diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1721Batch22.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1721Batch22.lean new file mode 100644 index 0000000000000000000000000000000000000000..bb3ef21c7488fcdf62b0bcd10571020a79483d55 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1721Batch22.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_22_17_21_0 : RowCompute.yRowIntegralFast 22 17 21 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_17_21_1 : RowCompute.yRowIntegralFast 22 17 21 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_17_21_2 : RowCompute.yRowIntegralFast 22 17 21 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_17_21_3 : RowCompute.yRowIntegralFast 22 17 21 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_17_21_4 : RowCompute.yRowIntegralFast 22 17 21 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_17_21_5 : RowCompute.yRowIntegralFast 22 17 21 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_17_21_6 : RowCompute.yRowIntegralFast 22 17 21 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1721Batch23.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1721Batch23.lean new file mode 100644 index 0000000000000000000000000000000000000000..28df47018b885b9b90543db96c6fc066f1ea1dee --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1721Batch23.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_23_17_21_0 : RowCompute.yRowIntegralFast 23 17 21 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_17_21_1 : RowCompute.yRowIntegralFast 23 17 21 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_17_21_2 : RowCompute.yRowIntegralFast 23 17 21 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_17_21_3 : RowCompute.yRowIntegralFast 23 17 21 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_17_21_4 : RowCompute.yRowIntegralFast 23 17 21 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_17_21_5 : RowCompute.yRowIntegralFast 23 17 21 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_17_21_6 : RowCompute.yRowIntegralFast 23 17 21 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1723Batch23.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1723Batch23.lean new file mode 100644 index 0000000000000000000000000000000000000000..4a806b528c90a12cf6ceb15bdcea23c4f6a10012 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1723Batch23.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_23_17_23_0 : RowCompute.yRowIntegralFast 23 17 23 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_17_23_1 : RowCompute.yRowIntegralFast 23 17 23 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_17_23_2 : RowCompute.yRowIntegralFast 23 17 23 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_17_23_3 : RowCompute.yRowIntegralFast 23 17 23 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_17_23_4 : RowCompute.yRowIntegralFast 23 17 23 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_17_23_5 : RowCompute.yRowIntegralFast 23 17 23 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_17_23_6 : RowCompute.yRowIntegralFast 23 17 23 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch19.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch19.lean new file mode 100644 index 0000000000000000000000000000000000000000..e4a74bb4c98f0cda2cc0a551b5b8b1787e0be0e7 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch19.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_19_19_19_0 : RowCompute.yRowIntegralFast 19 19 19 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_19_19_19_1 : RowCompute.yRowIntegralFast 19 19 19 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_19_19_19_2 : RowCompute.yRowIntegralFast 19 19 19 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_19_19_19_3 : RowCompute.yRowIntegralFast 19 19 19 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_19_19_19_4 : RowCompute.yRowIntegralFast 19 19 19 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_19_19_19_5 : RowCompute.yRowIntegralFast 19 19 19 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_19_19_19_6 : RowCompute.yRowIntegralFast 19 19 19 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch20.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch20.lean new file mode 100644 index 0000000000000000000000000000000000000000..16cb54d6912e1a4e011b4663c5164aeda8b4c23a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch20.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_20_19_19_0 : RowCompute.yRowIntegralFast 20 19 19 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_20_19_19_1 : RowCompute.yRowIntegralFast 20 19 19 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_20_19_19_2 : RowCompute.yRowIntegralFast 20 19 19 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_20_19_19_3 : RowCompute.yRowIntegralFast 20 19 19 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_20_19_19_4 : RowCompute.yRowIntegralFast 20 19 19 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_20_19_19_5 : RowCompute.yRowIntegralFast 20 19 19 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_20_19_19_6 : RowCompute.yRowIntegralFast 20 19 19 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch21.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch21.lean new file mode 100644 index 0000000000000000000000000000000000000000..4010eaaa40c6e583e4a043f4a1b357e730e75d13 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch21.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_21_19_19_0 : RowCompute.yRowIntegralFast 21 19 19 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_19_19_1 : RowCompute.yRowIntegralFast 21 19 19 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_19_19_2 : RowCompute.yRowIntegralFast 21 19 19 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_19_19_3 : RowCompute.yRowIntegralFast 21 19 19 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_19_19_4 : RowCompute.yRowIntegralFast 21 19 19 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_19_19_5 : RowCompute.yRowIntegralFast 21 19 19 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_19_19_6 : RowCompute.yRowIntegralFast 21 19 19 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch22.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch22.lean new file mode 100644 index 0000000000000000000000000000000000000000..075c86fb5ae217de5b29a8300f738cbb13252187 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch22.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_22_19_19_0 : RowCompute.yRowIntegralFast 22 19 19 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_19_19_1 : RowCompute.yRowIntegralFast 22 19 19 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_19_19_2 : RowCompute.yRowIntegralFast 22 19 19 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_19_19_3 : RowCompute.yRowIntegralFast 22 19 19 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_19_19_4 : RowCompute.yRowIntegralFast 22 19 19 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_19_19_5 : RowCompute.yRowIntegralFast 22 19 19 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_19_19_6 : RowCompute.yRowIntegralFast 22 19 19 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch23.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch23.lean new file mode 100644 index 0000000000000000000000000000000000000000..edae9dbe1a806fd0cbcb79019a233a6ffa66ce05 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1919Batch23.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_23_19_19_0 : RowCompute.yRowIntegralFast 23 19 19 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_19_1 : RowCompute.yRowIntegralFast 23 19 19 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_19_2 : RowCompute.yRowIntegralFast 23 19 19 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_19_3 : RowCompute.yRowIntegralFast 23 19 19 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_19_4 : RowCompute.yRowIntegralFast 23 19 19 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_19_5 : RowCompute.yRowIntegralFast 23 19 19 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_19_6 : RowCompute.yRowIntegralFast 23 19 19 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1921Batch21.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1921Batch21.lean new file mode 100644 index 0000000000000000000000000000000000000000..867074cc79c19d84bb452be7f1a88a1cb4500ecf --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1921Batch21.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_21_19_21_0 : RowCompute.yRowIntegralFast 21 19 21 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_19_21_1 : RowCompute.yRowIntegralFast 21 19 21 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_19_21_2 : RowCompute.yRowIntegralFast 21 19 21 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_19_21_3 : RowCompute.yRowIntegralFast 21 19 21 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_19_21_4 : RowCompute.yRowIntegralFast 21 19 21 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_19_21_5 : RowCompute.yRowIntegralFast 21 19 21 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_19_21_6 : RowCompute.yRowIntegralFast 21 19 21 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1921Batch22.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1921Batch22.lean new file mode 100644 index 0000000000000000000000000000000000000000..ac9d64720d4d75d20d5a368da939840596f3a412 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1921Batch22.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_22_19_21_0 : RowCompute.yRowIntegralFast 22 19 21 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_19_21_1 : RowCompute.yRowIntegralFast 22 19 21 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_19_21_2 : RowCompute.yRowIntegralFast 22 19 21 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_19_21_3 : RowCompute.yRowIntegralFast 22 19 21 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_19_21_4 : RowCompute.yRowIntegralFast 22 19 21 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_19_21_5 : RowCompute.yRowIntegralFast 22 19 21 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_19_21_6 : RowCompute.yRowIntegralFast 22 19 21 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1921Batch23.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1921Batch23.lean new file mode 100644 index 0000000000000000000000000000000000000000..deeadfc13f1bdf7c54e146c9963c1ff8b35fd106 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1921Batch23.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_23_19_21_0 : RowCompute.yRowIntegralFast 23 19 21 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_21_1 : RowCompute.yRowIntegralFast 23 19 21 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_21_2 : RowCompute.yRowIntegralFast 23 19 21 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_21_3 : RowCompute.yRowIntegralFast 23 19 21 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_21_4 : RowCompute.yRowIntegralFast 23 19 21 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_21_5 : RowCompute.yRowIntegralFast 23 19 21 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_21_6 : RowCompute.yRowIntegralFast 23 19 21 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1923Batch23.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1923Batch23.lean new file mode 100644 index 0000000000000000000000000000000000000000..2e15f4b13a4c4637fccbdbce283295ee531df393 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow1923Batch23.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_23_19_23_0 : RowCompute.yRowIntegralFast 23 19 23 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_23_1 : RowCompute.yRowIntegralFast 23 19 23 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_23_2 : RowCompute.yRowIntegralFast 23 19 23 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_23_3 : RowCompute.yRowIntegralFast 23 19 23 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_23_4 : RowCompute.yRowIntegralFast 23 19 23 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_23_5 : RowCompute.yRowIntegralFast 23 19 23 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_19_23_6 : RowCompute.yRowIntegralFast 23 19 23 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2121Batch21.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2121Batch21.lean new file mode 100644 index 0000000000000000000000000000000000000000..f55dd0f033ab8888bdf852c51035d7694ac6d7da --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2121Batch21.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_21_21_21_0 : RowCompute.yRowIntegralFast 21 21 21 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_21_21_1 : RowCompute.yRowIntegralFast 21 21 21 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_21_21_2 : RowCompute.yRowIntegralFast 21 21 21 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_21_21_3 : RowCompute.yRowIntegralFast 21 21 21 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_21_21_4 : RowCompute.yRowIntegralFast 21 21 21 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_21_21_5 : RowCompute.yRowIntegralFast 21 21 21 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_21_21_21_6 : RowCompute.yRowIntegralFast 21 21 21 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2121Batch22.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2121Batch22.lean new file mode 100644 index 0000000000000000000000000000000000000000..6526445ca8e1529112f956dd6bdb684507a713c9 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2121Batch22.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_22_21_21_0 : RowCompute.yRowIntegralFast 22 21 21 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_21_21_1 : RowCompute.yRowIntegralFast 22 21 21 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_21_21_2 : RowCompute.yRowIntegralFast 22 21 21 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_21_21_3 : RowCompute.yRowIntegralFast 22 21 21 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_21_21_4 : RowCompute.yRowIntegralFast 22 21 21 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_21_21_5 : RowCompute.yRowIntegralFast 22 21 21 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_22_21_21_6 : RowCompute.yRowIntegralFast 22 21 21 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2121Batch23.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2121Batch23.lean new file mode 100644 index 0000000000000000000000000000000000000000..58a40b5e7805cb82b14a1d090323ac84f242e771 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2121Batch23.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_23_21_21_0 : RowCompute.yRowIntegralFast 23 21 21 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_21_21_1 : RowCompute.yRowIntegralFast 23 21 21 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_21_21_2 : RowCompute.yRowIntegralFast 23 21 21 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_21_21_3 : RowCompute.yRowIntegralFast 23 21 21 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_21_21_4 : RowCompute.yRowIntegralFast 23 21 21 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_21_21_5 : RowCompute.yRowIntegralFast 23 21 21 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_21_21_6 : RowCompute.yRowIntegralFast 23 21 21 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2123Batch23.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2123Batch23.lean new file mode 100644 index 0000000000000000000000000000000000000000..0c9284027405ee26a619c5a9ad90f8e237536e3f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2123Batch23.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_23_21_23_0 : RowCompute.yRowIntegralFast 23 21 23 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_21_23_1 : RowCompute.yRowIntegralFast 23 21 23 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_21_23_2 : RowCompute.yRowIntegralFast 23 21 23 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_21_23_3 : RowCompute.yRowIntegralFast 23 21 23 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_21_23_4 : RowCompute.yRowIntegralFast 23 21 23 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_21_23_5 : RowCompute.yRowIntegralFast 23 21 23 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_21_23_6 : RowCompute.yRowIntegralFast 23 21 23 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2323Batch23.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2323Batch23.lean new file mode 100644 index 0000000000000000000000000000000000000000..ef346ef7c3f540c067a3a39a2eee14a4a3eaa999 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/ComputeRow2323Batch23.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem computeRow_23_23_23_0 : RowCompute.yRowIntegralFast 23 23 23 (RowCompute.rows[0]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_23_23_1 : RowCompute.yRowIntegralFast 23 23 23 (RowCompute.rows[1]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_23_23_2 : RowCompute.yRowIntegralFast 23 23 23 (RowCompute.rows[2]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_23_23_3 : RowCompute.yRowIntegralFast 23 23 23 (RowCompute.rows[3]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_23_23_4 : RowCompute.yRowIntegralFast 23 23 23 (RowCompute.rows[4]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_23_23_5 : RowCompute.yRowIntegralFast 23 23 23 (RowCompute.rows[5]!) = + (0 : ℤ) := by + decide +kernel + +theorem computeRow_23_23_23_6 : RowCompute.yRowIntegralFast 23 23 23 (RowCompute.rows[6]!) = + (0 : ℤ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data09.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data09.lean new file mode 100644 index 0000000000000000000000000000000000000000..1ad20bf03b79517a11c11ec4004ce6c3eef0eac8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data09.lean @@ -0,0 +1,76 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_9 : Matrix (Fin 5) (Fin 5) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => -12465910883340844333323483/6710886400000000000000 + | 0, 1 => -33961811903853786055197/838860800000000000000 + | 0, 2 => -670994343426034247927913/6710886400000000000000 + | 0, 3 => 4530779263986412498504797/3355443200000000000000 + | 0, 4 => 2064320406503781558919011/838860800000000000000 + | 1, 0 => -33961811903853786055197/838860800000000000000 + | 1, 1 => 2960534512700301116069433/23488102400000000000000 + | 1, 2 => -249132079557021880785303/11744051200000000000000 + | 1, 3 => -172612848420190308157317/419430400000000000000 + | 1, 4 => -460639144770506834240727/209715200000000000000 + | 2, 0 => -670994343426034247927913/6710886400000000000000 + | 2, 1 => -249132079557021880785303/11744051200000000000000 + | 2, 2 => -12391755266391716879263611/46976204800000000000000 + | 2, 3 => 202846259663372040293217/3355443200000000000000 + | 2, 4 => 1717697222431419971099331/838860800000000000000 + | 3, 0 => 4530779263986412498504797/3355443200000000000000 + | 3, 1 => -172612848420190308157317/419430400000000000000 + | 3, 2 => 202846259663372040293217/3355443200000000000000 + | 3, 3 => -3138981013037239731556773/1677721600000000000000 + | 3, 4 => -1034085603218724160418079/419430400000000000000 + | 4, 0 => 2064320406503781558919011/838860800000000000000 + | 4, 1 => -460639144770506834240727/209715200000000000000 + | 4, 2 => 1717697222431419971099331/838860800000000000000 + | 4, 3 => -1034085603218724160418079/419430400000000000000 + | 4, 4 => -9956547203160990435022917/104857600000000000000 + | _, _ => 0 +def candidateZ_9 : Matrix (Fin 5) (Fin 5) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 80640 + | 0, 3 => -10080 + | 0, 4 => 136080 + | 1, 1 => 4320 + | 1, 2 => -2160 + | 1, 4 => 22680 + | 2, 1 => -2160 + | 2, 2 => 1080 + | 2, 4 => -11340 + | 3, 0 => -10080 + | 3, 3 => 1260 + | 3, 4 => -17010 + | 4, 0 => 136080 + | 4, 1 => 22680 + | 4, 2 => -11340 + | 4, 3 => -17010 + | 4, 4 => 348705 + | _, _ => 0 +def lower_9 : Matrix (Fin 5) (Fin 5) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 0 => 23599862696142345457458519/3087682465193682626040960764 + | 1, 1 => 1 + | 2, 0 => -23599862696142345457458519/6175364930387365252081921528 + | 2, 1 => -1/2 + | 2, 2 => 1 + | 3, 0 => -1/8 + | 3, 3 => 1 + | 4, 0 => 2667181719584543372547889257/1543841232596841313020480382 + | 4, 1 => 21/4 + | 4, 4 => 1 + | _, _ => 0 +def pivots_9 : Fin 5 → ℚ := fun i => + match i.val with + | 0 => 2315761848895261969530720573/6710886400000000000000 + | 1 => 366163547971210521373295701801015256521000393308993/453273762007210333459693706370088960000000000000 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data10.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data10.lean new file mode 100644 index 0000000000000000000000000000000000000000..0a31f592bfc6c74d9f7a72e0c0882b8d1bf6a192 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data10.lean @@ -0,0 +1,63 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_10 : Matrix (Fin 5) (Fin 5) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 3252603773208384966897801/134217728000000000000 + | 0, 1 => -1219963203744052188572919/167772160000000000000 + | 0, 2 => 1233781148459940320874483/134217728000000000000 + | 0, 3 => -4673143458544379455879083/335544320000000000000 + | 0, 4 => 2012606963507139814961019/83886080000000000000 + | 1, 0 => -1219963203744052188572919/167772160000000000000 + | 1, 1 => 23917264894764854794377/16777216000000000000 + | 1, 2 => -13854999171694482915831/8388608000000000000 + | 1, 3 => 57805337880323795919969/16777216000000000000 + | 1, 4 => -52562004903703102850037/5242880000000000000 + | 2, 0 => 1233781148459940320874483/134217728000000000000 + | 2, 1 => -13854999171694482915831/8388608000000000000 + | 2, 2 => 2285267576183515842978393/939524096000000000000 + | 2, 3 => -121198635809384297528619/67108864000000000000 + | 2, 4 => 127922353790121014632767/16777216000000000000 + | 3, 0 => -4673143458544379455879083/335544320000000000000 + | 3, 1 => 57805337880323795919969/16777216000000000000 + | 3, 2 => -121198635809384297528619/67108864000000000000 + | 3, 3 => 51194502011873480782923/167772160000000000000 + | 3, 4 => 10203611212469228878953/41943040000000000000 + | 4, 0 => 2012606963507139814961019/83886080000000000000 + | 4, 1 => -52562004903703102850037/5242880000000000000 + | 4, 2 => 127922353790121014632767/16777216000000000000 + | 4, 3 => 10203611212469228878953/41943040000000000000 + | 4, 4 => -990036939147267786688413/10485760000000000000 + | _, _ => 0 +def candidateZ_10 : Matrix (Fin 5) (Fin 5) ℚ := fun i j => + match i.val, j.val with + | 1, 1 => 30240 + | 1, 3 => -22680 + | 1, 4 => 90720 + | 3, 1 => -22680 + | 3, 3 => 17010 + | 3, 4 => -68040 + | 4, 1 => 90720 + | 4, 3 => -68040 + | 4, 4 => 272160 + | _, _ => 0 +def lower_10 : Matrix (Fin 5) (Fin 5) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 1 => 1 + | 2, 2 => 1 + | 3, 1 => -3/4 + | 3, 3 => 1 + | 4, 1 => 3 + | 4, 4 => 1 + | _, _ => 0 +def pivots_10 : Fin 5 → ℚ := fun i => + match i.val with + | 1 => 7825536458311031147272977/536870912000000000000 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data11.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data11.lean new file mode 100644 index 0000000000000000000000000000000000000000..e5a9464c2df5722deccea509068a179e310a3612 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data11.lean @@ -0,0 +1,101 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_11 : Matrix (Fin 6) (Fin 6) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 15310420495743050456853357/134217728000000000000 + | 0, 1 => -21091981152473935416162441/335544320000000000000 + | 0, 2 => 1759644912412486678804947/134217728000000000000 + | 0, 3 => -7117902998608090523107887/335544320000000000000 + | 0, 4 => 2050140304557578762479287/16777216000000000000 + | 0, 5 => -3816671070411211699962099/8388608000000000000 + | 1, 0 => -21091981152473935416162441/335544320000000000000 + | 1, 1 => 3139824493398164330092707/167772160000000000000 + | 1, 2 => -110846050581407277067047/13421772800000000000 + | 1, 3 => -120000452149124136234801/167772160000000000000 + | 1, 4 => -804905973848069092119267/41943040000000000000 + | 1, 5 => -488664944191263381981813/20971520000000000000 + | 2, 0 => 1759644912412486678804947/134217728000000000000 + | 2, 1 => -110846050581407277067047/13421772800000000000 + | 2, 2 => 186561496958160530399967/134217728000000000000 + | 2, 3 => -132022995280028243088831/67108864000000000000 + | 2, 4 => 39011604836809336804287/16777216000000000000 + | 2, 5 => -536635508982633719381547/8388608000000000000 + | 3, 0 => -7117902998608090523107887/335544320000000000000 + | 3, 1 => -120000452149124136234801/167772160000000000000 + | 3, 2 => -132022995280028243088831/67108864000000000000 + | 3, 3 => 53081184869685889157043/167772160000000000000 + | 3, 4 => 581826960578730870868149/41943040000000000000 + | 3, 5 => 48169578758531066711919/20971520000000000000 + | 4, 0 => 2050140304557578762479287/16777216000000000000 + | 4, 1 => -804905973848069092119267/41943040000000000000 + | 4, 2 => 39011604836809336804287/16777216000000000000 + | 4, 3 => 581826960578730870868149/41943040000000000000 + | 4, 4 => -985704999590345844614157/10485760000000000000 + | 4, 5 => 390621018140645815377261/1048576000000000000 + | 5, 0 => -3816671070411211699962099/8388608000000000000 + | 5, 1 => -488664944191263381981813/20971520000000000000 + | 5, 2 => -536635508982633719381547/8388608000000000000 + | 5, 3 => 48169578758531066711919/20971520000000000000 + | 5, 4 => 390621018140645815377261/1048576000000000000 + | 5, 5 => -7434351034101698173344801/524288000000000000 + | _, _ => 0 +def candidateZ_11 : Matrix (Fin 6) (Fin 6) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 7257600 + | 0, 4 => -453600 + | 0, 5 => 9979200 + | 1, 1 => 241920 + | 1, 3 => -60480 + | 1, 5 => 2494800 + | 2, 2 => 54000 + | 2, 3 => -75600 + | 2, 4 => 113400 + | 3, 1 => -60480 + | 3, 2 => -75600 + | 3, 3 => 120960 + | 3, 4 => -158760 + | 3, 5 => -623700 + | 4, 0 => -453600 + | 4, 2 => 113400 + | 4, 3 => -158760 + | 4, 4 => 266490 + | 4, 5 => -623700 + | 5, 0 => 9979200 + | 5, 1 => 2494800 + | 5, 3 => -623700 + | 5, 4 => -623700 + | 5, 5 => 39449025 + | _, _ => 0 +def lower_11 : Matrix (Fin 6) (Fin 6) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 0 => 1925158773729525751974454/150990079174740777675305331 + | 1, 1 => 1 + | 2, 0 => -3936218478175539835501733/1207920633397926221402442648 + | 2, 1 => 97293768145330047583879356561582525137135743957/398751775291942480923180911595463390779768165464 + | 2, 2 => 1 + | 3, 0 => 8301941609933521328767591/6039603166989631107012213240 + | 3, 1 => -1179496096132238434241131635425406914434660414529/1993758876459712404615904557977316953898840827320 + | 3, 2 => -7/5 + | 3, 3 => 1 + | 4, 0 => -34900457663141259371752627/503300263915802592251017770 + | 4, 1 => 2043169131051930999261466487793233027879850623097/3987517752919424809231809115954633907797681654640 + | 4, 2 => 21/10 + | 4, 4 => 1 + | 5, 0 => 75821519573118101206927129/50330026391580259225101777 + | 5, 1 => 165/16 + | 5, 5 => 1 + | _, _ => 0 +def pivots_11 : Fin 6 → ℚ := fun i => + match i.val with + | 0 => 4076732137718000997233243937/134217728000000000000 + | 1 => 149531915734478430346192841848298771542413062049/4397904812798138491435026743296000000000000 + | 2 => 44365601556251097376769358134495883600481873025846129343811138887/167248616611409551550602139022849848180114473547831705600000000000 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data12.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data12.lean new file mode 100644 index 0000000000000000000000000000000000000000..c48a73516dac3dcc2d03bc5a414eb4b3b4aa02dd --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data12.lean @@ -0,0 +1,88 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_12 : Matrix (Fin 6) (Fin 6) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => -21758497948837526814361611/16777216000000000000 + | 0, 1 => 7514500960705467759694389/41943040000000000000 + | 0, 2 => 3165688667606660909537571/16777216000000000000 + | 0, 3 => -41707520784065633150907/8388608000000000000 + | 0, 4 => -2287894342236011100448461/10485760000000000000 + | 0, 5 => 974459105668097994666249/1048576000000000000 + | 1, 0 => 7514500960705467759694389/41943040000000000000 + | 1, 1 => -2755174567464265689714987/41943040000000000000 + | 1, 2 => 13005450739700130750669/8388608000000000000 + | 1, 3 => 81483121238154923538567/4194304000000000000 + | 1, 4 => 404785016635235824043973/5242880000000000000 + | 1, 5 => 6215584013984995241823/40960000000000000 + | 2, 0 => 3165688667606660909537571/16777216000000000000 + | 2, 1 => 13005450739700130750669/8388608000000000000 + | 2, 2 => 46805674377515194537803/3355443200000000000 + | 2, 3 => -41483885509932371903727/8388608000000000000 + | 2, 4 => -10240121934522536047317/419430400000000000 + | 2, 5 => -25627330574660171363787/1048576000000000000 + | 3, 0 => -41707520784065633150907/8388608000000000000 + | 3, 1 => 81483121238154923538567/4194304000000000000 + | 3, 2 => -41483885509932371903727/8388608000000000000 + | 3, 3 => -192219299280069275276433/4194304000000000000 + | 3, 4 => -42262827210616968341919/1048576000000000000 + | 3, 5 => 102387833991081458685459/524288000000000000 + | 4, 0 => -2287894342236011100448461/10485760000000000000 + | 4, 1 => 404785016635235824043973/5242880000000000000 + | 4, 2 => -10240121934522536047317/419430400000000000 + | 4, 3 => -42262827210616968341919/1048576000000000000 + | 4, 4 => 42184147125974825030859/1310720000000000000 + | 4, 5 => 18732467483584451907057/655360000000000000 + | 5, 0 => 974459105668097994666249/1048576000000000000 + | 5, 1 => 6215584013984995241823/40960000000000000 + | 5, 2 => -25627330574660171363787/1048576000000000000 + | 5, 3 => 102387833991081458685459/524288000000000000 + | 5, 4 => 18732467483584451907057/655360000000000000 + | 5, 5 => -330567209557174956464307/65536000000000000 + | _, _ => 0 +def candidateZ_12 : Matrix (Fin 6) (Fin 6) ℚ := fun i j => + match i.val, j.val with + | 1, 1 => 2177280 + | 1, 4 => -1088640 + | 1, 5 => 7484400 + | 2, 2 => 604800 + | 2, 3 => -453600 + | 2, 5 => 2494800 + | 3, 2 => -453600 + | 3, 3 => 340200 + | 3, 5 => -1871100 + | 4, 1 => -1088640 + | 4, 4 => 544320 + | 4, 5 => -3742200 + | 5, 1 => 7484400 + | 5, 2 => 2494800 + | 5, 3 => -1871100 + | 5, 4 => -3742200 + | 5, 5 => 36018675 + | _, _ => 0 +def lower_12 : Matrix (Fin 6) (Fin 6) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 1 => 1 + | 2, 1 => 204004003367800299891773/539865092478537355668714 + | 2, 2 => 1 + | 3, 1 => -204004003367800299891773/719820123304716474224952 + | 3, 2 => -3/4 + | 3, 3 => 1 + | 4, 1 => -1/2 + | 4, 4 => 1 + | 5, 1 => 449550461547858066194128/89977515413089559278119 + | 5, 2 => 33/8 + | 5, 5 => 1 + | _, _ => 0 +def pivots_12 : Fin 6 → ℚ := fun i => + match i.val with + | 1 => 21864536245380762904582917/83886080000000000000 + | 2 => 649683024815757908332880506062421317689132763/78623552668163164758010757120000000000000 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data13.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data13.lean new file mode 100644 index 0000000000000000000000000000000000000000..e19d2ed4a3988bb1e71b54a4285fb93fe3d21e6b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data13.lean @@ -0,0 +1,130 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_13 : Matrix (Fin 7) (Fin 7) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 121685493803305440547576917/8388608000000000000 + | 0, 1 => 7563908306608840424871171/8388608000000000000 + | 0, 2 => -66091999624888726298111247/16777216000000000000 + | 0, 3 => 2728798823338271240310567/1677721600000000000 + | 0, 4 => -13501297339814524797227781/10485760000000000000 + | 0, 5 => 12432022452888993488134359/1048576000000000000 + | 0, 6 => -165874530574631465579316753/1048576000000000000 + | 1, 0 => 7563908306608840424871171/8388608000000000000 + | 1, 1 => -2041302613950531427151763/8388608000000000000 + | 1, 2 => 126715690823288866730217/419430400000000000 + | 1, 3 => -500594098074230841463629/2097152000000000000 + | 1, 4 => -1215155073315811787592453/2621440000000000000 + | 1, 5 => -47337050492347165740927/524288000000000000 + | 1, 6 => -394753123867351949086959/131072000000000000 + | 2, 0 => -66091999624888726298111247/16777216000000000000 + | 2, 1 => 126715690823288866730217/419430400000000000 + | 2, 2 => -1379799513707028925041063/16777216000000000000 + | 2, 3 => 701982483744393187744923/8388608000000000000 + | 2, 4 => 672840394965225922256721/2097152000000000000 + | 2, 5 => 2506297034373528441573/1048576000000000000 + | 2, 6 => 5534718096701578046307903/1048576000000000000 + | 3, 0 => 2728798823338271240310567/1677721600000000000 + | 3, 1 => -500594098074230841463629/2097152000000000000 + | 3, 2 => 701982483744393187744923/8388608000000000000 + | 3, 3 => 126607865811947282465541/838860800000000000 + | 3, 4 => -175665130303631642663517/1048576000000000000 + | 3, 5 => 420722950805223871087107/524288000000000000 + | 3, 6 => -2485443250416390286101651/524288000000000000 + | 4, 0 => -13501297339814524797227781/10485760000000000000 + | 4, 1 => -1215155073315811787592453/2621440000000000000 + | 4, 2 => 672840394965225922256721/2097152000000000000 + | 4, 3 => -175665130303631642663517/1048576000000000000 + | 4, 4 => -125541053085493256369427/262144000000000000 + | 4, 5 => 1437479079722043725179197/655360000000000000 + | 4, 6 => -2022830025440980274156781/655360000000000000 + | 5, 0 => 12432022452888993488134359/1048576000000000000 + | 5, 1 => -47337050492347165740927/524288000000000000 + | 5, 2 => 2506297034373528441573/1048576000000000000 + | 5, 3 => 420722950805223871087107/524288000000000000 + | 5, 4 => 1437479079722043725179197/655360000000000000 + | 5, 5 => -184207969249874832456117/65536000000000000 + | 5, 6 => 252554056596275363975331/65536000000000000 + | 6, 0 => -165874530574631465579316753/1048576000000000000 + | 6, 1 => -394753123867351949086959/131072000000000000 + | 6, 2 => 5534718096701578046307903/1048576000000000000 + | 6, 3 => -2485443250416390286101651/524288000000000000 + | 6, 4 => -2022830025440980274156781/655360000000000000 + | 6, 5 => 252554056596275363975331/65536000000000000 + | 6, 6 => -17580701774552693245136811/13107200000000000 + | _, _ => 0 +def candidateZ_13 : Matrix (Fin 7) (Fin 7) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 958003200 + | 0, 5 => -29937600 + | 0, 6 => 972972000 + | 1, 1 => 21772800 + | 1, 4 => -2721600 + | 1, 6 => 291891600 + | 2, 2 => 4838400 + | 2, 3 => -907200 + | 2, 4 => -4082400 + | 2, 5 => 12474000 + | 2, 6 => 48648600 + | 3, 2 => -907200 + | 3, 3 => 453600 + | 3, 6 => -24324300 + | 4, 1 => -2721600 + | 4, 2 => -4082400 + | 4, 4 => 5851440 + | 4, 5 => -16839900 + | 4, 6 => -36486450 + | 5, 0 => -29937600 + | 5, 2 => 12474000 + | 5, 4 => -16839900 + | 5, 5 => 52390800 + | 5, 6 => -30405375 + | 6, 0 => 972972000 + | 6, 1 => 291891600 + | 6, 2 => 48648600 + | 6, 3 => -24324300 + | 6, 4 => -36486450 + | 6, 5 => -30405375 + | 6, 6 => 12411474075/2 + | _, _ => 0 +def lower_13 : Matrix (Fin 7) (Fin 7) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 0 => 1111855671728339030775679/197045554945531736379875742 + | 1, 1 => 1 + | 2, 0 => 1791249419107115395188367/1182273329673190418279254452 + | 2, 1 => -23158466219111904247947676151589232601649996629/349541975522142742932216682562005884893537644542 + | 2, 2 => 1 + | 3, 0 => -33408601617411273839585/35826464535551224796341044 + | 3, 1 => -7547483379072103020857744738955493237743278651/233027983681428495288144455041337256595691763028 + | 3, 2 => -21197452145059780073388475447411012177964120746217336845656524034634/265400427424486625635730094240887975974934890860545150367437796795333 + | 3, 3 => 1 + | 4, 0 => -114738360616464815616263/492613887363829340949689355 + | 4, 1 => 120923267605168300684507624514429840089303789453/2330279836814284952881444550413372565956917630280 + | 4, 2 => -401409941641860717880115658022918712914211968862598858017024547706917/353867236565982167514306792321183967966579854480726867156583729060444 + | 4, 3 => -27/10 + | 4, 4 => 1 + | 5, 0 => -292822950672807339915922/8956616133887806199085261 + | 5, 1 => -251905039959805173207865007026506417731839079201/466055967362856990576288910082674513191383526056 + | 5, 2 => 2453060754478037720378484576806725467809073143049215243437372235986715/707734473131964335028613584642367935933159708961453734313167458120888 + | 5, 3 => 33/4 + | 5, 5 => 1 + | 6, 0 => 1135776041819186628637426/995179570431978466565029 + | 6, 1 => 1764382601215946144725091581012207960554988007877/116513991840714247644072227520668628297845881514 + | 6, 2 => 1515617828371774275247275994489887370724434633354539584464441468476331/353867236565982167514306792321183967966579854480726867156583729060444 + | 6, 3 => -429/8 + | 6, 6 => 1 + | _, _ => 0 +def pivots_13 : Fin 7 → ℚ := fun i => + match i.val with + | 0 => 263351384184703165671703929183/67108864000000000000 + | 1 => 1572938889849642343194975071529026482020919400439/521760706622641126278445924352000000000000 + | 2 => 7165811540461138892164712544503975351323242053234719059920820513473991/7635860969273048933601917502794539224127627690901504000000000000 + | 3 => 22597095286098904465180990607174049148899538410734195998820269052085603485624016933/45295006280445717441831269417111547899722221373533038996042717319736832000000000000 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data14.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data14.lean new file mode 100644 index 0000000000000000000000000000000000000000..50f3e3a280f4b1aff87141237bea574874a4c7fd --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data14.lean @@ -0,0 +1,115 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_14 : Matrix (Fin 7) (Fin 7) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 165377041672743964897444611/4194304000000000000 + | 0, 1 => -99652836936417746642331957/4194304000000000000 + | 0, 2 => 198343656225197394663337443/8388608000000000000 + | 0, 3 => -10805495312804179528323783/4194304000000000000 + | 0, 4 => 21398938288605875882996397/1048576000000000000 + | 0, 5 => 3160468299521670425437149/104857600000000000 + | 0, 6 => -12750872962864833675394659/524288000000000000 + | 1, 0 => -99652836936417746642331957/4194304000000000000 + | 1, 1 => 23310418524081657499377/524288000000000000 + | 1, 2 => -347065711842922353039231/419430400000000000 + | 1, 3 => -138985253242272601987977/104857600000000000 + | 1, 4 => -567150585351068471238783/131072000000000000 + | 1, 5 => -141724874857705188581763/32768000000000000 + | 1, 6 => -841622022843306152134401/26214400000000000 + | 2, 0 => 198343656225197394663337443/8388608000000000000 + | 2, 1 => -347065711842922353039231/419430400000000000 + | 2, 2 => -948697485826720805007561/1677721600000000000 + | 2, 3 => 1776603855966711095862153/4194304000000000000 + | 2, 4 => 932798387166894000074907/1048576000000000000 + | 2, 5 => 269131392507015595229211/524288000000000000 + | 2, 6 => 6370357421543107418633493/524288000000000000 + | 3, 0 => -10805495312804179528323783/4194304000000000000 + | 3, 1 => -138985253242272601987977/104857600000000000 + | 3, 2 => 1776603855966711095862153/4194304000000000000 + | 3, 3 => -2225592748224580792706397/2097152000000000000 + | 3, 4 => 1701251773125333268329/20971520000000000 + | 3, 5 => -41108078112253038740007/52428800000000000 + | 3, 6 => -1332400286315383367619537/262144000000000000 + | 4, 0 => 21398938288605875882996397/1048576000000000000 + | 4, 1 => -567150585351068471238783/131072000000000000 + | 4, 2 => 932798387166894000074907/1048576000000000000 + | 4, 3 => 1701251773125333268329/20971520000000000 + | 4, 4 => 1451654095595659568163/26214400000000000 + | 4, 5 => 56731873890489317051103/65536000000000000 + | 4, 6 => 702921905295609015979677/65536000000000000 + | 5, 0 => 3160468299521670425437149/104857600000000000 + | 5, 1 => -141724874857705188581763/32768000000000000 + | 5, 2 => 269131392507015595229211/524288000000000000 + | 5, 3 => -41108078112253038740007/52428800000000000 + | 5, 4 => 56731873890489317051103/65536000000000000 + | 5, 5 => 15883626629942625122019/32768000000000000 + | 5, 6 => -304589521531696266272979/32768000000000000 + | 6, 0 => -12750872962864833675394659/524288000000000000 + | 6, 1 => -841622022843306152134401/26214400000000000 + | 6, 2 => 6370357421543107418633493/524288000000000000 + | 6, 3 => -1332400286315383367619537/262144000000000000 + | 6, 4 => 702921905295609015979677/65536000000000000 + | 6, 5 => -304589521531696266272979/32768000000000000 + | 6, 6 => -10250896235928348183825213/32768000000000000 + | _, _ => 0 +def candidateZ_14 : Matrix (Fin 7) (Fin 7) ℚ := fun i j => + match i.val, j.val with + | 1, 1 => 239500800 + | 1, 5 => -74844000 + | 1, 6 => 778377600 + | 2, 2 => 43545600 + | 2, 4 => -21772800 + | 2, 6 => 389188800 + | 3, 3 => 11113200 + | 3, 4 => -19051200 + | 3, 5 => 26195400 + | 4, 2 => -21772800 + | 4, 3 => -19051200 + | 4, 4 => 43545600 + | 4, 5 => -44906400 + | 4, 6 => -194594400 + | 5, 1 => -74844000 + | 5, 3 => 26195400 + | 5, 4 => -44906400 + | 5, 5 => 85135050 + | 5, 6 => -243243000 + | 6, 1 => 778377600 + | 6, 2 => 389188800 + | 6, 4 => -194594400 + | 6, 5 => -243243000 + | 6, 6 => 6008102100 + | _, _ => 0 +def lower_14 : Matrix (Fin 7) (Fin 7) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 1 => 1 + | 2, 1 => 120386933257136954636/536030904312722438251 + | 2, 2 => 1 + | 3, 1 => -4332122510776549572923/707560793692793618491320 + | 3, 2 => 307688534849122453100467601486871491946187/581648401554992803788669771158411492269968 + | 3, 3 => 1 + | 4, 1 => -206979540853306295379/2033220671531016145090 + | 4, 2 => -68190855043237431553166135915439263408323/48470700129582733649055814263200957689164 + | 4, 3 => -12/7 + | 4, 4 => 1 + | 5, 1 => -876227953263419430954/2680154521563612191255 + | 5, 2 => 483510554762906712015020516622226630201151/387765601036661869192446514105607661513312 + | 5, 3 => 33/14 + | 5, 5 => 1 + | 6, 1 => 2818058655002009456375/536030904312722438251 + | 6, 2 => 143/16 + | 6, 6 => 1 + | _, _ => 0 +def pivots_14 : Fin 7 → ℚ := fun i => + match i.val with + | 1 => 15760916679506977851894153/1677721600000000000 + | 2 => 2944595032872151069180140716489458179616713/2195582584064911107076096000000000000 + | 3 => 158050942662752402961772876954531015304963741122714063961053/2353019113846173357351497661891213306012631040000000000000 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data15.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data15.lean new file mode 100644 index 0000000000000000000000000000000000000000..281848bb00a01599c7c8048b6ef50077bb758f28 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data15.lean @@ -0,0 +1,161 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_15 : Matrix (Fin 8) (Fin 8) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1160239161688954312188380157/1048576000000000000 + | 0, 1 => 527769145158896263581537579/2097152000000000000 + | 0, 2 => -364633884256427977153375413/1677721600000000000 + | 0, 3 => 70800295830292526868599229/838860800000000000 + | 0, 4 => -213215905018995130639958571/1048576000000000000 + | 0, 5 => -236988935373506936612565573/524288000000000000 + | 0, 6 => 374746885492881333249210393/524288000000000000 + | 0, 7 => -1454272995490648196091417189/52428800000000000 + | 1, 0 => 527769145158896263581537579/2097152000000000000 + | 1, 1 => -79903889464778925306594867/2097152000000000000 + | 1, 2 => 10380910649344519579874271/838860800000000000 + | 1, 3 => 2399450471501791440121389/419430400000000000 + | 1, 4 => 7831247768240800098462597/524288000000000000 + | 1, 5 => 260365051976410952573409/52428800000000000 + | 1, 6 => 15417580069242120546303813/262144000000000000 + | 1, 7 => -19651317795670208550803901/26214400000000000 + | 2, 0 => -364633884256427977153375413/1677721600000000000 + | 2, 1 => 10380910649344519579874271/838860800000000000 + | 2, 2 => -544144788797698439940321/335544320000000000 + | 2, 3 => -1550173356554793074510931/838860800000000000 + | 2, 4 => -251612565167710626302493/209715200000000000 + | 2, 5 => 412467042517374252900789/104857600000000000 + | 2, 6 => -3917597116231063282740723/104857600000000000 + | 2, 7 => 6737890215993101774728119/10485760000000000 + | 3, 0 => 70800295830292526868599229/838860800000000000 + | 3, 1 => 2399450471501791440121389/419430400000000000 + | 3, 2 => -1550173356554793074510931/838860800000000000 + | 3, 3 => -11010455047903773080463201/2097152000000000000 + | 3, 4 => 483384920806779568744041/524288000000000000 + | 3, 5 => -2196385127442123145785873/262144000000000000 + | 3, 6 => -3020058706667129324414217/262144000000000000 + | 3, 7 => 6630571266894369608354541/26214400000000000 + | 4, 0 => -213215905018995130639958571/1048576000000000000 + | 4, 1 => 7831247768240800098462597/524288000000000000 + | 4, 2 => -251612565167710626302493/209715200000000000 + | 4, 3 => 483384920806779568744041/524288000000000000 + | 4, 4 => -733927230254603053476261/131072000000000000 + | 4, 5 => 144198476217622441333917/65536000000000000 + | 4, 6 => -270537545003843608530039/65536000000000000 + | 4, 7 => 488416974255188057862783/1310720000000000 + | 5, 0 => -236988935373506936612565573/524288000000000000 + | 5, 1 => 260365051976410952573409/52428800000000000 + | 5, 2 => 412467042517374252900789/104857600000000000 + | 5, 3 => -2196385127442123145785873/262144000000000000 + | 5, 4 => 144198476217622441333917/65536000000000000 + | 5, 5 => 103242122786757662097687/32768000000000000 + | 5, 6 => -1188419411670004290171681/32768000000000000 + | 5, 7 => -946932022961651320973379/3276800000000000 + | 6, 0 => 374746885492881333249210393/524288000000000000 + | 6, 1 => 15417580069242120546303813/262144000000000000 + | 6, 2 => -3917597116231063282740723/104857600000000000 + | 6, 3 => -3020058706667129324414217/262144000000000000 + | 6, 4 => -270537545003843608530039/65536000000000000 + | 6, 5 => -1188419411670004290171681/32768000000000000 + | 6, 6 => -13385634727914986582216457/32768000000000000 + | 6, 7 => 6044229669744752465993013/3276800000000000 + | 7, 0 => -1454272995490648196091417189/52428800000000000 + | 7, 1 => -19651317795670208550803901/26214400000000000 + | 7, 2 => 6737890215993101774728119/10485760000000000 + | 7, 3 => 6630571266894369608354541/26214400000000000 + | 7, 4 => 488416974255188057862783/1310720000000000 + | 7, 5 => -946932022961651320973379/3276800000000000 + | 7, 6 => 6044229669744752465993013/3276800000000000 + | 7, 7 => -31526289117493065494479881/327680000000000 + | _, _ => 0 +def candidateZ_15 : Matrix (Fin 8) (Fin 8) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 174356582400 + | 0, 6 => -2724321600 + | 0, 7 => 122594472000 + | 1, 1 => 2874009600 + | 1, 5 => -179625600 + | 1, 7 => 40864824000 + | 2, 2 => 435456000 + | 2, 4 => -40824000 + | 2, 5 => -299376000 + | 2, 6 => 1459458000 + | 2, 7 => 10216206000 + | 3, 3 => 177811200 + | 3, 4 => -171460800 + | 3, 6 => 681080400 + | 4, 2 => -40824000 + | 4, 3 => -171460800 + | 4, 4 => 175543200 + | 4, 6 => -656756100 + | 4, 7 => -2554051500 + | 5, 1 => -179625600 + | 5, 2 => -299376000 + | 5, 5 => 340540200 + | 5, 6 => -1605403800 + | 5, 7 => -2554051500 + | 6, 0 => -2724321600 + | 6, 2 => 1459458000 + | 6, 3 => 681080400 + | 6, 4 => -656756100 + | 6, 5 => -1605403800 + | 6, 6 => 10477692225 + | 6, 7 => -1915538625 + | 7, 0 => 122594472000 + | 7, 1 => 40864824000 + | 7, 2 => 10216206000 + | 7, 4 => -2554051500 + | 7, 5 => -2554051500 + | 7, 6 => -1915538625 + | 7, 7 => 1306397342250 + | _, _ => 0 +def lower_15 : Matrix (Fin 8) (Fin 8) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 0 => 197930700637414421837892/97247812005704593891661675 + | 1, 1 => 1 + | 2, 0 => 36261774332356403991399/77798249604563675113329340 + | 2, 1 => -1734106666864679455581400713948829255800237455/19797225624156201420121219315318097526857047788 + | 2, 2 => 1 + | 3, 0 => -23957260623299580546277/33342106973384432191426860 + | 3, 1 => -624196251755535956149438461279071991189114595/59391676872468604260363657945954292580571143364 + | 3, 2 => 303528572474207973463704744629937909376413767666986608473671375559/518665375860506760625961490756824848120953439349257906610363915955 + | 3, 3 => 1 + | 4, 0 => 496375964381946111357/1023661179007416777806965 + | 4, 1 => -486540140982570387792868750778417139890866395/26396300832208268560161625753757463369142730384 + | 4, 2 => -434406574781237967441900173220368084053771212269687136733349786553/691553834480675680834615321009099797494604585799010542147151887940 + | 4, 3 => -170642676494886817200553163565280791711087620144089633618121582441925509275929838011/171086617074875330697113852379164678624089998458380783511885582555597656081587924209 + | 4, 4 => 1 + | 5, 0 => 5351067720970075571982/19449562401140918778332335 + | 5, 1 => 1148569105109967564185374595147977467320161985/7198991136056800516407716114661126373402562832 + | 5, 2 => -283212392301264935312765751709162333082734798025620504193091613103/345776917240337840417307660504549898747302292899505271073575943970 + | 5, 3 => 49863402548204756592216006328416408447435927492586127181469410660015800021565046209/342173234149750661394227704758329357248179996916761567023771165111195312163175848418 + | 5, 4 => -22/5 + | 5, 5 => 1 + | 6, 0 => -1977883869664167079693446/97247812005704593891661675 + | 6, 1 => -505157650111198927113503706110557130686944676/449936946003550032275482257166320398337660177 + | 6, 2 => 36538005133794511969035965102506791153878259272812797414179484589/5860625715937929498598434923805930487242411744059411374128405830 + | 6, 3 => 2135123208195057797120959747964427415128021469041762264502063064505967180468355781093/684346468299501322788455409516658714496359993833523134047542330222390624326351696836 + | 6, 4 => 429/20 + | 6, 6 => 1 + | 7, 0 => 2178650591645921788996608/2778508914448702682618905 + | 7, 1 => 25637460033619581337817763456396286026941820605/1199831856009466752734619352443521062233760472 + | 7, 2 => 552496357271419294519425838185729534629755806181813234555850949939/34577691724033784041730766050454989874730229289950527107357594397 + | 7, 3 => 3241121165633309178494040411347066549083335287018098266795511692901027001401728003585/391055124742572184450545948295233551140777139333441790884309902984223213900772398192 + | 7, 4 => -1001/4 + | 7, 7 => 1 + | _, _ => 0 +def pivots_15 : Fin 8 → ℚ := fun i => + match i.val with + | 0 => 946193981428144101279578432481/1342177280000000000 + | 1 => 39688488070027144796988014422383956016966666552993/227615450271637723760140697600000000000000 + | 2 => 8402379088940209522140576150260562539559445717457978087087895438471/1572643610308728262144320277634771926691034525859840000000000 + | 3 => 32335370627151437501754518099662124259953009708633968083746375103007956999420117675501/4425944540676324357341538054458238703965469349113667469741772082816000000000000 + | 4 => 63969564659509058197628411283630898558162890371801893104190890068659388379197572494976593499596483/4004404477363939168773590510543191563681557906774443938655333406558445710343909357486080000000000 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data16.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data16.lean new file mode 100644 index 0000000000000000000000000000000000000000..74f0124b34cc78ebc041d8386fe24681a99140ab --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data16.lean @@ -0,0 +1,146 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_16 : Matrix (Fin 8) (Fin 8) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => -2276708101299057121652517561/52428800000000000 + | 0, 1 => -39034614015379387104670971/13107200000000000 + | 0, 2 => 78202406241711463127687271/83886080000000000 + | 0, 3 => 23832834670493732956060989/209715200000000000 + | 0, 4 => 22048584820368310367604441/52428800000000000 + | 0, 5 => 2553473034802720354150827/26214400000000000 + | 0, 6 => 108255415269241130506236621/26214400000000000 + | 0, 7 => -41435755574383986458435793/2621440000000000 + | 1, 0 => -39034614015379387104670971/13107200000000000 + | 1, 1 => -374098046732570322778463991/1048576000000000000 + | 1, 2 => 2737552373685628655395239/41943040000000000 + | 1, 3 => 22736583113602023500964129/524288000000000000 + | 1, 4 => 1851780972244557042321633/131072000000000000 + | 1, 5 => 507618379345280460543/1310720000000000 + | 1, 6 => 32584839756386941473215337/65536000000000000 + | 1, 7 => -12977256793584317385992841/6553600000000000 + | 2, 0 => 78202406241711463127687271/83886080000000000 + | 2, 1 => 2737552373685628655395239/41943040000000000 + | 2, 2 => -2533363535515609982834649/83886080000000000 + | 2, 3 => 1549750421445905525422653/209715200000000000 + | 2, 4 => -611154627229412014141701/52428800000000000 + | 2, 5 => -578745616368603039939/41943040000000 + | 2, 6 => -64505141078209101647091/1048576000000000 + | 2, 7 => -99002192076248555811717/524288000000000 + | 3, 0 => 23832834670493732956060989/209715200000000000 + | 3, 1 => 22736583113602023500964129/524288000000000000 + | 3, 2 => 1549750421445905525422653/209715200000000000 + | 3, 3 => -11434119007650938281635057/524288000000000000 + | 3, 4 => 1484433801775108633948569/131072000000000000 + | 3, 5 => 207943103777772680639091/13107200000000000 + | 3, 6 => -8974467290230038089021529/65536000000000000 + | 3, 7 => 4777756237785689667105597/6553600000000000 + | 4, 0 => 22048584820368310367604441/52428800000000000 + | 4, 1 => 1851780972244557042321633/131072000000000000 + | 4, 2 => -611154627229412014141701/52428800000000000 + | 4, 3 => 1484433801775108633948569/131072000000000000 + | 4, 4 => -621920505954394918130013/32768000000000000 + | 4, 5 => -28769175431642817466911/3276800000000000 + | 4, 6 => 1147904288009241919132977/16384000000000000 + | 4, 7 => 68877548037338038801803/1638400000000000 + | 5, 0 => 2553473034802720354150827/26214400000000000 + | 5, 1 => 507618379345280460543/1310720000000000 + | 5, 2 => -578745616368603039939/41943040000000 + | 5, 3 => 207943103777772680639091/13107200000000000 + | 5, 4 => -28769175431642817466911/3276800000000000 + | 5, 5 => -47586420975452552673183/1638400000000000 + | 5, 6 => 189274484540778686288811/1638400000000000 + | 5, 7 => -71581303517955662317887/163840000000000 + | 6, 0 => 108255415269241130506236621/26214400000000000 + | 6, 1 => 32584839756386941473215337/65536000000000000 + | 6, 2 => -64505141078209101647091/1048576000000000 + | 6, 3 => -8974467290230038089021529/65536000000000000 + | 6, 4 => 1147904288009241919132977/16384000000000000 + | 6, 5 => 189274484540778686288811/1638400000000000 + | 6, 6 => -7689933670205658822668289/8192000000000000 + | 6, 7 => 384276867404942369454597/819200000000000 + | 7, 0 => -41435755574383986458435793/2621440000000000 + | 7, 1 => -12977256793584317385992841/6553600000000000 + | 7, 2 => -99002192076248555811717/524288000000000 + | 7, 3 => 4777756237785689667105597/6553600000000000 + | 7, 4 => 68877548037338038801803/1638400000000000 + | 7, 5 => -71581303517955662317887/163840000000000 + | 7, 6 => 384276867404942369454597/819200000000000 + | 7, 7 => -2280462391086995129495481/81920000000000 + | _, _ => 0 +def candidateZ_16 : Matrix (Fin 8) (Fin 8) ℚ := fun i j => + match i.val, j.val with + | 1, 1 => 37362124800 + | 1, 6 => -7005398400 + | 1, 7 => 102162060000 + | 2, 2 => 4790016000 + | 2, 5 => -1496880000 + | 2, 7 => 61297236000 + | 3, 3 => 1828915200 + | 3, 4 => -685843200 + | 3, 5 => -1571724000 + | 3, 6 => 4086482400 + | 3, 7 => 15324309000 + | 4, 3 => -685843200 + | 4, 4 => 457228800 + | 4, 7 => -10216206000 + | 5, 2 => -1496880000 + | 5, 3 => -1571724000 + | 5, 5 => 3555090000 + | 5, 6 => -8027019000 + | 5, 7 => -19155386250 + | 6, 1 => -7005398400 + | 6, 3 => 4086482400 + | 6, 5 => -8027019000 + | 6, 6 => 22183761600 + | 6, 7 => -19155386250 + | 7, 1 => 102162060000 + | 7, 2 => 61297236000 + | 7, 3 => 15324309000 + | 7, 4 => -10216206000 + | 7, 5 => -19155386250 + | 7, 6 => -19155386250 + | 7, 7 => 2584061605125/2 + | _, _ => 0 +def lower_16 : Matrix (Fin 8) (Fin 8) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 1 => 1 + | 2, 1 => 3206343438656158285365/28684732320735088531813 + | 2, 2 => 1 + | 3, 1 => -54877189171649281865449/344216787848821062381756 + | 3, 2 => -19880867897726867470809330758846303284631/361700098638082573428816645249340132620844 + | 3, 3 => 1 + | 4, 1 => 349501055170489161415/28684732320735088531813 + | 4, 2 => 7974393916372040975712468793702276397163/180850049319041286714408322624670066310422 + | 4, 3 => -1829024744598826060427709473400208028305860576380374485804792/7345332138093951654543316940989723219670777360892472479457151 + | 4, 4 => 1 + | 5, 1 => 20853333024669907257460/86054196962205265595439 + | 5, 2 => -483886160701375938228598543593722155044225/1446800394552330293715266580997360530483376 + | 5, 3 => -253098726165764191014596400198917614746659257297705091291247965/205669299866630646327212874347712250150781766104989229424800228 + | 5, 4 => -165/56 + | 5, 5 => 1 + | 6, 1 => -16487932909993594598/18151064535373394979 + | 6, 2 => 3176103740377272144257773703204698926817/55646169021243472835202560807590789633976 + | 6, 3 => 658056688030986896637950640517185798341314068974033237357244709/205669299866630646327212874347712250150781766104989229424800228 + | 6, 4 => 429/56 + | 6, 6 => 1 + | 7, 1 => 111656826929597416061840/28684732320735088531813 + | 7, 2 => 657273111018667284729959547377935235866791/55646169021243472835202560807590789633976 + | 7, 3 => 163469086548520079150726534185143592529836289013995969668803285/29381328552375806618173267763958892878683109443569889917828604 + | 7, 4 => -715/32 + | 7, 7 => 1 + | _, _ => 0 +def pivots_16 : Fin 8 → ℚ := fun i => + match i.val with + | 1 => 8970891870719012322527729433/8388608000000000000 + | 2 => 65919842976790549007401833596692239170148819/854492098805315800918589440000000000 + | 3 => 87460869768284682350647274816364634376619946036146669812896296957/1481523604021586220764432978941297183214977024000000000000 + | 4 => 58443121758337845880938015150381796161824002859575616943582223394870562414699/117525314209503226472693071055835571514732437774279559671314416000000000000 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data17.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data17.lean new file mode 100644 index 0000000000000000000000000000000000000000..ac710dc72ef01fe21aba2f96baa35744ead0603a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data17.lean @@ -0,0 +1,184 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_17 : Matrix (Fin 9) (Fin 9) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => -27062893468327394953193285367/419430400000000000 + | 0, 1 => -34150355623889743675914477/104857600000000000 + | 0, 2 => 260924265129905899387586721/83886080000000000 + | 0, 3 => -67528457531024325424642053/41943040000000000 + | 0, 4 => -30137637143983305054521403/52428800000000000 + | 0, 5 => 95166999960067286140262373/26214400000000000 + | 0, 6 => -175538440354363800262225677/26214400000000000 + | 0, 7 => 69154353838247955125781933/2621440000000000 + | 1, 0 => -34150355623889743675914477/104857600000000000 + | 1, 1 => -259433233939629173544831711/1048576000000000000 + | 1, 2 => 10972785710270109216153663/104857600000000000 + | 1, 3 => -408068525315759942414781/13107200000000000 + | 1, 4 => 729849806595543331244547/65536000000000000 + | 1, 5 => 11113201543710491752527/13107200000000000 + | 1, 6 => -12885057439514659527475347/32768000000000000 + | 1, 7 => 1281998470570534260875331/1638400000000000 + | 2, 0 => 260924265129905899387586721/83886080000000000 + | 2, 1 => 10972785710270109216153663/104857600000000000 + | 2, 2 => -16291154585525363835188931/83886080000000000 + | 2, 3 => 4351689332062192591003071/41943040000000000 + | 2, 4 => 83301302217472013622717/10485760000000000 + | 2, 5 => -203973650747133817508343/1048576000000000 + | 2, 6 => 16866893128958580992747463/26214400000000000 + | 2, 7 => -99471136192512553900431/104857600000000 + | 3, 0 => -67528457531024325424642053/41943040000000000 + | 3, 1 => -408068525315759942414781/13107200000000000 + | 3, 2 => 4351689332062192591003071/41943040000000000 + | 3, 3 => -1404556469174930860536363/20971520000000000 + | 3, 4 => 138574461584170298662731/26214400000000000 + | 3, 5 => 322312699672503215100579/2621440000000000 + | 3, 6 => -5414374042135146758937267/13107200000000000 + | 3, 7 => 53455862611083189243987/1310720000000000 + | 4, 0 => -30137637143983305054521403/52428800000000000 + | 4, 1 => 729849806595543331244547/65536000000000000 + | 4, 2 => 83301302217472013622717/10485760000000000 + | 4, 3 => 138574461584170298662731/26214400000000000 + | 4, 4 => -560195899211802719046699/32768000000000000 + | 4, 5 => 1543576781120216089401/131072000000000 + | 4, 6 => 727025046163822366323363/16384000000000000 + | 4, 7 => 948970636189602992298333/1638400000000000 + | 5, 0 => 95166999960067286140262373/26214400000000000 + | 5, 1 => 11113201543710491752527/13107200000000000 + | 5, 2 => -203973650747133817508343/1048576000000000 + | 5, 3 => 322312699672503215100579/2621440000000000 + | 5, 4 => 1543576781120216089401/131072000000000 + | 5, 5 => -428477431290639456169917/1638400000000000 + | 5, 6 => 1054078060656605687920503/1638400000000000 + | 5, 7 => -99701519947816820212179/163840000000000 + | 6, 0 => -175538440354363800262225677/26214400000000000 + | 6, 1 => -12885057439514659527475347/32768000000000000 + | 6, 2 => 16866893128958580992747463/26214400000000000 + | 6, 3 => -5414374042135146758937267/13107200000000000 + | 6, 4 => 727025046163822366323363/16384000000000000 + | 6, 5 => 1054078060656605687920503/1638400000000000 + | 6, 6 => -13417206537411611280214011/8192000000000000 + | 6, 7 => 797255391734832796032267/819200000000000 + | 7, 0 => 69154353838247955125781933/2621440000000000 + | 7, 1 => 1281998470570534260875331/1638400000000000 + | 7, 2 => -99471136192512553900431/104857600000000 + | 7, 3 => 53455862611083189243987/1310720000000000 + | 7, 4 => 948970636189602992298333/1638400000000000 + | 7, 5 => -99701519947816820212179/163840000000000 + | 7, 6 => 797255391734832796032267/819200000000000 + | 7, 7 => -2081041110780259193873307/81920000000000 + | _, _ => 0 +def candidateZ_17 : Matrix (Fin 9) (Fin 9) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 41845579776000 + | 0, 7 => -326918592000 + | 0, 8 => 19451656224000 + | 1, 1 => 523069747200 + | 1, 6 => -16345929600 + | 1, 8 => 6947020080000 + | 2, 2 => 57480192000 + | 2, 5 => -2694384000 + | 2, 6 => -29189160000 + | 2, 7 => 204324120000 + | 2, 8 => 2084106024000 + | 3, 3 => 18289152000 + | 3, 4 => -1143072000 + | 3, 5 => -12573792000 + | 3, 7 => 143026884000 + | 3, 8 => 347351004000 + | 4, 3 => -1143072000 + | 4, 4 => 5372438400 + | 4, 5 => -9430344000 + | 4, 6 => 12259447200 + | 4, 8 => -173675502000 + | 5, 2 => -2694384000 + | 5, 3 => -12573792000 + | 5, 4 => -9430344000 + | 5, 5 => 28740096000 + | 5, 6 => -24081057000 + | 5, 7 => -112378266000 + | 5, 8 => -260513253000 + | 6, 1 => -16345929600 + | 6, 2 => -29189160000 + | 6, 4 => 12259447200 + | 6, 5 => -24081057000 + | 6, 6 => 55532376900 + | 6, 7 => -166013347500 + | 6, 8 => -217094377500 + | 7, 0 => -326918592000 + | 7, 2 => 204324120000 + | 7, 3 => 143026884000 + | 7, 5 => -112378266000 + | 7, 6 => -166013347500 + | 7, 7 => 2442950259750 + | 7, 8 => -151966064250 + | 8, 0 => 19451656224000 + | 8, 1 => 6947020080000 + | 8, 2 => 2084106024000 + | 8, 3 => 347351004000 + | 8, 4 => -173675502000 + | 8, 5 => -260513253000 + | 8, 6 => -217094377500 + | 8, 7 => -151966064250 + | 8, 8 => 355589735626125 + | _, _ => 0 +def lower_17 : Matrix (Fin 9) (Fin 9) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 0 => -17074299907403761141/3933206859654717967797816 + | 1, 1 => 1 + | 2, 0 => -29108706077229270416971/385454272246162360844185968 + | 2, 1 => -23903215896147783453722199043995011350002095/32315731140285268640562251998797048123441158 + | 2, 2 => 1 + | 3, 0 => 359147782598992292617/18354965345055350516389808 + | 3, 1 => -1020691970834637687700866031758787090035195/2308266510020376331468732285628360580245797 + | 3, 2 => -283538310838883583566340872312634146897359890258361021664296369/889442356638458559293052059188217299713741152168140352688919601 + | 3, 3 => 1 + | 4, 0 => 9363311208475594563/417158303296712511736132 + | 4, 1 => -336919552011183192929322540587846345723853/9233066040081505325874929142513442320983188 + | 4, 2 => -2674384864213951993148201591875982195006170634954906789080476291/8894423566384585592930520591882172997137411521681403526889196010 + | 4, 3 => 41271718399593646067579378636731561436803441798995959104813586715550592760494749/214038709054329274198044281167057989778399610209731044834516283303597544939778870 + | 4, 4 => 1 + | 5, 0 => -940578202163404210449/16060594676923431701841082 + | 5, 1 => 28024298102916842812030743772012710744210825/64631462280570537281124503997594096246882316 + | 5, 2 => 5900589436455135874651409741161668775599531241178082353073468491/7115538853107668474344416473505738397709929217345122821511356808 + | 5, 3 => -1401430526633342941929325287926515633420030875226867491768136634829265126585469267/1198616770704243935509047974535524742759037817174493851073291186500146251662761672 + | 5, 4 => -58174865625352179395573885943383634492656038867848316801777736660427658279911833085053323787115/28566515103070080496146958987164600609392781604764280759476047930393443055542870950818632109804 + | 5, 5 => 1 + | 6, 0 => 777567542845922824885/6883112004395756443646178 + | 6, 1 => 6178438691041407044933500593005506423239086/16157865570142634320281125999398524061720579 + | 6, 2 => -2057133941010983182319296466461545847795494641866516829142765187/1368372856366859321989310860289565076482678695643292850290645540 + | 6, 3 => 6270490517061553254110074721234477953828149660737619534303852637778396316275749107/11986167707042439355090479745355247427590378171744938510732911865001462516627616720 + | 6, 4 => 172700158881146687721172640811910407384075966784700668622385597436093506647049466396112581846499/57133030206140160992293917974329201218785563209528561518952095860786886111085741901637264219608 + | 6, 5 => -13/2 + | 6, 6 => 1 + | 7, 0 => -3946103659940235586480/491650857456839745974727 + | 7, 1 => -34622831454985827189343372085165616549621755/4616533020040752662937464571256721160491594 + | 7, 2 => 629345487290773004208066778654630075692558951177432017228794287/273674571273371864397862172057913015296535739128658570058129108 + | 7, 3 => 2987026582292976247742788505452556320158062929302914464670480903750512582333837841/342461934486926838716870849867292783645439376335569671735226053285756071903646192 + | 7, 4 => -3350860664879847076981333962361399641120354020046100771525544081090874237387296933589678125000/1020232682252502874862391392398735736049742200170152884267001711799765823412245391100665432493 + | 7, 5 => 91/2 + | 7, 7 => 1 + | 8, 0 => 228170651102924800000000/491650857456839745974727 + | 8, 1 => 4787760852129261109418493544468144000000000/2308266510020376331468732285628360580245797 + | 8, 2 => 626655198583298383926181935776276753064680559351863359200000000/68418642818342966099465543014478253824133934782164642514532277 + | 8, 3 => 78334892007928146619822509938646242027617215239754443742045819209115579699062500/21403870905432927419804428116705798977839961020973104483451628330359754493977887 + | 8, 4 => 56964631302957400308682677360143793899046018340783713115934249378544862035584047871024528125000/1020232682252502874862391392398735736049742200170152884267001711799765823412245391100665432493 + | 8, 5 => -1547/2 + | 8, 8 => 1 + | _, _ => 0 +def pivots_17 : Fin 9 → ℚ := fun i => + match i.val with + | 0 => 17579822539494988338529186390167/104857600000000000 + | 1 => 357298881352564072724376539224699562576827163427/1952777611775239369224224768000000000000 + | 2 => 7132438257883799186970984462630314526404490299236317488212446280419/10589218780048676828139438734965816729089198653440000000000 + | 3 => 764567672612969600362833976756847845287421247630180265253375615588780790279384101527/4553944865988907823580426543043672574534354699100878605767268357120000000000 + | 4 => 327993584784674896736635346350877153046895570190502280610114113324794914802979358539561829226742077/5479390951790829419469933597876684538327030021369114747763616852572097150458339072000000000000 + | 5 => 9670059656402727573219555154447076358618182987506578229349447920117676330673762758147876668370922239589/13372393812820005681396336458448709039551180966070227884664444836901890600628982790234641956772249600 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data18.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data18.lean new file mode 100644 index 0000000000000000000000000000000000000000..2ac54d22fe7b5d2451de6a03b8318a558d4c3fd1 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data18.lean @@ -0,0 +1,162 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_18 : Matrix (Fin 9) (Fin 9) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => -3559166385880423516847027379/41943040000000000 + | 0, 1 => 43700029260178412251303173/3276800000000000 + | 0, 2 => -157097886646298732847063351/41943040000000000 + | 0, 3 => 45795850251189055946275347/20971520000000000 + | 0, 4 => -15768543277252499592049191/5242880000000000 + | 0, 5 => 15774590706413201698776741/2621440000000000 + | 0, 6 => -111481601475376052708801013/13107200000000000 + | 0, 7 => -58408977661685586058262139/1310720000000000 + | 1, 0 => 43700029260178412251303173/3276800000000000 + | 1, 1 => -81940194402186836366199549/26214400000000000 + | 1, 2 => 5636036629375968042063837/5242880000000000 + | 1, 3 => -2298714004872189626128407/5242880000000000 + | 1, 4 => 297813059860269307535181/1638400000000000 + | 1, 5 => -427966983073658698687017/3276800000000000 + | 1, 6 => 460639052423449997118021/1638400000000000 + | 1, 7 => 856489912851915268585659/327680000000000 + | 2, 0 => -157097886646298732847063351/41943040000000000 + | 2, 1 => 5636036629375968042063837/5242880000000000 + | 2, 2 => -17038127051364859101889227/41943040000000000 + | 2, 3 => 3236875371562490528333463/20971520000000000 + | 2, 4 => 109159200441997398693/5242880000000000 + | 2, 5 => -76974792598120601955771/524288000000000 + | 2, 6 => 525900691396984091231043/2621440000000000 + | 2, 7 => 166478085484275751174989/262144000000000 + | 3, 0 => 45795850251189055946275347/20971520000000000 + | 3, 1 => -2298714004872189626128407/5242880000000000 + | 3, 2 => 3236875371562490528333463/20971520000000000 + | 3, 3 => -152920142255560594957119/2097152000000000 + | 3, 4 => 76480320836604209603463/2621440000000000 + | 3, 5 => 34507713700153945513647/1310720000000000 + | 3, 6 => -126720387057916007218863/1310720000000000 + | 3, 7 => -293804443074929463225549/655360000000000 + | 4, 0 => -15768543277252499592049191/5242880000000000 + | 4, 1 => 297813059860269307535181/1638400000000000 + | 4, 2 => 109159200441997398693/5242880000000000 + | 4, 3 => 76480320836604209603463/2621440000000000 + | 4, 4 => -59366777784768563477067/655360000000000 + | 4, 5 => 50562764756881342854273/327680000000000 + | 4, 6 => -141645844790470070219169/1638400000000000 + | 4, 7 => -70438571087878610696079/163840000000000 + | 5, 0 => 15774590706413201698776741/2621440000000000 + | 5, 1 => -427966983073658698687017/3276800000000000 + | 5, 2 => -76974792598120601955771/524288000000000 + | 5, 3 => 34507713700153945513647/1310720000000000 + | 5, 4 => 50562764756881342854273/327680000000000 + | 5, 5 => -60223184109272615717979/163840000000000 + | 5, 6 => 241267392281008969222347/819200000000000 + | 5, 7 => 153598002652096074585513/81920000000000 + | 6, 0 => -111481601475376052708801013/13107200000000000 + | 6, 1 => 460639052423449997118021/1638400000000000 + | 6, 2 => 525900691396984091231043/2621440000000000 + | 6, 3 => -126720387057916007218863/1310720000000000 + | 6, 4 => -141645844790470070219169/1638400000000000 + | 6, 5 => 241267392281008969222347/819200000000000 + | 6, 6 => -149658956021574385833447/819200000000000 + | 6, 7 => -32035926190597582065813/16384000000000 + | 7, 0 => -58408977661685586058262139/1310720000000000 + | 7, 1 => 856489912851915268585659/327680000000000 + | 7, 2 => 166478085484275751174989/262144000000000 + | 7, 3 => -293804443074929463225549/655360000000000 + | 7, 4 => -70438571087878610696079/163840000000000 + | 7, 5 => 153598002652096074585513/81920000000000 + | 7, 6 => -32035926190597582065813/16384000000000 + | 7, 7 => -884740548279231685308267/40960000000000 + | _, _ => 0 +def candidateZ_18 : Matrix (Fin 9) (Fin 9) ℚ := fun i j => + match i.val, j.val with + | 1, 1 => 7846046208000 + | 1, 7 => -858161304000 + | 1, 8 => 16672848192000 + | 2, 2 => 747242496000 + | 2, 6 => -140107968000 + | 2, 8 => 11115232128000 + | 3, 3 => 201180672000 + | 3, 5 => -47151720000 + | 3, 6 => -163459296000 + | 3, 7 => 643620978000 + | 3, 8 => 4168212048000 + | 4, 4 => 98761420800 + | 4, 5 => -113164128000 + | 4, 7 => 367783416000 + | 5, 3 => -47151720000 + | 5, 4 => -113164128000 + | 5, 5 => 149313780000 + | 5, 7 => -421418497500 + | 5, 8 => -1736755020000 + | 6, 2 => -140107968000 + | 6, 3 => -163459296000 + | 6, 6 => 329837508000 + | 6, 7 => -1195296102000 + | 6, 8 => -2084106024000 + | 7, 1 => -858161304000 + | 7, 3 => 643620978000 + | 7, 4 => 367783416000 + | 7, 5 => -421418497500 + | 7, 6 => -1195296102000 + | 7, 7 => 6169949911125 + | 7, 8 => -1823592771000 + | 8, 1 => 16672848192000 + | 8, 2 => 11115232128000 + | 8, 3 => 4168212048000 + | 8, 5 => -1736755020000 + | 8, 6 => -2084106024000 + | 8, 7 => -1823592771000 + | 8, 8 => 354298024080000 + | _, _ => 0 +def lower_18 : Matrix (Fin 9) (Fin 9) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 1 => 1 + | 2, 1 => -349137946238921854792/1525877070950641412829 + | 2, 2 => 1 + | 3, 1 => 2448474494275238057/871929754828937950188 + | 3, 2 => -28272705865850687826561643980455827573/32289923184509364807145527796719201480 + | 3, 3 => 1 + | 4, 1 => -10834989514912180131/72660812902411495849 + | 4, 2 => -979061977497069791996229265720311753/896942310680815689087375772131088930 + | 4, 3 => -440685757333367566070661575038916090137433038690979892/629581877147636158092152188207568795896263505459777553 + | 4, 4 => 1 + | 5, 1 => 34030303649537365180/217982438707234487547 + | 5, 2 => 12187338312118806997808062708304419093/8610646182535830615238807412458453728 + | 5, 3 => 1955080829813198644410494898659162001703219742000324505/2518327508590544632368608752830275183585054021839110212 + | 5, 4 => -134094910016360450773526967315269896725107554663849514202706685510965/109148753121288526125863247197819858970566946403445427530838707355024 + | 5, 5 => 1 + | 6, 1 => 157812974422168849522/1525877070950641412829 + | 6, 2 => 45513952742062515426150455606615999639/64579846369018729614291055593438402960 + | 6, 3 => -1097097007256332713510526764085515391074758346482444027/629581877147636158092152188207568795896263505459777553 + | 6, 4 => 5868609758841276148633964435715850408866403574769391852020100000000/15917526496854576726688390216348729433207679683835791514913978155941 + | 6, 5 => -156/35 + | 6, 6 => 1 + | 7, 1 => -65611877688532324320/72660812902411495849 + | 7, 2 => -54377807926711122382500801023294698143/7175538485446525512699006177048711440 + | 7, 3 => 2678724067668904800382475039040753287522149412899359696/629581877147636158092152188207568795896263505459777553 + | 7, 4 => 992051781081002513030703127326879805091498553059561527576614111642545/436595012485154104503452988791279435882267785613781710123354829420096 + | 7, 5 => 351/20 + | 7, 7 => 1 + | 8, 1 => 1832714240000000000/72660812902411495849 + | 8, 2 => 86328815377143985393057963520000000/269082693204244706726212731639326679 + | 8, 3 => 1430508497687333005102158111282728725862998579200000000/629581877147636158092152188207568795896263505459777553 + | 8, 4 => 49883182950150847263388697703584728475364430385539830742170850000000/6821797070080532882866452949863741185660434150215339220677419209689 + | 8, 5 => -442/5 + | 8, 8 => 1 + | _, _ => 0 +def pivots_18 : Fin 9 → ℚ := fun i => + match i.val with + | 1 => 3340430247323221822626880023/838860800000000000 + | 2 => 84153190555388693826262495905614664917139/297618689648277486997504000000000 + | 3 => 27486915174388647026145272384954246060034968384868428186427/587820112727779370000302586023830441164800000000000 + | 4 => 6579398154789361307939559277196232870110361943555737572149088472911120763/251832750859054463236860875283027518358505402183911021200000000000 + | 5 => 7480414033596234167413017594446696521620202424169281059330524956670415242021/186280538660332417921473275217612559309767588528546862985964727219240960 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data19.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data19.lean new file mode 100644 index 0000000000000000000000000000000000000000..470dd91819f9b1ff279232b4b94f71cfd40f0d45 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data19.lean @@ -0,0 +1,202 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_19 : Matrix (Fin 10) (Fin 10) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => -22693099803596038799039320263/209715200000000000 + | 0, 1 => 2702377258995069402702006051/104857600000000000 + | 0, 2 => -75142211033583596476200627/8388608000000000 + | 0, 3 => 14766383937965483058974739/4194304000000000 + | 0, 4 => -5511147190592216732622063/5242880000000000 + | 0, 5 => 7980474838179577610603727/13107200000000000 + | 0, 6 => -114214449015342819092842893/13107200000000000 + | 0, 7 => 15237169390990960795194813/262144000000000 + | 1, 0 => 2702377258995069402702006051/104857600000000000 + | 1, 1 => -333726928481320238730768903/52428800000000000 + | 1, 2 => 48289254450191241887451051/20971520000000000 + | 1, 3 => -10153357419755611709274627/10485760000000000 + | 1, 4 => 908184765784913635277259/2621440000000000 + | 1, 5 => -1019757214709519396489379/6553600000000000 + | 1, 6 => 11402120818106472624739569/6553600000000000 + | 1, 7 => -8025292448927789565871341/655360000000000 + | 2, 0 => -75142211033583596476200627/8388608000000000 + | 2, 1 => 48289254450191241887451051/20971520000000000 + | 2, 2 => -37648602224655100714998963/41943040000000000 + | 2, 3 => 9278879137014220083120771/20971520000000000 + | 2, 4 => -1279464695992326165509187/5242880000000000 + | 2, 5 => 488068742424207599021367/2621440000000000 + | 2, 6 => -1577990685084360947348949/2621440000000000 + | 2, 7 => 4397077893934901813915277/1310720000000000 + | 3, 0 => 14766383937965483058974739/4194304000000000 + | 3, 1 => -10153357419755611709274627/10485760000000000 + | 3, 2 => 9278879137014220083120771/20971520000000000 + | 3, 3 => -601273345026853390678479/2097152000000000 + | 3, 4 => 5095867887885096310527/20971520000000 + | 3, 5 => -66971412540394818930243/262144000000000 + | 3, 6 => 423492380929481504822181/1310720000000000 + | 3, 7 => -316097984120195393369253/655360000000000 + | 4, 0 => -5511147190592216732622063/5242880000000000 + | 4, 1 => 908184765784913635277259/2621440000000000 + | 4, 2 => -1279464695992326165509187/5242880000000000 + | 4, 3 => 5095867887885096310527/20971520000000 + | 4, 4 => -38268821834268590378583/131072000000000 + | 4, 5 => 120716948708384445134487/327680000000000 + | 4, 6 => -96794549499067619556357/327680000000000 + | 4, 7 => -152177568634600729759539/163840000000000 + | 5, 0 => 7980474838179577610603727/13107200000000000 + | 5, 1 => -1019757214709519396489379/6553600000000000 + | 5, 2 => 488068742424207599021367/2621440000000000 + | 5, 3 => -66971412540394818930243/262144000000000 + | 5, 4 => 120716948708384445134487/327680000000000 + | 5, 5 => -433804997186099031291183/819200000000000 + | 5, 6 => 429290867351544749347797/819200000000000 + | 5, 7 => 90088259697128585251359/81920000000000 + | 6, 0 => -114214449015342819092842893/13107200000000000 + | 6, 1 => 11402120818106472624739569/6553600000000000 + | 6, 2 => -1577990685084360947348949/2621440000000000 + | 6, 3 => 423492380929481504822181/1310720000000000 + | 6, 4 => -96794549499067619556357/327680000000000 + | 6, 5 => 429290867351544749347797/819200000000000 + | 6, 6 => -1253076332636888755282287/819200000000000 + | 6, 7 => 415758366080515083757131/81920000000000 + | 7, 0 => 15237169390990960795194813/262144000000000 + | 7, 1 => -8025292448927789565871341/655360000000000 + | 7, 2 => 4397077893934901813915277/1310720000000000 + | 7, 3 => -316097984120195393369253/655360000000000 + | 7, 4 => -152177568634600729759539/163840000000000 + | 7, 5 => 90088259697128585251359/81920000000000 + | 7, 6 => 415758366080515083757131/81920000000000 + | 7, 7 => -68818433127534301774563/1638400000000 + | _, _ => 0 +def candidateZ_19 : Matrix (Fin 10) (Fin 10) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 12804747411456000 + | 0, 8 => -50018544576000 + | 0, 9 => 3801409387776000 + | 1, 1 => 125536739328000 + | 1, 7 => -1961511552000 + | 1, 9 => 1425528520416000 + | 2, 2 => 10461394944000 + | 2, 6 => -245188944000 + | 2, 7 => -3677834160000 + | 2, 8 => 34735100400000 + | 2, 9 => 475176173472000 + | 3, 3 => 2414168064000 + | 3, 5 => -75442752000 + | 3, 6 => -1225944720000 + | 3, 8 => 29177484336000 + | 3, 9 => 118794043368000 + | 4, 4 => 1265380704000 + | 4, 5 => -678984768000 + | 4, 6 => -1103350248000 + | 4, 7 => 2574483912000 + | 4, 8 => 9378477108000 + | 5, 3 => -75442752000 + | 5, 4 => -678984768000 + | 5, 5 => 572107536000 + | 5, 8 => -7641722088000 + | 5, 9 => -29698510842000 + | 6, 2 => -245188944000 + | 6, 3 => -1225944720000 + | 6, 4 => -1103350248000 + | 6, 6 => 3544293753000 + | 6, 7 => -6574128561000 + | 6, 8 => -16933361445000 + | 6, 9 => -29698510842000 + | 7, 1 => -1961511552000 + | 7, 2 => -3677834160000 + | 7, 4 => 2574483912000 + | 7, 6 => -6574128561000 + | 7, 7 => 17439063642000 + | 7, 8 => -19538493975000 + | 7, 9 => -22273883131500 + | 8, 0 => -50018544576000 + | 8, 2 => 34735100400000 + | 8, 3 => 29177484336000 + | 8, 4 => 9378477108000 + | 8, 5 => -7641722088000 + | 8, 6 => -16933361445000 + | 8, 7 => -19538493975000 + | 8, 8 => 693290894546250 + | 8, 9 => -14849255421000 + | 9, 0 => 3801409387776000 + | 9, 1 => 1425528520416000 + | 9, 2 => 475176173472000 + | 9, 3 => 118794043368000 + | 9, 5 => -29698510842000 + | 9, 6 => -29698510842000 + | 9, 7 => -22273883131500 + | 9, 8 => -14849255421000 + | 9, 9 => 121635819624193875 + | _, _ => 0 +def lower_19 : Matrix (Fin 10) (Fin 10) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 0 => -2961386467910644914/3436008051774471467006057 + | 1, 1 => 1 + | 2, 0 => 32868502091063334461/54976128828391543472096912 + | 2, 1 => -382681628336533263172827585860911581922227/664405076952214538692620490978325294375408 + | 2, 2 => 1 + | 3, 0 => -12605880710080439027/54976128828391543472096912 + | 3, 1 => 161737392301757251513277454079926045377115/664405076952214538692620490978325294375408 + | 3, 2 => -50250215728550168294149709946214804555490003532691546631/1073340545827898416393588652894857493507658149711501015285 + | 3, 3 => 1 + | 4, 0 => -3030333728405132259/13744032207097885868024228 + | 4, 1 => 160523298500011983288271819972957034094987/1328810153904429077385240981956650588750816 + | 4, 2 => -2417829575181235969321246961770873991540939361714610356621/2146681091655796832787177305789714987015316299423002030570 + | 4, 3 => -22965661866173979128366345222917969142808057833824257675971717421026667/17979035256509678741586586582984183445732267398041101641709395188613418 + | 4, 4 => 1 + | 5, 0 => -174152127966390163/6872016103548942934012114 + | 5, 1 => 63173795145917582387221887164825763389205/1328810153904429077385240981956650588750816 + | 5, 2 => 257381482090328304440332959885953020569008045379687613094/1073340545827898416393588652894857493507658149711501015285 + | 5, 3 => 25609147132316783113580256703554979735227017555590674768001803342857627/26968552884764518112379879874476275168598401097061652462564092782920127 + | 5, 4 => -179211548793387697380180474676542143193021577375388073863862434243516388587231255/822217327179269096824488745375019221164303403948976369565640125598119135841515624 + | 5, 5 => 1 + | 6, 0 => 37119364338609142477/48104112724842600538084798 + | 6, 1 => -1383501467797740445417107983773565585170851/2325417769332750885424171718424138530313928 + | 6, 2 => 16103069103965665259682055101994537939308667687238368458239/7513383820795288914755120570264002454553607047980507106995 + | 6, 3 => -294804672437498922168256413775704224318702197343812657692819044881777563/1006825974364542009528848848647114272961006974290301691935726130562351408 + | 6, 4 => -14448862161388126485759117178453977351373474575407922522472660616272942502486528287/7674028387006511570361894956833512730866831770190446115945974505582445267854145824 + | 6, 5 => -1003184935151953416634223281268462615532647423841289158293770463036325500339108675798477289/320375745541799464072048113497256804323482244994208291721481509924111074377238562568353164 + | 6, 6 => 1 + | 7, 0 => -6140285291563728480/3436008051774471467006057 + | 7, 1 => 891363664038882269233634801038604137294155/664405076952214538692620490978325294375408 + | 7, 2 => -5842331865258346644158257101898369234067728509060109004448/1073340545827898416393588652894857493507658149711501015285 + | 7, 3 => -49059253193772961329746664366615898786316214020069688969975906294068087/71916141026038714966346346331936733782929069592164406566837580754453672 + | 7, 4 => 408866832458305351573659151621463148809590530760332785016532675145726508490254367/91357480797696566313832082819446580129367044883219596618404458399791015093501736 + | 7, 5 => 83396419025943334833770561841527230337997496793868644429800348698404397416799524488175607/11441990912207123716858861196330600154410080178364581847195768211575395513472805806012613 + | 7, 6 => -9 + | 7, 7 => 1 + | 8, 0 => -13421802836480000000000/3436008051774471467006057 + | 8, 1 => -1295686998080400818447338374729600000000/41525317309513408668288780686145330898463 + | 8, 2 => 134876713521216767239170334596868548136430347855078400000/214668109165579683278717730578971498701531629942300203057 + | 8, 3 => 22634898736030881597541500320992524541650678016921698093845936794437500/26968552884764518112379879874476275168598401097061652462564092782920127 + | 8, 4 => 6454554530171126601374164656915579337824189367448454919916324457545829979121008045/3288869308717076387297954981500076884657213615795905478262560502392476543366062496 + | 8, 5 => -621851393826751641183301789624188289755277715016465090228859509403781493934936397535624347/45767963648828494867435444785322400617640320713458327388783072846301582053891223224050452 + | 8, 6 => 85 + | 8, 8 => 1 + | 9, 0 => 1020057028074905600000000/3436008051774471467006057 + | 9, 1 => 165789376611013204396971335065112850000000/41525317309513408668288780686145330898463 + | 9, 2 => 3550303167275036238900210528190229417245897134919123200000/214668109165579683278717730578971498701531629942300203057 + | 9, 3 => -58643223061267437284649920144160396796768331325378044053105571334328125/17979035256509678741586586582984183445732267398041101641709395188613418 + | 9, 4 => 17464209939361954639662753282747761972857280764878129882714513507669482484305828555/730859846381572530510656662555572641034936359065756772947235667198328120748013888 + | 9, 5 => -470528345714752654295653291172328016180092196620919391389024803430615333210287220043706969/91535927297656989734870889570644801235280641426916654777566145692603164107782446448100904 + | 9, 6 => -1938 + | 9, 9 => 1 + | _, _ => 0 +def pivots_19 : Fin 10 → ℚ := fun i => + match i.val with + | 0 => 2685376904705879952676290239320263/52428800000000000 + | 1 => 1909040381322096342228407329403169208785883911201/351847224501705878221420236800000000000 + | 2 => 3289640437299075230685203627170908148295369470509460482408212613/8708490224628066401551915299351105298437347737600000000 + | 3 => 31790341360690220599246615736873511834817615024408596491303314623856765266711/137387589865970997298379347570541759168980243163072129956480000000000 + | 4 => 33041728287192005333626007782733694299111342129019058009411009792301715357819127055517/115065825641661943946154154131098774052686511347463050506940129207125875200000 + | 5 => 18501699305038919050160778554466580449681099648415528846915557198117414545285526988322395221/1539918688672284508730272474191165400040688954080936081271541817306765423139848192000 + | 6 => 98048496096756067261891323132563398837289446263970298601171328383568919254762877516980741523513427/2130290671654562670193358884553188101475622200480969420277903027027855455599300571883075584000 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data20.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data20.lean new file mode 100644 index 0000000000000000000000000000000000000000..b1198719f5bd7a003ed62c2c1cf8d9c634eaa864 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data20.lean @@ -0,0 +1,185 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_20 : Matrix (Fin 10) (Fin 10) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => -864345790529147882613755097/1638400000000000 + | 0, 1 => 21667622927027497262745903/204800000000000 + | 0, 2 => -11712315275254254792460329/327680000000000 + | 0, 3 => 665376664948039201360203/40960000000000 + | 0, 4 => -316262058979922913891033/40960000000000 + | 0, 5 => 5363979077413683764037/25600000000000 + | 0, 6 => 1356924469605003889899309/102400000000000 + | 0, 7 => -99760004425375579574289/2560000000000 + | 1, 0 => 21667622927027497262745903/204800000000000 + | 1, 1 => -23371021993295094552757323/819200000000000 + | 1, 2 => 1943037668945799386453493/163840000000000 + | 1, 3 => -1013982585631618048647201/163840000000000 + | 1, 4 => 30613754919741298283979/10240000000000 + | 1, 5 => 107082038149227953680869/102400000000000 + | 1, 6 => -520977417754125297368403/51200000000000 + | 1, 7 => 304457703228940211619669/10240000000000 + | 2, 0 => -11712315275254254792460329/327680000000000 + | 2, 1 => 1943037668945799386453493/163840000000000 + | 2, 2 => -355964824312558132018347/65536000000000 + | 2, 3 => 97684912586085571093347/32768000000000 + | 2, 4 => -11858364672253510424013/8192000000000 + | 2, 5 => -14013038479459638758139/20480000000000 + | 2, 6 => 117196994897535165704091/20480000000000 + | 2, 7 => -34211653005025978665183/2048000000000 + | 3, 0 => 665376664948039201360203/40960000000000 + | 3, 1 => -1013982585631618048647201/163840000000000 + | 3, 2 => 97684912586085571093347/32768000000000 + | 3, 3 => -54884862420967333061307/32768000000000 + | 3, 4 => 333816883149802681629/409600000000 + | 3, 5 => 8819254098389714698719/20480000000000 + | 3, 6 => -35062147478835063928341/10240000000000 + | 3, 7 => 20460760081953150590631/2048000000000 + | 4, 0 => -316262058979922913891033/40960000000000 + | 4, 1 => 30613754919741298283979/10240000000000 + | 4, 2 => -11858364672253510424013/8192000000000 + | 4, 3 => 333816883149802681629/409600000000 + | 4, 4 => -405636934175189416161/1024000000000 + | 4, 5 => -272920889814962733729/1280000000000 + | 4, 6 => 4300425691175779286121/2560000000000 + | 4, 7 => -627014474788464764001/128000000000 + | 5, 0 => 5363979077413683764037/25600000000000 + | 5, 1 => 107082038149227953680869/102400000000000 + | 5, 2 => -14013038479459638758139/20480000000000 + | 5, 3 => 8819254098389714698719/20480000000000 + | 5, 4 => -272920889814962733729/1280000000000 + | 5, 5 => -2024204103566300379339/12800000000000 + | 5, 6 => 7072091643721157882829/6400000000000 + | 5, 7 => -4132909998582898800267/1280000000000 + | 6, 0 => 1356924469605003889899309/102400000000000 + | 6, 1 => -520977417754125297368403/51200000000000 + | 6, 2 => 117196994897535165704091/20480000000000 + | 6, 3 => -35062147478835063928341/10240000000000 + | 6, 4 => 4300425691175779286121/2560000000000 + | 6, 5 => 7072091643721157882829/6400000000000 + | 6, 6 => -51489116962575084283491/6400000000000 + | 6, 7 => 15026634633786455969289/640000000000 + | 7, 0 => -99760004425375579574289/2560000000000 + | 7, 1 => 304457703228940211619669/10240000000000 + | 7, 2 => -34211653005025978665183/2048000000000 + | 7, 3 => 20460760081953150590631/2048000000000 + | 7, 4 => -627014474788464764001/128000000000 + | 7, 5 => -4132909998582898800267/1280000000000 + | 7, 6 => 15026634633786455969289/640000000000 + | 7, 7 => -8768897177979921681699/128000000000 + | _, _ => 0 +def candidateZ_20 : Matrix (Fin 10) (Fin 10) ℚ := fun i j => + match i.val, j.val with + | 1, 1 => 2134124568576000 + | 1, 8 => -133382785536000 + | 1, 9 => 3326233214304000 + | 2, 2 => 156920924160000 + | 2, 7 => -17163226080000 + | 2, 9 => 2375880867360000 + | 3, 3 => 31384184832000 + | 3, 6 => -4413400992000 + | 3, 7 => -21454032600000 + | 3, 8 => 116709937344000 + | 3, 9 => 1069146390312000 + | 4, 4 => 14485008384000 + | 4, 5 => -2263282560000 + | 4, 6 => -11769069312000 + | 4, 8 => 100037089152000 + | 4, 9 => 237588086736000 + | 5, 4 => -2263282560000 + | 5, 5 => 5148967824000 + | 5, 6 => -8091235152000 + | 5, 7 => 10114043940000 + | 5, 9 => -148492554210000 + | 6, 3 => -4413400992000 + | 6, 4 => -11769069312000 + | 6, 5 => -8091235152000 + | 6, 6 => 31384184832000 + | 6, 7 => -21913761870000 + | 6, 8 => -108373513248000 + | 6, 9 => -267286597578000 + | 7, 2 => -17163226080000 + | 7, 3 => -21454032600000 + | 7, 5 => 10114043940000 + | 7, 6 => -21913761870000 + | 7, 7 => 62791356127500 + | 7, 8 => -182359277100000 + | 7, 9 => -259861969867500 + | 8, 1 => -133382785536000 + | 8, 3 => 116709937344000 + | 8, 4 => 100037089152000 + | 8, 6 => -108373513248000 + | 8, 7 => -182359277100000 + | 8, 8 => 1921545754128000 + | 8, 9 => -207889575894000 + | 9, 1 => 3326233214304000 + | 9, 2 => 2375880867360000 + | 9, 3 => 1069146390312000 + | 9, 4 => 237588086736000 + | 9, 5 => -148492554210000 + | 9, 6 => -267286597578000 + | 9, 7 => -259861969867500 + | 9, 8 => -207889575894000 + | 9, 9 => 121494751697694375 + | _, _ => 0 +def lower_20 : Matrix (Fin 10) (Fin 10) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 1 => 1 + | 2, 1 => -35271522237113355/147707684316989588 + | 2, 2 => 1 + | 3, 1 => 13552063136396403/53711885206178032 + | 3, 2 => -26951235569631035647864429672331/63363303569163631484444183694484 + | 3, 3 => 1 + | 4, 1 => -27845094595539873/147707684316989588 + | 4, 2 => 6198614363370263024421143942010/15840825892290907871111045923621 + | 4, 3 => -5488928522115734285223809582285965948253331084/7080288448599026212327340384223832181879775341 + | 4, 4 => 1 + | 5, 1 => -37369443052409085/295415368633979176 + | 5, 2 => 32220490734518520519475982493591/126726607138327262968888367388968 + | 5, 3 => -53485551765591815944753102349372532681677976141/70802884485990262123273403842238321818797753410 + | 5, 4 => 155055478876273221503467781611480320610092472948218709/258592337393080717387838505162845046188018716700687080 + | 5, 5 => 1 + | 6, 1 => 69049063039899869/147707684316989588 + | 6, 2 => -61957215264707741137696949969195/63363303569163631484444183694484 + | 6, 3 => 8471070127087045295071733714616727047888131791/3453799243219037176745044089865283991160866020 + | 6, 4 => -963366712386391410456130993466415229299535440762277583/387888506089621076081757757744267569282028075051030620 + | 6, 5 => -13105986926343292700786978652372053726565753743555683428802/5846458902123404029581360979142345959067188987899263029263 + | 6, 6 => 1 + | 7, 1 => -94978031352709435/147707684316989588 + | 7, 2 => 80006742500841326724882139142513/63363303569163631484444183694484 + | 7, 3 => -324387224145991101150322110070575031860539967/93778654948331473010958150784421618303043382 + | 7, 4 => 700049595221624343959385951934715978288822982291462173/310310804871696860865406206195414055425622460040824496 + | 7, 5 => 18575780183308702392787205969949921234474746861647671946330/5846458902123404029581360979142345959067188987899263029263 + | 7, 6 => -25/4 + | 7, 7 => 1 + | 8, 1 => -814956800000000/36926921079247397 + | 8, 2 => -1816150174951180555904480000000/15840825892290907871111045923621 + | 8, 3 => 3886390958787136362754813016561109161256000000/7080288448599026212327340384223832181879775341 + | 8, 4 => 149213033060034671014822190201296242239403726466795399/25859233739308071738783850516284504618801871670068708 + | 8, 5 => -14914416372581188314263682050497007718619371838980860090227/5846458902123404029581360979142345959067188987899263029263 + | 8, 6 => 34 + | 8, 8 => 1 + | 9, 1 => 20947021200000000/36926921079247397 + | 9, 2 => 251408737722295139958793710000000/15840825892290907871111045923621 + | 9, 3 => 40984263831233174279840627463764636604961500000/7080288448599026212327340384223832181879775341 + | 9, 4 => 10135444848994695812098617396521887108295239968439950737/413747739828929147820541608260552073900829946721099328 + | 9, 5 => 283373911079042577971009958959443146653768064940636341714313/15590557072329077412216962611046255890845837301064701411368 + | 9, 6 => -969/4 + | 9, 9 => 1 + | _, _ => 0 +def pivots_20 : Fin 10 → ℚ := fun i => + match i.val with + | 1 => 28859857000887030552757323/819200000000000 + | 2 => 66204466578727251847483047558206891697/55000970451126304768000000000 + | 3 => 108500527995462094776803773196024729519269878176064369/64884022854823558640070844103151616000000000 + | 4 => 205758115091506213711939562636087280358501374303133291938747/906276921420675355177899569180650519280611243648000 + | 5 => 62025883457496784256180711274175290781140200177514623676486176031/1034369349572322869551354020651380184752074866802748320000 + | 6 => 99280203996433602814754380959974749006154407584400647898000155432387/61592324236361787307523802907837060309514418967169190760960000 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data21.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data21.lean new file mode 100644 index 0000000000000000000000000000000000000000..67c490d4a5e555a316f9304aec543e2005dc2842 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data21.lean @@ -0,0 +1,227 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_21 : Matrix (Fin 11) (Fin 11) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => -96711588542532735223983531/32768000000000 + | 0, 1 => 57038851132594341185352177/163840000000000 + | 0, 2 => -5636036476590197124447/327680000000 + | 0, 3 => -1952083051117812873373113/32768000000000 + | 0, 4 => 418641912860774562758799/4096000000000 + | 0, 5 => -644220666819787412766411/4096000000000 + | 0, 6 => 1256376941124933712895811/5120000000000 + | 0, 7 => -135618250205634004439631/409600000000 + | 1, 0 => 57038851132594341185352177/163840000000000 + | 1, 1 => -44082193767443568976121883/819200000000000 + | 1, 2 => 492577388419375083797973/40960000000000 + | 1, 3 => -281862084701495601299997/163840000000000 + | 1, 4 => -57918765188790724575357/20480000000000 + | 1, 5 => 143714000293113981147417/20480000000000 + | 1, 6 => -331513340018520454483689/25600000000000 + | 1, 7 => 195188481739185067894761/10240000000000 + | 2, 0 => -5636036476590197124447/327680000000 + | 2, 1 => 492577388419375083797973/40960000000000 + | 2, 2 => -16263180195796078115571/2048000000000 + | 2, 3 => 53358620528514863973411/8192000000000 + | 2, 4 => -6801410828588460561477/1024000000000 + | 2, 5 => 1665119090212013288853/204800000000 + | 2, 6 => -14227460106212415583521/1280000000000 + | 2, 7 => 7041025764192505558473/512000000000 + | 3, 0 => -1952083051117812873373113/32768000000000 + | 3, 1 => -281862084701495601299997/163840000000000 + | 3, 2 => 53358620528514863973411/8192000000000 + | 3, 3 => -9444449794627227102723/1310720000000 + | 3, 4 => 34389795345971868711909/4096000000000 + | 3, 5 => -45427929111821472609393/4096000000000 + | 3, 6 => 81562090823302666065489/5120000000000 + | 3, 7 => -41788312207893754536033/2048000000000 + | 4, 0 => 418641912860774562758799/4096000000000 + | 4, 1 => -57918765188790724575357/20480000000000 + | 4, 2 => -6801410828588460561477/1024000000000 + | 4, 3 => 34389795345971868711909/4096000000000 + | 4, 4 => -1046564151268430692359/102400000000 + | 4, 5 => 7064452961983792435599/512000000000 + | 4, 6 => -12849900797681178702471/640000000000 + | 4, 7 => 6640967897736757856271/256000000000 + | 5, 0 => -644220666819787412766411/4096000000000 + | 5, 1 => 143714000293113981147417/20480000000000 + | 5, 2 => 1665119090212013288853/204800000000 + | 5, 3 => -45427929111821472609393/4096000000000 + | 5, 4 => 7064452961983792435599/512000000000 + | 5, 5 => -9636033814007219448291/512000000000 + | 5, 6 => 17633221184266489332531/640000000000 + | 5, 7 => -365961031875624676491/10240000000 + | 6, 0 => 1256376941124933712895811/5120000000000 + | 6, 1 => -331513340018520454483689/25600000000000 + | 6, 2 => -14227460106212415583521/1280000000000 + | 6, 3 => 81562090823302666065489/5120000000000 + | 6, 4 => -12849900797681178702471/640000000000 + | 6, 5 => 17633221184266489332531/640000000000 + | 6, 6 => -32379448935674822168187/800000000000 + | 6, 7 => 16838009783175354176403/320000000000 + | 7, 0 => -135618250205634004439631/409600000000 + | 7, 1 => 195188481739185067894761/10240000000000 + | 7, 2 => 7041025764192505558473/512000000000 + | 7, 3 => -41788312207893754536033/2048000000000 + | 7, 4 => 6640967897736757856271/256000000000 + | 7, 5 => -365961031875624676491/10240000000 + | 7, 6 => 16838009783175354176403/320000000000 + | 7, 7 => -8768897177979921681699/128000000000 + | _, _ => 0 +def candidateZ_21 : Matrix (Fin 11) (Fin 11) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 4865804016353280000 + | 0, 9 => -9503523469440000 + | 0, 10 => 898082967862080000 + | 1, 1 => 38414242234368000 + | 1, 8 => -300111267456000 + | 1, 10 => 349254487501920000 + | 2, 2 => 2510734786560000 + | 2, 7 => -29422673280000 + | 2, 8 => -583549686720000 + | 2, 9 => 7127642602080000 + | 2, 10 => 124733745536400000 + | 3, 3 => 439378587648000 + | 3, 6 => -6865290432000 + | 3, 7 => -154469034720000 + | 3, 9 => 6652466428608000 + | 3, 10 => 37420123660920000 + | 4, 4 => 173820100608000 + | 4, 5 => -3394923840000 + | 4, 6 => -66201014880000 + | 4, 7 => -154469034720000 + | 4, 8 => 525194718048000 + | 4, 9 => 3207439170936000 + | 4, 10 => 6236687276820000 + | 5, 4 => -3394923840000 + | 5, 5 => 95057867520000 + | 5, 6 => -121368527280000 + | 5, 8 => 343877493960000 + | 5, 10 => -3118343638410000 + | 6, 3 => -6865290432000 + | 6, 4 => -66201014880000 + | 6, 5 => -121368527280000 + | 6, 6 => 198480450168000 + | 6, 8 => -447040742148000 + | 6, 9 => -1930403204730000 + | 6, 10 => -4677515457615000 + | 7, 2 => -29422673280000 + | 7, 3 => -154469034720000 + | 7, 4 => -154469034720000 + | 7, 7 => 481336545690000 + | 7, 8 => -1422402361380000 + | 7, 9 => -2672865975780000 + | 7, 10 => -3897929548012500 + | 8, 1 => -300111267456000 + | 8, 2 => -583549686720000 + | 8, 4 => 525194718048000 + | 8, 5 => 343877493960000 + | 8, 6 => -447040742148000 + | 8, 7 => -1422402361380000 + | 8, 8 => 6322135623804000 + | 8, 9 => -2650592092648500 + | 8, 10 => -2728550683608750 + | 9, 0 => -9503523469440000 + | 9, 2 => 7127642602080000 + | 9, 3 => 6652466428608000 + | 9, 4 => 3207439170936000 + | 9, 6 => -1930403204730000 + | 9, 7 => -2672865975780000 + | 9, 8 => -2650592092648500 + | 9, 9 => 241033113993672000 + | 9, 10 => -1754068296605625 + | 10, 0 => 898082967862080000 + | 10, 1 => 349254487501920000 + | 10, 2 => 124733745536400000 + | 10, 3 => 37420123660920000 + | 10, 4 => 6236687276820000 + | 10, 5 => -3118343638410000 + | 10, 6 => -4677515457615000 + | 10, 7 => -3897929548012500 + | 10, 8 => -2728550683608750 + | 10, 9 => -1754068296605625 + | 10, 10 => 102179740482167473125/2 + | _, _ => 0 +def lower_21 : Matrix (Fin 11) (Fin 11) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 0 => -3739586273669637/107374408857605613959110 + | 1, 1 => 1 + | 2, 0 => 42917021151345/42949763543042245583644 + | 2, 1 => -2754494102774409256708039938102406905/55101259836743085110111322759642888286 + | 2, 2 => 1 + | 3, 0 => 32603554581073/25264566790024850343320 + | 3, 1 => 19736944274324808448714748250673702531/661215118040917021321335873115714659432 + | 3, 2 => -28814354818578090714149102244859088577959391/135171633225332028090338934243100644999477932 + | 3, 3 => 1 + | 4, 0 => -1686576098456379/171799054172168982334576 + | 4, 1 => 6947516762454988509449222023584027875/440810078693944680880890582077143106288 + | 4, 2 => 111774107054151349634748526085288490733401633/270343266450664056180677868486201289998955864 + | 4, 3 => -814361992613372078815560084061530396046441414931169/1241480910030216053577478080906334013659843205408662 + | 4, 4 => 1 + | 5, 0 => 3949985641446423/171799054172168982334576 + | 5, 1 => -27562914327042743767342683176729852515/440810078693944680880890582077143106288 + | 5, 2 => -199843734971752637295958956381809621516336367/270343266450664056180677868486201289998955864 + | 5, 3 => 3635084314832807407670737096823288644793041676537775/2482961820060432107154956161812668027319686410817324 + | 5, 4 => -11762578660290143002961524155303416403787334288613634446055/7140240565457511713334448562032166963891212442895758704532 + | 5, 5 => 1 + | 6, 0 => -6350527481042977/214748817715211227918220 + | 6, 1 => 28069720902948540812738287817770730863/330607559020458510660667936557857329716 + | 6, 2 => 483078044414662133376940376935141175982383745/540686532901328112361355736972402579997911728 + | 6, 3 => -9332054263005462434092222127654035629551929659553663/4965923640120864214309912323625336054639372821634648 + | 6, 4 => 28621014367806154276237251134932844661524344524402516614433/14280481130915023426668897124064333927782424885791517409064 + | 6, 5 => -2521643197553287834812309698360522383524562167907761801910250473/1782723182987375871627803245970655706449461946171000734932853326 + | 6, 6 => 1 + | 7, 0 => 2109664577983545/85899527086084491167288 + | 7, 1 => -1438319909238975908129989378416372815/20036821758815667312767753730779232104 + | 7, 2 => -100253388196114199946281472255846144180996741/135171633225332028090338934243100644999477932 + | 7, 3 => 12375583665247951196671712849896820706470439075673695/9931847280241728428619824647250672109278745643269296 + | 7, 4 => -59577236123658401122530012013066481808505262394569657625815/28560962261830046853337794248128667855564849771583034818128 + | 7, 5 => 1829075310857617709386248164728766045661953288082367227681358445/3565446365974751743255606491941311412898923892342001469865706652 + | 7, 6 => -3789344048713596289788827118869104546566043125001683976933556642655/847987744905699066390032929775384688812915350304424007852946776316 + | 7, 7 => 1 + | 8, 0 => 91980000000/10737440885760561395911 + | 8, 1 => -253715258217967370961553275950000000/27550629918371542555055661379821444143 + | 8, 2 => -398624424849983184792966977318975752993506015/2162746131605312449445422947889610319991646912 + | 8, 3 => -673933961202360291677386519725721825860313661519355/19863694560483456857239649294501344218557491286538592 + | 8, 4 => 56478523870505941336981982628757993374237037496559269031763/57121924523660093706675588496257335711129699543166069636256 + | 8, 5 => 41883691881200042654310739187058600564182845041103740969954511519/21392678195848510459533638951647868477393543354052008819194239912 + | 8, 6 => 25315325874097613118136566301267759514083802076751642050268219707015/1695975489811398132780065859550769377625830700608848015705893552632 + | 8, 7 => -119/10 + | 8, 8 => 1 + | 9, 0 => -1233621593590000000/631614169750621258583 + | 9, 1 => -168878646683131688360719646525000000/27550629918371542555055661379821444143 + | 9, 2 => 166198003030821228223514443827573517712588529/67585816612666014045169467121550322499738966 + | 9, 3 => 521488036260118559948223123201671741114707738620088515/39727389120966913714479298589002688437114982573077184 + | 9, 4 => 830211347585029173861237247955247045180241202440377136819011/114243849047320187413351176992514671422259399086332139272512 + | 9, 5 => 74545061632926304019242939162748597843292006136030504893354932049/14261785463899006973022425967765245651595695569368005879462826608 + | 9, 6 => -148874317888028894553369314529627974724210036763511905165406266414107/3391950979622796265560131719101538755251661401217696031411787105264 + | 9, 7 => 2907/20 + | 9, 9 => 1 + | 10, 0 => 1981813099151655000000/10737440885760561395911 + | 10, 1 => 347165973775158904689165895528262500000/27550629918371542555055661379821444143 + | 10, 2 => 420529499754752051497112599939318321425224541057/8650984526421249797781691791558441279966587648 + | 10, 3 => 997911185751593128723721594130614722031480817250471215/11350682605990546775565513882572196696318566449450624 + | 10, 4 => -4075181008074170088866928631221058719537266348655119087649875/228487698094640374826702353985029342844518798172664278545024 + | 10, 5 => 266308250544531215894463353288926370962615274655156953863701013887/28523570927798013946044851935530491303191391138736011758925653216 + | 10, 6 => -902166246023909096592778923549092048117755890653318940795531098762805/6783901959245592531120263438203077510503322802435392062823574210528 + | 10, 7 => -33915/8 + | 10, 10 => 1 + | _, _ => 0 +def pivots_21 : Fin 11 → ℚ := fun i => + match i.val with + | 0 => 159443002280547058016234743983531/8192000000000 + | 1 => 11399247882371797962848706613961254721586449049/64677290982463616878899200000000000 + | 2 => 141232627880430997230888664300360595595770772862431/8014728703526266925107101492311692841600 + | 3 => 66586929790164805496236403433874818688867803599314827175953/17301969052842499595563383583116882559933175296000 + | 4 => 56813842778922157084402418710539193295096944427089335611491881663/11350682605990546775565513882572196696318566449450624000 + | 5 => 368806512387088227905578664088173995206305444582688058368064871360573409/91395079237856149930680941594011737137807519269065711418009600 + | 6 => 1140296001783246508096176269188676685849630816159197846184575254811978310261/28523570927798013946044851935530491303191391138736011758925653216000 + | 7 => 43249709135952940118581859654013822366164026698816076284093184456070451365487/8683394507834358439833937200899939213444253187117301840414174989475840 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data22.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data22.lean new file mode 100644 index 0000000000000000000000000000000000000000..a4e041cc9c10002ae9885d36b4d00ee3ccee5fd4 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data22.lean @@ -0,0 +1,139 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_22 : Matrix (Fin 11) (Fin 11) ℚ := fun i j => + match i.val, j.val with + | _, _ => 0 +def candidateZ_22 : Matrix (Fin 11) (Fin 11) ℚ := fun i j => + match i.val, j.val with + | 1, 1 => 729870602452992000 + | 1, 9 => -25659513367488000 + | 1, 10 => 798295971432960000 + | 2, 2 => 42682491371520000 + | 2, 8 => -2667655710720000 + | 2, 10 => 598721978574720000 + | 3, 3 => 6590678814720000 + | 3, 7 => -540641621520000 + | 3, 8 => -3501298120320000 + | 3, 9 => 24946749107280000 + | 3, 10 => 299360989287360000 + | 4, 4 => 2259661307904000 + | 4, 6 => -211843247616000 + | 4, 7 => -1544690347200000 + | 4, 9 => 25659513367488000 + | 4, 10 => 99786996429120000 + | 5, 5 => 1437750246240000 + | 5, 6 => -970948218240000 + | 5, 7 => -1274369536440000 + | 5, 8 => 2751019951680000 + | 5, 9 => 9800508577860000 + | 6, 4 => -211843247616000 + | 6, 5 => -970948218240000 + | 6, 6 => 997428624192000 + | 6, 9 => -9265935382704000 + | 6, 10 => -37420123660920000 + | 7, 3 => -540641621520000 + | 7, 4 => -1544690347200000 + | 7, 5 => -1274369536440000 + | 7, 7 => 5440206316545000 + | 7, 8 => -8534414168280000 + | 7, 9 => -23387577288075000 + | 7, 10 => -43656810937740000 + | 8, 2 => -2667655710720000 + | 8, 3 => -3501298120320000 + | 8, 5 => 2751019951680000 + | 8, 7 => -8534414168280000 + | 8, 8 => 22841802023040000 + | 8, 9 => -30292481058840000 + | 8, 10 => -37420123660920000 + | 9, 1 => -25659513367488000 + | 9, 3 => 24946749107280000 + | 9, 4 => 25659513367488000 + | 9, 5 => 9800508577860000 + | 9, 6 => -9265935382704000 + | 9, 7 => -23387577288075000 + | 9, 8 => -30292481058840000 + | 9, 9 => 698765124659852250 + | 9, 10 => -28065092745690000 + | 10, 1 => 798295971432960000 + | 10, 2 => 598721978574720000 + | 10, 3 => 299360989287360000 + | 10, 4 => 99786996429120000 + | 10, 6 => -37420123660920000 + | 10, 7 => -43656810937740000 + | 10, 8 => -37420123660920000 + | 10, 9 => -28065092745690000 + | 10, 10 => 51071452523969377500 + | _, _ => 0 +def lower_22 : Matrix (Fin 11) (Fin 11) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 1 => 1 + | 2, 1 => 840/66737 + | 2, 2 => 1 + | 3, 1 => 1365/266948 + | 3, 2 => 150800307/2039061058 + | 3, 3 => 1 + | 4, 1 => 59/66737 + | 4, 2 => 47591523/2039061058 + | 4, 3 => 15198870291372/93648863499905 + | 4, 4 => 1 + | 5, 1 => -45/97072 + | 5, 2 => -68696727/20390610580 + | 5, 3 => 660425774481/26756818142830 + | 5, 4 => 154645157313363/764453665033535 + | 5, 5 => 1 + | 6, 1 => -93/266948 + | 6, 2 => -713614293/81562442320 + | 6, 3 => -59927368152/1101751335293 + | 6, 4 => -1484762516855427/8408990315368885 + | 6, 5 => -746190355712094625176/1223003674500472600219 + | 6, 6 => 1 + | 7, 1 => 805/4271168 + | 7, 2 => 65693817/163124884640 + | 7, 3 => -31148397247191/214054545142640 + | 7, 4 => -68088830727895943/67271922522951080 + | 7, 5 => -5355557626784774638047/4892014698001890400876 + | 7, 6 => -1847528495687487453844185/575526667846139930071682 + | 7, 7 => 1 + | 8, 1 => 345/533896 + | 8, 2 => -7443144957/81562442320 + | 8, 3 => -6674712615021/11017513352930 + | 8, 4 => 36395025913148901/67271922522951080 + | 8, 5 => 8545737798499491261178/3669011023501417800657 + | 8, 6 => 329641681800251111369765/50781764809953523241619 + | 8, 7 => -408/49 + | 8, 8 => 1 + | 9, 1 => -1164591/17084672 + | 9, 2 => 7220729277/163124884640 + | 9, 3 => 507284045584347/88140106823440 + | 9, 4 => 116125139366547324/8408990315368885 + | 9, 5 => 63465354136001688316641/9784029396003780801752 + | 9, 6 => -198922152416610445086139/33854509873302348827746 + | 9, 7 => 2907/49 + | 9, 9 => 1 + | 10, 1 => 573685/266948 + | 10, 2 => 30939714679041/1304999077120 + | 10, 3 => 173420174307033/3147860957980 + | 10, 4 => 3909404991384728899/134543845045902160 + | 10, 5 => -7491126795250110445251/2446007349000945200438 + | 10, 6 => -5331080780369311833373095/135418039493209395310984 + | 10, 7 => -3876/7 + | 10, 10 => 1 + | _, _ => 0 +def pivots_22 : Fin 11 → ℚ := fun i => + match i.val with + | 1 => 8918952831281493/4000 + | 2 => 72436694902527501/485360 + | 3 => 18082311934319207702127/652499538560 + | 4 => 695854616241889310717511/66892045357075 + | 5 => 38925040602836761141408803009/6115629320268280000 + | 6 => 357191714080491816199102308268389/444728608909262763716000 + | 7 => 29690453297529080152425914264867187/184168533710764777622938240 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Data23.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data23.lean new file mode 100644 index 0000000000000000000000000000000000000000..e1d67a46ef8d29914b1c0571d770be2697d3922c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Data23.lean @@ -0,0 +1,189 @@ +import OAI.Analysis.Laughlin.FourBody.MatrixCompute + +namespace OAI + +namespace Laughlin.Certificate +def candidateY_23 : Matrix (Fin 12) (Fin 12) ℚ := fun i j => + match i.val, j.val with + | _, _ => 0 +def candidateZ_23 : Matrix (Fin 12) (Fin 12) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 2248001455555215360000 + | 0, 10 => -2195313921440640000 + | 0, 11 => 252461100965673600000 + | 1, 1 => 14597412049059840000 + | 1, 9 => -57021140816640000 + | 1, 11 => 100984440386269440000 + | 2, 2 => 768284844687360000 + | 2, 8 => -4501669011840000 + | 2, 9 => -114042281633280000 + | 2, 10 => 1746272437509600000 + | 2, 11 => 37869165144851040000 + | 3, 3 => 105450861035520000 + | 3, 7 => -823834851840000 + | 3, 8 => -24509086842240000 + | 3, 10 => 1746272437509600000 + | 3, 11 => 12623055048283680000 + | 4, 4 => 31635258310656000 + | 4, 6 => -308938069440000 + | 4, 7 => -8341327874880000 + | 4, 8 => -26259735902400000 + | 4, 9 => 119744395714944000 + | 4, 10 => 1010343338844840000 + | 4, 11 => 3155763762070920000 + | 5, 5 => 18896146093440000 + | 5, 6 => -4854741091200000 + | 5, 7 => -16991593819200000 + | 5, 9 => 117606102934320000 + | 5, 10 => 274414240180080000 + | 6, 4 => -308938069440000 + | 6, 5 => -4854741091200000 + | 6, 6 => 8396495387280000 + | 6, 7 => -11044535982480000 + | 6, 8 => 13411222264440000 + | 6, 10 => -202692336496650000 + | 6, 11 => -788940940517730000 + | 7, 3 => -823834851840000 + | 7, 4 => -8341327874880000 + | 7, 5 => -16991593819200000 + | 7, 6 => -11044535982480000 + | 7, 7 => 52725430517760000 + | 7, 8 => -31292851950360000 + | 7, 9 => -162153869197320000 + | 7, 10 => -420976391185350000 + | 7, 11 => -788940940517730000 + | 8, 2 => -4501669011840000 + | 8, 3 => -24509086842240000 + | 8, 4 => -26259735902400000 + | 8, 6 => 13411222264440000 + | 8, 7 => -31292851950360000 + | 8, 8 => 111009907368360000 + | 8, 9 => -302924810588400000 + | 8, 10 => -463853616213487500 + | 8, 11 => -591705705388297500 + | 9, 1 => -57021140816640000 + | 9, 2 => -114042281633280000 + | 9, 4 => 119744395714944000 + | 9, 5 => 117606102934320000 + | 9, 7 => -162153869197320000 + | 9, 8 => -302924810588400000 + | 9, 9 => 2530981340232345000 + | 9, 10 => -414739703908530000 + | 9, 11 => -394470470258865000 + | 10, 0 => -2195313921440640000 + | 10, 2 => 1746272437509600000 + | 10, 3 => 1746272437509600000 + | 10, 4 => 1010343338844840000 + | 10, 5 => 274414240180080000 + | 10, 6 => -202692336496650000 + | 10, 7 => -420976391185350000 + | 10, 8 => -463853616213487500 + | 10, 9 => -414739703908530000 + | 10, 10 => 101850365435360416875 + | 10, 11 => -246544043911790625 + | 11, 0 => 252461100965673600000 + | 11, 1 => 100984440386269440000 + | 11, 2 => 37869165144851040000 + | 11, 3 => 12623055048283680000 + | 11, 4 => 3155763762070920000 + | 11, 6 => -788940940517730000 + | 11, 7 => -788940940517730000 + | 11, 8 => -591705705388297500 + | 11, 9 => -394470470258865000 + | 11, 10 => -246544043911790625 + | 11, 11 => 25851868812458629565625 + | _, _ => 0 +def lower_23 : Matrix (Fin 12) (Fin 12) ℚ := fun i j => + match i.val, j.val with + | 0, 0 => 1 + | 1, 0 => 345/1048577573743 + | 1, 1 => 1 + | 2, 0 => 465/4194310294972 + | 2, 1 => 201963530395658/20166243897788951 + | 2, 2 => 1 + | 3, 0 => 30/1048577573743 + | 3, 1 => 265290126005179/80664975591155804 + | 3, 2 => 332148196734695751793/5894356643077481051949 + | 3, 3 => 1 + | 4, 0 => 51/16777241179888 + | 4, 1 => 13434900159550/20166243897788951 + | 4, 2 => 241839610991979869629/11788713286154962103898 + | 4, 3 => 558748096498957863063676946/3854866416052307060169897565 + | 4, 4 => 1 + | 5, 0 => -33/16777241179888 + | 5, 1 => -49432942720425/322659902364623216 + | 5, 2 => 816842823598526230/5894356643077481051949 + | 5, 3 => 271118458980709501504750913/7709732832104614120339795130 + | 5, 4 => 183460604356060440272919394566095/912492775553114299235651205336958 + | 5, 5 => 1 + | 6, 0 => -75/67108964719552 + | 6, 1 => -33161265757763/161329951182311608 + | 6, 2 => -75878744617480952119/13472815184177099547312 + | 6, 3 => -255914793917203570711756019/7709732832104614120339795130 + | 6, 4 => -52629204745453498067759412062635/1824985551106228598471302410673916 + | 6, 5 => -511161485774106343747899688487963641/4641715056261562091994311565431952959 + | 6, 6 => 1 + | 7, 0 => 15/33554482359776 + | 7, 1 => 7340042978251/1290639609458492864 + | 7, 2 => -53826474130765973461/31436568763079898943728 + | 7, 3 => -2691513774959985657046702857/61677862656836912962718361040 + | 7, 4 => -255301583103139618475404468620105/521424443173208170991800688763976 + | 7, 5 => -244281606388753916638146875851511556239/204235462475508732047749708879005930196 + | 7, 6 => -871270481830772945196296430021323257221815/389245422884705485467669569392415525492781 + | 7, 7 => 1 + | 8, 0 => 375/268435858878208 + | 8, 1 => 4849086132973/20166243897788951 + | 8, 2 => -126610091103297683417/31436568763079898943728 + | 8, 3 => -4669321454807479672372261089/15419465664209228240679590260 + | 8, 4 => -3350528227731030896574532676573595/3649971102212457196942604821347832 + | 8, 5 => 7226761974529335135951529165505220457/51058865618877183011937427219751482549 + | 8, 6 => 877517561683146974892250812004505270759033/389245422884705485467669569392415525492781 + | 8, 7 => -2149485405922476109461327803218860087576451580/357288100994165292101443563021377816034441037 + | 8, 8 => 1 + | 9, 0 => 453/268435858878208 + | 9, 1 => -37186155888609801/5162558437833971456 + | 9, 2 => -3929759593855251397667/15718284381539949471864 + | 9, 3 => 80235381091594789004152890837/308389313284184564813591805200 + | 9, 4 => 42206482799880566588067552672544509/7299942204424914393885209642695664 + | 9, 5 => 15206123889007365374367234449679334888503/2042354624755087320477497088790059301960 + | 9, 6 => 1728414985718012732165744553875995649337544/648742371474509142446115948987359209154635 + | 9, 7 => 47956834228992794970294642188728332076685865129/1786440504970826460507217815106889080172205185 + | 9, 8 => -76/5 + | 9, 9 => 1 + | 10, 0 => -1048578357607/1073743435512832 + | 10, 1 => 1394608297026685/2581279218916985728 + | 10, 2 => 6184830591167510390475025/1508955300627835149298944 + | 10, 3 => 292335005146257211435397680859/12335572531367382592543672208 + | 10, 4 => 68391187533320405733068453811892445/2085697772692832683967202755055904 + | 10, 5 => 3937712408681015175493709663951092602497/408470924951017464095499417758011860392 + | 10, 6 => -12493830276507879648736028481970837666070573/1037987794359214627913785518379774734647416 + | 10, 7 => -5525214534856393868865566110795649580988755063/51041157284880756014491937574482545147777291 + | 10, 8 => 931/4 + | 10, 10 => 1 + | 11, 0 => 30146627830105/268435858878208 + | 11, 1 => 278034133123027888827/20650233751335885824 + | 11, 2 => 129823823892450334408582601/1508955300627835149298944 + | 11, 3 => 143433987501531150697752909147377/986845802509390607403493776640 + | 11, 4 => 164070244050457811766440819336418545/4171395545385665367934405510111808 + | 11, 5 => -3474462440748244245422492818232190945903/148534881800369986943817970093822494688 + | 11, 6 => 19983224049978600492936320204846726907812909/1037987794359214627913785518379774734647416 + | 11, 7 => -190008968277167187380127733099574652696056726025/408329258279046048115935500595860361182218328 + | 11, 8 => -33649/4 + | 11, 11 => 1 + | _, _ => 0 +def pivots_23 : Fin 12 → ℚ := fun i => + match i.val with + | 0 => 3596807727106964372495493/400 + | 1 => 2695083358684056754955880339/59918718499600 + | 2 => 41460066632617412037005591462619/16132995118231160800 + | 3 => 1687804688951660387226431508125931/3991945239756177643648 + | 4 => 440474619464572437164875860934388795628693/3083893132841845648135918052000 + | 5 => 17875786513703508084674654426461795282409857029/208569777269283268396720275505590400 + | 6 => 161052762702264252299142605764190579764316339459883/7426744090018499347190898504691124734400 + | 7 => 3104434579359970407545821546788921635658478795883201511/830390235487371702331028414703819787717932800 + | 8 => 617253866866789232996626176408903607856598861326229375/816658516558092096231871001191720722364436656 + | _ => 0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Error05.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Error05.lean new file mode 100644 index 0000000000000000000000000000000000000000..60c5ee83154f76f10500ffaa38f3c98e103a8d6c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Error05.lean @@ -0,0 +1,61 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row05 +import OAI.Analysis.Laughlin.FiniteFlux.Row052 + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix +theorem error_five_11 : Y 5 1 1 = (-131383098735399323103/3355443200000000000000 : ℚ) := by + rw [Y_expand, yRow_5_1_1_0, yRow_5_1_1_1, yRow_5_1_1_2, yRow_5_1_1_3, yRow_5_1_1_4, yRow_5_1_1_5, yRow_5_1_1_6] + norm_num + +theorem error_five_13 : Y 5 1 3 = (-150940901726840366220441/187904819200000000000000 : ℚ) := by + rw [Y_expand, yRow_5_1_3_0, yRow_5_1_3_1, yRow_5_1_3_2, yRow_5_1_3_3, yRow_5_1_3_4, yRow_5_1_3_5, yRow_5_1_3_6] + norm_num + +theorem error_five_15 : Y 5 1 5 = (-68371964800993572891617/375809638400000000000000 : ℚ) := by + rw [Y_expand, yRow_5_1_5_0, yRow_5_1_5_1, yRow_5_1_5_2, yRow_5_1_5_3, yRow_5_1_5_4, yRow_5_1_5_5, yRow_5_1_5_6] + norm_num + +theorem error_five_31 : Y 5 3 1 = (-150940901726840366220441/187904819200000000000000 : ℚ) := by + rw [Y_expand, yRow_5_3_1_0, yRow_5_3_1_1, yRow_5_3_1_2, yRow_5_3_1_3, yRow_5_3_1_4, yRow_5_3_1_5, yRow_5_3_1_6] + norm_num + +theorem error_five_33 : Y 5 3 3 = (-157876378364069020620837/187904819200000000000000 : ℚ) := by + rw [Y_expand, yRow_5_3_3_0, yRow_5_3_3_1, yRow_5_3_3_2, yRow_5_3_3_3, yRow_5_3_3_4, yRow_5_3_3_5, yRow_5_3_3_6] + norm_num + +theorem error_five_35 : Y 5 3 5 = (-957095703323798289717/367001600000000000000 : ℚ) := by + rw [Y_expand, yRow_5_3_5_0, yRow_5_3_5_1, yRow_5_3_5_2, yRow_5_3_5_3, yRow_5_3_5_4, yRow_5_3_5_5, yRow_5_3_5_6] + norm_num + +theorem error_five_51 : Y 5 5 1 = (-68371964800993572891617/375809638400000000000000 : ℚ) := by + rw [Y_expand, yRow_5_5_1_0, yRow_5_5_1_1, yRow_5_5_1_2, yRow_5_5_1_3, yRow_5_5_1_4, yRow_5_5_1_5, yRow_5_5_1_6] + norm_num + +theorem error_five_53 : Y 5 5 3 = (-957095703323798289717/367001600000000000000 : ℚ) := by + rw [Y_expand, yRow_5_5_3_0, yRow_5_5_3_1, yRow_5_5_3_2, yRow_5_5_3_3, yRow_5_5_3_4, yRow_5_5_3_5, yRow_5_5_3_6] + norm_num + +theorem error_five_55 : Y 5 5 5 = (-6732043280507644550567857/375809638400000000000000 : ℚ) := by + rw [Y_expand, yRow_5_5_5_0, yRow_5_5_5_1, yRow_5_5_5_2, yRow_5_5_5_3, yRow_5_5_5_4, yRow_5_5_5_5, yRow_5_5_5_6] + norm_num +theorem error_five : errorRational 5 = + !![-131383098735399323103/3355443200000000000000, -150940901726840366220441/187904819200000000000000, -68371964800993572891617/375809638400000000000000; + -150940901726840366220441/187904819200000000000000, -157876378364069020620837/187904819200000000000000, -957095703323798289717/367001600000000000000; + -68371964800993572891617/375809638400000000000000, -957095703323798289717/367001600000000000000, -6732043280507644550567857/375809638400000000000000] := by + ext i j + fin_cases i <;> fin_cases j + · exact error_five_11 + · exact error_five_13 + · exact error_five_15 + · exact error_five_31 + · exact error_five_33 + · exact error_five_35 + · exact error_five_51 + · exact error_five_53 + · exact error_five_55 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Error07.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Error07.lean new file mode 100644 index 0000000000000000000000000000000000000000..d396525c4702bf76f3689ef4a904ec086e068e8c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Error07.lean @@ -0,0 +1,140 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row0301007 +import OAI.Analysis.Laughlin.FiniteFlux.Row0301107 +import OAI.Analysis.Laughlin.FiniteFlux.Row0301207 +import OAI.Analysis.Laughlin.FiniteFlux.Row0301307 +import OAI.Analysis.Laughlin.FiniteFlux.Row0301407 +import OAI.Analysis.Laughlin.FiniteFlux.Row0301507 +import OAI.Analysis.Laughlin.FiniteFlux.Row0301607 +import OAI.Analysis.Laughlin.FiniteFlux.Row0501007 +import OAI.Analysis.Laughlin.FiniteFlux.Row0501107 +import OAI.Analysis.Laughlin.FiniteFlux.Row0501207 +import OAI.Analysis.Laughlin.FiniteFlux.Row0501307 +import OAI.Analysis.Laughlin.FiniteFlux.Row0501407 +import OAI.Analysis.Laughlin.FiniteFlux.Row0501507 +import OAI.Analysis.Laughlin.FiniteFlux.Row0501607 +import OAI.Analysis.Laughlin.FiniteFlux.Row0503007 +import OAI.Analysis.Laughlin.FiniteFlux.Row0503107 +import OAI.Analysis.Laughlin.FiniteFlux.Row0503207 +import OAI.Analysis.Laughlin.FiniteFlux.Row0503307 +import OAI.Analysis.Laughlin.FiniteFlux.Row0503407 +import OAI.Analysis.Laughlin.FiniteFlux.Row0503507 +import OAI.Analysis.Laughlin.FiniteFlux.Row0503607 +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FiniteFlux.Row0701007 +import OAI.Analysis.Laughlin.FiniteFlux.Row0701107 +import OAI.Analysis.Laughlin.FiniteFlux.Row0701207 +import OAI.Analysis.Laughlin.FiniteFlux.Row0701307 +import OAI.Analysis.Laughlin.FiniteFlux.Row0701407 +import OAI.Analysis.Laughlin.FiniteFlux.Row0701507 +import OAI.Analysis.Laughlin.FiniteFlux.Row0701607 +import OAI.Analysis.Laughlin.FiniteFlux.Row0703007 +import OAI.Analysis.Laughlin.FiniteFlux.Row0703107 +import OAI.Analysis.Laughlin.FiniteFlux.Row0703207 +import OAI.Analysis.Laughlin.FiniteFlux.Row0703307 +import OAI.Analysis.Laughlin.FiniteFlux.Row0703407 +import OAI.Analysis.Laughlin.FiniteFlux.Row0703507 +import OAI.Analysis.Laughlin.FiniteFlux.Row0703607 +import OAI.Analysis.Laughlin.FiniteFlux.Row0705007 +import OAI.Analysis.Laughlin.FiniteFlux.Row0705107 +import OAI.Analysis.Laughlin.FiniteFlux.Row0705207 +import OAI.Analysis.Laughlin.FiniteFlux.Row0705307 +import OAI.Analysis.Laughlin.FiniteFlux.Row0705407 +import OAI.Analysis.Laughlin.FiniteFlux.Row0705507 +import OAI.Analysis.Laughlin.FiniteFlux.Row0705607 +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FiniteFlux.Row073 + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix +theorem error_7_1_1 : Y 7 1 1 = (-2223010934642432694336471/93952409600000000000000 : ℚ) := by + rw [Y_expand, yRow_7_1_1_0, yRow_7_1_1_1, yRow_7_1_1_2, yRow_7_1_1_3, yRow_7_1_1_4, yRow_7_1_1_5, yRow_7_1_1_6] + norm_num + +theorem error_7_1_3 : Y 7 1 3 = (108477953957456824077753/23488102400000000000000 : ℚ) := by + rw [Y_expand, yRow_7_1_3_0, yRow_7_1_3_1, yRow_7_1_3_2, yRow_7_1_3_3, yRow_7_1_3_4, yRow_7_1_3_5, yRow_7_1_3_6] + norm_num + +theorem error_7_1_5 : Y 7 1 5 = (-5196975194710104279852387/187904819200000000000000 : ℚ) := by + rw [Y_expand, yRow_7_1_5_0, yRow_7_1_5_1, yRow_7_1_5_2, yRow_7_1_5_3, yRow_7_1_5_4, yRow_7_1_5_5, yRow_7_1_5_6] + norm_num + +theorem error_7_1_7 : Y 7 1 7 = (-1651569710015033615111331/13421772800000000000000 : ℚ) := by + rw [Y_expand, yRow_7_1_7_0, yRow_7_1_7_1, yRow_7_1_7_2, yRow_7_1_7_3, yRow_7_1_7_4, yRow_7_1_7_5, yRow_7_1_7_6] + norm_num + +theorem error_7_3_1 : Y 7 3 1 = (108477953957456824077753/23488102400000000000000 : ℚ) := by + rw [Y_expand, yRow_7_3_1_0, yRow_7_3_1_1, yRow_7_3_1_2, yRow_7_3_1_3, yRow_7_3_1_4, yRow_7_3_1_5, yRow_7_3_1_6] + norm_num + +theorem error_7_3_3 : Y 7 3 3 = (-367191109045089385072113/46976204800000000000000 : ℚ) := by + rw [Y_expand, yRow_7_3_3_0, yRow_7_3_3_1, yRow_7_3_3_2, yRow_7_3_3_3, yRow_7_3_3_4, yRow_7_3_3_5, yRow_7_3_3_6] + norm_num + +theorem error_7_3_5 : Y 7 3 5 = (117278459962852511483289/18790481920000000000000 : ℚ) := by + rw [Y_expand, yRow_7_3_5_0, yRow_7_3_5_1, yRow_7_3_5_2, yRow_7_3_5_3, yRow_7_3_5_4, yRow_7_3_5_5, yRow_7_3_5_6] + norm_num + +theorem error_7_3_7 : Y 7 3 7 = (24425660136497504106789/1342177280000000000000 : ℚ) := by + rw [Y_expand, yRow_7_3_7_0, yRow_7_3_7_1, yRow_7_3_7_2, yRow_7_3_7_3, yRow_7_3_7_4, yRow_7_3_7_5, yRow_7_3_7_6] + norm_num + +theorem error_7_5_1 : Y 7 5 1 = (-5196975194710104279852387/187904819200000000000000 : ℚ) := by + rw [Y_expand, yRow_7_5_1_0, yRow_7_5_1_1, yRow_7_5_1_2, yRow_7_5_1_3, yRow_7_5_1_4, yRow_7_5_1_5, yRow_7_5_1_6] + norm_num + +theorem error_7_5_3 : Y 7 5 3 = (117278459962852511483289/18790481920000000000000 : ℚ) := by + rw [Y_expand, yRow_7_5_3_0, yRow_7_5_3_1, yRow_7_5_3_2, yRow_7_5_3_3, yRow_7_5_3_4, yRow_7_5_3_5, yRow_7_5_3_6] + norm_num + +theorem error_7_5_5 : Y 7 5 5 = (-9326100426131028195384507/187904819200000000000000 : ℚ) := by + rw [Y_expand, yRow_7_5_5_0, yRow_7_5_5_1, yRow_7_5_5_2, yRow_7_5_5_3, yRow_7_5_5_4, yRow_7_5_5_5, yRow_7_5_5_6] + norm_num + +theorem error_7_5_7 : Y 7 5 7 = (-1202717220838198373824731/13421772800000000000000 : ℚ) := by + rw [Y_expand, yRow_7_5_7_0, yRow_7_5_7_1, yRow_7_5_7_2, yRow_7_5_7_3, yRow_7_5_7_4, yRow_7_5_7_5, yRow_7_5_7_6] + norm_num + +theorem error_7_7_1 : Y 7 7 1 = (-1651569710015033615111331/13421772800000000000000 : ℚ) := by + rw [Y_expand, yRow_7_7_1_0, yRow_7_7_1_1, yRow_7_7_1_2, yRow_7_7_1_3, yRow_7_7_1_4, yRow_7_7_1_5, yRow_7_7_1_6] + norm_num + +theorem error_7_7_3 : Y 7 7 3 = (24425660136497504106789/1342177280000000000000 : ℚ) := by + rw [Y_expand, yRow_7_7_3_0, yRow_7_7_3_1, yRow_7_7_3_2, yRow_7_7_3_3, yRow_7_7_3_4, yRow_7_7_3_5, yRow_7_7_3_6] + norm_num + +theorem error_7_7_5 : Y 7 7 5 = (-1202717220838198373824731/13421772800000000000000 : ℚ) := by + rw [Y_expand, yRow_7_7_5_0, yRow_7_7_5_1, yRow_7_7_5_2, yRow_7_7_5_3, yRow_7_7_5_4, yRow_7_7_5_5, yRow_7_7_5_6] + norm_num + +theorem error_7_7_7 : Y 7 7 7 = (-3962174270025189289538421/6710886400000000000000 : ℚ) := by + rw [Y_expand, yRow_7_7_7_0, yRow_7_7_7_1, yRow_7_7_7_2, yRow_7_7_7_3, yRow_7_7_7_4, yRow_7_7_7_5, yRow_7_7_7_6] + norm_num +theorem error_7 : errorRational 7 = + !![-2223010934642432694336471/93952409600000000000000, 108477953957456824077753/23488102400000000000000, -5196975194710104279852387/187904819200000000000000, -1651569710015033615111331/13421772800000000000000; + 108477953957456824077753/23488102400000000000000, -367191109045089385072113/46976204800000000000000, 117278459962852511483289/18790481920000000000000, 24425660136497504106789/1342177280000000000000; + -5196975194710104279852387/187904819200000000000000, 117278459962852511483289/18790481920000000000000, -9326100426131028195384507/187904819200000000000000, -1202717220838198373824731/13421772800000000000000; + -1651569710015033615111331/13421772800000000000000, 24425660136497504106789/1342177280000000000000, -1202717220838198373824731/13421772800000000000000, -3962174270025189289538421/6710886400000000000000] := by + ext i j + fin_cases i <;> fin_cases j + · exact error_7_1_1 + · exact error_7_1_3 + · exact error_7_1_5 + · exact error_7_1_7 + · exact error_7_3_1 + · exact error_7_3_3 + · exact error_7_3_5 + · exact error_7_3_7 + · exact error_7_5_1 + · exact error_7_5_3 + · exact error_7_5_5 + · exact error_7_5_7 + · exact error_7_7_1 + · exact error_7_7_3 + · exact error_7_7_5 + · exact error_7_7_7 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Error08.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Error08.lean new file mode 100644 index 0000000000000000000000000000000000000000..eea1f476e3de50b519d23ebc6de351b7cb7228da --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Error08.lean @@ -0,0 +1,99 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row08 +import OAI.Analysis.Laughlin.FiniteFlux.Row082 +import OAI.Analysis.Laughlin.FiniteFlux.Row083 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix +theorem error_8_1_1 : Y 8 1 1 = (-67460768130800149252179/3355443200000000000000 : ℚ) := by + rw [Y_expand, yRow_8_1_1_0, yRow_8_1_1_1, yRow_8_1_1_2, yRow_8_1_1_3, yRow_8_1_1_4, yRow_8_1_1_5, yRow_8_1_1_6] + norm_num + +theorem error_8_1_3 : Y 8 1 3 = (-12646981826519267475639/1677721600000000000000 : ℚ) := by + rw [Y_expand, yRow_8_1_3_0, yRow_8_1_3_1, yRow_8_1_3_2, yRow_8_1_3_3, yRow_8_1_3_4, yRow_8_1_3_5, yRow_8_1_3_6] + norm_num + +theorem error_8_1_5 : Y 8 1 5 = (862312946559627131048937/6710886400000000000000 : ℚ) := by + rw [Y_expand, yRow_8_1_5_0, yRow_8_1_5_1, yRow_8_1_5_2, yRow_8_1_5_3, yRow_8_1_5_4, yRow_8_1_5_5, yRow_8_1_5_6] + norm_num + +theorem error_8_1_7 : Y 8 1 7 = (145152021796677708235047/3355443200000000000000 : ℚ) := by + rw [Y_expand, yRow_8_1_7_0, yRow_8_1_7_1, yRow_8_1_7_2, yRow_8_1_7_3, yRow_8_1_7_4, yRow_8_1_7_5, yRow_8_1_7_6] + norm_num + +theorem error_8_3_3 : Y 8 3 3 = (-227609666383850988434007/23488102400000000000000 : ℚ) := by + rw [Y_expand, yRow_8_3_3_0, yRow_8_3_3_1, yRow_8_3_3_2, yRow_8_3_3_3, yRow_8_3_3_4, yRow_8_3_3_5, yRow_8_3_3_6] + norm_num + +theorem error_8_3_5 : Y 8 3 5 = (-285716550006646092887421/23488102400000000000000 : ℚ) := by + rw [Y_expand, yRow_8_3_5_0, yRow_8_3_5_1, yRow_8_3_5_2, yRow_8_3_5_3, yRow_8_3_5_4, yRow_8_3_5_5, yRow_8_3_5_6] + norm_num + +theorem error_8_3_7 : Y 8 3 7 = (-140429284546716888797613/1677721600000000000000 : ℚ) := by + rw [Y_expand, yRow_8_3_7_0, yRow_8_3_7_1, yRow_8_3_7_2, yRow_8_3_7_3, yRow_8_3_7_4, yRow_8_3_7_5, yRow_8_3_7_6] + norm_num + +theorem error_8_5_5 : Y 8 5 5 = (1048952949137524188240279/46976204800000000000000 : ℚ) := by + rw [Y_expand, yRow_8_5_5_0, yRow_8_5_5_1, yRow_8_5_5_2, yRow_8_5_5_3, yRow_8_5_5_4, yRow_8_5_5_5, yRow_8_5_5_6] + norm_num + +theorem error_8_5_7 : Y 8 5 7 = (707573349496458024998847/3355443200000000000000 : ℚ) := by + rw [Y_expand, yRow_8_5_7_0, yRow_8_5_7_1, yRow_8_5_7_2, yRow_8_5_7_3, yRow_8_5_7_4, yRow_8_5_7_5, yRow_8_5_7_6] + norm_num + +theorem error_8_7_7 : Y 8 7 7 = (-2475302483264003426615343/1677721600000000000000 : ℚ) := by + rw [Y_expand, yRow_8_7_7_0, yRow_8_7_7_1, yRow_8_7_7_2, yRow_8_7_7_3, yRow_8_7_7_4, yRow_8_7_7_5, yRow_8_7_7_6] + norm_num + +theorem error_8_3_1 : Y 8 3 1 = (-12646981826519267475639/1677721600000000000000 : ℚ) := by + rw [Y_symm] + exact error_8_1_3 + +theorem error_8_5_1 : Y 8 5 1 = (862312946559627131048937/6710886400000000000000 : ℚ) := by + rw [Y_symm] + exact error_8_1_5 + +theorem error_8_5_3 : Y 8 5 3 = (-285716550006646092887421/23488102400000000000000 : ℚ) := by + rw [Y_symm] + exact error_8_3_5 + +theorem error_8_7_1 : Y 8 7 1 = (145152021796677708235047/3355443200000000000000 : ℚ) := by + rw [Y_symm] + exact error_8_1_7 + +theorem error_8_7_3 : Y 8 7 3 = (-140429284546716888797613/1677721600000000000000 : ℚ) := by + rw [Y_symm] + exact error_8_3_7 + +theorem error_8_7_5 : Y 8 7 5 = (707573349496458024998847/3355443200000000000000 : ℚ) := by + rw [Y_symm] + exact error_8_5_7 +theorem error_8 : errorRational 8 = + !![-67460768130800149252179/3355443200000000000000, -12646981826519267475639/1677721600000000000000, 862312946559627131048937/6710886400000000000000, 145152021796677708235047/3355443200000000000000; + -12646981826519267475639/1677721600000000000000, -227609666383850988434007/23488102400000000000000, -285716550006646092887421/23488102400000000000000, -140429284546716888797613/1677721600000000000000; + 862312946559627131048937/6710886400000000000000, -285716550006646092887421/23488102400000000000000, 1048952949137524188240279/46976204800000000000000, 707573349496458024998847/3355443200000000000000; + 145152021796677708235047/3355443200000000000000, -140429284546716888797613/1677721600000000000000, 707573349496458024998847/3355443200000000000000, -2475302483264003426615343/1677721600000000000000] := by + ext i j + fin_cases i <;> fin_cases j + · exact error_8_1_1 + · exact error_8_1_3 + · exact error_8_1_5 + · exact error_8_1_7 + · exact error_8_3_1 + · exact error_8_3_3 + · exact error_8_3_5 + · exact error_8_3_7 + · exact error_8_5_1 + · exact error_8_5_3 + · exact error_8_5_5 + · exact error_8_5_7 + · exact error_8_7_1 + · exact error_8_7_3 + · exact error_8_7_5 + · exact error_8_7_7 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Gram07.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Gram07.lean new file mode 100644 index 0000000000000000000000000000000000000000..11ce3bca8c142a05362cedf0f14cbe47b2b77e75 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Gram07.lean @@ -0,0 +1,33 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Gram072 + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix +theorem gram_7 : gramRational 7 = + !![1440, 0, -360, 2520; + 0, 0, 0, 0; + -360, 0, 90, -630; + 2520, 0, -630, 4410] := by + ext i j + fin_cases i <;> fin_cases j + · exact gram_7_1_1 + · exact gram_7_1_3 + · exact gram_7_1_5 + · exact gram_7_1_7 + · exact gram_7_3_1 + · exact gram_7_3_3 + · exact gram_7_3_5 + · exact gram_7_3_7 + · exact gram_7_5_1 + · exact gram_7_5_3 + · exact gram_7_5_5 + · exact gram_7_5_7 + · exact gram_7_7_1 + · exact gram_7_7_3 + · exact gram_7_7_5 + · exact gram_7_7_7 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Gram072.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Gram072.lean new file mode 100644 index 0000000000000000000000000000000000000000..f77bc77f59116b511e73a2844c4ddae536f91e9b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Gram072.lean @@ -0,0 +1,58 @@ +import OAI.Analysis.Laughlin.FourBody.Basic + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix + +theorem gram_7_1_1 : Z 7 1 1 = (1440 : ℚ) := by + decide +kernel + +theorem gram_7_1_3 : Z 7 1 3 = (0 : ℚ) := by + decide +kernel + +theorem gram_7_1_5 : Z 7 1 5 = (-360 : ℚ) := by + decide +kernel + +theorem gram_7_1_7 : Z 7 1 7 = (2520 : ℚ) := by + decide +kernel + +theorem gram_7_3_1 : Z 7 3 1 = (0 : ℚ) := by + decide +kernel + +theorem gram_7_3_3 : Z 7 3 3 = (0 : ℚ) := by + decide +kernel + +theorem gram_7_3_5 : Z 7 3 5 = (0 : ℚ) := by + decide +kernel + +theorem gram_7_3_7 : Z 7 3 7 = (0 : ℚ) := by + decide +kernel + +theorem gram_7_5_1 : Z 7 5 1 = (-360 : ℚ) := by + decide +kernel + +theorem gram_7_5_3 : Z 7 5 3 = (0 : ℚ) := by + decide +kernel + +theorem gram_7_5_5 : Z 7 5 5 = (90 : ℚ) := by + decide +kernel + +theorem gram_7_5_7 : Z 7 5 7 = (-630 : ℚ) := by + decide +kernel + +theorem gram_7_7_1 : Z 7 7 1 = (2520 : ℚ) := by + decide +kernel + +theorem gram_7_7_3 : Z 7 7 3 = (0 : ℚ) := by + decide +kernel + +theorem gram_7_7_5 : Z 7 7 5 = (-630 : ℚ) := by + decide +kernel + +theorem gram_7_7_7 : Z 7 7 7 = (4410 : ℚ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Gram08.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Gram08.lean new file mode 100644 index 0000000000000000000000000000000000000000..7cbba23efb8d572678c09b93cb292b71354d7fd5 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Gram08.lean @@ -0,0 +1,34 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Gram082 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix +theorem gram_8 : gramRational 8 = + !![0, 0, 0, 0; + 0, 720, -720, 1260; + 0, -720, 720, -1260; + 0, 1260, -1260, 2205] := by + ext i j + fin_cases i <;> fin_cases j + · exact gram_8_1_1 + · exact gram_8_1_3 + · exact gram_8_1_5 + · exact gram_8_1_7 + · exact (Z_symm 8 3 1).trans gram_8_1_3 + · exact gram_8_3_3 + · exact gram_8_3_5 + · exact gram_8_3_7 + · exact (Z_symm 8 5 1).trans gram_8_1_5 + · exact (Z_symm 8 5 3).trans gram_8_3_5 + · exact gram_8_5_5 + · exact gram_8_5_7 + · exact (Z_symm 8 7 1).trans gram_8_1_7 + · exact (Z_symm 8 7 3).trans gram_8_3_7 + · exact (Z_symm 8 7 5).trans gram_8_5_7 + · exact gram_8_7_7 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Gram082.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Gram082.lean new file mode 100644 index 0000000000000000000000000000000000000000..6aa2fc7fdd45892452414992083b4b32bc350fdb --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Gram082.lean @@ -0,0 +1,71 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Quadruples08 +import OAI.Analysis.Laughlin.FourBody.FastChoose + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix + +theorem gram_8_1_1 : Z 8 1 1 = (0 : ℚ) := by + rw [Z_eq_fast] + unfold ZFast + rw [quadruples_8] + decide +kernel + +theorem gram_8_1_3 : Z 8 1 3 = (0 : ℚ) := by + rw [Z_eq_fast] + unfold ZFast + rw [quadruples_8] + decide +kernel + +theorem gram_8_1_5 : Z 8 1 5 = (0 : ℚ) := by + rw [Z_eq_fast] + unfold ZFast + rw [quadruples_8] + decide +kernel + +theorem gram_8_1_7 : Z 8 1 7 = (0 : ℚ) := by + rw [Z_eq_fast] + unfold ZFast + rw [quadruples_8] + decide +kernel + +theorem gram_8_3_3 : Z 8 3 3 = (720 : ℚ) := by + rw [Z_eq_fast] + unfold ZFast + rw [quadruples_8] + decide +kernel + +theorem gram_8_3_5 : Z 8 3 5 = (-720 : ℚ) := by + rw [Z_eq_fast] + unfold ZFast + rw [quadruples_8] + decide +kernel + +theorem gram_8_3_7 : Z 8 3 7 = (1260 : ℚ) := by + rw [Z_eq_fast] + unfold ZFast + rw [quadruples_8] + decide +kernel + +theorem gram_8_5_5 : Z 8 5 5 = (720 : ℚ) := by + rw [Z_eq_fast] + unfold ZFast + rw [quadruples_8] + decide +kernel + +theorem gram_8_5_7 : Z 8 5 7 = (-1260 : ℚ) := by + rw [Z_eq_fast] + unfold ZFast + rw [quadruples_8] + decide +kernel + +theorem gram_8_7_7 : Z 8 7 7 = (2205 : ℚ) := by + rw [Z_eq_fast] + unfold ZFast + rw [quadruples_8] + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData09.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData09.lean new file mode 100644 index 0000000000000000000000000000000000000000..21785d293d4ae5e175e80b689f3b9349c82f07ec --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData09.lean @@ -0,0 +1,377 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow09 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow092 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow093 +import OAI.Analysis.Laughlin.FiniteFlux.Data09 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_9_1_1 : Y 9 1 1 = (-12465910883340844333323483/6710886400000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 1 1 0 (by decide), + source_yRow_eq_rowCompute 9 1 1 1 (by decide), + source_yRow_eq_rowCompute 9 1 1 2 (by decide), + source_yRow_eq_rowCompute 9 1 1 3 (by decide), + source_yRow_eq_rowCompute 9 1 1 4 (by decide), + source_yRow_eq_rowCompute 9 1 1 5 (by decide), + source_yRow_eq_rowCompute 9 1 1 6 (by decide), + computeRow_9_1_1_0, computeRow_9_1_1_1, computeRow_9_1_1_2, computeRow_9_1_1_3, computeRow_9_1_1_4, computeRow_9_1_1_5, computeRow_9_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_1_3 : Y 9 1 3 = (-33961811903853786055197/838860800000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 1 3 0 (by decide), + source_yRow_eq_rowCompute 9 1 3 1 (by decide), + source_yRow_eq_rowCompute 9 1 3 2 (by decide), + source_yRow_eq_rowCompute 9 1 3 3 (by decide), + source_yRow_eq_rowCompute 9 1 3 4 (by decide), + source_yRow_eq_rowCompute 9 1 3 5 (by decide), + source_yRow_eq_rowCompute 9 1 3 6 (by decide), + computeRow_9_1_3_0, computeRow_9_1_3_1, computeRow_9_1_3_2, computeRow_9_1_3_3, computeRow_9_1_3_4, computeRow_9_1_3_5, computeRow_9_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_1_5 : Y 9 1 5 = (-670994343426034247927913/6710886400000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 1 5 0 (by decide), + source_yRow_eq_rowCompute 9 1 5 1 (by decide), + source_yRow_eq_rowCompute 9 1 5 2 (by decide), + source_yRow_eq_rowCompute 9 1 5 3 (by decide), + source_yRow_eq_rowCompute 9 1 5 4 (by decide), + source_yRow_eq_rowCompute 9 1 5 5 (by decide), + source_yRow_eq_rowCompute 9 1 5 6 (by decide), + computeRow_9_1_5_0, computeRow_9_1_5_1, computeRow_9_1_5_2, computeRow_9_1_5_3, computeRow_9_1_5_4, computeRow_9_1_5_5, computeRow_9_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_1_7 : Y 9 1 7 = (4530779263986412498504797/3355443200000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 1 7 0 (by decide), + source_yRow_eq_rowCompute 9 1 7 1 (by decide), + source_yRow_eq_rowCompute 9 1 7 2 (by decide), + source_yRow_eq_rowCompute 9 1 7 3 (by decide), + source_yRow_eq_rowCompute 9 1 7 4 (by decide), + source_yRow_eq_rowCompute 9 1 7 5 (by decide), + source_yRow_eq_rowCompute 9 1 7 6 (by decide), + computeRow_9_1_7_0, computeRow_9_1_7_1, computeRow_9_1_7_2, computeRow_9_1_7_3, computeRow_9_1_7_4, computeRow_9_1_7_5, computeRow_9_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_1_9 : Y 9 1 9 = (2064320406503781558919011/838860800000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 1 9 0 (by decide), + source_yRow_eq_rowCompute 9 1 9 1 (by decide), + source_yRow_eq_rowCompute 9 1 9 2 (by decide), + source_yRow_eq_rowCompute 9 1 9 3 (by decide), + source_yRow_eq_rowCompute 9 1 9 4 (by decide), + source_yRow_eq_rowCompute 9 1 9 5 (by decide), + source_yRow_eq_rowCompute 9 1 9 6 (by decide), + computeRow_9_1_9_0, computeRow_9_1_9_1, computeRow_9_1_9_2, computeRow_9_1_9_3, computeRow_9_1_9_4, computeRow_9_1_9_5, computeRow_9_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_3_3 : Y 9 3 3 = (2960534512700301116069433/23488102400000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 3 3 0 (by decide), + source_yRow_eq_rowCompute 9 3 3 1 (by decide), + source_yRow_eq_rowCompute 9 3 3 2 (by decide), + source_yRow_eq_rowCompute 9 3 3 3 (by decide), + source_yRow_eq_rowCompute 9 3 3 4 (by decide), + source_yRow_eq_rowCompute 9 3 3 5 (by decide), + source_yRow_eq_rowCompute 9 3 3 6 (by decide), + computeRow_9_3_3_0, computeRow_9_3_3_1, computeRow_9_3_3_2, computeRow_9_3_3_3, computeRow_9_3_3_4, computeRow_9_3_3_5, computeRow_9_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_3_5 : Y 9 3 5 = (-249132079557021880785303/11744051200000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 3 5 0 (by decide), + source_yRow_eq_rowCompute 9 3 5 1 (by decide), + source_yRow_eq_rowCompute 9 3 5 2 (by decide), + source_yRow_eq_rowCompute 9 3 5 3 (by decide), + source_yRow_eq_rowCompute 9 3 5 4 (by decide), + source_yRow_eq_rowCompute 9 3 5 5 (by decide), + source_yRow_eq_rowCompute 9 3 5 6 (by decide), + computeRow_9_3_5_0, computeRow_9_3_5_1, computeRow_9_3_5_2, computeRow_9_3_5_3, computeRow_9_3_5_4, computeRow_9_3_5_5, computeRow_9_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_3_7 : Y 9 3 7 = (-172612848420190308157317/419430400000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 3 7 0 (by decide), + source_yRow_eq_rowCompute 9 3 7 1 (by decide), + source_yRow_eq_rowCompute 9 3 7 2 (by decide), + source_yRow_eq_rowCompute 9 3 7 3 (by decide), + source_yRow_eq_rowCompute 9 3 7 4 (by decide), + source_yRow_eq_rowCompute 9 3 7 5 (by decide), + source_yRow_eq_rowCompute 9 3 7 6 (by decide), + computeRow_9_3_7_0, computeRow_9_3_7_1, computeRow_9_3_7_2, computeRow_9_3_7_3, computeRow_9_3_7_4, computeRow_9_3_7_5, computeRow_9_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_3_9 : Y 9 3 9 = (-460639144770506834240727/209715200000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 3 9 0 (by decide), + source_yRow_eq_rowCompute 9 3 9 1 (by decide), + source_yRow_eq_rowCompute 9 3 9 2 (by decide), + source_yRow_eq_rowCompute 9 3 9 3 (by decide), + source_yRow_eq_rowCompute 9 3 9 4 (by decide), + source_yRow_eq_rowCompute 9 3 9 5 (by decide), + source_yRow_eq_rowCompute 9 3 9 6 (by decide), + computeRow_9_3_9_0, computeRow_9_3_9_1, computeRow_9_3_9_2, computeRow_9_3_9_3, computeRow_9_3_9_4, computeRow_9_3_9_5, computeRow_9_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_5_5 : Y 9 5 5 = (-12391755266391716879263611/46976204800000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 5 5 0 (by decide), + source_yRow_eq_rowCompute 9 5 5 1 (by decide), + source_yRow_eq_rowCompute 9 5 5 2 (by decide), + source_yRow_eq_rowCompute 9 5 5 3 (by decide), + source_yRow_eq_rowCompute 9 5 5 4 (by decide), + source_yRow_eq_rowCompute 9 5 5 5 (by decide), + source_yRow_eq_rowCompute 9 5 5 6 (by decide), + computeRow_9_5_5_0, computeRow_9_5_5_1, computeRow_9_5_5_2, computeRow_9_5_5_3, computeRow_9_5_5_4, computeRow_9_5_5_5, computeRow_9_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_5_7 : Y 9 5 7 = (202846259663372040293217/3355443200000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 5 7 0 (by decide), + source_yRow_eq_rowCompute 9 5 7 1 (by decide), + source_yRow_eq_rowCompute 9 5 7 2 (by decide), + source_yRow_eq_rowCompute 9 5 7 3 (by decide), + source_yRow_eq_rowCompute 9 5 7 4 (by decide), + source_yRow_eq_rowCompute 9 5 7 5 (by decide), + source_yRow_eq_rowCompute 9 5 7 6 (by decide), + computeRow_9_5_7_0, computeRow_9_5_7_1, computeRow_9_5_7_2, computeRow_9_5_7_3, computeRow_9_5_7_4, computeRow_9_5_7_5, computeRow_9_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_5_9 : Y 9 5 9 = (1717697222431419971099331/838860800000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 5 9 0 (by decide), + source_yRow_eq_rowCompute 9 5 9 1 (by decide), + source_yRow_eq_rowCompute 9 5 9 2 (by decide), + source_yRow_eq_rowCompute 9 5 9 3 (by decide), + source_yRow_eq_rowCompute 9 5 9 4 (by decide), + source_yRow_eq_rowCompute 9 5 9 5 (by decide), + source_yRow_eq_rowCompute 9 5 9 6 (by decide), + computeRow_9_5_9_0, computeRow_9_5_9_1, computeRow_9_5_9_2, computeRow_9_5_9_3, computeRow_9_5_9_4, computeRow_9_5_9_5, computeRow_9_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_7_7 : Y 9 7 7 = (-3138981013037239731556773/1677721600000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 7 7 0 (by decide), + source_yRow_eq_rowCompute 9 7 7 1 (by decide), + source_yRow_eq_rowCompute 9 7 7 2 (by decide), + source_yRow_eq_rowCompute 9 7 7 3 (by decide), + source_yRow_eq_rowCompute 9 7 7 4 (by decide), + source_yRow_eq_rowCompute 9 7 7 5 (by decide), + source_yRow_eq_rowCompute 9 7 7 6 (by decide), + computeRow_9_7_7_0, computeRow_9_7_7_1, computeRow_9_7_7_2, computeRow_9_7_7_3, computeRow_9_7_7_4, computeRow_9_7_7_5, computeRow_9_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_7_9 : Y 9 7 9 = (-1034085603218724160418079/419430400000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 7 9 0 (by decide), + source_yRow_eq_rowCompute 9 7 9 1 (by decide), + source_yRow_eq_rowCompute 9 7 9 2 (by decide), + source_yRow_eq_rowCompute 9 7 9 3 (by decide), + source_yRow_eq_rowCompute 9 7 9 4 (by decide), + source_yRow_eq_rowCompute 9 7 9 5 (by decide), + source_yRow_eq_rowCompute 9 7 9 6 (by decide), + computeRow_9_7_9_0, computeRow_9_7_9_1, computeRow_9_7_9_2, computeRow_9_7_9_3, computeRow_9_7_9_4, computeRow_9_7_9_5, computeRow_9_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_9_9_9 : Y 9 9 9 = (-9956547203160990435022917/104857600000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 9 9 9 0 (by decide), + source_yRow_eq_rowCompute 9 9 9 1 (by decide), + source_yRow_eq_rowCompute 9 9 9 2 (by decide), + source_yRow_eq_rowCompute 9 9 9 3 (by decide), + source_yRow_eq_rowCompute 9 9 9 4 (by decide), + source_yRow_eq_rowCompute 9 9 9 5 (by decide), + source_yRow_eq_rowCompute 9 9 9 6 (by decide), + computeRow_9_9_9_0, computeRow_9_9_9_1, computeRow_9_9_9_2, computeRow_9_9_9_3, computeRow_9_9_9_4, computeRow_9_9_9_5, computeRow_9_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_9_1_1 : Z 9 1 1 = (80640 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_1_1 + +theorem source_gram_9_1_3 : Z 9 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_1_3 + +theorem source_gram_9_1_5 : Z 9 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_1_5 + +theorem source_gram_9_1_7 : Z 9 1 7 = (-10080 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_1_7 + +theorem source_gram_9_1_9 : Z 9 1 9 = (136080 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_1_9 + +theorem source_gram_9_3_3 : Z 9 3 3 = (4320 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_3_3 + +theorem source_gram_9_3_5 : Z 9 3 5 = (-2160 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_3_5 + +theorem source_gram_9_3_7 : Z 9 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_3_7 + +theorem source_gram_9_3_9 : Z 9 3 9 = (22680 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_3_9 + +theorem source_gram_9_5_5 : Z 9 5 5 = (1080 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_5_5 + +theorem source_gram_9_5_7 : Z 9 5 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_5_7 + +theorem source_gram_9_5_9 : Z 9 5 9 = (-11340 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_5_9 + +theorem source_gram_9_7_7 : Z 9 7 7 = (1260 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_7_7 + +theorem source_gram_9_7_9 : Z 9 7 9 = (-17010 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_7_9 + +theorem source_gram_9_9_9 : Z 9 9 9 = (348705 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_9_9_9 + +theorem source_error_9_3_1 : Y 9 3 1 = (-33961811903853786055197/838860800000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_9_1_3 + +theorem source_gram_9_3_1 : Z 9 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_9_1_3 + +theorem source_error_9_5_1 : Y 9 5 1 = (-670994343426034247927913/6710886400000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_9_1_5 + +theorem source_gram_9_5_1 : Z 9 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_9_1_5 + +theorem source_error_9_5_3 : Y 9 5 3 = (-249132079557021880785303/11744051200000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_9_3_5 + +theorem source_gram_9_5_3 : Z 9 5 3 = (-2160 : ℚ) := by + rw [Z_symm] + exact source_gram_9_3_5 + +theorem source_error_9_7_1 : Y 9 7 1 = (4530779263986412498504797/3355443200000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_9_1_7 + +theorem source_gram_9_7_1 : Z 9 7 1 = (-10080 : ℚ) := by + rw [Z_symm] + exact source_gram_9_1_7 + +theorem source_error_9_7_3 : Y 9 7 3 = (-172612848420190308157317/419430400000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_9_3_7 + +theorem source_gram_9_7_3 : Z 9 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_9_3_7 + +theorem source_error_9_7_5 : Y 9 7 5 = (202846259663372040293217/3355443200000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_9_5_7 + +theorem source_gram_9_7_5 : Z 9 7 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_9_5_7 + +theorem source_error_9_9_1 : Y 9 9 1 = (2064320406503781558919011/838860800000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_9_1_9 + +theorem source_gram_9_9_1 : Z 9 9 1 = (136080 : ℚ) := by + rw [Z_symm] + exact source_gram_9_1_9 + +theorem source_error_9_9_3 : Y 9 9 3 = (-460639144770506834240727/209715200000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_9_3_9 + +theorem source_gram_9_9_3 : Z 9 9 3 = (22680 : ℚ) := by + rw [Z_symm] + exact source_gram_9_3_9 + +theorem source_error_9_9_5 : Y 9 9 5 = (1717697222431419971099331/838860800000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_9_5_9 + +theorem source_gram_9_9_5 : Z 9 9 5 = (-11340 : ℚ) := by + rw [Z_symm] + exact source_gram_9_5_9 + +theorem source_error_9_9_7 : Y 9 9 7 = (-1034085603218724160418079/419430400000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_9_7_9 + +theorem source_gram_9_9_7 : Z 9 9 7 = (-17010 : ℚ) := by + rw [Z_symm] + exact source_gram_9_7_9 + +theorem error_9 : errorRational 9 = candidateY_9 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_9_1_1 + · exact source_error_9_1_3 + · exact source_error_9_1_5 + · exact source_error_9_1_7 + · exact source_error_9_1_9 + · exact source_error_9_3_1 + · exact source_error_9_3_3 + · exact source_error_9_3_5 + · exact source_error_9_3_7 + · exact source_error_9_3_9 + · exact source_error_9_5_1 + · exact source_error_9_5_3 + · exact source_error_9_5_5 + · exact source_error_9_5_7 + · exact source_error_9_5_9 + · exact source_error_9_7_1 + · exact source_error_9_7_3 + · exact source_error_9_7_5 + · exact source_error_9_7_7 + · exact source_error_9_7_9 + · exact source_error_9_9_1 + · exact source_error_9_9_3 + · exact source_error_9_9_5 + · exact source_error_9_9_7 + · exact source_error_9_9_9 + +theorem gram_9 : gramRational 9 = candidateZ_9 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_9_1_1 + · exact source_gram_9_1_3 + · exact source_gram_9_1_5 + · exact source_gram_9_1_7 + · exact source_gram_9_1_9 + · exact source_gram_9_3_1 + · exact source_gram_9_3_3 + · exact source_gram_9_3_5 + · exact source_gram_9_3_7 + · exact source_gram_9_3_9 + · exact source_gram_9_5_1 + · exact source_gram_9_5_3 + · exact source_gram_9_5_5 + · exact source_gram_9_5_7 + · exact source_gram_9_5_9 + · exact source_gram_9_7_1 + · exact source_gram_9_7_3 + · exact source_gram_9_7_5 + · exact source_gram_9_7_7 + · exact source_gram_9_7_9 + · exact source_gram_9_9_1 + · exact source_gram_9_9_3 + · exact source_gram_9_9_5 + · exact source_gram_9_9_7 + · exact source_gram_9_9_9 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData10.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData10.lean new file mode 100644 index 0000000000000000000000000000000000000000..7e49067277c74aa9451a5bdee31023d4359f1810 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData10.lean @@ -0,0 +1,377 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram10 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow10 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow102 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow103 +import OAI.Analysis.Laughlin.FiniteFlux.Data10 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_10_1_1 : Y 10 1 1 = (3252603773208384966897801/134217728000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 1 1 0 (by decide), + source_yRow_eq_rowCompute 10 1 1 1 (by decide), + source_yRow_eq_rowCompute 10 1 1 2 (by decide), + source_yRow_eq_rowCompute 10 1 1 3 (by decide), + source_yRow_eq_rowCompute 10 1 1 4 (by decide), + source_yRow_eq_rowCompute 10 1 1 5 (by decide), + source_yRow_eq_rowCompute 10 1 1 6 (by decide), + computeRow_10_1_1_0, computeRow_10_1_1_1, computeRow_10_1_1_2, computeRow_10_1_1_3, computeRow_10_1_1_4, computeRow_10_1_1_5, computeRow_10_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_1_3 : Y 10 1 3 = (-1219963203744052188572919/167772160000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 1 3 0 (by decide), + source_yRow_eq_rowCompute 10 1 3 1 (by decide), + source_yRow_eq_rowCompute 10 1 3 2 (by decide), + source_yRow_eq_rowCompute 10 1 3 3 (by decide), + source_yRow_eq_rowCompute 10 1 3 4 (by decide), + source_yRow_eq_rowCompute 10 1 3 5 (by decide), + source_yRow_eq_rowCompute 10 1 3 6 (by decide), + computeRow_10_1_3_0, computeRow_10_1_3_1, computeRow_10_1_3_2, computeRow_10_1_3_3, computeRow_10_1_3_4, computeRow_10_1_3_5, computeRow_10_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_1_5 : Y 10 1 5 = (1233781148459940320874483/134217728000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 1 5 0 (by decide), + source_yRow_eq_rowCompute 10 1 5 1 (by decide), + source_yRow_eq_rowCompute 10 1 5 2 (by decide), + source_yRow_eq_rowCompute 10 1 5 3 (by decide), + source_yRow_eq_rowCompute 10 1 5 4 (by decide), + source_yRow_eq_rowCompute 10 1 5 5 (by decide), + source_yRow_eq_rowCompute 10 1 5 6 (by decide), + computeRow_10_1_5_0, computeRow_10_1_5_1, computeRow_10_1_5_2, computeRow_10_1_5_3, computeRow_10_1_5_4, computeRow_10_1_5_5, computeRow_10_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_1_7 : Y 10 1 7 = (-4673143458544379455879083/335544320000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 1 7 0 (by decide), + source_yRow_eq_rowCompute 10 1 7 1 (by decide), + source_yRow_eq_rowCompute 10 1 7 2 (by decide), + source_yRow_eq_rowCompute 10 1 7 3 (by decide), + source_yRow_eq_rowCompute 10 1 7 4 (by decide), + source_yRow_eq_rowCompute 10 1 7 5 (by decide), + source_yRow_eq_rowCompute 10 1 7 6 (by decide), + computeRow_10_1_7_0, computeRow_10_1_7_1, computeRow_10_1_7_2, computeRow_10_1_7_3, computeRow_10_1_7_4, computeRow_10_1_7_5, computeRow_10_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_1_9 : Y 10 1 9 = (2012606963507139814961019/83886080000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 1 9 0 (by decide), + source_yRow_eq_rowCompute 10 1 9 1 (by decide), + source_yRow_eq_rowCompute 10 1 9 2 (by decide), + source_yRow_eq_rowCompute 10 1 9 3 (by decide), + source_yRow_eq_rowCompute 10 1 9 4 (by decide), + source_yRow_eq_rowCompute 10 1 9 5 (by decide), + source_yRow_eq_rowCompute 10 1 9 6 (by decide), + computeRow_10_1_9_0, computeRow_10_1_9_1, computeRow_10_1_9_2, computeRow_10_1_9_3, computeRow_10_1_9_4, computeRow_10_1_9_5, computeRow_10_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_3_3 : Y 10 3 3 = (23917264894764854794377/16777216000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 3 3 0 (by decide), + source_yRow_eq_rowCompute 10 3 3 1 (by decide), + source_yRow_eq_rowCompute 10 3 3 2 (by decide), + source_yRow_eq_rowCompute 10 3 3 3 (by decide), + source_yRow_eq_rowCompute 10 3 3 4 (by decide), + source_yRow_eq_rowCompute 10 3 3 5 (by decide), + source_yRow_eq_rowCompute 10 3 3 6 (by decide), + computeRow_10_3_3_0, computeRow_10_3_3_1, computeRow_10_3_3_2, computeRow_10_3_3_3, computeRow_10_3_3_4, computeRow_10_3_3_5, computeRow_10_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_3_5 : Y 10 3 5 = (-13854999171694482915831/8388608000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 3 5 0 (by decide), + source_yRow_eq_rowCompute 10 3 5 1 (by decide), + source_yRow_eq_rowCompute 10 3 5 2 (by decide), + source_yRow_eq_rowCompute 10 3 5 3 (by decide), + source_yRow_eq_rowCompute 10 3 5 4 (by decide), + source_yRow_eq_rowCompute 10 3 5 5 (by decide), + source_yRow_eq_rowCompute 10 3 5 6 (by decide), + computeRow_10_3_5_0, computeRow_10_3_5_1, computeRow_10_3_5_2, computeRow_10_3_5_3, computeRow_10_3_5_4, computeRow_10_3_5_5, computeRow_10_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_3_7 : Y 10 3 7 = (57805337880323795919969/16777216000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 3 7 0 (by decide), + source_yRow_eq_rowCompute 10 3 7 1 (by decide), + source_yRow_eq_rowCompute 10 3 7 2 (by decide), + source_yRow_eq_rowCompute 10 3 7 3 (by decide), + source_yRow_eq_rowCompute 10 3 7 4 (by decide), + source_yRow_eq_rowCompute 10 3 7 5 (by decide), + source_yRow_eq_rowCompute 10 3 7 6 (by decide), + computeRow_10_3_7_0, computeRow_10_3_7_1, computeRow_10_3_7_2, computeRow_10_3_7_3, computeRow_10_3_7_4, computeRow_10_3_7_5, computeRow_10_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_3_9 : Y 10 3 9 = (-52562004903703102850037/5242880000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 3 9 0 (by decide), + source_yRow_eq_rowCompute 10 3 9 1 (by decide), + source_yRow_eq_rowCompute 10 3 9 2 (by decide), + source_yRow_eq_rowCompute 10 3 9 3 (by decide), + source_yRow_eq_rowCompute 10 3 9 4 (by decide), + source_yRow_eq_rowCompute 10 3 9 5 (by decide), + source_yRow_eq_rowCompute 10 3 9 6 (by decide), + computeRow_10_3_9_0, computeRow_10_3_9_1, computeRow_10_3_9_2, computeRow_10_3_9_3, computeRow_10_3_9_4, computeRow_10_3_9_5, computeRow_10_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_5_5 : Y 10 5 5 = (2285267576183515842978393/939524096000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 5 5 0 (by decide), + source_yRow_eq_rowCompute 10 5 5 1 (by decide), + source_yRow_eq_rowCompute 10 5 5 2 (by decide), + source_yRow_eq_rowCompute 10 5 5 3 (by decide), + source_yRow_eq_rowCompute 10 5 5 4 (by decide), + source_yRow_eq_rowCompute 10 5 5 5 (by decide), + source_yRow_eq_rowCompute 10 5 5 6 (by decide), + computeRow_10_5_5_0, computeRow_10_5_5_1, computeRow_10_5_5_2, computeRow_10_5_5_3, computeRow_10_5_5_4, computeRow_10_5_5_5, computeRow_10_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_5_7 : Y 10 5 7 = (-121198635809384297528619/67108864000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 5 7 0 (by decide), + source_yRow_eq_rowCompute 10 5 7 1 (by decide), + source_yRow_eq_rowCompute 10 5 7 2 (by decide), + source_yRow_eq_rowCompute 10 5 7 3 (by decide), + source_yRow_eq_rowCompute 10 5 7 4 (by decide), + source_yRow_eq_rowCompute 10 5 7 5 (by decide), + source_yRow_eq_rowCompute 10 5 7 6 (by decide), + computeRow_10_5_7_0, computeRow_10_5_7_1, computeRow_10_5_7_2, computeRow_10_5_7_3, computeRow_10_5_7_4, computeRow_10_5_7_5, computeRow_10_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_5_9 : Y 10 5 9 = (127922353790121014632767/16777216000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 5 9 0 (by decide), + source_yRow_eq_rowCompute 10 5 9 1 (by decide), + source_yRow_eq_rowCompute 10 5 9 2 (by decide), + source_yRow_eq_rowCompute 10 5 9 3 (by decide), + source_yRow_eq_rowCompute 10 5 9 4 (by decide), + source_yRow_eq_rowCompute 10 5 9 5 (by decide), + source_yRow_eq_rowCompute 10 5 9 6 (by decide), + computeRow_10_5_9_0, computeRow_10_5_9_1, computeRow_10_5_9_2, computeRow_10_5_9_3, computeRow_10_5_9_4, computeRow_10_5_9_5, computeRow_10_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_7_7 : Y 10 7 7 = (51194502011873480782923/167772160000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 7 7 0 (by decide), + source_yRow_eq_rowCompute 10 7 7 1 (by decide), + source_yRow_eq_rowCompute 10 7 7 2 (by decide), + source_yRow_eq_rowCompute 10 7 7 3 (by decide), + source_yRow_eq_rowCompute 10 7 7 4 (by decide), + source_yRow_eq_rowCompute 10 7 7 5 (by decide), + source_yRow_eq_rowCompute 10 7 7 6 (by decide), + computeRow_10_7_7_0, computeRow_10_7_7_1, computeRow_10_7_7_2, computeRow_10_7_7_3, computeRow_10_7_7_4, computeRow_10_7_7_5, computeRow_10_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_7_9 : Y 10 7 9 = (10203611212469228878953/41943040000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 7 9 0 (by decide), + source_yRow_eq_rowCompute 10 7 9 1 (by decide), + source_yRow_eq_rowCompute 10 7 9 2 (by decide), + source_yRow_eq_rowCompute 10 7 9 3 (by decide), + source_yRow_eq_rowCompute 10 7 9 4 (by decide), + source_yRow_eq_rowCompute 10 7 9 5 (by decide), + source_yRow_eq_rowCompute 10 7 9 6 (by decide), + computeRow_10_7_9_0, computeRow_10_7_9_1, computeRow_10_7_9_2, computeRow_10_7_9_3, computeRow_10_7_9_4, computeRow_10_7_9_5, computeRow_10_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_10_9_9 : Y 10 9 9 = (-990036939147267786688413/10485760000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 10 9 9 0 (by decide), + source_yRow_eq_rowCompute 10 9 9 1 (by decide), + source_yRow_eq_rowCompute 10 9 9 2 (by decide), + source_yRow_eq_rowCompute 10 9 9 3 (by decide), + source_yRow_eq_rowCompute 10 9 9 4 (by decide), + source_yRow_eq_rowCompute 10 9 9 5 (by decide), + source_yRow_eq_rowCompute 10 9 9 6 (by decide), + computeRow_10_9_9_0, computeRow_10_9_9_1, computeRow_10_9_9_2, computeRow_10_9_9_3, computeRow_10_9_9_4, computeRow_10_9_9_5, computeRow_10_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_10_1_1 : Z 10 1 1 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_1_1 + +theorem source_gram_10_1_3 : Z 10 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_1_3 + +theorem source_gram_10_1_5 : Z 10 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_1_5 + +theorem source_gram_10_1_7 : Z 10 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_1_7 + +theorem source_gram_10_1_9 : Z 10 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_1_9 + +theorem source_gram_10_3_3 : Z 10 3 3 = (30240 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_3_3 + +theorem source_gram_10_3_5 : Z 10 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_3_5 + +theorem source_gram_10_3_7 : Z 10 3 7 = (-22680 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_3_7 + +theorem source_gram_10_3_9 : Z 10 3 9 = (90720 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_3_9 + +theorem source_gram_10_5_5 : Z 10 5 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_5_5 + +theorem source_gram_10_5_7 : Z 10 5 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_5_7 + +theorem source_gram_10_5_9 : Z 10 5 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_5_9 + +theorem source_gram_10_7_7 : Z 10 7 7 = (17010 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_7_7 + +theorem source_gram_10_7_9 : Z 10 7 9 = (-68040 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_7_9 + +theorem source_gram_10_9_9 : Z 10 9 9 = (272160 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_10_9_9 + +theorem source_error_10_3_1 : Y 10 3 1 = (-1219963203744052188572919/167772160000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_10_1_3 + +theorem source_gram_10_3_1 : Z 10 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_10_1_3 + +theorem source_error_10_5_1 : Y 10 5 1 = (1233781148459940320874483/134217728000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_10_1_5 + +theorem source_gram_10_5_1 : Z 10 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_10_1_5 + +theorem source_error_10_5_3 : Y 10 5 3 = (-13854999171694482915831/8388608000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_10_3_5 + +theorem source_gram_10_5_3 : Z 10 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_10_3_5 + +theorem source_error_10_7_1 : Y 10 7 1 = (-4673143458544379455879083/335544320000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_10_1_7 + +theorem source_gram_10_7_1 : Z 10 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_10_1_7 + +theorem source_error_10_7_3 : Y 10 7 3 = (57805337880323795919969/16777216000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_10_3_7 + +theorem source_gram_10_7_3 : Z 10 7 3 = (-22680 : ℚ) := by + rw [Z_symm] + exact source_gram_10_3_7 + +theorem source_error_10_7_5 : Y 10 7 5 = (-121198635809384297528619/67108864000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_10_5_7 + +theorem source_gram_10_7_5 : Z 10 7 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_10_5_7 + +theorem source_error_10_9_1 : Y 10 9 1 = (2012606963507139814961019/83886080000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_10_1_9 + +theorem source_gram_10_9_1 : Z 10 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_10_1_9 + +theorem source_error_10_9_3 : Y 10 9 3 = (-52562004903703102850037/5242880000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_10_3_9 + +theorem source_gram_10_9_3 : Z 10 9 3 = (90720 : ℚ) := by + rw [Z_symm] + exact source_gram_10_3_9 + +theorem source_error_10_9_5 : Y 10 9 5 = (127922353790121014632767/16777216000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_10_5_9 + +theorem source_gram_10_9_5 : Z 10 9 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_10_5_9 + +theorem source_error_10_9_7 : Y 10 9 7 = (10203611212469228878953/41943040000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_10_7_9 + +theorem source_gram_10_9_7 : Z 10 9 7 = (-68040 : ℚ) := by + rw [Z_symm] + exact source_gram_10_7_9 + +theorem error_10 : errorRational 10 = candidateY_10 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_10_1_1 + · exact source_error_10_1_3 + · exact source_error_10_1_5 + · exact source_error_10_1_7 + · exact source_error_10_1_9 + · exact source_error_10_3_1 + · exact source_error_10_3_3 + · exact source_error_10_3_5 + · exact source_error_10_3_7 + · exact source_error_10_3_9 + · exact source_error_10_5_1 + · exact source_error_10_5_3 + · exact source_error_10_5_5 + · exact source_error_10_5_7 + · exact source_error_10_5_9 + · exact source_error_10_7_1 + · exact source_error_10_7_3 + · exact source_error_10_7_5 + · exact source_error_10_7_7 + · exact source_error_10_7_9 + · exact source_error_10_9_1 + · exact source_error_10_9_3 + · exact source_error_10_9_5 + · exact source_error_10_9_7 + · exact source_error_10_9_9 + +theorem gram_10 : gramRational 10 = candidateZ_10 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_10_1_1 + · exact source_gram_10_1_3 + · exact source_gram_10_1_5 + · exact source_gram_10_1_7 + · exact source_gram_10_1_9 + · exact source_gram_10_3_1 + · exact source_gram_10_3_3 + · exact source_gram_10_3_5 + · exact source_gram_10_3_7 + · exact source_gram_10_3_9 + · exact source_gram_10_5_1 + · exact source_gram_10_5_3 + · exact source_gram_10_5_5 + · exact source_gram_10_5_7 + · exact source_gram_10_5_9 + · exact source_gram_10_7_1 + · exact source_gram_10_7_3 + · exact source_gram_10_7_5 + · exact source_gram_10_7_7 + · exact source_gram_10_7_9 + · exact source_gram_10_9_1 + · exact source_gram_10_9_3 + · exact source_gram_10_9_5 + · exact source_gram_10_9_7 + · exact source_gram_10_9_9 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData11.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData11.lean new file mode 100644 index 0000000000000000000000000000000000000000..0f07aa6ae47a158cd67be29be4e9bda3e5907b43 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData11.lean @@ -0,0 +1,531 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram11 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow11 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow112 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow113 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow114 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow115 +import OAI.Analysis.Laughlin.FiniteFlux.Data11 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_11_1_1 : Y 11 1 1 = (15310420495743050456853357/134217728000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 1 1 0 (by decide), + source_yRow_eq_rowCompute 11 1 1 1 (by decide), + source_yRow_eq_rowCompute 11 1 1 2 (by decide), + source_yRow_eq_rowCompute 11 1 1 3 (by decide), + source_yRow_eq_rowCompute 11 1 1 4 (by decide), + source_yRow_eq_rowCompute 11 1 1 5 (by decide), + source_yRow_eq_rowCompute 11 1 1 6 (by decide), + computeRow_11_1_1_0, computeRow_11_1_1_1, computeRow_11_1_1_2, computeRow_11_1_1_3, computeRow_11_1_1_4, computeRow_11_1_1_5, computeRow_11_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_1_3 : Y 11 1 3 = (-21091981152473935416162441/335544320000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 1 3 0 (by decide), + source_yRow_eq_rowCompute 11 1 3 1 (by decide), + source_yRow_eq_rowCompute 11 1 3 2 (by decide), + source_yRow_eq_rowCompute 11 1 3 3 (by decide), + source_yRow_eq_rowCompute 11 1 3 4 (by decide), + source_yRow_eq_rowCompute 11 1 3 5 (by decide), + source_yRow_eq_rowCompute 11 1 3 6 (by decide), + computeRow_11_1_3_0, computeRow_11_1_3_1, computeRow_11_1_3_2, computeRow_11_1_3_3, computeRow_11_1_3_4, computeRow_11_1_3_5, computeRow_11_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_1_5 : Y 11 1 5 = (1759644912412486678804947/134217728000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 1 5 0 (by decide), + source_yRow_eq_rowCompute 11 1 5 1 (by decide), + source_yRow_eq_rowCompute 11 1 5 2 (by decide), + source_yRow_eq_rowCompute 11 1 5 3 (by decide), + source_yRow_eq_rowCompute 11 1 5 4 (by decide), + source_yRow_eq_rowCompute 11 1 5 5 (by decide), + source_yRow_eq_rowCompute 11 1 5 6 (by decide), + computeRow_11_1_5_0, computeRow_11_1_5_1, computeRow_11_1_5_2, computeRow_11_1_5_3, computeRow_11_1_5_4, computeRow_11_1_5_5, computeRow_11_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_1_7 : Y 11 1 7 = (-7117902998608090523107887/335544320000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 1 7 0 (by decide), + source_yRow_eq_rowCompute 11 1 7 1 (by decide), + source_yRow_eq_rowCompute 11 1 7 2 (by decide), + source_yRow_eq_rowCompute 11 1 7 3 (by decide), + source_yRow_eq_rowCompute 11 1 7 4 (by decide), + source_yRow_eq_rowCompute 11 1 7 5 (by decide), + source_yRow_eq_rowCompute 11 1 7 6 (by decide), + computeRow_11_1_7_0, computeRow_11_1_7_1, computeRow_11_1_7_2, computeRow_11_1_7_3, computeRow_11_1_7_4, computeRow_11_1_7_5, computeRow_11_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_1_9 : Y 11 1 9 = (2050140304557578762479287/16777216000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 1 9 0 (by decide), + source_yRow_eq_rowCompute 11 1 9 1 (by decide), + source_yRow_eq_rowCompute 11 1 9 2 (by decide), + source_yRow_eq_rowCompute 11 1 9 3 (by decide), + source_yRow_eq_rowCompute 11 1 9 4 (by decide), + source_yRow_eq_rowCompute 11 1 9 5 (by decide), + source_yRow_eq_rowCompute 11 1 9 6 (by decide), + computeRow_11_1_9_0, computeRow_11_1_9_1, computeRow_11_1_9_2, computeRow_11_1_9_3, computeRow_11_1_9_4, computeRow_11_1_9_5, computeRow_11_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_1_11 : Y 11 1 11 = (-3816671070411211699962099/8388608000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 1 11 0 (by decide), + source_yRow_eq_rowCompute 11 1 11 1 (by decide), + source_yRow_eq_rowCompute 11 1 11 2 (by decide), + source_yRow_eq_rowCompute 11 1 11 3 (by decide), + source_yRow_eq_rowCompute 11 1 11 4 (by decide), + source_yRow_eq_rowCompute 11 1 11 5 (by decide), + source_yRow_eq_rowCompute 11 1 11 6 (by decide), + computeRow_11_1_11_0, computeRow_11_1_11_1, computeRow_11_1_11_2, computeRow_11_1_11_3, computeRow_11_1_11_4, computeRow_11_1_11_5, computeRow_11_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_3_3 : Y 11 3 3 = (3139824493398164330092707/167772160000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 3 3 0 (by decide), + source_yRow_eq_rowCompute 11 3 3 1 (by decide), + source_yRow_eq_rowCompute 11 3 3 2 (by decide), + source_yRow_eq_rowCompute 11 3 3 3 (by decide), + source_yRow_eq_rowCompute 11 3 3 4 (by decide), + source_yRow_eq_rowCompute 11 3 3 5 (by decide), + source_yRow_eq_rowCompute 11 3 3 6 (by decide), + computeRow_11_3_3_0, computeRow_11_3_3_1, computeRow_11_3_3_2, computeRow_11_3_3_3, computeRow_11_3_3_4, computeRow_11_3_3_5, computeRow_11_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_3_5 : Y 11 3 5 = (-110846050581407277067047/13421772800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 3 5 0 (by decide), + source_yRow_eq_rowCompute 11 3 5 1 (by decide), + source_yRow_eq_rowCompute 11 3 5 2 (by decide), + source_yRow_eq_rowCompute 11 3 5 3 (by decide), + source_yRow_eq_rowCompute 11 3 5 4 (by decide), + source_yRow_eq_rowCompute 11 3 5 5 (by decide), + source_yRow_eq_rowCompute 11 3 5 6 (by decide), + computeRow_11_3_5_0, computeRow_11_3_5_1, computeRow_11_3_5_2, computeRow_11_3_5_3, computeRow_11_3_5_4, computeRow_11_3_5_5, computeRow_11_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_3_7 : Y 11 3 7 = (-120000452149124136234801/167772160000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 3 7 0 (by decide), + source_yRow_eq_rowCompute 11 3 7 1 (by decide), + source_yRow_eq_rowCompute 11 3 7 2 (by decide), + source_yRow_eq_rowCompute 11 3 7 3 (by decide), + source_yRow_eq_rowCompute 11 3 7 4 (by decide), + source_yRow_eq_rowCompute 11 3 7 5 (by decide), + source_yRow_eq_rowCompute 11 3 7 6 (by decide), + computeRow_11_3_7_0, computeRow_11_3_7_1, computeRow_11_3_7_2, computeRow_11_3_7_3, computeRow_11_3_7_4, computeRow_11_3_7_5, computeRow_11_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_3_9 : Y 11 3 9 = (-804905973848069092119267/41943040000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 3 9 0 (by decide), + source_yRow_eq_rowCompute 11 3 9 1 (by decide), + source_yRow_eq_rowCompute 11 3 9 2 (by decide), + source_yRow_eq_rowCompute 11 3 9 3 (by decide), + source_yRow_eq_rowCompute 11 3 9 4 (by decide), + source_yRow_eq_rowCompute 11 3 9 5 (by decide), + source_yRow_eq_rowCompute 11 3 9 6 (by decide), + computeRow_11_3_9_0, computeRow_11_3_9_1, computeRow_11_3_9_2, computeRow_11_3_9_3, computeRow_11_3_9_4, computeRow_11_3_9_5, computeRow_11_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_3_11 : Y 11 3 11 = (-488664944191263381981813/20971520000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 3 11 0 (by decide), + source_yRow_eq_rowCompute 11 3 11 1 (by decide), + source_yRow_eq_rowCompute 11 3 11 2 (by decide), + source_yRow_eq_rowCompute 11 3 11 3 (by decide), + source_yRow_eq_rowCompute 11 3 11 4 (by decide), + source_yRow_eq_rowCompute 11 3 11 5 (by decide), + source_yRow_eq_rowCompute 11 3 11 6 (by decide), + computeRow_11_3_11_0, computeRow_11_3_11_1, computeRow_11_3_11_2, computeRow_11_3_11_3, computeRow_11_3_11_4, computeRow_11_3_11_5, computeRow_11_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_5_5 : Y 11 5 5 = (186561496958160530399967/134217728000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 5 5 0 (by decide), + source_yRow_eq_rowCompute 11 5 5 1 (by decide), + source_yRow_eq_rowCompute 11 5 5 2 (by decide), + source_yRow_eq_rowCompute 11 5 5 3 (by decide), + source_yRow_eq_rowCompute 11 5 5 4 (by decide), + source_yRow_eq_rowCompute 11 5 5 5 (by decide), + source_yRow_eq_rowCompute 11 5 5 6 (by decide), + computeRow_11_5_5_0, computeRow_11_5_5_1, computeRow_11_5_5_2, computeRow_11_5_5_3, computeRow_11_5_5_4, computeRow_11_5_5_5, computeRow_11_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_5_7 : Y 11 5 7 = (-132022995280028243088831/67108864000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 5 7 0 (by decide), + source_yRow_eq_rowCompute 11 5 7 1 (by decide), + source_yRow_eq_rowCompute 11 5 7 2 (by decide), + source_yRow_eq_rowCompute 11 5 7 3 (by decide), + source_yRow_eq_rowCompute 11 5 7 4 (by decide), + source_yRow_eq_rowCompute 11 5 7 5 (by decide), + source_yRow_eq_rowCompute 11 5 7 6 (by decide), + computeRow_11_5_7_0, computeRow_11_5_7_1, computeRow_11_5_7_2, computeRow_11_5_7_3, computeRow_11_5_7_4, computeRow_11_5_7_5, computeRow_11_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_5_9 : Y 11 5 9 = (39011604836809336804287/16777216000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 5 9 0 (by decide), + source_yRow_eq_rowCompute 11 5 9 1 (by decide), + source_yRow_eq_rowCompute 11 5 9 2 (by decide), + source_yRow_eq_rowCompute 11 5 9 3 (by decide), + source_yRow_eq_rowCompute 11 5 9 4 (by decide), + source_yRow_eq_rowCompute 11 5 9 5 (by decide), + source_yRow_eq_rowCompute 11 5 9 6 (by decide), + computeRow_11_5_9_0, computeRow_11_5_9_1, computeRow_11_5_9_2, computeRow_11_5_9_3, computeRow_11_5_9_4, computeRow_11_5_9_5, computeRow_11_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_5_11 : Y 11 5 11 = (-536635508982633719381547/8388608000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 5 11 0 (by decide), + source_yRow_eq_rowCompute 11 5 11 1 (by decide), + source_yRow_eq_rowCompute 11 5 11 2 (by decide), + source_yRow_eq_rowCompute 11 5 11 3 (by decide), + source_yRow_eq_rowCompute 11 5 11 4 (by decide), + source_yRow_eq_rowCompute 11 5 11 5 (by decide), + source_yRow_eq_rowCompute 11 5 11 6 (by decide), + computeRow_11_5_11_0, computeRow_11_5_11_1, computeRow_11_5_11_2, computeRow_11_5_11_3, computeRow_11_5_11_4, computeRow_11_5_11_5, computeRow_11_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_7_7 : Y 11 7 7 = (53081184869685889157043/167772160000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 7 7 0 (by decide), + source_yRow_eq_rowCompute 11 7 7 1 (by decide), + source_yRow_eq_rowCompute 11 7 7 2 (by decide), + source_yRow_eq_rowCompute 11 7 7 3 (by decide), + source_yRow_eq_rowCompute 11 7 7 4 (by decide), + source_yRow_eq_rowCompute 11 7 7 5 (by decide), + source_yRow_eq_rowCompute 11 7 7 6 (by decide), + computeRow_11_7_7_0, computeRow_11_7_7_1, computeRow_11_7_7_2, computeRow_11_7_7_3, computeRow_11_7_7_4, computeRow_11_7_7_5, computeRow_11_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_7_9 : Y 11 7 9 = (581826960578730870868149/41943040000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 7 9 0 (by decide), + source_yRow_eq_rowCompute 11 7 9 1 (by decide), + source_yRow_eq_rowCompute 11 7 9 2 (by decide), + source_yRow_eq_rowCompute 11 7 9 3 (by decide), + source_yRow_eq_rowCompute 11 7 9 4 (by decide), + source_yRow_eq_rowCompute 11 7 9 5 (by decide), + source_yRow_eq_rowCompute 11 7 9 6 (by decide), + computeRow_11_7_9_0, computeRow_11_7_9_1, computeRow_11_7_9_2, computeRow_11_7_9_3, computeRow_11_7_9_4, computeRow_11_7_9_5, computeRow_11_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_7_11 : Y 11 7 11 = (48169578758531066711919/20971520000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 7 11 0 (by decide), + source_yRow_eq_rowCompute 11 7 11 1 (by decide), + source_yRow_eq_rowCompute 11 7 11 2 (by decide), + source_yRow_eq_rowCompute 11 7 11 3 (by decide), + source_yRow_eq_rowCompute 11 7 11 4 (by decide), + source_yRow_eq_rowCompute 11 7 11 5 (by decide), + source_yRow_eq_rowCompute 11 7 11 6 (by decide), + computeRow_11_7_11_0, computeRow_11_7_11_1, computeRow_11_7_11_2, computeRow_11_7_11_3, computeRow_11_7_11_4, computeRow_11_7_11_5, computeRow_11_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_9_9 : Y 11 9 9 = (-985704999590345844614157/10485760000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 9 9 0 (by decide), + source_yRow_eq_rowCompute 11 9 9 1 (by decide), + source_yRow_eq_rowCompute 11 9 9 2 (by decide), + source_yRow_eq_rowCompute 11 9 9 3 (by decide), + source_yRow_eq_rowCompute 11 9 9 4 (by decide), + source_yRow_eq_rowCompute 11 9 9 5 (by decide), + source_yRow_eq_rowCompute 11 9 9 6 (by decide), + computeRow_11_9_9_0, computeRow_11_9_9_1, computeRow_11_9_9_2, computeRow_11_9_9_3, computeRow_11_9_9_4, computeRow_11_9_9_5, computeRow_11_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_9_11 : Y 11 9 11 = (390621018140645815377261/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 9 11 0 (by decide), + source_yRow_eq_rowCompute 11 9 11 1 (by decide), + source_yRow_eq_rowCompute 11 9 11 2 (by decide), + source_yRow_eq_rowCompute 11 9 11 3 (by decide), + source_yRow_eq_rowCompute 11 9 11 4 (by decide), + source_yRow_eq_rowCompute 11 9 11 5 (by decide), + source_yRow_eq_rowCompute 11 9 11 6 (by decide), + computeRow_11_9_11_0, computeRow_11_9_11_1, computeRow_11_9_11_2, computeRow_11_9_11_3, computeRow_11_9_11_4, computeRow_11_9_11_5, computeRow_11_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_11_11_11 : Y 11 11 11 = (-7434351034101698173344801/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 11 11 11 0 (by decide), + source_yRow_eq_rowCompute 11 11 11 1 (by decide), + source_yRow_eq_rowCompute 11 11 11 2 (by decide), + source_yRow_eq_rowCompute 11 11 11 3 (by decide), + source_yRow_eq_rowCompute 11 11 11 4 (by decide), + source_yRow_eq_rowCompute 11 11 11 5 (by decide), + source_yRow_eq_rowCompute 11 11 11 6 (by decide), + computeRow_11_11_11_0, computeRow_11_11_11_1, computeRow_11_11_11_2, computeRow_11_11_11_3, computeRow_11_11_11_4, computeRow_11_11_11_5, computeRow_11_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_11_1_1 : Z 11 1 1 = (7257600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_1_1 + +theorem source_gram_11_1_3 : Z 11 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_1_3 + +theorem source_gram_11_1_5 : Z 11 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_1_5 + +theorem source_gram_11_1_7 : Z 11 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_1_7 + +theorem source_gram_11_1_9 : Z 11 1 9 = (-453600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_1_9 + +theorem source_gram_11_1_11 : Z 11 1 11 = (9979200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_1_11 + +theorem source_gram_11_3_3 : Z 11 3 3 = (241920 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_3_3 + +theorem source_gram_11_3_5 : Z 11 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_3_5 + +theorem source_gram_11_3_7 : Z 11 3 7 = (-60480 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_3_7 + +theorem source_gram_11_3_9 : Z 11 3 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_3_9 + +theorem source_gram_11_3_11 : Z 11 3 11 = (2494800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_3_11 + +theorem source_gram_11_5_5 : Z 11 5 5 = (54000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_5_5 + +theorem source_gram_11_5_7 : Z 11 5 7 = (-75600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_5_7 + +theorem source_gram_11_5_9 : Z 11 5 9 = (113400 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_5_9 + +theorem source_gram_11_5_11 : Z 11 5 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_5_11 + +theorem source_gram_11_7_7 : Z 11 7 7 = (120960 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_7_7 + +theorem source_gram_11_7_9 : Z 11 7 9 = (-158760 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_7_9 + +theorem source_gram_11_7_11 : Z 11 7 11 = (-623700 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_7_11 + +theorem source_gram_11_9_9 : Z 11 9 9 = (266490 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_9_9 + +theorem source_gram_11_9_11 : Z 11 9 11 = (-623700 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_9_11 + +theorem source_gram_11_11_11 : Z 11 11 11 = (39449025 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_11_11_11 + +theorem source_error_11_3_1 : Y 11 3 1 = (-21091981152473935416162441/335544320000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_1_3 + +theorem source_gram_11_3_1 : Z 11 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_11_1_3 + +theorem source_error_11_5_1 : Y 11 5 1 = (1759644912412486678804947/134217728000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_1_5 + +theorem source_gram_11_5_1 : Z 11 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_11_1_5 + +theorem source_error_11_5_3 : Y 11 5 3 = (-110846050581407277067047/13421772800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_3_5 + +theorem source_gram_11_5_3 : Z 11 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_11_3_5 + +theorem source_error_11_7_1 : Y 11 7 1 = (-7117902998608090523107887/335544320000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_1_7 + +theorem source_gram_11_7_1 : Z 11 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_11_1_7 + +theorem source_error_11_7_3 : Y 11 7 3 = (-120000452149124136234801/167772160000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_3_7 + +theorem source_gram_11_7_3 : Z 11 7 3 = (-60480 : ℚ) := by + rw [Z_symm] + exact source_gram_11_3_7 + +theorem source_error_11_7_5 : Y 11 7 5 = (-132022995280028243088831/67108864000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_5_7 + +theorem source_gram_11_7_5 : Z 11 7 5 = (-75600 : ℚ) := by + rw [Z_symm] + exact source_gram_11_5_7 + +theorem source_error_11_9_1 : Y 11 9 1 = (2050140304557578762479287/16777216000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_1_9 + +theorem source_gram_11_9_1 : Z 11 9 1 = (-453600 : ℚ) := by + rw [Z_symm] + exact source_gram_11_1_9 + +theorem source_error_11_9_3 : Y 11 9 3 = (-804905973848069092119267/41943040000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_3_9 + +theorem source_gram_11_9_3 : Z 11 9 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_11_3_9 + +theorem source_error_11_9_5 : Y 11 9 5 = (39011604836809336804287/16777216000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_5_9 + +theorem source_gram_11_9_5 : Z 11 9 5 = (113400 : ℚ) := by + rw [Z_symm] + exact source_gram_11_5_9 + +theorem source_error_11_9_7 : Y 11 9 7 = (581826960578730870868149/41943040000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_7_9 + +theorem source_gram_11_9_7 : Z 11 9 7 = (-158760 : ℚ) := by + rw [Z_symm] + exact source_gram_11_7_9 + +theorem source_error_11_11_1 : Y 11 11 1 = (-3816671070411211699962099/8388608000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_1_11 + +theorem source_gram_11_11_1 : Z 11 11 1 = (9979200 : ℚ) := by + rw [Z_symm] + exact source_gram_11_1_11 + +theorem source_error_11_11_3 : Y 11 11 3 = (-488664944191263381981813/20971520000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_3_11 + +theorem source_gram_11_11_3 : Z 11 11 3 = (2494800 : ℚ) := by + rw [Z_symm] + exact source_gram_11_3_11 + +theorem source_error_11_11_5 : Y 11 11 5 = (-536635508982633719381547/8388608000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_5_11 + +theorem source_gram_11_11_5 : Z 11 11 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_11_5_11 + +theorem source_error_11_11_7 : Y 11 11 7 = (48169578758531066711919/20971520000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_7_11 + +theorem source_gram_11_11_7 : Z 11 11 7 = (-623700 : ℚ) := by + rw [Z_symm] + exact source_gram_11_7_11 + +theorem source_error_11_11_9 : Y 11 11 9 = (390621018140645815377261/1048576000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_11_9_11 + +theorem source_gram_11_11_9 : Z 11 11 9 = (-623700 : ℚ) := by + rw [Z_symm] + exact source_gram_11_9_11 + +theorem error_11 : errorRational 11 = candidateY_11 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_11_1_1 + · exact source_error_11_1_3 + · exact source_error_11_1_5 + · exact source_error_11_1_7 + · exact source_error_11_1_9 + · exact source_error_11_1_11 + · exact source_error_11_3_1 + · exact source_error_11_3_3 + · exact source_error_11_3_5 + · exact source_error_11_3_7 + · exact source_error_11_3_9 + · exact source_error_11_3_11 + · exact source_error_11_5_1 + · exact source_error_11_5_3 + · exact source_error_11_5_5 + · exact source_error_11_5_7 + · exact source_error_11_5_9 + · exact source_error_11_5_11 + · exact source_error_11_7_1 + · exact source_error_11_7_3 + · exact source_error_11_7_5 + · exact source_error_11_7_7 + · exact source_error_11_7_9 + · exact source_error_11_7_11 + · exact source_error_11_9_1 + · exact source_error_11_9_3 + · exact source_error_11_9_5 + · exact source_error_11_9_7 + · exact source_error_11_9_9 + · exact source_error_11_9_11 + · exact source_error_11_11_1 + · exact source_error_11_11_3 + · exact source_error_11_11_5 + · exact source_error_11_11_7 + · exact source_error_11_11_9 + · exact source_error_11_11_11 + +theorem gram_11 : gramRational 11 = candidateZ_11 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_11_1_1 + · exact source_gram_11_1_3 + · exact source_gram_11_1_5 + · exact source_gram_11_1_7 + · exact source_gram_11_1_9 + · exact source_gram_11_1_11 + · exact source_gram_11_3_1 + · exact source_gram_11_3_3 + · exact source_gram_11_3_5 + · exact source_gram_11_3_7 + · exact source_gram_11_3_9 + · exact source_gram_11_3_11 + · exact source_gram_11_5_1 + · exact source_gram_11_5_3 + · exact source_gram_11_5_5 + · exact source_gram_11_5_7 + · exact source_gram_11_5_9 + · exact source_gram_11_5_11 + · exact source_gram_11_7_1 + · exact source_gram_11_7_3 + · exact source_gram_11_7_5 + · exact source_gram_11_7_7 + · exact source_gram_11_7_9 + · exact source_gram_11_7_11 + · exact source_gram_11_9_1 + · exact source_gram_11_9_3 + · exact source_gram_11_9_5 + · exact source_gram_11_9_7 + · exact source_gram_11_9_9 + · exact source_gram_11_9_11 + · exact source_gram_11_11_1 + · exact source_gram_11_11_3 + · exact source_gram_11_11_5 + · exact source_gram_11_11_7 + · exact source_gram_11_11_9 + · exact source_gram_11_11_11 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData12.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData12.lean new file mode 100644 index 0000000000000000000000000000000000000000..55d0cbdf5a461115524d69e74cf8d29dbbfefe59 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData12.lean @@ -0,0 +1,552 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram01Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram03Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram05Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram07Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram111112 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0101Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0103Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0105Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0107Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0109Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0111Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0303Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0305Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0307Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0309Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0311Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0505Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0507Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0509Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0511Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0707Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0709Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0711Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0909Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0911Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1111Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.Data12 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_12_1_1 : Y 12 1 1 = (-21758497948837526814361611/16777216000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 1 1 0 (by decide), + source_yRow_eq_rowCompute 12 1 1 1 (by decide), + source_yRow_eq_rowCompute 12 1 1 2 (by decide), + source_yRow_eq_rowCompute 12 1 1 3 (by decide), + source_yRow_eq_rowCompute 12 1 1 4 (by decide), + source_yRow_eq_rowCompute 12 1 1 5 (by decide), + source_yRow_eq_rowCompute 12 1 1 6 (by decide), + computeRow_12_1_1_0, computeRow_12_1_1_1, computeRow_12_1_1_2, computeRow_12_1_1_3, computeRow_12_1_1_4, computeRow_12_1_1_5, computeRow_12_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_1_3 : Y 12 1 3 = (7514500960705467759694389/41943040000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 1 3 0 (by decide), + source_yRow_eq_rowCompute 12 1 3 1 (by decide), + source_yRow_eq_rowCompute 12 1 3 2 (by decide), + source_yRow_eq_rowCompute 12 1 3 3 (by decide), + source_yRow_eq_rowCompute 12 1 3 4 (by decide), + source_yRow_eq_rowCompute 12 1 3 5 (by decide), + source_yRow_eq_rowCompute 12 1 3 6 (by decide), + computeRow_12_1_3_0, computeRow_12_1_3_1, computeRow_12_1_3_2, computeRow_12_1_3_3, computeRow_12_1_3_4, computeRow_12_1_3_5, computeRow_12_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_1_5 : Y 12 1 5 = (3165688667606660909537571/16777216000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 1 5 0 (by decide), + source_yRow_eq_rowCompute 12 1 5 1 (by decide), + source_yRow_eq_rowCompute 12 1 5 2 (by decide), + source_yRow_eq_rowCompute 12 1 5 3 (by decide), + source_yRow_eq_rowCompute 12 1 5 4 (by decide), + source_yRow_eq_rowCompute 12 1 5 5 (by decide), + source_yRow_eq_rowCompute 12 1 5 6 (by decide), + computeRow_12_1_5_0, computeRow_12_1_5_1, computeRow_12_1_5_2, computeRow_12_1_5_3, computeRow_12_1_5_4, computeRow_12_1_5_5, computeRow_12_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_1_7 : Y 12 1 7 = (-41707520784065633150907/8388608000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 1 7 0 (by decide), + source_yRow_eq_rowCompute 12 1 7 1 (by decide), + source_yRow_eq_rowCompute 12 1 7 2 (by decide), + source_yRow_eq_rowCompute 12 1 7 3 (by decide), + source_yRow_eq_rowCompute 12 1 7 4 (by decide), + source_yRow_eq_rowCompute 12 1 7 5 (by decide), + source_yRow_eq_rowCompute 12 1 7 6 (by decide), + computeRow_12_1_7_0, computeRow_12_1_7_1, computeRow_12_1_7_2, computeRow_12_1_7_3, computeRow_12_1_7_4, computeRow_12_1_7_5, computeRow_12_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_1_9 : Y 12 1 9 = (-2287894342236011100448461/10485760000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 1 9 0 (by decide), + source_yRow_eq_rowCompute 12 1 9 1 (by decide), + source_yRow_eq_rowCompute 12 1 9 2 (by decide), + source_yRow_eq_rowCompute 12 1 9 3 (by decide), + source_yRow_eq_rowCompute 12 1 9 4 (by decide), + source_yRow_eq_rowCompute 12 1 9 5 (by decide), + source_yRow_eq_rowCompute 12 1 9 6 (by decide), + computeRow_12_1_9_0, computeRow_12_1_9_1, computeRow_12_1_9_2, computeRow_12_1_9_3, computeRow_12_1_9_4, computeRow_12_1_9_5, computeRow_12_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_1_11 : Y 12 1 11 = (974459105668097994666249/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 1 11 0 (by decide), + source_yRow_eq_rowCompute 12 1 11 1 (by decide), + source_yRow_eq_rowCompute 12 1 11 2 (by decide), + source_yRow_eq_rowCompute 12 1 11 3 (by decide), + source_yRow_eq_rowCompute 12 1 11 4 (by decide), + source_yRow_eq_rowCompute 12 1 11 5 (by decide), + source_yRow_eq_rowCompute 12 1 11 6 (by decide), + computeRow_12_1_11_0, computeRow_12_1_11_1, computeRow_12_1_11_2, computeRow_12_1_11_3, computeRow_12_1_11_4, computeRow_12_1_11_5, computeRow_12_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_3_3 : Y 12 3 3 = (-2755174567464265689714987/41943040000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 3 3 0 (by decide), + source_yRow_eq_rowCompute 12 3 3 1 (by decide), + source_yRow_eq_rowCompute 12 3 3 2 (by decide), + source_yRow_eq_rowCompute 12 3 3 3 (by decide), + source_yRow_eq_rowCompute 12 3 3 4 (by decide), + source_yRow_eq_rowCompute 12 3 3 5 (by decide), + source_yRow_eq_rowCompute 12 3 3 6 (by decide), + computeRow_12_3_3_0, computeRow_12_3_3_1, computeRow_12_3_3_2, computeRow_12_3_3_3, computeRow_12_3_3_4, computeRow_12_3_3_5, computeRow_12_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_3_5 : Y 12 3 5 = (13005450739700130750669/8388608000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 3 5 0 (by decide), + source_yRow_eq_rowCompute 12 3 5 1 (by decide), + source_yRow_eq_rowCompute 12 3 5 2 (by decide), + source_yRow_eq_rowCompute 12 3 5 3 (by decide), + source_yRow_eq_rowCompute 12 3 5 4 (by decide), + source_yRow_eq_rowCompute 12 3 5 5 (by decide), + source_yRow_eq_rowCompute 12 3 5 6 (by decide), + computeRow_12_3_5_0, computeRow_12_3_5_1, computeRow_12_3_5_2, computeRow_12_3_5_3, computeRow_12_3_5_4, computeRow_12_3_5_5, computeRow_12_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_3_7 : Y 12 3 7 = (81483121238154923538567/4194304000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 3 7 0 (by decide), + source_yRow_eq_rowCompute 12 3 7 1 (by decide), + source_yRow_eq_rowCompute 12 3 7 2 (by decide), + source_yRow_eq_rowCompute 12 3 7 3 (by decide), + source_yRow_eq_rowCompute 12 3 7 4 (by decide), + source_yRow_eq_rowCompute 12 3 7 5 (by decide), + source_yRow_eq_rowCompute 12 3 7 6 (by decide), + computeRow_12_3_7_0, computeRow_12_3_7_1, computeRow_12_3_7_2, computeRow_12_3_7_3, computeRow_12_3_7_4, computeRow_12_3_7_5, computeRow_12_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_3_9 : Y 12 3 9 = (404785016635235824043973/5242880000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 3 9 0 (by decide), + source_yRow_eq_rowCompute 12 3 9 1 (by decide), + source_yRow_eq_rowCompute 12 3 9 2 (by decide), + source_yRow_eq_rowCompute 12 3 9 3 (by decide), + source_yRow_eq_rowCompute 12 3 9 4 (by decide), + source_yRow_eq_rowCompute 12 3 9 5 (by decide), + source_yRow_eq_rowCompute 12 3 9 6 (by decide), + computeRow_12_3_9_0, computeRow_12_3_9_1, computeRow_12_3_9_2, computeRow_12_3_9_3, computeRow_12_3_9_4, computeRow_12_3_9_5, computeRow_12_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_3_11 : Y 12 3 11 = (6215584013984995241823/40960000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 3 11 0 (by decide), + source_yRow_eq_rowCompute 12 3 11 1 (by decide), + source_yRow_eq_rowCompute 12 3 11 2 (by decide), + source_yRow_eq_rowCompute 12 3 11 3 (by decide), + source_yRow_eq_rowCompute 12 3 11 4 (by decide), + source_yRow_eq_rowCompute 12 3 11 5 (by decide), + source_yRow_eq_rowCompute 12 3 11 6 (by decide), + computeRow_12_3_11_0, computeRow_12_3_11_1, computeRow_12_3_11_2, computeRow_12_3_11_3, computeRow_12_3_11_4, computeRow_12_3_11_5, computeRow_12_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_5_5 : Y 12 5 5 = (46805674377515194537803/3355443200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 5 5 0 (by decide), + source_yRow_eq_rowCompute 12 5 5 1 (by decide), + source_yRow_eq_rowCompute 12 5 5 2 (by decide), + source_yRow_eq_rowCompute 12 5 5 3 (by decide), + source_yRow_eq_rowCompute 12 5 5 4 (by decide), + source_yRow_eq_rowCompute 12 5 5 5 (by decide), + source_yRow_eq_rowCompute 12 5 5 6 (by decide), + computeRow_12_5_5_0, computeRow_12_5_5_1, computeRow_12_5_5_2, computeRow_12_5_5_3, computeRow_12_5_5_4, computeRow_12_5_5_5, computeRow_12_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_5_7 : Y 12 5 7 = (-41483885509932371903727/8388608000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 5 7 0 (by decide), + source_yRow_eq_rowCompute 12 5 7 1 (by decide), + source_yRow_eq_rowCompute 12 5 7 2 (by decide), + source_yRow_eq_rowCompute 12 5 7 3 (by decide), + source_yRow_eq_rowCompute 12 5 7 4 (by decide), + source_yRow_eq_rowCompute 12 5 7 5 (by decide), + source_yRow_eq_rowCompute 12 5 7 6 (by decide), + computeRow_12_5_7_0, computeRow_12_5_7_1, computeRow_12_5_7_2, computeRow_12_5_7_3, computeRow_12_5_7_4, computeRow_12_5_7_5, computeRow_12_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_5_9 : Y 12 5 9 = (-10240121934522536047317/419430400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 5 9 0 (by decide), + source_yRow_eq_rowCompute 12 5 9 1 (by decide), + source_yRow_eq_rowCompute 12 5 9 2 (by decide), + source_yRow_eq_rowCompute 12 5 9 3 (by decide), + source_yRow_eq_rowCompute 12 5 9 4 (by decide), + source_yRow_eq_rowCompute 12 5 9 5 (by decide), + source_yRow_eq_rowCompute 12 5 9 6 (by decide), + computeRow_12_5_9_0, computeRow_12_5_9_1, computeRow_12_5_9_2, computeRow_12_5_9_3, computeRow_12_5_9_4, computeRow_12_5_9_5, computeRow_12_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_5_11 : Y 12 5 11 = (-25627330574660171363787/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 5 11 0 (by decide), + source_yRow_eq_rowCompute 12 5 11 1 (by decide), + source_yRow_eq_rowCompute 12 5 11 2 (by decide), + source_yRow_eq_rowCompute 12 5 11 3 (by decide), + source_yRow_eq_rowCompute 12 5 11 4 (by decide), + source_yRow_eq_rowCompute 12 5 11 5 (by decide), + source_yRow_eq_rowCompute 12 5 11 6 (by decide), + computeRow_12_5_11_0, computeRow_12_5_11_1, computeRow_12_5_11_2, computeRow_12_5_11_3, computeRow_12_5_11_4, computeRow_12_5_11_5, computeRow_12_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_7_7 : Y 12 7 7 = (-192219299280069275276433/4194304000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 7 7 0 (by decide), + source_yRow_eq_rowCompute 12 7 7 1 (by decide), + source_yRow_eq_rowCompute 12 7 7 2 (by decide), + source_yRow_eq_rowCompute 12 7 7 3 (by decide), + source_yRow_eq_rowCompute 12 7 7 4 (by decide), + source_yRow_eq_rowCompute 12 7 7 5 (by decide), + source_yRow_eq_rowCompute 12 7 7 6 (by decide), + computeRow_12_7_7_0, computeRow_12_7_7_1, computeRow_12_7_7_2, computeRow_12_7_7_3, computeRow_12_7_7_4, computeRow_12_7_7_5, computeRow_12_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_7_9 : Y 12 7 9 = (-42262827210616968341919/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 7 9 0 (by decide), + source_yRow_eq_rowCompute 12 7 9 1 (by decide), + source_yRow_eq_rowCompute 12 7 9 2 (by decide), + source_yRow_eq_rowCompute 12 7 9 3 (by decide), + source_yRow_eq_rowCompute 12 7 9 4 (by decide), + source_yRow_eq_rowCompute 12 7 9 5 (by decide), + source_yRow_eq_rowCompute 12 7 9 6 (by decide), + computeRow_12_7_9_0, computeRow_12_7_9_1, computeRow_12_7_9_2, computeRow_12_7_9_3, computeRow_12_7_9_4, computeRow_12_7_9_5, computeRow_12_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_7_11 : Y 12 7 11 = (102387833991081458685459/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 7 11 0 (by decide), + source_yRow_eq_rowCompute 12 7 11 1 (by decide), + source_yRow_eq_rowCompute 12 7 11 2 (by decide), + source_yRow_eq_rowCompute 12 7 11 3 (by decide), + source_yRow_eq_rowCompute 12 7 11 4 (by decide), + source_yRow_eq_rowCompute 12 7 11 5 (by decide), + source_yRow_eq_rowCompute 12 7 11 6 (by decide), + computeRow_12_7_11_0, computeRow_12_7_11_1, computeRow_12_7_11_2, computeRow_12_7_11_3, computeRow_12_7_11_4, computeRow_12_7_11_5, computeRow_12_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_9_9 : Y 12 9 9 = (42184147125974825030859/1310720000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 9 9 0 (by decide), + source_yRow_eq_rowCompute 12 9 9 1 (by decide), + source_yRow_eq_rowCompute 12 9 9 2 (by decide), + source_yRow_eq_rowCompute 12 9 9 3 (by decide), + source_yRow_eq_rowCompute 12 9 9 4 (by decide), + source_yRow_eq_rowCompute 12 9 9 5 (by decide), + source_yRow_eq_rowCompute 12 9 9 6 (by decide), + computeRow_12_9_9_0, computeRow_12_9_9_1, computeRow_12_9_9_2, computeRow_12_9_9_3, computeRow_12_9_9_4, computeRow_12_9_9_5, computeRow_12_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_9_11 : Y 12 9 11 = (18732467483584451907057/655360000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 9 11 0 (by decide), + source_yRow_eq_rowCompute 12 9 11 1 (by decide), + source_yRow_eq_rowCompute 12 9 11 2 (by decide), + source_yRow_eq_rowCompute 12 9 11 3 (by decide), + source_yRow_eq_rowCompute 12 9 11 4 (by decide), + source_yRow_eq_rowCompute 12 9 11 5 (by decide), + source_yRow_eq_rowCompute 12 9 11 6 (by decide), + computeRow_12_9_11_0, computeRow_12_9_11_1, computeRow_12_9_11_2, computeRow_12_9_11_3, computeRow_12_9_11_4, computeRow_12_9_11_5, computeRow_12_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_12_11_11 : Y 12 11 11 = (-330567209557174956464307/65536000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 12 11 11 0 (by decide), + source_yRow_eq_rowCompute 12 11 11 1 (by decide), + source_yRow_eq_rowCompute 12 11 11 2 (by decide), + source_yRow_eq_rowCompute 12 11 11 3 (by decide), + source_yRow_eq_rowCompute 12 11 11 4 (by decide), + source_yRow_eq_rowCompute 12 11 11 5 (by decide), + source_yRow_eq_rowCompute 12 11 11 6 (by decide), + computeRow_12_11_11_0, computeRow_12_11_11_1, computeRow_12_11_11_2, computeRow_12_11_11_3, computeRow_12_11_11_4, computeRow_12_11_11_5, computeRow_12_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_12_1_1 : Z 12 1 1 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_1_1 + +theorem source_gram_12_1_3 : Z 12 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_1_3 + +theorem source_gram_12_1_5 : Z 12 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_1_5 + +theorem source_gram_12_1_7 : Z 12 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_1_7 + +theorem source_gram_12_1_9 : Z 12 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_1_9 + +theorem source_gram_12_1_11 : Z 12 1 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_1_11 + +theorem source_gram_12_3_3 : Z 12 3 3 = (2177280 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_3_3 + +theorem source_gram_12_3_5 : Z 12 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_3_5 + +theorem source_gram_12_3_7 : Z 12 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_3_7 + +theorem source_gram_12_3_9 : Z 12 3 9 = (-1088640 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_3_9 + +theorem source_gram_12_3_11 : Z 12 3 11 = (7484400 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_3_11 + +theorem source_gram_12_5_5 : Z 12 5 5 = (604800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_5_5 + +theorem source_gram_12_5_7 : Z 12 5 7 = (-453600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_5_7 + +theorem source_gram_12_5_9 : Z 12 5 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_5_9 + +theorem source_gram_12_5_11 : Z 12 5 11 = (2494800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_5_11 + +theorem source_gram_12_7_7 : Z 12 7 7 = (340200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_7_7 + +theorem source_gram_12_7_9 : Z 12 7 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_7_9 + +theorem source_gram_12_7_11 : Z 12 7 11 = (-1871100 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_7_11 + +theorem source_gram_12_9_9 : Z 12 9 9 = (544320 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_9_9 + +theorem source_gram_12_9_11 : Z 12 9 11 = (-3742200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_9_11 + +theorem source_gram_12_11_11 : Z 12 11 11 = (36018675 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_12_11_11 + +theorem source_error_12_3_1 : Y 12 3 1 = (7514500960705467759694389/41943040000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_1_3 + +theorem source_gram_12_3_1 : Z 12 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_12_1_3 + +theorem source_error_12_5_1 : Y 12 5 1 = (3165688667606660909537571/16777216000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_1_5 + +theorem source_gram_12_5_1 : Z 12 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_12_1_5 + +theorem source_error_12_5_3 : Y 12 5 3 = (13005450739700130750669/8388608000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_3_5 + +theorem source_gram_12_5_3 : Z 12 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_12_3_5 + +theorem source_error_12_7_1 : Y 12 7 1 = (-41707520784065633150907/8388608000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_1_7 + +theorem source_gram_12_7_1 : Z 12 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_12_1_7 + +theorem source_error_12_7_3 : Y 12 7 3 = (81483121238154923538567/4194304000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_3_7 + +theorem source_gram_12_7_3 : Z 12 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_12_3_7 + +theorem source_error_12_7_5 : Y 12 7 5 = (-41483885509932371903727/8388608000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_5_7 + +theorem source_gram_12_7_5 : Z 12 7 5 = (-453600 : ℚ) := by + rw [Z_symm] + exact source_gram_12_5_7 + +theorem source_error_12_9_1 : Y 12 9 1 = (-2287894342236011100448461/10485760000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_1_9 + +theorem source_gram_12_9_1 : Z 12 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_12_1_9 + +theorem source_error_12_9_3 : Y 12 9 3 = (404785016635235824043973/5242880000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_3_9 + +theorem source_gram_12_9_3 : Z 12 9 3 = (-1088640 : ℚ) := by + rw [Z_symm] + exact source_gram_12_3_9 + +theorem source_error_12_9_5 : Y 12 9 5 = (-10240121934522536047317/419430400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_5_9 + +theorem source_gram_12_9_5 : Z 12 9 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_12_5_9 + +theorem source_error_12_9_7 : Y 12 9 7 = (-42262827210616968341919/1048576000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_7_9 + +theorem source_gram_12_9_7 : Z 12 9 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_12_7_9 + +theorem source_error_12_11_1 : Y 12 11 1 = (974459105668097994666249/1048576000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_1_11 + +theorem source_gram_12_11_1 : Z 12 11 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_12_1_11 + +theorem source_error_12_11_3 : Y 12 11 3 = (6215584013984995241823/40960000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_3_11 + +theorem source_gram_12_11_3 : Z 12 11 3 = (7484400 : ℚ) := by + rw [Z_symm] + exact source_gram_12_3_11 + +theorem source_error_12_11_5 : Y 12 11 5 = (-25627330574660171363787/1048576000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_5_11 + +theorem source_gram_12_11_5 : Z 12 11 5 = (2494800 : ℚ) := by + rw [Z_symm] + exact source_gram_12_5_11 + +theorem source_error_12_11_7 : Y 12 11 7 = (102387833991081458685459/524288000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_7_11 + +theorem source_gram_12_11_7 : Z 12 11 7 = (-1871100 : ℚ) := by + rw [Z_symm] + exact source_gram_12_7_11 + +theorem source_error_12_11_9 : Y 12 11 9 = (18732467483584451907057/655360000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_12_9_11 + +theorem source_gram_12_11_9 : Z 12 11 9 = (-3742200 : ℚ) := by + rw [Z_symm] + exact source_gram_12_9_11 + +theorem error_12 : errorRational 12 = candidateY_12 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_12_1_1 + · exact source_error_12_1_3 + · exact source_error_12_1_5 + · exact source_error_12_1_7 + · exact source_error_12_1_9 + · exact source_error_12_1_11 + · exact source_error_12_3_1 + · exact source_error_12_3_3 + · exact source_error_12_3_5 + · exact source_error_12_3_7 + · exact source_error_12_3_9 + · exact source_error_12_3_11 + · exact source_error_12_5_1 + · exact source_error_12_5_3 + · exact source_error_12_5_5 + · exact source_error_12_5_7 + · exact source_error_12_5_9 + · exact source_error_12_5_11 + · exact source_error_12_7_1 + · exact source_error_12_7_3 + · exact source_error_12_7_5 + · exact source_error_12_7_7 + · exact source_error_12_7_9 + · exact source_error_12_7_11 + · exact source_error_12_9_1 + · exact source_error_12_9_3 + · exact source_error_12_9_5 + · exact source_error_12_9_7 + · exact source_error_12_9_9 + · exact source_error_12_9_11 + · exact source_error_12_11_1 + · exact source_error_12_11_3 + · exact source_error_12_11_5 + · exact source_error_12_11_7 + · exact source_error_12_11_9 + · exact source_error_12_11_11 + +theorem gram_12 : gramRational 12 = candidateZ_12 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_12_1_1 + · exact source_gram_12_1_3 + · exact source_gram_12_1_5 + · exact source_gram_12_1_7 + · exact source_gram_12_1_9 + · exact source_gram_12_1_11 + · exact source_gram_12_3_1 + · exact source_gram_12_3_3 + · exact source_gram_12_3_5 + · exact source_gram_12_3_7 + · exact source_gram_12_3_9 + · exact source_gram_12_3_11 + · exact source_gram_12_5_1 + · exact source_gram_12_5_3 + · exact source_gram_12_5_5 + · exact source_gram_12_5_7 + · exact source_gram_12_5_9 + · exact source_gram_12_5_11 + · exact source_gram_12_7_1 + · exact source_gram_12_7_3 + · exact source_gram_12_7_5 + · exact source_gram_12_7_7 + · exact source_gram_12_7_9 + · exact source_gram_12_7_11 + · exact source_gram_12_9_1 + · exact source_gram_12_9_3 + · exact source_gram_12_9_5 + · exact source_gram_12_9_7 + · exact source_gram_12_9_9 + · exact source_gram_12_9_11 + · exact source_gram_12_11_1 + · exact source_gram_12_11_3 + · exact source_gram_12_11_5 + · exact source_gram_12_11_7 + · exact source_gram_12_11_9 + · exact source_gram_12_11_11 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData13.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData13.lean new file mode 100644 index 0000000000000000000000000000000000000000..8416c46e7d479f17eb761b140d7ba82a0596a790 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData13.lean @@ -0,0 +1,739 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram01Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram03Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram05Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram07Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram11Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram131313 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0101Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0103Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0105Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0107Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0109Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0111Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0113Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0303Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0305Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0307Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0309Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0311Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0313Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0505Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0507Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0509Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0511Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0513Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0707Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0709Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0711Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0713Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0909Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0911Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0913Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1111Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1113Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1313Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.Data13 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_13_1_1 : Y 13 1 1 = (121685493803305440547576917/8388608000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 1 1 0 (by decide), + source_yRow_eq_rowCompute 13 1 1 1 (by decide), + source_yRow_eq_rowCompute 13 1 1 2 (by decide), + source_yRow_eq_rowCompute 13 1 1 3 (by decide), + source_yRow_eq_rowCompute 13 1 1 4 (by decide), + source_yRow_eq_rowCompute 13 1 1 5 (by decide), + source_yRow_eq_rowCompute 13 1 1 6 (by decide), + computeRow_13_1_1_0, computeRow_13_1_1_1, computeRow_13_1_1_2, computeRow_13_1_1_3, computeRow_13_1_1_4, computeRow_13_1_1_5, computeRow_13_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_1_3 : Y 13 1 3 = (7563908306608840424871171/8388608000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 1 3 0 (by decide), + source_yRow_eq_rowCompute 13 1 3 1 (by decide), + source_yRow_eq_rowCompute 13 1 3 2 (by decide), + source_yRow_eq_rowCompute 13 1 3 3 (by decide), + source_yRow_eq_rowCompute 13 1 3 4 (by decide), + source_yRow_eq_rowCompute 13 1 3 5 (by decide), + source_yRow_eq_rowCompute 13 1 3 6 (by decide), + computeRow_13_1_3_0, computeRow_13_1_3_1, computeRow_13_1_3_2, computeRow_13_1_3_3, computeRow_13_1_3_4, computeRow_13_1_3_5, computeRow_13_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_1_5 : Y 13 1 5 = (-66091999624888726298111247/16777216000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 1 5 0 (by decide), + source_yRow_eq_rowCompute 13 1 5 1 (by decide), + source_yRow_eq_rowCompute 13 1 5 2 (by decide), + source_yRow_eq_rowCompute 13 1 5 3 (by decide), + source_yRow_eq_rowCompute 13 1 5 4 (by decide), + source_yRow_eq_rowCompute 13 1 5 5 (by decide), + source_yRow_eq_rowCompute 13 1 5 6 (by decide), + computeRow_13_1_5_0, computeRow_13_1_5_1, computeRow_13_1_5_2, computeRow_13_1_5_3, computeRow_13_1_5_4, computeRow_13_1_5_5, computeRow_13_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_1_7 : Y 13 1 7 = (2728798823338271240310567/1677721600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 1 7 0 (by decide), + source_yRow_eq_rowCompute 13 1 7 1 (by decide), + source_yRow_eq_rowCompute 13 1 7 2 (by decide), + source_yRow_eq_rowCompute 13 1 7 3 (by decide), + source_yRow_eq_rowCompute 13 1 7 4 (by decide), + source_yRow_eq_rowCompute 13 1 7 5 (by decide), + source_yRow_eq_rowCompute 13 1 7 6 (by decide), + computeRow_13_1_7_0, computeRow_13_1_7_1, computeRow_13_1_7_2, computeRow_13_1_7_3, computeRow_13_1_7_4, computeRow_13_1_7_5, computeRow_13_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_1_9 : Y 13 1 9 = (-13501297339814524797227781/10485760000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 1 9 0 (by decide), + source_yRow_eq_rowCompute 13 1 9 1 (by decide), + source_yRow_eq_rowCompute 13 1 9 2 (by decide), + source_yRow_eq_rowCompute 13 1 9 3 (by decide), + source_yRow_eq_rowCompute 13 1 9 4 (by decide), + source_yRow_eq_rowCompute 13 1 9 5 (by decide), + source_yRow_eq_rowCompute 13 1 9 6 (by decide), + computeRow_13_1_9_0, computeRow_13_1_9_1, computeRow_13_1_9_2, computeRow_13_1_9_3, computeRow_13_1_9_4, computeRow_13_1_9_5, computeRow_13_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_1_11 : Y 13 1 11 = (12432022452888993488134359/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 1 11 0 (by decide), + source_yRow_eq_rowCompute 13 1 11 1 (by decide), + source_yRow_eq_rowCompute 13 1 11 2 (by decide), + source_yRow_eq_rowCompute 13 1 11 3 (by decide), + source_yRow_eq_rowCompute 13 1 11 4 (by decide), + source_yRow_eq_rowCompute 13 1 11 5 (by decide), + source_yRow_eq_rowCompute 13 1 11 6 (by decide), + computeRow_13_1_11_0, computeRow_13_1_11_1, computeRow_13_1_11_2, computeRow_13_1_11_3, computeRow_13_1_11_4, computeRow_13_1_11_5, computeRow_13_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_1_13 : Y 13 1 13 = (-165874530574631465579316753/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 1 13 0 (by decide), + source_yRow_eq_rowCompute 13 1 13 1 (by decide), + source_yRow_eq_rowCompute 13 1 13 2 (by decide), + source_yRow_eq_rowCompute 13 1 13 3 (by decide), + source_yRow_eq_rowCompute 13 1 13 4 (by decide), + source_yRow_eq_rowCompute 13 1 13 5 (by decide), + source_yRow_eq_rowCompute 13 1 13 6 (by decide), + computeRow_13_1_13_0, computeRow_13_1_13_1, computeRow_13_1_13_2, computeRow_13_1_13_3, computeRow_13_1_13_4, computeRow_13_1_13_5, computeRow_13_1_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_3_3 : Y 13 3 3 = (-2041302613950531427151763/8388608000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 3 3 0 (by decide), + source_yRow_eq_rowCompute 13 3 3 1 (by decide), + source_yRow_eq_rowCompute 13 3 3 2 (by decide), + source_yRow_eq_rowCompute 13 3 3 3 (by decide), + source_yRow_eq_rowCompute 13 3 3 4 (by decide), + source_yRow_eq_rowCompute 13 3 3 5 (by decide), + source_yRow_eq_rowCompute 13 3 3 6 (by decide), + computeRow_13_3_3_0, computeRow_13_3_3_1, computeRow_13_3_3_2, computeRow_13_3_3_3, computeRow_13_3_3_4, computeRow_13_3_3_5, computeRow_13_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_3_5 : Y 13 3 5 = (126715690823288866730217/419430400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 3 5 0 (by decide), + source_yRow_eq_rowCompute 13 3 5 1 (by decide), + source_yRow_eq_rowCompute 13 3 5 2 (by decide), + source_yRow_eq_rowCompute 13 3 5 3 (by decide), + source_yRow_eq_rowCompute 13 3 5 4 (by decide), + source_yRow_eq_rowCompute 13 3 5 5 (by decide), + source_yRow_eq_rowCompute 13 3 5 6 (by decide), + computeRow_13_3_5_0, computeRow_13_3_5_1, computeRow_13_3_5_2, computeRow_13_3_5_3, computeRow_13_3_5_4, computeRow_13_3_5_5, computeRow_13_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_3_7 : Y 13 3 7 = (-500594098074230841463629/2097152000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 3 7 0 (by decide), + source_yRow_eq_rowCompute 13 3 7 1 (by decide), + source_yRow_eq_rowCompute 13 3 7 2 (by decide), + source_yRow_eq_rowCompute 13 3 7 3 (by decide), + source_yRow_eq_rowCompute 13 3 7 4 (by decide), + source_yRow_eq_rowCompute 13 3 7 5 (by decide), + source_yRow_eq_rowCompute 13 3 7 6 (by decide), + computeRow_13_3_7_0, computeRow_13_3_7_1, computeRow_13_3_7_2, computeRow_13_3_7_3, computeRow_13_3_7_4, computeRow_13_3_7_5, computeRow_13_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_3_9 : Y 13 3 9 = (-1215155073315811787592453/2621440000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 3 9 0 (by decide), + source_yRow_eq_rowCompute 13 3 9 1 (by decide), + source_yRow_eq_rowCompute 13 3 9 2 (by decide), + source_yRow_eq_rowCompute 13 3 9 3 (by decide), + source_yRow_eq_rowCompute 13 3 9 4 (by decide), + source_yRow_eq_rowCompute 13 3 9 5 (by decide), + source_yRow_eq_rowCompute 13 3 9 6 (by decide), + computeRow_13_3_9_0, computeRow_13_3_9_1, computeRow_13_3_9_2, computeRow_13_3_9_3, computeRow_13_3_9_4, computeRow_13_3_9_5, computeRow_13_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_3_11 : Y 13 3 11 = (-47337050492347165740927/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 3 11 0 (by decide), + source_yRow_eq_rowCompute 13 3 11 1 (by decide), + source_yRow_eq_rowCompute 13 3 11 2 (by decide), + source_yRow_eq_rowCompute 13 3 11 3 (by decide), + source_yRow_eq_rowCompute 13 3 11 4 (by decide), + source_yRow_eq_rowCompute 13 3 11 5 (by decide), + source_yRow_eq_rowCompute 13 3 11 6 (by decide), + computeRow_13_3_11_0, computeRow_13_3_11_1, computeRow_13_3_11_2, computeRow_13_3_11_3, computeRow_13_3_11_4, computeRow_13_3_11_5, computeRow_13_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_3_13 : Y 13 3 13 = (-394753123867351949086959/131072000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 3 13 0 (by decide), + source_yRow_eq_rowCompute 13 3 13 1 (by decide), + source_yRow_eq_rowCompute 13 3 13 2 (by decide), + source_yRow_eq_rowCompute 13 3 13 3 (by decide), + source_yRow_eq_rowCompute 13 3 13 4 (by decide), + source_yRow_eq_rowCompute 13 3 13 5 (by decide), + source_yRow_eq_rowCompute 13 3 13 6 (by decide), + computeRow_13_3_13_0, computeRow_13_3_13_1, computeRow_13_3_13_2, computeRow_13_3_13_3, computeRow_13_3_13_4, computeRow_13_3_13_5, computeRow_13_3_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_5_5 : Y 13 5 5 = (-1379799513707028925041063/16777216000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 5 5 0 (by decide), + source_yRow_eq_rowCompute 13 5 5 1 (by decide), + source_yRow_eq_rowCompute 13 5 5 2 (by decide), + source_yRow_eq_rowCompute 13 5 5 3 (by decide), + source_yRow_eq_rowCompute 13 5 5 4 (by decide), + source_yRow_eq_rowCompute 13 5 5 5 (by decide), + source_yRow_eq_rowCompute 13 5 5 6 (by decide), + computeRow_13_5_5_0, computeRow_13_5_5_1, computeRow_13_5_5_2, computeRow_13_5_5_3, computeRow_13_5_5_4, computeRow_13_5_5_5, computeRow_13_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_5_7 : Y 13 5 7 = (701982483744393187744923/8388608000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 5 7 0 (by decide), + source_yRow_eq_rowCompute 13 5 7 1 (by decide), + source_yRow_eq_rowCompute 13 5 7 2 (by decide), + source_yRow_eq_rowCompute 13 5 7 3 (by decide), + source_yRow_eq_rowCompute 13 5 7 4 (by decide), + source_yRow_eq_rowCompute 13 5 7 5 (by decide), + source_yRow_eq_rowCompute 13 5 7 6 (by decide), + computeRow_13_5_7_0, computeRow_13_5_7_1, computeRow_13_5_7_2, computeRow_13_5_7_3, computeRow_13_5_7_4, computeRow_13_5_7_5, computeRow_13_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_5_9 : Y 13 5 9 = (672840394965225922256721/2097152000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 5 9 0 (by decide), + source_yRow_eq_rowCompute 13 5 9 1 (by decide), + source_yRow_eq_rowCompute 13 5 9 2 (by decide), + source_yRow_eq_rowCompute 13 5 9 3 (by decide), + source_yRow_eq_rowCompute 13 5 9 4 (by decide), + source_yRow_eq_rowCompute 13 5 9 5 (by decide), + source_yRow_eq_rowCompute 13 5 9 6 (by decide), + computeRow_13_5_9_0, computeRow_13_5_9_1, computeRow_13_5_9_2, computeRow_13_5_9_3, computeRow_13_5_9_4, computeRow_13_5_9_5, computeRow_13_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_5_11 : Y 13 5 11 = (2506297034373528441573/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 5 11 0 (by decide), + source_yRow_eq_rowCompute 13 5 11 1 (by decide), + source_yRow_eq_rowCompute 13 5 11 2 (by decide), + source_yRow_eq_rowCompute 13 5 11 3 (by decide), + source_yRow_eq_rowCompute 13 5 11 4 (by decide), + source_yRow_eq_rowCompute 13 5 11 5 (by decide), + source_yRow_eq_rowCompute 13 5 11 6 (by decide), + computeRow_13_5_11_0, computeRow_13_5_11_1, computeRow_13_5_11_2, computeRow_13_5_11_3, computeRow_13_5_11_4, computeRow_13_5_11_5, computeRow_13_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_5_13 : Y 13 5 13 = (5534718096701578046307903/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 5 13 0 (by decide), + source_yRow_eq_rowCompute 13 5 13 1 (by decide), + source_yRow_eq_rowCompute 13 5 13 2 (by decide), + source_yRow_eq_rowCompute 13 5 13 3 (by decide), + source_yRow_eq_rowCompute 13 5 13 4 (by decide), + source_yRow_eq_rowCompute 13 5 13 5 (by decide), + source_yRow_eq_rowCompute 13 5 13 6 (by decide), + computeRow_13_5_13_0, computeRow_13_5_13_1, computeRow_13_5_13_2, computeRow_13_5_13_3, computeRow_13_5_13_4, computeRow_13_5_13_5, computeRow_13_5_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_7_7 : Y 13 7 7 = (126607865811947282465541/838860800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 7 7 0 (by decide), + source_yRow_eq_rowCompute 13 7 7 1 (by decide), + source_yRow_eq_rowCompute 13 7 7 2 (by decide), + source_yRow_eq_rowCompute 13 7 7 3 (by decide), + source_yRow_eq_rowCompute 13 7 7 4 (by decide), + source_yRow_eq_rowCompute 13 7 7 5 (by decide), + source_yRow_eq_rowCompute 13 7 7 6 (by decide), + computeRow_13_7_7_0, computeRow_13_7_7_1, computeRow_13_7_7_2, computeRow_13_7_7_3, computeRow_13_7_7_4, computeRow_13_7_7_5, computeRow_13_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_7_9 : Y 13 7 9 = (-175665130303631642663517/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 7 9 0 (by decide), + source_yRow_eq_rowCompute 13 7 9 1 (by decide), + source_yRow_eq_rowCompute 13 7 9 2 (by decide), + source_yRow_eq_rowCompute 13 7 9 3 (by decide), + source_yRow_eq_rowCompute 13 7 9 4 (by decide), + source_yRow_eq_rowCompute 13 7 9 5 (by decide), + source_yRow_eq_rowCompute 13 7 9 6 (by decide), + computeRow_13_7_9_0, computeRow_13_7_9_1, computeRow_13_7_9_2, computeRow_13_7_9_3, computeRow_13_7_9_4, computeRow_13_7_9_5, computeRow_13_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_7_11 : Y 13 7 11 = (420722950805223871087107/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 7 11 0 (by decide), + source_yRow_eq_rowCompute 13 7 11 1 (by decide), + source_yRow_eq_rowCompute 13 7 11 2 (by decide), + source_yRow_eq_rowCompute 13 7 11 3 (by decide), + source_yRow_eq_rowCompute 13 7 11 4 (by decide), + source_yRow_eq_rowCompute 13 7 11 5 (by decide), + source_yRow_eq_rowCompute 13 7 11 6 (by decide), + computeRow_13_7_11_0, computeRow_13_7_11_1, computeRow_13_7_11_2, computeRow_13_7_11_3, computeRow_13_7_11_4, computeRow_13_7_11_5, computeRow_13_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_7_13 : Y 13 7 13 = (-2485443250416390286101651/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 7 13 0 (by decide), + source_yRow_eq_rowCompute 13 7 13 1 (by decide), + source_yRow_eq_rowCompute 13 7 13 2 (by decide), + source_yRow_eq_rowCompute 13 7 13 3 (by decide), + source_yRow_eq_rowCompute 13 7 13 4 (by decide), + source_yRow_eq_rowCompute 13 7 13 5 (by decide), + source_yRow_eq_rowCompute 13 7 13 6 (by decide), + computeRow_13_7_13_0, computeRow_13_7_13_1, computeRow_13_7_13_2, computeRow_13_7_13_3, computeRow_13_7_13_4, computeRow_13_7_13_5, computeRow_13_7_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_9_9 : Y 13 9 9 = (-125541053085493256369427/262144000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 9 9 0 (by decide), + source_yRow_eq_rowCompute 13 9 9 1 (by decide), + source_yRow_eq_rowCompute 13 9 9 2 (by decide), + source_yRow_eq_rowCompute 13 9 9 3 (by decide), + source_yRow_eq_rowCompute 13 9 9 4 (by decide), + source_yRow_eq_rowCompute 13 9 9 5 (by decide), + source_yRow_eq_rowCompute 13 9 9 6 (by decide), + computeRow_13_9_9_0, computeRow_13_9_9_1, computeRow_13_9_9_2, computeRow_13_9_9_3, computeRow_13_9_9_4, computeRow_13_9_9_5, computeRow_13_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_9_11 : Y 13 9 11 = (1437479079722043725179197/655360000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 9 11 0 (by decide), + source_yRow_eq_rowCompute 13 9 11 1 (by decide), + source_yRow_eq_rowCompute 13 9 11 2 (by decide), + source_yRow_eq_rowCompute 13 9 11 3 (by decide), + source_yRow_eq_rowCompute 13 9 11 4 (by decide), + source_yRow_eq_rowCompute 13 9 11 5 (by decide), + source_yRow_eq_rowCompute 13 9 11 6 (by decide), + computeRow_13_9_11_0, computeRow_13_9_11_1, computeRow_13_9_11_2, computeRow_13_9_11_3, computeRow_13_9_11_4, computeRow_13_9_11_5, computeRow_13_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_9_13 : Y 13 9 13 = (-2022830025440980274156781/655360000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 9 13 0 (by decide), + source_yRow_eq_rowCompute 13 9 13 1 (by decide), + source_yRow_eq_rowCompute 13 9 13 2 (by decide), + source_yRow_eq_rowCompute 13 9 13 3 (by decide), + source_yRow_eq_rowCompute 13 9 13 4 (by decide), + source_yRow_eq_rowCompute 13 9 13 5 (by decide), + source_yRow_eq_rowCompute 13 9 13 6 (by decide), + computeRow_13_9_13_0, computeRow_13_9_13_1, computeRow_13_9_13_2, computeRow_13_9_13_3, computeRow_13_9_13_4, computeRow_13_9_13_5, computeRow_13_9_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_11_11 : Y 13 11 11 = (-184207969249874832456117/65536000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 11 11 0 (by decide), + source_yRow_eq_rowCompute 13 11 11 1 (by decide), + source_yRow_eq_rowCompute 13 11 11 2 (by decide), + source_yRow_eq_rowCompute 13 11 11 3 (by decide), + source_yRow_eq_rowCompute 13 11 11 4 (by decide), + source_yRow_eq_rowCompute 13 11 11 5 (by decide), + source_yRow_eq_rowCompute 13 11 11 6 (by decide), + computeRow_13_11_11_0, computeRow_13_11_11_1, computeRow_13_11_11_2, computeRow_13_11_11_3, computeRow_13_11_11_4, computeRow_13_11_11_5, computeRow_13_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_11_13 : Y 13 11 13 = (252554056596275363975331/65536000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 11 13 0 (by decide), + source_yRow_eq_rowCompute 13 11 13 1 (by decide), + source_yRow_eq_rowCompute 13 11 13 2 (by decide), + source_yRow_eq_rowCompute 13 11 13 3 (by decide), + source_yRow_eq_rowCompute 13 11 13 4 (by decide), + source_yRow_eq_rowCompute 13 11 13 5 (by decide), + source_yRow_eq_rowCompute 13 11 13 6 (by decide), + computeRow_13_11_13_0, computeRow_13_11_13_1, computeRow_13_11_13_2, computeRow_13_11_13_3, computeRow_13_11_13_4, computeRow_13_11_13_5, computeRow_13_11_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_13_13_13 : Y 13 13 13 = (-17580701774552693245136811/13107200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 13 13 13 0 (by decide), + source_yRow_eq_rowCompute 13 13 13 1 (by decide), + source_yRow_eq_rowCompute 13 13 13 2 (by decide), + source_yRow_eq_rowCompute 13 13 13 3 (by decide), + source_yRow_eq_rowCompute 13 13 13 4 (by decide), + source_yRow_eq_rowCompute 13 13 13 5 (by decide), + source_yRow_eq_rowCompute 13 13 13 6 (by decide), + computeRow_13_13_13_0, computeRow_13_13_13_1, computeRow_13_13_13_2, computeRow_13_13_13_3, computeRow_13_13_13_4, computeRow_13_13_13_5, computeRow_13_13_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_13_1_1 : Z 13 1 1 = (958003200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_1_1 + +theorem source_gram_13_1_3 : Z 13 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_1_3 + +theorem source_gram_13_1_5 : Z 13 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_1_5 + +theorem source_gram_13_1_7 : Z 13 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_1_7 + +theorem source_gram_13_1_9 : Z 13 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_1_9 + +theorem source_gram_13_1_11 : Z 13 1 11 = (-29937600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_1_11 + +theorem source_gram_13_1_13 : Z 13 1 13 = (972972000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_1_13 + +theorem source_gram_13_3_3 : Z 13 3 3 = (21772800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_3_3 + +theorem source_gram_13_3_5 : Z 13 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_3_5 + +theorem source_gram_13_3_7 : Z 13 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_3_7 + +theorem source_gram_13_3_9 : Z 13 3 9 = (-2721600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_3_9 + +theorem source_gram_13_3_11 : Z 13 3 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_3_11 + +theorem source_gram_13_3_13 : Z 13 3 13 = (291891600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_3_13 + +theorem source_gram_13_5_5 : Z 13 5 5 = (4838400 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_5_5 + +theorem source_gram_13_5_7 : Z 13 5 7 = (-907200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_5_7 + +theorem source_gram_13_5_9 : Z 13 5 9 = (-4082400 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_5_9 + +theorem source_gram_13_5_11 : Z 13 5 11 = (12474000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_5_11 + +theorem source_gram_13_5_13 : Z 13 5 13 = (48648600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_5_13 + +theorem source_gram_13_7_7 : Z 13 7 7 = (453600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_7_7 + +theorem source_gram_13_7_9 : Z 13 7 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_7_9 + +theorem source_gram_13_7_11 : Z 13 7 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_7_11 + +theorem source_gram_13_7_13 : Z 13 7 13 = (-24324300 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_7_13 + +theorem source_gram_13_9_9 : Z 13 9 9 = (5851440 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_9_9 + +theorem source_gram_13_9_11 : Z 13 9 11 = (-16839900 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_9_11 + +theorem source_gram_13_9_13 : Z 13 9 13 = (-36486450 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_9_13 + +theorem source_gram_13_11_11 : Z 13 11 11 = (52390800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_11_11 + +theorem source_gram_13_11_13 : Z 13 11 13 = (-30405375 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_11_13 + +theorem source_gram_13_13_13 : Z 13 13 13 = (12411474075/2 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_13_13_13 + +theorem source_error_13_3_1 : Y 13 3 1 = (7563908306608840424871171/8388608000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_1_3 + +theorem source_gram_13_3_1 : Z 13 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_13_1_3 + +theorem source_error_13_5_1 : Y 13 5 1 = (-66091999624888726298111247/16777216000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_1_5 + +theorem source_gram_13_5_1 : Z 13 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_13_1_5 + +theorem source_error_13_5_3 : Y 13 5 3 = (126715690823288866730217/419430400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_3_5 + +theorem source_gram_13_5_3 : Z 13 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_13_3_5 + +theorem source_error_13_7_1 : Y 13 7 1 = (2728798823338271240310567/1677721600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_1_7 + +theorem source_gram_13_7_1 : Z 13 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_13_1_7 + +theorem source_error_13_7_3 : Y 13 7 3 = (-500594098074230841463629/2097152000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_3_7 + +theorem source_gram_13_7_3 : Z 13 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_13_3_7 + +theorem source_error_13_7_5 : Y 13 7 5 = (701982483744393187744923/8388608000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_5_7 + +theorem source_gram_13_7_5 : Z 13 7 5 = (-907200 : ℚ) := by + rw [Z_symm] + exact source_gram_13_5_7 + +theorem source_error_13_9_1 : Y 13 9 1 = (-13501297339814524797227781/10485760000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_1_9 + +theorem source_gram_13_9_1 : Z 13 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_13_1_9 + +theorem source_error_13_9_3 : Y 13 9 3 = (-1215155073315811787592453/2621440000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_3_9 + +theorem source_gram_13_9_3 : Z 13 9 3 = (-2721600 : ℚ) := by + rw [Z_symm] + exact source_gram_13_3_9 + +theorem source_error_13_9_5 : Y 13 9 5 = (672840394965225922256721/2097152000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_5_9 + +theorem source_gram_13_9_5 : Z 13 9 5 = (-4082400 : ℚ) := by + rw [Z_symm] + exact source_gram_13_5_9 + +theorem source_error_13_9_7 : Y 13 9 7 = (-175665130303631642663517/1048576000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_7_9 + +theorem source_gram_13_9_7 : Z 13 9 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_13_7_9 + +theorem source_error_13_11_1 : Y 13 11 1 = (12432022452888993488134359/1048576000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_1_11 + +theorem source_gram_13_11_1 : Z 13 11 1 = (-29937600 : ℚ) := by + rw [Z_symm] + exact source_gram_13_1_11 + +theorem source_error_13_11_3 : Y 13 11 3 = (-47337050492347165740927/524288000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_3_11 + +theorem source_gram_13_11_3 : Z 13 11 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_13_3_11 + +theorem source_error_13_11_5 : Y 13 11 5 = (2506297034373528441573/1048576000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_5_11 + +theorem source_gram_13_11_5 : Z 13 11 5 = (12474000 : ℚ) := by + rw [Z_symm] + exact source_gram_13_5_11 + +theorem source_error_13_11_7 : Y 13 11 7 = (420722950805223871087107/524288000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_7_11 + +theorem source_gram_13_11_7 : Z 13 11 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_13_7_11 + +theorem source_error_13_11_9 : Y 13 11 9 = (1437479079722043725179197/655360000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_9_11 + +theorem source_gram_13_11_9 : Z 13 11 9 = (-16839900 : ℚ) := by + rw [Z_symm] + exact source_gram_13_9_11 + +theorem source_error_13_13_1 : Y 13 13 1 = (-165874530574631465579316753/1048576000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_1_13 + +theorem source_gram_13_13_1 : Z 13 13 1 = (972972000 : ℚ) := by + rw [Z_symm] + exact source_gram_13_1_13 + +theorem source_error_13_13_3 : Y 13 13 3 = (-394753123867351949086959/131072000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_3_13 + +theorem source_gram_13_13_3 : Z 13 13 3 = (291891600 : ℚ) := by + rw [Z_symm] + exact source_gram_13_3_13 + +theorem source_error_13_13_5 : Y 13 13 5 = (5534718096701578046307903/1048576000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_5_13 + +theorem source_gram_13_13_5 : Z 13 13 5 = (48648600 : ℚ) := by + rw [Z_symm] + exact source_gram_13_5_13 + +theorem source_error_13_13_7 : Y 13 13 7 = (-2485443250416390286101651/524288000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_7_13 + +theorem source_gram_13_13_7 : Z 13 13 7 = (-24324300 : ℚ) := by + rw [Z_symm] + exact source_gram_13_7_13 + +theorem source_error_13_13_9 : Y 13 13 9 = (-2022830025440980274156781/655360000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_9_13 + +theorem source_gram_13_13_9 : Z 13 13 9 = (-36486450 : ℚ) := by + rw [Z_symm] + exact source_gram_13_9_13 + +theorem source_error_13_13_11 : Y 13 13 11 = (252554056596275363975331/65536000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_13_11_13 + +theorem source_gram_13_13_11 : Z 13 13 11 = (-30405375 : ℚ) := by + rw [Z_symm] + exact source_gram_13_11_13 + +theorem error_13 : errorRational 13 = candidateY_13 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_13_1_1 + · exact source_error_13_1_3 + · exact source_error_13_1_5 + · exact source_error_13_1_7 + · exact source_error_13_1_9 + · exact source_error_13_1_11 + · exact source_error_13_1_13 + · exact source_error_13_3_1 + · exact source_error_13_3_3 + · exact source_error_13_3_5 + · exact source_error_13_3_7 + · exact source_error_13_3_9 + · exact source_error_13_3_11 + · exact source_error_13_3_13 + · exact source_error_13_5_1 + · exact source_error_13_5_3 + · exact source_error_13_5_5 + · exact source_error_13_5_7 + · exact source_error_13_5_9 + · exact source_error_13_5_11 + · exact source_error_13_5_13 + · exact source_error_13_7_1 + · exact source_error_13_7_3 + · exact source_error_13_7_5 + · exact source_error_13_7_7 + · exact source_error_13_7_9 + · exact source_error_13_7_11 + · exact source_error_13_7_13 + · exact source_error_13_9_1 + · exact source_error_13_9_3 + · exact source_error_13_9_5 + · exact source_error_13_9_7 + · exact source_error_13_9_9 + · exact source_error_13_9_11 + · exact source_error_13_9_13 + · exact source_error_13_11_1 + · exact source_error_13_11_3 + · exact source_error_13_11_5 + · exact source_error_13_11_7 + · exact source_error_13_11_9 + · exact source_error_13_11_11 + · exact source_error_13_11_13 + · exact source_error_13_13_1 + · exact source_error_13_13_3 + · exact source_error_13_13_5 + · exact source_error_13_13_7 + · exact source_error_13_13_9 + · exact source_error_13_13_11 + · exact source_error_13_13_13 + +theorem gram_13 : gramRational 13 = candidateZ_13 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_13_1_1 + · exact source_gram_13_1_3 + · exact source_gram_13_1_5 + · exact source_gram_13_1_7 + · exact source_gram_13_1_9 + · exact source_gram_13_1_11 + · exact source_gram_13_1_13 + · exact source_gram_13_3_1 + · exact source_gram_13_3_3 + · exact source_gram_13_3_5 + · exact source_gram_13_3_7 + · exact source_gram_13_3_9 + · exact source_gram_13_3_11 + · exact source_gram_13_3_13 + · exact source_gram_13_5_1 + · exact source_gram_13_5_3 + · exact source_gram_13_5_5 + · exact source_gram_13_5_7 + · exact source_gram_13_5_9 + · exact source_gram_13_5_11 + · exact source_gram_13_5_13 + · exact source_gram_13_7_1 + · exact source_gram_13_7_3 + · exact source_gram_13_7_5 + · exact source_gram_13_7_7 + · exact source_gram_13_7_9 + · exact source_gram_13_7_11 + · exact source_gram_13_7_13 + · exact source_gram_13_9_1 + · exact source_gram_13_9_3 + · exact source_gram_13_9_5 + · exact source_gram_13_9_7 + · exact source_gram_13_9_9 + · exact source_gram_13_9_11 + · exact source_gram_13_9_13 + · exact source_gram_13_11_1 + · exact source_gram_13_11_3 + · exact source_gram_13_11_5 + · exact source_gram_13_11_7 + · exact source_gram_13_11_9 + · exact source_gram_13_11_11 + · exact source_gram_13_11_13 + · exact source_gram_13_13_1 + · exact source_gram_13_13_3 + · exact source_gram_13_13_5 + · exact source_gram_13_13_7 + · exact source_gram_13_13_9 + · exact source_gram_13_13_11 + · exact source_gram_13_13_13 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData14.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData14.lean new file mode 100644 index 0000000000000000000000000000000000000000..eec46b4a6013514795e0623907b57fa155bc37d1 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData14.lean @@ -0,0 +1,739 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram01Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram03Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram05Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram07Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram11Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram131314 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0101Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0103Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0105Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0107Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0109Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0111Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0113Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0303Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0305Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0307Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0309Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0311Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0313Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0505Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0507Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0509Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0511Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0513Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0707Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0709Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0711Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0713Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0909Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0911Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0913Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1111Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1113Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1313Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.Data14 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_14_1_1 : Y 14 1 1 = (165377041672743964897444611/4194304000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 1 1 0 (by decide), + source_yRow_eq_rowCompute 14 1 1 1 (by decide), + source_yRow_eq_rowCompute 14 1 1 2 (by decide), + source_yRow_eq_rowCompute 14 1 1 3 (by decide), + source_yRow_eq_rowCompute 14 1 1 4 (by decide), + source_yRow_eq_rowCompute 14 1 1 5 (by decide), + source_yRow_eq_rowCompute 14 1 1 6 (by decide), + computeRow_14_1_1_0, computeRow_14_1_1_1, computeRow_14_1_1_2, computeRow_14_1_1_3, computeRow_14_1_1_4, computeRow_14_1_1_5, computeRow_14_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_1_3 : Y 14 1 3 = (-99652836936417746642331957/4194304000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 1 3 0 (by decide), + source_yRow_eq_rowCompute 14 1 3 1 (by decide), + source_yRow_eq_rowCompute 14 1 3 2 (by decide), + source_yRow_eq_rowCompute 14 1 3 3 (by decide), + source_yRow_eq_rowCompute 14 1 3 4 (by decide), + source_yRow_eq_rowCompute 14 1 3 5 (by decide), + source_yRow_eq_rowCompute 14 1 3 6 (by decide), + computeRow_14_1_3_0, computeRow_14_1_3_1, computeRow_14_1_3_2, computeRow_14_1_3_3, computeRow_14_1_3_4, computeRow_14_1_3_5, computeRow_14_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_1_5 : Y 14 1 5 = (198343656225197394663337443/8388608000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 1 5 0 (by decide), + source_yRow_eq_rowCompute 14 1 5 1 (by decide), + source_yRow_eq_rowCompute 14 1 5 2 (by decide), + source_yRow_eq_rowCompute 14 1 5 3 (by decide), + source_yRow_eq_rowCompute 14 1 5 4 (by decide), + source_yRow_eq_rowCompute 14 1 5 5 (by decide), + source_yRow_eq_rowCompute 14 1 5 6 (by decide), + computeRow_14_1_5_0, computeRow_14_1_5_1, computeRow_14_1_5_2, computeRow_14_1_5_3, computeRow_14_1_5_4, computeRow_14_1_5_5, computeRow_14_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_1_7 : Y 14 1 7 = (-10805495312804179528323783/4194304000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 1 7 0 (by decide), + source_yRow_eq_rowCompute 14 1 7 1 (by decide), + source_yRow_eq_rowCompute 14 1 7 2 (by decide), + source_yRow_eq_rowCompute 14 1 7 3 (by decide), + source_yRow_eq_rowCompute 14 1 7 4 (by decide), + source_yRow_eq_rowCompute 14 1 7 5 (by decide), + source_yRow_eq_rowCompute 14 1 7 6 (by decide), + computeRow_14_1_7_0, computeRow_14_1_7_1, computeRow_14_1_7_2, computeRow_14_1_7_3, computeRow_14_1_7_4, computeRow_14_1_7_5, computeRow_14_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_1_9 : Y 14 1 9 = (21398938288605875882996397/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 1 9 0 (by decide), + source_yRow_eq_rowCompute 14 1 9 1 (by decide), + source_yRow_eq_rowCompute 14 1 9 2 (by decide), + source_yRow_eq_rowCompute 14 1 9 3 (by decide), + source_yRow_eq_rowCompute 14 1 9 4 (by decide), + source_yRow_eq_rowCompute 14 1 9 5 (by decide), + source_yRow_eq_rowCompute 14 1 9 6 (by decide), + computeRow_14_1_9_0, computeRow_14_1_9_1, computeRow_14_1_9_2, computeRow_14_1_9_3, computeRow_14_1_9_4, computeRow_14_1_9_5, computeRow_14_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_1_11 : Y 14 1 11 = (3160468299521670425437149/104857600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 1 11 0 (by decide), + source_yRow_eq_rowCompute 14 1 11 1 (by decide), + source_yRow_eq_rowCompute 14 1 11 2 (by decide), + source_yRow_eq_rowCompute 14 1 11 3 (by decide), + source_yRow_eq_rowCompute 14 1 11 4 (by decide), + source_yRow_eq_rowCompute 14 1 11 5 (by decide), + source_yRow_eq_rowCompute 14 1 11 6 (by decide), + computeRow_14_1_11_0, computeRow_14_1_11_1, computeRow_14_1_11_2, computeRow_14_1_11_3, computeRow_14_1_11_4, computeRow_14_1_11_5, computeRow_14_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_1_13 : Y 14 1 13 = (-12750872962864833675394659/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 1 13 0 (by decide), + source_yRow_eq_rowCompute 14 1 13 1 (by decide), + source_yRow_eq_rowCompute 14 1 13 2 (by decide), + source_yRow_eq_rowCompute 14 1 13 3 (by decide), + source_yRow_eq_rowCompute 14 1 13 4 (by decide), + source_yRow_eq_rowCompute 14 1 13 5 (by decide), + source_yRow_eq_rowCompute 14 1 13 6 (by decide), + computeRow_14_1_13_0, computeRow_14_1_13_1, computeRow_14_1_13_2, computeRow_14_1_13_3, computeRow_14_1_13_4, computeRow_14_1_13_5, computeRow_14_1_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_3_3 : Y 14 3 3 = (23310418524081657499377/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 3 3 0 (by decide), + source_yRow_eq_rowCompute 14 3 3 1 (by decide), + source_yRow_eq_rowCompute 14 3 3 2 (by decide), + source_yRow_eq_rowCompute 14 3 3 3 (by decide), + source_yRow_eq_rowCompute 14 3 3 4 (by decide), + source_yRow_eq_rowCompute 14 3 3 5 (by decide), + source_yRow_eq_rowCompute 14 3 3 6 (by decide), + computeRow_14_3_3_0, computeRow_14_3_3_1, computeRow_14_3_3_2, computeRow_14_3_3_3, computeRow_14_3_3_4, computeRow_14_3_3_5, computeRow_14_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_3_5 : Y 14 3 5 = (-347065711842922353039231/419430400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 3 5 0 (by decide), + source_yRow_eq_rowCompute 14 3 5 1 (by decide), + source_yRow_eq_rowCompute 14 3 5 2 (by decide), + source_yRow_eq_rowCompute 14 3 5 3 (by decide), + source_yRow_eq_rowCompute 14 3 5 4 (by decide), + source_yRow_eq_rowCompute 14 3 5 5 (by decide), + source_yRow_eq_rowCompute 14 3 5 6 (by decide), + computeRow_14_3_5_0, computeRow_14_3_5_1, computeRow_14_3_5_2, computeRow_14_3_5_3, computeRow_14_3_5_4, computeRow_14_3_5_5, computeRow_14_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_3_7 : Y 14 3 7 = (-138985253242272601987977/104857600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 3 7 0 (by decide), + source_yRow_eq_rowCompute 14 3 7 1 (by decide), + source_yRow_eq_rowCompute 14 3 7 2 (by decide), + source_yRow_eq_rowCompute 14 3 7 3 (by decide), + source_yRow_eq_rowCompute 14 3 7 4 (by decide), + source_yRow_eq_rowCompute 14 3 7 5 (by decide), + source_yRow_eq_rowCompute 14 3 7 6 (by decide), + computeRow_14_3_7_0, computeRow_14_3_7_1, computeRow_14_3_7_2, computeRow_14_3_7_3, computeRow_14_3_7_4, computeRow_14_3_7_5, computeRow_14_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_3_9 : Y 14 3 9 = (-567150585351068471238783/131072000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 3 9 0 (by decide), + source_yRow_eq_rowCompute 14 3 9 1 (by decide), + source_yRow_eq_rowCompute 14 3 9 2 (by decide), + source_yRow_eq_rowCompute 14 3 9 3 (by decide), + source_yRow_eq_rowCompute 14 3 9 4 (by decide), + source_yRow_eq_rowCompute 14 3 9 5 (by decide), + source_yRow_eq_rowCompute 14 3 9 6 (by decide), + computeRow_14_3_9_0, computeRow_14_3_9_1, computeRow_14_3_9_2, computeRow_14_3_9_3, computeRow_14_3_9_4, computeRow_14_3_9_5, computeRow_14_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_3_11 : Y 14 3 11 = (-141724874857705188581763/32768000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 3 11 0 (by decide), + source_yRow_eq_rowCompute 14 3 11 1 (by decide), + source_yRow_eq_rowCompute 14 3 11 2 (by decide), + source_yRow_eq_rowCompute 14 3 11 3 (by decide), + source_yRow_eq_rowCompute 14 3 11 4 (by decide), + source_yRow_eq_rowCompute 14 3 11 5 (by decide), + source_yRow_eq_rowCompute 14 3 11 6 (by decide), + computeRow_14_3_11_0, computeRow_14_3_11_1, computeRow_14_3_11_2, computeRow_14_3_11_3, computeRow_14_3_11_4, computeRow_14_3_11_5, computeRow_14_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_3_13 : Y 14 3 13 = (-841622022843306152134401/26214400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 3 13 0 (by decide), + source_yRow_eq_rowCompute 14 3 13 1 (by decide), + source_yRow_eq_rowCompute 14 3 13 2 (by decide), + source_yRow_eq_rowCompute 14 3 13 3 (by decide), + source_yRow_eq_rowCompute 14 3 13 4 (by decide), + source_yRow_eq_rowCompute 14 3 13 5 (by decide), + source_yRow_eq_rowCompute 14 3 13 6 (by decide), + computeRow_14_3_13_0, computeRow_14_3_13_1, computeRow_14_3_13_2, computeRow_14_3_13_3, computeRow_14_3_13_4, computeRow_14_3_13_5, computeRow_14_3_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_5_5 : Y 14 5 5 = (-948697485826720805007561/1677721600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 5 5 0 (by decide), + source_yRow_eq_rowCompute 14 5 5 1 (by decide), + source_yRow_eq_rowCompute 14 5 5 2 (by decide), + source_yRow_eq_rowCompute 14 5 5 3 (by decide), + source_yRow_eq_rowCompute 14 5 5 4 (by decide), + source_yRow_eq_rowCompute 14 5 5 5 (by decide), + source_yRow_eq_rowCompute 14 5 5 6 (by decide), + computeRow_14_5_5_0, computeRow_14_5_5_1, computeRow_14_5_5_2, computeRow_14_5_5_3, computeRow_14_5_5_4, computeRow_14_5_5_5, computeRow_14_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_5_7 : Y 14 5 7 = (1776603855966711095862153/4194304000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 5 7 0 (by decide), + source_yRow_eq_rowCompute 14 5 7 1 (by decide), + source_yRow_eq_rowCompute 14 5 7 2 (by decide), + source_yRow_eq_rowCompute 14 5 7 3 (by decide), + source_yRow_eq_rowCompute 14 5 7 4 (by decide), + source_yRow_eq_rowCompute 14 5 7 5 (by decide), + source_yRow_eq_rowCompute 14 5 7 6 (by decide), + computeRow_14_5_7_0, computeRow_14_5_7_1, computeRow_14_5_7_2, computeRow_14_5_7_3, computeRow_14_5_7_4, computeRow_14_5_7_5, computeRow_14_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_5_9 : Y 14 5 9 = (932798387166894000074907/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 5 9 0 (by decide), + source_yRow_eq_rowCompute 14 5 9 1 (by decide), + source_yRow_eq_rowCompute 14 5 9 2 (by decide), + source_yRow_eq_rowCompute 14 5 9 3 (by decide), + source_yRow_eq_rowCompute 14 5 9 4 (by decide), + source_yRow_eq_rowCompute 14 5 9 5 (by decide), + source_yRow_eq_rowCompute 14 5 9 6 (by decide), + computeRow_14_5_9_0, computeRow_14_5_9_1, computeRow_14_5_9_2, computeRow_14_5_9_3, computeRow_14_5_9_4, computeRow_14_5_9_5, computeRow_14_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_5_11 : Y 14 5 11 = (269131392507015595229211/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 5 11 0 (by decide), + source_yRow_eq_rowCompute 14 5 11 1 (by decide), + source_yRow_eq_rowCompute 14 5 11 2 (by decide), + source_yRow_eq_rowCompute 14 5 11 3 (by decide), + source_yRow_eq_rowCompute 14 5 11 4 (by decide), + source_yRow_eq_rowCompute 14 5 11 5 (by decide), + source_yRow_eq_rowCompute 14 5 11 6 (by decide), + computeRow_14_5_11_0, computeRow_14_5_11_1, computeRow_14_5_11_2, computeRow_14_5_11_3, computeRow_14_5_11_4, computeRow_14_5_11_5, computeRow_14_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_5_13 : Y 14 5 13 = (6370357421543107418633493/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 5 13 0 (by decide), + source_yRow_eq_rowCompute 14 5 13 1 (by decide), + source_yRow_eq_rowCompute 14 5 13 2 (by decide), + source_yRow_eq_rowCompute 14 5 13 3 (by decide), + source_yRow_eq_rowCompute 14 5 13 4 (by decide), + source_yRow_eq_rowCompute 14 5 13 5 (by decide), + source_yRow_eq_rowCompute 14 5 13 6 (by decide), + computeRow_14_5_13_0, computeRow_14_5_13_1, computeRow_14_5_13_2, computeRow_14_5_13_3, computeRow_14_5_13_4, computeRow_14_5_13_5, computeRow_14_5_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_7_7 : Y 14 7 7 = (-2225592748224580792706397/2097152000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 7 7 0 (by decide), + source_yRow_eq_rowCompute 14 7 7 1 (by decide), + source_yRow_eq_rowCompute 14 7 7 2 (by decide), + source_yRow_eq_rowCompute 14 7 7 3 (by decide), + source_yRow_eq_rowCompute 14 7 7 4 (by decide), + source_yRow_eq_rowCompute 14 7 7 5 (by decide), + source_yRow_eq_rowCompute 14 7 7 6 (by decide), + computeRow_14_7_7_0, computeRow_14_7_7_1, computeRow_14_7_7_2, computeRow_14_7_7_3, computeRow_14_7_7_4, computeRow_14_7_7_5, computeRow_14_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_7_9 : Y 14 7 9 = (1701251773125333268329/20971520000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 7 9 0 (by decide), + source_yRow_eq_rowCompute 14 7 9 1 (by decide), + source_yRow_eq_rowCompute 14 7 9 2 (by decide), + source_yRow_eq_rowCompute 14 7 9 3 (by decide), + source_yRow_eq_rowCompute 14 7 9 4 (by decide), + source_yRow_eq_rowCompute 14 7 9 5 (by decide), + source_yRow_eq_rowCompute 14 7 9 6 (by decide), + computeRow_14_7_9_0, computeRow_14_7_9_1, computeRow_14_7_9_2, computeRow_14_7_9_3, computeRow_14_7_9_4, computeRow_14_7_9_5, computeRow_14_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_7_11 : Y 14 7 11 = (-41108078112253038740007/52428800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 7 11 0 (by decide), + source_yRow_eq_rowCompute 14 7 11 1 (by decide), + source_yRow_eq_rowCompute 14 7 11 2 (by decide), + source_yRow_eq_rowCompute 14 7 11 3 (by decide), + source_yRow_eq_rowCompute 14 7 11 4 (by decide), + source_yRow_eq_rowCompute 14 7 11 5 (by decide), + source_yRow_eq_rowCompute 14 7 11 6 (by decide), + computeRow_14_7_11_0, computeRow_14_7_11_1, computeRow_14_7_11_2, computeRow_14_7_11_3, computeRow_14_7_11_4, computeRow_14_7_11_5, computeRow_14_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_7_13 : Y 14 7 13 = (-1332400286315383367619537/262144000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 7 13 0 (by decide), + source_yRow_eq_rowCompute 14 7 13 1 (by decide), + source_yRow_eq_rowCompute 14 7 13 2 (by decide), + source_yRow_eq_rowCompute 14 7 13 3 (by decide), + source_yRow_eq_rowCompute 14 7 13 4 (by decide), + source_yRow_eq_rowCompute 14 7 13 5 (by decide), + source_yRow_eq_rowCompute 14 7 13 6 (by decide), + computeRow_14_7_13_0, computeRow_14_7_13_1, computeRow_14_7_13_2, computeRow_14_7_13_3, computeRow_14_7_13_4, computeRow_14_7_13_5, computeRow_14_7_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_9_9 : Y 14 9 9 = (1451654095595659568163/26214400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 9 9 0 (by decide), + source_yRow_eq_rowCompute 14 9 9 1 (by decide), + source_yRow_eq_rowCompute 14 9 9 2 (by decide), + source_yRow_eq_rowCompute 14 9 9 3 (by decide), + source_yRow_eq_rowCompute 14 9 9 4 (by decide), + source_yRow_eq_rowCompute 14 9 9 5 (by decide), + source_yRow_eq_rowCompute 14 9 9 6 (by decide), + computeRow_14_9_9_0, computeRow_14_9_9_1, computeRow_14_9_9_2, computeRow_14_9_9_3, computeRow_14_9_9_4, computeRow_14_9_9_5, computeRow_14_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_9_11 : Y 14 9 11 = (56731873890489317051103/65536000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 9 11 0 (by decide), + source_yRow_eq_rowCompute 14 9 11 1 (by decide), + source_yRow_eq_rowCompute 14 9 11 2 (by decide), + source_yRow_eq_rowCompute 14 9 11 3 (by decide), + source_yRow_eq_rowCompute 14 9 11 4 (by decide), + source_yRow_eq_rowCompute 14 9 11 5 (by decide), + source_yRow_eq_rowCompute 14 9 11 6 (by decide), + computeRow_14_9_11_0, computeRow_14_9_11_1, computeRow_14_9_11_2, computeRow_14_9_11_3, computeRow_14_9_11_4, computeRow_14_9_11_5, computeRow_14_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_9_13 : Y 14 9 13 = (702921905295609015979677/65536000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 9 13 0 (by decide), + source_yRow_eq_rowCompute 14 9 13 1 (by decide), + source_yRow_eq_rowCompute 14 9 13 2 (by decide), + source_yRow_eq_rowCompute 14 9 13 3 (by decide), + source_yRow_eq_rowCompute 14 9 13 4 (by decide), + source_yRow_eq_rowCompute 14 9 13 5 (by decide), + source_yRow_eq_rowCompute 14 9 13 6 (by decide), + computeRow_14_9_13_0, computeRow_14_9_13_1, computeRow_14_9_13_2, computeRow_14_9_13_3, computeRow_14_9_13_4, computeRow_14_9_13_5, computeRow_14_9_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_11_11 : Y 14 11 11 = (15883626629942625122019/32768000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 11 11 0 (by decide), + source_yRow_eq_rowCompute 14 11 11 1 (by decide), + source_yRow_eq_rowCompute 14 11 11 2 (by decide), + source_yRow_eq_rowCompute 14 11 11 3 (by decide), + source_yRow_eq_rowCompute 14 11 11 4 (by decide), + source_yRow_eq_rowCompute 14 11 11 5 (by decide), + source_yRow_eq_rowCompute 14 11 11 6 (by decide), + computeRow_14_11_11_0, computeRow_14_11_11_1, computeRow_14_11_11_2, computeRow_14_11_11_3, computeRow_14_11_11_4, computeRow_14_11_11_5, computeRow_14_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_11_13 : Y 14 11 13 = (-304589521531696266272979/32768000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 11 13 0 (by decide), + source_yRow_eq_rowCompute 14 11 13 1 (by decide), + source_yRow_eq_rowCompute 14 11 13 2 (by decide), + source_yRow_eq_rowCompute 14 11 13 3 (by decide), + source_yRow_eq_rowCompute 14 11 13 4 (by decide), + source_yRow_eq_rowCompute 14 11 13 5 (by decide), + source_yRow_eq_rowCompute 14 11 13 6 (by decide), + computeRow_14_11_13_0, computeRow_14_11_13_1, computeRow_14_11_13_2, computeRow_14_11_13_3, computeRow_14_11_13_4, computeRow_14_11_13_5, computeRow_14_11_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_14_13_13 : Y 14 13 13 = (-10250896235928348183825213/32768000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 14 13 13 0 (by decide), + source_yRow_eq_rowCompute 14 13 13 1 (by decide), + source_yRow_eq_rowCompute 14 13 13 2 (by decide), + source_yRow_eq_rowCompute 14 13 13 3 (by decide), + source_yRow_eq_rowCompute 14 13 13 4 (by decide), + source_yRow_eq_rowCompute 14 13 13 5 (by decide), + source_yRow_eq_rowCompute 14 13 13 6 (by decide), + computeRow_14_13_13_0, computeRow_14_13_13_1, computeRow_14_13_13_2, computeRow_14_13_13_3, computeRow_14_13_13_4, computeRow_14_13_13_5, computeRow_14_13_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_14_1_1 : Z 14 1 1 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_1_1 + +theorem source_gram_14_1_3 : Z 14 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_1_3 + +theorem source_gram_14_1_5 : Z 14 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_1_5 + +theorem source_gram_14_1_7 : Z 14 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_1_7 + +theorem source_gram_14_1_9 : Z 14 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_1_9 + +theorem source_gram_14_1_11 : Z 14 1 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_1_11 + +theorem source_gram_14_1_13 : Z 14 1 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_1_13 + +theorem source_gram_14_3_3 : Z 14 3 3 = (239500800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_3_3 + +theorem source_gram_14_3_5 : Z 14 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_3_5 + +theorem source_gram_14_3_7 : Z 14 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_3_7 + +theorem source_gram_14_3_9 : Z 14 3 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_3_9 + +theorem source_gram_14_3_11 : Z 14 3 11 = (-74844000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_3_11 + +theorem source_gram_14_3_13 : Z 14 3 13 = (778377600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_3_13 + +theorem source_gram_14_5_5 : Z 14 5 5 = (43545600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_5_5 + +theorem source_gram_14_5_7 : Z 14 5 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_5_7 + +theorem source_gram_14_5_9 : Z 14 5 9 = (-21772800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_5_9 + +theorem source_gram_14_5_11 : Z 14 5 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_5_11 + +theorem source_gram_14_5_13 : Z 14 5 13 = (389188800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_5_13 + +theorem source_gram_14_7_7 : Z 14 7 7 = (11113200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_7_7 + +theorem source_gram_14_7_9 : Z 14 7 9 = (-19051200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_7_9 + +theorem source_gram_14_7_11 : Z 14 7 11 = (26195400 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_7_11 + +theorem source_gram_14_7_13 : Z 14 7 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_7_13 + +theorem source_gram_14_9_9 : Z 14 9 9 = (43545600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_9_9 + +theorem source_gram_14_9_11 : Z 14 9 11 = (-44906400 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_9_11 + +theorem source_gram_14_9_13 : Z 14 9 13 = (-194594400 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_9_13 + +theorem source_gram_14_11_11 : Z 14 11 11 = (85135050 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_11_11 + +theorem source_gram_14_11_13 : Z 14 11 13 = (-243243000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_11_13 + +theorem source_gram_14_13_13 : Z 14 13 13 = (6008102100 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_14_13_13 + +theorem source_error_14_3_1 : Y 14 3 1 = (-99652836936417746642331957/4194304000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_1_3 + +theorem source_gram_14_3_1 : Z 14 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_14_1_3 + +theorem source_error_14_5_1 : Y 14 5 1 = (198343656225197394663337443/8388608000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_1_5 + +theorem source_gram_14_5_1 : Z 14 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_14_1_5 + +theorem source_error_14_5_3 : Y 14 5 3 = (-347065711842922353039231/419430400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_3_5 + +theorem source_gram_14_5_3 : Z 14 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_14_3_5 + +theorem source_error_14_7_1 : Y 14 7 1 = (-10805495312804179528323783/4194304000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_1_7 + +theorem source_gram_14_7_1 : Z 14 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_14_1_7 + +theorem source_error_14_7_3 : Y 14 7 3 = (-138985253242272601987977/104857600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_3_7 + +theorem source_gram_14_7_3 : Z 14 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_14_3_7 + +theorem source_error_14_7_5 : Y 14 7 5 = (1776603855966711095862153/4194304000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_5_7 + +theorem source_gram_14_7_5 : Z 14 7 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_14_5_7 + +theorem source_error_14_9_1 : Y 14 9 1 = (21398938288605875882996397/1048576000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_1_9 + +theorem source_gram_14_9_1 : Z 14 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_14_1_9 + +theorem source_error_14_9_3 : Y 14 9 3 = (-567150585351068471238783/131072000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_3_9 + +theorem source_gram_14_9_3 : Z 14 9 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_14_3_9 + +theorem source_error_14_9_5 : Y 14 9 5 = (932798387166894000074907/1048576000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_5_9 + +theorem source_gram_14_9_5 : Z 14 9 5 = (-21772800 : ℚ) := by + rw [Z_symm] + exact source_gram_14_5_9 + +theorem source_error_14_9_7 : Y 14 9 7 = (1701251773125333268329/20971520000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_7_9 + +theorem source_gram_14_9_7 : Z 14 9 7 = (-19051200 : ℚ) := by + rw [Z_symm] + exact source_gram_14_7_9 + +theorem source_error_14_11_1 : Y 14 11 1 = (3160468299521670425437149/104857600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_1_11 + +theorem source_gram_14_11_1 : Z 14 11 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_14_1_11 + +theorem source_error_14_11_3 : Y 14 11 3 = (-141724874857705188581763/32768000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_3_11 + +theorem source_gram_14_11_3 : Z 14 11 3 = (-74844000 : ℚ) := by + rw [Z_symm] + exact source_gram_14_3_11 + +theorem source_error_14_11_5 : Y 14 11 5 = (269131392507015595229211/524288000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_5_11 + +theorem source_gram_14_11_5 : Z 14 11 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_14_5_11 + +theorem source_error_14_11_7 : Y 14 11 7 = (-41108078112253038740007/52428800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_7_11 + +theorem source_gram_14_11_7 : Z 14 11 7 = (26195400 : ℚ) := by + rw [Z_symm] + exact source_gram_14_7_11 + +theorem source_error_14_11_9 : Y 14 11 9 = (56731873890489317051103/65536000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_9_11 + +theorem source_gram_14_11_9 : Z 14 11 9 = (-44906400 : ℚ) := by + rw [Z_symm] + exact source_gram_14_9_11 + +theorem source_error_14_13_1 : Y 14 13 1 = (-12750872962864833675394659/524288000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_1_13 + +theorem source_gram_14_13_1 : Z 14 13 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_14_1_13 + +theorem source_error_14_13_3 : Y 14 13 3 = (-841622022843306152134401/26214400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_3_13 + +theorem source_gram_14_13_3 : Z 14 13 3 = (778377600 : ℚ) := by + rw [Z_symm] + exact source_gram_14_3_13 + +theorem source_error_14_13_5 : Y 14 13 5 = (6370357421543107418633493/524288000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_5_13 + +theorem source_gram_14_13_5 : Z 14 13 5 = (389188800 : ℚ) := by + rw [Z_symm] + exact source_gram_14_5_13 + +theorem source_error_14_13_7 : Y 14 13 7 = (-1332400286315383367619537/262144000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_7_13 + +theorem source_gram_14_13_7 : Z 14 13 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_14_7_13 + +theorem source_error_14_13_9 : Y 14 13 9 = (702921905295609015979677/65536000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_9_13 + +theorem source_gram_14_13_9 : Z 14 13 9 = (-194594400 : ℚ) := by + rw [Z_symm] + exact source_gram_14_9_13 + +theorem source_error_14_13_11 : Y 14 13 11 = (-304589521531696266272979/32768000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_14_11_13 + +theorem source_gram_14_13_11 : Z 14 13 11 = (-243243000 : ℚ) := by + rw [Z_symm] + exact source_gram_14_11_13 + +theorem error_14 : errorRational 14 = candidateY_14 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_14_1_1 + · exact source_error_14_1_3 + · exact source_error_14_1_5 + · exact source_error_14_1_7 + · exact source_error_14_1_9 + · exact source_error_14_1_11 + · exact source_error_14_1_13 + · exact source_error_14_3_1 + · exact source_error_14_3_3 + · exact source_error_14_3_5 + · exact source_error_14_3_7 + · exact source_error_14_3_9 + · exact source_error_14_3_11 + · exact source_error_14_3_13 + · exact source_error_14_5_1 + · exact source_error_14_5_3 + · exact source_error_14_5_5 + · exact source_error_14_5_7 + · exact source_error_14_5_9 + · exact source_error_14_5_11 + · exact source_error_14_5_13 + · exact source_error_14_7_1 + · exact source_error_14_7_3 + · exact source_error_14_7_5 + · exact source_error_14_7_7 + · exact source_error_14_7_9 + · exact source_error_14_7_11 + · exact source_error_14_7_13 + · exact source_error_14_9_1 + · exact source_error_14_9_3 + · exact source_error_14_9_5 + · exact source_error_14_9_7 + · exact source_error_14_9_9 + · exact source_error_14_9_11 + · exact source_error_14_9_13 + · exact source_error_14_11_1 + · exact source_error_14_11_3 + · exact source_error_14_11_5 + · exact source_error_14_11_7 + · exact source_error_14_11_9 + · exact source_error_14_11_11 + · exact source_error_14_11_13 + · exact source_error_14_13_1 + · exact source_error_14_13_3 + · exact source_error_14_13_5 + · exact source_error_14_13_7 + · exact source_error_14_13_9 + · exact source_error_14_13_11 + · exact source_error_14_13_13 + +theorem gram_14 : gramRational 14 = candidateZ_14 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_14_1_1 + · exact source_gram_14_1_3 + · exact source_gram_14_1_5 + · exact source_gram_14_1_7 + · exact source_gram_14_1_9 + · exact source_gram_14_1_11 + · exact source_gram_14_1_13 + · exact source_gram_14_3_1 + · exact source_gram_14_3_3 + · exact source_gram_14_3_5 + · exact source_gram_14_3_7 + · exact source_gram_14_3_9 + · exact source_gram_14_3_11 + · exact source_gram_14_3_13 + · exact source_gram_14_5_1 + · exact source_gram_14_5_3 + · exact source_gram_14_5_5 + · exact source_gram_14_5_7 + · exact source_gram_14_5_9 + · exact source_gram_14_5_11 + · exact source_gram_14_5_13 + · exact source_gram_14_7_1 + · exact source_gram_14_7_3 + · exact source_gram_14_7_5 + · exact source_gram_14_7_7 + · exact source_gram_14_7_9 + · exact source_gram_14_7_11 + · exact source_gram_14_7_13 + · exact source_gram_14_9_1 + · exact source_gram_14_9_3 + · exact source_gram_14_9_5 + · exact source_gram_14_9_7 + · exact source_gram_14_9_9 + · exact source_gram_14_9_11 + · exact source_gram_14_9_13 + · exact source_gram_14_11_1 + · exact source_gram_14_11_3 + · exact source_gram_14_11_5 + · exact source_gram_14_11_7 + · exact source_gram_14_11_9 + · exact source_gram_14_11_11 + · exact source_gram_14_11_13 + · exact source_gram_14_13_1 + · exact source_gram_14_13_3 + · exact source_gram_14_13_5 + · exact source_gram_14_13_7 + · exact source_gram_14_13_9 + · exact source_gram_14_13_11 + · exact source_gram_14_13_13 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData15.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData15.lean new file mode 100644 index 0000000000000000000000000000000000000000..96ccf890088ab15d8e3901280773c6ea757f5c00 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData15.lean @@ -0,0 +1,954 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram01Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram03Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram05Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram07Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram11Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram13Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram151515 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0101Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0103Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0105Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0107Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0109Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0111Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0113Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0115Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0303Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0305Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0307Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0309Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0311Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0313Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0315Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0505Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0507Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0509Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0511Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0513Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0515Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0707Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0709Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0711Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0713Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0715Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0909Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0911Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0913Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0915Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1111Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1113Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1115Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1313Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1315Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1515Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.Data15 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_15_1_1 : Y 15 1 1 = (1160239161688954312188380157/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 1 1 0 (by decide), + source_yRow_eq_rowCompute 15 1 1 1 (by decide), + source_yRow_eq_rowCompute 15 1 1 2 (by decide), + source_yRow_eq_rowCompute 15 1 1 3 (by decide), + source_yRow_eq_rowCompute 15 1 1 4 (by decide), + source_yRow_eq_rowCompute 15 1 1 5 (by decide), + source_yRow_eq_rowCompute 15 1 1 6 (by decide), + computeRow_15_1_1_0, computeRow_15_1_1_1, computeRow_15_1_1_2, computeRow_15_1_1_3, computeRow_15_1_1_4, computeRow_15_1_1_5, computeRow_15_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_1_3 : Y 15 1 3 = (527769145158896263581537579/2097152000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 1 3 0 (by decide), + source_yRow_eq_rowCompute 15 1 3 1 (by decide), + source_yRow_eq_rowCompute 15 1 3 2 (by decide), + source_yRow_eq_rowCompute 15 1 3 3 (by decide), + source_yRow_eq_rowCompute 15 1 3 4 (by decide), + source_yRow_eq_rowCompute 15 1 3 5 (by decide), + source_yRow_eq_rowCompute 15 1 3 6 (by decide), + computeRow_15_1_3_0, computeRow_15_1_3_1, computeRow_15_1_3_2, computeRow_15_1_3_3, computeRow_15_1_3_4, computeRow_15_1_3_5, computeRow_15_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_1_5 : Y 15 1 5 = (-364633884256427977153375413/1677721600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 1 5 0 (by decide), + source_yRow_eq_rowCompute 15 1 5 1 (by decide), + source_yRow_eq_rowCompute 15 1 5 2 (by decide), + source_yRow_eq_rowCompute 15 1 5 3 (by decide), + source_yRow_eq_rowCompute 15 1 5 4 (by decide), + source_yRow_eq_rowCompute 15 1 5 5 (by decide), + source_yRow_eq_rowCompute 15 1 5 6 (by decide), + computeRow_15_1_5_0, computeRow_15_1_5_1, computeRow_15_1_5_2, computeRow_15_1_5_3, computeRow_15_1_5_4, computeRow_15_1_5_5, computeRow_15_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_1_7 : Y 15 1 7 = (70800295830292526868599229/838860800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 1 7 0 (by decide), + source_yRow_eq_rowCompute 15 1 7 1 (by decide), + source_yRow_eq_rowCompute 15 1 7 2 (by decide), + source_yRow_eq_rowCompute 15 1 7 3 (by decide), + source_yRow_eq_rowCompute 15 1 7 4 (by decide), + source_yRow_eq_rowCompute 15 1 7 5 (by decide), + source_yRow_eq_rowCompute 15 1 7 6 (by decide), + computeRow_15_1_7_0, computeRow_15_1_7_1, computeRow_15_1_7_2, computeRow_15_1_7_3, computeRow_15_1_7_4, computeRow_15_1_7_5, computeRow_15_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_1_9 : Y 15 1 9 = (-213215905018995130639958571/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 1 9 0 (by decide), + source_yRow_eq_rowCompute 15 1 9 1 (by decide), + source_yRow_eq_rowCompute 15 1 9 2 (by decide), + source_yRow_eq_rowCompute 15 1 9 3 (by decide), + source_yRow_eq_rowCompute 15 1 9 4 (by decide), + source_yRow_eq_rowCompute 15 1 9 5 (by decide), + source_yRow_eq_rowCompute 15 1 9 6 (by decide), + computeRow_15_1_9_0, computeRow_15_1_9_1, computeRow_15_1_9_2, computeRow_15_1_9_3, computeRow_15_1_9_4, computeRow_15_1_9_5, computeRow_15_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_1_11 : Y 15 1 11 = (-236988935373506936612565573/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 1 11 0 (by decide), + source_yRow_eq_rowCompute 15 1 11 1 (by decide), + source_yRow_eq_rowCompute 15 1 11 2 (by decide), + source_yRow_eq_rowCompute 15 1 11 3 (by decide), + source_yRow_eq_rowCompute 15 1 11 4 (by decide), + source_yRow_eq_rowCompute 15 1 11 5 (by decide), + source_yRow_eq_rowCompute 15 1 11 6 (by decide), + computeRow_15_1_11_0, computeRow_15_1_11_1, computeRow_15_1_11_2, computeRow_15_1_11_3, computeRow_15_1_11_4, computeRow_15_1_11_5, computeRow_15_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_1_13 : Y 15 1 13 = (374746885492881333249210393/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 1 13 0 (by decide), + source_yRow_eq_rowCompute 15 1 13 1 (by decide), + source_yRow_eq_rowCompute 15 1 13 2 (by decide), + source_yRow_eq_rowCompute 15 1 13 3 (by decide), + source_yRow_eq_rowCompute 15 1 13 4 (by decide), + source_yRow_eq_rowCompute 15 1 13 5 (by decide), + source_yRow_eq_rowCompute 15 1 13 6 (by decide), + computeRow_15_1_13_0, computeRow_15_1_13_1, computeRow_15_1_13_2, computeRow_15_1_13_3, computeRow_15_1_13_4, computeRow_15_1_13_5, computeRow_15_1_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_1_15 : Y 15 1 15 = (-1454272995490648196091417189/52428800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 1 15 0 (by decide), + source_yRow_eq_rowCompute 15 1 15 1 (by decide), + source_yRow_eq_rowCompute 15 1 15 2 (by decide), + source_yRow_eq_rowCompute 15 1 15 3 (by decide), + source_yRow_eq_rowCompute 15 1 15 4 (by decide), + source_yRow_eq_rowCompute 15 1 15 5 (by decide), + source_yRow_eq_rowCompute 15 1 15 6 (by decide), + computeRow_15_1_15_0, computeRow_15_1_15_1, computeRow_15_1_15_2, computeRow_15_1_15_3, computeRow_15_1_15_4, computeRow_15_1_15_5, computeRow_15_1_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_3_3 : Y 15 3 3 = (-79903889464778925306594867/2097152000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 3 3 0 (by decide), + source_yRow_eq_rowCompute 15 3 3 1 (by decide), + source_yRow_eq_rowCompute 15 3 3 2 (by decide), + source_yRow_eq_rowCompute 15 3 3 3 (by decide), + source_yRow_eq_rowCompute 15 3 3 4 (by decide), + source_yRow_eq_rowCompute 15 3 3 5 (by decide), + source_yRow_eq_rowCompute 15 3 3 6 (by decide), + computeRow_15_3_3_0, computeRow_15_3_3_1, computeRow_15_3_3_2, computeRow_15_3_3_3, computeRow_15_3_3_4, computeRow_15_3_3_5, computeRow_15_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_3_5 : Y 15 3 5 = (10380910649344519579874271/838860800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 3 5 0 (by decide), + source_yRow_eq_rowCompute 15 3 5 1 (by decide), + source_yRow_eq_rowCompute 15 3 5 2 (by decide), + source_yRow_eq_rowCompute 15 3 5 3 (by decide), + source_yRow_eq_rowCompute 15 3 5 4 (by decide), + source_yRow_eq_rowCompute 15 3 5 5 (by decide), + source_yRow_eq_rowCompute 15 3 5 6 (by decide), + computeRow_15_3_5_0, computeRow_15_3_5_1, computeRow_15_3_5_2, computeRow_15_3_5_3, computeRow_15_3_5_4, computeRow_15_3_5_5, computeRow_15_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_3_7 : Y 15 3 7 = (2399450471501791440121389/419430400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 3 7 0 (by decide), + source_yRow_eq_rowCompute 15 3 7 1 (by decide), + source_yRow_eq_rowCompute 15 3 7 2 (by decide), + source_yRow_eq_rowCompute 15 3 7 3 (by decide), + source_yRow_eq_rowCompute 15 3 7 4 (by decide), + source_yRow_eq_rowCompute 15 3 7 5 (by decide), + source_yRow_eq_rowCompute 15 3 7 6 (by decide), + computeRow_15_3_7_0, computeRow_15_3_7_1, computeRow_15_3_7_2, computeRow_15_3_7_3, computeRow_15_3_7_4, computeRow_15_3_7_5, computeRow_15_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_3_9 : Y 15 3 9 = (7831247768240800098462597/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 3 9 0 (by decide), + source_yRow_eq_rowCompute 15 3 9 1 (by decide), + source_yRow_eq_rowCompute 15 3 9 2 (by decide), + source_yRow_eq_rowCompute 15 3 9 3 (by decide), + source_yRow_eq_rowCompute 15 3 9 4 (by decide), + source_yRow_eq_rowCompute 15 3 9 5 (by decide), + source_yRow_eq_rowCompute 15 3 9 6 (by decide), + computeRow_15_3_9_0, computeRow_15_3_9_1, computeRow_15_3_9_2, computeRow_15_3_9_3, computeRow_15_3_9_4, computeRow_15_3_9_5, computeRow_15_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_3_11 : Y 15 3 11 = (260365051976410952573409/52428800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 3 11 0 (by decide), + source_yRow_eq_rowCompute 15 3 11 1 (by decide), + source_yRow_eq_rowCompute 15 3 11 2 (by decide), + source_yRow_eq_rowCompute 15 3 11 3 (by decide), + source_yRow_eq_rowCompute 15 3 11 4 (by decide), + source_yRow_eq_rowCompute 15 3 11 5 (by decide), + source_yRow_eq_rowCompute 15 3 11 6 (by decide), + computeRow_15_3_11_0, computeRow_15_3_11_1, computeRow_15_3_11_2, computeRow_15_3_11_3, computeRow_15_3_11_4, computeRow_15_3_11_5, computeRow_15_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_3_13 : Y 15 3 13 = (15417580069242120546303813/262144000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 3 13 0 (by decide), + source_yRow_eq_rowCompute 15 3 13 1 (by decide), + source_yRow_eq_rowCompute 15 3 13 2 (by decide), + source_yRow_eq_rowCompute 15 3 13 3 (by decide), + source_yRow_eq_rowCompute 15 3 13 4 (by decide), + source_yRow_eq_rowCompute 15 3 13 5 (by decide), + source_yRow_eq_rowCompute 15 3 13 6 (by decide), + computeRow_15_3_13_0, computeRow_15_3_13_1, computeRow_15_3_13_2, computeRow_15_3_13_3, computeRow_15_3_13_4, computeRow_15_3_13_5, computeRow_15_3_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_3_15 : Y 15 3 15 = (-19651317795670208550803901/26214400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 3 15 0 (by decide), + source_yRow_eq_rowCompute 15 3 15 1 (by decide), + source_yRow_eq_rowCompute 15 3 15 2 (by decide), + source_yRow_eq_rowCompute 15 3 15 3 (by decide), + source_yRow_eq_rowCompute 15 3 15 4 (by decide), + source_yRow_eq_rowCompute 15 3 15 5 (by decide), + source_yRow_eq_rowCompute 15 3 15 6 (by decide), + computeRow_15_3_15_0, computeRow_15_3_15_1, computeRow_15_3_15_2, computeRow_15_3_15_3, computeRow_15_3_15_4, computeRow_15_3_15_5, computeRow_15_3_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_5_5 : Y 15 5 5 = (-544144788797698439940321/335544320000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 5 5 0 (by decide), + source_yRow_eq_rowCompute 15 5 5 1 (by decide), + source_yRow_eq_rowCompute 15 5 5 2 (by decide), + source_yRow_eq_rowCompute 15 5 5 3 (by decide), + source_yRow_eq_rowCompute 15 5 5 4 (by decide), + source_yRow_eq_rowCompute 15 5 5 5 (by decide), + source_yRow_eq_rowCompute 15 5 5 6 (by decide), + computeRow_15_5_5_0, computeRow_15_5_5_1, computeRow_15_5_5_2, computeRow_15_5_5_3, computeRow_15_5_5_4, computeRow_15_5_5_5, computeRow_15_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_5_7 : Y 15 5 7 = (-1550173356554793074510931/838860800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 5 7 0 (by decide), + source_yRow_eq_rowCompute 15 5 7 1 (by decide), + source_yRow_eq_rowCompute 15 5 7 2 (by decide), + source_yRow_eq_rowCompute 15 5 7 3 (by decide), + source_yRow_eq_rowCompute 15 5 7 4 (by decide), + source_yRow_eq_rowCompute 15 5 7 5 (by decide), + source_yRow_eq_rowCompute 15 5 7 6 (by decide), + computeRow_15_5_7_0, computeRow_15_5_7_1, computeRow_15_5_7_2, computeRow_15_5_7_3, computeRow_15_5_7_4, computeRow_15_5_7_5, computeRow_15_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_5_9 : Y 15 5 9 = (-251612565167710626302493/209715200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 5 9 0 (by decide), + source_yRow_eq_rowCompute 15 5 9 1 (by decide), + source_yRow_eq_rowCompute 15 5 9 2 (by decide), + source_yRow_eq_rowCompute 15 5 9 3 (by decide), + source_yRow_eq_rowCompute 15 5 9 4 (by decide), + source_yRow_eq_rowCompute 15 5 9 5 (by decide), + source_yRow_eq_rowCompute 15 5 9 6 (by decide), + computeRow_15_5_9_0, computeRow_15_5_9_1, computeRow_15_5_9_2, computeRow_15_5_9_3, computeRow_15_5_9_4, computeRow_15_5_9_5, computeRow_15_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_5_11 : Y 15 5 11 = (412467042517374252900789/104857600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 5 11 0 (by decide), + source_yRow_eq_rowCompute 15 5 11 1 (by decide), + source_yRow_eq_rowCompute 15 5 11 2 (by decide), + source_yRow_eq_rowCompute 15 5 11 3 (by decide), + source_yRow_eq_rowCompute 15 5 11 4 (by decide), + source_yRow_eq_rowCompute 15 5 11 5 (by decide), + source_yRow_eq_rowCompute 15 5 11 6 (by decide), + computeRow_15_5_11_0, computeRow_15_5_11_1, computeRow_15_5_11_2, computeRow_15_5_11_3, computeRow_15_5_11_4, computeRow_15_5_11_5, computeRow_15_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_5_13 : Y 15 5 13 = (-3917597116231063282740723/104857600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 5 13 0 (by decide), + source_yRow_eq_rowCompute 15 5 13 1 (by decide), + source_yRow_eq_rowCompute 15 5 13 2 (by decide), + source_yRow_eq_rowCompute 15 5 13 3 (by decide), + source_yRow_eq_rowCompute 15 5 13 4 (by decide), + source_yRow_eq_rowCompute 15 5 13 5 (by decide), + source_yRow_eq_rowCompute 15 5 13 6 (by decide), + computeRow_15_5_13_0, computeRow_15_5_13_1, computeRow_15_5_13_2, computeRow_15_5_13_3, computeRow_15_5_13_4, computeRow_15_5_13_5, computeRow_15_5_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_5_15 : Y 15 5 15 = (6737890215993101774728119/10485760000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 5 15 0 (by decide), + source_yRow_eq_rowCompute 15 5 15 1 (by decide), + source_yRow_eq_rowCompute 15 5 15 2 (by decide), + source_yRow_eq_rowCompute 15 5 15 3 (by decide), + source_yRow_eq_rowCompute 15 5 15 4 (by decide), + source_yRow_eq_rowCompute 15 5 15 5 (by decide), + source_yRow_eq_rowCompute 15 5 15 6 (by decide), + computeRow_15_5_15_0, computeRow_15_5_15_1, computeRow_15_5_15_2, computeRow_15_5_15_3, computeRow_15_5_15_4, computeRow_15_5_15_5, computeRow_15_5_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_7_7 : Y 15 7 7 = (-11010455047903773080463201/2097152000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 7 7 0 (by decide), + source_yRow_eq_rowCompute 15 7 7 1 (by decide), + source_yRow_eq_rowCompute 15 7 7 2 (by decide), + source_yRow_eq_rowCompute 15 7 7 3 (by decide), + source_yRow_eq_rowCompute 15 7 7 4 (by decide), + source_yRow_eq_rowCompute 15 7 7 5 (by decide), + source_yRow_eq_rowCompute 15 7 7 6 (by decide), + computeRow_15_7_7_0, computeRow_15_7_7_1, computeRow_15_7_7_2, computeRow_15_7_7_3, computeRow_15_7_7_4, computeRow_15_7_7_5, computeRow_15_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_7_9 : Y 15 7 9 = (483384920806779568744041/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 7 9 0 (by decide), + source_yRow_eq_rowCompute 15 7 9 1 (by decide), + source_yRow_eq_rowCompute 15 7 9 2 (by decide), + source_yRow_eq_rowCompute 15 7 9 3 (by decide), + source_yRow_eq_rowCompute 15 7 9 4 (by decide), + source_yRow_eq_rowCompute 15 7 9 5 (by decide), + source_yRow_eq_rowCompute 15 7 9 6 (by decide), + computeRow_15_7_9_0, computeRow_15_7_9_1, computeRow_15_7_9_2, computeRow_15_7_9_3, computeRow_15_7_9_4, computeRow_15_7_9_5, computeRow_15_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_7_11 : Y 15 7 11 = (-2196385127442123145785873/262144000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 7 11 0 (by decide), + source_yRow_eq_rowCompute 15 7 11 1 (by decide), + source_yRow_eq_rowCompute 15 7 11 2 (by decide), + source_yRow_eq_rowCompute 15 7 11 3 (by decide), + source_yRow_eq_rowCompute 15 7 11 4 (by decide), + source_yRow_eq_rowCompute 15 7 11 5 (by decide), + source_yRow_eq_rowCompute 15 7 11 6 (by decide), + computeRow_15_7_11_0, computeRow_15_7_11_1, computeRow_15_7_11_2, computeRow_15_7_11_3, computeRow_15_7_11_4, computeRow_15_7_11_5, computeRow_15_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_7_13 : Y 15 7 13 = (-3020058706667129324414217/262144000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 7 13 0 (by decide), + source_yRow_eq_rowCompute 15 7 13 1 (by decide), + source_yRow_eq_rowCompute 15 7 13 2 (by decide), + source_yRow_eq_rowCompute 15 7 13 3 (by decide), + source_yRow_eq_rowCompute 15 7 13 4 (by decide), + source_yRow_eq_rowCompute 15 7 13 5 (by decide), + source_yRow_eq_rowCompute 15 7 13 6 (by decide), + computeRow_15_7_13_0, computeRow_15_7_13_1, computeRow_15_7_13_2, computeRow_15_7_13_3, computeRow_15_7_13_4, computeRow_15_7_13_5, computeRow_15_7_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_7_15 : Y 15 7 15 = (6630571266894369608354541/26214400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 7 15 0 (by decide), + source_yRow_eq_rowCompute 15 7 15 1 (by decide), + source_yRow_eq_rowCompute 15 7 15 2 (by decide), + source_yRow_eq_rowCompute 15 7 15 3 (by decide), + source_yRow_eq_rowCompute 15 7 15 4 (by decide), + source_yRow_eq_rowCompute 15 7 15 5 (by decide), + source_yRow_eq_rowCompute 15 7 15 6 (by decide), + computeRow_15_7_15_0, computeRow_15_7_15_1, computeRow_15_7_15_2, computeRow_15_7_15_3, computeRow_15_7_15_4, computeRow_15_7_15_5, computeRow_15_7_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_9_9 : Y 15 9 9 = (-733927230254603053476261/131072000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 9 9 0 (by decide), + source_yRow_eq_rowCompute 15 9 9 1 (by decide), + source_yRow_eq_rowCompute 15 9 9 2 (by decide), + source_yRow_eq_rowCompute 15 9 9 3 (by decide), + source_yRow_eq_rowCompute 15 9 9 4 (by decide), + source_yRow_eq_rowCompute 15 9 9 5 (by decide), + source_yRow_eq_rowCompute 15 9 9 6 (by decide), + computeRow_15_9_9_0, computeRow_15_9_9_1, computeRow_15_9_9_2, computeRow_15_9_9_3, computeRow_15_9_9_4, computeRow_15_9_9_5, computeRow_15_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_9_11 : Y 15 9 11 = (144198476217622441333917/65536000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 9 11 0 (by decide), + source_yRow_eq_rowCompute 15 9 11 1 (by decide), + source_yRow_eq_rowCompute 15 9 11 2 (by decide), + source_yRow_eq_rowCompute 15 9 11 3 (by decide), + source_yRow_eq_rowCompute 15 9 11 4 (by decide), + source_yRow_eq_rowCompute 15 9 11 5 (by decide), + source_yRow_eq_rowCompute 15 9 11 6 (by decide), + computeRow_15_9_11_0, computeRow_15_9_11_1, computeRow_15_9_11_2, computeRow_15_9_11_3, computeRow_15_9_11_4, computeRow_15_9_11_5, computeRow_15_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_9_13 : Y 15 9 13 = (-270537545003843608530039/65536000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 9 13 0 (by decide), + source_yRow_eq_rowCompute 15 9 13 1 (by decide), + source_yRow_eq_rowCompute 15 9 13 2 (by decide), + source_yRow_eq_rowCompute 15 9 13 3 (by decide), + source_yRow_eq_rowCompute 15 9 13 4 (by decide), + source_yRow_eq_rowCompute 15 9 13 5 (by decide), + source_yRow_eq_rowCompute 15 9 13 6 (by decide), + computeRow_15_9_13_0, computeRow_15_9_13_1, computeRow_15_9_13_2, computeRow_15_9_13_3, computeRow_15_9_13_4, computeRow_15_9_13_5, computeRow_15_9_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_9_15 : Y 15 9 15 = (488416974255188057862783/1310720000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 9 15 0 (by decide), + source_yRow_eq_rowCompute 15 9 15 1 (by decide), + source_yRow_eq_rowCompute 15 9 15 2 (by decide), + source_yRow_eq_rowCompute 15 9 15 3 (by decide), + source_yRow_eq_rowCompute 15 9 15 4 (by decide), + source_yRow_eq_rowCompute 15 9 15 5 (by decide), + source_yRow_eq_rowCompute 15 9 15 6 (by decide), + computeRow_15_9_15_0, computeRow_15_9_15_1, computeRow_15_9_15_2, computeRow_15_9_15_3, computeRow_15_9_15_4, computeRow_15_9_15_5, computeRow_15_9_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_11_11 : Y 15 11 11 = (103242122786757662097687/32768000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 11 11 0 (by decide), + source_yRow_eq_rowCompute 15 11 11 1 (by decide), + source_yRow_eq_rowCompute 15 11 11 2 (by decide), + source_yRow_eq_rowCompute 15 11 11 3 (by decide), + source_yRow_eq_rowCompute 15 11 11 4 (by decide), + source_yRow_eq_rowCompute 15 11 11 5 (by decide), + source_yRow_eq_rowCompute 15 11 11 6 (by decide), + computeRow_15_11_11_0, computeRow_15_11_11_1, computeRow_15_11_11_2, computeRow_15_11_11_3, computeRow_15_11_11_4, computeRow_15_11_11_5, computeRow_15_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_11_13 : Y 15 11 13 = (-1188419411670004290171681/32768000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 11 13 0 (by decide), + source_yRow_eq_rowCompute 15 11 13 1 (by decide), + source_yRow_eq_rowCompute 15 11 13 2 (by decide), + source_yRow_eq_rowCompute 15 11 13 3 (by decide), + source_yRow_eq_rowCompute 15 11 13 4 (by decide), + source_yRow_eq_rowCompute 15 11 13 5 (by decide), + source_yRow_eq_rowCompute 15 11 13 6 (by decide), + computeRow_15_11_13_0, computeRow_15_11_13_1, computeRow_15_11_13_2, computeRow_15_11_13_3, computeRow_15_11_13_4, computeRow_15_11_13_5, computeRow_15_11_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_11_15 : Y 15 11 15 = (-946932022961651320973379/3276800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 11 15 0 (by decide), + source_yRow_eq_rowCompute 15 11 15 1 (by decide), + source_yRow_eq_rowCompute 15 11 15 2 (by decide), + source_yRow_eq_rowCompute 15 11 15 3 (by decide), + source_yRow_eq_rowCompute 15 11 15 4 (by decide), + source_yRow_eq_rowCompute 15 11 15 5 (by decide), + source_yRow_eq_rowCompute 15 11 15 6 (by decide), + computeRow_15_11_15_0, computeRow_15_11_15_1, computeRow_15_11_15_2, computeRow_15_11_15_3, computeRow_15_11_15_4, computeRow_15_11_15_5, computeRow_15_11_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_13_13 : Y 15 13 13 = (-13385634727914986582216457/32768000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 13 13 0 (by decide), + source_yRow_eq_rowCompute 15 13 13 1 (by decide), + source_yRow_eq_rowCompute 15 13 13 2 (by decide), + source_yRow_eq_rowCompute 15 13 13 3 (by decide), + source_yRow_eq_rowCompute 15 13 13 4 (by decide), + source_yRow_eq_rowCompute 15 13 13 5 (by decide), + source_yRow_eq_rowCompute 15 13 13 6 (by decide), + computeRow_15_13_13_0, computeRow_15_13_13_1, computeRow_15_13_13_2, computeRow_15_13_13_3, computeRow_15_13_13_4, computeRow_15_13_13_5, computeRow_15_13_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_13_15 : Y 15 13 15 = (6044229669744752465993013/3276800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 13 15 0 (by decide), + source_yRow_eq_rowCompute 15 13 15 1 (by decide), + source_yRow_eq_rowCompute 15 13 15 2 (by decide), + source_yRow_eq_rowCompute 15 13 15 3 (by decide), + source_yRow_eq_rowCompute 15 13 15 4 (by decide), + source_yRow_eq_rowCompute 15 13 15 5 (by decide), + source_yRow_eq_rowCompute 15 13 15 6 (by decide), + computeRow_15_13_15_0, computeRow_15_13_15_1, computeRow_15_13_15_2, computeRow_15_13_15_3, computeRow_15_13_15_4, computeRow_15_13_15_5, computeRow_15_13_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_15_15_15 : Y 15 15 15 = (-31526289117493065494479881/327680000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 15 15 15 0 (by decide), + source_yRow_eq_rowCompute 15 15 15 1 (by decide), + source_yRow_eq_rowCompute 15 15 15 2 (by decide), + source_yRow_eq_rowCompute 15 15 15 3 (by decide), + source_yRow_eq_rowCompute 15 15 15 4 (by decide), + source_yRow_eq_rowCompute 15 15 15 5 (by decide), + source_yRow_eq_rowCompute 15 15 15 6 (by decide), + computeRow_15_15_15_0, computeRow_15_15_15_1, computeRow_15_15_15_2, computeRow_15_15_15_3, computeRow_15_15_15_4, computeRow_15_15_15_5, computeRow_15_15_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_15_1_1 : Z 15 1 1 = (174356582400 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_1_1 + +theorem source_gram_15_1_3 : Z 15 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_1_3 + +theorem source_gram_15_1_5 : Z 15 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_1_5 + +theorem source_gram_15_1_7 : Z 15 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_1_7 + +theorem source_gram_15_1_9 : Z 15 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_1_9 + +theorem source_gram_15_1_11 : Z 15 1 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_1_11 + +theorem source_gram_15_1_13 : Z 15 1 13 = (-2724321600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_1_13 + +theorem source_gram_15_1_15 : Z 15 1 15 = (122594472000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_1_15 + +theorem source_gram_15_3_3 : Z 15 3 3 = (2874009600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_3_3 + +theorem source_gram_15_3_5 : Z 15 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_3_5 + +theorem source_gram_15_3_7 : Z 15 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_3_7 + +theorem source_gram_15_3_9 : Z 15 3 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_3_9 + +theorem source_gram_15_3_11 : Z 15 3 11 = (-179625600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_3_11 + +theorem source_gram_15_3_13 : Z 15 3 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_3_13 + +theorem source_gram_15_3_15 : Z 15 3 15 = (40864824000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_3_15 + +theorem source_gram_15_5_5 : Z 15 5 5 = (435456000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_5_5 + +theorem source_gram_15_5_7 : Z 15 5 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_5_7 + +theorem source_gram_15_5_9 : Z 15 5 9 = (-40824000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_5_9 + +theorem source_gram_15_5_11 : Z 15 5 11 = (-299376000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_5_11 + +theorem source_gram_15_5_13 : Z 15 5 13 = (1459458000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_5_13 + +theorem source_gram_15_5_15 : Z 15 5 15 = (10216206000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_5_15 + +theorem source_gram_15_7_7 : Z 15 7 7 = (177811200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_7_7 + +theorem source_gram_15_7_9 : Z 15 7 9 = (-171460800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_7_9 + +theorem source_gram_15_7_11 : Z 15 7 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_7_11 + +theorem source_gram_15_7_13 : Z 15 7 13 = (681080400 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_7_13 + +theorem source_gram_15_7_15 : Z 15 7 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_7_15 + +theorem source_gram_15_9_9 : Z 15 9 9 = (175543200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_9_9 + +theorem source_gram_15_9_11 : Z 15 9 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_9_11 + +theorem source_gram_15_9_13 : Z 15 9 13 = (-656756100 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_9_13 + +theorem source_gram_15_9_15 : Z 15 9 15 = (-2554051500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_9_15 + +theorem source_gram_15_11_11 : Z 15 11 11 = (340540200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_11_11 + +theorem source_gram_15_11_13 : Z 15 11 13 = (-1605403800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_11_13 + +theorem source_gram_15_11_15 : Z 15 11 15 = (-2554051500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_11_15 + +theorem source_gram_15_13_13 : Z 15 13 13 = (10477692225 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_13_13 + +theorem source_gram_15_13_15 : Z 15 13 15 = (-1915538625 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_13_15 + +theorem source_gram_15_15_15 : Z 15 15 15 = (1306397342250 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_15_15_15 + +theorem source_error_15_3_1 : Y 15 3 1 = (527769145158896263581537579/2097152000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_1_3 + +theorem source_gram_15_3_1 : Z 15 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_1_3 + +theorem source_error_15_5_1 : Y 15 5 1 = (-364633884256427977153375413/1677721600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_1_5 + +theorem source_gram_15_5_1 : Z 15 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_1_5 + +theorem source_error_15_5_3 : Y 15 5 3 = (10380910649344519579874271/838860800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_3_5 + +theorem source_gram_15_5_3 : Z 15 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_3_5 + +theorem source_error_15_7_1 : Y 15 7 1 = (70800295830292526868599229/838860800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_1_7 + +theorem source_gram_15_7_1 : Z 15 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_1_7 + +theorem source_error_15_7_3 : Y 15 7 3 = (2399450471501791440121389/419430400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_3_7 + +theorem source_gram_15_7_3 : Z 15 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_3_7 + +theorem source_error_15_7_5 : Y 15 7 5 = (-1550173356554793074510931/838860800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_5_7 + +theorem source_gram_15_7_5 : Z 15 7 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_5_7 + +theorem source_error_15_9_1 : Y 15 9 1 = (-213215905018995130639958571/1048576000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_1_9 + +theorem source_gram_15_9_1 : Z 15 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_1_9 + +theorem source_error_15_9_3 : Y 15 9 3 = (7831247768240800098462597/524288000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_3_9 + +theorem source_gram_15_9_3 : Z 15 9 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_3_9 + +theorem source_error_15_9_5 : Y 15 9 5 = (-251612565167710626302493/209715200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_5_9 + +theorem source_gram_15_9_5 : Z 15 9 5 = (-40824000 : ℚ) := by + rw [Z_symm] + exact source_gram_15_5_9 + +theorem source_error_15_9_7 : Y 15 9 7 = (483384920806779568744041/524288000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_7_9 + +theorem source_gram_15_9_7 : Z 15 9 7 = (-171460800 : ℚ) := by + rw [Z_symm] + exact source_gram_15_7_9 + +theorem source_error_15_11_1 : Y 15 11 1 = (-236988935373506936612565573/524288000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_1_11 + +theorem source_gram_15_11_1 : Z 15 11 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_1_11 + +theorem source_error_15_11_3 : Y 15 11 3 = (260365051976410952573409/52428800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_3_11 + +theorem source_gram_15_11_3 : Z 15 11 3 = (-179625600 : ℚ) := by + rw [Z_symm] + exact source_gram_15_3_11 + +theorem source_error_15_11_5 : Y 15 11 5 = (412467042517374252900789/104857600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_5_11 + +theorem source_gram_15_11_5 : Z 15 11 5 = (-299376000 : ℚ) := by + rw [Z_symm] + exact source_gram_15_5_11 + +theorem source_error_15_11_7 : Y 15 11 7 = (-2196385127442123145785873/262144000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_7_11 + +theorem source_gram_15_11_7 : Z 15 11 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_7_11 + +theorem source_error_15_11_9 : Y 15 11 9 = (144198476217622441333917/65536000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_9_11 + +theorem source_gram_15_11_9 : Z 15 11 9 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_9_11 + +theorem source_error_15_13_1 : Y 15 13 1 = (374746885492881333249210393/524288000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_1_13 + +theorem source_gram_15_13_1 : Z 15 13 1 = (-2724321600 : ℚ) := by + rw [Z_symm] + exact source_gram_15_1_13 + +theorem source_error_15_13_3 : Y 15 13 3 = (15417580069242120546303813/262144000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_3_13 + +theorem source_gram_15_13_3 : Z 15 13 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_3_13 + +theorem source_error_15_13_5 : Y 15 13 5 = (-3917597116231063282740723/104857600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_5_13 + +theorem source_gram_15_13_5 : Z 15 13 5 = (1459458000 : ℚ) := by + rw [Z_symm] + exact source_gram_15_5_13 + +theorem source_error_15_13_7 : Y 15 13 7 = (-3020058706667129324414217/262144000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_7_13 + +theorem source_gram_15_13_7 : Z 15 13 7 = (681080400 : ℚ) := by + rw [Z_symm] + exact source_gram_15_7_13 + +theorem source_error_15_13_9 : Y 15 13 9 = (-270537545003843608530039/65536000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_9_13 + +theorem source_gram_15_13_9 : Z 15 13 9 = (-656756100 : ℚ) := by + rw [Z_symm] + exact source_gram_15_9_13 + +theorem source_error_15_13_11 : Y 15 13 11 = (-1188419411670004290171681/32768000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_11_13 + +theorem source_gram_15_13_11 : Z 15 13 11 = (-1605403800 : ℚ) := by + rw [Z_symm] + exact source_gram_15_11_13 + +theorem source_error_15_15_1 : Y 15 15 1 = (-1454272995490648196091417189/52428800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_1_15 + +theorem source_gram_15_15_1 : Z 15 15 1 = (122594472000 : ℚ) := by + rw [Z_symm] + exact source_gram_15_1_15 + +theorem source_error_15_15_3 : Y 15 15 3 = (-19651317795670208550803901/26214400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_3_15 + +theorem source_gram_15_15_3 : Z 15 15 3 = (40864824000 : ℚ) := by + rw [Z_symm] + exact source_gram_15_3_15 + +theorem source_error_15_15_5 : Y 15 15 5 = (6737890215993101774728119/10485760000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_5_15 + +theorem source_gram_15_15_5 : Z 15 15 5 = (10216206000 : ℚ) := by + rw [Z_symm] + exact source_gram_15_5_15 + +theorem source_error_15_15_7 : Y 15 15 7 = (6630571266894369608354541/26214400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_7_15 + +theorem source_gram_15_15_7 : Z 15 15 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_15_7_15 + +theorem source_error_15_15_9 : Y 15 15 9 = (488416974255188057862783/1310720000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_9_15 + +theorem source_gram_15_15_9 : Z 15 15 9 = (-2554051500 : ℚ) := by + rw [Z_symm] + exact source_gram_15_9_15 + +theorem source_error_15_15_11 : Y 15 15 11 = (-946932022961651320973379/3276800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_11_15 + +theorem source_gram_15_15_11 : Z 15 15 11 = (-2554051500 : ℚ) := by + rw [Z_symm] + exact source_gram_15_11_15 + +theorem source_error_15_15_13 : Y 15 15 13 = (6044229669744752465993013/3276800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_15_13_15 + +theorem source_gram_15_15_13 : Z 15 15 13 = (-1915538625 : ℚ) := by + rw [Z_symm] + exact source_gram_15_13_15 + +theorem error_15 : errorRational 15 = candidateY_15 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_15_1_1 + · exact source_error_15_1_3 + · exact source_error_15_1_5 + · exact source_error_15_1_7 + · exact source_error_15_1_9 + · exact source_error_15_1_11 + · exact source_error_15_1_13 + · exact source_error_15_1_15 + · exact source_error_15_3_1 + · exact source_error_15_3_3 + · exact source_error_15_3_5 + · exact source_error_15_3_7 + · exact source_error_15_3_9 + · exact source_error_15_3_11 + · exact source_error_15_3_13 + · exact source_error_15_3_15 + · exact source_error_15_5_1 + · exact source_error_15_5_3 + · exact source_error_15_5_5 + · exact source_error_15_5_7 + · exact source_error_15_5_9 + · exact source_error_15_5_11 + · exact source_error_15_5_13 + · exact source_error_15_5_15 + · exact source_error_15_7_1 + · exact source_error_15_7_3 + · exact source_error_15_7_5 + · exact source_error_15_7_7 + · exact source_error_15_7_9 + · exact source_error_15_7_11 + · exact source_error_15_7_13 + · exact source_error_15_7_15 + · exact source_error_15_9_1 + · exact source_error_15_9_3 + · exact source_error_15_9_5 + · exact source_error_15_9_7 + · exact source_error_15_9_9 + · exact source_error_15_9_11 + · exact source_error_15_9_13 + · exact source_error_15_9_15 + · exact source_error_15_11_1 + · exact source_error_15_11_3 + · exact source_error_15_11_5 + · exact source_error_15_11_7 + · exact source_error_15_11_9 + · exact source_error_15_11_11 + · exact source_error_15_11_13 + · exact source_error_15_11_15 + · exact source_error_15_13_1 + · exact source_error_15_13_3 + · exact source_error_15_13_5 + · exact source_error_15_13_7 + · exact source_error_15_13_9 + · exact source_error_15_13_11 + · exact source_error_15_13_13 + · exact source_error_15_13_15 + · exact source_error_15_15_1 + · exact source_error_15_15_3 + · exact source_error_15_15_5 + · exact source_error_15_15_7 + · exact source_error_15_15_9 + · exact source_error_15_15_11 + · exact source_error_15_15_13 + · exact source_error_15_15_15 + +theorem gram_15 : gramRational 15 = candidateZ_15 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_15_1_1 + · exact source_gram_15_1_3 + · exact source_gram_15_1_5 + · exact source_gram_15_1_7 + · exact source_gram_15_1_9 + · exact source_gram_15_1_11 + · exact source_gram_15_1_13 + · exact source_gram_15_1_15 + · exact source_gram_15_3_1 + · exact source_gram_15_3_3 + · exact source_gram_15_3_5 + · exact source_gram_15_3_7 + · exact source_gram_15_3_9 + · exact source_gram_15_3_11 + · exact source_gram_15_3_13 + · exact source_gram_15_3_15 + · exact source_gram_15_5_1 + · exact source_gram_15_5_3 + · exact source_gram_15_5_5 + · exact source_gram_15_5_7 + · exact source_gram_15_5_9 + · exact source_gram_15_5_11 + · exact source_gram_15_5_13 + · exact source_gram_15_5_15 + · exact source_gram_15_7_1 + · exact source_gram_15_7_3 + · exact source_gram_15_7_5 + · exact source_gram_15_7_7 + · exact source_gram_15_7_9 + · exact source_gram_15_7_11 + · exact source_gram_15_7_13 + · exact source_gram_15_7_15 + · exact source_gram_15_9_1 + · exact source_gram_15_9_3 + · exact source_gram_15_9_5 + · exact source_gram_15_9_7 + · exact source_gram_15_9_9 + · exact source_gram_15_9_11 + · exact source_gram_15_9_13 + · exact source_gram_15_9_15 + · exact source_gram_15_11_1 + · exact source_gram_15_11_3 + · exact source_gram_15_11_5 + · exact source_gram_15_11_7 + · exact source_gram_15_11_9 + · exact source_gram_15_11_11 + · exact source_gram_15_11_13 + · exact source_gram_15_11_15 + · exact source_gram_15_13_1 + · exact source_gram_15_13_3 + · exact source_gram_15_13_5 + · exact source_gram_15_13_7 + · exact source_gram_15_13_9 + · exact source_gram_15_13_11 + · exact source_gram_15_13_13 + · exact source_gram_15_13_15 + · exact source_gram_15_15_1 + · exact source_gram_15_15_3 + · exact source_gram_15_15_5 + · exact source_gram_15_15_7 + · exact source_gram_15_15_9 + · exact source_gram_15_15_11 + · exact source_gram_15_15_13 + · exact source_gram_15_15_15 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData16.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData16.lean new file mode 100644 index 0000000000000000000000000000000000000000..54868ca545b8618d3f2d8930ccdea04920bbb7e9 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData16.lean @@ -0,0 +1,954 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram01Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram03Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram05Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram07Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram11Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram13Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram151516 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0101Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0103Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0105Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0107Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0109Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0111Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0113Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0115Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0303Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0305Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0307Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0309Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0311Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0313Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0315Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0505Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0507Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0509Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0511Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0513Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0515Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0707Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0709Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0711Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0713Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0715Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0909Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0911Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0913Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0915Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1111Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1113Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1115Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1313Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1315Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1515Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.Data16 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_16_1_1 : Y 16 1 1 = (-2276708101299057121652517561/52428800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 1 1 0 (by decide), + source_yRow_eq_rowCompute 16 1 1 1 (by decide), + source_yRow_eq_rowCompute 16 1 1 2 (by decide), + source_yRow_eq_rowCompute 16 1 1 3 (by decide), + source_yRow_eq_rowCompute 16 1 1 4 (by decide), + source_yRow_eq_rowCompute 16 1 1 5 (by decide), + source_yRow_eq_rowCompute 16 1 1 6 (by decide), + computeRow_16_1_1_0, computeRow_16_1_1_1, computeRow_16_1_1_2, computeRow_16_1_1_3, computeRow_16_1_1_4, computeRow_16_1_1_5, computeRow_16_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_1_3 : Y 16 1 3 = (-39034614015379387104670971/13107200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 1 3 0 (by decide), + source_yRow_eq_rowCompute 16 1 3 1 (by decide), + source_yRow_eq_rowCompute 16 1 3 2 (by decide), + source_yRow_eq_rowCompute 16 1 3 3 (by decide), + source_yRow_eq_rowCompute 16 1 3 4 (by decide), + source_yRow_eq_rowCompute 16 1 3 5 (by decide), + source_yRow_eq_rowCompute 16 1 3 6 (by decide), + computeRow_16_1_3_0, computeRow_16_1_3_1, computeRow_16_1_3_2, computeRow_16_1_3_3, computeRow_16_1_3_4, computeRow_16_1_3_5, computeRow_16_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_1_5 : Y 16 1 5 = (78202406241711463127687271/83886080000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 1 5 0 (by decide), + source_yRow_eq_rowCompute 16 1 5 1 (by decide), + source_yRow_eq_rowCompute 16 1 5 2 (by decide), + source_yRow_eq_rowCompute 16 1 5 3 (by decide), + source_yRow_eq_rowCompute 16 1 5 4 (by decide), + source_yRow_eq_rowCompute 16 1 5 5 (by decide), + source_yRow_eq_rowCompute 16 1 5 6 (by decide), + computeRow_16_1_5_0, computeRow_16_1_5_1, computeRow_16_1_5_2, computeRow_16_1_5_3, computeRow_16_1_5_4, computeRow_16_1_5_5, computeRow_16_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_1_7 : Y 16 1 7 = (23832834670493732956060989/209715200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 1 7 0 (by decide), + source_yRow_eq_rowCompute 16 1 7 1 (by decide), + source_yRow_eq_rowCompute 16 1 7 2 (by decide), + source_yRow_eq_rowCompute 16 1 7 3 (by decide), + source_yRow_eq_rowCompute 16 1 7 4 (by decide), + source_yRow_eq_rowCompute 16 1 7 5 (by decide), + source_yRow_eq_rowCompute 16 1 7 6 (by decide), + computeRow_16_1_7_0, computeRow_16_1_7_1, computeRow_16_1_7_2, computeRow_16_1_7_3, computeRow_16_1_7_4, computeRow_16_1_7_5, computeRow_16_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_1_9 : Y 16 1 9 = (22048584820368310367604441/52428800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 1 9 0 (by decide), + source_yRow_eq_rowCompute 16 1 9 1 (by decide), + source_yRow_eq_rowCompute 16 1 9 2 (by decide), + source_yRow_eq_rowCompute 16 1 9 3 (by decide), + source_yRow_eq_rowCompute 16 1 9 4 (by decide), + source_yRow_eq_rowCompute 16 1 9 5 (by decide), + source_yRow_eq_rowCompute 16 1 9 6 (by decide), + computeRow_16_1_9_0, computeRow_16_1_9_1, computeRow_16_1_9_2, computeRow_16_1_9_3, computeRow_16_1_9_4, computeRow_16_1_9_5, computeRow_16_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_1_11 : Y 16 1 11 = (2553473034802720354150827/26214400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 1 11 0 (by decide), + source_yRow_eq_rowCompute 16 1 11 1 (by decide), + source_yRow_eq_rowCompute 16 1 11 2 (by decide), + source_yRow_eq_rowCompute 16 1 11 3 (by decide), + source_yRow_eq_rowCompute 16 1 11 4 (by decide), + source_yRow_eq_rowCompute 16 1 11 5 (by decide), + source_yRow_eq_rowCompute 16 1 11 6 (by decide), + computeRow_16_1_11_0, computeRow_16_1_11_1, computeRow_16_1_11_2, computeRow_16_1_11_3, computeRow_16_1_11_4, computeRow_16_1_11_5, computeRow_16_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_1_13 : Y 16 1 13 = (108255415269241130506236621/26214400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 1 13 0 (by decide), + source_yRow_eq_rowCompute 16 1 13 1 (by decide), + source_yRow_eq_rowCompute 16 1 13 2 (by decide), + source_yRow_eq_rowCompute 16 1 13 3 (by decide), + source_yRow_eq_rowCompute 16 1 13 4 (by decide), + source_yRow_eq_rowCompute 16 1 13 5 (by decide), + source_yRow_eq_rowCompute 16 1 13 6 (by decide), + computeRow_16_1_13_0, computeRow_16_1_13_1, computeRow_16_1_13_2, computeRow_16_1_13_3, computeRow_16_1_13_4, computeRow_16_1_13_5, computeRow_16_1_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_1_15 : Y 16 1 15 = (-41435755574383986458435793/2621440000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 1 15 0 (by decide), + source_yRow_eq_rowCompute 16 1 15 1 (by decide), + source_yRow_eq_rowCompute 16 1 15 2 (by decide), + source_yRow_eq_rowCompute 16 1 15 3 (by decide), + source_yRow_eq_rowCompute 16 1 15 4 (by decide), + source_yRow_eq_rowCompute 16 1 15 5 (by decide), + source_yRow_eq_rowCompute 16 1 15 6 (by decide), + computeRow_16_1_15_0, computeRow_16_1_15_1, computeRow_16_1_15_2, computeRow_16_1_15_3, computeRow_16_1_15_4, computeRow_16_1_15_5, computeRow_16_1_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_3_3 : Y 16 3 3 = (-374098046732570322778463991/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 3 3 0 (by decide), + source_yRow_eq_rowCompute 16 3 3 1 (by decide), + source_yRow_eq_rowCompute 16 3 3 2 (by decide), + source_yRow_eq_rowCompute 16 3 3 3 (by decide), + source_yRow_eq_rowCompute 16 3 3 4 (by decide), + source_yRow_eq_rowCompute 16 3 3 5 (by decide), + source_yRow_eq_rowCompute 16 3 3 6 (by decide), + computeRow_16_3_3_0, computeRow_16_3_3_1, computeRow_16_3_3_2, computeRow_16_3_3_3, computeRow_16_3_3_4, computeRow_16_3_3_5, computeRow_16_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_3_5 : Y 16 3 5 = (2737552373685628655395239/41943040000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 3 5 0 (by decide), + source_yRow_eq_rowCompute 16 3 5 1 (by decide), + source_yRow_eq_rowCompute 16 3 5 2 (by decide), + source_yRow_eq_rowCompute 16 3 5 3 (by decide), + source_yRow_eq_rowCompute 16 3 5 4 (by decide), + source_yRow_eq_rowCompute 16 3 5 5 (by decide), + source_yRow_eq_rowCompute 16 3 5 6 (by decide), + computeRow_16_3_5_0, computeRow_16_3_5_1, computeRow_16_3_5_2, computeRow_16_3_5_3, computeRow_16_3_5_4, computeRow_16_3_5_5, computeRow_16_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_3_7 : Y 16 3 7 = (22736583113602023500964129/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 3 7 0 (by decide), + source_yRow_eq_rowCompute 16 3 7 1 (by decide), + source_yRow_eq_rowCompute 16 3 7 2 (by decide), + source_yRow_eq_rowCompute 16 3 7 3 (by decide), + source_yRow_eq_rowCompute 16 3 7 4 (by decide), + source_yRow_eq_rowCompute 16 3 7 5 (by decide), + source_yRow_eq_rowCompute 16 3 7 6 (by decide), + computeRow_16_3_7_0, computeRow_16_3_7_1, computeRow_16_3_7_2, computeRow_16_3_7_3, computeRow_16_3_7_4, computeRow_16_3_7_5, computeRow_16_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_3_9 : Y 16 3 9 = (1851780972244557042321633/131072000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 3 9 0 (by decide), + source_yRow_eq_rowCompute 16 3 9 1 (by decide), + source_yRow_eq_rowCompute 16 3 9 2 (by decide), + source_yRow_eq_rowCompute 16 3 9 3 (by decide), + source_yRow_eq_rowCompute 16 3 9 4 (by decide), + source_yRow_eq_rowCompute 16 3 9 5 (by decide), + source_yRow_eq_rowCompute 16 3 9 6 (by decide), + computeRow_16_3_9_0, computeRow_16_3_9_1, computeRow_16_3_9_2, computeRow_16_3_9_3, computeRow_16_3_9_4, computeRow_16_3_9_5, computeRow_16_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_3_11 : Y 16 3 11 = (507618379345280460543/1310720000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 3 11 0 (by decide), + source_yRow_eq_rowCompute 16 3 11 1 (by decide), + source_yRow_eq_rowCompute 16 3 11 2 (by decide), + source_yRow_eq_rowCompute 16 3 11 3 (by decide), + source_yRow_eq_rowCompute 16 3 11 4 (by decide), + source_yRow_eq_rowCompute 16 3 11 5 (by decide), + source_yRow_eq_rowCompute 16 3 11 6 (by decide), + computeRow_16_3_11_0, computeRow_16_3_11_1, computeRow_16_3_11_2, computeRow_16_3_11_3, computeRow_16_3_11_4, computeRow_16_3_11_5, computeRow_16_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_3_13 : Y 16 3 13 = (32584839756386941473215337/65536000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 3 13 0 (by decide), + source_yRow_eq_rowCompute 16 3 13 1 (by decide), + source_yRow_eq_rowCompute 16 3 13 2 (by decide), + source_yRow_eq_rowCompute 16 3 13 3 (by decide), + source_yRow_eq_rowCompute 16 3 13 4 (by decide), + source_yRow_eq_rowCompute 16 3 13 5 (by decide), + source_yRow_eq_rowCompute 16 3 13 6 (by decide), + computeRow_16_3_13_0, computeRow_16_3_13_1, computeRow_16_3_13_2, computeRow_16_3_13_3, computeRow_16_3_13_4, computeRow_16_3_13_5, computeRow_16_3_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_3_15 : Y 16 3 15 = (-12977256793584317385992841/6553600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 3 15 0 (by decide), + source_yRow_eq_rowCompute 16 3 15 1 (by decide), + source_yRow_eq_rowCompute 16 3 15 2 (by decide), + source_yRow_eq_rowCompute 16 3 15 3 (by decide), + source_yRow_eq_rowCompute 16 3 15 4 (by decide), + source_yRow_eq_rowCompute 16 3 15 5 (by decide), + source_yRow_eq_rowCompute 16 3 15 6 (by decide), + computeRow_16_3_15_0, computeRow_16_3_15_1, computeRow_16_3_15_2, computeRow_16_3_15_3, computeRow_16_3_15_4, computeRow_16_3_15_5, computeRow_16_3_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_5_5 : Y 16 5 5 = (-2533363535515609982834649/83886080000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 5 5 0 (by decide), + source_yRow_eq_rowCompute 16 5 5 1 (by decide), + source_yRow_eq_rowCompute 16 5 5 2 (by decide), + source_yRow_eq_rowCompute 16 5 5 3 (by decide), + source_yRow_eq_rowCompute 16 5 5 4 (by decide), + source_yRow_eq_rowCompute 16 5 5 5 (by decide), + source_yRow_eq_rowCompute 16 5 5 6 (by decide), + computeRow_16_5_5_0, computeRow_16_5_5_1, computeRow_16_5_5_2, computeRow_16_5_5_3, computeRow_16_5_5_4, computeRow_16_5_5_5, computeRow_16_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_5_7 : Y 16 5 7 = (1549750421445905525422653/209715200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 5 7 0 (by decide), + source_yRow_eq_rowCompute 16 5 7 1 (by decide), + source_yRow_eq_rowCompute 16 5 7 2 (by decide), + source_yRow_eq_rowCompute 16 5 7 3 (by decide), + source_yRow_eq_rowCompute 16 5 7 4 (by decide), + source_yRow_eq_rowCompute 16 5 7 5 (by decide), + source_yRow_eq_rowCompute 16 5 7 6 (by decide), + computeRow_16_5_7_0, computeRow_16_5_7_1, computeRow_16_5_7_2, computeRow_16_5_7_3, computeRow_16_5_7_4, computeRow_16_5_7_5, computeRow_16_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_5_9 : Y 16 5 9 = (-611154627229412014141701/52428800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 5 9 0 (by decide), + source_yRow_eq_rowCompute 16 5 9 1 (by decide), + source_yRow_eq_rowCompute 16 5 9 2 (by decide), + source_yRow_eq_rowCompute 16 5 9 3 (by decide), + source_yRow_eq_rowCompute 16 5 9 4 (by decide), + source_yRow_eq_rowCompute 16 5 9 5 (by decide), + source_yRow_eq_rowCompute 16 5 9 6 (by decide), + computeRow_16_5_9_0, computeRow_16_5_9_1, computeRow_16_5_9_2, computeRow_16_5_9_3, computeRow_16_5_9_4, computeRow_16_5_9_5, computeRow_16_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_5_11 : Y 16 5 11 = (-578745616368603039939/41943040000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 5 11 0 (by decide), + source_yRow_eq_rowCompute 16 5 11 1 (by decide), + source_yRow_eq_rowCompute 16 5 11 2 (by decide), + source_yRow_eq_rowCompute 16 5 11 3 (by decide), + source_yRow_eq_rowCompute 16 5 11 4 (by decide), + source_yRow_eq_rowCompute 16 5 11 5 (by decide), + source_yRow_eq_rowCompute 16 5 11 6 (by decide), + computeRow_16_5_11_0, computeRow_16_5_11_1, computeRow_16_5_11_2, computeRow_16_5_11_3, computeRow_16_5_11_4, computeRow_16_5_11_5, computeRow_16_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_5_13 : Y 16 5 13 = (-64505141078209101647091/1048576000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 5 13 0 (by decide), + source_yRow_eq_rowCompute 16 5 13 1 (by decide), + source_yRow_eq_rowCompute 16 5 13 2 (by decide), + source_yRow_eq_rowCompute 16 5 13 3 (by decide), + source_yRow_eq_rowCompute 16 5 13 4 (by decide), + source_yRow_eq_rowCompute 16 5 13 5 (by decide), + source_yRow_eq_rowCompute 16 5 13 6 (by decide), + computeRow_16_5_13_0, computeRow_16_5_13_1, computeRow_16_5_13_2, computeRow_16_5_13_3, computeRow_16_5_13_4, computeRow_16_5_13_5, computeRow_16_5_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_5_15 : Y 16 5 15 = (-99002192076248555811717/524288000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 5 15 0 (by decide), + source_yRow_eq_rowCompute 16 5 15 1 (by decide), + source_yRow_eq_rowCompute 16 5 15 2 (by decide), + source_yRow_eq_rowCompute 16 5 15 3 (by decide), + source_yRow_eq_rowCompute 16 5 15 4 (by decide), + source_yRow_eq_rowCompute 16 5 15 5 (by decide), + source_yRow_eq_rowCompute 16 5 15 6 (by decide), + computeRow_16_5_15_0, computeRow_16_5_15_1, computeRow_16_5_15_2, computeRow_16_5_15_3, computeRow_16_5_15_4, computeRow_16_5_15_5, computeRow_16_5_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_7_7 : Y 16 7 7 = (-11434119007650938281635057/524288000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 7 7 0 (by decide), + source_yRow_eq_rowCompute 16 7 7 1 (by decide), + source_yRow_eq_rowCompute 16 7 7 2 (by decide), + source_yRow_eq_rowCompute 16 7 7 3 (by decide), + source_yRow_eq_rowCompute 16 7 7 4 (by decide), + source_yRow_eq_rowCompute 16 7 7 5 (by decide), + source_yRow_eq_rowCompute 16 7 7 6 (by decide), + computeRow_16_7_7_0, computeRow_16_7_7_1, computeRow_16_7_7_2, computeRow_16_7_7_3, computeRow_16_7_7_4, computeRow_16_7_7_5, computeRow_16_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_7_9 : Y 16 7 9 = (1484433801775108633948569/131072000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 7 9 0 (by decide), + source_yRow_eq_rowCompute 16 7 9 1 (by decide), + source_yRow_eq_rowCompute 16 7 9 2 (by decide), + source_yRow_eq_rowCompute 16 7 9 3 (by decide), + source_yRow_eq_rowCompute 16 7 9 4 (by decide), + source_yRow_eq_rowCompute 16 7 9 5 (by decide), + source_yRow_eq_rowCompute 16 7 9 6 (by decide), + computeRow_16_7_9_0, computeRow_16_7_9_1, computeRow_16_7_9_2, computeRow_16_7_9_3, computeRow_16_7_9_4, computeRow_16_7_9_5, computeRow_16_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_7_11 : Y 16 7 11 = (207943103777772680639091/13107200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 7 11 0 (by decide), + source_yRow_eq_rowCompute 16 7 11 1 (by decide), + source_yRow_eq_rowCompute 16 7 11 2 (by decide), + source_yRow_eq_rowCompute 16 7 11 3 (by decide), + source_yRow_eq_rowCompute 16 7 11 4 (by decide), + source_yRow_eq_rowCompute 16 7 11 5 (by decide), + source_yRow_eq_rowCompute 16 7 11 6 (by decide), + computeRow_16_7_11_0, computeRow_16_7_11_1, computeRow_16_7_11_2, computeRow_16_7_11_3, computeRow_16_7_11_4, computeRow_16_7_11_5, computeRow_16_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_7_13 : Y 16 7 13 = (-8974467290230038089021529/65536000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 7 13 0 (by decide), + source_yRow_eq_rowCompute 16 7 13 1 (by decide), + source_yRow_eq_rowCompute 16 7 13 2 (by decide), + source_yRow_eq_rowCompute 16 7 13 3 (by decide), + source_yRow_eq_rowCompute 16 7 13 4 (by decide), + source_yRow_eq_rowCompute 16 7 13 5 (by decide), + source_yRow_eq_rowCompute 16 7 13 6 (by decide), + computeRow_16_7_13_0, computeRow_16_7_13_1, computeRow_16_7_13_2, computeRow_16_7_13_3, computeRow_16_7_13_4, computeRow_16_7_13_5, computeRow_16_7_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_7_15 : Y 16 7 15 = (4777756237785689667105597/6553600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 7 15 0 (by decide), + source_yRow_eq_rowCompute 16 7 15 1 (by decide), + source_yRow_eq_rowCompute 16 7 15 2 (by decide), + source_yRow_eq_rowCompute 16 7 15 3 (by decide), + source_yRow_eq_rowCompute 16 7 15 4 (by decide), + source_yRow_eq_rowCompute 16 7 15 5 (by decide), + source_yRow_eq_rowCompute 16 7 15 6 (by decide), + computeRow_16_7_15_0, computeRow_16_7_15_1, computeRow_16_7_15_2, computeRow_16_7_15_3, computeRow_16_7_15_4, computeRow_16_7_15_5, computeRow_16_7_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_9_9 : Y 16 9 9 = (-621920505954394918130013/32768000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 9 9 0 (by decide), + source_yRow_eq_rowCompute 16 9 9 1 (by decide), + source_yRow_eq_rowCompute 16 9 9 2 (by decide), + source_yRow_eq_rowCompute 16 9 9 3 (by decide), + source_yRow_eq_rowCompute 16 9 9 4 (by decide), + source_yRow_eq_rowCompute 16 9 9 5 (by decide), + source_yRow_eq_rowCompute 16 9 9 6 (by decide), + computeRow_16_9_9_0, computeRow_16_9_9_1, computeRow_16_9_9_2, computeRow_16_9_9_3, computeRow_16_9_9_4, computeRow_16_9_9_5, computeRow_16_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_9_11 : Y 16 9 11 = (-28769175431642817466911/3276800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 9 11 0 (by decide), + source_yRow_eq_rowCompute 16 9 11 1 (by decide), + source_yRow_eq_rowCompute 16 9 11 2 (by decide), + source_yRow_eq_rowCompute 16 9 11 3 (by decide), + source_yRow_eq_rowCompute 16 9 11 4 (by decide), + source_yRow_eq_rowCompute 16 9 11 5 (by decide), + source_yRow_eq_rowCompute 16 9 11 6 (by decide), + computeRow_16_9_11_0, computeRow_16_9_11_1, computeRow_16_9_11_2, computeRow_16_9_11_3, computeRow_16_9_11_4, computeRow_16_9_11_5, computeRow_16_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_9_13 : Y 16 9 13 = (1147904288009241919132977/16384000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 9 13 0 (by decide), + source_yRow_eq_rowCompute 16 9 13 1 (by decide), + source_yRow_eq_rowCompute 16 9 13 2 (by decide), + source_yRow_eq_rowCompute 16 9 13 3 (by decide), + source_yRow_eq_rowCompute 16 9 13 4 (by decide), + source_yRow_eq_rowCompute 16 9 13 5 (by decide), + source_yRow_eq_rowCompute 16 9 13 6 (by decide), + computeRow_16_9_13_0, computeRow_16_9_13_1, computeRow_16_9_13_2, computeRow_16_9_13_3, computeRow_16_9_13_4, computeRow_16_9_13_5, computeRow_16_9_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_9_15 : Y 16 9 15 = (68877548037338038801803/1638400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 9 15 0 (by decide), + source_yRow_eq_rowCompute 16 9 15 1 (by decide), + source_yRow_eq_rowCompute 16 9 15 2 (by decide), + source_yRow_eq_rowCompute 16 9 15 3 (by decide), + source_yRow_eq_rowCompute 16 9 15 4 (by decide), + source_yRow_eq_rowCompute 16 9 15 5 (by decide), + source_yRow_eq_rowCompute 16 9 15 6 (by decide), + computeRow_16_9_15_0, computeRow_16_9_15_1, computeRow_16_9_15_2, computeRow_16_9_15_3, computeRow_16_9_15_4, computeRow_16_9_15_5, computeRow_16_9_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_11_11 : Y 16 11 11 = (-47586420975452552673183/1638400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 11 11 0 (by decide), + source_yRow_eq_rowCompute 16 11 11 1 (by decide), + source_yRow_eq_rowCompute 16 11 11 2 (by decide), + source_yRow_eq_rowCompute 16 11 11 3 (by decide), + source_yRow_eq_rowCompute 16 11 11 4 (by decide), + source_yRow_eq_rowCompute 16 11 11 5 (by decide), + source_yRow_eq_rowCompute 16 11 11 6 (by decide), + computeRow_16_11_11_0, computeRow_16_11_11_1, computeRow_16_11_11_2, computeRow_16_11_11_3, computeRow_16_11_11_4, computeRow_16_11_11_5, computeRow_16_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_11_13 : Y 16 11 13 = (189274484540778686288811/1638400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 11 13 0 (by decide), + source_yRow_eq_rowCompute 16 11 13 1 (by decide), + source_yRow_eq_rowCompute 16 11 13 2 (by decide), + source_yRow_eq_rowCompute 16 11 13 3 (by decide), + source_yRow_eq_rowCompute 16 11 13 4 (by decide), + source_yRow_eq_rowCompute 16 11 13 5 (by decide), + source_yRow_eq_rowCompute 16 11 13 6 (by decide), + computeRow_16_11_13_0, computeRow_16_11_13_1, computeRow_16_11_13_2, computeRow_16_11_13_3, computeRow_16_11_13_4, computeRow_16_11_13_5, computeRow_16_11_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_11_15 : Y 16 11 15 = (-71581303517955662317887/163840000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 11 15 0 (by decide), + source_yRow_eq_rowCompute 16 11 15 1 (by decide), + source_yRow_eq_rowCompute 16 11 15 2 (by decide), + source_yRow_eq_rowCompute 16 11 15 3 (by decide), + source_yRow_eq_rowCompute 16 11 15 4 (by decide), + source_yRow_eq_rowCompute 16 11 15 5 (by decide), + source_yRow_eq_rowCompute 16 11 15 6 (by decide), + computeRow_16_11_15_0, computeRow_16_11_15_1, computeRow_16_11_15_2, computeRow_16_11_15_3, computeRow_16_11_15_4, computeRow_16_11_15_5, computeRow_16_11_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_13_13 : Y 16 13 13 = (-7689933670205658822668289/8192000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 13 13 0 (by decide), + source_yRow_eq_rowCompute 16 13 13 1 (by decide), + source_yRow_eq_rowCompute 16 13 13 2 (by decide), + source_yRow_eq_rowCompute 16 13 13 3 (by decide), + source_yRow_eq_rowCompute 16 13 13 4 (by decide), + source_yRow_eq_rowCompute 16 13 13 5 (by decide), + source_yRow_eq_rowCompute 16 13 13 6 (by decide), + computeRow_16_13_13_0, computeRow_16_13_13_1, computeRow_16_13_13_2, computeRow_16_13_13_3, computeRow_16_13_13_4, computeRow_16_13_13_5, computeRow_16_13_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_13_15 : Y 16 13 15 = (384276867404942369454597/819200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 13 15 0 (by decide), + source_yRow_eq_rowCompute 16 13 15 1 (by decide), + source_yRow_eq_rowCompute 16 13 15 2 (by decide), + source_yRow_eq_rowCompute 16 13 15 3 (by decide), + source_yRow_eq_rowCompute 16 13 15 4 (by decide), + source_yRow_eq_rowCompute 16 13 15 5 (by decide), + source_yRow_eq_rowCompute 16 13 15 6 (by decide), + computeRow_16_13_15_0, computeRow_16_13_15_1, computeRow_16_13_15_2, computeRow_16_13_15_3, computeRow_16_13_15_4, computeRow_16_13_15_5, computeRow_16_13_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_16_15_15 : Y 16 15 15 = (-2280462391086995129495481/81920000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 16 15 15 0 (by decide), + source_yRow_eq_rowCompute 16 15 15 1 (by decide), + source_yRow_eq_rowCompute 16 15 15 2 (by decide), + source_yRow_eq_rowCompute 16 15 15 3 (by decide), + source_yRow_eq_rowCompute 16 15 15 4 (by decide), + source_yRow_eq_rowCompute 16 15 15 5 (by decide), + source_yRow_eq_rowCompute 16 15 15 6 (by decide), + computeRow_16_15_15_0, computeRow_16_15_15_1, computeRow_16_15_15_2, computeRow_16_15_15_3, computeRow_16_15_15_4, computeRow_16_15_15_5, computeRow_16_15_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_16_1_1 : Z 16 1 1 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_1_1 + +theorem source_gram_16_1_3 : Z 16 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_1_3 + +theorem source_gram_16_1_5 : Z 16 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_1_5 + +theorem source_gram_16_1_7 : Z 16 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_1_7 + +theorem source_gram_16_1_9 : Z 16 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_1_9 + +theorem source_gram_16_1_11 : Z 16 1 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_1_11 + +theorem source_gram_16_1_13 : Z 16 1 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_1_13 + +theorem source_gram_16_1_15 : Z 16 1 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_1_15 + +theorem source_gram_16_3_3 : Z 16 3 3 = (37362124800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_3_3 + +theorem source_gram_16_3_5 : Z 16 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_3_5 + +theorem source_gram_16_3_7 : Z 16 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_3_7 + +theorem source_gram_16_3_9 : Z 16 3 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_3_9 + +theorem source_gram_16_3_11 : Z 16 3 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_3_11 + +theorem source_gram_16_3_13 : Z 16 3 13 = (-7005398400 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_3_13 + +theorem source_gram_16_3_15 : Z 16 3 15 = (102162060000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_3_15 + +theorem source_gram_16_5_5 : Z 16 5 5 = (4790016000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_5_5 + +theorem source_gram_16_5_7 : Z 16 5 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_5_7 + +theorem source_gram_16_5_9 : Z 16 5 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_5_9 + +theorem source_gram_16_5_11 : Z 16 5 11 = (-1496880000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_5_11 + +theorem source_gram_16_5_13 : Z 16 5 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_5_13 + +theorem source_gram_16_5_15 : Z 16 5 15 = (61297236000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_5_15 + +theorem source_gram_16_7_7 : Z 16 7 7 = (1828915200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_7_7 + +theorem source_gram_16_7_9 : Z 16 7 9 = (-685843200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_7_9 + +theorem source_gram_16_7_11 : Z 16 7 11 = (-1571724000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_7_11 + +theorem source_gram_16_7_13 : Z 16 7 13 = (4086482400 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_7_13 + +theorem source_gram_16_7_15 : Z 16 7 15 = (15324309000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_7_15 + +theorem source_gram_16_9_9 : Z 16 9 9 = (457228800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_9_9 + +theorem source_gram_16_9_11 : Z 16 9 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_9_11 + +theorem source_gram_16_9_13 : Z 16 9 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_9_13 + +theorem source_gram_16_9_15 : Z 16 9 15 = (-10216206000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_9_15 + +theorem source_gram_16_11_11 : Z 16 11 11 = (3555090000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_11_11 + +theorem source_gram_16_11_13 : Z 16 11 13 = (-8027019000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_11_13 + +theorem source_gram_16_11_15 : Z 16 11 15 = (-19155386250 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_11_15 + +theorem source_gram_16_13_13 : Z 16 13 13 = (22183761600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_13_13 + +theorem source_gram_16_13_15 : Z 16 13 15 = (-19155386250 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_13_15 + +theorem source_gram_16_15_15 : Z 16 15 15 = (2584061605125/2 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_16_15_15 + +theorem source_error_16_3_1 : Y 16 3 1 = (-39034614015379387104670971/13107200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_1_3 + +theorem source_gram_16_3_1 : Z 16 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_1_3 + +theorem source_error_16_5_1 : Y 16 5 1 = (78202406241711463127687271/83886080000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_1_5 + +theorem source_gram_16_5_1 : Z 16 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_1_5 + +theorem source_error_16_5_3 : Y 16 5 3 = (2737552373685628655395239/41943040000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_3_5 + +theorem source_gram_16_5_3 : Z 16 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_3_5 + +theorem source_error_16_7_1 : Y 16 7 1 = (23832834670493732956060989/209715200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_1_7 + +theorem source_gram_16_7_1 : Z 16 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_1_7 + +theorem source_error_16_7_3 : Y 16 7 3 = (22736583113602023500964129/524288000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_3_7 + +theorem source_gram_16_7_3 : Z 16 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_3_7 + +theorem source_error_16_7_5 : Y 16 7 5 = (1549750421445905525422653/209715200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_5_7 + +theorem source_gram_16_7_5 : Z 16 7 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_5_7 + +theorem source_error_16_9_1 : Y 16 9 1 = (22048584820368310367604441/52428800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_1_9 + +theorem source_gram_16_9_1 : Z 16 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_1_9 + +theorem source_error_16_9_3 : Y 16 9 3 = (1851780972244557042321633/131072000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_3_9 + +theorem source_gram_16_9_3 : Z 16 9 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_3_9 + +theorem source_error_16_9_5 : Y 16 9 5 = (-611154627229412014141701/52428800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_5_9 + +theorem source_gram_16_9_5 : Z 16 9 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_5_9 + +theorem source_error_16_9_7 : Y 16 9 7 = (1484433801775108633948569/131072000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_7_9 + +theorem source_gram_16_9_7 : Z 16 9 7 = (-685843200 : ℚ) := by + rw [Z_symm] + exact source_gram_16_7_9 + +theorem source_error_16_11_1 : Y 16 11 1 = (2553473034802720354150827/26214400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_1_11 + +theorem source_gram_16_11_1 : Z 16 11 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_1_11 + +theorem source_error_16_11_3 : Y 16 11 3 = (507618379345280460543/1310720000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_3_11 + +theorem source_gram_16_11_3 : Z 16 11 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_3_11 + +theorem source_error_16_11_5 : Y 16 11 5 = (-578745616368603039939/41943040000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_5_11 + +theorem source_gram_16_11_5 : Z 16 11 5 = (-1496880000 : ℚ) := by + rw [Z_symm] + exact source_gram_16_5_11 + +theorem source_error_16_11_7 : Y 16 11 7 = (207943103777772680639091/13107200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_7_11 + +theorem source_gram_16_11_7 : Z 16 11 7 = (-1571724000 : ℚ) := by + rw [Z_symm] + exact source_gram_16_7_11 + +theorem source_error_16_11_9 : Y 16 11 9 = (-28769175431642817466911/3276800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_9_11 + +theorem source_gram_16_11_9 : Z 16 11 9 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_9_11 + +theorem source_error_16_13_1 : Y 16 13 1 = (108255415269241130506236621/26214400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_1_13 + +theorem source_gram_16_13_1 : Z 16 13 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_1_13 + +theorem source_error_16_13_3 : Y 16 13 3 = (32584839756386941473215337/65536000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_3_13 + +theorem source_gram_16_13_3 : Z 16 13 3 = (-7005398400 : ℚ) := by + rw [Z_symm] + exact source_gram_16_3_13 + +theorem source_error_16_13_5 : Y 16 13 5 = (-64505141078209101647091/1048576000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_5_13 + +theorem source_gram_16_13_5 : Z 16 13 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_5_13 + +theorem source_error_16_13_7 : Y 16 13 7 = (-8974467290230038089021529/65536000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_7_13 + +theorem source_gram_16_13_7 : Z 16 13 7 = (4086482400 : ℚ) := by + rw [Z_symm] + exact source_gram_16_7_13 + +theorem source_error_16_13_9 : Y 16 13 9 = (1147904288009241919132977/16384000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_9_13 + +theorem source_gram_16_13_9 : Z 16 13 9 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_9_13 + +theorem source_error_16_13_11 : Y 16 13 11 = (189274484540778686288811/1638400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_11_13 + +theorem source_gram_16_13_11 : Z 16 13 11 = (-8027019000 : ℚ) := by + rw [Z_symm] + exact source_gram_16_11_13 + +theorem source_error_16_15_1 : Y 16 15 1 = (-41435755574383986458435793/2621440000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_1_15 + +theorem source_gram_16_15_1 : Z 16 15 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_16_1_15 + +theorem source_error_16_15_3 : Y 16 15 3 = (-12977256793584317385992841/6553600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_3_15 + +theorem source_gram_16_15_3 : Z 16 15 3 = (102162060000 : ℚ) := by + rw [Z_symm] + exact source_gram_16_3_15 + +theorem source_error_16_15_5 : Y 16 15 5 = (-99002192076248555811717/524288000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_5_15 + +theorem source_gram_16_15_5 : Z 16 15 5 = (61297236000 : ℚ) := by + rw [Z_symm] + exact source_gram_16_5_15 + +theorem source_error_16_15_7 : Y 16 15 7 = (4777756237785689667105597/6553600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_7_15 + +theorem source_gram_16_15_7 : Z 16 15 7 = (15324309000 : ℚ) := by + rw [Z_symm] + exact source_gram_16_7_15 + +theorem source_error_16_15_9 : Y 16 15 9 = (68877548037338038801803/1638400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_9_15 + +theorem source_gram_16_15_9 : Z 16 15 9 = (-10216206000 : ℚ) := by + rw [Z_symm] + exact source_gram_16_9_15 + +theorem source_error_16_15_11 : Y 16 15 11 = (-71581303517955662317887/163840000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_11_15 + +theorem source_gram_16_15_11 : Z 16 15 11 = (-19155386250 : ℚ) := by + rw [Z_symm] + exact source_gram_16_11_15 + +theorem source_error_16_15_13 : Y 16 15 13 = (384276867404942369454597/819200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_16_13_15 + +theorem source_gram_16_15_13 : Z 16 15 13 = (-19155386250 : ℚ) := by + rw [Z_symm] + exact source_gram_16_13_15 + +theorem error_16 : errorRational 16 = candidateY_16 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_16_1_1 + · exact source_error_16_1_3 + · exact source_error_16_1_5 + · exact source_error_16_1_7 + · exact source_error_16_1_9 + · exact source_error_16_1_11 + · exact source_error_16_1_13 + · exact source_error_16_1_15 + · exact source_error_16_3_1 + · exact source_error_16_3_3 + · exact source_error_16_3_5 + · exact source_error_16_3_7 + · exact source_error_16_3_9 + · exact source_error_16_3_11 + · exact source_error_16_3_13 + · exact source_error_16_3_15 + · exact source_error_16_5_1 + · exact source_error_16_5_3 + · exact source_error_16_5_5 + · exact source_error_16_5_7 + · exact source_error_16_5_9 + · exact source_error_16_5_11 + · exact source_error_16_5_13 + · exact source_error_16_5_15 + · exact source_error_16_7_1 + · exact source_error_16_7_3 + · exact source_error_16_7_5 + · exact source_error_16_7_7 + · exact source_error_16_7_9 + · exact source_error_16_7_11 + · exact source_error_16_7_13 + · exact source_error_16_7_15 + · exact source_error_16_9_1 + · exact source_error_16_9_3 + · exact source_error_16_9_5 + · exact source_error_16_9_7 + · exact source_error_16_9_9 + · exact source_error_16_9_11 + · exact source_error_16_9_13 + · exact source_error_16_9_15 + · exact source_error_16_11_1 + · exact source_error_16_11_3 + · exact source_error_16_11_5 + · exact source_error_16_11_7 + · exact source_error_16_11_9 + · exact source_error_16_11_11 + · exact source_error_16_11_13 + · exact source_error_16_11_15 + · exact source_error_16_13_1 + · exact source_error_16_13_3 + · exact source_error_16_13_5 + · exact source_error_16_13_7 + · exact source_error_16_13_9 + · exact source_error_16_13_11 + · exact source_error_16_13_13 + · exact source_error_16_13_15 + · exact source_error_16_15_1 + · exact source_error_16_15_3 + · exact source_error_16_15_5 + · exact source_error_16_15_7 + · exact source_error_16_15_9 + · exact source_error_16_15_11 + · exact source_error_16_15_13 + · exact source_error_16_15_15 + +theorem gram_16 : gramRational 16 = candidateZ_16 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_16_1_1 + · exact source_gram_16_1_3 + · exact source_gram_16_1_5 + · exact source_gram_16_1_7 + · exact source_gram_16_1_9 + · exact source_gram_16_1_11 + · exact source_gram_16_1_13 + · exact source_gram_16_1_15 + · exact source_gram_16_3_1 + · exact source_gram_16_3_3 + · exact source_gram_16_3_5 + · exact source_gram_16_3_7 + · exact source_gram_16_3_9 + · exact source_gram_16_3_11 + · exact source_gram_16_3_13 + · exact source_gram_16_3_15 + · exact source_gram_16_5_1 + · exact source_gram_16_5_3 + · exact source_gram_16_5_5 + · exact source_gram_16_5_7 + · exact source_gram_16_5_9 + · exact source_gram_16_5_11 + · exact source_gram_16_5_13 + · exact source_gram_16_5_15 + · exact source_gram_16_7_1 + · exact source_gram_16_7_3 + · exact source_gram_16_7_5 + · exact source_gram_16_7_7 + · exact source_gram_16_7_9 + · exact source_gram_16_7_11 + · exact source_gram_16_7_13 + · exact source_gram_16_7_15 + · exact source_gram_16_9_1 + · exact source_gram_16_9_3 + · exact source_gram_16_9_5 + · exact source_gram_16_9_7 + · exact source_gram_16_9_9 + · exact source_gram_16_9_11 + · exact source_gram_16_9_13 + · exact source_gram_16_9_15 + · exact source_gram_16_11_1 + · exact source_gram_16_11_3 + · exact source_gram_16_11_5 + · exact source_gram_16_11_7 + · exact source_gram_16_11_9 + · exact source_gram_16_11_11 + · exact source_gram_16_11_13 + · exact source_gram_16_11_15 + · exact source_gram_16_13_1 + · exact source_gram_16_13_3 + · exact source_gram_16_13_5 + · exact source_gram_16_13_7 + · exact source_gram_16_13_9 + · exact source_gram_16_13_11 + · exact source_gram_16_13_13 + · exact source_gram_16_13_15 + · exact source_gram_16_15_1 + · exact source_gram_16_15_3 + · exact source_gram_16_15_5 + · exact source_gram_16_15_7 + · exact source_gram_16_15_9 + · exact source_gram_16_15_11 + · exact source_gram_16_15_13 + · exact source_gram_16_15_15 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData17.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData17.lean new file mode 100644 index 0000000000000000000000000000000000000000..b0e5ad822f23ba47e87a046814625fce9e4e0251 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData17.lean @@ -0,0 +1,1197 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram01Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram03Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram05Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram07Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram11Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram13Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram15Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram171717 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0101Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0103Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0105Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0107Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0109Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0111Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0113Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0115Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0117Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0303Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0305Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0307Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0309Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0311Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0313Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0315Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0317Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0505Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0507Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0509Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0511Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0513Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0515Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0517Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0707Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0709Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0711Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0713Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0715Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0717Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0909Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0911Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0913Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0915Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0917Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1111Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1113Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1115Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1117Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1313Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1315Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1317Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1515Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1517Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1717Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.Data17 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_17_1_1 : Y 17 1 1 = (-27062893468327394953193285367/419430400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 1 1 0 (by decide), + source_yRow_eq_rowCompute 17 1 1 1 (by decide), + source_yRow_eq_rowCompute 17 1 1 2 (by decide), + source_yRow_eq_rowCompute 17 1 1 3 (by decide), + source_yRow_eq_rowCompute 17 1 1 4 (by decide), + source_yRow_eq_rowCompute 17 1 1 5 (by decide), + source_yRow_eq_rowCompute 17 1 1 6 (by decide), + computeRow_17_1_1_0, computeRow_17_1_1_1, computeRow_17_1_1_2, computeRow_17_1_1_3, computeRow_17_1_1_4, computeRow_17_1_1_5, computeRow_17_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_1_3 : Y 17 1 3 = (-34150355623889743675914477/104857600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 1 3 0 (by decide), + source_yRow_eq_rowCompute 17 1 3 1 (by decide), + source_yRow_eq_rowCompute 17 1 3 2 (by decide), + source_yRow_eq_rowCompute 17 1 3 3 (by decide), + source_yRow_eq_rowCompute 17 1 3 4 (by decide), + source_yRow_eq_rowCompute 17 1 3 5 (by decide), + source_yRow_eq_rowCompute 17 1 3 6 (by decide), + computeRow_17_1_3_0, computeRow_17_1_3_1, computeRow_17_1_3_2, computeRow_17_1_3_3, computeRow_17_1_3_4, computeRow_17_1_3_5, computeRow_17_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_1_5 : Y 17 1 5 = (260924265129905899387586721/83886080000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 1 5 0 (by decide), + source_yRow_eq_rowCompute 17 1 5 1 (by decide), + source_yRow_eq_rowCompute 17 1 5 2 (by decide), + source_yRow_eq_rowCompute 17 1 5 3 (by decide), + source_yRow_eq_rowCompute 17 1 5 4 (by decide), + source_yRow_eq_rowCompute 17 1 5 5 (by decide), + source_yRow_eq_rowCompute 17 1 5 6 (by decide), + computeRow_17_1_5_0, computeRow_17_1_5_1, computeRow_17_1_5_2, computeRow_17_1_5_3, computeRow_17_1_5_4, computeRow_17_1_5_5, computeRow_17_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_1_7 : Y 17 1 7 = (-67528457531024325424642053/41943040000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 1 7 0 (by decide), + source_yRow_eq_rowCompute 17 1 7 1 (by decide), + source_yRow_eq_rowCompute 17 1 7 2 (by decide), + source_yRow_eq_rowCompute 17 1 7 3 (by decide), + source_yRow_eq_rowCompute 17 1 7 4 (by decide), + source_yRow_eq_rowCompute 17 1 7 5 (by decide), + source_yRow_eq_rowCompute 17 1 7 6 (by decide), + computeRow_17_1_7_0, computeRow_17_1_7_1, computeRow_17_1_7_2, computeRow_17_1_7_3, computeRow_17_1_7_4, computeRow_17_1_7_5, computeRow_17_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_1_9 : Y 17 1 9 = (-30137637143983305054521403/52428800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 1 9 0 (by decide), + source_yRow_eq_rowCompute 17 1 9 1 (by decide), + source_yRow_eq_rowCompute 17 1 9 2 (by decide), + source_yRow_eq_rowCompute 17 1 9 3 (by decide), + source_yRow_eq_rowCompute 17 1 9 4 (by decide), + source_yRow_eq_rowCompute 17 1 9 5 (by decide), + source_yRow_eq_rowCompute 17 1 9 6 (by decide), + computeRow_17_1_9_0, computeRow_17_1_9_1, computeRow_17_1_9_2, computeRow_17_1_9_3, computeRow_17_1_9_4, computeRow_17_1_9_5, computeRow_17_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_1_11 : Y 17 1 11 = (95166999960067286140262373/26214400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 1 11 0 (by decide), + source_yRow_eq_rowCompute 17 1 11 1 (by decide), + source_yRow_eq_rowCompute 17 1 11 2 (by decide), + source_yRow_eq_rowCompute 17 1 11 3 (by decide), + source_yRow_eq_rowCompute 17 1 11 4 (by decide), + source_yRow_eq_rowCompute 17 1 11 5 (by decide), + source_yRow_eq_rowCompute 17 1 11 6 (by decide), + computeRow_17_1_11_0, computeRow_17_1_11_1, computeRow_17_1_11_2, computeRow_17_1_11_3, computeRow_17_1_11_4, computeRow_17_1_11_5, computeRow_17_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_1_13 : Y 17 1 13 = (-175538440354363800262225677/26214400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 1 13 0 (by decide), + source_yRow_eq_rowCompute 17 1 13 1 (by decide), + source_yRow_eq_rowCompute 17 1 13 2 (by decide), + source_yRow_eq_rowCompute 17 1 13 3 (by decide), + source_yRow_eq_rowCompute 17 1 13 4 (by decide), + source_yRow_eq_rowCompute 17 1 13 5 (by decide), + source_yRow_eq_rowCompute 17 1 13 6 (by decide), + computeRow_17_1_13_0, computeRow_17_1_13_1, computeRow_17_1_13_2, computeRow_17_1_13_3, computeRow_17_1_13_4, computeRow_17_1_13_5, computeRow_17_1_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_1_15 : Y 17 1 15 = (69154353838247955125781933/2621440000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 1 15 0 (by decide), + source_yRow_eq_rowCompute 17 1 15 1 (by decide), + source_yRow_eq_rowCompute 17 1 15 2 (by decide), + source_yRow_eq_rowCompute 17 1 15 3 (by decide), + source_yRow_eq_rowCompute 17 1 15 4 (by decide), + source_yRow_eq_rowCompute 17 1 15 5 (by decide), + source_yRow_eq_rowCompute 17 1 15 6 (by decide), + computeRow_17_1_15_0, computeRow_17_1_15_1, computeRow_17_1_15_2, computeRow_17_1_15_3, computeRow_17_1_15_4, computeRow_17_1_15_5, computeRow_17_1_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_1_17 : Y 17 1 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 1 17 0 (by decide), + source_yRow_eq_rowCompute 17 1 17 1 (by decide), + source_yRow_eq_rowCompute 17 1 17 2 (by decide), + source_yRow_eq_rowCompute 17 1 17 3 (by decide), + source_yRow_eq_rowCompute 17 1 17 4 (by decide), + source_yRow_eq_rowCompute 17 1 17 5 (by decide), + source_yRow_eq_rowCompute 17 1 17 6 (by decide), + computeRow_17_1_17_0, computeRow_17_1_17_1, computeRow_17_1_17_2, computeRow_17_1_17_3, computeRow_17_1_17_4, computeRow_17_1_17_5, computeRow_17_1_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_3_3 : Y 17 3 3 = (-259433233939629173544831711/1048576000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 3 3 0 (by decide), + source_yRow_eq_rowCompute 17 3 3 1 (by decide), + source_yRow_eq_rowCompute 17 3 3 2 (by decide), + source_yRow_eq_rowCompute 17 3 3 3 (by decide), + source_yRow_eq_rowCompute 17 3 3 4 (by decide), + source_yRow_eq_rowCompute 17 3 3 5 (by decide), + source_yRow_eq_rowCompute 17 3 3 6 (by decide), + computeRow_17_3_3_0, computeRow_17_3_3_1, computeRow_17_3_3_2, computeRow_17_3_3_3, computeRow_17_3_3_4, computeRow_17_3_3_5, computeRow_17_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_3_5 : Y 17 3 5 = (10972785710270109216153663/104857600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 3 5 0 (by decide), + source_yRow_eq_rowCompute 17 3 5 1 (by decide), + source_yRow_eq_rowCompute 17 3 5 2 (by decide), + source_yRow_eq_rowCompute 17 3 5 3 (by decide), + source_yRow_eq_rowCompute 17 3 5 4 (by decide), + source_yRow_eq_rowCompute 17 3 5 5 (by decide), + source_yRow_eq_rowCompute 17 3 5 6 (by decide), + computeRow_17_3_5_0, computeRow_17_3_5_1, computeRow_17_3_5_2, computeRow_17_3_5_3, computeRow_17_3_5_4, computeRow_17_3_5_5, computeRow_17_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_3_7 : Y 17 3 7 = (-408068525315759942414781/13107200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 3 7 0 (by decide), + source_yRow_eq_rowCompute 17 3 7 1 (by decide), + source_yRow_eq_rowCompute 17 3 7 2 (by decide), + source_yRow_eq_rowCompute 17 3 7 3 (by decide), + source_yRow_eq_rowCompute 17 3 7 4 (by decide), + source_yRow_eq_rowCompute 17 3 7 5 (by decide), + source_yRow_eq_rowCompute 17 3 7 6 (by decide), + computeRow_17_3_7_0, computeRow_17_3_7_1, computeRow_17_3_7_2, computeRow_17_3_7_3, computeRow_17_3_7_4, computeRow_17_3_7_5, computeRow_17_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_3_9 : Y 17 3 9 = (729849806595543331244547/65536000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 3 9 0 (by decide), + source_yRow_eq_rowCompute 17 3 9 1 (by decide), + source_yRow_eq_rowCompute 17 3 9 2 (by decide), + source_yRow_eq_rowCompute 17 3 9 3 (by decide), + source_yRow_eq_rowCompute 17 3 9 4 (by decide), + source_yRow_eq_rowCompute 17 3 9 5 (by decide), + source_yRow_eq_rowCompute 17 3 9 6 (by decide), + computeRow_17_3_9_0, computeRow_17_3_9_1, computeRow_17_3_9_2, computeRow_17_3_9_3, computeRow_17_3_9_4, computeRow_17_3_9_5, computeRow_17_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_3_11 : Y 17 3 11 = (11113201543710491752527/13107200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 3 11 0 (by decide), + source_yRow_eq_rowCompute 17 3 11 1 (by decide), + source_yRow_eq_rowCompute 17 3 11 2 (by decide), + source_yRow_eq_rowCompute 17 3 11 3 (by decide), + source_yRow_eq_rowCompute 17 3 11 4 (by decide), + source_yRow_eq_rowCompute 17 3 11 5 (by decide), + source_yRow_eq_rowCompute 17 3 11 6 (by decide), + computeRow_17_3_11_0, computeRow_17_3_11_1, computeRow_17_3_11_2, computeRow_17_3_11_3, computeRow_17_3_11_4, computeRow_17_3_11_5, computeRow_17_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_3_13 : Y 17 3 13 = (-12885057439514659527475347/32768000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 3 13 0 (by decide), + source_yRow_eq_rowCompute 17 3 13 1 (by decide), + source_yRow_eq_rowCompute 17 3 13 2 (by decide), + source_yRow_eq_rowCompute 17 3 13 3 (by decide), + source_yRow_eq_rowCompute 17 3 13 4 (by decide), + source_yRow_eq_rowCompute 17 3 13 5 (by decide), + source_yRow_eq_rowCompute 17 3 13 6 (by decide), + computeRow_17_3_13_0, computeRow_17_3_13_1, computeRow_17_3_13_2, computeRow_17_3_13_3, computeRow_17_3_13_4, computeRow_17_3_13_5, computeRow_17_3_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_3_15 : Y 17 3 15 = (1281998470570534260875331/1638400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 3 15 0 (by decide), + source_yRow_eq_rowCompute 17 3 15 1 (by decide), + source_yRow_eq_rowCompute 17 3 15 2 (by decide), + source_yRow_eq_rowCompute 17 3 15 3 (by decide), + source_yRow_eq_rowCompute 17 3 15 4 (by decide), + source_yRow_eq_rowCompute 17 3 15 5 (by decide), + source_yRow_eq_rowCompute 17 3 15 6 (by decide), + computeRow_17_3_15_0, computeRow_17_3_15_1, computeRow_17_3_15_2, computeRow_17_3_15_3, computeRow_17_3_15_4, computeRow_17_3_15_5, computeRow_17_3_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_3_17 : Y 17 3 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 3 17 0 (by decide), + source_yRow_eq_rowCompute 17 3 17 1 (by decide), + source_yRow_eq_rowCompute 17 3 17 2 (by decide), + source_yRow_eq_rowCompute 17 3 17 3 (by decide), + source_yRow_eq_rowCompute 17 3 17 4 (by decide), + source_yRow_eq_rowCompute 17 3 17 5 (by decide), + source_yRow_eq_rowCompute 17 3 17 6 (by decide), + computeRow_17_3_17_0, computeRow_17_3_17_1, computeRow_17_3_17_2, computeRow_17_3_17_3, computeRow_17_3_17_4, computeRow_17_3_17_5, computeRow_17_3_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_5_5 : Y 17 5 5 = (-16291154585525363835188931/83886080000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 5 5 0 (by decide), + source_yRow_eq_rowCompute 17 5 5 1 (by decide), + source_yRow_eq_rowCompute 17 5 5 2 (by decide), + source_yRow_eq_rowCompute 17 5 5 3 (by decide), + source_yRow_eq_rowCompute 17 5 5 4 (by decide), + source_yRow_eq_rowCompute 17 5 5 5 (by decide), + source_yRow_eq_rowCompute 17 5 5 6 (by decide), + computeRow_17_5_5_0, computeRow_17_5_5_1, computeRow_17_5_5_2, computeRow_17_5_5_3, computeRow_17_5_5_4, computeRow_17_5_5_5, computeRow_17_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_5_7 : Y 17 5 7 = (4351689332062192591003071/41943040000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 5 7 0 (by decide), + source_yRow_eq_rowCompute 17 5 7 1 (by decide), + source_yRow_eq_rowCompute 17 5 7 2 (by decide), + source_yRow_eq_rowCompute 17 5 7 3 (by decide), + source_yRow_eq_rowCompute 17 5 7 4 (by decide), + source_yRow_eq_rowCompute 17 5 7 5 (by decide), + source_yRow_eq_rowCompute 17 5 7 6 (by decide), + computeRow_17_5_7_0, computeRow_17_5_7_1, computeRow_17_5_7_2, computeRow_17_5_7_3, computeRow_17_5_7_4, computeRow_17_5_7_5, computeRow_17_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_5_9 : Y 17 5 9 = (83301302217472013622717/10485760000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 5 9 0 (by decide), + source_yRow_eq_rowCompute 17 5 9 1 (by decide), + source_yRow_eq_rowCompute 17 5 9 2 (by decide), + source_yRow_eq_rowCompute 17 5 9 3 (by decide), + source_yRow_eq_rowCompute 17 5 9 4 (by decide), + source_yRow_eq_rowCompute 17 5 9 5 (by decide), + source_yRow_eq_rowCompute 17 5 9 6 (by decide), + computeRow_17_5_9_0, computeRow_17_5_9_1, computeRow_17_5_9_2, computeRow_17_5_9_3, computeRow_17_5_9_4, computeRow_17_5_9_5, computeRow_17_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_5_11 : Y 17 5 11 = (-203973650747133817508343/1048576000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 5 11 0 (by decide), + source_yRow_eq_rowCompute 17 5 11 1 (by decide), + source_yRow_eq_rowCompute 17 5 11 2 (by decide), + source_yRow_eq_rowCompute 17 5 11 3 (by decide), + source_yRow_eq_rowCompute 17 5 11 4 (by decide), + source_yRow_eq_rowCompute 17 5 11 5 (by decide), + source_yRow_eq_rowCompute 17 5 11 6 (by decide), + computeRow_17_5_11_0, computeRow_17_5_11_1, computeRow_17_5_11_2, computeRow_17_5_11_3, computeRow_17_5_11_4, computeRow_17_5_11_5, computeRow_17_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_5_13 : Y 17 5 13 = (16866893128958580992747463/26214400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 5 13 0 (by decide), + source_yRow_eq_rowCompute 17 5 13 1 (by decide), + source_yRow_eq_rowCompute 17 5 13 2 (by decide), + source_yRow_eq_rowCompute 17 5 13 3 (by decide), + source_yRow_eq_rowCompute 17 5 13 4 (by decide), + source_yRow_eq_rowCompute 17 5 13 5 (by decide), + source_yRow_eq_rowCompute 17 5 13 6 (by decide), + computeRow_17_5_13_0, computeRow_17_5_13_1, computeRow_17_5_13_2, computeRow_17_5_13_3, computeRow_17_5_13_4, computeRow_17_5_13_5, computeRow_17_5_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_5_15 : Y 17 5 15 = (-99471136192512553900431/104857600000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 5 15 0 (by decide), + source_yRow_eq_rowCompute 17 5 15 1 (by decide), + source_yRow_eq_rowCompute 17 5 15 2 (by decide), + source_yRow_eq_rowCompute 17 5 15 3 (by decide), + source_yRow_eq_rowCompute 17 5 15 4 (by decide), + source_yRow_eq_rowCompute 17 5 15 5 (by decide), + source_yRow_eq_rowCompute 17 5 15 6 (by decide), + computeRow_17_5_15_0, computeRow_17_5_15_1, computeRow_17_5_15_2, computeRow_17_5_15_3, computeRow_17_5_15_4, computeRow_17_5_15_5, computeRow_17_5_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_5_17 : Y 17 5 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 5 17 0 (by decide), + source_yRow_eq_rowCompute 17 5 17 1 (by decide), + source_yRow_eq_rowCompute 17 5 17 2 (by decide), + source_yRow_eq_rowCompute 17 5 17 3 (by decide), + source_yRow_eq_rowCompute 17 5 17 4 (by decide), + source_yRow_eq_rowCompute 17 5 17 5 (by decide), + source_yRow_eq_rowCompute 17 5 17 6 (by decide), + computeRow_17_5_17_0, computeRow_17_5_17_1, computeRow_17_5_17_2, computeRow_17_5_17_3, computeRow_17_5_17_4, computeRow_17_5_17_5, computeRow_17_5_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_7_7 : Y 17 7 7 = (-1404556469174930860536363/20971520000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 7 7 0 (by decide), + source_yRow_eq_rowCompute 17 7 7 1 (by decide), + source_yRow_eq_rowCompute 17 7 7 2 (by decide), + source_yRow_eq_rowCompute 17 7 7 3 (by decide), + source_yRow_eq_rowCompute 17 7 7 4 (by decide), + source_yRow_eq_rowCompute 17 7 7 5 (by decide), + source_yRow_eq_rowCompute 17 7 7 6 (by decide), + computeRow_17_7_7_0, computeRow_17_7_7_1, computeRow_17_7_7_2, computeRow_17_7_7_3, computeRow_17_7_7_4, computeRow_17_7_7_5, computeRow_17_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_7_9 : Y 17 7 9 = (138574461584170298662731/26214400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 7 9 0 (by decide), + source_yRow_eq_rowCompute 17 7 9 1 (by decide), + source_yRow_eq_rowCompute 17 7 9 2 (by decide), + source_yRow_eq_rowCompute 17 7 9 3 (by decide), + source_yRow_eq_rowCompute 17 7 9 4 (by decide), + source_yRow_eq_rowCompute 17 7 9 5 (by decide), + source_yRow_eq_rowCompute 17 7 9 6 (by decide), + computeRow_17_7_9_0, computeRow_17_7_9_1, computeRow_17_7_9_2, computeRow_17_7_9_3, computeRow_17_7_9_4, computeRow_17_7_9_5, computeRow_17_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_7_11 : Y 17 7 11 = (322312699672503215100579/2621440000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 7 11 0 (by decide), + source_yRow_eq_rowCompute 17 7 11 1 (by decide), + source_yRow_eq_rowCompute 17 7 11 2 (by decide), + source_yRow_eq_rowCompute 17 7 11 3 (by decide), + source_yRow_eq_rowCompute 17 7 11 4 (by decide), + source_yRow_eq_rowCompute 17 7 11 5 (by decide), + source_yRow_eq_rowCompute 17 7 11 6 (by decide), + computeRow_17_7_11_0, computeRow_17_7_11_1, computeRow_17_7_11_2, computeRow_17_7_11_3, computeRow_17_7_11_4, computeRow_17_7_11_5, computeRow_17_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_7_13 : Y 17 7 13 = (-5414374042135146758937267/13107200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 7 13 0 (by decide), + source_yRow_eq_rowCompute 17 7 13 1 (by decide), + source_yRow_eq_rowCompute 17 7 13 2 (by decide), + source_yRow_eq_rowCompute 17 7 13 3 (by decide), + source_yRow_eq_rowCompute 17 7 13 4 (by decide), + source_yRow_eq_rowCompute 17 7 13 5 (by decide), + source_yRow_eq_rowCompute 17 7 13 6 (by decide), + computeRow_17_7_13_0, computeRow_17_7_13_1, computeRow_17_7_13_2, computeRow_17_7_13_3, computeRow_17_7_13_4, computeRow_17_7_13_5, computeRow_17_7_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_7_15 : Y 17 7 15 = (53455862611083189243987/1310720000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 7 15 0 (by decide), + source_yRow_eq_rowCompute 17 7 15 1 (by decide), + source_yRow_eq_rowCompute 17 7 15 2 (by decide), + source_yRow_eq_rowCompute 17 7 15 3 (by decide), + source_yRow_eq_rowCompute 17 7 15 4 (by decide), + source_yRow_eq_rowCompute 17 7 15 5 (by decide), + source_yRow_eq_rowCompute 17 7 15 6 (by decide), + computeRow_17_7_15_0, computeRow_17_7_15_1, computeRow_17_7_15_2, computeRow_17_7_15_3, computeRow_17_7_15_4, computeRow_17_7_15_5, computeRow_17_7_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_7_17 : Y 17 7 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 7 17 0 (by decide), + source_yRow_eq_rowCompute 17 7 17 1 (by decide), + source_yRow_eq_rowCompute 17 7 17 2 (by decide), + source_yRow_eq_rowCompute 17 7 17 3 (by decide), + source_yRow_eq_rowCompute 17 7 17 4 (by decide), + source_yRow_eq_rowCompute 17 7 17 5 (by decide), + source_yRow_eq_rowCompute 17 7 17 6 (by decide), + computeRow_17_7_17_0, computeRow_17_7_17_1, computeRow_17_7_17_2, computeRow_17_7_17_3, computeRow_17_7_17_4, computeRow_17_7_17_5, computeRow_17_7_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_9_9 : Y 17 9 9 = (-560195899211802719046699/32768000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 9 9 0 (by decide), + source_yRow_eq_rowCompute 17 9 9 1 (by decide), + source_yRow_eq_rowCompute 17 9 9 2 (by decide), + source_yRow_eq_rowCompute 17 9 9 3 (by decide), + source_yRow_eq_rowCompute 17 9 9 4 (by decide), + source_yRow_eq_rowCompute 17 9 9 5 (by decide), + source_yRow_eq_rowCompute 17 9 9 6 (by decide), + computeRow_17_9_9_0, computeRow_17_9_9_1, computeRow_17_9_9_2, computeRow_17_9_9_3, computeRow_17_9_9_4, computeRow_17_9_9_5, computeRow_17_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_9_11 : Y 17 9 11 = (1543576781120216089401/131072000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 9 11 0 (by decide), + source_yRow_eq_rowCompute 17 9 11 1 (by decide), + source_yRow_eq_rowCompute 17 9 11 2 (by decide), + source_yRow_eq_rowCompute 17 9 11 3 (by decide), + source_yRow_eq_rowCompute 17 9 11 4 (by decide), + source_yRow_eq_rowCompute 17 9 11 5 (by decide), + source_yRow_eq_rowCompute 17 9 11 6 (by decide), + computeRow_17_9_11_0, computeRow_17_9_11_1, computeRow_17_9_11_2, computeRow_17_9_11_3, computeRow_17_9_11_4, computeRow_17_9_11_5, computeRow_17_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_9_13 : Y 17 9 13 = (727025046163822366323363/16384000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 9 13 0 (by decide), + source_yRow_eq_rowCompute 17 9 13 1 (by decide), + source_yRow_eq_rowCompute 17 9 13 2 (by decide), + source_yRow_eq_rowCompute 17 9 13 3 (by decide), + source_yRow_eq_rowCompute 17 9 13 4 (by decide), + source_yRow_eq_rowCompute 17 9 13 5 (by decide), + source_yRow_eq_rowCompute 17 9 13 6 (by decide), + computeRow_17_9_13_0, computeRow_17_9_13_1, computeRow_17_9_13_2, computeRow_17_9_13_3, computeRow_17_9_13_4, computeRow_17_9_13_5, computeRow_17_9_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_9_15 : Y 17 9 15 = (948970636189602992298333/1638400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 9 15 0 (by decide), + source_yRow_eq_rowCompute 17 9 15 1 (by decide), + source_yRow_eq_rowCompute 17 9 15 2 (by decide), + source_yRow_eq_rowCompute 17 9 15 3 (by decide), + source_yRow_eq_rowCompute 17 9 15 4 (by decide), + source_yRow_eq_rowCompute 17 9 15 5 (by decide), + source_yRow_eq_rowCompute 17 9 15 6 (by decide), + computeRow_17_9_15_0, computeRow_17_9_15_1, computeRow_17_9_15_2, computeRow_17_9_15_3, computeRow_17_9_15_4, computeRow_17_9_15_5, computeRow_17_9_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_9_17 : Y 17 9 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 9 17 0 (by decide), + source_yRow_eq_rowCompute 17 9 17 1 (by decide), + source_yRow_eq_rowCompute 17 9 17 2 (by decide), + source_yRow_eq_rowCompute 17 9 17 3 (by decide), + source_yRow_eq_rowCompute 17 9 17 4 (by decide), + source_yRow_eq_rowCompute 17 9 17 5 (by decide), + source_yRow_eq_rowCompute 17 9 17 6 (by decide), + computeRow_17_9_17_0, computeRow_17_9_17_1, computeRow_17_9_17_2, computeRow_17_9_17_3, computeRow_17_9_17_4, computeRow_17_9_17_5, computeRow_17_9_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_11_11 : Y 17 11 11 = (-428477431290639456169917/1638400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 11 11 0 (by decide), + source_yRow_eq_rowCompute 17 11 11 1 (by decide), + source_yRow_eq_rowCompute 17 11 11 2 (by decide), + source_yRow_eq_rowCompute 17 11 11 3 (by decide), + source_yRow_eq_rowCompute 17 11 11 4 (by decide), + source_yRow_eq_rowCompute 17 11 11 5 (by decide), + source_yRow_eq_rowCompute 17 11 11 6 (by decide), + computeRow_17_11_11_0, computeRow_17_11_11_1, computeRow_17_11_11_2, computeRow_17_11_11_3, computeRow_17_11_11_4, computeRow_17_11_11_5, computeRow_17_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_11_13 : Y 17 11 13 = (1054078060656605687920503/1638400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 11 13 0 (by decide), + source_yRow_eq_rowCompute 17 11 13 1 (by decide), + source_yRow_eq_rowCompute 17 11 13 2 (by decide), + source_yRow_eq_rowCompute 17 11 13 3 (by decide), + source_yRow_eq_rowCompute 17 11 13 4 (by decide), + source_yRow_eq_rowCompute 17 11 13 5 (by decide), + source_yRow_eq_rowCompute 17 11 13 6 (by decide), + computeRow_17_11_13_0, computeRow_17_11_13_1, computeRow_17_11_13_2, computeRow_17_11_13_3, computeRow_17_11_13_4, computeRow_17_11_13_5, computeRow_17_11_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_11_15 : Y 17 11 15 = (-99701519947816820212179/163840000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 11 15 0 (by decide), + source_yRow_eq_rowCompute 17 11 15 1 (by decide), + source_yRow_eq_rowCompute 17 11 15 2 (by decide), + source_yRow_eq_rowCompute 17 11 15 3 (by decide), + source_yRow_eq_rowCompute 17 11 15 4 (by decide), + source_yRow_eq_rowCompute 17 11 15 5 (by decide), + source_yRow_eq_rowCompute 17 11 15 6 (by decide), + computeRow_17_11_15_0, computeRow_17_11_15_1, computeRow_17_11_15_2, computeRow_17_11_15_3, computeRow_17_11_15_4, computeRow_17_11_15_5, computeRow_17_11_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_11_17 : Y 17 11 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 11 17 0 (by decide), + source_yRow_eq_rowCompute 17 11 17 1 (by decide), + source_yRow_eq_rowCompute 17 11 17 2 (by decide), + source_yRow_eq_rowCompute 17 11 17 3 (by decide), + source_yRow_eq_rowCompute 17 11 17 4 (by decide), + source_yRow_eq_rowCompute 17 11 17 5 (by decide), + source_yRow_eq_rowCompute 17 11 17 6 (by decide), + computeRow_17_11_17_0, computeRow_17_11_17_1, computeRow_17_11_17_2, computeRow_17_11_17_3, computeRow_17_11_17_4, computeRow_17_11_17_5, computeRow_17_11_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_13_13 : Y 17 13 13 = (-13417206537411611280214011/8192000000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 13 13 0 (by decide), + source_yRow_eq_rowCompute 17 13 13 1 (by decide), + source_yRow_eq_rowCompute 17 13 13 2 (by decide), + source_yRow_eq_rowCompute 17 13 13 3 (by decide), + source_yRow_eq_rowCompute 17 13 13 4 (by decide), + source_yRow_eq_rowCompute 17 13 13 5 (by decide), + source_yRow_eq_rowCompute 17 13 13 6 (by decide), + computeRow_17_13_13_0, computeRow_17_13_13_1, computeRow_17_13_13_2, computeRow_17_13_13_3, computeRow_17_13_13_4, computeRow_17_13_13_5, computeRow_17_13_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_13_15 : Y 17 13 15 = (797255391734832796032267/819200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 13 15 0 (by decide), + source_yRow_eq_rowCompute 17 13 15 1 (by decide), + source_yRow_eq_rowCompute 17 13 15 2 (by decide), + source_yRow_eq_rowCompute 17 13 15 3 (by decide), + source_yRow_eq_rowCompute 17 13 15 4 (by decide), + source_yRow_eq_rowCompute 17 13 15 5 (by decide), + source_yRow_eq_rowCompute 17 13 15 6 (by decide), + computeRow_17_13_15_0, computeRow_17_13_15_1, computeRow_17_13_15_2, computeRow_17_13_15_3, computeRow_17_13_15_4, computeRow_17_13_15_5, computeRow_17_13_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_13_17 : Y 17 13 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 13 17 0 (by decide), + source_yRow_eq_rowCompute 17 13 17 1 (by decide), + source_yRow_eq_rowCompute 17 13 17 2 (by decide), + source_yRow_eq_rowCompute 17 13 17 3 (by decide), + source_yRow_eq_rowCompute 17 13 17 4 (by decide), + source_yRow_eq_rowCompute 17 13 17 5 (by decide), + source_yRow_eq_rowCompute 17 13 17 6 (by decide), + computeRow_17_13_17_0, computeRow_17_13_17_1, computeRow_17_13_17_2, computeRow_17_13_17_3, computeRow_17_13_17_4, computeRow_17_13_17_5, computeRow_17_13_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_15_15 : Y 17 15 15 = (-2081041110780259193873307/81920000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 15 15 0 (by decide), + source_yRow_eq_rowCompute 17 15 15 1 (by decide), + source_yRow_eq_rowCompute 17 15 15 2 (by decide), + source_yRow_eq_rowCompute 17 15 15 3 (by decide), + source_yRow_eq_rowCompute 17 15 15 4 (by decide), + source_yRow_eq_rowCompute 17 15 15 5 (by decide), + source_yRow_eq_rowCompute 17 15 15 6 (by decide), + computeRow_17_15_15_0, computeRow_17_15_15_1, computeRow_17_15_15_2, computeRow_17_15_15_3, computeRow_17_15_15_4, computeRow_17_15_15_5, computeRow_17_15_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_15_17 : Y 17 15 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 15 17 0 (by decide), + source_yRow_eq_rowCompute 17 15 17 1 (by decide), + source_yRow_eq_rowCompute 17 15 17 2 (by decide), + source_yRow_eq_rowCompute 17 15 17 3 (by decide), + source_yRow_eq_rowCompute 17 15 17 4 (by decide), + source_yRow_eq_rowCompute 17 15 17 5 (by decide), + source_yRow_eq_rowCompute 17 15 17 6 (by decide), + computeRow_17_15_17_0, computeRow_17_15_17_1, computeRow_17_15_17_2, computeRow_17_15_17_3, computeRow_17_15_17_4, computeRow_17_15_17_5, computeRow_17_15_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_17_17_17 : Y 17 17 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 17 17 17 0 (by decide), + source_yRow_eq_rowCompute 17 17 17 1 (by decide), + source_yRow_eq_rowCompute 17 17 17 2 (by decide), + source_yRow_eq_rowCompute 17 17 17 3 (by decide), + source_yRow_eq_rowCompute 17 17 17 4 (by decide), + source_yRow_eq_rowCompute 17 17 17 5 (by decide), + source_yRow_eq_rowCompute 17 17 17 6 (by decide), + computeRow_17_17_17_0, computeRow_17_17_17_1, computeRow_17_17_17_2, computeRow_17_17_17_3, computeRow_17_17_17_4, computeRow_17_17_17_5, computeRow_17_17_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_17_1_1 : Z 17 1 1 = (41845579776000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_1_1 + +theorem source_gram_17_1_3 : Z 17 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_1_3 + +theorem source_gram_17_1_5 : Z 17 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_1_5 + +theorem source_gram_17_1_7 : Z 17 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_1_7 + +theorem source_gram_17_1_9 : Z 17 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_1_9 + +theorem source_gram_17_1_11 : Z 17 1 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_1_11 + +theorem source_gram_17_1_13 : Z 17 1 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_1_13 + +theorem source_gram_17_1_15 : Z 17 1 15 = (-326918592000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_1_15 + +theorem source_gram_17_1_17 : Z 17 1 17 = (19451656224000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_1_17 + +theorem source_gram_17_3_3 : Z 17 3 3 = (523069747200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_3_3 + +theorem source_gram_17_3_5 : Z 17 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_3_5 + +theorem source_gram_17_3_7 : Z 17 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_3_7 + +theorem source_gram_17_3_9 : Z 17 3 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_3_9 + +theorem source_gram_17_3_11 : Z 17 3 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_3_11 + +theorem source_gram_17_3_13 : Z 17 3 13 = (-16345929600 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_3_13 + +theorem source_gram_17_3_15 : Z 17 3 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_3_15 + +theorem source_gram_17_3_17 : Z 17 3 17 = (6947020080000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_3_17 + +theorem source_gram_17_5_5 : Z 17 5 5 = (57480192000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_5_5 + +theorem source_gram_17_5_7 : Z 17 5 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_5_7 + +theorem source_gram_17_5_9 : Z 17 5 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_5_9 + +theorem source_gram_17_5_11 : Z 17 5 11 = (-2694384000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_5_11 + +theorem source_gram_17_5_13 : Z 17 5 13 = (-29189160000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_5_13 + +theorem source_gram_17_5_15 : Z 17 5 15 = (204324120000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_5_15 + +theorem source_gram_17_5_17 : Z 17 5 17 = (2084106024000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_5_17 + +theorem source_gram_17_7_7 : Z 17 7 7 = (18289152000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_7_7 + +theorem source_gram_17_7_9 : Z 17 7 9 = (-1143072000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_7_9 + +theorem source_gram_17_7_11 : Z 17 7 11 = (-12573792000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_7_11 + +theorem source_gram_17_7_13 : Z 17 7 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_7_13 + +theorem source_gram_17_7_15 : Z 17 7 15 = (143026884000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_7_15 + +theorem source_gram_17_7_17 : Z 17 7 17 = (347351004000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_7_17 + +theorem source_gram_17_9_9 : Z 17 9 9 = (5372438400 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_9_9 + +theorem source_gram_17_9_11 : Z 17 9 11 = (-9430344000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_9_11 + +theorem source_gram_17_9_13 : Z 17 9 13 = (12259447200 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_9_13 + +theorem source_gram_17_9_15 : Z 17 9 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_9_15 + +theorem source_gram_17_9_17 : Z 17 9 17 = (-173675502000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_9_17 + +theorem source_gram_17_11_11 : Z 17 11 11 = (28740096000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_11_11 + +theorem source_gram_17_11_13 : Z 17 11 13 = (-24081057000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_11_13 + +theorem source_gram_17_11_15 : Z 17 11 15 = (-112378266000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_11_15 + +theorem source_gram_17_11_17 : Z 17 11 17 = (-260513253000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_11_17 + +theorem source_gram_17_13_13 : Z 17 13 13 = (55532376900 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_13_13 + +theorem source_gram_17_13_15 : Z 17 13 15 = (-166013347500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_13_15 + +theorem source_gram_17_13_17 : Z 17 13 17 = (-217094377500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_13_17 + +theorem source_gram_17_15_15 : Z 17 15 15 = (2442950259750 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_15_15 + +theorem source_gram_17_15_17 : Z 17 15 17 = (-151966064250 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_15_17 + +theorem source_gram_17_17_17 : Z 17 17 17 = (355589735626125 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_17_17_17 + +theorem source_error_17_3_1 : Y 17 3 1 = (-34150355623889743675914477/104857600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_1_3 + +theorem source_gram_17_3_1 : Z 17 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_1_3 + +theorem source_error_17_5_1 : Y 17 5 1 = (260924265129905899387586721/83886080000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_1_5 + +theorem source_gram_17_5_1 : Z 17 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_1_5 + +theorem source_error_17_5_3 : Y 17 5 3 = (10972785710270109216153663/104857600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_3_5 + +theorem source_gram_17_5_3 : Z 17 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_3_5 + +theorem source_error_17_7_1 : Y 17 7 1 = (-67528457531024325424642053/41943040000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_1_7 + +theorem source_gram_17_7_1 : Z 17 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_1_7 + +theorem source_error_17_7_3 : Y 17 7 3 = (-408068525315759942414781/13107200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_3_7 + +theorem source_gram_17_7_3 : Z 17 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_3_7 + +theorem source_error_17_7_5 : Y 17 7 5 = (4351689332062192591003071/41943040000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_5_7 + +theorem source_gram_17_7_5 : Z 17 7 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_5_7 + +theorem source_error_17_9_1 : Y 17 9 1 = (-30137637143983305054521403/52428800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_1_9 + +theorem source_gram_17_9_1 : Z 17 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_1_9 + +theorem source_error_17_9_3 : Y 17 9 3 = (729849806595543331244547/65536000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_3_9 + +theorem source_gram_17_9_3 : Z 17 9 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_3_9 + +theorem source_error_17_9_5 : Y 17 9 5 = (83301302217472013622717/10485760000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_5_9 + +theorem source_gram_17_9_5 : Z 17 9 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_5_9 + +theorem source_error_17_9_7 : Y 17 9 7 = (138574461584170298662731/26214400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_7_9 + +theorem source_gram_17_9_7 : Z 17 9 7 = (-1143072000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_7_9 + +theorem source_error_17_11_1 : Y 17 11 1 = (95166999960067286140262373/26214400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_1_11 + +theorem source_gram_17_11_1 : Z 17 11 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_1_11 + +theorem source_error_17_11_3 : Y 17 11 3 = (11113201543710491752527/13107200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_3_11 + +theorem source_gram_17_11_3 : Z 17 11 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_3_11 + +theorem source_error_17_11_5 : Y 17 11 5 = (-203973650747133817508343/1048576000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_5_11 + +theorem source_gram_17_11_5 : Z 17 11 5 = (-2694384000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_5_11 + +theorem source_error_17_11_7 : Y 17 11 7 = (322312699672503215100579/2621440000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_7_11 + +theorem source_gram_17_11_7 : Z 17 11 7 = (-12573792000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_7_11 + +theorem source_error_17_11_9 : Y 17 11 9 = (1543576781120216089401/131072000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_9_11 + +theorem source_gram_17_11_9 : Z 17 11 9 = (-9430344000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_9_11 + +theorem source_error_17_13_1 : Y 17 13 1 = (-175538440354363800262225677/26214400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_1_13 + +theorem source_gram_17_13_1 : Z 17 13 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_1_13 + +theorem source_error_17_13_3 : Y 17 13 3 = (-12885057439514659527475347/32768000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_3_13 + +theorem source_gram_17_13_3 : Z 17 13 3 = (-16345929600 : ℚ) := by + rw [Z_symm] + exact source_gram_17_3_13 + +theorem source_error_17_13_5 : Y 17 13 5 = (16866893128958580992747463/26214400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_5_13 + +theorem source_gram_17_13_5 : Z 17 13 5 = (-29189160000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_5_13 + +theorem source_error_17_13_7 : Y 17 13 7 = (-5414374042135146758937267/13107200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_7_13 + +theorem source_gram_17_13_7 : Z 17 13 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_7_13 + +theorem source_error_17_13_9 : Y 17 13 9 = (727025046163822366323363/16384000000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_9_13 + +theorem source_gram_17_13_9 : Z 17 13 9 = (12259447200 : ℚ) := by + rw [Z_symm] + exact source_gram_17_9_13 + +theorem source_error_17_13_11 : Y 17 13 11 = (1054078060656605687920503/1638400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_11_13 + +theorem source_gram_17_13_11 : Z 17 13 11 = (-24081057000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_11_13 + +theorem source_error_17_15_1 : Y 17 15 1 = (69154353838247955125781933/2621440000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_1_15 + +theorem source_gram_17_15_1 : Z 17 15 1 = (-326918592000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_1_15 + +theorem source_error_17_15_3 : Y 17 15 3 = (1281998470570534260875331/1638400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_3_15 + +theorem source_gram_17_15_3 : Z 17 15 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_3_15 + +theorem source_error_17_15_5 : Y 17 15 5 = (-99471136192512553900431/104857600000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_5_15 + +theorem source_gram_17_15_5 : Z 17 15 5 = (204324120000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_5_15 + +theorem source_error_17_15_7 : Y 17 15 7 = (53455862611083189243987/1310720000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_7_15 + +theorem source_gram_17_15_7 : Z 17 15 7 = (143026884000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_7_15 + +theorem source_error_17_15_9 : Y 17 15 9 = (948970636189602992298333/1638400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_9_15 + +theorem source_gram_17_15_9 : Z 17 15 9 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_17_9_15 + +theorem source_error_17_15_11 : Y 17 15 11 = (-99701519947816820212179/163840000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_11_15 + +theorem source_gram_17_15_11 : Z 17 15 11 = (-112378266000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_11_15 + +theorem source_error_17_15_13 : Y 17 15 13 = (797255391734832796032267/819200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_17_13_15 + +theorem source_gram_17_15_13 : Z 17 15 13 = (-166013347500 : ℚ) := by + rw [Z_symm] + exact source_gram_17_13_15 + +theorem source_error_17_17_1 : Y 17 17 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_17_1_17 + +theorem source_gram_17_17_1 : Z 17 17 1 = (19451656224000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_1_17 + +theorem source_error_17_17_3 : Y 17 17 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_17_3_17 + +theorem source_gram_17_17_3 : Z 17 17 3 = (6947020080000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_3_17 + +theorem source_error_17_17_5 : Y 17 17 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_17_5_17 + +theorem source_gram_17_17_5 : Z 17 17 5 = (2084106024000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_5_17 + +theorem source_error_17_17_7 : Y 17 17 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_17_7_17 + +theorem source_gram_17_17_7 : Z 17 17 7 = (347351004000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_7_17 + +theorem source_error_17_17_9 : Y 17 17 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_17_9_17 + +theorem source_gram_17_17_9 : Z 17 17 9 = (-173675502000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_9_17 + +theorem source_error_17_17_11 : Y 17 17 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_17_11_17 + +theorem source_gram_17_17_11 : Z 17 17 11 = (-260513253000 : ℚ) := by + rw [Z_symm] + exact source_gram_17_11_17 + +theorem source_error_17_17_13 : Y 17 17 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_17_13_17 + +theorem source_gram_17_17_13 : Z 17 17 13 = (-217094377500 : ℚ) := by + rw [Z_symm] + exact source_gram_17_13_17 + +theorem source_error_17_17_15 : Y 17 17 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_17_15_17 + +theorem source_gram_17_17_15 : Z 17 17 15 = (-151966064250 : ℚ) := by + rw [Z_symm] + exact source_gram_17_15_17 + +theorem error_17 : errorRational 17 = candidateY_17 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_17_1_1 + · exact source_error_17_1_3 + · exact source_error_17_1_5 + · exact source_error_17_1_7 + · exact source_error_17_1_9 + · exact source_error_17_1_11 + · exact source_error_17_1_13 + · exact source_error_17_1_15 + · exact source_error_17_1_17 + · exact source_error_17_3_1 + · exact source_error_17_3_3 + · exact source_error_17_3_5 + · exact source_error_17_3_7 + · exact source_error_17_3_9 + · exact source_error_17_3_11 + · exact source_error_17_3_13 + · exact source_error_17_3_15 + · exact source_error_17_3_17 + · exact source_error_17_5_1 + · exact source_error_17_5_3 + · exact source_error_17_5_5 + · exact source_error_17_5_7 + · exact source_error_17_5_9 + · exact source_error_17_5_11 + · exact source_error_17_5_13 + · exact source_error_17_5_15 + · exact source_error_17_5_17 + · exact source_error_17_7_1 + · exact source_error_17_7_3 + · exact source_error_17_7_5 + · exact source_error_17_7_7 + · exact source_error_17_7_9 + · exact source_error_17_7_11 + · exact source_error_17_7_13 + · exact source_error_17_7_15 + · exact source_error_17_7_17 + · exact source_error_17_9_1 + · exact source_error_17_9_3 + · exact source_error_17_9_5 + · exact source_error_17_9_7 + · exact source_error_17_9_9 + · exact source_error_17_9_11 + · exact source_error_17_9_13 + · exact source_error_17_9_15 + · exact source_error_17_9_17 + · exact source_error_17_11_1 + · exact source_error_17_11_3 + · exact source_error_17_11_5 + · exact source_error_17_11_7 + · exact source_error_17_11_9 + · exact source_error_17_11_11 + · exact source_error_17_11_13 + · exact source_error_17_11_15 + · exact source_error_17_11_17 + · exact source_error_17_13_1 + · exact source_error_17_13_3 + · exact source_error_17_13_5 + · exact source_error_17_13_7 + · exact source_error_17_13_9 + · exact source_error_17_13_11 + · exact source_error_17_13_13 + · exact source_error_17_13_15 + · exact source_error_17_13_17 + · exact source_error_17_15_1 + · exact source_error_17_15_3 + · exact source_error_17_15_5 + · exact source_error_17_15_7 + · exact source_error_17_15_9 + · exact source_error_17_15_11 + · exact source_error_17_15_13 + · exact source_error_17_15_15 + · exact source_error_17_15_17 + · exact source_error_17_17_1 + · exact source_error_17_17_3 + · exact source_error_17_17_5 + · exact source_error_17_17_7 + · exact source_error_17_17_9 + · exact source_error_17_17_11 + · exact source_error_17_17_13 + · exact source_error_17_17_15 + · exact source_error_17_17_17 + +theorem gram_17 : gramRational 17 = candidateZ_17 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_17_1_1 + · exact source_gram_17_1_3 + · exact source_gram_17_1_5 + · exact source_gram_17_1_7 + · exact source_gram_17_1_9 + · exact source_gram_17_1_11 + · exact source_gram_17_1_13 + · exact source_gram_17_1_15 + · exact source_gram_17_1_17 + · exact source_gram_17_3_1 + · exact source_gram_17_3_3 + · exact source_gram_17_3_5 + · exact source_gram_17_3_7 + · exact source_gram_17_3_9 + · exact source_gram_17_3_11 + · exact source_gram_17_3_13 + · exact source_gram_17_3_15 + · exact source_gram_17_3_17 + · exact source_gram_17_5_1 + · exact source_gram_17_5_3 + · exact source_gram_17_5_5 + · exact source_gram_17_5_7 + · exact source_gram_17_5_9 + · exact source_gram_17_5_11 + · exact source_gram_17_5_13 + · exact source_gram_17_5_15 + · exact source_gram_17_5_17 + · exact source_gram_17_7_1 + · exact source_gram_17_7_3 + · exact source_gram_17_7_5 + · exact source_gram_17_7_7 + · exact source_gram_17_7_9 + · exact source_gram_17_7_11 + · exact source_gram_17_7_13 + · exact source_gram_17_7_15 + · exact source_gram_17_7_17 + · exact source_gram_17_9_1 + · exact source_gram_17_9_3 + · exact source_gram_17_9_5 + · exact source_gram_17_9_7 + · exact source_gram_17_9_9 + · exact source_gram_17_9_11 + · exact source_gram_17_9_13 + · exact source_gram_17_9_15 + · exact source_gram_17_9_17 + · exact source_gram_17_11_1 + · exact source_gram_17_11_3 + · exact source_gram_17_11_5 + · exact source_gram_17_11_7 + · exact source_gram_17_11_9 + · exact source_gram_17_11_11 + · exact source_gram_17_11_13 + · exact source_gram_17_11_15 + · exact source_gram_17_11_17 + · exact source_gram_17_13_1 + · exact source_gram_17_13_3 + · exact source_gram_17_13_5 + · exact source_gram_17_13_7 + · exact source_gram_17_13_9 + · exact source_gram_17_13_11 + · exact source_gram_17_13_13 + · exact source_gram_17_13_15 + · exact source_gram_17_13_17 + · exact source_gram_17_15_1 + · exact source_gram_17_15_3 + · exact source_gram_17_15_5 + · exact source_gram_17_15_7 + · exact source_gram_17_15_9 + · exact source_gram_17_15_11 + · exact source_gram_17_15_13 + · exact source_gram_17_15_15 + · exact source_gram_17_15_17 + · exact source_gram_17_17_1 + · exact source_gram_17_17_3 + · exact source_gram_17_17_5 + · exact source_gram_17_17_7 + · exact source_gram_17_17_9 + · exact source_gram_17_17_11 + · exact source_gram_17_17_13 + · exact source_gram_17_17_15 + · exact source_gram_17_17_17 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData18.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData18.lean new file mode 100644 index 0000000000000000000000000000000000000000..d4281ece1d75c3c77a6170bd7b48c3cb8d34c2c8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData18.lean @@ -0,0 +1,1197 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram01Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram03Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram05Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram07Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram11Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram13Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram15Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram171718 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0101Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0103Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0105Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0107Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0109Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0111Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0113Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0115Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0117Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0303Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0305Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0307Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0309Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0311Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0313Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0315Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0317Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0505Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0507Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0509Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0511Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0513Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0515Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0517Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0707Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0709Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0711Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0713Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0715Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0717Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0909Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0911Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0913Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0915Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0917Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1111Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1113Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1115Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1117Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1313Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1315Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1317Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1515Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1517Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1717Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.Data18 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_18_1_1 : Y 18 1 1 = (-3559166385880423516847027379/41943040000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 1 1 0 (by decide), + source_yRow_eq_rowCompute 18 1 1 1 (by decide), + source_yRow_eq_rowCompute 18 1 1 2 (by decide), + source_yRow_eq_rowCompute 18 1 1 3 (by decide), + source_yRow_eq_rowCompute 18 1 1 4 (by decide), + source_yRow_eq_rowCompute 18 1 1 5 (by decide), + source_yRow_eq_rowCompute 18 1 1 6 (by decide), + computeRow_18_1_1_0, computeRow_18_1_1_1, computeRow_18_1_1_2, computeRow_18_1_1_3, computeRow_18_1_1_4, computeRow_18_1_1_5, computeRow_18_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_1_3 : Y 18 1 3 = (43700029260178412251303173/3276800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 1 3 0 (by decide), + source_yRow_eq_rowCompute 18 1 3 1 (by decide), + source_yRow_eq_rowCompute 18 1 3 2 (by decide), + source_yRow_eq_rowCompute 18 1 3 3 (by decide), + source_yRow_eq_rowCompute 18 1 3 4 (by decide), + source_yRow_eq_rowCompute 18 1 3 5 (by decide), + source_yRow_eq_rowCompute 18 1 3 6 (by decide), + computeRow_18_1_3_0, computeRow_18_1_3_1, computeRow_18_1_3_2, computeRow_18_1_3_3, computeRow_18_1_3_4, computeRow_18_1_3_5, computeRow_18_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_1_5 : Y 18 1 5 = (-157097886646298732847063351/41943040000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 1 5 0 (by decide), + source_yRow_eq_rowCompute 18 1 5 1 (by decide), + source_yRow_eq_rowCompute 18 1 5 2 (by decide), + source_yRow_eq_rowCompute 18 1 5 3 (by decide), + source_yRow_eq_rowCompute 18 1 5 4 (by decide), + source_yRow_eq_rowCompute 18 1 5 5 (by decide), + source_yRow_eq_rowCompute 18 1 5 6 (by decide), + computeRow_18_1_5_0, computeRow_18_1_5_1, computeRow_18_1_5_2, computeRow_18_1_5_3, computeRow_18_1_5_4, computeRow_18_1_5_5, computeRow_18_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_1_7 : Y 18 1 7 = (45795850251189055946275347/20971520000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 1 7 0 (by decide), + source_yRow_eq_rowCompute 18 1 7 1 (by decide), + source_yRow_eq_rowCompute 18 1 7 2 (by decide), + source_yRow_eq_rowCompute 18 1 7 3 (by decide), + source_yRow_eq_rowCompute 18 1 7 4 (by decide), + source_yRow_eq_rowCompute 18 1 7 5 (by decide), + source_yRow_eq_rowCompute 18 1 7 6 (by decide), + computeRow_18_1_7_0, computeRow_18_1_7_1, computeRow_18_1_7_2, computeRow_18_1_7_3, computeRow_18_1_7_4, computeRow_18_1_7_5, computeRow_18_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_1_9 : Y 18 1 9 = (-15768543277252499592049191/5242880000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 1 9 0 (by decide), + source_yRow_eq_rowCompute 18 1 9 1 (by decide), + source_yRow_eq_rowCompute 18 1 9 2 (by decide), + source_yRow_eq_rowCompute 18 1 9 3 (by decide), + source_yRow_eq_rowCompute 18 1 9 4 (by decide), + source_yRow_eq_rowCompute 18 1 9 5 (by decide), + source_yRow_eq_rowCompute 18 1 9 6 (by decide), + computeRow_18_1_9_0, computeRow_18_1_9_1, computeRow_18_1_9_2, computeRow_18_1_9_3, computeRow_18_1_9_4, computeRow_18_1_9_5, computeRow_18_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_1_11 : Y 18 1 11 = (15774590706413201698776741/2621440000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 1 11 0 (by decide), + source_yRow_eq_rowCompute 18 1 11 1 (by decide), + source_yRow_eq_rowCompute 18 1 11 2 (by decide), + source_yRow_eq_rowCompute 18 1 11 3 (by decide), + source_yRow_eq_rowCompute 18 1 11 4 (by decide), + source_yRow_eq_rowCompute 18 1 11 5 (by decide), + source_yRow_eq_rowCompute 18 1 11 6 (by decide), + computeRow_18_1_11_0, computeRow_18_1_11_1, computeRow_18_1_11_2, computeRow_18_1_11_3, computeRow_18_1_11_4, computeRow_18_1_11_5, computeRow_18_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_1_13 : Y 18 1 13 = (-111481601475376052708801013/13107200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 1 13 0 (by decide), + source_yRow_eq_rowCompute 18 1 13 1 (by decide), + source_yRow_eq_rowCompute 18 1 13 2 (by decide), + source_yRow_eq_rowCompute 18 1 13 3 (by decide), + source_yRow_eq_rowCompute 18 1 13 4 (by decide), + source_yRow_eq_rowCompute 18 1 13 5 (by decide), + source_yRow_eq_rowCompute 18 1 13 6 (by decide), + computeRow_18_1_13_0, computeRow_18_1_13_1, computeRow_18_1_13_2, computeRow_18_1_13_3, computeRow_18_1_13_4, computeRow_18_1_13_5, computeRow_18_1_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_1_15 : Y 18 1 15 = (-58408977661685586058262139/1310720000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 1 15 0 (by decide), + source_yRow_eq_rowCompute 18 1 15 1 (by decide), + source_yRow_eq_rowCompute 18 1 15 2 (by decide), + source_yRow_eq_rowCompute 18 1 15 3 (by decide), + source_yRow_eq_rowCompute 18 1 15 4 (by decide), + source_yRow_eq_rowCompute 18 1 15 5 (by decide), + source_yRow_eq_rowCompute 18 1 15 6 (by decide), + computeRow_18_1_15_0, computeRow_18_1_15_1, computeRow_18_1_15_2, computeRow_18_1_15_3, computeRow_18_1_15_4, computeRow_18_1_15_5, computeRow_18_1_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_1_17 : Y 18 1 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 1 17 0 (by decide), + source_yRow_eq_rowCompute 18 1 17 1 (by decide), + source_yRow_eq_rowCompute 18 1 17 2 (by decide), + source_yRow_eq_rowCompute 18 1 17 3 (by decide), + source_yRow_eq_rowCompute 18 1 17 4 (by decide), + source_yRow_eq_rowCompute 18 1 17 5 (by decide), + source_yRow_eq_rowCompute 18 1 17 6 (by decide), + computeRow_18_1_17_0, computeRow_18_1_17_1, computeRow_18_1_17_2, computeRow_18_1_17_3, computeRow_18_1_17_4, computeRow_18_1_17_5, computeRow_18_1_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_3_3 : Y 18 3 3 = (-81940194402186836366199549/26214400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 3 3 0 (by decide), + source_yRow_eq_rowCompute 18 3 3 1 (by decide), + source_yRow_eq_rowCompute 18 3 3 2 (by decide), + source_yRow_eq_rowCompute 18 3 3 3 (by decide), + source_yRow_eq_rowCompute 18 3 3 4 (by decide), + source_yRow_eq_rowCompute 18 3 3 5 (by decide), + source_yRow_eq_rowCompute 18 3 3 6 (by decide), + computeRow_18_3_3_0, computeRow_18_3_3_1, computeRow_18_3_3_2, computeRow_18_3_3_3, computeRow_18_3_3_4, computeRow_18_3_3_5, computeRow_18_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_3_5 : Y 18 3 5 = (5636036629375968042063837/5242880000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 3 5 0 (by decide), + source_yRow_eq_rowCompute 18 3 5 1 (by decide), + source_yRow_eq_rowCompute 18 3 5 2 (by decide), + source_yRow_eq_rowCompute 18 3 5 3 (by decide), + source_yRow_eq_rowCompute 18 3 5 4 (by decide), + source_yRow_eq_rowCompute 18 3 5 5 (by decide), + source_yRow_eq_rowCompute 18 3 5 6 (by decide), + computeRow_18_3_5_0, computeRow_18_3_5_1, computeRow_18_3_5_2, computeRow_18_3_5_3, computeRow_18_3_5_4, computeRow_18_3_5_5, computeRow_18_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_3_7 : Y 18 3 7 = (-2298714004872189626128407/5242880000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 3 7 0 (by decide), + source_yRow_eq_rowCompute 18 3 7 1 (by decide), + source_yRow_eq_rowCompute 18 3 7 2 (by decide), + source_yRow_eq_rowCompute 18 3 7 3 (by decide), + source_yRow_eq_rowCompute 18 3 7 4 (by decide), + source_yRow_eq_rowCompute 18 3 7 5 (by decide), + source_yRow_eq_rowCompute 18 3 7 6 (by decide), + computeRow_18_3_7_0, computeRow_18_3_7_1, computeRow_18_3_7_2, computeRow_18_3_7_3, computeRow_18_3_7_4, computeRow_18_3_7_5, computeRow_18_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_3_9 : Y 18 3 9 = (297813059860269307535181/1638400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 3 9 0 (by decide), + source_yRow_eq_rowCompute 18 3 9 1 (by decide), + source_yRow_eq_rowCompute 18 3 9 2 (by decide), + source_yRow_eq_rowCompute 18 3 9 3 (by decide), + source_yRow_eq_rowCompute 18 3 9 4 (by decide), + source_yRow_eq_rowCompute 18 3 9 5 (by decide), + source_yRow_eq_rowCompute 18 3 9 6 (by decide), + computeRow_18_3_9_0, computeRow_18_3_9_1, computeRow_18_3_9_2, computeRow_18_3_9_3, computeRow_18_3_9_4, computeRow_18_3_9_5, computeRow_18_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_3_11 : Y 18 3 11 = (-427966983073658698687017/3276800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 3 11 0 (by decide), + source_yRow_eq_rowCompute 18 3 11 1 (by decide), + source_yRow_eq_rowCompute 18 3 11 2 (by decide), + source_yRow_eq_rowCompute 18 3 11 3 (by decide), + source_yRow_eq_rowCompute 18 3 11 4 (by decide), + source_yRow_eq_rowCompute 18 3 11 5 (by decide), + source_yRow_eq_rowCompute 18 3 11 6 (by decide), + computeRow_18_3_11_0, computeRow_18_3_11_1, computeRow_18_3_11_2, computeRow_18_3_11_3, computeRow_18_3_11_4, computeRow_18_3_11_5, computeRow_18_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_3_13 : Y 18 3 13 = (460639052423449997118021/1638400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 3 13 0 (by decide), + source_yRow_eq_rowCompute 18 3 13 1 (by decide), + source_yRow_eq_rowCompute 18 3 13 2 (by decide), + source_yRow_eq_rowCompute 18 3 13 3 (by decide), + source_yRow_eq_rowCompute 18 3 13 4 (by decide), + source_yRow_eq_rowCompute 18 3 13 5 (by decide), + source_yRow_eq_rowCompute 18 3 13 6 (by decide), + computeRow_18_3_13_0, computeRow_18_3_13_1, computeRow_18_3_13_2, computeRow_18_3_13_3, computeRow_18_3_13_4, computeRow_18_3_13_5, computeRow_18_3_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_3_15 : Y 18 3 15 = (856489912851915268585659/327680000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 3 15 0 (by decide), + source_yRow_eq_rowCompute 18 3 15 1 (by decide), + source_yRow_eq_rowCompute 18 3 15 2 (by decide), + source_yRow_eq_rowCompute 18 3 15 3 (by decide), + source_yRow_eq_rowCompute 18 3 15 4 (by decide), + source_yRow_eq_rowCompute 18 3 15 5 (by decide), + source_yRow_eq_rowCompute 18 3 15 6 (by decide), + computeRow_18_3_15_0, computeRow_18_3_15_1, computeRow_18_3_15_2, computeRow_18_3_15_3, computeRow_18_3_15_4, computeRow_18_3_15_5, computeRow_18_3_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_3_17 : Y 18 3 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 3 17 0 (by decide), + source_yRow_eq_rowCompute 18 3 17 1 (by decide), + source_yRow_eq_rowCompute 18 3 17 2 (by decide), + source_yRow_eq_rowCompute 18 3 17 3 (by decide), + source_yRow_eq_rowCompute 18 3 17 4 (by decide), + source_yRow_eq_rowCompute 18 3 17 5 (by decide), + source_yRow_eq_rowCompute 18 3 17 6 (by decide), + computeRow_18_3_17_0, computeRow_18_3_17_1, computeRow_18_3_17_2, computeRow_18_3_17_3, computeRow_18_3_17_4, computeRow_18_3_17_5, computeRow_18_3_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_5_5 : Y 18 5 5 = (-17038127051364859101889227/41943040000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 5 5 0 (by decide), + source_yRow_eq_rowCompute 18 5 5 1 (by decide), + source_yRow_eq_rowCompute 18 5 5 2 (by decide), + source_yRow_eq_rowCompute 18 5 5 3 (by decide), + source_yRow_eq_rowCompute 18 5 5 4 (by decide), + source_yRow_eq_rowCompute 18 5 5 5 (by decide), + source_yRow_eq_rowCompute 18 5 5 6 (by decide), + computeRow_18_5_5_0, computeRow_18_5_5_1, computeRow_18_5_5_2, computeRow_18_5_5_3, computeRow_18_5_5_4, computeRow_18_5_5_5, computeRow_18_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_5_7 : Y 18 5 7 = (3236875371562490528333463/20971520000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 5 7 0 (by decide), + source_yRow_eq_rowCompute 18 5 7 1 (by decide), + source_yRow_eq_rowCompute 18 5 7 2 (by decide), + source_yRow_eq_rowCompute 18 5 7 3 (by decide), + source_yRow_eq_rowCompute 18 5 7 4 (by decide), + source_yRow_eq_rowCompute 18 5 7 5 (by decide), + source_yRow_eq_rowCompute 18 5 7 6 (by decide), + computeRow_18_5_7_0, computeRow_18_5_7_1, computeRow_18_5_7_2, computeRow_18_5_7_3, computeRow_18_5_7_4, computeRow_18_5_7_5, computeRow_18_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_5_9 : Y 18 5 9 = (109159200441997398693/5242880000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 5 9 0 (by decide), + source_yRow_eq_rowCompute 18 5 9 1 (by decide), + source_yRow_eq_rowCompute 18 5 9 2 (by decide), + source_yRow_eq_rowCompute 18 5 9 3 (by decide), + source_yRow_eq_rowCompute 18 5 9 4 (by decide), + source_yRow_eq_rowCompute 18 5 9 5 (by decide), + source_yRow_eq_rowCompute 18 5 9 6 (by decide), + computeRow_18_5_9_0, computeRow_18_5_9_1, computeRow_18_5_9_2, computeRow_18_5_9_3, computeRow_18_5_9_4, computeRow_18_5_9_5, computeRow_18_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_5_11 : Y 18 5 11 = (-76974792598120601955771/524288000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 5 11 0 (by decide), + source_yRow_eq_rowCompute 18 5 11 1 (by decide), + source_yRow_eq_rowCompute 18 5 11 2 (by decide), + source_yRow_eq_rowCompute 18 5 11 3 (by decide), + source_yRow_eq_rowCompute 18 5 11 4 (by decide), + source_yRow_eq_rowCompute 18 5 11 5 (by decide), + source_yRow_eq_rowCompute 18 5 11 6 (by decide), + computeRow_18_5_11_0, computeRow_18_5_11_1, computeRow_18_5_11_2, computeRow_18_5_11_3, computeRow_18_5_11_4, computeRow_18_5_11_5, computeRow_18_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_5_13 : Y 18 5 13 = (525900691396984091231043/2621440000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 5 13 0 (by decide), + source_yRow_eq_rowCompute 18 5 13 1 (by decide), + source_yRow_eq_rowCompute 18 5 13 2 (by decide), + source_yRow_eq_rowCompute 18 5 13 3 (by decide), + source_yRow_eq_rowCompute 18 5 13 4 (by decide), + source_yRow_eq_rowCompute 18 5 13 5 (by decide), + source_yRow_eq_rowCompute 18 5 13 6 (by decide), + computeRow_18_5_13_0, computeRow_18_5_13_1, computeRow_18_5_13_2, computeRow_18_5_13_3, computeRow_18_5_13_4, computeRow_18_5_13_5, computeRow_18_5_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_5_15 : Y 18 5 15 = (166478085484275751174989/262144000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 5 15 0 (by decide), + source_yRow_eq_rowCompute 18 5 15 1 (by decide), + source_yRow_eq_rowCompute 18 5 15 2 (by decide), + source_yRow_eq_rowCompute 18 5 15 3 (by decide), + source_yRow_eq_rowCompute 18 5 15 4 (by decide), + source_yRow_eq_rowCompute 18 5 15 5 (by decide), + source_yRow_eq_rowCompute 18 5 15 6 (by decide), + computeRow_18_5_15_0, computeRow_18_5_15_1, computeRow_18_5_15_2, computeRow_18_5_15_3, computeRow_18_5_15_4, computeRow_18_5_15_5, computeRow_18_5_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_5_17 : Y 18 5 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 5 17 0 (by decide), + source_yRow_eq_rowCompute 18 5 17 1 (by decide), + source_yRow_eq_rowCompute 18 5 17 2 (by decide), + source_yRow_eq_rowCompute 18 5 17 3 (by decide), + source_yRow_eq_rowCompute 18 5 17 4 (by decide), + source_yRow_eq_rowCompute 18 5 17 5 (by decide), + source_yRow_eq_rowCompute 18 5 17 6 (by decide), + computeRow_18_5_17_0, computeRow_18_5_17_1, computeRow_18_5_17_2, computeRow_18_5_17_3, computeRow_18_5_17_4, computeRow_18_5_17_5, computeRow_18_5_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_7_7 : Y 18 7 7 = (-152920142255560594957119/2097152000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 7 7 0 (by decide), + source_yRow_eq_rowCompute 18 7 7 1 (by decide), + source_yRow_eq_rowCompute 18 7 7 2 (by decide), + source_yRow_eq_rowCompute 18 7 7 3 (by decide), + source_yRow_eq_rowCompute 18 7 7 4 (by decide), + source_yRow_eq_rowCompute 18 7 7 5 (by decide), + source_yRow_eq_rowCompute 18 7 7 6 (by decide), + computeRow_18_7_7_0, computeRow_18_7_7_1, computeRow_18_7_7_2, computeRow_18_7_7_3, computeRow_18_7_7_4, computeRow_18_7_7_5, computeRow_18_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_7_9 : Y 18 7 9 = (76480320836604209603463/2621440000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 7 9 0 (by decide), + source_yRow_eq_rowCompute 18 7 9 1 (by decide), + source_yRow_eq_rowCompute 18 7 9 2 (by decide), + source_yRow_eq_rowCompute 18 7 9 3 (by decide), + source_yRow_eq_rowCompute 18 7 9 4 (by decide), + source_yRow_eq_rowCompute 18 7 9 5 (by decide), + source_yRow_eq_rowCompute 18 7 9 6 (by decide), + computeRow_18_7_9_0, computeRow_18_7_9_1, computeRow_18_7_9_2, computeRow_18_7_9_3, computeRow_18_7_9_4, computeRow_18_7_9_5, computeRow_18_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_7_11 : Y 18 7 11 = (34507713700153945513647/1310720000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 7 11 0 (by decide), + source_yRow_eq_rowCompute 18 7 11 1 (by decide), + source_yRow_eq_rowCompute 18 7 11 2 (by decide), + source_yRow_eq_rowCompute 18 7 11 3 (by decide), + source_yRow_eq_rowCompute 18 7 11 4 (by decide), + source_yRow_eq_rowCompute 18 7 11 5 (by decide), + source_yRow_eq_rowCompute 18 7 11 6 (by decide), + computeRow_18_7_11_0, computeRow_18_7_11_1, computeRow_18_7_11_2, computeRow_18_7_11_3, computeRow_18_7_11_4, computeRow_18_7_11_5, computeRow_18_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_7_13 : Y 18 7 13 = (-126720387057916007218863/1310720000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 7 13 0 (by decide), + source_yRow_eq_rowCompute 18 7 13 1 (by decide), + source_yRow_eq_rowCompute 18 7 13 2 (by decide), + source_yRow_eq_rowCompute 18 7 13 3 (by decide), + source_yRow_eq_rowCompute 18 7 13 4 (by decide), + source_yRow_eq_rowCompute 18 7 13 5 (by decide), + source_yRow_eq_rowCompute 18 7 13 6 (by decide), + computeRow_18_7_13_0, computeRow_18_7_13_1, computeRow_18_7_13_2, computeRow_18_7_13_3, computeRow_18_7_13_4, computeRow_18_7_13_5, computeRow_18_7_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_7_15 : Y 18 7 15 = (-293804443074929463225549/655360000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 7 15 0 (by decide), + source_yRow_eq_rowCompute 18 7 15 1 (by decide), + source_yRow_eq_rowCompute 18 7 15 2 (by decide), + source_yRow_eq_rowCompute 18 7 15 3 (by decide), + source_yRow_eq_rowCompute 18 7 15 4 (by decide), + source_yRow_eq_rowCompute 18 7 15 5 (by decide), + source_yRow_eq_rowCompute 18 7 15 6 (by decide), + computeRow_18_7_15_0, computeRow_18_7_15_1, computeRow_18_7_15_2, computeRow_18_7_15_3, computeRow_18_7_15_4, computeRow_18_7_15_5, computeRow_18_7_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_7_17 : Y 18 7 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 7 17 0 (by decide), + source_yRow_eq_rowCompute 18 7 17 1 (by decide), + source_yRow_eq_rowCompute 18 7 17 2 (by decide), + source_yRow_eq_rowCompute 18 7 17 3 (by decide), + source_yRow_eq_rowCompute 18 7 17 4 (by decide), + source_yRow_eq_rowCompute 18 7 17 5 (by decide), + source_yRow_eq_rowCompute 18 7 17 6 (by decide), + computeRow_18_7_17_0, computeRow_18_7_17_1, computeRow_18_7_17_2, computeRow_18_7_17_3, computeRow_18_7_17_4, computeRow_18_7_17_5, computeRow_18_7_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_9_9 : Y 18 9 9 = (-59366777784768563477067/655360000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 9 9 0 (by decide), + source_yRow_eq_rowCompute 18 9 9 1 (by decide), + source_yRow_eq_rowCompute 18 9 9 2 (by decide), + source_yRow_eq_rowCompute 18 9 9 3 (by decide), + source_yRow_eq_rowCompute 18 9 9 4 (by decide), + source_yRow_eq_rowCompute 18 9 9 5 (by decide), + source_yRow_eq_rowCompute 18 9 9 6 (by decide), + computeRow_18_9_9_0, computeRow_18_9_9_1, computeRow_18_9_9_2, computeRow_18_9_9_3, computeRow_18_9_9_4, computeRow_18_9_9_5, computeRow_18_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_9_11 : Y 18 9 11 = (50562764756881342854273/327680000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 9 11 0 (by decide), + source_yRow_eq_rowCompute 18 9 11 1 (by decide), + source_yRow_eq_rowCompute 18 9 11 2 (by decide), + source_yRow_eq_rowCompute 18 9 11 3 (by decide), + source_yRow_eq_rowCompute 18 9 11 4 (by decide), + source_yRow_eq_rowCompute 18 9 11 5 (by decide), + source_yRow_eq_rowCompute 18 9 11 6 (by decide), + computeRow_18_9_11_0, computeRow_18_9_11_1, computeRow_18_9_11_2, computeRow_18_9_11_3, computeRow_18_9_11_4, computeRow_18_9_11_5, computeRow_18_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_9_13 : Y 18 9 13 = (-141645844790470070219169/1638400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 9 13 0 (by decide), + source_yRow_eq_rowCompute 18 9 13 1 (by decide), + source_yRow_eq_rowCompute 18 9 13 2 (by decide), + source_yRow_eq_rowCompute 18 9 13 3 (by decide), + source_yRow_eq_rowCompute 18 9 13 4 (by decide), + source_yRow_eq_rowCompute 18 9 13 5 (by decide), + source_yRow_eq_rowCompute 18 9 13 6 (by decide), + computeRow_18_9_13_0, computeRow_18_9_13_1, computeRow_18_9_13_2, computeRow_18_9_13_3, computeRow_18_9_13_4, computeRow_18_9_13_5, computeRow_18_9_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_9_15 : Y 18 9 15 = (-70438571087878610696079/163840000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 9 15 0 (by decide), + source_yRow_eq_rowCompute 18 9 15 1 (by decide), + source_yRow_eq_rowCompute 18 9 15 2 (by decide), + source_yRow_eq_rowCompute 18 9 15 3 (by decide), + source_yRow_eq_rowCompute 18 9 15 4 (by decide), + source_yRow_eq_rowCompute 18 9 15 5 (by decide), + source_yRow_eq_rowCompute 18 9 15 6 (by decide), + computeRow_18_9_15_0, computeRow_18_9_15_1, computeRow_18_9_15_2, computeRow_18_9_15_3, computeRow_18_9_15_4, computeRow_18_9_15_5, computeRow_18_9_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_9_17 : Y 18 9 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 9 17 0 (by decide), + source_yRow_eq_rowCompute 18 9 17 1 (by decide), + source_yRow_eq_rowCompute 18 9 17 2 (by decide), + source_yRow_eq_rowCompute 18 9 17 3 (by decide), + source_yRow_eq_rowCompute 18 9 17 4 (by decide), + source_yRow_eq_rowCompute 18 9 17 5 (by decide), + source_yRow_eq_rowCompute 18 9 17 6 (by decide), + computeRow_18_9_17_0, computeRow_18_9_17_1, computeRow_18_9_17_2, computeRow_18_9_17_3, computeRow_18_9_17_4, computeRow_18_9_17_5, computeRow_18_9_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_11_11 : Y 18 11 11 = (-60223184109272615717979/163840000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 11 11 0 (by decide), + source_yRow_eq_rowCompute 18 11 11 1 (by decide), + source_yRow_eq_rowCompute 18 11 11 2 (by decide), + source_yRow_eq_rowCompute 18 11 11 3 (by decide), + source_yRow_eq_rowCompute 18 11 11 4 (by decide), + source_yRow_eq_rowCompute 18 11 11 5 (by decide), + source_yRow_eq_rowCompute 18 11 11 6 (by decide), + computeRow_18_11_11_0, computeRow_18_11_11_1, computeRow_18_11_11_2, computeRow_18_11_11_3, computeRow_18_11_11_4, computeRow_18_11_11_5, computeRow_18_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_11_13 : Y 18 11 13 = (241267392281008969222347/819200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 11 13 0 (by decide), + source_yRow_eq_rowCompute 18 11 13 1 (by decide), + source_yRow_eq_rowCompute 18 11 13 2 (by decide), + source_yRow_eq_rowCompute 18 11 13 3 (by decide), + source_yRow_eq_rowCompute 18 11 13 4 (by decide), + source_yRow_eq_rowCompute 18 11 13 5 (by decide), + source_yRow_eq_rowCompute 18 11 13 6 (by decide), + computeRow_18_11_13_0, computeRow_18_11_13_1, computeRow_18_11_13_2, computeRow_18_11_13_3, computeRow_18_11_13_4, computeRow_18_11_13_5, computeRow_18_11_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_11_15 : Y 18 11 15 = (153598002652096074585513/81920000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 11 15 0 (by decide), + source_yRow_eq_rowCompute 18 11 15 1 (by decide), + source_yRow_eq_rowCompute 18 11 15 2 (by decide), + source_yRow_eq_rowCompute 18 11 15 3 (by decide), + source_yRow_eq_rowCompute 18 11 15 4 (by decide), + source_yRow_eq_rowCompute 18 11 15 5 (by decide), + source_yRow_eq_rowCompute 18 11 15 6 (by decide), + computeRow_18_11_15_0, computeRow_18_11_15_1, computeRow_18_11_15_2, computeRow_18_11_15_3, computeRow_18_11_15_4, computeRow_18_11_15_5, computeRow_18_11_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_11_17 : Y 18 11 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 11 17 0 (by decide), + source_yRow_eq_rowCompute 18 11 17 1 (by decide), + source_yRow_eq_rowCompute 18 11 17 2 (by decide), + source_yRow_eq_rowCompute 18 11 17 3 (by decide), + source_yRow_eq_rowCompute 18 11 17 4 (by decide), + source_yRow_eq_rowCompute 18 11 17 5 (by decide), + source_yRow_eq_rowCompute 18 11 17 6 (by decide), + computeRow_18_11_17_0, computeRow_18_11_17_1, computeRow_18_11_17_2, computeRow_18_11_17_3, computeRow_18_11_17_4, computeRow_18_11_17_5, computeRow_18_11_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_13_13 : Y 18 13 13 = (-149658956021574385833447/819200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 13 13 0 (by decide), + source_yRow_eq_rowCompute 18 13 13 1 (by decide), + source_yRow_eq_rowCompute 18 13 13 2 (by decide), + source_yRow_eq_rowCompute 18 13 13 3 (by decide), + source_yRow_eq_rowCompute 18 13 13 4 (by decide), + source_yRow_eq_rowCompute 18 13 13 5 (by decide), + source_yRow_eq_rowCompute 18 13 13 6 (by decide), + computeRow_18_13_13_0, computeRow_18_13_13_1, computeRow_18_13_13_2, computeRow_18_13_13_3, computeRow_18_13_13_4, computeRow_18_13_13_5, computeRow_18_13_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_13_15 : Y 18 13 15 = (-32035926190597582065813/16384000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 13 15 0 (by decide), + source_yRow_eq_rowCompute 18 13 15 1 (by decide), + source_yRow_eq_rowCompute 18 13 15 2 (by decide), + source_yRow_eq_rowCompute 18 13 15 3 (by decide), + source_yRow_eq_rowCompute 18 13 15 4 (by decide), + source_yRow_eq_rowCompute 18 13 15 5 (by decide), + source_yRow_eq_rowCompute 18 13 15 6 (by decide), + computeRow_18_13_15_0, computeRow_18_13_15_1, computeRow_18_13_15_2, computeRow_18_13_15_3, computeRow_18_13_15_4, computeRow_18_13_15_5, computeRow_18_13_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_13_17 : Y 18 13 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 13 17 0 (by decide), + source_yRow_eq_rowCompute 18 13 17 1 (by decide), + source_yRow_eq_rowCompute 18 13 17 2 (by decide), + source_yRow_eq_rowCompute 18 13 17 3 (by decide), + source_yRow_eq_rowCompute 18 13 17 4 (by decide), + source_yRow_eq_rowCompute 18 13 17 5 (by decide), + source_yRow_eq_rowCompute 18 13 17 6 (by decide), + computeRow_18_13_17_0, computeRow_18_13_17_1, computeRow_18_13_17_2, computeRow_18_13_17_3, computeRow_18_13_17_4, computeRow_18_13_17_5, computeRow_18_13_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_15_15 : Y 18 15 15 = (-884740548279231685308267/40960000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 15 15 0 (by decide), + source_yRow_eq_rowCompute 18 15 15 1 (by decide), + source_yRow_eq_rowCompute 18 15 15 2 (by decide), + source_yRow_eq_rowCompute 18 15 15 3 (by decide), + source_yRow_eq_rowCompute 18 15 15 4 (by decide), + source_yRow_eq_rowCompute 18 15 15 5 (by decide), + source_yRow_eq_rowCompute 18 15 15 6 (by decide), + computeRow_18_15_15_0, computeRow_18_15_15_1, computeRow_18_15_15_2, computeRow_18_15_15_3, computeRow_18_15_15_4, computeRow_18_15_15_5, computeRow_18_15_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_15_17 : Y 18 15 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 15 17 0 (by decide), + source_yRow_eq_rowCompute 18 15 17 1 (by decide), + source_yRow_eq_rowCompute 18 15 17 2 (by decide), + source_yRow_eq_rowCompute 18 15 17 3 (by decide), + source_yRow_eq_rowCompute 18 15 17 4 (by decide), + source_yRow_eq_rowCompute 18 15 17 5 (by decide), + source_yRow_eq_rowCompute 18 15 17 6 (by decide), + computeRow_18_15_17_0, computeRow_18_15_17_1, computeRow_18_15_17_2, computeRow_18_15_17_3, computeRow_18_15_17_4, computeRow_18_15_17_5, computeRow_18_15_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_18_17_17 : Y 18 17 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 18 17 17 0 (by decide), + source_yRow_eq_rowCompute 18 17 17 1 (by decide), + source_yRow_eq_rowCompute 18 17 17 2 (by decide), + source_yRow_eq_rowCompute 18 17 17 3 (by decide), + source_yRow_eq_rowCompute 18 17 17 4 (by decide), + source_yRow_eq_rowCompute 18 17 17 5 (by decide), + source_yRow_eq_rowCompute 18 17 17 6 (by decide), + computeRow_18_17_17_0, computeRow_18_17_17_1, computeRow_18_17_17_2, computeRow_18_17_17_3, computeRow_18_17_17_4, computeRow_18_17_17_5, computeRow_18_17_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_18_1_1 : Z 18 1 1 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_1_1 + +theorem source_gram_18_1_3 : Z 18 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_1_3 + +theorem source_gram_18_1_5 : Z 18 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_1_5 + +theorem source_gram_18_1_7 : Z 18 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_1_7 + +theorem source_gram_18_1_9 : Z 18 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_1_9 + +theorem source_gram_18_1_11 : Z 18 1 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_1_11 + +theorem source_gram_18_1_13 : Z 18 1 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_1_13 + +theorem source_gram_18_1_15 : Z 18 1 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_1_15 + +theorem source_gram_18_1_17 : Z 18 1 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_1_17 + +theorem source_gram_18_3_3 : Z 18 3 3 = (7846046208000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_3_3 + +theorem source_gram_18_3_5 : Z 18 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_3_5 + +theorem source_gram_18_3_7 : Z 18 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_3_7 + +theorem source_gram_18_3_9 : Z 18 3 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_3_9 + +theorem source_gram_18_3_11 : Z 18 3 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_3_11 + +theorem source_gram_18_3_13 : Z 18 3 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_3_13 + +theorem source_gram_18_3_15 : Z 18 3 15 = (-858161304000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_3_15 + +theorem source_gram_18_3_17 : Z 18 3 17 = (16672848192000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_3_17 + +theorem source_gram_18_5_5 : Z 18 5 5 = (747242496000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_5_5 + +theorem source_gram_18_5_7 : Z 18 5 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_5_7 + +theorem source_gram_18_5_9 : Z 18 5 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_5_9 + +theorem source_gram_18_5_11 : Z 18 5 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_5_11 + +theorem source_gram_18_5_13 : Z 18 5 13 = (-140107968000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_5_13 + +theorem source_gram_18_5_15 : Z 18 5 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_5_15 + +theorem source_gram_18_5_17 : Z 18 5 17 = (11115232128000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_5_17 + +theorem source_gram_18_7_7 : Z 18 7 7 = (201180672000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_7_7 + +theorem source_gram_18_7_9 : Z 18 7 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_7_9 + +theorem source_gram_18_7_11 : Z 18 7 11 = (-47151720000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_7_11 + +theorem source_gram_18_7_13 : Z 18 7 13 = (-163459296000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_7_13 + +theorem source_gram_18_7_15 : Z 18 7 15 = (643620978000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_7_15 + +theorem source_gram_18_7_17 : Z 18 7 17 = (4168212048000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_7_17 + +theorem source_gram_18_9_9 : Z 18 9 9 = (98761420800 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_9_9 + +theorem source_gram_18_9_11 : Z 18 9 11 = (-113164128000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_9_11 + +theorem source_gram_18_9_13 : Z 18 9 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_9_13 + +theorem source_gram_18_9_15 : Z 18 9 15 = (367783416000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_9_15 + +theorem source_gram_18_9_17 : Z 18 9 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_9_17 + +theorem source_gram_18_11_11 : Z 18 11 11 = (149313780000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_11_11 + +theorem source_gram_18_11_13 : Z 18 11 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_11_13 + +theorem source_gram_18_11_15 : Z 18 11 15 = (-421418497500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_11_15 + +theorem source_gram_18_11_17 : Z 18 11 17 = (-1736755020000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_11_17 + +theorem source_gram_18_13_13 : Z 18 13 13 = (329837508000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_13_13 + +theorem source_gram_18_13_15 : Z 18 13 15 = (-1195296102000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_13_15 + +theorem source_gram_18_13_17 : Z 18 13 17 = (-2084106024000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_13_17 + +theorem source_gram_18_15_15 : Z 18 15 15 = (6169949911125 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_15_15 + +theorem source_gram_18_15_17 : Z 18 15 17 = (-1823592771000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_15_17 + +theorem source_gram_18_17_17 : Z 18 17 17 = (354298024080000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_18_17_17 + +theorem source_error_18_3_1 : Y 18 3 1 = (43700029260178412251303173/3276800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_1_3 + +theorem source_gram_18_3_1 : Z 18 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_1_3 + +theorem source_error_18_5_1 : Y 18 5 1 = (-157097886646298732847063351/41943040000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_1_5 + +theorem source_gram_18_5_1 : Z 18 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_1_5 + +theorem source_error_18_5_3 : Y 18 5 3 = (5636036629375968042063837/5242880000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_3_5 + +theorem source_gram_18_5_3 : Z 18 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_3_5 + +theorem source_error_18_7_1 : Y 18 7 1 = (45795850251189055946275347/20971520000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_1_7 + +theorem source_gram_18_7_1 : Z 18 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_1_7 + +theorem source_error_18_7_3 : Y 18 7 3 = (-2298714004872189626128407/5242880000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_3_7 + +theorem source_gram_18_7_3 : Z 18 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_3_7 + +theorem source_error_18_7_5 : Y 18 7 5 = (3236875371562490528333463/20971520000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_5_7 + +theorem source_gram_18_7_5 : Z 18 7 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_5_7 + +theorem source_error_18_9_1 : Y 18 9 1 = (-15768543277252499592049191/5242880000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_1_9 + +theorem source_gram_18_9_1 : Z 18 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_1_9 + +theorem source_error_18_9_3 : Y 18 9 3 = (297813059860269307535181/1638400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_3_9 + +theorem source_gram_18_9_3 : Z 18 9 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_3_9 + +theorem source_error_18_9_5 : Y 18 9 5 = (109159200441997398693/5242880000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_5_9 + +theorem source_gram_18_9_5 : Z 18 9 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_5_9 + +theorem source_error_18_9_7 : Y 18 9 7 = (76480320836604209603463/2621440000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_7_9 + +theorem source_gram_18_9_7 : Z 18 9 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_7_9 + +theorem source_error_18_11_1 : Y 18 11 1 = (15774590706413201698776741/2621440000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_1_11 + +theorem source_gram_18_11_1 : Z 18 11 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_1_11 + +theorem source_error_18_11_3 : Y 18 11 3 = (-427966983073658698687017/3276800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_3_11 + +theorem source_gram_18_11_3 : Z 18 11 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_3_11 + +theorem source_error_18_11_5 : Y 18 11 5 = (-76974792598120601955771/524288000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_5_11 + +theorem source_gram_18_11_5 : Z 18 11 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_5_11 + +theorem source_error_18_11_7 : Y 18 11 7 = (34507713700153945513647/1310720000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_7_11 + +theorem source_gram_18_11_7 : Z 18 11 7 = (-47151720000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_7_11 + +theorem source_error_18_11_9 : Y 18 11 9 = (50562764756881342854273/327680000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_9_11 + +theorem source_gram_18_11_9 : Z 18 11 9 = (-113164128000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_9_11 + +theorem source_error_18_13_1 : Y 18 13 1 = (-111481601475376052708801013/13107200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_1_13 + +theorem source_gram_18_13_1 : Z 18 13 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_1_13 + +theorem source_error_18_13_3 : Y 18 13 3 = (460639052423449997118021/1638400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_3_13 + +theorem source_gram_18_13_3 : Z 18 13 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_3_13 + +theorem source_error_18_13_5 : Y 18 13 5 = (525900691396984091231043/2621440000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_5_13 + +theorem source_gram_18_13_5 : Z 18 13 5 = (-140107968000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_5_13 + +theorem source_error_18_13_7 : Y 18 13 7 = (-126720387057916007218863/1310720000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_7_13 + +theorem source_gram_18_13_7 : Z 18 13 7 = (-163459296000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_7_13 + +theorem source_error_18_13_9 : Y 18 13 9 = (-141645844790470070219169/1638400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_9_13 + +theorem source_gram_18_13_9 : Z 18 13 9 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_9_13 + +theorem source_error_18_13_11 : Y 18 13 11 = (241267392281008969222347/819200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_11_13 + +theorem source_gram_18_13_11 : Z 18 13 11 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_11_13 + +theorem source_error_18_15_1 : Y 18 15 1 = (-58408977661685586058262139/1310720000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_1_15 + +theorem source_gram_18_15_1 : Z 18 15 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_1_15 + +theorem source_error_18_15_3 : Y 18 15 3 = (856489912851915268585659/327680000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_3_15 + +theorem source_gram_18_15_3 : Z 18 15 3 = (-858161304000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_3_15 + +theorem source_error_18_15_5 : Y 18 15 5 = (166478085484275751174989/262144000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_5_15 + +theorem source_gram_18_15_5 : Z 18 15 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_5_15 + +theorem source_error_18_15_7 : Y 18 15 7 = (-293804443074929463225549/655360000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_7_15 + +theorem source_gram_18_15_7 : Z 18 15 7 = (643620978000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_7_15 + +theorem source_error_18_15_9 : Y 18 15 9 = (-70438571087878610696079/163840000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_9_15 + +theorem source_gram_18_15_9 : Z 18 15 9 = (367783416000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_9_15 + +theorem source_error_18_15_11 : Y 18 15 11 = (153598002652096074585513/81920000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_11_15 + +theorem source_gram_18_15_11 : Z 18 15 11 = (-421418497500 : ℚ) := by + rw [Z_symm] + exact source_gram_18_11_15 + +theorem source_error_18_15_13 : Y 18 15 13 = (-32035926190597582065813/16384000000000 : ℚ) := by + rw [Y_symm] + exact source_error_18_13_15 + +theorem source_gram_18_15_13 : Z 18 15 13 = (-1195296102000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_13_15 + +theorem source_error_18_17_1 : Y 18 17 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_18_1_17 + +theorem source_gram_18_17_1 : Z 18 17 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_1_17 + +theorem source_error_18_17_3 : Y 18 17 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_18_3_17 + +theorem source_gram_18_17_3 : Z 18 17 3 = (16672848192000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_3_17 + +theorem source_error_18_17_5 : Y 18 17 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_18_5_17 + +theorem source_gram_18_17_5 : Z 18 17 5 = (11115232128000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_5_17 + +theorem source_error_18_17_7 : Y 18 17 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_18_7_17 + +theorem source_gram_18_17_7 : Z 18 17 7 = (4168212048000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_7_17 + +theorem source_error_18_17_9 : Y 18 17 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_18_9_17 + +theorem source_gram_18_17_9 : Z 18 17 9 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_18_9_17 + +theorem source_error_18_17_11 : Y 18 17 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_18_11_17 + +theorem source_gram_18_17_11 : Z 18 17 11 = (-1736755020000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_11_17 + +theorem source_error_18_17_13 : Y 18 17 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_18_13_17 + +theorem source_gram_18_17_13 : Z 18 17 13 = (-2084106024000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_13_17 + +theorem source_error_18_17_15 : Y 18 17 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_18_15_17 + +theorem source_gram_18_17_15 : Z 18 17 15 = (-1823592771000 : ℚ) := by + rw [Z_symm] + exact source_gram_18_15_17 + +theorem error_18 : errorRational 18 = candidateY_18 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_18_1_1 + · exact source_error_18_1_3 + · exact source_error_18_1_5 + · exact source_error_18_1_7 + · exact source_error_18_1_9 + · exact source_error_18_1_11 + · exact source_error_18_1_13 + · exact source_error_18_1_15 + · exact source_error_18_1_17 + · exact source_error_18_3_1 + · exact source_error_18_3_3 + · exact source_error_18_3_5 + · exact source_error_18_3_7 + · exact source_error_18_3_9 + · exact source_error_18_3_11 + · exact source_error_18_3_13 + · exact source_error_18_3_15 + · exact source_error_18_3_17 + · exact source_error_18_5_1 + · exact source_error_18_5_3 + · exact source_error_18_5_5 + · exact source_error_18_5_7 + · exact source_error_18_5_9 + · exact source_error_18_5_11 + · exact source_error_18_5_13 + · exact source_error_18_5_15 + · exact source_error_18_5_17 + · exact source_error_18_7_1 + · exact source_error_18_7_3 + · exact source_error_18_7_5 + · exact source_error_18_7_7 + · exact source_error_18_7_9 + · exact source_error_18_7_11 + · exact source_error_18_7_13 + · exact source_error_18_7_15 + · exact source_error_18_7_17 + · exact source_error_18_9_1 + · exact source_error_18_9_3 + · exact source_error_18_9_5 + · exact source_error_18_9_7 + · exact source_error_18_9_9 + · exact source_error_18_9_11 + · exact source_error_18_9_13 + · exact source_error_18_9_15 + · exact source_error_18_9_17 + · exact source_error_18_11_1 + · exact source_error_18_11_3 + · exact source_error_18_11_5 + · exact source_error_18_11_7 + · exact source_error_18_11_9 + · exact source_error_18_11_11 + · exact source_error_18_11_13 + · exact source_error_18_11_15 + · exact source_error_18_11_17 + · exact source_error_18_13_1 + · exact source_error_18_13_3 + · exact source_error_18_13_5 + · exact source_error_18_13_7 + · exact source_error_18_13_9 + · exact source_error_18_13_11 + · exact source_error_18_13_13 + · exact source_error_18_13_15 + · exact source_error_18_13_17 + · exact source_error_18_15_1 + · exact source_error_18_15_3 + · exact source_error_18_15_5 + · exact source_error_18_15_7 + · exact source_error_18_15_9 + · exact source_error_18_15_11 + · exact source_error_18_15_13 + · exact source_error_18_15_15 + · exact source_error_18_15_17 + · exact source_error_18_17_1 + · exact source_error_18_17_3 + · exact source_error_18_17_5 + · exact source_error_18_17_7 + · exact source_error_18_17_9 + · exact source_error_18_17_11 + · exact source_error_18_17_13 + · exact source_error_18_17_15 + · exact source_error_18_17_17 + +theorem gram_18 : gramRational 18 = candidateZ_18 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_18_1_1 + · exact source_gram_18_1_3 + · exact source_gram_18_1_5 + · exact source_gram_18_1_7 + · exact source_gram_18_1_9 + · exact source_gram_18_1_11 + · exact source_gram_18_1_13 + · exact source_gram_18_1_15 + · exact source_gram_18_1_17 + · exact source_gram_18_3_1 + · exact source_gram_18_3_3 + · exact source_gram_18_3_5 + · exact source_gram_18_3_7 + · exact source_gram_18_3_9 + · exact source_gram_18_3_11 + · exact source_gram_18_3_13 + · exact source_gram_18_3_15 + · exact source_gram_18_3_17 + · exact source_gram_18_5_1 + · exact source_gram_18_5_3 + · exact source_gram_18_5_5 + · exact source_gram_18_5_7 + · exact source_gram_18_5_9 + · exact source_gram_18_5_11 + · exact source_gram_18_5_13 + · exact source_gram_18_5_15 + · exact source_gram_18_5_17 + · exact source_gram_18_7_1 + · exact source_gram_18_7_3 + · exact source_gram_18_7_5 + · exact source_gram_18_7_7 + · exact source_gram_18_7_9 + · exact source_gram_18_7_11 + · exact source_gram_18_7_13 + · exact source_gram_18_7_15 + · exact source_gram_18_7_17 + · exact source_gram_18_9_1 + · exact source_gram_18_9_3 + · exact source_gram_18_9_5 + · exact source_gram_18_9_7 + · exact source_gram_18_9_9 + · exact source_gram_18_9_11 + · exact source_gram_18_9_13 + · exact source_gram_18_9_15 + · exact source_gram_18_9_17 + · exact source_gram_18_11_1 + · exact source_gram_18_11_3 + · exact source_gram_18_11_5 + · exact source_gram_18_11_7 + · exact source_gram_18_11_9 + · exact source_gram_18_11_11 + · exact source_gram_18_11_13 + · exact source_gram_18_11_15 + · exact source_gram_18_11_17 + · exact source_gram_18_13_1 + · exact source_gram_18_13_3 + · exact source_gram_18_13_5 + · exact source_gram_18_13_7 + · exact source_gram_18_13_9 + · exact source_gram_18_13_11 + · exact source_gram_18_13_13 + · exact source_gram_18_13_15 + · exact source_gram_18_13_17 + · exact source_gram_18_15_1 + · exact source_gram_18_15_3 + · exact source_gram_18_15_5 + · exact source_gram_18_15_7 + · exact source_gram_18_15_9 + · exact source_gram_18_15_11 + · exact source_gram_18_15_13 + · exact source_gram_18_15_15 + · exact source_gram_18_15_17 + · exact source_gram_18_17_1 + · exact source_gram_18_17_3 + · exact source_gram_18_17_5 + · exact source_gram_18_17_7 + · exact source_gram_18_17_9 + · exact source_gram_18_17_11 + · exact source_gram_18_17_13 + · exact source_gram_18_17_15 + · exact source_gram_18_17_17 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData19.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData19.lean new file mode 100644 index 0000000000000000000000000000000000000000..0e106f94fa65fae66b36350d9d0955702f80aaa9 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData19.lean @@ -0,0 +1,1468 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram01Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram03Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram05Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram07Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram11Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram13Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram15Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram17Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram191919 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0101Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0103Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0105Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0107Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0109Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0111Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0113Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0115Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0117Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0119Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0303Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0305Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0307Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0309Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0311Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0313Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0315Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0317Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0319Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0505Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0507Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0509Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0511Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0513Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0515Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0517Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0519Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0707Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0709Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0711Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0713Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0715Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0717Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0719Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0909Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0911Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0913Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0915Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0917Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0919Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1111Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1113Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1115Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1117Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1119Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1313Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1315Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1317Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1319Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1515Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1517Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1519Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1717Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1719Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1919Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.Data19 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_19_1_1 : Y 19 1 1 = (-22693099803596038799039320263/209715200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 1 1 0 (by decide), + source_yRow_eq_rowCompute 19 1 1 1 (by decide), + source_yRow_eq_rowCompute 19 1 1 2 (by decide), + source_yRow_eq_rowCompute 19 1 1 3 (by decide), + source_yRow_eq_rowCompute 19 1 1 4 (by decide), + source_yRow_eq_rowCompute 19 1 1 5 (by decide), + source_yRow_eq_rowCompute 19 1 1 6 (by decide), + computeRow_19_1_1_0, computeRow_19_1_1_1, computeRow_19_1_1_2, computeRow_19_1_1_3, computeRow_19_1_1_4, computeRow_19_1_1_5, computeRow_19_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_1_3 : Y 19 1 3 = (2702377258995069402702006051/104857600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 1 3 0 (by decide), + source_yRow_eq_rowCompute 19 1 3 1 (by decide), + source_yRow_eq_rowCompute 19 1 3 2 (by decide), + source_yRow_eq_rowCompute 19 1 3 3 (by decide), + source_yRow_eq_rowCompute 19 1 3 4 (by decide), + source_yRow_eq_rowCompute 19 1 3 5 (by decide), + source_yRow_eq_rowCompute 19 1 3 6 (by decide), + computeRow_19_1_3_0, computeRow_19_1_3_1, computeRow_19_1_3_2, computeRow_19_1_3_3, computeRow_19_1_3_4, computeRow_19_1_3_5, computeRow_19_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_1_5 : Y 19 1 5 = (-75142211033583596476200627/8388608000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 1 5 0 (by decide), + source_yRow_eq_rowCompute 19 1 5 1 (by decide), + source_yRow_eq_rowCompute 19 1 5 2 (by decide), + source_yRow_eq_rowCompute 19 1 5 3 (by decide), + source_yRow_eq_rowCompute 19 1 5 4 (by decide), + source_yRow_eq_rowCompute 19 1 5 5 (by decide), + source_yRow_eq_rowCompute 19 1 5 6 (by decide), + computeRow_19_1_5_0, computeRow_19_1_5_1, computeRow_19_1_5_2, computeRow_19_1_5_3, computeRow_19_1_5_4, computeRow_19_1_5_5, computeRow_19_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_1_7 : Y 19 1 7 = (14766383937965483058974739/4194304000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 1 7 0 (by decide), + source_yRow_eq_rowCompute 19 1 7 1 (by decide), + source_yRow_eq_rowCompute 19 1 7 2 (by decide), + source_yRow_eq_rowCompute 19 1 7 3 (by decide), + source_yRow_eq_rowCompute 19 1 7 4 (by decide), + source_yRow_eq_rowCompute 19 1 7 5 (by decide), + source_yRow_eq_rowCompute 19 1 7 6 (by decide), + computeRow_19_1_7_0, computeRow_19_1_7_1, computeRow_19_1_7_2, computeRow_19_1_7_3, computeRow_19_1_7_4, computeRow_19_1_7_5, computeRow_19_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_1_9 : Y 19 1 9 = (-5511147190592216732622063/5242880000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 1 9 0 (by decide), + source_yRow_eq_rowCompute 19 1 9 1 (by decide), + source_yRow_eq_rowCompute 19 1 9 2 (by decide), + source_yRow_eq_rowCompute 19 1 9 3 (by decide), + source_yRow_eq_rowCompute 19 1 9 4 (by decide), + source_yRow_eq_rowCompute 19 1 9 5 (by decide), + source_yRow_eq_rowCompute 19 1 9 6 (by decide), + computeRow_19_1_9_0, computeRow_19_1_9_1, computeRow_19_1_9_2, computeRow_19_1_9_3, computeRow_19_1_9_4, computeRow_19_1_9_5, computeRow_19_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_1_11 : Y 19 1 11 = (7980474838179577610603727/13107200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 1 11 0 (by decide), + source_yRow_eq_rowCompute 19 1 11 1 (by decide), + source_yRow_eq_rowCompute 19 1 11 2 (by decide), + source_yRow_eq_rowCompute 19 1 11 3 (by decide), + source_yRow_eq_rowCompute 19 1 11 4 (by decide), + source_yRow_eq_rowCompute 19 1 11 5 (by decide), + source_yRow_eq_rowCompute 19 1 11 6 (by decide), + computeRow_19_1_11_0, computeRow_19_1_11_1, computeRow_19_1_11_2, computeRow_19_1_11_3, computeRow_19_1_11_4, computeRow_19_1_11_5, computeRow_19_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_1_13 : Y 19 1 13 = (-114214449015342819092842893/13107200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 1 13 0 (by decide), + source_yRow_eq_rowCompute 19 1 13 1 (by decide), + source_yRow_eq_rowCompute 19 1 13 2 (by decide), + source_yRow_eq_rowCompute 19 1 13 3 (by decide), + source_yRow_eq_rowCompute 19 1 13 4 (by decide), + source_yRow_eq_rowCompute 19 1 13 5 (by decide), + source_yRow_eq_rowCompute 19 1 13 6 (by decide), + computeRow_19_1_13_0, computeRow_19_1_13_1, computeRow_19_1_13_2, computeRow_19_1_13_3, computeRow_19_1_13_4, computeRow_19_1_13_5, computeRow_19_1_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_1_15 : Y 19 1 15 = (15237169390990960795194813/262144000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 1 15 0 (by decide), + source_yRow_eq_rowCompute 19 1 15 1 (by decide), + source_yRow_eq_rowCompute 19 1 15 2 (by decide), + source_yRow_eq_rowCompute 19 1 15 3 (by decide), + source_yRow_eq_rowCompute 19 1 15 4 (by decide), + source_yRow_eq_rowCompute 19 1 15 5 (by decide), + source_yRow_eq_rowCompute 19 1 15 6 (by decide), + computeRow_19_1_15_0, computeRow_19_1_15_1, computeRow_19_1_15_2, computeRow_19_1_15_3, computeRow_19_1_15_4, computeRow_19_1_15_5, computeRow_19_1_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_1_17 : Y 19 1 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 1 17 0 (by decide), + source_yRow_eq_rowCompute 19 1 17 1 (by decide), + source_yRow_eq_rowCompute 19 1 17 2 (by decide), + source_yRow_eq_rowCompute 19 1 17 3 (by decide), + source_yRow_eq_rowCompute 19 1 17 4 (by decide), + source_yRow_eq_rowCompute 19 1 17 5 (by decide), + source_yRow_eq_rowCompute 19 1 17 6 (by decide), + computeRow_19_1_17_0, computeRow_19_1_17_1, computeRow_19_1_17_2, computeRow_19_1_17_3, computeRow_19_1_17_4, computeRow_19_1_17_5, computeRow_19_1_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_1_19 : Y 19 1 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 1 19 0 (by decide), + source_yRow_eq_rowCompute 19 1 19 1 (by decide), + source_yRow_eq_rowCompute 19 1 19 2 (by decide), + source_yRow_eq_rowCompute 19 1 19 3 (by decide), + source_yRow_eq_rowCompute 19 1 19 4 (by decide), + source_yRow_eq_rowCompute 19 1 19 5 (by decide), + source_yRow_eq_rowCompute 19 1 19 6 (by decide), + computeRow_19_1_19_0, computeRow_19_1_19_1, computeRow_19_1_19_2, computeRow_19_1_19_3, computeRow_19_1_19_4, computeRow_19_1_19_5, computeRow_19_1_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_3_3 : Y 19 3 3 = (-333726928481320238730768903/52428800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 3 3 0 (by decide), + source_yRow_eq_rowCompute 19 3 3 1 (by decide), + source_yRow_eq_rowCompute 19 3 3 2 (by decide), + source_yRow_eq_rowCompute 19 3 3 3 (by decide), + source_yRow_eq_rowCompute 19 3 3 4 (by decide), + source_yRow_eq_rowCompute 19 3 3 5 (by decide), + source_yRow_eq_rowCompute 19 3 3 6 (by decide), + computeRow_19_3_3_0, computeRow_19_3_3_1, computeRow_19_3_3_2, computeRow_19_3_3_3, computeRow_19_3_3_4, computeRow_19_3_3_5, computeRow_19_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_3_5 : Y 19 3 5 = (48289254450191241887451051/20971520000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 3 5 0 (by decide), + source_yRow_eq_rowCompute 19 3 5 1 (by decide), + source_yRow_eq_rowCompute 19 3 5 2 (by decide), + source_yRow_eq_rowCompute 19 3 5 3 (by decide), + source_yRow_eq_rowCompute 19 3 5 4 (by decide), + source_yRow_eq_rowCompute 19 3 5 5 (by decide), + source_yRow_eq_rowCompute 19 3 5 6 (by decide), + computeRow_19_3_5_0, computeRow_19_3_5_1, computeRow_19_3_5_2, computeRow_19_3_5_3, computeRow_19_3_5_4, computeRow_19_3_5_5, computeRow_19_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_3_7 : Y 19 3 7 = (-10153357419755611709274627/10485760000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 3 7 0 (by decide), + source_yRow_eq_rowCompute 19 3 7 1 (by decide), + source_yRow_eq_rowCompute 19 3 7 2 (by decide), + source_yRow_eq_rowCompute 19 3 7 3 (by decide), + source_yRow_eq_rowCompute 19 3 7 4 (by decide), + source_yRow_eq_rowCompute 19 3 7 5 (by decide), + source_yRow_eq_rowCompute 19 3 7 6 (by decide), + computeRow_19_3_7_0, computeRow_19_3_7_1, computeRow_19_3_7_2, computeRow_19_3_7_3, computeRow_19_3_7_4, computeRow_19_3_7_5, computeRow_19_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_3_9 : Y 19 3 9 = (908184765784913635277259/2621440000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 3 9 0 (by decide), + source_yRow_eq_rowCompute 19 3 9 1 (by decide), + source_yRow_eq_rowCompute 19 3 9 2 (by decide), + source_yRow_eq_rowCompute 19 3 9 3 (by decide), + source_yRow_eq_rowCompute 19 3 9 4 (by decide), + source_yRow_eq_rowCompute 19 3 9 5 (by decide), + source_yRow_eq_rowCompute 19 3 9 6 (by decide), + computeRow_19_3_9_0, computeRow_19_3_9_1, computeRow_19_3_9_2, computeRow_19_3_9_3, computeRow_19_3_9_4, computeRow_19_3_9_5, computeRow_19_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_3_11 : Y 19 3 11 = (-1019757214709519396489379/6553600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 3 11 0 (by decide), + source_yRow_eq_rowCompute 19 3 11 1 (by decide), + source_yRow_eq_rowCompute 19 3 11 2 (by decide), + source_yRow_eq_rowCompute 19 3 11 3 (by decide), + source_yRow_eq_rowCompute 19 3 11 4 (by decide), + source_yRow_eq_rowCompute 19 3 11 5 (by decide), + source_yRow_eq_rowCompute 19 3 11 6 (by decide), + computeRow_19_3_11_0, computeRow_19_3_11_1, computeRow_19_3_11_2, computeRow_19_3_11_3, computeRow_19_3_11_4, computeRow_19_3_11_5, computeRow_19_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_3_13 : Y 19 3 13 = (11402120818106472624739569/6553600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 3 13 0 (by decide), + source_yRow_eq_rowCompute 19 3 13 1 (by decide), + source_yRow_eq_rowCompute 19 3 13 2 (by decide), + source_yRow_eq_rowCompute 19 3 13 3 (by decide), + source_yRow_eq_rowCompute 19 3 13 4 (by decide), + source_yRow_eq_rowCompute 19 3 13 5 (by decide), + source_yRow_eq_rowCompute 19 3 13 6 (by decide), + computeRow_19_3_13_0, computeRow_19_3_13_1, computeRow_19_3_13_2, computeRow_19_3_13_3, computeRow_19_3_13_4, computeRow_19_3_13_5, computeRow_19_3_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_3_15 : Y 19 3 15 = (-8025292448927789565871341/655360000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 3 15 0 (by decide), + source_yRow_eq_rowCompute 19 3 15 1 (by decide), + source_yRow_eq_rowCompute 19 3 15 2 (by decide), + source_yRow_eq_rowCompute 19 3 15 3 (by decide), + source_yRow_eq_rowCompute 19 3 15 4 (by decide), + source_yRow_eq_rowCompute 19 3 15 5 (by decide), + source_yRow_eq_rowCompute 19 3 15 6 (by decide), + computeRow_19_3_15_0, computeRow_19_3_15_1, computeRow_19_3_15_2, computeRow_19_3_15_3, computeRow_19_3_15_4, computeRow_19_3_15_5, computeRow_19_3_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_3_17 : Y 19 3 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 3 17 0 (by decide), + source_yRow_eq_rowCompute 19 3 17 1 (by decide), + source_yRow_eq_rowCompute 19 3 17 2 (by decide), + source_yRow_eq_rowCompute 19 3 17 3 (by decide), + source_yRow_eq_rowCompute 19 3 17 4 (by decide), + source_yRow_eq_rowCompute 19 3 17 5 (by decide), + source_yRow_eq_rowCompute 19 3 17 6 (by decide), + computeRow_19_3_17_0, computeRow_19_3_17_1, computeRow_19_3_17_2, computeRow_19_3_17_3, computeRow_19_3_17_4, computeRow_19_3_17_5, computeRow_19_3_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_3_19 : Y 19 3 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 3 19 0 (by decide), + source_yRow_eq_rowCompute 19 3 19 1 (by decide), + source_yRow_eq_rowCompute 19 3 19 2 (by decide), + source_yRow_eq_rowCompute 19 3 19 3 (by decide), + source_yRow_eq_rowCompute 19 3 19 4 (by decide), + source_yRow_eq_rowCompute 19 3 19 5 (by decide), + source_yRow_eq_rowCompute 19 3 19 6 (by decide), + computeRow_19_3_19_0, computeRow_19_3_19_1, computeRow_19_3_19_2, computeRow_19_3_19_3, computeRow_19_3_19_4, computeRow_19_3_19_5, computeRow_19_3_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_5_5 : Y 19 5 5 = (-37648602224655100714998963/41943040000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 5 5 0 (by decide), + source_yRow_eq_rowCompute 19 5 5 1 (by decide), + source_yRow_eq_rowCompute 19 5 5 2 (by decide), + source_yRow_eq_rowCompute 19 5 5 3 (by decide), + source_yRow_eq_rowCompute 19 5 5 4 (by decide), + source_yRow_eq_rowCompute 19 5 5 5 (by decide), + source_yRow_eq_rowCompute 19 5 5 6 (by decide), + computeRow_19_5_5_0, computeRow_19_5_5_1, computeRow_19_5_5_2, computeRow_19_5_5_3, computeRow_19_5_5_4, computeRow_19_5_5_5, computeRow_19_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_5_7 : Y 19 5 7 = (9278879137014220083120771/20971520000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 5 7 0 (by decide), + source_yRow_eq_rowCompute 19 5 7 1 (by decide), + source_yRow_eq_rowCompute 19 5 7 2 (by decide), + source_yRow_eq_rowCompute 19 5 7 3 (by decide), + source_yRow_eq_rowCompute 19 5 7 4 (by decide), + source_yRow_eq_rowCompute 19 5 7 5 (by decide), + source_yRow_eq_rowCompute 19 5 7 6 (by decide), + computeRow_19_5_7_0, computeRow_19_5_7_1, computeRow_19_5_7_2, computeRow_19_5_7_3, computeRow_19_5_7_4, computeRow_19_5_7_5, computeRow_19_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_5_9 : Y 19 5 9 = (-1279464695992326165509187/5242880000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 5 9 0 (by decide), + source_yRow_eq_rowCompute 19 5 9 1 (by decide), + source_yRow_eq_rowCompute 19 5 9 2 (by decide), + source_yRow_eq_rowCompute 19 5 9 3 (by decide), + source_yRow_eq_rowCompute 19 5 9 4 (by decide), + source_yRow_eq_rowCompute 19 5 9 5 (by decide), + source_yRow_eq_rowCompute 19 5 9 6 (by decide), + computeRow_19_5_9_0, computeRow_19_5_9_1, computeRow_19_5_9_2, computeRow_19_5_9_3, computeRow_19_5_9_4, computeRow_19_5_9_5, computeRow_19_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_5_11 : Y 19 5 11 = (488068742424207599021367/2621440000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 5 11 0 (by decide), + source_yRow_eq_rowCompute 19 5 11 1 (by decide), + source_yRow_eq_rowCompute 19 5 11 2 (by decide), + source_yRow_eq_rowCompute 19 5 11 3 (by decide), + source_yRow_eq_rowCompute 19 5 11 4 (by decide), + source_yRow_eq_rowCompute 19 5 11 5 (by decide), + source_yRow_eq_rowCompute 19 5 11 6 (by decide), + computeRow_19_5_11_0, computeRow_19_5_11_1, computeRow_19_5_11_2, computeRow_19_5_11_3, computeRow_19_5_11_4, computeRow_19_5_11_5, computeRow_19_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_5_13 : Y 19 5 13 = (-1577990685084360947348949/2621440000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 5 13 0 (by decide), + source_yRow_eq_rowCompute 19 5 13 1 (by decide), + source_yRow_eq_rowCompute 19 5 13 2 (by decide), + source_yRow_eq_rowCompute 19 5 13 3 (by decide), + source_yRow_eq_rowCompute 19 5 13 4 (by decide), + source_yRow_eq_rowCompute 19 5 13 5 (by decide), + source_yRow_eq_rowCompute 19 5 13 6 (by decide), + computeRow_19_5_13_0, computeRow_19_5_13_1, computeRow_19_5_13_2, computeRow_19_5_13_3, computeRow_19_5_13_4, computeRow_19_5_13_5, computeRow_19_5_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_5_15 : Y 19 5 15 = (4397077893934901813915277/1310720000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 5 15 0 (by decide), + source_yRow_eq_rowCompute 19 5 15 1 (by decide), + source_yRow_eq_rowCompute 19 5 15 2 (by decide), + source_yRow_eq_rowCompute 19 5 15 3 (by decide), + source_yRow_eq_rowCompute 19 5 15 4 (by decide), + source_yRow_eq_rowCompute 19 5 15 5 (by decide), + source_yRow_eq_rowCompute 19 5 15 6 (by decide), + computeRow_19_5_15_0, computeRow_19_5_15_1, computeRow_19_5_15_2, computeRow_19_5_15_3, computeRow_19_5_15_4, computeRow_19_5_15_5, computeRow_19_5_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_5_17 : Y 19 5 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 5 17 0 (by decide), + source_yRow_eq_rowCompute 19 5 17 1 (by decide), + source_yRow_eq_rowCompute 19 5 17 2 (by decide), + source_yRow_eq_rowCompute 19 5 17 3 (by decide), + source_yRow_eq_rowCompute 19 5 17 4 (by decide), + source_yRow_eq_rowCompute 19 5 17 5 (by decide), + source_yRow_eq_rowCompute 19 5 17 6 (by decide), + computeRow_19_5_17_0, computeRow_19_5_17_1, computeRow_19_5_17_2, computeRow_19_5_17_3, computeRow_19_5_17_4, computeRow_19_5_17_5, computeRow_19_5_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_5_19 : Y 19 5 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 5 19 0 (by decide), + source_yRow_eq_rowCompute 19 5 19 1 (by decide), + source_yRow_eq_rowCompute 19 5 19 2 (by decide), + source_yRow_eq_rowCompute 19 5 19 3 (by decide), + source_yRow_eq_rowCompute 19 5 19 4 (by decide), + source_yRow_eq_rowCompute 19 5 19 5 (by decide), + source_yRow_eq_rowCompute 19 5 19 6 (by decide), + computeRow_19_5_19_0, computeRow_19_5_19_1, computeRow_19_5_19_2, computeRow_19_5_19_3, computeRow_19_5_19_4, computeRow_19_5_19_5, computeRow_19_5_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_7_7 : Y 19 7 7 = (-601273345026853390678479/2097152000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 7 7 0 (by decide), + source_yRow_eq_rowCompute 19 7 7 1 (by decide), + source_yRow_eq_rowCompute 19 7 7 2 (by decide), + source_yRow_eq_rowCompute 19 7 7 3 (by decide), + source_yRow_eq_rowCompute 19 7 7 4 (by decide), + source_yRow_eq_rowCompute 19 7 7 5 (by decide), + source_yRow_eq_rowCompute 19 7 7 6 (by decide), + computeRow_19_7_7_0, computeRow_19_7_7_1, computeRow_19_7_7_2, computeRow_19_7_7_3, computeRow_19_7_7_4, computeRow_19_7_7_5, computeRow_19_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_7_9 : Y 19 7 9 = (5095867887885096310527/20971520000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 7 9 0 (by decide), + source_yRow_eq_rowCompute 19 7 9 1 (by decide), + source_yRow_eq_rowCompute 19 7 9 2 (by decide), + source_yRow_eq_rowCompute 19 7 9 3 (by decide), + source_yRow_eq_rowCompute 19 7 9 4 (by decide), + source_yRow_eq_rowCompute 19 7 9 5 (by decide), + source_yRow_eq_rowCompute 19 7 9 6 (by decide), + computeRow_19_7_9_0, computeRow_19_7_9_1, computeRow_19_7_9_2, computeRow_19_7_9_3, computeRow_19_7_9_4, computeRow_19_7_9_5, computeRow_19_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_7_11 : Y 19 7 11 = (-66971412540394818930243/262144000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 7 11 0 (by decide), + source_yRow_eq_rowCompute 19 7 11 1 (by decide), + source_yRow_eq_rowCompute 19 7 11 2 (by decide), + source_yRow_eq_rowCompute 19 7 11 3 (by decide), + source_yRow_eq_rowCompute 19 7 11 4 (by decide), + source_yRow_eq_rowCompute 19 7 11 5 (by decide), + source_yRow_eq_rowCompute 19 7 11 6 (by decide), + computeRow_19_7_11_0, computeRow_19_7_11_1, computeRow_19_7_11_2, computeRow_19_7_11_3, computeRow_19_7_11_4, computeRow_19_7_11_5, computeRow_19_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_7_13 : Y 19 7 13 = (423492380929481504822181/1310720000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 7 13 0 (by decide), + source_yRow_eq_rowCompute 19 7 13 1 (by decide), + source_yRow_eq_rowCompute 19 7 13 2 (by decide), + source_yRow_eq_rowCompute 19 7 13 3 (by decide), + source_yRow_eq_rowCompute 19 7 13 4 (by decide), + source_yRow_eq_rowCompute 19 7 13 5 (by decide), + source_yRow_eq_rowCompute 19 7 13 6 (by decide), + computeRow_19_7_13_0, computeRow_19_7_13_1, computeRow_19_7_13_2, computeRow_19_7_13_3, computeRow_19_7_13_4, computeRow_19_7_13_5, computeRow_19_7_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_7_15 : Y 19 7 15 = (-316097984120195393369253/655360000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 7 15 0 (by decide), + source_yRow_eq_rowCompute 19 7 15 1 (by decide), + source_yRow_eq_rowCompute 19 7 15 2 (by decide), + source_yRow_eq_rowCompute 19 7 15 3 (by decide), + source_yRow_eq_rowCompute 19 7 15 4 (by decide), + source_yRow_eq_rowCompute 19 7 15 5 (by decide), + source_yRow_eq_rowCompute 19 7 15 6 (by decide), + computeRow_19_7_15_0, computeRow_19_7_15_1, computeRow_19_7_15_2, computeRow_19_7_15_3, computeRow_19_7_15_4, computeRow_19_7_15_5, computeRow_19_7_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_7_17 : Y 19 7 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 7 17 0 (by decide), + source_yRow_eq_rowCompute 19 7 17 1 (by decide), + source_yRow_eq_rowCompute 19 7 17 2 (by decide), + source_yRow_eq_rowCompute 19 7 17 3 (by decide), + source_yRow_eq_rowCompute 19 7 17 4 (by decide), + source_yRow_eq_rowCompute 19 7 17 5 (by decide), + source_yRow_eq_rowCompute 19 7 17 6 (by decide), + computeRow_19_7_17_0, computeRow_19_7_17_1, computeRow_19_7_17_2, computeRow_19_7_17_3, computeRow_19_7_17_4, computeRow_19_7_17_5, computeRow_19_7_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_7_19 : Y 19 7 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 7 19 0 (by decide), + source_yRow_eq_rowCompute 19 7 19 1 (by decide), + source_yRow_eq_rowCompute 19 7 19 2 (by decide), + source_yRow_eq_rowCompute 19 7 19 3 (by decide), + source_yRow_eq_rowCompute 19 7 19 4 (by decide), + source_yRow_eq_rowCompute 19 7 19 5 (by decide), + source_yRow_eq_rowCompute 19 7 19 6 (by decide), + computeRow_19_7_19_0, computeRow_19_7_19_1, computeRow_19_7_19_2, computeRow_19_7_19_3, computeRow_19_7_19_4, computeRow_19_7_19_5, computeRow_19_7_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_9_9 : Y 19 9 9 = (-38268821834268590378583/131072000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 9 9 0 (by decide), + source_yRow_eq_rowCompute 19 9 9 1 (by decide), + source_yRow_eq_rowCompute 19 9 9 2 (by decide), + source_yRow_eq_rowCompute 19 9 9 3 (by decide), + source_yRow_eq_rowCompute 19 9 9 4 (by decide), + source_yRow_eq_rowCompute 19 9 9 5 (by decide), + source_yRow_eq_rowCompute 19 9 9 6 (by decide), + computeRow_19_9_9_0, computeRow_19_9_9_1, computeRow_19_9_9_2, computeRow_19_9_9_3, computeRow_19_9_9_4, computeRow_19_9_9_5, computeRow_19_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_9_11 : Y 19 9 11 = (120716948708384445134487/327680000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 9 11 0 (by decide), + source_yRow_eq_rowCompute 19 9 11 1 (by decide), + source_yRow_eq_rowCompute 19 9 11 2 (by decide), + source_yRow_eq_rowCompute 19 9 11 3 (by decide), + source_yRow_eq_rowCompute 19 9 11 4 (by decide), + source_yRow_eq_rowCompute 19 9 11 5 (by decide), + source_yRow_eq_rowCompute 19 9 11 6 (by decide), + computeRow_19_9_11_0, computeRow_19_9_11_1, computeRow_19_9_11_2, computeRow_19_9_11_3, computeRow_19_9_11_4, computeRow_19_9_11_5, computeRow_19_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_9_13 : Y 19 9 13 = (-96794549499067619556357/327680000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 9 13 0 (by decide), + source_yRow_eq_rowCompute 19 9 13 1 (by decide), + source_yRow_eq_rowCompute 19 9 13 2 (by decide), + source_yRow_eq_rowCompute 19 9 13 3 (by decide), + source_yRow_eq_rowCompute 19 9 13 4 (by decide), + source_yRow_eq_rowCompute 19 9 13 5 (by decide), + source_yRow_eq_rowCompute 19 9 13 6 (by decide), + computeRow_19_9_13_0, computeRow_19_9_13_1, computeRow_19_9_13_2, computeRow_19_9_13_3, computeRow_19_9_13_4, computeRow_19_9_13_5, computeRow_19_9_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_9_15 : Y 19 9 15 = (-152177568634600729759539/163840000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 9 15 0 (by decide), + source_yRow_eq_rowCompute 19 9 15 1 (by decide), + source_yRow_eq_rowCompute 19 9 15 2 (by decide), + source_yRow_eq_rowCompute 19 9 15 3 (by decide), + source_yRow_eq_rowCompute 19 9 15 4 (by decide), + source_yRow_eq_rowCompute 19 9 15 5 (by decide), + source_yRow_eq_rowCompute 19 9 15 6 (by decide), + computeRow_19_9_15_0, computeRow_19_9_15_1, computeRow_19_9_15_2, computeRow_19_9_15_3, computeRow_19_9_15_4, computeRow_19_9_15_5, computeRow_19_9_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_9_17 : Y 19 9 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 9 17 0 (by decide), + source_yRow_eq_rowCompute 19 9 17 1 (by decide), + source_yRow_eq_rowCompute 19 9 17 2 (by decide), + source_yRow_eq_rowCompute 19 9 17 3 (by decide), + source_yRow_eq_rowCompute 19 9 17 4 (by decide), + source_yRow_eq_rowCompute 19 9 17 5 (by decide), + source_yRow_eq_rowCompute 19 9 17 6 (by decide), + computeRow_19_9_17_0, computeRow_19_9_17_1, computeRow_19_9_17_2, computeRow_19_9_17_3, computeRow_19_9_17_4, computeRow_19_9_17_5, computeRow_19_9_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_9_19 : Y 19 9 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 9 19 0 (by decide), + source_yRow_eq_rowCompute 19 9 19 1 (by decide), + source_yRow_eq_rowCompute 19 9 19 2 (by decide), + source_yRow_eq_rowCompute 19 9 19 3 (by decide), + source_yRow_eq_rowCompute 19 9 19 4 (by decide), + source_yRow_eq_rowCompute 19 9 19 5 (by decide), + source_yRow_eq_rowCompute 19 9 19 6 (by decide), + computeRow_19_9_19_0, computeRow_19_9_19_1, computeRow_19_9_19_2, computeRow_19_9_19_3, computeRow_19_9_19_4, computeRow_19_9_19_5, computeRow_19_9_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_11_11 : Y 19 11 11 = (-433804997186099031291183/819200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 11 11 0 (by decide), + source_yRow_eq_rowCompute 19 11 11 1 (by decide), + source_yRow_eq_rowCompute 19 11 11 2 (by decide), + source_yRow_eq_rowCompute 19 11 11 3 (by decide), + source_yRow_eq_rowCompute 19 11 11 4 (by decide), + source_yRow_eq_rowCompute 19 11 11 5 (by decide), + source_yRow_eq_rowCompute 19 11 11 6 (by decide), + computeRow_19_11_11_0, computeRow_19_11_11_1, computeRow_19_11_11_2, computeRow_19_11_11_3, computeRow_19_11_11_4, computeRow_19_11_11_5, computeRow_19_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_11_13 : Y 19 11 13 = (429290867351544749347797/819200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 11 13 0 (by decide), + source_yRow_eq_rowCompute 19 11 13 1 (by decide), + source_yRow_eq_rowCompute 19 11 13 2 (by decide), + source_yRow_eq_rowCompute 19 11 13 3 (by decide), + source_yRow_eq_rowCompute 19 11 13 4 (by decide), + source_yRow_eq_rowCompute 19 11 13 5 (by decide), + source_yRow_eq_rowCompute 19 11 13 6 (by decide), + computeRow_19_11_13_0, computeRow_19_11_13_1, computeRow_19_11_13_2, computeRow_19_11_13_3, computeRow_19_11_13_4, computeRow_19_11_13_5, computeRow_19_11_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_11_15 : Y 19 11 15 = (90088259697128585251359/81920000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 11 15 0 (by decide), + source_yRow_eq_rowCompute 19 11 15 1 (by decide), + source_yRow_eq_rowCompute 19 11 15 2 (by decide), + source_yRow_eq_rowCompute 19 11 15 3 (by decide), + source_yRow_eq_rowCompute 19 11 15 4 (by decide), + source_yRow_eq_rowCompute 19 11 15 5 (by decide), + source_yRow_eq_rowCompute 19 11 15 6 (by decide), + computeRow_19_11_15_0, computeRow_19_11_15_1, computeRow_19_11_15_2, computeRow_19_11_15_3, computeRow_19_11_15_4, computeRow_19_11_15_5, computeRow_19_11_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_11_17 : Y 19 11 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 11 17 0 (by decide), + source_yRow_eq_rowCompute 19 11 17 1 (by decide), + source_yRow_eq_rowCompute 19 11 17 2 (by decide), + source_yRow_eq_rowCompute 19 11 17 3 (by decide), + source_yRow_eq_rowCompute 19 11 17 4 (by decide), + source_yRow_eq_rowCompute 19 11 17 5 (by decide), + source_yRow_eq_rowCompute 19 11 17 6 (by decide), + computeRow_19_11_17_0, computeRow_19_11_17_1, computeRow_19_11_17_2, computeRow_19_11_17_3, computeRow_19_11_17_4, computeRow_19_11_17_5, computeRow_19_11_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_11_19 : Y 19 11 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 11 19 0 (by decide), + source_yRow_eq_rowCompute 19 11 19 1 (by decide), + source_yRow_eq_rowCompute 19 11 19 2 (by decide), + source_yRow_eq_rowCompute 19 11 19 3 (by decide), + source_yRow_eq_rowCompute 19 11 19 4 (by decide), + source_yRow_eq_rowCompute 19 11 19 5 (by decide), + source_yRow_eq_rowCompute 19 11 19 6 (by decide), + computeRow_19_11_19_0, computeRow_19_11_19_1, computeRow_19_11_19_2, computeRow_19_11_19_3, computeRow_19_11_19_4, computeRow_19_11_19_5, computeRow_19_11_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_13_13 : Y 19 13 13 = (-1253076332636888755282287/819200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 13 13 0 (by decide), + source_yRow_eq_rowCompute 19 13 13 1 (by decide), + source_yRow_eq_rowCompute 19 13 13 2 (by decide), + source_yRow_eq_rowCompute 19 13 13 3 (by decide), + source_yRow_eq_rowCompute 19 13 13 4 (by decide), + source_yRow_eq_rowCompute 19 13 13 5 (by decide), + source_yRow_eq_rowCompute 19 13 13 6 (by decide), + computeRow_19_13_13_0, computeRow_19_13_13_1, computeRow_19_13_13_2, computeRow_19_13_13_3, computeRow_19_13_13_4, computeRow_19_13_13_5, computeRow_19_13_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_13_15 : Y 19 13 15 = (415758366080515083757131/81920000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 13 15 0 (by decide), + source_yRow_eq_rowCompute 19 13 15 1 (by decide), + source_yRow_eq_rowCompute 19 13 15 2 (by decide), + source_yRow_eq_rowCompute 19 13 15 3 (by decide), + source_yRow_eq_rowCompute 19 13 15 4 (by decide), + source_yRow_eq_rowCompute 19 13 15 5 (by decide), + source_yRow_eq_rowCompute 19 13 15 6 (by decide), + computeRow_19_13_15_0, computeRow_19_13_15_1, computeRow_19_13_15_2, computeRow_19_13_15_3, computeRow_19_13_15_4, computeRow_19_13_15_5, computeRow_19_13_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_13_17 : Y 19 13 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 13 17 0 (by decide), + source_yRow_eq_rowCompute 19 13 17 1 (by decide), + source_yRow_eq_rowCompute 19 13 17 2 (by decide), + source_yRow_eq_rowCompute 19 13 17 3 (by decide), + source_yRow_eq_rowCompute 19 13 17 4 (by decide), + source_yRow_eq_rowCompute 19 13 17 5 (by decide), + source_yRow_eq_rowCompute 19 13 17 6 (by decide), + computeRow_19_13_17_0, computeRow_19_13_17_1, computeRow_19_13_17_2, computeRow_19_13_17_3, computeRow_19_13_17_4, computeRow_19_13_17_5, computeRow_19_13_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_13_19 : Y 19 13 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 13 19 0 (by decide), + source_yRow_eq_rowCompute 19 13 19 1 (by decide), + source_yRow_eq_rowCompute 19 13 19 2 (by decide), + source_yRow_eq_rowCompute 19 13 19 3 (by decide), + source_yRow_eq_rowCompute 19 13 19 4 (by decide), + source_yRow_eq_rowCompute 19 13 19 5 (by decide), + source_yRow_eq_rowCompute 19 13 19 6 (by decide), + computeRow_19_13_19_0, computeRow_19_13_19_1, computeRow_19_13_19_2, computeRow_19_13_19_3, computeRow_19_13_19_4, computeRow_19_13_19_5, computeRow_19_13_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_15_15 : Y 19 15 15 = (-68818433127534301774563/1638400000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 15 15 0 (by decide), + source_yRow_eq_rowCompute 19 15 15 1 (by decide), + source_yRow_eq_rowCompute 19 15 15 2 (by decide), + source_yRow_eq_rowCompute 19 15 15 3 (by decide), + source_yRow_eq_rowCompute 19 15 15 4 (by decide), + source_yRow_eq_rowCompute 19 15 15 5 (by decide), + source_yRow_eq_rowCompute 19 15 15 6 (by decide), + computeRow_19_15_15_0, computeRow_19_15_15_1, computeRow_19_15_15_2, computeRow_19_15_15_3, computeRow_19_15_15_4, computeRow_19_15_15_5, computeRow_19_15_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_15_17 : Y 19 15 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 15 17 0 (by decide), + source_yRow_eq_rowCompute 19 15 17 1 (by decide), + source_yRow_eq_rowCompute 19 15 17 2 (by decide), + source_yRow_eq_rowCompute 19 15 17 3 (by decide), + source_yRow_eq_rowCompute 19 15 17 4 (by decide), + source_yRow_eq_rowCompute 19 15 17 5 (by decide), + source_yRow_eq_rowCompute 19 15 17 6 (by decide), + computeRow_19_15_17_0, computeRow_19_15_17_1, computeRow_19_15_17_2, computeRow_19_15_17_3, computeRow_19_15_17_4, computeRow_19_15_17_5, computeRow_19_15_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_15_19 : Y 19 15 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 15 19 0 (by decide), + source_yRow_eq_rowCompute 19 15 19 1 (by decide), + source_yRow_eq_rowCompute 19 15 19 2 (by decide), + source_yRow_eq_rowCompute 19 15 19 3 (by decide), + source_yRow_eq_rowCompute 19 15 19 4 (by decide), + source_yRow_eq_rowCompute 19 15 19 5 (by decide), + source_yRow_eq_rowCompute 19 15 19 6 (by decide), + computeRow_19_15_19_0, computeRow_19_15_19_1, computeRow_19_15_19_2, computeRow_19_15_19_3, computeRow_19_15_19_4, computeRow_19_15_19_5, computeRow_19_15_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_17_17 : Y 19 17 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 17 17 0 (by decide), + source_yRow_eq_rowCompute 19 17 17 1 (by decide), + source_yRow_eq_rowCompute 19 17 17 2 (by decide), + source_yRow_eq_rowCompute 19 17 17 3 (by decide), + source_yRow_eq_rowCompute 19 17 17 4 (by decide), + source_yRow_eq_rowCompute 19 17 17 5 (by decide), + source_yRow_eq_rowCompute 19 17 17 6 (by decide), + computeRow_19_17_17_0, computeRow_19_17_17_1, computeRow_19_17_17_2, computeRow_19_17_17_3, computeRow_19_17_17_4, computeRow_19_17_17_5, computeRow_19_17_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_17_19 : Y 19 17 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 17 19 0 (by decide), + source_yRow_eq_rowCompute 19 17 19 1 (by decide), + source_yRow_eq_rowCompute 19 17 19 2 (by decide), + source_yRow_eq_rowCompute 19 17 19 3 (by decide), + source_yRow_eq_rowCompute 19 17 19 4 (by decide), + source_yRow_eq_rowCompute 19 17 19 5 (by decide), + source_yRow_eq_rowCompute 19 17 19 6 (by decide), + computeRow_19_17_19_0, computeRow_19_17_19_1, computeRow_19_17_19_2, computeRow_19_17_19_3, computeRow_19_17_19_4, computeRow_19_17_19_5, computeRow_19_17_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_19_19_19 : Y 19 19 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 19 19 19 0 (by decide), + source_yRow_eq_rowCompute 19 19 19 1 (by decide), + source_yRow_eq_rowCompute 19 19 19 2 (by decide), + source_yRow_eq_rowCompute 19 19 19 3 (by decide), + source_yRow_eq_rowCompute 19 19 19 4 (by decide), + source_yRow_eq_rowCompute 19 19 19 5 (by decide), + source_yRow_eq_rowCompute 19 19 19 6 (by decide), + computeRow_19_19_19_0, computeRow_19_19_19_1, computeRow_19_19_19_2, computeRow_19_19_19_3, computeRow_19_19_19_4, computeRow_19_19_19_5, computeRow_19_19_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_19_1_1 : Z 19 1 1 = (12804747411456000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_1_1 + +theorem source_gram_19_1_3 : Z 19 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_1_3 + +theorem source_gram_19_1_5 : Z 19 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_1_5 + +theorem source_gram_19_1_7 : Z 19 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_1_7 + +theorem source_gram_19_1_9 : Z 19 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_1_9 + +theorem source_gram_19_1_11 : Z 19 1 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_1_11 + +theorem source_gram_19_1_13 : Z 19 1 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_1_13 + +theorem source_gram_19_1_15 : Z 19 1 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_1_15 + +theorem source_gram_19_1_17 : Z 19 1 17 = (-50018544576000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_1_17 + +theorem source_gram_19_1_19 : Z 19 1 19 = (3801409387776000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_1_19 + +theorem source_gram_19_3_3 : Z 19 3 3 = (125536739328000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_3_3 + +theorem source_gram_19_3_5 : Z 19 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_3_5 + +theorem source_gram_19_3_7 : Z 19 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_3_7 + +theorem source_gram_19_3_9 : Z 19 3 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_3_9 + +theorem source_gram_19_3_11 : Z 19 3 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_3_11 + +theorem source_gram_19_3_13 : Z 19 3 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_3_13 + +theorem source_gram_19_3_15 : Z 19 3 15 = (-1961511552000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_3_15 + +theorem source_gram_19_3_17 : Z 19 3 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_3_17 + +theorem source_gram_19_3_19 : Z 19 3 19 = (1425528520416000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_3_19 + +theorem source_gram_19_5_5 : Z 19 5 5 = (10461394944000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_5_5 + +theorem source_gram_19_5_7 : Z 19 5 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_5_7 + +theorem source_gram_19_5_9 : Z 19 5 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_5_9 + +theorem source_gram_19_5_11 : Z 19 5 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_5_11 + +theorem source_gram_19_5_13 : Z 19 5 13 = (-245188944000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_5_13 + +theorem source_gram_19_5_15 : Z 19 5 15 = (-3677834160000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_5_15 + +theorem source_gram_19_5_17 : Z 19 5 17 = (34735100400000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_5_17 + +theorem source_gram_19_5_19 : Z 19 5 19 = (475176173472000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_5_19 + +theorem source_gram_19_7_7 : Z 19 7 7 = (2414168064000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_7_7 + +theorem source_gram_19_7_9 : Z 19 7 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_7_9 + +theorem source_gram_19_7_11 : Z 19 7 11 = (-75442752000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_7_11 + +theorem source_gram_19_7_13 : Z 19 7 13 = (-1225944720000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_7_13 + +theorem source_gram_19_7_15 : Z 19 7 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_7_15 + +theorem source_gram_19_7_17 : Z 19 7 17 = (29177484336000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_7_17 + +theorem source_gram_19_7_19 : Z 19 7 19 = (118794043368000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_7_19 + +theorem source_gram_19_9_9 : Z 19 9 9 = (1265380704000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_9_9 + +theorem source_gram_19_9_11 : Z 19 9 11 = (-678984768000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_9_11 + +theorem source_gram_19_9_13 : Z 19 9 13 = (-1103350248000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_9_13 + +theorem source_gram_19_9_15 : Z 19 9 15 = (2574483912000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_9_15 + +theorem source_gram_19_9_17 : Z 19 9 17 = (9378477108000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_9_17 + +theorem source_gram_19_9_19 : Z 19 9 19 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_9_19 + +theorem source_gram_19_11_11 : Z 19 11 11 = (572107536000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_11_11 + +theorem source_gram_19_11_13 : Z 19 11 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_11_13 + +theorem source_gram_19_11_15 : Z 19 11 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_11_15 + +theorem source_gram_19_11_17 : Z 19 11 17 = (-7641722088000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_11_17 + +theorem source_gram_19_11_19 : Z 19 11 19 = (-29698510842000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_11_19 + +theorem source_gram_19_13_13 : Z 19 13 13 = (3544293753000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_13_13 + +theorem source_gram_19_13_15 : Z 19 13 15 = (-6574128561000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_13_15 + +theorem source_gram_19_13_17 : Z 19 13 17 = (-16933361445000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_13_17 + +theorem source_gram_19_13_19 : Z 19 13 19 = (-29698510842000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_13_19 + +theorem source_gram_19_15_15 : Z 19 15 15 = (17439063642000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_15_15 + +theorem source_gram_19_15_17 : Z 19 15 17 = (-19538493975000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_15_17 + +theorem source_gram_19_15_19 : Z 19 15 19 = (-22273883131500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_15_19 + +theorem source_gram_19_17_17 : Z 19 17 17 = (693290894546250 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_17_17 + +theorem source_gram_19_17_19 : Z 19 17 19 = (-14849255421000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_17_19 + +theorem source_gram_19_19_19 : Z 19 19 19 = (121635819624193875 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_19_19_19 + +theorem source_error_19_3_1 : Y 19 3 1 = (2702377258995069402702006051/104857600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_1_3 + +theorem source_gram_19_3_1 : Z 19 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_1_3 + +theorem source_error_19_5_1 : Y 19 5 1 = (-75142211033583596476200627/8388608000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_1_5 + +theorem source_gram_19_5_1 : Z 19 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_1_5 + +theorem source_error_19_5_3 : Y 19 5 3 = (48289254450191241887451051/20971520000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_3_5 + +theorem source_gram_19_5_3 : Z 19 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_3_5 + +theorem source_error_19_7_1 : Y 19 7 1 = (14766383937965483058974739/4194304000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_1_7 + +theorem source_gram_19_7_1 : Z 19 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_1_7 + +theorem source_error_19_7_3 : Y 19 7 3 = (-10153357419755611709274627/10485760000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_3_7 + +theorem source_gram_19_7_3 : Z 19 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_3_7 + +theorem source_error_19_7_5 : Y 19 7 5 = (9278879137014220083120771/20971520000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_5_7 + +theorem source_gram_19_7_5 : Z 19 7 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_5_7 + +theorem source_error_19_9_1 : Y 19 9 1 = (-5511147190592216732622063/5242880000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_1_9 + +theorem source_gram_19_9_1 : Z 19 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_1_9 + +theorem source_error_19_9_3 : Y 19 9 3 = (908184765784913635277259/2621440000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_3_9 + +theorem source_gram_19_9_3 : Z 19 9 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_3_9 + +theorem source_error_19_9_5 : Y 19 9 5 = (-1279464695992326165509187/5242880000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_5_9 + +theorem source_gram_19_9_5 : Z 19 9 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_5_9 + +theorem source_error_19_9_7 : Y 19 9 7 = (5095867887885096310527/20971520000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_7_9 + +theorem source_gram_19_9_7 : Z 19 9 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_7_9 + +theorem source_error_19_11_1 : Y 19 11 1 = (7980474838179577610603727/13107200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_1_11 + +theorem source_gram_19_11_1 : Z 19 11 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_1_11 + +theorem source_error_19_11_3 : Y 19 11 3 = (-1019757214709519396489379/6553600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_3_11 + +theorem source_gram_19_11_3 : Z 19 11 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_3_11 + +theorem source_error_19_11_5 : Y 19 11 5 = (488068742424207599021367/2621440000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_5_11 + +theorem source_gram_19_11_5 : Z 19 11 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_5_11 + +theorem source_error_19_11_7 : Y 19 11 7 = (-66971412540394818930243/262144000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_7_11 + +theorem source_gram_19_11_7 : Z 19 11 7 = (-75442752000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_7_11 + +theorem source_error_19_11_9 : Y 19 11 9 = (120716948708384445134487/327680000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_9_11 + +theorem source_gram_19_11_9 : Z 19 11 9 = (-678984768000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_9_11 + +theorem source_error_19_13_1 : Y 19 13 1 = (-114214449015342819092842893/13107200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_1_13 + +theorem source_gram_19_13_1 : Z 19 13 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_1_13 + +theorem source_error_19_13_3 : Y 19 13 3 = (11402120818106472624739569/6553600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_3_13 + +theorem source_gram_19_13_3 : Z 19 13 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_3_13 + +theorem source_error_19_13_5 : Y 19 13 5 = (-1577990685084360947348949/2621440000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_5_13 + +theorem source_gram_19_13_5 : Z 19 13 5 = (-245188944000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_5_13 + +theorem source_error_19_13_7 : Y 19 13 7 = (423492380929481504822181/1310720000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_7_13 + +theorem source_gram_19_13_7 : Z 19 13 7 = (-1225944720000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_7_13 + +theorem source_error_19_13_9 : Y 19 13 9 = (-96794549499067619556357/327680000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_9_13 + +theorem source_gram_19_13_9 : Z 19 13 9 = (-1103350248000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_9_13 + +theorem source_error_19_13_11 : Y 19 13 11 = (429290867351544749347797/819200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_11_13 + +theorem source_gram_19_13_11 : Z 19 13 11 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_11_13 + +theorem source_error_19_15_1 : Y 19 15 1 = (15237169390990960795194813/262144000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_1_15 + +theorem source_gram_19_15_1 : Z 19 15 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_1_15 + +theorem source_error_19_15_3 : Y 19 15 3 = (-8025292448927789565871341/655360000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_3_15 + +theorem source_gram_19_15_3 : Z 19 15 3 = (-1961511552000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_3_15 + +theorem source_error_19_15_5 : Y 19 15 5 = (4397077893934901813915277/1310720000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_5_15 + +theorem source_gram_19_15_5 : Z 19 15 5 = (-3677834160000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_5_15 + +theorem source_error_19_15_7 : Y 19 15 7 = (-316097984120195393369253/655360000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_7_15 + +theorem source_gram_19_15_7 : Z 19 15 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_7_15 + +theorem source_error_19_15_9 : Y 19 15 9 = (-152177568634600729759539/163840000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_9_15 + +theorem source_gram_19_15_9 : Z 19 15 9 = (2574483912000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_9_15 + +theorem source_error_19_15_11 : Y 19 15 11 = (90088259697128585251359/81920000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_11_15 + +theorem source_gram_19_15_11 : Z 19 15 11 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_11_15 + +theorem source_error_19_15_13 : Y 19 15 13 = (415758366080515083757131/81920000000000 : ℚ) := by + rw [Y_symm] + exact source_error_19_13_15 + +theorem source_gram_19_15_13 : Z 19 15 13 = (-6574128561000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_13_15 + +theorem source_error_19_17_1 : Y 19 17 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_1_17 + +theorem source_gram_19_17_1 : Z 19 17 1 = (-50018544576000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_1_17 + +theorem source_error_19_17_3 : Y 19 17 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_3_17 + +theorem source_gram_19_17_3 : Z 19 17 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_3_17 + +theorem source_error_19_17_5 : Y 19 17 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_5_17 + +theorem source_gram_19_17_5 : Z 19 17 5 = (34735100400000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_5_17 + +theorem source_error_19_17_7 : Y 19 17 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_7_17 + +theorem source_gram_19_17_7 : Z 19 17 7 = (29177484336000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_7_17 + +theorem source_error_19_17_9 : Y 19 17 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_9_17 + +theorem source_gram_19_17_9 : Z 19 17 9 = (9378477108000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_9_17 + +theorem source_error_19_17_11 : Y 19 17 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_11_17 + +theorem source_gram_19_17_11 : Z 19 17 11 = (-7641722088000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_11_17 + +theorem source_error_19_17_13 : Y 19 17 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_13_17 + +theorem source_gram_19_17_13 : Z 19 17 13 = (-16933361445000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_13_17 + +theorem source_error_19_17_15 : Y 19 17 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_15_17 + +theorem source_gram_19_17_15 : Z 19 17 15 = (-19538493975000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_15_17 + +theorem source_error_19_19_1 : Y 19 19 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_1_19 + +theorem source_gram_19_19_1 : Z 19 19 1 = (3801409387776000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_1_19 + +theorem source_error_19_19_3 : Y 19 19 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_3_19 + +theorem source_gram_19_19_3 : Z 19 19 3 = (1425528520416000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_3_19 + +theorem source_error_19_19_5 : Y 19 19 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_5_19 + +theorem source_gram_19_19_5 : Z 19 19 5 = (475176173472000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_5_19 + +theorem source_error_19_19_7 : Y 19 19 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_7_19 + +theorem source_gram_19_19_7 : Z 19 19 7 = (118794043368000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_7_19 + +theorem source_error_19_19_9 : Y 19 19 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_9_19 + +theorem source_gram_19_19_9 : Z 19 19 9 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_19_9_19 + +theorem source_error_19_19_11 : Y 19 19 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_11_19 + +theorem source_gram_19_19_11 : Z 19 19 11 = (-29698510842000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_11_19 + +theorem source_error_19_19_13 : Y 19 19 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_13_19 + +theorem source_gram_19_19_13 : Z 19 19 13 = (-29698510842000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_13_19 + +theorem source_error_19_19_15 : Y 19 19 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_15_19 + +theorem source_gram_19_19_15 : Z 19 19 15 = (-22273883131500 : ℚ) := by + rw [Z_symm] + exact source_gram_19_15_19 + +theorem source_error_19_19_17 : Y 19 19 17 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_19_17_19 + +theorem source_gram_19_19_17 : Z 19 19 17 = (-14849255421000 : ℚ) := by + rw [Z_symm] + exact source_gram_19_17_19 + +theorem error_19 : errorRational 19 = candidateY_19 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_19_1_1 + · exact source_error_19_1_3 + · exact source_error_19_1_5 + · exact source_error_19_1_7 + · exact source_error_19_1_9 + · exact source_error_19_1_11 + · exact source_error_19_1_13 + · exact source_error_19_1_15 + · exact source_error_19_1_17 + · exact source_error_19_1_19 + · exact source_error_19_3_1 + · exact source_error_19_3_3 + · exact source_error_19_3_5 + · exact source_error_19_3_7 + · exact source_error_19_3_9 + · exact source_error_19_3_11 + · exact source_error_19_3_13 + · exact source_error_19_3_15 + · exact source_error_19_3_17 + · exact source_error_19_3_19 + · exact source_error_19_5_1 + · exact source_error_19_5_3 + · exact source_error_19_5_5 + · exact source_error_19_5_7 + · exact source_error_19_5_9 + · exact source_error_19_5_11 + · exact source_error_19_5_13 + · exact source_error_19_5_15 + · exact source_error_19_5_17 + · exact source_error_19_5_19 + · exact source_error_19_7_1 + · exact source_error_19_7_3 + · exact source_error_19_7_5 + · exact source_error_19_7_7 + · exact source_error_19_7_9 + · exact source_error_19_7_11 + · exact source_error_19_7_13 + · exact source_error_19_7_15 + · exact source_error_19_7_17 + · exact source_error_19_7_19 + · exact source_error_19_9_1 + · exact source_error_19_9_3 + · exact source_error_19_9_5 + · exact source_error_19_9_7 + · exact source_error_19_9_9 + · exact source_error_19_9_11 + · exact source_error_19_9_13 + · exact source_error_19_9_15 + · exact source_error_19_9_17 + · exact source_error_19_9_19 + · exact source_error_19_11_1 + · exact source_error_19_11_3 + · exact source_error_19_11_5 + · exact source_error_19_11_7 + · exact source_error_19_11_9 + · exact source_error_19_11_11 + · exact source_error_19_11_13 + · exact source_error_19_11_15 + · exact source_error_19_11_17 + · exact source_error_19_11_19 + · exact source_error_19_13_1 + · exact source_error_19_13_3 + · exact source_error_19_13_5 + · exact source_error_19_13_7 + · exact source_error_19_13_9 + · exact source_error_19_13_11 + · exact source_error_19_13_13 + · exact source_error_19_13_15 + · exact source_error_19_13_17 + · exact source_error_19_13_19 + · exact source_error_19_15_1 + · exact source_error_19_15_3 + · exact source_error_19_15_5 + · exact source_error_19_15_7 + · exact source_error_19_15_9 + · exact source_error_19_15_11 + · exact source_error_19_15_13 + · exact source_error_19_15_15 + · exact source_error_19_15_17 + · exact source_error_19_15_19 + · exact source_error_19_17_1 + · exact source_error_19_17_3 + · exact source_error_19_17_5 + · exact source_error_19_17_7 + · exact source_error_19_17_9 + · exact source_error_19_17_11 + · exact source_error_19_17_13 + · exact source_error_19_17_15 + · exact source_error_19_17_17 + · exact source_error_19_17_19 + · exact source_error_19_19_1 + · exact source_error_19_19_3 + · exact source_error_19_19_5 + · exact source_error_19_19_7 + · exact source_error_19_19_9 + · exact source_error_19_19_11 + · exact source_error_19_19_13 + · exact source_error_19_19_15 + · exact source_error_19_19_17 + · exact source_error_19_19_19 + +theorem gram_19 : gramRational 19 = candidateZ_19 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_19_1_1 + · exact source_gram_19_1_3 + · exact source_gram_19_1_5 + · exact source_gram_19_1_7 + · exact source_gram_19_1_9 + · exact source_gram_19_1_11 + · exact source_gram_19_1_13 + · exact source_gram_19_1_15 + · exact source_gram_19_1_17 + · exact source_gram_19_1_19 + · exact source_gram_19_3_1 + · exact source_gram_19_3_3 + · exact source_gram_19_3_5 + · exact source_gram_19_3_7 + · exact source_gram_19_3_9 + · exact source_gram_19_3_11 + · exact source_gram_19_3_13 + · exact source_gram_19_3_15 + · exact source_gram_19_3_17 + · exact source_gram_19_3_19 + · exact source_gram_19_5_1 + · exact source_gram_19_5_3 + · exact source_gram_19_5_5 + · exact source_gram_19_5_7 + · exact source_gram_19_5_9 + · exact source_gram_19_5_11 + · exact source_gram_19_5_13 + · exact source_gram_19_5_15 + · exact source_gram_19_5_17 + · exact source_gram_19_5_19 + · exact source_gram_19_7_1 + · exact source_gram_19_7_3 + · exact source_gram_19_7_5 + · exact source_gram_19_7_7 + · exact source_gram_19_7_9 + · exact source_gram_19_7_11 + · exact source_gram_19_7_13 + · exact source_gram_19_7_15 + · exact source_gram_19_7_17 + · exact source_gram_19_7_19 + · exact source_gram_19_9_1 + · exact source_gram_19_9_3 + · exact source_gram_19_9_5 + · exact source_gram_19_9_7 + · exact source_gram_19_9_9 + · exact source_gram_19_9_11 + · exact source_gram_19_9_13 + · exact source_gram_19_9_15 + · exact source_gram_19_9_17 + · exact source_gram_19_9_19 + · exact source_gram_19_11_1 + · exact source_gram_19_11_3 + · exact source_gram_19_11_5 + · exact source_gram_19_11_7 + · exact source_gram_19_11_9 + · exact source_gram_19_11_11 + · exact source_gram_19_11_13 + · exact source_gram_19_11_15 + · exact source_gram_19_11_17 + · exact source_gram_19_11_19 + · exact source_gram_19_13_1 + · exact source_gram_19_13_3 + · exact source_gram_19_13_5 + · exact source_gram_19_13_7 + · exact source_gram_19_13_9 + · exact source_gram_19_13_11 + · exact source_gram_19_13_13 + · exact source_gram_19_13_15 + · exact source_gram_19_13_17 + · exact source_gram_19_13_19 + · exact source_gram_19_15_1 + · exact source_gram_19_15_3 + · exact source_gram_19_15_5 + · exact source_gram_19_15_7 + · exact source_gram_19_15_9 + · exact source_gram_19_15_11 + · exact source_gram_19_15_13 + · exact source_gram_19_15_15 + · exact source_gram_19_15_17 + · exact source_gram_19_15_19 + · exact source_gram_19_17_1 + · exact source_gram_19_17_3 + · exact source_gram_19_17_5 + · exact source_gram_19_17_7 + · exact source_gram_19_17_9 + · exact source_gram_19_17_11 + · exact source_gram_19_17_13 + · exact source_gram_19_17_15 + · exact source_gram_19_17_17 + · exact source_gram_19_17_19 + · exact source_gram_19_19_1 + · exact source_gram_19_19_3 + · exact source_gram_19_19_5 + · exact source_gram_19_19_7 + · exact source_gram_19_19_9 + · exact source_gram_19_19_11 + · exact source_gram_19_19_13 + · exact source_gram_19_19_15 + · exact source_gram_19_19_17 + · exact source_gram_19_19_19 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData20.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData20.lean new file mode 100644 index 0000000000000000000000000000000000000000..afeca21cd36f51d1c3071f7144115d0d994035d4 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData20.lean @@ -0,0 +1,1468 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram01Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram03Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram05Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram07Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram11Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram13Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram15Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram17Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram191920 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0101Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0103Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0105Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0107Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0109Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0111Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0113Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0115Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0117Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0119Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0303Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0305Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0307Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0309Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0311Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0313Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0315Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0317Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0319Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0505Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0507Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0509Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0511Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0513Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0515Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0517Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0519Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0707Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0709Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0711Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0713Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0715Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0717Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0719Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0909Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0911Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0913Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0915Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0917Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0919Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1111Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1113Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1115Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1117Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1119Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1313Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1315Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1317Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1319Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1515Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1517Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1519Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1717Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1719Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1919Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.Data20 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_20_1_1 : Y 20 1 1 = (-864345790529147882613755097/1638400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 1 1 0 (by decide), + source_yRow_eq_rowCompute 20 1 1 1 (by decide), + source_yRow_eq_rowCompute 20 1 1 2 (by decide), + source_yRow_eq_rowCompute 20 1 1 3 (by decide), + source_yRow_eq_rowCompute 20 1 1 4 (by decide), + source_yRow_eq_rowCompute 20 1 1 5 (by decide), + source_yRow_eq_rowCompute 20 1 1 6 (by decide), + computeRow_20_1_1_0, computeRow_20_1_1_1, computeRow_20_1_1_2, computeRow_20_1_1_3, computeRow_20_1_1_4, computeRow_20_1_1_5, computeRow_20_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_1_3 : Y 20 1 3 = (21667622927027497262745903/204800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 1 3 0 (by decide), + source_yRow_eq_rowCompute 20 1 3 1 (by decide), + source_yRow_eq_rowCompute 20 1 3 2 (by decide), + source_yRow_eq_rowCompute 20 1 3 3 (by decide), + source_yRow_eq_rowCompute 20 1 3 4 (by decide), + source_yRow_eq_rowCompute 20 1 3 5 (by decide), + source_yRow_eq_rowCompute 20 1 3 6 (by decide), + computeRow_20_1_3_0, computeRow_20_1_3_1, computeRow_20_1_3_2, computeRow_20_1_3_3, computeRow_20_1_3_4, computeRow_20_1_3_5, computeRow_20_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_1_5 : Y 20 1 5 = (-11712315275254254792460329/327680000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 1 5 0 (by decide), + source_yRow_eq_rowCompute 20 1 5 1 (by decide), + source_yRow_eq_rowCompute 20 1 5 2 (by decide), + source_yRow_eq_rowCompute 20 1 5 3 (by decide), + source_yRow_eq_rowCompute 20 1 5 4 (by decide), + source_yRow_eq_rowCompute 20 1 5 5 (by decide), + source_yRow_eq_rowCompute 20 1 5 6 (by decide), + computeRow_20_1_5_0, computeRow_20_1_5_1, computeRow_20_1_5_2, computeRow_20_1_5_3, computeRow_20_1_5_4, computeRow_20_1_5_5, computeRow_20_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_1_7 : Y 20 1 7 = (665376664948039201360203/40960000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 1 7 0 (by decide), + source_yRow_eq_rowCompute 20 1 7 1 (by decide), + source_yRow_eq_rowCompute 20 1 7 2 (by decide), + source_yRow_eq_rowCompute 20 1 7 3 (by decide), + source_yRow_eq_rowCompute 20 1 7 4 (by decide), + source_yRow_eq_rowCompute 20 1 7 5 (by decide), + source_yRow_eq_rowCompute 20 1 7 6 (by decide), + computeRow_20_1_7_0, computeRow_20_1_7_1, computeRow_20_1_7_2, computeRow_20_1_7_3, computeRow_20_1_7_4, computeRow_20_1_7_5, computeRow_20_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_1_9 : Y 20 1 9 = (-316262058979922913891033/40960000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 1 9 0 (by decide), + source_yRow_eq_rowCompute 20 1 9 1 (by decide), + source_yRow_eq_rowCompute 20 1 9 2 (by decide), + source_yRow_eq_rowCompute 20 1 9 3 (by decide), + source_yRow_eq_rowCompute 20 1 9 4 (by decide), + source_yRow_eq_rowCompute 20 1 9 5 (by decide), + source_yRow_eq_rowCompute 20 1 9 6 (by decide), + computeRow_20_1_9_0, computeRow_20_1_9_1, computeRow_20_1_9_2, computeRow_20_1_9_3, computeRow_20_1_9_4, computeRow_20_1_9_5, computeRow_20_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_1_11 : Y 20 1 11 = (5363979077413683764037/25600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 1 11 0 (by decide), + source_yRow_eq_rowCompute 20 1 11 1 (by decide), + source_yRow_eq_rowCompute 20 1 11 2 (by decide), + source_yRow_eq_rowCompute 20 1 11 3 (by decide), + source_yRow_eq_rowCompute 20 1 11 4 (by decide), + source_yRow_eq_rowCompute 20 1 11 5 (by decide), + source_yRow_eq_rowCompute 20 1 11 6 (by decide), + computeRow_20_1_11_0, computeRow_20_1_11_1, computeRow_20_1_11_2, computeRow_20_1_11_3, computeRow_20_1_11_4, computeRow_20_1_11_5, computeRow_20_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_1_13 : Y 20 1 13 = (1356924469605003889899309/102400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 1 13 0 (by decide), + source_yRow_eq_rowCompute 20 1 13 1 (by decide), + source_yRow_eq_rowCompute 20 1 13 2 (by decide), + source_yRow_eq_rowCompute 20 1 13 3 (by decide), + source_yRow_eq_rowCompute 20 1 13 4 (by decide), + source_yRow_eq_rowCompute 20 1 13 5 (by decide), + source_yRow_eq_rowCompute 20 1 13 6 (by decide), + computeRow_20_1_13_0, computeRow_20_1_13_1, computeRow_20_1_13_2, computeRow_20_1_13_3, computeRow_20_1_13_4, computeRow_20_1_13_5, computeRow_20_1_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_1_15 : Y 20 1 15 = (-99760004425375579574289/2560000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 1 15 0 (by decide), + source_yRow_eq_rowCompute 20 1 15 1 (by decide), + source_yRow_eq_rowCompute 20 1 15 2 (by decide), + source_yRow_eq_rowCompute 20 1 15 3 (by decide), + source_yRow_eq_rowCompute 20 1 15 4 (by decide), + source_yRow_eq_rowCompute 20 1 15 5 (by decide), + source_yRow_eq_rowCompute 20 1 15 6 (by decide), + computeRow_20_1_15_0, computeRow_20_1_15_1, computeRow_20_1_15_2, computeRow_20_1_15_3, computeRow_20_1_15_4, computeRow_20_1_15_5, computeRow_20_1_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_1_17 : Y 20 1 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 1 17 0 (by decide), + source_yRow_eq_rowCompute 20 1 17 1 (by decide), + source_yRow_eq_rowCompute 20 1 17 2 (by decide), + source_yRow_eq_rowCompute 20 1 17 3 (by decide), + source_yRow_eq_rowCompute 20 1 17 4 (by decide), + source_yRow_eq_rowCompute 20 1 17 5 (by decide), + source_yRow_eq_rowCompute 20 1 17 6 (by decide), + computeRow_20_1_17_0, computeRow_20_1_17_1, computeRow_20_1_17_2, computeRow_20_1_17_3, computeRow_20_1_17_4, computeRow_20_1_17_5, computeRow_20_1_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_1_19 : Y 20 1 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 1 19 0 (by decide), + source_yRow_eq_rowCompute 20 1 19 1 (by decide), + source_yRow_eq_rowCompute 20 1 19 2 (by decide), + source_yRow_eq_rowCompute 20 1 19 3 (by decide), + source_yRow_eq_rowCompute 20 1 19 4 (by decide), + source_yRow_eq_rowCompute 20 1 19 5 (by decide), + source_yRow_eq_rowCompute 20 1 19 6 (by decide), + computeRow_20_1_19_0, computeRow_20_1_19_1, computeRow_20_1_19_2, computeRow_20_1_19_3, computeRow_20_1_19_4, computeRow_20_1_19_5, computeRow_20_1_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_3_3 : Y 20 3 3 = (-23371021993295094552757323/819200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 3 3 0 (by decide), + source_yRow_eq_rowCompute 20 3 3 1 (by decide), + source_yRow_eq_rowCompute 20 3 3 2 (by decide), + source_yRow_eq_rowCompute 20 3 3 3 (by decide), + source_yRow_eq_rowCompute 20 3 3 4 (by decide), + source_yRow_eq_rowCompute 20 3 3 5 (by decide), + source_yRow_eq_rowCompute 20 3 3 6 (by decide), + computeRow_20_3_3_0, computeRow_20_3_3_1, computeRow_20_3_3_2, computeRow_20_3_3_3, computeRow_20_3_3_4, computeRow_20_3_3_5, computeRow_20_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_3_5 : Y 20 3 5 = (1943037668945799386453493/163840000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 3 5 0 (by decide), + source_yRow_eq_rowCompute 20 3 5 1 (by decide), + source_yRow_eq_rowCompute 20 3 5 2 (by decide), + source_yRow_eq_rowCompute 20 3 5 3 (by decide), + source_yRow_eq_rowCompute 20 3 5 4 (by decide), + source_yRow_eq_rowCompute 20 3 5 5 (by decide), + source_yRow_eq_rowCompute 20 3 5 6 (by decide), + computeRow_20_3_5_0, computeRow_20_3_5_1, computeRow_20_3_5_2, computeRow_20_3_5_3, computeRow_20_3_5_4, computeRow_20_3_5_5, computeRow_20_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_3_7 : Y 20 3 7 = (-1013982585631618048647201/163840000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 3 7 0 (by decide), + source_yRow_eq_rowCompute 20 3 7 1 (by decide), + source_yRow_eq_rowCompute 20 3 7 2 (by decide), + source_yRow_eq_rowCompute 20 3 7 3 (by decide), + source_yRow_eq_rowCompute 20 3 7 4 (by decide), + source_yRow_eq_rowCompute 20 3 7 5 (by decide), + source_yRow_eq_rowCompute 20 3 7 6 (by decide), + computeRow_20_3_7_0, computeRow_20_3_7_1, computeRow_20_3_7_2, computeRow_20_3_7_3, computeRow_20_3_7_4, computeRow_20_3_7_5, computeRow_20_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_3_9 : Y 20 3 9 = (30613754919741298283979/10240000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 3 9 0 (by decide), + source_yRow_eq_rowCompute 20 3 9 1 (by decide), + source_yRow_eq_rowCompute 20 3 9 2 (by decide), + source_yRow_eq_rowCompute 20 3 9 3 (by decide), + source_yRow_eq_rowCompute 20 3 9 4 (by decide), + source_yRow_eq_rowCompute 20 3 9 5 (by decide), + source_yRow_eq_rowCompute 20 3 9 6 (by decide), + computeRow_20_3_9_0, computeRow_20_3_9_1, computeRow_20_3_9_2, computeRow_20_3_9_3, computeRow_20_3_9_4, computeRow_20_3_9_5, computeRow_20_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_3_11 : Y 20 3 11 = (107082038149227953680869/102400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 3 11 0 (by decide), + source_yRow_eq_rowCompute 20 3 11 1 (by decide), + source_yRow_eq_rowCompute 20 3 11 2 (by decide), + source_yRow_eq_rowCompute 20 3 11 3 (by decide), + source_yRow_eq_rowCompute 20 3 11 4 (by decide), + source_yRow_eq_rowCompute 20 3 11 5 (by decide), + source_yRow_eq_rowCompute 20 3 11 6 (by decide), + computeRow_20_3_11_0, computeRow_20_3_11_1, computeRow_20_3_11_2, computeRow_20_3_11_3, computeRow_20_3_11_4, computeRow_20_3_11_5, computeRow_20_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_3_13 : Y 20 3 13 = (-520977417754125297368403/51200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 3 13 0 (by decide), + source_yRow_eq_rowCompute 20 3 13 1 (by decide), + source_yRow_eq_rowCompute 20 3 13 2 (by decide), + source_yRow_eq_rowCompute 20 3 13 3 (by decide), + source_yRow_eq_rowCompute 20 3 13 4 (by decide), + source_yRow_eq_rowCompute 20 3 13 5 (by decide), + source_yRow_eq_rowCompute 20 3 13 6 (by decide), + computeRow_20_3_13_0, computeRow_20_3_13_1, computeRow_20_3_13_2, computeRow_20_3_13_3, computeRow_20_3_13_4, computeRow_20_3_13_5, computeRow_20_3_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_3_15 : Y 20 3 15 = (304457703228940211619669/10240000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 3 15 0 (by decide), + source_yRow_eq_rowCompute 20 3 15 1 (by decide), + source_yRow_eq_rowCompute 20 3 15 2 (by decide), + source_yRow_eq_rowCompute 20 3 15 3 (by decide), + source_yRow_eq_rowCompute 20 3 15 4 (by decide), + source_yRow_eq_rowCompute 20 3 15 5 (by decide), + source_yRow_eq_rowCompute 20 3 15 6 (by decide), + computeRow_20_3_15_0, computeRow_20_3_15_1, computeRow_20_3_15_2, computeRow_20_3_15_3, computeRow_20_3_15_4, computeRow_20_3_15_5, computeRow_20_3_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_3_17 : Y 20 3 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 3 17 0 (by decide), + source_yRow_eq_rowCompute 20 3 17 1 (by decide), + source_yRow_eq_rowCompute 20 3 17 2 (by decide), + source_yRow_eq_rowCompute 20 3 17 3 (by decide), + source_yRow_eq_rowCompute 20 3 17 4 (by decide), + source_yRow_eq_rowCompute 20 3 17 5 (by decide), + source_yRow_eq_rowCompute 20 3 17 6 (by decide), + computeRow_20_3_17_0, computeRow_20_3_17_1, computeRow_20_3_17_2, computeRow_20_3_17_3, computeRow_20_3_17_4, computeRow_20_3_17_5, computeRow_20_3_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_3_19 : Y 20 3 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 3 19 0 (by decide), + source_yRow_eq_rowCompute 20 3 19 1 (by decide), + source_yRow_eq_rowCompute 20 3 19 2 (by decide), + source_yRow_eq_rowCompute 20 3 19 3 (by decide), + source_yRow_eq_rowCompute 20 3 19 4 (by decide), + source_yRow_eq_rowCompute 20 3 19 5 (by decide), + source_yRow_eq_rowCompute 20 3 19 6 (by decide), + computeRow_20_3_19_0, computeRow_20_3_19_1, computeRow_20_3_19_2, computeRow_20_3_19_3, computeRow_20_3_19_4, computeRow_20_3_19_5, computeRow_20_3_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_5_5 : Y 20 5 5 = (-355964824312558132018347/65536000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 5 5 0 (by decide), + source_yRow_eq_rowCompute 20 5 5 1 (by decide), + source_yRow_eq_rowCompute 20 5 5 2 (by decide), + source_yRow_eq_rowCompute 20 5 5 3 (by decide), + source_yRow_eq_rowCompute 20 5 5 4 (by decide), + source_yRow_eq_rowCompute 20 5 5 5 (by decide), + source_yRow_eq_rowCompute 20 5 5 6 (by decide), + computeRow_20_5_5_0, computeRow_20_5_5_1, computeRow_20_5_5_2, computeRow_20_5_5_3, computeRow_20_5_5_4, computeRow_20_5_5_5, computeRow_20_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_5_7 : Y 20 5 7 = (97684912586085571093347/32768000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 5 7 0 (by decide), + source_yRow_eq_rowCompute 20 5 7 1 (by decide), + source_yRow_eq_rowCompute 20 5 7 2 (by decide), + source_yRow_eq_rowCompute 20 5 7 3 (by decide), + source_yRow_eq_rowCompute 20 5 7 4 (by decide), + source_yRow_eq_rowCompute 20 5 7 5 (by decide), + source_yRow_eq_rowCompute 20 5 7 6 (by decide), + computeRow_20_5_7_0, computeRow_20_5_7_1, computeRow_20_5_7_2, computeRow_20_5_7_3, computeRow_20_5_7_4, computeRow_20_5_7_5, computeRow_20_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_5_9 : Y 20 5 9 = (-11858364672253510424013/8192000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 5 9 0 (by decide), + source_yRow_eq_rowCompute 20 5 9 1 (by decide), + source_yRow_eq_rowCompute 20 5 9 2 (by decide), + source_yRow_eq_rowCompute 20 5 9 3 (by decide), + source_yRow_eq_rowCompute 20 5 9 4 (by decide), + source_yRow_eq_rowCompute 20 5 9 5 (by decide), + source_yRow_eq_rowCompute 20 5 9 6 (by decide), + computeRow_20_5_9_0, computeRow_20_5_9_1, computeRow_20_5_9_2, computeRow_20_5_9_3, computeRow_20_5_9_4, computeRow_20_5_9_5, computeRow_20_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_5_11 : Y 20 5 11 = (-14013038479459638758139/20480000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 5 11 0 (by decide), + source_yRow_eq_rowCompute 20 5 11 1 (by decide), + source_yRow_eq_rowCompute 20 5 11 2 (by decide), + source_yRow_eq_rowCompute 20 5 11 3 (by decide), + source_yRow_eq_rowCompute 20 5 11 4 (by decide), + source_yRow_eq_rowCompute 20 5 11 5 (by decide), + source_yRow_eq_rowCompute 20 5 11 6 (by decide), + computeRow_20_5_11_0, computeRow_20_5_11_1, computeRow_20_5_11_2, computeRow_20_5_11_3, computeRow_20_5_11_4, computeRow_20_5_11_5, computeRow_20_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_5_13 : Y 20 5 13 = (117196994897535165704091/20480000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 5 13 0 (by decide), + source_yRow_eq_rowCompute 20 5 13 1 (by decide), + source_yRow_eq_rowCompute 20 5 13 2 (by decide), + source_yRow_eq_rowCompute 20 5 13 3 (by decide), + source_yRow_eq_rowCompute 20 5 13 4 (by decide), + source_yRow_eq_rowCompute 20 5 13 5 (by decide), + source_yRow_eq_rowCompute 20 5 13 6 (by decide), + computeRow_20_5_13_0, computeRow_20_5_13_1, computeRow_20_5_13_2, computeRow_20_5_13_3, computeRow_20_5_13_4, computeRow_20_5_13_5, computeRow_20_5_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_5_15 : Y 20 5 15 = (-34211653005025978665183/2048000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 5 15 0 (by decide), + source_yRow_eq_rowCompute 20 5 15 1 (by decide), + source_yRow_eq_rowCompute 20 5 15 2 (by decide), + source_yRow_eq_rowCompute 20 5 15 3 (by decide), + source_yRow_eq_rowCompute 20 5 15 4 (by decide), + source_yRow_eq_rowCompute 20 5 15 5 (by decide), + source_yRow_eq_rowCompute 20 5 15 6 (by decide), + computeRow_20_5_15_0, computeRow_20_5_15_1, computeRow_20_5_15_2, computeRow_20_5_15_3, computeRow_20_5_15_4, computeRow_20_5_15_5, computeRow_20_5_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_5_17 : Y 20 5 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 5 17 0 (by decide), + source_yRow_eq_rowCompute 20 5 17 1 (by decide), + source_yRow_eq_rowCompute 20 5 17 2 (by decide), + source_yRow_eq_rowCompute 20 5 17 3 (by decide), + source_yRow_eq_rowCompute 20 5 17 4 (by decide), + source_yRow_eq_rowCompute 20 5 17 5 (by decide), + source_yRow_eq_rowCompute 20 5 17 6 (by decide), + computeRow_20_5_17_0, computeRow_20_5_17_1, computeRow_20_5_17_2, computeRow_20_5_17_3, computeRow_20_5_17_4, computeRow_20_5_17_5, computeRow_20_5_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_5_19 : Y 20 5 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 5 19 0 (by decide), + source_yRow_eq_rowCompute 20 5 19 1 (by decide), + source_yRow_eq_rowCompute 20 5 19 2 (by decide), + source_yRow_eq_rowCompute 20 5 19 3 (by decide), + source_yRow_eq_rowCompute 20 5 19 4 (by decide), + source_yRow_eq_rowCompute 20 5 19 5 (by decide), + source_yRow_eq_rowCompute 20 5 19 6 (by decide), + computeRow_20_5_19_0, computeRow_20_5_19_1, computeRow_20_5_19_2, computeRow_20_5_19_3, computeRow_20_5_19_4, computeRow_20_5_19_5, computeRow_20_5_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_7_7 : Y 20 7 7 = (-54884862420967333061307/32768000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 7 7 0 (by decide), + source_yRow_eq_rowCompute 20 7 7 1 (by decide), + source_yRow_eq_rowCompute 20 7 7 2 (by decide), + source_yRow_eq_rowCompute 20 7 7 3 (by decide), + source_yRow_eq_rowCompute 20 7 7 4 (by decide), + source_yRow_eq_rowCompute 20 7 7 5 (by decide), + source_yRow_eq_rowCompute 20 7 7 6 (by decide), + computeRow_20_7_7_0, computeRow_20_7_7_1, computeRow_20_7_7_2, computeRow_20_7_7_3, computeRow_20_7_7_4, computeRow_20_7_7_5, computeRow_20_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_7_9 : Y 20 7 9 = (333816883149802681629/409600000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 7 9 0 (by decide), + source_yRow_eq_rowCompute 20 7 9 1 (by decide), + source_yRow_eq_rowCompute 20 7 9 2 (by decide), + source_yRow_eq_rowCompute 20 7 9 3 (by decide), + source_yRow_eq_rowCompute 20 7 9 4 (by decide), + source_yRow_eq_rowCompute 20 7 9 5 (by decide), + source_yRow_eq_rowCompute 20 7 9 6 (by decide), + computeRow_20_7_9_0, computeRow_20_7_9_1, computeRow_20_7_9_2, computeRow_20_7_9_3, computeRow_20_7_9_4, computeRow_20_7_9_5, computeRow_20_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_7_11 : Y 20 7 11 = (8819254098389714698719/20480000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 7 11 0 (by decide), + source_yRow_eq_rowCompute 20 7 11 1 (by decide), + source_yRow_eq_rowCompute 20 7 11 2 (by decide), + source_yRow_eq_rowCompute 20 7 11 3 (by decide), + source_yRow_eq_rowCompute 20 7 11 4 (by decide), + source_yRow_eq_rowCompute 20 7 11 5 (by decide), + source_yRow_eq_rowCompute 20 7 11 6 (by decide), + computeRow_20_7_11_0, computeRow_20_7_11_1, computeRow_20_7_11_2, computeRow_20_7_11_3, computeRow_20_7_11_4, computeRow_20_7_11_5, computeRow_20_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_7_13 : Y 20 7 13 = (-35062147478835063928341/10240000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 7 13 0 (by decide), + source_yRow_eq_rowCompute 20 7 13 1 (by decide), + source_yRow_eq_rowCompute 20 7 13 2 (by decide), + source_yRow_eq_rowCompute 20 7 13 3 (by decide), + source_yRow_eq_rowCompute 20 7 13 4 (by decide), + source_yRow_eq_rowCompute 20 7 13 5 (by decide), + source_yRow_eq_rowCompute 20 7 13 6 (by decide), + computeRow_20_7_13_0, computeRow_20_7_13_1, computeRow_20_7_13_2, computeRow_20_7_13_3, computeRow_20_7_13_4, computeRow_20_7_13_5, computeRow_20_7_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_7_15 : Y 20 7 15 = (20460760081953150590631/2048000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 7 15 0 (by decide), + source_yRow_eq_rowCompute 20 7 15 1 (by decide), + source_yRow_eq_rowCompute 20 7 15 2 (by decide), + source_yRow_eq_rowCompute 20 7 15 3 (by decide), + source_yRow_eq_rowCompute 20 7 15 4 (by decide), + source_yRow_eq_rowCompute 20 7 15 5 (by decide), + source_yRow_eq_rowCompute 20 7 15 6 (by decide), + computeRow_20_7_15_0, computeRow_20_7_15_1, computeRow_20_7_15_2, computeRow_20_7_15_3, computeRow_20_7_15_4, computeRow_20_7_15_5, computeRow_20_7_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_7_17 : Y 20 7 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 7 17 0 (by decide), + source_yRow_eq_rowCompute 20 7 17 1 (by decide), + source_yRow_eq_rowCompute 20 7 17 2 (by decide), + source_yRow_eq_rowCompute 20 7 17 3 (by decide), + source_yRow_eq_rowCompute 20 7 17 4 (by decide), + source_yRow_eq_rowCompute 20 7 17 5 (by decide), + source_yRow_eq_rowCompute 20 7 17 6 (by decide), + computeRow_20_7_17_0, computeRow_20_7_17_1, computeRow_20_7_17_2, computeRow_20_7_17_3, computeRow_20_7_17_4, computeRow_20_7_17_5, computeRow_20_7_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_7_19 : Y 20 7 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 7 19 0 (by decide), + source_yRow_eq_rowCompute 20 7 19 1 (by decide), + source_yRow_eq_rowCompute 20 7 19 2 (by decide), + source_yRow_eq_rowCompute 20 7 19 3 (by decide), + source_yRow_eq_rowCompute 20 7 19 4 (by decide), + source_yRow_eq_rowCompute 20 7 19 5 (by decide), + source_yRow_eq_rowCompute 20 7 19 6 (by decide), + computeRow_20_7_19_0, computeRow_20_7_19_1, computeRow_20_7_19_2, computeRow_20_7_19_3, computeRow_20_7_19_4, computeRow_20_7_19_5, computeRow_20_7_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_9_9 : Y 20 9 9 = (-405636934175189416161/1024000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 9 9 0 (by decide), + source_yRow_eq_rowCompute 20 9 9 1 (by decide), + source_yRow_eq_rowCompute 20 9 9 2 (by decide), + source_yRow_eq_rowCompute 20 9 9 3 (by decide), + source_yRow_eq_rowCompute 20 9 9 4 (by decide), + source_yRow_eq_rowCompute 20 9 9 5 (by decide), + source_yRow_eq_rowCompute 20 9 9 6 (by decide), + computeRow_20_9_9_0, computeRow_20_9_9_1, computeRow_20_9_9_2, computeRow_20_9_9_3, computeRow_20_9_9_4, computeRow_20_9_9_5, computeRow_20_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_9_11 : Y 20 9 11 = (-272920889814962733729/1280000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 9 11 0 (by decide), + source_yRow_eq_rowCompute 20 9 11 1 (by decide), + source_yRow_eq_rowCompute 20 9 11 2 (by decide), + source_yRow_eq_rowCompute 20 9 11 3 (by decide), + source_yRow_eq_rowCompute 20 9 11 4 (by decide), + source_yRow_eq_rowCompute 20 9 11 5 (by decide), + source_yRow_eq_rowCompute 20 9 11 6 (by decide), + computeRow_20_9_11_0, computeRow_20_9_11_1, computeRow_20_9_11_2, computeRow_20_9_11_3, computeRow_20_9_11_4, computeRow_20_9_11_5, computeRow_20_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_9_13 : Y 20 9 13 = (4300425691175779286121/2560000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 9 13 0 (by decide), + source_yRow_eq_rowCompute 20 9 13 1 (by decide), + source_yRow_eq_rowCompute 20 9 13 2 (by decide), + source_yRow_eq_rowCompute 20 9 13 3 (by decide), + source_yRow_eq_rowCompute 20 9 13 4 (by decide), + source_yRow_eq_rowCompute 20 9 13 5 (by decide), + source_yRow_eq_rowCompute 20 9 13 6 (by decide), + computeRow_20_9_13_0, computeRow_20_9_13_1, computeRow_20_9_13_2, computeRow_20_9_13_3, computeRow_20_9_13_4, computeRow_20_9_13_5, computeRow_20_9_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_9_15 : Y 20 9 15 = (-627014474788464764001/128000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 9 15 0 (by decide), + source_yRow_eq_rowCompute 20 9 15 1 (by decide), + source_yRow_eq_rowCompute 20 9 15 2 (by decide), + source_yRow_eq_rowCompute 20 9 15 3 (by decide), + source_yRow_eq_rowCompute 20 9 15 4 (by decide), + source_yRow_eq_rowCompute 20 9 15 5 (by decide), + source_yRow_eq_rowCompute 20 9 15 6 (by decide), + computeRow_20_9_15_0, computeRow_20_9_15_1, computeRow_20_9_15_2, computeRow_20_9_15_3, computeRow_20_9_15_4, computeRow_20_9_15_5, computeRow_20_9_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_9_17 : Y 20 9 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 9 17 0 (by decide), + source_yRow_eq_rowCompute 20 9 17 1 (by decide), + source_yRow_eq_rowCompute 20 9 17 2 (by decide), + source_yRow_eq_rowCompute 20 9 17 3 (by decide), + source_yRow_eq_rowCompute 20 9 17 4 (by decide), + source_yRow_eq_rowCompute 20 9 17 5 (by decide), + source_yRow_eq_rowCompute 20 9 17 6 (by decide), + computeRow_20_9_17_0, computeRow_20_9_17_1, computeRow_20_9_17_2, computeRow_20_9_17_3, computeRow_20_9_17_4, computeRow_20_9_17_5, computeRow_20_9_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_9_19 : Y 20 9 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 9 19 0 (by decide), + source_yRow_eq_rowCompute 20 9 19 1 (by decide), + source_yRow_eq_rowCompute 20 9 19 2 (by decide), + source_yRow_eq_rowCompute 20 9 19 3 (by decide), + source_yRow_eq_rowCompute 20 9 19 4 (by decide), + source_yRow_eq_rowCompute 20 9 19 5 (by decide), + source_yRow_eq_rowCompute 20 9 19 6 (by decide), + computeRow_20_9_19_0, computeRow_20_9_19_1, computeRow_20_9_19_2, computeRow_20_9_19_3, computeRow_20_9_19_4, computeRow_20_9_19_5, computeRow_20_9_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_11_11 : Y 20 11 11 = (-2024204103566300379339/12800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 11 11 0 (by decide), + source_yRow_eq_rowCompute 20 11 11 1 (by decide), + source_yRow_eq_rowCompute 20 11 11 2 (by decide), + source_yRow_eq_rowCompute 20 11 11 3 (by decide), + source_yRow_eq_rowCompute 20 11 11 4 (by decide), + source_yRow_eq_rowCompute 20 11 11 5 (by decide), + source_yRow_eq_rowCompute 20 11 11 6 (by decide), + computeRow_20_11_11_0, computeRow_20_11_11_1, computeRow_20_11_11_2, computeRow_20_11_11_3, computeRow_20_11_11_4, computeRow_20_11_11_5, computeRow_20_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_11_13 : Y 20 11 13 = (7072091643721157882829/6400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 11 13 0 (by decide), + source_yRow_eq_rowCompute 20 11 13 1 (by decide), + source_yRow_eq_rowCompute 20 11 13 2 (by decide), + source_yRow_eq_rowCompute 20 11 13 3 (by decide), + source_yRow_eq_rowCompute 20 11 13 4 (by decide), + source_yRow_eq_rowCompute 20 11 13 5 (by decide), + source_yRow_eq_rowCompute 20 11 13 6 (by decide), + computeRow_20_11_13_0, computeRow_20_11_13_1, computeRow_20_11_13_2, computeRow_20_11_13_3, computeRow_20_11_13_4, computeRow_20_11_13_5, computeRow_20_11_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_11_15 : Y 20 11 15 = (-4132909998582898800267/1280000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 11 15 0 (by decide), + source_yRow_eq_rowCompute 20 11 15 1 (by decide), + source_yRow_eq_rowCompute 20 11 15 2 (by decide), + source_yRow_eq_rowCompute 20 11 15 3 (by decide), + source_yRow_eq_rowCompute 20 11 15 4 (by decide), + source_yRow_eq_rowCompute 20 11 15 5 (by decide), + source_yRow_eq_rowCompute 20 11 15 6 (by decide), + computeRow_20_11_15_0, computeRow_20_11_15_1, computeRow_20_11_15_2, computeRow_20_11_15_3, computeRow_20_11_15_4, computeRow_20_11_15_5, computeRow_20_11_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_11_17 : Y 20 11 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 11 17 0 (by decide), + source_yRow_eq_rowCompute 20 11 17 1 (by decide), + source_yRow_eq_rowCompute 20 11 17 2 (by decide), + source_yRow_eq_rowCompute 20 11 17 3 (by decide), + source_yRow_eq_rowCompute 20 11 17 4 (by decide), + source_yRow_eq_rowCompute 20 11 17 5 (by decide), + source_yRow_eq_rowCompute 20 11 17 6 (by decide), + computeRow_20_11_17_0, computeRow_20_11_17_1, computeRow_20_11_17_2, computeRow_20_11_17_3, computeRow_20_11_17_4, computeRow_20_11_17_5, computeRow_20_11_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_11_19 : Y 20 11 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 11 19 0 (by decide), + source_yRow_eq_rowCompute 20 11 19 1 (by decide), + source_yRow_eq_rowCompute 20 11 19 2 (by decide), + source_yRow_eq_rowCompute 20 11 19 3 (by decide), + source_yRow_eq_rowCompute 20 11 19 4 (by decide), + source_yRow_eq_rowCompute 20 11 19 5 (by decide), + source_yRow_eq_rowCompute 20 11 19 6 (by decide), + computeRow_20_11_19_0, computeRow_20_11_19_1, computeRow_20_11_19_2, computeRow_20_11_19_3, computeRow_20_11_19_4, computeRow_20_11_19_5, computeRow_20_11_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_13_13 : Y 20 13 13 = (-51489116962575084283491/6400000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 13 13 0 (by decide), + source_yRow_eq_rowCompute 20 13 13 1 (by decide), + source_yRow_eq_rowCompute 20 13 13 2 (by decide), + source_yRow_eq_rowCompute 20 13 13 3 (by decide), + source_yRow_eq_rowCompute 20 13 13 4 (by decide), + source_yRow_eq_rowCompute 20 13 13 5 (by decide), + source_yRow_eq_rowCompute 20 13 13 6 (by decide), + computeRow_20_13_13_0, computeRow_20_13_13_1, computeRow_20_13_13_2, computeRow_20_13_13_3, computeRow_20_13_13_4, computeRow_20_13_13_5, computeRow_20_13_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_13_15 : Y 20 13 15 = (15026634633786455969289/640000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 13 15 0 (by decide), + source_yRow_eq_rowCompute 20 13 15 1 (by decide), + source_yRow_eq_rowCompute 20 13 15 2 (by decide), + source_yRow_eq_rowCompute 20 13 15 3 (by decide), + source_yRow_eq_rowCompute 20 13 15 4 (by decide), + source_yRow_eq_rowCompute 20 13 15 5 (by decide), + source_yRow_eq_rowCompute 20 13 15 6 (by decide), + computeRow_20_13_15_0, computeRow_20_13_15_1, computeRow_20_13_15_2, computeRow_20_13_15_3, computeRow_20_13_15_4, computeRow_20_13_15_5, computeRow_20_13_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_13_17 : Y 20 13 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 13 17 0 (by decide), + source_yRow_eq_rowCompute 20 13 17 1 (by decide), + source_yRow_eq_rowCompute 20 13 17 2 (by decide), + source_yRow_eq_rowCompute 20 13 17 3 (by decide), + source_yRow_eq_rowCompute 20 13 17 4 (by decide), + source_yRow_eq_rowCompute 20 13 17 5 (by decide), + source_yRow_eq_rowCompute 20 13 17 6 (by decide), + computeRow_20_13_17_0, computeRow_20_13_17_1, computeRow_20_13_17_2, computeRow_20_13_17_3, computeRow_20_13_17_4, computeRow_20_13_17_5, computeRow_20_13_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_13_19 : Y 20 13 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 13 19 0 (by decide), + source_yRow_eq_rowCompute 20 13 19 1 (by decide), + source_yRow_eq_rowCompute 20 13 19 2 (by decide), + source_yRow_eq_rowCompute 20 13 19 3 (by decide), + source_yRow_eq_rowCompute 20 13 19 4 (by decide), + source_yRow_eq_rowCompute 20 13 19 5 (by decide), + source_yRow_eq_rowCompute 20 13 19 6 (by decide), + computeRow_20_13_19_0, computeRow_20_13_19_1, computeRow_20_13_19_2, computeRow_20_13_19_3, computeRow_20_13_19_4, computeRow_20_13_19_5, computeRow_20_13_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_15_15 : Y 20 15 15 = (-8768897177979921681699/128000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 15 15 0 (by decide), + source_yRow_eq_rowCompute 20 15 15 1 (by decide), + source_yRow_eq_rowCompute 20 15 15 2 (by decide), + source_yRow_eq_rowCompute 20 15 15 3 (by decide), + source_yRow_eq_rowCompute 20 15 15 4 (by decide), + source_yRow_eq_rowCompute 20 15 15 5 (by decide), + source_yRow_eq_rowCompute 20 15 15 6 (by decide), + computeRow_20_15_15_0, computeRow_20_15_15_1, computeRow_20_15_15_2, computeRow_20_15_15_3, computeRow_20_15_15_4, computeRow_20_15_15_5, computeRow_20_15_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_15_17 : Y 20 15 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 15 17 0 (by decide), + source_yRow_eq_rowCompute 20 15 17 1 (by decide), + source_yRow_eq_rowCompute 20 15 17 2 (by decide), + source_yRow_eq_rowCompute 20 15 17 3 (by decide), + source_yRow_eq_rowCompute 20 15 17 4 (by decide), + source_yRow_eq_rowCompute 20 15 17 5 (by decide), + source_yRow_eq_rowCompute 20 15 17 6 (by decide), + computeRow_20_15_17_0, computeRow_20_15_17_1, computeRow_20_15_17_2, computeRow_20_15_17_3, computeRow_20_15_17_4, computeRow_20_15_17_5, computeRow_20_15_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_15_19 : Y 20 15 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 15 19 0 (by decide), + source_yRow_eq_rowCompute 20 15 19 1 (by decide), + source_yRow_eq_rowCompute 20 15 19 2 (by decide), + source_yRow_eq_rowCompute 20 15 19 3 (by decide), + source_yRow_eq_rowCompute 20 15 19 4 (by decide), + source_yRow_eq_rowCompute 20 15 19 5 (by decide), + source_yRow_eq_rowCompute 20 15 19 6 (by decide), + computeRow_20_15_19_0, computeRow_20_15_19_1, computeRow_20_15_19_2, computeRow_20_15_19_3, computeRow_20_15_19_4, computeRow_20_15_19_5, computeRow_20_15_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_17_17 : Y 20 17 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 17 17 0 (by decide), + source_yRow_eq_rowCompute 20 17 17 1 (by decide), + source_yRow_eq_rowCompute 20 17 17 2 (by decide), + source_yRow_eq_rowCompute 20 17 17 3 (by decide), + source_yRow_eq_rowCompute 20 17 17 4 (by decide), + source_yRow_eq_rowCompute 20 17 17 5 (by decide), + source_yRow_eq_rowCompute 20 17 17 6 (by decide), + computeRow_20_17_17_0, computeRow_20_17_17_1, computeRow_20_17_17_2, computeRow_20_17_17_3, computeRow_20_17_17_4, computeRow_20_17_17_5, computeRow_20_17_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_17_19 : Y 20 17 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 17 19 0 (by decide), + source_yRow_eq_rowCompute 20 17 19 1 (by decide), + source_yRow_eq_rowCompute 20 17 19 2 (by decide), + source_yRow_eq_rowCompute 20 17 19 3 (by decide), + source_yRow_eq_rowCompute 20 17 19 4 (by decide), + source_yRow_eq_rowCompute 20 17 19 5 (by decide), + source_yRow_eq_rowCompute 20 17 19 6 (by decide), + computeRow_20_17_19_0, computeRow_20_17_19_1, computeRow_20_17_19_2, computeRow_20_17_19_3, computeRow_20_17_19_4, computeRow_20_17_19_5, computeRow_20_17_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_20_19_19 : Y 20 19 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 20 19 19 0 (by decide), + source_yRow_eq_rowCompute 20 19 19 1 (by decide), + source_yRow_eq_rowCompute 20 19 19 2 (by decide), + source_yRow_eq_rowCompute 20 19 19 3 (by decide), + source_yRow_eq_rowCompute 20 19 19 4 (by decide), + source_yRow_eq_rowCompute 20 19 19 5 (by decide), + source_yRow_eq_rowCompute 20 19 19 6 (by decide), + computeRow_20_19_19_0, computeRow_20_19_19_1, computeRow_20_19_19_2, computeRow_20_19_19_3, computeRow_20_19_19_4, computeRow_20_19_19_5, computeRow_20_19_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_20_1_1 : Z 20 1 1 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_1_1 + +theorem source_gram_20_1_3 : Z 20 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_1_3 + +theorem source_gram_20_1_5 : Z 20 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_1_5 + +theorem source_gram_20_1_7 : Z 20 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_1_7 + +theorem source_gram_20_1_9 : Z 20 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_1_9 + +theorem source_gram_20_1_11 : Z 20 1 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_1_11 + +theorem source_gram_20_1_13 : Z 20 1 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_1_13 + +theorem source_gram_20_1_15 : Z 20 1 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_1_15 + +theorem source_gram_20_1_17 : Z 20 1 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_1_17 + +theorem source_gram_20_1_19 : Z 20 1 19 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_1_19 + +theorem source_gram_20_3_3 : Z 20 3 3 = (2134124568576000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_3_3 + +theorem source_gram_20_3_5 : Z 20 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_3_5 + +theorem source_gram_20_3_7 : Z 20 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_3_7 + +theorem source_gram_20_3_9 : Z 20 3 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_3_9 + +theorem source_gram_20_3_11 : Z 20 3 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_3_11 + +theorem source_gram_20_3_13 : Z 20 3 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_3_13 + +theorem source_gram_20_3_15 : Z 20 3 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_3_15 + +theorem source_gram_20_3_17 : Z 20 3 17 = (-133382785536000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_3_17 + +theorem source_gram_20_3_19 : Z 20 3 19 = (3326233214304000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_3_19 + +theorem source_gram_20_5_5 : Z 20 5 5 = (156920924160000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_5_5 + +theorem source_gram_20_5_7 : Z 20 5 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_5_7 + +theorem source_gram_20_5_9 : Z 20 5 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_5_9 + +theorem source_gram_20_5_11 : Z 20 5 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_5_11 + +theorem source_gram_20_5_13 : Z 20 5 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_5_13 + +theorem source_gram_20_5_15 : Z 20 5 15 = (-17163226080000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_5_15 + +theorem source_gram_20_5_17 : Z 20 5 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_5_17 + +theorem source_gram_20_5_19 : Z 20 5 19 = (2375880867360000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_5_19 + +theorem source_gram_20_7_7 : Z 20 7 7 = (31384184832000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_7_7 + +theorem source_gram_20_7_9 : Z 20 7 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_7_9 + +theorem source_gram_20_7_11 : Z 20 7 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_7_11 + +theorem source_gram_20_7_13 : Z 20 7 13 = (-4413400992000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_7_13 + +theorem source_gram_20_7_15 : Z 20 7 15 = (-21454032600000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_7_15 + +theorem source_gram_20_7_17 : Z 20 7 17 = (116709937344000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_7_17 + +theorem source_gram_20_7_19 : Z 20 7 19 = (1069146390312000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_7_19 + +theorem source_gram_20_9_9 : Z 20 9 9 = (14485008384000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_9_9 + +theorem source_gram_20_9_11 : Z 20 9 11 = (-2263282560000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_9_11 + +theorem source_gram_20_9_13 : Z 20 9 13 = (-11769069312000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_9_13 + +theorem source_gram_20_9_15 : Z 20 9 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_9_15 + +theorem source_gram_20_9_17 : Z 20 9 17 = (100037089152000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_9_17 + +theorem source_gram_20_9_19 : Z 20 9 19 = (237588086736000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_9_19 + +theorem source_gram_20_11_11 : Z 20 11 11 = (5148967824000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_11_11 + +theorem source_gram_20_11_13 : Z 20 11 13 = (-8091235152000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_11_13 + +theorem source_gram_20_11_15 : Z 20 11 15 = (10114043940000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_11_15 + +theorem source_gram_20_11_17 : Z 20 11 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_11_17 + +theorem source_gram_20_11_19 : Z 20 11 19 = (-148492554210000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_11_19 + +theorem source_gram_20_13_13 : Z 20 13 13 = (31384184832000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_13_13 + +theorem source_gram_20_13_15 : Z 20 13 15 = (-21913761870000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_13_15 + +theorem source_gram_20_13_17 : Z 20 13 17 = (-108373513248000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_13_17 + +theorem source_gram_20_13_19 : Z 20 13 19 = (-267286597578000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_13_19 + +theorem source_gram_20_15_15 : Z 20 15 15 = (62791356127500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_15_15 + +theorem source_gram_20_15_17 : Z 20 15 17 = (-182359277100000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_15_17 + +theorem source_gram_20_15_19 : Z 20 15 19 = (-259861969867500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_15_19 + +theorem source_gram_20_17_17 : Z 20 17 17 = (1921545754128000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_17_17 + +theorem source_gram_20_17_19 : Z 20 17 19 = (-207889575894000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_17_19 + +theorem source_gram_20_19_19 : Z 20 19 19 = (121494751697694375 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_20_19_19 + +theorem source_error_20_3_1 : Y 20 3 1 = (21667622927027497262745903/204800000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_1_3 + +theorem source_gram_20_3_1 : Z 20 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_1_3 + +theorem source_error_20_5_1 : Y 20 5 1 = (-11712315275254254792460329/327680000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_1_5 + +theorem source_gram_20_5_1 : Z 20 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_1_5 + +theorem source_error_20_5_3 : Y 20 5 3 = (1943037668945799386453493/163840000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_3_5 + +theorem source_gram_20_5_3 : Z 20 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_3_5 + +theorem source_error_20_7_1 : Y 20 7 1 = (665376664948039201360203/40960000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_1_7 + +theorem source_gram_20_7_1 : Z 20 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_1_7 + +theorem source_error_20_7_3 : Y 20 7 3 = (-1013982585631618048647201/163840000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_3_7 + +theorem source_gram_20_7_3 : Z 20 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_3_7 + +theorem source_error_20_7_5 : Y 20 7 5 = (97684912586085571093347/32768000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_5_7 + +theorem source_gram_20_7_5 : Z 20 7 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_5_7 + +theorem source_error_20_9_1 : Y 20 9 1 = (-316262058979922913891033/40960000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_1_9 + +theorem source_gram_20_9_1 : Z 20 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_1_9 + +theorem source_error_20_9_3 : Y 20 9 3 = (30613754919741298283979/10240000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_3_9 + +theorem source_gram_20_9_3 : Z 20 9 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_3_9 + +theorem source_error_20_9_5 : Y 20 9 5 = (-11858364672253510424013/8192000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_5_9 + +theorem source_gram_20_9_5 : Z 20 9 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_5_9 + +theorem source_error_20_9_7 : Y 20 9 7 = (333816883149802681629/409600000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_7_9 + +theorem source_gram_20_9_7 : Z 20 9 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_7_9 + +theorem source_error_20_11_1 : Y 20 11 1 = (5363979077413683764037/25600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_1_11 + +theorem source_gram_20_11_1 : Z 20 11 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_1_11 + +theorem source_error_20_11_3 : Y 20 11 3 = (107082038149227953680869/102400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_3_11 + +theorem source_gram_20_11_3 : Z 20 11 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_3_11 + +theorem source_error_20_11_5 : Y 20 11 5 = (-14013038479459638758139/20480000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_5_11 + +theorem source_gram_20_11_5 : Z 20 11 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_5_11 + +theorem source_error_20_11_7 : Y 20 11 7 = (8819254098389714698719/20480000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_7_11 + +theorem source_gram_20_11_7 : Z 20 11 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_7_11 + +theorem source_error_20_11_9 : Y 20 11 9 = (-272920889814962733729/1280000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_9_11 + +theorem source_gram_20_11_9 : Z 20 11 9 = (-2263282560000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_9_11 + +theorem source_error_20_13_1 : Y 20 13 1 = (1356924469605003889899309/102400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_1_13 + +theorem source_gram_20_13_1 : Z 20 13 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_1_13 + +theorem source_error_20_13_3 : Y 20 13 3 = (-520977417754125297368403/51200000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_3_13 + +theorem source_gram_20_13_3 : Z 20 13 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_3_13 + +theorem source_error_20_13_5 : Y 20 13 5 = (117196994897535165704091/20480000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_5_13 + +theorem source_gram_20_13_5 : Z 20 13 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_5_13 + +theorem source_error_20_13_7 : Y 20 13 7 = (-35062147478835063928341/10240000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_7_13 + +theorem source_gram_20_13_7 : Z 20 13 7 = (-4413400992000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_7_13 + +theorem source_error_20_13_9 : Y 20 13 9 = (4300425691175779286121/2560000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_9_13 + +theorem source_gram_20_13_9 : Z 20 13 9 = (-11769069312000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_9_13 + +theorem source_error_20_13_11 : Y 20 13 11 = (7072091643721157882829/6400000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_11_13 + +theorem source_gram_20_13_11 : Z 20 13 11 = (-8091235152000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_11_13 + +theorem source_error_20_15_1 : Y 20 15 1 = (-99760004425375579574289/2560000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_1_15 + +theorem source_gram_20_15_1 : Z 20 15 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_1_15 + +theorem source_error_20_15_3 : Y 20 15 3 = (304457703228940211619669/10240000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_3_15 + +theorem source_gram_20_15_3 : Z 20 15 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_3_15 + +theorem source_error_20_15_5 : Y 20 15 5 = (-34211653005025978665183/2048000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_5_15 + +theorem source_gram_20_15_5 : Z 20 15 5 = (-17163226080000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_5_15 + +theorem source_error_20_15_7 : Y 20 15 7 = (20460760081953150590631/2048000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_7_15 + +theorem source_gram_20_15_7 : Z 20 15 7 = (-21454032600000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_7_15 + +theorem source_error_20_15_9 : Y 20 15 9 = (-627014474788464764001/128000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_9_15 + +theorem source_gram_20_15_9 : Z 20 15 9 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_9_15 + +theorem source_error_20_15_11 : Y 20 15 11 = (-4132909998582898800267/1280000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_11_15 + +theorem source_gram_20_15_11 : Z 20 15 11 = (10114043940000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_11_15 + +theorem source_error_20_15_13 : Y 20 15 13 = (15026634633786455969289/640000000000 : ℚ) := by + rw [Y_symm] + exact source_error_20_13_15 + +theorem source_gram_20_15_13 : Z 20 15 13 = (-21913761870000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_13_15 + +theorem source_error_20_17_1 : Y 20 17 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_1_17 + +theorem source_gram_20_17_1 : Z 20 17 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_1_17 + +theorem source_error_20_17_3 : Y 20 17 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_3_17 + +theorem source_gram_20_17_3 : Z 20 17 3 = (-133382785536000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_3_17 + +theorem source_error_20_17_5 : Y 20 17 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_5_17 + +theorem source_gram_20_17_5 : Z 20 17 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_5_17 + +theorem source_error_20_17_7 : Y 20 17 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_7_17 + +theorem source_gram_20_17_7 : Z 20 17 7 = (116709937344000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_7_17 + +theorem source_error_20_17_9 : Y 20 17 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_9_17 + +theorem source_gram_20_17_9 : Z 20 17 9 = (100037089152000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_9_17 + +theorem source_error_20_17_11 : Y 20 17 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_11_17 + +theorem source_gram_20_17_11 : Z 20 17 11 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_11_17 + +theorem source_error_20_17_13 : Y 20 17 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_13_17 + +theorem source_gram_20_17_13 : Z 20 17 13 = (-108373513248000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_13_17 + +theorem source_error_20_17_15 : Y 20 17 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_15_17 + +theorem source_gram_20_17_15 : Z 20 17 15 = (-182359277100000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_15_17 + +theorem source_error_20_19_1 : Y 20 19 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_1_19 + +theorem source_gram_20_19_1 : Z 20 19 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_20_1_19 + +theorem source_error_20_19_3 : Y 20 19 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_3_19 + +theorem source_gram_20_19_3 : Z 20 19 3 = (3326233214304000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_3_19 + +theorem source_error_20_19_5 : Y 20 19 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_5_19 + +theorem source_gram_20_19_5 : Z 20 19 5 = (2375880867360000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_5_19 + +theorem source_error_20_19_7 : Y 20 19 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_7_19 + +theorem source_gram_20_19_7 : Z 20 19 7 = (1069146390312000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_7_19 + +theorem source_error_20_19_9 : Y 20 19 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_9_19 + +theorem source_gram_20_19_9 : Z 20 19 9 = (237588086736000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_9_19 + +theorem source_error_20_19_11 : Y 20 19 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_11_19 + +theorem source_gram_20_19_11 : Z 20 19 11 = (-148492554210000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_11_19 + +theorem source_error_20_19_13 : Y 20 19 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_13_19 + +theorem source_gram_20_19_13 : Z 20 19 13 = (-267286597578000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_13_19 + +theorem source_error_20_19_15 : Y 20 19 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_15_19 + +theorem source_gram_20_19_15 : Z 20 19 15 = (-259861969867500 : ℚ) := by + rw [Z_symm] + exact source_gram_20_15_19 + +theorem source_error_20_19_17 : Y 20 19 17 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_20_17_19 + +theorem source_gram_20_19_17 : Z 20 19 17 = (-207889575894000 : ℚ) := by + rw [Z_symm] + exact source_gram_20_17_19 + +theorem error_20 : errorRational 20 = candidateY_20 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_20_1_1 + · exact source_error_20_1_3 + · exact source_error_20_1_5 + · exact source_error_20_1_7 + · exact source_error_20_1_9 + · exact source_error_20_1_11 + · exact source_error_20_1_13 + · exact source_error_20_1_15 + · exact source_error_20_1_17 + · exact source_error_20_1_19 + · exact source_error_20_3_1 + · exact source_error_20_3_3 + · exact source_error_20_3_5 + · exact source_error_20_3_7 + · exact source_error_20_3_9 + · exact source_error_20_3_11 + · exact source_error_20_3_13 + · exact source_error_20_3_15 + · exact source_error_20_3_17 + · exact source_error_20_3_19 + · exact source_error_20_5_1 + · exact source_error_20_5_3 + · exact source_error_20_5_5 + · exact source_error_20_5_7 + · exact source_error_20_5_9 + · exact source_error_20_5_11 + · exact source_error_20_5_13 + · exact source_error_20_5_15 + · exact source_error_20_5_17 + · exact source_error_20_5_19 + · exact source_error_20_7_1 + · exact source_error_20_7_3 + · exact source_error_20_7_5 + · exact source_error_20_7_7 + · exact source_error_20_7_9 + · exact source_error_20_7_11 + · exact source_error_20_7_13 + · exact source_error_20_7_15 + · exact source_error_20_7_17 + · exact source_error_20_7_19 + · exact source_error_20_9_1 + · exact source_error_20_9_3 + · exact source_error_20_9_5 + · exact source_error_20_9_7 + · exact source_error_20_9_9 + · exact source_error_20_9_11 + · exact source_error_20_9_13 + · exact source_error_20_9_15 + · exact source_error_20_9_17 + · exact source_error_20_9_19 + · exact source_error_20_11_1 + · exact source_error_20_11_3 + · exact source_error_20_11_5 + · exact source_error_20_11_7 + · exact source_error_20_11_9 + · exact source_error_20_11_11 + · exact source_error_20_11_13 + · exact source_error_20_11_15 + · exact source_error_20_11_17 + · exact source_error_20_11_19 + · exact source_error_20_13_1 + · exact source_error_20_13_3 + · exact source_error_20_13_5 + · exact source_error_20_13_7 + · exact source_error_20_13_9 + · exact source_error_20_13_11 + · exact source_error_20_13_13 + · exact source_error_20_13_15 + · exact source_error_20_13_17 + · exact source_error_20_13_19 + · exact source_error_20_15_1 + · exact source_error_20_15_3 + · exact source_error_20_15_5 + · exact source_error_20_15_7 + · exact source_error_20_15_9 + · exact source_error_20_15_11 + · exact source_error_20_15_13 + · exact source_error_20_15_15 + · exact source_error_20_15_17 + · exact source_error_20_15_19 + · exact source_error_20_17_1 + · exact source_error_20_17_3 + · exact source_error_20_17_5 + · exact source_error_20_17_7 + · exact source_error_20_17_9 + · exact source_error_20_17_11 + · exact source_error_20_17_13 + · exact source_error_20_17_15 + · exact source_error_20_17_17 + · exact source_error_20_17_19 + · exact source_error_20_19_1 + · exact source_error_20_19_3 + · exact source_error_20_19_5 + · exact source_error_20_19_7 + · exact source_error_20_19_9 + · exact source_error_20_19_11 + · exact source_error_20_19_13 + · exact source_error_20_19_15 + · exact source_error_20_19_17 + · exact source_error_20_19_19 + +theorem gram_20 : gramRational 20 = candidateZ_20 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_20_1_1 + · exact source_gram_20_1_3 + · exact source_gram_20_1_5 + · exact source_gram_20_1_7 + · exact source_gram_20_1_9 + · exact source_gram_20_1_11 + · exact source_gram_20_1_13 + · exact source_gram_20_1_15 + · exact source_gram_20_1_17 + · exact source_gram_20_1_19 + · exact source_gram_20_3_1 + · exact source_gram_20_3_3 + · exact source_gram_20_3_5 + · exact source_gram_20_3_7 + · exact source_gram_20_3_9 + · exact source_gram_20_3_11 + · exact source_gram_20_3_13 + · exact source_gram_20_3_15 + · exact source_gram_20_3_17 + · exact source_gram_20_3_19 + · exact source_gram_20_5_1 + · exact source_gram_20_5_3 + · exact source_gram_20_5_5 + · exact source_gram_20_5_7 + · exact source_gram_20_5_9 + · exact source_gram_20_5_11 + · exact source_gram_20_5_13 + · exact source_gram_20_5_15 + · exact source_gram_20_5_17 + · exact source_gram_20_5_19 + · exact source_gram_20_7_1 + · exact source_gram_20_7_3 + · exact source_gram_20_7_5 + · exact source_gram_20_7_7 + · exact source_gram_20_7_9 + · exact source_gram_20_7_11 + · exact source_gram_20_7_13 + · exact source_gram_20_7_15 + · exact source_gram_20_7_17 + · exact source_gram_20_7_19 + · exact source_gram_20_9_1 + · exact source_gram_20_9_3 + · exact source_gram_20_9_5 + · exact source_gram_20_9_7 + · exact source_gram_20_9_9 + · exact source_gram_20_9_11 + · exact source_gram_20_9_13 + · exact source_gram_20_9_15 + · exact source_gram_20_9_17 + · exact source_gram_20_9_19 + · exact source_gram_20_11_1 + · exact source_gram_20_11_3 + · exact source_gram_20_11_5 + · exact source_gram_20_11_7 + · exact source_gram_20_11_9 + · exact source_gram_20_11_11 + · exact source_gram_20_11_13 + · exact source_gram_20_11_15 + · exact source_gram_20_11_17 + · exact source_gram_20_11_19 + · exact source_gram_20_13_1 + · exact source_gram_20_13_3 + · exact source_gram_20_13_5 + · exact source_gram_20_13_7 + · exact source_gram_20_13_9 + · exact source_gram_20_13_11 + · exact source_gram_20_13_13 + · exact source_gram_20_13_15 + · exact source_gram_20_13_17 + · exact source_gram_20_13_19 + · exact source_gram_20_15_1 + · exact source_gram_20_15_3 + · exact source_gram_20_15_5 + · exact source_gram_20_15_7 + · exact source_gram_20_15_9 + · exact source_gram_20_15_11 + · exact source_gram_20_15_13 + · exact source_gram_20_15_15 + · exact source_gram_20_15_17 + · exact source_gram_20_15_19 + · exact source_gram_20_17_1 + · exact source_gram_20_17_3 + · exact source_gram_20_17_5 + · exact source_gram_20_17_7 + · exact source_gram_20_17_9 + · exact source_gram_20_17_11 + · exact source_gram_20_17_13 + · exact source_gram_20_17_15 + · exact source_gram_20_17_17 + · exact source_gram_20_17_19 + · exact source_gram_20_19_1 + · exact source_gram_20_19_3 + · exact source_gram_20_19_5 + · exact source_gram_20_19_7 + · exact source_gram_20_19_9 + · exact source_gram_20_19_11 + · exact source_gram_20_19_13 + · exact source_gram_20_19_15 + · exact source_gram_20_19_17 + · exact source_gram_20_19_19 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData21.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData21.lean new file mode 100644 index 0000000000000000000000000000000000000000..f6cadbb078add0a6e464bef5933c6b85dd8bfcbd --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData21.lean @@ -0,0 +1,1767 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram01Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram03Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram05Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram07Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram11Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram13Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram15Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram17Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram19Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram212121 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0101Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0103Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0105Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0107Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0109Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0111Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0113Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0115Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0117Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0119Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0121Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0303Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0305Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0307Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0309Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0311Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0313Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0315Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0317Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0319Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0321Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0505Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0507Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0509Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0511Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0513Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0515Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0517Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0519Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0521Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0707Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0709Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0711Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0713Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0715Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0717Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0719Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0721Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0909Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0911Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0913Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0915Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0917Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0919Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0921Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1111Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1113Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1115Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1117Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1119Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1121Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1313Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1315Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1317Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1319Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1321Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1515Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1517Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1519Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1521Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1717Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1719Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1721Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1919Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1921Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow2121Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.Data21 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_21_1_1 : Y 21 1 1 = (-96711588542532735223983531/32768000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 1 1 0 (by decide), + source_yRow_eq_rowCompute 21 1 1 1 (by decide), + source_yRow_eq_rowCompute 21 1 1 2 (by decide), + source_yRow_eq_rowCompute 21 1 1 3 (by decide), + source_yRow_eq_rowCompute 21 1 1 4 (by decide), + source_yRow_eq_rowCompute 21 1 1 5 (by decide), + source_yRow_eq_rowCompute 21 1 1 6 (by decide), + computeRow_21_1_1_0, computeRow_21_1_1_1, computeRow_21_1_1_2, computeRow_21_1_1_3, computeRow_21_1_1_4, computeRow_21_1_1_5, computeRow_21_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_1_3 : Y 21 1 3 = (57038851132594341185352177/163840000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 1 3 0 (by decide), + source_yRow_eq_rowCompute 21 1 3 1 (by decide), + source_yRow_eq_rowCompute 21 1 3 2 (by decide), + source_yRow_eq_rowCompute 21 1 3 3 (by decide), + source_yRow_eq_rowCompute 21 1 3 4 (by decide), + source_yRow_eq_rowCompute 21 1 3 5 (by decide), + source_yRow_eq_rowCompute 21 1 3 6 (by decide), + computeRow_21_1_3_0, computeRow_21_1_3_1, computeRow_21_1_3_2, computeRow_21_1_3_3, computeRow_21_1_3_4, computeRow_21_1_3_5, computeRow_21_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_1_5 : Y 21 1 5 = (-5636036476590197124447/327680000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 1 5 0 (by decide), + source_yRow_eq_rowCompute 21 1 5 1 (by decide), + source_yRow_eq_rowCompute 21 1 5 2 (by decide), + source_yRow_eq_rowCompute 21 1 5 3 (by decide), + source_yRow_eq_rowCompute 21 1 5 4 (by decide), + source_yRow_eq_rowCompute 21 1 5 5 (by decide), + source_yRow_eq_rowCompute 21 1 5 6 (by decide), + computeRow_21_1_5_0, computeRow_21_1_5_1, computeRow_21_1_5_2, computeRow_21_1_5_3, computeRow_21_1_5_4, computeRow_21_1_5_5, computeRow_21_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_1_7 : Y 21 1 7 = (-1952083051117812873373113/32768000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 1 7 0 (by decide), + source_yRow_eq_rowCompute 21 1 7 1 (by decide), + source_yRow_eq_rowCompute 21 1 7 2 (by decide), + source_yRow_eq_rowCompute 21 1 7 3 (by decide), + source_yRow_eq_rowCompute 21 1 7 4 (by decide), + source_yRow_eq_rowCompute 21 1 7 5 (by decide), + source_yRow_eq_rowCompute 21 1 7 6 (by decide), + computeRow_21_1_7_0, computeRow_21_1_7_1, computeRow_21_1_7_2, computeRow_21_1_7_3, computeRow_21_1_7_4, computeRow_21_1_7_5, computeRow_21_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_1_9 : Y 21 1 9 = (418641912860774562758799/4096000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 1 9 0 (by decide), + source_yRow_eq_rowCompute 21 1 9 1 (by decide), + source_yRow_eq_rowCompute 21 1 9 2 (by decide), + source_yRow_eq_rowCompute 21 1 9 3 (by decide), + source_yRow_eq_rowCompute 21 1 9 4 (by decide), + source_yRow_eq_rowCompute 21 1 9 5 (by decide), + source_yRow_eq_rowCompute 21 1 9 6 (by decide), + computeRow_21_1_9_0, computeRow_21_1_9_1, computeRow_21_1_9_2, computeRow_21_1_9_3, computeRow_21_1_9_4, computeRow_21_1_9_5, computeRow_21_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_1_11 : Y 21 1 11 = (-644220666819787412766411/4096000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 1 11 0 (by decide), + source_yRow_eq_rowCompute 21 1 11 1 (by decide), + source_yRow_eq_rowCompute 21 1 11 2 (by decide), + source_yRow_eq_rowCompute 21 1 11 3 (by decide), + source_yRow_eq_rowCompute 21 1 11 4 (by decide), + source_yRow_eq_rowCompute 21 1 11 5 (by decide), + source_yRow_eq_rowCompute 21 1 11 6 (by decide), + computeRow_21_1_11_0, computeRow_21_1_11_1, computeRow_21_1_11_2, computeRow_21_1_11_3, computeRow_21_1_11_4, computeRow_21_1_11_5, computeRow_21_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_1_13 : Y 21 1 13 = (1256376941124933712895811/5120000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 1 13 0 (by decide), + source_yRow_eq_rowCompute 21 1 13 1 (by decide), + source_yRow_eq_rowCompute 21 1 13 2 (by decide), + source_yRow_eq_rowCompute 21 1 13 3 (by decide), + source_yRow_eq_rowCompute 21 1 13 4 (by decide), + source_yRow_eq_rowCompute 21 1 13 5 (by decide), + source_yRow_eq_rowCompute 21 1 13 6 (by decide), + computeRow_21_1_13_0, computeRow_21_1_13_1, computeRow_21_1_13_2, computeRow_21_1_13_3, computeRow_21_1_13_4, computeRow_21_1_13_5, computeRow_21_1_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_1_15 : Y 21 1 15 = (-135618250205634004439631/409600000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 1 15 0 (by decide), + source_yRow_eq_rowCompute 21 1 15 1 (by decide), + source_yRow_eq_rowCompute 21 1 15 2 (by decide), + source_yRow_eq_rowCompute 21 1 15 3 (by decide), + source_yRow_eq_rowCompute 21 1 15 4 (by decide), + source_yRow_eq_rowCompute 21 1 15 5 (by decide), + source_yRow_eq_rowCompute 21 1 15 6 (by decide), + computeRow_21_1_15_0, computeRow_21_1_15_1, computeRow_21_1_15_2, computeRow_21_1_15_3, computeRow_21_1_15_4, computeRow_21_1_15_5, computeRow_21_1_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_1_17 : Y 21 1 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 1 17 0 (by decide), + source_yRow_eq_rowCompute 21 1 17 1 (by decide), + source_yRow_eq_rowCompute 21 1 17 2 (by decide), + source_yRow_eq_rowCompute 21 1 17 3 (by decide), + source_yRow_eq_rowCompute 21 1 17 4 (by decide), + source_yRow_eq_rowCompute 21 1 17 5 (by decide), + source_yRow_eq_rowCompute 21 1 17 6 (by decide), + computeRow_21_1_17_0, computeRow_21_1_17_1, computeRow_21_1_17_2, computeRow_21_1_17_3, computeRow_21_1_17_4, computeRow_21_1_17_5, computeRow_21_1_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_1_19 : Y 21 1 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 1 19 0 (by decide), + source_yRow_eq_rowCompute 21 1 19 1 (by decide), + source_yRow_eq_rowCompute 21 1 19 2 (by decide), + source_yRow_eq_rowCompute 21 1 19 3 (by decide), + source_yRow_eq_rowCompute 21 1 19 4 (by decide), + source_yRow_eq_rowCompute 21 1 19 5 (by decide), + source_yRow_eq_rowCompute 21 1 19 6 (by decide), + computeRow_21_1_19_0, computeRow_21_1_19_1, computeRow_21_1_19_2, computeRow_21_1_19_3, computeRow_21_1_19_4, computeRow_21_1_19_5, computeRow_21_1_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_1_21 : Y 21 1 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 1 21 0 (by decide), + source_yRow_eq_rowCompute 21 1 21 1 (by decide), + source_yRow_eq_rowCompute 21 1 21 2 (by decide), + source_yRow_eq_rowCompute 21 1 21 3 (by decide), + source_yRow_eq_rowCompute 21 1 21 4 (by decide), + source_yRow_eq_rowCompute 21 1 21 5 (by decide), + source_yRow_eq_rowCompute 21 1 21 6 (by decide), + computeRow_21_1_21_0, computeRow_21_1_21_1, computeRow_21_1_21_2, computeRow_21_1_21_3, computeRow_21_1_21_4, computeRow_21_1_21_5, computeRow_21_1_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_3_3 : Y 21 3 3 = (-44082193767443568976121883/819200000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 3 3 0 (by decide), + source_yRow_eq_rowCompute 21 3 3 1 (by decide), + source_yRow_eq_rowCompute 21 3 3 2 (by decide), + source_yRow_eq_rowCompute 21 3 3 3 (by decide), + source_yRow_eq_rowCompute 21 3 3 4 (by decide), + source_yRow_eq_rowCompute 21 3 3 5 (by decide), + source_yRow_eq_rowCompute 21 3 3 6 (by decide), + computeRow_21_3_3_0, computeRow_21_3_3_1, computeRow_21_3_3_2, computeRow_21_3_3_3, computeRow_21_3_3_4, computeRow_21_3_3_5, computeRow_21_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_3_5 : Y 21 3 5 = (492577388419375083797973/40960000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 3 5 0 (by decide), + source_yRow_eq_rowCompute 21 3 5 1 (by decide), + source_yRow_eq_rowCompute 21 3 5 2 (by decide), + source_yRow_eq_rowCompute 21 3 5 3 (by decide), + source_yRow_eq_rowCompute 21 3 5 4 (by decide), + source_yRow_eq_rowCompute 21 3 5 5 (by decide), + source_yRow_eq_rowCompute 21 3 5 6 (by decide), + computeRow_21_3_5_0, computeRow_21_3_5_1, computeRow_21_3_5_2, computeRow_21_3_5_3, computeRow_21_3_5_4, computeRow_21_3_5_5, computeRow_21_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_3_7 : Y 21 3 7 = (-281862084701495601299997/163840000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 3 7 0 (by decide), + source_yRow_eq_rowCompute 21 3 7 1 (by decide), + source_yRow_eq_rowCompute 21 3 7 2 (by decide), + source_yRow_eq_rowCompute 21 3 7 3 (by decide), + source_yRow_eq_rowCompute 21 3 7 4 (by decide), + source_yRow_eq_rowCompute 21 3 7 5 (by decide), + source_yRow_eq_rowCompute 21 3 7 6 (by decide), + computeRow_21_3_7_0, computeRow_21_3_7_1, computeRow_21_3_7_2, computeRow_21_3_7_3, computeRow_21_3_7_4, computeRow_21_3_7_5, computeRow_21_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_3_9 : Y 21 3 9 = (-57918765188790724575357/20480000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 3 9 0 (by decide), + source_yRow_eq_rowCompute 21 3 9 1 (by decide), + source_yRow_eq_rowCompute 21 3 9 2 (by decide), + source_yRow_eq_rowCompute 21 3 9 3 (by decide), + source_yRow_eq_rowCompute 21 3 9 4 (by decide), + source_yRow_eq_rowCompute 21 3 9 5 (by decide), + source_yRow_eq_rowCompute 21 3 9 6 (by decide), + computeRow_21_3_9_0, computeRow_21_3_9_1, computeRow_21_3_9_2, computeRow_21_3_9_3, computeRow_21_3_9_4, computeRow_21_3_9_5, computeRow_21_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_3_11 : Y 21 3 11 = (143714000293113981147417/20480000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 3 11 0 (by decide), + source_yRow_eq_rowCompute 21 3 11 1 (by decide), + source_yRow_eq_rowCompute 21 3 11 2 (by decide), + source_yRow_eq_rowCompute 21 3 11 3 (by decide), + source_yRow_eq_rowCompute 21 3 11 4 (by decide), + source_yRow_eq_rowCompute 21 3 11 5 (by decide), + source_yRow_eq_rowCompute 21 3 11 6 (by decide), + computeRow_21_3_11_0, computeRow_21_3_11_1, computeRow_21_3_11_2, computeRow_21_3_11_3, computeRow_21_3_11_4, computeRow_21_3_11_5, computeRow_21_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_3_13 : Y 21 3 13 = (-331513340018520454483689/25600000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 3 13 0 (by decide), + source_yRow_eq_rowCompute 21 3 13 1 (by decide), + source_yRow_eq_rowCompute 21 3 13 2 (by decide), + source_yRow_eq_rowCompute 21 3 13 3 (by decide), + source_yRow_eq_rowCompute 21 3 13 4 (by decide), + source_yRow_eq_rowCompute 21 3 13 5 (by decide), + source_yRow_eq_rowCompute 21 3 13 6 (by decide), + computeRow_21_3_13_0, computeRow_21_3_13_1, computeRow_21_3_13_2, computeRow_21_3_13_3, computeRow_21_3_13_4, computeRow_21_3_13_5, computeRow_21_3_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_3_15 : Y 21 3 15 = (195188481739185067894761/10240000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 3 15 0 (by decide), + source_yRow_eq_rowCompute 21 3 15 1 (by decide), + source_yRow_eq_rowCompute 21 3 15 2 (by decide), + source_yRow_eq_rowCompute 21 3 15 3 (by decide), + source_yRow_eq_rowCompute 21 3 15 4 (by decide), + source_yRow_eq_rowCompute 21 3 15 5 (by decide), + source_yRow_eq_rowCompute 21 3 15 6 (by decide), + computeRow_21_3_15_0, computeRow_21_3_15_1, computeRow_21_3_15_2, computeRow_21_3_15_3, computeRow_21_3_15_4, computeRow_21_3_15_5, computeRow_21_3_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_3_17 : Y 21 3 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 3 17 0 (by decide), + source_yRow_eq_rowCompute 21 3 17 1 (by decide), + source_yRow_eq_rowCompute 21 3 17 2 (by decide), + source_yRow_eq_rowCompute 21 3 17 3 (by decide), + source_yRow_eq_rowCompute 21 3 17 4 (by decide), + source_yRow_eq_rowCompute 21 3 17 5 (by decide), + source_yRow_eq_rowCompute 21 3 17 6 (by decide), + computeRow_21_3_17_0, computeRow_21_3_17_1, computeRow_21_3_17_2, computeRow_21_3_17_3, computeRow_21_3_17_4, computeRow_21_3_17_5, computeRow_21_3_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_3_19 : Y 21 3 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 3 19 0 (by decide), + source_yRow_eq_rowCompute 21 3 19 1 (by decide), + source_yRow_eq_rowCompute 21 3 19 2 (by decide), + source_yRow_eq_rowCompute 21 3 19 3 (by decide), + source_yRow_eq_rowCompute 21 3 19 4 (by decide), + source_yRow_eq_rowCompute 21 3 19 5 (by decide), + source_yRow_eq_rowCompute 21 3 19 6 (by decide), + computeRow_21_3_19_0, computeRow_21_3_19_1, computeRow_21_3_19_2, computeRow_21_3_19_3, computeRow_21_3_19_4, computeRow_21_3_19_5, computeRow_21_3_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_3_21 : Y 21 3 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 3 21 0 (by decide), + source_yRow_eq_rowCompute 21 3 21 1 (by decide), + source_yRow_eq_rowCompute 21 3 21 2 (by decide), + source_yRow_eq_rowCompute 21 3 21 3 (by decide), + source_yRow_eq_rowCompute 21 3 21 4 (by decide), + source_yRow_eq_rowCompute 21 3 21 5 (by decide), + source_yRow_eq_rowCompute 21 3 21 6 (by decide), + computeRow_21_3_21_0, computeRow_21_3_21_1, computeRow_21_3_21_2, computeRow_21_3_21_3, computeRow_21_3_21_4, computeRow_21_3_21_5, computeRow_21_3_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_5_5 : Y 21 5 5 = (-16263180195796078115571/2048000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 5 5 0 (by decide), + source_yRow_eq_rowCompute 21 5 5 1 (by decide), + source_yRow_eq_rowCompute 21 5 5 2 (by decide), + source_yRow_eq_rowCompute 21 5 5 3 (by decide), + source_yRow_eq_rowCompute 21 5 5 4 (by decide), + source_yRow_eq_rowCompute 21 5 5 5 (by decide), + source_yRow_eq_rowCompute 21 5 5 6 (by decide), + computeRow_21_5_5_0, computeRow_21_5_5_1, computeRow_21_5_5_2, computeRow_21_5_5_3, computeRow_21_5_5_4, computeRow_21_5_5_5, computeRow_21_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_5_7 : Y 21 5 7 = (53358620528514863973411/8192000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 5 7 0 (by decide), + source_yRow_eq_rowCompute 21 5 7 1 (by decide), + source_yRow_eq_rowCompute 21 5 7 2 (by decide), + source_yRow_eq_rowCompute 21 5 7 3 (by decide), + source_yRow_eq_rowCompute 21 5 7 4 (by decide), + source_yRow_eq_rowCompute 21 5 7 5 (by decide), + source_yRow_eq_rowCompute 21 5 7 6 (by decide), + computeRow_21_5_7_0, computeRow_21_5_7_1, computeRow_21_5_7_2, computeRow_21_5_7_3, computeRow_21_5_7_4, computeRow_21_5_7_5, computeRow_21_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_5_9 : Y 21 5 9 = (-6801410828588460561477/1024000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 5 9 0 (by decide), + source_yRow_eq_rowCompute 21 5 9 1 (by decide), + source_yRow_eq_rowCompute 21 5 9 2 (by decide), + source_yRow_eq_rowCompute 21 5 9 3 (by decide), + source_yRow_eq_rowCompute 21 5 9 4 (by decide), + source_yRow_eq_rowCompute 21 5 9 5 (by decide), + source_yRow_eq_rowCompute 21 5 9 6 (by decide), + computeRow_21_5_9_0, computeRow_21_5_9_1, computeRow_21_5_9_2, computeRow_21_5_9_3, computeRow_21_5_9_4, computeRow_21_5_9_5, computeRow_21_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_5_11 : Y 21 5 11 = (1665119090212013288853/204800000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 5 11 0 (by decide), + source_yRow_eq_rowCompute 21 5 11 1 (by decide), + source_yRow_eq_rowCompute 21 5 11 2 (by decide), + source_yRow_eq_rowCompute 21 5 11 3 (by decide), + source_yRow_eq_rowCompute 21 5 11 4 (by decide), + source_yRow_eq_rowCompute 21 5 11 5 (by decide), + source_yRow_eq_rowCompute 21 5 11 6 (by decide), + computeRow_21_5_11_0, computeRow_21_5_11_1, computeRow_21_5_11_2, computeRow_21_5_11_3, computeRow_21_5_11_4, computeRow_21_5_11_5, computeRow_21_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_5_13 : Y 21 5 13 = (-14227460106212415583521/1280000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 5 13 0 (by decide), + source_yRow_eq_rowCompute 21 5 13 1 (by decide), + source_yRow_eq_rowCompute 21 5 13 2 (by decide), + source_yRow_eq_rowCompute 21 5 13 3 (by decide), + source_yRow_eq_rowCompute 21 5 13 4 (by decide), + source_yRow_eq_rowCompute 21 5 13 5 (by decide), + source_yRow_eq_rowCompute 21 5 13 6 (by decide), + computeRow_21_5_13_0, computeRow_21_5_13_1, computeRow_21_5_13_2, computeRow_21_5_13_3, computeRow_21_5_13_4, computeRow_21_5_13_5, computeRow_21_5_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_5_15 : Y 21 5 15 = (7041025764192505558473/512000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 5 15 0 (by decide), + source_yRow_eq_rowCompute 21 5 15 1 (by decide), + source_yRow_eq_rowCompute 21 5 15 2 (by decide), + source_yRow_eq_rowCompute 21 5 15 3 (by decide), + source_yRow_eq_rowCompute 21 5 15 4 (by decide), + source_yRow_eq_rowCompute 21 5 15 5 (by decide), + source_yRow_eq_rowCompute 21 5 15 6 (by decide), + computeRow_21_5_15_0, computeRow_21_5_15_1, computeRow_21_5_15_2, computeRow_21_5_15_3, computeRow_21_5_15_4, computeRow_21_5_15_5, computeRow_21_5_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_5_17 : Y 21 5 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 5 17 0 (by decide), + source_yRow_eq_rowCompute 21 5 17 1 (by decide), + source_yRow_eq_rowCompute 21 5 17 2 (by decide), + source_yRow_eq_rowCompute 21 5 17 3 (by decide), + source_yRow_eq_rowCompute 21 5 17 4 (by decide), + source_yRow_eq_rowCompute 21 5 17 5 (by decide), + source_yRow_eq_rowCompute 21 5 17 6 (by decide), + computeRow_21_5_17_0, computeRow_21_5_17_1, computeRow_21_5_17_2, computeRow_21_5_17_3, computeRow_21_5_17_4, computeRow_21_5_17_5, computeRow_21_5_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_5_19 : Y 21 5 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 5 19 0 (by decide), + source_yRow_eq_rowCompute 21 5 19 1 (by decide), + source_yRow_eq_rowCompute 21 5 19 2 (by decide), + source_yRow_eq_rowCompute 21 5 19 3 (by decide), + source_yRow_eq_rowCompute 21 5 19 4 (by decide), + source_yRow_eq_rowCompute 21 5 19 5 (by decide), + source_yRow_eq_rowCompute 21 5 19 6 (by decide), + computeRow_21_5_19_0, computeRow_21_5_19_1, computeRow_21_5_19_2, computeRow_21_5_19_3, computeRow_21_5_19_4, computeRow_21_5_19_5, computeRow_21_5_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_5_21 : Y 21 5 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 5 21 0 (by decide), + source_yRow_eq_rowCompute 21 5 21 1 (by decide), + source_yRow_eq_rowCompute 21 5 21 2 (by decide), + source_yRow_eq_rowCompute 21 5 21 3 (by decide), + source_yRow_eq_rowCompute 21 5 21 4 (by decide), + source_yRow_eq_rowCompute 21 5 21 5 (by decide), + source_yRow_eq_rowCompute 21 5 21 6 (by decide), + computeRow_21_5_21_0, computeRow_21_5_21_1, computeRow_21_5_21_2, computeRow_21_5_21_3, computeRow_21_5_21_4, computeRow_21_5_21_5, computeRow_21_5_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_7_7 : Y 21 7 7 = (-9444449794627227102723/1310720000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 7 7 0 (by decide), + source_yRow_eq_rowCompute 21 7 7 1 (by decide), + source_yRow_eq_rowCompute 21 7 7 2 (by decide), + source_yRow_eq_rowCompute 21 7 7 3 (by decide), + source_yRow_eq_rowCompute 21 7 7 4 (by decide), + source_yRow_eq_rowCompute 21 7 7 5 (by decide), + source_yRow_eq_rowCompute 21 7 7 6 (by decide), + computeRow_21_7_7_0, computeRow_21_7_7_1, computeRow_21_7_7_2, computeRow_21_7_7_3, computeRow_21_7_7_4, computeRow_21_7_7_5, computeRow_21_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_7_9 : Y 21 7 9 = (34389795345971868711909/4096000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 7 9 0 (by decide), + source_yRow_eq_rowCompute 21 7 9 1 (by decide), + source_yRow_eq_rowCompute 21 7 9 2 (by decide), + source_yRow_eq_rowCompute 21 7 9 3 (by decide), + source_yRow_eq_rowCompute 21 7 9 4 (by decide), + source_yRow_eq_rowCompute 21 7 9 5 (by decide), + source_yRow_eq_rowCompute 21 7 9 6 (by decide), + computeRow_21_7_9_0, computeRow_21_7_9_1, computeRow_21_7_9_2, computeRow_21_7_9_3, computeRow_21_7_9_4, computeRow_21_7_9_5, computeRow_21_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_7_11 : Y 21 7 11 = (-45427929111821472609393/4096000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 7 11 0 (by decide), + source_yRow_eq_rowCompute 21 7 11 1 (by decide), + source_yRow_eq_rowCompute 21 7 11 2 (by decide), + source_yRow_eq_rowCompute 21 7 11 3 (by decide), + source_yRow_eq_rowCompute 21 7 11 4 (by decide), + source_yRow_eq_rowCompute 21 7 11 5 (by decide), + source_yRow_eq_rowCompute 21 7 11 6 (by decide), + computeRow_21_7_11_0, computeRow_21_7_11_1, computeRow_21_7_11_2, computeRow_21_7_11_3, computeRow_21_7_11_4, computeRow_21_7_11_5, computeRow_21_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_7_13 : Y 21 7 13 = (81562090823302666065489/5120000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 7 13 0 (by decide), + source_yRow_eq_rowCompute 21 7 13 1 (by decide), + source_yRow_eq_rowCompute 21 7 13 2 (by decide), + source_yRow_eq_rowCompute 21 7 13 3 (by decide), + source_yRow_eq_rowCompute 21 7 13 4 (by decide), + source_yRow_eq_rowCompute 21 7 13 5 (by decide), + source_yRow_eq_rowCompute 21 7 13 6 (by decide), + computeRow_21_7_13_0, computeRow_21_7_13_1, computeRow_21_7_13_2, computeRow_21_7_13_3, computeRow_21_7_13_4, computeRow_21_7_13_5, computeRow_21_7_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_7_15 : Y 21 7 15 = (-41788312207893754536033/2048000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 7 15 0 (by decide), + source_yRow_eq_rowCompute 21 7 15 1 (by decide), + source_yRow_eq_rowCompute 21 7 15 2 (by decide), + source_yRow_eq_rowCompute 21 7 15 3 (by decide), + source_yRow_eq_rowCompute 21 7 15 4 (by decide), + source_yRow_eq_rowCompute 21 7 15 5 (by decide), + source_yRow_eq_rowCompute 21 7 15 6 (by decide), + computeRow_21_7_15_0, computeRow_21_7_15_1, computeRow_21_7_15_2, computeRow_21_7_15_3, computeRow_21_7_15_4, computeRow_21_7_15_5, computeRow_21_7_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_7_17 : Y 21 7 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 7 17 0 (by decide), + source_yRow_eq_rowCompute 21 7 17 1 (by decide), + source_yRow_eq_rowCompute 21 7 17 2 (by decide), + source_yRow_eq_rowCompute 21 7 17 3 (by decide), + source_yRow_eq_rowCompute 21 7 17 4 (by decide), + source_yRow_eq_rowCompute 21 7 17 5 (by decide), + source_yRow_eq_rowCompute 21 7 17 6 (by decide), + computeRow_21_7_17_0, computeRow_21_7_17_1, computeRow_21_7_17_2, computeRow_21_7_17_3, computeRow_21_7_17_4, computeRow_21_7_17_5, computeRow_21_7_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_7_19 : Y 21 7 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 7 19 0 (by decide), + source_yRow_eq_rowCompute 21 7 19 1 (by decide), + source_yRow_eq_rowCompute 21 7 19 2 (by decide), + source_yRow_eq_rowCompute 21 7 19 3 (by decide), + source_yRow_eq_rowCompute 21 7 19 4 (by decide), + source_yRow_eq_rowCompute 21 7 19 5 (by decide), + source_yRow_eq_rowCompute 21 7 19 6 (by decide), + computeRow_21_7_19_0, computeRow_21_7_19_1, computeRow_21_7_19_2, computeRow_21_7_19_3, computeRow_21_7_19_4, computeRow_21_7_19_5, computeRow_21_7_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_7_21 : Y 21 7 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 7 21 0 (by decide), + source_yRow_eq_rowCompute 21 7 21 1 (by decide), + source_yRow_eq_rowCompute 21 7 21 2 (by decide), + source_yRow_eq_rowCompute 21 7 21 3 (by decide), + source_yRow_eq_rowCompute 21 7 21 4 (by decide), + source_yRow_eq_rowCompute 21 7 21 5 (by decide), + source_yRow_eq_rowCompute 21 7 21 6 (by decide), + computeRow_21_7_21_0, computeRow_21_7_21_1, computeRow_21_7_21_2, computeRow_21_7_21_3, computeRow_21_7_21_4, computeRow_21_7_21_5, computeRow_21_7_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_9_9 : Y 21 9 9 = (-1046564151268430692359/102400000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 9 9 0 (by decide), + source_yRow_eq_rowCompute 21 9 9 1 (by decide), + source_yRow_eq_rowCompute 21 9 9 2 (by decide), + source_yRow_eq_rowCompute 21 9 9 3 (by decide), + source_yRow_eq_rowCompute 21 9 9 4 (by decide), + source_yRow_eq_rowCompute 21 9 9 5 (by decide), + source_yRow_eq_rowCompute 21 9 9 6 (by decide), + computeRow_21_9_9_0, computeRow_21_9_9_1, computeRow_21_9_9_2, computeRow_21_9_9_3, computeRow_21_9_9_4, computeRow_21_9_9_5, computeRow_21_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_9_11 : Y 21 9 11 = (7064452961983792435599/512000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 9 11 0 (by decide), + source_yRow_eq_rowCompute 21 9 11 1 (by decide), + source_yRow_eq_rowCompute 21 9 11 2 (by decide), + source_yRow_eq_rowCompute 21 9 11 3 (by decide), + source_yRow_eq_rowCompute 21 9 11 4 (by decide), + source_yRow_eq_rowCompute 21 9 11 5 (by decide), + source_yRow_eq_rowCompute 21 9 11 6 (by decide), + computeRow_21_9_11_0, computeRow_21_9_11_1, computeRow_21_9_11_2, computeRow_21_9_11_3, computeRow_21_9_11_4, computeRow_21_9_11_5, computeRow_21_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_9_13 : Y 21 9 13 = (-12849900797681178702471/640000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 9 13 0 (by decide), + source_yRow_eq_rowCompute 21 9 13 1 (by decide), + source_yRow_eq_rowCompute 21 9 13 2 (by decide), + source_yRow_eq_rowCompute 21 9 13 3 (by decide), + source_yRow_eq_rowCompute 21 9 13 4 (by decide), + source_yRow_eq_rowCompute 21 9 13 5 (by decide), + source_yRow_eq_rowCompute 21 9 13 6 (by decide), + computeRow_21_9_13_0, computeRow_21_9_13_1, computeRow_21_9_13_2, computeRow_21_9_13_3, computeRow_21_9_13_4, computeRow_21_9_13_5, computeRow_21_9_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_9_15 : Y 21 9 15 = (6640967897736757856271/256000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 9 15 0 (by decide), + source_yRow_eq_rowCompute 21 9 15 1 (by decide), + source_yRow_eq_rowCompute 21 9 15 2 (by decide), + source_yRow_eq_rowCompute 21 9 15 3 (by decide), + source_yRow_eq_rowCompute 21 9 15 4 (by decide), + source_yRow_eq_rowCompute 21 9 15 5 (by decide), + source_yRow_eq_rowCompute 21 9 15 6 (by decide), + computeRow_21_9_15_0, computeRow_21_9_15_1, computeRow_21_9_15_2, computeRow_21_9_15_3, computeRow_21_9_15_4, computeRow_21_9_15_5, computeRow_21_9_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_9_17 : Y 21 9 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 9 17 0 (by decide), + source_yRow_eq_rowCompute 21 9 17 1 (by decide), + source_yRow_eq_rowCompute 21 9 17 2 (by decide), + source_yRow_eq_rowCompute 21 9 17 3 (by decide), + source_yRow_eq_rowCompute 21 9 17 4 (by decide), + source_yRow_eq_rowCompute 21 9 17 5 (by decide), + source_yRow_eq_rowCompute 21 9 17 6 (by decide), + computeRow_21_9_17_0, computeRow_21_9_17_1, computeRow_21_9_17_2, computeRow_21_9_17_3, computeRow_21_9_17_4, computeRow_21_9_17_5, computeRow_21_9_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_9_19 : Y 21 9 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 9 19 0 (by decide), + source_yRow_eq_rowCompute 21 9 19 1 (by decide), + source_yRow_eq_rowCompute 21 9 19 2 (by decide), + source_yRow_eq_rowCompute 21 9 19 3 (by decide), + source_yRow_eq_rowCompute 21 9 19 4 (by decide), + source_yRow_eq_rowCompute 21 9 19 5 (by decide), + source_yRow_eq_rowCompute 21 9 19 6 (by decide), + computeRow_21_9_19_0, computeRow_21_9_19_1, computeRow_21_9_19_2, computeRow_21_9_19_3, computeRow_21_9_19_4, computeRow_21_9_19_5, computeRow_21_9_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_9_21 : Y 21 9 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 9 21 0 (by decide), + source_yRow_eq_rowCompute 21 9 21 1 (by decide), + source_yRow_eq_rowCompute 21 9 21 2 (by decide), + source_yRow_eq_rowCompute 21 9 21 3 (by decide), + source_yRow_eq_rowCompute 21 9 21 4 (by decide), + source_yRow_eq_rowCompute 21 9 21 5 (by decide), + source_yRow_eq_rowCompute 21 9 21 6 (by decide), + computeRow_21_9_21_0, computeRow_21_9_21_1, computeRow_21_9_21_2, computeRow_21_9_21_3, computeRow_21_9_21_4, computeRow_21_9_21_5, computeRow_21_9_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_11_11 : Y 21 11 11 = (-9636033814007219448291/512000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 11 11 0 (by decide), + source_yRow_eq_rowCompute 21 11 11 1 (by decide), + source_yRow_eq_rowCompute 21 11 11 2 (by decide), + source_yRow_eq_rowCompute 21 11 11 3 (by decide), + source_yRow_eq_rowCompute 21 11 11 4 (by decide), + source_yRow_eq_rowCompute 21 11 11 5 (by decide), + source_yRow_eq_rowCompute 21 11 11 6 (by decide), + computeRow_21_11_11_0, computeRow_21_11_11_1, computeRow_21_11_11_2, computeRow_21_11_11_3, computeRow_21_11_11_4, computeRow_21_11_11_5, computeRow_21_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_11_13 : Y 21 11 13 = (17633221184266489332531/640000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 11 13 0 (by decide), + source_yRow_eq_rowCompute 21 11 13 1 (by decide), + source_yRow_eq_rowCompute 21 11 13 2 (by decide), + source_yRow_eq_rowCompute 21 11 13 3 (by decide), + source_yRow_eq_rowCompute 21 11 13 4 (by decide), + source_yRow_eq_rowCompute 21 11 13 5 (by decide), + source_yRow_eq_rowCompute 21 11 13 6 (by decide), + computeRow_21_11_13_0, computeRow_21_11_13_1, computeRow_21_11_13_2, computeRow_21_11_13_3, computeRow_21_11_13_4, computeRow_21_11_13_5, computeRow_21_11_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_11_15 : Y 21 11 15 = (-365961031875624676491/10240000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 11 15 0 (by decide), + source_yRow_eq_rowCompute 21 11 15 1 (by decide), + source_yRow_eq_rowCompute 21 11 15 2 (by decide), + source_yRow_eq_rowCompute 21 11 15 3 (by decide), + source_yRow_eq_rowCompute 21 11 15 4 (by decide), + source_yRow_eq_rowCompute 21 11 15 5 (by decide), + source_yRow_eq_rowCompute 21 11 15 6 (by decide), + computeRow_21_11_15_0, computeRow_21_11_15_1, computeRow_21_11_15_2, computeRow_21_11_15_3, computeRow_21_11_15_4, computeRow_21_11_15_5, computeRow_21_11_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_11_17 : Y 21 11 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 11 17 0 (by decide), + source_yRow_eq_rowCompute 21 11 17 1 (by decide), + source_yRow_eq_rowCompute 21 11 17 2 (by decide), + source_yRow_eq_rowCompute 21 11 17 3 (by decide), + source_yRow_eq_rowCompute 21 11 17 4 (by decide), + source_yRow_eq_rowCompute 21 11 17 5 (by decide), + source_yRow_eq_rowCompute 21 11 17 6 (by decide), + computeRow_21_11_17_0, computeRow_21_11_17_1, computeRow_21_11_17_2, computeRow_21_11_17_3, computeRow_21_11_17_4, computeRow_21_11_17_5, computeRow_21_11_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_11_19 : Y 21 11 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 11 19 0 (by decide), + source_yRow_eq_rowCompute 21 11 19 1 (by decide), + source_yRow_eq_rowCompute 21 11 19 2 (by decide), + source_yRow_eq_rowCompute 21 11 19 3 (by decide), + source_yRow_eq_rowCompute 21 11 19 4 (by decide), + source_yRow_eq_rowCompute 21 11 19 5 (by decide), + source_yRow_eq_rowCompute 21 11 19 6 (by decide), + computeRow_21_11_19_0, computeRow_21_11_19_1, computeRow_21_11_19_2, computeRow_21_11_19_3, computeRow_21_11_19_4, computeRow_21_11_19_5, computeRow_21_11_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_11_21 : Y 21 11 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 11 21 0 (by decide), + source_yRow_eq_rowCompute 21 11 21 1 (by decide), + source_yRow_eq_rowCompute 21 11 21 2 (by decide), + source_yRow_eq_rowCompute 21 11 21 3 (by decide), + source_yRow_eq_rowCompute 21 11 21 4 (by decide), + source_yRow_eq_rowCompute 21 11 21 5 (by decide), + source_yRow_eq_rowCompute 21 11 21 6 (by decide), + computeRow_21_11_21_0, computeRow_21_11_21_1, computeRow_21_11_21_2, computeRow_21_11_21_3, computeRow_21_11_21_4, computeRow_21_11_21_5, computeRow_21_11_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_13_13 : Y 21 13 13 = (-32379448935674822168187/800000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 13 13 0 (by decide), + source_yRow_eq_rowCompute 21 13 13 1 (by decide), + source_yRow_eq_rowCompute 21 13 13 2 (by decide), + source_yRow_eq_rowCompute 21 13 13 3 (by decide), + source_yRow_eq_rowCompute 21 13 13 4 (by decide), + source_yRow_eq_rowCompute 21 13 13 5 (by decide), + source_yRow_eq_rowCompute 21 13 13 6 (by decide), + computeRow_21_13_13_0, computeRow_21_13_13_1, computeRow_21_13_13_2, computeRow_21_13_13_3, computeRow_21_13_13_4, computeRow_21_13_13_5, computeRow_21_13_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_13_15 : Y 21 13 15 = (16838009783175354176403/320000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 13 15 0 (by decide), + source_yRow_eq_rowCompute 21 13 15 1 (by decide), + source_yRow_eq_rowCompute 21 13 15 2 (by decide), + source_yRow_eq_rowCompute 21 13 15 3 (by decide), + source_yRow_eq_rowCompute 21 13 15 4 (by decide), + source_yRow_eq_rowCompute 21 13 15 5 (by decide), + source_yRow_eq_rowCompute 21 13 15 6 (by decide), + computeRow_21_13_15_0, computeRow_21_13_15_1, computeRow_21_13_15_2, computeRow_21_13_15_3, computeRow_21_13_15_4, computeRow_21_13_15_5, computeRow_21_13_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_13_17 : Y 21 13 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 13 17 0 (by decide), + source_yRow_eq_rowCompute 21 13 17 1 (by decide), + source_yRow_eq_rowCompute 21 13 17 2 (by decide), + source_yRow_eq_rowCompute 21 13 17 3 (by decide), + source_yRow_eq_rowCompute 21 13 17 4 (by decide), + source_yRow_eq_rowCompute 21 13 17 5 (by decide), + source_yRow_eq_rowCompute 21 13 17 6 (by decide), + computeRow_21_13_17_0, computeRow_21_13_17_1, computeRow_21_13_17_2, computeRow_21_13_17_3, computeRow_21_13_17_4, computeRow_21_13_17_5, computeRow_21_13_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_13_19 : Y 21 13 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 13 19 0 (by decide), + source_yRow_eq_rowCompute 21 13 19 1 (by decide), + source_yRow_eq_rowCompute 21 13 19 2 (by decide), + source_yRow_eq_rowCompute 21 13 19 3 (by decide), + source_yRow_eq_rowCompute 21 13 19 4 (by decide), + source_yRow_eq_rowCompute 21 13 19 5 (by decide), + source_yRow_eq_rowCompute 21 13 19 6 (by decide), + computeRow_21_13_19_0, computeRow_21_13_19_1, computeRow_21_13_19_2, computeRow_21_13_19_3, computeRow_21_13_19_4, computeRow_21_13_19_5, computeRow_21_13_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_13_21 : Y 21 13 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 13 21 0 (by decide), + source_yRow_eq_rowCompute 21 13 21 1 (by decide), + source_yRow_eq_rowCompute 21 13 21 2 (by decide), + source_yRow_eq_rowCompute 21 13 21 3 (by decide), + source_yRow_eq_rowCompute 21 13 21 4 (by decide), + source_yRow_eq_rowCompute 21 13 21 5 (by decide), + source_yRow_eq_rowCompute 21 13 21 6 (by decide), + computeRow_21_13_21_0, computeRow_21_13_21_1, computeRow_21_13_21_2, computeRow_21_13_21_3, computeRow_21_13_21_4, computeRow_21_13_21_5, computeRow_21_13_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_15_15 : Y 21 15 15 = (-8768897177979921681699/128000000000 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 15 15 0 (by decide), + source_yRow_eq_rowCompute 21 15 15 1 (by decide), + source_yRow_eq_rowCompute 21 15 15 2 (by decide), + source_yRow_eq_rowCompute 21 15 15 3 (by decide), + source_yRow_eq_rowCompute 21 15 15 4 (by decide), + source_yRow_eq_rowCompute 21 15 15 5 (by decide), + source_yRow_eq_rowCompute 21 15 15 6 (by decide), + computeRow_21_15_15_0, computeRow_21_15_15_1, computeRow_21_15_15_2, computeRow_21_15_15_3, computeRow_21_15_15_4, computeRow_21_15_15_5, computeRow_21_15_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_15_17 : Y 21 15 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 15 17 0 (by decide), + source_yRow_eq_rowCompute 21 15 17 1 (by decide), + source_yRow_eq_rowCompute 21 15 17 2 (by decide), + source_yRow_eq_rowCompute 21 15 17 3 (by decide), + source_yRow_eq_rowCompute 21 15 17 4 (by decide), + source_yRow_eq_rowCompute 21 15 17 5 (by decide), + source_yRow_eq_rowCompute 21 15 17 6 (by decide), + computeRow_21_15_17_0, computeRow_21_15_17_1, computeRow_21_15_17_2, computeRow_21_15_17_3, computeRow_21_15_17_4, computeRow_21_15_17_5, computeRow_21_15_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_15_19 : Y 21 15 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 15 19 0 (by decide), + source_yRow_eq_rowCompute 21 15 19 1 (by decide), + source_yRow_eq_rowCompute 21 15 19 2 (by decide), + source_yRow_eq_rowCompute 21 15 19 3 (by decide), + source_yRow_eq_rowCompute 21 15 19 4 (by decide), + source_yRow_eq_rowCompute 21 15 19 5 (by decide), + source_yRow_eq_rowCompute 21 15 19 6 (by decide), + computeRow_21_15_19_0, computeRow_21_15_19_1, computeRow_21_15_19_2, computeRow_21_15_19_3, computeRow_21_15_19_4, computeRow_21_15_19_5, computeRow_21_15_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_15_21 : Y 21 15 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 15 21 0 (by decide), + source_yRow_eq_rowCompute 21 15 21 1 (by decide), + source_yRow_eq_rowCompute 21 15 21 2 (by decide), + source_yRow_eq_rowCompute 21 15 21 3 (by decide), + source_yRow_eq_rowCompute 21 15 21 4 (by decide), + source_yRow_eq_rowCompute 21 15 21 5 (by decide), + source_yRow_eq_rowCompute 21 15 21 6 (by decide), + computeRow_21_15_21_0, computeRow_21_15_21_1, computeRow_21_15_21_2, computeRow_21_15_21_3, computeRow_21_15_21_4, computeRow_21_15_21_5, computeRow_21_15_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_17_17 : Y 21 17 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 17 17 0 (by decide), + source_yRow_eq_rowCompute 21 17 17 1 (by decide), + source_yRow_eq_rowCompute 21 17 17 2 (by decide), + source_yRow_eq_rowCompute 21 17 17 3 (by decide), + source_yRow_eq_rowCompute 21 17 17 4 (by decide), + source_yRow_eq_rowCompute 21 17 17 5 (by decide), + source_yRow_eq_rowCompute 21 17 17 6 (by decide), + computeRow_21_17_17_0, computeRow_21_17_17_1, computeRow_21_17_17_2, computeRow_21_17_17_3, computeRow_21_17_17_4, computeRow_21_17_17_5, computeRow_21_17_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_17_19 : Y 21 17 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 17 19 0 (by decide), + source_yRow_eq_rowCompute 21 17 19 1 (by decide), + source_yRow_eq_rowCompute 21 17 19 2 (by decide), + source_yRow_eq_rowCompute 21 17 19 3 (by decide), + source_yRow_eq_rowCompute 21 17 19 4 (by decide), + source_yRow_eq_rowCompute 21 17 19 5 (by decide), + source_yRow_eq_rowCompute 21 17 19 6 (by decide), + computeRow_21_17_19_0, computeRow_21_17_19_1, computeRow_21_17_19_2, computeRow_21_17_19_3, computeRow_21_17_19_4, computeRow_21_17_19_5, computeRow_21_17_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_17_21 : Y 21 17 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 17 21 0 (by decide), + source_yRow_eq_rowCompute 21 17 21 1 (by decide), + source_yRow_eq_rowCompute 21 17 21 2 (by decide), + source_yRow_eq_rowCompute 21 17 21 3 (by decide), + source_yRow_eq_rowCompute 21 17 21 4 (by decide), + source_yRow_eq_rowCompute 21 17 21 5 (by decide), + source_yRow_eq_rowCompute 21 17 21 6 (by decide), + computeRow_21_17_21_0, computeRow_21_17_21_1, computeRow_21_17_21_2, computeRow_21_17_21_3, computeRow_21_17_21_4, computeRow_21_17_21_5, computeRow_21_17_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_19_19 : Y 21 19 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 19 19 0 (by decide), + source_yRow_eq_rowCompute 21 19 19 1 (by decide), + source_yRow_eq_rowCompute 21 19 19 2 (by decide), + source_yRow_eq_rowCompute 21 19 19 3 (by decide), + source_yRow_eq_rowCompute 21 19 19 4 (by decide), + source_yRow_eq_rowCompute 21 19 19 5 (by decide), + source_yRow_eq_rowCompute 21 19 19 6 (by decide), + computeRow_21_19_19_0, computeRow_21_19_19_1, computeRow_21_19_19_2, computeRow_21_19_19_3, computeRow_21_19_19_4, computeRow_21_19_19_5, computeRow_21_19_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_19_21 : Y 21 19 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 19 21 0 (by decide), + source_yRow_eq_rowCompute 21 19 21 1 (by decide), + source_yRow_eq_rowCompute 21 19 21 2 (by decide), + source_yRow_eq_rowCompute 21 19 21 3 (by decide), + source_yRow_eq_rowCompute 21 19 21 4 (by decide), + source_yRow_eq_rowCompute 21 19 21 5 (by decide), + source_yRow_eq_rowCompute 21 19 21 6 (by decide), + computeRow_21_19_21_0, computeRow_21_19_21_1, computeRow_21_19_21_2, computeRow_21_19_21_3, computeRow_21_19_21_4, computeRow_21_19_21_5, computeRow_21_19_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_21_21_21 : Y 21 21 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 21 21 21 0 (by decide), + source_yRow_eq_rowCompute 21 21 21 1 (by decide), + source_yRow_eq_rowCompute 21 21 21 2 (by decide), + source_yRow_eq_rowCompute 21 21 21 3 (by decide), + source_yRow_eq_rowCompute 21 21 21 4 (by decide), + source_yRow_eq_rowCompute 21 21 21 5 (by decide), + source_yRow_eq_rowCompute 21 21 21 6 (by decide), + computeRow_21_21_21_0, computeRow_21_21_21_1, computeRow_21_21_21_2, computeRow_21_21_21_3, computeRow_21_21_21_4, computeRow_21_21_21_5, computeRow_21_21_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_21_1_1 : Z 21 1 1 = (4865804016353280000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_1_1 + +theorem source_gram_21_1_3 : Z 21 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_1_3 + +theorem source_gram_21_1_5 : Z 21 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_1_5 + +theorem source_gram_21_1_7 : Z 21 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_1_7 + +theorem source_gram_21_1_9 : Z 21 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_1_9 + +theorem source_gram_21_1_11 : Z 21 1 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_1_11 + +theorem source_gram_21_1_13 : Z 21 1 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_1_13 + +theorem source_gram_21_1_15 : Z 21 1 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_1_15 + +theorem source_gram_21_1_17 : Z 21 1 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_1_17 + +theorem source_gram_21_1_19 : Z 21 1 19 = (-9503523469440000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_1_19 + +theorem source_gram_21_1_21 : Z 21 1 21 = (898082967862080000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_1_21 + +theorem source_gram_21_3_3 : Z 21 3 3 = (38414242234368000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_3_3 + +theorem source_gram_21_3_5 : Z 21 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_3_5 + +theorem source_gram_21_3_7 : Z 21 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_3_7 + +theorem source_gram_21_3_9 : Z 21 3 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_3_9 + +theorem source_gram_21_3_11 : Z 21 3 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_3_11 + +theorem source_gram_21_3_13 : Z 21 3 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_3_13 + +theorem source_gram_21_3_15 : Z 21 3 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_3_15 + +theorem source_gram_21_3_17 : Z 21 3 17 = (-300111267456000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_3_17 + +theorem source_gram_21_3_19 : Z 21 3 19 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_3_19 + +theorem source_gram_21_3_21 : Z 21 3 21 = (349254487501920000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_3_21 + +theorem source_gram_21_5_5 : Z 21 5 5 = (2510734786560000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_5_5 + +theorem source_gram_21_5_7 : Z 21 5 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_5_7 + +theorem source_gram_21_5_9 : Z 21 5 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_5_9 + +theorem source_gram_21_5_11 : Z 21 5 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_5_11 + +theorem source_gram_21_5_13 : Z 21 5 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_5_13 + +theorem source_gram_21_5_15 : Z 21 5 15 = (-29422673280000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_5_15 + +theorem source_gram_21_5_17 : Z 21 5 17 = (-583549686720000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_5_17 + +theorem source_gram_21_5_19 : Z 21 5 19 = (7127642602080000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_5_19 + +theorem source_gram_21_5_21 : Z 21 5 21 = (124733745536400000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_5_21 + +theorem source_gram_21_7_7 : Z 21 7 7 = (439378587648000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_7_7 + +theorem source_gram_21_7_9 : Z 21 7 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_7_9 + +theorem source_gram_21_7_11 : Z 21 7 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_7_11 + +theorem source_gram_21_7_13 : Z 21 7 13 = (-6865290432000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_7_13 + +theorem source_gram_21_7_15 : Z 21 7 15 = (-154469034720000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_7_15 + +theorem source_gram_21_7_17 : Z 21 7 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_7_17 + +theorem source_gram_21_7_19 : Z 21 7 19 = (6652466428608000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_7_19 + +theorem source_gram_21_7_21 : Z 21 7 21 = (37420123660920000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_7_21 + +theorem source_gram_21_9_9 : Z 21 9 9 = (173820100608000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_9_9 + +theorem source_gram_21_9_11 : Z 21 9 11 = (-3394923840000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_9_11 + +theorem source_gram_21_9_13 : Z 21 9 13 = (-66201014880000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_9_13 + +theorem source_gram_21_9_15 : Z 21 9 15 = (-154469034720000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_9_15 + +theorem source_gram_21_9_17 : Z 21 9 17 = (525194718048000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_9_17 + +theorem source_gram_21_9_19 : Z 21 9 19 = (3207439170936000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_9_19 + +theorem source_gram_21_9_21 : Z 21 9 21 = (6236687276820000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_9_21 + +theorem source_gram_21_11_11 : Z 21 11 11 = (95057867520000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_11_11 + +theorem source_gram_21_11_13 : Z 21 11 13 = (-121368527280000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_11_13 + +theorem source_gram_21_11_15 : Z 21 11 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_11_15 + +theorem source_gram_21_11_17 : Z 21 11 17 = (343877493960000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_11_17 + +theorem source_gram_21_11_19 : Z 21 11 19 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_11_19 + +theorem source_gram_21_11_21 : Z 21 11 21 = (-3118343638410000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_11_21 + +theorem source_gram_21_13_13 : Z 21 13 13 = (198480450168000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_13_13 + +theorem source_gram_21_13_15 : Z 21 13 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_13_15 + +theorem source_gram_21_13_17 : Z 21 13 17 = (-447040742148000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_13_17 + +theorem source_gram_21_13_19 : Z 21 13 19 = (-1930403204730000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_13_19 + +theorem source_gram_21_13_21 : Z 21 13 21 = (-4677515457615000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_13_21 + +theorem source_gram_21_15_15 : Z 21 15 15 = (481336545690000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_15_15 + +theorem source_gram_21_15_17 : Z 21 15 17 = (-1422402361380000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_15_17 + +theorem source_gram_21_15_19 : Z 21 15 19 = (-2672865975780000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_15_19 + +theorem source_gram_21_15_21 : Z 21 15 21 = (-3897929548012500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_15_21 + +theorem source_gram_21_17_17 : Z 21 17 17 = (6322135623804000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_17_17 + +theorem source_gram_21_17_19 : Z 21 17 19 = (-2650592092648500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_17_19 + +theorem source_gram_21_17_21 : Z 21 17 21 = (-2728550683608750 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_17_21 + +theorem source_gram_21_19_19 : Z 21 19 19 = (241033113993672000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_19_19 + +theorem source_gram_21_19_21 : Z 21 19 21 = (-1754068296605625 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_19_21 + +theorem source_gram_21_21_21 : Z 21 21 21 = (102179740482167473125/2 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_21_21_21 + +theorem source_error_21_3_1 : Y 21 3 1 = (57038851132594341185352177/163840000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_1_3 + +theorem source_gram_21_3_1 : Z 21 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_1_3 + +theorem source_error_21_5_1 : Y 21 5 1 = (-5636036476590197124447/327680000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_1_5 + +theorem source_gram_21_5_1 : Z 21 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_1_5 + +theorem source_error_21_5_3 : Y 21 5 3 = (492577388419375083797973/40960000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_3_5 + +theorem source_gram_21_5_3 : Z 21 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_3_5 + +theorem source_error_21_7_1 : Y 21 7 1 = (-1952083051117812873373113/32768000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_1_7 + +theorem source_gram_21_7_1 : Z 21 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_1_7 + +theorem source_error_21_7_3 : Y 21 7 3 = (-281862084701495601299997/163840000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_3_7 + +theorem source_gram_21_7_3 : Z 21 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_3_7 + +theorem source_error_21_7_5 : Y 21 7 5 = (53358620528514863973411/8192000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_5_7 + +theorem source_gram_21_7_5 : Z 21 7 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_5_7 + +theorem source_error_21_9_1 : Y 21 9 1 = (418641912860774562758799/4096000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_1_9 + +theorem source_gram_21_9_1 : Z 21 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_1_9 + +theorem source_error_21_9_3 : Y 21 9 3 = (-57918765188790724575357/20480000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_3_9 + +theorem source_gram_21_9_3 : Z 21 9 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_3_9 + +theorem source_error_21_9_5 : Y 21 9 5 = (-6801410828588460561477/1024000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_5_9 + +theorem source_gram_21_9_5 : Z 21 9 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_5_9 + +theorem source_error_21_9_7 : Y 21 9 7 = (34389795345971868711909/4096000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_7_9 + +theorem source_gram_21_9_7 : Z 21 9 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_7_9 + +theorem source_error_21_11_1 : Y 21 11 1 = (-644220666819787412766411/4096000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_1_11 + +theorem source_gram_21_11_1 : Z 21 11 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_1_11 + +theorem source_error_21_11_3 : Y 21 11 3 = (143714000293113981147417/20480000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_3_11 + +theorem source_gram_21_11_3 : Z 21 11 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_3_11 + +theorem source_error_21_11_5 : Y 21 11 5 = (1665119090212013288853/204800000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_5_11 + +theorem source_gram_21_11_5 : Z 21 11 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_5_11 + +theorem source_error_21_11_7 : Y 21 11 7 = (-45427929111821472609393/4096000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_7_11 + +theorem source_gram_21_11_7 : Z 21 11 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_7_11 + +theorem source_error_21_11_9 : Y 21 11 9 = (7064452961983792435599/512000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_9_11 + +theorem source_gram_21_11_9 : Z 21 11 9 = (-3394923840000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_9_11 + +theorem source_error_21_13_1 : Y 21 13 1 = (1256376941124933712895811/5120000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_1_13 + +theorem source_gram_21_13_1 : Z 21 13 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_1_13 + +theorem source_error_21_13_3 : Y 21 13 3 = (-331513340018520454483689/25600000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_3_13 + +theorem source_gram_21_13_3 : Z 21 13 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_3_13 + +theorem source_error_21_13_5 : Y 21 13 5 = (-14227460106212415583521/1280000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_5_13 + +theorem source_gram_21_13_5 : Z 21 13 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_5_13 + +theorem source_error_21_13_7 : Y 21 13 7 = (81562090823302666065489/5120000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_7_13 + +theorem source_gram_21_13_7 : Z 21 13 7 = (-6865290432000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_7_13 + +theorem source_error_21_13_9 : Y 21 13 9 = (-12849900797681178702471/640000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_9_13 + +theorem source_gram_21_13_9 : Z 21 13 9 = (-66201014880000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_9_13 + +theorem source_error_21_13_11 : Y 21 13 11 = (17633221184266489332531/640000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_11_13 + +theorem source_gram_21_13_11 : Z 21 13 11 = (-121368527280000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_11_13 + +theorem source_error_21_15_1 : Y 21 15 1 = (-135618250205634004439631/409600000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_1_15 + +theorem source_gram_21_15_1 : Z 21 15 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_1_15 + +theorem source_error_21_15_3 : Y 21 15 3 = (195188481739185067894761/10240000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_3_15 + +theorem source_gram_21_15_3 : Z 21 15 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_3_15 + +theorem source_error_21_15_5 : Y 21 15 5 = (7041025764192505558473/512000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_5_15 + +theorem source_gram_21_15_5 : Z 21 15 5 = (-29422673280000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_5_15 + +theorem source_error_21_15_7 : Y 21 15 7 = (-41788312207893754536033/2048000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_7_15 + +theorem source_gram_21_15_7 : Z 21 15 7 = (-154469034720000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_7_15 + +theorem source_error_21_15_9 : Y 21 15 9 = (6640967897736757856271/256000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_9_15 + +theorem source_gram_21_15_9 : Z 21 15 9 = (-154469034720000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_9_15 + +theorem source_error_21_15_11 : Y 21 15 11 = (-365961031875624676491/10240000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_11_15 + +theorem source_gram_21_15_11 : Z 21 15 11 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_11_15 + +theorem source_error_21_15_13 : Y 21 15 13 = (16838009783175354176403/320000000000 : ℚ) := by + rw [Y_symm] + exact source_error_21_13_15 + +theorem source_gram_21_15_13 : Z 21 15 13 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_13_15 + +theorem source_error_21_17_1 : Y 21 17 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_1_17 + +theorem source_gram_21_17_1 : Z 21 17 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_1_17 + +theorem source_error_21_17_3 : Y 21 17 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_3_17 + +theorem source_gram_21_17_3 : Z 21 17 3 = (-300111267456000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_3_17 + +theorem source_error_21_17_5 : Y 21 17 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_5_17 + +theorem source_gram_21_17_5 : Z 21 17 5 = (-583549686720000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_5_17 + +theorem source_error_21_17_7 : Y 21 17 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_7_17 + +theorem source_gram_21_17_7 : Z 21 17 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_7_17 + +theorem source_error_21_17_9 : Y 21 17 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_9_17 + +theorem source_gram_21_17_9 : Z 21 17 9 = (525194718048000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_9_17 + +theorem source_error_21_17_11 : Y 21 17 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_11_17 + +theorem source_gram_21_17_11 : Z 21 17 11 = (343877493960000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_11_17 + +theorem source_error_21_17_13 : Y 21 17 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_13_17 + +theorem source_gram_21_17_13 : Z 21 17 13 = (-447040742148000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_13_17 + +theorem source_error_21_17_15 : Y 21 17 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_15_17 + +theorem source_gram_21_17_15 : Z 21 17 15 = (-1422402361380000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_15_17 + +theorem source_error_21_19_1 : Y 21 19 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_1_19 + +theorem source_gram_21_19_1 : Z 21 19 1 = (-9503523469440000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_1_19 + +theorem source_error_21_19_3 : Y 21 19 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_3_19 + +theorem source_gram_21_19_3 : Z 21 19 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_3_19 + +theorem source_error_21_19_5 : Y 21 19 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_5_19 + +theorem source_gram_21_19_5 : Z 21 19 5 = (7127642602080000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_5_19 + +theorem source_error_21_19_7 : Y 21 19 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_7_19 + +theorem source_gram_21_19_7 : Z 21 19 7 = (6652466428608000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_7_19 + +theorem source_error_21_19_9 : Y 21 19 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_9_19 + +theorem source_gram_21_19_9 : Z 21 19 9 = (3207439170936000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_9_19 + +theorem source_error_21_19_11 : Y 21 19 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_11_19 + +theorem source_gram_21_19_11 : Z 21 19 11 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_21_11_19 + +theorem source_error_21_19_13 : Y 21 19 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_13_19 + +theorem source_gram_21_19_13 : Z 21 19 13 = (-1930403204730000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_13_19 + +theorem source_error_21_19_15 : Y 21 19 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_15_19 + +theorem source_gram_21_19_15 : Z 21 19 15 = (-2672865975780000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_15_19 + +theorem source_error_21_19_17 : Y 21 19 17 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_17_19 + +theorem source_gram_21_19_17 : Z 21 19 17 = (-2650592092648500 : ℚ) := by + rw [Z_symm] + exact source_gram_21_17_19 + +theorem source_error_21_21_1 : Y 21 21 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_1_21 + +theorem source_gram_21_21_1 : Z 21 21 1 = (898082967862080000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_1_21 + +theorem source_error_21_21_3 : Y 21 21 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_3_21 + +theorem source_gram_21_21_3 : Z 21 21 3 = (349254487501920000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_3_21 + +theorem source_error_21_21_5 : Y 21 21 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_5_21 + +theorem source_gram_21_21_5 : Z 21 21 5 = (124733745536400000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_5_21 + +theorem source_error_21_21_7 : Y 21 21 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_7_21 + +theorem source_gram_21_21_7 : Z 21 21 7 = (37420123660920000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_7_21 + +theorem source_error_21_21_9 : Y 21 21 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_9_21 + +theorem source_gram_21_21_9 : Z 21 21 9 = (6236687276820000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_9_21 + +theorem source_error_21_21_11 : Y 21 21 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_11_21 + +theorem source_gram_21_21_11 : Z 21 21 11 = (-3118343638410000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_11_21 + +theorem source_error_21_21_13 : Y 21 21 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_13_21 + +theorem source_gram_21_21_13 : Z 21 21 13 = (-4677515457615000 : ℚ) := by + rw [Z_symm] + exact source_gram_21_13_21 + +theorem source_error_21_21_15 : Y 21 21 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_15_21 + +theorem source_gram_21_21_15 : Z 21 21 15 = (-3897929548012500 : ℚ) := by + rw [Z_symm] + exact source_gram_21_15_21 + +theorem source_error_21_21_17 : Y 21 21 17 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_17_21 + +theorem source_gram_21_21_17 : Z 21 21 17 = (-2728550683608750 : ℚ) := by + rw [Z_symm] + exact source_gram_21_17_21 + +theorem source_error_21_21_19 : Y 21 21 19 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_21_19_21 + +theorem source_gram_21_21_19 : Z 21 21 19 = (-1754068296605625 : ℚ) := by + rw [Z_symm] + exact source_gram_21_19_21 + +theorem error_21 : errorRational 21 = candidateY_21 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_21_1_1 + · exact source_error_21_1_3 + · exact source_error_21_1_5 + · exact source_error_21_1_7 + · exact source_error_21_1_9 + · exact source_error_21_1_11 + · exact source_error_21_1_13 + · exact source_error_21_1_15 + · exact source_error_21_1_17 + · exact source_error_21_1_19 + · exact source_error_21_1_21 + · exact source_error_21_3_1 + · exact source_error_21_3_3 + · exact source_error_21_3_5 + · exact source_error_21_3_7 + · exact source_error_21_3_9 + · exact source_error_21_3_11 + · exact source_error_21_3_13 + · exact source_error_21_3_15 + · exact source_error_21_3_17 + · exact source_error_21_3_19 + · exact source_error_21_3_21 + · exact source_error_21_5_1 + · exact source_error_21_5_3 + · exact source_error_21_5_5 + · exact source_error_21_5_7 + · exact source_error_21_5_9 + · exact source_error_21_5_11 + · exact source_error_21_5_13 + · exact source_error_21_5_15 + · exact source_error_21_5_17 + · exact source_error_21_5_19 + · exact source_error_21_5_21 + · exact source_error_21_7_1 + · exact source_error_21_7_3 + · exact source_error_21_7_5 + · exact source_error_21_7_7 + · exact source_error_21_7_9 + · exact source_error_21_7_11 + · exact source_error_21_7_13 + · exact source_error_21_7_15 + · exact source_error_21_7_17 + · exact source_error_21_7_19 + · exact source_error_21_7_21 + · exact source_error_21_9_1 + · exact source_error_21_9_3 + · exact source_error_21_9_5 + · exact source_error_21_9_7 + · exact source_error_21_9_9 + · exact source_error_21_9_11 + · exact source_error_21_9_13 + · exact source_error_21_9_15 + · exact source_error_21_9_17 + · exact source_error_21_9_19 + · exact source_error_21_9_21 + · exact source_error_21_11_1 + · exact source_error_21_11_3 + · exact source_error_21_11_5 + · exact source_error_21_11_7 + · exact source_error_21_11_9 + · exact source_error_21_11_11 + · exact source_error_21_11_13 + · exact source_error_21_11_15 + · exact source_error_21_11_17 + · exact source_error_21_11_19 + · exact source_error_21_11_21 + · exact source_error_21_13_1 + · exact source_error_21_13_3 + · exact source_error_21_13_5 + · exact source_error_21_13_7 + · exact source_error_21_13_9 + · exact source_error_21_13_11 + · exact source_error_21_13_13 + · exact source_error_21_13_15 + · exact source_error_21_13_17 + · exact source_error_21_13_19 + · exact source_error_21_13_21 + · exact source_error_21_15_1 + · exact source_error_21_15_3 + · exact source_error_21_15_5 + · exact source_error_21_15_7 + · exact source_error_21_15_9 + · exact source_error_21_15_11 + · exact source_error_21_15_13 + · exact source_error_21_15_15 + · exact source_error_21_15_17 + · exact source_error_21_15_19 + · exact source_error_21_15_21 + · exact source_error_21_17_1 + · exact source_error_21_17_3 + · exact source_error_21_17_5 + · exact source_error_21_17_7 + · exact source_error_21_17_9 + · exact source_error_21_17_11 + · exact source_error_21_17_13 + · exact source_error_21_17_15 + · exact source_error_21_17_17 + · exact source_error_21_17_19 + · exact source_error_21_17_21 + · exact source_error_21_19_1 + · exact source_error_21_19_3 + · exact source_error_21_19_5 + · exact source_error_21_19_7 + · exact source_error_21_19_9 + · exact source_error_21_19_11 + · exact source_error_21_19_13 + · exact source_error_21_19_15 + · exact source_error_21_19_17 + · exact source_error_21_19_19 + · exact source_error_21_19_21 + · exact source_error_21_21_1 + · exact source_error_21_21_3 + · exact source_error_21_21_5 + · exact source_error_21_21_7 + · exact source_error_21_21_9 + · exact source_error_21_21_11 + · exact source_error_21_21_13 + · exact source_error_21_21_15 + · exact source_error_21_21_17 + · exact source_error_21_21_19 + · exact source_error_21_21_21 + +theorem gram_21 : gramRational 21 = candidateZ_21 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_21_1_1 + · exact source_gram_21_1_3 + · exact source_gram_21_1_5 + · exact source_gram_21_1_7 + · exact source_gram_21_1_9 + · exact source_gram_21_1_11 + · exact source_gram_21_1_13 + · exact source_gram_21_1_15 + · exact source_gram_21_1_17 + · exact source_gram_21_1_19 + · exact source_gram_21_1_21 + · exact source_gram_21_3_1 + · exact source_gram_21_3_3 + · exact source_gram_21_3_5 + · exact source_gram_21_3_7 + · exact source_gram_21_3_9 + · exact source_gram_21_3_11 + · exact source_gram_21_3_13 + · exact source_gram_21_3_15 + · exact source_gram_21_3_17 + · exact source_gram_21_3_19 + · exact source_gram_21_3_21 + · exact source_gram_21_5_1 + · exact source_gram_21_5_3 + · exact source_gram_21_5_5 + · exact source_gram_21_5_7 + · exact source_gram_21_5_9 + · exact source_gram_21_5_11 + · exact source_gram_21_5_13 + · exact source_gram_21_5_15 + · exact source_gram_21_5_17 + · exact source_gram_21_5_19 + · exact source_gram_21_5_21 + · exact source_gram_21_7_1 + · exact source_gram_21_7_3 + · exact source_gram_21_7_5 + · exact source_gram_21_7_7 + · exact source_gram_21_7_9 + · exact source_gram_21_7_11 + · exact source_gram_21_7_13 + · exact source_gram_21_7_15 + · exact source_gram_21_7_17 + · exact source_gram_21_7_19 + · exact source_gram_21_7_21 + · exact source_gram_21_9_1 + · exact source_gram_21_9_3 + · exact source_gram_21_9_5 + · exact source_gram_21_9_7 + · exact source_gram_21_9_9 + · exact source_gram_21_9_11 + · exact source_gram_21_9_13 + · exact source_gram_21_9_15 + · exact source_gram_21_9_17 + · exact source_gram_21_9_19 + · exact source_gram_21_9_21 + · exact source_gram_21_11_1 + · exact source_gram_21_11_3 + · exact source_gram_21_11_5 + · exact source_gram_21_11_7 + · exact source_gram_21_11_9 + · exact source_gram_21_11_11 + · exact source_gram_21_11_13 + · exact source_gram_21_11_15 + · exact source_gram_21_11_17 + · exact source_gram_21_11_19 + · exact source_gram_21_11_21 + · exact source_gram_21_13_1 + · exact source_gram_21_13_3 + · exact source_gram_21_13_5 + · exact source_gram_21_13_7 + · exact source_gram_21_13_9 + · exact source_gram_21_13_11 + · exact source_gram_21_13_13 + · exact source_gram_21_13_15 + · exact source_gram_21_13_17 + · exact source_gram_21_13_19 + · exact source_gram_21_13_21 + · exact source_gram_21_15_1 + · exact source_gram_21_15_3 + · exact source_gram_21_15_5 + · exact source_gram_21_15_7 + · exact source_gram_21_15_9 + · exact source_gram_21_15_11 + · exact source_gram_21_15_13 + · exact source_gram_21_15_15 + · exact source_gram_21_15_17 + · exact source_gram_21_15_19 + · exact source_gram_21_15_21 + · exact source_gram_21_17_1 + · exact source_gram_21_17_3 + · exact source_gram_21_17_5 + · exact source_gram_21_17_7 + · exact source_gram_21_17_9 + · exact source_gram_21_17_11 + · exact source_gram_21_17_13 + · exact source_gram_21_17_15 + · exact source_gram_21_17_17 + · exact source_gram_21_17_19 + · exact source_gram_21_17_21 + · exact source_gram_21_19_1 + · exact source_gram_21_19_3 + · exact source_gram_21_19_5 + · exact source_gram_21_19_7 + · exact source_gram_21_19_9 + · exact source_gram_21_19_11 + · exact source_gram_21_19_13 + · exact source_gram_21_19_15 + · exact source_gram_21_19_17 + · exact source_gram_21_19_19 + · exact source_gram_21_19_21 + · exact source_gram_21_21_1 + · exact source_gram_21_21_3 + · exact source_gram_21_21_5 + · exact source_gram_21_21_7 + · exact source_gram_21_21_9 + · exact source_gram_21_21_11 + · exact source_gram_21_21_13 + · exact source_gram_21_21_15 + · exact source_gram_21_21_17 + · exact source_gram_21_21_19 + · exact source_gram_21_21_21 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData22.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData22.lean new file mode 100644 index 0000000000000000000000000000000000000000..999ddc648e7addd12e7ed4af7f9a09c22dd7727a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData22.lean @@ -0,0 +1,1767 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram01Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram03Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram05Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram07Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram11Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram13Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram15Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram17Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram19Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram212122 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0101Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0103Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0105Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0107Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0109Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0111Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0113Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0115Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0117Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0119Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0121Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0303Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0305Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0307Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0309Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0311Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0313Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0315Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0317Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0319Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0321Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0505Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0507Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0509Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0511Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0513Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0515Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0517Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0519Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0521Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0707Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0709Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0711Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0713Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0715Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0717Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0719Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0721Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0909Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0911Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0913Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0915Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0917Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0919Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0921Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1111Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1113Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1115Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1117Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1119Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1121Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1313Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1315Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1317Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1319Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1321Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1515Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1517Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1519Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1521Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1717Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1719Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1721Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1919Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1921Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow2121Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.Data22 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_22_1_1 : Y 22 1 1 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 1 1 0 (by decide), + source_yRow_eq_rowCompute 22 1 1 1 (by decide), + source_yRow_eq_rowCompute 22 1 1 2 (by decide), + source_yRow_eq_rowCompute 22 1 1 3 (by decide), + source_yRow_eq_rowCompute 22 1 1 4 (by decide), + source_yRow_eq_rowCompute 22 1 1 5 (by decide), + source_yRow_eq_rowCompute 22 1 1 6 (by decide), + computeRow_22_1_1_0, computeRow_22_1_1_1, computeRow_22_1_1_2, computeRow_22_1_1_3, computeRow_22_1_1_4, computeRow_22_1_1_5, computeRow_22_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_1_3 : Y 22 1 3 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 1 3 0 (by decide), + source_yRow_eq_rowCompute 22 1 3 1 (by decide), + source_yRow_eq_rowCompute 22 1 3 2 (by decide), + source_yRow_eq_rowCompute 22 1 3 3 (by decide), + source_yRow_eq_rowCompute 22 1 3 4 (by decide), + source_yRow_eq_rowCompute 22 1 3 5 (by decide), + source_yRow_eq_rowCompute 22 1 3 6 (by decide), + computeRow_22_1_3_0, computeRow_22_1_3_1, computeRow_22_1_3_2, computeRow_22_1_3_3, computeRow_22_1_3_4, computeRow_22_1_3_5, computeRow_22_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_1_5 : Y 22 1 5 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 1 5 0 (by decide), + source_yRow_eq_rowCompute 22 1 5 1 (by decide), + source_yRow_eq_rowCompute 22 1 5 2 (by decide), + source_yRow_eq_rowCompute 22 1 5 3 (by decide), + source_yRow_eq_rowCompute 22 1 5 4 (by decide), + source_yRow_eq_rowCompute 22 1 5 5 (by decide), + source_yRow_eq_rowCompute 22 1 5 6 (by decide), + computeRow_22_1_5_0, computeRow_22_1_5_1, computeRow_22_1_5_2, computeRow_22_1_5_3, computeRow_22_1_5_4, computeRow_22_1_5_5, computeRow_22_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_1_7 : Y 22 1 7 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 1 7 0 (by decide), + source_yRow_eq_rowCompute 22 1 7 1 (by decide), + source_yRow_eq_rowCompute 22 1 7 2 (by decide), + source_yRow_eq_rowCompute 22 1 7 3 (by decide), + source_yRow_eq_rowCompute 22 1 7 4 (by decide), + source_yRow_eq_rowCompute 22 1 7 5 (by decide), + source_yRow_eq_rowCompute 22 1 7 6 (by decide), + computeRow_22_1_7_0, computeRow_22_1_7_1, computeRow_22_1_7_2, computeRow_22_1_7_3, computeRow_22_1_7_4, computeRow_22_1_7_5, computeRow_22_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_1_9 : Y 22 1 9 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 1 9 0 (by decide), + source_yRow_eq_rowCompute 22 1 9 1 (by decide), + source_yRow_eq_rowCompute 22 1 9 2 (by decide), + source_yRow_eq_rowCompute 22 1 9 3 (by decide), + source_yRow_eq_rowCompute 22 1 9 4 (by decide), + source_yRow_eq_rowCompute 22 1 9 5 (by decide), + source_yRow_eq_rowCompute 22 1 9 6 (by decide), + computeRow_22_1_9_0, computeRow_22_1_9_1, computeRow_22_1_9_2, computeRow_22_1_9_3, computeRow_22_1_9_4, computeRow_22_1_9_5, computeRow_22_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_1_11 : Y 22 1 11 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 1 11 0 (by decide), + source_yRow_eq_rowCompute 22 1 11 1 (by decide), + source_yRow_eq_rowCompute 22 1 11 2 (by decide), + source_yRow_eq_rowCompute 22 1 11 3 (by decide), + source_yRow_eq_rowCompute 22 1 11 4 (by decide), + source_yRow_eq_rowCompute 22 1 11 5 (by decide), + source_yRow_eq_rowCompute 22 1 11 6 (by decide), + computeRow_22_1_11_0, computeRow_22_1_11_1, computeRow_22_1_11_2, computeRow_22_1_11_3, computeRow_22_1_11_4, computeRow_22_1_11_5, computeRow_22_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_1_13 : Y 22 1 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 1 13 0 (by decide), + source_yRow_eq_rowCompute 22 1 13 1 (by decide), + source_yRow_eq_rowCompute 22 1 13 2 (by decide), + source_yRow_eq_rowCompute 22 1 13 3 (by decide), + source_yRow_eq_rowCompute 22 1 13 4 (by decide), + source_yRow_eq_rowCompute 22 1 13 5 (by decide), + source_yRow_eq_rowCompute 22 1 13 6 (by decide), + computeRow_22_1_13_0, computeRow_22_1_13_1, computeRow_22_1_13_2, computeRow_22_1_13_3, computeRow_22_1_13_4, computeRow_22_1_13_5, computeRow_22_1_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_1_15 : Y 22 1 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 1 15 0 (by decide), + source_yRow_eq_rowCompute 22 1 15 1 (by decide), + source_yRow_eq_rowCompute 22 1 15 2 (by decide), + source_yRow_eq_rowCompute 22 1 15 3 (by decide), + source_yRow_eq_rowCompute 22 1 15 4 (by decide), + source_yRow_eq_rowCompute 22 1 15 5 (by decide), + source_yRow_eq_rowCompute 22 1 15 6 (by decide), + computeRow_22_1_15_0, computeRow_22_1_15_1, computeRow_22_1_15_2, computeRow_22_1_15_3, computeRow_22_1_15_4, computeRow_22_1_15_5, computeRow_22_1_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_1_17 : Y 22 1 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 1 17 0 (by decide), + source_yRow_eq_rowCompute 22 1 17 1 (by decide), + source_yRow_eq_rowCompute 22 1 17 2 (by decide), + source_yRow_eq_rowCompute 22 1 17 3 (by decide), + source_yRow_eq_rowCompute 22 1 17 4 (by decide), + source_yRow_eq_rowCompute 22 1 17 5 (by decide), + source_yRow_eq_rowCompute 22 1 17 6 (by decide), + computeRow_22_1_17_0, computeRow_22_1_17_1, computeRow_22_1_17_2, computeRow_22_1_17_3, computeRow_22_1_17_4, computeRow_22_1_17_5, computeRow_22_1_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_1_19 : Y 22 1 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 1 19 0 (by decide), + source_yRow_eq_rowCompute 22 1 19 1 (by decide), + source_yRow_eq_rowCompute 22 1 19 2 (by decide), + source_yRow_eq_rowCompute 22 1 19 3 (by decide), + source_yRow_eq_rowCompute 22 1 19 4 (by decide), + source_yRow_eq_rowCompute 22 1 19 5 (by decide), + source_yRow_eq_rowCompute 22 1 19 6 (by decide), + computeRow_22_1_19_0, computeRow_22_1_19_1, computeRow_22_1_19_2, computeRow_22_1_19_3, computeRow_22_1_19_4, computeRow_22_1_19_5, computeRow_22_1_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_1_21 : Y 22 1 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 1 21 0 (by decide), + source_yRow_eq_rowCompute 22 1 21 1 (by decide), + source_yRow_eq_rowCompute 22 1 21 2 (by decide), + source_yRow_eq_rowCompute 22 1 21 3 (by decide), + source_yRow_eq_rowCompute 22 1 21 4 (by decide), + source_yRow_eq_rowCompute 22 1 21 5 (by decide), + source_yRow_eq_rowCompute 22 1 21 6 (by decide), + computeRow_22_1_21_0, computeRow_22_1_21_1, computeRow_22_1_21_2, computeRow_22_1_21_3, computeRow_22_1_21_4, computeRow_22_1_21_5, computeRow_22_1_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_3_3 : Y 22 3 3 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 3 3 0 (by decide), + source_yRow_eq_rowCompute 22 3 3 1 (by decide), + source_yRow_eq_rowCompute 22 3 3 2 (by decide), + source_yRow_eq_rowCompute 22 3 3 3 (by decide), + source_yRow_eq_rowCompute 22 3 3 4 (by decide), + source_yRow_eq_rowCompute 22 3 3 5 (by decide), + source_yRow_eq_rowCompute 22 3 3 6 (by decide), + computeRow_22_3_3_0, computeRow_22_3_3_1, computeRow_22_3_3_2, computeRow_22_3_3_3, computeRow_22_3_3_4, computeRow_22_3_3_5, computeRow_22_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_3_5 : Y 22 3 5 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 3 5 0 (by decide), + source_yRow_eq_rowCompute 22 3 5 1 (by decide), + source_yRow_eq_rowCompute 22 3 5 2 (by decide), + source_yRow_eq_rowCompute 22 3 5 3 (by decide), + source_yRow_eq_rowCompute 22 3 5 4 (by decide), + source_yRow_eq_rowCompute 22 3 5 5 (by decide), + source_yRow_eq_rowCompute 22 3 5 6 (by decide), + computeRow_22_3_5_0, computeRow_22_3_5_1, computeRow_22_3_5_2, computeRow_22_3_5_3, computeRow_22_3_5_4, computeRow_22_3_5_5, computeRow_22_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_3_7 : Y 22 3 7 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 3 7 0 (by decide), + source_yRow_eq_rowCompute 22 3 7 1 (by decide), + source_yRow_eq_rowCompute 22 3 7 2 (by decide), + source_yRow_eq_rowCompute 22 3 7 3 (by decide), + source_yRow_eq_rowCompute 22 3 7 4 (by decide), + source_yRow_eq_rowCompute 22 3 7 5 (by decide), + source_yRow_eq_rowCompute 22 3 7 6 (by decide), + computeRow_22_3_7_0, computeRow_22_3_7_1, computeRow_22_3_7_2, computeRow_22_3_7_3, computeRow_22_3_7_4, computeRow_22_3_7_5, computeRow_22_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_3_9 : Y 22 3 9 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 3 9 0 (by decide), + source_yRow_eq_rowCompute 22 3 9 1 (by decide), + source_yRow_eq_rowCompute 22 3 9 2 (by decide), + source_yRow_eq_rowCompute 22 3 9 3 (by decide), + source_yRow_eq_rowCompute 22 3 9 4 (by decide), + source_yRow_eq_rowCompute 22 3 9 5 (by decide), + source_yRow_eq_rowCompute 22 3 9 6 (by decide), + computeRow_22_3_9_0, computeRow_22_3_9_1, computeRow_22_3_9_2, computeRow_22_3_9_3, computeRow_22_3_9_4, computeRow_22_3_9_5, computeRow_22_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_3_11 : Y 22 3 11 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 3 11 0 (by decide), + source_yRow_eq_rowCompute 22 3 11 1 (by decide), + source_yRow_eq_rowCompute 22 3 11 2 (by decide), + source_yRow_eq_rowCompute 22 3 11 3 (by decide), + source_yRow_eq_rowCompute 22 3 11 4 (by decide), + source_yRow_eq_rowCompute 22 3 11 5 (by decide), + source_yRow_eq_rowCompute 22 3 11 6 (by decide), + computeRow_22_3_11_0, computeRow_22_3_11_1, computeRow_22_3_11_2, computeRow_22_3_11_3, computeRow_22_3_11_4, computeRow_22_3_11_5, computeRow_22_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_3_13 : Y 22 3 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 3 13 0 (by decide), + source_yRow_eq_rowCompute 22 3 13 1 (by decide), + source_yRow_eq_rowCompute 22 3 13 2 (by decide), + source_yRow_eq_rowCompute 22 3 13 3 (by decide), + source_yRow_eq_rowCompute 22 3 13 4 (by decide), + source_yRow_eq_rowCompute 22 3 13 5 (by decide), + source_yRow_eq_rowCompute 22 3 13 6 (by decide), + computeRow_22_3_13_0, computeRow_22_3_13_1, computeRow_22_3_13_2, computeRow_22_3_13_3, computeRow_22_3_13_4, computeRow_22_3_13_5, computeRow_22_3_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_3_15 : Y 22 3 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 3 15 0 (by decide), + source_yRow_eq_rowCompute 22 3 15 1 (by decide), + source_yRow_eq_rowCompute 22 3 15 2 (by decide), + source_yRow_eq_rowCompute 22 3 15 3 (by decide), + source_yRow_eq_rowCompute 22 3 15 4 (by decide), + source_yRow_eq_rowCompute 22 3 15 5 (by decide), + source_yRow_eq_rowCompute 22 3 15 6 (by decide), + computeRow_22_3_15_0, computeRow_22_3_15_1, computeRow_22_3_15_2, computeRow_22_3_15_3, computeRow_22_3_15_4, computeRow_22_3_15_5, computeRow_22_3_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_3_17 : Y 22 3 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 3 17 0 (by decide), + source_yRow_eq_rowCompute 22 3 17 1 (by decide), + source_yRow_eq_rowCompute 22 3 17 2 (by decide), + source_yRow_eq_rowCompute 22 3 17 3 (by decide), + source_yRow_eq_rowCompute 22 3 17 4 (by decide), + source_yRow_eq_rowCompute 22 3 17 5 (by decide), + source_yRow_eq_rowCompute 22 3 17 6 (by decide), + computeRow_22_3_17_0, computeRow_22_3_17_1, computeRow_22_3_17_2, computeRow_22_3_17_3, computeRow_22_3_17_4, computeRow_22_3_17_5, computeRow_22_3_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_3_19 : Y 22 3 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 3 19 0 (by decide), + source_yRow_eq_rowCompute 22 3 19 1 (by decide), + source_yRow_eq_rowCompute 22 3 19 2 (by decide), + source_yRow_eq_rowCompute 22 3 19 3 (by decide), + source_yRow_eq_rowCompute 22 3 19 4 (by decide), + source_yRow_eq_rowCompute 22 3 19 5 (by decide), + source_yRow_eq_rowCompute 22 3 19 6 (by decide), + computeRow_22_3_19_0, computeRow_22_3_19_1, computeRow_22_3_19_2, computeRow_22_3_19_3, computeRow_22_3_19_4, computeRow_22_3_19_5, computeRow_22_3_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_3_21 : Y 22 3 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 3 21 0 (by decide), + source_yRow_eq_rowCompute 22 3 21 1 (by decide), + source_yRow_eq_rowCompute 22 3 21 2 (by decide), + source_yRow_eq_rowCompute 22 3 21 3 (by decide), + source_yRow_eq_rowCompute 22 3 21 4 (by decide), + source_yRow_eq_rowCompute 22 3 21 5 (by decide), + source_yRow_eq_rowCompute 22 3 21 6 (by decide), + computeRow_22_3_21_0, computeRow_22_3_21_1, computeRow_22_3_21_2, computeRow_22_3_21_3, computeRow_22_3_21_4, computeRow_22_3_21_5, computeRow_22_3_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_5_5 : Y 22 5 5 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 5 5 0 (by decide), + source_yRow_eq_rowCompute 22 5 5 1 (by decide), + source_yRow_eq_rowCompute 22 5 5 2 (by decide), + source_yRow_eq_rowCompute 22 5 5 3 (by decide), + source_yRow_eq_rowCompute 22 5 5 4 (by decide), + source_yRow_eq_rowCompute 22 5 5 5 (by decide), + source_yRow_eq_rowCompute 22 5 5 6 (by decide), + computeRow_22_5_5_0, computeRow_22_5_5_1, computeRow_22_5_5_2, computeRow_22_5_5_3, computeRow_22_5_5_4, computeRow_22_5_5_5, computeRow_22_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_5_7 : Y 22 5 7 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 5 7 0 (by decide), + source_yRow_eq_rowCompute 22 5 7 1 (by decide), + source_yRow_eq_rowCompute 22 5 7 2 (by decide), + source_yRow_eq_rowCompute 22 5 7 3 (by decide), + source_yRow_eq_rowCompute 22 5 7 4 (by decide), + source_yRow_eq_rowCompute 22 5 7 5 (by decide), + source_yRow_eq_rowCompute 22 5 7 6 (by decide), + computeRow_22_5_7_0, computeRow_22_5_7_1, computeRow_22_5_7_2, computeRow_22_5_7_3, computeRow_22_5_7_4, computeRow_22_5_7_5, computeRow_22_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_5_9 : Y 22 5 9 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 5 9 0 (by decide), + source_yRow_eq_rowCompute 22 5 9 1 (by decide), + source_yRow_eq_rowCompute 22 5 9 2 (by decide), + source_yRow_eq_rowCompute 22 5 9 3 (by decide), + source_yRow_eq_rowCompute 22 5 9 4 (by decide), + source_yRow_eq_rowCompute 22 5 9 5 (by decide), + source_yRow_eq_rowCompute 22 5 9 6 (by decide), + computeRow_22_5_9_0, computeRow_22_5_9_1, computeRow_22_5_9_2, computeRow_22_5_9_3, computeRow_22_5_9_4, computeRow_22_5_9_5, computeRow_22_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_5_11 : Y 22 5 11 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 5 11 0 (by decide), + source_yRow_eq_rowCompute 22 5 11 1 (by decide), + source_yRow_eq_rowCompute 22 5 11 2 (by decide), + source_yRow_eq_rowCompute 22 5 11 3 (by decide), + source_yRow_eq_rowCompute 22 5 11 4 (by decide), + source_yRow_eq_rowCompute 22 5 11 5 (by decide), + source_yRow_eq_rowCompute 22 5 11 6 (by decide), + computeRow_22_5_11_0, computeRow_22_5_11_1, computeRow_22_5_11_2, computeRow_22_5_11_3, computeRow_22_5_11_4, computeRow_22_5_11_5, computeRow_22_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_5_13 : Y 22 5 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 5 13 0 (by decide), + source_yRow_eq_rowCompute 22 5 13 1 (by decide), + source_yRow_eq_rowCompute 22 5 13 2 (by decide), + source_yRow_eq_rowCompute 22 5 13 3 (by decide), + source_yRow_eq_rowCompute 22 5 13 4 (by decide), + source_yRow_eq_rowCompute 22 5 13 5 (by decide), + source_yRow_eq_rowCompute 22 5 13 6 (by decide), + computeRow_22_5_13_0, computeRow_22_5_13_1, computeRow_22_5_13_2, computeRow_22_5_13_3, computeRow_22_5_13_4, computeRow_22_5_13_5, computeRow_22_5_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_5_15 : Y 22 5 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 5 15 0 (by decide), + source_yRow_eq_rowCompute 22 5 15 1 (by decide), + source_yRow_eq_rowCompute 22 5 15 2 (by decide), + source_yRow_eq_rowCompute 22 5 15 3 (by decide), + source_yRow_eq_rowCompute 22 5 15 4 (by decide), + source_yRow_eq_rowCompute 22 5 15 5 (by decide), + source_yRow_eq_rowCompute 22 5 15 6 (by decide), + computeRow_22_5_15_0, computeRow_22_5_15_1, computeRow_22_5_15_2, computeRow_22_5_15_3, computeRow_22_5_15_4, computeRow_22_5_15_5, computeRow_22_5_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_5_17 : Y 22 5 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 5 17 0 (by decide), + source_yRow_eq_rowCompute 22 5 17 1 (by decide), + source_yRow_eq_rowCompute 22 5 17 2 (by decide), + source_yRow_eq_rowCompute 22 5 17 3 (by decide), + source_yRow_eq_rowCompute 22 5 17 4 (by decide), + source_yRow_eq_rowCompute 22 5 17 5 (by decide), + source_yRow_eq_rowCompute 22 5 17 6 (by decide), + computeRow_22_5_17_0, computeRow_22_5_17_1, computeRow_22_5_17_2, computeRow_22_5_17_3, computeRow_22_5_17_4, computeRow_22_5_17_5, computeRow_22_5_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_5_19 : Y 22 5 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 5 19 0 (by decide), + source_yRow_eq_rowCompute 22 5 19 1 (by decide), + source_yRow_eq_rowCompute 22 5 19 2 (by decide), + source_yRow_eq_rowCompute 22 5 19 3 (by decide), + source_yRow_eq_rowCompute 22 5 19 4 (by decide), + source_yRow_eq_rowCompute 22 5 19 5 (by decide), + source_yRow_eq_rowCompute 22 5 19 6 (by decide), + computeRow_22_5_19_0, computeRow_22_5_19_1, computeRow_22_5_19_2, computeRow_22_5_19_3, computeRow_22_5_19_4, computeRow_22_5_19_5, computeRow_22_5_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_5_21 : Y 22 5 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 5 21 0 (by decide), + source_yRow_eq_rowCompute 22 5 21 1 (by decide), + source_yRow_eq_rowCompute 22 5 21 2 (by decide), + source_yRow_eq_rowCompute 22 5 21 3 (by decide), + source_yRow_eq_rowCompute 22 5 21 4 (by decide), + source_yRow_eq_rowCompute 22 5 21 5 (by decide), + source_yRow_eq_rowCompute 22 5 21 6 (by decide), + computeRow_22_5_21_0, computeRow_22_5_21_1, computeRow_22_5_21_2, computeRow_22_5_21_3, computeRow_22_5_21_4, computeRow_22_5_21_5, computeRow_22_5_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_7_7 : Y 22 7 7 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 7 7 0 (by decide), + source_yRow_eq_rowCompute 22 7 7 1 (by decide), + source_yRow_eq_rowCompute 22 7 7 2 (by decide), + source_yRow_eq_rowCompute 22 7 7 3 (by decide), + source_yRow_eq_rowCompute 22 7 7 4 (by decide), + source_yRow_eq_rowCompute 22 7 7 5 (by decide), + source_yRow_eq_rowCompute 22 7 7 6 (by decide), + computeRow_22_7_7_0, computeRow_22_7_7_1, computeRow_22_7_7_2, computeRow_22_7_7_3, computeRow_22_7_7_4, computeRow_22_7_7_5, computeRow_22_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_7_9 : Y 22 7 9 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 7 9 0 (by decide), + source_yRow_eq_rowCompute 22 7 9 1 (by decide), + source_yRow_eq_rowCompute 22 7 9 2 (by decide), + source_yRow_eq_rowCompute 22 7 9 3 (by decide), + source_yRow_eq_rowCompute 22 7 9 4 (by decide), + source_yRow_eq_rowCompute 22 7 9 5 (by decide), + source_yRow_eq_rowCompute 22 7 9 6 (by decide), + computeRow_22_7_9_0, computeRow_22_7_9_1, computeRow_22_7_9_2, computeRow_22_7_9_3, computeRow_22_7_9_4, computeRow_22_7_9_5, computeRow_22_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_7_11 : Y 22 7 11 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 7 11 0 (by decide), + source_yRow_eq_rowCompute 22 7 11 1 (by decide), + source_yRow_eq_rowCompute 22 7 11 2 (by decide), + source_yRow_eq_rowCompute 22 7 11 3 (by decide), + source_yRow_eq_rowCompute 22 7 11 4 (by decide), + source_yRow_eq_rowCompute 22 7 11 5 (by decide), + source_yRow_eq_rowCompute 22 7 11 6 (by decide), + computeRow_22_7_11_0, computeRow_22_7_11_1, computeRow_22_7_11_2, computeRow_22_7_11_3, computeRow_22_7_11_4, computeRow_22_7_11_5, computeRow_22_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_7_13 : Y 22 7 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 7 13 0 (by decide), + source_yRow_eq_rowCompute 22 7 13 1 (by decide), + source_yRow_eq_rowCompute 22 7 13 2 (by decide), + source_yRow_eq_rowCompute 22 7 13 3 (by decide), + source_yRow_eq_rowCompute 22 7 13 4 (by decide), + source_yRow_eq_rowCompute 22 7 13 5 (by decide), + source_yRow_eq_rowCompute 22 7 13 6 (by decide), + computeRow_22_7_13_0, computeRow_22_7_13_1, computeRow_22_7_13_2, computeRow_22_7_13_3, computeRow_22_7_13_4, computeRow_22_7_13_5, computeRow_22_7_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_7_15 : Y 22 7 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 7 15 0 (by decide), + source_yRow_eq_rowCompute 22 7 15 1 (by decide), + source_yRow_eq_rowCompute 22 7 15 2 (by decide), + source_yRow_eq_rowCompute 22 7 15 3 (by decide), + source_yRow_eq_rowCompute 22 7 15 4 (by decide), + source_yRow_eq_rowCompute 22 7 15 5 (by decide), + source_yRow_eq_rowCompute 22 7 15 6 (by decide), + computeRow_22_7_15_0, computeRow_22_7_15_1, computeRow_22_7_15_2, computeRow_22_7_15_3, computeRow_22_7_15_4, computeRow_22_7_15_5, computeRow_22_7_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_7_17 : Y 22 7 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 7 17 0 (by decide), + source_yRow_eq_rowCompute 22 7 17 1 (by decide), + source_yRow_eq_rowCompute 22 7 17 2 (by decide), + source_yRow_eq_rowCompute 22 7 17 3 (by decide), + source_yRow_eq_rowCompute 22 7 17 4 (by decide), + source_yRow_eq_rowCompute 22 7 17 5 (by decide), + source_yRow_eq_rowCompute 22 7 17 6 (by decide), + computeRow_22_7_17_0, computeRow_22_7_17_1, computeRow_22_7_17_2, computeRow_22_7_17_3, computeRow_22_7_17_4, computeRow_22_7_17_5, computeRow_22_7_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_7_19 : Y 22 7 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 7 19 0 (by decide), + source_yRow_eq_rowCompute 22 7 19 1 (by decide), + source_yRow_eq_rowCompute 22 7 19 2 (by decide), + source_yRow_eq_rowCompute 22 7 19 3 (by decide), + source_yRow_eq_rowCompute 22 7 19 4 (by decide), + source_yRow_eq_rowCompute 22 7 19 5 (by decide), + source_yRow_eq_rowCompute 22 7 19 6 (by decide), + computeRow_22_7_19_0, computeRow_22_7_19_1, computeRow_22_7_19_2, computeRow_22_7_19_3, computeRow_22_7_19_4, computeRow_22_7_19_5, computeRow_22_7_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_7_21 : Y 22 7 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 7 21 0 (by decide), + source_yRow_eq_rowCompute 22 7 21 1 (by decide), + source_yRow_eq_rowCompute 22 7 21 2 (by decide), + source_yRow_eq_rowCompute 22 7 21 3 (by decide), + source_yRow_eq_rowCompute 22 7 21 4 (by decide), + source_yRow_eq_rowCompute 22 7 21 5 (by decide), + source_yRow_eq_rowCompute 22 7 21 6 (by decide), + computeRow_22_7_21_0, computeRow_22_7_21_1, computeRow_22_7_21_2, computeRow_22_7_21_3, computeRow_22_7_21_4, computeRow_22_7_21_5, computeRow_22_7_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_9_9 : Y 22 9 9 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 9 9 0 (by decide), + source_yRow_eq_rowCompute 22 9 9 1 (by decide), + source_yRow_eq_rowCompute 22 9 9 2 (by decide), + source_yRow_eq_rowCompute 22 9 9 3 (by decide), + source_yRow_eq_rowCompute 22 9 9 4 (by decide), + source_yRow_eq_rowCompute 22 9 9 5 (by decide), + source_yRow_eq_rowCompute 22 9 9 6 (by decide), + computeRow_22_9_9_0, computeRow_22_9_9_1, computeRow_22_9_9_2, computeRow_22_9_9_3, computeRow_22_9_9_4, computeRow_22_9_9_5, computeRow_22_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_9_11 : Y 22 9 11 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 9 11 0 (by decide), + source_yRow_eq_rowCompute 22 9 11 1 (by decide), + source_yRow_eq_rowCompute 22 9 11 2 (by decide), + source_yRow_eq_rowCompute 22 9 11 3 (by decide), + source_yRow_eq_rowCompute 22 9 11 4 (by decide), + source_yRow_eq_rowCompute 22 9 11 5 (by decide), + source_yRow_eq_rowCompute 22 9 11 6 (by decide), + computeRow_22_9_11_0, computeRow_22_9_11_1, computeRow_22_9_11_2, computeRow_22_9_11_3, computeRow_22_9_11_4, computeRow_22_9_11_5, computeRow_22_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_9_13 : Y 22 9 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 9 13 0 (by decide), + source_yRow_eq_rowCompute 22 9 13 1 (by decide), + source_yRow_eq_rowCompute 22 9 13 2 (by decide), + source_yRow_eq_rowCompute 22 9 13 3 (by decide), + source_yRow_eq_rowCompute 22 9 13 4 (by decide), + source_yRow_eq_rowCompute 22 9 13 5 (by decide), + source_yRow_eq_rowCompute 22 9 13 6 (by decide), + computeRow_22_9_13_0, computeRow_22_9_13_1, computeRow_22_9_13_2, computeRow_22_9_13_3, computeRow_22_9_13_4, computeRow_22_9_13_5, computeRow_22_9_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_9_15 : Y 22 9 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 9 15 0 (by decide), + source_yRow_eq_rowCompute 22 9 15 1 (by decide), + source_yRow_eq_rowCompute 22 9 15 2 (by decide), + source_yRow_eq_rowCompute 22 9 15 3 (by decide), + source_yRow_eq_rowCompute 22 9 15 4 (by decide), + source_yRow_eq_rowCompute 22 9 15 5 (by decide), + source_yRow_eq_rowCompute 22 9 15 6 (by decide), + computeRow_22_9_15_0, computeRow_22_9_15_1, computeRow_22_9_15_2, computeRow_22_9_15_3, computeRow_22_9_15_4, computeRow_22_9_15_5, computeRow_22_9_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_9_17 : Y 22 9 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 9 17 0 (by decide), + source_yRow_eq_rowCompute 22 9 17 1 (by decide), + source_yRow_eq_rowCompute 22 9 17 2 (by decide), + source_yRow_eq_rowCompute 22 9 17 3 (by decide), + source_yRow_eq_rowCompute 22 9 17 4 (by decide), + source_yRow_eq_rowCompute 22 9 17 5 (by decide), + source_yRow_eq_rowCompute 22 9 17 6 (by decide), + computeRow_22_9_17_0, computeRow_22_9_17_1, computeRow_22_9_17_2, computeRow_22_9_17_3, computeRow_22_9_17_4, computeRow_22_9_17_5, computeRow_22_9_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_9_19 : Y 22 9 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 9 19 0 (by decide), + source_yRow_eq_rowCompute 22 9 19 1 (by decide), + source_yRow_eq_rowCompute 22 9 19 2 (by decide), + source_yRow_eq_rowCompute 22 9 19 3 (by decide), + source_yRow_eq_rowCompute 22 9 19 4 (by decide), + source_yRow_eq_rowCompute 22 9 19 5 (by decide), + source_yRow_eq_rowCompute 22 9 19 6 (by decide), + computeRow_22_9_19_0, computeRow_22_9_19_1, computeRow_22_9_19_2, computeRow_22_9_19_3, computeRow_22_9_19_4, computeRow_22_9_19_5, computeRow_22_9_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_9_21 : Y 22 9 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 9 21 0 (by decide), + source_yRow_eq_rowCompute 22 9 21 1 (by decide), + source_yRow_eq_rowCompute 22 9 21 2 (by decide), + source_yRow_eq_rowCompute 22 9 21 3 (by decide), + source_yRow_eq_rowCompute 22 9 21 4 (by decide), + source_yRow_eq_rowCompute 22 9 21 5 (by decide), + source_yRow_eq_rowCompute 22 9 21 6 (by decide), + computeRow_22_9_21_0, computeRow_22_9_21_1, computeRow_22_9_21_2, computeRow_22_9_21_3, computeRow_22_9_21_4, computeRow_22_9_21_5, computeRow_22_9_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_11_11 : Y 22 11 11 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 11 11 0 (by decide), + source_yRow_eq_rowCompute 22 11 11 1 (by decide), + source_yRow_eq_rowCompute 22 11 11 2 (by decide), + source_yRow_eq_rowCompute 22 11 11 3 (by decide), + source_yRow_eq_rowCompute 22 11 11 4 (by decide), + source_yRow_eq_rowCompute 22 11 11 5 (by decide), + source_yRow_eq_rowCompute 22 11 11 6 (by decide), + computeRow_22_11_11_0, computeRow_22_11_11_1, computeRow_22_11_11_2, computeRow_22_11_11_3, computeRow_22_11_11_4, computeRow_22_11_11_5, computeRow_22_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_11_13 : Y 22 11 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 11 13 0 (by decide), + source_yRow_eq_rowCompute 22 11 13 1 (by decide), + source_yRow_eq_rowCompute 22 11 13 2 (by decide), + source_yRow_eq_rowCompute 22 11 13 3 (by decide), + source_yRow_eq_rowCompute 22 11 13 4 (by decide), + source_yRow_eq_rowCompute 22 11 13 5 (by decide), + source_yRow_eq_rowCompute 22 11 13 6 (by decide), + computeRow_22_11_13_0, computeRow_22_11_13_1, computeRow_22_11_13_2, computeRow_22_11_13_3, computeRow_22_11_13_4, computeRow_22_11_13_5, computeRow_22_11_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_11_15 : Y 22 11 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 11 15 0 (by decide), + source_yRow_eq_rowCompute 22 11 15 1 (by decide), + source_yRow_eq_rowCompute 22 11 15 2 (by decide), + source_yRow_eq_rowCompute 22 11 15 3 (by decide), + source_yRow_eq_rowCompute 22 11 15 4 (by decide), + source_yRow_eq_rowCompute 22 11 15 5 (by decide), + source_yRow_eq_rowCompute 22 11 15 6 (by decide), + computeRow_22_11_15_0, computeRow_22_11_15_1, computeRow_22_11_15_2, computeRow_22_11_15_3, computeRow_22_11_15_4, computeRow_22_11_15_5, computeRow_22_11_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_11_17 : Y 22 11 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 11 17 0 (by decide), + source_yRow_eq_rowCompute 22 11 17 1 (by decide), + source_yRow_eq_rowCompute 22 11 17 2 (by decide), + source_yRow_eq_rowCompute 22 11 17 3 (by decide), + source_yRow_eq_rowCompute 22 11 17 4 (by decide), + source_yRow_eq_rowCompute 22 11 17 5 (by decide), + source_yRow_eq_rowCompute 22 11 17 6 (by decide), + computeRow_22_11_17_0, computeRow_22_11_17_1, computeRow_22_11_17_2, computeRow_22_11_17_3, computeRow_22_11_17_4, computeRow_22_11_17_5, computeRow_22_11_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_11_19 : Y 22 11 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 11 19 0 (by decide), + source_yRow_eq_rowCompute 22 11 19 1 (by decide), + source_yRow_eq_rowCompute 22 11 19 2 (by decide), + source_yRow_eq_rowCompute 22 11 19 3 (by decide), + source_yRow_eq_rowCompute 22 11 19 4 (by decide), + source_yRow_eq_rowCompute 22 11 19 5 (by decide), + source_yRow_eq_rowCompute 22 11 19 6 (by decide), + computeRow_22_11_19_0, computeRow_22_11_19_1, computeRow_22_11_19_2, computeRow_22_11_19_3, computeRow_22_11_19_4, computeRow_22_11_19_5, computeRow_22_11_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_11_21 : Y 22 11 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 11 21 0 (by decide), + source_yRow_eq_rowCompute 22 11 21 1 (by decide), + source_yRow_eq_rowCompute 22 11 21 2 (by decide), + source_yRow_eq_rowCompute 22 11 21 3 (by decide), + source_yRow_eq_rowCompute 22 11 21 4 (by decide), + source_yRow_eq_rowCompute 22 11 21 5 (by decide), + source_yRow_eq_rowCompute 22 11 21 6 (by decide), + computeRow_22_11_21_0, computeRow_22_11_21_1, computeRow_22_11_21_2, computeRow_22_11_21_3, computeRow_22_11_21_4, computeRow_22_11_21_5, computeRow_22_11_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_13_13 : Y 22 13 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 13 13 0 (by decide), + source_yRow_eq_rowCompute 22 13 13 1 (by decide), + source_yRow_eq_rowCompute 22 13 13 2 (by decide), + source_yRow_eq_rowCompute 22 13 13 3 (by decide), + source_yRow_eq_rowCompute 22 13 13 4 (by decide), + source_yRow_eq_rowCompute 22 13 13 5 (by decide), + source_yRow_eq_rowCompute 22 13 13 6 (by decide), + computeRow_22_13_13_0, computeRow_22_13_13_1, computeRow_22_13_13_2, computeRow_22_13_13_3, computeRow_22_13_13_4, computeRow_22_13_13_5, computeRow_22_13_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_13_15 : Y 22 13 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 13 15 0 (by decide), + source_yRow_eq_rowCompute 22 13 15 1 (by decide), + source_yRow_eq_rowCompute 22 13 15 2 (by decide), + source_yRow_eq_rowCompute 22 13 15 3 (by decide), + source_yRow_eq_rowCompute 22 13 15 4 (by decide), + source_yRow_eq_rowCompute 22 13 15 5 (by decide), + source_yRow_eq_rowCompute 22 13 15 6 (by decide), + computeRow_22_13_15_0, computeRow_22_13_15_1, computeRow_22_13_15_2, computeRow_22_13_15_3, computeRow_22_13_15_4, computeRow_22_13_15_5, computeRow_22_13_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_13_17 : Y 22 13 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 13 17 0 (by decide), + source_yRow_eq_rowCompute 22 13 17 1 (by decide), + source_yRow_eq_rowCompute 22 13 17 2 (by decide), + source_yRow_eq_rowCompute 22 13 17 3 (by decide), + source_yRow_eq_rowCompute 22 13 17 4 (by decide), + source_yRow_eq_rowCompute 22 13 17 5 (by decide), + source_yRow_eq_rowCompute 22 13 17 6 (by decide), + computeRow_22_13_17_0, computeRow_22_13_17_1, computeRow_22_13_17_2, computeRow_22_13_17_3, computeRow_22_13_17_4, computeRow_22_13_17_5, computeRow_22_13_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_13_19 : Y 22 13 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 13 19 0 (by decide), + source_yRow_eq_rowCompute 22 13 19 1 (by decide), + source_yRow_eq_rowCompute 22 13 19 2 (by decide), + source_yRow_eq_rowCompute 22 13 19 3 (by decide), + source_yRow_eq_rowCompute 22 13 19 4 (by decide), + source_yRow_eq_rowCompute 22 13 19 5 (by decide), + source_yRow_eq_rowCompute 22 13 19 6 (by decide), + computeRow_22_13_19_0, computeRow_22_13_19_1, computeRow_22_13_19_2, computeRow_22_13_19_3, computeRow_22_13_19_4, computeRow_22_13_19_5, computeRow_22_13_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_13_21 : Y 22 13 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 13 21 0 (by decide), + source_yRow_eq_rowCompute 22 13 21 1 (by decide), + source_yRow_eq_rowCompute 22 13 21 2 (by decide), + source_yRow_eq_rowCompute 22 13 21 3 (by decide), + source_yRow_eq_rowCompute 22 13 21 4 (by decide), + source_yRow_eq_rowCompute 22 13 21 5 (by decide), + source_yRow_eq_rowCompute 22 13 21 6 (by decide), + computeRow_22_13_21_0, computeRow_22_13_21_1, computeRow_22_13_21_2, computeRow_22_13_21_3, computeRow_22_13_21_4, computeRow_22_13_21_5, computeRow_22_13_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_15_15 : Y 22 15 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 15 15 0 (by decide), + source_yRow_eq_rowCompute 22 15 15 1 (by decide), + source_yRow_eq_rowCompute 22 15 15 2 (by decide), + source_yRow_eq_rowCompute 22 15 15 3 (by decide), + source_yRow_eq_rowCompute 22 15 15 4 (by decide), + source_yRow_eq_rowCompute 22 15 15 5 (by decide), + source_yRow_eq_rowCompute 22 15 15 6 (by decide), + computeRow_22_15_15_0, computeRow_22_15_15_1, computeRow_22_15_15_2, computeRow_22_15_15_3, computeRow_22_15_15_4, computeRow_22_15_15_5, computeRow_22_15_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_15_17 : Y 22 15 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 15 17 0 (by decide), + source_yRow_eq_rowCompute 22 15 17 1 (by decide), + source_yRow_eq_rowCompute 22 15 17 2 (by decide), + source_yRow_eq_rowCompute 22 15 17 3 (by decide), + source_yRow_eq_rowCompute 22 15 17 4 (by decide), + source_yRow_eq_rowCompute 22 15 17 5 (by decide), + source_yRow_eq_rowCompute 22 15 17 6 (by decide), + computeRow_22_15_17_0, computeRow_22_15_17_1, computeRow_22_15_17_2, computeRow_22_15_17_3, computeRow_22_15_17_4, computeRow_22_15_17_5, computeRow_22_15_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_15_19 : Y 22 15 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 15 19 0 (by decide), + source_yRow_eq_rowCompute 22 15 19 1 (by decide), + source_yRow_eq_rowCompute 22 15 19 2 (by decide), + source_yRow_eq_rowCompute 22 15 19 3 (by decide), + source_yRow_eq_rowCompute 22 15 19 4 (by decide), + source_yRow_eq_rowCompute 22 15 19 5 (by decide), + source_yRow_eq_rowCompute 22 15 19 6 (by decide), + computeRow_22_15_19_0, computeRow_22_15_19_1, computeRow_22_15_19_2, computeRow_22_15_19_3, computeRow_22_15_19_4, computeRow_22_15_19_5, computeRow_22_15_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_15_21 : Y 22 15 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 15 21 0 (by decide), + source_yRow_eq_rowCompute 22 15 21 1 (by decide), + source_yRow_eq_rowCompute 22 15 21 2 (by decide), + source_yRow_eq_rowCompute 22 15 21 3 (by decide), + source_yRow_eq_rowCompute 22 15 21 4 (by decide), + source_yRow_eq_rowCompute 22 15 21 5 (by decide), + source_yRow_eq_rowCompute 22 15 21 6 (by decide), + computeRow_22_15_21_0, computeRow_22_15_21_1, computeRow_22_15_21_2, computeRow_22_15_21_3, computeRow_22_15_21_4, computeRow_22_15_21_5, computeRow_22_15_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_17_17 : Y 22 17 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 17 17 0 (by decide), + source_yRow_eq_rowCompute 22 17 17 1 (by decide), + source_yRow_eq_rowCompute 22 17 17 2 (by decide), + source_yRow_eq_rowCompute 22 17 17 3 (by decide), + source_yRow_eq_rowCompute 22 17 17 4 (by decide), + source_yRow_eq_rowCompute 22 17 17 5 (by decide), + source_yRow_eq_rowCompute 22 17 17 6 (by decide), + computeRow_22_17_17_0, computeRow_22_17_17_1, computeRow_22_17_17_2, computeRow_22_17_17_3, computeRow_22_17_17_4, computeRow_22_17_17_5, computeRow_22_17_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_17_19 : Y 22 17 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 17 19 0 (by decide), + source_yRow_eq_rowCompute 22 17 19 1 (by decide), + source_yRow_eq_rowCompute 22 17 19 2 (by decide), + source_yRow_eq_rowCompute 22 17 19 3 (by decide), + source_yRow_eq_rowCompute 22 17 19 4 (by decide), + source_yRow_eq_rowCompute 22 17 19 5 (by decide), + source_yRow_eq_rowCompute 22 17 19 6 (by decide), + computeRow_22_17_19_0, computeRow_22_17_19_1, computeRow_22_17_19_2, computeRow_22_17_19_3, computeRow_22_17_19_4, computeRow_22_17_19_5, computeRow_22_17_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_17_21 : Y 22 17 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 17 21 0 (by decide), + source_yRow_eq_rowCompute 22 17 21 1 (by decide), + source_yRow_eq_rowCompute 22 17 21 2 (by decide), + source_yRow_eq_rowCompute 22 17 21 3 (by decide), + source_yRow_eq_rowCompute 22 17 21 4 (by decide), + source_yRow_eq_rowCompute 22 17 21 5 (by decide), + source_yRow_eq_rowCompute 22 17 21 6 (by decide), + computeRow_22_17_21_0, computeRow_22_17_21_1, computeRow_22_17_21_2, computeRow_22_17_21_3, computeRow_22_17_21_4, computeRow_22_17_21_5, computeRow_22_17_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_19_19 : Y 22 19 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 19 19 0 (by decide), + source_yRow_eq_rowCompute 22 19 19 1 (by decide), + source_yRow_eq_rowCompute 22 19 19 2 (by decide), + source_yRow_eq_rowCompute 22 19 19 3 (by decide), + source_yRow_eq_rowCompute 22 19 19 4 (by decide), + source_yRow_eq_rowCompute 22 19 19 5 (by decide), + source_yRow_eq_rowCompute 22 19 19 6 (by decide), + computeRow_22_19_19_0, computeRow_22_19_19_1, computeRow_22_19_19_2, computeRow_22_19_19_3, computeRow_22_19_19_4, computeRow_22_19_19_5, computeRow_22_19_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_19_21 : Y 22 19 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 19 21 0 (by decide), + source_yRow_eq_rowCompute 22 19 21 1 (by decide), + source_yRow_eq_rowCompute 22 19 21 2 (by decide), + source_yRow_eq_rowCompute 22 19 21 3 (by decide), + source_yRow_eq_rowCompute 22 19 21 4 (by decide), + source_yRow_eq_rowCompute 22 19 21 5 (by decide), + source_yRow_eq_rowCompute 22 19 21 6 (by decide), + computeRow_22_19_21_0, computeRow_22_19_21_1, computeRow_22_19_21_2, computeRow_22_19_21_3, computeRow_22_19_21_4, computeRow_22_19_21_5, computeRow_22_19_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_22_21_21 : Y 22 21 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 22 21 21 0 (by decide), + source_yRow_eq_rowCompute 22 21 21 1 (by decide), + source_yRow_eq_rowCompute 22 21 21 2 (by decide), + source_yRow_eq_rowCompute 22 21 21 3 (by decide), + source_yRow_eq_rowCompute 22 21 21 4 (by decide), + source_yRow_eq_rowCompute 22 21 21 5 (by decide), + source_yRow_eq_rowCompute 22 21 21 6 (by decide), + computeRow_22_21_21_0, computeRow_22_21_21_1, computeRow_22_21_21_2, computeRow_22_21_21_3, computeRow_22_21_21_4, computeRow_22_21_21_5, computeRow_22_21_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_22_1_1 : Z 22 1 1 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_1_1 + +theorem source_gram_22_1_3 : Z 22 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_1_3 + +theorem source_gram_22_1_5 : Z 22 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_1_5 + +theorem source_gram_22_1_7 : Z 22 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_1_7 + +theorem source_gram_22_1_9 : Z 22 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_1_9 + +theorem source_gram_22_1_11 : Z 22 1 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_1_11 + +theorem source_gram_22_1_13 : Z 22 1 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_1_13 + +theorem source_gram_22_1_15 : Z 22 1 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_1_15 + +theorem source_gram_22_1_17 : Z 22 1 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_1_17 + +theorem source_gram_22_1_19 : Z 22 1 19 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_1_19 + +theorem source_gram_22_1_21 : Z 22 1 21 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_1_21 + +theorem source_gram_22_3_3 : Z 22 3 3 = (729870602452992000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_3_3 + +theorem source_gram_22_3_5 : Z 22 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_3_5 + +theorem source_gram_22_3_7 : Z 22 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_3_7 + +theorem source_gram_22_3_9 : Z 22 3 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_3_9 + +theorem source_gram_22_3_11 : Z 22 3 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_3_11 + +theorem source_gram_22_3_13 : Z 22 3 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_3_13 + +theorem source_gram_22_3_15 : Z 22 3 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_3_15 + +theorem source_gram_22_3_17 : Z 22 3 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_3_17 + +theorem source_gram_22_3_19 : Z 22 3 19 = (-25659513367488000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_3_19 + +theorem source_gram_22_3_21 : Z 22 3 21 = (798295971432960000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_3_21 + +theorem source_gram_22_5_5 : Z 22 5 5 = (42682491371520000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_5_5 + +theorem source_gram_22_5_7 : Z 22 5 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_5_7 + +theorem source_gram_22_5_9 : Z 22 5 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_5_9 + +theorem source_gram_22_5_11 : Z 22 5 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_5_11 + +theorem source_gram_22_5_13 : Z 22 5 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_5_13 + +theorem source_gram_22_5_15 : Z 22 5 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_5_15 + +theorem source_gram_22_5_17 : Z 22 5 17 = (-2667655710720000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_5_17 + +theorem source_gram_22_5_19 : Z 22 5 19 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_5_19 + +theorem source_gram_22_5_21 : Z 22 5 21 = (598721978574720000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_5_21 + +theorem source_gram_22_7_7 : Z 22 7 7 = (6590678814720000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_7_7 + +theorem source_gram_22_7_9 : Z 22 7 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_7_9 + +theorem source_gram_22_7_11 : Z 22 7 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_7_11 + +theorem source_gram_22_7_13 : Z 22 7 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_7_13 + +theorem source_gram_22_7_15 : Z 22 7 15 = (-540641621520000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_7_15 + +theorem source_gram_22_7_17 : Z 22 7 17 = (-3501298120320000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_7_17 + +theorem source_gram_22_7_19 : Z 22 7 19 = (24946749107280000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_7_19 + +theorem source_gram_22_7_21 : Z 22 7 21 = (299360989287360000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_7_21 + +theorem source_gram_22_9_9 : Z 22 9 9 = (2259661307904000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_9_9 + +theorem source_gram_22_9_11 : Z 22 9 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_9_11 + +theorem source_gram_22_9_13 : Z 22 9 13 = (-211843247616000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_9_13 + +theorem source_gram_22_9_15 : Z 22 9 15 = (-1544690347200000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_9_15 + +theorem source_gram_22_9_17 : Z 22 9 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_9_17 + +theorem source_gram_22_9_19 : Z 22 9 19 = (25659513367488000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_9_19 + +theorem source_gram_22_9_21 : Z 22 9 21 = (99786996429120000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_9_21 + +theorem source_gram_22_11_11 : Z 22 11 11 = (1437750246240000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_11_11 + +theorem source_gram_22_11_13 : Z 22 11 13 = (-970948218240000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_11_13 + +theorem source_gram_22_11_15 : Z 22 11 15 = (-1274369536440000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_11_15 + +theorem source_gram_22_11_17 : Z 22 11 17 = (2751019951680000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_11_17 + +theorem source_gram_22_11_19 : Z 22 11 19 = (9800508577860000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_11_19 + +theorem source_gram_22_11_21 : Z 22 11 21 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_11_21 + +theorem source_gram_22_13_13 : Z 22 13 13 = (997428624192000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_13_13 + +theorem source_gram_22_13_15 : Z 22 13 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_13_15 + +theorem source_gram_22_13_17 : Z 22 13 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_13_17 + +theorem source_gram_22_13_19 : Z 22 13 19 = (-9265935382704000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_13_19 + +theorem source_gram_22_13_21 : Z 22 13 21 = (-37420123660920000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_13_21 + +theorem source_gram_22_15_15 : Z 22 15 15 = (5440206316545000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_15_15 + +theorem source_gram_22_15_17 : Z 22 15 17 = (-8534414168280000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_15_17 + +theorem source_gram_22_15_19 : Z 22 15 19 = (-23387577288075000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_15_19 + +theorem source_gram_22_15_21 : Z 22 15 21 = (-43656810937740000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_15_21 + +theorem source_gram_22_17_17 : Z 22 17 17 = (22841802023040000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_17_17 + +theorem source_gram_22_17_19 : Z 22 17 19 = (-30292481058840000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_17_19 + +theorem source_gram_22_17_21 : Z 22 17 21 = (-37420123660920000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_17_21 + +theorem source_gram_22_19_19 : Z 22 19 19 = (698765124659852250 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_19_19 + +theorem source_gram_22_19_21 : Z 22 19 21 = (-28065092745690000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_19_21 + +theorem source_gram_22_21_21 : Z 22 21 21 = (51071452523969377500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_22_21_21 + +theorem source_error_22_3_1 : Y 22 3 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_1_3 + +theorem source_gram_22_3_1 : Z 22 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_1_3 + +theorem source_error_22_5_1 : Y 22 5 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_1_5 + +theorem source_gram_22_5_1 : Z 22 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_1_5 + +theorem source_error_22_5_3 : Y 22 5 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_3_5 + +theorem source_gram_22_5_3 : Z 22 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_3_5 + +theorem source_error_22_7_1 : Y 22 7 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_1_7 + +theorem source_gram_22_7_1 : Z 22 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_1_7 + +theorem source_error_22_7_3 : Y 22 7 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_3_7 + +theorem source_gram_22_7_3 : Z 22 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_3_7 + +theorem source_error_22_7_5 : Y 22 7 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_5_7 + +theorem source_gram_22_7_5 : Z 22 7 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_5_7 + +theorem source_error_22_9_1 : Y 22 9 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_1_9 + +theorem source_gram_22_9_1 : Z 22 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_1_9 + +theorem source_error_22_9_3 : Y 22 9 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_3_9 + +theorem source_gram_22_9_3 : Z 22 9 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_3_9 + +theorem source_error_22_9_5 : Y 22 9 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_5_9 + +theorem source_gram_22_9_5 : Z 22 9 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_5_9 + +theorem source_error_22_9_7 : Y 22 9 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_7_9 + +theorem source_gram_22_9_7 : Z 22 9 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_7_9 + +theorem source_error_22_11_1 : Y 22 11 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_1_11 + +theorem source_gram_22_11_1 : Z 22 11 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_1_11 + +theorem source_error_22_11_3 : Y 22 11 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_3_11 + +theorem source_gram_22_11_3 : Z 22 11 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_3_11 + +theorem source_error_22_11_5 : Y 22 11 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_5_11 + +theorem source_gram_22_11_5 : Z 22 11 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_5_11 + +theorem source_error_22_11_7 : Y 22 11 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_7_11 + +theorem source_gram_22_11_7 : Z 22 11 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_7_11 + +theorem source_error_22_11_9 : Y 22 11 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_9_11 + +theorem source_gram_22_11_9 : Z 22 11 9 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_9_11 + +theorem source_error_22_13_1 : Y 22 13 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_1_13 + +theorem source_gram_22_13_1 : Z 22 13 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_1_13 + +theorem source_error_22_13_3 : Y 22 13 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_3_13 + +theorem source_gram_22_13_3 : Z 22 13 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_3_13 + +theorem source_error_22_13_5 : Y 22 13 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_5_13 + +theorem source_gram_22_13_5 : Z 22 13 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_5_13 + +theorem source_error_22_13_7 : Y 22 13 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_7_13 + +theorem source_gram_22_13_7 : Z 22 13 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_7_13 + +theorem source_error_22_13_9 : Y 22 13 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_9_13 + +theorem source_gram_22_13_9 : Z 22 13 9 = (-211843247616000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_9_13 + +theorem source_error_22_13_11 : Y 22 13 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_11_13 + +theorem source_gram_22_13_11 : Z 22 13 11 = (-970948218240000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_11_13 + +theorem source_error_22_15_1 : Y 22 15 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_1_15 + +theorem source_gram_22_15_1 : Z 22 15 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_1_15 + +theorem source_error_22_15_3 : Y 22 15 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_3_15 + +theorem source_gram_22_15_3 : Z 22 15 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_3_15 + +theorem source_error_22_15_5 : Y 22 15 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_5_15 + +theorem source_gram_22_15_5 : Z 22 15 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_5_15 + +theorem source_error_22_15_7 : Y 22 15 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_7_15 + +theorem source_gram_22_15_7 : Z 22 15 7 = (-540641621520000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_7_15 + +theorem source_error_22_15_9 : Y 22 15 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_9_15 + +theorem source_gram_22_15_9 : Z 22 15 9 = (-1544690347200000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_9_15 + +theorem source_error_22_15_11 : Y 22 15 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_11_15 + +theorem source_gram_22_15_11 : Z 22 15 11 = (-1274369536440000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_11_15 + +theorem source_error_22_15_13 : Y 22 15 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_13_15 + +theorem source_gram_22_15_13 : Z 22 15 13 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_13_15 + +theorem source_error_22_17_1 : Y 22 17 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_1_17 + +theorem source_gram_22_17_1 : Z 22 17 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_1_17 + +theorem source_error_22_17_3 : Y 22 17 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_3_17 + +theorem source_gram_22_17_3 : Z 22 17 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_3_17 + +theorem source_error_22_17_5 : Y 22 17 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_5_17 + +theorem source_gram_22_17_5 : Z 22 17 5 = (-2667655710720000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_5_17 + +theorem source_error_22_17_7 : Y 22 17 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_7_17 + +theorem source_gram_22_17_7 : Z 22 17 7 = (-3501298120320000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_7_17 + +theorem source_error_22_17_9 : Y 22 17 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_9_17 + +theorem source_gram_22_17_9 : Z 22 17 9 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_9_17 + +theorem source_error_22_17_11 : Y 22 17 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_11_17 + +theorem source_gram_22_17_11 : Z 22 17 11 = (2751019951680000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_11_17 + +theorem source_error_22_17_13 : Y 22 17 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_13_17 + +theorem source_gram_22_17_13 : Z 22 17 13 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_13_17 + +theorem source_error_22_17_15 : Y 22 17 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_15_17 + +theorem source_gram_22_17_15 : Z 22 17 15 = (-8534414168280000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_15_17 + +theorem source_error_22_19_1 : Y 22 19 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_1_19 + +theorem source_gram_22_19_1 : Z 22 19 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_1_19 + +theorem source_error_22_19_3 : Y 22 19 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_3_19 + +theorem source_gram_22_19_3 : Z 22 19 3 = (-25659513367488000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_3_19 + +theorem source_error_22_19_5 : Y 22 19 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_5_19 + +theorem source_gram_22_19_5 : Z 22 19 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_5_19 + +theorem source_error_22_19_7 : Y 22 19 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_7_19 + +theorem source_gram_22_19_7 : Z 22 19 7 = (24946749107280000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_7_19 + +theorem source_error_22_19_9 : Y 22 19 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_9_19 + +theorem source_gram_22_19_9 : Z 22 19 9 = (25659513367488000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_9_19 + +theorem source_error_22_19_11 : Y 22 19 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_11_19 + +theorem source_gram_22_19_11 : Z 22 19 11 = (9800508577860000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_11_19 + +theorem source_error_22_19_13 : Y 22 19 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_13_19 + +theorem source_gram_22_19_13 : Z 22 19 13 = (-9265935382704000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_13_19 + +theorem source_error_22_19_15 : Y 22 19 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_15_19 + +theorem source_gram_22_19_15 : Z 22 19 15 = (-23387577288075000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_15_19 + +theorem source_error_22_19_17 : Y 22 19 17 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_17_19 + +theorem source_gram_22_19_17 : Z 22 19 17 = (-30292481058840000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_17_19 + +theorem source_error_22_21_1 : Y 22 21 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_1_21 + +theorem source_gram_22_21_1 : Z 22 21 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_1_21 + +theorem source_error_22_21_3 : Y 22 21 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_3_21 + +theorem source_gram_22_21_3 : Z 22 21 3 = (798295971432960000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_3_21 + +theorem source_error_22_21_5 : Y 22 21 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_5_21 + +theorem source_gram_22_21_5 : Z 22 21 5 = (598721978574720000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_5_21 + +theorem source_error_22_21_7 : Y 22 21 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_7_21 + +theorem source_gram_22_21_7 : Z 22 21 7 = (299360989287360000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_7_21 + +theorem source_error_22_21_9 : Y 22 21 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_9_21 + +theorem source_gram_22_21_9 : Z 22 21 9 = (99786996429120000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_9_21 + +theorem source_error_22_21_11 : Y 22 21 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_11_21 + +theorem source_gram_22_21_11 : Z 22 21 11 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_22_11_21 + +theorem source_error_22_21_13 : Y 22 21 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_13_21 + +theorem source_gram_22_21_13 : Z 22 21 13 = (-37420123660920000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_13_21 + +theorem source_error_22_21_15 : Y 22 21 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_15_21 + +theorem source_gram_22_21_15 : Z 22 21 15 = (-43656810937740000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_15_21 + +theorem source_error_22_21_17 : Y 22 21 17 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_17_21 + +theorem source_gram_22_21_17 : Z 22 21 17 = (-37420123660920000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_17_21 + +theorem source_error_22_21_19 : Y 22 21 19 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_22_19_21 + +theorem source_gram_22_21_19 : Z 22 21 19 = (-28065092745690000 : ℚ) := by + rw [Z_symm] + exact source_gram_22_19_21 + +theorem error_22 : errorRational 22 = candidateY_22 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_22_1_1 + · exact source_error_22_1_3 + · exact source_error_22_1_5 + · exact source_error_22_1_7 + · exact source_error_22_1_9 + · exact source_error_22_1_11 + · exact source_error_22_1_13 + · exact source_error_22_1_15 + · exact source_error_22_1_17 + · exact source_error_22_1_19 + · exact source_error_22_1_21 + · exact source_error_22_3_1 + · exact source_error_22_3_3 + · exact source_error_22_3_5 + · exact source_error_22_3_7 + · exact source_error_22_3_9 + · exact source_error_22_3_11 + · exact source_error_22_3_13 + · exact source_error_22_3_15 + · exact source_error_22_3_17 + · exact source_error_22_3_19 + · exact source_error_22_3_21 + · exact source_error_22_5_1 + · exact source_error_22_5_3 + · exact source_error_22_5_5 + · exact source_error_22_5_7 + · exact source_error_22_5_9 + · exact source_error_22_5_11 + · exact source_error_22_5_13 + · exact source_error_22_5_15 + · exact source_error_22_5_17 + · exact source_error_22_5_19 + · exact source_error_22_5_21 + · exact source_error_22_7_1 + · exact source_error_22_7_3 + · exact source_error_22_7_5 + · exact source_error_22_7_7 + · exact source_error_22_7_9 + · exact source_error_22_7_11 + · exact source_error_22_7_13 + · exact source_error_22_7_15 + · exact source_error_22_7_17 + · exact source_error_22_7_19 + · exact source_error_22_7_21 + · exact source_error_22_9_1 + · exact source_error_22_9_3 + · exact source_error_22_9_5 + · exact source_error_22_9_7 + · exact source_error_22_9_9 + · exact source_error_22_9_11 + · exact source_error_22_9_13 + · exact source_error_22_9_15 + · exact source_error_22_9_17 + · exact source_error_22_9_19 + · exact source_error_22_9_21 + · exact source_error_22_11_1 + · exact source_error_22_11_3 + · exact source_error_22_11_5 + · exact source_error_22_11_7 + · exact source_error_22_11_9 + · exact source_error_22_11_11 + · exact source_error_22_11_13 + · exact source_error_22_11_15 + · exact source_error_22_11_17 + · exact source_error_22_11_19 + · exact source_error_22_11_21 + · exact source_error_22_13_1 + · exact source_error_22_13_3 + · exact source_error_22_13_5 + · exact source_error_22_13_7 + · exact source_error_22_13_9 + · exact source_error_22_13_11 + · exact source_error_22_13_13 + · exact source_error_22_13_15 + · exact source_error_22_13_17 + · exact source_error_22_13_19 + · exact source_error_22_13_21 + · exact source_error_22_15_1 + · exact source_error_22_15_3 + · exact source_error_22_15_5 + · exact source_error_22_15_7 + · exact source_error_22_15_9 + · exact source_error_22_15_11 + · exact source_error_22_15_13 + · exact source_error_22_15_15 + · exact source_error_22_15_17 + · exact source_error_22_15_19 + · exact source_error_22_15_21 + · exact source_error_22_17_1 + · exact source_error_22_17_3 + · exact source_error_22_17_5 + · exact source_error_22_17_7 + · exact source_error_22_17_9 + · exact source_error_22_17_11 + · exact source_error_22_17_13 + · exact source_error_22_17_15 + · exact source_error_22_17_17 + · exact source_error_22_17_19 + · exact source_error_22_17_21 + · exact source_error_22_19_1 + · exact source_error_22_19_3 + · exact source_error_22_19_5 + · exact source_error_22_19_7 + · exact source_error_22_19_9 + · exact source_error_22_19_11 + · exact source_error_22_19_13 + · exact source_error_22_19_15 + · exact source_error_22_19_17 + · exact source_error_22_19_19 + · exact source_error_22_19_21 + · exact source_error_22_21_1 + · exact source_error_22_21_3 + · exact source_error_22_21_5 + · exact source_error_22_21_7 + · exact source_error_22_21_9 + · exact source_error_22_21_11 + · exact source_error_22_21_13 + · exact source_error_22_21_15 + · exact source_error_22_21_17 + · exact source_error_22_21_19 + · exact source_error_22_21_21 + +theorem gram_22 : gramRational 22 = candidateZ_22 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_22_1_1 + · exact source_gram_22_1_3 + · exact source_gram_22_1_5 + · exact source_gram_22_1_7 + · exact source_gram_22_1_9 + · exact source_gram_22_1_11 + · exact source_gram_22_1_13 + · exact source_gram_22_1_15 + · exact source_gram_22_1_17 + · exact source_gram_22_1_19 + · exact source_gram_22_1_21 + · exact source_gram_22_3_1 + · exact source_gram_22_3_3 + · exact source_gram_22_3_5 + · exact source_gram_22_3_7 + · exact source_gram_22_3_9 + · exact source_gram_22_3_11 + · exact source_gram_22_3_13 + · exact source_gram_22_3_15 + · exact source_gram_22_3_17 + · exact source_gram_22_3_19 + · exact source_gram_22_3_21 + · exact source_gram_22_5_1 + · exact source_gram_22_5_3 + · exact source_gram_22_5_5 + · exact source_gram_22_5_7 + · exact source_gram_22_5_9 + · exact source_gram_22_5_11 + · exact source_gram_22_5_13 + · exact source_gram_22_5_15 + · exact source_gram_22_5_17 + · exact source_gram_22_5_19 + · exact source_gram_22_5_21 + · exact source_gram_22_7_1 + · exact source_gram_22_7_3 + · exact source_gram_22_7_5 + · exact source_gram_22_7_7 + · exact source_gram_22_7_9 + · exact source_gram_22_7_11 + · exact source_gram_22_7_13 + · exact source_gram_22_7_15 + · exact source_gram_22_7_17 + · exact source_gram_22_7_19 + · exact source_gram_22_7_21 + · exact source_gram_22_9_1 + · exact source_gram_22_9_3 + · exact source_gram_22_9_5 + · exact source_gram_22_9_7 + · exact source_gram_22_9_9 + · exact source_gram_22_9_11 + · exact source_gram_22_9_13 + · exact source_gram_22_9_15 + · exact source_gram_22_9_17 + · exact source_gram_22_9_19 + · exact source_gram_22_9_21 + · exact source_gram_22_11_1 + · exact source_gram_22_11_3 + · exact source_gram_22_11_5 + · exact source_gram_22_11_7 + · exact source_gram_22_11_9 + · exact source_gram_22_11_11 + · exact source_gram_22_11_13 + · exact source_gram_22_11_15 + · exact source_gram_22_11_17 + · exact source_gram_22_11_19 + · exact source_gram_22_11_21 + · exact source_gram_22_13_1 + · exact source_gram_22_13_3 + · exact source_gram_22_13_5 + · exact source_gram_22_13_7 + · exact source_gram_22_13_9 + · exact source_gram_22_13_11 + · exact source_gram_22_13_13 + · exact source_gram_22_13_15 + · exact source_gram_22_13_17 + · exact source_gram_22_13_19 + · exact source_gram_22_13_21 + · exact source_gram_22_15_1 + · exact source_gram_22_15_3 + · exact source_gram_22_15_5 + · exact source_gram_22_15_7 + · exact source_gram_22_15_9 + · exact source_gram_22_15_11 + · exact source_gram_22_15_13 + · exact source_gram_22_15_15 + · exact source_gram_22_15_17 + · exact source_gram_22_15_19 + · exact source_gram_22_15_21 + · exact source_gram_22_17_1 + · exact source_gram_22_17_3 + · exact source_gram_22_17_5 + · exact source_gram_22_17_7 + · exact source_gram_22_17_9 + · exact source_gram_22_17_11 + · exact source_gram_22_17_13 + · exact source_gram_22_17_15 + · exact source_gram_22_17_17 + · exact source_gram_22_17_19 + · exact source_gram_22_17_21 + · exact source_gram_22_19_1 + · exact source_gram_22_19_3 + · exact source_gram_22_19_5 + · exact source_gram_22_19_7 + · exact source_gram_22_19_9 + · exact source_gram_22_19_11 + · exact source_gram_22_19_13 + · exact source_gram_22_19_15 + · exact source_gram_22_19_17 + · exact source_gram_22_19_19 + · exact source_gram_22_19_21 + · exact source_gram_22_21_1 + · exact source_gram_22_21_3 + · exact source_gram_22_21_5 + · exact source_gram_22_21_7 + · exact source_gram_22_21_9 + · exact source_gram_22_21_11 + · exact source_gram_22_21_13 + · exact source_gram_22_21_15 + · exact source_gram_22_21_17 + · exact source_gram_22_21_19 + · exact source_gram_22_21_21 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData23.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData23.lean new file mode 100644 index 0000000000000000000000000000000000000000..4640cbe9082cca545ed1bb41b71ab81012f8c688 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/GramData23.lean @@ -0,0 +1,2094 @@ +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram01Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram03Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram05Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram07Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram09Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram11Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram13Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram15Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram17Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram19Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram21Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeGram232323 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0101Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0103Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0105Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0107Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0109Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0111Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0113Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0115Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0117Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0119Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0121Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0123Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0303Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0305Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0307Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0309Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0311Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0313Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0315Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0317Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0319Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0321Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0323Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0505Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0507Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0509Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0511Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0513Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0515Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0517Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0519Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0521Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0523Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0707Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0709Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0711Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0713Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0715Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0717Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0719Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0721Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0723Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0909Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0911Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0913Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0915Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0917Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0919Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0921Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow0923Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1111Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1113Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1115Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1117Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1119Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1121Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1123Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1313Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1315Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1317Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1319Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1321Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1323Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1515Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1517Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1519Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1521Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1523Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1717Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1719Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1721Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1723Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1919Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1921Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow1923Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow2121Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow2123Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeRow2323Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.Data23 +import OAI.Analysis.Laughlin.FourBody.NumericBridge +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate +theorem source_error_23_1_1 : Y 23 1 1 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 1 1 0 (by decide), + source_yRow_eq_rowCompute 23 1 1 1 (by decide), + source_yRow_eq_rowCompute 23 1 1 2 (by decide), + source_yRow_eq_rowCompute 23 1 1 3 (by decide), + source_yRow_eq_rowCompute 23 1 1 4 (by decide), + source_yRow_eq_rowCompute 23 1 1 5 (by decide), + source_yRow_eq_rowCompute 23 1 1 6 (by decide), + computeRow_23_1_1_0, computeRow_23_1_1_1, computeRow_23_1_1_2, computeRow_23_1_1_3, computeRow_23_1_1_4, computeRow_23_1_1_5, computeRow_23_1_1_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_1_3 : Y 23 1 3 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 1 3 0 (by decide), + source_yRow_eq_rowCompute 23 1 3 1 (by decide), + source_yRow_eq_rowCompute 23 1 3 2 (by decide), + source_yRow_eq_rowCompute 23 1 3 3 (by decide), + source_yRow_eq_rowCompute 23 1 3 4 (by decide), + source_yRow_eq_rowCompute 23 1 3 5 (by decide), + source_yRow_eq_rowCompute 23 1 3 6 (by decide), + computeRow_23_1_3_0, computeRow_23_1_3_1, computeRow_23_1_3_2, computeRow_23_1_3_3, computeRow_23_1_3_4, computeRow_23_1_3_5, computeRow_23_1_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_1_5 : Y 23 1 5 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 1 5 0 (by decide), + source_yRow_eq_rowCompute 23 1 5 1 (by decide), + source_yRow_eq_rowCompute 23 1 5 2 (by decide), + source_yRow_eq_rowCompute 23 1 5 3 (by decide), + source_yRow_eq_rowCompute 23 1 5 4 (by decide), + source_yRow_eq_rowCompute 23 1 5 5 (by decide), + source_yRow_eq_rowCompute 23 1 5 6 (by decide), + computeRow_23_1_5_0, computeRow_23_1_5_1, computeRow_23_1_5_2, computeRow_23_1_5_3, computeRow_23_1_5_4, computeRow_23_1_5_5, computeRow_23_1_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_1_7 : Y 23 1 7 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 1 7 0 (by decide), + source_yRow_eq_rowCompute 23 1 7 1 (by decide), + source_yRow_eq_rowCompute 23 1 7 2 (by decide), + source_yRow_eq_rowCompute 23 1 7 3 (by decide), + source_yRow_eq_rowCompute 23 1 7 4 (by decide), + source_yRow_eq_rowCompute 23 1 7 5 (by decide), + source_yRow_eq_rowCompute 23 1 7 6 (by decide), + computeRow_23_1_7_0, computeRow_23_1_7_1, computeRow_23_1_7_2, computeRow_23_1_7_3, computeRow_23_1_7_4, computeRow_23_1_7_5, computeRow_23_1_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_1_9 : Y 23 1 9 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 1 9 0 (by decide), + source_yRow_eq_rowCompute 23 1 9 1 (by decide), + source_yRow_eq_rowCompute 23 1 9 2 (by decide), + source_yRow_eq_rowCompute 23 1 9 3 (by decide), + source_yRow_eq_rowCompute 23 1 9 4 (by decide), + source_yRow_eq_rowCompute 23 1 9 5 (by decide), + source_yRow_eq_rowCompute 23 1 9 6 (by decide), + computeRow_23_1_9_0, computeRow_23_1_9_1, computeRow_23_1_9_2, computeRow_23_1_9_3, computeRow_23_1_9_4, computeRow_23_1_9_5, computeRow_23_1_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_1_11 : Y 23 1 11 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 1 11 0 (by decide), + source_yRow_eq_rowCompute 23 1 11 1 (by decide), + source_yRow_eq_rowCompute 23 1 11 2 (by decide), + source_yRow_eq_rowCompute 23 1 11 3 (by decide), + source_yRow_eq_rowCompute 23 1 11 4 (by decide), + source_yRow_eq_rowCompute 23 1 11 5 (by decide), + source_yRow_eq_rowCompute 23 1 11 6 (by decide), + computeRow_23_1_11_0, computeRow_23_1_11_1, computeRow_23_1_11_2, computeRow_23_1_11_3, computeRow_23_1_11_4, computeRow_23_1_11_5, computeRow_23_1_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_1_13 : Y 23 1 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 1 13 0 (by decide), + source_yRow_eq_rowCompute 23 1 13 1 (by decide), + source_yRow_eq_rowCompute 23 1 13 2 (by decide), + source_yRow_eq_rowCompute 23 1 13 3 (by decide), + source_yRow_eq_rowCompute 23 1 13 4 (by decide), + source_yRow_eq_rowCompute 23 1 13 5 (by decide), + source_yRow_eq_rowCompute 23 1 13 6 (by decide), + computeRow_23_1_13_0, computeRow_23_1_13_1, computeRow_23_1_13_2, computeRow_23_1_13_3, computeRow_23_1_13_4, computeRow_23_1_13_5, computeRow_23_1_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_1_15 : Y 23 1 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 1 15 0 (by decide), + source_yRow_eq_rowCompute 23 1 15 1 (by decide), + source_yRow_eq_rowCompute 23 1 15 2 (by decide), + source_yRow_eq_rowCompute 23 1 15 3 (by decide), + source_yRow_eq_rowCompute 23 1 15 4 (by decide), + source_yRow_eq_rowCompute 23 1 15 5 (by decide), + source_yRow_eq_rowCompute 23 1 15 6 (by decide), + computeRow_23_1_15_0, computeRow_23_1_15_1, computeRow_23_1_15_2, computeRow_23_1_15_3, computeRow_23_1_15_4, computeRow_23_1_15_5, computeRow_23_1_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_1_17 : Y 23 1 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 1 17 0 (by decide), + source_yRow_eq_rowCompute 23 1 17 1 (by decide), + source_yRow_eq_rowCompute 23 1 17 2 (by decide), + source_yRow_eq_rowCompute 23 1 17 3 (by decide), + source_yRow_eq_rowCompute 23 1 17 4 (by decide), + source_yRow_eq_rowCompute 23 1 17 5 (by decide), + source_yRow_eq_rowCompute 23 1 17 6 (by decide), + computeRow_23_1_17_0, computeRow_23_1_17_1, computeRow_23_1_17_2, computeRow_23_1_17_3, computeRow_23_1_17_4, computeRow_23_1_17_5, computeRow_23_1_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_1_19 : Y 23 1 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 1 19 0 (by decide), + source_yRow_eq_rowCompute 23 1 19 1 (by decide), + source_yRow_eq_rowCompute 23 1 19 2 (by decide), + source_yRow_eq_rowCompute 23 1 19 3 (by decide), + source_yRow_eq_rowCompute 23 1 19 4 (by decide), + source_yRow_eq_rowCompute 23 1 19 5 (by decide), + source_yRow_eq_rowCompute 23 1 19 6 (by decide), + computeRow_23_1_19_0, computeRow_23_1_19_1, computeRow_23_1_19_2, computeRow_23_1_19_3, computeRow_23_1_19_4, computeRow_23_1_19_5, computeRow_23_1_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_1_21 : Y 23 1 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 1 21 0 (by decide), + source_yRow_eq_rowCompute 23 1 21 1 (by decide), + source_yRow_eq_rowCompute 23 1 21 2 (by decide), + source_yRow_eq_rowCompute 23 1 21 3 (by decide), + source_yRow_eq_rowCompute 23 1 21 4 (by decide), + source_yRow_eq_rowCompute 23 1 21 5 (by decide), + source_yRow_eq_rowCompute 23 1 21 6 (by decide), + computeRow_23_1_21_0, computeRow_23_1_21_1, computeRow_23_1_21_2, computeRow_23_1_21_3, computeRow_23_1_21_4, computeRow_23_1_21_5, computeRow_23_1_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_1_23 : Y 23 1 23 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 1 23 0 (by decide), + source_yRow_eq_rowCompute 23 1 23 1 (by decide), + source_yRow_eq_rowCompute 23 1 23 2 (by decide), + source_yRow_eq_rowCompute 23 1 23 3 (by decide), + source_yRow_eq_rowCompute 23 1 23 4 (by decide), + source_yRow_eq_rowCompute 23 1 23 5 (by decide), + source_yRow_eq_rowCompute 23 1 23 6 (by decide), + computeRow_23_1_23_0, computeRow_23_1_23_1, computeRow_23_1_23_2, computeRow_23_1_23_3, computeRow_23_1_23_4, computeRow_23_1_23_5, computeRow_23_1_23_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_3_3 : Y 23 3 3 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 3 3 0 (by decide), + source_yRow_eq_rowCompute 23 3 3 1 (by decide), + source_yRow_eq_rowCompute 23 3 3 2 (by decide), + source_yRow_eq_rowCompute 23 3 3 3 (by decide), + source_yRow_eq_rowCompute 23 3 3 4 (by decide), + source_yRow_eq_rowCompute 23 3 3 5 (by decide), + source_yRow_eq_rowCompute 23 3 3 6 (by decide), + computeRow_23_3_3_0, computeRow_23_3_3_1, computeRow_23_3_3_2, computeRow_23_3_3_3, computeRow_23_3_3_4, computeRow_23_3_3_5, computeRow_23_3_3_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_3_5 : Y 23 3 5 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 3 5 0 (by decide), + source_yRow_eq_rowCompute 23 3 5 1 (by decide), + source_yRow_eq_rowCompute 23 3 5 2 (by decide), + source_yRow_eq_rowCompute 23 3 5 3 (by decide), + source_yRow_eq_rowCompute 23 3 5 4 (by decide), + source_yRow_eq_rowCompute 23 3 5 5 (by decide), + source_yRow_eq_rowCompute 23 3 5 6 (by decide), + computeRow_23_3_5_0, computeRow_23_3_5_1, computeRow_23_3_5_2, computeRow_23_3_5_3, computeRow_23_3_5_4, computeRow_23_3_5_5, computeRow_23_3_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_3_7 : Y 23 3 7 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 3 7 0 (by decide), + source_yRow_eq_rowCompute 23 3 7 1 (by decide), + source_yRow_eq_rowCompute 23 3 7 2 (by decide), + source_yRow_eq_rowCompute 23 3 7 3 (by decide), + source_yRow_eq_rowCompute 23 3 7 4 (by decide), + source_yRow_eq_rowCompute 23 3 7 5 (by decide), + source_yRow_eq_rowCompute 23 3 7 6 (by decide), + computeRow_23_3_7_0, computeRow_23_3_7_1, computeRow_23_3_7_2, computeRow_23_3_7_3, computeRow_23_3_7_4, computeRow_23_3_7_5, computeRow_23_3_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_3_9 : Y 23 3 9 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 3 9 0 (by decide), + source_yRow_eq_rowCompute 23 3 9 1 (by decide), + source_yRow_eq_rowCompute 23 3 9 2 (by decide), + source_yRow_eq_rowCompute 23 3 9 3 (by decide), + source_yRow_eq_rowCompute 23 3 9 4 (by decide), + source_yRow_eq_rowCompute 23 3 9 5 (by decide), + source_yRow_eq_rowCompute 23 3 9 6 (by decide), + computeRow_23_3_9_0, computeRow_23_3_9_1, computeRow_23_3_9_2, computeRow_23_3_9_3, computeRow_23_3_9_4, computeRow_23_3_9_5, computeRow_23_3_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_3_11 : Y 23 3 11 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 3 11 0 (by decide), + source_yRow_eq_rowCompute 23 3 11 1 (by decide), + source_yRow_eq_rowCompute 23 3 11 2 (by decide), + source_yRow_eq_rowCompute 23 3 11 3 (by decide), + source_yRow_eq_rowCompute 23 3 11 4 (by decide), + source_yRow_eq_rowCompute 23 3 11 5 (by decide), + source_yRow_eq_rowCompute 23 3 11 6 (by decide), + computeRow_23_3_11_0, computeRow_23_3_11_1, computeRow_23_3_11_2, computeRow_23_3_11_3, computeRow_23_3_11_4, computeRow_23_3_11_5, computeRow_23_3_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_3_13 : Y 23 3 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 3 13 0 (by decide), + source_yRow_eq_rowCompute 23 3 13 1 (by decide), + source_yRow_eq_rowCompute 23 3 13 2 (by decide), + source_yRow_eq_rowCompute 23 3 13 3 (by decide), + source_yRow_eq_rowCompute 23 3 13 4 (by decide), + source_yRow_eq_rowCompute 23 3 13 5 (by decide), + source_yRow_eq_rowCompute 23 3 13 6 (by decide), + computeRow_23_3_13_0, computeRow_23_3_13_1, computeRow_23_3_13_2, computeRow_23_3_13_3, computeRow_23_3_13_4, computeRow_23_3_13_5, computeRow_23_3_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_3_15 : Y 23 3 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 3 15 0 (by decide), + source_yRow_eq_rowCompute 23 3 15 1 (by decide), + source_yRow_eq_rowCompute 23 3 15 2 (by decide), + source_yRow_eq_rowCompute 23 3 15 3 (by decide), + source_yRow_eq_rowCompute 23 3 15 4 (by decide), + source_yRow_eq_rowCompute 23 3 15 5 (by decide), + source_yRow_eq_rowCompute 23 3 15 6 (by decide), + computeRow_23_3_15_0, computeRow_23_3_15_1, computeRow_23_3_15_2, computeRow_23_3_15_3, computeRow_23_3_15_4, computeRow_23_3_15_5, computeRow_23_3_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_3_17 : Y 23 3 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 3 17 0 (by decide), + source_yRow_eq_rowCompute 23 3 17 1 (by decide), + source_yRow_eq_rowCompute 23 3 17 2 (by decide), + source_yRow_eq_rowCompute 23 3 17 3 (by decide), + source_yRow_eq_rowCompute 23 3 17 4 (by decide), + source_yRow_eq_rowCompute 23 3 17 5 (by decide), + source_yRow_eq_rowCompute 23 3 17 6 (by decide), + computeRow_23_3_17_0, computeRow_23_3_17_1, computeRow_23_3_17_2, computeRow_23_3_17_3, computeRow_23_3_17_4, computeRow_23_3_17_5, computeRow_23_3_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_3_19 : Y 23 3 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 3 19 0 (by decide), + source_yRow_eq_rowCompute 23 3 19 1 (by decide), + source_yRow_eq_rowCompute 23 3 19 2 (by decide), + source_yRow_eq_rowCompute 23 3 19 3 (by decide), + source_yRow_eq_rowCompute 23 3 19 4 (by decide), + source_yRow_eq_rowCompute 23 3 19 5 (by decide), + source_yRow_eq_rowCompute 23 3 19 6 (by decide), + computeRow_23_3_19_0, computeRow_23_3_19_1, computeRow_23_3_19_2, computeRow_23_3_19_3, computeRow_23_3_19_4, computeRow_23_3_19_5, computeRow_23_3_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_3_21 : Y 23 3 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 3 21 0 (by decide), + source_yRow_eq_rowCompute 23 3 21 1 (by decide), + source_yRow_eq_rowCompute 23 3 21 2 (by decide), + source_yRow_eq_rowCompute 23 3 21 3 (by decide), + source_yRow_eq_rowCompute 23 3 21 4 (by decide), + source_yRow_eq_rowCompute 23 3 21 5 (by decide), + source_yRow_eq_rowCompute 23 3 21 6 (by decide), + computeRow_23_3_21_0, computeRow_23_3_21_1, computeRow_23_3_21_2, computeRow_23_3_21_3, computeRow_23_3_21_4, computeRow_23_3_21_5, computeRow_23_3_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_3_23 : Y 23 3 23 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 3 23 0 (by decide), + source_yRow_eq_rowCompute 23 3 23 1 (by decide), + source_yRow_eq_rowCompute 23 3 23 2 (by decide), + source_yRow_eq_rowCompute 23 3 23 3 (by decide), + source_yRow_eq_rowCompute 23 3 23 4 (by decide), + source_yRow_eq_rowCompute 23 3 23 5 (by decide), + source_yRow_eq_rowCompute 23 3 23 6 (by decide), + computeRow_23_3_23_0, computeRow_23_3_23_1, computeRow_23_3_23_2, computeRow_23_3_23_3, computeRow_23_3_23_4, computeRow_23_3_23_5, computeRow_23_3_23_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_5_5 : Y 23 5 5 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 5 5 0 (by decide), + source_yRow_eq_rowCompute 23 5 5 1 (by decide), + source_yRow_eq_rowCompute 23 5 5 2 (by decide), + source_yRow_eq_rowCompute 23 5 5 3 (by decide), + source_yRow_eq_rowCompute 23 5 5 4 (by decide), + source_yRow_eq_rowCompute 23 5 5 5 (by decide), + source_yRow_eq_rowCompute 23 5 5 6 (by decide), + computeRow_23_5_5_0, computeRow_23_5_5_1, computeRow_23_5_5_2, computeRow_23_5_5_3, computeRow_23_5_5_4, computeRow_23_5_5_5, computeRow_23_5_5_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_5_7 : Y 23 5 7 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 5 7 0 (by decide), + source_yRow_eq_rowCompute 23 5 7 1 (by decide), + source_yRow_eq_rowCompute 23 5 7 2 (by decide), + source_yRow_eq_rowCompute 23 5 7 3 (by decide), + source_yRow_eq_rowCompute 23 5 7 4 (by decide), + source_yRow_eq_rowCompute 23 5 7 5 (by decide), + source_yRow_eq_rowCompute 23 5 7 6 (by decide), + computeRow_23_5_7_0, computeRow_23_5_7_1, computeRow_23_5_7_2, computeRow_23_5_7_3, computeRow_23_5_7_4, computeRow_23_5_7_5, computeRow_23_5_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_5_9 : Y 23 5 9 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 5 9 0 (by decide), + source_yRow_eq_rowCompute 23 5 9 1 (by decide), + source_yRow_eq_rowCompute 23 5 9 2 (by decide), + source_yRow_eq_rowCompute 23 5 9 3 (by decide), + source_yRow_eq_rowCompute 23 5 9 4 (by decide), + source_yRow_eq_rowCompute 23 5 9 5 (by decide), + source_yRow_eq_rowCompute 23 5 9 6 (by decide), + computeRow_23_5_9_0, computeRow_23_5_9_1, computeRow_23_5_9_2, computeRow_23_5_9_3, computeRow_23_5_9_4, computeRow_23_5_9_5, computeRow_23_5_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_5_11 : Y 23 5 11 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 5 11 0 (by decide), + source_yRow_eq_rowCompute 23 5 11 1 (by decide), + source_yRow_eq_rowCompute 23 5 11 2 (by decide), + source_yRow_eq_rowCompute 23 5 11 3 (by decide), + source_yRow_eq_rowCompute 23 5 11 4 (by decide), + source_yRow_eq_rowCompute 23 5 11 5 (by decide), + source_yRow_eq_rowCompute 23 5 11 6 (by decide), + computeRow_23_5_11_0, computeRow_23_5_11_1, computeRow_23_5_11_2, computeRow_23_5_11_3, computeRow_23_5_11_4, computeRow_23_5_11_5, computeRow_23_5_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_5_13 : Y 23 5 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 5 13 0 (by decide), + source_yRow_eq_rowCompute 23 5 13 1 (by decide), + source_yRow_eq_rowCompute 23 5 13 2 (by decide), + source_yRow_eq_rowCompute 23 5 13 3 (by decide), + source_yRow_eq_rowCompute 23 5 13 4 (by decide), + source_yRow_eq_rowCompute 23 5 13 5 (by decide), + source_yRow_eq_rowCompute 23 5 13 6 (by decide), + computeRow_23_5_13_0, computeRow_23_5_13_1, computeRow_23_5_13_2, computeRow_23_5_13_3, computeRow_23_5_13_4, computeRow_23_5_13_5, computeRow_23_5_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_5_15 : Y 23 5 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 5 15 0 (by decide), + source_yRow_eq_rowCompute 23 5 15 1 (by decide), + source_yRow_eq_rowCompute 23 5 15 2 (by decide), + source_yRow_eq_rowCompute 23 5 15 3 (by decide), + source_yRow_eq_rowCompute 23 5 15 4 (by decide), + source_yRow_eq_rowCompute 23 5 15 5 (by decide), + source_yRow_eq_rowCompute 23 5 15 6 (by decide), + computeRow_23_5_15_0, computeRow_23_5_15_1, computeRow_23_5_15_2, computeRow_23_5_15_3, computeRow_23_5_15_4, computeRow_23_5_15_5, computeRow_23_5_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_5_17 : Y 23 5 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 5 17 0 (by decide), + source_yRow_eq_rowCompute 23 5 17 1 (by decide), + source_yRow_eq_rowCompute 23 5 17 2 (by decide), + source_yRow_eq_rowCompute 23 5 17 3 (by decide), + source_yRow_eq_rowCompute 23 5 17 4 (by decide), + source_yRow_eq_rowCompute 23 5 17 5 (by decide), + source_yRow_eq_rowCompute 23 5 17 6 (by decide), + computeRow_23_5_17_0, computeRow_23_5_17_1, computeRow_23_5_17_2, computeRow_23_5_17_3, computeRow_23_5_17_4, computeRow_23_5_17_5, computeRow_23_5_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_5_19 : Y 23 5 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 5 19 0 (by decide), + source_yRow_eq_rowCompute 23 5 19 1 (by decide), + source_yRow_eq_rowCompute 23 5 19 2 (by decide), + source_yRow_eq_rowCompute 23 5 19 3 (by decide), + source_yRow_eq_rowCompute 23 5 19 4 (by decide), + source_yRow_eq_rowCompute 23 5 19 5 (by decide), + source_yRow_eq_rowCompute 23 5 19 6 (by decide), + computeRow_23_5_19_0, computeRow_23_5_19_1, computeRow_23_5_19_2, computeRow_23_5_19_3, computeRow_23_5_19_4, computeRow_23_5_19_5, computeRow_23_5_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_5_21 : Y 23 5 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 5 21 0 (by decide), + source_yRow_eq_rowCompute 23 5 21 1 (by decide), + source_yRow_eq_rowCompute 23 5 21 2 (by decide), + source_yRow_eq_rowCompute 23 5 21 3 (by decide), + source_yRow_eq_rowCompute 23 5 21 4 (by decide), + source_yRow_eq_rowCompute 23 5 21 5 (by decide), + source_yRow_eq_rowCompute 23 5 21 6 (by decide), + computeRow_23_5_21_0, computeRow_23_5_21_1, computeRow_23_5_21_2, computeRow_23_5_21_3, computeRow_23_5_21_4, computeRow_23_5_21_5, computeRow_23_5_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_5_23 : Y 23 5 23 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 5 23 0 (by decide), + source_yRow_eq_rowCompute 23 5 23 1 (by decide), + source_yRow_eq_rowCompute 23 5 23 2 (by decide), + source_yRow_eq_rowCompute 23 5 23 3 (by decide), + source_yRow_eq_rowCompute 23 5 23 4 (by decide), + source_yRow_eq_rowCompute 23 5 23 5 (by decide), + source_yRow_eq_rowCompute 23 5 23 6 (by decide), + computeRow_23_5_23_0, computeRow_23_5_23_1, computeRow_23_5_23_2, computeRow_23_5_23_3, computeRow_23_5_23_4, computeRow_23_5_23_5, computeRow_23_5_23_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_7_7 : Y 23 7 7 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 7 7 0 (by decide), + source_yRow_eq_rowCompute 23 7 7 1 (by decide), + source_yRow_eq_rowCompute 23 7 7 2 (by decide), + source_yRow_eq_rowCompute 23 7 7 3 (by decide), + source_yRow_eq_rowCompute 23 7 7 4 (by decide), + source_yRow_eq_rowCompute 23 7 7 5 (by decide), + source_yRow_eq_rowCompute 23 7 7 6 (by decide), + computeRow_23_7_7_0, computeRow_23_7_7_1, computeRow_23_7_7_2, computeRow_23_7_7_3, computeRow_23_7_7_4, computeRow_23_7_7_5, computeRow_23_7_7_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_7_9 : Y 23 7 9 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 7 9 0 (by decide), + source_yRow_eq_rowCompute 23 7 9 1 (by decide), + source_yRow_eq_rowCompute 23 7 9 2 (by decide), + source_yRow_eq_rowCompute 23 7 9 3 (by decide), + source_yRow_eq_rowCompute 23 7 9 4 (by decide), + source_yRow_eq_rowCompute 23 7 9 5 (by decide), + source_yRow_eq_rowCompute 23 7 9 6 (by decide), + computeRow_23_7_9_0, computeRow_23_7_9_1, computeRow_23_7_9_2, computeRow_23_7_9_3, computeRow_23_7_9_4, computeRow_23_7_9_5, computeRow_23_7_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_7_11 : Y 23 7 11 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 7 11 0 (by decide), + source_yRow_eq_rowCompute 23 7 11 1 (by decide), + source_yRow_eq_rowCompute 23 7 11 2 (by decide), + source_yRow_eq_rowCompute 23 7 11 3 (by decide), + source_yRow_eq_rowCompute 23 7 11 4 (by decide), + source_yRow_eq_rowCompute 23 7 11 5 (by decide), + source_yRow_eq_rowCompute 23 7 11 6 (by decide), + computeRow_23_7_11_0, computeRow_23_7_11_1, computeRow_23_7_11_2, computeRow_23_7_11_3, computeRow_23_7_11_4, computeRow_23_7_11_5, computeRow_23_7_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_7_13 : Y 23 7 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 7 13 0 (by decide), + source_yRow_eq_rowCompute 23 7 13 1 (by decide), + source_yRow_eq_rowCompute 23 7 13 2 (by decide), + source_yRow_eq_rowCompute 23 7 13 3 (by decide), + source_yRow_eq_rowCompute 23 7 13 4 (by decide), + source_yRow_eq_rowCompute 23 7 13 5 (by decide), + source_yRow_eq_rowCompute 23 7 13 6 (by decide), + computeRow_23_7_13_0, computeRow_23_7_13_1, computeRow_23_7_13_2, computeRow_23_7_13_3, computeRow_23_7_13_4, computeRow_23_7_13_5, computeRow_23_7_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_7_15 : Y 23 7 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 7 15 0 (by decide), + source_yRow_eq_rowCompute 23 7 15 1 (by decide), + source_yRow_eq_rowCompute 23 7 15 2 (by decide), + source_yRow_eq_rowCompute 23 7 15 3 (by decide), + source_yRow_eq_rowCompute 23 7 15 4 (by decide), + source_yRow_eq_rowCompute 23 7 15 5 (by decide), + source_yRow_eq_rowCompute 23 7 15 6 (by decide), + computeRow_23_7_15_0, computeRow_23_7_15_1, computeRow_23_7_15_2, computeRow_23_7_15_3, computeRow_23_7_15_4, computeRow_23_7_15_5, computeRow_23_7_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_7_17 : Y 23 7 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 7 17 0 (by decide), + source_yRow_eq_rowCompute 23 7 17 1 (by decide), + source_yRow_eq_rowCompute 23 7 17 2 (by decide), + source_yRow_eq_rowCompute 23 7 17 3 (by decide), + source_yRow_eq_rowCompute 23 7 17 4 (by decide), + source_yRow_eq_rowCompute 23 7 17 5 (by decide), + source_yRow_eq_rowCompute 23 7 17 6 (by decide), + computeRow_23_7_17_0, computeRow_23_7_17_1, computeRow_23_7_17_2, computeRow_23_7_17_3, computeRow_23_7_17_4, computeRow_23_7_17_5, computeRow_23_7_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_7_19 : Y 23 7 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 7 19 0 (by decide), + source_yRow_eq_rowCompute 23 7 19 1 (by decide), + source_yRow_eq_rowCompute 23 7 19 2 (by decide), + source_yRow_eq_rowCompute 23 7 19 3 (by decide), + source_yRow_eq_rowCompute 23 7 19 4 (by decide), + source_yRow_eq_rowCompute 23 7 19 5 (by decide), + source_yRow_eq_rowCompute 23 7 19 6 (by decide), + computeRow_23_7_19_0, computeRow_23_7_19_1, computeRow_23_7_19_2, computeRow_23_7_19_3, computeRow_23_7_19_4, computeRow_23_7_19_5, computeRow_23_7_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_7_21 : Y 23 7 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 7 21 0 (by decide), + source_yRow_eq_rowCompute 23 7 21 1 (by decide), + source_yRow_eq_rowCompute 23 7 21 2 (by decide), + source_yRow_eq_rowCompute 23 7 21 3 (by decide), + source_yRow_eq_rowCompute 23 7 21 4 (by decide), + source_yRow_eq_rowCompute 23 7 21 5 (by decide), + source_yRow_eq_rowCompute 23 7 21 6 (by decide), + computeRow_23_7_21_0, computeRow_23_7_21_1, computeRow_23_7_21_2, computeRow_23_7_21_3, computeRow_23_7_21_4, computeRow_23_7_21_5, computeRow_23_7_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_7_23 : Y 23 7 23 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 7 23 0 (by decide), + source_yRow_eq_rowCompute 23 7 23 1 (by decide), + source_yRow_eq_rowCompute 23 7 23 2 (by decide), + source_yRow_eq_rowCompute 23 7 23 3 (by decide), + source_yRow_eq_rowCompute 23 7 23 4 (by decide), + source_yRow_eq_rowCompute 23 7 23 5 (by decide), + source_yRow_eq_rowCompute 23 7 23 6 (by decide), + computeRow_23_7_23_0, computeRow_23_7_23_1, computeRow_23_7_23_2, computeRow_23_7_23_3, computeRow_23_7_23_4, computeRow_23_7_23_5, computeRow_23_7_23_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_9_9 : Y 23 9 9 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 9 9 0 (by decide), + source_yRow_eq_rowCompute 23 9 9 1 (by decide), + source_yRow_eq_rowCompute 23 9 9 2 (by decide), + source_yRow_eq_rowCompute 23 9 9 3 (by decide), + source_yRow_eq_rowCompute 23 9 9 4 (by decide), + source_yRow_eq_rowCompute 23 9 9 5 (by decide), + source_yRow_eq_rowCompute 23 9 9 6 (by decide), + computeRow_23_9_9_0, computeRow_23_9_9_1, computeRow_23_9_9_2, computeRow_23_9_9_3, computeRow_23_9_9_4, computeRow_23_9_9_5, computeRow_23_9_9_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_9_11 : Y 23 9 11 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 9 11 0 (by decide), + source_yRow_eq_rowCompute 23 9 11 1 (by decide), + source_yRow_eq_rowCompute 23 9 11 2 (by decide), + source_yRow_eq_rowCompute 23 9 11 3 (by decide), + source_yRow_eq_rowCompute 23 9 11 4 (by decide), + source_yRow_eq_rowCompute 23 9 11 5 (by decide), + source_yRow_eq_rowCompute 23 9 11 6 (by decide), + computeRow_23_9_11_0, computeRow_23_9_11_1, computeRow_23_9_11_2, computeRow_23_9_11_3, computeRow_23_9_11_4, computeRow_23_9_11_5, computeRow_23_9_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_9_13 : Y 23 9 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 9 13 0 (by decide), + source_yRow_eq_rowCompute 23 9 13 1 (by decide), + source_yRow_eq_rowCompute 23 9 13 2 (by decide), + source_yRow_eq_rowCompute 23 9 13 3 (by decide), + source_yRow_eq_rowCompute 23 9 13 4 (by decide), + source_yRow_eq_rowCompute 23 9 13 5 (by decide), + source_yRow_eq_rowCompute 23 9 13 6 (by decide), + computeRow_23_9_13_0, computeRow_23_9_13_1, computeRow_23_9_13_2, computeRow_23_9_13_3, computeRow_23_9_13_4, computeRow_23_9_13_5, computeRow_23_9_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_9_15 : Y 23 9 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 9 15 0 (by decide), + source_yRow_eq_rowCompute 23 9 15 1 (by decide), + source_yRow_eq_rowCompute 23 9 15 2 (by decide), + source_yRow_eq_rowCompute 23 9 15 3 (by decide), + source_yRow_eq_rowCompute 23 9 15 4 (by decide), + source_yRow_eq_rowCompute 23 9 15 5 (by decide), + source_yRow_eq_rowCompute 23 9 15 6 (by decide), + computeRow_23_9_15_0, computeRow_23_9_15_1, computeRow_23_9_15_2, computeRow_23_9_15_3, computeRow_23_9_15_4, computeRow_23_9_15_5, computeRow_23_9_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_9_17 : Y 23 9 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 9 17 0 (by decide), + source_yRow_eq_rowCompute 23 9 17 1 (by decide), + source_yRow_eq_rowCompute 23 9 17 2 (by decide), + source_yRow_eq_rowCompute 23 9 17 3 (by decide), + source_yRow_eq_rowCompute 23 9 17 4 (by decide), + source_yRow_eq_rowCompute 23 9 17 5 (by decide), + source_yRow_eq_rowCompute 23 9 17 6 (by decide), + computeRow_23_9_17_0, computeRow_23_9_17_1, computeRow_23_9_17_2, computeRow_23_9_17_3, computeRow_23_9_17_4, computeRow_23_9_17_5, computeRow_23_9_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_9_19 : Y 23 9 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 9 19 0 (by decide), + source_yRow_eq_rowCompute 23 9 19 1 (by decide), + source_yRow_eq_rowCompute 23 9 19 2 (by decide), + source_yRow_eq_rowCompute 23 9 19 3 (by decide), + source_yRow_eq_rowCompute 23 9 19 4 (by decide), + source_yRow_eq_rowCompute 23 9 19 5 (by decide), + source_yRow_eq_rowCompute 23 9 19 6 (by decide), + computeRow_23_9_19_0, computeRow_23_9_19_1, computeRow_23_9_19_2, computeRow_23_9_19_3, computeRow_23_9_19_4, computeRow_23_9_19_5, computeRow_23_9_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_9_21 : Y 23 9 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 9 21 0 (by decide), + source_yRow_eq_rowCompute 23 9 21 1 (by decide), + source_yRow_eq_rowCompute 23 9 21 2 (by decide), + source_yRow_eq_rowCompute 23 9 21 3 (by decide), + source_yRow_eq_rowCompute 23 9 21 4 (by decide), + source_yRow_eq_rowCompute 23 9 21 5 (by decide), + source_yRow_eq_rowCompute 23 9 21 6 (by decide), + computeRow_23_9_21_0, computeRow_23_9_21_1, computeRow_23_9_21_2, computeRow_23_9_21_3, computeRow_23_9_21_4, computeRow_23_9_21_5, computeRow_23_9_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_9_23 : Y 23 9 23 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 9 23 0 (by decide), + source_yRow_eq_rowCompute 23 9 23 1 (by decide), + source_yRow_eq_rowCompute 23 9 23 2 (by decide), + source_yRow_eq_rowCompute 23 9 23 3 (by decide), + source_yRow_eq_rowCompute 23 9 23 4 (by decide), + source_yRow_eq_rowCompute 23 9 23 5 (by decide), + source_yRow_eq_rowCompute 23 9 23 6 (by decide), + computeRow_23_9_23_0, computeRow_23_9_23_1, computeRow_23_9_23_2, computeRow_23_9_23_3, computeRow_23_9_23_4, computeRow_23_9_23_5, computeRow_23_9_23_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_11_11 : Y 23 11 11 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 11 11 0 (by decide), + source_yRow_eq_rowCompute 23 11 11 1 (by decide), + source_yRow_eq_rowCompute 23 11 11 2 (by decide), + source_yRow_eq_rowCompute 23 11 11 3 (by decide), + source_yRow_eq_rowCompute 23 11 11 4 (by decide), + source_yRow_eq_rowCompute 23 11 11 5 (by decide), + source_yRow_eq_rowCompute 23 11 11 6 (by decide), + computeRow_23_11_11_0, computeRow_23_11_11_1, computeRow_23_11_11_2, computeRow_23_11_11_3, computeRow_23_11_11_4, computeRow_23_11_11_5, computeRow_23_11_11_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_11_13 : Y 23 11 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 11 13 0 (by decide), + source_yRow_eq_rowCompute 23 11 13 1 (by decide), + source_yRow_eq_rowCompute 23 11 13 2 (by decide), + source_yRow_eq_rowCompute 23 11 13 3 (by decide), + source_yRow_eq_rowCompute 23 11 13 4 (by decide), + source_yRow_eq_rowCompute 23 11 13 5 (by decide), + source_yRow_eq_rowCompute 23 11 13 6 (by decide), + computeRow_23_11_13_0, computeRow_23_11_13_1, computeRow_23_11_13_2, computeRow_23_11_13_3, computeRow_23_11_13_4, computeRow_23_11_13_5, computeRow_23_11_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_11_15 : Y 23 11 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 11 15 0 (by decide), + source_yRow_eq_rowCompute 23 11 15 1 (by decide), + source_yRow_eq_rowCompute 23 11 15 2 (by decide), + source_yRow_eq_rowCompute 23 11 15 3 (by decide), + source_yRow_eq_rowCompute 23 11 15 4 (by decide), + source_yRow_eq_rowCompute 23 11 15 5 (by decide), + source_yRow_eq_rowCompute 23 11 15 6 (by decide), + computeRow_23_11_15_0, computeRow_23_11_15_1, computeRow_23_11_15_2, computeRow_23_11_15_3, computeRow_23_11_15_4, computeRow_23_11_15_5, computeRow_23_11_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_11_17 : Y 23 11 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 11 17 0 (by decide), + source_yRow_eq_rowCompute 23 11 17 1 (by decide), + source_yRow_eq_rowCompute 23 11 17 2 (by decide), + source_yRow_eq_rowCompute 23 11 17 3 (by decide), + source_yRow_eq_rowCompute 23 11 17 4 (by decide), + source_yRow_eq_rowCompute 23 11 17 5 (by decide), + source_yRow_eq_rowCompute 23 11 17 6 (by decide), + computeRow_23_11_17_0, computeRow_23_11_17_1, computeRow_23_11_17_2, computeRow_23_11_17_3, computeRow_23_11_17_4, computeRow_23_11_17_5, computeRow_23_11_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_11_19 : Y 23 11 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 11 19 0 (by decide), + source_yRow_eq_rowCompute 23 11 19 1 (by decide), + source_yRow_eq_rowCompute 23 11 19 2 (by decide), + source_yRow_eq_rowCompute 23 11 19 3 (by decide), + source_yRow_eq_rowCompute 23 11 19 4 (by decide), + source_yRow_eq_rowCompute 23 11 19 5 (by decide), + source_yRow_eq_rowCompute 23 11 19 6 (by decide), + computeRow_23_11_19_0, computeRow_23_11_19_1, computeRow_23_11_19_2, computeRow_23_11_19_3, computeRow_23_11_19_4, computeRow_23_11_19_5, computeRow_23_11_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_11_21 : Y 23 11 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 11 21 0 (by decide), + source_yRow_eq_rowCompute 23 11 21 1 (by decide), + source_yRow_eq_rowCompute 23 11 21 2 (by decide), + source_yRow_eq_rowCompute 23 11 21 3 (by decide), + source_yRow_eq_rowCompute 23 11 21 4 (by decide), + source_yRow_eq_rowCompute 23 11 21 5 (by decide), + source_yRow_eq_rowCompute 23 11 21 6 (by decide), + computeRow_23_11_21_0, computeRow_23_11_21_1, computeRow_23_11_21_2, computeRow_23_11_21_3, computeRow_23_11_21_4, computeRow_23_11_21_5, computeRow_23_11_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_11_23 : Y 23 11 23 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 11 23 0 (by decide), + source_yRow_eq_rowCompute 23 11 23 1 (by decide), + source_yRow_eq_rowCompute 23 11 23 2 (by decide), + source_yRow_eq_rowCompute 23 11 23 3 (by decide), + source_yRow_eq_rowCompute 23 11 23 4 (by decide), + source_yRow_eq_rowCompute 23 11 23 5 (by decide), + source_yRow_eq_rowCompute 23 11 23 6 (by decide), + computeRow_23_11_23_0, computeRow_23_11_23_1, computeRow_23_11_23_2, computeRow_23_11_23_3, computeRow_23_11_23_4, computeRow_23_11_23_5, computeRow_23_11_23_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_13_13 : Y 23 13 13 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 13 13 0 (by decide), + source_yRow_eq_rowCompute 23 13 13 1 (by decide), + source_yRow_eq_rowCompute 23 13 13 2 (by decide), + source_yRow_eq_rowCompute 23 13 13 3 (by decide), + source_yRow_eq_rowCompute 23 13 13 4 (by decide), + source_yRow_eq_rowCompute 23 13 13 5 (by decide), + source_yRow_eq_rowCompute 23 13 13 6 (by decide), + computeRow_23_13_13_0, computeRow_23_13_13_1, computeRow_23_13_13_2, computeRow_23_13_13_3, computeRow_23_13_13_4, computeRow_23_13_13_5, computeRow_23_13_13_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_13_15 : Y 23 13 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 13 15 0 (by decide), + source_yRow_eq_rowCompute 23 13 15 1 (by decide), + source_yRow_eq_rowCompute 23 13 15 2 (by decide), + source_yRow_eq_rowCompute 23 13 15 3 (by decide), + source_yRow_eq_rowCompute 23 13 15 4 (by decide), + source_yRow_eq_rowCompute 23 13 15 5 (by decide), + source_yRow_eq_rowCompute 23 13 15 6 (by decide), + computeRow_23_13_15_0, computeRow_23_13_15_1, computeRow_23_13_15_2, computeRow_23_13_15_3, computeRow_23_13_15_4, computeRow_23_13_15_5, computeRow_23_13_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_13_17 : Y 23 13 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 13 17 0 (by decide), + source_yRow_eq_rowCompute 23 13 17 1 (by decide), + source_yRow_eq_rowCompute 23 13 17 2 (by decide), + source_yRow_eq_rowCompute 23 13 17 3 (by decide), + source_yRow_eq_rowCompute 23 13 17 4 (by decide), + source_yRow_eq_rowCompute 23 13 17 5 (by decide), + source_yRow_eq_rowCompute 23 13 17 6 (by decide), + computeRow_23_13_17_0, computeRow_23_13_17_1, computeRow_23_13_17_2, computeRow_23_13_17_3, computeRow_23_13_17_4, computeRow_23_13_17_5, computeRow_23_13_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_13_19 : Y 23 13 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 13 19 0 (by decide), + source_yRow_eq_rowCompute 23 13 19 1 (by decide), + source_yRow_eq_rowCompute 23 13 19 2 (by decide), + source_yRow_eq_rowCompute 23 13 19 3 (by decide), + source_yRow_eq_rowCompute 23 13 19 4 (by decide), + source_yRow_eq_rowCompute 23 13 19 5 (by decide), + source_yRow_eq_rowCompute 23 13 19 6 (by decide), + computeRow_23_13_19_0, computeRow_23_13_19_1, computeRow_23_13_19_2, computeRow_23_13_19_3, computeRow_23_13_19_4, computeRow_23_13_19_5, computeRow_23_13_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_13_21 : Y 23 13 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 13 21 0 (by decide), + source_yRow_eq_rowCompute 23 13 21 1 (by decide), + source_yRow_eq_rowCompute 23 13 21 2 (by decide), + source_yRow_eq_rowCompute 23 13 21 3 (by decide), + source_yRow_eq_rowCompute 23 13 21 4 (by decide), + source_yRow_eq_rowCompute 23 13 21 5 (by decide), + source_yRow_eq_rowCompute 23 13 21 6 (by decide), + computeRow_23_13_21_0, computeRow_23_13_21_1, computeRow_23_13_21_2, computeRow_23_13_21_3, computeRow_23_13_21_4, computeRow_23_13_21_5, computeRow_23_13_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_13_23 : Y 23 13 23 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 13 23 0 (by decide), + source_yRow_eq_rowCompute 23 13 23 1 (by decide), + source_yRow_eq_rowCompute 23 13 23 2 (by decide), + source_yRow_eq_rowCompute 23 13 23 3 (by decide), + source_yRow_eq_rowCompute 23 13 23 4 (by decide), + source_yRow_eq_rowCompute 23 13 23 5 (by decide), + source_yRow_eq_rowCompute 23 13 23 6 (by decide), + computeRow_23_13_23_0, computeRow_23_13_23_1, computeRow_23_13_23_2, computeRow_23_13_23_3, computeRow_23_13_23_4, computeRow_23_13_23_5, computeRow_23_13_23_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_15_15 : Y 23 15 15 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 15 15 0 (by decide), + source_yRow_eq_rowCompute 23 15 15 1 (by decide), + source_yRow_eq_rowCompute 23 15 15 2 (by decide), + source_yRow_eq_rowCompute 23 15 15 3 (by decide), + source_yRow_eq_rowCompute 23 15 15 4 (by decide), + source_yRow_eq_rowCompute 23 15 15 5 (by decide), + source_yRow_eq_rowCompute 23 15 15 6 (by decide), + computeRow_23_15_15_0, computeRow_23_15_15_1, computeRow_23_15_15_2, computeRow_23_15_15_3, computeRow_23_15_15_4, computeRow_23_15_15_5, computeRow_23_15_15_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_15_17 : Y 23 15 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 15 17 0 (by decide), + source_yRow_eq_rowCompute 23 15 17 1 (by decide), + source_yRow_eq_rowCompute 23 15 17 2 (by decide), + source_yRow_eq_rowCompute 23 15 17 3 (by decide), + source_yRow_eq_rowCompute 23 15 17 4 (by decide), + source_yRow_eq_rowCompute 23 15 17 5 (by decide), + source_yRow_eq_rowCompute 23 15 17 6 (by decide), + computeRow_23_15_17_0, computeRow_23_15_17_1, computeRow_23_15_17_2, computeRow_23_15_17_3, computeRow_23_15_17_4, computeRow_23_15_17_5, computeRow_23_15_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_15_19 : Y 23 15 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 15 19 0 (by decide), + source_yRow_eq_rowCompute 23 15 19 1 (by decide), + source_yRow_eq_rowCompute 23 15 19 2 (by decide), + source_yRow_eq_rowCompute 23 15 19 3 (by decide), + source_yRow_eq_rowCompute 23 15 19 4 (by decide), + source_yRow_eq_rowCompute 23 15 19 5 (by decide), + source_yRow_eq_rowCompute 23 15 19 6 (by decide), + computeRow_23_15_19_0, computeRow_23_15_19_1, computeRow_23_15_19_2, computeRow_23_15_19_3, computeRow_23_15_19_4, computeRow_23_15_19_5, computeRow_23_15_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_15_21 : Y 23 15 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 15 21 0 (by decide), + source_yRow_eq_rowCompute 23 15 21 1 (by decide), + source_yRow_eq_rowCompute 23 15 21 2 (by decide), + source_yRow_eq_rowCompute 23 15 21 3 (by decide), + source_yRow_eq_rowCompute 23 15 21 4 (by decide), + source_yRow_eq_rowCompute 23 15 21 5 (by decide), + source_yRow_eq_rowCompute 23 15 21 6 (by decide), + computeRow_23_15_21_0, computeRow_23_15_21_1, computeRow_23_15_21_2, computeRow_23_15_21_3, computeRow_23_15_21_4, computeRow_23_15_21_5, computeRow_23_15_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_15_23 : Y 23 15 23 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 15 23 0 (by decide), + source_yRow_eq_rowCompute 23 15 23 1 (by decide), + source_yRow_eq_rowCompute 23 15 23 2 (by decide), + source_yRow_eq_rowCompute 23 15 23 3 (by decide), + source_yRow_eq_rowCompute 23 15 23 4 (by decide), + source_yRow_eq_rowCompute 23 15 23 5 (by decide), + source_yRow_eq_rowCompute 23 15 23 6 (by decide), + computeRow_23_15_23_0, computeRow_23_15_23_1, computeRow_23_15_23_2, computeRow_23_15_23_3, computeRow_23_15_23_4, computeRow_23_15_23_5, computeRow_23_15_23_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_17_17 : Y 23 17 17 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 17 17 0 (by decide), + source_yRow_eq_rowCompute 23 17 17 1 (by decide), + source_yRow_eq_rowCompute 23 17 17 2 (by decide), + source_yRow_eq_rowCompute 23 17 17 3 (by decide), + source_yRow_eq_rowCompute 23 17 17 4 (by decide), + source_yRow_eq_rowCompute 23 17 17 5 (by decide), + source_yRow_eq_rowCompute 23 17 17 6 (by decide), + computeRow_23_17_17_0, computeRow_23_17_17_1, computeRow_23_17_17_2, computeRow_23_17_17_3, computeRow_23_17_17_4, computeRow_23_17_17_5, computeRow_23_17_17_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_17_19 : Y 23 17 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 17 19 0 (by decide), + source_yRow_eq_rowCompute 23 17 19 1 (by decide), + source_yRow_eq_rowCompute 23 17 19 2 (by decide), + source_yRow_eq_rowCompute 23 17 19 3 (by decide), + source_yRow_eq_rowCompute 23 17 19 4 (by decide), + source_yRow_eq_rowCompute 23 17 19 5 (by decide), + source_yRow_eq_rowCompute 23 17 19 6 (by decide), + computeRow_23_17_19_0, computeRow_23_17_19_1, computeRow_23_17_19_2, computeRow_23_17_19_3, computeRow_23_17_19_4, computeRow_23_17_19_5, computeRow_23_17_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_17_21 : Y 23 17 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 17 21 0 (by decide), + source_yRow_eq_rowCompute 23 17 21 1 (by decide), + source_yRow_eq_rowCompute 23 17 21 2 (by decide), + source_yRow_eq_rowCompute 23 17 21 3 (by decide), + source_yRow_eq_rowCompute 23 17 21 4 (by decide), + source_yRow_eq_rowCompute 23 17 21 5 (by decide), + source_yRow_eq_rowCompute 23 17 21 6 (by decide), + computeRow_23_17_21_0, computeRow_23_17_21_1, computeRow_23_17_21_2, computeRow_23_17_21_3, computeRow_23_17_21_4, computeRow_23_17_21_5, computeRow_23_17_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_17_23 : Y 23 17 23 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 17 23 0 (by decide), + source_yRow_eq_rowCompute 23 17 23 1 (by decide), + source_yRow_eq_rowCompute 23 17 23 2 (by decide), + source_yRow_eq_rowCompute 23 17 23 3 (by decide), + source_yRow_eq_rowCompute 23 17 23 4 (by decide), + source_yRow_eq_rowCompute 23 17 23 5 (by decide), + source_yRow_eq_rowCompute 23 17 23 6 (by decide), + computeRow_23_17_23_0, computeRow_23_17_23_1, computeRow_23_17_23_2, computeRow_23_17_23_3, computeRow_23_17_23_4, computeRow_23_17_23_5, computeRow_23_17_23_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_19_19 : Y 23 19 19 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 19 19 0 (by decide), + source_yRow_eq_rowCompute 23 19 19 1 (by decide), + source_yRow_eq_rowCompute 23 19 19 2 (by decide), + source_yRow_eq_rowCompute 23 19 19 3 (by decide), + source_yRow_eq_rowCompute 23 19 19 4 (by decide), + source_yRow_eq_rowCompute 23 19 19 5 (by decide), + source_yRow_eq_rowCompute 23 19 19 6 (by decide), + computeRow_23_19_19_0, computeRow_23_19_19_1, computeRow_23_19_19_2, computeRow_23_19_19_3, computeRow_23_19_19_4, computeRow_23_19_19_5, computeRow_23_19_19_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_19_21 : Y 23 19 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 19 21 0 (by decide), + source_yRow_eq_rowCompute 23 19 21 1 (by decide), + source_yRow_eq_rowCompute 23 19 21 2 (by decide), + source_yRow_eq_rowCompute 23 19 21 3 (by decide), + source_yRow_eq_rowCompute 23 19 21 4 (by decide), + source_yRow_eq_rowCompute 23 19 21 5 (by decide), + source_yRow_eq_rowCompute 23 19 21 6 (by decide), + computeRow_23_19_21_0, computeRow_23_19_21_1, computeRow_23_19_21_2, computeRow_23_19_21_3, computeRow_23_19_21_4, computeRow_23_19_21_5, computeRow_23_19_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_19_23 : Y 23 19 23 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 19 23 0 (by decide), + source_yRow_eq_rowCompute 23 19 23 1 (by decide), + source_yRow_eq_rowCompute 23 19 23 2 (by decide), + source_yRow_eq_rowCompute 23 19 23 3 (by decide), + source_yRow_eq_rowCompute 23 19 23 4 (by decide), + source_yRow_eq_rowCompute 23 19 23 5 (by decide), + source_yRow_eq_rowCompute 23 19 23 6 (by decide), + computeRow_23_19_23_0, computeRow_23_19_23_1, computeRow_23_19_23_2, computeRow_23_19_23_3, computeRow_23_19_23_4, computeRow_23_19_23_5, computeRow_23_19_23_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_21_21 : Y 23 21 21 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 21 21 0 (by decide), + source_yRow_eq_rowCompute 23 21 21 1 (by decide), + source_yRow_eq_rowCompute 23 21 21 2 (by decide), + source_yRow_eq_rowCompute 23 21 21 3 (by decide), + source_yRow_eq_rowCompute 23 21 21 4 (by decide), + source_yRow_eq_rowCompute 23 21 21 5 (by decide), + source_yRow_eq_rowCompute 23 21 21 6 (by decide), + computeRow_23_21_21_0, computeRow_23_21_21_1, computeRow_23_21_21_2, computeRow_23_21_21_3, computeRow_23_21_21_4, computeRow_23_21_21_5, computeRow_23_21_21_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_21_23 : Y 23 21 23 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 21 23 0 (by decide), + source_yRow_eq_rowCompute 23 21 23 1 (by decide), + source_yRow_eq_rowCompute 23 21 23 2 (by decide), + source_yRow_eq_rowCompute 23 21 23 3 (by decide), + source_yRow_eq_rowCompute 23 21 23 4 (by decide), + source_yRow_eq_rowCompute 23 21 23 5 (by decide), + source_yRow_eq_rowCompute 23 21 23 6 (by decide), + computeRow_23_21_23_0, computeRow_23_21_23_1, computeRow_23_21_23_2, computeRow_23_21_23_3, computeRow_23_21_23_4, computeRow_23_21_23_5, computeRow_23_21_23_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_error_23_23_23 : Y 23 23 23 = (0 : ℚ) := by + rw [Y_expand, source_yRow_eq_rowCompute 23 23 23 0 (by decide), + source_yRow_eq_rowCompute 23 23 23 1 (by decide), + source_yRow_eq_rowCompute 23 23 23 2 (by decide), + source_yRow_eq_rowCompute 23 23 23 3 (by decide), + source_yRow_eq_rowCompute 23 23 23 4 (by decide), + source_yRow_eq_rowCompute 23 23 23 5 (by decide), + source_yRow_eq_rowCompute 23 23 23 6 (by decide), + computeRow_23_23_23_0, computeRow_23_23_23_1, computeRow_23_23_23_2, computeRow_23_23_23_3, computeRow_23_23_23_4, computeRow_23_23_23_5, computeRow_23_23_23_6] + norm_num [arithmeticScale, Nat.factorial] + +theorem source_gram_23_1_1 : Z 23 1 1 = (2248001455555215360000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_1_1 + +theorem source_gram_23_1_3 : Z 23 1 3 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_1_3 + +theorem source_gram_23_1_5 : Z 23 1 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_1_5 + +theorem source_gram_23_1_7 : Z 23 1 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_1_7 + +theorem source_gram_23_1_9 : Z 23 1 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_1_9 + +theorem source_gram_23_1_11 : Z 23 1 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_1_11 + +theorem source_gram_23_1_13 : Z 23 1 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_1_13 + +theorem source_gram_23_1_15 : Z 23 1 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_1_15 + +theorem source_gram_23_1_17 : Z 23 1 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_1_17 + +theorem source_gram_23_1_19 : Z 23 1 19 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_1_19 + +theorem source_gram_23_1_21 : Z 23 1 21 = (-2195313921440640000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_1_21 + +theorem source_gram_23_1_23 : Z 23 1 23 = (252461100965673600000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_1_23 + +theorem source_gram_23_3_3 : Z 23 3 3 = (14597412049059840000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_3_3 + +theorem source_gram_23_3_5 : Z 23 3 5 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_3_5 + +theorem source_gram_23_3_7 : Z 23 3 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_3_7 + +theorem source_gram_23_3_9 : Z 23 3 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_3_9 + +theorem source_gram_23_3_11 : Z 23 3 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_3_11 + +theorem source_gram_23_3_13 : Z 23 3 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_3_13 + +theorem source_gram_23_3_15 : Z 23 3 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_3_15 + +theorem source_gram_23_3_17 : Z 23 3 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_3_17 + +theorem source_gram_23_3_19 : Z 23 3 19 = (-57021140816640000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_3_19 + +theorem source_gram_23_3_21 : Z 23 3 21 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_3_21 + +theorem source_gram_23_3_23 : Z 23 3 23 = (100984440386269440000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_3_23 + +theorem source_gram_23_5_5 : Z 23 5 5 = (768284844687360000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_5_5 + +theorem source_gram_23_5_7 : Z 23 5 7 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_5_7 + +theorem source_gram_23_5_9 : Z 23 5 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_5_9 + +theorem source_gram_23_5_11 : Z 23 5 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_5_11 + +theorem source_gram_23_5_13 : Z 23 5 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_5_13 + +theorem source_gram_23_5_15 : Z 23 5 15 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_5_15 + +theorem source_gram_23_5_17 : Z 23 5 17 = (-4501669011840000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_5_17 + +theorem source_gram_23_5_19 : Z 23 5 19 = (-114042281633280000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_5_19 + +theorem source_gram_23_5_21 : Z 23 5 21 = (1746272437509600000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_5_21 + +theorem source_gram_23_5_23 : Z 23 5 23 = (37869165144851040000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_5_23 + +theorem source_gram_23_7_7 : Z 23 7 7 = (105450861035520000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_7_7 + +theorem source_gram_23_7_9 : Z 23 7 9 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_7_9 + +theorem source_gram_23_7_11 : Z 23 7 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_7_11 + +theorem source_gram_23_7_13 : Z 23 7 13 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_7_13 + +theorem source_gram_23_7_15 : Z 23 7 15 = (-823834851840000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_7_15 + +theorem source_gram_23_7_17 : Z 23 7 17 = (-24509086842240000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_7_17 + +theorem source_gram_23_7_19 : Z 23 7 19 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_7_19 + +theorem source_gram_23_7_21 : Z 23 7 21 = (1746272437509600000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_7_21 + +theorem source_gram_23_7_23 : Z 23 7 23 = (12623055048283680000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_7_23 + +theorem source_gram_23_9_9 : Z 23 9 9 = (31635258310656000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_9_9 + +theorem source_gram_23_9_11 : Z 23 9 11 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_9_11 + +theorem source_gram_23_9_13 : Z 23 9 13 = (-308938069440000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_9_13 + +theorem source_gram_23_9_15 : Z 23 9 15 = (-8341327874880000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_9_15 + +theorem source_gram_23_9_17 : Z 23 9 17 = (-26259735902400000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_9_17 + +theorem source_gram_23_9_19 : Z 23 9 19 = (119744395714944000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_9_19 + +theorem source_gram_23_9_21 : Z 23 9 21 = (1010343338844840000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_9_21 + +theorem source_gram_23_9_23 : Z 23 9 23 = (3155763762070920000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_9_23 + +theorem source_gram_23_11_11 : Z 23 11 11 = (18896146093440000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_11_11 + +theorem source_gram_23_11_13 : Z 23 11 13 = (-4854741091200000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_11_13 + +theorem source_gram_23_11_15 : Z 23 11 15 = (-16991593819200000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_11_15 + +theorem source_gram_23_11_17 : Z 23 11 17 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_11_17 + +theorem source_gram_23_11_19 : Z 23 11 19 = (117606102934320000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_11_19 + +theorem source_gram_23_11_21 : Z 23 11 21 = (274414240180080000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_11_21 + +theorem source_gram_23_11_23 : Z 23 11 23 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_11_23 + +theorem source_gram_23_13_13 : Z 23 13 13 = (8396495387280000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_13_13 + +theorem source_gram_23_13_15 : Z 23 13 15 = (-11044535982480000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_13_15 + +theorem source_gram_23_13_17 : Z 23 13 17 = (13411222264440000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_13_17 + +theorem source_gram_23_13_19 : Z 23 13 19 = (0 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_13_19 + +theorem source_gram_23_13_21 : Z 23 13 21 = (-202692336496650000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_13_21 + +theorem source_gram_23_13_23 : Z 23 13 23 = (-788940940517730000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_13_23 + +theorem source_gram_23_15_15 : Z 23 15 15 = (52725430517760000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_15_15 + +theorem source_gram_23_15_17 : Z 23 15 17 = (-31292851950360000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_15_17 + +theorem source_gram_23_15_19 : Z 23 15 19 = (-162153869197320000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_15_19 + +theorem source_gram_23_15_21 : Z 23 15 21 = (-420976391185350000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_15_21 + +theorem source_gram_23_15_23 : Z 23 15 23 = (-788940940517730000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_15_23 + +theorem source_gram_23_17_17 : Z 23 17 17 = (111009907368360000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_17_17 + +theorem source_gram_23_17_19 : Z 23 17 19 = (-302924810588400000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_17_19 + +theorem source_gram_23_17_21 : Z 23 17 21 = (-463853616213487500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_17_21 + +theorem source_gram_23_17_23 : Z 23 17 23 = (-591705705388297500 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_17_23 + +theorem source_gram_23_19_19 : Z 23 19 19 = (2530981340232345000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_19_19 + +theorem source_gram_23_19_21 : Z 23 19 21 = (-414739703908530000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_19_21 + +theorem source_gram_23_19_23 : Z 23 19 23 = (-394470470258865000 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_19_23 + +theorem source_gram_23_21_21 : Z 23 21 21 = (101850365435360416875 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_21_21 + +theorem source_gram_23_21_23 : Z 23 21 23 = (-246544043911790625 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_21_23 + +theorem source_gram_23_23_23 : Z 23 23 23 = (25851868812458629565625 : ℚ) := by + rw [Z_eq_gramCompute] + exact computeGram_23_23_23 + +theorem source_error_23_3_1 : Y 23 3 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_1_3 + +theorem source_gram_23_3_1 : Z 23 3 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_1_3 + +theorem source_error_23_5_1 : Y 23 5 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_1_5 + +theorem source_gram_23_5_1 : Z 23 5 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_1_5 + +theorem source_error_23_5_3 : Y 23 5 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_3_5 + +theorem source_gram_23_5_3 : Z 23 5 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_3_5 + +theorem source_error_23_7_1 : Y 23 7 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_1_7 + +theorem source_gram_23_7_1 : Z 23 7 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_1_7 + +theorem source_error_23_7_3 : Y 23 7 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_3_7 + +theorem source_gram_23_7_3 : Z 23 7 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_3_7 + +theorem source_error_23_7_5 : Y 23 7 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_5_7 + +theorem source_gram_23_7_5 : Z 23 7 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_5_7 + +theorem source_error_23_9_1 : Y 23 9 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_1_9 + +theorem source_gram_23_9_1 : Z 23 9 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_1_9 + +theorem source_error_23_9_3 : Y 23 9 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_3_9 + +theorem source_gram_23_9_3 : Z 23 9 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_3_9 + +theorem source_error_23_9_5 : Y 23 9 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_5_9 + +theorem source_gram_23_9_5 : Z 23 9 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_5_9 + +theorem source_error_23_9_7 : Y 23 9 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_7_9 + +theorem source_gram_23_9_7 : Z 23 9 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_7_9 + +theorem source_error_23_11_1 : Y 23 11 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_1_11 + +theorem source_gram_23_11_1 : Z 23 11 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_1_11 + +theorem source_error_23_11_3 : Y 23 11 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_3_11 + +theorem source_gram_23_11_3 : Z 23 11 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_3_11 + +theorem source_error_23_11_5 : Y 23 11 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_5_11 + +theorem source_gram_23_11_5 : Z 23 11 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_5_11 + +theorem source_error_23_11_7 : Y 23 11 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_7_11 + +theorem source_gram_23_11_7 : Z 23 11 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_7_11 + +theorem source_error_23_11_9 : Y 23 11 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_9_11 + +theorem source_gram_23_11_9 : Z 23 11 9 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_9_11 + +theorem source_error_23_13_1 : Y 23 13 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_1_13 + +theorem source_gram_23_13_1 : Z 23 13 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_1_13 + +theorem source_error_23_13_3 : Y 23 13 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_3_13 + +theorem source_gram_23_13_3 : Z 23 13 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_3_13 + +theorem source_error_23_13_5 : Y 23 13 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_5_13 + +theorem source_gram_23_13_5 : Z 23 13 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_5_13 + +theorem source_error_23_13_7 : Y 23 13 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_7_13 + +theorem source_gram_23_13_7 : Z 23 13 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_7_13 + +theorem source_error_23_13_9 : Y 23 13 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_9_13 + +theorem source_gram_23_13_9 : Z 23 13 9 = (-308938069440000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_9_13 + +theorem source_error_23_13_11 : Y 23 13 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_11_13 + +theorem source_gram_23_13_11 : Z 23 13 11 = (-4854741091200000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_11_13 + +theorem source_error_23_15_1 : Y 23 15 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_1_15 + +theorem source_gram_23_15_1 : Z 23 15 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_1_15 + +theorem source_error_23_15_3 : Y 23 15 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_3_15 + +theorem source_gram_23_15_3 : Z 23 15 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_3_15 + +theorem source_error_23_15_5 : Y 23 15 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_5_15 + +theorem source_gram_23_15_5 : Z 23 15 5 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_5_15 + +theorem source_error_23_15_7 : Y 23 15 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_7_15 + +theorem source_gram_23_15_7 : Z 23 15 7 = (-823834851840000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_7_15 + +theorem source_error_23_15_9 : Y 23 15 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_9_15 + +theorem source_gram_23_15_9 : Z 23 15 9 = (-8341327874880000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_9_15 + +theorem source_error_23_15_11 : Y 23 15 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_11_15 + +theorem source_gram_23_15_11 : Z 23 15 11 = (-16991593819200000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_11_15 + +theorem source_error_23_15_13 : Y 23 15 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_13_15 + +theorem source_gram_23_15_13 : Z 23 15 13 = (-11044535982480000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_13_15 + +theorem source_error_23_17_1 : Y 23 17 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_1_17 + +theorem source_gram_23_17_1 : Z 23 17 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_1_17 + +theorem source_error_23_17_3 : Y 23 17 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_3_17 + +theorem source_gram_23_17_3 : Z 23 17 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_3_17 + +theorem source_error_23_17_5 : Y 23 17 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_5_17 + +theorem source_gram_23_17_5 : Z 23 17 5 = (-4501669011840000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_5_17 + +theorem source_error_23_17_7 : Y 23 17 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_7_17 + +theorem source_gram_23_17_7 : Z 23 17 7 = (-24509086842240000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_7_17 + +theorem source_error_23_17_9 : Y 23 17 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_9_17 + +theorem source_gram_23_17_9 : Z 23 17 9 = (-26259735902400000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_9_17 + +theorem source_error_23_17_11 : Y 23 17 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_11_17 + +theorem source_gram_23_17_11 : Z 23 17 11 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_11_17 + +theorem source_error_23_17_13 : Y 23 17 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_13_17 + +theorem source_gram_23_17_13 : Z 23 17 13 = (13411222264440000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_13_17 + +theorem source_error_23_17_15 : Y 23 17 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_15_17 + +theorem source_gram_23_17_15 : Z 23 17 15 = (-31292851950360000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_15_17 + +theorem source_error_23_19_1 : Y 23 19 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_1_19 + +theorem source_gram_23_19_1 : Z 23 19 1 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_1_19 + +theorem source_error_23_19_3 : Y 23 19 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_3_19 + +theorem source_gram_23_19_3 : Z 23 19 3 = (-57021140816640000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_3_19 + +theorem source_error_23_19_5 : Y 23 19 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_5_19 + +theorem source_gram_23_19_5 : Z 23 19 5 = (-114042281633280000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_5_19 + +theorem source_error_23_19_7 : Y 23 19 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_7_19 + +theorem source_gram_23_19_7 : Z 23 19 7 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_7_19 + +theorem source_error_23_19_9 : Y 23 19 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_9_19 + +theorem source_gram_23_19_9 : Z 23 19 9 = (119744395714944000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_9_19 + +theorem source_error_23_19_11 : Y 23 19 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_11_19 + +theorem source_gram_23_19_11 : Z 23 19 11 = (117606102934320000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_11_19 + +theorem source_error_23_19_13 : Y 23 19 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_13_19 + +theorem source_gram_23_19_13 : Z 23 19 13 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_13_19 + +theorem source_error_23_19_15 : Y 23 19 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_15_19 + +theorem source_gram_23_19_15 : Z 23 19 15 = (-162153869197320000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_15_19 + +theorem source_error_23_19_17 : Y 23 19 17 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_17_19 + +theorem source_gram_23_19_17 : Z 23 19 17 = (-302924810588400000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_17_19 + +theorem source_error_23_21_1 : Y 23 21 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_1_21 + +theorem source_gram_23_21_1 : Z 23 21 1 = (-2195313921440640000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_1_21 + +theorem source_error_23_21_3 : Y 23 21 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_3_21 + +theorem source_gram_23_21_3 : Z 23 21 3 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_3_21 + +theorem source_error_23_21_5 : Y 23 21 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_5_21 + +theorem source_gram_23_21_5 : Z 23 21 5 = (1746272437509600000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_5_21 + +theorem source_error_23_21_7 : Y 23 21 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_7_21 + +theorem source_gram_23_21_7 : Z 23 21 7 = (1746272437509600000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_7_21 + +theorem source_error_23_21_9 : Y 23 21 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_9_21 + +theorem source_gram_23_21_9 : Z 23 21 9 = (1010343338844840000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_9_21 + +theorem source_error_23_21_11 : Y 23 21 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_11_21 + +theorem source_gram_23_21_11 : Z 23 21 11 = (274414240180080000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_11_21 + +theorem source_error_23_21_13 : Y 23 21 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_13_21 + +theorem source_gram_23_21_13 : Z 23 21 13 = (-202692336496650000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_13_21 + +theorem source_error_23_21_15 : Y 23 21 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_15_21 + +theorem source_gram_23_21_15 : Z 23 21 15 = (-420976391185350000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_15_21 + +theorem source_error_23_21_17 : Y 23 21 17 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_17_21 + +theorem source_gram_23_21_17 : Z 23 21 17 = (-463853616213487500 : ℚ) := by + rw [Z_symm] + exact source_gram_23_17_21 + +theorem source_error_23_21_19 : Y 23 21 19 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_19_21 + +theorem source_gram_23_21_19 : Z 23 21 19 = (-414739703908530000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_19_21 + +theorem source_error_23_23_1 : Y 23 23 1 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_1_23 + +theorem source_gram_23_23_1 : Z 23 23 1 = (252461100965673600000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_1_23 + +theorem source_error_23_23_3 : Y 23 23 3 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_3_23 + +theorem source_gram_23_23_3 : Z 23 23 3 = (100984440386269440000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_3_23 + +theorem source_error_23_23_5 : Y 23 23 5 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_5_23 + +theorem source_gram_23_23_5 : Z 23 23 5 = (37869165144851040000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_5_23 + +theorem source_error_23_23_7 : Y 23 23 7 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_7_23 + +theorem source_gram_23_23_7 : Z 23 23 7 = (12623055048283680000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_7_23 + +theorem source_error_23_23_9 : Y 23 23 9 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_9_23 + +theorem source_gram_23_23_9 : Z 23 23 9 = (3155763762070920000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_9_23 + +theorem source_error_23_23_11 : Y 23 23 11 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_11_23 + +theorem source_gram_23_23_11 : Z 23 23 11 = (0 : ℚ) := by + rw [Z_symm] + exact source_gram_23_11_23 + +theorem source_error_23_23_13 : Y 23 23 13 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_13_23 + +theorem source_gram_23_23_13 : Z 23 23 13 = (-788940940517730000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_13_23 + +theorem source_error_23_23_15 : Y 23 23 15 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_15_23 + +theorem source_gram_23_23_15 : Z 23 23 15 = (-788940940517730000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_15_23 + +theorem source_error_23_23_17 : Y 23 23 17 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_17_23 + +theorem source_gram_23_23_17 : Z 23 23 17 = (-591705705388297500 : ℚ) := by + rw [Z_symm] + exact source_gram_23_17_23 + +theorem source_error_23_23_19 : Y 23 23 19 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_19_23 + +theorem source_gram_23_23_19 : Z 23 23 19 = (-394470470258865000 : ℚ) := by + rw [Z_symm] + exact source_gram_23_19_23 + +theorem source_error_23_23_21 : Y 23 23 21 = (0 : ℚ) := by + rw [Y_symm] + exact source_error_23_21_23 + +theorem source_gram_23_23_21 : Z 23 23 21 = (-246544043911790625 : ℚ) := by + rw [Z_symm] + exact source_gram_23_21_23 + +theorem error_23 : errorRational 23 = candidateY_23 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_error_23_1_1 + · exact source_error_23_1_3 + · exact source_error_23_1_5 + · exact source_error_23_1_7 + · exact source_error_23_1_9 + · exact source_error_23_1_11 + · exact source_error_23_1_13 + · exact source_error_23_1_15 + · exact source_error_23_1_17 + · exact source_error_23_1_19 + · exact source_error_23_1_21 + · exact source_error_23_1_23 + · exact source_error_23_3_1 + · exact source_error_23_3_3 + · exact source_error_23_3_5 + · exact source_error_23_3_7 + · exact source_error_23_3_9 + · exact source_error_23_3_11 + · exact source_error_23_3_13 + · exact source_error_23_3_15 + · exact source_error_23_3_17 + · exact source_error_23_3_19 + · exact source_error_23_3_21 + · exact source_error_23_3_23 + · exact source_error_23_5_1 + · exact source_error_23_5_3 + · exact source_error_23_5_5 + · exact source_error_23_5_7 + · exact source_error_23_5_9 + · exact source_error_23_5_11 + · exact source_error_23_5_13 + · exact source_error_23_5_15 + · exact source_error_23_5_17 + · exact source_error_23_5_19 + · exact source_error_23_5_21 + · exact source_error_23_5_23 + · exact source_error_23_7_1 + · exact source_error_23_7_3 + · exact source_error_23_7_5 + · exact source_error_23_7_7 + · exact source_error_23_7_9 + · exact source_error_23_7_11 + · exact source_error_23_7_13 + · exact source_error_23_7_15 + · exact source_error_23_7_17 + · exact source_error_23_7_19 + · exact source_error_23_7_21 + · exact source_error_23_7_23 + · exact source_error_23_9_1 + · exact source_error_23_9_3 + · exact source_error_23_9_5 + · exact source_error_23_9_7 + · exact source_error_23_9_9 + · exact source_error_23_9_11 + · exact source_error_23_9_13 + · exact source_error_23_9_15 + · exact source_error_23_9_17 + · exact source_error_23_9_19 + · exact source_error_23_9_21 + · exact source_error_23_9_23 + · exact source_error_23_11_1 + · exact source_error_23_11_3 + · exact source_error_23_11_5 + · exact source_error_23_11_7 + · exact source_error_23_11_9 + · exact source_error_23_11_11 + · exact source_error_23_11_13 + · exact source_error_23_11_15 + · exact source_error_23_11_17 + · exact source_error_23_11_19 + · exact source_error_23_11_21 + · exact source_error_23_11_23 + · exact source_error_23_13_1 + · exact source_error_23_13_3 + · exact source_error_23_13_5 + · exact source_error_23_13_7 + · exact source_error_23_13_9 + · exact source_error_23_13_11 + · exact source_error_23_13_13 + · exact source_error_23_13_15 + · exact source_error_23_13_17 + · exact source_error_23_13_19 + · exact source_error_23_13_21 + · exact source_error_23_13_23 + · exact source_error_23_15_1 + · exact source_error_23_15_3 + · exact source_error_23_15_5 + · exact source_error_23_15_7 + · exact source_error_23_15_9 + · exact source_error_23_15_11 + · exact source_error_23_15_13 + · exact source_error_23_15_15 + · exact source_error_23_15_17 + · exact source_error_23_15_19 + · exact source_error_23_15_21 + · exact source_error_23_15_23 + · exact source_error_23_17_1 + · exact source_error_23_17_3 + · exact source_error_23_17_5 + · exact source_error_23_17_7 + · exact source_error_23_17_9 + · exact source_error_23_17_11 + · exact source_error_23_17_13 + · exact source_error_23_17_15 + · exact source_error_23_17_17 + · exact source_error_23_17_19 + · exact source_error_23_17_21 + · exact source_error_23_17_23 + · exact source_error_23_19_1 + · exact source_error_23_19_3 + · exact source_error_23_19_5 + · exact source_error_23_19_7 + · exact source_error_23_19_9 + · exact source_error_23_19_11 + · exact source_error_23_19_13 + · exact source_error_23_19_15 + · exact source_error_23_19_17 + · exact source_error_23_19_19 + · exact source_error_23_19_21 + · exact source_error_23_19_23 + · exact source_error_23_21_1 + · exact source_error_23_21_3 + · exact source_error_23_21_5 + · exact source_error_23_21_7 + · exact source_error_23_21_9 + · exact source_error_23_21_11 + · exact source_error_23_21_13 + · exact source_error_23_21_15 + · exact source_error_23_21_17 + · exact source_error_23_21_19 + · exact source_error_23_21_21 + · exact source_error_23_21_23 + · exact source_error_23_23_1 + · exact source_error_23_23_3 + · exact source_error_23_23_5 + · exact source_error_23_23_7 + · exact source_error_23_23_9 + · exact source_error_23_23_11 + · exact source_error_23_23_13 + · exact source_error_23_23_15 + · exact source_error_23_23_17 + · exact source_error_23_23_19 + · exact source_error_23_23_21 + · exact source_error_23_23_23 + +theorem gram_23 : gramRational 23 = candidateZ_23 := by + ext i j + fin_cases i <;> fin_cases j + · exact source_gram_23_1_1 + · exact source_gram_23_1_3 + · exact source_gram_23_1_5 + · exact source_gram_23_1_7 + · exact source_gram_23_1_9 + · exact source_gram_23_1_11 + · exact source_gram_23_1_13 + · exact source_gram_23_1_15 + · exact source_gram_23_1_17 + · exact source_gram_23_1_19 + · exact source_gram_23_1_21 + · exact source_gram_23_1_23 + · exact source_gram_23_3_1 + · exact source_gram_23_3_3 + · exact source_gram_23_3_5 + · exact source_gram_23_3_7 + · exact source_gram_23_3_9 + · exact source_gram_23_3_11 + · exact source_gram_23_3_13 + · exact source_gram_23_3_15 + · exact source_gram_23_3_17 + · exact source_gram_23_3_19 + · exact source_gram_23_3_21 + · exact source_gram_23_3_23 + · exact source_gram_23_5_1 + · exact source_gram_23_5_3 + · exact source_gram_23_5_5 + · exact source_gram_23_5_7 + · exact source_gram_23_5_9 + · exact source_gram_23_5_11 + · exact source_gram_23_5_13 + · exact source_gram_23_5_15 + · exact source_gram_23_5_17 + · exact source_gram_23_5_19 + · exact source_gram_23_5_21 + · exact source_gram_23_5_23 + · exact source_gram_23_7_1 + · exact source_gram_23_7_3 + · exact source_gram_23_7_5 + · exact source_gram_23_7_7 + · exact source_gram_23_7_9 + · exact source_gram_23_7_11 + · exact source_gram_23_7_13 + · exact source_gram_23_7_15 + · exact source_gram_23_7_17 + · exact source_gram_23_7_19 + · exact source_gram_23_7_21 + · exact source_gram_23_7_23 + · exact source_gram_23_9_1 + · exact source_gram_23_9_3 + · exact source_gram_23_9_5 + · exact source_gram_23_9_7 + · exact source_gram_23_9_9 + · exact source_gram_23_9_11 + · exact source_gram_23_9_13 + · exact source_gram_23_9_15 + · exact source_gram_23_9_17 + · exact source_gram_23_9_19 + · exact source_gram_23_9_21 + · exact source_gram_23_9_23 + · exact source_gram_23_11_1 + · exact source_gram_23_11_3 + · exact source_gram_23_11_5 + · exact source_gram_23_11_7 + · exact source_gram_23_11_9 + · exact source_gram_23_11_11 + · exact source_gram_23_11_13 + · exact source_gram_23_11_15 + · exact source_gram_23_11_17 + · exact source_gram_23_11_19 + · exact source_gram_23_11_21 + · exact source_gram_23_11_23 + · exact source_gram_23_13_1 + · exact source_gram_23_13_3 + · exact source_gram_23_13_5 + · exact source_gram_23_13_7 + · exact source_gram_23_13_9 + · exact source_gram_23_13_11 + · exact source_gram_23_13_13 + · exact source_gram_23_13_15 + · exact source_gram_23_13_17 + · exact source_gram_23_13_19 + · exact source_gram_23_13_21 + · exact source_gram_23_13_23 + · exact source_gram_23_15_1 + · exact source_gram_23_15_3 + · exact source_gram_23_15_5 + · exact source_gram_23_15_7 + · exact source_gram_23_15_9 + · exact source_gram_23_15_11 + · exact source_gram_23_15_13 + · exact source_gram_23_15_15 + · exact source_gram_23_15_17 + · exact source_gram_23_15_19 + · exact source_gram_23_15_21 + · exact source_gram_23_15_23 + · exact source_gram_23_17_1 + · exact source_gram_23_17_3 + · exact source_gram_23_17_5 + · exact source_gram_23_17_7 + · exact source_gram_23_17_9 + · exact source_gram_23_17_11 + · exact source_gram_23_17_13 + · exact source_gram_23_17_15 + · exact source_gram_23_17_17 + · exact source_gram_23_17_19 + · exact source_gram_23_17_21 + · exact source_gram_23_17_23 + · exact source_gram_23_19_1 + · exact source_gram_23_19_3 + · exact source_gram_23_19_5 + · exact source_gram_23_19_7 + · exact source_gram_23_19_9 + · exact source_gram_23_19_11 + · exact source_gram_23_19_13 + · exact source_gram_23_19_15 + · exact source_gram_23_19_17 + · exact source_gram_23_19_19 + · exact source_gram_23_19_21 + · exact source_gram_23_19_23 + · exact source_gram_23_21_1 + · exact source_gram_23_21_3 + · exact source_gram_23_21_5 + · exact source_gram_23_21_7 + · exact source_gram_23_21_9 + · exact source_gram_23_21_11 + · exact source_gram_23_21_13 + · exact source_gram_23_21_15 + · exact source_gram_23_21_17 + · exact source_gram_23_21_19 + · exact source_gram_23_21_21 + · exact source_gram_23_21_23 + · exact source_gram_23_23_1 + · exact source_gram_23_23_3 + · exact source_gram_23_23_5 + · exact source_gram_23_23_7 + · exact source_gram_23_23_9 + · exact source_gram_23_23_11 + · exact source_gram_23_23_13 + · exact source_gram_23_23_15 + · exact source_gram_23_23_17 + · exact source_gram_23_23_19 + · exact source_gram_23_23_21 + · exact source_gram_23_23_23 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDL08.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDL08.lean new file mode 100644 index 0000000000000000000000000000000000000000..c8ec9d7b1162e55ee62ed9a9122846adb754b080 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDL08.lean @@ -0,0 +1,109 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Error08 +import OAI.Analysis.Laughlin.FiniteFlux.Gram08 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData08 +import OAI.Analysis.Laughlin.FourBody.NumericBridge + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix + +theorem ldl_8_0_0 : compressedRational 8 0 0 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 0 0 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_0_1 : compressedRational 8 0 1 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 0 1 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_0_2 : compressedRational 8 0 2 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 0 2 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_0_3 : compressedRational 8 0 3 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 0 3 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_1_0 : compressedRational 8 1 0 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 1 0 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_1_1 : compressedRational 8 1 1 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 1 1 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_1_2 : compressedRational 8 1 2 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 1 2 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_1_3 : compressedRational 8 1 3 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 1 3 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_2_0 : compressedRational 8 2 0 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 2 0 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_2_1 : compressedRational 8 2 1 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 2 1 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_2_2 : compressedRational 8 2 2 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 2 2 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_2_3 : compressedRational 8 2 3 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 2 3 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_3_0 : compressedRational 8 3 0 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 3 0 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_3_1 : compressedRational 8 3 1 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 3 1 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_3_2 : compressedRational 8 3 2 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 3 2 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +theorem ldl_8_3_3 : compressedRational 8 3 3 = + (lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose) 3 3 := by + rw [compressedRational_eq_compute, error_8, gram_8] + rw [MatrixCompute.compressed_apply, MatrixCompute.ldl_apply] + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData08.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData08.lean new file mode 100644 index 0000000000000000000000000000000000000000..e395006035ba0eab518fcf5008828333c2da8eb5 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData08.lean @@ -0,0 +1,17 @@ +import OAI.Analysis.Laughlin.FourBody.Matrix + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix +def lower_8 : Matrix (Fin 4) (Fin 4) ℚ := + !![1, 0, 0, 0; + 0, 1, 0, 0; + 0, -1, 1, 0; + 0, 7/4, 0, 1] +def pivots_8 : Fin 4 → ℚ := + ![0, 38057801156652456127253649/187904819200000000000000, 0, 0] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData09.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData09.lean new file mode 100644 index 0000000000000000000000000000000000000000..e7e0b8b3b170004f7fd2dbdbcfd7686b26c9a4ad --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData09.lean @@ -0,0 +1,39 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL09 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_9 : MatrixCompute.compressed 9 candidateY_9 candidateZ_9 = + lower_9 * Matrix.diagonal pivots_9 * lower_9.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_9_0_0 + · exact computeLDL_9_0_1 + · exact computeLDL_9_0_2 + · exact computeLDL_9_0_3 + · exact computeLDL_9_0_4 + · exact computeLDL_9_1_0 + · exact computeLDL_9_1_1 + · exact computeLDL_9_1_2 + · exact computeLDL_9_1_3 + · exact computeLDL_9_1_4 + · exact computeLDL_9_2_0 + · exact computeLDL_9_2_1 + · exact computeLDL_9_2_2 + · exact computeLDL_9_2_3 + · exact computeLDL_9_2_4 + · exact computeLDL_9_3_0 + · exact computeLDL_9_3_1 + · exact computeLDL_9_3_2 + · exact computeLDL_9_3_3 + · exact computeLDL_9_3_4 + · exact computeLDL_9_4_0 + · exact computeLDL_9_4_1 + · exact computeLDL_9_4_2 + · exact computeLDL_9_4_3 + · exact computeLDL_9_4_4 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData10.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData10.lean new file mode 100644 index 0000000000000000000000000000000000000000..471a0345a6b77eceddff4a5022ec8de1b958fd3b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData10.lean @@ -0,0 +1,39 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL10 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_10 : MatrixCompute.compressed 10 candidateY_10 candidateZ_10 = + lower_10 * Matrix.diagonal pivots_10 * lower_10.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_10_0_0 + · exact computeLDL_10_0_1 + · exact computeLDL_10_0_2 + · exact computeLDL_10_0_3 + · exact computeLDL_10_0_4 + · exact computeLDL_10_1_0 + · exact computeLDL_10_1_1 + · exact computeLDL_10_1_2 + · exact computeLDL_10_1_3 + · exact computeLDL_10_1_4 + · exact computeLDL_10_2_0 + · exact computeLDL_10_2_1 + · exact computeLDL_10_2_2 + · exact computeLDL_10_2_3 + · exact computeLDL_10_2_4 + · exact computeLDL_10_3_0 + · exact computeLDL_10_3_1 + · exact computeLDL_10_3_2 + · exact computeLDL_10_3_3 + · exact computeLDL_10_3_4 + · exact computeLDL_10_4_0 + · exact computeLDL_10_4_1 + · exact computeLDL_10_4_2 + · exact computeLDL_10_4_3 + · exact computeLDL_10_4_4 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData11.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData11.lean new file mode 100644 index 0000000000000000000000000000000000000000..ae03142c5cf5b23f5d905e2097d0b7af9e2d979c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData11.lean @@ -0,0 +1,51 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL050511 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL11 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_11 : MatrixCompute.compressed 11 candidateY_11 candidateZ_11 = + lower_11 * Matrix.diagonal pivots_11 * lower_11.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_11_0_0 + · exact computeLDL_11_0_1 + · exact computeLDL_11_0_2 + · exact computeLDL_11_0_3 + · exact computeLDL_11_0_4 + · exact computeLDL_11_0_5 + · exact computeLDL_11_1_0 + · exact computeLDL_11_1_1 + · exact computeLDL_11_1_2 + · exact computeLDL_11_1_3 + · exact computeLDL_11_1_4 + · exact computeLDL_11_1_5 + · exact computeLDL_11_2_0 + · exact computeLDL_11_2_1 + · exact computeLDL_11_2_2 + · exact computeLDL_11_2_3 + · exact computeLDL_11_2_4 + · exact computeLDL_11_2_5 + · exact computeLDL_11_3_0 + · exact computeLDL_11_3_1 + · exact computeLDL_11_3_2 + · exact computeLDL_11_3_3 + · exact computeLDL_11_3_4 + · exact computeLDL_11_3_5 + · exact computeLDL_11_4_0 + · exact computeLDL_11_4_1 + · exact computeLDL_11_4_2 + · exact computeLDL_11_4_3 + · exact computeLDL_11_4_4 + · exact computeLDL_11_4_5 + · exact computeLDL_11_5_0 + · exact computeLDL_11_5_1 + · exact computeLDL_11_5_2 + · exact computeLDL_11_5_3 + · exact computeLDL_11_5_4 + · exact computeLDL_11_5_5 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData12.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData12.lean new file mode 100644 index 0000000000000000000000000000000000000000..c7cf587e364020dd5a3e7dfadfd9df050ddd2d54 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData12.lean @@ -0,0 +1,55 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL00Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL01Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL02Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL03Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL04Batch12 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL05Batch12 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_12 : MatrixCompute.compressed 12 candidateY_12 candidateZ_12 = + lower_12 * Matrix.diagonal pivots_12 * lower_12.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_12_0_0 + · exact computeLDL_12_0_1 + · exact computeLDL_12_0_2 + · exact computeLDL_12_0_3 + · exact computeLDL_12_0_4 + · exact computeLDL_12_0_5 + · exact computeLDL_12_1_0 + · exact computeLDL_12_1_1 + · exact computeLDL_12_1_2 + · exact computeLDL_12_1_3 + · exact computeLDL_12_1_4 + · exact computeLDL_12_1_5 + · exact computeLDL_12_2_0 + · exact computeLDL_12_2_1 + · exact computeLDL_12_2_2 + · exact computeLDL_12_2_3 + · exact computeLDL_12_2_4 + · exact computeLDL_12_2_5 + · exact computeLDL_12_3_0 + · exact computeLDL_12_3_1 + · exact computeLDL_12_3_2 + · exact computeLDL_12_3_3 + · exact computeLDL_12_3_4 + · exact computeLDL_12_3_5 + · exact computeLDL_12_4_0 + · exact computeLDL_12_4_1 + · exact computeLDL_12_4_2 + · exact computeLDL_12_4_3 + · exact computeLDL_12_4_4 + · exact computeLDL_12_4_5 + · exact computeLDL_12_5_0 + · exact computeLDL_12_5_1 + · exact computeLDL_12_5_2 + · exact computeLDL_12_5_3 + · exact computeLDL_12_5_4 + · exact computeLDL_12_5_5 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData13.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData13.lean new file mode 100644 index 0000000000000000000000000000000000000000..dedc2e2594218b030b51bfdc961f37a0dc0da0a8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData13.lean @@ -0,0 +1,69 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL00Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL01Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL02Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL03Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL04Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL05Batch13 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL06Batch13 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_13 : MatrixCompute.compressed 13 candidateY_13 candidateZ_13 = + lower_13 * Matrix.diagonal pivots_13 * lower_13.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_13_0_0 + · exact computeLDL_13_0_1 + · exact computeLDL_13_0_2 + · exact computeLDL_13_0_3 + · exact computeLDL_13_0_4 + · exact computeLDL_13_0_5 + · exact computeLDL_13_0_6 + · exact computeLDL_13_1_0 + · exact computeLDL_13_1_1 + · exact computeLDL_13_1_2 + · exact computeLDL_13_1_3 + · exact computeLDL_13_1_4 + · exact computeLDL_13_1_5 + · exact computeLDL_13_1_6 + · exact computeLDL_13_2_0 + · exact computeLDL_13_2_1 + · exact computeLDL_13_2_2 + · exact computeLDL_13_2_3 + · exact computeLDL_13_2_4 + · exact computeLDL_13_2_5 + · exact computeLDL_13_2_6 + · exact computeLDL_13_3_0 + · exact computeLDL_13_3_1 + · exact computeLDL_13_3_2 + · exact computeLDL_13_3_3 + · exact computeLDL_13_3_4 + · exact computeLDL_13_3_5 + · exact computeLDL_13_3_6 + · exact computeLDL_13_4_0 + · exact computeLDL_13_4_1 + · exact computeLDL_13_4_2 + · exact computeLDL_13_4_3 + · exact computeLDL_13_4_4 + · exact computeLDL_13_4_5 + · exact computeLDL_13_4_6 + · exact computeLDL_13_5_0 + · exact computeLDL_13_5_1 + · exact computeLDL_13_5_2 + · exact computeLDL_13_5_3 + · exact computeLDL_13_5_4 + · exact computeLDL_13_5_5 + · exact computeLDL_13_5_6 + · exact computeLDL_13_6_0 + · exact computeLDL_13_6_1 + · exact computeLDL_13_6_2 + · exact computeLDL_13_6_3 + · exact computeLDL_13_6_4 + · exact computeLDL_13_6_5 + · exact computeLDL_13_6_6 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData14.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData14.lean new file mode 100644 index 0000000000000000000000000000000000000000..c17c7f46fc65f5bd5178721c07a69e2e07fd7af5 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData14.lean @@ -0,0 +1,69 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL00Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL01Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL02Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL03Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL04Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL05Batch14 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL06Batch14 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_14 : MatrixCompute.compressed 14 candidateY_14 candidateZ_14 = + lower_14 * Matrix.diagonal pivots_14 * lower_14.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_14_0_0 + · exact computeLDL_14_0_1 + · exact computeLDL_14_0_2 + · exact computeLDL_14_0_3 + · exact computeLDL_14_0_4 + · exact computeLDL_14_0_5 + · exact computeLDL_14_0_6 + · exact computeLDL_14_1_0 + · exact computeLDL_14_1_1 + · exact computeLDL_14_1_2 + · exact computeLDL_14_1_3 + · exact computeLDL_14_1_4 + · exact computeLDL_14_1_5 + · exact computeLDL_14_1_6 + · exact computeLDL_14_2_0 + · exact computeLDL_14_2_1 + · exact computeLDL_14_2_2 + · exact computeLDL_14_2_3 + · exact computeLDL_14_2_4 + · exact computeLDL_14_2_5 + · exact computeLDL_14_2_6 + · exact computeLDL_14_3_0 + · exact computeLDL_14_3_1 + · exact computeLDL_14_3_2 + · exact computeLDL_14_3_3 + · exact computeLDL_14_3_4 + · exact computeLDL_14_3_5 + · exact computeLDL_14_3_6 + · exact computeLDL_14_4_0 + · exact computeLDL_14_4_1 + · exact computeLDL_14_4_2 + · exact computeLDL_14_4_3 + · exact computeLDL_14_4_4 + · exact computeLDL_14_4_5 + · exact computeLDL_14_4_6 + · exact computeLDL_14_5_0 + · exact computeLDL_14_5_1 + · exact computeLDL_14_5_2 + · exact computeLDL_14_5_3 + · exact computeLDL_14_5_4 + · exact computeLDL_14_5_5 + · exact computeLDL_14_5_6 + · exact computeLDL_14_6_0 + · exact computeLDL_14_6_1 + · exact computeLDL_14_6_2 + · exact computeLDL_14_6_3 + · exact computeLDL_14_6_4 + · exact computeLDL_14_6_5 + · exact computeLDL_14_6_6 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData15.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData15.lean new file mode 100644 index 0000000000000000000000000000000000000000..c39d1b7e79069156ac818289fc70eda224775660 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData15.lean @@ -0,0 +1,85 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL00Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL01Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL02Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL03Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL04Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL05Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL06Batch15 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL07Batch15 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_15 : MatrixCompute.compressed 15 candidateY_15 candidateZ_15 = + lower_15 * Matrix.diagonal pivots_15 * lower_15.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_15_0_0 + · exact computeLDL_15_0_1 + · exact computeLDL_15_0_2 + · exact computeLDL_15_0_3 + · exact computeLDL_15_0_4 + · exact computeLDL_15_0_5 + · exact computeLDL_15_0_6 + · exact computeLDL_15_0_7 + · exact computeLDL_15_1_0 + · exact computeLDL_15_1_1 + · exact computeLDL_15_1_2 + · exact computeLDL_15_1_3 + · exact computeLDL_15_1_4 + · exact computeLDL_15_1_5 + · exact computeLDL_15_1_6 + · exact computeLDL_15_1_7 + · exact computeLDL_15_2_0 + · exact computeLDL_15_2_1 + · exact computeLDL_15_2_2 + · exact computeLDL_15_2_3 + · exact computeLDL_15_2_4 + · exact computeLDL_15_2_5 + · exact computeLDL_15_2_6 + · exact computeLDL_15_2_7 + · exact computeLDL_15_3_0 + · exact computeLDL_15_3_1 + · exact computeLDL_15_3_2 + · exact computeLDL_15_3_3 + · exact computeLDL_15_3_4 + · exact computeLDL_15_3_5 + · exact computeLDL_15_3_6 + · exact computeLDL_15_3_7 + · exact computeLDL_15_4_0 + · exact computeLDL_15_4_1 + · exact computeLDL_15_4_2 + · exact computeLDL_15_4_3 + · exact computeLDL_15_4_4 + · exact computeLDL_15_4_5 + · exact computeLDL_15_4_6 + · exact computeLDL_15_4_7 + · exact computeLDL_15_5_0 + · exact computeLDL_15_5_1 + · exact computeLDL_15_5_2 + · exact computeLDL_15_5_3 + · exact computeLDL_15_5_4 + · exact computeLDL_15_5_5 + · exact computeLDL_15_5_6 + · exact computeLDL_15_5_7 + · exact computeLDL_15_6_0 + · exact computeLDL_15_6_1 + · exact computeLDL_15_6_2 + · exact computeLDL_15_6_3 + · exact computeLDL_15_6_4 + · exact computeLDL_15_6_5 + · exact computeLDL_15_6_6 + · exact computeLDL_15_6_7 + · exact computeLDL_15_7_0 + · exact computeLDL_15_7_1 + · exact computeLDL_15_7_2 + · exact computeLDL_15_7_3 + · exact computeLDL_15_7_4 + · exact computeLDL_15_7_5 + · exact computeLDL_15_7_6 + · exact computeLDL_15_7_7 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData16.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData16.lean new file mode 100644 index 0000000000000000000000000000000000000000..1ea6dd0917d94460b43202ca724925f8c51d6486 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData16.lean @@ -0,0 +1,85 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL00Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL01Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL02Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL03Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL04Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL05Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL06Batch16 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL07Batch16 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_16 : MatrixCompute.compressed 16 candidateY_16 candidateZ_16 = + lower_16 * Matrix.diagonal pivots_16 * lower_16.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_16_0_0 + · exact computeLDL_16_0_1 + · exact computeLDL_16_0_2 + · exact computeLDL_16_0_3 + · exact computeLDL_16_0_4 + · exact computeLDL_16_0_5 + · exact computeLDL_16_0_6 + · exact computeLDL_16_0_7 + · exact computeLDL_16_1_0 + · exact computeLDL_16_1_1 + · exact computeLDL_16_1_2 + · exact computeLDL_16_1_3 + · exact computeLDL_16_1_4 + · exact computeLDL_16_1_5 + · exact computeLDL_16_1_6 + · exact computeLDL_16_1_7 + · exact computeLDL_16_2_0 + · exact computeLDL_16_2_1 + · exact computeLDL_16_2_2 + · exact computeLDL_16_2_3 + · exact computeLDL_16_2_4 + · exact computeLDL_16_2_5 + · exact computeLDL_16_2_6 + · exact computeLDL_16_2_7 + · exact computeLDL_16_3_0 + · exact computeLDL_16_3_1 + · exact computeLDL_16_3_2 + · exact computeLDL_16_3_3 + · exact computeLDL_16_3_4 + · exact computeLDL_16_3_5 + · exact computeLDL_16_3_6 + · exact computeLDL_16_3_7 + · exact computeLDL_16_4_0 + · exact computeLDL_16_4_1 + · exact computeLDL_16_4_2 + · exact computeLDL_16_4_3 + · exact computeLDL_16_4_4 + · exact computeLDL_16_4_5 + · exact computeLDL_16_4_6 + · exact computeLDL_16_4_7 + · exact computeLDL_16_5_0 + · exact computeLDL_16_5_1 + · exact computeLDL_16_5_2 + · exact computeLDL_16_5_3 + · exact computeLDL_16_5_4 + · exact computeLDL_16_5_5 + · exact computeLDL_16_5_6 + · exact computeLDL_16_5_7 + · exact computeLDL_16_6_0 + · exact computeLDL_16_6_1 + · exact computeLDL_16_6_2 + · exact computeLDL_16_6_3 + · exact computeLDL_16_6_4 + · exact computeLDL_16_6_5 + · exact computeLDL_16_6_6 + · exact computeLDL_16_6_7 + · exact computeLDL_16_7_0 + · exact computeLDL_16_7_1 + · exact computeLDL_16_7_2 + · exact computeLDL_16_7_3 + · exact computeLDL_16_7_4 + · exact computeLDL_16_7_5 + · exact computeLDL_16_7_6 + · exact computeLDL_16_7_7 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData17.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData17.lean new file mode 100644 index 0000000000000000000000000000000000000000..95ede1516eaf671ca0155b723a1cebd8e4e23899 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData17.lean @@ -0,0 +1,103 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL00Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL01Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL02Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL03Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL04Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL05Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL06Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL07Batch17 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL08Batch17 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_17 : MatrixCompute.compressed 17 candidateY_17 candidateZ_17 = + lower_17 * Matrix.diagonal pivots_17 * lower_17.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_17_0_0 + · exact computeLDL_17_0_1 + · exact computeLDL_17_0_2 + · exact computeLDL_17_0_3 + · exact computeLDL_17_0_4 + · exact computeLDL_17_0_5 + · exact computeLDL_17_0_6 + · exact computeLDL_17_0_7 + · exact computeLDL_17_0_8 + · exact computeLDL_17_1_0 + · exact computeLDL_17_1_1 + · exact computeLDL_17_1_2 + · exact computeLDL_17_1_3 + · exact computeLDL_17_1_4 + · exact computeLDL_17_1_5 + · exact computeLDL_17_1_6 + · exact computeLDL_17_1_7 + · exact computeLDL_17_1_8 + · exact computeLDL_17_2_0 + · exact computeLDL_17_2_1 + · exact computeLDL_17_2_2 + · exact computeLDL_17_2_3 + · exact computeLDL_17_2_4 + · exact computeLDL_17_2_5 + · exact computeLDL_17_2_6 + · exact computeLDL_17_2_7 + · exact computeLDL_17_2_8 + · exact computeLDL_17_3_0 + · exact computeLDL_17_3_1 + · exact computeLDL_17_3_2 + · exact computeLDL_17_3_3 + · exact computeLDL_17_3_4 + · exact computeLDL_17_3_5 + · exact computeLDL_17_3_6 + · exact computeLDL_17_3_7 + · exact computeLDL_17_3_8 + · exact computeLDL_17_4_0 + · exact computeLDL_17_4_1 + · exact computeLDL_17_4_2 + · exact computeLDL_17_4_3 + · exact computeLDL_17_4_4 + · exact computeLDL_17_4_5 + · exact computeLDL_17_4_6 + · exact computeLDL_17_4_7 + · exact computeLDL_17_4_8 + · exact computeLDL_17_5_0 + · exact computeLDL_17_5_1 + · exact computeLDL_17_5_2 + · exact computeLDL_17_5_3 + · exact computeLDL_17_5_4 + · exact computeLDL_17_5_5 + · exact computeLDL_17_5_6 + · exact computeLDL_17_5_7 + · exact computeLDL_17_5_8 + · exact computeLDL_17_6_0 + · exact computeLDL_17_6_1 + · exact computeLDL_17_6_2 + · exact computeLDL_17_6_3 + · exact computeLDL_17_6_4 + · exact computeLDL_17_6_5 + · exact computeLDL_17_6_6 + · exact computeLDL_17_6_7 + · exact computeLDL_17_6_8 + · exact computeLDL_17_7_0 + · exact computeLDL_17_7_1 + · exact computeLDL_17_7_2 + · exact computeLDL_17_7_3 + · exact computeLDL_17_7_4 + · exact computeLDL_17_7_5 + · exact computeLDL_17_7_6 + · exact computeLDL_17_7_7 + · exact computeLDL_17_7_8 + · exact computeLDL_17_8_0 + · exact computeLDL_17_8_1 + · exact computeLDL_17_8_2 + · exact computeLDL_17_8_3 + · exact computeLDL_17_8_4 + · exact computeLDL_17_8_5 + · exact computeLDL_17_8_6 + · exact computeLDL_17_8_7 + · exact computeLDL_17_8_8 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData18.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData18.lean new file mode 100644 index 0000000000000000000000000000000000000000..9a29fbcf1e5331f42d29ccf45b00f6ae44fb1c71 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData18.lean @@ -0,0 +1,103 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL00Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL01Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL02Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL03Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL04Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL05Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL06Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL07Batch18 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL08Batch18 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_18 : MatrixCompute.compressed 18 candidateY_18 candidateZ_18 = + lower_18 * Matrix.diagonal pivots_18 * lower_18.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_18_0_0 + · exact computeLDL_18_0_1 + · exact computeLDL_18_0_2 + · exact computeLDL_18_0_3 + · exact computeLDL_18_0_4 + · exact computeLDL_18_0_5 + · exact computeLDL_18_0_6 + · exact computeLDL_18_0_7 + · exact computeLDL_18_0_8 + · exact computeLDL_18_1_0 + · exact computeLDL_18_1_1 + · exact computeLDL_18_1_2 + · exact computeLDL_18_1_3 + · exact computeLDL_18_1_4 + · exact computeLDL_18_1_5 + · exact computeLDL_18_1_6 + · exact computeLDL_18_1_7 + · exact computeLDL_18_1_8 + · exact computeLDL_18_2_0 + · exact computeLDL_18_2_1 + · exact computeLDL_18_2_2 + · exact computeLDL_18_2_3 + · exact computeLDL_18_2_4 + · exact computeLDL_18_2_5 + · exact computeLDL_18_2_6 + · exact computeLDL_18_2_7 + · exact computeLDL_18_2_8 + · exact computeLDL_18_3_0 + · exact computeLDL_18_3_1 + · exact computeLDL_18_3_2 + · exact computeLDL_18_3_3 + · exact computeLDL_18_3_4 + · exact computeLDL_18_3_5 + · exact computeLDL_18_3_6 + · exact computeLDL_18_3_7 + · exact computeLDL_18_3_8 + · exact computeLDL_18_4_0 + · exact computeLDL_18_4_1 + · exact computeLDL_18_4_2 + · exact computeLDL_18_4_3 + · exact computeLDL_18_4_4 + · exact computeLDL_18_4_5 + · exact computeLDL_18_4_6 + · exact computeLDL_18_4_7 + · exact computeLDL_18_4_8 + · exact computeLDL_18_5_0 + · exact computeLDL_18_5_1 + · exact computeLDL_18_5_2 + · exact computeLDL_18_5_3 + · exact computeLDL_18_5_4 + · exact computeLDL_18_5_5 + · exact computeLDL_18_5_6 + · exact computeLDL_18_5_7 + · exact computeLDL_18_5_8 + · exact computeLDL_18_6_0 + · exact computeLDL_18_6_1 + · exact computeLDL_18_6_2 + · exact computeLDL_18_6_3 + · exact computeLDL_18_6_4 + · exact computeLDL_18_6_5 + · exact computeLDL_18_6_6 + · exact computeLDL_18_6_7 + · exact computeLDL_18_6_8 + · exact computeLDL_18_7_0 + · exact computeLDL_18_7_1 + · exact computeLDL_18_7_2 + · exact computeLDL_18_7_3 + · exact computeLDL_18_7_4 + · exact computeLDL_18_7_5 + · exact computeLDL_18_7_6 + · exact computeLDL_18_7_7 + · exact computeLDL_18_7_8 + · exact computeLDL_18_8_0 + · exact computeLDL_18_8_1 + · exact computeLDL_18_8_2 + · exact computeLDL_18_8_3 + · exact computeLDL_18_8_4 + · exact computeLDL_18_8_5 + · exact computeLDL_18_8_6 + · exact computeLDL_18_8_7 + · exact computeLDL_18_8_8 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData19.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData19.lean new file mode 100644 index 0000000000000000000000000000000000000000..9ee5c09dc4899339b96259e9a1b2098238fb2d86 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData19.lean @@ -0,0 +1,123 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL00Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL01Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL02Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL03Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL04Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL05Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL06Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL07Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL08Batch19 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL09Batch19 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_19 : MatrixCompute.compressed 19 candidateY_19 candidateZ_19 = + lower_19 * Matrix.diagonal pivots_19 * lower_19.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_19_0_0 + · exact computeLDL_19_0_1 + · exact computeLDL_19_0_2 + · exact computeLDL_19_0_3 + · exact computeLDL_19_0_4 + · exact computeLDL_19_0_5 + · exact computeLDL_19_0_6 + · exact computeLDL_19_0_7 + · exact computeLDL_19_0_8 + · exact computeLDL_19_0_9 + · exact computeLDL_19_1_0 + · exact computeLDL_19_1_1 + · exact computeLDL_19_1_2 + · exact computeLDL_19_1_3 + · exact computeLDL_19_1_4 + · exact computeLDL_19_1_5 + · exact computeLDL_19_1_6 + · exact computeLDL_19_1_7 + · exact computeLDL_19_1_8 + · exact computeLDL_19_1_9 + · exact computeLDL_19_2_0 + · exact computeLDL_19_2_1 + · exact computeLDL_19_2_2 + · exact computeLDL_19_2_3 + · exact computeLDL_19_2_4 + · exact computeLDL_19_2_5 + · exact computeLDL_19_2_6 + · exact computeLDL_19_2_7 + · exact computeLDL_19_2_8 + · exact computeLDL_19_2_9 + · exact computeLDL_19_3_0 + · exact computeLDL_19_3_1 + · exact computeLDL_19_3_2 + · exact computeLDL_19_3_3 + · exact computeLDL_19_3_4 + · exact computeLDL_19_3_5 + · exact computeLDL_19_3_6 + · exact computeLDL_19_3_7 + · exact computeLDL_19_3_8 + · exact computeLDL_19_3_9 + · exact computeLDL_19_4_0 + · exact computeLDL_19_4_1 + · exact computeLDL_19_4_2 + · exact computeLDL_19_4_3 + · exact computeLDL_19_4_4 + · exact computeLDL_19_4_5 + · exact computeLDL_19_4_6 + · exact computeLDL_19_4_7 + · exact computeLDL_19_4_8 + · exact computeLDL_19_4_9 + · exact computeLDL_19_5_0 + · exact computeLDL_19_5_1 + · exact computeLDL_19_5_2 + · exact computeLDL_19_5_3 + · exact computeLDL_19_5_4 + · exact computeLDL_19_5_5 + · exact computeLDL_19_5_6 + · exact computeLDL_19_5_7 + · exact computeLDL_19_5_8 + · exact computeLDL_19_5_9 + · exact computeLDL_19_6_0 + · exact computeLDL_19_6_1 + · exact computeLDL_19_6_2 + · exact computeLDL_19_6_3 + · exact computeLDL_19_6_4 + · exact computeLDL_19_6_5 + · exact computeLDL_19_6_6 + · exact computeLDL_19_6_7 + · exact computeLDL_19_6_8 + · exact computeLDL_19_6_9 + · exact computeLDL_19_7_0 + · exact computeLDL_19_7_1 + · exact computeLDL_19_7_2 + · exact computeLDL_19_7_3 + · exact computeLDL_19_7_4 + · exact computeLDL_19_7_5 + · exact computeLDL_19_7_6 + · exact computeLDL_19_7_7 + · exact computeLDL_19_7_8 + · exact computeLDL_19_7_9 + · exact computeLDL_19_8_0 + · exact computeLDL_19_8_1 + · exact computeLDL_19_8_2 + · exact computeLDL_19_8_3 + · exact computeLDL_19_8_4 + · exact computeLDL_19_8_5 + · exact computeLDL_19_8_6 + · exact computeLDL_19_8_7 + · exact computeLDL_19_8_8 + · exact computeLDL_19_8_9 + · exact computeLDL_19_9_0 + · exact computeLDL_19_9_1 + · exact computeLDL_19_9_2 + · exact computeLDL_19_9_3 + · exact computeLDL_19_9_4 + · exact computeLDL_19_9_5 + · exact computeLDL_19_9_6 + · exact computeLDL_19_9_7 + · exact computeLDL_19_9_8 + · exact computeLDL_19_9_9 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData20.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData20.lean new file mode 100644 index 0000000000000000000000000000000000000000..5ca0daccc4f6d9da168c1d19a3ebc609f9b85f92 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData20.lean @@ -0,0 +1,123 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL00Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL01Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL02Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL03Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL04Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL05Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL06Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL07Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL08Batch20 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL09Batch20 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_20 : MatrixCompute.compressed 20 candidateY_20 candidateZ_20 = + lower_20 * Matrix.diagonal pivots_20 * lower_20.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_20_0_0 + · exact computeLDL_20_0_1 + · exact computeLDL_20_0_2 + · exact computeLDL_20_0_3 + · exact computeLDL_20_0_4 + · exact computeLDL_20_0_5 + · exact computeLDL_20_0_6 + · exact computeLDL_20_0_7 + · exact computeLDL_20_0_8 + · exact computeLDL_20_0_9 + · exact computeLDL_20_1_0 + · exact computeLDL_20_1_1 + · exact computeLDL_20_1_2 + · exact computeLDL_20_1_3 + · exact computeLDL_20_1_4 + · exact computeLDL_20_1_5 + · exact computeLDL_20_1_6 + · exact computeLDL_20_1_7 + · exact computeLDL_20_1_8 + · exact computeLDL_20_1_9 + · exact computeLDL_20_2_0 + · exact computeLDL_20_2_1 + · exact computeLDL_20_2_2 + · exact computeLDL_20_2_3 + · exact computeLDL_20_2_4 + · exact computeLDL_20_2_5 + · exact computeLDL_20_2_6 + · exact computeLDL_20_2_7 + · exact computeLDL_20_2_8 + · exact computeLDL_20_2_9 + · exact computeLDL_20_3_0 + · exact computeLDL_20_3_1 + · exact computeLDL_20_3_2 + · exact computeLDL_20_3_3 + · exact computeLDL_20_3_4 + · exact computeLDL_20_3_5 + · exact computeLDL_20_3_6 + · exact computeLDL_20_3_7 + · exact computeLDL_20_3_8 + · exact computeLDL_20_3_9 + · exact computeLDL_20_4_0 + · exact computeLDL_20_4_1 + · exact computeLDL_20_4_2 + · exact computeLDL_20_4_3 + · exact computeLDL_20_4_4 + · exact computeLDL_20_4_5 + · exact computeLDL_20_4_6 + · exact computeLDL_20_4_7 + · exact computeLDL_20_4_8 + · exact computeLDL_20_4_9 + · exact computeLDL_20_5_0 + · exact computeLDL_20_5_1 + · exact computeLDL_20_5_2 + · exact computeLDL_20_5_3 + · exact computeLDL_20_5_4 + · exact computeLDL_20_5_5 + · exact computeLDL_20_5_6 + · exact computeLDL_20_5_7 + · exact computeLDL_20_5_8 + · exact computeLDL_20_5_9 + · exact computeLDL_20_6_0 + · exact computeLDL_20_6_1 + · exact computeLDL_20_6_2 + · exact computeLDL_20_6_3 + · exact computeLDL_20_6_4 + · exact computeLDL_20_6_5 + · exact computeLDL_20_6_6 + · exact computeLDL_20_6_7 + · exact computeLDL_20_6_8 + · exact computeLDL_20_6_9 + · exact computeLDL_20_7_0 + · exact computeLDL_20_7_1 + · exact computeLDL_20_7_2 + · exact computeLDL_20_7_3 + · exact computeLDL_20_7_4 + · exact computeLDL_20_7_5 + · exact computeLDL_20_7_6 + · exact computeLDL_20_7_7 + · exact computeLDL_20_7_8 + · exact computeLDL_20_7_9 + · exact computeLDL_20_8_0 + · exact computeLDL_20_8_1 + · exact computeLDL_20_8_2 + · exact computeLDL_20_8_3 + · exact computeLDL_20_8_4 + · exact computeLDL_20_8_5 + · exact computeLDL_20_8_6 + · exact computeLDL_20_8_7 + · exact computeLDL_20_8_8 + · exact computeLDL_20_8_9 + · exact computeLDL_20_9_0 + · exact computeLDL_20_9_1 + · exact computeLDL_20_9_2 + · exact computeLDL_20_9_3 + · exact computeLDL_20_9_4 + · exact computeLDL_20_9_5 + · exact computeLDL_20_9_6 + · exact computeLDL_20_9_7 + · exact computeLDL_20_9_8 + · exact computeLDL_20_9_9 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData21.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData21.lean new file mode 100644 index 0000000000000000000000000000000000000000..e86b5adec1c8f13669fbd8415e20c2c8993dcdc1 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData21.lean @@ -0,0 +1,145 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL00Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL01Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL02Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL03Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL04Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL05Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL06Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL07Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL08Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL09Batch21 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL10Batch21 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_21 : MatrixCompute.compressed 21 candidateY_21 candidateZ_21 = + lower_21 * Matrix.diagonal pivots_21 * lower_21.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_21_0_0 + · exact computeLDL_21_0_1 + · exact computeLDL_21_0_2 + · exact computeLDL_21_0_3 + · exact computeLDL_21_0_4 + · exact computeLDL_21_0_5 + · exact computeLDL_21_0_6 + · exact computeLDL_21_0_7 + · exact computeLDL_21_0_8 + · exact computeLDL_21_0_9 + · exact computeLDL_21_0_10 + · exact computeLDL_21_1_0 + · exact computeLDL_21_1_1 + · exact computeLDL_21_1_2 + · exact computeLDL_21_1_3 + · exact computeLDL_21_1_4 + · exact computeLDL_21_1_5 + · exact computeLDL_21_1_6 + · exact computeLDL_21_1_7 + · exact computeLDL_21_1_8 + · exact computeLDL_21_1_9 + · exact computeLDL_21_1_10 + · exact computeLDL_21_2_0 + · exact computeLDL_21_2_1 + · exact computeLDL_21_2_2 + · exact computeLDL_21_2_3 + · exact computeLDL_21_2_4 + · exact computeLDL_21_2_5 + · exact computeLDL_21_2_6 + · exact computeLDL_21_2_7 + · exact computeLDL_21_2_8 + · exact computeLDL_21_2_9 + · exact computeLDL_21_2_10 + · exact computeLDL_21_3_0 + · exact computeLDL_21_3_1 + · exact computeLDL_21_3_2 + · exact computeLDL_21_3_3 + · exact computeLDL_21_3_4 + · exact computeLDL_21_3_5 + · exact computeLDL_21_3_6 + · exact computeLDL_21_3_7 + · exact computeLDL_21_3_8 + · exact computeLDL_21_3_9 + · exact computeLDL_21_3_10 + · exact computeLDL_21_4_0 + · exact computeLDL_21_4_1 + · exact computeLDL_21_4_2 + · exact computeLDL_21_4_3 + · exact computeLDL_21_4_4 + · exact computeLDL_21_4_5 + · exact computeLDL_21_4_6 + · exact computeLDL_21_4_7 + · exact computeLDL_21_4_8 + · exact computeLDL_21_4_9 + · exact computeLDL_21_4_10 + · exact computeLDL_21_5_0 + · exact computeLDL_21_5_1 + · exact computeLDL_21_5_2 + · exact computeLDL_21_5_3 + · exact computeLDL_21_5_4 + · exact computeLDL_21_5_5 + · exact computeLDL_21_5_6 + · exact computeLDL_21_5_7 + · exact computeLDL_21_5_8 + · exact computeLDL_21_5_9 + · exact computeLDL_21_5_10 + · exact computeLDL_21_6_0 + · exact computeLDL_21_6_1 + · exact computeLDL_21_6_2 + · exact computeLDL_21_6_3 + · exact computeLDL_21_6_4 + · exact computeLDL_21_6_5 + · exact computeLDL_21_6_6 + · exact computeLDL_21_6_7 + · exact computeLDL_21_6_8 + · exact computeLDL_21_6_9 + · exact computeLDL_21_6_10 + · exact computeLDL_21_7_0 + · exact computeLDL_21_7_1 + · exact computeLDL_21_7_2 + · exact computeLDL_21_7_3 + · exact computeLDL_21_7_4 + · exact computeLDL_21_7_5 + · exact computeLDL_21_7_6 + · exact computeLDL_21_7_7 + · exact computeLDL_21_7_8 + · exact computeLDL_21_7_9 + · exact computeLDL_21_7_10 + · exact computeLDL_21_8_0 + · exact computeLDL_21_8_1 + · exact computeLDL_21_8_2 + · exact computeLDL_21_8_3 + · exact computeLDL_21_8_4 + · exact computeLDL_21_8_5 + · exact computeLDL_21_8_6 + · exact computeLDL_21_8_7 + · exact computeLDL_21_8_8 + · exact computeLDL_21_8_9 + · exact computeLDL_21_8_10 + · exact computeLDL_21_9_0 + · exact computeLDL_21_9_1 + · exact computeLDL_21_9_2 + · exact computeLDL_21_9_3 + · exact computeLDL_21_9_4 + · exact computeLDL_21_9_5 + · exact computeLDL_21_9_6 + · exact computeLDL_21_9_7 + · exact computeLDL_21_9_8 + · exact computeLDL_21_9_9 + · exact computeLDL_21_9_10 + · exact computeLDL_21_10_0 + · exact computeLDL_21_10_1 + · exact computeLDL_21_10_2 + · exact computeLDL_21_10_3 + · exact computeLDL_21_10_4 + · exact computeLDL_21_10_5 + · exact computeLDL_21_10_6 + · exact computeLDL_21_10_7 + · exact computeLDL_21_10_8 + · exact computeLDL_21_10_9 + · exact computeLDL_21_10_10 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData22.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData22.lean new file mode 100644 index 0000000000000000000000000000000000000000..c42df0b34b6dfccbb506a9b6976d098c97de04ef --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData22.lean @@ -0,0 +1,145 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL00Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL01Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL02Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL03Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL04Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL05Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL06Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL07Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL08Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL09Batch22 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL10Batch22 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_22 : MatrixCompute.compressed 22 candidateY_22 candidateZ_22 = + lower_22 * Matrix.diagonal pivots_22 * lower_22.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_22_0_0 + · exact computeLDL_22_0_1 + · exact computeLDL_22_0_2 + · exact computeLDL_22_0_3 + · exact computeLDL_22_0_4 + · exact computeLDL_22_0_5 + · exact computeLDL_22_0_6 + · exact computeLDL_22_0_7 + · exact computeLDL_22_0_8 + · exact computeLDL_22_0_9 + · exact computeLDL_22_0_10 + · exact computeLDL_22_1_0 + · exact computeLDL_22_1_1 + · exact computeLDL_22_1_2 + · exact computeLDL_22_1_3 + · exact computeLDL_22_1_4 + · exact computeLDL_22_1_5 + · exact computeLDL_22_1_6 + · exact computeLDL_22_1_7 + · exact computeLDL_22_1_8 + · exact computeLDL_22_1_9 + · exact computeLDL_22_1_10 + · exact computeLDL_22_2_0 + · exact computeLDL_22_2_1 + · exact computeLDL_22_2_2 + · exact computeLDL_22_2_3 + · exact computeLDL_22_2_4 + · exact computeLDL_22_2_5 + · exact computeLDL_22_2_6 + · exact computeLDL_22_2_7 + · exact computeLDL_22_2_8 + · exact computeLDL_22_2_9 + · exact computeLDL_22_2_10 + · exact computeLDL_22_3_0 + · exact computeLDL_22_3_1 + · exact computeLDL_22_3_2 + · exact computeLDL_22_3_3 + · exact computeLDL_22_3_4 + · exact computeLDL_22_3_5 + · exact computeLDL_22_3_6 + · exact computeLDL_22_3_7 + · exact computeLDL_22_3_8 + · exact computeLDL_22_3_9 + · exact computeLDL_22_3_10 + · exact computeLDL_22_4_0 + · exact computeLDL_22_4_1 + · exact computeLDL_22_4_2 + · exact computeLDL_22_4_3 + · exact computeLDL_22_4_4 + · exact computeLDL_22_4_5 + · exact computeLDL_22_4_6 + · exact computeLDL_22_4_7 + · exact computeLDL_22_4_8 + · exact computeLDL_22_4_9 + · exact computeLDL_22_4_10 + · exact computeLDL_22_5_0 + · exact computeLDL_22_5_1 + · exact computeLDL_22_5_2 + · exact computeLDL_22_5_3 + · exact computeLDL_22_5_4 + · exact computeLDL_22_5_5 + · exact computeLDL_22_5_6 + · exact computeLDL_22_5_7 + · exact computeLDL_22_5_8 + · exact computeLDL_22_5_9 + · exact computeLDL_22_5_10 + · exact computeLDL_22_6_0 + · exact computeLDL_22_6_1 + · exact computeLDL_22_6_2 + · exact computeLDL_22_6_3 + · exact computeLDL_22_6_4 + · exact computeLDL_22_6_5 + · exact computeLDL_22_6_6 + · exact computeLDL_22_6_7 + · exact computeLDL_22_6_8 + · exact computeLDL_22_6_9 + · exact computeLDL_22_6_10 + · exact computeLDL_22_7_0 + · exact computeLDL_22_7_1 + · exact computeLDL_22_7_2 + · exact computeLDL_22_7_3 + · exact computeLDL_22_7_4 + · exact computeLDL_22_7_5 + · exact computeLDL_22_7_6 + · exact computeLDL_22_7_7 + · exact computeLDL_22_7_8 + · exact computeLDL_22_7_9 + · exact computeLDL_22_7_10 + · exact computeLDL_22_8_0 + · exact computeLDL_22_8_1 + · exact computeLDL_22_8_2 + · exact computeLDL_22_8_3 + · exact computeLDL_22_8_4 + · exact computeLDL_22_8_5 + · exact computeLDL_22_8_6 + · exact computeLDL_22_8_7 + · exact computeLDL_22_8_8 + · exact computeLDL_22_8_9 + · exact computeLDL_22_8_10 + · exact computeLDL_22_9_0 + · exact computeLDL_22_9_1 + · exact computeLDL_22_9_2 + · exact computeLDL_22_9_3 + · exact computeLDL_22_9_4 + · exact computeLDL_22_9_5 + · exact computeLDL_22_9_6 + · exact computeLDL_22_9_7 + · exact computeLDL_22_9_8 + · exact computeLDL_22_9_9 + · exact computeLDL_22_9_10 + · exact computeLDL_22_10_0 + · exact computeLDL_22_10_1 + · exact computeLDL_22_10_2 + · exact computeLDL_22_10_3 + · exact computeLDL_22_10_4 + · exact computeLDL_22_10_5 + · exact computeLDL_22_10_6 + · exact computeLDL_22_10_7 + · exact computeLDL_22_10_8 + · exact computeLDL_22_10_9 + · exact computeLDL_22_10_10 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData23.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData23.lean new file mode 100644 index 0000000000000000000000000000000000000000..d93a4ee26c1876388fc473099476a6946c149601 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/LDLData23.lean @@ -0,0 +1,169 @@ +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL00Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL01Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL02Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL03Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL04Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL05Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL06Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL07Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL08Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL09Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL10Batch23 +import OAI.Analysis.Laughlin.FiniteFlux.ComputeLDL11Batch23 + +namespace OAI + +namespace Laughlin.Certificate +theorem candidateLDL_23 : MatrixCompute.compressed 23 candidateY_23 candidateZ_23 = + lower_23 * Matrix.diagonal pivots_23 * lower_23.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact computeLDL_23_0_0 + · exact computeLDL_23_0_1 + · exact computeLDL_23_0_2 + · exact computeLDL_23_0_3 + · exact computeLDL_23_0_4 + · exact computeLDL_23_0_5 + · exact computeLDL_23_0_6 + · exact computeLDL_23_0_7 + · exact computeLDL_23_0_8 + · exact computeLDL_23_0_9 + · exact computeLDL_23_0_10 + · exact computeLDL_23_0_11 + · exact computeLDL_23_1_0 + · exact computeLDL_23_1_1 + · exact computeLDL_23_1_2 + · exact computeLDL_23_1_3 + · exact computeLDL_23_1_4 + · exact computeLDL_23_1_5 + · exact computeLDL_23_1_6 + · exact computeLDL_23_1_7 + · exact computeLDL_23_1_8 + · exact computeLDL_23_1_9 + · exact computeLDL_23_1_10 + · exact computeLDL_23_1_11 + · exact computeLDL_23_2_0 + · exact computeLDL_23_2_1 + · exact computeLDL_23_2_2 + · exact computeLDL_23_2_3 + · exact computeLDL_23_2_4 + · exact computeLDL_23_2_5 + · exact computeLDL_23_2_6 + · exact computeLDL_23_2_7 + · exact computeLDL_23_2_8 + · exact computeLDL_23_2_9 + · exact computeLDL_23_2_10 + · exact computeLDL_23_2_11 + · exact computeLDL_23_3_0 + · exact computeLDL_23_3_1 + · exact computeLDL_23_3_2 + · exact computeLDL_23_3_3 + · exact computeLDL_23_3_4 + · exact computeLDL_23_3_5 + · exact computeLDL_23_3_6 + · exact computeLDL_23_3_7 + · exact computeLDL_23_3_8 + · exact computeLDL_23_3_9 + · exact computeLDL_23_3_10 + · exact computeLDL_23_3_11 + · exact computeLDL_23_4_0 + · exact computeLDL_23_4_1 + · exact computeLDL_23_4_2 + · exact computeLDL_23_4_3 + · exact computeLDL_23_4_4 + · exact computeLDL_23_4_5 + · exact computeLDL_23_4_6 + · exact computeLDL_23_4_7 + · exact computeLDL_23_4_8 + · exact computeLDL_23_4_9 + · exact computeLDL_23_4_10 + · exact computeLDL_23_4_11 + · exact computeLDL_23_5_0 + · exact computeLDL_23_5_1 + · exact computeLDL_23_5_2 + · exact computeLDL_23_5_3 + · exact computeLDL_23_5_4 + · exact computeLDL_23_5_5 + · exact computeLDL_23_5_6 + · exact computeLDL_23_5_7 + · exact computeLDL_23_5_8 + · exact computeLDL_23_5_9 + · exact computeLDL_23_5_10 + · exact computeLDL_23_5_11 + · exact computeLDL_23_6_0 + · exact computeLDL_23_6_1 + · exact computeLDL_23_6_2 + · exact computeLDL_23_6_3 + · exact computeLDL_23_6_4 + · exact computeLDL_23_6_5 + · exact computeLDL_23_6_6 + · exact computeLDL_23_6_7 + · exact computeLDL_23_6_8 + · exact computeLDL_23_6_9 + · exact computeLDL_23_6_10 + · exact computeLDL_23_6_11 + · exact computeLDL_23_7_0 + · exact computeLDL_23_7_1 + · exact computeLDL_23_7_2 + · exact computeLDL_23_7_3 + · exact computeLDL_23_7_4 + · exact computeLDL_23_7_5 + · exact computeLDL_23_7_6 + · exact computeLDL_23_7_7 + · exact computeLDL_23_7_8 + · exact computeLDL_23_7_9 + · exact computeLDL_23_7_10 + · exact computeLDL_23_7_11 + · exact computeLDL_23_8_0 + · exact computeLDL_23_8_1 + · exact computeLDL_23_8_2 + · exact computeLDL_23_8_3 + · exact computeLDL_23_8_4 + · exact computeLDL_23_8_5 + · exact computeLDL_23_8_6 + · exact computeLDL_23_8_7 + · exact computeLDL_23_8_8 + · exact computeLDL_23_8_9 + · exact computeLDL_23_8_10 + · exact computeLDL_23_8_11 + · exact computeLDL_23_9_0 + · exact computeLDL_23_9_1 + · exact computeLDL_23_9_2 + · exact computeLDL_23_9_3 + · exact computeLDL_23_9_4 + · exact computeLDL_23_9_5 + · exact computeLDL_23_9_6 + · exact computeLDL_23_9_7 + · exact computeLDL_23_9_8 + · exact computeLDL_23_9_9 + · exact computeLDL_23_9_10 + · exact computeLDL_23_9_11 + · exact computeLDL_23_10_0 + · exact computeLDL_23_10_1 + · exact computeLDL_23_10_2 + · exact computeLDL_23_10_3 + · exact computeLDL_23_10_4 + · exact computeLDL_23_10_5 + · exact computeLDL_23_10_6 + · exact computeLDL_23_10_7 + · exact computeLDL_23_10_8 + · exact computeLDL_23_10_9 + · exact computeLDL_23_10_10 + · exact computeLDL_23_10_11 + · exact computeLDL_23_11_0 + · exact computeLDL_23_11_1 + · exact computeLDL_23_11_2 + · exact computeLDL_23_11_3 + · exact computeLDL_23_11_4 + · exact computeLDL_23_11_5 + · exact computeLDL_23_11_6 + · exact computeLDL_23_11_7 + · exact computeLDL_23_11_8 + · exact computeLDL_23_11_9 + · exact computeLDL_23_11_10 + · exact computeLDL_23_11_11 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive05.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive05.lean new file mode 100644 index 0000000000000000000000000000000000000000..01403d6e87a048886db90f40d955ca68ad66782f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive05.lean @@ -0,0 +1,30 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Error05 +import OAI.Analysis.Laughlin.FourBody.Matrix + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix + +def lowerFive : Matrix (Fin 3) (Fin 3) ℚ := + !![1, 0, 0; -1/2, 1, 0; 5/4, 0, 1] + +def pivotsFive : Fin 3 → ℚ := + ![56737668577815655510619653/300647710720000000000000, 0, 0] + + +theorem ldl_five : compressedRational 5 = + lowerFive * Matrix.diagonal pivotsFive * lowerFive.transpose := by + unfold compressedRational middleRational + rw [gram_five, error_five] + decide +kernel + +theorem four_body_five_positive : + ((compressedRational 5).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lowerFive pivotsFive ldl_five + intro i + fin_cases i <;> norm_num [pivotsFive] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive07.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive07.lean new file mode 100644 index 0000000000000000000000000000000000000000..b104a6a34ce71bf4304aba746cc29776533a1de0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive07.lean @@ -0,0 +1,30 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Error07 +import OAI.Analysis.Laughlin.FiniteFlux.Gram07 +import OAI.Analysis.Laughlin.FourBody.Matrix + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix +def lower_7 : Matrix (Fin 4) (Fin 4) ℚ := + !![1, 0, 0, 0; + 0, 1, 0, 0; + -1/4, 0, 1, 0; + 7/4, 0, 0, 1] +def pivots_7 : Fin 4 → ℚ := + ![4554569876705321270859037803/751619276800000000000000, 0, 0, 0] + +theorem ldl_7 : compressedRational 7 = + lower_7 * Matrix.diagonal pivots_7 * lower_7.transpose := by + unfold compressedRational middleRational + rw [gram_7, error_7] + decide +kernel +theorem four_body_7_positive : + ((compressedRational 7).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_7 pivots_7 ldl_7 + intro i + fin_cases i <;> norm_num [pivots_7] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive08.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive08.lean new file mode 100644 index 0000000000000000000000000000000000000000..b06e0ac35fc9d24528d76cd3e60514ca65d1c630 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive08.lean @@ -0,0 +1,36 @@ +import OAI.Analysis.Laughlin.FiniteFlux.LDL08 + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix + +theorem ldl_8 : compressedRational 8 = + lower_8 * Matrix.diagonal pivots_8 * lower_8.transpose := by + ext i j + fin_cases i <;> fin_cases j + · exact ldl_8_0_0 + · exact ldl_8_0_1 + · exact ldl_8_0_2 + · exact ldl_8_0_3 + · exact ldl_8_1_0 + · exact ldl_8_1_1 + · exact ldl_8_1_2 + · exact ldl_8_1_3 + · exact ldl_8_2_0 + · exact ldl_8_2_1 + · exact ldl_8_2_2 + · exact ldl_8_2_3 + · exact ldl_8_3_0 + · exact ldl_8_3_1 + · exact ldl_8_3_2 + · exact ldl_8_3_3 +theorem four_body_8_positive : + ((compressedRational 8).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_8 pivots_8 ldl_8 + intro i + fin_cases i <;> norm_num [pivots_8] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive09.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive09.lean new file mode 100644 index 0000000000000000000000000000000000000000..ab571c317106bb5078ef0d92abb7b36b6305482d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive09.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData09 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData09 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_9 : compressedRational 9 = + lower_9 * Matrix.diagonal pivots_9 * lower_9.transpose := by + rw [compressedRational_eq_compute, error_9, gram_9] + exact candidateLDL_9 + +theorem four_body_9_positive : + ((compressedRational 9).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_9 pivots_9 ldl_9 + intro i + fin_cases i <;> norm_num [pivots_9] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive10.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive10.lean new file mode 100644 index 0000000000000000000000000000000000000000..ac7abd56e444a6b325a73b1b1a533b0578fc83d2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive10.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData10 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData10 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_10 : compressedRational 10 = + lower_10 * Matrix.diagonal pivots_10 * lower_10.transpose := by + rw [compressedRational_eq_compute, error_10, gram_10] + exact candidateLDL_10 + +theorem four_body_10_positive : + ((compressedRational 10).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_10 pivots_10 ldl_10 + intro i + fin_cases i <;> norm_num [pivots_10] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive11.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive11.lean new file mode 100644 index 0000000000000000000000000000000000000000..aec80392bc414e2f3a87d26b87fd703cdeaed3a2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive11.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData11 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData11 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_11 : compressedRational 11 = + lower_11 * Matrix.diagonal pivots_11 * lower_11.transpose := by + rw [compressedRational_eq_compute, error_11, gram_11] + exact candidateLDL_11 + +theorem four_body_11_positive : + ((compressedRational 11).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_11 pivots_11 ldl_11 + intro i + fin_cases i <;> norm_num [pivots_11] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive12.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive12.lean new file mode 100644 index 0000000000000000000000000000000000000000..85d5b024d22ad000a94a219329acd38e3acadcc0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive12.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData12 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData12 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_12 : compressedRational 12 = + lower_12 * Matrix.diagonal pivots_12 * lower_12.transpose := by + rw [compressedRational_eq_compute, error_12, gram_12] + exact candidateLDL_12 + +theorem four_body_12_positive : + ((compressedRational 12).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_12 pivots_12 ldl_12 + intro i + fin_cases i <;> norm_num [pivots_12] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive13.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive13.lean new file mode 100644 index 0000000000000000000000000000000000000000..d73daeb8239dcef786b6035e1ee9ca6ac676bb38 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive13.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData13 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData13 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_13 : compressedRational 13 = + lower_13 * Matrix.diagonal pivots_13 * lower_13.transpose := by + rw [compressedRational_eq_compute, error_13, gram_13] + exact candidateLDL_13 + +theorem four_body_13_positive : + ((compressedRational 13).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_13 pivots_13 ldl_13 + intro i + fin_cases i <;> norm_num [pivots_13] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive14.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive14.lean new file mode 100644 index 0000000000000000000000000000000000000000..33b7a58f20d4c415f1128b90286b04560ab12739 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive14.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData14 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData14 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_14 : compressedRational 14 = + lower_14 * Matrix.diagonal pivots_14 * lower_14.transpose := by + rw [compressedRational_eq_compute, error_14, gram_14] + exact candidateLDL_14 + +theorem four_body_14_positive : + ((compressedRational 14).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_14 pivots_14 ldl_14 + intro i + fin_cases i <;> norm_num [pivots_14] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive15.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive15.lean new file mode 100644 index 0000000000000000000000000000000000000000..d349c0f9a606dc5534d1e1ff6fb488e5762fb946 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive15.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData15 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData15 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_15 : compressedRational 15 = + lower_15 * Matrix.diagonal pivots_15 * lower_15.transpose := by + rw [compressedRational_eq_compute, error_15, gram_15] + exact candidateLDL_15 + +theorem four_body_15_positive : + ((compressedRational 15).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_15 pivots_15 ldl_15 + intro i + fin_cases i <;> norm_num [pivots_15] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive16.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive16.lean new file mode 100644 index 0000000000000000000000000000000000000000..768854d411db28ef5f2c29db325145333fc1d991 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive16.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData16 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData16 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_16 : compressedRational 16 = + lower_16 * Matrix.diagonal pivots_16 * lower_16.transpose := by + rw [compressedRational_eq_compute, error_16, gram_16] + exact candidateLDL_16 + +theorem four_body_16_positive : + ((compressedRational 16).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_16 pivots_16 ldl_16 + intro i + fin_cases i <;> norm_num [pivots_16] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive17.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive17.lean new file mode 100644 index 0000000000000000000000000000000000000000..9f59a9ba3db0f5f3c39df68325b8bf660a109ba3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive17.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData17 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData17 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_17 : compressedRational 17 = + lower_17 * Matrix.diagonal pivots_17 * lower_17.transpose := by + rw [compressedRational_eq_compute, error_17, gram_17] + exact candidateLDL_17 + +theorem four_body_17_positive : + ((compressedRational 17).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_17 pivots_17 ldl_17 + intro i + fin_cases i <;> norm_num [pivots_17] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive18.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive18.lean new file mode 100644 index 0000000000000000000000000000000000000000..17666ffa8ad6e34189ea74cf3347e96eb1b75431 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive18.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData18 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData18 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_18 : compressedRational 18 = + lower_18 * Matrix.diagonal pivots_18 * lower_18.transpose := by + rw [compressedRational_eq_compute, error_18, gram_18] + exact candidateLDL_18 + +theorem four_body_18_positive : + ((compressedRational 18).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_18 pivots_18 ldl_18 + intro i + fin_cases i <;> norm_num [pivots_18] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive19.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive19.lean new file mode 100644 index 0000000000000000000000000000000000000000..148db31d2dca83c32ba3880e6d80d823264c9e00 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive19.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData19 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData19 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_19 : compressedRational 19 = + lower_19 * Matrix.diagonal pivots_19 * lower_19.transpose := by + rw [compressedRational_eq_compute, error_19, gram_19] + exact candidateLDL_19 + +theorem four_body_19_positive : + ((compressedRational 19).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_19 pivots_19 ldl_19 + intro i + fin_cases i <;> norm_num [pivots_19] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive20.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive20.lean new file mode 100644 index 0000000000000000000000000000000000000000..39c5141fe1526bf62fdc6ffdcc7cf3e77585c87b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive20.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData20 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData20 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_20 : compressedRational 20 = + lower_20 * Matrix.diagonal pivots_20 * lower_20.transpose := by + rw [compressedRational_eq_compute, error_20, gram_20] + exact candidateLDL_20 + +theorem four_body_20_positive : + ((compressedRational 20).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_20 pivots_20 ldl_20 + intro i + fin_cases i <;> norm_num [pivots_20] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive21.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive21.lean new file mode 100644 index 0000000000000000000000000000000000000000..ac8e47384d22e69d7bb44c31920a283420ff9ca0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive21.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData21 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData21 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_21 : compressedRational 21 = + lower_21 * Matrix.diagonal pivots_21 * lower_21.transpose := by + rw [compressedRational_eq_compute, error_21, gram_21] + exact candidateLDL_21 + +theorem four_body_21_positive : + ((compressedRational 21).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_21 pivots_21 ldl_21 + intro i + fin_cases i <;> norm_num [pivots_21] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive22.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive22.lean new file mode 100644 index 0000000000000000000000000000000000000000..18c1205599668501227d3bd764af4b6bf1f9253f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive22.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData22 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData22 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_22 : compressedRational 22 = + lower_22 * Matrix.diagonal pivots_22 * lower_22.transpose := by + rw [compressedRational_eq_compute, error_22, gram_22] + exact candidateLDL_22 + +theorem four_body_22_positive : + ((compressedRational 22).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_22 pivots_22 ldl_22 + intro i + fin_cases i <;> norm_num [pivots_22] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive23.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive23.lean new file mode 100644 index 0000000000000000000000000000000000000000..33d080653fe9c2dd1486c0c1c7dfa658094ab03d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Positive23.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FiniteFlux.GramData23 +import OAI.Analysis.Laughlin.FiniteFlux.LDLData23 + +namespace OAI + +namespace Laughlin.Certificate + +theorem ldl_23 : compressedRational 23 = + lower_23 * Matrix.diagonal pivots_23 * lower_23.transpose := by + rw [compressedRational_eq_compute, error_23, gram_23] + exact candidateLDL_23 + +theorem four_body_23_positive : + ((compressedRational 23).map (Rat.castHom ℝ)).PosSemidef := by + apply rational_ldl_positive _ lower_23 pivots_23 ldl_23 + intro i + fin_cases i <;> norm_num [pivots_23] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Quadruples08.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Quadruples08.lean new file mode 100644 index 0000000000000000000000000000000000000000..9084531e27eb2cebcdd086fca272cb511069eae0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Quadruples08.lean @@ -0,0 +1,12 @@ +import OAI.Analysis.Laughlin.FourBody.Basic + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix +theorem quadruples_8 : quadruples 8 = [(0,1,2,6), (0,1,3,5), (0,2,3,4)] := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301007.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301007.lean new file mode 100644 index 0000000000000000000000000000000000000000..20fb50b33915adea202e533bdf4811c057ae71fa --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301007.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_3_1_0 : yRow 7 3 1 (rows[0]!) = (-3670890702116855625 / 8192 : ℚ) := by + rw [yRow_swap 7 3 1 (rows[0]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_3_0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301107.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301107.lean new file mode 100644 index 0000000000000000000000000000000000000000..a04ca507edec039a3654eb363fb33bfd44d3d220 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301107.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_3_1_1 : yRow 7 3 1 (rows[1]!) = (-28502538608116390869 / 33554432 : ℚ) := by + rw [yRow_swap 7 3 1 (rows[1]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_3_1 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301207.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301207.lean new file mode 100644 index 0000000000000000000000000000000000000000..4e9a31e9f73b8b029c84b6e83f5af521d92b51c2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301207.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_3_1_2 : yRow 7 3 1 (rows[2]!) = (2988849553778345597235 / 134217728 : ℚ) := by + rw [yRow_swap 7 3 1 (rows[2]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_3_2 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301307.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301307.lean new file mode 100644 index 0000000000000000000000000000000000000000..542afa82decbcc58ab7a612e575e5a42be10e89c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301307.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_3_1_3 : yRow 7 3 1 (rows[3]!) = (-12918373159386147536445 / 234881024 : ℚ) := by + rw [yRow_swap 7 3 1 (rows[3]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_3_3 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301407.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301407.lean new file mode 100644 index 0000000000000000000000000000000000000000..5d1176f683cab9dd8c9494648d3c9a76372b3c73 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301407.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_3_1_4 : yRow 7 3 1 (rows[4]!) = (3528819936117742548165 / 58720256 : ℚ) := by + rw [yRow_swap 7 3 1 (rows[4]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_3_4 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301507.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301507.lean new file mode 100644 index 0000000000000000000000000000000000000000..79ffb1f94b2838388c73242647055a9f062e7db0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301507.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_3_1_5 : yRow 7 3 1 (rows[5]!) = (-29217720453316236095145 / 939524096 : ℚ) := by + rw [yRow_swap 7 3 1 (rows[5]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_3_5 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301607.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301607.lean new file mode 100644 index 0000000000000000000000000000000000000000..fed6c5ee8ee759c31f6ba2fe68f8e1f7747b17ff --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0301607.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_3_1_6 : yRow 7 3 1 (rows[6]!) = (-76772184534764046045 / 8388608 : ℚ) := by + rw [yRow_swap 7 3 1 (rows[6]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_3_6 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row05.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row05.lean new file mode 100644 index 0000000000000000000000000000000000000000..e44b6521596a3b3dca2dba2f271b918eb3205451 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row05.lean @@ -0,0 +1,123 @@ +import OAI.Analysis.Laughlin.FourBody.Basic + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_5_1_1_0 : yRow 5 1 1 (rows[0]!) = (288217185514048371 / 32768 : ℚ) := by + decide +kernel + +theorem yRow_5_1_1_1 : yRow 5 1 1 (rows[1]!) = (117686364357605208465 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_1_1_2 : yRow 5 1 1 (rows[2]!) = (45543850761592353716265 / 3758096384 : ℚ) := by + decide +kernel + +theorem yRow_5_1_1_3 : yRow 5 1 1 (rows[3]!) = (-33527805633645391850149 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_1_1_4 : yRow 5 1 1 (rows[4]!) = (307361222967220883631 / 67108864 : ℚ) := by + decide +kernel + +theorem yRow_5_1_1_5 : yRow 5 1 1 (rows[5]!) = (10589763940221275062345 / 536870912 : ℚ) := by + decide +kernel + +theorem yRow_5_1_1_6 : yRow 5 1 1 (rows[6]!) = (-192715136303794262991 / 33554432 : ℚ) := by + decide +kernel + +theorem yRow_5_1_3_0 : yRow 5 1 3 (rows[0]!) = (1227892611554313699 / 32768 : ℚ) := by + decide +kernel + +theorem yRow_5_1_3_1 : yRow 5 1 3 (rows[1]!) = (-40217208208139155215 / 469762048 : ℚ) := by + decide +kernel + +theorem yRow_5_1_3_2 : yRow 5 1 3 (rows[2]!) = (3609794378028611869977 / 1879048192 : ℚ) := by + decide +kernel + +theorem yRow_5_1_3_3 : yRow 5 1 3 (rows[3]!) = (15972179718835785494373 / 469762048 : ℚ) := by + decide +kernel + +theorem yRow_5_1_3_4 : yRow 5 1 3 (rows[4]!) = (973139460225276068975 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_1_3_5 : yRow 5 1 3 (rows[5]!) = (8556207819014717270965 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_1_3_6 : yRow 5 1 3 (rows[6]!) = (-26195139147988314471 / 8388608 : ℚ) := by + decide +kernel + +theorem yRow_5_1_5_0 : yRow 5 1 5 (rows[0]!) = (517229739078330765 / 4096 : ℚ) := by + decide +kernel + +theorem yRow_5_1_5_1 : yRow 5 1 5 (rows[1]!) = (33354143675585625297 / 234881024 : ℚ) := by + decide +kernel + +theorem yRow_5_1_5_2 : yRow 5 1 5 (rows[2]!) = (-39698825671225989422295 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_1_5_3 : yRow 5 1 5 (rows[3]!) = (-24352127547028721893585 / 234881024 : ℚ) := by + decide +kernel + +theorem yRow_5_1_5_4 : yRow 5 1 5 (rows[4]!) = (-18686933965106262007505 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_1_5_5 : yRow 5 1 5 (rows[5]!) = (209580109115659324643705 / 3758096384 : ℚ) := by + decide +kernel + +theorem yRow_5_1_5_6 : yRow 5 1 5 (rows[6]!) = (122766324303368643735 / 67108864 : ℚ) := by + decide +kernel + +theorem yRow_5_3_1_0 : yRow 5 3 1 (rows[0]!) = (1227892611554313699 / 32768 : ℚ) := by + decide +kernel + +theorem yRow_5_3_1_1 : yRow 5 3 1 (rows[1]!) = (-40217208208139155215 / 469762048 : ℚ) := by + decide +kernel + +theorem yRow_5_3_1_2 : yRow 5 3 1 (rows[2]!) = (3609794378028611869977 / 1879048192 : ℚ) := by + decide +kernel + +theorem yRow_5_3_1_3 : yRow 5 3 1 (rows[3]!) = (15972179718835785494373 / 469762048 : ℚ) := by + decide +kernel + +theorem yRow_5_3_1_4 : yRow 5 3 1 (rows[4]!) = (973139460225276068975 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_3_1_5 : yRow 5 3 1 (rows[5]!) = (8556207819014717270965 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_3_1_6 : yRow 5 3 1 (rows[6]!) = (-26195139147988314471 / 8388608 : ℚ) := by + decide +kernel + +theorem yRow_5_3_3_0 : yRow 5 3 3 (rows[0]!) = (828106156763491761 / 16384 : ℚ) := by + decide +kernel + +theorem yRow_5_3_3_1 : yRow 5 3 3 (rows[1]!) = (12057655206433421045 / 234881024 : ℚ) := by + decide +kernel + +theorem yRow_5_3_3_2 : yRow 5 3 3 (rows[2]!) = (-6457052018534822018791 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_3_3_3 : yRow 5 3 3 (rows[3]!) = (885506700796361417871 / 234881024 : ℚ) := by + decide +kernel + +theorem yRow_5_3_3_4 : yRow 5 3 3 (rows[4]!) = (-543574257899971267101 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_3_3_5 : yRow 5 3 3 (rows[5]!) = (10662554367612487256863 / 268435456 : ℚ) := by + decide +kernel + +theorem yRow_5_3_3_6 : yRow 5 3 3 (rows[6]!) = (-175521550402232335797 / 67108864 : ℚ) := by + decide +kernel + +theorem yRow_5_3_5_0 : yRow 5 3 5 (rows[0]!) = (2088880360412782875 / 8192 : ℚ) := by + decide +kernel + +theorem yRow_5_3_5_1 : yRow 5 3 5 (rows[1]!) = (9078017688703880489 / 117440512 : ℚ) := by + decide +kernel + +theorem yRow_5_3_5_2 : yRow 5 3 5 (rows[2]!) = (4154519314999427044985 / 469762048 : ℚ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501007.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501007.lean new file mode 100644 index 0000000000000000000000000000000000000000..424b820ab80c7981c510f588ae972f9e8c7885bc --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501007.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_1_0 : yRow 7 5 1 (rows[0]!) = (205314913297683315 / 256 : ℚ) := by + rw [yRow_swap 7 5 1 (rows[0]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_5_0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501107.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501107.lean new file mode 100644 index 0000000000000000000000000000000000000000..fe7ace39cfaefdab8f2cc7d221a3e552febddc93 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501107.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_1_1 : yRow 7 5 1 (rows[1]!) = (-2180568515710116549 / 16777216 : ℚ) := by + rw [yRow_swap 7 5 1 (rows[1]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_5_1 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501207.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501207.lean new file mode 100644 index 0000000000000000000000000000000000000000..d6e57b058959d40d68d2932c0290567d6ac8f32b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501207.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_1_2 : yRow 7 5 1 (rows[2]!) = (50011870045872224797155 / 67108864 : ℚ) := by + rw [yRow_swap 7 5 1 (rows[2]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_5_2 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501307.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501307.lean new file mode 100644 index 0000000000000000000000000000000000000000..3a35f1b608e6a369afd5f5e66d27ec6a05f962a7 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501307.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_1_3 : yRow 7 5 1 (rows[3]!) = (126559883614713029393025 / 117440512 : ℚ) := by + rw [yRow_swap 7 5 1 (rows[3]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_5_3 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501407.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501407.lean new file mode 100644 index 0000000000000000000000000000000000000000..8dbc3e547aff3e4ea18e145976b158e1e4d390f2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501407.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_1_4 : yRow 7 5 1 (rows[4]!) = (-46679206856806148273295 / 469762048 : ℚ) := by + rw [yRow_swap 7 5 1 (rows[4]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_5_4 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501507.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501507.lean new file mode 100644 index 0000000000000000000000000000000000000000..6376789cc56dbd05aecf09a48a92bda59c705069 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501507.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_1_5 : yRow 7 5 1 (rows[5]!) = (486363383031076447124835 / 1879048192 : ℚ) := by + rw [yRow_swap 7 5 1 (rows[5]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_5_5 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501607.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501607.lean new file mode 100644 index 0000000000000000000000000000000000000000..43857d822c308cc3afe7c979276b39183b219648 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0501607.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_1_6 : yRow 7 5 1 (rows[6]!) = (-620279821822140423225 / 33554432 : ℚ) := by + rw [yRow_swap 7 5 1 (rows[6]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_5_6 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503007.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503007.lean new file mode 100644 index 0000000000000000000000000000000000000000..bc245bc90fc3ad751d10a310f0c0b7dec20039ff --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503007.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_3_0 : yRow 7 5 3 (rows[0]!) = (11065428419616135 / 1024 : ℚ) := by + rw [yRow_swap 7 5 3 (rows[0]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_5_0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503107.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503107.lean new file mode 100644 index 0000000000000000000000000000000000000000..139dfc994419e233353624eb921ea5c0edaafe05 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503107.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_3_1 : yRow 7 5 3 (rows[1]!) = (2141394541249492635 / 8388608 : ℚ) := by + rw [yRow_swap 7 5 3 (rows[1]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_5_1 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503207.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503207.lean new file mode 100644 index 0000000000000000000000000000000000000000..f4c3b0ee2f6f1177694bc25473818759eb532d8d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503207.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_3_2 : yRow 7 5 3 (rows[2]!) = (-23803270741598517863565 / 33554432 : ℚ) := by + rw [yRow_swap 7 5 3 (rows[2]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_5_2 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503307.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503307.lean new file mode 100644 index 0000000000000000000000000000000000000000..9cf677b164d8db63565fc22b5cba69c7ad8f88b4 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503307.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_3_3 : yRow 7 5 3 (rows[3]!) = (-14416679890174213591545 / 58720256 : ℚ) := by + rw [yRow_swap 7 5 3 (rows[3]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_5_3 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503407.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503407.lean new file mode 100644 index 0000000000000000000000000000000000000000..687610d63b819850c69e1a4a63b2df4e3f06ff6d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503407.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_3_4 : yRow 7 5 3 (rows[4]!) = (-54234982718013152865 / 7340032 : ℚ) := by + rw [yRow_swap 7 5 3 (rows[4]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_5_4 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503507.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503507.lean new file mode 100644 index 0000000000000000000000000000000000000000..38179c6910d20aab1953f448715c72c5e8252a8d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503507.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_3_5 : yRow 7 5 3 (rows[5]!) = (310146766753353391486215 / 939524096 : ℚ) := by + rw [yRow_swap 7 5 3 (rows[5]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_5_5 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503607.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503607.lean new file mode 100644 index 0000000000000000000000000000000000000000..0dfed86d8863a89637c3a3fffc420d6249cf6db0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0503607.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_3_6 : yRow 7 5 3 (rows[6]!) = (-50552514240995949885 / 16777216 : ℚ) := by + rw [yRow_swap 7 5 3 (rows[6]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_5_6 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row052.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row052.lean new file mode 100644 index 0000000000000000000000000000000000000000..03032ef6f3dc01f10e0c405411ec63c9a8ec49c3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row052.lean @@ -0,0 +1,84 @@ +import OAI.Analysis.Laughlin.FourBody.Basic + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_5_3_5_3 : yRow 5 3 5 (rows[3]!) = (-1676596742006268315615 / 117440512 : ℚ) := by + decide +kernel + +theorem yRow_5_3_5_4 : yRow 5 3 5 (rows[4]!) = (1122516649266680657945 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_3_5_5 : yRow 5 3 5 (rows[5]!) = (11113921888615690197695 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_3_5_6 : yRow 5 3 5 (rows[6]!) = (-125595578390684976075 / 67108864 : ℚ) := by + decide +kernel + +theorem yRow_5_5_1_0 : yRow 5 5 1 (rows[0]!) = (517229739078330765 / 4096 : ℚ) := by + decide +kernel + +theorem yRow_5_5_1_1 : yRow 5 5 1 (rows[1]!) = (33354143675585625297 / 234881024 : ℚ) := by + decide +kernel + +theorem yRow_5_5_1_2 : yRow 5 5 1 (rows[2]!) = (-39698825671225989422295 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_5_1_3 : yRow 5 5 1 (rows[3]!) = (-24352127547028721893585 / 234881024 : ℚ) := by + decide +kernel + +theorem yRow_5_5_1_4 : yRow 5 5 1 (rows[4]!) = (-18686933965106262007505 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_5_1_5 : yRow 5 5 1 (rows[5]!) = (209580109115659324643705 / 3758096384 : ℚ) := by + decide +kernel + +theorem yRow_5_5_1_6 : yRow 5 5 1 (rows[6]!) = (122766324303368643735 / 67108864 : ℚ) := by + decide +kernel + +theorem yRow_5_5_3_0 : yRow 5 5 3 (rows[0]!) = (2088880360412782875 / 8192 : ℚ) := by + decide +kernel + +theorem yRow_5_5_3_1 : yRow 5 5 3 (rows[1]!) = (9078017688703880489 / 117440512 : ℚ) := by + decide +kernel + +theorem yRow_5_5_3_2 : yRow 5 5 3 (rows[2]!) = (4154519314999427044985 / 469762048 : ℚ) := by + decide +kernel + +theorem yRow_5_5_3_3 : yRow 5 5 3 (rows[3]!) = (-1676596742006268315615 / 117440512 : ℚ) := by + decide +kernel + +theorem yRow_5_5_3_4 : yRow 5 5 3 (rows[4]!) = (1122516649266680657945 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_5_3_5 : yRow 5 5 3 (rows[5]!) = (11113921888615690197695 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_5_3_6 : yRow 5 5 3 (rows[6]!) = (-125595578390684976075 / 67108864 : ℚ) := by + decide +kernel + +theorem yRow_5_5_5_0 : yRow 5 5 5 (rows[0]!) = (2127370824716077635 / 2048 : ℚ) := by + decide +kernel + +theorem yRow_5_5_5_1 : yRow 5 5 5 (rows[1]!) = (105906315909713386913 / 58720256 : ℚ) := by + decide +kernel + +theorem yRow_5_5_5_2 : yRow 5 5 5 (rows[2]!) = (79674709640186975436905 / 234881024 : ℚ) := by + decide +kernel + +theorem yRow_5_5_5_3 : yRow 5 5 5 (rows[3]!) = (16556987918363989467635 / 58720256 : ℚ) := by + decide +kernel + +theorem yRow_5_5_5_4 : yRow 5 5 5 (rows[4]!) = (35865503886652808531045 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_5_5_5_5 : yRow 5 5 5 (rows[5]!) = (52813174350218993123795 / 536870912 : ℚ) := by + decide +kernel + +theorem yRow_5_5_5_6 : yRow 5 5 5 (rows[6]!) = (-465607554421578820545 / 67108864 : ℚ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row07.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row07.lean new file mode 100644 index 0000000000000000000000000000000000000000..62578cbf98cf6e5d4323e9c0b1a3e741190a7955 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row07.lean @@ -0,0 +1,84 @@ +import OAI.Analysis.Laughlin.FourBody.Basic + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_1_1_0 : yRow 7 1 1 (rows[0]!) = (7813395192175504245 / 4096 : ℚ) := by + decide +kernel + +theorem yRow_7_1_1_1 : yRow 7 1 1 (rows[1]!) = (36323988982144322139 / 67108864 : ℚ) := by + decide +kernel + +theorem yRow_7_1_1_2 : yRow 7 1 1 (rows[2]!) = (56489461722547816265955 / 268435456 : ℚ) := by + decide +kernel + +theorem yRow_7_1_1_3 : yRow 7 1 1 (rows[3]!) = (-181450975756044921243195 / 469762048 : ℚ) := by + decide +kernel + +theorem yRow_7_1_1_4 : yRow 7 1 1 (rows[4]!) = (-2508628320709374018255 / 29360128 : ℚ) := by + decide +kernel + +theorem yRow_7_1_1_5 : yRow 7 1 1 (rows[5]!) = (1591029590813751708821385 / 1879048192 : ℚ) := by + decide +kernel + +theorem yRow_7_1_1_6 : yRow 7 1 1 (rows[6]!) = (-4276885373741756719485 / 33554432 : ℚ) := by + decide +kernel + +theorem yRow_7_1_3_0 : yRow 7 1 3 (rows[0]!) = (-3670890702116855625 / 8192 : ℚ) := by + decide +kernel + +theorem yRow_7_1_3_1 : yRow 7 1 3 (rows[1]!) = (-28502538608116390869 / 33554432 : ℚ) := by + decide +kernel + +theorem yRow_7_1_3_2 : yRow 7 1 3 (rows[2]!) = (2988849553778345597235 / 134217728 : ℚ) := by + decide +kernel + +theorem yRow_7_1_3_3 : yRow 7 1 3 (rows[3]!) = (-12918373159386147536445 / 234881024 : ℚ) := by + decide +kernel + +theorem yRow_7_1_3_4 : yRow 7 1 3 (rows[4]!) = (3528819936117742548165 / 58720256 : ℚ) := by + decide +kernel + +theorem yRow_7_1_3_5 : yRow 7 1 3 (rows[5]!) = (-29217720453316236095145 / 939524096 : ℚ) := by + decide +kernel + +theorem yRow_7_1_3_6 : yRow 7 1 3 (rows[6]!) = (-76772184534764046045 / 8388608 : ℚ) := by + decide +kernel + +theorem yRow_7_1_5_0 : yRow 7 1 5 (rows[0]!) = (205314913297683315 / 256 : ℚ) := by + decide +kernel + +theorem yRow_7_1_5_1 : yRow 7 1 5 (rows[1]!) = (-2180568515710116549 / 16777216 : ℚ) := by + decide +kernel + +theorem yRow_7_1_5_2 : yRow 7 1 5 (rows[2]!) = (50011870045872224797155 / 67108864 : ℚ) := by + decide +kernel + +theorem yRow_7_1_5_3 : yRow 7 1 5 (rows[3]!) = (126559883614713029393025 / 117440512 : ℚ) := by + decide +kernel + +theorem yRow_7_1_5_4 : yRow 7 1 5 (rows[4]!) = (-46679206856806148273295 / 469762048 : ℚ) := by + decide +kernel + +theorem yRow_7_1_5_5 : yRow 7 1 5 (rows[5]!) = (486363383031076447124835 / 1879048192 : ℚ) := by + decide +kernel + +theorem yRow_7_1_5_6 : yRow 7 1 5 (rows[6]!) = (-620279821822140423225 / 33554432 : ℚ) := by + decide +kernel + +theorem yRow_7_1_7_0 : yRow 7 1 7 (rows[0]!) = (15514482988745341335 / 2048 : ℚ) := by + decide +kernel + +theorem yRow_7_1_7_1 : yRow 7 1 7 (rows[1]!) = (34459028886161906571 / 8388608 : ℚ) := by + decide +kernel + +theorem yRow_7_1_7_2 : yRow 7 1 7 (rows[2]!) = (207794480500460556638835 / 33554432 : ℚ) := by + decide +kernel + +theorem yRow_7_1_7_3 : yRow 7 1 7 (rows[3]!) = (-12487246647748499348535 / 8388608 : ℚ) := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701007.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701007.lean new file mode 100644 index 0000000000000000000000000000000000000000..e7a731dcb3f35fc94e34b8778303cfa4850bd81f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701007.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_1_0 : yRow 7 7 1 (rows[0]!) = (15514482988745341335 / 2048 : ℚ) := by + rw [yRow_swap 7 7 1 (rows[0]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_7_0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701107.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701107.lean new file mode 100644 index 0000000000000000000000000000000000000000..0bbd6fdb2fdf7a0f8fc2d80796a05e68b3f01834 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701107.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_1_1 : yRow 7 7 1 (rows[1]!) = (34459028886161906571 / 8388608 : ℚ) := by + rw [yRow_swap 7 7 1 (rows[1]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_7_1 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701207.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701207.lean new file mode 100644 index 0000000000000000000000000000000000000000..121734915ed9a8c67c24bb2b35a4ef57e2477e3d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701207.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_1_2 : yRow 7 7 1 (rows[2]!) = (207794480500460556638835 / 33554432 : ℚ) := by + rw [yRow_swap 7 7 1 (rows[2]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_7_2 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701307.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701307.lean new file mode 100644 index 0000000000000000000000000000000000000000..2a5111c6176ac87104a3237f5764452082b01800 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701307.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row07 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_1_3 : yRow 7 7 1 (rows[3]!) = (-12487246647748499348535 / 8388608 : ℚ) := by + rw [yRow_swap 7 7 1 (rows[3]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_7_3 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701407.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701407.lean new file mode 100644 index 0000000000000000000000000000000000000000..085b2ee885dfa20533a14e4e9293348b7f83d76d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701407.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_1_4 : yRow 7 7 1 (rows[4]!) = (20867558445854020401465 / 33554432 : ℚ) := by + rw [yRow_swap 7 7 1 (rows[4]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_7_4 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701507.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701507.lean new file mode 100644 index 0000000000000000000000000000000000000000..7d9b7c8666b5c1c475d75bc593a69df23bc28969 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701507.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_1_5 : yRow 7 7 1 (rows[5]!) = (-87026179675834894580205 / 134217728 : ℚ) := by + rw [yRow_swap 7 7 1 (rows[5]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_7_5 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701607.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701607.lean new file mode 100644 index 0000000000000000000000000000000000000000..d300ea77c884c881107cac4bfbd951b8fd6bcf54 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0701607.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_1_6 : yRow 7 7 1 (rows[6]!) = (201099333031028464725 / 4194304 : ℚ) := by + rw [yRow_swap 7 7 1 (rows[6]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_1_7_6 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703007.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703007.lean new file mode 100644 index 0000000000000000000000000000000000000000..bc3a0aadaadc32eefa83e4476b4d687f5cbdfd8b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703007.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_3_0 : yRow 7 7 3 (rows[0]!) = (-1488415248143087355 / 2048 : ℚ) := by + rw [yRow_swap 7 7 3 (rows[0]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_7_0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703107.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703107.lean new file mode 100644 index 0000000000000000000000000000000000000000..62c4451b50226060fbf1e78bd2f79216a7c63865 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703107.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_3_1 : yRow 7 7 3 (rows[1]!) = (9225871950243624195 / 4194304 : ℚ) := by + rw [yRow_swap 7 7 3 (rows[1]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_7_1 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703207.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703207.lean new file mode 100644 index 0000000000000000000000000000000000000000..d93fd75733046b5faa9e241267135308a7b5d8af --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703207.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_3_2 : yRow 7 7 3 (rows[2]!) = (-3990280684502974026525 / 16777216 : ℚ) := by + rw [yRow_swap 7 7 3 (rows[2]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_7_2 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703307.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703307.lean new file mode 100644 index 0000000000000000000000000000000000000000..14b5cbd6b3e9a26aa500c1d7089d96fccd688e4e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703307.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_3_3 : yRow 7 7 3 (rows[3]!) = (-6304209573025048032825 / 4194304 : ℚ) := by + rw [yRow_swap 7 7 3 (rows[3]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_7_3 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703407.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703407.lean new file mode 100644 index 0000000000000000000000000000000000000000..88aba9a3b2e846ddb6ea55339c024bc72e9a13a8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703407.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_3_4 : yRow 7 7 3 (rows[4]!) = (-1462389462807293524305 / 8388608 : ℚ) := by + rw [yRow_swap 7 7 3 (rows[4]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_7_4 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703507.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703507.lean new file mode 100644 index 0000000000000000000000000000000000000000..11cce94fb6d0541fe018e94773bfe0d252c7144d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703507.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_3_5 : yRow 7 7 3 (rows[5]!) = (51986196748062068309475 / 67108864 : ℚ) := by + rw [yRow_swap 7 7 3 (rows[5]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_7_5 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703607.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703607.lean new file mode 100644 index 0000000000000000000000000000000000000000..486f6874b22832679c719e583049bdf6e5906736 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0703607.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_3_6 : yRow 7 7 3 (rows[6]!) = (47466735597972069435 / 1048576 : ℚ) := by + rw [yRow_swap 7 7 3 (rows[6]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_3_7_6 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705007.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705007.lean new file mode 100644 index 0000000000000000000000000000000000000000..e8a5e6d757f2b87b747b7562cea4627d9f3cba7d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705007.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_5_0 : yRow 7 7 5 (rows[0]!) = (1153158553770801165 / 128 : ℚ) := by + rw [yRow_swap 7 7 5 (rows[0]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_5_7_0 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705107.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705107.lean new file mode 100644 index 0000000000000000000000000000000000000000..cf6e058c3939f83f86d5fd48e6dfe5a12664cc2f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705107.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_5_1 : yRow 7 7 5 (rows[1]!) = (398875219468930779 / 2097152 : ℚ) := by + rw [yRow_swap 7 7 5 (rows[1]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_5_7_1 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705207.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705207.lean new file mode 100644 index 0000000000000000000000000000000000000000..5093a1c8a1839061dbdc1e06fdf2b5c5cd021200 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705207.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_5_2 : yRow 7 7 5 (rows[2]!) = (-3344728266700356251085 / 8388608 : ℚ) := by + rw [yRow_swap 7 7 5 (rows[2]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_5_7_2 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705307.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705307.lean new file mode 100644 index 0000000000000000000000000000000000000000..edd375627a8d227faf96ae5db96c2f1f88f7f8a0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705307.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row072 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_5_3 : yRow 7 7 5 (rows[3]!) = (2694741498446716664085 / 2097152 : ℚ) := by + rw [yRow_swap 7 7 5 (rows[3]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_5_7_3 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705407.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705407.lean new file mode 100644 index 0000000000000000000000000000000000000000..61b98bf999aa0199f171fcbfe50b1e8886b5ebeb --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705407.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row073 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_5_4 : yRow 7 7 5 (rows[4]!) = (-3701247860527868239965 / 33554432 : ℚ) := by + rw [yRow_swap 7 7 5 (rows[4]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_5_7_4 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705507.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705507.lean new file mode 100644 index 0000000000000000000000000000000000000000..ed4b0712a4d568b7c32363a4467549b38a384ac6 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705507.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row073 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_5_5 : yRow 7 7 5 (rows[5]!) = (-111316765905740996833665 / 134217728 : ℚ) := by + rw [yRow_swap 7 7 5 (rows[5]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_5_7_5 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705607.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705607.lean new file mode 100644 index 0000000000000000000000000000000000000000..08c7cc14f60de88a354579af437ace1041dc5325 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row0705607.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FiniteFlux.Row073 +import OAI.Analysis.Laughlin.FourBody.Symmetry + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_7_5_6 : yRow 7 7 5 (rows[6]!) = (21601964370283224165 / 4194304 : ℚ) := by + rw [yRow_swap 7 7 5 (rows[6]!) (rows_valid _ (by decide +kernel))] + exact yRow_7_5_7_6 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row072.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row072.lean new file mode 100644 index 0000000000000000000000000000000000000000..5232d9541557005690562de09efc40bc12654d60 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row072.lean @@ -0,0 +1,149 @@ +import OAI.Analysis.Laughlin.FourBody.Fast + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_1_7_4 : yRow 7 1 7 (rows[4]!) = (20867558445854020401465 / 33554432 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_1_7_5 : yRow 7 1 7 (rows[5]!) = (-87026179675834894580205 / 134217728 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_1_7_6 : yRow 7 1 7 (rows[6]!) = (201099333031028464725 / 4194304 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_3_0 : yRow 7 3 3 (rows[0]!) = (1339467956678017935 / 8192 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_3_1 : yRow 7 3 3 (rows[1]!) = (6048833004624160083 / 16777216 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_3_2 : yRow 7 3 3 (rows[2]!) = (21081146259965870818659 / 67108864 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_3_3 : yRow 7 3 3 (rows[3]!) = (11539020213471479679117 / 117440512 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_3_4 : yRow 7 3 3 (rows[4]!) = (5238129656277557731281 / 234881024 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_3_5 : yRow 7 3 3 (rows[5]!) = (44738130881813395918293 / 234881024 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_3_6 : yRow 7 3 3 (rows[6]!) = (-61880973868094171805 / 8388608 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_5_0 : yRow 7 3 5 (rows[0]!) = (11065428419616135 / 1024 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_5_1 : yRow 7 3 5 (rows[1]!) = (2141394541249492635 / 8388608 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_5_2 : yRow 7 3 5 (rows[2]!) = (-23803270741598517863565 / 33554432 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_5_3 : yRow 7 3 5 (rows[3]!) = (-14416679890174213591545 / 58720256 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_5_4 : yRow 7 3 5 (rows[4]!) = (-54234982718013152865 / 7340032 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_5_5 : yRow 7 3 5 (rows[5]!) = (310146766753353391486215 / 939524096 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_5_6 : yRow 7 3 5 (rows[6]!) = (-50552514240995949885 / 16777216 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_7_0 : yRow 7 3 7 (rows[0]!) = (-1488415248143087355 / 2048 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_7_1 : yRow 7 3 7 (rows[1]!) = (9225871950243624195 / 4194304 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_7_2 : yRow 7 3 7 (rows[2]!) = (-3990280684502974026525 / 16777216 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_7_3 : yRow 7 3 7 (rows[3]!) = (-6304209573025048032825 / 4194304 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_7_4 : yRow 7 3 7 (rows[4]!) = (-1462389462807293524305 / 8388608 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_7_5 : yRow 7 3 7 (rows[5]!) = (51986196748062068309475 / 67108864 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_3_7_6 : yRow 7 3 7 (rows[6]!) = (47466735597972069435 / 1048576 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_5_0 : yRow 7 5 5 (rows[0]!) = (1647590914974091305 / 512 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_5_1 : yRow 7 5 5 (rows[1]!) = (-1941155336440971141 / 4194304 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_5_2 : yRow 7 5 5 (rows[2]!) = (13696035226878429190755 / 16777216 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_5_3 : yRow 7 5 5 (rows[3]!) = (21555340744289352133005 / 29360128 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_5_4 : yRow 7 5 5 (rows[4]!) = (23982864216689624871615 / 469762048 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_5_5 : yRow 7 5 5 (rows[5]!) = (298255256745963536707095 / 1879048192 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_5_6 : yRow 7 5 5 (rows[6]!) = (-489275399025456543315 / 33554432 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_7_0 : yRow 7 5 7 (rows[0]!) = (1153158553770801165 / 128 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_7_1 : yRow 7 5 7 (rows[1]!) = (398875219468930779 / 2097152 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_7_2 : yRow 7 5 7 (rows[2]!) = (-3344728266700356251085 / 8388608 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_7_3 : yRow 7 5 7 (rows[3]!) = (2694741498446716664085 / 2097152 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row073.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row073.lean new file mode 100644 index 0000000000000000000000000000000000000000..3e7e600b5221aa0d00329792911bdda4bdc3969b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row073.lean @@ -0,0 +1,49 @@ +import OAI.Analysis.Laughlin.FourBody.Fast + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_7_5_7_4 : yRow 7 5 7 (rows[4]!) = (-3701247860527868239965 / 33554432 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_7_5 : yRow 7 5 7 (rows[5]!) = (-111316765905740996833665 / 134217728 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_5_7_6 : yRow 7 5 7 (rows[6]!) = (21601964370283224165 / 4194304 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_7_7_0 : yRow 7 7 7 (rows[0]!) = (23600622017985557895 / 512 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_7_7_1 : yRow 7 7 7 (rows[1]!) = (48841871261567267859 / 1048576 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_7_7_2 : yRow 7 7 7 (rows[2]!) = (-21796542666481881573405 / 4194304 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_7_7_3 : yRow 7 7 7 (rows[3]!) = (23162047839316984778355 / 1048576 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_7_7_4 : yRow 7 7 7 (rows[4]!) = (66973353174085436915265 / 16777216 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_7_7_5 : yRow 7 7 7 (rows[5]!) = (-501028086213336269895615 / 67108864 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +theorem yRow_7_7_7_6 : yRow 7 7 7 (rows[6]!) = (-272062846972941081435 / 524288 : ℚ) := by + rw [yRow_eq_fast] + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row08.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row08.lean new file mode 100644 index 0000000000000000000000000000000000000000..83f806a1f40d38910b45afc63e290bee47a4082c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row08.lean @@ -0,0 +1,184 @@ +import OAI.Analysis.Laughlin.FourBody.Integral + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_8_1_1_0 : yRow 8 1 1 (rows[0]!) = (-1542335899954614345/2048 : ℚ) := by + rw [source_yRow_eq_integral 8 1 1 0 (by decide)] + have h : yRowIntegral 8 1 1 (rows[0]!) = (-8619347850272953673098966182318281602089400786118246400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_1_1 : yRow 8 1 1 (rows[1]!) = (-75316015709295173739/8388608 : ℚ) := by + rw [source_yRow_eq_integral 8 1 1 1 (by decide)] + have h : yRowIntegral 8 1 1 (rows[1]!) = (-102759700481278136454049635014896858919534980057006080000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_1_2 : yRow 8 1 1 (rows[2]!) = (-9136760184633772519965/33554432 : ℚ) := by + rw [source_yRow_eq_integral 8 1 1 2 (by decide)] + have h : yRowIntegral 8 1 1 (rows[2]!) = (-3116504275684753840824333987016605727399506032669491200000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_1_3 : yRow 8 1 1 (rows[3]!) = (526208461257856971342675/67108864 : ℚ) := by + rw [source_yRow_eq_integral 8 1 1 3 (by decide)] + have h : yRowIntegral 8 1 1 (rows[3]!) = (89743568084978664405363388204529436242875518101225472000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_1_4 : yRow 8 1 1 (rows[4]!) = (14597567158110194070375/16777216 : ℚ) := by + rw [source_yRow_eq_integral 8 1 1 4 (by decide)] + have h : yRowIntegral 8 1 1 (rows[4]!) = (9958317728281114061683907653004378575256490564648960000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_1_5 : yRow 8 1 1 (rows[5]!) = (-347441421785295611479515/67108864 : ℚ) := by + rw [source_yRow_eq_integral 8 1 1 5 (by decide)] + have h : yRowIntegral 8 1 1 (rows[5]!) = (-59255286045754170219483300870860577850712898244549017600000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_1_6 : yRow 8 1 1 (rows[6]!) = (-8205115144686782088375/16777216 : ℚ) := by + rw [source_yRow_eq_integral 8 1 1 6 (by decide)] + have h : yRowIntegral 8 1 1 (rows[6]!) = (-5597449405295309043794642493309726317975774366269440000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_3_0 : yRow 8 1 3 (rows[0]!) = (-11387494346113586295/8192 : ℚ) := by + rw [source_yRow_eq_integral 8 1 3 0 (by decide)] + have h : yRowIntegral 8 1 3 (rows[0]!) = (-15909759818703865639420918948060704312505350737205657600000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_3_1 : yRow 8 1 3 (rows[1]!) = (197119650262423977/524288 : ℚ) := by + rw [source_yRow_eq_integral 8 1 3 1 (by decide)] + have h : yRowIntegral 8 1 3 (rows[1]!) = (4303139199104731278274793995541665105689055372247040000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_3_2 : yRow 8 1 3 (rows[2]!) = (36872577681837689686995/16777216 : ℚ) := by + rw [source_yRow_eq_integral 8 1 3 2 (by decide)] + have h : yRowIntegral 8 1 3 (rows[2]!) = (25154112328400015358321224590538739271019887395550003200000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_3_3 : yRow 8 1 3 (rows[3]!) = (15064379418747419024745/33554432 : ℚ) := by + rw [source_yRow_eq_integral 8 1 3 3 (by decide)] + have h : yRowIntegral 8 1 3 (rows[3]!) = (5138386246365681146408405211272447483086217886144921600000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_3_4 : yRow 8 1 3 (rows[4]!) = (-441299603451117593115/33554432 : ℚ) := by + rw [source_yRow_eq_integral 8 1 3 4 (by decide)] + have h : yRowIntegral 8 1 3 (rows[4]!) = (-150525139460965372092090500551256731669027559256883200000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_3_5 : yRow 8 1 3 (rows[5]!) = (-6630239381949782627055/16777216 : ℚ) := by + rw [source_yRow_eq_integral 8 1 3 5 (by decide)] + have h : yRowIntegral 8 1 3 (rows[5]!) = (-4523084543120943521189449142964840775985106302848204800000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_3_6 : yRow 8 1 3 (rows[6]!) = (-397903947246140783805/4194304 : ℚ) := by + rw [source_yRow_eq_integral 8 1 3 6 (by decide)] + have h : yRowIntegral 8 1 3 (rows[6]!) = (-1085784744566232926682825961496439763504947159839539200000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_5_0 : yRow 8 1 5 (rows[0]!) = (-14645438327407983795/2048 : ℚ) := by + rw [source_yRow_eq_integral 8 1 5 0 (by decide)] + have h : yRowIntegral 8 1 5 (rows[0]!) = (-81846066973714198535257051527707951684592003606537830400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_5_1 : yRow 8 1 5 (rows[1]!) = (-18171099948981591081/2097152 : ℚ) := by + rw [source_yRow_eq_integral 8 1 5 1 (by decide)] + have h : yRowIntegral 8 1 5 (rows[1]!) = (-99169175139585513026729613548820931756850687539937280000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_5_2 : yRow 8 1 5 (rows[2]!) = (-35901747833688299761245/8388608 : ℚ) := by + rw [source_yRow_eq_integral 8 1 5 2 (by decide)] + have h : yRowIntegral 8 1 5 (rows[2]!) = (-48983643377843663525738690465967873761696349774308966400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_5_3 : yRow 8 1 5 (rows[3]!) = (13068275739016009424895/16777216 : ℚ) := by + rw [source_yRow_eq_integral 8 1 5 3 (by decide)] + have h : yRowIntegral 8 1 5 (rows[3]!) = (8915050060078423264496009358264607986567716386583347200000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_5_4 : yRow 8 1 5 (rows[4]!) = (-102541802088869818905/2097152 : ℚ) := by + rw [source_yRow_eq_integral 8 1 5 4 (by decide)] + have h : yRowIntegral 8 1 5 (rows[4]!) = (-559624126169080528107859221332441491696940415870566400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_5_5 : yRow 8 1 5 (rows[5]!) = (-142185036639416818007445/67108864 : ℚ) := by + rw [source_yRow_eq_integral 8 1 5 5 (by decide)] + have h : yRowIntegral 8 1 5 (rows[5]!) = (-24249310787995549471600525782497902890479770894388428800000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_5_6 : yRow 8 1 5 (rows[6]!) = (-177811778631486817125/8388608 : ℚ) := by + rw [source_yRow_eq_integral 8 1 5 6 (by decide)] + have h : yRowIntegral 8 1 5 (rows[6]!) = (-242602917083940767689579220014547693785978062766080000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_7_0 : yRow 8 1 7 (rows[0]!) = (-29482763785841653245/2048 : ℚ) := by + rw [source_yRow_eq_integral 8 1 7 0 (by decide)] + have h : yRowIntegral 8 1 7 (rows[0]!) = (-164764495636182421456560607435114239038750987318093414400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_7_1 : yRow 8 1 7 (rows[1]!) = (7866895664760765897/524288 : ℚ) := by + rw [source_yRow_eq_integral 8 1 7 1 (by decide)] + have h : yRowIntegral 8 1 7 (rows[1]!) = (171735020152642000678453243482343046239215668365885440000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_7_2 : yRow 8 1 7 (rows[2]!) = (-825991533879872150445/4194304 : ℚ) := by + rw [source_yRow_eq_integral 8 1 7 2 (by decide)] + have h : yRowIntegral 8 1 7 (rows[2]!) = (-2253933424975156060465058265096229214598307691416780800000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_7_3 : yRow 8 1 7 (rows[3]!) = (58901045380419353591445/8388608 : ℚ) := by + rw [source_yRow_eq_integral 8 1 7 3 (by decide)] + have h : yRowIntegral 8 1 7 (rows[3]!) = (80363435642800099800973330645718861695432544989111910400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row082.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row082.lean new file mode 100644 index 0000000000000000000000000000000000000000..0df7a4fa7e0eb4c4b705046fea7935f0ce079f53 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row082.lean @@ -0,0 +1,205 @@ +import OAI.Analysis.Laughlin.FourBody.FastChoose + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_8_1_7_4 : yRow 8 1 7 (rows[4]!) = (898662178057610818425/8388608 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 1 7 4 (by decide)] + have h : yRowIntegralFast 8 1 7 (rows[4]!) = (1226117119730434135579945337146359789819184929570816000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_7_5 : yRow 8 1 7 (rows[5]!) = (100330787491458237454185/33554432 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 1 7 5 (by decide)] + have h : yRowIntegralFast 8 1 7 (rows[5]!) = (34222341604830156437390681988973533353986549319781580800000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_1_7_6 : yRow 8 1 7 (rows[6]!) = (139637915427504113235/1048576 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 1 7 6 (by decide)] + have h : yRowIntegralFast 8 1 7 (rows[6]!) = (1524153951058190208281381424542084824467012314569113600000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_3_0 : yRow 8 3 3 (rows[0]!) = (15977720834090203455/8192 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 3 0 (by decide)] + have h : yRowIntegralFast 8 3 3 (rows[0]!) = (22322882733850216101237666734600677605481762670405222400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_3_1 : yRow 8 3 3 (rows[1]!) = (3142036540605854661/2097152 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 3 1 (by decide)] + have h : yRowIntegralFast 8 3 3 (rows[1]!) = (17147733096244555833634088409268874847094058967367680000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_3_2 : yRow 8 3 3 (rows[2]!) = (685667686484171871195/8388608 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 3 2 (by decide)] + have h : yRowIntegralFast 8 3 3 (rows[2]!) = (935511596428071271256193942280031406802407155721830400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_3_3 : yRow 8 3 3 (rows[3]!) = (-18744793144766932510845/16777216 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 3 3 (by decide)] + have h : yRowIntegralFast 8 3 3 (rows[3]!) = (-12787514786858549425344796377195048608240794860729139200000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_3_4 : yRow 8 3 3 (rows[4]!) = (-6097593366856360539375/234881024 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 3 4 (by decide)] + have h : yRowIntegralFast 8 3 3 (rows[4]!) = (-297122759602537588518861771098439094257983894323200000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_3_5 : yRow 8 3 3 (rows[5]!) = (32391427003169138594775/234881024 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 3 5 (by decide)] + have h : yRowIntegralFast 8 3 3 (rows[5]!) = (1578365364761537085254234510698954482866065816682496000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_3_6 : yRow 8 3 3 (rows[6]!) = (-1988696899266245149545/33554432 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 3 6 (by decide)] + have h : yRowIntegralFast 8 3 3 (rows[6]!) = (-678334799683996527711351806702633338084636298418585600000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_5_0 : yRow 8 3 5 (rows[0]!) = (76640875416000675/1024 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 5 0 (by decide)] + have h : yRowIntegralFast 8 3 5 (rows[0]!) = (856615429595306325025256914923187604516818661670912000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_5_1 : yRow 8 3 5 (rows[1]!) = (174426263694933807/524288 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 5 1 (by decide)] + have h : yRowIntegralFast 8 3 5 (rows[1]!) = (3807740586287595884710452381718919859920364518768640000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_5_2 : yRow 8 3 5 (rows[2]!) = (2761275840379361416995/4194304 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 5 2 (by decide)] + have h : yRowIntegralFast 8 3 5 (rows[2]!) = (7534861626211962036591583876263875363608284577451212800000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_5_3 : yRow 8 3 5 (rows[3]!) = (702428309218164239085/8388608 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 5 3 (by decide)] + have h : yRowIntegralFast 8 3 5 (rows[3]!) = (958379462655522227776546507336903612321559804588851200000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_5_4 : yRow 8 3 5 (rows[4]!) = (2911950561638159921355/33554432 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 5 4 (by decide)] + have h : yRowIntegralFast 8 3 5 (rows[4]!) = (993252114813135149443158640425212610753801639847526400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_5_5 : yRow 8 3 5 (rows[5]!) = (20424443618431088962035/58720256 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 5 5 (by decide)] + have h : yRowIntegralFast 8 3 5 (rows[5]!) = (3980958838115082923031199520266531892326567020960153600000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_5_6 : yRow 8 3 5 (rows[6]!) = (-74303915387983228845/2097152 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 5 6 (by decide)] + have h : yRowIntegralFast 8 3 5 (rows[6]!) = (-405515242299948507369798187993398981045996312172953600000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_7_0 : yRow 8 3 7 (rows[0]!) = (1990312643635120665/2048 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 7 0 (by decide)] + have h : yRowIntegralFast 8 3 7 (rows[0]!) = (11122866949276273240494885445024757470322608040627404800000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_7_1 : yRow 8 3 7 (rows[1]!) = (-1095344391635191101/524288 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 7 1 (by decide)] + have h : yRowIntegralFast 8 3 7 (rows[1]!) = (-23911463833717104904155617528637173818730653176299520000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_7_2 : yRow 8 3 7 (rows[2]!) = (11311749600528369600555/2097152 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 7 2 (by decide)] + have h : yRowIntegralFast 8 3 7 (rows[2]!) = (61734120687218218053787138616255934133213958544713318400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_7_3 : yRow 8 3 7 (rows[3]!) = (8603647500660654488295/4194304 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 7 3 (by decide)] + have h : yRowIntegralFast 8 3 7 (rows[3]!) = (23477297142930871074039406428360714858159574168161484800000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_7_4 : yRow 8 3 7 (rows[4]!) = (3519874183592373572895/16777216 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 7 4 (by decide)] + have h : yRowIntegralFast 8 3 7 (rows[4]!) = (2401223786411049713220922466624398209967081271800627200000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_7_5 : yRow 8 3 7 (rows[5]!) = (-3479431231969799395785/8388608 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 7 5 (by decide)] + have h : yRowIntegralFast 8 3 7 (rows[5]!) = (-4747267999710378909098188438704975869751880355885875200000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_3_7_6 : yRow 8 3 7 (rows[6]!) = (672523966016989221555/4194304 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 3 7 6 (by decide)] + have h : yRowIntegralFast 8 3 7 (rows[6]!) = (1835157121989341670710322442697238660354473731502899200000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_5_0 : yRow 8 5 5 (rows[0]!) = (-2191463802492555735/512 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 5 0 (by decide)] + have h : yRowIntegralFast 8 5 5 (rows[0]!) = (-48988002718528541435005798209203201739968688205647052800000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_5_1 : yRow 8 5 5 (rows[1]!) = (2321948566914231201/524288 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 5 1 (by decide)] + have h : yRowIntegralFast 8 5 5 (rows[1]!) = (50688340220225875834055464782591602111445800079851520000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_5_2 : yRow 8 5 5 (rows[2]!) = (106818877845876879555/2097152 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 5 2 (by decide)] + have h : yRowIntegralFast 8 5 5 (rows[2]!) = (582966360597529667058459936508264130344641949492838400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_5_3 : yRow 8 5 5 (rows[3]!) = (2894465599178455021275/4194304 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 5 3 (by decide)] + have h : yRowIntegralFast 8 5 5 (rows[3]!) = (7898304636107648937531058100797533823195362870951936000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FiniteFlux/Row083.lean b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row083.lean new file mode 100644 index 0000000000000000000000000000000000000000..133f63deb7f4a763a6fd4f34cf910c737437731a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FiniteFlux/Row083.lean @@ -0,0 +1,128 @@ +import OAI.Analysis.Laughlin.FourBody.FastChoose + +namespace OAI + +namespace Laughlin.Certificate + +theorem yRow_8_5_5_4 : yRow 8 5 5 (rows[4]!) = (17756957755544037975/16777216 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 5 4 (by decide)] + have h : yRowIntegralFast 8 5 5 (rows[4]!) = (12113623133367752972587743288446773259962045956096000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_5_5 : yRow 8 5 5 (rows[5]!) = (607875903328624705389525/469762048 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 5 5 (by decide)] + have h : yRowIntegralFast 8 5 5 (rows[5]!) = (14810250128732551946479860109388307697762371914170368000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_5_6 : yRow 8 5 5 (rows[6]!) = (14119266506282124255/2097152 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 5 6 (by decide)] + have h : yRowIntegralFast 8 5 5 (rows[6]!) = (77056205564619678704021234047790246774509031286374400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_7_0 : yRow 8 5 7 (rows[0]!) = (-2272256943023826045/256 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 7 0 (by decide)] + have h : yRowIntegralFast 8 5 7 (rows[0]!) = (-101588106703327277768404585735202496511763361314321203200000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_7_1 : yRow 8 5 7 (rows[1]!) = (265856006788524411/16384 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 7 1 (by decide)] + have h : yRowIntegralFast 8 5 7 (rows[1]!) = (185717115890761117907991264301533337132741044511703040000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_7_2 : yRow 8 5 7 (rows[2]!) = (-9014338390167069525885/1048576 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 7 2 (by decide)] + have h : yRowIntegralFast 8 5 7 (rows[2]!) = (-98391897583730922009041504617868937065755206491937177600000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_7_3 : yRow 8 5 7 (rows[3]!) = (-6216612413350207898295/2097152 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 7 3 (by decide)] + have h : yRowIntegralFast 8 5 7 (rows[3]!) = (-33927298123138660043769111171450955625046914576783769600000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_7_4 : yRow 8 5 7 (rows[4]!) = (27270331387166645325/262144 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 7 4 (by decide)] + have h : yRowIntegralFast 8 5 7 (rows[4]!) = (1190627436772217281909258082054284765385603508338688000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_7_5 : yRow 8 5 7 (rows[5]!) = (-26878866420346632296175/33554432 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 7 5 (by decide)] + have h : yRowIntegralFast 8 5 7 (rows[5]!) = (-9168250061487993259349020436235780108988519047757824000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_5_7_6 : yRow 8 5 7 (rows[6]!) = (16005164678075894895/524288 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 5 7 6 (by decide)] + have h : yRowIntegralFast 8 5 7 (rows[6]!) = (349394144229991478302979905337497461001824323921510400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_7_7_0 : yRow 8 7 7 (rows[0]!) = (42321625347011687775/512 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 7 7 0 (by decide)] + have h : yRowIntegralFast 8 7 7 (rows[0]!) = (946058016196230415752027336404918886222132921218629632000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_7_7_1 : yRow 8 7 7 (rows[1]!) = (-7376057539791286839/131072 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 7 7 1 (by decide)] + have h : yRowIntegralFast 8 7 7 (rows[1]!) = (-644079923885262353649015021574536610266031989058437120000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_7_7_2 : yRow 8 7 7 (rows[2]!) = (20829685222835364120795/524288 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 7 7 2 (by decide)] + have h : yRowIntegralFast 8 7 7 (rows[2]!) = (454713849522701608096165768651365279143842787883378278400000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_7_7_3 : yRow 8 7 7 (rows[3]!) = (30544199608275577479675/1048576 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 7 7 3 (by decide)] + have h : yRowIntegralFast 8 7 7 (rows[3]!) = (333391273941157787431481591034581183654347604207075328000000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_7_7_4 : yRow 8 7 7 (rows[4]!) = (-1243929398768283753645/4194304 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 7 7 4 (by decide)] + have h : yRowIntegralFast 8 7 7 (rows[4]!) = (-3394385941249665107509736601572607530416212886211788800000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_7_7_5 : yRow 8 7 7 (rows[5]!) = (-45894925152507618987405/16777216 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 7 7 5 (by decide)] + have h : yRowIntegralFast 8 7 7 (rows[5]!) = (-31309069643870677701452949891793221572349284445899980800000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +theorem yRow_8_7_7_6 : yRow 8 7 7 (rows[6]!) = (-466714964291950350585/524288 : ℚ) := by + rw [source_yRow_eq_fastIntegral 8 7 7 6 (by decide)] + have h : yRowIntegralFast 8 7 7 (rows[6]!) = (-10188428474684124940652669537868107900326856055010099200000 : ℤ) := by + decide +kernel + rw [h] + norm_num [arithmeticScale, Nat.factorial] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/Adjoint.lean b/lean/OAI/Analysis/Laughlin/Fock/Adjoint.lean new file mode 100644 index 0000000000000000000000000000000000000000..9f15d86f4e273be201ead5b0e2166116148bf478 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/Adjoint.lean @@ -0,0 +1,39 @@ +import OAI.Analysis.Laughlin.Fock.ContractionBound + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +noncomputable def occupationInner (Q : ℕ) (x y : Space Q) : ℂ := + ∑ A : Finset (Fin (Q+1)), star ((occupationBasis Q).repr x A) * (occupationBasis Q).repr y A + +theorem insertionSign_star (Q : ℕ) (i : Fin (Q+1)) (A : Finset (Fin (Q+1))) : + star (insertionSign Q i A) = insertionSign Q i A := by + rcases insertionSign_spec Q i A with h | h <;> simp [h] + +theorem create_annihilate_adjoint (Q : ℕ) (i : Fin (Q+1)) (x y : Space Q) : + occupationInner Q (create i x) y = occupationInner Q x (annihilate i y) := by + let f : Finset (Fin (Q+1)) → ℂ := fun A => + insertionSign Q i (A.erase i) * + (star ((occupationBasis Q).repr x (A.erase i)) * (occupationBasis Q).repr y A) + have hl : occupationInner Q (create i x) y = + ∑ A ∈ Finset.univ.filter (fun A : Finset (Fin (Q+1)) => i ∈ A), f A := by + rw [Finset.sum_filter] + unfold occupationInner + apply Finset.sum_congr rfl + intro A hA + by_cases hi : i ∈ A <;> + simp only [f, create_coordinate, hi, ite_true, ite_false, star_mul, + insertionSign_star, star_zero, zero_mul, mul_comm, mul_left_comm] + rw [hl, ← sum_unoccupied_insert i f, Finset.sum_filter] + unfold occupationInner + apply Finset.sum_congr rfl + intro A hA + by_cases hi : i ∈ A <;> + simp only [f, hi, annihilate_coordinate, not_true_eq_false, not_false_eq_true, + ite_true, ite_false, Finset.erase_insert, zero_mul, mul_assoc, mul_comm] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/Annihilation.lean b/lean/OAI/Analysis/Laughlin/Fock/Annihilation.lean new file mode 100644 index 0000000000000000000000000000000000000000..af0168a0c12768fa5241d0f9d8e4889a3bf5e40d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/Annihilation.lean @@ -0,0 +1,59 @@ +import OAI.Analysis.Laughlin.Fock.Creation + +namespace OAI + +namespace Laughlin.Fock + +noncomputable def insertionSign (Q : ℕ) (i : Fin (Q+1)) (A : Finset (Fin (Q+1))) : ℂ := + if h : i ∉ A then (create_unoccupied_sign Q i A h).choose else 1 + +theorem insertionSign_spec (Q : ℕ) (i : Fin (Q+1)) (A : Finset (Fin (Q+1))) : + insertionSign Q i A = 1 ∨ insertionSign Q i A = -1 := by + by_cases h : i ∉ A + · simpa [insertionSign,h] using (create_unoccupied_sign Q i A h).choose_spec.1 + · simp [insertionSign,h] + +theorem insertionSign_sq (Q : ℕ) (i : Fin (Q+1)) (A : Finset (Fin (Q+1))) : + insertionSign Q i A * insertionSign Q i A = 1 := by + rcases insertionSign_spec Q i A with h | h <;> simp [h] + +theorem insertionSign_norm (Q : ℕ) (i : Fin (Q+1)) (A : Finset (Fin (Q+1))) : + ‖insertionSign Q i A‖ = 1 := by + rcases insertionSign_spec Q i A with h | h <;> simp [h] + +theorem create_unoccupied (Q : ℕ) (i : Fin (Q+1)) + (A : Finset (Fin (Q+1))) (hi : i ∉ A) : + create i (occupationBasis Q A) = insertionSign Q i A • occupationBasis Q (insert i A) := by + simpa [insertionSign,hi] using (create_unoccupied_sign Q i A hi).choose_spec.2 + +theorem annihilate_insert (Q : ℕ) (i : Fin (Q+1)) + (A : Finset (Fin (Q+1))) (hi : i ∉ A) : + annihilate i (occupationBasis Q (insert i A)) = insertionSign Q i A • occupationBasis Q A := by + have h := LinearMap.congr_fun (mixed_car i i) (occupationBasis Q A) + change annihilate i (create i (occupationBasis Q A)) + + create i (annihilate i (occupationBasis Q A)) = (if i = i then (1 : ℂ) else 0) • occupationBasis Q A at h + rw [create_unoccupied Q i A hi, map_smul, annihilate_unoccupied Q i A hi, map_zero] at h + simp only [add_zero, ite_true, one_smul] at h + have he := congrArg (fun x => insertionSign Q i A • x) h + simpa only [smul_smul, insertionSign_sq, one_smul] using he + +theorem annihilate_occupied (Q : ℕ) (i : Fin (Q+1)) + (A : Finset (Fin (Q+1))) (hi : i ∈ A) : + annihilate i (occupationBasis Q A) = + insertionSign Q i (A.erase i) • occupationBasis Q (A.erase i) := by + simpa only [Finset.insert_erase hi] using + annihilate_insert Q i (A.erase i) (Finset.notMem_erase i A) + +theorem number_occupation (Q : ℕ) (i : Fin (Q+1)) (A : Finset (Fin (Q+1))) : + (create i * annihilate i) (occupationBasis Q A) = + if i ∈ A then occupationBasis Q A else 0 := by + by_cases hi : i ∈ A + · have h := LinearMap.congr_fun (mixed_car i i) (occupationBasis Q A) + change annihilate i (create i (occupationBasis Q A)) + + create i (annihilate i (occupationBasis Q A)) = (if i = i then (1 : ℂ) else 0) • occupationBasis Q A at h + simpa [hi,create_occupied Q i A hi] using h + · simpa [hi] using congrArg (create i) (annihilate_unoccupied Q i A hi) + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/Bidegree.lean b/lean/OAI/Analysis/Laughlin/Fock/Bidegree.lean new file mode 100644 index 0000000000000000000000000000000000000000..a0baddb363e58e9835b9a3ea044103b29126d4c2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/Bidegree.lean @@ -0,0 +1,49 @@ +import OAI.Analysis.Laughlin.Fock.Inner + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem occupation_empty (Q : ℕ) : occupationBasis Q ∅ = (1 : Space Q) := by + let A : Set.powersetCard (Fin (Q+1)) 0 := ⟨∅,rfl⟩ + change (Pi.basisFun ℂ (Fin (Q+1))).ExteriorAlgebra A.val = _ + rw [ExteriorAlgebra.basis_apply_powersetCard] + simp [ExteriorAlgebra.ιMulti_family,ExteriorAlgebra.ιMulti_zero_apply] + +def OccupationBidegree (Q n w : ℕ) (x : Space Q) : Prop := + ∀ A : Finset (Fin (Q+1)), (A.card ≠ n ∨ (∑ i ∈ A, i.val) ≠ w) → + (occupationBasis Q).repr x A = 0 + +theorem vacuum_bidegree (Q : ℕ) : OccupationBidegree Q 0 0 (1 : Space Q) := by + intro A hA + have hn : (∅ : Finset (Fin (Q+1))) ≠ A := by intro he; subst A; simp at hA + rw [← occupation_empty] + simp [Module.Basis.repr_self,hn] + +theorem create_bidegree (Q n w : ℕ) (x : Space Q) (hx : OccupationBidegree Q n w x) + (i : Fin (Q+1)) : OccupationBidegree Q (n+1) (w+i.val) (create i x) := by + intro A hA + rw [create_coordinate] + by_cases hi : i ∈ A + · rw [ite_eq_left hi] + have hc := Finset.card_erase_of_mem hi + have hw := Finset.sum_erase_add A (fun j : Fin (Q+1) => j.val) hi + have hlow : (A.erase i).card ≠ n ∨ (∑ j ∈ A.erase i, j.val) ≠ w := by + rcases hA with hA | hA + · left; have hp := Finset.card_pos.mpr ⟨i,hi⟩; omega + · right; omega + rw [hx (A.erase i) hlow,mul_zero] + · rw [ite_eq_right hi] + +theorem four_create_bidegree (Q : ℕ) (a b c d : Fin (Q+1)) : + OccupationBidegree Q 4 (a.val+b.val+c.val+d.val) + (create a (create b (create c (create d (1 : Space Q))))) := by + have h := create_bidegree Q _ _ _ + (create_bidegree Q _ _ _ (create_bidegree Q _ _ _ + (create_bidegree Q 0 0 _ (vacuum_bidegree Q) d) c) b) a + convert h using 1; omega + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/ContractionBound.lean b/lean/OAI/Analysis/Laughlin/Fock/ContractionBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..26d0715e8b53771fb6264351ae7a1ef187788898 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/ContractionBound.lean @@ -0,0 +1,65 @@ +import OAI.Analysis.Laughlin.Fock.Coordinates + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem sum_unoccupied_insert {Q : ℕ} {R : Type*} [AddCommMonoid R] + (i : Fin (Q+1)) (f : Finset (Fin (Q+1)) → R) : + (∑ A ∈ Finset.univ.filter (fun A : Finset (Fin (Q+1)) => i ∉ A), f (insert i A)) = + ∑ A ∈ Finset.univ.filter (fun A : Finset (Fin (Q+1)) => i ∈ A), f A := by + classical + apply Finset.sum_bij (fun A _ => insert i A) + · intro A hA + simp + · intro A hA B hB h + have ha := (Finset.mem_filter.mp hA).2 + have hb := (Finset.mem_filter.mp hB).2 + have he := congrArg (fun C => C.erase i) h + simpa [Finset.erase_insert,ha,hb] using he + · intro B hB + have hb := (Finset.mem_filter.mp hB).2 + exact ⟨B.erase i,by simp,Finset.insert_erase hb⟩ + · intro A hA + rfl + +theorem annihilate_normSq (Q : ℕ) (i : Fin (Q+1)) (x : Space Q) : + occupationNormSq Q (annihilate i x) = + ∑ A : Finset (Fin (Q+1)), if i ∈ A then ‖(occupationBasis Q).repr x A‖^2 else 0 := by + have h (A : Finset (Fin (Q+1))) : + ‖(occupationBasis Q).repr (annihilate i x) A‖^2 = + if i ∉ A then ‖(occupationBasis Q).repr x (insert i A)‖^2 else 0 := by + by_cases hi : i ∈ A <;> simp [annihilate_coordinate,hi,insertionSign_norm] + unfold occupationNormSq + simp_rw [h] + simpa only [Finset.sum_filter] using + sum_unoccupied_insert (R := ℝ) i (fun A => ‖(occupationBasis Q).repr x A‖^2) + +theorem annihilate_normSq_le (Q : ℕ) (i : Fin (Q+1)) (x : Space Q) : + occupationNormSq Q (annihilate i x) ≤ occupationNormSq Q x := by + rw [annihilate_normSq] + unfold occupationNormSq + apply Finset.sum_le_sum + intro A hA + split_ifs + · exact le_rfl + · positivity + +theorem two_annihilate_normSq_le (Q : ℕ) (j k : Fin (Q+1)) (x : Space Q) : + occupationNormSq Q (annihilate k (annihilate j x)) ≤ occupationNormSq Q x := + (annihilate_normSq_le Q k _).trans (annihilate_normSq_le Q j x) + +theorem sourceFour_normSq_le_pair (Q p : ℕ) (j k : Fin (Q+1)) (x : Space Q) : + occupationNormSq Q (sourceFourEnd Q p j k x) ≤ + occupationNormSq Q (sourcePairEnd Q p x) := + two_annihilate_normSq_le Q j k (sourcePairEnd Q p x) + +theorem limitFour_normSq_le_pair (Q p : ℕ) (j k : Fin (Q+1)) (x : Space Q) : + occupationNormSq Q (limitFourEnd Q p j k x) ≤ + occupationNormSq Q (limitPairEnd Q p x) := + two_annihilate_normSq_le Q j k (limitPairEnd Q p x) + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/Coordinates.lean b/lean/OAI/Analysis/Laughlin/Fock/Coordinates.lean new file mode 100644 index 0000000000000000000000000000000000000000..e914512be66de08405387a45bebf6916f6115fa7 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/Coordinates.lean @@ -0,0 +1,70 @@ +import OAI.Analysis.Laughlin.Fock.Annihilation + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem annihilate_coordinate (Q : ℕ) (i : Fin (Q+1)) (x : Space Q) + (A : Finset (Fin (Q+1))) : + (occupationBasis Q).repr (annihilate i x) A = + if i ∈ A then 0 else insertionSign Q i A * (occupationBasis Q).repr x (insert i A) := by + let e : ℂ := if i ∈ A then 0 else insertionSign Q i A + have h : ((occupationBasis Q).coord A).comp (annihilate i) = + e • (occupationBasis Q).coord (insert i A) := by + apply (occupationBasis Q).ext + intro B + change (occupationBasis Q).repr (annihilate i (occupationBasis Q B)) A = + e * (occupationBasis Q).repr (occupationBasis Q B) (insert i A) + by_cases hiB : i ∈ B + · rw [annihilate_occupied Q i B hiB, map_smul, Finsupp.smul_apply] + by_cases hiA : i ∈ A + · have hBA : B.erase i ≠ A := by intro h; rw [← h] at hiA; exact Finset.notMem_erase i B hiA + simp [e,hiA,Module.Basis.repr_self,Finsupp.single_apply,hBA] + · by_cases hBA : B = insert i A + · subst B + simp [e,hiA,Module.Basis.repr_self] + · have herase : B.erase i ≠ A := by + intro h + apply hBA + rw [← h,Finset.insert_erase hiB] + simp [e,hiA,Module.Basis.repr_self,herase,hBA] + · rw [annihilate_unoccupied Q i B hiB] + have hBA : B ≠ insert i A := by intro h; subst B; simp at hiB + simp [e,Module.Basis.repr_self,hBA] + have hx := LinearMap.congr_fun h x + by_cases hi : i ∈ A <;> simpa [e,hi] using hx + +theorem create_coordinate (Q : ℕ) (i : Fin (Q+1)) (x : Space Q) + (A : Finset (Fin (Q+1))) : + (occupationBasis Q).repr (create i x) A = + if i ∈ A then insertionSign Q i (A.erase i) * (occupationBasis Q).repr x (A.erase i) else 0 := by + let e : ℂ := if i ∈ A then insertionSign Q i (A.erase i) else 0 + have h : ((occupationBasis Q).coord A).comp (create i) = + e • (occupationBasis Q).coord (A.erase i) := by + apply (occupationBasis Q).ext + intro B + change (occupationBasis Q).repr (create i (occupationBasis Q B)) A = + e * (occupationBasis Q).repr (occupationBasis Q B) (A.erase i) + by_cases hiB : i ∈ B + · rw [create_occupied Q i B hiB] + have hBA : B ≠ A.erase i := by intro h; rw [h] at hiB; exact Finset.notMem_erase i A hiB + simp [e,Module.Basis.repr_self,hBA] + · rw [create_unoccupied Q i B hiB,map_smul,Finsupp.smul_apply] + by_cases hiA : i ∈ A + · by_cases hBA : B = A.erase i + · subst B + simp [e,hiA,Module.Basis.repr_self] + · have hins : insert i B ≠ A := by + intro h + apply hBA + rw [← h,Finset.erase_insert hiB] + simp [e,hiA,Module.Basis.repr_self,hBA,hins] + · have hins : insert i B ≠ A := by intro h; rw [← h] at hiA; simp at hiA + simp [e,hiA,Module.Basis.repr_self,Finsupp.single_apply,hins] + have hx := LinearMap.congr_fun h x + by_cases hi : i ∈ A <;> simpa [e,hi] using hx + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/Creation.lean b/lean/OAI/Analysis/Laughlin/Fock/Creation.lean new file mode 100644 index 0000000000000000000000000000000000000000..ac29de2313babf0e9892931a49429c42192196bc --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/Creation.lean @@ -0,0 +1,62 @@ +import Mathlib.Algebra.Ring.Int.Units +import OAI.Analysis.Laughlin.Exterior.OccupationMetric + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem occupation_singleton (Q : ℕ) (i : Fin (Q+1)) : + occupationBasis Q {i} = ExteriorAlgebra.ι ℂ (mode i) := by + let A : Set.powersetCard (Fin (Q+1)) 1 := ⟨{i},Finset.card_singleton i⟩ + have hi : Set.powersetCard.ofFinEmbEquiv.symm A 0 = i := by + have hm := (Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem A + (Set.powersetCard.ofFinEmbEquiv.symm A 0)).mp ⟨0,rfl⟩ + exact Finset.mem_singleton.mp hm + change (Pi.basisFun ℂ (Fin (Q+1))).ExteriorAlgebra A.val = _ + rw [ExteriorAlgebra.basis_apply_powersetCard] + simp only [ExteriorAlgebra.ιMulti_family, ExteriorAlgebra.ιMulti_succ_apply, + ExteriorAlgebra.ιMulti_zero_apply, mul_one, Function.comp_apply, hi] + simp [Pi.basisFun_apply, mode] + +theorem annihilate_unoccupied (Q : ℕ) (i : Fin (Q+1)) + (A : Finset (Fin (Q+1))) (hi : i ∉ A) : annihilate i (occupationBasis Q A) = 0 := by + let d : Fin (Q+1) → ℂ := fun j => if j = i then 0 else 1 + have hd : (∏ j ∈ A, d j) = 1 := by + apply Finset.prod_eq_one + intro j hj + simp [d, show j ≠ i by intro h; subst j; exact hi hj] + have h := annihilate_scaling Q d i (occupationBasis Q A) + rw [exteriorScaling_occupation,hd,one_smul] at h + simpa [d] using h + +theorem create_occupied (Q : ℕ) (i : Fin (Q+1)) + (A : Finset (Fin (Q+1))) (hi : i ∈ A) : create i (occupationBasis Q A) = 0 := by + have hd : ¬Disjoint ({i} : Finset (Fin (Q+1))) A := by simpa using hi + have h := ExteriorAlgebra.basis_mul_of_not_disjoint + (Pi.basisFun ℂ (Fin (Q+1))) + (⟨{i},Finset.card_singleton i⟩ : Set.powersetCard (Fin (Q+1)) 1) + (⟨A,rfl⟩ : Set.powersetCard (Fin (Q+1)) A.card) hd + change occupationBasis Q {i} * occupationBasis Q A = 0 at h + rw [occupation_singleton] at h + exact h + +theorem create_unoccupied_sign (Q : ℕ) (i : Fin (Q+1)) + (A : Finset (Fin (Q+1))) (hi : i ∉ A) : + ∃ ε : ℂ, (ε = 1 ∨ ε = -1) ∧ + create i (occupationBasis Q A) = ε • occupationBasis Q (insert i A) := by + let S : Set.powersetCard (Fin (Q+1)) 1 := ⟨{i},Finset.card_singleton i⟩ + let T : Set.powersetCard (Fin (Q+1)) A.card := ⟨A,rfl⟩ + have hd : Disjoint S.val T.val := by simpa [S,T] using hi + have h := ExteriorAlgebra.basis_mul_of_disjoint (Pi.basisFun ℂ (Fin (Q+1))) S T hd + rcases Int.units_eq_one_or (Set.powersetCard.permOfDisjoint hd).sign with hs | hs + · refine ⟨1,Or.inl rfl,?_⟩ + simpa [hs,S,T,occupationBasis,Set.powersetCard.disjUnion, + ← occupation_singleton Q i, create] using h + · refine ⟨-1,Or.inr rfl,?_⟩ + simpa [hs,S,T,occupationBasis,Set.powersetCard.disjUnion, + ← occupation_singleton Q i, create] using h + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/EigenvalueGap.lean b/lean/OAI/Analysis/Laughlin/Fock/EigenvalueGap.lean new file mode 100644 index 0000000000000000000000000000000000000000..32733ab9820b05f4b22bf068b174c909de79bb69 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/EigenvalueGap.lean @@ -0,0 +1,71 @@ +import OAI.Analysis.Laughlin.Operators.PhysicalFockGap + +namespace OAI + +namespace Laughlin.Fock +open Filter +open scoped BigOperators + +theorem sourceFockHamiltonian_symmetric (Q : ℕ) (x y : Space Q) : + occupationInner Q (sourceFockHamiltonian Q x) y = + occupationInner Q x (sourceFockHamiltonian Q y) := by + simp only [sourceFockHamiltonian,LinearMap.sum_apply,Module.End.mul_apply, + occupationInner_sum_left,occupationInner_sum_right,pair_annihilate_create_inner] + apply Finset.sum_congr rfl + intro p hp + exact pairCreate_pair_adjoint Q _ _ _ + +theorem sourceFockHamiltonian_kernel (Q : ℕ) (x : Space Q) : + sourceFockHamiltonian Q x=0 ↔ sourceFockEnergy Q x=0 := by + constructor + · intro h + have he := sourceFockHamiltonian_quadratic Q x + rw [h] at he + have hz : occupationInner Q 0 x=0 := by simp [occupationInner] + rw [hz] at he + exact Complex.ofReal_injective he.symm + · intro h + have he := (sourceFockEnergy_eq_zero Q x).mp h + simp only [sourceFockHamiltonian,LinearMap.sum_apply,Module.End.mul_apply] + apply Finset.sum_eq_zero + intro p hp + rw [he p hp,map_zero] + +theorem sourceFock_eigen_energy (Q : ℕ) (x : Space Q) (a : ℝ) + (he : sourceFockHamiltonian Q x=(a : ℂ) • x) : + sourceFockEnergy Q x=a*occupationNormSq Q x := by + have h := sourceFockHamiltonian_quadratic Q x + rw [he,occupationInner_smul_left,occupationInner_self] at h + simp only [Complex.star_def,Complex.conj_ofReal,← Complex.ofReal_mul] at h + exact Complex.ofReal_injective h.symm + +theorem sourceFock_eigen_nonneg (Q : ℕ) (x : Space Q) (hx : x≠0) (a : ℝ) + (he : sourceFockHamiltonian Q x=(a : ℂ) • x) : 0 ≤ a := by + have hn : 0 < occupationNormSq Q x := + lt_of_le_of_ne (occupationNormSq_nonneg Q x) (Ne.symm (mt (occupationNormSq_eq_zero Q x).mp hx)) + have hE : 0 ≤ sourceFockEnergy Q x := Finset.sum_nonneg (fun p hp => occupationNormSq_nonneg Q _) + rw [sourceFock_eigen_energy Q x a he] at hE + exact nonneg_of_mul_nonneg_left hE hn + +theorem physical_fock_eigenvalue_gap_uniform : + ∃ Q₀ : ℕ, 25 ≤ Q₀ ∧ ∀ Q : ℕ, Q₀ ≤ Q → ∀ x : Space Q, x≠0 → ∀ a : ℝ, + sourceFockHamiltonian Q x=(a : ℂ) • x → a=0 ∨ (1/100 : ℝ) ≤ a := by + obtain ⟨Q₀,h25,h⟩ := physical_fock_square_uniform + refine ⟨Q₀,h25,fun Q hQ x hx a he => ?_⟩ + have hn : 0 < occupationNormSq Q x := + lt_of_le_of_ne (occupationNormSq_nonneg Q x) (Ne.symm (mt (occupationNormSq_eq_zero Q x).mp hx)) + have ha := sourceFock_eigen_nonneg Q x hx a he + have hs := h Q hQ x + rw [sourceFock_eigen_energy Q x a he,he,occupationNormSq_smul] at hs + have hnorm : ‖(a : ℂ)‖^2=a^2 := by simp + rw [hnorm] at hs + have hs' : (1/100 : ℝ)*a ≤ a^2 := by nlinarith + by_cases hz : a=0 + · exact Or.inl hz + · right + have hp : 0 < a := lt_of_le_of_ne ha (Ne.symm hz) + nlinarith + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/EnergyRotation.lean b/lean/OAI/Analysis/Laughlin/Fock/EnergyRotation.lean new file mode 100644 index 0000000000000000000000000000000000000000..ad312c66753622714c7f7b925177638fd7b973a1 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/EnergyRotation.lean @@ -0,0 +1,42 @@ +import OAI.Analysis.Laughlin.Fock.UnitaryFamilies +import OAI.Analysis.Laughlin.Pair.FockCovariance + +namespace OAI + +namespace Laughlin.Fock +open Rotation +open scoped BigOperators Matrix + +theorem sourceFockEnergy_eq_fin (Q : ℕ) (hQ : 0 < Q) (x : Space Q) : + sourceFockEnergy Q x = ∑ p : Fin (2*Q-2+1), occupationNormSq Q (sourcePairEnd Q p.val x) := by + unfold sourceFockEnergy + rw [show 2*Q-1=2*Q-2+1 by omega] + exact (Fin.sum_univ_eq_sum_range _ _).symm + +theorem sourceFockEnergy_rotation (Q : ℕ) (hQ : 0 < Q) (g : SourceSU2) (x : Space Q) : + sourceFockEnergy Q (exteriorRotation Q g x) = sourceFockEnergy Q x := by + rw [sourceFockEnergy_eq_fin Q hQ,sourceFockEnergy_eq_fin Q hQ] + simp_rw [sourcePairEnd_rotation Q hQ g] + have hu := Matrix.mem_unitaryGroup_iff'.mp (sourceSpinRepresentation_unitary (2*Q-2) g) + rw [Matrix.star_eq_conjTranspose] at hu + rw [unitary_sum_occupationNormSq Q _ hu] + simp only [exteriorRotation_norm] + +theorem sourceFockHamiltonian_apply_fin (Q : ℕ) (hQ : 0 < Q) (x : Space Q) : + sourceFockHamiltonian Q x = ∑ p : Fin (2*Q-2+1), + sourcePairVector Q p.val * sourcePairEnd Q p.val x := by + simp only [sourceFockHamiltonian,LinearMap.sum_apply,Module.End.mul_apply,sourcePairCreateEnd_mul] + rw [show 2*Q-1=2*Q-2+1 by omega] + exact (Fin.sum_univ_eq_sum_range _ _).symm + +theorem sourceFockHamiltonian_rotation (Q : ℕ) (hQ : 0 < Q) (g : SourceSU2) (x : Space Q) : + sourceFockHamiltonian Q (exteriorRotation Q g x) = + exteriorRotation Q g (sourceFockHamiltonian Q x) := by + rw [sourceFockHamiltonian_apply_fin Q hQ,sourceFockHamiltonian_apply_fin Q hQ] + simp only [sourcePairEnd_rotation Q hQ g,map_sum,map_mul,sourcePairVector_rotation Q hQ, + Finset.sum_mul,Finset.mul_sum,smul_mul_assoc,mul_smul_comm] + rw [Finset.sum_comm] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/FourLabels.lean b/lean/OAI/Analysis/Laughlin/Fock/FourLabels.lean new file mode 100644 index 0000000000000000000000000000000000000000..b9dc723917dca49822a15b9d59ccd01e9fd3bf77 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/FourLabels.lean @@ -0,0 +1,39 @@ +import OAI.Analysis.Laughlin.Fock.Bidegree + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +noncomputable def occupationFourLabels (Q : ℕ) (A : Finset (Fin (Q+1))) (hA : A.card=4) : + Fin 4 ↪o Fin (Q+1) := Set.powersetCard.ofFinEmbEquiv.symm ⟨A,hA⟩ + +theorem occupationBasis_four (Q : ℕ) (A : Finset (Fin (Q+1))) (hA : A.card=4) : + occupationBasis Q A = + create (occupationFourLabels Q A hA 0) (create (occupationFourLabels Q A hA 1) + (create (occupationFourLabels Q A hA 2) (create (occupationFourLabels Q A hA 3) (1 : Space Q)))) := by + let B : Set.powersetCard (Fin (Q+1)) 4 := ⟨A,hA⟩ + change (Pi.basisFun ℂ (Fin (Q+1))).ExteriorAlgebra B.val = _ + rw [ExteriorAlgebra.basis_apply_powersetCard] + simp [ExteriorAlgebra.ιMulti_family,ExteriorAlgebra.ιMulti_succ_apply, + ExteriorAlgebra.ιMulti_zero_apply,occupationFourLabels,B,create,Pi.basisFun_apply,mode,Matrix.vecTail,Function.comp_def] + +theorem occupationFourLabels_range (Q : ℕ) (A : Finset (Fin (Q+1))) (hA : A.card=4) : + Finset.univ.image (occupationFourLabels Q A hA) = A := by + ext i + simp only [Finset.mem_image,Finset.mem_univ,true_and] + exact Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem ⟨A,hA⟩ i + +theorem occupationFourLabels_sum (Q : ℕ) (A : Finset (Fin (Q+1))) (hA : A.card=4) : + (∑ i ∈ A, i.val) = + (occupationFourLabels Q A hA 0).val + (occupationFourLabels Q A hA 1).val + + (occupationFourLabels Q A hA 2).val + (occupationFourLabels Q A hA 3).val := by + conv_lhs => rw [← occupationFourLabels_range Q A hA] + rw [Finset.sum_image] + · simp [Fin.sum_univ_succ,Nat.add_assoc] + · intro i hi j hj he + exact (occupationFourLabels Q A hA).injective he + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/HaarQuadratic.lean b/lean/OAI/Analysis/Laughlin/Fock/HaarQuadratic.lean new file mode 100644 index 0000000000000000000000000000000000000000..f6141a8f8a10c5d668c8832f87aec013db55b2de --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/HaarQuadratic.lean @@ -0,0 +1,52 @@ +import OAI.Analysis.Laughlin.Exterior.FamilyCovariance +import OAI.Analysis.Laughlin.Fock.MatrixQuadratic +import OAI.Analysis.Laughlin.Spin.CompactAverage + +namespace OAI + +namespace Laughlin.Fock +open Rotation MeasureTheory +open scoped BigOperators Matrix + +noncomputable def contractionForm {I : Type*} [Fintype I] (Q : ℕ) + (minus : I → Module.End ℂ (Space Q)) (M : Matrix I I ℂ) (x : Space Q) : ℂ := + ∑ i, ∑ j, M i j * occupationInner Q (minus i x) (minus j x) + +theorem contractionForm_rotation {I : Type*} [Fintype I] [DecidableEq I] + (Q : ℕ) (ρ : SourceSU2 →* Matrix I I ℂ) + (hρ : ∀ g, ρ g⁻¹=(ρ g)ᴴ) + (minus : I → Module.End ℂ (Space Q)) + (hm : ∀ g i x, minus i (exteriorRotation Q g x) = + ∑ j, ρ g i j • exteriorRotation Q g (minus j x)) + (M : Matrix I I ℂ) (g : SourceSU2) (x : Space Q) : + contractionForm Q minus M (exteriorRotation Q g⁻¹ x) = + contractionForm Q minus (conjugateOrbit ρ M g) x := by + unfold contractionForm + simp_rw [hm,hρ,Matrix.conjTranspose_apply] + rw [occupation_matrix_quadratic_factor] + simp_rw [exteriorRotation_unitary] + simp only [conjugateOrbit,hρ] + +theorem contractionForm_haar {I : Type*} [Fintype I] [DecidableEq I] + (Q : ℕ) (ρ : SourceSU2 →* Matrix I I ℂ) + (hρ : ∀ g, ρ g⁻¹=(ρ g)ᴴ) + (hc : ∀ i j, Continuous (fun g => ρ g i j)) + (minus : I → Module.End ℂ (Space Q)) + (hm : ∀ g i x, minus i (exteriorRotation Q g x) = + ∑ j, ρ g i j • exteriorRotation Q g (minus j x)) + (M : Matrix I I ℂ) (x : Space Q) : + (∫ g, contractionForm Q minus M (exteriorRotation Q g⁻¹ x) ∂sourceHaar) = + contractionForm Q minus (matrixIntegral sourceHaar (conjugateOrbit ρ M)) x := by + simp_rw [contractionForm_rotation Q ρ hρ minus hm] + unfold contractionForm + have hi := compact_conjugateOrbit_integrable sourceHaar ρ hc M + rw [integral_finsetSum _ (fun i hi' => integrable_finsetSum _ + (fun j hj => (hi i j).mul_const _))] + apply Finset.sum_congr rfl + intro i hi' + rw [integral_finsetSum _ (fun j hj => (hi i j).mul_const _)] + simp only [integral_mul_const,matrixIntegral] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/Hamiltonian.lean b/lean/OAI/Analysis/Laughlin/Fock/Hamiltonian.lean new file mode 100644 index 0000000000000000000000000000000000000000..5bc8c400224dbb0f52bcf25558ff341245bc3c11 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/Hamiltonian.lean @@ -0,0 +1,48 @@ +import OAI.Analysis.Laughlin.Fock.Inner + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +noncomputable def pairCreateEnd (Q : ℕ) (c : Fin (Q+1) → Fin (Q+1) → ℂ) : + Module.End ℂ (Space Q) := ∑ i, ∑ j, star (c i j) • (create i * create j) + +theorem pairCreate_pair_adjoint (Q : ℕ) (c : Fin (Q+1) → Fin (Q+1) → ℂ) + (x y : Space Q) : + occupationInner Q (pairCreateEnd Q c x) y = occupationInner Q x (pairEnd Q c y) := by + simp only [pairCreateEnd,pairEnd,LinearMap.sum_apply,LinearMap.smul_apply,Module.End.mul_apply, + occupationInner_sum_left,occupationInner_sum_right,occupationInner_smul_left, + occupationInner_smul_right,star_star,create_annihilate_adjoint] + +noncomputable def sourcePairCreateEnd (Q p : ℕ) : Module.End ℂ (Space Q) := + pairCreateEnd Q (fun i j => ((pairCoefficient Q p i j / Real.sqrt 2 : ℝ) : ℂ)) + +noncomputable def sourceFockHamiltonian (Q : ℕ) : Module.End ℂ (Space Q) := + ∑ p ∈ Finset.range (2*Q-1), sourcePairCreateEnd Q p * sourcePairEnd Q p + +noncomputable def sourceFockEnergy (Q : ℕ) (x : Space Q) : ℝ := + ∑ p ∈ Finset.range (2*Q-1), occupationNormSq Q (sourcePairEnd Q p x) + +theorem sourceFockHamiltonian_quadratic (Q : ℕ) (x : Space Q) : + occupationInner Q (sourceFockHamiltonian Q x) x = (sourceFockEnergy Q x : ℂ) := by + simp only [sourceFockHamiltonian,LinearMap.sum_apply,Module.End.mul_apply, + occupationInner_sum_left,sourcePairCreateEnd,sourcePairEnd,pairCreate_pair_adjoint, + occupationInner_self,sourceFockEnergy,Complex.ofReal_sum] + +theorem sourceFockHamiltonian_positive (Q : ℕ) (x : Space Q) : + 0 ≤ (occupationInner Q (sourceFockHamiltonian Q x) x).re := by + rw [sourceFockHamiltonian_quadratic] + simp only [Complex.ofReal_re] + unfold sourceFockEnergy + exact Finset.sum_nonneg (fun p hp => occupationNormSq_nonneg Q _) + +theorem sourceFockEnergy_eq_zero (Q : ℕ) (x : Space Q) : + sourceFockEnergy Q x = 0 ↔ ∀ p ∈ Finset.range (2*Q-1), sourcePairEnd Q p x = 0 := by + unfold sourceFockEnergy + rw [Finset.sum_eq_zero_iff_of_nonneg (fun p hp => occupationNormSq_nonneg Q _)] + simp only [occupationNormSq_eq_zero] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/Inner.lean b/lean/OAI/Analysis/Laughlin/Fock/Inner.lean new file mode 100644 index 0000000000000000000000000000000000000000..72383d9f567cf1cd1bfcf0464915c415f8fd54f5 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/Inner.lean @@ -0,0 +1,55 @@ +import OAI.Analysis.Laughlin.Fock.Adjoint + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem occupationInner_smul_left (Q : ℕ) (c : ℂ) (x y : Space Q) : + occupationInner Q (c • x) y = star c * occupationInner Q x y := by + simp [occupationInner,star_mul,Finset.mul_sum,mul_comm,mul_left_comm] + +theorem occupationInner_smul_right (Q : ℕ) (c : ℂ) (x y : Space Q) : + occupationInner Q x (c • y) = c * occupationInner Q x y := by + simp [occupationInner,Finset.mul_sum,mul_left_comm] + +theorem occupationInner_sum_left {I : Type*} (Q : ℕ) (s : Finset I) + (x : I → Space Q) (y : Space Q) : + occupationInner Q (∑ a ∈ s, x a) y = ∑ a ∈ s, occupationInner Q (x a) y := by + simp only [occupationInner,map_sum,Finsupp.finsetSum_apply,star_sum,Finset.sum_mul] + rw [Finset.sum_comm] + +theorem occupationInner_sum_right {I : Type*} (Q : ℕ) (s : Finset I) + (x : Space Q) (y : I → Space Q) : + occupationInner Q x (∑ a ∈ s, y a) = ∑ a ∈ s, occupationInner Q x (y a) := by + simp only [occupationInner,map_sum,Finsupp.finsetSum_apply,Finset.mul_sum] + rw [Finset.sum_comm] + +theorem occupationInner_self (Q : ℕ) (x : Space Q) : + occupationInner Q x x = (occupationNormSq Q x : ℂ) := by + unfold occupationInner occupationNormSq + simp only [Complex.ofReal_sum] + apply Finset.sum_congr rfl + intro A hA + rw [← Complex.normSq_eq_norm_sq,Complex.normSq_eq_conj_mul_self] + rfl + +theorem occupationNormSq_eq_zero (Q : ℕ) (x : Space Q) : + occupationNormSq Q x = 0 ↔ x = 0 := by + constructor + · intro h + have hc : ∀ A, (occupationBasis Q).repr x A = 0 := by + have hs := (Finset.sum_eq_zero_iff_of_nonneg + (fun A (_ : A ∈ Finset.univ) => sq_nonneg ‖(occupationBasis Q).repr x A‖)).mp h + intro A + have ha := hs A (Finset.mem_univ A) + simpa using ha + apply (occupationBasis Q).repr.injective + ext A + simp [hc] + · intro h + simp [h,occupationNormSq] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/LaughlinGap.lean b/lean/OAI/Analysis/Laughlin/Fock/LaughlinGap.lean new file mode 100644 index 0000000000000000000000000000000000000000..4f07975fb82f48dd47f92a47a10409ddf5481d92 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/LaughlinGap.lean @@ -0,0 +1,47 @@ +import OAI.Analysis.Laughlin.Fock.SharpGap +import OAI.Analysis.Laughlin.Main + +namespace OAI + +namespace Laughlin +open Fock +open scoped BigOperators + +def HaldaneKernelInput : Prop := + ∀ N : ℕ, 2 ≤ N → ∀ ψ : State N (3*(N-1)), Antisymmetric ψ → + energy ψ = 0 → ∃ c : ℂ, ψ = fun a => c * laughlinVector N (3*(N-1)) a + +def SharpMainTarget : Prop := + ∃ N₀ : ℕ, 2 ≤ N₀ ∧ ∀ N : ℕ, N₀ ≤ N → + ∀ ψ : State N (3*(N-1)), Antisymmetric ψ → + (1/25 : ℝ) * distanceToLaughlinSq ψ ≤ energy ψ + +theorem sharpMainTarget_of_haldane (hkernel : HaldaneKernelInput) : SharpMainTarget := by + obtain ⟨Q₀,h25,hgap⟩ := physical_fock_kernel_distance_uniform_sharp (1/25) + (by norm_num) one_twenty_fifth_lt_gammaStar + refine ⟨Q₀+2,by omega,fun N hN ψ hψ => ?_⟩ + have hN2 : 2 ≤ N := by omega + obtain ⟨n,rfl⟩ : ∃ n, N=n+2 := ⟨N-2,by omega⟩ + have hQ : Q₀ ≤ 3*(n+2-1) := by omega + let Q := 3*(n+2-1) + let x := normalizedTensorExterior (n+2) Q ψ + obtain ⟨y,hy,hb⟩ := hgap Q hQ x + have hyE : sourceFockEnergy Q y=0 := (sourceFockHamiltonian_kernel Q y).mp hy + have hrE : energy (normalizedTensorReadout (n+2) Q y)=0 := + normalizedTensorReadout_zero_energy n Q y hyE + have hrA := normalizedTensorReadout_antisymmetric (n+2) Q y + obtain ⟨c,hc⟩ := (hkernel (n+2) (show 2 ≤ n+2 by omega) + (normalizedTensorReadout (n+2) Q y) hrA) hrE + have hread : normalizedTensorReadout (n+2) Q (x-y) = + fun a => ψ a-c*laughlinVector (n+2) Q a := by + rw [normalizedTensorReadout_sub,normalizedTensorReadout_left_inverse (n+2) Q ψ hψ,hc] + have hnorm := normalizedTensorReadout_norm_le (n+2) Q (x-y) + rw [hread] at hnorm + have hdist := distanceToLaughlinSq_le ψ c + have hE : sourceFockEnergy Q x=energy ψ := normalizedTensorExterior_energy n Q ψ hψ + rw [hE] at hb + exact (mul_le_mul_of_nonneg_left (hdist.trans hnorm) (by norm_num : (0 : ℝ) ≤ 1/25)).trans hb + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/MatrixQuadratic.lean b/lean/OAI/Analysis/Laughlin/Fock/MatrixQuadratic.lean new file mode 100644 index 0000000000000000000000000000000000000000..adaaa86e9020543433d2b3cb8ee69135231a658b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/MatrixQuadratic.lean @@ -0,0 +1,47 @@ +import OAI.Analysis.Laughlin.Operators.PositiveFockLift + +namespace OAI + +namespace Laughlin.Fock +open scoped Matrix BigOperators ComplexOrder +open Matrix + +theorem occupation_matrix_quadratic_positive {I : Type*} [Fintype I] + (Q : ℕ) (M : Matrix I I ℂ) (hM : M.PosSemidef) (v : I → Space Q) : + 0 ≤ (∑ i, ∑ j, M i j * occupationInner Q (v i) (v j)).re := by + have he : (∑ i, ∑ j, M i j * occupationInner Q (v i) (v j)) = + ∑ A : Finset (Fin (Q+1)), star (fun i => (occupationBasis Q).repr (v i) A) ⬝ᵥ + (M*ᵥ (fun i => (occupationBasis Q).repr (v i) A)) := by + simp only [occupationInner,dotProduct,Matrix.mulVec,Finset.mul_sum,Pi.star_apply] + symm + rw [Finset.sum_comm] + apply Finset.sum_congr rfl; intro i hi + rw [Finset.sum_comm] + apply Finset.sum_congr rfl; intro j hj + apply Finset.sum_congr rfl; intro A hA + ring + rw [he,Complex.re_sum] + exact Finset.sum_nonneg (fun A hA => (Complex.nonneg_iff.mp (hM.dotProduct_mulVec_nonneg _)).1) + +theorem occupation_matrix_quadratic_factor {I J : Type*} [Fintype I] [Fintype J] + (Q : ℕ) (W : Matrix J I ℂ) (C : Matrix I I ℂ) (v : J → Space Q) : + (∑ i, ∑ j, C i j * occupationInner Q + (∑ a, star (W a i) • v a) (∑ b, star (W b j) • v b)) = + ∑ a, ∑ b, (W*C*Wᴴ) a b * occupationInner Q (v a) (v b) := by + simp_rw [occupationInner_sum_left,occupationInner_smul_left,star_star, + occupationInner_sum_right,occupationInner_smul_right] + simp only [Matrix.mul_apply,Matrix.conjTranspose_apply,Finset.mul_sum,Finset.sum_mul] + conv_lhs => arg 2; ext i; rw [Finset.sum_comm] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl; intro a ha + conv_lhs => arg 2; ext i; rw [Finset.sum_comm] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl; intro b hb + conv_rhs => rw [Finset.sum_comm] + apply Finset.sum_congr rfl; intro i hi + apply Finset.sum_congr rfl; intro j hj + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/ModeEmbedding.lean b/lean/OAI/Analysis/Laughlin/Fock/ModeEmbedding.lean new file mode 100644 index 0000000000000000000000000000000000000000..d8e114c1fe838ae943faefa97eb5e062c90f2a52 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/ModeEmbedding.lean @@ -0,0 +1,146 @@ +import OAI.Analysis.Laughlin.Fock.SpinRepresentation + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +noncomputable def modeInclusion (L Q : ℕ) (_h : L ≤ Q) : Orbital L →ₗ[ℂ] Orbital Q where + toFun v j := if hj : j.val ≤ L then v ⟨j.val,by omega⟩ else 0 + map_add' v w := by ext j; dsimp; split_ifs <;> simp + map_smul' c v := by ext j; dsimp; split_ifs <;> simp + +noncomputable def fockInclusion (L Q : ℕ) (h : L ≤ Q) : Space L →ₐ[ℂ] Space Q := + ExteriorAlgebra.map (modeInclusion L Q h) + +def includedOccupations (L Q : ℕ) (h : L ≤ Q) (A : Finset (Fin (L+1))) : + Finset (Fin (Q+1)) := A.map (Fin.castLEEmb (Nat.add_le_add_right h 1)) + +theorem modeInclusion_mode (L Q : ℕ) (h : L ≤ Q) (i : Fin (L+1)) : + modeInclusion L Q h (mode i) = mode (Fin.castLE (Nat.add_le_add_right h 1) i) := by + ext j + change (if hj : j.val ≤ L then (Pi.single i (1 : ℂ) : Orbital L) ⟨j.val,by omega⟩ else 0) = + (Pi.single (Fin.castLE (Nat.add_le_add_right h 1) i) (1 : ℂ) : Orbital Q) j + by_cases hj : j.val ≤ L + · rw [dite_eq_left hj] + have he : (⟨j.val,by omega⟩ : Fin (L+1)) = i ↔ + j = Fin.castLE (Nat.add_le_add_right h 1) i := by + constructor <;> intro hh <;> apply Fin.ext + · exact congrArg (fun k : Fin (L+1) => k.val) hh + · exact congrArg (fun k : Fin (Q+1) => k.val) hh + simp only [Pi.single_apply,he] + · rw [dite_eq_right hj] + have he : j ≠ Fin.castLE (Nat.add_le_add_right h 1) i := by + intro hh + have hv := congrArg (fun k : Fin (Q+1) => k.val) hh + have := i.isLt + simp only [Fin.val_castLE] at hv + omega + simp [he] + +theorem fockInclusion_create (L Q : ℕ) (h : L ≤ Q) (i : Fin (L+1)) (x : Space L) : + fockInclusion L Q h (create i x) = + create (Fin.castLE (Nat.add_le_add_right h 1) i) (fockInclusion L Q h x) := by + change ExteriorAlgebra.map (modeInclusion L Q h) (ExteriorAlgebra.ι ℂ (mode i) * x) = _ + rw [map_mul,ExteriorAlgebra.map_apply_ι,modeInclusion_mode] + rfl + +theorem contraction_map_between (L Q : ℕ) (f : Orbital L →ₗ[ℂ] Orbital Q) + (d : Module.Dual ℂ (Orbital Q)) (x : Space L) : + CliffordAlgebra.contractLeft d (ExteriorAlgebra.map f x) = + ExteriorAlgebra.map f (CliffordAlgebra.contractLeft (d.comp f) x) := by + induction x using CliffordAlgebra.left_induction with + | algebraMap r => simp + | add x y hx hy => simp only [map_add,hx,hy] + | ι_mul x m hx => + change CliffordAlgebra.contractLeft d (ExteriorAlgebra.map f (ExteriorAlgebra.ι ℂ m*x)) = + ExteriorAlgebra.map f (CliffordAlgebra.contractLeft (d.comp f) (ExteriorAlgebra.ι ℂ m*x)) + simp only [map_mul,ExteriorAlgebra.map_apply_ι,CliffordAlgebra.contractLeft_ι_mul, + LinearMap.comp_apply,map_sub,map_smul,hx] + +theorem fockInclusion_annihilate (L Q : ℕ) (h : L ≤ Q) (i : Fin (L+1)) (x : Space L) : + annihilate (Fin.castLE (Nat.add_le_add_right h 1) i) (fockInclusion L Q h x) = + fockInclusion L Q h (annihilate i x) := by + unfold annihilate fockInclusion + rw [contraction_map_between] + have hp : (LinearMap.proj (Fin.castLE (Nat.add_le_add_right h 1) i)).comp + (modeInclusion L Q h) = LinearMap.proj i := by + apply LinearMap.ext + intro v + change (if hj : i.val ≤ L then v ⟨i.val,by omega⟩ else 0) = v i + rw [dite_eq_left (show i.val ≤ L by omega)] + rw [hp] + +theorem fockInclusion_annihilate_high (L Q : ℕ) (h : L ≤ Q) (i : Fin (Q+1)) + (hi : L < i.val) (x : Space L) : + annihilate i (fockInclusion L Q h x) = 0 := by + unfold annihilate fockInclusion + rw [contraction_map_between] + have he : (LinearMap.proj i).comp (modeInclusion L Q h) = 0 := by + ext v + simp [modeInclusion,show ¬i.val ≤ L by omega] + rw [he] + simp + +theorem fockInclusion_occupation (L Q : ℕ) (h : L ≤ Q) (A : Finset (Fin (L+1))) : + fockInclusion L Q h (occupationBasis L A) = + occupationBasis Q (includedOccupations L Q h A) := by + let S : Set.powersetCard (Fin (L+1)) A.card := ⟨A,rfl⟩ + let e := (Set.powersetCard.ofFinEmbEquiv.symm S).trans + (Fin.castLEOrderEmb (Nat.add_le_add_right h 1)) + let T : Set.powersetCard (Fin (Q+1)) A.card := Set.powersetCard.ofFinEmbEquiv e + have hT : T.val = includedOccupations L Q h A := by + ext j + change j ∈ Set.powersetCard.ofFinEmbEquiv e ↔ _ + rw [Set.powersetCard.mem_ofFinEmbEquiv_iff_mem_range] + simp only [Set.mem_range,includedOccupations,Finset.mem_map] + constructor + · rintro ⟨i,rfl⟩ + refine ⟨Set.powersetCard.ofFinEmbEquiv.symm S i,?_,rfl⟩ + exact (Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem S _).mp ⟨i,rfl⟩ + · rintro ⟨i,hi,rfl⟩ + obtain ⟨a,ha⟩ := (Set.powersetCard.mem_range_ofFinEmbEquiv_symm_iff_mem S i).mpr hi + exact ⟨a,congrArg (Fin.castLE (Nat.add_le_add_right h 1)) ha⟩ + change fockInclusion L Q h ((Pi.basisFun ℂ (Fin (L+1))).ExteriorAlgebra S.val) = _ + rw [← hT] + change ExteriorAlgebra.map (modeInclusion L Q h) + ((Pi.basisFun ℂ (Fin (L+1))).ExteriorAlgebra S.val) = + (Pi.basisFun ℂ (Fin (Q+1))).ExteriorAlgebra T.val + rw [ExteriorAlgebra.basis_apply_powersetCard,ExteriorAlgebra.basis_apply_powersetCard] + simp only [ExteriorAlgebra.ιMulti_family,ExteriorAlgebra.map_apply_ιMulti] + have he : Set.powersetCard.ofFinEmbEquiv.symm T = e := + Set.powersetCard.ofFinEmbEquiv.symm_apply_apply e + rw [he] + congr 1 + funext i + simp only [Function.comp_apply,Pi.basisFun_apply] + change modeInclusion L Q h (mode (Set.powersetCard.ofFinEmbEquiv.symm S i)) = + mode (Fin.castLE (Nat.add_le_add_right h 1) (Set.powersetCard.ofFinEmbEquiv.symm S i)) + exact modeInclusion_mode L Q h (Set.powersetCard.ofFinEmbEquiv.symm S i) + +theorem includedOccupations_injective (L Q : ℕ) (h : L ≤ Q) : + Function.Injective (includedOccupations L Q h) := Finset.map_injective _ + +theorem fockInclusion_inner (L Q : ℕ) (h : L ≤ Q) (x y : Space L) : + occupationInner Q (fockInclusion L Q h x) (fockInclusion L Q h y) = + occupationInner L x y := by + have hb (A B : Finset (Fin (L+1))) : + occupationInner Q (fockInclusion L Q h (occupationBasis L A)) + (fockInclusion L Q h (occupationBasis L B)) = + occupationInner L (occupationBasis L A) (occupationBasis L B) := by + rw [fockInclusion_occupation,fockInclusion_occupation,occupationInner_basis,occupationInner_basis] + simp only [(includedOccupations_injective L Q h).eq_iff] + conv_lhs => rw [← (occupationBasis L).sum_repr x,← (occupationBasis L).sum_repr y] + conv_rhs => rw [← (occupationBasis L).sum_repr x,← (occupationBasis L).sum_repr y] + simp only [map_sum,map_smul,occupationInner_sum_left,occupationInner_sum_right, + occupationInner_smul_left,occupationInner_smul_right,hb] + +theorem fockInclusion_normSq (L Q : ℕ) (h : L ≤ Q) (x : Space L) : + occupationNormSq Q (fockInclusion L Q h x) = occupationNormSq L x := by + have hi := fockInclusion_inner L Q h x x + rw [occupationInner_self,occupationInner_self] at hi + exact Complex.ofReal_injective hi + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/NormalSquare.lean b/lean/OAI/Analysis/Laughlin/Fock/NormalSquare.lean new file mode 100644 index 0000000000000000000000000000000000000000..83842a973869e506ad9e08858ca170ea14c9195c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/NormalSquare.lean @@ -0,0 +1,82 @@ +import OAI.Analysis.Laughlin.Fock.EnergyRotation +import OAI.Analysis.Laughlin.Operators.PairNormalOrder +import OAI.Analysis.Laughlin.ThreeBody.FockHaar + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators Matrix + +theorem annihilate_create_inner (Q : ℕ) (i : Fin (Q+1)) (x y : Space Q) : + occupationInner Q x (create i y) = occupationInner Q (annihilate i x) y := by + have h := congrArg star (create_annihilate_adjoint Q i y x) + simpa only [occupationInner_star] using h + +theorem pair_annihilate_create_inner (Q p : ℕ) (x y : Space Q) : + occupationInner Q x (sourcePairCreateEnd Q p y) = + occupationInner Q (sourcePairEnd Q p x) y := by + have h := congrArg star (pairCreate_pair_adjoint Q + (fun i j => ((pairCoefficient Q p i j / Real.sqrt 2 : ℝ) : ℂ)) y x) + simpa only [occupationInner_star,sourcePairCreateEnd,sourcePairEnd] using h + +theorem sourcePairCreate_inner (Q : ℕ) (hQ : 2 ≤ Q) + (p q : Fin (2*Q-2+1)) (y z : Space Q) : + occupationInner Q (sourcePairCreateEnd Q p.val y) (sourcePairCreateEnd Q q.val z) = + (if p=q then (1 : ℂ) else 0) * occupationInner Q y z + + (∑ i, ∑ j, (complexThreeGram Q-1) (p,i) (q,j) * + occupationInner Q (annihilate i y) (annihilate j z)) + + occupationInner Q (sourcePairEnd Q q.val y) (sourcePairEnd Q p.val z) := by + rw [sourcePairCreateEnd,pairCreate_pair_adjoint] + change occupationInner Q y ((sourcePairEnd Q p.val * sourcePairCreateEnd Q q.val) z) = _ + rw [sourcePair_normal_order Q p.val q.val hQ (by omega)] + simp only [LinearMap.add_apply,LinearMap.sub_apply,LinearMap.smul_apply, + Module.End.one_apply,LinearMap.sum_apply,Module.End.mul_apply, + occupationInner_add_right,occupationInner_sub_right,occupationInner_smul_right, + occupationInner_sum_right,annihilate_create_inner,pair_annihilate_create_inner, + complexThreeGram_sub_one_entry,Finset.sum_mul,Finset.mul_sum] + have he : p.val=q.val ↔ p=q := Fin.val_inj + simp only [he] + ring_nf + simp only [Finset.sum_neg_distrib] + ring + +theorem sourceFockHamiltonian_normal_square (Q : ℕ) (hQ : 2 ≤ Q) (x : Space Q) : + occupationNormSq Q (sourceFockHamiltonian Q x) = sourceFockEnergy Q x + + (contractionForm Q (sourceThreeEnd Q) (complexThreeGram Q-1) x).re + + ∑ p : Fin (2*Q-2+1), ∑ q : Fin (2*Q-2+1), + occupationNormSq Q (sourcePairEnd Q q.val (sourcePairEnd Q p.val x)) := by + have hc (p q : Fin (2*Q-2+1)) : + sourcePairEnd Q p.val (sourcePairEnd Q q.val x) = + sourcePairEnd Q q.val (sourcePairEnd Q p.val x) := + LinearMap.congr_fun (pairEnd_commute Q _ _) x + have hH : sourceFockHamiltonian Q x = ∑ p : Fin (2*Q-2+1), + sourcePairCreateEnd Q p.val (sourcePairEnd Q p.val x) := by + rw [sourceFockHamiltonian_apply_fin Q (by omega)] + simp only [sourcePairCreateEnd_mul] + have he : (occupationNormSq Q (sourceFockHamiltonian Q x) : ℂ) = + (sourceFockEnergy Q x : ℂ) + + contractionForm Q (sourceThreeEnd Q) (complexThreeGram Q-1) x + + ∑ p : Fin (2*Q-2+1), ∑ q : Fin (2*Q-2+1), + (occupationNormSq Q (sourcePairEnd Q q.val (sourcePairEnd Q p.val x)) : ℂ) := by + rw [← occupationInner_self,hH,occupationInner_sum_left] + simp_rw [occupationInner_sum_right,sourcePairCreate_inner Q hQ] + have hl (p q : Fin (2*Q-2+1)) : occupationInner Q + (sourcePairEnd Q q.val (sourcePairEnd Q p.val x)) + (sourcePairEnd Q p.val (sourcePairEnd Q q.val x)) = + (occupationNormSq Q (sourcePairEnd Q q.val (sourcePairEnd Q p.val x)) : ℂ) := by + rw [hc p q,occupationInner_self] + simp only [Finset.sum_add_distrib,hl] + congr 1 + · congr 1 + · rw [sourceFockEnergy_eq_fin Q (by omega),Complex.ofReal_sum] + simp [occupationInner_self] + · simp only [contractionForm,Fintype.sum_prod_type,sourceThreeEnd,Module.End.mul_apply] + apply Finset.sum_congr rfl + intro p hp + rw [Finset.sum_comm] + have hr := congrArg Complex.re he + simpa only [Complex.add_re,Complex.ofReal_re,Complex.re_sum] using hr + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/OrbitIntegration.lean b/lean/OAI/Analysis/Laughlin/Fock/OrbitIntegration.lean new file mode 100644 index 0000000000000000000000000000000000000000..a5701ffbe9f65fca4a38e5b8a837f002deea61df --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/OrbitIntegration.lean @@ -0,0 +1,61 @@ +import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap +import OAI.Analysis.Laughlin.Operators.CollectionAnnihilatorBound +import OAI.Analysis.Laughlin.Pair.FockHaar + +namespace OAI + +namespace Laughlin.Fock +open Rotation MeasureTheory +open scoped BigOperators + +theorem linearMap_rotation_coordinate_continuous (Q : ℕ) (L : Module.End ℂ (Space Q)) + (x : Space Q) (A : Finset (Fin (Q+1))) : + Continuous (fun g : SourceSU2 => (occupationBasis Q).repr (L (exteriorRotation Q g⁻¹ x)) A) := by + have he (g : SourceSU2) : (occupationBasis Q).repr (L (exteriorRotation Q g⁻¹ x)) A = + ∑ B, (occupationBasis Q).repr (exteriorRotation Q g⁻¹ x) B * + (occupationBasis Q).repr (L (occupationBasis Q B)) A := by + conv_lhs => rw [← (occupationBasis Q).sum_repr (exteriorRotation Q g⁻¹ x)] + simp only [map_sum,map_smul,Finsupp.finsetSum_apply,Finsupp.smul_apply,smul_eq_mul] + simp_rw [he] + apply continuous_finsetSum + intro B hB + exact ((exteriorRotation_coordinate_continuous Q x B).comp continuous_inv).mul continuous_const + +theorem linearMap_rotation_norm_continuous (Q : ℕ) (L : Module.End ℂ (Space Q)) (x : Space Q) : + Continuous (fun g : SourceSU2 => occupationNormSq Q (L (exteriorRotation Q g⁻¹ x))) := by + unfold occupationNormSq + apply continuous_finsetSum + intro A hA + exact (linearMap_rotation_coordinate_continuous Q L x A).norm.pow 2 + +theorem linearMap_rotation_norm_integrable (Q : ℕ) (L : Module.End ℂ (Space Q)) (x : Space Q) : + Integrable (fun g : SourceSU2 => occupationNormSq Q (L (exteriorRotation Q g⁻¹ x))) sourceHaar := + (linearMap_rotation_norm_continuous Q L x).integrable_of_hasCompactSupport + (isClosed_tsupport _).isCompact + +theorem physical_pair_norm_haar_real (Q : ℕ) (hQ : 0 < Q) (p : Fin (2*Q-2+1)) (x : Space Q) : + (∫ g, occupationNormSq Q (sourcePairEnd Q p.val (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) = + sourceFockEnergy Q x/(2*Q-2+1 : ℕ) := by + apply Complex.ofReal_injective + rw [← integral_complex_ofReal,physical_pair_norm_haar Q hQ] + push_cast + rfl + +theorem sourcePairWindow_haar (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + (2*Q-2+1 : ℕ) * (∫ g, sourcePairWindow Q (exteriorRotation Q g⁻¹ x) ∂sourceHaar) = + 24 * sourceFockEnergy Q x := by + unfold sourcePairWindow + rw [integral_finsetSum _ (fun p hp => linearMap_rotation_norm_integrable Q _ x)] + have hp (p : ℕ) (h : p ∈ Finset.range 24) : + (∫ g, occupationNormSq Q (sourcePairEnd Q p (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) = + sourceFockEnergy Q x/(2*Q-2+1 : ℕ) := + physical_pair_norm_haar_real Q (by omega) ⟨p,by simp only [Finset.mem_range] at h; omega⟩ x + rw [Finset.sum_congr rfl hp] + simp only [Finset.sum_const,Finset.card_range,nsmul_eq_mul] + have hd : ((2*Q-2+1 : ℕ) : ℝ) ≠ 0 := by positivity + field_simp + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/PairNormalization.lean b/lean/OAI/Analysis/Laughlin/Fock/PairNormalization.lean new file mode 100644 index 0000000000000000000000000000000000000000..b9c8d2cee9966d8dd2f7c4f45129ff72dc169ff6 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/PairNormalization.lean @@ -0,0 +1,72 @@ +import OAI.Analysis.Laughlin.Exterior.PairConjugation +import OAI.Analysis.Laughlin.Operators.NormalOrderFour +import OAI.Analysis.Laughlin.Pair.Orthonormality + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem annihilate_vacuum {Q : ℕ} (i : Fin (Q+1)) : annihilate i (1 : Space Q) = 0 := by + simp [annihilate] + +theorem two_annihilate_two_create {Q : ℕ} (a b i j : Fin (Q+1)) : + annihilate b (annihilate a (create i (create j (1 : Space Q)))) = + (delta a i*delta b j-delta b i*delta a j) • (1 : Space Q) := by + have h := LinearMap.congr_fun (normal_order_four a b i j) (1 : Space Q) + simpa [Module.End.mul_apply, annihilate_vacuum, smul_smul, sub_smul] using h + +theorem pairEnd_two_create (Q : ℕ) (c : Fin (Q+1) → Fin (Q+1) → ℂ) + (i j : Fin (Q+1)) : + pairEnd Q c (create i (create j (1 : Space Q))) = (c i j-c j i) • (1 : Space Q) := by + simp only [pairEnd, LinearMap.sum_apply, LinearMap.smul_apply, Module.End.mul_apply, + two_annihilate_two_create, smul_smul] + simp [delta, mul_sub, sub_smul, mul_ite, ite_smul, Finset.sum_sub_distrib] + +theorem sourcePairEnd_two_create (Q p : ℕ) (i j : Fin (Q+1)) : + sourcePairEnd Q p (create i (create j (1 : Space Q))) = + ((Real.sqrt 2*pairCoefficient Q p i j : ℝ) : ℂ) • (1 : Space Q) := by + unfold sourcePairEnd + rw [pairEnd_two_create] + have hne : Real.sqrt (2 : ℝ) ≠ 0 := by positivity + have hc : pairCoefficient Q p i j / Real.sqrt 2 - pairCoefficient Q p j i / Real.sqrt 2 = + Real.sqrt 2*pairCoefficient Q p i j := by + rw [pairCoefficient_swap Q p i j] + calc + _ = 2*pairCoefficient Q p i j / Real.sqrt 2 := by ring + _ = (Real.sqrt 2*Real.sqrt 2)*pairCoefficient Q p i j / Real.sqrt 2 := by + rw [Real.mul_self_sqrt (by norm_num)] + _ = _ := by field_simp + have h := congrArg (fun r : ℝ => (r : ℂ)) hc + push_cast at h ⊢ + exact congrArg (fun c : ℂ => c • (1 : Space Q)) h + +noncomputable def sourcePairVector (Q p : ℕ) : Space Q := + ∑ i, ∑ j, ((pairCoefficient Q p i j / Real.sqrt 2 : ℝ) : ℂ) • + create i (create j (1 : Space Q)) + +theorem sourcePairEnd_pairVector (Q p q : ℕ) (hQ : 2 ≤ Q) (hp : p ≤ 2*Q-2) : + sourcePairEnd Q p (sourcePairVector Q q) = (if p = q then (1 : ℂ) else 0) • (1 : Space Q) := by + have hne : (Real.sqrt 2 : ℂ) ≠ 0 := by + exact_mod_cast (show Real.sqrt (2 : ℝ) ≠ 0 by positivity) + unfold sourcePairVector + simp only [map_sum, map_smul, sourcePairEnd_two_create, smul_smul] + have he (i j : Fin (Q+1)) : + ((pairCoefficient Q q i j / Real.sqrt 2 : ℝ) : ℂ)* + ((Real.sqrt 2*pairCoefficient Q p i j : ℝ) : ℂ) = + ((pairCoefficient Q p i j : ℂ)*(pairCoefficient Q q i j : ℂ)) := by + push_cast + field_simp + simp_rw [he] + simp only [← Finset.sum_smul] + have hg := congrArg (fun r : ℝ => (r : ℂ)) (pairCoefficient_gram Q p q hQ hp) + push_cast at hg + by_cases h : p = q + · simp only [ite_eq_left h, Complex.ofReal_one] at hg ⊢ + rw [hg] + · simp only [ite_eq_right h, Complex.ofReal_zero] at hg ⊢ + rw [hg] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/Perturbation.lean b/lean/OAI/Analysis/Laughlin/Fock/Perturbation.lean new file mode 100644 index 0000000000000000000000000000000000000000..0fcda993cf6d6811ccecd70a29a97307256334c2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/Perturbation.lean @@ -0,0 +1,41 @@ +import Mathlib.Analysis.InnerProductSpace.Basic +import OAI.Analysis.Laughlin.Asymptotics.Perturbation +import OAI.Analysis.Laughlin.Asymptotics.TruncatedScaling +import OAI.Analysis.Laughlin.Fock.Inner + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators InnerProductSpace + +theorem occupation_coefficient_perturbation {I : Type*} [Fintype I] (Q : ℕ) + (R : Finset (Fin (Q+1)) → I → I → ℝ) (v : I → Space Q) + (ε : ℝ) (hε : 0 ≤ ε) (hR : ∀ A i j, |R A i j| ≤ ε) : + |∑ A : Finset (Fin (Q+1)), ∑ i, ∑ j, R A i j * + ⟪(occupationBasis Q).repr (v i) A,(occupationBasis Q).repr (v j) A⟫_ℝ| ≤ + ε * (Fintype.card I : ℝ) * ∑ i, occupationNormSq Q (v i) := by + calc + _ ≤ ∑ A : Finset (Fin (Q+1)), |∑ i, ∑ j, R A i j * + ⟪(occupationBasis Q).repr (v i) A,(occupationBasis Q).repr (v j) A⟫_ℝ| := + Finset.abs_sum_le_sum_abs _ _ + _ ≤ ∑ A : Finset (Fin (Q+1)), ε * (Fintype.card I : ℝ) * + ∑ i, ‖(occupationBasis Q).repr (v i) A‖^2 := + Finset.sum_le_sum (fun A hA => quadratic_perturbation_bound (R A) + (fun i => (occupationBasis Q).repr (v i) A) ε hε (hR A)) + _ = _ := by + rw [← Finset.mul_sum,Finset.sum_comm] + rfl + +theorem truncatedInverse_inner (L Q : ℕ) (x y : Space Q) : + occupationInner Q (truncatedScalingInv L Q x) (truncatedScalingInv L Q y) = + ∑ A : Finset (Fin (Q+1)), (((truncatedDiagonals L Q A)⁻¹)^2 : ℝ) * + (star ((occupationBasis Q).repr x A) * (occupationBasis Q).repr y A) := by + simp only [occupationInner,truncatedScalingInv_coordinate,star_mul, + Complex.star_def,Complex.conj_ofReal] + apply Finset.sum_congr rfl; intro A hA + push_cast + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/Quadruple.lean b/lean/OAI/Analysis/Laughlin/Fock/Quadruple.lean new file mode 100644 index 0000000000000000000000000000000000000000..8d82ac2d01a5061a8443544bac3c73d899f0a7d8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/Quadruple.lean @@ -0,0 +1,47 @@ +import OAI.Analysis.Laughlin.Fock.FourLabels +import OAI.Analysis.Laughlin.FourBody.Quadruples + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +abbrev FourOccupation (Q D : ℕ) := + {A : Finset (Fin (Q+1)) // A.card=4 ∧ (∑ i ∈ A, i.val)=D+1} + +noncomputable def occupationQuadruple (Q D : ℕ) (A : FourOccupation Q D) : + {t : ℕ×ℕ×ℕ×ℕ // t ∈ Certificate.quadruples D} := + let l := occupationFourLabels Q A.val A.property.1 + ⟨((l 0).val,(l 1).val,(l 2).val,(l 3).val), + (Certificate.mem_quadruples D _ _ _ _).mpr + ⟨l.strictMono (by decide),l.strictMono (by decide),l.strictMono (by decide), + (occupationFourLabels_sum Q A.val A.property.1).symm.trans A.property.2⟩⟩ + +theorem occupationQuadruple_injective (Q D : ℕ) : Function.Injective (occupationQuadruple Q D) := by + intro A B h + have ht := congrArg Subtype.val h + simp only [occupationQuadruple,Prod.mk.injEq] at ht + have hl : occupationFourLabels Q A.val A.property.1 = occupationFourLabels Q B.val B.property.1 := by + ext i + fin_cases i + · exact ht.1 + · exact ht.2.1 + · exact ht.2.2.1 + · exact ht.2.2.2 + apply Subtype.ext + rw [← occupationFourLabels_range Q A.val A.property.1, + ← occupationFourLabels_range Q B.val B.property.1,hl] + +noncomputable def quadrupleEmbedding (Q D a b c d : ℕ) (hQ : D+1 ≤ Q) + (h : (a,b,c,d) ∈ Certificate.quadruples D) : Fin 4 ↪o Fin (Q+1) := by + have hh := (Certificate.mem_quadruples D a b c d).mp h + let f : Fin 4 → Fin (Q+1) := ![⟨a,by omega⟩,⟨b,by omega⟩,⟨c,by omega⟩,⟨d,by omega⟩] + have hf : StrictMono f := by + apply Fin.strictMono_iff_lt_succ.mpr + intro i + fin_cases i <;> simp [f,Fin.lt_def] <;> omega + exact OrderEmbedding.ofStrictMono f hf + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/RankOneHaar.lean b/lean/OAI/Analysis/Laughlin/Fock/RankOneHaar.lean new file mode 100644 index 0000000000000000000000000000000000000000..c53d1ff615f118e2466fb913f9b9882f3a054f2e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/RankOneHaar.lean @@ -0,0 +1,62 @@ +import OAI.Analysis.Laughlin.Pair.FockHaar +import OAI.Analysis.Laughlin.Spin.EmbeddedSpinHaar + +namespace OAI + +namespace Laughlin.Fock +open Rotation MeasureTheory +open scoped BigOperators Matrix + +noncomputable def complexOuter {I : Type*} (v w : I → ℂ) : Matrix I I ℂ := + fun i j => v i * star (w j) + +theorem contractionForm_outer {I : Type*} [Fintype I] (Q : ℕ) + (minus : I → Module.End ℂ (Space Q)) (v : I → ℂ) (x : Space Q) : + contractionForm Q minus (complexOuter v v) x = + (occupationNormSq Q (∑ i, star (v i) • minus i x) : ℂ) := by + rw [← occupationInner_self] + simp only [occupationInner_sum_left,occupationInner_sum_right,occupationInner_smul_left, + occupationInner_smul_right,star_star,contractionForm,complexOuter,Finset.mul_sum,mul_assoc] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + ring + +noncomputable def diagonalUnit {J : Type*} [DecidableEq J] (p : J) : Matrix J J ℂ := + fun i j => if i=p ∧ j=p then 1 else 0 + +theorem matrix_sandwich_single {I J : Type*} [Fintype I] [Fintype J] [DecidableEq J] + (W : Matrix I J ℂ) (p : J) : + W*diagonalUnit p*Wᴴ = + complexOuter (fun i => W i p) (fun i => W i p) := by + ext i j + simp [diagonalUnit,Matrix.mul_apply,complexOuter,Matrix.conjTranspose_apply,ite_and] + +theorem physical_family_spin_norm_haar {I : Type*} [Fintype I] [DecidableEq I] + (Q : ℕ) (ρ : SourceSU2 →* Matrix I I ℂ) + (hρ : ∀ g, ρ g⁻¹=(ρ g)ᴴ) (hc : ∀ i j, Continuous (fun g => ρ g i j)) + (minus : I → Module.End ℂ (Space Q)) + (hm : ∀ g i x, minus i (exteriorRotation Q g x) = + ∑ j, ρ g i j • exteriorRotation Q g (minus j x)) + (m : ℕ) (W : Matrix I (Fin (m+1)) ℂ) + (hW : ∀ g, ρ g*W=W*sourceSpinRepresentation m g) + (p : Fin (m+1)) (x : Space Q) : + ((m+1 : ℕ) : ℂ) * (∫ g, + (occupationNormSq Q (∑ i, star (W i p) • minus i (exteriorRotation Q g⁻¹ x)) : ℂ) + ∂sourceHaar) = contractionForm Q minus (W*Wᴴ) x := by + let M : Matrix (Fin (m+1)) (Fin (m+1)) ℂ := fun i j => if i=p ∧ j=p then 1 else 0 + have h := contractionForm_haar Q ρ hρ hc minus hm (W*M*Wᴴ) x + rw [embedded_spin_haar ρ hρ m W hW,contractionForm_smul] at h + have ht : Matrix.trace M=1 := by simp [M,Matrix.trace,Matrix.diag] + rw [ht] at h + have he : W*M*Wᴴ=complexOuter (fun i => W i p) (fun i => W i p) := matrix_sandwich_single W p + simp_rw [he,contractionForm_outer] at h + rw [h] + have hd : ((m+1 : ℕ) : ℂ) ≠ 0 := by exact_mod_cast Nat.succ_ne_zero m + field_simp + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/SharpGap.lean b/lean/OAI/Analysis/Laughlin/Fock/SharpGap.lean new file mode 100644 index 0000000000000000000000000000000000000000..6045ab25eb2e81b4316d1cdc3329c7b2e48851f3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/SharpGap.lean @@ -0,0 +1,114 @@ +import OAI.Analysis.Laughlin.FourBody.BesselAllowance +import OAI.Analysis.Laughlin.Fock.SpectralDistance + +namespace OAI + +namespace Laughlin +open Filter +open scoped Topology BigOperators + +noncomputable def gammaStar : ℝ := 4616733319001 / 10^14 + +theorem gammaStar_budget : + 1 - (93527408868499 / 10^14 : ℝ) - 61/4096 - 1222*(3/10^6) = gammaStar := by + norm_num [gammaStar] + +theorem one_twenty_fifth_lt_gammaStar : (1/25 : ℝ) < gammaStar := by + norm_num [gammaStar] + +theorem sharp_scalar_budget (error : ℕ → ℝ) + (he : Tendsto error atTop (𝓝 0)) (γ : ℝ) (hγ : γ < gammaStar) : + ∀ᶠ Q : ℕ in atTop, γ ≤ + 1-93527408868499/10^14-deltaFormula Q-1222*(3/10^6)-error Q := by + have ht : Tendsto (fun Q : ℕ => + 1-93527408868499/10^14-deltaFormula Q-1222*(3/10^6)-error Q) atTop + (𝓝 ((1-93527408868499/10^14)-61/4096-1222*(3/10^6)-(0 : ℝ))) := + ((tendsto_const_nhds.sub deltaFormula_tendsto).sub tendsto_const_nhds).sub he + have hlim : γ < (1-93527408868499/10^14)-61/4096-1222*(3/10^6)-(0 : ℝ) := by + simpa only [sub_zero, gammaStar_budget] using hγ + exact ((tendsto_order.mp ht).1 _ hlim).mono fun _ hQ => le_of_lt hQ + +namespace Fock + +theorem physical_fock_sharp_budget_eventually : + ∀ᶠ Q : ℕ in atTop, ∃ hQ : 25 ≤ Q, ∀ x : Space Q, + sourceKForm Q (by omega) x + + (1-93527408868499/10^14-deltaFormula Q-1222*(3/10^6)-averagedFourTransferError Q) * + sourceFockEnergy Q x ≤ occupationNormSq Q (sourceFockHamiltonian Q x) := by + filter_upwards [physical_threeBody_budget_eventually,eventually_ge_atTop 25] with Q h3 h25 + obtain ⟨h15,h3⟩ := h3 + refine ⟨h25,fun x => ?_⟩ + have h3x := h3 x + change sourceA3Form Q x-deltaFormula Q*sourceFockEnergy Q x ≤ _ at h3x + have h4 := sourceA4Form_bessel_bound Q h25 x + have hs := sourceFockHamiltonian_normal_square Q (by omega) x + rw [sourceKForm_decomposition Q h25] + nlinarith + +theorem physical_fock_square_eventually_sharp (γ : ℝ) (hγ : γ < gammaStar) : + ∀ᶠ Q : ℕ in atTop, ∀ x : Space Q, + γ*sourceFockEnergy Q x ≤ occupationNormSq Q (sourceFockHamiltonian Q x) := by + filter_upwards [physical_fock_sharp_budget_eventually, + sharp_scalar_budget averagedFourTransferError averagedFourTransferError_tendsto γ hγ] + with Q h hs + obtain ⟨hQ,h⟩ := h + intro x + have hE : 0 ≤ sourceFockEnergy Q x := Finset.sum_nonneg (fun p hp => occupationNormSq_nonneg Q _) + have hm := mul_le_mul_of_nonneg_right hs hE + have hk := sourceKForm_nonneg Q (by omega) x + have hx := h x + linarith + +theorem physical_fock_square_uniform_sharp (γ : ℝ) (hγ : γ < gammaStar) : + ∃ Q₀ : ℕ, 25 ≤ Q₀ ∧ ∀ Q : ℕ, Q₀ ≤ Q → ∀ x : Space Q, + γ*sourceFockEnergy Q x ≤ occupationNormSq Q (sourceFockHamiltonian Q x) := by + obtain ⟨q,hq⟩ := eventually_atTop.mp (physical_fock_square_eventually_sharp γ hγ) + exact ⟨max 25 q,le_max_left _ _,fun Q hQ => hq Q (le_trans (le_max_right _ _) hQ)⟩ + +theorem physical_fock_eigenvalue_gap_uniform_sharp (γ : ℝ) (hγ : γ < gammaStar) : + ∃ Q₀ : ℕ, 25 ≤ Q₀ ∧ ∀ Q : ℕ, Q₀ ≤ Q → ∀ x : Space Q, x ≠ 0 → ∀ a : ℝ, + sourceFockHamiltonian Q x=(a : ℂ) • x → a=0 ∨ γ ≤ a := by + obtain ⟨Q₀,h25,h⟩ := physical_fock_square_uniform_sharp γ hγ + refine ⟨Q₀,h25,fun Q hQ x hx a he => ?_⟩ + have hn : 0 < occupationNormSq Q x := + lt_of_le_of_ne (occupationNormSq_nonneg Q x) (Ne.symm (mt (occupationNormSq_eq_zero Q x).mp hx)) + have ha := sourceFock_eigen_nonneg Q x hx a he + have hs := h Q hQ x + rw [sourceFock_eigen_energy Q x a he,he,occupationNormSq_smul] at hs + have hnorm : ‖(a : ℂ)‖^2=a^2 := by simp + rw [hnorm] at hs + have hs' : γ*a ≤ a^2 := by nlinarith + by_cases hz : a=0 + · exact Or.inl hz + · right + have hp : 0 < a := lt_of_le_of_ne ha (Ne.symm hz) + nlinarith + +theorem physical_fock_kernel_distance_uniform_sharp (γ : ℝ) + (hγ0 : 0 ≤ γ) (hγ : γ < gammaStar) : + ∃ Q₀ : ℕ, 25 ≤ Q₀ ∧ ∀ Q : ℕ, Q₀ ≤ Q → ∀ x : Space Q, + ∃ y : Space Q, sourceFockHamiltonian Q y=0 ∧ + γ*occupationNormSq Q (x-y) ≤ sourceFockEnergy Q x := by + obtain ⟨Q₀,h25,hgap⟩ := physical_fock_eigenvalue_gap_uniform_sharp γ hγ + refine ⟨Q₀,h25,fun Q hQ x => ?_⟩ + have hg : ∀ v : EuclideanSpace ℂ (Finset (Fin (Q+1))), v≠0 → ∀ a : ℝ, + euclideanFockHamiltonian Q v=(a : ℂ) • v → a=0 ∨ γ≤a := by + intro v hv a he + obtain ⟨u,rfl⟩ := (occupationEuclidean Q).surjective v + apply hgap Q hQ u (by intro hu; simp [hu] at hv) a + apply (occupationEuclidean Q).injective + simpa only [euclideanFockHamiltonian_apply,map_smul] using he + obtain ⟨z,hz,hb⟩ := spectral_kernel_distance (euclideanFockHamiltonian Q) + (euclideanFockHamiltonian_symmetric Q) γ hγ0 hg (occupationEuclidean Q x) + obtain ⟨y,rfl⟩ := (occupationEuclidean Q).surjective z + refine ⟨y,?_,?_⟩ + · apply (occupationEuclidean Q).injective + simpa only [euclideanFockHamiltonian_apply,map_zero] using hz + · rw [← map_sub,occupationEuclidean_norm,euclideanFockHamiltonian_apply, + occupationEuclidean_inner,sourceFockHamiltonian_quadratic,Complex.ofReal_re] at hb + exact hb + +end Fock +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/SpectralDistance.lean b/lean/OAI/Analysis/Laughlin/Fock/SpectralDistance.lean new file mode 100644 index 0000000000000000000000000000000000000000..e240534cf4b14e86379a37226e649c6f42098780 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/SpectralDistance.lean @@ -0,0 +1,72 @@ +import OAI.Analysis.Laughlin.Fock.EigenvalueGap +import OAI.Analysis.Laughlin.Operators.SpectralKernelDistance + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators InnerProductSpace + +noncomputable def occupationEuclidean (Q : ℕ) : + Space Q ≃ₗ[ℂ] EuclideanSpace ℂ (Finset (Fin (Q+1))) := + (occupationBasis Q).equivFun.trans (WithLp.linearEquiv 2 ℂ (Finset (Fin (Q+1)) → ℂ)).symm + +theorem occupationEuclidean_inner (Q : ℕ) (x y : Space Q) : + inner ℂ (occupationEuclidean Q x) (occupationEuclidean Q y) = occupationInner Q x y := by + simp only [occupationEuclidean,LinearEquiv.trans_apply,PiLp.inner_apply, + Module.Basis.equivFun_apply,occupationInner] + apply Finset.sum_congr rfl + intro A hA + change (occupationBasis Q).repr y A * star ((occupationBasis Q).repr x A) = _ + ring + +theorem occupationEuclidean_norm (Q : ℕ) (x : Space Q) : + ‖occupationEuclidean Q x‖^2 = occupationNormSq Q x := by + have h := occupationEuclidean_inner Q x x + rw [inner_self_eq_norm_sq_to_K,occupationInner_self] at h + change (‖occupationEuclidean Q x‖ : ℂ)^2 = (occupationNormSq Q x : ℂ) at h + exact_mod_cast h + +noncomputable def euclideanFockHamiltonian (Q : ℕ) : + Module.End ℂ (EuclideanSpace ℂ (Finset (Fin (Q+1)))) := + (occupationEuclidean Q).toLinearMap.comp + ((sourceFockHamiltonian Q).comp (occupationEuclidean Q).symm.toLinearMap) + +theorem euclideanFockHamiltonian_apply (Q : ℕ) (x : Space Q) : + euclideanFockHamiltonian Q (occupationEuclidean Q x) = + occupationEuclidean Q (sourceFockHamiltonian Q x) := by + simp [euclideanFockHamiltonian] + +theorem euclideanFockHamiltonian_symmetric (Q : ℕ) : + (euclideanFockHamiltonian Q).IsSymmetric := by + intro x y + obtain ⟨u,rfl⟩ := (occupationEuclidean Q).surjective x + obtain ⟨v,rfl⟩ := (occupationEuclidean Q).surjective y + simp only [euclideanFockHamiltonian_apply,occupationEuclidean_inner] + exact sourceFockHamiltonian_symmetric Q u v + +theorem physical_fock_kernel_distance_uniform : + ∃ Q₀ : ℕ, 25 ≤ Q₀ ∧ ∀ Q : ℕ, Q₀ ≤ Q → ∀ x : Space Q, + ∃ y : Space Q, sourceFockHamiltonian Q y=0 ∧ + (1/100 : ℝ)*occupationNormSq Q (x-y) ≤ sourceFockEnergy Q x := by + obtain ⟨Q₀,h25,hgap⟩ := physical_fock_eigenvalue_gap_uniform + refine ⟨Q₀,h25,fun Q hQ x => ?_⟩ + have hg : ∀ v : EuclideanSpace ℂ (Finset (Fin (Q+1))), v≠0 → ∀ a : ℝ, + euclideanFockHamiltonian Q v=(a : ℂ) • v → a=0 ∨ (1/100 : ℝ)≤a := by + intro v hv a he + obtain ⟨u,rfl⟩ := (occupationEuclidean Q).surjective v + apply hgap Q hQ u (by intro hu; simp [hu] at hv) a + apply (occupationEuclidean Q).injective + simpa only [euclideanFockHamiltonian_apply,map_smul] using he + obtain ⟨z,hz,hb⟩ := spectral_kernel_distance (euclideanFockHamiltonian Q) + (euclideanFockHamiltonian_symmetric Q) (1/100) (by norm_num) hg (occupationEuclidean Q x) + obtain ⟨y,rfl⟩ := (occupationEuclidean Q).surjective z + refine ⟨y,?_,?_⟩ + · apply (occupationEuclidean Q).injective + simpa only [euclideanFockHamiltonian_apply,map_zero] using hz + · rw [← map_sub,occupationEuclidean_norm,euclideanFockHamiltonian_apply, + occupationEuclidean_inner,sourceFockHamiltonian_quadratic,Complex.ofReal_re] at hb + exact hb + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/SpinContinuity.lean b/lean/OAI/Analysis/Laughlin/Fock/SpinContinuity.lean new file mode 100644 index 0000000000000000000000000000000000000000..2eb60381d4b0f3358e22115b678a2047ed232b51 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/SpinContinuity.lean @@ -0,0 +1,41 @@ +import OAI.Analysis.Laughlin.Tensor.ExteriorRotation + +namespace OAI + +namespace Laughlin.Fock +open Rotation +open scoped BigOperators + +theorem occupationBasis_wedge (Q : ℕ) (A : Finset (Fin (Q+1))) : + occupationBasis Q A = ExteriorAlgebra.ιMulti ℂ A.card + (fun k => mode (Set.powersetCard.ofFinEmbEquiv.symm (⟨A,rfl⟩ : Set.powersetCard (Fin (Q+1)) A.card) k)) := by + change (Pi.basisFun ℂ (Fin (Q+1))).ExteriorAlgebra + (⟨A,rfl⟩ : Set.powersetCard (Fin (Q+1)) A.card).val = _ + rw [ExteriorAlgebra.basis_apply_powersetCard] + simp only [ExteriorAlgebra.ιMulti_family,Function.comp_def,Pi.basisFun_apply,mode] + +theorem exteriorRotation_basis_continuous (Q : ℕ) (A B : Finset (Fin (Q+1))) : + Continuous (fun g : SourceSU2 => (occupationBasis Q).repr + (exteriorRotation Q g (occupationBasis Q B)) A) := by + simp only [occupationBasis_wedge Q B,exteriorRotation_basis_wedge,map_sum,map_smul, + Finsupp.finsetSum_apply,Finsupp.smul_apply,smul_eq_mul] + apply continuous_finsetSum + intro b hb + apply Continuous.mul _ continuous_const + apply continuous_finsetProd + intro k hk + exact sourceSpinRepresentation_continuous Q _ _ + +theorem exteriorRotation_coordinate_continuous (Q : ℕ) (x : Space Q) + (A : Finset (Fin (Q+1))) : + Continuous (fun g : SourceSU2 => (occupationBasis Q).repr (exteriorRotation Q g x) A) := by + have hx := (occupationBasis Q).sum_repr x + conv in exteriorRotation Q _ x => rw [← hx] + simp only [map_sum,map_smul,Finsupp.finsetSum_apply,Finsupp.smul_apply,smul_eq_mul] + apply continuous_finsetSum + intro b hb + exact continuous_const.mul (exteriorRotation_basis_continuous Q A b) + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/SpinRepresentation.lean b/lean/OAI/Analysis/Laughlin/Fock/SpinRepresentation.lean new file mode 100644 index 0000000000000000000000000000000000000000..92a55fffe4979d70207b411948a9b271d83e3072 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/SpinRepresentation.lean @@ -0,0 +1,68 @@ +import OAI.Analysis.Laughlin.Fock.SpinContinuity + +namespace OAI + +namespace Laughlin.Fock +open Rotation +open scoped BigOperators Matrix + +noncomputable def fockSpinMatrix (Q : ℕ) (g : SourceSU2) : + Matrix (Finset (Fin (Q+1))) (Finset (Fin (Q+1))) ℂ := + fun A B => (occupationBasis Q).repr (exteriorRotation Q g (occupationBasis Q B)) A + +theorem fockSpinMatrix_mul (Q : ℕ) (g h : SourceSU2) : + fockSpinMatrix Q (g*h) = fockSpinMatrix Q g*fockSpinMatrix Q h := by + funext A B + change (occupationBasis Q).repr (exteriorRotation Q (g*h) (occupationBasis Q B)) A = _ + rw [← exteriorRotation_mul] + have hx := (occupationBasis Q).sum_repr (exteriorRotation Q h (occupationBasis Q B)) + conv_lhs => rw [← hx] + simp only [map_sum,map_smul,Finsupp.finsetSum_apply,Finsupp.smul_apply,smul_eq_mul, + Matrix.mul_apply,fockSpinMatrix] + apply Finset.sum_congr rfl + intro C hC + exact mul_comm _ _ + +theorem fockSpinMatrix_one (Q : ℕ) : fockSpinMatrix Q 1 = 1 := by + funext A B + simp [fockSpinMatrix,exteriorRotation_one,Module.Basis.repr_self,Finsupp.single_apply,Matrix.one_apply,eq_comm] + +noncomputable def fockSpinRepresentation (Q : ℕ) : + SourceSU2 →* Matrix (Finset (Fin (Q+1))) (Finset (Fin (Q+1))) ℂ where + toFun := fockSpinMatrix Q + map_one' := fockSpinMatrix_one Q + map_mul' := fockSpinMatrix_mul Q + +theorem occupationInner_basis (Q : ℕ) (A B : Finset (Fin (Q+1))) : + occupationInner Q (occupationBasis Q A) (occupationBasis Q B) = if A=B then 1 else 0 := by + simp [occupationInner,Module.Basis.repr_self,Finsupp.single_apply] + +theorem fockSpinRepresentation_unitary (Q : ℕ) (g : SourceSU2) : + fockSpinRepresentation Q g ∈ Matrix.unitaryGroup (Finset (Fin (Q+1))) ℂ := by + apply Matrix.mem_unitaryGroup_iff'.mpr + rw [Matrix.star_eq_conjTranspose] + funext A B + have h := exteriorRotation_unitary Q g (occupationBasis Q A) (occupationBasis Q B) + rw [occupationInner_basis] at h + simpa only [occupationInner,fockSpinRepresentation,fockSpinMatrix,MonoidHom.coe_mk,OneHom.coe_mk, + Matrix.mul_apply,Matrix.conjTranspose_apply,Matrix.one_apply] using h + +theorem fockSpinRepresentation_continuous (Q : ℕ) (A B : Finset (Fin (Q+1))) : + Continuous (fun g => fockSpinRepresentation Q g A B) := + exteriorRotation_basis_continuous Q A B + +theorem fockSpinRepresentation_coordinates (Q : ℕ) (g : SourceSU2) (x : Space Q) : + (fun A => (occupationBasis Q).repr (exteriorRotation Q g x) A) = + fockSpinRepresentation Q g *ᵥ (fun A => (occupationBasis Q).repr x A) := by + have hx := (occupationBasis Q).sum_repr x + conv_lhs => rw [← hx] + funext A + simp only [map_sum,map_smul,Finsupp.finsetSum_apply,Finsupp.smul_apply,smul_eq_mul, + Matrix.mulVec,dotProduct,fockSpinRepresentation,fockSpinMatrix,MonoidHom.coe_mk,OneHom.coe_mk] + apply Finset.sum_congr rfl + intro B hB + exact mul_comm _ _ + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Fock/UnitaryFamilies.lean b/lean/OAI/Analysis/Laughlin/Fock/UnitaryFamilies.lean new file mode 100644 index 0000000000000000000000000000000000000000..f9fa3129fd8ea229e92f96f33321bf8d15bb4e0d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Fock/UnitaryFamilies.lean @@ -0,0 +1,30 @@ +import OAI.Analysis.Laughlin.Fock.SpinRepresentation + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators Matrix + +variable {I : Type*} [Fintype I] [DecidableEq I] + +theorem unitary_sum_norm_sq (A : Matrix I I ℂ) (hA : Aᴴ*A=1) (v : I → ℂ) : + (∑ i, ‖(A *ᵥ v) i‖^2) = ∑ i, ‖v i‖^2 := by + have h : star (A *ᵥ v) ⬝ᵥ (A *ᵥ v) = star v ⬝ᵥ v := by + rw [Matrix.star_mulVec,Matrix.dotProduct_mulVec,Matrix.vecMul_vecMul,hA,Matrix.vecMul_one] + apply Complex.ofReal_injective + simpa only [Complex.ofReal_sum,← Complex.normSq_eq_norm_sq,Complex.normSq_eq_conj_mul_self, + dotProduct,Pi.star_apply,Complex.star_def] using h + +theorem unitary_sum_occupationNormSq (Q : ℕ) (A : Matrix I I ℂ) (hA : Aᴴ*A=1) + (v : I → Space Q) : + (∑ i, occupationNormSq Q (∑ j, A i j • v j)) = ∑ i, occupationNormSq Q (v i) := by + simp only [occupationNormSq,map_sum,map_smul,Finsupp.finsetSum_apply,Finsupp.smul_apply,smul_eq_mul] + rw [Finset.sum_comm] + conv_rhs => rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro B hB + exact unitary_sum_norm_sq A hA (fun j => (occupationBasis Q).repr (v j) B) + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/All.lean b/lean/OAI/Analysis/Laughlin/FourBody/All.lean new file mode 100644 index 0000000000000000000000000000000000000000..0c0ea9c445d8fa2caae5c652136f45a665fbecc2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/All.lean @@ -0,0 +1,54 @@ +import Mathlib.Tactic.IntervalCases +import OAI.Analysis.Laughlin.FiniteFlux.Positive05 +import OAI.Analysis.Laughlin.FiniteFlux.Positive07 +import OAI.Analysis.Laughlin.FiniteFlux.Positive08 +import OAI.Analysis.Laughlin.FiniteFlux.Positive09 +import OAI.Analysis.Laughlin.FiniteFlux.Positive10 +import OAI.Analysis.Laughlin.FiniteFlux.Positive11 +import OAI.Analysis.Laughlin.FiniteFlux.Positive12 +import OAI.Analysis.Laughlin.FiniteFlux.Positive13 +import OAI.Analysis.Laughlin.FiniteFlux.Positive14 +import OAI.Analysis.Laughlin.FiniteFlux.Positive15 +import OAI.Analysis.Laughlin.FiniteFlux.Positive16 +import OAI.Analysis.Laughlin.FiniteFlux.Positive17 +import OAI.Analysis.Laughlin.FiniteFlux.Positive18 +import OAI.Analysis.Laughlin.FiniteFlux.Positive19 +import OAI.Analysis.Laughlin.FiniteFlux.Positive20 +import OAI.Analysis.Laughlin.FiniteFlux.Positive21 +import OAI.Analysis.Laughlin.FiniteFlux.Positive22 +import OAI.Analysis.Laughlin.FiniteFlux.Positive23 + +namespace OAI + +namespace Laughlin.Certificate + +theorem four_body_certificates (D : ℕ) (hD₁ : 1 ≤ D) (hD₂ : D ≤ 23) : + ((compressedRational D).map (Rat.castHom ℝ)).PosSemidef := by + interval_cases D + · exact zero_blocks_positive 1 (by decide) + · exact zero_blocks_positive 2 (by decide) + · exact zero_blocks_positive 3 (by decide) + · exact zero_blocks_positive 4 (by decide) + · exact four_body_five_positive + · exact zero_blocks_positive 6 (by decide) + · exact four_body_7_positive + · exact four_body_8_positive + · exact four_body_9_positive + · exact four_body_10_positive + · exact four_body_11_positive + · exact four_body_12_positive + · exact four_body_13_positive + · exact four_body_14_positive + · exact four_body_15_positive + · exact four_body_16_positive + · exact four_body_17_positive + · exact four_body_18_positive + · exact four_body_19_positive + · exact four_body_20_positive + · exact four_body_21_positive + · exact four_body_22_positive + · exact four_body_23_positive + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Assembly.lean b/lean/OAI/Analysis/Laughlin/FourBody/Assembly.lean new file mode 100644 index 0000000000000000000000000000000000000000..a8b9f436936594204c7e41fbaa2027a70ccc770a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Assembly.lean @@ -0,0 +1,86 @@ +import OAI.Analysis.Laughlin.FourBody.Square +import OAI.Analysis.Laughlin.ThreeBody.SourceExpansion + +namespace OAI + +namespace Laughlin.Fock +open Spin +open scoped BigOperators Matrix + +theorem rowLevel_sum {A : Type*} [AddCommMonoid A] (t : ℕ) (f : ℕ → A) : + (∑ T : RowLevel t, f T.val.val) = + (((List.range 16).filter (fun T => t ≤ T)).map f).sum := by + classical + rw [← Finset.sum_subtype (Finset.univ.filter (fun T : Fin 16 => t ≤ T.val)) + (by simp) (fun T : Fin 16 => f T.val),Finset.sum_filter, + Fin.sum_univ_eq_sum_range (fun n : ℕ => if t ≤ n then f n else 0) 16] + have hs (n : ℕ) (g : ℕ → A) : (∑ i ∈ Finset.range n, g i) = + ((List.range n).map g).sum := by + induction n with + | zero => simp + | succ n ih => simp only [Finset.sum_range_succ,List.range_succ,List.map_append, + List.sum_append,List.map_singleton,List.sum_singleton,ih] + rw [hs,list_map_ite_sum] + +theorem contractionForm_list {I J : Type*} [Fintype I] (Q : ℕ) + (L : I → Module.End ℂ (Space Q)) (l : List J) (M : J → Matrix I I ℂ) (x : Space Q) : + contractionForm Q L (l.map M).sum x = (l.map (fun j => contractionForm Q L (M j) x)).sum := by + induction l with + | nil => simp [contractionForm] + | cons j l ih => simp only [List.map_cons,List.sum_cons,contractionForm_add,ih] + +theorem matrix_ofReal_list {I J : Type*} (l : List J) (M : J → Matrix I I ℝ) : + ((l.map M).sum).map Complex.ofReal = (l.map (fun j => (M j).map Complex.ofReal)).sum := by + induction l with + | nil => ext i j; simp + | cons k l ih => + simp only [List.map_cons,List.sum_cons] + have he (A B : Matrix I I ℝ) : (A+B).map Complex.ofReal = + A.map Complex.ofReal+B.map Complex.ofReal := by ext i j; simp + rw [he,ih] + +theorem physicalThreeBodyMatrix_row_sum (Q : ℕ) (x : Space Q) : + contractionForm Q (sourceThreeEnd Q) ((physicalThreeBodyMatrix Q).map Complex.ofReal) x = + (Certificate.rows.map (fun row => ∑ T : RowLevel row.1, + contractionForm Q (sourceThreeEnd Q) + ((threeBodyLevelMatrix Q row.1 T.val.val row.2.1 row.2.2).map Complex.ofReal) x)).sum := by + simp only [physicalThreeBodyMatrix,matrix_ofReal_list,contractionForm_list] + congr 1 + +theorem physicalPairRowMatrix_Fock (Q : ℕ) (hQ : 15 ≤ Q) + (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) (ht : row.1 ≤ 7) (x : Space Q) : + contractionForm Q (fun p : Fin (2*Q-2+1) => sourcePairEnd Q p.val) + (physicalPairRowMatrix Q row) x = + ((row.2.1 : ℂ)/10^7)^2 * (occupationNormSq Q (sourcePairEnd Q row.1 x) : ℂ) := by + let p : Fin (2*Q-2+1) := ⟨row.1,by omega⟩ + have he (i : Fin (2*Q-2+1)) : i.val=row.1 ↔ i=p := by + constructor + · intro h; exact Fin.ext h + · intro h; subst i; rfl + simp only [contractionForm,physicalPairRowMatrix,he,ite_mul,zero_mul] + simp only [ite_and,Finset.sum_ite_irrel,Finset.sum_const_zero,Finset.sum_ite_eq', + Finset.mem_univ,ite_true,occupationInner_self] + rfl + +theorem source_rows_normal_two_three (Q : ℕ) (hQ : 15 ≤ Q) (x : Space Q) : + (Certificate.rows.map (fun row => (occupationNormSq Q (sourceRowSquareVector Q hQ row x) : ℂ))).sum = + contractionForm Q (fun p : Fin (2*Q-2+1) => sourcePairEnd Q p.val) + (physicalTwoBodyMatrix Q) x + + contractionForm Q (sourceThreeEnd Q) ((physicalThreeBodyMatrix Q).map Complex.ofReal) x + + (Certificate.rows.map (fun row => sourceRowFourForm Q hQ row x)).sum := by + rw [physicalTwoBodyMatrix,contractionForm_list,physicalThreeBodyMatrix_row_sum] + have hr (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) (hrow : row ∈ Certificate.rows) : + (occupationNormSq Q (sourceRowSquareVector Q hQ row x) : ℂ) = + contractionForm Q (fun p : Fin (2*Q-2+1) => sourcePairEnd Q p.val) + (physicalPairRowMatrix Q row) x + + (∑ T : RowLevel row.1, contractionForm Q (sourceThreeEnd Q) + ((threeBodyLevelMatrix Q row.1 T.val.val row.2.1 row.2.2).map Complex.ofReal) x) + + sourceRowFourForm Q hQ row x := by + have ht := (source_threeBody_rows_support row hrow).1 + rw [sourceRowSquareVector_normal Q hQ row ht,physicalPairRowMatrix_Fock Q hQ row ht] + rw [List.map_congr_left hr] + simp only [List.sum_map_add] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Basic.lean b/lean/OAI/Analysis/Laughlin/FourBody/Basic.lean new file mode 100644 index 0000000000000000000000000000000000000000..5c38bce17fa11fc3b51d36b5ee4053cea08e63dd --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Basic.lean @@ -0,0 +1,76 @@ +import Mathlib.Data.Matrix.Basic +import Mathlib.LinearAlgebra.Matrix.PosDef +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.Operators.Certificate + +namespace OAI + +namespace Laughlin.Certificate +open scoped BigOperators Matrix + +def V (r D T p j k : ℕ) : ℤ := + if r ≤ j+k then U 1 r (j+k) j * U 1 (D-r) (T-r) p else 0 + +def yEntry (D r s t : ℕ) (e f : ℕ × ℕ × ℤ) : ℚ := + let (p,j,a) := e + let (q,l,b) := f + let i := p+j-t + let k := q+l-t + let T := p+j+k + if D ≤ T then + (a : ℚ) * (b : ℚ) * (V r D T p j k : ℚ) * (V s D T q l i : ℚ) * + (2 : ℚ) ^ (1-2*(T : ℤ)+(p : ℤ)+(q : ℤ)-(t : ℤ)+((r+s)/2 : ℕ)) * + ((i.factorial : ℚ) * (k.factorial : ℚ) * (t.factorial : ℚ) / + ((T-D).factorial : ℚ)) + else 0 + +def yRow (D r s : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) : ℚ := + (row.2.2.map (fun e => (row.2.2.map (fun f => yEntry D r s row.1 e f)).sum)).sum + +def Y (D r s : ℕ) : ℚ := + -(rows.map (yRow D r s)).sum / (10^14 : ℚ) + +theorem Y_expand (D r s : ℕ) : Y D r s = + -(yRow D r s (rows[0]!) + (yRow D r s (rows[1]!) + + (yRow D r s (rows[2]!) + (yRow D r s (rows[3]!) + + (yRow D r s (rows[4]!) + (yRow D r s (rows[5]!) + + (yRow D r s (rows[6]!) + 0))))))) / (10^14 : ℚ) := by rfl + +def quadruples (D : ℕ) : List (ℕ × ℕ × ℕ × ℕ) := + (List.range (D+2)).flatMap (fun a => + (List.range (D+2)).flatMap (fun b => + (List.range (D+2)).filterMap (fun c => + let d := D+1-a-b-c + if a < b ∧ b < c ∧ c < d ∧ a+b+c ≤ D+1 then some (a,b,c,d) else none))) + +def L (D r : ℕ) (A : ℕ × ℕ × ℕ × ℕ) : ℚ := + let (a,b,c,d) := A + let term := fun (x y j k : ℕ) => ((x : ℤ)-(y : ℤ)) * + ((x+y-1).factorial : ℤ) * (j.factorial : ℤ) * (k.factorial : ℤ) * + V r D D (x+y-1) j k + (2 : ℚ)^(((1 : ℤ)-2*(D : ℤ)+(r : ℤ))/2) * + ((term a b c d - term a c b d + term a d b c + term b c a d - + term b d a c + term c d a b : ℤ) : ℚ) + +def Z (D r s : ℕ) : ℚ := + ((quadruples D).map (fun A => + let (a,b,c,d) := A + L D r A * L D s A / + ((a.factorial : ℚ)*(b.factorial : ℚ)*(c.factorial : ℚ)*(d.factorial : ℚ)))).sum + +def copyLabel {D : ℕ} (i : Fin ((D+1)/2)) : ℕ := 2*i.val+1 + +def gramRational (D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ := + fun i j => Z D (copyLabel i) (copyLabel j) + +def errorRational (D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ := + fun i j => Y D (copyLabel i) (copyLabel j) + + +theorem gram_five : gramRational 5 = + !![48, -24, 60; -24, 12, -30; 60, -30, 75] := by + decide +kernel + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/BesselAllowance.lean b/lean/OAI/Analysis/Laughlin/FourBody/BesselAllowance.lean new file mode 100644 index 0000000000000000000000000000000000000000..12e4c25268241a7fa87fc9a1c9f7f1f31bc22920 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/BesselAllowance.lean @@ -0,0 +1,186 @@ +import OAI.Analysis.Laughlin.Operators.OrthonormalRows +import OAI.Analysis.Laughlin.FourBody.PairTarget +import OAI.Analysis.Laughlin.FourBody.CopyOrthogonality + +namespace OAI + +namespace Laughlin.Fock +open Spin Rotation MeasureTheory +open scoped BigOperators + +theorem orthonormal_occupation_sum_bound {I J : Type*} [Fintype I] [Fintype J] + [DecidableEq I] (Q : ℕ) (c : I → J → ℝ) (v : J → Space Q) + (hc : ∀ i k, (∑ j, c i j * c k j) = if i = k then 1 else 0) : + (∑ i, occupationNormSq Q (∑ j, (c i j : ℂ) • v j)) ≤ + ∑ j, occupationNormSq Q (v j) := by + unfold occupationNormSq + simp only [map_sum,Finsupp.finsetSum_apply,map_smul,Finsupp.smul_apply,smul_eq_mul] + rw [Finset.sum_comm] + conv_rhs => rw [Finset.sum_comm] + apply Finset.sum_le_sum + intro A hA + exact orthonormal_rows_complex_bound c (fun j => (occupationBasis Q).repr (v j) A) hc + +end Laughlin.Fock + +namespace Laughlin.Spin +open scoped BigOperators + +theorem source_fourBody_local_orthonormal (Q D : ℕ) (hQ : D+2 ≤ Q) + (r s : OddPairLabel D) : + (∑ b : LocalFourIndex D, + fourBodyCoefficient Q (oddPairDeficit r) D D b.val.1.val b.val.2.1.val b.val.2.2.val * + fourBodyCoefficient Q (oddPairDeficit s) D D b.val.1.val b.val.2.1.val b.val.2.2.val) = + if r = s then 1 else 0 := by + classical + by_cases hrs : r = s + · subst s + simp only [ite_true] + simpa only [pow_two] using source_fourBody_local_normalization Q (oddPairDeficit r) D + (oddPairDeficit_le r) (oddPairDeficit_odd r) hQ + · rw [ite_eq_right hrs] + have hr : oddPairDeficit r ≤ Q := le_trans (oddPairDeficit_le r) (by omega) + have hs : oddPairDeficit s ≤ Q := le_trans (oddPairDeficit_le s) (by omega) + have hA : D-oddPairDeficit r ≤ 2*Q-2 := by have := oddPairDeficit_le r; omega + have hB : D-oddPairDeficit r ≤ genericCoupledWeight Q Q (oddPairDeficit r) := by + have := oddPairDeficit_le r; unfold genericCoupledWeight; omega + have hC : D-oddPairDeficit s ≤ 2*Q-2 := by have := oddPairDeficit_le s; omega + have hE : D-oddPairDeficit s ≤ genericCoupledWeight Q Q (oddPairDeficit s) := by + have := oddPairDeficit_le s; unfold genericCoupledWeight; omega + have hne : oddPairDeficit r ≠ oddPairDeficit s := by + intro he + exact hrs (Fin.ext (by unfold oddPairDeficit at he; omega)) + have ho := fourBodyCopy_orthogonal_pair Q (oddPairDeficit r) (oddPairDeficit s) D D 0 0 + hr hs (oddPairDeficit_odd r) (oddPairDeficit_odd s) hne hA hB hC hE + rw [Fintype.sum_prod_type] at ho + rw [← fourWeightSlice_sum Q D hQ (fun p j k => + fourBodyCoefficient Q (oddPairDeficit r) D D p j.val k.val * + fourBodyCoefficient Q (oddPairDeficit s) D D p j.val k.val)] + convert ho using 1 + apply Finset.sum_congr rfl + intro p hp + apply Finset.sum_congr rfl + intro i hi + by_cases he : p.val+i.val.1.val+i.val.2.val=D + · rw [ite_eq_left he] + have h1 := fourBodyCopy_source_coefficient Q (oddPairDeficit r) D D + (oddPairDeficit_le r) (le_refl D) hQ p i he + have h2 := fourBodyCopy_source_coefficient Q (oddPairDeficit s) D D + (oddPairDeficit_le s) (le_refl D) hQ p i he + simpa only [Nat.sub_self] using congrArg₂ (fun a b : ℝ => a*b) h1.symm h2.symm + · rw [ite_eq_right he, fourBodyCopy_off Q (oddPairDeficit r) D 0 hr + (oddPairDeficit_le r) hA hB p i (by simpa only [add_zero] using he),zero_mul] + +end Laughlin.Spin + +namespace Laughlin.Fock +open Spin Rotation MeasureTheory +open scoped BigOperators + +theorem source_fourBody_bessel_allowance (Q D : ℕ) (hQ : D+2 ≤ Q) (x : Space Q) : + (∑ r : OddPairLabel D, occupationNormSq Q + (physicalFourCopyEnd Q (oddPairDeficit r) D (by have := oddPairDeficit_le r; omega) x)) ≤ + ∑ b : LocalFourIndex D, occupationNormSq Q (sourcePairEnd Q b.val.1.val x) := by + simp only [physicalFourCopyEnd,LinearMap.sum_apply,LinearMap.smul_apply] + apply (orthonormal_occupation_sum_bound Q + (fun r : OddPairLabel D => fun b : LocalFourIndex D => + fourBodyCoefficient Q (oddPairDeficit r) D D b.val.1.val b.val.2.1.val b.val.2.2.val) + (fun b => sourceFourEnd Q b.val.1.val ⟨b.val.2.1.val,by omega⟩ ⟨b.val.2.2.val,by omega⟩ x) + (source_fourBody_local_orthonormal Q D hQ)).trans + exact Finset.sum_le_sum (fun b hb => sourceFour_normSq_le_pair Q b.val.1.val _ _ x) + +theorem physical_fourBody_bessel_haar_allowance (Q D : ℕ) (hQ : D+2 ≤ Q) + (x : Space Q) : + (∑ r : OddPairLabel D, (2*Q-2+1 : ℕ) * (∫ g, occupationNormSq Q + (physicalFourCopyEnd Q (oddPairDeficit r) D + (by have := oddPairDeficit_le r; omega) (exteriorRotation Q g⁻¹ x)) ∂sourceHaar)) ≤ + (Fintype.card (LocalFourIndex D) : ℝ) * sourceFockEnergy Q x := by + have hL (r : OddPairLabel D) : Integrable + (fun g => occupationNormSq Q (physicalFourCopyEnd Q (oddPairDeficit r) D + (by have := oddPairDeficit_le r; omega) (exteriorRotation Q g⁻¹ x))) sourceHaar := + linearMap_rotation_norm_integrable Q _ x + have hP (b : LocalFourIndex D) : Integrable + (fun g => occupationNormSq Q (sourcePairEnd Q b.val.1.val + (exteriorRotation Q g⁻¹ x))) sourceHaar := + linearMap_rotation_norm_integrable Q _ x + have hi := integral_mono + (integrable_finsetSum _ (fun (r : OddPairLabel D) hr => hL r)) + (integrable_finsetSum _ (fun (b : LocalFourIndex D) hb => hP b)) + (fun g => source_fourBody_bessel_allowance Q D hQ (exteriorRotation Q g⁻¹ x)) + rw [integral_finsetSum _ (fun (r : OddPairLabel D) hr => hL r)] at hi + rw [← Finset.mul_sum] + apply (mul_le_mul_of_nonneg_left hi (by positivity : (0 : ℝ) ≤ (2*Q-2+1 : ℕ))).trans_eq + rw [integral_finsetSum _ (fun (b : LocalFourIndex D) hb => hP b)] + have hp (b : LocalFourIndex D) : + (∫ g, occupationNormSq Q (sourcePairEnd Q b.val.1.val (exteriorRotation Q g⁻¹ x)) + ∂sourceHaar) = sourceFockEnergy Q x/(2*Q-2+1 : ℕ) := + physical_pair_norm_haar_real Q (by omega) ⟨b.val.1.val,by have := b.val.1.isLt; omega⟩ x + simp_rw [hp] + simp only [Finset.sum_const,Finset.card_univ,nsmul_eq_mul] + have hd : ((2*Q-2+1 : ℕ) : ℝ) ≠ 0 := by positivity + field_simp + +theorem source_bessel_allowance_count_fin : + (∑ d : Fin 23, (d.val+2)^2/4) = 1222 := by decide +kernel + +theorem physical_fourBody_total_bessel_haar_allowance (Q : ℕ) (hQ : 25 ≤ Q) + (x : Space Q) : + (∑ d : Fin 23, ∑ r : OddPairLabel (d.val+1), + (2*Q-2+1 : ℕ) * (∫ g, occupationNormSq Q + (physicalFourCopyEnd Q (oddPairDeficit r) (d.val+1) + (by have := oddPairDeficit_le r; omega) (exteriorRotation Q g⁻¹ x)) ∂sourceHaar)) ≤ + 1222 * sourceFockEnergy Q x := by + calc + _ ≤ ∑ d : Fin 23, ((d.val+2)^2/4 : ℕ) * sourceFockEnergy Q x := by + apply Finset.sum_le_sum + intro d hd + simpa only [localFourIndex_card_retained (d.val+1) (by omega),Nat.add_assoc] using + physical_fourBody_bessel_haar_allowance Q (d.val+1) (by omega) x + _ = _ := by + rw [← Finset.sum_mul,← Nat.cast_sum,source_bessel_allowance_count_fin,Nat.cast_ofNat] + +theorem retainedFourAllowance_bessel_bound (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + retainedFourAllowance Q hQ x ≤ 1222*sourceFockEnergy Q x := by + unfold retainedFourAllowance + simp_rw [fourCopyForm_allowance_identity] + exact physical_fourBody_total_bessel_haar_allowance Q hQ x + +theorem sourceA4Form_retained_bessel_bound (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + sourceA4Form Q x ≤ retainedFourTarget Q hQ x + + (1222*(3/10^6 : ℝ)+averagedFourTransferError Q)*sourceFockEnergy Q x := by + have ht := physical_fourBody_total_haar_transfer Q hQ x + have ha := retainedFourAllowance_bessel_bound Q hQ x + have he : (∑ d : Fin 23, + (((2*Q-2+1 : ℕ) : ℝ)/((4*Q-1-2*(d.val+1) : ℕ) : ℝ)) * + (contractionForm Q (sourceFourFamilyEnd Q) + (fourCopyOperator Q (d.val+1) (by omega) (finiteFourMiddle Q (d.val+1))) x).re) = + retainedFourTarget Q hQ x+(3/10^6 : ℝ)*retainedFourAllowance Q hQ x-sourceA4Form Q x := by + conv_lhs => arg 2; ext d; erw [fourCopyMiddleForm Q _ (by omega) (by omega) x] + rw [Finset.sum_sub_distrib,Finset.sum_add_distrib,sourceA4Form_retained Q hQ x] + unfold retainedFourTarget retainedFourAllowance + rw [Finset.mul_sum] + congr 1 + congr 1 + apply Finset.sum_congr rfl + intro d hd + ring + have hi : -(averagedFourTransferError Q*sourceFockEnergy Q x) ≤ + retainedFourTarget Q hQ x+(3/10^6 : ℝ)*retainedFourAllowance Q hQ x-sourceA4Form Q x := by + rw [← he] + conv_rhs => arg 2; ext d; erw [fourCopyForm_scaled_haar] + exact ht + nlinarith + +theorem sourceA4Form_bessel_bound (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + sourceA4Form Q x ≤ + (∑ p : Fin (2*Q-2+1), ∑ q : Fin (2*Q-2+1), + occupationNormSq Q (sourcePairEnd Q q.val (sourcePairEnd Q p.val x))) + + (1222*(3/10^6 : ℝ)+averagedFourTransferError Q)*sourceFockEnergy Q x := by + have ht := retainedFourTarget_le_full Q hQ x + rw [fourPairTargetMatrix_Fock] at ht + have hb := sourceA4Form_retained_bessel_bound Q hQ x + linarith + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/CARReadout.lean b/lean/OAI/Analysis/Laughlin/FourBody/CARReadout.lean new file mode 100644 index 0000000000000000000000000000000000000000..577d2a6645c5499020d4ee1aedce4be1537faba7 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/CARReadout.lean @@ -0,0 +1,52 @@ +import Mathlib.Tactic.Abel +import OAI.Analysis.Laughlin.Fock.PairNormalization + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem annihilate_create_apply (Q : ℕ) (a b : Fin (Q+1)) (x : Space Q) : + annihilate a (create b x) = delta a b • x - create b (annihilate a x) := by + have h := LinearMap.congr_fun (annihilate_create a b) x + simpa only [Module.End.mul_apply,LinearMap.sub_apply,LinearMap.smul_apply, + Module.End.one_apply] using h + +theorem annihilate_three_create (Q : ℕ) (a x y z : Fin (Q+1)) : + annihilate a (create x (create y (create z (1 : Space Q)))) = + delta a x • create y (create z (1 : Space Q)) - + delta a y • create x (create z (1 : Space Q)) + + delta a z • create x (create y (1 : Space Q)) := by + simp only [annihilate_create_apply,annihilate_vacuum,map_zero,sub_zero,map_sub,map_smul] + abel + +theorem annihilate_four_create (Q : ℕ) (a x y z w : Fin (Q+1)) : + annihilate a (create x (create y (create z (create w (1 : Space Q))))) = + delta a x • create y (create z (create w (1 : Space Q))) - + delta a y • create x (create z (create w (1 : Space Q))) + + delta a z • create x (create y (create w (1 : Space Q))) - + delta a w • create x (create y (create z (1 : Space Q))) := by + rw [annihilate_create_apply,annihilate_three_create] + simp only [map_sub,map_add,map_smul] + abel + +theorem pairEnd_four_create (Q : ℕ) (c : Fin (Q+1) → Fin (Q+1) → ℂ) + (x y z w : Fin (Q+1)) : + pairEnd Q c (create x (create y (create z (create w (1 : Space Q))))) = + (c x y-c y x) • create z (create w (1 : Space Q)) - + (c x z-c z x) • create y (create w (1 : Space Q)) + + (c x w-c w x) • create y (create z (1 : Space Q)) + + (c y z-c z y) • create x (create w (1 : Space Q)) - + (c y w-c w y) • create x (create z (1 : Space Q)) + + (c z w-c w z) • create x (create y (1 : Space Q)) := by + simp only [pairEnd,LinearMap.sum_apply,LinearMap.smul_apply,Module.End.mul_apply, + annihilate_four_create,map_sub,map_add,map_smul,annihilate_three_create, + smul_sub,smul_add,smul_smul,Finset.sum_sub_distrib,Finset.sum_add_distrib] + simp only [delta,mul_ite,mul_one,mul_zero,ite_smul,zero_smul, + Finset.sum_ite_eq',Finset.mem_univ,ite_true] + simp only [sub_smul] + abel + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/CoefficientLimit.lean b/lean/OAI/Analysis/Laughlin/FourBody/CoefficientLimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..9332eb769831824204ae8450fcd1a0cf18b18eae --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/CoefficientLimit.lean @@ -0,0 +1,31 @@ +import OAI.Analysis.Laughlin.FourBody.Coefficients +import OAI.Analysis.Laughlin.Spin.Specializations + +namespace OAI + +namespace Laughlin.Spin +open scoped Topology +open Filter + +noncomputable def fourBodyLimitCoefficient (r D T p j k : ℕ) : ℝ := + if r ≤ j+k then Real.sqrt 2 * + couplingPolynomialCoefficient (Real.sqrt (1/2)) (Real.sqrt (1/2)) r (j+k-r) j * + couplingPolynomialCoefficient (Real.sqrt (1/2)) (Real.sqrt (1/2)) (D-r) (T-D) p else 0 + +theorem source_fourBody_coefficient_tendsto (r D T p j k : ℕ) + (hrD : r ≤ D) (hDT : D ≤ T) (hT : p+j+k=T) : + Tendsto (fun Q : ℕ => fourBodyCoefficient Q r D T p j k) atTop + (𝓝 (fourBodyLimitCoefficient r D T p j k)) := by + by_cases hr : r ≤ j+k + · simp only [fourBodyCoefficient,fourBodyLimitCoefficient,ite_eq_left hr] + have hI := source_fourBody_inner_coupling_tendsto r (j+k) j hr (by omega) + have hO := source_fourBody_outer_coupling_tendsto r (D-r) (T-r) p (by omega) (by omega) + have he : T-r-(D-r)=T-D := by omega + rw [he] at hO + exact (tendsto_const_nhds.mul hI).mul hO + · simp only [fourBodyCoefficient,fourBodyLimitCoefficient,ite_eq_right hr] + exact tendsto_const_nhds + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/CoefficientNorm.lean b/lean/OAI/Analysis/Laughlin/FourBody/CoefficientNorm.lean new file mode 100644 index 0000000000000000000000000000000000000000..458c550084a850c6a5b46bb259bcc2fe7cb20c84 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/CoefficientNorm.lean @@ -0,0 +1,40 @@ +import OAI.Analysis.Laughlin.FourBody.Coefficients + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +theorem fourBodyCopy_off (Q r D n : ℕ) (hr : r ≤ Q) (hrD : r ≤ D) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) + (p : Fin ((2*Q-2)+1)) (i : WedgePairIndex Q) + (hi : p.val+i.val.1.val+i.val.2.val ≠ D+n) : + fourBodyCopy Q r D hr hA hB n (p,i) = 0 := by + rw [fourBodyCopy_coordinate] + apply Finset.sum_eq_zero + intro b hb + by_cases hi' : i.val.1.val+i.val.2.val=r+b.val + · rw [genericUnitDescendant_off _ _ _ _ hA hB (p,b) (by dsimp; omega),mul_zero,mul_zero] + · rw [pairCoupledWedge_off Q r b.val hr i hi',zero_mul] + +theorem source_fourBody_coefficients_norm (Q r D T : ℕ) (ho : Odd r) + (hrD : r ≤ D) (hDT : D ≤ T) (hQT : T+2 ≤ Q) : + (∑ p : Fin ((2*Q-2)+1), ∑ i : WedgePairIndex Q, + if p.val+i.val.1.val+i.val.2.val=T then + (fourBodyCoefficient Q r D T p.val i.val.1.val i.val.2.val)^2 else 0) = 1 := by + have hn : T-D ≤ genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q r) (D-r) := by + unfold genericCoupledWeight; omega + have hnorm := fourBodyCopy_norm Q r D (T-D) (by omega) ho (by omega) + (by unfold genericCoupledWeight; omega) hn + rw [vectorNormSq,Fintype.sum_prod_type] at hnorm + rw [← hnorm] + apply Finset.sum_congr rfl; intro p hp + apply Finset.sum_congr rfl; intro i hi + by_cases he : p.val+i.val.1.val+i.val.2.val=T + · rw [ite_eq_left he,fourBodyCopy_source_coefficient Q r D T hrD hDT hQT p i he] + · rw [ite_eq_right he,fourBodyCopy_off Q r D (T-D) (by omega) hrD (by omega) + (by unfold genericCoupledWeight; omega) p i (by omega),zero_pow (by omega)] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Coefficients.lean b/lean/OAI/Analysis/Laughlin/FourBody/Coefficients.lean new file mode 100644 index 0000000000000000000000000000000000000000..2731ec8a82a7ef44f87f543c7d6067368a4d6046 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Coefficients.lean @@ -0,0 +1,66 @@ +import OAI.Analysis.Laughlin.FourBody.Copies +import OAI.Analysis.Laughlin.Operators.PhysicalCoupling + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +noncomputable def fourBodyCoefficient (Q r D T p j k : ℕ) : ℝ := + if r ≤ j+k then Real.sqrt 2 * physicalCouplingCoefficient Q Q r (j+k) j * + physicalCouplingCoefficient (2*Q-2) (2*Q-2*r) (D-r) (T-r) p else 0 + +theorem pairCoupledWedge_off (Q r n : ℕ) (hr : r ≤ Q) (i : WedgePairIndex Q) + (hi : i.val.1.val+i.val.2.val ≠ r+n) : + pairCoupledWedge Q r hr n i = 0 := by + simp only [pairCoupledWedge,tensorToWedgePair,pairCoupledTensor,Pi.smul_apply,smul_eq_mul, + genericUnitDescendant_off Q Q r n hr hr i.val hi,mul_zero] + +theorem genericUnitDescendant_transport_right (A B B' z n : ℕ) (he : B=B') + (hA : z ≤ A) (hB : z ≤ B) (hB' : z ≤ B') (i : SpinIndex A B) : + genericUnitDescendant A B z hA hB n i = + genericUnitDescendant A B' z hA hB' n (i.1,Fin.cast (congrArg (fun k => k+1) he) i.2) := by + subst B'; rfl + +theorem fourBodyCopy_source_coefficient (Q r D T : ℕ) (hrD : r ≤ D) (hDT : D ≤ T) + (hQT : T+2 ≤ Q) (p : Fin ((2*Q-2)+1)) (i : WedgePairIndex Q) + (hT : p.val+i.val.1.val+i.val.2.val=T) : + fourBodyCopy Q r D (by omega) (by omega) (by unfold genericCoupledWeight; omega) + (T-D) (p,i) = fourBodyCoefficient Q r D T p.val i.val.1.val i.val.2.val := by + have hcw : genericCoupledWeight Q Q r = 2*Q-2*r := by unfold genericCoupledWeight; omega + rw [fourBodyCopy_coordinate] + by_cases hri : r ≤ i.val.1.val+i.val.2.val + · let b : Fin (genericCoupledWeight Q Q r+1) := ⟨i.val.1.val+i.val.2.val-r,by + rw [hcw]; omega⟩ + rw [Finset.sum_eq_single b] + · unfold fourBodyCoefficient + rw [ite_eq_left hri] + have hI : r ≤ i.val.1.val+i.val.2.val ∧ i.val.1.val ≤ i.val.1.val+i.val.2.val ∧ + i.val.1.val+i.val.2.val ≤ Q ∧ i.val.1.val+i.val.2.val ≤ Q := by omega + have hO : D-r ≤ T-r ∧ p.val ≤ T-r ∧ T-r ≤ 2*Q-2 ∧ T-r ≤ 2*Q-2*r := by omega + rw [physicalCouplingCoefficient,dite_eq_left hI,physicalCouplingCoefficient,dite_eq_left hO] + simp only [pairCoupledWedge,tensorToWedgePair,pairCoupledTensor,Pi.smul_apply,smul_eq_mul] + have hi2 : i.val.1.val+i.val.2.val-i.val.1.val=i.val.2.val := by omega + have hb : T-r-p.val=b.val := by dsimp [b]; omega + have hn : T-r-(D-r)=T-D := by omega + try simp only [hi2,hn] + have hbfin : (⟨T-r-p.val,by omega⟩ : Fin (2*Q-2*r+1)) = + ⟨b.val,by rw [← hcw]; exact b.isLt⟩ := by apply Fin.ext; exact hb + rw [hbfin] + have hout := genericUnitDescendant_transport_right (2*Q-2) (genericCoupledWeight Q Q r) + (2*Q-2*r) (D-r) (T-D) hcw (by omega) (by unfold genericCoupledWeight; omega) + (by omega) (p,b) + rw [hout] + rfl + · intro c hc hcb + rw [pairCoupledWedge_off Q r c.val (by omega) i (by + intro he; apply hcb; apply Fin.ext; dsimp [b]; omega),zero_mul] + · simp + · rw [fourBodyCoefficient,ite_eq_right hri] + apply Finset.sum_eq_zero + intro c hc + rw [pairCoupledWedge_off Q r c.val (by omega) i (by omega),zero_mul] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/ColumnExpansion.lean b/lean/OAI/Analysis/Laughlin/FourBody/ColumnExpansion.lean new file mode 100644 index 0000000000000000000000000000000000000000..21a7f3e06d48893edc450879ceb92294adf957a6 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/ColumnExpansion.lean @@ -0,0 +1,67 @@ +import OAI.Analysis.Laughlin.FourBody.PhysicalGram +import OAI.Analysis.Laughlin.Operators.PositiveFockLift + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators +open Spin + +noncomputable def fourOccupationCreate (Q D : ℕ) (A : FourOccupation Q D) : Module.End ℂ (Space Q) := + let l := occupationFourLabels Q A.val A.property.1 + create (l 0)*create (l 1)*create (l 2)*create (l 3) + +noncomputable def fourOccupationEnd (Q D : ℕ) (A : FourOccupation Q D) : Module.End ℂ (Space Q) := + let l := occupationFourLabels Q A.val A.property.1 + annihilate (l 3)*annihilate (l 2)*annihilate (l 1)*annihilate (l 0) + +theorem fourOccupation_adjoint (Q D : ℕ) (A : FourOccupation Q D) (x y : Space Q) : + occupationInner Q x (fourOccupationCreate Q D A y) = + occupationInner Q (fourOccupationEnd Q D A x) y := by + simp only [fourOccupationCreate,fourOccupationEnd,Module.End.mul_apply,create_annihilate_adjoint_right] + +theorem fourOccupationCreate_mul (Q D : ℕ) (A : FourOccupation Q D) (x : Space Q) : + fourOccupationCreate Q D A x = occupationBasis Q A.val * x := by + rw [occupationBasis_four Q A.val A.property.1] + simp [fourOccupationCreate,create,mul_assoc] + +theorem limitFourColumn_mul_adjoint (Q r D : ℕ) (x y : Space Q) : + occupationInner Q x (limitFourColumn Q r D * y) = + occupationInner Q (limitFourCopyEnd Q r D x) y := by + simp only [limitFourColumn,Finset.sum_mul,smul_mul_assoc] + simp only [limitFourCopyEnd,weightedFourEnd,limitFourEnd,limitPairEnd,pairEnd, + LinearMap.sum_apply,LinearMap.smul_apply,Module.End.mul_apply,map_sum,map_smul, + occupationInner_sum_left,occupationInner_sum_right,occupationInner_smul_left, + occupationInner_smul_right,Complex.star_def,Complex.conj_ofReal] + simp only [create,LinearMap.coe_mk,AddHom.coe_mk,mul_one,mul_assoc] + simp only [show ∀ (i : Fin (Q+1)) (v : Space Q), (ExteriorAlgebra.ι ℂ) (mode i)*v=create i v from by intros; rfl, + create_annihilate_adjoint_right] + apply Finset.sum_congr rfl; intro p hp + apply Finset.sum_congr rfl; intro j hj + apply Finset.sum_congr rfl; intro k hk + simp only [Finset.mul_sum] + apply Finset.sum_congr rfl; intro a ha + apply Finset.sum_congr rfl; intro b hb + push_cast + ring + +theorem limitFourColumn_expansion (Q r D : ℕ) (hr : r ≤ D) (hor : Odd r) : + limitFourColumn Q r D = ∑ A : FourOccupation Q D, + (fourOccupationCoefficient Q r D A.val : ℂ) • occupationBasis Q A.val := by + classical + conv_lhs => rw [← (occupationBasis Q).sum_repr (limitFourColumn Q r D)] + simp_rw [limitFourColumn_occupation_coefficient Q r D hr hor] + let P := fun A : Finset (Fin (Q+1)) => A.card=4 ∧ (∑ i ∈ A, i.val)=D+1 + rw [← Finset.sum_subset (Finset.filter_subset P Finset.univ) (f := fun A => + (fourOccupationCoefficient Q r D A : ℂ) • occupationBasis Q A)] + · exact Finset.sum_subtype _ (by simp [P]) _ + · intro A hA hn + simp only [Finset.mem_filter,Finset.mem_univ,true_and] at hn + by_cases hc : A.card=4 + · have hw : (∑ i ∈ A, i.val) ≠ D+1 := by intro hw; exact hn ⟨hc,hw⟩ + simp [fourOccupationCoefficient,hc,hw] + · simp [fourOccupationCoefficient,hc] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Copies.lean b/lean/OAI/Analysis/Laughlin/FourBody/Copies.lean new file mode 100644 index 0000000000000000000000000000000000000000..434ca2104aa9cf0cbea83267d50b3998931da03b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Copies.lean @@ -0,0 +1,75 @@ +import OAI.Analysis.Laughlin.Pair.CoupledIsometry +import OAI.Analysis.Laughlin.Spin.Support + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix Kronecker + +noncomputable def tensorPairInclusion (A Q r : ℕ) (hr : r ≤ Q) : + Matrix (Fin (A+1) × WedgePairIndex Q) (SpinIndex A (genericCoupledWeight Q Q r)) ℝ := + (1 : Matrix (Fin (A+1)) (Fin (A+1)) ℝ) ⊗ₖ pairCoupledInclusion Q r hr + +theorem tensorPairInclusion_isometry (A Q r : ℕ) (hr : r ≤ Q) (ho : Odd r) : + (tensorPairInclusion A Q r hr)ᵀ * tensorPairInclusion A Q r hr = 1 := by + unfold tensorPairInclusion + have ht : ((1 : Matrix (Fin (A+1)) (Fin (A+1)) ℝ) ⊗ₖ pairCoupledInclusion Q r hr)ᵀ = + (1 : Matrix (Fin (A+1)) (Fin (A+1)) ℝ) ⊗ₖ (pairCoupledInclusion Q r hr)ᵀ := by + ext i j + simp [Matrix.kroneckerMap,Matrix.transpose_apply,Matrix.one_apply,eq_comm] + rw [ht,← Matrix.mul_kronecker_mul, + Matrix.one_mul,pairCoupledInclusion_isometry Q r hr ho, + Matrix.one_kronecker_one] + +theorem isometry_vectorNormSq {I J : Type*} [Fintype I] [Fintype J] + [DecidableEq I] [DecidableEq J] (W : Matrix I J ℝ) (hW : Wᵀ*W=1) (f : J → ℝ) : + vectorNormSq (W *ᵥ f) = vectorNormSq f := by + unfold vectorNormSq + simp only [pow_two] + have hp (v : J → ℝ) (w : I → ℝ) : + (∑ i, (W *ᵥ v) i*w i) = ∑ i, v i*(Wᵀ *ᵥ w) i := by + simp only [Matrix.mulVec,dotProduct,Matrix.transpose_apply,Finset.sum_mul,Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl; intro i hi + apply Finset.sum_congr rfl; intro j hj; ring + rw [hp,Matrix.mulVec_mulVec,hW,Matrix.one_mulVec] + +noncomputable def fourBodyCopy (Q r D : ℕ) (hr : r ≤ Q) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) (n : ℕ) : + Fin ((2*Q-2)+1) × WedgePairIndex Q → ℝ := + tensorPairInclusion (2*Q-2) Q r hr *ᵥ + ((-1 : ℝ)^(D-r) • genericUnitDescendant (2*Q-2) (genericCoupledWeight Q Q r) + (D-r) hA hB n) + +theorem phased_generic_norm (A B z n : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hn : n ≤ genericCoupledWeight A B z) : + vectorNormSq ((-1 : ℝ)^z • genericUnitDescendant A B z hA hB n) = 1 := by + unfold vectorNormSq + simp only [Pi.smul_apply,smul_eq_mul,mul_pow,← Finset.mul_sum] + have h : ((-1 : ℝ)^z)^2 = 1 := by rw [← pow_mul,mul_comm z 2,pow_mul]; norm_num + rw [h,one_mul] + exact genericUnitDescendant_norm A B z n hA hB hn + +theorem fourBodyCopy_norm (Q r D n : ℕ) (hr : r ≤ Q) (ho : Odd r) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) + (hn : n ≤ genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q r) (D-r)) : + vectorNormSq (fourBodyCopy Q r D hr hA hB n) = 1 := by + rw [fourBodyCopy,isometry_vectorNormSq _ (tensorPairInclusion_isometry _ Q r hr ho)] + exact phased_generic_norm _ _ _ _ hA hB hn + +theorem fourBodyCopy_coordinate (Q r D n : ℕ) (hr : r ≤ Q) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) + (p : Fin ((2*Q-2)+1)) (i : WedgePairIndex Q) : + fourBodyCopy Q r D hr hA hB n (p,i) = + ∑ b : Fin (genericCoupledWeight Q Q r+1), pairCoupledWedge Q r hr b.val i * + ((-1 : ℝ)^(D-r) * genericUnitDescendant (2*Q-2) (genericCoupledWeight Q Q r) + (D-r) hA hB n (p,b)) := by + simp only [fourBodyCopy,Matrix.mulVec,dotProduct,Fintype.sum_prod_type,tensorPairInclusion, + Matrix.kroneckerMap,Matrix.of_apply,Matrix.one_apply,ite_mul, + one_mul,zero_mul,pairCoupledInclusion,Pi.smul_apply,smul_eq_mul] + rw [Finset.sum_comm] + simp only [Finset.sum_ite_eq,Finset.mem_univ,ite_true] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/CopyAlgebra.lean b/lean/OAI/Analysis/Laughlin/FourBody/CopyAlgebra.lean new file mode 100644 index 0000000000000000000000000000000000000000..3a89fef5dcc1fe3d9caa6d6e5fce509a5431ce47 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/CopyAlgebra.lean @@ -0,0 +1,58 @@ +import OAI.Analysis.Laughlin.FourBody.CopyOperatorHaar + +namespace OAI + +namespace Laughlin.Fock +open Spin +open scoped BigOperators Matrix + +def firstOddPairLabel (D : ℕ) (hD : 1 ≤ D) : OddPairLabel D := ⟨0,by omega⟩ + +theorem fourCopyOperator_diagonal (Q D : ℕ) (hQ : D+2 ≤ Q) (c : OddPairLabel D → ℝ) : + fourCopyOperator Q D hQ (Matrix.diagonal c) = ∑ r, + (c r : ℂ) • (retainedFourInclusion Q D hQ r * (retainedFourInclusion Q D hQ r)ᴴ) := by + classical + simp [fourCopyOperator,Matrix.diagonal_apply,apply_ite,ite_smul] + +theorem fourCopyOperator_sub (Q D : ℕ) (hQ : D+2 ≤ Q) + (C E : OddPairLabel D → OddPairLabel D → ℝ) : + fourCopyOperator Q D hQ (C-E) = fourCopyOperator Q D hQ C-fourCopyOperator Q D hQ E := by + simp only [fourCopyOperator,Pi.sub_apply,Complex.ofReal_sub,sub_smul,Finset.sum_sub_distrib] + +theorem fourCopyOperator_middle (Q D : ℕ) (hQ : D+2 ≤ Q) (hD : 1 ≤ D) : + fourCopyOperator Q D hQ (finiteFourMiddle Q D) = + (fourDimensionRatio Q D : ℂ) • + (retainedFourInclusion Q D hQ (firstOddPairLabel D hD) * + (retainedFourInclusion Q D hQ (firstOddPairLabel D hD))ᴴ) + + ((3/10^6 : ℝ) : ℂ) • (∑ r : OddPairLabel D, + retainedFourInclusion Q D hQ r * (retainedFourInclusion Q D hQ r)ᴴ) - + fourCopyOperator Q D hQ (fun r s => physicalFourError Q D (oddPairDeficit r) (oddPairDeficit s)) := by + classical + unfold finiteFourMiddle + erw [fourCopyOperator_sub,fourCopyOperator_diagonal] + have he (r : OddPairLabel D) : Certificate.copyLabel r=1 ↔ r=firstOddPairLabel D hD := by + dsimp [Certificate.copyLabel,firstOddPairLabel] + constructor + · intro h; apply Fin.ext; dsimp; omega + · intro h; have := congrArg Fin.val h; dsimp at this; omega + simp only [Complex.ofReal_add,add_smul,Finset.sum_add_distrib] + simp_rw [he] + simp only [apply_ite,Complex.ofReal_zero,ite_smul,zero_smul,Finset.sum_ite_eq', + Finset.mem_univ,ite_true,← Finset.smul_sum] + rfl + +theorem fourDimensionRatio_exact (Q D : ℕ) (hQ : D+2 ≤ Q) : + fourDimensionRatio Q D = + ((4*Q-1-2*D : ℕ) : ℝ)/((2*Q-2+1 : ℕ) : ℝ) := by + unfold fourDimensionRatio + congr 1 + · rw [Nat.cast_sub (by omega : 2*D ≤ 4*Q-1),Nat.cast_sub (by omega : 1 ≤ 4*Q)] + push_cast + ring + · rw [Nat.cast_add,Nat.cast_sub (by omega : 2 ≤ 2*Q)] + push_cast + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/CopyFormAllowance.lean b/lean/OAI/Analysis/Laughlin/FourBody/CopyFormAllowance.lean new file mode 100644 index 0000000000000000000000000000000000000000..d3de761c8ebe417c0b10ac113e088c7b84521a35 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/CopyFormAllowance.lean @@ -0,0 +1,55 @@ +import OAI.Analysis.Laughlin.FourBody.CopyAlgebra +import OAI.Analysis.Laughlin.FourBody.TotalAllowance + +namespace OAI + +namespace Laughlin.Fock +open Spin Rotation MeasureTheory +open scoped BigOperators Matrix + +private theorem scaled_sum_of_haar_identity {ι : Type*} [Fintype ι] + (a d t : ℝ) (f : ι → ℝ) (hd : d ≠ 0) (h : d * ∑ i, f i = t) : + (a / d) * t = ∑ i, a * f i := by + rw [← h, ← Finset.mul_sum] + field_simp + +theorem fourCopyForm_allowance_identity (Q D : ℕ) (hQ : D+2 ≤ Q) (x : Space Q) : + (((2*Q-2+1 : ℕ) : ℝ)/((4*Q-1-2*D : ℕ) : ℝ)) * + (∑ r : OddPairLabel D, (contractionForm Q (sourceFourFamilyEnd Q) + (retainedFourInclusion Q D hQ r*(retainedFourInclusion Q D hQ r)ᴴ) x).re) = + ∑ r : OddPairLabel D, ((2*Q-2+1 : ℕ) : ℝ) * (∫ g, occupationNormSq Q + (physicalFourCopyEnd Q (oddPairDeficit r) D (by omega) + (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) := by + classical + have hd : ((4*Q-1-2*D : ℕ) : ℝ) ≠ 0 := + Nat.cast_ne_zero.mpr (by omega) + have h := physical_fourCopyOperator_haar Q D hQ (Matrix.diagonal (fun _ : OddPairLabel D => (1 : ℝ))) x + rw [fourCopyOperator_diagonal] at h + simp only [Complex.ofReal_one,one_smul,contractionForm_sum,Complex.re_sum] at h + have he (g : SourceSU2) : occupationQuadratic Q (Matrix.diagonal (fun _ : OddPairLabel D => (1 : ℝ))) + (fun r => physicalFourCopyEnd Q (oddPairDeficit r) D (by omega) (exteriorRotation Q g⁻¹ x)) = + ∑ r : OddPairLabel D, occupationNormSq Q + (physicalFourCopyEnd Q (oddPairDeficit r) D (by omega) (exteriorRotation Q g⁻¹ x)) := by + simp only [occupationQuadratic,Matrix.diagonal_apply,apply_ite,Complex.ofReal_one, + Complex.ofReal_zero,ite_mul,one_mul,zero_mul,Finset.sum_ite_eq,Finset.mem_univ, + ite_true,occupationInner_self,Complex.re_sum,Complex.ofReal_re] + simp_rw [he] at h + rw [integral_finsetSum _ (fun (r : OddPairLabel D) hr => linearMap_rotation_norm_integrable Q + (physicalFourCopyEnd Q (oddPairDeficit r) D (by omega)) x)] at h + exact scaled_sum_of_haar_identity _ _ _ _ hd h + +noncomputable def retainedFourAllowance (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : ℝ := + ∑ d : Fin 23, (((2*Q-2+1 : ℕ) : ℝ)/((4*Q-1-2*(d.val+1) : ℕ) : ℝ)) * + (∑ r : OddPairLabel (d.val+1), (contractionForm Q (sourceFourFamilyEnd Q) + (retainedFourInclusion Q (d.val+1) (by omega) r* + (retainedFourInclusion Q (d.val+1) (by omega) r)ᴴ) x).re) + +theorem retainedFourAllowance_bound (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + retainedFourAllowance Q hQ x ≤ 10946*sourceFockEnergy Q x := by + unfold retainedFourAllowance + simp_rw [fourCopyForm_allowance_identity] + exact physical_fourBody_total_haar_allowance Q hQ x + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/CopyOperatorHaar.lean b/lean/OAI/Analysis/Laughlin/FourBody/CopyOperatorHaar.lean new file mode 100644 index 0000000000000000000000000000000000000000..7926cd8409cb022162ce5ca63a4ef433f5484e01 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/CopyOperatorHaar.lean @@ -0,0 +1,81 @@ +import OAI.Analysis.Laughlin.FourBody.HaarTransfer +import OAI.Analysis.Laughlin.FourBody.HighestFock + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory +open scoped BigOperators Matrix + +noncomputable def fourCopyOperator (Q D : ℕ) (hQ : D+2 ≤ Q) + (C : OddPairLabel D → OddPairLabel D → ℝ) : Matrix (FourWedgeIndex Q) (FourWedgeIndex Q) ℂ := + ∑ r, ∑ s, (C r s : ℂ) • + (retainedFourInclusion Q D hQ r * (retainedFourInclusion Q D hQ s)ᴴ) + +theorem linearMap_rotation_inner_integrable (Q : ℕ) (L R : Module.End ℂ (Space Q)) (x : Space Q) : + Integrable (fun g : SourceSU2 => occupationInner Q + (L (exteriorRotation Q g⁻¹ x)) (R (exteriorRotation Q g⁻¹ x))) sourceHaar := by + apply Continuous.integrable_of_hasCompactSupport _ (isClosed_tsupport _).isCompact + unfold occupationInner + apply continuous_finsetSum + intro A hA + exact (linearMap_rotation_coordinate_continuous Q L x A).star.mul + (linearMap_rotation_coordinate_continuous Q R x A) + +theorem physical_fourCopyOperator_haar (Q D : ℕ) (hQ : D+2 ≤ Q) + (C : OddPairLabel D → OddPairLabel D → ℝ) (x : Space Q) : + ((4*Q-1-2*D : ℕ) : ℝ) * (∫ g, occupationQuadratic Q C + (fun r => physicalFourCopyEnd Q (oddPairDeficit r) D (by omega) + (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) = + (contractionForm Q (sourceFourFamilyEnd Q) (fourCopyOperator Q D hQ C) x).re := by + let L : OddPairLabel D → Module.End ℂ (Space Q) := + fun r => physicalFourCopyEnd Q (oddPairDeficit r) D (by omega) + have hi (r s : OddPairLabel D) := linearMap_rotation_inner_integrable Q (L r) (L s) x + have hisum : Integrable (fun g : SourceSU2 => ∑ r, ∑ s, + (C r s : ℂ) * occupationInner Q (L r (exteriorRotation Q g⁻¹ x)) + (L s (exteriorRotation Q g⁻¹ x))) sourceHaar := + integrable_finsetSum _ (fun r hr => integrable_finsetSum _ (fun s hs => (hi r s).const_mul _)) + have hc : ((4*Q-1-2*D : ℕ) : ℂ) * (∫ g, ∑ r, ∑ s, + (C r s : ℂ) * occupationInner Q (L r (exteriorRotation Q g⁻¹ x)) + (L s (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) = + contractionForm Q (sourceFourFamilyEnd Q) (fourCopyOperator Q D hQ C) x := by + rw [integral_finsetSum _ (fun r hr => integrable_finsetSum _ (fun s hs => (hi r s).const_mul _))] + simp_rw [integral_finsetSum _ (fun s hs => (hi _ s).const_mul _),integral_const_mul] + simp only [fourCopyOperator,contractionForm_sum,contractionForm_smul,Finset.mul_sum] + apply Finset.sum_congr rfl + intro r hr + apply Finset.sum_congr rfl + intro s hs + calc + _ = (C r s : ℂ) * (((4*Q-1-2*D : ℕ) : ℂ) * (∫ g, occupationInner Q + (L r (exteriorRotation Q g⁻¹ x)) (L s (exteriorRotation Q g⁻¹ x)) ∂sourceHaar)) := by ring + _ = _ := by rw [physicalFourCopyEnd_cross_haar Q D hQ r s] + have hr := congrArg Complex.re hc + simp only [Complex.mul_re,Complex.natCast_re,Complex.natCast_im,zero_mul,sub_zero] at hr + have hre := integral_re hisum + change (∫ g, (∑ r, ∑ s, (C r s : ℂ) * occupationInner Q + (L r (exteriorRotation Q g⁻¹ x)) (L s (exteriorRotation Q g⁻¹ x))).re ∂sourceHaar) = + (∫ g, ∑ r, ∑ s, (C r s : ℂ) * occupationInner Q + (L r (exteriorRotation Q g⁻¹ x)) (L s (exteriorRotation Q g⁻¹ x)) ∂sourceHaar).re at hre + rw [← hre] at hr + simpa only [occupationQuadratic,L,Complex.mul_re,Complex.natCast_re,Complex.natCast_im, + zero_mul,sub_zero] using hr + +theorem physical_fourCopyOperator_transfer (Q D : ℕ) (hQ : 25 ≤ Q) (hD₁ : 1 ≤ D) (hD₂ : D ≤ 23) + (x : Space Q) : + -(24*fourBodyRho D Q*sourceFockEnergy Q x) ≤ + (((2*Q-2+1 : ℕ) : ℝ)/((4*Q-1-2*D : ℕ) : ℝ)) * + (contractionForm Q (sourceFourFamilyEnd Q) + (fourCopyOperator Q D (by omega) (finiteFourMiddle Q D)) x).re := by + have h := physical_fourBody_haar_transfer Q D hQ hD₁ hD₂ x + have he := physical_fourCopyOperator_haar Q D (by omega) (finiteFourMiddle Q D) x + have hd : ((4*Q-1-2*D : ℕ) : ℝ) ≠ 0 := by exact_mod_cast (show 4*Q-1-2*D ≠ 0 by omega) + rw [← he] + have hm : (((2*Q-2+1 : ℕ) : ℝ)/((4*Q-1-2*D : ℕ) : ℝ))*((4*Q-1-2*D : ℕ) : ℝ) = + ((2*Q-2+1 : ℕ) : ℝ) := by field_simp + rw [← mul_assoc,hm] + exact h + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/CopyOrthogonality.lean b/lean/OAI/Analysis/Laughlin/FourBody/CopyOrthogonality.lean new file mode 100644 index 0000000000000000000000000000000000000000..5ce791ba0831ad56dcd722f4d5ff20334e124248 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/CopyOrthogonality.lean @@ -0,0 +1,91 @@ +import OAI.Analysis.Laughlin.FourBody.Copies +import OAI.Analysis.Laughlin.Spin.Basis2 + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix Kronecker + +noncomputable def fourBodyInclusion (Q r D : ℕ) (hr : r ≤ Q) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) : + Matrix (Fin (2*Q-2+1) × WedgePairIndex Q) + (Fin (genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q r) (D-r)+1)) ℝ := + tensorPairInclusion (2*Q-2) Q r hr * + ((-1 : ℝ)^(D-r) • genericCoupledInclusion (2*Q-2) (genericCoupledWeight Q Q r) (D-r) hA hB) + +theorem fourBodyInclusion_column (Q r D : ℕ) (hr : r ≤ Q) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) + (n : Fin (genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q r) (D-r)+1)) + (i : Fin (2*Q-2+1) × WedgePairIndex Q) : + fourBodyInclusion Q r D hr hA hB i n = fourBodyCopy Q r D hr hA hB n.val i := rfl + +theorem pairCoupledInclusion_cross (Q r s : ℕ) (hr : r ≤ Q) (hs : s ≤ Q) + (hor : Odd r) (hos : Odd s) (hne : r ≠ s) : + (pairCoupledInclusion Q r hr)ᵀ * pairCoupledInclusion Q s hs = 0 := by + ext n m + exact pairCoupledWedge_orthogonal Q r s n.val m.val hr hs hor hos (Or.inl hne) + +theorem tensorPairInclusion_cross (A Q r s : ℕ) (hr : r ≤ Q) (hs : s ≤ Q) + (hor : Odd r) (hos : Odd s) (hne : r ≠ s) : + (tensorPairInclusion A Q r hr)ᵀ * tensorPairInclusion A Q s hs = 0 := by + unfold tensorPairInclusion + have ht : ((1 : Matrix (Fin (A+1)) (Fin (A+1)) ℝ) ⊗ₖ pairCoupledInclusion Q r hr)ᵀ = + (1 : Matrix (Fin (A+1)) (Fin (A+1)) ℝ) ⊗ₖ (pairCoupledInclusion Q r hr)ᵀ := by + ext i j + simp [Matrix.kroneckerMap,Matrix.transpose_apply,Matrix.one_apply,eq_comm] + rw [ht,← Matrix.mul_kronecker_mul,pairCoupledInclusion_cross Q r s hr hs hor hos hne] + simp + +theorem fourBodyInclusion_isometry (Q r D : ℕ) (hr : r ≤ Q) (hor : Odd r) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) : + (fourBodyInclusion Q r D hr hA hB)ᵀ * fourBodyInclusion Q r D hr hA hB = 1 := by + have hs : (-1 : ℝ)^(D-r) * (-1 : ℝ)^(D-r) = 1 := by rw [← mul_pow]; norm_num + unfold fourBodyInclusion + rw [Matrix.transpose_mul,Matrix.mul_assoc,← Matrix.mul_assoc + (tensorPairInclusion (2*Q-2) Q r hr)ᵀ, + tensorPairInclusion_isometry _ Q r hr hor,Matrix.one_mul] + simp only [Matrix.transpose_smul,Matrix.smul_mul,Matrix.mul_smul,smul_smul, + genericCoupledInclusion_isometry,hs,one_smul] + +theorem fourBodyCopy_orthogonal_pair (Q r s D E n m : ℕ) + (hr : r ≤ Q) (hs : s ≤ Q) (hor : Odd r) (hos : Odd s) (hne : r ≠ s) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) + (hC : E-s ≤ 2*Q-2) (hD : E-s ≤ genericCoupledWeight Q Q s) : + (∑ i, fourBodyCopy Q r D hr hA hB n i * fourBodyCopy Q s E hs hC hD m i) = 0 := by + have hp {I J K : Type} [Fintype I] [Fintype J] [Fintype K] + (A : Matrix I J ℝ) (B : Matrix I K ℝ) (v : J → ℝ) (w : K → ℝ) : + (∑ i, (A *ᵥ v) i * (B *ᵥ w) i) = ∑ j, v j * ((Aᵀ*B) *ᵥ w) j := by + change (A *ᵥ v) ⬝ᵥ (B *ᵥ w) = v ⬝ᵥ ((Aᵀ*B) *ᵥ w) + rw [← Matrix.mulVec_mulVec,Matrix.dotProduct_transpose_mulVec] + exact dotProduct_comm _ _ + rw [fourBodyCopy,fourBodyCopy,hp,tensorPairInclusion_cross _ Q r s hr hs hor hos hne] + simp + +theorem fourBodyCopy_orthogonal_outer (Q r D E n m : ℕ) + (hr : r ≤ Q) (hor : Odd r) (hrD : r ≤ D) (hrE : r ≤ E) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) + (hC : E-r ≤ 2*Q-2) (hD : E-r ≤ genericCoupledWeight Q Q r) + (hne : D ≠ E ∨ n ≠ m) : + (∑ i, fourBodyCopy Q r D hr hA hB n i * fourBodyCopy Q r E hr hC hD m i) = 0 := by + have hp {I J : Type} [Fintype I] [Fintype J] [DecidableEq J] + (A : Matrix I J ℝ) (h : Aᵀ*A=1) (v w : J → ℝ) : + (∑ i, (A *ᵥ v) i * (A *ᵥ w) i) = ∑ j, v j*w j := by + change (A *ᵥ v) ⬝ᵥ (A *ᵥ w) = v ⬝ᵥ w + rw [← Matrix.dotProduct_transpose_mulVec,Matrix.mulVec_mulVec,h,Matrix.one_mulVec] + exact dotProduct_comm _ _ + rw [fourBodyCopy,fourBodyCopy,hp _ (tensorPairInclusion_isometry _ Q r hr hor)] + simp only [Pi.smul_apply,smul_eq_mul] + calc + _ = ((-1 : ℝ)^(D-r) * (-1 : ℝ)^(E-r)) * + (∑ i, genericUnitDescendant (2*Q-2) (genericCoupledWeight Q Q r) (D-r) hA hB n i * + genericUnitDescendant (2*Q-2) (genericCoupledWeight Q Q r) (E-r) hC hD m i) := by + rw [Finset.mul_sum]; apply Finset.sum_congr rfl; intro i hi; ring + _ = 0 := by + rw [genericUnitDescendant_orthogonal _ _ _ _ _ _ hA hB hC hD (by + rcases hne with h | h + · left; omega + · exact Or.inr h),mul_zero] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/CoupledBasis.lean b/lean/OAI/Analysis/Laughlin/FourBody/CoupledBasis.lean new file mode 100644 index 0000000000000000000000000000000000000000..5ce120dc4217700334703b2b085ba507719d5d91 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/CoupledBasis.lean @@ -0,0 +1,66 @@ +import OAI.Analysis.Laughlin.FourBody.CopyOrthogonality +import OAI.Analysis.Laughlin.Pair.CoupledBasis + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +abbrev FourCoupledIndex (Q : ℕ) := + Σ r : OddPairLabel Q, GenericCoupledIndex (2*Q-2) (genericCoupledWeight Q Q (oddPairDeficit r)) + +noncomputable def fourCoupledBasis (Q : ℕ) : + Matrix (Fin (2*Q-2+1) × WedgePairIndex Q) (FourCoupledIndex Q) ℝ := + fun i s => fourBodyCopy Q (oddPairDeficit s.1) (oddPairDeficit s.1+s.2.1.val) + (oddPairDeficit_le s.1) (by have := s.2.1.isLt; omega) + (by have := s.2.1.isLt; omega) s.2.2.val i + +theorem fourCoupledIndex_card (Q : ℕ) : + Fintype.card (FourCoupledIndex Q) = Fintype.card (Fin (2*Q-2+1) × WedgePairIndex Q) := by + rw [Fintype.card_sigma] + simp_rw [genericCoupledIndex_card,Fintype.card_prod,Fintype.card_fin] + rw [← Finset.mul_sum] + congr 1 + simpa only [Fintype.card_sigma,Fintype.card_fin] using pairCoupledIndex_card Q + +theorem fourCoupledBasis_isometry (Q : ℕ) : + (fourCoupledBasis Q)ᵀ * fourCoupledBasis Q = 1 := by + ext s t + simp only [Matrix.mul_apply,Matrix.transpose_apply,fourCoupledBasis,Matrix.one_apply] + by_cases h : s=t + · subst t + rw [ite_eq_left rfl] + simpa only [vectorNormSq,pow_two] using + fourBodyCopy_norm Q (oddPairDeficit s.1) (oddPairDeficit s.1+s.2.1.val) + s.2.2.val (oddPairDeficit_le s.1) (oddPairDeficit_odd s.1) _ _ + (by have := s.2.2.isLt; simpa only [Nat.add_sub_cancel_left] using Nat.le_of_lt_succ this) + · rw [ite_eq_right h] + rcases s with ⟨r,⟨z,n⟩⟩ + rcases t with ⟨s,⟨w,m⟩⟩ + dsimp only at * + by_cases hrs : r=s + · subst s + apply fourBodyCopy_orthogonal_outer _ _ _ _ _ _ _ (oddPairDeficit_odd r) + (by omega) (by omega) + by_cases hzw : z=w + · subst w + right + intro he + exact h (by have hn : n=m := Fin.ext he; subst m; rfl) + · left + intro he + exact hzw (Fin.ext (by omega)) + · apply fourBodyCopy_orthogonal_pair _ _ _ _ _ _ _ _ _ + (oddPairDeficit_odd r) (oddPairDeficit_odd s) + intro he + exact hrs (Fin.ext (by dsimp [oddPairDeficit] at he; omega)) + +theorem fourCoupledBasis_complete (Q : ℕ) : + fourCoupledBasis Q * (fourCoupledBasis Q)ᵀ = 1 := + (Matrix.mul_eq_one_comm_of_card_eq (m := FourCoupledIndex Q) + (n := Fin (2*Q-2+1) × WedgePairIndex Q) (R := ℝ) + (fourCoupledIndex_card Q)).mp (fourCoupledBasis_isometry Q) + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/EndExpansion.lean b/lean/OAI/Analysis/Laughlin/FourBody/EndExpansion.lean new file mode 100644 index 0000000000000000000000000000000000000000..8a44ceef0611456aec01f194272635bb96cc8afc --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/EndExpansion.lean @@ -0,0 +1,29 @@ +import OAI.Analysis.Laughlin.FourBody.ColumnExpansion + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators +open Spin + +theorem occupationInner_left_ext (Q : ℕ) (x y : Space Q) + (h : ∀ z, occupationInner Q x z = occupationInner Q y z) : x=y := by + apply (occupationBasis Q).repr.injective + ext A + have hA := h (occupationBasis Q A) + rw [occupationInner_basis_right,occupationInner_basis_right] at hA + exact star_injective hA + +theorem limitFourCopyEnd_expansion (Q r D : ℕ) (hr : r ≤ D) (hor : Odd r) (x : Space Q) : + limitFourCopyEnd Q r D x = ∑ A : FourOccupation Q D, + (fourOccupationCoefficient Q r D A.val : ℂ) • fourOccupationEnd Q D A x := by + apply occupationInner_left_ext + intro y + rw [← limitFourColumn_mul_adjoint,limitFourColumn_expansion Q r D hr hor] + simp only [Finset.sum_mul,smul_mul_assoc,occupationInner_sum_right,occupationInner_sum_left, + occupationInner_smul_right,occupationInner_smul_left,Complex.star_def,Complex.conj_ofReal, + ← fourOccupationCreate_mul,fourOccupation_adjoint] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/ErrorCertificate.lean b/lean/OAI/Analysis/Laughlin/FourBody/ErrorCertificate.lean new file mode 100644 index 0000000000000000000000000000000000000000..cc919f35803d6a54fe1695ac7b33673a39367ec2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/ErrorCertificate.lean @@ -0,0 +1,104 @@ +import OAI.Analysis.Laughlin.FourBody.ErrorLimit +import OAI.Analysis.Laughlin.FourBody.RadicalCancellation + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +theorem sourceAlpha_factor (t : ℕ) (e : ℕ × ℕ × ℤ) : + sourceAlpha t e = (e.2.2 : ℝ)/(10^7) * alphaRadical t e.1 e.2.1 := rfl + +theorem fourErrorLimitEntry_certificate (D r s t : ℕ) (e f : ℕ × ℕ × ℤ) + (hr : r ≤ D) (hs : s ≤ D) (hor : Odd r) (hos : Odd s) + (he : t ≤ e.1+e.2.1) (hf : t ≤ f.1+f.2.1) : + fourErrorLimitEntry D r s t e f = + (Real.sqrt (sourceCopyWeight D r * sourceCopyWeight D s)/(10^14)) * + (Certificate.yEntry D r s t e f : ℝ) := by + rcases e with ⟨p,j,a⟩ + rcases f with ⟨q,l,b⟩ + dsimp only at he hf ⊢ + let i := p+j-t + let k := q+l-t + let T := p+j+k + have hT' : q+l+i=T := by dsimp [i,k,T]; omega + by_cases hD : D ≤ T + · have heq : fourErrorLimitEntry D r s t (p,j,a) (q,l,b) = + sourceAlpha t (p,j,a) * sourceAlpha t (q,l,b) * + fourBodyLimitCoefficient r D T p j k * fourBodyLimitCoefficient s D T q l i := by + simp only [fourErrorLimitEntry]; exact ite_eq_left hD + rw [heq,sourceAlpha_factor,sourceAlpha_factor, + source_fourBody_radical_coefficient r D T p j k hr hD rfl, + source_fourBody_radical_coefficient s D T q l i hs hD hT'] + dsimp only + calc + _ = ((a : ℝ)*(b : ℝ)*(Certificate.V r D T p j k : ℝ)*(Certificate.V s D T q l i : ℝ)/(10^14)) * + (alphaRadical t p j * alphaRadical t q l * fourBodyRadical r D T p j k * fourBodyRadical s D T q l i) := by ring + _ = ((a : ℝ)*(b : ℝ)*(Certificate.V r D T p j k : ℝ)*(Certificate.V s D T q l i : ℝ)/(10^14)) * + (Real.sqrt (sourceCopyWeight D r * sourceCopyWeight D s)*sourceYFactor D r s t p j q l) := by + rw [source_Y_radical_cancellation D r s t p j q l hor hos he hf] + _ = _ := by + simp only [Certificate.yEntry] + rw [ite_eq_left hD] + push_cast + dsimp [sourceYFactor,i,k,T] + ring + · simp only [fourErrorLimitEntry,Certificate.yEntry] + rw [ite_eq_right hD,ite_eq_right hD] + simp + +theorem real_list_sum_scale {I : Type*} (l : List I) (c : ℝ) (f : I → ℝ) : + (l.map (fun i => c*f i)).sum = c*(l.map f).sum := by + induction l with + | nil => simp + | cons a l ih => simp only [List.map_cons,List.sum_cons,ih]; ring + +theorem fourErrorLimitRow_certificate (D r s : ℕ) (hr : r ≤ D) (hs : s ≤ D) + (hor : Odd r) (hos : Odd s) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) (hrow : row ∈ Certificate.rows) : + fourErrorLimitRow D r s row = + (Real.sqrt (sourceCopyWeight D r * sourceCopyWeight D s)/(10^14)) * + (Certificate.yRow D r s row : ℝ) := by + unfold fourErrorLimitRow + have he : ∀ e ∈ row.2.2, ∀ f ∈ row.2.2, + fourErrorLimitEntry D r s row.1 e f = + (Real.sqrt (sourceCopyWeight D r * sourceCopyWeight D s)/(10^14)) * + (Certificate.yEntry D r s row.1 e f : ℝ) := by + intro e he f hf + exact fourErrorLimitEntry_certificate D r s row.1 e f hr hs hor hos + (source_rows_admissible row hrow e he) (source_rows_admissible row hrow f hf) + calc + _ = (row.2.2.map (fun e => (row.2.2.map (fun f => + (Real.sqrt (sourceCopyWeight D r * sourceCopyWeight D s)/(10^14)) * + (Certificate.yEntry D r s row.1 e f : ℝ))).sum)).sum := by + apply congrArg List.sum + apply List.map_congr_left; intro e he' + apply congrArg List.sum + apply List.map_congr_left; intro f hf' + exact he e he' f hf' + _ = _ := by + simp_rw [real_list_sum_scale] + unfold Certificate.yRow + push_cast + simp only [List.map_map,Function.comp_def] + push_cast + simp only [List.map_map,Function.comp_def] + +theorem source_fourBody_error_certificate_identity (D r s : ℕ) (hr : r ≤ D) (hs : s ≤ D) + (hor : Odd r) (hos : Odd s) : + limitFourError D r s = Real.sqrt (sourceCopyWeight D r * sourceCopyWeight D s) * + (Certificate.Y D r s : ℝ) := by + unfold limitFourError + have he : Certificate.rows.map (fourErrorLimitRow D r s) = Certificate.rows.map (fun row => + (Real.sqrt (sourceCopyWeight D r * sourceCopyWeight D s)/(10^14)) * + (Certificate.yRow D r s row : ℝ)) := by + apply List.map_congr_left; intro row hrow + exact fourErrorLimitRow_certificate D r s hr hs hor hos row hrow + rw [he,real_list_sum_scale] + unfold Certificate.Y + push_cast + simp only [List.map_map,Function.comp_def] + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/ErrorLimit.lean b/lean/OAI/Analysis/Laughlin/FourBody/ErrorLimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..c3c4360b5e0a3fb86b0a2926174f162ba4e8eebc --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/ErrorLimit.lean @@ -0,0 +1,77 @@ +import OAI.Analysis.Laughlin.FourBody.CoefficientLimit +import OAI.Analysis.Laughlin.Operators.Certificate + +namespace OAI + +namespace Laughlin.Spin +open scoped Topology +open Filter + +noncomputable def sourceAlpha (t : ℕ) (e : ℕ × ℕ × ℤ) : ℝ := + (e.2.2 : ℝ)/(10^7) * Real.sqrt ((2 : ℝ)^((e.1 : ℤ)-t) * + ((t.factorial : ℝ)*((e.1+e.2.1-t).factorial : ℝ) / + ((e.1.factorial : ℝ)*(e.2.1.factorial : ℝ)))) + +noncomputable def fourErrorEntry (Q D r s t : ℕ) (e f : ℕ × ℕ × ℤ) : ℝ := + let i := e.1+e.2.1-t + let k := f.1+f.2.1-t + let T := e.1+e.2.1+k + if D ≤ T then sourceAlpha t e * sourceAlpha t f * + fourBodyCoefficient Q r D T e.1 e.2.1 k * fourBodyCoefficient Q s D T f.1 f.2.1 i else 0 + +noncomputable def fourErrorLimitEntry (D r s t : ℕ) (e f : ℕ × ℕ × ℤ) : ℝ := + let i := e.1+e.2.1-t + let k := f.1+f.2.1-t + let T := e.1+e.2.1+k + if D ≤ T then sourceAlpha t e * sourceAlpha t f * + fourBodyLimitCoefficient r D T e.1 e.2.1 k * fourBodyLimitCoefficient s D T f.1 f.2.1 i else 0 + +theorem fourErrorEntry_tendsto (D r s t : ℕ) (e f : ℕ × ℕ × ℤ) + (hr : r ≤ D) (hs : s ≤ D) (he : t ≤ e.1+e.2.1) (hf : t ≤ f.1+f.2.1) : + Tendsto (fun Q => fourErrorEntry Q D r s t e f) atTop (𝓝 (fourErrorLimitEntry D r s t e f)) := by + unfold fourErrorEntry fourErrorLimitEntry + dsimp only + by_cases hD : D ≤ e.1+e.2.1+(f.1+f.2.1-t) + · simp only [ite_eq_left hD] + exact (tendsto_const_nhds.mul + (source_fourBody_coefficient_tendsto r D _ e.1 e.2.1 _ hr hD rfl)).mul + (source_fourBody_coefficient_tendsto s D _ f.1 f.2.1 _ hs hD (by omega)) + · simp only [ite_eq_right hD]; exact tendsto_const_nhds + +theorem physical_list_sum_tendsto {I : Type*} (l : List I) (f : ℕ → I → ℝ) (g : I → ℝ) + (h : ∀ i ∈ l, Tendsto (fun Q => f Q i) atTop (𝓝 (g i))) : + Tendsto (fun Q => (l.map (f Q)).sum) atTop (𝓝 ((l.map g).sum)) := by + induction l with + | nil => simp + | cons a l ih => + simp only [List.map_cons,List.sum_cons] + exact (h a (by simp)).add (ih (fun i hi => h i (by simp [hi]))) + +theorem source_rows_admissible : ∀ row ∈ Certificate.rows, ∀ e ∈ row.2.2, + row.1 ≤ e.1+e.2.1 := by decide + +noncomputable def fourErrorRow (Q D r s : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) : ℝ := + (row.2.2.map (fun e => (row.2.2.map (fun f => fourErrorEntry Q D r s row.1 e f)).sum)).sum +noncomputable def fourErrorLimitRow (D r s : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) : ℝ := + (row.2.2.map (fun e => (row.2.2.map (fun f => fourErrorLimitEntry D r s row.1 e f)).sum)).sum + +noncomputable def physicalFourError (Q D r s : ℕ) : ℝ := + -(Certificate.rows.map (fourErrorRow Q D r s)).sum +noncomputable def limitFourError (D r s : ℕ) : ℝ := + -(Certificate.rows.map (fourErrorLimitRow D r s)).sum + +theorem physicalFourError_tendsto (D r s : ℕ) (hr : r ≤ D) (hs : s ≤ D) : + Tendsto (fun Q => physicalFourError Q D r s) atTop (𝓝 (limitFourError D r s)) := by + apply Filter.Tendsto.neg + apply physical_list_sum_tendsto + intro row hrow + apply physical_list_sum_tendsto + intro e he + apply physical_list_sum_tendsto + intro f hf + exact fourErrorEntry_tendsto D r s row.1 e f hr hs + (source_rows_admissible row hrow e he) (source_rows_admissible row hrow f hf) + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/ErrorMatrix.lean b/lean/OAI/Analysis/Laughlin/FourBody/ErrorMatrix.lean new file mode 100644 index 0000000000000000000000000000000000000000..cb41714eb902a9beb0223ec7b5a86944f5b184d3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/ErrorMatrix.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.Laughlin.FourBody.ErrorCertificate +import OAI.Analysis.Laughlin.FourBody.Scaled + +namespace OAI + +namespace Laughlin.Spin +open scoped Matrix Topology +open Filter + +theorem sourceCopyWeight_certificate (D : ℕ) (i : Fin ((D+1)/2)) : + sourceCopyWeight D (Certificate.copyLabel i) = (Certificate.copyWeight D i : ℝ) := by + simp [sourceCopyWeight,Certificate.copyWeight] + +theorem source_fourBody_error_matrix (D : ℕ) (i j : Fin ((D+1)/2)) : + limitFourError D (Certificate.copyLabel i) (Certificate.copyLabel j) = Certificate.scaledError D i j := by + have hi : Certificate.copyLabel i ≤ D := by unfold Certificate.copyLabel; have := i.isLt; omega + have hj : Certificate.copyLabel j ≤ D := by unfold Certificate.copyLabel; have := j.isLt; omega + have hoi : Odd (Certificate.copyLabel i) := ⟨i.val,by unfold Certificate.copyLabel; omega⟩ + have hoj : Odd (Certificate.copyLabel j) := ⟨j.val,by unfold Certificate.copyLabel; omega⟩ + rw [source_fourBody_error_certificate_identity D _ _ hi hj hoi hoj, + sourceCopyWeight_certificate,sourceCopyWeight_certificate, + Real.sqrt_mul (Certificate.copyWeight_nonneg D i)] + simp only [Certificate.scaledError,Certificate.weightSqrtDiagonal,Matrix.diagonal_mul, + Matrix.mul_diagonal,Matrix.map_apply,Certificate.errorRational,Rat.coe_castHom] + ring + +theorem physicalFourError_certificate_tendsto (D : ℕ) (i j : Fin ((D+1)/2)) : + Tendsto (fun Q => physicalFourError Q D (Certificate.copyLabel i) (Certificate.copyLabel j)) + atTop (𝓝 (Certificate.scaledError D i j)) := by + rw [← source_fourBody_error_matrix D i j] + apply physicalFourError_tendsto D + · unfold Certificate.copyLabel; have := i.isLt; omega + · unfold Certificate.copyLabel; have := j.isLt; omega + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Estimate.lean b/lean/OAI/Analysis/Laughlin/FourBody/Estimate.lean new file mode 100644 index 0000000000000000000000000000000000000000..15e056dc3adcfae1fc8d1797b1203482a22e80f3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Estimate.lean @@ -0,0 +1,21 @@ +import OAI.Analysis.Laughlin.FourBody.PairTarget + +namespace OAI + +namespace Laughlin.Fock +open Filter +open scoped BigOperators Topology + +theorem physical_fourBody_estimate : + ∃ e : ℕ → ℝ, (∀ Q, 0 ≤ e Q) ∧ Tendsto e atTop (𝓝 0) ∧ + ∀ Q : ℕ, 25 ≤ Q → ∀ x : Space Q, + sourceA4Form Q x ≤ + (∑ p : Fin (2*Q-2+1), ∑ q : Fin (2*Q-2+1), + occupationNormSq Q (sourcePairEnd Q q.val (sourcePairEnd Q p.val x))) + + (10946*(3/10^6 : ℝ)+e Q)*sourceFockEnergy Q x := + ⟨averagedFourTransferError,averagedFourTransferError_nonneg, + averagedFourTransferError_tendsto,sourceA4Form_bound⟩ + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Expansion.lean b/lean/OAI/Analysis/Laughlin/FourBody/Expansion.lean new file mode 100644 index 0000000000000000000000000000000000000000..3d10a934178712d7e25c5daecbbc042e80a2baae --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Expansion.lean @@ -0,0 +1,67 @@ +import OAI.Analysis.Laughlin.FourBody.Assembly + +namespace OAI + +namespace Laughlin.Fock +open Spin +open scoped BigOperators Matrix + +noncomputable def sourceEntryThree (Q : ℕ) (e : ℕ × ℕ × ℤ) (x : Space Q) : Space Q := + ∑ i, (pairOrbitalUnit Q e.1 e.2.1 i : ℂ) • sourceThreeEnd Q i x + +theorem sourceEntryThree_eq (Q : ℕ) (e : ℕ × ℕ × ℤ) + (hp : e.1 < 2*Q-2+1) (hj : e.2.1 ≤ Q) (x : Space Q) : + sourceEntryThree Q e x = annihilate ⟨e.2.1,by omega⟩ (sourcePairEnd Q e.1 x) := by + rw [sourceEntryThree,pairOrbitalUnit_family_sum Q e.1 e.2.1 hp hj] + rfl + +theorem sourceRowLevel_entries (Q t T : ℕ) (entries : List (ℕ × ℕ × ℤ)) (x : Space Q) : + sourceRowLevel Q t T entries x = + (entries.map (fun e => if e.1+e.2.1=T then + (sourceAlpha t e : ℂ) • sourceEntryThree Q e x else 0)).sum := by + induction entries with + | nil => simp [sourceRowLevel,threeBodyLevelVector] + | cons e entries ih => + simp only [sourceRowLevel,threeBodyLevelVector,List.map_cons,List.sum_cons, + Pi.add_apply,Complex.ofReal_add,add_smul,Finset.sum_add_distrib] at ih ⊢ + rw [ih] + congr 1 + by_cases h : e.1+e.2.1=T + · simp only [ite_eq_left h,Pi.smul_apply,smul_eq_mul,Complex.ofReal_mul,sourceEntryThree, + Finset.smul_sum,smul_smul] + · simp [h] + +theorem occupationInner_list_left {I : Type*} (Q : ℕ) (l : List I) + (f : I → Space Q) (x : Space Q) : + occupationInner Q (l.map f).sum x = (l.map (fun i => occupationInner Q (f i) x)).sum := by + induction l with + | nil => simp [occupationInner] + | cons i l ih => simp only [List.map_cons,List.sum_cons,occupationInner_add_left,ih] + +theorem occupationInner_list_right {I : Type*} (Q : ℕ) (l : List I) + (f : I → Space Q) (x : Space Q) : + occupationInner Q x (l.map f).sum = (l.map (fun i => occupationInner Q x (f i))).sum := by + induction l with + | nil => simp [occupationInner] + | cons i l ih => simp only [List.map_cons,List.sum_cons,occupationInner_add_right,ih] + +theorem finset_list_sum_swap {I J A : Type*} [AddCommMonoid A] + (s : Finset I) (l : List J) (f : I → J → A) : + (∑ i ∈ s, (l.map (f i)).sum) = (l.map (fun j => ∑ i ∈ s, f i j)).sum := by + induction l with + | nil => simp + | cons j l ih => simp only [List.map_cons,List.sum_cons,Finset.sum_add_distrib,ih] + +theorem rowLevel_sum_select {A : Type*} [AddCommMonoid A] (t n : ℕ) + (ht : t ≤ n) (hn : n < 16) (f : RowLevel t → A) : + (∑ T : RowLevel t, if n=T.val.val then f T else 0) = f ⟨⟨n,hn⟩,ht⟩ := by + classical + have he (T : RowLevel t) : n=T.val.val ↔ T=⟨⟨n,hn⟩,ht⟩ := by + constructor + · intro h; exact Subtype.ext (Fin.ext h.symm) + · intro h; subst T; rfl + simp only [he,Finset.sum_ite_eq',Finset.mem_univ,ite_true] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/FactorialCoefficient.lean b/lean/OAI/Analysis/Laughlin/FourBody/FactorialCoefficient.lean new file mode 100644 index 0000000000000000000000000000000000000000..16e4ba39cc38dace9932218b6ee85307656e1cd8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/FactorialCoefficient.lean @@ -0,0 +1,32 @@ +import OAI.Analysis.Laughlin.FourBody.Basic +import OAI.Analysis.Laughlin.FourBody.CoefficientLimit +import OAI.Analysis.Laughlin.Polynomial.SourceEqualSpinPolynomial + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +theorem source_fourBody_factorial_coefficient (r D T p j k : ℕ) + (hrD : r ≤ D) (hDT : D ≤ T) (hT : p+j+k=T) (hr : r ≤ j+k) : + fourBodyLimitCoefficient r D T p j k = + Real.sqrt 2 * (Real.sqrt (1/2))^(j+k+(T-r)) * (Certificate.V r D T p j k : ℝ) * + sqrtFactorial j * sqrtFactorial k * sqrtFactorial p / + (sqrtFactorial r * sqrtFactorial (D-r) * sqrtFactorial (T-D)) := by + have hi : r+(j+k-r)=j+k := by omega + have ho : (D-r)+(T-D)=T-r := by omega + have hk : j+k-j=k := by omega + have hb : T-r-p=j+k-r := by omega + rw [fourBodyLimitCoefficient,ite_eq_left hr, + equalSpin_polynomialCoefficient _ r (j+k-r) j (by omega), + equalSpin_polynomialCoefficient _ (D-r) (T-D) p (by omega)] + rw [hi,ho,hk,hb] + simp only [Certificate.V,ite_eq_left hr,Int.cast_mul] + rw [pow_add] + field_simp [ne_of_gt (sqrtFactorial_pos r),ne_of_gt (sqrtFactorial_pos (D-r)), + ne_of_gt (sqrtFactorial_pos (T-D)),ne_of_gt (sqrtFactorial_pos (j+k-r))] + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Fast.lean b/lean/OAI/Analysis/Laughlin/FourBody/Fast.lean new file mode 100644 index 0000000000000000000000000000000000000000..5ae5c029de291090a64f6150ac5bb02fa59d4e24 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Fast.lean @@ -0,0 +1,43 @@ +import Mathlib.Tactic.Ring +import OAI.Analysis.Laughlin.FourBody.Basic + +namespace OAI + +namespace Laughlin.Certificate + +def yEntryFast (D r s t : ℕ) (e f : ℕ × ℕ × ℤ) : ℚ := + let (p,j,a) := e + let (q,l,b) := f + let i := p+j-t + let k := q+l-t + let T := p+j+k + if D ≤ T then + let vr := V r D T p j k + let vs := V s D T q l i + if vr = 0 ∨ vs = 0 then 0 else + ((a*b*vr*vs*(i.factorial : ℤ)*(k.factorial : ℤ)*(t.factorial : ℤ) : ℤ) : ℚ) * + (2 : ℚ) ^ (1-2*(T : ℤ)+(p : ℤ)+(q : ℤ)-(t : ℤ)+((r+s)/2 : ℕ)) / + ((T-D).factorial : ℚ) + else 0 + +theorem yEntry_eq_fast (D r s t : ℕ) (e f : ℕ × ℕ × ℤ) : + yEntry D r s t e f = yEntryFast D r s t e f := by + rcases e with ⟨p,j,a⟩ + rcases f with ⟨q,l,b⟩ + dsimp [yEntry, yEntryFast] + split_ifs with hD hz + · rcases hz with hz | hz <;> simp [hz] + · push_cast + ring + · rfl + +def yRowFast (D r s : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) : ℚ := + (row.2.2.map (fun e => (row.2.2.map (fun f => yEntryFast D r s row.1 e f)).sum)).sum + +theorem yRow_eq_fast (D r s : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) : + yRow D r s row = yRowFast D r s row := by + simp only [yRow, yRowFast, yEntry_eq_fast] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/FastChoose.lean b/lean/OAI/Analysis/Laughlin/FourBody/FastChoose.lean new file mode 100644 index 0000000000000000000000000000000000000000..8805d742e1a145a1d66a59e2b1c1bccd018e5aee --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/FastChoose.lean @@ -0,0 +1,74 @@ +import OAI.Analysis.Laughlin.FourBody.Integral + +namespace OAI + +namespace Laughlin.Certificate + +def UFast (c z T p : ℕ) : ℤ := + if z ≤ T ∧ p ≤ T then + (((List.range (min p z + 1)).filter (fun h => p + z ≤ T + h)).map + (fun h => (-1 : ℤ) ^ (z-h) * (Nat.fast_choose z h : ℤ) * + (Nat.fast_choose (T-z) (p-h) : ℤ) * (c : ℤ) ^ (p-h))).sum + else 0 + +theorem U_eq_fast (c z T p : ℕ) : U c z T p = UFast c z T p := by + simp only [U, UFast, Nat.choose_eq_fast_choose] + +def VFast (r D T p j k : ℕ) : ℤ := + if r ≤ j+k then UFast 1 r (j+k) j * UFast 1 (D-r) (T-r) p else 0 + +theorem V_eq_fast (r D T p j k : ℕ) : V r D T p j k = VFast r D T p j k := by + simp only [V, VFast, U_eq_fast] + +def yEntryIntegralFast (D r s t : ℕ) (e f : ℕ × ℕ × ℤ) : ℤ := + let (p,j,a) := e + let (q,l,b) := f + let i := p+j-t + let k := q+l-t + let T := p+j+k + if D ≤ T then + a*b*VFast r D T p j k*VFast s D T q l i * + (2 : ℤ)^((65-2*(T : ℤ)+(p : ℤ)+(q : ℤ)-(t : ℤ)+((r+s)/2 : ℕ)).toNat) * + (i.factorial : ℤ)*(k.factorial : ℤ)*(t.factorial : ℤ) * + ((24 : ℕ).descFactorial (24-(T-D)) : ℤ) + else 0 + +theorem yEntryIntegral_eq_fast (D r s t : ℕ) (e f : ℕ × ℕ × ℤ) : + yEntryIntegral D r s t e f = yEntryIntegralFast D r s t e f := by + simp only [yEntryIntegral, yEntryIntegralFast, V_eq_fast] + +def yRowIntegralFast (D r s : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) : ℤ := + (row.2.2.map (fun e => (row.2.2.map (fun f => yEntryIntegralFast D r s row.1 e f)).sum)).sum + +theorem yRowIntegral_eq_fast (D r s : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) : + yRowIntegral D r s row = yRowIntegralFast D r s row := by + simp only [yRowIntegral, yRowIntegralFast, yEntryIntegral_eq_fast] + +theorem source_yRow_eq_fastIntegral (D r s n : ℕ) (hn : n < 7) : + yRow D r s (rows[n]!) = (yRowIntegralFast D r s (rows[n]!) : ℚ) / arithmeticScale := by + rw [source_yRow_eq_integral D r s n hn, yRowIntegral_eq_fast] + +def LFast (D r : ℕ) (A : ℕ × ℕ × ℕ × ℕ) : ℚ := + let (a,b,c,d) := A + let term := fun (x y j k : ℕ) => ((x : ℤ)-(y : ℤ)) * + ((x+y-1).factorial : ℤ) * (j.factorial : ℤ) * (k.factorial : ℤ) * + VFast r D D (x+y-1) j k + (2 : ℚ)^(((1 : ℤ)-2*(D : ℤ)+(r : ℤ))/2) * + ((term a b c d - term a c b d + term a d b c + term b c a d - + term b d a c + term c d a b : ℤ) : ℚ) + +def ZFast (D r s : ℕ) : ℚ := + ((quadruples D).map (fun A => + let (a,b,c,d) := A + LFast D r A * LFast D s A / + ((a.factorial : ℚ)*(b.factorial : ℚ)*(c.factorial : ℚ)*(d.factorial : ℚ)))).sum + +theorem L_eq_fast (D r : ℕ) (A : ℕ × ℕ × ℕ × ℕ) : L D r A = LFast D r A := by + simp only [L, LFast, V_eq_fast] + +theorem Z_eq_fast (D r s : ℕ) : Z D r s = ZFast D r s := by + simp only [Z, ZFast, L_eq_fast] + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/FockCovariance.lean b/lean/OAI/Analysis/Laughlin/FourBody/FockCovariance.lean new file mode 100644 index 0000000000000000000000000000000000000000..db8e84f5c61e9d9eebb6d0a47d6b11156d08706b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/FockCovariance.lean @@ -0,0 +1,82 @@ +import OAI.Analysis.Laughlin.Exterior.FourConjugation +import OAI.Analysis.Laughlin.FourBody.GroupIntertwining +import OAI.Analysis.Laughlin.Pair.FockHaar + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin +open scoped BigOperators Matrix Kronecker + +theorem antisymmetric_exterior_sum (Q : ℕ) (f : SpinIndex Q Q → Space Q) + (hf : ∀ i j, f (j,i) = -f (i,j)) (a : SpinIndex Q Q → ℂ) : + (∑ i, a i • f i) = ∑ i : WedgePairIndex Q, (a i.val-a i.val.swap) • f i.val := by + apply (occupationBasis Q).repr.injective + ext A + have h := antisymmetric_ordered_sum Q + (fun i => (occupationBasis Q).repr (f i) A) a (by + intro i j; rw [hf,map_neg]; rfl) + simpa only [map_sum,map_smul,Finset.sum_apply',Finsupp.smul_apply,smul_eq_mul,mul_comm] using h + +noncomputable def wedgePairVector (Q : ℕ) (i : WedgePairIndex Q) : Space Q := + create i.val.1 (create i.val.2 1) + +theorem wedgePairVector_rotation (Q : ℕ) (g : SourceSU2) (i : WedgePairIndex Q) : + exteriorRotation Q g (wedgePairVector Q i) = + ∑ j, wedgePairRepresentation Q g j i • wedgePairVector Q j := by + have ha (i j : Fin (Q+1)) : create j (create i (1 : Space Q)) = -create i (create j 1) := by + have h := LinearMap.congr_fun (create_anticommute j i) (1 : Space Q) + exact eq_neg_of_add_eq_zero_left h + rw [wedgePairVector,exteriorRotation_pair_basis] + have h := antisymmetric_exterior_sum Q + (fun k : SpinIndex Q Q => create k.1 (create k.2 (1 : Space Q))) ha + (fun j : SpinIndex Q Q => sourceSpinRepresentation Q g j.1 i.val.1 * + sourceSpinRepresentation Q g j.2 i.val.2) + rw [h] + apply Finset.sum_congr rfl + intro j hj + change (_ - _) • wedgePairVector Q j = _ • wedgePairVector Q j + congr 1 + dsimp [wedgePairRepresentation,wedgePairMatrix] + ring + +noncomputable def sourceFourVector (Q : ℕ) (i : FourWedgeIndex Q) : Space Q := + sourcePairVector Q i.1.val * wedgePairVector Q i.2 + +noncomputable def sourceFourFamilyEnd (Q : ℕ) (i : FourWedgeIndex Q) : Module.End ℂ (Space Q) := + sourceFourEnd Q i.1.val i.2.val.1 i.2.val.2 + +theorem sourceFourVector_adjoint (Q : ℕ) (i : FourWedgeIndex Q) (x y : Space Q) : + occupationInner Q (sourceFourVector Q i*x) y = + occupationInner Q x (sourceFourFamilyEnd Q i y) := by + have he : sourceFourVector Q i*x = sourcePairVector Q i.1.val * + create i.2.val.1 (create i.2.val.2 x) := by + change (sourcePairVector Q i.1.val * + (ExteriorAlgebra.ι ℂ (mode i.2.val.1)*(ExteriorAlgebra.ι ℂ (mode i.2.val.2)*1)))*x = + sourcePairVector Q i.1.val * + (ExteriorAlgebra.ι ℂ (mode i.2.val.1)*(ExteriorAlgebra.ι ℂ (mode i.2.val.2)*x)) + simp only [mul_one,mul_assoc] + rw [he,sourcePairVector_adjoint,create_annihilate_adjoint,create_annihilate_adjoint] + rfl + +theorem sourceFourVector_rotation (Q : ℕ) (hQ : 0 < Q) (g : SourceSU2) (i : FourWedgeIndex Q) : + exteriorRotation Q g (sourceFourVector Q i) = + ∑ j, fourBodySpinRepresentation Q g j i • sourceFourVector Q j := by + rw [sourceFourVector,map_mul,sourcePairVector_rotation Q hQ,wedgePairVector_rotation] + simp only [Finset.sum_mul,Finset.mul_sum,smul_mul_smul,Fintype.sum_prod_type, + fourBodySpinRepresentation,MonoidHom.coe_mk,OneHom.coe_mk,Matrix.kroneckerMap, + Matrix.of_apply,sourceFourVector] + rw [Finset.sum_comm] + +theorem sourceFourFamilyEnd_rotation (Q : ℕ) (hQ : 0 < Q) (g : SourceSU2) + (i : FourWedgeIndex Q) (x : Space Q) : + sourceFourFamilyEnd Q i (exteriorRotation Q g x) = + ∑ j, fourBodySpinRepresentation Q g i j • + exteriorRotation Q g (sourceFourFamilyEnd Q j x) := + exteriorFamily_contraction_rotation Q (fourBodySpinRepresentation Q) + (fourBodySpinRepresentation_inv Q) (sourceFourVector Q) (sourceFourFamilyEnd Q) + (sourceFourVector_adjoint Q) (sourceFourVector_rotation Q hQ) g i x + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Formula.lean b/lean/OAI/Analysis/Laughlin/FourBody/Formula.lean new file mode 100644 index 0000000000000000000000000000000000000000..42b6b4995171b8297d67d83559a9bddb5d86c188 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Formula.lean @@ -0,0 +1,45 @@ +import OAI.Analysis.Laughlin.FourBody.Ungroup + +namespace OAI + +namespace Laughlin.Fock +open Spin +open scoped BigOperators + +noncomputable def boundedCreate (Q n : ℕ) : Module.End ℂ (Space Q) := + if h : n ≤ Q then create ⟨n,by omega⟩ else 0 + +theorem boundedCreate_rowOutput (Q t : ℕ) (hQ : 15 ≤ Q) (T : RowLevel t) : + boundedCreate Q (T.val.val-t) = create (rowOutputMode Q t hQ T) := by + have ht : T.val.val-t ≤ Q := by have h := T.val.isLt; omega + rw [boundedCreate,dite_eq_left ht] + rfl + +theorem sourceRowSquareVector_eq_F (Q : ℕ) (hQ : 15 ≤ Q) + (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) (hr : row ∈ Certificate.rows) (x : Space Q) : + sourceRowSquareVector Q hQ row x = ((row.2.1 : ℂ)/10^7) • sourcePairEnd Q row.1 x + + (row.2.2.map (fun e => (sourceAlpha row.1 e : ℂ) • + boundedCreate Q (e.1+e.2.1-row.1) + (boundedAnnihilate Q e.2.1 (sourcePairEnd Q e.1 x)))).sum := by + rw [sourceRowSquareVector] + congr 1 + simp only [sourceRowLevel_entries,linearMap_list_sum] + have ht (T : RowLevel row.1) (e : ℕ × ℕ × ℤ) : + create (rowOutputMode Q row.1 hQ T) + (if e.1+e.2.1=T.val.val then (sourceAlpha row.1 e : ℂ) • sourceEntryThree Q e x else 0) = + if e.1+e.2.1=T.val.val then (sourceAlpha row.1 e : ℂ) • + boundedCreate Q (T.val.val-row.1) (sourceEntryThree Q e x) else 0 := by + rw [boundedCreate_rowOutput Q row.1 hQ T] + by_cases he : e.1+e.2.1=T.val.val <;> simp only [he,ite_true,ite_false,map_smul,map_zero] + simp_rw [ht,finset_list_sum_swap] + congr 1 + apply List.map_congr_left + intro e he + obtain ⟨het,he15,he8⟩ := (source_threeBody_rows_support row hr).2 e he + rw [rowLevel_sum_select row.1 (e.1+e.2.1) het (by omega)] + rw [sourceEntryThree_eq Q e (by omega) (by omega),boundedAnnihilate, + dite_eq_left (show e.2.1 ≤ Q by omega)] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/GlobalFock.lean b/lean/OAI/Analysis/Laughlin/FourBody/GlobalFock.lean new file mode 100644 index 0000000000000000000000000000000000000000..108f3be8f96bbc63b4760fdbe7505321682133d7 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/GlobalFock.lean @@ -0,0 +1,43 @@ +import OAI.Analysis.Laughlin.FourBody.GlobalHaar + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory +open scoped BigOperators Matrix + +theorem physical_fourBody_global_Fock_haar (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + (∫ g, contractionForm Q (sourceFourFamilyEnd Q) ((physicalFourBodyMatrix Q).map Complex.ofReal) + (exteriorRotation Q g⁻¹ x) ∂sourceHaar) = + ∑ d : Fin 23, (1 / ((4*Q-1-2*(d.val+1) : ℕ) : ℂ)) * + contractionForm Q (sourceFourFamilyEnd Q) + (fourCopyOperator Q (d.val+1) (by omega) + (fun r s => physicalFourError Q (d.val+1) (oddPairDeficit r) (oddPairDeficit s))) x := by + rw [contractionForm_haar Q (fourBodySpinRepresentation Q) + (fourBodySpinRepresentation_inv Q) (fourBodySpinRepresentation_continuous Q) + _ (sourceFourFamilyEnd_rotation Q (by omega)),physicalFourBodyHaar_retained_sum Q hQ, + contractionForm_sum] + simp only [contractionForm_smul] + +noncomputable def sourceA4Form (Q : ℕ) (x : Space Q) : ℝ := + ((2*Q-2+1 : ℕ) : ℝ) * (∫ g, contractionForm Q (sourceFourFamilyEnd Q) + ((physicalFourBodyMatrix Q).map Complex.ofReal) (exteriorRotation Q g⁻¹ x) ∂sourceHaar).re + +theorem sourceA4Form_retained (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + sourceA4Form Q x = ∑ d : Fin 23, + (((2*Q-2+1 : ℕ) : ℝ)/((4*Q-1-2*(d.val+1) : ℕ) : ℝ)) * + (contractionForm Q (sourceFourFamilyEnd Q) + (fourCopyOperator Q (d.val+1) (by omega) + (fun r s => physicalFourError Q (d.val+1) (oddPairDeficit r) (oddPairDeficit s))) x).re := by + rw [sourceA4Form,physical_fourBody_global_Fock_haar Q hQ x,Complex.re_sum,Finset.mul_sum] + apply Finset.sum_congr rfl + intro d hd + have he : (1 / ((4*Q-1-2*(d.val+1) : ℕ) : ℂ)) = + ((1 / ((4*Q-1-2*(d.val+1) : ℕ) : ℝ) : ℝ) : ℂ) := by push_cast; rfl + rw [he] + simp only [Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im,zero_mul,sub_zero] + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/GlobalHaar.lean b/lean/OAI/Analysis/Laughlin/FourBody/GlobalHaar.lean new file mode 100644 index 0000000000000000000000000000000000000000..93ba5570e9b5c53a2e82788206a084a1e8a475da --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/GlobalHaar.lean @@ -0,0 +1,72 @@ +import OAI.Analysis.Laughlin.FourBody.CopyOperatorHaar +import OAI.Analysis.Laughlin.FourBody.Hermitian +import OAI.Analysis.Laughlin.FourBody.RetainedReconstruction + +namespace OAI + +namespace Laughlin.Spin +open Rotation Fock +open scoped BigOperators Matrix + +theorem physicalFourBodyHaar_retained_sum (Q : ℕ) (hQ : 25 ≤ Q) : + matrixIntegral sourceHaar + (conjugateOrbit (fourBodySpinRepresentation Q) ((physicalFourBodyMatrix Q).map Complex.ofReal)) = + ∑ d : Fin 23, (1 / ((4*Q-1-2*(d.val+1) : ℕ) : ℂ)) • + fourCopyOperator Q (d.val+1) (by omega) + (fun r s => physicalFourError Q (d.val+1) (oddPairDeficit r) (oddPairDeficit s)) := by + classical + let A : Matrix (FourWedgeIndex Q) (FourWedgeIndex Q) ℂ := matrixIntegral sourceHaar + (conjugateOrbit (fourBodySpinRepresentation Q) ((physicalFourBodyMatrix Q).map Complex.ofReal)) + let U (d : Fin 23) (r : OddPairLabel (d.val+1)) : + Matrix (FourWedgeIndex Q) (Fin (fourSpinWeight Q (d.val+1)+1)) ℂ := + retainedFourInclusion Q (d.val+1) (by omega) r + have hr : A = ∑ d : Fin 23, ∑ r : OddPairLabel (d.val+1), A*U d r*(U d r)ᴴ := + fourBody_retained_reconstruction Q hQ A (physicalFourBodyHaar_high_column Q) + have hl : A = ∑ d : Fin 23, ∑ r : OddPairLabel (d.val+1), U d r*(U d r)ᴴ*A := by + have ha : Aᴴ=A := physicalFourBodyHaar_hermitian Q + have h := congrArg Matrix.conjTranspose hr + simpa only [Matrix.conjTranspose_sum,Matrix.conjTranspose_mul, + Matrix.conjTranspose_conjTranspose,ha,← Matrix.mul_assoc] using h + have he (d : Fin 23) (r : OddPairLabel (d.val+1)) : + U d r*(U d r)ᴴ*A = ∑ s : OddPairLabel (d.val+1), + ((physicalFourError Q (d.val+1) (oddPairDeficit r) (oddPairDeficit s) : ℂ) / + ((4*Q-1-2*(d.val+1) : ℕ) : ℂ)) • (U d r*(U d s)ᴴ) := by + calc + _ = ∑ e : Fin 23, ∑ s : OddPairLabel (e.val+1), + U d r*((U d r)ᴴ*A*U e s)*(U e s)ᴴ := by + conv_lhs => rw [hr] + simp only [Matrix.mul_sum,Matrix.mul_assoc] + _ = ∑ s : OddPairLabel (d.val+1), + U d r*((U d r)ᴴ*A*U d s)*(U d s)ᴴ := by + apply Finset.sum_eq_single d + · intro e he hed + apply Finset.sum_eq_zero + intro s hs + have hz : (U d r)ᴴ*A*U e s=0 := + fourBody_haar_unequal_spin Q (d.val+1) (e.val+1) (by omega) (by omega) + (by intro hv; exact hed (Fin.ext (by omega))) r s _ + rw [hz,Matrix.mul_zero,Matrix.zero_mul] + · simp + _ = _ := by + apply Finset.sum_congr rfl + intro s hs + have hb : (U d r)ᴴ*A*U d s = + ((physicalFourError Q (d.val+1) (oddPairDeficit r) (oddPairDeficit s) : ℂ) / + ((4*Q-1-2*(d.val+1) : ℕ) : ℂ)) • 1 := + physical_fourBody_haar_multiplicity Q (d.val+1) hQ (by omega) r s + rw [hb,Matrix.mul_smul,Matrix.mul_one,Matrix.smul_mul] + change A = _ + rw [hl] + apply Finset.sum_congr rfl + intro d hd + simp only [he,fourCopyOperator,Finset.smul_sum,smul_smul] + apply Finset.sum_congr rfl + intro r hr + apply Finset.sum_congr rfl + intro s hs + congr 1 + simp only [div_eq_mul_inv,one_mul,mul_comm] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/GramCompute.lean b/lean/OAI/Analysis/Laughlin/FourBody/GramCompute.lean new file mode 100644 index 0000000000000000000000000000000000000000..b9f7e37803794f1f9a4f226677ce7c691bd20132 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/GramCompute.lean @@ -0,0 +1,31 @@ +import Mathlib.Algebra.Field.Rat +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate.GramCompute + +def quadruples (D : ℕ) : List (ℕ × ℕ × ℕ × ℕ) := + (List.range (D+2)).flatMap (fun a => + (List.range (D+2)).flatMap (fun b => + (List.range (D+2)).filterMap (fun c => + let d := D+1-a-b-c + if a < b ∧ b < c ∧ c < d ∧ a+b+c ≤ D+1 then some (a,b,c,d) else none))) + +def LFast (D r : ℕ) (A : ℕ × ℕ × ℕ × ℕ) : ℚ := + let (a,b,c,d) := A + let term := fun (x y j k : ℕ) => ((x : ℤ)-(y : ℤ)) * + ((x+y-1).factorial : ℤ) * (j.factorial : ℤ) * (k.factorial : ℤ) * + RowCompute.VFast r D D (x+y-1) j k + (2 : ℚ)^(((1 : ℤ)-2*(D : ℤ)+(r : ℤ))/2) * + ((term a b c d - term a c b d + term a d b c + term b c a d - + term b d a c + term c d a b : ℤ) : ℚ) + +def ZFast (D r s : ℕ) : ℚ := + ((quadruples D).map (fun A => + let (a,b,c,d) := A + LFast D r A * LFast D s A / + ((a.factorial : ℚ)*(b.factorial : ℚ)*(c.factorial : ℚ)*(d.factorial : ℚ)))).sum +end Laughlin.Certificate.GramCompute + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/GroupIntertwining.lean b/lean/OAI/Analysis/Laughlin/FourBody/GroupIntertwining.lean new file mode 100644 index 0000000000000000000000000000000000000000..571a60ac12af4dda7e32d473d0a4a01e38e43767 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/GroupIntertwining.lean @@ -0,0 +1,78 @@ +import OAI.Analysis.Laughlin.FourBody.CoupledBasis +import OAI.Analysis.Laughlin.FourBody.TensorIntertwining +import OAI.Analysis.Laughlin.Operators.WedgePairRepresentation + +namespace OAI + +namespace Laughlin.Spin +open Rotation +open scoped BigOperators Matrix Kronecker + +abbrev FourWedgeIndex (Q : ℕ) := Fin (2*Q-2+1) × WedgePairIndex Q + +noncomputable def fourBodySpinRepresentation (Q : ℕ) : + SourceSU2 →* Matrix (FourWedgeIndex Q) (FourWedgeIndex Q) ℂ where + toFun g := sourceSpinRepresentation (2*Q-2) g ⊗ₖ wedgePairRepresentation Q g + map_one' := by simp only [map_one,Matrix.one_kronecker_one] + map_mul' g h := by simp only [map_mul,Matrix.mul_kronecker_mul] + +theorem fourBodySpinRepresentation_continuous (Q : ℕ) (i j : FourWedgeIndex Q) : + Continuous (fun g => fourBodySpinRepresentation Q g i j) := + (sourceSpinRepresentation_continuous (2*Q-2) i.1 j.1).mul + (wedgePairRepresentation_continuous Q i.2 j.2) + +theorem fourBodySpinRepresentation_inv (Q : ℕ) (g : SourceSU2) : + fourBodySpinRepresentation Q g⁻¹ = (fourBodySpinRepresentation Q g)ᴴ := by + change _ ⊗ₖ _ = (_ ⊗ₖ _)ᴴ + rw [Matrix.conjTranspose_kronecker,sourceSpinRepresentation_inv,wedgePairRepresentation_inv] + +theorem fourWedgeInclusion_factor (Q r D : ℕ) (hr : r ≤ Q) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) : + fourWedgeInclusion Q r D hr hA hB = + ((1 : Matrix (Fin (2*Q-2+1)) (Fin (2*Q-2+1)) ℂ) ⊗ₖ + (pairCoupledInclusion Q r hr).map Complex.ofReal) * + physicalCoupledInclusion (2*Q-2) (genericCoupledWeight Q Q r) (D-r) hA hB := by + ext i n + rw [fourWedgeInclusion,fourBodyCopy_coordinate] + simp only [Complex.ofReal_sum,Complex.ofReal_mul,Complex.ofReal_pow,Complex.ofReal_neg, + Complex.ofReal_one,Matrix.mul_apply,Fintype.sum_prod_type,Matrix.kroneckerMap, + Matrix.of_apply,Matrix.one_apply,ite_mul,one_mul,zero_mul,physicalCoupledInclusion, + Matrix.smul_apply,smul_eq_mul,Matrix.map_apply,genericCoupledInclusion,pairCoupledInclusion] + rw [Finset.sum_comm] + simp only [Finset.sum_ite_eq,Finset.mem_univ,ite_true] + +theorem fourWedgeInclusion_SU2 (Q r D : ℕ) (hr : r ≤ Q) (hor : Odd r) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) (g : SourceSU2) : + fourBodySpinRepresentation Q g * fourWedgeInclusion Q r D hr hA hB = + fourWedgeInclusion Q r D hr hA hB * sourceSpinRepresentation + (genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q r) (D-r)) g := by + rw [fourWedgeInclusion_factor] + change (_ ⊗ₖ wedgePairMatrix Q g) * ((_ ⊗ₖ _) * _) = _ + rw [← Matrix.mul_assoc,← Matrix.mul_kronecker_mul,Matrix.mul_one, + pairCoupledInclusion_SU2 Q r hr hor] + have he : sourceSpinRepresentation (2*Q-2) g ⊗ₖ + ((pairCoupledInclusion Q r hr).map Complex.ofReal * + sourceSpinRepresentation (genericCoupledWeight Q Q r) g) = + ((1 : Matrix (Fin (2*Q-2+1)) (Fin (2*Q-2+1)) ℂ) ⊗ₖ + (pairCoupledInclusion Q r hr).map Complex.ofReal) * + (sourceSpinRepresentation (2*Q-2) g ⊗ₖ + sourceSpinRepresentation (genericCoupledWeight Q Q r) g) := by + rw [← Matrix.mul_kronecker_mul,Matrix.one_mul] + rw [he,Matrix.mul_assoc,physicalCoupledInclusion_SU2,Matrix.mul_assoc] + +theorem fourWedgeInclusion_isometry (Q r D : ℕ) (hr : r ≤ Q) (hor : Odd r) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) : + (fourWedgeInclusion Q r D hr hA hB)ᴴ * fourWedgeInclusion Q r D hr hA hB = 1 := by + have he : fourWedgeInclusion Q r D hr hA hB = + (fourBodyInclusion Q r D hr hA hB).map Complex.ofReal := rfl + rw [he,real_matrix_adjoint] + exact real_matrix_inverse_complex _ _ (fourBodyInclusion_isometry Q r D hr hor hA hB) + +theorem fourCoupledBasis_complex_complete (Q : ℕ) : + (fourCoupledBasis Q).map Complex.ofReal * ((fourCoupledBasis Q).map Complex.ofReal)ᴴ = 1 := by + rw [real_matrix_adjoint] + exact real_matrix_inverse_complex _ _ (fourCoupledBasis_complete Q) + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/HaarAllowance.lean b/lean/OAI/Analysis/Laughlin/FourBody/HaarAllowance.lean new file mode 100644 index 0000000000000000000000000000000000000000..17adf201a02e5891499a46b2f42b9c174c41f8b2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/HaarAllowance.lean @@ -0,0 +1,42 @@ +import OAI.Analysis.Laughlin.Fock.OrbitIntegration +import OAI.Analysis.Laughlin.FourBody.PhysicalAllowance +import OAI.Analysis.Laughlin.Operators.LocalFourCardinality + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory +open scoped BigOperators + +theorem physical_fourBody_haar_allowance (Q r D : ℕ) (hr : r ≤ D) (hor : Odd r) + (hQ : D+2 ≤ Q) (x : Space Q) : + (2*Q-2+1 : ℕ) * (∫ g, occupationNormSq Q + (physicalFourCopyEnd Q r D (by omega) (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) ≤ + (Fintype.card (LocalFourIndex D) : ℝ) * sourceFockEnergy Q x := by + have hi := integral_mono + (linearMap_rotation_norm_integrable Q (physicalFourCopyEnd Q r D (by omega)) x) + (integrable_finsetSum _ (fun (b : LocalFourIndex D) hb => linearMap_rotation_norm_integrable Q + (sourcePairEnd Q b.val.1.val) x)) + (fun g => source_fourBody_normalized_allowance Q r D hr hor hQ (exteriorRotation Q g⁻¹ x)) + apply (mul_le_mul_of_nonneg_left hi (by positivity : (0 : ℝ) ≤ (2*Q-2+1 : ℕ))).trans_eq + rw [integral_finsetSum _ (fun (b : LocalFourIndex D) hb => linearMap_rotation_norm_integrable Q _ x)] + have hp (b : LocalFourIndex D) : + (∫ g, occupationNormSq Q (sourcePairEnd Q b.val.1.val (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) = + sourceFockEnergy Q x/(2*Q-2+1 : ℕ) := + physical_pair_norm_haar_real Q (by omega) ⟨b.val.1.val,by have := b.val.1.isLt; omega⟩ x + simp_rw [hp] + simp only [Finset.sum_const,Finset.card_univ,nsmul_eq_mul] + have hd : ((2*Q-2+1 : ℕ) : ℝ) ≠ 0 := by positivity + field_simp + +theorem physical_fourBody_haar_allowance_retained (Q r D : ℕ) (hr : r ≤ D) (hor : Odd r) + (hQ : 25 ≤ Q) (hD : D ≤ 23) (x : Space Q) : + (2*Q-2+1 : ℕ) * (∫ g, occupationNormSq Q + (physicalFourCopyEnd Q r D (by omega) (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) ≤ + ((D+1)^2/4 : ℕ) * sourceFockEnergy Q x := by + simpa only [localFourIndex_card_retained D hD] using + physical_fourBody_haar_allowance Q r D hr hor (by omega) x + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/HaarTransfer.lean b/lean/OAI/Analysis/Laughlin/FourBody/HaarTransfer.lean new file mode 100644 index 0000000000000000000000000000000000000000..6b0a833580a4fda04472dc15d38e82e447834d14 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/HaarTransfer.lean @@ -0,0 +1,65 @@ +import OAI.Analysis.Laughlin.Fock.OrbitIntegration +import OAI.Analysis.Laughlin.FourBody.UniformTransfer + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory +open scoped BigOperators Topology + +theorem occupationQuadratic_rotation_integrable {I : Type*} [Fintype I] + (Q : ℕ) (R : I → I → ℝ) (L : I → Module.End ℂ (Space Q)) (x : Space Q) : + Integrable (fun g : SourceSU2 => occupationQuadratic Q R + (fun i => L i (exteriorRotation Q g⁻¹ x))) sourceHaar := by + apply Continuous.integrable_of_hasCompactSupport _ (isClosed_tsupport _).isCompact + unfold occupationQuadratic occupationInner + apply Complex.continuous_re.comp + apply continuous_finsetSum + intro i hi + apply continuous_finsetSum + intro j hj + apply continuous_const.mul + apply continuous_finsetSum + intro A hA + exact (linearMap_rotation_coordinate_continuous Q (L i) x A).star.mul + (linearMap_rotation_coordinate_continuous Q (L j) x A) + +theorem physical_fourBody_haar_transfer (Q D : ℕ) (hQ : 25 ≤ Q) + (hD₁ : 1 ≤ D) (hD₂ : D ≤ 23) (x : Space Q) : + -(24 * fourBodyRho D Q * sourceFockEnergy Q x) ≤ + (2*Q-2+1 : ℕ) * (∫ g, occupationQuadratic Q (finiteFourMiddle Q D) + (fun i : Fin ((D+1)/2) => physicalFourCopyEnd Q (Certificate.copyLabel i) D + (by omega) (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) := by + have hw : Integrable (fun g : SourceSU2 => sourcePairWindow Q (exteriorRotation Q g⁻¹ x)) sourceHaar := + integrable_finsetSum _ (fun (p : ℕ) hp => + linearMap_rotation_norm_integrable Q (sourcePairEnd Q p) x) + let L : Fin ((D+1)/2) → Module.End ℂ (Space Q) := fun i => + physicalFourCopyEnd Q (Certificate.copyLabel i) D (by omega) + have hi := integral_mono ((hw.const_mul (fourBodyRho D Q)).neg) + (occupationQuadratic_rotation_integrable Q (finiteFourMiddle Q D) L x) + (fun g => source_fourBody_uniform_transfer Q D (by omega) hD₁ hD₂ (exteriorRotation Q g⁻¹ x)) + have hi := mul_le_mul_of_nonneg_left hi (by positivity : (0 : ℝ) ≤ (2*Q-2+1 : ℕ)) + simp only [Pi.neg_apply] at hi + rw [integral_neg,integral_const_mul] at hi + have he : ((2*Q-2+1 : ℕ) : ℝ) * + -(fourBodyRho D Q * (∫ g, sourcePairWindow Q (exteriorRotation Q g⁻¹ x) ∂sourceHaar)) = + -(24 * fourBodyRho D Q * sourceFockEnergy Q x) := by + calc + _ = -(fourBodyRho D Q * ((2*Q-2+1 : ℕ) * + (∫ g, sourcePairWindow Q (exteriorRotation Q g⁻¹ x) ∂sourceHaar))) := by ring + _ = _ := by rw [sourcePairWindow_haar Q hQ]; ring + rwa [he] at hi + +noncomputable def averagedFourTransferError (Q : ℕ) : ℝ := 24 * uniformFourBodyRho Q + +theorem averagedFourTransferError_nonneg (Q : ℕ) : 0 ≤ averagedFourTransferError Q := + mul_nonneg (by norm_num) (uniformFourBodyRho_nonneg Q) + +theorem averagedFourTransferError_tendsto : + Filter.Tendsto averagedFourTransferError Filter.atTop (𝓝 0) := by + change Filter.Tendsto (fun Q => 24 * uniformFourBodyRho Q) Filter.atTop (𝓝 0) + simpa only [mul_zero] using uniformFourBodyRho_tendsto.const_mul 24 + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Hermitian.lean b/lean/OAI/Analysis/Laughlin/FourBody/Hermitian.lean new file mode 100644 index 0000000000000000000000000000000000000000..64463d6dc2abe723a715eaa330cb05d9514bcc2b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Hermitian.lean @@ -0,0 +1,60 @@ +import Mathlib.MeasureTheory.Integral.Bochner.ContinuousLinearMap +import OAI.Analysis.Laughlin.FourBody.Support + +namespace OAI + +namespace Laughlin.Spin +open Rotation MeasureTheory +open scoped BigOperators Matrix + +theorem list_double_sum_swap {I A : Type*} [AddCommMonoid A] + (l k : List I) (f : I → I → A) : + (l.map (fun i => (k.map (f i)).sum)).sum = + (k.map (fun j => (l.map (fun i => f i j)).sum)).sum := by + induction l with + | nil => simp + | cons i l ih => simp only [List.map_cons,List.sum_cons,ih,List.sum_map_add] + +theorem fourBodyTermMatrix_transpose (Q t : ℕ) (e f : ℕ × ℕ × ℤ) : + (fourBodyTermMatrix Q t e f)ᵀ = fourBodyTermMatrix Q t f e := by + ext i j + simp only [fourBodyTermMatrix,Matrix.transpose_apply,Matrix.smul_apply,smul_eq_mul,realOuter] + ring + +theorem physicalFourBodyMatrix_transpose (Q : ℕ) : + (physicalFourBodyMatrix Q)ᵀ = physicalFourBodyMatrix Q := by + unfold physicalFourBodyMatrix + simp only [Matrix.transpose_list_sum,List.map_map,Function.comp_def,fourBodyTermMatrix_transpose] + congr 1 + apply List.map_congr_left + intro row hrow + exact list_double_sum_swap row.2.2 row.2.2 (fun e f => fourBodyTermMatrix Q row.1 f e) + +theorem physicalFourBodyMatrix_hermitian (Q : ℕ) : + ((physicalFourBodyMatrix Q).map Complex.ofReal)ᴴ = (physicalFourBodyMatrix Q).map Complex.ofReal := by + rw [real_matrix_adjoint,physicalFourBodyMatrix_transpose] + +theorem physicalFourBodyHaar_hermitian (Q : ℕ) : + (matrixIntegral sourceHaar + (conjugateOrbit (fourBodySpinRepresentation Q) ((physicalFourBodyMatrix Q).map Complex.ofReal)))ᴴ = + matrixIntegral sourceHaar + (conjugateOrbit (fourBodySpinRepresentation Q) ((physicalFourBodyMatrix Q).map Complex.ofReal)) := by + have he (g : SourceSU2) : + (conjugateOrbit (fourBodySpinRepresentation Q) ((physicalFourBodyMatrix Q).map Complex.ofReal) g)ᴴ = + conjugateOrbit (fourBodySpinRepresentation Q) ((physicalFourBodyMatrix Q).map Complex.ofReal) g := by + simp only [conjugateOrbit,Matrix.conjTranspose_mul,fourBodySpinRepresentation_inv, + Matrix.conjTranspose_conjTranspose,physicalFourBodyMatrix_hermitian,Matrix.mul_assoc] + ext i j + change star (∫ g, conjugateOrbit (fourBodySpinRepresentation Q) + ((physicalFourBodyMatrix Q).map Complex.ofReal) g j i ∂sourceHaar) = _ + calc + _ = ∫ g, star (conjugateOrbit (fourBodySpinRepresentation Q) + ((physicalFourBodyMatrix Q).map Complex.ofReal) g j i) ∂sourceHaar := integral_conj.symm + _ = _ := by + apply integral_congr_ae + filter_upwards [] with g + exact congrFun (congrFun (he g) i) j + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/HighestFock.lean b/lean/OAI/Analysis/Laughlin/FourBody/HighestFock.lean new file mode 100644 index 0000000000000000000000000000000000000000..a5eeaaf7b28e97b4ab18914a9c81f39399c5beb3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/HighestFock.lean @@ -0,0 +1,83 @@ +import OAI.Analysis.Laughlin.Fock.RankOneHaar +import OAI.Analysis.Laughlin.FourBody.FockCovariance +import OAI.Analysis.Laughlin.FourBody.MultiplicityHaar +import OAI.Analysis.Laughlin.FourBody.WeightSlice + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory +open scoped BigOperators Matrix + +theorem physicalFourCopyEnd_column (Q D : ℕ) (hQ : D+2 ≤ Q) (r : OddPairLabel D) (x : Space Q) : + (∑ i, star (retainedFourInclusion Q D hQ r i 0) • sourceFourFamilyEnd Q i x) = + physicalFourCopyEnd Q (oddPairDeficit r) D (by omega) x := by + have hc (i : FourWedgeIndex Q) : + star (retainedFourInclusion Q D hQ r i 0) • sourceFourFamilyEnd Q i x = + if i.1.val+i.2.val.1.val+i.2.val.2.val=D then + (fourBodyCoefficient Q (oddPairDeficit r) D D i.1.val i.2.val.1.val i.2.val.2.val : ℂ) • + sourceFourEnd Q i.1.val i.2.val.1 i.2.val.2 x else 0 := by + rw [retainedFourInclusion_column] + simp only [Fin.val_zero,Complex.star_def,Complex.conj_ofReal] + by_cases h : i.1.val+i.2.val.1.val+i.2.val.2.val=D + · have he := fourBodyCopy_source_coefficient Q (oddPairDeficit r) D D + (oddPairDeficit_le r) (le_refl D) hQ i.1 i.2 h + simp only [Nat.sub_self] at he + rw [ite_eq_left h,he] + rfl + · rw [ite_eq_right h,fourBodyCopy_off Q (oddPairDeficit r) D 0 _ (oddPairDeficit_le r) + _ _ i.1 i.2 (by simpa using h)] + simp + simp_rw [hc] + rw [Fintype.sum_prod_type] + dsimp only + rw [fourWeightSlice_sum Q D hQ (fun p j k => + (fourBodyCoefficient Q (oddPairDeficit r) D D p j.val k.val : ℂ) • sourceFourEnd Q p j k x)] + simp only [physicalFourCopyEnd,LinearMap.sum_apply,LinearMap.smul_apply] + +theorem contractionForm_outer_cross {I : Type*} [Fintype I] (Q : ℕ) + (minus : I → Module.End ℂ (Space Q)) (v w : I → ℂ) (x : Space Q) : + contractionForm Q minus (complexOuter v w) x = + occupationInner Q (∑ i, star (v i) • minus i x) (∑ j, star (w j) • minus j x) := by + simp only [occupationInner_sum_left,occupationInner_sum_right,occupationInner_smul_left, + occupationInner_smul_right,star_star,contractionForm,complexOuter,Finset.mul_sum,mul_assoc] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + ring + +theorem matrix_cross_sandwich_single {I J : Type*} [Fintype I] [Fintype J] [DecidableEq J] + (V W : Matrix I J ℂ) (p : J) : + V*diagonalUnit p*Wᴴ = complexOuter (fun i => V i p) (fun i => W i p) := by + ext i j + simp [diagonalUnit,Matrix.mul_apply,complexOuter,Matrix.conjTranspose_apply,ite_and] + +theorem physicalFourCopyEnd_cross_haar (Q D : ℕ) (hQ : D+2 ≤ Q) (r s : OddPairLabel D) + (x : Space Q) : + ((4*Q-1-2*D : ℕ) : ℂ) * (∫ g, occupationInner Q + (physicalFourCopyEnd Q (oddPairDeficit r) D (by omega) (exteriorRotation Q g⁻¹ x)) + (physicalFourCopyEnd Q (oddPairDeficit s) D (by omega) (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) = + contractionForm Q (sourceFourFamilyEnd Q) + (retainedFourInclusion Q D hQ r * (retainedFourInclusion Q D hQ s)ᴴ) x := by + let M : Matrix (Fin (fourSpinWeight Q D+1)) (Fin (fourSpinWeight Q D+1)) ℂ := diagonalUnit 0 + have h := contractionForm_haar Q (fourBodySpinRepresentation Q) + (fourBodySpinRepresentation_inv Q) (fourBodySpinRepresentation_continuous Q) + (sourceFourFamilyEnd Q) (sourceFourFamilyEnd_rotation Q (by omega)) + (retainedFourInclusion Q D hQ r*M*(retainedFourInclusion Q D hQ s)ᴴ) x + rw [fourBody_cross_orbit,contractionForm_smul] at h + have ht : Matrix.trace M=1 := by simp [M,diagonalUnit,Matrix.trace,Matrix.diag] + rw [ht] at h + have he := matrix_cross_sandwich_single (retainedFourInclusion Q D hQ r) + (retainedFourInclusion Q D hQ s) (0 : Fin (fourSpinWeight Q D+1)) + change retainedFourInclusion Q D hQ r*M*(retainedFourInclusion Q D hQ s)ᴴ = _ at he + simp_rw [he,contractionForm_outer_cross,physicalFourCopyEnd_column] at h + rw [h] + have hd : ((4*Q-1-2*D : ℕ) : ℂ) ≠ 0 := by + exact_mod_cast (show 4*Q-1-2*D ≠ 0 by omega) + field_simp + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Integral.lean b/lean/OAI/Analysis/Laughlin/FourBody/Integral.lean new file mode 100644 index 0000000000000000000000000000000000000000..1fffb0538dfe640d05998702f04beba4ca3d9dda --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Integral.lean @@ -0,0 +1,101 @@ +import Mathlib.Tactic.FieldSimp +import Mathlib.Tactic.IntervalCases +import Mathlib.Tactic.Ring +import OAI.Analysis.Laughlin.FourBody.Basic + +namespace OAI + +namespace Laughlin.Certificate + +def arithmeticScale : ℚ := 2^64 * (Nat.factorial 24 : ℚ) + +def yEntryIntegral (D r s t : ℕ) (e f : ℕ × ℕ × ℤ) : ℤ := + let (p,j,a) := e + let (q,l,b) := f + let i := p+j-t + let k := q+l-t + let T := p+j+k + if D ≤ T then + a*b*V r D T p j k*V s D T q l i * + (2 : ℤ)^((65-2*(T : ℤ)+(p : ℤ)+(q : ℤ)-(t : ℤ)+((r+s)/2 : ℕ)).toNat) * + (i.factorial : ℤ)*(k.factorial : ℤ)*(t.factorial : ℤ) * + ((24 : ℕ).descFactorial (24-(T-D)) : ℤ) + else 0 + +theorem yEntry_eq_integral (D r s t : ℕ) (e f : ℕ × ℕ × ℤ) + (ht : t ≤ 16) (hT : e.1 + e.2.1 + (f.1 + f.2.1 - t) ≤ 24) : + yEntry D r s t e f = (yEntryIntegral D r s t e f : ℚ) / arithmeticScale := by + rcases e with ⟨p,j,a⟩ + rcases f with ⟨q,l,b⟩ + dsimp at hT + let T := p+j+(q+l-t) + let z : ℤ := 1-2*((p : ℤ)+(j : ℤ)+(q+l-t : ℕ))+(p : ℤ)+(q : ℤ)-(t : ℤ)+((r : ℤ)+(s : ℤ))/2 + have hz : 0 ≤ 64+z := by dsimp [z,T]; omega + have hexp : 65-2*((p : ℤ)+(j : ℤ)+(q+l-t : ℕ))+(p : ℤ)+(q : ℤ)-(t : ℤ)+((r : ℤ)+(s : ℤ))/2 = 64+z := by dsimp [z]; ring + have hp : (2 : ℚ)^((64+z).toNat) = (2 : ℚ)^64 * (2 : ℚ)^z := by + rw [← zpow_natCast, Int.toNat_of_nonneg hz, zpow_add₀ (by norm_num)] + norm_num + have hTD : T-D ≤ 24 := by dsimp [T]; omega + have hf : ((T-D).factorial : ℚ) * ((24 : ℕ).descFactorial (24-(T-D)) : ℚ) = (Nat.factorial 24 : ℚ) := by + have hn := Nat.factorial_mul_descFactorial (n := 24) (k := 24-(T-D)) (by omega) + rw [Nat.sub_sub_self hTD] at hn + exact_mod_cast hn + dsimp [yEntry, yEntryIntegral] + split_ifs with hd + · change _ = _ / arithmeticScale + rw [hexp] + push_cast + rw [hp] + change _ = _ / ((2 : ℚ)^64 * (Nat.factorial 24 : ℚ)) + rw [← hf] + have hn : ((T-D).factorial : ℚ) ≠ 0 := by positivity + have hm : ((24 : ℕ).descFactorial (24-(T-D)) : ℚ) ≠ 0 := by + intro h + rw [h, mul_zero] at hf + exact (ne_of_gt (show (0 : ℚ) < (Nat.factorial 24 : ℚ) by positivity)) hf.symm + change _ = _ / ((2 : ℚ)^64 * (((T-D).factorial : ℚ) * ((24 : ℕ).descFactorial (24-(T-D)) : ℚ))) + field_simp + ring + · simp + +def yRowIntegral (D r s : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) : ℤ := + (row.2.2.map (fun e => (row.2.2.map (fun f => yEntryIntegral D r s row.1 e f)).sum)).sum + +private theorem sum_integral {Element : Type*} (xs : List Element) (f : Element → ℤ) (c : ℚ) : + (xs.map (fun x => (f x : ℚ)/c)).sum = ((xs.map f).sum : ℚ)/c := by + induction xs with + | nil => simp + | cons x xs ih => simp [ih, add_div] + +theorem yRow_eq_integral (D r s : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) + (ht : row.1 ≤ 16) + (hT : ∀ e ∈ row.2.2, ∀ f ∈ row.2.2, + e.1 + e.2.1 + (f.1 + f.2.1 - row.1) ≤ 24) : + yRow D r s row = (yRowIntegral D r s row : ℚ) / arithmeticScale := by + unfold yRow yRowIntegral + calc + _ = (row.2.2.map (fun e => (row.2.2.map (fun f => + (yEntryIntegral D r s row.1 e f : ℚ)/arithmeticScale)).sum)).sum := by + congr 1 + apply List.map_congr_left + intro e he + congr 1 + apply List.map_congr_left + intro f hf + exact yEntry_eq_integral D r s row.1 e f ht (hT e he f hf) + _ = _ := by simp_rw [sum_integral] + +theorem rows_integral_bounds : ∀ row ∈ rows, row.1 ≤ 16 ∧ + ∀ e ∈ row.2.2, ∀ f ∈ row.2.2, + e.1 + e.2.1 + (f.1 + f.2.1 - row.1) ≤ 24 := by + decide +kernel + +theorem source_yRow_eq_integral (D r s n : ℕ) (hn : n < 7) : + yRow D r s (rows[n]!) = (yRowIntegral D r s (rows[n]!) : ℚ) / arithmeticScale := by + have hm : rows[n]! ∈ rows := by + interval_cases n <;> decide +kernel + exact yRow_eq_integral D r s _ (rows_integral_bounds _ hm).1 (rows_integral_bounds _ hm).2 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Levels.lean b/lean/OAI/Analysis/Laughlin/FourBody/Levels.lean new file mode 100644 index 0000000000000000000000000000000000000000..a2c9dca01d1afea98509c70d5149d1d445b4798e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Levels.lean @@ -0,0 +1,64 @@ +import OAI.Analysis.Laughlin.FourBody.MiddleForm +import OAI.Analysis.Laughlin.FourBody.NormalForm +import OAI.Analysis.Laughlin.Operators.RowNormalSquare +import OAI.Analysis.Laughlin.Spin.TwoBodyCertificateHaar + +namespace OAI + +namespace Laughlin.Fock +open Spin +open scoped BigOperators Matrix + +theorem pairOrbitalUnit_family_sum (Q p j : ℕ) (hp : p < 2*Q-2+1) (hj : j ≤ Q) + (v : PairOrbitalIndex Q → Space Q) : + (∑ i, (pairOrbitalUnit Q p j i : ℂ) • v i) = v (⟨p,hp⟩,⟨j,by omega⟩) := by + classical + have he (i : PairOrbitalIndex Q) : (i.1.val=p ∧ i.2.val=j) ↔ + i=(⟨p,hp⟩,⟨j,by omega⟩) := by + constructor + · rintro ⟨h1,h2⟩; exact Prod.ext (Fin.ext h1) (Fin.ext h2) + · intro h; subst i; exact ⟨rfl,rfl⟩ + simp only [pairOrbitalUnit,apply_ite,Complex.ofReal_one,Complex.ofReal_zero, + ite_smul,one_smul,zero_smul,he] + simp + +noncomputable def sourceRowLevel (Q t T : ℕ) (entries : List (ℕ × ℕ × ℤ)) + (x : Space Q) : Space Q := + ∑ i, (threeBodyLevelVector Q t T entries i : ℂ) • sourceThreeEnd Q i x + +theorem contractionForm_realOuter {I : Type*} [Fintype I] (Q : ℕ) + (L : I → Module.End ℂ (Space Q)) (u v : I → ℝ) (x : Space Q) : + contractionForm Q L ((realOuter u v).map Complex.ofReal) x = + occupationInner Q (∑ i, (u i : ℂ) • L i x) (∑ j, (v j : ℂ) • L j x) := by + have he : (realOuter u v).map Complex.ofReal = + complexOuter (fun i => (u i : ℂ)) (fun i => (v i : ℂ)) := by + ext i j + simp [realOuter,complexOuter] + rw [he,contractionForm_outer_cross] + simp only [Complex.star_def,Complex.conj_ofReal] + +theorem threeBodyLevelMatrix_Fock (Q t T : ℕ) (ell : ℤ) + (entries : List (ℕ × ℕ × ℤ)) (ht : t < 2*Q-2+1) (hT : T-t ≤ Q) (x : Space Q) : + contractionForm Q (sourceThreeEnd Q) + ((threeBodyLevelMatrix Q t T ell entries).map Complex.ofReal) x = + ((ell : ℂ)/10^7) * + (occupationInner Q (annihilate ⟨T-t,by omega⟩ (sourcePairEnd Q t x)) + (sourceRowLevel Q t T entries x) + + occupationInner Q (sourceRowLevel Q t T entries x) + (annihilate ⟨T-t,by omega⟩ (sourcePairEnd Q t x))) + + (occupationNormSq Q (sourceRowLevel Q t T entries x) : ℂ) := by + have hadd (M N : Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℝ) : + (M+N).map Complex.ofReal = M.map Complex.ofReal + N.map Complex.ofReal := by + ext i j; simp + have hsmul (r : ℝ) (M : Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℝ) : + (r • M).map Complex.ofReal = (r : ℂ) • M.map Complex.ofReal := by + ext i j; simp + simp only [threeBodyLevelMatrix,hadd,hsmul,contractionForm_add,contractionForm_smul, + contractionForm_realOuter,pairOrbitalUnit_family_sum Q t (T-t) ht hT] + simp only [sourceRowLevel,sourceThreeEnd,Module.End.mul_apply,occupationInner_self, + Complex.ofReal_div,Complex.ofReal_pow,Complex.ofReal_ofNat, + Complex.ofReal_intCast] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/LimitCARReadout.lean b/lean/OAI/Analysis/Laughlin/FourBody/LimitCARReadout.lean new file mode 100644 index 0000000000000000000000000000000000000000..2c86e59f319460d2615f56f96da04cdfff6ccc09 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/LimitCARReadout.lean @@ -0,0 +1,65 @@ +import OAI.Analysis.Laughlin.Exterior.FourConjugation +import OAI.Analysis.Laughlin.FourBody.CARReadout + +namespace OAI + +namespace Laughlin + +theorem pairLimitCoefficient_swap (p x y : ℕ) : + pairLimitCoefficient p y x = -pairLimitCoefficient p x y := by + unfold pairLimitCoefficient + rw [Nat.add_comm y x] + split_ifs + · rw [show ((2 : ℕ) : ℝ)^p * y.factorial*x.factorial = + ((2 : ℕ) : ℝ)^p*x.factorial*y.factorial by ring] + ring + · simp + +theorem pairLimitCoefficient_difference (p x y : ℕ) : + pairLimitCoefficient p x y / Real.sqrt 2 - pairLimitCoefficient p y x / Real.sqrt 2 = + Real.sqrt 2 * pairLimitCoefficient p x y := by + rw [pairLimitCoefficient_swap p x y] + have h : Real.sqrt 2 * Real.sqrt 2 = 2 := Real.mul_self_sqrt (by norm_num) + calc + _ = 2 * pairLimitCoefficient p x y / Real.sqrt 2 := by ring + _ = (Real.sqrt 2 * Real.sqrt 2) * pairLimitCoefficient p x y / Real.sqrt 2 := by rw [h] + _ = _ := by field_simp + +end Laughlin + +namespace Laughlin.Fock +open scoped BigOperators + +theorem limitPairEnd_four_create (Q p : ℕ) (a b c d : Fin (Q+1)) : + limitPairEnd Q p (create a (create b (create c (create d (1 : Space Q))))) = + ((Real.sqrt 2*pairLimitCoefficient p a.val b.val : ℝ) : ℂ) • create c (create d (1 : Space Q)) - + ((Real.sqrt 2*pairLimitCoefficient p a.val c.val : ℝ) : ℂ) • create b (create d (1 : Space Q)) + + ((Real.sqrt 2*pairLimitCoefficient p a.val d.val : ℝ) : ℂ) • create b (create c (1 : Space Q)) + + ((Real.sqrt 2*pairLimitCoefficient p b.val c.val : ℝ) : ℂ) • create a (create d (1 : Space Q)) - + ((Real.sqrt 2*pairLimitCoefficient p b.val d.val : ℝ) : ℂ) • create a (create c (1 : Space Q)) + + ((Real.sqrt 2*pairLimitCoefficient p c.val d.val : ℝ) : ℂ) • create a (create b (1 : Space Q)) := by + unfold limitPairEnd + rw [pairEnd_four_create] + have he (x y : ℕ) : ((pairLimitCoefficient p x y / Real.sqrt 2 : ℝ) : ℂ) - + ((pairLimitCoefficient p y x / Real.sqrt 2 : ℝ) : ℂ) = + ((Real.sqrt 2 * pairLimitCoefficient p x y : ℝ) : ℂ) := by + rw [← Complex.ofReal_sub,pairLimitCoefficient_difference] + simp only [he] + +noncomputable def wedgeDelta (Q : ℕ) (j k a b : Fin (Q+1)) : ℂ := + delta j a * delta k b - delta k a * delta j b + +theorem limitFourEnd_four_create (Q p : ℕ) (j k a b c d : Fin (Q+1)) : + limitFourEnd Q p j k (create a (create b (create c (create d (1 : Space Q))))) = + (((Real.sqrt 2*pairLimitCoefficient p a.val b.val : ℝ) : ℂ) * wedgeDelta Q j k c d - + ((Real.sqrt 2*pairLimitCoefficient p a.val c.val : ℝ) : ℂ) * wedgeDelta Q j k b d + + ((Real.sqrt 2*pairLimitCoefficient p a.val d.val : ℝ) : ℂ) * wedgeDelta Q j k b c + + ((Real.sqrt 2*pairLimitCoefficient p b.val c.val : ℝ) : ℂ) * wedgeDelta Q j k a d - + ((Real.sqrt 2*pairLimitCoefficient p b.val d.val : ℝ) : ℂ) * wedgeDelta Q j k a c + + ((Real.sqrt 2*pairLimitCoefficient p c.val d.val : ℝ) : ℂ) * wedgeDelta Q j k a b) • (1 : Space Q) := by + simp only [limitFourEnd,Module.End.mul_apply,limitPairEnd_four_create,map_sub,map_add,map_smul, + two_annihilate_two_create,smul_smul,wedgeDelta,sub_smul,add_smul,smul_sub,mul_sub] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/LimitPositive.lean b/lean/OAI/Analysis/Laughlin/FourBody/LimitPositive.lean new file mode 100644 index 0000000000000000000000000000000000000000..e8decf5361d60fa5b0c64e5417b23e8bd5949a42 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/LimitPositive.lean @@ -0,0 +1,46 @@ +import OAI.Analysis.Laughlin.Fock.MatrixQuadratic +import OAI.Analysis.Laughlin.FourBody.EndExpansion +import OAI.Analysis.Laughlin.FourBody.WedgeCompression + +namespace OAI + +namespace Laughlin.Fock +open scoped Matrix BigOperators ComplexOrder +open Matrix Spin + +noncomputable def physicalFourOccupationColumns (Q D : ℕ) : + Matrix (FourOccupation Q D) (Fin ((D+1)/2)) ℂ := + fun A i => physicalWedgeColumns Q D A.val i + +theorem physicalFourOccupationColumns_positive (Q D : ℕ) (hQ : D+1 ≤ Q) + (hD₁ : 1 ≤ D) (hD₂ : D ≤ 23) : + (physicalFourOccupationColumns Q D * physicalLimitMiddle D * + (physicalFourOccupationColumns Q D)ᴴ).PosSemidef := by + have h := (source_physical_wedge_compression Q D hQ hD₁ hD₂).submatrix + (fun A : FourOccupation Q D => A.val) + convert h using 1 + ext A B + simp [physicalFourOccupationColumns,Matrix.mul_apply,Matrix.conjTranspose_apply,Matrix.submatrix_apply] + +theorem limitFourCopyEnd_matrix_expansion (Q D : ℕ) (i : Fin ((D+1)/2)) (x : Space Q) : + limitFourCopyEnd Q (Certificate.copyLabel i) D x = + ∑ A : FourOccupation Q D, star (physicalFourOccupationColumns Q D A i) • fourOccupationEnd Q D A x := by + have hi : Certificate.copyLabel i ≤ D := by unfold Certificate.copyLabel; have := i.isLt; omega + have hoi : Odd (Certificate.copyLabel i) := ⟨i.val,by unfold Certificate.copyLabel; omega⟩ + rw [limitFourCopyEnd_expansion Q _ D hi hoi] + simp only [physicalFourOccupationColumns,physicalWedgeColumns, + limitFourColumn_occupation_coefficient Q _ D hi hoi,Complex.star_def,Complex.conj_ofReal] + +theorem source_fourBody_limitpositive (Q D : ℕ) (hQ : D+1 ≤ Q) + (hD₁ : 1 ≤ D) (hD₂ : D ≤ 23) (x : Space Q) : + 0 ≤ (∑ i : Fin ((D+1)/2), ∑ j : Fin ((D+1)/2), physicalLimitMiddle D i j * + occupationInner Q (limitFourCopyEnd Q (Certificate.copyLabel i) D x) + (limitFourCopyEnd Q (Certificate.copyLabel j) D x)).re := by + simp_rw [limitFourCopyEnd_matrix_expansion] + rw [occupation_matrix_quadratic_factor] + exact occupation_matrix_quadratic_positive Q _ + (physicalFourOccupationColumns_positive Q D hQ hD₁ hD₂) _ + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/LocalNormalization.lean b/lean/OAI/Analysis/Laughlin/FourBody/LocalNormalization.lean new file mode 100644 index 0000000000000000000000000000000000000000..ef2a74dc75b7779d8012fe94bcf3db2222b6415a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/LocalNormalization.lean @@ -0,0 +1,43 @@ +import OAI.Analysis.Laughlin.FourBody.CoefficientNorm +import OAI.Analysis.Laughlin.Operators.LocalFourIndexEquiv + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +theorem source_fourBody_local_normalization (Q r D : ℕ) (hr : r ≤ D) (hor : Odd r) (hQ : D+2 ≤ Q) : + (∑ b : LocalFourIndex D, + (fourBodyCoefficient Q r D D b.val.1.val b.val.2.1.val b.val.2.2.val)^2) = 1 := by + classical + let f := fun p : ℕ => ∑ j : Fin (Q+1), ∑ k : Fin (Q+1), + if p+j.val+k.val=D ∧ j < k then (fourBodyCoefficient Q r D D p j.val k.val)^2 else 0 + have hi (p : ℕ) : (∑ i : WedgePairIndex Q, + if p+i.val.1.val+i.val.2.val=D then (fourBodyCoefficient Q r D D p i.val.1.val i.val.2.val)^2 else 0) = f p := by + have hs := Finset.sum_subtype (F := inferInstance) (p := fun i : SpinIndex Q Q => i.1 < i.2) + (Finset.univ.filter (fun i : SpinIndex Q Q => i.1 < i.2)) (by simp) + (fun i => if p+i.1.val+i.2.val=D then (fourBodyCoefficient Q r D D p i.1.val i.2.val)^2 else 0) + rw [← hs,Finset.sum_filter,Fintype.sum_prod_type] + apply Finset.sum_congr rfl; intro j hj + apply Finset.sum_congr rfl; intro k hk + by_cases h₁ : j < k <;> by_cases h₂ : p+j.val+k.val=D <;> simp [h₁,h₂] + have hn := source_fourBody_coefficients_norm Q r D D hor hr (le_refl _) hQ + simp_rw [hi] at hn + rw [Fin.sum_univ_eq_sum_range] at hn + have hsub : (∑ p ∈ Finset.range (D+1), f p) = ∑ p ∈ Finset.range ((2*Q-2)+1), f p := by + apply Finset.sum_subset (Finset.range_mono (by omega)) + intro p hp hn + have hpD : D < p := by simpa using hn + apply Finset.sum_eq_zero; intro j hj + apply Finset.sum_eq_zero; intro k hk + simp [show p+j.val+k.val≠D by omega] + have he := localFourIndex_sum Q D (by omega) + (fun p j k => (fourBodyCoefficient Q r D D p j.val k.val)^2) + rw [← he] + change (∑ p : Fin (D+1), f p.val)=1 + rw [Fin.sum_univ_eq_sum_range,hsub] + exact hn + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Matrix.lean b/lean/OAI/Analysis/Laughlin/FourBody/Matrix.lean new file mode 100644 index 0000000000000000000000000000000000000000..cb4a5897992507839004fbbab24a9cefb038faca --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Matrix.lean @@ -0,0 +1,46 @@ +import OAI.Analysis.Laughlin.FourBody.Basic +import OAI.Analysis.Laughlin.Operators.RationalPSD + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix + +def copyWeight (D : ℕ) (i : Fin ((D+1)/2)) : ℚ := + 1 / ((copyLabel i).factorial * (D-copyLabel i).factorial : ℕ) + +def middleRational (D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ := + Matrix.diagonal (fun i => ((if copyLabel i = 1 then 2 else 0) + (3/10^6 : ℚ)) * + copyWeight D i) - Matrix.diagonal (copyWeight D) * errorRational D * + Matrix.diagonal (copyWeight D) + +def compressedRational (D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ := + gramRational D * middleRational D * gramRational D + +theorem compressed_positive_of_gram_zero (D : ℕ) (h : gramRational D = 0) : + ((compressedRational D).map (Rat.castHom ℝ)).PosSemidef := by + have he : compressedRational D = 0 := by simp [compressedRational, h] + rw [he] + simpa using (Matrix.PosSemidef.zero : + (0 : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℝ).PosSemidef) + + +theorem gram_one_zero : gramRational 1 = 0 := by decide +kernel +theorem gram_two_zero : gramRational 2 = 0 := by decide +kernel +theorem gram_three_zero : gramRational 3 = 0 := by decide +kernel +theorem gram_four_zero : gramRational 4 = 0 := by decide +kernel +theorem gram_six_zero : gramRational 6 = 0 := by decide +kernel + +theorem zero_blocks_positive (D : ℕ) (hD : D ∈ [1,2,3,4,6]) : + ((compressedRational D).map (Rat.castHom ℝ)).PosSemidef := by + simp only [List.mem_cons, List.not_mem_nil, or_false] at hD + rcases hD with rfl | rfl | rfl | rfl | rfl + · exact compressed_positive_of_gram_zero 1 gram_one_zero + · exact compressed_positive_of_gram_zero 2 gram_two_zero + · exact compressed_positive_of_gram_zero 3 gram_three_zero + · exact compressed_positive_of_gram_zero 4 gram_four_zero + · exact compressed_positive_of_gram_zero 6 gram_six_zero + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/MatrixCompute.lean b/lean/OAI/Analysis/Laughlin/FourBody/MatrixCompute.lean new file mode 100644 index 0000000000000000000000000000000000000000..a95c905116fd6325a5e176ff03e9d438d57e9a20 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/MatrixCompute.lean @@ -0,0 +1,48 @@ +import Mathlib.Algebra.Field.Rat +import Mathlib.Data.Matrix.Mul +import Mathlib.Data.Nat.Factorial.Basic + +namespace OAI + +namespace Laughlin.Certificate.MatrixCompute + +def copyLabel {D : ℕ} (i : Fin ((D+1)/2)) : ℕ := 2*i.val+1 + +def copyWeight (D : ℕ) (i : Fin ((D+1)/2)) : ℚ := + 1 / ((copyLabel i).factorial * (D-copyLabel i).factorial : ℕ) + +def middle (D : ℕ) (Y : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ) : + Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ := + Matrix.diagonal (fun i => ((if copyLabel i = 1 then 2 else 0) + (3/10^6 : ℚ)) * + copyWeight D i) - Matrix.diagonal (copyWeight D) * Y * Matrix.diagonal (copyWeight D) + +def compressed (D : ℕ) (Y Z : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ) : + Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ := Z * middle D Y * Z + +open scoped BigOperators + +theorem middle_apply (D : ℕ) (Y : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ) + (i j : Fin ((D+1)/2)) : + middle D Y i j = + (if i = j then ((if copyLabel i = 1 then 2 else 0) + (3/10^6 : ℚ)) * copyWeight D i else 0) - + copyWeight D i * Y i j * copyWeight D j := by + simp only [middle, Matrix.sub_apply, Matrix.diagonal_mul, Matrix.mul_diagonal, + Matrix.diagonal_apply] + +theorem compressed_apply (D : ℕ) (Y Z : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ) + (i j : Fin ((D+1)/2)) : + compressed D Y Z i j = + ∑ k, (∑ l, Z i l * + ((if l = k then ((if copyLabel l = 1 then 2 else 0) + (3/10^6 : ℚ)) * copyWeight D l else 0) - + copyWeight D l * Y l k * copyWeight D k)) * Z k j := by + simp only [compressed, Matrix.mul_apply, middle_apply] + +theorem ldl_apply {n : ℕ} (L : Matrix (Fin n) (Fin n) ℚ) (d : Fin n → ℚ) + (i j : Fin n) : + (L * Matrix.diagonal d * L.transpose) i j = ∑ k, L i k * d k * L j k := by + rw [Matrix.mul_apply] + simp only [Matrix.mul_diagonal, Matrix.transpose_apply] + +end Laughlin.Certificate.MatrixCompute + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/MiddleForm.lean b/lean/OAI/Analysis/Laughlin/FourBody/MiddleForm.lean new file mode 100644 index 0000000000000000000000000000000000000000..4aefa295bbee3b8160ee6d01fd9c1e8aee74ee8b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/MiddleForm.lean @@ -0,0 +1,41 @@ +import OAI.Analysis.Laughlin.FourBody.CopyAlgebra + +namespace OAI + +namespace Laughlin.Fock +open Spin +open scoped BigOperators Matrix + +theorem contractionForm_add {I : Type*} [Fintype I] (Q : ℕ) + (L : I → Module.End ℂ (Space Q)) (M N : Matrix I I ℂ) (x : Space Q) : + contractionForm Q L (M+N) x = contractionForm Q L M x+contractionForm Q L N x := by + simp only [contractionForm,Matrix.add_apply,add_mul,Finset.sum_add_distrib] + +theorem contractionForm_sub {I : Type*} [Fintype I] (Q : ℕ) + (L : I → Module.End ℂ (Space Q)) (M N : Matrix I I ℂ) (x : Space Q) : + contractionForm Q L (M-N) x = contractionForm Q L M x-contractionForm Q L N x := by + simp only [contractionForm,Matrix.sub_apply,sub_mul,Finset.sum_sub_distrib] + +theorem fourCopyMiddleForm (Q D : ℕ) (hQ : D+2 ≤ Q) (hD : 1 ≤ D) (x : Space Q) : + (((2*Q-2+1 : ℕ) : ℝ)/((4*Q-1-2*D : ℕ) : ℝ)) * + (contractionForm Q (sourceFourFamilyEnd Q) (fourCopyOperator Q D hQ (finiteFourMiddle Q D)) x).re = + (contractionForm Q (sourceFourFamilyEnd Q) + (retainedFourInclusion Q D hQ (firstOddPairLabel D hD) * + (retainedFourInclusion Q D hQ (firstOddPairLabel D hD))ᴴ) x).re + + (3/10^6 : ℝ) * (((2*Q-2+1 : ℕ) : ℝ)/((4*Q-1-2*D : ℕ) : ℝ)) * + (∑ r : OddPairLabel D, (contractionForm Q (sourceFourFamilyEnd Q) + (retainedFourInclusion Q D hQ r*(retainedFourInclusion Q D hQ r)ᴴ) x).re) - + (((2*Q-2+1 : ℕ) : ℝ)/((4*Q-1-2*D : ℕ) : ℝ)) * + (contractionForm Q (sourceFourFamilyEnd Q) + (fourCopyOperator Q D hQ (fun r s => physicalFourError Q D (oddPairDeficit r) (oddPairDeficit s))) x).re := by + rw [fourCopyOperator_middle Q D hQ hD,contractionForm_sub,contractionForm_add] + simp only [contractionForm_smul,contractionForm_sum,Complex.sub_re,Complex.add_re, + Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im,zero_mul,sub_zero,Complex.re_sum] + rw [fourDimensionRatio_exact Q D hQ] + have ha : ((2*Q-2+1 : ℕ) : ℝ) ≠ 0 := by positivity + have hd : ((4*Q-1-2*D : ℕ) : ℝ) ≠ 0 := by exact_mod_cast (show 4*Q-1-2*D ≠ 0 by omega) + field_simp + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/MiddleLimit.lean b/lean/OAI/Analysis/Laughlin/FourBody/MiddleLimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..50945ca597a444828e83b39f065f743974772209 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/MiddleLimit.lean @@ -0,0 +1,55 @@ +import OAI.Analysis.Laughlin.FourBody.ErrorMatrix +import OAI.Analysis.Laughlin.FourBody.WedgeCompression + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators Matrix Topology +open Filter Spin + +noncomputable def fourDimensionRatio (Q D : ℕ) : ℝ := + (4*(Q : ℝ)-1-2*(D : ℝ))/(2*(Q : ℝ)-1) + +theorem fourDimensionRatio_tendsto (D : ℕ) : Tendsto (fun Q => fourDimensionRatio Q D) atTop (𝓝 2) := by + have hi : Tendsto (fun Q : ℕ => (Q : ℝ)⁻¹) atTop (𝓝 0) := + tendsto_inv_atTop_zero.comp tendsto_natCast_atTop_atTop + have hn := (tendsto_const_nhds (x := (4 : ℝ))).sub (hi.const_mul (1+2*(D : ℝ))) + have hd := (tendsto_const_nhds (x := (2 : ℝ))).sub hi + have hh := hn.div hd (by norm_num : (2 : ℝ)-0 ≠ 0) + have he : (fun Q : ℕ => fourDimensionRatio Q D) =ᶠ[atTop] + (fun Q => (4-(1+2*(D : ℝ))*(Q : ℝ)⁻¹)/(2-(Q : ℝ)⁻¹)) := by + filter_upwards [eventually_ge_atTop 1] with Q hQ + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (by omega : Q ≠ 0) + unfold fourDimensionRatio + field_simp + ring + apply Tendsto.congr' he.symm + norm_num at hh + apply hh.congr + intro Q + rfl + +noncomputable def finiteFourMiddle (Q D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℝ := + Matrix.diagonal (fun i : Fin ((D+1)/2) => (if Certificate.copyLabel i=1 then fourDimensionRatio Q D else 0) + (3/10^6 : ℝ)) - + Matrix.of (fun i j : Fin ((D+1)/2) => physicalFourError Q D (Certificate.copyLabel i) (Certificate.copyLabel j)) + +noncomputable def limitFourMiddle (D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℝ := + Certificate.certificateDiagonal D - physicalLimitError D + +theorem finiteFourMiddle_tendsto (D : ℕ) (i j : Fin ((D+1)/2)) : + Tendsto (fun Q => finiteFourMiddle Q D i j) atTop (𝓝 (limitFourMiddle D i j)) := by + have he := physicalFourError_certificate_tendsto D i j + rw [← physicalLimitError_eq D] at he + unfold finiteFourMiddle limitFourMiddle + apply Tendsto.sub _ he + by_cases hij : i=j + · subst j + by_cases hi : Certificate.copyLabel i=1 + · simpa [Matrix.diagonal_apply,hi,Certificate.certificateDiagonal,Matrix.map_apply] using + (fourDimensionRatio_tendsto D).add_const (3/10^6 : ℝ) + · simp [hi,Certificate.certificateDiagonal,Matrix.map_apply] + · simp [hij,Certificate.certificateDiagonal,Matrix.map_apply] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/MultiplicityHaar.lean b/lean/OAI/Analysis/Laughlin/FourBody/MultiplicityHaar.lean new file mode 100644 index 0000000000000000000000000000000000000000..933c6ebd89368cbdba020f02f7e2b46a6bf05296 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/MultiplicityHaar.lean @@ -0,0 +1,93 @@ +import OAI.Analysis.Laughlin.FourBody.RetainedInclusions +import OAI.Analysis.Laughlin.Spin.HaarOrthogonality +import OAI.Analysis.Laughlin.Spin.Sandwich + +namespace OAI + +namespace Laughlin.Spin +open Rotation MeasureTheory +open scoped BigOperators Matrix + +theorem retainedFourInclusion_adjoint_SU2 (Q D : ℕ) (hQ : D+2 ≤ Q) + (r : OddPairLabel D) (g : SourceSU2) : + (retainedFourInclusion Q D hQ r)ᴴ * fourBodySpinRepresentation Q g = + sourceSpinRepresentation (fourSpinWeight Q D) g * (retainedFourInclusion Q D hQ r)ᴴ := by + have h := congrArg Matrix.conjTranspose (retainedFourInclusion_SU2 Q D hQ r g⁻¹) + simpa only [Matrix.conjTranspose_mul,fourBodySpinRepresentation_inv,sourceSpinRepresentation_inv, + Matrix.conjTranspose_conjTranspose] using h + +theorem fourBody_haar_compressed (Q D E : ℕ) (hD : D+2 ≤ Q) (hE : E+2 ≤ Q) + (r : OddPairLabel D) (s : OddPairLabel E) (M : Matrix (FourWedgeIndex Q) (FourWedgeIndex Q) ℂ) : + (retainedFourInclusion Q D hD r)ᴴ * matrixIntegral sourceHaar + (conjugateOrbit (fourBodySpinRepresentation Q) M) * retainedFourInclusion Q E hE s = + rectangularIntegral sourceHaar (rectangularOrbit + (sourceSpinRepresentation (fourSpinWeight Q D)) (sourceSpinRepresentation (fourSpinWeight Q E)) + ((retainedFourInclusion Q D hD r)ᴴ * M * retainedFourInclusion Q E hE s)) := by + change (retainedFourInclusion Q D hD r)ᴴ * entrywiseIntegral sourceHaar + (conjugateOrbit (fourBodySpinRepresentation Q) M) * retainedFourInclusion Q E hE s = _ + rw [← integral_matrix_sandwich sourceHaar _ + (compact_conjugateOrbit_integrable sourceHaar _ (fourBodySpinRepresentation_continuous Q) M)] + funext i j + apply integral_congr_ae + filter_upwards [] with g + have hs := retainedFourInclusion_SU2 Q E hE s g⁻¹ + simp only [conjugateOrbit,rectangularOrbit] + rw [← Matrix.mul_assoc,← Matrix.mul_assoc,retainedFourInclusion_adjoint_SU2, + Matrix.mul_assoc,Matrix.mul_assoc,hs] + simp only [Matrix.mul_assoc] + +theorem fourBody_haar_multiplicity_block (Q D : ℕ) (hD : D+2 ≤ Q) + (r s : OddPairLabel D) (M : Matrix (FourWedgeIndex Q) (FourWedgeIndex Q) ℂ) : + (retainedFourInclusion Q D hD r)ᴴ * matrixIntegral sourceHaar + (conjugateOrbit (fourBodySpinRepresentation Q) M) * retainedFourInclusion Q D hD s = + (Matrix.trace ((retainedFourInclusion Q D hD r)ᴴ*M*retainedFourInclusion Q D hD s) / + (4*Q-1-2*D : ℕ)) • 1 := by + rw [fourBody_haar_compressed,source_equal_spin_haar_trace] + have hd : ((fourSpinWeight Q D+1 : ℕ) : ℂ) = ((4*Q-1-2*D : ℕ) : ℂ) := by + exact_mod_cast fourSpinWeight_dimension Q D hD + rw [hd] + +theorem fourBody_haar_unequal_spin (Q D E : ℕ) (hD : D+2 ≤ Q) (hE : E+2 ≤ Q) + (hDE : D ≠ E) (r : OddPairLabel D) (s : OddPairLabel E) + (M : Matrix (FourWedgeIndex Q) (FourWedgeIndex Q) ℂ) : + (retainedFourInclusion Q D hD r)ᴴ * matrixIntegral sourceHaar + (conjugateOrbit (fourBodySpinRepresentation Q) M) * retainedFourInclusion Q E hE s = 0 := by + rw [fourBody_haar_compressed] + apply source_unequal_spin_haar_zero + unfold fourSpinWeight + omega + +theorem fourBody_cross_orbit (Q D : ℕ) (hD : D+2 ≤ Q) (r s : OddPairLabel D) + (M : Matrix (Fin (fourSpinWeight Q D+1)) (Fin (fourSpinWeight Q D+1)) ℂ) : + matrixIntegral sourceHaar (conjugateOrbit (fourBodySpinRepresentation Q) + (retainedFourInclusion Q D hD r * M * (retainedFourInclusion Q D hD s)ᴴ)) = + (Matrix.trace M / (4*Q-1-2*D : ℕ)) • + (retainedFourInclusion Q D hD r * (retainedFourInclusion Q D hD s)ᴴ) := by + have he (g : SourceSU2) : conjugateOrbit (fourBodySpinRepresentation Q) + (retainedFourInclusion Q D hD r * M * (retainedFourInclusion Q D hD s)ᴴ) g = + retainedFourInclusion Q D hD r * + conjugateOrbit (sourceSpinRepresentation (fourSpinWeight Q D)) M g * + (retainedFourInclusion Q D hD s)ᴴ := by + unfold conjugateOrbit + calc + _ = (fourBodySpinRepresentation Q g*retainedFourInclusion Q D hD r)*M* + ((retainedFourInclusion Q D hD s)ᴴ*fourBodySpinRepresentation Q g⁻¹) := by + simp only [Matrix.mul_assoc] + _ = _ := by + rw [retainedFourInclusion_SU2,retainedFourInclusion_adjoint_SU2] + simp only [Matrix.mul_assoc] + unfold matrixIntegral + simp_rw [he] + rw [integral_matrix_sandwich sourceHaar _ (compact_conjugateOrbit_integrable sourceHaar _ + (sourceSpinRepresentation_continuous (fourSpinWeight Q D)) M)] + change retainedFourInclusion Q D hD r * matrixIntegral sourceHaar + (conjugateOrbit (sourceSpinRepresentation (fourSpinWeight Q D)) M) * + (retainedFourInclusion Q D hD s)ᴴ = _ + rw [source_spin_haar_schur,Matrix.mul_smul,Matrix.mul_one,Matrix.smul_mul] + have hd : ((fourSpinWeight Q D+1 : ℕ) : ℂ) = ((4*Q-1-2*D : ℕ) : ℂ) := by + exact_mod_cast fourSpinWeight_dimension Q D hD + rw [hd] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/NormalForm.lean b/lean/OAI/Analysis/Laughlin/FourBody/NormalForm.lean new file mode 100644 index 0000000000000000000000000000000000000000..436074d9e55c11ccef0859996a8003d2ec3f3e45 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/NormalForm.lean @@ -0,0 +1,70 @@ +import OAI.Analysis.Laughlin.FourBody.HighestFock +import OAI.Analysis.Laughlin.FourBody.PhysicalTrace + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin +open scoped BigOperators Matrix + +theorem fourWedgeUnit_family_sum (Q p j k : ℕ) (hp : p < 2*Q-2+1) (hj : j ≤ Q) (hk : k ≤ Q) + (hjk : j < k) (v : FourWedgeIndex Q → Space Q) : + (∑ i, (fourWedgeUnit Q p j k i : ℂ) • v i) = + v (⟨p,hp⟩,⟨(⟨j,by omega⟩,⟨k,by omega⟩),hjk⟩) := by + have he (i : FourWedgeIndex Q) : + (i.1.val=p ∧ i.2.val.1.val=j ∧ i.2.val.2.val=k) ↔ + i=(⟨p,hp⟩,⟨(⟨j,by omega⟩,⟨k,by omega⟩),hjk⟩) := by + constructor + · rintro ⟨h1,h2,h3⟩ + exact Prod.ext (Fin.ext h1) (Subtype.ext (Prod.ext (Fin.ext h2) (Fin.ext h3))) + · intro h; subst i; exact ⟨rfl,rfl,rfl⟩ + simp only [fourWedgeUnit,apply_ite,Complex.ofReal_one,Complex.ofReal_zero,ite_smul,one_smul,zero_smul] + simp_rw [he] + simp + +theorem sourceFourEnd_swap (Q p : ℕ) (j k : Fin (Q+1)) : + sourceFourEnd Q p k j = -sourceFourEnd Q p j k := by + have h : annihilate j*annihilate k = -(annihilate k*annihilate j) := + eq_neg_of_add_eq_zero_left (annihilate_anticommute j k) + rw [sourceFourEnd,sourceFourEnd,h] + ext x + rfl + +theorem fourSignedUnit_family_sum (Q p j k : ℕ) (hp : p < 2*Q-2+1) (hj : j ≤ Q) (hk : k ≤ Q) + (x : Space Q) : + (∑ i, (fourSignedUnit Q p j k i : ℂ) • sourceFourFamilyEnd Q i x) = + sourceFourEnd Q p ⟨j,by omega⟩ ⟨k,by omega⟩ x := by + simp only [fourSignedUnit,Pi.sub_apply,Complex.ofReal_sub,sub_smul,Finset.sum_sub_distrib] + rcases lt_trichotomy j k with h | h | h + · rw [fourWedgeUnit_family_sum Q p j k hp hj hk h,fourWedgeUnit_zero Q p k j (by omega)] + simp only [Pi.zero_apply,Complex.ofReal_zero,zero_smul,Finset.sum_const_zero,sub_zero] + rfl + · subst k + rw [sub_self] + simp only [sourceFourEnd,annihilate_sq,zero_mul,LinearMap.zero_apply] + · rw [fourWedgeUnit_zero Q p j k (by omega),fourWedgeUnit_family_sum Q p k j hp hk hj h] + simp only [Pi.zero_apply,Complex.ofReal_zero,zero_smul,Finset.sum_const_zero,zero_sub, + sourceFourFamilyEnd,sourceFourEnd_swap Q p ⟨j,by omega⟩ ⟨k,by omega⟩, + LinearMap.neg_apply,neg_neg] + +theorem fourBodyTermMatrix_Fock (Q t : ℕ) (e f : ℕ × ℕ × ℤ) + (he : t ≤ e.1+e.2.1) (hf : t ≤ f.1+f.2.1) + (hQ : e.1+e.2.1+(f.1+f.2.1-t)+2 ≤ Q) (x : Space Q) : + contractionForm Q (sourceFourFamilyEnd Q) ((fourBodyTermMatrix Q t e f).map Complex.ofReal) x = + -(sourceAlpha t e * sourceAlpha t f : ℝ) * occupationInner Q + (sourceFourEnd Q e.1 ⟨e.2.1,by omega⟩ ⟨f.1+f.2.1-t,by omega⟩ x) + (sourceFourEnd Q f.1 ⟨f.2.1,by omega⟩ ⟨e.1+e.2.1-t,by omega⟩ x) := by + have hm : (fourBodyTermMatrix Q t e f).map Complex.ofReal = + (-(sourceAlpha t e * sourceAlpha t f : ℝ) : ℂ) • + complexOuter (fun i => (fourSignedUnit Q e.1 e.2.1 (f.1+f.2.1-t) i : ℂ)) + (fun i => (fourSignedUnit Q f.1 f.2.1 (e.1+e.2.1-t) i : ℂ)) := by + ext i j + simp [fourBodyTermMatrix,realOuter,complexOuter] + rw [hm,contractionForm_smul,contractionForm_outer_cross] + simp only [Complex.star_def,Complex.conj_ofReal] + rw [fourSignedUnit_family_sum Q e.1 e.2.1 (f.1+f.2.1-t) (by omega) (by omega) (by omega), + fourSignedUnit_family_sum Q f.1 f.2.1 (e.1+e.2.1-t) (by omega) (by omega) (by omega)] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/NumericBridge.lean b/lean/OAI/Analysis/Laughlin/FourBody/NumericBridge.lean new file mode 100644 index 0000000000000000000000000000000000000000..5e39ae47e5d8d772d830c8fc61b5d11f9b61211a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/NumericBridge.lean @@ -0,0 +1,19 @@ +import OAI.Analysis.Laughlin.FourBody.GramCompute +import OAI.Analysis.Laughlin.FourBody.Matrix +import OAI.Analysis.Laughlin.FourBody.MatrixCompute +import OAI.Analysis.Laughlin.FourBody.RowBridge + +namespace OAI + +namespace Laughlin.Certificate + +theorem Z_eq_gramCompute (D r s : ℕ) : Z D r s = GramCompute.ZFast D r s := by + exact Z_eq_fast D r s + +theorem compressedRational_eq_compute (D : ℕ) : + compressedRational D = MatrixCompute.compressed D (errorRational D) (gramRational D) := by + rfl + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/OccupationCoefficient.lean b/lean/OAI/Analysis/Laughlin/FourBody/OccupationCoefficient.lean new file mode 100644 index 0000000000000000000000000000000000000000..db3de41a644376d046d6e716909f10148e648ff6 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/OccupationCoefficient.lean @@ -0,0 +1,51 @@ +import OAI.Analysis.Laughlin.Fock.FourLabels +import OAI.Analysis.Laughlin.FourBody.PhysicalColumn + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators +open Spin + +theorem occupationInner_basis_right (Q : ℕ) (x : Space Q) (A : Finset (Fin (Q+1))) : + occupationInner Q x (occupationBasis Q A) = star ((occupationBasis Q).repr x A) := by + simp [occupationInner,Module.Basis.repr_self,Finsupp.single_apply] + +noncomputable def fourOccupationCoefficient (Q r D : ℕ) (A : Finset (Fin (Q+1))) : ℝ := + if hA : A.card=4 then + if (∑ i ∈ A, i.val)=D+1 then + let l := occupationFourLabels Q A hA + Real.sqrt (sourceCopyWeight D r / + ((l 0).val.factorial*(l 1).val.factorial*(l 2).val.factorial*(l 3).val.factorial : ℝ)) * + (Certificate.L D r ((l 0).val,(l 1).val,(l 2).val,(l 3).val) : ℝ) + else 0 + else 0 + +theorem limitFourColumn_occupation_coefficient (Q r D : ℕ) (hr : r ≤ D) (hor : Odd r) + (A : Finset (Fin (Q+1))) : + (occupationBasis Q).repr (limitFourColumn Q r D) A = (fourOccupationCoefficient Q r D A : ℂ) := by + by_cases hA : A.card=4 + · by_cases hw : (∑ i ∈ A, i.val)=D+1 + · let l := occupationFourLabels Q A hA + have h := limitFourColumn_physical_L Q r D hr hor (l 0) (l 1) (l 2) (l 3) + (l.strictMono (by decide)) (l.strictMono (by decide)) (l.strictMono (by decide)) + (by rw [← occupationFourLabels_sum Q A hA]; exact hw) + rw [← occupationBasis_four Q A hA,occupationInner_basis_right] at h + have hs := congrArg star h + simpa [fourOccupationCoefficient,hA,hw,l] using hs + · rw [limitFourColumn_bidegree Q r D A (Or.inr hw)] + simp [fourOccupationCoefficient,hA,hw] + · rw [limitFourColumn_bidegree Q r D A (Or.inl hA)] + simp [fourOccupationCoefficient,hA] + +theorem limitFourColumn_gram_occupation (Q r s D : ℕ) (hr : r ≤ D) (hs : s ≤ D) + (hor : Odd r) (hos : Odd s) : + occupationInner Q (limitFourColumn Q r D) (limitFourColumn Q s D) = + ((∑ A : Finset (Fin (Q+1)), fourOccupationCoefficient Q r D A * + fourOccupationCoefficient Q s D A : ℝ) : ℂ) := by + simp [occupationInner,limitFourColumn_occupation_coefficient Q r D hr hor, + limitFourColumn_occupation_coefficient Q s D hs hos] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/PairTarget.lean b/lean/OAI/Analysis/Laughlin/FourBody/PairTarget.lean new file mode 100644 index 0000000000000000000000000000000000000000..51641041c0c15c2525962a36c861f054864c5f64 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/PairTarget.lean @@ -0,0 +1,95 @@ +import OAI.Analysis.Laughlin.FourBody.TargetBound +import OAI.Analysis.Laughlin.Pair.CoupledOne + +namespace OAI + +namespace Laughlin.Fock +open Spin +open scoped BigOperators Matrix Kronecker + +theorem pairCoupledOne_contract (Q : ℕ) (hQ : 1 ≤ Q) + (n : Fin (genericCoupledWeight Q Q 1+1)) (x : Space Q) : + (∑ i : WedgePairIndex Q, (pairCoupledInclusion Q 1 hQ i n : ℂ) • + annihilate i.val.2 (annihilate i.val.1 x)) = sourcePairEnd Q n.val x := by + have hf (i j : Fin (Q+1)) : annihilate i (annihilate j x) = + -annihilate j (annihilate i x) := by + have h := LinearMap.congr_fun (annihilate_anticommute i j) x + exact eq_neg_of_add_eq_zero_left h + have he := antisymmetric_exterior_sum Q + (fun i => annihilate i.2 (annihilate i.1 x)) hf + (fun i => ((pairCoefficient Q n.val i.1 i.2 / Real.sqrt 2 : ℝ) : ℂ)) + have hn : n.val ≤ 2*Q-2 := by have := n.isLt; unfold genericCoupledWeight at this; omega + have hc (i : WedgePairIndex Q) : + ((pairCoefficient Q n.val i.val.1 i.val.2 / Real.sqrt 2 : ℝ) : ℂ) - + ((pairCoefficient Q n.val i.val.2 i.val.1 / Real.sqrt 2 : ℝ) : ℂ) = + (pairCoupledInclusion Q 1 hQ i n : ℂ) := by + rw [pairCoefficient_swap Q n.val i.val.1 i.val.2] + have hs : Real.sqrt 2 ≠ 0 := by positivity + have hreal : pairCoefficient Q n.val i.val.1 i.val.2 / Real.sqrt 2 - + -pairCoefficient Q n.val i.val.1 i.val.2 / Real.sqrt 2 = + Real.sqrt 2*pairCoefficient Q n.val i.val.1 i.val.2 := by + field_simp + rw [Real.sq_sqrt (by norm_num)] + ring + rw [← Complex.ofReal_sub,hreal] + simp only [pairCoupledInclusion,pairCoupledWedge,tensorToWedgePair,pairCoupledTensor_one Q n.val hQ hn] + have he' := he.trans (Finset.sum_congr rfl (fun i hi => + congrArg (fun c : ℂ => c • annihilate i.val.2 (annihilate i.val.1 x)) (hc i))) + calc + _ = ∑ i : SpinIndex Q Q, ((pairCoefficient Q n.val i.1 i.2 / Real.sqrt 2 : ℝ) : ℂ) • + annihilate i.2 (annihilate i.1 x) := he'.symm + _ = _ := by + simp only [sourcePairEnd,pairEnd,LinearMap.sum_apply,LinearMap.smul_apply, + Module.End.mul_apply,Fintype.sum_prod_type] + +theorem fourPairEmbedding_contract (Q : ℕ) (hQ : 1 ≤ Q) + (j : SpinIndex (2*Q-2) (genericCoupledWeight Q Q 1)) (x : Space Q) : + (∑ i : FourWedgeIndex Q, star (fourPairEmbedding Q 1 hQ i j) • sourceFourFamilyEnd Q i x) = + sourcePairEnd Q j.2.val (sourcePairEnd Q j.1.val x) := by + simp only [fourPairEmbedding,Matrix.kroneckerMap,Matrix.of_apply,Matrix.one_apply, + Matrix.map_apply,apply_ite,star_zero,Complex.star_def,Complex.conj_ofReal, + ite_mul,one_mul,zero_mul,ite_smul,zero_smul,Fintype.sum_prod_type] + rw [Finset.sum_comm] + simp only [Finset.sum_ite_eq',Finset.mem_univ,ite_true] + exact pairCoupledOne_contract Q hQ j.2 (sourcePairEnd Q j.1.val x) + +theorem contractionForm_factor_one {I J : Type*} [Fintype I] [Fintype J] [DecidableEq J] + (Q : ℕ) (L : I → Module.End ℂ (Space Q)) (W : Matrix I J ℂ) (x : Space Q) : + contractionForm Q L (W*Wᴴ) x = + (∑ j, (occupationNormSq Q (∑ i, star (W i j) • L i x) : ℂ)) := by + have h := occupation_matrix_quadratic_factor Q W (1 : Matrix J J ℂ) (fun i => L i x) + rw [Matrix.mul_one] at h + change (∑ a, ∑ b, (W*Wᴴ) a b * occupationInner Q (L a x) (L b x)) = _ + rw [← h] + simp [Matrix.one_apply,occupationInner_self] + +theorem fourPairTargetMatrix_Fock (Q : ℕ) (hQ : 1 ≤ Q) (x : Space Q) : + (contractionForm Q (sourceFourFamilyEnd Q) (fourPairTargetMatrix Q hQ) x).re = + ∑ p : Fin (2*Q-2+1), ∑ q : Fin (2*Q-2+1), + occupationNormSq Q (sourcePairEnd Q q.val (sourcePairEnd Q p.val x)) := by + rw [fourPairTargetMatrix,contractionForm_factor_one] + simp only [Complex.re_sum,Complex.ofReal_re] + have he : (∑ j : SpinIndex (2*Q-2) (genericCoupledWeight Q Q 1), + occupationNormSq Q (∑ i, star (fourPairEmbedding Q 1 hQ i j) • sourceFourFamilyEnd Q i x)) = + ∑ j : SpinIndex (2*Q-2) (genericCoupledWeight Q Q 1), + occupationNormSq Q (sourcePairEnd Q j.2.val (sourcePairEnd Q j.1.val x)) := + Finset.sum_congr rfl (fun j hj => congrArg (occupationNormSq Q) (fourPairEmbedding_contract Q hQ j x)) + rw [he,Fintype.sum_prod_type] + have hw : genericCoupledWeight Q Q 1=2*Q-2 := by unfold genericCoupledWeight; omega + apply Finset.sum_congr rfl + intro p hp + exact Fintype.sum_equiv (finCongr (congrArg (fun m => m+1) hw)) _ _ (fun q => rfl) + +theorem sourceA4Form_bound (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + sourceA4Form Q x ≤ + (∑ p : Fin (2*Q-2+1), ∑ q : Fin (2*Q-2+1), + occupationNormSq Q (sourcePairEnd Q q.val (sourcePairEnd Q p.val x))) + + (10946*(3/10^6 : ℝ)+averagedFourTransferError Q)*sourceFockEnergy Q x := by + have ht := retainedFourTarget_le_full Q hQ x + rw [fourPairTargetMatrix_Fock] at ht + have hb := sourceA4Form_retained_bound Q hQ x + linarith + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Parity.lean b/lean/OAI/Analysis/Laughlin/FourBody/Parity.lean new file mode 100644 index 0000000000000000000000000000000000000000..d4c5fe17dc347311d353e96b72fd2a863353e1bc --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Parity.lean @@ -0,0 +1,45 @@ +import OAI.Analysis.Laughlin.FourBody.CoefficientLimit + +namespace OAI + +namespace Laughlin.Spin +open scoped Topology +open Filter + +theorem physicalPairCoupling_antisymmetric (Q r j k : ℕ) (ho : Odd r) : + physicalCouplingCoefficient Q Q r (j+k) k = + -physicalCouplingCoefficient Q Q r (j+k) j := by + by_cases h : r ≤ j+k ∧ j+k ≤ Q + · have h1 : r ≤ j+k ∧ k ≤ j+k ∧ j+k ≤ Q ∧ j+k ≤ Q := by omega + have h2 : r ≤ j+k ∧ j ≤ j+k ∧ j+k ≤ Q ∧ j+k ≤ Q := by omega + rw [physicalCouplingCoefficient,dite_eq_left h1,physicalCouplingCoefficient,dite_eq_left h2] + have hj : j+k-k=j := by omega + have hk : j+k-j=k := by omega + simp only [hj,hk] + exact pairCoupledTensor_antisymmetric Q r (j+k-r) (by omega) ho + ⟨j,by omega⟩ ⟨k,by omega⟩ + · have h1 : ¬(r ≤ j+k ∧ k ≤ j+k ∧ j+k ≤ Q ∧ j+k ≤ Q) := by omega + have h2 : ¬(r ≤ j+k ∧ j ≤ j+k ∧ j+k ≤ Q ∧ j+k ≤ Q) := by omega + simp only [physicalCouplingCoefficient,dite_eq_right h1,dite_eq_right h2,neg_zero] + +theorem fourBodyCoefficient_antisymmetric (Q r D T p j k : ℕ) (ho : Odd r) : + fourBodyCoefficient Q r D T p k j = -fourBodyCoefficient Q r D T p j k := by + unfold fourBodyCoefficient + rw [Nat.add_comm k j] + by_cases hr : r ≤ j+k + · rw [ite_eq_left hr,ite_eq_left hr,physicalPairCoupling_antisymmetric Q r j k ho] + ring + · rw [ite_eq_right hr,ite_eq_right hr,neg_zero] + +theorem fourBodyLimitCoefficient_antisymmetric (r D T p j k : ℕ) (ho : Odd r) + (hrD : r ≤ D) (hDT : D ≤ T) (hT : p+j+k=T) : + fourBodyLimitCoefficient r D T p k j = -fourBodyLimitCoefficient r D T p j k := by + apply tendsto_nhds_unique (source_fourBody_coefficient_tendsto r D T p k j hrD hDT (by omega)) + have h := (source_fourBody_coefficient_tendsto r D T p j k hrD hDT hT).neg + apply h.congr + intro Q + exact (fourBodyCoefficient_antisymmetric Q r D T p j k ho).symm + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/PhysicalAllowance.lean b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalAllowance.lean new file mode 100644 index 0000000000000000000000000000000000000000..f2f47c8626a561c902d73e2f614ad93520f40cca --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalAllowance.lean @@ -0,0 +1,26 @@ +import OAI.Analysis.Laughlin.FourBody.LocalNormalization +import OAI.Analysis.Laughlin.FourBody.TransferConjugation +import OAI.Analysis.Laughlin.Operators.WeightedOccupationNorm + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators +open Spin + +theorem source_fourBody_normalized_allowance (Q r D : ℕ) (hr : r ≤ D) (hor : Odd r) + (hQ : D+2 ≤ Q) (x : Space Q) : + occupationNormSq Q (physicalFourCopyEnd Q r D (by omega) x) ≤ + ∑ b : LocalFourIndex D, occupationNormSq Q (sourcePairEnd Q b.val.1.val x) := by + simp only [physicalFourCopyEnd,LinearMap.sum_apply,LinearMap.smul_apply] + apply (normalized_occupation_sum_bound Q + (fun b : LocalFourIndex D => fourBodyCoefficient Q r D D b.val.1.val b.val.2.1.val b.val.2.2.val) + (fun b => sourceFourEnd Q b.val.1.val ⟨b.val.2.1.val,by omega⟩ ⟨b.val.2.2.val,by omega⟩ x) + (source_fourBody_local_normalization Q r D hr hor hQ)).trans + apply Finset.sum_le_sum + intro b hb + exact sourceFour_normSq_le_pair Q b.val.1.val _ _ x + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/PhysicalCertificate.lean b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalCertificate.lean new file mode 100644 index 0000000000000000000000000000000000000000..a85b2771a5a2c1d69e91a91ef59bb2ec5e01a571 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalCertificate.lean @@ -0,0 +1,34 @@ +import OAI.Analysis.Laughlin.FourBody.PhysicalGram +import OAI.Analysis.Laughlin.FourBody.ScaledAll + +namespace OAI + +namespace Laughlin.Fock +open scoped Matrix + +noncomputable def physicalLimitGram (Q D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℝ := + fun i j => (occupationInner Q (limitFourColumn Q (Certificate.copyLabel i) D) + (limitFourColumn Q (Certificate.copyLabel j) D)).re + +noncomputable def physicalLimitError (D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℝ := + fun i j => Spin.limitFourError D (Certificate.copyLabel i) (Certificate.copyLabel j) + +theorem physicalLimitGram_eq (Q D : ℕ) (hQ : D+1 ≤ Q) : + physicalLimitGram Q D = Certificate.scaledGram D := by + ext i j + simp [physicalLimitGram,source_fourBody_physical_scaledGram Q D hQ] + +theorem physicalLimitError_eq (D : ℕ) : physicalLimitError D = Certificate.scaledError D := by + ext i j + exact Spin.source_fourBody_error_matrix D i j + +theorem source_physical_four_body_certificates (Q D : ℕ) (hQ : D+1 ≤ Q) + (hD₁ : 1 ≤ D) (hD₂ : D ≤ 23) : + (physicalLimitGram Q D * (Certificate.certificateDiagonal D-physicalLimitError D) * + physicalLimitGram Q D).PosSemidef := by + rw [physicalLimitGram_eq Q D hQ,physicalLimitError_eq] + exact Certificate.scaled_four_body_certificates D hD₁ hD₂ + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/PhysicalColumn.lean b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalColumn.lean new file mode 100644 index 0000000000000000000000000000000000000000..850ca6c2d3ab721a0986b0d7bff9b44941ef624c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalColumn.lean @@ -0,0 +1,67 @@ +import OAI.Analysis.Laughlin.Fock.Bidegree +import OAI.Analysis.Laughlin.FourBody.PhysicalSlaterReadout + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators +open Spin + +noncomputable def limitFourColumn (Q r D : ℕ) : Space Q := + ∑ p ∈ Finset.range (D+1), ∑ j : Fin (Q+1), ∑ k : Fin (Q+1), + ∑ x : Fin (Q+1), ∑ y : Fin (Q+1), + (((limitSliceCoefficient r D p j.val k.val / 2) * + (pairLimitCoefficient p x.val y.val / Real.sqrt 2) : ℝ) : ℂ) • + create x (create y (create j (create k (1 : Space Q)))) + +theorem limitFourColumn_adjoint (Q r D : ℕ) (x : Space Q) : + occupationInner Q (limitFourColumn Q r D) x = occupationInner Q (1 : Space Q) (limitFourCopyEnd Q r D x) := by + simp only [limitFourColumn,limitFourCopyEnd,weightedFourEnd,limitFourEnd,limitPairEnd,pairEnd, + LinearMap.sum_apply,LinearMap.smul_apply,Module.End.mul_apply,map_sum,map_smul, + occupationInner_sum_left,occupationInner_sum_right,occupationInner_smul_left, + occupationInner_smul_right,create_annihilate_adjoint,Complex.star_def,Complex.conj_ofReal] + apply Finset.sum_congr rfl; intro p hp + apply Finset.sum_congr rfl; intro j hj + apply Finset.sum_congr rfl; intro k hk + simp only [Finset.mul_sum] + apply Finset.sum_congr rfl; intro a ha + apply Finset.sum_congr rfl; intro b hb + push_cast + ring + +theorem limitFourColumn_bidegree (Q r D : ℕ) : OccupationBidegree Q 4 (D+1) (limitFourColumn Q r D) := by + intro A hA + simp only [limitFourColumn,map_sum,Finsupp.finsetSum_apply,map_smul,Finsupp.smul_apply,smul_eq_mul] + apply Finset.sum_eq_zero; intro p hp + apply Finset.sum_eq_zero; intro j hj + apply Finset.sum_eq_zero; intro k hk + apply Finset.sum_eq_zero; intro x hx + apply Finset.sum_eq_zero; intro y hy + by_cases hS : p+j.val+k.val=D + · by_cases hP : x.val+y.val=p+1 + · have hv := four_create_bidegree Q x y j k A (by + rcases hA with hA | hA + · exact Or.inl hA + · exact Or.inr (by omega)) + rw [hv,mul_zero] + · simp [pairLimitCoefficient,hP] + · simp [limitSliceCoefficient,hS] + +theorem occupationInner_vacuum (Q : ℕ) : occupationInner Q (1 : Space Q) 1 = 1 := by + rw [← occupation_empty Q] + simp [occupationInner,Module.Basis.repr_self,Finsupp.single_apply] + +theorem limitFourColumn_physical_L (Q r D : ℕ) (hr : r ≤ D) (hor : Odd r) + (a b c d : Fin (Q+1)) (hab : a < b) (hbc : b < c) (hcd : c < d) + (hT : a.val+b.val+c.val+d.val=D+1) : + occupationInner Q (limitFourColumn Q r D) + (create a (create b (create c (create d (1 : Space Q))))) = + ((Real.sqrt (sourceCopyWeight D r / + ((a.val.factorial : ℝ)*b.val.factorial*c.val.factorial*d.val.factorial)) * + (Certificate.L D r (a.val,b.val,c.val,d.val) : ℝ) : ℝ) : ℂ) := by + rw [limitFourColumn_adjoint,source_fourBody_physical_L Q r D hr hor a b c d hab hbc hcd hT, + occupationInner_smul_right,occupationInner_vacuum,mul_one] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/PhysicalGram.lean b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalGram.lean new file mode 100644 index 0000000000000000000000000000000000000000..91e517009771f83811dbdd2da8d9c82d1b79c62b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalGram.lean @@ -0,0 +1,85 @@ +import OAI.Analysis.Laughlin.FourBody.ErrorMatrix +import OAI.Analysis.Laughlin.FourBody.OccupationCoefficient +import OAI.Analysis.Laughlin.Operators.FourOccupationEquiv + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators Matrix +open Spin + +private theorem sqrt_weight_product (u v f : ℝ) (hu : 0 ≤ u) (hv : 0 ≤ v) (hf : 0 ≤ f) : + Real.sqrt (u/f)*Real.sqrt (v/f) = Real.sqrt (u*v)/f := by + rw [Real.sqrt_div hu,Real.sqrt_div hv] + + rw [div_mul_div_comm,Real.mul_self_sqrt hf,← Real.sqrt_mul hu] + +private theorem fourOccupation_product (Q r s D : ℕ) (A : FourOccupation Q D) : + fourOccupationCoefficient Q r D A.val * fourOccupationCoefficient Q s D A.val = + let t := (occupationQuadruple Q D A).val + Real.sqrt (sourceCopyWeight D r * sourceCopyWeight D s) * + ((Certificate.L D r t : ℝ)*(Certificate.L D s t : ℝ) / + ((t.1.factorial : ℝ)*t.2.1.factorial*t.2.2.1.factorial*t.2.2.2.factorial)) := by + simp only [fourOccupationCoefficient,dite_eq_left A.property.1,ite_eq_left A.property.2,occupationQuadruple] + have hr : 0 ≤ sourceCopyWeight D r := by unfold sourceCopyWeight; positivity + have hs : 0 ≤ sourceCopyWeight D s := by unfold sourceCopyWeight; positivity + have hf : 0 ≤ (((occupationFourLabels Q A.val A.property.1 0).val.factorial : ℝ) * + (occupationFourLabels Q A.val A.property.1 1).val.factorial * + (occupationFourLabels Q A.val A.property.1 2).val.factorial * + (occupationFourLabels Q A.val A.property.1 3).val.factorial) := by positivity + rw [show ∀ a b c d : ℝ, (a*b)*(c*d)=(a*c)*(b*d) from by intros; ring, + sqrt_weight_product _ _ _ hr hs hf] + ring + +theorem source_fourBody_physical_Gram (Q r s D : ℕ) (hQ : D+1 ≤ Q) + (hr : r ≤ D) (hs : s ≤ D) (hor : Odd r) (hos : Odd s) : + occupationInner Q (limitFourColumn Q r D) (limitFourColumn Q s D) = + ((Real.sqrt (sourceCopyWeight D r * sourceCopyWeight D s) * + (Certificate.Z D r s : ℝ) : ℝ) : ℂ) := by + classical + rw [limitFourColumn_gram_occupation Q r s D hr hs hor hos] + congr 1 + let P := fun A : Finset (Fin (Q+1)) => A.card=4 ∧ (∑ i ∈ A, i.val)=D+1 + let f := fun A => fourOccupationCoefficient Q r D A * fourOccupationCoefficient Q s D A + have hsum : ∑ A, f A = ∑ A ∈ Finset.univ.filter P, f A := by + symm + apply Finset.sum_subset (Finset.filter_subset _ _) + intro A hA hn + simp only [Finset.mem_filter,Finset.mem_univ,true_and] at hn + by_cases hc : A.card=4 + · have hw : (∑ i ∈ A, i.val) ≠ D+1 := by intro hw; exact hn ⟨hc,hw⟩ + simp [f,fourOccupationCoefficient,hc,hw] + · simp [f,fourOccupationCoefficient,hc] + change ∑ A, f A = _ + rw [hsum,Finset.sum_subtype (p := P) (Finset.univ.filter P) (by simp)] + change (∑ A : FourOccupation Q D, fourOccupationCoefficient Q r D A.val * + fourOccupationCoefficient Q s D A.val) = _ + simp_rw [fourOccupation_product] + rw [← Finset.mul_sum,sum_fourOccupations Q D hQ (fun t => + (Certificate.L D r t : ℝ)*(Certificate.L D s t : ℝ) / + ((t.1.factorial : ℝ)*t.2.1.factorial*t.2.2.1.factorial*t.2.2.2.factorial))] + simp only [Certificate.Z] + push_cast + simp only [List.map_map,Function.comp_def] + push_cast + rfl + +theorem source_fourBody_physical_scaledGram (Q D : ℕ) (hQ : D+1 ≤ Q) + (i j : Fin ((D+1)/2)) : + occupationInner Q (limitFourColumn Q (Certificate.copyLabel i) D) + (limitFourColumn Q (Certificate.copyLabel j) D) = + (Certificate.scaledGram D i j : ℂ) := by + have hi : Certificate.copyLabel i ≤ D := by unfold Certificate.copyLabel; have := i.isLt; omega + have hj : Certificate.copyLabel j ≤ D := by unfold Certificate.copyLabel; have := j.isLt; omega + rw [source_fourBody_physical_Gram Q _ _ D hQ hi hj + ⟨i.val,by unfold Certificate.copyLabel; omega⟩ ⟨j.val,by unfold Certificate.copyLabel; omega⟩, + sourceCopyWeight_certificate,sourceCopyWeight_certificate, + Real.sqrt_mul (Certificate.copyWeight_nonneg D i)] + simp only [Certificate.scaledGram,Certificate.weightSqrtDiagonal,Matrix.diagonal_mul, + Matrix.mul_diagonal,Matrix.map_apply,Certificate.gramRational,Rat.coe_castHom] + push_cast + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/PhysicalMatrix.lean b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalMatrix.lean new file mode 100644 index 0000000000000000000000000000000000000000..d832c934160e29e812aa2d52dc669c2b996863ed --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalMatrix.lean @@ -0,0 +1,36 @@ +import OAI.Analysis.Laughlin.FourBody.ErrorLimit +import OAI.Analysis.Laughlin.FourBody.SignedCoordinates + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +noncomputable def fourBodyTermMatrix (Q t : ℕ) (e f : ℕ × ℕ × ℤ) : + Matrix (Fin (2*Q-2+1) × WedgePairIndex Q) (Fin (2*Q-2+1) × WedgePairIndex Q) ℝ := + -(sourceAlpha t e * sourceAlpha t f) • + realOuter (fourSignedUnit Q e.1 e.2.1 (f.1+f.2.1-t)) + (fourSignedUnit Q f.1 f.2.1 (e.1+e.2.1-t)) + +noncomputable def physicalFourBodyMatrix (Q : ℕ) : + Matrix (Fin (2*Q-2+1) × WedgePairIndex Q) (Fin (2*Q-2+1) × WedgePairIndex Q) ℝ := + (Certificate.rows.map (fun row => (row.2.2.map (fun e => + (row.2.2.map (fun f => fourBodyTermMatrix Q row.1 e f)).sum)).sum)).sum + +theorem trace_cross_outer {I J : Type*} [Fintype I] [Fintype J] + (V W : Matrix I J ℝ) (u v : I → ℝ) : + Matrix.trace (Vᵀ * realOuter u v * W) = + ∑ n, dotProduct (fun i => V i n) u * dotProduct (fun i => W i n) v := by + simp only [Matrix.trace,Matrix.diag,Matrix.mul_apply,Matrix.transpose_apply,realOuter, + dotProduct,Finset.sum_mul,Finset.mul_sum] + apply Finset.sum_congr rfl + intro n hn + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/PhysicalSlaterReadout.lean b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalSlaterReadout.lean new file mode 100644 index 0000000000000000000000000000000000000000..6404b3d858fda172c0d62ba9eb48d0ca1eb05452 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalSlaterReadout.lean @@ -0,0 +1,44 @@ +import OAI.Analysis.Laughlin.FourBody.SliceCoefficient +import OAI.Analysis.Laughlin.FourBody.WeightedReadout + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators +open Spin + +noncomputable def limitFourCopyEnd (Q r D : ℕ) : Module.End ℂ (Space Q) := + ∑ p ∈ Finset.range (D+1), weightedFourEnd Q p (fun j k => limitSliceCoefficient r D p j.val k.val) + +theorem limitFourCopyEnd_Slater_readout (Q r D : ℕ) (hr : r ≤ D) (hor : Odd r) + (a b c d : Fin (Q+1)) (hab : a < b) (hbc : b < c) (hcd : c < d) + (hT : a.val+b.val+c.val+d.val=D+1) : + limitFourCopyEnd Q r D (create a (create b (create c (create d (1 : Space Q))))) = + (limitSlaterCoefficient D r a.val b.val c.val d.val : ℂ) • (1 : Space Q) := by + simp only [limitFourCopyEnd,LinearMap.sum_apply] + simp_rw [weightedFourEnd_readout Q _ _ + (fun j k => limitSliceCoefficient_antisymmetric r D _ j.val k.val hr hor)] + rw [← Finset.sum_smul,← Complex.ofReal_sum] + apply congrArg (fun v : ℝ => (v : ℂ) • (1 : Space Q)) + simp only [Finset.sum_sub_distrib,Finset.sum_add_distrib] + rw [sum_pairLimit_slice D r a.val b.val c.val d.val hab hT, + sum_pairLimit_slice D r a.val c.val b.val d.val (by exact_mod_cast lt_trans hab hbc) (by omega), + sum_pairLimit_slice D r a.val d.val b.val c.val (by exact_mod_cast lt_trans hab (lt_trans hbc hcd)) (by omega), + sum_pairLimit_slice D r b.val c.val a.val d.val hbc (by omega), + sum_pairLimit_slice D r b.val d.val a.val c.val (by exact_mod_cast lt_trans hbc hcd) (by omega), + sum_pairLimit_slice D r c.val d.val a.val b.val hcd (by omega)] + rfl + +theorem source_fourBody_physical_L (Q r D : ℕ) (hr : r ≤ D) (hor : Odd r) + (a b c d : Fin (Q+1)) (hab : a < b) (hbc : b < c) (hcd : c < d) + (hT : a.val+b.val+c.val+d.val=D+1) : + limitFourCopyEnd Q r D (create a (create b (create c (create d (1 : Space Q))))) = + ((Real.sqrt (sourceCopyWeight D r / + ((a.val.factorial : ℝ)*b.val.factorial*c.val.factorial*d.val.factorial)) * + (Certificate.L D r (a.val,b.val,c.val,d.val) : ℝ) : ℝ) : ℂ) • (1 : Space Q) := by + rw [limitFourCopyEnd_Slater_readout Q r D hr hor a b c d hab hbc hcd hT, + source_fourBody_Slater_coefficient D r a.val b.val c.val d.val hr hor hab hbc hcd hT] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/PhysicalTrace.lean b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalTrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..63d8f58b5fa823e03c782be8609decbaefbb79b0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/PhysicalTrace.lean @@ -0,0 +1,71 @@ +import OAI.Analysis.Laughlin.FourBody.MultiplicityHaar +import OAI.Analysis.Laughlin.FourBody.TraceReadout + +namespace OAI + +namespace Laughlin.Spin +open Rotation +open scoped BigOperators Matrix + +theorem trace_sandwich_list_sum {I J : Type*} [Fintype I] [Fintype J] + (V W : Matrix I J ℝ) (l : List (Matrix I I ℝ)) : + Matrix.trace (Vᵀ*l.sum*W) = (l.map (fun M => Matrix.trace (Vᵀ*M*W))).sum := by + induction l with + | nil => simp + | cons a l ih => + simp only [List.sum_cons,List.map_cons,Matrix.mul_add,Matrix.add_mul,Matrix.trace_add,ih] + +theorem negative_list_sum {I : Type*} (l : List I) (a b : I → ℝ) + (h : ∀ i ∈ l, a i = -b i) : (l.map a).sum = -(l.map b).sum := by + induction l with + | nil => simp + | cons i l ih => + simp only [List.map_cons,List.sum_cons,h i (by simp),ih (fun j hj => h j (by simp [hj]))] + ring + +theorem source_fourBody_rows_support : ∀ row ∈ Certificate.rows, ∀ e ∈ row.2.2, ∀ f ∈ row.2.2, + e.1+e.2.1+(f.1+f.2.1-row.1) ≤ 23 := by decide + +theorem source_physical_fourBody_trace_identity (Q D : ℕ) (hQ : 25 ≤ Q) (hD : D+2 ≤ Q) + (r s : OddPairLabel D) : + Matrix.trace ((retainedFourReal Q D hD r)ᵀ * physicalFourBodyMatrix Q * retainedFourReal Q D hD s) = + physicalFourError Q D (oddPairDeficit r) (oddPairDeficit s) := by + unfold physicalFourBodyMatrix physicalFourError + rw [trace_sandwich_list_sum] + simp only [List.map_map,Function.comp_def] + apply negative_list_sum + intro row hrow + unfold fourErrorRow + rw [trace_sandwich_list_sum] + simp only [List.map_map,Function.comp_def] + apply negative_list_sum + intro e he + rw [trace_sandwich_list_sum] + simp only [List.map_map,Function.comp_def] + apply negative_list_sum + intro f hf + exact fourBodyTermMatrix_trace Q D row.1 hD r s e f + (source_rows_admissible row hrow e he) (source_rows_admissible row hrow f hf) + (by have := source_fourBody_rows_support row hrow e he f hf; omega) + +theorem trace_real_sandwich_complex {I J : Type*} [Fintype I] [Fintype J] + (V W : Matrix I J ℝ) (M : Matrix I I ℝ) : + Matrix.trace ((V.map Complex.ofReal)ᴴ*M.map Complex.ofReal*W.map Complex.ofReal) = + Complex.ofReal (Matrix.trace (Vᵀ*M*W)) := by + simp only [Matrix.trace,Matrix.diag,Matrix.mul_apply,Matrix.conjTranspose_apply, + Matrix.transpose_apply,Matrix.map_apply,Complex.star_def,Complex.conj_ofReal, + Complex.ofReal_sum,Complex.ofReal_mul] + +theorem physical_fourBody_haar_multiplicity (Q D : ℕ) (hQ : 25 ≤ Q) (hD : D+2 ≤ Q) + (r s : OddPairLabel D) : + (retainedFourInclusion Q D hD r)ᴴ * matrixIntegral sourceHaar + (conjugateOrbit (fourBodySpinRepresentation Q) ((physicalFourBodyMatrix Q).map Complex.ofReal)) * + retainedFourInclusion Q D hD s = + ((physicalFourError Q D (oddPairDeficit r) (oddPairDeficit s) : ℂ) / (4*Q-1-2*D : ℕ)) • 1 := by + rw [fourBody_haar_multiplicity_block,← retainedFourReal_complex Q D hD r, + ← retainedFourReal_complex Q D hD s,trace_real_sandwich_complex, + source_physical_fourBody_trace_identity Q D hQ hD] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Quadruples.lean b/lean/OAI/Analysis/Laughlin/FourBody/Quadruples.lean new file mode 100644 index 0000000000000000000000000000000000000000..cc83f581f527eee2b657c6d5c3e54109601921bb --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Quadruples.lean @@ -0,0 +1,77 @@ +import Mathlib.Data.List.Nodup +import OAI.Analysis.Laughlin.FourBody.Basic + +namespace OAI + +namespace Laughlin.Certificate + +private def quadTail (D a b : ℕ) := + (List.range (D+2)).filterMap (fun c => + let d := D+1-a-b-c + if a (List.range (D+2)).flatMap (quadTail D x)) ↔ _ + simp only [List.mem_flatMap,List.mem_range,mem_quadTail] + constructor + · rintro ⟨x,hx,y,hy,rfl,rfl,h⟩ + exact h + · rintro ⟨hab,hbc,hcd,hs⟩ + exact ⟨a,by omega,b,by omega,rfl,rfl,hab,hbc,hcd,hs⟩ + +private theorem quadTail_nodup (D a b : ℕ) : (quadTail D a b).Nodup := by + apply List.Nodup.filterMap _ List.nodup_range + intro c c' t hc hc' + dsimp only at hc hc' + split_ifs at hc with h + · split_ifs at hc' with h' + · simp only [Option.mem_def,Option.some.injEq] at hc hc' + have he := hc.trans hc'.symm + exact congrArg (fun u : ℕ×ℕ×ℕ×ℕ => u.2.2.1) he + · simp at hc' + · simp at hc + +theorem quadruples_nodup (D : ℕ) : (quadruples D).Nodup := by + change ((List.range (D+2)).flatMap + (fun a => (List.range (D+2)).flatMap (quadTail D a))).Nodup + apply List.nodup_flatMap.mpr + constructor + · intro a ha + apply List.nodup_flatMap.mpr + constructor + · intro b hb; exact quadTail_nodup D a b + · apply List.nodup_range.imp + intro b b' hne t ht ht' + obtain ⟨x,y,z,w⟩ := t + have h := (mem_quadTail D a b x y z w).mp ht + have h' := (mem_quadTail D a b' x y z w).mp ht' + exact hne (h.2.1.symm.trans h'.2.1) + · apply List.nodup_range.imp + intro a a' hne t ht ht' + obtain ⟨b,hb,ht⟩ := List.mem_flatMap.mp ht + obtain ⟨b',hb',ht'⟩ := List.mem_flatMap.mp ht' + obtain ⟨x,y,z,w⟩ := t + have h := (mem_quadTail D a b x y z w).mp ht + have h' := (mem_quadTail D a' b' x y z w).mp ht' + exact hne (h.1.symm.trans h'.1) + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/RadicalCancellation.lean b/lean/OAI/Analysis/Laughlin/FourBody/RadicalCancellation.lean new file mode 100644 index 0000000000000000000000000000000000000000..0667a906bd8d4dec87eab7e047f90ae01eed60bd --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/RadicalCancellation.lean @@ -0,0 +1,78 @@ +import OAI.Analysis.Laughlin.FourBody.RadicalCoefficient + +namespace OAI + +namespace Laughlin.Spin + +noncomputable def alphaRadical (t p j : ℕ) : ℝ := + Real.sqrt ((2 : ℝ)^((p : ℤ)-t) * ((t.factorial : ℝ)*((p+j-t).factorial : ℝ) / + ((p.factorial : ℝ)*(j.factorial : ℝ)))) +noncomputable def sourceCopyWeight (D r : ℕ) : ℝ := + 1 / ((r.factorial : ℝ)*((D-r).factorial : ℝ)) +noncomputable def sourceYFactor (D r s t p j q l : ℕ) : ℝ := + let i := p+j-t + let k := q+l-t + let T := p+j+k + (2 : ℝ)^((1 : ℤ)-2*T+p+q-t+((r+s)/2 : ℕ)) * + ((i.factorial : ℝ)*(k.factorial : ℝ)*(t.factorial : ℝ) / ((T-D).factorial : ℝ)) + +theorem source_Y_radical_cancellation (D r s t p j q l : ℕ) + (hor : Odd r) (hos : Odd s) (he : t ≤ p+j) (hf : t ≤ q+l) : + alphaRadical t p j * alphaRadical t q l * + fourBodyRadical r D (p+j+(q+l-t)) p j (q+l-t) * + fourBodyRadical s D (p+j+(q+l-t)) q l (p+j-t) = + Real.sqrt (sourceCopyWeight D r * sourceCopyWeight D s) * sourceYFactor D r s t p j q l := by + let i := p+j-t + let k := q+l-t + let T := p+j+k + let e : ℤ := 1-2*(T : ℤ)+p+q-t+((r+s)/2 : ℕ) + have hT : p+j+k=T := rfl + have hT' : q+l+i=T := by dsimp [i,k,T]; omega + have hTr : (p : ℤ)+j+k=T := by exact_mod_cast hT + have hTr' : (q : ℤ)+l+i=T := by exact_mod_cast hT' + have heven : (((r+s)/2 : ℕ) : ℤ)*2=(r : ℤ)+s := by + rcases hor with ⟨a,ha⟩; rcases hos with ⟨b,hb⟩ + omega + have hex : ((p : ℤ)-t)+((q : ℤ)-t)+((1 : ℤ)-j-k-T+r)+((1 : ℤ)-l-i-T+s)=e*2 := by + dsimp [e]; omega + have hpowers : (2 : ℝ)^((p : ℤ)-t) * (2 : ℝ)^((q : ℤ)-t) * + (2 : ℝ)^((1 : ℤ)-j-k-T+r) * (2 : ℝ)^((1 : ℤ)-l-i-T+s) = ((2 : ℝ)^e)^2 := by + rw [← zpow_add₀ (by norm_num : (2 : ℝ) ≠ 0),← zpow_add₀ (by norm_num : (2 : ℝ) ≠ 0), + ← zpow_add₀ (by norm_num : (2 : ℝ) ≠ 0),hex,zpow_mul] + norm_num + let F : ℝ := ((i.factorial : ℝ)*(k.factorial : ℝ)*(t.factorial : ℝ))^2 / + ((r.factorial : ℝ)*((D-r).factorial : ℝ)*(s.factorial : ℝ)*((D-s).factorial : ℝ)*((T-D).factorial : ℝ)^2) + have hsq : (alphaRadical t p j * alphaRadical t q l * fourBodyRadical r D T p j k * + fourBodyRadical s D T q l i)^2 = + (Real.sqrt (sourceCopyWeight D r * sourceCopyWeight D s) * sourceYFactor D r s t p j q l)^2 := by + simp only [alphaRadical,fourBodyRadical,mul_pow] + have hc0 : 0 ≤ sourceCopyWeight D r * sourceCopyWeight D s := by + unfold sourceCopyWeight; positivity + rw [Real.sq_sqrt hc0] + repeat rw [Real.sq_sqrt (by positivity)] + change (2^((p : ℤ)-t)*((t.factorial : ℝ)*i.factorial/(p.factorial*j.factorial))) * + (2^((q : ℤ)-t)*((t.factorial : ℝ)*k.factorial/(q.factorial*l.factorial))) * + (2^((1 : ℤ)-j-k-T+r)*((j.factorial : ℝ)*k.factorial*p.factorial / + (r.factorial*(D-r).factorial*(T-D).factorial))) * + (2^((1 : ℤ)-l-i-T+s)*((l.factorial : ℝ)*i.factorial*q.factorial / + (s.factorial*(D-s).factorial*(T-D).factorial))) = _ + calc + _ = (2^((p : ℤ)-t)*2^((q : ℤ)-t)*2^((1 : ℤ)-j-k-T+r)*2^((1 : ℤ)-l-i-T+s))*F := by + dsimp [F] + field_simp + _ = ((2 : ℝ)^e)^2*F := by rw [hpowers] + _ = _ := by + dsimp [F,sourceYFactor,sourceCopyWeight] + change ((2 : ℝ)^e)^2 * _ = (1/((r.factorial : ℝ)*(D-r).factorial) * + (1/((s.factorial : ℝ)*(D-s).factorial))) * + ((2 : ℝ)^e * ((i.factorial : ℝ)*k.factorial*t.factorial/(T-D).factorial))^2 + field_simp + have hl : 0 ≤ alphaRadical t p j * alphaRadical t q l * fourBodyRadical r D T p j k * + fourBodyRadical s D T q l i := by unfold alphaRadical fourBodyRadical; positivity + have hr : 0 ≤ Real.sqrt (sourceCopyWeight D r * sourceCopyWeight D s) * sourceYFactor D r s t p j q l := by + unfold sourceYFactor; positivity + nlinarith only [hsq,hl,hr] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/RadicalCoefficient.lean b/lean/OAI/Analysis/Laughlin/FourBody/RadicalCoefficient.lean new file mode 100644 index 0000000000000000000000000000000000000000..c2542d8be4ac83e315cbe43948aa0e6295da7e05 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/RadicalCoefficient.lean @@ -0,0 +1,55 @@ +import OAI.Analysis.Laughlin.FourBody.FactorialCoefficient + +namespace OAI + +namespace Laughlin.Spin + +noncomputable def fourBodyRadical (r D T p j k : ℕ) : ℝ := + Real.sqrt ((2 : ℝ)^((1 : ℤ)-(j : ℤ)-k-T+r) * + ((j.factorial : ℝ)*(k.factorial : ℝ)*(p.factorial : ℝ) / + ((r.factorial : ℝ)*((D-r).factorial : ℝ)*((T-D).factorial : ℝ)))) + +theorem fourBodyRadical_factorial (r D T p j k : ℕ) (hr : r ≤ T) : + fourBodyRadical r D T p j k = + Real.sqrt 2 * (Real.sqrt (1/2))^(j+k+(T-r)) * + sqrtFactorial j * sqrtFactorial k * sqrtFactorial p / + (sqrtFactorial r * sqrtFactorial (D-r) * sqrtFactorial (T-D)) := by + let m := j+k+(T-r) + have hm : (1 : ℤ)-(j : ℤ)-k-T+r = 1-(m : ℤ) := by + dsimp [m] + simp only [Nat.cast_sub hr] + omega + have hp : (2 : ℝ)^((1 : ℤ)-(j : ℤ)-k-T+r) = 2*(1/2 : ℝ)^m := by + rw [hm,zpow_sub₀ (by norm_num : (2 : ℝ) ≠ 0),zpow_one,zpow_natCast] + simp [div_eq_mul_inv] + let a := Real.sqrt 2 * (Real.sqrt (1/2))^m * + sqrtFactorial j * sqrtFactorial k * sqrtFactorial p / + (sqrtFactorial r * sqrtFactorial (D-r) * sqrtFactorial (T-D)) + have ha : 0 ≤ a := by dsimp [a]; unfold sqrtFactorial; positivity + have hs : a^2 = (2 : ℝ)^((1 : ℤ)-(j : ℤ)-k-T+r) * + ((j.factorial : ℝ)*(k.factorial : ℝ)*(p.factorial : ℝ) / + ((r.factorial : ℝ)*((D-r).factorial : ℝ)*((T-D).factorial : ℝ))) := by + rw [hp] + dsimp [a] + simp only [div_pow,mul_pow,sqrtFactorial] + rw [show ((Real.sqrt (1/2))^m)^2 = (1/2 : ℝ)^m by + rw [← pow_mul,mul_comm m 2,pow_mul,Real.sq_sqrt (by norm_num)]] + simp only [Real.sq_sqrt (by norm_num : (0 : ℝ) ≤ 2),Real.sq_sqrt (Nat.cast_nonneg _)] + ring_nf + norm_num + change Real.sqrt _ = a + rw [← hs,Real.sqrt_sq ha] + +theorem source_fourBody_radical_coefficient (r D T p j k : ℕ) + (hrD : r ≤ D) (hDT : D ≤ T) (hT : p+j+k=T) : + fourBodyLimitCoefficient r D T p j k = + (Certificate.V r D T p j k : ℝ) * fourBodyRadical r D T p j k := by + by_cases hr : r ≤ j+k + · rw [source_fourBody_factorial_coefficient r D T p j k hrD hDT hT hr, + fourBodyRadical_factorial r D T p j k (by omega)] + ring + · simp [fourBodyLimitCoefficient,Certificate.V,hr] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/RetainedComparison.lean b/lean/OAI/Analysis/Laughlin/FourBody/RetainedComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..99639c8b777deb212a943ba7f473999ef9c48017 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/RetainedComparison.lean @@ -0,0 +1,56 @@ +import OAI.Analysis.Laughlin.FourBody.CopyFormAllowance +import OAI.Analysis.Laughlin.FourBody.GlobalFock +import OAI.Analysis.Laughlin.FourBody.MiddleForm +import OAI.Analysis.Laughlin.FourBody.TotalTransfer + +namespace OAI + +namespace Laughlin.Fock +open Spin Rotation MeasureTheory +open scoped BigOperators Matrix + +noncomputable def retainedFourTarget (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : ℝ := + ∑ d : Fin 23, (contractionForm Q (sourceFourFamilyEnd Q) + (retainedFourInclusion Q (d.val+1) (by omega) (firstOddPairLabel (d.val+1) (by omega)) * + (retainedFourInclusion Q (d.val+1) (by omega) (firstOddPairLabel (d.val+1) (by omega)))ᴴ) x).re + +theorem fourCopyForm_scaled_haar (Q D : ℕ) (hQ : D+2 ≤ Q) + (C : OddPairLabel D → OddPairLabel D → ℝ) (x : Space Q) : + (((2*Q-2+1 : ℕ) : ℝ)/((4*Q-1-2*D : ℕ) : ℝ)) * + (contractionForm Q (sourceFourFamilyEnd Q) (fourCopyOperator Q D hQ C) x).re = + ((2*Q-2+1 : ℕ) : ℝ) * (∫ g, occupationQuadratic Q C + (fun r => physicalFourCopyEnd Q (oddPairDeficit r) D (by omega) + (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) := by + rw [← physical_fourCopyOperator_haar Q D hQ C x] + have hd : ((4*Q-1-2*D : ℕ) : ℝ) ≠ 0 := by exact_mod_cast (show 4*Q-1-2*D ≠ 0 by omega) + field_simp + +theorem sourceA4Form_retained_bound (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + sourceA4Form Q x ≤ retainedFourTarget Q hQ x + + (10946*(3/10^6 : ℝ)+averagedFourTransferError Q)*sourceFockEnergy Q x := by + have ht := physical_fourBody_total_haar_transfer Q hQ x + have ha := retainedFourAllowance_bound Q hQ x + have he : (∑ d : Fin 23, + (((2*Q-2+1 : ℕ) : ℝ)/((4*Q-1-2*(d.val+1) : ℕ) : ℝ)) * + (contractionForm Q (sourceFourFamilyEnd Q) + (fourCopyOperator Q (d.val+1) (by omega) (finiteFourMiddle Q (d.val+1))) x).re) = + retainedFourTarget Q hQ x+(3/10^6 : ℝ)*retainedFourAllowance Q hQ x-sourceA4Form Q x := by + conv_lhs => arg 2; ext d; erw [fourCopyMiddleForm Q _ (by omega) (by omega) x] + rw [Finset.sum_sub_distrib,Finset.sum_add_distrib,sourceA4Form_retained Q hQ x] + unfold retainedFourTarget retainedFourAllowance + rw [Finset.mul_sum] + congr 1 + congr 1 + apply Finset.sum_congr rfl + intro d hd + ring + have hi : -(averagedFourTransferError Q*sourceFockEnergy Q x) ≤ + retainedFourTarget Q hQ x+(3/10^6 : ℝ)*retainedFourAllowance Q hQ x-sourceA4Form Q x := by + rw [← he] + conv_rhs => arg 2; ext d; erw [fourCopyForm_scaled_haar] + exact ht + nlinarith + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/RetainedInclusions.lean b/lean/OAI/Analysis/Laughlin/FourBody/RetainedInclusions.lean new file mode 100644 index 0000000000000000000000000000000000000000..2b75fcd6b669a06659a406bbca0695445f85e75b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/RetainedInclusions.lean @@ -0,0 +1,69 @@ +import OAI.Analysis.Laughlin.FourBody.GroupIntertwining + +namespace OAI + +namespace Laughlin.Spin +open Rotation +open scoped BigOperators Matrix + +noncomputable def castSpinColumns {I : Type*} (m n : ℕ) (h : m=n) + (W : Matrix I (Fin (m+1)) ℂ) : Matrix I (Fin (n+1)) ℂ := + fun i j => W i (Fin.cast (congrArg (fun k => k+1) h.symm) j) + +theorem castSpinColumns_SU2 {I : Type*} [Fintype I] + (m n : ℕ) (h : m=n) (W : Matrix I (Fin (m+1)) ℂ) + (R : Matrix I I ℂ) (g : SourceSU2) + (hW : R*W=W*sourceSpinRepresentation m g) : + R*castSpinColumns m n h W = castSpinColumns m n h W*sourceSpinRepresentation n g := by + subst n + exact hW + +theorem castSpinColumns_isometry {I : Type*} [Fintype I] + (m n : ℕ) (h : m=n) (W : Matrix I (Fin (m+1)) ℂ) (hW : Wᴴ*W=1) : + (castSpinColumns m n h W)ᴴ*castSpinColumns m n h W=1 := by + subst n + exact hW + +def fourSpinWeight (Q D : ℕ) : ℕ := 4*Q-2-2*D + +theorem four_nested_weight (Q D r : ℕ) (hQ : D+2 ≤ Q) (hr : r ≤ D) : + genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q r) (D-r) = fourSpinWeight Q D := by + unfold genericCoupledWeight fourSpinWeight + omega + +theorem fourSpinWeight_dimension (Q D : ℕ) (hQ : D+2 ≤ Q) : + fourSpinWeight Q D+1=4*Q-1-2*D := by unfold fourSpinWeight; omega + +noncomputable def retainedFourInclusion (Q D : ℕ) (hQ : D+2 ≤ Q) (r : OddPairLabel D) : + Matrix (FourWedgeIndex Q) (Fin (fourSpinWeight Q D+1)) ℂ := + castSpinColumns _ _ (four_nested_weight Q D (oddPairDeficit r) hQ (oddPairDeficit_le r)) + (fourWedgeInclusion Q (oddPairDeficit r) D + (by have := oddPairDeficit_le r; omega) + (by have := oddPairDeficit_le r; omega) + (by have := oddPairDeficit_le r; unfold genericCoupledWeight; omega)) + +theorem retainedFourInclusion_column (Q D : ℕ) (hQ : D+2 ≤ Q) (r : OddPairLabel D) + (n : Fin (fourSpinWeight Q D+1)) (i : FourWedgeIndex Q) : + retainedFourInclusion Q D hQ r i n = + (fourBodyCopy Q (oddPairDeficit r) D + (by have := oddPairDeficit_le r; omega) + (by have := oddPairDeficit_le r; omega) + (by have := oddPairDeficit_le r; unfold genericCoupledWeight; omega) n.val i : ℂ) := rfl + +theorem retainedFourInclusion_SU2 (Q D : ℕ) (hQ : D+2 ≤ Q) (r : OddPairLabel D) + (g : SourceSU2) : + fourBodySpinRepresentation Q g * retainedFourInclusion Q D hQ r = + retainedFourInclusion Q D hQ r * sourceSpinRepresentation (fourSpinWeight Q D) g := by + unfold retainedFourInclusion + apply castSpinColumns_SU2 + exact fourWedgeInclusion_SU2 Q (oddPairDeficit r) D _ (oddPairDeficit_odd r) _ _ g + +theorem retainedFourInclusion_isometry (Q D : ℕ) (hQ : D+2 ≤ Q) (r : OddPairLabel D) : + (retainedFourInclusion Q D hQ r)ᴴ * retainedFourInclusion Q D hQ r = 1 := by + unfold retainedFourInclusion + apply castSpinColumns_isometry + exact fourWedgeInclusion_isometry Q (oddPairDeficit r) D _ (oddPairDeficit_odd r) _ _ + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/RetainedIndex.lean b/lean/OAI/Analysis/Laughlin/FourBody/RetainedIndex.lean new file mode 100644 index 0000000000000000000000000000000000000000..adb2ecaa8e2e2dd4d7f18c8b49907feaca4970e8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/RetainedIndex.lean @@ -0,0 +1,74 @@ +import OAI.Analysis.Laughlin.FourBody.RetainedInclusions + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +def fourCoupledDeficit {Q : ℕ} (s : FourCoupledIndex Q) : ℕ := + oddPairDeficit s.1+s.2.1.val + +def retainedFourIndex (Q D : ℕ) (hQ : D+2 ≤ Q) + (r : OddPairLabel D) (n : Fin (fourSpinWeight Q D+1)) : FourCoupledIndex Q := + ⟨⟨r.val, by have := r.isLt; omega⟩, + ⟨⟨D-oddPairDeficit r, by + have := oddPairDeficit_le r + dsimp [genericCoupledWeight,oddPairDeficit] at * + omega⟩, + ⟨n.val, by + have h := four_nested_weight Q D (oddPairDeficit r) hQ (oddPairDeficit_le r) + change n.val < genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q (oddPairDeficit r)) (D-oddPairDeficit r)+1 + rw [h] + exact n.isLt⟩⟩⟩ + +theorem retainedFourIndex_deficit (Q D : ℕ) (hQ : D+2 ≤ Q) + (r : OddPairLabel D) (n : Fin (fourSpinWeight Q D+1)) : + fourCoupledDeficit (retainedFourIndex Q D hQ r n) = D := by + dsimp [fourCoupledDeficit,retainedFourIndex] + have := oddPairDeficit_le r + dsimp [oddPairDeficit] at * + omega + +theorem retainedFourIndex_column (Q D : ℕ) (hQ : D+2 ≤ Q) + (r : OddPairLabel D) (n : Fin (fourSpinWeight Q D+1)) (i : FourWedgeIndex Q) : + (fourCoupledBasis Q i (retainedFourIndex Q D hQ r n) : ℂ) = + retainedFourInclusion Q D hQ r i n := by + have hd := retainedFourIndex_deficit Q D hQ r n + change (fourBodyCopy Q (oddPairDeficit r) _ _ _ _ n.val i : ℂ) = _ + rw [retainedFourInclusion_column] + unfold fourCoupledDeficit at hd + simp only [hd] + +def retainedFourIndexEquiv (Q D : ℕ) (hQ : D+2 ≤ Q) : + (OddPairLabel D × Fin (fourSpinWeight Q D+1)) ≃ + {s : FourCoupledIndex Q // fourCoupledDeficit s = D} where + toFun x := ⟨retainedFourIndex Q D hQ x.1 x.2,retainedFourIndex_deficit Q D hQ x.1 x.2⟩ + invFun s := + (⟨s.val.1.val, by have := s.property; dsimp [fourCoupledDeficit,oddPairDeficit] at *; omega⟩, + ⟨s.val.2.2.val, by + have hd := s.property + have hw := four_nested_weight Q D (oddPairDeficit s.val.1) hQ + (by dsimp [fourCoupledDeficit] at hd; omega) + have hz : D-oddPairDeficit s.val.1=s.val.2.1.val := by + dsimp [fourCoupledDeficit] at hd; omega + rw [hz] at hw + rw [← hw] + exact s.val.2.2.isLt⟩) + left_inv x := by apply Prod.ext <;> apply Fin.ext <;> rfl + right_inv s := by + apply Subtype.ext + rcases s with ⟨⟨r,⟨z,n⟩⟩,hd⟩ + dsimp [fourCoupledDeficit] at hd + have hz : D-oddPairDeficit r=z.val := by omega + dsimp [retainedFourIndex] + congr 2 + · exact Fin.ext hz + · apply (Fin.heq_ext_iff (by congr 2)).mpr + rfl + +theorem fourCoupledDeficit_pos {Q : ℕ} (s : FourCoupledIndex Q) : + 1 ≤ fourCoupledDeficit s := by dsimp [fourCoupledDeficit,oddPairDeficit]; omega + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/RetainedReconstruction.lean b/lean/OAI/Analysis/Laughlin/FourBody/RetainedReconstruction.lean new file mode 100644 index 0000000000000000000000000000000000000000..4c28722b6e16b8673653eb9d60f34179c03e4cd3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/RetainedReconstruction.lean @@ -0,0 +1,48 @@ +import OAI.Analysis.Laughlin.FourBody.RetainedSum +import OAI.Analysis.Laughlin.FourBody.Support + +namespace OAI + +namespace Laughlin.Spin +open Rotation +open scoped BigOperators Matrix + +theorem fourBody_retained_reconstruction (Q : ℕ) (hQ : 25 ≤ Q) + (A : Matrix (FourWedgeIndex Q) (FourWedgeIndex Q) ℂ) + (hz : ∀ s : FourCoupledIndex Q, 23 < fourCoupledDeficit s → + A *ᵥ (fun i => (fourCoupledBasis Q i s : ℂ)) = 0) : + A = ∑ d : Fin 23, ∑ r : OddPairLabel (d.val+1), + A * retainedFourInclusion Q (d.val+1) (by omega) r * + (retainedFourInclusion Q (d.val+1) (by omega) r)ᴴ := by + classical + have hc : A = (A * (fourCoupledBasis Q).map Complex.ofReal) * + ((fourCoupledBasis Q).map Complex.ofReal)ᴴ := by + rw [Matrix.mul_assoc,fourCoupledBasis_complex_complete,Matrix.mul_one] + ext i j + have he := congrFun (congrFun hc i) j + simp only [Matrix.mul_apply,Matrix.map_apply,Matrix.conjTranspose_apply] at he + rw [he] + rw [sum_fourCoupled_retained Q hQ + (fun s => (∑ k, A i k*(fourCoupledBasis Q k s : ℂ))*star (fourCoupledBasis Q j s : ℂ)) + (by intro s hs; have h := congrFun (hz s hs) i; change (∑ k, A i k*_) = 0 at h; rw [h,zero_mul])] + simp only [Matrix.sum_apply,Matrix.mul_apply,Matrix.conjTranspose_apply,retainedFourIndex_column] + +theorem physicalFourBodyHaar_high_column (Q : ℕ) (s : FourCoupledIndex Q) + (hs : 23 < fourCoupledDeficit s) : + matrixIntegral sourceHaar + (conjugateOrbit (fourBodySpinRepresentation Q) ((physicalFourBodyMatrix Q).map Complex.ofReal)) *ᵥ + (fun i => (fourCoupledBasis Q i s : ℂ)) = 0 := by + let r := oddPairDeficit s.1 + let D := r+s.2.1.val + have he := physicalFourBodyHaar_high_copy Q r D (oddPairDeficit_le s.1) + (oddPairDeficit_odd s.1) (by dsimp [D,r]; omega) + (by have := s.2.1.isLt; dsimp [D,r]; omega) + (by have := s.2.1.isLt; dsimp [D,r]; omega) hs + let n : Fin (genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q r) (D-r)+1) := + ⟨s.2.2.val,by simpa only [D,Nat.add_sub_cancel_left] using s.2.2.isLt⟩ + funext i + exact congrFun (congrFun he i) n + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/RetainedSum.lean b/lean/OAI/Analysis/Laughlin/FourBody/RetainedSum.lean new file mode 100644 index 0000000000000000000000000000000000000000..5c2682e2ff74ae054c8ae25df0be195adfac7bd9 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/RetainedSum.lean @@ -0,0 +1,59 @@ +import OAI.Analysis.Laughlin.FourBody.RetainedIndex + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +abbrev RetainedFourColumns (Q : ℕ) := + Σ d : Fin 23, OddPairLabel (d.val+1) × Fin (fourSpinWeight Q (d.val+1)+1) + +noncomputable def retainedFourColumnsEquiv (Q : ℕ) (hQ : 25 ≤ Q) : + RetainedFourColumns Q ≃ {s : FourCoupledIndex Q // fourCoupledDeficit s ≤ 23} := by + let f : RetainedFourColumns Q → {s : FourCoupledIndex Q // fourCoupledDeficit s ≤ 23} := + fun x => ⟨retainedFourIndex Q (x.1.val+1) (by have := x.1.isLt; omega) x.2.1 x.2.2, + by rw [retainedFourIndex_deficit]; have := x.1.isLt; omega⟩ + apply Equiv.ofBijective f + constructor + · rintro ⟨d,x⟩ ⟨e,y⟩ h + have hv := congrArg (fun s => fourCoupledDeficit s.val) h + change fourCoupledDeficit (retainedFourIndex Q _ (by omega) x.1 x.2) = + fourCoupledDeficit (retainedFourIndex Q _ (by omega) y.1 y.2) at hv + simp only [retainedFourIndex_deficit] at hv + have hd : d=e := Fin.ext (by omega) + subst e + have he : (retainedFourIndexEquiv Q (d.val+1) (by omega)) x = + (retainedFourIndexEquiv Q (d.val+1) (by omega)) y := by + apply Subtype.ext + exact congrArg (fun s => s.val) h + exact congrArg (Sigma.mk d) ((retainedFourIndexEquiv Q (d.val+1) (by omega)).injective he) + · intro s + let d : Fin 23 := ⟨fourCoupledDeficit s.val-1,by + have := fourCoupledDeficit_pos s.val; have := s.property; omega⟩ + let t : {t : FourCoupledIndex Q // fourCoupledDeficit t=d.val+1} := + ⟨s.val,by have := fourCoupledDeficit_pos s.val; dsimp [d]; omega⟩ + refine ⟨⟨d,(retainedFourIndexEquiv Q (d.val+1) (by omega)).symm t⟩,?_⟩ + apply Subtype.ext + exact congrArg (fun x : {t : FourCoupledIndex Q // fourCoupledDeficit t=d.val+1} => x.val) + ((retainedFourIndexEquiv Q (d.val+1) (by omega)).apply_symm_apply t) + +theorem sum_fourCoupled_retained {A : Type*} [AddCommMonoid A] + (Q : ℕ) (hQ : 25 ≤ Q) (f : FourCoupledIndex Q → A) + (hz : ∀ s, 23 < fourCoupledDeficit s → f s=0) : + (∑ s, f s) = ∑ d : Fin 23, ∑ r : OddPairLabel (d.val+1), + ∑ n : Fin (fourSpinWeight Q (d.val+1)+1), + f (retainedFourIndex Q (d.val+1) (by have := d.isLt; omega) r n) := by + classical + rw [Finset.sum_congr_set (s := {s : FourCoupledIndex Q | fourCoupledDeficit s ≤ 23}) + f (fun s => f s.val) (fun _ _ => rfl) (by intro s hs; exact hz s (by simpa using hs))] + have h := Fintype.sum_equiv (retainedFourColumnsEquiv Q hQ) + (fun x => f (retainedFourIndex Q (x.1.val+1) (by have := x.1.isLt; omega) x.2.1 x.2.2)) + (fun s => f s.val) (fun _ => rfl) + convert (by simpa only [Fintype.sum_sigma,Fintype.sum_prod_type] using h.symm) using 1 + apply Fintype.sum_equiv (Equiv.refl _) + intro s + rfl + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/RowBridge.lean b/lean/OAI/Analysis/Laughlin/FourBody/RowBridge.lean new file mode 100644 index 0000000000000000000000000000000000000000..609cabdaad96335e208e9d191afc4b02ec153409 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/RowBridge.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FourBody.FastChoose +import OAI.Analysis.Laughlin.FourBody.RowCompute + +namespace OAI + +namespace Laughlin.Certificate + +theorem source_yRow_eq_rowCompute (D r s n : ℕ) (hn : n < 7) : + yRow D r s (rows[n]!) = (RowCompute.yRowIntegralFast D r s (RowCompute.rows[n]!) : ℚ) / arithmeticScale := by + exact source_yRow_eq_fastIntegral D r s n hn + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/RowCompute.lean b/lean/OAI/Analysis/Laughlin/FourBody/RowCompute.lean new file mode 100644 index 0000000000000000000000000000000000000000..82808d87998f8b75db26c2ebc81f5e3065de226d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/RowCompute.lean @@ -0,0 +1,43 @@ +import Mathlib.Data.Nat.Choose.Basic + +namespace OAI + +namespace Laughlin.Certificate.RowCompute + +def rows : List (ℕ × ℤ × List (ℕ × ℕ × ℤ)) := + [(0, 7181518, [(0, 5, -849651), (0, 7, -2958744), (1, 5, 751659), (1, 6, -43084), (1, 7, -146216), (3, 2, 720949), (3, 5, -127514), (4, 2, 222437), (4, 3, -262822), (5, 3, -117700), (6, 1, -55024), (7, 1, -166049)]), + (1, -112991, [(0, 5, 142772), (0, 6, -142342), (0, 7, 527055), (0, 8, 50742), (1, 6, 197917), (1, 8, -18343), (2, 4, 5764), (2, 7, -21183), (3, 2, 75832), (3, 5, -6115), (4, 5, 2660), (5, 3, -9455), (6, 1, -27091), (6, 3, -3494), (7, 1, 479), (7, 2, -15331)]), + (1, -4247311, [(0, 5, -12207250), (0, 6, -14064191), (0, 7, -14063663), (0, 8, -15662679), (1, 6, 483831), (1, 8, 3987214), (2, 4, -814558), (2, 7, 888887), (3, 2, 966462), (3, 5, 145978), (4, 5, -171722), (5, 3, 34350), (6, 1, 389319), (6, 3, 97603), (7, 1, 412447), (7, 2, -53786)]), + (2, 3438746, [(1, 4, 6689266), (1, 5, 6620205), (1, 6, 6625065), (1, 7, 4969272), (1, 8, 4878238), (2, 7, -1387380), (3, 6, -586188), (3, 7, 344087), (4, 2, -1120634), (4, 5, -318530), (4, 6, 559169), (5, 5, 157455), (6, 1, 1207103), (6, 3, 211617), (6, 4, 33240), (7, 1, 577001), (7, 3, -142578)]), + (5, -98645, [(0, 5, -2719776), (0, 8, -8519913), (1, 4, -949523), (1, 7, -1952105), (1, 8, -1562606), (2, 8, -8919966), (3, 2, 248826), (3, 5, -1017623), (3, 7, 3656005), (3, 8, -2081871), (4, 2, -33163), (4, 3, -305905), (4, 6, 35677), (4, 7, -1320749), (4, 8, -1040378), (5, 3, 502094), (5, 5, 1060633), (5, 8, -998003), (6, 1, -113617), (6, 3, 184919), (6, 4, 209239), (6, 5, -68198), (6, 7, -266297), (7, 2, -606696), (7, 3, -563620), (7, 4, 437345), (7, 6, -432189)]), + (5, -3160276, [(0, 5, -1698129), (0, 8, 10575875), (1, 4, -252576), (1, 7, -8002616), (1, 8, 22592844), (2, 8, 7370640), (3, 2, 289294), (3, 5, 1400647), (3, 7, 1987740), (3, 8, 4030699), (4, 2, -1731401), (4, 3, -1034062), (4, 6, -1106371), (4, 7, -1257051), (4, 8, 1461735), (5, 3, 1408149), (5, 5, 1136847), (5, 8, 1878501), (6, 1, -2838516), (6, 3, -734099), (6, 4, 1062416), (6, 5, 11745), (6, 7, 611312), (7, 2, -480776), (7, 3, 20459), (7, 4, 316925), (7, 6, 37092)]), + (7, 1441784, [(0, 7, 3441286), (0, 8, -6097155), (3, 7, -1002399), (4, 7, -251321), (5, 8, 1143225), (6, 6, -17397), (7, 1, -1007464), (7, 3, -662286), (7, 6, -344621), (7, 8, -1115284)])] + +def UFast (c z T p : ℕ) : ℤ := + if z ≤ T ∧ p ≤ T then + (((List.range (min p z + 1)).filter (fun h => p + z ≤ T + h)).map + (fun h => (-1 : ℤ) ^ (z-h) * (Nat.fast_choose z h : ℤ) * + (Nat.fast_choose (T-z) (p-h) : ℤ) * (c : ℤ) ^ (p-h))).sum + else 0 + +def VFast (r D T p j k : ℕ) : ℤ := + if r ≤ j+k then UFast 1 r (j+k) j * UFast 1 (D-r) (T-r) p else 0 + +def yEntryIntegralFast (D r s t : ℕ) (e f : ℕ × ℕ × ℤ) : ℤ := + let (p,j,a) := e + let (q,l,b) := f + let i := p+j-t + let k := q+l-t + let T := p+j+k + if D ≤ T then + a*b*VFast r D T p j k*VFast s D T q l i * + (2 : ℤ)^((65-2*(T : ℤ)+(p : ℤ)+(q : ℤ)-(t : ℤ)+((r+s)/2 : ℕ)).toNat) * + (i.factorial : ℤ)*(k.factorial : ℤ)*(t.factorial : ℤ) * + ((24 : ℕ).descFactorial (24-(T-D)) : ℤ) + else 0 + +def yRowIntegralFast (D r s : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) : ℤ := + (row.2.2.map (fun e => (row.2.2.map (fun f => yEntryIntegralFast D r s row.1 e f)).sum)).sum +end Laughlin.Certificate.RowCompute + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Scaled.lean b/lean/OAI/Analysis/Laughlin/FourBody/Scaled.lean new file mode 100644 index 0000000000000000000000000000000000000000..39c82eacff90f3c352600a537ad5f4b3da247b55 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Scaled.lean @@ -0,0 +1,78 @@ +import Mathlib.Analysis.SpecialFunctions.Sqrt +import OAI.Analysis.Laughlin.FourBody.Matrix +import OAI.Analysis.Laughlin.Operators.MatrixCongruence + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix + +noncomputable def weightSqrtDiagonal (D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℝ := + Matrix.diagonal (fun i => Real.sqrt (copyWeight D i : ℝ)) + +noncomputable def certificateDiagonal (D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℝ := + (Matrix.diagonal (fun i : Fin ((D+1)/2) => + (if copyLabel i = 1 then 2 else 0) + (3/10^6 : ℚ))).map (Rat.castHom ℝ) + +noncomputable def scaledError (D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℝ := + weightSqrtDiagonal D * (errorRational D).map (Rat.castHom ℝ) * weightSqrtDiagonal D + +noncomputable def scaledGram (D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℝ := + weightSqrtDiagonal D * (gramRational D).map (Rat.castHom ℝ) * weightSqrtDiagonal D + +theorem cast_rat_diagonal {n : ℕ} (v : Fin n → ℚ) : + (Matrix.diagonal v).map (Rat.castHom ℝ) = Matrix.diagonal (fun i => (v i : ℝ)) := by + ext i j + by_cases h : i = j <;> simp [Matrix.map_apply,h] + +theorem cast_rat_sub {n : ℕ} (A B : Matrix (Fin n) (Fin n) ℚ) : + (A-B).map (Rat.castHom ℝ) = A.map (Rat.castHom ℝ)-B.map (Rat.castHom ℝ) := by + ext i j + simp [Matrix.map_apply,Matrix.sub_apply] + +theorem copyWeight_nonneg (D : ℕ) (i : Fin ((D+1)/2)) : 0 ≤ (copyWeight D i : ℝ) := by + unfold copyWeight + positivity + +theorem weightSqrtDiagonal_sq (D : ℕ) : + weightSqrtDiagonal D * weightSqrtDiagonal D = + (Matrix.diagonal (copyWeight D)).map (Rat.castHom ℝ) := by + rw [weightSqrtDiagonal,Matrix.diagonal_mul_diagonal,cast_rat_diagonal] + congr 1 + funext i + simpa [pow_two] using Real.sq_sqrt (copyWeight_nonneg D i) + +theorem weightSqrtDiagonal_middle_diagonal (D : ℕ) : + weightSqrtDiagonal D * certificateDiagonal D * weightSqrtDiagonal D = + (Matrix.diagonal (fun i => ((if copyLabel i = 1 then 2 else 0) + (3/10^6 : ℚ))*copyWeight D i)).map + (Rat.castHom ℝ) := by + simp only [weightSqrtDiagonal,certificateDiagonal,cast_rat_diagonal, + Matrix.diagonal_mul_diagonal] + congr 1 + funext i + change Real.sqrt (copyWeight D i : ℝ) * + (((if copyLabel i = 1 then 2 else 0) + (3/10^6 : ℚ) : ℚ) : ℝ) * Real.sqrt (copyWeight D i : ℝ) = _ + rw [Rat.cast_mul] + calc + _ = (((if copyLabel i = 1 then 2 else 0) + (3/10^6 : ℚ) : ℚ) : ℝ) * + (Real.sqrt (copyWeight D i : ℝ))^2 := by ring + _ = _ := by rw [Real.sq_sqrt (copyWeight_nonneg D i)] + +theorem scaled_compression_identity (D : ℕ) : + scaledGram D * (certificateDiagonal D-scaledError D) * scaledGram D = + weightSqrtDiagonal D * (compressedRational D).map (Rat.castHom ℝ) * weightSqrtDiagonal D := by + rw [scaledGram,scaledError,compressed_congruence_identity, + weightSqrtDiagonal_middle_diagonal,weightSqrtDiagonal_sq] + simp only [compressedRational,middleRational,Matrix.map_mul,cast_rat_sub] + +theorem scaled_compression_positive (D : ℕ) + (hM : ((compressedRational D).map (Rat.castHom ℝ)).PosSemidef) : + (scaledGram D * (certificateDiagonal D-scaledError D) * scaledGram D).PosSemidef := by + rw [scaled_compression_identity] + have hd : (weightSqrtDiagonal D).IsHermitian := by + simp [weightSqrtDiagonal,Matrix.IsHermitian] + simpa only [hd.eq] using hM.mul_mul_conjTranspose_same (weightSqrtDiagonal D) + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/ScaledAll.lean b/lean/OAI/Analysis/Laughlin/FourBody/ScaledAll.lean new file mode 100644 index 0000000000000000000000000000000000000000..b1c5aaa8b3bfbadf35faaf271359ff7967671c6b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/ScaledAll.lean @@ -0,0 +1,14 @@ +import OAI.Analysis.Laughlin.FourBody.All +import OAI.Analysis.Laughlin.FourBody.Scaled + +namespace OAI + +namespace Laughlin.Certificate + +theorem scaled_four_body_certificates (D : ℕ) (hD₁ : 1 ≤ D) (hD₂ : D ≤ 23) : + (scaledGram D * (certificateDiagonal D-scaledError D) * scaledGram D).PosSemidef := + scaled_compression_positive D (four_body_certificates D hD₁ hD₂) + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/SignedCoordinates.lean b/lean/OAI/Analysis/Laughlin/FourBody/SignedCoordinates.lean new file mode 100644 index 0000000000000000000000000000000000000000..70f96f72a0c5295ba62d656e440c1d025d605159 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/SignedCoordinates.lean @@ -0,0 +1,91 @@ +import OAI.Analysis.Laughlin.FourBody.CoefficientNorm +import OAI.Analysis.Laughlin.ThreeBody.RankTrace + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +theorem physicalCouplingCoefficient_pair_swap (Q r j k : ℕ) (hr : r ≤ Q) + (hor : Odd r) (hjk : j+k ≤ Q) : + physicalCouplingCoefficient Q Q r (j+k) k = -physicalCouplingCoefficient Q Q r (j+k) j := by + by_cases h : r ≤ j+k + · rw [physicalCouplingCoefficient,dite_eq_left ⟨h,by omega,hjk,hjk⟩, + physicalCouplingCoefficient,dite_eq_left ⟨h,by omega,hjk,hjk⟩] + have hp := pairCoupledTensor_antisymmetric Q r (j+k-r) hr hor ⟨j,by omega⟩ ⟨k,by omega⟩ + simpa only [pairCoupledTensor,Pi.smul_apply,smul_eq_mul,Nat.add_sub_cancel,Nat.add_sub_cancel_left] using hp + · simp [physicalCouplingCoefficient,h] + +theorem fourBodyCoefficient_swap (Q r D T p j k : ℕ) (hr : r ≤ Q) (hor : Odd r) + (hjk : j+k ≤ Q) : + fourBodyCoefficient Q r D T p k j = -fourBodyCoefficient Q r D T p j k := by + unfold fourBodyCoefficient + rw [Nat.add_comm k j] + split_ifs + · rw [physicalCouplingCoefficient_pair_swap Q r j k hr hor hjk] + ring + · simp + +noncomputable def fourWedgeUnit (Q p j k : ℕ) : Fin (2*Q-2+1) × WedgePairIndex Q → ℝ := + fun i => if i.1.val=p ∧ i.2.val.1.val=j ∧ i.2.val.2.val=k then 1 else 0 + +noncomputable def fourSignedUnit (Q p j k : ℕ) : Fin (2*Q-2+1) × WedgePairIndex Q → ℝ := + fourWedgeUnit Q p j k - fourWedgeUnit Q p k j + +theorem fourWedgeUnit_dot (Q p j k : ℕ) (hp : p < 2*Q-2+1) (hj : j ≤ Q) (hk : k ≤ Q) + (hjk : j < k) (v : Fin (2*Q-2+1) × WedgePairIndex Q → ℝ) : + dotProduct v (fourWedgeUnit Q p j k) = v (⟨p,hp⟩,⟨(⟨j,by omega⟩,⟨k,by omega⟩),hjk⟩) := by + classical + simp only [dotProduct,fourWedgeUnit,mul_ite,mul_one,mul_zero] + have he (i : Fin (2*Q-2+1) × WedgePairIndex Q) : + (i.1.val=p ∧ i.2.val.1.val=j ∧ i.2.val.2.val=k) ↔ + i=(⟨p,hp⟩,⟨(⟨j,by omega⟩,⟨k,by omega⟩),hjk⟩) := by + constructor + · rintro ⟨h1,h2,h3⟩ + exact Prod.ext (Fin.ext h1) (Subtype.ext (Prod.ext (Fin.ext h2) (Fin.ext h3))) + · intro h; subst i; exact ⟨rfl,rfl,rfl⟩ + simp_rw [he] + simp + +theorem fourWedgeUnit_zero (Q p j k : ℕ) (hkj : k ≤ j) : fourWedgeUnit Q p j k=0 := by + funext i + have h := i.2.property + simp only [fourWedgeUnit,Pi.zero_apply] + rw [ite_eq_right (by rintro ⟨_,hj,hk⟩; change i.2.val.1.val < i.2.val.2.val at h; omega)] + +theorem fourBodyCopy_signed_at_level (Q r D T p j k : ℕ) (hor : Odd r) + (hrD : r ≤ D) (hDT : D ≤ T) (hQ : T+2 ≤ Q) (hT : p+j+k=T) : + dotProduct (fourBodyCopy Q r D (by omega) (by omega) + (by unfold genericCoupledWeight; omega) (T-D)) (fourSignedUnit Q p j k) = + fourBodyCoefficient Q r D T p j k := by + rw [fourSignedUnit,dotProduct_sub] + rcases lt_trichotomy j k with h | h | h + · rw [fourWedgeUnit_dot Q p j k (by omega) (by omega) (by omega) h, + fourWedgeUnit_zero Q p k j (by omega),dotProduct_zero,sub_zero] + exact fourBodyCopy_source_coefficient Q r D T hrD hDT hQ _ _ hT + · subst k + rw [sub_self] + have he := fourBodyCoefficient_swap Q r D T p j j (by omega) hor (by omega) + linarith + · rw [fourWedgeUnit_zero Q p j k (by omega),dotProduct_zero,zero_sub, + fourWedgeUnit_dot Q p k j (by omega) (by omega) (by omega) h, + fourBodyCopy_source_coefficient Q r D T hrD hDT hQ _ _ (by dsimp; omega), + fourBodyCoefficient_swap Q r D T p j k (by omega) hor (by omega),neg_neg] + +theorem fourBodyCopy_signed_off (Q r D n p j k : ℕ) (hr : r ≤ Q) (hrD : r ≤ D) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) + (hT : p+j+k ≠ D+n) : + dotProduct (fourBodyCopy Q r D hr hA hB n) (fourSignedUnit Q p j k) = 0 := by + have hz (j k : ℕ) (hT : p+j+k ≠ D+n) : + dotProduct (fourBodyCopy Q r D hr hA hB n) (fourWedgeUnit Q p j k) = 0 := by + apply Finset.sum_eq_zero + intro i hi + simp only [fourWedgeUnit] + split_ifs with he + · rw [fourBodyCopy_off Q r D n hr hrD hA hB i.1 i.2 (by omega),zero_mul] + · exact mul_zero _ + rw [fourSignedUnit,dotProduct_sub,hz j k hT,hz k j (by omega),sub_self] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/SlaterCoefficient.lean b/lean/OAI/Analysis/Laughlin/FourBody/SlaterCoefficient.lean new file mode 100644 index 0000000000000000000000000000000000000000..c4d9b89be49de1dfa2c836de9fc648cb003f9748 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/SlaterCoefficient.lean @@ -0,0 +1,41 @@ +import OAI.Analysis.Laughlin.FourBody.SlaterRadical + +namespace OAI + +namespace Laughlin.Spin + +noncomputable def limitSlaterCoefficient (D r a b c d : ℕ) : ℝ := + limitSlaterTerm D r a b c d - limitSlaterTerm D r a c b d + + limitSlaterTerm D r a d b c + limitSlaterTerm D r b c a d - + limitSlaterTerm D r b d a c + limitSlaterTerm D r c d a b + +theorem source_fourBody_Slater_coefficient (D r a b c d : ℕ) (hr : r ≤ D) (hor : Odd r) + (hab : a < b) (hbc : b < c) (hcd : c < d) (hT : a+b+c+d=D+1) : + limitSlaterCoefficient D r a b c d = + Real.sqrt (sourceCopyWeight D r / ((a.factorial : ℝ)*b.factorial*c.factorial*d.factorial)) * + (Certificate.L D r (a,b,c,d) : ℝ) := by + unfold limitSlaterCoefficient + rw [limitSlaterTerm_rational D r a b c d hr hor hab hT, + limitSlaterTerm_rational D r a c b d hr hor (by omega) (by omega), + limitSlaterTerm_rational D r a d b c hr hor (by omega) (by omega), + limitSlaterTerm_rational D r b c a d hr hor hbc (by omega), + limitSlaterTerm_rational D r b d a c hr hor (by omega) (by omega), + limitSlaterTerm_rational D r c d a b hr hor hcd (by omega)] + have h1 : (a.factorial : ℝ)*c.factorial*b.factorial*d.factorial = + (a.factorial : ℝ)*b.factorial*c.factorial*d.factorial := by ring + have h2 : (a.factorial : ℝ)*d.factorial*b.factorial*c.factorial = + (a.factorial : ℝ)*b.factorial*c.factorial*d.factorial := by ring + have h3 : (b.factorial : ℝ)*c.factorial*a.factorial*d.factorial = + (a.factorial : ℝ)*b.factorial*c.factorial*d.factorial := by ring + have h4 : (b.factorial : ℝ)*d.factorial*a.factorial*c.factorial = + (a.factorial : ℝ)*b.factorial*c.factorial*d.factorial := by ring + have h5 : (c.factorial : ℝ)*d.factorial*a.factorial*b.factorial = + (a.factorial : ℝ)*b.factorial*c.factorial*d.factorial := by ring + rw [h1,h2,h3,h4,h5] + simp only [Certificate.L] + push_cast + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/SlaterRadical.lean b/lean/OAI/Analysis/Laughlin/FourBody/SlaterRadical.lean new file mode 100644 index 0000000000000000000000000000000000000000..5802f7dcb086aab96fd9b41132a637f7e3a86c7e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/SlaterRadical.lean @@ -0,0 +1,71 @@ +import OAI.Analysis.Laughlin.FourBody.RadicalCancellation +import OAI.Analysis.Laughlin.Pair.Conjugation + +namespace OAI + +namespace Laughlin.Spin + +theorem source_L_radical_cancellation (D r p x y j k : ℕ) (hor : Odd r) + (hT : p+j+k=D) : + Real.sqrt ((p.factorial : ℝ)/((2 : ℝ)^p*x.factorial*y.factorial)) * fourBodyRadical r D D p j k = + Real.sqrt (sourceCopyWeight D r / ((x.factorial : ℝ)*y.factorial*j.factorial*k.factorial)) * + (2 : ℝ)^(((1 : ℤ)-2*D+r)/2) * + ((p.factorial : ℝ)*j.factorial*k.factorial) := by + let e : ℤ := ((1 : ℤ)-2*D+r)/2 + have he : e*2=(1 : ℤ)-2*D+r := by + rcases hor with ⟨a,ha⟩ + dsimp [e]; omega + have hTr : (p : ℤ)+j+k=D := by exact_mod_cast hT + have hpow : (2 : ℝ)^((1 : ℤ)-j-k-D+r) / (2 : ℝ)^p = ((2 : ℝ)^e)^2 := by + rw [← zpow_natCast,← zpow_sub₀ (by norm_num : (2 : ℝ) ≠ 0)] + rw [show (1 : ℤ)-j-k-D+r-(p : ℤ)=e*2 by omega,zpow_mul] + norm_num + have hsq : (Real.sqrt ((p.factorial : ℝ)/((2 : ℝ)^p*x.factorial*y.factorial)) * + fourBodyRadical r D D p j k)^2 = + (Real.sqrt (sourceCopyWeight D r / ((x.factorial : ℝ)*y.factorial*j.factorial*k.factorial)) * + (2 : ℝ)^e * ((p.factorial : ℝ)*j.factorial*k.factorial))^2 := by + simp only [fourBodyRadical,mul_pow] + rw [Real.sq_sqrt (by positivity),Real.sq_sqrt (by positivity), + Real.sq_sqrt (by unfold sourceCopyWeight; positivity)] + simp only [Nat.sub_self,Nat.factorial_zero,Nat.cast_one,mul_one] + calc + _ = ((2 : ℝ)^((1 : ℤ)-j-k-D+r)/(2 : ℝ)^p) * + (((p.factorial : ℝ)*j.factorial*k.factorial)^2 / + ((r.factorial : ℝ)*(D-r).factorial*x.factorial*y.factorial*j.factorial*k.factorial)) := by + field_simp + _ = ((2 : ℝ)^e)^2 * + (((p.factorial : ℝ)*j.factorial*k.factorial)^2 / + ((r.factorial : ℝ)*(D-r).factorial*x.factorial*y.factorial*j.factorial*k.factorial)) := by rw [hpow] + _ = _ := by unfold sourceCopyWeight; field_simp + have hl : 0 ≤ Real.sqrt ((p.factorial : ℝ)/((2 : ℝ)^p*x.factorial*y.factorial)) * + fourBodyRadical r D D p j k := by unfold fourBodyRadical; positivity + have hr : 0 ≤ Real.sqrt (sourceCopyWeight D r / ((x.factorial : ℝ)*y.factorial*j.factorial*k.factorial)) * + (2 : ℝ)^e * ((p.factorial : ℝ)*j.factorial*k.factorial) := by positivity + nlinarith only [hsq,hl,hr] + +noncomputable def limitSlaterTerm (D r x y j k : ℕ) : ℝ := + (Real.sqrt 2 * pairLimitCoefficient (x+y-1) x y) * + fourBodyLimitCoefficient r D D (x+y-1) j k + +theorem limitSlaterTerm_rational (D r x y j k : ℕ) (hr : r ≤ D) (hor : Odd r) + (hxy : x < y) (hT : x+y+j+k=D+1) : + limitSlaterTerm D r x y j k = + Real.sqrt (sourceCopyWeight D r / ((x.factorial : ℝ)*y.factorial*j.factorial*k.factorial)) * + (2 : ℝ)^(((1 : ℤ)-2*D+r)/2) * + ((x : ℝ)-y) * ((x+y-1).factorial : ℝ)*j.factorial*k.factorial * + (Certificate.V r D D (x+y-1) j k : ℝ) := by + have hp : x+y-1+j+k=D := by omega + rw [limitSlaterTerm,source_fourBody_radical_coefficient r D D (x+y-1) j k hr (le_refl _) hp] + rw [pairLimitCoefficient,ite_eq_left (by omega : x+y=x+y-1+1)] + have hc := source_L_radical_cancellation D r (x+y-1) x y j k hor hp + calc + _ = ((x : ℝ)-y)*(Certificate.V r D D (x+y-1) j k : ℝ) * + (Real.sqrt (((x+y-1).factorial : ℝ)/((2 : ℝ)^(x+y-1)*x.factorial*y.factorial)) * + fourBodyRadical r D D (x+y-1) j k) := by + simp only [Nat.cast_ofNat] + field_simp + _ = _ := by rw [hc]; ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/SliceCoefficient.lean b/lean/OAI/Analysis/Laughlin/FourBody/SliceCoefficient.lean new file mode 100644 index 0000000000000000000000000000000000000000..6b05433f71b0ac0d4211befc5c61f6cc4bb98a04 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/SliceCoefficient.lean @@ -0,0 +1,35 @@ +import OAI.Analysis.Laughlin.FourBody.Parity +import OAI.Analysis.Laughlin.FourBody.SlaterCoefficient + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +noncomputable def limitSliceCoefficient (r D p j k : ℕ) : ℝ := + if p+j+k=D then fourBodyLimitCoefficient r D D p j k else 0 + +theorem limitSliceCoefficient_antisymmetric (r D p j k : ℕ) (hr : r ≤ D) (ho : Odd r) : + limitSliceCoefficient r D p k j = -limitSliceCoefficient r D p j k := by + unfold limitSliceCoefficient + by_cases h : p+j+k=D + · rw [ite_eq_left (by omega : p+k+j=D),ite_eq_left h, + fourBodyLimitCoefficient_antisymmetric r D D p j k ho hr (le_refl _) h] + · rw [ite_eq_right (by omega : p+k+j ≠ D),ite_eq_right h,neg_zero] + +theorem sum_pairLimit_slice (D r a b c d : ℕ) (hab : a < b) (hT : a+b+c+d=D+1) : + (∑ p ∈ Finset.range (D+1), Real.sqrt 2 * pairLimitCoefficient p a b * + limitSliceCoefficient r D p c d) = limitSlaterTerm D r a b c d := by + rw [Finset.sum_eq_single (a+b-1)] + · rw [limitSliceCoefficient,ite_eq_left (by omega)] + rfl + · intro p hp hne + have h : a+b ≠ p+1 := by omega + simp [pairLimitCoefficient,h] + · intro h + have hm : a+b-1 ∈ Finset.range (D+1) := Finset.mem_range.mpr (by omega) + exact (h hm).elim + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Square.lean b/lean/OAI/Analysis/Laughlin/FourBody/Square.lean new file mode 100644 index 0000000000000000000000000000000000000000..b78dd6b07ab03aa6dfa209c5e017904a29b4cee7 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Square.lean @@ -0,0 +1,59 @@ +import OAI.Analysis.Laughlin.FourBody.Levels + +namespace OAI + +namespace Laughlin.Fock +open Spin +open scoped BigOperators Matrix + +abbrev RowLevel (t : ℕ) := {T : Fin 16 // t ≤ T.val} + +def rowOutputMode (Q t : ℕ) (hQ : 15 ≤ Q) (T : RowLevel t) : Fin (Q+1) := + ⟨T.val.val-t,by have h := T.val.isLt; omega⟩ + +theorem rowOutputMode_injective (Q t : ℕ) (hQ : 15 ≤ Q) : + Function.Injective (rowOutputMode Q t hQ) := by + intro T S h + have he := congrArg Fin.val h + dsimp [rowOutputMode] at he + have hT := T.property + have hS := S.property + apply Subtype.ext + apply Fin.ext + omega + +noncomputable def sourceRowSquareVector (Q : ℕ) (hQ : 15 ≤ Q) + (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) (x : Space Q) : Space Q := + ((row.2.1 : ℂ)/10^7) • sourcePairEnd Q row.1 x + + ∑ T : RowLevel row.1, create (rowOutputMode Q row.1 hQ T) + (sourceRowLevel Q row.1 T.val.val row.2.2 x) + +noncomputable def sourceRowFourForm (Q : ℕ) (hQ : 15 ≤ Q) + (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) (x : Space Q) : ℂ := + -∑ T : RowLevel row.1, ∑ S : RowLevel row.1, + occupationInner Q + (annihilate (rowOutputMode Q row.1 hQ S) (sourceRowLevel Q row.1 T.val.val row.2.2 x)) + (annihilate (rowOutputMode Q row.1 hQ T) (sourceRowLevel Q row.1 S.val.val row.2.2 x)) + +theorem sourceRowSquareVector_normal (Q : ℕ) (hQ : 15 ≤ Q) + (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) (ht : row.1 ≤ 7) (x : Space Q) : + (occupationNormSq Q (sourceRowSquareVector Q hQ row x) : ℂ) = + ((row.2.1 : ℂ)/10^7)^2 * (occupationNormSq Q (sourcePairEnd Q row.1 x) : ℂ) + + (∑ T : RowLevel row.1, contractionForm Q (sourceThreeEnd Q) + ((threeBodyLevelMatrix Q row.1 T.val.val row.2.1 row.2.2).map Complex.ofReal) x) + + sourceRowFourForm Q hQ row x := by + have h := row_normal_square Q (rowOutputMode Q row.1 hQ) + (rowOutputMode_injective Q row.1 hQ) ((row.2.1 : ℝ)/10^7) + (sourcePairEnd Q row.1 x) (fun T => sourceRowLevel Q row.1 T.val.val row.2.2 x) + have hc : (((row.2.1 : ℝ)/10^7 : ℝ) : ℂ) = (row.2.1 : ℂ)/10^7 := by push_cast; rfl + rw [hc] at h + rw [sourceRowSquareVector,h] + have hl (T : RowLevel row.1) := threeBodyLevelMatrix_Fock Q row.1 T.val.val + row.2.1 row.2.2 (by omega) (by have hT := T.val.isLt; omega) x + simp_rw [hl] + simp only [sourceRowFourForm,rowOutputMode,Finset.sum_add_distrib] + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Support.lean b/lean/OAI/Analysis/Laughlin/FourBody/Support.lean new file mode 100644 index 0000000000000000000000000000000000000000..93fc3bbe71d9011ebe84c5729b9ee804cdee4fc8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Support.lean @@ -0,0 +1,86 @@ +import OAI.Analysis.Laughlin.FourBody.PhysicalTrace + +namespace OAI + +namespace Laughlin.Spin +open Rotation MeasureTheory +open scoped BigOperators Matrix + +theorem realOuter_mulVec_row {I : Type*} [Fintype I] (u v w : I → ℝ) (i : I) : + (realOuter u v *ᵥ w) i = u i * dotProduct w v := by + simp only [Matrix.mulVec,dotProduct,realOuter,Finset.mul_sum] + apply Finset.sum_congr rfl + intro j hj + ring + +theorem fourBodyTermMatrix_high_copy (Q r D t : ℕ) (hr : r ≤ Q) (hrD : r ≤ D) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) + (e f : ℕ × ℕ × ℤ) (he : t ≤ e.1+e.2.1) (hf : t ≤ f.1+f.2.1) + (hT : e.1+e.2.1+(f.1+f.2.1-t) < D) : + fourBodyTermMatrix Q t e f * fourBodyInclusion Q r D hr hA hB = 0 := by + ext i n + change (fourBodyTermMatrix Q t e f *ᵥ fourBodyCopy Q r D hr hA hB n.val) i=0 + rw [fourBodyTermMatrix,Matrix.smul_mulVec] + simp only [Pi.smul_apply,smul_eq_mul] + rw [realOuter_mulVec_row,fourBodyCopy_signed_off Q r D n.val f.1 f.2.1 + (e.1+e.2.1-t) hr hrD hA hB (by omega),mul_zero,mul_zero] + +theorem list_sum_mul_zero {I J K : Type*} [Fintype J] + (l : List (Matrix I J ℝ)) (W : Matrix J K ℝ) (h : ∀ M ∈ l, M*W=0) : l.sum*W=0 := by + induction l with + | nil => simp + | cons M l ih => + rw [List.sum_cons,Matrix.add_mul,h M (by simp),ih (fun A hA => h A (by simp [hA])),zero_add] + +theorem physicalFourBodyMatrix_high_copy (Q r D : ℕ) (hr : r ≤ Q) (hrD : r ≤ D) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) (hD : 23 < D) : + physicalFourBodyMatrix Q * fourBodyInclusion Q r D hr hA hB = 0 := by + unfold physicalFourBodyMatrix + apply list_sum_mul_zero + intro M hM + rcases List.mem_map.mp hM with ⟨row,hrow,rfl⟩ + apply list_sum_mul_zero + intro A hA' + rcases List.mem_map.mp hA' with ⟨e,he,rfl⟩ + apply list_sum_mul_zero + intro B hB' + rcases List.mem_map.mp hB' with ⟨f,hf,rfl⟩ + exact fourBodyTermMatrix_high_copy Q r D row.1 hr hrD hA hB e f + (source_rows_admissible row hrow e he) (source_rows_admissible row hrow f hf) + (by have := source_fourBody_rows_support row hrow e he f hf; omega) + +theorem real_matrix_mul_zero_complex {I J K : Type*} [Fintype J] + (A : Matrix I J ℝ) (B : Matrix J K ℝ) (h : A*B=0) : + A.map Complex.ofReal * B.map Complex.ofReal=0 := by + ext i k + have he := congrArg Complex.ofReal (congrFun (congrFun h i) k) + simpa only [Matrix.mul_apply,Matrix.map_apply,Complex.ofReal_sum,Complex.ofReal_mul, + Matrix.zero_apply,Complex.ofReal_zero] using he + +theorem physicalFourBodyMatrix_high_wedge_copy (Q r D : ℕ) (hr : r ≤ Q) (hrD : r ≤ D) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) (hD : 23 < D) : + (physicalFourBodyMatrix Q).map Complex.ofReal * fourWedgeInclusion Q r D hr hA hB = 0 := + real_matrix_mul_zero_complex _ _ (physicalFourBodyMatrix_high_copy Q r D hr hrD hA hB hD) + +theorem physicalFourBodyHaar_high_copy (Q r D : ℕ) (hr : r ≤ Q) (hor : Odd r) (hrD : r ≤ D) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) (hD : 23 < D) : + matrixIntegral sourceHaar + (conjugateOrbit (fourBodySpinRepresentation Q) ((physicalFourBodyMatrix Q).map Complex.ofReal)) * + fourWedgeInclusion Q r D hr hA hB = 0 := by + have hz (g : SourceSU2) : + conjugateOrbit (fourBodySpinRepresentation Q) ((physicalFourBodyMatrix Q).map Complex.ofReal) g * + fourWedgeInclusion Q r D hr hA hB = 0 := by + unfold conjugateOrbit + rw [Matrix.mul_assoc, fourWedgeInclusion_SU2 Q r D hr hor hA hB, Matrix.mul_assoc, + ← Matrix.mul_assoc ((physicalFourBodyMatrix Q).map Complex.ofReal), + physicalFourBodyMatrix_high_wedge_copy Q r D hr hrD hA hB hD,Matrix.zero_mul,Matrix.mul_zero] + have hi := integral_matrix_sandwich sourceHaar + (conjugateOrbit (fourBodySpinRepresentation Q) ((physicalFourBodyMatrix Q).map Complex.ofReal)) + (compact_conjugateOrbit_integrable sourceHaar _ (fourBodySpinRepresentation_continuous Q) _) + (1 : Matrix (FourWedgeIndex Q) (FourWedgeIndex Q) ℂ) (fourWedgeInclusion Q r D hr hA hB) + simp only [Matrix.one_mul,hz,Matrix.zero_apply,integral_zero] at hi + exact hi.symm + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Symmetry.lean b/lean/OAI/Analysis/Laughlin/FourBody/Symmetry.lean new file mode 100644 index 0000000000000000000000000000000000000000..29beca7c372f4b9057a93421107c93e5b172ead8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Symmetry.lean @@ -0,0 +1,66 @@ +import Mathlib.Tactic.Ring +import OAI.Analysis.Laughlin.FourBody.Basic + +namespace OAI + +namespace Laughlin.Certificate + +theorem yEntry_swap (D r s t : ℕ) (e f : ℕ × ℕ × ℤ) + (he : t ≤ e.1 + e.2.1) (hf : t ≤ f.1 + f.2.1) : + yEntry D r s t e f = yEntry D s r t f e := by + rcases e with ⟨p,j,a⟩ + rcases f with ⟨q,l,b⟩ + dsimp at he hf + have hT : q+l+(p+j-t) = p+j+(q+l-t) := by omega + simp only [yEntry, hT, Nat.add_comm s r] + split_ifs <;> ring_nf + +private theorem sum_add {Element : Type*} (xs : List Element) (f g : Element → ℚ) : + (xs.map (fun x => f x + g x)).sum = (xs.map f).sum + (xs.map g).sum := by + induction xs with + | nil => simp + | cons x xs ih => simp only [List.map_cons, List.sum_cons, ih]; ring + +private theorem sum_swap {Element : Type*} (xs ys : List Element) + (f : Element → Element → ℚ) : + (xs.map (fun x => (ys.map (f x)).sum)).sum = + (ys.map (fun y => (xs.map (fun x => f x y)).sum)).sum := by + induction xs with + | nil => simp + | cons x xs ih => + simp only [List.map_cons, List.sum_cons, ih, sum_add] + +theorem yRow_swap (D r s : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) + (h : ∀ e ∈ row.2.2, row.1 ≤ e.1 + e.2.1) : + yRow D r s row = yRow D s r row := by + unfold yRow + rw [sum_swap] + congr 1 + apply List.map_congr_left + intro f hf + congr 1 + apply List.map_congr_left + intro e he + exact yEntry_swap D r s row.1 e f (h e he) (h f hf) + +theorem rows_valid : ∀ row ∈ rows, ∀ e ∈ row.2.2, row.1 ≤ e.1 + e.2.1 := by + decide +kernel + +theorem Y_symm (D r s : ℕ) : Y D r s = Y D s r := by + unfold Y + congr 3 + apply List.map_congr_left + intro row hr + exact yRow_swap D r s row (rows_valid row hr) + +theorem Z_symm (D r s : ℕ) : Z D r s = Z D s r := by + unfold Z + congr 1 + apply List.map_congr_left + intro A hA + dsimp + ring + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/TargetBound.lean b/lean/OAI/Analysis/Laughlin/FourBody/TargetBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..fd9fd1317b055f6edd753643ae5636caae98f339 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/TargetBound.lean @@ -0,0 +1,77 @@ +import OAI.Analysis.Laughlin.FourBody.RetainedComparison +import OAI.Analysis.Laughlin.FourBody.TargetResolution + +namespace OAI + +namespace Laughlin.Fock +open Spin +open scoped BigOperators Matrix ComplexOrder + +theorem castSpinColumns_mul_adjoint {I : Type*} (m n : ℕ) (h : m=n) + (W : Matrix I (Fin (m+1)) ℂ) : + castSpinColumns m n h W * (castSpinColumns m n h W)ᴴ = W*Wᴴ := by + subst n + rfl + +theorem fourWedgeProjector_congr (Q r D E : ℕ) (hr : r ≤ Q) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) + (hA' : E-r ≤ 2*Q-2) (hB' : E-r ≤ genericCoupledWeight Q Q r) (h : D=E) : + fourWedgeInclusion Q r D hr hA hB*(fourWedgeInclusion Q r D hr hA hB)ᴴ = + fourWedgeInclusion Q r E hr hA' hB'*(fourWedgeInclusion Q r E hr hA' hB')ᴴ := by + subst E + rfl + +theorem retainedFirst_projector (Q D : ℕ) (hQ : D+2 ≤ Q) (hD : 1 ≤ D) : + retainedFourInclusion Q D hQ (firstOddPairLabel D hD) * + (retainedFourInclusion Q D hQ (firstOddPairLabel D hD))ᴴ = + fourWedgeInclusion Q 1 D (by omega) (by omega) (by unfold genericCoupledWeight; omega) * + (fourWedgeInclusion Q 1 D (by omega) (by omega) (by unfold genericCoupledWeight; omega))ᴴ := by + unfold retainedFourInclusion + rw [castSpinColumns_mul_adjoint] + rfl + +theorem contractionForm_projector_nonneg {I J : Type*} [Fintype I] [Fintype J] + (Q : ℕ) (L : I → Module.End ℂ (Space Q)) (W : Matrix I J ℂ) (x : Space Q) : + 0 ≤ (contractionForm Q L (W*Wᴴ) x).re := + occupation_matrix_quadratic_positive Q _ (Matrix.posSemidef_self_mul_conjTranspose W) _ + +theorem sum_fin_castLE_le (m n : ℕ) (hmn : m ≤ n) (f : Fin n → ℝ) + (hf : ∀ i, 0 ≤ f i) : (∑ i : Fin m, f (Fin.castLE hmn i)) ≤ ∑ i : Fin n, f i := by + classical + calc + _ = ∑ i ∈ Finset.univ.image (Fin.castLE hmn), f i := by + rw [Finset.sum_image] + intro i hi j hj he + exact Fin.ext (congrArg (fun x : Fin n => x.val) he) + _ ≤ _ := Finset.sum_le_sum_of_subset_of_nonneg (Finset.subset_univ _) + (fun i hi hnot => hf i) + +theorem retainedFourTarget_le_full (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + retainedFourTarget Q hQ x ≤ + (contractionForm Q (sourceFourFamilyEnd Q) (fourPairTargetMatrix Q (by omega)) x).re := by + let f (z : Fin (min (2*Q-2) (genericCoupledWeight Q Q 1)+1)) : ℝ := + (contractionForm Q (sourceFourFamilyEnd Q) + (fourWedgeInclusion Q 1 (1+z.val) (by omega) (by omega) (by omega) * + (fourWedgeInclusion Q 1 (1+z.val) (by omega) (by omega) (by omega))ᴴ) x).re + have hn : 23 ≤ min (2*Q-2) (genericCoupledWeight Q Q 1)+1 := by + unfold genericCoupledWeight + omega + have hs := sum_fin_castLE_le 23 _ hn f (fun z => contractionForm_projector_nonneg Q _ _ x) + have hl : (∑ d : Fin 23, f (Fin.castLE hn d)) = retainedFourTarget Q hQ x := by + unfold retainedFourTarget + apply Finset.sum_congr rfl + intro d hd + rw [retainedFirst_projector] + dsimp only [f,Fin.val_castLE] + exact congrArg (fun M => (contractionForm Q (sourceFourFamilyEnd Q) M x).re) + (fourWedgeProjector_congr Q 1 (1+d.val) (d.val+1) (by omega) + (by omega) (by unfold genericCoupledWeight; omega) + (by omega) (by unfold genericCoupledWeight; omega) (Nat.add_comm 1 d.val)) + have hr : (∑ z, f z) = + (contractionForm Q (sourceFourFamilyEnd Q) (fourPairTargetMatrix Q (by omega)) x).re := by + rw [fourPairTargetMatrix,fourPairEmbedding_resolution,contractionForm_sum,Complex.re_sum] + rwa [hl,hr] at hs + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/TargetResolution.lean b/lean/OAI/Analysis/Laughlin/FourBody/TargetResolution.lean new file mode 100644 index 0000000000000000000000000000000000000000..6b084524a5c0b11c5170241ef938c6731038251a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/TargetResolution.lean @@ -0,0 +1,56 @@ +import OAI.Analysis.Laughlin.FourBody.RetainedInclusions +import OAI.Analysis.Laughlin.Operators.GenericPhysicalResolution + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix Kronecker + +noncomputable def fourPairEmbedding (Q r : ℕ) (hr : r ≤ Q) : + Matrix (FourWedgeIndex Q) (SpinIndex (2*Q-2) (genericCoupledWeight Q Q r)) ℂ := + (1 : Matrix (Fin (2*Q-2+1)) (Fin (2*Q-2+1)) ℂ) ⊗ₖ + (pairCoupledInclusion Q r hr).map Complex.ofReal + +theorem fourPairEmbedding_resolution (Q r : ℕ) (hr : r ≤ Q) : + fourPairEmbedding Q r hr*(fourPairEmbedding Q r hr)ᴴ = + ∑ z : Fin (min (2*Q-2) (genericCoupledWeight Q Q r)+1), + fourWedgeInclusion Q r (r+z.val) hr (by omega) (by omega) * + (fourWedgeInclusion Q r (r+z.val) hr (by omega) (by omega))ᴴ := by + let F : Matrix (FourWedgeIndex Q) (SpinIndex (2*Q-2) (genericCoupledWeight Q Q r)) ℂ := + fourPairEmbedding Q r hr + have hA (z : Fin (min (2*Q-2) (genericCoupledWeight Q Q r)+1)) : z.val ≤ 2*Q-2 := + (Nat.le_of_lt_succ z.isLt).trans (Nat.min_le_left _ _) + have hB (z : Fin (min (2*Q-2) (genericCoupledWeight Q Q r)+1)) : z.val ≤ genericCoupledWeight Q Q r := + (Nat.le_of_lt_succ z.isLt).trans (Nat.min_le_right _ _) + have hp (z : Fin (min (2*Q-2) (genericCoupledWeight Q Q r)+1)) : + fourWedgeInclusion Q r (r+z.val) hr (by simpa only [Nat.add_sub_cancel_left] using hA z) (by simpa only [Nat.add_sub_cancel_left] using hB z) * + (fourWedgeInclusion Q r (r+z.val) hr (by simpa only [Nat.add_sub_cancel_left] using hA z) (by simpa only [Nat.add_sub_cancel_left] using hB z))ᴴ = + (F*physicalCoupledInclusion (2*Q-2) (genericCoupledWeight Q Q r) z.val (hA z) (hB z)) * + (F*physicalCoupledInclusion (2*Q-2) (genericCoupledWeight Q Q r) z.val (hA z) (hB z))ᴴ := by + rw [fourWedgeInclusion_factor] + let v : {k : ℕ // k ≤ 2*Q-2 ∧ k ≤ genericCoupledWeight Q Q r} → + Matrix (FourWedgeIndex Q) (FourWedgeIndex Q) ℂ := fun k => + (F*physicalCoupledInclusion (2*Q-2) (genericCoupledWeight Q Q r) k.val k.property.1 k.property.2) * + (F*physicalCoupledInclusion (2*Q-2) (genericCoupledWeight Q Q r) k.val k.property.1 k.property.2)ᴴ + exact congrArg v (show (⟨r+z.val-r,by constructor <;> omega⟩ : + {k : ℕ // k ≤ 2*Q-2 ∧ k ≤ genericCoupledWeight Q Q r}) = ⟨z.val,by constructor <;> omega⟩ + from Subtype.ext (Nat.add_sub_cancel_left r z.val)) + change F*Fᴴ = _ + calc + _ = F*(∑ z : Fin (min (2*Q-2) (genericCoupledWeight Q Q r)+1), + physicalCoupledInclusion (2*Q-2) (genericCoupledWeight Q Q r) z.val (hA z) (hB z) * + (physicalCoupledInclusion (2*Q-2) (genericCoupledWeight Q Q r) z.val (hA z) (hB z))ᴴ)*Fᴴ := by + rw [physicalCoupledInclusion_complete,Matrix.mul_one] + _ = ∑ z : Fin (min (2*Q-2) (genericCoupledWeight Q Q r)+1), + (F*physicalCoupledInclusion (2*Q-2) (genericCoupledWeight Q Q r) z.val (hA z) (hB z)) * + (F*physicalCoupledInclusion (2*Q-2) (genericCoupledWeight Q Q r) z.val (hA z) (hB z))ᴴ := by + simp only [Matrix.mul_sum,Matrix.sum_mul,Matrix.conjTranspose_mul,Matrix.mul_assoc] + _ = _ := Finset.sum_congr rfl (fun z hz => (hp z).symm) + +noncomputable def fourPairTargetMatrix (Q : ℕ) (hQ : 1 ≤ Q) : + Matrix (FourWedgeIndex Q) (FourWedgeIndex Q) ℂ := + fourPairEmbedding Q 1 hQ*(fourPairEmbedding Q 1 hQ)ᴴ + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/TensorIntertwining.lean b/lean/OAI/Analysis/Laughlin/FourBody/TensorIntertwining.lean new file mode 100644 index 0000000000000000000000000000000000000000..b4a45543c5a8b730d648679e046d0398b28a6af2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/TensorIntertwining.lean @@ -0,0 +1,98 @@ +import OAI.Analysis.Laughlin.FourBody.Copies +import OAI.Analysis.Laughlin.Spin.Disjoint +import OAI.Analysis.Laughlin.Spin.Intertwining + +namespace OAI + +namespace Laughlin.Spin +open Rotation +open scoped BigOperators Matrix Kronecker + +abbrev FourTensorIndex (Q : ℕ) := Fin (2*Q-2+1) × SpinIndex Q Q + +noncomputable def fourTensorInclusion (Q r D : ℕ) (hr : r ≤ Q) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) : + Matrix (FourTensorIndex Q) + (Fin (genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q r) (D-r)+1)) ℂ := + ((1 : Matrix (Fin (2*Q-2+1)) (Fin (2*Q-2+1)) ℂ) ⊗ₖ + physicalCoupledInclusion Q Q r hr hr) * + physicalCoupledInclusion (2*Q-2) (genericCoupledWeight Q Q r) (D-r) hA hB + +noncomputable def fourTensorRepresentation (Q : ℕ) : + SourceSU2 →* Matrix (FourTensorIndex Q) (FourTensorIndex Q) ℂ where + toFun g := sourceSpinRepresentation (2*Q-2) g ⊗ₖ + (sourceSpinRepresentation Q g ⊗ₖ sourceSpinRepresentation Q g) + map_one' := by simp only [map_one,Matrix.one_kronecker_one] + map_mul' g h := by simp only [map_mul,Matrix.mul_kronecker_mul] + +theorem fourTensorRepresentation_continuous (Q : ℕ) (i j : FourTensorIndex Q) : + Continuous (fun g => fourTensorRepresentation Q g i j) := + (sourceSpinRepresentation_continuous (2*Q-2) i.1 j.1).mul + ((sourceSpinRepresentation_continuous Q i.2.1 j.2.1).mul + (sourceSpinRepresentation_continuous Q i.2.2 j.2.2)) + +theorem fourTensorRepresentation_inv (Q : ℕ) (g : SourceSU2) : + fourTensorRepresentation Q g⁻¹ = (fourTensorRepresentation Q g)ᴴ := by + change _ ⊗ₖ (_ ⊗ₖ _) = (_ ⊗ₖ (_ ⊗ₖ _))ᴴ + simp only [Matrix.conjTranspose_kronecker,sourceSpinRepresentation_inv] + +theorem fourTensorInclusion_SU2 (Q r D : ℕ) (hr : r ≤ Q) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) + (g : SourceSU2) : + fourTensorRepresentation Q g * fourTensorInclusion Q r D hr hA hB = + fourTensorInclusion Q r D hr hA hB * + sourceSpinRepresentation + (genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q r) (D-r)) g := by + unfold fourTensorInclusion + change (_ ⊗ₖ _) * ((_ ⊗ₖ _) * _) = _ + rw [← Matrix.mul_assoc,← Matrix.mul_kronecker_mul,Matrix.mul_one, + physicalCoupledInclusion_SU2] + have he : sourceSpinRepresentation (2*Q-2) g ⊗ₖ + (physicalCoupledInclusion Q Q r hr hr * sourceSpinRepresentation (genericCoupledWeight Q Q r) g) = + ((1 : Matrix (Fin (2*Q-2+1)) (Fin (2*Q-2+1)) ℂ) ⊗ₖ + physicalCoupledInclusion Q Q r hr hr) * + (sourceSpinRepresentation (2*Q-2) g ⊗ₖ sourceSpinRepresentation (genericCoupledWeight Q Q r) g) := by + rw [← Matrix.mul_kronecker_mul,Matrix.one_mul] + rw [he,Matrix.mul_assoc,physicalCoupledInclusion_SU2,Matrix.mul_assoc] + +noncomputable def fourWedgeInclusion (Q r D : ℕ) (hr : r ≤ Q) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) : + Matrix (Fin (2*Q-2+1) × WedgePairIndex Q) + (Fin (genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q r) (D-r)+1)) ℂ := + fun i n => (fourBodyCopy Q r D hr hA hB n.val i : ℂ) + +theorem fourTensorInclusion_coordinate (Q r D : ℕ) (hr : r ≤ Q) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) + (i : FourTensorIndex Q) + (n : Fin (genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q r) (D-r)+1)) : + fourTensorInclusion Q r D hr hA hB i n = + ∑ b : Fin (genericCoupledWeight Q Q r+1), + (pairCoupledTensor Q r hr b.val i.2 : ℂ) * + ((-1 : ℂ)^(D-r) * (genericUnitDescendant (2*Q-2) + (genericCoupledWeight Q Q r) (D-r) hA hB n.val (i.1,b) : ℂ)) := by + simp only [fourTensorInclusion,Matrix.mul_apply,Fintype.sum_prod_type, + Matrix.kroneckerMap,Matrix.of_apply,Matrix.one_apply, + ite_mul,one_mul,zero_mul,physicalCoupledInclusion,Matrix.smul_apply, + smul_eq_mul,Matrix.map_apply,genericCoupledInclusion, + pairCoupledTensor,Pi.smul_apply,Complex.ofReal_mul,Complex.ofReal_pow, + Complex.ofReal_neg,Complex.ofReal_one] + rw [Finset.sum_comm] + simp only [Finset.sum_ite_eq,Finset.mem_univ,ite_true] + +theorem fourWedgeInclusion_tensor_coordinate (Q r D : ℕ) (hr : r ≤ Q) + (hA : D-r ≤ 2*Q-2) (hB : D-r ≤ genericCoupledWeight Q Q r) + (i : Fin (2*Q-2+1) × WedgePairIndex Q) + (n : Fin (genericCoupledWeight (2*Q-2) (genericCoupledWeight Q Q r) (D-r)+1)) : + fourWedgeInclusion Q r D hr hA hB i n = + (Real.sqrt 2 : ℂ) * fourTensorInclusion Q r D hr hA hB (i.1,i.2.val) n := by + rw [fourWedgeInclusion,fourBodyCopy_coordinate,fourTensorInclusion_coordinate] + simp only [Complex.ofReal_sum,Complex.ofReal_mul,Complex.ofReal_pow, + Complex.ofReal_neg,Complex.ofReal_one,pairCoupledWedge,tensorToWedgePair, + Complex.ofReal_mul,Finset.mul_sum] + apply Finset.sum_congr rfl + intro b hb + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/TotalAllowance.lean b/lean/OAI/Analysis/Laughlin/FourBody/TotalAllowance.lean new file mode 100644 index 0000000000000000000000000000000000000000..64e6c3ecdaadc7703ae1b16bad9d53cd913eb3e6 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/TotalAllowance.lean @@ -0,0 +1,43 @@ +import OAI.Analysis.Laughlin.FourBody.Basic +import OAI.Analysis.Laughlin.FourBody.HaarAllowance + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory +open scoped BigOperators + +theorem source_allowance_count_fin : + (∑ n : Fin 23, ((n.val+2)/2) * ((n.val+2)^2/4)) = 10946 := by + have he (n : ℕ) (f : ℕ → ℕ) : + (∑ i ∈ Finset.range n, f i) = ((List.range n).map f).sum := by + induction n with + | zero => simp + | succ n ih => simp only [Finset.sum_range_succ,List.range_succ,List.map_append, + List.sum_append,List.map_singleton,List.sum_singleton,ih] + rw [Fin.sum_univ_eq_sum_range (fun n : ℕ => ((n+2)/2) * ((n+2)^2/4)) 23,he] + exact Certificate.allowance_count + +theorem physical_fourBody_total_haar_allowance (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + (∑ d : Fin 23, ∑ i : Fin ((d.val+2)/2), + (2*Q-2+1 : ℕ) * (∫ g, occupationNormSq Q + (physicalFourCopyEnd Q (Certificate.copyLabel (D := d.val+1) i) (d.val+1) (by omega) + (exteriorRotation Q g⁻¹ x)) ∂sourceHaar)) ≤ + 10946 * sourceFockEnergy Q x := by + calc + _ ≤ ∑ d : Fin 23, ∑ _i : Fin ((d.val+2)/2), + ((d.val+2)^2/4 : ℕ) * sourceFockEnergy Q x := by + apply Finset.sum_le_sum + intro d hd + apply Finset.sum_le_sum + intro i hi + exact physical_fourBody_haar_allowance_retained Q (Certificate.copyLabel (D := d.val+1) i) (d.val+1) + (by unfold Certificate.copyLabel; have := i.isLt; omega) + (by exact ⟨i.val,by unfold Certificate.copyLabel; omega⟩) hQ (by omega) x + _ = 10946 * sourceFockEnergy Q x := by + simp only [Finset.sum_const,Finset.card_univ,Fintype.card_fin,nsmul_eq_mul,← mul_assoc, + ← Nat.cast_mul,← Finset.sum_mul,← Nat.cast_sum,source_allowance_count_fin,Nat.cast_ofNat] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/TotalTransfer.lean b/lean/OAI/Analysis/Laughlin/FourBody/TotalTransfer.lean new file mode 100644 index 0000000000000000000000000000000000000000..dc5d1ea258630172d8b7419e8b4d5972e00e873b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/TotalTransfer.lean @@ -0,0 +1,34 @@ +import OAI.Analysis.Laughlin.FourBody.HaarTransfer + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory +open scoped BigOperators + +theorem physical_fourBody_total_haar_transfer (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + -(averagedFourTransferError Q * sourceFockEnergy Q x) ≤ + ∑ d : Fin 23, (2*Q-2+1 : ℕ) * (∫ g, occupationQuadratic Q (finiteFourMiddle Q (d.val+1)) + (fun i : Fin ((d.val+2)/2) => physicalFourCopyEnd Q + (Certificate.copyLabel (D := d.val+1) i) (d.val+1) (by omega) + (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) := by + have hs : (∑ d : Fin 23, fourBodyRho (d.val+1) Q) ≤ uniformFourBodyRho Q := by + rw [Fin.sum_univ_eq_sum_range (fun d => fourBodyRho (d+1) Q) 23] + unfold uniformFourBodyRho + rw [Finset.sum_range_succ' (fun D => fourBodyRho D Q) 23] + exact le_add_of_nonneg_right (fourBodyRho_nonneg 0 Q) + have hE : 0 ≤ sourceFockEnergy Q x := + Finset.sum_nonneg (fun p hp => occupationNormSq_nonneg Q _) + calc + _ ≤ -(24 * (∑ d : Fin 23, fourBodyRho (d.val+1) Q) * sourceFockEnergy Q x) := + neg_le_neg (mul_le_mul_of_nonneg_right (mul_le_mul_of_nonneg_left hs (by norm_num)) hE) + _ = ∑ d : Fin 23, -(24 * fourBodyRho (d.val+1) Q * sourceFockEnergy Q x) := by + rw [Finset.mul_sum,Finset.sum_mul,Finset.sum_neg_distrib] + _ ≤ _ := by + apply Finset.sum_le_sum + intro d hd + exact physical_fourBody_haar_transfer Q (d.val+1) hQ (by omega) (by omega) x + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/TraceReadout.lean b/lean/OAI/Analysis/Laughlin/FourBody/TraceReadout.lean new file mode 100644 index 0000000000000000000000000000000000000000..2811ccd1d3c57b98de008a6ca73d900f15f566ba --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/TraceReadout.lean @@ -0,0 +1,60 @@ +import OAI.Analysis.Laughlin.FourBody.PhysicalMatrix +import OAI.Analysis.Laughlin.FourBody.RetainedInclusions + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +noncomputable def retainedFourReal (Q D : ℕ) (hQ : D+2 ≤ Q) (r : OddPairLabel D) : + Matrix (FourWedgeIndex Q) (Fin (fourSpinWeight Q D+1)) ℝ := + fun i n => fourBodyCopy Q (oddPairDeficit r) D + (by have := oddPairDeficit_le r; omega) + (by have := oddPairDeficit_le r; omega) + (by have := oddPairDeficit_le r; unfold genericCoupledWeight; omega) n.val i + +theorem retainedFourReal_complex (Q D : ℕ) (hQ : D+2 ≤ Q) (r : OddPairLabel D) : + (retainedFourReal Q D hQ r).map Complex.ofReal = retainedFourInclusion Q D hQ r := rfl + +theorem retainedFourReal_outer_trace (Q D T p j k q l i : ℕ) (hQ : D+2 ≤ Q) + (hTQ : T+2 ≤ Q) (r s : OddPairLabel D) (hp : p+j+k=T) (hq : q+l+i=T) : + Matrix.trace ((retainedFourReal Q D hQ r)ᵀ * + realOuter (fourSignedUnit Q p j k) (fourSignedUnit Q q l i) * retainedFourReal Q D hQ s) = + if D ≤ T then fourBodyCoefficient Q (oddPairDeficit r) D T p j k * + fourBodyCoefficient Q (oddPairDeficit s) D T q l i else 0 := by + rw [trace_cross_outer] + by_cases hDT : D ≤ T + · rw [ite_eq_left hDT] + let n : Fin (fourSpinWeight Q D+1) := ⟨T-D,by unfold fourSpinWeight; omega⟩ + rw [Finset.sum_eq_single n] + · change dotProduct (fourBodyCopy Q (oddPairDeficit r) D _ _ _ (T-D)) (fourSignedUnit Q p j k) * + dotProduct (fourBodyCopy Q (oddPairDeficit s) D _ _ _ (T-D)) (fourSignedUnit Q q l i) = _ + rw [fourBodyCopy_signed_at_level Q (oddPairDeficit r) D T p j k + (oddPairDeficit_odd r) (oddPairDeficit_le r) hDT hTQ hp, + fourBodyCopy_signed_at_level Q (oddPairDeficit s) D T q l i + (oddPairDeficit_odd s) (oddPairDeficit_le s) hDT hTQ hq] + · intro m hm hmn + change dotProduct (fourBodyCopy Q (oddPairDeficit r) D _ _ _ m.val) (fourSignedUnit Q p j k) * _ = 0 + rw [fourBodyCopy_signed_off Q (oddPairDeficit r) D m.val p j k _ (oddPairDeficit_le r) _ _ (by + intro he; apply hmn; apply Fin.ext; dsimp [n]; omega),zero_mul] + · simp + · rw [ite_eq_right hDT] + apply Finset.sum_eq_zero + intro n hn + change dotProduct (fourBodyCopy Q (oddPairDeficit r) D _ _ _ n.val) (fourSignedUnit Q p j k) * _ = 0 + rw [fourBodyCopy_signed_off Q (oddPairDeficit r) D n.val p j k _ (oddPairDeficit_le r) _ _ (by omega),zero_mul] + +theorem fourBodyTermMatrix_trace (Q D t : ℕ) (hQ : D+2 ≤ Q) (r s : OddPairLabel D) + (e f : ℕ × ℕ × ℤ) (he : t ≤ e.1+e.2.1) (hf : t ≤ f.1+f.2.1) + (hTQ : e.1+e.2.1+(f.1+f.2.1-t)+2 ≤ Q) : + Matrix.trace ((retainedFourReal Q D hQ r)ᵀ * fourBodyTermMatrix Q t e f * + retainedFourReal Q D hQ s) = -fourErrorEntry Q D (oddPairDeficit r) (oddPairDeficit s) t e f := by + rw [fourBodyTermMatrix,Matrix.mul_smul,Matrix.smul_mul,Matrix.trace_smul, + retainedFourReal_outer_trace Q D (e.1+e.2.1+(f.1+f.2.1-t)) _ _ _ _ _ _ hQ hTQ r s rfl (by omega)] + unfold fourErrorEntry + dsimp only + split_ifs <;> simp only [smul_eq_mul] <;> ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/TransferCoefficients.lean b/lean/OAI/Analysis/Laughlin/FourBody/TransferCoefficients.lean new file mode 100644 index 0000000000000000000000000000000000000000..e1016ee6d910d5c89bfc9130fbdc9c75964d4625 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/TransferCoefficients.lean @@ -0,0 +1,50 @@ +import OAI.Analysis.Laughlin.FourBody.MiddleLimit +import OAI.Analysis.Laughlin.FourBody.TransferConjugation +import OAI.Analysis.Laughlin.Operators.CopyQuadraticMatrix +import OAI.Analysis.Laughlin.Operators.MatrixMetricError + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators Topology +open Filter Spin + +noncomputable def finiteLocalFourMatrix (Q D : ℕ) : LocalFourIndex D → LocalFourIndex D → ℝ := + copyQuadraticMatrix (finiteFourMiddle Q D) + (fun i b => physicalFourBeta Q (Certificate.copyLabel i) D b) + +noncomputable def limitLocalFourMatrix (D : ℕ) : LocalFourIndex D → LocalFourIndex D → ℝ := + copyQuadraticMatrix (limitFourMiddle D) + (fun i b => fourBodyLimitCoefficient (Certificate.copyLabel i) D D + b.val.1.val b.val.2.1.val b.val.2.2.val) + +theorem finiteLocalFourMatrix_tendsto (D : ℕ) (a b : LocalFourIndex D) : + Tendsto (fun Q => finiteLocalFourMatrix Q D a b) atTop (𝓝 (limitLocalFourMatrix D a b)) := by + unfold finiteLocalFourMatrix limitLocalFourMatrix copyQuadraticMatrix + apply tendsto_finsetSum + intro i hi + apply tendsto_finsetSum + intro j hj + have hiD : Certificate.copyLabel i ≤ D := by unfold Certificate.copyLabel; have := i.isLt; omega + have hjD : Certificate.copyLabel j ≤ D := by unfold Certificate.copyLabel; have := j.isLt; omega + exact ((finiteFourMiddle_tendsto D i j).mul (physicalFourBeta_tendsto _ D hiD a)).mul + (physicalFourBeta_tendsto _ D hjD b) + +noncomputable def fourBodyRho (D Q : ℕ) : ℝ := + matrixMetricError 24 Q (finiteLocalFourMatrix Q D) (limitLocalFourMatrix D) * + (Fintype.card (LocalFourIndex D) : ℝ)^2 + +theorem fourBodyRho_nonneg (D Q : ℕ) : 0 ≤ fourBodyRho D Q := + mul_nonneg (matrixMetricError_nonneg _ _ _ _) (sq_nonneg _) + +theorem fourBodyRho_tendsto (D : ℕ) : Tendsto (fourBodyRho D) atTop (𝓝 0) := by + have h := (matrixMetricError_tendsto 24 (fun Q => finiteLocalFourMatrix Q D) + (limitLocalFourMatrix D) (finiteLocalFourMatrix_tendsto D)).mul_const + ((Fintype.card (LocalFourIndex D) : ℝ)^2) + change Tendsto (fun Q => matrixMetricError 24 Q (finiteLocalFourMatrix Q D) + (limitLocalFourMatrix D) * (Fintype.card (LocalFourIndex D) : ℝ)^2) atTop (𝓝 0) + simpa using h + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/TransferConjugation.lean b/lean/OAI/Analysis/Laughlin/FourBody/TransferConjugation.lean new file mode 100644 index 0000000000000000000000000000000000000000..45ca2297924b92ed50e78061e509b027980510d9 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/TransferConjugation.lean @@ -0,0 +1,61 @@ +import OAI.Analysis.Laughlin.Exterior.FourConjugation +import OAI.Analysis.Laughlin.FourBody.CoefficientLimit +import OAI.Analysis.Laughlin.Pair.FactorLimit + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Topology +open Filter + +abbrev LocalFourIndex (D : ℕ) := + {b : Fin (D+1) × Fin (D+1) × Fin (D+1) // b.1.val+b.2.1.val+b.2.2.val=D ∧ b.2.1 < b.2.2} + +noncomputable def physicalFourBeta (Q r D : ℕ) (b : LocalFourIndex D) : ℝ := + fourBodyCoefficient Q r D D b.val.1.val b.val.2.1.val b.val.2.2.val * + pairFactor Q b.val.1.val / (modeFactor Q b.val.2.1.val * modeFactor Q b.val.2.2.val) + +theorem physicalFourBeta_tendsto (r D : ℕ) (hrD : r ≤ D) (b : LocalFourIndex D) : + Tendsto (fun Q => physicalFourBeta Q r D b) atTop + (𝓝 (fourBodyLimitCoefficient r D D b.val.1.val b.val.2.1.val b.val.2.2.val)) := by + have hs := source_fourBody_coefficient_tendsto r D D b.val.1.val b.val.2.1.val b.val.2.2.val + hrD (le_refl _) b.property.1 + have hp := pairFactor_tendsto b.val.1.val + have hj := modeFactor_tendsto b.val.2.1.val + have hk := modeFactor_tendsto b.val.2.2.val + have hh := (hs.mul hp).div (hj.mul hk) (by norm_num) + simp only [mul_one,div_one] at hh + apply hh.congr + intro Q + rfl + +end Laughlin.Spin + +namespace Laughlin.Fock +open scoped BigOperators +open Spin + +noncomputable def physicalFourCopyEnd (Q r D : ℕ) (hDQ : D ≤ Q) : Module.End ℂ (Space Q) := + ∑ b : LocalFourIndex D, + (fourBodyCoefficient Q r D D b.val.1.val b.val.2.1.val b.val.2.2.val : ℂ) • + sourceFourEnd Q b.val.1.val ⟨b.val.2.1.val,by omega⟩ ⟨b.val.2.2.val,by omega⟩ + +theorem physicalFourCopyEnd_conjugation (Q r D : ℕ) (hDQ : D ≤ Q) (hQ : 2 ≤ Q) + (x : Space Q) : + physicalFourCopyEnd Q r D hDQ x = physicalScalingInv Q + (∑ b : LocalFourIndex D, (physicalFourBeta Q r D b : ℂ) • + limitFourEnd Q b.val.1.val ⟨b.val.2.1.val,by omega⟩ ⟨b.val.2.2.val,by omega⟩ + (physicalScaling Q x)) := by + simp only [physicalFourCopyEnd,LinearMap.sum_apply,LinearMap.smul_apply,map_sum,map_smul] + apply Finset.sum_congr rfl + intro b hb + rw [sourceFour_conjugation Q b.val.1.val (by omega) (by omega)] + rw [smul_smul] + congr 1 + simp only [physicalFourBeta] + push_cast + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/Ungroup.lean b/lean/OAI/Analysis/Laughlin/FourBody/Ungroup.lean new file mode 100644 index 0000000000000000000000000000000000000000..5a385e73e3b246b8b4f4b174dfcb1d6b64b8ff05 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/Ungroup.lean @@ -0,0 +1,83 @@ +import OAI.Analysis.Laughlin.FourBody.Expansion + +namespace OAI + +namespace Laughlin.Fock +open Spin +open scoped BigOperators Matrix + +noncomputable def boundedAnnihilate (Q n : ℕ) : Module.End ℂ (Space Q) := + if h : n ≤ Q then annihilate ⟨n,by omega⟩ else 0 + +theorem boundedAnnihilate_rowOutput (Q t : ℕ) (hQ : 15 ≤ Q) (T : RowLevel t) : + boundedAnnihilate Q (T.val.val-t) = annihilate (rowOutputMode Q t hQ T) := by + have ht : T.val.val-t ≤ Q := by have h := T.val.isLt; omega + rw [boundedAnnihilate,dite_eq_left ht] + rfl + +theorem linearMap_list_sum {I : Type*} (Q : ℕ) (L : Module.End ℂ (Space Q)) + (l : List I) (v : I → Space Q) : + L (l.map v).sum = (l.map (fun i => L (v i))).sum := by + induction l with + | nil => simp + | cons i l ih => simp only [List.map_cons,List.sum_cons,map_add,ih] + +noncomputable def sourceRowFourEntry (Q t : ℕ) (e f : ℕ × ℕ × ℤ) (x : Space Q) : ℂ := + -(sourceAlpha t e : ℂ)*(sourceAlpha t f : ℂ) * occupationInner Q + (boundedAnnihilate Q (f.1+f.2.1-t) (sourceEntryThree Q e x)) + (boundedAnnihilate Q (e.1+e.2.1-t) (sourceEntryThree Q f x)) + +theorem sourceRowFourForm_entries (Q : ℕ) (hQ : 15 ≤ Q) + (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) (hr : row ∈ Certificate.rows) (x : Space Q) : + sourceRowFourForm Q hQ row x = + (row.2.2.map (fun e => (row.2.2.map (fun f => sourceRowFourEntry Q row.1 e f x)).sum)).sum := by + classical + let term := fun (T S : RowLevel row.1) (e f : ℕ × ℕ × ℤ) => + if e.1+e.2.1=T.val.val then if f.1+f.2.1=S.val.val then + -(sourceAlpha row.1 e : ℂ)*(sourceAlpha row.1 f : ℂ) * occupationInner Q + (boundedAnnihilate Q (S.val.val-row.1) (sourceEntryThree Q e x)) + (boundedAnnihilate Q (T.val.val-row.1) (sourceEntryThree Q f x)) else 0 else 0 + have ht (T S : RowLevel row.1) : + -occupationInner Q + (annihilate (rowOutputMode Q row.1 hQ S) (sourceRowLevel Q row.1 T.val.val row.2.2 x)) + (annihilate (rowOutputMode Q row.1 hQ T) (sourceRowLevel Q row.1 S.val.val row.2.2 x)) = + (row.2.2.map (fun e => (row.2.2.map (fun f => term T S e f)).sum)).sum := by + rw [← boundedAnnihilate_rowOutput,← boundedAnnihilate_rowOutput] + simp only [sourceRowLevel_entries,linearMap_list_sum] + rw [occupationInner_list_left] + simp_rw [occupationInner_list_right] + rw [List.sum_neg] + simp only [List.map_map,Function.comp_def] + congr 1 + apply List.map_congr_left + intro e he + rw [List.sum_neg] + simp only [List.map_map,Function.comp_def] + congr 1 + apply List.map_congr_left + intro f hf + dsimp only [term] + by_cases heT : e.1+e.2.1=T.val.val <;> by_cases hfS : f.1+f.2.1=S.val.val + · simp only [ite_eq_left heT,ite_eq_left hfS,map_smul,occupationInner_smul_left, + occupationInner_smul_right,Complex.star_def,Complex.conj_ofReal] + ring + all_goals simp [heT,hfS,occupationInner] + rw [sourceRowFourForm,← Finset.sum_neg_distrib] + simp only [← Finset.sum_neg_distrib,ht] + simp_rw [finset_list_sum_swap] + congr 1 + apply List.map_congr_left + intro e he + congr 1 + apply List.map_congr_left + intro f hf + obtain ⟨het,he15,he8⟩ := (source_threeBody_rows_support row hr).2 e he + obtain ⟨hft,hf15,hf8⟩ := (source_threeBody_rows_support row hr).2 f hf + simp only [term,Finset.sum_ite_irrel,Finset.sum_const_zero] + rw [rowLevel_sum_select row.1 (e.1+e.2.1) het (by omega)] + rw [rowLevel_sum_select row.1 (f.1+f.2.1) hft (by omega)] + rfl + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/UniformTransfer.lean b/lean/OAI/Analysis/Laughlin/FourBody/UniformTransfer.lean new file mode 100644 index 0000000000000000000000000000000000000000..9f264b6dd8aff124122b22599a95e5e83866110a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/UniformTransfer.lean @@ -0,0 +1,84 @@ +import OAI.Analysis.Laughlin.Asymptotics.LimitFourLocalSum +import OAI.Analysis.Laughlin.FourBody.LimitPositive +import OAI.Analysis.Laughlin.FourBody.TransferCoefficients +import OAI.Analysis.Laughlin.Operators.TruncatedFourCopy +import OAI.Analysis.Laughlin.Operators.TruncatedPairReturn + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators Topology +open Filter Spin + +theorem source_fourBody_uniform_transfer (Q D : ℕ) (hQ : 24 ≤ Q) + (hD₁ : 1 ≤ D) (hD₂ : D ≤ 23) (x : Space Q) : + -(fourBodyRho D Q * sourcePairWindow Q x) ≤ + occupationQuadratic Q (finiteFourMiddle Q D) + (fun i : Fin ((D+1)/2) => physicalFourCopyEnd Q (Certificate.copyLabel i) D (by omega) x) := by + let hDQ : D ≤ Q := by omega + let v : LocalFourIndex D → Space Q := fun b => + localFourOperators Q D hDQ b (truncatedScaling 24 Q x) + let ε := matrixMetricError 24 Q (finiteLocalFourMatrix Q D) (limitLocalFourMatrix D) + let n : ℝ := Fintype.card (LocalFourIndex D) + have hε : 0 ≤ ε := matrixMetricError_nonneg _ _ _ _ + have hn : 0 ≤ n := by positivity + have hfinite : occupationQuadratic Q (finiteFourMiddle Q D) + (fun i : Fin ((D+1)/2) => physicalFourCopyEnd Q (Certificate.copyLabel i) D hDQ x) = + occupationQuadratic Q (finiteLocalFourMatrix Q D) (fun b => truncatedScalingInv 24 Q (v b)) := by + simp_rw [physicalFourCopyEnd_truncated Q _ D hDQ hQ hD₂ x,map_sum,map_smul] + exact occupationQuadratic_factor Q (finiteFourMiddle Q D) _ _ + rw [hfinite] + have hbase := source_fourBody_limitpositive Q D (by omega) hD₁ hD₂ (truncatedScaling 24 Q x) + change 0 ≤ occupationQuadratic Q (limitFourMiddle D) + (fun i => limitFourCopyEnd Q (Certificate.copyLabel i) D (truncatedScaling 24 Q x)) at hbase + have hends (i : Fin ((D+1)/2)) : + limitFourCopyEnd Q (Certificate.copyLabel i) D (truncatedScaling 24 Q x) = + ∑ b : LocalFourIndex D, + (fourBodyLimitCoefficient (Certificate.copyLabel i) D D + b.val.1.val b.val.2.1.val b.val.2.2.val : ℂ) • v b := by + apply limitFourCopyEnd_local_sum Q _ D hDQ + · unfold Certificate.copyLabel; have := i.isLt; omega + · exact ⟨i.val,by unfold Certificate.copyLabel; omega⟩ + simp_rw [hends] at hbase + have hbase := hbase.trans_eq (occupationQuadratic_factor Q (limitFourMiddle D) + (fun (i : Fin ((D+1)/2)) (b : LocalFourIndex D) => + fourBodyLimitCoefficient (Certificate.copyLabel i) D D b.val.1.val b.val.2.1.val b.val.2.2.val) v) + change 0 ≤ occupationQuadratic Q (limitLocalFourMatrix D) v at hbase + have herr := truncatedQuadratic_error 24 Q (finiteLocalFourMatrix Q D) + (limitLocalFourMatrix D) v ε hε (matrixMetricError_bound 24 Q hQ _ _) + have hpair : (∑ b, occupationNormSq Q (v b)) ≤ n * sourcePairWindow Q x := by + apply (localFourOperators_bound Q D hDQ hD₂ (truncatedScaling 24 Q x)).trans + exact mul_le_mul_of_nonneg_left (truncated_pair_window_return Q hQ x) hn + have hbound : |occupationQuadratic Q (finiteLocalFourMatrix Q D) (fun b => truncatedScalingInv 24 Q (v b)) - + occupationQuadratic Q (limitLocalFourMatrix D) v| ≤ fourBodyRho D Q * sourcePairWindow Q x := by + apply herr.trans + calc + _ ≤ ε*n*(n*sourcePairWindow Q x) := mul_le_mul_of_nonneg_left hpair (mul_nonneg hε hn) + _ = _ := by change ε*n*(n*sourcePairWindow Q x)=(ε*n^2)*sourcePairWindow Q x; ring + have hl := (abs_le.mp hbound).1 + linarith + +noncomputable def uniformFourBodyRho (Q : ℕ) : ℝ := ∑ D ∈ Finset.range 24, fourBodyRho D Q + +theorem uniformFourBodyRho_nonneg (Q : ℕ) : 0 ≤ uniformFourBodyRho Q := + Finset.sum_nonneg (fun degree _ => fourBodyRho_nonneg degree Q) + +theorem uniformFourBodyRho_tendsto : Tendsto uniformFourBodyRho atTop (𝓝 0) := by + have h := tendsto_finsetSum (s := Finset.range 24) (fun D hD => fourBodyRho_tendsto D) + change Tendsto (fun Q => ∑ D ∈ Finset.range 24, fourBodyRho D Q) atTop (𝓝 0) + simpa using h + +theorem source_fourBody_uniform_transfer_all (Q D : ℕ) (hQ : 25 ≤ Q) + (hD₁ : 1 ≤ D) (hD₂ : D ≤ 23) (x : Space Q) : + -(uniformFourBodyRho Q * sourcePairWindow Q x) ≤ + occupationQuadratic Q (finiteFourMiddle Q D) + (fun i : Fin ((D+1)/2) => physicalFourCopyEnd Q (Certificate.copyLabel i) D (by omega) x) := by + have hρ : fourBodyRho D Q ≤ uniformFourBodyRho Q := + Finset.single_le_sum (fun d hd => fourBodyRho_nonneg d Q) (Finset.mem_range.mpr (by omega)) + have he : 0 ≤ sourcePairWindow Q x := Finset.sum_nonneg (fun p hp => occupationNormSq_nonneg Q _) + exact (neg_le_neg (mul_le_mul_of_nonneg_right hρ he)).trans + (source_fourBody_uniform_transfer Q D (by omega) hD₁ hD₂ x) + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/WedgeCompression.lean b/lean/OAI/Analysis/Laughlin/FourBody/WedgeCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..8ef114d84a0769ad2177a2d4179a03ad625a2359 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/WedgeCompression.lean @@ -0,0 +1,55 @@ +import OAI.Analysis.Laughlin.FourBody.PhysicalCertificate +import OAI.Analysis.Laughlin.FourBody.Symmetry +import OAI.Analysis.Laughlin.Operators.MatrixPhysicalCompression +import OAI.Analysis.Laughlin.Operators.RealComplexMatrixPositive + +namespace OAI + +namespace Laughlin.Fock +open scoped Matrix BigOperators ComplexOrder +open Matrix Spin + +noncomputable def physicalWedgeColumns (Q D : ℕ) : + Matrix (Finset (Fin (Q+1))) (Fin ((D+1)/2)) ℂ := + fun A i => (occupationBasis Q).repr (limitFourColumn Q (Certificate.copyLabel i) D) A + +noncomputable def physicalLimitMiddle (D : ℕ) : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℂ := + (Certificate.certificateDiagonal D - physicalLimitError D).map Complex.ofReal + +theorem physicalWedgeColumns_gram (Q D : ℕ) (hQ : D+1 ≤ Q) : + (physicalWedgeColumns Q D)ᴴ * physicalWedgeColumns Q D = + (physicalLimitGram Q D).map Complex.ofReal := by + rw [physicalLimitGram_eq Q D hQ] + ext i j + change occupationInner Q (limitFourColumn Q (Certificate.copyLabel i) D) + (limitFourColumn Q (Certificate.copyLabel j) D) = _ + exact source_fourBody_physical_scaledGram Q D hQ i j + +theorem physicalLimitMiddle_hermitian (D : ℕ) : (physicalLimitMiddle D).IsHermitian := by + apply real_complex_matrix_hermitian + apply Matrix.IsHermitian.sub + · simp [Certificate.certificateDiagonal,Matrix.IsHermitian] + · rw [physicalLimitError_eq] + ext i j + simp only [Matrix.conjTranspose_apply,star_trivial,Certificate.scaledError, + Certificate.weightSqrtDiagonal,Matrix.diagonal_mul,Matrix.mul_diagonal, + Matrix.map_apply,Certificate.errorRational,Rat.coe_castHom] + rw [Certificate.Y_symm D (Certificate.copyLabel j) (Certificate.copyLabel i)] + ring + +theorem source_physical_wedge_compression (Q D : ℕ) (hQ : D+1 ≤ Q) + (hD₁ : 1 ≤ D) (hD₂ : D ≤ 23) : + (physicalWedgeColumns Q D * physicalLimitMiddle D * (physicalWedgeColumns Q D)ᴴ).PosSemidef := by + apply matrix_physical_compression _ _ (physicalLimitMiddle_hermitian D) + rw [physicalWedgeColumns_gram Q D hQ] + have h := real_complex_matrix_positive _ (source_physical_four_body_certificates Q D hQ hD₁ hD₂) + have hm : ∀ A B : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℝ, + (A*B).map Complex.ofReal = A.map Complex.ofReal * B.map Complex.ofReal := by + intro A B + ext i j + simp [Matrix.mul_apply,Matrix.map_apply,Complex.ofReal_sum] + simpa only [physicalLimitMiddle,hm] using h + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/WeightSlice.lean b/lean/OAI/Analysis/Laughlin/FourBody/WeightSlice.lean new file mode 100644 index 0000000000000000000000000000000000000000..70b1dec06b4c8c6d6b1c43dc7cac5327eaf683b1 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/WeightSlice.lean @@ -0,0 +1,40 @@ +import OAI.Analysis.Laughlin.FourBody.CoefficientNorm +import OAI.Analysis.Laughlin.Operators.LocalFourIndexEquiv + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +theorem fourWeightSlice_sum {M : Type*} [AddCommMonoid M] (Q D : ℕ) (hQ : D+2 ≤ Q) + (f : ℕ → Fin (Q+1) → Fin (Q+1) → M) : + (∑ p : Fin (2*Q-2+1), ∑ i : WedgePairIndex Q, + if p.val+i.val.1.val+i.val.2.val=D then f p.val i.val.1 i.val.2 else 0) = + ∑ b : LocalFourIndex D, f b.val.1.val ⟨b.val.2.1.val,by omega⟩ ⟨b.val.2.2.val,by omega⟩ := by + classical + let F := fun p : ℕ => ∑ j : Fin (Q+1), ∑ k : Fin (Q+1), + if p+j.val+k.val=D ∧ j < k then f p j k else 0 + have hi (p : ℕ) : (∑ i : WedgePairIndex Q, + if p+i.val.1.val+i.val.2.val=D then f p i.val.1 i.val.2 else 0) = F p := by + have hs := Finset.sum_subtype (F := inferInstance) (p := fun i : SpinIndex Q Q => i.1 < i.2) + (Finset.univ.filter (fun i : SpinIndex Q Q => i.1 < i.2)) (by simp) + (fun i => if p+i.1.val+i.2.val=D then f p i.1 i.2 else 0) + rw [← hs,Finset.sum_filter,Fintype.sum_prod_type] + apply Finset.sum_congr rfl; intro j hj + apply Finset.sum_congr rfl; intro k hk + by_cases h₁ : j < k <;> by_cases h₂ : p+j.val+k.val=D <;> simp [h₁,h₂] + simp_rw [hi] + rw [Fin.sum_univ_eq_sum_range] + have hsub : (∑ p ∈ Finset.range (D+1), F p) = ∑ p ∈ Finset.range (2*Q-2+1), F p := by + apply Finset.sum_subset (Finset.range_mono (by omega)) + intro p hp hn + have hpD : D < p := by simpa using hn + apply Finset.sum_eq_zero; intro j hj + apply Finset.sum_eq_zero; intro k hk + simp [show p+j.val+k.val≠D by omega] + rw [← hsub,← Fin.sum_univ_eq_sum_range] + exact localFourIndex_sum Q D (by omega) f + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/FourBody/WeightedReadout.lean b/lean/OAI/Analysis/Laughlin/FourBody/WeightedReadout.lean new file mode 100644 index 0000000000000000000000000000000000000000..b833d9a41de6b322440b47c1dc9ad39c15e66582 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/FourBody/WeightedReadout.lean @@ -0,0 +1,51 @@ +import OAI.Analysis.Laughlin.FourBody.LimitCARReadout + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem sum_weighted_wedgeDelta (Q : ℕ) (S : Fin (Q+1) → Fin (Q+1) → ℝ) + (hS : ∀ j k, S k j = -S j k) (a b : Fin (Q+1)) : + (∑ j, ∑ k, ((S j k / 2 : ℝ) : ℂ)*wedgeDelta Q j k a b) = (S a b : ℂ) := by + simp only [wedgeDelta,delta,mul_sub,mul_ite,mul_one,mul_zero, + Finset.sum_sub_distrib,Finset.sum_ite_eq',Finset.mem_univ,ite_true] + simp only [Finset.sum_ite_irrel,Finset.sum_const_zero,Finset.sum_ite_eq',Finset.mem_univ,ite_true] + rw [hS a b] + push_cast + ring + +theorem sum_weighted_wedgeDelta_factor (Q : ℕ) (S : Fin (Q+1) → Fin (Q+1) → ℝ) + (hS : ∀ j k, S k j = -S j k) (c : ℂ) (a b : Fin (Q+1)) : + (∑ j, ∑ k, ((S j k / 2 : ℝ) : ℂ)*(c*wedgeDelta Q j k a b)) = c*(S a b : ℂ) := by + calc + _ = c*(∑ j, ∑ k, ((S j k / 2 : ℝ) : ℂ)*wedgeDelta Q j k a b) := by + simp only [Finset.mul_sum] + apply Finset.sum_congr rfl; intro j hj + apply Finset.sum_congr rfl; intro k hk; ring + _ = _ := by rw [sum_weighted_wedgeDelta Q S hS a b] + +noncomputable def weightedFourEnd (Q p : ℕ) (S : Fin (Q+1) → Fin (Q+1) → ℝ) : + Module.End ℂ (Space Q) := + ∑ j, ∑ k, ((S j k / 2 : ℝ) : ℂ) • limitFourEnd Q p j k + +theorem weightedFourEnd_readout (Q p : ℕ) (S : Fin (Q+1) → Fin (Q+1) → ℝ) + (hS : ∀ j k, S k j = -S j k) (a b c d : Fin (Q+1)) : + weightedFourEnd Q p S (create a (create b (create c (create d (1 : Space Q))))) = + ((Real.sqrt 2*pairLimitCoefficient p a.val b.val*S c d - + Real.sqrt 2*pairLimitCoefficient p a.val c.val*S b d + + Real.sqrt 2*pairLimitCoefficient p a.val d.val*S b c + + Real.sqrt 2*pairLimitCoefficient p b.val c.val*S a d - + Real.sqrt 2*pairLimitCoefficient p b.val d.val*S a c + + Real.sqrt 2*pairLimitCoefficient p c.val d.val*S a b : ℝ) : ℂ) • (1 : Space Q) := by + simp only [weightedFourEnd,LinearMap.sum_apply,LinearMap.smul_apply,limitFourEnd_four_create, + smul_smul,← Finset.sum_smul] + congr 1 + simp only [mul_sub,mul_add,Finset.sum_sub_distrib,Finset.sum_add_distrib, + sum_weighted_wedgeDelta_factor Q S hS] + push_cast + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/GapEstimates.lean b/lean/OAI/Analysis/Laughlin/GapEstimates.lean new file mode 100644 index 0000000000000000000000000000000000000000..a7477726252e0227b0fcae33edea53ef7b160aa3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/GapEstimates.lean @@ -0,0 +1,3 @@ +import OAI.Analysis.Laughlin.Fock.LaughlinGap +import OAI.Analysis.Laughlin.Planar.Forms +import OAI.Analysis.Laughlin.Charge.UniformGap diff --git a/lean/OAI/Analysis/Laughlin/Main.lean b/lean/OAI/Analysis/Laughlin/Main.lean new file mode 100644 index 0000000000000000000000000000000000000000..9f6bb591d42b0f1a5ea3408526e63a8e1927d699 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Main.lean @@ -0,0 +1,46 @@ +import OAI.Analysis.Laughlin.Fock.SpectralDistance +import OAI.Analysis.Laughlin.Polynomial.PhysicalLaughlinKernel +import OAI.Analysis.Laughlin.Tensor.KernelReadout + +namespace OAI + +namespace Laughlin +open scoped BigOperators +open Fock + +theorem distanceToLaughlinSq_le {N Q : ℕ} (ψ : State N Q) (c : ℂ) : + distanceToLaughlinSq ψ ≤ ∑ a, ‖ψ a-c*laughlinVector N Q a‖^2 := by + apply csInf_le + · refine ⟨0,?_⟩ + rintro t ⟨d,rfl⟩ + exact Finset.sum_nonneg (fun a ha => sq_nonneg _) + · exact ⟨c,rfl⟩ + +theorem mainTarget_proved : MainTarget := by + obtain ⟨Q₀,h25,hgap⟩ := physical_fock_kernel_distance_uniform + refine ⟨Q₀+2,by omega,fun N hN ψ hψ => ?_⟩ + have hN2 : 2 ≤ N := by omega + obtain ⟨n,rfl⟩ : ∃ n, N=n+2 := ⟨N-2,by omega⟩ + have hQ : Q₀ ≤ 3*(n+2-1) := by omega + let Q := 3*(n+2-1) + let x := normalizedTensorExterior (n+2) Q ψ + obtain ⟨y,hy,hb⟩ := hgap Q hQ x + have hyE : sourceFockEnergy Q y=0 := (sourceFockHamiltonian_kernel Q y).mp hy + have hrE : energy (normalizedTensorReadout (n+2) Q y)=0 := + normalizedTensorReadout_zero_energy n Q y hyE + have hrA := normalizedTensorReadout_antisymmetric (n+2) Q y + obtain ⟨c,hc⟩ := (physical_Laughlin_kernel (show 2 ≤ n+2 by omega) + (normalizedTensorReadout (n+2) Q y) hrA).mp hrE + have hread : normalizedTensorReadout (n+2) Q (x-y) = + fun a => ψ a-c*laughlinVector (n+2) Q a := by + rw [normalizedTensorReadout_sub,normalizedTensorReadout_left_inverse (n+2) Q ψ hψ,hc] + have hnorm := normalizedTensorReadout_norm_le (n+2) Q (x-y) + rw [hread] at hnorm + have hdist := distanceToLaughlinSq_le ψ c + have hE : sourceFockEnergy Q x=energy ψ := normalizedTensorExterior_energy n Q ψ hψ + rw [hE] at hb + exact (mul_le_mul_of_nonneg_left (hdist.trans hnorm) (by norm_num : (0 : ℝ) ≤ 1/100)).trans hb + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Model.lean b/lean/OAI/Analysis/Laughlin/Model.lean new file mode 100644 index 0000000000000000000000000000000000000000..9b85281fb0766061ef910847f1362d275151eb3c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Model.lean @@ -0,0 +1,63 @@ +import Mathlib + +namespace OAI + +namespace Laughlin +open scoped BigOperators + +abbrev Configuration (N Q : ℕ) := Fin N → Fin (Q+1) +abbrev State (N Q : ℕ) := Configuration N Q → ℂ + +def Antisymmetric {N Q : ℕ} (ψ : State N Q) : Prop := + ∀ (i j : Fin N), i ≠ j → ∀ a, ψ (a ∘ Equiv.swap i j) = -ψ a + +noncomputable def pairCoefficient (Q p : ℕ) (x y : Fin (Q+1)) : ℝ := + if x.val + y.val = p+1 then + ((x.val : ℝ) - (y.val : ℝ)) * + Real.sqrt (((Q.descFactorial x.val : ℝ) * (Q.descFactorial y.val : ℝ) * + (p.factorial : ℝ)) / + ((Q : ℝ) * ((2*Q-2).descFactorial p : ℝ) * + (x.val.factorial : ℝ) * (y.val.factorial : ℝ))) / Real.sqrt 2 + else 0 + +noncomputable def pairAmplitude {N Q : ℕ} (ψ : State N Q) + (i j : Fin N) (p : ℕ) (a : Configuration N Q) : ℂ := + ∑ x : Fin (Q+1), ∑ y : Fin (Q+1), + (pairCoefficient Q p x y : ℂ) * ψ (Function.update (Function.update a i x) j y) + +noncomputable def energy {N Q : ℕ} (ψ : State N Q) : ℝ := + ∑ i : Fin N, ∑ j : Fin N, if i < j then + ∑ p ∈ Finset.range (2*Q-1), ∑ a : Configuration N Q, + if a i = 0 ∧ a j = 0 then ‖pairAmplitude ψ i j p a‖ ^ 2 else 0 + else 0 + +abbrev SpinorVariables (N : ℕ) := Fin N × Bool + +noncomputable def bracket {N : ℕ} (i j : Fin N) : MvPolynomial (SpinorVariables N) ℂ := + MvPolynomial.X (i,false) * MvPolynomial.X (j,true) - + MvPolynomial.X (j,false) * MvPolynomial.X (i,true) + +noncomputable def laughlinPolynomial (N : ℕ) : MvPolynomial (SpinorVariables N) ℂ := + ∏ i : Fin N, ∏ j : Fin N, if i < j then bracket i j ^ 3 else 1 + +noncomputable def monomialExponent {N Q : ℕ} (a : Configuration N Q) : SpinorVariables N →₀ ℕ := + Finsupp.onFinset Finset.univ + (fun ib => if ib.2 then (a ib.1).val else Q - (a ib.1).val) + (by intro; simp) + +noncomputable def laughlinVector (N Q : ℕ) : State N Q := fun a => + (laughlinPolynomial N).coeff (monomialExponent a) / + ((∏ i : Fin N, Real.sqrt (Nat.choose Q (a i).val : ℝ) : ℝ) : ℂ) + +noncomputable def distanceToLaughlinSq {N Q : ℕ} (ψ : State N Q) : ℝ := + sInf (Set.range (fun c : ℂ => ∑ a : Configuration N Q, + ‖ψ a - c * laughlinVector N Q a‖ ^ 2)) + +def MainTarget : Prop := + ∃ N₀ : ℕ, 2 ≤ N₀ ∧ ∀ N : ℕ, N₀ ≤ N → + ∀ ψ : State N (3*(N-1)), Antisymmetric ψ → + (1/100 : ℝ) * distanceToLaughlinSq ψ ≤ energy ψ + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/CAR.lean b/lean/OAI/Analysis/Laughlin/Operators/CAR.lean new file mode 100644 index 0000000000000000000000000000000000000000..c27a22d4774ff3ff6324905475b03b125a22ccb0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/CAR.lean @@ -0,0 +1,66 @@ +import Mathlib.Analysis.Complex.Basic +import Mathlib.LinearAlgebra.CliffordAlgebra.Contraction +import Mathlib.LinearAlgebra.ExteriorAlgebra.Basic +import Mathlib.LinearAlgebra.Pi + +namespace OAI + +namespace Laughlin.Fock + +abbrev Orbital (Q : ℕ) := Fin (Q+1) → ℂ +abbrev Space (Q : ℕ) := ExteriorAlgebra ℂ (Orbital Q) + +noncomputable def mode {Q : ℕ} (i : Fin (Q+1)) : Orbital Q := Pi.single i 1 + +noncomputable def create {Q : ℕ} (i : Fin (Q+1)) : Module.End ℂ (Space Q) where + toFun x := ExteriorAlgebra.ι ℂ (mode i) * x + map_add' x y := mul_add _ x y + map_smul' c x := by simp + +noncomputable def annihilate {Q : ℕ} (i : Fin (Q+1)) : Module.End ℂ (Space Q) := + CliffordAlgebra.contractLeft (Q := (0 : QuadraticForm ℂ (Orbital Q))) (LinearMap.proj i) + +theorem annihilate_anticommute {Q : ℕ} (i j : Fin (Q+1)) : + annihilate i * annihilate j + annihilate j * annihilate i = 0 := by + ext x + change CliffordAlgebra.contractLeft (LinearMap.proj i) + (CliffordAlgebra.contractLeft (LinearMap.proj j) x) + + CliffordAlgebra.contractLeft (LinearMap.proj j) + (CliffordAlgebra.contractLeft (LinearMap.proj i) x) = 0 + rw [CliffordAlgebra.contractLeft_comm] + exact neg_add_cancel _ + +theorem create_anticommute {Q : ℕ} (i j : Fin (Q+1)) : + create i * create j + create j * create i = 0 := by + ext x + change ExteriorAlgebra.ι ℂ (mode i) * (ExteriorAlgebra.ι ℂ (mode j) * x) + + ExteriorAlgebra.ι ℂ (mode j) * (ExteriorAlgebra.ι ℂ (mode i) * x) = 0 + rw [← mul_assoc, ← mul_assoc, ← add_mul, ExteriorAlgebra.ι_add_mul_swap, zero_mul] + +theorem mixed_car {Q : ℕ} (i j : Fin (Q+1)) : + annihilate i * create j + create j * annihilate i = + (if i = j then (1 : ℂ) else 0) • (1 : Module.End ℂ (Space Q)) := by + ext x + change CliffordAlgebra.contractLeft (LinearMap.proj i) + (ExteriorAlgebra.ι ℂ (mode j) * x) + + ExteriorAlgebra.ι ℂ (mode j) * CliffordAlgebra.contractLeft (LinearMap.proj i) x = + (if i = j then (1 : ℂ) else 0) • x + rw [CliffordAlgebra.contractLeft_ι_mul, sub_add_cancel] + by_cases h : i = j + · subst j + simp [mode, LinearMap.proj] + · simp [mode, LinearMap.proj, h] + +theorem annihilate_sq {Q : ℕ} (i : Fin (Q+1)) : annihilate i * annihilate i = 0 := by + have h : (2 : ℂ) • (annihilate i * annihilate i) = 0 := by + simpa only [two_smul] using annihilate_anticommute i i + exact (smul_eq_zero.mp h).resolve_left two_ne_zero + +theorem create_sq {Q : ℕ} (i : Fin (Q+1)) : create i * create i = 0 := by + ext x + change ExteriorAlgebra.ι ℂ (mode i) * (ExteriorAlgebra.ι ℂ (mode i) * x) = 0 + rw [← mul_assoc, ExteriorAlgebra.ι_sq_zero, zero_mul] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/Certificate.lean b/lean/OAI/Analysis/Laughlin/Operators/Certificate.lean new file mode 100644 index 0000000000000000000000000000000000000000..66d815094c2c1103f3ab3a0211b5e90ef2c076bf --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/Certificate.lean @@ -0,0 +1,55 @@ +import Mathlib.Data.Nat.Choose.Basic +import Mathlib.Data.Rat.Defs +import Mathlib.Tactic.NormNum + +namespace OAI + +namespace Laughlin.Certificate + +def rows : List (ℕ × ℤ × List (ℕ × ℕ × ℤ)) := + [(0, 7181518, [(0, 5, -849651), (0, 7, -2958744), (1, 5, 751659), (1, 6, -43084), (1, 7, -146216), (3, 2, 720949), (3, 5, -127514), (4, 2, 222437), (4, 3, -262822), (5, 3, -117700), (6, 1, -55024), (7, 1, -166049)]), + (1, -112991, [(0, 5, 142772), (0, 6, -142342), (0, 7, 527055), (0, 8, 50742), (1, 6, 197917), (1, 8, -18343), (2, 4, 5764), (2, 7, -21183), (3, 2, 75832), (3, 5, -6115), (4, 5, 2660), (5, 3, -9455), (6, 1, -27091), (6, 3, -3494), (7, 1, 479), (7, 2, -15331)]), + (1, -4247311, [(0, 5, -12207250), (0, 6, -14064191), (0, 7, -14063663), (0, 8, -15662679), (1, 6, 483831), (1, 8, 3987214), (2, 4, -814558), (2, 7, 888887), (3, 2, 966462), (3, 5, 145978), (4, 5, -171722), (5, 3, 34350), (6, 1, 389319), (6, 3, 97603), (7, 1, 412447), (7, 2, -53786)]), + (2, 3438746, [(1, 4, 6689266), (1, 5, 6620205), (1, 6, 6625065), (1, 7, 4969272), (1, 8, 4878238), (2, 7, -1387380), (3, 6, -586188), (3, 7, 344087), (4, 2, -1120634), (4, 5, -318530), (4, 6, 559169), (5, 5, 157455), (6, 1, 1207103), (6, 3, 211617), (6, 4, 33240), (7, 1, 577001), (7, 3, -142578)]), + (5, -98645, [(0, 5, -2719776), (0, 8, -8519913), (1, 4, -949523), (1, 7, -1952105), (1, 8, -1562606), (2, 8, -8919966), (3, 2, 248826), (3, 5, -1017623), (3, 7, 3656005), (3, 8, -2081871), (4, 2, -33163), (4, 3, -305905), (4, 6, 35677), (4, 7, -1320749), (4, 8, -1040378), (5, 3, 502094), (5, 5, 1060633), (5, 8, -998003), (6, 1, -113617), (6, 3, 184919), (6, 4, 209239), (6, 5, -68198), (6, 7, -266297), (7, 2, -606696), (7, 3, -563620), (7, 4, 437345), (7, 6, -432189)]), + (5, -3160276, [(0, 5, -1698129), (0, 8, 10575875), (1, 4, -252576), (1, 7, -8002616), (1, 8, 22592844), (2, 8, 7370640), (3, 2, 289294), (3, 5, 1400647), (3, 7, 1987740), (3, 8, 4030699), (4, 2, -1731401), (4, 3, -1034062), (4, 6, -1106371), (4, 7, -1257051), (4, 8, 1461735), (5, 3, 1408149), (5, 5, 1136847), (5, 8, 1878501), (6, 1, -2838516), (6, 3, -734099), (6, 4, 1062416), (6, 5, 11745), (6, 7, 611312), (7, 2, -480776), (7, 3, 20459), (7, 4, 316925), (7, 6, 37092)]), + (7, 1441784, [(0, 7, 3441286), (0, 8, -6097155), (3, 7, -1002399), (4, 7, -251321), (5, 8, 1143225), (6, 6, -17397), (7, 1, -1007464), (7, 3, -662286), (7, 6, -344621), (7, 8, -1115284)])] + +def U (c z T p : ℕ) : ℤ := + if z ≤ T ∧ p ≤ T then + (((List.range (min p z + 1)).filter (fun h => p + z ≤ T + h)).map + (fun h => (-1 : ℤ) ^ (z-h) * (Nat.choose z h : ℤ) * + (Nat.choose (T-z) (p-h) : ℤ) * (c : ℤ) ^ (p-h))).sum + else 0 + +def X (entries : List (ℕ × ℕ × ℤ)) (z T : ℕ) : ℤ := + (entries.map (fun (p,j,a) => if p+j = T then a * U 2 z T p else 0)).sum + +def e (z : ℕ) : ℚ := + (rows.map (fun (t,ell,entries) => + (((List.range 16).filter (fun T => max z t ≤ T)).map (fun T => + ((2 : ℚ)^z * (Nat.choose T z : ℚ) / + ((3 : ℚ)^T * (2 : ℚ)^t * (Nat.choose T t : ℚ))) * + (X entries z T : ℚ) * + ((X entries z T : ℚ) + 2 * (ell : ℚ) * (U 2 z T t : ℚ)))).sum)).sum / + (10^14 : ℚ) + +def limitBound (z : ℕ) : ℚ := (3/2 : ℚ) * (3 * (z : ℚ) - 1) * (-1/2 : ℚ)^z + + +theorem eta_numerator : (rows.map (fun r => r.2.1 ^ 2)).sum = 93527408868499 := by + decide + +theorem allowance_count : + ((List.range 23).map (fun n => ((n+2)/2) * ((n+2)^2/4))).sum = 10946 := by + decide + +theorem final_margin : + (1 - 93527408868499 / 10^14 - 61 / 4096 - 10946 * (3 / 10^6) : ℚ) = + 1699533319001 / 10^14 := by norm_num + +theorem final_margin_gt : (1/100 : ℚ) < 1699533319001 / 10^14 := by norm_num + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/CollectionAnnihilatorBound.lean b/lean/OAI/Analysis/Laughlin/Operators/CollectionAnnihilatorBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..9a76793cb70868c2fc51ac0be82a351c0d8c3dd4 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/CollectionAnnihilatorBound.lean @@ -0,0 +1,48 @@ +import OAI.Analysis.Laughlin.Fock.ContractionBound + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +noncomputable def limitPairWindow (Q : ℕ) (x : Space Q) : ℝ := + ∑ p ∈ Finset.range 24, occupationNormSq Q (limitPairEnd Q p x) + +noncomputable def sourcePairWindow (Q : ℕ) (x : Space Q) : ℝ := + ∑ p ∈ Finset.range 24, occupationNormSq Q (sourcePairEnd Q p x) + +theorem collection_limit_annihilator_bound {I : Type*} [Fintype I] (Q : ℕ) + (p : I → ℕ) (j k : I → Fin (Q+1)) (hp : ∀ i, p i ≤ 23) (x : Space Q) : + (∑ i, occupationNormSq Q (limitFourEnd Q (p i) (j i) (k i) x)) ≤ + (Fintype.card I : ℝ) * limitPairWindow Q x := by + calc + _ ≤ ∑ i : I, limitPairWindow Q x := by + apply Finset.sum_le_sum + intro i hi + apply (limitFour_normSq_le_pair Q (p i) (j i) (k i) x).trans + change occupationNormSq Q (limitPairEnd Q (p i) x) ≤ + ∑ r ∈ Finset.range 24, occupationNormSq Q (limitPairEnd Q r x) + exact Finset.single_le_sum + (f := fun r => occupationNormSq Q (limitPairEnd Q r x)) + (fun r hr => occupationNormSq_nonneg Q _) (Finset.mem_range.mpr (by have h := hp i; omega)) + _ = _ := by simp + +theorem collection_source_annihilator_bound {I : Type*} [Fintype I] (Q : ℕ) + (p : I → ℕ) (j k : I → Fin (Q+1)) (hp : ∀ i, p i ≤ 23) (x : Space Q) : + (∑ i, occupationNormSq Q (sourceFourEnd Q (p i) (j i) (k i) x)) ≤ + (Fintype.card I : ℝ) * sourcePairWindow Q x := by + calc + _ ≤ ∑ i : I, sourcePairWindow Q x := by + apply Finset.sum_le_sum + intro i hi + apply (sourceFour_normSq_le_pair Q (p i) (j i) (k i) x).trans + change occupationNormSq Q (sourcePairEnd Q (p i) x) ≤ + ∑ r ∈ Finset.range 24, occupationNormSq Q (sourcePairEnd Q r x) + exact Finset.single_le_sum + (f := fun r => occupationNormSq Q (sourcePairEnd Q r x)) + (fun r hr => occupationNormSq_nonneg Q _) (Finset.mem_range.mpr (by have h := hp i; omega)) + _ = _ := by simp + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/ComplexCompression.lean b/lean/OAI/Analysis/Laughlin/Operators/ComplexCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..50ee49d4484e908998227f9f781ce8464791f3f3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/ComplexCompression.lean @@ -0,0 +1,30 @@ +import Mathlib.Analysis.Complex.Basic +import Mathlib.Analysis.InnerProductSpace.Adjoint + +namespace OAI + +namespace Laughlin +open scoped InnerProductSpace + +variable {E F : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] + [NormedAddCommGroup F] [InnerProductSpace ℂ F] + [FiniteDimensional ℂ E] [FiniteDimensional ℂ F] + +theorem complex_compression_positive_iff (W : E →ₗ[ℂ] F) (C : E →ₗ[ℂ] E) : + (∀ x : E, 0 ≤ (⟪x, W.adjoint (W (C (W.adjoint (W x))))⟫_ℂ).re) ↔ + (∀ y : F, 0 ≤ (⟪y, W (C (W.adjoint y))⟫_ℂ).re) := by + simp only [W.adjoint_inner_right, ← W.adjoint_inner_left] + constructor + · intro h y + have hy : W.adjoint y ∈ (W.adjoint ∘ₗ W).range := by + rw [W.range_adjoint_comp_self] + exact ⟨y, rfl⟩ + obtain ⟨x, hx⟩ := hy + change W.adjoint (W x) = W.adjoint y at hx + simpa only [hx] using h x + · intro h x + exact h (W x) + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/CopyQuadraticMatrix.lean b/lean/OAI/Analysis/Laughlin/Operators/CopyQuadraticMatrix.lean new file mode 100644 index 0000000000000000000000000000000000000000..7c5dabcde81d41981a2b78e6eb8ad9aca72d255f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/CopyQuadraticMatrix.lean @@ -0,0 +1,33 @@ +import OAI.Analysis.Laughlin.Asymptotics.TruncatedMetricPerturbation +import OAI.Analysis.Laughlin.Fock.MatrixQuadratic + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators Matrix +open Matrix + +noncomputable def copyQuadraticMatrix {I J : Type*} [Fintype I] + (C : I → I → ℝ) (β : I → J → ℝ) : J → J → ℝ := + fun a b => ∑ i, ∑ j, C i j * β i a * β j b + +theorem occupationQuadratic_factor {I J : Type*} [Fintype I] [Fintype J] + (Q : ℕ) (C : I → I → ℝ) (β : I → J → ℝ) (v : J → Space Q) : + occupationQuadratic Q C (fun i => ∑ a, (β i a : ℂ) • v a) = + occupationQuadratic Q (copyQuadraticMatrix C β) v := by + let W : Matrix J I ℂ := fun a i => (β i a : ℂ) + let C' : Matrix I I ℂ := fun i j => (C i j : ℂ) + have hm (a b : J) : (W*C'*Wᴴ) a b = (copyQuadraticMatrix C β a b : ℂ) := by + simp only [Matrix.mul_apply,Matrix.conjTranspose_apply,Finset.sum_mul] + simp only [W,C',Complex.star_def,Complex.conj_ofReal,copyQuadraticMatrix,Complex.ofReal_sum,Complex.ofReal_mul] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl; intro i hi + apply Finset.sum_congr rfl; intro j hj + ring + have h := occupation_matrix_quadratic_factor Q W C' v + simp only [W,Complex.star_def,Complex.conj_ofReal,hm] at h + exact congrArg Complex.re h + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/Energy.lean b/lean/OAI/Analysis/Laughlin/Operators/Energy.lean new file mode 100644 index 0000000000000000000000000000000000000000..a46d842fcfe323396ad145a0b53823e176837be5 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/Energy.lean @@ -0,0 +1,17 @@ +import Mathlib.Algebra.Order.BigOperators.Group.Finset +import OAI.Analysis.Laughlin.EnergyNonnegative + +namespace OAI + +namespace Laughlin +open scoped BigOperators + +theorem energy_eq_zero_iff {N Q : ℕ} (ψ : State N Q) : + energy ψ = 0 ↔ ∀ (i j : Fin N), i < j → ∀ p : ℕ, p < 2*Q-1 → + ∀ a : Configuration N Q, a i = 0 → a j = 0 → pairAmplitude ψ i j p a = 0 := by + unfold energy + simp (disch := intros; positivity) [Finset.sum_eq_zero_iff_of_nonneg] + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/FourOccupationEquiv.lean b/lean/OAI/Analysis/Laughlin/Operators/FourOccupationEquiv.lean new file mode 100644 index 0000000000000000000000000000000000000000..05c15a2bc4a3a29ed00f6306c66514199b1a27b9 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/FourOccupationEquiv.lean @@ -0,0 +1,40 @@ +import OAI.Analysis.Laughlin.Fock.Quadruple + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem occupationQuadruple_surjective (Q D : ℕ) (hQ : D+1 ≤ Q) : + Function.Surjective (occupationQuadruple Q D) := by + rintro ⟨⟨a,b,c,d⟩,h⟩ + let l := quadrupleEmbedding Q D a b c d hQ h + let A := Set.powersetCard.ofFinEmbEquiv l + have hl : occupationFourLabels Q A.val A.property = l := + Set.powersetCard.ofFinEmbEquiv.symm_apply_apply l + have hw : (∑ i ∈ A.val, i.val)=D+1 := by + rw [occupationFourLabels_sum Q A.val A.property,hl] + exact (Certificate.mem_quadruples D a b c d).mp h |>.2.2.2 + refine ⟨⟨A.val,A.property,hw⟩,?_⟩ + apply Subtype.ext + simp only [occupationQuadruple,hl] + rfl + +noncomputable def fourOccupationEquiv (Q D : ℕ) (hQ : D+1 ≤ Q) : + FourOccupation Q D ≃ {t : ℕ×ℕ×ℕ×ℕ // t ∈ Certificate.quadruples D} := + Equiv.ofBijective (occupationQuadruple Q D) + ⟨occupationQuadruple_injective Q D,occupationQuadruple_surjective Q D hQ⟩ + +theorem sum_fourOccupations (Q D : ℕ) (hQ : D+1 ≤ Q) (f : (ℕ×ℕ×ℕ×ℕ) → ℝ) : + ∑ A : FourOccupation Q D, f (occupationQuadruple Q D A).val = + ((Certificate.quadruples D).map f).sum := by + classical + let : Fintype {t : ℕ×ℕ×ℕ×ℕ // t ∈ Certificate.quadruples D} := + Fintype.ofFinset (Certificate.quadruples D).toFinset (by intro t; change t ∈ (Certificate.quadruples D).toFinset ↔ t ∈ Certificate.quadruples D; simp) + rw [← List.sum_toFinset f (Certificate.quadruples_nodup D)] + rw [Finset.sum_subtype (p := fun t => t ∈ Certificate.quadruples D) (Certificate.quadruples D).toFinset (by simp)] + exact (fourOccupationEquiv Q D hQ).sum_comp (fun t => f t.val) + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/GenericPhysicalResolution.lean b/lean/OAI/Analysis/Laughlin/Operators/GenericPhysicalResolution.lean new file mode 100644 index 0000000000000000000000000000000000000000..3a4d7b3c99265ea9ffeeb8fdbae9a1aa599f2bf5 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/GenericPhysicalResolution.lean @@ -0,0 +1,40 @@ +import OAI.Analysis.Laughlin.Spin.Basis2 + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +theorem physicalCoupledInclusion_complete (A B : ℕ) : + (∑ z : Fin (min A B+1), + physicalCoupledInclusion A B z.val (by omega) (by omega) * + (physicalCoupledInclusion A B z.val (by omega) (by omega))ᴴ) = 1 := by + have hc : (genericCoupledBasis A B).map Complex.ofReal * + ((genericCoupledBasis A B).map Complex.ofReal)ᴴ = 1 := by + ext i j + have h := congrArg Complex.ofReal (congrFun (congrFun (genericCoupledBasis_complete A B) i) j) + simpa only [Matrix.mul_apply,Matrix.map_apply,Matrix.conjTranspose_apply,Matrix.transpose_apply, + Complex.star_def,Complex.conj_ofReal,Complex.ofReal_sum,Complex.ofReal_mul,Matrix.one_apply, + apply_ite,Complex.ofReal_one,Complex.ofReal_zero] using h + rw [← hc] + ext i j + simp only [Matrix.sum_apply,Matrix.mul_apply,Matrix.conjTranspose_apply,Matrix.map_apply, + Fintype.sum_sigma,physicalCoupledInclusion,Matrix.smul_apply,smul_eq_mul, + genericCoupledInclusion,genericCoupledBasis] + apply Finset.sum_congr rfl + intro z hz + apply Finset.sum_congr rfl + intro n hn + have hp : ((-1 : ℂ)^z.val)*star ((-1 : ℂ)^z.val)=1 := by + simp only [star_pow,star_neg,star_one,← mul_pow] + norm_num + simp only [star_mul] + calc + _ = (((-1 : ℂ)^z.val)*star ((-1 : ℂ)^z.val)) * + ((genericUnitDescendant A B z.val (by omega) (by omega) n.val i : ℂ)* + star (genericUnitDescendant A B z.val (by omega) (by omega) n.val j : ℂ)) := by ring + _ = _ := by rw [hp,one_mul] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/GlobalPairCube.lean b/lean/OAI/Analysis/Laughlin/Operators/GlobalPairCube.lean new file mode 100644 index 0000000000000000000000000000000000000000..8b1cecdae9032e0a9b6d314e72219b1e1ff55828 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/GlobalPairCube.lean @@ -0,0 +1,73 @@ +import OAI.Analysis.Laughlin.Pair.AffineChart +import OAI.Analysis.Laughlin.Spin.PairDecomposition + +namespace OAI + +namespace Laughlin +open MvPolynomial +open scoped BigOperators + +theorem pairAffineChart_coefficient {N Q : ℕ} (ψ : State N Q) + (i j : Fin N) (hij : i ≠ j) (a : PairSpectators (Q := Q) i j) : + (pairAffineChart i j (spinPolynomial ψ)).coeff (affineExponent a.val) = + Polynomial.C (Polynomial.C (spectatorWeight i j a.val)) * + pairAffinePolynomial Q (pairSlice ψ i j a.val) := by + classical + rw [spinPolynomial_pair_decomposition ψ i j hij] + simp only [map_sum, map_mul] + simp_rw [pairAffineChart_spectator i j hij, pairAffineChart_pair i j hij] + simp only [coeff_sum] + simp_rw [mul_comm (monomial _ _) (C _), coeff_C_mul, coeff_monomial, mul_ite, mul_zero] + have he (b : PairSpectators (Q := Q) i j) : + affineExponent b.val = affineExponent a.val ↔ b = a := by + rw [(affineExponent_injective N Q).eq_iff] + exact Subtype.val_injective.eq_iff + simp_rw [he] + simp [mul_comm] + +theorem affine_pair_cubes_of_bracket_dvd {N Q : ℕ} (ψ : State N Q) + (i j : Fin N) (hij : i ≠ j) (hc : bracket i j^3 ∣ spinPolynomial ψ) + (a : Configuration N Q) : + PairDiagonal.diagonal^3 ∣ pairAffinePolynomial Q (pairSlice ψ i j a) := by + let a0 : PairSpectators (Q := Q) i j := + ⟨Function.update (Function.update a i 0) j 0, by simp [hij]⟩ + have hd := map_dvd (pairAffineChart i j) hc + rw [map_pow, pairAffineChart_bracket i j hij, ← map_pow] at hd + obtain ⟨g,hg⟩ := hd + have he : Polynomial.C (Polynomial.C (spectatorWeight i j a0.val)) * + pairAffinePolynomial Q (pairSlice ψ i j a0.val) = + PairDiagonal.diagonal^3 * g.coeff (affineExponent a0.val) := by + rw [← pairAffineChart_coefficient ψ i j hij a0, hg, coeff_C_mul] + have hunit : Polynomial.C (Polynomial.C (spectatorWeight i j a0.val)) * + Polynomial.C (Polynomial.C (spectatorWeight i j a0.val)⁻¹) = (1 : PairDiagonal.Poly) := by + rw [← map_mul, ← map_mul, mul_inv_cancel₀ (spectatorWeight_ne_zero i j a0.val), + map_one, map_one] + have hdiv : PairDiagonal.diagonal^3 ∣ + (Polynomial.C (Polynomial.C (spectatorWeight i j a0.val)) * + pairAffinePolynomial Q (pairSlice ψ i j a0.val)) * + Polynomial.C (Polynomial.C (spectatorWeight i j a0.val)⁻¹) := + dvd_mul_of_dvd_left ⟨g.coeff (affineExponent a0.val), he⟩ _ + rw [mul_right_comm, hunit, one_mul] at hdiv + simpa only [a0, pairSlice_anchor] using hdiv + +theorem affine_pair_cubes_iff_bracket_dvd {N Q : ℕ} (ψ : State N Q) + (i j : Fin N) (hij : i ≠ j) : + (∀ a : Configuration N Q, + PairDiagonal.diagonal^3 ∣ pairAffinePolynomial Q (pairSlice ψ i j a)) ↔ + bracket i j^3 ∣ spinPolynomial ψ := + ⟨bracket_cube_dvd_spinPolynomial_of_slices ψ i j hij, + fun h => affine_pair_cubes_of_bracket_dvd ψ i j hij h⟩ + +theorem energy_eq_zero_iff_global_pair_cubes {N Q : ℕ} (hQ : 2 ≤ Q) + (ψ : State N Q) (hψ : Antisymmetric ψ) : + energy ψ = 0 ↔ ∀ i j : Fin N, i < j → bracket i j^3 ∣ spinPolynomial ψ := by + rw [energy_eq_zero_iff_affine_pair_cubes hQ ψ hψ] + constructor + · intro h i j hij + exact (affine_pair_cubes_iff_bracket_dvd ψ i j (ne_of_lt hij)).mp (h i j hij) + · intro h i j hij + exact (affine_pair_cubes_iff_bracket_dvd ψ i j (ne_of_lt hij)).mpr (h i j hij) + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/GramReadout.lean b/lean/OAI/Analysis/Laughlin/Operators/GramReadout.lean new file mode 100644 index 0000000000000000000000000000000000000000..4a44a464a706f0dc1a6cd2e136b43ba67acd79a9 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/GramReadout.lean @@ -0,0 +1,75 @@ +import OAI.Analysis.Laughlin.Asymptotics.Bound +import OAI.Analysis.Laughlin.Spin.Highest + +namespace OAI + +namespace Laughlin.Spin + +noncomputable def highestReadout (Q z : ℕ) : ℝ := + if z = 0 then -highestUnit (2*Q-2) Q z 0 else + -highestUnit (2*Q-2) Q z (z-1) * (z : ℝ) * + Real.sqrt ((Q.choose z : ℝ)/((Q : ℝ)*((2*Q-2).choose (z-1) : ℝ))) + + highestUnit (2*Q-2) Q z z * ((z : ℝ)-1) * + Real.sqrt ((Q.choose z : ℝ)/((2*Q-2).choose z : ℝ)) + +theorem source_readout_rational_identity (Q z : ℕ) (hQ : 2 ≤ Q) + (hz : z ≤ Q) (hz₀ : 1 ≤ z) : + (z : ℝ)^2*(Q.choose z : ℝ)/((Q : ℝ)*((2*Q-2).choose (z-1) : ℝ)) + + ((z : ℝ)-1)*(Q.choose z : ℝ)/((2*Q-2).choose z : ℝ) = + (Q.choose z : ℝ)/((2*Q-2).choose z : ℝ)* + (3*(z : ℝ)-1-(z : ℝ)*((z : ℝ)+1)/Q) := by + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (by omega : Q ≠ 0) + have hc : (((2*Q-2).choose z : ℝ)) ≠ 0 := by + exact_mod_cast Nat.ne_of_gt (Nat.choose_pos (by omega : z ≤ 2*Q-2)) + have hp : (((2*Q-2).choose (z-1) : ℝ)) ≠ 0 := by + exact_mod_cast Nat.ne_of_gt (Nat.choose_pos (by omega : z-1 ≤ 2*Q-2)) + have he := choose_step_real (2*Q-2) (z-1) (by omega) + rw [show z-1+1=z by omega] at he + have hcast : ((z-1 : ℕ) : ℝ)+1 = (z : ℝ) := by + rw [Nat.cast_sub hz₀]; push_cast; ring + have hcast' : ((2*Q-2-(z-1) : ℕ) : ℝ) = 2*(Q : ℝ)-1-z := by + rw [Nat.cast_sub (by omega : z-1 ≤ 2*Q-2),Nat.cast_sub (by omega : 2 ≤ 2*Q), + Nat.cast_sub hz₀]; push_cast; ring + rw [hcast,hcast'] at he + field_simp + linear_combination (z : ℝ)*(Q.choose z : ℝ)*he + +theorem highestReadout_eq_formula (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + highestReadout Q z = gramEigenvalueFormula Q z * highestUnit (2*Q-2) Q z 0 := by + by_cases hz₀ : z = 0 + · subst z + simp [highestReadout,gramEigenvalueFormula,fallingRatio] + have hzpos : 1 ≤ z := by omega + have hA : z ≤ 2*Q-2 := by omega + have hs := highestUnit_ne_zero (2*Q-2) Q z 0 hA hz (by omega) + have hend := highest_end_ratio (2*Q-2) Q z hA hz + have hprev := highest_penultimate_ratio (2*Q-2) Q z hA hz hzpos + have hsign : (-1 : ℝ)^z = -((-1 : ℝ)^(z-1)) := by + have hh : z = (z-1)+1 := by omega + conv_lhs => rw [hh,pow_succ] + ring + have hprev' := (div_eq_iff hs).mp hprev + have hend' := (div_eq_iff hs).mp hend + rw [highestReadout,ite_eq_right hz₀,hprev',hend'] + rw [show ((2*Q-2).choose (z-1) : ℝ)*(Q : ℝ) = + (Q : ℝ)*((2*Q-2).choose (z-1) : ℝ) by ring] + have he := source_readout_rational_identity Q z hQ hz hzpos + have hc := choose_ratio_descFactorial (2*Q-2) Q z + change (Q.choose z : ℝ)/((2*Q-2).choose z : ℝ) = fallingRatio Q z at hc + calc + _ = (-1 : ℝ)^z * ((z : ℝ)^2 * (Q.choose z : ℝ) / + ((Q : ℝ)*((2*Q-2).choose (z-1) : ℝ)) + + ((z : ℝ)-1)*(Q.choose z : ℝ)/((2*Q-2).choose z : ℝ)) * + highestUnit (2*Q-2) Q z 0 := by + rw [hsign] + have h₁ := Real.sq_sqrt (show 0 ≤ (Q.choose z : ℝ)/ + ((Q : ℝ)*((2*Q-2).choose (z-1) : ℝ)) by positivity) + have h₂ := Real.sq_sqrt (show 0 ≤ (Q.choose z : ℝ)/((2*Q-2).choose z : ℝ) by positivity) + linear_combination + -((-1 : ℝ)^(z-1))*(z : ℝ)^2*highestUnit (2*Q-2) Q z 0*h₁ + + -((-1 : ℝ)^(z-1))*((z : ℝ)-1)*highestUnit (2*Q-2) Q z 0*h₂ + _ = _ := by rw [he,hc]; unfold gramEigenvalueFormula; ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/LocalFourCardinality.lean b/lean/OAI/Analysis/Laughlin/Operators/LocalFourCardinality.lean new file mode 100644 index 0000000000000000000000000000000000000000..23586c3bc35dfd4cb7759b68a23fe7479b226ed8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/LocalFourCardinality.lean @@ -0,0 +1,49 @@ +import Mathlib.Data.Fin.Basic +import OAI.Analysis.Laughlin.Operators.LocalFourIndexEquiv + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +def localFourCountEquiv (D : ℕ) : + LocalFourIndex D ≃ (n : Fin (D+1)) × Fin ((n.val+1)/2) where + toFun b := ⟨⟨b.val.2.1.val+b.val.2.2.val,by have := b.property.1; omega⟩, + ⟨b.val.2.1.val,by dsimp; have := b.property.2; omega⟩⟩ + invFun b := ⟨(⟨D-b.1.val,by omega⟩,⟨b.2.val,by have := b.2.isLt; omega⟩, + ⟨b.1.val-b.2.val,by omega⟩),by + have := b.2.isLt + constructor + · dsimp; omega + · change b.2.val < b.1.val-b.2.val + omega⟩ + left_inv b := by + apply Subtype.ext + apply Prod.ext + · apply Fin.ext; dsimp; have := b.property.1; omega + · apply Prod.ext + · rfl + · apply Fin.ext; dsimp; omega + right_inv b := by + rcases b with ⟨n,j⟩ + have hj : j.val ≤ n.val := by have := j.isLt; omega + dsimp + have hn : j.val+(n.val-j.val)=n.val := by omega + apply Sigma.ext + · exact Fin.ext hn + · apply (Fin.heq_ext_iff (by dsimp; rw [hn])).mpr + rfl + +theorem localFourIndex_card_sum (D : ℕ) : + Fintype.card (LocalFourIndex D) = ∑ n : Fin (D+1), (n.val+1)/2 := by + rw [Fintype.card_congr (localFourCountEquiv D),Fintype.card_sigma] + simp only [Fintype.card_fin] + +theorem localFourIndex_card_retained (D : ℕ) (hD : D ≤ 23) : + Fintype.card (LocalFourIndex D) = (D+1)^2/4 := by + rw [localFourIndex_card_sum] + interval_cases D <;> norm_num [Fin.sum_univ_succ] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/LocalFourIndexEquiv.lean b/lean/OAI/Analysis/Laughlin/Operators/LocalFourIndexEquiv.lean new file mode 100644 index 0000000000000000000000000000000000000000..ea613c1d130610095235bdb4e30e8bff92e8c59f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/LocalFourIndexEquiv.lean @@ -0,0 +1,38 @@ +import OAI.Analysis.Laughlin.FourBody.TransferConjugation + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +abbrev EmbeddedLocalFourIndex (Q D : ℕ) := + {b : Fin (D+1) × Fin (Q+1) × Fin (Q+1) // b.1.val+b.2.1.val+b.2.2.val=D ∧ b.2.1 + b.1.val+b.2.1.val+b.2.2.val=D ∧ b.2.1 f b.val.1.val b.val.2.1 b.val.2.2) |>.symm + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/MatrixCongruence.lean b/lean/OAI/Analysis/Laughlin/Operators/MatrixCongruence.lean new file mode 100644 index 0000000000000000000000000000000000000000..22b2fa575d54aaf2fb38713ec98a699924acadb0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/MatrixCongruence.lean @@ -0,0 +1,25 @@ +import Mathlib.Algebra.Order.Star.Real +import Mathlib.LinearAlgebra.Matrix.PosDef +import Mathlib.Tactic.NoncommRing + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix + +theorem compressed_congruence_identity {n : ℕ} + (D Z Y K : Matrix (Fin n) (Fin n) ℝ) : + (D*Z*D) * (K-D*Y*D) * (D*Z*D) = + D * (Z * (D*K*D-(D*D)*Y*(D*D)) * Z) * D := by + noncomm_ring + +theorem compressed_congruence_positive {n : ℕ} + (D Z Y K : Matrix (Fin n) (Fin n) ℝ) (hD : D.IsHermitian) + (hM : (Z * (D*K*D-(D*D)*Y*(D*D)) * Z).PosSemidef) : + ((D*Z*D) * (K-D*Y*D) * (D*Z*D)).PosSemidef := by + rw [compressed_congruence_identity] + simpa only [hD.eq] using hM.mul_mul_conjTranspose_same D + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/MatrixMetricError.lean b/lean/OAI/Analysis/Laughlin/Operators/MatrixMetricError.lean new file mode 100644 index 0000000000000000000000000000000000000000..73a6540b069fd6b20f9cecad2ece24b693c17aa5 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/MatrixMetricError.lean @@ -0,0 +1,61 @@ +import OAI.Analysis.Laughlin.Asymptotics.TruncatedMetricPerturbation + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators Topology +open Filter + +noncomputable def entrySum {I : Type*} [Fintype I] (R : I → I → ℝ) : ℝ := ∑ i, ∑ j, |R i j| + +theorem entrySum_nonneg {I : Type*} [Fintype I] (R : I → I → ℝ) : 0 ≤ entrySum R := by + unfold entrySum + positivity + +theorem abs_le_entrySum {I : Type*} [Fintype I] (R : I → I → ℝ) (i j : I) : |R i j| ≤ entrySum R := by + apply (Finset.single_le_sum (fun k hk => abs_nonneg (R i k)) (Finset.mem_univ j)).trans + exact Finset.single_le_sum (fun k hk => Finset.sum_nonneg (fun l hl => abs_nonneg (R k l))) (Finset.mem_univ i) + +noncomputable def matrixMetricError {I : Type*} [Fintype I] (L Q : ℕ) (R S : I → I → ℝ) : ℝ := + entrySum (fun i j => R i j-S i j) + localMetricError L Q * entrySum R + +theorem matrixMetricError_nonneg {I : Type*} [Fintype I] (L Q : ℕ) (R S : I → I → ℝ) : + 0 ≤ matrixMetricError L Q R S := + add_nonneg (entrySum_nonneg _) (mul_nonneg (localMetricError_nonneg L Q) (entrySum_nonneg R)) + +theorem matrixMetricError_bound {I : Type*} [Fintype I] (L Q : ℕ) (hL : L ≤ Q) + (R S : I → I → ℝ) (A : Finset (Fin (Q+1))) (i j : I) : + |((truncatedDiagonals L Q A)⁻¹)^2*R i j-S i j| ≤ matrixMetricError L Q R S := by + have he : ((truncatedDiagonals L Q A)⁻¹)^2*R i j-S i j = + (((truncatedDiagonals L Q A)⁻¹)^2-1)*R i j+(R i j-S i j) := by ring + rw [he] + apply (abs_add_le _ _).trans + rw [abs_mul] + have h₁ := mul_le_mul (truncatedMetricError_bound L Q hL A) (abs_le_entrySum R i j) + (abs_nonneg _) (localMetricError_nonneg L Q) + have h₂ := abs_le_entrySum (fun i j => R i j-S i j) i j + unfold matrixMetricError + linarith + +theorem entrySum_tendsto {I : Type*} [Fintype I] (R : ℕ → I → I → ℝ) (S : I → I → ℝ) + (hR : ∀ i j, Tendsto (fun Q => R Q i j) atTop (𝓝 (S i j))) : + Tendsto (fun Q => entrySum (R Q)) atTop (𝓝 (entrySum S)) := by + apply tendsto_finsetSum + intro i hi + apply tendsto_finsetSum + intro j hj + exact (hR i j).abs + +theorem matrixMetricError_tendsto {I : Type*} [Fintype I] (L : ℕ) + (R : ℕ → I → I → ℝ) (S : I → I → ℝ) + (hR : ∀ i j, Tendsto (fun Q => R Q i j) atTop (𝓝 (S i j))) : + Tendsto (fun Q => matrixMetricError L Q (R Q) S) atTop (𝓝 0) := by + have hd := entrySum_tendsto (fun Q i j => R Q i j-S i j) (fun _ _ => 0) + (fun i j => by simpa using (hR i j).sub_const (S i j)) + have hr := entrySum_tendsto R S hR + have h := hd.add ((localMetricError_tendsto L).mul hr) + simpa [matrixMetricError,entrySum] using h + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/MatrixPhysicalCompression.lean b/lean/OAI/Analysis/Laughlin/Operators/MatrixPhysicalCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..6ed916e7ef2e1c22b964ac0a0d4ccd5ae9d20c4b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/MatrixPhysicalCompression.lean @@ -0,0 +1,38 @@ +import Mathlib.Analysis.InnerProductSpace.Positive +import OAI.Analysis.Laughlin.Operators.ComplexCompression + +namespace OAI + +namespace Laughlin +open scoped Matrix InnerProductSpace ComplexOrder +open Matrix + +theorem matrix_physical_compression {I J : Type*} [Fintype I] [Fintype J] + [DecidableEq I] [DecidableEq J] (W : Matrix J I ℂ) (C : Matrix I I ℂ) + (hC : C.IsHermitian) (hG : ((Wᴴ*W)*C*(Wᴴ*W)).PosSemidef) : + (W*C*Wᴴ).PosSemidef := by + have hc : (W*C*Wᴴ).IsHermitian := isHermitian_mul_mul_conjTranspose W hC + have hpos : ∀ x : EuclideanSpace ℂ I, + 0 ≤ (⟪x,W.toEuclideanLin.adjoint (W.toEuclideanLin + (C.toEuclideanLin (W.toEuclideanLin.adjoint (W.toEuclideanLin x))))⟫_ℂ).re := by + intro x + have hp := hG.dotProduct_mulVec_nonneg (WithLp.ofLp x) + have hp' := (Complex.nonneg_iff.mp hp).1 + simpa only [← Matrix.toEuclideanLin_conjTranspose_eq_adjoint, + EuclideanSpace.inner_eq_star_dotProduct,Matrix.ofLp_toLpLin,Matrix.toLin'_apply, + Matrix.mulVec_mulVec,Matrix.mul_assoc,dotProduct_comm] using hp' + have hout := (complex_compression_positive_iff W.toEuclideanLin C.toEuclideanLin).mp hpos + rw [← Matrix.isPositive_toEuclideanLin_iff,LinearMap.IsPositive, + Matrix.isSymmetric_toEuclideanLin_iff] + refine ⟨hc,?_⟩ + intro y + have hy := hout y + rw [inner_re_symm] + change 0 ≤ (⟪y,(W*C*Wᴴ).toEuclideanLin y⟫_ℂ).re + simpa only [← Matrix.toEuclideanLin_conjTranspose_eq_adjoint, + EuclideanSpace.inner_eq_star_dotProduct,Matrix.ofLp_toLpLin,Matrix.toLin'_apply, + Matrix.mulVec_mulVec,Matrix.mul_assoc] using hy + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/NormalCertificate.lean b/lean/OAI/Analysis/Laughlin/Operators/NormalCertificate.lean new file mode 100644 index 0000000000000000000000000000000000000000..d8f0422878de65c271f970e59b238a37cffb3dce --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/NormalCertificate.lean @@ -0,0 +1,65 @@ +import OAI.Analysis.Laughlin.FourBody.Ungroup + +namespace OAI + +namespace Laughlin.Fock +open Spin +open scoped BigOperators Matrix + +theorem sourceRowFourEntry_physical (Q : ℕ) (hQ : 25 ≤ Q) + (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) (hr : row ∈ Certificate.rows) + (e f : ℕ × ℕ × ℤ) (he : e ∈ row.2.2) (hf : f ∈ row.2.2) (x : Space Q) : + sourceRowFourEntry Q row.1 e f x = contractionForm Q (sourceFourFamilyEnd Q) + ((fourBodyTermMatrix Q row.1 e f).map Complex.ofReal) x := by + obtain ⟨het,he15,he8⟩ := (source_threeBody_rows_support row hr).2 e he + obtain ⟨hft,hf15,hf8⟩ := (source_threeBody_rows_support row hr).2 f hf + rw [fourBodyTermMatrix_Fock Q row.1 e f het hft (by omega),sourceRowFourEntry, + boundedAnnihilate,dite_eq_left (show f.1+f.2.1-row.1 ≤ Q by omega), + boundedAnnihilate,dite_eq_left (show e.1+e.2.1-row.1 ≤ Q by omega), + sourceEntryThree_eq Q e (by omega) (by omega),sourceEntryThree_eq Q f (by omega) (by omega)] + simp only [sourceFourEnd,Module.End.mul_apply,Complex.ofReal_mul] + ring + +theorem source_rows_four_form (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + (Certificate.rows.map (fun row => sourceRowFourForm Q (by omega) row x)).sum = + contractionForm Q (sourceFourFamilyEnd Q) ((physicalFourBodyMatrix Q).map Complex.ofReal) x := by + simp only [physicalFourBodyMatrix,matrix_ofReal_list,contractionForm_list] + congr 1 + apply List.map_congr_left + intro row hr + rw [sourceRowFourForm_entries Q (by omega) row hr] + congr 1 + apply List.map_congr_left + intro e he + congr 1 + apply List.map_congr_left + intro f hf + exact sourceRowFourEntry_physical Q hQ row hr e f he hf x + +theorem source_seven_squares_normal_form (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + (Certificate.rows.map (fun row => (occupationNormSq Q + (sourceRowSquareVector Q (by omega) row x) : ℂ))).sum = + contractionForm Q (fun p : Fin (2*Q-2+1) => sourcePairEnd Q p.val) + (physicalTwoBodyMatrix Q) x + + contractionForm Q (sourceThreeEnd Q) ((physicalThreeBodyMatrix Q).map Complex.ofReal) x + + contractionForm Q (sourceFourFamilyEnd Q) ((physicalFourBodyMatrix Q).map Complex.ofReal) x := by + rw [source_rows_normal_two_three Q (by omega),source_rows_four_form Q hQ] + +theorem source_seven_normal_form_nonneg (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + 0 ≤ (contractionForm Q (fun p : Fin (2*Q-2+1) => sourcePairEnd Q p.val) + (physicalTwoBodyMatrix Q) x + + contractionForm Q (sourceThreeEnd Q) ((physicalThreeBodyMatrix Q).map Complex.ofReal) x + + contractionForm Q (sourceFourFamilyEnd Q) ((physicalFourBodyMatrix Q).map Complex.ofReal) x).re := by + rw [← source_seven_squares_normal_form Q hQ] + have hl (l : List (ℕ × ℤ × List (ℕ × ℕ × ℤ))) : + 0 ≤ (l.map (fun row => (occupationNormSq Q (sourceRowSquareVector Q (by omega) row x) : ℂ))).sum.re := by + induction l with + | nil => simp + | cons row l ih => + simp only [List.map_cons,List.sum_cons,Complex.add_re,Complex.ofReal_re] + exact add_nonneg (occupationNormSq_nonneg Q _) ih + exact hl _ + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/NormalOrder.lean b/lean/OAI/Analysis/Laughlin/Operators/NormalOrder.lean new file mode 100644 index 0000000000000000000000000000000000000000..eb11bf676afaba85efec2252d2788f8cf8b7d9aa --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/NormalOrder.lean @@ -0,0 +1,47 @@ +import Mathlib.Tactic.NoncommRing +import OAI.Analysis.Laughlin.Operators.CAR + +namespace OAI + +namespace Laughlin.Fock + +noncomputable def delta {Q : ℕ} (i j : Fin (Q+1)) : ℂ := if i = j then 1 else 0 + +theorem annihilate_create {Q : ℕ} (i j : Fin (Q+1)) : + annihilate i * create j = delta i j • (1 : Module.End ℂ (Space Q)) - + create j * annihilate i := by + exact eq_sub_of_add_eq (mixed_car i j) + +theorem normal_order_entry {Q : ℕ} (P R : Module.End ℂ (Space Q)) + (i j k l : Fin (Q+1)) : + (P * create j * annihilate i) * (create k * annihilate l * R) = + delta i k • (P * create j * annihilate l * R) - + P * create j * create k * annihilate i * annihilate l * R := by + calc + _ = P * create j * (annihilate i * create k) * annihilate l * R := by + noncomm_ring + _ = _ := by + rw [annihilate_create] + simp only [mul_sub, sub_mul, mul_smul_comm, smul_mul_assoc, mul_one] + noncomm_ring + +theorem normal_order_two_inner {Q : ℕ} (a b c d : Fin (Q+1)) : + annihilate b * annihilate a * create c * create d = + delta a c • (annihilate b * create d) - + delta b c • (annihilate a * create d) + + create c * annihilate b * annihilate a * create d := by + calc + _ = annihilate b * (annihilate a * create c) * create d := by noncomm_ring + _ = delta a c • (annihilate b * create d) - + (annihilate b * create c) * annihilate a * create d := by + rw [annihilate_create] + simp only [mul_sub, sub_mul, mul_smul_comm, smul_mul_assoc, mul_one] + noncomm_ring + _ = _ := by + rw [annihilate_create b c] + simp only [sub_mul, smul_mul_assoc, one_mul] + noncomm_ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/NormalOrderFour.lean b/lean/OAI/Analysis/Laughlin/Operators/NormalOrderFour.lean new file mode 100644 index 0000000000000000000000000000000000000000..fcf22d9a5df0c2dfabce18f9ab2b20d17745fbe8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/NormalOrderFour.lean @@ -0,0 +1,40 @@ +import OAI.Analysis.Laughlin.Operators.NormalOrder + +namespace OAI + +namespace Laughlin.Fock + +theorem normal_order_two_one {Q : ℕ} (a b d : Fin (Q+1)) : + annihilate b * annihilate a * create d = + delta a d • annihilate b - delta b d • annihilate a + + create d * annihilate b * annihilate a := by + calc + _ = annihilate b * (annihilate a * create d) := by noncomm_ring + _ = delta a d • annihilate b - (annihilate b * create d) * annihilate a := by + rw [annihilate_create] + simp only [mul_sub, mul_smul_comm, mul_one] + noncomm_ring + _ = _ := by + rw [annihilate_create b d] + simp only [sub_mul, smul_mul_assoc, one_mul] + noncomm_ring + +theorem normal_order_four {Q : ℕ} (a b c d : Fin (Q+1)) : + annihilate b * annihilate a * create c * create d = + delta a c • (delta b d • (1 : Module.End ℂ (Space Q))) - + delta b c • (delta a d • (1 : Module.End ℂ (Space Q))) - + delta a c • (create d * annihilate b) + + delta b c • (create d * annihilate a) + + delta a d • (create c * annihilate b) - + delta b d • (create c * annihilate a) + + create c * create d * annihilate b * annihilate a := by + rw [normal_order_two_inner, annihilate_create b d, annihilate_create a d] + have h : create c * annihilate b * annihilate a * create d = + create c * (annihilate b * annihilate a * create d) := by noncomm_ring + rw [h, normal_order_two_one] + simp only [smul_sub, mul_add, mul_sub, mul_smul_comm] + noncomm_ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/OrthonormalRows.lean b/lean/OAI/Analysis/Laughlin/Operators/OrthonormalRows.lean new file mode 100644 index 0000000000000000000000000000000000000000..5378d7ffc37a19b082a538d85cc8a67906fd7b8e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/OrthonormalRows.lean @@ -0,0 +1,27 @@ +import Mathlib.Analysis.InnerProductSpace.PiL2 + +namespace OAI + +namespace Laughlin +open scoped BigOperators + +theorem orthonormal_rows_complex_bound {I J : Type*} [Fintype I] [Fintype J] + [DecidableEq I] (c : I → J → ℝ) (v : J → ℂ) + (hc : ∀ i k, (∑ j, c i j * c k j) = if i = k then 1 else 0) : + (∑ i, ‖∑ j, (c i j : ℂ) * v j‖^2) ≤ ∑ j, ‖v j‖^2 := by + let u : I → EuclideanSpace ℂ J := fun i => WithLp.toLp 2 (fun j => (c i j : ℂ)) + have hu : Orthonormal ℂ u := by + rw [orthonormal_iff_ite] + intro i k + simp only [u,PiLp.inner_apply,RCLike.inner_apply, + Complex.conj_ofReal] + have h := congrArg Complex.ofReal (hc k i) + simpa only [Complex.ofReal_sum,Complex.ofReal_mul, + apply_ite,Complex.ofReal_one,Complex.ofReal_zero,eq_comm] using h + have h := hu.sum_inner_products_le (WithLp.toLp 2 v) (s := Finset.univ) + simpa only [u,PiLp.inner_apply,PiLp.toLp_apply,RCLike.inner_apply, + Complex.star_def,Complex.conj_ofReal,EuclideanSpace.norm_sq_eq,mul_comm] using h + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/PairNormalOrder.lean b/lean/OAI/Analysis/Laughlin/Operators/PairNormalOrder.lean new file mode 100644 index 0000000000000000000000000000000000000000..e5edf1d032094e68a5f0f829a4e442015d4861ac --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/PairNormalOrder.lean @@ -0,0 +1,84 @@ +import OAI.Analysis.Laughlin.Pair.NormalOrder +import OAI.Analysis.Laughlin.ThreeBody.PhysicalKernel + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators Matrix + +theorem sourcePair_normal_order (Q p q : ℕ) (hQ : 2 ≤ Q) (hp : p ≤ 2*Q-2) : + sourcePairEnd Q p * sourcePairCreateEnd Q q = + (if p=q then (1 : ℂ) else 0) • (1 : Module.End ℂ (Space Q)) - + (2 : ℂ) • (∑ i, ∑ j, ∑ t, + ((pairCoefficient Q p j t : ℂ)*(pairCoefficient Q q i t : ℂ)) • + (create i * annihilate j)) + + sourcePairCreateEnd Q q * sourcePairEnd Q p := by + let F : Module.End ℂ (Space Q) := ∑ i, ∑ j, + ((pairCoefficient Q q i j : ℂ)*(pairCoefficient Q p i j : ℂ)) • 1 + let U : Module.End ℂ (Space Q) := ∑ i, ∑ j, ∑ b, + ((pairCoefficient Q q i j : ℂ)*(pairCoefficient Q p i b : ℂ)) • (create j * annihilate b) + let V : Module.End ℂ (Space Q) := ∑ i, ∑ j, ∑ b, + ((pairCoefficient Q q i j : ℂ)*(pairCoefficient Q p j b : ℂ)) • (create i * annihilate b) + have hexp : sourcePairEnd Q p * sourcePairCreateEnd Q q = + F-U+V+sourcePairCreateEnd Q q * sourcePairEnd Q p := by + simp only [sourcePairCreateEnd,pairCreateEnd,Complex.star_def,Complex.conj_ofReal, + Finset.mul_sum,mul_smul_comm,← mul_assoc,sourcePairEnd,pairEnd_create_create, + smul_add,smul_sub,Finset.smul_sum,smul_smul,pair_weight_product, + Finset.sum_add_distrib,Finset.sum_sub_distrib, + Finset.sum_mul,smul_mul_assoc,F,U,V] + have hF : F = (if p=q then (1 : ℂ) else 0) • (1 : Module.End ℂ (Space Q)) := by + dsimp [F] + simp only [← Finset.sum_smul] + have hg := congrArg Complex.ofReal (pairCoefficient_gram Q p q hQ hp) + push_cast at hg + congr 1 + by_cases he : p=q <;> simpa [he,mul_comm] using hg + have hV : V = -U := by + dsimp [V,U] + rw [Finset.sum_comm] + simp only [← Finset.sum_neg_distrib] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + apply Finset.sum_congr rfl + intro b hb + rw [pairCoefficient_swap Q q i j] + simp only [Complex.ofReal_neg,neg_mul] + apply LinearMap.ext + intro x + exact neg_smul ((pairCoefficient Q q i j : ℂ)*(pairCoefficient Q p i b : ℂ)) + ((create j * annihilate b) x) + have hU : U = ∑ i, ∑ j, ∑ t, + ((pairCoefficient Q p j t : ℂ)*(pairCoefficient Q q i t : ℂ)) • + (create i * annihilate j) := by + dsimp [U] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i hi + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro j hj + apply Finset.sum_congr rfl + intro t ht + rw [pairCoefficient_swap Q q t i,pairCoefficient_swap Q p t j] + simp [mul_comm] + rw [hexp,hF,hV,hU] + module + +theorem complexThreeGram_sub_one_entry (Q : ℕ) (a b : Spin.PairOrbitalIndex Q) : + (complexThreeGram Q-1) a b = -2 * ∑ t, + (pairCoefficient Q a.1.val b.2 t : ℂ)*(pairCoefficient Q b.1.val a.2 t : ℂ) := by + simp only [complexThreeGram,Spin.threeGram,Matrix.sub_apply,Matrix.smul_apply, + smul_eq_mul,Spin.swapCompression_entry,Complex.ofReal_sub,Complex.ofReal_mul, + Complex.ofReal_ofNat,Complex.ofReal_sum] + have h : ((1 : Matrix (Spin.PairOrbitalIndex Q) (Spin.PairOrbitalIndex Q) ℝ) a b : ℂ) = + (1 : Matrix (Spin.PairOrbitalIndex Q) (Spin.PairOrbitalIndex Q) ℂ) a b := by + classical + by_cases hab : a=b <;> simp [hab,Matrix.one_apply] + rw [h] + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/PhysicalCoupling.lean b/lean/OAI/Analysis/Laughlin/Operators/PhysicalCoupling.lean new file mode 100644 index 0000000000000000000000000000000000000000..ed15c6cd0b077cdc0ca1eca7d8ec2d0a6ffe35b0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/PhysicalCoupling.lean @@ -0,0 +1,35 @@ +import OAI.Analysis.Laughlin.Spin.Polynomial + +namespace OAI + +namespace Laughlin.Spin +open scoped Topology +open Filter + +noncomputable def physicalCouplingCoefficient (A B z T p : ℕ) : ℝ := + if h : z ≤ T ∧ p ≤ T ∧ T ≤ A ∧ T ≤ B then + (-1 : ℝ)^z * genericUnitDescendant A B z (by omega) (by omega) (T-z) + (⟨p,by omega⟩,⟨T-p,by omega⟩) + else 0 + +theorem physicalCouplingCoefficient_eq_array (A B z T p : ℕ) + (hz : z ≤ T) (hp : p ≤ T) (hA : T ≤ A) (hB : T ≤ B) : + physicalCouplingCoefficient A B z T p = couplingArray A B z (T-z) p := by + rw [physicalCouplingCoefficient,dite_eq_left ⟨hz,hp,hA,hB⟩] + exact couplingArray_physical A B z (T-z) (by omega) (by omega) (by omega) (by omega) + (⟨p,by omega⟩,⟨T-p,by omega⟩) (by dsimp; omega) + +theorem source_physical_coupling_tendsto (A B : ℕ → ℕ) (b : ℝ) + (hA : Tendsto A atTop atTop) (hB : Tendsto B atTop atTop) + (hb0 : 0 < b) (hb1 : b < 1) + (hfrac : Tendsto (fun j => (B j : ℝ)/((A j : ℝ)+B j)) atTop (𝓝 b)) + (z T p : ℕ) (hz : z ≤ T) (hp : p ≤ T) : + Tendsto (fun j => physicalCouplingCoefficient (A j) (B j) z T p) atTop + (𝓝 (couplingPolynomialCoefficient (Real.sqrt b) (Real.sqrt (1-b)) z (T-z) p)) := by + apply (source_coupling_polynomial_tendsto A B b hA hB hb0 hb1 hfrac z T p hz hp).congr' + filter_upwards [hA.eventually (eventually_ge_atTop T),hB.eventually (eventually_ge_atTop T)] with j hjA hjB + exact (physicalCouplingCoefficient_eq_array (A j) (B j) z T p hz hp hjA hjB).symm + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/PhysicalFockGap.lean b/lean/OAI/Analysis/Laughlin/Operators/PhysicalFockGap.lean new file mode 100644 index 0000000000000000000000000000000000000000..42e3eed1f32077295401c68f4344ee53da3e02ea --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/PhysicalFockGap.lean @@ -0,0 +1,48 @@ +import OAI.Analysis.Laughlin.Asymptotics.ScalarBudget +import OAI.Analysis.Laughlin.FourBody.Estimate +import OAI.Analysis.Laughlin.Operators.SevenSquareAverage +import OAI.Analysis.Laughlin.ThreeBody.FockBudget + +namespace OAI + +namespace Laughlin.Fock +open Filter +open scoped BigOperators Topology + +theorem physical_fock_budget_eventually : + ∀ᶠ Q : ℕ in atTop, ∃ hQ : 25 ≤ Q, ∀ x : Space Q, + sourceKForm Q (by omega) x + + (1-93527408868499/10^14-deltaFormula Q-10946*(3/10^6)-averagedFourTransferError Q) * + sourceFockEnergy Q x ≤ occupationNormSq Q (sourceFockHamiltonian Q x) := by + filter_upwards [physical_threeBody_budget_eventually,eventually_ge_atTop 25] with Q h3 h25 + obtain ⟨h15,h3⟩ := h3 + refine ⟨h25,fun x => ?_⟩ + have h3x := h3 x + change sourceA3Form Q x-deltaFormula Q*sourceFockEnergy Q x ≤ _ at h3x + have h4 := sourceA4Form_bound Q h25 x + have hs := sourceFockHamiltonian_normal_square Q (by omega) x + rw [sourceKForm_decomposition Q h25] + nlinarith + +theorem physical_fock_square_eventually : + ∀ᶠ Q : ℕ in atTop, ∀ x : Space Q, + (1/100 : ℝ)*sourceFockEnergy Q x ≤ occupationNormSq Q (sourceFockHamiltonian Q x) := by + filter_upwards [physical_fock_budget_eventually, + eventual_scalar_budget averagedFourTransferError averagedFourTransferError_tendsto] with Q h hs + obtain ⟨hQ,h⟩ := h + intro x + have hE : 0 ≤ sourceFockEnergy Q x := Finset.sum_nonneg (fun p hp => occupationNormSq_nonneg Q _) + have hm := mul_le_mul_of_nonneg_right hs hE + have hk := sourceKForm_nonneg Q (by omega) x + have hx := h x + linarith + +theorem physical_fock_square_uniform : + ∃ Q₀ : ℕ, 25 ≤ Q₀ ∧ ∀ Q : ℕ, Q₀ ≤ Q → ∀ x : Space Q, + (1/100 : ℝ)*sourceFockEnergy Q x ≤ occupationNormSq Q (sourceFockHamiltonian Q x) := by + obtain ⟨q,hq⟩ := eventually_atTop.mp physical_fock_square_eventually + exact ⟨max 25 q,le_max_left _ _,fun Q hQ => hq Q (le_trans (le_max_right _ _) hQ)⟩ + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/PhysicalPairCounting.lean b/lean/OAI/Analysis/Laughlin/Operators/PhysicalPairCounting.lean new file mode 100644 index 0000000000000000000000000000000000000000..bc95256d256936cfe0c679dae7b38c05fd596dd2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/PhysicalPairCounting.lean @@ -0,0 +1,88 @@ +import OAI.Analysis.Laughlin.Tensor.PairContraction + +namespace OAI + +namespace Laughlin +open scoped BigOperators + +theorem pair_update_insert {n Q : ℕ} (i : Fin (n+2)) (j : Fin (n+1)) + (u v x y : Fin (Q+1)) (b : Configuration n Q) : + Function.update (Function.update (i.insertNth u (j.insertNth v b) : Configuration (n+2) Q) i x) + (i.succAbove j) y = i.insertNth x (j.insertNth y b) := by + rw [Fin.update_insertNth, ← Fin.insertNth_update, Fin.update_insertNth] + +theorem pairAmplitude_insert {n Q : ℕ} (ψ : State (n+2) Q) (hψ : Antisymmetric ψ) + (i : Fin (n+2)) (j : Fin (n+1)) (p : ℕ) + (u v : Fin (Q+1)) (b : Configuration n Q) : + pairAmplitude ψ i (i.succAbove j) p (i.insertNth u (j.insertNth v b)) = + ((-1 : ℂ)^i.val * (-1 : ℂ)^j.val) * headPairAmplitude ψ p b := by + simp only [pairAmplitude,pair_update_insert,antisymmetric_insertNth hψ] + have he (x y : Fin (Q+1)) : + ψ (Fin.cons x (j.insertNth y b)) = + (-1 : ℂ)^j.val * ψ (Fin.cons x (Fin.cons y b)) := + antisymmetric_insertNth (antisymmetric_cons hψ x) j y b + simp only [he,headPairAmplitude,Finset.mul_sum] + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + ring + +theorem anchored_pair_sum {n Q : ℕ} (ψ : State (n+2) Q) (hψ : Antisymmetric ψ) + (i : Fin (n+2)) (j : Fin (n+1)) (p : ℕ) : + (∑ a : Configuration (n+2) Q, + if a i = 0 ∧ a (i.succAbove j) = 0 then + ‖pairAmplitude ψ i (i.succAbove j) p a‖^2 else 0) = + ∑ b : Configuration n Q, ‖headPairAmplitude ψ p b‖^2 := by + rw [sum_config_insert i] + simp only [Fin.insertNth_apply_same,Fin.insertNth_apply_succAbove] + simp_rw [sum_config_insert j] + simp only [Fin.insertNth_apply_same,pairAmplitude_insert ψ hψ] + simp [norm_pow,ite_and] + +theorem unordered_position_count (n : ℕ) : + (∑ i : Fin n, ∑ j : Fin n, if i < j then (1 : ℝ) else 0) = + (n : ℝ)*((n : ℝ)-1)/2 := by + induction n with + | zero => simp + | succ n ih => + rw [Fin.sum_univ_succ] + simp only [Fin.sum_univ_succ,Fin.lt_def,Fin.val_zero,Fin.val_succ, + Nat.zero_lt_succ,Nat.not_lt_zero,ite_true,ite_false,Nat.add_lt_add_iff_right] + simp only [Finset.sum_const,Finset.card_univ,Fintype.card_fin,nsmul_eq_mul,mul_one, + zero_add] + change (n : ℝ) + (∑ i : Fin n, ∑ j : Fin n, if i < j then (1 : ℝ) else 0) = _ + rw [ih] + push_cast + ring + +theorem energy_head_pair (n Q : ℕ) (ψ : State (n+2) Q) (hψ : Antisymmetric ψ) : + energy ψ = ((n+2 : ℝ)*(n+1)/2) * + ∑ p ∈ Finset.range (2*Q-1), ∑ b : Configuration n Q, ‖headPairAmplitude ψ p b‖^2 := by + have he (i j : Fin (n+2)) (hij : i < j) (p : ℕ) : + (∑ a : Configuration (n+2) Q, + if a i = 0 ∧ a j = 0 then ‖pairAmplitude ψ i j p a‖^2 else 0) = + ∑ b : Configuration n Q, ‖headPairAmplitude ψ p b‖^2 := by + obtain ⟨k,hk⟩ := (Fin.exists_succAbove_eq (ne_of_lt hij).symm) + subst j + exact anchored_pair_sum ψ hψ i k p + unfold energy + have hs : (∑ i : Fin (n+2), ∑ j : Fin (n+2), if i < j then (1 : ℝ) else 0) = + (n+2 : ℝ)*(n+1)/2 := by + rw [unordered_position_count] + push_cast + ring + rw [← hs,Finset.sum_mul] + apply Finset.sum_congr rfl + intro i hi + rw [Finset.sum_mul] + apply Finset.sum_congr rfl + intro j hj + by_cases hij : i < j + · simp only [ite_eq_left hij,one_mul] + exact Finset.sum_congr rfl (fun p hp => he i j hij p) + · simp [hij] + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/PhysicalPairKernel.lean b/lean/OAI/Analysis/Laughlin/Operators/PhysicalPairKernel.lean new file mode 100644 index 0000000000000000000000000000000000000000..04b04ac185b36a74019362e11604dc243af0592f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/PhysicalPairKernel.lean @@ -0,0 +1,68 @@ +import OAI.Analysis.Laughlin.Operators.Energy +import OAI.Analysis.Laughlin.Pair.AffineKernel + +namespace OAI + +namespace Laughlin +open scoped BigOperators + +def pairSlice {N Q : ℕ} (ψ : State N Q) (i j : Fin N) (a : Configuration N Q) + (x y : Fin (Q+1)) : ℂ := ψ (Function.update (Function.update a i x) j y) + +theorem pairSlice_antisymmetric {N Q : ℕ} (ψ : State N Q) (hψ : Antisymmetric ψ) + (i j : Fin N) (hij : i ≠ j) (a : Configuration N Q) : + ∀ x y, pairSlice ψ i j a y x = -pairSlice ψ i j a x y := by + intro x y + have h := hψ i j hij (Function.update (Function.update a i x) j y) + have hs : (Function.update (Function.update a i x) j y) ∘ Equiv.swap i j = + Function.update (Function.update a i y) j x := by + funext k + by_cases hki : k = i + · subst k; simp [hij] + · by_cases hkj : k = j + · subst k; simp [hij] + · simp [Equiv.swap_apply_of_ne_of_ne hki hkj,hki,hkj] + simpa only [hs,pairSlice] using h + +theorem pairSlice_anchor {N Q : ℕ} (ψ : State N Q) (i j : Fin N) + (a : Configuration N Q) : + pairSlice ψ i j (Function.update (Function.update a i 0) j 0) = pairSlice ψ i j a := by + funext x y + unfold pairSlice + congr 1 + funext k + by_cases hki : k = i <;> by_cases hkj : k = j <;> + simp_all + +theorem energy_eq_zero_iff_pair_slices {N Q : ℕ} (ψ : State N Q) : + energy ψ = 0 ↔ ∀ (i j : Fin N), i < j → ∀ a : Configuration N Q, + ∀ p ∈ Finset.range (2*Q-1), + (∑ x, ∑ y, (pairCoefficient Q p x y : ℂ)*pairSlice ψ i j a x y) = 0 := by + rw [energy_eq_zero_iff] + constructor + · intro h i j hij a p hp + have h0 := h i j hij p (Finset.mem_range.mp hp) + (Function.update (Function.update a i 0) j 0) + (by simp [ne_of_lt hij]) (by simp) + change (∑ x, ∑ y, (pairCoefficient Q p x y : ℂ)* + pairSlice ψ i j (Function.update (Function.update a i 0) j 0) x y) = 0 at h0 + simpa only [pairSlice_anchor] using h0 + · intro h i j hij p hp a hai haj + exact h i j hij a p (Finset.mem_range.mpr hp) + +theorem energy_eq_zero_iff_affine_pair_cubes {N Q : ℕ} (hQ : 2 ≤ Q) + (ψ : State N Q) (hψ : Antisymmetric ψ) : + energy ψ = 0 ↔ ∀ (i j : Fin N), i < j → ∀ a : Configuration N Q, + PairDiagonal.diagonal^3 ∣ pairAffinePolynomial Q (pairSlice ψ i j a) := by + rw [energy_eq_zero_iff_pair_slices] + constructor + · intro h i j hij a + exact (pair_kernel_iff_affine_cube Q hQ _ + (pairSlice_antisymmetric ψ hψ i j (ne_of_lt hij) a)).mp (h i j hij a) + · intro h i j hij a + exact (pair_kernel_iff_affine_cube Q hQ _ + (pairSlice_antisymmetric ψ hψ i j (ne_of_lt hij) a)).mpr (h i j hij a) + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/PhysicalPairRotation.lean b/lean/OAI/Analysis/Laughlin/Operators/PhysicalPairRotation.lean new file mode 100644 index 0000000000000000000000000000000000000000..4173638775987bf14f97a84188ea920eb32be61e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/PhysicalPairRotation.lean @@ -0,0 +1,65 @@ +import OAI.Analysis.Laughlin.Pair.LadderIntertwining +import OAI.Analysis.Laughlin.Spin.LadderGroupIntertwining + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix Kronecker + +noncomputable def physicalPairInclusion (Q : ℕ) := (Spin.pairInclusion Q).map Complex.ofReal + +theorem physicalPairInclusion_SU2 (Q : ℕ) (hQ : 0 < Q) (g : SourceSU2) : + (sourceSpinRepresentation Q g ⊗ₖ sourceSpinRepresentation Q g)*physicalPairInclusion Q = + physicalPairInclusion Q*sourceSpinRepresentation (2*Q-2) g := by + apply ladder_intertwiner_SU2 Q Q 1 (2*Q-2) (by omega) + · intro i n hi + have hn : i.1.val+i.2.val ≠ n.val+1 := by omega + simp [physicalPairInclusion,Spin.pairInclusion,pairCoefficient,hn] + · ext i n + have h := congrArg Complex.ofReal (congrFun (congrFun (Spin.pairInclusion_raising Q hQ) i) n) + simpa [physicalPairInclusion,totalRaiseComplex,spinRaiseComplex,Matrix.mul_apply] using h + · ext i n + have h := congrArg Complex.ofReal (congrFun (congrFun (Spin.pairInclusion_lowering Q hQ) i) n) + simpa [physicalPairInclusion,totalRaiseComplex,spinRaiseComplex,Matrix.mul_apply,Matrix.transpose_apply] using h + +theorem physicalPairInclusion_isometry (Q : ℕ) (hQ : 2 ≤ Q) : + (physicalPairInclusion Q)ᴴ*physicalPairInclusion Q=1 := by + ext p q + have h := congrArg Complex.ofReal (congrFun (congrFun (Spin.pairInclusion_isometry Q hQ) p) q) + simpa [physicalPairInclusion,Matrix.mul_apply,Matrix.conjTranspose_apply,Matrix.transpose_apply, + Matrix.one_apply,apply_ite] using h + +theorem physicalPairProjector_SU2 (Q : ℕ) (hQ : 0 < Q) (g : SourceSU2) : + (sourceSpinRepresentation Q g ⊗ₖ sourceSpinRepresentation Q g)* + (physicalPairInclusion Q*(physicalPairInclusion Q)ᴴ) = + (physicalPairInclusion Q*(physicalPairInclusion Q)ᴴ)* + (sourceSpinRepresentation Q g ⊗ₖ sourceSpinRepresentation Q g) := by + have h := physicalPairInclusion_SU2 Q hQ g + have hi := physicalPairInclusion_SU2 Q hQ g⁻¹ + have hinv (A : ℕ) : (sourceSpinRepresentation A g⁻¹)ᴴ=sourceSpinRepresentation A g := by + have hu := Matrix.mem_unitaryGroup_iff.mp (sourceSpinRepresentation_unitary A g) + rw [Matrix.star_eq_conjTranspose] at hu + have hm : sourceSpinRepresentation A g⁻¹*sourceSpinRepresentation A g=1 := by + rw [← map_mul,inv_mul_cancel,map_one] + have he : sourceSpinRepresentation A g⁻¹=(sourceSpinRepresentation A g)ᴴ := by + calc + _ = sourceSpinRepresentation A g⁻¹*1 := by rw [Matrix.mul_one] + _ = sourceSpinRepresentation A g⁻¹*(sourceSpinRepresentation A g*(sourceSpinRepresentation A g)ᴴ) := by rw [hu] + _ = (sourceSpinRepresentation A g⁻¹*sourceSpinRepresentation A g)*(sourceSpinRepresentation A g)ᴴ := by rw [Matrix.mul_assoc] + _ = _ := by rw [hm,Matrix.one_mul] + rw [he,Matrix.conjTranspose_conjTranspose] + have hs := hinv Q + have hj := hinv (2*Q-2) + have ht := congrArg Matrix.conjTranspose hi + have hk : (sourceSpinRepresentation Q g⁻¹ ⊗ₖ sourceSpinRepresentation Q g⁻¹)ᴴ = + sourceSpinRepresentation Q g ⊗ₖ sourceSpinRepresentation Q g := by + ext i j + simp only [Matrix.conjTranspose_apply,Matrix.kroneckerMap,Matrix.of_apply] + simpa only [Matrix.conjTranspose_apply,star_mul,mul_comm] using + congrArg₂ (·*·) (congrFun (congrFun hs i.1) j.1) (congrFun (congrFun hs i.2) j.2) + rw [Matrix.conjTranspose_mul,Matrix.conjTranspose_mul,hk,hj] at ht + rw [← Matrix.mul_assoc,h,Matrix.mul_assoc,← ht,← Matrix.mul_assoc] + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/PositiveFockLift.lean b/lean/OAI/Analysis/Laughlin/Operators/PositiveFockLift.lean new file mode 100644 index 0000000000000000000000000000000000000000..ea5b5e098599f9ac523e3cd36a81f47be1de1570 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/PositiveFockLift.lean @@ -0,0 +1,79 @@ +import Mathlib.Analysis.Complex.Order +import Mathlib.LinearAlgebra.Matrix.PosDef +import OAI.Analysis.Laughlin.Fock.Hamiltonian + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators ComplexOrder +open Matrix + +theorem occupationInner_star (Q : ℕ) (x y : Space Q) : + star (occupationInner Q x y) = occupationInner Q y x := by + simp [occupationInner,star_mul,mul_comm] + +theorem create_annihilate_adjoint_right (Q : ℕ) (i : Fin (Q+1)) (x y : Space Q) : + occupationInner Q x (create i y) = occupationInner Q (annihilate i x) y := by + have h := congrArg star (create_annihilate_adjoint Q i y x) + simpa only [occupationInner_star] using h + +theorem pairCreate_pair_adjoint_right (Q : ℕ) (c : Fin (Q+1) → Fin (Q+1) → ℂ) + (x y : Space Q) : + occupationInner Q x (pairCreateEnd Q c y) = occupationInner Q (pairEnd Q c x) y := by + have h := congrArg star (pairCreate_pair_adjoint Q c y x) + simpa only [occupationInner_star] using h + +noncomputable def operatorLift {I : Type*} [Fintype I] (Q : ℕ) + (plus minus : I → Module.End ℂ (Space Q)) (M : Matrix I I ℂ) : Module.End ℂ (Space Q) := + ∑ i, ∑ j, M i j • (plus i * minus j) + +theorem operatorLift_quadratic {I : Type*} [Fintype I] (Q : ℕ) + (plus minus : I → Module.End ℂ (Space Q)) (M : Matrix I I ℂ) + (ha : ∀ i x y, occupationInner Q x (plus i y) = occupationInner Q (minus i x) y) + (x : Space Q) : + occupationInner Q x (operatorLift Q plus minus M x) = + ∑ A : Finset (Fin (Q+1)), star (fun i => (occupationBasis Q).repr (minus i x) A) ⬝ᵥ + (M *ᵥ (fun i => (occupationBasis Q).repr (minus i x) A)) := by + simp only [operatorLift,LinearMap.sum_apply,LinearMap.smul_apply,Module.End.mul_apply, + occupationInner_sum_right,occupationInner_smul_right,ha] + simp only [occupationInner, dotProduct,Matrix.mulVec,Finset.mul_sum,Pi.star_apply] + symm + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i hi + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro j hj + apply Finset.sum_congr rfl + intro A hA + ring + +theorem operatorLift_positive {I : Type*} [Fintype I] (Q : ℕ) + (plus minus : I → Module.End ℂ (Space Q)) (M : Matrix I I ℂ) + (ha : ∀ i x y, occupationInner Q x (plus i y) = occupationInner Q (minus i x) y) + (hM : M.PosSemidef) (x : Space Q) : + 0 ≤ (occupationInner Q x (operatorLift Q plus minus M x)).re := by + rw [operatorLift_quadratic Q plus minus M ha x, Complex.re_sum] + exact Finset.sum_nonneg (fun A hA => + (Complex.nonneg_iff.mp (hM.dotProduct_mulVec_nonneg _)).1) + +noncomputable def sourceFourCreateEnd (Q p : ℕ) (j k : Fin (Q+1)) : Module.End ℂ (Space Q) := + sourcePairCreateEnd Q p * create j * create k + +theorem sourceFour_adjoint_right (Q p : ℕ) (j k : Fin (Q+1)) (x y : Space Q) : + occupationInner Q x (sourceFourCreateEnd Q p j k y) = + occupationInner Q (sourceFourEnd Q p j k x) y := by + simp only [sourceFourCreateEnd,sourceFourEnd,sourcePairCreateEnd,sourcePairEnd, + Module.End.mul_apply,pairCreate_pair_adjoint_right,create_annihilate_adjoint_right] + +theorem sourceFourLift_positive {I : Type*} [Fintype I] (Q : ℕ) + (p : I → ℕ) (j k : I → Fin (Q+1)) (M : Matrix I I ℂ) (hM : M.PosSemidef) + (x : Space Q) : + 0 ≤ (occupationInner Q x (operatorLift Q + (fun a => sourceFourCreateEnd Q (p a) (j a) (k a)) + (fun a => sourceFourEnd Q (p a) (j a) (k a)) M x)).re := + operatorLift_positive Q _ _ M (fun a => sourceFour_adjoint_right Q (p a) (j a) (k a)) hM x + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/RationalPSD.lean b/lean/OAI/Analysis/Laughlin/Operators/RationalPSD.lean new file mode 100644 index 0000000000000000000000000000000000000000..f97c0e9eb9514a571fa2daab33d3544ebdaace28 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/RationalPSD.lean @@ -0,0 +1,32 @@ +import Mathlib.Algebra.Order.Star.Real +import Mathlib.Data.Matrix.Basic +import Mathlib.LinearAlgebra.Matrix.PosDef +import Mathlib.Tactic.NormNum + +namespace OAI + +namespace Laughlin.Certificate +open scoped Matrix + +theorem rational_ldl_positive {n : ℕ} (A L : Matrix (Fin n) (Fin n) ℚ) + (d : Fin n → ℚ) (h : A = L * Matrix.diagonal d * L.transpose) + (hd : ∀ i, 0 ≤ d i) : (A.map (Rat.castHom ℝ)).PosSemidef := by + rw [h, Matrix.map_mul, Matrix.map_mul] + have hdiag : (Matrix.diagonal d).map (Rat.castHom ℝ) = + Matrix.diagonal (fun i => (d i : ℝ)) := by + ext i j + by_cases hij : i = j <;> simp [Matrix.diagonal, hij] + have htrans : L.transpose.map (Rat.castHom ℝ) = + (L.map (Rat.castHom ℝ)).conjTranspose := by + ext i j + simp + rw [hdiag, htrans] + apply Matrix.PosSemidef.mul_mul_conjTranspose_same + apply Matrix.PosSemidef.diagonal + intro i + change (0 : ℝ) ≤ (d i : ℝ) + exact_mod_cast hd i + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/RealComplexMatrixPositive.lean b/lean/OAI/Analysis/Laughlin/Operators/RealComplexMatrixPositive.lean new file mode 100644 index 0000000000000000000000000000000000000000..14537d39d0a5150b74e504c585b4ee71265dbe70 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/RealComplexMatrixPositive.lean @@ -0,0 +1,39 @@ +import Mathlib.Analysis.Complex.Order +import Mathlib.Analysis.Matrix.Hermitian +import Mathlib.LinearAlgebra.Matrix.PosDef +import Mathlib.Tactic.Ring + +namespace OAI + +namespace Laughlin +open scoped Matrix BigOperators ComplexOrder +open Matrix + +theorem real_complex_matrix_hermitian {I : Type*} (M : Matrix I I ℝ) (hM : M.IsHermitian) : + (M.map Complex.ofReal).IsHermitian := by + ext i j + have h := congrFun (congrFun hM.eq i) j + simpa [Matrix.conjTranspose_apply,Matrix.map_apply] using congrArg Complex.ofReal h + +theorem real_complex_matrix_positive {I : Type*} [Fintype I] + (M : Matrix I I ℝ) (hM : M.PosSemidef) : (M.map Complex.ofReal).PosSemidef := by + have hh := real_complex_matrix_hermitian M hM.isHermitian + apply Matrix.PosSemidef.of_dotProduct_mulVec_nonneg hh + intro z + apply Complex.nonneg_iff.mpr + constructor + · have hr := hM.dotProduct_mulVec_nonneg (fun i => (z i).re) + have hi := hM.dotProduct_mulVec_nonneg (fun i => (z i).im) + have he : (star z ⬝ᵥ ((M.map Complex.ofReal)*ᵥ z)).re = + (star (fun i => (z i).re) ⬝ᵥ (M*ᵥ (fun i => (z i).re))) + + (star (fun i => (z i).im) ⬝ᵥ (M*ᵥ (fun i => (z i).im))) := by + simp [dotProduct,Matrix.mulVec,Complex.mul_re,Complex.mul_im,Complex.re_sum, + Matrix.map_apply, + Finset.mul_sum,Finset.sum_add_distrib,sub_eq_add_neg] + rw [he] + exact add_nonneg hr hi + · exact (hh.im_star_dotProduct_mulVec_self z).symm + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/RowNormalSquare.lean b/lean/OAI/Analysis/Laughlin/Operators/RowNormalSquare.lean new file mode 100644 index 0000000000000000000000000000000000000000..1b31d8fb4ade7e4a0d51f2865c7fcd8a479cf65c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/RowNormalSquare.lean @@ -0,0 +1,48 @@ +import OAI.Analysis.Laughlin.Fock.NormalSquare + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem create_create_inner (Q : ℕ) (i j : Fin (Q+1)) (y z : Space Q) : + occupationInner Q (create i y) (create j z) = + delta i j * occupationInner Q y z - + occupationInner Q (annihilate j y) (annihilate i z) := by + rw [create_annihilate_adjoint] + change occupationInner Q y ((annihilate i * create j) z) = _ + rw [annihilate_create] + simp only [LinearMap.sub_apply,LinearMap.smul_apply,Module.End.one_apply, + Module.End.mul_apply,occupationInner_sub_right,occupationInner_smul_right, + annihilate_create_inner] + +theorem row_normal_square {I : Type*} [Fintype I] [DecidableEq I] + (Q : ℕ) (m : I → Fin (Q+1)) (hm : Function.Injective m) + (ell : ℝ) (u : Space Q) (v : I → Space Q) : + (occupationNormSq Q ((ell : ℂ) • u + ∑ i, create (m i) (v i)) : ℂ) = + (ell : ℂ)^2 * (occupationNormSq Q u : ℂ) + + (∑ i, (ell : ℂ) * (occupationInner Q (annihilate (m i) u) (v i) + + occupationInner Q (v i) (annihilate (m i) u))) + + (∑ i, (occupationNormSq Q (v i) : ℂ)) - + ∑ i, ∑ j, occupationInner Q (annihilate (m j) (v i)) (annihilate (m i) (v j)) := by + rw [← occupationInner_self] + simp only [occupationInner_add_left,occupationInner_add_right,occupationInner_smul_left, + occupationInner_smul_right,Complex.star_def,Complex.conj_ofReal, + occupationInner_sum_left,occupationInner_sum_right] + have hd (i j : I) : delta (m i) (m j) = if i=j then (1 : ℂ) else 0 := by + simp only [delta,hm.eq_iff] + have he : (∑ i, ∑ j, occupationInner Q (create (m i) (v i)) (create (m j) (v j))) = + (∑ i, (occupationNormSq Q (v i) : ℂ)) - + ∑ i, ∑ j, occupationInner Q (annihilate (m j) (v i)) (annihilate (m i) (v j)) := by + simp_rw [create_create_inner,hd] + simp [Finset.sum_sub_distrib,occupationInner_self] + rw [Finset.sum_comm] at he + simp only [Finset.sum_add_distrib] + rw [he] + simp only [create_annihilate_adjoint,annihilate_create_inner,occupationInner_self, + Finset.mul_sum,mul_add,Finset.sum_add_distrib] + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/SevenSquareAverage.lean b/lean/OAI/Analysis/Laughlin/Operators/SevenSquareAverage.lean new file mode 100644 index 0000000000000000000000000000000000000000..06e389727364d42231722d5923a790cebd64bc72 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/SevenSquareAverage.lean @@ -0,0 +1,85 @@ +import OAI.Analysis.Laughlin.FourBody.Formula +import OAI.Analysis.Laughlin.FourBody.GlobalFock +import OAI.Analysis.Laughlin.Operators.NormalCertificate + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory +open scoped BigOperators Matrix + +theorem contractionForm_rotation_integrable {I : Type*} [Fintype I] + (Q : ℕ) (L : I → Module.End ℂ (Space Q)) (M : Matrix I I ℂ) (x : Space Q) : + Integrable (fun g : SourceSU2 => contractionForm Q L M (exteriorRotation Q g⁻¹ x)) sourceHaar := by + unfold contractionForm + exact integrable_finsetSum _ (fun i hi => integrable_finsetSum _ + (fun j hj => (linearMap_rotation_inner_integrable Q (L i) (L j) x).const_mul _)) + +noncomputable def sourceKForm (Q : ℕ) (hQ : 15 ≤ Q) (x : Space Q) : ℝ := + ((2*Q-2+1 : ℕ) : ℝ) * ∫ g, (Certificate.rows.map (fun row => + occupationNormSq Q (sourceRowSquareVector Q hQ row (exteriorRotation Q g⁻¹ x)))).sum ∂sourceHaar + +noncomputable def sourceA3Form (Q : ℕ) (x : Space Q) : ℝ := + ((2*Q-2+1 : ℕ) : ℝ) * (∫ g, contractionForm Q (sourceThreeEnd Q) + ((physicalThreeBodyMatrix Q).map Complex.ofReal) (exteriorRotation Q g⁻¹ x) ∂sourceHaar).re + +theorem sourceKForm_nonneg (Q : ℕ) (hQ : 15 ≤ Q) (x : Space Q) : 0 ≤ sourceKForm Q hQ x := by + apply mul_nonneg (by positivity) + apply integral_nonneg + intro g + apply List.sum_nonneg + intro a ha + obtain ⟨row,hr,rfl⟩ := List.mem_map.mp ha + exact occupationNormSq_nonneg Q _ + +theorem sourceKForm_decomposition (Q : ℕ) (hQ : 25 ≤ Q) (x : Space Q) : + sourceKForm Q (by omega) x = (93527408868499/10^14 : ℝ)*sourceFockEnergy Q x + + sourceA3Form Q x + sourceA4Form Q x := by + let L2 := fun p : Fin (2*Q-2+1) => sourcePairEnd Q p.val + let M2 := physicalTwoBodyMatrix Q + let M3 := (physicalThreeBodyMatrix Q).map Complex.ofReal + let M4 := (physicalFourBodyMatrix Q).map Complex.ofReal + have hp (y : Space Q) : + (Certificate.rows.map (fun row => occupationNormSq Q (sourceRowSquareVector Q (by omega) row y))).sum = + (contractionForm Q L2 M2 y + contractionForm Q (sourceThreeEnd Q) M3 y + + contractionForm Q (sourceFourFamilyEnd Q) M4 y).re := by + have h := congrArg Complex.re (source_seven_squares_normal_form Q hQ y) + have hs (l : List (ℕ × ℤ × List (ℕ × ℕ × ℤ))) : + (l.map (fun row => (occupationNormSq Q (sourceRowSquareVector Q (by omega) row y) : ℂ))).sum.re = + (l.map (fun row => occupationNormSq Q (sourceRowSquareVector Q (by omega) row y))).sum := by + induction l with + | nil => simp + | cons row l ih => simp only [List.map_cons,List.sum_cons,Complex.add_re,Complex.ofReal_re,ih] + rw [hs] at h + exact h + have hi2 := contractionForm_rotation_integrable Q L2 M2 x + have hi3 := contractionForm_rotation_integrable Q (sourceThreeEnd Q) M3 x + have hi4 := contractionForm_rotation_integrable Q (sourceFourFamilyEnd Q) M4 x + have h2 := congrArg Complex.re (physical_twoBody_certificate_haar Q (by omega) x) + norm_num [Complex.mul_re] at h2 + rw [sourceKForm] + simp_rw [hp] + have hre := integral_re ((hi2.add hi3).add hi4) + change (∫ g, (contractionForm Q L2 M2 (exteriorRotation Q g⁻¹ x) + + contractionForm Q (sourceThreeEnd Q) M3 (exteriorRotation Q g⁻¹ x) + + contractionForm Q (sourceFourFamilyEnd Q) M4 (exteriorRotation Q g⁻¹ x)).re ∂sourceHaar) = + (∫ g, contractionForm Q L2 M2 (exteriorRotation Q g⁻¹ x) + + contractionForm Q (sourceThreeEnd Q) M3 (exteriorRotation Q g⁻¹ x) + + contractionForm Q (sourceFourFamilyEnd Q) M4 (exteriorRotation Q g⁻¹ x) ∂sourceHaar).re at hre + have hi23 : Integrable (fun g : SourceSU2 => + contractionForm Q L2 M2 (exteriorRotation Q g⁻¹ x) + + contractionForm Q (sourceThreeEnd Q) M3 (exteriorRotation Q g⁻¹ x)) sourceHaar := hi2.add hi3 + rw [hre,integral_add hi23 hi4, + integral_add hi2 hi3,Complex.add_re,Complex.add_re] + change _ = _ + ((2*Q-2+1 : ℕ) : ℝ) * (∫ g, contractionForm Q (sourceThreeEnd Q) M3 + (exteriorRotation Q g⁻¹ x) ∂sourceHaar).re + + ((2*Q-2+1 : ℕ) : ℝ) * (∫ g, contractionForm Q (sourceFourFamilyEnd Q) M4 + (exteriorRotation Q g⁻¹ x) ∂sourceHaar).re + rw [mul_add,mul_add] + congr 2 + norm_num [L2,M2] + exact h2 + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/SpectralKernelDistance.lean b/lean/OAI/Analysis/Laughlin/Operators/SpectralKernelDistance.lean new file mode 100644 index 0000000000000000000000000000000000000000..b3b52ba9070f04b2efca56e83a5f1ee628e48c00 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/SpectralKernelDistance.lean @@ -0,0 +1,62 @@ +import Mathlib.Analysis.InnerProductSpace.Spectrum + +namespace OAI + +namespace Laughlin +open scoped BigOperators InnerProductSpace + +theorem spectral_kernel_distance {E : Type*} [NormedAddCommGroup E] + [InnerProductSpace ℂ E] [FiniteDimensional ℂ E] + (T : Module.End ℂ E) (hT : T.IsSymmetric) (c : ℝ) (hc : 0 ≤ c) + (hgap : ∀ v : E, v≠0 → ∀ a : ℝ, T v=(a : ℂ) • v → a=0 ∨ c≤a) + (x : E) : ∃ y : E, T y=0 ∧ c*‖x-y‖^2 ≤ (inner ℂ (T x) x).re := by + classical + let d := Module.finrank ℂ E + let b := hT.eigenvectorBasis (n := d) rfl + let a := hT.eigenvalues (n := d) rfl + let z : EuclideanSpace ℂ (Fin d) := WithLp.toLp 2 (fun i => if a i=0 then b.repr x i else 0) + let y := b.repr.symm z + have hyrepr (i : Fin d) : b.repr y i = if a i=0 then b.repr x i else 0 := by + simp [y,z] + have hdiag (v : E) (i : Fin d) : b.repr (T v) i = (a i : ℂ)*b.repr v i := + hT.eigenvectorBasis_apply_self_apply rfl v i + have hy : T y=0 := by + apply b.repr.injective + ext i + rw [hdiag,hyrepr] + by_cases hi : a i=0 <;> simp [hi] + have hnorm : ‖x-y‖^2 = ∑ i : Fin d, if a i=0 then 0 else ‖b.repr x i‖^2 := by + rw [← b.repr.norm_map,EuclideanSpace.norm_sq_eq] + apply Finset.sum_congr rfl + intro i hi + simp only [map_sub,PiLp.sub_apply,hyrepr] + by_cases ha : a i=0 <;> simp [ha] + have he : (inner ℂ (T x) x).re = ∑ i : Fin d, a i*‖b.repr x i‖^2 := by + rw [← b.repr.inner_map_map,PiLp.inner_apply,Complex.re_sum] + apply Finset.sum_congr rfl + intro i hi + rw [hdiag] + simp only [RCLike.inner_apply,map_mul,Complex.conj_ofReal] + have hn : (star (b.repr x i)*b.repr x i).re = ‖b.repr x i‖^2 := by + change (((starRingEnd ℂ) (b.repr x i))*b.repr x i).re = _ + rw [← Complex.normSq_eq_conj_mul_self] + simp only [Complex.ofReal_re,Complex.normSq_eq_norm_sq] + have hh : b.repr x i * ((a i : ℂ) * star (b.repr x i)) = + (a i : ℂ)*(star (b.repr x i)*b.repr x i) := by ring + change (b.repr x i * ((a i : ℂ) * star (b.repr x i))).re = _ + rw [hh,Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im,zero_mul,sub_zero,hn] + refine ⟨y,hy,?_⟩ + rw [hnorm,he,Finset.mul_sum] + apply Finset.sum_le_sum + intro i hi + have hb : b i ≠ 0 := b.orthonormal.ne_zero i + have hgi := hgap (b i) hb (a i) (hT.apply_eigenvectorBasis rfl i) + by_cases ha : a i=0 + · simp [ha] + · rw [ite_eq_right ha] + exact mul_le_mul (hgi.resolve_left ha) le_rfl (sq_nonneg _) + (hc.trans (hgi.resolve_left ha)) + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/SymmetricPairSum.lean b/lean/OAI/Analysis/Laughlin/Operators/SymmetricPairSum.lean new file mode 100644 index 0000000000000000000000000000000000000000..364784c8de86f620b91593e112c773d72febbde2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/SymmetricPairSum.lean @@ -0,0 +1,56 @@ +import OAI.Analysis.Laughlin.FourBody.WeightedReadout + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +private theorem symmetric_pair_sum {I M : Type*} [Fintype I] [LinearOrder I] + [AddCommGroup M] (F : I → I → M) (hF : ∀ i j, F j i=F i j) (h0 : ∀ i, F i i=0) : + (∑ i, ∑ j, F i j) = (∑ i, ∑ j, if i < j then F i j else 0) + + (∑ i, ∑ j, if i < j then F i j else 0) := by + have he (i j : I) : F i j = (if i < j then F i j else 0) + (if j < i then F j i else 0) := by + rcases lt_trichotomy i j with h | h | h + · simp [h,not_lt_of_gt h] + · subst j; simp [h0] + · simp [h,not_lt_of_gt h,hF] + conv_lhs => arg 2; ext i; arg 2; ext j; rw [he i j] + simp only [Finset.sum_add_distrib] + rw [Finset.sum_comm (f := fun i j : I => if j < i then F j i else 0)] + +theorem limitFourEnd_swap (Q p : ℕ) (j k : Fin (Q+1)) (x : Space Q) : + limitFourEnd Q p k j x = -limitFourEnd Q p j k x := by + have h := LinearMap.congr_fun (annihilate_anticommute j k) (limitPairEnd Q p x) + simpa only [limitFourEnd,Module.End.mul_apply,LinearMap.add_apply,LinearMap.zero_apply, + add_eq_zero_iff_eq_neg] using h + +theorem weightedFourEnd_ordered (Q p : ℕ) (S : ℕ → ℕ → ℝ) + (hS : ∀ j k, S k j = -S j k) (x : Space Q) : + weightedFourEnd Q p (fun j k => S j.val k.val) x = ∑ j : Fin (Q+1), ∑ k : Fin (Q+1), + if j ((S j.val k.val / 2 : ℝ) : ℂ) • limitFourEnd Q p j k x + have hf : ∀ j k, F k j=F j k := by + intro j k + simp [F,hS j.val k.val,limitFourEnd_swap Q p j k x,neg_div] + have h0 : ∀ j, F j j=0 := by + intro j + have hs := hS j.val j.val + have hz : S j.val j.val=0 := by linarith + simp [F,hz] + have h := symmetric_pair_sum F hf h0 + simp only [weightedFourEnd,LinearMap.sum_apply,LinearMap.smul_apply] + change (∑ j, ∑ k, F j k) = _ + rw [h,← Finset.sum_add_distrib] + apply Finset.sum_congr rfl; intro j hj + rw [← Finset.sum_add_distrib] + apply Finset.sum_congr rfl; intro k hk + split_ifs + · simp only [F,← add_smul] + congr 1 + push_cast + ring + · simp + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/TruncatedConjugation.lean b/lean/OAI/Analysis/Laughlin/Operators/TruncatedConjugation.lean new file mode 100644 index 0000000000000000000000000000000000000000..fbfa1c9de11054c83b92168d7d6f5bf015df7f22 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/TruncatedConjugation.lean @@ -0,0 +1,51 @@ +import OAI.Analysis.Laughlin.Asymptotics.TruncatedScaling + +namespace OAI + +namespace Laughlin.Fock + +theorem truncated_sourcePair_intertwining (L Q p : ℕ) (hQ : 0 < Q) + (hp : p ≤ 2*Q-2) (hL : p+1 ≤ L) (x : Space Q) : + truncatedScaling L Q (sourcePairEnd Q p x) = + (pairFactor Q p : ℂ) • limitPairEnd Q p (truncatedScaling L Q x) := by + have hc : (fun i j : Fin (Q+1) => ((pairCoefficient Q p i j / Real.sqrt 2 : ℝ) : ℂ)) = + (fun i j => (pairFactor Q p : ℂ)* + (((pairLimitCoefficient p i.val j.val / Real.sqrt 2 : ℝ) : ℂ)* + (truncatedModeFactor L Q i : ℂ)*(truncatedModeFactor L Q j : ℂ))) := by + funext i j + rw [pairCoefficient_conjugation Q p hQ hp] + by_cases hs : i.val+j.val=p+1 + · simp only [truncatedModeFactor,ite_eq_left (show i.val≤L by omega),ite_eq_left (show j.val≤L by omega)] + push_cast + ring + · simp [pairLimitCoefficient,hs] + unfold sourcePairEnd limitPairEnd truncatedScaling + rw [hc,pairEnd_smul,LinearMap.smul_apply,map_smul,pairEnd_scaling] + +theorem truncated_sourceFour_conjugation (L Q p : ℕ) (hQ : 0 < Q) + (hp : p ≤ 2*Q-2) (hL : p+1 ≤ L) (j k : Fin (Q+1)) + (hjL : j.val ≤ L) (hkL : k.val ≤ L) (x : Space Q) : + sourceFourEnd Q p j k x = + ((pairFactor Q p : ℂ)/((modeFactor Q j.val : ℂ)*(modeFactor Q k.val : ℂ))) • + truncatedScalingInv L Q (limitFourEnd Q p j k (truncatedScaling L Q x)) := by + have h := congrArg (fun y => annihilate k (annihilate j y)) + (truncated_sourcePair_intertwining L Q p hQ hp hL x) + have he : ((modeFactor Q j.val : ℂ)*(modeFactor Q k.val : ℂ)) • + truncatedScaling L Q (sourceFourEnd Q p j k x) = + (pairFactor Q p : ℂ) • limitFourEnd Q p j k (truncatedScaling L Q x) := by + simpa only [sourceFourEnd,limitFourEnd,Module.End.mul_apply,truncatedScaling, + annihilate_scaling,map_smul,smul_smul,truncatedModeFactor,ite_eq_left hjL,ite_eq_left hkL] using h + have h' := congrArg (truncatedScalingInv L Q) he + rw [map_smul,truncatedScaling_left_inverse L Q hQ,map_smul] at h' + have hj : (modeFactor Q j.val : ℂ) ≠ 0 := by exact_mod_cast ne_of_gt (modeFactor_pos Q hQ j) + have hk : (modeFactor Q k.val : ℂ) ≠ 0 := by exact_mod_cast ne_of_gt (modeFactor_pos Q hQ k) + have hd := mul_ne_zero hj hk + calc + _ = ((modeFactor Q j.val : ℂ)*(modeFactor Q k.val : ℂ))⁻¹ • + (((modeFactor Q j.val : ℂ)*(modeFactor Q k.val : ℂ)) • sourceFourEnd Q p j k x) := by + rw [smul_smul,inv_mul_cancel₀ hd,one_smul] + _ = _ := by rw [h',smul_smul]; congr 1; ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/TruncatedFourCopy.lean b/lean/OAI/Analysis/Laughlin/Operators/TruncatedFourCopy.lean new file mode 100644 index 0000000000000000000000000000000000000000..956fd1b1a4b1711b140fd6e003139d73199430b2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/TruncatedFourCopy.lean @@ -0,0 +1,38 @@ +import OAI.Analysis.Laughlin.FourBody.TransferConjugation +import OAI.Analysis.Laughlin.Operators.TruncatedConjugation + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators +open Spin + +noncomputable def localFourOperators (Q D : ℕ) (hDQ : D ≤ Q) (b : LocalFourIndex D) : Module.End ℂ (Space Q) := + limitFourEnd Q b.val.1.val ⟨b.val.2.1.val,by omega⟩ ⟨b.val.2.2.val,by omega⟩ + +theorem physicalFourCopyEnd_truncated (Q r D : ℕ) (hDQ : D ≤ Q) (hQ : 24 ≤ Q) + (hD : D ≤ 23) (x : Space Q) : + physicalFourCopyEnd Q r D hDQ x = truncatedScalingInv 24 Q + (∑ b : LocalFourIndex D, (physicalFourBeta Q r D b : ℂ) • + localFourOperators Q D hDQ b (truncatedScaling 24 Q x)) := by + simp only [physicalFourCopyEnd,LinearMap.sum_apply,LinearMap.smul_apply,map_sum,map_smul,localFourOperators] + apply Finset.sum_congr rfl + intro b hb + rw [truncated_sourceFour_conjugation 24 Q b.val.1.val (by omega) (by omega) (by omega) + _ _ (by change b.val.2.1.val ≤ 24; omega) (by change b.val.2.2.val ≤ 24; omega)] + rw [smul_smul] + congr 1 + simp only [physicalFourBeta] + push_cast + ring + +theorem localFourOperators_bound (Q D : ℕ) (hDQ : D ≤ Q) (hD : D ≤ 23) (x : Space Q) : + (∑ b : LocalFourIndex D, occupationNormSq Q (localFourOperators Q D hDQ b x)) ≤ + (Fintype.card (LocalFourIndex D) : ℝ) * limitPairWindow Q x := by + exact collection_limit_annihilator_bound Q (fun b : LocalFourIndex D => b.val.1.val) + (fun b => ⟨b.val.2.1.val,by omega⟩) (fun b => ⟨b.val.2.2.val,by omega⟩) + (fun b => by have := b.val.1.isLt; omega) x + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/TruncatedPairReturn.lean b/lean/OAI/Analysis/Laughlin/Operators/TruncatedPairReturn.lean new file mode 100644 index 0000000000000000000000000000000000000000..0bf0e4bd712575c3671e90f5d52bfbdd3f471081 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/TruncatedPairReturn.lean @@ -0,0 +1,53 @@ +import OAI.Analysis.Laughlin.Operators.TruncatedConjugation + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem truncatedScaling_normSq_le (L Q : ℕ) (hQ : 0 < Q) (x : Space Q) : + occupationNormSq Q (truncatedScaling L Q x) ≤ occupationNormSq Q x := by + unfold occupationNormSq truncatedScaling + apply Finset.sum_le_sum + intro A hA + rw [exteriorScaling_coordinate,norm_mul,mul_pow] + have hb : ‖∏ i ∈ A, (truncatedModeFactor L Q i : ℂ)‖ ≤ 1 := by + rw [norm_prod] + apply Finset.prod_le_one₀ + · intro i hi; exact norm_nonneg _ + · intro i hi + rw [Complex.norm_real,Real.norm_eq_abs,abs_of_pos (truncatedModeFactor_pos L Q hQ i)] + unfold truncatedModeFactor + split_ifs + · exact modeFactor_le_one Q i.val hQ + · exact le_rfl + have hsq : ‖∏ i ∈ A, (truncatedModeFactor L Q i : ℂ)‖^2 ≤ 1 := by + simpa using pow_le_pow_left₀ (norm_nonneg _) hb 2 + exact (mul_le_mul_of_nonneg_right hsq (sq_nonneg _)).trans_eq (one_mul _) + +theorem truncated_pair_energy_return (L Q p : ℕ) (hQ : 0 < Q) + (hp : p ≤ 2*Q-2) (hL : p+1 ≤ L) (x : Space Q) : + occupationNormSq Q (limitPairEnd Q p (truncatedScaling L Q x)) ≤ + occupationNormSq Q (sourcePairEnd Q p x) := by + have he := congrArg (occupationNormSq Q) (truncated_sourcePair_intertwining L Q p hQ hp hL x) + rw [occupationNormSq_smul,Complex.norm_real,Real.norm_eq_abs, + abs_of_nonneg (show 0 ≤ pairFactor Q p from Real.sqrt_nonneg _)] at he + have hr := pairFactor_one_le Q p hp + have hsq : 1 ≤ (pairFactor Q p)^2 := by nlinarith + calc + _ ≤ (pairFactor Q p)^2 * occupationNormSq Q (limitPairEnd Q p (truncatedScaling L Q x)) := by + simpa using mul_le_mul_of_nonneg_right hsq (occupationNormSq_nonneg Q _) + _ = occupationNormSq Q (truncatedScaling L Q (sourcePairEnd Q p x)) := he.symm + _ ≤ _ := truncatedScaling_normSq_le L Q hQ _ + +theorem truncated_pair_window_return (Q : ℕ) (hQ : 24 ≤ Q) (x : Space Q) : + limitPairWindow Q (truncatedScaling 24 Q x) ≤ sourcePairWindow Q x := by + unfold limitPairWindow sourcePairWindow + apply Finset.sum_le_sum + intro p hp + have hp' := Finset.mem_range.mp hp + exact truncated_pair_energy_return 24 Q p (by omega) (by omega) (by omega) x + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/WedgePairRepresentation.lean b/lean/OAI/Analysis/Laughlin/Operators/WedgePairRepresentation.lean new file mode 100644 index 0000000000000000000000000000000000000000..55300644352ff7ad7db09657e8b47cb726ee27b6 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/WedgePairRepresentation.lean @@ -0,0 +1,101 @@ +import OAI.Analysis.Laughlin.Operators.WedgePairRotation + +namespace OAI + +namespace Laughlin.Spin +open Rotation +open scoped BigOperators Matrix + +theorem real_matrix_inverse_complex {I J : Type*} [Fintype I] [Fintype J] + [DecidableEq I] (A : Matrix I J ℝ) (B : Matrix J I ℝ) (h : A*B=1) : + A.map Complex.ofReal * B.map Complex.ofReal = 1 := by + ext i j + have he := congrArg Complex.ofReal (congrFun (congrFun h i) j) + simpa only [Matrix.mul_apply,Matrix.map_apply,Complex.ofReal_sum,Complex.ofReal_mul, + Matrix.one_apply,apply_ite,Complex.ofReal_one,Complex.ofReal_zero] using he + +theorem real_matrix_adjoint {I J : Type*} (A : Matrix I J ℝ) : + (A.map Complex.ofReal)ᴴ = Aᵀ.map Complex.ofReal := by + ext i j + simp [Matrix.conjTranspose_apply,Matrix.transpose_apply] + +noncomputable def complexPairBasis (Q : ℕ) := (pairCoupledBasis Q).map Complex.ofReal + +theorem complexPairBasis_isometry (Q : ℕ) : + (complexPairBasis Q)ᴴ * complexPairBasis Q = 1 := by + rw [complexPairBasis,real_matrix_adjoint] + exact real_matrix_inverse_complex _ _ (pairCoupledBasis_isometry Q) + +theorem complexPairBasis_complete (Q : ℕ) : + complexPairBasis Q * (complexPairBasis Q)ᴴ = 1 := by + rw [complexPairBasis,real_matrix_adjoint] + exact real_matrix_inverse_complex _ _ (pairCoupledBasis_complete Q) + +noncomputable def pairBasisAction (Q : ℕ) (g : SourceSU2) : + Matrix (PairCoupledIndex Q) (PairCoupledIndex Q) ℂ := + Matrix.blockDiagonal' (fun r : OddPairLabel Q => + sourceSpinRepresentation (genericCoupledWeight Q Q (oddPairDeficit r)) g) + +theorem wedgePairMatrix_basis (Q : ℕ) (g : SourceSU2) : + wedgePairMatrix Q g * complexPairBasis Q = complexPairBasis Q * pairBasisAction Q g := by + ext i s + have hb : (complexPairBasis Q * pairBasisAction Q g) i s = + ∑ n, complexPairBasis Q i ⟨s.1,n⟩ * + sourceSpinRepresentation (genericCoupledWeight Q Q (oddPairDeficit s.1)) g n s.2 := by + rw [Matrix.mul_apply,Fintype.sum_sigma,Finset.sum_eq_single s.1] + · cases s; simp only [pairBasisAction,Matrix.blockDiagonal'_apply_eq] + · intro r hr hrs + simp only [pairBasisAction,Matrix.blockDiagonal'_apply_ne _ _ _ hrs,mul_zero,Finset.sum_const_zero] + · simp + rw [hb] + exact congrFun (congrFun (pairCoupledInclusion_SU2 Q (oddPairDeficit s.1) + (oddPairDeficit_le s.1) (oddPairDeficit_odd s.1) g) i) s.2 + +theorem wedgePairMatrix_factor (Q : ℕ) (g : SourceSU2) : + wedgePairMatrix Q g = complexPairBasis Q * pairBasisAction Q g * (complexPairBasis Q)ᴴ := by + rw [← wedgePairMatrix_basis,Matrix.mul_assoc,complexPairBasis_complete,Matrix.mul_one] + +theorem pairBasisAction_one (Q : ℕ) : pairBasisAction Q 1=1 := by + simp only [pairBasisAction,map_one] + exact Matrix.blockDiagonal'_one + +theorem pairBasisAction_mul (Q : ℕ) (g h : SourceSU2) : + pairBasisAction Q (g*h) = pairBasisAction Q g * pairBasisAction Q h := by + simp only [pairBasisAction,map_mul,Matrix.blockDiagonal'_mul] + +theorem wedgePairMatrix_one (Q : ℕ) : wedgePairMatrix Q 1=1 := by + rw [wedgePairMatrix_factor,pairBasisAction_one,Matrix.mul_one,complexPairBasis_complete] + +theorem wedgePairMatrix_mul (Q : ℕ) (g h : SourceSU2) : + wedgePairMatrix Q (g*h) = wedgePairMatrix Q g * wedgePairMatrix Q h := by + rw [wedgePairMatrix_factor,wedgePairMatrix_factor Q g,wedgePairMatrix_factor Q h,pairBasisAction_mul] + calc + _ = complexPairBasis Q * pairBasisAction Q g * + ((complexPairBasis Q)ᴴ * complexPairBasis Q) * pairBasisAction Q h * (complexPairBasis Q)ᴴ := by + rw [complexPairBasis_isometry,Matrix.mul_one] + simp only [Matrix.mul_assoc] + _ = _ := by simp only [Matrix.mul_assoc] + +noncomputable def wedgePairRepresentation (Q : ℕ) : + SourceSU2 →* Matrix (WedgePairIndex Q) (WedgePairIndex Q) ℂ where + toFun := wedgePairMatrix Q + map_one' := wedgePairMatrix_one Q + map_mul' := wedgePairMatrix_mul Q + +theorem wedgePairRepresentation_continuous (Q : ℕ) (i j : WedgePairIndex Q) : + Continuous (fun g => wedgePairRepresentation Q g i j) := + ((sourceSpinRepresentation_continuous Q i.val.1 j.val.1).mul + (sourceSpinRepresentation_continuous Q i.val.2 j.val.2)).sub + ((sourceSpinRepresentation_continuous Q i.val.1 j.val.2).mul + (sourceSpinRepresentation_continuous Q i.val.2 j.val.1)) + +theorem wedgePairRepresentation_inv (Q : ℕ) (g : SourceSU2) : + wedgePairRepresentation Q g⁻¹ = (wedgePairRepresentation Q g)ᴴ := by + ext i j + simp only [wedgePairRepresentation,MonoidHom.coe_mk,OneHom.coe_mk,wedgePairMatrix, + Matrix.conjTranspose_apply,sourceSpinRepresentation_inv,star_sub,star_mul] + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/WedgePairRotation.lean b/lean/OAI/Analysis/Laughlin/Operators/WedgePairRotation.lean new file mode 100644 index 0000000000000000000000000000000000000000..0fe70288179613ed1c799e9c026efa216811be35 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/WedgePairRotation.lean @@ -0,0 +1,97 @@ +import OAI.Analysis.Laughlin.Pair.CoupledBasis +import OAI.Analysis.Laughlin.Spin.Disjoint +import OAI.Analysis.Laughlin.Spin.Intertwining + +namespace OAI + +namespace Laughlin.Spin +open Rotation +open scoped BigOperators Matrix Kronecker + +theorem antisymmetric_ordered_sum (Q : ℕ) (f g : SpinIndex Q Q → ℂ) + (hf : ∀ i j, f (j,i) = -f (i,j)) : + (∑ i, f i*g i) = ∑ i : WedgePairIndex Q, f i.val * (g i.val-g i.val.swap) := by + have hd (i : Fin (Q+1)) : f (i,i)=0 := by have := hf i i; linear_combination this / 2 + have he (i j : Fin (Q+1)) : f (i,j)*g (i,j) = + (if i < j then f (i,j)*g (i,j) else 0) - + (if j < i then f (j,i)*g (i,j) else 0) := by + rcases lt_trichotomy i j with h | h | h + · simp [h,not_lt_of_gt h] + · subst j; simp [hd] + · simp [h,not_lt_of_gt h,hf i j] + calc + _ = ∑ i : Fin (Q+1), ∑ j : Fin (Q+1), + ((if i < j then f (i,j)*g (i,j) else 0) - + (if j < i then f (j,i)*g (i,j) else 0)) := by + rw [Fintype.sum_prod_type] + apply Finset.sum_congr rfl; intro i hi + apply Finset.sum_congr rfl; intro j hj + exact he i j + _ = ∑ i : SpinIndex Q Q, if i.1 < i.2 then f i*(g i-g i.swap) else 0 := by + simp only [Finset.sum_sub_distrib,Fintype.sum_prod_type] + rw [Finset.sum_comm (f := fun i j : Fin (Q+1) => if j < i then f (j,i)*g (i,j) else 0)] + rw [← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl; intro i hi + rw [← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl; intro j hj + split_ifs <;> simp [mul_sub] + _ = _ := by + rw [← Finset.sum_filter] + exact (Finset.sum_subtype (p := fun i : SpinIndex Q Q => i.1 < i.2) (Finset.univ.filter (fun i : SpinIndex Q Q => i.1 < i.2)) + (by simp) (fun i => f i*(g i-g i.swap))) + +noncomputable def wedgePairMatrix (Q : ℕ) (g : SourceSU2) : + Matrix (WedgePairIndex Q) (WedgePairIndex Q) ℂ := fun i j => + sourceSpinRepresentation Q g i.val.1 j.val.1 * sourceSpinRepresentation Q g i.val.2 j.val.2 - + sourceSpinRepresentation Q g i.val.1 j.val.2 * sourceSpinRepresentation Q g i.val.2 j.val.1 + +theorem wedgePairMatrix_tensor (Q : ℕ) (g : SourceSU2) (f : SpinIndex Q Q → ℂ) + (hf : ∀ i j, f (j,i) = -f (i,j)) (i : WedgePairIndex Q) : + (wedgePairMatrix Q g *ᵥ (fun j => (Real.sqrt 2 : ℂ)*f j.val)) i = + (Real.sqrt 2 : ℂ) * + ((sourceSpinRepresentation Q g ⊗ₖ sourceSpinRepresentation Q g) *ᵥ f) i.val := by + have h := antisymmetric_ordered_sum Q f + (fun j => sourceSpinRepresentation Q g i.val.1 j.1 * sourceSpinRepresentation Q g i.val.2 j.2) hf + simp only [Matrix.mulVec,dotProduct,Matrix.kroneckerMap,Matrix.of_apply] + conv_rhs => rw [show (∑ j : SpinIndex Q Q, + sourceSpinRepresentation Q g i.val.1 j.1 * sourceSpinRepresentation Q g i.val.2 j.2 * f j) = + ∑ j : SpinIndex Q Q, f j*(sourceSpinRepresentation Q g i.val.1 j.1 * + sourceSpinRepresentation Q g i.val.2 j.2) by apply Finset.sum_congr rfl; intro j hj; ring] + rw [h,Finset.mul_sum] + apply Finset.sum_congr rfl + intro j hj + dsimp [wedgePairMatrix] + ring + +theorem pairCoupledInclusion_SU2 (Q r : ℕ) (hr : r ≤ Q) (hor : Odd r) (g : SourceSU2) : + wedgePairMatrix Q g * (pairCoupledInclusion Q r hr).map Complex.ofReal = + (pairCoupledInclusion Q r hr).map Complex.ofReal * + sourceSpinRepresentation (genericCoupledWeight Q Q r) g := by + ext i n + have hp : physicalCoupledInclusion Q Q r hr hr = + (fun j k => (pairCoupledTensor Q r hr k.val j : ℂ)) := by + ext j k + simp [physicalCoupledInclusion,genericCoupledInclusion,pairCoupledTensor] + have h := congrFun (congrFun (physicalCoupledInclusion_SU2 Q Q r hr hr g) i.val) n + rw [hp] at h + have hf (a b : Fin (Q+1)) : + (pairCoupledTensor Q r hr n.val (b,a) : ℂ) = -(pairCoupledTensor Q r hr n.val (a,b) : ℂ) := by + exact_mod_cast pairCoupledTensor_antisymmetric Q r n.val hr hor a b + change (wedgePairMatrix Q g *ᵥ + (fun j => (pairCoupledWedge Q r hr n.val j : ℂ))) i = _ + simp only [pairCoupledWedge,tensorToWedgePair,Complex.ofReal_mul] + rw [wedgePairMatrix_tensor Q g (fun j : SpinIndex Q Q => (pairCoupledTensor Q r hr n.val j : ℂ)) hf i] + change ((sourceSpinRepresentation Q g ⊗ₖ sourceSpinRepresentation Q g) *ᵥ + (fun j : SpinIndex Q Q => (pairCoupledTensor Q r hr n.val j : ℂ))) i.val = + ∑ k, (pairCoupledTensor Q r hr k.val i.val : ℂ) * + sourceSpinRepresentation (genericCoupledWeight Q Q r) g k n at h + rw [h] + simp only [Matrix.mul_apply,Matrix.map_apply,pairCoupledInclusion,pairCoupledWedge, + tensorToWedgePair,Complex.ofReal_mul,Finset.mul_sum] + apply Finset.sum_congr rfl + intro k hk + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Operators/WeightedOccupationNorm.lean b/lean/OAI/Analysis/Laughlin/Operators/WeightedOccupationNorm.lean new file mode 100644 index 0000000000000000000000000000000000000000..7d95f6c8355e9942119e2480d998664847489afd --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Operators/WeightedOccupationNorm.lean @@ -0,0 +1,28 @@ +import Mathlib.Algebra.Order.BigOperators.Ring.Finset +import OAI.Analysis.Laughlin.Pair.EnergyReturn + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem normalized_occupation_sum_bound {I : Type*} [Fintype I] (Q : ℕ) + (c : I → ℝ) (v : I → Space Q) (hc : (∑ i, (c i)^2)=1) : + occupationNormSq Q (∑ i, (c i : ℂ) • v i) ≤ ∑ i, occupationNormSq Q (v i) := by + unfold occupationNormSq + simp only [map_sum,Finsupp.finsetSum_apply,map_smul,Finsupp.smul_apply,smul_eq_mul] + rw [Finset.sum_comm (f := fun i A => ‖(occupationBasis Q).repr (v i) A‖^2)] + apply Finset.sum_le_sum + intro A hA + have ht : ‖∑ i, (c i : ℂ) * (occupationBasis Q).repr (v i) A‖ ≤ + ∑ i, |c i| * ‖(occupationBasis Q).repr (v i) A‖ := by + simpa only [norm_mul,Complex.norm_real,Real.norm_eq_abs] using + (norm_sum_le Finset.univ (fun i => (c i : ℂ) * (occupationBasis Q).repr (v i) A)) + have hs := Finset.sum_mul_sq_le_sq_mul_sq Finset.univ (fun i => |c i|) + (fun i => ‖(occupationBasis Q).repr (v i) A‖) + simp only [sq_abs,hc,one_mul] at hs + exact (pow_le_pow_left₀ (norm_nonneg _) ht 2).trans hs + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/AffineChart.lean b/lean/OAI/Analysis/Laughlin/Pair/AffineChart.lean new file mode 100644 index 0000000000000000000000000000000000000000..385b3699a84f23857edb9fc31bc587f689bbb33e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/AffineChart.lean @@ -0,0 +1,83 @@ +import OAI.Analysis.Laughlin.Pair.SpinorCube +import OAI.Analysis.Laughlin.Spin.OrbitalExpansion + +namespace OAI + +namespace Laughlin +open MvPolynomial +open scoped BigOperators + +noncomputable def pairAffineChart {N : ℕ} (i j : Fin N) : + MvPolynomial (SpinorVariables N) ℂ →+* MvPolynomial (Fin N) PairDiagonal.Poly := + eval₂Hom (C.comp (Polynomial.C.comp Polynomial.C)) (fun kb => + if kb.2 then + if kb.1=i then C (Polynomial.C Polynomial.X) + else if kb.1=j then C Polynomial.X else X kb.1 + else 1) + +theorem pairAffineChart_bracket {N : ℕ} (i j : Fin N) (hij : i ≠ j) : + pairAffineChart i j (bracket i j) = C PairDiagonal.diagonal := by + unfold bracket + rw [map_sub, map_mul, map_mul] + simp [pairAffineChart, Ne.symm hij, PairDiagonal.diagonal] + +theorem pairAffineChart_pair {N Q : ℕ} (i j : Fin N) (hij : i ≠ j) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : + pairAffineChart i j + (pairSpinorPolynomial C (X (i,false)) (X (i,true)) (X (j,false)) (X (j,true)) Q ψ) = + C (pairAffinePolynomial Q ψ) := by + unfold pairSpinorPolynomial pairAffinePolynomial + simp only [map_sum] + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + simp [pairAffineChart, eval₂Hom, Ne.symm hij, + ← Polynomial.C_mul_X_pow_eq_monomial, map_mul, map_pow] + +noncomputable def spectatorWeight {N Q : ℕ} (i j : Fin N) (a : Configuration N Q) : ℂ := + ∏ k ∈ (Finset.univ.erase i).erase j, (Real.sqrt (Nat.choose Q (a k).val : ℝ) : ℂ) + +noncomputable def affineExponent {N Q : ℕ} (a : Configuration N Q) : Fin N →₀ ℕ := + Finsupp.onFinset Finset.univ (fun k => (a k).val) (by simp) + +theorem affineExponent_injective (N Q : ℕ) : + Function.Injective (affineExponent (N := N) (Q := Q)) := by + intro a b h + funext k + apply Fin.ext + exact congrArg (fun d => d k) h + +theorem spectatorWeight_ne_zero {N Q : ℕ} (i j : Fin N) (a : Configuration N Q) : + spectatorWeight i j a ≠ 0 := by + apply Finset.prod_ne_zero_iff.mpr + intro k hk + apply Complex.ofReal_ne_zero.mpr + apply Real.sqrt_ne_zero'.mpr + exact_mod_cast Nat.choose_pos (Nat.le_of_lt_succ (a k).isLt) + +theorem pairAffineChart_spectator {N Q : ℕ} (i j : Fin N) (hij : i ≠ j) + (a : PairSpectators (Q := Q) i j) : + pairAffineChart i j (spectatorPolynomial i j a.val) = + monomial (affineExponent a.val) (Polynomial.C (Polynomial.C (spectatorWeight i j a.val))) := by + classical + unfold spectatorPolynomial + simp only [map_prod] + have he (k : Fin N) (hk : k ∈ (Finset.univ.erase i).erase j) : + pairAffineChart i j (spinOrbitalPolynomial Q k (a.val k)) = + C (Polynomial.C (Polynomial.C (Real.sqrt (Nat.choose Q (a.val k).val : ℝ) : ℂ))) * + X k^(a.val k).val := by + have hki := (Finset.mem_erase.mp (Finset.mem_erase.mp hk).2).1 + have hkj := (Finset.mem_erase.mp hk).1 + simp [pairAffineChart, spinOrbitalPolynomial, eval₂Hom, hki, hkj] + rw [Finset.prod_congr rfl he, Finset.prod_mul_distrib, monomial_eq] + simp only [← map_prod, ← RingHom.comp_apply, spectatorWeight] + congr 1 + rw [Finsupp.prod_fintype _ _ (fun _ => pow_zero _)] + simp only [affineExponent, Finsupp.onFinset_apply] + rw [prod_pair_split i j hij] + simp [a.property.1, a.property.2] + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/AffineKernel.lean b/lean/OAI/Analysis/Laughlin/Pair/AffineKernel.lean new file mode 100644 index 0000000000000000000000000000000000000000..e4182a30b42af0a7274f3b6f479933a9cdbd320e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/AffineKernel.lean @@ -0,0 +1,69 @@ +import OAI.Analysis.Laughlin.Pair.AffinePolynomial + +namespace OAI + +namespace Laughlin +open Polynomial +open scoped BigOperators + +theorem pairMoment_eq_jet (Q n : ℕ) (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) + (ha : ∀ x y, ψ y x = -ψ x y) : + pairMoment Q n ψ = -2 * ((pairAffinePolynomial Q ψ).derivative.eval + (X : Polynomial ℂ)).coeff n := by + rw [pairAffinePolynomial_jet_coeff] + let I : ℂ := ∑ x, ∑ y, if x.val+y.val = n+1 then + (x.val : ℂ)*weightedPairCoordinate Q ψ x y else 0 + let J : ℂ := ∑ x, ∑ y, if x.val+y.val = n+1 then + (y.val : ℂ)*weightedPairCoordinate Q ψ x y else 0 + have hs : I = -J := by + dsimp [I,J] + rw [Finset.sum_comm] + simp only [← Finset.sum_neg_distrib] + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + rw [weightedPairCoordinate_swap Q ψ ha x y, Nat.add_comm y.val x.val] + split_ifs <;> ring + have hmom : pairMoment Q n ψ = I-J := by + dsimp [pairMoment,I,J] + rw [← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro x hx + rw [← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro y hy + split_ifs <;> ring + change pairMoment Q n ψ = -2*J + rw [hmom,hs] + ring + +theorem pair_kernel_of_affine_cube (Q : ℕ) (hQ : 2 ≤ Q) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) (ha : ∀ x y, ψ y x = -ψ x y) + (hcube : PairDiagonal.diagonal^3 ∣ pairAffinePolynomial Q ψ) : + ∀ p ∈ Finset.range (2*Q-1), + (∑ x, ∑ y, (pairCoefficient Q p x y : ℂ)*ψ x y) = 0 := by + obtain ⟨g,hg⟩ := hcube + have hj : (pairAffinePolynomial Q ψ).derivative.eval (X : Polynomial ℂ) = 0 := by + rw [hg, derivative_mul] + simp [PairDiagonal.diagonal, derivative_pow] + intro p hp + have hp' : p ≤ 2*Q-2 := by have h := Finset.mem_range.mp hp; omega + have hm : pairMoment Q p ψ = 0 := by + rw [pairMoment_eq_jet Q p ψ ha, hj, coeff_zero] + ring + rw [pairMoment_eq_amplitude Q p (by omega) hp' ψ] at hm + have hn : (pairNormalization Q p : ℂ) ≠ 0 := by + exact_mod_cast (ne_of_gt (pairNormalization_pos Q p (by omega) hp')) + exact (mul_eq_zero.mp hm).resolve_left hn + +theorem pair_kernel_iff_affine_cube (Q : ℕ) (hQ : 2 ≤ Q) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) (ha : ∀ x y, ψ y x = -ψ x y) : + (∀ p ∈ Finset.range (2*Q-1), + (∑ x, ∑ y, (pairCoefficient Q p x y : ℂ)*ψ x y) = 0) ↔ + PairDiagonal.diagonal^3 ∣ pairAffinePolynomial Q ψ := + ⟨pair_kernel_affine_cube Q hQ ψ ha, pair_kernel_of_affine_cube Q hQ ψ ha⟩ + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/AffinePolynomial.lean b/lean/OAI/Analysis/Laughlin/Pair/AffinePolynomial.lean new file mode 100644 index 0000000000000000000000000000000000000000..11ddb201c33085b3288e8c710a2cb8f967f511a6 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/AffinePolynomial.lean @@ -0,0 +1,69 @@ +import OAI.Analysis.Laughlin.Pair.DiagonalCube +import OAI.Analysis.Laughlin.Pair.MomentKernel + +namespace OAI + +namespace Laughlin +open Polynomial +open scoped BigOperators Polynomial.Bivariate + +noncomputable def pairAffinePolynomial (Q : ℕ) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : PairDiagonal.Poly := + ∑ x, ∑ y, monomial y.val (monomial x.val (weightedPairCoordinate Q ψ x y)) + +theorem pairAffinePolynomial_antisymmetric (Q : ℕ) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) (ha : ∀ x y, ψ y x = -ψ x y) : + Bivariate.swap (pairAffinePolynomial Q ψ) = -pairAffinePolynomial Q ψ := by + unfold pairAffinePolynomial + simp only [map_sum, Bivariate.swap_monomial_monomial] + rw [Finset.sum_comm] + simp only [← Finset.sum_neg_distrib] + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + rw [weightedPairCoordinate_swap Q ψ ha x y] + simp + +theorem diagonal_jet_monomial_coeff (i j n : ℕ) (a : ℂ) : + ((monomial j (monomial i a)).derivative.eval (X : Polynomial ℂ)).coeff n = + if i+j = n+1 then (j : ℂ)*a else 0 := by + cases j with + | zero => simp + | succ j => + rw [derivative_monomial, eval_monomial] + have hm : (monomial i a : Polynomial ℂ)*(j.succ : Polynomial ℂ) = + monomial i (a*(j.succ : ℂ)) := by + have hc : (j.succ : Polynomial ℂ) = C (j.succ : ℂ) := by simp + rw [hc, monomial_mul_C] + rw [Nat.succ_sub_one, hm, monomial_mul_X_pow, coeff_monomial] + have he : i+j = n ↔ i+j.succ = n+1 := by omega + simp only [he, mul_comm] + +theorem pairAffinePolynomial_jet_coeff (Q n : ℕ) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : + ((pairAffinePolynomial Q ψ).derivative.eval (X : Polynomial ℂ)).coeff n = + ∑ x, ∑ y, if x.val+y.val = n+1 then + (y.val : ℂ)*weightedPairCoordinate Q ψ x y else 0 := by + unfold pairAffinePolynomial + simp only [derivative_sum, eval_finsetSum, finsetSum_coeff] + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + exact diagonal_jet_monomial_coeff x.val y.val n _ + +theorem pair_kernel_affine_cube (Q : ℕ) (hQ : 2 ≤ Q) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) (ha : ∀ x y, ψ y x = -ψ x y) + (hk : ∀ p ∈ Finset.range (2*Q-1), + (∑ x, ∑ y, (pairCoefficient Q p x y : ℂ)*ψ x y) = 0) : + PairDiagonal.diagonal^3 ∣ pairAffinePolynomial Q ψ := by + apply PairDiagonal.cube_dvd_of_antisymmetric_first_jet + · exact pairAffinePolynomial_antisymmetric Q ψ ha + · ext n + rw [pairAffinePolynomial_jet_coeff, coeff_zero] + exact pair_jet_coefficient_zero Q n ψ ha (pairMoment_zero_of_pair_kernel Q hQ ψ hk n) + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/Binomial.lean b/lean/OAI/Analysis/Laughlin/Pair/Binomial.lean new file mode 100644 index 0000000000000000000000000000000000000000..f4175921665d01d866fc7f86f6a105b33325d840 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/Binomial.lean @@ -0,0 +1,185 @@ +import Mathlib.Data.Nat.Choose.Vandermonde +import Mathlib.Basic.Real.Basic +import Mathlib.Tactic.NormNum +import Mathlib.Tactic.Ring + +namespace OAI + +namespace Laughlin.PairNormalization +open scoped BigOperators +open Finset Finset.Nat + +theorem binomial_convolution (m n k : ℕ) : + (∑ ij ∈ antidiagonal k, (m.choose ij.1 : ℝ) * (n.choose ij.2 : ℝ)) = + ((m+n).choose k : ℝ) := by + exact_mod_cast (Nat.add_choose_eq m n k).symm + +theorem weighted_choose (m i : ℕ) : + ((i+1 : ℕ) : ℝ) * ((m+1).choose (i+1) : ℝ) = + ((m+1 : ℕ) : ℝ) * (m.choose i : ℝ) := by + have h : (i+1) * (m+1).choose (i+1) = (m+1) * m.choose i := by + simpa only [mul_comm] using (Nat.add_one_mul_choose_eq m i).symm + exact_mod_cast h + +theorem weighted_shift (m k : ℕ) (f : ℕ → ℕ → ℝ) : + (∑ ij ∈ antidiagonal (k+1), (ij.1 : ℝ) * ((m+1).choose ij.1 : ℝ) * f ij.1 ij.2) = + ((m+1 : ℕ) : ℝ) * + ∑ ij ∈ antidiagonal k, (m.choose ij.1 : ℝ) * f (ij.1+1) ij.2 := by + rw [sum_antidiagonal_succ] + simp only [Nat.cast_zero, zero_mul, zero_add] + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + rintro ⟨i,j⟩ hij + dsimp only + rw [weighted_choose] + ring + +theorem binomial_first_moment (m n k : ℕ) : + (∑ ij ∈ antidiagonal (k+1), (ij.1 : ℝ) * ((m+1).choose ij.1 : ℝ) * (n.choose ij.2 : ℝ)) = + ((m+1 : ℕ) : ℝ) * ((m+n).choose k : ℝ) := by + rw [weighted_shift m k (fun _ j => (n.choose j : ℝ)), binomial_convolution] + +theorem weighted_shift_right (n k : ℕ) (f : ℕ → ℕ → ℝ) : + (∑ ij ∈ antidiagonal (k+1), (ij.2 : ℝ) * ((n+1).choose ij.2 : ℝ) * f ij.1 ij.2) = + ((n+1 : ℕ) : ℝ) * + ∑ ij ∈ antidiagonal k, (n.choose ij.2 : ℝ) * f ij.1 (ij.2+1) := by + rw [sum_antidiagonal_succ'] + simp only [Nat.cast_zero, zero_mul, zero_add] + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + rintro ⟨i,j⟩ hij + dsimp only + rw [weighted_choose] + ring + +theorem binomial_second_falling (m n k : ℕ) : + (∑ ij ∈ antidiagonal (k+2), (ij.1 : ℝ) * ((ij.1 : ℝ)-1) * + ((m+2).choose ij.1 : ℝ) * (n.choose ij.2 : ℝ)) = + ((m+2 : ℕ) : ℝ) * ((m+1 : ℕ) : ℝ) * ((m+n).choose k : ℝ) := by + calc + _ = ∑ ij ∈ antidiagonal (k+2), (ij.1 : ℝ) * ((m+2).choose ij.1 : ℝ) * + (((ij.1 : ℝ)-1) * (n.choose ij.2 : ℝ)) := by + apply Finset.sum_congr rfl + intro ij hij + ring + _ = ((m+2 : ℕ) : ℝ) * ∑ ij ∈ antidiagonal (k+1), + ((m+1).choose ij.1 : ℝ) * + (((ij.1+1 : ℕ) : ℝ)-1) * (n.choose ij.2 : ℝ) := by + simpa only [mul_assoc] using weighted_shift (m+1) (k+1) + (fun i j => ((i : ℝ)-1) * (n.choose j : ℝ)) + _ = ((m+2 : ℕ) : ℝ) * ∑ ij ∈ antidiagonal (k+1), + (ij.1 : ℝ) * ((m+1).choose ij.1 : ℝ) * (n.choose ij.2 : ℝ) := by + congr 1 + apply Finset.sum_congr rfl + intro ij hij + push_cast + ring + _ = _ := by rw [binomial_first_moment]; ring + +theorem binomial_cross_moment (m n k : ℕ) : + (∑ ij ∈ antidiagonal (k+2), (ij.1 : ℝ) * (ij.2 : ℝ) * + ((m+1).choose ij.1 : ℝ) * ((n+1).choose ij.2 : ℝ)) = + ((m+1 : ℕ) : ℝ) * ((n+1 : ℕ) : ℝ) * ((m+n).choose k : ℝ) := by + calc + _ = ∑ ij ∈ antidiagonal (k+2), (ij.1 : ℝ) * ((m+1).choose ij.1 : ℝ) * + ((ij.2 : ℝ) * ((n+1).choose ij.2 : ℝ)) := by + apply Finset.sum_congr rfl + intro ij hij + ring + _ = ((m+1 : ℕ) : ℝ) * ∑ ij ∈ antidiagonal (k+1), (m.choose ij.1 : ℝ) * + ((ij.2 : ℝ) * ((n+1).choose ij.2 : ℝ)) := + weighted_shift m (k+1) (fun _ j => (j : ℝ) * ((n+1).choose j : ℝ)) + _ = ((m+1 : ℕ) : ℝ) * ∑ ij ∈ antidiagonal (k+1), (ij.2 : ℝ) * + ((n+1).choose ij.2 : ℝ) * (m.choose ij.1 : ℝ) := by + congr 1 + apply Finset.sum_congr rfl + intro ij hij + ring + _ = ((m+1 : ℕ) : ℝ) * (((n+1 : ℕ) : ℝ) * + ∑ ij ∈ antidiagonal k, (n.choose ij.2 : ℝ) * (m.choose ij.1 : ℝ)) := by + rw [weighted_shift_right n k (fun i _ => (m.choose i : ℝ))] + _ = ((m+1 : ℕ) : ℝ) * (((n+1 : ℕ) : ℝ) * + ∑ ij ∈ antidiagonal k, (m.choose ij.1 : ℝ) * (n.choose ij.2 : ℝ)) := by + congr 2 + apply Finset.sum_congr rfl + intro ij hij + ring + _ = _ := by rw [binomial_convolution]; ring + +theorem difference_decomposition (Q n : ℕ) : + (∑ ij ∈ antidiagonal n, ((ij.1 : ℝ)-(ij.2 : ℝ))^2 * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) = + 2 * (∑ ij ∈ antidiagonal n, (ij.1 : ℝ) * ((ij.1 : ℝ)-1) * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) + + 2 * (∑ ij ∈ antidiagonal n, (ij.1 : ℝ) * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) - + 2 * (∑ ij ∈ antidiagonal n, (ij.1 : ℝ) * (ij.2 : ℝ) * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) := by + have hfirst : (∑ ij ∈ antidiagonal n, (ij.2 : ℝ) * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) = + ∑ ij ∈ antidiagonal n, (ij.1 : ℝ) * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ) := by + calc + _ = ∑ ij ∈ antidiagonal n, (ij.2 : ℝ) * + (Q.choose ij.2 : ℝ) * (Q.choose ij.1 : ℝ) := by + apply Finset.sum_congr rfl + intro ij hij + ring + _ = _ := sum_antidiagonal_swap (n := n) + (f := fun ij => (ij.1 : ℝ) * (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) + have hfall : (∑ ij ∈ antidiagonal n, (ij.2 : ℝ) * ((ij.2 : ℝ)-1) * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) = + ∑ ij ∈ antidiagonal n, (ij.1 : ℝ) * ((ij.1 : ℝ)-1) * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ) := by + calc + _ = ∑ ij ∈ antidiagonal n, (ij.2 : ℝ) * ((ij.2 : ℝ)-1) * + (Q.choose ij.2 : ℝ) * (Q.choose ij.1 : ℝ) := by + apply Finset.sum_congr rfl + intro ij hij + ring + _ = _ := sum_antidiagonal_swap (n := n) + (f := fun ij => (ij.1 : ℝ) * ((ij.1 : ℝ)-1) * (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) + have hpoint : (∑ ij ∈ antidiagonal n, ((ij.1 : ℝ)-(ij.2 : ℝ))^2 * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) = + (∑ ij ∈ antidiagonal n, (ij.1 : ℝ) * ((ij.1 : ℝ)-1) * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) + + (∑ ij ∈ antidiagonal n, (ij.1 : ℝ) * (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) + + (∑ ij ∈ antidiagonal n, (ij.2 : ℝ) * ((ij.2 : ℝ)-1) * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) + + (∑ ij ∈ antidiagonal n, (ij.2 : ℝ) * (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) - + 2 * (∑ ij ∈ antidiagonal n, (ij.1 : ℝ) * (ij.2 : ℝ) * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) := by + rw [Finset.mul_sum, ← Finset.sum_add_distrib, ← Finset.sum_add_distrib, + ← Finset.sum_add_distrib, ← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro ij hij + ring + rw [hpoint, hfirst, hfall] + ring + +theorem pair_binomial_moment (m p : ℕ) : + (∑ ij ∈ antidiagonal (p+1), ((ij.1 : ℝ)-(ij.2 : ℝ))^2 * + ((m+2).choose ij.1 : ℝ) * ((m+2).choose ij.2 : ℝ)) = + 2 * ((m+2 : ℕ) : ℝ) * ((2*m+2).choose p : ℝ) := by + cases p with + | zero => + rw [sum_antidiagonal_succ] + simp [Nat.choose_one_right] + ring + | succ k => + rw [difference_decomposition, binomial_second_falling m (m+2) k, + binomial_first_moment (m+1) (m+2) (k+1), binomial_cross_moment (m+1) (m+1) k] + have hA : m+(m+2) = 2*m+2 := by omega + have hB : m+1+(m+2) = (2*m+2)+1 := by omega + have hC : m+1+(m+1) = 2*m+2 := by omega + rw [hA, hB, hC] + have hp : (((2*m+2)+1).choose (k+1) : ℝ) = + ((2*m+2).choose k : ℝ) + ((2*m+2).choose (k+1) : ℝ) := by + exact_mod_cast Nat.choose_succ_succ (2*m+2) k + rw [hp] + push_cast + ring + +end Laughlin.PairNormalization + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/CoefficientSquare.lean b/lean/OAI/Analysis/Laughlin/Pair/CoefficientSquare.lean new file mode 100644 index 0000000000000000000000000000000000000000..a41cd264bcd4fa146d2fc2012e630afa442607c1 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/CoefficientSquare.lean @@ -0,0 +1,32 @@ +import Mathlib.Tactic.FieldSimp +import Mathlib.Tactic.NormNum +import Mathlib.Tactic.Ring +import OAI.Analysis.Laughlin.EnergyNonnegative + +namespace OAI + +namespace Laughlin + +theorem pairCoefficient_sq_choose (Q p : ℕ) (hQ : 1 ≤ Q) (hp : p ≤ 2*Q-2) + (x y : Fin (Q+1)) : + (pairCoefficient Q p x y)^2 = + if x.val+y.val = p+1 then + (((x.val : ℝ)-(y.val : ℝ))^2 * (Q.choose x.val : ℝ) * (Q.choose y.val : ℝ)) / + (2*(Q : ℝ)*((2*Q-2).choose p : ℝ)) + else 0 := by + have hx : (x.val.factorial : ℝ) ≠ 0 := by positivity + have hy : (y.val.factorial : ℝ) ≠ 0 := by positivity + have hpf : (p.factorial : ℝ) ≠ 0 := by positivity + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + have hc : ((2*Q-2).choose p : ℝ) ≠ 0 := by + exact_mod_cast (Nat.ne_of_gt (Nat.choose_pos hp)) + unfold pairCoefficient + split_ifs with h + · rw [div_pow, mul_pow, Real.sq_sqrt (by positivity), Real.sq_sqrt (by norm_num)] + simp only [Nat.descFactorial_eq_factorial_mul_choose, Nat.cast_mul] + field_simp + · simp + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/Conjugation.lean b/lean/OAI/Analysis/Laughlin/Pair/Conjugation.lean new file mode 100644 index 0000000000000000000000000000000000000000..8eb0600ddcf456d4cbd93d50500cc94c7aed00bd --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/Conjugation.lean @@ -0,0 +1,59 @@ +import Mathlib.Tactic.FieldSimp +import Mathlib.Tactic.NormNum +import Mathlib.Tactic.Ring +import OAI.Analysis.Laughlin.EnergyNonnegative + +namespace OAI + +namespace Laughlin + +noncomputable def modeFactor (Q x : ℕ) : ℝ := + Real.sqrt ((Q.descFactorial x : ℝ) / (Q : ℝ)^x) + +noncomputable def pairFactor (Q p : ℕ) : ℝ := + Real.sqrt (((2 : ℝ)*Q)^p / ((2*Q-2).descFactorial p : ℝ)) + +noncomputable def pairLimitCoefficient (p x y : ℕ) : ℝ := + if x+y = p+1 then + ((x : ℝ)-(y : ℝ)) * Real.sqrt ((p.factorial : ℝ) / + (((2 : ℕ) : ℝ)^p * (x.factorial : ℝ) * (y.factorial : ℝ))) / Real.sqrt (2 : ℕ) + else 0 + +theorem pair_radicand_factorization (Q p x y : ℕ) (hQ : 0 < Q) + (hp : p ≤ 2*Q-2) (hxy : x+y = p+1) : + ((Q.descFactorial x : ℝ) / (Q : ℝ)^x) * + ((Q.descFactorial y : ℝ) / (Q : ℝ)^y) * + (((2 : ℝ)*Q)^p / ((2*Q-2).descFactorial p : ℝ)) * + ((p.factorial : ℝ) / ((2 : ℝ)^p * (x.factorial : ℝ) * (y.factorial : ℝ))) = + ((Q.descFactorial x : ℝ)*(Q.descFactorial y : ℝ)*(p.factorial : ℝ)) / + ((Q : ℝ)*((2*Q-2).descFactorial p : ℝ)*(x.factorial : ℝ)*(y.factorial : ℝ)) := by + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (Nat.ne_of_gt hQ) + have hd : ((2*Q-2).descFactorial p : ℝ) ≠ 0 := by + exact_mod_cast (Nat.ne_of_gt (Nat.descFactorial_pos.mpr hp)) + have hx : (x.factorial : ℝ) ≠ 0 := by positivity + have hy : (y.factorial : ℝ) ≠ 0 := by positivity + have hh : (Q : ℝ)^x * (Q : ℝ)^y = (Q : ℝ)^p * Q := by + rw [← pow_add, hxy, pow_succ] + rw [mul_pow] + field_simp + have he := congrArg (fun t : ℝ => (Q.descFactorial x : ℝ) * (Q.descFactorial y : ℝ) * t) hh + nlinarith only [he] + +theorem pairCoefficient_conjugation (Q p : ℕ) (hQ : 0 < Q) + (hp : p ≤ 2*Q-2) (x y : Fin (Q+1)) : + pairCoefficient Q p x y = + modeFactor Q x.val * modeFactor Q y.val * pairFactor Q p * + pairLimitCoefficient p x.val y.val := by + unfold pairCoefficient pairLimitCoefficient modeFactor pairFactor + split_ifs with h + · have hr := pair_radicand_factorization Q p x.val y.val hQ hp h + have hs := congrArg Real.sqrt hr + rw [Real.sqrt_mul (by positivity), Real.sqrt_mul (by positivity), + Real.sqrt_mul (by positivity)] at hs + rw [← hs] + ring_nf + · simp + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/CoupledBasis.lean b/lean/OAI/Analysis/Laughlin/Pair/CoupledBasis.lean new file mode 100644 index 0000000000000000000000000000000000000000..3c9a7c2243a8d83a36da782f9386c2e926e9ed88 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/CoupledBasis.lean @@ -0,0 +1,97 @@ +import OAI.Analysis.Laughlin.Pair.CoupledIsometry +import OAI.Analysis.Laughlin.Spin.Basis + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +abbrev OddPairLabel (Q : ℕ) := Fin ((Q+1)/2) +def oddPairDeficit {Q : ℕ} (r : OddPairLabel Q) : ℕ := 2*r.val+1 + +theorem oddPairDeficit_le {Q : ℕ} (r : OddPairLabel Q) : oddPairDeficit r ≤ Q := by + have := r.isLt + dsimp [oddPairDeficit] + omega + +theorem oddPairDeficit_odd {Q : ℕ} (r : OddPairLabel Q) : Odd (oddPairDeficit r) := + ⟨r.val,rfl⟩ + +abbrev PairCoupledIndex (Q : ℕ) := + Σ r : OddPairLabel Q, Fin (genericCoupledWeight Q Q (oddPairDeficit r)+1) + +noncomputable def pairCoupledBasis (Q : ℕ) : Matrix (WedgePairIndex Q) (PairCoupledIndex Q) ℝ := + fun i s => pairCoupledWedge Q (oddPairDeficit s.1) (oddPairDeficit_le s.1) s.2.val i + +def wedgePairEquiv (Q : ℕ) : WedgePairIndex Q ≃ Σ j : Fin (Q+1), Fin j.val where + toFun i := ⟨i.val.2,⟨i.val.1.val,i.property⟩⟩ + invFun s := ⟨(⟨s.2.val,by have := s.1.isLt; have := s.2.isLt; omega⟩,s.1),s.2.isLt⟩ + left_inv i := by apply Subtype.ext; rfl + right_inv s := by cases s; rfl + +theorem wedgePairIndex_card_real (Q : ℕ) : + (Fintype.card (WedgePairIndex Q) : ℝ) = (Q : ℝ)*(Q+1)/2 := by + rw [Fintype.card_congr (wedgePairEquiv Q)] + simp only [Fintype.card_sigma,Fintype.card_fin,Nat.cast_sum] + rw [fin_sum_values] + push_cast + ring + +theorem pairCoupledIndex_card (Q : ℕ) : + Fintype.card (PairCoupledIndex Q) = Fintype.card (WedgePairIndex Q) := by + have h : (Fintype.card (PairCoupledIndex Q) : ℝ) = (Fintype.card (WedgePairIndex Q) : ℝ) := by + rw [wedgePairIndex_card_real] + simp only [Fintype.card_sigma,Fintype.card_fin,Nat.cast_sum] + have hc (r : OddPairLabel Q) : + ((genericCoupledWeight Q Q (oddPairDeficit r)+1 : ℕ) : ℝ) = + 2*(Q : ℝ)-1-4*(r.val : ℝ) := by + have hr := oddPairDeficit_le r + unfold genericCoupledWeight + rw [Nat.cast_add,Nat.cast_sub (by omega : 2*oddPairDeficit r ≤ Q+Q)] + simp only [oddPairDeficit,Nat.cast_add,Nat.cast_mul,Nat.cast_ofNat] + ring + simp_rw [hc] + rw [Finset.sum_sub_distrib,Finset.sum_const,← Finset.mul_sum,fin_sum_values] + simp only [Finset.card_univ,Fintype.card_fin,nsmul_eq_mul] + have hp : Q+1=2*((Q+1)/2) ∨ Q=2*((Q+1)/2) := by omega + rcases hp with hp | hp + · have he : (Q : ℝ)+1=2*(((Q+1)/2 : ℕ) : ℝ) := by exact_mod_cast hp + nlinarith + · have he : (Q : ℝ)=2*(((Q+1)/2 : ℕ) : ℝ) := by exact_mod_cast hp + nlinarith + exact_mod_cast h + +theorem pairCoupledBasis_isometry (Q : ℕ) : + (pairCoupledBasis Q)ᵀ * pairCoupledBasis Q = 1 := by + ext s t + simp only [Matrix.mul_apply,Matrix.transpose_apply,pairCoupledBasis,Matrix.one_apply] + by_cases h : s=t + · subst t + rw [ite_eq_left rfl] + simpa only [vectorNormSq,pow_two] using + pairCoupledWedge_norm Q (oddPairDeficit s.1) s.2.val (oddPairDeficit_le s.1) + (oddPairDeficit_odd s.1) (by have := s.2.isLt; omega) + · rw [ite_eq_right h] + apply pairCoupledWedge_orthogonal _ _ _ _ _ _ _ (oddPairDeficit_odd s.1) (oddPairDeficit_odd t.1) + rcases s with ⟨r,n⟩ + rcases t with ⟨s,m⟩ + by_cases hrs : r=s + · subst s + right + intro he + exact h (by have hn : n=m := Fin.ext he; subst m; rfl) + · left + intro he + apply hrs + apply Fin.ext + dsimp [oddPairDeficit] at he + omega + +theorem pairCoupledBasis_complete (Q : ℕ) : + pairCoupledBasis Q * (pairCoupledBasis Q)ᵀ = 1 := + (Matrix.mul_eq_one_comm_of_card_eq (m := PairCoupledIndex Q) (n := WedgePairIndex Q) + (R := ℝ) (pairCoupledIndex_card Q)).mp (pairCoupledBasis_isometry Q) + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/CoupledIsometry.lean b/lean/OAI/Analysis/Laughlin/Pair/CoupledIsometry.lean new file mode 100644 index 0000000000000000000000000000000000000000..0fa4089d05e46b3ed5343c2947b4c0ffe41b0996 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/CoupledIsometry.lean @@ -0,0 +1,45 @@ +import OAI.Analysis.Laughlin.Polynomial.AntisymmetricCoordinates +import OAI.Analysis.Laughlin.Spin.GenericOrthogonality + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +theorem pairCoupledTensor_orthogonal (Q r s n m : ℕ) (hr : r ≤ Q) (hs : s ≤ Q) + (hne : r ≠ s ∨ n ≠ m) : + (∑ i, pairCoupledTensor Q r hr n i * pairCoupledTensor Q s hs m i) = 0 := by + unfold pairCoupledTensor + simp only [Pi.smul_apply,smul_eq_mul] + calc + _ = ((-1 : ℝ)^r * (-1 : ℝ)^s) * + (∑ i, genericUnitDescendant Q Q r hr hr n i * genericUnitDescendant Q Q s hs hs m i) := by + rw [Finset.mul_sum]; apply Finset.sum_congr rfl; intro i hi; ring + _ = 0 := by rw [genericUnitDescendant_orthogonal Q Q r s n m hr hr hs hs hne,mul_zero] + +theorem pairCoupledWedge_orthogonal (Q r s n m : ℕ) (hr : r ≤ Q) (hs : s ≤ Q) + (hor : Odd r) (hos : Odd s) (hne : r ≠ s ∨ n ≠ m) : + (∑ i, pairCoupledWedge Q r hr n i * pairCoupledWedge Q s hs m i) = 0 := by + rw [pairCoupledWedge,pairCoupledWedge,antisymmetric_pairing Q _ _ + (pairCoupledTensor_antisymmetric Q r n hr hor) (pairCoupledTensor_antisymmetric Q s m hs hos)] + exact pairCoupledTensor_orthogonal Q r s n m hr hs hne + +noncomputable def pairCoupledInclusion (Q r : ℕ) (hr : r ≤ Q) : + Matrix (WedgePairIndex Q) (Fin (genericCoupledWeight Q Q r+1)) ℝ := + fun i n => pairCoupledWedge Q r hr n.val i + +theorem pairCoupledInclusion_isometry (Q r : ℕ) (hr : r ≤ Q) (ho : Odd r) : + (pairCoupledInclusion Q r hr)ᵀ * pairCoupledInclusion Q r hr = 1 := by + ext n m + simp only [Matrix.mul_apply,Matrix.transpose_apply,pairCoupledInclusion,Matrix.one_apply] + by_cases h : n=m + · subst m + rw [ite_eq_left rfl] + simpa only [pow_two,vectorNormSq] using pairCoupledWedge_norm Q r n.val hr ho (by omega) + · rw [ite_eq_right h] + exact pairCoupledWedge_orthogonal Q r r n.val m.val hr hr ho ho + (Or.inr (fun he => h (Fin.ext he))) + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/CoupledOne.lean b/lean/OAI/Analysis/Laughlin/Pair/CoupledOne.lean new file mode 100644 index 0000000000000000000000000000000000000000..819000826b345a951b440b01a34acc7f63d3a518 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/CoupledOne.lean @@ -0,0 +1,97 @@ +import OAI.Analysis.Laughlin.Pair.CoupledParity +import OAI.Analysis.Laughlin.Pair.LadderIntertwining + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +theorem highestUnit_one_zero (Q : ℕ) (hQ : 1 ≤ Q) : + highestUnit Q Q 1 0 = 1 / Real.sqrt 2 := by + have hn := highestUnit_norm Q Q 1 hQ hQ + have hr := highestUnit_reverse Q 1 0 (by omega) + norm_num at hr + simp only [show 1+1=2 by omega,Finset.sum_range_succ,Finset.sum_range_zero,zero_add] at hn + rw [hr] at hn + have hp : 0 < highestUnit Q Q 1 0 := by + rw [highestUnit,highestRaw_zero] + have hqr : (0 : ℝ) < Q := by exact_mod_cast (by omega : 0 < Q) + simp only [Nat.choose_one_right] + exact div_pos (by positivity) (highestNorm_pos Q Q 1 hQ hQ) + have ht : 0 < (1 : ℝ)/Real.sqrt 2 := by positivity + have hs : ((1 : ℝ)/Real.sqrt 2)^2 = 1/2 := by + rw [div_pow,Real.sq_sqrt (by norm_num)]; norm_num + nlinarith only [hn,hp,ht,hs] + +theorem pairCoupledTensor_one_zero (Q : ℕ) (hQ : 1 ≤ Q) (i : SpinIndex Q Q) : + pairCoupledTensor Q 1 hQ 0 i = pairCoefficient Q 0 i.1 i.2 := by + rw [pairCoupledTensor,genericUnitDescendant_zero] + simp only [pow_one,Pi.smul_apply,smul_eq_mul,neg_one_mul] + by_cases hi : i.1.val+i.2.val=1 + · let p : Fin 2 := ⟨i.1.val,by omega⟩ + have he : i = weightSliceIndex Q Q 1 hQ hQ p := by + apply Prod.ext + · rfl + · apply Fin.ext; dsimp [weightSliceIndex,p]; omega + have hv : genericHighest Q Q 1 hQ hQ i = highestUnit Q Q 1 i.1.val := by + change extendWeightSlice Q Q 1 hQ hQ _ i = _ + rw [he,extendWeightSlice_at]; rfl + rw [hv] + have hqr : (Q : ℝ) ≠ 0 := by exact_mod_cast (by omega : Q ≠ 0) + rcases (show i.1.val=0 ∨ i.1.val=1 by omega) with h0 | h1 + · have hj : i.2.val=1 := by omega + simp [pairCoefficient,h0,hj,highestUnit_one_zero Q hQ,hqr,div_eq_mul_inv] + · have hj : i.2.val=0 := by omega + have hr := highestUnit_reverse Q 1 0 (by omega) + norm_num at hr + rw [h1,hr,highestUnit_one_zero Q hQ] + simp [pairCoefficient,h1,hj,hqr] + · have hv : genericHighest Q Q 1 hQ hQ i = 0 := + extendWeightSlice_off Q Q 1 hQ hQ _ i hi + simp [hv,pairCoefficient,hi] + +theorem pairCoupledTensor_lowering (Q r n : ℕ) (hr : r ≤ Q) + (hn : n < genericCoupledWeight Q Q r) : + (totalRaise Q Q)ᵀ *ᵥ pairCoupledTensor Q r hr n = + Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight Q Q r : ℝ)-n)) • + pairCoupledTensor Q r hr (n+1) := by + rw [pairCoupledTensor,Matrix.mulVec_smul,genericUnitDescendant_lowering Q Q r n hr hr hn] + exact smul_comm _ _ _ + +theorem pairCoupledTensor_one (Q n : ℕ) (hQ : 1 ≤ Q) (hn : n ≤ 2*Q-2) + (i : SpinIndex Q Q) : + pairCoupledTensor Q 1 hQ n i = pairCoefficient Q n i.1 i.2 := by + induction n generalizing i with + | zero => exact pairCoupledTensor_one_zero Q hQ i + | succ n ih => + have hcw : genericCoupledWeight Q Q 1 = 2*Q-2 := by unfold genericCoupledWeight; omega + have hlt : n < genericCoupledWeight Q Q 1 := by rw [hcw]; omega + have hreal : (n : ℝ) < genericCoupledWeight Q Q 1 := by exact_mod_cast hlt + have hd : Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight Q Q 1 : ℝ)-n)) ≠ 0 := by positivity + have he := congrFun (pairCoupledTensor_lowering Q 1 n hQ hlt) i + have hf : pairCoupledTensor Q 1 hQ n = fun j => pairCoefficient Q n j.1 j.2 := by + funext j; exact ih (by omega) j + rw [hf] at he + change (∑ j, totalRaise Q Q j i * pairCoefficient Q n j.1 j.2) = + Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight Q Q 1 : ℝ)-n))* + pairCoupledTensor Q 1 hQ (n+1) i at he + rw [totalRaise_transpose_apply,raiseMatrix_column,raiseMatrix_column] at he + have hc := pairCoefficient_tensor_lowering Q n (by omega) (by omega) i.1 i.2 + have hl : pairTensorLower Q n i.1 i.2 = + (∑ j, totalRaise Q Q j i * pairCoefficient Q n j.1 j.2) := by + rw [totalRaise_transpose_apply,raiseMatrix_column,raiseMatrix_column] + unfold pairTensorLower; split_ifs <;> ring + rw [hcw] at he hd + have hw : ladder (2*Q-2) n = Real.sqrt (((n : ℝ)+1)*(((2*Q-2 : ℕ) : ℝ)-n)) := by + unfold ladder + rw [Nat.cast_sub (by omega : n ≤ 2*Q-2)] + rw [hw] at hc + have he' : pairTensorLower Q n i.1 i.2 = + Real.sqrt (((n : ℝ)+1)*(((2*Q-2 : ℕ) : ℝ)-n))*pairCoupledTensor Q 1 hQ (n+1) i := by + rw [hl,totalRaise_transpose_apply,raiseMatrix_column,raiseMatrix_column] + exact he + exact (mul_left_cancel₀ hd) (he'.symm.trans hc) + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/CoupledParity.lean b/lean/OAI/Analysis/Laughlin/Pair/CoupledParity.lean new file mode 100644 index 0000000000000000000000000000000000000000..df5d4763f494fc0e919c4795d1232a31bdddd67c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/CoupledParity.lean @@ -0,0 +1,90 @@ +import OAI.Analysis.Laughlin.Spin.GenericNormalizedLadder + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +theorem sign_reverse (r p : ℕ) (hp : p ≤ r) : + (-1 : ℝ)^(r-p) = (-1 : ℝ)^r * (-1 : ℝ)^p := by + have h : (-1 : ℝ)^p * (-1 : ℝ)^p = 1 := by + rw [← mul_pow]; norm_num + calc + _ = (-1 : ℝ)^(r-p) * ((-1 : ℝ)^p * (-1 : ℝ)^p) := by rw [h,mul_one] + _ = _ := by rw [← mul_assoc,← pow_add,Nat.sub_add_cancel hp] + +theorem highestUnit_reverse (Q r p : ℕ) (hp : p ≤ r) : + highestUnit Q Q r (r-p) = (-1 : ℝ)^r * highestUnit Q Q r p := by + unfold highestUnit highestRaw + rw [ite_eq_left (by omega : r-p ≤ r),ite_eq_left hp,Nat.sub_sub_self hp, + Nat.choose_symm hp,sign_reverse r p hp] + rw [mul_comm (Q.choose (r-p) : ℝ) (Q.choose p : ℝ)] + ring + +theorem genericHighest_swap (Q r : ℕ) (hr : r ≤ Q) (i : SpinIndex Q Q) : + genericHighest Q Q r hr hr i.swap = (-1 : ℝ)^r * genericHighest Q Q r hr hr i := by + by_cases hi : i.1.val+i.2.val=r + · let p : Fin (r+1) := ⟨i.1.val,by omega⟩ + let q : Fin (r+1) := ⟨r-i.1.val,by omega⟩ + have h1 : i = weightSliceIndex Q Q r hr hr p := by + apply Prod.ext + · rfl + · apply Fin.ext; dsimp [weightSliceIndex,p]; omega + have h2 : i.swap = weightSliceIndex Q Q r hr hr q := by + apply Prod.ext <;> apply Fin.ext <;> dsimp [weightSliceIndex,q] <;> omega + change extendWeightSlice Q Q r hr hr _ i.swap = _ * extendWeightSlice Q Q r hr hr _ i + rw [h2,h1,extendWeightSlice_at,extendWeightSlice_at] + exact highestUnit_reverse Q r i.1.val (by omega) + · change extendWeightSlice Q Q r hr hr _ i.swap = _ * extendWeightSlice Q Q r hr hr _ i + rw [extendWeightSlice_off _ _ _ _ _ _ i hi, + extendWeightSlice_off _ _ _ _ _ _ i.swap (by simpa [Nat.add_comm] using hi),mul_zero] + +theorem totalLower_swap (Q : ℕ) (f : SpinIndex Q Q → ℝ) (i : SpinIndex Q Q) : + ((totalRaise Q Q)ᵀ *ᵥ (fun j => f j.swap)) i = + ((totalRaise Q Q)ᵀ *ᵥ f) i.swap := by + change (∑ j, totalRaise Q Q j i * f j.swap) = + ∑ j, totalRaise Q Q j i.swap * f j + rw [totalRaise_transpose_apply,totalRaise_transpose_apply] + exact add_comm _ _ + +theorem genericDescendant_swap (Q r n : ℕ) (hr : r ≤ Q) (i : SpinIndex Q Q) : + genericDescendant Q Q r hr hr n i.swap = + (-1 : ℝ)^r * genericDescendant Q Q r hr hr n i := by + induction n generalizing i with + | zero => simpa [genericDescendant] using genericHighest_swap Q r hr i + | succ n ih => + rw [genericDescendant_succ] + rw [← totalLower_swap] + have he : (fun j => genericDescendant Q Q r hr hr n j.swap) = + (-1 : ℝ)^r • genericDescendant Q Q r hr hr n := by funext j; exact ih j + rw [he,Matrix.mulVec_smul] + rfl + +theorem genericUnitDescendant_swap (Q r n : ℕ) (hr : r ≤ Q) (i : SpinIndex Q Q) : + genericUnitDescendant Q Q r hr hr n i.swap = + (-1 : ℝ)^r * genericUnitDescendant Q Q r hr hr n i := by + simp only [genericUnitDescendant,Pi.smul_apply,smul_eq_mul,genericDescendant_swap] + ring + +noncomputable def pairCoupledTensor (Q r : ℕ) (hr : r ≤ Q) (n : ℕ) : SpinIndex Q Q → ℝ := + (-1 : ℝ)^r • genericUnitDescendant Q Q r hr hr n + +theorem pairCoupledTensor_norm (Q r n : ℕ) (hr : r ≤ Q) + (hn : n ≤ genericCoupledWeight Q Q r) : + vectorNormSq (pairCoupledTensor Q r hr n) = 1 := by + unfold pairCoupledTensor vectorNormSq + simp only [Pi.smul_apply,smul_eq_mul,mul_pow,← Finset.mul_sum] + have h : ((-1 : ℝ)^r)^2 = 1 := by rw [← pow_mul,mul_comm r 2,pow_mul]; norm_num + rw [h,one_mul] + exact genericUnitDescendant_norm Q Q r n hr hr hn + +theorem pairCoupledTensor_antisymmetric (Q r n : ℕ) (hr : r ≤ Q) (ho : Odd r) + (i j : Fin (Q+1)) : + pairCoupledTensor Q r hr n (j,i) = -pairCoupledTensor Q r hr n (i,j) := by + have h := genericUnitDescendant_swap Q r n hr (i,j) + have hs : (-1 : ℝ)^r = -1 := ho.neg_one_pow + simpa [pairCoupledTensor,hs] using congrArg (fun x : ℝ => -x) h + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/DiagonalCube.lean b/lean/OAI/Analysis/Laughlin/Pair/DiagonalCube.lean new file mode 100644 index 0000000000000000000000000000000000000000..ccd7e4d825c284296cd4b7641db22d6727ff0a53 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/DiagonalCube.lean @@ -0,0 +1,73 @@ +import Mathlib.Algebra.Polynomial.Bivariate +import Mathlib.Algebra.Polynomial.Derivative +import Mathlib.Analysis.Complex.Basic +import Mathlib.Tactic.Ring + +namespace OAI + +namespace Laughlin.PairDiagonal +open Polynomial +open scoped Polynomial.Bivariate + +abbrev Poly := Polynomial (Polynomial ℂ) +noncomputable def diagonal : Poly := X - C (X : Polynomial ℂ) + +theorem eval_swap_diagonal (p : Poly) : + (Bivariate.swap p).eval (X : Polynomial ℂ) = p.eval X := by + have he : (evalRingHom (X : Polynomial ℂ)).comp Bivariate.swap.toRingHom = + evalRingHom (X : Polynomial ℂ) := by + ext <;> simp [Bivariate.swap_X, Bivariate.swap_Y, Bivariate.swap_C_C] + exact congrArg (fun f : Poly →+* Polynomial ℂ => f p) he + +theorem antisymmetric_eval_zero (p : Poly) (ha : Bivariate.swap p = -p) : + p.eval (X : Polynomial ℂ) = 0 := by + have he := eval_swap_diagonal p + rw [ha, eval_neg] at he + have hz : (2 : ℂ) • p.eval (X : Polynomial ℂ) = 0 := by + simp only [two_smul] + calc + _ = -p.eval (X : Polynomial ℂ) + p.eval X := + congrArg (fun z : Polynomial ℂ => z+p.eval X) he.symm + _ = 0 := neg_add_cancel _ + exact (smul_eq_zero.mp hz).resolve_left two_ne_zero + +theorem swap_diagonal : Bivariate.swap diagonal = -diagonal := by + simp only [diagonal, map_sub, Bivariate.swap_X, Bivariate.swap_Y] + ring + +theorem cube_dvd_of_antisymmetric_first_jet (p : Poly) + (ha : Bivariate.swap p = -p) (hj : p.derivative.eval (X : Polynomial ℂ) = 0) : + diagonal^3 ∣ p := by + have hd : diagonal ∣ p := by + apply dvd_iff_isRoot.mpr + exact antisymmetric_eval_zero p ha + obtain ⟨g,hg⟩ := hd + have hg0 : g.eval (X : Polynomial ℂ) = 0 := by + rw [hg, derivative_mul] at hj + simpa [diagonal] using hj + have hdg : diagonal ∣ g := by + apply dvd_iff_isRoot.mpr + exact hg0 + obtain ⟨h,hh⟩ := hdg + have hp : p = diagonal^2*h := by rw [hg,hh]; ring + have hb : diagonal ≠ 0 := by + exact X_sub_C_ne_zero (X : Polynomial ℂ) + have hanti : Bivariate.swap h = -h := by + rw [hp, map_mul, map_pow, swap_diagonal] at ha + have hsq : (-diagonal)^2 = diagonal^2 := by ring + rw [hsq] at ha + apply mul_left_cancel₀ (pow_ne_zero 2 hb) + calc + _ = -(diagonal^2*h) := ha + _ = _ := by ring + have hdh : diagonal ∣ h := by + apply dvd_iff_isRoot.mpr + exact antisymmetric_eval_zero h hanti + obtain ⟨k,hk⟩ := hdh + refine ⟨k, ?_⟩ + rw [hp,hk] + ring + +end Laughlin.PairDiagonal + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/EnergyReturn.lean b/lean/OAI/Analysis/Laughlin/Pair/EnergyReturn.lean new file mode 100644 index 0000000000000000000000000000000000000000..2de8955b444282fd099333ad49f6102951e43653 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/EnergyReturn.lean @@ -0,0 +1,55 @@ +import OAI.Analysis.Laughlin.Operators.CollectionAnnihilatorBound +import OAI.Analysis.Laughlin.Pair.FactorBounds + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem occupationNormSq_smul (Q : ℕ) (c : ℂ) (x : Space Q) : + occupationNormSq Q (c • x) = ‖c‖^2 * occupationNormSq Q x := by + simp [occupationNormSq,mul_pow,Finset.mul_sum] + +theorem physicalScaling_normSq_le (Q : ℕ) (hQ : 0 < Q) (x : Space Q) : + occupationNormSq Q (physicalScaling Q x) ≤ occupationNormSq Q x := by + unfold occupationNormSq physicalScaling + apply Finset.sum_le_sum + intro A hA + rw [exteriorScaling_coordinate,norm_mul,mul_pow] + have hb : ‖∏ i ∈ A, (modeFactor Q i.val : ℂ)‖ ≤ 1 := by + rw [norm_prod] + apply Finset.prod_le_one₀ + · intro i hi + exact norm_nonneg _ + · intro i hi + simpa only [Complex.norm_real,Real.norm_eq_abs,abs_of_nonneg (modeFactor_nonneg Q i.val)] using + modeFactor_le_one Q i.val hQ + have hsq : ‖∏ i ∈ A, (modeFactor Q i.val : ℂ)‖^2 ≤ 1 := by + simpa using pow_le_pow_left₀ (norm_nonneg _) hb 2 + exact (mul_le_mul_of_nonneg_right hsq (sq_nonneg _)).trans_eq (one_mul _) + +theorem pair_energy_return (Q p : ℕ) (hQ : 0 < Q) (hp : p ≤ 2*Q-2) (x : Space Q) : + occupationNormSq Q (limitPairEnd Q p (physicalScaling Q x)) ≤ + occupationNormSq Q (sourcePairEnd Q p x) := by + have he := congrArg (occupationNormSq Q) (sourcePair_intertwining Q p hQ hp x) + rw [occupationNormSq_smul,Complex.norm_real,Real.norm_eq_abs, + abs_of_nonneg (show 0 ≤ pairFactor Q p from Real.sqrt_nonneg _)] at he + have hr := pairFactor_one_le Q p hp + have hsq : 1 ≤ (pairFactor Q p)^2 := by nlinarith + calc + _ ≤ (pairFactor Q p)^2 * occupationNormSq Q (limitPairEnd Q p (physicalScaling Q x)) := by + simpa using mul_le_mul_of_nonneg_right hsq (occupationNormSq_nonneg Q _) + _ = occupationNormSq Q (physicalScaling Q (sourcePairEnd Q p x)) := he.symm + _ ≤ _ := physicalScaling_normSq_le Q hQ _ + +theorem pair_window_return (Q : ℕ) (hQ : 24 ≤ Q) (x : Space Q) : + limitPairWindow Q (physicalScaling Q x) ≤ sourcePairWindow Q x := by + unfold limitPairWindow sourcePairWindow + apply Finset.sum_le_sum + intro p hp + exact pair_energy_return Q p (by omega) + (by have h := Finset.mem_range.mp hp; omega) x + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/ExteriorRotation.lean b/lean/OAI/Analysis/Laughlin/Pair/ExteriorRotation.lean new file mode 100644 index 0000000000000000000000000000000000000000..1e9ac8c6c5095a0ef40ea7ae9f799b3d9a547228 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/ExteriorRotation.lean @@ -0,0 +1,70 @@ +import OAI.Analysis.Laughlin.Exterior.SpinUnitary +import OAI.Analysis.Laughlin.Fock.PairNormalization +import OAI.Analysis.Laughlin.Operators.PhysicalPairRotation + +namespace OAI + +namespace Laughlin.Fock +open Rotation +open scoped BigOperators Matrix Kronecker + +noncomputable def pairExterior (Q : ℕ) (v : Spin.SpinIndex Q Q → ℂ) : Space Q := + ∑ i, v i • create i.1 (create i.2 (1 : Space Q)) + +theorem exteriorRotation_pair_basis (Q : ℕ) (g : SourceSU2) (i j : Fin (Q+1)) : + exteriorRotation Q g (create i (create j (1 : Space Q))) = + ∑ k : Spin.SpinIndex Q Q, (sourceSpinRepresentation Q g k.1 i * sourceSpinRepresentation Q g k.2 j) • + create k.1 (create k.2 (1 : Space Q)) := by + rw [create_exteriorRotation,create_exteriorRotation] + simp only [map_one,map_sum,map_smul,Finset.smul_sum,smul_smul,Fintype.sum_prod_type] + +theorem pairExterior_rotation (Q : ℕ) (g : SourceSU2) (v : Spin.SpinIndex Q Q → ℂ) : + exteriorRotation Q g (pairExterior Q v) = + pairExterior Q ((sourceSpinRepresentation Q g ⊗ₖ sourceSpinRepresentation Q g) *ᵥ v) := by + simp only [pairExterior,map_sum,map_smul,exteriorRotation_pair_basis,Finset.smul_sum,smul_smul] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro k hk + rw [← Finset.sum_smul] + congr 1 + simp only [Matrix.mulVec,dotProduct,Matrix.kroneckerMap,Matrix.of_apply] + apply Finset.sum_congr rfl + intro i hi + ring + +theorem pairExterior_sum {I : Type*} [Fintype I] (Q : ℕ) (v : I → Spin.SpinIndex Q Q → ℂ) : + pairExterior Q (∑ a, v a) = ∑ a, pairExterior Q (v a) := by + simp only [pairExterior,Finset.sum_apply,Finset.sum_smul] + rw [Finset.sum_comm] + +theorem pairExterior_smul (Q : ℕ) (c : ℂ) (v : Spin.SpinIndex Q Q → ℂ) : + pairExterior Q (c • v) = c • pairExterior Q v := by + simp only [pairExterior,Pi.smul_apply,smul_eq_mul,Finset.smul_sum,smul_smul] + +theorem sourcePairVector_pairExterior (Q p : ℕ) : + sourcePairVector Q p = (Real.sqrt 2 : ℂ)⁻¹ • + pairExterior Q (fun i => (pairCoefficient Q p i.1 i.2 : ℂ)) := by + simp only [sourcePairVector,pairExterior,Fintype.sum_prod_type,Finset.smul_sum,smul_smul, + div_eq_mul_inv,Complex.ofReal_mul,Complex.ofReal_inv,mul_comm] + +theorem sourcePairVector_rotation (Q : ℕ) (hQ : 0 < Q) (g : SourceSU2) + (p : Fin (2*Q-2+1)) : + exteriorRotation Q g (sourcePairVector Q p.val) = + ∑ q : Fin (2*Q-2+1), sourceSpinRepresentation (2*Q-2) g q p • sourcePairVector Q q.val := by + have hc : ((sourceSpinRepresentation Q g ⊗ₖ sourceSpinRepresentation Q g) *ᵥ + (fun i => (pairCoefficient Q p.val i.1 i.2 : ℂ))) = + ∑ q : Fin (2*Q-2+1), sourceSpinRepresentation (2*Q-2) g q p • + (fun i : Spin.SpinIndex Q Q => (pairCoefficient Q q.val i.1 i.2 : ℂ)) := by + funext i + have h := congrFun (congrFun (physicalPairInclusion_SU2 Q hQ g) i) p + simpa only [physicalPairInclusion,Spin.pairInclusion,Matrix.map_apply,Matrix.mul_apply, + Matrix.mulVec,dotProduct,Finset.sum_apply,Pi.smul_apply,smul_eq_mul,mul_comm] using h + rw [sourcePairVector_pairExterior,map_smul,pairExterior_rotation,hc,pairExterior_sum] + simp only [pairExterior_smul,Finset.smul_sum,sourcePairVector_pairExterior] + apply Finset.sum_congr rfl + intro q hq + exact smul_comm _ _ _ + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/FactorBounds.lean b/lean/OAI/Analysis/Laughlin/Pair/FactorBounds.lean new file mode 100644 index 0000000000000000000000000000000000000000..c63111e7c975f53665cd0e9909db1f0fb477fc95 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/FactorBounds.lean @@ -0,0 +1,27 @@ +import OAI.Analysis.Laughlin.Pair.Conjugation + +namespace OAI + +namespace Laughlin + +theorem modeFactor_nonneg (Q x : ℕ) : 0 ≤ modeFactor Q x := Real.sqrt_nonneg _ + +theorem modeFactor_le_one (Q x : ℕ) (hQ : 0 < Q) : modeFactor Q x ≤ 1 := by + have hpow : (0 : ℝ) < (Q : ℝ)^x := pow_pos (by exact_mod_cast hQ) _ + have hd : (Q.descFactorial x : ℝ) ≤ (Q : ℝ)^x := by + exact_mod_cast Nat.descFactorial_le_pow Q x + have h := Real.sqrt_le_sqrt ((div_le_one hpow).mpr hd) + simpa [modeFactor] using h + +theorem pairFactor_one_le (Q p : ℕ) (hp : p ≤ 2*Q-2) : 1 ≤ pairFactor Q p := by + have hd : (0 : ℝ) < (2*Q-2).descFactorial p := by exact_mod_cast Nat.descFactorial_pos.mpr hp + have hn : (2*Q-2).descFactorial p ≤ (2*Q)^p := by + apply (Nat.descFactorial_le_pow (2*Q-2) p).trans + exact Nat.pow_le_pow_left (Nat.sub_le _ _) p + have hr : ((2*Q-2).descFactorial p : ℝ) ≤ ((2 : ℝ)*Q)^p := by exact_mod_cast hn + have h := Real.sqrt_le_sqrt ((one_le_div hd).mpr hr) + simpa [pairFactor] using h + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/FactorLimit.lean b/lean/OAI/Analysis/Laughlin/Pair/FactorLimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..d506a9ed95777547048d42df4bcc633c3d0a172a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/FactorLimit.lean @@ -0,0 +1,69 @@ +import Mathlib.Analysis.SpecificLimits.Normed +import Mathlib.Data.Nat.Factorial.BigOperators +import OAI.Analysis.Laughlin.Pair.Conjugation + +namespace OAI + +namespace Laughlin +open scoped BigOperators Topology +open Filter + +theorem modeFactor_sq_tendsto (x : ℕ) : + Tendsto (fun Q : ℕ => (Q.descFactorial x : ℝ)/(Q : ℝ)^x) + atTop (𝓝 1) := by + have hp : Tendsto (fun Q : ℕ => ∏ i ∈ Finset.range x, + ((-(i : ℝ)+1*(Q : ℝ))/(0+1*(Q : ℝ)))) atTop + (𝓝 (∏ _i ∈ Finset.range x, (1/1 : ℝ))) := by + apply tendsto_finsetProd + intro i hi + exact tendsto_add_mul_div_add_mul_atTop_nhds (-(i : ℝ)) 0 1 (by norm_num) + have he : (fun Q : ℕ => ∏ i ∈ Finset.range x, + ((-(i : ℝ)+1*(Q : ℝ))/(0+1*(Q : ℝ)))) =ᶠ[atTop] + (fun Q : ℕ => (Q.descFactorial x : ℝ)/(Q : ℝ)^x) := by + filter_upwards [eventually_ge_atTop x] with Q hQ + rw [Nat.descFactorial_eq_prod_range, Nat.cast_prod] + have hd : (Q : ℝ)^x = ∏ _i ∈ Finset.range x, (Q : ℝ) := by simp + rw [hd, ← Finset.prod_div_distrib] + · apply Finset.prod_congr rfl + intro i hi + have hi := Finset.mem_range.mp hi + rw [Nat.cast_sub (by omega : i ≤ Q)] + congr 1 <;> ring + simpa using hp.congr' he + +theorem pairFactor_inv_sq_tendsto (p : ℕ) : + Tendsto (fun Q : ℕ => ((2*Q-2).descFactorial p : ℝ)/((2 : ℝ)*Q)^p) + atTop (𝓝 1) := by + have hp : Tendsto (fun Q : ℕ => ∏ i ∈ Finset.range p, + ((-(2+(i : ℝ))+2*(Q : ℝ))/(0+2*(Q : ℝ)))) atTop + (𝓝 (∏ _i ∈ Finset.range p, (2/2 : ℝ))) := by + apply tendsto_finsetProd + intro i hi + exact tendsto_add_mul_div_add_mul_atTop_nhds (-(2+(i : ℝ))) 0 2 (by norm_num) + have he : (fun Q : ℕ => ∏ i ∈ Finset.range p, + ((-(2+(i : ℝ))+2*(Q : ℝ))/(0+2*(Q : ℝ)))) =ᶠ[atTop] + (fun Q : ℕ => ((2*Q-2).descFactorial p : ℝ)/((2 : ℝ)*Q)^p) := by + filter_upwards [eventually_ge_atTop (p+2)] with Q hQ + rw [Nat.descFactorial_eq_prod_range, Nat.cast_prod] + have hd : ((2 : ℝ)*Q)^p = ∏ _i ∈ Finset.range p, (2 : ℝ)*Q := by simp + rw [hd, ← Finset.prod_div_distrib] + · apply Finset.prod_congr rfl + intro i hi + have hi := Finset.mem_range.mp hi + rw [Nat.cast_sub (by omega : i ≤ 2*Q-2), Nat.cast_sub (by omega : 2 ≤ 2*Q)] + push_cast + congr 1 <;> ring + simpa using hp.congr' he + +theorem modeFactor_tendsto (x : ℕ) : + Tendsto (fun Q : ℕ => modeFactor Q x) atTop (𝓝 1) := by + simpa [modeFactor] using (modeFactor_sq_tendsto x).sqrt + +theorem pairFactor_tendsto (p : ℕ) : + Tendsto (fun Q : ℕ => pairFactor Q p) atTop (𝓝 1) := by + have h := ((pairFactor_inv_sq_tendsto p).inv₀ (by norm_num)).sqrt + simpa [pairFactor, inv_div] using h + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/FockCovariance.lean b/lean/OAI/Analysis/Laughlin/Pair/FockCovariance.lean new file mode 100644 index 0000000000000000000000000000000000000000..bcb7194c6791c2e06233417aad2bb759d9a24ad4 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/FockCovariance.lean @@ -0,0 +1,43 @@ +import OAI.Analysis.Laughlin.Exterior.FamilyCovariance +import OAI.Analysis.Laughlin.Pair.ExteriorRotation + +namespace OAI + +namespace Laughlin.Fock +open Rotation +open scoped BigOperators Matrix + +theorem sourcePairCreateEnd_mul (Q p : ℕ) (x : Space Q) : + sourcePairCreateEnd Q p x = sourcePairVector Q p*x := by + simp only [sourcePairCreateEnd,pairCreateEnd,sourcePairVector,LinearMap.sum_apply, + LinearMap.smul_apply,Module.End.mul_apply,Finset.sum_mul,smul_mul_assoc, + Complex.star_def,Complex.conj_ofReal] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + congr 1 + change ExteriorAlgebra.ι ℂ (mode i)*(ExteriorAlgebra.ι ℂ (mode j)*x) = + (ExteriorAlgebra.ι ℂ (mode i)*(ExteriorAlgebra.ι ℂ (mode j)*1))*x + simp only [mul_one,mul_assoc] + +theorem sourcePairVector_adjoint (Q p : ℕ) (x y : Space Q) : + occupationInner Q (sourcePairVector Q p*x) y = occupationInner Q x (sourcePairEnd Q p y) := by + rw [← sourcePairCreateEnd_mul] + exact pairCreate_pair_adjoint Q _ x y + +theorem sourcePairEnd_rotation (Q : ℕ) (hQ : 0 < Q) (g : SourceSU2) + (p : Fin (2*Q-2+1)) (x : Space Q) : + sourcePairEnd Q p.val (exteriorRotation Q g x) = + ∑ q : Fin (2*Q-2+1), sourceSpinRepresentation (2*Q-2) g p q • + exteriorRotation Q g (sourcePairEnd Q q.val x) := by + exact exteriorFamily_contraction_rotation Q (sourceSpinRepresentation (2*Q-2)) + (sourceSpinRepresentation_inv (2*Q-2)) + (fun p : Fin (2*Q-2+1) => sourcePairVector Q p.val) + (fun p => sourcePairEnd Q p.val) + (fun p => sourcePairVector_adjoint Q p.val) + (fun g p => sourcePairVector_rotation Q hQ g p) g p x + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/FockHaar.lean b/lean/OAI/Analysis/Laughlin/Pair/FockHaar.lean new file mode 100644 index 0000000000000000000000000000000000000000..fb724c105c0c6f76a10a0124f90237defe8a5611 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/FockHaar.lean @@ -0,0 +1,54 @@ +import OAI.Analysis.Laughlin.Fock.EnergyRotation +import OAI.Analysis.Laughlin.Fock.HaarQuadratic +import OAI.Analysis.Laughlin.Spin.Schur + +namespace OAI + +namespace Laughlin.Fock +open Rotation MeasureTheory +open scoped BigOperators Matrix + +theorem contractionForm_smul {I : Type*} [Fintype I] (Q : ℕ) + (minus : I → Module.End ℂ (Space Q)) (c : ℂ) (M : Matrix I I ℂ) (x : Space Q) : + contractionForm Q minus (c • M) x = c * contractionForm Q minus M x := by + simp only [contractionForm,Matrix.smul_apply,smul_eq_mul,Finset.mul_sum,mul_assoc] + +theorem contractionForm_sum {I J : Type*} [Fintype I] [Fintype J] (Q : ℕ) + (minus : I → Module.End ℂ (Space Q)) (M : J → Matrix I I ℂ) (x : Space Q) : + contractionForm Q minus (∑ j, M j) x = ∑ j, contractionForm Q minus (M j) x := by + simp only [contractionForm,Matrix.sum_apply,Finset.sum_mul] + conv_lhs => arg 2; ext i; rw [Finset.sum_comm] + rw [Finset.sum_comm] + +theorem pair_contractionForm_one (Q : ℕ) (hQ : 0 < Q) (x : Space Q) : + contractionForm Q (fun p : Fin (2*Q-2+1) => sourcePairEnd Q p.val) 1 x = + (sourceFockEnergy Q x : ℂ) := by + rw [sourceFockEnergy_eq_fin Q hQ] + simp [contractionForm,Matrix.one_apply,occupationInner_self,Complex.ofReal_sum] + +theorem physical_pairFock_haar (Q : ℕ) (hQ : 0 < Q) + (M : Matrix (Fin (2*Q-2+1)) (Fin (2*Q-2+1)) ℂ) (x : Space Q) : + (∫ g, contractionForm Q (fun p : Fin (2*Q-2+1) => sourcePairEnd Q p.val) M + (exteriorRotation Q g⁻¹ x) ∂sourceHaar) = + (Matrix.trace M/(2*Q-2+1 : ℕ)) * (sourceFockEnergy Q x : ℂ) := by + rw [contractionForm_haar Q (sourceSpinRepresentation (2*Q-2)) + (sourceSpinRepresentation_inv (2*Q-2)) (sourceSpinRepresentation_continuous (2*Q-2)) + _ (sourcePairEnd_rotation Q hQ),source_spin_haar_schur,contractionForm_smul, + pair_contractionForm_one Q hQ] + +theorem physical_pair_norm_haar (Q : ℕ) (hQ : 0 < Q) (p : Fin (2*Q-2+1)) (x : Space Q) : + (∫ g, (occupationNormSq Q (sourcePairEnd Q p.val (exteriorRotation Q g⁻¹ x)) : ℂ) + ∂sourceHaar) = (sourceFockEnergy Q x : ℂ)/(2*Q-2+1 : ℕ) := by + let M : Matrix (Fin (2*Q-2+1)) (Fin (2*Q-2+1)) ℂ := + fun i j => if i=p ∧ j=p then 1 else 0 + have hm (y : Space Q) : contractionForm Q + (fun p : Fin (2*Q-2+1) => sourcePairEnd Q p.val) M y = + (occupationNormSq Q (sourcePairEnd Q p.val y) : ℂ) := by + simp [contractionForm,M,occupationInner_self,ite_and] + have ht : Matrix.trace M=1 := by simp [Matrix.trace,Matrix.diag,M] + have h := physical_pairFock_haar Q hQ M x + simpa only [hm,ht,one_div,mul_comm,div_eq_mul_inv,one_mul] using h + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/HomogeneousCube.lean b/lean/OAI/Analysis/Laughlin/Pair/HomogeneousCube.lean new file mode 100644 index 0000000000000000000000000000000000000000..c0778f0f9ba0415c037064ce541949a38b31bed3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/HomogeneousCube.lean @@ -0,0 +1,90 @@ +import OAI.Analysis.Laughlin.Pair.Homogenize + +namespace OAI + +namespace Laughlin +open Polynomial +open scoped BigOperators + +theorem homogeneousEval_cube {R S : Type*} [CommRing R] [CommRing S] + (f : R →+* S) (u v : S) (p : Polynomial R) (hp : p.natDegree ≤ 1) : + homogeneousEval f u v 3 (p^3) = (homogeneousEval f u v 1 p)^3 := by + have h := homogenize_finsetProd (s := Finset.range 3) (p := fun _ => p) + (n := fun _ => 1) (fun _ _ => hp) + have he : (p^3).homogenize 3 = (p.homogenize 1)^3 := by simpa using h + simp [homogeneousEval, he] + +theorem homogeneousEval_linear {R S : Type*} [CommRing R] [CommRing S] + (f : R →+* S) (u v : S) (a b : R) : + homogeneousEval f u v 1 (C a - X * C b) = f a * u - v * f b := by + simp [homogeneousEval, homogenize_sub, show X * C b = C b * X by ring, + MvPolynomial.eval₂_mul] + ring + +theorem linear_natDegree {R : Type*} [CommRing R] [IsDomain R] + (a b : R) (hb : b ≠ 0) : (C a - X * C b).natDegree = 1 := by + apply natDegree_eq_of_le_of_coeff_ne_zero + · exact (natDegree_sub_le _ _).trans (max_le (by simp) + ((natDegree_mul_le).trans (by simp))) + · simpa using neg_ne_zero.mpr hb + +noncomputable def pairPartialPolynomial {R : Type*} [CommRing R] + (f : ℂ →+* R) (uj vj : R) (Q : ℕ) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : Polynomial R := + homogeneousEval (Polynomial.mapRingHom f) (C uj) (C vj) Q + (pairAffinePolynomial Q ψ) + +theorem pairPartialPolynomial_expansion {R : Type*} [CommRing R] + (f : ℂ →+* R) (uj vj : R) (Q : ℕ) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : + pairPartialPolynomial f uj vj Q ψ = ∑ x, ∑ y, + monomial x.val (f (weightedPairCoordinate Q ψ x y) * vj^y.val * uj^(Q-y.val)) := by + unfold pairPartialPolynomial pairAffinePolynomial + simp only [homogeneousEval_sum] + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + rw [homogeneousEval_monomial _ _ _ _ _ (Nat.le_of_lt_succ y.isLt)] + change (monomial x.val (weightedPairCoordinate Q ψ x y)).map f * + C vj ^ y.val * C uj ^ (Q-y.val) = _ + simp only [map_monomial, ← map_pow, monomial_mul_C] + +theorem pairPartialPolynomial_degree {R : Type*} [CommRing R] + (f : ℂ →+* R) (uj vj : R) (Q : ℕ) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : + (pairPartialPolynomial f uj vj Q ψ).natDegree ≤ Q := by + rw [pairPartialPolynomial_expansion] + apply natDegree_sum_le_of_forall_le + intro x hx + apply natDegree_sum_le_of_forall_le + intro y hy + exact (natDegree_monomial_le _).trans (Nat.le_of_lt_succ x.isLt) + +theorem pairAffinePolynomial_degree (Q : ℕ) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : + (pairAffinePolynomial Q ψ).natDegree ≤ Q := by + apply natDegree_sum_le_of_forall_le + intro x hx + apply natDegree_sum_le_of_forall_le + intro y hy + exact (natDegree_monomial_le _).trans (Nat.le_of_lt_succ y.isLt) + +theorem pairPartialPolynomial_cube {R : Type*} [CommRing R] + (f : ℂ →+* R) (uj vj : R) (Q : ℕ) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) + (hc : PairDiagonal.diagonal^3 ∣ pairAffinePolynomial Q ψ) : + (C vj - X * C uj)^3 ∣ pairPartialPolynomial f uj vj Q ψ := by + have hd := homogeneousEval_dvd (Polynomial.mapRingHom f) (C uj) (C vj) + hc (pairAffinePolynomial_degree Q ψ) + have hdeg : (PairDiagonal.diagonal^3).natDegree = 3 := by + simp [PairDiagonal.diagonal, natDegree_pow] + rw [hdeg, homogeneousEval_cube _ _ _ _ (by simp [PairDiagonal.diagonal])] at hd + have he : homogeneousEval (Polynomial.mapRingHom f) (C uj) (C vj) 1 + PairDiagonal.diagonal = C vj - X * C uj := by + simp [homogeneousEval, PairDiagonal.diagonal] + simpa only [he, pairPartialPolynomial] using hd + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/Homogenize.lean b/lean/OAI/Analysis/Laughlin/Pair/Homogenize.lean new file mode 100644 index 0000000000000000000000000000000000000000..fee21958a183aa858e23804d4f7234846393a4da --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/Homogenize.lean @@ -0,0 +1,44 @@ +import Mathlib.Algebra.Polynomial.Homogenize +import OAI.Analysis.Laughlin.Pair.AffinePolynomial + +namespace OAI + +namespace Laughlin +open Polynomial +open scoped BigOperators + +theorem homogenize_dvd_of_degree_le {R : Type*} [CommRing R] [IsDomain R] + {p q : Polynomial R} {n : ℕ} (hd : p ∣ q) (hn : q.natDegree ≤ n) : + p.homogenize p.natDegree ∣ q.homogenize n := by + have he : q.homogenize n = q.homogenize q.natDegree * + (1 : Polynomial R).homogenize (n-q.natDegree) := by + rw [← homogenize_mul q 1 le_rfl (by simp), mul_one, + Nat.add_sub_of_le hn] + rw [he] + exact (homogenize_dvd hd).trans (dvd_mul_right _ _) + +noncomputable def homogeneousEval {R S : Type*} [CommRing R] [CommRing S] + (f : R →+* S) (u v : S) (n : ℕ) (p : Polynomial R) : S := + MvPolynomial.eval₂ f (fun k : Fin 2 => if k = 0 then v else u) (p.homogenize n) + +theorem homogeneousEval_monomial {R S : Type*} [CommRing R] [CommRing S] + (f : R →+* S) (u v : S) (n k : ℕ) (h : k ≤ n) (a : R) : + homogeneousEval f u v n (monomial k a) = f a * v^k * u^(n-k) := by + simp [homogeneousEval, homogenize_monomial h, MvPolynomial.eval₂_monomial, + Finsupp.prod_fintype, Fin.prod_univ_two, mul_assoc] + +theorem homogeneousEval_sum {R S ι : Type*} [CommRing R] [CommRing S] + (f : R →+* S) (u v : S) (n : ℕ) (s : Finset ι) (p : ι → Polynomial R) : + homogeneousEval f u v n (∑ k ∈ s, p k) = + ∑ k ∈ s, homogeneousEval f u v n (p k) := by + simp [homogeneousEval] + +theorem homogeneousEval_dvd {R S : Type*} [CommRing R] [IsDomain R] [CommRing S] + (f : R →+* S) (u v : S) {p q : Polynomial R} {n : ℕ} + (hd : p ∣ q) (hn : q.natDegree ≤ n) : + homogeneousEval f u v p.natDegree p ∣ homogeneousEval f u v n q := + MvPolynomial.eval₂_dvd _ _ (homogenize_dvd_of_degree_le hd hn) + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/LadderIntertwining.lean b/lean/OAI/Analysis/Laughlin/Pair/LadderIntertwining.lean new file mode 100644 index 0000000000000000000000000000000000000000..24c9e7491fe9391cb26e613ffcf5645e519d0a4e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/LadderIntertwining.lean @@ -0,0 +1,66 @@ +import OAI.Analysis.Laughlin.Pair.Orthonormality +import OAI.Analysis.Laughlin.Pair.TensorBoundary +import OAI.Analysis.Laughlin.Spin.LadderMatrix + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +noncomputable def pairInclusion (Q : ℕ) : + Matrix (Fin (Q+1) × Fin (Q+1)) (Fin ((2*Q-2)+1)) ℝ := + fun i p => pairCoefficient Q p.val i.1 i.2 + +theorem pairInclusion_raising (Q : ℕ) (hQ : 0 < Q) : + totalRaise Q Q * pairInclusion Q = pairInclusion Q * raiseMatrix (2*Q-2) := by + ext i p + change (∑ j, totalRaise Q Q i j*pairCoefficient Q p.val j.1 j.2) = + ∑ k, pairCoefficient Q k.val i.1 i.2 * raiseMatrix (2*Q-2) k p + rw [totalRaise_apply,raiseMatrix_row,raiseMatrix_row,raiseMatrix_column] + change pairTensorRaise Q p.val i.1 i.2 = _ + by_cases hp : 0 < p.val + · rw [dite_eq_left hp] + have he := pairCoefficient_tensor_raising Q (p.val-1) hQ (by omega) i.1 i.2 + rw [show p.val-1+1=p.val by omega] at he + simpa only [mul_comm] using he + · rw [dite_eq_right hp] + have hz : p.val=0 := by omega + rw [hz,pairCoefficient_tensor_highest Q hQ] + +theorem pairInclusion_lowering (Q : ℕ) (hQ : 0 < Q) : + (totalRaise Q Q)ᵀ * pairInclusion Q = pairInclusion Q * (raiseMatrix (2*Q-2))ᵀ := by + ext i p + change (∑ j, totalRaise Q Q j i*pairCoefficient Q p.val j.1 j.2) = + ∑ k, pairCoefficient Q k.val i.1 i.2 * raiseMatrix (2*Q-2) p k + conv_rhs => simp only [mul_comm (pairCoefficient Q _ _ _)] + rw [totalRaise_transpose_apply,raiseMatrix_column,raiseMatrix_column,raiseMatrix_row] + have heq : + (if h : 0 < i.1.val then pairCoefficient Q p.val ⟨i.1.val-1,by omega⟩ i.2 * + ladder Q (i.1.val-1) else 0) + + (if h : 0 < i.2.val then pairCoefficient Q p.val i.1 ⟨i.2.val-1,by omega⟩ * + ladder Q (i.2.val-1) else 0) = pairTensorLower Q p.val i.1 i.2 := by + unfold pairTensorLower + split_ifs <;> ring + rw [heq] + by_cases hp : p.val < 2*Q-2 + · rw [dite_eq_left hp,pairCoefficient_tensor_lowering Q p.val hQ hp] + · rw [dite_eq_right hp] + have hz : p.val=2*Q-2 := by omega + rw [hz,pairCoefficient_tensor_lowest Q hQ] + +theorem pairInclusion_isometry (Q : ℕ) (hQ : 2 ≤ Q) : + (pairInclusion Q)ᵀ * pairInclusion Q = 1 := by + ext p q + rw [Matrix.mul_apply,Fintype.sum_prod_type] + simp only [Matrix.transpose_apply,pairInclusion,Matrix.one_apply] + have h := pairCoefficient_gram Q p.val q.val hQ (by omega) + simpa only [Fin.ext_iff] using h + +theorem pairInclusion_transpose_raising (Q : ℕ) (hQ : 0 < Q) : + (pairInclusion Q)ᵀ * totalRaise Q Q = raiseMatrix (2*Q-2) * (pairInclusion Q)ᵀ := by + have h := congrArg Matrix.transpose (pairInclusion_lowering Q hQ) + simpa only [Matrix.transpose_mul,Matrix.transpose_transpose] using h + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/LoweringAlgebra.lean b/lean/OAI/Analysis/Laughlin/Pair/LoweringAlgebra.lean new file mode 100644 index 0000000000000000000000000000000000000000..f88e6a4aaf3d89b8760e78265cfdb45b3394648b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/LoweringAlgebra.lean @@ -0,0 +1,60 @@ +import Mathlib.Data.Nat.Choose.Basic +import Mathlib.Basic.Real.Basic +import Mathlib.Tactic.Linarith +import Mathlib.Tactic.NormNum +import Mathlib.Tactic.Ring + +namespace OAI + +namespace Laughlin + +noncomputable def pairPolynomialCoefficient (Q i j : ℕ) : ℝ := + ((i : ℝ)-(j : ℝ)) * (Q.choose i : ℝ) * (Q.choose j : ℝ) + +theorem choose_lowering (Q i : ℕ) (hi : 0 < i) (hiQ : i ≤ Q+1) : + ((Q : ℝ)-(i : ℝ)+1) * (Q.choose (i-1) : ℝ) = + (i : ℝ) * (Q.choose i : ℝ) := by + obtain ⟨k,rfl⟩ := Nat.exists_eq_succ_of_ne_zero (Nat.ne_of_gt hi) + have hk : k ≤ Q := by omega + have h := Nat.choose_succ_right_eq Q k + have hc := congrArg (fun x : ℕ => (x : ℝ)) h + simp only [Nat.cast_mul, Nat.cast_add, Nat.cast_one, Nat.cast_sub hk] at hc + simp only [Nat.succ_eq_add_one, Nat.add_sub_cancel, Nat.cast_add, Nat.cast_one] + nlinarith only [hc] + +theorem pairPolynomialCoefficient_lowering (Q i j : ℕ) + (hiQ : i ≤ Q) (hjQ : j ≤ Q) : + (if 0 < i then ((Q : ℝ)-(i : ℝ)+1)*pairPolynomialCoefficient Q (i-1) j else 0) + + (if 0 < j then ((Q : ℝ)-(j : ℝ)+1)*pairPolynomialCoefficient Q i (j-1) else 0) = + ((i : ℝ)+(j : ℝ)-1)*pairPolynomialCoefficient Q i j := by + have left : (if 0 < i then ((Q : ℝ)-(i : ℝ)+1)*pairPolynomialCoefficient Q (i-1) j else 0) = + (i : ℝ)*((i : ℝ)-1-(j : ℝ))*(Q.choose i : ℝ)*(Q.choose j : ℝ) := by + by_cases hi : 0 < i + · rw [ite_eq_left hi] + unfold pairPolynomialCoefficient + rw [Nat.cast_sub (by omega : 1 ≤ i), Nat.cast_one] + calc + _ = ((i : ℝ)-1-(j : ℝ))*(Q.choose j : ℝ)* + (((Q : ℝ)-(i : ℝ)+1)*(Q.choose (i-1) : ℝ)) := by ring + _ = _ := by rw [choose_lowering Q i hi (by omega)]; ring + · have hz : i = 0 := by omega + simp [hz] + have right : (if 0 < j then ((Q : ℝ)-(j : ℝ)+1)*pairPolynomialCoefficient Q i (j-1) else 0) = + (j : ℝ)*((i : ℝ)-((j : ℝ)-1))*(Q.choose i : ℝ)*(Q.choose j : ℝ) := by + by_cases hj : 0 < j + · rw [ite_eq_left hj] + unfold pairPolynomialCoefficient + rw [Nat.cast_sub (by omega : 1 ≤ j), Nat.cast_one] + calc + _ = ((i : ℝ)-((j : ℝ)-1))*(Q.choose i : ℝ)* + (((Q : ℝ)-(j : ℝ)+1)*(Q.choose (j-1) : ℝ)) := by ring + _ = _ := by rw [choose_lowering Q j hj (by omega)]; ring + · have hz : j = 0 := by omega + simp [hz] + rw [left, right] + unfold pairPolynomialCoefficient + ring + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/Moment.lean b/lean/OAI/Analysis/Laughlin/Pair/Moment.lean new file mode 100644 index 0000000000000000000000000000000000000000..5a15ab8305a2151e4b88f0f8fbb3d668f073a599 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/Moment.lean @@ -0,0 +1,67 @@ +import OAI.Analysis.Laughlin.Pair.NormalizedLadder + +namespace OAI + +namespace Laughlin +open scoped BigOperators + +theorem pairCoefficient_scaled (Q p : ℕ) (hQ : 0 < Q) (hp : p ≤ 2*Q-2) + (x y : Fin (Q+1)) : + pairCoefficient Q p x y * pairNormalization Q p = + if x.val+y.val = p+1 then ((x.val : ℝ)-(y.val : ℝ))* + Real.sqrt (Q.choose x.val : ℝ)*Real.sqrt (Q.choose y.val : ℝ) else 0 := by + have hd : pairNormalization Q p ≠ 0 := ne_of_gt (pairNormalization_pos Q p hQ hp) + rw [pairCoefficient_choose Q p hQ hp] + unfold pairNormalization at hd ⊢ + split_ifs + · rw [Real.sqrt_div (by positivity), Real.sqrt_mul (by positivity)] + field_simp + · simp + +noncomputable def weightedPairCoordinate (Q : ℕ) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) (x y : Fin (Q+1)) : ℂ := + ((Real.sqrt (Q.choose x.val : ℝ)*Real.sqrt (Q.choose y.val : ℝ) : ℝ) : ℂ)*ψ x y + +noncomputable def pairMoment (Q p : ℕ) (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : ℂ := + ∑ x, ∑ y, if x.val+y.val = p+1 then + ((x.val : ℂ)-(y.val : ℂ))*weightedPairCoordinate Q ψ x y else 0 + +theorem pairMoment_eq_amplitude (Q p : ℕ) (hQ : 0 < Q) (hp : p ≤ 2*Q-2) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : + pairMoment Q p ψ = (pairNormalization Q p : ℂ)* + (∑ x, ∑ y, (pairCoefficient Q p x y : ℂ)*ψ x y) := by + unfold pairMoment + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro x hx + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro y hy + have h := congrArg (fun r : ℝ => (r : ℂ)) (pairCoefficient_scaled Q p hQ hp x y) + push_cast at h + by_cases hs : x.val+y.val = p+1 + · rw [ite_eq_left hs] at h ⊢ + push_cast at h + unfold weightedPairCoordinate + push_cast + calc + _ = ((x.val : ℂ)-(y.val : ℂ))*(Real.sqrt (Q.choose x.val : ℝ) : ℂ)* + (Real.sqrt (Q.choose y.val : ℝ) : ℂ)*ψ x y := by ring + _ = _ := by rw [← h]; ring + · rw [ite_eq_right hs] + simp only [ite_eq_right hs, Complex.ofReal_zero] at h + calc + _ = ((pairCoefficient Q p x y : ℂ)*(pairNormalization Q p : ℂ))*ψ x y := by rw [h]; simp + _ = _ := by ring + +theorem weightedPairCoordinate_swap (Q : ℕ) (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) + (ha : ∀ x y, ψ y x = -ψ x y) (x y : Fin (Q+1)) : + weightedPairCoordinate Q ψ y x = -weightedPairCoordinate Q ψ x y := by + unfold weightedPairCoordinate + rw [ha] + push_cast + ring + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/MomentKernel.lean b/lean/OAI/Analysis/Laughlin/Pair/MomentKernel.lean new file mode 100644 index 0000000000000000000000000000000000000000..854c8793e6022cdba51c231416ebe63eba6fccc1 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/MomentKernel.lean @@ -0,0 +1,65 @@ +import OAI.Analysis.Laughlin.Pair.Moment + +namespace OAI + +namespace Laughlin +open scoped BigOperators + +theorem pairMoment_zero_outside (Q p : ℕ) (hp : 2*Q-2 < p) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : pairMoment Q p ψ = 0 := by + unfold pairMoment + apply Finset.sum_eq_zero + intro x hx + apply Finset.sum_eq_zero + intro y hy + by_cases hs : x.val+y.val = p+1 + · rw [ite_eq_left hs] + have hxy : x.val = y.val := by omega + simp [hxy] + · simp [hs] + +theorem pairMoment_zero_of_pair_kernel (Q : ℕ) (hQ : 2 ≤ Q) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) + (hk : ∀ p ∈ Finset.range (2*Q-1), + (∑ x, ∑ y, (pairCoefficient Q p x y : ℂ)*ψ x y) = 0) (p : ℕ) : + pairMoment Q p ψ = 0 := by + by_cases hp : p ≤ 2*Q-2 + · rw [pairMoment_eq_amplitude Q p (by omega) hp ψ, hk p (by simpa using (show p < 2*Q-1 by omega)), mul_zero] + · exact pairMoment_zero_outside Q p (by omega) ψ + +theorem pair_jet_coefficient_zero (Q n : ℕ) (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) + (ha : ∀ x y, ψ y x = -ψ x y) (hm : pairMoment Q n ψ = 0) : + (∑ x, ∑ y, if x.val+y.val = n+1 then + (y.val : ℂ)*weightedPairCoordinate Q ψ x y else 0) = 0 := by + let I : ℂ := ∑ x, ∑ y, if x.val+y.val = n+1 then + (x.val : ℂ)*weightedPairCoordinate Q ψ x y else 0 + let J : ℂ := ∑ x, ∑ y, if x.val+y.val = n+1 then + (y.val : ℂ)*weightedPairCoordinate Q ψ x y else 0 + have hs : I = -J := by + dsimp [I,J] + rw [Finset.sum_comm] + simp only [← Finset.sum_neg_distrib] + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + rw [weightedPairCoordinate_swap Q ψ ha x y, Nat.add_comm y.val x.val] + split_ifs <;> ring + have hmom : pairMoment Q n ψ = I-J := by + dsimp [pairMoment,I,J] + rw [← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro x hx + rw [← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro y hy + split_ifs <;> ring + have hz : (2 : ℂ)*J = 0 := by + calc + _ = -(I-J) := by rw [hs]; ring + _ = 0 := by rw [← hmom, hm]; simp + exact (mul_eq_zero.mp hz).resolve_left two_ne_zero + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/NormalOrder.lean b/lean/OAI/Analysis/Laughlin/Pair/NormalOrder.lean new file mode 100644 index 0000000000000000000000000000000000000000..e8df5f74a4bfb12f8118031deb9aa7e0262b5d1c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/NormalOrder.lean @@ -0,0 +1,60 @@ +import OAI.Analysis.Laughlin.ThreeBody.PairAction + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem pairEnd_create_create (Q : ℕ) (c : Fin (Q+1) → Fin (Q+1) → ℂ) + (i j : Fin (Q+1)) : + pairEnd Q c * create i * create j = + (c i j-c j i) • (1 : Module.End ℂ (Space Q)) - + (∑ b, (c i b-c b i) • (create j * annihilate b)) + + (∑ b, (c j b-c b j) • (create i * annihilate b)) + + create i * create j * pairEnd Q c := by + classical + simp only [pairEnd,Finset.sum_mul,smul_mul_assoc,normal_order_four, + smul_add,smul_sub,smul_smul,Finset.sum_add_distrib,Finset.sum_sub_distrib] + simp only [delta,mul_ite,mul_one,mul_zero,ite_smul,zero_smul, + Finset.sum_ite_eq',Finset.mem_univ,ite_true] + simp only [Finset.mul_sum,mul_smul_comm] + simp only [Finset.sum_ite_irrel,Finset.sum_const_zero,Finset.sum_ite_eq', + Finset.mem_univ,ite_true,mul_assoc] + have hs (a b : ℂ) (v : Module.End ℂ (Space Q)) : (a-b) • v = a • v-b • v := by + apply LinearMap.ext + intro x + exact sub_smul a b (v x) + simp only [hs,Finset.sum_sub_distrib] + module + +theorem pairEnd_annihilate_commute (Q : ℕ) (c : Fin (Q+1) → Fin (Q+1) → ℂ) + (i : Fin (Q+1)) : pairEnd Q c * annihilate i = annihilate i * pairEnd Q c := by + have h (a b : Fin (Q+1)) : annihilate b * annihilate a * annihilate i = + annihilate i * (annihilate b * annihilate a) := by + calc + _ = annihilate b * (annihilate a * annihilate i) := mul_assoc _ _ _ + _ = annihilate b * -(annihilate i * annihilate a) := by rw [eq_neg_of_add_eq_zero_left (annihilate_anticommute a i)] + _ = -(annihilate b * (annihilate i * annihilate a)) := by + apply LinearMap.ext + intro x + exact map_neg (annihilate b) ((annihilate i * annihilate a) x) + _ = -((annihilate b * annihilate i) * annihilate a) := by rw [mul_assoc] + _ = -(-(annihilate i * annihilate b) * annihilate a) := by rw [eq_neg_of_add_eq_zero_left (annihilate_anticommute b i)] + _ = _ := by + apply LinearMap.ext + intro x + change -(-(annihilate i (annihilate b (annihilate a x)))) = _ + exact neg_neg _ + simp only [pairEnd,Finset.sum_mul,Finset.mul_sum,smul_mul_assoc,mul_smul_comm,h] + +theorem pairEnd_commute (Q : ℕ) (c d : Fin (Q+1) → Fin (Q+1) → ℂ) : + pairEnd Q c * pairEnd Q d = pairEnd Q d * pairEnd Q c := by + conv_lhs => arg 2; unfold pairEnd + conv_rhs => arg 1; unfold pairEnd + simp only [Finset.mul_sum,Finset.sum_mul,mul_smul_comm,smul_mul_assoc, + ← mul_assoc,pairEnd_annihilate_commute] + simp only [mul_assoc,pairEnd_annihilate_commute] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/Normalization.lean b/lean/OAI/Analysis/Laughlin/Pair/Normalization.lean new file mode 100644 index 0000000000000000000000000000000000000000..49d80bcbbbfac30797ce3e73ee37c1d1a3c14fec --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/Normalization.lean @@ -0,0 +1,76 @@ +import OAI.Analysis.Laughlin.Pair.Binomial +import OAI.Analysis.Laughlin.Pair.CoefficientSquare + +namespace OAI + +namespace Laughlin +open scoped BigOperators +open Finset Finset.Nat + +theorem finite_pair_antidiagonal (Q n : ℕ) (f : ℕ → ℕ → ℝ) + (hz : ∀ i j, Q < i ∨ Q < j → f i j = 0) : + (∑ x : Fin (Q+1), ∑ y : Fin (Q+1), + if x.val+y.val = n then f x.val y.val else 0) = + ∑ ij ∈ antidiagonal n, f ij.1 ij.2 := by + classical + rw [← Fintype.sum_prod_type (f := fun a : Fin (Q+1) × Fin (Q+1) => + if a.1.val+a.2.val = n then f a.1.val a.2.val else 0)] + refine Finset.sum_bij_ne_zero (fun a _ _ => (a.1.val,a.2.val)) ?_ ?_ ?_ ?_ + · intro a ha hn + apply HasAntidiagonal.mem_antidiagonal.mpr + by_contra h + exact hn (by simp [h]) + · intro a ha hna b hb hnb hab + apply Prod.ext + · exact Fin.ext (congrArg Prod.fst hab) + · exact Fin.ext (congrArg Prod.snd hab) + · rintro ⟨i,j⟩ hij hn + have hi : i < Q+1 := by + by_contra h + exact hn (hz i j (Or.inl (by omega))) + have hj : j < Q+1 := by + by_contra h + exact hn (hz i j (Or.inr (by omega))) + have hs : i+j = n := HasAntidiagonal.mem_antidiagonal.mp hij + let a : Fin (Q+1) × Fin (Q+1) := (⟨i,hi⟩,⟨j,hj⟩) + refine ⟨a, mem_univ a, ?_, rfl⟩ + simpa [a, hs] using hn + · intro a ha hn + have hs : a.1.val+a.2.val = n := by + by_contra h + exact hn (by simp [h]) + simp [hs] + +theorem pairCoefficient_unit_norm (Q p : ℕ) (hQ : 2 ≤ Q) (hp : p ≤ 2*Q-2) : + (∑ x : Fin (Q+1), ∑ y : Fin (Q+1), (pairCoefficient Q p x y)^2) = 1 := by + let f : ℕ → ℕ → ℝ := fun i j => + ((i : ℝ)-(j : ℝ))^2 * (Q.choose i : ℝ) * (Q.choose j : ℝ) / + (2*(Q : ℝ)*((2*Q-2).choose p : ℝ)) + have hz : ∀ i j, Q < i ∨ Q < j → f i j = 0 := by + intro i j h + rcases h with h | h + · simp [f, Nat.choose_eq_zero_of_lt h] + · simp [f, Nat.choose_eq_zero_of_lt h] + simp_rw [pairCoefficient_sq_choose Q p (by omega) hp] + change (∑ x : Fin (Q+1), ∑ y : Fin (Q+1), + if x.val+y.val = p+1 then f x.val y.val else 0) = 1 + rw [finite_pair_antidiagonal Q (p+1) f hz] + simp only [f, div_eq_mul_inv] + rw [← Finset.sum_mul, ← div_eq_mul_inv] + have hmoment : (∑ ij ∈ antidiagonal (p+1), ((ij.1 : ℝ)-(ij.2 : ℝ))^2 * + (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) = + 2*(Q : ℝ)*((2*Q-2).choose p : ℝ) := by + have h := PairNormalization.pair_binomial_moment (Q-2) p + have h₁ : Q-2+2 = Q := by omega + have h₂ : 2*(Q-2)+2 = 2*Q-2 := by omega + simpa only [h₁, h₂] using h + rw [hmoment] + apply div_self + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + have hc : ((2*Q-2).choose p : ℝ) ≠ 0 := by + exact_mod_cast (Nat.ne_of_gt (Nat.choose_pos hp)) + exact mul_ne_zero (mul_ne_zero (by norm_num) hq) hc + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/NormalizedLadder.lean b/lean/OAI/Analysis/Laughlin/Pair/NormalizedLadder.lean new file mode 100644 index 0000000000000000000000000000000000000000..b12c7032c4798560ad6a9e3d901c2128e64d1c15 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/NormalizedLadder.lean @@ -0,0 +1,66 @@ +import Mathlib.Tactic.LinearCombination +import OAI.Analysis.Laughlin.Pair.PolynomialLadder + +namespace OAI + +namespace Laughlin + +noncomputable def pairNormalization (Q p : ℕ) : ℝ := + Real.sqrt (2*(Q : ℝ)*((2*Q-2).choose p : ℝ)) + +noncomputable def normalizedPairState (Q p i j : ℕ) : ℝ := + rawPairState Q p i j / pairNormalization Q p + +theorem pairNormalization_pos (Q p : ℕ) (hQ : 0 < Q) (hp : p ≤ 2*Q-2) : + 0 < pairNormalization Q p := by + unfold pairNormalization + apply Real.sqrt_pos.mpr + have hq : (0 : ℝ) < Q := by exact_mod_cast hQ + have hc : (0 : ℝ) < (2*Q-2).choose p := by exact_mod_cast Nat.choose_pos hp + positivity + +theorem pairNormalization_ratio (Q p : ℕ) (hQ : 0 < Q) (hp : p < 2*Q-2) : + ((p : ℝ)+1) / pairNormalization Q p = + Real.sqrt (((p : ℝ)+1)*((2*Q-2-p : ℕ) : ℝ)) / pairNormalization Q (p+1) := by + have hdn := pairNormalization_pos Q (p+1) hQ (by omega) + have hd := pairNormalization_pos Q p hQ (by omega) + apply (div_eq_div_iff (ne_of_gt hd) (ne_of_gt hdn)).mpr + have hc := congrArg (fun n : ℕ => (n : ℝ)) (Nat.choose_succ_right_eq (2*Q-2) p) + push_cast at hc + have he : (((p : ℝ)+1)*pairNormalization Q (p+1))^2 = + (Real.sqrt (((p : ℝ)+1)*((2*Q-2-p : ℕ) : ℝ))*pairNormalization Q p)^2 := by + unfold pairNormalization + rw [mul_pow, mul_pow, Real.sq_sqrt (by positivity), + Real.sq_sqrt (by positivity), Real.sq_sqrt (by positivity)] + linear_combination (2*(Q : ℝ)*((p : ℝ)+1))*hc + have hn₁ : 0 ≤ ((p : ℝ)+1)*pairNormalization Q (p+1) := by positivity + have hn₂ : 0 ≤ Real.sqrt (((p : ℝ)+1)*((2*Q-2-p : ℕ) : ℝ))*pairNormalization Q p := by positivity + nlinarith only [he,hn₁,hn₂] + +theorem lowerPair_div (Q : ℕ) (f : ℕ → ℕ → ℝ) (d : ℝ) (i j : ℕ) : + lowerPair Q (fun i j => f i j / d) i j = lowerPair Q f i j / d := by + unfold lowerPair + split_ifs <;> ring + +theorem normalizedPairState_lowering (Q p i j : ℕ) (hQ : 0 < Q) + (hp : p < 2*Q-2) (hi : i ≤ Q) (hj : j ≤ Q) : + lowerPair Q (normalizedPairState Q p) i j = + Real.sqrt (((p : ℝ)+1)*((2*Q-2-p : ℕ) : ℝ))*normalizedPairState Q (p+1) i j := by + unfold normalizedPairState + rw [lowerPair_div, rawPairState_lowering Q p i j hi hj] + push_cast + calc + _ = (((p : ℝ)+1)/pairNormalization Q p)*rawPairState Q (p+1) i j := by ring + _ = _ := by rw [pairNormalization_ratio Q p hQ hp]; ring + +theorem normalizedPairState_eq_coefficients (Q p : ℕ) (hQ : 0 < Q) + (hp : p ≤ 2*Q-2) (x y : Fin (Q+1)) : + normalizedPairState Q p x.val y.val = pairCoefficient Q p x y * + Real.sqrt (Q.choose x.val : ℝ)*Real.sqrt (Q.choose y.val : ℝ) := by + unfold normalizedPairState rawPairState + apply (div_eq_iff (ne_of_gt (pairNormalization_pos Q p hQ hp))).mpr + exact (pairCoefficient_polynomial_weight Q p hQ hp x y).symm + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/Orthonormality.lean b/lean/OAI/Analysis/Laughlin/Pair/Orthonormality.lean new file mode 100644 index 0000000000000000000000000000000000000000..66d1902b651a2f91e7e821de9b45b3056057caeb --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/Orthonormality.lean @@ -0,0 +1,46 @@ +import OAI.Analysis.Laughlin.Pair.Normalization + +namespace OAI + +namespace Laughlin +open scoped BigOperators + +theorem pairCoefficient_orthogonal (Q p q : ℕ) (hpq : p ≠ q) : + (∑ x : Fin (Q+1), ∑ y : Fin (Q+1), + pairCoefficient Q p x y * pairCoefficient Q q x y) = 0 := by + apply Finset.sum_eq_zero + intro x hx + apply Finset.sum_eq_zero + intro y hy + by_cases hp : x.val+y.val = p+1 + · have hq : x.val+y.val ≠ q+1 := by omega + simp [pairCoefficient, hq] + · simp [pairCoefficient, hp] + +theorem pairCoefficient_gram (Q p q : ℕ) (hQ : 2 ≤ Q) + (hp : p ≤ 2*Q-2) : + (∑ x : Fin (Q+1), ∑ y : Fin (Q+1), + pairCoefficient Q p x y * pairCoefficient Q q x y) = if p = q then 1 else 0 := by + by_cases h : p = q + · subst q + simp only [ite_true] + simpa only [pow_two] using pairCoefficient_unit_norm Q p hQ hp + · rw [ite_eq_right h] + exact pairCoefficient_orthogonal Q p q h + +theorem pairCoefficient_swap (Q p : ℕ) (x y : Fin (Q+1)) : + pairCoefficient Q p y x = -pairCoefficient Q p x y := by + unfold pairCoefficient + rw [Nat.add_comm y.val x.val] + split_ifs + · have hn : ((Q.descFactorial y.val : ℝ) * (Q.descFactorial x.val : ℝ) * (p.factorial : ℝ)) = + ((Q.descFactorial x.val : ℝ) * (Q.descFactorial y.val : ℝ) * (p.factorial : ℝ)) := by ring + have hd : ((Q : ℝ) * ((2*Q-2).descFactorial p : ℝ) * (y.val.factorial : ℝ) * (x.val.factorial : ℝ)) = + ((Q : ℝ) * ((2*Q-2).descFactorial p : ℝ) * (x.val.factorial : ℝ) * (y.val.factorial : ℝ)) := by ring + rw [hn, hd] + ring + · simp + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/PolynomialBridge.lean b/lean/OAI/Analysis/Laughlin/Pair/PolynomialBridge.lean new file mode 100644 index 0000000000000000000000000000000000000000..67169b4bc395f6502d4df897c1da6141e943b1b2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/PolynomialBridge.lean @@ -0,0 +1,58 @@ +import OAI.Analysis.Laughlin.Pair.CoefficientSquare +import OAI.Analysis.Laughlin.Pair.LoweringAlgebra + +namespace OAI + +namespace Laughlin + +theorem pairCoefficient_choose (Q p : ℕ) (hQ : 0 < Q) (hp : p ≤ 2*Q-2) + (x y : Fin (Q+1)) : + pairCoefficient Q p x y = if x.val+y.val = p+1 then + ((x.val : ℝ)-(y.val : ℝ)) * + Real.sqrt ((Q.choose x.val : ℝ)*(Q.choose y.val : ℝ) / + (2*(Q : ℝ)*((2*Q-2).choose p : ℝ))) else 0 := by + have hx : (x.val.factorial : ℝ) ≠ 0 := by positivity + have hy : (y.val.factorial : ℝ) ≠ 0 := by positivity + have hpf : (p.factorial : ℝ) ≠ 0 := by positivity + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (Nat.ne_of_gt hQ) + have hc : ((2*Q-2).choose p : ℝ) ≠ 0 := by + exact_mod_cast (Nat.ne_of_gt (Nat.choose_pos hp)) + unfold pairCoefficient + split_ifs + · have hr : (((Q.descFactorial x.val : ℝ)*(Q.descFactorial y.val : ℝ)*(p.factorial : ℝ)) / + ((Q : ℝ)*((2*Q-2).descFactorial p : ℝ)*(x.val.factorial : ℝ)*(y.val.factorial : ℝ))) / 2 = + (Q.choose x.val : ℝ)*(Q.choose y.val : ℝ)/(2*(Q : ℝ)*((2*Q-2).choose p : ℝ)) := by + simp only [Nat.descFactorial_eq_factorial_mul_choose, Nat.cast_mul] + field_simp + have hs := congrArg Real.sqrt hr + rw [Real.sqrt_div (by positivity) (2 : ℝ)] at hs + rw [← hs] + ring + · rfl + +theorem pairCoefficient_polynomial_weight (Q p : ℕ) (hQ : 0 < Q) + (hp : p ≤ 2*Q-2) (x y : Fin (Q+1)) : + pairCoefficient Q p x y * Real.sqrt (Q.choose x.val : ℝ) * + Real.sqrt (Q.choose y.val : ℝ) * Real.sqrt (2*(Q : ℝ)*((2*Q-2).choose p : ℝ)) = + if x.val+y.val = p+1 then pairPolynomialCoefficient Q x.val y.val else 0 := by + have hd : Real.sqrt (2*(Q : ℝ)*((2*Q-2).choose p : ℝ)) ≠ 0 := by + apply Real.sqrt_ne_zero'.mpr + have hq : (0 : ℝ) < Q := by exact_mod_cast hQ + have hc : (0 : ℝ) < (2*Q-2).choose p := by exact_mod_cast Nat.choose_pos hp + positivity + rw [pairCoefficient_choose Q p hQ hp] + split_ifs + · rw [Real.sqrt_div (by positivity), Real.sqrt_mul (by positivity)] + unfold pairPolynomialCoefficient + have hx := Real.sq_sqrt (show (0 : ℝ) ≤ Q.choose x.val by positivity) + have hy := Real.sq_sqrt (show (0 : ℝ) ≤ Q.choose y.val by positivity) + field_simp + calc + _ = ((x.val : ℝ)-(y.val : ℝ)) * (Real.sqrt (Q.choose x.val : ℝ))^2 * + (Real.sqrt (Q.choose y.val : ℝ))^2 := by ring + _ = _ := by rw [hx,hy] + · simp + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/PolynomialLadder.lean b/lean/OAI/Analysis/Laughlin/Pair/PolynomialLadder.lean new file mode 100644 index 0000000000000000000000000000000000000000..0b504abd0646724aeb333a366002cbc348c8d7b6 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/PolynomialLadder.lean @@ -0,0 +1,40 @@ +import OAI.Analysis.Laughlin.Pair.PolynomialBridge + +namespace OAI + +namespace Laughlin + +noncomputable def rawPairState (Q p i j : ℕ) : ℝ := + if i+j = p+1 then pairPolynomialCoefficient Q i j else 0 + +noncomputable def lowerPair (Q : ℕ) (f : ℕ → ℕ → ℝ) (i j : ℕ) : ℝ := + (if 0 < i then ((Q : ℝ)-(i : ℝ)+1)*f (i-1) j else 0) + + (if 0 < j then ((Q : ℝ)-(j : ℝ)+1)*f i (j-1) else 0) + +theorem rawPairState_lowering (Q p i j : ℕ) (hiQ : i ≤ Q) (hjQ : j ≤ Q) : + lowerPair Q (rawPairState Q p) i j = (p+1 : ℕ)*rawPairState Q (p+1) i j := by + by_cases h : i+j = p+2 + · have hx : 0 < i → i-1+j = p+1 := by omega + have hy : 0 < j → i+(j-1) = p+1 := by omega + have hr : ((i : ℝ)+(j : ℝ)-1) = (p+1 : ℕ) := by + have hc := congrArg (fun n : ℕ => (n : ℝ)) h + push_cast at hc ⊢ + linarith + have ha := pairPolynomialCoefficient_lowering Q i j hiQ hjQ + rw [hr] at ha + by_cases hi : 0 < i <;> by_cases hj : 0 < j + · simpa [lowerPair, rawPairState, h, hx hi, hy hj, hi, hj, Nat.add_assoc] using ha + · simpa [lowerPair, rawPairState, h, hx hi, hi, hj, Nat.add_assoc] using ha + · simpa [lowerPair, rawPairState, h, hy hj, hi, hj, Nat.add_assoc] using ha + · simpa [lowerPair, rawPairState, h, hi, hj, Nat.add_assoc] using ha + · have hx : 0 < i → i-1+j ≠ p+1 := by omega + have hy : 0 < j → i+(j-1) ≠ p+1 := by omega + by_cases hi : 0 < i <;> by_cases hj : 0 < j + · simp [lowerPair, rawPairState, h, hx hi, hy hj, hi, hj, Nat.add_assoc] + · simp [lowerPair, rawPairState, h, hx hi, hi, hj, Nat.add_assoc] + · simp [lowerPair, rawPairState, h, hy hj, hi, hj, Nat.add_assoc] + · simp [lowerPair, rawPairState, h, hi, hj, Nat.add_assoc] + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/PolynomialRaising.lean b/lean/OAI/Analysis/Laughlin/Pair/PolynomialRaising.lean new file mode 100644 index 0000000000000000000000000000000000000000..0692f4967368830ff97f4927edfc08e3c7e8d3d0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/PolynomialRaising.lean @@ -0,0 +1,70 @@ +import OAI.Analysis.Laughlin.Pair.NormalizedLadder +import OAI.Analysis.Laughlin.Spin.Highest2 + +namespace OAI + +namespace Laughlin + +noncomputable def raisePair (f : ℕ → ℕ → ℝ) (i j : ℕ) : ℝ := + ((i : ℝ)+1)*f (i+1) j + ((j : ℝ)+1)*f i (j+1) + +theorem pairPolynomialCoefficient_raising (Q i j : ℕ) (hi : i ≤ Q) (hj : j ≤ Q) : + ((i : ℝ)+1)*pairPolynomialCoefficient Q (i+1) j + + ((j : ℝ)+1)*pairPolynomialCoefficient Q i (j+1) = + (2*(Q : ℝ)-i-j-1)*pairPolynomialCoefficient Q i j := by + have hx := Spin.choose_step_real Q i hi + have hy := Spin.choose_step_real Q j hj + rw [Nat.cast_sub hi] at hx + rw [Nat.cast_sub hj] at hy + unfold pairPolynomialCoefficient + push_cast + linear_combination + ((i : ℝ)+1-j)*(Q.choose j : ℝ)*hx + + ((i : ℝ)-j-1)*(Q.choose i : ℝ)*hy + +theorem rawPairState_raising (Q p i j : ℕ) (hi : i ≤ Q) (hj : j ≤ Q) : + raisePair (rawPairState Q (p+1)) i j = + (2*(Q : ℝ)-2-p)*rawPairState Q p i j := by + have hs : i+1+j = p+1+1 ↔ i+j=p+1 := by omega + have ht : i+(j+1) = p+1+1 ↔ i+j=p+1 := by omega + unfold raisePair rawPairState + by_cases h : i+j=p+1 + · rw [ite_eq_left (hs.mpr h),ite_eq_left (ht.mpr h),ite_eq_left h] + have hc : (i : ℝ)+j = (p : ℝ)+1 := by exact_mod_cast h + rw [pairPolynomialCoefficient_raising Q i j hi hj] + congr 1 + linarith + · simp only [ite_eq_right h,ite_eq_right (mt hs.mp h),ite_eq_right (mt ht.mp h),mul_zero,add_zero] + +theorem pairNormalization_raising_ratio (Q p : ℕ) (hQ : 0 < Q) (hp : p < 2*Q-2) : + (2*(Q : ℝ)-2-p)/pairNormalization Q (p+1) = + Spin.ladder (2*Q-2) p / pairNormalization Q p := by + have h := Spin.sqrt_choose_step (2*Q-2) p hp + have hc : ((2*Q-2-p : ℕ) : ℝ) = 2*(Q : ℝ)-2-p := by + rw [Nat.cast_sub (by omega : p ≤ 2*Q-2),Nat.cast_sub (by omega : 2 ≤ 2*Q)] + push_cast; ring + rw [hc] at h + have hn₀ := ne_of_gt (pairNormalization_pos Q p hQ (by omega)) + have hn₁ := ne_of_gt (pairNormalization_pos Q (p+1) hQ (by omega)) + apply (div_eq_div_iff hn₁ hn₀).mpr + unfold pairNormalization + simp only [Real.sqrt_mul (by positivity : 0 ≤ 2*(Q : ℝ))] + linear_combination -(Real.sqrt (2*(Q : ℝ)))*h + +theorem normalizedPairState_raising (Q p i j : ℕ) (hQ : 0 < Q) (hp : p < 2*Q-2) + (hi : i ≤ Q) (hj : j ≤ Q) : + raisePair (normalizedPairState Q (p+1)) i j = + Spin.ladder (2*Q-2) p * normalizedPairState Q p i j := by + have hdiv : raisePair (normalizedPairState Q (p+1)) i j = + raisePair (rawPairState Q (p+1)) i j / pairNormalization Q (p+1) := by + unfold normalizedPairState raisePair + ring + rw [hdiv,rawPairState_raising Q p i j hi hj] + unfold normalizedPairState + calc + _ = ((2*(Q : ℝ)-2-p)/pairNormalization Q (p+1))*rawPairState Q p i j := by ring + _ = _ := by rw [pairNormalization_raising_ratio Q p hQ hp]; ring + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/Spectators.lean b/lean/OAI/Analysis/Laughlin/Pair/Spectators.lean new file mode 100644 index 0000000000000000000000000000000000000000..fd6cb8c602bddb5144913d1eae35ba23e4a2e7ff --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/Spectators.lean @@ -0,0 +1,46 @@ +import OAI.Analysis.Laughlin.Operators.PhysicalPairKernel +import OAI.Analysis.Laughlin.Spin.Polynomial2 + +namespace OAI + +namespace Laughlin +open scoped BigOperators + +abbrev PairSpectators {N Q : ℕ} (i j : Fin N) := + {a : Configuration N Q // a i = 0 ∧ a j = 0} + +noncomputable def pairConfigurationEquiv {N Q : ℕ} (i j : Fin N) (hij : i ≠ j) : + PairSpectators (Q := Q) i j × (Fin (Q+1) × Fin (Q+1)) ≃ Configuration N Q where + toFun b := Function.update (Function.update b.1.val i b.2.1) j b.2.2 + invFun a := (⟨Function.update (Function.update a i 0) j 0, by simp [hij]⟩, a i, a j) + left_inv := by + rintro ⟨⟨a,hai,haj⟩,x,y⟩ + apply Prod.ext + · apply Subtype.ext + funext k + by_cases hki : k=i + · subst k; simp [hij,hai] + · by_cases hkj : k=j + · subst k; simp [haj] + · simp [hki,hkj] + · simp [hij] + right_inv := by + intro a + funext k + by_cases hki : k=i + · subst k; simp [hij] + · by_cases hkj : k=j + · subst k; simp + · simp [hki,hkj] + +theorem sum_pair_configurations {N Q : ℕ} {R : Type*} [AddCommMonoid R] + (i j : Fin N) (hij : i ≠ j) (F : Configuration N Q → R) : + (∑ a, F a) = ∑ a : PairSpectators (Q := Q) i j, ∑ x, ∑ y, + F (Function.update (Function.update a.val i x) j y) := by + classical + rw [← Equiv.sum_comp (pairConfigurationEquiv (Q := Q) i j hij)] + simp only [Fintype.sum_prod_type, pairConfigurationEquiv, Equiv.coe_fn_mk] + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/SpinorCube.lean b/lean/OAI/Analysis/Laughlin/Pair/SpinorCube.lean new file mode 100644 index 0000000000000000000000000000000000000000..6156b2280e1a3ab6592e22f20eba476cbfb7c806 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/SpinorCube.lean @@ -0,0 +1,56 @@ +import OAI.Analysis.Laughlin.Pair.HomogeneousCube +import OAI.Analysis.Laughlin.Polynomial.Polynomial + +namespace OAI + +namespace Laughlin +open Polynomial +open scoped BigOperators + +noncomputable def pairSpinorPolynomial {R : Type*} [CommRing R] + (f : ℂ →+* R) (ui vi uj vj : R) (Q : ℕ) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : R := + ∑ x, ∑ y, f (weightedPairCoordinate Q ψ x y) * + (ui^(Q-x.val) * vi^x.val) * (uj^(Q-y.val) * vj^y.val) + +theorem pairSpinorPolynomial_homogeneousEval {R : Type*} [CommRing R] + (f : ℂ →+* R) (ui vi uj vj : R) (Q : ℕ) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : + pairSpinorPolynomial f ui vi uj vj Q ψ = + homogeneousEval (RingHom.id R) ui vi Q (pairPartialPolynomial f uj vj Q ψ) := by + rw [pairPartialPolynomial_expansion] + simp only [homogeneousEval_sum, pairSpinorPolynomial] + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + rw [homogeneousEval_monomial _ _ _ _ _ (Nat.le_of_lt_succ x.isLt)] + simp only [RingHom.id_apply] + ring + +theorem pairSpinorPolynomial_cube {R : Type*} [CommRing R] [IsDomain R] + (f : ℂ →+* R) (ui vi uj vj : R) (huj : uj ≠ 0) (Q : ℕ) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) + (hc : PairDiagonal.diagonal^3 ∣ pairAffinePolynomial Q ψ) : + (ui*vj-uj*vi)^3 ∣ pairSpinorPolynomial f ui vi uj vj Q ψ := by + have hd := homogeneousEval_dvd (RingHom.id R) ui vi + (pairPartialPolynomial_cube f uj vj Q ψ hc) + (pairPartialPolynomial_degree f uj vj Q ψ) + have hdeg : ((C vj-X*C uj)^3).natDegree = 3 := by + rw [natDegree_pow, linear_natDegree vj uj huj] + rw [hdeg, homogeneousEval_cube _ _ _ _ (by rw [linear_natDegree vj uj huj]), + homogeneousEval_linear] at hd + rw [pairSpinorPolynomial_homogeneousEval] + simpa only [RingHom.id_apply, mul_comm vj ui, mul_comm vi uj] using hd + +theorem pairSpinorPolynomial_bracket_cube {N Q : ℕ} (i j : Fin N) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) + (hc : PairDiagonal.diagonal^3 ∣ pairAffinePolynomial Q ψ) : + bracket i j^3 ∣ pairSpinorPolynomial MvPolynomial.C + (MvPolynomial.X (i,false)) (MvPolynomial.X (i,true)) + (MvPolynomial.X (j,false)) (MvPolynomial.X (j,true)) Q ψ := by + exact pairSpinorPolynomial_cube _ _ _ _ _ (MvPolynomial.X_ne_zero _) Q ψ hc + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/TensorBoundary.lean b/lean/OAI/Analysis/Laughlin/Pair/TensorBoundary.lean new file mode 100644 index 0000000000000000000000000000000000000000..9ac242d70ccd1b8cd52ada995c3c360e089cc9de --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/TensorBoundary.lean @@ -0,0 +1,66 @@ +import OAI.Analysis.Laughlin.Pair.TensorRaise + +namespace OAI + +namespace Laughlin.Spin + +theorem rawPairState_highest (Q i j : ℕ) : + raisePair (rawPairState Q 0) i j = 0 := by + by_cases h : i+j=0 + · have hi : i=0 := by omega + have hj : j=0 := by omega + simp [hi,hj,raisePair,rawPairState,pairPolynomialCoefficient] + · have hi : i+1+j ≠ 0+1 := by omega + have hj : i+(j+1) ≠ 0+1 := by omega + simp [raisePair,rawPairState,hi,hj] + +theorem normalizedPairState_highest (Q i j : ℕ) : + raisePair (normalizedPairState Q 0) i j = 0 := by + have he : raisePair (normalizedPairState Q 0) i j = + raisePair (rawPairState Q 0) i j / pairNormalization Q 0 := by + unfold raisePair normalizedPairState; ring + rw [he,rawPairState_highest,zero_div] + +theorem rawPairState_past_lowest (Q i j : ℕ) (hQ : 0 < Q) + (hi : i ≤ Q) (hj : j ≤ Q) : + rawPairState Q (2*Q-2+1) i j = 0 := by + by_cases h : i+j=2*Q-2+1+1 + · have he : i=j := by omega + simp [rawPairState,pairPolynomialCoefficient,he] + · simp [rawPairState,h] + +theorem normalizedPairState_lowest (Q i j : ℕ) (hQ : 0 < Q) + (hi : i ≤ Q) (hj : j ≤ Q) : + lowerPair Q (normalizedPairState Q (2*Q-2)) i j = 0 := by + unfold normalizedPairState + rw [lowerPair_div,rawPairState_lowering Q (2*Q-2) i j hi hj, + rawPairState_past_lowest Q i j hQ hi hj] + simp + +theorem pairCoefficient_tensor_highest (Q : ℕ) (hQ : 0 < Q) + (x y : Fin (Q+1)) : pairTensorRaise Q 0 x y = 0 := by + have he := pairTensorRaise_weight Q 0 hQ (by omega) x y + rw [normalizedPairState_highest] at he + have hx : Real.sqrt (Q.choose x.val : ℝ) ≠ 0 := by + apply ne_of_gt; apply Real.sqrt_pos.mpr + exact_mod_cast Nat.choose_pos (by omega : x.val ≤ Q) + have hy : Real.sqrt (Q.choose y.val : ℝ) ≠ 0 := by + apply ne_of_gt; apply Real.sqrt_pos.mpr + exact_mod_cast Nat.choose_pos (by omega : y.val ≤ Q) + exact (mul_eq_zero.mp ((mul_eq_zero.mp he).resolve_right hy)).resolve_right hx + +theorem pairCoefficient_tensor_lowest (Q : ℕ) (hQ : 0 < Q) + (x y : Fin (Q+1)) : pairTensorLower Q (2*Q-2) x y = 0 := by + have he := pairTensorLower_weight Q (2*Q-2) hQ (by omega) x y + rw [normalizedPairState_lowest Q x.val y.val hQ (by omega) (by omega)] at he + have hx : Real.sqrt (Q.choose x.val : ℝ) ≠ 0 := by + apply ne_of_gt; apply Real.sqrt_pos.mpr + exact_mod_cast Nat.choose_pos (by omega : x.val ≤ Q) + have hy : Real.sqrt (Q.choose y.val : ℝ) ≠ 0 := by + apply ne_of_gt; apply Real.sqrt_pos.mpr + exact_mod_cast Nat.choose_pos (by omega : y.val ≤ Q) + exact (mul_eq_zero.mp ((mul_eq_zero.mp he).resolve_right hy)).resolve_right hx + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/TensorLower.lean b/lean/OAI/Analysis/Laughlin/Pair/TensorLower.lean new file mode 100644 index 0000000000000000000000000000000000000000..721273dc90fb389ee4bffcbc5fde81d6a46e36b2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/TensorLower.lean @@ -0,0 +1,72 @@ +import OAI.Analysis.Laughlin.Pair.NormalizedLadder +import OAI.Analysis.Laughlin.Spin.Highest2 + +namespace OAI + +namespace Laughlin.Spin + +noncomputable def pairTensorLower (Q p : ℕ) (x y : Fin (Q+1)) : ℝ := + (if h : 0 < x.val then ladder Q (x.val-1) * + pairCoefficient Q p ⟨x.val-1,by omega⟩ y else 0) + + (if h : 0 < y.val then ladder Q (y.val-1) * + pairCoefficient Q p x ⟨y.val-1,by omega⟩ else 0) + +theorem ladder_weight_previous (Q : ℕ) (x : Fin (Q+1)) (hx : 0 < x.val) : + ladder Q (x.val-1)*Real.sqrt (Q.choose x.val : ℝ) = + ((Q : ℝ)-x.val+1)*Real.sqrt (Q.choose (x.val-1) : ℝ) := by + have h := sqrt_choose_step Q (x.val-1) (by omega) + rw [show x.val-1+1=x.val by omega] at h + have hc : ((Q-(x.val-1) : ℕ) : ℝ) = (Q : ℝ)-x.val+1 := by + rw [Nat.cast_sub (by omega : x.val-1 ≤ Q),Nat.cast_sub (by omega : 1 ≤ x.val)] + push_cast; ring + rwa [hc] at h + +theorem pairTensorLower_weight (Q p : ℕ) (hQ : 0 < Q) (hp : p ≤ 2*Q-2) + (x y : Fin (Q+1)) : + pairTensorLower Q p x y * Real.sqrt (Q.choose x.val : ℝ)*Real.sqrt (Q.choose y.val : ℝ) = + lowerPair Q (normalizedPairState Q p) x.val y.val := by + have hl : + (if h : 0 < x.val then ladder Q (x.val-1)*pairCoefficient Q p ⟨x.val-1,by omega⟩ y else 0) * + Real.sqrt (Q.choose x.val : ℝ)*Real.sqrt (Q.choose y.val : ℝ) = + (if 0 < x.val then ((Q : ℝ)-x.val+1)*normalizedPairState Q p (x.val-1) y.val else 0) := by + by_cases hx : 0 < x.val + · rw [dite_eq_left hx,ite_eq_left hx,normalizedPairState_eq_coefficients Q p hQ hp ⟨x.val-1,by omega⟩ y] + calc + _ = pairCoefficient Q p ⟨x.val-1,by omega⟩ y * Real.sqrt (Q.choose y.val : ℝ)* + (ladder Q (x.val-1)*Real.sqrt (Q.choose x.val : ℝ)) := by ring + _ = _ := by rw [ladder_weight_previous Q x hx]; ring + · simp only [dite_eq_right hx,ite_eq_right hx,zero_mul] + have hr : + (if h : 0 < y.val then ladder Q (y.val-1)*pairCoefficient Q p x ⟨y.val-1,by omega⟩ else 0) * + Real.sqrt (Q.choose x.val : ℝ)*Real.sqrt (Q.choose y.val : ℝ) = + (if 0 < y.val then ((Q : ℝ)-y.val+1)*normalizedPairState Q p x.val (y.val-1) else 0) := by + by_cases hy : 0 < y.val + · rw [dite_eq_left hy,ite_eq_left hy,normalizedPairState_eq_coefficients Q p hQ hp x ⟨y.val-1,by omega⟩] + calc + _ = pairCoefficient Q p x ⟨y.val-1,by omega⟩ * Real.sqrt (Q.choose x.val : ℝ)* + (ladder Q (y.val-1)*Real.sqrt (Q.choose y.val : ℝ)) := by ring + _ = _ := by rw [ladder_weight_previous Q y hy]; ring + · simp only [dite_eq_right hy,ite_eq_right hy,zero_mul] + unfold pairTensorLower lowerPair + rw [add_mul,add_mul,hl,hr] + +theorem pairCoefficient_tensor_lowering (Q p : ℕ) (hQ : 0 < Q) (hp : p < 2*Q-2) + (x y : Fin (Q+1)) : + pairTensorLower Q p x y = ladder (2*Q-2) p * pairCoefficient Q (p+1) x y := by + have hx : Real.sqrt (Q.choose x.val : ℝ) ≠ 0 := by + apply ne_of_gt; apply Real.sqrt_pos.mpr + exact_mod_cast Nat.choose_pos (by omega : x.val ≤ Q) + have hy : Real.sqrt (Q.choose y.val : ℝ) ≠ 0 := by + apply ne_of_gt; apply Real.sqrt_pos.mpr + exact_mod_cast Nat.choose_pos (by omega : y.val ≤ Q) + apply (mul_right_cancel₀ hy) + apply (mul_right_cancel₀ hx) + have he := pairTensorLower_weight Q p hQ (by omega) x y + rw [normalizedPairState_lowering Q p x.val y.val hQ hp (by omega) (by omega), + normalizedPairState_eq_coefficients Q (p+1) hQ (by omega) x y] at he + unfold ladder + linear_combination he + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Pair/TensorRaise.lean b/lean/OAI/Analysis/Laughlin/Pair/TensorRaise.lean new file mode 100644 index 0000000000000000000000000000000000000000..d7e646152472878783a156f67a6f529e622b837f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Pair/TensorRaise.lean @@ -0,0 +1,82 @@ +import OAI.Analysis.Laughlin.Pair.PolynomialRaising +import OAI.Analysis.Laughlin.Pair.TensorLower + +namespace OAI + +namespace Laughlin.Spin + +noncomputable def pairTensorRaise (Q p : ℕ) (x y : Fin (Q+1)) : ℝ := + (if h : x.val < Q then ladder Q x.val * + pairCoefficient Q p ⟨x.val+1,by omega⟩ y else 0) + + (if h : y.val < Q then ladder Q y.val * + pairCoefficient Q p x ⟨y.val+1,by omega⟩ else 0) + +theorem ladder_weight_next (Q : ℕ) (x : Fin (Q+1)) (hx : x.val < Q) : + ladder Q x.val*Real.sqrt (Q.choose x.val : ℝ) = + ((x.val : ℝ)+1)*Real.sqrt (Q.choose (x.val+1) : ℝ) := by + have h₀ : Real.sqrt (Q.choose x.val : ℝ) ≠ 0 := by + apply ne_of_gt; apply Real.sqrt_pos.mpr + exact_mod_cast Nat.choose_pos (by omega : x.val ≤ Q) + have h₁ : Real.sqrt (Q.choose (x.val+1) : ℝ) ≠ 0 := by + apply ne_of_gt; apply Real.sqrt_pos.mpr + exact_mod_cast Nat.choose_pos (by omega : x.val+1 ≤ Q) + exact (div_eq_div_iff h₁ h₀).mp (ladder_div_sqrt_choose Q x.val hx) + +theorem normalizedPairState_out_left (Q p i j : ℕ) (hi : Q < i) : + normalizedPairState Q p i j = 0 := by + simp [normalizedPairState,rawPairState,pairPolynomialCoefficient,Nat.choose_eq_zero_of_lt hi] + +theorem normalizedPairState_out_right (Q p i j : ℕ) (hj : Q < j) : + normalizedPairState Q p i j = 0 := by + simp [normalizedPairState,rawPairState,pairPolynomialCoefficient,Nat.choose_eq_zero_of_lt hj] + +theorem pairTensorRaise_weight (Q p : ℕ) (hQ : 0 < Q) (hp : p ≤ 2*Q-2) + (x y : Fin (Q+1)) : + pairTensorRaise Q p x y * Real.sqrt (Q.choose x.val : ℝ)*Real.sqrt (Q.choose y.val : ℝ) = + raisePair (normalizedPairState Q p) x.val y.val := by + have hl : + (if h : x.val < Q then ladder Q x.val*pairCoefficient Q p ⟨x.val+1,by omega⟩ y else 0) * + Real.sqrt (Q.choose x.val : ℝ)*Real.sqrt (Q.choose y.val : ℝ) = + ((x.val : ℝ)+1)*normalizedPairState Q p (x.val+1) y.val := by + by_cases hx : x.val < Q + · rw [dite_eq_left hx,normalizedPairState_eq_coefficients Q p hQ hp ⟨x.val+1,by omega⟩ y] + calc + _ = pairCoefficient Q p ⟨x.val+1,by omega⟩ y * Real.sqrt (Q.choose y.val : ℝ)* + (ladder Q x.val*Real.sqrt (Q.choose x.val : ℝ)) := by ring + _ = _ := by rw [ladder_weight_next Q x hx]; ring + · rw [dite_eq_right hx,normalizedPairState_out_left Q p (x.val+1) y.val (by omega)] + ring + have hr : + (if h : y.val < Q then ladder Q y.val*pairCoefficient Q p x ⟨y.val+1,by omega⟩ else 0) * + Real.sqrt (Q.choose x.val : ℝ)*Real.sqrt (Q.choose y.val : ℝ) = + ((y.val : ℝ)+1)*normalizedPairState Q p x.val (y.val+1) := by + by_cases hy : y.val < Q + · rw [dite_eq_left hy,normalizedPairState_eq_coefficients Q p hQ hp x ⟨y.val+1,by omega⟩] + calc + _ = pairCoefficient Q p x ⟨y.val+1,by omega⟩ * Real.sqrt (Q.choose x.val : ℝ)* + (ladder Q y.val*Real.sqrt (Q.choose y.val : ℝ)) := by ring + _ = _ := by rw [ladder_weight_next Q y hy]; ring + · rw [dite_eq_right hy,normalizedPairState_out_right Q p x.val (y.val+1) (by omega)] + ring + unfold pairTensorRaise raisePair + rw [add_mul,add_mul,hl,hr] + +theorem pairCoefficient_tensor_raising (Q p : ℕ) (hQ : 0 < Q) (hp : p < 2*Q-2) + (x y : Fin (Q+1)) : + pairTensorRaise Q (p+1) x y = ladder (2*Q-2) p * pairCoefficient Q p x y := by + have hx : Real.sqrt (Q.choose x.val : ℝ) ≠ 0 := by + apply ne_of_gt; apply Real.sqrt_pos.mpr + exact_mod_cast Nat.choose_pos (by omega : x.val ≤ Q) + have hy : Real.sqrt (Q.choose y.val : ℝ) ≠ 0 := by + apply ne_of_gt; apply Real.sqrt_pos.mpr + exact_mod_cast Nat.choose_pos (by omega : y.val ≤ Q) + apply (mul_right_cancel₀ hy) + apply (mul_right_cancel₀ hx) + have he := pairTensorRaise_weight Q (p+1) hQ (by omega) x y + rw [normalizedPairState_raising Q p x.val y.val hQ hp (by omega) (by omega), + normalizedPairState_eq_coefficients Q p hQ (by omega) x y] at he + linear_combination he + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Planar/DegreeRestriction.lean b/lean/OAI/Analysis/Laughlin/Planar/DegreeRestriction.lean new file mode 100644 index 0000000000000000000000000000000000000000..1c1be7e21fda15401b19fe7cf6e3efe221917eec --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Planar/DegreeRestriction.lean @@ -0,0 +1,218 @@ +import OAI.Analysis.Laughlin.Fock.ModeEmbedding +import OAI.Analysis.Laughlin.Fock.Hamiltonian +import OAI.Analysis.Laughlin.Planar.Model + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem sum_fin_castLE_of_high_zero {R : Type*} [AddCommMonoid R] + (L Q : ℕ) (h : L ≤ Q) (f : Fin (Q+1) → R) + (hf : ∀ i, L < i.val → f i = 0) : + (∑ i, f i) = ∑ i : Fin (L+1), f (Fin.castLE (Nat.add_le_add_right h 1) i) := by + classical + let e := Fin.castLEEmb (Nat.add_le_add_right h 1) + have hz : ∑ i ∈ Finset.univ.map e, f i = ∑ i : Fin (Q+1), f i := by + apply Finset.sum_subset (Finset.subset_univ _) + intro i hi hin + apply hf + by_contra hh + have hiL : i.val ≤ L := by omega + apply hin + exact Finset.mem_map.mpr ⟨⟨i.val,by omega⟩,Finset.mem_univ _,Fin.ext rfl⟩ + rw [← hz,Finset.sum_map] + rfl + +theorem pairEnd_fockInclusion (L Q : ℕ) (h : L ≤ Q) + (c : Fin (Q+1) → Fin (Q+1) → ℂ) (x : Space L) : + pairEnd Q c (fockInclusion L Q h x) = + fockInclusion L Q h (pairEnd L + (fun i j => c (Fin.castLE (Nat.add_le_add_right h 1) i) + (Fin.castLE (Nat.add_le_add_right h 1) j)) x) := by + simp only [pairEnd,LinearMap.sum_apply,LinearMap.smul_apply,Module.End.mul_apply,map_sum,map_smul] + rw [sum_fin_castLE_of_high_zero L Q h _ (by + intro i hi + simp [fockInclusion_annihilate_high L Q h i hi])] + apply Finset.sum_congr rfl + intro i hi + rw [sum_fin_castLE_of_high_zero L Q h _ (by + intro j hj + rw [fockInclusion_annihilate] + simp [fockInclusion_annihilate_high L Q h j hj])] + apply Finset.sum_congr rfl + intro j hj + rw [fockInclusion_annihilate,fockInclusion_annihilate] + +theorem pairCreateEnd_fockInclusion (L Q : ℕ) (h : L ≤ Q) + (c : Fin (Q+1) → Fin (Q+1) → ℂ) + (hc : ∀ i j, L < i.val ∨ L < j.val → c i j = 0) (x : Space L) : + pairCreateEnd Q c (fockInclusion L Q h x) = + fockInclusion L Q h (pairCreateEnd L + (fun i j => c (Fin.castLE (Nat.add_le_add_right h 1) i) + (Fin.castLE (Nat.add_le_add_right h 1) j)) x) := by + simp only [pairCreateEnd,LinearMap.sum_apply,LinearMap.smul_apply,Module.End.mul_apply, + map_sum,map_smul] + rw [sum_fin_castLE_of_high_zero L Q h _ (by + intro i hi + simp only [hc i _ (Or.inl hi),star_zero,zero_smul,Finset.sum_const_zero])] + apply Finset.sum_congr rfl + intro i hi + rw [sum_fin_castLE_of_high_zero L Q h _ (by + intro j hj + simp only [hc _ j (Or.inr hj),star_zero,zero_smul])] + apply Finset.sum_congr rfl + intro j hj + rw [← fockInclusion_create,← fockInclusion_create] + +def DegreeAtMost (Q d : ℕ) (x : Space Q) : Prop := + ∀ A : Finset (Fin (Q+1)), d < ∑ i ∈ A, i.val → (occupationBasis Q).repr x A = 0 + +theorem two_mem_weight_le (Q : ℕ) (A : Finset (Fin (Q+1))) (i j : Fin (Q+1)) + (hi : i ∈ A) (hj : j ∈ A) (hij : i ≠ j) : + i.val+j.val ≤ ∑ k ∈ A, k.val := by + have hs : ({i,j} : Finset (Fin (Q+1))) ⊆ A := by + intro k hk + rcases Finset.mem_insert.mp hk with hk | hk + · simpa only [hk] using hi + · have he := Finset.mem_singleton.mp hk + simpa only [he] using hj + have hsum := Finset.sum_le_sum_of_subset_of_nonneg hs + (fun k hk hnot => Nat.zero_le k.val) + simpa [hij] using hsum + +theorem pair_annihilate_high_degree (Q d : ℕ) (x : Space Q) (hx : DegreeAtMost Q d x) + (i j : Fin (Q+1)) (hij : d < i.val+j.val) : + annihilate j (annihilate i x) = 0 := by + by_cases he : i=j + · subst j + exact LinearMap.congr_fun (annihilate_sq i) x + conv_lhs => rw [← (occupationBasis Q).sum_repr x] + simp only [map_sum,map_smul] + apply Finset.sum_eq_zero + intro A hA + by_cases hd : d < ∑ k ∈ A, k.val + · rw [hx A hd,zero_smul] + by_cases hi : i ∈ A + · rw [annihilate_occupied Q i A hi,map_smul] + have hj : j ∉ A.erase i := by + intro hj + have hjA := (Finset.mem_erase.mp hj).2 + have hh := two_mem_weight_le Q A i j hi hjA he + omega + rw [annihilate_unoccupied Q j (A.erase i) hj,smul_zero,smul_zero] + · rw [annihilate_unoccupied Q i A hi,map_zero,smul_zero] + +theorem pairEnd_high_degree (Q d p : ℕ) (x : Space Q) (hx : DegreeAtMost Q d x) + (hp : d < p+1) (c : Fin (Q+1) → Fin (Q+1) → ℂ) + (hc : ∀ i j, i.val+j.val ≠ p+1 → c i j = 0) : pairEnd Q c x = 0 := by + simp only [pairEnd,LinearMap.sum_apply,LinearMap.smul_apply,Module.End.mul_apply] + apply Finset.sum_eq_zero + intro i hi + apply Finset.sum_eq_zero + intro j hj + by_cases he : i.val+j.val=p+1 + · rw [pair_annihilate_high_degree Q d x hx i j (by omega),smul_zero] + · rw [hc i j he,zero_smul] + +noncomputable def restrictedSpherePairEnd (L Q p : ℕ) : Module.End ℂ (Space L) := + pairEnd L (fun i j => Planar.sphereCoefficient Q p i.val j.val) + +noncomputable def restrictedSpherePairCreateEnd (L Q p : ℕ) : Module.End ℂ (Space L) := + pairCreateEnd L (fun i j => Planar.sphereCoefficient Q p i.val j.val) + +noncomputable def restrictedSphereHamiltonian (L Q : ℕ) : Module.End ℂ (Space L) := + ∑ p ∈ Finset.range (2*L+1), restrictedSpherePairCreateEnd L Q p * restrictedSpherePairEnd L Q p + +noncomputable def restrictedSphereEnergy (L Q : ℕ) (x : Space L) : ℝ := + ∑ p ∈ Finset.range (2*L+1), occupationNormSq L (restrictedSpherePairEnd L Q p x) + +theorem sourcePairEnd_fockInclusion (L Q p : ℕ) (h : L ≤ Q) + (hQ : 0 < Q) (hp : p ≤ 2*Q-2) (x : Space L) : + sourcePairEnd Q p (fockInclusion L Q h x) = + fockInclusion L Q h (restrictedSpherePairEnd L Q p x) := by + unfold sourcePairEnd + rw [pairEnd_fockInclusion] + unfold restrictedSpherePairEnd + congr 2 + congr 1 + funext i j + exact (Planar.sphereCoefficient_eq Q p hQ hp + (Fin.castLE (Nat.add_le_add_right h 1) i) (Fin.castLE (Nat.add_le_add_right h 1) j)).symm + +theorem restrictedSpherePairEnd_high_degree (L Q d p : ℕ) (x : Space L) + (hx : DegreeAtMost L d x) (hp : d < p+1) : restrictedSpherePairEnd L Q p x = 0 := by + apply pairEnd_high_degree L d p x hx hp + intro i j hij + simp [Planar.sphereCoefficient,pairLimitCoefficient,hij] + +theorem sourcePairCreateEnd_fockInclusion (L Q p : ℕ) (h : L ≤ Q) + (hQ : 0 < Q) (hp : p+1 ≤ L) (x : Space L) : + sourcePairCreateEnd Q p (fockInclusion L Q h x) = + fockInclusion L Q h (restrictedSpherePairCreateEnd L Q p x) := by + have hpQ : p ≤ 2*Q-2 := by omega + unfold sourcePairCreateEnd + rw [pairCreateEnd_fockInclusion L Q h _ (by + intro i j hij + have hne : i.val+j.val ≠ p+1 := by rcases hij with hi | hj <;> omega + simp [pairCoefficient,hne])] + unfold restrictedSpherePairCreateEnd + congr 2 + congr 1 + funext i j + exact (Planar.sphereCoefficient_eq Q p hQ hpQ + (Fin.castLE (Nat.add_le_add_right h 1) i) (Fin.castLE (Nat.add_le_add_right h 1) j)).symm + +theorem sum_range_eq_short {M : Type*} [AddCommMonoid M] (n m : ℕ) (hnm : n ≤ m) + (f : ℕ → M) (hf : ∀ k, n ≤ k → k < m → f k = 0) : + (∑ k ∈ Finset.range m, f k) = ∑ k ∈ Finset.range n, f k := by + symm + apply Finset.sum_subset (Finset.range_mono hnm) + intro k hk hkn + exact hf k (by simpa using hkn) (Finset.mem_range.mp hk) + +theorem sourceFockHamiltonian_fockInclusion (L Q : ℕ) (hQ : L+2 ≤ Q) + (x : Space L) (hx : DegreeAtMost L L x) : + sourceFockHamiltonian Q (fockInclusion L Q (by omega) x) = + fockInclusion L Q (by omega) (restrictedSphereHamiltonian L Q x) := by + have h : L ≤ Q := by omega + have hsource (p : ℕ) (hp : L ≤ p) (hpQ : p < 2*Q-1) : + sourcePairEnd Q p (fockInclusion L Q h x) = 0 := by + rw [sourcePairEnd_fockInclusion L Q p h (by omega) (by omega), + restrictedSpherePairEnd_high_degree L Q L p x hx (by omega),map_zero] + simp only [sourceFockHamiltonian,restrictedSphereHamiltonian,LinearMap.sum_apply, + Module.End.mul_apply,map_sum] + rw [sum_range_eq_short L (2*Q-1) (by omega) _ (by + intro p hp hpQ + rw [hsource p hp hpQ,map_zero])] + rw [sum_range_eq_short L (2*L+1) (by omega) _ (by + intro p hp hpL + rw [restrictedSpherePairEnd_high_degree L Q L p x hx (by omega),map_zero,map_zero])] + apply Finset.sum_congr rfl + intro p hp + have hpL := Finset.mem_range.mp hp + rw [sourcePairEnd_fockInclusion L Q p h (by omega) (by omega), + sourcePairCreateEnd_fockInclusion L Q p h (by omega) (by omega)] + +theorem sourceFockEnergy_fockInclusion (L Q : ℕ) (hQ : L+2 ≤ Q) + (x : Space L) (hx : DegreeAtMost L L x) : + sourceFockEnergy Q (fockInclusion L Q (by omega) x) = restrictedSphereEnergy L Q x := by + have h : L ≤ Q := by omega + unfold sourceFockEnergy restrictedSphereEnergy + rw [sum_range_eq_short L (2*Q-1) (by omega) _ (by + intro p hp hpQ + rw [sourcePairEnd_fockInclusion L Q p h (by omega) (by omega), + restrictedSpherePairEnd_high_degree L Q L p x hx (by omega),map_zero] + simp [occupationNormSq])] + rw [sum_range_eq_short L (2*L+1) (by omega) _ (by + intro p hp hpL + rw [restrictedSpherePairEnd_high_degree L Q L p x hx (by omega)] + simp [occupationNormSq])] + apply Finset.sum_congr rfl + intro p hp + have hpL := Finset.mem_range.mp hp + rw [sourcePairEnd_fockInclusion L Q p h (by omega) (by omega),fockInclusion_normSq] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Planar/Forms.lean b/lean/OAI/Analysis/Laughlin/Planar/Forms.lean new file mode 100644 index 0000000000000000000000000000000000000000..cc0dc091887ffcc08697fccb5ce1561fbea2fc17 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Planar/Forms.lean @@ -0,0 +1,45 @@ +import OAI.Analysis.Laughlin.Planar.Restriction +import OAI.Analysis.Laughlin.Fock.Bidegree +import Mathlib.Topology.Algebra.InfiniteSum.ENNReal + +namespace OAI + +namespace Laughlin.Planar +open Fock +open scoped BigOperators ENNReal + +structure HomogeneousState (N : ℕ) where + block : (L : ℕ) → Space L + homogeneous : ∀ L, OccupationBidegree L N L (block L) + +noncomputable def fullNormSq {N : ℕ} (ψ : HomogeneousState N) : ℝ≥0∞ := + ∑' L, ENNReal.ofReal (occupationNormSq L (ψ.block L)) + +def IsHilbertState {N : ℕ} (ψ : HomogeneousState N) : Prop := fullNormSq ψ < ⊤ + +noncomputable def fullEnergy {N : ℕ} (ψ : HomogeneousState N) : ℝ≥0∞ := + ∑' L, ENNReal.ofReal (pairEnergy L (planarPairMatrix L) + (fun A => (occupationBasis L).repr (ψ.block L) A)) + +noncomputable def fullSquareNorm {N : ℕ} (ψ : HomogeneousState N) : ℝ≥0∞ := + ∑' L, ENNReal.ofReal (squareNorm L (planarHamiltonian L) + (fun A => (occupationBasis L).repr (ψ.block L) A)) + +theorem full_planar_endpoint {N : ℕ} (ψ : HomogeneousState N) : + ENNReal.ofReal gammaStar * fullEnergy ψ ≤ fullSquareNorm ψ := by + unfold fullEnergy fullSquareNorm + rw [← ENNReal.tsum_mul_left] + apply ENNReal.tsum_le_tsum + intro L + have hd : DegreeAtMost L L (ψ.block L) := by + intro A hA + exact ψ.homogeneous L A (Or.inr (ne_of_gt hA)) + have h := finite_degree_endpoint L (ψ.block L) hd + have hγ : 0 ≤ gammaStar := + le_of_lt (lt_trans (by norm_num : (0 : ℝ) < 1/25) one_twenty_fifth_lt_gammaStar) + rw [← ENNReal.ofReal_mul hγ] + exact ENNReal.ofReal_le_ofReal h + +end Laughlin.Planar + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Planar/Model.lean b/lean/OAI/Analysis/Laughlin/Planar/Model.lean new file mode 100644 index 0000000000000000000000000000000000000000..dee990c6af7853cbda135337af0e8a79b1131ab0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Planar/Model.lean @@ -0,0 +1,130 @@ +import OAI.Analysis.Laughlin.Pair.FactorLimit +import OAI.Analysis.Laughlin.Fock.Hamiltonian +import Mathlib.Topology.Instances.Matrix + +namespace OAI + +namespace Laughlin.Planar +open Fock Filter +open scoped BigOperators Topology Matrix + +abbrev Occupations (L : ℕ) := Finset (Fin (L+1)) + +noncomputable def pairMatrix (L : ℕ) (c : Fin (L+1) → Fin (L+1) → ℂ) : + Matrix (Occupations L) (Occupations L) ℂ := fun A B => + ∑ i, ∑ j, c i j * (occupationBasis L).repr + (annihilate j (annihilate i (occupationBasis L B))) A + +noncomputable def planarCoefficient (p i j : ℕ) : ℂ := + ((pairLimitCoefficient p i j / Real.sqrt (2 : ℕ) : ℝ) : ℂ) + +noncomputable def sphereCoefficient (Q p i j : ℕ) : ℂ := + ((modeFactor Q i * modeFactor Q j * pairFactor Q p * + pairLimitCoefficient p i j / Real.sqrt 2 : ℝ) : ℂ) + +theorem sphereCoefficient_eq (Q p : ℕ) (hQ : 0 < Q) (hp : p ≤ 2*Q-2) + (i j : Fin (Q+1)) : + sphereCoefficient Q p i.val j.val = ((pairCoefficient Q p i j / Real.sqrt 2 : ℝ) : ℂ) := by + rw [sphereCoefficient,pairCoefficient_conjugation Q p hQ hp] + +theorem sphereCoefficient_tendsto (p i j : ℕ) : + Tendsto (fun Q => sphereCoefficient Q p i j) atTop (𝓝 (planarCoefficient p i j)) := by + have h := ((((modeFactor_tendsto i).mul (modeFactor_tendsto j)).mul + (pairFactor_tendsto p)).mul_const (pairLimitCoefficient p i j)).div_const (Real.sqrt 2) + simpa only [one_mul,sphereCoefficient,planarCoefficient,Nat.cast_ofNat,Function.comp_def] using + Complex.continuous_ofReal.continuousAt.tendsto.comp h + +noncomputable def planarPairMatrix (L p : ℕ) : Matrix (Occupations L) (Occupations L) ℂ := + pairMatrix L (fun i j => planarCoefficient p i.val j.val) + +noncomputable def spherePairMatrix (L Q p : ℕ) : Matrix (Occupations L) (Occupations L) ℂ := + pairMatrix L (fun i j => sphereCoefficient Q p i.val j.val) + +theorem spherePairMatrix_tendsto (L p : ℕ) (A B : Occupations L) : + Tendsto (fun Q => spherePairMatrix L Q p A B) atTop + (𝓝 (planarPairMatrix L p A B)) := by + unfold spherePairMatrix planarPairMatrix pairMatrix + apply tendsto_finsetSum + intro i hi + apply tendsto_finsetSum + intro j hj + exact (sphereCoefficient_tendsto p i.val j.val).mul_const _ + +noncomputable def planarHamiltonian (L : ℕ) : Matrix (Occupations L) (Occupations L) ℂ := + ∑ p ∈ Finset.range (2*L+1), (planarPairMatrix L p)ᴴ * planarPairMatrix L p + +noncomputable def sphereHamiltonian (L Q : ℕ) : Matrix (Occupations L) (Occupations L) ℂ := + ∑ p ∈ Finset.range (2*L+1), (spherePairMatrix L Q p)ᴴ * spherePairMatrix L Q p + +theorem sphereHamiltonian_tendsto (L : ℕ) (A B : Occupations L) : + Tendsto (fun Q => sphereHamiltonian L Q A B) atTop (𝓝 (planarHamiltonian L A B)) := by + simp only [sphereHamiltonian,planarHamiltonian,Matrix.sum_apply,Matrix.mul_apply, + Matrix.conjTranspose_apply] + apply tendsto_finsetSum + intro p hp + apply tendsto_finsetSum + intro C hC + exact ((spherePairMatrix_tendsto L p C A).star).mul (spherePairMatrix_tendsto L p C B) + +noncomputable def pairEnergy (L : ℕ) + (P : ℕ → Matrix (Occupations L) (Occupations L) ℂ) (x : Occupations L → ℂ) : ℝ := + ∑ p ∈ Finset.range (2*L+1), ∑ A, ‖(P p *ᵥ x) A‖^2 + +noncomputable def squareNorm (L : ℕ) (H : Matrix (Occupations L) (Occupations L) ℂ) + (x : Occupations L → ℂ) : ℝ := ∑ A, ‖(H *ᵥ x) A‖^2 + +theorem sphere_pairEnergy_tendsto (L : ℕ) (x : Occupations L → ℂ) : + Tendsto (fun Q => pairEnergy L (spherePairMatrix L Q) x) atTop + (𝓝 (pairEnergy L (planarPairMatrix L) x)) := by + unfold pairEnergy + apply tendsto_finsetSum + intro p hp + apply tendsto_finsetSum + intro A hA + apply Filter.Tendsto.pow + apply Filter.Tendsto.norm + simp only [Matrix.mulVec,dotProduct] + apply tendsto_finsetSum + intro B hB + exact (spherePairMatrix_tendsto L p A B).mul_const (x B) + +theorem sphere_squareNorm_tendsto (L : ℕ) (x : Occupations L → ℂ) : + Tendsto (fun Q => squareNorm L (sphereHamiltonian L Q) x) atTop + (𝓝 (squareNorm L (planarHamiltonian L) x)) := by + unfold squareNorm + apply tendsto_finsetSum + intro A hA + apply Filter.Tendsto.pow + apply Filter.Tendsto.norm + simp only [Matrix.mulVec,dotProduct] + apply tendsto_finsetSum + intro B hB + exact (sphereHamiltonian_tendsto L A B).mul_const (x B) + +theorem endpoint_of_sphere_blocks (L : ℕ) (γstar : ℝ) (hγstar : 0 < γstar) + (x : Occupations L → ℂ) + (hSphere : ∀ γ : ℝ, 0 < γ → γ < γstar → ∀ᶠ Q : ℕ in atTop, + γ * pairEnergy L (spherePairMatrix L Q) x ≤ squareNorm L (sphereHamiltonian L Q) x) : + γstar * pairEnergy L (planarPairMatrix L) x ≤ squareNorm L (planarHamiltonian L) x := by + have hGap (γ : ℝ) (hγ : 0 < γ) (hγ' : γ < γstar) : + γ * pairEnergy L (planarPairMatrix L) x ≤ squareNorm L (planarHamiltonian L) x := + le_of_tendsto_of_tendsto ((sphere_pairEnergy_tendsto L x).const_mul γ) + (sphere_squareNorm_tendsto L x) (hSphere γ hγ hγ') + by_contra hn + have hlt : squareNorm L (planarHamiltonian L) x < + γstar * pairEnergy L (planarPairMatrix L) x := lt_of_not_ge hn + have hE : 0 < pairEnergy L (planarPairMatrix L) x := by + have hS : 0 ≤ squareNorm L (planarHamiltonian L) x := + Finset.sum_nonneg (fun A hA => sq_nonneg _) + nlinarith + obtain ⟨γ,hγ,hγ'⟩ := exists_between (div_lt_iff₀ hE |>.mpr hlt) + have hS : 0 ≤ squareNorm L (planarHamiltonian L) x := + Finset.sum_nonneg (fun A hA => sq_nonneg _) + have hγpos : 0 < γ := lt_of_le_of_lt (div_nonneg hS hE.le) hγ + have hc := hGap γ hγpos hγ' + have hd := (div_lt_iff₀ hE).mp hγ + linarith + +end Laughlin.Planar + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Planar/Restriction.lean b/lean/OAI/Analysis/Laughlin/Planar/Restriction.lean new file mode 100644 index 0000000000000000000000000000000000000000..f12b5d9b21742c8f117647b24e28482387b62071 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Planar/Restriction.lean @@ -0,0 +1,87 @@ +import OAI.Analysis.Laughlin.Planar.DegreeRestriction +import OAI.Analysis.Laughlin.Fock.SharpGap +import Mathlib.LinearAlgebra.Matrix.ToLin + +namespace OAI + +namespace Laughlin.Planar +open Fock Filter +open scoped BigOperators Topology Matrix + +theorem pairMatrix_toMatrix (L : ℕ) (c : Fin (L+1) → Fin (L+1) → ℂ) : + pairMatrix L c = LinearMap.toMatrix (occupationBasis L) (occupationBasis L) (pairEnd L c) := by + ext A B + simp only [pairMatrix,LinearMap.toMatrix_apply,pairEnd,LinearMap.sum_apply, + LinearMap.smul_apply,Module.End.mul_apply,map_sum,Finsupp.finsetSum_apply, + map_smul,Finsupp.smul_apply,smul_eq_mul] + +theorem occupationInner_basis_left (L : ℕ) (A : Occupations L) (x : Space L) : + occupationInner L (occupationBasis L A) x = (occupationBasis L).repr x A := by + simp [occupationInner,Module.Basis.repr_self,Finsupp.single_apply] + +theorem occupationInner_basis_right (L : ℕ) (A : Occupations L) (x : Space L) : + occupationInner L x (occupationBasis L A) = star ((occupationBasis L).repr x A) := by + simp [occupationInner,Module.Basis.repr_self,Finsupp.single_apply] + +theorem pairCreateMatrix_toMatrix (L : ℕ) (c : Fin (L+1) → Fin (L+1) → ℂ) : + (pairMatrix L c)ᴴ = + LinearMap.toMatrix (occupationBasis L) (occupationBasis L) (pairCreateEnd L c) := by + rw [pairMatrix_toMatrix] + ext A B + simp only [Matrix.conjTranspose_apply,LinearMap.toMatrix_apply] + have h := pairCreate_pair_adjoint L c (occupationBasis L B) (occupationBasis L A) + rw [occupationInner_basis_left,occupationInner_basis_right] at h + simpa only [star_star] using (congrArg star h).symm + +theorem sphereHamiltonian_toMatrix (L Q : ℕ) : + sphereHamiltonian L Q = LinearMap.toMatrix (occupationBasis L) (occupationBasis L) + (restrictedSphereHamiltonian L Q) := by + unfold sphereHamiltonian restrictedSphereHamiltonian + rw [map_sum] + apply Finset.sum_congr rfl + intro p hp + rw [LinearMap.toMatrix_mul] + change (pairMatrix L _)ᴴ * pairMatrix L _ = _ + rw [pairCreateMatrix_toMatrix,pairMatrix_toMatrix] + rfl + +theorem sphere_pairEnergy_eq (L Q : ℕ) (x : Space L) : + pairEnergy L (spherePairMatrix L Q) (fun A => (occupationBasis L).repr x A) = + restrictedSphereEnergy L Q x := by + unfold pairEnergy restrictedSphereEnergy + apply Finset.sum_congr rfl + intro p hp + change (∑ A, ‖(pairMatrix L _ *ᵥ fun B => (occupationBasis L).repr x B) A‖^2) = _ + rw [pairMatrix_toMatrix,LinearMap.toMatrix_mulVec_repr] + rfl + +theorem sphere_squareNorm_eq (L Q : ℕ) (x : Space L) : + squareNorm L (sphereHamiltonian L Q) (fun A => (occupationBasis L).repr x A) = + occupationNormSq L (restrictedSphereHamiltonian L Q x) := by + rw [squareNorm,sphereHamiltonian_toMatrix,LinearMap.toMatrix_mulVec_repr] + rfl + +theorem finite_degree_endpoint_of_fock_square (γstar : ℝ) (hγstar : 0 < γstar) + (hSphere : ∀ γ : ℝ, 0 < γ → γ < γstar → ∀ᶠ Q : ℕ in atTop, + ∀ x : Space Q, γ * sourceFockEnergy Q x ≤ occupationNormSq Q (sourceFockHamiltonian Q x)) + (L : ℕ) (x : Space L) (hx : DegreeAtMost L L x) : + γstar * pairEnergy L (planarPairMatrix L) (fun A => (occupationBasis L).repr x A) ≤ + squareNorm L (planarHamiltonian L) (fun A => (occupationBasis L).repr x A) := by + apply endpoint_of_sphere_blocks L γstar hγstar + intro γ hγ hγstar' + filter_upwards [hSphere γ hγ hγstar',eventually_ge_atTop (L+2)] with Q hs hQ + have h := hs (fockInclusion L Q (by omega) x) + rw [sourceFockEnergy_fockInclusion L Q hQ x hx, + sourceFockHamiltonian_fockInclusion L Q hQ x hx,fockInclusion_normSq] at h + simpa only [sphere_pairEnergy_eq,sphere_squareNorm_eq] using h + +theorem finite_degree_endpoint (L : ℕ) (x : Space L) (hx : DegreeAtMost L L x) : + gammaStar * pairEnergy L (planarPairMatrix L) (fun A => (occupationBasis L).repr x A) ≤ + squareNorm L (planarHamiltonian L) (fun A => (occupationBasis L).repr x A) := by + apply finite_degree_endpoint_of_fock_square gammaStar + (lt_trans (by norm_num : (0 : ℝ) < 1/25) one_twenty_fifth_lt_gammaStar) + (fun γ _hγ hγstar => physical_fock_square_eventually_sharp γ hγstar) L x hx + +end Laughlin.Planar + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/AntisymmetricCoordinates.lean b/lean/OAI/Analysis/Laughlin/Polynomial/AntisymmetricCoordinates.lean new file mode 100644 index 0000000000000000000000000000000000000000..fee87f9abccf1c940073d66eab70bdb52bda1cdb --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/AntisymmetricCoordinates.lean @@ -0,0 +1,68 @@ +import OAI.Analysis.Laughlin.Pair.CoupledParity + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +abbrev WedgePairIndex (Q : ℕ) := {i : SpinIndex Q Q // i.1 < i.2} + +noncomputable def tensorToWedgePair (Q : ℕ) (f : SpinIndex Q Q → ℝ) : + WedgePairIndex Q → ℝ := fun i => Real.sqrt 2 * f i.val + +theorem antisymmetric_pairing (Q : ℕ) (f g : SpinIndex Q Q → ℝ) + (hf : ∀ i j, f (j,i) = -f (i,j)) (hg : ∀ i j, g (j,i) = -g (i,j)) : + (∑ i : WedgePairIndex Q, tensorToWedgePair Q f i * tensorToWedgePair Q g i) = + ∑ i, f i * g i := by + have hd (i : Fin (Q+1)) : f (i,i) = 0 := by have h := hf i i; linarith + have he (i j : Fin (Q+1)) : f (i,j)*g (i,j) = + (if i < j then f (i,j)*g (i,j) else 0) + + (if j < i then f (j,i)*g (j,i) else 0) := by + rcases lt_trichotomy i j with h | h | h + · simp [h,not_lt_of_gt h] + · subst j; simp [hd] + · simp [h,not_lt_of_gt h,hf i j,hg i j] + have hs : (∑ i, f i*g i) = 2 * ∑ i : SpinIndex Q Q, if i.1 < i.2 then f i*g i else 0 := by + calc + _ = ∑ i : Fin (Q+1), ∑ j : Fin (Q+1), + ((if i < j then f (i,j)*g (i,j) else 0) + + (if j < i then f (j,i)*g (j,i) else 0)) := by + rw [Fintype.sum_prod_type] + apply Finset.sum_congr rfl; intro i hi + apply Finset.sum_congr rfl; intro j hj + exact he i j + _ = _ := by + simp only [Finset.sum_add_distrib,Fintype.sum_prod_type] + rw [Finset.sum_comm (f := fun i j : Fin (Q+1) => if j < i then f (j,i)*g (j,i) else 0)] + ring + rw [hs] + simp only [tensorToWedgePair] + have hm (i : WedgePairIndex Q) : + Real.sqrt 2*f i.val*(Real.sqrt 2*g i.val) = 2*(f i.val*g i.val) := by + have h : Real.sqrt 2 * Real.sqrt 2 = 2 := Real.mul_self_sqrt (by norm_num) + calc + _ = (Real.sqrt 2 * Real.sqrt 2) * (f i.val * g i.val) := by ring + _ = _ := by rw [h] + simp_rw [hm] + rw [← Finset.mul_sum] + congr 1 + rw [← Finset.sum_filter] + exact (Finset.sum_subtype (Finset.univ.filter (fun i : SpinIndex Q Q => i.1 < i.2)) (by simp) (fun i => f i*g i)).symm + +theorem tensorToWedgePair_norm (Q : ℕ) (f : SpinIndex Q Q → ℝ) + (hf : ∀ i j, f (j,i) = -f (i,j)) : + vectorNormSq (tensorToWedgePair Q f) = vectorNormSq f := by + simpa only [vectorNormSq,pow_two] using antisymmetric_pairing Q f f hf hf + +noncomputable def pairCoupledWedge (Q r : ℕ) (hr : r ≤ Q) (n : ℕ) : WedgePairIndex Q → ℝ := + tensorToWedgePair Q (pairCoupledTensor Q r hr n) + +theorem pairCoupledWedge_norm (Q r n : ℕ) (hr : r ≤ Q) (ho : Odd r) + (hn : n ≤ genericCoupledWeight Q Q r) : + vectorNormSq (pairCoupledWedge Q r hr n) = 1 := by + rw [pairCoupledWedge,tensorToWedgePair_norm Q _ (pairCoupledTensor_antisymmetric Q r n hr ho)] + exact pairCoupledTensor_norm Q r n hr hn + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/BracketCoprime.lean b/lean/OAI/Analysis/Laughlin/Polynomial/BracketCoprime.lean new file mode 100644 index 0000000000000000000000000000000000000000..972ca70f157cd790ca7e24fd6a30bbb6ea3cf5ce --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/BracketCoprime.lean @@ -0,0 +1,52 @@ +import OAI.Analysis.Laughlin.Polynomial.BracketIrreducible + +namespace OAI + +namespace Laughlin +open MvPolynomial + +theorem pair_outside_endpoint {N : ℕ} (i j k l : Fin N) (hij : i < j) (hkl : k < l) + (hne : (i,j) ≠ (k,l)) : (k ≠ i ∧ k ≠ j) ∨ (l ≠ i ∧ l ≠ j) := by + by_cases hk : k = i ∨ k = j + · right + rcases hk with rfl | rfl + · constructor + · exact ne_of_gt hkl + · intro h + subst l + exact hne rfl + · constructor + · intro h + subst l + exact (lt_asymm hij hkl) + · exact ne_of_gt hkl + · exact Or.inl (not_or.mp hk) + +theorem bracket_not_dvd_distinct {N : ℕ} (i j k l : Fin N) (hij : i < j) (hkl : k < l) + (hne : (i,j) ≠ (k,l)) : ¬ bracket i j ∣ bracket k l := by + intro hd + rcases pair_outside_endpoint i j k l hij hkl hne with hk | hl + · let point : SpinorVariables N → ℂ := fun z => + if z.2 then (if z.1 = k then 1 else 0) else (if z.1 = k then 0 else 1) + let ev : MvPolynomial (SpinorVariables N) ℂ →+* ℂ := eval₂Hom (RingHom.id ℂ) point + have h := map_dvd ev hd + norm_num [ev,point,bracket,eval₂Hom,hk.1,hk.2,Ne.symm hk.1,Ne.symm hk.2,ne_of_gt hkl] at h + · let point : SpinorVariables N → ℂ := fun z => + if z.2 then (if z.1 = l then 1 else 0) else (if z.1 = l then 0 else 1) + let ev : MvPolynomial (SpinorVariables N) ℂ →+* ℂ := eval₂Hom (RingHom.id ℂ) point + have h := map_dvd ev hd + norm_num [ev,point,bracket,eval₂Hom,hl.1,hl.2,Ne.symm hl.1,Ne.symm hl.2,ne_of_lt hkl] at h + +theorem bracket_isRelPrime {N : ℕ} (i j k l : Fin N) (hij : i < j) (hkl : k < l) + (hne : (i,j) ≠ (k,l)) : IsRelPrime (bracket i j) (bracket k l) := + (bracket_irreducible i j (ne_of_lt hij)).isRelPrime_iff_not_dvd.mpr + (bracket_not_dvd_distinct i j k l hij hkl hne) + +theorem bracket_not_associated {N : ℕ} (i j k l : Fin N) (hij : i < j) (hkl : k < l) + (hne : (i,j) ≠ (k,l)) : ¬ Associated (bracket i j) (bracket k l) := by + intro h + exact bracket_not_dvd_distinct i j k l hij hkl hne h.dvd + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/BracketIrreducible.lean b/lean/OAI/Analysis/Laughlin/Polynomial/BracketIrreducible.lean new file mode 100644 index 0000000000000000000000000000000000000000..d8e79477db2e1cf0e5bc025f3be52fb08861082c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/BracketIrreducible.lean @@ -0,0 +1,42 @@ +import Mathlib.Algebra.MvPolynomial.Division +import Mathlib.RingTheory.MvPolynomial.IrreducibleQuadratic +import Mathlib.RingTheory.Polynomial.UniqueFactorization +import Mathlib.Tactic.NormNum +import Mathlib.Tactic.Ring +import OAI.Analysis.Laughlin.EnergyNonnegative + +namespace OAI + +namespace Laughlin +open MvPolynomial + +theorem bracket_irreducible {N : ℕ} (i j : Fin N) (hij : i ≠ j) : + Irreducible (bracket i j) := by + let f : MvPolynomial (SpinorVariables N) ℂ := X (j,true) + let g : MvPolynomial (SpinorVariables N) ℂ := -(X (j,false)*X (i,true)) + have hf : f ≠ 0 := X_ne_zero _ + have hif : (i,false) ∉ f.vars := by simp [f] + have hig : (i,false) ∉ g.vars := by + simp only [g, vars_neg] + intro h + have hu := vars_mul (X (j,false) : MvPolynomial (SpinorVariables N) ℂ) (X (i,true)) h + simp [hij] at hu + have hnd : ¬ f ∣ g := by + intro hd + let ev : MvPolynomial (SpinorVariables N) ℂ →+* ℂ := + eval₂Hom (RingHom.id ℂ) (fun z => if z = (j,true) then 0 else 1) + have h := map_dvd ev hd + norm_num [ev,f,g,eval₂Hom,hij,Ne.symm hij] at h + have hr : IsRelPrime f g := + (X_prime (R := ℂ) (i := (j,true))).irreducible.isRelPrime_iff_not_dvd.mpr hnd + have h := irreducible_mul_X_add f g (i,false) hf hif hig hr + convert h using 1 + unfold bracket f g + ring + +theorem bracket_prime {N : ℕ} (i j : Fin N) (hij : i ≠ j) : Prime (bracket i j) := + irreducible_iff_prime.mp (bracket_irreducible i j hij) + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/BracketProductDivisibility.lean b/lean/OAI/Analysis/Laughlin/Polynomial/BracketProductDivisibility.lean new file mode 100644 index 0000000000000000000000000000000000000000..69e72ac1dcdcaf052867a7d2d663c6ff466e41b1 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/BracketProductDivisibility.lean @@ -0,0 +1,40 @@ +import Mathlib.RingTheory.Coprime.Lemmas +import OAI.Analysis.Laughlin.Polynomial.BracketCoprime +import OAI.Analysis.Laughlin.Polynomial.Polynomial + +namespace OAI + +namespace Laughlin +open scoped BigOperators + +def orderedPairs (N : ℕ) : Finset (Fin N × Fin N) := + Finset.univ.filter (fun ij => ij.1 < ij.2) + +theorem laughlinPolynomial_eq_orderedProduct (N : ℕ) : + laughlinPolynomial N = ∏ ij ∈ orderedPairs N, bracket ij.1 ij.2 ^ 3 := by + unfold laughlinPolynomial orderedPairs + rw [Finset.prod_filter, Fintype.prod_prod_type] + +theorem laughlinPolynomial_dvd_of_pair_cubes {N : ℕ} + (P : MvPolynomial (SpinorVariables N) ℂ) + (h : ∀ i j : Fin N, i < j → bracket i j ^ 3 ∣ P) : + laughlinPolynomial N ∣ P := by + rw [laughlinPolynomial_eq_orderedProduct] + apply Finset.prod_dvd_of_isRelPrime + · rintro ⟨i,j⟩ hij ⟨k,l⟩ hkl hne + exact (bracket_isRelPrime i j k l (Finset.mem_filter.mp hij).2 + (Finset.mem_filter.mp hkl).2 hne).pow + · rintro ⟨i,j⟩ hij + exact h i j (Finset.mem_filter.mp hij).2 + +theorem laughlinPolynomial_dvd_iff_pair_cubes {N : ℕ} + (P : MvPolynomial (SpinorVariables N) ℂ) : + laughlinPolynomial N ∣ P ↔ ∀ i j : Fin N, i < j → bracket i j ^ 3 ∣ P := by + constructor + · intro h i j hij + exact (bracket_cube_dvd_laughlin hij).trans h + · exact laughlinPolynomial_dvd_of_pair_cubes P + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/LaughlinAntisymmetry.lean b/lean/OAI/Analysis/Laughlin/Polynomial/LaughlinAntisymmetry.lean new file mode 100644 index 0000000000000000000000000000000000000000..e3ad4b415eb6f6ad60e0e7246ccee38209b4ee54 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/LaughlinAntisymmetry.lean @@ -0,0 +1,65 @@ +import Mathlib.Algebra.MvPolynomial.Rename +import Mathlib.GroupTheory.Perm.Fin +import OAI.Analysis.Laughlin.Polynomial.LaughlinMultidegree + +namespace OAI + +namespace Laughlin +open MvPolynomial +open scoped BigOperators + +def spinorPermutation {N : ℕ} (σ : Equiv.Perm (Fin N)) : Equiv.Perm (SpinorVariables N) := + σ.prodCongr (Equiv.refl Bool) + +theorem bracket_rename {N : ℕ} (σ : Equiv.Perm (Fin N)) (i j : Fin N) : + rename (spinorPermutation σ) (bracket i j)=bracket (σ i) (σ j) := by + simp [bracket,spinorPermutation] + +theorem laughlinPolynomial_eq_Ioi (N : ℕ) : + laughlinPolynomial N=∏ i : Fin N, ∏ j ∈ Finset.Ioi i, bracket i j^3 := by + unfold laughlinPolynomial + apply Finset.prod_congr rfl + intro i hi + rw [← Finset.prod_filter] + congr 1 + ext j + simp + +theorem laughlinPolynomial_rename_swap {N : ℕ} (i j : Fin N) (hij : i ≠ j) : + rename (spinorPermutation (Equiv.swap i j)) (laughlinPolynomial N) = -laughlinPolynomial N := by + rw [laughlinPolynomial_eq_Ioi] + simp only [map_prod,map_pow,bracket_rename] + rw [(Equiv.swap i j).prod_Ioi_comp_eq_sign_mul_prod (f := fun a b => bracket a b^3)] + · simp [Equiv.Perm.sign_swap hij] + · intro a b + rw [bracket_swap b a] + ring + +theorem monomialExponent_rename {N Q : ℕ} (σ : Equiv.Perm (Fin N)) (a : Configuration N Q) : + (monomialExponent a).mapDomain (spinorPermutation σ)=monomialExponent (a ∘ σ.symm) := by + ext ⟨k,b⟩ + rw [Finsupp.mapDomain_equiv_apply] + simp [monomialExponent,spinorPermutation] + +theorem spinWeight_permute {N Q : ℕ} (σ : Equiv.Perm (Fin N)) (a : Configuration N Q) : + spinWeight (a ∘ σ)=spinWeight a := by + unfold spinWeight + congr 1 + exact Equiv.prod_comp σ (fun k => Real.sqrt (Nat.choose Q (a k).val : ℝ)) + +theorem laughlinVector_antisymmetric (N : ℕ) : Antisymmetric (laughlinVector N (3*(N-1))) := by + intro i j hij a + have hc := coeff_rename_mapDomain (spinorPermutation (Equiv.swap i j)) + (spinorPermutation (Equiv.swap i j)).injective (laughlinPolynomial N) (monomialExponent a) + rw [laughlinPolynomial_rename_swap i j hij,monomialExponent_rename] at hc + simp only [coeff_neg,Equiv.symm_swap] at hc + change (laughlinPolynomial N).coeff (monomialExponent (a ∘ Equiv.swap i j)) / + spinWeight (a ∘ Equiv.swap i j) = -((laughlinPolynomial N).coeff (monomialExponent a)/spinWeight a) + rw [spinWeight_permute] + have he : (laughlinPolynomial N).coeff (monomialExponent (a ∘ Equiv.swap i j)) = + -(laughlinPolynomial N).coeff (monomialExponent a) := by linear_combination -hc + rw [he,neg_div] + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/LaughlinDegree.lean b/lean/OAI/Analysis/Laughlin/Polynomial/LaughlinDegree.lean new file mode 100644 index 0000000000000000000000000000000000000000..b2c7097487ac2a49073405a2e81cb409ba767bc3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/LaughlinDegree.lean @@ -0,0 +1,70 @@ +import Mathlib.Algebra.MvPolynomial.NoZeroDivisors +import Mathlib.Data.Fintype.Prod +import Mathlib.RingTheory.MvPolynomial.Homogeneous +import Mathlib.Tactic.Linarith +import OAI.Analysis.Laughlin.Polynomial.BracketProductDivisibility + +namespace OAI + +namespace Laughlin +open MvPolynomial +open scoped BigOperators + +theorem bracket_isHomogeneous {N : ℕ} (i j : Fin N) : + (bracket i j).IsHomogeneous 2 := + ((isHomogeneous_X ℂ (i,false)).mul (isHomogeneous_X ℂ (j,true))).sub + ((isHomogeneous_X ℂ (j,false)).mul (isHomogeneous_X ℂ (i,true))) + +theorem orderedPairs_card (N : ℕ) : (orderedPairs N).card = N.choose 2 := by + simpa [orderedPairs] using (Fintype.card_product_filter_lt (α := Fin N)) + +theorem laughlinPolynomial_isHomogeneous (N : ℕ) : + (laughlinPolynomial N).IsHomogeneous (6 * N.choose 2) := by + rw [laughlinPolynomial_eq_orderedProduct] + have h := IsHomogeneous.prod (orderedPairs N) + (fun ij => bracket ij.1 ij.2 ^ 3) (fun _ => 6) + (fun ij _ => (bracket_isHomogeneous ij.1 ij.2).pow 3) + simpa [orderedPairs_card, Nat.mul_comm] using h + +theorem laughlinPolynomial_totalDegree (N : ℕ) : + (laughlinPolynomial N).totalDegree = 6 * N.choose 2 := + (laughlinPolynomial_isHomogeneous N).totalDegree (laughlinPolynomial_ne_zero N) + +theorem laughlin_degree_at_flux (N : ℕ) : 6 * N.choose 2 = N * (3 * (N-1)) := by + cases N with + | zero => simp + | succ n => + have h := Nat.add_one_mul_choose_eq n 1 + simp only [Nat.choose_one_right, Nat.reduceAdd] at h + simp only [Nat.add_sub_cancel] + nlinarith + +theorem laughlinPolynomial_totalDegree_flux (N : ℕ) : + (laughlinPolynomial N).totalDegree = N * (3 * (N-1)) := by + rw [laughlinPolynomial_totalDegree, laughlin_degree_at_flux] + +theorem scalar_laughlin_of_degree_and_pair_cubes {N : ℕ} + (P : MvPolynomial (SpinorVariables N) ℂ) + (hdegree : P.totalDegree ≤ 6 * N.choose 2) + (hcubes : ∀ i j : Fin N, i < j → bracket i j ^ 3 ∣ P) : + ∃ c : ℂ, P = C c * laughlinPolynomial N := by + obtain ⟨g,hg⟩ := laughlinPolynomial_dvd_of_pair_cubes P hcubes + by_cases hzero : g = 0 + · exact ⟨0, by simp [hg,hzero]⟩ + · have hdeg : g.totalDegree = 0 := by + rw [hg, totalDegree_mul_of_isDomain (laughlinPolynomial_ne_zero N) hzero, + laughlinPolynomial_totalDegree] at hdegree + omega + exact ⟨g.coeff 0, by rw [hg, mul_comm]; exact congrArg (fun z => z * laughlinPolynomial N) (totalDegree_eq_zero_iff_eq_C.mp hdeg)⟩ + +theorem scalar_laughlin_at_flux {N : ℕ} + (P : MvPolynomial (SpinorVariables N) ℂ) + (hdegree : P.totalDegree ≤ N * (3 * (N-1))) + (hcubes : ∀ i j : Fin N, i < j → bracket i j ^ 3 ∣ P) : + ∃ c : ℂ, P = C c * laughlinPolynomial N := + scalar_laughlin_of_degree_and_pair_cubes P + (by simpa [laughlin_degree_at_flux] using hdegree) hcubes + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/LaughlinMultidegree.lean b/lean/OAI/Analysis/Laughlin/Polynomial/LaughlinMultidegree.lean new file mode 100644 index 0000000000000000000000000000000000000000..62380f9a95211d0dd3ec458ba3706f6485a5072f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/LaughlinMultidegree.lean @@ -0,0 +1,75 @@ +import OAI.Analysis.Laughlin.Spin.Multidegree + +namespace OAI + +namespace Laughlin +open MvPolynomial +open scoped BigOperators + +theorem bracket_particle_degree {N : ℕ} (k i j : Fin N) : + (bracket i j).IsWeightedHomogeneous (particleDegreeWeight k) + ((if i=k then 1 else 0)+(if j=k then 1 else 0) : ℕ) := by + have h (a : Fin N) (b : Bool) := isWeightedHomogeneous_X (R := ℂ) (particleDegreeWeight k) (a,b) + have h1 := (h i false).mul (h j true) + have h2 := (h j false).mul (h i true) + exact h1.sub (by simpa only [particleDegreeWeight,Nat.add_comm] using h2) + +theorem particle_pair_degree_count {N : ℕ} (k : Fin N) : + (∑ i : Fin N, ∑ j : Fin N, if i omega + simp_rw [he,Finset.sum_add_distrib] + simp + rw [hsplit,← Finset.sum_add_distrib] + have hentry (j : Fin N) : (if k omega + simp_rw [hentry] + simp [Finset.sum_ite,Finset.filter_ne'] + +theorem laughlinPolynomial_particle_degree (N : ℕ) (k : Fin N) : + (laughlinPolynomial N).IsWeightedHomogeneous (particleDegreeWeight k) (3*(N-1)) := by + have hp := IsWeightedHomogeneous.prod (Finset.univ : Finset (Fin N)) + (fun i => ∏ j : Fin N, if i ∑ j : Fin N, if i simp [h] + simp_rw [he,← Finset.mul_sum] + rw [particle_pair_degree_count] + rw [hs] at hp + exact hp + +theorem spinPolynomial_laughlinVector (N : ℕ) : + spinPolynomial (laughlinVector N (3*(N-1)))=laughlinPolynomial N := by + exact spinPolynomial_reconstruct _ (laughlinPolynomial_particle_degree N) + +theorem laughlinVector_ne_zero (N : ℕ) : laughlinVector N (3*(N-1)) ≠ 0 := by + intro h + have he := spinPolynomial_laughlinVector N + rw [h] at he + have hz : spinPolynomial (0 : State N (3*(N-1)))=0 := by simp [spinPolynomial] + rw [hz] at he + exact laughlinPolynomial_ne_zero N he.symm + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/OscillatorPolynomial.lean b/lean/OAI/Analysis/Laughlin/Polynomial/OscillatorPolynomial.lean new file mode 100644 index 0000000000000000000000000000000000000000..13d5a605a780411745e6a4604e200325662b5a4d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/OscillatorPolynomial.lean @@ -0,0 +1,93 @@ +import Mathlib.Algebra.Polynomial.Coeff +import OAI.Analysis.Laughlin.Spin.OscillatorHighest + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators +open Polynomial + +noncomputable def sqrtFactorial (n : ℕ) : ℝ := Real.sqrt (n.factorial : ℝ) +noncomputable def monomialNormFactor (T p : ℕ) : ℝ := sqrtFactorial p * sqrtFactorial (T-p) + +noncomputable def couplingPolynomial (u v : ℝ) (z n : ℕ) : Polynomial ℝ := + (C u * X-C v)^z * (C v * X+C u)^n + +noncomputable def couplingPolynomialCoefficient (u v : ℝ) (z n p : ℕ) : ℝ := + (couplingPolynomial u v z n).coeff p * monomialNormFactor (z+n) p / + (sqrtFactorial z * sqrtFactorial n) + +theorem sqrtFactorial_pos (n : ℕ) : 0 < sqrtFactorial n := by + apply Real.sqrt_pos.mpr + exact_mod_cast Nat.factorial_pos n + +theorem sqrtFactorial_succ (n : ℕ) : + sqrtFactorial (n+1) = Real.sqrt ((n : ℝ)+1) * sqrtFactorial n := by + unfold sqrtFactorial + rw [Nat.factorial_succ,Nat.cast_mul,Real.sqrt_mul (by positivity)] + push_cast; rfl + +theorem sqrt_choose_factorial (z p : ℕ) (hp : p ≤ z) : + (z.choose p : ℝ) * monomialNormFactor z p / sqrtFactorial z = + Real.sqrt (z.choose p : ℝ) := by + have he : (z.choose p : ℝ) * (p.factorial : ℝ) * ((z-p).factorial : ℝ) = (z.factorial : ℝ) := by + exact_mod_cast Nat.choose_mul_factorial_mul_factorial hp + have hc : 0 < (z.choose p : ℝ) := by exact_mod_cast Nat.choose_pos hp + have hs : sqrtFactorial z = Real.sqrt (z.choose p : ℝ) * monomialNormFactor z p := by + unfold monomialNormFactor sqrtFactorial + rw [← he,Real.sqrt_mul (by positivity),Real.sqrt_mul (by positivity)] + ring + have hn := ne_of_gt (sqrtFactorial_pos z) + apply (div_eq_iff hn).mpr + rw [hs] + rw [← mul_assoc,← pow_two,Real.sq_sqrt (le_of_lt hc)] + +theorem couplingPolynomial_base_coeff (u v : ℝ) (hu : u ≠ 0) (z p : ℕ) : + (couplingPolynomial u v z 0).coeff p = + u^z * ((-v/u)^(z-p) * (z.choose p : ℝ)) := by + have he : C u * X-C v = C u * (X+C (-v/u)) := by + rw [mul_add,← C_mul] + have hc : u*(-v/u) = -v := by field_simp + rw [hc,C_neg]; ring + simp only [couplingPolynomial,pow_zero,mul_one,he,mul_pow,← C_pow,coeff_C_mul,coeff_X_add_C_pow] + +theorem couplingPolynomial_base_normalized (u v : ℝ) (hu : u ≠ 0) (z p : ℕ) (hp : p ≤ z) : + couplingPolynomialCoefficient u v z 0 p = oscillatorHighest u v z p := by + have hz : z=p+(z-p) := by omega + have hupow : u^z = u^p*u^(z-p) := by rw [← pow_add,← hz] + unfold couplingPolynomialCoefficient + rw [couplingPolynomial_base_coeff u v hu] + simp only [Nat.add_zero,sqrtFactorial,Nat.factorial_zero,Nat.cast_one,Real.sqrt_one,mul_one] + change _ = (-1 : ℝ)^(z-p)*Real.sqrt (z.choose p : ℝ)*u^p*v^(z-p) + have he : u^z*(-v/u)^(z-p) = (-1 : ℝ)^(z-p)*u^p*v^(z-p) := by + rw [hupow,div_pow,neg_eq_neg_one_mul,mul_pow] + field_simp + calc + _ = (u^z*(-v/u)^(z-p))*((z.choose p : ℝ)*monomialNormFactor z p / sqrtFactorial z) := by unfold sqrtFactorial; ring + _ = _ := by rw [he,sqrt_choose_factorial z p hp]; ring + +theorem couplingPolynomial_succ_coeff (u v : ℝ) (z n p : ℕ) : + (couplingPolynomial u v z (n+1)).coeff p = + (if p=0 then 0 else v*(couplingPolynomial u v z n).coeff (p-1)) + + u*(couplingPolynomial u v z n).coeff p := by + have he : couplingPolynomial u v z (n+1) = + C v * (couplingPolynomial u v z n * X) + C u * couplingPolynomial u v z n := by + unfold couplingPolynomial + rw [pow_succ] + ring + rw [he,coeff_add,coeff_C_mul,coeff_C_mul] + cases p with + | zero => simp + | succ p => simp [coeff_mul_X] + +theorem couplingPolynomial_coeff_off (u v : ℝ) (hu : u ≠ 0) (z n p : ℕ) (hp : z+n < p) : + (couplingPolynomial u v z n).coeff p = 0 := by + induction n generalizing p with + | zero => rw [couplingPolynomial_base_coeff u v hu,Nat.choose_eq_zero_of_lt (by omega)]; simp + | succ n ih => + rw [couplingPolynomial_succ_coeff,ite_eq_right (by omega : p ≠ 0),ih (p-1) (by omega),ih p (by omega)] + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/OscillatorPolynomialLadder.lean b/lean/OAI/Analysis/Laughlin/Polynomial/OscillatorPolynomialLadder.lean new file mode 100644 index 0000000000000000000000000000000000000000..45a294edce18ce6b5b0c9cb64e3bb0fb7f369a52 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/OscillatorPolynomialLadder.lean @@ -0,0 +1,65 @@ +import OAI.Analysis.Laughlin.Polynomial.OscillatorPolynomial + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + + theorem monomialNormFactor_first (T p : ℕ) (hp : 0 < p) : + monomialNormFactor (T+1) p = Real.sqrt (p : ℝ)*monomialNormFactor T (p-1) := by + have he : sqrtFactorial p = Real.sqrt (p : ℝ)*sqrtFactorial (p-1) := by + have hh := sqrtFactorial_succ (p-1) + have hk : p-1+1=p := by omega + have hc : ((p-1 : ℕ) : ℝ)+1=p := by exact_mod_cast hk + rwa [hk,hc] at hh + unfold monomialNormFactor + rw [he,show T+1-p=T-(p-1) by omega] + ring + + theorem monomialNormFactor_second (T p : ℕ) (hp : p ≤ T) : + monomialNormFactor (T+1) p = Real.sqrt ((T+1-p : ℕ) : ℝ)*monomialNormFactor T p := by + have hk : T+1-p=(T-p)+1 := by omega + have hc : ((T-p : ℕ) : ℝ)+1=(T+1-p : ℕ) := by exact_mod_cast hk.symm + have hf : sqrtFactorial (T+1-p) = Real.sqrt ((T+1-p : ℕ) : ℝ)*sqrtFactorial (T-p) := by + calc + _ = sqrtFactorial ((T-p)+1) := by rw [hk] + _ = _ := by rw [sqrtFactorial_succ,hc] + unfold monomialNormFactor + rw [hf]; ring + +theorem couplingPolynomialCoefficient_lowering (u v : ℝ) (hu : u ≠ 0) + (z n p : ℕ) (hp : p ≤ z+n+1) : + couplingPolynomialCoefficient u v z (n+1) p = + ((if p=0 then 0 else v*Real.sqrt (p : ℝ)*couplingPolynomialCoefficient u v z n (p-1)) + + (if p ≤ z+n then u*Real.sqrt ((z+n+1-p : ℕ) : ℝ)*couplingPolynomialCoefficient u v z n p else 0)) / + Real.sqrt ((n : ℝ)+1) := by + unfold couplingPolynomialCoefficient + rw [couplingPolynomial_succ_coeff,sqrtFactorial_succ] + have ht : z+(n+1)=z+n+1 := by omega + rw [ht] + by_cases hp0 : p=0 + · subst p + simp only [ite_eq_left (by omega : 0 ≤ z+n)] + rw [monomialNormFactor_second (z+n) 0 (by omega)] + simp only [Nat.sub_zero] + simp [div_eq_mul_inv,mul_inv_rev]; ring + · simp only [ite_eq_right hp0] + by_cases hpn : p ≤ z+n + · simp only [ite_eq_left hpn] + have hfirst := monomialNormFactor_first (z+n) p (by omega) + have hsecond := monomialNormFactor_second (z+n) p hpn + rw [add_mul] + simp only [add_div] + congr 1 + · rw [hfirst] + simp only [div_eq_mul_inv,mul_inv_rev]; ring + · rw [hsecond] + simp only [div_eq_mul_inv,mul_inv_rev]; ring + · simp only [ite_eq_right hpn] + rw [couplingPolynomial_coeff_off u v hu z n p (by omega),mul_zero,add_zero, + monomialNormFactor_first (z+n) p (by omega)] + simp only [div_eq_mul_inv,mul_inv_rev]; ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/PhysicalLaughlinKernel.lean b/lean/OAI/Analysis/Laughlin/Polynomial/PhysicalLaughlinKernel.lean new file mode 100644 index 0000000000000000000000000000000000000000..86254c0514765cccafb1ddc644f7724c48f80c65 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/PhysicalLaughlinKernel.lean @@ -0,0 +1,47 @@ +import OAI.Analysis.Laughlin.Operators.GlobalPairCube +import OAI.Analysis.Laughlin.Polynomial.LaughlinAntisymmetry + +namespace OAI + +namespace Laughlin +open MvPolynomial +open scoped BigOperators + +theorem spinPolynomial_scalar {N Q : ℕ} (c : ℂ) (ψ : State N Q) : + spinPolynomial (fun a => c * ψ a) = C c * spinPolynomial ψ := by + unfold spinPolynomial + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro a ha + rw [C_mul_monomial] + congr 1 + ring + +theorem physical_Laughlin_kernel {N : ℕ} (hN : 2 ≤ N) + (ψ : State N (3*(N-1))) (hψ : Antisymmetric ψ) : + energy ψ = 0 ↔ ∃ c : ℂ, ψ = fun a => c * laughlinVector N (3*(N-1)) a := by + constructor + · exact zero_energy_state_eq_laughlin hN ψ hψ + · rintro ⟨c,hc⟩ + apply (energy_eq_zero_iff_global_pair_cubes (by omega) ψ hψ).mpr + intro i j hij + rw [hc, spinPolynomial_scalar, spinPolynomial_laughlinVector] + exact dvd_mul_of_dvd_right (bracket_cube_dvd_laughlin hij) _ + +theorem laughlinVector_zero_energy {N : ℕ} (hN : 2 ≤ N) : + energy (laughlinVector N (3*(N-1))) = 0 := by + apply (physical_Laughlin_kernel hN _ (laughlinVector_antisymmetric N)).mpr + exact ⟨1, by funext a; simp⟩ + +theorem physical_Laughlin_ground_line {N : ℕ} (hN : 2 ≤ N) : + laughlinVector N (3*(N-1)) ≠ 0 ∧ + Antisymmetric (laughlinVector N (3*(N-1))) ∧ + energy (laughlinVector N (3*(N-1))) = 0 ∧ + ∀ ψ : State N (3*(N-1)), Antisymmetric ψ → + (energy ψ = 0 ↔ ∃ c : ℂ, ψ = fun a => c * laughlinVector N (3*(N-1)) a) := + ⟨laughlinVector_ne_zero N, laughlinVector_antisymmetric N, + laughlinVector_zero_energy hN, fun ψ hψ => physical_Laughlin_kernel hN ψ hψ⟩ + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/Polynomial.lean b/lean/OAI/Analysis/Laughlin/Polynomial/Polynomial.lean new file mode 100644 index 0000000000000000000000000000000000000000..5463529dfce0c867e17802ad761326016dfbf8c6 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/Polynomial.lean @@ -0,0 +1,47 @@ +import Mathlib.Algebra.MvPolynomial.Eval +import Mathlib.Tactic.Ring +import OAI.Analysis.Laughlin.EnergyNonnegative + +namespace OAI + +namespace Laughlin + +theorem bracket_swap {N : ℕ} (i j : Fin N) : bracket j i = -bracket i j := by + unfold bracket + ring + +theorem bracket_ne_zero {N : ℕ} {i j : Fin N} (hij : i ≠ j) : + bracket i j ≠ 0 := by + intro h + let f : SpinorVariables N → ℂ := fun kb => + if (kb.1 = i ∧ kb.2 = false) ∨ (kb.1 = j ∧ kb.2 = true) then 1 else 0 + have := congrArg (MvPolynomial.eval f) h + have hji : j ≠ i := Ne.symm hij + simp [bracket, f, hij, hji] at this + +theorem laughlinPolynomial_ne_zero (N : ℕ) : laughlinPolynomial N ≠ 0 := by + classical + unfold laughlinPolynomial + apply Finset.prod_ne_zero_iff.mpr + intro i _ + apply Finset.prod_ne_zero_iff.mpr + intro j _ + split_ifs with hij + · exact pow_ne_zero 3 (bracket_ne_zero (ne_of_lt hij)) + · exact one_ne_zero + +theorem bracket_cube_dvd_laughlin {N : ℕ} {i j : Fin N} (hij : i < j) : + bracket i j ^ 3 ∣ laughlinPolynomial N := by + classical + unfold laughlinPolynomial + have h₁ : bracket i j ^ 3 ∣ ∏ k : Fin N, if i < k then bracket i k ^ 3 else 1 := by + simpa [hij] using + (Finset.dvd_prod_of_mem (fun j => if i < j then bracket i j ^ 3 else 1) + (Finset.mem_univ j)) + exact h₁.trans + (Finset.dvd_prod_of_mem (fun i => ∏ j : Fin N, if i < j then bracket i j ^ 3 else 1) + (Finset.mem_univ i)) + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/PolynomialMatrixODE.lean b/lean/OAI/Analysis/Laughlin/Polynomial/PolynomialMatrixODE.lean new file mode 100644 index 0000000000000000000000000000000000000000..a027cf28ce4b6512e7eb373ec9681efdc25bb3d4 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/PolynomialMatrixODE.lean @@ -0,0 +1,96 @@ +import Mathlib.Algebra.Polynomial.Derivative +import Mathlib.Analysis.Complex.Basic +import Mathlib.Data.Matrix.Mul + +namespace OAI + +namespace Laughlin.Rotation +open Polynomial +open scoped BigOperators Matrix + +noncomputable def polynomialMatrixDerivative {ι κ : Type*} + (P : Matrix ι κ (Polynomial ℂ)) : Matrix ι κ (Polynomial ℂ) := fun i j => (P i j).derivative +noncomputable def polynomialMatrixCoeff {ι κ : Type*} + (P : Matrix ι κ (Polynomial ℂ)) (n : ℕ) : Matrix ι κ ℂ := fun i j => (P i j).coeff n + +theorem polynomialMatrixDerivative_coeff {ι κ : Type*} (P : Matrix ι κ (Polynomial ℂ)) (n : ℕ) : + polynomialMatrixCoeff (polynomialMatrixDerivative P) n = + (n+1 : ℂ) • polynomialMatrixCoeff P (n+1) := by + ext i j + simp [polynomialMatrixCoeff,polynomialMatrixDerivative,coeff_derivative,mul_comm] + +theorem polynomialMatrixCoeff_mul_constant {ι κ τ : Type*} [Fintype κ] + (P : Matrix ι κ (Polynomial ℂ)) (G : Matrix κ τ ℂ) (n : ℕ) : + polynomialMatrixCoeff (P * G.map C) n = polynomialMatrixCoeff P n * G := by + ext i j + simp [polynomialMatrixCoeff,Matrix.mul_apply,coeff_mul_C] + +theorem polynomialMatrixCoeff_constant_mul {ι κ τ : Type*} [Fintype κ] + (G : Matrix ι κ ℂ) (P : Matrix κ τ (Polynomial ℂ)) (n : ℕ) : + polynomialMatrixCoeff (G.map C * P) n = G * polynomialMatrixCoeff P n := by + ext i j + simp [polynomialMatrixCoeff,Matrix.mul_apply,coeff_C_mul] + +theorem polynomialMatrixDerivative_mul {ι κ τ : Type*} [Fintype κ] + (P : Matrix ι κ (Polynomial ℂ)) (Q : Matrix κ τ (Polynomial ℂ)) : + polynomialMatrixDerivative (P*Q) = polynomialMatrixDerivative P*Q+P*polynomialMatrixDerivative Q := by + ext i j + simp [polynomialMatrixDerivative,Matrix.mul_apply,derivative_mul,Finset.sum_add_distrib] + +theorem polynomialMatrixDerivative_constant {ι κ : Type*} (G : Matrix ι κ ℂ) : + polynomialMatrixDerivative (G.map C)=0 := by + ext i j + simp [polynomialMatrixDerivative] + +theorem polynomialMatrixDerivative_sub {ι κ : Type*} + (P Q : Matrix ι κ (Polynomial ℂ)) : + polynomialMatrixDerivative (P-Q)=polynomialMatrixDerivative P-polynomialMatrixDerivative Q := by + ext i j + simp [polynomialMatrixDerivative] + +theorem polynomialMatrixCoeff_sub {ι κ : Type*} + (P Q : Matrix ι κ (Polynomial ℂ)) (n : ℕ) : + polynomialMatrixCoeff (P-Q) n=polynomialMatrixCoeff P n-polynomialMatrixCoeff Q n := by + ext i j + simp [polynomialMatrixCoeff] + +theorem polynomialMatrix_zero_of_derivative_right {ι κ : Type*} [Fintype κ] + (P : Matrix ι κ (Polynomial ℂ)) (G : Matrix κ κ ℂ) + (hd : polynomialMatrixDerivative P=P*G.map C) + (h0 : polynomialMatrixCoeff P 0=0) : P=0 := by + have hc : ∀ n, polynomialMatrixCoeff P n=0 := by + intro n + induction n with + | zero => exact h0 + | succ n ih => + have h := congrArg (fun M => polynomialMatrixCoeff M n) hd + rw [polynomialMatrixDerivative_coeff,polynomialMatrixCoeff_mul_constant,ih,Matrix.zero_mul] at h + exact (smul_eq_zero.mp h).resolve_left (by exact_mod_cast Nat.succ_ne_zero n) + ext i j n + exact congrFun (congrFun (hc n) i) j + +theorem polynomialMatrix_intertwining {ι κ : Type*} + [Fintype ι] [DecidableEq ι] [Fintype κ] [DecidableEq κ] + (U : Matrix ι ι (Polynomial ℂ)) (V : Matrix κ κ (Polynomial ℂ)) + (G : Matrix ι ι ℂ) (H : Matrix κ κ ℂ) (W : Matrix ι κ ℂ) + (hU : polynomialMatrixDerivative U=U*G.map C) + (hV : polynomialMatrixDerivative V=V*H.map C) + (hU0 : polynomialMatrixCoeff U 0=1) (hV0 : polynomialMatrixCoeff V 0=1) + (hW : G*W=W*H) : U*W.map C=W.map C*V := by + have hWC : G.map C*W.map C=W.map C*H.map C := by + simpa only [Matrix.map_mul] using congrArg (fun M => M.map C) hW + have hd : polynomialMatrixDerivative (U*W.map C-W.map C*V) = + (U*W.map C-W.map C*V)*H.map C := by + rw [polynomialMatrixDerivative_sub,polynomialMatrixDerivative_mul,polynomialMatrixDerivative_mul, + polynomialMatrixDerivative_constant,hU,hV,Matrix.mul_zero,Matrix.zero_mul,add_zero,zero_add, + Matrix.sub_mul] + simp only [Matrix.mul_assoc] + rw [hWC] + have h0 : polynomialMatrixCoeff (U*W.map C-W.map C*V) 0=0 := by + rw [polynomialMatrixCoeff_sub,polynomialMatrixCoeff_mul_constant, + polynomialMatrixCoeff_constant_mul,hU0,hV0,Matrix.one_mul,Matrix.mul_one,sub_self] + exact sub_eq_zero.mp (polynomialMatrix_zero_of_derivative_right _ H hd h0) + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/SourceEqualSpinPolynomial.lean b/lean/OAI/Analysis/Laughlin/Polynomial/SourceEqualSpinPolynomial.lean new file mode 100644 index 0000000000000000000000000000000000000000..f7b426a73508046a7312fb750521178cbc8c9402 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/SourceEqualSpinPolynomial.lean @@ -0,0 +1,31 @@ +import Mathlib.Algebra.Polynomial.Eval.Coeff +import OAI.Analysis.Laughlin.Polynomial.OscillatorPolynomial +import OAI.Analysis.Laughlin.Polynomial.SourceIntegerPolynomial + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators +open Polynomial + +theorem equalSpin_polynomial (u : ℝ) (z n : ℕ) : + couplingPolynomial u u z n = C (u^(z+n)) * + (Certificate.integerCouplingPolynomial z n).map (Int.castRingHom ℝ) := by + simp only [couplingPolynomial,Certificate.integerCouplingPolynomial,Polynomial.map_mul,Polynomial.map_pow, + Polynomial.map_sub,Polynomial.map_add,Polynomial.map_X,Polynomial.map_one,pow_add,C_mul,C_pow] + rw [show C u * X-C u = C u*(X-1) by ring, + show C u * X+C u = C u*(X+1) by ring,mul_pow,mul_pow] + ring + +theorem equalSpin_polynomialCoefficient (u : ℝ) (z n p : ℕ) (hp : p ≤ z+n) : + couplingPolynomialCoefficient u u z n p = + u^(z+n) * (Certificate.U 1 z (z+n) p : ℝ) * + sqrtFactorial p * sqrtFactorial (z+n-p) / (sqrtFactorial z * sqrtFactorial n) := by + unfold couplingPolynomialCoefficient + rw [equalSpin_polynomial,coeff_C_mul,coeff_map,Certificate.integerCouplingPolynomial_coeff z n p hp] + simp only [Int.coe_castRingHom,monomialNormFactor] + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/SourceIntegerPolynomial.lean b/lean/OAI/Analysis/Laughlin/Polynomial/SourceIntegerPolynomial.lean new file mode 100644 index 0000000000000000000000000000000000000000..229316587fae3c1b61279818ec700b2e9f3ec057 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/SourceIntegerPolynomial.lean @@ -0,0 +1,51 @@ +import Mathlib.Algebra.BigOperators.Group.Finset.Basic +import Mathlib.Algebra.BigOperators.NatAntidiagonal +import Mathlib.Algebra.Polynomial.Coeff +import Mathlib.Tactic.Ring +import OAI.Analysis.Laughlin.Operators.Certificate + +namespace OAI + +namespace Laughlin.Certificate +open scoped BigOperators +open Polynomial + +theorem U_one_sum (z T p : ℕ) (hz : z ≤ T) (hp : p ≤ T) : + U 1 z T p = ∑ h ∈ Finset.range (p+1), + (-1 : ℤ)^(z-h) * (z.choose h : ℤ) * ((T-z).choose (p-h) : ℤ) := by + unfold U + rw [ite_eq_left ⟨hz,hp⟩] + simp only [Int.natCast_one,one_pow,mul_one] + rw [← List.sum_toFinset _ (List.nodup_range.filter _)] + simp only [List.toFinset_filter,List.toFinset_range] + apply Finset.sum_subset + · intro h hh + simp only [Finset.mem_filter,Finset.mem_range] at hh ⊢ + omega + · intro h hh hn + simp only [Finset.mem_range,Finset.mem_filter,decide_eq_true_eq,not_and] at hh hn + by_cases hhz : h ≤ z + · have hbound : ¬ p+z ≤ T+h := hn (by omega) + rw [Nat.choose_eq_zero_of_lt (by omega : T-z < p-h)] + simp + · rw [Nat.choose_eq_zero_of_lt (by omega : z < h)] + simp + +noncomputable def integerCouplingPolynomial (z n : ℕ) : Polynomial ℤ := (Polynomial.X-1)^z * (Polynomial.X+1)^n + +theorem integerCouplingPolynomial_coeff (z n p : ℕ) (hp : p ≤ z+n) : + (integerCouplingPolynomial z n).coeff p = U 1 z (z+n) p := by + rw [U_one_sum z (z+n) p (by omega) hp] + simp only [Nat.add_sub_cancel_left] + unfold integerCouplingPolynomial + rw [coeff_mul,Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk] + apply Finset.sum_congr rfl + intro h hh + have hneg : (Polynomial.X-1 : Polynomial ℤ) = Polynomial.X+C (-1) := by simp [sub_eq_add_neg] + have hpos : (Polynomial.X+1 : Polynomial ℤ) = Polynomial.X+C 1 := by simp + rw [hneg,hpos,coeff_X_add_C_pow,coeff_X_add_C_pow] + simp + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/SymmetricTensorCoordinates.lean b/lean/OAI/Analysis/Laughlin/Polynomial/SymmetricTensorCoordinates.lean new file mode 100644 index 0000000000000000000000000000000000000000..3ad4b49569fa4fa705f06ade2b0741f46c1d4bf3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/SymmetricTensorCoordinates.lean @@ -0,0 +1,72 @@ +import Mathlib.Data.Finset.Powerset +import Mathlib.Tactic.FinCases +import OAI.Analysis.Laughlin.Spin.TensorAction + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + +noncomputable def tensorBits (Q : ℕ) (a : Fin Q → Fin 2) : Finset (Fin Q) := + Finset.univ.filter (fun i => a i=1) +noncomputable def subsetTensorBits (Q : ℕ) (s : Finset (Fin Q)) : Fin Q → Fin 2 := + fun i => if i ∈ s then 1 else 0 + +noncomputable def tensorSubsetEquiv (Q : ℕ) : (Fin Q → Fin 2) ≃ Finset (Fin Q) where + toFun := tensorBits Q + invFun := subsetTensorBits Q + left_inv a := by + funext i + simp only [subsetTensorBits,tensorBits,Finset.mem_filter,Finset.mem_univ,true_and] + have hi : a i=0 ∨ a i=1 := by omega + rcases hi with hi | hi <;> simp [hi] + right_inv s := by + ext i + simp [tensorBits,subsetTensorBits] + +noncomputable def tensorWeight (Q : ℕ) (a : Fin Q → Fin 2) : ℕ := (tensorBits Q a).card + + theorem tensorWeight_count (Q p : ℕ) : + (∑ a : Fin Q → Fin 2, if tensorWeight Q a=p then (1 : ℝ) else 0) = Q.choose p := by + classical + have he : (∑ a : Fin Q → Fin 2, if tensorWeight Q a=p then (1 : ℝ) else 0) = + ∑ s : Finset (Fin Q), if s.card=p then (1 : ℝ) else 0 := + (tensorSubsetEquiv Q).sum_comp (fun s => if s.card=p then (1 : ℝ) else 0) + rw [he] + have hs : (Finset.univ.filter (fun s : Finset (Fin Q) => s.card=p)) = + (Finset.univ : Finset (Fin Q)).powersetCard p := by + ext s + simp [Finset.mem_powersetCard] + rw [← Finset.sum_filter] + rw [hs] + simp + +noncomputable def symmetricTensorInclusionReal (Q : ℕ) : + Matrix (Fin Q → Fin 2) (Fin (Q+1)) ℝ := + fun a p => if tensorWeight Q a=p.val then (Real.sqrt (Q.choose p.val : ℝ))⁻¹ else 0 + +theorem symmetricTensorInclusionReal_isometry (Q : ℕ) : + (symmetricTensorInclusionReal Q)ᵀ*symmetricTensorInclusionReal Q=1 := by + classical + ext p q + simp only [Matrix.mul_apply,Matrix.transpose_apply,Matrix.one_apply,symmetricTensorInclusionReal] + by_cases hpq : p=q + · subst q + rw [ite_eq_left rfl] + have hn : (Q.choose p.val : ℝ) ≠ 0 := by exact_mod_cast (ne_of_gt (Nat.choose_pos (by omega : p.val ≤ Q))) + have he (a : Fin Q → Fin 2) : + (if tensorWeight Q a=p.val then (Real.sqrt (Q.choose p.val : ℝ))⁻¹ else 0) * + (if tensorWeight Q a=p.val then (Real.sqrt (Q.choose p.val : ℝ))⁻¹ else 0) = + ((Real.sqrt (Q.choose p.val : ℝ))⁻¹)^2 * (if tensorWeight Q a=p.val then 1 else 0) := by + split_ifs <;> ring + simp_rw [he,← Finset.mul_sum,tensorWeight_count] + rw [inv_pow,Real.sq_sqrt (by positivity),inv_mul_cancel₀ hn] + · rw [ite_eq_right hpq] + apply Finset.sum_eq_zero + intro a ha + have h : p.val ≠ q.val := fun h => hpq (Fin.ext h) + split_ifs <;> simp_all + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/SymmetricTensorOrbit.lean b/lean/OAI/Analysis/Laughlin/Polynomial/SymmetricTensorOrbit.lean new file mode 100644 index 0000000000000000000000000000000000000000..d95bdacd123a85f8245e2f2fc73e59583caf36c3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/SymmetricTensorOrbit.lean @@ -0,0 +1,61 @@ +import Mathlib.Logic.Equiv.Fintype +import OAI.Analysis.Laughlin.Polynomial.SymmetricTensorCoordinates + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + +noncomputable def tensorPermutation (Q : ℕ) (σ : Equiv.Perm (Fin Q)) : + (Fin Q → Fin 2) ≃ (Fin Q → Fin 2) where + toFun a := a ∘ σ + invFun a := a ∘ σ.symm + left_inv a := by funext i; simp + right_inv a := by funext i; simp + + theorem tensorWeight_perm (Q : ℕ) (a : Fin Q → Fin 2) (σ : Equiv.Perm (Fin Q)) : + tensorWeight Q (a ∘ σ)=tensorWeight Q a := by + have he : tensorBits Q (a ∘ σ) = (tensorBits Q a).map σ.symm.toEmbedding := by + ext i + simp [tensorBits] + unfold tensorWeight + rw [he,Finset.card_map] + +theorem tensorWeight_eq_exists_perm (Q : ℕ) (a b : Fin Q → Fin 2) + (h : tensorWeight Q a=tensorWeight Q b) : + ∃ σ : Equiv.Perm (Fin Q), a ∘ σ=b := by + obtain ⟨σ,hσ⟩ := Equiv.Perm.exists_map_finset_eq (tensorBits Q a) (tensorBits Q b) h + refine ⟨σ.symm,?_⟩ + funext i + have hm := congrArg (fun s : Finset (Fin Q) => i ∈ s) hσ + have hh : a (σ.symm i)=1 ↔ b i=1 := by simpa [tensorBits] using Iff.of_eq hm + apply Fin.ext + simp only [Fin.ext_iff,Fin.val_one] at hh + have ha := (a (σ.symm i)).isLt + have hb := (b i).isLt + dsimp [Function.comp_def] + omega + + theorem tensorMatrix_perm (Q : ℕ) (A : Matrix (Fin 2) (Fin 2) ℂ) + (a b : Fin Q → Fin 2) (σ : Equiv.Perm (Fin Q)) : + tensorMatrix Q A (a ∘ σ) (b ∘ σ)=tensorMatrix Q A a b := by + exact Equiv.prod_comp σ (fun i => A (a i) (b i)) + +theorem tensorMatrix_preserves_symmetric (Q : ℕ) (A : Matrix (Fin 2) (Fin 2) ℂ) + (v : (Fin Q → Fin 2) → ℂ) + (hv : ∀ a b, tensorWeight Q a=tensorWeight Q b → v a=v b) : + ∀ a b, tensorWeight Q a=tensorWeight Q b → + (tensorMatrix Q A *ᵥ v) a=(tensorMatrix Q A *ᵥ v) b := by + intro a b hab + obtain ⟨σ,rfl⟩ := tensorWeight_eq_exists_perm Q a b hab + have he := (tensorPermutation Q σ).sum_comp (fun c => tensorMatrix Q A (a ∘ σ) c*v c) + change (∑ c, tensorMatrix Q A a c*v c) = ∑ c, tensorMatrix Q A (a ∘ σ) c*v c + rw [← he] + apply Finset.sum_congr rfl + intro c hc + change tensorMatrix Q A a c*v c = tensorMatrix Q A (a ∘ σ) (c ∘ σ)*v (c ∘ σ) + rw [tensorMatrix_perm,hv (c ∘ σ) c (tensorWeight_perm Q c σ)] + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Polynomial/SymmetricTensorRange.lean b/lean/OAI/Analysis/Laughlin/Polynomial/SymmetricTensorRange.lean new file mode 100644 index 0000000000000000000000000000000000000000..f3ed0862aed8c73985a8a899d2c856148e31f521 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Polynomial/SymmetricTensorRange.lean @@ -0,0 +1,74 @@ +import OAI.Analysis.Laughlin.Polynomial.SymmetricTensorOrbit + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + + theorem tensorWeight_le (Q : ℕ) (a : Fin Q → Fin 2) : tensorWeight Q a ≤ Q := by + have h := Finset.card_le_card (Finset.filter_subset (fun i => a i=1) (Finset.univ : Finset (Fin Q))) + simpa [tensorWeight,tensorBits] using h + + theorem tensorWeight_surjective (Q : ℕ) (p : Fin (Q+1)) : ∃ a : Fin Q → Fin 2, tensorWeight Q a=p.val := by + by_contra h + push Not at h + have hc := tensorWeight_count Q p.val + simp only [ite_eq_right (h _),Finset.sum_const_zero] at hc + have hp : (0 : ℝ) < Q.choose p.val := by exact_mod_cast Nat.choose_pos (by omega : p.val ≤ Q) + linarith + +noncomputable def tensorWeightRepresentative (Q : ℕ) (p : Fin (Q+1)) : Fin Q → Fin 2 := + Classical.choose (tensorWeight_surjective Q p) + theorem tensorWeightRepresentative_weight (Q : ℕ) (p : Fin (Q+1)) : + tensorWeight Q (tensorWeightRepresentative Q p)=p.val := Classical.choose_spec (tensorWeight_surjective Q p) + +noncomputable def symmetricTensorInclusion (Q : ℕ) : Matrix (Fin Q → Fin 2) (Fin (Q+1)) ℂ := + (symmetricTensorInclusionReal Q).map Complex.ofReal + +theorem symmetricTensorInclusion_isometry (Q : ℕ) : + (symmetricTensorInclusion Q)ᴴ * symmetricTensorInclusion Q=1 := by + ext p q + have h := congrArg Complex.ofReal (congrFun (congrFun (symmetricTensorInclusionReal_isometry Q) p) q) + simpa [symmetricTensorInclusion,Matrix.mul_apply,Matrix.conjTranspose_apply,Matrix.transpose_apply, + Matrix.one_apply,apply_ite] using h + + theorem symmetricTensorInclusion_mulVec (Q : ℕ) (w : Fin (Q+1) → ℂ) (a : Fin Q → Fin 2) : + (symmetricTensorInclusion Q *ᵥ w) a = + ((Real.sqrt (Q.choose (tensorWeight Q a) : ℝ))⁻¹ : ℂ) * + w ⟨tensorWeight Q a,by have := tensorWeight_le Q a; omega⟩ := by + classical + let p : Fin (Q+1) := ⟨tensorWeight Q a,by have := tensorWeight_le Q a; omega⟩ + change (∑ q, (symmetricTensorInclusion Q) a q * w q) = _ + rw [Finset.sum_eq_single p] + · simp [symmetricTensorInclusion,symmetricTensorInclusionReal,p] + · intro q hq hqp + have hn : tensorWeight Q a ≠ q.val := by intro h; exact hqp (Fin.ext h.symm) + simp [symmetricTensorInclusion,symmetricTensorInclusionReal,hn] + · simp + +theorem symmetricTensor_range (Q : ℕ) (v : (Fin Q → Fin 2) → ℂ) + (hv : ∀ a b, tensorWeight Q a=tensorWeight Q b → v a=v b) : + ∃ w : Fin (Q+1) → ℂ, symmetricTensorInclusion Q *ᵥ w=v := by + let w : Fin (Q+1) → ℂ := fun p => (Real.sqrt (Q.choose p.val : ℝ) : ℂ) * + v (tensorWeightRepresentative Q p) + refine ⟨w,?_⟩ + funext a + rw [symmetricTensorInclusion_mulVec] + dsimp [w] + have hn : (Real.sqrt (Q.choose (tensorWeight Q a) : ℝ) : ℂ) ≠ 0 := by + apply Complex.ofReal_ne_zero.mpr + apply Real.sqrt_ne_zero'.mpr + exact_mod_cast Nat.choose_pos (tensorWeight_le Q a) + rw [← mul_assoc,inv_mul_cancel₀ hn,one_mul] + apply hv + exact tensorWeightRepresentative_weight Q _ + + theorem symmetricTensor_projector_fixed (Q : ℕ) (v : (Fin Q → Fin 2) → ℂ) + (hv : ∀ a b, tensorWeight Q a=tensorWeight Q b → v a=v b) : + (symmetricTensorInclusion Q*(symmetricTensorInclusion Q)ᴴ) *ᵥ v=v := by + obtain ⟨w,rfl⟩ := symmetricTensor_range Q v hv + rw [Matrix.mulVec_mulVec,Matrix.mul_assoc,symmetricTensorInclusion_isometry,Matrix.mul_one] + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Array.lean b/lean/OAI/Analysis/Laughlin/Spin/Array.lean new file mode 100644 index 0000000000000000000000000000000000000000..a13c95c614e40c4bb71dca05d9c9559b65fddca1 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Array.lean @@ -0,0 +1,77 @@ +import OAI.Analysis.Laughlin.Spin.GenericNormalizedLadder + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +noncomputable def couplingArray (A B z : ℕ) : ℕ → ℕ → ℝ + | 0, p => (-1 : ℝ)^z * highestUnit A B z p + | n+1, p => + ((if p=0 then 0 else ladder A (p-1)*couplingArray A B z n (p-1)) + + (if p ≤ z+n then ladder B (z+n-p)*couplingArray A B z n p else 0)) / + Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n)) + +theorem couplingArray_off (A B z n p : ℕ) (hp : z+n < p) : + couplingArray A B z n p = 0 := by + induction n generalizing p with + | zero => + simp only [couplingArray,highestUnit,highestRaw] + rw [ite_eq_right (by omega)]; simp + | succ n ih => + simp only [couplingArray] + rw [ite_eq_right (by omega : p ≠ 0),ite_eq_right (by omega : ¬ p ≤ z+n),ih (p-1) (by omega)] + simp + +theorem couplingArray_physical (A B z n : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hTA : z+n ≤ A) (hTB : z+n ≤ B) (i : SpinIndex A B) (hi : i.1.val+i.2.val=z+n) : + (-1 : ℝ)^z * genericUnitDescendant A B z hA hB n i = couplingArray A B z n i.1.val := by + induction n generalizing i with + | zero => + rw [genericUnitDescendant_zero] + let p : Fin (z+1) := ⟨i.1.val,by omega⟩ + have he : i = weightSliceIndex A B z hA hB p := by + apply Prod.ext + · rfl + · apply Fin.ext; dsimp [weightSliceIndex,p]; omega + rw [he] + change (-1 : ℝ)^z * extendWeightSlice A B z hA hB (fun q => highestUnit A B z q.val) + (weightSliceIndex A B z hA hB p) = (-1 : ℝ)^z * highestUnit A B z p.val + rw [extendWeightSlice_at] + | succ n ih => + have hn : n < genericCoupledWeight A B z := by unfold genericCoupledWeight; omega + have hnreal : (n : ℝ) < genericCoupledWeight A B z := by exact_mod_cast hn + have hd : Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n)) ≠ 0 := by positivity + have he := congrFun (genericUnitDescendant_lowering A B z n hA hB hn) i + change (∑ j, totalRaise A B j i * genericUnitDescendant A B z hA hB n j) = + Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n))* + genericUnitDescendant A B z hA hB (n+1) i at he + rw [totalRaise_transpose_apply,raiseMatrix_column,raiseMatrix_column] at he + have h1 : (-1 : ℝ)^z * + (if h : 0 < i.1.val then genericUnitDescendant A B z hA hB n (⟨i.1.val-1,by omega⟩,i.2) * + ladder A (i.1.val-1) else 0) = + (if i.1.val=0 then 0 else ladder A (i.1.val-1)*couplingArray A B z n (i.1.val-1)) := by + by_cases hp : 0 < i.1.val + · rw [dite_eq_left hp,ite_eq_right (by omega : i.1.val ≠ 0)] + have hh := ih (by omega) (by omega) (⟨i.1.val-1,by omega⟩,i.2) (by dsimp; omega) + dsimp at hh + rw [← hh]; ring + · rw [dite_eq_right hp,ite_eq_left (by omega : i.1.val=0),mul_zero] + have h2 : (-1 : ℝ)^z * + (if h : 0 < i.2.val then genericUnitDescendant A B z hA hB n (i.1,⟨i.2.val-1,by omega⟩) * + ladder B (i.2.val-1) else 0) = + (if i.1.val ≤ z+n then ladder B (z+n-i.1.val)*couplingArray A B z n i.1.val else 0) := by + by_cases hp : 0 < i.2.val + · rw [dite_eq_left hp,ite_eq_left (by omega : i.1.val ≤ z+n)] + have hh := ih (by omega) (by omega) (i.1,⟨i.2.val-1,by omega⟩) (by dsimp; omega) + dsimp at hh + have hl : ladder B (i.2.val-1) = ladder B (z+n-i.1.val) := congrArg (ladder B) (by omega) + rw [← hh,hl]; ring + · rw [dite_eq_right hp,ite_eq_right (by omega : ¬ i.1.val ≤ z+n),mul_zero] + change _ = (_ + _) / _ + apply (eq_div_iff hd).mpr + linear_combination h1+h2-(-1 : ℝ)^z*he + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/ArrayLimit.lean b/lean/OAI/Analysis/Laughlin/Spin/ArrayLimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..62506616ac0a6cffb5813ff616e6486f46a37f76 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/ArrayLimit.lean @@ -0,0 +1,62 @@ +import OAI.Analysis.Laughlin.Asymptotics.HighestCouplingLimit +import OAI.Analysis.Laughlin.Spin.Array +import OAI.Analysis.Laughlin.Spin.LoweringLimit + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Topology +open Filter + +noncomputable def oscillatorArray (b : ℝ) (z : ℕ) : ℕ → ℕ → ℝ + | 0, p => oscillatorHighest (Real.sqrt b) (Real.sqrt (1-b)) z p + | n+1, p => + (if p=0 then 0 else Real.sqrt ((((p-1 : ℕ)+1 : ℝ)*(1-b))/((n : ℝ)+1))* + oscillatorArray b z n (p-1)) + + (if p ≤ z+n then Real.sqrt ((((z+n-p : ℕ)+1 : ℝ)*b)/((n : ℝ)+1))* + oscillatorArray b z n p else 0) + +theorem couplingArray_tendsto (A B : ℕ → ℕ) (b : ℝ) + (hA : Tendsto A atTop atTop) (hB : Tendsto B atTop atTop) + (hb0 : 0 < b) (hb1 : b < 1) + (hfrac : Tendsto (fun j => (B j : ℝ)/((A j : ℝ)+B j)) atTop (𝓝 b)) + (z n p : ℕ) (hp : p ≤ z+n) : + Tendsto (fun j => couplingArray (A j) (B j) z n p) atTop (𝓝 (oscillatorArray b z n p)) := by + have hS : Tendsto (fun j => A j+B j) atTop atTop := + tendsto_atTop_mono (fun j => Nat.le_add_right (A j) (B j)) hA + induction n generalizing p with + | zero => + exact source_highest_coupling_tendsto A B b hA hB hb0 hb1 hfrac z p (by omega) + | succ n ih => + let d : ℕ → ℝ := fun j => Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight (A j) (B j) z : ℝ)-n)) + have hfirst : Tendsto (fun j => if p=0 then 0 else + (ladder (A j) (p-1)/d j)*couplingArray (A j) (B j) z n (p-1)) atTop + (𝓝 (if p=0 then 0 else Real.sqrt ((((p-1 : ℕ)+1 : ℝ)*(1-b))/((n : ℝ)+1))* + oscillatorArray b z n (p-1))) := by + by_cases hp0 : p=0 + · simp only [hp0,ite_true]; exact tendsto_const_nhds + · simp only [hp0,ite_false] + have hf := normalized_ladder_factor_tendsto A (fun j => A j+B j) (1-b) hA hS + (by simpa only [Nat.cast_add] using first_spin_fraction_tendsto A B b hA hfrac) z n (p-1) + exact hf.mul (ih (p-1) (by omega)) + have hsecond : Tendsto (fun j => if p ≤ z+n then + (ladder (B j) (z+n-p)/d j)*couplingArray (A j) (B j) z n p else 0) atTop + (𝓝 (if p ≤ z+n then Real.sqrt ((((z+n-p : ℕ)+1 : ℝ)*b)/((n : ℝ)+1))* + oscillatorArray b z n p else 0)) := by + by_cases hpn : p ≤ z+n + · simp only [hpn,ite_true] + have hf := normalized_ladder_factor_tendsto B (fun j => A j+B j) b hB hS + (by simpa only [Nat.cast_add] using hfrac) z n (z+n-p) + exact hf.mul (ih p hpn) + · simp only [hpn,ite_false]; exact tendsto_const_nhds + have ht := hfirst.add hsecond + apply ht.congr' + exact Filter.Eventually.of_forall (fun j => by + change (if p=0 then 0 else (ladder (A j) (p-1)/d j)*couplingArray (A j) (B j) z n (p-1)) + + (if p ≤ z+n then (ladder (B j) (z+n-p)/d j)*couplingArray (A j) (B j) z n p else 0) = _ + change _ = ((if p=0 then 0 else _) + (if p ≤ z+n then _ else 0))/d j + split_ifs <;> ring) + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Basic.lean b/lean/OAI/Analysis/Laughlin/Spin/Basic.lean new file mode 100644 index 0000000000000000000000000000000000000000..cd5d28a2c664e9336ede31b9d4d75a6eaa822c8c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Basic.lean @@ -0,0 +1,101 @@ +import OAI.Analysis.Laughlin.Spin.Sl2DescendantNorm +import OAI.Analysis.Laughlin.Spin.TotalSl2Matrix + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +def genericCoupledWeight (A B z : ℕ) : ℕ := A+B-2*z + +noncomputable def genericHighest (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + SpinIndex A B → ℝ := + extendWeightSlice A B z hA hB (fun p => highestUnit A B z p.val) + +theorem genericHighest_norm (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + vectorNormSq (genericHighest A B z hA hB) = 1 := by + unfold vectorNormSq genericHighest + simp only [pow_two] + rw [sum_extendWeightSlice] + simp_rw [extendWeightSlice_at,← pow_two] + simpa only [← Fin.sum_univ_eq_sum_range] using highestUnit_norm A B z hA hB + +theorem genericHighest_weight (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + totalWeight A B *ᵥ genericHighest A B z hA hB = + (genericCoupledWeight A B z : ℝ) • genericHighest A B z hA hB := by + rw [totalWeight_diagonal] + funext i + simp only [Matrix.mulVec,dotProduct,Matrix.diagonal_apply,ite_mul,zero_mul, + Finset.sum_ite_eq,Finset.mem_univ,ite_true] + change ((A : ℝ)+B-2*((i.1.val : ℝ)+i.2.val))*genericHighest A B z hA hB i = + (genericCoupledWeight A B z : ℝ)*genericHighest A B z hA hB i + by_cases hi : i.1.val+i.2.val=z + · have hc : (i.1.val : ℝ)+i.2.val=z := by exact_mod_cast hi + rw [hc] + congr 1 + unfold genericCoupledWeight + rw [Nat.cast_sub (by omega : 2*z ≤ A+B)] + push_cast; ring + · have he : genericHighest A B z hA hB i = 0 := + extendWeightSlice_off A B z hA hB _ i hi + rw [he]; ring + +theorem genericHighest_raising_zero (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + totalRaise A B *ᵥ genericHighest A B z hA hB = 0 := by + apply extendWeightSlice_highest + intro p + exact highestUnit_raising A B z p.val hA hB p.isLt + +noncomputable def genericDescendant (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) (n : ℕ) : + SpinIndex A B → ℝ := + ((totalRaise A B)ᵀ ^ n) *ᵥ genericHighest A B z hA hB + +theorem genericDescendant_succ (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) (n : ℕ) : + genericDescendant A B z hA hB (n+1) = + (totalRaise A B)ᵀ *ᵥ genericDescendant A B z hA hB n := by + simp only [genericDescendant,pow_succ',Matrix.mulVec_mulVec] + +theorem genericDescendant_norm_pos (A B z n : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hn : n ≤ genericCoupledWeight A B z) : + 0 < vectorNormSq (genericDescendant A B z hA hB n) := by + apply descendant_norm_pos (totalRaise A B) (totalWeight A B) ((totalRaise A B)ᵀ) + (genericHighest A B z hA hB) (genericCoupledWeight A B z) n + · exact total_raise_lower_commutator _ _ + · exact total_weight_lower_commutator _ _ + · exact Matrix.transpose_transpose _ + · exact genericHighest_weight A B z hA hB + · exact genericHighest_raising_zero A B z hA hB + · rw [genericHighest_norm]; norm_num + · exact hn + +theorem genericDescendant_norm_step (A B z n : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + vectorNormSq (genericDescendant A B z hA hB (n+1)) = + (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n))* + vectorNormSq (genericDescendant A B z hA hB n) := by + exact descendant_norm_step (totalRaise A B) (totalWeight A B) ((totalRaise A B)ᵀ) + (genericHighest A B z hA hB) (genericCoupledWeight A B z) + (total_raise_lower_commutator _ _) (total_weight_lower_commutator _ _) + (Matrix.transpose_transpose _) (genericHighest_weight A B z hA hB) + (genericHighest_raising_zero A B z hA hB) n + +noncomputable def genericUnitDescendant (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) (n : ℕ) : + SpinIndex A B → ℝ := + (Real.sqrt (vectorNormSq (genericDescendant A B z hA hB n)))⁻¹ • genericDescendant A B z hA hB n + +theorem genericUnitDescendant_norm (A B z n : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hn : n ≤ genericCoupledWeight A B z) : + vectorNormSq (genericUnitDescendant A B z hA hB n) = 1 := by + have hp := genericDescendant_norm_pos A B z n hA hB hn + unfold genericUnitDescendant vectorNormSq + simp only [Pi.smul_apply,smul_eq_mul,mul_pow,← Finset.mul_sum] + change (Real.sqrt (vectorNormSq (genericDescendant A B z hA hB n)))⁻¹ ^ 2 * + vectorNormSq (genericDescendant A B z hA hB n) = 1 + rw [inv_pow,Real.sq_sqrt (le_of_lt hp),inv_mul_cancel₀ (ne_of_gt hp)] + +theorem genericUnitDescendant_zero (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + genericUnitDescendant A B z hA hB 0 = genericHighest A B z hA hB := by + simp [genericUnitDescendant,genericDescendant,genericHighest_norm] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Basis.lean b/lean/OAI/Analysis/Laughlin/Spin/Basis.lean new file mode 100644 index 0000000000000000000000000000000000000000..78332216e4c0ef81a932bf9824d4592e7467e1b1 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Basis.lean @@ -0,0 +1,89 @@ +import OAI.Analysis.Laughlin.Spin.Orthogonal + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +abbrev CoupledIndex (Q : ℕ) := Σ z : Fin (Q+1), Fin (coupledWeight Q z.val+1) + +theorem fin_sum_values (n : ℕ) : (∑ i : Fin n, (i.val : ℝ)) = (n : ℝ)*(n-1)/2 := by + induction n with + | zero => simp + | succ n ih => + rw [Fin.sum_univ_succ] + simp only [Fin.val_zero,Nat.cast_zero,zero_add,Fin.val_succ,Nat.cast_add,Nat.cast_one, + Finset.sum_add_distrib,Finset.sum_const,Finset.card_univ,Fintype.card_fin,nsmul_eq_mul,mul_one,ih] + ring + +theorem coupledIndex_card (Q : ℕ) (hQ : 2 ≤ Q) : + Fintype.card (CoupledIndex Q) = Fintype.card (PairOrbitalIndex Q) := by + have hr : (Fintype.card (CoupledIndex Q) : ℝ) = (Fintype.card (PairOrbitalIndex Q) : ℝ) := by + simp only [Fintype.card_sigma,Fintype.card_fin,Fintype.card_prod,Nat.cast_sum] + have hc (z : Fin (Q+1)) : ((coupledWeight Q z.val+1 : ℕ) : ℝ) = 3*(Q : ℝ)-1-2*z.val := by + unfold coupledWeight + rw [Nat.cast_add,Nat.cast_one,Nat.cast_sub (by omega : 2*z.val ≤ 3*Q-2), + Nat.cast_sub (by omega : 2 ≤ 3*Q)] + push_cast; ring + simp_rw [hc] + rw [Finset.sum_sub_distrib,Finset.sum_const,← Finset.mul_sum,fin_sum_values] + simp only [Finset.card_univ,Fintype.card_fin,nsmul_eq_mul,Nat.cast_mul,Nat.cast_add,Nat.cast_one] + rw [Nat.cast_sub (by omega : 2 ≤ 2*Q)] + push_cast + ring + exact_mod_cast hr + +noncomputable def coupledBasisMatrix (Q : ℕ) (hQ : 2 ≤ Q) : + Matrix (PairOrbitalIndex Q) (CoupledIndex Q) ℝ := fun i s => + normalizedCoupledDescendant Q s.1.val hQ (by omega) s.2.val i + +theorem coupledBasis_isometry (Q : ℕ) (hQ : 2 ≤ Q) : + (coupledBasisMatrix Q hQ)ᵀ * coupledBasisMatrix Q hQ = 1 := by + ext s t + rw [Matrix.mul_apply] + simp only [Matrix.transpose_apply,coupledBasisMatrix,Matrix.one_apply] + by_cases hst : s=t + · subst t + rw [ite_eq_left rfl] + simpa only [vectorNormSq,pow_two] using + normalizedCoupledDescendant_norm Q s.1.val s.2.val hQ (by omega) (by omega) + · rw [ite_eq_right hst] + apply normalizedCoupledDescendant_orthogonal + rcases s with ⟨z,n⟩ + rcases t with ⟨w,m⟩ + by_cases hzw : z=w + · subst w + right + intro hnm + apply hst + have he : n=m := Fin.ext hnm + rw [he] + · left + intro h + exact hzw (Fin.ext h) + +theorem coupledBasis_complete (Q : ℕ) (hQ : 2 ≤ Q) : + coupledBasisMatrix Q hQ * (coupledBasisMatrix Q hQ)ᵀ = 1 := by + exact (Matrix.mul_eq_one_comm_of_card_eq (m := CoupledIndex Q) (n := PairOrbitalIndex Q) + (R := ℝ) (coupledIndex_card Q hQ)).mp (coupledBasis_isometry Q hQ) + +theorem coupledBasis_eigen (Q : ℕ) (hQ : 2 ≤ Q) : + (threeGram Q-1)*coupledBasisMatrix Q hQ = + coupledBasisMatrix Q hQ * Matrix.diagonal (fun s : CoupledIndex Q => gramEigenvalueFormula Q s.1.val) := by + ext i s + rw [Matrix.mul_apply,Matrix.mul_diagonal] + have he := congrFun (normalizedCoupledDescendant_eigen Q s.1.val s.2.val hQ (by omega)) i + simpa only [Matrix.mulVec,dotProduct,Pi.smul_apply,smul_eq_mul,coupledBasisMatrix,mul_comm] using he + +theorem threeGram_diagonalization (Q : ℕ) (hQ : 2 ≤ Q) : + threeGram Q-1 = coupledBasisMatrix Q hQ * + Matrix.diagonal (fun s : CoupledIndex Q => gramEigenvalueFormula Q s.1.val) * + (coupledBasisMatrix Q hQ)ᵀ := by + calc + _ = (threeGram Q-1)*(coupledBasisMatrix Q hQ*(coupledBasisMatrix Q hQ)ᵀ) := by + rw [coupledBasis_complete Q hQ,Matrix.mul_one] + _ = _ := by rw [← Matrix.mul_assoc,coupledBasis_eigen Q hQ] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Basis2.lean b/lean/OAI/Analysis/Laughlin/Spin/Basis2.lean new file mode 100644 index 0000000000000000000000000000000000000000..c87c6629586670db8ffd3da0d5aa37d9730a7a1a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Basis2.lean @@ -0,0 +1,98 @@ +import OAI.Analysis.Laughlin.Spin.Basis +import OAI.Analysis.Laughlin.Spin.GenericOrthogonality +import OAI.Analysis.Laughlin.Spin.Intertwining + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +abbrev GenericCoupledIndex (A B : ℕ) := + Σ z : Fin (min A B+1), Fin (genericCoupledWeight A B z.val+1) + +noncomputable def genericCoupledBasis (A B : ℕ) : + Matrix (SpinIndex A B) (GenericCoupledIndex A B) ℝ := + fun i s => genericUnitDescendant A B s.1.val (by have := s.1.isLt; omega) + (by have := s.1.isLt; omega) s.2.val i + +theorem genericCoupledIndex_card (A B : ℕ) : + Fintype.card (GenericCoupledIndex A B) = Fintype.card (SpinIndex A B) := by + have hr : (Fintype.card (GenericCoupledIndex A B) : ℝ) = + (Fintype.card (SpinIndex A B) : ℝ) := by + simp only [Fintype.card_sigma,Fintype.card_fin,Fintype.card_prod,Nat.cast_sum] + have hc (z : Fin (min A B+1)) : + ((genericCoupledWeight A B z.val+1 : ℕ) : ℝ) = A+B+1-2*(z.val : ℝ) := by + have hz := z.isLt + unfold genericCoupledWeight + rw [Nat.cast_add,Nat.cast_sub (by omega : 2*z.val ≤ A+B)] + push_cast + ring + simp_rw [hc] + rw [Finset.sum_sub_distrib,Finset.sum_const,← Finset.mul_sum,fin_sum_values] + simp only [Finset.card_univ,Fintype.card_fin,nsmul_eq_mul,Nat.cast_mul,Nat.cast_add,Nat.cast_one] + rcases le_total A B with h | h + · rw [Nat.min_eq_left h]; ring + · rw [Nat.min_eq_right h]; ring + exact_mod_cast hr + +theorem genericCoupledBasis_isometry (A B : ℕ) : + (genericCoupledBasis A B)ᵀ * genericCoupledBasis A B = 1 := by + ext s t + simp only [Matrix.mul_apply,Matrix.transpose_apply,genericCoupledBasis,Matrix.one_apply] + by_cases h : s=t + · subst t + rw [ite_eq_left rfl] + simpa only [vectorNormSq,pow_two] using + genericUnitDescendant_norm A B s.1.val s.2.val _ _ (by have := s.2.isLt; omega) + · rw [ite_eq_right h] + apply genericUnitDescendant_orthogonal + rcases s with ⟨z,n⟩ + rcases t with ⟨w,m⟩ + by_cases hzw : z=w + · subst w + right + intro hnm + exact h (by have he : n=m := Fin.ext hnm; subst m; rfl) + · left + intro he + exact hzw (Fin.ext he) + +theorem genericCoupledBasis_complete (A B : ℕ) : + genericCoupledBasis A B * (genericCoupledBasis A B)ᵀ = 1 := + (Matrix.mul_eq_one_comm_of_card_eq (m := GenericCoupledIndex A B) (n := SpinIndex A B) (R := ℝ) (genericCoupledIndex_card A B)).mp + (genericCoupledBasis_isometry A B) + +theorem genericCoupledInclusion_isometry (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + (genericCoupledInclusion A B z hA hB)ᵀ * genericCoupledInclusion A B z hA hB = 1 := by + ext n m + simp only [Matrix.mul_apply,Matrix.transpose_apply,genericCoupledInclusion,Matrix.one_apply] + by_cases h : n=m + · subst m + rw [ite_eq_left rfl] + simpa only [vectorNormSq,pow_two] using genericUnitDescendant_norm A B z n.val hA hB (by omega) + · rw [ite_eq_right h] + exact genericUnitDescendant_orthogonal A B z z n.val m.val hA hB hA hB + (Or.inr (fun he => h (Fin.ext he))) + +theorem physicalCoupledInclusion_isometry (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + (physicalCoupledInclusion A B z hA hB)ᴴ * physicalCoupledInclusion A B z hA hB = 1 := by + have hs : star ((-1 : ℂ)^z) * (-1 : ℂ)^z = 1 := by + simp only [star_pow,star_neg,star_one,← mul_pow] + norm_num + have hg : ((genericCoupledInclusion A B z hA hB).map Complex.ofReal)ᴴ * + (genericCoupledInclusion A B z hA hB).map Complex.ofReal = 1 := by + ext n m + have h := congrArg Complex.ofReal + (congrFun (congrFun (genericCoupledInclusion_isometry A B z hA hB) n) m) + simpa only [Matrix.mul_apply,Matrix.transpose_apply,Matrix.conjTranspose_apply, + Matrix.map_apply,Complex.star_def,Complex.conj_ofReal,Complex.ofReal_sum, + Complex.ofReal_mul,Matrix.one_apply,apply_ite,Complex.ofReal_one, + Complex.ofReal_zero] using h + simp only [physicalCoupledInclusion,Matrix.conjTranspose_smul,Matrix.smul_mul,Matrix.mul_smul, + smul_smul,hg] + simp only [star_pow,star_neg,star_one] at hs ⊢ + rw [hs,one_smul] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/BinomialWeights.lean b/lean/OAI/Analysis/Laughlin/Spin/BinomialWeights.lean new file mode 100644 index 0000000000000000000000000000000000000000..aea0ab020980ce73b79dfe1ca6eaedcc68144d3c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/BinomialWeights.lean @@ -0,0 +1,38 @@ +import OAI.Analysis.Laughlin.Spin.GeneralSpinAction +import OAI.Analysis.Laughlin.Spin.LadderMatrix + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators + +noncomputable def spinBinomialWeight (Q : ℕ) (p : Fin (Q+1)) : ℂ := + (Real.sqrt (Q.choose p.val : ℝ) : ℂ) + +theorem spinBinomialWeight_ne_zero (Q : ℕ) (p : Fin (Q+1)) : spinBinomialWeight Q p ≠ 0 := by + apply Complex.ofReal_ne_zero.mpr + apply Real.sqrt_ne_zero'.mpr + exact_mod_cast Nat.choose_pos (Nat.le_of_lt_succ p.isLt) + +theorem spinBinomialWeight_step (Q : ℕ) (p : Fin Q) : + spinBinomialWeight Q p.succ * ((p.val : ℂ)+1) = + spinBinomialWeight Q p.castSucc * (Spin.ladder Q p.val : ℂ) := by + have hr : Real.sqrt (Q.choose (p.val+1) : ℝ)*((p.val : ℝ)+1) = + Real.sqrt (Q.choose p.val : ℝ)*Spin.ladder Q p.val := by + have hc := congrArg (fun n : ℕ => (n : ℝ)) (Nat.choose_succ_right_eq Q p.val) + push_cast at hc + have he : (Real.sqrt (Q.choose (p.val+1) : ℝ)*((p.val : ℝ)+1))^2 = + (Real.sqrt (Q.choose p.val : ℝ)*Spin.ladder Q p.val)^2 := by + unfold Spin.ladder + rw [mul_pow,mul_pow,Real.sq_sqrt (by positivity),Real.sq_sqrt (by positivity), + Real.sq_sqrt (by positivity)] + linear_combination ((p.val : ℝ)+1)*hc + have h1 : 0 ≤ Real.sqrt (Q.choose (p.val+1) : ℝ)*((p.val : ℝ)+1) := by positivity + have h2 : 0 ≤ Real.sqrt (Q.choose p.val : ℝ)*Spin.ladder Q p.val := by + unfold Spin.ladder; positivity + nlinarith only [he,h1,h2] + simpa [spinBinomialWeight] using congrArg Complex.ofReal hr + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Compact.lean b/lean/OAI/Analysis/Laughlin/Spin/Compact.lean new file mode 100644 index 0000000000000000000000000000000000000000..12f9bc16ec017d7410b12e1a27520a4e1d2b96f8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Compact.lean @@ -0,0 +1,62 @@ +import Mathlib.Analysis.Complex.Basic +import Mathlib.Topology.Algebra.Star.Unitary +import Mathlib.Topology.Instances.Matrix +import Mathlib.Topology.MetricSpace.ProperSpace +import OAI.Analysis.Laughlin.Spin.TensorAction + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + +instance sourceSU2_continuousInv : ContinuousInv SourceSU2 where + continuous_inv := by + apply continuous_induced_rng.mpr + change Continuous (fun g : SourceSU2 => (g.val)ᴴ) + fun_prop + +instance sourceSU2_topologicalGroup : IsTopologicalGroup SourceSU2 where + + theorem unitary_entry_norm_le_one (A : Matrix (Fin 2) (Fin 2) ℂ) + (hA : A ∈ Matrix.unitaryGroup (Fin 2) ℂ) (i j : Fin 2) : ‖A i j‖ ≤ 1 := by + have h := congrFun (congrFun (Matrix.mem_unitaryGroup_iff.mp hA) i) i + rw [Matrix.star_eq_conjTranspose] at h + have hs : ∑ k, ‖A i k‖^2 = (1 : ℝ) := by + have hr := congrArg Complex.re h + simpa [Matrix.mul_apply,Matrix.conjTranspose_apply,Complex.mul_conj,Complex.normSq_eq_norm_sq,← Complex.ofReal_pow] using hr + have hj : ‖A i j‖^2 ≤ ∑ k, ‖A i k‖^2 := + Finset.single_le_sum (fun k hk => sq_nonneg ‖A i k‖) (Finset.mem_univ j) + rw [hs] at hj + nlinarith [norm_nonneg (A i j)] + + theorem sourceSU2_isClosed : + IsClosed (Matrix.specialUnitaryGroup (Fin 2) ℂ : Set (Matrix (Fin 2) (Fin 2) ℂ)) := by + have he : (Matrix.specialUnitaryGroup (Fin 2) ℂ : Set (Matrix (Fin 2) (Fin 2) ℂ)) = + (unitary (Matrix (Fin 2) (Fin 2) ℂ) : Set _) ∩ {A | A.det=1} := rfl + rw [he] + exact isClosed_unitary.inter (isClosed_eq (by fun_prop) continuous_const) + + theorem sourceSU2_isCompact : + IsCompact (Matrix.specialUnitaryGroup (Fin 2) ℂ : Set (Matrix (Fin 2) (Fin 2) ℂ)) := by + let K : Set (Matrix (Fin 2) (Fin 2) ℂ) := + {A | ∀ i j, A i j ∈ Metric.closedBall (0 : ℂ) 1} + have hK : IsCompact K := by + exact isCompact_pi_infinite (fun i : Fin 2 => + isCompact_pi_infinite (fun j : Fin 2 => isCompact_closedBall (0 : ℂ) 1)) + apply hK.of_isClosed_subset sourceSU2_isClosed + intro A hA i j + simp only [Metric.mem_closedBall,dist_zero_right] + exact unitary_entry_norm_le_one A hA.1 i j + +instance sourceSU2_compactSpace : CompactSpace SourceSU2 := + isCompact_iff_compactSpace.mp sourceSU2_isCompact + + theorem sourceTensorRepresentation_continuous (Q : ℕ) (a b : Fin Q → Fin 2) : + Continuous (fun g : SourceSU2 => sourceTensorRepresentation Q g a b) := by + change Continuous (fun g : SourceSU2 => ∏ i, g.val (a i) (b i)) + exact continuous_finsetProd _ (fun i hi => (continuous_apply (b i)).comp + ((continuous_apply (a i)).comp continuous_subtype_val)) + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/CompactAverage.lean b/lean/OAI/Analysis/Laughlin/Spin/CompactAverage.lean new file mode 100644 index 0000000000000000000000000000000000000000..587f043bb953da63190093e596ca50e56d8b84a2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/CompactAverage.lean @@ -0,0 +1,40 @@ +import Mathlib.Tactic.FunProp +import OAI.Analysis.Laughlin.Spin.MatrixAverage + +namespace OAI + +namespace Laughlin.Rotation +open MeasureTheory MeasureTheory.Measure + +variable {G I : Type*} [Group G] [TopologicalSpace G] [IsTopologicalGroup G] + [Fintype I] [DecidableEq I] + + theorem conjugateOrbit_continuous (ρ : G →* Matrix I I ℂ) + (hρ : ∀ i j, Continuous (fun g => ρ g i j)) (M : Matrix I I ℂ) (i j : I) : + Continuous (fun g => conjugateOrbit ρ M g i j) := by + simp only [conjugateOrbit,Matrix.mul_apply] + fun_prop + +variable [MeasurableSpace G] [BorelSpace G] [CompactSpace G] + + theorem compact_conjugateOrbit_integrable (μ : Measure G) [IsFiniteMeasure μ] + (ρ : G →* Matrix I I ℂ) (hρ : ∀ i j, Continuous (fun g => ρ g i j)) (M : Matrix I I ℂ) : + ∀ i j, Integrable (fun g => conjugateOrbit ρ M g i j) μ := by + intro i j + exact (conjugateOrbit_continuous ρ hρ M i j).integrable_of_hasCompactSupport + (isClosed_tsupport _).isCompact + +theorem compact_haar_average_commutes (μ : Measure G) [IsProbabilityMeasure μ] [IsMulLeftInvariant μ] + (ρ : G →* Matrix I I ℂ) (hρ : ∀ i j, Continuous (fun g => ρ g i j)) + (M : Matrix I I ℂ) (g : G) : + ρ g*matrixIntegral μ (conjugateOrbit ρ M) = matrixIntegral μ (conjugateOrbit ρ M)*ρ g := by + exact haar_average_commutes μ ρ M (compact_conjugateOrbit_integrable μ ρ hρ M) g + +theorem compact_haar_average_trace (μ : Measure G) [IsProbabilityMeasure μ] + (ρ : G →* Matrix I I ℂ) (hρ : ∀ i j, Continuous (fun g => ρ g i j)) (M : Matrix I I ℂ) : + Matrix.trace (matrixIntegral μ (conjugateOrbit ρ M)) = Matrix.trace M := by + exact haar_average_trace μ ρ M (compact_conjugateOrbit_integrable μ ρ hρ M) + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/CopySchur.lean b/lean/OAI/Analysis/Laughlin/Spin/CopySchur.lean new file mode 100644 index 0000000000000000000000000000000000000000..29448c0e2e8ad0a7d0f48d11fa98c4cbc8aaf35c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/CopySchur.lean @@ -0,0 +1,69 @@ +import OAI.Analysis.Laughlin.Spin.Schur + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + +variable {C I : Type*} [Fintype C] [DecidableEq C] [Fintype I] [DecidableEq I] + +noncomputable def copyMatrix (A : Matrix I I ℂ) : Matrix (C × I) (C × I) ℂ := + fun i j => if i.1=j.1 then A i.2 j.2 else 0 + +omit [DecidableEq I] in +theorem copyMatrix_mul (A B : Matrix I I ℂ) : + copyMatrix (C := C) (A*B)=copyMatrix A*copyMatrix B := by + ext a b + simp only [copyMatrix,Matrix.mul_apply,Fintype.sum_prod_type,ite_mul,zero_mul,mul_ite,mul_zero, + Finset.sum_ite_irrel,Finset.sum_const_zero,Finset.sum_ite_eq',Finset.mem_univ,ite_true] + +omit [Fintype C] [Fintype I] in +theorem copyMatrix_one : copyMatrix (C := C) (1 : Matrix I I ℂ)=1 := by + ext a b + simp only [copyMatrix,Matrix.one_apply] + by_cases h : a=b + · subst b; simp + · have hh : ¬ (a.1=b.1 ∧ a.2=b.2) := by rintro ⟨h1,h2⟩; exact h (Prod.ext h1 h2) + simp [h] + tauto + +noncomputable def copiedSpinRepresentation (C : Type*) [Fintype C] [DecidableEq C] (Q : ℕ) : + SourceSU2 →* Matrix (C × Fin (Q+1)) (C × Fin (Q+1)) ℂ where + toFun g := copyMatrix (sourceSpinRepresentation Q g) + map_one' := by rw [map_one,copyMatrix_one] + map_mul' g h := by rw [map_mul,copyMatrix_mul] + + theorem copied_conjugateOrbit_block (Q : ℕ) + (M : Matrix (C × Fin (Q+1)) (C × Fin (Q+1)) ℂ) (g : SourceSU2) + (r s : C) (p q : Fin (Q+1)) : + conjugateOrbit (copiedSpinRepresentation C Q) M g (r,p) (s,q) = + conjugateOrbit (sourceSpinRepresentation Q) (fun i j => M (r,i) (s,j)) g p q := by + simp only [conjugateOrbit,Matrix.mul_apply,Fintype.sum_prod_type,copiedSpinRepresentation, + MonoidHom.coe_mk,OneHom.coe_mk,copyMatrix,ite_mul,zero_mul,mul_ite,mul_zero, + Finset.sum_ite_irrel,Finset.sum_const_zero,Finset.sum_ite_eq,Finset.sum_ite_eq',Finset.mem_univ,ite_true] + rfl + +theorem source_spin_copy_haar_schur (Q : ℕ) + (M : Matrix (C × Fin (Q+1)) (C × Fin (Q+1)) ℂ) (r s : C) (p q : Fin (Q+1)) : + matrixIntegral sourceHaar (conjugateOrbit (copiedSpinRepresentation C Q) M) (r,p) (s,q) = + ((∑ k : Fin (Q+1), M (r,k) (s,k))/(Q+1 : ℕ)) * (if p=q then 1 else 0) := by + have h := congrFun (congrFun (source_spin_haar_schur Q (fun i j => M (r,i) (s,j))) p) q + simpa only [matrixIntegral,copied_conjugateOrbit_block,Matrix.smul_apply,smul_eq_mul,Matrix.one_apply, + Matrix.trace,Matrix.diag] using h + +theorem source_highest_copy_orbit_resolution (Q : ℕ) (r s : C) (a b : C) (p q : Fin (Q+1)) : + ((Q+1 : ℕ) : ℂ) * matrixIntegral sourceHaar + (conjugateOrbit (copiedSpinRepresentation C Q) + (fun i j => if i=(r,(0 : Fin (Q+1))) ∧ j=(s,(0 : Fin (Q+1))) then 1 else 0)) (a,p) (b,q) = + if a=r ∧ b=s ∧ p=q then 1 else 0 := by + rw [source_spin_copy_haar_schur Q + (fun (i j : C × Fin (Q+1)) => if i=(r,0) ∧ j=(s,0) then 1 else 0) a b p q] + have hn : ((Q+1 : ℕ) : ℂ) ≠ 0 := by exact_mod_cast Nat.succ_ne_zero Q + have hn' : (Q : ℂ)+1 ≠ 0 := by simpa only [Nat.cast_add,Nat.cast_one] using hn + simp only [Prod.mk.injEq] + by_cases ha : a=r <;> by_cases hb : b=s <;> by_cases hpq : p=q <;> + simp [ha,hb,hpq,hn'] + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/DescendantNorm.lean b/lean/OAI/Analysis/Laughlin/Spin/DescendantNorm.lean new file mode 100644 index 0000000000000000000000000000000000000000..aaa524d3a55b8574e2e47c90bc3104fcd9b7db6b --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/DescendantNorm.lean @@ -0,0 +1,82 @@ +import OAI.Analysis.Laughlin.Spin.Sl2DescendantNorm +import OAI.Analysis.Laughlin.Spin.TotalSl2Matrix +import OAI.Analysis.Laughlin.ThreeBody.Descendants + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +def coupledWeight (Q z : ℕ) : ℕ := 3*Q-2-2*z + +theorem coupledHighest_weight (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + totalWeight (2*Q-2) Q *ᵥ coupledHighest Q z hQ hz = + (coupledWeight Q z : ℝ) • coupledHighest Q z hQ hz := by + rw [totalWeight_diagonal] + funext i + simp only [Matrix.mulVec,dotProduct,Matrix.diagonal_apply,ite_mul,zero_mul, + Finset.sum_ite_eq,Finset.mem_univ,ite_true] + change ((2*Q-2 : ℕ)+ (Q : ℝ)-2*((i.1.val : ℝ)+i.2.val))*coupledHighest Q z hQ hz i = + (coupledWeight Q z : ℝ)*coupledHighest Q z hQ hz i + by_cases hi : i.1.val+i.2.val=z + · have hc : (i.1.val : ℝ)+i.2.val=z := by exact_mod_cast hi + rw [hc] + congr 1 + unfold coupledWeight + rw [Nat.cast_sub (by omega : 2*z ≤ 3*Q-2),Nat.cast_sub (by omega : 2 ≤ 3*Q), + Nat.cast_sub (by omega : 2 ≤ 2*Q)] + push_cast; ring + · have he : coupledHighest Q z hQ hz i = 0 := + extendWeightSlice_off (2*Q-2) Q z (by omega) hz _ i hi + rw [he]; ring + +theorem coupledHighest_raising_zero (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + totalRaise (2*Q-2) Q *ᵥ coupledHighest Q z hQ hz = 0 := by + apply extendWeightSlice_highest + intro p + exact highestUnit_raising (2*Q-2) Q z p.val (by omega) hz p.isLt + +theorem coupledDescendant_norm_pos (Q z n : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) + (hn : n ≤ coupledWeight Q z) : 0 < vectorNormSq (coupledDescendant Q z hQ hz n) := by + apply descendant_norm_pos (totalRaise (2*Q-2) Q) (totalWeight (2*Q-2) Q) + ((totalRaise (2*Q-2) Q)ᵀ) (coupledHighest Q z hQ hz) (coupledWeight Q z) n + · exact total_raise_lower_commutator _ _ + · exact total_weight_lower_commutator _ _ + · exact Matrix.transpose_transpose _ + · exact coupledHighest_weight Q z hQ hz + · exact coupledHighest_raising_zero Q z hQ hz + · change 0 < ∑ i, (coupledHighest Q z hQ hz i)^2 + rw [coupledHighest_norm Q z hQ hz]; norm_num + · exact hn + +theorem coupledDescendant_norm_step (Q z n : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + vectorNormSq (coupledDescendant Q z hQ hz (n+1)) = + (((n : ℝ)+1)*((coupledWeight Q z : ℝ)-n))*vectorNormSq (coupledDescendant Q z hQ hz n) := by + exact descendant_norm_step (totalRaise (2*Q-2) Q) (totalWeight (2*Q-2) Q) + ((totalRaise (2*Q-2) Q)ᵀ) (coupledHighest Q z hQ hz) (coupledWeight Q z) + (total_raise_lower_commutator _ _) (total_weight_lower_commutator _ _) + (Matrix.transpose_transpose _) (coupledHighest_weight Q z hQ hz) + (coupledHighest_raising_zero Q z hQ hz) n + +noncomputable def normalizedCoupledDescendant (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) (n : ℕ) : + PairOrbitalIndex Q → ℝ := + (Real.sqrt (vectorNormSq (coupledDescendant Q z hQ hz n)))⁻¹ • coupledDescendant Q z hQ hz n + +theorem normalizedCoupledDescendant_norm (Q z n : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) + (hn : n ≤ coupledWeight Q z) : vectorNormSq (normalizedCoupledDescendant Q z hQ hz n) = 1 := by + have hp := coupledDescendant_norm_pos Q z n hQ hz hn + unfold normalizedCoupledDescendant vectorNormSq + simp only [Pi.smul_apply,smul_eq_mul,mul_pow,← Finset.mul_sum] + change (Real.sqrt (vectorNormSq (coupledDescendant Q z hQ hz n)))⁻¹ ^ 2 * + vectorNormSq (coupledDescendant Q z hQ hz n) = 1 + rw [inv_pow,Real.sq_sqrt (le_of_lt hp),inv_mul_cancel₀ (ne_of_gt hp)] + +theorem normalizedCoupledDescendant_eigen (Q z n : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + (threeGram Q-1) *ᵥ normalizedCoupledDescendant Q z hQ hz n = + gramEigenvalueFormula Q z • normalizedCoupledDescendant Q z hQ hz n := by + unfold normalizedCoupledDescendant + rw [Matrix.mulVec_smul,threeGram_sub_one_descendant_eigen,smul_comm] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Disjoint.lean b/lean/OAI/Analysis/Laughlin/Spin/Disjoint.lean new file mode 100644 index 0000000000000000000000000000000000000000..2a0d41820c9bcfdcbbbde22f70cb88e742b64a73 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Disjoint.lean @@ -0,0 +1,66 @@ +import Mathlib.Analysis.RCLike.Basic +import Mathlib.LinearAlgebra.Matrix.DotProduct +import OAI.Analysis.Laughlin.Spin.Schur + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix ComplexOrder + + theorem sourceSpinRepresentation_inv (Q : ℕ) (g : SourceSU2) : + sourceSpinRepresentation Q g⁻¹=(sourceSpinRepresentation Q g)ᴴ := by + have hu := Matrix.mem_unitaryGroup_iff'.mp (sourceSpinRepresentation_unitary Q g) + rw [Matrix.star_eq_conjTranspose] at hu + calc + _ = 1*sourceSpinRepresentation Q g⁻¹ := by rw [Matrix.one_mul] + _ = ((sourceSpinRepresentation Q g)ᴴ*sourceSpinRepresentation Q g)*sourceSpinRepresentation Q g⁻¹ := by rw [hu] + _ = _ := by rw [Matrix.mul_assoc,← map_mul,mul_inv_cancel,map_one,Matrix.mul_one] + + theorem source_spin_intertwiner_adjoint (m n : ℕ) + (M : Matrix (Fin (m+1)) (Fin (n+1)) ℂ) + (hM : ∀ g : SourceSU2, sourceSpinRepresentation m g*M=M*sourceSpinRepresentation n g) : + ∀ g : SourceSU2, sourceSpinRepresentation n g*Mᴴ=Mᴴ*sourceSpinRepresentation m g := by + intro g + have h := congrArg Matrix.conjTranspose (hM g⁻¹) + simpa only [Matrix.conjTranspose_mul,sourceSpinRepresentation_inv, + Matrix.conjTranspose_conjTranspose] using h.symm + +theorem source_spin_intertwiner_zero (m n : ℕ) (hmn : m ≠ n) + (M : Matrix (Fin (m+1)) (Fin (n+1)) ℂ) + (hM : ∀ g : SourceSU2, sourceSpinRepresentation m g*M=M*sourceSpinRepresentation n g) : M=0 := by + have hA := source_spin_intertwiner_adjoint m n M hM + have hl := source_spin_commutant_scalar m (M*Mᴴ) (by + intro g + rw [← Matrix.mul_assoc,hM,Matrix.mul_assoc,hA,← Matrix.mul_assoc]) + have hr := source_spin_commutant_scalar n (Mᴴ*M) (by + intro g + rw [← Matrix.mul_assoc,hA,Matrix.mul_assoc,hM,← Matrix.mul_assoc]) + by_contra h0 + obtain ⟨i,j,hij⟩ : ∃ i j, M i j ≠ 0 := by + by_contra h + apply h0 + ext i j + simpa using not_exists.mp (not_exists.mp h i) j + let c := (M*Mᴴ) 0 0 + let d := (Mᴴ*M) 0 0 + have hc : c ≠ 0 := by + intro hc + have hz : M*Mᴴ=0 := by rw [hl]; change c • _=0; rw [hc,zero_smul] + exact h0 (Matrix.self_mul_conjTranspose_eq_zero.mp hz) + have hd : c=d := by + have h := Matrix.mul_assoc M Mᴴ M + rw [hl,hr,Matrix.smul_mul,Matrix.mul_smul,Matrix.one_mul,Matrix.mul_one] at h + have he := congrFun (congrFun h i) j + simp only [Matrix.smul_apply,smul_eq_mul] at he + exact mul_right_cancel₀ hij he + have ht := Matrix.trace_mul_comm M Mᴴ + rw [hl,hr] at ht + simp only [Matrix.trace_smul,Matrix.trace_one,Fintype.card_fin,smul_eq_mul] at ht + change c*((m+1 : ℕ) : ℂ)=d*((n+1 : ℕ) : ℂ) at ht + rw [← hd] at ht + have he : m+1=n+1 := by exact_mod_cast mul_left_cancel₀ hc ht + omega + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/EmbeddedSpinHaar.lean b/lean/OAI/Analysis/Laughlin/Spin/EmbeddedSpinHaar.lean new file mode 100644 index 0000000000000000000000000000000000000000..26d5378567d2ae0d2b50b68b41e07f63b560ba42 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/EmbeddedSpinHaar.lean @@ -0,0 +1,35 @@ +import OAI.Analysis.Laughlin.Spin.Disjoint +import OAI.Analysis.Laughlin.Spin.Sandwich + +namespace OAI + +namespace Laughlin.Rotation +open MeasureTheory +open scoped BigOperators Matrix + +theorem embedded_spin_haar {I : Type*} [Fintype I] [DecidableEq I] + (ρ : SourceSU2 →* Matrix I I ℂ) (hρ : ∀ g, ρ g⁻¹=(ρ g)ᴴ) + (m : ℕ) (W : Matrix I (Fin (m+1)) ℂ) + (hW : ∀ g, ρ g*W=W*sourceSpinRepresentation m g) + (M : Matrix (Fin (m+1)) (Fin (m+1)) ℂ) : + matrixIntegral sourceHaar (conjugateOrbit ρ (W*M*Wᴴ)) = + (Matrix.trace M/(m+1 : ℕ)) • (W*Wᴴ) := by + have ha (g : SourceSU2) : Wᴴ*ρ g⁻¹=sourceSpinRepresentation m g⁻¹*Wᴴ := by + have h := congrArg Matrix.conjTranspose (hW g) + simpa only [Matrix.conjTranspose_mul,← hρ,← sourceSpinRepresentation_inv] using h + have he (g : SourceSU2) : conjugateOrbit ρ (W*M*Wᴴ) g = + W*conjugateOrbit (sourceSpinRepresentation m) M g*Wᴴ := by + unfold conjugateOrbit + calc + _ = (ρ g*W)*M*(Wᴴ*ρ g⁻¹) := by simp only [Matrix.mul_assoc] + _ = _ := by rw [hW,ha]; simp only [Matrix.mul_assoc] + unfold matrixIntegral + simp_rw [he] + rw [integral_matrix_sandwich sourceHaar _ + (compact_conjugateOrbit_integrable sourceHaar _ (sourceSpinRepresentation_continuous m) M)] + change W*matrixIntegral sourceHaar (conjugateOrbit (sourceSpinRepresentation m) M)*Wᴴ = _ + rw [source_spin_haar_schur,Matrix.mul_smul,Matrix.mul_one,Matrix.smul_mul] + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Endpoint.lean b/lean/OAI/Analysis/Laughlin/Spin/Endpoint.lean new file mode 100644 index 0000000000000000000000000000000000000000..19711217f42944a4570623ef6779b4cc0a38bafb --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Endpoint.lean @@ -0,0 +1,56 @@ +import OAI.Analysis.Laughlin.Spin.GenericNormalizedLadder +import OAI.Analysis.Laughlin.Spin.Support + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +theorem genericUnitDescendant_raising_succ (A B z n : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hn : n < genericCoupledWeight A B z) : + totalRaise A B *ᵥ genericUnitDescendant A B z hA hB (n+1) = + Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n)) • + genericUnitDescendant A B z hA hB n := by + have hr : totalRaise A B *ᵥ genericDescendant A B z hA hB (n+1) = + (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n)) • genericDescendant A B z hA hB n := by + exact descendant_raising (totalRaise A B) (totalWeight A B) (totalRaise A B)ᵀ + (genericHighest A B z hA hB) (genericCoupledWeight A B z) + (total_raise_lower_commutator A B) (total_weight_lower_commutator A B) + (genericHighest_weight A B z hA hB) (genericHighest_raising_zero A B z hA hB) n + have hc : 0 < ((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n) := by + have hn' : (n : ℝ) < genericCoupledWeight A B z := by exact_mod_cast hn + positivity + have hden : Real.sqrt (vectorNormSq (genericDescendant A B z hA hB (n+1))) = + Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n))* + Real.sqrt (vectorNormSq (genericDescendant A B z hA hB n)) := by + rw [genericDescendant_norm_step,Real.sqrt_mul (le_of_lt hc)] + have hx : (Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n)))⁻¹ * + (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n)) = + Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n)) := by + apply mul_left_cancel₀ (ne_of_gt (Real.sqrt_pos.mpr hc)) + rw [mul_inv_cancel_left₀ (ne_of_gt (Real.sqrt_pos.mpr hc))] + exact (Real.mul_self_sqrt (le_of_lt hc)).symm + unfold genericUnitDescendant + rw [Matrix.mulVec_smul,hr,smul_smul,smul_smul,hden,mul_inv_rev] + rw [mul_assoc,hx,mul_comm] + +theorem genericDescendant_past_lowest (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + genericDescendant A B z hA hB (genericCoupledWeight A B z+1)=0 := by + have h := genericDescendant_norm_step A B z (genericCoupledWeight A B z) hA hB + simp only [sub_self,mul_zero,zero_mul] at h + funext i + have hi : (genericDescendant A B z hA hB (genericCoupledWeight A B z+1) i)^2 ≤ + vectorNormSq (genericDescendant A B z hA hB (genericCoupledWeight A B z+1)) := + Finset.single_le_sum (fun k hk => sq_nonneg _) (Finset.mem_univ i) + rw [h] at hi + change genericDescendant A B z hA hB (genericCoupledWeight A B z+1) i=0 + nlinarith [sq_nonneg (genericDescendant A B z hA hB (genericCoupledWeight A B z+1) i)] + +theorem genericUnitDescendant_lowest (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + (totalRaise A B)ᵀ *ᵥ genericUnitDescendant A B z hA hB (genericCoupledWeight A B z)=0 := by + unfold genericUnitDescendant + rw [Matrix.mulVec_smul,← genericDescendant_succ,genericDescendant_past_lowest,smul_zero] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/GeneralSpinAction.lean b/lean/OAI/Analysis/Laughlin/Spin/GeneralSpinAction.lean new file mode 100644 index 0000000000000000000000000000000000000000..81fb84da1a75a2594d39a251ca83f62175483ca4 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/GeneralSpinAction.lean @@ -0,0 +1,98 @@ +import OAI.Analysis.Laughlin.Spin.Torus +import OAI.Analysis.Laughlin.Tensor.PolynomialRealization + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + +noncomputable def generalSpinMatrix (Q : ℕ) (A : Matrix (Fin 2) (Fin 2) ℂ) : + Matrix (Fin (Q+1)) (Fin (Q+1)) ℂ := + (symmetricTensorInclusion Q)ᴴ * tensorMatrix Q A * symmetricTensorInclusion Q + +theorem general_tensor_spin_intertwining (Q : ℕ) (A : Matrix (Fin 2) (Fin 2) ℂ) : + symmetricTensorInclusion Q*generalSpinMatrix Q A = tensorMatrix Q A*symmetricTensorInclusion Q := by + ext a p + let v : (Fin Q → Fin 2) → ℂ := fun b => symmetricTensorInclusion Q b p + have hv : ∀ b c, tensorWeight Q b=tensorWeight Q c → v b=v c := by + intro b c h + simp only [v,symmetricTensorInclusion,Matrix.map_apply,symmetricTensorInclusionReal,h] + have hf := tensorMatrix_preserves_symmetric Q A v hv + have he := congrFun (symmetricTensor_projector_fixed Q (tensorMatrix Q A *ᵥ v) hf) a + change (symmetricTensorInclusion Q*((symmetricTensorInclusion Q)ᴴ*tensorMatrix Q A*symmetricTensorInclusion Q)) a p = _ + calc + _ = ((symmetricTensorInclusion Q*(symmetricTensorInclusion Q)ᴴ)* + (tensorMatrix Q A*symmetricTensorInclusion Q)) a p := by simp only [Matrix.mul_assoc] + _ = _ := he + +theorem generalSpinMatrix_mul (Q : ℕ) (A B : Matrix (Fin 2) (Fin 2) ℂ) : + generalSpinMatrix Q (A*B) = generalSpinMatrix Q A*generalSpinMatrix Q B := by + unfold generalSpinMatrix + rw [tensorMatrix_mul] + have he := general_tensor_spin_intertwining Q B + unfold generalSpinMatrix at he + calc + _ = (symmetricTensorInclusion Q)ᴴ*tensorMatrix Q A* + (tensorMatrix Q B*symmetricTensorInclusion Q) := by simp only [Matrix.mul_assoc] + _ = _ := by rw [← he]; simp only [Matrix.mul_assoc] + +theorem generalSpinMatrix_one (Q : ℕ) : generalSpinMatrix Q 1=1 := by + simp [generalSpinMatrix,tensorMatrix_one,symmetricTensorInclusion_isometry] + +theorem generalSpinMatrix_source (Q : ℕ) (g : SourceSU2) : + generalSpinMatrix Q g.val=sourceSpinRepresentation Q g := rfl + +theorem generalSpinMatrix_diagonal (Q : ℕ) (x y : ℂ) : + generalSpinMatrix Q (Matrix.diagonal (fun i : Fin 2 => if i=0 then x else y)) = + Matrix.diagonal (fun p : Fin (Q+1) => y^p.val*x^(Q-p.val)) := by + unfold generalSpinMatrix + rw [tensorMatrix_diagonal,Matrix.mul_assoc, + symmetricTensor_diagonal_intertwining Q (fun k => y^k*x^(Q-k)), + ← Matrix.mul_assoc,symmetricTensorInclusion_isometry,Matrix.one_mul] + +theorem generalSpinMatrix_transpose (Q : ℕ) (A : Matrix (Fin 2) (Fin 2) ℂ) : + generalSpinMatrix Q Aᵀ=(generalSpinMatrix Q A)ᵀ := by + have hI : (symmetricTensorInclusion Q)ᴴ=(symmetricTensorInclusion Q)ᵀ := by + ext a b + simp [symmetricTensorInclusion,Matrix.conjTranspose_apply,Matrix.transpose_apply] + have hT : tensorMatrix Q Aᵀ=(tensorMatrix Q A)ᵀ := rfl + simp only [generalSpinMatrix,hI,hT,Matrix.transpose_mul,Matrix.transpose_transpose] + simp only [Matrix.mul_assoc] + +theorem generalSpinMatrix_polynomial {R : Type*} [CommRing R] + (f : ℂ →+* R) (Q : ℕ) (A : Matrix (Fin 2) (Fin 2) ℂ) (u v : R) (p : Fin (Q+1)) : + (∑ q : Fin (Q+1), f (generalSpinMatrix Q A q p) * + (f (Real.sqrt (Q.choose q.val : ℝ) : ℂ) * v^q.val*u^(Q-q.val))) = + f (Real.sqrt (Q.choose p.val : ℝ) : ℂ) * + (f (A 0 1)*u+f (A 1 1)*v)^p.val * + (f (A 0 0)*u+f (A 1 0)*v)^(Q-p.val) := by + have h := general_tensor_spin_intertwining Q A + have hm := congrArg (fun M : Matrix (Fin Q → Fin 2) (Fin (Q+1)) ℂ => + ∑ a, f (M a p) * (v^(tensorWeight Q a)*u^(Q-tensorWeight Q a))) h + simp only [Matrix.mul_apply, map_sum, map_mul, Finset.sum_mul] at hm + rw [Finset.sum_comm] at hm + have hl (q : Fin (Q+1)) : (∑ a, f (symmetricTensorInclusion Q a q) * + f (generalSpinMatrix Q A q p) * (v^(tensorWeight Q a)*u^(Q-tensorWeight Q a))) = + f (generalSpinMatrix Q A q p) * + (f (Real.sqrt (Q.choose q.val : ℝ) : ℂ)*v^q.val*u^(Q-q.val)) := by + simp_rw [mul_right_comm _ (f (generalSpinMatrix Q A q p)), ← Finset.sum_mul] + rw [symmetricTensor_weighted_column f Q q (fun n => v^n*u^(Q-n))] + ring + simp_rw [hl] at hm + rw [Finset.sum_comm] at hm + have hr (b : Fin Q → Fin 2) : (∑ a, f (tensorMatrix Q A a b) * + f (symmetricTensorInclusion Q b p) * (v^(tensorWeight Q a)*u^(Q-tensorWeight Q a))) = + f (symmetricTensorInclusion Q b p) * + ((f (A 0 1)*u+f (A 1 1)*v)^(tensorWeight Q b) * + (f (A 0 0)*u+f (A 1 0)*v)^(Q-tensorWeight Q b)) := by + simp_rw [mul_right_comm _ (f (symmetricTensorInclusion Q b p)), ← Finset.sum_mul] + rw [tensorMatrix_polynomial] + ring + simp_rw [hr] at hm + rw [symmetricTensor_weighted_column f Q p (fun n => + (f (A 0 1)*u+f (A 1 1)*v)^n*(f (A 0 0)*u+f (A 1 0)*v)^(Q-n))] at hm + simpa only [mul_assoc] using hm + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/GenericNormalizedLadder.lean b/lean/OAI/Analysis/Laughlin/Spin/GenericNormalizedLadder.lean new file mode 100644 index 0000000000000000000000000000000000000000..a5c754eb3ac8628cf2414c38950ff33877b6a98f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/GenericNormalizedLadder.lean @@ -0,0 +1,31 @@ +import OAI.Analysis.Laughlin.Spin.Basic + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +theorem genericUnitDescendant_lowering (A B z n : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hn : n < genericCoupledWeight A B z) : + (totalRaise A B)ᵀ *ᵥ genericUnitDescendant A B z hA hB n = + Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n)) • + genericUnitDescendant A B z hA hB (n+1) := by + have hp := genericDescendant_norm_pos A B z n hA hB (by omega) + have hp₁ := genericDescendant_norm_pos A B z (n+1) hA hB (by omega) + have hnreal : (n : ℝ) < genericCoupledWeight A B z := by exact_mod_cast hn + have hc : 0 < ((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n) := by positivity + have hden : Real.sqrt (vectorNormSq (genericDescendant A B z hA hB (n+1))) = + Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n))* + Real.sqrt (vectorNormSq (genericDescendant A B z hA hB n)) := by + rw [genericDescendant_norm_step A B z n hA hB,Real.sqrt_mul (le_of_lt hc)] + have hs : (Real.sqrt (vectorNormSq (genericDescendant A B z hA hB n)))⁻¹ = + Real.sqrt (((n : ℝ)+1)*((genericCoupledWeight A B z : ℝ)-n))* + (Real.sqrt (vectorNormSq (genericDescendant A B z hA hB (n+1))))⁻¹ := by + rw [hden,mul_inv_rev] + field_simp [ne_of_gt (Real.sqrt_pos.mpr hc)] + unfold genericUnitDescendant + rw [Matrix.mulVec_smul,← genericDescendant_succ,smul_smul,hs] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/GenericOrthogonality.lean b/lean/OAI/Analysis/Laughlin/Spin/GenericOrthogonality.lean new file mode 100644 index 0000000000000000000000000000000000000000..5b4fcc94c18157a3d188cd2f9996f36c95514c63 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/GenericOrthogonality.lean @@ -0,0 +1,51 @@ +import OAI.Analysis.Laughlin.Spin.Basic +import OAI.Analysis.Laughlin.Spin.Sl2Orthogonal + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +theorem genericHighest_orthogonal (A B z w : ℕ) (hzA : z ≤ A) (hzB : z ≤ B) (hwA : w ≤ A) (hwB : w ≤ B) + (hzw : z ≠ w) : + (∑ i, genericHighest A B z hzA hzB i*genericHighest A B w hwA hwB i) = 0 := by + apply Finset.sum_eq_zero + intro i hi + by_cases he : i.1.val+i.2.val=z + · have hh : i.1.val+i.2.val ≠ w := by omega + have hv : genericHighest A B w hwA hwB i = 0 := + extendWeightSlice_off A B w hwA hwB _ i hh + rw [hv,mul_zero] + · have hv : genericHighest A B z hzA hzB i = 0 := + extendWeightSlice_off A B z hzA hzB _ i he + rw [hv,zero_mul] + +theorem genericDescendant_orthogonal (A B z w n m : ℕ) (hzA : z ≤ A) (hzB : z ≤ B) (hwA : w ≤ A) (hwB : w ≤ B) + (hne : z ≠ w ∨ n ≠ m) : + (∑ i, genericDescendant A B z hzA hzB n i*genericDescendant A B w hwA hwB m i) = 0 := by + apply descendants_orthogonal (totalRaise A B) (totalWeight A B) + ((totalRaise A B)ᵀ) (genericHighest A B z hzA hzB) (genericHighest A B w hwA hwB) + (genericCoupledWeight A B w) (total_raise_lower_commutator _ _) (total_weight_lower_commutator _ _) + (Matrix.transpose_transpose _) (genericHighest_weight A B w hwA hwB) + (genericHighest_raising_zero A B z hzA hzB) (genericHighest_raising_zero A B w hwA hwB) n m + rcases hne with h | h + · exact Or.inl (genericHighest_orthogonal A B z w hzA hzB hwA hwB h) + · exact Or.inr h + +theorem genericUnitDescendant_orthogonal (A B z w n m : ℕ) (hzA : z ≤ A) (hzB : z ≤ B) (hwA : w ≤ A) (hwB : w ≤ B) + (hne : z ≠ w ∨ n ≠ m) : + (∑ i, genericUnitDescendant A B z hzA hzB n i * + genericUnitDescendant A B w hwA hwB m i) = 0 := by + unfold genericUnitDescendant + simp only [Pi.smul_apply,smul_eq_mul] + calc + _ = (Real.sqrt (vectorNormSq (genericDescendant A B z hzA hzB n)))⁻¹ * + (Real.sqrt (vectorNormSq (genericDescendant A B w hwA hwB m)))⁻¹ * + (∑ i, genericDescendant A B z hzA hzB n i*genericDescendant A B w hwA hwB m i) := by + rw [Finset.mul_sum] + apply Finset.sum_congr rfl; intro i hi; ring + _ = 0 := by rw [genericDescendant_orthogonal A B z w n m hzA hzB hwA hwB hne,mul_zero] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Haar.lean b/lean/OAI/Analysis/Laughlin/Spin/Haar.lean new file mode 100644 index 0000000000000000000000000000000000000000..cdd09985144a5fd0160fd3ca38a0b97e8bbf98a8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Haar.lean @@ -0,0 +1,40 @@ +import Mathlib.MeasureTheory.Measure.Haar.Basic +import OAI.Analysis.Laughlin.Spin.Compact +import OAI.Analysis.Laughlin.Spin.CompactAverage + +namespace OAI + +namespace Laughlin.Rotation +open MeasureTheory MeasureTheory.Measure TopologicalSpace + +noncomputable instance sourceSU2_measurableSpace : MeasurableSpace SourceSU2 := borel SourceSU2 +instance sourceSU2_borelSpace : BorelSpace SourceSU2 := ⟨rfl⟩ + +noncomputable def sourceHaar : Measure SourceSU2 := + haarMeasure (⊤ : PositiveCompacts SourceSU2) + +instance sourceHaar_isHaar : IsHaarMeasure sourceHaar := + inferInstanceAs (IsHaarMeasure (haarMeasure (⊤ : PositiveCompacts SourceSU2))) + +instance sourceHaar_isProbability : IsProbabilityMeasure sourceHaar where + measure_univ := by + simpa [sourceHaar] using (haarMeasure_self (K₀ := (⊤ : PositiveCompacts SourceSU2))) + +theorem sourceHaar_univ : sourceHaar Set.univ=1 := measure_univ + +theorem source_tensor_haar_average_commutes (Q : ℕ) + (M : Matrix (Fin Q → Fin 2) (Fin Q → Fin 2) ℂ) (g : SourceSU2) : + sourceTensorRepresentation Q g * matrixIntegral sourceHaar (conjugateOrbit (sourceTensorRepresentation Q) M) = + matrixIntegral sourceHaar (conjugateOrbit (sourceTensorRepresentation Q) M) * sourceTensorRepresentation Q g := by + exact compact_haar_average_commutes sourceHaar (sourceTensorRepresentation Q) + (sourceTensorRepresentation_continuous Q) M g + +theorem source_tensor_haar_average_trace (Q : ℕ) + (M : Matrix (Fin Q → Fin 2) (Fin Q → Fin 2) ℂ) : + Matrix.trace (matrixIntegral sourceHaar (conjugateOrbit (sourceTensorRepresentation Q) M)) = Matrix.trace M := by + exact compact_haar_average_trace sourceHaar (sourceTensorRepresentation Q) + (sourceTensorRepresentation_continuous Q) M + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/HaarOrthogonality.lean b/lean/OAI/Analysis/Laughlin/Spin/HaarOrthogonality.lean new file mode 100644 index 0000000000000000000000000000000000000000..920ef8c4592674862050f9680e223ecff7a64144 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/HaarOrthogonality.lean @@ -0,0 +1,26 @@ +import OAI.Analysis.Laughlin.Spin.CopySchur +import OAI.Analysis.Laughlin.Spin.Disjoint +import OAI.Analysis.Laughlin.Spin.RectangularAverage + +namespace OAI + +namespace Laughlin.Rotation +open scoped Matrix + +theorem source_unequal_spin_haar_zero (m n : ℕ) (hmn : m ≠ n) + (M : Matrix (Fin (m+1)) (Fin (n+1)) ℂ) : + rectangularIntegral sourceHaar + (rectangularOrbit (sourceSpinRepresentation m) (sourceSpinRepresentation n) M)=0 := by + exact source_spin_intertwiner_zero m n hmn _ + (compact_rectangular_average_intertwines sourceHaar _ _ + (sourceSpinRepresentation_continuous m) (sourceSpinRepresentation_continuous n) M) + +theorem source_equal_spin_haar_trace (Q : ℕ) (M : Matrix (Fin (Q+1)) (Fin (Q+1)) ℂ) : + rectangularIntegral sourceHaar + (rectangularOrbit (sourceSpinRepresentation Q) (sourceSpinRepresentation Q) M)= + (Matrix.trace M/(Q+1 : ℕ)) • (1 : Matrix (Fin (Q+1)) (Fin (Q+1)) ℂ) := + source_spin_haar_schur Q M + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Highest.lean b/lean/OAI/Analysis/Laughlin/Spin/Highest.lean new file mode 100644 index 0000000000000000000000000000000000000000..dec0e6beee252b89df01b2aaa0ee7fe6516d2cfa --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Highest.lean @@ -0,0 +1,69 @@ +import Mathlib.Data.Nat.Factorial.Basic +import OAI.Analysis.Laughlin.Spin.HighestSpace + +namespace OAI + +namespace Laughlin.Spin + +theorem highestUnit_div_eq_raw (A B z p q : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + highestUnit A B z p / highestUnit A B z q = + highestRaw A B z p / highestRaw A B z q := by + unfold highestUnit + exact div_div_div_cancel_right₀ (ne_of_gt (highestNorm_pos A B z hA hB)) _ _ + +theorem source_highest_ratio (Q z p : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) (hp : p < z) : + highestUnit (2*Q-2) Q z (p+1) / highestUnit (2*Q-2) Q z p = + -Real.sqrt (((z : ℝ)-p)*((Q : ℝ)-z+p+1) / + (((p : ℝ)+1)*(2*(Q : ℝ)-2-p))) := by + rw [highestUnit_ratio (2*Q-2) Q z p (by omega) hz hp] + unfold ladder + rw [← Real.sqrt_div (by positivity)] + have h₁ : ((z-p-1 : ℕ) : ℝ)+1 = (z : ℝ)-p := by + rw [Nat.cast_sub (by omega : 1 ≤ z-p),Nat.cast_sub (by omega : p ≤ z)] + push_cast; ring + have h₂ : ((Q-(z-p-1) : ℕ) : ℝ) = (Q : ℝ)-z+p+1 := by + rw [Nat.cast_sub (by omega : z-p-1 ≤ Q),Nat.cast_sub (by omega : 1 ≤ z-p), + Nat.cast_sub (by omega : p ≤ z)] + push_cast; ring + have h₃ : ((2*Q-2-p : ℕ) : ℝ) = 2*(Q : ℝ)-2-p := by + rw [Nat.cast_sub (by omega : p ≤ 2*Q-2),Nat.cast_sub (by omega : 2 ≤ 2*Q)] + push_cast; ring + rw [h₁,h₂,h₃] + +theorem highest_end_ratio (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + highestUnit A B z z / highestUnit A B z 0 = + (-1 : ℝ)^z * Real.sqrt ((B.choose z : ℝ)/(A.choose z : ℝ)) := by + rw [highestUnit_div_eq_raw A B z z 0 hA hB,highestRaw_zero] + simp only [highestRaw,le_refl,ite_true,Nat.choose_self,Nat.sub_self, + Nat.choose_zero_right,Nat.cast_one,mul_one] + rw [Real.sqrt_div (by positivity)] + simp only [div_eq_mul_inv,one_mul,inv_inv] + ring + +theorem highest_penultimate_ratio (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hz : 1 ≤ z) : + highestUnit A B z (z-1) / highestUnit A B z 0 = + (-1 : ℝ)^(z-1) * (z : ℝ) * + Real.sqrt ((B.choose z : ℝ)/((A.choose (z-1) : ℝ)*B)) := by + rw [highestUnit_div_eq_raw A B z (z-1) 0 hA hB,highestRaw_zero] + simp only [highestRaw,ite_eq_left (show z-1 ≤ z by omega)] + rw [show z-(z-1)=1 by omega,Nat.choose_one_right, + Nat.choose_symm hz,Nat.choose_one_right] + rw [Real.sqrt_div (by positivity)] + simp only [div_eq_mul_inv,one_mul,inv_inv] + ring + +theorem choose_ratio_descFactorial (A B z : ℕ) : + (B.choose z : ℝ)/(A.choose z : ℝ) = + (B.descFactorial z : ℝ)/(A.descFactorial z : ℝ) := by + simp only [Nat.descFactorial_eq_factorial_mul_choose,Nat.cast_mul] + rw [mul_div_mul_left _ _ (by positivity : (z.factorial : ℝ) ≠ 0)] + +theorem source_highest_end_ratio (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + highestUnit (2*Q-2) Q z z / highestUnit (2*Q-2) Q z 0 = + (-1 : ℝ)^z * Real.sqrt ((Q.descFactorial z : ℝ)/((2*Q-2).descFactorial z : ℝ)) := by + rw [highest_end_ratio _ _ _ (by omega) hz,choose_ratio_descFactorial] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Highest2.lean b/lean/OAI/Analysis/Laughlin/Spin/Highest2.lean new file mode 100644 index 0000000000000000000000000000000000000000..4759cb34ddf893a672ab44329d522addacea7da7 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Highest2.lean @@ -0,0 +1,101 @@ +import Mathlib.Algebra.BigOperators.Group.Finset.Basic +import Mathlib.Analysis.Real.Sqrt +import Mathlib.Data.Nat.Choose.Basic +import Mathlib.Tactic.FieldSimp +import Mathlib.Tactic.Linarith +import Mathlib.Tactic.LinearCombination +import Mathlib.Tactic.NormNum +import Mathlib.Tactic.Positivity +import Mathlib.Tactic.Ring + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +noncomputable def ladder (A p : ℕ) : ℝ := + Real.sqrt (((p : ℝ)+1)*(A-p : ℕ)) + +noncomputable def highestRaw (A B z p : ℕ) : ℝ := + if p ≤ z then (-1 : ℝ)^p * (z.choose p : ℝ) / + Real.sqrt ((A.choose p : ℝ)*(B.choose (z-p) : ℝ)) else 0 + +theorem ladder_pos (A p : ℕ) (hp : p < A) : 0 < ladder A p := by + unfold ladder + apply Real.sqrt_pos.mpr + have h : (0 : ℝ) < (A-p : ℕ) := by exact_mod_cast (show 0 < A-p by omega) + positivity + +theorem choose_step_real (A p : ℕ) (hp : p ≤ A) : + ((p : ℝ)+1)*(A.choose (p+1) : ℝ) = + (A-p : ℕ)*(A.choose p : ℝ) := by + have h := Nat.choose_succ_right_eq A p + simpa only [Nat.cast_mul,Nat.cast_add,Nat.cast_one,Nat.cast_sub hp,mul_comm] using + congrArg (fun n : ℕ => (n : ℝ)) h + +theorem sqrt_choose_step (A p : ℕ) (hp : p < A) : + ladder A p * Real.sqrt (A.choose (p+1) : ℝ) = + (A-p : ℕ)*Real.sqrt (A.choose p : ℝ) := by + have hc := choose_step_real A p (by omega) + have he : (ladder A p * Real.sqrt (A.choose (p+1) : ℝ))^2 = + ((A-p : ℕ)*Real.sqrt (A.choose p : ℝ))^2 := by + unfold ladder + rw [mul_pow,mul_pow,Real.sq_sqrt (by positivity),Real.sq_sqrt (by positivity), + Real.sq_sqrt (by positivity)] + nlinarith [hc] + have h₁ : 0 ≤ ladder A p * Real.sqrt (A.choose (p+1) : ℝ) := by + exact mul_nonneg (le_of_lt (ladder_pos A p hp)) (Real.sqrt_nonneg _) + have h₂ : 0 ≤ (A-p : ℕ)*Real.sqrt (A.choose p : ℝ) := by positivity + nlinarith + +theorem ladder_div_sqrt_choose (A p : ℕ) (hp : p < A) : + ladder A p / Real.sqrt (A.choose (p+1) : ℝ) = + ((p : ℝ)+1) / Real.sqrt (A.choose p : ℝ) := by + have h₀ : 0 < (A.choose p : ℝ) := by exact_mod_cast Nat.choose_pos (by omega : p ≤ A) + have h₁ : 0 < (A.choose (p+1) : ℝ) := by exact_mod_cast Nat.choose_pos (by omega : p+1 ≤ A) + apply (div_eq_div_iff (ne_of_gt (Real.sqrt_pos.mpr h₁)) + (ne_of_gt (Real.sqrt_pos.mpr h₀))).mpr + have hc := choose_step_real A p (by omega) + have he : (ladder A p * Real.sqrt (A.choose p : ℝ))^2 = + (((p : ℝ)+1)*Real.sqrt (A.choose (p+1) : ℝ))^2 := by + unfold ladder + rw [mul_pow,mul_pow,Real.sq_sqrt (by positivity),Real.sq_sqrt (by positivity), + Real.sq_sqrt (by positivity)] + nlinarith [hc] + have hn₀ : 0 ≤ ladder A p * Real.sqrt (A.choose p : ℝ) := + mul_nonneg (le_of_lt (ladder_pos A p hp)) (Real.sqrt_nonneg _) + have hn₁ : 0 ≤ ((p : ℝ)+1)*Real.sqrt (A.choose (p+1) : ℝ) := by positivity + nlinarith + +theorem highestRaw_raising (A B z p : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hp : p < z) : + ladder A p * highestRaw A B z (p+1) + + ladder B (z-p-1) * highestRaw A B z p = 0 := by + have hpA : p < A := by omega + have hkB : z-p-1 < B := by omega + have hk : z-(p+1) = z-p-1 := by omega + have hk' : z-p = (z-p-1)+1 := by omega + have hca : (Real.sqrt (A.choose p : ℝ)) ≠ 0 := by + apply ne_of_gt; apply Real.sqrt_pos.mpr; exact_mod_cast Nat.choose_pos (by omega : p ≤ A) + have hcb : (Real.sqrt (B.choose (z-p-1) : ℝ)) ≠ 0 := by + apply ne_of_gt; apply Real.sqrt_pos.mpr; exact_mod_cast Nat.choose_pos (by omega : z-p-1 ≤ B) + simp only [highestRaw,ite_eq_left (show p+1 ≤ z by omega),ite_eq_left (show p ≤ z by omega),hk] + rw [Real.sqrt_mul (by positivity),Real.sqrt_mul (by positivity)] + have hleft := ladder_div_sqrt_choose A p hpA + have hright := ladder_div_sqrt_choose B (z-p-1) hkB + rw [← hk'] at hright + have hz := choose_step_real z p (by omega) + have castk : ((z-p-1 : ℕ) : ℝ)+1 = (z-p : ℕ) := by exact_mod_cast hk'.symm + rw [castk] at hright + calc + _ = (-1 : ℝ)^(p+1)*(z.choose (p+1) : ℝ) / + Real.sqrt (B.choose (z-p-1) : ℝ) * + (ladder A p / Real.sqrt (A.choose (p+1) : ℝ)) + + (-1 : ℝ)^p*(z.choose p : ℝ) / Real.sqrt (A.choose p : ℝ) * + (ladder B (z-p-1) / Real.sqrt (B.choose (z-p) : ℝ)) := by ring + _ = _ := by rw [hleft,hright] + _ = 0 := by rw [pow_succ]; field_simp; linear_combination -((-1 : ℝ)^p)*hz + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/HighestSpace.lean b/lean/OAI/Analysis/Laughlin/Spin/HighestSpace.lean new file mode 100644 index 0000000000000000000000000000000000000000..107be6ec86e3922cbc6d7a27d139eafd2418b685 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/HighestSpace.lean @@ -0,0 +1,114 @@ +import Mathlib.Algebra.BigOperators.Field +import OAI.Analysis.Laughlin.Spin.Highest2 + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +theorem highestRaw_zero (A B z : ℕ) : + highestRaw A B z 0 = 1 / Real.sqrt (B.choose z : ℝ) := by + simp [highestRaw] + +theorem highestRaw_ne_zero (A B z p : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hp : p ≤ z) : highestRaw A B z p ≠ 0 := by + rw [highestRaw,ite_eq_left hp] + apply div_ne_zero + · exact mul_ne_zero (pow_ne_zero _ (by norm_num)) + (by exact_mod_cast Nat.ne_of_gt (Nat.choose_pos hp)) + · apply ne_of_gt; apply Real.sqrt_pos.mpr + have ha : 0 < (A.choose p : ℝ) := by exact_mod_cast Nat.choose_pos (by omega : p ≤ A) + have hb : 0 < (B.choose (z-p) : ℝ) := by exact_mod_cast Nat.choose_pos (by omega : z-p ≤ B) + positivity + +theorem highest_unique (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (f : ℕ → ℝ) + (hf : ∀ p < z, ladder A p*f (p+1)+ladder B (z-p-1)*f p = 0) : + ∀ p ≤ z, f p = (f 0 / highestRaw A B z 0)*highestRaw A B z p := by + intro p hp + induction p with + | zero => field_simp [highestRaw_ne_zero A B z 0 hA hB (by omega)] + | succ p ih => + have hlt : p < z := by omega + have he := highestRaw_raising A B z p hA hB hlt + have hh := hf p hlt + have hi := ih (by omega) + have ha : ladder A p ≠ 0 := ne_of_gt (ladder_pos A p (by omega)) + apply (mul_left_cancel₀ ha) + linear_combination hh - (f 0 / highestRaw A B z 0)*he - ladder B (z-p-1)*hi + +noncomputable def highestNorm (A B z : ℕ) : ℝ := + Real.sqrt (∑ p ∈ Finset.range (z+1), (highestRaw A B z p)^2) + +noncomputable def highestUnit (A B z p : ℕ) : ℝ := + highestRaw A B z p / highestNorm A B z + +theorem highestNorm_pos (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + 0 < highestNorm A B z := by + apply Real.sqrt_pos.mpr + apply Finset.sum_pos' + · intro p hp; exact sq_nonneg _ + · exact ⟨0,Finset.mem_range.mpr (by omega),sq_pos_of_ne_zero + (highestRaw_ne_zero A B z 0 hA hB (by omega))⟩ + +theorem highestUnit_norm (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + (∑ p ∈ Finset.range (z+1), (highestUnit A B z p)^2) = 1 := by + simp only [highestUnit,div_pow,← Finset.sum_div] + rw [highestNorm,Real.sq_sqrt (Finset.sum_nonneg (fun _ _ => sq_nonneg _))] + apply div_self + have h := highestNorm_pos A B z hA hB + exact ne_of_gt (Real.sqrt_pos.mp h) + +theorem highestUnit_raising (A B z p : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hp : p < z) : + ladder A p*highestUnit A B z (p+1)+ladder B (z-p-1)*highestUnit A B z p = 0 := by + simp only [highestUnit,← mul_div_assoc,← add_div] + rw [highestRaw_raising A B z p hA hB hp,zero_div] + +theorem highestUnit_ne_zero (A B z p : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hp : p ≤ z) : highestUnit A B z p ≠ 0 := + div_ne_zero (highestRaw_ne_zero A B z p hA hB hp) + (ne_of_gt (highestNorm_pos A B z hA hB)) + +theorem highestUnit_ratio (A B z p : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hp : p < z) : + highestUnit A B z (p+1) / highestUnit A B z p = + -(ladder B (z-p-1) / ladder A p) := by + have he := highestUnit_raising A B z p hA hB hp + have ha := ne_of_gt (ladder_pos A p (by omega)) + have hs := highestUnit_ne_zero A B z p hA hB (by omega) + apply (div_eq_iff hs).mpr + apply (mul_left_cancel₀ ha) + field_simp + nlinarith only [he] + +noncomputable def raiseSlice (A B z : ℕ) (f : Fin (z+1) → ℝ) (p : Fin z) : ℝ := + ladder A p.val * f ⟨p.val+1,by omega⟩ + + ladder B (z-p.val-1)*f ⟨p.val,by omega⟩ + +theorem raiseSlice_kernel (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (f : Fin (z+1) → ℝ) : + (∀ p, raiseSlice A B z f p = 0) ↔ + ∃ c : ℝ, ∀ p, f p = c*highestUnit A B z p.val := by + constructor + · intro hf + let g : ℕ → ℝ := fun p => if h : p < z+1 then f ⟨p,h⟩ else 0 + have hg : ∀ p < z, ladder A p*g (p+1)+ladder B (z-p-1)*g p = 0 := by + intro p hp + simpa [g,raiseSlice,hp,show p ≤ z by omega] using hf ⟨p,hp⟩ + refine ⟨(g 0 / highestRaw A B z 0)*highestNorm A B z,?_⟩ + intro p + have he := highest_unique A B z hA hB g hg p.val (by omega) + have hn := ne_of_gt (highestNorm_pos A B z hA hB) + have hfval : g p.val = f p := by simp [g,show p.val ≤ z by omega] + rw [hfval] at he + rw [he] + unfold highestUnit + field_simp + · rintro ⟨c,hc⟩ p + simp only [raiseSlice,hc] + linear_combination c * highestUnit_raising A B z p.val hA hB p.isLt + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Intertwining.lean b/lean/OAI/Analysis/Laughlin/Spin/Intertwining.lean new file mode 100644 index 0000000000000000000000000000000000000000..8f7f2cc5070e557af086580db24cdd1b59fb9240 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Intertwining.lean @@ -0,0 +1,79 @@ +import OAI.Analysis.Laughlin.Spin.Endpoint +import OAI.Analysis.Laughlin.Spin.LadderGroupIntertwining + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix Kronecker + +noncomputable def genericCoupledInclusion (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + Matrix (SpinIndex A B) (Fin (genericCoupledWeight A B z+1)) ℝ := + fun i n => genericUnitDescendant A B z hA hB n.val i + +theorem genericCoupledInclusion_raising (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + totalRaise A B*genericCoupledInclusion A B z hA hB = + genericCoupledInclusion A B z hA hB*raiseMatrix (genericCoupledWeight A B z) := by + funext i n + change (totalRaise A B *ᵥ genericUnitDescendant A B z hA hB n.val) i = + ∑ k, genericUnitDescendant A B z hA hB k.val i * raiseMatrix (genericCoupledWeight A B z) k n + rw [raiseMatrix_column] + by_cases hn : 0 < n.val + · rw [dite_eq_left hn] + have h := genericUnitDescendant_raising_succ A B z (n.val-1) hA hB (by omega) + rw [show n.val-1+1=n.val by omega] at h + have he := congrFun h i + simpa [ladder,Nat.cast_sub (show n.val-1 ≤ genericCoupledWeight A B z by omega),mul_comm] using he + · rw [dite_eq_right hn] + have hz : n.val=0 := by omega + rw [hz,genericUnitDescendant_zero,genericHighest_raising_zero] + rfl + +theorem genericCoupledInclusion_lowering (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + (totalRaise A B)ᵀ*genericCoupledInclusion A B z hA hB = + genericCoupledInclusion A B z hA hB*(raiseMatrix (genericCoupledWeight A B z))ᵀ := by + funext i n + change ((totalRaise A B)ᵀ *ᵥ genericUnitDescendant A B z hA hB n.val) i = + ∑ k, genericUnitDescendant A B z hA hB k.val i * raiseMatrix (genericCoupledWeight A B z) n k + conv_rhs => simp only [mul_comm (genericUnitDescendant A B z hA hB _ i)] + rw [raiseMatrix_row] + by_cases hn : n.val < genericCoupledWeight A B z + · rw [dite_eq_left hn] + have h := congrFun (genericUnitDescendant_lowering A B z n.val hA hB hn) i + simpa [ladder,Nat.cast_sub (Nat.le_of_lt hn)] using h + · rw [dite_eq_right hn] + have hz : n.val=genericCoupledWeight A B z := by omega + rw [hz,genericUnitDescendant_lowest] + rfl + +theorem genericCoupledInclusion_SU2 (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (g : Rotation.SourceSU2) : + (Rotation.sourceSpinRepresentation A g ⊗ₖ Rotation.sourceSpinRepresentation B g)* + (genericCoupledInclusion A B z hA hB).map Complex.ofReal = + (genericCoupledInclusion A B z hA hB).map Complex.ofReal* + Rotation.sourceSpinRepresentation (genericCoupledWeight A B z) g := by + apply Rotation.ladder_intertwiner_SU2 A B z (genericCoupledWeight A B z) + (by unfold genericCoupledWeight; omega) + · intro i n hn + simp only [Matrix.map_apply,genericCoupledInclusion,genericUnitDescendant_off A B z n.val hA hB i hn, + Complex.ofReal_zero] + · ext i n + have h := congrArg Complex.ofReal (congrFun (congrFun (genericCoupledInclusion_raising A B z hA hB) i) n) + simpa [Rotation.totalRaiseComplex,Rotation.spinRaiseComplex,Matrix.mul_apply] using h + · ext i n + have h := congrArg Complex.ofReal (congrFun (congrFun (genericCoupledInclusion_lowering A B z hA hB) i) n) + simpa [Rotation.totalRaiseComplex,Rotation.spinRaiseComplex,Matrix.mul_apply,Matrix.transpose_apply] using h + +noncomputable def physicalCoupledInclusion (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) := + (-1 : ℂ)^z • (genericCoupledInclusion A B z hA hB).map Complex.ofReal + +theorem physicalCoupledInclusion_SU2 (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (g : Rotation.SourceSU2) : + (Rotation.sourceSpinRepresentation A g ⊗ₖ Rotation.sourceSpinRepresentation B g)* + physicalCoupledInclusion A B z hA hB = + physicalCoupledInclusion A B z hA hB* + Rotation.sourceSpinRepresentation (genericCoupledWeight A B z) g := by + simp only [physicalCoupledInclusion,Matrix.mul_smul,Matrix.smul_mul,genericCoupledInclusion_SU2] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/LadderGroupIntertwining.lean b/lean/OAI/Analysis/Laughlin/Spin/LadderGroupIntertwining.lean new file mode 100644 index 0000000000000000000000000000000000000000..1c76635ce53836e58fd490777c1ab12671b46161 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/LadderGroupIntertwining.lean @@ -0,0 +1,75 @@ +import OAI.Analysis.Laughlin.Asymptotics.UpperSpinDynamics + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix Kronecker + +theorem weight_support_diagonal_intertwining (A B z J : ℕ) (hz : 2*z+J=A+B) + (W : Matrix (Fin (A+1) × Fin (B+1)) (Fin (J+1)) ℂ) + (hs : ∀ i n, i.1.val+i.2.val ≠ z+n.val → W i n=0) + (x y : ℂ) (hxy : x*y=1) : + (generalSpinMatrix A (Matrix.diagonal (fun i : Fin 2 => if i=0 then x else y)) ⊗ₖ + generalSpinMatrix B (Matrix.diagonal (fun i : Fin 2 => if i=0 then x else y)))*W = + W*generalSpinMatrix J (Matrix.diagonal (fun i : Fin 2 => if i=0 then x else y)) := by + rw [generalSpinMatrix_diagonal,generalSpinMatrix_diagonal,generalSpinMatrix_diagonal, + Matrix.diagonal_kronecker_diagonal] + ext i n + rw [Matrix.diagonal_mul,Matrix.mul_diagonal] + by_cases hi : i.1.val+i.2.val=z+n.val + · have he : A-i.1.val+(B-i.2.val)=z+(J-n.val) := by + have h1 := i.1.isLt + have h2 := i.2.isLt + have hn := n.isLt + omega + have hf : (y^i.1.val*x^(A-i.1.val))*(y^i.2.val*x^(B-i.2.val)) = y^n.val*x^(J-n.val) := by + calc + _ = y^(i.1.val+i.2.val)*x^(A-i.1.val+(B-i.2.val)) := by simp only [pow_add]; ring + _ = (x*y)^z*(y^n.val*x^(J-n.val)) := by rw [hi,he]; simp only [pow_add,mul_pow]; ring + _ = _ := by rw [hxy,one_pow,one_mul] + rw [hf] + ring + · rw [hs i n hi] + simp + +theorem ladder_intertwiner_SU2 (A B z J : ℕ) (hz : 2*z+J=A+B) + (W : Matrix (Fin (A+1) × Fin (B+1)) (Fin (J+1)) ℂ) + (hs : ∀ i n, i.1.val+i.2.val ≠ z+n.val → W i n=0) + (hr : totalRaiseComplex A B*W=W*spinRaiseComplex J) + (hl : (totalRaiseComplex A B)ᵀ*W=W*(spinRaiseComplex J)ᵀ) + (g : SourceSU2) : + (sourceSpinRepresentation A g ⊗ₖ sourceSpinRepresentation B g)*W = + W*sourceSpinRepresentation J g := by + let P : Matrix (Fin 2) (Fin 2) ℂ → Prop := fun M => + (generalSpinMatrix A M ⊗ₖ generalSpinMatrix B M)*W=W*generalSpinMatrix J M + have h : P g.val := by + apply Matrix.diagonal_transvection_induction P g.val + · intro D hD + have hxy : D 0*D 1=1 := by + simpa [Matrix.det_diagonal,Fin.prod_univ_two] using hD.trans g.property.2 + have he : D=(fun i : Fin 2 => if i=0 then D 0 else D 1) := by + funext i + fin_cases i <;> simp + change (generalSpinMatrix A (Matrix.diagonal D) ⊗ₖ + generalSpinMatrix B (Matrix.diagonal D))*W=W*generalSpinMatrix J (Matrix.diagonal D) + rw [he] + exact weight_support_diagonal_intertwining A B z J hz W hs _ _ hxy + · rintro ⟨i,j,hij,c⟩ + change (generalSpinMatrix A (Matrix.transvection i j c) ⊗ₖ + generalSpinMatrix B (Matrix.transvection i j c))*W=W*generalSpinMatrix J (Matrix.transvection i j c) + fin_cases i <;> fin_cases j + · exact False.elim (hij rfl) + · exact raising_intertwiner_upper A B J W hr c + · exact lowering_intertwiner_lower A B J W hl c + · exact False.elim (hij rfl) + · intro M L hM hL + change (generalSpinMatrix A (M*L) ⊗ₖ generalSpinMatrix B (M*L))*W=W*generalSpinMatrix J (M*L) + rw [generalSpinMatrix_mul,generalSpinMatrix_mul,generalSpinMatrix_mul,Matrix.mul_kronecker_mul] + change (generalSpinMatrix A M ⊗ₖ generalSpinMatrix B M)* + (generalSpinMatrix A L ⊗ₖ generalSpinMatrix B L)*W=W*(generalSpinMatrix J M*generalSpinMatrix J L) + rw [Matrix.mul_assoc,hL,← Matrix.mul_assoc,hM,Matrix.mul_assoc] + exact h + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/LadderMatrix.lean b/lean/OAI/Analysis/Laughlin/Spin/LadderMatrix.lean new file mode 100644 index 0000000000000000000000000000000000000000..8b64d83294123ec0212cffa17f50afa5acb69bec --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/LadderMatrix.lean @@ -0,0 +1,86 @@ +import Mathlib.Data.Matrix.Mul +import OAI.Analysis.Laughlin.Spin.Highest2 + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +noncomputable def raiseMatrix (A : ℕ) : Matrix (Fin (A+1)) (Fin (A+1)) ℝ := + fun i j => if i.val+1=j.val then ladder A i.val else 0 + +theorem raiseMatrix_row (A : ℕ) (i : Fin (A+1)) (f : Fin (A+1) → ℝ) : + (∑ j, raiseMatrix A i j*f j) = + if hi : i.val < A then ladder A i.val*f ⟨i.val+1,by omega⟩ else 0 := by + by_cases hi : i.val < A + · rw [dite_eq_left hi] + let next : Fin (A+1) := ⟨i.val+1,by omega⟩ + have he (j : Fin (A+1)) : i.val+1=j.val ↔ next=j := by + constructor + · intro h; exact Fin.ext h + · intro h; exact congrArg Fin.val h + simp only [raiseMatrix,he,ite_mul,zero_mul,Finset.sum_ite_eq,Finset.mem_univ,ite_true] + rfl + · rw [dite_eq_right hi] + apply Finset.sum_eq_zero + intro j hj + have hn : i.val+1 ≠ j.val := by omega + simp [raiseMatrix,hn] + +theorem raiseMatrix_column (A : ℕ) (j : Fin (A+1)) (f : Fin (A+1) → ℝ) : + (∑ i, f i*raiseMatrix A i j) = + if hj : 0 < j.val then f ⟨j.val-1,by omega⟩*ladder A (j.val-1) else 0 := by + by_cases hj : 0 < j.val + · rw [dite_eq_left hj] + let prev : Fin (A+1) := ⟨j.val-1,by omega⟩ + rw [Finset.sum_eq_single prev] + · simp [raiseMatrix,prev,show j.val-1+1=j.val by omega] + · intro i hi hn + have hne : i.val+1 ≠ j.val := by + intro h; apply hn; apply Fin.ext; dsimp [prev]; omega + simp [raiseMatrix,hne] + · simp + · rw [dite_eq_right hj] + apply Finset.sum_eq_zero + intro i hi + have hn : i.val+1 ≠ j.val := by omega + simp [raiseMatrix,hn] + +noncomputable def totalRaise (A B : ℕ) : + Matrix (Fin (A+1) × Fin (B+1)) (Fin (A+1) × Fin (B+1)) ℝ := fun i j => + raiseMatrix A i.1 j.1 * (if i.2=j.2 then 1 else 0) + + (if i.1=j.1 then 1 else 0)*raiseMatrix B i.2 j.2 + +theorem totalRaise_apply (A B : ℕ) (f : Fin (A+1) × Fin (B+1) → ℝ) + (i : Fin (A+1) × Fin (B+1)) : + (∑ j, totalRaise A B i j*f j) = + (∑ x, raiseMatrix A i.1 x*f (x,i.2)) + + (∑ y, raiseMatrix B i.2 y*f (i.1,y)) := by + rw [Fintype.sum_prod_type] + simp only [totalRaise,add_mul,Finset.sum_add_distrib] + congr 1 + · simp only [mul_ite,mul_one,mul_zero,ite_mul,zero_mul,Finset.sum_ite_eq, + Finset.mem_univ,ite_true] + · rw [Finset.sum_comm] + simp only [ite_mul,one_mul,zero_mul,Finset.sum_ite_eq,Finset.mem_univ,ite_true] + +theorem totalRaise_transpose_apply (A B : ℕ) (f : Fin (A+1) × Fin (B+1) → ℝ) + (i : Fin (A+1) × Fin (B+1)) : + (∑ j, totalRaise A B j i*f j) = + (∑ x, f (x,i.2)*raiseMatrix A x i.1) + + (∑ y, f (i.1,y)*raiseMatrix B y i.2) := by + rw [Fintype.sum_prod_type] + simp only [totalRaise,add_mul,Finset.sum_add_distrib] + congr 1 + · simp only [mul_ite,mul_one,mul_zero,ite_mul,zero_mul,Finset.sum_ite_eq', + Finset.mem_univ,ite_true] + apply Finset.sum_congr rfl + intro x hx; ring + · rw [Finset.sum_comm] + simp only [ite_mul,one_mul,zero_mul,Finset.sum_ite_eq',Finset.mem_univ,ite_true] + apply Finset.sum_congr rfl + intro y hy; ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/LoweringLimit.lean b/lean/OAI/Analysis/Laughlin/Spin/LoweringLimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..7db0746d7416f0987b59752dabd9afff9d8436fa --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/LoweringLimit.lean @@ -0,0 +1,47 @@ +import OAI.Analysis.Laughlin.Spin.ScaleLimit + +namespace OAI + +namespace Laughlin.Spin +open scoped Topology +open Filter + +theorem coupled_denominator_scale_tendsto (S : ℕ → ℕ) (hS : Tendsto S atTop atTop) + (z n : ℕ) : + Tendsto (fun j => ((((S j-2*z : ℕ) : ℝ)-(n : ℝ))/(S j : ℝ))) atTop (𝓝 1) := by + have hself : Tendsto (fun j => (S j : ℝ)/(S j : ℝ)) atTop (𝓝 (1 : ℝ)) := by + apply (tendsto_const_nhds (x := (1 : ℝ))).congr' + filter_upwards [hS.eventually (eventually_ge_atTop 1)] with j hj + have hn : (S j : ℝ) ≠ 0 := by exact_mod_cast (show S j ≠ 0 by omega) + rw [div_self hn] + have ht := spin_fraction_sub_tendsto S S 1 hS hS hself (2*z+n) + apply ht.congr' + filter_upwards [hS.eventually (eventually_ge_atTop (2*z+n))] with j hj + rw [Nat.cast_sub (by omega : 2*z+n ≤ S j),Nat.cast_sub (by omega : 2*z ≤ S j)] + push_cast + ring + +theorem normalized_ladder_factor_tendsto (C S : ℕ → ℕ) (c : ℝ) + (hC : Tendsto C atTop atTop) (hS : Tendsto S atTop atTop) + (hc : Tendsto (fun j => (C j : ℝ)/(S j : ℝ)) atTop (𝓝 c)) (z n k : ℕ) : + Tendsto (fun j => ladder (C j) k / + Real.sqrt (((n : ℝ)+1)*(((S j-2*z : ℕ) : ℝ)-n))) atTop + (𝓝 (Real.sqrt ((((k : ℝ)+1)*c)/((n : ℝ)+1)))) := by + have hnum := (spin_fraction_sub_tendsto C S c hC hS hc k).const_mul ((k : ℝ)+1) + have hden := (coupled_denominator_scale_tendsto S hS z n).const_mul ((n : ℝ)+1) + have ht := (hnum.div hden (by positivity)).sqrt + simp only [mul_one] at ht + apply ht.congr' + filter_upwards [hS.eventually (eventually_ge_atTop 1)] with j hj + have hp : (S j : ℝ) ≠ 0 := by exact_mod_cast (show S j ≠ 0 by omega) + simp only [Pi.div_apply] + have he : (((k : ℝ)+1)*(((C j-k : ℕ) : ℝ)/(S j : ℝ))) / + (((n : ℝ)+1)*((((S j-2*z : ℕ) : ℝ)-n)/(S j : ℝ))) = + (((k : ℝ)+1)*((C j-k : ℕ) : ℝ)) / + (((n : ℝ)+1)*(((S j-2*z : ℕ) : ℝ)-n)) := by field_simp + rw [he,Real.sqrt_div (by positivity)] + rfl + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/MatrixAverage.lean b/lean/OAI/Analysis/Laughlin/Spin/MatrixAverage.lean new file mode 100644 index 0000000000000000000000000000000000000000..35d65a25cd4d189c875905652a53f488e0ebc025 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/MatrixAverage.lean @@ -0,0 +1,85 @@ +import Mathlib.Analysis.Complex.Basic +import Mathlib.LinearAlgebra.Matrix.Trace +import Mathlib.MeasureTheory.Function.LocallyIntegrable +import Mathlib.MeasureTheory.Group.Integral + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators +open MeasureTheory MeasureTheory.Measure + +variable {G I : Type*} [MeasurableSpace G] [Fintype I] + +noncomputable def matrixIntegral (μ : Measure G) (f : G → Matrix I I ℂ) : Matrix I I ℂ := + fun i j => ∫ g, f g i j ∂μ + +theorem matrixIntegral_mul_left (μ : Measure G) (f : G → Matrix I I ℂ) + (hf : ∀ i j, Integrable (fun g => f g i j) μ) (A : Matrix I I ℂ) : + matrixIntegral μ (fun g => A*f g) = A*matrixIntegral μ f := by + ext i j + simp only [matrixIntegral,Matrix.mul_apply] + rw [integral_finsetSum _ (fun k hk => (hf k j).const_mul (A i k))] + simp only [integral_const_mul] + +theorem matrixIntegral_mul_right (μ : Measure G) (f : G → Matrix I I ℂ) + (hf : ∀ i j, Integrable (fun g => f g i j) μ) (A : Matrix I I ℂ) : + matrixIntegral μ (fun g => f g*A) = matrixIntegral μ f*A := by + ext i j + simp only [matrixIntegral,Matrix.mul_apply] + rw [integral_finsetSum _ (fun k hk => (hf i k).mul_const (A k j))] + simp only [integral_mul_const] + +theorem matrixIntegral_trace (μ : Measure G) (f : G → Matrix I I ℂ) + (hf : ∀ i j, Integrable (fun g => f g i j) μ) : + Matrix.trace (matrixIntegral μ f) = ∫ g, Matrix.trace (f g) ∂μ := by + simp only [Matrix.trace,Matrix.diag,matrixIntegral] + rw [integral_finsetSum _ (fun i hi => hf i i)] + +variable [DecidableEq I] + +noncomputable def conjugateOrbit [Group G] (ρ : G →* Matrix I I ℂ) (M : Matrix I I ℂ) + (g : G) : Matrix I I ℂ := ρ g*M*ρ g⁻¹ + +omit [MeasurableSpace G] in +theorem conjugateOrbit_mul [Group G] (ρ : G →* Matrix I I ℂ) (M : Matrix I I ℂ) (g h : G) : + conjugateOrbit ρ M (g*h) = ρ g*conjugateOrbit ρ M h*ρ g⁻¹ := by + simp only [conjugateOrbit,map_mul,mul_inv_rev,Matrix.mul_assoc] + +omit [MeasurableSpace G] in +theorem conjugateOrbit_trace [Group G] (ρ : G →* Matrix I I ℂ) (M : Matrix I I ℂ) (g : G) : + Matrix.trace (conjugateOrbit ρ M g) = Matrix.trace M := by + unfold conjugateOrbit + rw [Matrix.trace_mul_cycle] + rw [← map_mul,inv_mul_cancel,map_one,Matrix.one_mul] + +theorem haar_average_invariant [Group G] [MeasurableMul G] (μ : Measure G) [IsMulLeftInvariant μ] + (ρ : G →* Matrix I I ℂ) (M : Matrix I I ℂ) + (hf : ∀ i j, Integrable (fun g => conjugateOrbit ρ M g i j) μ) (h : G) : + ρ h*matrixIntegral μ (conjugateOrbit ρ M)*ρ h⁻¹ = matrixIntegral μ (conjugateOrbit ρ M) := by + have hl : ∀ i j, Integrable (fun g => (ρ h*conjugateOrbit ρ M g) i j) μ := by + intro i j + simp only [Matrix.mul_apply] + exact integrable_finsetSum _ (fun k hk => (hf k j).const_mul _) + rw [← matrixIntegral_mul_left μ _ hf,← matrixIntegral_mul_right μ _ hl] + ext i j + simp only [matrixIntegral,← conjugateOrbit_mul] + exact integral_mul_left_eq_self (fun g => conjugateOrbit ρ M g i j) h + +theorem haar_average_commutes [Group G] [MeasurableMul G] (μ : Measure G) [IsMulLeftInvariant μ] + (ρ : G →* Matrix I I ℂ) (M : Matrix I I ℂ) + (hf : ∀ i j, Integrable (fun g => conjugateOrbit ρ M g i j) μ) (h : G) : + ρ h*matrixIntegral μ (conjugateOrbit ρ M) = matrixIntegral μ (conjugateOrbit ρ M)*ρ h := by + have hh := congrArg (fun A : Matrix I I ℂ => A*ρ h) (haar_average_invariant μ ρ M hf h) + simpa only [Matrix.mul_assoc,← map_mul,inv_mul_cancel,map_one,Matrix.mul_one] using hh + +theorem haar_average_trace [Group G] (μ : Measure G) [IsProbabilityMeasure μ] + (ρ : G →* Matrix I I ℂ) (M : Matrix I I ℂ) + (hf : ∀ i j, Integrable (fun g => conjugateOrbit ρ M g i j) μ) : + Matrix.trace (matrixIntegral μ (conjugateOrbit ρ M)) = Matrix.trace M := by + rw [matrixIntegral_trace μ _ hf] + simp [conjugateOrbit_trace] + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Mixing.lean b/lean/OAI/Analysis/Laughlin/Spin/Mixing.lean new file mode 100644 index 0000000000000000000000000000000000000000..897b0ddae8c4e28ad8bd75d711b2b47261d0f450 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Mixing.lean @@ -0,0 +1,90 @@ +import OAI.Analysis.Laughlin.Spin.Torus + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + + theorem tensorWeight_sum_const (Q p : ℕ) (c : ℂ) : + (∑ a : Fin Q → Fin 2, if tensorWeight Q a=p then c else 0) = (Q.choose p : ℂ)*c := by + have he (a : Fin Q → Fin 2) : (if tensorWeight Q a=p then c else 0) = + ((if tensorWeight Q a=p then (1 : ℝ) else 0) : ℂ)*c := by split_ifs <;> simp + simp_rw [he] + rw [← Finset.sum_mul] + have hc := congrArg Complex.ofReal (tensorWeight_count Q p) + simp only [Complex.ofReal_sum,apply_ite,Complex.ofReal_one,Complex.ofReal_zero,Complex.ofReal_natCast] at hc + simpa only [Complex.ofReal_one] using congrArg (fun z : ℂ => z*c) hc + + theorem symmetricTensorInclusion_column_sum (Q : ℕ) (p : Fin (Q+1)) : + (∑ a, symmetricTensorInclusion Q a p) = (Real.sqrt (Q.choose p.val : ℝ) : ℂ) := by + simp only [symmetricTensorInclusion,Matrix.map_apply,symmetricTensorInclusionReal,apply_ite, + Complex.ofReal_zero] + rw [tensorWeight_sum_const] + have hs : (Real.sqrt (Q.choose p.val : ℝ) : ℂ)^2=(Q.choose p.val : ℂ) := by + exact_mod_cast Real.sq_sqrt (show (0 : ℝ) ≤ Q.choose p.val by positivity) + have hn : (Real.sqrt (Q.choose p.val : ℝ) : ℂ) ≠ 0 := by + apply Complex.ofReal_ne_zero.mpr + apply Real.sqrt_ne_zero'.mpr + exact_mod_cast Nat.choose_pos (by omega : p.val ≤ Q) + rw [Complex.ofReal_inv,← hs] + field_simp + + theorem tensorMatrix_uniform_first_column (Q : ℕ) (A : Matrix (Fin 2) (Fin 2) ℂ) (c : ℂ) + (h0 : A 0 0=c) (h1 : A 1 0=c) (a : Fin Q → Fin 2) : + (tensorMatrix Q A*symmetricTensorInclusion Q) a 0=c^Q := by + classical + rw [Matrix.mul_apply,Finset.sum_eq_single (fun _ => (0 : Fin 2))] + · rw [symmetricTensor_zero_column,ite_eq_left rfl,mul_one] + have he (i : Fin Q) : A (a i) 0=c := by + have h : a i=0 ∨ a i=1 := by omega + rcases h with h | h + · rw [h]; exact h0 + · rw [h]; exact h1 + simp [tensorMatrix,he] + · intro b hb hne + rw [symmetricTensor_zero_column,ite_eq_right hne,mul_zero] + · simp + +noncomputable def sourceMixer : SourceSU2 := by + let c : ℝ := Real.sqrt (1/2) + have hc : (c : ℂ)^2=(1/2 : ℂ) := by + have hs : c^2=(1/2 : ℝ) := Real.sq_sqrt (by norm_num) + have h := congrArg Complex.ofReal hs + push_cast at h + exact h + refine ⟨!![(c : ℂ),-(c : ℂ);(c : ℂ),(c : ℂ)],?_⟩ + constructor + · apply Matrix.mem_unitaryGroup_iff.mpr + ext i j + fin_cases i <;> fin_cases j <;> + simp [Matrix.mul_apply,Matrix.star_eq_conjTranspose,Matrix.conjTranspose_apply] <;> + linear_combination 2*hc + · simp [Matrix.det_fin_two] + linear_combination 2*hc + +theorem sourceSpinRepresentation_mixer_column (Q : ℕ) (p : Fin (Q+1)) : + sourceSpinRepresentation Q sourceMixer p 0 = + (Real.sqrt (Q.choose p.val : ℝ) : ℂ)*(Real.sqrt (1/2) : ℂ)^Q := by + change ((symmetricTensorInclusion Q)ᴴ*tensorMatrix Q sourceMixer.val*symmetricTensorInclusion Q) p 0 = _ + rw [Matrix.mul_assoc,Matrix.mul_apply] + have he (a : Fin Q → Fin 2) : (tensorMatrix Q sourceMixer.val*symmetricTensorInclusion Q) a 0 = + (Real.sqrt (1/2) : ℂ)^Q := tensorMatrix_uniform_first_column Q _ _ rfl rfl a + simp_rw [he,Matrix.conjTranspose_apply] + have hr (a : Fin Q → Fin 2) : star (symmetricTensorInclusion Q a p)=symmetricTensorInclusion Q a p := by + simp [symmetricTensorInclusion] + simp_rw [hr] + rw [← Finset.sum_mul,symmetricTensorInclusion_column_sum] + + theorem sourceSpinRepresentation_mixer_column_ne_zero (Q : ℕ) (p : Fin (Q+1)) : + sourceSpinRepresentation Q sourceMixer p 0 ≠ 0 := by + rw [sourceSpinRepresentation_mixer_column] + apply mul_ne_zero + · apply Complex.ofReal_ne_zero.mpr + apply Real.sqrt_ne_zero'.mpr + exact_mod_cast Nat.choose_pos (by omega : p.val ≤ Q) + · apply pow_ne_zero + exact Complex.ofReal_ne_zero.mpr (by positivity) + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Multidegree.lean b/lean/OAI/Analysis/Laughlin/Spin/Multidegree.lean new file mode 100644 index 0000000000000000000000000000000000000000..8b2837267a6b2d568bf1dab70bd723a02e5b5b81 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Multidegree.lean @@ -0,0 +1,61 @@ +import Mathlib.RingTheory.MvPolynomial.WeightedHomogeneous +import OAI.Analysis.Laughlin.Spin.PolynomialDegree + +namespace OAI + +namespace Laughlin +open MvPolynomial +open scoped BigOperators + +noncomputable def particleDegreeWeight {N : ℕ} (k : Fin N) (ib : SpinorVariables N) : ℕ := + if ib.1=k then 1 else 0 + +theorem particleDegreeWeight_apply {N : ℕ} (k : Fin N) (d : SpinorVariables N →₀ ℕ) : + Finsupp.weight (particleDegreeWeight k) d=d (k,false)+d (k,true) := by + rw [Finsupp.weight_eq_sum,Fintype.sum_prod_type] + simp [particleDegreeWeight,Nat.add_comm] + +theorem monomialExponent_particle_degree {N Q : ℕ} (a : Configuration N Q) (k : Fin N) : + Finsupp.weight (particleDegreeWeight k) (monomialExponent a)=Q := by + rw [particleDegreeWeight_apply] + simp only [monomialExponent,Finsupp.onFinset_apply,Bool.false_eq_true,↓reduceIte] + omega + +theorem spinPolynomial_particle_degree {N Q : ℕ} (ψ : State N Q) (k : Fin N) : + (spinPolynomial ψ).IsWeightedHomogeneous (particleDegreeWeight k) Q := by + apply IsWeightedHomogeneous.sum + intro a ha + exact isWeightedHomogeneous_monomial _ _ _ (monomialExponent_particle_degree a k) + +theorem exponent_eq_configuration {N Q : ℕ} (d : SpinorVariables N →₀ ℕ) + (hd : ∀ k : Fin N, d (k,false)+d (k,true)=Q) : + ∃ a : Configuration N Q, monomialExponent a=d := by + let a : Configuration N Q := fun k => ⟨d (k,true),by have h := hd k; omega⟩ + refine ⟨a,?_⟩ + ext ⟨k,b⟩ + cases b <;> simp only [monomialExponent,Finsupp.onFinset_apply,Bool.false_eq_true,↓reduceIte,a] + have h := hd k + omega + +theorem spinPolynomial_reconstruct {N Q : ℕ} (P : MvPolynomial (SpinorVariables N) ℂ) + (hP : ∀ k : Fin N, P.IsWeightedHomogeneous (particleDegreeWeight k) Q) : + spinPolynomial (fun a : Configuration N Q => P.coeff (monomialExponent a)/spinWeight a)=P := by + ext d + by_cases hd : P.coeff d=0 + · by_cases he : ∃ a : Configuration N Q, monomialExponent a=d + · obtain ⟨a,rfl⟩ := he + rw [spinPolynomial_coeff] + simp [hd] + · rw [hd] + simp only [spinPolynomial,coeff_sum,coeff_monomial] + apply Finset.sum_eq_zero + intro a ha + simp only [ite_eq_right (fun h => he ⟨a,h⟩)] + · obtain ⟨a,rfl⟩ := exponent_eq_configuration d (fun k => by + rw [← particleDegreeWeight_apply]; exact hP k hd) + rw [spinPolynomial_coeff] + field_simp [spinWeight_ne_zero a] + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/OrbitalExpansion.lean b/lean/OAI/Analysis/Laughlin/Spin/OrbitalExpansion.lean new file mode 100644 index 0000000000000000000000000000000000000000..2ae7a19ff50a6f5051e3ca94979b85da2f157540 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/OrbitalExpansion.lean @@ -0,0 +1,61 @@ +import OAI.Analysis.Laughlin.Pair.Spectators + +namespace OAI + +namespace Laughlin +open MvPolynomial +open scoped BigOperators + +noncomputable def spinOrbitalPolynomial {N : ℕ} (Q : ℕ) (i : Fin N) (x : Fin (Q+1)) : + MvPolynomial (SpinorVariables N) ℂ := + C (Real.sqrt (Nat.choose Q x.val : ℝ) : ℂ) * + (X (i,false)^(Q-x.val)*X (i,true)^x.val) + +theorem spinPolynomial_expansion {N Q : ℕ} (ψ : State N Q) : + spinPolynomial ψ = ∑ a, C (ψ a) * ∏ k, spinOrbitalPolynomial Q k (a k) := by + classical + unfold spinPolynomial + apply Finset.sum_congr rfl + intro a ha + rw [monomial_eq] + rw [Finsupp.prod_fintype _ _ (fun _ => pow_zero _), Fintype.prod_prod_type] + have he (k : Fin N) : (∏ b : Bool, X (k,b)^monomialExponent a (k,b)) = + (X (k,false)^(Q-(a k).val)*X (k,true)^(a k).val : MvPolynomial _ ℂ) := by + simp [monomialExponent, mul_comm] + simp_rw [he] + simp only [spinOrbitalPolynomial, Finset.prod_mul_distrib, ← map_prod, map_mul] + have hw : spinWeight a = ∏ k : Fin N, + (Real.sqrt (Nat.choose Q (a k).val : ℝ) : ℂ) := by + simp [spinWeight] + rw [hw] + ring + +theorem prod_pair_split {N : ℕ} {R : Type*} [CommMonoid R] + (i j : Fin N) (hij : i ≠ j) (f : Fin N → R) : + (∏ k, f k) = (∏ k ∈ (Finset.univ.erase i).erase j, f k) * f i * f j := by + classical + have hj : j ∈ Finset.univ.erase i := by simp [Ne.symm hij] + rw [← Finset.prod_erase_mul _ _ (Finset.mem_univ i), + ← Finset.prod_erase_mul _ _ hj] + ac_rfl + +noncomputable def spectatorPolynomial {N Q : ℕ} (i j : Fin N) (a : Configuration N Q) : + MvPolynomial (SpinorVariables N) ℂ := + ∏ k ∈ (Finset.univ.erase i).erase j, spinOrbitalPolynomial Q k (a k) + +theorem spinOrbital_update_product {N Q : ℕ} (i j : Fin N) (hij : i ≠ j) + (a : Configuration N Q) (x y : Fin (Q+1)) : + (∏ k, spinOrbitalPolynomial Q k ((Function.update (Function.update a i x) j y) k)) = + spectatorPolynomial i j a * spinOrbitalPolynomial Q i x * spinOrbitalPolynomial Q j y := by + rw [prod_pair_split i j hij] + simp only [Function.update_self, Function.update_of_ne hij] + congr 2 + apply Finset.prod_congr rfl + intro k hk + have hki : k ≠ i := (Finset.mem_erase.mp (Finset.mem_erase.mp hk).2).1 + have hkj : k ≠ j := (Finset.mem_erase.mp hk).1 + simp [Function.update_of_ne, hki,hkj] + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Orthogonal.lean b/lean/OAI/Analysis/Laughlin/Spin/Orthogonal.lean new file mode 100644 index 0000000000000000000000000000000000000000..a99d2f355579435919aab87dc4cf0920cfafdacb --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Orthogonal.lean @@ -0,0 +1,51 @@ +import OAI.Analysis.Laughlin.Spin.DescendantNorm +import OAI.Analysis.Laughlin.Spin.Sl2Orthogonal + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +theorem coupledHighest_orthogonal (Q z w : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) (hw : w ≤ Q) + (hzw : z ≠ w) : + (∑ i, coupledHighest Q z hQ hz i*coupledHighest Q w hQ hw i) = 0 := by + apply Finset.sum_eq_zero + intro i hi + by_cases he : i.1.val+i.2.val=z + · have hh : i.1.val+i.2.val ≠ w := by omega + have hv : coupledHighest Q w hQ hw i = 0 := + extendWeightSlice_off (2*Q-2) Q w (by omega) hw _ i hh + rw [hv,mul_zero] + · have hv : coupledHighest Q z hQ hz i = 0 := + extendWeightSlice_off (2*Q-2) Q z (by omega) hz _ i he + rw [hv,zero_mul] + +theorem coupledDescendant_orthogonal (Q z w n m : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) (hw : w ≤ Q) + (hne : z ≠ w ∨ n ≠ m) : + (∑ i, coupledDescendant Q z hQ hz n i*coupledDescendant Q w hQ hw m i) = 0 := by + apply descendants_orthogonal (totalRaise (2*Q-2) Q) (totalWeight (2*Q-2) Q) + ((totalRaise (2*Q-2) Q)ᵀ) (coupledHighest Q z hQ hz) (coupledHighest Q w hQ hw) + (coupledWeight Q w) (total_raise_lower_commutator _ _) (total_weight_lower_commutator _ _) + (Matrix.transpose_transpose _) (coupledHighest_weight Q w hQ hw) + (coupledHighest_raising_zero Q z hQ hz) (coupledHighest_raising_zero Q w hQ hw) n m + rcases hne with h | h + · exact Or.inl (coupledHighest_orthogonal Q z w hQ hz hw h) + · exact Or.inr h + +theorem normalizedCoupledDescendant_orthogonal (Q z w n m : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) (hw : w ≤ Q) + (hne : z ≠ w ∨ n ≠ m) : + (∑ i, normalizedCoupledDescendant Q z hQ hz n i * + normalizedCoupledDescendant Q w hQ hw m i) = 0 := by + unfold normalizedCoupledDescendant + simp only [Pi.smul_apply,smul_eq_mul] + calc + _ = (Real.sqrt (vectorNormSq (coupledDescendant Q z hQ hz n)))⁻¹ * + (Real.sqrt (vectorNormSq (coupledDescendant Q w hQ hw m)))⁻¹ * + (∑ i, coupledDescendant Q z hQ hz n i*coupledDescendant Q w hQ hw m i) := by + rw [Finset.mul_sum] + apply Finset.sum_congr rfl; intro i hi; ring + _ = 0 := by rw [coupledDescendant_orthogonal Q z w n m hQ hz hw hne,mul_zero] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/OscillatorHighest.lean b/lean/OAI/Analysis/Laughlin/Spin/OscillatorHighest.lean new file mode 100644 index 0000000000000000000000000000000000000000..66874440112cc44328c20be3104064c29e64bfda --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/OscillatorHighest.lean @@ -0,0 +1,70 @@ +import Mathlib.Data.Nat.Choose.Sum +import OAI.Analysis.Laughlin.Spin.RelativeHighest + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +noncomputable def oscillatorHighest (u v : ℝ) (z p : ℕ) : ℝ := + (-1 : ℝ)^(z-p) * Real.sqrt (z.choose p : ℝ) * u^p * v^(z-p) + +noncomputable def oscillatorRelative (t : ℝ) (z p : ℕ) : ℝ := + (-1 : ℝ)^p * Real.sqrt (z.choose p : ℝ) * t^p + +theorem oscillatorRelative_zero (t : ℝ) (z : ℕ) : + oscillatorRelative t z 0 = 1 := by simp [oscillatorRelative] + +theorem sqrt_choose_ratio (z p : ℕ) (hp : p < z) : + Real.sqrt (z.choose (p+1) : ℝ) = + Real.sqrt ((z-p : ℕ)/(p+1 : ℝ)) * Real.sqrt (z.choose p : ℝ) := by + rw [← Real.sqrt_mul (by positivity)] + congr 1 + have he := choose_step_real z p (by omega) + apply (mul_left_cancel₀ (show (p+1 : ℝ) ≠ 0 by positivity)) + field_simp + nlinarith only [he] + +theorem oscillatorRelative_succ (b : ℝ) (hb : 0 ≤ b) (z p : ℕ) (hp : p < z) : + oscillatorRelative (Real.sqrt (b/(1-b))) z (p+1) = + -Real.sqrt ((((z-p : ℕ) : ℝ)*b)/(((p : ℝ)+1)*(1-b))) * + oscillatorRelative (Real.sqrt (b/(1-b))) z p := by + have he : (((z-p : ℕ) : ℝ)*b)/(((p : ℝ)+1)*(1-b)) = + ((z-p : ℕ)/(p+1 : ℝ))*(b/(1-b)) := by rw [mul_div_mul_comm] + rw [he,Real.sqrt_mul (by positivity),Real.sqrt_div hb] + unfold oscillatorRelative + rw [sqrt_choose_ratio z p hp,pow_succ,pow_succ] + ring + +theorem oscillatorHighest_norm (u v : ℝ) (huv : u^2+v^2=1) (z : ℕ) : + (∑ p ∈ Finset.range (z+1), (oscillatorHighest u v z p)^2) = 1 := by + have hs := add_pow (u^2) (v^2) z + rw [huv,one_pow] at hs + apply Eq.trans ?_ hs.symm + apply Finset.sum_congr rfl + intro p hp + unfold oscillatorHighest + rw [mul_pow,mul_pow,mul_pow,Real.sq_sqrt (by positivity)] + have hn : ((-1 : ℝ)^(z-p))^2 = 1 := by rw [← pow_mul,mul_comm _ 2,pow_mul]; norm_num + rw [hn,one_mul] + ring + +theorem oscillatorHighest_relative (u v : ℝ) (hv : v ≠ 0) (z p : ℕ) (hp : p ≤ z) : + (-1 : ℝ)^z * oscillatorRelative (u/v) z p * v^z = oscillatorHighest u v z p := by + have hz : z=p+(z-p) := by omega + have hsign : (-1 : ℝ)^z*(-1 : ℝ)^p = (-1 : ℝ)^(z-p) := by + conv_lhs => arg 1; rw [hz,pow_add] + have he : ((-1 : ℝ)^p)^2 = 1 := by rw [← pow_mul,mul_comm _ 2,pow_mul]; norm_num + calc + _ = ((-1 : ℝ)^p)^2 * (-1 : ℝ)^(z-p) := by ring + _ = _ := by rw [he,one_mul] + unfold oscillatorRelative oscillatorHighest + calc + _ = ((-1 : ℝ)^z*(-1 : ℝ)^p)*Real.sqrt (z.choose p : ℝ)*u^p*(v^z/v^p) := by rw [div_pow]; ring + _ = _ := by + have hpows : v^z = v^p*v^(z-p) := by rw [← pow_add,← hz] + rw [hsign,hpows]; field_simp + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/OscillatorHighestNormalization.lean b/lean/OAI/Analysis/Laughlin/Spin/OscillatorHighestNormalization.lean new file mode 100644 index 0000000000000000000000000000000000000000..f23bb2f229d39e997072689d7ccda76b98f8ceff --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/OscillatorHighestNormalization.lean @@ -0,0 +1,52 @@ +import OAI.Analysis.Laughlin.Spin.OscillatorHighest + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +noncomputable def oscillatorRelativeNorm (t : ℝ) (z : ℕ) : ℝ := + Real.sqrt (∑ p ∈ Finset.range (z+1), (oscillatorRelative t z p)^2) + +theorem oscillatorRelativeNorm_pos (t : ℝ) (z : ℕ) : 0 < oscillatorRelativeNorm t z := by + apply Real.sqrt_pos.mpr + apply Finset.sum_pos' + · intro p hp; exact sq_nonneg _ + · refine ⟨0,Finset.mem_range.mpr (by omega),?_⟩ + rw [oscillatorRelative_zero]; norm_num + +theorem oscillatorRelativeNorm_scale (u v : ℝ) (hv : 0 < v) (huv : u^2+v^2=1) (z : ℕ) : + v^z * oscillatorRelativeNorm (u/v) z = 1 := by + have hvz : 0 < v^z := pow_pos hv z + have he : (v^z)^2 * ∑ p ∈ Finset.range (z+1), (oscillatorRelative (u/v) z p)^2 = 1 := by + rw [Finset.mul_sum,← oscillatorHighest_norm u v huv z] + apply Finset.sum_congr rfl + intro p hp + have hh := congrArg (fun x : ℝ => x^2) + (oscillatorHighest_relative u v (ne_of_gt hv) z p (by have := Finset.mem_range.mp hp; omega)) + have hsign : ((-1 : ℝ)^z)^2 = 1 := by rw [← pow_mul,mul_comm _ 2,pow_mul]; norm_num + simp only [mul_pow,hsign,one_mul] at hh + nlinarith only [hh] + have hs : (oscillatorRelativeNorm (u/v) z)^2 = + ∑ p ∈ Finset.range (z+1), (oscillatorRelative (u/v) z p)^2 := + Real.sq_sqrt (Finset.sum_nonneg (fun _ _ => sq_nonneg _)) + have hn := oscillatorRelativeNorm_pos (u/v) z + have hproduct : 0 < v^z*oscillatorRelativeNorm (u/v) z := mul_pos hvz hn + rw [← hs] at he + nlinarith only [he,hproduct] + +theorem oscillatorHighest_from_relative (u v : ℝ) (hv : 0 < v) (huv : u^2+v^2=1) + (z p : ℕ) (hp : p ≤ z) : + (-1 : ℝ)^z * (oscillatorRelative (u/v) z p / oscillatorRelativeNorm (u/v) z) = + oscillatorHighest u v z p := by + have hs := oscillatorRelativeNorm_scale u v hv huv z + have hn := ne_of_gt (oscillatorRelativeNorm_pos (u/v) z) + have he := oscillatorHighest_relative u v (ne_of_gt hv) z p hp + have hvz : v^z = 1 / oscillatorRelativeNorm (u/v) z := (eq_div_iff hn).mpr hs + calc + _ = (-1 : ℝ)^z * oscillatorRelative (u/v) z p * v^z := by rw [hvz]; ring + _ = _ := he + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/PairDecomposition.lean b/lean/OAI/Analysis/Laughlin/Spin/PairDecomposition.lean new file mode 100644 index 0000000000000000000000000000000000000000..dc74ee3d09038b6d35f04e2701a5738e9d9aa67e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/PairDecomposition.lean @@ -0,0 +1,67 @@ +import OAI.Analysis.Laughlin.Pair.SpinorCube +import OAI.Analysis.Laughlin.Spin.OrbitalExpansion +import OAI.Analysis.Laughlin.Spin.PolynomialDegree + +namespace OAI + +namespace Laughlin +open MvPolynomial +open scoped BigOperators + +theorem pairSpinorPolynomial_orbitals {N Q : ℕ} (i j : Fin N) + (ψ : Fin (Q+1) → Fin (Q+1) → ℂ) : + pairSpinorPolynomial C (X (i,false)) (X (i,true)) (X (j,false)) (X (j,true)) Q ψ = + ∑ x, ∑ y, C (ψ x y) * spinOrbitalPolynomial Q i x * spinOrbitalPolynomial Q j y := by + unfold pairSpinorPolynomial + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + simp only [weightedPairCoordinate, Complex.ofReal_mul, map_mul, spinOrbitalPolynomial] + ring + +theorem spinPolynomial_pair_decomposition {N Q : ℕ} (ψ : State N Q) + (i j : Fin N) (hij : i ≠ j) : + spinPolynomial ψ = ∑ a : PairSpectators (Q := Q) i j, + spectatorPolynomial i j a.val * + pairSpinorPolynomial C (X (i,false)) (X (i,true)) (X (j,false)) (X (j,true)) Q + (pairSlice ψ i j a.val) := by + rw [spinPolynomial_expansion, sum_pair_configurations i j hij] + apply Finset.sum_congr rfl + intro a ha + rw [pairSpinorPolynomial_orbitals] + simp only [Finset.mul_sum] + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + rw [spinOrbital_update_product i j hij] + unfold pairSlice + ring + +theorem bracket_cube_dvd_spinPolynomial_of_slices {N Q : ℕ} (ψ : State N Q) + (i j : Fin N) (hij : i ≠ j) + (hc : ∀ a : Configuration N Q, + PairDiagonal.diagonal^3 ∣ pairAffinePolynomial Q (pairSlice ψ i j a)) : + bracket i j^3 ∣ spinPolynomial ψ := by + rw [spinPolynomial_pair_decomposition ψ i j hij] + apply Finset.dvd_sum + intro a ha + exact dvd_mul_of_dvd_right (pairSpinorPolynomial_bracket_cube i j _ (hc a.val)) _ + +theorem energy_zero_global_pair_cubes {N Q : ℕ} (hQ : 2 ≤ Q) + (ψ : State N Q) (hψ : Antisymmetric ψ) (hE : energy ψ = 0) : + ∀ i j : Fin N, i < j → bracket i j^3 ∣ spinPolynomial ψ := by + intro i j hij + exact bracket_cube_dvd_spinPolynomial_of_slices ψ i j (ne_of_lt hij) + ((energy_eq_zero_iff_affine_pair_cubes hQ ψ hψ).mp hE i j hij) + +theorem zero_energy_state_eq_laughlin {N : ℕ} (hN : 2 ≤ N) + (ψ : State N (3*(N-1))) (hψ : Antisymmetric ψ) (hE : energy ψ = 0) : + ∃ c : ℂ, ψ = fun a => c * laughlinVector N (3*(N-1)) a := by + exact state_eq_laughlin_of_pair_cubes ψ + (energy_zero_global_pair_cubes (by omega) ψ hψ hE) + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/ParticleSpinAction.lean b/lean/OAI/Analysis/Laughlin/Spin/ParticleSpinAction.lean new file mode 100644 index 0000000000000000000000000000000000000000..87b28168b93bc857b6e3cf9d5b40dbae06af1852 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/ParticleSpinAction.lean @@ -0,0 +1,62 @@ +import OAI.Analysis.Laughlin.EnergyNonnegative +import OAI.Analysis.Laughlin.Spin.Representation + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + +noncomputable def tensorPowerMatrix {ι κ : Type*} [Fintype ι] [DecidableEq ι] + (A : Matrix κ κ ℂ) : Matrix (ι → κ) (ι → κ) ℂ := fun a b => ∏ i, A (a i) (b i) + +theorem tensorPowerMatrix_mul {ι κ : Type*} [Fintype ι] [DecidableEq ι] [Fintype κ] + (A B : Matrix κ κ ℂ) : + tensorPowerMatrix (ι := ι) (A*B) = tensorPowerMatrix (ι := ι) A * tensorPowerMatrix (ι := ι) B := by + ext a c + simp only [tensorPowerMatrix,Matrix.mul_apply,← Finset.prod_mul_distrib] + exact Fintype.prod_sum (fun i b => A (a i) b*B b (c i)) + +theorem tensorPowerMatrix_one {ι κ : Type*} [Fintype ι] [DecidableEq ι] [DecidableEq κ] : + tensorPowerMatrix (ι := ι) (1 : Matrix κ κ ℂ) = 1 := by + classical + ext a b + simp only [tensorPowerMatrix,Matrix.one_apply] + by_cases h : a=b + · subst b; simp + · rw [ite_eq_right h] + obtain ⟨i,hi⟩ := Function.ne_iff.mp h + exact Finset.prod_eq_zero (Finset.mem_univ i) (ite_eq_right hi) + +theorem tensorPowerMatrix_conjTranspose {ι κ : Type*} [Fintype ι] [DecidableEq ι] + (A : Matrix κ κ ℂ) : tensorPowerMatrix (ι := ι) Aᴴ = (tensorPowerMatrix A)ᴴ := by + ext a b + simp [tensorPowerMatrix,Matrix.conjTranspose_apply] + +theorem tensorPowerMatrix_unitary {ι κ : Type*} [Fintype ι] [DecidableEq ι] [Fintype κ] [DecidableEq κ] + (A : Matrix κ κ ℂ) (hA : A ∈ Matrix.unitaryGroup κ ℂ) : + tensorPowerMatrix (ι := ι) A ∈ Matrix.unitaryGroup (ι → κ) ℂ := by + classical + apply Matrix.mem_unitaryGroup_iff'.mpr + rw [Matrix.star_eq_conjTranspose,← tensorPowerMatrix_conjTranspose,← tensorPowerMatrix_mul] + have h := Matrix.mem_unitaryGroup_iff'.mp hA + rw [Matrix.star_eq_conjTranspose] at h + rw [h,tensorPowerMatrix_one] + +noncomputable def sourceParticleRepresentation (N Q : ℕ) : SourceSU2 →* + Matrix (Configuration N Q) (Configuration N Q) ℂ where + toFun g := tensorPowerMatrix (sourceSpinRepresentation Q g) + map_one' := by rw [map_one, tensorPowerMatrix_one] + map_mul' g h := by rw [map_mul, tensorPowerMatrix_mul] + +theorem sourceParticleRepresentation_unitary (N Q : ℕ) (g : SourceSU2) : + sourceParticleRepresentation N Q g ∈ Matrix.unitaryGroup (Configuration N Q) ℂ := + tensorPowerMatrix_unitary _ (sourceSpinRepresentation_unitary Q g) + +theorem sourceParticleRepresentation_continuous (N Q : ℕ) + (a b : Configuration N Q) : Continuous (fun g => sourceParticleRepresentation N Q g a b) := by + change Continuous (fun g => ∏ k, sourceSpinRepresentation Q g (a k) (b k)) + exact continuous_finsetProd _ (fun k hk => sourceSpinRepresentation_continuous Q _ _) + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Polynomial.lean b/lean/OAI/Analysis/Laughlin/Spin/Polynomial.lean new file mode 100644 index 0000000000000000000000000000000000000000..8d766ff81ff8d442eb43e09ec2b24b273cbf6629 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Polynomial.lean @@ -0,0 +1,58 @@ +import OAI.Analysis.Laughlin.Polynomial.OscillatorPolynomialLadder +import OAI.Analysis.Laughlin.Spin.ArrayLimit + +namespace OAI + +namespace Laughlin.Spin +open scoped Topology +open Filter + +theorem oscillatorArray_polynomial (b : ℝ) (hb0 : 0 < b) (hb1 : b < 1) + (z n p : ℕ) (hp : p ≤ z+n) : + oscillatorArray b z n p = + couplingPolynomialCoefficient (Real.sqrt b) (Real.sqrt (1-b)) z n p := by + have hu : Real.sqrt b ≠ 0 := ne_of_gt (Real.sqrt_pos.mpr hb0) + induction n generalizing p with + | zero => exact (couplingPolynomial_base_normalized _ _ hu z p (by omega)).symm + | succ n ih => + have hf (c : ℝ) (hc : 0 ≤ c) (k : ℕ) : + Real.sqrt ((((k : ℝ)+1)*c)/((n : ℝ)+1)) = + Real.sqrt c * Real.sqrt ((k : ℝ)+1) / Real.sqrt ((n : ℝ)+1) := by + rw [Real.sqrt_div (by positivity),Real.sqrt_mul (by positivity)] + ring + have hfirst : + (if p=0 then 0 else Real.sqrt ((((p-1 : ℕ)+1 : ℝ)*(1-b))/((n : ℝ)+1))*oscillatorArray b z n (p-1)) = + (if p=0 then 0 else Real.sqrt (1-b)*Real.sqrt (p : ℝ)* + couplingPolynomialCoefficient (Real.sqrt b) (Real.sqrt (1-b)) z n (p-1)) / Real.sqrt ((n : ℝ)+1) := by + by_cases hp0 : p=0 + · simp only [hp0,ite_true,zero_div] + · simp only [hp0,ite_false] + have hk : ((p-1 : ℕ) : ℝ)+1=p := by exact_mod_cast (show p-1+1=p by omega) + rw [ih (p-1) (by omega),hf (1-b) (by linarith),hk] + ring + have hsecond : + (if p ≤ z+n then Real.sqrt ((((z+n-p : ℕ)+1 : ℝ)*b)/((n : ℝ)+1))*oscillatorArray b z n p else 0) = + (if p ≤ z+n then Real.sqrt b*Real.sqrt ((z+n+1-p : ℕ) : ℝ)* + couplingPolynomialCoefficient (Real.sqrt b) (Real.sqrt (1-b)) z n p else 0) / Real.sqrt ((n : ℝ)+1) := by + by_cases hpn : p ≤ z+n + · simp only [hpn,ite_true] + have hk : ((z+n-p : ℕ) : ℝ)+1=(z+n+1-p : ℕ) := by + exact_mod_cast (show z+n-p+1=z+n+1-p by omega) + rw [ih p hpn,hf b (le_of_lt hb0),hk] + ring + · simp only [hpn,ite_false,zero_div] + rw [oscillatorArray,couplingPolynomialCoefficient_lowering _ _ hu z n p (by omega),hfirst,hsecond,← add_div] + +theorem source_coupling_polynomial_tendsto (A B : ℕ → ℕ) (b : ℝ) + (hA : Tendsto A atTop atTop) (hB : Tendsto B atTop atTop) + (hb0 : 0 < b) (hb1 : b < 1) + (hfrac : Tendsto (fun j => (B j : ℝ)/((A j : ℝ)+B j)) atTop (𝓝 b)) + (z T p : ℕ) (hz : z ≤ T) (hp : p ≤ T) : + Tendsto (fun j => couplingArray (A j) (B j) z (T-z) p) atTop + (𝓝 (couplingPolynomialCoefficient (Real.sqrt b) (Real.sqrt (1-b)) z (T-z) p)) := by + rw [← oscillatorArray_polynomial b hb0 hb1 z (T-z) p (by omega)] + exact couplingArray_tendsto A B b hA hB hb0 hb1 hfrac z (T-z) p (by omega) + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Polynomial2.lean b/lean/OAI/Analysis/Laughlin/Spin/Polynomial2.lean new file mode 100644 index 0000000000000000000000000000000000000000..cce9e7e10aa3dfd0aba38c24a1aa273f8b652872 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Polynomial2.lean @@ -0,0 +1,62 @@ +import Mathlib.Algebra.BigOperators.Fin +import OAI.Analysis.Laughlin.Polynomial.LaughlinDegree + +namespace OAI + +namespace Laughlin +open MvPolynomial +open scoped BigOperators + +noncomputable def spinWeight {N Q : ℕ} (a : Configuration N Q) : ℂ := + ((∏ i : Fin N, Real.sqrt (Nat.choose Q (a i).val : ℝ) : ℝ) : ℂ) + +noncomputable def spinPolynomial {N Q : ℕ} (ψ : State N Q) : + MvPolynomial (SpinorVariables N) ℂ := + ∑ a : Configuration N Q, monomial (monomialExponent a) (spinWeight a * ψ a) + +theorem monomialExponent_injective (N Q : ℕ) : + Function.Injective (monomialExponent (N := N) (Q := Q)) := by + intro a b hab + funext i + apply Fin.ext + have h := congrArg (fun d => d (i,true)) hab + simpa [monomialExponent] using h + +theorem spinWeight_ne_zero {N Q : ℕ} (a : Configuration N Q) : spinWeight a ≠ 0 := by + apply Complex.ofReal_ne_zero.mpr + apply Finset.prod_ne_zero_iff.mpr + intro i hi + apply Real.sqrt_ne_zero'.mpr + exact_mod_cast Nat.choose_pos (Nat.le_of_lt_succ (a i).isLt) + +theorem spinPolynomial_coeff {N Q : ℕ} (ψ : State N Q) (a : Configuration N Q) : + (spinPolynomial ψ).coeff (monomialExponent a) = spinWeight a * ψ a := by + classical + simp only [spinPolynomial, coeff_sum, coeff_monomial] + have he (b : Configuration N Q) : monomialExponent b = monomialExponent a ↔ b = a := + (monomialExponent_injective N Q).eq_iff + simp_rw [he] + simp + +theorem spinPolynomial_injective (N Q : ℕ) : + Function.Injective (spinPolynomial (N := N) (Q := Q)) := by + intro ψ φ h + funext a + have hc := congrArg (fun p => p.coeff (monomialExponent a)) h + simp only [spinPolynomial_coeff] at hc + exact mul_left_cancel₀ (spinWeight_ne_zero a) hc + +theorem state_eq_laughlin_of_polynomial {N Q : ℕ} (ψ : State N Q) (c : ℂ) + (h : spinPolynomial ψ = C c * laughlinPolynomial N) : + ψ = fun a => c * laughlinVector N Q a := by + funext a + have hc := congrArg (fun p => p.coeff (monomialExponent a)) h + rw [spinPolynomial_coeff, coeff_C_mul] at hc + change ψ a = c * ((laughlinPolynomial N).coeff (monomialExponent a) / spinWeight a) + apply (mul_left_cancel₀ (spinWeight_ne_zero a)) + rw [hc] + field_simp [spinWeight_ne_zero a] + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/PolynomialDegree.lean b/lean/OAI/Analysis/Laughlin/Spin/PolynomialDegree.lean new file mode 100644 index 0000000000000000000000000000000000000000..99a0c68ad8940cd8f640f2d4a4b91e1fae12824c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/PolynomialDegree.lean @@ -0,0 +1,36 @@ +import OAI.Analysis.Laughlin.Spin.Polynomial2 + +namespace OAI + +namespace Laughlin +open MvPolynomial +open scoped BigOperators + +theorem monomialExponent_degree {N Q : ℕ} (a : Configuration N Q) : + (monomialExponent a).degree = N * Q := by + rw [Finsupp.degree_eq_sum, Fintype.sum_prod_type] + have h (i : Fin N) : ∑ b : Bool, monomialExponent a (i,b) = Q := by + simpa [monomialExponent, Nat.add_comm] using Nat.sub_add_cancel (Nat.le_of_lt_succ (a i).isLt) + simp_rw [h] + simp + +theorem spinPolynomial_isHomogeneous {N Q : ℕ} (ψ : State N Q) : + (spinPolynomial ψ).IsHomogeneous (N * Q) := by + apply IsHomogeneous.sum + intro a ha + exact isHomogeneous_monomial _ (monomialExponent_degree a) + +theorem spinPolynomial_totalDegree_le {N Q : ℕ} (ψ : State N Q) : + (spinPolynomial ψ).totalDegree ≤ N * Q := + (spinPolynomial_isHomogeneous ψ).totalDegree_le + +theorem state_eq_laughlin_of_pair_cubes {N : ℕ} (ψ : State N (3*(N-1))) + (hcubes : ∀ i j : Fin N, i < j → bracket i j ^ 3 ∣ spinPolynomial ψ) : + ∃ c : ℂ, ψ = fun a => c * laughlinVector N (3*(N-1)) a := by + obtain ⟨c,hc⟩ := scalar_laughlin_at_flux (spinPolynomial ψ) + (spinPolynomial_totalDegree_le ψ) hcubes + exact ⟨c,state_eq_laughlin_of_polynomial ψ c hc⟩ + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/RectangularAverage.lean b/lean/OAI/Analysis/Laughlin/Spin/RectangularAverage.lean new file mode 100644 index 0000000000000000000000000000000000000000..78c08dbf0049f8011d41e3340c3451dac2f84052 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/RectangularAverage.lean @@ -0,0 +1,75 @@ +import OAI.Analysis.Laughlin.Spin.CompactAverage + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators +open MeasureTheory MeasureTheory.Measure +variable {G I J : Type*} [Group G] [TopologicalSpace G] [IsTopologicalGroup G] + [MeasurableSpace G] [BorelSpace G] [CompactSpace G] + [Fintype I] [DecidableEq I] [Fintype J] [DecidableEq J] + +noncomputable def rectangularIntegral (μ : Measure G) (f : G → Matrix I J ℂ) : Matrix I J ℂ := + fun i j => ∫ g, f g i j ∂μ +noncomputable def rectangularOrbit (ρ : G →* Matrix I I ℂ) (σ : G →* Matrix J J ℂ) + (M : Matrix I J ℂ) (g : G) : Matrix I J ℂ := ρ g*M*σ g⁻¹ + +omit [TopologicalSpace G] [IsTopologicalGroup G] [MeasurableSpace G] [BorelSpace G] + [CompactSpace G] in +theorem rectangularOrbit_mul (ρ : G →* Matrix I I ℂ) (σ : G →* Matrix J J ℂ) + (M : Matrix I J ℂ) (g h : G) : + rectangularOrbit ρ σ M (g*h)=ρ g*rectangularOrbit ρ σ M h*σ g⁻¹ := by + simp only [rectangularOrbit,map_mul,mul_inv_rev,Matrix.mul_assoc] + +theorem compact_rectangularOrbit_integrable (μ : Measure G) [IsFiniteMeasure μ] + (ρ : G →* Matrix I I ℂ) (σ : G →* Matrix J J ℂ) + (hρ : ∀ i j, Continuous (fun g => ρ g i j)) (hσ : ∀ i j, Continuous (fun g => σ g i j)) + (M : Matrix I J ℂ) (i : I) (j : J) : Integrable (fun g => rectangularOrbit ρ σ M g i j) μ := by + have hc : Continuous (fun g => rectangularOrbit ρ σ M g i j) := by + simp only [rectangularOrbit,Matrix.mul_apply] + fun_prop + exact hc.integrable_of_hasCompactSupport (isClosed_tsupport _).isCompact + +omit [Group G] [TopologicalSpace G] [IsTopologicalGroup G] [BorelSpace G] [CompactSpace G] + [DecidableEq I] [Fintype J] [DecidableEq J] in +theorem rectangularIntegral_mul_left (μ : Measure G) (f : G → Matrix I J ℂ) + (hf : ∀ i j, Integrable (fun g => f g i j) μ) (A : Matrix I I ℂ) : + rectangularIntegral μ (fun g => A*f g)=A*rectangularIntegral μ f := by + ext i j + simp only [rectangularIntegral,Matrix.mul_apply] + rw [integral_finsetSum _ (fun k hk => (hf k j).const_mul (A i k))] + simp only [integral_const_mul] + +omit [Group G] [TopologicalSpace G] [IsTopologicalGroup G] [BorelSpace G] [CompactSpace G] + [Fintype I] [DecidableEq I] [DecidableEq J] in +theorem rectangularIntegral_mul_right (μ : Measure G) (f : G → Matrix I J ℂ) + (hf : ∀ i j, Integrable (fun g => f g i j) μ) (A : Matrix J J ℂ) : + rectangularIntegral μ (fun g => f g*A)=rectangularIntegral μ f*A := by + ext i j + simp only [rectangularIntegral,Matrix.mul_apply] + rw [integral_finsetSum _ (fun k hk => (hf i k).mul_const (A k j))] + simp only [integral_mul_const] + +theorem compact_rectangular_average_intertwines (μ : Measure G) [IsProbabilityMeasure μ] + [IsMulLeftInvariant μ] (ρ : G →* Matrix I I ℂ) (σ : G →* Matrix J J ℂ) + (hρ : ∀ i j, Continuous (fun g => ρ g i j)) (hσ : ∀ i j, Continuous (fun g => σ g i j)) + (M : Matrix I J ℂ) (h : G) : + ρ h*rectangularIntegral μ (rectangularOrbit ρ σ M)= + rectangularIntegral μ (rectangularOrbit ρ σ M)*σ h := by + have hf := compact_rectangularOrbit_integrable μ ρ σ hρ hσ M + have hl : ∀ i j, Integrable (fun g => (ρ h*rectangularOrbit ρ σ M g) i j) μ := by + intro i j + simp only [Matrix.mul_apply] + exact integrable_finsetSum _ (fun k hk => (hf k j).const_mul _) + have he : ρ h*rectangularIntegral μ (rectangularOrbit ρ σ M)*σ h⁻¹ = + rectangularIntegral μ (rectangularOrbit ρ σ M) := by + rw [← rectangularIntegral_mul_left μ _ hf,← rectangularIntegral_mul_right μ _ hl] + ext i j + simp only [rectangularIntegral,← rectangularOrbit_mul] + exact integral_mul_left_eq_self (fun g => rectangularOrbit ρ σ M g i j) h + have hh := congrArg (fun A : Matrix I J ℂ => A*σ h) he + simpa only [Matrix.mul_assoc,← map_mul,inv_mul_cancel,map_one,Matrix.mul_one] using hh + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/RelativeHighest.lean b/lean/OAI/Analysis/Laughlin/Spin/RelativeHighest.lean new file mode 100644 index 0000000000000000000000000000000000000000..d018d0c3c1a1a526f2c70c6b25a8384e1bcd84e6 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/RelativeHighest.lean @@ -0,0 +1,65 @@ +import OAI.Analysis.Laughlin.Spin.HighestSpace + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators + +noncomputable def relativeHighest (A B z p : ℕ) : ℝ := + highestRaw A B z p / highestRaw A B z 0 + +noncomputable def relativeHighestNorm (A B z : ℕ) : ℝ := + Real.sqrt (∑ p ∈ Finset.range (z+1), (relativeHighest A B z p)^2) + +theorem highestRaw_zero_pos (A B z : ℕ) (hB : z ≤ B) : + 0 < highestRaw A B z 0 := by + rw [highestRaw_zero] + apply one_div_pos.mpr + apply Real.sqrt_pos.mpr + exact_mod_cast Nat.choose_pos hB + +theorem relativeHighest_zero (A B z : ℕ) (hB : z ≤ B) : + relativeHighest A B z 0 = 1 := by + exact div_self (ne_of_gt (highestRaw_zero_pos A B z hB)) + +theorem relativeHighest_succ (A B z p : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (hp : p < z) : + relativeHighest A B z (p+1) = + -(ladder B (z-p-1)/ladder A p)*relativeHighest A B z p := by + have he := highestRaw_raising A B z p hA hB hp + have ha := ne_of_gt (ladder_pos A p (by omega)) + have hr := ne_of_gt (highestRaw_zero_pos A B z hB) + unfold relativeHighest + field_simp + nlinarith only [he] + +theorem relativeHighestNorm_pos (A B z : ℕ) (hB : z ≤ B) : + 0 < relativeHighestNorm A B z := by + apply Real.sqrt_pos.mpr + apply Finset.sum_pos' + · intro p hp; exact sq_nonneg _ + · refine ⟨0,Finset.mem_range.mpr (by omega),?_⟩ + rw [relativeHighest_zero A B z hB]; norm_num + +theorem highestNorm_relative (A B z : ℕ) (hB : z ≤ B) : + highestNorm A B z = highestRaw A B z 0 * relativeHighestNorm A B z := by + have hp := highestRaw_zero_pos A B z hB + have he : (∑ p ∈ Finset.range (z+1), (highestRaw A B z p)^2) = + (highestRaw A B z 0)^2 * ∑ p ∈ Finset.range (z+1), (relativeHighest A B z p)^2 := by + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro p hp' + unfold relativeHighest + field_simp + unfold highestNorm relativeHighestNorm + rw [he,Real.sqrt_mul (sq_nonneg _),Real.sqrt_sq (le_of_lt hp)] + +theorem highestUnit_eq_relative (A B z p : ℕ) (hB : z ≤ B) : + highestUnit A B z p = relativeHighest A B z p / relativeHighestNorm A B z := by + unfold highestUnit relativeHighest + rw [highestNorm_relative A B z hB] + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Representation.lean b/lean/OAI/Analysis/Laughlin/Spin/Representation.lean new file mode 100644 index 0000000000000000000000000000000000000000..dcc728253fc2eb30c7cd0ae768d6ce7efff82ce9 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Representation.lean @@ -0,0 +1,79 @@ +import OAI.Analysis.Laughlin.Polynomial.SymmetricTensorRange +import OAI.Analysis.Laughlin.Spin.Haar + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + +noncomputable def sourceSpinMatrix (Q : ℕ) (g : SourceSU2) : Matrix (Fin (Q+1)) (Fin (Q+1)) ℂ := + (symmetricTensorInclusion Q)ᴴ * sourceTensorRepresentation Q g * symmetricTensorInclusion Q + + theorem tensor_spin_intertwining (Q : ℕ) (g : SourceSU2) : + symmetricTensorInclusion Q*sourceSpinMatrix Q g = sourceTensorRepresentation Q g*symmetricTensorInclusion Q := by + ext a p + let v : (Fin Q → Fin 2) → ℂ := fun b => symmetricTensorInclusion Q b p + have hv : ∀ b c, tensorWeight Q b=tensorWeight Q c → v b=v c := by + intro b c h + simp only [v,symmetricTensorInclusion,Matrix.map_apply,symmetricTensorInclusionReal,h] + have hf := tensorMatrix_preserves_symmetric Q g.val v hv + have he := congrFun (symmetricTensor_projector_fixed Q (sourceTensorRepresentation Q g *ᵥ v) hf) a + change (symmetricTensorInclusion Q*((symmetricTensorInclusion Q)ᴴ*sourceTensorRepresentation Q g*symmetricTensorInclusion Q)) a p = _ + calc + _ = ((symmetricTensorInclusion Q*(symmetricTensorInclusion Q)ᴴ)* + (sourceTensorRepresentation Q g*symmetricTensorInclusion Q)) a p := by simp only [Matrix.mul_assoc] + _ = _ := he + + theorem sourceSpinMatrix_mul (Q : ℕ) (g h : SourceSU2) : + sourceSpinMatrix Q (g*h)=sourceSpinMatrix Q g*sourceSpinMatrix Q h := by + unfold sourceSpinMatrix + rw [map_mul] + have he := tensor_spin_intertwining Q h + unfold sourceSpinMatrix at he + calc + _ = (symmetricTensorInclusion Q)ᴴ*sourceTensorRepresentation Q g* + (sourceTensorRepresentation Q h*symmetricTensorInclusion Q) := by simp only [Matrix.mul_assoc] + _ = _ := by rw [← he]; simp only [Matrix.mul_assoc] + + theorem sourceSpinMatrix_one (Q : ℕ) : sourceSpinMatrix Q 1=1 := by + simp only [sourceSpinMatrix,map_one,Matrix.mul_one,symmetricTensorInclusion_isometry] + +noncomputable def sourceSpinRepresentation (Q : ℕ) : SourceSU2 →* Matrix (Fin (Q+1)) (Fin (Q+1)) ℂ where + toFun := sourceSpinMatrix Q + map_one' := sourceSpinMatrix_one Q + map_mul' := sourceSpinMatrix_mul Q + + theorem sourceSpinRepresentation_unitary (Q : ℕ) (g : SourceSU2) : + sourceSpinRepresentation Q g ∈ Matrix.unitaryGroup (Fin (Q+1)) ℂ := by + have he := congrArg (fun M => Mᴴ*M) (tensor_spin_intertwining Q g) + have hu := Matrix.mem_unitaryGroup_iff'.mp (sourceTensorRepresentation_unitary Q g) + rw [Matrix.star_eq_conjTranspose] at hu + simp only [Matrix.conjTranspose_mul] at he + have hleft : (sourceSpinMatrix Q g)ᴴ*(symmetricTensorInclusion Q)ᴴ* + (symmetricTensorInclusion Q*sourceSpinMatrix Q g) = (sourceSpinMatrix Q g)ᴴ*sourceSpinMatrix Q g := by + rw [Matrix.mul_assoc,← Matrix.mul_assoc (symmetricTensorInclusion Q)ᴴ, + symmetricTensorInclusion_isometry,Matrix.one_mul] + have hright : (symmetricTensorInclusion Q)ᴴ*(sourceTensorRepresentation Q g)ᴴ* + (sourceTensorRepresentation Q g*symmetricTensorInclusion Q) = 1 := by + rw [Matrix.mul_assoc,← Matrix.mul_assoc (sourceTensorRepresentation Q g)ᴴ,hu, + Matrix.one_mul,symmetricTensorInclusion_isometry] + rw [hleft,hright] at he + exact Matrix.mem_unitaryGroup_iff'.mpr he + + theorem sourceSpinRepresentation_continuous (Q : ℕ) (p q : Fin (Q+1)) : + Continuous (fun g => sourceSpinRepresentation Q g p q) := by + change Continuous (fun g : SourceSU2 => + ((symmetricTensorInclusion Q)ᴴ*sourceTensorRepresentation Q g*symmetricTensorInclusion Q) p q) + simp only [Matrix.mul_apply] + have h := sourceTensorRepresentation_continuous Q + fun_prop + + theorem source_spin_haar_average_commutes (Q : ℕ) (M : Matrix (Fin (Q+1)) (Fin (Q+1)) ℂ) (g : SourceSU2) : + sourceSpinRepresentation Q g * matrixIntegral sourceHaar (conjugateOrbit (sourceSpinRepresentation Q) M) = + matrixIntegral sourceHaar (conjugateOrbit (sourceSpinRepresentation Q) M) * sourceSpinRepresentation Q g := by + exact compact_haar_average_commutes sourceHaar (sourceSpinRepresentation Q) + (sourceSpinRepresentation_continuous Q) M g + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Sandwich.lean b/lean/OAI/Analysis/Laughlin/Spin/Sandwich.lean new file mode 100644 index 0000000000000000000000000000000000000000..761324341492b1ea3223c85924792efe4691f449 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Sandwich.lean @@ -0,0 +1,32 @@ +import OAI.Analysis.Laughlin.Spin.RectangularAverage + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators +open MeasureTheory + +variable {G I J K L : Type*} [MeasurableSpace G] + [Fintype I] [Fintype J] [Fintype K] [Fintype L] + +noncomputable def entrywiseIntegral (μ : Measure G) (f : G → Matrix I J ℂ) : Matrix I J ℂ := + fun i j => ∫ g, f g i j ∂μ + +omit [Fintype K] [Fintype L] in +theorem integral_matrix_sandwich (μ : Measure G) (f : G → Matrix I J ℂ) + (hf : ∀ i j, Integrable (fun g => f g i j) μ) + (A : Matrix K I ℂ) (B : Matrix J L ℂ) : + (fun k l => ∫ g, (A*f g*B) k l ∂μ) = + A*entrywiseIntegral μ f*B := by + funext k l + simp only [Matrix.mul_apply,entrywiseIntegral,Finset.sum_mul] + rw [integral_finsetSum _ (fun j hj => integrable_finsetSum _ + (fun i hi => ((hf i j).const_mul (A k i)).mul_const (B j l)))] + apply Finset.sum_congr rfl + intro j hj + rw [integral_finsetSum _ (fun i hi => ((hf i j).const_mul (A k i)).mul_const (B j l))] + simp only [integral_mul_const,integral_const_mul] + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/ScaleLimit.lean b/lean/OAI/Analysis/Laughlin/Spin/ScaleLimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..eba05d389aab4a6655104782b7035cf832561e98 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/ScaleLimit.lean @@ -0,0 +1,68 @@ +import Mathlib.Analysis.SpecificLimits.Basic +import OAI.Analysis.Laughlin.Spin.Highest2 + +namespace OAI + +namespace Laughlin.Spin +open scoped Topology +open Filter + +theorem spin_fraction_sub_tendsto (B S : ℕ → ℕ) (b : ℝ) + (hB : Tendsto B atTop atTop) (hS : Tendsto S atTop atTop) + (hfrac : Tendsto (fun n => (B n : ℝ)/(S n : ℝ)) atTop (𝓝 b)) (k : ℕ) : + Tendsto (fun n => ((B n-k : ℕ) : ℝ)/(S n : ℝ)) atTop (𝓝 b) := by + have hi := (tendsto_inv_atTop_nhds_zero_nat (𝕜 := ℝ)).comp hS + have ht := hfrac.sub (hi.const_mul (k : ℝ)) + have he : (fun n => (B n : ℝ)/(S n : ℝ)-(k : ℝ)*(S n : ℝ)⁻¹) =ᶠ[atTop] + (fun n => ((B n-k : ℕ) : ℝ)/(S n : ℝ)) := by + filter_upwards [hB.eventually (eventually_ge_atTop k)] with n hn + rw [Nat.cast_sub hn] + ring + simpa using ht.congr' he + +theorem first_spin_fraction_tendsto (A B : ℕ → ℕ) (b : ℝ) + (hA : Tendsto A atTop atTop) + (hfrac : Tendsto (fun n => (B n : ℝ)/((A n : ℝ)+B n)) atTop (𝓝 b)) : + Tendsto (fun n => (A n : ℝ)/((A n : ℝ)+B n)) atTop (𝓝 (1-b)) := by + have ht := (tendsto_const_nhds (x := (1 : ℝ))).sub hfrac + apply ht.congr' + filter_upwards [hA.eventually (eventually_ge_atTop 1)] with n hn + have hp : (0 : ℝ) < (A n : ℝ)+B n := by + have h : (0 : ℝ) < A n := by exact_mod_cast (show 0 < A n by omega) + positivity + field_simp + ring + +theorem ladder_ratio_tendsto (A B : ℕ → ℕ) (b : ℝ) + (hA : Tendsto A atTop atTop) (hB : Tendsto B atTop atTop) + (hb : b < 1) + (hfrac : Tendsto (fun n => (B n : ℝ)/((A n : ℝ)+B n)) atTop (𝓝 b)) + (p k : ℕ) : + Tendsto (fun n => ladder (B n) k / ladder (A n) p) atTop + (𝓝 (Real.sqrt ((((k : ℝ)+1)*b)/(((p : ℝ)+1)*(1-b))))) := by + have hS : Tendsto (fun n => A n+B n) atTop atTop := + tendsto_atTop_mono (fun n => Nat.le_add_right (A n) (B n)) hA + have hb' : Tendsto (fun n => ((B n-k : ℕ) : ℝ)/((A n : ℝ)+B n)) atTop (𝓝 b) := by + simpa only [Nat.cast_add] using spin_fraction_sub_tendsto B (fun n => A n+B n) b hB hS + (by simpa only [Nat.cast_add] using hfrac) k + have ha' : Tendsto (fun n => ((A n-p : ℕ) : ℝ)/((A n : ℝ)+B n)) atTop (𝓝 (1-b)) := by + simpa only [Nat.cast_add] using spin_fraction_sub_tendsto A (fun n => A n+B n) (1-b) hA hS + (by simpa only [Nat.cast_add] using first_spin_fraction_tendsto A B b hA hfrac) p + have hnz : ((p : ℝ)+1)*(1-b) ≠ 0 := by positivity + have ht := ((hb'.const_mul ((k : ℝ)+1)).div (ha'.const_mul ((p : ℝ)+1)) hnz).sqrt + apply ht.congr' + filter_upwards [hA.eventually (eventually_ge_atTop 1)] with n hn + have hp : (0 : ℝ) < (A n : ℝ)+B n := by + have h : (0 : ℝ) < A n := by exact_mod_cast (show 0 < A n by omega) + positivity + have he : (((k : ℝ)+1)*(((B n-k : ℕ) : ℝ)/((A n : ℝ)+B n))) / + (((p : ℝ)+1)*(((A n-p : ℕ) : ℝ)/((A n : ℝ)+B n))) = + (((k : ℝ)+1)*((B n-k : ℕ) : ℝ))/(((p : ℝ)+1)*((A n-p : ℕ) : ℝ)) := by + field_simp + simp only [Pi.div_apply] + rw [he,Real.sqrt_div (by positivity)] + rfl + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Schur.lean b/lean/OAI/Analysis/Laughlin/Spin/Schur.lean new file mode 100644 index 0000000000000000000000000000000000000000..cfe4aca11cb110dec5829a3ab87f7208c7d461da --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Schur.lean @@ -0,0 +1,92 @@ +import Mathlib.RingTheory.RootsOfUnity.Complex +import OAI.Analysis.Laughlin.Spin.Mixing + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + +noncomputable def spinSeparatingRoot (Q : ℕ) : ℂ := Complex.exp (2*Real.pi*Complex.I/(2*Q+1 : ℕ)) + theorem spinSeparatingRoot_primitive (Q : ℕ) : IsPrimitiveRoot (spinSeparatingRoot Q) (2*Q+1) := + Complex.isPrimitiveRoot_exp _ (by omega) + theorem spinSeparatingRoot_norm (Q : ℕ) : ‖spinSeparatingRoot Q‖=1 := by + simp [spinSeparatingRoot,Complex.norm_exp,Complex.div_re] + + theorem torus_weight_fraction (Q : ℕ) (z : ℂ) (hz : ‖z‖=1) (p : Fin (Q+1)) : + (star z)^p.val*z^(Q-p.val) = z^Q/z^(2*p.val) := by + have hz0 : z ≠ 0 := by intro h; simp [h] at hz + have hinv : star z=z⁻¹ := by + simp [Complex.inv_def,Complex.normSq_eq_norm_sq,hz] + rw [hinv,inv_pow] + have hQ : Q=(Q-p.val)+p.val := by omega + have hp : z^Q=z^(Q-p.val)*z^p.val := by rw [← pow_add,← hQ] + rw [hp,show 2*p.val=p.val+p.val by omega,pow_add] + field_simp + + theorem spinSeparatingRoot_weights_injective (Q : ℕ) : Function.Injective + (fun p : Fin (Q+1) => (star (spinSeparatingRoot Q))^p.val*(spinSeparatingRoot Q)^(Q-p.val)) := by + intro p q hpq + dsimp only at hpq + let z := spinSeparatingRoot Q + have hz := spinSeparatingRoot_norm Q + have hz0 : z ≠ 0 := Complex.exp_ne_zero _ + rw [torus_weight_fraction Q _ hz p,torus_weight_fraction Q _ hz q] at hpq + have he := (div_eq_div_iff (pow_ne_zero (2*p.val) hz0) (pow_ne_zero (2*q.val) hz0)).mp hpq + have hpows : z^(2*p.val)=z^(2*q.val) := (mul_left_cancel₀ (pow_ne_zero Q hz0) he).symm + have h := (spinSeparatingRoot_primitive Q).pow_inj (by omega : 2*p.val < 2*Q+1) + (by omega : 2*q.val < 2*Q+1) hpows + exact Fin.ext (by omega) + +theorem source_spin_commutant_scalar (Q : ℕ) (M : Matrix (Fin (Q+1)) (Fin (Q+1)) ℂ) + (hM : ∀ g : SourceSU2, sourceSpinRepresentation Q g*M=M*sourceSpinRepresentation Q g) : + M=M 0 0 • (1 : Matrix (Fin (Q+1)) (Fin (Q+1)) ℂ) := by + have ht := hM (sourceTorus (spinSeparatingRoot Q) (spinSeparatingRoot_norm Q)) + rw [sourceSpinRepresentation_torus] at ht + have hd : M=Matrix.diagonal (fun p => M p p) := by + ext p q + by_cases hpq : p=q + · subst q; simp + · rw [Matrix.diagonal_apply_ne _ hpq] + have he := congrFun (congrFun ht p) q + simp only [Matrix.diagonal_mul,Matrix.mul_diagonal] at he + have hn := (spinSeparatingRoot_weights_injective Q).ne hpq + exact (mul_eq_zero.mp (show + ((star (spinSeparatingRoot Q))^p.val*(spinSeparatingRoot Q)^(Q-p.val)- + (star (spinSeparatingRoot Q))^q.val*(spinSeparatingRoot Q)^(Q-q.val))*M p q=0 by + linear_combination he)).resolve_left (sub_ne_zero.mpr hn) + have hm := hM sourceMixer + rw [hd] at hm + have hc (p : Fin (Q+1)) : M p p=M 0 0 := by + have he := congrFun (congrFun hm p) 0 + simp only [Matrix.mul_diagonal,Matrix.diagonal_mul] at he + apply (mul_left_cancel₀ (sourceSpinRepresentation_mixer_column_ne_zero Q p)) + calc + _ = M p p*sourceSpinRepresentation Q sourceMixer p 0 := by ring + _ = _ := he.symm + rw [hd] + ext p q + by_cases hpq : p=q + · subst q; simp [hc] + · simp [hpq] + +theorem source_spin_haar_schur (Q : ℕ) (M : Matrix (Fin (Q+1)) (Fin (Q+1)) ℂ) : + matrixIntegral sourceHaar (conjugateOrbit (sourceSpinRepresentation Q) M) = + (Matrix.trace M / (Q+1 : ℕ)) • (1 : Matrix (Fin (Q+1)) (Fin (Q+1)) ℂ) := by + let H := matrixIntegral sourceHaar (conjugateOrbit (sourceSpinRepresentation Q) M) + have hc := source_spin_commutant_scalar Q H (source_spin_haar_average_commutes Q M) + have ht := compact_haar_average_trace sourceHaar (sourceSpinRepresentation Q) + (sourceSpinRepresentation_continuous Q) M + have he := congrArg Matrix.trace hc + simp only [Matrix.trace_smul,Matrix.trace_one,Fintype.card_fin,smul_eq_mul] at he + have hdim : ((Q+1 : ℕ) : ℂ) ≠ 0 := by exact_mod_cast Nat.succ_ne_zero Q + have hs : Matrix.trace M / ((Q+1 : ℕ) : ℂ) = H 0 0 := by + rw [← ht] + change Matrix.trace H / ((Q+1 : ℕ) : ℂ)=H 0 0 + rw [he] + field_simp + rw [hs] + exact hc + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Sl2DescendantNorm.lean b/lean/OAI/Analysis/Laughlin/Spin/Sl2DescendantNorm.lean new file mode 100644 index 0000000000000000000000000000000000000000..c48bb1e9a42127bc81e39abd02d55db7d3e7cc6a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Sl2DescendantNorm.lean @@ -0,0 +1,84 @@ +import OAI.Analysis.Laughlin.Spin.LadderMatrix + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +variable {I : Type*} [Fintype I] [DecidableEq I] + +noncomputable def vectorNormSq (v : I → ℝ) : ℝ := ∑ i, (v i)^2 + +omit [DecidableEq I] in +theorem matrix_transpose_pairing (L : Matrix I I ℝ) (v w : I → ℝ) : + (∑ i, (L *ᵥ v) i*w i) = ∑ i, v i*((Lᵀ) *ᵥ w) i := by + simp only [Matrix.mulVec,dotProduct,Matrix.transpose_apply,Finset.sum_mul,Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + ring + +theorem descendant_weight (H L : Matrix I I ℝ) (v : I → ℝ) (μ : ℝ) + (hHL : H*L=L*H-(2 : ℝ) • L) (hv : H *ᵥ v=μ • v) (n : ℕ) : + H *ᵥ (L^n *ᵥ v) = (μ-2*(n : ℝ)) • (L^n *ᵥ v) := by + have hs (n : ℕ) : L^(n+1) *ᵥ v = L *ᵥ (L^n *ᵥ v) := by + rw [Matrix.mulVec_mulVec,pow_succ'] + induction n with + | zero => simpa using hv + | succ n ih => + rw [hs,Matrix.mulVec_mulVec,hHL,Matrix.sub_mulVec,Matrix.smul_mulVec, + ← Matrix.mulVec_mulVec,ih,Matrix.mulVec_smul] + funext i + simp only [Pi.sub_apply,Pi.smul_apply,smul_eq_mul,Nat.cast_add,Nat.cast_one] + ring + +theorem descendant_raising (R H L : Matrix I I ℝ) (v : I → ℝ) (μ : ℝ) + (hRL : R*L=L*R+H) (hHL : H*L=L*H-(2 : ℝ) • L) + (hv : H *ᵥ v=μ • v) (hr : R *ᵥ v=0) (n : ℕ) : + R *ᵥ (L^(n+1) *ᵥ v) = (((n : ℝ)+1)*(μ-n)) • (L^n *ᵥ v) := by + have hs (n : ℕ) : L^(n+1) *ᵥ v = L *ᵥ (L^n *ᵥ v) := by + rw [Matrix.mulVec_mulVec,pow_succ'] + induction n with + | zero => + simp only [pow_one,pow_zero,Matrix.one_mulVec,Nat.cast_zero,zero_add,sub_zero,one_mul] + rw [Matrix.mulVec_mulVec,hRL,Matrix.add_mulVec,← Matrix.mulVec_mulVec,hr, + Matrix.mulVec_zero,zero_add,hv] + | succ n ih => + rw [hs (n+1),Matrix.mulVec_mulVec,hRL,Matrix.add_mulVec,← Matrix.mulVec_mulVec, + ih,Matrix.mulVec_smul,descendant_weight H L v μ hHL hv (n+1),hs n] + funext i + simp only [Pi.add_apply,Pi.smul_apply,smul_eq_mul,Nat.cast_add,Nat.cast_one] + ring + +theorem descendant_norm_step (R H L : Matrix I I ℝ) (v : I → ℝ) (μ : ℝ) + (hRL : R*L=L*R+H) (hHL : H*L=L*H-(2 : ℝ) • L) (ht : Lᵀ=R) + (hv : H *ᵥ v=μ • v) (hr : R *ᵥ v=0) (n : ℕ) : + vectorNormSq (L^(n+1) *ᵥ v) = (((n : ℝ)+1)*(μ-n))*vectorNormSq (L^n *ᵥ v) := by + have hs : L^(n+1) *ᵥ v = L *ᵥ (L^n *ᵥ v) := by + rw [Matrix.mulVec_mulVec,pow_succ'] + unfold vectorNormSq + simp only [pow_two] + conv_lhs => arg 2; ext i; arg 1; rw [hs] + rw [matrix_transpose_pairing,ht,descendant_raising R H L v μ hRL hHL hv hr n] + simp only [Pi.smul_apply,smul_eq_mul,Finset.mul_sum] + apply Finset.sum_congr rfl + intro i hi + ring + +theorem descendant_norm_pos (R H L : Matrix I I ℝ) (v : I → ℝ) (μ n : ℕ) + (hRL : R*L=L*R+H) (hHL : H*L=L*H-(2 : ℝ) • L) (ht : Lᵀ=R) + (hv : H *ᵥ v=(μ : ℝ) • v) (hr : R *ᵥ v=0) + (hnorm : 0 < vectorNormSq v) (hn : n ≤ μ) : 0 < vectorNormSq (L^n *ᵥ v) := by + induction n with + | zero => simpa using hnorm + | succ n ih => + rw [descendant_norm_step R H L v μ hRL hHL ht hv hr n] + have hp : (n : ℝ) < μ := by exact_mod_cast (show n < μ by omega) + have hi := ih (by omega) + positivity + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Sl2Matrix.lean b/lean/OAI/Analysis/Laughlin/Spin/Sl2Matrix.lean new file mode 100644 index 0000000000000000000000000000000000000000..3b25e22aa735907447db207f1555226870ac4573 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Sl2Matrix.lean @@ -0,0 +1,77 @@ +import OAI.Analysis.Laughlin.Spin.LadderMatrix + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +noncomputable def weightMatrix (A : ℕ) : Matrix (Fin (A+1)) (Fin (A+1)) ℝ := + Matrix.diagonal (fun i => (A : ℝ)-2*i.val) + +theorem raise_mul_transpose_entry (A : ℕ) (i j : Fin (A+1)) : + (raiseMatrix A * (raiseMatrix A)ᵀ) i j = + if i=j then ((i.val : ℝ)+1)*(A-i.val : ℕ) else 0 := by + change (∑ k, raiseMatrix A i k*raiseMatrix A j k) = _ + rw [raiseMatrix_row] + by_cases hi : i.val < A + · rw [dite_eq_left hi] + by_cases hij : i=j + · subst j + simp only [raiseMatrix,ite_true] + unfold ladder + rw [Real.mul_self_sqrt (by positivity)] + · have hne : j.val+1 ≠ i.val+1 := by intro h; apply hij; apply Fin.ext; omega + simp only [raiseMatrix,ite_eq_right hne,ite_eq_right hij,mul_zero] + · rw [dite_eq_right hi] + have hz : i.val=A := by omega + simp [hz] + +theorem transpose_mul_raise_entry (A : ℕ) (i j : Fin (A+1)) : + ((raiseMatrix A)ᵀ * raiseMatrix A) i j = + if i=j then (i.val : ℝ)*((A : ℝ)-i.val+1) else 0 := by + change (∑ k, raiseMatrix A k i*raiseMatrix A k j) = _ + have he : (∑ k, raiseMatrix A k i*raiseMatrix A k j) = + ∑ k, raiseMatrix A k j*raiseMatrix A k i := by + apply Finset.sum_congr rfl; intro k hk; ring + rw [he,raiseMatrix_column] + by_cases hi : 0 < i.val + · rw [dite_eq_left hi] + by_cases hij : i=j + · subst j + simp only [raiseMatrix,ite_eq_left (show i.val-1+1=i.val by omega),ite_true] + unfold ladder + rw [Real.mul_self_sqrt (by positivity)] + rw [Nat.cast_sub (by omega : i.val-1 ≤ A),Nat.cast_sub (by omega : 1 ≤ i.val)] + push_cast; ring + · have hne : i.val-1+1 ≠ j.val := by intro h; apply hij; apply Fin.ext; omega + simp only [raiseMatrix,ite_eq_right hne,ite_eq_right hij,zero_mul] + · rw [dite_eq_right hi] + have hz : i.val=0 := by omega + simp [hz] + +theorem raise_lower_commutator (A : ℕ) : + raiseMatrix A * (raiseMatrix A)ᵀ - (raiseMatrix A)ᵀ * raiseMatrix A = weightMatrix A := by + ext i j + rw [Matrix.sub_apply,raise_mul_transpose_entry,transpose_mul_raise_entry] + by_cases hij : i=j + · subst j + simp only [ite_true,weightMatrix,Matrix.diagonal_apply_eq] + rw [Nat.cast_sub (by omega : i.val ≤ A)] + ring + · simp [hij,weightMatrix] + +theorem weight_lower_commutator (A : ℕ) : + weightMatrix A * (raiseMatrix A)ᵀ = + (raiseMatrix A)ᵀ * weightMatrix A - (2 : ℝ) • (raiseMatrix A)ᵀ := by + ext i j + simp only [weightMatrix,Matrix.diagonal_mul,Matrix.mul_diagonal,Matrix.sub_apply, + Matrix.smul_apply,Matrix.transpose_apply,smul_eq_mul,raiseMatrix] + by_cases h : j.val+1=i.val + · rw [ite_eq_left h] + have hc : (j.val : ℝ)+1=i.val := by exact_mod_cast h + linear_combination 2*ladder A j.val*hc + · rw [ite_eq_right h]; ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Sl2Orthogonal.lean b/lean/OAI/Analysis/Laughlin/Spin/Sl2Orthogonal.lean new file mode 100644 index 0000000000000000000000000000000000000000..04bf18d1e54c41741c0831a7a519382b12ba3b10 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Sl2Orthogonal.lean @@ -0,0 +1,50 @@ +import OAI.Analysis.Laughlin.Spin.Sl2DescendantNorm + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +variable {I : Type*} [Fintype I] [DecidableEq I] + +theorem descendants_orthogonal (R H L : Matrix I I ℝ) (v w : I → ℝ) (ν : ℝ) + (hRL : R*L=L*R+H) (hHL : H*L=L*H-(2 : ℝ) • L) (ht : Lᵀ=R) + (hw : H *ᵥ w=ν • w) (hvR : R *ᵥ v=0) (hwR : R *ᵥ w=0) + (n m : ℕ) (h : (∑ i, v i*w i)=0 ∨ n ≠ m) : + (∑ i, (L^n *ᵥ v) i*(L^m *ᵥ w) i) = 0 := by + have hs (k : ℕ) (u : I → ℝ) : L^(k+1) *ᵥ u = L *ᵥ (L^k *ᵥ u) := by + rw [Matrix.mulVec_mulVec,pow_succ'] + induction n generalizing m with + | zero => + cases m with + | zero => simpa using h.resolve_right (by simp) + | succ m => + simp only [pow_zero,Matrix.one_mulVec] + calc + _ = ∑ i, (L *ᵥ (L^m *ᵥ w)) i*v i := by + rw [hs m w] + apply Finset.sum_congr rfl; intro i hi; ring + _ = ∑ i, (L^m *ᵥ w) i*(R *ᵥ v) i := by rw [matrix_transpose_pairing,ht] + _ = 0 := by rw [hvR]; simp + | succ n ih => + cases m with + | zero => + simp only [pow_zero,Matrix.one_mulVec] + rw [hs n v,matrix_transpose_pairing,ht,hwR] + simp + | succ m => + rw [hs n v,matrix_transpose_pairing,ht,descendant_raising R H L w ν hRL hHL hw hwR m] + have hp : (∑ i, v i*w i)=0 ∨ n ≠ m := by + rcases h with h | h + · exact Or.inl h + · exact Or.inr (by omega) + calc + _ = (((m : ℝ)+1)*(ν-m))*(∑ i, (L^n *ᵥ v) i*(L^m *ᵥ w) i) := by + rw [Finset.mul_sum] + apply Finset.sum_congr rfl; intro i hi + simp only [Pi.smul_apply,smul_eq_mul]; ring + _ = 0 := by rw [ih m hp,mul_zero] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Specializations.lean b/lean/OAI/Analysis/Laughlin/Spin/Specializations.lean new file mode 100644 index 0000000000000000000000000000000000000000..2ead87a903c9f1fefbbf66a96140e2918b0239fc --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Specializations.lean @@ -0,0 +1,82 @@ +import Mathlib.Analysis.SpecificLimits.Normed +import OAI.Analysis.Laughlin.Operators.PhysicalCoupling +import OAI.Analysis.Laughlin.Spin.DescendantNorm + +namespace OAI + +namespace Laughlin.Spin +open scoped Topology +open Filter + +theorem affine_spin_tendsto (a c : ℕ) (ha : 0 < a) : + Tendsto (fun Q : ℕ => a*Q-c) atTop atTop := by + apply tendsto_atTop.mpr + intro k + filter_upwards [eventually_ge_atTop (k+c)] with Q hQ + have hm : Q ≤ a*Q := by + simpa using Nat.mul_le_mul_right Q (show 1 ≤ a by omega) + omega + +theorem affine_spin_fraction_tendsto (a b c d : ℕ) (ha : 0 < a) (hb : 0 < b) : + Tendsto (fun Q : ℕ => ((b*Q-d : ℕ) : ℝ)/(((a*Q-c : ℕ) : ℝ)+((b*Q-d : ℕ) : ℝ))) + atTop (𝓝 ((b : ℝ)/((a : ℝ)+b))) := by + have har : (0 : ℝ) < a := by exact_mod_cast ha + have hbr : (0 : ℝ) < b := by exact_mod_cast hb + have ht : Tendsto (fun Q : ℕ => (-(d : ℝ)+(b : ℝ)*Q)/ + (-(c : ℝ)-(d : ℝ)+((a : ℝ)+b)*Q)) atTop (𝓝 ((b : ℝ)/((a : ℝ)+b))) := + tendsto_add_mul_div_add_mul_atTop_nhds (-(d : ℝ)) (-(c : ℝ)-(d : ℝ)) (b : ℝ) (by positivity) + apply ht.congr' + filter_upwards [eventually_ge_atTop (c+d)] with Q hQ + have hmA : Q ≤ a*Q := by simpa using Nat.mul_le_mul_right Q (show 1 ≤ a by omega) + have hmB : Q ≤ b*Q := by simpa using Nat.mul_le_mul_right Q (show 1 ≤ b by omega) + rw [Nat.cast_sub (by omega : c ≤ a*Q),Nat.cast_sub (by omega : d ≤ b*Q)] + push_cast + congr 1 <;> ring + +theorem genericUnitDescendant_threeBody (Q z n : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + genericUnitDescendant (2*Q-2) Q z (by omega) hz n = + normalizedCoupledDescendant Q z hQ hz n := by rfl + +theorem source_threeBody_coupling_tendsto (z T p : ℕ) (hz : z ≤ T) (hp : p ≤ T) : + Tendsto (fun Q : ℕ => physicalCouplingCoefficient (2*Q-2) Q z T p) atTop + (𝓝 (couplingPolynomialCoefficient (Real.sqrt (1/3)) (Real.sqrt (2/3)) z (T-z) p)) := by + have hA := affine_spin_tendsto 2 2 (by omega) + have hB : Tendsto (fun Q : ℕ => Q) atTop atTop := tendsto_id + have hf : Tendsto (fun Q : ℕ => (Q : ℝ)/(((2*Q-2 : ℕ) : ℝ)+Q)) atTop (𝓝 (1/3 : ℝ)) := by + have h := affine_spin_fraction_tendsto 2 1 2 0 (by omega) (by omega) + norm_num at h ⊢ + exact h + have hh := source_physical_coupling_tendsto (fun Q => 2*Q-2) (fun Q => Q) (1/3) hA hB + (by norm_num) (by norm_num) hf z T p hz hp + norm_num at hh ⊢ + exact hh + +theorem source_fourBody_inner_coupling_tendsto (r T p : ℕ) (hr : r ≤ T) (hp : p ≤ T) : + Tendsto (fun Q : ℕ => physicalCouplingCoefficient Q Q r T p) atTop + (𝓝 (couplingPolynomialCoefficient (Real.sqrt (1/2)) (Real.sqrt (1/2)) r (T-r) p)) := by + have hf : Tendsto (fun Q : ℕ => (Q : ℝ)/((Q : ℝ)+Q)) atTop (𝓝 (1/2 : ℝ)) := by + have h := affine_spin_fraction_tendsto 1 1 0 0 (by omega) (by omega) + norm_num at h ⊢ + exact h + have hh := source_physical_coupling_tendsto (fun Q => Q) (fun Q => Q) (1/2) tendsto_id tendsto_id + (by norm_num) (by norm_num) hf r T p hr hp + norm_num at hh ⊢ + exact hh + +theorem source_fourBody_outer_coupling_tendsto (r z T p : ℕ) (hz : z ≤ T) (hp : p ≤ T) : + Tendsto (fun Q : ℕ => physicalCouplingCoefficient (2*Q-2) (2*Q-2*r) z T p) atTop + (𝓝 (couplingPolynomialCoefficient (Real.sqrt (1/2)) (Real.sqrt (1/2)) z (T-z) p)) := by + have hf : Tendsto (fun Q : ℕ => ((2*Q-2*r : ℕ) : ℝ)/ + (((2*Q-2 : ℕ) : ℝ)+((2*Q-2*r : ℕ) : ℝ))) atTop (𝓝 (1/2 : ℝ)) := by + have h := affine_spin_fraction_tendsto 2 2 2 (2*r) (by omega) (by omega) + norm_num at h ⊢ + exact h + have hh := source_physical_coupling_tendsto (fun Q => 2*Q-2) (fun Q => 2*Q-2*r) (1/2) + (affine_spin_tendsto 2 2 (by omega)) (affine_spin_tendsto 2 (2*r) (by omega)) + (by norm_num) (by norm_num) hf z T p hz hp + norm_num at hh ⊢ + exact hh + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Support.lean b/lean/OAI/Analysis/Laughlin/Spin/Support.lean new file mode 100644 index 0000000000000000000000000000000000000000..8857aab20131e1e4ac62bd5b771f080ec81d9e52 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Support.lean @@ -0,0 +1,38 @@ +import OAI.Analysis.Laughlin.Spin.Basic + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +theorem genericDescendant_off (A B z n : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (i : SpinIndex A B) (hi : i.1.val+i.2.val ≠ z+n) : + genericDescendant A B z hA hB n i = 0 := by + induction n generalizing i with + | zero => + simpa [genericDescendant,genericHighest] using + extendWeightSlice_off A B z hA hB (fun p => highestUnit A B z p.val) i (by omega) + | succ n ih => + rw [genericDescendant_succ] + change (∑ j, totalRaise A B j i * genericDescendant A B z hA hB n j) = 0 + rw [totalRaise_transpose_apply,raiseMatrix_column,raiseMatrix_column] + have h1 : (if h : 0 < i.1.val then + genericDescendant A B z hA hB n (⟨i.1.val-1,by omega⟩,i.2) * ladder A (i.1.val-1) else 0) = 0 := by + split_ifs with h + · rw [ih _ (by dsimp; omega),zero_mul] + · rfl + have h2 : (if h : 0 < i.2.val then + genericDescendant A B z hA hB n (i.1,⟨i.2.val-1,by omega⟩) * ladder B (i.2.val-1) else 0) = 0 := by + split_ifs with h + · rw [ih _ (by dsimp; omega),zero_mul] + · rfl + rw [h1,h2,add_zero] + +theorem genericUnitDescendant_off (A B z n : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (i : SpinIndex A B) (hi : i.1.val+i.2.val ≠ z+n) : + genericUnitDescendant A B z hA hB n i = 0 := by + simp only [genericUnitDescendant,Pi.smul_apply,smul_eq_mul,genericDescendant_off A B z n hA hB i hi,mul_zero] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/TensorAction.lean b/lean/OAI/Analysis/Laughlin/Spin/TensorAction.lean new file mode 100644 index 0000000000000000000000000000000000000000..c06eefd08d551785aaf7a92d03c3bcb6d80da08e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/TensorAction.lean @@ -0,0 +1,57 @@ +import Mathlib.Algebra.BigOperators.Ring.Finset +import Mathlib.Analysis.Complex.Basic +import Mathlib.LinearAlgebra.UnitaryGroup + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + +noncomputable def tensorMatrix (N : ℕ) (A : Matrix (Fin 2) (Fin 2) ℂ) : + Matrix (Fin N → Fin 2) (Fin N → Fin 2) ℂ := fun a b => ∏ i, A (a i) (b i) + +theorem tensorMatrix_mul (N : ℕ) (A B : Matrix (Fin 2) (Fin 2) ℂ) : + tensorMatrix N (A*B) = tensorMatrix N A * tensorMatrix N B := by + ext a c + simp only [tensorMatrix,Matrix.mul_apply,← Finset.prod_mul_distrib] + exact Fintype.prod_sum (fun i b => A (a i) b*B b (c i)) + +theorem tensorMatrix_one (N : ℕ) : tensorMatrix N 1 = 1 := by + classical + ext a b + simp only [tensorMatrix,Matrix.one_apply] + by_cases h : a=b + · subst b; simp + · rw [ite_eq_right h] + obtain ⟨i,hi⟩ := Function.ne_iff.mp h + exact Finset.prod_eq_zero (Finset.mem_univ i) (ite_eq_right hi) + +theorem tensorMatrix_conjTranspose (N : ℕ) (A : Matrix (Fin 2) (Fin 2) ℂ) : + tensorMatrix N Aᴴ = (tensorMatrix N A)ᴴ := by + ext a b + simp [tensorMatrix,Matrix.conjTranspose_apply] + +theorem tensorMatrix_unitary (N : ℕ) (A : Matrix (Fin 2) (Fin 2) ℂ) + (hA : A ∈ Matrix.unitaryGroup (Fin 2) ℂ) : + tensorMatrix N A ∈ Matrix.unitaryGroup (Fin N → Fin 2) ℂ := by + apply Matrix.mem_unitaryGroup_iff'.mpr + rw [Matrix.star_eq_conjTranspose,← tensorMatrix_conjTranspose,← tensorMatrix_mul] + have h := Matrix.mem_unitaryGroup_iff'.mp hA + rw [Matrix.star_eq_conjTranspose] at h + rw [h,tensorMatrix_one] + +abbrev SourceSU2 := Matrix.specialUnitaryGroup (Fin 2) ℂ + +noncomputable def sourceTensorRepresentation (Q : ℕ) : SourceSU2 →* + Matrix (Fin Q → Fin 2) (Fin Q → Fin 2) ℂ where + toFun g := tensorMatrix Q g.val + map_one' := tensorMatrix_one Q + map_mul' g h := tensorMatrix_mul Q g.val h.val + + theorem sourceTensorRepresentation_unitary (Q : ℕ) (g : SourceSU2) : + sourceTensorRepresentation Q g ∈ Matrix.unitaryGroup (Fin Q → Fin 2) ℂ := + tensorMatrix_unitary Q g.val g.property.1 + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/Torus.lean b/lean/OAI/Analysis/Laughlin/Spin/Torus.lean new file mode 100644 index 0000000000000000000000000000000000000000..ca3debd52651c27be30c9ddd44168e653585559e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/Torus.lean @@ -0,0 +1,41 @@ +import OAI.Analysis.Laughlin.Spin.Representation +import OAI.Analysis.Laughlin.Tensor.WeightProducts + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + +noncomputable def sourceTorus (z : ℂ) (hz : ‖z‖=1) : SourceSU2 := by + let A : Matrix (Fin 2) (Fin 2) ℂ := Matrix.diagonal (fun i => if i=0 then z else star z) + have hzz : z*(starRingEnd ℂ) z=1 := by simpa [hz] using Complex.mul_conj' z + have hzz' : (starRingEnd ℂ) z*z=1 := by rw [mul_comm]; exact hzz + refine ⟨A,?_⟩ + constructor + · apply Matrix.mem_unitaryGroup_iff.mpr + ext i j + fin_cases i <;> fin_cases j <;> + simp [A,Matrix.mul_apply,Matrix.star_eq_conjTranspose,hzz,hzz'] + · simp [A,Matrix.det_diagonal,Fin.prod_univ_two,hzz] + + theorem symmetricTensor_diagonal_intertwining (Q : ℕ) (f : ℕ → ℂ) : + Matrix.diagonal (fun a => f (tensorWeight Q a))*symmetricTensorInclusion Q = + symmetricTensorInclusion Q*Matrix.diagonal (fun p : Fin (Q+1) => f p.val) := by + ext a p + simp only [Matrix.diagonal_mul,Matrix.mul_diagonal,symmetricTensorInclusion,Matrix.map_apply, + symmetricTensorInclusionReal] + by_cases h : tensorWeight Q a=p.val + · simp [h,mul_comm] + · simp [h] + +theorem sourceSpinRepresentation_torus (Q : ℕ) (z : ℂ) (hz : ‖z‖=1) : + sourceSpinRepresentation Q (sourceTorus z hz) = + Matrix.diagonal (fun p : Fin (Q+1) => (star z)^p.val*z^(Q-p.val)) := by + change (symmetricTensorInclusion Q)ᴴ * tensorMatrix Q + (Matrix.diagonal (fun i : Fin 2 => if i=0 then z else star z)) * symmetricTensorInclusion Q = _ + rw [tensorMatrix_diagonal,Matrix.mul_assoc,symmetricTensor_diagonal_intertwining Q (fun k => (star z)^k*z^(Q-k)), + ← Matrix.mul_assoc,symmetricTensorInclusion_isometry,Matrix.one_mul] + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/TotalSl2Matrix.lean b/lean/OAI/Analysis/Laughlin/Spin/TotalSl2Matrix.lean new file mode 100644 index 0000000000000000000000000000000000000000..08ee3715062a83f36674ee10a680071731dcf622 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/TotalSl2Matrix.lean @@ -0,0 +1,70 @@ +import Mathlib.Tactic.Abel +import OAI.Analysis.Laughlin.Spin.Sl2Matrix +import OAI.Analysis.Laughlin.Spin.TripleLadderIntertwining +import OAI.Analysis.Laughlin.Spin.WeightSlice + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix Kronecker + +noncomputable def totalWeight (A B : ℕ) : Matrix (SpinIndex A B) (SpinIndex A B) ℝ := + weightMatrix A ⊗ₖ (1 : Matrix (Fin (B+1)) (Fin (B+1)) ℝ) + + (1 : Matrix (Fin (A+1)) (Fin (A+1)) ℝ) ⊗ₖ weightMatrix B + +theorem totalRaise_transpose_kronecker (A B : ℕ) : + (totalRaise A B)ᵀ = (raiseMatrix A)ᵀ ⊗ₖ (1 : Matrix (Fin (B+1)) (Fin (B+1)) ℝ) + + (1 : Matrix (Fin (A+1)) (Fin (A+1)) ℝ) ⊗ₖ (raiseMatrix B)ᵀ := by + ext i j + simp [totalRaise,Matrix.kroneckerMap,Matrix.transpose_apply,Matrix.one_apply,eq_comm] + +theorem total_raise_lower_commutator (A B : ℕ) : + totalRaise A B * (totalRaise A B)ᵀ = + (totalRaise A B)ᵀ * totalRaise A B + totalWeight A B := by + have ha : raiseMatrix A*(raiseMatrix A)ᵀ = (raiseMatrix A)ᵀ*raiseMatrix A+weightMatrix A := by + calc + _ = (raiseMatrix A*(raiseMatrix A)ᵀ - (raiseMatrix A)ᵀ*raiseMatrix A) + + (raiseMatrix A)ᵀ*raiseMatrix A := by abel + _ = _ := by rw [raise_lower_commutator A]; abel + have hb : raiseMatrix B*(raiseMatrix B)ᵀ = (raiseMatrix B)ᵀ*raiseMatrix B+weightMatrix B := by + calc + _ = (raiseMatrix B*(raiseMatrix B)ᵀ - (raiseMatrix B)ᵀ*raiseMatrix B) + + (raiseMatrix B)ᵀ*raiseMatrix B := by abel + _ = _ := by rw [raise_lower_commutator B]; abel + rw [totalRaise_transpose_kronecker,totalRaise_kronecker] + unfold totalWeight + simp only [Matrix.add_mul,Matrix.mul_add,← Matrix.mul_kronecker_mul, + Matrix.one_mul,Matrix.mul_one,ha,hb,Matrix.add_kronecker,Matrix.kronecker_add] + abel + +theorem total_weight_lower_commutator (A B : ℕ) : + totalWeight A B * (totalRaise A B)ᵀ = + (totalRaise A B)ᵀ * totalWeight A B - (2 : ℝ) • (totalRaise A B)ᵀ := by + have ha : weightMatrix A*(raiseMatrix A)ᵀ = + (raiseMatrix A)ᵀ*weightMatrix A+(-2 : ℝ) • (raiseMatrix A)ᵀ := by + simpa only [sub_eq_add_neg,neg_smul] using weight_lower_commutator A + have hb : weightMatrix B*(raiseMatrix B)ᵀ = + (raiseMatrix B)ᵀ*weightMatrix B+(-2 : ℝ) • (raiseMatrix B)ᵀ := by + simpa only [sub_eq_add_neg,neg_smul] using weight_lower_commutator B + rw [totalRaise_transpose_kronecker] + unfold totalWeight + simp only [Matrix.add_mul,Matrix.mul_add,← Matrix.mul_kronecker_mul, + Matrix.one_mul,Matrix.mul_one,ha,hb,Matrix.add_kronecker,Matrix.kronecker_add, + smul_add,neg_smul,sub_eq_add_neg] + ext i j + simp only [Matrix.add_apply,Matrix.neg_apply,Matrix.smul_apply,Matrix.kroneckerMap, + Matrix.of_apply,smul_eq_mul] + ring + +theorem totalWeight_diagonal (A B : ℕ) : + totalWeight A B = Matrix.diagonal (fun i : SpinIndex A B => + (A : ℝ)+B-2*((i.1.val : ℝ)+i.2.val)) := by + ext i j + by_cases h₁ : i.1=j.1 <;> by_cases h₂ : i.2=j.2 <;> + simp [totalWeight,weightMatrix,Matrix.kroneckerMap, + Matrix.one_apply,Matrix.diagonal_apply,Prod.ext_iff,h₁,h₂] + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/TripleLadderIntertwining.lean b/lean/OAI/Analysis/Laughlin/Spin/TripleLadderIntertwining.lean new file mode 100644 index 0000000000000000000000000000000000000000..23953cc30def9742394a08f374034a78b2977c9c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/TripleLadderIntertwining.lean @@ -0,0 +1,83 @@ +import Mathlib.LinearAlgebra.Matrix.Kronecker +import OAI.Analysis.Laughlin.Pair.LadderIntertwining + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix Kronecker + +abbrev Orbital (Q : ℕ) := Fin (Q+1) +abbrev TripleIndex (Q : ℕ) := (Orbital Q × Orbital Q) × Orbital Q +abbrev PairOrbitalIndex (Q : ℕ) := Fin ((2*Q-2)+1) × Orbital Q + +theorem totalRaise_kronecker (A B : ℕ) : + totalRaise A B = raiseMatrix A ⊗ₖ (1 : Matrix (Fin (B+1)) (Fin (B+1)) ℝ) + + (1 : Matrix (Fin (A+1)) (Fin (A+1)) ℝ) ⊗ₖ raiseMatrix B := by + rfl + +noncomputable def tripleInclusion (Q : ℕ) : Matrix (TripleIndex Q) (PairOrbitalIndex Q) ℝ := + pairInclusion Q ⊗ₖ (1 : Matrix (Orbital Q) (Orbital Q) ℝ) + +noncomputable def tripleRaise (Q : ℕ) : Matrix (TripleIndex Q) (TripleIndex Q) ℝ := + totalRaise Q Q ⊗ₖ (1 : Matrix (Orbital Q) (Orbital Q) ℝ) + + (1 : Matrix (Orbital Q × Orbital Q) (Orbital Q × Orbital Q) ℝ) ⊗ₖ raiseMatrix Q + +theorem tripleInclusion_raising (Q : ℕ) (hQ : 0 < Q) : + tripleRaise Q * tripleInclusion Q = tripleInclusion Q * totalRaise (2*Q-2) Q := by + rw [totalRaise_kronecker] + unfold tripleRaise tripleInclusion + simp only [Matrix.add_mul,Matrix.mul_add,← Matrix.mul_kronecker_mul, + Matrix.mul_one,Matrix.one_mul,pairInclusion_raising Q hQ] + +theorem tripleInclusion_transpose (Q : ℕ) : + (tripleInclusion Q)ᵀ = (pairInclusion Q)ᵀ ⊗ₖ (1 : Matrix (Orbital Q) (Orbital Q) ℝ) := by + ext i j + simp [tripleInclusion,Matrix.kroneckerMap,Matrix.transpose_apply,Matrix.one_apply,eq_comm] + +theorem tripleInclusion_transpose_raising (Q : ℕ) (hQ : 0 < Q) : + (tripleInclusion Q)ᵀ * tripleRaise Q = totalRaise (2*Q-2) Q * (tripleInclusion Q)ᵀ := by + rw [tripleInclusion_transpose,totalRaise_kronecker] + unfold tripleRaise + simp only [Matrix.add_mul,Matrix.mul_add,← Matrix.mul_kronecker_mul, + Matrix.mul_one,Matrix.one_mul,pairInclusion_transpose_raising Q hQ] + +theorem tripleInclusion_isometry (Q : ℕ) (hQ : 2 ≤ Q) : + (tripleInclusion Q)ᵀ * tripleInclusion Q = 1 := by + rw [tripleInclusion_transpose] + unfold tripleInclusion + rw [← Matrix.mul_kronecker_mul,pairInclusion_isometry Q hQ,Matrix.mul_one, + Matrix.one_kronecker_one] + +def swap23 {Q : ℕ} (i : TripleIndex Q) : TripleIndex Q := ((i.1.1,i.2),i.1.2) + +@[simp] theorem swap23_involutive {Q : ℕ} (i : TripleIndex Q) : swap23 (swap23 i) = i := by + rcases i with ⟨⟨i,j⟩,k⟩; rfl + +noncomputable def swap23Matrix (Q : ℕ) : Matrix (TripleIndex Q) (TripleIndex Q) ℝ := + fun i j => if swap23 i=j then 1 else 0 + +theorem swap23Matrix_mul (Q : ℕ) (M : Matrix (TripleIndex Q) (TripleIndex Q) ℝ) + (i j : TripleIndex Q) : (swap23Matrix Q * M) i j = M (swap23 i) j := by + simp [Matrix.mul_apply,swap23Matrix] + +theorem mul_swap23Matrix (Q : ℕ) (M : Matrix (TripleIndex Q) (TripleIndex Q) ℝ) + (i j : TripleIndex Q) : (M * swap23Matrix Q) i j = M i (swap23 j) := by + have he (k : TripleIndex Q) : swap23 k=j ↔ k=swap23 j := by + constructor + · intro h; simpa using congrArg swap23 h + · intro h; rw [h,swap23_involutive] + simp [Matrix.mul_apply,swap23Matrix,he] + +theorem swap23_raising (Q : ℕ) : swap23Matrix Q * tripleRaise Q = tripleRaise Q * swap23Matrix Q := by + ext a b + rw [swap23Matrix_mul,mul_swap23Matrix] + rcases a with ⟨⟨i,j⟩,k⟩ + rcases b with ⟨⟨l,m⟩,n⟩ + simp only [tripleRaise,totalRaise,Matrix.add_apply,Matrix.kroneckerMap, + Matrix.one_apply,Matrix.of_apply,swap23,Prod.mk.injEq] + split_ifs <;> simp_all + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/TwoBodyCertificateHaar.lean b/lean/OAI/Analysis/Laughlin/Spin/TwoBodyCertificateHaar.lean new file mode 100644 index 0000000000000000000000000000000000000000..00e047b97d8c4d8a46ae349980f20b1c58b2edf7 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/TwoBodyCertificateHaar.lean @@ -0,0 +1,62 @@ +import OAI.Analysis.Laughlin.Operators.Certificate +import OAI.Analysis.Laughlin.Pair.FockHaar + +namespace OAI + +namespace Laughlin.Fock +open Rotation MeasureTheory +open scoped BigOperators Matrix + +noncomputable def physicalPairRowMatrix (Q : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) : + Matrix (Fin (2*Q-2+1)) (Fin (2*Q-2+1)) ℂ := + fun i j => if i.val=row.1 ∧ j.val=row.1 then ((row.2.1 : ℂ)/10^7)^2 else 0 + +noncomputable def physicalTwoBodyMatrix (Q : ℕ) : + Matrix (Fin (2*Q-2+1)) (Fin (2*Q-2+1)) ℂ := + (Certificate.rows.map (physicalPairRowMatrix Q)).sum + +theorem physicalTwoBodyMatrix_trace (Q : ℕ) (hQ : 5 ≤ Q) : + Matrix.trace (physicalTwoBodyMatrix Q) = (93527408868499/10^14 : ℂ) := by + have htr (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) (hr : row ∈ Certificate.rows) : + Matrix.trace (physicalPairRowMatrix Q row) = + ((row.2.1 : ℂ)/10^7)^2 := by + have ht : row.1 ≤ 7 := (show ∀ row ∈ Certificate.rows, row.1 ≤ 7 from by decide) row hr + let p : Fin (2*Q-2+1) := ⟨row.1,by omega⟩ + have he (i : Fin (2*Q-2+1)) : i.val=row.1 ↔ i=p := by + constructor + · intro h; exact Fin.ext h + · intro h; subst i; rfl + simp only [Matrix.trace,Matrix.diag,physicalPairRowMatrix,he,and_self,Finset.sum_ite_eq',Finset.mem_univ,ite_true] + have hsum (l : List (Matrix (Fin (2*Q-2+1)) (Fin (2*Q-2+1)) ℂ)) : + Matrix.trace l.sum = (l.map Matrix.trace).sum := by + induction l with + | nil => simp + | cons a l ih => simp only [List.sum_cons,List.map_cons,Matrix.trace_add,ih] + rw [physicalTwoBodyMatrix,hsum,List.map_map] + have he : Certificate.rows.map (fun row => Matrix.trace (physicalPairRowMatrix Q row)) = + Certificate.rows.map (fun row => ((row.2.1 : ℂ)/10^7)^2) := List.map_congr_left htr + change (Certificate.rows.map (fun row => Matrix.trace (physicalPairRowMatrix Q row))).sum = _ + rw [he] + have hl (l : List (ℕ × ℤ × List (ℕ × ℕ × ℤ))) : + (l.map (fun row => ((row.2.1 : ℂ)/10^7)^2)).sum = + ((l.map (fun row => row.2.1^2)).sum : ℤ)/(10^14 : ℂ) := by + induction l with + | nil => simp + | cons a l ih => + simp only [List.map_cons,List.sum_cons,Int.cast_add,Int.cast_pow,ih] + ring + rw [hl,Certificate.eta_numerator] + norm_num + +theorem physical_twoBody_certificate_haar (Q : ℕ) (hQ : 5 ≤ Q) (x : Space Q) : + ((2*Q-2+1 : ℕ) : ℂ) * (∫ g, contractionForm Q + (fun p : Fin (2*Q-2+1) => sourcePairEnd Q p.val) (physicalTwoBodyMatrix Q) + (exteriorRotation Q g⁻¹ x) ∂sourceHaar) = + (93527408868499/10^14 : ℂ) * (sourceFockEnergy Q x : ℂ) := by + rw [physical_pairFock_haar Q (by omega),physicalTwoBodyMatrix_trace Q hQ] + have hd : ((2*Q-2+1 : ℕ) : ℂ) ≠ 0 := by exact_mod_cast Nat.succ_ne_zero (2*Q-2) + field_simp + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Spin/WeightSlice.lean b/lean/OAI/Analysis/Laughlin/Spin/WeightSlice.lean new file mode 100644 index 0000000000000000000000000000000000000000..0f46688205e1cc19a1199d4c9c7ecc37a33511d5 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Spin/WeightSlice.lean @@ -0,0 +1,91 @@ +import OAI.Analysis.Laughlin.Spin.HighestSpace +import OAI.Analysis.Laughlin.Spin.LadderMatrix + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +abbrev SpinIndex (A B : ℕ) := Fin (A+1) × Fin (B+1) + +def weightSliceIndex (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (p : Fin (z+1)) : SpinIndex A B := (⟨p.val,by omega⟩,⟨z-p.val,by omega⟩) + +theorem weightSliceIndex_injective (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) : + Function.Injective (weightSliceIndex A B z hA hB) := by + intro p q h + exact Fin.ext (congrArg (fun i => i.1.val) h) + +noncomputable def extendWeightSlice (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (f : Fin (z+1) → ℝ) (i : SpinIndex A B) : ℝ := + ∑ p, if weightSliceIndex A B z hA hB p=i then f p else 0 + +theorem extendWeightSlice_at (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (f : Fin (z+1) → ℝ) (p : Fin (z+1)) : + extendWeightSlice A B z hA hB f (weightSliceIndex A B z hA hB p) = f p := by + simp only [extendWeightSlice,(weightSliceIndex_injective A B z hA hB).eq_iff, + Finset.sum_ite_eq',Finset.mem_univ,ite_true] + +theorem extendWeightSlice_off (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (f : Fin (z+1) → ℝ) (i : SpinIndex A B) (hi : i.1.val+i.2.val ≠ z) : + extendWeightSlice A B z hA hB f i = 0 := by + apply Finset.sum_eq_zero + intro p hp + have hne : weightSliceIndex A B z hA hB p ≠ i := by + intro he + have h₁ := congrArg (fun x => x.1.val) he + have h₂ := congrArg (fun x => x.2.val) he + dsimp [weightSliceIndex] at h₁ h₂ + omega + simp [hne] + +theorem sum_extendWeightSlice (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (f : Fin (z+1) → ℝ) (g : SpinIndex A B → ℝ) : + (∑ i, g i*extendWeightSlice A B z hA hB f i) = + ∑ p, g (weightSliceIndex A B z hA hB p)*f p := by + simp only [extendWeightSlice,Finset.mul_sum,mul_ite,mul_zero] + rw [Finset.sum_comm] + simp only [Finset.sum_ite_eq,Finset.mem_univ,ite_true] + +theorem totalRaise_below_slice (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (f : SpinIndex A B → ℝ) (p : Fin z) : + (totalRaise A B *ᵥ f) (⟨p.val,by omega⟩,⟨z-p.val-1,by omega⟩) = + ladder A p.val * f (weightSliceIndex A B z hA hB ⟨p.val+1,by omega⟩) + + ladder B (z-p.val-1)*f (weightSliceIndex A B z hA hB ⟨p.val,by omega⟩) := by + change (∑ j, totalRaise A B _ j * f j) = _ + rw [totalRaise_apply,raiseMatrix_row,raiseMatrix_row] + rw [dite_eq_left (show p.val < A by omega),dite_eq_left (show z-p.val-1 < B by omega)] + have h₁ : z-(p.val+1)=z-p.val-1 := by omega + have h₂ : z-p.val-1+1=z-p.val := by omega + simp only [weightSliceIndex,h₁,h₂] + +theorem extendWeightSlice_highest (A B z : ℕ) (hA : z ≤ A) (hB : z ≤ B) + (f : Fin (z+1) → ℝ) (hf : ∀ p, raiseSlice A B z f p=0) : + totalRaise A B *ᵥ extendWeightSlice A B z hA hB f = 0 := by + funext i + change (∑ j, totalRaise A B i j * extendWeightSlice A B z hA hB f j) = 0 + by_cases hi : i.1.val+i.2.val+1=z + · let p : Fin z := ⟨i.1.val,by omega⟩ + have he : i = (⟨p.val,by omega⟩,⟨z-p.val-1,by omega⟩) := by + apply Prod.ext + · rfl + · apply Fin.ext; dsimp [p]; omega + change (totalRaise A B *ᵥ extendWeightSlice A B z hA hB f) i = 0 + rw [he,totalRaise_below_slice A B z hA hB,extendWeightSlice_at,extendWeightSlice_at] + exact hf p + · rw [totalRaise_apply,raiseMatrix_row,raiseMatrix_row] + have hx (h : i.1.val < A) : + extendWeightSlice A B z hA hB f (⟨i.1.val+1,by omega⟩,i.2)=0 := by + apply extendWeightSlice_off + change i.1.val+1+i.2.val ≠ z + omega + have hy (h : i.2.val < B) : + extendWeightSlice A B z hA hB f (i.1,⟨i.2.val+1,by omega⟩)=0 := by + apply extendWeightSlice_off + change i.1.val+(i.2.val+1) ≠ z + omega + split_ifs with h₁ h₂ h₂ <;> simp_all only [mul_zero,add_zero] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Tensor/Antisymmetry.lean b/lean/OAI/Analysis/Laughlin/Tensor/Antisymmetry.lean new file mode 100644 index 0000000000000000000000000000000000000000..fc9710fe768367729d17f8d05f0dc4bdc259829f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Tensor/Antisymmetry.lean @@ -0,0 +1,49 @@ +import Mathlib.Algebra.BigOperators.Fin +import Mathlib.Data.Fin.VecNotation +import Mathlib.GroupTheory.Perm.Fin +import OAI.Analysis.Laughlin.EnergyNonnegative + +namespace OAI + +namespace Laughlin +open scoped BigOperators + +theorem antisymmetric_perm {N Q : ℕ} {ψ : State N Q} (hψ : Antisymmetric ψ) + (σ : Equiv.Perm (Fin N)) (a : Configuration N Q) : + ψ (a ∘ σ) = σ.sign • ψ a := by + induction σ using Equiv.Perm.swap_induction_on' generalizing a with + | one => simp + | mul_swap σ i j hij ih => + change ψ ((a ∘ σ) ∘ Equiv.swap i j) = _ + rw [hψ i j hij, ih] + simp [map_mul, Equiv.Perm.sign_swap hij] + +theorem antisymmetric_insertNth {n Q : ℕ} {ψ : State (n+1) Q} + (hψ : Antisymmetric ψ) (k : Fin (n+1)) (i : Fin (Q+1)) (a : Configuration n Q) : + ψ (k.insertNth i a) = (-1 : ℂ)^k.val * ψ (Fin.cons i a) := by + rw [← Fin.cons_comp_cycleRange, antisymmetric_perm hψ] + simp [Units.smul_def] + +theorem antisymmetric_cons {n Q : ℕ} {ψ : State (n+1) Q} + (hψ : Antisymmetric ψ) (i : Fin (Q+1)) : + Antisymmetric (fun a : Configuration n Q => ψ (Fin.cons i a)) := by + intro j k hjk a + change ψ (Fin.cons i (a ∘ Equiv.swap j k)) = _ + rw [show Fin.cons i (a ∘ Equiv.swap j k) = + Fin.cons i a ∘ Equiv.swap j.succ k.succ from Matrix.cons_swap i a j k] + exact hψ j.succ k.succ (by simpa using hjk) (Fin.cons i a) + +theorem sum_config_insert {n Q : ℕ} {M : Type*} [AddCommMonoid M] + (k : Fin (n+1)) (f : Configuration (n+1) Q → M) : + ∑ a, f a = ∑ i : Fin (Q+1), ∑ b : Configuration n Q, f (k.insertNth i b) := by + rw [← (Fin.insertNthEquiv (fun _ : Fin (n+1) => Fin (Q+1)) k).sum_comp] + exact Fintype.sum_prod_type _ + +theorem sum_config_cons {n Q : ℕ} {M : Type*} [AddCommMonoid M] + (f : Configuration (n+1) Q → M) : + ∑ a, f a = ∑ i : Fin (Q+1), ∑ b : Configuration n Q, f (Fin.cons i b) := by + simpa using sum_config_insert (0 : Fin (n+1)) f + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Tensor/ExteriorAdjoint.lean b/lean/OAI/Analysis/Laughlin/Tensor/ExteriorAdjoint.lean new file mode 100644 index 0000000000000000000000000000000000000000..4da068f67778fe16a33779ba6d4c6a970335234e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Tensor/ExteriorAdjoint.lean @@ -0,0 +1,87 @@ +import OAI.Analysis.Laughlin.Tensor.FockEnergy + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +noncomputable def normalizedTensorReadout (n Q : ℕ) (x : Space Q) : State n Q := + fun a => ((Real.sqrt (n.factorial : ℝ))⁻¹ : ℂ) * occupationInner Q (orderedWedge a) x + +theorem orderedWedge_swap {n Q : ℕ} (a : Configuration n Q) (i j : Fin n) (hij : i≠j) : + orderedWedge (a ∘ Equiv.swap i j) = -orderedWedge a := by + exact (ExteriorAlgebra.ιMulti ℂ n).map_swap (fun k => mode (a k)) hij + +theorem normalizedTensorReadout_antisymmetric (n Q : ℕ) (x : Space Q) : + Antisymmetric (normalizedTensorReadout n Q x) := by + intro i j hij a + simp [normalizedTensorReadout,orderedWedge_swap a i j hij,occupationInner] + +theorem tensorExterior_single (n Q : ℕ) (a : Configuration n Q) : + tensorExterior n Q (Pi.single a 1) = orderedWedge a := by + simp [tensorExterior,Pi.single_apply,orderedWedge] + +theorem normalizedTensorReadout_left_inverse (n Q : ℕ) (ψ : State n Q) + (hψ : Antisymmetric ψ) : + normalizedTensorReadout n Q (normalizedTensorExterior n Q ψ) = ψ := by + funext a + have h := normalizedTensorExterior_inner n Q (Pi.single a 1) ψ hψ + rw [normalizedTensorExterior,tensorExterior_single,occupationInner_smul_left] at h + have hr : star (((Real.sqrt (n.factorial : ℝ))⁻¹ : ℂ)) = + ((Real.sqrt (n.factorial : ℝ))⁻¹ : ℂ) := by simp + rw [hr] at h + simpa [normalizedTensorReadout,Pi.single_apply] using h + +theorem normalizedTensorExterior_adjoint (n Q : ℕ) (ψ : State n Q) (x : Space Q) : + occupationInner Q (normalizedTensorExterior n Q ψ) x = + ∑ a, star (ψ a)*normalizedTensorReadout n Q x a := by + simp only [normalizedTensorExterior,tensorExterior,occupationInner_smul_left, + occupationInner_sum_left,normalizedTensorReadout,orderedWedge] + simp only [Complex.star_def,map_inv₀,Complex.conj_ofReal,Finset.mul_sum] + apply Finset.sum_congr rfl + intro a ha + ring + +theorem normalizedTensorReadout_sub (n Q : ℕ) (x y : Space Q) : + normalizedTensorReadout n Q (x-y) = + fun a => normalizedTensorReadout n Q x a - normalizedTensorReadout n Q y a := by + funext a + simp [normalizedTensorReadout,occupationInner,mul_sub,Finset.sum_sub_distrib] + +theorem normalizedTensorReadout_norm_le (n Q : ℕ) (x : Space Q) : + (∑ a, ‖normalizedTensorReadout n Q x a‖^2) ≤ occupationNormSq Q x := by + let ψ := normalizedTensorReadout n Q x + let z := normalizedTensorExterior n Q ψ + let S : ℝ := ∑ a, ‖ψ a‖^2 + have he (a : Configuration n Q) : star (ψ a)*ψ a = ((‖ψ a‖^2 : ℝ) : ℂ) := by + rw [← Complex.normSq_eq_norm_sq,Complex.normSq_eq_conj_mul_self] + rfl + have hzx : occupationInner Q z x = (S : ℂ) := by + rw [normalizedTensorExterior_adjoint] + change (∑ a, star (ψ a)*ψ a) = (S : ℂ) + simp only [he,← Complex.ofReal_sum] + rfl + have hzz : occupationInner Q z z = (S : ℂ) := by + rw [occupationInner_self,normalizedTensorExterior_norm n Q ψ + (normalizedTensorReadout_antisymmetric n Q x)] + have hxz : occupationInner Q x z = (S : ℂ) := by + rw [← occupationInner_star,hzx] + simp + have hs : occupationNormSq Q (x-z) = occupationNormSq Q x-S := by + apply Complex.ofReal_injective + rw [← occupationInner_self] + have hsub : occupationInner Q (x-z) (x-z) = + occupationInner Q x x - occupationInner Q x z - + occupationInner Q z x + occupationInner Q z z := by + simp [occupationInner,sub_mul,mul_sub,Finset.sum_sub_distrib] + ring + rw [hsub,occupationInner_self,hzx,hxz,hzz] + push_cast + ring + have hp := occupationNormSq_nonneg Q (x-z) + rw [hs] at hp + exact sub_nonneg.mp hp + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Tensor/ExteriorContraction.lean b/lean/OAI/Analysis/Laughlin/Tensor/ExteriorContraction.lean new file mode 100644 index 0000000000000000000000000000000000000000..19db5806bae1621c5cb64752085a0e846f2c566c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Tensor/ExteriorContraction.lean @@ -0,0 +1,94 @@ +import OAI.Analysis.Laughlin.FourBody.CARReadout +import OAI.Analysis.Laughlin.Tensor.Antisymmetry +import OAI.Analysis.Laughlin.Tensor.ExteriorRotation + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +noncomputable def orderedWedge {n Q : ℕ} (a : Configuration n Q) : Space Q := + ExteriorAlgebra.ιMulti ℂ n (fun k => mode (a k)) + +theorem orderedWedge_cons {n Q : ℕ} (i : Fin (Q+1)) (a : Configuration n Q) : + orderedWedge (Fin.cons i a) = create i (orderedWedge a) := by + simp only [orderedWedge, ExteriorAlgebra.ιMulti_succ_apply, Fin.cons_zero] + rfl + +theorem orderedWedge_head {n Q : ℕ} (a : Configuration (n+1) Q) : + orderedWedge a = create (a 0) (orderedWedge (fun j => a j.succ)) := by + rw [← orderedWedge_cons] + congr 1 + exact (Fin.cons_self_tail a).symm + +theorem annihilate_orderedWedge (n Q : ℕ) (i : Fin (Q+1)) + (a : Configuration (n+1) Q) : + annihilate i (orderedWedge a) = + ∑ k : Fin (n+1), ((-1 : ℂ)^k.val * delta i (a k)) • + orderedWedge (k.removeNth a) := by + induction n with + | zero => + rw [orderedWedge_head, annihilate_create_apply] + simp [orderedWedge, ExteriorAlgebra.ιMulti_zero_apply, annihilate_vacuum] + | succ n ih => + rw [orderedWedge_head, annihilate_create_apply, ih, map_sum] + conv_rhs => rw [Fin.sum_univ_succ] + simp only [Fin.val_zero, pow_zero, one_mul, Fin.val_succ, pow_succ, + map_smul] + have h0 : (0 : Fin (n+2)).removeNth a = fun j => a j.succ := by rfl + rw [h0] + rw [sub_eq_add_neg, ← Finset.sum_neg_distrib] + congr 1 + apply Finset.sum_congr rfl + intro k hk + have hw : orderedWedge (k.succ.removeNth a) = + create (a 0) (orderedWedge (k.removeNth (fun j => a j.succ))) := by + rw [← orderedWedge_cons] + congr 1 + have h := Fin.cons_comp_succ_succAbove (a 0) (fun j => a j.succ) k + have ha : Fin.cons (a 0) (fun j => a j.succ) = a := Fin.cons_self_tail a + rw [ha] at h + exact h + rw [hw] + simp only [mul_neg_one, neg_mul, neg_smul] + +theorem tensorExterior_cons (n Q : ℕ) (ψ : State (n+1) Q) : + tensorExterior (n+1) Q ψ = + ∑ i : Fin (Q+1), create i (tensorExterior n Q (fun a => ψ (Fin.cons i a))) := by + change (∑ a, ψ a • orderedWedge a) = _ + rw [sum_config_cons] + change (∑ i, ∑ b, ψ (Fin.cons i b) • orderedWedge (Fin.cons i b)) = _ + simp only [orderedWedge_cons,tensorExterior,map_sum,map_smul] + rfl + +theorem annihilate_tensorExterior (n Q : ℕ) (ψ : State (n+1) Q) + (hψ : Antisymmetric ψ) (i : Fin (Q+1)) : + annihilate i (tensorExterior (n+1) Q ψ) = + (n+1 : ℂ) • tensorExterior n Q (fun a => ψ (Fin.cons i a)) := by + change annihilate i (∑ a, ψ a • orderedWedge a) = _ + simp only [map_sum,map_smul,annihilate_orderedWedge,Finset.smul_sum,smul_smul] + rw [Finset.sum_comm] + have hs (k : Fin (n+1)) : + (∑ a : Configuration (n+1) Q, + (ψ a * ((-1 : ℂ)^k.val * delta i (a k))) • orderedWedge (k.removeNth a)) = + tensorExterior n Q (fun a => ψ (Fin.cons i a)) := by + rw [sum_config_insert k] + simp only [Fin.insertNth_apply_same, Fin.removeNth_insertNth, + antisymmetric_insertNth hψ] + have he (x : Fin (Q+1)) (b : Configuration n Q) : + ((-1 : ℂ)^k.val * ψ (Fin.cons x b) * ((-1 : ℂ)^k.val * delta i x)) = + delta i x * ψ (Fin.cons x b) := by + have hpow : ((-1 : ℂ)^k.val)^2 = 1 := by + rw [← pow_mul, Nat.mul_comm, pow_mul]; norm_num + calc + _ = ((-1 : ℂ)^k.val)^2 * (delta i x * ψ (Fin.cons x b)) := by ring + _ = _ := by rw [hpow,one_mul] + simp only [he] + simp [delta,tensorExterior,orderedWedge] + simp only [hs,Finset.sum_const,Finset.card_univ,Fintype.card_fin] + rw [← Nat.cast_smul_eq_nsmul ℂ] + simp + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Tensor/ExteriorIsometry.lean b/lean/OAI/Analysis/Laughlin/Tensor/ExteriorIsometry.lean new file mode 100644 index 0000000000000000000000000000000000000000..52a2af49ceebcbd26aaa2d67c3c3f00727ecf944 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Tensor/ExteriorIsometry.lean @@ -0,0 +1,73 @@ +import OAI.Analysis.Laughlin.Fock.Bidegree +import OAI.Analysis.Laughlin.Tensor.ExteriorContraction + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem tensorExterior_inner (n Q : ℕ) (ψ φ : State n Q) (hφ : Antisymmetric φ) : + occupationInner Q (tensorExterior n Q ψ) (tensorExterior n Q φ) = + (n.factorial : ℂ) * ∑ a, star (ψ a) * φ a := by + induction n with + | zero => + simp only [tensorExterior, ExteriorAlgebra.ιMulti_zero_apply] + simp only [occupationInner_sum_left,occupationInner_sum_right] + simp only [occupationInner_smul_left,occupationInner_smul_right] + have h1 : occupationInner Q 1 1 = 1 := by + rw [← occupation_empty] + simp [occupationInner,Module.Basis.repr_self,Finsupp.single_apply] + simp [h1,mul_comm] + | succ n ih => + rw [tensorExterior_cons,occupationInner_sum_left] + simp only [create_annihilate_adjoint,annihilate_tensorExterior n Q φ hφ, + occupationInner_smul_right] + simp_rw [ih _ _ (antisymmetric_cons hφ _)] + rw [sum_config_cons] + simp only [Nat.factorial_succ,Nat.cast_mul,Nat.cast_add,Nat.cast_one, + Finset.mul_sum] + ring_nf + +theorem tensorExterior_norm (n Q : ℕ) (ψ : State n Q) (hψ : Antisymmetric ψ) : + occupationNormSq Q (tensorExterior n Q ψ) = + (n.factorial : ℝ) * ∑ a, ‖ψ a‖^2 := by + have h := tensorExterior_inner n Q ψ ψ hψ + rw [occupationInner_self] at h + have he (a : Configuration n Q) : star (ψ a)*ψ a = ((‖ψ a‖^2 : ℝ) : ℂ) := by + rw [← Complex.normSq_eq_norm_sq,Complex.normSq_eq_conj_mul_self] + rfl + simp only [he,← Complex.ofReal_sum,← Complex.ofReal_natCast,← Complex.ofReal_mul] at h + exact Complex.ofReal_injective h + +noncomputable def normalizedTensorExterior (n Q : ℕ) (ψ : State n Q) : Space Q := + ((Real.sqrt (n.factorial : ℝ))⁻¹ : ℂ) • tensorExterior n Q ψ + +theorem normalizedTensorExterior_inner (n Q : ℕ) (ψ φ : State n Q) + (hφ : Antisymmetric φ) : + occupationInner Q (normalizedTensorExterior n Q ψ) (normalizedTensorExterior n Q φ) = + ∑ a, star (ψ a)*φ a := by + have hp : 0 < (n.factorial : ℝ) := by exact_mod_cast Nat.factorial_pos n + have hs : Real.sqrt (n.factorial : ℝ) ≠ 0 := ne_of_gt (Real.sqrt_pos.2 hp) + have he : ((Real.sqrt (n.factorial : ℝ) : ℂ))^2 = (n.factorial : ℂ) := by + exact_mod_cast Real.sq_sqrt (le_of_lt hp) + simp only [normalizedTensorExterior,occupationInner_smul_left,occupationInner_smul_right, + tensorExterior_inner n Q ψ φ hφ] + simp only [Complex.star_def, map_inv₀, Complex.conj_ofReal] + have hsc : (Real.sqrt (n.factorial : ℝ) : ℂ) ≠ 0 := by exact_mod_cast hs + rw [← he] + field_simp + +theorem normalizedTensorExterior_norm (n Q : ℕ) (ψ : State n Q) + (hψ : Antisymmetric ψ) : + occupationNormSq Q (normalizedTensorExterior n Q ψ) = ∑ a, ‖ψ a‖^2 := by + have h := normalizedTensorExterior_inner n Q ψ ψ hψ + rw [occupationInner_self] at h + have he (a : Configuration n Q) : star (ψ a)*ψ a = ((‖ψ a‖^2 : ℝ) : ℂ) := by + rw [← Complex.normSq_eq_norm_sq,Complex.normSq_eq_conj_mul_self] + rfl + simp only [he,← Complex.ofReal_sum] at h + exact Complex.ofReal_injective h + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Tensor/ExteriorRotation.lean b/lean/OAI/Analysis/Laughlin/Tensor/ExteriorRotation.lean new file mode 100644 index 0000000000000000000000000000000000000000..d925a3acdcd597488c475dfe73c44b9a1f85f52c --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Tensor/ExteriorRotation.lean @@ -0,0 +1,51 @@ +import OAI.Analysis.Laughlin.Exterior.SpinUnitary +import OAI.Analysis.Laughlin.Spin.ParticleSpinAction + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators Matrix +open Rotation + +noncomputable def tensorExterior (N Q : ℕ) (ψ : State N Q) : Space Q := + ∑ a, ψ a • ExteriorAlgebra.ιMulti ℂ N (fun k => mode (a k)) + +theorem orbitalRotation_mode (Q : ℕ) (g : SourceSU2) (i : Fin (Q+1)) : + orbitalRotation Q g (mode i) = ∑ j, sourceSpinRepresentation Q g j i • mode j := by + rw [orbital_sum_modes Q (orbitalRotation Q g (mode i))] + apply Finset.sum_congr rfl + intro j hj + congr 1 + simp [orbitalRotation,mode,Matrix.mulVec,dotProduct,Pi.single_apply] + +theorem exteriorRotation_basis_wedge (N Q : ℕ) (g : SourceSU2) (a : Configuration N Q) : + exteriorRotation Q g (ExteriorAlgebra.ιMulti ℂ N (fun k => mode (a k))) = + ∑ b : Configuration N Q, (∏ k, sourceSpinRepresentation Q g (b k) (a k)) • + ExteriorAlgebra.ιMulti ℂ N (fun k => mode (b k)) := by + unfold exteriorRotation + rw [ExteriorAlgebra.map_apply_ιMulti] + change ExteriorAlgebra.ιMulti ℂ N (fun k => orbitalRotation Q g (mode (a k))) = _ + simp_rw [orbitalRotation_mode] + change (ExteriorAlgebra.ιMulti ℂ N).toMultilinearMap + (fun k => ∑ j, sourceSpinRepresentation Q g j (a k) • mode j) = _ + rw [MultilinearMap.map_sum] + apply Finset.sum_congr rfl + intro b hb + exact (ExteriorAlgebra.ιMulti ℂ N).map_smul_univ _ _ + +theorem tensorExterior_rotation (N Q : ℕ) (g : SourceSU2) (ψ : State N Q) : + exteriorRotation Q g (tensorExterior N Q ψ) = + tensorExterior N Q (sourceParticleRepresentation N Q g *ᵥ ψ) := by + simp only [tensorExterior,map_sum,map_smul,exteriorRotation_basis_wedge,Finset.smul_sum,smul_smul] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro b hb + rw [← Finset.sum_smul] + congr 1 + change (∑ a, ψ a * ∏ k, sourceSpinRepresentation Q g (b k) (a k)) = + ∑ a, (∏ k, sourceSpinRepresentation Q g (b k) (a k))*ψ a + simp only [mul_comm] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Tensor/FockEnergy.lean b/lean/OAI/Analysis/Laughlin/Tensor/FockEnergy.lean new file mode 100644 index 0000000000000000000000000000000000000000..a99f8dbef783e2a75bd5e285002f2d8417d464c2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Tensor/FockEnergy.lean @@ -0,0 +1,47 @@ +import OAI.Analysis.Laughlin.Operators.PhysicalPairCounting +import OAI.Analysis.Laughlin.Pair.EnergyReturn + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem tensorExterior_energy (n Q : ℕ) (ψ : State (n+2) Q) (hψ : Antisymmetric ψ) : + sourceFockEnergy Q (tensorExterior (n+2) Q ψ) = ((n+2).factorial : ℝ)*energy ψ := by + have hn : ‖((n+2 : ℂ)*(n+1))/(Real.sqrt 2 : ℂ)‖^2 = + ((n+2 : ℝ)*(n+1))^2/2 := by + rw [norm_div,norm_mul,div_pow,mul_pow] + have h2 : ‖(Real.sqrt 2 : ℂ)‖^2 = (2 : ℝ) := by + rw [Complex.norm_real,Real.norm_eq_abs,abs_of_nonneg (Real.sqrt_nonneg _), + Real.sq_sqrt (by norm_num)] + rw [h2] + have hn2 : (n+2 : ℂ) = ((n+2 : ℝ) : ℂ) := by push_cast; rfl + have hn1 : (n+1 : ℂ) = ((n+1 : ℝ) : ℂ) := by push_cast; rfl + rw [hn2,hn1,Complex.norm_of_nonneg (by positivity),Complex.norm_of_nonneg (by positivity)] + ring + simp only [sourceFockEnergy,sourcePairEnd_tensorExterior n Q ψ hψ, + occupationNormSq_smul,hn,tensorExterior_norm n Q _ (headPairAmplitude_antisymmetric ψ hψ _)] + rw [energy_head_pair n Q ψ hψ] + simp only [Nat.factorial_succ,Nat.cast_mul,Nat.cast_add,Nat.cast_one,← Finset.mul_sum] + ring + +theorem normalizedTensorExterior_energy (n Q : ℕ) (ψ : State (n+2) Q) + (hψ : Antisymmetric ψ) : + sourceFockEnergy Q (normalizedTensorExterior (n+2) Q ψ) = energy ψ := by + have hp : 0 < ((n+2).factorial : ℝ) := by exact_mod_cast Nat.factorial_pos (n+2) + have hs : (Real.sqrt ((n+2).factorial : ℝ))^2 = ((n+2).factorial : ℝ) := + Real.sq_sqrt (le_of_lt hp) + have he (c : ℂ) (x : Space Q) : sourceFockEnergy Q (c • x) = ‖c‖^2*sourceFockEnergy Q x := by + simp only [sourceFockEnergy,map_smul,occupationNormSq_smul,Finset.mul_sum] + rw [normalizedTensorExterior,he,tensorExterior_energy n Q ψ hψ] + have hn : ‖((Real.sqrt ((n+2).factorial : ℝ))⁻¹ : ℂ)‖^2 = + (((n+2).factorial : ℝ))⁻¹ := by + rw [norm_inv,inv_pow] + congr 1 + simpa only [Complex.norm_real,Real.norm_eq_abs,sq_abs] using hs + rw [hn] + field_simp + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Tensor/KernelReadout.lean b/lean/OAI/Analysis/Laughlin/Tensor/KernelReadout.lean new file mode 100644 index 0000000000000000000000000000000000000000..bce6e0ee5e1123e59fbfc4661c20ffff6675dd09 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Tensor/KernelReadout.lean @@ -0,0 +1,42 @@ +import OAI.Analysis.Laughlin.Tensor.ExteriorAdjoint + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem headPairAmplitude_readout (n Q : ℕ) (x : Space Q) (p : ℕ) + (b : Configuration n Q) : + headPairAmplitude (normalizedTensorReadout (n+2) Q x) p b = + (((Real.sqrt ((n+2).factorial : ℝ))⁻¹ : ℂ)*(Real.sqrt 2 : ℂ)) * + occupationInner Q (orderedWedge b) (sourcePairEnd Q p x) := by + have he (i j : Fin (Q+1)) : + occupationInner Q (orderedWedge (Fin.cons i (Fin.cons j b))) x = + occupationInner Q (orderedWedge b) (annihilate j (annihilate i x)) := by + rw [orderedWedge_cons,orderedWedge_cons,create_annihilate_adjoint,create_annihilate_adjoint] + simp only [headPairAmplitude,normalizedTensorReadout,he,sourcePairEnd,pairEnd, + LinearMap.sum_apply,LinearMap.smul_apply,Module.End.mul_apply, + occupationInner_sum_right,occupationInner_smul_right,Finset.mul_sum] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + have h2 : (Real.sqrt 2 : ℂ) ≠ 0 := by exact_mod_cast (show Real.sqrt (2 : ℝ) ≠ 0 by positivity) + push_cast + field_simp + +theorem normalizedTensorReadout_zero_energy (n Q : ℕ) (x : Space Q) + (hx : sourceFockEnergy Q x=0) : + energy (normalizedTensorReadout (n+2) Q x)=0 := by + rw [energy_head_pair n Q _ (normalizedTensorReadout_antisymmetric (n+2) Q x)] + have hp := (sourceFockEnergy_eq_zero Q x).mp hx + have hs : (∑ p ∈ Finset.range (2*Q-1), ∑ b : Configuration n Q, + ‖headPairAmplitude (normalizedTensorReadout (n+2) Q x) p b‖^2) = 0 := by + apply Finset.sum_eq_zero + intro p hpr + simp [headPairAmplitude_readout,hp p hpr,occupationInner] + rw [hs,mul_zero] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Tensor/PairContraction.lean b/lean/OAI/Analysis/Laughlin/Tensor/PairContraction.lean new file mode 100644 index 0000000000000000000000000000000000000000..cb5a5876c62f21991a587ec7c210f14e84630a24 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Tensor/PairContraction.lean @@ -0,0 +1,62 @@ +import OAI.Analysis.Laughlin.Fock.Hamiltonian +import OAI.Analysis.Laughlin.Tensor.ExteriorIsometry + +namespace OAI + +namespace Laughlin +open scoped BigOperators + +noncomputable def headPairAmplitude {n Q : ℕ} (ψ : State (n+2) Q) + (p : ℕ) (b : Configuration n Q) : ℂ := + ∑ x, ∑ y, (pairCoefficient Q p x y : ℂ) * ψ (Fin.cons x (Fin.cons y b)) + +theorem headPairAmplitude_antisymmetric {n Q : ℕ} (ψ : State (n+2) Q) + (hψ : Antisymmetric ψ) (p : ℕ) : Antisymmetric (headPairAmplitude ψ p) := by + intro i j hij b + unfold headPairAmplitude + simp_rw [(antisymmetric_cons (antisymmetric_cons hψ _) _) i j hij, + mul_neg,Finset.sum_neg_distrib] + +namespace Fock + +theorem tensorExterior_sum {I : Type*} (n Q : ℕ) (s : Finset I) (ψ : I → State n Q) : + tensorExterior n Q (fun a => ∑ i ∈ s, ψ i a) = ∑ i ∈ s, tensorExterior n Q (ψ i) := by + simp only [tensorExterior,Finset.sum_smul] + rw [Finset.sum_comm] + +theorem tensorExterior_smul (n Q : ℕ) (c : ℂ) (ψ : State n Q) : + tensorExterior n Q (fun a => c * ψ a) = c • tensorExterior n Q ψ := by + simp only [tensorExterior,Finset.smul_sum,smul_smul] + +theorem two_annihilate_tensorExterior (n Q : ℕ) (ψ : State (n+2) Q) + (hψ : Antisymmetric ψ) (i j : Fin (Q+1)) : + annihilate j (annihilate i (tensorExterior (n+2) Q ψ)) = + ((n+2 : ℂ)*(n+1)) • tensorExterior n Q (fun a => ψ (Fin.cons i (Fin.cons j a))) := by + rw [annihilate_tensorExterior (n+1) Q ψ hψ,map_smul, + annihilate_tensorExterior n Q _ (antisymmetric_cons hψ i),smul_smul] + congr 1 + push_cast + ring + +theorem sourcePairEnd_tensorExterior (n Q : ℕ) (ψ : State (n+2) Q) + (hψ : Antisymmetric ψ) (p : ℕ) : + sourcePairEnd Q p (tensorExterior (n+2) Q ψ) = + (((n+2 : ℂ)*(n+1))/(Real.sqrt 2 : ℂ)) • + tensorExterior n Q (headPairAmplitude ψ p) := by + simp only [sourcePairEnd,pairEnd,LinearMap.sum_apply,LinearMap.smul_apply, + Module.End.mul_apply,two_annihilate_tensorExterior n Q ψ hψ,smul_smul] + unfold headPairAmplitude + simp only [tensorExterior_sum,tensorExterior_smul,Finset.smul_sum,smul_smul] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + congr 1 + push_cast + ring + +end Fock + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Tensor/PolynomialRealization.lean b/lean/OAI/Analysis/Laughlin/Tensor/PolynomialRealization.lean new file mode 100644 index 0000000000000000000000000000000000000000..cc03f8de0c910391d8af860648a1a8e73f55b5ab --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Tensor/PolynomialRealization.lean @@ -0,0 +1,95 @@ +import OAI.Analysis.Laughlin.Spin.Representation +import OAI.Analysis.Laughlin.Tensor.WeightProducts + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators Matrix + +theorem symmetricTensor_column_sum (Q : ℕ) (p : Fin (Q+1)) : + (∑ a, symmetricTensorInclusion Q a p) = (Real.sqrt (Q.choose p.val : ℝ) : ℂ) := by + have hr : (∑ a : Fin Q → Fin 2, symmetricTensorInclusionReal Q a p) = + Real.sqrt (Q.choose p.val : ℝ) := by + have hn : Real.sqrt (Q.choose p.val : ℝ) ≠ 0 := + Real.sqrt_ne_zero'.mpr (by exact_mod_cast Nat.choose_pos (Nat.le_of_lt_succ p.isLt)) + have he (a : Fin Q → Fin 2) : symmetricTensorInclusionReal Q a p = + (Real.sqrt (Q.choose p.val : ℝ))⁻¹ * + (if tensorWeight Q a=p.val then 1 else 0) := by + simp [symmetricTensorInclusionReal, mul_ite] + simp_rw [he, ← Finset.mul_sum, tensorWeight_count] + apply (mul_left_cancel₀ hn) + rw [mul_inv_cancel_left₀ hn] + nlinarith [Real.sq_sqrt (show (0 : ℝ) ≤ Q.choose p.val by positivity)] + simpa [symmetricTensorInclusion] using congrArg Complex.ofReal hr + +theorem symmetricTensor_weighted_column {R : Type*} [CommRing R] + (f : ℂ →+* R) (Q : ℕ) (p : Fin (Q+1)) (m : ℕ → R) : + (∑ a, f (symmetricTensorInclusion Q a p) * m (tensorWeight Q a)) = + f (Real.sqrt (Q.choose p.val : ℝ) : ℂ) * m p.val := by + have he (a : Fin Q → Fin 2) : f (symmetricTensorInclusion Q a p) * m (tensorWeight Q a) = + f (symmetricTensorInclusion Q a p) * m p.val := by + by_cases h : tensorWeight Q a=p.val + · rw [h] + · simp [symmetricTensorInclusion, symmetricTensorInclusionReal,h] + simp_rw [he, ← Finset.sum_mul, ← map_sum, symmetricTensor_column_sum] + +theorem tensorMatrix_polynomial {R : Type*} [CommRing R] + (f : ℂ →+* R) (Q : ℕ) (A : Matrix (Fin 2) (Fin 2) ℂ) + (u v : R) (b : Fin Q → Fin 2) : + (∑ a, f (tensorMatrix Q A a b) * + (v^(tensorWeight Q a)*u^(Q-tensorWeight Q a))) = + (f (A 0 1)*u+f (A 1 1)*v)^(tensorWeight Q b) * + (f (A 0 0)*u+f (A 1 0)*v)^(Q-tensorWeight Q b) := by + have he (a : Fin Q → Fin 2) : f (tensorMatrix Q A a b) * + (v^(tensorWeight Q a)*u^(Q-tensorWeight Q a)) = + ∏ k, f (A (a k) (b k)) * (if a k=1 then v else u) := by + rw [Finset.prod_mul_distrib, tensorWeight_product] + simp [tensorMatrix] + simp_rw [he] + rw [← Fintype.prod_sum (fun k x => f (A x (b k)) * (if x=1 then v else u))] + have he' (k : Fin Q) : (∑ x : Fin 2, f (A x (b k)) * (if x=1 then v else u)) = + if b k=1 then f (A 0 1)*u+f (A 1 1)*v else f (A 0 0)*u+f (A 1 0)*v := by + have h : b k=0 ∨ b k=1 := by omega + rcases h with h | h <;> simp [h, Fin.sum_univ_two] + simp_rw [he'] + exact tensorWeight_product Q b _ _ + +theorem sourceSpinRepresentation_polynomial {R : Type*} [CommRing R] + (f : ℂ →+* R) (Q : ℕ) (g : SourceSU2) (u v : R) (p : Fin (Q+1)) : + (∑ q : Fin (Q+1), f (sourceSpinRepresentation Q g q p) * + (f (Real.sqrt (Q.choose q.val : ℝ) : ℂ) * v^q.val*u^(Q-q.val))) = + f (Real.sqrt (Q.choose p.val : ℝ) : ℂ) * + (f (g.val 0 1)*u+f (g.val 1 1)*v)^p.val * + (f (g.val 0 0)*u+f (g.val 1 0)*v)^(Q-p.val) := by + have h := tensor_spin_intertwining Q g + have hm := congrArg (fun M : Matrix (Fin Q → Fin 2) (Fin (Q+1)) ℂ => + ∑ a, f (M a p) * (v^(tensorWeight Q a)*u^(Q-tensorWeight Q a))) h + simp only [Matrix.mul_apply, map_sum, map_mul, Finset.sum_mul] at hm + rw [Finset.sum_comm] at hm + have hl (q : Fin (Q+1)) : (∑ a, f (symmetricTensorInclusion Q a q) * + f (sourceSpinMatrix Q g q p) * (v^(tensorWeight Q a)*u^(Q-tensorWeight Q a))) = + f (sourceSpinMatrix Q g q p) * + (f (Real.sqrt (Q.choose q.val : ℝ) : ℂ)*v^q.val*u^(Q-q.val)) := by + simp_rw [mul_right_comm _ (f (sourceSpinMatrix Q g q p)), ← Finset.sum_mul] + rw [symmetricTensor_weighted_column f Q q (fun n => v^n*u^(Q-n))] + ring + simp_rw [hl] at hm + rw [Finset.sum_comm] at hm + have hr (b : Fin Q → Fin 2) : (∑ a, f (sourceTensorRepresentation Q g a b) * + f (symmetricTensorInclusion Q b p) * (v^(tensorWeight Q a)*u^(Q-tensorWeight Q a))) = + f (symmetricTensorInclusion Q b p) * + ((f (g.val 0 1)*u+f (g.val 1 1)*v)^(tensorWeight Q b) * + (f (g.val 0 0)*u+f (g.val 1 0)*v)^(Q-tensorWeight Q b)) := by + simp_rw [mul_right_comm _ (f (symmetricTensorInclusion Q b p)), ← Finset.sum_mul] + rw [show sourceTensorRepresentation Q g = tensorMatrix Q g.val from rfl, + tensorMatrix_polynomial] + ring + simp_rw [hr] at hm + rw [symmetricTensor_weighted_column f Q p (fun n => + (f (g.val 0 1)*u+f (g.val 1 1)*v)^n * + (f (g.val 0 0)*u+f (g.val 1 0)*v)^(Q-n))] at hm + simpa only [sourceSpinRepresentation, MonoidHom.coe_mk, OneHom.coe_mk, mul_assoc] using hm + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/Tensor/WeightProducts.lean b/lean/OAI/Analysis/Laughlin/Tensor/WeightProducts.lean new file mode 100644 index 0000000000000000000000000000000000000000..4bf903e24700aca217047c1fc0b1739475b17211 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/Tensor/WeightProducts.lean @@ -0,0 +1,64 @@ +import OAI.Analysis.Laughlin.Polynomial.SymmetricTensorRange + +namespace OAI + +namespace Laughlin.Rotation +open scoped BigOperators + + theorem tensorWeight_product {R : Type*} [CommMonoid R] (Q : ℕ) (a : Fin Q → Fin 2) (x y : R) : + (∏ i, if a i=1 then y else x) = y^(tensorWeight Q a)*x^(Q-tensorWeight Q a) := by + classical + rw [Finset.prod_ite] + simp only [Finset.prod_const] + have hc : (Finset.univ.filter (fun i => ¬ a i=1)).card=Q-tensorWeight Q a := by + have h := Finset.card_filter_add_card_filter_not (s := Finset.univ) (fun i : Fin Q => a i=1) + simp only [Finset.card_univ,Fintype.card_fin] at h + change (Finset.univ.filter (fun i => ¬ a i=1)).card=Q-(tensorBits Q a).card + unfold tensorBits + omega + rw [hc] + rfl + + theorem tensorWeight_zero_iff (Q : ℕ) (a : Fin Q → Fin 2) : + tensorWeight Q a=0 ↔ a=fun _ => 0 := by + constructor + · intro h + have he : tensorBits Q a=∅ := Finset.card_eq_zero.mp h + funext i + have hn : a i ≠ 1 := by + intro hi + have hm : i ∈ tensorBits Q a := by simp [tensorBits,hi] + rw [he] at hm + exact Finset.notMem_empty _ hm + apply Fin.ext + have ha := (a i).isLt + have hn' : (a i).val ≠ 1 := by intro he; exact hn (Fin.ext he) + simp only [Fin.val_zero] + omega + · rintro rfl + simp [tensorWeight,tensorBits] + + theorem symmetricTensor_zero_column (Q : ℕ) (a : Fin Q → Fin 2) : + symmetricTensorInclusion Q a 0 = if a=(fun _ => 0) then 1 else 0 := by + simp [symmetricTensorInclusion,symmetricTensorInclusionReal,tensorWeight_zero_iff,apply_ite] + + theorem tensorMatrix_diagonal (Q : ℕ) (x y : ℂ) : + tensorMatrix Q (Matrix.diagonal (fun i : Fin 2 => if i=0 then x else y)) = + Matrix.diagonal (fun a => y^(tensorWeight Q a)*x^(Q-tensorWeight Q a)) := by + classical + ext a b + by_cases hab : a=b + · subst b + simp only [tensorMatrix,Matrix.diagonal_apply_eq] + have he (i : Fin Q) : (if a i=0 then x else y)=(if a i=1 then y else x) := by + have h : a i=0 ∨ a i=1 := by omega + rcases h with h | h <;> simp [h] + simp_rw [he] + exact tensorWeight_product Q a x y + · rw [Matrix.diagonal_apply_ne _ hab] + obtain ⟨i,hi⟩ := Function.ne_iff.mp hab + exact Finset.prod_eq_zero (Finset.mem_univ i) (Matrix.diagonal_apply_ne _ hi) + +end Laughlin.Rotation + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/Basic.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/Basic.lean new file mode 100644 index 0000000000000000000000000000000000000000..92e630a83b316ec7aea5a50dd6c0a3d46d283aee --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/Basic.lean @@ -0,0 +1,53 @@ +import OAI.Analysis.Laughlin.Operators.Certificate + +namespace OAI + +namespace Laughlin.Certificate + +theorem threeBody_2 : e 2 < limitBound 2 := by decide +kernel + +theorem threeBody_4 : e 4 < limitBound 4 := by decide +kernel + +theorem threeBody_5 : e 5 < limitBound 5 := by decide +kernel + +theorem threeBody_6 : e 6 < limitBound 6 := by decide +kernel + +theorem threeBody_7 : e 7 < limitBound 7 := by decide +kernel + +theorem threeBody_8 : e 8 < limitBound 8 := by decide +kernel + +theorem threeBody_9 : e 9 < limitBound 9 := by decide +kernel + +theorem threeBody_10 : e 10 < limitBound 10 := by decide +kernel + +theorem threeBody_11 : e 11 < limitBound 11 := by decide +kernel + +theorem threeBody_12 : e 12 < limitBound 12 := by decide +kernel + +theorem threeBody_13 : e 13 < limitBound 13 := by decide +kernel + +theorem threeBody_14 : e 14 < limitBound 14 := by decide +kernel + +theorem threeBody_15 : e 15 < limitBound 15 := by decide +kernel + +theorem threeBody_certificate (z : ℕ) + (hz : z ∈ [2, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15]) : e z < limitBound z := by + simp only [List.mem_cons, List.not_mem_nil, or_false] at hz + rcases hz with rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl | rfl + · exact threeBody_2 + · exact threeBody_4 + · exact threeBody_5 + · exact threeBody_6 + · exact threeBody_7 + · exact threeBody_8 + · exact threeBody_9 + · exact threeBody_10 + · exact threeBody_11 + · exact threeBody_12 + · exact threeBody_13 + · exact threeBody_14 + · exact threeBody_15 + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/Contraction.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/Contraction.lean new file mode 100644 index 0000000000000000000000000000000000000000..41e41007313ac03c0eaa1e331bd22402fa23f806 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/Contraction.lean @@ -0,0 +1,39 @@ +import Mathlib.Tactic.Module +import OAI.Analysis.Laughlin.Fock.PairNormalization + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem annihilate_create_vacuum {Q : ℕ} (a i : Fin (Q+1)) : + annihilate a (create i (1 : Space Q)) = delta a i • (1 : Space Q) := by + have h := LinearMap.congr_fun (mixed_car a i) (1 : Space Q) + by_cases ha : a = i <;> simpa [Module.End.mul_apply,annihilate_vacuum,delta,ha] using h + +theorem two_annihilate_three_create {Q : ℕ} (a b i j k : Fin (Q+1)) : + annihilate b (annihilate a (create i (create j (create k (1 : Space Q))))) = + (delta a i*delta b j-delta b i*delta a j) • create k (1 : Space Q) - + (delta a i*delta b k-delta b i*delta a k) • create j (1 : Space Q) + + (delta a j*delta b k-delta b j*delta a k) • create i (1 : Space Q) := by + have h := LinearMap.congr_fun (normal_order_four a b i j) (create k (1 : Space Q)) + simp only [Module.End.mul_apply,LinearMap.add_apply,LinearMap.sub_apply, + LinearMap.smul_apply,Module.End.one_apply,annihilate_create_vacuum,map_smul, + annihilate_vacuum,smul_zero,map_zero,add_zero,smul_smul] at h + rw [h] + module + +theorem pairEnd_three_create (Q : ℕ) (c : Fin (Q+1) → Fin (Q+1) → ℂ) + (i j k : Fin (Q+1)) : + pairEnd Q c (create i (create j (create k (1 : Space Q)))) = + (c i j-c j i) • create k (1 : Space Q) - + (c i k-c k i) • create j (1 : Space Q) + + (c j k-c k j) • create i (1 : Space Q) := by + simp only [pairEnd,LinearMap.sum_apply,LinearMap.smul_apply,Module.End.mul_apply, + two_annihilate_three_create,smul_add,smul_sub,smul_smul] + simp [delta,mul_sub,sub_smul,mul_ite,ite_smul, + Finset.sum_sub_distrib,Finset.sum_add_distrib] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/Descendants.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/Descendants.lean new file mode 100644 index 0000000000000000000000000000000000000000..98461fd32e9e0c4f4265527adbc8cdbd3791ebbd --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/Descendants.lean @@ -0,0 +1,54 @@ +import OAI.Analysis.Laughlin.ThreeBody.HighestEigen + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +theorem threeGram_transpose (Q : ℕ) : (threeGram Q)ᵀ = threeGram Q := by + ext a b + simp only [Matrix.transpose_apply,threeGram_entry] + have hd : (if b=a then (1 : ℝ) else 0) = (if a=b then 1 else 0) := by + by_cases h : a=b + · simp [h] + · simp [h,Ne.symm h] + rw [hd] + congr 2 + apply Finset.sum_congr rfl + intro t ht + ring + +theorem threeGram_lowering (Q : ℕ) (hQ : 0 < Q) : + threeGram Q * (totalRaise (2*Q-2) Q)ᵀ = (totalRaise (2*Q-2) Q)ᵀ * threeGram Q := by + have h := congrArg Matrix.transpose (threeGram_raising Q hQ) + simpa only [Matrix.transpose_mul,threeGram_transpose] using h.symm + +noncomputable def coupledDescendant (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) (n : ℕ) : + PairOrbitalIndex Q → ℝ := + ((totalRaise (2*Q-2) Q)ᵀ ^ n) *ᵥ coupledHighest Q z hQ hz + +theorem coupledDescendant_succ (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) (n : ℕ) : + coupledDescendant Q z hQ hz (n+1) = + (totalRaise (2*Q-2) Q)ᵀ *ᵥ coupledDescendant Q z hQ hz n := by + simp only [coupledDescendant,pow_succ',Matrix.mulVec_mulVec] + +theorem threeGram_descendant_eigen (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) (n : ℕ) : + threeGram Q *ᵥ coupledDescendant Q z hQ hz n = + (1+gramEigenvalueFormula Q z) • coupledDescendant Q z hQ hz n := by + induction n with + | zero => simpa [coupledDescendant] using threeGram_highest_eigen Q z hQ hz + | succ n ih => + rw [coupledDescendant_succ,Matrix.mulVec_mulVec,threeGram_lowering Q (by omega), + ← Matrix.mulVec_mulVec,ih,Matrix.mulVec_smul] + +theorem threeGram_sub_one_descendant_eigen (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) (n : ℕ) : + (threeGram Q-1) *ᵥ coupledDescendant Q z hQ hz n = + gramEigenvalueFormula Q z • coupledDescendant Q z hQ hz n := by + rw [Matrix.sub_mulVec,threeGram_descendant_eigen,Matrix.one_mulVec] + funext i + simp only [Pi.sub_apply,Pi.smul_apply,smul_eq_mul] + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/FockBudget.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/FockBudget.lean new file mode 100644 index 0000000000000000000000000000000000000000..1957a5371255ba2da1830648ec284606f3edf4a3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/FockBudget.lean @@ -0,0 +1,49 @@ +import OAI.Analysis.Laughlin.ThreeBody.FockComparison + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory Filter +open scoped BigOperators Matrix + +theorem complexThreeGram_sub_one_spectral (Q : ℕ) (hQ : 2 ≤ Q) : + complexThreeGram Q-1 = ∑ z : Fin (Q+1), (gramEigenvalueFormula Q z.val : ℂ) • + (threeSpinProjector Q hQ z).map Complex.ofReal := by + ext i j + have h := congrArg Complex.ofReal (congrFun (congrFun (source_threeBody_spectral_decomposition Q hQ) i) j) + simpa only [Matrix.sub_apply,Matrix.sum_apply,Matrix.smul_apply,smul_eq_mul, + Complex.ofReal_sub,Complex.ofReal_sum,Complex.ofReal_mul,Matrix.one_apply, + apply_ite,Complex.ofReal_one,Complex.ofReal_zero,complexThreeGram,Matrix.map_apply] using h + +theorem physical_threeBody_budget_eventually : + ∀ᶠ Q : ℕ in atTop, ∃ _ : 15 ≤ Q, ∀ x : Space Q, + (2*Q-2+1 : ℕ) * (∫ g, contractionForm Q (sourceThreeEnd Q) + ((physicalThreeBodyMatrix Q).map Complex.ofReal) (exteriorRotation Q g⁻¹ x) ∂sourceHaar).re - + deltaFormula Q * sourceFockEnergy Q x ≤ + (contractionForm Q (sourceThreeEnd Q) (complexThreeGram Q-1) x).re := by + filter_upwards [physical_threeBody_Fock_comparison_eventually] with Q h + obtain ⟨hQ,h⟩ := h + refine ⟨hQ,fun x => ?_⟩ + have hlo := h x + have htail := physical_threeBody_tail_sum Q (by omega) x + rw [complexThreeGram_sub_one_spectral Q (by omega),contractionForm_sum,Complex.re_sum] + simp only [contractionForm_smul,Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im,zero_mul,sub_zero] + let f := fun z : Fin (Q+1) => gramEigenvalueFormula Q z.val * + (contractionForm Q (sourceThreeEnd Q) ((threeSpinProjector Q (by omega) z).map Complex.ofReal) x).re + have he : (∑ z, f z) = (∑ z, if z.val ≤ 15 then f z else 0) + + (∑ z, if 16 ≤ z.val then f z else 0) := by + rw [← Finset.sum_add_distrib] + apply Finset.sum_congr rfl + intro z hz + by_cases h15 : z.val ≤ 15 + · simp [h15,show ¬16 ≤ z.val by omega] + · simp [h15,show 16 ≤ z.val by omega] + change _ ≤ ∑ z, f z + rw [he] + change _ ≤ ∑ z, if z.val ≤ 15 then f z else 0 at hlo + change _ ≤ ∑ z, if 16 ≤ z.val then f z else 0 at htail + linarith + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/FockComparison.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/FockComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..75d4d2de565952ae229429e0e604927a733b9418 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/FockComparison.lean @@ -0,0 +1,80 @@ +import OAI.Analysis.Laughlin.ThreeBody.FockNull +import OAI.Analysis.Laughlin.ThreeBody.FockTail +import OAI.Analysis.Laughlin.ThreeBody.TraceComparison + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory Filter +open scoped BigOperators Matrix + +theorem physicalThreeBodyTraceFormula_high (Q z : ℕ) (hz : 15 < z) : + physicalThreeBodyTraceFormula Q z=0 := by + have he (t : ℕ) : (List.range 16).filter (fun T => max z t ≤ T) = [] := by + apply List.filter_eq_nil_iff.mpr + intro T hT + simp only [List.mem_range] at hT + simp only [decide_eq_true_eq,max_le_iff] + omega + simp only [physicalThreeBodyTraceFormula,threeBodyTraceFormula,he,List.map_nil,List.sum_nil, + List.map_const',List.sum_replicate,nsmul_zero] + +theorem physical_threeBody_Fock_haar_real (Q : ℕ) (hQ : 15 ≤ Q) (x : Space Q) : + (∫ g, contractionForm Q (sourceThreeEnd Q) ((physicalThreeBodyMatrix Q).map Complex.ofReal) + (exteriorRotation Q g⁻¹ x) ∂sourceHaar).re = + ∑ z : Fin (Q+1), (physicalThreeBodyTraceFormula Q z.val/(coupledWeight Q z.val+1 : ℕ)) * + (contractionForm Q (sourceThreeEnd Q) ((threeSpinProjector Q (by omega) z).map Complex.ofReal) x).re := by + rw [physical_threeBody_Fock_haar Q hQ,Complex.re_sum] + apply Finset.sum_congr rfl + intro z hz + rw [← Complex.ofReal_natCast,← Complex.ofReal_div] + simp only [Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im,zero_mul,sub_zero] + +theorem physical_threeBody_Fock_comparison_eventually : + ∀ᶠ Q : ℕ in atTop, ∃ hQ : 15 ≤ Q, ∀ x : Space Q, + (2*Q-2+1 : ℕ) * (∫ g, contractionForm Q (sourceThreeEnd Q) + ((physicalThreeBodyMatrix Q).map Complex.ofReal) (exteriorRotation Q g⁻¹ x) ∂sourceHaar).re ≤ + ∑ z : Fin (Q+1), if z.val ≤ 15 then gramEigenvalueFormula Q z.val * + (contractionForm Q (sourceThreeEnd Q) + ((threeSpinProjector Q (by omega) z).map Complex.ofReal) x).re else 0 := by + filter_upwards [source_threeBody_physical_traces_strict_eventually] with Q h + obtain ⟨hQ,hs⟩ := h + refine ⟨hQ,fun x => ?_⟩ + rw [physical_threeBody_Fock_haar_real Q hQ,Finset.mul_sum] + apply Finset.sum_le_sum + intro z hz + by_cases h15 : z.val ≤ 15 + · rw [ite_eq_left h15] + by_cases hn : z.val=0 ∨ z.val=1 ∨ z.val=3 + · rw [physical_threeBody_Fock_null Q (by omega) z hn] + simp + · have hm : z.val ∈ [2,4,5,6,7,8,9,10,11,12,13,14,15] := by + simp only [List.mem_cons] + omega + have ht := hs z hm + rw [source_physical_threeBody_trace_identity Q hQ] at ht + have hr := threeBody_dimension_ratio Q z.val (by omega) (by omega) + change _ = threeBodyDimensionRatio Q z.val at hr + rw [← hr] at ht + have ha : (0 : ℝ) < (2*Q-2+1 : ℕ) := by positivity + have hd : (0 : ℝ) < (coupledWeight Q z.val+1 : ℕ) := by positivity + have hc : (2*Q-2+1 : ℕ) * + (physicalThreeBodyTraceFormula Q z.val/(coupledWeight Q z.val+1 : ℕ)) ≤ + gramEigenvalueFormula Q z.val := by + rw [← mul_div_assoc] + apply (div_le_iff₀ hd).mpr + have hh := mul_lt_mul_of_pos_left ht ha + have he : ((2*Q-2+1 : ℕ) : ℝ) * + (((coupledWeight Q z.val+1 : ℕ)/(2*Q-2+1 : ℕ) : ℝ) * gramEigenvalueFormula Q z.val) = + gramEigenvalueFormula Q z.val*(coupledWeight Q z.val+1 : ℕ) := by + field_simp + rw [he] at hh + exact hh.le + simpa only [mul_assoc] using mul_le_mul_of_nonneg_right hc + (physical_threeBody_projector_nonneg Q (by omega) z x) + · rw [ite_eq_right h15,physicalThreeBodyTraceFormula_high Q z.val (by omega)] + simp + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/FockHaar.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/FockHaar.lean new file mode 100644 index 0000000000000000000000000000000000000000..731a4aadf2b30df9fca76ceaa8daa5e5d3ba8c05 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/FockHaar.lean @@ -0,0 +1,50 @@ +import OAI.Analysis.Laughlin.Pair.FockHaar +import OAI.Analysis.Laughlin.ThreeBody.HaarNormalization + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory +open scoped BigOperators Matrix Kronecker + +noncomputable def sourceThreeEnd (Q : ℕ) (i : PairOrbitalIndex Q) : Module.End ℂ (Space Q) := + annihilate i.2 * sourcePairEnd Q i.1.val + +noncomputable def sourceThreeVector (Q : ℕ) (i : PairOrbitalIndex Q) : Space Q := + sourcePairVector Q i.1.val * create i.2 (1 : Space Q) + +theorem sourceThreeVector_adjoint (Q : ℕ) (i : PairOrbitalIndex Q) (x y : Space Q) : + occupationInner Q (sourceThreeVector Q i*x) y = + occupationInner Q x (sourceThreeEnd Q i y) := by + have he : sourceThreeVector Q i*x = sourcePairVector Q i.1.val * create i.2 x := by + change (sourcePairVector Q i.1.val * (ExteriorAlgebra.ι ℂ (mode i.2)*1))*x = + sourcePairVector Q i.1.val * (ExteriorAlgebra.ι ℂ (mode i.2)*x) + simp only [mul_one,mul_assoc] + rw [he,sourcePairVector_adjoint,create_annihilate_adjoint] + rfl + +theorem sourceThreeEnd_rotation (Q : ℕ) (hQ : 0 < Q) (g : SourceSU2) + (i : PairOrbitalIndex Q) (x : Space Q) : + sourceThreeEnd Q i (exteriorRotation Q g x) = + ∑ j, threeBodySpinRepresentation Q g i j • exteriorRotation Q g (sourceThreeEnd Q j x) := by + simp only [sourceThreeEnd,Module.End.mul_apply,sourcePairEnd_rotation Q hQ g, + map_sum,map_smul,annihilate_exteriorRotation,Finset.smul_sum,smul_smul] + simp only [threeBodySpinRepresentation,MonoidHom.coe_mk,OneHom.coe_mk, + Matrix.kroneckerMap,Matrix.of_apply,Fintype.sum_prod_type] + +theorem physical_threeBody_Fock_haar (Q : ℕ) (hQ : 15 ≤ Q) (x : Space Q) : + (∫ g, contractionForm Q (sourceThreeEnd Q) ((physicalThreeBodyMatrix Q).map Complex.ofReal) + (exteriorRotation Q g⁻¹ x) ∂sourceHaar) = + ∑ z : Fin (Q+1), + ((physicalThreeBodyTraceFormula Q z.val : ℂ)/(coupledWeight Q z.val+1 : ℕ)) * + contractionForm Q (sourceThreeEnd Q) + ((threeSpinProjector Q (by omega) z).map Complex.ofReal) x := by + rw [contractionForm_haar Q (threeBodySpinRepresentation Q) + (threeBodySpinRepresentation_inv Q) (threeBodySpinRepresentation_continuous Q) + _ (sourceThreeEnd_rotation Q (by omega)),physical_threeBody_certificate_haar Q hQ, + contractionForm_sum] + simp only [contractionForm_smul] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/FockNull.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/FockNull.lean new file mode 100644 index 0000000000000000000000000000000000000000..7ff1e4c4597002b3015134fe7a7adf906517eb3d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/FockNull.lean @@ -0,0 +1,51 @@ +import OAI.Analysis.Laughlin.ThreeBody.FockHaar +import OAI.Analysis.Laughlin.ThreeBody.NullSectors + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin +open scoped BigOperators Matrix + +theorem threeBodyColumn_sourceThreeVector (Q : ℕ) (i : PairOrbitalIndex Q) : + threeBodyColumn Q i.1.val i.2 = sourceThreeVector Q i := by + rw [threeBodyColumn,sourcePairCreateEnd_mul] + rfl + +theorem threeWedge_contraction_zero (Q : ℕ) (v : PairOrbitalIndex Q → ℂ) + (hv : threeWedge Q v=0) (x : Space Q) : + (∑ i, star (v i) • sourceThreeEnd Q i x)=0 := by + apply occupationInner_ext_right Q + intro y + have h : occupationInner Q (threeWedge Q v*y) x = + occupationInner Q y (∑ i, star (v i) • sourceThreeEnd Q i x) := by + simp only [threeWedge,Finset.sum_mul,smul_mul_assoc,occupationInner_sum_left, + occupationInner_smul_left,threeBodyColumn_sourceThreeVector,sourceThreeVector_adjoint, + occupationInner_sum_right,occupationInner_smul_right] + rw [← h,hv,zero_mul] + simp [occupationInner] + +theorem physical_threeBody_Fock_null (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) + (hz : z.val=0 ∨ z.val=1 ∨ z.val=3) (x : Space Q) : + contractionForm Q (sourceThreeEnd Q) ((threeSpinProjector Q hQ z).map Complex.ofReal) x = 0 := by + let R := (threeSpinProjector Q hQ z).map Complex.ofReal + have hc (j : PairOrbitalIndex Q) : (∑ i, star (R i j) • sourceThreeEnd Q i x)=0 := by + apply threeWedge_contraction_zero + have h := source_threeBody_null_sectors Q hQ z hz (Pi.single j 1) + have he : complexThreeSpinProjector Q hQ z *ᵥ Pi.single j 1 = (fun i => R i j) := by + funext i + simp [Matrix.mulVec,dotProduct,Pi.single_apply,complexThreeSpinProjector,R] + rw [he] at h + exact h + have he : contractionForm Q (sourceThreeEnd Q) R x = + ∑ j, occupationInner Q (∑ i, star (R i j) • sourceThreeEnd Q i x) (sourceThreeEnd Q j x) := by + simp only [contractionForm,occupationInner_sum_left,occupationInner_smul_left,star_star] + rw [Finset.sum_comm] + change contractionForm Q (sourceThreeEnd Q) R x=0 + rw [he] + simp only [hc] + simp [occupationInner] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/FockTail.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/FockTail.lean new file mode 100644 index 0000000000000000000000000000000000000000..fb57e6bc0ce5f54c17e88fda4049095183868473 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/FockTail.lean @@ -0,0 +1,85 @@ +import OAI.Analysis.Laughlin.Asymptotics.FiniteReindex +import OAI.Analysis.Laughlin.ThreeBody.ProjectorBound + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory +open scoped BigOperators Matrix + +theorem threeBody_dimension_ratio (Q z : ℕ) (hQ : 4 ≤ Q) (hz : z ≤ Q) : + ((coupledWeight Q z+1 : ℕ)/(2*Q-2+1 : ℕ) : ℝ) = + (3*(Q : ℝ)-1-2*(z : ℝ))/(2*(Q : ℝ)-1) := by + have hn : ((coupledWeight Q z+1 : ℕ) : ℝ)=3*(Q : ℝ)-1-2*(z : ℝ) := by + unfold coupledWeight + rw [Nat.cast_add,Nat.cast_sub (by omega : 2*z ≤ 3*Q-2), + Nat.cast_sub (by omega : 2 ≤ 3*Q)] + push_cast + ring + have hd : ((2*Q-2+1 : ℕ) : ℝ)=2*(Q : ℝ)-1 := by + rw [Nat.cast_add,Nat.cast_sub (by omega : 2 ≤ 2*Q)] + push_cast + ring + rw [hn,hd] + +theorem physical_threeBody_tail_sum (Q : ℕ) (hQ : 4 ≤ Q) (x : Space Q) : + -(deltaFormula Q * sourceFockEnergy Q x) ≤ + ∑ z : Fin (Q+1), if 16 ≤ z.val then gramEigenvalueFormula Q z.val * + (contractionForm Q (sourceThreeEnd Q) + ((threeSpinProjector Q (by omega) z).map Complex.ofReal) x).re else 0 := by + let P := fun z : Fin (Q+1) => (contractionForm Q (sourceThreeEnd Q) + ((threeSpinProjector Q (by omega) z).map Complex.ofReal) x).re + have hP (z : Fin (Q+1)) : 0 ≤ P z := physical_threeBody_projector_nonneg Q (by omega) z x + have hb (z : Fin (Q+1)) : P z ≤ + ((3*(Q : ℝ)-1-2*(z.val : ℝ))/(2*(Q : ℝ)-1))* + (z.val+1 : ℕ)*sourceFockEnergy Q x := by + simpa only [threeBody_dimension_ratio Q z.val hQ (by omega)] using + physical_threeBody_projector_bound Q (by omega) z x + have ht (z : Fin (Q+1)) : + -(if 17 ≤ z.val ∧ Odd z.val then tailWeight Q z.val else 0) * sourceFockEnergy Q x ≤ + if 16 ≤ z.val then gramEigenvalueFormula Q z.val * P z else 0 := by + by_cases hz : 16 ≤ z.val + · rw [ite_eq_left hz] + by_cases ho : Odd z.val + · have hz17 : 17 ≤ z.val := by obtain ⟨k,hk⟩ := ho; omega + rw [ite_eq_left ⟨hz17,ho⟩] + have h₁ := mul_le_mul_of_nonneg_left (hb z) (abs_nonneg (gramEigenvalueFormula Q z.val)) + have h₂ := mul_le_mul_of_nonneg_right (neg_abs_le (gramEigenvalueFormula Q z.val)) (hP z) + unfold tailWeight + push_cast at h₁ ⊢ + nlinarith + · rw [ite_eq_right (by tauto)] + have he : Even z.val := Nat.not_odd_iff_even.mp ho + have hpow : (-1 : ℝ)^z.val=1 := he.neg_one_pow + have hg : 0 ≤ gramEigenvalueFormula Q z.val := by + unfold gramEigenvalueFormula + rw [hpow,one_mul] + exact mul_nonneg (by unfold fallingRatio; positivity) (tail_bracket_bounds hQ hz (by omega)).1 + simpa using mul_nonneg hg (hP z) + · have hn : ¬ (17 ≤ z.val ∧ Odd z.val) := by omega + simp only [ite_eq_right hz,ite_eq_right hn,neg_zero,zero_mul,le_refl] + have hs : (∑ z : Fin (Q+1), if 17 ≤ z.val ∧ Odd z.val then tailWeight Q z.val else 0)=deltaFormula Q := by + rw [Fin.sum_univ_eq_sum_range (fun z => if 17 ≤ z ∧ Odd z then tailWeight Q z else 0) (Q+1), + ← Finset.sum_filter,← deltaFormula_eq_odd_finite_sum] + have h := Finset.sum_le_sum (s := Finset.univ) (fun z hz => ht z) + simpa only [← Finset.sum_mul,Finset.sum_neg_distrib,hs,neg_mul] using h + +theorem physical_threeBody_Fock_tail (Q : ℕ) (hQ : 4 ≤ Q) (x : Space Q) : + -(deltaFormula Q * sourceFockEnergy Q x) ≤ + (contractionForm Q (sourceThreeEnd Q) + (∑ z : Fin (Q+1), if 16 ≤ z.val then (gramEigenvalueFormula Q z.val : ℂ) • + (threeSpinProjector Q (by omega) z).map Complex.ofReal else 0) x).re := by + rw [contractionForm_sum,Complex.re_sum] + have hz : contractionForm Q (sourceThreeEnd Q) (0 : Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℂ) x=0 := by + simp [contractionForm] + apply (physical_threeBody_tail_sum Q hQ x).trans_eq + apply Finset.sum_congr rfl + intro z hz' + by_cases h16 : 16 ≤ z.val + · simp only [ite_eq_left h16,contractionForm_smul,Complex.mul_re, + Complex.ofReal_re,Complex.ofReal_im,zero_mul,sub_zero] + · simp only [ite_eq_right h16,hz,Complex.zero_re] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/Gram.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/Gram.lean new file mode 100644 index 0000000000000000000000000000000000000000..1933d10bc7751b92bf6689a3578362d48e8c87d2 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/Gram.lean @@ -0,0 +1,43 @@ +import OAI.Analysis.Laughlin.ThreeBody.PairAction + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem occupationInner_sub_right (Q : ℕ) (x y z : Space Q) : + occupationInner Q x (y-z) = occupationInner Q x y-occupationInner Q x z := by + simp [occupationInner,mul_sub,Finset.sum_sub_distrib] + +theorem occupationInner_oneMode (Q : ℕ) (i j : Fin (Q+1)) : + occupationInner Q (create i (1 : Space Q)) (create j (1 : Space Q)) = + if i = j then 1 else 0 := by + have h (k : Fin (Q+1)) : create k (1 : Space Q) = occupationBasis Q {k} := by + rw [occupation_singleton] + simp [create] + rw [h i,h j] + simp [occupationInner,Module.Basis.repr_self,Finsupp.single_apply] + +theorem threeBodyColumn_gram (Q p q : ℕ) (hQ : 2 ≤ Q) (hp : p ≤ 2*Q-2) + (i j : Fin (Q+1)) : + occupationInner Q (threeBodyColumn Q p i) (threeBodyColumn Q q j) = + (if p = q then (1 : ℂ) else 0)*(if i = j then (1 : ℂ) else 0) - + 2 * ∑ t, (pairCoefficient Q p j t : ℂ)*(pairCoefficient Q q i t : ℂ) := by + rw [threeBodyColumn,sourcePairCreateEnd,pairCreate_pair_adjoint] + change occupationInner Q (create i (1 : Space Q)) + (sourcePairEnd Q p (threeBodyColumn Q q j)) = _ + rw [sourcePair_threeBodyColumn Q p q hQ hp j,occupationInner_sub_right, + occupationInner_smul_right,occupationInner_smul_right] + simp only [occupationInner_sum_right,occupationInner_smul_right,occupationInner_oneMode] + simp only [mul_ite,mul_one,mul_zero] + congr 2 + apply Finset.sum_congr rfl + intro t ht + simp only [Finset.sum_ite_eq,Finset.mem_univ,ite_true] + rw [pairCoefficient_swap Q q i t,pairCoefficient_swap Q p j t] + push_cast + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/GramSlice.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/GramSlice.lean new file mode 100644 index 0000000000000000000000000000000000000000..ec52e048deb009f170ddf93eec2c06736d6b1c6d --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/GramSlice.lean @@ -0,0 +1,69 @@ +import OAI.Analysis.Laughlin.Pair.PolynomialBridge +import OAI.Analysis.Laughlin.ThreeBody.Gram + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +noncomputable def sliceOrbital (Q z : ℕ) (hz : z ≤ Q) (p : Fin (z+1)) : Fin (Q+1) := + ⟨z-p.val,by omega⟩ + +noncomputable def threeBodyGramSlice (Q z : ℕ) (hz : z ≤ Q) + (p q : Fin (z+1)) : ℝ := + (if p = q then 1 else 0) - 2*∑ t : Fin (Q+1), + pairCoefficient Q p.val (sliceOrbital Q z hz q) t * + pairCoefficient Q q.val (sliceOrbital Q z hz p) t + +theorem threeBodyGramSlice_physical (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) + (p q : Fin (z+1)) : + (threeBodyGramSlice Q z hz p q : ℂ) = + occupationInner Q (threeBodyColumn Q p.val (sliceOrbital Q z hz p)) + (threeBodyColumn Q q.val (sliceOrbital Q z hz q)) := by + rw [threeBodyColumn_gram Q p.val q.val hQ (by omega)] + unfold threeBodyGramSlice + push_cast + congr 1 + by_cases h : p = q + · subst q; simp + · have hv : p.val ≠ q.val := by simpa only [Fin.ext_iff] using h + simp [h,hv] + +theorem pairCoefficient_base (Q : ℕ) (hQ : 2 ≤ Q) (x y : Fin (Q+1)) : + pairCoefficient Q 0 x y = + if x.val = 0 ∧ y.val = 1 then -(1/Real.sqrt 2) else + if x.val = 1 ∧ y.val = 0 then 1/Real.sqrt 2 else 0 := by + rw [pairCoefficient_choose Q 0 (by omega) (by omega)] + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (by omega : Q ≠ 0) + have hr : (Q : ℝ)/(2*Q) = 1/2 := by field_simp + by_cases hs : x.val+y.val=1 + · have hc : (x.val=0 ∧ y.val=1) ∨ (x.val=1 ∧ y.val=0) := by omega + rcases hc with ⟨hx,hy⟩ | ⟨hx,hy⟩ + · simp [hx,hy,hr] + · simp [hx,hy,hr] + · have h₀ : ¬(x.val=0 ∧ y.val=1) := by omega + have h₁ : ¬(x.val=1 ∧ y.val=0) := by omega + rw [ite_eq_right hs,ite_eq_right h₀,ite_eq_right h₁] + +theorem swap_base_row (Q q : ℕ) (hQ : 2 ≤ Q) (i j : Fin (Q+1)) : + (∑ t : Fin (Q+1), pairCoefficient Q 0 j t * pairCoefficient Q q i t) = + if j.val=0 then -pairCoefficient Q q i ⟨1,by omega⟩ / Real.sqrt 2 else + if j.val=1 then pairCoefficient Q q i ⟨0,by omega⟩ / Real.sqrt 2 else 0 := by + simp_rw [pairCoefficient_base Q hQ] + have ht₀ (t : Fin (Q+1)) : t.val=0 ↔ t=(⟨0,Nat.zero_lt_succ Q⟩ : Fin (Q+1)) := by + constructor + · intro h; exact Fin.ext h + · intro h; exact congrArg Fin.val h + have ht₁ (t : Fin (Q+1)) : t.val=1 ↔ t=(⟨1,Nat.lt_succ_of_le (le_trans (by decide : 1 ≤ 2) hQ)⟩ : Fin (Q+1)) := by + constructor + · intro h; exact Fin.ext h + · intro h; exact congrArg Fin.val h + by_cases hj₀ : j.val=0 + · simp [hj₀,ht₁]; ring + · by_cases hj₁ : j.val=1 + · simp [hj₁,ht₀]; ring + · simp [hj₀,hj₁] + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/GroupIntertwining.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/GroupIntertwining.lean new file mode 100644 index 0000000000000000000000000000000000000000..da12a367bdd48e967bc0c2339196eefdfbd35155 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/GroupIntertwining.lean @@ -0,0 +1,44 @@ +import OAI.Analysis.Laughlin.Spin.Intertwining +import OAI.Analysis.Laughlin.Spin.Specializations +import OAI.Analysis.Laughlin.ThreeBody.SpinProjectors + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix Kronecker + +noncomputable def threeCoupledInclusion (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) : + Matrix (PairOrbitalIndex Q) (Fin (coupledWeight Q z.val+1)) ℂ := + fun i n => (normalizedCoupledDescendant Q z.val hQ (by omega) n.val i : ℂ) + +theorem threeCoupledInclusion_SU2 (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) + (g : Rotation.SourceSU2) : + (Rotation.sourceSpinRepresentation (2*Q-2) g ⊗ₖ Rotation.sourceSpinRepresentation Q g)* + threeCoupledInclusion Q hQ z = + threeCoupledInclusion Q hQ z*Rotation.sourceSpinRepresentation (coupledWeight Q z.val) g := by + have hw : genericCoupledWeight (2*Q-2) Q z.val = coupledWeight Q z.val := by + unfold genericCoupledWeight coupledWeight + omega + have h := genericCoupledInclusion_SU2 (2*Q-2) Q z.val (by omega) (by omega) g + unfold genericCoupledInclusion at h + simp only [genericUnitDescendant_threeBody Q z.val _ hQ] at h + rw [hw] at h + exact h + +theorem threeSpinProjector_complex_factor (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) : + (threeSpinProjector Q hQ z).map Complex.ofReal = + threeCoupledInclusion Q hQ z*(threeCoupledInclusion Q hQ z)ᴴ := by + funext i j + change (↑(∑ s, (coupledBasisMatrix Q hQ * coupledSelector Q z) i s * + coupledBasisMatrix Q hQ j s) : ℂ) = _ + simp only [coupledSelector,Matrix.mul_diagonal] + simp only [Matrix.mul_apply,Matrix.conjTranspose_apply,threeCoupledInclusion, + Complex.star_def,Complex.conj_ofReal] + rw [Fintype.sum_sigma] + simp only [mul_ite,mul_one,mul_zero,ite_mul,zero_mul,Finset.sum_ite_irrel, + Finset.sum_const_zero,Finset.sum_ite_eq',Finset.mem_univ,ite_true,Complex.ofReal_sum, + Complex.ofReal_mul,coupledBasisMatrix] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/HaarBlocks.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/HaarBlocks.lean new file mode 100644 index 0000000000000000000000000000000000000000..8f6b010444e22ec8f1b3bf0b1849d21f6cc6d956 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/HaarBlocks.lean @@ -0,0 +1,91 @@ +import OAI.Analysis.Laughlin.Spin.HaarOrthogonality +import OAI.Analysis.Laughlin.Spin.Sandwich +import OAI.Analysis.Laughlin.ThreeBody.GroupIntertwining + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix Kronecker +open Rotation MeasureTheory + +noncomputable def threeBodySpinRepresentation (Q : ℕ) : + SourceSU2 →* Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℂ where + toFun g := sourceSpinRepresentation (2*Q-2) g ⊗ₖ sourceSpinRepresentation Q g + map_one' := by simp only [map_one,Matrix.one_kronecker_one] + map_mul' g h := by simp only [map_mul,Matrix.mul_kronecker_mul] + +theorem threeBodySpinRepresentation_continuous (Q : ℕ) (i j : PairOrbitalIndex Q) : + Continuous (fun g => threeBodySpinRepresentation Q g i j) := + (sourceSpinRepresentation_continuous (2*Q-2) i.1 j.1).mul + (sourceSpinRepresentation_continuous Q i.2 j.2) + +theorem threeBodySpinRepresentation_inv (Q : ℕ) (g : SourceSU2) : + threeBodySpinRepresentation Q g⁻¹=(threeBodySpinRepresentation Q g)ᴴ := by + change _ ⊗ₖ _ = (_ ⊗ₖ _)ᴴ + rw [Matrix.conjTranspose_kronecker,sourceSpinRepresentation_inv,sourceSpinRepresentation_inv] + +theorem threeCoupledInclusion_adjoint_SU2 (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) + (g : SourceSU2) : + (threeCoupledInclusion Q hQ z)ᴴ * threeBodySpinRepresentation Q g = + sourceSpinRepresentation (coupledWeight Q z.val) g * (threeCoupledInclusion Q hQ z)ᴴ := by + have h : threeBodySpinRepresentation Q g⁻¹ * threeCoupledInclusion Q hQ z = + threeCoupledInclusion Q hQ z * sourceSpinRepresentation (coupledWeight Q z.val) g⁻¹ := + threeCoupledInclusion_SU2 Q hQ z g⁻¹ + have ht := congrArg Matrix.conjTranspose h + simpa only [Matrix.conjTranspose_mul,threeBodySpinRepresentation_inv,sourceSpinRepresentation_inv, + Matrix.conjTranspose_conjTranspose] using ht + +theorem threeBody_haar_compressed (Q : ℕ) (hQ : 2 ≤ Q) (z w : Fin (Q+1)) + (M : Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℂ) : + (threeCoupledInclusion Q hQ z)ᴴ * matrixIntegral sourceHaar + (conjugateOrbit (threeBodySpinRepresentation Q) M) * threeCoupledInclusion Q hQ w = + rectangularIntegral sourceHaar (rectangularOrbit + (sourceSpinRepresentation (coupledWeight Q z.val)) + (sourceSpinRepresentation (coupledWeight Q w.val)) + ((threeCoupledInclusion Q hQ z)ᴴ*M*threeCoupledInclusion Q hQ w)) := by + change (threeCoupledInclusion Q hQ z)ᴴ * entrywiseIntegral sourceHaar + (conjugateOrbit (threeBodySpinRepresentation Q) M) * threeCoupledInclusion Q hQ w = _ + rw [← integral_matrix_sandwich sourceHaar _ + (compact_conjugateOrbit_integrable sourceHaar _ (threeBodySpinRepresentation_continuous Q) M)] + funext i j + apply integral_congr_ae + filter_upwards [] with g + have hw : threeBodySpinRepresentation Q g⁻¹*threeCoupledInclusion Q hQ w = + threeCoupledInclusion Q hQ w*sourceSpinRepresentation (coupledWeight Q w.val) g⁻¹ := + threeCoupledInclusion_SU2 Q hQ w g⁻¹ + simp only [conjugateOrbit,rectangularOrbit] + rw [← Matrix.mul_assoc,← Matrix.mul_assoc,threeCoupledInclusion_adjoint_SU2, + Matrix.mul_assoc,Matrix.mul_assoc,hw] + simp only [Matrix.mul_assoc] + +theorem threeBody_haar_diagonal_block (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) + (M : Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℂ) : + (threeCoupledInclusion Q hQ z)ᴴ * matrixIntegral sourceHaar + (conjugateOrbit (threeBodySpinRepresentation Q) M) * threeCoupledInclusion Q hQ z = + (Matrix.trace ((threeSpinProjector Q hQ z).map Complex.ofReal*M)/ + (coupledWeight Q z.val+1 : ℕ)) • 1 := by + rw [threeBody_haar_compressed,source_equal_spin_haar_trace] + congr 2 + rw [threeSpinProjector_complex_factor] + calc + _ = Matrix.trace (threeCoupledInclusion Q hQ z*((threeCoupledInclusion Q hQ z)ᴴ*M)) := + Matrix.trace_mul_comm _ _ + _ = _ := by simp only [Matrix.mul_assoc] + +theorem threeBody_haar_offdiagonal_block (Q : ℕ) (hQ : 2 ≤ Q) (z w : Fin (Q+1)) + (hzw : z ≠ w) (M : Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℂ) : + (threeCoupledInclusion Q hQ z)ᴴ * matrixIntegral sourceHaar + (conjugateOrbit (threeBodySpinRepresentation Q) M) * threeCoupledInclusion Q hQ w = 0 := by + rw [threeBody_haar_compressed] + apply source_unequal_spin_haar_zero + intro h + apply hzw + apply Fin.ext + unfold coupledWeight at h + have hz := z.isLt + have hw := w.isLt + omega + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/HaarNormalization.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/HaarNormalization.lean new file mode 100644 index 0000000000000000000000000000000000000000..cfcb211a75d74485868137d57648ff99b73b9aff --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/HaarNormalization.lean @@ -0,0 +1,68 @@ +import OAI.Analysis.Laughlin.ThreeBody.HaarBlocks +import OAI.Analysis.Laughlin.ThreeBody.PhysicalTrace + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix +open Rotation + +theorem threeSpinProjector_complex_sum (Q : ℕ) (hQ : 2 ≤ Q) : + (∑ z : Fin (Q+1), (threeSpinProjector Q hQ z).map Complex.ofReal) = 1 := by + funext i j + have h := congrArg Complex.ofReal (congrFun (congrFun (threeSpinProjector_sum Q hQ) i) j) + simpa only [Matrix.sum_apply,Matrix.map_apply,Complex.ofReal_sum,Matrix.one_apply, + apply_ite,Complex.ofReal_one,Complex.ofReal_zero] using h + +theorem physical_threeBody_haar_normalization (Q : ℕ) (hQ : 2 ≤ Q) + (M : Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℂ) : + matrixIntegral sourceHaar (conjugateOrbit (threeBodySpinRepresentation Q) M) = + ∑ z : Fin (Q+1), + (Matrix.trace ((threeSpinProjector Q hQ z).map Complex.ofReal*M)/ + (coupledWeight Q z.val+1 : ℕ)) • (threeSpinProjector Q hQ z).map Complex.ofReal := by + let H := matrixIntegral sourceHaar (conjugateOrbit (threeBodySpinRepresentation Q) M) + let R := fun z => (threeSpinProjector Q hQ z).map Complex.ofReal + have hblock (z w : Fin (Q+1)) : R z*H*R w = + if z=w then (Matrix.trace (R z*M)/(coupledWeight Q z.val+1 : ℕ)) • R z else 0 := by + change (threeSpinProjector Q hQ z).map Complex.ofReal*H* + (threeSpinProjector Q hQ w).map Complex.ofReal = _ + rw [threeSpinProjector_complex_factor,threeSpinProjector_complex_factor] + have he : threeCoupledInclusion Q hQ z*(threeCoupledInclusion Q hQ z)ᴴ*H* + (threeCoupledInclusion Q hQ w*(threeCoupledInclusion Q hQ w)ᴴ) = + threeCoupledInclusion Q hQ z* + ((threeCoupledInclusion Q hQ z)ᴴ*H*threeCoupledInclusion Q hQ w)* + (threeCoupledInclusion Q hQ w)ᴴ := by simp only [Matrix.mul_assoc] + rw [he] + by_cases hzw : z=w + · subst w + rw [ite_eq_left rfl] + change _ = (Matrix.trace ((threeSpinProjector Q hQ z).map Complex.ofReal*M)/_) • _ + rw [threeBody_haar_diagonal_block,Matrix.mul_smul,Matrix.mul_one,Matrix.smul_mul, + ← threeSpinProjector_complex_factor] + · rw [ite_eq_right hzw,threeBody_haar_offdiagonal_block Q hQ z w hzw,Matrix.mul_zero,Matrix.zero_mul] + calc + _ = (∑ z, R z)*H*(∑ w, R w) := by + change H = _ + rw [show (∑ z, R z)=1 from threeSpinProjector_complex_sum Q hQ,Matrix.one_mul,Matrix.mul_one] + _ = ∑ z, ∑ w, R z*H*R w := by rw [Matrix.sum_mul,Matrix.sum_mul]; simp only [Matrix.mul_sum] + _ = _ := by simp only [hblock,Finset.sum_ite_eq,Finset.mem_univ,ite_true,R] + +theorem complex_trace_mul_real {I : Type*} [Fintype I] (A B : Matrix I I ℝ) : + Matrix.trace (A.map Complex.ofReal * B.map Complex.ofReal) = ((Matrix.trace (A*B) : ℝ) : ℂ) := by + simp only [Matrix.trace,Matrix.diag,Matrix.mul_apply,Matrix.map_apply, + Complex.ofReal_sum,Complex.ofReal_mul] + +theorem physical_threeBody_certificate_haar (Q : ℕ) (hQ : 15 ≤ Q) : + matrixIntegral sourceHaar (conjugateOrbit (threeBodySpinRepresentation Q) + ((physicalThreeBodyMatrix Q).map Complex.ofReal)) = + ∑ z : Fin (Q+1), + ((physicalThreeBodyTraceFormula Q z.val : ℂ)/(coupledWeight Q z.val+1 : ℕ)) • + (threeSpinProjector Q (by omega) z).map Complex.ofReal := by + rw [physical_threeBody_haar_normalization Q (by omega)] + apply Finset.sum_congr rfl + intro z hz + rw [complex_trace_mul_real,source_physical_threeBody_trace_identity Q hQ] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/HighestEigen.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/HighestEigen.lean new file mode 100644 index 0000000000000000000000000000000000000000..06395b728d4199cbb73f2e8f0bf774bd12fa16f0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/HighestEigen.lean @@ -0,0 +1,88 @@ +import OAI.Analysis.Laughlin.Spin.WeightSlice +import OAI.Analysis.Laughlin.ThreeBody.HighestReadout +import OAI.Analysis.Laughlin.ThreeBody.SpinCovariance + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +noncomputable def coupledHighest (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : PairOrbitalIndex Q → ℝ := + extendWeightSlice (2*Q-2) Q z (by omega) hz (fun p => highestUnit (2*Q-2) Q z p.val) + +theorem threeGram_on_slice (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) (p q : Fin (z+1)) : + threeGram Q (weightSliceIndex (2*Q-2) Q z (by omega) hz p) + (weightSliceIndex (2*Q-2) Q z (by omega) hz q) = Fock.threeBodyGramSlice Q z hz p q := by + apply Complex.ofReal_injective + rw [threeGram_physical Q hQ,Fock.threeBodyGramSlice_physical Q z hQ hz] + rfl + +theorem threeGram_extend_off (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) + (f : Fin (z+1) → ℝ) (i : PairOrbitalIndex Q) (hi : i.1.val+i.2.val ≠ z) : + (threeGram Q *ᵥ extendWeightSlice (2*Q-2) Q z (by omega) hz f) i = 0 := by + change (∑ j, threeGram Q i j * extendWeightSlice (2*Q-2) Q z (by omega) hz f j) = 0 + rw [sum_extendWeightSlice] + apply Finset.sum_eq_zero + intro p hp + rw [threeGram_weight] + · ring + · dsimp [weightSliceIndex] + omega + +theorem threeGram_highest_eigen (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + threeGram Q *ᵥ coupledHighest Q z hQ hz = + (1+gramEigenvalueFormula Q z) • coupledHighest Q z hQ hz := by + let v := coupledHighest Q z hQ hz + let g := threeGram Q *ᵥ v + let f : Fin (z+1) → ℝ := fun p => g (weightSliceIndex (2*Q-2) Q z (by omega) hz p) + have hv : totalRaise (2*Q-2) Q *ᵥ v = 0 := by + apply extendWeightSlice_highest + intro p + exact highestUnit_raising (2*Q-2) Q z p.val (by omega) hz p.isLt + have hg : totalRaise (2*Q-2) Q *ᵥ g = 0 := by + dsimp [g] + rw [Matrix.mulVec_mulVec,← threeGram_raising Q (by omega),← Matrix.mulVec_mulVec,hv, + Matrix.mulVec_zero] + have hf : ∀ p, raiseSlice (2*Q-2) Q z f p = 0 := by + intro p + have he := congrFun hg ((⟨p.val,by omega⟩,⟨z-p.val-1,by omega⟩) : PairOrbitalIndex Q) + rw [totalRaise_below_slice (2*Q-2) Q z (by omega) hz] at he + exact he + obtain ⟨c,hc⟩ := (raiseSlice_kernel (2*Q-2) Q z (by omega) hz f).mp hf + have hfirst : f ⟨0,by omega⟩ = + (1+gramEigenvalueFormula Q z)*highestUnit (2*Q-2) Q z 0 := by + dsimp [f,g,v,coupledHighest] + change (∑ j,threeGram Q _ j*extendWeightSlice (2*Q-2) Q z (by omega) hz _ j) = _ + rw [sum_extendWeightSlice] + simp_rw [threeGram_on_slice Q z hQ hz] + exact Fock.threeBodyGram_highest_first_coordinate Q z hQ hz + have hcz : c = 1+gramEigenvalueFormula Q z := by + apply (mul_right_cancel₀ (highestUnit_ne_zero (2*Q-2) Q z 0 (by omega) hz (by omega))) + exact (hc ⟨0,by omega⟩).symm.trans hfirst + funext i + change g i = (1+gramEigenvalueFormula Q z)*v i + by_cases hi : i.1.val+i.2.val=z + · let p : Fin (z+1) := ⟨i.1.val,by omega⟩ + have he : i = weightSliceIndex (2*Q-2) Q z (by omega) hz p := by + apply Prod.ext + · rfl + · apply Fin.ext; dsimp [weightSliceIndex,p]; omega + rw [he] + change f p = (1+gramEigenvalueFormula Q z)*extendWeightSlice (2*Q-2) Q z (by omega) hz _ _ + rw [extendWeightSlice_at,hc p,hcz] + · have hg₀ : g i = 0 := threeGram_extend_off Q z hQ hz _ i hi + have hv₀ : v i = 0 := extendWeightSlice_off (2*Q-2) Q z (by omega) hz _ i hi + rw [hg₀,hv₀,mul_zero] + +theorem coupledHighest_norm (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + (∑ i : PairOrbitalIndex Q, (coupledHighest Q z hQ hz i)^2) = 1 := by + simp only [pow_two] + unfold coupledHighest + rw [sum_extendWeightSlice] + simp_rw [extendWeightSlice_at,← pow_two] + have hs := highestUnit_norm (2*Q-2) Q z (by omega) hz + simpa only [← Fin.sum_univ_eq_sum_range] using hs + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/HighestFock.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/HighestFock.lean new file mode 100644 index 0000000000000000000000000000000000000000..51c661858934b2b10843aa3c59e71f14196a68cf --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/HighestFock.lean @@ -0,0 +1,63 @@ +import OAI.Analysis.Laughlin.Fock.OrbitIntegration +import OAI.Analysis.Laughlin.Fock.RankOneHaar +import OAI.Analysis.Laughlin.Operators.WeightedOccupationNorm +import OAI.Analysis.Laughlin.ThreeBody.FockHaar + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory +open scoped BigOperators Matrix + +noncomputable def sourceThreeHighestEnd (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + Module.End ℂ (Space Q) := + ∑ p : Fin (z+1), (highestUnit (2*Q-2) Q z p.val : ℂ) • + sourceThreeEnd Q (weightSliceIndex (2*Q-2) Q z (by omega) hz p) + +theorem threeCoupledInclusion_highest (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) + (i : PairOrbitalIndex Q) : + threeCoupledInclusion Q hQ z i 0 = (coupledHighest Q z.val hQ (by omega) i : ℂ) := by + have hn : vectorNormSq (coupledHighest Q z.val hQ (by omega))=1 := + coupledHighest_norm Q z.val hQ (by omega) + simp only [threeCoupledInclusion,normalizedCoupledDescendant,coupledDescendant, + Fin.val_zero,pow_zero,Matrix.one_mulVec,hn,Real.sqrt_one,inv_one,one_smul] + +theorem sourceThreeHighestEnd_column (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (x : Space Q) : + (∑ i, star (threeCoupledInclusion Q hQ z i 0) • sourceThreeEnd Q i x) = + sourceThreeHighestEnd Q z.val hQ (by omega) x := by + simp only [threeCoupledInclusion_highest,coupledHighest,extendWeightSlice, + Complex.ofReal_sum,star_sum,Finset.sum_smul] + rw [Finset.sum_comm] + simp only [apply_ite,Complex.ofReal_zero,star_zero,Complex.star_def,Complex.conj_ofReal, + ite_smul,zero_smul,Finset.sum_ite_eq,Finset.mem_univ,ite_true,sourceThreeHighestEnd, + LinearMap.sum_apply,LinearMap.smul_apply] + +theorem sourceThreeHighestEnd_norm_bound (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) (x : Space Q) : + occupationNormSq Q (sourceThreeHighestEnd Q z hQ hz x) ≤ + ∑ p : Fin (z+1), occupationNormSq Q (sourcePairEnd Q p.val x) := by + have hn : (∑ p : Fin (z+1), (highestUnit (2*Q-2) Q z p.val)^2)=1 := by + rw [Fin.sum_univ_eq_sum_range (fun p => (highestUnit (2*Q-2) Q z p)^2) (z+1)] + exact highestUnit_norm (2*Q-2) Q z (by omega) hz + simp only [sourceThreeHighestEnd,LinearMap.sum_apply,LinearMap.smul_apply] + apply (normalized_occupation_sum_bound Q _ _ hn).trans + apply Finset.sum_le_sum + intro p hp + exact annihilate_normSq_le Q _ (sourcePairEnd Q p.val x) + +theorem sourceThreeHighestEnd_haar (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (x : Space Q) : + (coupledWeight Q z.val+1 : ℕ) * (∫ g, occupationNormSq Q + (sourceThreeHighestEnd Q z.val hQ (by omega) (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) = + (contractionForm Q (sourceThreeEnd Q) ((threeSpinProjector Q hQ z).map Complex.ofReal) x).re := by + have h := physical_family_spin_norm_haar Q (threeBodySpinRepresentation Q) + (threeBodySpinRepresentation_inv Q) (threeBodySpinRepresentation_continuous Q) + (sourceThreeEnd Q) (sourceThreeEnd_rotation Q (by omega)) + (coupledWeight Q z.val) (threeCoupledInclusion Q hQ z) + (threeCoupledInclusion_SU2 Q hQ z) 0 x + simp_rw [sourceThreeHighestEnd_column] at h + rw [← threeSpinProjector_complex_factor,integral_complex_ofReal] at h + have hh := congrArg Complex.re h + simpa only [Complex.mul_re,Complex.ofReal_re,Complex.ofReal_im,Complex.natCast_re,Complex.natCast_im,zero_mul,mul_zero,sub_zero] using hh + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/HighestReadout.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/HighestReadout.lean new file mode 100644 index 0000000000000000000000000000000000000000..01d14577e29d13b90df26234267baeb893d64f26 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/HighestReadout.lean @@ -0,0 +1,54 @@ +import OAI.Analysis.Laughlin.ThreeBody.HighestRow + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem threeBodyGram_highest_first_coordinate (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + (∑ q : Fin (z+1), threeBodyGramSlice Q z hz ⟨0,by omega⟩ q * + Spin.highestUnit (2*Q-2) Q z q.val) = + (1+gramEigenvalueFormula Q z)*Spin.highestUnit (2*Q-2) Q z 0 := by + by_cases hz₀ : z=0 + · subst z + simp only [Fin.sum_univ_succ,Fin.sum_univ_zero] + change (1-2*∑ t : Fin (Q+1), + pairCoefficient Q 0 ⟨0,Nat.zero_lt_succ Q⟩ t * + pairCoefficient Q 0 ⟨0,Nat.zero_lt_succ Q⟩ t) * + Spin.highestUnit (2*Q-2) Q 0 0 + 0 = _ + rw [swap_base_row Q 0 hQ] + simp [pairCoefficient_base Q hQ,gramEigenvalueFormula,fallingRatio] + left + have hn : Real.sqrt (2 : ℝ) ≠ 0 := by positivity + field_simp + rw [Real.sq_sqrt (by norm_num)] + norm_num + · rw [threeBodyGramSlice_first_row_pos Q z hQ hz (by omega)] + have he := Spin.highestReadout_eq_formula Q z hQ hz + unfold Spin.highestReadout at he + rw [ite_eq_right hz₀] at he + linear_combination he + +noncomputable def threeBodyHighest (Q z : ℕ) (hz : z ≤ Q) : Space Q := + ∑ p : Fin (z+1), (Spin.highestUnit (2*Q-2) Q z p.val : ℂ) • + threeBodyColumn Q p.val (sliceOrbital Q z hz p) + +theorem threeBodyHighest_first_inner (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + occupationInner Q (threeBodyColumn Q 0 ⟨z,by omega⟩) (threeBodyHighest Q z hz) = + (((1+gramEigenvalueFormula Q z)*Spin.highestUnit (2*Q-2) Q z 0 : ℝ) : ℂ) := by + unfold threeBodyHighest + rw [occupationInner_sum_right] + simp only [occupationInner_smul_right] + have hrow := congrArg (fun x : ℝ => (x : ℂ)) + (threeBodyGram_highest_first_coordinate Q z hQ hz) + push_cast at hrow + push_cast + rw [← hrow] + apply Finset.sum_congr rfl + intro p hp + rw [threeBodyGramSlice_physical Q z hQ hz] + exact mul_comm _ _ + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/HighestRow.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/HighestRow.lean new file mode 100644 index 0000000000000000000000000000000000000000..4677b716be4089cc2bcc3150eb93ff5dd9f4f148 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/HighestRow.lean @@ -0,0 +1,87 @@ +import OAI.Analysis.Laughlin.Operators.GramReadout +import OAI.Analysis.Laughlin.ThreeBody.GramSlice + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +theorem pairCoefficient_endpoint_zero (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) + (hz₀ : 1 ≤ z) : + pairCoefficient Q (z-1) ⟨z,by omega⟩ ⟨0,by omega⟩ = + (z : ℝ)/Real.sqrt 2 * Real.sqrt ((Q.choose z : ℝ)/ + ((Q : ℝ)*((2*Q-2).choose (z-1) : ℝ))) := by + rw [pairCoefficient_choose Q (z-1) (by omega) (by omega)] + rw [ite_eq_left (show z+0=z-1+1 by omega)] + simp only [Nat.cast_zero,sub_zero, + Nat.choose_zero_right,Nat.cast_one,mul_one] + rw [show (Q.choose z : ℝ)/(2*(Q : ℝ)*((2*Q-2).choose (z-1) : ℝ)) = + ((Q.choose z : ℝ)/((Q : ℝ)*((2*Q-2).choose (z-1) : ℝ)))/2 by ring] + rw [Real.sqrt_div (by positivity)] + ring + +theorem pairCoefficient_endpoint_one (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) : + pairCoefficient Q z ⟨z,by omega⟩ ⟨1,by omega⟩ = + ((z : ℝ)-1)/Real.sqrt 2 * + Real.sqrt ((Q.choose z : ℝ)/((2*Q-2).choose z : ℝ)) := by + rw [pairCoefficient_choose Q z (by omega) (by omega)] + simp only [ite_true,Nat.choose_one_right,Nat.cast_one] + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (by omega : Q ≠ 0) + have hr : (Q.choose z : ℝ)*Q/(2*(Q : ℝ)*((2*Q-2).choose z : ℝ)) = + ((Q.choose z : ℝ)/((2*Q-2).choose z : ℝ))/2 := by field_simp + rw [hr,Real.sqrt_div (by positivity)] + ring + +theorem swap_slice_first_row (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) + (hz₀ : 1 ≤ z) (f : Fin (z+1) → ℝ) : + (∑ q : Fin (z+1), (∑ t : Fin (Q+1), + pairCoefficient Q 0 (sliceOrbital Q z hz q) t * + pairCoefficient Q q.val ⟨z,by omega⟩ t)*f q) = + (-pairCoefficient Q z ⟨z,by omega⟩ ⟨1,by omega⟩ /Real.sqrt 2)*f ⟨z,by omega⟩ + + (pairCoefficient Q (z-1) ⟨z,by omega⟩ ⟨0,by omega⟩ /Real.sqrt 2)*f ⟨z-1,by omega⟩ := by + let last : Fin (z+1) := ⟨z,by omega⟩ + let prev : Fin (z+1) := ⟨z-1,by omega⟩ + have hne : last ≠ prev := by intro h; have := congrArg Fin.val h; dsimp [last,prev] at this; omega + have he (q : Fin (z+1)) : + (∑ t : Fin (Q+1), pairCoefficient Q 0 (sliceOrbital Q z hz q) t * + pairCoefficient Q q.val ⟨z,by omega⟩ t) = + (if q=last then -pairCoefficient Q z ⟨z,by omega⟩ ⟨1,by omega⟩ /Real.sqrt 2 else 0) + + (if q=prev then pairCoefficient Q (z-1) ⟨z,by omega⟩ ⟨0,by omega⟩ /Real.sqrt 2 else 0) := by + rw [swap_base_row Q q.val hQ] + by_cases hl : q=last + · subst q + simp [last,prev,sliceOrbital,show z ≠ z-1 by omega] + · by_cases hp : q=prev + · subst q + simp [last,prev,sliceOrbital,show z-(z-1)=1 by omega,show z-1 ≠ z by omega] + · have hlv : q.val ≠ z := by intro h; apply hl; exact Fin.ext h + have hpv : q.val ≠ z-1 := by intro h; apply hp; exact Fin.ext h + have hzero : z-q.val ≠ 0 := by omega + have hone : z-q.val ≠ 1 := by omega + simp [hl,hp,sliceOrbital,hzero,hone] + simp_rw [he,add_mul,ite_mul,zero_mul] + rw [Finset.sum_add_distrib] + simp [last,prev] + +theorem threeBodyGramSlice_first_row_pos (Q z : ℕ) (hQ : 2 ≤ Q) (hz : z ≤ Q) + (hz₀ : 1 ≤ z) (f : Fin (z+1) → ℝ) : + (∑ q : Fin (z+1), threeBodyGramSlice Q z hz ⟨0,by omega⟩ q*f q) = + f ⟨0,by omega⟩ - f ⟨z-1,by omega⟩ * (z : ℝ) * + Real.sqrt ((Q.choose z : ℝ)/((Q : ℝ)*((2*Q-2).choose (z-1) : ℝ))) + + f ⟨z,by omega⟩*((z : ℝ)-1)* + Real.sqrt ((Q.choose z : ℝ)/((2*Q-2).choose z : ℝ)) := by + simp only [threeBodyGramSlice,sub_mul,mul_assoc] + rw [Finset.sum_sub_distrib,← Finset.mul_sum] + have horb : sliceOrbital Q z hz ⟨0,by omega⟩ = ⟨z,by omega⟩ := by rfl + rw [horb,swap_slice_first_row Q z hQ hz hz₀ f] + simp only [ite_mul,one_mul,zero_mul,Finset.sum_ite_eq,Finset.mem_univ,ite_true] + rw [pairCoefficient_endpoint_zero Q z hQ hz hz₀,pairCoefficient_endpoint_one Q z hQ hz] + have hs : Real.sqrt (2 : ℝ) ≠ 0 := by positivity + have hsq := Real.sq_sqrt (show (0 : ℝ) ≤ 2 by norm_num) + field_simp + rw [hsq] + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/IntegerPolynomial.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/IntegerPolynomial.lean new file mode 100644 index 0000000000000000000000000000000000000000..b2ebaaea824ecd3b095b9315822f4ffef7db7582 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/IntegerPolynomial.lean @@ -0,0 +1,50 @@ +import Mathlib.Algebra.Polynomial.Eval.Degree +import OAI.Analysis.Laughlin.Polynomial.SourceIntegerPolynomial + +namespace OAI + +namespace Laughlin.Certificate +open scoped BigOperators +open Polynomial + +theorem U_general_sum (c z T p : ℕ) (hz : z ≤ T) (hp : p ≤ T) : + U c z T p = ∑ h ∈ Finset.range (p+1), + (-1 : ℤ)^(z-h) * (z.choose h : ℤ) * ((T-z).choose (p-h) : ℤ) * (c : ℤ)^(p-h) := by + unfold U + rw [ite_eq_left ⟨hz,hp⟩,← List.sum_toFinset _ (List.nodup_range.filter _)] + simp only [List.toFinset_filter,List.toFinset_range] + apply Finset.sum_subset + · intro h hh + simp only [Finset.mem_filter,Finset.mem_range] at hh ⊢ + omega + · intro h hh hn + simp only [Finset.mem_range,Finset.mem_filter,decide_eq_true_eq,not_and] at hh hn + by_cases hhz : h ≤ z + · have hbound : ¬ p+z ≤ T+h := hn (by omega) + rw [Nat.choose_eq_zero_of_lt (by omega : T-z < p-h)] + simp + · rw [Nat.choose_eq_zero_of_lt (by omega : z < h)] + simp + +noncomputable def weightedIntegerCouplingPolynomial (c z n : ℕ) : Polynomial ℤ := + (Polynomial.X-1)^z * (C (c : ℤ)*Polynomial.X+1)^n + +theorem weightedIntegerCouplingPolynomial_coeff (c z n p : ℕ) (hp : p ≤ z+n) : + (weightedIntegerCouplingPolynomial c z n).coeff p = U c z (z+n) p := by + rw [U_general_sum c z (z+n) p (by omega) hp] + simp only [Nat.add_sub_cancel_left] + unfold weightedIntegerCouplingPolynomial + rw [coeff_mul,Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk] + apply Finset.sum_congr rfl + intro h hh + have hneg : (Polynomial.X-1 : Polynomial ℤ) = Polynomial.X+C (-1) := by simp [sub_eq_add_neg] + rw [hneg,coeff_X_add_C_pow] + rw [show (C (c : ℤ)*Polynomial.X+1 : Polynomial ℤ)^n = ((Polynomial.X+1)^n).comp (C (c : ℤ)*Polynomial.X) by simp] + rw [comp_C_mul_X_coeff] + rw [show (Polynomial.X+1 : Polynomial ℤ) = Polynomial.X+C 1 by simp,coeff_X_add_C_pow] + simp + ring + +end Laughlin.Certificate + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/LevelTrace.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/LevelTrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..169ce0604d4d54117701097d3e14e9b400ab8a02 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/LevelTrace.lean @@ -0,0 +1,65 @@ +import OAI.Analysis.Laughlin.ThreeBody.TraceReadout + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + + theorem phasedThreeDescendant_quadratic (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (n : ℕ) + (M : Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℝ) : + dotProduct (phasedThreeDescendant Q hQ z n) (M *ᵥ phasedThreeDescendant Q hQ z n) = + dotProduct (normalizedCoupledDescendant Q z.val hQ (by omega) n) + (M *ᵥ normalizedCoupledDescendant Q z.val hQ (by omega) n) := by + simp only [phasedThreeDescendant,Matrix.mulVec_smul,smul_dotProduct,dotProduct_smul,smul_eq_mul] + have hs : ((-1 : ℝ)^z.val)^2=1 := by rw [← pow_mul,mul_comm z.val 2,pow_mul]; norm_num + nlinarith only [congrArg (fun s : ℝ => s * dotProduct + (normalizedCoupledDescendant Q z.val hQ (by omega) n) + (M *ᵥ normalizedCoupledDescendant Q z.val hQ (by omega) n)) hs] + +noncomputable def physicalThreeBodyLevel (Q z T t : ℕ) (ell : ℤ) (entries : List (ℕ × ℕ × ℤ)) : ℝ := + let a := threeBodyInner (physicalCouplingCoefficient (2*Q-2) Q) z T t entries + 2*((ell : ℝ)/10^7)*physicalCouplingCoefficient (2*Q-2) Q z T t*a+a^2 + +theorem threeBodyLevelMatrix_descendant_off (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (n t T : ℕ) + (ell : ℤ) (entries : List (ℕ × ℕ × ℤ)) (h : T ≠ z.val+n) : + dotProduct (phasedThreeDescendant Q hQ z n) + (threeBodyLevelMatrix Q t T ell entries *ᵥ phasedThreeDescendant Q hQ z n) = 0 := by + rw [threeBodyLevelMatrix_quadratic,threeBodyLevelVector_descendant_off Q hQ z n t T entries h] + ring + +theorem threeBodyLevelMatrix_descendant (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (t T : ℕ) + (ell : ℤ) (entries : List (ℕ × ℕ × ℤ)) (hz : z.val ≤ T) (hT : T ≤ Q) (ht : t ≤ T) : + dotProduct (phasedThreeDescendant Q hQ z (T-z.val)) + (threeBodyLevelMatrix Q t T ell entries *ᵥ phasedThreeDescendant Q hQ z (T-z.val)) = + physicalThreeBodyLevel Q z.val T t ell entries := by + rw [threeBodyLevelMatrix_quadratic,threeBodyLevelVector_descendant Q hQ z t T entries hz hT, + pairOrbitalUnit_dot Q t (T-t) (by omega) (by omega), + phasedThreeDescendant_at_level Q hQ z T t (T-t) hz hT (by omega)] + rfl + +theorem threeBodyLevelMatrix_trace (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (t T : ℕ) + (ell : ℤ) (entries : List (ℕ × ℕ × ℤ)) (hT : T ≤ Q) (ht : t ≤ T) : + Matrix.trace (threeSpinProjector Q hQ z * threeBodyLevelMatrix Q t T ell entries) = + if z.val ≤ T then physicalThreeBodyLevel Q z.val T t ell entries else 0 := by + classical + rw [threeSpinProjector_trace] + simp_rw [← phasedThreeDescendant_quadratic] + by_cases hz : z.val ≤ T + · rw [ite_eq_left hz] + have hn : T-z.val < coupledWeight Q z.val+1 := by unfold coupledWeight; omega + rw [Finset.sum_eq_single (⟨T-z.val,hn⟩ : Fin (coupledWeight Q z.val+1))] + · exact threeBodyLevelMatrix_descendant Q hQ z t T ell entries hz hT ht + · intro n hn' hne + apply threeBodyLevelMatrix_descendant_off + intro he + apply hne + exact Fin.ext (by dsimp; omega) + · simp + · rw [ite_eq_right hz] + apply Finset.sum_eq_zero + intro n hn + exact threeBodyLevelMatrix_descendant_off Q hQ z n.val t T ell entries (by omega) + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/NullFormula.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/NullFormula.lean new file mode 100644 index 0000000000000000000000000000000000000000..dda9398e051c0e90b274dd14084eb9a6b6747545 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/NullFormula.lean @@ -0,0 +1,56 @@ +import Mathlib.Tactic.FieldSimp +import OAI.Analysis.Laughlin.Asymptotics.Bound + +namespace OAI + +namespace Laughlin + +theorem gramEigenvalueFormula_zero (Q : ℕ) : gramEigenvalueFormula Q 0 = -1 := by + simp [gramEigenvalueFormula,fallingRatio] + +theorem gramEigenvalueFormula_one (Q : ℕ) (hQ : 2 ≤ Q) : gramEigenvalueFormula Q 1 = -1 := by + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (by omega : Q ≠ 0) + have hd : (2*(Q : ℝ)-2) ≠ 0 := by + have h : (2 : ℝ) ≤ Q := by exact_mod_cast hQ + linarith + have hq1 : -1+(Q : ℝ) ≠ 0 := by + have hh : (2 : ℝ) ≤ Q := by exact_mod_cast hQ + linarith + norm_num [gramEigenvalueFormula,fallingRatio,Nat.descFactorial] + rw [Nat.cast_sub (by omega : 2 ≤ 2*Q)] + push_cast + field_simp + ring_nf + field_simp [hq1] + ring + +theorem descFactorial_three_real (n : ℕ) (hn : 2 ≤ n) : + (n.descFactorial 3 : ℝ) = (n : ℝ)*(n-1)*(n-2) := by + norm_num [Nat.descFactorial] + rw [Nat.cast_sub hn,Nat.cast_sub (by omega : 1 ≤ n)] + push_cast + ring + +theorem gramEigenvalueFormula_three (Q : ℕ) (hQ : 3 ≤ Q) : gramEigenvalueFormula Q 3 = -1 := by + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (by omega : Q ≠ 0) + have h : (3 : ℝ) ≤ Q := by exact_mod_cast hQ + have hd₀ : (2*(Q : ℝ)-2) ≠ 0 := by linarith + have hd₁ : (2*(Q : ℝ)-2-1) ≠ 0 := by linarith + have hd₂ : (2*(Q : ℝ)-2-2) ≠ 0 := by linarith + have hpoly : -6+(Q : ℝ)*13-(Q : ℝ)^2*9+(Q : ℝ)^3*2 ≠ 0 := by + have hp : 0 < ((Q : ℝ)-1)*((Q : ℝ)-2)*(2*(Q : ℝ)-3) := + mul_pos (mul_pos (by linarith) (by linarith)) (by linarith) + nlinarith + unfold gramEigenvalueFormula fallingRatio + rw [descFactorial_three_real Q (by omega),descFactorial_three_real (2*Q-2) (by omega), + Nat.cast_sub (by omega : 2 ≤ 2*Q)] + push_cast + norm_num + field_simp + ring_nf + field_simp [hpoly] + ring + +end Laughlin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/NullSectors.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/NullSectors.lean new file mode 100644 index 0000000000000000000000000000000000000000..6e9c7225021054581bf7c203f34de8c0998d1e40 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/NullSectors.lean @@ -0,0 +1,38 @@ +import OAI.Analysis.Laughlin.ThreeBody.NullFormula +import OAI.Analysis.Laughlin.ThreeBody.PhysicalKernel +import OAI.Analysis.Laughlin.ThreeBody.SpinProjectors + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators Matrix + +noncomputable def complexThreeSpinProjector (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) : + Matrix (Spin.PairOrbitalIndex Q) (Spin.PairOrbitalIndex Q) ℂ := + fun a b => (Spin.threeSpinProjector Q hQ z a b : ℂ) + +theorem complexThreeSpinProjector_eigen (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) : + complexThreeGram Q * complexThreeSpinProjector Q hQ z = + ((1+gramEigenvalueFormula Q z.val : ℝ) : ℂ) • complexThreeSpinProjector Q hQ z := by + ext a b + have he := congrArg (fun M : Matrix (Spin.PairOrbitalIndex Q) (Spin.PairOrbitalIndex Q) ℝ => + (M a b : ℂ)) (Spin.threeSpinProjector_eigen Q hQ z) + simp only [Matrix.mul_apply,Matrix.smul_apply,smul_eq_mul] at he ⊢ + push_cast at he + simpa only [complexThreeGram,complexThreeSpinProjector,Complex.ofReal_add,Complex.ofReal_one] using he + +theorem source_threeBody_null_sectors (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) + (hz : z.val=0 ∨ z.val=1 ∨ z.val=3) (u : Spin.PairOrbitalIndex Q → ℂ) : + threeWedge Q (complexThreeSpinProjector Q hQ z *ᵥ u) = 0 := by + have hval : gramEigenvalueFormula Q z.val = -1 := by + rcases hz with hz | hz | hz + · rw [hz,gramEigenvalueFormula_zero] + · rw [hz,gramEigenvalueFormula_one Q hQ] + · rw [hz,gramEigenvalueFormula_three Q (by omega)] + apply threeWedge_zero_of_gram_zero Q hQ + rw [Matrix.mulVec_mulVec,complexThreeSpinProjector_eigen,hval] + simp + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/PairAction.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/PairAction.lean new file mode 100644 index 0000000000000000000000000000000000000000..6848f163d2eeff165ef06f627b44ff3bfee59a72 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/PairAction.lean @@ -0,0 +1,75 @@ +import OAI.Analysis.Laughlin.Fock.Hamiltonian +import OAI.Analysis.Laughlin.ThreeBody.Contraction + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators + +noncomputable def threeBodyColumn (Q p : ℕ) (k : Fin (Q+1)) : Space Q := + sourcePairCreateEnd Q p (create k (1 : Space Q)) + +theorem sourcePairCreate_apply (Q p : ℕ) (x : Space Q) : + sourcePairCreateEnd Q p x = ∑ i, ∑ j, + ((pairCoefficient Q p i j / Real.sqrt 2 : ℝ) : ℂ) • create i (create j x) := by + simp [sourcePairCreateEnd,pairCreateEnd,LinearMap.sum_apply,LinearMap.smul_apply,Module.End.mul_apply] + +theorem pair_weight_difference (Q p : ℕ) (i j : Fin (Q+1)) : + pairCoefficient Q p i j / Real.sqrt 2 - pairCoefficient Q p j i / Real.sqrt 2 = + Real.sqrt 2 * pairCoefficient Q p i j := by + rw [pairCoefficient_swap Q p i j] + have hne : Real.sqrt (2 : ℝ) ≠ 0 := by positivity + calc + _ = 2*pairCoefficient Q p i j / Real.sqrt 2 := by ring + _ = (Real.sqrt 2*Real.sqrt 2)*pairCoefficient Q p i j / Real.sqrt 2 := by + rw [Real.mul_self_sqrt (by norm_num)] + _ = _ := by field_simp + +theorem pair_weight_product (Q p q : ℕ) (i j k l : Fin (Q+1)) : + ((pairCoefficient Q q i j / Real.sqrt 2 : ℝ) : ℂ) * + (((pairCoefficient Q p k l / Real.sqrt 2 : ℝ) : ℂ) - + ((pairCoefficient Q p l k / Real.sqrt 2 : ℝ) : ℂ)) = + (pairCoefficient Q q i j : ℂ) * (pairCoefficient Q p k l : ℂ) := by + rw [← Complex.ofReal_sub,pair_weight_difference] + have hne : (Real.sqrt 2 : ℂ) ≠ 0 := by exact_mod_cast (show Real.sqrt (2 : ℝ) ≠ 0 by positivity) + push_cast + field_simp + +theorem sourcePair_threeBodyColumn (Q p q : ℕ) (hQ : 2 ≤ Q) (hp : p ≤ 2*Q-2) + (k : Fin (Q+1)) : + sourcePairEnd Q p (threeBodyColumn Q q k) = + (if p = q then (1 : ℂ) else 0) • create k (1 : Space Q) - + (2 : ℂ) • (∑ i, ∑ j, ((pairCoefficient Q q i j : ℂ) * (pairCoefficient Q p i k : ℂ)) • + create j (1 : Space Q)) := by + let F : Space Q := ∑ i, ∑ j, ((pairCoefficient Q q i j : ℂ)*(pairCoefficient Q p i j : ℂ)) • create k (1 : Space Q) + let U : Space Q := ∑ i, ∑ j, ((pairCoefficient Q q i j : ℂ)*(pairCoefficient Q p i k : ℂ)) • create j (1 : Space Q) + let V : Space Q := ∑ i, ∑ j, ((pairCoefficient Q q i j : ℂ)*(pairCoefficient Q p j k : ℂ)) • create i (1 : Space Q) + have hexp : sourcePairEnd Q p (threeBodyColumn Q q k) = F-U+V := by + rw [threeBodyColumn,sourcePairCreate_apply] + simp only [map_sum,map_smul,sourcePairEnd,pairEnd_three_create, + smul_add,smul_sub,smul_smul,pair_weight_product] + simp only [F,U,V,Finset.sum_add_distrib,Finset.sum_sub_distrib] + have hF : F = (if p = q then (1 : ℂ) else 0) • create k (1 : Space Q) := by + dsimp [F] + simp only [← Finset.sum_smul] + have hg := congrArg (fun r : ℝ => (r : ℂ)) (pairCoefficient_gram Q p q hQ hp) + push_cast at hg + rw [show (∑ i, ∑ j, (pairCoefficient Q q i j : ℂ)*(pairCoefficient Q p i j : ℂ)) = + (if p = q then 1 else 0) by by_cases he : p = q <;> simpa [he,mul_comm] using hg] + have hV : V = -U := by + dsimp [V,U] + rw [Finset.sum_comm] + simp only [← Finset.sum_neg_distrib] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + rw [pairCoefficient_swap Q q i j] + simp + rw [hexp,hF,hV] + change _ = _ - (2 : ℂ) • U + module + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/PhysicalKernel.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/PhysicalKernel.lean new file mode 100644 index 0000000000000000000000000000000000000000..79262be7496454cbe5f667c3d791a9a0cc9685bc --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/PhysicalKernel.lean @@ -0,0 +1,58 @@ +import OAI.Analysis.Laughlin.ThreeBody.SpinCovariance + +namespace OAI + +namespace Laughlin.Fock +open scoped BigOperators Matrix + +noncomputable def threeWedge (Q : ℕ) (u : Spin.PairOrbitalIndex Q → ℂ) : Space Q := + ∑ a, u a • threeBodyColumn Q a.1.val a.2 + +noncomputable def complexThreeGram (Q : ℕ) : + Matrix (Spin.PairOrbitalIndex Q) (Spin.PairOrbitalIndex Q) ℂ := + fun a b => (Spin.threeGram Q a b : ℂ) + +theorem threeWedge_inner (Q : ℕ) (hQ : 2 ≤ Q) (u v : Spin.PairOrbitalIndex Q → ℂ) : + occupationInner Q (threeWedge Q u) (threeWedge Q v) = + ∑ a, star (u a)*(complexThreeGram Q *ᵥ v) a := by + unfold threeWedge + rw [occupationInner_sum_left] + simp_rw [occupationInner_smul_left,occupationInner_sum_right,occupationInner_smul_right] + simp only [Matrix.mulVec,dotProduct,Finset.mul_sum,complexThreeGram] + apply Finset.sum_congr rfl + intro a ha + apply Finset.sum_congr rfl + intro b hb + rw [Spin.threeGram_physical Q hQ a b] + ring + +theorem threeWedge_zero_of_gram_zero (Q : ℕ) (hQ : 2 ≤ Q) (u : Spin.PairOrbitalIndex Q → ℂ) + (hu : complexThreeGram Q *ᵥ u=0) : threeWedge Q u=0 := by + apply (occupationNormSq_eq_zero Q _).mp + apply Complex.ofReal_injective + rw [← occupationInner_self,threeWedge_inner Q hQ,hu] + simp + +theorem complexThreeGram_apply (Q : ℕ) (hQ : 2 ≤ Q) (u : Spin.PairOrbitalIndex Q → ℂ) + (a : Spin.PairOrbitalIndex Q) : + (complexThreeGram Q *ᵥ u) a = occupationInner Q (threeBodyColumn Q a.1.val a.2) (threeWedge Q u) := by + unfold threeWedge + rw [occupationInner_sum_right] + simp only [occupationInner_smul_right,Matrix.mulVec,dotProduct,complexThreeGram] + apply Finset.sum_congr rfl + intro b hb + rw [Spin.threeGram_physical Q hQ a b] + ring + +theorem threeWedge_kernel_iff (Q : ℕ) (hQ : 2 ≤ Q) (u : Spin.PairOrbitalIndex Q → ℂ) : + threeWedge Q u=0 ↔ complexThreeGram Q *ᵥ u=0 := by + constructor + · intro hu + funext a + rw [complexThreeGram_apply Q hQ,hu] + simp [occupationInner] + · exact threeWedge_zero_of_gram_zero Q hQ u + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/PhysicalMatrix.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/PhysicalMatrix.lean new file mode 100644 index 0000000000000000000000000000000000000000..8fdc0e688cc8d56ffe826cf90de9db0ac92f57b3 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/PhysicalMatrix.lean @@ -0,0 +1,54 @@ +import OAI.Analysis.Laughlin.Spin.Support +import OAI.Analysis.Laughlin.ThreeBody.RankTrace +import OAI.Analysis.Laughlin.ThreeBody.TraceLimit + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +noncomputable def pairOrbitalUnit (Q p j : ℕ) : PairOrbitalIndex Q → ℝ := + fun i => if i.1.val=p ∧ i.2.val=j then 1 else 0 + +theorem pairOrbitalUnit_dot (Q p j : ℕ) (hp : p < 2*Q-2+1) (hj : j ≤ Q) + (v : PairOrbitalIndex Q → ℝ) : + dotProduct v (pairOrbitalUnit Q p j) = v (⟨p,hp⟩,⟨j,by omega⟩) := by + classical + simp only [dotProduct,pairOrbitalUnit,mul_ite,mul_one,mul_zero] + have he : ∀ i : PairOrbitalIndex Q, (i.1.val=p ∧ i.2.val=j) ↔ i=(⟨p,hp⟩,⟨j,by omega⟩) := by + intro i + constructor + · rintro ⟨h1,h2⟩; exact Prod.ext (Fin.ext h1) (Fin.ext h2) + · intro h; subst i; exact ⟨rfl,rfl⟩ + simp_rw [he] + simp + +noncomputable def threeBodyLevelVector (Q t T : ℕ) (entries : List (ℕ × ℕ × ℤ)) : + PairOrbitalIndex Q → ℝ := + (entries.map (fun e => if e.1+e.2.1=T then sourceAlpha t e • pairOrbitalUnit Q e.1 e.2.1 else 0)).sum + +noncomputable def threeBodyLevelMatrix (Q t T : ℕ) (ell : ℤ) (entries : List (ℕ × ℕ × ℤ)) : + Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℝ := + let u := pairOrbitalUnit Q t (T-t) + let a := threeBodyLevelVector Q t T entries + ((ell : ℝ)/10^7) • (realOuter u a + realOuter a u) + realOuter a a + +noncomputable def physicalThreeBodyMatrix (Q : ℕ) : + Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℝ := + (Certificate.rows.map (fun row => + (((List.range 16).filter (fun T => row.1 ≤ T)).map + (fun T => threeBodyLevelMatrix Q row.1 T row.2.1 row.2.2)).sum)).sum + +theorem threeBodyLevelMatrix_quadratic (Q t T : ℕ) (ell : ℤ) (entries : List (ℕ × ℕ × ℤ)) + (v : PairOrbitalIndex Q → ℝ) : + dotProduct v (threeBodyLevelMatrix Q t T ell entries *ᵥ v) = + 2*((ell : ℝ)/10^7)*dotProduct v (pairOrbitalUnit Q t (T-t))* + dotProduct v (threeBodyLevelVector Q t T entries) + + (dotProduct v (threeBodyLevelVector Q t T entries))^2 := by + simp only [threeBodyLevelMatrix,Matrix.add_mulVec,Matrix.smul_mulVec, + dotProduct_add,dotProduct_smul,realOuter_quadratic,smul_eq_mul] + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/PhysicalTrace.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/PhysicalTrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..1285a27287fa8cebcd7983f5aed9a7e0923dd3be --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/PhysicalTrace.lean @@ -0,0 +1,58 @@ +import OAI.Analysis.Laughlin.ThreeBody.LevelTrace +import OAI.Analysis.Laughlin.ThreeBody.TraceCertificate + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix Topology + + theorem trace_mul_list_sum {I : Type*} [Fintype I] (P : Matrix I I ℝ) + (l : List (Matrix I I ℝ)) : + Matrix.trace (P*l.sum) = (l.map (fun M => Matrix.trace (P*M))).sum := by + induction l with + | nil => simp + | cons a l ih => simp only [List.sum_cons,List.map_cons,Matrix.mul_add,Matrix.trace_add,ih] + + theorem list_filter_sum_if {I : Type*} (l : List I) (p q : I → Prop) + [DecidablePred p] [DecidablePred q] (f : I → ℝ) : + ((l.filter p).map (fun i => if q i then f i else 0)).sum = + ((l.filter (fun i => p i ∧ q i)).map f).sum := by + induction l with + | nil => simp + | cons a l ih => + by_cases hp : p a <;> by_cases hq : q a <;> simp [hp,hq,ih] + +theorem source_physical_threeBody_trace_identity (Q : ℕ) (hQ : 15 ≤ Q) (z : Fin (Q+1)) : + Matrix.trace (threeSpinProjector Q (by omega) z * physicalThreeBodyMatrix Q) = + physicalThreeBodyTraceFormula Q z.val := by + unfold physicalThreeBodyMatrix + rw [trace_mul_list_sum] + simp only [List.map_map,Function.comp_def] + unfold physicalThreeBodyTraceFormula threeBodyTraceFormula + apply congrArg List.sum + apply List.map_congr_left + intro row hrow + rw [trace_mul_list_sum] + simp only [List.map_map,Function.comp_def] + have he : (((List.range 16).filter (fun T => row.1 ≤ T)).map + (fun T => Matrix.trace (threeSpinProjector Q (by omega) z * threeBodyLevelMatrix Q row.1 T row.2.1 row.2.2))) = + (((List.range 16).filter (fun T => row.1 ≤ T)).map + (fun T => if z.val ≤ T then physicalThreeBodyLevel Q z.val T row.1 row.2.1 row.2.2 else 0)) := by + apply List.map_congr_left + intro T hT + simp only [List.mem_filter,List.mem_range,decide_eq_true_eq] at hT + exact threeBodyLevelMatrix_trace Q (by omega) z row.1 T row.2.1 row.2.2 (by omega) hT.2 + rw [he,list_filter_sum_if] + simp only [physicalThreeBodyLevel,max_le_iff,and_comm] + +theorem source_physical_threeBody_trace_tendsto (z : ℕ) : + Filter.Tendsto (fun Q => if h : 15 ≤ Q ∧ z ≤ Q then + Matrix.trace (threeSpinProjector Q (by omega) ⟨z,by omega⟩ * physicalThreeBodyMatrix Q) else 0) + Filter.atTop (𝓝 (Certificate.e z : ℝ)) := by + apply (source_physical_threeBody_trace_formula_tendsto z).congr' + filter_upwards [Filter.eventually_ge_atTop (max 15 z)] with Q hQ + rw [dite_eq_left (show 15 ≤ Q ∧ z ≤ Q by omega),source_physical_threeBody_trace_identity Q (by omega)] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/PolynomialCoefficient.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/PolynomialCoefficient.lean new file mode 100644 index 0000000000000000000000000000000000000000..e62335a979ab6c6c055ea791fbb310e4afa64a83 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/PolynomialCoefficient.lean @@ -0,0 +1,51 @@ +import OAI.Analysis.Laughlin.Polynomial.OscillatorPolynomial +import OAI.Analysis.Laughlin.ThreeBody.IntegerPolynomial + +namespace OAI + +namespace Laughlin.Spin +open Polynomial + +theorem threeBody_scaled_polynomial (u w : ℝ) (hw : w^2=2) (hw0 : w ≠ 0) (z n : ℕ) : + couplingPolynomial u (w*u) z n = C (u^(z+n)*w^z) * + ((Certificate.weightedIntegerCouplingPolynomial 2 z n).map (Int.castRingHom ℝ)).comp (C w⁻¹*X) := by + have h2 : (2 : ℝ)*w⁻¹=w := by + field_simp + nlinarith only [hw] + simp only [Certificate.weightedIntegerCouplingPolynomial,Polynomial.map_mul,Polynomial.map_pow, + Polynomial.map_sub,Polynomial.map_add,Polynomial.map_X,Polynomial.map_one,Polynomial.map_C, + Int.coe_castRingHom,Polynomial.mul_comp,Polynomial.pow_comp,Polynomial.sub_comp,Polynomial.add_comp, + Polynomial.X_comp,Polynomial.C_comp,Polynomial.one_comp] + norm_num only [Nat.cast_ofNat,Int.cast_natCast] + rw [show C (2 : ℝ)*(C w⁻¹*X) = C w*X by rw [← mul_assoc,← C_mul,h2]] + have he : C u*X-C (w*u) = C (u*w)*(C w⁻¹*X-1) := by + have hc : u*w*w⁻¹=u := by field_simp + simp only [mul_sub,← mul_assoc,← C_mul,mul_one,hc] + rw [mul_comm w u] + have hf : C (w*u)*X+C u = C u*(C w*X+1) := by + simp only [mul_add,← mul_assoc,← C_mul,mul_one] + rw [mul_comm w u] + unfold couplingPolynomial + rw [he,hf,mul_pow,mul_pow,← C_pow,← C_pow] + simp only [pow_add,mul_pow,C_mul] + ring + +theorem threeBody_polynomialCoefficient_factorial (z T p : ℕ) (hz : z ≤ T) (hp : p ≤ T) : + couplingPolynomialCoefficient (Real.sqrt (1/3)) (Real.sqrt (2/3)) z (T-z) p = + (Certificate.U 2 z T p : ℝ) * (Real.sqrt (1/3))^T * + (Real.sqrt 2)^z / (Real.sqrt 2)^p * + sqrtFactorial p * sqrtFactorial (T-p) / (sqrtFactorial z*sqrtFactorial (T-z)) := by + have hs : Real.sqrt (2/3) = Real.sqrt 2 * Real.sqrt (1/3) := by + rw [← Real.sqrt_mul (by norm_num : (0 : ℝ) ≤ 2)] + norm_num + have hT : z+(T-z)=T := by omega + unfold couplingPolynomialCoefficient + rw [hs,threeBody_scaled_polynomial _ _ (Real.sq_sqrt (by norm_num)) (by positivity), + coeff_C_mul,comp_C_mul_X_coeff,coeff_map, + Certificate.weightedIntegerCouplingPolynomial_coeff 2 z (T-z) p (by omega)] + simp only [Int.coe_castRingHom,hT,monomialNormFactor,inv_pow] + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/ProjectorBound.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/ProjectorBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..a3cfae924367e15e0239deef2e326d28d0118ea1 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/ProjectorBound.lean @@ -0,0 +1,40 @@ +import OAI.Analysis.Laughlin.ThreeBody.HighestFock + +namespace OAI + +namespace Laughlin.Fock +open Rotation Spin MeasureTheory +open scoped BigOperators Matrix + +theorem physical_threeBody_projector_nonneg (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (x : Space Q) : + 0 ≤ (contractionForm Q (sourceThreeEnd Q) + ((threeSpinProjector Q hQ z).map Complex.ofReal) x).re := by + rw [← sourceThreeHighestEnd_haar Q hQ z] + exact mul_nonneg (by positivity) (integral_nonneg (fun g => occupationNormSq_nonneg Q _)) + +theorem physical_threeBody_projector_bound (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (x : Space Q) : + (contractionForm Q (sourceThreeEnd Q) + ((threeSpinProjector Q hQ z).map Complex.ofReal) x).re ≤ + ((coupledWeight Q z.val+1 : ℕ) / (2*Q-2+1 : ℕ) : ℝ) * + (z.val+1 : ℕ) * sourceFockEnergy Q x := by + rw [← sourceThreeHighestEnd_haar Q hQ z] + have hi := integral_mono + (linearMap_rotation_norm_integrable Q (sourceThreeHighestEnd Q z.val hQ (by omega)) x) + (integrable_finsetSum _ (fun (p : Fin (z.val+1)) hp => + linearMap_rotation_norm_integrable Q (sourcePairEnd Q p.val) x)) + (fun g => sourceThreeHighestEnd_norm_bound Q z.val hQ (by omega) (exteriorRotation Q g⁻¹ x)) + apply (mul_le_mul_of_nonneg_left hi + (by positivity : (0 : ℝ) ≤ (coupledWeight Q z.val+1 : ℕ))).trans_eq + rw [integral_finsetSum _ (fun (p : Fin (z.val+1)) hp => + linearMap_rotation_norm_integrable Q (sourcePairEnd Q p.val) x)] + have hp (p : Fin (z.val+1)) : + (∫ g, occupationNormSq Q (sourcePairEnd Q p.val (exteriorRotation Q g⁻¹ x)) ∂sourceHaar) = + sourceFockEnergy Q x/(2*Q-2+1 : ℕ) := + physical_pair_norm_haar_real Q (by omega) ⟨p.val,by have := p.isLt; have := z.isLt; omega⟩ x + simp_rw [hp] + simp only [Finset.sum_const,Finset.card_univ,Fintype.card_fin,nsmul_eq_mul] + ring + +end Laughlin.Fock + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/Radical.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/Radical.lean new file mode 100644 index 0000000000000000000000000000000000000000..404a0f533f16949ac9f824ddd9258fa51e508dd6 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/Radical.lean @@ -0,0 +1,75 @@ +import OAI.Analysis.Laughlin.FourBody.RadicalCancellation +import OAI.Analysis.Laughlin.ThreeBody.PolynomialCoefficient + +namespace OAI + +namespace Laughlin.Spin + +noncomputable def threeBodyRadical (z T p : ℕ) : ℝ := + Real.sqrt ((2 : ℝ)^((z : ℤ)-p) * + ((p.factorial : ℝ)*((T-p).factorial : ℝ) / + ((3 : ℝ)^T * (z.factorial : ℝ)*((T-z).factorial : ℝ)))) + +theorem threeBodyRadical_factorial (z T p : ℕ) : + threeBodyRadical z T p = + (Real.sqrt (1/3))^T * (Real.sqrt 2)^z / (Real.sqrt 2)^p * + sqrtFactorial p * sqrtFactorial (T-p) / (sqrtFactorial z*sqrtFactorial (T-z)) := by + let a := (Real.sqrt (1/3))^T * (Real.sqrt 2)^z / (Real.sqrt 2)^p * + sqrtFactorial p * sqrtFactorial (T-p) / (sqrtFactorial z*sqrtFactorial (T-z)) + have ha : 0 ≤ a := by dsimp [a]; unfold sqrtFactorial; positivity + have hs : a^2 = (2 : ℝ)^((z : ℤ)-p) * + ((p.factorial : ℝ)*((T-p).factorial : ℝ) / + ((3 : ℝ)^T * (z.factorial : ℝ)*((T-z).factorial : ℝ))) := by + dsimp [a] + simp only [div_pow,mul_pow,sqrtFactorial] + have hr (c : ℝ) (hc : 0 ≤ c) (n : ℕ) : (Real.sqrt c ^ n)^2 = c^n := by + rw [← pow_mul,mul_comm n 2,pow_mul,Real.sq_sqrt hc] + rw [hr _ (by norm_num),hr _ (by norm_num),hr _ (by norm_num)] + simp only [Real.sq_sqrt (Nat.cast_nonneg _)] + rw [zpow_sub₀ (by norm_num : (2 : ℝ) ≠ 0)] + simp only [zpow_natCast,div_pow,one_pow] + ring + change Real.sqrt _ = a + rw [← hs,Real.sqrt_sq ha] + +theorem source_threeBody_radical_coefficient (z T p : ℕ) (hz : z ≤ T) (hp : p ≤ T) : + couplingPolynomialCoefficient (Real.sqrt (1/3)) (Real.sqrt (2/3)) z (T-z) p = + (Certificate.U 2 z T p : ℝ) * threeBodyRadical z T p := by + rw [threeBody_polynomialCoefficient_factorial z T p hz hp,threeBodyRadical_factorial] + ring + +theorem threeBody_alpha_radical_cancel (z T t p j : ℕ) (hT : p+j=T) : + alphaRadical t p j * threeBodyRadical z T p = threeBodyRadical z T t := by + have hj : T-p=j := by omega + have he : ((p : ℤ)-t)+((z : ℤ)-p)=(z : ℤ)-t := by omega + have hs : (alphaRadical t p j * threeBodyRadical z T p)^2 = (threeBodyRadical z T t)^2 := by + simp only [alphaRadical,threeBodyRadical,mul_pow] + repeat rw [Real.sq_sqrt (by positivity)] + rw [hT,hj] + calc + _ = ((2 : ℝ)^((p : ℤ)-t)*(2 : ℝ)^((z : ℤ)-p)) * + ((t.factorial : ℝ)*(T-t).factorial/(3^T*z.factorial*(T-z).factorial)) := by field_simp + _ = _ := by rw [← zpow_add₀ (by norm_num : (2 : ℝ) ≠ 0),he] + have hl : 0 ≤ alphaRadical t p j * threeBodyRadical z T p := by + unfold alphaRadical threeBodyRadical; positivity + have hr : 0 ≤ threeBodyRadical z T t := Real.sqrt_nonneg _ + nlinarith only [hs,hl,hr] + +theorem threeBodyRadical_sq_choose (z T p : ℕ) (hz : z ≤ T) (hp : p ≤ T) : + (threeBodyRadical z T p)^2 = + (2 : ℝ)^z * (T.choose z : ℝ) / ((3 : ℝ)^T * (2 : ℝ)^p * (T.choose p : ℝ)) := by + have hc (k : ℕ) (hk : k ≤ T) : (T.choose k : ℝ) * (k.factorial : ℝ) * ((T-k).factorial : ℝ) = T.factorial := by + exact_mod_cast Nat.choose_mul_factorial_mul_factorial hk + have hcp : (T.choose p : ℝ) ≠ 0 := by exact_mod_cast (ne_of_gt (Nat.choose_pos hp)) + unfold threeBodyRadical + rw [Real.sq_sqrt (by positivity),zpow_sub₀ (by norm_num : (2 : ℝ) ≠ 0)] + simp only [zpow_natCast] + apply (eq_div_iff (by positivity : (3 : ℝ)^T*2^p*(T.choose p : ℝ) ≠ 0)).mpr + have hzfac := hc z hz + have hpfac := hc p hp + field_simp + nlinarith only [hzfac,hpfac] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/RankTrace.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/RankTrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..f63c6ce94879636e25f0bbe2a52b8f170616ffb0 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/RankTrace.lean @@ -0,0 +1,67 @@ +import Mathlib.LinearAlgebra.Matrix.Trace +import OAI.Analysis.Laughlin.ThreeBody.SpinProjectors + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +noncomputable def realOuter {I : Type*} (u v : I → ℝ) : Matrix I I ℝ := + fun i j => u i * v j + +theorem realOuter_quadratic {I : Type*} [Fintype I] (u v x : I → ℝ) : + dotProduct x (realOuter u v *ᵥ x) = dotProduct x u * dotProduct x v := by + simp only [dotProduct,Matrix.mulVec,realOuter] + rw [Finset.sum_mul] + apply Finset.sum_congr rfl + intro i hi + simp only [Finset.mul_sum] + apply Finset.sum_congr rfl + intro j hj + ring + +theorem trace_outer {I : Type*} [Fintype I] (M : Matrix I I ℝ) (u v : I → ℝ) : + Matrix.trace (M * realOuter u v) = dotProduct v (M *ᵥ u) := by + simp only [Matrix.trace,Matrix.diag,Matrix.mul_apply,realOuter,Matrix.mulVec,dotProduct, + Finset.mul_sum] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + ring + +theorem threeSpinProjector_trace (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) + (M : Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℝ) : + Matrix.trace (threeSpinProjector Q hQ z * M) = + ∑ n : Fin (coupledWeight Q z.val+1), + dotProduct (normalizedCoupledDescendant Q z.val hQ (by omega) n.val) + (M *ᵥ normalizedCoupledDescendant Q z.val hQ (by omega) n.val) := by + let B := coupledBasisMatrix Q hQ + have he : Matrix.trace (threeSpinProjector Q hQ z * M) = + Matrix.trace (coupledSelector Q z * (Bᵀ*M*B)) := by + change Matrix.trace (B*coupledSelector Q z*Bᵀ*M) = _ + calc + _ = Matrix.trace ((B*coupledSelector Q z)*(Bᵀ*M)) := by simp only [Matrix.mul_assoc] + _ = Matrix.trace ((Bᵀ*M)*(B*coupledSelector Q z)) := Matrix.trace_mul_comm _ _ + _ = Matrix.trace ((Bᵀ*M*B)*coupledSelector Q z) := by simp only [Matrix.mul_assoc] + _ = _ := Matrix.trace_mul_comm _ _ + rw [he] + unfold coupledSelector + simp only [Matrix.trace,Matrix.diag,Matrix.diagonal_mul] + rw [Fintype.sum_sigma] + simp only [ite_mul,one_mul,zero_mul,Finset.sum_ite_irrel,Finset.sum_const_zero, + Finset.sum_ite_eq',Finset.mem_univ,ite_true] + apply Finset.sum_congr rfl + intro n hn + simp only [Matrix.mul_apply,Matrix.transpose_apply,B,coupledBasisMatrix,Matrix.mulVec,dotProduct] + simp only [Finset.sum_mul,Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/SourceExpansion.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/SourceExpansion.lean new file mode 100644 index 0000000000000000000000000000000000000000..2c32ed156e384342488982433371a66f9e05609a --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/SourceExpansion.lean @@ -0,0 +1,65 @@ +import OAI.Analysis.Laughlin.ThreeBody.PhysicalTrace + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + + theorem realOuter_add_left {I : Type*} (u v w : I → ℝ) : + realOuter (u+v) w = realOuter u w + realOuter v w := by ext i j; simp [realOuter,add_mul] + theorem realOuter_add_right {I : Type*} (u v w : I → ℝ) : + realOuter u (v+w) = realOuter u v + realOuter u w := by ext i j; simp [realOuter,mul_add] + theorem realOuter_smul_left {I : Type*} (c : ℝ) (u v : I → ℝ) : + realOuter (c • u) v = c • realOuter u v := by ext i j; simp [realOuter,mul_assoc] + theorem realOuter_smul_right {I : Type*} (c : ℝ) (u v : I → ℝ) : + realOuter u (c • v) = c • realOuter u v := by ext i j; simp [realOuter]; ring + theorem realOuter_list_sum_left {I : Type*} (l : List (I → ℝ)) (v : I → ℝ) : + realOuter l.sum v = (l.map (fun u => realOuter u v)).sum := by + induction l with + | nil => ext i j; simp [realOuter] + | cons a l ih => simp only [List.sum_cons,List.map_cons,realOuter_add_left,ih] + theorem realOuter_list_sum_right {I : Type*} (l : List (I → ℝ)) (u : I → ℝ) : + realOuter u l.sum = (l.map (realOuter u)).sum := by + induction l with + | nil => ext i j; simp [realOuter] + | cons a l ih => simp only [List.sum_cons,List.map_cons,realOuter_add_right,ih] + + theorem source_threeBody_normal3_delta (t p j q l : ℕ) (he : t ≤ p+j) (hf : t ≤ q+l) : + p+j-t=q+l-t ↔ p+j=q+l := by omega + + theorem source_threeBody_rows_support : ∀ row ∈ Certificate.rows, + row.1 ≤ 7 ∧ ∀ e ∈ row.2.2, row.1 ≤ e.1+e.2.1 ∧ e.1+e.2.1 ≤ 15 ∧ e.1+e.2.1-row.1 ≤ 8 := by decide + + theorem list_map_ite_sum {I A : Type*} [AddMonoid A] (l : List I) (p : I → Prop) + [DecidablePred p] (f : I → A) : + (l.map (fun i => if p i then f i else 0)).sum = ((l.filter p).map f).sum := by + induction l with + | nil => simp + | cons a l ih => by_cases h : p a <;> simp [h,ih] + + theorem threeBodyLevelVector_filtered (Q t T : ℕ) (entries : List (ℕ × ℕ × ℤ)) : + threeBodyLevelVector Q t T entries = + ((entries.filter (fun e => e.1+e.2.1=T)).map + (fun e => sourceAlpha t e • pairOrbitalUnit Q e.1 e.2.1)).sum := by + exact list_map_ite_sum _ _ _ + +theorem source_threeBody_normal3_level_expansion (Q t T : ℕ) (ell : ℤ) + (entries : List (ℕ × ℕ × ℤ)) : + threeBodyLevelMatrix Q t T ell entries = + ((ell : ℝ)/10^7) • + ((((entries.filter (fun e => e.1+e.2.1=T)).map (fun e => + sourceAlpha t e • realOuter (pairOrbitalUnit Q t (T-t)) (pairOrbitalUnit Q e.1 e.2.1))).sum) + + (((entries.filter (fun e => e.1+e.2.1=T)).map (fun e => + sourceAlpha t e • realOuter (pairOrbitalUnit Q e.1 e.2.1) (pairOrbitalUnit Q t (T-t)))).sum)) + + (((entries.filter (fun e => e.1+e.2.1=T)).map (fun e => + (((entries.filter (fun f => f.1+f.2.1=T)).map (fun f => + (sourceAlpha t e * sourceAlpha t f) • + realOuter (pairOrbitalUnit Q e.1 e.2.1) (pairOrbitalUnit Q f.1 f.2.1))).sum))).sum) := by + unfold threeBodyLevelMatrix + rw [threeBodyLevelVector_filtered] + simp_rw [realOuter_list_sum_left,realOuter_list_sum_right,List.map_map,Function.comp_def, + realOuter_smul_left,realOuter_smul_right,smul_smul] + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/SpinCovariance.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/SpinCovariance.lean new file mode 100644 index 0000000000000000000000000000000000000000..0cf01e0f8836c63048db1ab7b14c4ee7446ad115 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/SpinCovariance.lean @@ -0,0 +1,93 @@ +import OAI.Analysis.Laughlin.Spin.TripleLadderIntertwining +import OAI.Analysis.Laughlin.ThreeBody.GramSlice + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix Kronecker + +noncomputable def swapCompression (Q : ℕ) : Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℝ := + (tripleInclusion Q)ᵀ * swap23Matrix Q * tripleInclusion Q + +noncomputable def threeGram (Q : ℕ) : Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℝ := + 1 - (2 : ℝ) • swapCompression Q + +theorem swapCompression_raising (Q : ℕ) (hQ : 0 < Q) : + swapCompression Q * totalRaise (2*Q-2) Q = totalRaise (2*Q-2) Q * swapCompression Q := by + unfold swapCompression + calc + _ = (tripleInclusion Q)ᵀ * swap23Matrix Q * + (tripleInclusion Q * totalRaise (2*Q-2) Q) := by simp only [Matrix.mul_assoc] + _ = (tripleInclusion Q)ᵀ * swap23Matrix Q * + (tripleRaise Q * tripleInclusion Q) := by rw [tripleInclusion_raising Q hQ] + _ = (tripleInclusion Q)ᵀ * (swap23Matrix Q * tripleRaise Q) * tripleInclusion Q := by + simp only [Matrix.mul_assoc] + _ = (tripleInclusion Q)ᵀ * (tripleRaise Q * swap23Matrix Q) * tripleInclusion Q := by + rw [swap23_raising] + _ = ((tripleInclusion Q)ᵀ * tripleRaise Q) * swap23Matrix Q * tripleInclusion Q := by + simp only [Matrix.mul_assoc] + _ = _ := by rw [tripleInclusion_transpose_raising Q hQ]; simp only [Matrix.mul_assoc] + +theorem threeGram_raising (Q : ℕ) (hQ : 0 < Q) : + threeGram Q * totalRaise (2*Q-2) Q = totalRaise (2*Q-2) Q * threeGram Q := by + simp only [threeGram,Matrix.sub_mul,Matrix.mul_sub,Matrix.one_mul,Matrix.mul_one, + Matrix.smul_mul,Matrix.mul_smul,swapCompression_raising Q hQ] + +theorem swapCompression_entry (Q : ℕ) (a b : PairOrbitalIndex Q) : + swapCompression Q a b = ∑ t : Orbital Q, + pairCoefficient Q a.1.val b.2 t * pairCoefficient Q b.1.val a.2 t := by + have he (i : TripleIndex Q) : + ((tripleInclusion Q)ᵀ * swap23Matrix Q) a i = tripleInclusion Q (swap23 i) a := by + have hi (k : TripleIndex Q) : swap23 k=i ↔ k=swap23 i := by + constructor + · intro h; simpa using congrArg swap23 h + · intro h; rw [h,swap23_involutive] + simp [Matrix.mul_apply,swap23Matrix,hi,Matrix.transpose_apply] + unfold swapCompression + rw [Matrix.mul_apply] + simp_rw [he] + rw [Fintype.sum_prod_type] + simp_rw [Fintype.sum_prod_type] + simp only [tripleInclusion,pairInclusion,Matrix.kroneckerMap, + Matrix.of_apply,Matrix.one_apply,swap23] + simp only [mul_ite,mul_one,mul_zero,ite_mul,zero_mul,Finset.sum_ite_eq', + Finset.mem_univ,ite_true] + apply Finset.sum_congr rfl + intro t ht + rw [pairCoefficient_swap Q a.1.val t b.2,pairCoefficient_swap Q b.1.val t a.2] + ring + +theorem threeGram_entry (Q : ℕ) (a b : PairOrbitalIndex Q) : + threeGram Q a b = (if a=b then 1 else 0) - 2*∑ t : Orbital Q, + pairCoefficient Q a.1.val b.2 t * pairCoefficient Q b.1.val a.2 t := by + simp only [threeGram,Matrix.sub_apply,Matrix.one_apply,Matrix.smul_apply,smul_eq_mul, + swapCompression_entry] + +theorem threeGram_physical (Q : ℕ) (hQ : 2 ≤ Q) (a b : PairOrbitalIndex Q) : + (threeGram Q a b : ℂ) = + Fock.occupationInner Q (Fock.threeBodyColumn Q a.1.val a.2) + (Fock.threeBodyColumn Q b.1.val b.2) := by + rw [threeGram_entry,Fock.threeBodyColumn_gram Q a.1.val b.1.val hQ (by omega)] + push_cast + congr 1 + by_cases ha : a.1=b.1 <;> by_cases hb : a.2=b.2 <;> + simp [Prod.ext_iff,ha,hb] + simp_all [Fin.ext_iff] + +theorem threeGram_weight (Q : ℕ) (a b : PairOrbitalIndex Q) + (h : a.1.val+a.2.val ≠ b.1.val+b.2.val) : threeGram Q a b = 0 := by + have hab : a ≠ b := by intro he; apply h; rw [he] + rw [threeGram_entry,ite_eq_right hab] + have hz : (∑ t : Orbital Q, pairCoefficient Q a.1.val b.2 t * + pairCoefficient Q b.1.val a.2 t) = 0 := by + apply Finset.sum_eq_zero + intro t ht + by_cases ha : b.2.val+t.val=a.1.val+1 + · have hb : a.2.val+t.val ≠ b.1.val+1 := by omega + simp [pairCoefficient,hb] + · simp [pairCoefficient,ha] + rw [hz]; ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/SpinProjectors.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/SpinProjectors.lean new file mode 100644 index 0000000000000000000000000000000000000000..d6e77792a8fbcbcb34ad7b322e20ef0e116e345f --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/SpinProjectors.lean @@ -0,0 +1,118 @@ +import OAI.Analysis.Laughlin.Spin.Basis + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +noncomputable def coupledSelector (Q : ℕ) (z : Fin (Q+1)) : + Matrix (CoupledIndex Q) (CoupledIndex Q) ℝ := + Matrix.diagonal (fun s => if s.1=z then 1 else 0) + +noncomputable def threeSpinProjector (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) : + Matrix (PairOrbitalIndex Q) (PairOrbitalIndex Q) ℝ := + coupledBasisMatrix Q hQ * coupledSelector Q z * (coupledBasisMatrix Q hQ)ᵀ + +theorem coupledSelector_sum (Q : ℕ) : (∑ z : Fin (Q+1), coupledSelector Q z) = 1 := by + ext s t + by_cases h : s=t + · subst t + simp [coupledSelector,Matrix.sum_apply] + · simp [coupledSelector,Matrix.sum_apply,h] + +theorem coupledSelector_eigenvalue_sum (Q : ℕ) : + Matrix.diagonal (fun s : CoupledIndex Q => gramEigenvalueFormula Q s.1.val) = + ∑ z : Fin (Q+1), gramEigenvalueFormula Q z.val • coupledSelector Q z := by + ext s t + by_cases h : s=t + · subst t + simp [coupledSelector,Matrix.sum_apply] + · simp [coupledSelector,Matrix.sum_apply,h] + +theorem threeSpinProjector_sum (Q : ℕ) (hQ : 2 ≤ Q) : + (∑ z : Fin (Q+1), threeSpinProjector Q hQ z) = 1 := by + unfold threeSpinProjector + rw [← Matrix.sum_mul,← Matrix.mul_sum,coupledSelector_sum,Matrix.mul_one,coupledBasis_complete Q hQ] + +theorem threeSpinProjector_transpose (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) : + (threeSpinProjector Q hQ z)ᵀ = threeSpinProjector Q hQ z := by + simp only [threeSpinProjector,coupledSelector,Matrix.transpose_mul,Matrix.transpose_transpose, + Matrix.diagonal_transpose,Matrix.mul_assoc] + +theorem coupledSelector_mul (Q : ℕ) (z w : Fin (Q+1)) : + coupledSelector Q z * coupledSelector Q w = if z=w then coupledSelector Q z else 0 := by + unfold coupledSelector + rw [Matrix.diagonal_mul_diagonal] + ext s t + by_cases hzw : z=w + · subst w + simp only [ite_true,Matrix.diagonal_apply] + split_ifs <;> norm_num + · simp only [ite_eq_right hzw,Matrix.diagonal_apply,Matrix.zero_apply] + by_cases hst : s=t + · subst t + simp only [ite_true] + by_cases hz : s.1=z + · simp [hz,hzw] + · simp [hz] + · simp [hst] + +theorem threeSpinProjector_mul (Q : ℕ) (hQ : 2 ≤ Q) (z w : Fin (Q+1)) : + threeSpinProjector Q hQ z * threeSpinProjector Q hQ w = + if z=w then threeSpinProjector Q hQ z else 0 := by + unfold threeSpinProjector + calc + _ = coupledBasisMatrix Q hQ * coupledSelector Q z * + ((coupledBasisMatrix Q hQ)ᵀ * coupledBasisMatrix Q hQ) * coupledSelector Q w * + (coupledBasisMatrix Q hQ)ᵀ := by simp only [Matrix.mul_assoc] + _ = coupledBasisMatrix Q hQ * (coupledSelector Q z * coupledSelector Q w) * + (coupledBasisMatrix Q hQ)ᵀ := by rw [coupledBasis_isometry Q hQ,Matrix.mul_one]; simp only [Matrix.mul_assoc] + _ = _ := by rw [coupledSelector_mul]; split_ifs <;> simp + +theorem source_threeBody_spectral_decomposition (Q : ℕ) (hQ : 2 ≤ Q) : + threeGram Q-1 = ∑ z : Fin (Q+1), gramEigenvalueFormula Q z.val • threeSpinProjector Q hQ z := by + rw [threeGram_diagonalization Q hQ,coupledSelector_eigenvalue_sum] + rw [Matrix.mul_sum,Matrix.sum_mul] + apply Finset.sum_congr rfl + intro z hz + simp only [threeSpinProjector,Matrix.mul_smul,Matrix.smul_mul] + +theorem coupledSelector_eigen (Q : ℕ) (z : Fin (Q+1)) : + Matrix.diagonal (fun s : CoupledIndex Q => gramEigenvalueFormula Q s.1.val) * + coupledSelector Q z = gramEigenvalueFormula Q z.val • coupledSelector Q z := by + unfold coupledSelector + rw [Matrix.diagonal_mul_diagonal] + ext s t + by_cases hst : s=t + · subst t + simp only [Matrix.diagonal_apply_eq,Matrix.smul_apply,smul_eq_mul] + by_cases h : s.1=z + · simp [h] + · simp [h] + · simp [hst] + +theorem threeSpinProjector_sub_one_eigen (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) : + (threeGram Q-1)*threeSpinProjector Q hQ z = + gramEigenvalueFormula Q z.val • threeSpinProjector Q hQ z := by + unfold threeSpinProjector + calc + _ = ((threeGram Q-1)*coupledBasisMatrix Q hQ)*coupledSelector Q z*(coupledBasisMatrix Q hQ)ᵀ := by + simp only [Matrix.mul_assoc] + _ = coupledBasisMatrix Q hQ * + (Matrix.diagonal (fun s : CoupledIndex Q => gramEigenvalueFormula Q s.1.val)*coupledSelector Q z)* + (coupledBasisMatrix Q hQ)ᵀ := by rw [coupledBasis_eigen]; simp only [Matrix.mul_assoc] + _ = _ := by rw [coupledSelector_eigen]; simp only [Matrix.mul_smul,Matrix.smul_mul] + +theorem threeSpinProjector_eigen (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) : + threeGram Q*threeSpinProjector Q hQ z = + (1+gramEigenvalueFormula Q z.val) • threeSpinProjector Q hQ z := by + have he := threeSpinProjector_sub_one_eigen Q hQ z + rw [Matrix.sub_mul,Matrix.one_mul] at he + calc + _ = (threeGram Q*threeSpinProjector Q hQ z-threeSpinProjector Q hQ z)+threeSpinProjector Q hQ z := by abel + _ = gramEigenvalueFormula Q z.val • threeSpinProjector Q hQ z+threeSpinProjector Q hQ z := by rw [he] + _ = _ := by ext i j; simp only [Matrix.add_apply,Matrix.smul_apply,smul_eq_mul]; ring + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/TraceCertificate.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/TraceCertificate.lean new file mode 100644 index 0000000000000000000000000000000000000000..e4e458f724dc1e58d0700ee37824c2102541a529 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/TraceCertificate.lean @@ -0,0 +1,92 @@ +import OAI.Analysis.Laughlin.FourBody.ErrorCertificate +import OAI.Analysis.Laughlin.ThreeBody.Radical +import OAI.Analysis.Laughlin.ThreeBody.TraceLimit + +namespace OAI + +namespace Laughlin.Spin + + theorem threeBodyInner_certificate (z T t : ℕ) (hz : z ≤ T) + (entries : List (ℕ × ℕ × ℤ)) : + threeBodyInner (fun z T p => couplingPolynomialCoefficient + (Real.sqrt (1/3)) (Real.sqrt (2/3)) z (T-z) p) z T t entries = + (threeBodyRadical z T t / 10^7) * (Certificate.X entries z T : ℝ) := by + induction entries with + | nil => simp [threeBodyInner,Certificate.X] + | cons e es ih => + simp only [threeBodyInner,List.map_cons,List.sum_cons] at ih ⊢ + rw [ih] + change _ = (threeBodyRadical z T t/10^7) * + (((if e.1+e.2.1=T then e.2.2*Certificate.U 2 z T e.1 else 0)+Certificate.X es z T : ℤ) : ℝ) + rw [Int.cast_add] + by_cases he : e.1+e.2.1=T + · rw [ite_eq_left he,ite_eq_left he,sourceAlpha_factor, + source_threeBody_radical_coefficient z T e.1 hz (by omega)] + simp only [Int.cast_mul] + have hc := threeBody_alpha_radical_cancel z T t e.1 e.2.1 he + calc + _ = ((e.2.2 : ℝ)*(Certificate.U 2 z T e.1 : ℝ)/10^7) * + (alphaRadical t e.1 e.2.1 * threeBodyRadical z T e.1) + + threeBodyRadical z T t/10^7 * (Certificate.X es z T : ℝ) := by ring + _ = _ := by rw [hc]; ring + · simp [he] + +noncomputable def rationalThreeBodyLevel (z T : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) : ℚ := + ((2 : ℚ)^z * (T.choose z : ℚ) / ((3 : ℚ)^T * (2 : ℚ)^row.1 * (T.choose row.1 : ℚ))) * + (Certificate.X row.2.2 z T : ℚ) * + ((Certificate.X row.2.2 z T : ℚ)+2*(row.2.1 : ℚ)*(Certificate.U 2 z T row.1 : ℚ)) + +theorem threeBodyLevel_certificate (z T : ℕ) (row : ℕ × ℤ × List (ℕ × ℕ × ℤ)) + (hz : z ≤ T) (ht : row.1 ≤ T) : + (let a := threeBodyInner (fun z T p => couplingPolynomialCoefficient + (Real.sqrt (1/3)) (Real.sqrt (2/3)) z (T-z) p) z T row.1 row.2.2; + 2*((row.2.1 : ℝ)/10^7)*couplingPolynomialCoefficient + (Real.sqrt (1/3)) (Real.sqrt (2/3)) z (T-z) row.1*a+a^2) = + (1/(10^14) : ℝ)*(rationalThreeBodyLevel z T row : ℝ) := by + dsimp only + rw [threeBodyInner_certificate z T row.1 hz, + source_threeBody_radical_coefficient z T row.1 hz ht] + calc + _ = (1/(10^14) : ℝ)*(threeBodyRadical z T row.1)^2 * (Certificate.X row.2.2 z T : ℝ) * + ((Certificate.X row.2.2 z T : ℝ)+2*(row.2.1 : ℝ)*(Certificate.U 2 z T row.1 : ℝ)) := by ring + _ = _ := by + rw [threeBodyRadical_sq_choose z T row.1 hz ht] + unfold rationalThreeBodyLevel + push_cast + ring + +theorem source_threeBody_trace_certificate_identity (z : ℕ) : + limitThreeBodyTraceFormula z = (Certificate.e z : ℝ) := by + unfold limitThreeBodyTraceFormula threeBodyTraceFormula + have he : Certificate.rows.map (fun row => + (((List.range 16).filter (fun T => max z row.1 ≤ T)).map (fun T => + let a := threeBodyInner (fun z T p => couplingPolynomialCoefficient + (Real.sqrt (1/3)) (Real.sqrt (2/3)) z (T-z) p) z T row.1 row.2.2; + 2*((row.2.1 : ℝ)/10^7)*couplingPolynomialCoefficient + (Real.sqrt (1/3)) (Real.sqrt (2/3)) z (T-z) row.1*a+a^2)).sum) = + Certificate.rows.map (fun row => (((List.range 16).filter (fun T => max z row.1 ≤ T)).map + (fun T => (1/(10^14) : ℝ)*(rationalThreeBodyLevel z T row : ℝ))).sum) := by + apply List.map_congr_left; intro row hrow + apply congrArg List.sum + apply List.map_congr_left; intro T hT + simp only [List.mem_filter,decide_eq_true_eq,max_le_iff] at hT + exact threeBodyLevel_certificate z T row hT.2.1 hT.2.2 + rw [he] + simp_rw [real_list_sum_scale] + unfold Certificate.e rationalThreeBodyLevel + push_cast + simp only [List.map_map,Function.comp_def] + push_cast + simp only [List.map_map,Function.comp_def] + push_cast + ring + + theorem source_physical_threeBody_trace_formula_tendsto (z : ℕ) : + Filter.Tendsto (fun Q => physicalThreeBodyTraceFormula Q z) Filter.atTop + (nhds (Certificate.e z : ℝ)) := by + rw [← source_threeBody_trace_certificate_identity] + exact physicalThreeBodyTraceFormula_tendsto z + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/TraceComparison.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/TraceComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..a918d2e9978431dfb15bfa30011f3527416b1198 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/TraceComparison.lean @@ -0,0 +1,59 @@ +import OAI.Analysis.Laughlin.Asymptotics.ScalarBudget +import OAI.Analysis.Laughlin.ThreeBody.PhysicalTrace + +namespace OAI + +namespace Laughlin.Spin +open scoped Topology +open Filter + +noncomputable def threeBodyDimensionRatio (Q z : ℕ) : ℝ := + (3*(Q : ℝ)-1-2*z)/(2*(Q : ℝ)-1) + +theorem threeBodyDimensionRatio_tendsto (z : ℕ) : + Tendsto (fun Q => threeBodyDimensionRatio Q z) atTop (𝓝 (3/2 : ℝ)) := by + have h := tendsto_add_mul_div_add_mul_atTop_nhds (-1-2*(z : ℝ)) (-1 : ℝ) 3 (d := 2) (by norm_num) + convert h using 1 + ext Q + unfold threeBodyDimensionRatio + congr 1 <;> ring + +theorem source_threeBody_trace_strict_eventually (z : ℕ) + (hz : z ∈ [2,4,5,6,7,8,9,10,11,12,13,14,15]) : + ∀ᶠ Q : ℕ in atTop, physicalThreeBodyTraceFormula Q z < + threeBodyDimensionRatio Q z * gramEigenvalueFormula Q z := by + have h := ((threeBodyDimensionRatio_tendsto z).mul (gramEigenvalueFormula_tendsto z)).sub + (source_physical_threeBody_trace_formula_tendsto z) + have hl : 0 < (3/2 : ℝ)*((3*(z : ℝ)-1)*(-1/2 : ℝ)^z)-(Certificate.e z : ℝ) := by + have hh := three_body_real z hz + nlinarith only [hh] + exact ((tendsto_order.mp h).1 0 hl).mono (fun Q hQ => by linarith) + +theorem eventually_list_all {I : Type*} (l : List I) (P : ℕ → I → Prop) + (h : ∀ i ∈ l, ∀ᶠ Q in atTop, P Q i) : ∀ᶠ Q in atTop, ∀ i ∈ l, P Q i := by + induction l with + | nil => simp + | cons a l ih => + filter_upwards [h a (by simp),ih (fun i hi => h i (by simp [hi]))] with Q ha hl + intro i hi + rcases List.mem_cons.mp hi with rfl | hi + · exact ha + · exact hl i hi + +theorem source_threeBody_physical_traces_strict_eventually : + ∀ᶠ Q : ℕ in atTop, ∃ hQ : 15 ≤ Q, ∀ z : Fin (Q+1), + z.val ∈ [2,4,5,6,7,8,9,10,11,12,13,14,15] → + Matrix.trace (threeSpinProjector Q (by omega) z * physicalThreeBodyMatrix Q) < + threeBodyDimensionRatio Q z.val * gramEigenvalueFormula Q z.val := by + have hall := eventually_list_all [2,4,5,6,7,8,9,10,11,12,13,14,15] + (fun Q z => physicalThreeBodyTraceFormula Q z < threeBodyDimensionRatio Q z * gramEigenvalueFormula Q z) + source_threeBody_trace_strict_eventually + filter_upwards [eventually_ge_atTop 15,hall] with Q hQ h + refine ⟨hQ,?_⟩ + intro z hz + rw [source_physical_threeBody_trace_identity Q hQ] + exact h z.val hz + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/TraceLimit.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/TraceLimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..5dfa196f5c7ff5621cc893677a67c84765aa2743 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/TraceLimit.lean @@ -0,0 +1,55 @@ +import OAI.Analysis.Laughlin.FourBody.ErrorLimit +import OAI.Analysis.Laughlin.Spin.Specializations + +namespace OAI + +namespace Laughlin.Spin +open scoped Topology +open Filter + +noncomputable def threeBodyInner (s : ℕ → ℕ → ℕ → ℝ) (z T t : ℕ) + (entries : List (ℕ × ℕ × ℤ)) : ℝ := + (entries.map (fun e => if e.1+e.2.1=T then sourceAlpha t e * s z T e.1 else 0)).sum + +noncomputable def threeBodyTraceFormula (s : ℕ → ℕ → ℕ → ℝ) (z : ℕ) : ℝ := + (Certificate.rows.map (fun row => + (((List.range 16).filter (fun T => max z row.1 ≤ T)).map (fun T => + let a := threeBodyInner s z T row.1 row.2.2 + 2*((row.2.1 : ℝ)/10^7)*s z T row.1*a+a^2)).sum)).sum + +noncomputable def physicalThreeBodyTraceFormula (Q z : ℕ) : ℝ := + threeBodyTraceFormula (physicalCouplingCoefficient (2*Q-2) Q) z +noncomputable def limitThreeBodyTraceFormula (z : ℕ) : ℝ := + threeBodyTraceFormula (fun z T p => couplingPolynomialCoefficient + (Real.sqrt (1/3)) (Real.sqrt (2/3)) z (T-z) p) z + +theorem threeBodyInner_tendsto (z T t : ℕ) (entries : List (ℕ × ℕ × ℤ)) (hz : z ≤ T) : + Tendsto (fun Q => threeBodyInner (physicalCouplingCoefficient (2*Q-2) Q) z T t entries) + atTop (𝓝 (threeBodyInner (fun z T p => couplingPolynomialCoefficient + (Real.sqrt (1/3)) (Real.sqrt (2/3)) z (T-z) p) z T t entries)) := by + apply physical_list_sum_tendsto + intro e he + by_cases h : e.1+e.2.1=T + · simp only [ite_eq_left h] + exact tendsto_const_nhds.mul (source_threeBody_coupling_tendsto z T e.1 hz (by omega)) + · simp only [ite_eq_right h] + exact tendsto_const_nhds + +theorem physicalThreeBodyTraceFormula_tendsto (z : ℕ) : + Tendsto (fun Q => physicalThreeBodyTraceFormula Q z) atTop + (𝓝 (limitThreeBodyTraceFormula z)) := by + unfold physicalThreeBodyTraceFormula limitThreeBodyTraceFormula threeBodyTraceFormula + apply physical_list_sum_tendsto + intro row hrow + apply physical_list_sum_tendsto + intro T hT + have h : z ≤ T ∧ row.1 ≤ T := by + simp only [List.mem_filter,decide_eq_true_eq, max_le_iff] at hT + exact hT.2 + exact ((tendsto_const_nhds.mul (source_threeBody_coupling_tendsto z T row.1 h.1 h.2)).mul + (threeBodyInner_tendsto z T row.1 row.2.2 h.1)).add + ((threeBodyInner_tendsto z T row.1 row.2.2 h.1).pow 2) + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/ThreeBody/TraceReadout.lean b/lean/OAI/Analysis/Laughlin/ThreeBody/TraceReadout.lean new file mode 100644 index 0000000000000000000000000000000000000000..8706944e8231ccbcca3819fb28a5ec81468e8d1e --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/ThreeBody/TraceReadout.lean @@ -0,0 +1,81 @@ +import OAI.Analysis.Laughlin.ThreeBody.PhysicalMatrix + +namespace OAI + +namespace Laughlin.Spin +open scoped BigOperators Matrix + +noncomputable def phasedThreeDescendant (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (n : ℕ) : + PairOrbitalIndex Q → ℝ := + (-1 : ℝ)^z.val • normalizedCoupledDescendant Q z.val hQ (by omega) n + +theorem phasedThreeDescendant_off (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (n : ℕ) + (i : PairOrbitalIndex Q) (hi : i.1.val+i.2.val ≠ z.val+n) : + phasedThreeDescendant Q hQ z n i = 0 := by + have hh := genericUnitDescendant_off (2*Q-2) Q z.val n (by omega) (by omega) i hi + change (-1 : ℝ)^z.val * genericUnitDescendant (2*Q-2) Q z.val (by omega) (by omega) n i = 0 + rw [hh,mul_zero] + +theorem phasedThreeDescendant_at_level (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (T p j : ℕ) + (hz : z.val ≤ T) (hT : T ≤ Q) (hpj : p+j=T) : + phasedThreeDescendant Q hQ z (T-z.val) (⟨p,by omega⟩,⟨j,by omega⟩) = + physicalCouplingCoefficient (2*Q-2) Q z.val T p := by + rw [physicalCouplingCoefficient,dite_eq_left ⟨hz,by omega,by omega,hT⟩] + have hj : T-p=j := by omega + subst j + rfl + +theorem threeBodyLevelVector_dot {Q : ℕ} (v : PairOrbitalIndex Q → ℝ) (t T : ℕ) + (entries : List (ℕ × ℕ × ℤ)) : + dotProduct v (threeBodyLevelVector Q t T entries) = + (entries.map (fun e => if e.1+e.2.1=T then sourceAlpha t e * + dotProduct v (pairOrbitalUnit Q e.1 e.2.1) else 0)).sum := by + induction entries with + | nil => simp [threeBodyLevelVector] + | cons e es ih => + simp only [threeBodyLevelVector,List.map_cons,List.sum_cons] at ih ⊢ + rw [dotProduct_add,ih] + by_cases h : e.1+e.2.1=T + · simp [h,dotProduct_smul,mul_comm] + · simp [h] + +theorem phasedThreeDescendant_unit_off (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (n p j : ℕ) + (h : p+j ≠ z.val+n) : + dotProduct (phasedThreeDescendant Q hQ z n) (pairOrbitalUnit Q p j) = 0 := by + apply Finset.sum_eq_zero + intro i hi + simp only [pairOrbitalUnit] + split_ifs with he + · rw [phasedThreeDescendant_off Q hQ z n i (by omega),zero_mul] + · exact mul_zero _ + +theorem threeBodyLevelVector_descendant_off (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (n t T : ℕ) + (entries : List (ℕ × ℕ × ℤ)) (h : T ≠ z.val+n) : + dotProduct (phasedThreeDescendant Q hQ z n) (threeBodyLevelVector Q t T entries) = 0 := by + rw [threeBodyLevelVector_dot] + have he : entries.map (fun e => if e.1+e.2.1=T then sourceAlpha t e * + dotProduct (phasedThreeDescendant Q hQ z n) (pairOrbitalUnit Q e.1 e.2.1) else 0) = entries.map (fun _ => (0 : ℝ)) := by + apply List.map_congr_left + intro e he + split_ifs with hT + · rw [phasedThreeDescendant_unit_off Q hQ z n e.1 e.2.1 (by omega),mul_zero] + · rfl + rw [he] + simp + +theorem threeBodyLevelVector_descendant (Q : ℕ) (hQ : 2 ≤ Q) (z : Fin (Q+1)) (t T : ℕ) + (entries : List (ℕ × ℕ × ℤ)) (hz : z.val ≤ T) (hT : T ≤ Q) : + dotProduct (phasedThreeDescendant Q hQ z (T-z.val)) (threeBodyLevelVector Q t T entries) = + threeBodyInner (physicalCouplingCoefficient (2*Q-2) Q) z.val T t entries := by + rw [threeBodyLevelVector_dot] + apply congrArg List.sum + apply List.map_congr_left + intro e he + split_ifs with h + · rw [pairOrbitalUnit_dot Q e.1 e.2.1 (by omega) (by omega), + phasedThreeDescendant_at_level Q hQ z T e.1 e.2.1 hz hT h] + · rfl + +end Laughlin.Spin + +end OAI diff --git a/lean/OAI/Analysis/Laughlin/UniformGap.lean b/lean/OAI/Analysis/Laughlin/UniformGap.lean new file mode 100644 index 0000000000000000000000000000000000000000..aad1bf4c9a3157151db98b0718a8118055d5c3e8 --- /dev/null +++ b/lean/OAI/Analysis/Laughlin/UniformGap.lean @@ -0,0 +1,35 @@ +import OAI.Analysis.Laughlin.GapEstimates +import OAI.Analysis.Laughlin.Charge.LaughlinGround +import OAI.Analysis.Laughlin.Charge.Overlap + +namespace OAI + +namespace Laughlin +open Fock + +theorem uniform_fock_gap (γ : ℝ) (_hγ0 : 0<γ) (hγ : γ p.val) + (by intro p; have := p.isLt; omega) + simpa only [Fintype.card_fin, partialHamiltonian, + Fin.sum_univ_eq_sum_range (fun p => (pairAnnihilator Q p)ᴴ * pairAnnihilator Q p) P] using h + + + +theorem fockAverage_local_error {Q : ℕ} (hQ : 24 ≤ Q) : + ((2*Q-1 : ℕ) : ℂ) • fockAverage Q (partialHamiltonian Q 24) = (24 : ℂ) • hamiltonian Q := by + rw [fockAverage_partialHamiltonian (by omega) (by omega), smul_smul] + have hn : ((2*Q-1 : ℕ) : ℂ) ≠ 0 := by exact_mod_cast (show 2*Q-1 ≠ 0 by omega) + congr 1 + field_simp + norm_num + + +def fourCopyAllowance (Q : ℕ) : FockMatrix Q := + ((2*Q-1 : ℕ) : ℂ) • ∑ D ∈ Finset.Icc 1 23, + fockAverage Q (∑ r : CopyLabel D, + (highestFourAnnihilator Q D r)ᴴ * highestFourAnnihilator Q D r) + + + +theorem fourCopyAllowance_bound {Q : ℕ} (hQ : 24 ≤ Q) : + ((1222 : ℂ) • hamiltonian Q - fourCopyAllowance Q).PosSemidef := by + have hb (D : ℕ) (hD : D ∈ Finset.Icc 1 23) : + ((Fintype.card (FourHighestShell Q D) : ℂ) • hamiltonian Q - + ((2*Q-1 : ℕ) : ℂ) • fockAverage Q (∑ r : CopyLabel D, + (highestFourAnnihilator Q D r)ᴴ * highestFourAnnihilator Q D r)).PosSemidef := by + have hd : D ≤ Q := by have := (Finset.mem_Icc.mp hD).2; omega + have he := fockAverage_posSemidef Q _ (highestFourAnnihilator_pair_posSemidef hd) + rw [map_sub, fockAverage_pair_family (by omega : 1 ≤ Q) + (fun b : FourHighestShell Q D => b.val.1.val) + (by intro b; have := b.val.1.isLt; omega)] at he + have hs := he.smul (show (0:ℂ) ≤ ((2*Q-1 : ℕ) : ℂ) by exact_mod_cast Nat.zero_le _) + have hn : ((2*Q-1 : ℕ) : ℂ) ≠ 0 := by exact_mod_cast (show 2*Q-1 ≠ 0 by omega) + simpa only [smul_sub, smul_smul, mul_div_cancel₀ _ hn] using hs + have hs := Matrix.posSemidef_sum (Finset.Icc 1 23) hb + have hc := congrArg (fun n : ℕ => (n : ℂ)) (fourHighestShell_count (by omega : 23 ≤ Q)) + push_cast at hc + simpa only [Finset.sum_sub_distrib, ← Finset.sum_smul, hc, ← Finset.smul_sum, + fourCopyAllowance] using hs + + + +def averagedFourComparison {ι : Type*} [Fintype ι] (rows : ι → ComparisonRow) + (ε : ℝ) (Q : ℕ) : FockMatrix Q := + ((2*Q-1 : ℕ) : ℂ) • ∑ D ∈ Finset.Icc 1 23, + fockAverage Q (∑ r, ∑ s, fourComparison rows ε Q D r s • + ((highestFourAnnihilator Q D r)ᴴ * highestFourAnnihilator Q D s)) + + + +theorem averagedFourComparison_transfer {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) (ε : ℝ) + (hCertificate : ∀ D, 1 ≤ D → D ≤ 23 → + (planarFourGram D * planarFourComparison rows ε D * planarFourGram D).PosSemidef) : + ∃ e : ℕ → ℝ, (∀ Q, 0 ≤ e Q) ∧ Tendsto e atTop (𝓝 0) ∧ + ∀ Q, 24 ≤ Q → (averagedFourComparison rows ε Q + e Q • hamiltonian Q).PosSemidef := by + obtain ⟨ρ, hρpos, hρlim, hρ⟩ := fourComparison_uniform_transfer rows ε hCertificate + refine ⟨fun Q => 552 * ρ Q, fun Q => mul_nonneg (by norm_num) (hρpos Q), ?_, ?_⟩ + · simpa using hρlim.const_mul 552 + intro Q hQ + have he (D : ℕ) (hD : D ∈ Finset.Icc 1 23) : + (((2*Q-1 : ℕ) : ℂ) • fockAverage Q + (∑ r, ∑ s, fourComparison rows ε Q D r s • + ((highestFourAnnihilator Q D r)ᴴ * highestFourAnnihilator Q D s)) + + (24*ρ Q : ℝ) • hamiltonian Q).PosSemidef := by + have hs := fockAverage_posSemidef Q _ + (hρ D (Finset.mem_Icc.mp hD).1 (Finset.mem_Icc.mp hD).2 Q hQ) + rw [map_add, (fockAverage Q).map_smul_of_tower] at hs + have ht := hs.smul (show (0:ℂ) ≤ ((2*Q-1 : ℕ) : ℂ) by exact_mod_cast Nat.zero_le _) + rw [smul_add, smul_comm _ (ρ Q), fockAverage_local_error hQ] at ht + convert ht using 1 + rw [RCLike.real_smul_eq_coe_smul (K:=ℂ) (ρ Q), smul_smul, + RCLike.real_smul_eq_coe_smul (K:=ℂ) (24*ρ Q)] + push_cast + congr 1 + ring_nf + have hs := Matrix.posSemidef_sum (Finset.Icc 1 23) he + simp only [Finset.sum_add_distrib, ← Finset.smul_sum, Finset.sum_const, + Nat.card_Icc, show 23+1-1=23 by omega] at hs + rw [← Nat.cast_smul_eq_nsmul ℝ, smul_smul] at hs + norm_num only [Nat.cast_ofNat] at hs + have hc : (24*ρ Q : ℝ)*23 = 552*ρ Q := by ring + simpa only [hc, averagedFourComparison] using hs + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Assembly.lean b/lean/OAI/Analysis/LaughlinFock/Assembly.lean new file mode 100644 index 0000000000000000000000000000000000000000..46188ba5ae35c13a7d24e0b30aade9e73a04da04 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Assembly.lean @@ -0,0 +1,43 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.CertificateRows +import OAI.Analysis.LaughlinFock.FourBound + +namespace OAI + +/-! Assembly. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder +open Filter Topology + + + +theorem integer_threshold_of_certificates_le {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) + (hEta : rowsEta rows ≤ 93527408868499 / 10^14) + (hThree : ∀ z : ComparedThreeBlock, + planarRowsThreeTrace rows z.val.val < + (3/2 : ℝ)*(3*(z.val.val : ℝ)-1)*(-1/2)^z.val.val) + (hFour : ∀ D, 1 ≤ D → D ≤ 23 → + (planarFourGram D * planarFourComparison rows (3/10^6) D * planarFourGram D).PosSemidef) + (γ : ℝ) (hγ : γ < gammaStar) : + ∃ Qγ : ℤ, 1 ≤ Qγ ∧ ∀ Q : ℤ, Qγ ≤ Q → FockInequality Q.toNat γ := by + obtain ⟨e, _, helim, hb⟩ := + fockInequality_eventual_of_certificates rows (3/10^6) (by norm_num) hThree hFour + have hl : Tendsto (fun Q => 1-(93527408868499 / 10^14 : ℝ)- + tailCoefficient Q-1222*(3/10^6)-e Q) atTop (𝓝 gammaStar) := by + have h := (((tendsto_const_nhds (x := 1-(93527408868499 / 10^14 : ℝ))).sub + tailCoefficient_tendsto).sub_const (1222*(3/10^6))).sub helim + simpa only [sub_zero, final_margin_arithmetic] using h + apply uniform_integer_threshold_of_eventual_bound _ hl _ γ hγ + filter_upwards [hb] with Q hQ + exact hQ.mono (by linarith only [hEta]) + +theorem certificateEta_le : rowsEta certificateRows ≤ 93527408868499 / 10^14 := by + rw [certificateEta] + norm_num + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/AveragedOperators.lean b/lean/OAI/Analysis/LaughlinFock/AveragedOperators.lean new file mode 100644 index 0000000000000000000000000000000000000000..296ee6b4625586d03044048e1ed884634204a657 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/AveragedOperators.lean @@ -0,0 +1,131 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PositiveIntegrals + +namespace OAI + +/-! Averaged Operators. -/ +noncomputable section +namespace LaughlinFock +open scoped Matrix Matrix.Norms.Elementwise ComplexOrder BigOperators +open MeasureTheory +local instance averagedOperatorsContinuousENorm {ι κ : Type*} [Fintype ι] [Fintype κ] : + ContinuousENorm (Matrix ι κ ℂ) := + inferInstanceAs (ContinuousENorm (ι → κ → ℂ)) + + +theorem matrixIntegral_mul_left_right {G ι κ α β : Type*} + [MeasurableSpace G] [Fintype ι] [Fintype κ] [Fintype α] [Fintype β] + (μ : Measure G) {M : G → Matrix ι κ ℂ} (hM : Integrable M μ) + (A : Matrix α ι ℂ) (B : Matrix κ β ℂ) : + A * (∫ g, M g ∂μ) * B = ∫ g, A * M g * B ∂μ := by + let L : Matrix ι κ ℂ →ₗ[ℂ] Matrix α β ℂ := + { toFun := fun X => A * X * B + map_add' _ _ := by simp [Matrix.mul_add, Matrix.add_mul] + map_smul' _ _ := by simp [Matrix.mul_smul, Matrix.smul_mul] } + exact (L.toContinuousLinearMap.integral_comp_comm hM).symm + + +theorem matrixIntegral_trace {G ι : Type*} [MeasurableSpace G] [Fintype ι] + (μ : Measure G) {M : G → Matrix ι ι ℂ} (hM : Integrable M μ) : + (∫ g, M g ∂μ).trace = ∫ g, (M g).trace ∂μ := + ((Matrix.traceLinearMap ι ℂ ℂ).toContinuousLinearMap.integral_comp_comm hM).symm + + + +def matrixConjugationAverage {G ι : Type*} [MeasurableSpace G] [Fintype ι] + (μ : Measure G) (U : G → Matrix ι ι ℂ) (M : Matrix ι ι ℂ) : Matrix ι ι ℂ := + ∫ g, U g * M * (U g)ᴴ ∂μ + +theorem matrixConjugationAverage_posSemidef {G ι : Type*} + [MeasurableSpace G] [Fintype ι] (μ : Measure G) (U : G → Matrix ι ι ℂ) + (M : Matrix ι ι ℂ) (hM : M.PosSemidef) + (hI : Integrable (fun g => U g * M * (U g)ᴴ) μ) : + (matrixConjugationAverage μ U M).PosSemidef := + conjugationIntegral_posSemidef μ U M hM hI + + +theorem matrixConjugationAverage_invariant {G ι : Type*} + [Group G] [MeasurableSpace G] [MeasurableMul G] [Fintype ι] [DecidableEq ι] + (μ : Measure G) [μ.IsMulLeftInvariant] (U : G →* Matrix ι ι ℂ) + (M : Matrix ι ι ℂ) (hI : Integrable (fun g => U g * M * (U g)ᴴ) μ) (h : G) : + U h * matrixConjugationAverage μ U M * (U h)ᴴ = + matrixConjugationAverage μ U M := by + unfold matrixConjugationAverage + rw [matrixIntegral_mul_left_right μ hI] + calc + _ = ∫ g, U (h*g) * M * (U (h*g))ᴴ ∂μ := by + apply integral_congr_ae + exact Filter.Eventually.of_forall fun g => by + simp only [map_mul, Matrix.conjTranspose_mul, Matrix.mul_assoc] + _ = _ := integral_mul_left_eq_self (μ := μ) (fun g => U g * M * (U g)ᴴ) h + + + +theorem matrixConjugationAverage_commutes {G ι : Type*} + [Group G] [MeasurableSpace G] [MeasurableMul G] [Fintype ι] [DecidableEq ι] + (μ : Measure G) [μ.IsMulLeftInvariant] (U : G →* Matrix ι ι ℂ) + (hU : ∀ g, (U g)ᴴ * U g = 1) (M : Matrix ι ι ℂ) + (hI : Integrable (fun g => U g * M * (U g)ᴴ) μ) (h : G) : + matrixConjugationAverage μ U M * U h = U h * matrixConjugationAverage μ U M := by + have hv := congrArg (fun A => A * U h) (matrixConjugationAverage_invariant μ U M hI h) + simpa only [Matrix.mul_assoc, hU, Matrix.mul_one] using hv.symm + + +theorem matrixConjugationAverage_trace {G ι : Type*} + [MeasurableSpace G] [Fintype ι] [DecidableEq ι] + (μ : Measure G) [IsProbabilityMeasure μ] (U : G → Matrix ι ι ℂ) + (hU : ∀ g, (U g)ᴴ * U g = 1) (M : Matrix ι ι ℂ) + (hI : Integrable (fun g => U g * M * (U g)ᴴ) μ) : + (matrixConjugationAverage μ U M).trace = M.trace := by + rw [matrixConjugationAverage, matrixIntegral_trace μ hI] + have ht (g : G) : (U g * M * (U g)ᴴ).trace = M.trace := by + rw [Matrix.trace_mul_cycle, hU, Matrix.one_mul] + simp only [ht, integral_const, probReal_univ, one_smul] + + +def matrixRepresentation {G ι : Type*} [Monoid G] [Fintype ι] [DecidableEq ι] + (U : G →* Matrix ι ι ℂ) : Representation ℂ G (ι → ℂ) := + (Matrix.toLinAlgEquiv' : Matrix ι ι ℂ ≃ₐ[ℂ] Module.End ℂ (ι → ℂ)).toMonoidHom.comp U + + +theorem matrix_scalar_of_commutes {G ι : Type*} [Monoid G] [Fintype ι] [DecidableEq ι] + (U : G →* Matrix ι ι ℂ) [Representation.IsIrreducible (matrixRepresentation U)] + (A : Matrix ι ι ℂ) (hA : ∀ g, A * U g = U g * A) : ∃ z : ℂ, A = z • 1 := by + let ρ := matrixRepresentation U + let f : Representation.IntertwiningMap ρ ρ := + { toLinearMap := Matrix.toLin' A + isIntertwining' g := by + change Matrix.toLin' A ∘ₗ Matrix.toLin' (U g) = Matrix.toLin' (U g) ∘ₗ Matrix.toLin' A + simp only [← Matrix.toLin'_mul, hA] } + obtain ⟨z, hz⟩ := + (Representation.IsIrreducible.algebraMap_intertwiningMap_bijective_of_isAlgClosed + (ρ := ρ)).surjective f + refine ⟨z, ?_⟩ + apply Matrix.toLin'.injective + have hz' := congrArg Representation.IntertwiningMap.toLinearMap hz + rw [Representation.IntertwiningMap.algebraMap_apply, + Representation.IntertwiningMap.toLinearMap_smul] at hz' + change z • LinearMap.id = Matrix.toLin' A at hz' + simpa only [map_smul, Matrix.toLin'_one] using hz'.symm + + + +theorem schur_matrix_average {G ι : Type*} + [Group G] [MeasurableSpace G] [MeasurableMul G] [Fintype ι] [DecidableEq ι] + [Nonempty ι] (μ : Measure G) [μ.IsMulLeftInvariant] [IsProbabilityMeasure μ] + (U : G →* Matrix ι ι ℂ) [Representation.IsIrreducible (matrixRepresentation U)] + (hU : ∀ g, (U g)ᴴ * U g = 1) (M : Matrix ι ι ℂ) + (hI : Integrable (fun g => U g * M * (U g)ᴴ) μ) : + matrixConjugationAverage μ U M = (M.trace / (Fintype.card ι : ℂ)) • 1 := by + obtain ⟨z, hz⟩ := matrix_scalar_of_commutes U _ + (matrixConjugationAverage_commutes μ U hU M hI) + have ht := matrixConjugationAverage_trace μ (U : G → Matrix ι ι ℂ) hU M hI + rw [hz, Matrix.trace_smul, Matrix.trace_one, smul_eq_mul] at ht + have hn : (Fintype.card ι : ℂ) ≠ 0 := by exact_mod_cast Fintype.card_ne_zero + have he : z = M.trace / (Fintype.card ι : ℂ) := (eq_div_iff hn).mpr ht + rw [hz, he] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Averaging.lean b/lean/OAI/Analysis/LaughlinFock/Averaging.lean new file mode 100644 index 0000000000000000000000000000000000000000..4a05a736f9e073c854e87818a03c35f230dd5d2c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Averaging.lean @@ -0,0 +1,131 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.AveragedOperators +import OAI.Analysis.LaughlinFock.Rotations + +namespace OAI + +/-! Averaging. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix Matrix.Norms.Elementwise ComplexOrder +open NormedSpace MeasureTheory Topology +local instance averagingContinuousENorm {ι κ : Type*} [Fintype ι] [Fintype κ] : + ContinuousENorm (Matrix ι κ ℂ) := + inferInstanceAs (ContinuousENorm (ι → κ → ℂ)) + +section +variable {J σ : Type*} {I : J → Type*} + [∀ j, Fintype (I j)] [∀ j, DecidableEq (I j)] + (X : σ → ∀ j, Matrix (I j) (I j) ℂ) + (hX : ∀ s j, (X s j)ᴴ = -X s j) + +local instance averagingRotationMeasurableSpace : MeasurableSpace (rotationGroup X hX) := borel _ +local instance averagingRotationBorelSpace : BorelSpace (rotationGroup X hX) := ⟨rfl⟩ + + + +def rotationHaar : Measure (rotationGroup X hX) := + Measure.haarMeasure (⊤ : TopologicalSpace.PositiveCompacts (rotationGroup X hX)) + +instance rotationHaar_probability : IsProbabilityMeasure (rotationHaar X hX) := + ⟨by exact Measure.haarMeasure_self⟩ + +instance rotationHaar_leftInvariant : (rotationHaar X hX).IsMulLeftInvariant := + Measure.isMulLeftInvariant_haarMeasure _ + + +def rotationEvaluation (j : J) : rotationGroup X hX →* Matrix (I j) (I j) ℂ where + toFun g := (g.val j).val + map_one' := rfl + map_mul' _ _ := rfl + +theorem rotationEvaluation_continuous (j : J) : Continuous (rotationEvaluation X hX j) := by + unfold rotationEvaluation + exact continuous_subtype_val.comp ((continuous_apply j).comp continuous_subtype_val) + +theorem rotationEvaluation_unitary (j : J) (g : rotationGroup X hX) : + (rotationEvaluation X hX j g)ᴴ * rotationEvaluation X hX j g = 1 := by + exact Unitary.star_mul_self_of_mem (g.val j).property + + + +theorem rotationOrbit_integrable (j : J) (M : Matrix (I j) (I j) ℂ) : + Integrable (fun g => rotationEvaluation X hX j g * M * + (rotationEvaluation X hX j g)ᴴ) (rotationHaar X hX) := by + have hc : Continuous (fun g => rotationEvaluation X hX j g * M * + (rotationEvaluation X hX j g)ᴴ) := + ((rotationEvaluation_continuous X hX j).mul continuous_const).mul + (rotationEvaluation_continuous X hX j).matrix_conjTranspose + exact integrableOn_univ.mp (hc.continuousOn.integrableOn_compact isCompact_univ) + + +def rotationAverage (j : J) (M : Matrix (I j) (I j) ℂ) : Matrix (I j) (I j) ℂ := + matrixConjugationAverage (rotationHaar X hX) (rotationEvaluation X hX j) M + +theorem rotationAverage_posSemidef (j : J) (M : Matrix (I j) (I j) ℂ) + (hM : M.PosSemidef) : (rotationAverage X hX j M).PosSemidef := + matrixConjugationAverage_posSemidef _ _ _ hM (rotationOrbit_integrable X hX j M) + +theorem rotationAverage_trace (j : J) (M : Matrix (I j) (I j) ℂ) : + (rotationAverage X hX j M).trace = M.trace := + matrixConjugationAverage_trace _ _ (rotationEvaluation_unitary X hX j) M + (rotationOrbit_integrable X hX j M) + +theorem rotationAverage_commutes (j : J) (M : Matrix (I j) (I j) ℂ) + (g : rotationGroup X hX) : + rotationAverage X hX j M * rotationEvaluation X hX j g = + rotationEvaluation X hX j g * rotationAverage X hX j M := + matrixConjugationAverage_commutes _ _ (rotationEvaluation_unitary X hX j) M + (rotationOrbit_integrable X hX j M) g + + + +theorem rotationAverage_covariance {i j : J} + (L : Matrix (I i) (I i) ℂ →ₗ[ℂ] Matrix (I j) (I j) ℂ) + (hL : ∀ s M, L (X s i * M - M * X s i) = X s j * L M - L M * X s j) + (M : Matrix (I i) (I i) ℂ) : + L (rotationAverage X hX i M) = rotationAverage X hX j (L M) := by + unfold rotationAverage matrixConjugationAverage + refine (L.toContinuousLinearMap.integral_comp_comm + (rotationOrbit_integrable X hX i M)).symm.trans ?_ + apply integral_congr_ae + exact Filter.Eventually.of_forall fun g => rotationGroup_covariance X hX L hL g M + +theorem rotationAverage_one (j : J) : + rotationAverage X hX j 1 = 1 := by + have hU (g : rotationGroup X hX) : + rotationEvaluation X hX j g * (rotationEvaluation X hX j g)ᴴ = 1 := + Unitary.mul_star_self_of_mem (g.val j).property + simp [rotationAverage, matrixConjugationAverage, hU] + +theorem rotationAverage_add (j : J) (M N : Matrix (I j) (I j) ℂ) : + rotationAverage X hX j (M+N) = rotationAverage X hX j M + rotationAverage X hX j N := by + simp only [rotationAverage, matrixConjugationAverage, Matrix.mul_add, Matrix.add_mul] + exact integral_add (rotationOrbit_integrable X hX j M) (rotationOrbit_integrable X hX j N) + +theorem rotationAverage_smul (j : J) (c : ℂ) (M : Matrix (I j) (I j) ℂ) : + rotationAverage X hX j (c • M) = c • rotationAverage X hX j M := by + simp only [rotationAverage, matrixConjugationAverage, Matrix.mul_smul, Matrix.smul_mul, + integral_smul] + + +def rotationAverageLinear (j : J) : Matrix (I j) (I j) ℂ →ₗ[ℂ] Matrix (I j) (I j) ℂ where + toFun := rotationAverage X hX j + map_add' := rotationAverage_add X hX j + map_smul' := rotationAverage_smul X hX j + +theorem rotationAverage_real_smul (j : J) (r : ℝ) (M : Matrix (I j) (I j) ℂ) : + rotationAverage X hX j (r • M) = r • rotationAverage X hX j M := + (rotationAverageLinear X hX j).map_smul_of_tower r M + +theorem rotationAverage_relative (j : J) (A H : Matrix (I j) (I j) ℂ) (r : ℝ) + (h : (A + r • H).PosSemidef) : + (rotationAverage X hX j A + r • rotationAverage X hX j H).PosSemidef := by + have hp := rotationAverage_posSemidef X hX j (A+r•H) h + rwa [rotationAverage_add, rotationAverage_real_smul] at hp + +end +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/BesselComparison.lean b/lean/OAI/Analysis/LaughlinFock/BesselComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..3eba037543538f8af86949318ea0f459c6828a67 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/BesselComparison.lean @@ -0,0 +1,185 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.CopyNormalization + +namespace OAI + +/-! Bessel Comparison. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder + + +abbrev CopyLabel (D : ℕ) := {r : Fin (D+1) // Odd r.val} + + +abbrev FourUncoupled (Q : ℕ) := Fin (2*Q-2+1) × IncreasingPair Q + + +abbrev FourHighestShell (Q D : ℕ) := + {b : FourUncoupled Q // b.1.val+b.2.val.1.val+b.2.val.2.val=D} + + +theorem sum_subtype_support {ι M : Type*} [Fintype ι] [AddCommMonoid M] + (P : ι → Prop) [DecidablePred P] (f : ι → M) + (hf : ∀ i, ¬P i → f i=0) : (∑ i : {i // P i}, f i.val) = ∑ i, f i := by + classical + rw [← Finset.sum_subtype (Finset.univ.filter P) (by simp) f, Finset.sum_filter] + apply Finset.sum_congr rfl + intro i _ + split_ifs with h + · rfl + · exact (hf i h).symm + + + +def highestCopyMatrix (Q D : ℕ) : Matrix (CopyLabel D) (FourHighestShell Q D) ℂ := + fun r b => sphericalCopyCoefficient Q D D r.val.val + b.val.1.val b.val.2.val.1.val b.val.2.val.2.val + + + +theorem highestCopyMatrix_gram {Q D : ℕ} (hD : D ≤ Q) : + highestCopyMatrix Q D * (highestCopyMatrix Q D)ᴴ = 1 := by + classical + ext r s + have h := sphericalCopyCoefficient_highest_gram hD + (Nat.le_of_lt_succ r.val.isLt) (Nat.le_of_lt_succ s.val.isLt) r.property s.property + have he : (r.val.val=s.val.val) ↔ r=s := by + constructor + · intro h + exact Subtype.ext (Fin.ext h) + · rintro rfl + rfl + simp only [he] at h + rw [← sum_subtype_support + (fun b : FourUncoupled Q => b.1.val+b.2.val.1.val+b.2.val.2.val=D) + (fun b => sphericalCopyCoefficient Q D D r.val.val b.1.val b.2.val.1.val b.2.val.2.val * + sphericalCopyCoefficient Q D D s.val.val b.1.val b.2.val.1.val b.2.val.2.val)] at h + · have hc := congrArg (fun t : ℝ => (t : ℂ)) h + simpa only [Matrix.mul_apply, Matrix.conjTranspose_apply, highestCopyMatrix, + Complex.star_def, Complex.conj_ofReal, Complex.ofReal_sum, Complex.ofReal_mul, + Matrix.one_apply, apply_ite, Complex.ofReal_one, Complex.ofReal_zero] using hc + · intro b hb + simp [sphericalCopyCoefficient, hb] + + +def shellFourAnnihilator (Q D : ℕ) (b : FourHighestShell Q D) : FockMatrix Q := + annihilator Q b.val.2.val.2 * annihilator Q b.val.2.val.1 * pairAnnihilator Q b.val.1.val + + + +def highestFourAnnihilator (Q D : ℕ) (r : CopyLabel D) : FockMatrix Q := + ∑ b : FourHighestShell Q D, highestCopyMatrix Q D r b • shellFourAnnihilator Q D b + + + +theorem highestFourAnnihilator_bessel {Q D : ℕ} (hD : D ≤ Q) + (ψ : Occupation Q → ℂ) : + (∑ r : CopyLabel D, ∑ A, ‖(highestFourAnnihilator Q D r *ᵥ ψ) A‖^2) ≤ + ∑ b : FourHighestShell Q D, ∑ A, ‖(shellFourAnnihilator Q D b *ᵥ ψ) A‖^2 := by + have h := row_isometry_contracts_family (highestCopyMatrix Q D) (highestCopyMatrix_gram hD) + (fun b A => (shellFourAnnihilator Q D b *ᵥ ψ) A) + simpa only [highestFourAnnihilator, Matrix.sum_mulVec, Matrix.smul_mulVec, + Finset.sum_apply, Pi.smul_apply, smul_eq_mul] using h + + + +theorem highestFourAnnihilator_pair_bound {Q D : ℕ} (hD : D ≤ Q) + (ψ : Occupation Q → ℂ) : + (∑ r : CopyLabel D, ∑ A, ‖(highestFourAnnihilator Q D r *ᵥ ψ) A‖^2) ≤ + ∑ b : FourHighestShell Q D, ∑ A, + ‖(pairAnnihilator Q b.val.1.val *ᵥ ψ) A‖^2 := by + refine (highestFourAnnihilator_bessel hD ψ).trans ?_ + exact Finset.sum_le_sum fun b _ => + twoAnnihilators_contract Q b.val.2.val.1 b.val.2.val.2 _ ψ + + + +def fourHighestShellEquiv {Q D : ℕ} (hQ : 1 ≤ Q) (hD : D ≤ Q) : + FourHighestShell Q D ≃ ((n : Fin (D+1)) × Fin ((n.val+1)/2)) where + toFun b := ⟨⟨b.val.2.val.1.val+b.val.2.val.2.val, by have := b.property; omega⟩, + ⟨b.val.2.val.1.val, by + change b.val.2.val.1.val < (b.val.2.val.1.val+b.val.2.val.2.val+1)/2 + have hlt : b.val.2.val.1.val < b.val.2.val.2.val := b.val.2.property + omega⟩⟩ + invFun c := by + let n := c.1.val + let j := c.2.val + have hn := c.1.isLt + have hj := c.2.isLt + refine ⟨(⟨D-n, by dsimp [n] at *; omega⟩, + ⟨(⟨j, by dsimp [n,j] at *; omega⟩, + ⟨n-j, by dsimp [n,j] at *; omega⟩), ?_⟩), ?_⟩ + · change j < n-j + dsimp [n,j] at * + omega + · change D-n+j+(n-j)=D + dsimp [n,j] at * + omega + left_inv b := by + apply Subtype.ext + apply Prod.ext + · apply Fin.ext + dsimp + have := b.property + omega + · apply Subtype.ext + apply Prod.ext + · apply Fin.ext + rfl + · apply Fin.ext + dsimp + omega + right_inv c := by + rcases c with ⟨n,j⟩ + apply Sigma.ext + · apply Fin.ext + dsimp + have := j.isLt + omega + · apply (Fin.heq_ext_iff ?_).mpr + · rfl + · dsimp + have := j.isLt + omega + +theorem fourHighestShell_card_sum {Q D : ℕ} (hQ : 1 ≤ Q) (hD : D ≤ Q) : + Fintype.card (FourHighestShell Q D) = ∑ n ∈ Finset.range (D+1), (n+1)/2 := by + rw [Fintype.card_congr (fourHighestShellEquiv hQ hD)] + simp only [Fintype.card_sigma, Fintype.card_fin] + exact Fin.sum_univ_eq_sum_range (fun n => (n+1)/2) (D+1) + + +theorem shell_count_formula (D : ℕ) : + (∑ n ∈ Finset.range (D+1), (n+1)/2) = (D+1)^2/4 := by + induction D using Nat.twoStepInduction with + | zero => norm_num + | one => norm_num + | more D ih _ => + rw [show D+2+1 = (D+1)+1+1 by omega, + Finset.sum_range_succ, Finset.sum_range_succ, ih] + have he : (D+2)/2 + (D+3)/2 = D+2 := by omega + have hh : (D+3)^2 = (D+1)^2 + (D+2)*4 := by ring + rw [show D+1+1 = D+2 by omega, show D+1+1+1 = D+3 by omega, + add_assoc, he, hh, Nat.add_mul_div_right] + norm_num + +theorem fourHighestShell_card {Q D : ℕ} (hQ : 1 ≤ Q) (hD : D ≤ Q) : + Fintype.card (FourHighestShell Q D) = (D+1)^2/4 := by + rw [fourHighestShell_card_sum hQ hD, shell_count_formula] + + + +theorem fourHighestShell_count {Q : ℕ} (hQ : 23 ≤ Q) : + (∑ D ∈ Finset.Icc 1 23, Fintype.card (FourHighestShell Q D)) = 1222 := by + calc + _ = ∑ D ∈ Finset.Icc 1 23, (D+1)^2/4 := by + apply Finset.sum_congr rfl + intro D hD + exact fourHighestShell_card (by omega) (by have := (Finset.mem_Icc.mp hD).2; omega) + _ = 1222 := by norm_num [Finset.sum_Icc_succ_top] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate01.lean b/lean/OAI/Analysis/LaughlinFock/Certificate01.lean new file mode 100644 index 0000000000000000000000000000000000000000..d9974b8b46ff1eea79e79bc63a959637813e610f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate01.lean @@ -0,0 +1,63 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.LDL + +namespace OAI + +/-! Certificate01. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourZData_1 : Matrix (CopyLabel 1) (CopyLabel 1) ℚ := + copyMatrixData 1 [ + [0] + ] + +def fourLData_1 : Matrix (CopyLabel 1) (CopyLabel 1) ℚ := + copyMatrixData 1 [ + [1] + ] + +def fourPivotData_1 : CopyLabel 1 → ℚ := + copyDiagonalData 1 [0] + +theorem fourOccupations_1 : highestFourOccupations 1 = ∅ := by + decide +kernel + +def fourHighestCache_1 : List (Occupation 24 × List ℚ) := [ + +] + +theorem fourHighestChecked_1 : ∀ r : CopyLabel 1, ∀ A∈highestFourOccupations 1, + kernelHighestEntry 1 r A = highestLookup fourHighestCache_1 r.val.val A := by + rw [fourOccupations_1] + apply @of_decide_eq_true _ (boundedMatrixEntriesDecidable _ _ _) + decide +kernel + +theorem fourZChecked_1 (r s : CopyLabel 1) : + integerFourGram 1 r s = fourZData_1 r s := by + rw [integerFourGram_cached 1 fourHighestCache_1 fourHighestChecked_1] + have h : ∀ r s : CopyLabel 1, cachedFourGram 1 fourHighestCache_1 r s = fourZData_1 r s := by + simp only [cachedFourGram, fourOccupations_1] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem integer_certificate_1 : + ((integerCompression 1).map (algebraMap ℚ ℂ)).PosSemidef := by + have he : integerFourGram 1 = 0 := by + rw [show integerFourGram 1 = fourZData_1 from Matrix.ext fourZChecked_1] + have h : ∀ r s : CopyLabel 1, fourZData_1 r s = (0:ℚ) := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + simp only [integerCompression, he, Matrix.zero_mul, Matrix.map_zero _ (map_zero _)] + exact Matrix.PosSemidef.zero + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate02.lean b/lean/OAI/Analysis/LaughlinFock/Certificate02.lean new file mode 100644 index 0000000000000000000000000000000000000000..7045fefc2b4fc70938ab2b21584a1b7eb7044ee3 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate02.lean @@ -0,0 +1,63 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.LDL + +namespace OAI + +/-! Certificate02. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourZData_2 : Matrix (CopyLabel 2) (CopyLabel 2) ℚ := + copyMatrixData 2 [ + [0] + ] + +def fourLData_2 : Matrix (CopyLabel 2) (CopyLabel 2) ℚ := + copyMatrixData 2 [ + [1] + ] + +def fourPivotData_2 : CopyLabel 2 → ℚ := + copyDiagonalData 2 [0] + +theorem fourOccupations_2 : highestFourOccupations 2 = ∅ := by + decide +kernel + +def fourHighestCache_2 : List (Occupation 24 × List ℚ) := [ + +] + +theorem fourHighestChecked_2 : ∀ r : CopyLabel 2, ∀ A∈highestFourOccupations 2, + kernelHighestEntry 2 r A = highestLookup fourHighestCache_2 r.val.val A := by + rw [fourOccupations_2] + apply @of_decide_eq_true _ (boundedMatrixEntriesDecidable _ _ _) + decide +kernel + +theorem fourZChecked_2 (r s : CopyLabel 2) : + integerFourGram 2 r s = fourZData_2 r s := by + rw [integerFourGram_cached 2 fourHighestCache_2 fourHighestChecked_2] + have h : ∀ r s : CopyLabel 2, cachedFourGram 2 fourHighestCache_2 r s = fourZData_2 r s := by + simp only [cachedFourGram, fourOccupations_2] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem integer_certificate_2 : + ((integerCompression 2).map (algebraMap ℚ ℂ)).PosSemidef := by + have he : integerFourGram 2 = 0 := by + rw [show integerFourGram 2 = fourZData_2 from Matrix.ext fourZChecked_2] + have h : ∀ r s : CopyLabel 2, fourZData_2 r s = (0:ℚ) := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + simp only [integerCompression, he, Matrix.zero_mul, Matrix.map_zero _ (map_zero _)] + exact Matrix.PosSemidef.zero + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate03.lean b/lean/OAI/Analysis/LaughlinFock/Certificate03.lean new file mode 100644 index 0000000000000000000000000000000000000000..bfcce095dae801668a1a9507956decfa83a17cea --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate03.lean @@ -0,0 +1,65 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.LDL + +namespace OAI + +/-! Certificate03. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourZData_3 : Matrix (CopyLabel 3) (CopyLabel 3) ℚ := + copyMatrixData 3 [ + [0, 0], + [0, 0] + ] + +def fourLData_3 : Matrix (CopyLabel 3) (CopyLabel 3) ℚ := + copyMatrixData 3 [ + [1, 0], + [0, 1] + ] + +def fourPivotData_3 : CopyLabel 3 → ℚ := + copyDiagonalData 3 [0, 0] + +theorem fourOccupations_3 : highestFourOccupations 3 = ∅ := by + decide +kernel + +def fourHighestCache_3 : List (Occupation 24 × List ℚ) := [ + +] + +theorem fourHighestChecked_3 : ∀ r : CopyLabel 3, ∀ A∈highestFourOccupations 3, + kernelHighestEntry 3 r A = highestLookup fourHighestCache_3 r.val.val A := by + rw [fourOccupations_3] + apply @of_decide_eq_true _ (boundedMatrixEntriesDecidable _ _ _) + decide +kernel + +theorem fourZChecked_3 (r s : CopyLabel 3) : + integerFourGram 3 r s = fourZData_3 r s := by + rw [integerFourGram_cached 3 fourHighestCache_3 fourHighestChecked_3] + have h : ∀ r s : CopyLabel 3, cachedFourGram 3 fourHighestCache_3 r s = fourZData_3 r s := by + simp only [cachedFourGram, fourOccupations_3] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem integer_certificate_3 : + ((integerCompression 3).map (algebraMap ℚ ℂ)).PosSemidef := by + have he : integerFourGram 3 = 0 := by + rw [show integerFourGram 3 = fourZData_3 from Matrix.ext fourZChecked_3] + have h : ∀ r s : CopyLabel 3, fourZData_3 r s = (0:ℚ) := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + simp only [integerCompression, he, Matrix.zero_mul, Matrix.map_zero _ (map_zero _)] + exact Matrix.PosSemidef.zero + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate04.lean b/lean/OAI/Analysis/LaughlinFock/Certificate04.lean new file mode 100644 index 0000000000000000000000000000000000000000..1e56a5a990f244b9a5e2b194af50e23fb820eda6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate04.lean @@ -0,0 +1,65 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.LDL + +namespace OAI + +/-! Certificate04. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourZData_4 : Matrix (CopyLabel 4) (CopyLabel 4) ℚ := + copyMatrixData 4 [ + [0, 0], + [0, 0] + ] + +def fourLData_4 : Matrix (CopyLabel 4) (CopyLabel 4) ℚ := + copyMatrixData 4 [ + [1, 0], + [0, 1] + ] + +def fourPivotData_4 : CopyLabel 4 → ℚ := + copyDiagonalData 4 [0, 0] + +theorem fourOccupations_4 : highestFourOccupations 4 = ∅ := by + decide +kernel + +def fourHighestCache_4 : List (Occupation 24 × List ℚ) := [ + +] + +theorem fourHighestChecked_4 : ∀ r : CopyLabel 4, ∀ A∈highestFourOccupations 4, + kernelHighestEntry 4 r A = highestLookup fourHighestCache_4 r.val.val A := by + rw [fourOccupations_4] + apply @of_decide_eq_true _ (boundedMatrixEntriesDecidable _ _ _) + decide +kernel + +theorem fourZChecked_4 (r s : CopyLabel 4) : + integerFourGram 4 r s = fourZData_4 r s := by + rw [integerFourGram_cached 4 fourHighestCache_4 fourHighestChecked_4] + have h : ∀ r s : CopyLabel 4, cachedFourGram 4 fourHighestCache_4 r s = fourZData_4 r s := by + simp only [cachedFourGram, fourOccupations_4] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem integer_certificate_4 : + ((integerCompression 4).map (algebraMap ℚ ℂ)).PosSemidef := by + have he : integerFourGram 4 = 0 := by + rw [show integerFourGram 4 = fourZData_4 from Matrix.ext fourZChecked_4] + have h : ∀ r s : CopyLabel 4, fourZData_4 r s = (0:ℚ) := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + simp only [integerCompression, he, Matrix.zero_mul, Matrix.map_zero _ (map_zero _)] + exact Matrix.PosSemidef.zero + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate05.lean b/lean/OAI/Analysis/LaughlinFock/Certificate05.lean new file mode 100644 index 0000000000000000000000000000000000000000..56252cc24f17c8f5aba30bce9f45f5f7de5834f4 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate05.lean @@ -0,0 +1,92 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate05Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate05. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_5 (r s : CopyLabel 5) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 5 r s = fourYData_5 r s := by + rw [integerRowsFourTrace_short (by decide)] + fin_cases r <;> fin_cases s + · exact fourYNumber_5_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_5_3_1 + · exact fourYNumber_5_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_5_5_1 + · exact fourYNumber_5_5_3 + · exact fourYNumber_5_5_5 + +theorem fourYChecked_5 (r s : CopyLabel 5) : + integerRowsFourTrace 5 r s = fourYData_5 r s := by + have hh : ∀ r s : CopyLabel 5, fourYData_5 r s = fourYData_5 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_5 r s h + · rw [integerRowsFourTrace_symm, fourYLower_5 s r (by omega), hh] + +def fourHighestCache_5_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,3}, [384, -96, 120]) +] + +def fourHighestCache_5 : List (Occupation 24 × List ℚ) := fourHighestCache_5_0 + +theorem fourHighestChecked_5 : ∀ r : CopyLabel 5, ∀ A∈highestFourOccupations 5, + kernelHighestEntry 5 r A = highestLookup fourHighestCache_5 r.val.val A := by + rw [fourOccupations_5] + apply @of_decide_eq_true _ (boundedMatrixEntriesDecidable _ _ _) + decide +kernel + +theorem fourZChecked_5 (r s : CopyLabel 5) : + integerFourGram 5 r s = fourZData_5 r s := by + rw [integerFourGram_cached 5 fourHighestCache_5 fourHighestChecked_5] + have h : ∀ r s : CopyLabel 5, cachedFourGram 5 fourHighestCache_5 r s = fourZData_5 r s := by + simp only [cachedFourGram, fourOccupations_5] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_5 : + fourZData_5 * (Matrix.diagonal (fun r : CopyLabel 5 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 5 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 5 => rationalCopyDiagonal 5 r.val.val) * + fourYData_5 * Matrix.diagonal (fun r : CopyLabel 5 => rationalCopyDiagonal 5 r.val.val)) * + fourZData_5 = fourLData_5 * Matrix.diagonal fourPivotData_5 * (fourLData_5)ᵀ := by + have h : ∀ r s : CopyLabel 5, + (fourZData_5 * (Matrix.diagonal (fun r : CopyLabel 5 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 5 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 5 => rationalCopyDiagonal 5 r.val.val) * + fourYData_5 * Matrix.diagonal (fun r : CopyLabel 5 => rationalCopyDiagonal 5 r.val.val)) * + fourZData_5 : Matrix (CopyLabel 5) (CopyLabel 5) ℚ) r s = + (fourLData_5 * Matrix.diagonal fourPivotData_5 * (fourLData_5)ᵀ : Matrix (CopyLabel 5) (CopyLabel 5) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_5 : ∀ r, 0 ≤ fourPivotData_5 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_5, copyDiagonalData] + +theorem integer_certificate_5 : + ((integerCompression 5).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_5) (fourPivotData_5) _ fourPivotChecked_5 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 5 = fourYData_5 from Matrix.ext fourYChecked_5, + show integerFourGram 5 = fourZData_5 from Matrix.ext fourZChecked_5] + exact fourLDLChecked_5 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate05Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate05Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..d113845a335514c92a13fd5e9e904d48da0ef225 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate05Data.lean @@ -0,0 +1,68 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FasterTrace +import OAI.Analysis.LaughlinFock.LDL + +namespace OAI + +/-! Certificate05 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_5 : Matrix (CopyLabel 5) (CopyLabel 5) ℚ := + copyMatrixData 5 [ + [(-2024172058688009719584426783/60129542144000000000000000000), (61749543313564923991586775801/601295421440000000000000000000), (-371682523763530720573033623/12025908428800000000000000000)], + [(61749543313564923991586775801/601295421440000000000000000000), (-81625478502088057676049676411/1202590842880000000000000000000), (6370708288009007294968493697/120259084288000000000000000000)], + [(-371682523763530720573033623/12025908428800000000000000000), (6370708288009007294968493697/120259084288000000000000000000), (-400615328776296560234415701/3006477107200000000000000000)] + ] + +def fourZData_5 : Matrix (CopyLabel 5) (CopyLabel 5) ℚ := + copyMatrixData 5 [ + [24, -6, (15/2)], + [-6, (3/2), (-15/8)], + [(15/2), (-15/8), (75/32)] + ] + +def fourLData_5 : Matrix (CopyLabel 5) (CopyLabel 5) ℚ := + copyMatrixData 5 [ + [1, 0, 0], + [(-1/4), 1, 0], + [(5/16), 0, 1] + ] + +def fourPivotData_5 : CopyLabel 5 → ℚ := + copyDiagonalData 5 [(1888290710477919674814730887537/18790481920000000000000000000), 0, 0] + +theorem fourOccupations_5 : highestFourOccupations 5 = {{0,1,2,3}} := by + decide +kernel + +theorem fourYNumber_5_1_1 : + (shortNumericRowsFourTrace 5 1 1 : ℚ) / fourCommonDenominator = (-2024172058688009719584426783/60129542144000000000000000000) := by + decide +kernel + +theorem fourYNumber_5_3_1 : + (shortNumericRowsFourTrace 5 3 1 : ℚ) / fourCommonDenominator = (61749543313564923991586775801/601295421440000000000000000000) := by + decide +kernel + +theorem fourYNumber_5_3_3 : + (shortNumericRowsFourTrace 5 3 3 : ℚ) / fourCommonDenominator = (-81625478502088057676049676411/1202590842880000000000000000000) := by + decide +kernel + +theorem fourYNumber_5_5_1 : + (shortNumericRowsFourTrace 5 5 1 : ℚ) / fourCommonDenominator = (-371682523763530720573033623/12025908428800000000000000000) := by + decide +kernel + +theorem fourYNumber_5_5_3 : + (shortNumericRowsFourTrace 5 5 3 : ℚ) / fourCommonDenominator = (6370708288009007294968493697/120259084288000000000000000000) := by + decide +kernel + +theorem fourYNumber_5_5_5 : + (shortNumericRowsFourTrace 5 5 5 : ℚ) / fourCommonDenominator = (-400615328776296560234415701/3006477107200000000000000000) := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate06.lean b/lean/OAI/Analysis/LaughlinFock/Certificate06.lean new file mode 100644 index 0000000000000000000000000000000000000000..b5524ccc337ea0da6b8ab1b7768d3643fdf647f8 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate06.lean @@ -0,0 +1,67 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.LDL + +namespace OAI + +/-! Certificate06. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourZData_6 : Matrix (CopyLabel 6) (CopyLabel 6) ℚ := + copyMatrixData 6 [ + [0, 0, 0], + [0, 0, 0], + [0, 0, 0] + ] + +def fourLData_6 : Matrix (CopyLabel 6) (CopyLabel 6) ℚ := + copyMatrixData 6 [ + [1, 0, 0], + [0, 1, 0], + [0, 0, 1] + ] + +def fourPivotData_6 : CopyLabel 6 → ℚ := + copyDiagonalData 6 [0, 0, 0] + +theorem fourOccupations_6 : highestFourOccupations 6 = {{0,1,2,4}} := by + decide +kernel + +def fourHighestCache_6 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,4}, [0, 0, 0]) +] + +theorem fourHighestChecked_6 : ∀ r : CopyLabel 6, ∀ A∈highestFourOccupations 6, + kernelHighestEntry 6 r A = highestLookup fourHighestCache_6 r.val.val A := by + rw [fourOccupations_6] + apply @of_decide_eq_true _ (boundedMatrixEntriesDecidable _ _ _) + decide +kernel + +theorem fourZChecked_6 (r s : CopyLabel 6) : + integerFourGram 6 r s = fourZData_6 r s := by + rw [integerFourGram_cached 6 fourHighestCache_6 fourHighestChecked_6] + have h : ∀ r s : CopyLabel 6, cachedFourGram 6 fourHighestCache_6 r s = fourZData_6 r s := by + simp only [cachedFourGram, fourOccupations_6] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem integer_certificate_6 : + ((integerCompression 6).map (algebraMap ℚ ℂ)).PosSemidef := by + have he : integerFourGram 6 = 0 := by + rw [show integerFourGram 6 = fourZData_6 from Matrix.ext fourZChecked_6] + have h : ∀ r s : CopyLabel 6, fourZData_6 r s = (0:ℚ) := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + simp only [integerCompression, he, Matrix.zero_mul, Matrix.map_zero _ (map_zero _)] + exact Matrix.PosSemidef.zero + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate07.lean b/lean/OAI/Analysis/LaughlinFock/Certificate07.lean new file mode 100644 index 0000000000000000000000000000000000000000..cc307e960c884cb74967986eab8ddce53d0b9c1c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate07.lean @@ -0,0 +1,103 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate07Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate07. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_7 (r s : CopyLabel 7) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 7 r s = fourYData_7 r s := by + rw [integerRowsFourTrace_short (by decide)] + fin_cases r <;> fin_cases s + · exact fourYNumber_7_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_7_3_1 + · exact fourYNumber_7_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_7_5_1 + · exact fourYNumber_7_5_3 + · exact fourYNumber_7_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_7_7_1 + · exact fourYNumber_7_7_3 + · exact fourYNumber_7_7_5 + · exact fourYNumber_7_7_7 + +theorem fourYChecked_7 (r s : CopyLabel 7) : + integerRowsFourTrace 7 r s = fourYData_7 r s := by + have hh : ∀ r s : CopyLabel 7, fourYData_7 r s = fourYData_7 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_7 r s h + · rw [integerRowsFourTrace_symm, fourYLower_7 s r (by omega), hh] + +def fourHighestCache_7_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,5}, [23040, 0, -1440, 5040]), + ({0,1,3,4}, [-23040, 0, 1440, -5040]) +] + +def fourHighestCache_7 : List (Occupation 24 × List ℚ) := fourHighestCache_7_0 + +theorem fourHighestChecked_7 : ∀ r : CopyLabel 7, ∀ A∈highestFourOccupations 7, + kernelHighestEntry 7 r A = highestLookup fourHighestCache_7 r.val.val A := by + rw [fourOccupations_7] + apply @of_decide_eq_true _ (boundedMatrixEntriesDecidable _ _ _) + decide +kernel + +theorem fourZChecked_7 (r s : CopyLabel 7) : + integerFourGram 7 r s = fourZData_7 r s := by + rw [integerFourGram_cached 7 fourHighestCache_7 fourHighestChecked_7] + have h : ∀ r s : CopyLabel 7, cachedFourGram 7 fourHighestCache_7 r s = fourZData_7 r s := by + simp only [cachedFourGram, fourOccupations_7] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_7 : + fourZData_7 * (Matrix.diagonal (fun r : CopyLabel 7 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 7 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 7 => rationalCopyDiagonal 7 r.val.val) * + fourYData_7 * Matrix.diagonal (fun r : CopyLabel 7 => rationalCopyDiagonal 7 r.val.val)) * + fourZData_7 = fourLData_7 * Matrix.diagonal fourPivotData_7 * (fourLData_7)ᵀ := by + have h : ∀ r s : CopyLabel 7, + (fourZData_7 * (Matrix.diagonal (fun r : CopyLabel 7 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 7 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 7 => rationalCopyDiagonal 7 r.val.val) * + fourYData_7 * Matrix.diagonal (fun r : CopyLabel 7 => rationalCopyDiagonal 7 r.val.val)) * + fourZData_7 : Matrix (CopyLabel 7) (CopyLabel 7) ℚ) r s = + (fourLData_7 * Matrix.diagonal fourPivotData_7 * (fourLData_7)ᵀ : Matrix (CopyLabel 7) (CopyLabel 7) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_7 : ∀ r, 0 ≤ fourPivotData_7 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_7, copyDiagonalData] + +theorem integer_certificate_7 : + ((integerCompression 7).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_7) (fourPivotData_7) _ fourPivotChecked_7 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 7 = fourYData_7 from Matrix.ext fourYChecked_7, + show integerFourGram 7 = fourZData_7 from Matrix.ext fourZChecked_7] + exact fourLDLChecked_7 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate07Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate07Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..8c5379e6151168b29607f7a0f913b9becb11720a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate07Data.lean @@ -0,0 +1,87 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FasterTrace +import OAI.Analysis.LaughlinFock.LDL + +namespace OAI + +/-! Certificate07 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_7 : Matrix (CopyLabel 7) (CopyLabel 7) ℚ := + copyMatrixData 7 [ + [(-166434639714168948577730130927/3758096384000000000000000000), (45995705370248318526416296167/7516192768000000000000000000), (-106335364725988709134966359/53687091200000000000000000), (-51594657218957307370313483247/4294967296000000000000000000)], + [(45995705370248318526416296167/7516192768000000000000000000), (-87211931042683137626019530763/75161927680000000000000000000), (1568403660783923680978370343/3006477107200000000000000000), (3815628101661385334514451191/1717986918400000000000000000)], + [(-106335364725988709134966359/53687091200000000000000000), (1568403660783923680978370343/3006477107200000000000000000), (-11751684800182621092199856481/30064771072000000000000000000), (-10949361788140579505956340379/8589934592000000000000000000)], + [(-51594657218957307370313483247/4294967296000000000000000000), (3815628101661385334514451191/1717986918400000000000000000), (-10949361788140579505956340379/8589934592000000000000000000), (-148920474389511901767358542711/34359738368000000000000000000)] + ] + +def fourZData_7 : Matrix (CopyLabel 7) (CopyLabel 7) ℚ := + copyMatrixData 7 [ + [720, 0, -45, (315/2)], + [0, 0, 0, 0], + [-45, 0, (45/16), (-315/32)], + [(315/2), 0, (-315/32), (2205/64)] + ] + +def fourLData_7 : Matrix (CopyLabel 7) (CopyLabel 7) ℚ := + copyMatrixData 7 [ + [1, 0, 0, 0], + [0, 1, 0, 0], + [(-1/16), 0, 1, 0], + [(7/32), 0, 0, 1] + ] + +def fourPivotData_7 : CopyLabel 7 → ℚ := + copyDiagonalData 7 [(48465284516682192798125037847983/15032385536000000000000000000), 0, 0, 0] + +theorem fourOccupations_7 : highestFourOccupations 7 = {{0,1,2,5}, {0,1,3,4}} := by + decide +kernel + +theorem fourYNumber_7_1_1 : + (shortNumericRowsFourTrace 7 1 1 : ℚ) / fourCommonDenominator = (-166434639714168948577730130927/3758096384000000000000000000) := by + decide +kernel + +theorem fourYNumber_7_3_1 : + (shortNumericRowsFourTrace 7 3 1 : ℚ) / fourCommonDenominator = (45995705370248318526416296167/7516192768000000000000000000) := by + decide +kernel + +theorem fourYNumber_7_3_3 : + (shortNumericRowsFourTrace 7 3 3 : ℚ) / fourCommonDenominator = (-87211931042683137626019530763/75161927680000000000000000000) := by + decide +kernel + +theorem fourYNumber_7_5_1 : + (shortNumericRowsFourTrace 7 5 1 : ℚ) / fourCommonDenominator = (-106335364725988709134966359/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_7_5_3 : + (shortNumericRowsFourTrace 7 5 3 : ℚ) / fourCommonDenominator = (1568403660783923680978370343/3006477107200000000000000000) := by + decide +kernel + +theorem fourYNumber_7_5_5 : + (shortNumericRowsFourTrace 7 5 5 : ℚ) / fourCommonDenominator = (-11751684800182621092199856481/30064771072000000000000000000) := by + decide +kernel + +theorem fourYNumber_7_7_1 : + (shortNumericRowsFourTrace 7 7 1 : ℚ) / fourCommonDenominator = (-51594657218957307370313483247/4294967296000000000000000000) := by + decide +kernel + +theorem fourYNumber_7_7_3 : + (shortNumericRowsFourTrace 7 7 3 : ℚ) / fourCommonDenominator = (3815628101661385334514451191/1717986918400000000000000000) := by + decide +kernel + +theorem fourYNumber_7_7_5 : + (shortNumericRowsFourTrace 7 7 5 : ℚ) / fourCommonDenominator = (-10949361788140579505956340379/8589934592000000000000000000) := by + decide +kernel + +theorem fourYNumber_7_7_7 : + (shortNumericRowsFourTrace 7 7 7 : ℚ) / fourCommonDenominator = (-148920474389511901767358542711/34359738368000000000000000000) := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate08.lean b/lean/OAI/Analysis/LaughlinFock/Certificate08.lean new file mode 100644 index 0000000000000000000000000000000000000000..49ba00633b2278379ddd1e37cb1f8f68c2ec2d5d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate08.lean @@ -0,0 +1,131 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate08Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate08. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_8 (r s : CopyLabel 8) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 8 r s = fourYData_8 r s := by + rw [integerRowsFourTrace_parts (by decide) collectedFourData_8 collectedFourChecked_8] + fin_cases r <;> fin_cases s + · exact fourYNumber_8_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_8_3_1 + · exact fourYNumber_8_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_8_5_1 + · exact fourYNumber_8_5_3 + · exact fourYNumber_8_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_8_7_1 + · exact fourYNumber_8_7_3 + · exact fourYNumber_8_7_5 + · exact fourYNumber_8_7_7 + +theorem fourYChecked_8 (r s : CopyLabel 8) : + integerRowsFourTrace 8 r s = fourYData_8 r s := by + have hh : ∀ r s : CopyLabel 8, fourYData_8 r s = fourYData_8 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_8 r s h + · rw [integerRowsFourTrace_symm, fourYLower_8 s r (by omega), hh] + +def fourHighestCache_8_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,6}, [0, -23040, 11520, -10080]), + ({0,1,3,5}, [0, 23040, -11520, 10080]), + ({0,2,3,4}, [0, -23040, 11520, -10080]) +] + +def fourHighestCache_8 : List (Occupation 24 × List ℚ) := fourHighestCache_8_0 + +theorem fourHighestNumber_8_1 : ∀ A∈highestFourOccupations 8, + kernelHighestEntry 8 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_8 1 A := by + rw [fourOccupations_8] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_8_3 : ∀ A∈highestFourOccupations 8, + kernelHighestEntry 8 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_8 3 A := by + rw [fourOccupations_8] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_8_5 : ∀ A∈highestFourOccupations 8, + kernelHighestEntry 8 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_8 5 A := by + rw [fourOccupations_8] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_8_7 : ∀ A∈highestFourOccupations 8, + kernelHighestEntry 8 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_8 7 A := by + rw [fourOccupations_8] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_8 : ∀ r : CopyLabel 8, ∀ A∈highestFourOccupations 8, + kernelHighestEntry 8 r A = highestLookup fourHighestCache_8 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_8_1 + · exact fourHighestNumber_8_3 + · exact fourHighestNumber_8_5 + · exact fourHighestNumber_8_7 + +theorem fourZChecked_8 (r s : CopyLabel 8) : + integerFourGram 8 r s = fourZData_8 r s := by + rw [integerFourGram_cached 8 fourHighestCache_8 fourHighestChecked_8] + have h : ∀ r s : CopyLabel 8, cachedFourGram 8 fourHighestCache_8 r s = fourZData_8 r s := by + simp only [cachedFourGram, fourOccupations_8] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_8 : + fourZData_8 * (Matrix.diagonal (fun r : CopyLabel 8 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 8 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 8 => rationalCopyDiagonal 8 r.val.val) * + fourYData_8 * Matrix.diagonal (fun r : CopyLabel 8 => rationalCopyDiagonal 8 r.val.val)) * + fourZData_8 = fourLData_8 * Matrix.diagonal fourPivotData_8 * (fourLData_8)ᵀ := by + have h : ∀ r s : CopyLabel 8, + (fourZData_8 * (Matrix.diagonal (fun r : CopyLabel 8 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 8 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 8 => rationalCopyDiagonal 8 r.val.val) * + fourYData_8 * Matrix.diagonal (fun r : CopyLabel 8 => rationalCopyDiagonal 8 r.val.val)) * + fourZData_8 : Matrix (CopyLabel 8) (CopyLabel 8) ℚ) r s = + (fourLData_8 * Matrix.diagonal fourPivotData_8 * (fourLData_8)ᵀ : Matrix (CopyLabel 8) (CopyLabel 8) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_8 : ∀ r, 0 ≤ fourPivotData_8 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_8, copyDiagonalData] + +theorem integer_certificate_8 : + ((integerCompression 8).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_8) (fourPivotData_8) _ fourPivotChecked_8 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 8 = fourYData_8 from Matrix.ext fourYChecked_8, + show integerFourGram 8 = fourZData_8 from Matrix.ext fourZChecked_8] + exact fourLDLChecked_8 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate08Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate08Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..e30f65f3f80900c1e9b50e26df2066268d06fed6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate08Data.lean @@ -0,0 +1,87 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse0833 + +namespace OAI + +/-! Certificate08 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_8 : Matrix (CopyLabel 8) (CopyLabel 8) ℚ := + copyMatrixData 8 [ + [(-63725659480009131775992546879/536870912000000000000000000), (-1915756407095537127488603541/268435456000000000000000000), (5848046872621070751629176509/536870912000000000000000000), (-15409311511841483890426595631/2147483648000000000000000000)], + [(-1915756407095537127488603541/268435456000000000000000000), (-20669734241111819247651968649/7516192768000000000000000000), (9455940384238314087831042759/3758096384000000000000000000), (-12382701644617792221325809759/4294967296000000000000000000)], + [(5848046872621070751629176509/536870912000000000000000000), (9455940384238314087831042759/3758096384000000000000000000), (-2472410179928723052502001181/1073741824000000000000000000), (1770955193734196297743289949/536870912000000000000000000)], + [(-15409311511841483890426595631/2147483648000000000000000000), (-12382701644617792221325809759/4294967296000000000000000000), (1770955193734196297743289949/536870912000000000000000000), (-178020445962132587387054522433/17179869184000000000000000000)] + ] + +def fourZData_8 : Matrix (CopyLabel 8) (CopyLabel 8) ℚ := + copyMatrixData 8 [ + [0, 0, 0, 0], + [0, 90, -45, (315/8)], + [0, -45, (45/2), (-315/16)], + [0, (315/8), (-315/16), (2205/128)] + ] + +def fourLData_8 : Matrix (CopyLabel 8) (CopyLabel 8) ℚ := + copyMatrixData 8 [ + [1, 0, 0, 0], + [0, 1, 0, 0], + [0, (-1/2), 1, 0], + [0, (7/16), 0, 1] + ] + +def fourPivotData_8 : CopyLabel 8 → ℚ := + copyDiagonalData 8 [0, (6175145290577572637607316298463/120259084288000000000000000000), 0, 0] + +theorem fourOccupations_8 : highestFourOccupations 8 = {{0,1,2,6}, {0,1,3,5}, {0,2,3,4}} := by + decide +kernel + +theorem fourYNumber_8_1_1 : + (collectedFourPartsTrace 8 1 1 collectedFourData_8 : ℚ) / fourCommonDenominator = (-63725659480009131775992546879/536870912000000000000000000) := by + decide +kernel + +theorem fourYNumber_8_3_1 : + (collectedFourPartsTrace 8 3 1 collectedFourData_8 : ℚ) / fourCommonDenominator = (-1915756407095537127488603541/268435456000000000000000000) := by + decide +kernel + +theorem fourYNumber_8_3_3 : + (collectedFourPartsTrace 8 3 3 collectedFourData_8 : ℚ) / fourCommonDenominator = (-20669734241111819247651968649/7516192768000000000000000000) := by + decide +kernel + +theorem fourYNumber_8_5_1 : + (collectedFourPartsTrace 8 5 1 collectedFourData_8 : ℚ) / fourCommonDenominator = (5848046872621070751629176509/536870912000000000000000000) := by + decide +kernel + +theorem fourYNumber_8_5_3 : + (collectedFourPartsTrace 8 5 3 collectedFourData_8 : ℚ) / fourCommonDenominator = (9455940384238314087831042759/3758096384000000000000000000) := by + decide +kernel + +theorem fourYNumber_8_5_5 : + (collectedFourPartsTrace 8 5 5 collectedFourData_8 : ℚ) / fourCommonDenominator = (-2472410179928723052502001181/1073741824000000000000000000) := by + decide +kernel + +theorem fourYNumber_8_7_1 : + (collectedFourPartsTrace 8 7 1 collectedFourData_8 : ℚ) / fourCommonDenominator = (-15409311511841483890426595631/2147483648000000000000000000) := by + decide +kernel + +theorem fourYNumber_8_7_3 : + (collectedFourPartsTrace 8 7 3 collectedFourData_8 : ℚ) / fourCommonDenominator = (-12382701644617792221325809759/4294967296000000000000000000) := by + decide +kernel + +theorem fourYNumber_8_7_5 : + (collectedFourPartsTrace 8 7 5 collectedFourData_8 : ℚ) / fourCommonDenominator = (1770955193734196297743289949/536870912000000000000000000) := by + decide +kernel + +theorem fourYNumber_8_7_7 : + (collectedFourPartsTrace 8 7 7 collectedFourData_8 : ℚ) / fourCommonDenominator = (-178020445962132587387054522433/17179869184000000000000000000) := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate09.lean b/lean/OAI/Analysis/LaughlinFock/Certificate09.lean new file mode 100644 index 0000000000000000000000000000000000000000..f8d4cb6099a7f7c7efb86b09e12fb977c3ad64ea --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate09.lean @@ -0,0 +1,156 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate09Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate09. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_9 (r s : CopyLabel 9) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 9 r s = fourYData_9 r s := by + rw [integerRowsFourTrace_parts (by decide) collectedFourData_9 collectedFourChecked_9] + fin_cases r <;> fin_cases s + · exact fourYNumber_9_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_9_3_1 + · exact fourYNumber_9_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_9_5_1 + · exact fourYNumber_9_5_3 + · exact fourYNumber_9_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_9_7_1 + · exact fourYNumber_9_7_3 + · exact fourYNumber_9_7_5 + · exact fourYNumber_9_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_9_9_1 + · exact fourYNumber_9_9_3 + · exact fourYNumber_9_9_5 + · exact fourYNumber_9_9_7 + · exact fourYNumber_9_9_9 + +theorem fourYChecked_9 (r s : CopyLabel 9) : + integerRowsFourTrace 9 r s = fourYData_9 r s := by + have hh : ∀ r s : CopyLabel 9, fourYData_9 r s = fourYData_9 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_9 r s h + · rw [integerRowsFourTrace_symm, fourYLower_9 s r (by omega), hh] + +def fourHighestCache_9_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,7}, [1935360, 241920, -60480, -30240, 362880]), + ({0,1,3,6}, [-1935360, -241920, 60480, 30240, -362880]), + ({0,1,4,5}, [2580480, 138240, -34560, -40320, 362880]), + ({0,2,3,5}, [-645120, 103680, -25920, 10080, 0]) +] + +def fourHighestCache_9_1 : List (Occupation 24 × List ℚ) := [ + ({1,2,3,4}, [645120, -103680, 25920, -10080, 0]) +] + +def fourHighestCache_9 : List (Occupation 24 × List ℚ) := fourHighestCache_9_0 ++ fourHighestCache_9_1 + +theorem fourHighestNumber_9_1 : ∀ A∈highestFourOccupations 9, + kernelHighestEntry 9 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_9 1 A := by + rw [fourOccupations_9] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_9_3 : ∀ A∈highestFourOccupations 9, + kernelHighestEntry 9 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_9 3 A := by + rw [fourOccupations_9] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_9_5 : ∀ A∈highestFourOccupations 9, + kernelHighestEntry 9 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_9 5 A := by + rw [fourOccupations_9] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_9_7 : ∀ A∈highestFourOccupations 9, + kernelHighestEntry 9 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_9 7 A := by + rw [fourOccupations_9] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_9_9 : ∀ A∈highestFourOccupations 9, + kernelHighestEntry 9 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_9 9 A := by + rw [fourOccupations_9] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_9 : ∀ r : CopyLabel 9, ∀ A∈highestFourOccupations 9, + kernelHighestEntry 9 r A = highestLookup fourHighestCache_9 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_9_1 + · exact fourHighestNumber_9_3 + · exact fourHighestNumber_9_5 + · exact fourHighestNumber_9_7 + · exact fourHighestNumber_9_9 + +theorem fourZChecked_9 (r s : CopyLabel 9) : + integerFourGram 9 r s = fourZData_9 r s := by + rw [integerFourGram_cached 9 fourHighestCache_9 fourHighestChecked_9] + have h : ∀ r s : CopyLabel 9, cachedFourGram 9 fourHighestCache_9 r s = fourZData_9 r s := by + simp only [cachedFourGram, fourOccupations_9] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_9 : + fourZData_9 * (Matrix.diagonal (fun r : CopyLabel 9 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 9 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 9 => rationalCopyDiagonal 9 r.val.val) * + fourYData_9 * Matrix.diagonal (fun r : CopyLabel 9 => rationalCopyDiagonal 9 r.val.val)) * + fourZData_9 = fourLData_9 * Matrix.diagonal fourPivotData_9 * (fourLData_9)ᵀ := by + have h : ∀ r s : CopyLabel 9, + (fourZData_9 * (Matrix.diagonal (fun r : CopyLabel 9 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 9 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 9 => rationalCopyDiagonal 9 r.val.val) * + fourYData_9 * Matrix.diagonal (fun r : CopyLabel 9 => rationalCopyDiagonal 9 r.val.val)) * + fourZData_9 : Matrix (CopyLabel 9) (CopyLabel 9) ℚ) r s = + (fourLData_9 * Matrix.diagonal fourPivotData_9 * (fourLData_9)ᵀ : Matrix (CopyLabel 9) (CopyLabel 9) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_9 : ∀ r, 0 ≤ fourPivotData_9 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_9, copyDiagonalData] + +theorem integer_certificate_9 : + ((integerCompression 9).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_9) (fourPivotData_9) _ fourPivotChecked_9 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 9 = fourYData_9 from Matrix.ext fourYChecked_9, + show integerFourGram 9 = fourZData_9 from Matrix.ext fourZChecked_9] + exact fourLDLChecked_9 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate09Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate09Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..38911bf91af86de374956aedeb10136721e23fdf --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate09Data.lean @@ -0,0 +1,110 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse0930 + +namespace OAI + +/-! Certificate09 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_9 : Matrix (CopyLabel 9) (CopyLabel 9) ℚ := + copyMatrixData 9 [ + [(-146091607413928872790325971761/268435456000000000000000000), (-27122971776637241097052043481/536870912000000000000000000), (260469020419292216479075761/53687091200000000000000000), (30789416395436608069256092953/2147483648000000000000000000), (-129703291268636859530657931099/536870912000000000000000000)], + [(-27122971776637241097052043481/536870912000000000000000000), (-128380238690076998480031524721/7516192768000000000000000000), (39773187663702578771741264079/3758096384000000000000000000), (-1837610439668880684708642399/171798691840000000000000000), (-20806144524092430933966807651/1073741824000000000000000000)], + [(260469020419292216479075761/53687091200000000000000000), (39773187663702578771741264079/3758096384000000000000000000), (-46478716744801148895226746231/7516192768000000000000000000), (1660933205203877918300823867/268435456000000000000000000), (7156024769090901250266984873/536870912000000000000000000)], + [(30789416395436608069256092953/2147483648000000000000000000), (-1837610439668880684708642399/171798691840000000000000000), (1660933205203877918300823867/268435456000000000000000000), (-105495675446941487863399344237/17179869184000000000000000000), (-85051785275352886328867049021/4294967296000000000000000000)], + [(-129703291268636859530657931099/536870912000000000000000000), (-20806144524092430933966807651/1073741824000000000000000000), (7156024769090901250266984873/536870912000000000000000000), (-85051785275352886328867049021/4294967296000000000000000000), (-99131997774302568689042771217/1073741824000000000000000000)] + ] + +def fourZData_9 : Matrix (CopyLabel 9) (CopyLabel 9) ℚ := + copyMatrixData 9 [ + [40320, 0, 0, -630, (8505/2)], + [0, 540, -135, 0, (2835/8)], + [0, -135, (135/4), 0, (-2835/32)], + [-630, 0, 0, (315/32), (-8505/128)], + [(8505/2), (2835/8), (-2835/32), (-8505/128), (348705/512)] + ] + +def fourLData_9 : Matrix (CopyLabel 9) (CopyLabel 9) ℚ := + copyMatrixData 9 [ + [1, 0, 0, 0, 0], + [(37662092511230861665070264137/10232154760876942507977290094024), 1, 0, 0, 0], + [(-37662092511230861665070264137/40928619043507770031909160376096), (-1/4), 1, 0, 0], + [(-1/64), 0, 0, 1, 0], + [(91990693387227940258827681287/852679563406411875664774174502), (21/32), 0, 0, 1] + ] + +def fourPivotData_9 : CopyLabel 9 → ℚ := + copyDiagonalData 9 [(11511174105986560321474451355777/67108864000000000000000000), (224998014131384802568074889313302515150854695443477453969327/1831115419399048681343111669355743543296000000000000000000), 0, 0, 0] + +theorem fourOccupations_9 : highestFourOccupations 9 = {{0,1,2,7}, {0,1,3,6}, {0,1,4,5}, {0,2,3,5}, {1,2,3,4}} := by + decide +kernel + +theorem fourYNumber_9_1_1 : + (collectedFourPartsTrace 9 1 1 collectedFourData_9 : ℚ) / fourCommonDenominator = (-146091607413928872790325971761/268435456000000000000000000) := by + decide +kernel + +theorem fourYNumber_9_3_1 : + (collectedFourPartsTrace 9 3 1 collectedFourData_9 : ℚ) / fourCommonDenominator = (-27122971776637241097052043481/536870912000000000000000000) := by + decide +kernel + +theorem fourYNumber_9_3_3 : + (collectedFourPartsTrace 9 3 3 collectedFourData_9 : ℚ) / fourCommonDenominator = (-128380238690076998480031524721/7516192768000000000000000000) := by + decide +kernel + +theorem fourYNumber_9_5_1 : + (collectedFourPartsTrace 9 5 1 collectedFourData_9 : ℚ) / fourCommonDenominator = (260469020419292216479075761/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_9_5_3 : + (collectedFourPartsTrace 9 5 3 collectedFourData_9 : ℚ) / fourCommonDenominator = (39773187663702578771741264079/3758096384000000000000000000) := by + decide +kernel + +theorem fourYNumber_9_5_5 : + (collectedFourPartsTrace 9 5 5 collectedFourData_9 : ℚ) / fourCommonDenominator = (-46478716744801148895226746231/7516192768000000000000000000) := by + decide +kernel + +theorem fourYNumber_9_7_1 : + (collectedFourPartsTrace 9 7 1 collectedFourData_9 : ℚ) / fourCommonDenominator = (30789416395436608069256092953/2147483648000000000000000000) := by + decide +kernel + +theorem fourYNumber_9_7_3 : + (collectedFourPartsTrace 9 7 3 collectedFourData_9 : ℚ) / fourCommonDenominator = (-1837610439668880684708642399/171798691840000000000000000) := by + decide +kernel + +theorem fourYNumber_9_7_5 : + (collectedFourPartsTrace 9 7 5 collectedFourData_9 : ℚ) / fourCommonDenominator = (1660933205203877918300823867/268435456000000000000000000) := by + decide +kernel + +theorem fourYNumber_9_7_7 : + (collectedFourPartsTrace 9 7 7 collectedFourData_9 : ℚ) / fourCommonDenominator = (-105495675446941487863399344237/17179869184000000000000000000) := by + decide +kernel + +theorem fourYNumber_9_9_1 : + (collectedFourPartsTrace 9 9 1 collectedFourData_9 : ℚ) / fourCommonDenominator = (-129703291268636859530657931099/536870912000000000000000000) := by + decide +kernel + +theorem fourYNumber_9_9_3 : + (collectedFourPartsTrace 9 9 3 collectedFourData_9 : ℚ) / fourCommonDenominator = (-20806144524092430933966807651/1073741824000000000000000000) := by + decide +kernel + +theorem fourYNumber_9_9_5 : + (collectedFourPartsTrace 9 9 5 collectedFourData_9 : ℚ) / fourCommonDenominator = (7156024769090901250266984873/536870912000000000000000000) := by + decide +kernel + +theorem fourYNumber_9_9_7 : + (collectedFourPartsTrace 9 9 7 collectedFourData_9 : ℚ) / fourCommonDenominator = (-85051785275352886328867049021/4294967296000000000000000000) := by + decide +kernel + +theorem fourYNumber_9_9_9 : + (collectedFourPartsTrace 9 9 9 collectedFourData_9 : ℚ) / fourCommonDenominator = (-99131997774302568689042771217/1073741824000000000000000000) := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate10.lean b/lean/OAI/Analysis/LaughlinFock/Certificate10.lean new file mode 100644 index 0000000000000000000000000000000000000000..3fe092cb1e8f2f20e4a995173eb3e6d3ee876f9c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate10.lean @@ -0,0 +1,157 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate10Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate10. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_10 (r s : CopyLabel 10) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 10 r s = fourYData_10 r s := by + rw [integerRowsFourTrace_parts (by decide) collectedFourData_10 collectedFourChecked_10] + fin_cases r <;> fin_cases s + · exact fourYNumber_10_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_10_3_1 + · exact fourYNumber_10_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_10_5_1 + · exact fourYNumber_10_5_3 + · exact fourYNumber_10_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_10_7_1 + · exact fourYNumber_10_7_3 + · exact fourYNumber_10_7_5 + · exact fourYNumber_10_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_10_9_1 + · exact fourYNumber_10_9_3 + · exact fourYNumber_10_9_5 + · exact fourYNumber_10_9_7 + · exact fourYNumber_10_9_9 + +theorem fourYChecked_10 (r s : CopyLabel 10) : + integerRowsFourTrace 10 r s = fourYData_10 r s := by + have hh : ∀ r s : CopyLabel 10, fourYData_10 r s = fourYData_10 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_10 r s h + · rw [integerRowsFourTrace_symm, fourYLower_10 s r (by omega), hh] + +def fourHighestCache_10_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,8}, [0, -3870720, 0, 725760, -1451520]), + ({0,1,3,7}, [0, 3870720, 0, -725760, 1451520]), + ({0,1,4,6}, [0, -1935360, 0, 362880, -725760]), + ({0,2,3,6}, [0, -1935360, 0, 362880, -725760]) +] + +def fourHighestCache_10_1 : List (Occupation 24 × List ℚ) := [ + ({0,2,4,5}, [0, 1935360, 0, -362880, 725760]), + ({1,2,3,5}, [0, 0, 0, 0, 0]) +] + +def fourHighestCache_10 : List (Occupation 24 × List ℚ) := fourHighestCache_10_0 ++ fourHighestCache_10_1 + +theorem fourHighestNumber_10_1 : ∀ A∈highestFourOccupations 10, + kernelHighestEntry 10 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_10 1 A := by + rw [fourOccupations_10] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_10_3 : ∀ A∈highestFourOccupations 10, + kernelHighestEntry 10 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_10 3 A := by + rw [fourOccupations_10] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_10_5 : ∀ A∈highestFourOccupations 10, + kernelHighestEntry 10 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_10 5 A := by + rw [fourOccupations_10] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_10_7 : ∀ A∈highestFourOccupations 10, + kernelHighestEntry 10 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_10 7 A := by + rw [fourOccupations_10] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_10_9 : ∀ A∈highestFourOccupations 10, + kernelHighestEntry 10 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_10 9 A := by + rw [fourOccupations_10] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_10 : ∀ r : CopyLabel 10, ∀ A∈highestFourOccupations 10, + kernelHighestEntry 10 r A = highestLookup fourHighestCache_10 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_10_1 + · exact fourHighestNumber_10_3 + · exact fourHighestNumber_10_5 + · exact fourHighestNumber_10_7 + · exact fourHighestNumber_10_9 + +theorem fourZChecked_10 (r s : CopyLabel 10) : + integerFourGram 10 r s = fourZData_10 r s := by + rw [integerFourGram_cached 10 fourHighestCache_10 fourHighestChecked_10] + have h : ∀ r s : CopyLabel 10, cachedFourGram 10 fourHighestCache_10 r s = fourZData_10 r s := by + simp only [cachedFourGram, fourOccupations_10] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_10 : + fourZData_10 * (Matrix.diagonal (fun r : CopyLabel 10 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 10 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 10 => rationalCopyDiagonal 10 r.val.val) * + fourYData_10 * Matrix.diagonal (fun r : CopyLabel 10 => rationalCopyDiagonal 10 r.val.val)) * + fourZData_10 = fourLData_10 * Matrix.diagonal fourPivotData_10 * (fourLData_10)ᵀ := by + have h : ∀ r s : CopyLabel 10, + (fourZData_10 * (Matrix.diagonal (fun r : CopyLabel 10 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 10 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 10 => rationalCopyDiagonal 10 r.val.val) * + fourYData_10 * Matrix.diagonal (fun r : CopyLabel 10 => rationalCopyDiagonal 10 r.val.val)) * + fourZData_10 : Matrix (CopyLabel 10) (CopyLabel 10) ℚ) r s = + (fourLData_10 * Matrix.diagonal fourPivotData_10 * (fourLData_10)ᵀ : Matrix (CopyLabel 10) (CopyLabel 10) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_10 : ∀ r, 0 ≤ fourPivotData_10 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_10, copyDiagonalData] + +theorem integer_certificate_10 : + ((integerCompression 10).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_10) (fourPivotData_10) _ fourPivotChecked_10 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 10 = fourYData_10 from Matrix.ext fourYChecked_10, + show integerFourGram 10 = fourZData_10 from Matrix.ext fourZChecked_10] + exact fourLDLChecked_10 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate10Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate10Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..b5db22aa9ab0d53c0632da62b4feb6e5d0cd496b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate10Data.lean @@ -0,0 +1,110 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse1027 + +namespace OAI + +/-! Certificate10 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_10 : Matrix (CopyLabel 10) (CopyLabel 10) ℚ := + copyMatrixData 10 [ + [(737670548859399948830388711147/33554432000000000000000000), (-340762940414160772908009142467/134217728000000000000000000), (148518328795926257133899451/134217728000000000000000), (-424730358650114657260778608119/536870912000000000000000000), (74331768409382616339850430283/134217728000000000000000000)], + [(-340762940414160772908009142467/134217728000000000000000000), (6753716923485661803328277187/67108864000000000000000000), (-133847515145750760226034487/1342177280000000000000000), (27875776847130353195239319289/214748364800000000000000000), (-62712565299322420555264659867/268435456000000000000000000)], + [(148518328795926257133899451/134217728000000000000000), (-133847515145750760226034487/1342177280000000000000000), (4916058814322941309449723117/107374182400000000000000000), (-8781593118050446480941197751/214748364800000000000000000), (79913088812449654011001179/1342177280000000000000000)], + [(-424730358650114657260778608119/536870912000000000000000000), (27875776847130353195239319289/214748364800000000000000000), (-8781593118050446480941197751/214748364800000000000000000), (88212964072712605466404249449/4294967296000000000000000000), (-4590411174217141231271545953/1073741824000000000000000000)], + [(74331768409382616339850430283/134217728000000000000000000), (-62712565299322420555264659867/268435456000000000000000000), (79913088812449654011001179/1342177280000000000000000), (-4590411174217141231271545953/1073741824000000000000000000), (-34263985364968403855161804941/268435456000000000000000000)] + ] + +def fourZData_10 : Matrix (CopyLabel 10) (CopyLabel 10) ℚ := + copyMatrixData 10 [ + [0, 0, 0, 0, 0], + [0, 3780, 0, (-2835/4), (2835/2)], + [0, 0, 0, 0, 0], + [0, (-2835/4), 0, (8505/64), (-8505/32)], + [0, (2835/2), 0, (-8505/32), (8505/16)] + ] + +def fourLData_10 : Matrix (CopyLabel 10) (CopyLabel 10) ℚ := + copyMatrixData 10 [ + [1, 0, 0, 0, 0], + [0, 1, 0, 0, 0], + [0, 0, 1, 0, 0], + [0, (-3/16), 0, 1, 0], + [0, (3/8), 0, 0, 1] + ] + +def fourPivotData_10 : CopyLabel 10 → ℚ := + copyDiagonalData 10 [0, (8105210798198965041984329871639/4294967296000000000000000000), 0, 0, 0] + +theorem fourOccupations_10 : highestFourOccupations 10 = {{0,1,2,8}, {0,1,3,7}, {0,1,4,6}, {0,2,3,6}, {0,2,4,5}, {1,2,3,5}} := by + decide +kernel + +theorem fourYNumber_10_1_1 : + (collectedFourPartsTrace 10 1 1 collectedFourData_10 : ℚ) / fourCommonDenominator = (737670548859399948830388711147/33554432000000000000000000) := by + decide +kernel + +theorem fourYNumber_10_3_1 : + (collectedFourPartsTrace 10 3 1 collectedFourData_10 : ℚ) / fourCommonDenominator = (-340762940414160772908009142467/134217728000000000000000000) := by + decide +kernel + +theorem fourYNumber_10_3_3 : + (collectedFourPartsTrace 10 3 3 collectedFourData_10 : ℚ) / fourCommonDenominator = (6753716923485661803328277187/67108864000000000000000000) := by + decide +kernel + +theorem fourYNumber_10_5_1 : + (collectedFourPartsTrace 10 5 1 collectedFourData_10 : ℚ) / fourCommonDenominator = (148518328795926257133899451/134217728000000000000000) := by + decide +kernel + +theorem fourYNumber_10_5_3 : + (collectedFourPartsTrace 10 5 3 collectedFourData_10 : ℚ) / fourCommonDenominator = (-133847515145750760226034487/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_10_5_5 : + (collectedFourPartsTrace 10 5 5 collectedFourData_10 : ℚ) / fourCommonDenominator = (4916058814322941309449723117/107374182400000000000000000) := by + decide +kernel + +theorem fourYNumber_10_7_1 : + (collectedFourPartsTrace 10 7 1 collectedFourData_10 : ℚ) / fourCommonDenominator = (-424730358650114657260778608119/536870912000000000000000000) := by + decide +kernel + +theorem fourYNumber_10_7_3 : + (collectedFourPartsTrace 10 7 3 collectedFourData_10 : ℚ) / fourCommonDenominator = (27875776847130353195239319289/214748364800000000000000000) := by + decide +kernel + +theorem fourYNumber_10_7_5 : + (collectedFourPartsTrace 10 7 5 collectedFourData_10 : ℚ) / fourCommonDenominator = (-8781593118050446480941197751/214748364800000000000000000) := by + decide +kernel + +theorem fourYNumber_10_7_7 : + (collectedFourPartsTrace 10 7 7 collectedFourData_10 : ℚ) / fourCommonDenominator = (88212964072712605466404249449/4294967296000000000000000000) := by + decide +kernel + +theorem fourYNumber_10_9_1 : + (collectedFourPartsTrace 10 9 1 collectedFourData_10 : ℚ) / fourCommonDenominator = (74331768409382616339850430283/134217728000000000000000000) := by + decide +kernel + +theorem fourYNumber_10_9_3 : + (collectedFourPartsTrace 10 9 3 collectedFourData_10 : ℚ) / fourCommonDenominator = (-62712565299322420555264659867/268435456000000000000000000) := by + decide +kernel + +theorem fourYNumber_10_9_5 : + (collectedFourPartsTrace 10 9 5 collectedFourData_10 : ℚ) / fourCommonDenominator = (79913088812449654011001179/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_10_9_7 : + (collectedFourPartsTrace 10 9 7 collectedFourData_10 : ℚ) / fourCommonDenominator = (-4590411174217141231271545953/1073741824000000000000000000) := by + decide +kernel + +theorem fourYNumber_10_9_9 : + (collectedFourPartsTrace 10 9 9 collectedFourData_10 : ℚ) / fourCommonDenominator = (-34263985364968403855161804941/268435456000000000000000000) := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate11.lean b/lean/OAI/Analysis/LaughlinFock/Certificate11.lean new file mode 100644 index 0000000000000000000000000000000000000000..0ad507201b879c116a454013cd2a3743e9d49be9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate11.lean @@ -0,0 +1,186 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate11Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate11. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_11 (r s : CopyLabel 11) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 11 r s = fourYData_11 r s := by + rw [integerRowsFourTrace_parts (by decide) collectedFourData_11 collectedFourChecked_11] + fin_cases r <;> fin_cases s + · exact fourYNumber_11_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_11_3_1 + · exact fourYNumber_11_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_11_5_1 + · exact fourYNumber_11_5_3 + · exact fourYNumber_11_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_11_7_1 + · exact fourYNumber_11_7_3 + · exact fourYNumber_11_7_5 + · exact fourYNumber_11_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_11_9_1 + · exact fourYNumber_11_9_3 + · exact fourYNumber_11_9_5 + · exact fourYNumber_11_9_7 + · exact fourYNumber_11_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_11_11_1 + · exact fourYNumber_11_11_3 + · exact fourYNumber_11_11_5 + · exact fourYNumber_11_11_7 + · exact fourYNumber_11_11_9 + · exact fourYNumber_11_11_11 + +theorem fourYChecked_11 (r s : CopyLabel 11) : + integerRowsFourTrace 11 r s = fourYData_11 r s := by + have hh : ∀ r s : CopyLabel 11, fourYData_11 r s = fourYData_11 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_11 r s h + · rw [integerRowsFourTrace_symm, fourYLower_11 s r (by omega), hh] + +def fourHighestCache_11_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,9}, [232243200, 46448640, 7257600, -7983360, 2903040, 39916800]), + ({0,1,3,8}, [-232243200, -46448640, -7257600, 7983360, -2903040, -39916800]), + ({0,1,4,7}, [348364800, 38707200, 1209600, -3265920, -725760, 39916800]), + ({0,1,5,6}, [-348364800, -38707200, 4320000, -604800, 3628800, -39916800]) +] + +def fourHighestCache_11_1 : List (Occupation 24 × List ℚ) := [ + ({0,2,3,7}, [-116121600, 7741440, 6048000, -4717440, 3628800, 0]), + ({0,2,4,6}, [0, 0, -5529600, 3870720, -2903040, 0]), + ({0,3,4,5}, [116121600, -7741440, 5011200, -3024000, 2177280, 0]), + ({1,2,3,6}, [116121600, -7741440, -518400, 846720, -725760, 0]) +] + +def fourHighestCache_11_2 : List (Occupation 24 × List ℚ) := [ + ({1,2,4,5}, [-116121600, 7741440, 518400, -846720, 725760, 0]) +] + +def fourHighestCache_11 : List (Occupation 24 × List ℚ) := fourHighestCache_11_0 ++ fourHighestCache_11_1 ++ fourHighestCache_11_2 + +theorem fourHighestNumber_11_1 : ∀ A∈highestFourOccupations 11, + kernelHighestEntry 11 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_11 1 A := by + rw [fourOccupations_11] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_11_3 : ∀ A∈highestFourOccupations 11, + kernelHighestEntry 11 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_11 3 A := by + rw [fourOccupations_11] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_11_5 : ∀ A∈highestFourOccupations 11, + kernelHighestEntry 11 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_11 5 A := by + rw [fourOccupations_11] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_11_7 : ∀ A∈highestFourOccupations 11, + kernelHighestEntry 11 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_11 7 A := by + rw [fourOccupations_11] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_11_9 : ∀ A∈highestFourOccupations 11, + kernelHighestEntry 11 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_11 9 A := by + rw [fourOccupations_11] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_11_11 : ∀ A∈highestFourOccupations 11, + kernelHighestEntry 11 ⟨⟨11,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_11 11 A := by + rw [fourOccupations_11] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_11 : ∀ r : CopyLabel 11, ∀ A∈highestFourOccupations 11, + kernelHighestEntry 11 r A = highestLookup fourHighestCache_11 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_11_1 + · exact fourHighestNumber_11_3 + · exact fourHighestNumber_11_5 + · exact fourHighestNumber_11_7 + · exact fourHighestNumber_11_9 + · exact fourHighestNumber_11_11 + +theorem fourZChecked_11 (r s : CopyLabel 11) : + integerFourGram 11 r s = fourZData_11 r s := by + rw [integerFourGram_cached 11 fourHighestCache_11 fourHighestChecked_11] + have h : ∀ r s : CopyLabel 11, cachedFourGram 11 fourHighestCache_11 r s = fourZData_11 r s := by + simp only [cachedFourGram, fourOccupations_11] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_11 : + fourZData_11 * (Matrix.diagonal (fun r : CopyLabel 11 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 11 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 11 => rationalCopyDiagonal 11 r.val.val) * + fourYData_11 * Matrix.diagonal (fun r : CopyLabel 11 => rationalCopyDiagonal 11 r.val.val)) * + fourZData_11 = fourLData_11 * Matrix.diagonal fourPivotData_11 * (fourLData_11)ᵀ := by + have h : ∀ r s : CopyLabel 11, + (fourZData_11 * (Matrix.diagonal (fun r : CopyLabel 11 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 11 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 11 => rationalCopyDiagonal 11 r.val.val) * + fourYData_11 * Matrix.diagonal (fun r : CopyLabel 11 => rationalCopyDiagonal 11 r.val.val)) * + fourZData_11 : Matrix (CopyLabel 11) (CopyLabel 11) ℚ) r s = + (fourLData_11 * Matrix.diagonal fourPivotData_11 * (fourLData_11)ᵀ : Matrix (CopyLabel 11) (CopyLabel 11) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_11 : ∀ r, 0 ≤ fourPivotData_11 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_11, copyDiagonalData] + +theorem integer_certificate_11 : + ((integerCompression 11).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_11) (fourPivotData_11) _ fourPivotChecked_11 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 11 = fourYData_11 from Matrix.ext fourYChecked_11, + show integerFourGram 11 = fourZData_11 from Matrix.ext fourZChecked_11] + exact fourLDLChecked_11 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate11Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate11Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..c4de66a88c5cf6a563db23718dc27fcfe27f7c5b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate11Data.lean @@ -0,0 +1,137 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse1124 + +namespace OAI + +/-! Certificate11 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_11 : Matrix (CopyLabel 11) (CopyLabel 11) ℚ := + copyMatrixData 11 [ + [(355506999534679510671910366977/2684354560000000000000000), (-492518176620867562155352785603/26843545600000000000000000), (4138293745048202697976148691/2684354560000000000000000), (-462687962608795946399629749/107374182400000000000000000), (11348337457149032083099347/8589934592000000000000), (9515299162481273462940221121/53687091200000000000000000)], + [(-492518176620867562155352785603/26843545600000000000000000), (147990015194717604324970401939/53687091200000000000000000), (-32142369690011994391738675341/53687091200000000000000000), (152067258827467245508923213633/1073741824000000000000000000), (-24550910356013172596362249197/268435456000000000000000000), (-6054978439653477518247063561/4294967296000000000000000)], + [(4138293745048202697976148691/2684354560000000000000000), (-32142369690011994391738675341/53687091200000000000000000), (34715791944194177659480181307/751619276800000000000000000), (6557195925083744855698330017/214748364800000000000000000), (-54074165446495408903733637/1342177280000000000000000), (7480163841350538966655866399/107374182400000000000000000)], + [(-462687962608795946399629749/107374182400000000000000000), (152067258827467245508923213633/1073741824000000000000000000), (6557195925083744855698330017/214748364800000000000000000), (-237367962714551377912277743917/4294967296000000000000000000), (81330512041049837325818730273/1073741824000000000000000000), (5164978977978401789071684677/429496729600000000000000000)], + [(11348337457149032083099347/8589934592000000000000), (-24550910356013172596362249197/268435456000000000000000000), (-54074165446495408903733637/1342177280000000000000000), (81330512041049837325818730273/1073741824000000000000000000), (-33338233529668386729470042271/268435456000000000000000000), (-3621872144856940147989219393/107374182400000000000000000)], + [(9515299162481273462940221121/53687091200000000000000000), (-6054978439653477518247063561/4294967296000000000000000), (7480163841350538966655866399/107374182400000000000000000), (5164978977978401789071684677/429496729600000000000000000), (-3621872144856940147989219393/107374182400000000000000000), (-485970561658224932619441308769/214748364800000000000000000)] + ] + +def fourZData_11 : Matrix (CopyLabel 11) (CopyLabel 11) ℚ := + copyMatrixData 11 [ + [3628800, 0, 0, 0, -14175, 155925], + [0, 30240, 0, -1890, 0, (155925/8)], + [0, 0, (3375/2), (-4725/4), (14175/16), 0], + [0, -1890, (-4725/4), 945, (-19845/32), (-155925/128)], + [-14175, 0, (14175/16), (-19845/32), (133245/256), (-155925/256)], + [155925, (155925/8), 0, (-155925/128), (-155925/256), (39449025/2048)] + ] + +def fourLData_11 : Matrix (CopyLabel 11) (CopyLabel 11) ℚ := + copyMatrixData 11 [ + [1, 0, 0, 0, 0, 0], + [(31383047013636756733203467204/7051155903302383413526567079169), 1, 0, 0, 0, 0], + [(-9939372038972515368176183805/25070776545075141025872238503712), (125765185144970030615819379031746558389214906329570600851695/403913072730290964655802469730964386629273989007811824607184), 1, 0, 0, 0], + [(-296100363493333293793952873/451273977811352538465700293066816), (-226560393294244413444122439360815730073560117487375319268271/807826145460581929311604939461928773258547978015623649214368), (-7/10), 1, 0, 0], + [(-58943366399805908686060530373/14326158025757223443355564859264), (528213777608874128586441391933335545234702606584196523577119/3231304581842327717246419757847715093034191912062494596857472), (21/40), 0, 1, 0], + [(27580305897858760803256936653173/601698637081803384620933724089088), (165/256), 0, 0, 0, 1] + ] + +def fourPivotData_11 : CopyLabel 11 → ℚ := + copyDiagonalData 11 [(190381209389164352165217311137563/13421772800000000000000000), (75733701136929555872962963074555822492988872938964717113847/26288614586528711076345008361268314112000000000000000000), (31160160353385400741807881710332433700203771124666113757322271747415105611829819889953/948715161298772175963026916321379196390157829147195853630437756764160000000000000000), 0, 0, 0] + +theorem fourOccupations_11 : highestFourOccupations 11 = {{0,1,2,9}, {0,1,3,8}, {0,1,4,7}, {0,1,5,6}, {0,2,3,7}, {0,2,4,6}, {0,3,4,5}, {1,2,3,6}, {1,2,4,5}} := by + decide +kernel + +theorem fourYNumber_11_1_1 : + (collectedFourPartsTrace 11 1 1 collectedFourData_11 : ℚ) / fourCommonDenominator = (355506999534679510671910366977/2684354560000000000000000) := by + decide +kernel + +theorem fourYNumber_11_3_1 : + (collectedFourPartsTrace 11 3 1 collectedFourData_11 : ℚ) / fourCommonDenominator = (-492518176620867562155352785603/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_11_3_3 : + (collectedFourPartsTrace 11 3 3 collectedFourData_11 : ℚ) / fourCommonDenominator = (147990015194717604324970401939/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_11_5_1 : + (collectedFourPartsTrace 11 5 1 collectedFourData_11 : ℚ) / fourCommonDenominator = (4138293745048202697976148691/2684354560000000000000000) := by + decide +kernel + +theorem fourYNumber_11_5_3 : + (collectedFourPartsTrace 11 5 3 collectedFourData_11 : ℚ) / fourCommonDenominator = (-32142369690011994391738675341/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_11_5_5 : + (collectedFourPartsTrace 11 5 5 collectedFourData_11 : ℚ) / fourCommonDenominator = (34715791944194177659480181307/751619276800000000000000000) := by + decide +kernel + +theorem fourYNumber_11_7_1 : + (collectedFourPartsTrace 11 7 1 collectedFourData_11 : ℚ) / fourCommonDenominator = (-462687962608795946399629749/107374182400000000000000000) := by + decide +kernel + +theorem fourYNumber_11_7_3 : + (collectedFourPartsTrace 11 7 3 collectedFourData_11 : ℚ) / fourCommonDenominator = (152067258827467245508923213633/1073741824000000000000000000) := by + decide +kernel + +theorem fourYNumber_11_7_5 : + (collectedFourPartsTrace 11 7 5 collectedFourData_11 : ℚ) / fourCommonDenominator = (6557195925083744855698330017/214748364800000000000000000) := by + decide +kernel + +theorem fourYNumber_11_7_7 : + (collectedFourPartsTrace 11 7 7 collectedFourData_11 : ℚ) / fourCommonDenominator = (-237367962714551377912277743917/4294967296000000000000000000) := by + decide +kernel + +theorem fourYNumber_11_9_1 : + (collectedFourPartsTrace 11 9 1 collectedFourData_11 : ℚ) / fourCommonDenominator = (11348337457149032083099347/8589934592000000000000) := by + decide +kernel + +theorem fourYNumber_11_9_3 : + (collectedFourPartsTrace 11 9 3 collectedFourData_11 : ℚ) / fourCommonDenominator = (-24550910356013172596362249197/268435456000000000000000000) := by + decide +kernel + +theorem fourYNumber_11_9_5 : + (collectedFourPartsTrace 11 9 5 collectedFourData_11 : ℚ) / fourCommonDenominator = (-54074165446495408903733637/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_11_9_7 : + (collectedFourPartsTrace 11 9 7 collectedFourData_11 : ℚ) / fourCommonDenominator = (81330512041049837325818730273/1073741824000000000000000000) := by + decide +kernel + +theorem fourYNumber_11_9_9 : + (collectedFourPartsTrace 11 9 9 collectedFourData_11 : ℚ) / fourCommonDenominator = (-33338233529668386729470042271/268435456000000000000000000) := by + decide +kernel + +theorem fourYNumber_11_11_1 : + (collectedFourPartsTrace 11 11 1 collectedFourData_11 : ℚ) / fourCommonDenominator = (9515299162481273462940221121/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_11_11_3 : + (collectedFourPartsTrace 11 11 3 collectedFourData_11 : ℚ) / fourCommonDenominator = (-6054978439653477518247063561/4294967296000000000000000) := by + decide +kernel + +theorem fourYNumber_11_11_5 : + (collectedFourPartsTrace 11 11 5 collectedFourData_11 : ℚ) / fourCommonDenominator = (7480163841350538966655866399/107374182400000000000000000) := by + decide +kernel + +theorem fourYNumber_11_11_7 : + (collectedFourPartsTrace 11 11 7 collectedFourData_11 : ℚ) / fourCommonDenominator = (5164978977978401789071684677/429496729600000000000000000) := by + decide +kernel + +theorem fourYNumber_11_11_9 : + (collectedFourPartsTrace 11 11 9 collectedFourData_11 : ℚ) / fourCommonDenominator = (-3621872144856940147989219393/107374182400000000000000000) := by + decide +kernel + +theorem fourYNumber_11_11_11 : + (collectedFourPartsTrace 11 11 11 collectedFourData_11 : ℚ) / fourCommonDenominator = (-485970561658224932619441308769/214748364800000000000000000) := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate12.lean b/lean/OAI/Analysis/LaughlinFock/Certificate12.lean new file mode 100644 index 0000000000000000000000000000000000000000..2659cabab3e2b1ed5a90ac407ce074933169ed35 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate12.lean @@ -0,0 +1,147 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate12Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate12. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_12 (r s : CopyLabel 12) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 12 r s = fourYData_12 r s := by + rw [integerRowsFourTrace_short (by decide)] + fin_cases r <;> fin_cases s + · exact fourYNumber_12_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_12_3_1 + · exact fourYNumber_12_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_12_5_1 + · exact fourYNumber_12_5_3 + · exact fourYNumber_12_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_12_7_1 + · exact fourYNumber_12_7_3 + · exact fourYNumber_12_7_5 + · exact fourYNumber_12_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_12_9_1 + · exact fourYNumber_12_9_3 + · exact fourYNumber_12_9_5 + · exact fourYNumber_12_9_7 + · exact fourYNumber_12_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_12_11_1 + · exact fourYNumber_12_11_3 + · exact fourYNumber_12_11_5 + · exact fourYNumber_12_11_7 + · exact fourYNumber_12_11_9 + · exact fourYNumber_12_11_11 + +theorem fourYChecked_12 (r s : CopyLabel 12) : + integerRowsFourTrace 12 r s = fourYData_12 r s := by + have hh : ∀ r s : CopyLabel 12, fourYData_12 r s = fourYData_12 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_12 r s h + · rw [integerRowsFourTrace_symm, fourYLower_12 s r (by omega), hh] + +def fourHighestCache_12_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,10}, [0, -696729600, -174182400, 65318400, 43545600, -239500800]), + ({0,1,3,9}, [0, 696729600, 174182400, -65318400, -43545600, 239500800]), + ({0,1,4,8}, [0, -557383680, -77414400, 29030400, 34836480, -159667200]), + ({0,1,5,7}, [0, 348364800, 9676800, -3628800, -21772800, 79833600]) +] + +def fourHighestCache_12_1 : List (Occupation 24 × List ℚ) := [ + ({0,2,3,8}, [0, -139345920, -96768000, 36288000, 8709120, -79833600]), + ({0,2,4,7}, [0, 209018880, 67737600, -25401600, -13063680, 79833600]), + ({0,2,5,6}, [0, -348364800, -9676800, 3628800, 21772800, -79833600]), + ({0,3,4,6}, [0, 69672960, -29030400, 10886400, -4354560, 0]) +] + +def fourHighestCache_12_2 : List (Occupation 24 × List ℚ) := [ + ({1,2,3,7}, [0, -69672960, 29030400, -10886400, 4354560, 0]), + ({1,2,4,6}, [0, 69672960, -29030400, 10886400, -4354560, 0]), + ({1,3,4,5}, [0, -69672960, 29030400, -10886400, 4354560, 0]) +] + +def fourHighestCache_12 : List (Occupation 24 × List ℚ) := fourHighestCache_12_0 ++ fourHighestCache_12_1 ++ fourHighestCache_12_2 + +theorem fourHighestChecked_12 : ∀ r : CopyLabel 12, ∀ A∈highestFourOccupations 12, + kernelHighestEntry 12 r A = highestLookup fourHighestCache_12 r.val.val A := by + rw [fourOccupations_12] + apply @of_decide_eq_true _ (boundedMatrixEntriesDecidable _ _ _) + decide +kernel + +theorem fourZChecked_12 (r s : CopyLabel 12) : + integerFourGram 12 r s = fourZData_12 r s := by + rw [integerFourGram_cached 12 fourHighestCache_12 fourHighestChecked_12] + have h : ∀ r s : CopyLabel 12, cachedFourGram 12 fourHighestCache_12 r s = fourZData_12 r s := by + simp only [cachedFourGram, fourOccupations_12] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_12 : + fourZData_12 * (Matrix.diagonal (fun r : CopyLabel 12 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 12 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 12 => rationalCopyDiagonal 12 r.val.val) * + fourYData_12 * Matrix.diagonal (fun r : CopyLabel 12 => rationalCopyDiagonal 12 r.val.val)) * + fourZData_12 = fourLData_12 * Matrix.diagonal fourPivotData_12 * (fourLData_12)ᵀ := by + have h : ∀ r s : CopyLabel 12, + (fourZData_12 * (Matrix.diagonal (fun r : CopyLabel 12 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 12 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 12 => rationalCopyDiagonal 12 r.val.val) * + fourYData_12 * Matrix.diagonal (fun r : CopyLabel 12 => rationalCopyDiagonal 12 r.val.val)) * + fourZData_12 : Matrix (CopyLabel 12) (CopyLabel 12) ℚ) r s = + (fourLData_12 * Matrix.diagonal fourPivotData_12 * (fourLData_12)ᵀ : Matrix (CopyLabel 12) (CopyLabel 12) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_12 : ∀ r, 0 ≤ fourPivotData_12 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_12, copyDiagonalData] + +theorem integer_certificate_12 : + ((integerCompression 12).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_12) (fourPivotData_12) _ fourPivotChecked_12 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 12 = fourYData_12 from Matrix.ext fourYChecked_12, + show integerFourGram 12 = fourZData_12 from Matrix.ext fourZChecked_12] + exact fourLDLChecked_12 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate12Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate12Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..d0ec3429984247246cecce126009684aa96eac1a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate12Data.lean @@ -0,0 +1,137 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FasterTrace +import OAI.Analysis.LaughlinFock.LDL + +namespace OAI + +/-! Certificate12 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_12 : Matrix (CopyLabel 12) (CopyLabel 12) ℚ := + copyMatrixData 12 [ + [(-3212210757512321485599281916753/3355443200000000000000000), (895702254134345728636174721541/13421772800000000000000000), (68097845461495289881861573857/1677721600000000000000000), (-752813653217822024111461724931/53687091200000000000000000), (-134829903556655679763808374617/13421772800000000000000000), (811936640191894240871622253347/26843545600000000000000000)], + [(895702254134345728636174721541/13421772800000000000000000), (-1159911251074617621122089942749/134217728000000000000000000), (213044818522802951430393957/13421772800000000000000000), (36837551380530207007795982913/107374182400000000000000000), (60751252291694576857824915477/134217728000000000000000000), (-54800676639953961331845380733/53687091200000000000000000)], + [(68097845461495289881861573857/1677721600000000000000000), (213044818522802951430393957/13421772800000000000000000), (-3478046950764018380506002147/13421772800000000000000000), (10762345455625583105572253637/53687091200000000000000000), (-366529537329497692072793991/2684354560000000000000000), (-19801282521664131308141766093/26843545600000000000000000)], + [(-752813653217822024111461724931/53687091200000000000000000), (36837551380530207007795982913/107374182400000000000000000), (10762345455625583105572253637/53687091200000000000000000), (-39177728661094886378053727181/429496729600000000000000000), (-3189821925618051152448113649/107374182400000000000000000), (143533377069418623133561028193/214748364800000000000000000)], + [(-134829903556655679763808374617/13421772800000000000000000), (60751252291694576857824915477/134217728000000000000000000), (-366529537329497692072793991/2684354560000000000000000), (-3189821925618051152448113649/107374182400000000000000000), (18536046179056210622306506059/134217728000000000000000000), (-23867512086636946827723967299/53687091200000000000000000)], + [(811936640191894240871622253347/26843545600000000000000000), (-54800676639953961331845380733/53687091200000000000000000), (-19801282521664131308141766093/26843545600000000000000000), (143533377069418623133561028193/214748364800000000000000000), (-23867512086636946827723967299/53687091200000000000000000), (-17023195688011355418191427537/21474836480000000000000000)] + ] + +def fourZData_12 : Matrix (CopyLabel 12) (CopyLabel 12) ℚ := + copyMatrixData 12 [ + [0, 0, 0, 0, 0, 0], + [0, 272160, 0, 0, -17010, (467775/8)], + [0, 0, 18900, (-14175/2), 0, (155925/16)], + [0, 0, (-14175/2), (42525/16), 0, (-467775/128)], + [0, -17010, 0, 0, (8505/8), (-467775/128)], + [0, (467775/8), (155925/16), (-467775/128), (-467775/128), (36018675/2048)] + ] + +def fourLData_12 : Matrix (CopyLabel 12) (CopyLabel 12) ℚ := + copyMatrixData 12 [ + [1, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0], + [0, (163364364513064607528121281645/335222978107285455528947287236), 1, 0, 0, 0], + [0, (-163364364513064607528121281645/893927941619427881410526099296), (-3/8), 1, 0, 0], + [0, (-1/16), 0, 0, 1, 0], + [0, (833361664825525588495918957815/1787855883238855762821052198592), (33/64), 0, 0, 1] + ] + +def fourPivotData_12 : CopyLabel 12 → ℚ := + copyDiagonalData 12 [0, (6788265306672530474461182566529/536870912000000000000000000), (13166444846555554646802017772530214918706281995746569/9373513853115332101779238150954024960000000000000000), 0, 0, 0] + +theorem fourOccupations_12 : highestFourOccupations 12 = {{0,1,2,10}, {0,1,3,9}, {0,1,4,8}, {0,1,5,7}, {0,2,3,8}, {0,2,4,7}, {0,2,5,6}, {0,3,4,6}, {1,2,3,7}, {1,2,4,6}, {1,3,4,5}} := by + decide +kernel + +theorem fourYNumber_12_1_1 : + (shortNumericRowsFourTrace 12 1 1 : ℚ) / fourCommonDenominator = (-3212210757512321485599281916753/3355443200000000000000000) := by + decide +kernel + +theorem fourYNumber_12_3_1 : + (shortNumericRowsFourTrace 12 3 1 : ℚ) / fourCommonDenominator = (895702254134345728636174721541/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_12_3_3 : + (shortNumericRowsFourTrace 12 3 3 : ℚ) / fourCommonDenominator = (-1159911251074617621122089942749/134217728000000000000000000) := by + decide +kernel + +theorem fourYNumber_12_5_1 : + (shortNumericRowsFourTrace 12 5 1 : ℚ) / fourCommonDenominator = (68097845461495289881861573857/1677721600000000000000000) := by + decide +kernel + +theorem fourYNumber_12_5_3 : + (shortNumericRowsFourTrace 12 5 3 : ℚ) / fourCommonDenominator = (213044818522802951430393957/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_12_5_5 : + (shortNumericRowsFourTrace 12 5 5 : ℚ) / fourCommonDenominator = (-3478046950764018380506002147/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_12_7_1 : + (shortNumericRowsFourTrace 12 7 1 : ℚ) / fourCommonDenominator = (-752813653217822024111461724931/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_12_7_3 : + (shortNumericRowsFourTrace 12 7 3 : ℚ) / fourCommonDenominator = (36837551380530207007795982913/107374182400000000000000000) := by + decide +kernel + +theorem fourYNumber_12_7_5 : + (shortNumericRowsFourTrace 12 7 5 : ℚ) / fourCommonDenominator = (10762345455625583105572253637/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_12_7_7 : + (shortNumericRowsFourTrace 12 7 7 : ℚ) / fourCommonDenominator = (-39177728661094886378053727181/429496729600000000000000000) := by + decide +kernel + +theorem fourYNumber_12_9_1 : + (shortNumericRowsFourTrace 12 9 1 : ℚ) / fourCommonDenominator = (-134829903556655679763808374617/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_12_9_3 : + (shortNumericRowsFourTrace 12 9 3 : ℚ) / fourCommonDenominator = (60751252291694576857824915477/134217728000000000000000000) := by + decide +kernel + +theorem fourYNumber_12_9_5 : + (shortNumericRowsFourTrace 12 9 5 : ℚ) / fourCommonDenominator = (-366529537329497692072793991/2684354560000000000000000) := by + decide +kernel + +theorem fourYNumber_12_9_7 : + (shortNumericRowsFourTrace 12 9 7 : ℚ) / fourCommonDenominator = (-3189821925618051152448113649/107374182400000000000000000) := by + decide +kernel + +theorem fourYNumber_12_9_9 : + (shortNumericRowsFourTrace 12 9 9 : ℚ) / fourCommonDenominator = (18536046179056210622306506059/134217728000000000000000000) := by + decide +kernel + +theorem fourYNumber_12_11_1 : + (shortNumericRowsFourTrace 12 11 1 : ℚ) / fourCommonDenominator = (811936640191894240871622253347/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_12_11_3 : + (shortNumericRowsFourTrace 12 11 3 : ℚ) / fourCommonDenominator = (-54800676639953961331845380733/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_12_11_5 : + (shortNumericRowsFourTrace 12 11 5 : ℚ) / fourCommonDenominator = (-19801282521664131308141766093/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_12_11_7 : + (shortNumericRowsFourTrace 12 11 7 : ℚ) / fourCommonDenominator = (143533377069418623133561028193/214748364800000000000000000) := by + decide +kernel + +theorem fourYNumber_12_11_9 : + (shortNumericRowsFourTrace 12 11 9 : ℚ) / fourCommonDenominator = (-23867512086636946827723967299/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_12_11_11 : + (shortNumericRowsFourTrace 12 11 11 : ℚ) / fourCommonDenominator = (-17023195688011355418191427537/21474836480000000000000000) := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate13.lean b/lean/OAI/Analysis/LaughlinFock/Certificate13.lean new file mode 100644 index 0000000000000000000000000000000000000000..405ed7de0108d2e7b9406ba195337d647019ca08 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate13.lean @@ -0,0 +1,221 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate13Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate13. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_13 (r s : CopyLabel 13) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 13 r s = fourYData_13 r s := by + rw [integerRowsFourTrace_parts (by decide) collectedFourData_13 collectedFourChecked_13] + fin_cases r <;> fin_cases s + · exact fourYNumber_13_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · have h : (13:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_13_3_1 + · exact fourYNumber_13_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · have h : (13:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_13_5_1 + · exact fourYNumber_13_5_3 + · exact fourYNumber_13_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · have h : (13:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_13_7_1 + · exact fourYNumber_13_7_3 + · exact fourYNumber_13_7_5 + · exact fourYNumber_13_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · have h : (13:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_13_9_1 + · exact fourYNumber_13_9_3 + · exact fourYNumber_13_9_5 + · exact fourYNumber_13_9_7 + · exact fourYNumber_13_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · have h : (13:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_13_11_1 + · exact fourYNumber_13_11_3 + · exact fourYNumber_13_11_5 + · exact fourYNumber_13_11_7 + · exact fourYNumber_13_11_9 + · exact fourYNumber_13_11_11 + · have h : (13:ℕ) ≤ 11 := hrs + omega + · exact fourYNumber_13_13_1 + · exact fourYNumber_13_13_3 + · exact fourYNumber_13_13_5 + · exact fourYNumber_13_13_7 + · exact fourYNumber_13_13_9 + · exact fourYNumber_13_13_11 + · exact fourYNumber_13_13_13 + +theorem fourYChecked_13 (r s : CopyLabel 13) : + integerRowsFourTrace 13 r s = fourYData_13 r s := by + have hh : ∀ r s : CopyLabel 13, fourYData_13 r s = fourYData_13 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_13 r s h + · rw [integerRowsFourTrace_symm, fourYLower_13 s r (by omega), hh] + +def fourHighestCache_13_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,11}, [38320128000, 9580032000, 3353011200, -239500800, -958003200, 1197504000, 6227020800]), + ({0,1,3,10}, [-38320128000, -9580032000, -3353011200, 239500800, 958003200, -1197504000, -6227020800]), + ({0,1,4,9}, [61312204800, 9754214400, 1741824000, -174182400, -505128960, 479001600, 6227020800]), + ({0,1,5,8}, [-61312204800, -9754214400, -503193600, 174182400, 87091200, 159667200, -6227020800]) +] + +def fourHighestCache_13_1 : List (Occupation 24 × List ℚ) := [ + ({0,1,6,7}, [68976230400, 8883302400, 43545600, -210470400, 130636800, -479001600, 6227020800]), + ({0,2,3,9}, [-22992076800, -174182400, 1611187200, -65318400, -452874240, 718502400, 0]), + ({0,2,4,8}, [0, 0, -1238630400, 0, 418037760, -638668800, 0]), + ({0,2,5,7}, [-7664025600, 870912000, 459648000, 36288000, -217728000, 319334400, 0]) +] + +def fourHighestCache_13_2 : List (Occupation 24 × List ℚ) := [ + ({0,3,4,7}, [30656102400, -696729600, 406425600, 29030400, -165473280, 239500800, 0]), + ({0,3,5,6}, [-22992076800, -174182400, -246758400, -65318400, 174182400, -239500800, 0]), + ({1,2,3,8}, [22992076800, 174182400, -372556800, 65318400, 34836480, -79833600, 0]), + ({1,2,4,7}, [-22992076800, -174182400, 372556800, -65318400, -34836480, 79833600, 0]) +] + +def fourHighestCache_13_3 : List (Occupation 24 × List ℚ) := [ + ({1,2,5,6}, [30656102400, -696729600, -212889600, 29030400, 43545600, -79833600, 0]), + ({1,3,4,6}, [-7664025600, 870912000, -159667200, 36288000, -8709120, 0, 0]), + ({2,3,4,5}, [7664025600, -870912000, 159667200, -36288000, 8709120, 0, 0]) +] + +def fourHighestCache_13 : List (Occupation 24 × List ℚ) := fourHighestCache_13_0 ++ fourHighestCache_13_1 ++ fourHighestCache_13_2 ++ fourHighestCache_13_3 + +theorem fourHighestNumber_13_1 : ∀ A∈highestFourOccupations 13, + kernelHighestEntry 13 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_13 1 A := by + rw [fourOccupations_13] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_13_3 : ∀ A∈highestFourOccupations 13, + kernelHighestEntry 13 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_13 3 A := by + rw [fourOccupations_13] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_13_5 : ∀ A∈highestFourOccupations 13, + kernelHighestEntry 13 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_13 5 A := by + rw [fourOccupations_13] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_13_7 : ∀ A∈highestFourOccupations 13, + kernelHighestEntry 13 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_13 7 A := by + rw [fourOccupations_13] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_13_9 : ∀ A∈highestFourOccupations 13, + kernelHighestEntry 13 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_13 9 A := by + rw [fourOccupations_13] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_13_11 : ∀ A∈highestFourOccupations 13, + kernelHighestEntry 13 ⟨⟨11,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_13 11 A := by + rw [fourOccupations_13] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_13_13 : ∀ A∈highestFourOccupations 13, + kernelHighestEntry 13 ⟨⟨13,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_13 13 A := by + rw [fourOccupations_13] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_13 : ∀ r : CopyLabel 13, ∀ A∈highestFourOccupations 13, + kernelHighestEntry 13 r A = highestLookup fourHighestCache_13 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_13_1 + · exact fourHighestNumber_13_3 + · exact fourHighestNumber_13_5 + · exact fourHighestNumber_13_7 + · exact fourHighestNumber_13_9 + · exact fourHighestNumber_13_11 + · exact fourHighestNumber_13_13 + +theorem fourZChecked_13 (r s : CopyLabel 13) : + integerFourGram 13 r s = fourZData_13 r s := by + rw [integerFourGram_cached 13 fourHighestCache_13 fourHighestChecked_13] + have h : ∀ r s : CopyLabel 13, cachedFourGram 13 fourHighestCache_13 r s = fourZData_13 r s := by + simp only [cachedFourGram, fourOccupations_13] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_13 : + fourZData_13 * (Matrix.diagonal (fun r : CopyLabel 13 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 13 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 13 => rationalCopyDiagonal 13 r.val.val) * + fourYData_13 * Matrix.diagonal (fun r : CopyLabel 13 => rationalCopyDiagonal 13 r.val.val)) * + fourZData_13 = fourLData_13 * Matrix.diagonal fourPivotData_13 * (fourLData_13)ᵀ := by + have h : ∀ r s : CopyLabel 13, + (fourZData_13 * (Matrix.diagonal (fun r : CopyLabel 13 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 13 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 13 => rationalCopyDiagonal 13 r.val.val) * + fourYData_13 * Matrix.diagonal (fun r : CopyLabel 13 => rationalCopyDiagonal 13 r.val.val)) * + fourZData_13 : Matrix (CopyLabel 13) (CopyLabel 13) ℚ) r s = + (fourLData_13 * Matrix.diagonal fourPivotData_13 * (fourLData_13)ᵀ : Matrix (CopyLabel 13) (CopyLabel 13) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_13 : ∀ r, 0 ≤ fourPivotData_13 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_13, copyDiagonalData] + +theorem integer_certificate_13 : + ((integerCompression 13).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_13) (fourPivotData_13) _ fourPivotChecked_13 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 13 = fourYData_13 from Matrix.ext fourYChecked_13, + show integerFourGram 13 = fourZData_13 from Matrix.ext fourZChecked_13] + exact fourLDLChecked_13 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate13Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate13Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..566634fb680393b2c072101eb0586b09449d496e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate13Data.lean @@ -0,0 +1,168 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse1317 + +namespace OAI + +/-! Certificate13 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_13 : Matrix (CopyLabel 13) (CopyLabel 13) ℚ := + copyMatrixData 13 [ + [(54392955842088185147902038019563/6710886400000000000000000), (1123748024618949361656403709187/2684354560000000000000000), (-3952251593651960125174045120041/6710886400000000000000000), (8652633863278216781156747661189/53687091200000000000000000), (-355081805318944629813716960967/13421772800000000000000000), (2144660569773776567544859885431/26843545600000000000000000), (-10573066740063296657251598628951/13421772800000000000000000)], + [(1123748024618949361656403709187/2684354560000000000000000), (549287455032456681750279702831/26843545600000000000000000), (272608352002224246803257304523/13421772800000000000000000), (-336594871328110409131740050319/107374182400000000000000000), (-83467340369805263164603981947/26843545600000000000000000), (-53741237690979222629963864157/53687091200000000000000000), (-322958874522253767236148992139/26843545600000000000000000)], + [(-3952251593651960125174045120041/6710886400000000000000000), (272608352002224246803257304523/13421772800000000000000000), (-12877898930642977749820839573/2684354560000000000000000), (-5970782558191454823931610373/53687091200000000000000000), (4274996279199192620771589153/2684354560000000000000000), (-68930057095502634567023048451/26843545600000000000000000), (946650494523480527937150423/268435456000000000000000)], + [(8652633863278216781156747661189/53687091200000000000000000), (-336594871328110409131740050319/107374182400000000000000000), (-5970782558191454823931610373/53687091200000000000000000), (36229772664258699428237933199/85899345920000000000000000), (-45868939007172219785430914913/107374182400000000000000000), (70075598168791046625716962809/214748364800000000000000000), (-6961929908725446971605721289/21474836480000000000000000)], + [(-355081805318944629813716960967/13421772800000000000000000), (-83467340369805263164603981947/26843545600000000000000000), (4274996279199192620771589153/2684354560000000000000000), (-45868939007172219785430914913/107374182400000000000000000), (-6983205275787585443985353589/26843545600000000000000000), (59787590378753456451814088133/53687091200000000000000000), (-32349288923635241335157434197/26843545600000000000000000)], + [(2144660569773776567544859885431/26843545600000000000000000), (-53741237690979222629963864157/53687091200000000000000000), (-68930057095502634567023048451/26843545600000000000000000), (70075598168791046625716962809/214748364800000000000000000), (59787590378753456451814088133/53687091200000000000000000), (-57551507789343683809289940729/21474836480000000000000000), (111617540419977191224126903401/53687091200000000000000000)], + [(-10573066740063296657251598628951/13421772800000000000000000), (-322958874522253767236148992139/26843545600000000000000000), (946650494523480527937150423/268435456000000000000000), (-6961929908725446971605721289/21474836480000000000000000), (-32349288923635241335157434197/26843545600000000000000000), (111617540419977191224126903401/53687091200000000000000000), (-1524949629653034503076717749619/26843545600000000000000000)] + ] + +def fourZData_13 : Matrix (CopyLabel 13) (CopyLabel 13) ℚ := + copyMatrixData 13 [ + [479001600, 0, 0, 0, 0, -467775, (30405375/4)], + [0, 2721600, 0, 0, -42525, 0, (18243225/16)], + [0, 0, 151200, -14175, (-127575/4), (779625/16), (6081075/64)], + [0, 0, -14175, (14175/4), 0, 0, (-6081075/256)], + [0, -42525, (-127575/4), 0, (365715/32), (-4209975/256), (-18243225/1024)], + [-467775, 0, (779625/16), 0, (-4209975/256), (3274425/128), (-30405375/4096)], + [(30405375/4), (18243225/16), (6081075/64), (-6081075/256), (-18243225/1024), (-30405375/4096), (12411474075/16384)] + ] + +def fourLData_13 : Matrix (CopyLabel 13) (CopyLabel 13) ℚ := + copyMatrixData 13 [ + [1, 0, 0, 0, 0, 0, 0], + [(11689849916810741289906063583/9668394871427482199961857042500), 1, 0, 0, 0, 0, 0], + [(13589354797225438138011294791/23204147691425957279908456902000), (-5722733975085987028604046653929956243704293874849103118195/34281240482376075690109946909475716511496984077694073918916), 1, 0, 0, 0, 0], + [(-509502443091073156788337649/4640829538285191455981691380400), (-133331179119516533068778683019503316626683544854170179925/45708320643168100920146595879300955348662645436925431891888), (-21706288275812938364385693437825764627858127435592841870260081720101251237530632919/517343355656801378818908150437551439728860213722088824246042411156204427158872474621), 1, 0, 0, 0], + [(-21141801667723258155053469941/309388635885679430398779425360000), (8164139482202159622549526622922929439160404777133065091103/182833282572672403680586383517203821394650581747701727567552), (-2324798293789167976951373034105741258574109601490474266531011255089316879927249691903/8277493690508822061102530407000823035661763419553421187936678578499270834541959593936), (-27/20), 1, 0, 0], + [(-10136985870043872385759156641/11250495850388342923591979104000), (-33675001318444951452957104866436564064713894801763875118835/365666565145344807361172767034407642789301163495403455135104), (14207100684267137636925057430646196580175114231330676073245068781101380932888748117185/33109974762035288244410121628003292142647053678213684751746714313997083338167838375744), (33/16), 0, 1, 0], + [(481284793213666874729611098291/28126239625970857308979947760000), (80172088942951081162996041064320236757429026345000134361817/182833282572672403680586383517203821394650581747701727567552), (9311997670323750558321462484827253025351136669869329162341575057923436780900641522251/33109974762035288244410121628003292142647053678213684751746714313997083338167838375744), (-429/64), 0, 0, 1] + ] + +def fourPivotData_13 : CopyLabel 13 → ℚ := + copyDiagonalData 13 [(10337447796530263968199217549841/5368709120000000000000), (694195119768115532724726424916883259357813927573304996858049/5898499968408403534724191540477952000000000000000000000), (13968270602733637228110520061813888872679225770496398254643145101217519533289556814767/599108100334132932380545461509173481945991026270869020893354393600000000000000000), (5883696273719332012203518889149014794794346104783014799260478072665637020854974785901422275094899856437/2169895306004744650385661731012823753860517309855412043890472669282112853650167455792758784000000000000000), 0, 0, 0] + +theorem fourOccupations_13 : highestFourOccupations 13 = {{0,1,2,11}, {0,1,3,10}, {0,1,4,9}, {0,1,5,8}, {0,1,6,7}, {0,2,3,9}, {0,2,4,8}, {0,2,5,7}, {0,3,4,7}, {0,3,5,6}, {1,2,3,8}, {1,2,4,7}, {1,2,5,6}, {1,3,4,6}, {2,3,4,5}} := by + decide +kernel + +theorem fourYNumber_13_1_1 : + (collectedFourPartsTrace 13 1 1 collectedFourData_13 : ℚ) / fourCommonDenominator = (54392955842088185147902038019563/6710886400000000000000000) := by + decide +kernel + +theorem fourYNumber_13_3_1 : + (collectedFourPartsTrace 13 3 1 collectedFourData_13 : ℚ) / fourCommonDenominator = (1123748024618949361656403709187/2684354560000000000000000) := by + decide +kernel + +theorem fourYNumber_13_3_3 : + (collectedFourPartsTrace 13 3 3 collectedFourData_13 : ℚ) / fourCommonDenominator = (549287455032456681750279702831/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_13_5_1 : + (collectedFourPartsTrace 13 5 1 collectedFourData_13 : ℚ) / fourCommonDenominator = (-3952251593651960125174045120041/6710886400000000000000000) := by + decide +kernel + +theorem fourYNumber_13_5_3 : + (collectedFourPartsTrace 13 5 3 collectedFourData_13 : ℚ) / fourCommonDenominator = (272608352002224246803257304523/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_13_5_5 : + (collectedFourPartsTrace 13 5 5 collectedFourData_13 : ℚ) / fourCommonDenominator = (-12877898930642977749820839573/2684354560000000000000000) := by + decide +kernel + +theorem fourYNumber_13_7_1 : + (collectedFourPartsTrace 13 7 1 collectedFourData_13 : ℚ) / fourCommonDenominator = (8652633863278216781156747661189/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_13_7_3 : + (collectedFourPartsTrace 13 7 3 collectedFourData_13 : ℚ) / fourCommonDenominator = (-336594871328110409131740050319/107374182400000000000000000) := by + decide +kernel + +theorem fourYNumber_13_7_5 : + (collectedFourPartsTrace 13 7 5 collectedFourData_13 : ℚ) / fourCommonDenominator = (-5970782558191454823931610373/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_13_7_7 : + (collectedFourPartsTrace 13 7 7 collectedFourData_13 : ℚ) / fourCommonDenominator = (36229772664258699428237933199/85899345920000000000000000) := by + decide +kernel + +theorem fourYNumber_13_9_1 : + (collectedFourPartsTrace 13 9 1 collectedFourData_13 : ℚ) / fourCommonDenominator = (-355081805318944629813716960967/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_13_9_3 : + (collectedFourPartsTrace 13 9 3 collectedFourData_13 : ℚ) / fourCommonDenominator = (-83467340369805263164603981947/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_13_9_5 : + (collectedFourPartsTrace 13 9 5 collectedFourData_13 : ℚ) / fourCommonDenominator = (4274996279199192620771589153/2684354560000000000000000) := by + decide +kernel + +theorem fourYNumber_13_9_7 : + (collectedFourPartsTrace 13 9 7 collectedFourData_13 : ℚ) / fourCommonDenominator = (-45868939007172219785430914913/107374182400000000000000000) := by + decide +kernel + +theorem fourYNumber_13_9_9 : + (collectedFourPartsTrace 13 9 9 collectedFourData_13 : ℚ) / fourCommonDenominator = (-6983205275787585443985353589/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_13_11_1 : + (collectedFourPartsTrace 13 11 1 collectedFourData_13 : ℚ) / fourCommonDenominator = (2144660569773776567544859885431/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_13_11_3 : + (collectedFourPartsTrace 13 11 3 collectedFourData_13 : ℚ) / fourCommonDenominator = (-53741237690979222629963864157/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_13_11_5 : + (collectedFourPartsTrace 13 11 5 collectedFourData_13 : ℚ) / fourCommonDenominator = (-68930057095502634567023048451/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_13_11_7 : + (collectedFourPartsTrace 13 11 7 collectedFourData_13 : ℚ) / fourCommonDenominator = (70075598168791046625716962809/214748364800000000000000000) := by + decide +kernel + +theorem fourYNumber_13_11_9 : + (collectedFourPartsTrace 13 11 9 collectedFourData_13 : ℚ) / fourCommonDenominator = (59787590378753456451814088133/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_13_11_11 : + (collectedFourPartsTrace 13 11 11 collectedFourData_13 : ℚ) / fourCommonDenominator = (-57551507789343683809289940729/21474836480000000000000000) := by + decide +kernel + +theorem fourYNumber_13_13_1 : + (collectedFourPartsTrace 13 13 1 collectedFourData_13 : ℚ) / fourCommonDenominator = (-10573066740063296657251598628951/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_13_13_3 : + (collectedFourPartsTrace 13 13 3 collectedFourData_13 : ℚ) / fourCommonDenominator = (-322958874522253767236148992139/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_13_13_5 : + (collectedFourPartsTrace 13 13 5 collectedFourData_13 : ℚ) / fourCommonDenominator = (946650494523480527937150423/268435456000000000000000) := by + decide +kernel + +theorem fourYNumber_13_13_7 : + (collectedFourPartsTrace 13 13 7 collectedFourData_13 : ℚ) / fourCommonDenominator = (-6961929908725446971605721289/21474836480000000000000000) := by + decide +kernel + +theorem fourYNumber_13_13_9 : + (collectedFourPartsTrace 13 13 9 collectedFourData_13 : ℚ) / fourCommonDenominator = (-32349288923635241335157434197/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_13_13_11 : + (collectedFourPartsTrace 13 13 11 collectedFourData_13 : ℚ) / fourCommonDenominator = (111617540419977191224126903401/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_13_13_13 : + (collectedFourPartsTrace 13 13 13 collectedFourData_13 : ℚ) / fourCommonDenominator = (-1524949629653034503076717749619/26843545600000000000000000) := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate14.lean b/lean/OAI/Analysis/LaughlinFock/Certificate14.lean new file mode 100644 index 0000000000000000000000000000000000000000..743f181f0a71f760fff3f327ffd81a5a2f66608e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate14.lean @@ -0,0 +1,227 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate14Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate14. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_14 (r s : CopyLabel 14) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 14 r s = fourYData_14 r s := by + rw [integerRowsFourTrace_parts (by decide) collectedFourData_14 collectedFourChecked_14] + fin_cases r <;> fin_cases s + · exact fourYNumber_14_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · have h : (13:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_14_3_1 + · exact fourYNumber_14_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · have h : (13:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_14_5_1 + · exact fourYNumber_14_5_3 + · exact fourYNumber_14_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · have h : (13:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_14_7_1 + · exact fourYNumber_14_7_3 + · exact fourYNumber_14_7_5 + · exact fourYNumber_14_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · have h : (13:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_14_9_1 + · exact fourYNumber_14_9_3 + · exact fourYNumber_14_9_5 + · exact fourYNumber_14_9_7 + · exact fourYNumber_14_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · have h : (13:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_14_11_1 + · exact fourYNumber_14_11_3 + · exact fourYNumber_14_11_5 + · exact fourYNumber_14_11_7 + · exact fourYNumber_14_11_9 + · exact fourYNumber_14_11_11 + · have h : (13:ℕ) ≤ 11 := hrs + omega + · exact fourYNumber_14_13_1 + · exact fourYNumber_14_13_3 + · exact fourYNumber_14_13_5 + · exact fourYNumber_14_13_7 + · exact fourYNumber_14_13_9 + · exact fourYNumber_14_13_11 + · exact fourYNumber_14_13_13 + +theorem fourYChecked_14 (r s : CopyLabel 14) : + integerRowsFourTrace 14 r s = fourYData_14 r s := by + have hh : ∀ r s : CopyLabel 14, fourYData_14 r s = fourYData_14 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_14 r s h + · rw [integerRowsFourTrace_symm, fourYLower_14 s r (by omega), hh] + +def fourHighestCache_14_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,12}, [0, -153280512000, -61312204800, -6706022400, 13412044800, -958003200, -49816166400]), + ({0,1,3,11}, [0, 153280512000, 61312204800, 6706022400, -13412044800, 958003200, 49816166400]), + ({0,1,4,10}, [0, -153280512000, -39016857600, -1828915200, 6444748800, 1916006400, -37362124800]), + ({0,1,5,9}, [0, 122624409600, 22295347200, -2438553600, -696729600, -3832012800, 24908083200]) +] + +def fourHighestCache_14_1 : List (Occupation 24 × List ℚ) := [ + ({0,1,6,8}, [0, -61312204800, -11147673600, 2844979200, -1045094400, 2874009600, -12454041600]), + ({0,2,3,10}, [0, 0, -22295347200, -4877107200, 6967296000, -2874009600, -12454041600]), + ({0,2,4,9}, [0, 30656102400, 16721510400, 4267468800, -5748019200, 1916006400, 12454041600]), + ({0,2,5,8}, [0, -61312204800, -11147673600, -406425600, 1741824000, 958003200, -12454041600]) +] + +def fourHighestCache_14_2 : List (Occupation 24 × List ℚ) := [ + ({0,2,6,7}, [0, 61312204800, 11147673600, -2844979200, 1045094400, -2874009600, 12454041600]), + ({0,3,4,8}, [0, 0, 0, -3251404800, 2786918400, -1916006400, 0]), + ({0,3,5,7}, [0, 15328051200, -2786918400, 2946585600, -2177280000, 1437004800, 0]), + ({0,4,5,6}, [0, -30656102400, 5573836800, -2641766400, 1567641600, -958003200, 0]) +] + +def fourHighestCache_14_3 : List (Occupation 24 × List ℚ) := [ + ({1,2,3,9}, [0, -30656102400, 5573836800, 609638400, -1219276800, 958003200, 0]), + ({1,2,4,8}, [0, 30656102400, -5573836800, -609638400, 1219276800, -958003200, 0]), + ({1,2,5,7}, [0, -15328051200, 2786918400, 304819200, -609638400, 479001600, 0]), + ({1,3,4,7}, [0, -15328051200, 2786918400, 304819200, -609638400, 479001600, 0]) +] + +def fourHighestCache_14_4 : List (Occupation 24 × List ℚ) := [ + ({1,3,5,6}, [0, 15328051200, -2786918400, -304819200, 609638400, -479001600, 0]), + ({2,3,4,6}, [0, 0, 0, 0, 0, 0, 0]) +] + +def fourHighestCache_14 : List (Occupation 24 × List ℚ) := fourHighestCache_14_0 ++ fourHighestCache_14_1 ++ fourHighestCache_14_2 ++ fourHighestCache_14_3 ++ fourHighestCache_14_4 + +theorem fourHighestNumber_14_1 : ∀ A∈highestFourOccupations 14, + kernelHighestEntry 14 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_14 1 A := by + rw [fourOccupations_14] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_14_3 : ∀ A∈highestFourOccupations 14, + kernelHighestEntry 14 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_14 3 A := by + rw [fourOccupations_14] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_14_5 : ∀ A∈highestFourOccupations 14, + kernelHighestEntry 14 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_14 5 A := by + rw [fourOccupations_14] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_14_7 : ∀ A∈highestFourOccupations 14, + kernelHighestEntry 14 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_14 7 A := by + rw [fourOccupations_14] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_14_9 : ∀ A∈highestFourOccupations 14, + kernelHighestEntry 14 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_14 9 A := by + rw [fourOccupations_14] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_14_11 : ∀ A∈highestFourOccupations 14, + kernelHighestEntry 14 ⟨⟨11,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_14 11 A := by + rw [fourOccupations_14] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_14_13 : ∀ A∈highestFourOccupations 14, + kernelHighestEntry 14 ⟨⟨13,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_14 13 A := by + rw [fourOccupations_14] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_14 : ∀ r : CopyLabel 14, ∀ A∈highestFourOccupations 14, + kernelHighestEntry 14 r A = highestLookup fourHighestCache_14 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_14_1 + · exact fourHighestNumber_14_3 + · exact fourHighestNumber_14_5 + · exact fourHighestNumber_14_7 + · exact fourHighestNumber_14_9 + · exact fourHighestNumber_14_11 + · exact fourHighestNumber_14_13 + +theorem fourZChecked_14 (r s : CopyLabel 14) : + integerFourGram 14 r s = fourZData_14 r s := by + rw [integerFourGram_cached 14 fourHighestCache_14 fourHighestChecked_14] + have h : ∀ r s : CopyLabel 14, cachedFourGram 14 fourHighestCache_14 r s = fourZData_14 r s := by + simp only [cachedFourGram, fourOccupations_14] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_14 : + fourZData_14 * (Matrix.diagonal (fun r : CopyLabel 14 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 14 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 14 => rationalCopyDiagonal 14 r.val.val) * + fourYData_14 * Matrix.diagonal (fun r : CopyLabel 14 => rationalCopyDiagonal 14 r.val.val)) * + fourZData_14 = fourLData_14 * Matrix.diagonal fourPivotData_14 * (fourLData_14)ᵀ := by + have h : ∀ r s : CopyLabel 14, + (fourZData_14 * (Matrix.diagonal (fun r : CopyLabel 14 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 14 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 14 => rationalCopyDiagonal 14 r.val.val) * + fourYData_14 * Matrix.diagonal (fun r : CopyLabel 14 => rationalCopyDiagonal 14 r.val.val)) * + fourZData_14 : Matrix (CopyLabel 14) (CopyLabel 14) ℚ) r s = + (fourLData_14 * Matrix.diagonal fourPivotData_14 * (fourLData_14)ᵀ : Matrix (CopyLabel 14) (CopyLabel 14) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_14 : ∀ r, 0 ≤ fourPivotData_14 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_14, copyDiagonalData] + +theorem integer_certificate_14 : + ((integerCompression 14).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_14) (fourPivotData_14) _ fourPivotChecked_14 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 14 = fourYData_14 from Matrix.ext fourYChecked_14, + show integerFourGram 14 = fourZData_14 from Matrix.ext fourZChecked_14] + exact fourLDLChecked_14 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate14Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate14Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..f3880c9dd507e1013d47c70766a001a6632f0fee --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate14Data.lean @@ -0,0 +1,168 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse1413 + +namespace OAI + +/-! Certificate14 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_14 : Matrix (CopyLabel 14) (CopyLabel 14) ℚ := + copyMatrixData 14 [ + [(-73743456216689631429868109022867/1677721600000000000000000), (-13596265456695017190695318466177/838860800000000000000000), (4218556651632078178090845049587/1677721600000000000000000), (-601758946497245207677320475161/1342177280000000000000000), (-65792859630351313043704679559/838860800000000000000000), (137254565014346724354426453723/671088640000000000000000), (-72085225343410427749643785743/104857600000000000000000)], + [(-13596265456695017190695318466177/838860800000000000000000), (13386782195228438740574170659/67108864000000000000000), (-2673895873363342088813998569/104857600000000000000000), (80258770793485913472210966291/13421772800000000000000000), (11396787485992128812442905901/3355443200000000000000000), (158234983123199496672321772983/6710886400000000000000000), (-339970341033955238226872051943/3355443200000000000000000)], + [(4218556651632078178090845049587/1677721600000000000000000), (-2673895873363342088813998569/104857600000000000000000), (-118599109885276691436463501647/6710886400000000000000000), (51791883792723030621502729521/13421772800000000000000000), (447947864118505342038286071/1677721600000000000000000), (-199373232582573167162137599/1342177280000000000000000), (-15546338707404656166201221607/6710886400000000000000000)], + [(-601758946497245207677320475161/1342177280000000000000000), (80258770793485913472210966291/13421772800000000000000000), (51791883792723030621502729521/13421772800000000000000000), (-124352718990572049190706318301/53687091200000000000000000), (11786587097020001481424088313/13421772800000000000000000), (1148019225793308762774727077/26843545600000000000000000), (-472886193342561862517016363/671088640000000000000000)], + [(-65792859630351313043704679559/838860800000000000000000), (11396787485992128812442905901/3355443200000000000000000), (447947864118505342038286071/1677721600000000000000000), (11786587097020001481424088313/13421772800000000000000000), (-2511231860904985581654902337/3355443200000000000000000), (-245216406486237366219564393/268435456000000000000000), (18739058037442034351954893713/3355443200000000000000000)], + [(137254565014346724354426453723/671088640000000000000000), (158234983123199496672321772983/6710886400000000000000000), (-199373232582573167162137599/1342177280000000000000000), (1148019225793308762774727077/26843545600000000000000000), (-245216406486237366219564393/268435456000000000000000), (19121697292235405186772511839/13421772800000000000000000), (-96382029030050639819612097/26843545600000000000000)], + [(-72085225343410427749643785743/104857600000000000000000), (-339970341033955238226872051943/3355443200000000000000000), (-15546338707404656166201221607/6710886400000000000000000), (-472886193342561862517016363/671088640000000000000000), (18739058037442034351954893713/3355443200000000000000000), (-96382029030050639819612097/26843545600000000000000), (-109065237409747857476663108541/6710886400000000000000000)] + ] + +def fourZData_14 : Matrix (CopyLabel 14) (CopyLabel 14) ℚ := + copyMatrixData 14 [ + [0, 0, 0, 0, 0, 0, 0], + [0, 29937600, 0, 0, 0, (-2338875/4), (6081075/2)], + [0, 0, 1360800, 0, -170100, 0, (6081075/8)], + [0, 0, 0, (694575/8), (-297675/4), (3274425/64), 0], + [0, 0, -170100, (-297675/4), 85050, (-1403325/32), (-6081075/64)], + [0, (-2338875/4), 0, (3274425/64), (-1403325/32), (42567525/1024), (-30405375/512)], + [0, (6081075/2), (6081075/8), 0, (-6081075/64), (-30405375/512), (1502025525/2048)] + ] + +def fourLData_14 : Matrix (CopyLabel 14) (CopyLabel 14) ℚ := + copyMatrixData 14 [ + [1, 0, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0, 0], + [0, (1220225850803980188695600294/4658665020569184332878103901), 1, 0, 0, 0, 0], + [0, (11717788938700055281155750553/447231841974641695956297974496), (2528507447792559602104460610889800179577158385469111/11527282328038776223543938804720313165114066416035616), 1, 0, 0, 0], + [0, (-4114421549993682560413450667/74538640329106949326049662416), (-601367064852125876386374050463549407069946629210615/1921213721339796037257323134120052194185677736005936), (-6/7), 1, 0, 0], + [0, (-110901290240976764798767469/27104960119675254300381695424), (3973368846531165089021295245683971710764106034308603/30739419541436736596117170145920835106970843776094976), (33/56), 0, 1, 0], + [0, (6718581527267453628143216897/27104960119675254300381695424), (143/256), 0, 0, 0, 1] + ] + +def fourPivotData_14 : CopyLabel 14 → ℚ := + copyDiagonalData 14 [0, (12452611599981429721783171727373/13421772800000000000000000), (9726144464282717438615198366482764233064993538530051/7401461110012656107624228297113600000000000000000), (756220433458987106260911093151509838908241844881935813830292724684837401603/1611630879254078375650507890146454279656352974168128277708800000000000000000), 0, 0, 0] + +theorem fourOccupations_14 : highestFourOccupations 14 = {{0,1,2,12}, {0,1,3,11}, {0,1,4,10}, {0,1,5,9}, {0,1,6,8}, {0,2,3,10}, {0,2,4,9}, {0,2,5,8}, {0,2,6,7}, {0,3,4,8}, {0,3,5,7}, {0,4,5,6}, {1,2,3,9}, {1,2,4,8}, {1,2,5,7}, {1,3,4,7}, {1,3,5,6}, {2,3,4,6}} := by + decide +kernel + +theorem fourYNumber_14_1_1 : + (collectedFourPartsTrace 14 1 1 collectedFourData_14 : ℚ) / fourCommonDenominator = (-73743456216689631429868109022867/1677721600000000000000000) := by + decide +kernel + +theorem fourYNumber_14_3_1 : + (collectedFourPartsTrace 14 3 1 collectedFourData_14 : ℚ) / fourCommonDenominator = (-13596265456695017190695318466177/838860800000000000000000) := by + decide +kernel + +theorem fourYNumber_14_3_3 : + (collectedFourPartsTrace 14 3 3 collectedFourData_14 : ℚ) / fourCommonDenominator = (13386782195228438740574170659/67108864000000000000000) := by + decide +kernel + +theorem fourYNumber_14_5_1 : + (collectedFourPartsTrace 14 5 1 collectedFourData_14 : ℚ) / fourCommonDenominator = (4218556651632078178090845049587/1677721600000000000000000) := by + decide +kernel + +theorem fourYNumber_14_5_3 : + (collectedFourPartsTrace 14 5 3 collectedFourData_14 : ℚ) / fourCommonDenominator = (-2673895873363342088813998569/104857600000000000000000) := by + decide +kernel + +theorem fourYNumber_14_5_5 : + (collectedFourPartsTrace 14 5 5 collectedFourData_14 : ℚ) / fourCommonDenominator = (-118599109885276691436463501647/6710886400000000000000000) := by + decide +kernel + +theorem fourYNumber_14_7_1 : + (collectedFourPartsTrace 14 7 1 collectedFourData_14 : ℚ) / fourCommonDenominator = (-601758946497245207677320475161/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_14_7_3 : + (collectedFourPartsTrace 14 7 3 collectedFourData_14 : ℚ) / fourCommonDenominator = (80258770793485913472210966291/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_14_7_5 : + (collectedFourPartsTrace 14 7 5 collectedFourData_14 : ℚ) / fourCommonDenominator = (51791883792723030621502729521/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_14_7_7 : + (collectedFourPartsTrace 14 7 7 collectedFourData_14 : ℚ) / fourCommonDenominator = (-124352718990572049190706318301/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_14_9_1 : + (collectedFourPartsTrace 14 9 1 collectedFourData_14 : ℚ) / fourCommonDenominator = (-65792859630351313043704679559/838860800000000000000000) := by + decide +kernel + +theorem fourYNumber_14_9_3 : + (collectedFourPartsTrace 14 9 3 collectedFourData_14 : ℚ) / fourCommonDenominator = (11396787485992128812442905901/3355443200000000000000000) := by + decide +kernel + +theorem fourYNumber_14_9_5 : + (collectedFourPartsTrace 14 9 5 collectedFourData_14 : ℚ) / fourCommonDenominator = (447947864118505342038286071/1677721600000000000000000) := by + decide +kernel + +theorem fourYNumber_14_9_7 : + (collectedFourPartsTrace 14 9 7 collectedFourData_14 : ℚ) / fourCommonDenominator = (11786587097020001481424088313/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_14_9_9 : + (collectedFourPartsTrace 14 9 9 collectedFourData_14 : ℚ) / fourCommonDenominator = (-2511231860904985581654902337/3355443200000000000000000) := by + decide +kernel + +theorem fourYNumber_14_11_1 : + (collectedFourPartsTrace 14 11 1 collectedFourData_14 : ℚ) / fourCommonDenominator = (137254565014346724354426453723/671088640000000000000000) := by + decide +kernel + +theorem fourYNumber_14_11_3 : + (collectedFourPartsTrace 14 11 3 collectedFourData_14 : ℚ) / fourCommonDenominator = (158234983123199496672321772983/6710886400000000000000000) := by + decide +kernel + +theorem fourYNumber_14_11_5 : + (collectedFourPartsTrace 14 11 5 collectedFourData_14 : ℚ) / fourCommonDenominator = (-199373232582573167162137599/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_14_11_7 : + (collectedFourPartsTrace 14 11 7 collectedFourData_14 : ℚ) / fourCommonDenominator = (1148019225793308762774727077/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_14_11_9 : + (collectedFourPartsTrace 14 11 9 collectedFourData_14 : ℚ) / fourCommonDenominator = (-245216406486237366219564393/268435456000000000000000) := by + decide +kernel + +theorem fourYNumber_14_11_11 : + (collectedFourPartsTrace 14 11 11 collectedFourData_14 : ℚ) / fourCommonDenominator = (19121697292235405186772511839/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_14_13_1 : + (collectedFourPartsTrace 14 13 1 collectedFourData_14 : ℚ) / fourCommonDenominator = (-72085225343410427749643785743/104857600000000000000000) := by + decide +kernel + +theorem fourYNumber_14_13_3 : + (collectedFourPartsTrace 14 13 3 collectedFourData_14 : ℚ) / fourCommonDenominator = (-339970341033955238226872051943/3355443200000000000000000) := by + decide +kernel + +theorem fourYNumber_14_13_5 : + (collectedFourPartsTrace 14 13 5 collectedFourData_14 : ℚ) / fourCommonDenominator = (-15546338707404656166201221607/6710886400000000000000000) := by + decide +kernel + +theorem fourYNumber_14_13_7 : + (collectedFourPartsTrace 14 13 7 collectedFourData_14 : ℚ) / fourCommonDenominator = (-472886193342561862517016363/671088640000000000000000) := by + decide +kernel + +theorem fourYNumber_14_13_9 : + (collectedFourPartsTrace 14 13 9 collectedFourData_14 : ℚ) / fourCommonDenominator = (18739058037442034351954893713/3355443200000000000000000) := by + decide +kernel + +theorem fourYNumber_14_13_11 : + (collectedFourPartsTrace 14 13 11 collectedFourData_14 : ℚ) / fourCommonDenominator = (-96382029030050639819612097/26843545600000000000000) := by + decide +kernel + +theorem fourYNumber_14_13_13 : + (collectedFourPartsTrace 14 13 13 collectedFourData_14 : ℚ) / fourCommonDenominator = (-109065237409747857476663108541/6710886400000000000000000) := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate15.lean b/lean/OAI/Analysis/LaughlinFock/Certificate15.lean new file mode 100644 index 0000000000000000000000000000000000000000..18b01e45b796b24bbf93bba34f6eaaabf2193db7 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate15.lean @@ -0,0 +1,264 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate15Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate15. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_15 (r s : CopyLabel 15) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 15 r s = fourYData_15 r s := by + rw [integerRowsFourTrace_collected (by decide) collectedFourData_15 collectedFourChecked_15] + fin_cases r <;> fin_cases s + · exact fourYNumber_15_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · have h : (13:ℕ) ≤ 1 := hrs + omega + · have h : (15:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_15_3_1 + · exact fourYNumber_15_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · have h : (13:ℕ) ≤ 3 := hrs + omega + · have h : (15:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_15_5_1 + · exact fourYNumber_15_5_3 + · exact fourYNumber_15_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · have h : (13:ℕ) ≤ 5 := hrs + omega + · have h : (15:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_15_7_1 + · exact fourYNumber_15_7_3 + · exact fourYNumber_15_7_5 + · exact fourYNumber_15_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · have h : (13:ℕ) ≤ 7 := hrs + omega + · have h : (15:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_15_9_1 + · exact fourYNumber_15_9_3 + · exact fourYNumber_15_9_5 + · exact fourYNumber_15_9_7 + · exact fourYNumber_15_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · have h : (13:ℕ) ≤ 9 := hrs + omega + · have h : (15:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_15_11_1 + · exact fourYNumber_15_11_3 + · exact fourYNumber_15_11_5 + · exact fourYNumber_15_11_7 + · exact fourYNumber_15_11_9 + · exact fourYNumber_15_11_11 + · have h : (13:ℕ) ≤ 11 := hrs + omega + · have h : (15:ℕ) ≤ 11 := hrs + omega + · exact fourYNumber_15_13_1 + · exact fourYNumber_15_13_3 + · exact fourYNumber_15_13_5 + · exact fourYNumber_15_13_7 + · exact fourYNumber_15_13_9 + · exact fourYNumber_15_13_11 + · exact fourYNumber_15_13_13 + · have h : (15:ℕ) ≤ 13 := hrs + omega + · exact fourYNumber_15_15_1 + · exact fourYNumber_15_15_3 + · exact fourYNumber_15_15_5 + · exact fourYNumber_15_15_7 + · exact fourYNumber_15_15_9 + · exact fourYNumber_15_15_11 + · exact fourYNumber_15_15_13 + · exact fourYNumber_15_15_15 + +theorem fourYChecked_15 (r s : CopyLabel 15) : + integerRowsFourTrace 15 r s = fourYData_15 r s := by + have hh : ∀ r s : CopyLabel 15, fourYData_15 r s = fourYData_15 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_15 r s h + · rw [integerRowsFourTrace_symm, fourYLower_15 s r (by omega), hh] + +def fourHighestCache_15_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,13}, [8369115955200, 2391175987200, 1120863744000, 261534873600, -149448499200, -112086374400, 373621248000, 1307674368000]), + ({0,1,3,12}, [-8369115955200, -2391175987200, -1120863744000, -261534873600, 149448499200, 112086374400, -373621248000, -1307674368000]), + ({0,1,4,11}, [13948526592000, 2759049216000, 795142656000, 114002380800, -74724249600, -76640256000, 211718707200, 1307674368000]), + ({0,1,5,10}, [-13948526592000, -2759049216000, -516450816000, 3048192000, 18289152000, 38320128000, -62270208000, -1307674368000]) +] + +def fourHighestCache_15_1 : List (Occupation 24 × List ℚ) := [ + ({0,1,6,9}, [16738231910400, 2575112601600, 276950016000, -32920473600, -4702924800, -2874009600, -37362124800, 1307674368000]), + ({0,1,7,8}, [-16738231910400, -2575112601600, -109734912000, 19914854400, 10973491200, -20118067200, 87178291200, -1307674368000]), + ({0,2,3,11}, [-5579410636800, -367873228800, 325721088000, 147532492800, -74724249600, -35446118400, 161902540800, 0]), + ({0,2,4,10}, [0, 0, -278691840000, -117050572800, 56435097600, 38320128000, -149448499200, 0]) +] + +def fourHighestCache_15_2 : List (Occupation 24 × List ℚ) := [ + ({0,2,5,9}, [-2789705318400, 183936614400, 239500800000, 29872281600, -13586227200, -35446118400, 99632332800, 0]), + ({0,2,6,8}, [0, 0, -167215104000, 13005619200, -6270566400, 22992076800, -49816166400, 0]), + ({0,3,4,9}, [8369115955200, 183936614400, -7838208000, 56696371200, -24559718400, -5748019200, 37362124800, 0]), + ({0,3,5,8}, [-5579410636800, -367873228800, -8709120000, -34546176000, 13063680000, 10538035200, -37362124800, 0]) +] + +def fourHighestCache_15_3 : List (Occupation 24 × List ℚ) := [ + ({0,3,6,7}, [8369115955200, 183936614400, 75769344000, -1828915200, 3657830400, -17244057600, 37362124800, 0]), + ({0,4,5,7}, [-2789705318400, 183936614400, -39191040000, 16866662400, -7315660800, 2874009600, 0, 0]), + ({1,2,3,10}, [5579410636800, 367873228800, -47029248000, -30481920000, 18289152000, -2874009600, -12454041600, 0]), + ({1,2,4,9}, [-5579410636800, -367873228800, 47029248000, 30481920000, -18289152000, 2874009600, 12454041600, 0]) +] + +def fourHighestCache_15_4 : List (Occupation 24 × List ℚ) := [ + ({1,2,5,8}, [8369115955200, 183936614400, -63576576000, -8331724800, 6793113600, 1916006400, -12454041600, 0]), + ({1,2,6,7}, [-8369115955200, -183936614400, 91445760000, -11176704000, 2612736000, -5748019200, 12454041600, 0]), + ({1,3,4,8}, [-2789705318400, 183936614400, 16547328000, -22150195200, 11496038400, -4790016000, 0, 0]), + ({1,3,5,7}, [0, 0, -27869184000, 19508428800, -9405849600, 3832012800, 0, 0]) +] + +def fourHighestCache_15_5 : List (Occupation 24 × List ℚ) := [ + ({1,4,5,6}, [2789705318400, -183936614400, 39191040000, -16866662400, 7315660800, -2874009600, 0, 0]), + ({2,3,4,7}, [2789705318400, -183936614400, 11321856000, 2641766400, -2090188800, 958003200, 0, 0]), + ({2,3,5,6}, [-2789705318400, 183936614400, -11321856000, -2641766400, 2090188800, -958003200, 0, 0]) +] + +def fourHighestCache_15 : List (Occupation 24 × List ℚ) := fourHighestCache_15_0 ++ fourHighestCache_15_1 ++ fourHighestCache_15_2 ++ fourHighestCache_15_3 ++ fourHighestCache_15_4 ++ fourHighestCache_15_5 + +theorem fourHighestNumber_15_1 : ∀ A∈highestFourOccupations 15, + kernelHighestEntry 15 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_15 1 A := by + rw [fourOccupations_15] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_15_3 : ∀ A∈highestFourOccupations 15, + kernelHighestEntry 15 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_15 3 A := by + rw [fourOccupations_15] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_15_5 : ∀ A∈highestFourOccupations 15, + kernelHighestEntry 15 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_15 5 A := by + rw [fourOccupations_15] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_15_7 : ∀ A∈highestFourOccupations 15, + kernelHighestEntry 15 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_15 7 A := by + rw [fourOccupations_15] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_15_9 : ∀ A∈highestFourOccupations 15, + kernelHighestEntry 15 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_15 9 A := by + rw [fourOccupations_15] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_15_11 : ∀ A∈highestFourOccupations 15, + kernelHighestEntry 15 ⟨⟨11,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_15 11 A := by + rw [fourOccupations_15] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_15_13 : ∀ A∈highestFourOccupations 15, + kernelHighestEntry 15 ⟨⟨13,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_15 13 A := by + rw [fourOccupations_15] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_15_15 : ∀ A∈highestFourOccupations 15, + kernelHighestEntry 15 ⟨⟨15,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_15 15 A := by + rw [fourOccupations_15] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_15 : ∀ r : CopyLabel 15, ∀ A∈highestFourOccupations 15, + kernelHighestEntry 15 r A = highestLookup fourHighestCache_15 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_15_1 + · exact fourHighestNumber_15_3 + · exact fourHighestNumber_15_5 + · exact fourHighestNumber_15_7 + · exact fourHighestNumber_15_9 + · exact fourHighestNumber_15_11 + · exact fourHighestNumber_15_13 + · exact fourHighestNumber_15_15 + +theorem fourZChecked_15 (r s : CopyLabel 15) : + integerFourGram 15 r s = fourZData_15 r s := by + rw [integerFourGram_cached 15 fourHighestCache_15 fourHighestChecked_15] + have h : ∀ r s : CopyLabel 15, cachedFourGram 15 fourHighestCache_15 r s = fourZData_15 r s := by + simp only [cachedFourGram, fourOccupations_15] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_15 : + fourZData_15 * (Matrix.diagonal (fun r : CopyLabel 15 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 15 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 15 => rationalCopyDiagonal 15 r.val.val) * + fourYData_15 * Matrix.diagonal (fun r : CopyLabel 15 => rationalCopyDiagonal 15 r.val.val)) * + fourZData_15 = fourLData_15 * Matrix.diagonal fourPivotData_15 * (fourLData_15)ᵀ := by + have h : ∀ r s : CopyLabel 15, + (fourZData_15 * (Matrix.diagonal (fun r : CopyLabel 15 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 15 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 15 => rationalCopyDiagonal 15 r.val.val) * + fourYData_15 * Matrix.diagonal (fun r : CopyLabel 15 => rationalCopyDiagonal 15 r.val.val)) * + fourZData_15 : Matrix (CopyLabel 15) (CopyLabel 15) ℚ) r s = + (fourLData_15 * Matrix.diagonal fourPivotData_15 * (fourLData_15)ᵀ : Matrix (CopyLabel 15) (CopyLabel 15) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_15 : ∀ r, 0 ≤ fourPivotData_15 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_15, copyDiagonalData] + +theorem integer_certificate_15 : + ((integerCompression 15).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_15) (fourPivotData_15) _ fourPivotChecked_15 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 15 = fourYData_15 from Matrix.ext fourYChecked_15, + show integerFourGram 15 = fourZData_15 from Matrix.ext fourZChecked_15] + exact fourLDLChecked_15 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate15Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate15Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..ea21691ed11f9271e1c143c523f5a8142df2f320 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate15Data.lean @@ -0,0 +1,203 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse1508 + +namespace OAI + +/-! Certificate15 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_15 : Matrix (CopyLabel 15) (CopyLabel 15) ℚ := + copyMatrixData 15 [ + [(1308564550559617459628590378527219/838860800000000000000000), (55806599899143061188549474278133/335544320000000000000000), (-121594567745064868354589107419/5242880000000000000000), (12612366434934957846304143447453/6710886400000000000000000), (2848733507955651141700122589341/1677721600000000000000000), (-5040016539767018277289956355221/3355443200000000000000000), (6898076709287361794034590374623/1677721600000000000000000), (-69774527590501029164523237379797/1342177280000000000000000)], + [(55806599899143061188549474278133/335544320000000000000000), (-24176107214630877161809676787561/3355443200000000000000000), (154555932129637874044488648237/671088640000000000000000), (773582640636166926582031618527/13421772800000000000000000), (-53299623602193211938552243903/3355443200000000000000000), (-430660873720800228400034708007/6710886400000000000000000), (40471219671864835802931462051/209715200000000000000000), (-3452926424016985931403148463703/2684354560000000000000000)], + [(-121594567745064868354589107419/5242880000000000000000), (154555932129637874044488648237/671088640000000000000000), (-22143837937571892482195405511/268435456000000000000000), (-23566822031129421592118634903/2684354560000000000000000), (803212446786638973149111013/167772160000000000000000), (41605607408434531382555260659/1342177280000000000000000), (-104668576082860227329572569603/1342177280000000000000000), (30373191163661118559130314971/107374182400000000000000)], + [(12612366434934957846304143447453/6710886400000000000000000), (773582640636166926582031618527/13421772800000000000000000), (-23566822031129421592118634903/2684354560000000000000000), (-571499890221638338551002497491/53687091200000000000000000), (117089877007690980042457656891/13421772800000000000000000), (-97616174744145272084505558153/26843545600000000000000000), (6517014895586416110380281791/6710886400000000000000000), (424557985372508681956282503483/10737418240000000000000000)], + [(2848733507955651141700122589341/1677721600000000000000000), (-53299623602193211938552243903/3355443200000000000000000), (803212446786638973149111013/167772160000000000000000), (117089877007690980042457656891/13421772800000000000000000), (-14666630048429445130453017813/3355443200000000000000000), (-1547373619860320277277256763/1342177280000000000000000), (28963210226166726601713556077/3355443200000000000000000), (26896636911492553061456701101/2684354560000000000000000)], + [(-5040016539767018277289956355221/3355443200000000000000000), (-430660873720800228400034708007/6710886400000000000000000), (41605607408434531382555260659/1342177280000000000000000), (-97616174744145272084505558153/26843545600000000000000000), (-1547373619860320277277256763/1342177280000000000000000), (-3262167284765114930518367559/2684354560000000000000000), (2503653400615248264299638293/671088640000000000000000), (-39622599808406172905598670419/1073741824000000000000000)], + [(6898076709287361794034590374623/1677721600000000000000000), (40471219671864835802931462051/209715200000000000000000), (-104668576082860227329572569603/1342177280000000000000000), (6517014895586416110380281791/6710886400000000000000000), (28963210226166726601713556077/3355443200000000000000000), (2503653400615248264299638293/671088640000000000000000), (-171164208681192557791375250121/6710886400000000000000000), (131081604324030412414565143941/1342177280000000000000000)], + [(-69774527590501029164523237379797/1342177280000000000000000), (-3452926424016985931403148463703/2684354560000000000000000), (30373191163661118559130314971/107374182400000000000000), (424557985372508681956282503483/10737418240000000000000000), (26896636911492553061456701101/2684354560000000000000000), (-39622599808406172905598670419/1073741824000000000000000), (131081604324030412414565143941/1342177280000000000000000), (-4368271789417477428222669736803/2147483648000000000000000)] + ] + +def fourZData_15 : Matrix (CopyLabel 15) (CopyLabel 15) ℚ := + copyMatrixData 15 [ + [87178291200, 0, 0, 0, 0, 0, (-42567525/2), (1915538625/4)], + [0, 359251200, 0, 0, 0, -1403325, 0, (638512875/8)], + [0, 0, 13608000, 0, (-637875/2), (-2338875/2), (91216125/32), (638512875/64)], + [0, 0, 0, 1389150, (-2679075/4), 0, (42567525/64), 0], + [0, 0, (-637875/2), (-2679075/4), (5485725/16), 0, (-164189025/512), (-638512875/1024)], + [0, -1403325, (-2338875/2), 0, 0, (42567525/256), (-200675475/512), (-638512875/2048)], + [(-42567525/2), 0, (91216125/32), (42567525/64), (-164189025/512), (-200675475/512), (10477692225/8192), (-1915538625/16384)], + [(1915538625/4), (638512875/8), (638512875/64), 0, (-638512875/1024), (-638512875/2048), (-1915538625/16384), (653198671125/16384)] + ] + +def fourLData_15 : Matrix (CopyLabel 15) (CopyLabel 15) ℚ := + copyMatrixData 15 [ + [1, 0, 0, 0, 0, 0, 0, 0], + [(-903438684010875969128016324/4766456886497595705324219429695), 1, 0, 0, 0, 0, 0, 0], + [(2181748140413327287704680687/15252662036792306257037502175024), (-839284167782826637336798582215608429782738456643209697345/39209246608307481907730403048484279450717315996545395736728), 1, 0, 0, 0, 0, 0], + [(-4638194302278633425529650527/457579861103769187711125065250720), (-3408516694277191749723087117239793155754236842928466325361/235255479649844891446382418290905676704303895979272374420368), (71656892856790538406735701222302444279424234419186090373566269113789033906034044951/488039880518471995256197731532813414687553775179186540061784395315354925944327335430), 1, 0, 0, 0, 0], + [(-1283061901458295762036944609/305053240735846125140750043500480), (2264917168509309363816845420200186656145038180643139076977/627347945732919710523686448775748471211477055944726331787648), (-109404692249026573035944561500220172240113837945672314383597700624215449694070366857/1301439681382591987349860617420835772500143400477830773498091720840946469184872894480), (-38927999864278238054172525514129483505548083155055263967651445708004148030174457320258597118637205783208743/77198170996373200148393044911650050968176987487237256434803376966843881844836720952363986575258295523154864), 1, 0, 0, 0], + [(657308877942706528399897837/610106481471692250281500087000960), (737138621931585436937463695653857858136770077711587276909/114063262860530856458852081595590631129359464717222969415936), (-140944273037169746217723068766536025038033537156634723911588688592787988948747228767/1301439681382591987349860617420835772500143400477830773498091720840946469184872894480), (3756396894544836418919790635513202506675192642159205153345312846349722423824855665811399329388589257427111/77198170996373200148393044911650050968176987487237256434803376966843881844836720952363986575258295523154864), (-11/5), 1, 0, 0], + [(-76206946154756167727800606687/305053240735846125140750043500480), (-1837044885037467827778127596432078744637240539296895126269/57031631430265428229426040797795315564679732358611484707968), (870084325315506923385742911572385435131086092244730188415780151233981300563765390739/2602879362765183974699721234841671545000286800955661546996183441681892938369745788960), (63556236070811683991683146732492442833595170667217038152103279240684264127044562536816464554594718982685271/176452962277424457482041245512342973641547399970828014708122004495643158502483933605403397886304675481496832), (429/80), 0, 1, 0], + [(1399706483799772687035184194183/244042592588676900112600034800384), (74768530699453445178605502284458110638336526052638553519755/228126525721061712917704163191181262258718929434445938831872), (216145947932327208493895732357714332809187026076568604840018874692414731333732767149/520575872553036794939944246968334309000057360191132309399236688336378587673949157792), (244165798145414367229786391308358162933887521740348334967445335012731957548615618277740956410258301732762215/352905924554848914964082491024685947283094799941656029416244008991286317004967867210806795772609350962993664), (-1001/32), 0, 0, 1] + ] + +def fourPivotData_15 : CopyLabel 15 → ℚ := + copyDiagonalData 15 [(231881454488466934430035821347460177/671088640000000000000000), (39302368569002212177261262755724429614412769622037191051602729/1999196918486441165722419485084745728000000000000000000), (3953123032199623161575201625415788658969185578951410974500453602054374900149051416983/7475249994827750208887330019448627601693701879707924523642781696000000000000000), (911903394894658426752892843018866227061590664692990091636114890420843354292133766249799591420238615867266831/26653484674715483900925145444778716620802936841785974241240918442822583688906196878950400000000000000000), (162108513660461990130482535809420900589792904998602621403248683009437560448720649909678006322786899622980548102029237636780043/5782010667906644622771527532948454560286225202244092385955741843313235017809393536381858541938431606177688190976000000000000000), 0, 0, 0] + +theorem fourOccupations_15 : highestFourOccupations 15 = {{0,1,2,13}, {0,1,3,12}, {0,1,4,11}, {0,1,5,10}, {0,1,6,9}, {0,1,7,8}, {0,2,3,11}, {0,2,4,10}, {0,2,5,9}, {0,2,6,8}, {0,3,4,9}, {0,3,5,8}, {0,3,6,7}, {0,4,5,7}, {1,2,3,10}, {1,2,4,9}, {1,2,5,8}, {1,2,6,7}, {1,3,4,8}, {1,3,5,7}, {1,4,5,6}, {2,3,4,7}, {2,3,5,6}} := by + decide +kernel + +theorem fourYNumber_15_1_1 : + (collectedFourTrace 15 1 1 collectedFourData_15 : ℚ) / fourCommonDenominator = (1308564550559617459628590378527219/838860800000000000000000) := by + decide +kernel + +theorem fourYNumber_15_3_1 : + (collectedFourTrace 15 3 1 collectedFourData_15 : ℚ) / fourCommonDenominator = (55806599899143061188549474278133/335544320000000000000000) := by + decide +kernel + +theorem fourYNumber_15_3_3 : + (collectedFourTrace 15 3 3 collectedFourData_15 : ℚ) / fourCommonDenominator = (-24176107214630877161809676787561/3355443200000000000000000) := by + decide +kernel + +theorem fourYNumber_15_5_1 : + (collectedFourTrace 15 5 1 collectedFourData_15 : ℚ) / fourCommonDenominator = (-121594567745064868354589107419/5242880000000000000000) := by + decide +kernel + +theorem fourYNumber_15_5_3 : + (collectedFourTrace 15 5 3 collectedFourData_15 : ℚ) / fourCommonDenominator = (154555932129637874044488648237/671088640000000000000000) := by + decide +kernel + +theorem fourYNumber_15_5_5 : + (collectedFourTrace 15 5 5 collectedFourData_15 : ℚ) / fourCommonDenominator = (-22143837937571892482195405511/268435456000000000000000) := by + decide +kernel + +theorem fourYNumber_15_7_1 : + (collectedFourTrace 15 7 1 collectedFourData_15 : ℚ) / fourCommonDenominator = (12612366434934957846304143447453/6710886400000000000000000) := by + decide +kernel + +theorem fourYNumber_15_7_3 : + (collectedFourTrace 15 7 3 collectedFourData_15 : ℚ) / fourCommonDenominator = (773582640636166926582031618527/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_15_7_5 : + (collectedFourTrace 15 7 5 collectedFourData_15 : ℚ) / fourCommonDenominator = (-23566822031129421592118634903/2684354560000000000000000) := by + decide +kernel + +theorem fourYNumber_15_7_7 : + (collectedFourTrace 15 7 7 collectedFourData_15 : ℚ) / fourCommonDenominator = (-571499890221638338551002497491/53687091200000000000000000) := by + decide +kernel + +theorem fourYNumber_15_9_1 : + (collectedFourTrace 15 9 1 collectedFourData_15 : ℚ) / fourCommonDenominator = (2848733507955651141700122589341/1677721600000000000000000) := by + decide +kernel + +theorem fourYNumber_15_9_3 : + (collectedFourTrace 15 9 3 collectedFourData_15 : ℚ) / fourCommonDenominator = (-53299623602193211938552243903/3355443200000000000000000) := by + decide +kernel + +theorem fourYNumber_15_9_5 : + (collectedFourTrace 15 9 5 collectedFourData_15 : ℚ) / fourCommonDenominator = (803212446786638973149111013/167772160000000000000000) := by + decide +kernel + +theorem fourYNumber_15_9_7 : + (collectedFourTrace 15 9 7 collectedFourData_15 : ℚ) / fourCommonDenominator = (117089877007690980042457656891/13421772800000000000000000) := by + decide +kernel + +theorem fourYNumber_15_9_9 : + (collectedFourTrace 15 9 9 collectedFourData_15 : ℚ) / fourCommonDenominator = (-14666630048429445130453017813/3355443200000000000000000) := by + decide +kernel + +theorem fourYNumber_15_11_1 : + (collectedFourTrace 15 11 1 collectedFourData_15 : ℚ) / fourCommonDenominator = (-5040016539767018277289956355221/3355443200000000000000000) := by + decide +kernel + +theorem fourYNumber_15_11_3 : + (collectedFourTrace 15 11 3 collectedFourData_15 : ℚ) / fourCommonDenominator = (-430660873720800228400034708007/6710886400000000000000000) := by + decide +kernel + +theorem fourYNumber_15_11_5 : + (collectedFourTrace 15 11 5 collectedFourData_15 : ℚ) / fourCommonDenominator = (41605607408434531382555260659/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_15_11_7 : + (collectedFourTrace 15 11 7 collectedFourData_15 : ℚ) / fourCommonDenominator = (-97616174744145272084505558153/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_15_11_9 : + (collectedFourTrace 15 11 9 collectedFourData_15 : ℚ) / fourCommonDenominator = (-1547373619860320277277256763/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_15_11_11 : + (collectedFourTrace 15 11 11 collectedFourData_15 : ℚ) / fourCommonDenominator = (-3262167284765114930518367559/2684354560000000000000000) := by + decide +kernel + +theorem fourYNumber_15_13_1 : + (collectedFourTrace 15 13 1 collectedFourData_15 : ℚ) / fourCommonDenominator = (6898076709287361794034590374623/1677721600000000000000000) := by + decide +kernel + +theorem fourYNumber_15_13_3 : + (collectedFourTrace 15 13 3 collectedFourData_15 : ℚ) / fourCommonDenominator = (40471219671864835802931462051/209715200000000000000000) := by + decide +kernel + +theorem fourYNumber_15_13_5 : + (collectedFourTrace 15 13 5 collectedFourData_15 : ℚ) / fourCommonDenominator = (-104668576082860227329572569603/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_15_13_7 : + (collectedFourTrace 15 13 7 collectedFourData_15 : ℚ) / fourCommonDenominator = (6517014895586416110380281791/6710886400000000000000000) := by + decide +kernel + +theorem fourYNumber_15_13_9 : + (collectedFourTrace 15 13 9 collectedFourData_15 : ℚ) / fourCommonDenominator = (28963210226166726601713556077/3355443200000000000000000) := by + decide +kernel + +theorem fourYNumber_15_13_11 : + (collectedFourTrace 15 13 11 collectedFourData_15 : ℚ) / fourCommonDenominator = (2503653400615248264299638293/671088640000000000000000) := by + decide +kernel + +theorem fourYNumber_15_13_13 : + (collectedFourTrace 15 13 13 collectedFourData_15 : ℚ) / fourCommonDenominator = (-171164208681192557791375250121/6710886400000000000000000) := by + decide +kernel + +theorem fourYNumber_15_15_1 : + (collectedFourTrace 15 15 1 collectedFourData_15 : ℚ) / fourCommonDenominator = (-69774527590501029164523237379797/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_15_15_3 : + (collectedFourTrace 15 15 3 collectedFourData_15 : ℚ) / fourCommonDenominator = (-3452926424016985931403148463703/2684354560000000000000000) := by + decide +kernel + +theorem fourYNumber_15_15_5 : + (collectedFourTrace 15 15 5 collectedFourData_15 : ℚ) / fourCommonDenominator = (30373191163661118559130314971/107374182400000000000000) := by + decide +kernel + +theorem fourYNumber_15_15_7 : + (collectedFourTrace 15 15 7 collectedFourData_15 : ℚ) / fourCommonDenominator = (424557985372508681956282503483/10737418240000000000000000) := by + decide +kernel + +theorem fourYNumber_15_15_9 : + (collectedFourTrace 15 15 9 collectedFourData_15 : ℚ) / fourCommonDenominator = (26896636911492553061456701101/2684354560000000000000000) := by + decide +kernel + +theorem fourYNumber_15_15_11 : + (collectedFourTrace 15 15 11 collectedFourData_15 : ℚ) / fourCommonDenominator = (-39622599808406172905598670419/1073741824000000000000000) := by + decide +kernel + +theorem fourYNumber_15_15_13 : + (collectedFourTrace 15 15 13 collectedFourData_15 : ℚ) / fourCommonDenominator = (131081604324030412414565143941/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_15_15_15 : + (collectedFourTrace 15 15 15 collectedFourData_15 : ℚ) / fourCommonDenominator = (-4368271789417477428222669736803/2147483648000000000000000) := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate16.lean b/lean/OAI/Analysis/LaughlinFock/Certificate16.lean new file mode 100644 index 0000000000000000000000000000000000000000..a96a63f05b9728abeb17adbcedf3684813f60bda --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate16.lean @@ -0,0 +1,271 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate16Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate16. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_16 (r s : CopyLabel 16) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 16 r s = fourYData_16 r s := by + rw [integerRowsFourTrace_collected (by decide) collectedFourData_16 collectedFourChecked_16] + fin_cases r <;> fin_cases s + · exact fourYNumber_16_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · have h : (13:ℕ) ≤ 1 := hrs + omega + · have h : (15:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_16_3_1 + · exact fourYNumber_16_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · have h : (13:ℕ) ≤ 3 := hrs + omega + · have h : (15:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_16_5_1 + · exact fourYNumber_16_5_3 + · exact fourYNumber_16_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · have h : (13:ℕ) ≤ 5 := hrs + omega + · have h : (15:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_16_7_1 + · exact fourYNumber_16_7_3 + · exact fourYNumber_16_7_5 + · exact fourYNumber_16_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · have h : (13:ℕ) ≤ 7 := hrs + omega + · have h : (15:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_16_9_1 + · exact fourYNumber_16_9_3 + · exact fourYNumber_16_9_5 + · exact fourYNumber_16_9_7 + · exact fourYNumber_16_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · have h : (13:ℕ) ≤ 9 := hrs + omega + · have h : (15:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_16_11_1 + · exact fourYNumber_16_11_3 + · exact fourYNumber_16_11_5 + · exact fourYNumber_16_11_7 + · exact fourYNumber_16_11_9 + · exact fourYNumber_16_11_11 + · have h : (13:ℕ) ≤ 11 := hrs + omega + · have h : (15:ℕ) ≤ 11 := hrs + omega + · exact fourYNumber_16_13_1 + · exact fourYNumber_16_13_3 + · exact fourYNumber_16_13_5 + · exact fourYNumber_16_13_7 + · exact fourYNumber_16_13_9 + · exact fourYNumber_16_13_11 + · exact fourYNumber_16_13_13 + · have h : (15:ℕ) ≤ 13 := hrs + omega + · exact fourYNumber_16_15_1 + · exact fourYNumber_16_15_3 + · exact fourYNumber_16_15_5 + · exact fourYNumber_16_15_7 + · exact fourYNumber_16_15_9 + · exact fourYNumber_16_15_11 + · exact fourYNumber_16_15_13 + · exact fourYNumber_16_15_15 + +theorem fourYChecked_16 (r s : CopyLabel 16) : + integerRowsFourTrace 16 r s = fourYData_16 r s := by + have hh : ∀ r s : CopyLabel 16, fourYData_16 r s = fourYData_16 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_16 r s h + · rw [integerRowsFourTrace_symm, fourYLower_16 s r (by omega), hh] + +def fourHighestCache_16_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,14}, [0, -41845579776000, -20922789888000, -6799906713600, 1046139494400, 2615348736000, -2092278988800, -13076743680000]), + ({0,1,3,13}, [0, 41845579776000, 20922789888000, 6799906713600, -1046139494400, -2615348736000, 2092278988800, 13076743680000]), + ({0,1,4,12}, [0, -47823519744000, -16554295296000, -3540779827200, 643778150400, 1437004800000, -747242496000, -10461394944000]), + ({0,1,5,11}, [0, 41845579776000, 12339081216000, 1005903360000, -402361344000, -383201280000, -373621248000, 7846046208000]) +] + +def fourHighestCache_16_1 : List (Occupation 24 × List ℚ) := [ + ({0,1,6,10}, [0, -29889699840000, -7587385344000, -91445760000, 329204736000, -143700480000, 747242496000, -5230697472000]), + ({0,1,7,9}, [0, 16738231910400, 3218890752000, -7315660800, -219469824000, 201180672000, -523069747200, 2615348736000]), + ({0,2,3,12}, [0, 5977939968000, -4368494592000, -3259126886400, 402361344000, 1178343936000, -1345036492800, -2615348736000]), + ({0,2,4,11}, [0, 5977939968000, 4215214080000, 2534876467200, -241416806400, -1053803520000, 1120863744000, 2615348736000]) +] + +def fourHighestCache_16_2 : List (Occupation 24 × List ℚ) := [ + ({0,2,5,10}, [0, -11955879936000, -4751695872000, -914457600000, 73156608000, 526901760000, -373621248000, -2615348736000]), + ({0,2,6,9}, [0, 13151467929600, 4368494592000, 98761420800, -109734912000, -57480192000, -224172748800, 2615348736000]), + ({0,2,7,8}, [0, -16738231910400, -3218890752000, 7315660800, 219469824000, -201180672000, 523069747200, -2615348736000]), + ({0,3,4,10}, [0, -5977939968000, 689762304000, -896168448000, 7315660800, 402361344000, -523069747200, 0]) +] + +def fourHighestCache_16_3 : List (Occupation 24 × List ℚ) := [ + ({0,3,5,9}, [0, 8369115955200, -229920768000, 493807104000, 95103590400, -373621248000, 448345497600, 0]), + ({0,3,6,8}, [0, -2391175987200, -459841536000, -65840947200, -102419251200, 201180672000, -224172748800, 0]), + ({0,4,5,8}, [0, -9564703948800, 613122048000, -146313216000, -58525286400, 134120448000, -149448499200, 0]), + ({0,4,6,7}, [0, 8369115955200, -229920768000, 25604812800, 95103590400, -143700480000, 149448499200, 0]) +] + +def fourHighestCache_16_4 : List (Occupation 24 × List ℚ) := [ + ({1,2,3,11}, [0, -11955879936000, 153280512000, 724250419200, -160944537600, -124540416000, 224172748800, 0]), + ({1,2,4,10}, [0, 11955879936000, -153280512000, -724250419200, 160944537600, 124540416000, -224172748800, 0]), + ({1,2,5,9}, [0, -9564703948800, 613122048000, 321889075200, -58525286400, -95800320000, 149448499200, 0]), + ({1,2,6,8}, [0, 5977939968000, -689762304000, -40236134400, -7315660800, 57480192000, -74724249600, 0]) +] + +def fourHighestCache_16_5 : List (Occupation 24 × List ℚ) := [ + ({1,3,4,9}, [0, -2391175987200, -459841536000, 402361344000, -102419251200, -28740096000, 74724249600, 0]), + ({1,3,5,8}, [0, 3586763980800, 76640256000, -281652940800, 65840947200, 38320128000, -74724249600, 0]), + ({1,3,6,7}, [0, -5977939968000, 689762304000, 40236134400, 7315660800, -57480192000, 74724249600, 0]), + ({1,4,5,7}, [0, 1195587993600, -383201280000, 120708403200, -36578304000, 9580032000, 0, 0]) +] + +def fourHighestCache_16_6 : List (Occupation 24 × List ℚ) := [ + ({2,3,4,8}, [0, -1195587993600, 383201280000, -120708403200, 36578304000, -9580032000, 0, 0]), + ({2,3,5,7}, [0, 1195587993600, -383201280000, 120708403200, -36578304000, 9580032000, 0, 0]), + ({2,4,5,6}, [0, -1195587993600, 383201280000, -120708403200, 36578304000, -9580032000, 0, 0]) +] + +def fourHighestCache_16 : List (Occupation 24 × List ℚ) := fourHighestCache_16_0 ++ fourHighestCache_16_1 ++ fourHighestCache_16_2 ++ fourHighestCache_16_3 ++ fourHighestCache_16_4 ++ fourHighestCache_16_5 ++ fourHighestCache_16_6 + +theorem fourHighestNumber_16_1 : ∀ A∈highestFourOccupations 16, + kernelHighestEntry 16 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_16 1 A := by + rw [fourOccupations_16] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_16_3 : ∀ A∈highestFourOccupations 16, + kernelHighestEntry 16 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_16 3 A := by + rw [fourOccupations_16] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_16_5 : ∀ A∈highestFourOccupations 16, + kernelHighestEntry 16 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_16 5 A := by + rw [fourOccupations_16] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_16_7 : ∀ A∈highestFourOccupations 16, + kernelHighestEntry 16 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_16 7 A := by + rw [fourOccupations_16] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_16_9 : ∀ A∈highestFourOccupations 16, + kernelHighestEntry 16 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_16 9 A := by + rw [fourOccupations_16] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_16_11 : ∀ A∈highestFourOccupations 16, + kernelHighestEntry 16 ⟨⟨11,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_16 11 A := by + rw [fourOccupations_16] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_16_13 : ∀ A∈highestFourOccupations 16, + kernelHighestEntry 16 ⟨⟨13,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_16 13 A := by + rw [fourOccupations_16] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_16_15 : ∀ A∈highestFourOccupations 16, + kernelHighestEntry 16 ⟨⟨15,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_16 15 A := by + rw [fourOccupations_16] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_16 : ∀ r : CopyLabel 16, ∀ A∈highestFourOccupations 16, + kernelHighestEntry 16 r A = highestLookup fourHighestCache_16 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_16_1 + · exact fourHighestNumber_16_3 + · exact fourHighestNumber_16_5 + · exact fourHighestNumber_16_7 + · exact fourHighestNumber_16_9 + · exact fourHighestNumber_16_11 + · exact fourHighestNumber_16_13 + · exact fourHighestNumber_16_15 + +theorem fourZChecked_16 (r s : CopyLabel 16) : + integerFourGram 16 r s = fourZData_16 r s := by + rw [integerFourGram_cached 16 fourHighestCache_16 fourHighestChecked_16] + have h : ∀ r s : CopyLabel 16, cachedFourGram 16 fourHighestCache_16 r s = fourZData_16 r s := by + simp only [cachedFourGram, fourOccupations_16] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_16 : + fourZData_16 * (Matrix.diagonal (fun r : CopyLabel 16 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 16 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 16 => rationalCopyDiagonal 16 r.val.val) * + fourYData_16 * Matrix.diagonal (fun r : CopyLabel 16 => rationalCopyDiagonal 16 r.val.val)) * + fourZData_16 = fourLData_16 * Matrix.diagonal fourPivotData_16 * (fourLData_16)ᵀ := by + have h : ∀ r s : CopyLabel 16, + (fourZData_16 * (Matrix.diagonal (fun r : CopyLabel 16 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 16 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 16 => rationalCopyDiagonal 16 r.val.val) * + fourYData_16 * Matrix.diagonal (fun r : CopyLabel 16 => rationalCopyDiagonal 16 r.val.val)) * + fourZData_16 : Matrix (CopyLabel 16) (CopyLabel 16) ℚ) r s = + (fourLData_16 * Matrix.diagonal fourPivotData_16 * (fourLData_16)ᵀ : Matrix (CopyLabel 16) (CopyLabel 16) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_16 : ∀ r, 0 ≤ fourPivotData_16 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_16, copyDiagonalData] + +theorem integer_certificate_16 : + ((integerCompression 16).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_16) (fourPivotData_16) _ fourPivotChecked_16 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 16 = fourYData_16 from Matrix.ext fourYChecked_16, + show integerFourGram 16 = fourZData_16 from Matrix.ext fourZChecked_16] + exact fourLDLChecked_16 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate16Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate16Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..eb32f69d5c77d12911695dc19ba50fe7a9a2e218 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate16Data.lean @@ -0,0 +1,203 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse1605 + +namespace OAI + +/-! Certificate16 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_16 : Matrix (CopyLabel 16) (CopyLabel 16) ℚ := + copyMatrixData 16 [ + [(-3023300183640213893190968391086889/167772160000000000000000), (-1842284299727598695958363192819/4194304000000000000000), (4978857332568431590081678121247/33554432000000000000000), (-495035435219731541754508880991/134217728000000000000000), (-379088797146560907753377563533/83886080000000000000000), (-1950638107811679763870313499579/335544320000000000000000), (830433036679330373158862049057/83886080000000000000000), (-780293120878982200971277577781/134217728000000000000000)], + [(-1842284299727598695958363192819/4194304000000000000000), (-23811117256265722049574939091203/1677721600000000000000000), (451840005330447003265547996301/167772160000000000000000), (765033524894004427226426290029/1342177280000000000000000), (-299360130730835687934042178557/1677721600000000000000000), (-54641732479826306851381037121/134217728000000000000000), (1596360042122635609616004677469/1677721600000000000000000), (-1867439584107586370782878530553/1342177280000000000000000)], + [(4978857332568431590081678121247/33554432000000000000000), (451840005330447003265547996301/167772160000000000000000), (-83970211150334552496385437351/67108864000000000000000), (48488780217799936547817299631/335544320000000000000000), (-142712675539696745387515611/10485760000000000000000), (55761689248689962568566349/2097152000000000000000), (-14386490313579701778931067169/335544320000000000000000), (-26878148679024614358884359863/67108864000000000000000)], + [(-495035435219731541754508880991/134217728000000000000000), (765033524894004427226426290029/1342177280000000000000000), (48488780217799936547817299631/335544320000000000000000), (-3262158077323107028703896377657/26843545600000000000000000), (52643089387008932592230169867/1342177280000000000000000), (53630278770653547050750239809/2684354560000000000000000), (-501723637603154001058680647991/6710886400000000000000000), (1593230986748752248427033240737/5368709120000000000000000)], + [(-379088797146560907753377563533/83886080000000000000000), (-299360130730835687934042178557/1677721600000000000000000), (-142712675539696745387515611/10485760000000000000000), (52643089387008932592230169867/1342177280000000000000000), (-35077411519799463622935034803/1677721600000000000000000), (1492590838618072536119968653/671088640000000000000000), (40370172661050112192774463001/1677721600000000000000000), (-86392805913427500216351869247/1342177280000000000000000)], + [(-1950638107811679763870313499579/335544320000000000000000), (-54641732479826306851381037121/134217728000000000000000), (55761689248689962568566349/2097152000000000000000), (53630278770653547050750239809/2684354560000000000000000), (1492590838618072536119968653/671088640000000000000000), (-18951724542978071115384073653/1342177280000000000000000), (3060950838759256839852570543/134217728000000000000000), (-8106039764158833303443597961/536870912000000000000000)], + [(830433036679330373158862049057/83886080000000000000000), (1596360042122635609616004677469/1677721600000000000000000), (-14386490313579701778931067169/335544320000000000000000), (-501723637603154001058680647991/6710886400000000000000000), (40370172661050112192774463001/1677721600000000000000000), (3060950838759256839852570543/134217728000000000000000), (-184942013999244668370911421/4194304000000000000000), (18946767647015678576766350691/268435456000000000000000)], + [(-780293120878982200971277577781/134217728000000000000000), (-1867439584107586370782878530553/1342177280000000000000000), (-26878148679024614358884359863/67108864000000000000000), (1593230986748752248427033240737/5368709120000000000000000), (-86392805913427500216351869247/1342177280000000000000000), (-8106039764158833303443597961/536870912000000000000000), (18946767647015678576766350691/268435456000000000000000), (-28303565196748876363274618673/42949672960000000000000)] + ] + +def fourZData_16 : Matrix (CopyLabel 16) (CopyLabel 16) ℚ := + copyMatrixData 16 [ + [0, 0, 0, 0, 0, 0, 0, 0], + [0, 4670265600, 0, 0, 0, 0, (-54729675/2), (3192564375/16)], + [0, 0, 149688000, 0, 0, (-11694375/2), 0, (1915538625/32)], + [0, 0, 0, 14288400, -2679075, (-49116375/16), (127702575/32), (1915538625/256)], + [0, 0, 0, -2679075, 893025, 0, 0, (-638512875/256)], + [0, 0, (-11694375/2), (-49116375/16), 0, (222193125/128), (-1003377375/512), (-9577693125/4096)], + [0, (-54729675/2), 0, (127702575/32), 0, (-1003377375/512), (346621275/128), (-9577693125/8192)], + [0, (3192564375/16), (1915538625/32), (1915538625/256), (-638512875/256), (-9577693125/4096), (-9577693125/8192), (2584061605125/65536)] + ] + +def fourLData_16 : Matrix (CopyLabel 16) (CopyLabel 16) ℚ := + copyMatrixData 16 [ + [1, 0, 0, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0, 0, 0], + [0, (2662114609823252321446554735/31846883619456444318310735886), 1, 0, 0, 0, 0, 0], + [0, (-17360028699934957438187203593/254775068955651554546485887088), (8465590199751968259176205997398130465255792473891241/1203382170043606369261657898744251670892140198195617080), 1, 0, 0, 0, 0], + [0, (640570914407014793429222681/127387534477825777273242943544), (436797514031755906616504442343241048612038835260569/80225478002907091284110526582950111392809346546374472), (-1275194507514036637278365937230604879105104344465161974052430467237510230580/11008773474816855464614116596323385562037106374777989640768967739311575751573), 1, 0, 0, 0], + [0, (11611413667826677607464701735/509550137911303109092971774176), (-194613665775878056818579803761786280887342230583992893/3850822944139540381637305275981605346854848634225974656), (-56439349625015857914692290450676628694242661968005386360520314081135354041545/176140375597069687433825865541174168992593701996447834252303483828985212025168), (-165/112), 1, 0, 0], + [0, (-1840313747998192277792824497/46322739810118464462997434016), (287240814382777194295671681721906343167860587762014927/19254114720697701908186526379908026734274243171129873280), (146742309025041230578199955171759234605030921116814004537352816610951920508017/352280751194139374867651731082348337985187403992895668504606967657970424050336), (429/224), 0, 1, 0], + [0, (63294652727275802726767645065/1019100275822606218185943548352), (987596636001863499622501810331762538010156135684222467/2567215296093026921091536850654403564569899089483983104), (227941018218134048913507911279970622140037401573147702861871946018704953716175/704561502388278749735303462164696675970374807985791337009213935315940848100672), (-715/256), 0, 0, 1] + ] + +def fourPivotData_16 : CopyLabel 16 → ℚ := + copyDiagonalData 16 [0, (1659971038338737975425469641953921/26843545600000000000000000), (21931640049044726079793715204613986702009255112115121283/6071614152391847374093999671345152000000000000000), (18725923680663471145308612330346078841025117943497360378948014124568990353425673/210306277055940765375818698805608740009566133410527895879680000000000000000), (1258193430655446810881478335223852733907966615729102098881517572221031021658883374072770186347847/1803677446113993599322376863141623490484159508443625822743587674408808571137720320000000000000000), 0, 0, 0] + +theorem fourOccupations_16 : highestFourOccupations 16 = {{0,1,2,14}, {0,1,3,13}, {0,1,4,12}, {0,1,5,11}, {0,1,6,10}, {0,1,7,9}, {0,2,3,12}, {0,2,4,11}, {0,2,5,10}, {0,2,6,9}, {0,2,7,8}, {0,3,4,10}, {0,3,5,9}, {0,3,6,8}, {0,4,5,8}, {0,4,6,7}, {1,2,3,11}, {1,2,4,10}, {1,2,5,9}, {1,2,6,8}, {1,3,4,9}, {1,3,5,8}, {1,3,6,7}, {1,4,5,7}, {2,3,4,8}, {2,3,5,7}, {2,4,5,6}} := by + decide +kernel + +theorem fourYNumber_16_1_1 : + (collectedFourTrace 16 1 1 collectedFourData_16 : ℚ) / fourCommonDenominator = (-3023300183640213893190968391086889/167772160000000000000000) := by + decide +kernel + +theorem fourYNumber_16_3_1 : + (collectedFourTrace 16 3 1 collectedFourData_16 : ℚ) / fourCommonDenominator = (-1842284299727598695958363192819/4194304000000000000000) := by + decide +kernel + +theorem fourYNumber_16_3_3 : + (collectedFourTrace 16 3 3 collectedFourData_16 : ℚ) / fourCommonDenominator = (-23811117256265722049574939091203/1677721600000000000000000) := by + decide +kernel + +theorem fourYNumber_16_5_1 : + (collectedFourTrace 16 5 1 collectedFourData_16 : ℚ) / fourCommonDenominator = (4978857332568431590081678121247/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_16_5_3 : + (collectedFourTrace 16 5 3 collectedFourData_16 : ℚ) / fourCommonDenominator = (451840005330447003265547996301/167772160000000000000000) := by + decide +kernel + +theorem fourYNumber_16_5_5 : + (collectedFourTrace 16 5 5 collectedFourData_16 : ℚ) / fourCommonDenominator = (-83970211150334552496385437351/67108864000000000000000) := by + decide +kernel + +theorem fourYNumber_16_7_1 : + (collectedFourTrace 16 7 1 collectedFourData_16 : ℚ) / fourCommonDenominator = (-495035435219731541754508880991/134217728000000000000000) := by + decide +kernel + +theorem fourYNumber_16_7_3 : + (collectedFourTrace 16 7 3 collectedFourData_16 : ℚ) / fourCommonDenominator = (765033524894004427226426290029/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_16_7_5 : + (collectedFourTrace 16 7 5 collectedFourData_16 : ℚ) / fourCommonDenominator = (48488780217799936547817299631/335544320000000000000000) := by + decide +kernel + +theorem fourYNumber_16_7_7 : + (collectedFourTrace 16 7 7 collectedFourData_16 : ℚ) / fourCommonDenominator = (-3262158077323107028703896377657/26843545600000000000000000) := by + decide +kernel + +theorem fourYNumber_16_9_1 : + (collectedFourTrace 16 9 1 collectedFourData_16 : ℚ) / fourCommonDenominator = (-379088797146560907753377563533/83886080000000000000000) := by + decide +kernel + +theorem fourYNumber_16_9_3 : + (collectedFourTrace 16 9 3 collectedFourData_16 : ℚ) / fourCommonDenominator = (-299360130730835687934042178557/1677721600000000000000000) := by + decide +kernel + +theorem fourYNumber_16_9_5 : + (collectedFourTrace 16 9 5 collectedFourData_16 : ℚ) / fourCommonDenominator = (-142712675539696745387515611/10485760000000000000000) := by + decide +kernel + +theorem fourYNumber_16_9_7 : + (collectedFourTrace 16 9 7 collectedFourData_16 : ℚ) / fourCommonDenominator = (52643089387008932592230169867/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_16_9_9 : + (collectedFourTrace 16 9 9 collectedFourData_16 : ℚ) / fourCommonDenominator = (-35077411519799463622935034803/1677721600000000000000000) := by + decide +kernel + +theorem fourYNumber_16_11_1 : + (collectedFourTrace 16 11 1 collectedFourData_16 : ℚ) / fourCommonDenominator = (-1950638107811679763870313499579/335544320000000000000000) := by + decide +kernel + +theorem fourYNumber_16_11_3 : + (collectedFourTrace 16 11 3 collectedFourData_16 : ℚ) / fourCommonDenominator = (-54641732479826306851381037121/134217728000000000000000) := by + decide +kernel + +theorem fourYNumber_16_11_5 : + (collectedFourTrace 16 11 5 collectedFourData_16 : ℚ) / fourCommonDenominator = (55761689248689962568566349/2097152000000000000000) := by + decide +kernel + +theorem fourYNumber_16_11_7 : + (collectedFourTrace 16 11 7 collectedFourData_16 : ℚ) / fourCommonDenominator = (53630278770653547050750239809/2684354560000000000000000) := by + decide +kernel + +theorem fourYNumber_16_11_9 : + (collectedFourTrace 16 11 9 collectedFourData_16 : ℚ) / fourCommonDenominator = (1492590838618072536119968653/671088640000000000000000) := by + decide +kernel + +theorem fourYNumber_16_11_11 : + (collectedFourTrace 16 11 11 collectedFourData_16 : ℚ) / fourCommonDenominator = (-18951724542978071115384073653/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_16_13_1 : + (collectedFourTrace 16 13 1 collectedFourData_16 : ℚ) / fourCommonDenominator = (830433036679330373158862049057/83886080000000000000000) := by + decide +kernel + +theorem fourYNumber_16_13_3 : + (collectedFourTrace 16 13 3 collectedFourData_16 : ℚ) / fourCommonDenominator = (1596360042122635609616004677469/1677721600000000000000000) := by + decide +kernel + +theorem fourYNumber_16_13_5 : + (collectedFourTrace 16 13 5 collectedFourData_16 : ℚ) / fourCommonDenominator = (-14386490313579701778931067169/335544320000000000000000) := by + decide +kernel + +theorem fourYNumber_16_13_7 : + (collectedFourTrace 16 13 7 collectedFourData_16 : ℚ) / fourCommonDenominator = (-501723637603154001058680647991/6710886400000000000000000) := by + decide +kernel + +theorem fourYNumber_16_13_9 : + (collectedFourTrace 16 13 9 collectedFourData_16 : ℚ) / fourCommonDenominator = (40370172661050112192774463001/1677721600000000000000000) := by + decide +kernel + +theorem fourYNumber_16_13_11 : + (collectedFourTrace 16 13 11 collectedFourData_16 : ℚ) / fourCommonDenominator = (3060950838759256839852570543/134217728000000000000000) := by + decide +kernel + +theorem fourYNumber_16_13_13 : + (collectedFourTrace 16 13 13 collectedFourData_16 : ℚ) / fourCommonDenominator = (-184942013999244668370911421/4194304000000000000000) := by + decide +kernel + +theorem fourYNumber_16_15_1 : + (collectedFourTrace 16 15 1 collectedFourData_16 : ℚ) / fourCommonDenominator = (-780293120878982200971277577781/134217728000000000000000) := by + decide +kernel + +theorem fourYNumber_16_15_3 : + (collectedFourTrace 16 15 3 collectedFourData_16 : ℚ) / fourCommonDenominator = (-1867439584107586370782878530553/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_16_15_5 : + (collectedFourTrace 16 15 5 collectedFourData_16 : ℚ) / fourCommonDenominator = (-26878148679024614358884359863/67108864000000000000000) := by + decide +kernel + +theorem fourYNumber_16_15_7 : + (collectedFourTrace 16 15 7 collectedFourData_16 : ℚ) / fourCommonDenominator = (1593230986748752248427033240737/5368709120000000000000000) := by + decide +kernel + +theorem fourYNumber_16_15_9 : + (collectedFourTrace 16 15 9 collectedFourData_16 : ℚ) / fourCommonDenominator = (-86392805913427500216351869247/1342177280000000000000000) := by + decide +kernel + +theorem fourYNumber_16_15_11 : + (collectedFourTrace 16 15 11 collectedFourData_16 : ℚ) / fourCommonDenominator = (-8106039764158833303443597961/536870912000000000000000) := by + decide +kernel + +theorem fourYNumber_16_15_13 : + (collectedFourTrace 16 15 13 collectedFourData_16 : ℚ) / fourCommonDenominator = (18946767647015678576766350691/268435456000000000000000) := by + decide +kernel + +theorem fourYNumber_16_15_15 : + (collectedFourTrace 16 15 15 collectedFourData_16 : ℚ) / fourCommonDenominator = (-28303565196748876363274618673/42949672960000000000000) := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate17.lean b/lean/OAI/Analysis/LaughlinFock/Certificate17.lean new file mode 100644 index 0000000000000000000000000000000000000000..64e08b4eff22b05f42b14deb213eab55eaf2497a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate17.lean @@ -0,0 +1,316 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate17Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate17. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_17 (r s : CopyLabel 17) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 17 r s = fourYData_17 r s := by + rw [integerRowsFourTrace_collected (by decide) collectedFourData_17 collectedFourChecked_17] + fin_cases r <;> fin_cases s + · exact fourYNumber_17_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · have h : (13:ℕ) ≤ 1 := hrs + omega + · have h : (15:ℕ) ≤ 1 := hrs + omega + · have h : (17:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_17_3_1 + · exact fourYNumber_17_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · have h : (13:ℕ) ≤ 3 := hrs + omega + · have h : (15:ℕ) ≤ 3 := hrs + omega + · have h : (17:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_17_5_1 + · exact fourYNumber_17_5_3 + · exact fourYNumber_17_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · have h : (13:ℕ) ≤ 5 := hrs + omega + · have h : (15:ℕ) ≤ 5 := hrs + omega + · have h : (17:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_17_7_1 + · exact fourYNumber_17_7_3 + · exact fourYNumber_17_7_5 + · exact fourYNumber_17_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · have h : (13:ℕ) ≤ 7 := hrs + omega + · have h : (15:ℕ) ≤ 7 := hrs + omega + · have h : (17:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_17_9_1 + · exact fourYNumber_17_9_3 + · exact fourYNumber_17_9_5 + · exact fourYNumber_17_9_7 + · exact fourYNumber_17_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · have h : (13:ℕ) ≤ 9 := hrs + omega + · have h : (15:ℕ) ≤ 9 := hrs + omega + · have h : (17:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_17_11_1 + · exact fourYNumber_17_11_3 + · exact fourYNumber_17_11_5 + · exact fourYNumber_17_11_7 + · exact fourYNumber_17_11_9 + · exact fourYNumber_17_11_11 + · have h : (13:ℕ) ≤ 11 := hrs + omega + · have h : (15:ℕ) ≤ 11 := hrs + omega + · have h : (17:ℕ) ≤ 11 := hrs + omega + · exact fourYNumber_17_13_1 + · exact fourYNumber_17_13_3 + · exact fourYNumber_17_13_5 + · exact fourYNumber_17_13_7 + · exact fourYNumber_17_13_9 + · exact fourYNumber_17_13_11 + · exact fourYNumber_17_13_13 + · have h : (15:ℕ) ≤ 13 := hrs + omega + · have h : (17:ℕ) ≤ 13 := hrs + omega + · exact fourYNumber_17_15_1 + · exact fourYNumber_17_15_3 + · exact fourYNumber_17_15_5 + · exact fourYNumber_17_15_7 + · exact fourYNumber_17_15_9 + · exact fourYNumber_17_15_11 + · exact fourYNumber_17_15_13 + · exact fourYNumber_17_15_15 + · have h : (17:ℕ) ≤ 15 := hrs + omega + · exact fourYNumber_17_17_1 + · exact fourYNumber_17_17_3 + · exact fourYNumber_17_17_5 + · exact fourYNumber_17_17_7 + · exact fourYNumber_17_17_9 + · exact fourYNumber_17_17_11 + · exact fourYNumber_17_17_13 + · exact fourYNumber_17_17_15 + · exact fourYNumber_17_17_17 + +theorem fourYChecked_17 (r s : CopyLabel 17) : + integerRowsFourTrace 17 r s = fourYData_17 r s := by + have hh : ∀ r s : CopyLabel 17, fourYData_17 r s = fourYData_17 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_17 r s h + · rw [integerRowsFourTrace_symm, fourYLower_17 s r (by omega), hh] + +def fourHighestCache_17_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,15}, [2343352467456000, 732297646080000, 402763705344000, 159536272896000, 10461394944000, -44460928512000, -5230697472000, 128152088064000, 355687428096000]), + ({0,1,3,14}, [-2343352467456000, -732297646080000, -402763705344000, -159536272896000, -10461394944000, 44460928512000, 5230697472000, -128152088064000, -355687428096000]), + ({0,1,4,13}, [4017175658496000, 920602755072000, 343731548160000, 94152554496000, 2092278988800, -23164517376000, -8518564454400, 83691159552000, 355687428096000]), + ({0,1,5,12}, [-4017175658496000, -920602755072000, -270156902400000, -42650302464000, 5633058816000, 5460618240000, 9714152448000, -41845579776000, -355687428096000]) +] + +def fourHighestCache_17_1 : List (Occupation 24 × List ℚ) := [ + ({0,1,6,11}, [5021469573120000, 899679965184000, 176981511168000, 16295634432000, -7242504192000, 1293304320000, -5977939968000, 10461394944000, 355687428096000]), + ({0,1,7,10}, [-5021469573120000, -899679965184000, -103406865408000, -2249565696000, 3730987008000, -603542016000, 0, 10461394944000, -355687428096000]), + ({0,1,8,9}, [5356234211328000, 870388059340800, 70815596544000, -5559902208000, 58525286400, -1609445376000, 4184557977600, -20922789888000, 355687428096000]), + ({0,2,3,13}, [-1673823191040000, -188305108992000, 59032157184000, 65383718400000, 8369115955200, -21296411136000, 3287866982400, 44460928512000, 0]) +] + +def fourHighestCache_17_2 : List (Occupation 24 × List ℚ) := [ + ({0,2,4,12}, [0, 0, -73574645760000, -51502252032000, -7725337804800, 17703899136000, -1195587993600, -41845579776000, 0]), + ({0,2,5,11}, [-1004293914624000, 20922789888000, 93175391232000, 26354668032000, 1609445376000, -6753922560000, -3736212480000, 31384184832000, 0]), + ({0,2,6,10}, [0, 0, -73574645760000, -14046068736000, 3511517184000, -689762304000, 5977939968000, -20922789888000, 0]), + ({0,2,7,9}, [-334764638208000, 29291905843200, 32591268864000, 7809467904000, -3789512294400, 2212987392000, -4184557977600, 10461394944000, 0]) +] + +def fourHighestCache_17_3 : List (Occupation 24 × List ℚ) := [ + ({0,3,4,11}, [2678117105664000, 167382319104000, -5058256896000, 11266117632000, 5472114278400, -7357464576000, 2839521484800, 7846046208000, 0]), + ({0,3,5,10}, [-1673823191040000, -188305108992000, -14542488576000, -4846625280000, -4974649344000, 5604318720000, -1494484992000, -7846046208000, 0]), + ({0,3,6,9}, [3012881743872000, 138090413260800, 21210190848000, 3456649728000, 833985331200, -1293304320000, -1345036492800, 7846046208000, 0]), + ({0,3,7,8}, [-2678117105664000, -167382319104000, -9656672256000, -6584094720000, 2721425817600, -1609445376000, 3138418483200, -7846046208000, 0]) +] + +def fourHighestCache_17_4 : List (Occupation 24 × List ℚ) := [ + ({0,4,5,9}, [-1339058552832000, 50214695731200, 8047226880000, -3292047360000, 3438360576000, -2701569024000, 1643933491200, 0, 0]), + ({0,4,6,8}, [0, 0, -14714929152000, 4682022912000, -3043314892800, 2069286912000, -1195587993600, 0, 0]), + ({0,5,6,7}, [1004293914624000, -20922789888000, 17186577408000, -5285564928000, 2487324672000, -1408264704000, 747242496000, 0, 0]), + ({1,2,3,12}, [1673823191040000, 188305108992000, 14542488576000, -13881466368000, -643778150400, 3592512000000, -2092278988800, -2615348736000, 0]) +] + +def fourHighestCache_17_5 : List (Occupation 24 × List ℚ) := [ + ({1,2,4,11}, [-1673823191040000, -188305108992000, -14542488576000, 13881466368000, 643778150400, -3592512000000, 2092278988800, 2615348736000, 0]), + ({1,2,5,10}, [2678117105664000, 167382319104000, -5058256896000, -7461974016000, -146313216000, 1839366144000, -747242496000, -2615348736000, 0]), + ({1,2,6,9}, [-2678117105664000, -167382319104000, 19773186048000, 2779951104000, -555990220800, -229920768000, -448345497600, 2615348736000, 0]), + ({1,2,7,8}, [3012881743872000, 138090413260800, -22934596608000, -1225373184000, 1068086476800, -603542016000, 1046139494400, -2615348736000, 0]) +] + +def fourHighestCache_17_6 : List (Occupation 24 × List ℚ) := [ + ({1,3,4,10}, [-1004293914624000, 20922789888000, 19600745472000, -6419492352000, -497464934400, 1753145856000, -1345036492800, 0, 0]), + ({1,3,5,9}, [0, 0, -14714929152000, 4682022912000, 702303436800, -1609445376000, 1195587993600, 0, 0]), + ({1,3,6,8}, [-334764638208000, 29291905843200, 3161410560000, -1554577920000, -512096256000, 833462784000, -597793996800, 0, 0]), + ({1,4,5,8}, [1339058552832000, -50214695731200, 6667702272000, -1389975552000, -395045683200, 632282112000, -448345497600, 0, 0]) +] + +def fourHighestCache_17_7 : List (Occupation 24 × List ℚ) := [ + ({1,4,6,7}, [-1004293914624000, 20922789888000, -2471648256000, 603542016000, 555990220800, -661022208000, 448345497600, 0, 0]), + ({2,3,4,9}, [1004293914624000, -20922789888000, -4885816320000, 1737469440000, -204838502400, -143700480000, 149448499200, 0, 0]), + ({2,3,5,8}, [-1004293914624000, 20922789888000, 4885816320000, -1737469440000, 204838502400, 143700480000, -149448499200, 0, 0]), + ({2,3,6,7}, [1339058552832000, -50214695731200, -689762304000, 951035904000, -43893964800, -172440576000, 149448499200, 0, 0]) +] + +def fourHighestCache_17_8 : List (Occupation 24 × List ℚ) := [ + ({2,4,5,7}, [-334764638208000, 29291905843200, -4196054016000, 786433536000, -160944537600, 28740096000, 0, 0, 0]), + ({3,4,5,6}, [334764638208000, -29291905843200, 4196054016000, -786433536000, 160944537600, -28740096000, 0, 0, 0]) +] + +def fourHighestCache_17 : List (Occupation 24 × List ℚ) := fourHighestCache_17_0 ++ fourHighestCache_17_1 ++ fourHighestCache_17_2 ++ fourHighestCache_17_3 ++ fourHighestCache_17_4 ++ fourHighestCache_17_5 ++ fourHighestCache_17_6 ++ fourHighestCache_17_7 ++ fourHighestCache_17_8 + +theorem fourHighestNumber_17_1 : ∀ A∈highestFourOccupations 17, + kernelHighestEntry 17 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_17 1 A := by + rw [fourOccupations_17] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_17_3 : ∀ A∈highestFourOccupations 17, + kernelHighestEntry 17 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_17 3 A := by + rw [fourOccupations_17] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_17_5 : ∀ A∈highestFourOccupations 17, + kernelHighestEntry 17 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_17 5 A := by + rw [fourOccupations_17] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_17_7 : ∀ A∈highestFourOccupations 17, + kernelHighestEntry 17 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_17 7 A := by + rw [fourOccupations_17] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_17_9 : ∀ A∈highestFourOccupations 17, + kernelHighestEntry 17 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_17 9 A := by + rw [fourOccupations_17] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_17_11 : ∀ A∈highestFourOccupations 17, + kernelHighestEntry 17 ⟨⟨11,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_17 11 A := by + rw [fourOccupations_17] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_17_13 : ∀ A∈highestFourOccupations 17, + kernelHighestEntry 17 ⟨⟨13,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_17 13 A := by + rw [fourOccupations_17] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_17_15 : ∀ A∈highestFourOccupations 17, + kernelHighestEntry 17 ⟨⟨15,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_17 15 A := by + rw [fourOccupations_17] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_17_17 : ∀ A∈highestFourOccupations 17, + kernelHighestEntry 17 ⟨⟨17,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_17 17 A := by + rw [fourOccupations_17] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_17 : ∀ r : CopyLabel 17, ∀ A∈highestFourOccupations 17, + kernelHighestEntry 17 r A = highestLookup fourHighestCache_17 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_17_1 + · exact fourHighestNumber_17_3 + · exact fourHighestNumber_17_5 + · exact fourHighestNumber_17_7 + · exact fourHighestNumber_17_9 + · exact fourHighestNumber_17_11 + · exact fourHighestNumber_17_13 + · exact fourHighestNumber_17_15 + · exact fourHighestNumber_17_17 + +theorem fourZChecked_17 (r s : CopyLabel 17) : + integerFourGram 17 r s = fourZData_17 r s := by + rw [integerFourGram_cached 17 fourHighestCache_17 fourHighestChecked_17] + have h : ∀ r s : CopyLabel 17, cachedFourGram 17 fourHighestCache_17 r s = fourZData_17 r s := by + simp only [cachedFourGram, fourOccupations_17] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_17 : + fourZData_17 * (Matrix.diagonal (fun r : CopyLabel 17 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 17 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 17 => rationalCopyDiagonal 17 r.val.val) * + fourYData_17 * Matrix.diagonal (fun r : CopyLabel 17 => rationalCopyDiagonal 17 r.val.val)) * + fourZData_17 = fourLData_17 * Matrix.diagonal fourPivotData_17 * (fourLData_17)ᵀ := by + have h : ∀ r s : CopyLabel 17, + (fourZData_17 * (Matrix.diagonal (fun r : CopyLabel 17 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 17 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 17 => rationalCopyDiagonal 17 r.val.val) * + fourYData_17 * Matrix.diagonal (fun r : CopyLabel 17 => rationalCopyDiagonal 17 r.val.val)) * + fourZData_17 : Matrix (CopyLabel 17) (CopyLabel 17) ℚ) r s = + (fourLData_17 * Matrix.diagonal fourPivotData_17 * (fourLData_17)ᵀ : Matrix (CopyLabel 17) (CopyLabel 17) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_17 : ∀ r, 0 ≤ fourPivotData_17 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_17, copyDiagonalData] + +theorem integer_certificate_17 : + ((integerCompression 17).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_17) (fourPivotData_17) _ fourPivotChecked_17 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 17 = fourYData_17 from Matrix.ext fourYChecked_17, + show integerFourGram 17 = fourZData_17 from Matrix.ext fourZChecked_17] + exact fourLDLChecked_17 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate17Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate17Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..72dfb8bc65fd01dd743ab8a6f35bfc4830d24075 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate17Data.lean @@ -0,0 +1,242 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse1703 + +namespace OAI + +/-! Certificate17 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_17 : Matrix (CopyLabel 17) (CopyLabel 17) ℚ := + copyMatrixData 17 [ + [(-80532574708892899999366914086133/3355443200000000000000), (52168314199581417516891452106867/167772160000000000000000), (3416941451122696842894790053813/16777216000000000000000), (-1780399758192138186776437952187/26843545600000000000000), (-147580447016100579129054473067/33554432000000000000000), (484754681413657976207114779551/13421772800000000000000), (-8998787136844095341470376163507/167772160000000000000000), (13585035090756473170103083369563/134217728000000000000000), 0], + [(52168314199581417516891452106867/167772160000000000000000), (-1936359965196807219209198649591/335544320000000000000000), (-42279505429943443249978853463/33554432000000000000000), (80383774372540182022310744913/268435456000000000000000), (7501433511302274776260777749/67108864000000000000000), (-213828608195027061344135968941/671088640000000000000000), (277309144397718714739016580021/335544320000000000000000), (-255854381753090751185768626413/268435456000000000000000), 0], + [(3416941451122696842894790053813/16777216000000000000000), (-42279505429943443249978853463/33554432000000000000000), (-6128074571331463431937198371/2684354560000000000000), (10281592378696087538598060783/13421772800000000000000), (-251301453661421637165143991/33554432000000000000000), (-2988845641835365468393449333/8388608000000000000000), (1478457672704508300479559027/2684354560000000000000), (-9486946401639002079898757643/13421772800000000000000), 0], + [(-1780399758192138186776437952187/26843545600000000000000), (80383774372540182022310744913/268435456000000000000000), (10281592378696087538598060783/13421772800000000000000), (-56338902649996905268880020737/214748364800000000000000), (3801942718922194741310789331/268435456000000000000000), (12371464740075924792908192517/107374182400000000000000), (-57128772289770289745633735739/268435456000000000000000), (34846908517875080159788075821/214748364800000000000000), 0], + [(-147580447016100579129054473067/33554432000000000000000), (7501433511302274776260777749/67108864000000000000000), (-251301453661421637165143991/33554432000000000000000), (3801942718922194741310789331/268435456000000000000000), (-880826387722113202317841761/67108864000000000000000), (778359374321012227957500441/134217728000000000000000), (1542736257700531168437068907/335544320000000000000000), (11878850604017989335381270633/268435456000000000000000), 0], + [(484754681413657976207114779551/13421772800000000000000), (-213828608195027061344135968941/671088640000000000000000), (-2988845641835365468393449333/8388608000000000000000), (12371464740075924792908192517/107374182400000000000000), (778359374321012227957500441/134217728000000000000000), (-3469951889789090759165765169/53687091200000000000000), (67600551228997897843877987271/671088640000000000000000), (-55816204555305340589721547269/536870912000000000000000), 0], + [(-8998787136844095341470376163507/167772160000000000000000), (277309144397718714739016580021/335544320000000000000000), (1478457672704508300479559027/2684354560000000000000), (-57128772289770289745633735739/268435456000000000000000), (1542736257700531168437068907/335544320000000000000000), (67600551228997897843877987271/671088640000000000000000), (-5335051448812934030171092389/41943040000000000000000), (49207289089932048557142307647/268435456000000000000000), 0], + [(13585035090756473170103083369563/134217728000000000000000), (-255854381753090751185768626413/268435456000000000000000), (-9486946401639002079898757643/13421772800000000000000), (34846908517875080159788075821/214748364800000000000000), (11878850604017989335381270633/268435456000000000000000), (-55816204555305340589721547269/536870912000000000000000), (49207289089932048557142307647/268435456000000000000000), (-25213653324476267050918226709/42949672960000000000000), 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0] + ] + +def fourZData_17 : Matrix (CopyLabel 17) (CopyLabel 17) ℚ := + copyMatrixData 17 [ + [20922789888000, 0, 0, 0, 0, 0, 0, -1277025750, (75983032125/2)], + [0, 65383718400, 0, 0, 0, 0, (-127702575/2), 0, (54273594375/8)], + [0, 0, 1796256000, 0, 0, (-21049875/2), (-456080625/8), (3192564375/16), (32564156625/32)], + [0, 0, 0, 142884000, -4465125, (-49116375/2), 0, (4469590125/64), (10854718875/128)], + [0, 0, 0, -4465125, (41972175/4), (-147349125/16), (383107725/64), 0, (-10854718875/512)], + [0, 0, (-21049875/2), (-49116375/2), (-147349125/16), 14033250, (-3010132125/512), (-7023641625/512), (-32564156625/2048)], + [0, (-127702575/2), (-456080625/8), 0, (383107725/64), (-3010132125/512), (13883094225/2048), (-41503336875/4096), (-54273594375/8192)], + [-1277025750, 0, (3192564375/16), (4469590125/64), 0, (-7023641625/512), (-41503336875/4096), (1221475129875/16384), (-75983032125/32768)], + [(75983032125/2), (54273594375/8), (32564156625/32), (10854718875/128), (-10854718875/512), (-32564156625/2048), (-54273594375/8192), (-75983032125/32768), (355589735626125/131072)] + ] + +def fourLData_17 : Matrix (CopyLabel 17) (CopyLabel 17) ℚ := + copyMatrixData 17 [ + [1, 0, 0, 0, 0, 0, 0, 0, 0], + [(-117551264169584824801695701/9632539259029384797337239268080), 1, 0, 0, 0, 0, 0, 0, 0], + [(-37924296738363526674373909/2568677135741169279289930471488), (47118794471883626975050859394034423161530498507205602325/59127304175414171271171470320360289721589942153620741596), 1, 0, 0, 0, 0, 0, 0], + [(1588624636284321645585129/1712451423827446186193286980992), (-3574390678441118233187761656898628539053244136567356845/59127304175414171271171470320360289721589942153620741596), (-232723468888604157341303010280893399007903488637042302097831415530994981655461/5557016493988524890617677582494356155560315146280885694528065366755862212807418), 1, 0, 0, 0, 0, 0], + [(19293947999278735721493109/19265078518058769594674478536160), (-30452780383080492658048360980272214698485054504985278951/473018433403313370169371762562882317772719537228965932768), (-4733752136139313751781082456429438817411153654670017636287425241230908371534527/111140329879770497812353551649887123111206302925617713890561307335117244256148360), (2994296799359379675970335423857005313135833295213372394960554955829237440270701376972449213402679691/27062668890449347039789492867733128959680730998064413675113087348032475774648284613842083735276242180), 1, 0, 0, 0, 0], + [(-17815538580168323323917761/15412062814447015675739582828928), (70677821751760383296076535081211420678544864180652912955/946036866806626740338743525125764635545439074457931865536), (8712367356269257991172970819322521772790782092856121564497433781029681611388583/177824527807632796499765682639819396977930084680988342224898091736187590809837376), (-1016478261622833582103890131007273343392081666197497162946248131739720045937322658333179342472936367/3330790017286073481820245276028692795037628430531004760013918442834766249187481183242102613572460576), (-96135302426917635873191131299256392665577897050571594599602147410352650602440903024984217217257661474358830047555776165/97672778486944754637311264260713876130916549837706903435686594875080084979164917369696374367519788498353641721147699368), 1, 0, 0, 0], + [(105484771648377976339183819/77060314072235078378697914144640), (-38437128935850371942212389425316885203089401141060583189/473018433403313370169371762562882317772719537228965932768), (-66251894878278801520868485654579260974571202859115919121259362675097805376540177/889122639038163982498828413199096984889650423404941711124490458680937954049186880), (4722741724519108096698689916219531272704636021680610476576360150961277144062831171792273478204210943/66615800345721469636404905520573855900752568610620095200278368856695324983749623664842052271449211520), (252101265576136415413233936227327084172436474029424501844600554396266446973118654762896142784683188076338307323645018029/390691113947779018549245057042855504523666199350827613742746379500320339916659669478785497470079153993414566884590797472), (-13/4), 1, 0, 0], + [(-1942799299014989555583336253/30824125628894031351479165657856), (195588798156802390658650606509901082151665802472348461805/1892073733613253480677487050251529271090878148915863731072), (50586461043426630179029557735398538805377385653097398370310544165102862076501649/355649055615265592999531365279638793955860169361976684449796183472375181619674752), (14860082434011024823640793127031288834936744868051992123018514732896396042964135926443351454401933199/26646320138288587854561962208229542360301027444248038080111347542678129993499849465936820908579684608), (-41982016917003166854238180649618422694022298787858513391308029870108504038521619100335508199477895371198226562500000/1744156758695442047094844004655604930909224104244766132780117765626430088913659238744578113705710508899172173591923203), (91/8), 0, 1, 0], + [(218366443438346000000000000/120406740737867309966715490851), (2098684213723329960706490736712721462811680000000000000/14781826043853542817792867580090072430397485538405185399), (285861478788004340060601627011164057199246250352531405406751354299625000000000/2778508246994262445308838791247178077780157573140442847264032683377931106403709), (809673334988228164332568659712589021660492334020315958969953603251788598771778105247086328125000/104087188040189796306882664875896649844925888454093898750434951338586445287108786976315706674139393), (356847143794526918261024535521756592899189539696797363826118253895922284327433762352851819695562110655184925781250000/1744156758695442047094844004655604930909224104244766132780117765626430088913659238744578113705710508899172173591923203), (-1547/16), 0, 0, 1] + ] + +def fourPivotData_17 : CopyLabel 17 → ℚ := + copyDiagonalData 17 [(87864290511903174234701328423209379/1048576000000000000000), (108956839769244464109951226932843923884459865903584621576029/8161979382687673691517327679003033600000000000000000), (22280857632646990548931578267011121005719083579013211192210278088007629542251342471/3099973605151954502741994783132105557755294759183751136988364800000000000000), (48335279771787056280416023736414754978437769599092946044435729657953403357310568734552653655390132345589/72836926590006393446304023609270025002160162685332824975318258375142437195709389209600000000000000), (11775271456121018333847960388467241246294586509040458004488292887422983039950031295099869137139838481705205221233769770794607/3547158136808976815199288409159516679003272773378298829224422584881312664734699960905509599350127615016960000000000000000), (22296391454799418208944267100323807615506431152732876070624896007485482989797570438567739119199486707179791568451405742005633419/46819351485589295103347792563859343258446606702913533246618746014963188656965866238101369348021225026034134044065906291428556800), 0, 0, 0] + +theorem fourOccupations_17 : highestFourOccupations 17 = {{0,1,2,15}, {0,1,3,14}, {0,1,4,13}, {0,1,5,12}, {0,1,6,11}, {0,1,7,10}, {0,1,8,9}, {0,2,3,13}, {0,2,4,12}, {0,2,5,11}, {0,2,6,10}, {0,2,7,9}, {0,3,4,11}, {0,3,5,10}, {0,3,6,9}, {0,3,7,8}, {0,4,5,9}, {0,4,6,8}, {0,5,6,7}, {1,2,3,12}, {1,2,4,11}, {1,2,5,10}, {1,2,6,9}, {1,2,7,8}, {1,3,4,10}, {1,3,5,9}, {1,3,6,8}, {1,4,5,8}, {1,4,6,7}, {2,3,4,9}, {2,3,5,8}, {2,3,6,7}, {2,4,5,7}, {3,4,5,6}} := by + decide +kernel + +theorem fourYNumber_17_1_1 : + (collectedFourTrace 17 1 1 collectedFourData_17 : ℚ) / fourCommonDenominator = (-80532574708892899999366914086133/3355443200000000000000) := by + decide +kernel + +theorem fourYNumber_17_3_1 : + (collectedFourTrace 17 3 1 collectedFourData_17 : ℚ) / fourCommonDenominator = (52168314199581417516891452106867/167772160000000000000000) := by + decide +kernel + +theorem fourYNumber_17_3_3 : + (collectedFourTrace 17 3 3 collectedFourData_17 : ℚ) / fourCommonDenominator = (-1936359965196807219209198649591/335544320000000000000000) := by + decide +kernel + +theorem fourYNumber_17_5_1 : + (collectedFourTrace 17 5 1 collectedFourData_17 : ℚ) / fourCommonDenominator = (3416941451122696842894790053813/16777216000000000000000) := by + decide +kernel + +theorem fourYNumber_17_5_3 : + (collectedFourTrace 17 5 3 collectedFourData_17 : ℚ) / fourCommonDenominator = (-42279505429943443249978853463/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_17_5_5 : + (collectedFourTrace 17 5 5 collectedFourData_17 : ℚ) / fourCommonDenominator = (-6128074571331463431937198371/2684354560000000000000) := by + decide +kernel + +theorem fourYNumber_17_7_1 : + (collectedFourTrace 17 7 1 collectedFourData_17 : ℚ) / fourCommonDenominator = (-1780399758192138186776437952187/26843545600000000000000) := by + decide +kernel + +theorem fourYNumber_17_7_3 : + (collectedFourTrace 17 7 3 collectedFourData_17 : ℚ) / fourCommonDenominator = (80383774372540182022310744913/268435456000000000000000) := by + decide +kernel + +theorem fourYNumber_17_7_5 : + (collectedFourTrace 17 7 5 collectedFourData_17 : ℚ) / fourCommonDenominator = (10281592378696087538598060783/13421772800000000000000) := by + decide +kernel + +theorem fourYNumber_17_7_7 : + (collectedFourTrace 17 7 7 collectedFourData_17 : ℚ) / fourCommonDenominator = (-56338902649996905268880020737/214748364800000000000000) := by + decide +kernel + +theorem fourYNumber_17_9_1 : + (collectedFourTrace 17 9 1 collectedFourData_17 : ℚ) / fourCommonDenominator = (-147580447016100579129054473067/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_17_9_3 : + (collectedFourTrace 17 9 3 collectedFourData_17 : ℚ) / fourCommonDenominator = (7501433511302274776260777749/67108864000000000000000) := by + decide +kernel + +theorem fourYNumber_17_9_5 : + (collectedFourTrace 17 9 5 collectedFourData_17 : ℚ) / fourCommonDenominator = (-251301453661421637165143991/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_17_9_7 : + (collectedFourTrace 17 9 7 collectedFourData_17 : ℚ) / fourCommonDenominator = (3801942718922194741310789331/268435456000000000000000) := by + decide +kernel + +theorem fourYNumber_17_9_9 : + (collectedFourTrace 17 9 9 collectedFourData_17 : ℚ) / fourCommonDenominator = (-880826387722113202317841761/67108864000000000000000) := by + decide +kernel + +theorem fourYNumber_17_11_1 : + (collectedFourTrace 17 11 1 collectedFourData_17 : ℚ) / fourCommonDenominator = (484754681413657976207114779551/13421772800000000000000) := by + decide +kernel + +theorem fourYNumber_17_11_3 : + (collectedFourTrace 17 11 3 collectedFourData_17 : ℚ) / fourCommonDenominator = (-213828608195027061344135968941/671088640000000000000000) := by + decide +kernel + +theorem fourYNumber_17_11_5 : + (collectedFourTrace 17 11 5 collectedFourData_17 : ℚ) / fourCommonDenominator = (-2988845641835365468393449333/8388608000000000000000) := by + decide +kernel + +theorem fourYNumber_17_11_7 : + (collectedFourTrace 17 11 7 collectedFourData_17 : ℚ) / fourCommonDenominator = (12371464740075924792908192517/107374182400000000000000) := by + decide +kernel + +theorem fourYNumber_17_11_9 : + (collectedFourTrace 17 11 9 collectedFourData_17 : ℚ) / fourCommonDenominator = (778359374321012227957500441/134217728000000000000000) := by + decide +kernel + +theorem fourYNumber_17_11_11 : + (collectedFourTrace 17 11 11 collectedFourData_17 : ℚ) / fourCommonDenominator = (-3469951889789090759165765169/53687091200000000000000) := by + decide +kernel + +theorem fourYNumber_17_13_1 : + (collectedFourTrace 17 13 1 collectedFourData_17 : ℚ) / fourCommonDenominator = (-8998787136844095341470376163507/167772160000000000000000) := by + decide +kernel + +theorem fourYNumber_17_13_3 : + (collectedFourTrace 17 13 3 collectedFourData_17 : ℚ) / fourCommonDenominator = (277309144397718714739016580021/335544320000000000000000) := by + decide +kernel + +theorem fourYNumber_17_13_5 : + (collectedFourTrace 17 13 5 collectedFourData_17 : ℚ) / fourCommonDenominator = (1478457672704508300479559027/2684354560000000000000) := by + decide +kernel + +theorem fourYNumber_17_13_7 : + (collectedFourTrace 17 13 7 collectedFourData_17 : ℚ) / fourCommonDenominator = (-57128772289770289745633735739/268435456000000000000000) := by + decide +kernel + +theorem fourYNumber_17_13_9 : + (collectedFourTrace 17 13 9 collectedFourData_17 : ℚ) / fourCommonDenominator = (1542736257700531168437068907/335544320000000000000000) := by + decide +kernel + +theorem fourYNumber_17_13_11 : + (collectedFourTrace 17 13 11 collectedFourData_17 : ℚ) / fourCommonDenominator = (67600551228997897843877987271/671088640000000000000000) := by + decide +kernel + +theorem fourYNumber_17_13_13 : + (collectedFourTrace 17 13 13 collectedFourData_17 : ℚ) / fourCommonDenominator = (-5335051448812934030171092389/41943040000000000000000) := by + decide +kernel + +theorem fourYNumber_17_15_1 : + (collectedFourTrace 17 15 1 collectedFourData_17 : ℚ) / fourCommonDenominator = (13585035090756473170103083369563/134217728000000000000000) := by + decide +kernel + +theorem fourYNumber_17_15_3 : + (collectedFourTrace 17 15 3 collectedFourData_17 : ℚ) / fourCommonDenominator = (-255854381753090751185768626413/268435456000000000000000) := by + decide +kernel + +theorem fourYNumber_17_15_5 : + (collectedFourTrace 17 15 5 collectedFourData_17 : ℚ) / fourCommonDenominator = (-9486946401639002079898757643/13421772800000000000000) := by + decide +kernel + +theorem fourYNumber_17_15_7 : + (collectedFourTrace 17 15 7 collectedFourData_17 : ℚ) / fourCommonDenominator = (34846908517875080159788075821/214748364800000000000000) := by + decide +kernel + +theorem fourYNumber_17_15_9 : + (collectedFourTrace 17 15 9 collectedFourData_17 : ℚ) / fourCommonDenominator = (11878850604017989335381270633/268435456000000000000000) := by + decide +kernel + +theorem fourYNumber_17_15_11 : + (collectedFourTrace 17 15 11 collectedFourData_17 : ℚ) / fourCommonDenominator = (-55816204555305340589721547269/536870912000000000000000) := by + decide +kernel + +theorem fourYNumber_17_15_13 : + (collectedFourTrace 17 15 13 collectedFourData_17 : ℚ) / fourCommonDenominator = (49207289089932048557142307647/268435456000000000000000) := by + decide +kernel + +theorem fourYNumber_17_15_15 : + (collectedFourTrace 17 15 15 collectedFourData_17 : ℚ) / fourCommonDenominator = (-25213653324476267050918226709/42949672960000000000000) := by + decide +kernel + +theorem fourYNumber_17_17_1 : + (collectedFourTrace 17 17 1 collectedFourData_17 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_17_17_3 : + (collectedFourTrace 17 17 3 collectedFourData_17 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_17_17_5 : + (collectedFourTrace 17 17 5 collectedFourData_17 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_17_17_7 : + (collectedFourTrace 17 17 7 collectedFourData_17 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_17_17_9 : + (collectedFourTrace 17 17 9 collectedFourData_17 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_17_17_11 : + (collectedFourTrace 17 17 11 collectedFourData_17 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_17_17_13 : + (collectedFourTrace 17 17 13 collectedFourData_17 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_17_17_15 : + (collectedFourTrace 17 17 15 collectedFourData_17 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_17_17_17 : + (collectedFourTrace 17 17 17 collectedFourData_17 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate18.lean b/lean/OAI/Analysis/LaughlinFock/Certificate18.lean new file mode 100644 index 0000000000000000000000000000000000000000..6afe67abce223b64f3a21cead9551b6c6024d21e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate18.lean @@ -0,0 +1,324 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate18Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate18. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_18 (r s : CopyLabel 18) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 18 r s = fourYData_18 r s := by + rw [integerRowsFourTrace_collected (by decide) collectedFourData_18 collectedFourChecked_18] + fin_cases r <;> fin_cases s + · exact fourYNumber_18_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · have h : (13:ℕ) ≤ 1 := hrs + omega + · have h : (15:ℕ) ≤ 1 := hrs + omega + · have h : (17:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_18_3_1 + · exact fourYNumber_18_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · have h : (13:ℕ) ≤ 3 := hrs + omega + · have h : (15:ℕ) ≤ 3 := hrs + omega + · have h : (17:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_18_5_1 + · exact fourYNumber_18_5_3 + · exact fourYNumber_18_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · have h : (13:ℕ) ≤ 5 := hrs + omega + · have h : (15:ℕ) ≤ 5 := hrs + omega + · have h : (17:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_18_7_1 + · exact fourYNumber_18_7_3 + · exact fourYNumber_18_7_5 + · exact fourYNumber_18_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · have h : (13:ℕ) ≤ 7 := hrs + omega + · have h : (15:ℕ) ≤ 7 := hrs + omega + · have h : (17:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_18_9_1 + · exact fourYNumber_18_9_3 + · exact fourYNumber_18_9_5 + · exact fourYNumber_18_9_7 + · exact fourYNumber_18_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · have h : (13:ℕ) ≤ 9 := hrs + omega + · have h : (15:ℕ) ≤ 9 := hrs + omega + · have h : (17:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_18_11_1 + · exact fourYNumber_18_11_3 + · exact fourYNumber_18_11_5 + · exact fourYNumber_18_11_7 + · exact fourYNumber_18_11_9 + · exact fourYNumber_18_11_11 + · have h : (13:ℕ) ≤ 11 := hrs + omega + · have h : (15:ℕ) ≤ 11 := hrs + omega + · have h : (17:ℕ) ≤ 11 := hrs + omega + · exact fourYNumber_18_13_1 + · exact fourYNumber_18_13_3 + · exact fourYNumber_18_13_5 + · exact fourYNumber_18_13_7 + · exact fourYNumber_18_13_9 + · exact fourYNumber_18_13_11 + · exact fourYNumber_18_13_13 + · have h : (15:ℕ) ≤ 13 := hrs + omega + · have h : (17:ℕ) ≤ 13 := hrs + omega + · exact fourYNumber_18_15_1 + · exact fourYNumber_18_15_3 + · exact fourYNumber_18_15_5 + · exact fourYNumber_18_15_7 + · exact fourYNumber_18_15_9 + · exact fourYNumber_18_15_11 + · exact fourYNumber_18_15_13 + · exact fourYNumber_18_15_15 + · have h : (17:ℕ) ≤ 15 := hrs + omega + · exact fourYNumber_18_17_1 + · exact fourYNumber_18_17_3 + · exact fourYNumber_18_17_5 + · exact fourYNumber_18_17_7 + · exact fourYNumber_18_17_9 + · exact fourYNumber_18_17_11 + · exact fourYNumber_18_17_13 + · exact fourYNumber_18_17_15 + · exact fourYNumber_18_17_17 + +theorem fourYChecked_18 (r s : CopyLabel 18) : + integerRowsFourTrace 18 r s = fourYData_18 r s := by + have hh : ∀ r s : CopyLabel 18, fourYData_18 r s = fourYData_18 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_18 r s h + · rw [integerRowsFourTrace_symm, fourYLower_18 s r (by omega), hh] + +def fourHighestCache_18_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,16}, [0, -14060114804736000, -8034351316992000, -3640565440512000, -753220435968000, 627683696640000, 502146957312000, -1129830653952000, -4268249137152000]), + ({0,1,3,15}, [0, 14060114804736000, 8034351316992000, 3640565440512000, 753220435968000, -627683696640000, -502146957312000, 1129830653952000, 4268249137152000]), + ({0,1,4,14}, [0, -17575143505920000, -7364822040576000, -2374736652288000, -338949196185600, 334764638208000, 324303243264000, -596299511808000, -3556874280960000]), + ({0,1,5,13}, [0, 16068702633984000, 6121410527232000, 1339058552832000, 0, -104613949440000, -149448499200000, 125536739328000, 2845499424768000]) +] + +def fourHighestCache_18_1 : List (Occupation 24 × List ℚ) := [ + ({0,1,6,12}, [0, -13557967847424000, -4304116776960000, -668724553728000, 101395058688000, 24141680640000, 22417274880000, 125536739328000, -2134124568576000]), + ({0,1,7,11}, [0, 10042939146240000, 2678117105664000, 234979024896000, -57940033536000, -24141680640000, 41845579776000, -188305108992000, 1422749712384000]), + ({0,1,8,10}, [0, -5021469573120000, -1339058552832000, -27360571392000, 7900913664000, 24141680640000, -41845579776000, 125536739328000, -711374856192000]), + ({0,2,3,14}, [0, 3515028701184000, -669529276416000, -1265828788224000, -414271239782400, 292919058432000, 177843714048000, -533531142144000, -711374856192000]) +] + +def fourHighestCache_18_2 : List (Occupation 24 × List ℚ) := [ + ({0,2,4,13}, [0, 1506440871936000, 1243411513344000, 1035678099456000, 338949196185600, -230150688768000, -174854744064000, 470762772480000, 711374856192000]), + ({0,2,5,12}, [0, -2510734786560000, -1817293750272000, -670333999104000, -101395058688000, 80472268800000, 127031224320000, -251073478656000, -711374856192000]), + ({0,2,6,11}, [0, 3515028701184000, 1625999671296000, 433745528832000, -43455025152000, 0, -64262854656000, 62768369664000, 711374856192000]), + ({0,2,7,10}, [0, -5021469573120000, -1339058552832000, -207618453504000, 50039119872000, 0, 0, 62768369664000, -711374856192000]) +] + +def fourHighestCache_18_3 : List (Occupation 24 × List ℚ) := [ + ({0,2,8,9}, [0, 5021469573120000, 1339058552832000, 27360571392000, -7900913664000, -24141680640000, 41845579776000, -125536739328000, 711374856192000]), + ({0,3,4,12}, [0, -4017175658496000, 0, -135193411584000, -162232093900800, 86910050304000, 44834549760000, -156920924160000, 0]), + ({0,3,5,11}, [0, 4017175658496000, 382588157952000, 70815596544000, 115880067072000, -52306974720000, -52306974720000, 141228831744000, 0]), + ({0,3,6,10}, [0, -2510734786560000, -286941118464000, -103809226752000, -17118646272000, 0, 49318004736000, -94152554496000, 0]) +] + +def fourHighestCache_18_4 : List (Occupation 24 × List ℚ) := [ + ({0,3,7,9}, [0, 2008587829248000, 0, 106223394816000, -24229468569600, 16899176448000, -31384184832000, 47076277248000, 0]), + ({0,4,5,10}, [0, -2510734786560000, -286941118464000, 76448655360000, -59256852480000, 24141680640000, 7472424960000, -31384184832000, 0]), + ({0,4,6,9}, [0, 2510734786560000, 286941118464000, -50697529344000, 33973928755200, -9656672256000, -13450364928000, 31384184832000, 0]), + ({0,4,7,8}, [0, -4017175658496000, 0, -32188907520000, 6320730931200, -9656672256000, 20922789888000, -31384184832000, 0]) +] + +def fourHighestCache_18_5 : List (Occupation 24 × List ℚ) := [ + ({0,5,6,8}, [0, 1004293914624000, -191294078976000, 46673915904000, -18435465216000, 8047226880000, -2988969984000, 0, 0]), + ({1,2,3,13}, [0, -5021469573120000, -573882236928000, 230150688768000, 75322043596800, -62768369664000, -2988969984000, 62768369664000, 0]), + ({1,2,4,12}, [0, 5021469573120000, 573882236928000, -230150688768000, -75322043596800, 62768369664000, 2988969984000, -62768369664000, 0]), + ({1,2,5,11}, [0, -5021469573120000, -191294078976000, 165772873728000, 28970016768000, -28165294080000, -10461394944000, 47076277248000, 0]) +] + +def fourHighestCache_18_6 : List (Occupation 24 × List ℚ) := [ + ({1,2,6,10}, [0, 4017175658496000, 0, -122317848576000, 10534551552000, 0, 14944849920000, -31384184832000, 0]), + ({1,2,7,9}, [0, -2008587829248000, 0, 74034487296000, -17908737638400, 7242504192000, -10461394944000, 15692092416000, 0]), + ({1,3,4,11}, [0, 0, -382588157952000, 64377815040000, 46352026828800, -34603075584000, 7472424960000, 15692092416000, 0]), + ({1,3,5,10}, [0, 1004293914624000, 191294078976000, -43455025152000, -39504568320000, 28165294080000, -4483454976000, -15692092416000, 0]) +] + +def fourHighestCache_18_7 : List (Occupation 24 × List ℚ) := [ + ({1,3,6,9}, [0, -2008587829248000, 0, 48283361280000, 7374186086400, -7242504192000, -4483454976000, 15692092416000, 0]), + ({1,3,7,8}, [0, 2008587829248000, 0, -74034487296000, 17908737638400, -7242504192000, 10461394944000, -15692092416000, 0]), + ({1,4,5,9}, [0, 0, 0, -25751126016000, 25282923724800, -14485008384000, 5977939968000, 0, 0]), + ({1,4,6,8}, [0, 502146957312000, -95647039488000, 36212520960000, -21859194470400, 11266117632000, -4483454976000, 0, 0]) +] + +def fourHighestCache_18_8 : List (Occupation 24 × List ℚ) := [ + ({1,5,6,7}, [0, -1004293914624000, 191294078976000, -46673915904000, 18435465216000, -8047226880000, 2988969984000, 0, 0]), + ({2,3,4,10}, [0, -1004293914624000, 191294078976000, -20922789888000, -6847458508800, 6437781504000, -2988969984000, 0, 0]), + ({2,3,5,9}, [0, 1004293914624000, -191294078976000, 20922789888000, 6847458508800, -6437781504000, 2988969984000, 0, 0]), + ({2,3,6,8}, [0, -502146957312000, 95647039488000, -10461394944000, -3423729254400, 3218890752000, -1494484992000, 0, 0]) +] + +def fourHighestCache_18_9 : List (Occupation 24 × List ℚ) := [ + ({2,4,5,8}, [0, -502146957312000, 95647039488000, -10461394944000, -3423729254400, 3218890752000, -1494484992000, 0, 0]), + ({2,4,6,7}, [0, 502146957312000, -95647039488000, 10461394944000, 3423729254400, -3218890752000, 1494484992000, 0, 0]), + ({3,4,5,7}, [0, 0, 0, 0, 0, 0, 0, 0, 0]) +] + +def fourHighestCache_18 : List (Occupation 24 × List ℚ) := fourHighestCache_18_0 ++ fourHighestCache_18_1 ++ fourHighestCache_18_2 ++ fourHighestCache_18_3 ++ fourHighestCache_18_4 ++ fourHighestCache_18_5 ++ fourHighestCache_18_6 ++ fourHighestCache_18_7 ++ fourHighestCache_18_8 ++ fourHighestCache_18_9 + +theorem fourHighestNumber_18_1 : ∀ A∈highestFourOccupations 18, + kernelHighestEntry 18 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_18 1 A := by + rw [fourOccupations_18] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_18_3 : ∀ A∈highestFourOccupations 18, + kernelHighestEntry 18 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_18 3 A := by + rw [fourOccupations_18] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_18_5 : ∀ A∈highestFourOccupations 18, + kernelHighestEntry 18 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_18 5 A := by + rw [fourOccupations_18] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_18_7 : ∀ A∈highestFourOccupations 18, + kernelHighestEntry 18 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_18 7 A := by + rw [fourOccupations_18] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_18_9 : ∀ A∈highestFourOccupations 18, + kernelHighestEntry 18 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_18 9 A := by + rw [fourOccupations_18] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_18_11 : ∀ A∈highestFourOccupations 18, + kernelHighestEntry 18 ⟨⟨11,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_18 11 A := by + rw [fourOccupations_18] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_18_13 : ∀ A∈highestFourOccupations 18, + kernelHighestEntry 18 ⟨⟨13,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_18 13 A := by + rw [fourOccupations_18] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_18_15 : ∀ A∈highestFourOccupations 18, + kernelHighestEntry 18 ⟨⟨15,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_18 15 A := by + rw [fourOccupations_18] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_18_17 : ∀ A∈highestFourOccupations 18, + kernelHighestEntry 18 ⟨⟨17,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_18 17 A := by + rw [fourOccupations_18] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_18 : ∀ r : CopyLabel 18, ∀ A∈highestFourOccupations 18, + kernelHighestEntry 18 r A = highestLookup fourHighestCache_18 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_18_1 + · exact fourHighestNumber_18_3 + · exact fourHighestNumber_18_5 + · exact fourHighestNumber_18_7 + · exact fourHighestNumber_18_9 + · exact fourHighestNumber_18_11 + · exact fourHighestNumber_18_13 + · exact fourHighestNumber_18_15 + · exact fourHighestNumber_18_17 + +theorem fourZChecked_18 (r s : CopyLabel 18) : + integerFourGram 18 r s = fourZData_18 r s := by + rw [integerFourGram_cached 18 fourHighestCache_18 fourHighestChecked_18] + have h : ∀ r s : CopyLabel 18, cachedFourGram 18 fourHighestCache_18 r s = fourZData_18 r s := by + simp only [cachedFourGram, fourOccupations_18] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_18 : + fourZData_18 * (Matrix.diagonal (fun r : CopyLabel 18 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 18 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 18 => rationalCopyDiagonal 18 r.val.val) * + fourYData_18 * Matrix.diagonal (fun r : CopyLabel 18 => rationalCopyDiagonal 18 r.val.val)) * + fourZData_18 = fourLData_18 * Matrix.diagonal fourPivotData_18 * (fourLData_18)ᵀ := by + have h : ∀ r s : CopyLabel 18, + (fourZData_18 * (Matrix.diagonal (fun r : CopyLabel 18 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 18 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 18 => rationalCopyDiagonal 18 r.val.val) * + fourYData_18 * Matrix.diagonal (fun r : CopyLabel 18 => rationalCopyDiagonal 18 r.val.val)) * + fourZData_18 : Matrix (CopyLabel 18) (CopyLabel 18) ℚ) r s = + (fourLData_18 * Matrix.diagonal fourPivotData_18 * (fourLData_18)ᵀ : Matrix (CopyLabel 18) (CopyLabel 18) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_18 : ∀ r, 0 ≤ fourPivotData_18 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_18, copyDiagonalData] + +theorem integer_certificate_18 : + ((integerCompression 18).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_18) (fourPivotData_18) _ fourPivotChecked_18 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 18 = fourYData_18 from Matrix.ext fourYChecked_18, + show integerFourGram 18 = fourZData_18 from Matrix.ext fourZChecked_18] + exact fourLDLChecked_18 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate18Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate18Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..839bffb52f913d80b152f10b3a4ad874645eeb68 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate18Data.lean @@ -0,0 +1,242 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse1802 + +namespace OAI + +/-! Certificate18 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_18 : Matrix (CopyLabel 18) (CopyLabel 18) ℚ := + copyMatrixData 18 [ + [(-66521135019707973636148739444823/838860800000000000000), (252807337181468791157280462398781/41943040000000000000000), (-3252673886370851574147845456127/4194304000000000000000), (5486362141771333842849073567323/33554432000000000000000), (-2995000631158705240266068943069/41943040000000000000000), (969639349882794261211214675001/16777216000000000000000), (-1825892225284111905489652320237/41943040000000000000000), (-1826945530642202491518005975967/33554432000000000000000), 0], + [(252807337181468791157280462398781/41943040000000000000000), (-4007199514466721234466894776687/10485760000000000000000), (3372146185937105246632585623/83886080000000000000), (-537252564751161309170239296177/67108864000000000000000), (326882437778322963441861875919/83886080000000000000000), (-446863114834040129604253847973/167772160000000000000000), (94926062405918105309169939717/83886080000000000000000), (-57423478077219023517144295899/67108864000000000000000), 0], + [(-3252673886370851574147845456127/4194304000000000000000), (3372146185937105246632585623/83886080000000000000), (-23486105657561204635588697229/6710886400000000000000), (13080008728723829467798462239/13421772800000000000000), (-561883338175515088890230073/838860800000000000000), (13256817221098100127860348967/33554432000000000000000), (-529685184269295692581892949/6710886400000000000000), (13124154212646099108768591309/13421772800000000000000), 0], + [(5486362141771333842849073567323/33554432000000000000000), (-537252564751161309170239296177/67108864000000000000000), (13080008728723829467798462239/13421772800000000000000), (-26821902960980170260006245841/53687091200000000000000), (5261464120361048458016212593/13421772800000000000000), (-38369036592682761923577485019/134217728000000000000000), (5710729709386883525559892677/33554432000000000000000), (-18505980504524000026333045251/53687091200000000000000), 0], + [(-2995000631158705240266068943069/41943040000000000000000), (326882437778322963441861875919/83886080000000000000000), (-561883338175515088890230073/838860800000000000000), (5261464120361048458016212593/13421772800000000000000), (-5378965725447864249453406611/16777216000000000000000), (45327067783268824664031633867/167772160000000000000000), (-16829807573720669915736782433/83886080000000000000000), (6451412435501569773360954831/67108864000000000000000), 0], + [(969639349882794261211214675001/16777216000000000000000), (-446863114834040129604253847973/167772160000000000000000), (13256817221098100127860348967/33554432000000000000000), (-38369036592682761923577485019/134217728000000000000000), (45327067783268824664031633867/167772160000000000000000), (-16696042828466646120838082721/67108864000000000000000), (8083429949860810590580083549/41943040000000000000000), (-3918367451570737029679703889/134217728000000000000000), 0], + [(-1825892225284111905489652320237/41943040000000000000000), (94926062405918105309169939717/83886080000000000000000), (-529685184269295692581892949/6710886400000000000000), (5710729709386883525559892677/33554432000000000000000), (-16829807573720669915736782433/83886080000000000000000), (8083429949860810590580083549/41943040000000000000000), (-26274961134789366068159533443/167772160000000000000000), (3426033838439075057449574319/33554432000000000000000), 0], + [(-1826945530642202491518005975967/33554432000000000000000), (-57423478077219023517144295899/67108864000000000000000), (13124154212646099108768591309/13421772800000000000000), (-18505980504524000026333045251/53687091200000000000000), (6451412435501569773360954831/67108864000000000000000), (-3918367451570737029679703889/134217728000000000000000), (3426033838439075057449574319/33554432000000000000000), (-23010186633185192976943168761/53687091200000000000000), 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0] + ] + +def fourZData_18 : Matrix (CopyLabel 18) (CopyLabel 18) ℚ := + copyMatrixData 18 [ + [0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 980755776000, 0, 0, 0, 0, 0, (-13408770375/8), (32564156625/2)], + [0, 0, 23351328000, 0, 0, 0, -273648375, 0, (10854718875/2)], + [0, 0, 0, 1571724000, 0, (-736745625/8), (-638512875/4), (40226311125/128), (32564156625/32)], + [0, 0, 0, 0, 192893400, (-442047375/4), 0, (5746615875/64), 0], + [0, 0, 0, (-736745625/8), (-442047375/4), (4666055625/64), 0, (-105354624375/2048), (-54273594375/512)], + [0, 0, -273648375, (-638512875/4), 0, 0, (10307422125/256), (-74706006375/1024), (-32564156625/512)], + [0, (-13408770375/8), 0, (40226311125/128), (5746615875/64), (-105354624375/2048), (-74706006375/1024), (6169949911125/32768), (-227949096375/8192)], + [0, (32564156625/2), (10854718875/2), (32564156625/32), 0, (-54273594375/512), (-32564156625/512), (-227949096375/8192), (2767953313125/1024)] + ] + +def fourLData_18 : Matrix (CopyLabel 18) (CopyLabel 18) ℚ := + copyMatrixData 18 [ + [1, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0, 0, 0, 0], + [0, (-19622685426805868627669012/241834110471751660293852243), 1, 0, 0, 0, 0, 0, 0], + [0, (11907899514743343096973993/3869345767548026564701635888), (-942959943853497737532933439001756109065712828299/2521638922497384864691980677182886104546196483056), 1, 0, 0, 0, 0, 0], + [0, (-1088215349783697235979995/71654551250889380827808072), (-579204823628016596624476603524201143561035964799/1260819461248692432345990338591443052273098241528), (-322101729697288344392147952249607776977585870663556408186825263663526/896556691289636709022246400557524688955271263723517547157923999074815), 1, 0, 0, 0, 0], + [0, (65578238647888838567920175/7738691535096053129403271776), (11390305541518521331259601334244984541751526760805/40346222759958157835071690834926177672739143728896), (1764525143126657426552304672749480878308638515903065614115538950149393/8606944236380512406613565445352237013970604131745768452716070391118224), (-746964701974071644619763663296766133499353785736298568429784445370119583960533835042401385/1257803672830877627227527488195898541504022219668692957498233729040566442330578330255827872), 1, 0, 0, 0], + [0, (5741174184871059350371589/7738691535096053129403271776), (1310160080619562486842653224134698432946302730817/40346222759958157835071690834926177672739143728896), (-330394004973020203955159581918403323443812496648608511748486056799217/1434490706063418734435594240892039502328434021957628075452678398519704), (611650334627304855241497353688554267704941174400765416464543741776492457522000000000000/13102121591988308616953411335373943140666898121548884973939934677505900440943524273498207), (-78/35), 1, 0, 0], + [0, (-4796259647520084320930065/573236410007115046622464576), (-24275911090440877486016355576015295113520593409485/80692445519916315670143381669852355345478287457792), (821129026386347956739303799931901501603816085711306781981372049648123/2868981412126837468871188481784079004656868043915256150905356797039408), (2506128775452890259623800369079393746679030015173179378992757673094868541242697285183739335/6708286255098014011880146603711458888021451838233029106657246554883021025763084428031081984), (351/80), 0, 1, 0], + [0, (20045312000000000000000/80611370157250553431284081), (3327001416275461411445027332595808000000000000/157602432656086554043248792323930381534137280191), (4858111925195910439364072755509308781395355553047854473600000000000/537934014773782025413347840334514813373162758234110528294754399444889), (9098298727581159721717273136117244732110999969211385569910088158925325305639750000000000/39306364775964925850860234006121829422000694364646654921819804032517701322830572820494621), (-221/20), 0, 0, 1] + ] + +def fourPivotData_18 : CopyLabel 18 → ℚ := + copyDiagonalData 18 [0, (529420090801322601943717510296441/1342177280000000000000000), (1825508977455450555482950761488085609309912116452353/939190534155657292386245961318400000000000000), (634112851077230835083076540751443720400590647267061851980158422784839038977/264413005479661783187925833055772197996063252341692825600000000000000), (1805223415065741149552457967199157259864225890085126920594418139801440468653639717926856458667/14689184830089407840620485026734484503843164384846111492635426800841768960000000000000000), (44794141803382999890132162011222314683603629634860904805225482207148310449269562829938841063801523/732723746690172410470962146368056949475623112784066325889815517034689443240682501792408314839040), 0, 0, 0] + +theorem fourOccupations_18 : highestFourOccupations 18 = {{0,1,2,16}, {0,1,3,15}, {0,1,4,14}, {0,1,5,13}, {0,1,6,12}, {0,1,7,11}, {0,1,8,10}, {0,2,3,14}, {0,2,4,13}, {0,2,5,12}, {0,2,6,11}, {0,2,7,10}, {0,2,8,9}, {0,3,4,12}, {0,3,5,11}, {0,3,6,10}, {0,3,7,9}, {0,4,5,10}, {0,4,6,9}, {0,4,7,8}, {0,5,6,8}, {1,2,3,13}, {1,2,4,12}, {1,2,5,11}, {1,2,6,10}, {1,2,7,9}, {1,3,4,11}, {1,3,5,10}, {1,3,6,9}, {1,3,7,8}, {1,4,5,9}, {1,4,6,8}, {1,5,6,7}, {2,3,4,10}, {2,3,5,9}, {2,3,6,8}, {2,4,5,8}, {2,4,6,7}, {3,4,5,7}} := by + decide +kernel + +theorem fourYNumber_18_1_1 : + (collectedFourTrace 18 1 1 collectedFourData_18 : ℚ) / fourCommonDenominator = (-66521135019707973636148739444823/838860800000000000000) := by + decide +kernel + +theorem fourYNumber_18_3_1 : + (collectedFourTrace 18 3 1 collectedFourData_18 : ℚ) / fourCommonDenominator = (252807337181468791157280462398781/41943040000000000000000) := by + decide +kernel + +theorem fourYNumber_18_3_3 : + (collectedFourTrace 18 3 3 collectedFourData_18 : ℚ) / fourCommonDenominator = (-4007199514466721234466894776687/10485760000000000000000) := by + decide +kernel + +theorem fourYNumber_18_5_1 : + (collectedFourTrace 18 5 1 collectedFourData_18 : ℚ) / fourCommonDenominator = (-3252673886370851574147845456127/4194304000000000000000) := by + decide +kernel + +theorem fourYNumber_18_5_3 : + (collectedFourTrace 18 5 3 collectedFourData_18 : ℚ) / fourCommonDenominator = (3372146185937105246632585623/83886080000000000000) := by + decide +kernel + +theorem fourYNumber_18_5_5 : + (collectedFourTrace 18 5 5 collectedFourData_18 : ℚ) / fourCommonDenominator = (-23486105657561204635588697229/6710886400000000000000) := by + decide +kernel + +theorem fourYNumber_18_7_1 : + (collectedFourTrace 18 7 1 collectedFourData_18 : ℚ) / fourCommonDenominator = (5486362141771333842849073567323/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_18_7_3 : + (collectedFourTrace 18 7 3 collectedFourData_18 : ℚ) / fourCommonDenominator = (-537252564751161309170239296177/67108864000000000000000) := by + decide +kernel + +theorem fourYNumber_18_7_5 : + (collectedFourTrace 18 7 5 collectedFourData_18 : ℚ) / fourCommonDenominator = (13080008728723829467798462239/13421772800000000000000) := by + decide +kernel + +theorem fourYNumber_18_7_7 : + (collectedFourTrace 18 7 7 collectedFourData_18 : ℚ) / fourCommonDenominator = (-26821902960980170260006245841/53687091200000000000000) := by + decide +kernel + +theorem fourYNumber_18_9_1 : + (collectedFourTrace 18 9 1 collectedFourData_18 : ℚ) / fourCommonDenominator = (-2995000631158705240266068943069/41943040000000000000000) := by + decide +kernel + +theorem fourYNumber_18_9_3 : + (collectedFourTrace 18 9 3 collectedFourData_18 : ℚ) / fourCommonDenominator = (326882437778322963441861875919/83886080000000000000000) := by + decide +kernel + +theorem fourYNumber_18_9_5 : + (collectedFourTrace 18 9 5 collectedFourData_18 : ℚ) / fourCommonDenominator = (-561883338175515088890230073/838860800000000000000) := by + decide +kernel + +theorem fourYNumber_18_9_7 : + (collectedFourTrace 18 9 7 collectedFourData_18 : ℚ) / fourCommonDenominator = (5261464120361048458016212593/13421772800000000000000) := by + decide +kernel + +theorem fourYNumber_18_9_9 : + (collectedFourTrace 18 9 9 collectedFourData_18 : ℚ) / fourCommonDenominator = (-5378965725447864249453406611/16777216000000000000000) := by + decide +kernel + +theorem fourYNumber_18_11_1 : + (collectedFourTrace 18 11 1 collectedFourData_18 : ℚ) / fourCommonDenominator = (969639349882794261211214675001/16777216000000000000000) := by + decide +kernel + +theorem fourYNumber_18_11_3 : + (collectedFourTrace 18 11 3 collectedFourData_18 : ℚ) / fourCommonDenominator = (-446863114834040129604253847973/167772160000000000000000) := by + decide +kernel + +theorem fourYNumber_18_11_5 : + (collectedFourTrace 18 11 5 collectedFourData_18 : ℚ) / fourCommonDenominator = (13256817221098100127860348967/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_18_11_7 : + (collectedFourTrace 18 11 7 collectedFourData_18 : ℚ) / fourCommonDenominator = (-38369036592682761923577485019/134217728000000000000000) := by + decide +kernel + +theorem fourYNumber_18_11_9 : + (collectedFourTrace 18 11 9 collectedFourData_18 : ℚ) / fourCommonDenominator = (45327067783268824664031633867/167772160000000000000000) := by + decide +kernel + +theorem fourYNumber_18_11_11 : + (collectedFourTrace 18 11 11 collectedFourData_18 : ℚ) / fourCommonDenominator = (-16696042828466646120838082721/67108864000000000000000) := by + decide +kernel + +theorem fourYNumber_18_13_1 : + (collectedFourTrace 18 13 1 collectedFourData_18 : ℚ) / fourCommonDenominator = (-1825892225284111905489652320237/41943040000000000000000) := by + decide +kernel + +theorem fourYNumber_18_13_3 : + (collectedFourTrace 18 13 3 collectedFourData_18 : ℚ) / fourCommonDenominator = (94926062405918105309169939717/83886080000000000000000) := by + decide +kernel + +theorem fourYNumber_18_13_5 : + (collectedFourTrace 18 13 5 collectedFourData_18 : ℚ) / fourCommonDenominator = (-529685184269295692581892949/6710886400000000000000) := by + decide +kernel + +theorem fourYNumber_18_13_7 : + (collectedFourTrace 18 13 7 collectedFourData_18 : ℚ) / fourCommonDenominator = (5710729709386883525559892677/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_18_13_9 : + (collectedFourTrace 18 13 9 collectedFourData_18 : ℚ) / fourCommonDenominator = (-16829807573720669915736782433/83886080000000000000000) := by + decide +kernel + +theorem fourYNumber_18_13_11 : + (collectedFourTrace 18 13 11 collectedFourData_18 : ℚ) / fourCommonDenominator = (8083429949860810590580083549/41943040000000000000000) := by + decide +kernel + +theorem fourYNumber_18_13_13 : + (collectedFourTrace 18 13 13 collectedFourData_18 : ℚ) / fourCommonDenominator = (-26274961134789366068159533443/167772160000000000000000) := by + decide +kernel + +theorem fourYNumber_18_15_1 : + (collectedFourTrace 18 15 1 collectedFourData_18 : ℚ) / fourCommonDenominator = (-1826945530642202491518005975967/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_18_15_3 : + (collectedFourTrace 18 15 3 collectedFourData_18 : ℚ) / fourCommonDenominator = (-57423478077219023517144295899/67108864000000000000000) := by + decide +kernel + +theorem fourYNumber_18_15_5 : + (collectedFourTrace 18 15 5 collectedFourData_18 : ℚ) / fourCommonDenominator = (13124154212646099108768591309/13421772800000000000000) := by + decide +kernel + +theorem fourYNumber_18_15_7 : + (collectedFourTrace 18 15 7 collectedFourData_18 : ℚ) / fourCommonDenominator = (-18505980504524000026333045251/53687091200000000000000) := by + decide +kernel + +theorem fourYNumber_18_15_9 : + (collectedFourTrace 18 15 9 collectedFourData_18 : ℚ) / fourCommonDenominator = (6451412435501569773360954831/67108864000000000000000) := by + decide +kernel + +theorem fourYNumber_18_15_11 : + (collectedFourTrace 18 15 11 collectedFourData_18 : ℚ) / fourCommonDenominator = (-3918367451570737029679703889/134217728000000000000000) := by + decide +kernel + +theorem fourYNumber_18_15_13 : + (collectedFourTrace 18 15 13 collectedFourData_18 : ℚ) / fourCommonDenominator = (3426033838439075057449574319/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_18_15_15 : + (collectedFourTrace 18 15 15 collectedFourData_18 : ℚ) / fourCommonDenominator = (-23010186633185192976943168761/53687091200000000000000) := by + decide +kernel + +theorem fourYNumber_18_17_1 : + (collectedFourTrace 18 17 1 collectedFourData_18 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_18_17_3 : + (collectedFourTrace 18 17 3 collectedFourData_18 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_18_17_5 : + (collectedFourTrace 18 17 5 collectedFourData_18 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_18_17_7 : + (collectedFourTrace 18 17 7 collectedFourData_18 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_18_17_9 : + (collectedFourTrace 18 17 9 collectedFourData_18 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_18_17_11 : + (collectedFourTrace 18 17 11 collectedFourData_18 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_18_17_13 : + (collectedFourTrace 18 17 13 collectedFourData_18 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_18_17_15 : + (collectedFourTrace 18 17 15 collectedFourData_18 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_18_17_17 : + (collectedFourTrace 18 17 17 collectedFourData_18 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate19.lean b/lean/OAI/Analysis/LaughlinFock/Certificate19.lean new file mode 100644 index 0000000000000000000000000000000000000000..e6c4361c2d35634bfce95d6429303f83922f2bce --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate19.lean @@ -0,0 +1,373 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate19Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate19. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_19 (r s : CopyLabel 19) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 19 r s = fourYData_19 r s := by + rw [integerRowsFourTrace_collected (by decide) collectedFourData_19 collectedFourChecked_19] + fin_cases r <;> fin_cases s + · exact fourYNumber_19_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · have h : (13:ℕ) ≤ 1 := hrs + omega + · have h : (15:ℕ) ≤ 1 := hrs + omega + · have h : (17:ℕ) ≤ 1 := hrs + omega + · have h : (19:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_19_3_1 + · exact fourYNumber_19_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · have h : (13:ℕ) ≤ 3 := hrs + omega + · have h : (15:ℕ) ≤ 3 := hrs + omega + · have h : (17:ℕ) ≤ 3 := hrs + omega + · have h : (19:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_19_5_1 + · exact fourYNumber_19_5_3 + · exact fourYNumber_19_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · have h : (13:ℕ) ≤ 5 := hrs + omega + · have h : (15:ℕ) ≤ 5 := hrs + omega + · have h : (17:ℕ) ≤ 5 := hrs + omega + · have h : (19:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_19_7_1 + · exact fourYNumber_19_7_3 + · exact fourYNumber_19_7_5 + · exact fourYNumber_19_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · have h : (13:ℕ) ≤ 7 := hrs + omega + · have h : (15:ℕ) ≤ 7 := hrs + omega + · have h : (17:ℕ) ≤ 7 := hrs + omega + · have h : (19:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_19_9_1 + · exact fourYNumber_19_9_3 + · exact fourYNumber_19_9_5 + · exact fourYNumber_19_9_7 + · exact fourYNumber_19_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · have h : (13:ℕ) ≤ 9 := hrs + omega + · have h : (15:ℕ) ≤ 9 := hrs + omega + · have h : (17:ℕ) ≤ 9 := hrs + omega + · have h : (19:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_19_11_1 + · exact fourYNumber_19_11_3 + · exact fourYNumber_19_11_5 + · exact fourYNumber_19_11_7 + · exact fourYNumber_19_11_9 + · exact fourYNumber_19_11_11 + · have h : (13:ℕ) ≤ 11 := hrs + omega + · have h : (15:ℕ) ≤ 11 := hrs + omega + · have h : (17:ℕ) ≤ 11 := hrs + omega + · have h : (19:ℕ) ≤ 11 := hrs + omega + · exact fourYNumber_19_13_1 + · exact fourYNumber_19_13_3 + · exact fourYNumber_19_13_5 + · exact fourYNumber_19_13_7 + · exact fourYNumber_19_13_9 + · exact fourYNumber_19_13_11 + · exact fourYNumber_19_13_13 + · have h : (15:ℕ) ≤ 13 := hrs + omega + · have h : (17:ℕ) ≤ 13 := hrs + omega + · have h : (19:ℕ) ≤ 13 := hrs + omega + · exact fourYNumber_19_15_1 + · exact fourYNumber_19_15_3 + · exact fourYNumber_19_15_5 + · exact fourYNumber_19_15_7 + · exact fourYNumber_19_15_9 + · exact fourYNumber_19_15_11 + · exact fourYNumber_19_15_13 + · exact fourYNumber_19_15_15 + · have h : (17:ℕ) ≤ 15 := hrs + omega + · have h : (19:ℕ) ≤ 15 := hrs + omega + · exact fourYNumber_19_17_1 + · exact fourYNumber_19_17_3 + · exact fourYNumber_19_17_5 + · exact fourYNumber_19_17_7 + · exact fourYNumber_19_17_9 + · exact fourYNumber_19_17_11 + · exact fourYNumber_19_17_13 + · exact fourYNumber_19_17_15 + · exact fourYNumber_19_17_17 + · have h : (19:ℕ) ≤ 17 := hrs + omega + · exact fourYNumber_19_19_1 + · exact fourYNumber_19_19_3 + · exact fourYNumber_19_19_5 + · exact fourYNumber_19_19_7 + · exact fourYNumber_19_19_9 + · exact fourYNumber_19_19_11 + · exact fourYNumber_19_19_13 + · exact fourYNumber_19_19_15 + · exact fourYNumber_19_19_17 + · exact fourYNumber_19_19_19 + +theorem fourYChecked_19 (r s : CopyLabel 19) : + integerRowsFourTrace 19 r s = fourYData_19 r s := by + have hh : ∀ r s : CopyLabel 19, fourYData_19 r s = fourYData_19 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_19 r s h + · rw [integerRowsFourTrace_symm, fourYLower_19 s r (by omega), hh] + +def fourHighestCache_19_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,17}, [819503834333184000, 273167944777728000, 166461716348928000, 83230858174464000, 25609494822912000, -6402373705728000, -12804747411456000, 6402373705728000, 51218989645824000, 121645100408832000]), + ({0,1,3,16}, [-819503834333184000, -273167944777728000, -166461716348928000, -83230858174464000, -25609494822912000, 6402373705728000, 12804747411456000, -6402373705728000, -51218989645824000, -121645100408832000]), + ({0,1,4,15}, [1434131710083072000, 365562984923136000, 161251941666816000, 59033651668992000, 13369662738432000, -3828870549504000, -7249746696192000, 1977203644416000, 36280117665792000, 121645100408832000]), + ({0,1,5,14}, [-1434131710083072000, -365562984923136000, -137818416992256000, -37943479461888000, -3577797070848000, 1987665039360000, 2353813862400000, 1537825056768000, -22052620541952000, -121645100408832000]) +] + +def fourHighestCache_19_1 : List (Occupation 24 × List ℚ) := [ + ({0,1,6,13}, [1843883627249664000, 373597336240128000, 101873063964672000, 21309861500928000, -188305108992000, -1255367393280000, 112086374400000, -2385198047232000, 10670622842880000, 121645100408832000]), + ({0,1,7,12}, [-1843883627249664000, -373597336240128000, -71744246525952000, -9026574391296000, 593885343744000, 830473814016000, -596299511808000, 1380904132608000, -2134124568576000, -121645100408832000]), + ({0,1,8,11}, [2048759585832960000, 361545809264640000, 49921776672768000, 2351399694336000, -463520268288000, -275215159296000, 125536739328000, 125536739328000, -3556874280960000, 121645100408832000]), + ({0,1,9,10}, [-2048759585832960000, -361545809264640000, -36531191144448000, -188305108992000, 568865783808000, -188305108992000, 376610217984000, -1129830653952000, 6402373705728000, -121645100408832000]) +] + +def fourHighestCache_19_2 : List (Occupation 24 × List ℚ) := [ + ({0,2,3,15}, [-614627875749888000, -92395040145408000, 5209774682112000, 24197206505472000, 12239832084480000, -2573503156224000, -5555000715264000, 4425170061312000, 14938871980032000, 0]), + ({0,2,4,14}, [0, 0, -23433524674560000, -21090172207104000, -9791865667584000, 1841205510144000, 4895932833792000, -3515028701184000, -14227497123840000, 0]), + ({0,2,5,13}, [-409751917166592000, -8034351316992000, 35945353027584000, 16633617960960000, 3766102179840000, -732297646080000, -2465900236800000, 847372990464000, 11381997699072000, 0]), + ({0,2,6,12}, [0, 0, -30128817438720000, -12283287109632000, -405580234752000, 424893579264000, 484213137408000, 1004293914624000, -8536498274304000, 0]) +] + +def fourHighestCache_19_3 : List (Occupation 24 × List ℚ) := [ + ({0,2,7,11}, [-204875958583296000, 12051526975488000, 21822469853184000, 6675174696960000, -130365075456000, -555258654720000, 470762772480000, -1506440871936000, 5690998849536000, 0]), + ({0,2,8,10}, [0, 0, -13390585528320000, -2163094585344000, -105345515520000, 463520268288000, -502146957312000, 1004293914624000, -2845499424768000, 0]), + ({0,3,4,13}, [1024379792916480000, 100429391462400000, 5711921639424000, 1349519947776000, 3577797070848000, -376610217984000, -1770964715520000, 1757514350592000, 2134124568576000, 0]), + ({0,3,5,12}, [-614627875749888000, -92395040145408000, -14876103610368000, -1296408250368000, -2245176299520000, -24141680640000, 1546791966720000, -1349519947776000, -2134124568576000, 0]) +] + +def fourHighestCache_19_4 : List (Occupation 24 × List ℚ) := [ + ({0,3,6,11}, [1229255751499776000, 88377864486912000, 10670622842880000, 2708696567808000, 463520268288000, 178648436736000, -753220435968000, 376610217984000, 2134124568576000, 0]), + ({0,3,7,10}, [-1024379792916480000, -100429391462400000, -5711921639424000, -2585573996544000, 46088663040000, 67596705792000, 31384184832000, 376610217984000, -2134124568576000, 0]), + ({0,3,8,9}, [1229255751499776000, 88377864486912000, 6653447184384000, 1318135762944000, 179087376384000, -362125209600000, 376610217984000, -753220435968000, 2134124568576000, 0]), + ({0,4,5,11}, [-614627875749888000, 4017175658496000, 10900773531648000, -1566795073536000, 738735427584000, 128755630080000, -560431872000000, 596299511808000, 0, 0]) +] + +def fourHighestCache_19_5 : List (Occupation 24 × List ℚ) := [ + ({0,4,6,10}, [0, 0, -10042939146240000, 849787158528000, -247561961472000, -270386823168000, 520080777216000, -502146957312000, 0, 0]), + ({0,4,7,9}, [-204875958583296000, 12051526975488000, 3075650113536000, 185890940928000, -109295972352000, 217275125760000, -282457663488000, 251073478656000, 0, 0]), + ({0,5,6,9}, [614627875749888000, -4017175658496000, 5837458378752000, -673552889856000, 67157766144000, 115880067072000, -174854744064000, 156920924160000, 0, 0]), + ({0,5,7,8}, [-409751917166592000, -8034351316992000, -4226403557376000, 255901814784000, 79009136640000, -165772873728000, 188305108992000, -156920924160000, 0, 0]) +] + +def fourHighestCache_19_6 : List (Occupation 24 × List ℚ) := [ + ({1,2,3,14}, [614627875749888000, 92395040145408000, 18223749992448000, -3107034298368000, -2447966416896000, 732297646080000, 659067881472000, -910141360128000, -711374856192000, 0]), + ({1,2,4,13}, [-614627875749888000, -92395040145408000, -18223749992448000, 3107034298368000, 2447966416896000, -732297646080000, -659067881472000, 910141360128000, 711374856192000, 0]), + ({1,2,5,12}, [1024379792916480000, 100429391462400000, 9059568021504000, -3053922600960000, -1115345645568000, 331545747456000, 434895132672000, -502146957312000, -711374856192000, 0]), + ({1,2,6,11}, [-1024379792916480000, -100429391462400000, -2364275257344000, 2899415844864000, 72425041920000, -48283361280000, -201755473920000, 125536739328000, 711374856192000, 0]) +] + +def fourHighestCache_19_7 : List (Occupation 24 × List ℚ) := [ + ({1,2,7,10}, [1229255751499776000, 88377864486912000, -2719962685440000, -1926506115072000, 189621927936000, 24141680640000, 0, 125536739328000, -711374856192000, 0]), + ({1,2,8,9}, [-1229255751499776000, -88377864486912000, 6737138343936000, 844958822400000, -73741860864000, -101395058688000, 125536739328000, -251073478656000, 711374856192000, 0]), + ({1,3,4,12}, [-409751917166592000, -8034351316992000, 9164181970944000, -53111697408000, -1332620771328000, 400751898624000, 224172748800000, -407994402816000, 0, 0]), + ({1,3,5,11}, [0, 0, -6695292764160000, 154506756096000, 1042920603648000, -283262386176000, -233139658752000, 376610217984000, 0, 0]) +] + +def fourHighestCache_19_8 : List (Occupation 24 × List ℚ) := [ + ({1,3,6,10}, [-204875958583296000, 12051526975488000, 5084237942784000, -972909729792000, -262046969856000, 24141680640000, 201755473920000, -251073478656000, 0, 0]), + ({1,3,7,9}, [0, 0, -4017175658496000, 1081547292672000, -115880067072000, 77253378048000, -125536739328000, 125536739328000, 0, 0]), + ({1,4,5,10}, [614627875749888000, -4017175658496000, -857834385408000, 717007915008000, -491173466112000, 141631193088000, 40351094784000, -94152554496000, 0, 0]), + ({1,4,6,9}, [-409751917166592000, -8034351316992000, 1129830653952000, -362125209600000, 289700167680000, -62768369664000, -62768369664000, 94152554496000, 0, 0]) +] + +def fourHighestCache_19_9 : List (Occupation 24 × List ℚ) := [ + ({1,4,7,8}, [614627875749888000, -4017175658496000, 1150753443840000, -441792755712000, 30286835712000, -51502252032000, 94152554496000, -94152554496000, 0, 0]), + ({1,5,6,8}, [-204875958583296000, 12051526975488000, -1611054821376000, 417651075072000, -146166902784000, 49892806656000, -13450364928000, 0, 0, 0]), + ({2,3,4,11}, [409751917166592000, 8034351316992000, -2468889206784000, -101395058688000, 289700167680000, -117489512448000, 8966909952000, 31384184832000, 0, 0]), + ({2,3,5,10}, [-409751917166592000, -8034351316992000, 2468889206784000, 101395058688000, -289700167680000, 117489512448000, -8966909952000, -31384184832000, 0, 0]) +] + +def fourHighestCache_19_10 : List (Occupation 24 × List ℚ) := [ + ({2,3,6,9}, [614627875749888000, -4017175658496000, -2196892938240000, 253487646720000, 88226869248000, -38626689024000, -13450364928000, 31384184832000, 0, 0]), + ({2,3,7,8}, [-614627875749888000, 4017175658496000, 2866422214656000, -639754536960000, 85593231360000, -25751126016000, 31384184832000, -31384184832000, 0, 0]), + ({2,4,5,9}, [-204875958583296000, 12051526975488000, -271996268544000, -354882705408000, 201473298432000, -78862823424000, 22417274880000, 0, 0, 0]), + ({2,4,6,8}, [0, 0, -669529276416000, 386266890240000, -173820100608000, 64377815040000, -17933819904000, 0, 0, 0]) +] + +def fourHighestCache_19_11 : List (Occupation 24 × List ℚ) := [ + ({2,5,6,7}, [204875958583296000, -12051526975488000, 1611054821376000, -417651075072000, 146166902784000, -49892806656000, 13450364928000, 0, 0, 0]), + ({3,4,5,8}, [204875958583296000, -12051526975488000, 941525544960000, -31384184832000, -27653197824000, 14485008384000, -4483454976000, 0, 0, 0]), + ({3,4,6,7}, [-204875958583296000, 12051526975488000, -941525544960000, 31384184832000, 27653197824000, -14485008384000, 4483454976000, 0, 0, 0]) +] + +def fourHighestCache_19 : List (Occupation 24 × List ℚ) := fourHighestCache_19_0 ++ fourHighestCache_19_1 ++ fourHighestCache_19_2 ++ fourHighestCache_19_3 ++ fourHighestCache_19_4 ++ fourHighestCache_19_5 ++ fourHighestCache_19_6 ++ fourHighestCache_19_7 ++ fourHighestCache_19_8 ++ fourHighestCache_19_9 ++ fourHighestCache_19_10 ++ fourHighestCache_19_11 + +theorem fourHighestNumber_19_1 : ∀ A∈highestFourOccupations 19, + kernelHighestEntry 19 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_19 1 A := by + rw [fourOccupations_19] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_19_3 : ∀ A∈highestFourOccupations 19, + kernelHighestEntry 19 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_19 3 A := by + rw [fourOccupations_19] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_19_5 : ∀ A∈highestFourOccupations 19, + kernelHighestEntry 19 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_19 5 A := by + rw [fourOccupations_19] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_19_7 : ∀ A∈highestFourOccupations 19, + kernelHighestEntry 19 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_19 7 A := by + rw [fourOccupations_19] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_19_9 : ∀ A∈highestFourOccupations 19, + kernelHighestEntry 19 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_19 9 A := by + rw [fourOccupations_19] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_19_11 : ∀ A∈highestFourOccupations 19, + kernelHighestEntry 19 ⟨⟨11,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_19 11 A := by + rw [fourOccupations_19] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_19_13 : ∀ A∈highestFourOccupations 19, + kernelHighestEntry 19 ⟨⟨13,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_19 13 A := by + rw [fourOccupations_19] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_19_15 : ∀ A∈highestFourOccupations 19, + kernelHighestEntry 19 ⟨⟨15,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_19 15 A := by + rw [fourOccupations_19] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_19_17 : ∀ A∈highestFourOccupations 19, + kernelHighestEntry 19 ⟨⟨17,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_19 17 A := by + rw [fourOccupations_19] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_19_19 : ∀ A∈highestFourOccupations 19, + kernelHighestEntry 19 ⟨⟨19,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_19 19 A := by + rw [fourOccupations_19] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_19 : ∀ r : CopyLabel 19, ∀ A∈highestFourOccupations 19, + kernelHighestEntry 19 r A = highestLookup fourHighestCache_19 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_19_1 + · exact fourHighestNumber_19_3 + · exact fourHighestNumber_19_5 + · exact fourHighestNumber_19_7 + · exact fourHighestNumber_19_9 + · exact fourHighestNumber_19_11 + · exact fourHighestNumber_19_13 + · exact fourHighestNumber_19_15 + · exact fourHighestNumber_19_17 + · exact fourHighestNumber_19_19 + +theorem fourZChecked_19 (r s : CopyLabel 19) : + integerFourGram 19 r s = fourZData_19 r s := by + rw [integerFourGram_cached 19 fourHighestCache_19 fourHighestChecked_19] + have h : ∀ r s : CopyLabel 19, cachedFourGram 19 fourHighestCache_19 r s = fourZData_19 r s := by + simp only [cachedFourGram, fourOccupations_19] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_19 : + fourZData_19 * (Matrix.diagonal (fun r : CopyLabel 19 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 19 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 19 => rationalCopyDiagonal 19 r.val.val) * + fourYData_19 * Matrix.diagonal (fun r : CopyLabel 19 => rationalCopyDiagonal 19 r.val.val)) * + fourZData_19 = fourLData_19 * Matrix.diagonal fourPivotData_19 * (fourLData_19)ᵀ := by + have h : ∀ r s : CopyLabel 19, + (fourZData_19 * (Matrix.diagonal (fun r : CopyLabel 19 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 19 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 19 => rationalCopyDiagonal 19 r.val.val) * + fourYData_19 * Matrix.diagonal (fun r : CopyLabel 19 => rationalCopyDiagonal 19 r.val.val)) * + fourZData_19 : Matrix (CopyLabel 19) (CopyLabel 19) ℚ) r s = + (fourLData_19 * Matrix.diagonal fourPivotData_19 * (fourLData_19)ᵀ : Matrix (CopyLabel 19) (CopyLabel 19) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_19 : ∀ r, 0 ≤ fourPivotData_19 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_19, copyDiagonalData] + +theorem integer_certificate_19 : + ((integerCompression 19).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_19) (fourPivotData_19) _ fourPivotChecked_19 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 19 = fourYData_19 from Matrix.ext fourYChecked_19, + show integerFourGram 19 = fourZData_19 from Matrix.ext fourZChecked_19] + exact fourLDLChecked_19 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate19Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate19Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..1fbd816d96a7f3917f43ed09372993fc4f6dc62b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate19Data.lean @@ -0,0 +1,285 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse19 + +namespace OAI + +/-! Certificate19 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_19 : Matrix (CopyLabel 19) (CopyLabel 19) ℚ := + copyMatrixData 19 [ + [(-5179636017239466145793848200719937/20971520000000000000000), (187434720909027305797300194104127/8388608000000000000000), (-2655089774899248756771754225173/838860800000000000000), (16881332854132320143988817820421/33554432000000000000000), (-194634222784906412908126173447/8388608000000000000000), (-4278863868672885847019994838509/83886080000000000000000), (-92711834507674027889855562951/8388608000000000000000), (6869519969496381960085415099007/33554432000000000000000), 0, 0], + [(187434720909027305797300194104127/8388608000000000000000), (-178409637091064952160509455064531/83886080000000000000000), (5621260360207772838458389165677/16777216000000000000000), (-4717729566947090956657038913269/67108864000000000000000), (284747204857559498276849187561/16777216000000000000000), (-36590419351896827609695794291/6710886400000000000000), (78521760071585338639486774419/10485760000000000000000), (-1321637020094633023479152437983/67108864000000000000000), 0, 0], + [(-2655089774899248756771754225173/838860800000000000000), (5621260360207772838458389165677/16777216000000000000000), (-426035399881728630302625737421/6710886400000000000000), (245031192885525934544085492063/13421772800000000000000), (-1557730163651995099526246487/209715200000000000000), (27876208643370085842832469481/6710886400000000000000), (-105195415768801818681315887793/33554432000000000000000), (38229925041583923398630108229/13421772800000000000000), 0, 0], + [(16881332854132320143988817820421/33554432000000000000000), (-4717729566947090956657038913269/67108864000000000000000), (245031192885525934544085492063/13421772800000000000000), (-384466433084035638058510508259/53687091200000000000000), (10123087280082182882087994459/2684354560000000000000), (-322902858771556364114391557133/134217728000000000000000), (26165622301296628386942262557/16777216000000000000000), (-23973293068487386195658999913/53687091200000000000000), 0, 0], + [(-194634222784906412908126173447/8388608000000000000000), (284747204857559498276849187561/16777216000000000000000), (-1557730163651995099526246487/209715200000000000000), (10123087280082182882087994459/2684354560000000000000), (-7622943311608357206631060953/3355443200000000000000), (51386596016276650248544081041/33554432000000000000000), (-15903873537826236008064465447/16777216000000000000000), (125491751932979281769752833/2684354560000000000000), 0, 0], + [(-4278863868672885847019994838509/83886080000000000000000), (-36590419351896827609695794291/6710886400000000000000), (27876208643370085842832469481/6710886400000000000000), (-322902858771556364114391557133/134217728000000000000000), (51386596016276650248544081041/33554432000000000000000), (-357286302839183067236886747363/335544320000000000000000), (1423697597371070492775004701/2097152000000000000000), (-8162389557098350440321766311/134217728000000000000000), 0, 0], + [(-92711834507674027889855562951/8388608000000000000000), (78521760071585338639486774419/10485760000000000000000), (-105195415768801818681315887793/33554432000000000000000), (26165622301296628386942262557/16777216000000000000000), (-15903873537826236008064465447/16777216000000000000000), (1423697597371070492775004701/2097152000000000000000), (-86861544457766197928712646743/167772160000000000000000), (4888844510450527600329505149/16777216000000000000000), 0, 0], + [(6869519969496381960085415099007/33554432000000000000000), (-1321637020094633023479152437983/67108864000000000000000), (38229925041583923398630108229/13421772800000000000000), (-23973293068487386195658999913/53687091200000000000000), (125491751932979281769752833/2684354560000000000000), (-8162389557098350440321766311/134217728000000000000000), (4888844510450527600329505149/16777216000000000000000), (-42318688162572652589522350587/53687091200000000000000), 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] + ] + +def fourZData_19 : Matrix (CopyLabel 19) (CopyLabel 19) ℚ := + copyMatrixData 19 [ + [6402373705728000, 0, 0, 0, 0, 0, 0, 0, -97692469875, 3712313855250], + [0, 15692092416000, 0, 0, 0, 0, 0, -3831077250, 0, (5568470782875/8)], + [0, 0, 326918592000, 0, 0, 0, (-1915538625/4), (-28733079375/8), (271367971875/16), (1856156927625/16)], + [0, 0, 0, 18860688000, 0, -147349125, (-9577693125/8), 0, (227949096375/32), (1856156927625/128)], + [0, 0, 0, 0, (4942893375/2), (-1326142125/2), (-17239847625/32), (40226311125/64), (293077409625/256), 0], + [0, 0, 0, -147349125, (-1326142125/2), (4469590125/16), 0, 0, (-119401907625/256), (-1856156927625/2048)], + [0, 0, (-1915538625/4), (-9577693125/8), (-17239847625/32), 0, (443036719125/1024), (-821766070125/2048), (-2116670180625/4096), (-1856156927625/4096)], + [0, -3831077250, (-28733079375/8), 0, (40226311125/64), 0, (-821766070125/2048), (1089941477625/2048), (-2442311746875/8192), (-5568470782875/32768)], + [-97692469875, 0, (271367971875/16), (227949096375/32), (293077409625/256), (-119401907625/256), (-2116670180625/4096), (-2442311746875/8192), (346645447273125/65536), (-1856156927625/32768)], + [3712313855250, (5568470782875/8), (1856156927625/16), (1856156927625/128), 0, (-1856156927625/2048), (-1856156927625/4096), (-5568470782875/32768), (-1856156927625/32768), (121635819624193875/524288)] + ] + +def fourLData_19 : Matrix (CopyLabel 19) (CopyLabel 19) ℚ := + copyMatrixData 19 [ + [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [(-2020011531631846969177200/1202639047713818742631803172201), 1, 0, 0, 0, 0, 0, 0, 0, 0], + [(23595088792077008460858915/76968899053684399528435403020864), (-5822692808407349938912024178421113542355995713624115777/31262571384967907735769652165612355825696278835743059616), 1, 0, 0, 0, 0, 0, 0, 0], + [(-6451764561601397527869641/153937798107368799056870806041728), (2503750154892137909913496822537882251630356635271327065/62525142769935815471539304331224711651392557671486119232), (-92774401214903063949344590108787205519457990348578712381666279529750347731/168418625539847275664136167095522878077741314813553176311666683135166901682), 1, 0, 0, 0, 0, 0, 0], + [(-3991241748017824922059479/307875596214737598113741612083456), (-424440986191928747792654883979978928826133369553726583/250100571079743261886157217324898846605570230685944476928), (292552408649523873184750356531382741673385640896547717852755738972549700203/3368372510796945513282723341910457561554826296271063526233333662703338033640), (-9686261414621178345199795745128428396957249184590196228783883175168413330877698894846027553/13809778020376421591169151541712996318383052045070770607444688987375008635459809794761716924), 1, 0, 0, 0, 0, 0], + [(772800113721185652704523/615751192429475196227483224166912), (1385142357177886757041123943329631902700428160389838855/500201142159486523772314434649797693211140461371888953856), (-32581241124941751750352214972586545115893793027678406661240754676955279473/336837251079694551328272334191045756155482629627106352623333366270333803364), (3251016691257014358611121593521969021370373108242937325123146042503015433752498856034179231/13809778020376421591169151541712996318383052045070770607444688987375008635459809794761716924), (-2122231202756391713145325083545292842288303167896135143392823227018143507956047460325521849288415365/15870638051051129919271535319839481602043326225695621661360980618060215480300545072063250228599005104), 1, 0, 0, 0, 0], + [(2811778187557848892254875/307875596214737598113741612083456), (-1509785959510237917930593179397250973442741161169160203/250100571079743261886157217324898846605570230685944476928), (6401774252120685662357585571886157870975114629754590565441298796897955427111/47157215151157237185958126786746405861767568147794889367266671277846732470960), (18729047246966666079667574135347429918773885130339118875816720849736745793810665416263379983/3093390276564318436421889945343711175317803658095852616067610333172001934342997394026624590976), (-128094774302086004238884690032304206718133114297639347331085824516047259085717351746740342242370764701/296251910286287758493068659303670323238142089546318271012071638203790688965610174678514004267181428608), (-6702785262915535022085814294995920066692670055957138446674674798735073316329511157131562446168655168296380347/4264045600302034874792061579880963129330136297602065715110861053443518810565784897268444808748010548014575944), 1, 0, 0, 0], + [(-13993580349908417522901555/1231502384858950392454966448333824), (6272560116072020767460314837271369997611582439691541385/1000402284318973047544628869299595386422280922743777907712), (-53994202807818727880203037240236812292585294681520751894397546531524863076/421046563849618189160340417738807195194353287033882940779166707837917254205), (-40098902593236325891789226096139882314755846076938467183475906989123414139838158185502713333/441912896652045490917412849334815882188257665442264659438230047596000276334713913432374941568), (32770074676248522710006638816111908772902096028501605030943516753614473499893798307524222067677526869/63482552204204519677086141279357926408173304902782486645443922472240861921202180288253000914396020416), (563607842048940847817534681407895588619244881444636054709299988710470948500694807584354119739423491219929061/304574685735859633913718684277211652095009735543004693936490075245965629326127492662031772053429324858183996), (-9/2), 1, 0, 0], + [(-18350121065500000000000000/1202639047713818742631803172201), (-313600733812462986419512299537214253490000000000000/976955355780247116742801630175386119553008713616970613), (441570846180885198909046659227810858111826365890906336956256556000000000/84209312769923637832068083547761439038870657406776588155833341567583450841), (131645772084642511409985537258103541019401171342814414409646572578055364474948577099609375/6904889010188210795584575770856498159191526022535385303722344493687504317729904897380858462), (11312548259316076855245775593721245396374151409654469795096913062573833380412020467169874330265475505/72551488233376593916669875747837630180769491317465699023364482825418127909945348900860572473595451904), (-4464100423831520588262797324649000680699963188046352726804700693944857034202148761387233561981806136560432081/2436597485886877071309749474217693216760077884344037551491920601967725034609019941296254176427434598865471968), (85/4), 0, 1, 0], + [(697304609035580000000000000/1202639047713818742631803172201), (13978478272021385777459991602037106843824375000000000/976955355780247116742801630175386119553008713616970613), (6717416019148967780259088242587558144193978697225759002148282681500000000/84209312769923637832068083547761439038870657406776588155833341567583450841), (7705138308084153675883035243414537786376683952106186448166916362765958097789103370666015625/110478224163011372729353212333703970547064416360566164859557511899000069083678478358093735392), (578594629283587183301293481989396418779507290411938707222981396191981046305649679474498620292164629795/677147223511514876555585506979817881687181918963013190884735173037235860492823256408032009753557551104), (11726613515986148404227844711992671967876439443152177866396077750214029128556582266077138798517899565228513013/9746389943547508285238997896870772867040311537376150205967682407870900138436079765185016705709738395461887872), (-969/4), 0, 0, 1] + ] + +def fourPivotData_19 : CopyLabel 19 → ℚ := + copyDiagonalData 19 [(134272890216321057298020353848200719937/5242880000000000000000), (6416213893363475534282471017076289038717677460210985136084893/3152646105238913004684714107734589440000000000000000), (1290449529563955732542701421323712550116316965134583130865730278684193183973793869/65562364105128217643884797578418283244570602552936228959813632000000000000), (4069717415493395784179764413327622017283928267341277224165386816373687138604893891849137144498183/689842690211214441120301740423261708606428425476313810172586734121643629289472000000000000), (10523360835063401957396916150532242395316070491506110656596640614459093767501830240262118396280510200752203/22625940308584729134971537885942573168038792470643950563237378436915214148337352367737597008281600000), (12822518125808256622859078178399541250286886113926611863552748045336341503222635909198372095506361219198331685601/3169822888575045639281917984673524621017939588654288034130143164297734953804118923711198985086367690653696000), (698847760952378595541191690326365080417166967358647868797028146956772497602403809764930020401490316492538821468124921/116134438425514455087531448394422358293518883075178796345145097142223147540463076998393682695526075542725506105344000), 0, 0, 0] + +theorem fourOccupations_19 : highestFourOccupations 19 = {{0,1,2,17}, {0,1,3,16}, {0,1,4,15}, {0,1,5,14}, {0,1,6,13}, {0,1,7,12}, {0,1,8,11}, {0,1,9,10}, {0,2,3,15}, {0,2,4,14}, {0,2,5,13}, {0,2,6,12}, {0,2,7,11}, {0,2,8,10}, {0,3,4,13}, {0,3,5,12}, {0,3,6,11}, {0,3,7,10}, {0,3,8,9}, {0,4,5,11}, {0,4,6,10}, {0,4,7,9}, {0,5,6,9}, {0,5,7,8}, {1,2,3,14}, {1,2,4,13}, {1,2,5,12}, {1,2,6,11}, {1,2,7,10}, {1,2,8,9}, {1,3,4,12}, {1,3,5,11}, {1,3,6,10}, {1,3,7,9}, {1,4,5,10}, {1,4,6,9}, {1,4,7,8}, {1,5,6,8}, {2,3,4,11}, {2,3,5,10}, {2,3,6,9}, {2,3,7,8}, {2,4,5,9}, {2,4,6,8}, {2,5,6,7}, {3,4,5,8}, {3,4,6,7}} := by + decide +kernel + +theorem fourYNumber_19_1_1 : + (collectedFourTrace 19 1 1 collectedFourData_19 : ℚ) / fourCommonDenominator = (-5179636017239466145793848200719937/20971520000000000000000) := by + decide +kernel + +theorem fourYNumber_19_3_1 : + (collectedFourTrace 19 3 1 collectedFourData_19 : ℚ) / fourCommonDenominator = (187434720909027305797300194104127/8388608000000000000000) := by + decide +kernel + +theorem fourYNumber_19_3_3 : + (collectedFourTrace 19 3 3 collectedFourData_19 : ℚ) / fourCommonDenominator = (-178409637091064952160509455064531/83886080000000000000000) := by + decide +kernel + +theorem fourYNumber_19_5_1 : + (collectedFourTrace 19 5 1 collectedFourData_19 : ℚ) / fourCommonDenominator = (-2655089774899248756771754225173/838860800000000000000) := by + decide +kernel + +theorem fourYNumber_19_5_3 : + (collectedFourTrace 19 5 3 collectedFourData_19 : ℚ) / fourCommonDenominator = (5621260360207772838458389165677/16777216000000000000000) := by + decide +kernel + +theorem fourYNumber_19_5_5 : + (collectedFourTrace 19 5 5 collectedFourData_19 : ℚ) / fourCommonDenominator = (-426035399881728630302625737421/6710886400000000000000) := by + decide +kernel + +theorem fourYNumber_19_7_1 : + (collectedFourTrace 19 7 1 collectedFourData_19 : ℚ) / fourCommonDenominator = (16881332854132320143988817820421/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_19_7_3 : + (collectedFourTrace 19 7 3 collectedFourData_19 : ℚ) / fourCommonDenominator = (-4717729566947090956657038913269/67108864000000000000000) := by + decide +kernel + +theorem fourYNumber_19_7_5 : + (collectedFourTrace 19 7 5 collectedFourData_19 : ℚ) / fourCommonDenominator = (245031192885525934544085492063/13421772800000000000000) := by + decide +kernel + +theorem fourYNumber_19_7_7 : + (collectedFourTrace 19 7 7 collectedFourData_19 : ℚ) / fourCommonDenominator = (-384466433084035638058510508259/53687091200000000000000) := by + decide +kernel + +theorem fourYNumber_19_9_1 : + (collectedFourTrace 19 9 1 collectedFourData_19 : ℚ) / fourCommonDenominator = (-194634222784906412908126173447/8388608000000000000000) := by + decide +kernel + +theorem fourYNumber_19_9_3 : + (collectedFourTrace 19 9 3 collectedFourData_19 : ℚ) / fourCommonDenominator = (284747204857559498276849187561/16777216000000000000000) := by + decide +kernel + +theorem fourYNumber_19_9_5 : + (collectedFourTrace 19 9 5 collectedFourData_19 : ℚ) / fourCommonDenominator = (-1557730163651995099526246487/209715200000000000000) := by + decide +kernel + +theorem fourYNumber_19_9_7 : + (collectedFourTrace 19 9 7 collectedFourData_19 : ℚ) / fourCommonDenominator = (10123087280082182882087994459/2684354560000000000000) := by + decide +kernel + +theorem fourYNumber_19_9_9 : + (collectedFourTrace 19 9 9 collectedFourData_19 : ℚ) / fourCommonDenominator = (-7622943311608357206631060953/3355443200000000000000) := by + decide +kernel + +theorem fourYNumber_19_11_1 : + (collectedFourTrace 19 11 1 collectedFourData_19 : ℚ) / fourCommonDenominator = (-4278863868672885847019994838509/83886080000000000000000) := by + decide +kernel + +theorem fourYNumber_19_11_3 : + (collectedFourTrace 19 11 3 collectedFourData_19 : ℚ) / fourCommonDenominator = (-36590419351896827609695794291/6710886400000000000000) := by + decide +kernel + +theorem fourYNumber_19_11_5 : + (collectedFourTrace 19 11 5 collectedFourData_19 : ℚ) / fourCommonDenominator = (27876208643370085842832469481/6710886400000000000000) := by + decide +kernel + +theorem fourYNumber_19_11_7 : + (collectedFourTrace 19 11 7 collectedFourData_19 : ℚ) / fourCommonDenominator = (-322902858771556364114391557133/134217728000000000000000) := by + decide +kernel + +theorem fourYNumber_19_11_9 : + (collectedFourTrace 19 11 9 collectedFourData_19 : ℚ) / fourCommonDenominator = (51386596016276650248544081041/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_19_11_11 : + (collectedFourTrace 19 11 11 collectedFourData_19 : ℚ) / fourCommonDenominator = (-357286302839183067236886747363/335544320000000000000000) := by + decide +kernel + +theorem fourYNumber_19_13_1 : + (collectedFourTrace 19 13 1 collectedFourData_19 : ℚ) / fourCommonDenominator = (-92711834507674027889855562951/8388608000000000000000) := by + decide +kernel + +theorem fourYNumber_19_13_3 : + (collectedFourTrace 19 13 3 collectedFourData_19 : ℚ) / fourCommonDenominator = (78521760071585338639486774419/10485760000000000000000) := by + decide +kernel + +theorem fourYNumber_19_13_5 : + (collectedFourTrace 19 13 5 collectedFourData_19 : ℚ) / fourCommonDenominator = (-105195415768801818681315887793/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_19_13_7 : + (collectedFourTrace 19 13 7 collectedFourData_19 : ℚ) / fourCommonDenominator = (26165622301296628386942262557/16777216000000000000000) := by + decide +kernel + +theorem fourYNumber_19_13_9 : + (collectedFourTrace 19 13 9 collectedFourData_19 : ℚ) / fourCommonDenominator = (-15903873537826236008064465447/16777216000000000000000) := by + decide +kernel + +theorem fourYNumber_19_13_11 : + (collectedFourTrace 19 13 11 collectedFourData_19 : ℚ) / fourCommonDenominator = (1423697597371070492775004701/2097152000000000000000) := by + decide +kernel + +theorem fourYNumber_19_13_13 : + (collectedFourTrace 19 13 13 collectedFourData_19 : ℚ) / fourCommonDenominator = (-86861544457766197928712646743/167772160000000000000000) := by + decide +kernel + +theorem fourYNumber_19_15_1 : + (collectedFourTrace 19 15 1 collectedFourData_19 : ℚ) / fourCommonDenominator = (6869519969496381960085415099007/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_19_15_3 : + (collectedFourTrace 19 15 3 collectedFourData_19 : ℚ) / fourCommonDenominator = (-1321637020094633023479152437983/67108864000000000000000) := by + decide +kernel + +theorem fourYNumber_19_15_5 : + (collectedFourTrace 19 15 5 collectedFourData_19 : ℚ) / fourCommonDenominator = (38229925041583923398630108229/13421772800000000000000) := by + decide +kernel + +theorem fourYNumber_19_15_7 : + (collectedFourTrace 19 15 7 collectedFourData_19 : ℚ) / fourCommonDenominator = (-23973293068487386195658999913/53687091200000000000000) := by + decide +kernel + +theorem fourYNumber_19_15_9 : + (collectedFourTrace 19 15 9 collectedFourData_19 : ℚ) / fourCommonDenominator = (125491751932979281769752833/2684354560000000000000) := by + decide +kernel + +theorem fourYNumber_19_15_11 : + (collectedFourTrace 19 15 11 collectedFourData_19 : ℚ) / fourCommonDenominator = (-8162389557098350440321766311/134217728000000000000000) := by + decide +kernel + +theorem fourYNumber_19_15_13 : + (collectedFourTrace 19 15 13 collectedFourData_19 : ℚ) / fourCommonDenominator = (4888844510450527600329505149/16777216000000000000000) := by + decide +kernel + +theorem fourYNumber_19_15_15 : + (collectedFourTrace 19 15 15 collectedFourData_19 : ℚ) / fourCommonDenominator = (-42318688162572652589522350587/53687091200000000000000) := by + decide +kernel + +theorem fourYNumber_19_17_1 : + (collectedFourTrace 19 17 1 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_17_3 : + (collectedFourTrace 19 17 3 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_17_5 : + (collectedFourTrace 19 17 5 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_17_7 : + (collectedFourTrace 19 17 7 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_17_9 : + (collectedFourTrace 19 17 9 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_17_11 : + (collectedFourTrace 19 17 11 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_17_13 : + (collectedFourTrace 19 17 13 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_17_15 : + (collectedFourTrace 19 17 15 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_17_17 : + (collectedFourTrace 19 17 17 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_19_1 : + (collectedFourTrace 19 19 1 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_19_3 : + (collectedFourTrace 19 19 3 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_19_5 : + (collectedFourTrace 19 19 5 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_19_7 : + (collectedFourTrace 19 19 7 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_19_9 : + (collectedFourTrace 19 19 9 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_19_11 : + (collectedFourTrace 19 19 11 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_19_13 : + (collectedFourTrace 19 19 13 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_19_15 : + (collectedFourTrace 19 19 15 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_19_17 : + (collectedFourTrace 19 19 17 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_19_19_19 : + (collectedFourTrace 19 19 19 collectedFourData_19 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate20.lean b/lean/OAI/Analysis/LaughlinFock/Certificate20.lean new file mode 100644 index 0000000000000000000000000000000000000000..02b4d331ccb0577562de2ffdf1ec1bbd592692b7 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate20.lean @@ -0,0 +1,386 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate20Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate20. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_20 (r s : CopyLabel 20) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 20 r s = fourYData_20 r s := by + rw [integerRowsFourTrace_collected (by decide) collectedFourData_20 collectedFourChecked_20] + fin_cases r <;> fin_cases s + · exact fourYNumber_20_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · have h : (13:ℕ) ≤ 1 := hrs + omega + · have h : (15:ℕ) ≤ 1 := hrs + omega + · have h : (17:ℕ) ≤ 1 := hrs + omega + · have h : (19:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_20_3_1 + · exact fourYNumber_20_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · have h : (13:ℕ) ≤ 3 := hrs + omega + · have h : (15:ℕ) ≤ 3 := hrs + omega + · have h : (17:ℕ) ≤ 3 := hrs + omega + · have h : (19:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_20_5_1 + · exact fourYNumber_20_5_3 + · exact fourYNumber_20_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · have h : (13:ℕ) ≤ 5 := hrs + omega + · have h : (15:ℕ) ≤ 5 := hrs + omega + · have h : (17:ℕ) ≤ 5 := hrs + omega + · have h : (19:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_20_7_1 + · exact fourYNumber_20_7_3 + · exact fourYNumber_20_7_5 + · exact fourYNumber_20_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · have h : (13:ℕ) ≤ 7 := hrs + omega + · have h : (15:ℕ) ≤ 7 := hrs + omega + · have h : (17:ℕ) ≤ 7 := hrs + omega + · have h : (19:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_20_9_1 + · exact fourYNumber_20_9_3 + · exact fourYNumber_20_9_5 + · exact fourYNumber_20_9_7 + · exact fourYNumber_20_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · have h : (13:ℕ) ≤ 9 := hrs + omega + · have h : (15:ℕ) ≤ 9 := hrs + omega + · have h : (17:ℕ) ≤ 9 := hrs + omega + · have h : (19:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_20_11_1 + · exact fourYNumber_20_11_3 + · exact fourYNumber_20_11_5 + · exact fourYNumber_20_11_7 + · exact fourYNumber_20_11_9 + · exact fourYNumber_20_11_11 + · have h : (13:ℕ) ≤ 11 := hrs + omega + · have h : (15:ℕ) ≤ 11 := hrs + omega + · have h : (17:ℕ) ≤ 11 := hrs + omega + · have h : (19:ℕ) ≤ 11 := hrs + omega + · exact fourYNumber_20_13_1 + · exact fourYNumber_20_13_3 + · exact fourYNumber_20_13_5 + · exact fourYNumber_20_13_7 + · exact fourYNumber_20_13_9 + · exact fourYNumber_20_13_11 + · exact fourYNumber_20_13_13 + · have h : (15:ℕ) ≤ 13 := hrs + omega + · have h : (17:ℕ) ≤ 13 := hrs + omega + · have h : (19:ℕ) ≤ 13 := hrs + omega + · exact fourYNumber_20_15_1 + · exact fourYNumber_20_15_3 + · exact fourYNumber_20_15_5 + · exact fourYNumber_20_15_7 + · exact fourYNumber_20_15_9 + · exact fourYNumber_20_15_11 + · exact fourYNumber_20_15_13 + · exact fourYNumber_20_15_15 + · have h : (17:ℕ) ≤ 15 := hrs + omega + · have h : (19:ℕ) ≤ 15 := hrs + omega + · exact fourYNumber_20_17_1 + · exact fourYNumber_20_17_3 + · exact fourYNumber_20_17_5 + · exact fourYNumber_20_17_7 + · exact fourYNumber_20_17_9 + · exact fourYNumber_20_17_11 + · exact fourYNumber_20_17_13 + · exact fourYNumber_20_17_15 + · exact fourYNumber_20_17_17 + · have h : (19:ℕ) ≤ 17 := hrs + omega + · exact fourYNumber_20_19_1 + · exact fourYNumber_20_19_3 + · exact fourYNumber_20_19_5 + · exact fourYNumber_20_19_7 + · exact fourYNumber_20_19_9 + · exact fourYNumber_20_19_11 + · exact fourYNumber_20_19_13 + · exact fourYNumber_20_19_15 + · exact fourYNumber_20_19_17 + · exact fourYNumber_20_19_19 + +theorem fourYChecked_20 (r s : CopyLabel 20) : + integerRowsFourTrace 20 r s = fourYData_20 r s := by + have hh : ∀ r s : CopyLabel 20, fourYData_20 r s = fourYData_20 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_20 r s h + · rw [integerRowsFourTrace_symm, fourYLower_20 s r (by omega), hh] + +def fourHighestCache_20_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,18}, [0, -5736526840332288000, -3585329275207680000, -1933516859129856000, -742675349864448000, -12804747411456000, 256094948229120000, 64023737057280000, -589018380926976000, -1703031405723648000]), + ({0,1,3,17}, [0, 5736526840332288000, 3585329275207680000, 1933516859129856000, 742675349864448000, 12804747411456000, -256094948229120000, -64023737057280000, 589018380926976000, 1703031405723648000]), + ({0,1,4,16}, [0, -7648702453776384000, -3655629849231360000, -1473299172753408000, -427829207629824000, 7532204359680000, 140099001090048000, 60257634877440000, -358532927520768000, -1459741204905984000]), + ({0,1,5,15}, [0, 7170658550415360000, 3216251261583360000, 1033481206517760000, 175123751362560000, -28245766348800000, -42996333219840000, -49273170186240000, 149388719800320000, 1216451004088320000]) +] + +def fourHighestCache_20_1 : List (Occupation 24 × List ℚ) := [ + ({0,1,6,14}, [0, -6692614647054336000, -2495670377840640000, -630822115123200000, -54985091825664000, 32011868528640000, 1255367393280000, 26048873410560000, -17072996548608000, -973160803270656000]), + ({0,1,7,13}, [0, 5531650881748992000, 1830325659402240000, 319930380177408000, 9415255449600000, -19583731335168000, 2824576634880000, -1255367393280000, -46950740508672000, 729870602452992000]), + ({0,1,8,12}, [0, -3824351226888192000, -1185066819256320000, -142107588919296000, 8575124963328000, 4229622448128000, 3766102179840000, -12553673932800000, 59755487920128000, -486580401635328000]), + ({0,1,9,11}, [0, 2048759585832960000, 557383122616320000, 56114922479616000, -10487146070016000, 2462451425280000, -5272543051776000, 11298306539520000, -38414242234368000, 243290200817664000]) +] + +def fourHighestCache_20_2 : List (Occupation 24 × List ℚ) := [ + ({0,2,3,16}, [0, 1912175613444096000, 70300574023680000, -460217686376448000, -314846142234624000, -20336951771136000, 115995947139072000, 3766102179840000, -230485453406208000, -243290200817664000]), + ({0,2,4,15}, [0, 478043903361024000, 439378587648000000, 439817966235648000, 252705456267264000, 20713561989120000, -97102667870208000, -10984464691200000, 209144207720448000, 243290200817664000]), + ({0,2,5,14}, [0, -478043903361024000, -720580883742720000, -402659091394560000, -120138659536896000, -3766102179840000, 41740965826560000, 23224296775680000, -132315723251712000, -243290200817664000]), + ({0,2,6,13}, [0, 1160963765305344000, 665344718438400000, 310891734945792000, 45569836376064000, -12428137193472000, -4079944028160000, -24793506017280000, 64023737057280000, 243290200817664000]) +] + +def fourHighestCache_20_3 : List (Occupation 24 × List ℚ) := [ + ({0,2,7,12}, [0, -1707299654860800000, -645258840145920000, -177822791258112000, -17990380412928000, 15354108887040000, -6590678814720000, 13809041326080000, -12804747411456000, -243290200817664000]), + ({0,2,8,11}, [0, 1775591641055232000, 627683696640000000, 85992666439680000, 1912021106688000, -6692073873408000, 1506440871936000, 1255367393280000, -21341245685760000, 243290200817664000]), + ({0,2,9,10}, [0, -2048759585832960000, -557383122616320000, -56114922479616000, 10487146070016000, -2462451425280000, 5272543051776000, -11298306539520000, 38414242234368000, -243290200817664000]), + ({0,3,4,14}, [0, -2390219516805120000, -228476865576960000, -16759154700288000, -70426110763008000, -17324070027264000, 36468422774784000, -5021469573120000, -55487238782976000, 0]) +] + +def fourHighestCache_20_4 : List (Occupation 24 × List ℚ) := [ + ({0,3,5,13}, [0, 2048759585832960000, 396696096276480000, 44063395504128000, 41427123978240000, 16947459809280000, -27618082652160000, -313841848320000, 51218989645824000, 0]), + ({0,3,6,12}, [0, -1843883627249664000, -248562743869440000, -69484585218048000, -16425999507456000, -4953872867328000, 8473729904640000, 8473729904640000, -38414242234368000, 0]), + ({0,3,7,11}, [0, 1639007668666368000, 140601148047360000, 43686785286144000, 12746807377920000, -5620183252992000, 3515028701184000, -11298306539520000, 25609494822912000, 0]), + ({0,3,8,10}, [0, -682919861944320000, -105450861035520000, -8662035013632000, -10718906204160000, 6807953940480000, -5021469573120000, 7532204359680000, -12804747411456000, 0]) +] + +def fourHighestCache_20_5 : List (Occupation 24 × List ℚ) := [ + ({0,4,5,12}, [0, -546335889555456000, -261116417802240000, 9540792188928000, -3012881743872000, -10718906204160000, 11298306539520000, -3766102179840000, -8536498274304000, 0]), + ({0,4,6,11}, [0, 887795820527616000, 213412456857600000, 10356780994560000, -4142712397824000, 9560105533440000, -8222656425984000, 1569209241600000, 8536498274304000, 0]), + ({0,4,7,10}, [0, -1707299654860800000, -123026004541440000, -8097119686656000, -376610217984000, -1883051089920000, 1318135762944000, 2510734786560000, -8536498274304000, 0]), + ({0,4,8,9}, [0, 1639007668666368000, 140601148047360000, -12553673932800000, 9038645231616000, -4461382582272000, 3263955222528000, -5021469573120000, 8536498274304000, 0]) +] + +def fourHighestCache_20_6 : List (Occupation 24 × List ℚ) := [ + ({0,5,6,10}, [0, 341459930972160000, -47703960944640000, -12239832084480000, 7677054443520000, -5794003353600000, 4079944028160000, -2196892938240000, 0, 0]), + ({0,5,7,9}, [0, 204875958583296000, -12553673932800000, 18767742529536000, -8372334845952000, 4924902850560000, -3075650113536000, 1569209241600000, 0, 0]), + ({0,6,7,8}, [0, -682919861944320000, 55236165304320000, -20713561989120000, 7821904527360000, -3737132163072000, 2008587829248000, -941525544960000, 0, 0]), + ({1,2,3,15}, [0, -2390219516805120000, -509679161671680000, 20399720140800000, 62140685967360000, -376610217984000, -18893279268864000, 7218362511360000, 21341245685760000, 0]) +] + +def fourHighestCache_20_7 : List (Occupation 24 × List ℚ) := [ + ({1,2,4,14}, [0, 2390219516805120000, 509679161671680000, -20399720140800000, -62140685967360000, 376610217984000, 18893279268864000, -7218362511360000, -21341245685760000, 0]), + ({1,2,5,13}, [0, -2731679447777280000, -341459930972160000, 47703960944640000, 33141699182592000, -753220435968000, -10042939146240000, 1883051089920000, 17072996548608000, 0]), + ({1,2,6,12}, [0, 2390219516805120000, 228476865576960000, -63584358469632000, -11153456455680000, 2027901173760000, 2196892938240000, 2510734786560000, -12804747411456000, 0]), + ({1,2,7,11}, [0, -1707299654860800000, -123026004541440000, 48143339532288000, 3331551928320000, -3041851760640000, 1569209241600000, -3766102179840000, 8536498274304000, 0]) +] + +def fourHighestCache_20_8 : List (Occupation 24 × List ℚ) := [ + ({1,2,8,10}, [0, 956087806722048000, 35150287011840000, -21215708946432000, -1680260972544000, 2346571358208000, -1757514350592000, 2510734786560000, -4268249137152000, 0]), + ({1,3,4,13}, [0, 341459930972160000, -168219230699520000, -27304240803840000, 28998986784768000, 376610217984000, -8850340122624000, 5335311421440000, 4268249137152000, 0]), + ({1,3,5,12}, [0, 341459930972160000, 112983065395200000, 15880397524992000, -21988242726912000, -1274680737792000, 7846046208000000, -4393785876480000, -4268249137152000, 0]), + ({1,3,6,11}, [0, -682919861944320000, -105450861035520000, 15441018937344000, 7821904527360000, 1013950586880000, -3766102179840000, 1255367393280000, 4268249137152000, 0]) +] + +def fourHighestCache_20_9 : List (Occupation 24 × List ℚ) := [ + ({1,3,7,10}, [0, 751211848138752000, 87875717529600000, -26927630585856000, -1651290955776000, 695280402432000, 188305108992000, 1255367393280000, -4268249137152000, 0]), + ({1,3,8,9}, [0, -956087806722048000, -35150287011840000, 21215708946432000, 1680260972544000, -2346571358208000, 1757514350592000, -2510734786560000, 4268249137152000, 0]), + ({1,4,5,11}, [0, -341459930972160000, 47703960944640000, -19897573183488000, 7155594141696000, 1158800670720000, -3075650113536000, 2196892938240000, 0, 0]), + ({1,4,6,10}, [0, 478043903361024000, -42682491371520000, 9980170776576000, -3157731827712000, -1883051089920000, 2824576634880000, -1883051089920000, 0, 0]) +] + +def fourHighestCache_20_10 : List (Occupation 24 × List ℚ) := [ + ({1,4,7,9}, [0, -136583972388864000, -5021469573120000, 1883051089920000, -289700167680000, 1419530821632000, -1506440871936000, 941525544960000, 0, 0]), + ({1,5,6,9}, [0, -546335889555456000, 60257634877440000, -6527910445056000, 695280402432000, 869100503040000, -1004293914624000, 627683696640000, 0, 0]), + ({1,5,7,8}, [0, 478043903361024000, -42682491371520000, 1945819459584000, 550430318592000, -1187770687488000, 1067062284288000, -627683696640000, 0, 0]), + ({2,3,4,12}, [0, -682919861944320000, 55236165304320000, 11423843278848000, -7010744057856000, 898070519808000, 1004293914624000, -941525544960000, 0, 0]) +] + +def fourHighestCache_20_11 : List (Occupation 24 × List ℚ) := [ + ({2,3,5,11}, [0, 682919861944320000, -55236165304320000, -11423843278848000, 7010744057856000, -898070519808000, -1004293914624000, 941525544960000, 0, 0]), + ({2,3,6,10}, [0, -546335889555456000, 60257634877440000, 1506440871936000, -3012881743872000, 173820100608000, 753220435968000, -627683696640000, 0, 0]), + ({2,3,7,9}, [0, 341459930972160000, -47703960944640000, 3828870549504000, 260730150912000, 231760134144000, -439378587648000, 313841848320000, 0, 0]), + ({2,4,5,10}, [0, -136583972388864000, -5021469573120000, 9917402406912000, -3997862313984000, 724250419200000, 251073478656000, -313841848320000, 0, 0]) +] + +def fourHighestCache_20_12 : List (Occupation 24 × List ℚ) := [ + ({2,4,6,9}, [0, 204875958583296000, -12553673932800000, -5335311421440000, 2752151592960000, -405580234752000, -313841848320000, 313841848320000, 0, 0]), + ({2,4,7,8}, [0, -341459930972160000, 47703960944640000, -3828870549504000, -260730150912000, -231760134144000, 439378587648000, -313841848320000, 0, 0]), + ({2,5,6,8}, [0, 68291986194432000, -17575143505920000, 4582090985472000, -1245710721024000, 318670184448000, -62768369664000, 0, 0, 0]), + ({3,4,5,9}, [0, -68291986194432000, 17575143505920000, -4582090985472000, 1245710721024000, -318670184448000, 62768369664000, 0, 0, 0]) +] + +def fourHighestCache_20_13 : List (Occupation 24 × List ℚ) := [ + ({3,4,6,8}, [0, 68291986194432000, -17575143505920000, 4582090985472000, -1245710721024000, 318670184448000, -62768369664000, 0, 0, 0]), + ({3,5,6,7}, [0, -68291986194432000, 17575143505920000, -4582090985472000, 1245710721024000, -318670184448000, 62768369664000, 0, 0, 0]) +] + +def fourHighestCache_20 : List (Occupation 24 × List ℚ) := fourHighestCache_20_0 ++ fourHighestCache_20_1 ++ fourHighestCache_20_2 ++ fourHighestCache_20_3 ++ fourHighestCache_20_4 ++ fourHighestCache_20_5 ++ fourHighestCache_20_6 ++ fourHighestCache_20_7 ++ fourHighestCache_20_8 ++ fourHighestCache_20_9 ++ fourHighestCache_20_10 ++ fourHighestCache_20_11 ++ fourHighestCache_20_12 ++ fourHighestCache_20_13 + +theorem fourHighestNumber_20_1 : ∀ A∈highestFourOccupations 20, + kernelHighestEntry 20 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_20 1 A := by + rw [fourOccupations_20] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_20_3 : ∀ A∈highestFourOccupations 20, + kernelHighestEntry 20 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_20 3 A := by + rw [fourOccupations_20] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_20_5 : ∀ A∈highestFourOccupations 20, + kernelHighestEntry 20 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_20 5 A := by + rw [fourOccupations_20] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_20_7 : ∀ A∈highestFourOccupations 20, + kernelHighestEntry 20 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_20 7 A := by + rw [fourOccupations_20] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_20_9 : ∀ A∈highestFourOccupations 20, + kernelHighestEntry 20 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_20 9 A := by + rw [fourOccupations_20] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_20_11 : ∀ A∈highestFourOccupations 20, + kernelHighestEntry 20 ⟨⟨11,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_20 11 A := by + rw [fourOccupations_20] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_20_13 : ∀ A∈highestFourOccupations 20, + kernelHighestEntry 20 ⟨⟨13,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_20 13 A := by + rw [fourOccupations_20] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_20_15 : ∀ A∈highestFourOccupations 20, + kernelHighestEntry 20 ⟨⟨15,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_20 15 A := by + rw [fourOccupations_20] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_20_17 : ∀ A∈highestFourOccupations 20, + kernelHighestEntry 20 ⟨⟨17,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_20 17 A := by + rw [fourOccupations_20] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_20_19 : ∀ A∈highestFourOccupations 20, + kernelHighestEntry 20 ⟨⟨19,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_20 19 A := by + rw [fourOccupations_20] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_20 : ∀ r : CopyLabel 20, ∀ A∈highestFourOccupations 20, + kernelHighestEntry 20 r A = highestLookup fourHighestCache_20 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_20_1 + · exact fourHighestNumber_20_3 + · exact fourHighestNumber_20_5 + · exact fourHighestNumber_20_7 + · exact fourHighestNumber_20_9 + · exact fourHighestNumber_20_11 + · exact fourHighestNumber_20_13 + · exact fourHighestNumber_20_15 + · exact fourHighestNumber_20_17 + · exact fourHighestNumber_20_19 + +theorem fourZChecked_20 (r s : CopyLabel 20) : + integerFourGram 20 r s = fourZData_20 r s := by + rw [integerFourGram_cached 20 fourHighestCache_20 fourHighestChecked_20] + have h : ∀ r s : CopyLabel 20, cachedFourGram 20 fourHighestCache_20 r s = fourZData_20 r s := by + simp only [cachedFourGram, fourOccupations_20] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_20 : + fourZData_20 * (Matrix.diagonal (fun r : CopyLabel 20 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 20 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 20 => rationalCopyDiagonal 20 r.val.val) * + fourYData_20 * Matrix.diagonal (fun r : CopyLabel 20 => rationalCopyDiagonal 20 r.val.val)) * + fourZData_20 = fourLData_20 * Matrix.diagonal fourPivotData_20 * (fourLData_20)ᵀ := by + have h : ∀ r s : CopyLabel 20, + (fourZData_20 * (Matrix.diagonal (fun r : CopyLabel 20 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 20 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 20 => rationalCopyDiagonal 20 r.val.val) * + fourYData_20 * Matrix.diagonal (fun r : CopyLabel 20 => rationalCopyDiagonal 20 r.val.val)) * + fourZData_20 : Matrix (CopyLabel 20) (CopyLabel 20) ℚ) r s = + (fourLData_20 * Matrix.diagonal fourPivotData_20 * (fourLData_20)ᵀ : Matrix (CopyLabel 20) (CopyLabel 20) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_20 : ∀ r, 0 ≤ fourPivotData_20 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_20, copyDiagonalData] + +theorem integer_certificate_20 : + ((integerCompression 20).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_20) (fourPivotData_20) _ fourPivotChecked_20 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 20 = fourYData_20 from Matrix.ext fourYChecked_20, + show integerFourGram 20 = fourZData_20 from Matrix.ext fourZChecked_20] + exact fourLDLChecked_20 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate20Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate20Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..ccd8973836aa9aa891eebfbfe61fdd42ba5770a5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate20Data.lean @@ -0,0 +1,285 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse20 + +namespace OAI + +/-! Certificate20 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_20 : Matrix (CopyLabel 20) (CopyLabel 20) ℚ := + copyMatrixData 20 [ + [(-5425434932455263271311794102417343/2097152000000000000000), (179418905051802025654157882778009/838860800000000000000), (-11723708051921673633253439432421/419430400000000000000), (13864922655913073136265005303171/3355443200000000000000), (-13277763324745580223308038293/167772160000000000000), (-5957610413352344509215553231131/8388608000000000000000), (683874918374867258301621850491/838860800000000000000), (-2091544795318033449783795052647/3355443200000000000000), 0, 0], + [(179418905051802025654157882778009/838860800000000000000), (-834115719323087675418764349012483/41943040000000000000000), (12881735552398269417898166992863/4194304000000000000000), (-20662582833925800835803040061757/33554432000000000000000), (923018611270173374732366614023/8388608000000000000000), (503718895711039797688496710113/16777216000000000000000), (-3562452616542808964288980155489/41943040000000000000000), (3405146765776144196267117498841/33554432000000000000000), 0, 0], + [(-11723708051921673633253439432421/419430400000000000000), (12881735552398269417898166992863/4194304000000000000000), (-118469950634932051982395097529/209715200000000000000), (469185654095355642726736632177/3355443200000000000000), (-31129257954026396319571959543/838860800000000000000), (931665634290193477885889679/335544320000000000000), (59811152248639925369457400179/4194304000000000000000), (-78411052632888756633548076381/3355443200000000000000), 0, 0], + [(13864922655913073136265005303171/3355443200000000000000), (-20662582833925800835803040061757/33554432000000000000000), (469185654095355642726736632177/3355443200000000000000), (-1108741085510629637805875018883/26843545600000000000000), (90944316095019535880541746937/6710886400000000000000), (-40083328549786255395843422241/13421772800000000000000), (-96834753595294023711234063231/33554432000000000000000), (177472155556961120068579204839/26843545600000000000000), 0, 0], + [(-13277763324745580223308038293/167772160000000000000), (923018611270173374732366614023/8388608000000000000000), (-31129257954026396319571959543/838860800000000000000), (90944316095019535880541746937/6710886400000000000000), (-9010857355442849356413184683/1677721600000000000000), (6156096576995889112242847347/3355443200000000000000), (2488970661229237488568173909/8388608000000000000000), (-12165091907974821838928406501/6710886400000000000000), 0, 0], + [(-5957610413352344509215553231131/8388608000000000000000), (503718895711039797688496710113/16777216000000000000000), (931665634290193477885889679/335544320000000000000), (-40083328549786255395843422241/13421772800000000000000), (6156096576995889112242847347/3355443200000000000000), (-36159738791356336455643126167/33554432000000000000000), (9179254744275982446329067819/16777216000000000000000), (-194619785792343914883807927/2684354560000000000000), 0, 0], + [(683874918374867258301621850491/838860800000000000000), (-3562452616542808964288980155489/41943040000000000000000), (59811152248639925369457400179/4194304000000000000000), (-96834753595294023711234063231/33554432000000000000000), (2488970661229237488568173909/8388608000000000000000), (9179254744275982446329067819/16777216000000000000000), (-41690584097328109332167065287/41943040000000000000000), (39976011044472042963992972403/33554432000000000000000), 0, 0], + [(-2091544795318033449783795052647/3355443200000000000000), (3405146765776144196267117498841/33554432000000000000000), (-78411052632888756633548076381/3355443200000000000000), (177472155556961120068579204839/26843545600000000000000), (-12165091907974821838928406501/6710886400000000000000), (-194619785792343914883807927/2684354560000000000000), (39976011044472042963992972403/33554432000000000000000), (-50456789410054114597827183867/26843545600000000000000), 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0] + ] + +def fourZData_20 : Matrix (CopyLabel 20) (CopyLabel 20) ℚ := + copyMatrixData 20 [ + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 266765571072000, 0, 0, 0, 0, 0, 0, -130256626500, (12993098493375/8)], + [0, 0, 4903778880000, 0, 0, 0, 0, (-67043851875/4), 0, (9280784638125/16)], + [0, 0, 0, 245188944000, 0, 0, (-17239847625/4), (-335219259375/32), (227949096375/8), (16705412348625/128)], + [0, 0, 0, 0, 28291032000, -2210236875, -5746615875, 0, (97692469875/8), (1856156927625/128)], + [0, 0, 0, 0, -2210236875, (40226311125/16), (-63212774625/32), (316063873125/256), 0, (-9280784638125/2048)], + [0, 0, 0, (-17239847625/4), -5746615875, (-63212774625/32), 3831077250, (-1369610116875/1024), (-423334036125/128), (-16705412348625/4096)], + [0, 0, (-67043851875/4), (-335219259375/32), 0, (316063873125/256), (-1369610116875/1024), (15697839031875/8192), (-5698727409375/2048), (-64965492466875/32768)], + [0, -130256626500, 0, (227949096375/8), (97692469875/8), 0, (-423334036125/128), (-5698727409375/2048), (15012076204125/1024), (-12993098493375/16384)], + [0, (12993098493375/8), (9280784638125/16), (16705412348625/128), (1856156927625/128), (-9280784638125/2048), (-16705412348625/4096), (-64965492466875/32768), (-12993098493375/16384), (121494751697694375/524288)] + ] + +def fourLData_20 : Matrix (CopyLabel 20) (CopyLabel 20) ℚ := + copyMatrixData 20 [ + [1, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0, 0, 0, 0, 0], + [0, (-8126138115145743032553165/62284328069371912383859672), 1, 0, 0, 0, 0, 0, 0, 0], + [0, (1626803167008096359790661/45297693141361390824625216), (-17449910457629697811253768910994745334764785247/36126952092093301262412516311431044434338593352), 1, 0, 0, 0, 0, 0, 0], + [0, (-2741391634246070130778671/249137312277487649535438688), (1710747011218568525172761259487667720823745509/9031738023023325315603129077857761108584648338), (-1409880132621320206328277901568423102070009205103214981952464878/3672486685330114611812244238666481186928923369975629714230340569), 1, 0, 0, 0, 0, 0], + [0, (-3468403531570060272169437/996549249109950598141754752), (-54206663627697249243209181831639780932965256217/1445078083683732050496500652457241777373543734080), (-2682669873345268677667448439108508517833436035126757303806715923/48966489137734861490829923182219749159052311599675062856404540920), (390940692538680577286483357680346542717307071740235885579397866444341/1011471242142306678707331123629264075534347116402293932285940459557840), 1, 0, 0, 0, 0], + [0, (6404262476599127023962681/996549249109950598141754752), (-12271060906794183557615921331520007198784539277/1445078083683732050496500652457241777373543734080), (280398844021620654558483485855868622071510682688491918102282355137/1762793608958455013669877234559910969725883217588302262830563473120), (-1788682496537489510987861678551568040817933777893676875060518069228257241/2497322496849355189728400544240653002494303030397263718813986994648306960), (-205442230950505060736566456171910121044619455031873133064218660750573987/187661331655209709927001310658363823865769463148584900488167563297275181), 1, 0, 0, 0], + [0, (-8779322327759465983491715/1993098498219901196283509504), (6687041020002338097601109864075674474307238385/578031233473492820198600260982896710949417493632), (-42814016882767727606104144332365856781212582674220992676967182959/352558721791691002733975446911982193945176643517660452566112694624), (1378947132065935572460680545276594936012831841923306016261338517800366171/3995715994958968303565440870785044803990884848635621950102379191437291136), (802545190924812102496849755024902631767861005683116612021376985492540565/1125967989931258259562007863950182943194616778891509402929005379783651086), (-25/8), 1, 0, 0], + [0, (-5821120000000000000/158888592013703858122091), (-3768460864257326460101079607735000000000000/4515869011511662657801564538928880554292324169), (10368215532090329941304000763197677462009911340790522500000000/1224162228443371537270748079555493728976307789991876571410113523), (13657845482385131284239371109165770160170064532345695293305985047596369/39173686225087924544759224223382792195989067143486489706886070504287168), (-437060818101686496392267403571259618767317470664856137215575304419278347/4503871959725033038248031455800731772778467115566037611716021519134604344), (17/2), 0, 1, 0], + [0, (74810790000000000000/158888592013703858122091), (237273681736773465102203726552459568750000000/4515869011511662657801564538928880554292324169), (473756356311740932404506082590313071478423778982982285390625000/3672486685330114611812244238666481186928923369975629714230340569), (1013166684682223083025523920336107583474332845429774647175845986566229847/1253557959202813585432295175148249350271650148591567670620354256137189376), (8304155543932043431453080667853932756579031942632266607095930783966288593/24020650451866842870656167764270569454818491283018867262485448102051223168), (-969/32), 0, 0, 1] + ] + +def fourPivotData_20 : CopyLabel 20 → ℚ := + copyDiagonalData 20 [0, (869244263371676065818764349012483/41943040000000000000000), (385172015598864243071868844218861009117255205346517/4240899453874657298689483079680000000000000), (506504886879459989851432926271154150860670244829450849894026924491326389/23676159323074265915334666689859449280488140539166720000000000000), (454294178708108325951467664004177789316244900017142236248749409163960139861/990453034608207371192293162243812802743102559566760777579422220288000), (2442864701541646919176317341151732237970348495765660569758482956637734977606633919/4142986207814888155985228282385465653388685788783795946643212122348912640000), (718567282981337674007366669002548593087012201710765379962596158858384241414384953062941/3238952193537869690068996271307928151869950906519474627711061817423979588364533760000), 0, 0, 0] + +theorem fourOccupations_20 : highestFourOccupations 20 = {{0,1,2,18}, {0,1,3,17}, {0,1,4,16}, {0,1,5,15}, {0,1,6,14}, {0,1,7,13}, {0,1,8,12}, {0,1,9,11}, {0,2,3,16}, {0,2,4,15}, {0,2,5,14}, {0,2,6,13}, {0,2,7,12}, {0,2,8,11}, {0,2,9,10}, {0,3,4,14}, {0,3,5,13}, {0,3,6,12}, {0,3,7,11}, {0,3,8,10}, {0,4,5,12}, {0,4,6,11}, {0,4,7,10}, {0,4,8,9}, {0,5,6,10}, {0,5,7,9}, {0,6,7,8}, {1,2,3,15}, {1,2,4,14}, {1,2,5,13}, {1,2,6,12}, {1,2,7,11}, {1,2,8,10}, {1,3,4,13}, {1,3,5,12}, {1,3,6,11}, {1,3,7,10}, {1,3,8,9}, {1,4,5,11}, {1,4,6,10}, {1,4,7,9}, {1,5,6,9}, {1,5,7,8}, {2,3,4,12}, {2,3,5,11}, {2,3,6,10}, {2,3,7,9}, {2,4,5,10}, {2,4,6,9}, {2,4,7,8}, {2,5,6,8}, {3,4,5,9}, {3,4,6,8}, {3,5,6,7}} := by + decide +kernel + +theorem fourYNumber_20_1_1 : + (collectedFourTrace 20 1 1 collectedFourData_20 : ℚ) / fourCommonDenominator = (-5425434932455263271311794102417343/2097152000000000000000) := by + decide +kernel + +theorem fourYNumber_20_3_1 : + (collectedFourTrace 20 3 1 collectedFourData_20 : ℚ) / fourCommonDenominator = (179418905051802025654157882778009/838860800000000000000) := by + decide +kernel + +theorem fourYNumber_20_3_3 : + (collectedFourTrace 20 3 3 collectedFourData_20 : ℚ) / fourCommonDenominator = (-834115719323087675418764349012483/41943040000000000000000) := by + decide +kernel + +theorem fourYNumber_20_5_1 : + (collectedFourTrace 20 5 1 collectedFourData_20 : ℚ) / fourCommonDenominator = (-11723708051921673633253439432421/419430400000000000000) := by + decide +kernel + +theorem fourYNumber_20_5_3 : + (collectedFourTrace 20 5 3 collectedFourData_20 : ℚ) / fourCommonDenominator = (12881735552398269417898166992863/4194304000000000000000) := by + decide +kernel + +theorem fourYNumber_20_5_5 : + (collectedFourTrace 20 5 5 collectedFourData_20 : ℚ) / fourCommonDenominator = (-118469950634932051982395097529/209715200000000000000) := by + decide +kernel + +theorem fourYNumber_20_7_1 : + (collectedFourTrace 20 7 1 collectedFourData_20 : ℚ) / fourCommonDenominator = (13864922655913073136265005303171/3355443200000000000000) := by + decide +kernel + +theorem fourYNumber_20_7_3 : + (collectedFourTrace 20 7 3 collectedFourData_20 : ℚ) / fourCommonDenominator = (-20662582833925800835803040061757/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_20_7_5 : + (collectedFourTrace 20 7 5 collectedFourData_20 : ℚ) / fourCommonDenominator = (469185654095355642726736632177/3355443200000000000000) := by + decide +kernel + +theorem fourYNumber_20_7_7 : + (collectedFourTrace 20 7 7 collectedFourData_20 : ℚ) / fourCommonDenominator = (-1108741085510629637805875018883/26843545600000000000000) := by + decide +kernel + +theorem fourYNumber_20_9_1 : + (collectedFourTrace 20 9 1 collectedFourData_20 : ℚ) / fourCommonDenominator = (-13277763324745580223308038293/167772160000000000000) := by + decide +kernel + +theorem fourYNumber_20_9_3 : + (collectedFourTrace 20 9 3 collectedFourData_20 : ℚ) / fourCommonDenominator = (923018611270173374732366614023/8388608000000000000000) := by + decide +kernel + +theorem fourYNumber_20_9_5 : + (collectedFourTrace 20 9 5 collectedFourData_20 : ℚ) / fourCommonDenominator = (-31129257954026396319571959543/838860800000000000000) := by + decide +kernel + +theorem fourYNumber_20_9_7 : + (collectedFourTrace 20 9 7 collectedFourData_20 : ℚ) / fourCommonDenominator = (90944316095019535880541746937/6710886400000000000000) := by + decide +kernel + +theorem fourYNumber_20_9_9 : + (collectedFourTrace 20 9 9 collectedFourData_20 : ℚ) / fourCommonDenominator = (-9010857355442849356413184683/1677721600000000000000) := by + decide +kernel + +theorem fourYNumber_20_11_1 : + (collectedFourTrace 20 11 1 collectedFourData_20 : ℚ) / fourCommonDenominator = (-5957610413352344509215553231131/8388608000000000000000) := by + decide +kernel + +theorem fourYNumber_20_11_3 : + (collectedFourTrace 20 11 3 collectedFourData_20 : ℚ) / fourCommonDenominator = (503718895711039797688496710113/16777216000000000000000) := by + decide +kernel + +theorem fourYNumber_20_11_5 : + (collectedFourTrace 20 11 5 collectedFourData_20 : ℚ) / fourCommonDenominator = (931665634290193477885889679/335544320000000000000) := by + decide +kernel + +theorem fourYNumber_20_11_7 : + (collectedFourTrace 20 11 7 collectedFourData_20 : ℚ) / fourCommonDenominator = (-40083328549786255395843422241/13421772800000000000000) := by + decide +kernel + +theorem fourYNumber_20_11_9 : + (collectedFourTrace 20 11 9 collectedFourData_20 : ℚ) / fourCommonDenominator = (6156096576995889112242847347/3355443200000000000000) := by + decide +kernel + +theorem fourYNumber_20_11_11 : + (collectedFourTrace 20 11 11 collectedFourData_20 : ℚ) / fourCommonDenominator = (-36159738791356336455643126167/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_20_13_1 : + (collectedFourTrace 20 13 1 collectedFourData_20 : ℚ) / fourCommonDenominator = (683874918374867258301621850491/838860800000000000000) := by + decide +kernel + +theorem fourYNumber_20_13_3 : + (collectedFourTrace 20 13 3 collectedFourData_20 : ℚ) / fourCommonDenominator = (-3562452616542808964288980155489/41943040000000000000000) := by + decide +kernel + +theorem fourYNumber_20_13_5 : + (collectedFourTrace 20 13 5 collectedFourData_20 : ℚ) / fourCommonDenominator = (59811152248639925369457400179/4194304000000000000000) := by + decide +kernel + +theorem fourYNumber_20_13_7 : + (collectedFourTrace 20 13 7 collectedFourData_20 : ℚ) / fourCommonDenominator = (-96834753595294023711234063231/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_20_13_9 : + (collectedFourTrace 20 13 9 collectedFourData_20 : ℚ) / fourCommonDenominator = (2488970661229237488568173909/8388608000000000000000) := by + decide +kernel + +theorem fourYNumber_20_13_11 : + (collectedFourTrace 20 13 11 collectedFourData_20 : ℚ) / fourCommonDenominator = (9179254744275982446329067819/16777216000000000000000) := by + decide +kernel + +theorem fourYNumber_20_13_13 : + (collectedFourTrace 20 13 13 collectedFourData_20 : ℚ) / fourCommonDenominator = (-41690584097328109332167065287/41943040000000000000000) := by + decide +kernel + +theorem fourYNumber_20_15_1 : + (collectedFourTrace 20 15 1 collectedFourData_20 : ℚ) / fourCommonDenominator = (-2091544795318033449783795052647/3355443200000000000000) := by + decide +kernel + +theorem fourYNumber_20_15_3 : + (collectedFourTrace 20 15 3 collectedFourData_20 : ℚ) / fourCommonDenominator = (3405146765776144196267117498841/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_20_15_5 : + (collectedFourTrace 20 15 5 collectedFourData_20 : ℚ) / fourCommonDenominator = (-78411052632888756633548076381/3355443200000000000000) := by + decide +kernel + +theorem fourYNumber_20_15_7 : + (collectedFourTrace 20 15 7 collectedFourData_20 : ℚ) / fourCommonDenominator = (177472155556961120068579204839/26843545600000000000000) := by + decide +kernel + +theorem fourYNumber_20_15_9 : + (collectedFourTrace 20 15 9 collectedFourData_20 : ℚ) / fourCommonDenominator = (-12165091907974821838928406501/6710886400000000000000) := by + decide +kernel + +theorem fourYNumber_20_15_11 : + (collectedFourTrace 20 15 11 collectedFourData_20 : ℚ) / fourCommonDenominator = (-194619785792343914883807927/2684354560000000000000) := by + decide +kernel + +theorem fourYNumber_20_15_13 : + (collectedFourTrace 20 15 13 collectedFourData_20 : ℚ) / fourCommonDenominator = (39976011044472042963992972403/33554432000000000000000) := by + decide +kernel + +theorem fourYNumber_20_15_15 : + (collectedFourTrace 20 15 15 collectedFourData_20 : ℚ) / fourCommonDenominator = (-50456789410054114597827183867/26843545600000000000000) := by + decide +kernel + +theorem fourYNumber_20_17_1 : + (collectedFourTrace 20 17 1 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_17_3 : + (collectedFourTrace 20 17 3 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_17_5 : + (collectedFourTrace 20 17 5 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_17_7 : + (collectedFourTrace 20 17 7 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_17_9 : + (collectedFourTrace 20 17 9 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_17_11 : + (collectedFourTrace 20 17 11 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_17_13 : + (collectedFourTrace 20 17 13 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_17_15 : + (collectedFourTrace 20 17 15 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_17_17 : + (collectedFourTrace 20 17 17 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_19_1 : + (collectedFourTrace 20 19 1 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_19_3 : + (collectedFourTrace 20 19 3 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_19_5 : + (collectedFourTrace 20 19 5 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_19_7 : + (collectedFourTrace 20 19 7 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_19_9 : + (collectedFourTrace 20 19 9 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_19_11 : + (collectedFourTrace 20 19 11 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_19_13 : + (collectedFourTrace 20 19 13 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_19_15 : + (collectedFourTrace 20 19 15 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_19_17 : + (collectedFourTrace 20 19 17 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_20_19_19 : + (collectedFourTrace 20 19 19 collectedFourData_20 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate21.lean b/lean/OAI/Analysis/LaughlinFock/Certificate21.lean new file mode 100644 index 0000000000000000000000000000000000000000..efc7eee7d97e984e962d1323f37c71b635fe4e56 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate21.lean @@ -0,0 +1,440 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate21Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate21. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_21 (r s : CopyLabel 21) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 21 r s = fourYData_21 r s := by + rw [integerRowsFourTrace_collected (by decide) collectedFourData_21 collectedFourChecked_21] + fin_cases r <;> fin_cases s + · exact fourYNumber_21_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · have h : (13:ℕ) ≤ 1 := hrs + omega + · have h : (15:ℕ) ≤ 1 := hrs + omega + · have h : (17:ℕ) ≤ 1 := hrs + omega + · have h : (19:ℕ) ≤ 1 := hrs + omega + · have h : (21:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_21_3_1 + · exact fourYNumber_21_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · have h : (13:ℕ) ≤ 3 := hrs + omega + · have h : (15:ℕ) ≤ 3 := hrs + omega + · have h : (17:ℕ) ≤ 3 := hrs + omega + · have h : (19:ℕ) ≤ 3 := hrs + omega + · have h : (21:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_21_5_1 + · exact fourYNumber_21_5_3 + · exact fourYNumber_21_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · have h : (13:ℕ) ≤ 5 := hrs + omega + · have h : (15:ℕ) ≤ 5 := hrs + omega + · have h : (17:ℕ) ≤ 5 := hrs + omega + · have h : (19:ℕ) ≤ 5 := hrs + omega + · have h : (21:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_21_7_1 + · exact fourYNumber_21_7_3 + · exact fourYNumber_21_7_5 + · exact fourYNumber_21_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · have h : (13:ℕ) ≤ 7 := hrs + omega + · have h : (15:ℕ) ≤ 7 := hrs + omega + · have h : (17:ℕ) ≤ 7 := hrs + omega + · have h : (19:ℕ) ≤ 7 := hrs + omega + · have h : (21:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_21_9_1 + · exact fourYNumber_21_9_3 + · exact fourYNumber_21_9_5 + · exact fourYNumber_21_9_7 + · exact fourYNumber_21_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · have h : (13:ℕ) ≤ 9 := hrs + omega + · have h : (15:ℕ) ≤ 9 := hrs + omega + · have h : (17:ℕ) ≤ 9 := hrs + omega + · have h : (19:ℕ) ≤ 9 := hrs + omega + · have h : (21:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_21_11_1 + · exact fourYNumber_21_11_3 + · exact fourYNumber_21_11_5 + · exact fourYNumber_21_11_7 + · exact fourYNumber_21_11_9 + · exact fourYNumber_21_11_11 + · have h : (13:ℕ) ≤ 11 := hrs + omega + · have h : (15:ℕ) ≤ 11 := hrs + omega + · have h : (17:ℕ) ≤ 11 := hrs + omega + · have h : (19:ℕ) ≤ 11 := hrs + omega + · have h : (21:ℕ) ≤ 11 := hrs + omega + · exact fourYNumber_21_13_1 + · exact fourYNumber_21_13_3 + · exact fourYNumber_21_13_5 + · exact fourYNumber_21_13_7 + · exact fourYNumber_21_13_9 + · exact fourYNumber_21_13_11 + · exact fourYNumber_21_13_13 + · have h : (15:ℕ) ≤ 13 := hrs + omega + · have h : (17:ℕ) ≤ 13 := hrs + omega + · have h : (19:ℕ) ≤ 13 := hrs + omega + · have h : (21:ℕ) ≤ 13 := hrs + omega + · exact fourYNumber_21_15_1 + · exact fourYNumber_21_15_3 + · exact fourYNumber_21_15_5 + · exact fourYNumber_21_15_7 + · exact fourYNumber_21_15_9 + · exact fourYNumber_21_15_11 + · exact fourYNumber_21_15_13 + · exact fourYNumber_21_15_15 + · have h : (17:ℕ) ≤ 15 := hrs + omega + · have h : (19:ℕ) ≤ 15 := hrs + omega + · have h : (21:ℕ) ≤ 15 := hrs + omega + · exact fourYNumber_21_17_1 + · exact fourYNumber_21_17_3 + · exact fourYNumber_21_17_5 + · exact fourYNumber_21_17_7 + · exact fourYNumber_21_17_9 + · exact fourYNumber_21_17_11 + · exact fourYNumber_21_17_13 + · exact fourYNumber_21_17_15 + · exact fourYNumber_21_17_17 + · have h : (19:ℕ) ≤ 17 := hrs + omega + · have h : (21:ℕ) ≤ 17 := hrs + omega + · exact fourYNumber_21_19_1 + · exact fourYNumber_21_19_3 + · exact fourYNumber_21_19_5 + · exact fourYNumber_21_19_7 + · exact fourYNumber_21_19_9 + · exact fourYNumber_21_19_11 + · exact fourYNumber_21_19_13 + · exact fourYNumber_21_19_15 + · exact fourYNumber_21_19_17 + · exact fourYNumber_21_19_19 + · have h : (21:ℕ) ≤ 19 := hrs + omega + · exact fourYNumber_21_21_1 + · exact fourYNumber_21_21_3 + · exact fourYNumber_21_21_5 + · exact fourYNumber_21_21_7 + · exact fourYNumber_21_21_9 + · exact fourYNumber_21_21_11 + · exact fourYNumber_21_21_13 + · exact fourYNumber_21_21_15 + · exact fourYNumber_21_21_17 + · exact fourYNumber_21_21_19 + · exact fourYNumber_21_21_21 + +theorem fourYChecked_21 (r s : CopyLabel 21) : + integerRowsFourTrace 21 r s = fourYData_21 r s := by + have hh : ∀ r s : CopyLabel 21, fourYData_21 r s = fourYData_21 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_21 r s h + · rw [integerRowsFourTrace_symm, fourYLower_21 s r (by omega), hh] + +def fourHighestCache_21_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,19}, [350337889177436160000, 122618261212102656000, 80285766269829120000, 45981847954538496000, 20436376868683776000, 3649353012264960000, -4379223614717952000, -3649353012264960000, 5838964819623936000, 24085729880948736000, 51090942171709440000]), + ({0,1,3,18}, [-350337889177436160000, -122618261212102656000, -80285766269829120000, -45981847954538496000, -20436376868683776000, -3649353012264960000, 4379223614717952000, 3649353012264960000, -5838964819623936000, -24085729880948736000, -51090942171709440000]), + ({0,1,4,17}, [622822914093219840000, 172095805209968640000, 85364982743040000000, 37287424462159872000, 12753528421810176000, 1664617163489280000, -2432902008176640000, -2304854534062080000, 2970701399457792000, 18003474860507136000, 51090942171709440000]), + ({0,1,5,16}, [-622822914093219840000, -172095805209968640000, -76366509268008960000, -27839027313377280000, -6462631340605440000, -7532204359680000, 866203501363200000, 1039444201635840000, -512189896458240000, -12164510040883200000, -51090942171709440000]) +] + +def fourHighestCache_21_1 : List (Occupation 24 × List ℚ) := [ + ({0,1,6,15}, [817455074747351040000, 182851793035591680000, 61636028275261440000, 18058459952332800000, 2881068167577600000, -547967867166720000, -222200028610560000, -217492400885760000, -640237370572800000, 7298706024529920000, 51090942171709440000]), + ({0,1,7,14}, [-817455074747351040000, -182851793035591680000, -48138318062714880000, -10184795661680640000, -964875378475008000, 382259371253760000, 117753461489664000, -151585612738560000, 776821342961664000, -3406062811447296000, -51090942171709440000]), + ({0,1,8,13}, [934234371139829760000, 179471339718967296000, 35491746942812160000, 5202242477752320000, 40673903542272000, -109216963215360000, -110221257129984000, 173240700272640000, -401215418892288000, 486580401635328000, 51090942171709440000]), + ({0,1,9,12}, [-934234371139829760000, -179471339718967296000, -25850525362421760000, -2277738598367232000, 190159190065152000, 19989311569920000, 33894919618560000, -22596613079040000, -76828484468736000, 1459741204905984000, -51090942171709440000]) +] + +def fourHighestCache_21_2 : List (Occupation 24 × List ℚ) := [ + ({0,1,10,11}, [973160803270656000000, 176705514278092800000, 21353799359692800000, 764518742507520000, -118197668413440000, -51276929679360000, 52725430517760000, -112983065395200000, 384142422343680000, -2432902008176640000, 51090942171709440000]), + ({0,2,3,17}, [-272485024915783680000, -49477543997865984000, -5079216473210880000, 8694423492378624000, 7682848446873600000, 1984735848775680000, -1946321606541312000, -1344498478202880000, 2868263420166144000, 6082255020441600000, 0]), + ({0,2,4,16}, [0, 0, -8998473475031040000, -9448397148782592000, -6290897081204736000, -1657084959129600000, 1566698506813440000, 1265410332426240000, -2458511502999552000, -5838964819623936000, 0]), + ({0,2,5,15}, [-194632160654131200000, -10755987825623040000, 14730480992747520000, 9780567361044480000, 3581563173027840000, 555500071526400000, -644003472752640000, -821951800750080000, 1152427267031040000, 4865804016353280000, 0]) +] + +def fourHighestCache_21_3 : List (Occupation 24 × List ℚ) := [ + ({0,2,6,14}, [0, 0, -13497710212546560000, -7873664290652160000, -1916192789102592000, 165708495912960000, 104446567120896000, 369078013624320000, -136583972388864000, -3892643213082624000, 0]), + ({0,2,7,13}, [-116779296392478720000, 3380453316624384000, 12646571119902720000, 4982553183928320000, 924201474932736000, -273042408038400000, -7532204359680000, -21655087534080000, -375605924069376000, 2919482409811968000, 0]), + ({0,2,8,12}, [0, 0, -9641221580390400000, -2924503879385088000, -230833093607424000, 89227651645440000, 76326337511424000, -150644087193600000, 478043903361024000, -1946321606541312000, 0]), + ({0,2,9,11}, [-38926432130826240000, 2765825440874496000, 4496726002728960000, 1513219855859712000, -71961521651712000, 31287618109440000, -86620350136320000, 135579678474240000, -307313937874944000, 973160803270656000, 0]) +] + +def fourHighestCache_21_4 : List (Occupation 24 × List ℚ) := [ + ({0,3,4,15}, [467117185569914880000, 60233531823489024000, 8345682430525440000, 421803444142080000, 1317382542508032000, 773933997957120000, -543071934332928000, -364370385899520000, 896332318801920000, 729870602452992000, 0]), + ({0,3,5,14}, [-272485024915783680000, -49477543997865984000, -11828071579484160000, -1541340085469184000, -795400780382208000, -583745837875200000, 351502870118400000, 369078013624320000, -751211848138752000, -729870602452992000, 0]), + ({0,3,6,13}, [583896481962393600000, 56853078506864640000, 8232699365130240000, 1850662611173376000, 519722100817920000, 135579678474240000, -65530177929216000, -271159356948480000, 384142422343680000, 729870602452992000, 0]), + ({0,3,7,12}, [-467117185569914880000, -60233531823489024000, -6417438114447360000, -1096688954769408000, -452453721882624000, 105595711119360000, -47452887465984000, 130872050749440000, -76828484468736000, -729870602452992000, 0]) +] + +def fourHighestCache_21_5 : List (Occupation 24 × List ℚ) := [ + ({0,3,8,11}, [622822914093219840000, 54087253065990144000, 5342843625799680000, 674885510627328000, 237090617229312000, -80536646615040000, 5021469573120000, 11298306539520000, -128047474114560000, 729870602452992000, 0]), + ({0,3,9,10}, [-583896481962393600000, -56853078506864640000, -3412088574935040000, -838334345232384000, 18424930664448000, -22596613079040000, 65530177929216000, -101684758855680000, 230485453406208000, -729870602452992000, 0]), + ({0,4,5,13}, [-311411457046609920000, -7375534508998656000, 6809112741150720000, 365562984923136000, -122021710626816000, 282457663488000000, -129302841507840000, -90386452316160000, 230485453406208000, 0, 0]), + ({0,4,6,12}, [0, 0, -5784732948234240000, -674885510627328000, 164086174973952000, -191202110668800000, 60257634877440000, 105450861035520000, -204875958583296000, 0, 0]) +] + +def fourHighestCache_21_6 : List (Occupation 24 × List ℚ) := [ + ({0,4,7,11}, [-155705728523304960000, 6146278757498880000, 4288335015444480000, 196841607266304000, 40152443240448000, 13181357629440000, 26362715258880000, -96977131130880000, 136583972388864000, 0, 0]), + ({0,4,8,10}, [0, 0, -3213740526796800000, 224961836875776000, -136274958876672000, 54463631523840000, -44188932243456000, 60257634877440000, -68291986194432000, 0, 0]), + ({0,5,6,11}, [350337889177436160000, 4609709068124160000, 1227749310627840000, 483316446412800000, -191202110668800000, 100525958184960000, -35150287011840000, -15064408719360000, 42682491371520000, 0, 0]), + ({0,5,7,10}, [-194632160654131200000, -10755987825623040000, -1338221641236480000, -342715298365440000, 119066768916480000, -52870280601600000, 8787571752960000, 25421189713920000, -42682491371520000, 0, 0]) +] + +def fourHighestCache_21_7 : List (Occupation 24 × List ℚ) := [ + ({0,5,8,9}, [311411457046609920000, 7375534508998656000, 2832108839239680000, -140601148047360000, 41369183944704000, -19409911234560000, 24856274386944000, -37661021798400000, 42682491371520000, 0, 0]), + ({0,6,7,9}, [-116779296392478720000, 3380453316624384000, -851139092643840000, 258354609537024000, -79783426179072000, 31722168360960000, -13557967847424000, 4707627724800000, 0, 0, 0]), + ({1,2,3,16}, [272485024915783680000, 49477543997865984000, 14077689948241920000, 753973656403968000, -1391951365668864000, -327650889646080000, 379623099727872000, 79088145776640000, -409751917166592000, -243290200817664000, 0]), + ({1,2,4,15}, [-272485024915783680000, -49477543997865984000, -14077689948241920000, -753973656403968000, 1391951365668864000, 327650889646080000, -379623099727872000, -79088145776640000, 409751917166592000, 243290200817664000, 0]) +] + +def fourHighestCache_21_8 : List (Occupation 24 × List ℚ) := [ + ({1,2,5,14}, [467117185569914880000, 60233531823489024000, 10595300799283200000, -365562984923136000, -869969603543040000, -137462729564160000, 188054035513344000, 83795773501440000, -264631446503424000, -243290200817664000, 0]), + ({1,2,6,13}, [-467117185569914880000, -60233531823489024000, -7381560272486400000, 1040448495550464000, 472269213351936000, -28245766348800000, -31384184832000000, -76263569141760000, 128047474114560000, 243290200817664000, 0]), + ({1,2,7,12}, [583896481962393600000, 56853078506864640000, 3412088574935040000, -961360349773824000, -240914659442688000, 78219045273600000, -21341245685760000, 41427123978240000, -25609494822912000, -243290200817664000, 0]), + ({1,2,8,11}, [-583896481962393600000, -56853078506864640000, -198348048138240000, 736398512898048000, 65703998029824000, -39978623139840000, 5272543051776000, 3766102179840000, -42682491371520000, 243290200817664000, 0]) +] + +def fourHighestCache_21_9 : List (Occupation 24 × List ℚ) := [ + ({1,2,9,10}, [622822914093219840000, 54087253065990144000, -1084637427793920000, -674885510627328000, 53536590987264000, -8691005030400000, 21090172207104000, -33894919618560000, 76828484468736000, -243290200817664000, 0]), + ({1,3,4,14}, [-194632160654131200000, -10755987825623040000, 3482389148958720000, 1119536641327104000, -521981762125824000, -190188160081920000, 191569064214528000, -4707627724800000, -145120470663168000, 0, 0]), + ({1,3,5,13}, [0, 0, -3213740526796800000, -674885510627328000, 397700390191104000, 165708495912960000, -156669850681344000, -7532204359680000, 136583972388864000, 0, 0]), + ({1,3,6,12}, [-116779296392478720000, 3380453316624384000, 3969471697551360000, -79088145776640000, -231354553909248000, -49973278924800000, 52725430517760000, 34836445163520000, -102437979291648000, 0, 0]) +] + +def fourHighestCache_21_10 : List (Occupation 24 × List ℚ) := [ + ({1,3,7,11}, [0, 0, -3213740526796800000, 224961836875776000, 175210661412864000, -38240422133760000, 16068702633984000, -45193226158080000, 68291986194432000, 0, 0]), + ({1,3,8,10}, [-38926432130826240000, 2765825440874496000, 1282985475932160000, -61513002270720000, -119240589017088000, 48669628170240000, -26362715258880000, 30128817438720000, -34145993097216000, 0, 0]), + ({1,4,5,12}, [311411457046609920000, 7375534508998656000, -1024379792916480000, 309322525704192000, -42064464347136000, -91255552819200000, 69045206630400000, -15064408719360000, -25609494822912000, 0, 0]), + ({1,4,6,11}, [-194632160654131200000, -10755987825623040000, 268648622161920000, -5272543051776000, -13036507545600000, 77494794854400000, -51470063124480000, 6590678814720000, 25609494822912000, 0, 0]) +] + +def fourHighestCache_21_11 : List (Occupation 24 × List ℚ) := [ + ({1,4,7,10}, [350337889177436160000, 4609709068124160000, 263627152588800000, -79088145776640000, -22944253280256000, -14774708551680000, 9038645231616000, 11298306539520000, -25609494822912000, 0, 0]), + ({1,4,8,9}, [-311411457046609920000, -7375534508998656000, 381631687557120000, -84360688828416000, 94905774931968000, -35053720289280000, 19332657856512000, -22596613079040000, 25609494822912000, 0, 0]), + ({1,5,6,10}, [-155705728523304960000, 6146278757498880000, 110472330608640000, -140601148047360000, 72135341752320000, -47655677583360000, 26362715258880000, -10356780994560000, 0, 0, 0]), + ({1,5,7,9}, [0, 0, -642748105359360000, 224961836875776000, -80652526682112000, 40558023475200000, -20085878292480000, 7532204359680000, 0, 0, 0]) +] + +def fourHighestCache_21_12 : List (Occupation 24 × List ℚ) := [ + ({1,6,7,8}, [116779296392478720000, -3380453316624384000, 851139092643840000, -258354609537024000, 79783426179072000, -31722168360960000, 13557967847424000, -4707627724800000, 0, 0, 0]), + ({2,3,4,13}, [194632160654131200000, 10755987825623040000, -268648622161920000, -444651130699776000, 124281371934720000, 24479664168960000, -34899213533184000, 12239832084480000, 8536498274304000, 0, 0]), + ({2,3,5,12}, [-194632160654131200000, -10755987825623040000, 268648622161920000, 444651130699776000, -124281371934720000, -24479664168960000, 34899213533184000, -12239832084480000, -8536498274304000, 0, 0]), + ({2,3,6,11}, [311411457046609920000, 7375534508998656000, -1024379792916480000, -140601148047360000, 69180400041984000, 10718906204160000, -17324070027264000, 3766102179840000, 8536498274304000, 0, 0]) +] + +def fourHighestCache_21_13 : List (Occupation 24 × List ℚ) := [ + ({2,3,7,10}, [-311411457046609920000, -7375534508998656000, 1667127898275840000, -84360688828416000, -33025819115520000, 4345502515200000, 1255367393280000, 3766102179840000, -8536498274304000, 0, 0]), + ({2,3,8,9}, [350337889177436160000, 4609709068124160000, -1664617163489280000, 145873691099136000, 24334814085120000, -13615907880960000, 7030057402368000, -7532204359680000, 8536498274304000, 0, 0]), + ({2,4,5,11}, [-116779296392478720000, 3380453316624384000, 755731170754560000, -304049982652416000, 55100971892736000, 13760757964800000, -17575143505920000, 8473729904640000, 0, 0, 0]), + ({2,4,6,10}, [0, 0, -642748105359360000, 224961836875776000, -36154580926464000, -15064408719360000, 16068702633984000, -7532204359680000, 0, 0, 0]) +] + +def fourHighestCache_21_14 : List (Occupation 24 × List ℚ) := [ + ({2,4,7,9}, [-38926432130826240000, 2765825440874496000, -2510734786560000, -61513002270720000, 8691005030400000, 9270405365760000, -8285424795648000, 3766102179840000, 0, 0, 0]), + ({2,5,6,9}, [155705728523304960000, -6146278757498880000, 532275774750720000, -84360688828416000, 8517184929792000, 7097654108160000, -6276836966400000, 2824576634880000, 0, 0, 0]), + ({2,5,7,8}, [-116779296392478720000, 3380453316624384000, -208390987284480000, 33392772661248000, 869100503040000, -8835855114240000, 6527910445056000, -2824576634880000, 0, 0, 0]), + ({3,4,5,10}, [116779296392478720000, -3380453316624384000, -112983065395200000, 79088145776640000, -18946390966272000, 1303650754560000, 1506440871936000, -941525544960000, 0, 0, 0]) +] + +def fourHighestCache_21_15 : List (Occupation 24 × List ℚ) := [ + ({3,4,6,9}, [-116779296392478720000, 3380453316624384000, 112983065395200000, -79088145776640000, 18946390966272000, -1303650754560000, -1506440871936000, 941525544960000, 0, 0, 0]), + ({3,4,7,8}, [155705728523304960000, -6146278757498880000, 210901722071040000, 28120229609472000, -9560105533440000, -434550251520000, 1757514350592000, -941525544960000, 0, 0, 0]), + ({3,5,6,8}, [-38926432130826240000, 2765825440874496000, -323884787466240000, 50967916167168000, -9386285432832000, 1738201006080000, -251073478656000, 0, 0, 0, 0]), + ({4,5,6,7}, [38926432130826240000, -2765825440874496000, 323884787466240000, -50967916167168000, 9386285432832000, -1738201006080000, 251073478656000, 0, 0, 0, 0]) +] + +def fourHighestCache_21 : List (Occupation 24 × List ℚ) := fourHighestCache_21_0 ++ fourHighestCache_21_1 ++ fourHighestCache_21_2 ++ fourHighestCache_21_3 ++ fourHighestCache_21_4 ++ fourHighestCache_21_5 ++ fourHighestCache_21_6 ++ fourHighestCache_21_7 ++ fourHighestCache_21_8 ++ fourHighestCache_21_9 ++ fourHighestCache_21_10 ++ fourHighestCache_21_11 ++ fourHighestCache_21_12 ++ fourHighestCache_21_13 ++ fourHighestCache_21_14 ++ fourHighestCache_21_15 + +theorem fourHighestNumber_21_1 : ∀ A∈highestFourOccupations 21, + kernelHighestEntry 21 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_21 1 A := by + rw [fourOccupations_21] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_21_3 : ∀ A∈highestFourOccupations 21, + kernelHighestEntry 21 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_21 3 A := by + rw [fourOccupations_21] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_21_5 : ∀ A∈highestFourOccupations 21, + kernelHighestEntry 21 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_21 5 A := by + rw [fourOccupations_21] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_21_7 : ∀ A∈highestFourOccupations 21, + kernelHighestEntry 21 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_21 7 A := by + rw [fourOccupations_21] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_21_9 : ∀ A∈highestFourOccupations 21, + kernelHighestEntry 21 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_21 9 A := by + rw [fourOccupations_21] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_21_11 : ∀ A∈highestFourOccupations 21, + kernelHighestEntry 21 ⟨⟨11,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_21 11 A := by + rw [fourOccupations_21] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_21_13 : ∀ A∈highestFourOccupations 21, + kernelHighestEntry 21 ⟨⟨13,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_21 13 A := by + rw [fourOccupations_21] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_21_15 : ∀ A∈highestFourOccupations 21, + kernelHighestEntry 21 ⟨⟨15,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_21 15 A := by + rw [fourOccupations_21] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_21_17 : ∀ A∈highestFourOccupations 21, + kernelHighestEntry 21 ⟨⟨17,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_21 17 A := by + rw [fourOccupations_21] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_21_19 : ∀ A∈highestFourOccupations 21, + kernelHighestEntry 21 ⟨⟨19,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_21 19 A := by + rw [fourOccupations_21] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_21_21 : ∀ A∈highestFourOccupations 21, + kernelHighestEntry 21 ⟨⟨21,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_21 21 A := by + rw [fourOccupations_21] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_21 : ∀ r : CopyLabel 21, ∀ A∈highestFourOccupations 21, + kernelHighestEntry 21 r A = highestLookup fourHighestCache_21 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_21_1 + · exact fourHighestNumber_21_3 + · exact fourHighestNumber_21_5 + · exact fourHighestNumber_21_7 + · exact fourHighestNumber_21_9 + · exact fourHighestNumber_21_11 + · exact fourHighestNumber_21_13 + · exact fourHighestNumber_21_15 + · exact fourHighestNumber_21_17 + · exact fourHighestNumber_21_19 + · exact fourHighestNumber_21_21 + +theorem fourZChecked_21 (r s : CopyLabel 21) : + integerFourGram 21 r s = fourZData_21 r s := by + rw [integerFourGram_cached 21 fourHighestCache_21 fourHighestChecked_21] + have h : ∀ r s : CopyLabel 21, cachedFourGram 21 fourHighestCache_21 r s = fourZData_21 r s := by + simp only [cachedFourGram, fourOccupations_21] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_21 : + fourZData_21 * (Matrix.diagonal (fun r : CopyLabel 21 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 21 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 21 => rationalCopyDiagonal 21 r.val.val) * + fourYData_21 * Matrix.diagonal (fun r : CopyLabel 21 => rationalCopyDiagonal 21 r.val.val)) * + fourZData_21 = fourLData_21 * Matrix.diagonal fourPivotData_21 * (fourLData_21)ᵀ := by + have h : ∀ r s : CopyLabel 21, + (fourZData_21 * (Matrix.diagonal (fun r : CopyLabel 21 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 21 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 21 => rationalCopyDiagonal 21 r.val.val) * + fourYData_21 * Matrix.diagonal (fun r : CopyLabel 21 => rationalCopyDiagonal 21 r.val.val)) * + fourZData_21 : Matrix (CopyLabel 21) (CopyLabel 21) ℚ) r s = + (fourLData_21 * Matrix.diagonal fourPivotData_21 * (fourLData_21)ᵀ : Matrix (CopyLabel 21) (CopyLabel 21) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_21 : ∀ r, 0 ≤ fourPivotData_21 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_21, copyDiagonalData] + +theorem integer_certificate_21 : + ((integerCompression 21).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_21) (fourPivotData_21) _ fourPivotChecked_21 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 21 = fourYData_21 from Matrix.ext fourYChecked_21, + show integerFourGram 21 = fourZData_21 from Matrix.ext fourZChecked_21] + exact fourLDLChecked_21 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate21Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate21Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..a5ebf6fe02e81f4d5165468ee7c56bfdfad754ca --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate21Data.lean @@ -0,0 +1,332 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse21 + +namespace OAI + +/-! Certificate21 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_21 : Matrix (CopyLabel 21) (CopyLabel 21) ℚ := + copyMatrixData 21 [ + [(-234648598012788536548705681690743/83886080000000000000), (128874713188638154430356187885361/838860800000000000000), (6270682580043219642783111633/16777216000000000000), (-6042544634844584151223719109329/671088640000000000000), (1187993206113164578676205684027/167772160000000000000), (-1778372107681260395143472115483/335544320000000000000), (3421529235582403416771066790023/838860800000000000000), (-366368465148827393952514902087/134217728000000000000), 0, 0, 0], + [(128874713188638154430356187885361/838860800000000000000), (-89109343832838073782565478877927/8388608000000000000000), (140306726251072355149640506041/167772160000000000000), (803074471330315088847985265223/6710886400000000000000), (-320742271871519438351384482509/1677721600000000000000), (562059596029051670113407784941/3355443200000000000000), (-1160433329158398969375622681761/8388608000000000000000), (129343096918795330831303876833/1342177280000000000000), 0, 0, 0], + [(6270682580043219642783111633/16777216000000000000), (140306726251072355149640506041/167772160000000000000), (-5638121704563113630737651779/16777216000000000000), (19891972635951350629406534823/134217728000000000000), (-526714179453404230953465801/6710886400000000000), (3299803841527864774758187533/67108864000000000000), (-5728719801694801014637510977/167772160000000000000), (2867595547173532199600893317/134217728000000000000), 0, 0, 0], + [(-6042544634844584151223719109329/671088640000000000000), (803074471330315088847985265223/6710886400000000000000), (19891972635951350629406534823/134217728000000000000), (-500887997448748544894883831207/5368709120000000000000), (76124470629698703209013437421/1342177280000000000000), (-102710567885345352527324078349/2684354560000000000000), (186761849648099558221472372289/6710886400000000000000), (-19299770582440975858393235073/1073741824000000000000), 0, 0, 0], + [(1187993206113164578676205684027/167772160000000000000), (-320742271871519438351384482509/1677721600000000000000), (-526714179453404230953465801/6710886400000000000), (76124470629698703209013437421/1342177280000000000000), (-12018851946390543258370025583/335544320000000000000), (16508910094239456529035425487/671088640000000000000), (-30331843016349867488456747787/1677721600000000000000), (3155784219706520761092961227/268435456000000000000), 0, 0, 0], + [(-1778372107681260395143472115483/335544320000000000000), (562059596029051670113407784941/3355443200000000000000), (3299803841527864774758187533/67108864000000000000), (-102710567885345352527324078349/2684354560000000000000), (16508910094239456529035425487/671088640000000000000), (-22859632155862339731192645423/1342177280000000000000), (42192733869700877570394249963/3355443200000000000000), (-4402799920270527426300877227/536870912000000000000), 0, 0, 0], + [(3421529235582403416771066790023/838860800000000000000), (-1160433329158398969375622681761/8388608000000000000000), (-5728719801694801014637510977/167772160000000000000), (186761849648099558221472372289/6710886400000000000000), (-30331843016349867488456747787/1677721600000000000000), (42192733869700877570394249963/3355443200000000000000), (-78077457933297171053368086423/8388608000000000000000), (8160844785649882576623812439/1342177280000000000000), 0, 0, 0], + [(-366368465148827393952514902087/134217728000000000000), (129343096918795330831303876833/1342177280000000000000), (2867595547173532199600893317/134217728000000000000), (-19299770582440975858393235073/1073741824000000000000), (3155784219706520761092961227/268435456000000000000), (-4402799920270527426300877227/536870912000000000000), (8160844785649882576623812439/1342177280000000000000), (-4269467008484810944634153331/1073741824000000000000), 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] + ] + +def fourZData_21 : Matrix (CopyLabel 21) (CopyLabel 21) ℚ := + copyMatrixData 21 [ + [2432902008176640000, 0, 0, 0, 0, 0, 0, 0, 0, -9280784638125, (1754068296605625/4)], + [0, 4801780279296000, 0, 0, 0, 0, 0, 0, -293077409625, 0, (1364275341804375/16)], + [0, 0, 78460462080000, 0, 0, 0, 0, -28733079375, (-1139745481875/4), (27842353914375/16), (974482387003125/64)], + [0, 0, 0, 3432645216000, 0, 0, (-13408770375/2), (-603394666875/8), 0, (12993098493375/16), (584689432201875/256)], + [0, 0, 0, 0, 339492384000, (-6630710625/2), (-258597714375/8), (-603394666875/16), (2051541867375/32), (50116237045875/256), (194896477400625/1024)], + [0, 0, 0, 0, (-6630710625/2), 46414974375, (-948191619375/32), 0, (5373085843125/256), 0, (-194896477400625/4096)], + [0, 0, 0, (-13408770375/2), (-258597714375/8), (-948191619375/32), (3101257033875/128), 0, (-13970023192125/1024), (-120650200295625/4096), (-584689432201875/16384)], + [0, 0, -28733079375, (-603394666875/8), (-603394666875/16), 0, 0, (30083534105625/2048), (-44450073793125/2048), (-83527061743125/4096), (-974482387003125/65536)], + [0, -293077409625, (-1139745481875/4), 0, (2051541867375/32), (5373085843125/256), (-13970023192125/1024), (-44450073793125/2048), (197566738243875/4096), (-662648023162125/65536), (-1364275341804375/262144)], + [-9280784638125, 0, (27842353914375/16), (12993098493375/16), (50116237045875/256), 0, (-120650200295625/4096), (-83527061743125/4096), (-662648023162125/65536), (3766142406151125/8192), (-1754068296605625/1048576)], + [(1754068296605625/4), (1364275341804375/16), (974482387003125/64), (584689432201875/256), (194896477400625/1024), (-194896477400625/4096), (-584689432201875/16384), (-974482387003125/65536), (-1364275341804375/262144), (-1754068296605625/1048576), (102179740482167473125/4194304)] + ] + +def fourLData_21 : Matrix (CopyLabel 21) (CopyLabel 21) ℚ := + copyMatrixData 21 [ + [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [(-8548810830947288451141/274878635986343591102561497660), 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [(-124033985403178175655/219902908789074872882049198128), (-14757153203417715518299991021934558935177667165/664024150087302063112879796744004241924426401196), 1, 0, 0, 0, 0, 0, 0, 0, 0], + [(2502160081413933716363/4398058175781497457640983962560), (3717840143772810771232079066398195689997611923/758884742956916643557576910564576276485058744224), (-272120122881938716411038525475117483470012132201638363/1944332809753462405897919792357279092639701896778055352), 1, 0, 0, 0, 0, 0, 0, 0], + [(-4780377743058242070237/3518446540625197966112787170048), (148130422718292903990730772372544184241501467375/21248772802793666019612153495808135741581644838272), (1060352093934662093745636740340484304893072449165496869/7777331239013849623591679169429116370558807587112221408), (-8696142136303731809503584984093518274929264230276958063583717/20356877660929408298126406948592442600862047332351177536071132), 1, 0, 0, 0, 0, 0, 0], + [(10830972661073344317609/7036893081250395932225574340096), (-57677155233072884366416276570083396963443536985/6071077943655333148460615284516610211880469953792), (-1970344530863121207550101349261994845945854550790137131/15554662478027699247183358338858232741117615174224442816), (38207069769285224485772860920057454973853491492633905148388075/81427510643717633192505627794369770403448189329404710144284528), (-138329320388805368201372891238915548986397179867976432281875152058115/155701753873727721118627377208199250545659698359367240448402652202952), 1, 0, 0, 0, 0, 0], + [(-17311727787538344820711/17592232703125989830563935850240), (132254071891215471295105810273731761612249021753/21248772802793666019612153495808135741581644838272), (4821425922303353707480669215275945173579945024230113285/62218649912110796988733433355432930964470460696897771264), (-97709222793993804444913676366268135892960181911157904449585659/325710042574870532770022511177479081613792757317618840577138112), (341084326270111014094851110796381720994679419404112880192884076287269/622807015494910884474509508832797002182638793437468961793610608811808), (-30113940812185690096786889911085352658321628449549602053881427639667038989/42502993933828826340640487872958883980979259340828174783761707040935098636), 1, 0, 0, 0, 0], + [(5740134976371624297975/14073786162500791864451148680192), (-20095565573109783113174308549806538916670646795/7726826473743151279858964907566594815120598123008), (-996785994407829034966439075010854702175460163381861913/31109324956055398494366716677716465482235230348448885632), (139261359168545739689039703818210473377229189472973893422828635/1302840170299482131080090044709916326455171029270475362308552448), (-674790097504517865140318623403218646850793520710174505343090952175795/2491228061979643537898038035331188008730555173749875847174442435247232), (22283909766527630160101788746935083691737896861232873693998231553010260385/170011975735315305362561951491835535923917037363312699135046828163740394544), (-45590055979219358411386711012075048322811174736837613418901268346051295341915/20405411281542024974131140470047325652742245613561572522118498602025493474776), 1, 0, 0, 0], + [(459900000000000/13743931799317179555128074883), (-1449802258970314775428257010308392187500000/23715148217403645111174278455143008640158085757), (-2395255250761331989568356939773718639755575142402034395/995498398593772751819734933686926895431527371150364340224), (-13418176075736194356537502364762088341877229146860666334375015/5211360681197928524320360178839665305820684117081901449234209792), (487865575284756334992773906895746705106398651519135056854571107548959/9964912247918574151592152141324752034922220694999503388697769740988928), (489775601242945684391979977752120194834021229547456876965929983663917306267/2040143708823783664350743417902026431087004448359752389620561937964884734528), (43505192969491182132926799872582277695073580574000721485545373586935100532485/11660235018024014270932080268598471801566997493463755726924856344014567699872), (-119/20), 1, 0, 0], + [(-3084053983975000000000/808466576430422326772239699), (-6630744430914671133930860629859883984375000/166006037521825515778219949186001060481106600299), (997633968783156110923401994511741399639161255134118197/62218649912110796988733433355432930964470460696897771264), (3971793243161119563670601187158757516771615055247800795636706895/20845442724791714097281440715358661223282736468327605796936839168), (8039897538616978997115340898140436139443964333369611655401031990883023/39859648991674296606368608565299008139688882779998013554791078963955712), (906375549329927009412754792175289405907055876156100252396610809398220865557/2720191611765044885800991223869368574782672597813003186160749250619846312704), (-1790004131550357230463889888075609897998371992570933724333165984690844140466951/326486580504672399586098247520757210443875929816985160353895977632407895596416), (2907/80), 0, 1, 0], + [(2477266373939568750000000/13743931799317179555128074883), (517910555825304382493487680612287469628906250/23715148217403645111174278455143008640158085757), (2545009274178797313715242194361019417755624297612648023301/15927974377500364029115758938990830326904437938405829443584), (8605765564944287811353984318618871043684221188569515573437797995/11911681557023836627017966123062092127590135124758631883963908096), (-7011887382412585013867388065737146253750710922098621848169972681187625/22776942280956740917924919180170861794107933017141722031309187979403264), (3359044370757364557384621321141036500278741566062717005569520857539523946491/10880766447060179543203964895477474299130690391252012744642997002479385250816), (-1560668513592208246078480195599799647936263394859855442167637748711884810323695/186563760288384228334913284297575548825071959895420091630797701504233083197952), (-33915/64), 0, 0, 1] + ] + +def fourPivotData_21 : CopyLabel 21 → ℚ := + copyDiagonalData 21 [(204087153776864912607415934305681690743/20971520000000000000), (68686051000951308092485085224845625578784487532876946557/2649183277647207880367275045683200000000000000), (145108231049514310362969863743338229942453332146654340745869/220766470678375750853113283073331280432017089228800), (545921396214739089908393066994960984590653939463756496884072177308629/15927974377500364029115758938990830326904437938405829443584000), (619447964244996785266991661282173764626085685727450857710891938144176089659/47646726228095346508071864492248368510360540499034527535855632384000), (628067262021864256238767162144689872333259282275344863924787846024809203999130291/291544861196246283749438965506187030964581542619414042000757606136361779200), (13719661067550378937930651710372384060889169133346919609631684465615105930952230819273/2785476210447405963060215013242233420577456740160515262628607232634722624208896000), (74340884648338837367812460820456447521614018774423081875531150438350664268838708663613/489065703770381951526275079989036446711996638548250045004638326631256773618439290880), 0, 0, 0] + +theorem fourOccupations_21 : highestFourOccupations 21 = {{0,1,2,19}, {0,1,3,18}, {0,1,4,17}, {0,1,5,16}, {0,1,6,15}, {0,1,7,14}, {0,1,8,13}, {0,1,9,12}, {0,1,10,11}, {0,2,3,17}, {0,2,4,16}, {0,2,5,15}, {0,2,6,14}, {0,2,7,13}, {0,2,8,12}, {0,2,9,11}, {0,3,4,15}, {0,3,5,14}, {0,3,6,13}, {0,3,7,12}, {0,3,8,11}, {0,3,9,10}, {0,4,5,13}, {0,4,6,12}, {0,4,7,11}, {0,4,8,10}, {0,5,6,11}, {0,5,7,10}, {0,5,8,9}, {0,6,7,9}, {1,2,3,16}, {1,2,4,15}, {1,2,5,14}, {1,2,6,13}, {1,2,7,12}, {1,2,8,11}, {1,2,9,10}, {1,3,4,14}, {1,3,5,13}, {1,3,6,12}, {1,3,7,11}, {1,3,8,10}, {1,4,5,12}, {1,4,6,11}, {1,4,7,10}, {1,4,8,9}, {1,5,6,10}, {1,5,7,9}, {1,6,7,8}, {2,3,4,13}, {2,3,5,12}, {2,3,6,11}, {2,3,7,10}, {2,3,8,9}, {2,4,5,11}, {2,4,6,10}, {2,4,7,9}, {2,5,6,9}, {2,5,7,8}, {3,4,5,10}, {3,4,6,9}, {3,4,7,8}, {3,5,6,8}, {4,5,6,7}} := by + decide +kernel + +theorem fourYNumber_21_1_1 : + (collectedFourTrace 21 1 1 collectedFourData_21 : ℚ) / fourCommonDenominator = (-234648598012788536548705681690743/83886080000000000000) := by + decide +kernel + +theorem fourYNumber_21_3_1 : + (collectedFourTrace 21 3 1 collectedFourData_21 : ℚ) / fourCommonDenominator = (128874713188638154430356187885361/838860800000000000000) := by + decide +kernel + +theorem fourYNumber_21_3_3 : + (collectedFourTrace 21 3 3 collectedFourData_21 : ℚ) / fourCommonDenominator = (-89109343832838073782565478877927/8388608000000000000000) := by + decide +kernel + +theorem fourYNumber_21_5_1 : + (collectedFourTrace 21 5 1 collectedFourData_21 : ℚ) / fourCommonDenominator = (6270682580043219642783111633/16777216000000000000) := by + decide +kernel + +theorem fourYNumber_21_5_3 : + (collectedFourTrace 21 5 3 collectedFourData_21 : ℚ) / fourCommonDenominator = (140306726251072355149640506041/167772160000000000000) := by + decide +kernel + +theorem fourYNumber_21_5_5 : + (collectedFourTrace 21 5 5 collectedFourData_21 : ℚ) / fourCommonDenominator = (-5638121704563113630737651779/16777216000000000000) := by + decide +kernel + +theorem fourYNumber_21_7_1 : + (collectedFourTrace 21 7 1 collectedFourData_21 : ℚ) / fourCommonDenominator = (-6042544634844584151223719109329/671088640000000000000) := by + decide +kernel + +theorem fourYNumber_21_7_3 : + (collectedFourTrace 21 7 3 collectedFourData_21 : ℚ) / fourCommonDenominator = (803074471330315088847985265223/6710886400000000000000) := by + decide +kernel + +theorem fourYNumber_21_7_5 : + (collectedFourTrace 21 7 5 collectedFourData_21 : ℚ) / fourCommonDenominator = (19891972635951350629406534823/134217728000000000000) := by + decide +kernel + +theorem fourYNumber_21_7_7 : + (collectedFourTrace 21 7 7 collectedFourData_21 : ℚ) / fourCommonDenominator = (-500887997448748544894883831207/5368709120000000000000) := by + decide +kernel + +theorem fourYNumber_21_9_1 : + (collectedFourTrace 21 9 1 collectedFourData_21 : ℚ) / fourCommonDenominator = (1187993206113164578676205684027/167772160000000000000) := by + decide +kernel + +theorem fourYNumber_21_9_3 : + (collectedFourTrace 21 9 3 collectedFourData_21 : ℚ) / fourCommonDenominator = (-320742271871519438351384482509/1677721600000000000000) := by + decide +kernel + +theorem fourYNumber_21_9_5 : + (collectedFourTrace 21 9 5 collectedFourData_21 : ℚ) / fourCommonDenominator = (-526714179453404230953465801/6710886400000000000) := by + decide +kernel + +theorem fourYNumber_21_9_7 : + (collectedFourTrace 21 9 7 collectedFourData_21 : ℚ) / fourCommonDenominator = (76124470629698703209013437421/1342177280000000000000) := by + decide +kernel + +theorem fourYNumber_21_9_9 : + (collectedFourTrace 21 9 9 collectedFourData_21 : ℚ) / fourCommonDenominator = (-12018851946390543258370025583/335544320000000000000) := by + decide +kernel + +theorem fourYNumber_21_11_1 : + (collectedFourTrace 21 11 1 collectedFourData_21 : ℚ) / fourCommonDenominator = (-1778372107681260395143472115483/335544320000000000000) := by + decide +kernel + +theorem fourYNumber_21_11_3 : + (collectedFourTrace 21 11 3 collectedFourData_21 : ℚ) / fourCommonDenominator = (562059596029051670113407784941/3355443200000000000000) := by + decide +kernel + +theorem fourYNumber_21_11_5 : + (collectedFourTrace 21 11 5 collectedFourData_21 : ℚ) / fourCommonDenominator = (3299803841527864774758187533/67108864000000000000) := by + decide +kernel + +theorem fourYNumber_21_11_7 : + (collectedFourTrace 21 11 7 collectedFourData_21 : ℚ) / fourCommonDenominator = (-102710567885345352527324078349/2684354560000000000000) := by + decide +kernel + +theorem fourYNumber_21_11_9 : + (collectedFourTrace 21 11 9 collectedFourData_21 : ℚ) / fourCommonDenominator = (16508910094239456529035425487/671088640000000000000) := by + decide +kernel + +theorem fourYNumber_21_11_11 : + (collectedFourTrace 21 11 11 collectedFourData_21 : ℚ) / fourCommonDenominator = (-22859632155862339731192645423/1342177280000000000000) := by + decide +kernel + +theorem fourYNumber_21_13_1 : + (collectedFourTrace 21 13 1 collectedFourData_21 : ℚ) / fourCommonDenominator = (3421529235582403416771066790023/838860800000000000000) := by + decide +kernel + +theorem fourYNumber_21_13_3 : + (collectedFourTrace 21 13 3 collectedFourData_21 : ℚ) / fourCommonDenominator = (-1160433329158398969375622681761/8388608000000000000000) := by + decide +kernel + +theorem fourYNumber_21_13_5 : + (collectedFourTrace 21 13 5 collectedFourData_21 : ℚ) / fourCommonDenominator = (-5728719801694801014637510977/167772160000000000000) := by + decide +kernel + +theorem fourYNumber_21_13_7 : + (collectedFourTrace 21 13 7 collectedFourData_21 : ℚ) / fourCommonDenominator = (186761849648099558221472372289/6710886400000000000000) := by + decide +kernel + +theorem fourYNumber_21_13_9 : + (collectedFourTrace 21 13 9 collectedFourData_21 : ℚ) / fourCommonDenominator = (-30331843016349867488456747787/1677721600000000000000) := by + decide +kernel + +theorem fourYNumber_21_13_11 : + (collectedFourTrace 21 13 11 collectedFourData_21 : ℚ) / fourCommonDenominator = (42192733869700877570394249963/3355443200000000000000) := by + decide +kernel + +theorem fourYNumber_21_13_13 : + (collectedFourTrace 21 13 13 collectedFourData_21 : ℚ) / fourCommonDenominator = (-78077457933297171053368086423/8388608000000000000000) := by + decide +kernel + +theorem fourYNumber_21_15_1 : + (collectedFourTrace 21 15 1 collectedFourData_21 : ℚ) / fourCommonDenominator = (-366368465148827393952514902087/134217728000000000000) := by + decide +kernel + +theorem fourYNumber_21_15_3 : + (collectedFourTrace 21 15 3 collectedFourData_21 : ℚ) / fourCommonDenominator = (129343096918795330831303876833/1342177280000000000000) := by + decide +kernel + +theorem fourYNumber_21_15_5 : + (collectedFourTrace 21 15 5 collectedFourData_21 : ℚ) / fourCommonDenominator = (2867595547173532199600893317/134217728000000000000) := by + decide +kernel + +theorem fourYNumber_21_15_7 : + (collectedFourTrace 21 15 7 collectedFourData_21 : ℚ) / fourCommonDenominator = (-19299770582440975858393235073/1073741824000000000000) := by + decide +kernel + +theorem fourYNumber_21_15_9 : + (collectedFourTrace 21 15 9 collectedFourData_21 : ℚ) / fourCommonDenominator = (3155784219706520761092961227/268435456000000000000) := by + decide +kernel + +theorem fourYNumber_21_15_11 : + (collectedFourTrace 21 15 11 collectedFourData_21 : ℚ) / fourCommonDenominator = (-4402799920270527426300877227/536870912000000000000) := by + decide +kernel + +theorem fourYNumber_21_15_13 : + (collectedFourTrace 21 15 13 collectedFourData_21 : ℚ) / fourCommonDenominator = (8160844785649882576623812439/1342177280000000000000) := by + decide +kernel + +theorem fourYNumber_21_15_15 : + (collectedFourTrace 21 15 15 collectedFourData_21 : ℚ) / fourCommonDenominator = (-4269467008484810944634153331/1073741824000000000000) := by + decide +kernel + +theorem fourYNumber_21_17_1 : + (collectedFourTrace 21 17 1 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_17_3 : + (collectedFourTrace 21 17 3 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_17_5 : + (collectedFourTrace 21 17 5 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_17_7 : + (collectedFourTrace 21 17 7 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_17_9 : + (collectedFourTrace 21 17 9 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_17_11 : + (collectedFourTrace 21 17 11 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_17_13 : + (collectedFourTrace 21 17 13 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_17_15 : + (collectedFourTrace 21 17 15 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_17_17 : + (collectedFourTrace 21 17 17 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_19_1 : + (collectedFourTrace 21 19 1 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_19_3 : + (collectedFourTrace 21 19 3 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_19_5 : + (collectedFourTrace 21 19 5 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_19_7 : + (collectedFourTrace 21 19 7 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_19_9 : + (collectedFourTrace 21 19 9 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_19_11 : + (collectedFourTrace 21 19 11 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_19_13 : + (collectedFourTrace 21 19 13 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_19_15 : + (collectedFourTrace 21 19 15 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_19_17 : + (collectedFourTrace 21 19 17 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_19_19 : + (collectedFourTrace 21 19 19 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_21_1 : + (collectedFourTrace 21 21 1 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_21_3 : + (collectedFourTrace 21 21 3 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_21_5 : + (collectedFourTrace 21 21 5 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_21_7 : + (collectedFourTrace 21 21 7 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_21_9 : + (collectedFourTrace 21 21 9 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_21_11 : + (collectedFourTrace 21 21 11 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_21_13 : + (collectedFourTrace 21 21 13 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_21_15 : + (collectedFourTrace 21 21 15 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_21_17 : + (collectedFourTrace 21 21 17 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_21_19 : + (collectedFourTrace 21 21 19 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_21_21_21 : + (collectedFourTrace 21 21 21 collectedFourData_21 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate22.lean b/lean/OAI/Analysis/LaughlinFock/Certificate22.lean new file mode 100644 index 0000000000000000000000000000000000000000..65b156370d37ed9c100a18cdd5a0722bf0637cdc --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate22.lean @@ -0,0 +1,454 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate22Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate22. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_22 (r s : CopyLabel 22) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 22 r s = fourYData_22 r s := by + rw [integerRowsFourTrace_collected (by decide) collectedFourData_22 collectedFourChecked_22] + fin_cases r <;> fin_cases s + · exact fourYNumber_22_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · have h : (13:ℕ) ≤ 1 := hrs + omega + · have h : (15:ℕ) ≤ 1 := hrs + omega + · have h : (17:ℕ) ≤ 1 := hrs + omega + · have h : (19:ℕ) ≤ 1 := hrs + omega + · have h : (21:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_22_3_1 + · exact fourYNumber_22_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · have h : (13:ℕ) ≤ 3 := hrs + omega + · have h : (15:ℕ) ≤ 3 := hrs + omega + · have h : (17:ℕ) ≤ 3 := hrs + omega + · have h : (19:ℕ) ≤ 3 := hrs + omega + · have h : (21:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_22_5_1 + · exact fourYNumber_22_5_3 + · exact fourYNumber_22_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · have h : (13:ℕ) ≤ 5 := hrs + omega + · have h : (15:ℕ) ≤ 5 := hrs + omega + · have h : (17:ℕ) ≤ 5 := hrs + omega + · have h : (19:ℕ) ≤ 5 := hrs + omega + · have h : (21:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_22_7_1 + · exact fourYNumber_22_7_3 + · exact fourYNumber_22_7_5 + · exact fourYNumber_22_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · have h : (13:ℕ) ≤ 7 := hrs + omega + · have h : (15:ℕ) ≤ 7 := hrs + omega + · have h : (17:ℕ) ≤ 7 := hrs + omega + · have h : (19:ℕ) ≤ 7 := hrs + omega + · have h : (21:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_22_9_1 + · exact fourYNumber_22_9_3 + · exact fourYNumber_22_9_5 + · exact fourYNumber_22_9_7 + · exact fourYNumber_22_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · have h : (13:ℕ) ≤ 9 := hrs + omega + · have h : (15:ℕ) ≤ 9 := hrs + omega + · have h : (17:ℕ) ≤ 9 := hrs + omega + · have h : (19:ℕ) ≤ 9 := hrs + omega + · have h : (21:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_22_11_1 + · exact fourYNumber_22_11_3 + · exact fourYNumber_22_11_5 + · exact fourYNumber_22_11_7 + · exact fourYNumber_22_11_9 + · exact fourYNumber_22_11_11 + · have h : (13:ℕ) ≤ 11 := hrs + omega + · have h : (15:ℕ) ≤ 11 := hrs + omega + · have h : (17:ℕ) ≤ 11 := hrs + omega + · have h : (19:ℕ) ≤ 11 := hrs + omega + · have h : (21:ℕ) ≤ 11 := hrs + omega + · exact fourYNumber_22_13_1 + · exact fourYNumber_22_13_3 + · exact fourYNumber_22_13_5 + · exact fourYNumber_22_13_7 + · exact fourYNumber_22_13_9 + · exact fourYNumber_22_13_11 + · exact fourYNumber_22_13_13 + · have h : (15:ℕ) ≤ 13 := hrs + omega + · have h : (17:ℕ) ≤ 13 := hrs + omega + · have h : (19:ℕ) ≤ 13 := hrs + omega + · have h : (21:ℕ) ≤ 13 := hrs + omega + · exact fourYNumber_22_15_1 + · exact fourYNumber_22_15_3 + · exact fourYNumber_22_15_5 + · exact fourYNumber_22_15_7 + · exact fourYNumber_22_15_9 + · exact fourYNumber_22_15_11 + · exact fourYNumber_22_15_13 + · exact fourYNumber_22_15_15 + · have h : (17:ℕ) ≤ 15 := hrs + omega + · have h : (19:ℕ) ≤ 15 := hrs + omega + · have h : (21:ℕ) ≤ 15 := hrs + omega + · exact fourYNumber_22_17_1 + · exact fourYNumber_22_17_3 + · exact fourYNumber_22_17_5 + · exact fourYNumber_22_17_7 + · exact fourYNumber_22_17_9 + · exact fourYNumber_22_17_11 + · exact fourYNumber_22_17_13 + · exact fourYNumber_22_17_15 + · exact fourYNumber_22_17_17 + · have h : (19:ℕ) ≤ 17 := hrs + omega + · have h : (21:ℕ) ≤ 17 := hrs + omega + · exact fourYNumber_22_19_1 + · exact fourYNumber_22_19_3 + · exact fourYNumber_22_19_5 + · exact fourYNumber_22_19_7 + · exact fourYNumber_22_19_9 + · exact fourYNumber_22_19_11 + · exact fourYNumber_22_19_13 + · exact fourYNumber_22_19_15 + · exact fourYNumber_22_19_17 + · exact fourYNumber_22_19_19 + · have h : (21:ℕ) ≤ 19 := hrs + omega + · exact fourYNumber_22_21_1 + · exact fourYNumber_22_21_3 + · exact fourYNumber_22_21_5 + · exact fourYNumber_22_21_7 + · exact fourYNumber_22_21_9 + · exact fourYNumber_22_21_11 + · exact fourYNumber_22_21_13 + · exact fourYNumber_22_21_15 + · exact fourYNumber_22_21_17 + · exact fourYNumber_22_21_19 + · exact fourYNumber_22_21_21 + +theorem fourYChecked_22 (r s : CopyLabel 22) : + integerRowsFourTrace 22 r s = fourYData_22 r s := by + have hh : ∀ r s : CopyLabel 22, fourYData_22 r s = fourYData_22 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_22 r s h + · rw [integerRowsFourTrace_symm, fourYLower_22 s r (by omega), hh] + +def fourHighestCache_22_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,20}, [0, -2802703113419489280000, -1868468742279659520000, -1124000727777607680000, -554701657864273920000, -160571532539658240000, 58389648196239360000, 102181884343418880000, -29194824098119680000, -335740477128376320000, -817455074747351040000]), + ({0,1,3,19}, [0, 2802703113419489280000, 1868468742279659520000, 1124000727777607680000, 554701657864273920000, 160571532539658240000, -58389648196239360000, -102181884343418880000, 29194824098119680000, 335740477128376320000, 817455074747351040000]), + ({0,1,4,18}, [0, -3923784358787284992000, -2065149662519623680000, -962660910393262080000, -370927923015057408000, -84511332915609600000, 34880131948806144000, 59157933040926720000, -6146278757498880000, -221880663145709568000, -715273190403932160000]), + ({0,1,5,17}, [0, 3736937484559319040000, 1879395460070768640000, 752919147793612800000, 215119756512460800000, 22536355444162560000, -16902266583121920000, -21511975651246080000, -11268177722081280000, 116779296392478720000, 613091306060513280000]) +] + +def fourHighestCache_22_1 : List (Occupation 24 × List ℚ) := [ + ({0,1,6,16}, [0, -3736937484559319040000, -1573447361919713280000, -514178398409195520000, -111717655062773760000, 2485627438694400000, 8903065553141760000, 2214468081745920000, 13829127204372480000, -43792236147179520000, -510909421717094400000]), + ({0,1,7,15}, [0, 3269820298989404160000, 1262035904873103360000, 317565268008468480000, 46503829716664320000, -5219817621258240000, -5377993912811520000, 2768085102182400000, -7170658550415360000, 0, 408727537373675520000]), + ({0,1,8,14}, [0, -2615856239191523328000, -917844294453166080000, -183273596479733760000, -12401021257777152000, 2899898678476800000, 2372644373299200000, -1107234040872960000, -597554879201280000, 20436376868683776000, -306545653030256640000]), + ({0,1,9,13}, [0, 1868468742279659520000, 590042760719892480000, 93007659433328640000, 1120792008720384000, -1988501950955520000, 153656968937472000, -1265410332426240000, 4609709068124160000, -23355859278495744000, 204363768686837760000]) +] + +def fourHighestCache_22_2 : List (Occupation 24 × List ℚ) := [ + ({0,1,10,12}, [0, -934234371139829760000, -295021380359946240000, -35115136724828160000, 90386452316160000, 1472256252149760000, -926461136240640000, 1581762915532800000, -3841424223436800000, 14597412049059840000, -102181884343418880000]), + ({0,2,3,18}, [0, 1121081245367795712000, 196680920239964160000, -161339817384345600000, -183773734849216512000, -76060199624048640000, 23509516247433216000, 43023951302492160000, -23048545340620800000, -113859813982666752000, -102181884343418880000]), + ({0,2,4,17}, [0, 186846874227965952000, 185754202448855040000, 209741762599649280000, 155808166502596608000, 61974977471447040000, -17977865365684224000, -37645957389680640000, 17414456479580160000, 105101366753230848000, 102181884343418880000]), + ({0,2,5,16}, [0, 0, -305948098151055360000, -238740749384417280000, -103402101449687040000, -25021982882856960000, 7999201029980160000, 19297507569500160000, -2560949482291200000, -72987060245299200000, -102181884343418880000]) +] + +def fourHighestCache_22_3 : List (Occupation 24 × List ℚ) := [ + ({0,2,6,15}, [0, 467117185569914880000, 311411457046609920000, 196613130400727040000, 65213825346109440000, 2734190182563840000, -3525071640330240000, -4982553183928320000, -6658468653957120000, 43792236147179520000, 102181884343418880000]), + ({0,2,7,14}, [0, -653964059797880832000, -344191610419937280000, -134291671528734720000, -34102808458887168000, 2319918942781440000, 3005349539512320000, -1660851061309440000, 7768213429616640000, -20436376868683776000, -102181884343418880000]), + ({0,2,8,13}, [0, 747387496911863808000, 327801533733273600000, 90265937046405120000, 11280229249056768000, -911396727521280000, -2526301342236672000, 2372644373299200000, -4012154188922880000, 2919482409811968000, 102181884343418880000]), + ({0,2,9,12}, [0, -934234371139829760000, -295021380359946240000, -57892522708500480000, -1211178461036544000, 516245698805760000, 772804167303168000, -316352583106560000, -768284844687360000, 8758447229435904000, -102181884343418880000]) +] + +def fourHighestCache_22_4 : List (Occupation 24 × List ℚ) := [ + ({0,2,10,11}, [0, 934234371139829760000, 295021380359946240000, 35115136724828160000, -90386452316160000, -1472256252149760000, 926461136240640000, -1581762915532800000, 3841424223436800000, -14597412049059840000, 102181884343418880000]), + ({0,3,4,16}, [0, -1494774993823727616000, -262241226986618880000, -19402958430535680000, -24440496706289664000, -22867772435988480000, 4447013453955072000, 12970455907368960000, -9219418136248320000, -23355859278495744000, 0]), + ({0,3,5,15}, [0, 1167792963924787200000, 319606495389941760000, 54966261314764800000, 17331602231623680000, 15535171491840000000, -1694745980928000000, -10953708190064640000, 6402373705728000000, 21896118073589760000, 0]), + ({0,3,6,14}, [0, -1307928119595761664000, -229461073613291520000, -52198176212582400000, -16070711221813248000, -4225566645780480000, -203369517711360000, 5219817621258240000, -768284844687360000, -17516894458871808000, 0]) +] + +def fourHighestCache_22_5 : List (Occupation 24 × List ℚ) := [ + ({0,3,7,13}, [0, 1167792963924787200000, 188485881896632320000, 27970840889671680000, 13571525815271424000, -372844115804160000, -275678679564288000, -619523808583680000, -2817044430520320000, 13137670844153856000, 0]), + ({0,3,8,12}, [0, -747387496911863808000, -131120613493309440000, -16450334321541120000, -6435515404910592000, -114721266401280000, 1355796784742400000, -1529037485015040000, 3585329275207680000, -8758447229435904000, 0]), + ({0,3,9,11}, [0, 467117185569914880000, 49170230059991040000, 11863221866496000000, 858671297003520000, 860409498009600000, -1301564913352704000, 1423586623979520000, -2304854534062080000, 4379223614717952000, 0]), + ({0,4,5,14}, [0, 0, -152974049075527680000, -25730010092666880000, 4555477196734464000, -5385526117171200000, -158176291553280000, 3796230997278720000, -3158504361492480000, -2919482409811968000, 0]) +] + +def fourHighestCache_22_6 : List (Occupation 24 × List ℚ) := [ + ({0,4,6,13}, [0, 373693748455931904000, 131120613493309440000, 30158946256158720000, -3290066864308224000, 2734190182563840000, 998770298093568000, -3268976692101120000, 2304854534062080000, 2919482409811968000, 0]), + ({0,4,7,12}, [0, -747387496911863808000, -131120613493309440000, -11388692991836160000, -1518492398911488000, -38240422133760000, -885787232698368000, 1529037485015040000, -512189896458240000, -2919482409811968000, 0]), + ({0,4,8,11}, [0, 747387496911863808000, 131120613493309440000, -421803444142080000, 2386202341146624000, -140214881157120000, -54231871389696000, 52725430517760000, -853649827430400000, 2919482409811968000, 0]), + ({0,4,9,10}, [0, -934234371139829760000, -98340460119982080000, -949057749319680000, -415777680654336000, -764808442675200000, 903864523161600000, -949057749319680000, 1536569689374720000, -2919482409811968000, 0]) +] + +def fourHighestCache_22_7 : List (Occupation 24 × List ℚ) := [ + ({0,5,6,12}, [0, 0, 0, -17715744653967360000, 3615458092646400000, -879529709076480000, -542318713896960000, 1159959471390720000, -1024379792916480000, 0, 0]), + ({0,5,7,11}, [0, 233558592784957440000, 2731679447777280000, 12680466039521280000, -1739939207086080000, -28680316600320000, 790881457766400000, -1067689967984640000, 853649827430400000, 0, 0]), + ({0,5,8,10}, [0, 0, -21853435582218240000, -2109017220710400000, -361545809264640000, 478005276672000000, -564915326976000000, 579979735695360000, -426824913715200000, 0, 0]), + ({0,6,7,10}, [0, -467117185569914880000, 16390076686663680000, -6379777092648960000, 949057749319680000, 38240422133760000, -293755970027520000, 342715298365440000, -256094948229120000, 0, 0]) +] + +def fourHighestCache_22_8 : List (Occupation 24 × List ℚ) := [ + ({0,6,8,9}, [0, 373693748455931904000, 0, 3163525831065600000, -108463742779392000, -325043588136960000, 393181067575296000, -369078013624320000, 256094948229120000, 0, 0]), + ({1,2,3,17}, [0, -1307928119595761664000, -382435122688819200000, -48401945215303680000, 27965568346619904000, 14085222152601600000, -5531650881748992000, -5377993912811520000, 5634088861040640000, 8758447229435904000, 0]), + ({1,2,4,16}, [0, 1307928119595761664000, 382435122688819200000, 48401945215303680000, -27965568346619904000, -14085222152601600000, 5531650881748992000, 5377993912811520000, -5634088861040640000, -8758447229435904000, 0]), + ({1,2,5,15}, [0, -1634910149494702080000, -325069854285496320000, -12838642331074560000, 20856673871953920000, 6752621208453120000, -2779383408721920000, -3361246195507200000, 2817044430520320000, 7298706024529920000, 0]) +] + +def fourHighestCache_22_9 : List (Occupation 24 × List ℚ) := [ + ({1,2,6,14}, [0, 1494774993823727616000, 262241226986618880000, -10123282659409920000, -15040305665409024000, -828542479564800000, 723091618529280000, 1423586623979520000, -341459930972160000, -5838964819623936000, 0]), + ({1,2,7,13}, [0, -1261216401038770176000, -172095805209968640000, 16054893592657920000, 9251053394558976000, -1035678099456000000, -203369517711360000, -92269503406080000, -939014810173440000, 4379223614717952000, 0]), + ({1,2,8,12}, [0, 934234371139829760000, 98340460119982080000, -15923080016363520000, -3633535383109632000, 509872295116800000, 397700390191104000, -527254305177600000, 1195109758402560000, -2919482409811968000, 0]), + ({1,2,9,11}, [0, -467117185569914880000, -49170230059991040000, 10914164117176320000, 442893616349184000, 95601055334400000, -397700390191104000, 474528874659840000, -768284844687360000, 1459741204905984000, 0]) +] + +def fourHighestCache_22_10 : List (Occupation 24 × List ℚ) := [ + ({1,3,4,15}, [0, 326982029898940416000, -57365268403322880000, -35563302884229120000, 7108894474665984000, 7332600944148480000, -2752267473027072000, -2016747717304320000, 2817044430520320000, 1459741204905984000, 0]), + ({1,3,5,14}, [0, 140135155670974464000, 62828627298877440000, 22961924990484480000, -5816368206544896000, -5924078728888320000, 2056291790192640000, 1937659571527680000, -2475584499548160000, -1459741204905984000, 0]), + ({1,3,6,13}, [0, -233558592784957440000, -90145421776650240000, -5931610933248000000, 5789252270850048000, 1864220579020800000, -519722100817920000, -1331317120573440000, 1280474741145600000, 1459741204905984000, 0]), + ({1,3,7,12}, [0, 326982029898940416000, 73755345089986560000, -131813576294400000, -5617518011449344000, 525805804339200000, -194330872479744000, 619523808583680000, -256094948229120000, -1459741204905984000, 0]) +] + +def fourHighestCache_22_11 : List (Occupation 24 × List ℚ) := [ + ({1,3,8,11}, [0, -467117185569914880000, -49170230059991040000, 5008915899187200000, 3190641766760448000, -605473350451200000, 0, 52725430517760000, -426824913715200000, 1459741204905984000, 0]), + ({1,3,9,10}, [0, 467117185569914880000, 49170230059991040000, -10914164117176320000, -442893616349184000, -95601055334400000, 397700390191104000, -474528874659840000, 768284844687360000, -1459741204905984000, 0]), + ({1,4,5,13}, [0, -373693748455931904000, 21853435582218240000, -4428936163491840000, -1265410332426240000, 2651335934607360000, -840594006540288000, -527254305177600000, 853649827430400000, 0, 0]), + ({1,4,6,12}, [0, 373693748455931904000, 0, -1054508610355200000, 1193101170573312000, -1816420051353600000, 429335648501760000, 579979735695360000, -768284844687360000, 0, 0]) +] + +def fourHighestCache_22_12 : List (Occupation 24 × List ℚ) := [ + ({1,4,7,11}, [0, -233558592784957440000, -2731679447777280000, -869969603543040000, 872229264850944000, 207135619891200000, 149137646321664000, -514072947548160000, 512189896458240000, 0, 0]), + ({1,4,8,10}, [0, 186846874227965952000, -10926717791109120000, 3479878414172160000, -1608878851227648000, 427018047160320000, -284717324795904000, 316352583106560000, -256094948229120000, 0, 0]), + ({1,5,6,11}, [0, -233558592784957440000, -2731679447777280000, 5035278614446080000, -1875518885560320000, 908210025676800000, -248562743869440000, -92269503406080000, 170729965486080000, 0, 0]), + ({1,5,7,10}, [0, 233558592784957440000, 2731679447777280000, -4191671726161920000, 1152427267031040000, -487565382205440000, 67789839237120000, 144994933923840000, -170729965486080000, 0, 0]) +] + +def fourHighestCache_22_13 : List (Occupation 24 × List ℚ) := [ + ({1,5,8,9}, [0, -373693748455931904000, 21853435582218240000, -1054508610355200000, 470009552044032000, -152961688535040000, 171734259400704000, -210901722071040000, 170729965486080000, 0, 0]), + ({1,6,7,9}, [0, 93423437113982976000, -16390076686663680000, 3216251261583360000, -840594006540288000, 286803166003200000, -99425097547776000, 26362715258880000, 0, 0, 0]), + ({2,3,4,14}, [0, -467117185569914880000, -5463358895554560000, 12601377893744640000, -1292526268121088000, -1408522215260160000, 695975682834432000, 79088145776640000, -341459930972160000, 0, 0]), + ({2,3,5,13}, [0, 467117185569914880000, 5463358895554560000, -12601377893744640000, 1292526268121088000, 1408522215260160000, -695975682834432000, -79088145776640000, 341459930972160000, 0, 0]) +] + +def fourHighestCache_22_14 : List (Occupation 24 × List ℚ) := [ + ({2,3,6,12}, [0, -467117185569914880000, 16390076686663680000, 7117933119897600000, -1364835429974016000, -573606332006400000, 284717324795904000, 131813576294400000, -256094948229120000, 0, 0]), + ({2,3,7,11}, [0, 373693748455931904000, -21853435582218240000, -4007132719349760000, 1554646979837952000, -127468073779200000, 45193226158080000, -158176291553280000, 170729965486080000, 0, 0]), + ({2,3,8,10}, [0, -186846874227965952000, 10926717791109120000, 2425369803816960000, -1138869299183616000, 274056358625280000, -112983065395200000, 105450861035520000, -85364982743040000, 0, 0]), + ({2,4,5,12}, [0, 0, -21853435582218240000, 5483444773847040000, 72309161852928000, -834915883253760000, 411258358038528000, -52725430517760000, -85364982743040000, 0, 0]) +] + +def fourHighestCache_22_15 : List (Occupation 24 × List ℚ) := [ + ({2,4,6,11}, [0, 93423437113982976000, 5463358895554560000, -3110800400547840000, -189811549863936000, 701074405785600000, -329910550953984000, 26362715258880000, 85364982743040000, 0, 0]), + ({2,4,7,10}, [0, -186846874227965952000, 10926717791109120000, 1581762915532800000, -415777680654336000, -146588284846080000, 67789839237120000, 52725430517760000, -85364982743040000, 0, 0]), + ({2,4,8,9}, [0, 186846874227965952000, -10926717791109120000, -2425369803816960000, 1138869299183616000, -274056358625280000, 112983065395200000, -105450861035520000, 85364982743040000, 0, 0]), + ({2,5,6,10}, [0, 0, 0, -843606888284160000, 723091618529280000, -420644643471360000, 180772904632320000, -52725430517760000, 0, 0, 0]) +] + +def fourHighestCache_22_16 : List (Occupation 24 × List ℚ) := [ + ({2,5,7,9}, [0, 46711718556991488000, -8195038343331840000, 2029929074933760000, -781842812534784000, 353723904737280000, -140099001090048000, 39544072888320000, 0, 0, 0]), + ({2,6,7,8}, [0, -93423437113982976000, 16390076686663680000, -3216251261583360000, 840594006540288000, -286803166003200000, 99425097547776000, -26362715258880000, 0, 0, 0]), + ({3,4,5,11}, [0, -93423437113982976000, 16390076686663680000, -2372644373299200000, 117502388011008000, 133841477468160000, -81347807084544000, 26362715258880000, 0, 0, 0]), + ({3,4,6,10}, [0, 93423437113982976000, -16390076686663680000, 2372644373299200000, -117502388011008000, -133841477468160000, 81347807084544000, -26362715258880000, 0, 0, 0]) +] + +def fourHighestCache_22_17 : List (Occupation 24 × List ℚ) := [ + ({3,4,7,9}, [0, -46711718556991488000, 8195038343331840000, -1186322186649600000, 58751194005504000, 66920738734080000, -40673903542272000, 13181357629440000, 0, 0, 0]), + ({3,5,6,9}, [0, -46711718556991488000, 8195038343331840000, -1186322186649600000, 58751194005504000, 66920738734080000, -40673903542272000, 13181357629440000, 0, 0, 0]), + ({3,5,7,8}, [0, 46711718556991488000, -8195038343331840000, 1186322186649600000, -58751194005504000, -66920738734080000, 40673903542272000, -13181357629440000, 0, 0, 0]), + ({4,5,6,8}, [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]) +] + +def fourHighestCache_22 : List (Occupation 24 × List ℚ) := fourHighestCache_22_0 ++ fourHighestCache_22_1 ++ fourHighestCache_22_2 ++ fourHighestCache_22_3 ++ fourHighestCache_22_4 ++ fourHighestCache_22_5 ++ fourHighestCache_22_6 ++ fourHighestCache_22_7 ++ fourHighestCache_22_8 ++ fourHighestCache_22_9 ++ fourHighestCache_22_10 ++ fourHighestCache_22_11 ++ fourHighestCache_22_12 ++ fourHighestCache_22_13 ++ fourHighestCache_22_14 ++ fourHighestCache_22_15 ++ fourHighestCache_22_16 ++ fourHighestCache_22_17 + +theorem fourHighestNumber_22_1 : ∀ A∈highestFourOccupations 22, + kernelHighestEntry 22 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_22 1 A := by + rw [fourOccupations_22] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_22_3 : ∀ A∈highestFourOccupations 22, + kernelHighestEntry 22 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_22 3 A := by + rw [fourOccupations_22] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_22_5 : ∀ A∈highestFourOccupations 22, + kernelHighestEntry 22 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_22 5 A := by + rw [fourOccupations_22] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_22_7 : ∀ A∈highestFourOccupations 22, + kernelHighestEntry 22 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_22 7 A := by + rw [fourOccupations_22] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_22_9 : ∀ A∈highestFourOccupations 22, + kernelHighestEntry 22 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_22 9 A := by + rw [fourOccupations_22] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_22_11 : ∀ A∈highestFourOccupations 22, + kernelHighestEntry 22 ⟨⟨11,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_22 11 A := by + rw [fourOccupations_22] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_22_13 : ∀ A∈highestFourOccupations 22, + kernelHighestEntry 22 ⟨⟨13,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_22 13 A := by + rw [fourOccupations_22] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_22_15 : ∀ A∈highestFourOccupations 22, + kernelHighestEntry 22 ⟨⟨15,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_22 15 A := by + rw [fourOccupations_22] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_22_17 : ∀ A∈highestFourOccupations 22, + kernelHighestEntry 22 ⟨⟨17,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_22 17 A := by + rw [fourOccupations_22] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_22_19 : ∀ A∈highestFourOccupations 22, + kernelHighestEntry 22 ⟨⟨19,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_22 19 A := by + rw [fourOccupations_22] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_22_21 : ∀ A∈highestFourOccupations 22, + kernelHighestEntry 22 ⟨⟨21,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_22 21 A := by + rw [fourOccupations_22] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_22 : ∀ r : CopyLabel 22, ∀ A∈highestFourOccupations 22, + kernelHighestEntry 22 r A = highestLookup fourHighestCache_22 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_22_1 + · exact fourHighestNumber_22_3 + · exact fourHighestNumber_22_5 + · exact fourHighestNumber_22_7 + · exact fourHighestNumber_22_9 + · exact fourHighestNumber_22_11 + · exact fourHighestNumber_22_13 + · exact fourHighestNumber_22_15 + · exact fourHighestNumber_22_17 + · exact fourHighestNumber_22_19 + · exact fourHighestNumber_22_21 + +theorem fourZChecked_22 (r s : CopyLabel 22) : + integerFourGram 22 r s = fourZData_22 r s := by + rw [integerFourGram_cached 22 fourHighestCache_22 fourHighestChecked_22] + have h : ∀ r s : CopyLabel 22, cachedFourGram 22 fourHighestCache_22 r s = fourZData_22 r s := by + simp only [cachedFourGram, fourOccupations_22] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_22 : + fourZData_22 * (Matrix.diagonal (fun r : CopyLabel 22 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 22 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 22 => rationalCopyDiagonal 22 r.val.val) * + fourYData_22 * Matrix.diagonal (fun r : CopyLabel 22 => rationalCopyDiagonal 22 r.val.val)) * + fourZData_22 = fourLData_22 * Matrix.diagonal fourPivotData_22 * (fourLData_22)ᵀ := by + have h : ∀ r s : CopyLabel 22, + (fourZData_22 * (Matrix.diagonal (fun r : CopyLabel 22 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 22 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 22 => rationalCopyDiagonal 22 r.val.val) * + fourYData_22 * Matrix.diagonal (fun r : CopyLabel 22 => rationalCopyDiagonal 22 r.val.val)) * + fourZData_22 : Matrix (CopyLabel 22) (CopyLabel 22) ℚ) r s = + (fourLData_22 * Matrix.diagonal fourPivotData_22 * (fourLData_22)ᵀ : Matrix (CopyLabel 22) (CopyLabel 22) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_22 : ∀ r, 0 ≤ fourPivotData_22 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_22, copyDiagonalData] + +theorem integer_certificate_22 : + ((integerCompression 22).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_22) (fourPivotData_22) _ fourPivotChecked_22 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 22 = fourYData_22 from Matrix.ext fourYChecked_22, + show integerFourGram 22 = fourZData_22 from Matrix.ext fourZChecked_22] + exact fourLDLChecked_22 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate22Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate22Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..c510d9850df2d20d198688494c9038c8e73961c5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate22Data.lean @@ -0,0 +1,332 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse22 + +namespace OAI + +/-! Certificate22 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_22 : Matrix (CopyLabel 22) (CopyLabel 22) ℚ := + copyMatrixData 22 [ + [(-215945136211697789352769368338283/1310720000000000000), (215945136211697789352769368338283/13107200000000000000), (-3788511161608733146539813479619/1310720000000000000), (1559975184191831295634040844549/2097152000000000000), (-668560793225070555271731790521/2621440000000000000), (565705286575059700614542284287/5242880000000000000), (-668560793225070555271731790521/13107200000000000000), (222853597741690185090577263507/10485760000000000000), 0, 0, 0], + [(215945136211697789352769368338283/13107200000000000000), (-215945136211697789352769368338283/131072000000000000000), (3788511161608733146539813479619/13107200000000000000), (-1559975184191831295634040844549/20971520000000000000), (668560793225070555271731790521/26214400000000000000), (-565705286575059700614542284287/52428800000000000000), (668560793225070555271731790521/131072000000000000000), (-222853597741690185090577263507/104857600000000000000), 0, 0, 0], + [(-3788511161608733146539813479619/1310720000000000000), (3788511161608733146539813479619/13107200000000000000), (-66465108098398827132277429467/1310720000000000000), (27367985687575987642702470957/2097152000000000000), (-11729136723246851846872487553/2621440000000000000), (9924654150439643870430566391/5242880000000000000), (-11729136723246851846872487553/13107200000000000000), (3909712241082283948957495851/10485760000000000000), 0, 0, 0], + [(1559975184191831295634040844549/2097152000000000000), (-1559975184191831295634040844549/20971520000000000000), (27367985687575987642702470957/2097152000000000000), (-11269170577237171382289252747/3355443200000000000), (4829644533101644878123965463/4194304000000000000), (-4086622297239853358412586161/8388608000000000000), (4829644533101644878123965463/20971520000000000000), (-1609881511033881626041321821/16777216000000000000), 0, 0, 0], + [(-668560793225070555271731790521/2621440000000000000), (668560793225070555271731790521/26214400000000000000), (-11729136723246851846872487553/2621440000000000000), (4829644533101644878123965463/4194304000000000000), (-2069847657043562090624556627/5242880000000000000), (1751409555959937153605394069/10485760000000000000), (-2069847657043562090624556627/26214400000000000000), (689949219014520696874852209/20971520000000000000), 0, 0, 0], + [(565705286575059700614542284287/5242880000000000000), (-565705286575059700614542284287/52428800000000000000), (9924654150439643870430566391/5242880000000000000), (-4086622297239853358412586161/8388608000000000000), (1751409555959937153605394069/10485760000000000000), (-1481961931966100668435333443/20971520000000000000), (1751409555959937153605394069/52428800000000000000), (-583803185319979051201798023/41943040000000000000), 0, 0, 0], + [(-668560793225070555271731790521/13107200000000000000), (668560793225070555271731790521/131072000000000000000), (-11729136723246851846872487553/13107200000000000000), (4829644533101644878123965463/20971520000000000000), (-2069847657043562090624556627/26214400000000000000), (1751409555959937153605394069/52428800000000000000), (-2069847657043562090624556627/131072000000000000000), (689949219014520696874852209/104857600000000000000), 0, 0, 0], + [(222853597741690185090577263507/10485760000000000000), (-222853597741690185090577263507/104857600000000000000), (3909712241082283948957495851/10485760000000000000), (-1609881511033881626041321821/16777216000000000000), (689949219014520696874852209/20971520000000000000), (-583803185319979051201798023/41943040000000000000), (689949219014520696874852209/104857600000000000000), (-229983073004840232291617403/83886080000000000000), 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] + ] + +def fourZData_22 : Matrix (CopyLabel 22) (CopyLabel 22) ℚ := + copyMatrixData 22 [ + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 91233825306624000, 0, 0, 0, 0, 0, 0, 0, (-50116237045875/4), 194896477400625], + [0, 0, 1333827855360000, 0, 0, 0, 0, 0, -1302566265000, 0, (584689432201875/8)], + [0, 0, 0, 51489678240000, 0, 0, 0, (-4223762668125/16), (-3419236445625/4), (194896477400625/64), (584689432201875/32)], + [0, 0, 0, 0, 4413400992000, 0, -103439085750, (-3016973334375/8), 0, (50116237045875/32), (194896477400625/64)], + [0, 0, 0, 0, 0, (5616211899375/8), (-948191619375/4), (-19912024006875/128), (5373085843125/32), (306265893058125/1024), 0], + [0, 0, 0, 0, -103439085750, (-948191619375/4), (1948102781625/16), 0, 0, (-72390120177375/512), (-584689432201875/2048)], + [0, 0, 0, (-4223762668125/16), (-3016973334375/8), (-19912024006875/128), 0, (680025789568125/4096), (-133350221379375/1024), (-2923447161009375/16384), (-1364275341804375/8192)], + [0, 0, -1302566265000, (-3419236445625/4), 0, (5373085843125/32), 0, (-133350221379375/1024), (22306447288125/128), (-473320016544375/4096), (-584689432201875/8192)], + [0, (-50116237045875/4), 0, (194896477400625/64), (50116237045875/32), (306265893058125/1024), (-72390120177375/512), (-2923447161009375/16384), (-473320016544375/4096), (349382562329926125/262144), (-1754068296605625/65536)], + [0, 194896477400625, (584689432201875/8), (584689432201875/32), (194896477400625/64), 0, (-584689432201875/2048), (-1364275341804375/8192), (-584689432201875/8192), (-1754068296605625/65536), (12767863130992344375/524288)] + ] + +def fourLData_22 : Matrix (CopyLabel 22) (CopyLabel 22) ℚ := + copyMatrixData 22 [ + [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, (-281759001143527504710/1889186882518106776847), 1, 0, 0, 0, 0, 0, 0, 0, 0], + [0, (4516345162834156618785/120907960481158833718208), (-163845303147667745278173597/1241300715662491208518027376), 1, 0, 0, 0, 0, 0, 0, 0], + [0, (-864479036197004558497/60453980240579416859104), (93704257580975353717016787/1551625894578114010647534220), (-107209907723209102697370623360346/902760519093081289878957414547685), 1, 0, 0, 0, 0, 0, 0], + [0, (71144428250976364305/10991632771014439428928), (-656009087179626239457820719/24826014313249824170360547520), (40888012561406657173603830318939/515863153767475022787975665455820), (-50351149458651936478777592120931795/438763676641540108390949454759117472), 1, 0, 0, 0, 0, 0], + [0, (-155175095919694458459/60453980240579416859104), (1005262441971194191709101149/99304057252999296681442190080), (-31307006481528102413340575283189/902760519093081289878957414547685), (24605740536733806567629897446205343/603300055382117649037555500293786524), (-99014764382294804145890057625027304458528/291107268883302171114657206843225690858255), 1, 0, 0, 0, 0], + [0, (175193208941590517615/241815920962317667436416), (-578048670176143455403598799/198608114505998593362884380160), (32725041219376190027990739453963/8253810460279600364607610647293120), (-15168802217910587715934674483744511055/154444814177822118153614208075209350144), (-404387875247230340023283618623839111143595/1863086520853133895133806123796644421492832), (-241594650436252992171996347847338760300930435/150435247616908832584135131604999972144928122), 1, 0, 0, 0], + [0, (1380000000000000/1889186882518106776847), (-203770575252764288855849127/397216229011997186725768760320), (-176764375836144120789986212342329/14444168305489300638063318632762960), (103616033331847848585777943769681895/38611203544455529538403552018802337536), (325262114945183327776230776455747800344935/1397314890639850421350354592847483316119624), (1468151455180036203053520846993983347811393285/902611485701452995504810789629999832869568732), (-204/49), 1, 0, 0], + [0, (-72786937500000000/1889186882518106776847), (-52949955015551930470202619/66899575412546894606445264896), (45077441214468065884503493526001537/924426771551315240836052392496829440), (101065376724840752328215248891832154141/308889628355644236307228416150418700288), (8130072555576470941981350029772918139593441/18630865208531338951338061237966444214928320), (-449948144786238924459884042334773513376322589/601740990467635330336540526419999888579712488), (2907/196), 0, 1, 0], + [0, (1147370000000000000/1889186882518106776847), (65503599217649001326101461669/1337991508250937892128905297920), (22798619955980752149014522559487803/66030483682236802916860885178344960), (8513386380551269323296066713692619085/19305601772227764769201776009401168768), (-62827488129543903360339675724249542131409/1863086520853133895133806123796644421492832), (-23092887666265972052450246932154400504514993995/9627855847482165285384648422719998217275399808), (-969/14), 0, 0, 1] + ] + +def fourPivotData_22 : CopyLabel 22 → ℚ := + copyDiagonalData 22 [0, (252477167008626784680769368338283/131072000000000000000), (5512078762303357411618169673832059/439665310840577577157120), (174310682459542995847618821831459734200779/406749418508285119207187210567680), (62404806161650616515384108365273134448230433/1650762092055920072921522129458624000), (1853038138367273847451704609262271325740924925561/359435203904749656793865793338669033062400), (93365306868407495301616487806062763484680988634866769/867182089706185958462280668530801767094845440000), (248386774123325334530722962536243545224925735855560001827/50477692865647294731437465522510224253388848145367040), 0, 0, 0] + +theorem fourOccupations_22 : highestFourOccupations 22 = {{0,1,2,20}, {0,1,3,19}, {0,1,4,18}, {0,1,5,17}, {0,1,6,16}, {0,1,7,15}, {0,1,8,14}, {0,1,9,13}, {0,1,10,12}, {0,2,3,18}, {0,2,4,17}, {0,2,5,16}, {0,2,6,15}, {0,2,7,14}, {0,2,8,13}, {0,2,9,12}, {0,2,10,11}, {0,3,4,16}, {0,3,5,15}, {0,3,6,14}, {0,3,7,13}, {0,3,8,12}, {0,3,9,11}, {0,4,5,14}, {0,4,6,13}, {0,4,7,12}, {0,4,8,11}, {0,4,9,10}, {0,5,6,12}, {0,5,7,11}, {0,5,8,10}, {0,6,7,10}, {0,6,8,9}, {1,2,3,17}, {1,2,4,16}, {1,2,5,15}, {1,2,6,14}, {1,2,7,13}, {1,2,8,12}, {1,2,9,11}, {1,3,4,15}, {1,3,5,14}, {1,3,6,13}, {1,3,7,12}, {1,3,8,11}, {1,3,9,10}, {1,4,5,13}, {1,4,6,12}, {1,4,7,11}, {1,4,8,10}, {1,5,6,11}, {1,5,7,10}, {1,5,8,9}, {1,6,7,9}, {2,3,4,14}, {2,3,5,13}, {2,3,6,12}, {2,3,7,11}, {2,3,8,10}, {2,4,5,12}, {2,4,6,11}, {2,4,7,10}, {2,4,8,9}, {2,5,6,10}, {2,5,7,9}, {2,6,7,8}, {3,4,5,11}, {3,4,6,10}, {3,4,7,9}, {3,5,6,9}, {3,5,7,8}, {4,5,6,8}} := by + decide +kernel + +theorem fourYNumber_22_1_1 : + (collectedFourTrace 22 1 1 collectedFourData_22 : ℚ) / fourCommonDenominator = (-215945136211697789352769368338283/1310720000000000000) := by + decide +kernel + +theorem fourYNumber_22_3_1 : + (collectedFourTrace 22 3 1 collectedFourData_22 : ℚ) / fourCommonDenominator = (215945136211697789352769368338283/13107200000000000000) := by + decide +kernel + +theorem fourYNumber_22_3_3 : + (collectedFourTrace 22 3 3 collectedFourData_22 : ℚ) / fourCommonDenominator = (-215945136211697789352769368338283/131072000000000000000) := by + decide +kernel + +theorem fourYNumber_22_5_1 : + (collectedFourTrace 22 5 1 collectedFourData_22 : ℚ) / fourCommonDenominator = (-3788511161608733146539813479619/1310720000000000000) := by + decide +kernel + +theorem fourYNumber_22_5_3 : + (collectedFourTrace 22 5 3 collectedFourData_22 : ℚ) / fourCommonDenominator = (3788511161608733146539813479619/13107200000000000000) := by + decide +kernel + +theorem fourYNumber_22_5_5 : + (collectedFourTrace 22 5 5 collectedFourData_22 : ℚ) / fourCommonDenominator = (-66465108098398827132277429467/1310720000000000000) := by + decide +kernel + +theorem fourYNumber_22_7_1 : + (collectedFourTrace 22 7 1 collectedFourData_22 : ℚ) / fourCommonDenominator = (1559975184191831295634040844549/2097152000000000000) := by + decide +kernel + +theorem fourYNumber_22_7_3 : + (collectedFourTrace 22 7 3 collectedFourData_22 : ℚ) / fourCommonDenominator = (-1559975184191831295634040844549/20971520000000000000) := by + decide +kernel + +theorem fourYNumber_22_7_5 : + (collectedFourTrace 22 7 5 collectedFourData_22 : ℚ) / fourCommonDenominator = (27367985687575987642702470957/2097152000000000000) := by + decide +kernel + +theorem fourYNumber_22_7_7 : + (collectedFourTrace 22 7 7 collectedFourData_22 : ℚ) / fourCommonDenominator = (-11269170577237171382289252747/3355443200000000000) := by + decide +kernel + +theorem fourYNumber_22_9_1 : + (collectedFourTrace 22 9 1 collectedFourData_22 : ℚ) / fourCommonDenominator = (-668560793225070555271731790521/2621440000000000000) := by + decide +kernel + +theorem fourYNumber_22_9_3 : + (collectedFourTrace 22 9 3 collectedFourData_22 : ℚ) / fourCommonDenominator = (668560793225070555271731790521/26214400000000000000) := by + decide +kernel + +theorem fourYNumber_22_9_5 : + (collectedFourTrace 22 9 5 collectedFourData_22 : ℚ) / fourCommonDenominator = (-11729136723246851846872487553/2621440000000000000) := by + decide +kernel + +theorem fourYNumber_22_9_7 : + (collectedFourTrace 22 9 7 collectedFourData_22 : ℚ) / fourCommonDenominator = (4829644533101644878123965463/4194304000000000000) := by + decide +kernel + +theorem fourYNumber_22_9_9 : + (collectedFourTrace 22 9 9 collectedFourData_22 : ℚ) / fourCommonDenominator = (-2069847657043562090624556627/5242880000000000000) := by + decide +kernel + +theorem fourYNumber_22_11_1 : + (collectedFourTrace 22 11 1 collectedFourData_22 : ℚ) / fourCommonDenominator = (565705286575059700614542284287/5242880000000000000) := by + decide +kernel + +theorem fourYNumber_22_11_3 : + (collectedFourTrace 22 11 3 collectedFourData_22 : ℚ) / fourCommonDenominator = (-565705286575059700614542284287/52428800000000000000) := by + decide +kernel + +theorem fourYNumber_22_11_5 : + (collectedFourTrace 22 11 5 collectedFourData_22 : ℚ) / fourCommonDenominator = (9924654150439643870430566391/5242880000000000000) := by + decide +kernel + +theorem fourYNumber_22_11_7 : + (collectedFourTrace 22 11 7 collectedFourData_22 : ℚ) / fourCommonDenominator = (-4086622297239853358412586161/8388608000000000000) := by + decide +kernel + +theorem fourYNumber_22_11_9 : + (collectedFourTrace 22 11 9 collectedFourData_22 : ℚ) / fourCommonDenominator = (1751409555959937153605394069/10485760000000000000) := by + decide +kernel + +theorem fourYNumber_22_11_11 : + (collectedFourTrace 22 11 11 collectedFourData_22 : ℚ) / fourCommonDenominator = (-1481961931966100668435333443/20971520000000000000) := by + decide +kernel + +theorem fourYNumber_22_13_1 : + (collectedFourTrace 22 13 1 collectedFourData_22 : ℚ) / fourCommonDenominator = (-668560793225070555271731790521/13107200000000000000) := by + decide +kernel + +theorem fourYNumber_22_13_3 : + (collectedFourTrace 22 13 3 collectedFourData_22 : ℚ) / fourCommonDenominator = (668560793225070555271731790521/131072000000000000000) := by + decide +kernel + +theorem fourYNumber_22_13_5 : + (collectedFourTrace 22 13 5 collectedFourData_22 : ℚ) / fourCommonDenominator = (-11729136723246851846872487553/13107200000000000000) := by + decide +kernel + +theorem fourYNumber_22_13_7 : + (collectedFourTrace 22 13 7 collectedFourData_22 : ℚ) / fourCommonDenominator = (4829644533101644878123965463/20971520000000000000) := by + decide +kernel + +theorem fourYNumber_22_13_9 : + (collectedFourTrace 22 13 9 collectedFourData_22 : ℚ) / fourCommonDenominator = (-2069847657043562090624556627/26214400000000000000) := by + decide +kernel + +theorem fourYNumber_22_13_11 : + (collectedFourTrace 22 13 11 collectedFourData_22 : ℚ) / fourCommonDenominator = (1751409555959937153605394069/52428800000000000000) := by + decide +kernel + +theorem fourYNumber_22_13_13 : + (collectedFourTrace 22 13 13 collectedFourData_22 : ℚ) / fourCommonDenominator = (-2069847657043562090624556627/131072000000000000000) := by + decide +kernel + +theorem fourYNumber_22_15_1 : + (collectedFourTrace 22 15 1 collectedFourData_22 : ℚ) / fourCommonDenominator = (222853597741690185090577263507/10485760000000000000) := by + decide +kernel + +theorem fourYNumber_22_15_3 : + (collectedFourTrace 22 15 3 collectedFourData_22 : ℚ) / fourCommonDenominator = (-222853597741690185090577263507/104857600000000000000) := by + decide +kernel + +theorem fourYNumber_22_15_5 : + (collectedFourTrace 22 15 5 collectedFourData_22 : ℚ) / fourCommonDenominator = (3909712241082283948957495851/10485760000000000000) := by + decide +kernel + +theorem fourYNumber_22_15_7 : + (collectedFourTrace 22 15 7 collectedFourData_22 : ℚ) / fourCommonDenominator = (-1609881511033881626041321821/16777216000000000000) := by + decide +kernel + +theorem fourYNumber_22_15_9 : + (collectedFourTrace 22 15 9 collectedFourData_22 : ℚ) / fourCommonDenominator = (689949219014520696874852209/20971520000000000000) := by + decide +kernel + +theorem fourYNumber_22_15_11 : + (collectedFourTrace 22 15 11 collectedFourData_22 : ℚ) / fourCommonDenominator = (-583803185319979051201798023/41943040000000000000) := by + decide +kernel + +theorem fourYNumber_22_15_13 : + (collectedFourTrace 22 15 13 collectedFourData_22 : ℚ) / fourCommonDenominator = (689949219014520696874852209/104857600000000000000) := by + decide +kernel + +theorem fourYNumber_22_15_15 : + (collectedFourTrace 22 15 15 collectedFourData_22 : ℚ) / fourCommonDenominator = (-229983073004840232291617403/83886080000000000000) := by + decide +kernel + +theorem fourYNumber_22_17_1 : + (collectedFourTrace 22 17 1 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_17_3 : + (collectedFourTrace 22 17 3 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_17_5 : + (collectedFourTrace 22 17 5 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_17_7 : + (collectedFourTrace 22 17 7 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_17_9 : + (collectedFourTrace 22 17 9 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_17_11 : + (collectedFourTrace 22 17 11 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_17_13 : + (collectedFourTrace 22 17 13 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_17_15 : + (collectedFourTrace 22 17 15 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_17_17 : + (collectedFourTrace 22 17 17 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_19_1 : + (collectedFourTrace 22 19 1 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_19_3 : + (collectedFourTrace 22 19 3 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_19_5 : + (collectedFourTrace 22 19 5 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_19_7 : + (collectedFourTrace 22 19 7 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_19_9 : + (collectedFourTrace 22 19 9 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_19_11 : + (collectedFourTrace 22 19 11 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_19_13 : + (collectedFourTrace 22 19 13 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_19_15 : + (collectedFourTrace 22 19 15 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_19_17 : + (collectedFourTrace 22 19 17 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_19_19 : + (collectedFourTrace 22 19 19 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_21_1 : + (collectedFourTrace 22 21 1 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_21_3 : + (collectedFourTrace 22 21 3 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_21_5 : + (collectedFourTrace 22 21 5 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_21_7 : + (collectedFourTrace 22 21 7 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_21_9 : + (collectedFourTrace 22 21 9 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_21_11 : + (collectedFourTrace 22 21 11 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_21_13 : + (collectedFourTrace 22 21 13 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_21_15 : + (collectedFourTrace 22 21 15 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_21_17 : + (collectedFourTrace 22 21 17 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_21_19 : + (collectedFourTrace 22 21 19 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_22_21_21 : + (collectedFourTrace 22 21 21 collectedFourData_22 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate23.lean b/lean/OAI/Analysis/LaughlinFock/Certificate23.lean new file mode 100644 index 0000000000000000000000000000000000000000..f4ac3cb4fb82d0b1ee37d3ead3afbdf22a520124 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate23.lean @@ -0,0 +1,516 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Certificate23Data +import OAI.Analysis.LaughlinFock.GramCache +import OAI.Analysis.LaughlinFock.TraceSymmetry + +namespace OAI + +/-! Certificate23. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fourYLower_23 (r s : CopyLabel 23) (hrs : s.val.val ≤ r.val.val) : + integerRowsFourTrace 23 r s = fourYData_23 r s := by + rw [integerRowsFourTrace_collected (by decide) collectedFourData_23 collectedFourChecked_23] + fin_cases r <;> fin_cases s + · exact fourYNumber_23_1_1 + · have h : (3:ℕ) ≤ 1 := hrs + omega + · have h : (5:ℕ) ≤ 1 := hrs + omega + · have h : (7:ℕ) ≤ 1 := hrs + omega + · have h : (9:ℕ) ≤ 1 := hrs + omega + · have h : (11:ℕ) ≤ 1 := hrs + omega + · have h : (13:ℕ) ≤ 1 := hrs + omega + · have h : (15:ℕ) ≤ 1 := hrs + omega + · have h : (17:ℕ) ≤ 1 := hrs + omega + · have h : (19:ℕ) ≤ 1 := hrs + omega + · have h : (21:ℕ) ≤ 1 := hrs + omega + · have h : (23:ℕ) ≤ 1 := hrs + omega + · exact fourYNumber_23_3_1 + · exact fourYNumber_23_3_3 + · have h : (5:ℕ) ≤ 3 := hrs + omega + · have h : (7:ℕ) ≤ 3 := hrs + omega + · have h : (9:ℕ) ≤ 3 := hrs + omega + · have h : (11:ℕ) ≤ 3 := hrs + omega + · have h : (13:ℕ) ≤ 3 := hrs + omega + · have h : (15:ℕ) ≤ 3 := hrs + omega + · have h : (17:ℕ) ≤ 3 := hrs + omega + · have h : (19:ℕ) ≤ 3 := hrs + omega + · have h : (21:ℕ) ≤ 3 := hrs + omega + · have h : (23:ℕ) ≤ 3 := hrs + omega + · exact fourYNumber_23_5_1 + · exact fourYNumber_23_5_3 + · exact fourYNumber_23_5_5 + · have h : (7:ℕ) ≤ 5 := hrs + omega + · have h : (9:ℕ) ≤ 5 := hrs + omega + · have h : (11:ℕ) ≤ 5 := hrs + omega + · have h : (13:ℕ) ≤ 5 := hrs + omega + · have h : (15:ℕ) ≤ 5 := hrs + omega + · have h : (17:ℕ) ≤ 5 := hrs + omega + · have h : (19:ℕ) ≤ 5 := hrs + omega + · have h : (21:ℕ) ≤ 5 := hrs + omega + · have h : (23:ℕ) ≤ 5 := hrs + omega + · exact fourYNumber_23_7_1 + · exact fourYNumber_23_7_3 + · exact fourYNumber_23_7_5 + · exact fourYNumber_23_7_7 + · have h : (9:ℕ) ≤ 7 := hrs + omega + · have h : (11:ℕ) ≤ 7 := hrs + omega + · have h : (13:ℕ) ≤ 7 := hrs + omega + · have h : (15:ℕ) ≤ 7 := hrs + omega + · have h : (17:ℕ) ≤ 7 := hrs + omega + · have h : (19:ℕ) ≤ 7 := hrs + omega + · have h : (21:ℕ) ≤ 7 := hrs + omega + · have h : (23:ℕ) ≤ 7 := hrs + omega + · exact fourYNumber_23_9_1 + · exact fourYNumber_23_9_3 + · exact fourYNumber_23_9_5 + · exact fourYNumber_23_9_7 + · exact fourYNumber_23_9_9 + · have h : (11:ℕ) ≤ 9 := hrs + omega + · have h : (13:ℕ) ≤ 9 := hrs + omega + · have h : (15:ℕ) ≤ 9 := hrs + omega + · have h : (17:ℕ) ≤ 9 := hrs + omega + · have h : (19:ℕ) ≤ 9 := hrs + omega + · have h : (21:ℕ) ≤ 9 := hrs + omega + · have h : (23:ℕ) ≤ 9 := hrs + omega + · exact fourYNumber_23_11_1 + · exact fourYNumber_23_11_3 + · exact fourYNumber_23_11_5 + · exact fourYNumber_23_11_7 + · exact fourYNumber_23_11_9 + · exact fourYNumber_23_11_11 + · have h : (13:ℕ) ≤ 11 := hrs + omega + · have h : (15:ℕ) ≤ 11 := hrs + omega + · have h : (17:ℕ) ≤ 11 := hrs + omega + · have h : (19:ℕ) ≤ 11 := hrs + omega + · have h : (21:ℕ) ≤ 11 := hrs + omega + · have h : (23:ℕ) ≤ 11 := hrs + omega + · exact fourYNumber_23_13_1 + · exact fourYNumber_23_13_3 + · exact fourYNumber_23_13_5 + · exact fourYNumber_23_13_7 + · exact fourYNumber_23_13_9 + · exact fourYNumber_23_13_11 + · exact fourYNumber_23_13_13 + · have h : (15:ℕ) ≤ 13 := hrs + omega + · have h : (17:ℕ) ≤ 13 := hrs + omega + · have h : (19:ℕ) ≤ 13 := hrs + omega + · have h : (21:ℕ) ≤ 13 := hrs + omega + · have h : (23:ℕ) ≤ 13 := hrs + omega + · exact fourYNumber_23_15_1 + · exact fourYNumber_23_15_3 + · exact fourYNumber_23_15_5 + · exact fourYNumber_23_15_7 + · exact fourYNumber_23_15_9 + · exact fourYNumber_23_15_11 + · exact fourYNumber_23_15_13 + · exact fourYNumber_23_15_15 + · have h : (17:ℕ) ≤ 15 := hrs + omega + · have h : (19:ℕ) ≤ 15 := hrs + omega + · have h : (21:ℕ) ≤ 15 := hrs + omega + · have h : (23:ℕ) ≤ 15 := hrs + omega + · exact fourYNumber_23_17_1 + · exact fourYNumber_23_17_3 + · exact fourYNumber_23_17_5 + · exact fourYNumber_23_17_7 + · exact fourYNumber_23_17_9 + · exact fourYNumber_23_17_11 + · exact fourYNumber_23_17_13 + · exact fourYNumber_23_17_15 + · exact fourYNumber_23_17_17 + · have h : (19:ℕ) ≤ 17 := hrs + omega + · have h : (21:ℕ) ≤ 17 := hrs + omega + · have h : (23:ℕ) ≤ 17 := hrs + omega + · exact fourYNumber_23_19_1 + · exact fourYNumber_23_19_3 + · exact fourYNumber_23_19_5 + · exact fourYNumber_23_19_7 + · exact fourYNumber_23_19_9 + · exact fourYNumber_23_19_11 + · exact fourYNumber_23_19_13 + · exact fourYNumber_23_19_15 + · exact fourYNumber_23_19_17 + · exact fourYNumber_23_19_19 + · have h : (21:ℕ) ≤ 19 := hrs + omega + · have h : (23:ℕ) ≤ 19 := hrs + omega + · exact fourYNumber_23_21_1 + · exact fourYNumber_23_21_3 + · exact fourYNumber_23_21_5 + · exact fourYNumber_23_21_7 + · exact fourYNumber_23_21_9 + · exact fourYNumber_23_21_11 + · exact fourYNumber_23_21_13 + · exact fourYNumber_23_21_15 + · exact fourYNumber_23_21_17 + · exact fourYNumber_23_21_19 + · exact fourYNumber_23_21_21 + · have h : (23:ℕ) ≤ 21 := hrs + omega + · exact fourYNumber_23_23_1 + · exact fourYNumber_23_23_3 + · exact fourYNumber_23_23_5 + · exact fourYNumber_23_23_7 + · exact fourYNumber_23_23_9 + · exact fourYNumber_23_23_11 + · exact fourYNumber_23_23_13 + · exact fourYNumber_23_23_15 + · exact fourYNumber_23_23_17 + · exact fourYNumber_23_23_19 + · exact fourYNumber_23_23_21 + · exact fourYNumber_23_23_23 + +theorem fourYChecked_23 (r s : CopyLabel 23) : + integerRowsFourTrace 23 r s = fourYData_23 r s := by + have hh : ∀ r s : CopyLabel 23, fourYData_23 r s = fourYData_23 s r := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + by_cases h : s.val.val ≤ r.val.val + · exact fourYLower_23 r s h + · rw [integerRowsFourTrace_symm, fourYLower_23 s r (by omega), hh] + +def fourHighestCache_23_0 : List (Occupation 24 × List ℚ) := [ + ({0,1,2,21}, [179840116444417228800000, 65396405979788083200000, 45164392879791144960000, 28304381963127029760000, 15122918882825994240000, 5620003638888038400000, -204363768686837760000, -2350183339898634240000, -817455074747351040000, 4393821026767011840000, 13283644964644454400000, 25852016738884976640000]), + ({0,1,3,20}, [-179840116444417228800000, -65396405979788083200000, -45164392879791144960000, -28304381963127029760000, -15122918882825994240000, -5620003638888038400000, 204363768686837760000, 2350183339898634240000, 817455074747351040000, -4393821026767011840000, -13283644964644454400000, -25852016738884976640000]), + ({0,1,4,19}, [323712209599951011840000, 95291905856262635520000, 51587254181377474560000, 25443289201511301120000, 10749534232927666176000, 3211430650793164800000, -218961180735897600000, -1328364496464445440000, -642286130158632960000, 2574983485454155776000, 10320370318685306880000, 25852016738884976640000]), + ({0,1,5,18}, [-323712209599951011840000, -95291905856262635520000, -47456954856338227200000, -20624606655632179200000, -6851564244921876480000, -1250767727151022080000, 258911992659640320000, 467885470414602240000, 433312652403671040000, -963429195237949440000, -7459277557069578240000, -25852016738884976640000]) +] + +def fourHighestCache_23_1 : List (Occupation 24 × List ℚ) := [ + ({0,1,6,17}, [431616279466601349120000, 104634249567660933120000, 41001825591275028480000, 14707020686901903360000, 3904423580701163520000, 329594198370877440000, -243546295765893120000, -69913920866549760000, -205900338376212480000, 43792236147179520000, 5006912332827525120000, 25852016738884976640000]), + ({0,1,7,16}, [-431616279466601349120000, -104634249567660933120000, -34117993382876282880000, -9699370198047129600000, -1862051304165212160000, -31318905727549440000, 156594528637747200000, -11072340408729600000, 21511975651246080000, 306545653030256640000, -2963274645959147520000, -25852016738884976640000]), + ({0,1,8,15}, [503552326044368240640000, 104634249567660933120000, 26610313880591400960000, 5980961936212623360000, 717804011068784640000, -50458237005496320000, -54570820585881600000, -15132198558597120000, 66328591591342080000, -306545653030256640000, 1328364496464445440000, 25852016738884976640000]), + ({0,1,9,14}, [-503552326044368240640000, -104634249567660933120000, -20414864893032529920000, -3288168748809584640000, -224040899356065792000, 64377750662184960000, -3005349539512320000, 28629908771143680000, -59157933040926720000, 143054638080786432000, -102181884343418880000, -25852016738884976640000]) +] + +def fourHighestCache_23_2 : List (Occupation 24 × List ℚ) := [ + ({0,1,10,13}, [539520349333251686400000, 102765780825381273600000, 16132445168745185280000, 1623837809085972480000, 28155379896483840000, -37035848836546560000, 6033295692103680000, -7908814577664000000, 3841424223436800000, 43792236147179520000, -715273190403932160000, 25852016738884976640000]), + ({0,1,11,12}, [-539520349333251686400000, -102765780825381273600000, -13673933665745633280000, -915208022927278080000, 59157933040926720000, 2313545539092480000, 10688197986385920000, -17399392070860800000, 42255666457804800000, -160571532539658240000, 1124000727777607680000, -25852016738884976640000]), + ({0,2,3,19}, [-143872093155533783040000, -29895499876474552320000, -6422861301586329600000, 2861092761615728640000, 4373384649898328064000, 2408572988094873600000, 14597412049059840000, -1021818843434188800000, -175168944588718080000, 1818837541312856064000, 2963274645959147520000, 0]), + ({0,2,4,18}, [0, 0, -4130299325039247360000, -4818682545879121920000, -3897969988005789696000, -1960662923642142720000, -39950811923742720000, 860479026049843200000, 208973477754961920000, -1611554290216206336000, -2861092761615728640000, 0]) +] + +def fourHighestCache_23_3 : List (Occupation 24 × List ℚ) := [ + ({0,2,5,17}, [-107904069866650337280000, -9342343711398297600000, 6455129265063198720000, 5917585968730275840000, 2947140664220712960000, 921173528780144640000, -15365696893747200000, -397971549548052480000, -227412314027458560000, 919636959090769920000, 2452365224242053120000, 0]), + ({0,2,6,16}, [0, 0, -6883832208398745600000, -5007650488854773760000, -2042372276535951360000, -298275292643328000000, 86951767128145920000, 80986261275279360000, 184388362724966400000, -350337889177436160000, -2043637686868377600000, 0]), + ({0,2,7,15}, [-71936046577766891520000, 0, 7507679502284881920000, 3718408261834506240000, 1144247293096427520000, 81777142733045760000, -102023708051865600000, 26204538967326720000, -87840567242588160000, 0, 1634910149494702080000, 0]), + ({0,2,8,14}, [0, 0, -6195448987558871040000, -2692793187403038720000, -493763111712718848000, -13919513656688640000, 57576170125393920000, -13497710212546560000, -7170658550415360000, 163491014949470208000, -1226182612121026560000, 0]) +] + +def fourHighestCache_23_4 : List (Occupation 24 × List ℚ) := [ + ({0,2,9,13}, [-35968023288883445760000, 1868468742279659520000, 4282419724287344640000, 1664330939723612160000, 195885519459581952000, -27341901825638400000, -3027946152591360000, -20721094193479680000, 55316508817489920000, -186846874227965952000, 817455074747351040000, 0]), + ({0,2,10,12}, [0, 0, -2458511502999552000000, -708629786158694400000, -87313312937410560000, 34722303297454080000, -16721493678489600000, 25308206648524800000, -46097090681241600000, 116779296392478720000, -408727537373675520000, 0]), + ({0,3,4,17}, [251776163022184120320000, 39237843587872849920000, 8228330686601625600000, 858686361412239360000, 475414661892538368000, 591579330409267200000, 80669908692172800000, -301167659117445120000, -15365696893747200000, 484634080028786688000, 306545653030256640000, 0]), + ({0,3,5,16}, [-143872093155533783040000, -29895499876474552320000, -9176394184945827840000, -1863105812775567360000, -452384193842380800000, -383283751046676480000, -88804689400627200000, 228406565002936320000, 46097090681241600000, -423324949422735360000, -306545653030256640000, 0]) +] + +def fourHighestCache_23_5 : List (Occupation 24 × List ℚ) := [ + ({0,3,6,15}, [323712209599951011840000, 39237843587872849920000, 7260291782295552000000, 1557403766633594880000, 486866625400995840000, 140935075773972480000, 31115536209838080000, -82093495316152320000, -76060199624048640000, 262753416883077120000, 306545653030256640000, 0]), + ({0,3,7,14}, [-251776163022184120320000, -39237843587872849920000, -6507372634501939200000, -929549340028108800000, -366715914337124352000, -55678054626754560000, 26257264397844480000, -7381560272486400000, 71706585504153600000, -122618261212102656000, -306545653030256640000, 0]), + ({0,3,8,13}, [359680232888834457600000, 37369374845593190400000, 4895511030347857920000, 699561012109639680000, 165325859931488256000, 40018601762979840000, -39883022084505600000, 24886403204382720000, -36109387700305920000, 17516894458871808000, 306545653030256640000, 0]), + ({0,3,9,12}, [-323712209599951011840000, -39237843587872849920000, -3277503147436277760000, -555198783352012800000, -66623854002241536000, -10841159674920960000, 15252713828352000000, -3321702122618880000, -6914563602186240000, 52550683376615424000, -306545653030256640000, 0]) +] + +def fourHighestCache_23_6 : List (Occupation 24 × List ℚ) := [ + ({0,3,10,11}, [359680232888834457600000, 37369374845593190400000, 2928701827948216320000, 348620546583429120000, 71179331198976000000, -24225307421736960000, 12179574449602560000, -18981154986393600000, 34572818010931200000, -87584472294359040000, 306545653030256640000, 0]), + ({0,4,5,15}, [-179840116444417228800000, -9342343711398297600000, 3637060454749962240000, 990710839428710400000, -75608267362467840000, 78297264318873600000, 58864177070899200000, -82831651343400960000, 6402373705728000000, 102181884343418880000, 0, 0]), + ({0,4,6,14}, [0, 0, -3441916104199372800000, -992081700622172160000, 7339379928072192000, -21873521460510720000, -55226122365173760000, 59052482179891200000, 7170658550415360000, -93423437113982976000, 0, 0]), + ({0,4,7,13}, [-107904069866650337280000, 1868468742279659520000, 3824521956853678080000, 462823829084897280000, 50173519680700416000, 4722692133519360000, 17150829326991360000, -13497710212546560000, -24329020081766400000, 70067577835487232000, 0, 0]) +] + +def fourHighestCache_23_7 : List (Occupation 24 × List ℚ) := [ + ({0,4,8,12}, [0, 0, -3146894723839426560000, -215963363400744960000, -8098626127527936000, -24473870165606400000, 14461832370585600000, -13497710212546560000, 28682634201661440000, -46711718556991488000, 0, 0]), + ({0,4,9,11}, [-35968023288883445760000, 1868468742279659520000, 1332205920687882240000, 166085106130944000000, -30369847978229760000, 28030229424046080000, -18393643046338560000, 14710395114455040000, -18438836272496640000, 23355859278495744000, 0, 0]), + ({0,5,6,13}, [215808139733300674560000, 7473874969118638080000, 144437550801223680000, 435933859520839680000, -20562917901926400000, -15162327376035840000, 29940512329728000000, -25097304926453760000, 6914563602186240000, 14597412049059840000, 0, 0]), + ({0,5,7,12}, [-107904069866650337280000, -9342343711398297600000, -920405243935457280000, -257616453509775360000, -17715744653967360000, 24359148899205120000, -25308206648524800000, 17504842931896320000, -2048759585832960000, -14597412049059840000, 0, 0]) +] + +def fourHighestCache_23_8 : List (Occupation 24 × List ℚ) := [ + ({0,5,8,11}, [215808139733300674560000, 7473874969118638080000, 1619544452600954880000, 105239959313448960000, 3479878414172160000, -3690200735907840000, 4722692133519360000, -1476312054497280000, -6402373705728000000, 14597412049059840000, 0, 0]), + ({0,5,9,10}, [-179840116444417228800000, -9342343711398297600000, -1279962551249141760000, -156594528637747200000, 43340303885598720000, -21127833228902400000, 11411289604915200000, -9016048618536960000, 11524272670310400000, -14597412049059840000, 0, 0]), + ({0,6,7,11}, [-107904069866650337280000, 1868468742279659520000, 38414242234368000000, 14024964517724160000, 31318905727549440000, -21051352384634880000, 14168076400558080000, -9068774049054720000, 4353614119895040000, 0, 0, 0]), + ({0,6,8,10}, [0, 0, -491702300599910400000, 74237406169006080000, -41758540970065920000, 20649827952230400000, -11659852348784640000, 6748855106273280000, -3073139378749440000, 0, 0, 0]) +] + +def fourHighestCache_23_9 : List (Occupation 24 × List ℚ) := [ + ({0,7,8,9}, [71936046577766891520000, 0, 752919147793612800000, -128017345297121280000, 43213762852356096000, -17533233548328960000, 8383343452323840000, -4270759871938560000, 1792664637603840000, 0, 0, 0]), + ({1,2,3,18}, [143872093155533783040000, 29895499876474552320000, 10553160626625576960000, 1957589784263393280000, -475414661892538368000, -447910064452730880000, 25353399874682880000, 161339817384345600000, -33804533166243840000, -207283251096649728000, -102181884343418880000, 0]), + ({1,2,4,17}, [-143872093155533783040000, -29895499876474552320000, -10553160626625576960000, -1957589784263393280000, 475414661892538368000, 447910064452730880000, -25353399874682880000, -161339817384345600000, 33804533166243840000, 207283251096649728000, 102181884343418880000, 0]), + ({1,2,5,16}, [251776163022184120320000, 39237843587872849920000, 9605097128281374720000, 953170332900065280000, -452384193842380800000, -239614485090140160000, 17218619166228480000, 88578723269836800000, -3073139378749440000, -145974120490598400000, -102181884343418880000, 0]) +] + +def fourHighestCache_23_10 : List (Occupation 24 × List ℚ) := [ + ({1,2,6,15}, [-251776163022184120320000, -39237843587872849920000, -7884139076181688320000, -268161539613327360000, 411258358038528000000, 75563074136309760000, -16043595286118400000, -25097304926453760000, -20487595858329600000, 87584472294359040000, 102181884343418880000, 0]), + ({1,2,7,14}, [323712209599951011840000, 39237843587872849920000, 5195142119775928320000, -96065734403358720000, -283768267046584320000, -12179574449602560000, 18190273528627200000, -5325268482293760000, 23304640288849920000, -40872753737367552000, -102181884343418880000, 0]), + ({1,2,8,13}, [-323712209599951011840000, -39237843587872849920000, -2982481767076331520000, 328901235569786880000, 132551732321648640000, 1242813719347200000, -14665201888296960000, 9332401201643520000, -12036462566768640000, 5838964819623936000, 102181884343418880000, 0]), + ({1,2,9,12}, [359680232888834457600000, 37369374845593190400000, 1453594926148485120000, -400502370212904960000, -41948352519929856000, 3460758203105280000, 4496726002728960000, -1265410332426240000, -2304854534062080000, 17516894458871808000, -102181884343418880000, 0]) +] + +def fourHighestCache_23_11 : List (Occupation 24 × List ℚ) := [ + ({1,2,10,11}, [-359680232888834457600000, -37369374845593190400000, -470190324948664320000, 360009239575265280000, 16133981738434560000, -10496995875717120000, 4541919228887040000, -6327051662131200000, 11524272670310400000, -29194824098119680000, 102181884343418880000, 0]), + ({1,3,4,16}, [-107904069866650337280000, -9342343711398297600000, 948063498344202240000, 1004419451363328000000, -23030468050157568000, -208295579362590720000, 8134780708454400000, 72761094114508800000, -30731393787494400000, -61309130606051328000, 0, 0]), + ({1,3,5,15}, [0, 0, -1720958052099686400000, -685008793286737920000, 41125835803852800000, 164051410953830400000, -1175023880110080000, -63481418343383040000, 23560735237079040000, 58389648196239360000, 0, 0]), + ({1,3,6,14}, [-71936046577766891520000, 0, 2688996956405760000000, 364227274016686080000, -127490090991943680000, -63383499686707200000, -2146678242508800000, 30422573408747520000, -2817044430520320000, -46711718556991488000, 0, 0]) +] + +def fourHighestCache_23_12 : List (Occupation 24 × List ℚ) := [ + ({1,3,7,13}, [0, 0, -2212660352699596800000, -232835501166428160000, 151216534724935680000, 10936760730255360000, -3525071640330240000, -4007132719349760000, -11268177722081280000, 35033788917743616000, 0, 0]), + ({1,3,8,12}, [-35968023288883445760000, 1868468742279659520000, 1528886840927846400000, 71601134643118080000, -90603379801718784000, -4703571922452480000, 10168475885568000000, -8066990869217280000, 14341317100830720000, -23355859278495744000, 0, 0]), + ({1,3,9,11}, [0, 0, -983404601199820800000, 40493130637639680000, 25814370781495296000, 7036237672611840000, -9038645231616000000, 7592461994557440000, -9219418136248320000, 11677929639247872000, 0, 0]), + ({1,4,5,14}, [179840116444417228800000, 9342343711398297600000, -195144350550589440000, 1370861193461760000, 68268887434395648000, -56423742858362880000, -3638054705725440000, 23779169163509760000, -13573032256143360000, -8758447229435904000, 0, 0]) +] + +def fourHighestCache_23_13 : List (Occupation 24 × List ℚ) := [ + ({1,4,6,13}, [-107904069866650337280000, -9342343711398297600000, -527043403455528960000, 93324012016435200000, -36949981706846208000, 32313156703027200000, 8134780708454400000, -20457467040890880000, 10243797929164800000, 8758447229435904000, 0, 0]), + ({1,4,7,12}, [215808139733300674560000, 7473874969118638080000, 242778010921205760000, 10755987825623040000, -24359148899205120000, -4607970867118080000, -6304455049052160000, 9490577493196800000, -2304854534062080000, -8758447229435904000, 0, 0]), + ({1,4,8,11}, [-179840116444417228800000, -9342343711398297600000, 195144350550589440000, -55361702043648000000, 34988595691585536000, 133841477468160000, -790881457766400000, 263627152588800000, -3841424223436800000, 8758447229435904000, 0, 0]), + ({1,4,9,10}, [215808139733300674560000, 7473874969118638080000, -52243369438740480000, -9490577493196800000, -12970455907368960000, -6902396195143680000, 6982353441423360000, -5694346495918080000, 6914563602186240000, -8758447229435904000, 0, 0]) +] + +def fourHighestCache_23_14 : List (Occupation 24 × List ℚ) := [ + ({1,5,6,12}, [-107904069866650337280000, 1868468742279659520000, 775967693134233600000, -178317406011064320000, 38278662555893760000, -9196821523169280000, -4632305681203200000, 7592461994557440000, -4865804016353280000, 0, 0, 0]), + ({1,5,7,11}, [0, 0, -737553450899865600000, 138351529678602240000, -17083039487754240000, 382404221337600000, 6417438114447360000, -6959756828344320000, 4097519171665920000, 0, 0, 0]), + ({1,5,8,10}, [-35968023288883445760000, 1868468742279659520000, 152120399248097280000, -22882836844707840000, -5061641329704960000, 4168206012579840000, -4474129389649920000, 3743505566760960000, -2048759585832960000, 0, 0, 0]), + ({1,6,7,10}, [107904069866650337280000, -1868468742279659520000, 453288058365542400000, -88262370686730240000, 10439635242516480000, 401524432404480000, -2508224051773440000, 2319918942781440000, -1280474741145600000, 0, 0, 0]) +] + +def fourHighestCache_23_15 : List (Occupation 24 × List ℚ) := [ + ({1,6,8,9}, [-71936046577766891520000, 0, -261216847193702400000, 53779939128115200000, -1455221882290176000, -3116594403901440000, 3276508896460800000, -2478095234334720000, 1280474741145600000, 0, 0, 0]), + ({2,3,4,15}, [107904069866650337280000, 9342343711398297600000, 772894553755484160000, -319410658076590080000, -18095367753695232000, 44244168408760320000, -6959756828344320000, -9279675771125760000, 7170658550415360000, 2919482409811968000, 0, 0]), + ({2,3,5,14}, [-107904069866650337280000, -9342343711398297600000, -772894553755484160000, 319410658076590080000, 18095367753695232000, -44244168408760320000, 6959756828344320000, 9279675771125760000, -7170658550415360000, -2919482409811968000, 0, 0]), + ({2,3,6,13}, [179840116444417228800000, 9342343711398297600000, 50706799749365760000, -224715784866693120000, 13223537973854208000, 20133582253424640000, -2463030825615360000, -5957973648506880000, 3841424223436800000, 2919482409811968000, 0, 0]) +] + +def fourHighestCache_23_16 : List (Occupation 24 × List ℚ) := [ + ({2,3,7,12}, [-179840116444417228800000, -9342343711398297600000, 440995500850544640000, 150478378697687040000, -36254006024011776000, -1625217940684800000, -338949196185600000, 2583546095370240000, -768284844687360000, -2919482409811968000, 0, 0]), + ({2,3,8,11}, [215808139733300674560000, 7473874969118638080000, -740626590278615040000, -56732563237109760000, 29800413328637952000, -2466507227627520000, -338949196185600000, 210901722071040000, -1280474741145600000, 2919482409811968000, 0, 0]), + ({2,3,9,10}, [-215808139733300674560000, -7473874969118638080000, 1035647970638561280000, -31002553144442880000, -12843914874126336000, -133841477468160000, 2056291790192640000, -1898115498639360000, 2304854534062080000, -2919482409811968000, 0, 0]), + ({2,4,5,13}, [-71936046577766891520000, 0, 722187754006118400000, -94694873209896960000, -31318905727549440000, 24110586155335680000, -4496726002728960000, -3321702122618880000, 3329234326978560000, 0, 0, 0]) +] + +def fourHighestCache_23_17 : List (Occupation 24 × List ℚ) := [ + ({2,4,6,12}, [0, 0, -491702300599910400000, 74237406169006080000, 23030468050157568000, -18508364312739840000, 2801980021800960000, 3374427553136640000, -3073139378749440000, 0, 0, 0]), + ({2,4,7,11}, [-35968023288883445760000, 1868468742279659520000, 299631089428070400000, -93745815460577280000, 6453592695373824000, 4091725168312320000, 677898392371200000, -2794447817441280000, 2048759585832960000, 0, 0, 0]), + ({2,4,8,10}, [0, 0, -295021380359946240000, 87735116381552640000, -16956498454511616000, 2600348705095680000, -1717342594007040000, 1687213776568320000, -1024379792916480000, 0, 0, 0]), + ({2,5,6,11}, [107904069866650337280000, -1868468742279659520000, -38414242234368000000, 39965876332462080000, -21195623068139520000, 8814417301831680000, -1785132433244160000, -632705166213120000, 768284844687360000, 0, 0, 0]) +] + +def fourHighestCache_23_18 : List (Occupation 24 × List ℚ) := [ + ({2,5,7,10}, [-71936046577766891520000, 0, 132144993286225920000, -27206322147164160000, 11705045574942720000, -4952134666321920000, 564915326976000000, 896332318801920000, -768284844687360000, 0, 0, 0]), + ({2,5,8,9}, [107904069866650337280000, -1868468742279659520000, 109096447945605120000, -30897102283407360000, 6516863211995136000, -1051611608678400000, 1197620493189120000, -1265410332426240000, 768284844687360000, 0, 0, 0]), + ({2,6,7,9}, [-35968023288883445760000, 1868468742279659520000, -192071211171840000000, 34482431558615040000, -8984413360226304000, 2715069971496960000, -768284844687360000, 158176291553280000, 0, 0, 0, 0]), + ({3,4,5,12}, [71936046577766891520000, 0, -230485453406208000000, 20457467040890880000, 8288437677391872000, -5602221842595840000, 1694745980928000000, -52725430517760000, -256094948229120000, 0, 0, 0]) +] + +def fourHighestCache_23_19 : List (Occupation 24 × List ℚ) := [ + ({3,4,6,11}, [-71936046577766891520000, 0, 230485453406208000000, -20457467040890880000, -8288437677391872000, 5602221842595840000, -1694745980928000000, 52725430517760000, 256094948229120000, 0, 0, 0]), + ({3,4,7,10}, [107904069866650337280000, -1868468742279659520000, -136754702354350080000, 33217021226188800000, -1202139815804928000, -1739939207086080000, 474528874659840000, 210901722071040000, -256094948229120000, 0, 0, 0]), + ({3,4,8,9}, [-107904069866650337280000, 1868468742279659520000, 185924932414341120000, -56838014098145280000, 10439635242516480000, -1548737096417280000, 519722100817920000, -421803444142080000, 256094948229120000, 0, 0, 0]), + ({3,5,6,10}, [-35968023288883445760000, 1868468742279659520000, -93730751051857920000, -12759554185297920000, 9490577493196800000, -3862282635509760000, 1220217106268160000, -263627152588800000, 0, 0, 0, 0]) +] + +def fourHighestCache_23_20 : List (Occupation 24 × List ℚ) := [ + ({3,5,7,9}, [0, 0, -49170230059991040000, 23620992871956480000, -9237495426711552000, 3288676303503360000, -994250975477760000, 210901722071040000, 0, 0, 0, 0]), + ({3,6,7,8}, [35968023288883445760000, -1868468742279659520000, 192071211171840000000, -34482431558615040000, 8984413360226304000, -2715069971496960000, 768284844687360000, -158176291553280000, 0, 0, 0, 0]), + ({4,5,6,9}, [35968023288883445760000, -1868468742279659520000, 142900981111848960000, -10861438686658560000, -253082066485248000, 573606332006400000, -225966130790400000, 52725430517760000, 0, 0, 0, 0]), + ({4,5,7,8}, [-35968023288883445760000, 1868468742279659520000, -142900981111848960000, 10861438686658560000, 253082066485248000, -573606332006400000, 225966130790400000, -52725430517760000, 0, 0, 0, 0]) +] + +def fourHighestCache_23 : List (Occupation 24 × List ℚ) := fourHighestCache_23_0 ++ fourHighestCache_23_1 ++ fourHighestCache_23_2 ++ fourHighestCache_23_3 ++ fourHighestCache_23_4 ++ fourHighestCache_23_5 ++ fourHighestCache_23_6 ++ fourHighestCache_23_7 ++ fourHighestCache_23_8 ++ fourHighestCache_23_9 ++ fourHighestCache_23_10 ++ fourHighestCache_23_11 ++ fourHighestCache_23_12 ++ fourHighestCache_23_13 ++ fourHighestCache_23_14 ++ fourHighestCache_23_15 ++ fourHighestCache_23_16 ++ fourHighestCache_23_17 ++ fourHighestCache_23_18 ++ fourHighestCache_23_19 ++ fourHighestCache_23_20 + +theorem fourHighestNumber_23_1 : ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 ⟨⟨1,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_23 1 A := by + rw [fourOccupations_23] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_23_3 : ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 ⟨⟨3,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_23 3 A := by + rw [fourOccupations_23] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_23_5 : ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 ⟨⟨5,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_23 5 A := by + rw [fourOccupations_23] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_23_7 : ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 ⟨⟨7,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_23 7 A := by + rw [fourOccupations_23] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_23_9 : ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 ⟨⟨9,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_23 9 A := by + rw [fourOccupations_23] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_23_11 : ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 ⟨⟨11,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_23 11 A := by + rw [fourOccupations_23] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_23_13 : ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 ⟨⟨13,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_23 13 A := by + rw [fourOccupations_23] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_23_15 : ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 ⟨⟨15,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_23 15 A := by + rw [fourOccupations_23] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_23_17 : ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 ⟨⟨17,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_23 17 A := by + rw [fourOccupations_23] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_23_19 : ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 ⟨⟨19,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_23 19 A := by + rw [fourOccupations_23] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_23_21 : ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 ⟨⟨21,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_23 21 A := by + rw [fourOccupations_23] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestNumber_23_23 : ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 ⟨⟨23,by decide⟩,by decide⟩ A = highestLookup fourHighestCache_23 23 A := by + rw [fourOccupations_23] + apply @of_decide_eq_true _ (boundedEntriesDecidable _ _ _) + decide +kernel + +theorem fourHighestChecked_23 : ∀ r : CopyLabel 23, ∀ A∈highestFourOccupations 23, + kernelHighestEntry 23 r A = highestLookup fourHighestCache_23 r.val.val A := by + intro r + fin_cases r + · exact fourHighestNumber_23_1 + · exact fourHighestNumber_23_3 + · exact fourHighestNumber_23_5 + · exact fourHighestNumber_23_7 + · exact fourHighestNumber_23_9 + · exact fourHighestNumber_23_11 + · exact fourHighestNumber_23_13 + · exact fourHighestNumber_23_15 + · exact fourHighestNumber_23_17 + · exact fourHighestNumber_23_19 + · exact fourHighestNumber_23_21 + · exact fourHighestNumber_23_23 + +theorem fourZChecked_23 (r s : CopyLabel 23) : + integerFourGram 23 r s = fourZData_23 r s := by + rw [integerFourGram_cached 23 fourHighestCache_23 fourHighestChecked_23] + have h : ∀ r s : CopyLabel 23, cachedFourGram 23 fourHighestCache_23 r s = fourZData_23 r s := by + simp only [cachedFourGram, fourOccupations_23] + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact h r s + +theorem fourLDLChecked_23 : + fourZData_23 * (Matrix.diagonal (fun r : CopyLabel 23 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 23 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 23 => rationalCopyDiagonal 23 r.val.val) * + fourYData_23 * Matrix.diagonal (fun r : CopyLabel 23 => rationalCopyDiagonal 23 r.val.val)) * + fourZData_23 = fourLData_23 * Matrix.diagonal fourPivotData_23 * (fourLData_23)ᵀ := by + have h : ∀ r s : CopyLabel 23, + (fourZData_23 * (Matrix.diagonal (fun r : CopyLabel 23 => + ((if r.val.val=1 then 2 else 0)+3/10^6) * rationalCopyDiagonal 23 r.val.val) - + Matrix.diagonal (fun r : CopyLabel 23 => rationalCopyDiagonal 23 r.val.val) * + fourYData_23 * Matrix.diagonal (fun r : CopyLabel 23 => rationalCopyDiagonal 23 r.val.val)) * + fourZData_23 : Matrix (CopyLabel 23) (CopyLabel 23) ℚ) r s = + (fourLData_23 * Matrix.diagonal fourPivotData_23 * (fourLData_23)ᵀ : Matrix (CopyLabel 23) (CopyLabel 23) ℚ) r s := by + apply @of_decide_eq_true _ (matrixEntriesDecidable _ _) + decide +kernel + exact Matrix.ext h + +theorem fourPivotChecked_23 : ∀ r, 0 ≤ fourPivotData_23 r := by + intro r + fin_cases r <;> norm_num [fourPivotData_23, copyDiagonalData] + +theorem integer_certificate_23 : + ((integerCompression 23).map (algebraMap ℚ ℂ)).PosSemidef := by + apply rational_ldl_posSemidef _ (fourLData_23) (fourPivotData_23) _ fourPivotChecked_23 + unfold integerCompression integerFourMiddle + rw [show integerRowsFourTrace 23 = fourYData_23 from Matrix.ext fourYChecked_23, + show integerFourGram 23 = fourZData_23 from Matrix.ext fourZChecked_23] + exact fourLDLChecked_23 + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Certificate23Data.lean b/lean/OAI/Analysis/LaughlinFock/Certificate23Data.lean new file mode 100644 index 0000000000000000000000000000000000000000..169dbb5df600bc60454d7d13c57adc9861f22ece --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Certificate23Data.lean @@ -0,0 +1,383 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LDL +import OAI.Analysis.LaughlinFock.Sparse23 + +namespace OAI + +/-! Certificate23 Data. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def fourYData_23 : Matrix (CopyLabel 23) (CopyLabel 23) ℚ := + copyMatrixData 23 [ + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] + ] + +def fourZData_23 : Matrix (CopyLabel 23) (CopyLabel 23) ℚ := + copyMatrixData 23 [ + [1124000727777607680000, 0, 0, 0, 0, 0, 0, 0, 0, 0, (-2143861251406875/2), (246544043911790625/4)], + [0, 1824676506132480000, 0, 0, 0, 0, 0, 0, 0, -27842353914375, 0, (49308808782358125/4)], + [0, 0, 24008901396480000, 0, 0, 0, 0, 0, (-4396161144375/2), -27842353914375, (6821376709021875/32), (147926426347074375/64)], + [0, 0, 0, 823834851840000, 0, 0, 0, -402263111250, (-23934655119375/4), 0, (6821376709021875/64), (49308808782358125/128)], + [0, 0, 0, 0, 61787613888000, 0, (-603394666875/4), (-16291656005625/8), (-51288546684375/16), (116937886440375/16), (15786614669450625/512), (49308808782358125/1024)], + [0, 0, 0, 0, 0, (18453267669375/2), (-4740958096875/4), (-33186706678125/16), 0, (918797679174375/256), (2143861251406875/512), 0], + [0, 0, 0, 0, (-603394666875/4), (-4740958096875/4), (65597620213125/64), (-86285437363125/128), (209550347881875/512), 0, (-12668271031040625/8192), (-49308808782358125/16384)], + [0, 0, 0, -402263111250, (-16291656005625/8), (-33186706678125/16), (-86285437363125/128), 1609052445000, (-488950811724375/1024), (-2533654206208125/2048), (-26311024449084375/16384), (-49308808782358125/32768)], + [0, 0, (-4396161144375/2), (-23934655119375/4), (-51288546684375/16), 0, (209550347881875/512), (-488950811724375/1024), (1734529802630625/2048), (-2366600082721875/2048), (-115963404053371875/131072), (-147926426347074375/262144)], + [0, -27842353914375, -27842353914375, 0, (116937886440375/16), (918797679174375/256), 0, (-2533654206208125/2048), (-2366600082721875/2048), (316372667529043125/65536), (-25921231494283125/65536), (-49308808782358125/262144)], + [(-2143861251406875/2), 0, (6821376709021875/32), (6821376709021875/64), (15786614669450625/512), (2143861251406875/512), (-12668271031040625/8192), (-26311024449084375/16384), (-115963404053371875/131072), (-25921231494283125/65536), (101850365435360416875/2097152), (-246544043911790625/4194304)], + [(246544043911790625/4), (49308808782358125/4), (147926426347074375/64), (49308808782358125/128), (49308808782358125/1024), 0, (-49308808782358125/16384), (-49308808782358125/32768), (-147926426347074375/262144), (-49308808782358125/262144), (-246544043911790625/4194304), (25851868812458629565625/8388608)] + ] + +def fourLData_23 : Matrix (CopyLabel 23) (CopyLabel 23) ℚ := + copyMatrixData 23 [ + [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [(345/2097155147486), 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [(465/16777241179888), (100981765197829/20166243897788951), 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], + [(15/4194310294972), (265290126005179/322659902364623216), (332148196734695751793/11788713286154962103898), 1, 0, 0, 0, 0, 0, 0, 0, 0], + [(51/268435858878208), (6717450079775/80664975591155804), (241839610991979869629/47154853144619848415592), (279374048249478931531838473/3854866416052307060169897565), 1, 0, 0, 0, 0, 0, 0, 0], + [(-33/536871717756416), (-49432942720425/5162558437833971456), (408421411799263115/23577426572309924207796), (271118458980709501504750913/30838931328418456481359180520), (183460604356060440272919394566095/1824985551106228598471302410673916), 1, 0, 0, 0, 0, 0, 0], + [(-75/4294973742051328), (-33161265757763/5162558437833971456), (-75878744617480952119/215565042946833592756992), (-255914793917203570711756019/61677862656836912962718361040), (-52629204745453498067759412062635/7299942204424914393885209642695664), (-511161485774106343747899688487963641/9283430112523124183988623130863905918), 1, 0, 0, 0, 0, 0], + [(15/4294973742051328), (7340042978251/82600935005343543296), (-53826474130765973461/1005970200418556766199296), (-2691513774959985657046702857/986845802509390607403493776640), (-255301583103139618475404468620105/4171395545385665367934405510111808), (-244281606388753916638146875851511556239/816941849902034928190998835516023720784), (-871270481830772945196296430021323257221815/778490845769410970935339138784831050985562), 1, 0, 0, 0, 0], + [(375/68719579872821248), (4849086132973/2581279218916985728), (-126610091103297683417/2011940400837113532398592), (-4669321454807479672372261089/493422901254695303701746888320), (-3350528227731030896574532676573595/58399537635399315151081677141565312), (7226761974529335135951529165505220457/408470924951017464095499417758011860392), (877517561683146974892250812004505270759033/1556981691538821941870678277569662101971124), (-1074742702961238054730663901609430043788225790/357288100994165292101443563021377816034441037), 1, 0, 0, 0], + [(453/137439159745642496), (-37186155888609801/1321614960085496692736), (-3929759593855251397667/2011940400837113532398592), (80235381091594789004152890837/19736916050187812148069875532800), (42206482799880566588067552672544509/233598150541597260604326708566261248), (15206123889007365374367234449679334888503/32677673996081397127639953420640948831360), (216051873214751591520718069234499456167193/648742371474509142446115948987359209154635), (47956834228992794970294642188728332076685865129/7145762019883305842028871260427556320688820740), (-38/5), 1, 0, 0], + [(-1048578357607/1099513277965139968), (1394608297026685/1321614960085496692736), (6184830591167510390475025/386292556960725798220529664), (292335005146257211435397680859/1578953284015024971845590042624), (68391187533320405733068453811892445/133484657452341291773900976323577856), (3937712408681015175493709663951092602497/13071069598432558851055981368256379532544), (-12493830276507879648736028481970837666070573/16607804709747434046620568294076395754358656), (-5525214534856393868865566110795649580988755063/408329258279046048115935500595860361182218328), (931/16), 0, 1, 0], + [(30146627830105/549756638982569984), (278034133123027888827/21145839361367947083776), (129823823892450334408582601/772585113921451596441059328), (143433987501531150697752909147377/252632525442403995495294406819840), (164070244050457811766440819336418545/533938629809365167095603905294311424), (-3474462440748244245422492818232190945903/9506232435223679164404350086004639660032), (19983224049978600492936320204846726907812909/33215609419494868093241136588152791508717312), (-190008968277167187380127733099574652696056726025/6533268132464736769854968009533765778915493248), (-33649/32), 0, 0, 1] + ] + +def fourPivotData_23 : CopyLabel 23 → ℚ := + copyDiagonalData 23 [(3596807727106964372495493/800), (2695083358684056754955880339/479349747996800), (41460066632617412037005591462619/516255843783397145600), (1687804688951660387226431508125931/510968990688790738386944), (440474619464572437164875860934388795628693/1578953284015024971845590042624000), (17875786513703508084674654426461795282409857029/427150903847492133676483124235449139200), (161052762702264252299142605764190579764316339459883/60839887585431546652187840550429693824204800), (3104434579359970407545821546788921635658478795883201511/27210227236450195941983139093014766803941221990400), (617253866866789232996626176408903607856598861326229375/107041065082302247237303795868201218521751441375232), 0, 0, 0] + +theorem fourOccupations_23 : highestFourOccupations 23 = {{0,1,2,21}, {0,1,3,20}, {0,1,4,19}, {0,1,5,18}, {0,1,6,17}, {0,1,7,16}, {0,1,8,15}, {0,1,9,14}, {0,1,10,13}, {0,1,11,12}, {0,2,3,19}, {0,2,4,18}, {0,2,5,17}, {0,2,6,16}, {0,2,7,15}, {0,2,8,14}, {0,2,9,13}, {0,2,10,12}, {0,3,4,17}, {0,3,5,16}, {0,3,6,15}, {0,3,7,14}, {0,3,8,13}, {0,3,9,12}, {0,3,10,11}, {0,4,5,15}, {0,4,6,14}, {0,4,7,13}, {0,4,8,12}, {0,4,9,11}, {0,5,6,13}, {0,5,7,12}, {0,5,8,11}, {0,5,9,10}, {0,6,7,11}, {0,6,8,10}, {0,7,8,9}, {1,2,3,18}, {1,2,4,17}, {1,2,5,16}, {1,2,6,15}, {1,2,7,14}, {1,2,8,13}, {1,2,9,12}, {1,2,10,11}, {1,3,4,16}, {1,3,5,15}, {1,3,6,14}, {1,3,7,13}, {1,3,8,12}, {1,3,9,11}, {1,4,5,14}, {1,4,6,13}, {1,4,7,12}, {1,4,8,11}, {1,4,9,10}, {1,5,6,12}, {1,5,7,11}, {1,5,8,10}, {1,6,7,10}, {1,6,8,9}, {2,3,4,15}, {2,3,5,14}, {2,3,6,13}, {2,3,7,12}, {2,3,8,11}, {2,3,9,10}, {2,4,5,13}, {2,4,6,12}, {2,4,7,11}, {2,4,8,10}, {2,5,6,11}, {2,5,7,10}, {2,5,8,9}, {2,6,7,9}, {3,4,5,12}, {3,4,6,11}, {3,4,7,10}, {3,4,8,9}, {3,5,6,10}, {3,5,7,9}, {3,6,7,8}, {4,5,6,9}, {4,5,7,8}} := by + decide +kernel + +theorem fourYNumber_23_1_1 : + (collectedFourTrace 23 1 1 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_3_1 : + (collectedFourTrace 23 3 1 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_3_3 : + (collectedFourTrace 23 3 3 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_5_1 : + (collectedFourTrace 23 5 1 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_5_3 : + (collectedFourTrace 23 5 3 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_5_5 : + (collectedFourTrace 23 5 5 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_7_1 : + (collectedFourTrace 23 7 1 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_7_3 : + (collectedFourTrace 23 7 3 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_7_5 : + (collectedFourTrace 23 7 5 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_7_7 : + (collectedFourTrace 23 7 7 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_9_1 : + (collectedFourTrace 23 9 1 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_9_3 : + (collectedFourTrace 23 9 3 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_9_5 : + (collectedFourTrace 23 9 5 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_9_7 : + (collectedFourTrace 23 9 7 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_9_9 : + (collectedFourTrace 23 9 9 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_11_1 : + (collectedFourTrace 23 11 1 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_11_3 : + (collectedFourTrace 23 11 3 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_11_5 : + (collectedFourTrace 23 11 5 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_11_7 : + (collectedFourTrace 23 11 7 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_11_9 : + (collectedFourTrace 23 11 9 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_11_11 : + (collectedFourTrace 23 11 11 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_13_1 : + (collectedFourTrace 23 13 1 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_13_3 : + (collectedFourTrace 23 13 3 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_13_5 : + (collectedFourTrace 23 13 5 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_13_7 : + (collectedFourTrace 23 13 7 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_13_9 : + (collectedFourTrace 23 13 9 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_13_11 : + (collectedFourTrace 23 13 11 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_13_13 : + (collectedFourTrace 23 13 13 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_15_1 : + (collectedFourTrace 23 15 1 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_15_3 : + (collectedFourTrace 23 15 3 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_15_5 : + (collectedFourTrace 23 15 5 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_15_7 : + (collectedFourTrace 23 15 7 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_15_9 : + (collectedFourTrace 23 15 9 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_15_11 : + (collectedFourTrace 23 15 11 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_15_13 : + (collectedFourTrace 23 15 13 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_15_15 : + (collectedFourTrace 23 15 15 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_17_1 : + (collectedFourTrace 23 17 1 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_17_3 : + (collectedFourTrace 23 17 3 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_17_5 : + (collectedFourTrace 23 17 5 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_17_7 : + (collectedFourTrace 23 17 7 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_17_9 : + (collectedFourTrace 23 17 9 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_17_11 : + (collectedFourTrace 23 17 11 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_17_13 : + (collectedFourTrace 23 17 13 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_17_15 : + (collectedFourTrace 23 17 15 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_17_17 : + (collectedFourTrace 23 17 17 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_19_1 : + (collectedFourTrace 23 19 1 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_19_3 : + (collectedFourTrace 23 19 3 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_19_5 : + (collectedFourTrace 23 19 5 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_19_7 : + (collectedFourTrace 23 19 7 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_19_9 : + (collectedFourTrace 23 19 9 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_19_11 : + (collectedFourTrace 23 19 11 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_19_13 : + (collectedFourTrace 23 19 13 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_19_15 : + (collectedFourTrace 23 19 15 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_19_17 : + (collectedFourTrace 23 19 17 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_19_19 : + (collectedFourTrace 23 19 19 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_21_1 : + (collectedFourTrace 23 21 1 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_21_3 : + (collectedFourTrace 23 21 3 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_21_5 : + (collectedFourTrace 23 21 5 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_21_7 : + (collectedFourTrace 23 21 7 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_21_9 : + (collectedFourTrace 23 21 9 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_21_11 : + (collectedFourTrace 23 21 11 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_21_13 : + (collectedFourTrace 23 21 13 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_21_15 : + (collectedFourTrace 23 21 15 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_21_17 : + (collectedFourTrace 23 21 17 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_21_19 : + (collectedFourTrace 23 21 19 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_21_21 : + (collectedFourTrace 23 21 21 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_23_1 : + (collectedFourTrace 23 23 1 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_23_3 : + (collectedFourTrace 23 23 3 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_23_5 : + (collectedFourTrace 23 23 5 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_23_7 : + (collectedFourTrace 23 23 7 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_23_9 : + (collectedFourTrace 23 23 9 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_23_11 : + (collectedFourTrace 23 23 11 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_23_13 : + (collectedFourTrace 23 23 13 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_23_15 : + (collectedFourTrace 23 23 15 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_23_17 : + (collectedFourTrace 23 23 17 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_23_19 : + (collectedFourTrace 23 23 19 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_23_21 : + (collectedFourTrace 23 23 21 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +theorem fourYNumber_23_23_23 : + (collectedFourTrace 23 23 23 collectedFourData_23 : ℚ) / fourCommonDenominator = 0 := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/CertificateRows.lean b/lean/OAI/Analysis/LaughlinFock/CertificateRows.lean new file mode 100644 index 0000000000000000000000000000000000000000..544ef35d29de2effc30a51a2504c480af37089d9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/CertificateRows.lean @@ -0,0 +1,98 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FiniteComparison +import OAI.Analysis.LaughlinFock.RationalThree + +namespace OAI + +/-! Certificate Rows. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def certificateEllData : Fin 8 → ℤ := ![711263444, 341669889, 383742518, 275246624, 176011065, 178799366, 29656603, 153354554] + +def certificateAlphaData : Fin 8 → Fin 8 → Fin 9 → ℤ := ![ + ![![-1458000, -1303000, 1475944, 3608220, 43844714, -184490641, -142169573, 1489137, -100397507], + ![781353, -3890972, -194326, -13071015, -49364910, 44700932, 51534774, -41946820, 0], + ![2056486, -760626, 4305543, -36416268, -8021896, -2613330, -1141300, 0, 0], + ![3923145, -4779646, 49466660, -6088990, 5250044, -9079480, 0, 0, 0], + ![3991791, -6855540, 9257380, -9310399, 6494980, 0, 0, 0, 0], + ![-39241199, -7152680, 9042278, -4542700, 0, 0, 0, 0, 0], + ![5245792, -12421683, 8099967, 0, 0, 0, 0, 0, 0], + ![21052655, -7572580, 0, 0, 0, 0, 0, 0, 0]], + ![![0, -2158090, 10930045, -20794124, -10149386, 597895303, 834366316, 765947384, 1283859555], + ![-5627000, -5402022, 9973000, 24359402, 91996112, -136745470, -141127842, -50782825, -366942013], + ![-5127489, 6909968, -9505204, 72222049, 51361561, -1267754, -15925422, -78778293, 0], + ![-5983211, -106483, -96337602, -7668424, 10264188, -19098454, 2115155, 0, 0], + ![10208704, 618400, -7918740, -6479832, 4936997, 14394828, 0, 0, 0], + ![99243497, -1336744, 7033004, 2815777, 3603042, 0, 0, 0, 0], + ![35489766, -6585714, 9964326, -9564997, 0, 0, 0, 0, 0], + ![-977099, -25775399, 1881084, 0, 0, 0, 0, 0, 0]], + ![![0, 0, 2286849, 19304798, 72232229, -661988975, -694800860, -7185493, -295108017], + ![0, -8424424, 2832670, -21562963, 316632327, 538338959, 592775303, 493483565, 530121321], + ![-677288, 5188364, -2632251, -109820524, -71765788, -51844671, -17032491, -15649485, -126493796], + ![2276756, -7542800, 36208527, 45768030, 35084799, 20746753, -6109724, -38742315, 0], + ![14442833, -16716287, -76293178, -1636292, -4793945, -10517615, 24708653, 0, 0], + ![10039299, 36778073, -63545981, -887901, 3332305, 4129678, 0, 0, 0], + ![57374228, 40592205, -31810373, 4995989, -3075894, 0, 0, 0, 0], + ![88550482, 31531302, -4435968, -7365918, 0, 0, 0, 0, 0]], + ![![0, 0, 0, 39091021, -4327630, 213162965, 45619843, -654459233, -49355411], + ![0, 0, -7645272, 8738979, -367337826, -305799567, -733169191, 195732122, 71375471], + ![0, -3949210, 762818, 68452276, 199108377, 46517664, 68403288, 47754272, 127976176], + ![11033607, -2140475, 18301715, -133068288, -15957882, -12923425, -63267429, -35729612, -80840875], + ![8563509, 21124181, 91082225, -17834095, 23279016, 25167823, 5867255, -14358409, 0], + ![-78804551, -37818356, 61096591, -30356506, 14193156, 7769542, -14948988, 0, 0], + ![-10297948, -16392402, -224637, -26277133, -1390692, 7844148, 0, 0, 0], + ![-156393617, 5235902, 12966156, -29134694, -7754810, 0, 0, 0, 0]], + ![![0, 0, 0, 0, 19350310, -256570426, 437882921, -166877023, 644065588], + ![0, 0, 0, 7604311, -56036955, -106906398, 395640853, -375570014, -1474842820], + ![0, 0, 3171752, -42320168, -196928392, 84182344, 123805380, -377993673, 446685144], + ![0, 5083588, 54525539, 112160315, -4586199, 169842096, 129314466, 473546, -43309042], + ![8117035, -12273926, -13371505, -33864426, -63645420, 39205032, 47849173, -57278002, 30676490], + ![-32345547, 6924448, -21143042, -30323348, 13003067, 19986152, 9072780, -25147087, 0], + ![-62327236, -2573763, 19203739, -59245571, -6662966, 28341971, 18781561, 0, 0], + ![135264167, 9223722, 1641094, -16817961, 11019210, 24257380, 0, 0, 0]], + ![![0, 0, 0, 0, 0, 160543938, -772096646, 150680285, -122410154], + ![0, 0, 0, 0, 57714191, -84055787, -173419469, 817621606, -1272768087], + ![0, 0, 0, 11295230, 36541316, -181828330, -133076448, 86288265, -861124623], + ![0, 0, -24815988, -50599547, 6698654, -132907956, 35137762, 33919179, -293036253], + ![0, -10241680, 43618923, 71239842, 27177342, -45431218, 41533885, 63934128, -214411360], + ![31688993, 9888664, -4845107, 34212037, -3172205, 5715090, 54142081, -48900364, -147596784], + ![-53903546, 40649652, 19129337, 39646640, -23829198, -2574933, -7391939, -19892913, 0], + ![-165809403, -87926915, -20371590, -16611293, -44679775, 13277906, -14870629, 0, 0]], + ![![0, 0, 0, 0, 0, 0, -67829135, 720057917, -875530193], + ![0, 0, 0, 0, 0, -51790296, 175876646, -200676925, -10152433], + ![0, 0, 0, 0, -7378820, 52323471, -211371229, 182388432, -61003176], + ![0, 0, 0, -656201, 14264883, 26191317, -100136184, -183883082, 121658379], + ![0, 0, 2431803, -22478098, 1654355, -93663294, 109018199, 36347410, -91971370], + ![0, 937204, -2276330, 13793516, 47941518, 28279597, -40367840, 55740134, 13007596], + ![-10808966, -25113301, -4615426, 31886801, -27442867, 40912313, -18147728, -21491028, 127556721], + ![78650298, 34037298, 58687256, 49941189, 61860018, 9377295, 26910871, 48292819, 0]], + ![![0, 0, 0, 0, 0, 0, 0, 90151251, 41493601], + ![0, 0, 0, 0, 0, 0, 5671034, 217565363, -239274251], + ![0, 0, 0, 0, 0, -13713832, 128996036, -145424091, -81564855], + ![0, 0, 0, 0, 4354537, 53285313, -28885070, -101829212, -59154681], + ![0, 0, 0, 8355807, -30008008, -6707391, -116951489, -67400418, 234283414], + ![0, 0, -7051082, -28653824, 17782076, -19218169, 30912487, -3984978, 110000521], + ![0, 2562590, 35701498, 4486260, 45335753, -25079048, 18952126, 51942067, 32561769], + ![-12496841, -51081249, -10849108, -40398862, -51858623, -10716483, -28108965, -5754196, -77199525]] + ] + +def certificateEll (t : Fin 8) : ℚ := certificateEllData t / 10^9 + +def certificateAlpha (t : Fin 8) (b : RowEntry t.val) : ℚ := + certificateAlphaData t b.val.1 b.val.2 / 10^9 + +def certificateRows (t : Fin 8) : ComparisonRow := + rationalComparisonRow t (certificateEll t) (certificateAlpha t) + +theorem certificateEta : rowsEta certificateRows = 932999265582865863 / 10^18 := by + norm_num [rowsEta, certificateRows, rationalComparisonRow, + certificateEll, certificateEllData, Fin.sum_univ_succ] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/CopyAverage.lean b/lean/OAI/Analysis/LaughlinFock/CopyAverage.lean new file mode 100644 index 0000000000000000000000000000000000000000..010a82c38fccb011738646bc2b1ce6d278355fa0 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/CopyAverage.lean @@ -0,0 +1,125 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FourBasis +import OAI.Analysis.LaughlinFock.FourCopies +import OAI.Analysis.LaughlinFock.ThreeRows + +namespace OAI + +/-! Copy Average. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +theorem sectorAverage_of_complete_copies {ι μ : Type*} [Fintype ι] + [Fintype μ] [DecidableEq μ] (κ : ι → Type*) [∀ i, Fintype (κ i)] + {Q k : ℕ} (n : ι → ℕ) (hn : Function.Injective n) + (C : ∀ i, κ i → Matrix μ (Fin (n i+1)) ℂ) + (hC : ∑ i, ∑ r, C i r * (C i r)ᴴ = 1) + (W : Matrix (SectorOccupation Q k) μ ℂ) + (hW : ∀ i r s, sectorOneBody Q k (spinGenerator Q s)*(W*C i r) = + (W*C i r)*spinGenerator (n i) s) + (M : Matrix μ μ ℂ) : + sectorAverage Q k (W*M*Wᴴ) = ∑ i, ∑ r, ∑ s, + (((C i r)ᴴ*M*C i s).trace / (n i+1 : ℂ)) • ((W*C i r)*(W*C i s)ᴴ) := by + classical + have hh : (∑ b : Sigma κ, C b.1 b.2 * (C b.1 b.2)ᴴ) = 1 := by + simpa only [Fintype.sum_sigma] using hC + rw [matrix_complete_column_sandwich (fun b : Sigma κ => n b.1) + (fun b => C b.1 b.2) hh W M] + simp only [Fintype.sum_sigma, map_sum] + apply Finset.sum_congr rfl + intro i _ + rw [Finset.sum_comm, Finset.sum_eq_single i] + · apply Finset.sum_congr rfl + intro r _ + apply Finset.sum_congr rfl + intro s _ + exact sectorAverage_spin_mixed_sandwich (W*C i r) (W*C i s) (hW i r) (hW i s) _ + · intro j _ hji + apply Finset.sum_eq_zero + intro r _ + apply Finset.sum_eq_zero + intro s _ + exact sectorAverage_spin_cross_sandwich (fun hij => hji (hn hij).symm) + (W*C i r) (W*C j s) (hW i r) (hW j s) _ + · simp + + +theorem full_column_gram_cast {ι : Type*} {n m : ℕ} (h : n=m) + (C : Matrix ι (Fin m) ℂ) : + C.submatrix id (Fin.cast h) * (C.submatrix id (Fin.cast h))ᴴ = C*Cᴴ := by + subst m + rfl + + + +theorem fourSpinColumns_complete {Q : ℕ} (hQ : 1 ≤ Q) : + (∑ b : FourSpinIndex Q, fourSpinColumns Q b * (fourSpinColumns Q b)ᴴ) = 1 := by + classical + rw [Fintype.sum_sigma] + have hi (r : CopyLabel Q) : + (∑ z : Fin (2*Q-2*r.val.val+1), fourSpinColumns Q ⟨r,z⟩ * + (fourSpinColumns Q ⟨r,z⟩)ᴴ) = + composedCouplingMatrix Q r.val.val * (composedCouplingMatrix Q r.val.val)ᴴ := by + have hr := r.val.isLt + have hr0 := r.property.pos + have hmin : min (2*Q-2) (2*Q-2*r.val.val) = 2*Q-2*r.val.val := by omega + ext x y + simp only [Matrix.sum_apply, Matrix.mul_apply, Matrix.conjTranspose_apply, + composedCouplingMatrix, fourSpinColumns, CoupledIndex, Fintype.sum_sigma] + rw [hmin] + simp_rw [hi] + exact composedCouplingMatrix_complete Q + + + +theorem fourCopyColumns_complete {Q : ℕ} (hQ : 1 ≤ Q) : + (∑ D : Fin (2*Q), ∑ r : CopyLabel D.val, + fourCopyColumns Q D.val r * (fourCopyColumns Q D.val r)ᴴ) = 1 := by + classical + let f : ((D : Fin (2*Q)) × CopyLabel D.val) → + Matrix (FourUncoupled Q) (FourUncoupled Q) ℂ := + fun b => fourCopyColumns Q b.1.val b.2 * (fourCopyColumns Q b.1.val b.2)ᴴ + change (∑ D, ∑ r, f ⟨D,r⟩) = 1 + rw [← Fintype.sum_sigma f] + rw [← sum_subtype_support (fun b : (D : Fin (2*Q)) × CopyLabel D.val => + b.1.val+b.2.val.val ≤ 2*Q) f] + · rw [← (fourSpinCopyEquiv hQ).sum_comp] + have hh (b : FourSpinIndex Q) : f (fourSpinCopyEquiv hQ b).val = + fourSpinColumns Q b * (fourSpinColumns Q b)ᴴ := by + rw [fourSpinColumns_eq_copy hQ, full_column_gram_cast] + simp_rw [hh] + exact fourSpinColumns_complete hQ + · intro b hb + simp [f, fourCopyColumns, hb] + + +theorem fourSpinDegree_injective {Q : ℕ} (_hQ : 1 ≤ Q) : + Function.Injective (fun D : Fin (2*Q) => fourSpinDegree Q D.val) := by + intro a b hab + apply Fin.ext + have := a.isLt + have := b.isLt + dsimp [fourSpinDegree] at hab + omega + + + +theorem sectorAverage_four_kernel {Q : ℕ} (hQ : 1 ≤ Q) + (M : Matrix (FourUncoupled Q) (FourUncoupled Q) ℂ) : + sectorAverage Q 4 (wideFourWedgeMatrix Q*M*(wideFourWedgeMatrix Q)ᴴ) = + ∑ D : Fin (2*Q), ∑ r : CopyLabel D.val, ∑ s : CopyLabel D.val, + (((fourCopyColumns Q D.val r)ᴴ*M*fourCopyColumns Q D.val s).trace / + (fourSpinDegree Q D.val+1 : ℂ)) • + (fourCopyWedge Q D.val r*(fourCopyWedge Q D.val s)ᴴ) := by + exact sectorAverage_of_complete_copies (fun D : Fin (2*Q) => CopyLabel D.val) + (fun D => fourSpinDegree Q D.val) (fourSpinDegree_injective hQ) + (fun D => fourCopyColumns Q D.val) (fourCopyColumns_complete hQ) + (wideFourWedgeMatrix Q) (fun D r s => fourCopyWedge_intertwines hQ r s) M + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/CopyNormalization.lean b/lean/OAI/Analysis/LaughlinFock/CopyNormalization.lean new file mode 100644 index 0000000000000000000000000000000000000000..b9656a88567680aff960ea1ec58ac5e78c7b9347 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/CopyNormalization.lean @@ -0,0 +1,215 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.NormalOrdering +import OAI.Analysis.LaughlinFock.TensorBasis + +namespace OAI + +/-! Copy Normalization. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators + + + +theorem antisymmetric_wedge_inner (Q : ℕ) (f g : Orbital Q → Orbital Q → ℝ) + (hf : ∀ i j, f j i = -f i j) (hg : ∀ i j, g j i = -g i j) : + (∑ ij : IncreasingPair Q, + (Real.sqrt 2 * f ij.val.1 ij.val.2) * (Real.sqrt 2 * g ij.val.1 ij.val.2)) = + ∑ i : Orbital Q, ∑ j : Orbital Q, f i j * g i j := by + have hdiag (i : Orbital Q) : f i i = 0 := by have h := hf i i; linarith + have hterm (i j : Orbital Q) : f i j * g i j = + (if i < j then f i j * g i j else 0) + (if j < i then f j i * g j i else 0) := by + rcases lt_trichotomy i j with h | rfl | h + · simp [h, not_lt.mpr h.le] + · simp [hdiag] + · simp only [ite_eq_left h, ite_eq_right (not_lt.mpr h.le), zero_add, hf i j, hg i j, neg_mul_neg] + have hsum : (∑ i : Orbital Q, ∑ j : Orbital Q, f i j * g i j) = + 2 * ∑ i : Orbital Q, ∑ j : Orbital Q, if i < j then f i j * g i j else 0 := by + calc + _ = ∑ i : Orbital Q, ∑ j : Orbital Q, + ((if i < j then f i j * g i j else 0) + (if j < i then f j i * g j i else 0)) := by + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + exact hterm i j + _ = _ := by + simp only [Finset.sum_add_distrib] + rw [Finset.sum_comm (f := fun i j : Orbital Q => if j < i then f j i * g j i else 0)] + ring + rw [increasingPair_sum Q (fun i j => (Real.sqrt 2 * f i j) * (Real.sqrt 2 * g i j)), hsum, Finset.mul_sum] + apply Finset.sum_congr rfl + intro i _ + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro j _ + split_ifs + · calc + _ = (Real.sqrt 2)^2 * (f i j * g i j) := by ring + _ = _ := by rw [Real.sq_sqrt (by norm_num : (0:ℝ) ≤ 2)] + · simp + + + +def wedgeCoupledCoefficient (Q r k : ℕ) (ij : IncreasingPair Q) : ℝ := + Real.sqrt 2 * coupledVector Q Q r k ij.val.1.val ij.val.2.val + +theorem gridInner_eq_fin_sum (n m : ℕ) (f g : GridVector) : + gridInner n m f g = ∑ p : Fin (n+1), ∑ q : Fin (m+1), f p.val q.val * g p.val q.val := by + symm + calc + _ = ∑ p : Fin (n+1), ∑ q ∈ Finset.range (m+1), f p.val q * g p.val q := by + apply Finset.sum_congr rfl + intro p _ + exact Fin.sum_univ_eq_sum_range (fun q => f p.val q * g p.val q) (m+1) + _ = _ := Fin.sum_univ_eq_sum_range + (fun p => ∑ q ∈ Finset.range (m+1), f p q * g p q) (n+1) + + + +theorem wedgeCoupledCoefficient_gram {Q r s k l : ℕ} + (hr : r ≤ Q) (hs : s ≤ Q) (hor : Odd r) (hos : Odd s) + (hk : k ≤ 2*Q-2*r) (hl : l ≤ 2*Q-2*s) : + (∑ ij : IncreasingPair Q, wedgeCoupledCoefficient Q r k ij * + wedgeCoupledCoefficient Q s l ij) = if r=s ∧ k=l then 1 else 0 := by + unfold wedgeCoupledCoefficient + rw [antisymmetric_wedge_inner Q + (fun i j => coupledVector Q Q r k i.val j.val) + (fun i j => coupledVector Q Q s l i.val j.val) + (fun i j => coupledVector_antisymm hr hor k i.val j.val) + (fun i j => coupledVector_antisymm hs hos l i.val j.val)] + rw [← gridInner_eq_fin_sum] + exact coupledVector_gram hr hr hs hs (by omega) (by omega) + + + +theorem tensor_contraction_inner {P I A B : Type*} + [Fintype P] [Fintype I] [Fintype A] [Fintype B] + (x : P → A → ℝ) (y : P → B → ℝ) (u : A → I → ℝ) (v : B → I → ℝ) : + (∑ p, ∑ i, (∑ a, x p a * u a i) * (∑ b, y p b * v b i)) = + ∑ p, ∑ a, ∑ b, (x p a * y p b) * (∑ i, u a i * v b i) := by + apply Finset.sum_congr rfl + intro p _ + have ht (i : I) : (∑ a, x p a * u a i) * (∑ b, y p b * v b i) = + ∑ a, ∑ b, (x p a * u a i) * (y p b * v b i) := by + rw [Finset.sum_mul] + apply Finset.sum_congr rfl + intro a _ + rw [Finset.mul_sum] + simp only [ht] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro a _ + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro b _ + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro i _ + ring + + + +def composedCoupledVector (Q r z k : ℕ) + (b : Fin (2*Q-2+1) × IncreasingPair Q) : ℝ := + ∑ a : Fin (2*Q-2*r+1), + coupledVector (2*Q-2) (2*Q-2*r) z k b.1.val a.val * + wedgeCoupledCoefficient Q r a.val b.2 + + + +theorem composedCoupledVector_gram {Q r s z w k l : ℕ} + (hr : r ≤ Q) (hs : s ≤ Q) (hor : Odd r) (hos : Odd s) + (hz₁ : z ≤ 2*Q-2) (hz₂ : z ≤ 2*Q-2*r) + (hw₁ : w ≤ 2*Q-2) (hw₂ : w ≤ 2*Q-2*s) + (hk : k ≤ (2*Q-2)+(2*Q-2*r)-2*z) + (hl : l ≤ (2*Q-2)+(2*Q-2*s)-2*w) : + (∑ b : Fin (2*Q-2+1) × IncreasingPair Q, + composedCoupledVector Q r z k b * composedCoupledVector Q s w l b) = + if r=s ∧ z=w ∧ k=l then 1 else 0 := by + classical + simp only [Fintype.sum_prod_type, composedCoupledVector] + rw [tensor_contraction_inner] + simp_rw [wedgeCoupledCoefficient_gram hr hs hor hos + (Nat.le_of_lt_succ (Fin.isLt _)) (Nat.le_of_lt_succ (Fin.isLt _))] + by_cases hrs : r=s + · subst s + have hsimp (p : Fin (2*Q-2+1)) (a : Fin (2*Q-2*r+1)) : + (∑ b : Fin (2*Q-2*r+1), + (coupledVector (2*Q-2) (2*Q-2*r) z k p.val a.val * + coupledVector (2*Q-2) (2*Q-2*r) w l p.val b.val) * + (if a.val=b.val then (1:ℝ) else 0)) = + coupledVector (2*Q-2) (2*Q-2*r) z k p.val a.val * + coupledVector (2*Q-2) (2*Q-2*r) w l p.val a.val := by + simp only [Fin.val_inj, mul_ite, mul_one, mul_zero] + simp + simp only [true_and, hsimp] + rw [← gridInner_eq_fin_sum, coupledVector_gram hz₁ hz₂ hw₁ hw₂ hk hl] + · simp [hrs] + + + +theorem composedCoupledVector_eq_sphericalCopy {Q D T r : ℕ} + (hr : r ≤ D) (hD : D ≤ T) (hT : T ≤ Q) (hor : Odd r) + (b : Fin (2*Q-2+1) × IncreasingPair Q) : + composedCoupledVector Q r (D-r) (T-D) b = + sphericalCopyCoefficient Q D T r b.1.val b.2.val.1.val b.2.val.2.val := by + classical + let p := b.1.val + let j := b.2.val.1.val + let k := b.2.val.2.val + change (∑ a : Fin (2*Q-2*r+1), + coupledVector (2*Q-2) (2*Q-2*r) (D-r) (T-D) p a.val * + (Real.sqrt 2 * coupledVector Q Q r a.val j k)) = + sphericalCopyCoefficient Q D T r p j k + by_cases hjk : r ≤ j+k + · by_cases ht : p+j+k=T + · let a : Fin (2*Q-2*r+1) := ⟨j+k-r, by omega⟩ + rw [Finset.sum_eq_single a] + · rw [sphericalCopyCoefficient, ite_eq_left ⟨hor, hr, hD, hjk, ht⟩] + rw [coupledVector, ite_eq_left (show p+a.val = D-r+(T-D) by dsimp [a]; omega), + coupledVector, ite_eq_left (show j+k = r+a.val by dsimp [a]; omega)] + dsimp [a] + ring + · intro a' _ hne + have he : j+k ≠ r+a'.val := by + intro he + apply hne + apply Fin.ext + dsimp [a] + omega + simp only [coupledVector, ite_eq_right he, mul_zero] + · simp + · rw [sphericalCopyCoefficient, ite_eq_right (by tauto)] + apply Finset.sum_eq_zero + intro a _ + by_cases he : j+k = r+a.val + · have he' : p+a.val ≠ D-r+(T-D) := by omega + simp only [coupledVector, ite_eq_right he', zero_mul] + · simp only [coupledVector, ite_eq_right he, mul_zero] + · rw [sphericalCopyCoefficient, ite_eq_right (by tauto)] + apply Finset.sum_eq_zero + intro a _ + have he : j+k ≠ r+a.val := by omega + simp only [coupledVector, ite_eq_right he, mul_zero] + + + +theorem sphericalCopyCoefficient_highest_gram {Q D r s : ℕ} + (hD : D ≤ Q) (hr : r ≤ D) (hs : s ≤ D) (hor : Odd r) (hos : Odd s) : + (∑ b : Fin (2*Q-2+1) × IncreasingPair Q, + sphericalCopyCoefficient Q D D r b.1.val b.2.val.1.val b.2.val.2.val * + sphericalCopyCoefficient Q D D s b.1.val b.2.val.1.val b.2.val.2.val) = + if r=s then 1 else 0 := by + have hr0 : 1 ≤ r := by obtain ⟨a, ha⟩ := hor; omega + have hs0 : 1 ≤ s := by obtain ⟨a, ha⟩ := hos; omega + simp_rw [← composedCoupledVector_eq_sphericalCopy hr (le_refl D) hD hor, + ← composedCoupledVector_eq_sphericalCopy hs (le_refl D) hD hos] + rw [composedCoupledVector_gram (by omega) (by omega) hor hos + (by omega) (by omega) (by omega) (by omega) (by omega) (by omega)] + split_ifs <;> simp_all + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/CopyVectors.lean b/lean/OAI/Analysis/LaughlinFock/CopyVectors.lean new file mode 100644 index 0000000000000000000000000000000000000000..344c22ee2df0b9905864b7be53a94f3bb18ffdb8 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/CopyVectors.lean @@ -0,0 +1,153 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PairDecomposition + +namespace OAI + +/-! Copy Vectors. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder + + +theorem pairAnnihilator_increasing (Q p : ℕ) : + pairAnnihilator Q p = ∑ ij : IncreasingPair Q, + (pairCoefficient Q p ij.val.1 ij.val.2 : ℂ) • + (annihilator Q ij.val.2 * annihilator Q ij.val.1) := by + rw [increasingPair_sum Q (fun i j => + (pairCoefficient Q p i j : ℂ) • (annihilator Q j * annihilator Q i))] + rfl + + + +theorem wedgeCoupledCoefficient_one_eq_pair {Q p : ℕ} (hQ : 1 ≤ Q) + (hp : p ≤ 2*Q-2) (ij : IncreasingPair Q) : + wedgeCoupledCoefficient Q 1 p ij = pairCoefficient Q p ij.val.1 ij.val.2 := by + rw [pairCoefficient_eq_coupled hQ hp] + rfl + + + +def wideFourWedgeMatrix (Q : ℕ) : + Matrix (SectorOccupation Q 4) (FourUncoupled Q) ℂ := fun A b => + annihilatorVector Q 4 + (annihilator Q b.2.val.2 * annihilator Q b.2.val.1 * pairAnnihilator Q b.1.val) A + +theorem wideFourAnnihilator_mem (Q : ℕ) (b : FourUncoupled Q) : + annihilator Q b.2.val.2 * annihilator Q b.2.val.1 * pairAnnihilator Q b.1.val ∈ + AnnihilationSpace Q 4 := + annihilationSpace_mul Q 2 2 (pairAnnihilator_mem Q b.1.val) + (annihilationSpace_mul Q 1 1 (annihilator_mem Q b.2.val.1) (annihilator_mem Q b.2.val.2)) + +theorem wideFourWedgeMatrix_annihilator_column (Q : ℕ) (b : FourUncoupled Q) : + wedgeAnnihilator Q 4 (fun A => wideFourWedgeMatrix Q A b) = + annihilator Q b.2.val.2 * annihilator Q b.2.val.1 * pairAnnihilator Q b.1.val := + wedgeAnnihilator_annihilatorVector Q 4 _ (wideFourAnnihilator_mem Q b) + + + +def composedFourWedgeColumn (Q r z k : ℕ) : SectorOccupation Q 4 → ℂ := + wideFourWedgeMatrix Q *ᵥ fun b => (composedCoupledVector Q r z k b : ℂ) + + +def composedFourAnnihilator (Q r z k : ℕ) : FockMatrix Q := + ∑ b : FourUncoupled Q, (composedCoupledVector Q r z k b : ℂ) • + (annihilator Q b.2.val.2 * annihilator Q b.2.val.1 * pairAnnihilator Q b.1.val) + +theorem composedFourAnnihilator_eq_wedge (Q r z k : ℕ) : + composedFourAnnihilator Q r z k = wedgeAnnihilator Q 4 (composedFourWedgeColumn Q r z k) := by + unfold composedFourWedgeColumn + rw [wedgeAnnihilator_mulVec] + simp only [wideFourWedgeMatrix_annihilator_column, Complex.star_def, + Complex.conj_ofReal, composedFourAnnihilator] + + + +theorem highestFourAnnihilator_eq_composed {Q D : ℕ} (hD : D ≤ Q) (r : CopyLabel D) : + highestFourAnnihilator Q D r = composedFourAnnihilator Q r.val.val (D-r.val.val) 0 := by + classical + have hr : r.val.val ≤ D := Nat.le_of_lt_succ r.val.isLt + have h := sum_subtype_support + (fun b : FourUncoupled Q => b.1.val+b.2.val.1.val+b.2.val.2.val=D) + (fun b : FourUncoupled Q => + (sphericalCopyCoefficient Q D D r.val.val b.1.val b.2.val.1.val b.2.val.2.val : ℂ) • + (annihilator Q b.2.val.2 * annihilator Q b.2.val.1 * pairAnnihilator Q b.1.val)) + (by intro b hb; simp [sphericalCopyCoefficient, hb]) + change (∑ b : FourHighestShell Q D, + (sphericalCopyCoefficient Q D D r.val.val b.val.1.val b.val.2.val.1.val b.val.2.val.2.val : ℂ) • + (annihilator Q b.val.2.val.2 * annihilator Q b.val.2.val.1 * pairAnnihilator Q b.val.1.val)) = _ + rw [h] + unfold composedFourAnnihilator + apply Finset.sum_congr rfl + intro b _ + rw [← composedCoupledVector_eq_sphericalCopy hr (le_refl D) hD r.property b] + simp only [Nat.sub_self] + + +theorem highestFourAnnihilator_eq_wedge {Q D : ℕ} (hD : D ≤ Q) (r : CopyLabel D) : + highestFourAnnihilator Q D r = + wedgeAnnihilator Q 4 (composedFourWedgeColumn Q r.val.val (D-r.val.val) 0) := by + rw [highestFourAnnihilator_eq_composed hD, composedFourAnnihilator_eq_wedge] + + + +theorem composedFourAnnihilator_one {Q : ℕ} (hQ : 1 ≤ Q) (z k : ℕ) : + composedFourAnnihilator Q 1 z k = fourCoupledAnnihilator Q z k := by + classical + calc + _ = ∑ p : Fin (2*Q-2+1), ∑ a : Fin (2*Q-2+1), + (coupledVector (2*Q-2) (2*Q-2) z k p.val a.val : ℂ) • + (pairAnnihilator Q a.val * pairAnnihilator Q p.val) := by + simp only [composedFourAnnihilator, Fintype.sum_prod_type, composedCoupledVector, + Nat.mul_one, Complex.ofReal_sum, Finset.sum_smul, Complex.ofReal_mul] + apply Finset.sum_congr rfl + intro p _ + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro a _ + rw [pairAnnihilator_increasing Q a.val, Matrix.sum_mul, Finset.smul_sum] + apply Finset.sum_congr rfl + intro ij _ + rw [wedgeCoupledCoefficient_one_eq_pair hQ (Nat.le_of_lt_succ a.isLt)] + simp only [Matrix.smul_mul, smul_smul] + _ = _ := by + rw [show 2*Q-2+1 = 2*Q-1 by omega] + rfl + + +theorem annihilatorVector_wedgeAnnihilator (Q k : ℕ) (v : SectorOccupation Q k → ℂ) : + annihilatorVector Q k (wedgeAnnihilator Q k v) = v := by + classical + funext A + simp only [annihilatorVector, wedgeAnnihilator, Matrix.sum_apply, Matrix.smul_apply, + smul_eq_mul, basisAnnihilator_vacuum, Subtype.val_inj, mul_ite, mul_one, mul_zero] + simp + + +theorem wedgeAnnihilator_injective (Q k : ℕ) : Function.Injective (wedgeAnnihilator Q k) := by + intro v w h + have hv := congrArg (annihilatorVector Q k) h + simpa only [annihilatorVector_wedgeAnnihilator] using hv + + + +theorem composedFourWedgeColumn_one {Q : ℕ} (hQ : 1 ≤ Q) + (c : CoupledIndex (2*Q-2) (2*Q-2)) : + composedFourWedgeColumn Q 1 c.1.val c.2.val = + fun A => fourCoupledWedgeMatrix Q A c := by + apply wedgeAnnihilator_injective Q 4 + rw [← composedFourAnnihilator_eq_wedge, composedFourAnnihilator_one hQ, + fourCoupledAnnihilator_eq_wedge] + + +theorem fourCoupledWedgeMatrix_even_deficit_zero (Q : ℕ) + (c : CoupledIndex (2*Q-2) (2*Q-2)) (ho : Odd c.1.val) : + (fun A => fourCoupledWedgeMatrix Q A c) = 0 := by + apply wedgeAnnihilator_injective Q 4 + rw [← fourCoupledAnnihilator_eq_wedge, + fourCoupledAnnihilator_odd_zero (coupledIndex_bounds c).1 ho] + simp [wedgeAnnihilator] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/CoupledLie.lean b/lean/OAI/Analysis/LaughlinFock/CoupledLie.lean new file mode 100644 index 0000000000000000000000000000000000000000..33d5219ec0ee07e2676ccac3ec5328d1137c4a2d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/CoupledLie.lean @@ -0,0 +1,175 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.WedgeLie + +namespace OAI + +/-! Coupled Lie. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem spinLower_sum (n : ℕ) (i : Fin (n+1)) (f : ℕ → ℂ) : + (∑ a : Fin (n+1), spinLowerMatrix n i a * f a.val) = + (spinStep n i.val : ℂ) * f (i.val-1) := by + classical + by_cases hi : i.val=0 + · simp [spinLowerMatrix, hi] + · have hip : 0 < i.val := by omega + rw [Finset.sum_eq_single (⟨i.val-1, by omega⟩ : Fin (n+1))] + · simp [spinLowerMatrix, Nat.sub_add_cancel hip] + · intro b _ hb + have hn : i.val ≠ b.val+1 := by + intro he; apply hb; apply Fin.ext; dsimp only; omega + simp [spinLowerMatrix, hn] + · simp + +theorem spinRaise_sum (n : ℕ) (i : Fin (n+1)) (f : ℕ → ℂ) : + (∑ a : Fin (n+1), (spinLowerMatrix n)ᴴ i a * f a.val) = + (spinStep n (i.val+1) : ℂ) * f (i.val+1) := by + classical + by_cases hi : i.val < n + · rw [Finset.sum_eq_single (⟨i.val+1, by omega⟩ : Fin (n+1))] + · simp [Matrix.conjTranspose_apply, spinLowerMatrix] + · intro b _ hb + have hn : b.val ≠ i.val+1 := fun he => hb (Fin.ext he) + simp [Matrix.conjTranspose_apply, spinLowerMatrix, hn] + · simp + · have he : i.val=n := by omega + have hz (b : Fin (n+1)) : b.val ≠ i.val+1 := by omega + simp only [Matrix.conjTranspose_apply, spinLowerMatrix, ite_eq_right (hz _)] + simp [he] + +theorem sum_spinLower (n : ℕ) (j : Fin (n+1)) (f : ℕ → ℂ) : + (∑ a : Fin (n+1), f a.val * spinLowerMatrix n a j) = + (spinStep n (j.val+1) : ℂ) * f (j.val+1) := by + have he (a : Fin (n+1)) : spinLowerMatrix n a j = (spinLowerMatrix n)ᴴ j a := by + simp only [spinLowerMatrix, Matrix.conjTranspose_apply] + split_ifs <;> simp + simpa only [he, mul_comm] using spinRaise_sum n j f + +theorem sum_spinRaise (n : ℕ) (j : Fin (n+1)) (f : ℕ → ℂ) : + (∑ a : Fin (n+1), f a.val * (spinLowerMatrix n)ᴴ a j) = + (spinStep n j.val : ℂ) * f (j.val-1) := by + have he (a : Fin (n+1)) : (spinLowerMatrix n)ᴴ a j = spinLowerMatrix n j a := by + simp only [spinLowerMatrix, Matrix.conjTranspose_apply] + split_ifs <;> simp + simpa only [he, mul_comm] using spinLower_sum n j f + +theorem tensorSum_mul_apply {ι κ β : Type*} [Fintype ι] [Fintype κ] + [DecidableEq ι] [DecidableEq κ] + (X : Matrix ι ι ℂ) (Y : Matrix κ κ ℂ) (C : Matrix (ι × κ) β ℂ) + (i : ι) (j : κ) (k : β) : + (tensorSum X Y * C) (i,j) k = + (∑ a, X i a * C (a,j) k) + ∑ b, Y j b * C (i,b) k := by + classical + simp only [Matrix.mul_apply, tensorSum_apply, add_mul, Finset.sum_add_distrib, + Fintype.sum_prod_type, ite_mul, zero_mul] + simp only [Finset.sum_ite_eq, Finset.mem_univ, ite_true] + congr 1 + rw [Finset.sum_comm] + simp + + + +def coupledSpinMatrix (n m z : ℕ) : + Matrix (Fin (n+1) × Fin (m+1)) (Fin (n+m-2*z+1)) ℂ := fun ij k => + (coupledVector n m z k.val ij.1.val ij.2.val : ℂ) + +theorem tensorLower_coupled_apply (n m z : ℕ) (i : Fin (n+1)) (j : Fin (m+1)) + (k : Fin (n+m-2*z+1)) : + (tensorSum (spinLowerMatrix n) (spinLowerMatrix m) * coupledSpinMatrix n m z) (i,j) k = + (gridLower n m (coupledVector n m z k.val) i.val j.val : ℂ) := by + rw [tensorSum_mul_apply] + change (∑ a : Fin (n+1), spinLowerMatrix n i a * + (coupledVector n m z k.val a.val j.val : ℂ)) + + (∑ a : Fin (m+1), spinLowerMatrix m j a * + (coupledVector n m z k.val i.val a.val : ℂ)) = _ + rw [spinLower_sum n i (fun a => (coupledVector n m z k.val a j.val : ℂ)), + spinLower_sum m j (fun a => (coupledVector n m z k.val i.val a : ℂ))] + by_cases hi : i.val=0 <;> by_cases hj : j.val=0 <;> + simp [gridLower, hi, hj] + +theorem tensorRaise_coupled_apply (n m z : ℕ) (i : Fin (n+1)) (j : Fin (m+1)) + (k : Fin (n+m-2*z+1)) : + (tensorSum (spinLowerMatrix n)ᴴ (spinLowerMatrix m)ᴴ * coupledSpinMatrix n m z) (i,j) k = + (gridRaise n m (coupledVector n m z k.val) i.val j.val : ℂ) := by + rw [tensorSum_mul_apply] + change (∑ a : Fin (n+1), (spinLowerMatrix n)ᴴ i a * + (coupledVector n m z k.val a.val j.val : ℂ)) + + (∑ a : Fin (m+1), (spinLowerMatrix m)ᴴ j a * + (coupledVector n m z k.val i.val a.val : ℂ)) = _ + rw [spinRaise_sum n i (fun a => (coupledVector n m z k.val a j.val : ℂ)), + spinRaise_sum m j (fun a => (coupledVector n m z k.val i.val a : ℂ))] + simp [gridRaise] + +theorem coupledSpinMatrix_lower {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) : + tensorSum (spinLowerMatrix n) (spinLowerMatrix m) * coupledSpinMatrix n m z = + coupledSpinMatrix n m z * spinLowerMatrix (n+m-2*z) := by + ext ⟨i,j⟩ k + rw [tensorLower_coupled_apply, coupledVector_lower_all hn hm] + simp only [Pi.smul_apply, smul_eq_mul, Complex.ofReal_mul, Matrix.mul_apply, + coupledSpinMatrix] + exact (sum_spinLower (n+m-2*z) k (fun t => (coupledVector n m z t i.val j.val : ℂ))).symm + +theorem coupledSpinMatrix_raise {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) : + tensorSum (spinLowerMatrix n)ᴴ (spinLowerMatrix m)ᴴ * coupledSpinMatrix n m z = + coupledSpinMatrix n m z * (spinLowerMatrix (n+m-2*z))ᴴ := by + ext ⟨i,j⟩ k + rw [tensorRaise_coupled_apply, coupledVector_raise_all hn hm] + simp only [Pi.smul_apply, smul_eq_mul, Complex.ofReal_mul, Matrix.mul_apply, + coupledSpinMatrix] + exact (sum_spinRaise (n+m-2*z) k (fun t => (coupledVector n m z t i.val j.val : ℂ))).symm + +theorem coupledSpinMatrix_weight {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) : + tensorSum (spinWeightMatrix n) (spinWeightMatrix m) * coupledSpinMatrix n m z = + coupledSpinMatrix n m z * spinWeightMatrix (n+m-2*z) := by + ext ⟨i,j⟩ k + rw [tensorSum_mul_apply] + simp only [spinWeightMatrix, Matrix.diagonal_apply, ite_mul, zero_mul, + Finset.sum_ite_eq, Finset.mem_univ, ite_true, Matrix.mul_diagonal, coupledSpinMatrix] + by_cases hl : i.val+j.val=z+k.val + · have he : (n : ℂ) - 2*i.val + ((m : ℂ)-2*j.val) = + ((n+m-2*z : ℕ) : ℂ) - 2*k.val := by + push_cast [Nat.cast_sub (show 2*z ≤ n+m by omega)] + have hh : (i.val : ℂ)+j.val = z+k.val := by exact_mod_cast hl + linear_combination -2 * hh + rw [← add_mul, he, mul_comm] + · simp [coupledVector, hl] + +theorem tensorSum_add {ι κ : Type*} [DecidableEq ι] [DecidableEq κ] + (X X' : Matrix ι ι ℂ) (Y Y' : Matrix κ κ ℂ) : + tensorSum (X+X') (Y+Y') = tensorSum X Y + tensorSum X' Y' := by + ext i j + simp only [tensorSum_apply, Matrix.add_apply] + split_ifs <;> ring + +theorem tensorSum_smul {ι κ : Type*} [DecidableEq ι] [DecidableEq κ] + (X : Matrix ι ι ℂ) (Y : Matrix κ κ ℂ) (c : ℂ) : + tensorSum (c•X) (c•Y) = c • tensorSum X Y := by + ext i j + simp only [tensorSum_apply, Matrix.smul_apply, smul_eq_mul] + split_ifs <;> ring + +theorem tensorSum_sub {ι κ : Type*} [DecidableEq ι] [DecidableEq κ] + (X X' : Matrix ι ι ℂ) (Y Y' : Matrix κ κ ℂ) : + tensorSum (X-X') (Y-Y') = tensorSum X Y - tensorSum X' Y' := by + ext i j + simp only [tensorSum_apply, Matrix.sub_apply] + split_ifs <;> ring + + +theorem coupledSpinMatrix_intertwines {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) (s : Fin 3) : + tensorSum (spinGenerator n s) (spinGenerator m s) * coupledSpinMatrix n m z = + coupledSpinMatrix n m z * spinGenerator (n+m-2*z) s := by + fin_cases s <;> simp only [spinGenerator, Fin.reduceFinMk, Fin.isValue, Fin.reduceEq, ↓reduceIte] + · rw [tensorSum_sub, Matrix.sub_mul, coupledSpinMatrix_lower hn hm, + coupledSpinMatrix_raise hn hm, Matrix.mul_sub] + · rw [tensorSum_smul, tensorSum_add, Matrix.smul_mul, Matrix.add_mul, + coupledSpinMatrix_lower hn hm, coupledSpinMatrix_raise hn hm, + Matrix.mul_smul, Matrix.mul_add] + · rw [tensorSum_smul, Matrix.smul_mul, coupledSpinMatrix_weight hn hm, Matrix.mul_smul] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/CouplingTables.lean b/lean/OAI/Analysis/LaughlinFock/CouplingTables.lean new file mode 100644 index 0000000000000000000000000000000000000000..5bd7098edf0b5fc053ace7033df6770f7d6ae5a3 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/CouplingTables.lean @@ -0,0 +1,788 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FastCoupling + +namespace OAI + +/-! Coupling Tables. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder +def unitCouplingData_0 : List (List ℤ) := [ + [1, 0, 0, 0, 0, 0, 0, 0, 0], + [1, 1, 0, 0, 0, 0, 0, 0, 0], + [1, 2, 1, 0, 0, 0, 0, 0, 0], + [1, 3, 3, 1, 0, 0, 0, 0, 0], + [1, 4, 6, 4, 1, 0, 0, 0, 0], + [1, 5, 10, 10, 5, 1, 0, 0, 0], + [1, 6, 15, 20, 15, 6, 1, 0, 0], + [1, 7, 21, 35, 35, 21, 7, 1, 0], + [1, 8, 28, 56, 70, 56, 28, 8, 1], + [1, 9, 36, 84, 126, 126, 84, 36, 9], + [1, 10, 45, 120, 210, 252, 210, 120, 45], + [1, 11, 55, 165, 330, 462, 462, 330, 165], + [1, 12, 66, 220, 495, 792, 924, 792, 495], + [1, 13, 78, 286, 715, 1287, 1716, 1716, 1287], + [1, 14, 91, 364, 1001, 2002, 3003, 3432, 3003], + [1, 15, 105, 455, 1365, 3003, 5005, 6435, 6435], + [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870], + [1, 17, 136, 680, 2380, 6188, 12376, 19448, 24310], + [1, 18, 153, 816, 3060, 8568, 18564, 31824, 43758], + [1, 19, 171, 969, 3876, 11628, 27132, 50388, 75582], + [1, 20, 190, 1140, 4845, 15504, 38760, 77520, 125970], + [1, 21, 210, 1330, 5985, 20349, 54264, 116280, 203490], + [1, 22, 231, 1540, 7315, 26334, 74613, 170544, 319770], + [1, 23, 253, 1771, 8855, 33649, 100947, 245157, 490314] +] + +def unitCouplingData_1 : List (List ℤ) := [ + [-1, 1, 0, 0, 0, 0, 0, 0, 0], + [-1, 0, 1, 0, 0, 0, 0, 0, 0], + [-1, -1, 1, 1, 0, 0, 0, 0, 0], + [-1, -2, 0, 2, 1, 0, 0, 0, 0], + [-1, -3, -2, 2, 3, 1, 0, 0, 0], + [-1, -4, -5, 0, 5, 4, 1, 0, 0], + [-1, -5, -9, -5, 5, 9, 5, 1, 0], + [-1, -6, -14, -14, 0, 14, 14, 6, 1], + [-1, -7, -20, -28, -14, 14, 28, 20, 7], + [-1, -8, -27, -48, -42, 0, 42, 48, 27], + [-1, -9, -35, -75, -90, -42, 42, 90, 75], + [-1, -10, -44, -110, -165, -132, 0, 132, 165], + [-1, -11, -54, -154, -275, -297, -132, 132, 297], + [-1, -12, -65, -208, -429, -572, -429, 0, 429], + [-1, -13, -77, -273, -637, -1001, -1001, -429, 429], + [-1, -14, -90, -350, -910, -1638, -2002, -1430, 0], + [-1, -15, -104, -440, -1260, -2548, -3640, -3432, -1430], + [-1, -16, -119, -544, -1700, -3808, -6188, -7072, -4862], + [-1, -17, -135, -663, -2244, -5508, -9996, -13260, -11934], + [-1, -18, -152, -798, -2907, -7752, -15504, -23256, -25194], + [-1, -19, -170, -950, -3705, -10659, -23256, -38760, -48450], + [-1, -20, -189, -1120, -4655, -14364, -33915, -62016, -87210], + [-1, -21, -209, -1309, -5775, -19019, -48279, -95931, -149226], + [-1, -22, -230, -1518, -7084, -24794, -67298, -144210, -245157] +] + +def unitCouplingData_2 : List (List ℤ) := [ + [1, -2, 1, 0, 0, 0, 0, 0, 0], + [1, -1, -1, 1, 0, 0, 0, 0, 0], + [1, 0, -2, 0, 1, 0, 0, 0, 0], + [1, 1, -2, -2, 1, 1, 0, 0, 0], + [1, 2, -1, -4, -1, 2, 1, 0, 0], + [1, 3, 1, -5, -5, 1, 3, 1, 0], + [1, 4, 4, -4, -10, -4, 4, 4, 1], + [1, 5, 8, 0, -14, -14, 0, 8, 5], + [1, 6, 13, 8, -14, -28, -14, 8, 13], + [1, 7, 19, 21, -6, -42, -42, -6, 21], + [1, 8, 26, 40, 15, -48, -84, -48, 15], + [1, 9, 34, 66, 55, -33, -132, -132, -33], + [1, 10, 43, 100, 121, 22, -165, -264, -165], + [1, 11, 53, 143, 221, 143, -143, -429, -429], + [1, 12, 64, 196, 364, 364, 0, -572, -858], + [1, 13, 76, 260, 560, 728, 364, -572, -1430], + [1, 14, 89, 336, 820, 1288, 1092, -208, -2002], + [1, 15, 103, 425, 1156, 2108, 2380, 884, -2210], + [1, 16, 118, 528, 1581, 3264, 4488, 3264, -1326], + [1, 17, 134, 646, 2109, 4845, 7752, 7752, 1938], + [1, 18, 151, 780, 2755, 6954, 12597, 15504, 9690], + [1, 19, 169, 931, 3535, 9709, 19551, 28101, 25194], + [1, 20, 188, 1100, 4466, 13244, 29260, 47652, 53295], + [1, 21, 208, 1288, 5566, 17710, 42504, 76912, 100947] +] + +def unitCouplingData_3 : List (List ℤ) := [ + [-1, 3, -3, 1, 0, 0, 0, 0, 0], + [-1, 2, 0, -2, 1, 0, 0, 0, 0], + [-1, 1, 2, -2, -1, 1, 0, 0, 0], + [-1, 0, 3, 0, -3, 0, 1, 0, 0], + [-1, -1, 3, 3, -3, -3, 1, 1, 0], + [-1, -2, 2, 6, 0, -6, -2, 2, 1], + [-1, -3, 0, 8, 6, -6, -8, 0, 3], + [-1, -4, -3, 8, 14, 0, -14, -8, 3], + [-1, -5, -7, 5, 22, 14, -14, -22, -5], + [-1, -6, -12, -2, 27, 36, 0, -36, -27], + [-1, -7, -18, -14, 25, 63, 36, -36, -63], + [-1, -8, -25, -32, 11, 88, 99, 0, -99], + [-1, -9, -33, -57, -21, 99, 187, 99, -99], + [-1, -10, -42, -90, -78, 78, 286, 286, 0], + [-1, -11, -52, -132, -168, 0, 364, 572, 286], + [-1, -12, -63, -184, -300, -168, 364, 936, 858], + [-1, -13, -75, -247, -484, -468, 196, 1300, 1794], + [-1, -14, -88, -322, -731, -952, -272, 1496, 3094], + [-1, -15, -102, -410, -1053, -1683, -1224, 1224, 4590], + [-1, -16, -117, -512, -1463, -2736, -2907, 0, 5814], + [-1, -17, -133, -629, -1975, -4199, -5643, -2907, 5814], + [-1, -18, -150, -762, -2604, -6174, -9842, -8550, 2907], + [-1, -19, -168, -912, -3366, -8778, -16016, -18392, -5643], + [-1, -20, -187, -1080, -4278, -12144, -24794, -34408, -24035] +] + +def unitCouplingData_4 : List (List ℤ) := [ + [1, -4, 6, -4, 1, 0, 0, 0, 0], + [1, -3, 2, 2, -3, 1, 0, 0, 0], + [1, -2, -1, 4, -1, -2, 1, 0, 0], + [1, -1, -3, 3, 3, -3, -1, 1, 0], + [1, 0, -4, 0, 6, 0, -4, 0, 1], + [1, 1, -4, -4, 6, 6, -4, -4, 1], + [1, 2, -3, -8, 2, 12, 2, -8, -3], + [1, 3, -1, -11, -6, 14, 14, -6, -11], + [1, 4, 2, -12, -17, 8, 28, 8, -17], + [1, 5, 6, -10, -29, -9, 36, 36, -9], + [1, 6, 11, -4, -39, -38, 27, 72, 27], + [1, 7, 17, 7, -43, -77, -11, 99, 99], + [1, 8, 24, 24, -36, -120, -88, 88, 198], + [1, 9, 32, 48, -12, -156, -208, 0, 286], + [1, 10, 41, 80, 36, -168, -364, -208, 286], + [1, 11, 51, 121, 116, -132, -532, -572, 78], + [1, 12, 62, 172, 237, -16, -664, -1104, -494], + [1, 13, 74, 234, 409, 221, -680, -1768, -1598], + [1, 14, 87, 308, 643, 630, -459, -2448, -3366], + [1, 15, 101, 395, 951, 1273, 171, -2907, -5814], + [1, 16, 116, 496, 1346, 2224, 1444, -2736, -8721], + [1, 17, 132, 612, 1842, 3570, 3668, -1292, -11457], + [1, 18, 149, 744, 2454, 5412, 7238, 2376, -12749], + [1, 19, 167, 893, 3198, 7866, 12650, 9614, -10373] +] + +def unitCouplingData_5 : List (List ℤ) := [ + [-1, 5, -10, 10, -5, 1, 0, 0, 0], + [-1, 4, -5, 0, 5, -4, 1, 0, 0], + [-1, 3, -1, -5, 5, 1, -3, 1, 0], + [-1, 2, 2, -6, 0, 6, -2, -2, 1], + [-1, 1, 4, -4, -6, 6, 4, -4, -1], + [-1, 0, 5, 0, -10, 0, 10, 0, -5], + [-1, -1, 5, 5, -10, -10, 10, 10, -5], + [-1, -2, 4, 10, -5, -20, 0, 20, 5], + [-1, -3, 2, 14, 5, -25, -20, 20, 25], + [-1, -4, -1, 16, 19, -20, -45, 0, 45], + [-1, -5, -5, 15, 35, -1, -65, -45, 45], + [-1, -6, -10, 10, 50, 34, -66, -110, 0], + [-1, -7, -16, 0, 60, 84, -32, -176, -110], + [-1, -8, -23, -16, 60, 144, 52, -208, -286], + [-1, -9, -31, -39, 44, 204, 196, -156, -494], + [-1, -10, -40, -70, 5, 248, 400, 40, -650], + [-1, -11, -50, -110, -65, 253, 648, 440, -610], + [-1, -12, -61, -160, -175, 188, 901, 1088, -170], + [-1, -13, -73, -221, -335, 13, 1089, 1989, 918], + [-1, -14, -86, -294, -556, -322, 1102, 3078, 2907], + [-1, -15, -100, -380, -850, -878, 780, 4180, 5985], + [-1, -16, -115, -480, -1230, -1728, -98, 4960, 10165], + [-1, -17, -131, -595, -1710, -2958, -1826, 4862, 15125], + [-1, -18, -148, -726, -2305, -4668, -4784, 3036, 19987] +] + +def unitCouplingData_6 : List (List ℤ) := [ + [1, -6, 15, -20, 15, -6, 1, 0, 0], + [1, -5, 9, -5, -5, 9, -5, 1, 0], + [1, -4, 4, 4, -10, 4, 4, -4, 1], + [1, -3, 0, 8, -6, -6, 8, 0, -3], + [1, -2, -3, 8, 2, -12, 2, 8, -3], + [1, -1, -5, 5, 10, -10, -10, 10, 5], + [1, 0, -6, 0, 15, 0, -20, 0, 15], + [1, 1, -6, -6, 15, 15, -20, -20, 15], + [1, 2, -5, -12, 9, 30, -5, -40, -5], + [1, 3, -3, -17, -3, 39, 25, -45, -45], + [1, 4, 0, -20, -20, 36, 64, -20, -90], + [1, 5, 4, -20, -40, 16, 100, 44, -110], + [1, 6, 9, -16, -60, -24, 116, 144, -66], + [1, 7, 15, -7, -76, -84, 92, 260, 78], + [1, 8, 22, 8, -83, -160, 8, 352, 338], + [1, 9, 30, 30, -75, -243, -152, 360, 690], + [1, 10, 39, 60, -45, -318, -395, 208, 1050], + [1, 11, 49, 99, 15, -363, -713, -187, 1258], + [1, 12, 60, 148, 114, -348, -1076, -900, 1071], + [1, 13, 72, 208, 262, -234, -1424, -1976, 171], + [1, 14, 85, 280, 470, 28, -1658, -3400, -1805], + [1, 15, 99, 365, 750, 498, -1630, -5058, -5205], + [1, 16, 114, 464, 1115, 1248, -1132, -6688, -10263], + [1, 17, 130, 578, 1579, 2363, 116, -7820, -16951] +] + +def unitCouplingData_7 : List (List ℤ) := [ + [-1, 7, -21, 35, -35, 21, -7, 1, 0], + [-1, 6, -14, 14, 0, -14, 14, -6, 1], + [-1, 5, -8, 0, 14, -14, 0, 8, -5], + [-1, 4, -3, -8, 14, 0, -14, 8, 3], + [-1, 3, 1, -11, 6, 14, -14, -6, 11], + [-1, 2, 4, -10, -5, 20, 0, -20, 5], + [-1, 1, 6, -6, -15, 15, 20, -20, -15], + [-1, 0, 7, 0, -21, 0, 35, 0, -35], + [-1, -1, 7, 7, -21, -21, 35, 35, -35], + [-1, -2, 6, 14, -14, -42, 14, 70, 0], + [-1, -3, 4, 20, 0, -56, -28, 84, 70], + [-1, -4, 1, 24, 20, -56, -84, 56, 154], + [-1, -5, -3, 25, 44, -36, -140, -28, 210], + [-1, -6, -8, 22, 69, 8, -176, -168, 182], + [-1, -7, -14, 14, 91, 77, -168, -344, 14], + [-1, -8, -21, 0, 105, 168, -91, -512, -330], + [-1, -9, -29, -21, 105, 273, 77, -603, -842], + [-1, -10, -38, -50, 84, 378, 350, -526, -1445], + [-1, -11, -48, -88, 34, 462, 728, -176, -1971], + [-1, -12, -59, -136, -54, 496, 1190, 552, -2147], + [-1, -13, -71, -195, -190, 442, 1686, 1742, -1595], + [-1, -14, -84, -266, -385, 252, 2128, 3428, 147], + [-1, -15, -98, -350, -651, -133, 2380, 5556, 3575], + [-1, -16, -113, -448, -1001, -784, 2247, 7936, 9131] +] + +def unitCouplingData_8 : List (List ℤ) := [ + [1, -8, 28, -56, 70, -56, 28, -8, 1], + [1, -7, 20, -28, 14, 14, -28, 20, -7], + [1, -6, 13, -8, -14, 28, -14, -8, 13], + [1, -5, 7, 5, -22, 14, 14, -22, 5], + [1, -4, 2, 12, -17, -8, 28, -8, -17], + [1, -3, -2, 14, -5, -25, 20, 20, -25], + [1, -2, -5, 12, 9, -30, -5, 40, -5], + [1, -1, -7, 7, 21, -21, -35, 35, 35], + [1, 0, -8, 0, 28, 0, -56, 0, 70], + [1, 1, -8, -8, 28, 28, -56, -56, 70], + [1, 2, -7, -16, 20, 56, -28, -112, 14], + [1, 3, -5, -23, 4, 76, 28, -140, -98], + [1, 4, -2, -28, -19, 80, 104, -112, -238], + [1, 5, 2, -30, -47, 61, 184, -8, -350], + [1, 6, 7, -28, -77, 14, 245, 176, -358], + [1, 7, 13, -21, -105, -63, 259, 421, -182], + [1, 8, 20, -8, -126, -168, 196, 680, 239], + [1, 9, 28, 12, -134, -294, 28, 876, 919], + [1, 10, 37, 40, -122, -428, -266, 904, 1795], + [1, 11, 47, 77, -82, -550, -694, 638, 2699], + [1, 12, 58, 124, -5, -632, -1244, -56, 3337], + [1, 13, 70, 182, 119, -637, -1876, -1300, 3281], + [1, 14, 83, 252, 301, -518, -2513, -3176, 1981], + [1, 15, 97, 335, 553, -217, -3031, -5689, -1195] +] + +def unitCouplingData_9 : List (List ℤ) := [ + [-1, 9, -36, 84, -126, 126, -84, 36, -9], + [-1, 8, -27, 48, -42, 0, 42, -48, 27], + [-1, 7, -19, 21, 6, -42, 42, -6, -21], + [-1, 6, -12, 2, 27, -36, 0, 36, -27], + [-1, 5, -6, -10, 29, -9, -36, 36, 9], + [-1, 4, -1, -16, 19, 20, -45, 0, 45], + [-1, 3, 3, -17, 3, 39, -25, -45, 45], + [-1, 2, 6, -14, -14, 42, 14, -70, 0], + [-1, 1, 8, -8, -28, 28, 56, -56, -70], + [-1, 0, 9, 0, -36, 0, 84, 0, -126], + [-1, -1, 9, 9, -36, -36, 84, 84, -126], + [-1, -2, 8, 18, -27, -72, 48, 168, -42], + [-1, -3, 6, 26, -9, -99, -24, 216, 126], + [-1, -4, 3, 32, 17, -108, -123, 192, 342], + [-1, -5, -1, 35, 49, -91, -231, 69, 534], + [-1, -6, -6, 34, 84, -42, -322, -162, 603], + [-1, -7, -12, 28, 118, 42, -364, -484, 441], + [-1, -8, -19, 16, 146, 160, -322, -848, -43], + [-1, -9, -27, -3, 162, 306, -162, -1170, -891], + [-1, -10, -36, -30, 159, 468, 144, -1332, -2061], + [-1, -11, -46, -66, 129, 627, 612, -1188, -3393], + [-1, -12, -57, -112, 63, 756, 1239, -576, -4581], + [-1, -13, -69, -169, -49, 819, 1995, 663, -5157], + [-1, -14, -82, -238, -218, 770, 2814, 2658, -4494] +] + +def unitCouplingData_10 : List (List ℤ) := [ + [1, -10, 45, -120, 210, -252, 210, -120, 45], + [1, -9, 35, -75, 90, -42, -42, 90, -75], + [1, -8, 26, -40, 15, 48, -84, 48, 15], + [1, -7, 18, -14, -25, 63, -36, -36, 63], + [1, -6, 11, 4, -39, 38, 27, -72, 27], + [1, -5, 5, 15, -35, -1, 65, -45, -45], + [1, -4, 0, 20, -20, -36, 64, 20, -90], + [1, -3, -4, 20, 0, -56, 28, 84, -70], + [1, -2, -7, 16, 20, -56, -28, 112, 14], + [1, -1, -9, 9, 36, -36, -84, 84, 126], + [1, 0, -10, 0, 45, 0, -120, 0, 210], + [1, 1, -10, -10, 45, 45, -120, -120, 210], + [1, 2, -9, -20, 35, 90, -75, -240, 90], + [1, 3, -7, -29, 15, 125, 15, -315, -150], + [1, 4, -4, -36, -14, 140, 140, -300, -465], + [1, 5, 0, -40, -50, 126, 280, -160, -765], + [1, 6, 5, -40, -90, 76, 406, 120, -925], + [1, 7, 11, -35, -130, -14, 482, 526, -805], + [1, 8, 18, -24, -165, -144, 468, 1008, -279], + [1, 9, 26, -6, -189, -309, 324, 1476, 729], + [1, 10, 35, 20, -195, -498, 15, 1800, 2205], + [1, 11, 45, 55, -175, -693, -483, 1815, 4005], + [1, 12, 56, 100, -120, -868, -1176, 1332, 5820], + [1, 13, 68, 156, -20, -988, -2044, 156, 7152] +] + +def unitCouplingData_11 : List (List ℤ) := [ + [-1, 11, -55, 165, -330, 462, -462, 330, -165], + [-1, 10, -44, 110, -165, 132, 0, -132, 165], + [-1, 9, -34, 66, -55, -33, 132, -132, 33], + [-1, 8, -25, 32, 11, -88, 99, 0, -99], + [-1, 7, -17, 7, 43, -77, 11, 99, -99], + [-1, 6, -10, -10, 50, -34, -66, 110, 0], + [-1, 5, -4, -20, 40, 16, -100, 44, 110], + [-1, 4, 1, -24, 20, 56, -84, -56, 154], + [-1, 3, 5, -23, -4, 76, -28, -140, 98], + [-1, 2, 8, -18, -27, 72, 48, -168, -42], + [-1, 1, 10, -10, -45, 45, 120, -120, -210], + [-1, 0, 11, 0, -55, 0, 165, 0, -330], + [-1, -1, 11, 11, -55, -55, 165, 165, -330], + [-1, -2, 10, 22, -44, -110, 110, 330, -165], + [-1, -3, 8, 32, -22, -154, 0, 440, 165], + [-1, -4, 5, 40, 10, -176, -154, 440, 605], + [-1, -5, 1, 45, 50, -166, -330, 286, 1045], + [-1, -6, -4, 46, 95, -116, -496, -44, 1331], + [-1, -7, -10, 42, 141, -21, -612, -540, 1287], + [-1, -8, -17, 32, 183, 120, -633, -1152, 747], + [-1, -9, -25, 15, 215, 303, -513, -1785, -405], + [-1, -10, -34, -10, 230, 518, -210, -2298, -2190], + [-1, -11, -44, -44, 220, 748, 308, -2508, -4488], + [-1, -12, -55, -88, 176, 968, 1056, -2200, -6996] +] + +def unitCouplingData_12 : List (List ℤ) := [ + [1, -12, 66, -220, 495, -792, 924, -792, 495], + [1, -11, 54, -154, 275, -297, 132, 132, -297], + [1, -10, 43, -100, 121, -22, -165, 264, -165], + [1, -9, 33, -57, 21, 99, -187, 99, 99], + [1, -8, 24, -24, -36, 120, -88, -88, 198], + [1, -7, 16, 0, -60, 84, 32, -176, 110], + [1, -6, 9, 16, -60, 24, 116, -144, -66], + [1, -5, 3, 25, -44, -36, 140, -28, -210], + [1, -4, -2, 28, -19, -80, 104, 112, -238], + [1, -3, -6, 26, 9, -99, 24, 216, -126], + [1, -2, -9, 20, 35, -90, -75, 240, 90], + [1, -1, -11, 11, 55, -55, -165, 165, 330], + [1, 0, -12, 0, 66, 0, -220, 0, 495], + [1, 1, -12, -12, 66, 66, -220, -220, 495], + [1, 2, -11, -24, 54, 132, -154, -440, 275], + [1, 3, -9, -35, 30, 186, -22, -594, -165], + [1, 4, -6, -44, -5, 216, 164, -616, -759], + [1, 5, -2, -50, -49, 211, 380, -452, -1375], + [1, 6, 3, -52, -99, 162, 591, -72, -1827], + [1, 7, 9, -49, -151, 63, 753, 519, -1899], + [1, 8, 16, -40, -200, -88, 816, 1272, -1380], + [1, 9, 24, -24, -240, -288, 728, 2088, -108], + [1, 10, 33, 0, -264, -528, 440, 2816, 1980], + [1, 11, 43, 33, -264, -792, -88, 3256, 4796] +] + +def unitCouplingData_13 : List (List ℤ) := [ + [-1, 13, -78, 286, -715, 1287, -1716, 1716, -1287], + [-1, 12, -65, 208, -429, 572, -429, 0, 429], + [-1, 11, -53, 143, -221, 143, 143, -429, 429], + [-1, 10, -42, 90, -78, -78, 286, -286, 0], + [-1, 9, -32, 48, 12, -156, 208, 0, -286], + [-1, 8, -23, 16, 60, -144, 52, 208, -286], + [-1, 7, -15, -7, 76, -84, -92, 260, -78], + [-1, 6, -8, -22, 69, -8, -176, 168, 182], + [-1, 5, -2, -30, 47, 61, -184, -8, 350], + [-1, 4, 3, -32, 17, 108, -123, -192, 342], + [-1, 3, 7, -29, -15, 125, -15, -315, 150], + [-1, 2, 10, -22, -44, 110, 110, -330, -165], + [-1, 1, 12, -12, -66, 66, 220, -220, -495], + [-1, 0, 13, 0, -78, 0, 286, 0, -715], + [-1, -1, 13, 13, -78, -78, 286, 286, -715], + [-1, -2, 12, 26, -65, -156, 208, 572, -429], + [-1, -3, 10, 38, -39, -221, 52, 780, 143], + [-1, -4, 7, 48, -1, -260, -169, 832, 923], + [-1, -5, 3, 55, 47, -261, -429, 663, 1755], + [-1, -6, -2, 58, 102, -214, -690, 234, 2418], + [-1, -7, -8, 56, 160, -112, -904, -456, 2652], + [-1, -8, -15, 48, 216, 48, -1016, -1360, 2196], + [-1, -9, -23, 33, 264, 264, -968, -2376, 836], + [-1, -10, -32, 10, 297, 528, -704, -3344, -1540] +] + +def unitCouplingData_14 : List (List ℤ) := [ + [1, -14, 91, -364, 1001, -2002, 3003, -3432, 3003], + [1, -13, 77, -273, 637, -1001, 1001, -429, -429], + [1, -12, 64, -196, 364, -364, 0, 572, -858], + [1, -11, 52, -132, 168, 0, -364, 572, -286], + [1, -10, 41, -80, 36, 168, -364, 208, 286], + [1, -9, 31, -39, -44, 204, -196, -156, 494], + [1, -8, 22, -8, -83, 160, 8, -352, 338], + [1, -7, 14, 14, -91, 77, 168, -344, -14], + [1, -6, 7, 28, -77, -14, 245, -176, -358], + [1, -5, 1, 35, -49, -91, 231, 69, -534], + [1, -4, -4, 36, -14, -140, 140, 300, -465], + [1, -3, -8, 32, 22, -154, 0, 440, -165], + [1, -2, -11, 24, 54, -132, -154, 440, 275], + [1, -1, -13, 13, 78, -78, -286, 286, 715], + [1, 0, -14, 0, 91, 0, -364, 0, 1001], + [1, 1, -14, -14, 91, 91, -364, -364, 1001], + [1, 2, -13, -28, 77, 182, -273, -728, 637], + [1, 3, -11, -41, 49, 259, -91, -1001, -91], + [1, 4, -8, -52, 8, 308, 168, -1092, -1092], + [1, 5, -4, -60, -44, 316, 476, -924, -2184], + [1, 6, 1, -64, -104, 272, 792, -448, -3108], + [1, 7, 7, -63, -168, 168, 1064, 344, -3556], + [1, 8, 14, -56, -231, 0, 1232, 1408, -3212], + [1, 9, 22, -42, -287, -231, 1232, 2640, -1804] +] + +def unitCouplingData_15 : List (List ℤ) := [ + [-1, 15, -105, 455, -1365, 3003, -5005, 6435, -6435], + [-1, 14, -90, 350, -910, 1638, -2002, 1430, 0], + [-1, 13, -76, 260, -560, 728, -364, -572, 1430], + [-1, 12, -63, 184, -300, 168, 364, -936, 858], + [-1, 11, -51, 121, -116, -132, 532, -572, -78], + [-1, 10, -40, 70, 5, -248, 400, -40, -650], + [-1, 9, -30, 30, 75, -243, 152, 360, -690], + [-1, 8, -21, 0, 105, -168, -91, 512, -330], + [-1, 7, -13, -21, 105, -63, -259, 421, 182], + [-1, 6, -6, -34, 84, 42, -322, 162, 603], + [-1, 5, 0, -40, 50, 126, -280, -160, 765], + [-1, 4, 5, -40, 10, 176, -154, -440, 605], + [-1, 3, 9, -35, -30, 186, 22, -594, 165], + [-1, 2, 12, -26, -65, 156, 208, -572, -429], + [-1, 1, 14, -14, -91, 91, 364, -364, -1001], + [-1, 0, 15, 0, -105, 0, 455, 0, -1365], + [-1, -1, 15, 15, -105, -105, 455, 455, -1365], + [-1, -2, 14, 30, -90, -210, 350, 910, -910], + [-1, -3, 12, 44, -60, -300, 140, 1260, 0], + [-1, -4, 9, 56, -16, -360, -160, 1400, 1260], + [-1, -5, 5, 65, 40, -376, -520, 1240, 2660], + [-1, -6, 0, 70, 105, -336, -896, 720, 3900], + [-1, -7, -6, 70, 175, -231, -1232, -176, 4620], + [-1, -8, -13, 64, 245, -56, -1463, -1408, 4444] +] + +def unitCouplingData_16 : List (List ℤ) := [ + [1, -16, 120, -560, 1820, -4368, 8008, -11440, 12870], + [1, -15, 104, -440, 1260, -2548, 3640, -3432, 1430], + [1, -14, 89, -336, 820, -1288, 1092, 208, -2002], + [1, -13, 75, -247, 484, -468, -196, 1300, -1794], + [1, -12, 62, -172, 237, 16, -664, 1104, -494], + [1, -11, 50, -110, 65, 253, -648, 440, 610], + [1, -10, 39, -60, -45, 318, -395, -208, 1050], + [1, -9, 29, -21, -105, 273, -77, -603, 842], + [1, -8, 20, 8, -126, 168, 196, -680, 239], + [1, -7, 12, 28, -118, 42, 364, -484, -441], + [1, -6, 5, 40, -90, -76, 406, -120, -925], + [1, -5, -1, 45, -50, -166, 330, 286, -1045], + [1, -4, -6, 44, -5, -216, 164, 616, -759], + [1, -3, -10, 38, 39, -221, -52, 780, -143], + [1, -2, -13, 28, 77, -182, -273, 728, 637], + [1, -1, -15, 15, 105, -105, -455, 455, 1365], + [1, 0, -16, 0, 120, 0, -560, 0, 1820], + [1, 1, -16, -16, 120, 120, -560, -560, 1820], + [1, 2, -15, -32, 104, 240, -440, -1120, 1260], + [1, 3, -13, -47, 72, 344, -200, -1560, 140], + [1, 4, -10, -60, 25, 416, 144, -1760, -1420], + [1, 5, -6, -70, -35, 441, 560, -1616, -3180], + [1, 6, -1, -76, -105, 406, 1001, -1056, -4796], + [1, 7, 5, -77, -181, 301, 1407, -55, -5852] +] + +def unitCouplingData_17 : List (List ℤ) := [ + [-1, 17, -136, 680, -2380, 6188, -12376, 19448, -24310], + [-1, 16, -119, 544, -1700, 3808, -6188, 7072, -4862], + [-1, 15, -103, 425, -1156, 2108, -2380, 884, 2210], + [-1, 14, -88, 322, -731, 952, -272, -1496, 3094], + [-1, 13, -74, 234, -409, 221, 680, -1768, 1598], + [-1, 12, -61, 160, -175, -188, 901, -1088, -170], + [-1, 11, -49, 99, -15, -363, 713, -187, -1258], + [-1, 10, -38, 50, 84, -378, 350, 526, -1445], + [-1, 9, -28, 12, 134, -294, -28, 876, -919], + [-1, 8, -19, -16, 146, -160, -322, 848, -43], + [-1, 7, -11, -35, 130, -14, -482, 526, 805], + [-1, 6, -4, -46, 95, 116, -496, 44, 1331], + [-1, 5, 2, -50, 49, 211, -380, -452, 1375], + [-1, 4, 7, -48, -1, 260, -169, -832, 923], + [-1, 3, 11, -41, -49, 259, 91, -1001, 91], + [-1, 2, 14, -30, -90, 210, 350, -910, -910], + [-1, 1, 16, -16, -120, 120, 560, -560, -1820], + [-1, 0, 17, 0, -136, 0, 680, 0, -2380], + [-1, -1, 17, 17, -136, -136, 680, 680, -2380], + [-1, -2, 16, 34, -119, -272, 544, 1360, -1700], + [-1, -3, 14, 50, -85, -391, 272, 1904, -340], + [-1, -4, 11, 64, -35, -476, -119, 2176, 1564], + [-1, -5, 7, 75, 29, -511, -595, 2057, 3740], + [-1, -6, 2, 82, 104, -482, -1106, 1462, 5797] +] + +def unitCouplingData_18 : List (List ℤ) := [ + [1, -18, 153, -816, 3060, -8568, 18564, -31824, 43758], + [1, -17, 135, -663, 2244, -5508, 9996, -13260, 11934], + [1, -16, 118, -528, 1581, -3264, 4488, -3264, -1326], + [1, -15, 102, -410, 1053, -1683, 1224, 1224, -4590], + [1, -14, 87, -308, 643, -630, -459, 2448, -3366], + [1, -13, 73, -221, 335, 13, -1089, 1989, -918], + [1, -12, 60, -148, 114, 348, -1076, 900, 1071], + [1, -11, 48, -88, -34, 462, -728, -176, 1971], + [1, -10, 37, -40, -122, 428, -266, -904, 1795], + [1, -9, 27, -3, -162, 306, 162, -1170, 891], + [1, -8, 18, 24, -165, 144, 468, -1008, -279], + [1, -7, 10, 42, -141, -21, 612, -540, -1287], + [1, -6, 3, 52, -99, -162, 591, 72, -1827], + [1, -5, -3, 55, -47, -261, 429, 663, -1755], + [1, -4, -8, 52, 8, -308, 168, 1092, -1092], + [1, -3, -12, 44, 60, -300, -140, 1260, 0], + [1, -2, -15, 32, 104, -240, -440, 1120, 1260], + [1, -1, -17, 17, 136, -136, -680, 680, 2380], + [1, 0, -18, 0, 153, 0, -816, 0, 3060], + [1, 1, -18, -18, 153, 153, -816, -816, 3060], + [1, 2, -17, -36, 135, 306, -663, -1632, 2244], + [1, 3, -15, -53, 99, 441, -357, -2295, 612], + [1, 4, -12, -68, 46, 540, 84, -2652, -1683], + [1, 5, -8, -80, -22, 586, 624, -2568, -4335] +] + +def unitCouplingData_19 : List (List ℤ) := [ + [-1, 19, -171, 969, -3876, 11628, -27132, 50388, -75582], + [-1, 18, -152, 798, -2907, 7752, -15504, 23256, -25194], + [-1, 17, -134, 646, -2109, 4845, -7752, 7752, -1938], + [-1, 16, -117, 512, -1463, 2736, -2907, 0, 5814], + [-1, 15, -101, 395, -951, 1273, -171, -2907, 5814], + [-1, 14, -86, 294, -556, 322, 1102, -3078, 2907], + [-1, 13, -72, 208, -262, -234, 1424, -1976, -171], + [-1, 12, -59, 136, -54, -496, 1190, -552, -2147], + [-1, 11, -47, 77, 82, -550, 694, 638, -2699], + [-1, 10, -36, 30, 159, -468, 144, 1332, -2061], + [-1, 9, -26, -6, 189, -309, -324, 1476, -729], + [-1, 8, -17, -32, 183, -120, -633, 1152, 747], + [-1, 7, -9, -49, 151, 63, -753, 519, 1899], + [-1, 6, -2, -58, 102, 214, -690, -234, 2418], + [-1, 5, 4, -60, 44, 316, -476, -924, 2184], + [-1, 4, 9, -56, -16, 360, -160, -1400, 1260], + [-1, 3, 13, -47, -72, 344, 200, -1560, -140], + [-1, 2, 16, -34, -119, 272, 544, -1360, -1700], + [-1, 1, 18, -18, -153, 153, 816, -816, -3060], + [-1, 0, 19, 0, -171, 0, 969, 0, -3876], + [-1, -1, 19, 19, -171, -171, 969, 969, -3876], + [-1, -2, 18, 38, -152, -342, 798, 1938, -2907], + [-1, -3, 16, 56, -114, -494, 456, 2736, -969], + [-1, -4, 13, 72, -58, -608, -38, 3192, 1767] +] + +def unitCouplingData_20 : List (List ℤ) := [ + [1, -20, 190, -1140, 4845, -15504, 38760, -77520, 125970], + [1, -19, 170, -950, 3705, -10659, 23256, -38760, 48450], + [1, -18, 151, -780, 2755, -6954, 12597, -15504, 9690], + [1, -17, 133, -629, 1975, -4199, 5643, -2907, -5814], + [1, -16, 116, -496, 1346, -2224, 1444, 2736, -8721], + [1, -15, 100, -380, 850, -878, -780, 4180, -5985], + [1, -14, 85, -280, 470, -28, -1658, 3400, -1805], + [1, -13, 71, -195, 190, 442, -1686, 1742, 1595], + [1, -12, 58, -124, -5, 632, -1244, 56, 3337], + [1, -11, 46, -66, -129, 627, -612, -1188, 3393], + [1, -10, 35, -20, -195, 498, 15, -1800, 2205], + [1, -9, 25, 15, -215, 303, 513, -1785, 405], + [1, -8, 16, 40, -200, 88, 816, -1272, -1380], + [1, -7, 8, 56, -160, -112, 904, -456, -2652], + [1, -6, 1, 64, -104, -272, 792, 448, -3108], + [1, -5, -5, 65, -40, -376, 520, 1240, -2660], + [1, -4, -10, 60, 25, -416, 144, 1760, -1420], + [1, -3, -14, 50, 85, -391, -272, 1904, 340], + [1, -2, -17, 36, 135, -306, -663, 1632, 2244], + [1, -1, -19, 19, 171, -171, -969, 969, 3876], + [1, 0, -20, 0, 190, 0, -1140, 0, 4845], + [1, 1, -20, -20, 190, 190, -1140, -1140, 4845], + [1, 2, -19, -40, 170, 380, -950, -2280, 3705], + [1, 3, -17, -59, 130, 550, -570, -3230, 1425] +] + +def unitCouplingData_21 : List (List ℤ) := [ + [-1, 21, -210, 1330, -5985, 20349, -54264, 116280, -203490], + [-1, 20, -189, 1120, -4655, 14364, -33915, 62016, -87210], + [-1, 19, -169, 931, -3535, 9709, -19551, 28101, -25194], + [-1, 18, -150, 762, -2604, 6174, -9842, 8550, 2907], + [-1, 17, -132, 612, -1842, 3570, -3668, -1292, 11457], + [-1, 16, -115, 480, -1230, 1728, -98, -4960, 10165], + [-1, 15, -99, 365, -750, 498, 1630, -5058, 5205], + [-1, 14, -84, 266, -385, -252, 2128, -3428, 147], + [-1, 13, -70, 182, -119, -637, 1876, -1300, -3281], + [-1, 12, -57, 112, 63, -756, 1239, 576, -4581], + [-1, 11, -45, 55, 175, -693, 483, 1815, -4005], + [-1, 10, -34, 10, 230, -518, -210, 2298, -2190], + [-1, 9, -24, -24, 240, -288, -728, 2088, 108], + [-1, 8, -15, -48, 216, -48, -1016, 1360, 2196], + [-1, 7, -7, -63, 168, 168, -1064, 344, 3556], + [-1, 6, 0, -70, 105, 336, -896, -720, 3900], + [-1, 5, 6, -70, 35, 441, -560, -1616, 3180], + [-1, 4, 11, -64, -35, 476, -119, -2176, 1564], + [-1, 3, 15, -53, -99, 441, 357, -2295, -612], + [-1, 2, 18, -38, -152, 342, 798, -1938, -2907], + [-1, 1, 20, -20, -190, 190, 1140, -1140, -4845], + [-1, 0, 21, 0, -210, 0, 1330, 0, -5985], + [-1, -1, 21, 21, -210, -210, 1330, 1330, -5985], + [-1, -2, 20, 42, -189, -420, 1120, 2660, -4655] +] + +def unitCouplingData_22 : List (List ℤ) := [ + [1, -22, 231, -1540, 7315, -26334, 74613, -170544, 319770], + [1, -21, 209, -1309, 5775, -19019, 48279, -95931, 149226], + [1, -20, 188, -1100, 4466, -13244, 29260, -47652, 53295], + [1, -19, 168, -912, 3366, -8778, 16016, -18392, 5643], + [1, -18, 149, -744, 2454, -5412, 7238, -2376, -12749], + [1, -17, 131, -595, 1710, -2958, 1826, 4862, -15125], + [1, -16, 114, -464, 1115, -1248, -1132, 6688, -10263], + [1, -15, 98, -350, 651, -133, -2380, 5556, -3575], + [1, -14, 83, -252, 301, 518, -2513, 3176, 1981], + [1, -13, 69, -169, 49, 819, -1995, 663, 5157], + [1, -12, 56, -100, -120, 868, -1176, -1332, 5820], + [1, -11, 44, -44, -220, 748, -308, -2508, 4488], + [1, -10, 33, 0, -264, 528, 440, -2816, 1980], + [1, -9, 23, 33, -264, 264, 968, -2376, -836], + [1, -8, 14, 56, -231, 0, 1232, -1408, -3212], + [1, -7, 6, 70, -175, -231, 1232, -176, -4620], + [1, -6, -1, 76, -105, -406, 1001, 1056, -4796], + [1, -5, -7, 75, -29, -511, 595, 2057, -3740], + [1, -4, -12, 68, 46, -540, 84, 2652, -1683], + [1, -3, -16, 56, 114, -494, -456, 2736, 969], + [1, -2, -19, 40, 170, -380, -950, 2280, 3705], + [1, -1, -21, 21, 210, -210, -1330, 1330, 5985], + [1, 0, -22, 0, 231, 0, -1540, 0, 7315], + [1, 1, -22, -22, 231, 231, -1540, -1540, 7315] +] + +def unitCouplingData_23 : List (List ℤ) := [ + [-1, 23, -253, 1771, -8855, 33649, -100947, 245157, -490314], + [-1, 22, -230, 1518, -7084, 24794, -67298, 144210, -245157], + [-1, 21, -208, 1288, -5566, 17710, -42504, 76912, -100947], + [-1, 20, -187, 1080, -4278, 12144, -24794, 34408, -24035], + [-1, 19, -167, 893, -3198, 7866, -12650, 9614, 10373], + [-1, 18, -148, 726, -2305, 4668, -4784, -3036, 19987], + [-1, 17, -130, 578, -1579, 2363, -116, -7820, 16951], + [-1, 16, -113, 448, -1001, 784, 2247, -7936, 9131], + [-1, 15, -97, 335, -553, -217, 3031, -5689, 1195], + [-1, 14, -82, 238, -218, -770, 2814, -2658, -4494], + [-1, 13, -68, 156, 20, -988, 2044, 156, -7152], + [-1, 12, -55, 88, 176, -968, 1056, 2200, -6996], + [-1, 11, -43, 33, 264, -792, 88, 3256, -4796], + [-1, 10, -32, -10, 297, -528, -704, 3344, -1540], + [-1, 9, -22, -42, 287, -231, -1232, 2640, 1804], + [-1, 8, -13, -64, 245, 56, -1463, 1408, 4444], + [-1, 7, -5, -77, 181, 301, -1407, -55, 5852], + [-1, 6, 2, -82, 104, 482, -1106, -1462, 5797], + [-1, 5, 8, -80, 22, 586, -624, -2568, 4335], + [-1, 4, 13, -72, -58, 608, -38, -3192, 1767], + [-1, 3, 17, -59, -130, 550, 570, -3230, -1425], + [-1, 2, 20, -42, -189, 420, 1120, -2660, -4655], + [-1, 1, 22, -22, -231, 231, 1540, -1540, -7315], + [-1, 0, 23, 0, -253, 0, 1771, 0, -8855] +] + +def unitCouplingData : List (List (List ℤ)) := [unitCouplingData_0, unitCouplingData_1, unitCouplingData_2, unitCouplingData_3, unitCouplingData_4, unitCouplingData_5, unitCouplingData_6, unitCouplingData_7, unitCouplingData_8, unitCouplingData_9, unitCouplingData_10, unitCouplingData_11, unitCouplingData_12, unitCouplingData_13, unitCouplingData_14, unitCouplingData_15, unitCouplingData_16, unitCouplingData_17, unitCouplingData_18, unitCouplingData_19, unitCouplingData_20, unitCouplingData_21, unitCouplingData_22, unitCouplingData_23] + +def memoUnitCoupling (z k p : ℕ) : ℤ := (((unitCouplingData.getD z []).getD k []).getD p 0) + +theorem unitCouplingChecked_0 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 0 k.val p.val = memoUnitCoupling 0 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_1 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 1 k.val p.val = memoUnitCoupling 1 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_2 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 2 k.val p.val = memoUnitCoupling 2 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_3 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 3 k.val p.val = memoUnitCoupling 3 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_4 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 4 k.val p.val = memoUnitCoupling 4 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_5 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 5 k.val p.val = memoUnitCoupling 5 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_6 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 6 k.val p.val = memoUnitCoupling 6 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_7 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 7 k.val p.val = memoUnitCoupling 7 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_8 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 8 k.val p.val = memoUnitCoupling 8 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_9 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 9 k.val p.val = memoUnitCoupling 9 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_10 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 10 k.val p.val = memoUnitCoupling 10 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_11 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 11 k.val p.val = memoUnitCoupling 11 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_12 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 12 k.val p.val = memoUnitCoupling 12 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_13 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 13 k.val p.val = memoUnitCoupling 13 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_14 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 14 k.val p.val = memoUnitCoupling 14 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_15 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 15 k.val p.val = memoUnitCoupling 15 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_16 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 16 k.val p.val = memoUnitCoupling 16 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_17 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 17 k.val p.val = memoUnitCoupling 17 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_18 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 18 k.val p.val = memoUnitCoupling 18 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_19 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 19 k.val p.val = memoUnitCoupling 19 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_20 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 20 k.val p.val = memoUnitCoupling 20 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_21 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 21 k.val p.val = memoUnitCoupling 21 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_22 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 22 k.val p.val = memoUnitCoupling 22 k.val p.val := by + decide +kernel + +theorem unitCouplingChecked_23 : ∀ (k : Fin 24) (p : Fin 9), + fastIntegerCoupling 1 23 k.val p.val = memoUnitCoupling 23 k.val p.val := by + decide +kernel + +theorem memoUnitCoupling_spec (z k p : ℕ) (hz : z < 24) (hk : k < 24) (hp : p < 9) : + fastIntegerCoupling 1 z k p = memoUnitCoupling z k p := by + interval_cases z + · exact unitCouplingChecked_0 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_1 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_2 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_3 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_4 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_5 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_6 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_7 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_8 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_9 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_10 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_11 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_12 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_13 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_14 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_15 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_16 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_17 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_18 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_19 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_20 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_21 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_22 ⟨k, hk⟩ ⟨p, hp⟩ + · exact unitCouplingChecked_23 ⟨k, hk⟩ ⟨p, hp⟩ +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Covariance.lean b/lean/OAI/Analysis/LaughlinFock/Covariance.lean new file mode 100644 index 0000000000000000000000000000000000000000..f19b11ff450fdaf4bb53d0ede844d26b853ce06b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Covariance.lean @@ -0,0 +1,325 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.ThreeGram + +namespace OAI + +/-! Covariance. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder + + + +def oneBodyLift (Q : ℕ) (A : Matrix (Orbital Q) (Orbital Q) ℂ) : FockMatrix Q := + ∑ i, ∑ j, A i j • ((annihilator Q i)ᴴ * annihilator Q j) + +theorem oneBodyLift_add (Q : ℕ) (A B : Matrix (Orbital Q) (Orbital Q) ℂ) : + oneBodyLift Q (A+B) = oneBodyLift Q A + oneBodyLift Q B := by + simp [oneBodyLift, add_smul, Finset.sum_add_distrib] + +theorem oneBodyLift_smul (Q : ℕ) (c : ℂ) (A : Matrix (Orbital Q) (Orbital Q) ℂ) : + oneBodyLift Q (c • A) = c • oneBodyLift Q A := by + simp [oneBodyLift, smul_smul, Finset.smul_sum] + +def oneBodyLiftLinear (Q : ℕ) : + Matrix (Orbital Q) (Orbital Q) ℂ →ₗ[ℂ] FockMatrix Q where + toFun := oneBodyLift Q + map_add' := oneBodyLift_add Q + map_smul' := oneBodyLift_smul Q + +theorem oneBodyLift_adjoint (Q : ℕ) (A : Matrix (Orbital Q) (Orbital Q) ℂ) : + (oneBodyLift Q A)ᴴ = oneBodyLift Q Aᴴ := by + simp only [oneBodyLift, Matrix.conjTranspose_sum, Matrix.conjTranspose_smul, + Matrix.conjTranspose_mul, Matrix.conjTranspose_conjTranspose, + Matrix.conjTranspose_apply] + rw [Finset.sum_comm] + +theorem oneBodyLift_hermitian (Q : ℕ) (A : Matrix (Orbital Q) (Orbital Q) ℂ) + (hA : A.IsHermitian) : (oneBodyLift Q A).IsHermitian := by + change (oneBodyLift Q A)ᴴ = _ + rw [oneBodyLift_adjoint, hA.eq] + + +theorem annihilator_oneBody_unit_commutator (Q : ℕ) (k i j : Orbital Q) : + annihilator Q k * ((annihilator Q i)ᴴ * annihilator Q j) - + ((annihilator Q i)ᴴ * annihilator Q j) * annihilator Q k = + if k=i then annihilator Q j else 0 := by + have h1 := congrArg (fun X : FockMatrix Q => X * annihilator Q j) + (annihilator_adjoint_anticommute Q k i) + have h2 := congrArg (fun X : FockMatrix Q => (annihilator Q i)ᴴ * X) + (annihilator_anticommute Q k j) + simp only [Matrix.add_mul, Matrix.mul_assoc, ite_mul, Matrix.one_mul, + Matrix.zero_mul] at h1 + simp only [Matrix.mul_add, Matrix.mul_zero] at h2 + calc + _ = annihilator Q k * ((annihilator Q i)ᴴ * annihilator Q j) + + (annihilator Q i)ᴴ * (annihilator Q k * annihilator Q j) - + ((annihilator Q i)ᴴ * (annihilator Q k * annihilator Q j) + + (annihilator Q i)ᴴ * (annihilator Q j * annihilator Q k)) := by noncomm_ring + _ = _ := by rw [h1, h2, sub_zero] + +theorem annihilator_oneBody_commutator (Q : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (k : Orbital Q) : + annihilator Q k * oneBodyLift Q A - oneBodyLift Q A * annihilator Q k = + ∑ j, A k j • annihilator Q j := by + classical + simp only [oneBodyLift, Matrix.mul_sum, Matrix.sum_mul, + Matrix.mul_smul, Matrix.smul_mul, ← Finset.sum_sub_distrib, ← smul_sub] + simp_rw [annihilator_oneBody_unit_commutator, smul_ite, smul_zero] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro j _ + simp + +theorem oneBody_creator_commutator (Q : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (k : Orbital Q) : + oneBodyLift Q A * (annihilator Q k)ᴴ - (annihilator Q k)ᴴ * oneBodyLift Q A = + ∑ i, A i k • (annihilator Q i)ᴴ := by + have h := congrArg Matrix.conjTranspose (annihilator_oneBody_commutator Q Aᴴ k) + simpa only [Matrix.conjTranspose_sub, Matrix.conjTranspose_mul, oneBodyLift_adjoint, + Matrix.conjTranspose_conjTranspose, Matrix.conjTranspose_sum, + Matrix.conjTranspose_smul, Matrix.conjTranspose_apply, star_star] using h + + +theorem matrix_commutator_mul {ι : Type*} [Fintype ι] + (X Y Z : Matrix ι ι ℂ) : + X * (Y*Z) - (Y*Z) * X = + (X*Y-Y*X)*Z + Y*(X*Z-Z*X) := by noncomm_ring + + + +theorem oneBody_annihilator_commutator_mem (Q : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (j : Orbital Q) : + oneBodyLift Q A * annihilator Q j - annihilator Q j * oneBodyLift Q A ∈ + AnnihilationSpace Q 1 := by + rw [← neg_sub, annihilator_oneBody_commutator] + apply Submodule.neg_mem + apply Submodule.sum_mem + intro i _ + exact Submodule.smul_mem _ _ (annihilator_mem Q i) + +theorem oneBody_annihilatorList_commutator_mem (Q : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (js : List (Orbital Q)) : + oneBodyLift Q A * annihilatorList Q js - annihilatorList Q js * oneBodyLift Q A ∈ + AnnihilationSpace Q js.length := by + induction js with + | nil => simp only [annihilatorList_nil, Matrix.mul_one, Matrix.one_mul, sub_self]; exact Submodule.zero_mem _ + | cons j js ih => + rw [annihilatorList_cons, matrix_commutator_mul] + apply Submodule.add_mem + · simpa only [List.length_cons, Nat.add_comm] using + annihilationSpace_mul Q 1 js.length (annihilator_mem Q j) ih + · simpa only [List.length_cons, Nat.add_comm] using + annihilationSpace_mul Q 1 js.length + (oneBody_annihilator_commutator_mem Q A j) (annihilatorList_mem Q js _ rfl) + +theorem oneBody_annihilationSpace_commutator_mem (Q k : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (M : FockMatrix Q) + (hM : M ∈ AnnihilationSpace Q k) : + oneBodyLift Q A * M - M * oneBodyLift Q A ∈ AnnihilationSpace Q k := by + rw [annihilationSpace_normal_form Q k M hM] + simp only [Matrix.mul_sum, Matrix.sum_mul, Matrix.mul_smul, Matrix.smul_mul, + ← Finset.sum_sub_distrib, ← smul_sub] + apply Submodule.sum_mem + intro S _ + apply Submodule.smul_mem + have h := oneBody_annihilatorList_commutator_mem Q A (S.val.sort (· ≤ ·)) + simpa only [Finset.length_sort, S.property, basisAnnihilator] using h + + +theorem oneBodyLift_vacuum_row (Q : ℕ) (A : Matrix (Orbital Q) (Orbital Q) ℂ) + (S : Occupation Q) : oneBodyLift Q A ∅ S = 0 := by + simp only [oneBodyLift, Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, + ← creator_eq_adjoint, creator_mul_vacuum_zero, mul_zero, Finset.sum_const_zero] + + +theorem oneBodyLift_vacuum_column (Q : ℕ) (A : Matrix (Orbital Q) (Orbital Q) ℂ) + (S : Occupation Q) : oneBodyLift Q A S ∅ = 0 := by + simp only [oneBodyLift, Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, + mul_annihilator_vacuum_zero, mul_zero, Finset.sum_const_zero] + + + +theorem oneBodyLift_entry_eq_zero (Q : ℕ) (A : Matrix (Orbital Q) (Orbital Q) ℂ) + (S T : Occupation Q) (h : S.card ≠ T.card) : oneBodyLift Q A S T = 0 := by + classical + simp only [oneBodyLift, Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul] + apply Finset.sum_eq_zero + intro i _ + apply Finset.sum_eq_zero + intro j _ + suffices hh : ((annihilator Q i)ᴴ * annihilator Q j) S T = 0 by rw [hh, mul_zero] + rw [Matrix.mul_apply] + apply Finset.sum_eq_zero + intro R _ + rw [Matrix.conjTranspose_apply] + by_cases hR : R.card+1=S.card + · rw [annihilator_entry_eq_zero j R T (by omega), mul_zero] + · rw [annihilator_entry_eq_zero i R S hR, star_zero, zero_mul] + + +def sectorOneBody (Q k : ℕ) (A : Matrix (Orbital Q) (Orbital Q) ℂ) : + Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ := + (oneBodyLift Q A).submatrix Subtype.val Subtype.val + +theorem sectorOneBody_adjoint (Q k : ℕ) (A : Matrix (Orbital Q) (Orbital Q) ℂ) : + (sectorOneBody Q k A)ᴴ = sectorOneBody Q k Aᴴ := by + rw [sectorOneBody, Matrix.conjTranspose_submatrix, oneBodyLift_adjoint] + rfl + + + +theorem oneBody_basis_commutator (Q k : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (T : SectorOccupation Q k) : + oneBodyLift Q A * basisAnnihilator Q T.val - + basisAnnihilator Q T.val * oneBodyLift Q A = + -∑ S, sectorOneBody Q k A T S • basisAnnihilator Q S.val := by + classical + apply annihilationSpace_ext Q k + (oneBody_annihilationSpace_commutator_mem Q k A _ (basisAnnihilator_mem Q k T)) + (Submodule.neg_mem _ (Submodule.sum_mem _ fun S _ => + Submodule.smul_mem _ _ (basisAnnihilator_mem Q k S))) + intro S + simp only [Matrix.sub_apply, Matrix.mul_apply, oneBodyLift_vacuum_row, + zero_mul, Finset.sum_const_zero, zero_sub, basisAnnihilator_vacuum, + ite_mul, one_mul, Finset.sum_ite_eq, Finset.mem_univ, ite_true, + Matrix.neg_apply, Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, + Subtype.val_inj, mul_ite, mul_one, mul_zero, Finset.sum_ite_eq'] + rfl + + +theorem oneBody_basisCreator_commutator (Q k : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (T : SectorOccupation Q k) : + oneBodyLift Q A * (basisAnnihilator Q T.val)ᴴ - + (basisAnnihilator Q T.val)ᴴ * oneBodyLift Q A = + ∑ S, sectorOneBody Q k A S T • (basisAnnihilator Q S.val)ᴴ := by + have h := congrArg Matrix.conjTranspose (oneBody_basis_commutator Q k Aᴴ T) + simp only [Matrix.conjTranspose_sub, Matrix.conjTranspose_mul, oneBodyLift_adjoint, + Matrix.conjTranspose_conjTranspose, Matrix.conjTranspose_neg, Matrix.conjTranspose_sum, + Matrix.conjTranspose_smul] at h + rw [← neg_sub, h, neg_neg] + congr 1 + funext S + congr 1 + rw [← sectorOneBody_adjoint, Matrix.conjTranspose_apply, star_star] + + + +theorem oneBody_wedgeAnnihilator_commutator (Q k : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (v : SectorOccupation Q k → ℂ) : + oneBodyLift Q A * wedgeAnnihilator Q k v - + wedgeAnnihilator Q k v * oneBodyLift Q A = + -wedgeAnnihilator Q k ((sectorOneBody Q k A)ᴴ *ᵥ v) := by + classical + simp only [wedgeAnnihilator, Matrix.mul_sum, Matrix.sum_mul, + Matrix.mul_smul, Matrix.smul_mul, ← Finset.sum_sub_distrib, ← smul_sub, + oneBody_basis_commutator, smul_neg, Finset.sum_neg_distrib, Matrix.mulVec, + dotProduct, Matrix.conjTranspose_apply, star_sum, star_mul, star_star, + Finset.smul_sum, Finset.sum_smul, smul_smul] + rw [Finset.sum_comm] + + + +theorem oneBody_exteriorLift_commutator (Q k : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) + (M : Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ) : + oneBodyLift Q A * exteriorLift Q k M - exteriorLift Q k M * oneBodyLift Q A = + exteriorLift Q k (sectorOneBody Q k A * M - M * sectorOneBody Q k A) := by + classical + let R := sectorOneBody Q k A + let C (S T : SectorOccupation Q k) := + (basisAnnihilator Q S.val)ᴴ * basisAnnihilator Q T.val + have hprod (S T : SectorOccupation Q k) : + oneBodyLift Q A * C S T - C S T * oneBodyLift Q A = + (∑ U, R U S • C U T) - ∑ U, R T U • C S U := by + dsimp only [C] + rw [matrix_commutator_mul, oneBody_basisCreator_commutator, oneBody_basis_commutator] + simp only [Matrix.sum_mul, Matrix.smul_mul, Matrix.mul_neg, + Matrix.mul_sum, Matrix.mul_smul, sub_eq_add_neg, R] + have hleft : (∑ S, ∑ T, ∑ U, (M S T * R U S) • C U T) = + exteriorLift Q k (R*M) := by + unfold exteriorLift + simp only [Matrix.mul_apply, Finset.sum_smul] + rw [Finset.sum_comm] + conv_lhs => + arg 2 + ext T + rw [Finset.sum_comm] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro U _ + apply Finset.sum_congr rfl + intro T _ + apply Finset.sum_congr rfl + intro S _ + rw [mul_comm] + have hright : (∑ S, ∑ T, ∑ U, (M S T * R T U) • C S U) = + exteriorLift Q k (M*R) := by + unfold exteriorLift + simp only [Matrix.mul_apply, Finset.sum_smul] + apply Finset.sum_congr rfl + intro S _ + exact Finset.sum_comm + calc + _ = ∑ S, ∑ T, M S T • + (oneBodyLift Q A * C S T - C S T * oneBodyLift Q A) := by + simp only [exteriorLift, Matrix.mul_sum, Matrix.sum_mul, Matrix.mul_smul, + Matrix.smul_mul, ← Finset.sum_sub_distrib, smul_sub, C] + _ = exteriorLift Q k (R*M) - exteriorLift Q k (M*R) := by + simp only [hprod, smul_sub, Finset.smul_sum, smul_smul, Finset.sum_sub_distrib] + rw [hleft, hright] + _ = _ := ((exteriorLiftLinear Q k).map_sub (R*M) (M*R)).symm + + + +theorem oneBodyLift_commutator (Q : ℕ) (A B : Matrix (Orbital Q) (Orbital Q) ℂ) : + oneBodyLift Q A * oneBodyLift Q B - oneBodyLift Q B * oneBodyLift Q A = + oneBodyLift Q (A*B-B*A) := by + classical + let C (i j : Orbital Q) := (annihilator Q i)ᴴ * annihilator Q j + have hp (i j : Orbital Q) : + oneBodyLift Q A * C i j - C i j * oneBodyLift Q A = + (∑ r, A r i • C r j) - ∑ r, A j r • C i r := by + dsimp only [C] + rw [matrix_commutator_mul, oneBody_creator_commutator, + ← neg_sub (annihilator Q j * oneBodyLift Q A) (oneBodyLift Q A * annihilator Q j), + annihilator_oneBody_commutator] + simp only [Matrix.sum_mul, Matrix.smul_mul, Matrix.mul_neg, + Matrix.mul_sum, Matrix.mul_smul, sub_eq_add_neg] + have hl : (∑ i, ∑ j, ∑ r, (B i j * A r i) • C r j) = oneBodyLift Q (A*B) := by + unfold oneBodyLift + simp only [Matrix.mul_apply, Finset.sum_smul] + rw [Finset.sum_comm] + conv_lhs => + arg 2 + ext j + rw [Finset.sum_comm] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro r _ + apply Finset.sum_congr rfl + intro j _ + apply Finset.sum_congr rfl + intro i _ + rw [mul_comm] + have hr : (∑ i, ∑ j, ∑ r, (B i j * A j r) • C i r) = oneBodyLift Q (B*A) := by + unfold oneBodyLift + simp only [Matrix.mul_apply, Finset.sum_smul] + apply Finset.sum_congr rfl + intro i _ + exact Finset.sum_comm + calc + _ = ∑ i, ∑ j, B i j • (oneBodyLift Q A * C i j - C i j * oneBodyLift Q A) := by + change oneBodyLift Q A * (∑ i, ∑ j, B i j • C i j) - + (∑ i, ∑ j, B i j • C i j) * oneBodyLift Q A = _ + simp only [Matrix.mul_sum, Matrix.sum_mul, Matrix.mul_smul, + Matrix.smul_mul, ← Finset.sum_sub_distrib, smul_sub] + _ = oneBodyLift Q (A*B) - oneBodyLift Q (B*A) := by + simp only [hp, smul_sub, Finset.smul_sum, smul_smul, Finset.sum_sub_distrib] + rw [hl, hr] + _ = _ := ((oneBodyLiftLinear Q).map_sub (A*B) (B*A)).symm + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/CreationRows.lean b/lean/OAI/Analysis/LaughlinFock/CreationRows.lean new file mode 100644 index 0000000000000000000000000000000000000000..8979553d48fcd23c1bfe0350370d37bb33f02886 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/CreationRows.lean @@ -0,0 +1,173 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.NormalOrdering + +namespace OAI + +/-! Creation Rows. -/ +noncomputable section +namespace LaughlinFock +open scoped Matrix ComplexOrder Kronecker BigOperators + + + +theorem creationRow_product (Q : ℕ) (i k : Orbital Q) (X Y : FockMatrix Q) : + ((annihilator Q i)ᴴ * X)ᴴ * ((annihilator Q k)ᴴ * Y) = + (if i = k then Xᴴ * Y else 0) - + (annihilator Q k * X)ᴴ * (annihilator Q i * Y) := by + have hCAR := eq_sub_of_add_eq (annihilator_adjoint_anticommute Q i k) + rw [Matrix.conjTranspose_mul, Matrix.conjTranspose_conjTranspose, + Matrix.conjTranspose_mul] + calc + _ = Xᴴ * (annihilator Q i * (annihilator Q k)ᴴ) * Y := by + simp only [Matrix.mul_assoc] + _ = Xᴴ * ((if i = k then 1 else 0) - (annihilator Q k)ᴴ * annihilator Q i) * Y := by + rw [hCAR] + _ = _ := by + split_ifs <;> simp only [Matrix.mul_sub, Matrix.sub_mul, Matrix.mul_one, + Matrix.mul_zero, Matrix.zero_mul, Matrix.mul_assoc] + + + +theorem square_sum_expansion {β : Type*} [Fintype β] (Q : ℕ) (B : FockMatrix Q) + (Y : β → FockMatrix Q) (ℓ : ℝ) (a : β → ℝ) : + (ℓ • B + ∑ b, a b • Y b)ᴴ * (ℓ • B + ∑ b, a b • Y b) = + ℓ^2 • (Bᴴ * B) + + ∑ b, (ℓ * a b) • (Bᴴ * Y b + (Y b)ᴴ * B) + + ∑ b, ∑ c, (a b * a c) • ((Y b)ᴴ * Y c) := by + simp only [Matrix.conjTranspose_add, Matrix.conjTranspose_smul, + Matrix.conjTranspose_sum, star_trivial, Matrix.add_mul, Matrix.mul_add, + Matrix.sum_mul, Matrix.mul_sum, Matrix.smul_mul, Matrix.mul_smul, smul_smul, + smul_add, Finset.sum_add_distrib, Finset.smul_sum, pow_two] + have hcomm : ∑ c, ∑ b, (a c * a b) • ((Y b)ᴴ * Y c) = + ∑ b, ∑ c, (a b * a c) • ((Y b)ᴴ * Y c) := by + rw [Finset.sum_comm] + simp only [mul_comm] + rw [hcomm] + simp only [mul_comm ℓ] + abel + + + +def auxiliaryRow {β : Type*} [Fintype β] (Q t : ℕ) (ℓ : ℝ) + (p : β → ℕ) (i j : β → Orbital Q) (a : β → ℝ) : FockMatrix Q := + ℓ • pairAnnihilator Q t + ∑ b, a b • + ((annihilator Q (i b))ᴴ * (annihilator Q (j b) * pairAnnihilator Q (p b))) + + +def rowTwoBody (Q t : ℕ) (ℓ : ℝ) : FockMatrix Q := + ℓ^2 • ((pairAnnihilator Q t)ᴴ * pairAnnihilator Q t) + + +def rowThreeBody {β : Type*} [Fintype β] (Q t : ℕ) (ℓ : ℝ) + (p : β → ℕ) (i j : β → Orbital Q) (a : β → ℝ) : FockMatrix Q := + (∑ b, (ℓ*a b) • + ((annihilator Q (i b) * pairAnnihilator Q t)ᴴ * + (annihilator Q (j b) * pairAnnihilator Q (p b)) + + (annihilator Q (j b) * pairAnnihilator Q (p b))ᴴ * + (annihilator Q (i b) * pairAnnihilator Q t))) + + ∑ b, ∑ c, (a b*a c) • + (if i b = i c then + (annihilator Q (j b) * pairAnnihilator Q (p b))ᴴ * + (annihilator Q (j c) * pairAnnihilator Q (p c)) else 0) + + +def rowFourBody {β : Type*} [Fintype β] (Q : ℕ) + (p : β → ℕ) (i j : β → Orbital Q) (a : β → ℝ) : FockMatrix Q := + -(∑ b, ∑ c, (a b*a c) • + (annihilator Q (i c) * (annihilator Q (j b) * pairAnnihilator Q (p b)))ᴴ * + (annihilator Q (i b) * (annihilator Q (j c) * pairAnnihilator Q (p c)))) + + + +theorem auxiliaryRow_square {β : Type*} [Fintype β] (Q t : ℕ) (ℓ : ℝ) + (p : β → ℕ) (i j : β → Orbital Q) (a : β → ℝ) : + (auxiliaryRow Q t ℓ p i j a)ᴴ * auxiliaryRow Q t ℓ p i j a = + rowTwoBody Q t ℓ + rowThreeBody Q t ℓ p i j a + rowFourBody Q p i j a := by + rw [auxiliaryRow, square_sum_expansion] + simp_rw [creationRow_product] + simp only [rowTwoBody, rowThreeBody, rowFourBody, + Matrix.conjTranspose_mul, Matrix.conjTranspose_conjTranspose, + Matrix.mul_assoc, Matrix.smul_mul, smul_sub, Finset.sum_sub_distrib] + abel + + + +theorem rowTwoBody_mem (Q t : ℕ) (ℓ : ℝ) : rowTwoBody Q t ℓ ∈ BodySpace Q 2 := + Submodule.smul_of_tower_mem _ _ (bodySpace_product Q 2 + (pairAnnihilator_mem Q t) (pairAnnihilator_mem Q t)) + +theorem orbitalPair_mem (Q p : ℕ) (j : Orbital Q) : + annihilator Q j * pairAnnihilator Q p ∈ AnnihilationSpace Q 3 := + annihilationSpace_mul Q 2 1 (pairAnnihilator_mem Q p) (annihilator_mem Q j) + +theorem rowThreeBody_mem {β : Type*} [Fintype β] (Q t : ℕ) (ℓ : ℝ) + (p : β → ℕ) (i j : β → Orbital Q) (a : β → ℝ) : + rowThreeBody Q t ℓ p i j a ∈ BodySpace Q 3 := by + classical + apply Submodule.add_mem + · apply Submodule.sum_mem + intro b _ + apply Submodule.smul_of_tower_mem + exact Submodule.add_mem _ + (bodySpace_product Q 3 (orbitalPair_mem Q t _) (orbitalPair_mem Q (p b) _)) + (bodySpace_product Q 3 (orbitalPair_mem Q (p b) _) (orbitalPair_mem Q t _)) + · apply Submodule.sum_mem + intro b _ + apply Submodule.sum_mem + intro c _ + apply Submodule.smul_of_tower_mem + split_ifs + · exact bodySpace_product Q 3 (orbitalPair_mem Q (p b) _) (orbitalPair_mem Q (p c) _) + · exact Submodule.zero_mem _ + +theorem rowFourBody_mem {β : Type*} [Fintype β] (Q : ℕ) + (p : β → ℕ) (i j : β → Orbital Q) (a : β → ℝ) : + rowFourBody Q p i j a ∈ BodySpace Q 4 := by + classical + apply Submodule.neg_mem + apply Submodule.sum_mem + intro b _ + apply Submodule.sum_mem + intro c _ + rw [Matrix.smul_mul] + apply Submodule.smul_of_tower_mem + apply bodySpace_product + · exact annihilationSpace_mul Q 3 1 (orbitalPair_mem Q (p b) (j b)) + (annihilator_mem Q (i c)) + · exact annihilationSpace_mul Q 3 1 (orbitalPair_mem Q (p c) (j c)) + (annihilator_mem Q (i b)) + + + +theorem auxiliaryRow_decomposition_posSemidef {β : Type*} [Fintype β] + (Q t : ℕ) (ℓ : ℝ) (p : β → ℕ) (i j : β → Orbital Q) (a : β → ℝ) : + (rowTwoBody Q t ℓ + rowThreeBody Q t ℓ p i j a + rowFourBody Q p i j a).PosSemidef := by + rw [← auxiliaryRow_square] + exact Matrix.posSemidef_conjTranspose_mul_self _ + + + +def rowsComparison {ρ β : Type*} [Fintype ρ] [Fintype β] + (Q : ℕ) (t : ρ → ℕ) (ℓ : ρ → ℝ) (p : ρ → β → ℕ) + (i j : ρ → β → Orbital Q) (a : ρ → β → ℝ) : FockMatrix Q := + ∑ r, (auxiliaryRow Q (t r) (ℓ r) (p r) (i r) (j r) (a r))ᴴ * + auxiliaryRow Q (t r) (ℓ r) (p r) (i r) (j r) (a r) + +theorem rowsComparison_posSemidef {ρ β : Type*} [Fintype ρ] [Fintype β] + (Q : ℕ) (t : ρ → ℕ) (ℓ : ρ → ℝ) (p : ρ → β → ℕ) + (i j : ρ → β → Orbital Q) (a : ρ → β → ℝ) : + (rowsComparison Q t ℓ p i j a).PosSemidef := + Matrix.posSemidef_sum _ (fun _ _ => Matrix.posSemidef_conjTranspose_mul_self _) + +theorem rowsComparison_decomposition {ρ β : Type*} [Fintype ρ] [Fintype β] + (Q : ℕ) (t : ρ → ℕ) (ℓ : ρ → ℝ) (p : ρ → β → ℕ) + (i j : ρ → β → Orbital Q) (a : ρ → β → ℝ) : + rowsComparison Q t ℓ p i j a = (∑ r, rowTwoBody Q (t r) (ℓ r)) + + (∑ r, rowThreeBody Q (t r) (ℓ r) (p r) (i r) (j r) (a r)) + + (∑ r, rowFourBody Q (p r) (i r) (j r) (a r)) := by + simp only [rowsComparison, auxiliaryRow_square, Finset.sum_add_distrib] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/CrossOrbit.lean b/lean/OAI/Analysis/LaughlinFock/CrossOrbit.lean new file mode 100644 index 0000000000000000000000000000000000000000..29a6bda064db29f4fef6f1c46711ddd2d0cabd61 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/CrossOrbit.lean @@ -0,0 +1,148 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FockRotations +import OAI.Analysis.LaughlinFock.RectangularOrbit + +namespace OAI + +/-! Cross Orbit. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix Matrix.Norms.Elementwise ComplexOrder +open MeasureTheory Topology +local instance crossOrbitContinuousENorm {ι κ : Type*} [Fintype ι] [Fintype κ] : + ContinuousENorm (Matrix ι κ ℂ) := + inferInstanceAs (ContinuousENorm (ι → κ → ℂ)) + +section +variable {J σ : Type*} {I : J → Type*} + [∀ j, Fintype (I j)] [∀ j, DecidableEq (I j)] + (X : σ → ∀ j, Matrix (I j) (I j) ℂ) + (hX : ∀ s j, (X s j)ᴴ = -X s j) +local instance crossOrbitRotationMeasurableSpace : MeasurableSpace (rotationGroup X hX) := borel _ +local instance crossOrbitRotationBorelSpace : BorelSpace (rotationGroup X hX) := ⟨rfl⟩ + + +def rotationCrossAverage (i j : J) (M : Matrix (I i) (I j) ℂ) : Matrix (I i) (I j) ℂ := + ∫ g, rotationEvaluation X hX i g * M * (rotationEvaluation X hX j g)ᴴ ∂rotationHaar X hX + +theorem rotationCrossOrbit_integrable (i j : J) (M : Matrix (I i) (I j) ℂ) : + Integrable (fun g => rotationEvaluation X hX i g * M * (rotationEvaluation X hX j g)ᴴ) + (rotationHaar X hX) := by + have hc : Continuous (fun g => rotationEvaluation X hX i g * M * + (rotationEvaluation X hX j g)ᴴ) := + ((rotationEvaluation_continuous X hX i).matrix_mul continuous_const).matrix_mul + (rotationEvaluation_continuous X hX j).matrix_conjTranspose + exact integrableOn_univ.mp (hc.continuousOn.integrableOn_compact isCompact_univ) + + +theorem rotationCrossAverage_invariant (i j : J) (M : Matrix (I i) (I j) ℂ) + (h : rotationGroup X hX) : + rotationEvaluation X hX i h * rotationCrossAverage X hX i j M * + (rotationEvaluation X hX j h)ᴴ = rotationCrossAverage X hX i j M := by + unfold rotationCrossAverage + rw [matrixIntegral_mul_left_right _ (rotationCrossOrbit_integrable X hX i j M)] + calc + _ = ∫ g, rotationEvaluation X hX i (h*g) * M * (rotationEvaluation X hX j (h*g))ᴴ + ∂rotationHaar X hX := by + apply integral_congr_ae + exact Filter.Eventually.of_forall fun g => by + simp only [map_mul, Matrix.conjTranspose_mul, Matrix.mul_assoc] + _ = _ := integral_mul_left_eq_self (μ:=rotationHaar X hX) + (fun g => rotationEvaluation X hX i g * M * (rotationEvaluation X hX j g)ᴴ) h + +theorem rotationCrossAverage_intertwines (i j : J) (M : Matrix (I i) (I j) ℂ) + (h : rotationGroup X hX) : + rotationEvaluation X hX i h * rotationCrossAverage X hX i j M = + rotationCrossAverage X hX i j M * rotationEvaluation X hX j h := by + have he := congrArg (fun A => A * rotationEvaluation X hX j h) + (rotationCrossAverage_invariant X hX i j M h) + simpa only [Matrix.mul_assoc, rotationEvaluation_unitary, Matrix.mul_one] using he + + + +theorem rotationCrossAverage_intertwines_generator (i j : J) (M : Matrix (I i) (I j) ℂ) + (s : σ) : X s i * rotationCrossAverage X hX i j M = + rotationCrossAverage X hX i j M * X s j := by + apply matrix_intertwiner_generator_of_flow + intro t + exact rotationCrossAverage_intertwines X hX i j M + ⟨rotationFlow X hX s t, rotationFlow_mem_group X hX s t⟩ + + + +theorem rotationAverage_mixed_sandwich {i j k : J} + (C : Matrix (I k) (I i) ℂ) (D : Matrix (I k) (I j) ℂ) + (hC : ∀ s, X s k*C = C*X s i) (hD : ∀ s, X s k*D = D*X s j) + (M : Matrix (I i) (I j) ℂ) : + rotationAverage X hX k (C*M*Dᴴ) = C * rotationCrossAverage X hX i j M * Dᴴ := by + unfold rotationAverage matrixConjugationAverage rotationCrossAverage + rw [matrixIntegral_mul_left_right _ (rotationCrossOrbit_integrable X hX i j M)] + apply integral_congr_ae + apply Filter.Eventually.of_forall + intro g + have hc := rotationGroup_intertwiner X hX C hC g + have hd : Dᴴ * (rotationEvaluation X hX k g)ᴴ = + (rotationEvaluation X hX j g)ᴴ * Dᴴ := by + have he := congrArg Matrix.conjTranspose (rotationGroup_intertwiner X hX D hD g) + simp only [Matrix.conjTranspose_mul] at he + exact he + change rotationEvaluation X hX k g*C = C*rotationEvaluation X hX i g at hc + simp only [Matrix.mul_assoc] + rw [← Matrix.mul_assoc (rotationEvaluation X hX k g) C, hc] + simp only [Matrix.mul_assoc, hd] + +end + + +theorem spinRotationCrossAverage_zero {Q n m : ℕ} (hnm : n ≠ m) + (M : Matrix (Fin (n+1)) (Fin (m+1)) ℂ) : + rotationCrossAverage (fockRotationGenerator Q) (fockRotationGenerator_skew Q) + (.spin n) (.spin m) M = 0 := by + apply spin_intertwiner_zero_of_ne hnm + intro s + exact rotationCrossAverage_intertwines_generator + (fockRotationGenerator Q) (fockRotationGenerator_skew Q) (.spin n) (.spin m) M s + + + +theorem sectorAverage_spin_mixed_sandwich {Q k n : ℕ} + (C D : Matrix (SectorOccupation Q k) (Fin (n+1)) ℂ) + (hC : ∀ s, sectorOneBody Q k (spinGenerator Q s)*C = C*spinGenerator n s) + (hD : ∀ s, sectorOneBody Q k (spinGenerator Q s)*D = D*spinGenerator n s) + (M : Matrix (Fin (n+1)) (Fin (n+1)) ℂ) : + sectorAverage Q k (C*M*Dᴴ) = (M.trace / (n+1 : ℂ)) • (C*Dᴴ) := by + have h := rotationAverage_mixed_sandwich (fockRotationGenerator Q) + (fockRotationGenerator_skew Q) (i:=.spin n) (j:=.spin n) (k:=.sector k) C D hC hD M + change sectorAverage Q k (C*M*Dᴴ) = C * rotationAverage (fockRotationGenerator Q) + (fockRotationGenerator_skew Q) (.spin n) M * Dᴴ at h + rw [h, spinRotationAverage] + simp only [Matrix.mul_smul, Matrix.smul_mul, Matrix.mul_one] + + +theorem sectorAverage_spin_cross_sandwich {Q k n m : ℕ} (hnm : n ≠ m) + (C : Matrix (SectorOccupation Q k) (Fin (n+1)) ℂ) + (D : Matrix (SectorOccupation Q k) (Fin (m+1)) ℂ) + (hC : ∀ s, sectorOneBody Q k (spinGenerator Q s)*C = C*spinGenerator n s) + (hD : ∀ s, sectorOneBody Q k (spinGenerator Q s)*D = D*spinGenerator m s) + (M : Matrix (Fin (n+1)) (Fin (m+1)) ℂ) : + sectorAverage Q k (C*M*Dᴴ) = 0 := by + have h := rotationAverage_mixed_sandwich (fockRotationGenerator Q) + (fockRotationGenerator_skew Q) (i:=.spin n) (j:=.spin m) (k:=.sector k) C D hC hD M + rw [spinRotationCrossAverage_zero hnm, Matrix.mul_zero, Matrix.zero_mul] at h + exact h + + +theorem fockAverage_spin_mixed_sandwich {Q k n : ℕ} + (C D : Matrix (SectorOccupation Q k) (Fin (n+1)) ℂ) + (hC : ∀ s, sectorOneBody Q k (spinGenerator Q s)*C = C*spinGenerator n s) + (hD : ∀ s, sectorOneBody Q k (spinGenerator Q s)*D = D*spinGenerator n s) + (M : Matrix (Fin (n+1)) (Fin (n+1)) ℂ) : + fockAverage Q (exteriorLift Q k (C*M*Dᴴ)) = + (M.trace / (n+1 : ℂ)) • exteriorLift Q k (C*Dᴴ) := by + rw [fockAverage_exteriorLift, sectorAverage_spin_mixed_sandwich C D hC hD] + exact (exteriorLiftLinear Q k).map_smul _ _ + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/EntryEnumeration.lean b/lean/OAI/Analysis/LaughlinFock/EntryEnumeration.lean new file mode 100644 index 0000000000000000000000000000000000000000..138511d3a298c7bcf58b159b6ff80291b273c138 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/EntryEnumeration.lean @@ -0,0 +1,69 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.RowTraces + +namespace OAI + +/-! Entry Enumeration. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder +def rowEntryList_0 : List (RowEntry 0) := [⟨(⟨0, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨1, by decide⟩), by decide⟩] + +def rowEntryData_0 : Finset (RowEntry 0) := ⟨rowEntryList_0, by decide⟩ + +theorem rowEntryChecked_0 : (Finset.univ : Finset (RowEntry 0)) = rowEntryData_0 := by + decide +kernel + +def rowEntryList_1 : List (RowEntry 1) := [⟨(⟨0, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨2, by decide⟩), by decide⟩] + +def rowEntryData_1 : Finset (RowEntry 1) := ⟨rowEntryList_1, by decide⟩ + +theorem rowEntryChecked_1 : (Finset.univ : Finset (RowEntry 1)) = rowEntryData_1 := by + decide +kernel + +def rowEntryList_2 : List (RowEntry 2) := [⟨(⟨0, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨3, by decide⟩), by decide⟩] + +def rowEntryData_2 : Finset (RowEntry 2) := ⟨rowEntryList_2, by decide⟩ + +theorem rowEntryChecked_2 : (Finset.univ : Finset (RowEntry 2)) = rowEntryData_2 := by + decide +kernel + +def rowEntryList_3 : List (RowEntry 3) := [⟨(⟨0, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨4, by decide⟩), by decide⟩] + +def rowEntryData_3 : Finset (RowEntry 3) := ⟨rowEntryList_3, by decide⟩ + +theorem rowEntryChecked_3 : (Finset.univ : Finset (RowEntry 3)) = rowEntryData_3 := by + decide +kernel + +def rowEntryList_4 : List (RowEntry 4) := [⟨(⟨0, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨5, by decide⟩), by decide⟩] + +def rowEntryData_4 : Finset (RowEntry 4) := ⟨rowEntryList_4, by decide⟩ + +theorem rowEntryChecked_4 : (Finset.univ : Finset (RowEntry 4)) = rowEntryData_4 := by + decide +kernel + +def rowEntryList_5 : List (RowEntry 5) := [⟨(⟨0, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨6, by decide⟩), by decide⟩] + +def rowEntryData_5 : Finset (RowEntry 5) := ⟨rowEntryList_5, by decide⟩ + +theorem rowEntryChecked_5 : (Finset.univ : Finset (RowEntry 5)) = rowEntryData_5 := by + decide +kernel + +def rowEntryList_6 : List (RowEntry 6) := [⟨(⟨0, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨7, by decide⟩), by decide⟩] + +def rowEntryData_6 : Finset (RowEntry 6) := ⟨rowEntryList_6, by decide⟩ + +theorem rowEntryChecked_6 : (Finset.univ : Finset (RowEntry 6)) = rowEntryData_6 := by + decide +kernel + +def rowEntryList_7 : List (RowEntry 7) := [⟨(⟨0, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨0, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨1, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨2, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨3, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨4, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨5, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨6, by decide⟩, ⟨8, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨0, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨1, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨2, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨3, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨4, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨5, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨6, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨7, by decide⟩), by decide⟩, ⟨(⟨7, by decide⟩, ⟨8, by decide⟩), by decide⟩] + +def rowEntryData_7 : Finset (RowEntry 7) := ⟨rowEntryList_7, by decide⟩ + +theorem rowEntryChecked_7 : (Finset.univ : Finset (RowEntry 7)) = rowEntryData_7 := by + decide +kernel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/ExchangeSpectrum.lean b/lean/OAI/Analysis/LaughlinFock/ExchangeSpectrum.lean new file mode 100644 index 0000000000000000000000000000000000000000..e3a0a9fe125b9891988eda3f27f846e86d011289 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/ExchangeSpectrum.lean @@ -0,0 +1,215 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PairIdentification +import OAI.Analysis.LaughlinFock.SpinTails +import OAI.Analysis.LaughlinFock.SwapCompression + +namespace OAI + +/-! Exchange Spectrum. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators + +theorem sphericalPairCoefficient_coupled {Q p : ℕ} (hQ : 1 ≤ Q) + (hp : p ≤ 2*Q-2) (i j : ℕ) : + Real.sqrt 2 * coupledVector Q Q 1 p i j = sphericalPairCoefficient Q p i j := by + rw [sphericalPairCoefficient_eq_normalized hQ hp, normalizedPairGrid_eq_coupled hQ hp] + +theorem sphericalPairCoefficient_top {Q : ℕ} (hQ : 1 ≤ Q) (i j : ℕ) : + sphericalPairCoefficient Q 0 i j = + (if i=1 ∧ j=0 then 1 else 0) - (if i=0 ∧ j=1 then 1 else 0) := by + have hq : (Q:ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + by_cases ht : i+j=1 + · have hcases : (i=0 ∧ j=1) ∨ (i=1 ∧ j=0) := by omega + rcases hcases with ⟨rfl,rfl⟩ | ⟨rfl,rfl⟩ <;> simp [sphericalPairCoefficient, hq] + · simp only [sphericalPairCoefficient, zero_add, ite_eq_right ht] + rw [ite_eq_right (by omega : ¬(i=1 ∧ j=0)), ite_eq_right (by omega : ¬(i=0 ∧ j=1))] + ring + +theorem pairCoupled_top {Q : ℕ} (hQ : 1 ≤ Q) (i j : ℕ) : + coupledVector Q Q 1 0 i j = + ((if i=1 ∧ j=0 then 1 else 0) - (if i=0 ∧ j=1 then 1 else 0)) / Real.sqrt 2 := by + apply (eq_div_iff (by positivity : Real.sqrt (2:ℝ) ≠ 0)).mpr + rw [mul_comm, sphericalPairCoefficient_coupled hQ (by omega), sphericalPairCoefficient_top hQ] + + + +theorem pairTensorProject_top {Q : ℕ} (hQ : 1 ≤ Q) (f : CubeVector) (k : ℕ) : + pairTensorProject Q f 0 k = (f 1 0 k - f 0 1 k) / Real.sqrt 2 := by + simp only [pairTensorProject, LinearMap.coe_mk, AddHom.coe_mk, gridInner, pairCoupled_top hQ] + simp only [sub_div, sub_mul, Finset.sum_sub_distrib] + simp only [ite_and, ite_div, zero_div, ite_mul, zero_mul, one_div] + simp only [Finset.sum_ite_irrel, Finset.sum_ite_eq', Finset.mem_range, + show 0 < Q+1 by omega, show 1 < Q+1 by omega, ite_true, Finset.sum_const_zero] + ring + + +theorem pairTensorEmbed_apply {Q p i j : ℕ} (hij : i+j=p+1) (hp : p ≤ 2*Q-2) + (f : GridVector) (k : ℕ) : + pairTensorEmbed Q f i j k = coupledVector Q Q 1 p i j * f p k := by + simp only [pairTensorEmbed, LinearMap.coe_mk, AddHom.coe_mk] + apply Finset.sum_eq_single p + · intro r _ hr + rw [coupledVector_layer Q Q 1 r i j (by omega), zero_mul] + · intro h + exact (h (Finset.mem_range.mpr (by omega))).elim + +theorem pairTensorEmbed_zero_zero (Q : ℕ) (f : GridVector) (k : ℕ) : + pairTensorEmbed Q f 0 0 k = 0 := by + simp only [pairTensorEmbed, LinearMap.coe_mk, AddHom.coe_mk] + apply Finset.sum_eq_zero + intro p _ + rw [coupledVector_layer Q Q 1 p 0 0 (by omega), zero_mul] + + + +theorem pairSwapCompression_highest {Q z : ℕ} (hQ : 2 ≤ Q) + (hz : z ≤ Q) (hz0 : 1 ≤ z) : + pairSwapCompression Q (coupledVector (2*Q-2) Q z 0) 0 z = + (sphericalPairCoefficient Q z 1 z * highestCoefficient (2*Q-2) Q z z - + sphericalPairCoefficient Q (z-1) 0 z * highestCoefficient (2*Q-2) Q z (z-1))/2 := by + have h2 : Real.sqrt (2:ℝ) ^ 2 = 2 := Real.sq_sqrt (by norm_num) + simp only [pairSwapCompression, LinearMap.comp_apply, pairTensorProject_top (by omega : 1 ≤ Q), + swap23, LinearMap.coe_mk, AddHom.coe_mk] + rw [pairTensorEmbed_apply (by omega : 1+z=z+1) (by omega), + pairTensorEmbed_apply (by omega : 0+z=(z-1)+1) (by omega)] + rw [show coupledVector (2*Q-2) Q z 0 z 0 = highestCoefficient (2*Q-2) Q z z by + simp [coupledVector, coupledCoefficient], + show coupledVector (2*Q-2) Q z 0 (z-1) 1 = highestCoefficient (2*Q-2) Q z (z-1) by + simp [coupledVector, coupledCoefficient, show z-1+1=z by omega]] + rw [← sphericalPairCoefficient_coupled (by omega : 1 ≤ Q) (by omega), + ← sphericalPairCoefficient_coupled (by omega : 1 ≤ Q) (by omega)] + field_simp + rw [h2] + + +theorem pairSwapCompression_highest_zero {Q : ℕ} (hQ : 2 ≤ Q) : + pairSwapCompression Q (coupledVector (2*Q-2) Q 0 0) 0 0 = + highestCoefficient (2*Q-2) Q 0 0 / 2 := by + have h2 : Real.sqrt (2:ℝ) ^ 2 = 2 := Real.sq_sqrt (by norm_num) + simp only [pairSwapCompression, LinearMap.comp_apply, pairTensorProject_top (by omega : 1 ≤ Q), + swap23, LinearMap.coe_mk, AddHom.coe_mk] + rw [pairTensorEmbed_apply (p := 0) (i := 1) (j := 0) rfl (by omega), pairTensorEmbed_zero_zero, + pairCoupled_top (by omega : 1 ≤ Q)] + simp only [coupledVector, coupledCoefficient, add_zero, ite_true, sub_zero, and_self, + zero_ne_one, and_false, ite_false, div_mul_eq_mul_div] + field_simp + rw [h2] + + +theorem sphericalPairCoefficient_edge_one {Q : ℕ} (hQ : 1 ≤ Q) (z : ℕ) : + sphericalPairCoefficient Q z 1 z = (1-z : ℝ) * Real.sqrt (fallingRatio Q z) := by + have hq : (Q:ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + have hz : (z.factorial : ℝ) ≠ 0 := by exact_mod_cast Nat.factorial_ne_zero z + simp only [sphericalPairCoefficient, add_comm 1 z, ite_true, + Nat.descFactorial_one, Nat.factorial_one, Nat.cast_one, mul_one] + congr 2 + unfold fallingRatio + field_simp + + + +theorem sphericalPairCoefficient_edge_zero {Q z : ℕ} (hQ : 1 ≤ Q) (hz0 : 1 ≤ z) : + sphericalPairCoefficient Q (z-1) 0 z = -(z:ℝ) * + Real.sqrt ((((Q-1).descFactorial (z-1) : ℝ) / (2*Q-2).descFactorial (z-1)) / z) := by + have hq : (Q:ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + have hf : ((z-1).factorial : ℝ) ≠ 0 := by exact_mod_cast Nat.factorial_ne_zero (z-1) + have he : Q.descFactorial z = Q * (Q-1).descFactorial (z-1) := by + conv_lhs => rw [← Nat.sub_add_cancel hQ, ← Nat.sub_add_cancel hz0] + rw [Nat.succ_descFactorial_succ, Nat.sub_add_cancel hQ] + have hez : z.factorial = z * (z-1).factorial := by + conv_lhs => rw [← Nat.sub_add_cancel hz0] + rw [Nat.factorial_succ, Nat.sub_add_cancel hz0] + simp only [sphericalPairCoefficient, Nat.zero_add, Nat.sub_add_cancel hz0, ite_true, + Nat.cast_zero, zero_sub, Nat.descFactorial_zero, Nat.factorial_zero, Nat.cast_one, one_mul, mul_one] + congr 2 + rw [he, hez, Nat.cast_mul, Nat.cast_mul] + field_simp + + +theorem sqrt_mul_sqrt_div {x y : ℝ} (hx : 0 ≤ x) (hy : 0 < y) : + Real.sqrt (y*x) * Real.sqrt (x/y) = x := by + rw [← Real.sqrt_mul (mul_nonneg hy.le hx)] + convert Real.sqrt_mul_self hx using 2 + field_simp + + + +theorem fallingRatio_penultimate {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) (hz0 : 1 ≤ z) : + ((Q-1).descFactorial (z-1) : ℝ) / (2*Q-2).descFactorial (z-1) = + fallingRatio Q z * ((2*Q-1-z : ℝ)/Q) := by + have hq : (Q:ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + have hd : ((2*Q-2).descFactorial (z-1) : ℝ) ≠ 0 := by + exact_mod_cast (Nat.descFactorial_pos.mpr (show z-1 ≤ 2*Q-2 by omega)).ne' + have he : Q.descFactorial z = Q * (Q-1).descFactorial (z-1) := by + conv_lhs => rw [← Nat.sub_add_cancel (by omega : 1 ≤ Q), ← Nat.sub_add_cancel hz0] + rw [Nat.succ_descFactorial_succ, Nat.sub_add_cancel (by omega : 1 ≤ Q)] + have he' : (2*Q-2).descFactorial z = (2*Q-2-(z-1)) * (2*Q-2).descFactorial (z-1) := by + conv_lhs => rw [← Nat.sub_add_cancel hz0] + rw [Nat.descFactorial_succ] + have hw : (2*Q-2-(z-1) : ℕ) = 2*Q-1-z := by omega + have hc : ((2*Q-1-z : ℕ) : ℝ) = 2*(Q:ℝ)-1-z := by + rw [Nat.cast_sub (by omega : z ≤ 2*Q-1), Nat.cast_sub (by omega : 1 ≤ 2*Q)] + push_cast + rfl + have hdz : (2*(Q:ℝ)-1-z) ≠ 0 := by + rw [← hc] + exact_mod_cast (show 2*Q-1-z ≠ 0 by omega) + rw [fallingRatio, he, he', hw, Nat.cast_mul, Nat.cast_mul, hc] + field_simp [hq, hd, hdz, mul_comm (Q:ℝ) 2] + + + +theorem pairSwapCompression_scalar {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + pairSwapCompression Q (coupledVector (2*Q-2) Q z 0) 0 z = + (-gramShift Q z / 2) * highestCoefficient (2*Q-2) Q z 0 := by + by_cases hz0 : z=0 + · subst z + rw [pairSwapCompression_highest_zero hQ] + simp [gramShift, fallingRatio, div_eq_mul_inv, mul_comm] + · have hzp : 1 ≤ z := by omega + have hzn : z ≤ 2*Q-2 := by omega + rw [pairSwapCompression_highest hQ hz hzp, sphericalPairCoefficient_edge_one (by omega), + sphericalPairCoefficient_edge_zero (by omega) hzp, + highestCoefficient_last hzn hz, highestCoefficient_penultimate hzn hz hzp] + let x : ℝ := ((Q-1).descFactorial (z-1) : ℝ) / (2*Q-2).descFactorial (z-1) + have hx : 0 ≤ x := by dsimp [x]; positivity + have hroot : Real.sqrt ((z:ℝ) * (Q-1).descFactorial (z-1) / (2*Q-2).descFactorial (z-1)) = + Real.sqrt ((z:ℝ)*x) := by congr 1; dsimp [x]; ring + rw [hroot] + change ((1-(z:ℝ))*Real.sqrt (fallingRatio Q z) * + ((-1:ℝ)^z * Real.sqrt (fallingRatio Q z) * highestCoefficient (2*Q-2) Q z 0) - + (-(z:ℝ)*Real.sqrt (x/z)) * ((-1:ℝ)^(z-1) * Real.sqrt ((z:ℝ)*x) * + highestCoefficient (2*Q-2) Q z 0)) / 2 = _ + have hsign : (-1:ℝ)^(z-1) = -(-1:ℝ)^z := by + conv_rhs => rw [← Nat.sub_add_cancel hzp, pow_succ] + ring + have hs : Real.sqrt (fallingRatio Q z) ^ 2 = fallingRatio Q z := + Real.sq_sqrt (fallingRatio_nonneg Q z) + have hs' : Real.sqrt ((z:ℝ)*x) * Real.sqrt (x/z) = x := + sqrt_mul_sqrt_div hx (by exact_mod_cast hzp) + calc + _ = ((-1:ℝ)^z * ((1-(z:ℝ)) * Real.sqrt (fallingRatio Q z)^2 - + (z:ℝ)*(Real.sqrt ((z:ℝ)*x)*Real.sqrt (x/z)))) / 2 * + highestCoefficient (2*Q-2) Q z 0 := by rw [hsign]; ring + _ = ((-1:ℝ)^z * ((1-(z:ℝ))*fallingRatio Q z - (z:ℝ)*x)) / 2 * + highestCoefficient (2*Q-2) Q z 0 := by rw [hs, hs'] + _ = _ := by + rw [show x = fallingRatio Q z * ((2*Q-1-z : ℝ)/Q) from fallingRatio_penultimate hQ hz hzp] + unfold gramShift + have hq : (Q:ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + field_simp + ring + + + +theorem pairSwapCompression_eigenvector {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) (k : ℕ) : + pairSwapCompression Q (coupledVector (2*Q-2) Q z k) = + (-gramShift Q z / 2) • coupledVector (2*Q-2) Q z k := by + rw [pairSwapCompression_coupled hQ hz, pairSwapCompression_scalar hQ hz, + mul_div_cancel_right₀ _ (highestCoefficient_first_ne_zero (by omega))] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FastCoupling.lean b/lean/OAI/Analysis/LaughlinFock/FastCoupling.lean new file mode 100644 index 0000000000000000000000000000000000000000..47d98bfd1175343310b60269150628318443e61e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FastCoupling.lean @@ -0,0 +1,30 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.IntegerFour + +namespace OAI + +/-! Fast Coupling. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +def fastIntegerCoupling (c : ℤ) (z k p : ℕ) : ℤ := + ∑ h ∈ Finset.range (p+1), (-1)^(z-h) * (Nat.fast_choose z h : ℤ) * + (Nat.fast_choose k (p-h) : ℤ) * c^(p-h) + +theorem integerCoupling_fast (c : ℤ) (z k p : ℕ) : + integerCoupling c z k p = fastIntegerCoupling c z k p := by + simp only [integerCoupling, fastIntegerCoupling, Nat.choose_eq_fast_choose] + +def fastIntegerCopyPolynomial (D T r p j k : ℕ) : ℤ := + if r ≤ j+k then + fastIntegerCoupling 1 r (j+k-r) j * fastIntegerCoupling 1 (D-r) (T-D) p + else 0 + +theorem integerCopyPolynomial_fast (D T r p j k : ℕ) : + integerCopyPolynomial D T r p j k = fastIntegerCopyPolynomial D T r p j k := by + simp only [integerCopyPolynomial, fastIntegerCopyPolynomial, integerCoupling_fast] +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FastTrace.lean b/lean/OAI/Analysis/LaughlinFock/FastTrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..e14b5fcdd184b8d379998b02fb4678630f6a047e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FastTrace.lean @@ -0,0 +1,75 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FastCoupling + +namespace OAI + +/-! Fast Trace. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +def fourCommonDenominator : ℕ := 2^53 * (23).factorial * 10^18 + +def scaledFourFactor (D : ℕ) (t : Fin 8) (b c : RowEntry t.val) : ℕ := + 2 * 2^(53+rowP b+rowP c-(t.val+2*rowFourLevel b c)) * + t.val.factorial * (rowI b).factorial * (rowI c).factorial * + ((23).factorial / (rowFourLevel b c-D).factorial) + +theorem scaledFourFactor_spec (D : ℕ) (t : Fin 8) (b c : RowEntry t.val) : + (scaledFourFactor D t b c : ℚ) / (2^53 * (23).factorial) = rationalFourFactor D b c := by + have hT := rowFourLevel_le b c + have ht := t.isLt + have hdvd : (rowFourLevel b c-D).factorial ∣ (23).factorial := + Nat.factorial_dvd_factorial (by omega) + have hpow : (2:ℚ)^(53+rowP b+rowP c-(t.val+2*rowFourLevel b c)) * + 2^(t.val+2*rowFourLevel b c) = 2^(53+rowP b+rowP c) := by + rw [← pow_add, Nat.sub_add_cancel (by omega)] + unfold scaledFourFactor rationalFourFactor + push_cast + rw [Nat.cast_div hdvd (by positivity : ((rowFourLevel b c-D).factorial : ℚ) ≠ 0)] + apply (div_eq_div_iff (by positivity) (by positivity)).mpr + have hfac : ((rowFourLevel b c-D).factorial : ℚ) ≠ 0 := by positivity + field_simp + simp only [← pow_mul, ← pow_add] at * + ring_nf at * + exact hpow + +def scaledFourTrace (D : ℕ) (t : Fin 8) (r s : CopyLabel D) : ℤ := + -(∑ b : RowEntry t.val, ∑ c : RowEntry t.val, if D ≤ rowFourLevel b c then + certificateAlphaData t b.val.1 b.val.2 * certificateAlphaData t c.val.1 c.val.2 * + (scaledFourFactor D t b c : ℤ) * + fastIntegerCopyPolynomial D (rowFourLevel b c) r.val.val (rowP b) (rowJ b) (rowI c) * + fastIntegerCopyPolynomial D (rowFourLevel b c) s.val.val (rowP c) (rowJ c) (rowI b) + else 0) + +theorem integerFourTrace_scaled (D : ℕ) (t : Fin 8) (r s : CopyLabel D) : + integerFourTrace D t.val (certificateAlpha t) r s = + (scaledFourTrace D t r s : ℚ) / fourCommonDenominator := by + unfold integerFourTrace scaledFourTrace + simp only [integerCopyPolynomial_fast] + simp only [Int.cast_neg, Int.cast_sum, neg_div, Finset.sum_div] + congr 1 + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro c _ + split_ifs with hh + · simp only [Int.cast_mul, Int.cast_natCast] + rw [← scaledFourFactor_spec D t b c] + unfold certificateAlpha fourCommonDenominator + push_cast + ring + · simp + +def scaledRowsFourTrace (D : ℕ) (r s : CopyLabel D) : ℤ := + ∑ t : Fin 8, scaledFourTrace D t r s + +theorem integerRowsFourTrace_scaled (D : ℕ) (r s : CopyLabel D) : + integerRowsFourTrace D r s = (scaledRowsFourTrace D r s : ℚ) / fourCommonDenominator := by + simp only [integerRowsFourTrace, Matrix.sum_apply, integerFourTrace_scaled, + scaledRowsFourTrace, Int.cast_sum, Finset.sum_div] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FastWedge.lean b/lean/OAI/Analysis/LaughlinFock/FastWedge.lean new file mode 100644 index 0000000000000000000000000000000000000000..21404e2d86a62c7780c11ac7c9961c65a60b4907 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FastWedge.lean @@ -0,0 +1,203 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.RationalWedge + +namespace OAI + +/-! Fast Wedge. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + +def occupationWeight {Q : ℕ} (A : Occupation Q) : ℕ := ∑ x ∈ A, x.val + + +def fastHighestTerm (D : ℕ) (r : CopyLabel D) (A : Occupation 24) + (x y j k : Orbital 24) : ℚ := + if x b.1.val+b.2.val.1.val+b.2.val.2.val=D)) (by simp) f] + simp only [Finset.sum_filter, Fintype.sum_prod_type] + +theorem highest_pair_weight_sum (D : ℕ) (r : CopyLabel D) (A : Occupation 24) + (xy jk : IncreasingPair 24) : + (∑ p : Fin 47, if p.val+jk.val.1.val+jk.val.2.val=D then + rationalHighestTerm D r p.val jk.val.1.val jk.val.2.val xy.val.1.val xy.val.2.val * + rationalWordVacuum [xy.val.1,xy.val.2,jk.val.1,jk.val.2] A else 0) = + fastHighestTerm D r A xy.val.1 xy.val.2 jk.val.1 jk.val.2 := by + have hp : xy.val.1.val+xy.val.2.val-1 < 47 := by + have hx := xy.val.1.isLt + have hy := xy.val.2.isLt + have hxy := xy.property + change xy.val.1.val < xy.val.2.val at hxy + omega + let p : Fin 47 := ⟨xy.val.1.val+xy.val.2.val-1, hp⟩ + rw [Finset.sum_eq_single p] + · simp [fastHighestTerm, xy.property, jk.property, p] + · intro b _ hn + have hd : xy.val.1.val+xy.val.2.val ≠ b.val+1 := by + intro h + apply hn + apply Fin.ext + dsimp [p] + omega + simp [rationalHighestTerm, hd] + · simp + +theorem rationalHighestEntry_expand (D : ℕ) (r : CopyLabel D) (A : Occupation 24) : + rationalHighestEntry D r A = + ∑ j : Orbital 24, ∑ k : Orbital 24, ∑ x : Orbital 24, ∑ y : Orbital 24, + fastHighestTerm D r A x y j k := by + classical + unfold rationalHighestEntry + rw [fourHighestShell_sum D (fun b => ∑ xy : IncreasingPair 24, + rationalHighestTerm D r b.1.val b.2.val.1.val b.2.val.2.val xy.val.1.val xy.val.2.val * + rationalWordVacuum [xy.val.1,xy.val.2,b.2.val.1,b.2.val.2] A)] + have he : (∑ p : Fin 47, ∑ jk : IncreasingPair 24, + if p.val+jk.val.1.val+jk.val.2.val=D then + ∑ xy : IncreasingPair 24, + rationalHighestTerm D r p.val jk.val.1.val jk.val.2.val xy.val.1.val xy.val.2.val * + rationalWordVacuum [xy.val.1,xy.val.2,jk.val.1,jk.val.2] A else 0) = + ∑ jk : IncreasingPair 24, ∑ xy : IncreasingPair 24, + fastHighestTerm D r A xy.val.1 xy.val.2 jk.val.1 jk.val.2 := by + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro jk _ + have hh (p : Fin 47) : + (if p.val+jk.val.1.val+jk.val.2.val=D then + ∑ xy : IncreasingPair 24, + rationalHighestTerm D r p.val jk.val.1.val jk.val.2.val xy.val.1.val xy.val.2.val * + rationalWordVacuum [xy.val.1,xy.val.2,jk.val.1,jk.val.2] A else 0) = + ∑ xy : IncreasingPair 24, if p.val+jk.val.1.val+jk.val.2.val=D then + rationalHighestTerm D r p.val jk.val.1.val jk.val.2.val xy.val.1.val xy.val.2.val * + rationalWordVacuum [xy.val.1,xy.val.2,jk.val.1,jk.val.2] A else 0 := by + split_ifs <;> simp + simp_rw [hh] + rw [Finset.sum_comm] + exact Finset.sum_congr rfl (fun xy _ => highest_pair_weight_sum D r A xy jk) + rw [he, increasingPair_sum 24 (fun j k => ∑ xy : IncreasingPair 24, + fastHighestTerm D r A xy.val.1 xy.val.2 j k)] + apply Finset.sum_congr rfl + intro j _ + apply Finset.sum_congr rfl + intro k _ + by_cases hjk : j fastHighestTerm D r A x y j k)] + apply Finset.sum_congr rfl + intro x _ + apply Finset.sum_congr rfl + intro y _ + by_cases hxy : x hn (by rw [hm, mul_zero]) + obtain ⟨_,hs⟩ := rationalWordVacuum_support _ _ hn' + simp [← hs] + · simp at hn + +theorem rationalHighestEntry_fast (D : ℕ) (r : CopyLabel D) (A : Occupation 24) : + rationalHighestEntry D r A = fastHighestEntry D r A := by + classical + rw [rationalHighestEntry_expand] + unfold fastHighestEntry + symm + let f : Orbital 24 × (Orbital 24 × (Orbital 24 × Orbital 24)) → ℚ := fun b => + fastHighestTerm D r A b.2.2.1 b.2.2.2 b.1 b.2.1 + have hs : (∑ b ∈ A ×ˢ (A ×ˢ (A ×ˢ A)), f b) = + ∑ b ∈ Finset.univ ×ˢ (Finset.univ ×ˢ (Finset.univ ×ˢ Finset.univ)), f b := by + apply Finset.sum_subset (by simp only [Finset.univ_product_univ]; exact Finset.subset_univ _) + intro b _ hb + by_contra hn + obtain ⟨hx,hy,hj,hk⟩ := fastHighestTerm_support D r A b.2.2.1 b.2.2.2 b.1 b.2.1 hn + exact hb (by simp [hx,hy,hj,hk]) + simpa only [Finset.sum_product] using hs + +end LaughlinFock +end + +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem fastHighestTerm_weight (D : ℕ) (r : CopyLabel D) (A : Occupation 24) + (x y j k : Orbital 24) (hn : fastHighestTerm D r A x y j k ≠ 0) : + occupationWeight A = D+1 := by + unfold fastHighestTerm at hn + split_ifs at hn with hh + · have hn' : rationalWordVacuum [x,y,j,k] A ≠ 0 := fun hm => hn (by rw [hm, mul_zero]) + obtain ⟨hnd,hs⟩ := rationalWordVacuum_support _ _ hn' + simp only [List.nodup_cons, List.mem_cons, not_or, + List.not_mem_nil, not_false_eq_true, List.nodup_nil, and_self, and_true] at hnd + have hw : occupationWeight A = x.val+y.val+j.val+k.val := by + unfold occupationWeight + rw [← hs] + simp [hnd.1.1, hnd.1.2.1, hnd.1.2.2, hnd.2.1.1, hnd.2.1.2, hnd.2.2, + Finset.sum_insert, add_assoc] + rw [hw] + have hxy : x.val < y.val := hh.1 + omega + · simp at hn + +theorem rationalHighestEntry_weight (D : ℕ) (r : CopyLabel D) (A : Occupation 24) + (hw : occupationWeight A ≠ D+1) : rationalHighestEntry D r A = 0 := by + rw [rationalHighestEntry_fast] + unfold fastHighestEntry + apply Finset.sum_eq_zero + intro j _ + apply Finset.sum_eq_zero + intro k _ + apply Finset.sum_eq_zero + intro x _ + apply Finset.sum_eq_zero + intro y _ + by_contra hn + exact hw (fastHighestTerm_weight D r A x y j k hn) + + +def highestFourOccupations (D : ℕ) : Finset (Occupation 24) := + ((Finset.univ : Finset (Orbital 24)).powersetCard 4).filter + (fun A => occupationWeight A = D+1) + +def fastFourGram (D : ℕ) : Matrix (CopyLabel D) (CopyLabel D) ℚ := fun r s => + ∑ A ∈ highestFourOccupations D, + 2 * fastHighestEntry D r A * fastHighestEntry D s A / + (2^(2*D) * occupationFactorial A) + +theorem rationalFourGram_fast (D : ℕ) : rationalFourGram D = fastFourGram D := by + ext r s + classical + unfold rationalFourGram fastFourGram highestFourOccupations + rw [← Finset.sum_subtype ((Finset.univ : Finset (Orbital 24)).powersetCard 4) + (by intro A; simp [Finset.mem_powersetCard]) + (fun A => 2 * rationalHighestEntry D r A * rationalHighestEntry D s A / + (2^(2*D) * occupationFactorial A))] + rw [Finset.sum_filter] + apply Finset.sum_congr rfl + intro A _ + split_ifs with h + · rw [rationalHighestEntry_fast, rationalHighestEntry_fast] + · simp [rationalHighestEntry_weight D r A h] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FasterTrace.lean b/lean/OAI/Analysis/LaughlinFock/FasterTrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..fb9ab4e39e62576b0a00326878f48b01921bb9a0 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FasterTrace.lean @@ -0,0 +1,62 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.NumericTrace + +namespace OAI + +/-! Faster Trace. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +def shortNumericRowTerm (D t r s : ℕ) (b c : NumericRowEntry) : ℤ := + if D ≤ b.p+b.j+c.i then + let x := memoIntegerCopyPolynomial D (b.p+b.j+c.i) r b.p b.j c.i + if x = 0 then 0 else + let y := memoIntegerCopyPolynomial D (b.p+b.j+c.i) s c.p c.j b.i + if y = 0 then 0 else + b.a*c.a * (numericRowFactor D t b c : ℤ) * x * y + else 0 + +theorem numericRowTerm_short (D t r s : ℕ) (b c : NumericRowEntry) : + numericRowTerm D t r s b c = shortNumericRowTerm D t r s b c := by + unfold numericRowTerm shortNumericRowTerm + dsimp only + split_ifs <;> simp_all + +def directIntegerSum {α : Type*} (f : α → ℤ) : List α → ℤ + | [] => 0 + | a::as => f a + directIntegerSum f as + +theorem directIntegerSum_spec {α : Type*} (f : α → ℤ) (ls : List α) : + (ls.map f).sum = directIntegerSum f ls := by + induction ls with + | nil => rfl + | cons a as ih => simp only [List.map_cons, List.sum_cons, directIntegerSum, ih] + +def shortNumericFourTrace (D : ℕ) (t : Fin 8) (r s : ℕ) : ℤ := + -(directIntegerSum (fun b => directIntegerSum (shortNumericRowTerm D t.val r s b) + (numericRowData t)) (numericRowData t)) + +theorem numericFourTrace_short (D : ℕ) (t : Fin 8) (r s : ℕ) : + numericFourTrace D t r s = shortNumericFourTrace D t r s := by + simp only [numericFourTrace, shortNumericFourTrace, numericRowTerm_short, directIntegerSum_spec] + +def shortNumericRowsFourTrace (D r s : ℕ) : ℤ := + shortNumericFourTrace D 0 r s + shortNumericFourTrace D 1 r s + + shortNumericFourTrace D 2 r s + shortNumericFourTrace D 3 r s + + shortNumericFourTrace D 4 r s + shortNumericFourTrace D 5 r s + + shortNumericFourTrace D 6 r s + shortNumericFourTrace D 7 r s + +theorem integerRowsFourTrace_short {D : ℕ} (hD : D ≤ 23) (r s : CopyLabel D) : + integerRowsFourTrace D r s = (shortNumericRowsFourTrace D r.val.val s.val.val : ℚ) / fourCommonDenominator := by + rw [integerRowsFourTrace_numeric hD] + simp only [numericRowsFourTrace, numericFourTrace_short, Fin.sum_univ_succ] + simp only [shortNumericRowsFourTrace] + congr 2 + simp only [Fin.isValue, Fin.succ_zero_eq_one] + abel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FermionOperators.lean b/lean/OAI/Analysis/LaughlinFock/FermionOperators.lean new file mode 100644 index 0000000000000000000000000000000000000000..0b05b49dcb348a0358682269d22dc1336fd62002 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FermionOperators.lean @@ -0,0 +1,292 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Model + +namespace OAI + +/-! Fermion Operators. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open scoped BigOperators Polynomial +open Polynomial +def fermionSign {Q : ℕ} (j : Orbital Q) (B : Occupation Q) : ℂ := + (-1 : ℂ) ^ (B.filter (fun i => i < j)).card + +theorem annihilator_apply {Q : ℕ} (j : Orbital Q) (A B : Occupation Q) : + annihilator Q j A B = + if j ∈ B ∧ A = B.erase j then fermionSign j B else 0 := rfl + +@[simp] theorem fermionSign_star {Q : ℕ} (j : Orbital Q) (B : Occupation Q) : + star (fermionSign j B) = fermionSign j B := by simp [fermionSign] + +@[simp] theorem fermionSign_mul_self {Q : ℕ} (j : Orbital Q) (B : Occupation Q) : + fermionSign j B * fermionSign j B = 1 := by + unfold fermionSign + rw [← mul_pow] + simp + +private theorem sign_insert_lt {Q : ℕ} (i j : Orbital Q) (B : Occupation Q) + (hi : i ∉ B) (hij : i < j) : + fermionSign j (insert i B) = -fermionSign j B := by + simp [fermionSign, Finset.filter_insert, hi, hij, pow_succ] + +private theorem sign_insert_not_lt {Q : ℕ} (i j : Orbital Q) (B : Occupation Q) + (hij : ¬ i < j) : fermionSign j (insert i B) = fermionSign j B := by + simp [fermionSign, Finset.filter_insert, hij] + +private theorem sign_erase_lt {Q : ℕ} (i j : Orbital Q) (B : Occupation Q) + (hi : i ∈ B) (hij : i < j) : + fermionSign j (B.erase i) = -fermionSign j B := by + have h := sign_insert_lt i j (B.erase i) (Finset.notMem_erase i B) hij + rw [Finset.insert_erase hi] at h + rw [h] + simp + +private theorem sign_erase_not_lt {Q : ℕ} (i j : Orbital Q) (B : Occupation Q) + (hij : ¬ i < j) : fermionSign j (B.erase i) = fermionSign j B := by + by_cases hi : i ∈ B + · have h := sign_insert_not_lt i j (B.erase i) hij + rw [Finset.insert_erase hi] at h + exact h.symm + · rw [Finset.erase_eq_of_notMem hi] + + +def creator (Q : ℕ) (j : Orbital Q) : FockMatrix Q := fun A B => + if j ∉ B ∧ A = insert j B then fermionSign j B else 0 + + +theorem mul_annihilator_apply {Q : ℕ} (M : FockMatrix Q) (j : Orbital Q) + (A B : Occupation Q) : + (M * annihilator Q j) A B = + if j ∈ B then M A (B.erase j) * fermionSign j B else 0 := by + classical + rw [Matrix.mul_apply] + by_cases hj : j ∈ B + · simp [annihilator, hj, mul_ite, fermionSign] + · simp [annihilator, hj] + + +theorem mul_creator_apply {Q : ℕ} (M : FockMatrix Q) (j : Orbital Q) + (A B : Occupation Q) : + (M * creator Q j) A B = + if j ∉ B then M A (insert j B) * fermionSign j B else 0 := by + classical + rw [Matrix.mul_apply] + by_cases hj : j ∈ B + · simp [creator, hj] + · simp [creator, hj, mul_ite] + + +theorem creator_eq_adjoint (Q : ℕ) (j : Orbital Q) : + creator Q j = (annihilator Q j)ᴴ := by + classical + ext A B + by_cases hc : j ∉ B ∧ A = insert j B + · rcases hc with ⟨hj, rfl⟩ + simp [creator, annihilator_apply, Matrix.conjTranspose_apply, hj, sign_insert_not_lt j j B (lt_irrefl j)] + · have hd : ¬ (j ∈ A ∧ B = A.erase j) := by + rintro ⟨hj, rfl⟩ + apply hc + exact ⟨Finset.notMem_erase _ _, (Finset.insert_erase hj).symm⟩ + simp [creator, annihilator, Matrix.conjTranspose_apply, hc, hd] + + +theorem annihilator_square (Q : ℕ) (j : Orbital Q) : + annihilator Q j * annihilator Q j = 0 := by + classical + ext A B + rw [mul_annihilator_apply] + by_cases hj : j ∈ B <;> simp [annihilator, hj] + + +theorem annihilator_anticommute (Q : ℕ) (i j : Orbital Q) : + annihilator Q i * annihilator Q j + annihilator Q j * annihilator Q i = 0 := by + classical + by_cases hij : i=j + · subst j; rw [annihilator_square]; simp + ext A B + simp only [Matrix.add_apply, Matrix.zero_apply, mul_annihilator_apply] + by_cases hi : i ∈ B + · by_cases hj : j ∈ B + · simp only [hi, hj, ite_true, annihilator_apply, + Finset.mem_erase, ne_eq, hij, Ne.symm hij, not_false_eq_true, true_and, and_true] + rw [Finset.erase_right_comm] + by_cases hab : A = (B.erase i).erase j + · simp only [hab, ite_true] + rcases lt_or_gt_of_ne hij with hij | hji + · rw [sign_erase_lt i j B hi hij, + sign_erase_not_lt j i B (not_lt.mpr hij.le)] + ring + · rw [sign_erase_lt j i B hj hji, + sign_erase_not_lt i j B (not_lt.mpr hji.le)] + ring + · simp [hab] + · simp [hi, hj, annihilator, Finset.mem_erase] + · simp [hi, annihilator, Finset.mem_erase] + + +theorem creator_mul_annihilator (Q : ℕ) (j : Orbital Q) : + creator Q j * annihilator Q j = + Matrix.diagonal (fun B : Occupation Q => if j ∈ B then (1 : ℂ) else 0) := by + classical + ext A B + rw [mul_annihilator_apply] + by_cases hAB : A = B + · subst A + by_cases hj : j ∈ B <;> + simp [hj, creator, + sign_erase_not_lt j j B (lt_irrefl j)] + · by_cases hj : j ∈ B <;> simp [creator, hj, hAB] + + +theorem annihilator_mul_creator (Q : ℕ) (j : Orbital Q) : + annihilator Q j * creator Q j = + Matrix.diagonal (fun B : Occupation Q => if j ∈ B then (0 : ℂ) else 1) := by + classical + ext A B + rw [mul_creator_apply] + by_cases hAB : A = B + · subst A + by_cases hj : j ∈ B <;> + simp [annihilator_apply, hj, + sign_insert_not_lt j j B (lt_irrefl j)] + · by_cases hj : j ∈ B <;> simp [annihilator_apply, hj, hAB] + + +theorem annihilator_creator_anticommute (Q : ℕ) (i j : Orbital Q) : + annihilator Q i * creator Q j + creator Q j * annihilator Q i = + if i = j then 1 else 0 := by + classical + by_cases hij : i = j + · subst j + rw [ite_eq_left rfl, annihilator_mul_creator, creator_mul_annihilator] + ext A B + by_cases hi : i ∈ A <;> simp [Matrix.diagonal_apply, Matrix.one_apply, hi] + rw [ite_eq_right hij] + ext A B + simp only [Matrix.add_apply, Matrix.zero_apply, mul_annihilator_apply, mul_creator_apply] + by_cases hi : i ∈ B + · by_cases hj : j ∈ B + · simp [hi, hj, creator, Finset.mem_erase, Ne.symm hij] + · simp only [hi, hj, not_false_eq_true, ite_true, annihilator_apply, creator, + Finset.mem_insert, Finset.mem_erase, hij, Ne.symm hij, false_or, + ne_eq, not_false_eq_true, true_and] + have he : (insert j B).erase i = insert j (B.erase i) := by + ext k + simp only [Finset.mem_erase, Finset.mem_insert] + by_cases hki : k=i <;> by_cases hkj : k=j <;> simp_all + rw [he] + by_cases hAB : A = insert j (B.erase i) + · simp only [hAB, ite_true] + rcases lt_or_gt_of_ne hij with hij | hji + · rw [sign_insert_not_lt j i B (not_lt.mpr hij.le), sign_erase_lt i j B hi hij] + ring + · rw [sign_insert_lt j i B hj hji, sign_erase_not_lt i j B (not_lt.mpr hji.le)] + ring + · simp [hAB] + · by_cases hj : j ∈ B <;> simp [hi, hj, annihilator_apply, hij] + + +theorem annihilator_adjoint_anticommute (Q : ℕ) (i j : Orbital Q) : + annihilator Q i * (annihilator Q j)ᴴ + (annihilator Q j)ᴴ * annihilator Q i = + if i = j then 1 else 0 := by + rw [← creator_eq_adjoint] + exact annihilator_creator_anticommute Q i j + + + +theorem annihilator_norm_sq (Q : ℕ) (j : Orbital Q) (ψ : Occupation Q → ℂ) : + (∑ A : Occupation Q, ‖(annihilator Q j *ᵥ ψ) A‖^2) = + ∑ B : Occupation Q, if j ∈ B then ‖ψ B‖^2 else 0 := by + classical + have hg := congrArg Complex.re (gram_quadratic_form (annihilator Q j) ψ) + rw [← creator_eq_adjoint, creator_mul_annihilator] at hg + have hs : (star (annihilator Q j *ᵥ ψ) ⬝ᵥ (annihilator Q j *ᵥ ψ)).re = + ∑ A : Occupation Q, ‖(annihilator Q j *ᵥ ψ) A‖^2 := by + simp [dotProduct, RCLike.star_def, RCLike.conj_mul, ← Complex.ofReal_pow] + rw [hs] at hg + rw [← hg] + simp only [Matrix.mulVec_diagonal, dotProduct, Complex.re_sum, Pi.star_apply] + apply Finset.sum_congr rfl + intro B _ + by_cases hj : j ∈ B <;> + simp [hj, RCLike.star_def, RCLike.conj_mul, ← Complex.ofReal_pow] + + +theorem annihilator_contracts (Q : ℕ) (j : Orbital Q) (ψ : Occupation Q → ℂ) : + (∑ A : Occupation Q, ‖(annihilator Q j *ᵥ ψ) A‖^2) ≤ + ∑ B : Occupation Q, ‖ψ B‖^2 := by + rw [annihilator_norm_sq] + apply Finset.sum_le_sum + intro B _ + split_ifs + · exact le_rfl + · exact sq_nonneg _ + + + +theorem fourAnnihilator_norm_le_pair (Q p : ℕ) (j k : Orbital Q) + (ψ : Occupation Q → ℂ) : + (∑ A : Occupation Q, + ‖((annihilator Q k * annihilator Q j * pairAnnihilator Q p) *ᵥ ψ) A‖^2) ≤ + ∑ A : Occupation Q, ‖(pairAnnihilator Q p *ᵥ ψ) A‖^2 := by + have hk := annihilator_contracts Q k (annihilator Q j *ᵥ (pairAnnihilator Q p *ᵥ ψ)) + have hj := annihilator_contracts Q j (pairAnnihilator Q p *ᵥ ψ) + simpa only [← Matrix.mulVec_mulVec] using hk.trans hj + + +def orbitalDelta (Q : ℕ) (i j : Orbital Q) : FockMatrix Q := if i=j then 1 else 0 + +private theorem delta_comm (Q : ℕ) (i j : Orbital Q) (M : FockMatrix Q) : + M * orbitalDelta Q i j = orbitalDelta Q i j * M := by + classical + by_cases hij : i=j <;> simp [orbitalDelta, hij] + +private theorem annihilator_creator_swap (Q : ℕ) (i j : Orbital Q) : + annihilator Q i * creator Q j = + orbitalDelta Q i j - creator Q j * annihilator Q i := + eq_sub_of_add_eq (annihilator_creator_anticommute Q i j) + + + +theorem pair_normal_order (Q : ℕ) (i j k l : Orbital Q) : + (annihilator Q j * annihilator Q i) * (creator Q k * creator Q l) = + orbitalDelta Q i k * orbitalDelta Q j l - + orbitalDelta Q j k * orbitalDelta Q i l - + orbitalDelta Q i k * creator Q l * annihilator Q j + + orbitalDelta Q j k * creator Q l * annihilator Q i + + orbitalDelta Q i l * creator Q k * annihilator Q j - + orbitalDelta Q j l * creator Q k * annihilator Q i + + creator Q k * creator Q l * annihilator Q j * annihilator Q i := by + classical + let I := annihilator Q i + let J := annihilator Q j + let K := creator Q k + let L := creator Q l + let E := orbitalDelta Q i k + let F := orbitalDelta Q j k + let G := orbitalDelta Q i l + let H := orbitalDelta Q j l + have hIK : I*K = E-K*I := annihilator_creator_swap Q i k + have hJK : J*K = F-K*J := annihilator_creator_swap Q j k + have hIL : I*L = G-L*I := annihilator_creator_swap Q i l + have hJL : J*L = H-L*J := annihilator_creator_swap Q j l + have hJE : J*E = E*J := delta_comm Q i k J + have hKJG : (K*J)*G = G*(K*J) := delta_comm Q i l (K*J) + have hKH : K*H = H*K := delta_comm Q j l K + change (J*I)*(K*L) = E*H-F*G-E*L*J+F*L*I+G*K*J-H*K*I+K*L*J*I + calc + _ = J*(I*K)*L := by noncomm_ring + _ = J*(E-K*I)*L := by rw [hIK] + _ = J*E*L-(J*K)*(I*L) := by noncomm_ring + _ = E*J*L-(F-K*J)*(G-L*I) := by rw [hJE, hJK, hIL] + _ = E*(J*L)-(F-K*J)*(G-L*I) := by noncomm_ring + _ = E*(H-L*J)-(F-K*J)*(G-L*I) := by rw [hJL] + _ = E*H-F*G-E*L*J+F*L*I+(K*J)*G-K*(J*L)*I := by noncomm_ring + _ = E*H-F*G-E*L*J+F*L*I+G*(K*J)-K*(H-L*J)*I := by rw [hKJG, hJL] + _ = E*H-F*G-E*L*J+F*L*I+G*K*J-(K*H)*I+K*L*J*I := by noncomm_ring + _ = _ := by rw [hKH] +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FiniteComparison.lean b/lean/OAI/Analysis/LaughlinFock/FiniteComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..25652e97a4474d8bcbf759ac501cdd443be9c70d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FiniteComparison.lean @@ -0,0 +1,124 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.NullComponents +import OAI.Analysis.LaughlinFock.RelativeTransfer + +namespace OAI + +/-! Finite Comparison. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open Filter Topology + + +def rowsEta {ι : Type*} [Fintype ι] (rows : ι → ComparisonRow) : ℝ := + ∑ i, (rows i).ell ^ 2 + + +def rowsThreeTrace {ι : Type*} [Fintype ι] (rows : ι → ComparisonRow) (Q z : ℕ) : ℝ := + ∑ i, rowThreeTrace Q z (rows i).t.val (rows i).ell (rows i).alpha + + +def planarRowsThreeTrace {ι : Type*} [Fintype ι] (rows : ι → ComparisonRow) (z : ℕ) : ℝ := + ∑ i, planarRowThreeTrace z (rows i).t.val (rows i).ell (rows i).alpha + +theorem rowsThreeTrace_tendsto {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) (z : ℕ) : + Tendsto (fun Q => rowsThreeTrace rows Q z) atTop (𝓝 (planarRowsThreeTrace rows z)) := + tendsto_finsetSum Finset.univ (fun i _ => + rowThreeTrace_tendsto z (rows i).t.val (rows i).ell (rows i).alpha) + + +abbrev ComparedThreeBlock := {z : Fin 16 // z.val=2 ∨ 4 ≤ z.val} + + + +theorem rowsThreeTrace_eventual_bound {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) + (hCertificate : ∀ z : ComparedThreeBlock, + planarRowsThreeTrace rows z.val.val < + (3/2 : ℝ)*(3*(z.val.val : ℝ)-1)*(-1/2) ^ z.val.val) : + ∀ᶠ Q in atTop, ∀ z : ComparedThreeBlock, + rowsThreeTrace rows Q z.val.val / spinRatio Q z.val.val < gramShift Q z.val.val := by + apply eventually_all.mpr + intro z + have hlim : Tendsto (fun Q => spinRatio Q z.val.val * gramShift Q z.val.val) + atTop (𝓝 ((3/2 : ℝ)*(3*(z.val.val : ℝ)-1)*(-1/2)^z.val.val)) := by + simpa only [mul_assoc] using + (spinRatio_tendsto z.val.val).mul (gramShift_tendsto z.val.val) + have he := (rowsThreeTrace_tendsto rows z.val.val).eventually_lt hlim (hCertificate z) + filter_upwards [he, eventually_ge_atTop 16] with Q hlt hQ + have hn : (z.val.val : ℝ) ≤ (Q : ℝ) := by exact_mod_cast (by omega : z.val.val ≤ Q) + have hq : (16 : ℝ) ≤ Q := by exact_mod_cast hQ + have hp : 0 < spinRatio Q z.val.val := by + unfold spinRatio + apply div_pos <;> linarith + rw [div_lt_iff₀ hp] + simpa only [mul_comm] using hlt + + +def finiteThreeTarget (Q : ℕ) : FockMatrix Q := + exteriorLift Q 3 (threeWedgeMatrix Q * + (∑ z ∈ Finset.range 16, (gramShift Q z : ℂ) • threeSpinProjection Q z) * + (threeWedgeMatrix Q)ᴴ) + + +def fullThreeTarget (Q : ℕ) : FockMatrix Q := + exteriorLift Q 3 (threeWedgeMatrix Q * + (∑ z ∈ Finset.range (Q+1), (gramShift Q z : ℂ) • threeSpinProjection Q z) * + (threeWedgeMatrix Q)ᴴ) + + + +def threeTraceForm {ι : Type*} [Fintype ι] (rows : ι → ComparisonRow) (Q : ℕ) : FockMatrix Q := + exteriorLift Q 3 (threeWedgeMatrix Q * + (∑ z ∈ Finset.range 16, (rowsThreeTrace rows Q z / spinRatio Q z : ℂ) • + threeSpinProjection Q z) * (threeWedgeMatrix Q)ᴴ) + + +theorem threeWedgeMatrix_null_sandwich {Q z : ℕ} (hQ : 3 ≤ Q) + (hz : z=0 ∨ z=1 ∨ z=3) (a : ℂ) : + threeWedgeMatrix Q * (a • threeSpinProjection Q z) * (threeWedgeMatrix Q)ᴴ = 0 := by + have hle : z ≤ Q := by rcases hz with rfl | rfl | rfl <;> omega + rw [Matrix.mul_smul, threeWedgeMatrix_null_projection (by omega) hle hz, + smul_zero, Matrix.zero_mul] + + + +theorem threeTraceForm_le_finite_of_coefficients {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) {Q : ℕ} (hQ : 16 ≤ Q) + (hbound : ∀ z : ComparedThreeBlock, + rowsThreeTrace rows Q z.val.val / spinRatio Q z.val.val ≤ gramShift Q z.val.val) : + (finiteThreeTarget Q - threeTraceForm rows Q).PosSemidef := by + classical + unfold finiteThreeTarget threeTraceForm + rw [← exteriorLift_sub, ← Matrix.sub_mul, ← Matrix.mul_sub, ← Finset.sum_sub_distrib] + apply exteriorLift_posSemidef + rw [Matrix.mul_sum, Matrix.sum_mul] + apply Matrix.posSemidef_sum + intro z hz + rw [← sub_smul, ← Complex.ofReal_div, ← Complex.ofReal_sub] + by_cases hn : z=0 ∨ z=1 ∨ z=3 + · rw [threeWedgeMatrix_null_sandwich (by omega) hn] + exact Matrix.PosSemidef.zero + · have hzlt : z < 16 := Finset.mem_range.mp hz + have hg : z=2 ∨ 4 ≤ z := by omega + have h := hbound ⟨⟨z,hzlt⟩,hg⟩ + apply Matrix.PosSemidef.mul_mul_conjTranspose_same + exact (threeSpinProjection_posSemidef Q z).smul (by exact_mod_cast sub_nonneg.mpr h) + + + +theorem threeTraceForm_eventual_bound {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) + (hCertificate : ∀ z : ComparedThreeBlock, + planarRowsThreeTrace rows z.val.val < + (3/2 : ℝ)*(3*(z.val.val : ℝ)-1)*(-1/2)^z.val.val) : + ∀ᶠ Q in atTop, (finiteThreeTarget Q - threeTraceForm rows Q).PosSemidef := by + filter_upwards [rowsThreeTrace_eventual_bound rows hCertificate, eventually_ge_atTop 16] with Q h hQ + exact threeTraceForm_le_finite_of_coefficients rows hQ (fun z => (h z).le) + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FiniteCoupling.lean b/lean/OAI/Analysis/LaughlinFock/FiniteCoupling.lean new file mode 100644 index 0000000000000000000000000000000000000000..263b61aef6e7b2e93ea3af3cfd06738e558f671f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FiniteCoupling.lean @@ -0,0 +1,405 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SphereScaling + +namespace OAI + +/-! Finite Coupling. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators +open Filter Topology + + + +def highestWeight (n m z p : ℕ) : ℕ := + z.choose p * (n-p).descFactorial (z-p) * (m-z+p).descFactorial p + +def highestTotal (n m z : ℕ) : ℕ := + ∑ p ∈ Finset.range (z+1), highestWeight n m z p + + +def highestCoefficient (n m z p : ℕ) : ℝ := + (-1)^(z-p) * Real.sqrt ((highestWeight n m z p : ℝ) / highestTotal n m z) + +theorem highestWeight_zero (n m z p : ℕ) (hp : z < p) : + highestWeight n m z p = 0 := by + simp [highestWeight, Nat.choose_eq_zero_of_lt hp] + +theorem highestCoefficient_zero (n m z p : ℕ) (hp : z < p) : + highestCoefficient n m z p = 0 := by + simp [highestCoefficient, highestWeight_zero n m z p hp] + +theorem highestTotal_pos {n m z : ℕ} (hz : z ≤ n) : 0 < highestTotal n m z := by + unfold highestTotal + apply Finset.sum_pos' + · exact fun _ _ => Nat.zero_le _ + · refine ⟨0, by simp, ?_⟩ + simpa [highestWeight] using Nat.descFactorial_pos.mpr hz + +theorem highestCoefficient_sq (n m z p : ℕ) : + highestCoefficient n m z p ^ 2 = (highestWeight n m z p : ℝ) / highestTotal n m z := by + rw [highestCoefficient, mul_pow, ← pow_mul, mul_comm (z-p) 2, pow_mul] + norm_num only [neg_sq, one_pow, one_mul] + exact Real.sq_sqrt (by positivity) + + + +theorem highestCoefficient_norm {n m z : ℕ} (hz : z ≤ n) : + ∑ p ∈ Finset.range (z+1), highestCoefficient n m z p ^ 2 = 1 := by + simp_rw [highestCoefficient_sq] + rw [← Finset.sum_div] + have ht : (∑ p ∈ Finset.range (z+1), (highestWeight n m z p : ℝ)) = + (highestTotal n m z : ℝ) := by simp [highestTotal] + rw [ht, div_self (by exact_mod_cast (highestTotal_pos (m := m) hz).ne')] + + +theorem highestWeight_adjacent {n m z p : ℕ} (hz : z ≤ n) (hp : p < z) : + highestWeight n m z (p+1) * ((p+1)*(n-p)) = + highestWeight n m z p * ((z-p)*(m-z+p+1)) := by + have hnp : n-p = (n-(p+1))+1 := by omega + have hzp : z-p = (z-(p+1))+1 := by omega + have hnfall : (n-p).descFactorial (z-p) = + (n-p) * (n-(p+1)).descFactorial (z-(p+1)) := by + rw [hnp, hzp, Nat.succ_descFactorial_succ] + have hmfall : (m-z+(p+1)).descFactorial (p+1) = + (m-z+p+1) * (m-z+p).descFactorial p := by + rw [show m-z+(p+1) = (m-z+p)+1 by omega, Nat.succ_descFactorial_succ] + unfold highestWeight + rw [hnfall, hmfall] + have hch := Nat.choose_succ_right_eq z p + calc + _ = (z.choose (p+1) * (p+1)) * (n-p) * + (n-(p+1)).descFactorial (z-(p+1)) * + ((m-z+p+1) * (m-z+p).descFactorial p) := by ring + _ = _ := by rw [hch]; ring + + + +theorem highestCoefficient_raising {n m z p : ℕ} (hz : z ≤ n) (hp : p < z) : + highestCoefficient n m z (p+1) * Real.sqrt ((p+1 : ℕ) * (n-p : ℕ) : ℝ) + + highestCoefficient n m z p * Real.sqrt ((z-p : ℕ) * (m-z+p+1 : ℕ) : ℝ) = 0 := by + have he : (highestWeight n m z (p+1) : ℝ) / highestTotal n m z * + ((p+1 : ℕ) * (n-p : ℕ) : ℝ) = + (highestWeight n m z p : ℝ) / highestTotal n m z * + ((z-p : ℕ) * (m-z+p+1 : ℕ) : ℝ) := by + have h := congrArg (fun a : ℕ => (a : ℝ)) (highestWeight_adjacent (m := m) hz hp) + push_cast at h + simpa only [div_mul_eq_mul_div, Nat.cast_add, Nat.cast_one] using congrArg (fun a : ℝ => a / highestTotal n m z) h + have hs : + Real.sqrt ((highestWeight n m z (p+1) : ℝ) / highestTotal n m z) * + Real.sqrt ((p+1 : ℕ) * (n-p : ℕ) : ℝ) = + Real.sqrt ((highestWeight n m z p : ℝ) / highestTotal n m z) * + Real.sqrt ((z-p : ℕ) * (m-z+p+1 : ℕ) : ℝ) := by + calc + _ = Real.sqrt ((highestWeight n m z (p+1) : ℝ) / highestTotal n m z * + ((p+1 : ℕ) * (n-p : ℕ) : ℝ)) := (Real.sqrt_mul (by positivity) _).symm + _ = _ := congrArg Real.sqrt he + _ = _ := Real.sqrt_mul (by positivity) _ + have hpar : (-1 : ℝ)^(z-p) = -((-1 : ℝ)^(z-(p+1))) := by + rw [show z-p = z-(p+1)+1 by omega, pow_succ] + ring + unfold highestCoefficient + rw [hpar] + calc + _ = (-1 : ℝ)^(z-(p+1)) * + (Real.sqrt ((highestWeight n m z (p+1) : ℝ) / highestTotal n m z) * + Real.sqrt ((p+1 : ℕ) * (n-p : ℕ) : ℝ) - + Real.sqrt ((highestWeight n m z p : ℝ) / highestTotal n m z) * + Real.sqrt ((z-p : ℕ) * (m-z+p+1 : ℕ) : ℝ)) := by ring + _ = 0 := by rw [hs, sub_self, mul_zero] + + +theorem spin_complement_ratio_tendsto (n m : ℕ → ℕ) (r : ℝ) + (hn : Tendsto n atTop atTop) + (h : Tendsto (fun Q => (m Q : ℝ) / (n Q + m Q)) atTop (𝓝 r)) : + Tendsto (fun Q => (n Q : ℝ) / (n Q + m Q)) atTop (𝓝 (1-r)) := by + apply ((tendsto_const_nhds (x := (1 : ℝ))).sub h).congr' + filter_upwards [hn.eventually (eventually_ge_atTop 1)] with Q hQ + have hnQ : (n Q : ℝ) > 0 := by exact_mod_cast hQ + field_simp + ring + + + +theorem highestWeight_factorization {n m z p : ℕ} (hn : 0 < n) (hm : 0 < m) + (hmz : z ≤ m) (hp : p ≤ z) : + (highestWeight n m z p : ℝ) / ((n : ℝ)+m)^z = + (z.choose p : ℝ) * scaledDescFactorial n p (z-p) * + scaledDescFactorial m (z-p) p * + ((n : ℝ)/(n+m))^(z-p) * ((m : ℝ)/(n+m))^p := by + have hs : m-z+p = m-(z-p) := by omega + have hn' : (n : ℝ) ≠ 0 := by exact_mod_cast hn.ne' + have hm' : (m : ℝ) ≠ 0 := by exact_mod_cast hm.ne' + have hN : (n : ℝ)+m ≠ 0 := ne_of_gt (by positivity) + have hpw : ((n : ℝ)+m)^z = ((n : ℝ)+m)^(z-p) * ((n : ℝ)+m)^p := by + rw [← pow_add, Nat.sub_add_cancel hp] + simp only [highestWeight, Nat.cast_mul, hs, scaledDescFactorial, div_pow] + rw [hpw] + field_simp + + + +theorem highestWeight_scaled_tendsto (n m : ℕ → ℕ) (r : ℝ) + (hn : Tendsto n atTop atTop) (hm : Tendsto m atTop atTop) + (hr : Tendsto (fun Q => (m Q : ℝ) / (n Q + m Q)) atTop (𝓝 r)) + (z p : ℕ) (hp : p ≤ z) : + Tendsto (fun Q => (highestWeight (n Q) (m Q) z p : ℝ) / + ((n Q : ℝ)+m Q)^z) atTop (𝓝 ((z.choose p : ℝ) * (1-r)^(z-p) * r^p)) := by + have hc := spin_complement_ratio_tendsto n m r hn hr + have h := (((((tendsto_const_nhds (x := (z.choose p : ℝ))).mul + ((scaledDescFactorial_tendsto p (z-p)).comp hn)).mul + ((scaledDescFactorial_tendsto (z-p) p).comp hm)).mul (hc.pow (z-p))).mul (hr.pow p)) + simp only [mul_one] at h + apply h.congr' + filter_upwards [hn.eventually (eventually_ge_atTop 1), + hm.eventually (eventually_ge_atTop (z+1))] with Q hnQ hmQ + exact (highestWeight_factorization (by omega) (by omega) (by omega) hp).symm + + + +theorem highestTotal_scaled_tendsto (n m : ℕ → ℕ) (r : ℝ) + (hn : Tendsto n atTop atTop) (hm : Tendsto m atTop atTop) + (hr : Tendsto (fun Q => (m Q : ℝ) / (n Q + m Q)) atTop (𝓝 r)) (z : ℕ) : + Tendsto (fun Q => (highestTotal (n Q) (m Q) z : ℝ) / + ((n Q : ℝ)+m Q)^z) atTop (𝓝 1) := by + have h := tendsto_finsetSum (Finset.range (z+1)) + (fun p hp => highestWeight_scaled_tendsto n m r hn hm hr z p (by + have := Finset.mem_range.mp hp; omega)) + have hsum : ∑ p ∈ Finset.range (z+1), + (z.choose p : ℝ) * (1-r)^(z-p) * r^p = 1 := by + calc + _ = (r + (1-r))^z := by + rw [add_pow] + apply Finset.sum_congr rfl + intro p _ + ring + _ = 1 := by simp + simpa only [hsum, ← Finset.sum_div, highestTotal, Nat.cast_sum] using h + + + +theorem highestCoefficient_tendsto (n m : ℕ → ℕ) (r : ℝ) + (hn : Tendsto n atTop atTop) (hm : Tendsto m atTop atTop) + (hr : Tendsto (fun Q => (m Q : ℝ) / (n Q + m Q)) atTop (𝓝 r)) + (z p : ℕ) (hp : p ≤ z) : + Tendsto (fun Q => highestCoefficient (n Q) (m Q) z p) atTop + (𝓝 ((-1 : ℝ)^(z-p) * Real.sqrt ((z.choose p : ℝ) * (1-r)^(z-p) * r^p))) := by + have hratio := (highestWeight_scaled_tendsto n m r hn hm hr z p hp).div + (highestTotal_scaled_tendsto n m r hn hm hr z) (by norm_num) + simp only [div_one] at hratio + have hrat : Tendsto (fun Q => (highestWeight (n Q) (m Q) z p : ℝ) / + highestTotal (n Q) (m Q) z) atTop + (𝓝 ((z.choose p : ℝ) * (1-r)^(z-p) * r^p)) := by + apply hratio.congr' + filter_upwards [hn.eventually (eventually_ge_atTop 1)] with Q hnQ + have hn' : (n Q : ℝ) > 0 := by exact_mod_cast hnQ + have hN : ((n Q : ℝ)+m Q)^z ≠ 0 := pow_ne_zero _ (ne_of_gt (by positivity)) + exact div_div_div_cancel_right₀ hN _ _ + exact (Real.continuous_sqrt.tendsto _ |>.comp hrat).const_mul ((-1 : ℝ)^(z-p)) + + +theorem highestCoefficient_tendsto_all (n m : ℕ → ℕ) (r : ℝ) + (hn : Tendsto n atTop atTop) (hm : Tendsto m atTop atTop) + (hr : Tendsto (fun Q => (m Q : ℝ) / (n Q + m Q)) atTop (𝓝 r)) + (z p : ℕ) : + Tendsto (fun Q => highestCoefficient (n Q) (m Q) z p) atTop + (𝓝 ((-1 : ℝ)^(z-p) * Real.sqrt ((z.choose p : ℝ) * (1-r)^(z-p) * r^p))) := by + by_cases hp : p ≤ z + · exact highestCoefficient_tendsto n m r hn hm hr z p hp + · simpa only [highestCoefficient_zero _ _ _ _ (by omega : z < p), + Nat.choose_eq_zero_of_lt (by omega : z < p), Nat.cast_zero, zero_mul, + Real.sqrt_zero, mul_zero] using + (tendsto_const_nhds : Tendsto (fun _ : ℕ => (0 : ℝ)) atTop (𝓝 0)) + + + +theorem root_affine_ratio_tendsto (N a : ℕ → ℕ) (r b c : ℝ) + (hN : Tendsto N atTop atTop) + (ha : Tendsto (fun Q => (a Q : ℝ) / N Q) atTop (𝓝 r)) : + Tendsto (fun Q => Real.sqrt (b*((a Q : ℝ)+c)) / Real.sqrt (N Q)) + atTop (𝓝 (Real.sqrt (b*r))) := by + have hlim := (ha.add ((tendsto_const_div_atTop_nhds_zero_nat c).comp hN)).const_mul b + simp only [add_zero] at hlim + have hscaled := Real.continuous_sqrt.tendsto _ |>.comp hlim + convert hscaled using 1 + funext Q + rw [← Real.sqrt_div' _ (Nat.cast_nonneg (N Q)), mul_div_assoc, add_div] + rfl + + + +def coupledCoefficient (n m z : ℕ) : ℕ → ℕ → ℝ + | 0, p => highestCoefficient n m z p + | k+1, p => + ((if p = 0 then 0 else + Real.sqrt ((p : ℝ)*((n : ℝ)+1-p)) * coupledCoefficient n m z k (p-1)) + + Real.sqrt (((z+k+1 : ℕ) : ℝ)-p) * + Real.sqrt ((m : ℝ)+p-z-k) * coupledCoefficient n m z k p) / + Real.sqrt (((k+1 : ℕ) : ℝ)*((n : ℝ)+m-2*z-k)) + + + +theorem coupledCoefficient_zero (n m z k p : ℕ) (hp : z+k < p) : + coupledCoefficient n m z k p = 0 := by + induction k generalizing p with + | zero => exact highestCoefficient_zero n m z p (by simpa using hp) + | succ k ih => + rw [coupledCoefficient, ih p (by omega)] + by_cases hp0 : p = 0 + · simp [hp0] + · rw [ite_eq_right hp0, ih (p-1) (by omega)] + simp + + +def oscillatorCoefficient (r : ℝ) (z : ℕ) : ℕ → ℕ → ℝ + | 0, p => (-1 : ℝ)^(z-p) * Real.sqrt ((z.choose p : ℝ) * (1-r)^(z-p) * r^p) + | k+1, p => + ((if p = 0 then 0 else Real.sqrt ((p : ℝ)*(1-r)) * oscillatorCoefficient r z k (p-1)) + + Real.sqrt (((z+k+1 : ℕ) : ℝ)-p) * Real.sqrt r * oscillatorCoefficient r z k p) / + Real.sqrt (k+1 : ℕ) + + +theorem oscillatorCoefficient_zero (r : ℝ) (z k p : ℕ) (hp : z+k < p) : + oscillatorCoefficient r z k p = 0 := by + induction k generalizing p with + | zero => + simp [oscillatorCoefficient, Nat.choose_eq_zero_of_lt (by omega : z < p)] + | succ k ih => + rw [oscillatorCoefficient, ih p (by omega)] + by_cases hp0 : p = 0 + · simp [hp0] + · rw [ite_eq_right hp0, ih (p-1) (by omega)] + simp + + + +theorem coupledCoefficient_tendsto (n m : ℕ → ℕ) (r : ℝ) + (hn : Tendsto n atTop atTop) (hm : Tendsto m atTop atTop) + (hr : Tendsto (fun Q => (m Q : ℝ) / (n Q + m Q)) atTop (𝓝 r)) + (z k p : ℕ) : + Tendsto (fun Q => coupledCoefficient (n Q) (m Q) z k p) + atTop (𝓝 (oscillatorCoefficient r z k p)) := by + let N : ℕ → ℕ := fun Q => n Q + m Q + have hN : Tendsto N atTop atTop := hn.atTop_add_atTop hm + have hNratio : Tendsto (fun Q => (N Q : ℝ) / N Q) atTop (𝓝 1) := by + apply tendsto_const_nhds.congr' + filter_upwards [hN.eventually (eventually_ge_atTop 1)] with Q hQ + exact (div_self (by exact_mod_cast (by omega : N Q ≠ 0))).symm + have hr' : Tendsto (fun Q => (m Q : ℝ) / N Q) atTop (𝓝 r) := by simpa [N] using hr + have hc' : Tendsto (fun Q => (n Q : ℝ) / N Q) atTop (𝓝 (1-r)) := by + simpa [N] using spin_complement_ratio_tendsto n m r hn hr + induction k generalizing p with + | zero => exact highestCoefficient_tendsto_all n m r hn hm hr z p + | succ k ih => + have hfirst : Tendsto (fun Q => + (if p = 0 then 0 else + (Real.sqrt ((p : ℝ)*((n Q : ℝ)+1-p)) / Real.sqrt (N Q)) * + coupledCoefficient (n Q) (m Q) z k (p-1))) atTop + (𝓝 (if p = 0 then 0 else + Real.sqrt ((p : ℝ)*(1-r)) * oscillatorCoefficient r z k (p-1))) := by + by_cases hp : p = 0 + · simp only [hp, ite_true] + exact tendsto_const_nhds + · simp only [hp, ite_false] + have h := (root_affine_ratio_tendsto N n (1-r) p (1-p) hN hc').mul (ih (p-1)) + simpa only [add_sub_assoc] using h + have hsecond : Tendsto (fun Q => + (Real.sqrt (((z+k+1 : ℕ) : ℝ)-p) * + (Real.sqrt ((m Q : ℝ)+p-z-k) / Real.sqrt (N Q))) * + coupledCoefficient (n Q) (m Q) z k p) atTop + (𝓝 (Real.sqrt (((z+k+1 : ℕ) : ℝ)-p) * Real.sqrt r * + oscillatorCoefficient r z k p)) := by + have h := root_affine_ratio_tendsto N m r 1 ((p : ℝ)-z-k) hN hr' + simp only [one_mul] at h + have h' := (h.const_mul (Real.sqrt (((z+k+1 : ℕ) : ℝ)-p))).mul (ih p) + simpa only [← add_sub_assoc] using h' + have hden : Tendsto (fun Q => + Real.sqrt (((k+1 : ℕ) : ℝ)*((n Q : ℝ)+m Q-2*z-k)) / Real.sqrt (N Q)) + atTop (𝓝 (Real.sqrt (k+1 : ℕ))) := by + have h := root_affine_ratio_tendsto N N 1 (k+1 : ℕ) (-2*z-k) hN hNratio + simp only [mul_one] at h + convert h using 1 + funext Q + congr 2 + simp only [N, Nat.cast_add] + ring + have hden0 : Real.sqrt (k+1 : ℕ) ≠ 0 := Real.sqrt_ne_zero'.mpr (by positivity) + have h := (hfirst.add hsecond).div hden hden0 + apply h.congr' + filter_upwards [hN.eventually (eventually_ge_atTop 1)] with Q hQ + have hN0 : Real.sqrt (N Q) ≠ 0 := Real.sqrt_ne_zero'.mpr (by exact_mod_cast (by omega : 0 < N Q)) + simp only [Pi.div_apply, coupledCoefficient] + by_cases hp : p = 0 + · simp only [hp, ite_true, zero_add] + field_simp [hN0] + · simp only [hp, ite_false] + field_simp [hN0] + + + +theorem highestWeight_mul_descFactorial (n m z p : ℕ) (hp : p ≤ z) : + highestWeight n m z p * n.descFactorial p = + highestWeight n m z 0 * (z.choose p * (m-z+p).descFactorial p) := by + simp only [highestWeight, Nat.sub_zero, Nat.choose_zero_right, one_mul, + Nat.add_zero, Nat.descFactorial_zero, mul_one] + calc + _ = (z.choose p * (m-z+p).descFactorial p) * + ((n-p).descFactorial (z-p) * n.descFactorial p) := by ring + _ = _ := by rw [Nat.descFactorial_mul_descFactorial hp]; ring + + + +theorem highestCoefficient_ratio {n m z p : ℕ} (hz : z ≤ n) (hp : p ≤ z) : + highestCoefficient n m z p = (-1 : ℝ)^p * + Real.sqrt ((z.choose p : ℝ) * (m-z+p).descFactorial p / + n.descFactorial p) * highestCoefficient n m z 0 := by + have hnp : (n.descFactorial p : ℝ) ≠ 0 := by + exact_mod_cast (Nat.descFactorial_pos.mpr (hp.trans hz)).ne' + have he : (highestWeight n m z p : ℝ) / highestTotal n m z = + ((z.choose p : ℝ) * (m-z+p).descFactorial p / n.descFactorial p) * + ((highestWeight n m z 0 : ℝ) / highestTotal n m z) := by + have h := congrArg (fun a : ℕ => (a : ℝ)) + (highestWeight_mul_descFactorial n m z p hp) + push_cast at h + have heq : (highestWeight n m z p : ℝ) = + (z.choose p : ℝ) * (m-z+p).descFactorial p * highestWeight n m z 0 / + n.descFactorial p := (eq_div_iff hnp).mpr (by nlinarith only [h]) + rw [heq] + ring + have hsign : (-1 : ℝ)^p * (-1 : ℝ)^z = (-1 : ℝ)^(z-p) := by + calc + _ = (-1 : ℝ)^p * ((-1 : ℝ)^(z-p) * (-1 : ℝ)^p) := by + rw [← pow_add (-1 : ℝ) (z-p) p, Nat.sub_add_cancel hp] + _ = ((-1 : ℝ)^p * (-1 : ℝ)^p) * (-1 : ℝ)^(z-p) := by ring + _ = _ := by rw [← mul_pow]; norm_num + simp only [highestCoefficient, Nat.sub_zero] + rw [he, Real.sqrt_mul (by positivity)] + calc + _ = ((-1 : ℝ)^p * (-1 : ℝ)^z) * + (Real.sqrt ((z.choose p : ℝ) * (m-z+p).descFactorial p / + n.descFactorial p) * + Real.sqrt ((highestWeight n m z 0 : ℝ) / highestTotal n m z)) := by rw [hsign] + _ = _ := by ring + + +theorem highestCoefficient_last {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) : + highestCoefficient n m z z = (-1 : ℝ)^z * + Real.sqrt ((m.descFactorial z : ℝ) / n.descFactorial z) * + highestCoefficient n m z 0 := by + simpa only [Nat.sub_add_cancel hm, Nat.choose_self, Nat.cast_one, one_mul] using + highestCoefficient_ratio (m := m) hn (le_refl z) + + +theorem highestCoefficient_penultimate {n m z : ℕ} (hn : z ≤ n) + (hm : z ≤ m) (hz : 1 ≤ z) : + highestCoefficient n m z (z-1) = (-1 : ℝ)^(z-1) * + Real.sqrt ((z : ℝ) * (m-1).descFactorial (z-1) / + n.descFactorial (z-1)) * highestCoefficient n m z 0 := by + have hs : m-z+(z-1) = m-1 := by omega + simpa only [hs, Nat.choose_symm hz, Nat.choose_one_right] using + highestCoefficient_ratio (m := m) hn (Nat.sub_le z 1) + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Flow.lean b/lean/OAI/Analysis/LaughlinFock/Flow.lean new file mode 100644 index 0000000000000000000000000000000000000000..5425fb0b15b384e949506a32921a7a4d8ce79cc5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Flow.lean @@ -0,0 +1,128 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Covariance + +namespace OAI + +/-! Flow. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix Matrix.Norms.Operator ComplexConjugate ComplexOrder +open NormedSpace + + +theorem matrixExp_conjugation_hasDerivAt {ι : Type*} [Fintype ι] [DecidableEq ι] + (A M : Matrix ι ι ℂ) (t : ℂ) : + HasDerivAt (fun u : ℂ => exp (u • A) * M * exp (u • (-A))) + (A * (exp (t • A) * M * exp (t • (-A))) - + (exp (t • A) * M * exp (t • (-A))) * A) t := by + have h := ((hasDerivAt_exp_smul_const' A t).mul_const M).mul + (hasDerivAt_exp_smul_const (-A) t) + convert! h using 1 + noncomm_ring + + + +theorem matrixExp_conjugation_naturality {ι κ : Type*} + [Fintype ι] [DecidableEq ι] [Fintype κ] [DecidableEq κ] + (X : Matrix ι ι ℂ) (Y : Matrix κ κ ℂ) + (L : Matrix ι ι ℂ →ₗ[ℂ] Matrix κ κ ℂ) + (hL : ∀ M, L (X*M-M*X) = Y*L M-L M*Y) + (M : Matrix ι ι ℂ) (t : ℂ) : + L (exp (t • X) * M * exp (t • (-X))) = + exp (t • Y) * L M * exp (t • (-Y)) := by + let m (u : ℂ) := exp (u • X) * M * exp (u • (-X)) + let f (u : ℂ) := exp (u • (-Y)) * L (m u) * exp (u • Y) + have hd (u : ℂ) : HasDerivAt f 0 u := by + have hm : HasDerivAt (fun v => L (m v)) (Y*L (m u)-L (m u)*Y) u := by + have h := L.toContinuousLinearMap.hasFDerivAt.comp_hasDerivAt u + (matrixExp_conjugation_hasDerivAt X M u) + change HasDerivAt (fun v => L (m v)) (L (X*m u-m u*X)) u at h + rwa [hL] at h + have h := ((hasDerivAt_exp_smul_const (-Y) u).mul hm).mul + (hasDerivAt_exp_smul_const' Y u) + simp only [Pi.mul_apply] at h + convert! h using 1 + noncomm_ring + have he := is_const_of_deriv_eq_zero (fun u => (hd u).differentiableAt) + (fun u => (hd u).deriv) t 0 + have he' : exp (t • (-Y)) * L (m t) * exp (t • Y) = L M := by + simpa only [f, m, zero_smul, exp_zero, Matrix.one_mul, Matrix.mul_one] using he + have hi₁ : exp (t • Y) * exp (t • (-Y)) = 1 := by + have h := (exp_add_of_commute (Commute.refl (t • Y)).neg_right).symm + simpa only [← smul_neg, ← smul_add, add_neg_cancel, smul_zero, exp_zero] using! h + calc + L (m t) = 1 * L (m t) * 1 := by simp + _ = (exp (t • Y) * exp (t • (-Y))) * L (m t) * + (exp (t • Y) * exp (t • (-Y))) := by rw [hi₁] + _ = exp (t • Y) * (exp (t • (-Y)) * L (m t) * exp (t • Y)) * + exp (t • (-Y)) := by noncomm_ring + _ = _ := by rw [he'] + + + +theorem exteriorLift_exp_conjugation (Q k : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) + (M : Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ) (t : ℂ) : + exteriorLift Q k (exp (t • sectorOneBody Q k A) * M * + exp (t • (-sectorOneBody Q k A))) = + exp (t • oneBodyLift Q A) * exteriorLift Q k M * + exp (t • (-oneBodyLift Q A)) := + matrixExp_conjugation_naturality _ _ (exteriorLiftLinear Q k) + (fun M => (oneBody_exteriorLift_commutator Q k A M).symm) M t + + + +private theorem matrixExp_smul_unitary {ι : Type*} [Fintype ι] [DecidableEq ι] + (B : Matrix ι ι ℂ) (hB : Bᴴ = B) (t : ℝ) : + exp (((t : ℂ) * Complex.I) • B) ∈ Matrix.unitaryGroup ι ℂ := by + let X : Matrix ι ι ℂ := ((t : ℂ) * Complex.I) • B + have hX : Xᴴ = -X := by + dsimp only [X] + rw [Matrix.conjTranspose_smul, hB] + simp [star_mul, mul_comm] + have hstar : (exp X)ᴴ = exp (-X) := by + rw [← Matrix.exp_conjTranspose, hX] + change (exp X) ∈ unitary (Matrix ι ι ℂ) + rw [Unitary.mem_iff] + change (exp X)ᴴ * exp X = 1 ∧ exp X * (exp X)ᴴ = 1 + rw [hstar] + constructor + · simpa only [neg_add_cancel, exp_zero] using! + (exp_add_of_commute (Commute.refl X).neg_left).symm + · simpa only [add_neg_cancel, exp_zero] using! + (exp_add_of_commute (Commute.refl X).neg_right).symm + + +theorem oneBodyLift_exp_unitary (Q : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (hA : A.IsHermitian) (t : ℝ) : + exp ((t * Complex.I) • oneBodyLift Q A) ∈ + Matrix.unitaryGroup (Occupation Q) ℂ := + matrixExp_smul_unitary (oneBodyLift Q A) (oneBodyLift_hermitian Q A hA).eq t + + +theorem exteriorLift_unitary_conjugation (Q k : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (hA : A.IsHermitian) + (M : Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ) (t : ℝ) : + exteriorLift Q k (exp ((t * Complex.I) • sectorOneBody Q k A) * M * + (exp ((t * Complex.I) • sectorOneBody Q k A))ᴴ) = + exp ((t * Complex.I) • oneBodyLift Q A) * exteriorLift Q k M * + (exp ((t * Complex.I) • oneBodyLift Q A))ᴴ := by + have hf : (oneBodyLift Q A)ᴴ = oneBodyLift Q A := + (oneBodyLift_hermitian Q A hA).eq + have hs : (sectorOneBody Q k A)ᴴ = sectorOneBody Q k A := by + rw [sectorOneBody_adjoint, hA.eq] + have hB {ι : Type} [Fintype ι] [DecidableEq ι] + (B : Matrix ι ι ℂ) (hB : Bᴴ = B) : + (exp (((t : ℂ) * Complex.I) • B))ᴴ = + exp (((t : ℂ) * Complex.I) • (-B)) := by + rw [← Matrix.exp_conjTranspose] + congr 1 + rw [Matrix.conjTranspose_smul, hB] + simp [star_mul, mul_comm] + rw [hB _ hs, hB _ hf] + exact exteriorLift_exp_conjugation Q k A M _ + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FockRotations.lean b/lean/OAI/Analysis/LaughlinFock/FockRotations.lean new file mode 100644 index 0000000000000000000000000000000000000000..5018037dc5eb7cefb5ee4bb110ac51bb59ea34b4 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FockRotations.lean @@ -0,0 +1,151 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SpinSchur + +namespace OAI + +/-! Fock Rotations. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + +def sectorOneBodyLinear (Q k : ℕ) : + Matrix (Orbital Q) (Orbital Q) ℂ →ₗ[ℂ] + Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ where + toFun := sectorOneBody Q k + map_add' A B := by ext S T; exact congrFun (congrFun (oneBodyLift_add Q A B) S.val) T.val + map_smul' c A := by ext S T; exact congrFun (congrFun (oneBodyLift_smul Q c A) S.val) T.val + + + +inductive FockRotationIndex + | spin (n : ℕ) + | sector (k : ℕ) + | fock + deriving DecidableEq + + + +abbrev FockRotationSpace (Q : ℕ) : FockRotationIndex → Type + | .spin n => Fin (n+1) + | .sector k => SectorOccupation Q k + | .fock => Occupation Q + +instance (Q : ℕ) (j : FockRotationIndex) : Fintype (FockRotationSpace Q j) := by + cases j <;> unfold FockRotationSpace <;> infer_instance +instance (Q : ℕ) (j : FockRotationIndex) : DecidableEq (FockRotationSpace Q j) := by + cases j <;> unfold FockRotationSpace <;> infer_instance + + +def fockRotationGenerator (Q : ℕ) (s : Fin 3) : + ∀ j, Matrix (FockRotationSpace Q j) (FockRotationSpace Q j) ℂ + | .spin n => spinGenerator n s + | .sector k => sectorOneBody Q k (spinGenerator Q s) + | .fock => oneBodyLift Q (spinGenerator Q s) + +theorem fockRotationGenerator_skew (Q : ℕ) (s : Fin 3) (j : FockRotationIndex) : + (fockRotationGenerator Q s j)ᴴ = -fockRotationGenerator Q s j := by + cases j with + | spin n => exact spinGenerator_skew n s + | sector k => + change (sectorOneBody Q k _)ᴴ = _ + rw [sectorOneBody_adjoint, spinGenerator_skew] + exact (sectorOneBodyLinear Q k).map_neg _ + | fock => + change (oneBodyLift Q _)ᴴ = _ + rw [oneBodyLift_adjoint, spinGenerator_skew] + exact (oneBodyLiftLinear Q).map_neg _ + + +def fockAverage (Q : ℕ) : FockMatrix Q →ₗ[ℂ] FockMatrix Q := + rotationAverageLinear (fockRotationGenerator Q) (fockRotationGenerator_skew Q) .fock + + +def sectorAverage (Q k : ℕ) : + Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ →ₗ[ℂ] + Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ := + rotationAverageLinear (fockRotationGenerator Q) (fockRotationGenerator_skew Q) (.sector k) + + +theorem fockAverage_exteriorLift (Q k : ℕ) + (M : Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ) : + fockAverage Q (exteriorLift Q k M) = exteriorLift Q k (sectorAverage Q k M) := by + exact (rotationAverage_covariance (fockRotationGenerator Q) (fockRotationGenerator_skew Q) + (i:=.sector k) (j:=.fock) (exteriorLiftLinear Q k) + (fun s M => (oneBody_exteriorLift_commutator Q k (spinGenerator Q s) M).symm) M).symm + +theorem fockAverage_posSemidef (Q : ℕ) (M : FockMatrix Q) (hM : M.PosSemidef) : + (fockAverage Q M).PosSemidef := + rotationAverage_posSemidef (fockRotationGenerator Q) (fockRotationGenerator_skew Q) .fock M hM + +theorem sectorAverage_posSemidef (Q k : ℕ) + (M : Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ) (hM : M.PosSemidef) : + (sectorAverage Q k M).PosSemidef := + rotationAverage_posSemidef (fockRotationGenerator Q) (fockRotationGenerator_skew Q) (.sector k) M hM + + + +theorem spinRotationAverage (Q n : ℕ) (M : Matrix (Fin (n+1)) (Fin (n+1)) ℂ) : + rotationAverage (fockRotationGenerator Q) (fockRotationGenerator_skew Q) (.spin n) M = + (M.trace / (n+1 : ℂ)) • 1 := by + have he := spin_intertwiner_trace_scalar + (rotationAverage (fockRotationGenerator Q) (fockRotationGenerator_skew Q) (.spin n) M) + (fun s => (rotationAverage_commutes_generator (fockRotationGenerator Q) + (fockRotationGenerator_skew Q) (.spin n) M s).symm) + rw [rotationAverage_trace] at he + exact he + + +def congruenceLinear {ι κ : Type*} [Fintype ι] (C : Matrix κ ι ℂ) : + Matrix ι ι ℂ →ₗ[ℂ] Matrix κ κ ℂ where + toFun M := C * M * Cᴴ + map_add' A B := by simp only [Matrix.mul_add, Matrix.add_mul] + map_smul' c M := by simp only [Matrix.mul_smul, Matrix.smul_mul, RingHom.id_apply] + + + +theorem congruenceLinear_commutator {ι κ : Type*} [Fintype ι] [Fintype κ] + (X : Matrix ι ι ℂ) (Y : Matrix κ κ ℂ) (C : Matrix κ ι ℂ) + (hX : Xᴴ = -X) (hY : Yᴴ = -Y) (hC : Y*C = C*X) + (M : Matrix ι ι ℂ) : + congruenceLinear C (X*M-M*X) = Y * congruenceLinear C M - congruenceLinear C M * Y := by + have hC' : Cᴴ * Y = X * Cᴴ := by + have hh := congrArg Matrix.conjTranspose hC + simpa only [Matrix.conjTranspose_mul, hX, hY, Matrix.mul_neg, Matrix.neg_mul, + neg_inj] using hh + change C * (X*M-M*X) * Cᴴ = Y*(C*M*Cᴴ) - (C*M*Cᴴ)*Y + simp only [Matrix.mul_sub, Matrix.sub_mul, Matrix.mul_assoc] + rw [← Matrix.mul_assoc Y C, hC, Matrix.mul_assoc, hC'] + + + +theorem sectorAverage_spin_sandwich {Q k n : ℕ} + (C : Matrix (SectorOccupation Q k) (Fin (n+1)) ℂ) + (hC : ∀ s, sectorOneBody Q k (spinGenerator Q s) * C = C * spinGenerator n s) + (M : Matrix (Fin (n+1)) (Fin (n+1)) ℂ) : + sectorAverage Q k (C*M*Cᴴ) = (M.trace / (n+1 : ℂ)) • (C*Cᴴ) := by + have hc := rotationAverage_covariance (fockRotationGenerator Q) + (fockRotationGenerator_skew Q) (i:=.spin n) (j:=.sector k) + (congruenceLinear C) (fun s M => congruenceLinear_commutator _ _ C + (spinGenerator_skew n s) (fockRotationGenerator_skew Q s (.sector k)) (hC s) M) M + change C * rotationAverage (fockRotationGenerator Q) (fockRotationGenerator_skew Q) (.spin n) M * Cᴴ = + rotationAverage (fockRotationGenerator Q) (fockRotationGenerator_skew Q) (.sector k) (C*M*Cᴴ) at hc + change rotationAverage (fockRotationGenerator Q) (fockRotationGenerator_skew Q) (.sector k) (C*M*Cᴴ) = _ + rw [← hc, spinRotationAverage] + simp only [Matrix.mul_smul, Matrix.smul_mul, Matrix.mul_one] + + + +theorem fockAverage_spin_sandwich {Q k n : ℕ} + (C : Matrix (SectorOccupation Q k) (Fin (n+1)) ℂ) + (hC : ∀ s, sectorOneBody Q k (spinGenerator Q s) * C = C * spinGenerator n s) + (M : Matrix (Fin (n+1)) (Fin (n+1)) ℂ) : + fockAverage Q (exteriorLift Q k (C*M*Cᴴ)) = + (M.trace / (n+1 : ℂ)) • exteriorLift Q k (C*Cᴴ) := by + rw [fockAverage_exteriorLift, sectorAverage_spin_sandwich C hC] + exact (exteriorLiftLinear Q k).map_smul _ _ + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FourBasis.lean b/lean/OAI/Analysis/LaughlinFock/FourBasis.lean new file mode 100644 index 0000000000000000000000000000000000000000..d2d212ec5d56ba2499f1142bea1fd90c822626c3 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FourBasis.lean @@ -0,0 +1,144 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.BesselComparison +import OAI.Analysis.LaughlinFock.ThreeSpectrum + +namespace OAI + +/-! Four Basis. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +theorem wedgeCoupledCoefficient_resolution (Q : ℕ) (ij kl : IncreasingPair Q) : + (∑ r : CopyLabel Q, ∑ k : Fin (2*Q-2*r.val.val+1), + wedgeCoupledCoefficient Q r.val.val k.val ij * + wedgeCoupledCoefficient Q r.val.val k.val kl) = if ij=kl then 1 else 0 := by + classical + have h₁ := coupledVector_resolution Q Q ij.val kl.val + have h₂ := coupledVector_resolution Q Q (ij.val.2,ij.val.1) kl.val + have hn : (ij.val.2,ij.val.1) ≠ kl.val := by + intro h + have ha := congrArg Prod.fst h + have hb := congrArg Prod.snd h + have hi := ij.property + have hk := kl.property + dsimp only [Prod.fst, Prod.snd] at ha hb + rw [← ha, ← hb] at hk + exact lt_asymm hi hk + rw [ite_eq_right hn] at h₂ + have hv := congrArg₂ (fun x y : ℝ => x-y) h₁ h₂ + rw [← Finset.sum_sub_distrib] at hv + have ht (c : CoupledIndex Q Q) : + coupledVector Q Q c.1.val c.2.val ij.val.1.val ij.val.2.val * + coupledVector Q Q c.1.val c.2.val kl.val.1.val kl.val.2.val - + coupledVector Q Q c.1.val c.2.val ij.val.2.val ij.val.1.val * + coupledVector Q Q c.1.val c.2.val kl.val.1.val kl.val.2.val = + if Odd c.1.val then wedgeCoupledCoefficient Q c.1.val c.2.val ij * + wedgeCoupledCoefficient Q c.1.val c.2.val kl else 0 := by + rw [coupledVector_swap (coupledIndex_bounds c).1 c.2.val ij.val.1.val ij.val.2.val] + by_cases ho : Odd c.1.val + · rw [ite_eq_left ho, ho.neg_one_pow] + unfold wedgeCoupledCoefficient + have hs := Real.mul_self_sqrt (by norm_num : (0:ℝ) ≤ 2) + linear_combination -(coupledVector Q Q c.1.val c.2.val ij.val.1.val ij.val.2.val * + coupledVector Q Q c.1.val c.2.val kl.val.1.val kl.val.2.val) * hs + · rw [ite_eq_right ho, (Nat.not_odd_iff_even.mp ho).neg_one_pow] + ring + simp only [ht, sub_zero, Subtype.val_inj] at hv + rw [Fintype.sum_sigma] at hv + rw [Nat.min_self, ← two_mul Q] at hv + have he : (∑ r : CopyLabel Q, ∑ k : Fin (2*Q-2*r.val.val+1), + wedgeCoupledCoefficient Q r.val.val k.val ij * + wedgeCoupledCoefficient Q r.val.val k.val kl) = + ∑ r : Fin (Q+1), if Odd r.val then ∑ k : Fin (2*Q-2*r.val+1), + wedgeCoupledCoefficient Q r.val k.val ij * + wedgeCoupledCoefficient Q r.val k.val kl else 0 := by + rw [← Finset.sum_subtype (Finset.univ.filter (fun r : Fin (Q+1) => Odd r.val)) + (by intro r; simp) (fun r : Fin (Q+1) => ∑ k : Fin (2*Q-2*r.val+1), + wedgeCoupledCoefficient Q r.val k.val ij * wedgeCoupledCoefficient Q r.val k.val kl)] + rw [Finset.sum_filter] + rw [he] + simpa only [Nat.min_self, Finset.sum_ite_irrel, Finset.sum_const_zero, two_mul] using hv + + +def fullCouplingMatrix (n m : ℕ) : + Matrix (Fin (n+1) × Fin (m+1)) (CoupledIndex n m) ℂ := + fun b c => coupledVector n m c.1.val c.2.val b.1.val b.2.val + +theorem fullCouplingMatrix_complete (n m : ℕ) : + fullCouplingMatrix n m * (fullCouplingMatrix n m)ᴴ = 1 := by + classical + ext b c + have h := congrArg (fun x : ℝ => (x : ℂ)) (coupledVector_resolution n m b c) + simpa only [Matrix.mul_apply, Matrix.conjTranspose_apply, fullCouplingMatrix, + Complex.star_def, Complex.conj_ofReal, Matrix.one_apply, + Complex.ofReal_sum, Complex.ofReal_mul, apply_ite, Complex.ofReal_one, + Complex.ofReal_zero] using h + + +def oddPairColumns (Q r : ℕ) : + Matrix (IncreasingPair Q) (Fin (2*Q-2*r+1)) ℂ := + fun b k => wedgeCoupledCoefficient Q r k.val b + + +theorem oddPairColumns_complete (Q : ℕ) : + (∑ r : CopyLabel Q, oddPairColumns Q r.val.val * (oddPairColumns Q r.val.val)ᴴ) = 1 := by + classical + ext ij kl + have h := congrArg (fun x : ℝ => (x : ℂ)) (wedgeCoupledCoefficient_resolution Q ij kl) + simpa only [Matrix.sum_apply, Matrix.mul_apply, Matrix.conjTranspose_apply, oddPairColumns, + Complex.star_def, Complex.conj_ofReal, Matrix.one_apply, + Complex.ofReal_sum, Complex.ofReal_mul, apply_ite, Complex.ofReal_one, + Complex.ofReal_zero] using h + + +def fourFactorEmbedding (Q r : ℕ) : + Matrix (FourUncoupled Q) (Fin (2*Q-2+1) × Fin (2*Q-2*r+1)) ℂ := + Matrix.kronecker 1 (oddPairColumns Q r) + + +def composedCouplingMatrix (Q r : ℕ) : + Matrix (FourUncoupled Q) (CoupledIndex (2*Q-2) (2*Q-2*r)) ℂ := + fun b c => composedCoupledVector Q r c.1.val c.2.val b + +theorem composedCouplingMatrix_eq_product (Q r : ℕ) : + composedCouplingMatrix Q r = + fourFactorEmbedding Q r * fullCouplingMatrix (2*Q-2) (2*Q-2*r) := by + classical + ext b c + simp only [Matrix.mul_apply, fourFactorEmbedding, Matrix.kronecker, Matrix.kroneckerMap_apply, Matrix.one_apply, + ite_mul, one_mul, zero_mul, Fintype.sum_prod_type, fullCouplingMatrix] + rw [Finset.sum_comm] + simp only [Finset.sum_ite_eq, Finset.mem_univ, ite_true, + composedCouplingMatrix, composedCoupledVector, Complex.ofReal_sum, Complex.ofReal_mul, + oddPairColumns] + apply Finset.sum_congr rfl + intro k _ + ring + + + +theorem composedCouplingMatrix_complete (Q : ℕ) : + (∑ r : CopyLabel Q, composedCouplingMatrix Q r.val.val * + (composedCouplingMatrix Q r.val.val)ᴴ) = 1 := by + simp_rw [composedCouplingMatrix_eq_product, Matrix.conjTranspose_mul] + conv_lhs => arg 2; ext r; rw [Matrix.mul_assoc, ← Matrix.mul_assoc + (fullCouplingMatrix _ _), fullCouplingMatrix_complete, Matrix.one_mul] + simp only [fourFactorEmbedding, Matrix.kronecker, Matrix.conjTranspose_kronecker, + Matrix.conjTranspose_one, ← Matrix.mul_kronecker_mul, Matrix.mul_one] + have hs : (∑ r : CopyLabel Q, Matrix.kronecker 1 + (oddPairColumns Q r.val.val * (oddPairColumns Q r.val.val)ᴴ)) = + Matrix.kronecker (1 : Matrix (Fin (2*Q-2+1)) (Fin (2*Q-2+1)) ℂ) + (∑ r : CopyLabel Q, oddPairColumns Q r.val.val * (oddPairColumns Q r.val.val)ᴴ) := by + ext b c + simp only [Matrix.sum_apply, Matrix.kronecker, Matrix.kroneckerMap_apply, Finset.mul_sum] + simp only [Matrix.kronecker] at hs + rw [hs, oddPairColumns_complete] + exact Matrix.one_kronecker_one + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FourBound.lean b/lean/OAI/Analysis/LaughlinFock/FourBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..3eb43da9c8181896a3ab2f191974a882e86c262c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FourBound.lean @@ -0,0 +1,82 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FourRetained +import OAI.Analysis.LaughlinFock.TailOrbit + +namespace OAI + +/-! Four Bound. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder +open Filter Topology + + + +theorem averagedRowsFour_eventual_bound {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) (ε : ℝ) (hε : 0 ≤ ε) + (hCertificate : ∀ D, 1 ≤ D → D ≤ 23 → + (planarFourGram D * planarFourComparison rows ε D * planarFourGram D).PosSemidef) : + ∃ e : ℕ → ℝ, (∀ Q, 0 ≤ e Q) ∧ Tendsto e atTop (𝓝 0) ∧ + ∀ Q, (hQ : 24 ≤ Q) → + (exteriorLift Q 4 (fourWedgeMatrix Q * (fourWedgeMatrix Q)ᴴ) + + (1222*ε+e Q) • hamiltonian Q - + averagedRowsFour (by omega : 8 ≤ Q) rows).PosSemidef := by + obtain ⟨e, hepos, helim, he⟩ := averagedFourComparison_transfer rows ε hCertificate + refine ⟨e, hepos, helim, ?_⟩ + intro Q hQ + have h := he Q hQ + rw [averagedFourComparison_eq rows ε hQ] at h + have hr : (1222 : ℂ) • hamiltonian Q = (1222 : ℝ) • hamiltonian Q := by + rw [RCLike.real_smul_eq_coe_smul (K:=ℂ)] + norm_num [RCLike.ofReal_eq_complex_ofReal] + have hallow := (fourCopyAllowance_bound hQ).smul hε + rw [hr] at hallow + have hdisc := discardedFourTarget_lift_posSemidef Q 23 (by omega) + convert (h.add hallow).add hdisc using 1 + simp only [smul_sub, smul_smul, add_smul, mul_comm ε (1222:ℝ)] + abel + + + +theorem fockInequality_eventual_of_certificates {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) (ε : ℝ) (hε : 0 ≤ ε) + (hThree : ∀ z : ComparedThreeBlock, + planarRowsThreeTrace rows z.val.val < + (3/2 : ℝ)*(3*(z.val.val : ℝ)-1)*(-1/2)^z.val.val) + (hFour : ∀ D, 1 ≤ D → D ≤ 23 → + (planarFourGram D * planarFourComparison rows ε D * planarFourGram D).PosSemidef) : + ∃ e : ℕ → ℝ, (∀ Q, 0 ≤ e Q) ∧ Tendsto e atTop (𝓝 0) ∧ + ∀ᶠ Q in atTop, FockInequality Q (1-rowsEta rows-tailCoefficient Q-1222*ε-e Q) := by + obtain ⟨e, hepos, helim, he⟩ := averagedRowsFour_eventual_bound rows ε hε hFour + refine ⟨e, hepos, helim, ?_⟩ + filter_upwards [threeTraceForm_eventual_bound rows hThree, eventually_ge_atTop 24] with Q h3 hQ + have htail : (tailThreeTarget Q + tailCoefficient Q • hamiltonian Q).PosSemidef := by + rw [RCLike.real_smul_eq_coe_smul (K:=ℂ), RCLike.ofReal_eq_complex_ofReal] + exact tailThreeTarget_relative_bound (Q:=Q) (by omega) + have hf := fockInequality_of_finite_comparisons rows (by omega : 16 ≤ Q) + (averagedRowsFour (by omega : 8 ≤ Q) rows) (tailCoefficient Q) (1222*ε+e Q) + (averagedRows_positive rows (by omega)) h3 (he Q hQ) htail + convert hf using 1 + ring + + + +theorem integer_threshold_of_certificates {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) + (hEta : rowsEta rows = 93527408868499 / 10^14) + (hThree : ∀ z : ComparedThreeBlock, + planarRowsThreeTrace rows z.val.val < + (3/2 : ℝ)*(3*(z.val.val : ℝ)-1)*(-1/2)^z.val.val) + (hFour : ∀ D, 1 ≤ D → D ≤ 23 → + (planarFourGram D * planarFourComparison rows (3/10^6) D * planarFourGram D).PosSemidef) + (γ : ℝ) (hγ : γ < gammaStar) : + ∃ Qγ : ℤ, 1 ≤ Qγ ∧ ∀ Q : ℤ, Qγ ≤ Q → FockInequality Q.toNat γ := by + obtain ⟨e, _, helim, hb⟩ := + fockInequality_eventual_of_certificates rows (3/10^6) (by norm_num) hThree hFour + exact uniform_integer_threshold_of_eventual_bound _ + (final_coefficient_tendsto rows hEta e helim) hb γ hγ + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FourCoefficients.lean b/lean/OAI/Analysis/LaughlinFock/FourCoefficients.lean new file mode 100644 index 0000000000000000000000000000000000000000..f872cb295a594c5000b364e0cfe83bfcfdda2f66 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FourCoefficients.lean @@ -0,0 +1,165 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.OscillatorLimit + +namespace OAI + +/-! Four Coefficients. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators +open Filter Topology + + +theorem coupledCoefficient_left_support {n m z : ℕ} (hz : z ≤ n) + (k p : ℕ) (hp : n < p) : coupledCoefficient n m z k p = 0 := by + induction k generalizing p with + | zero => exact highestCoefficient_zero _ _ _ _ (by omega) + | succ k ih => + rw [coupledCoefficient, ih p hp] + simp only [mul_zero, add_zero] + by_cases he : p = n+1 + · rw [he] + have he' : (n : ℝ)+1-(n+1 : ℕ) = 0 := by push_cast; ring + simp only [he', mul_zero, Real.sqrt_zero, zero_mul] + split_ifs <;> simp + · rw [ite_eq_right (by omega : p ≠ 0), ih (p-1) (by omega)] + simp + + + +theorem coupledCoefficient_right_support {n m z : ℕ} (hz : z ≤ m) + (k p : ℕ) (hp : m+p < z+k) : coupledCoefficient n m z k p = 0 := by + induction k generalizing p with + | zero => omega + | succ k ih => + rw [coupledCoefficient] + have hfirst : (if p = 0 then 0 else + Real.sqrt ((p : ℝ)*((n : ℝ)+1-p)) * coupledCoefficient n m z k (p-1)) = 0 := by + split_ifs with hp0 + · rfl + · rw [ih (p-1) (by omega), mul_zero] + rw [hfirst, zero_add] + by_cases he : m+p = z+k + · have he' : (m : ℝ)+p-z-k = 0 := by exact_mod_cast sub_eq_zero.mpr (show (m+p : ℤ)-z=k by omega) + simp [he'] + · rw [ih p (by omega)] + simp + + + +theorem coupledCoefficient_lower (n m z k p : ℕ) : + coupledCoefficient n m z (k+1) p = + (Real.sqrt (p : ℝ) * Real.sqrt ((n : ℝ)+1-p) * coupledCoefficient n m z k (p-1) + + Real.sqrt (((z+k+1 : ℕ) : ℝ)-p) * Real.sqrt ((m : ℝ)+p-z-k) * + coupledCoefficient n m z k p) / + Real.sqrt (((k+1 : ℕ) : ℝ)*((n : ℝ)+m-2*z-k)) := by + rw [coupledCoefficient] + by_cases hp : p = 0 + · simp [hp] + · rw [ite_eq_right hp, Real.sqrt_mul (Nat.cast_nonneg p)] + + +theorem affineSpin_atTop (a b : ℕ) (ha : 0 < a) : + Tendsto (fun Q : ℕ => a*Q-b) atTop atTop := by + refine tendsto_atTop.mpr fun k => ?_ + filter_upwards [eventually_ge_atTop (k+b)] with Q hQ + have hm : Q ≤ a*Q := by nlinarith only [ha] + omega + + + +theorem affineSpin_scaled_tendsto (a b : ℕ) (ha : 0 < a) : + Tendsto (fun Q : ℕ => ((a*Q-b : ℕ) : ℝ) / Q) atTop (𝓝 (a : ℝ)) := by + have h := tendsto_const_nhds (x := (a : ℝ)) |>.sub + (tendsto_const_div_atTop_nhds_zero_nat (b : ℝ)) + simp only [sub_zero] at h + apply h.congr' + filter_upwards [eventually_ge_atTop (b+1)] with Q hQ + have hm : Q ≤ a*Q := by nlinarith only [ha] + have hQ0 : (Q : ℝ) ≠ 0 := by exact_mod_cast (by omega : Q ≠ 0) + rw [Nat.cast_sub (by omega : b ≤ a*Q), Nat.cast_mul] + field_simp + + + +theorem affineSpin_ratio_tendsto (a b c d : ℕ) (ha : 0 < a) (hc : 0 < c) : + Tendsto (fun Q : ℕ => ((c*Q-d : ℕ) : ℝ) / + (((a*Q-b : ℕ) : ℝ) + ((c*Q-d : ℕ) : ℝ))) atTop + (𝓝 ((c : ℝ) / (a+c : ℕ))) := by + have h1 := affineSpin_scaled_tendsto a b ha + have h2 := affineSpin_scaled_tendsto c d hc + have h := h2.div (h1.add h2) (by positivity : (a : ℝ)+(c : ℝ) ≠ 0) + simp only [Nat.cast_add] + apply h.congr' + filter_upwards [eventually_ge_atTop 1] with Q hQ + have hQ0 : (Q : ℝ) ≠ 0 := by exact_mod_cast (by omega : Q ≠ 0) + simp only [Pi.div_apply] + rw [← add_div] + exact div_div_div_cancel_right₀ hQ0 _ _ + + +theorem threeCoupling_tendsto (z k p : ℕ) : + Tendsto (fun Q : ℕ => coupledCoefficient (2*Q-2) Q z k p) atTop + (𝓝 (polynomialCouplingCoefficient (Real.sqrt (1/3)) (Real.sqrt (2/3)) z k p)) := by + have h := coupledCoefficient_tendsto (fun Q => 2*Q-2) (fun Q => Q) (1/3) + (affineSpin_atTop 2 2 (by norm_num)) tendsto_id + (by simpa using affineSpin_ratio_tendsto 2 2 1 0 (by norm_num) (by norm_num)) z k p + rw [oscillatorCoefficient_eq_polynomial _ (by norm_num) (by norm_num)] at h + norm_num only [show (1 : ℝ)-1/3 = 2/3 by norm_num] at h + exact h + + + +theorem singlePairCoupling_tendsto (z k p : ℕ) : + Tendsto (fun Q : ℕ => coupledCoefficient Q Q z k p) atTop + (𝓝 (polynomialCouplingCoefficient (Real.sqrt (1/2)) (Real.sqrt (1/2)) z k p)) := by + have h := coupledCoefficient_tendsto (fun Q => Q) (fun Q => Q) (1/2) + tendsto_id tendsto_id + (by simpa using affineSpin_ratio_tendsto 1 0 1 0 (by norm_num) (by norm_num)) z k p + rw [oscillatorCoefficient_eq_polynomial _ (by norm_num) (by norm_num)] at h + norm_num only [show (1 : ℝ)-1/2 = 1/2 by norm_num] at h + exact h + + + +theorem doublePairCoupling_tendsto (r z k p : ℕ) : + Tendsto (fun Q : ℕ => coupledCoefficient (2*Q-2) (2*Q-2*r) z k p) atTop + (𝓝 (polynomialCouplingCoefficient (Real.sqrt (1/2)) (Real.sqrt (1/2)) z k p)) := by + have h := coupledCoefficient_tendsto (fun Q => 2*Q-2) (fun Q => 2*Q-2*r) (1/2) + (affineSpin_atTop 2 2 (by norm_num)) (affineSpin_atTop 2 (2*r) (by norm_num)) + (by convert affineSpin_ratio_tendsto 2 2 2 (2*r) (by norm_num) (by norm_num) using 1; norm_num) z k p + rw [oscillatorCoefficient_eq_polynomial _ (by norm_num) (by norm_num)] at h + norm_num only [show (1 : ℝ)-1/2 = 1/2 by norm_num] at h + exact h + + + +def sphericalCopyCoefficient (Q D T r p j k : ℕ) : ℝ := + if Odd r ∧ r ≤ D ∧ D ≤ T ∧ r ≤ j+k ∧ p+j+k = T then + Real.sqrt 2 * coupledCoefficient Q Q r (j+k-r) j * + coupledCoefficient (2*Q-2) (2*Q-2*r) (D-r) (T-D) p + else 0 + + + +def planarCopyCoefficient (D T r p j k : ℕ) : ℝ := + if Odd r ∧ r ≤ D ∧ D ≤ T ∧ r ≤ j+k ∧ p+j+k = T then + Real.sqrt 2 * polynomialCouplingCoefficient (Real.sqrt (1/2)) (Real.sqrt (1/2)) r (j+k-r) j * + polynomialCouplingCoefficient (Real.sqrt (1/2)) (Real.sqrt (1/2)) (D-r) (T-D) p + else 0 + + + +theorem sphericalCopyCoefficient_tendsto (D T r p j k : ℕ) : + Tendsto (fun Q => sphericalCopyCoefficient Q D T r p j k) atTop + (𝓝 (planarCopyCoefficient D T r p j k)) := by + unfold sphericalCopyCoefficient planarCopyCoefficient + split_ifs + · exact ((singlePairCoupling_tendsto r (j+k-r) j).const_mul (Real.sqrt 2)).mul + (doublePairCoupling_tendsto r (D-r) (T-D) p) + · exact tendsto_const_nhds + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FourCopies.lean b/lean/OAI/Analysis/LaughlinFock/FourCopies.lean new file mode 100644 index 0000000000000000000000000000000000000000..f3656aef1c79263464f2496357d52dfe00b625a9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FourCopies.lean @@ -0,0 +1,133 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FourLie + +namespace OAI + +/-! Four Copies. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +abbrev FourSpinIndex (Q : ℕ) := (r : CopyLabel Q) × Fin (2*Q-2*r.val.val+1) + + + +abbrev ValidFourCopy (Q : ℕ) := + {b : (D : Fin (2*Q)) × CopyLabel D.val // b.1.val + b.2.val.val ≤ 2*Q} + + +def fourSpinCopyEquiv {Q : ℕ} (_hQ : 1 ≤ Q) : FourSpinIndex Q ≃ ValidFourCopy Q where + toFun b := by + have hr := b.1.val.isLt + have hz := b.2.isLt + have hr0 := b.1.property.pos + refine ⟨⟨⟨b.1.val.val+b.2.val, by omega⟩, + ⟨⟨b.1.val.val, by dsimp; omega⟩, b.1.property⟩⟩, ?_⟩ + dsimp + omega + invFun b := by + have hr := b.val.2.val.isLt + have hd := b.property + have hr0 := b.val.2.property.pos + refine ⟨⟨⟨b.val.2.val.val, by omega⟩, b.val.2.property⟩, + ⟨b.val.1.val-b.val.2.val.val, ?_⟩⟩ + dsimp only + omega + left_inv b := by + apply Sigma.ext + · apply Subtype.ext + apply Fin.ext + rfl + · apply (Fin.heq_ext_iff rfl).mpr + dsimp + omega + right_inv b := by + rcases b with ⟨⟨⟨D,hD⟩,⟨⟨r,hr⟩,hor⟩⟩,h⟩ + have he : r+(D-r)=D := by dsimp only at hr; omega + apply Subtype.ext + dsimp + have hs {d e : Fin (2*Q)} (u : CopyLabel d.val) (v : CopyLabel e.val) + (hde : d=e) (huv : u.val.val=v.val.val) : (⟨d,u⟩ : (D : Fin (2*Q)) × CopyLabel D.val) = ⟨e,v⟩ := by + subst e + congr 1 + exact Subtype.ext (Fin.ext huv) + exact hs _ _ (Fin.ext he) rfl + + +def fourSpinDegree (Q D : ℕ) : ℕ := 4*Q-2-2*D + + + +def fourCopyColumns (Q D : ℕ) (r : CopyLabel D) : + Matrix (FourUncoupled Q) (Fin (fourSpinDegree Q D+1)) ℂ := + if D+r.val.val ≤ 2*Q then + fun b k => (composedCoupledVector Q r.val.val (D-r.val.val) k.val b : ℂ) + else 0 + + +def fourSpinColumns (Q : ℕ) (b : FourSpinIndex Q) : + Matrix (FourUncoupled Q) + (Fin ((2*Q-2)+(2*Q-2*b.1.val.val)-2*b.2.val+1)) ℂ := + fun x k => (composedCoupledVector Q b.1.val.val b.2.val k.val x : ℂ) + + +theorem fourSpinColumns_eq_copy {Q : ℕ} (hQ : 1 ≤ Q) (b : FourSpinIndex Q) : + fourSpinColumns Q b = + (fourCopyColumns Q (fourSpinCopyEquiv hQ b).val.1.val + (fourSpinCopyEquiv hQ b).val.2).submatrix id (Fin.cast (by + have := b.1.val.isLt + have := b.2.isLt + have := b.1.property.pos + dsimp [fourSpinDegree, fourSpinCopyEquiv] + omega)) := by + have hd := (fourSpinCopyEquiv hQ b).property + rw [fourCopyColumns] + erw [ite_eq_left hd] + ext x k + simp only [fourSpinCopyEquiv, Equiv.coe_fn_mk, fourSpinColumns, Nat.add_sub_cancel_left] + rfl + + +def fourCopyWedge (Q D : ℕ) (r : CopyLabel D) : + Matrix (SectorOccupation Q 4) (Fin (fourSpinDegree Q D+1)) ℂ := + wideFourWedgeMatrix Q * fourCopyColumns Q D r + + + +theorem fourCopyWedge_intertwines {Q D : ℕ} (hQ : 1 ≤ Q) (r : CopyLabel D) (s : Fin 3) : + sectorOneBody Q 4 (spinGenerator Q s)*fourCopyWedge Q D r = + fourCopyWedge Q D r*spinGenerator (fourSpinDegree Q D) s := by + by_cases hd : D+r.val.val ≤ 2*Q + · have hr := r.val.isLt + have hr0 := r.property.pos + have he : (2*Q-2)+(2*Q-2*r.val.val)-2*(D-r.val.val) = fourSpinDegree Q D := by + dsimp [fourSpinDegree] + omega + have hw : fourCopyWedge Q D r = + (fourSpinWedge Q r.val.val (D-r.val.val)).submatrix id + (Fin.cast (congrArg (·+1) he.symm)) := by + rw [fourCopyWedge, fourCopyColumns] + erw [ite_eq_left hd] + ext S k + simp only [Matrix.submatrix_apply, id_eq, Fin.val_cast, fourSpinWedge, + composedFourWedgeColumn, Matrix.mulVec, dotProduct] + rfl + rw [hw] + have hi := fourSpinWedge_intertwines hQ (by omega : r.val.val ≤ Q) r.property + (by omega : D-r.val.val ≤ 2*Q-2) (by omega : D-r.val.val ≤ 2*Q-2*r.val.val) s + have hc (n m : ℕ) (he : n=m) + (C : Matrix (SectorOccupation Q 4) (Fin (n+1)) ℂ) + (hi : sectorOneBody Q 4 (spinGenerator Q s)*C = C*spinGenerator n s) : + sectorOneBody Q 4 (spinGenerator Q s)*C.submatrix id (Fin.cast (congrArg (·+1) he.symm)) = + C.submatrix id (Fin.cast (congrArg (·+1) he.symm))*spinGenerator m s := by + subst m + simpa only [Fin.cast_refl, Matrix.submatrix_id_id] using hi + exact hc _ _ he _ hi + · simp [fourCopyWedge, fourCopyColumns, hd] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FourHighest.lean b/lean/OAI/Analysis/LaughlinFock/FourHighest.lean new file mode 100644 index 0000000000000000000000000000000000000000..42eda958f07eaf2b8472084e1caa8ea0d9342d0c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FourHighest.lean @@ -0,0 +1,112 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FourTrace + +namespace OAI + +/-! Four Highest. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + +theorem exteriorLift_mixed_single {ι κ : Type*} [Fintype ι] [Fintype κ] + [DecidableEq ι] [DecidableEq κ] (Q k : ℕ) + (C : Matrix (SectorOccupation Q k) ι ℂ) (D : Matrix (SectorOccupation Q k) κ ℂ) + (p : ι) (q : κ) : + exteriorLift Q k (C*Matrix.single p q (1 : ℂ)*Dᴴ) = + (wedgeAnnihilator Q k (fun A => C A p))ᴴ * + wedgeAnnihilator Q k (fun A => D A q) := by + have h : C*Matrix.single p q (1 : ℂ)*Dᴴ = + Matrix.vecMulVec (fun A => C A p) (star (fun A => D A q)) := by + ext A B + simp [Matrix.mul_apply, Matrix.single_apply, ite_and, Matrix.vecMulVec_apply] + rw [h, exteriorLift_rankOne] + + + +theorem fockAverage_spin_mixed_column {Q k n : ℕ} + (C D : Matrix (SectorOccupation Q k) (Fin (n+1)) ℂ) + (hC : ∀ s, sectorOneBody Q k (spinGenerator Q s)*C = C*spinGenerator n s) + (hD : ∀ s, sectorOneBody Q k (spinGenerator Q s)*D = D*spinGenerator n s) + (p : Fin (n+1)) : + fockAverage Q ((wedgeAnnihilator Q k (fun A => C A p))ᴴ * + wedgeAnnihilator Q k (fun A => D A p)) = + (1/(n+1 : ℂ)) • exteriorLift Q k (C*Dᴴ) := by + rw [← exteriorLift_mixed_single Q k C D p p, + fockAverage_spin_mixed_sandwich C D hC hD, Matrix.trace_single_eq_same] + + + +theorem fourCopyWedge_column {Q D : ℕ} (hr : D ≤ Q) (r : CopyLabel D) + (k : Fin (fourSpinDegree Q D+1)) : + (fun A => fourCopyWedge Q D r A k) = + composedFourWedgeColumn Q r.val.val (D-r.val.val) k.val := by + have hrl := r.val.isLt + unfold fourCopyWedge fourCopyColumns + erw [ite_eq_left (by omega : D+r.val.val ≤ 2*Q)] + rfl + + +theorem fockAverage_highestFour {Q D : ℕ} (hQ : 1 ≤ Q) (hD : D ≤ Q) + (r s : CopyLabel D) : + fockAverage Q ((highestFourAnnihilator Q D r)ᴴ * highestFourAnnihilator Q D s) = + (1/(fourSpinDegree Q D+1 : ℂ)) • fourCopyLift Q D r s := by + have h := fockAverage_spin_mixed_column (fourCopyWedge Q D r) (fourCopyWedge Q D s) + (fourCopyWedge_intertwines hQ r) (fourCopyWedge_intertwines hQ s) + (⟨0, by omega⟩ : Fin (fourSpinDegree Q D+1)) + rw [fourCopyWedge_column hD, fourCopyWedge_column hD, + ← highestFourAnnihilator_eq_wedge hD r, ← highestFourAnnihilator_eq_wedge hD s] at h + exact h + + +theorem exteriorLift_mixed_gram {ι : Type*} [Fintype ι] + (Q k : ℕ) (C D : Matrix (SectorOccupation Q k) ι ℂ) : + exteriorLift Q k (C*Dᴴ) = ∑ p, + (wedgeAnnihilator Q k (fun A => C A p))ᴴ * + wedgeAnnihilator Q k (fun A => D A p) := by + have h : C*Dᴴ = ∑ p, Matrix.vecMulVec (fun A => C A p) (star (fun A => D A p)) := by + ext A B + simp only [Matrix.sum_apply, Matrix.mul_apply, Matrix.conjTranspose_apply, + Matrix.vecMulVec_apply, Pi.star_apply] + rw [h, exteriorLift_sum] + simp only [exteriorLift_rankOne] + + +theorem fourCopyLift_eq_weights {Q D : ℕ} (hD : D ≤ Q) (r s : CopyLabel D) : + fourCopyLift Q D r s = ∑ k : Fin (fourSpinDegree Q D+1), + (composedFourAnnihilator Q r.val.val (D-r.val.val) k.val)ᴴ * + composedFourAnnihilator Q s.val.val (D-s.val.val) k.val := by + rw [fourCopyLift, exteriorLift_mixed_gram] + simp only [fourCopyWedge_column hD, ← composedFourAnnihilator_eq_wedge] + + +def firstFourCopy {D : ℕ} (hD : 1 ≤ D) : CopyLabel D := ⟨⟨1,by omega⟩, by change Odd (1:ℕ); decide⟩ + + + +theorem targetCopy_sum {Q D : ℕ} (hD : 1 ≤ D) (f : CopyLabel D → CopyLabel D → FockMatrix Q) : + (∑ r, ∑ s, targetCopy D r s • f r s) = f (firstFourCopy hD) (firstFourCopy hD) := by + classical + have he (r : CopyLabel D) : r.val.val=1 ↔ r=firstFourCopy hD := by + constructor + · intro h + exact Subtype.ext (Fin.ext h) + · rintro rfl + rfl + simp [targetCopy, he, ite_and, ite_smul] + + + +theorem fourCopyLift_first {Q D : ℕ} (hQ : 1 ≤ Q) (hD : 1 ≤ D) (hd : D ≤ Q) : + fourCopyLift Q D (firstFourCopy hD) (firstFourCopy hD) = + ∑ k ∈ Finset.range (fourSpinDegree Q D+1), + (fourCoupledAnnihilator Q (D-1) k)ᴴ * fourCoupledAnnihilator Q (D-1) k := by + rw [fourCopyLift_eq_weights hd] + simp only [firstFourCopy, composedFourAnnihilator_one hQ] + exact Fin.sum_univ_eq_sum_range (fun k => + (fourCoupledAnnihilator Q (D-1) k)ᴴ * fourCoupledAnnihilator Q (D-1) k) _ + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FourLie.lean b/lean/OAI/Analysis/LaughlinFock/FourLie.lean new file mode 100644 index 0000000000000000000000000000000000000000..53db18b3098a8311db3de04cef64b71291f2a729 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FourLie.lean @@ -0,0 +1,141 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PairLie + +namespace OAI + +/-! Four Lie. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + +def oddPairSpinMatrix (Q r : ℕ) : + Matrix (SectorOccupation Q 2) (Fin (2*Q-2*r+1)) ℂ := + fun S k => wedgeCoupledCoefficient Q r k.val ((increasingPairEquiv Q).symm S) + +theorem oddPairSpinMatrix_contraction (Q r : ℕ) (k : Fin (2*Q-2*r+1)) : + wedgeAnnihilator Q 2 (fun S => oddPairSpinMatrix Q r S k) = + (Real.sqrt 2 : ℂ) • coefficientPairAnnihilator Q + (fun i j => (coupledVector Q Q r k.val i.val j.val : ℂ)) := by + classical + rw [coefficientPair_basis_expansion, Finset.smul_sum] + unfold wedgeAnnihilator + rw [← (increasingPairEquiv Q).sum_comp] + apply Finset.sum_congr rfl + intro ij _ + have hi : (increasingPairEquiv Q).symm (increasingPairSector Q ij) = ij := + (increasingPairEquiv Q).symm_apply_apply ij + simp only [oddPairSpinMatrix, increasingPairEquiv_apply, hi, wedgeCoupledCoefficient, + Complex.ofReal_mul, star_mul, Complex.star_def, Complex.conj_ofReal, smul_smul, mul_comm] + + + +theorem tensorWedge_oddPairSpinMatrix {Q r : ℕ} (hr : r ≤ Q) (hor : Odd r) : + wedgeProductMatrix Q 1 1 (oneParticleMatrix Q) (oneParticleMatrix Q) * + coupledSpinMatrix Q Q r = + (Real.sqrt 2 : ℂ) • + (oddPairSpinMatrix Q r).submatrix id (Fin.cast (by omega)) := by + ext S k + have hv : wedgeAnnihilator Q 2 + (wedgeProductMatrix Q 1 1 (oneParticleMatrix Q) (oneParticleMatrix Q) *ᵥ + (fun ij => coupledSpinMatrix Q Q r ij k)) = + wedgeAnnihilator Q 2 ((Real.sqrt 2 : ℂ) • + fun T => oddPairSpinMatrix Q r T (Fin.cast (by omega) k)) := by + rw [tensorWedge_contraction] + · rw [wedgeAnnihilator_smul] + rw [oddPairSpinMatrix_contraction Q r (Fin.cast (by omega) k)] + rw [smul_smul] + simp only [Complex.star_def, Complex.conj_ofReal, coupledSpinMatrix, Fin.val_cast] + have hs : (Real.sqrt 2 : ℂ) * (Real.sqrt 2 : ℂ) = 2 := by + exact_mod_cast (Real.mul_self_sqrt (by norm_num : (0:ℝ) ≤ 2)) + rw [hs] + · intro i j + dsimp [coupledSpinMatrix] + rw [coupledVector_antisymm hr hor] + simp + exact congrFun (wedgeAnnihilator_injective Q 2 hv) S + + +theorem oddPairSpinMatrix_intertwines {Q r : ℕ} (hr : r ≤ Q) (hor : Odd r) (s : Fin 3) : + sectorOneBody Q 2 (spinGenerator Q s) * oddPairSpinMatrix Q r = + oddPairSpinMatrix Q r * spinGenerator (2*Q-2*r) s := by + have he : sectorOneBody Q 2 (spinGenerator Q s) * + (wedgeProductMatrix Q 1 1 (oneParticleMatrix Q) (oneParticleMatrix Q) * coupledSpinMatrix Q Q r) = + (wedgeProductMatrix Q 1 1 (oneParticleMatrix Q) (oneParticleMatrix Q) * coupledSpinMatrix Q Q r) * + spinGenerator (Q+Q-2*r) s := by + rw [← Matrix.mul_assoc, tensorWedge_intertwines, Matrix.mul_assoc, + coupledSpinMatrix_intertwines hr hr, Matrix.mul_assoc] + rw [tensorWedge_oddPairSpinMatrix hr hor] at he + simp only [Matrix.mul_smul, Matrix.smul_mul] at he + have hn : (Real.sqrt 2 : ℂ) ≠ 0 := by exact_mod_cast (show Real.sqrt 2 ≠ 0 by positivity) + have hf := smul_right_injective _ hn he + have hc (n : ℕ) (e : n = 2*Q-2*r) + (hc : sectorOneBody Q 2 (spinGenerator Q s) * + (oddPairSpinMatrix Q r).submatrix id (Fin.cast (congrArg (·+1) e)) = + (oddPairSpinMatrix Q r).submatrix id (Fin.cast (congrArg (·+1) e)) * spinGenerator n s) : + sectorOneBody Q 2 (spinGenerator Q s) * oddPairSpinMatrix Q r = + oddPairSpinMatrix Q r * spinGenerator (2*Q-2*r) s := by + subst n + simpa only [Fin.cast_refl, Matrix.submatrix_id_id] using hc + exact hc _ (by omega) hf + + +def fourSpinWedge (Q r z : ℕ) : + Matrix (SectorOccupation Q 4) (Fin ((2*Q-2)+(2*Q-2*r)-2*z+1)) ℂ := + fun S k => composedFourWedgeColumn Q r z k.val S + + +theorem oddPairSpinMatrix_contraction_increasing (Q r : ℕ) (k : Fin (2*Q-2*r+1)) : + wedgeAnnihilator Q 2 (fun S => oddPairSpinMatrix Q r S k) = + ∑ ij : IncreasingPair Q, (wedgeCoupledCoefficient Q r k.val ij : ℂ) • + (annihilator Q ij.val.2 * annihilator Q ij.val.1) := by + rw [oddPairSpinMatrix_contraction, coefficientPair_basis_expansion, Finset.smul_sum] + apply Finset.sum_congr rfl + intro ij _ + rw [show (increasingPairSector Q ij).val = {ij.val.1,ij.val.2} from rfl, + basisAnnihilator_pair _ _ ij.property, smul_smul] + simp only [wedgeCoupledCoefficient, Complex.ofReal_mul] + + + +theorem fourSpinWedge_eq_tensor (Q r z : ℕ) : + fourSpinWedge Q r z = + wedgeProductMatrix Q 2 2 (pairSpinMatrix Q) (oddPairSpinMatrix Q r) * + coupledSpinMatrix (2*Q-2) (2*Q-2*r) z := by + ext S k + have hv : wedgeAnnihilator Q 4 (composedFourWedgeColumn Q r z k.val) = + wedgeAnnihilator Q 4 + (wedgeProductMatrix Q 2 2 (pairSpinMatrix Q) (oddPairSpinMatrix Q r) *ᵥ + fun b => coupledSpinMatrix (2*Q-2) (2*Q-2*r) z b k) := by + rw [← composedFourAnnihilator_eq_wedge, wedgeAnnihilator_mulVec] + have hh (b : Fin (2*Q-2+1) × Fin (2*Q-2*r+1)) := + wedgeProductMatrix_contraction Q 2 2 (pairSpinMatrix Q) (oddPairSpinMatrix Q r) b + have ho (a : Fin (2*Q-2*r+1)) := oddPairSpinMatrix_contraction_increasing Q r a + simp only [hh, ho, + pairSpinMatrix, pairVector, + wedgeAnnihilator_annihilatorVector Q 2 _ (pairAnnihilator_mem Q _), + coupledSpinMatrix, Complex.star_def, Complex.conj_ofReal, + composedFourAnnihilator, composedCoupledVector, Fintype.sum_prod_type, + Complex.ofReal_sum, Finset.sum_smul, Complex.ofReal_mul, + Matrix.sum_mul, Matrix.smul_mul, Finset.smul_sum, smul_smul] + apply Finset.sum_congr rfl + intro p _ + rw [Finset.sum_comm] + exact congrFun (wedgeAnnihilator_injective Q 4 hv) S + + + +theorem fourSpinWedge_intertwines {Q r z : ℕ} (hQ : 1 ≤ Q) + (hr : r ≤ Q) (hor : Odd r) (hz₁ : z ≤ 2*Q-2) (hz₂ : z ≤ 2*Q-2*r) (s : Fin 3) : + sectorOneBody Q 4 (spinGenerator Q s) * fourSpinWedge Q r z = + fourSpinWedge Q r z * spinGenerator ((2*Q-2)+(2*Q-2*r)-2*z) s := by + rw [fourSpinWedge_eq_tensor] + rw [← Matrix.mul_assoc, + wedgeProductMatrix_intertwines Q 2 2 _ (spinGenerator_skew Q s) _ _ _ _ + (pairSpinMatrix_intertwines hQ s) (oddPairSpinMatrix_intertwines hr hor s), + Matrix.mul_assoc, coupledSpinMatrix_intertwines hz₁ hz₂, Matrix.mul_assoc] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FourRetained.lean b/lean/OAI/Analysis/LaughlinFock/FourRetained.lean new file mode 100644 index 0000000000000000000000000000000000000000..356b6c44a82decd322a55e0e90334170117a7381 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FourRetained.lean @@ -0,0 +1,151 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.AllowanceOrbit +import OAI.Analysis.LaughlinFock.FourHighest + +namespace OAI + +/-! Four Retained. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +theorem retainedFourTarget_copy_sum {Q : ℕ} (hQ : 24 ≤ Q) : + exteriorLift Q 4 (retainedFourTarget Q 23) = + ∑ D ∈ Finset.Icc 1 23, ∑ r : CopyLabel D, ∑ s : CopyLabel D, + targetCopy D r s • fourCopyLift Q D r s := by + classical + let f (z : ℕ) := ∑ k ∈ Finset.range ((2*Q-2)+(2*Q-2)-2*z+1), + (fourCoupledAnnihilator Q z k)ᴴ * fourCoupledAnnihilator Q z k + have h1 : exteriorLift Q 4 (retainedFourTarget Q 23) = + ∑ z ∈ Finset.range (2*Q-2+1), if z+1 ≤ 23 then f z else 0 := by + rw [retainedFourTarget_lift] + change (∑ c : (z : Fin (min (2*Q-2) (2*Q-2)+1)) × + Fin ((2*Q-2)+(2*Q-2)-2*z.val+1), if c.1.val+1 ≤ 23 then + (fourCoupledAnnihilator Q c.1.val c.2.val)ᴴ * + fourCoupledAnnihilator Q c.1.val c.2.val else 0) = _ + rw [Fintype.sum_sigma, min_self] + rw [← Fin.sum_univ_eq_sum_range (fun z => if z+1 ≤ 23 then f z else 0)] + apply Finset.sum_congr rfl + intro z _ + by_cases hz : z.val+1 ≤ 23 + · simp only [hz, ite_true] + exact Fin.sum_univ_eq_sum_range (fun k => + (fourCoupledAnnihilator Q z.val k)ᴴ * fourCoupledAnnihilator Q z.val k) _ + · simp only [hz, ite_false, Finset.sum_const_zero] + rw [h1, ← Finset.sum_filter] + have he : (Finset.range (2*Q-2+1)).filter (fun z => z+1 ≤ 23) = Finset.range 23 := by + ext z + simp only [Finset.mem_filter, Finset.mem_range] + omega + rw [he] + apply Finset.sum_bij (fun z _ => z+1) + · intro z hz + have := Finset.mem_range.mp hz + simp only [Finset.mem_Icc] + omega + · intro z hz w hw hzw + omega + · intro D hD + have hD' := Finset.mem_Icc.mp hD + refine ⟨D-1, Finset.mem_range.mpr (by omega), by omega⟩ + · intro z hz + have hz' := Finset.mem_range.mp hz + rw [targetCopy_sum (by omega : 1 ≤ z+1), + fourCopyLift_first (by omega : 1 ≤ Q) (by omega : 1 ≤ z+1) (by omega : z+1 ≤ Q)] + have hd : (2*Q-2)+(2*Q-2)-2*z+1 = fourSpinDegree Q (z+1)+1 := by + dsimp [fourSpinDegree] + omega + simp only [Nat.add_sub_cancel, f, hd] + + + +theorem averagedRowsFour_copy_sum {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) {Q : ℕ} (hQ : 24 ≤ Q) : + averagedRowsFour (by omega : 8 ≤ Q) rows = + ∑ D ∈ Finset.Icc 1 23, ∑ r : CopyLabel D, ∑ s : CopyLabel D, + (((2*Q-1 : ℕ) : ℂ) * + ((∑ i, rowFourTrace Q D (rows i).t.val (rows i).alpha r s : ℝ) : ℂ) / + (fourSpinDegree Q D+1 : ℂ)) • fourCopyLift Q D r s := by + rw [averagedRowsFour, map_sum] + simp_rw [fockAverage_rowFourBody hQ] + simp only [Finset.smul_sum, smul_smul, ← mul_div_assoc] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro D hD + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro r _ + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro s _ + rw [← Finset.sum_smul] + simp only [← Finset.sum_div, ← Finset.mul_sum, ← Complex.ofReal_sum] + + +theorem fourCopyAllowance_copy_sum {Q : ℕ} (hQ : 24 ≤ Q) : + fourCopyAllowance Q = ∑ D ∈ Finset.Icc 1 23, ∑ r : CopyLabel D, ∑ s : CopyLabel D, + ((((2*Q-1 : ℕ) : ℂ) * (1 : Matrix (CopyLabel D) (CopyLabel D) ℂ) r s) / + (fourSpinDegree Q D+1 : ℂ)) • fourCopyLift Q D r s := by + classical + unfold fourCopyAllowance + rw [Finset.smul_sum] + apply Finset.sum_congr rfl + intro D hD + have hd : D ≤ Q := by have := (Finset.mem_Icc.mp hD).2; omega + rw [map_sum, Finset.smul_sum] + simp_rw [fockAverage_highestFour (by omega : 1 ≤ Q) hd] + apply Finset.sum_congr rfl + intro r _ + simp [Matrix.one_apply, ite_smul, smul_smul, div_eq_mul_inv] + + + +theorem fourSpinRatio_common_dimensions {Q D : ℕ} (hQ : 1 ≤ Q) (hD : D ≤ Q) : + (fourSpinRatio Q D : ℂ) = (fourSpinDegree Q D+1 : ℂ) / ((2*Q-1 : ℕ) : ℂ) := by + rw [fourSpinRatio_eq_dimensions hQ hD, Complex.ofReal_div, + Complex.ofReal_natCast, Complex.ofReal_natCast] + have hd : 4*Q-1-2*D = fourSpinDegree Q D+1 := by + dsimp [fourSpinDegree] + omega + rw [hd, Nat.cast_add_one] + + + +theorem averagedFourComparison_eq {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) (ε : ℝ) {Q : ℕ} (hQ : 24 ≤ Q) : + averagedFourComparison rows ε Q = + exteriorLift Q 4 (retainedFourTarget Q 23) - + averagedRowsFour (by omega : 8 ≤ Q) rows + ε • fourCopyAllowance Q := by + classical + rw [retainedFourTarget_copy_sum hQ, averagedRowsFour_copy_sum rows hQ, + fourCopyAllowance_copy_sum hQ, averagedFourComparison] + simp only [Finset.smul_sum, ← Finset.sum_sub_distrib, ← Finset.sum_add_distrib] + apply Finset.sum_congr rfl + intro D hD + have hd : D ≤ Q := by have := (Finset.mem_Icc.mp hD).2; omega + rw [map_sum, Finset.smul_sum] + apply Finset.sum_congr rfl + intro r _ + rw [map_sum, Finset.smul_sum] + apply Finset.sum_congr rfl + intro s _ + rw [map_smul, fockAverage_highestFour (by omega : 1 ≤ Q) hd] + rw [RCLike.real_smul_eq_coe_smul (K:=ℂ) ε] + simp only [fourComparison, Matrix.add_apply, Matrix.sub_apply, Matrix.smul_apply, + Matrix.of_apply, smul_eq_mul, smul_smul, ← sub_smul, ← add_smul] + rw [fourSpinRatio_common_dimensions (by omega) hd] + congr 1 + have hn : ((2*Q-1 : ℕ) : ℂ) ≠ 0 := by exact_mod_cast (show 2*Q-1 ≠ 0 by omega) + have hm : (fourSpinDegree Q D+1 : ℂ) ≠ 0 := by + rw [← Nat.cast_add_one] + exact_mod_cast (show fourSpinDegree Q D+1 ≠ 0 by omega) + simp only [Matrix.one_apply] + simp only [RCLike.ofReal_eq_complex_ofReal] + split_ifs <;> field_simp + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FourTrace.lean b/lean/OAI/Analysis/LaughlinFock/FourTrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..72c153fa297c0f6bff922c1c0dbd696945b426d1 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FourTrace.lean @@ -0,0 +1,121 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.CopyAverage +import OAI.Analysis.LaughlinFock.FourTraces + +namespace OAI + +/-! Four Trace. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + +theorem trace_column_bilinear {ι κ : Type*} [Fintype ι] [Fintype κ] + (C D : Matrix ι κ ℂ) (M : Matrix ι ι ℂ) : + (Cᴴ*M*D).trace = ∑ k, star (fun b => C b k) ⬝ᵥ (M *ᵥ fun b => D b k) := by + rw [Matrix.mul_assoc] + rfl + + + +theorem fourCopy_row_trace {Q D t : ℕ} (hQ : 24 ≤ Q) (hD : D ≤ 23) + (a : RowEntry t → ℝ) (r s : CopyLabel D) : + ((fourCopyColumns Q D r)ᴴ * sourceRowFourKernel (by omega : 8 ≤ Q) a * + fourCopyColumns Q D s).trace = (rowFourTrace Q D t a r s : ℂ) := by + have hr := r.val.isLt + have hs := s.val.isLt + rw [trace_column_bilinear] + erw [fourCopyColumns, ite_eq_left (by omega : D+r.val.val ≤ 2*Q), + fourCopyColumns, ite_eq_left (by omega : D+s.val.val ≤ 2*Q)] + have hd : fourSpinDegree Q D+1 = 4*Q-1-2*D := by + dsimp [fourSpinDegree] + omega + convert sourceRowFourKernel_copyTrace hQ hD a r s using 1 + rw [hd] + + + +theorem fourCopy_row_trace_above_support {Q D t : ℕ} (hQ : 24 ≤ Q) (hD : 23 < D) + (a : RowEntry t → ℝ) (r s : CopyLabel D) : + ((fourCopyColumns Q D r)ᴴ * sourceRowFourKernel (by omega : 8 ≤ Q) a * + fourCopyColumns Q D s).trace = 0 := by + by_cases hr : D+r.val.val ≤ 2*Q + · by_cases hs : D+s.val.val ≤ 2*Q + · rw [trace_column_bilinear] + erw [fourCopyColumns, ite_eq_left hr, fourCopyColumns, ite_eq_left hs] + apply Finset.sum_eq_zero + intro k _ + have hrl : r.val.val ≤ D := Nat.le_of_lt_succ r.val.isLt + have hsl : s.val.val ≤ D := Nat.le_of_lt_succ s.val.isLt + have he := rowFourPrewedge_coupled_bilinear hrl hsl (by omega : D ≤ D+k.val) + (by omega : r.val.val ≤ Q) (by omega : s.val.val ≤ Q) r.property s.property + (sourceRowFourP (by omega : 8 ≤ Q)) (sourceRowI (by omega : 8 ≤ Q)) + (sourceRowJ (by omega : 8 ≤ Q)) a + simp only [Nat.add_sub_cancel_left] at he + rw [sourceRowFourKernel, he] + have hz : (∑ b : RowEntry t, ∑ c : RowEntry t, a b*a c * + sphericalCopyCoefficient Q D (D+k.val) r.val.val (rowP b) (rowJ b) (rowI c) * + sphericalCopyCoefficient Q D (D+k.val) s.val.val (rowP c) (rowJ c) (rowI b)) = 0 := by + apply Finset.sum_eq_zero + intro b _ + apply Finset.sum_eq_zero + intro c _ + have hl := rowFourLevel_le b c + have hn : rowP b+rowJ b+rowI c ≠ D+k.val := by + dsimp [rowFourLevel] at hl + omega + rw [sphericalCopyCoefficient_level _ _ _ _ _ _ _ hn, mul_zero, zero_mul] + simp only [sourceRowFourP, sourceRowI, sourceRowJ, hz, neg_zero, Complex.ofReal_zero] + · simp [fourCopyColumns, hs] + · simp [fourCopyColumns, hr] + + + +def fourCopyLift (Q D : ℕ) (r s : CopyLabel D) : FockMatrix Q := + exteriorLift Q 4 (fourCopyWedge Q D r*(fourCopyWedge Q D s)ᴴ) + + + +theorem fockAverage_rowFourBody {Q t : ℕ} (hQ : 24 ≤ Q) (a : RowEntry t → ℝ) : + fockAverage Q (rowFourBody Q rowP (sourceRowI (by omega : 8 ≤ Q)) + (sourceRowJ (by omega : 8 ≤ Q)) a) = + ∑ D ∈ Finset.Icc 1 23, ∑ r : CopyLabel D, ∑ s : CopyLabel D, + ((rowFourTrace Q D t a r s : ℂ)/(fourSpinDegree Q D+1 : ℂ)) • + fourCopyLift Q D r s := by + have hs (c : ℂ) (M : Matrix (SectorOccupation Q 4) (SectorOccupation Q 4) ℂ) : + exteriorLift Q 4 (c • M) = c • exteriorLift Q 4 M := (exteriorLiftLinear Q 4).map_smul c M + rw [← sourceRowFourKernel_lift (by omega : 8 ≤ Q) a, fockAverage_exteriorLift, + sectorAverage_four_kernel (by omega)] + simp only [exteriorLift_sum, hs] + let f (D : ℕ) := ∑ r : CopyLabel D, ∑ s : CopyLabel D, + (((fourCopyColumns Q D r)ᴴ * sourceRowFourKernel (by omega : 8 ≤ Q) a * + fourCopyColumns Q D s).trace / (fourSpinDegree Q D+1 : ℂ)) • fourCopyLift Q D r s + change (∑ D : Fin (2*Q), f D.val) = _ + rw [Fin.sum_univ_eq_sum_range f (2*Q)] + calc + _ = ∑ D ∈ Finset.Icc 1 23, f D := by + symm + apply Finset.sum_subset + · intro D hD + simp only [Finset.mem_Icc] at hD + simp only [Finset.mem_range] + omega + · intro D hDr hD + by_cases hz : D=0 + · subst D + have he : IsEmpty (CopyLabel 0) := ⟨fun r => by have := r.val.isLt; have := r.property.pos; omega⟩ + let := he + simp [f] + · have hd : 23 < D := by simp only [Finset.mem_Icc] at hD; omega + dsimp [f] + simp only [fourCopy_row_trace_above_support hQ hd, zero_div, zero_smul, Finset.sum_const_zero] + _ = _ := by + apply Finset.sum_congr rfl + intro D hD + dsimp [f] + simp only [fourCopy_row_trace hQ (Finset.mem_Icc.mp hD).2] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/FourTraces.lean b/lean/OAI/Analysis/LaughlinFock/FourTraces.lean new file mode 100644 index 0000000000000000000000000000000000000000..2600a4c44c670c10c22ae28a38b8c436322edc09 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/FourTraces.lean @@ -0,0 +1,305 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.CopyVectors +import OAI.Analysis.LaughlinFock.ThreeTraces + +namespace OAI + +/-! Four Traces. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder + + + +theorem composedCoupledVector_eq_sphericalCopy_all {Q D T r : ℕ} + (hr : r ≤ D) (hD : D ≤ T) (hrQ : r ≤ Q) (hor : Odd r) + (b : FourUncoupled Q) : + composedCoupledVector Q r (D-r) (T-D) b = + sphericalCopyCoefficient Q D T r b.1.val b.2.val.1.val b.2.val.2.val := by + classical + let p := b.1.val + let j := b.2.val.1.val + let k := b.2.val.2.val + change (∑ a : Fin (2*Q-2*r+1), + coupledVector (2*Q-2) (2*Q-2*r) (D-r) (T-D) p a.val * + (Real.sqrt 2 * coupledVector Q Q r a.val j k)) = + sphericalCopyCoefficient Q D T r p j k + by_cases hjk : r ≤ j+k + · by_cases ht : p+j+k=T + · by_cases ha : j+k-r ≤ 2*Q-2*r + · let a : Fin (2*Q-2*r+1) := ⟨j+k-r, by omega⟩ + rw [Finset.sum_eq_single a] + · rw [sphericalCopyCoefficient, ite_eq_left ⟨hor, hr, hD, hjk, ht⟩] + rw [coupledVector, ite_eq_left (show p+a.val = D-r+(T-D) by dsimp [a]; omega), + coupledVector, ite_eq_left (show j+k = r+a.val by dsimp [a]; omega)] + dsimp [a] + ring + · intro a' _ hne + have he : j+k ≠ r+a'.val := by + intro he + apply hne + apply Fin.ext + dsimp [a] + omega + simp only [coupledVector, ite_eq_right he, mul_zero] + · simp + · have hc : coupledCoefficient Q Q r (j+k-r) j = 0 := by + have h := congrFun (congrFun (coupledVector_outside_ladder + (by omega : 2*r ≤ Q+Q) (by omega : Q+Q-2*r < j+k-r)) j) k + dsimp only [coupledVector] at h + rw [ite_eq_left (by omega : j+k = r+(j+k-r))] at h + exact h + rw [sphericalCopyCoefficient, ite_eq_left ⟨hor, hr, hD, hjk, ht⟩, hc, mul_zero, zero_mul] + apply Finset.sum_eq_zero + intro a _ + have hn : j+k ≠ r+a.val := by have := a.isLt; omega + simp only [coupledVector, ite_eq_right hn, mul_zero] + · rw [sphericalCopyCoefficient, ite_eq_right (by tauto)] + apply Finset.sum_eq_zero + intro a _ + by_cases he : j+k = r+a.val + · have he' : p+a.val ≠ D-r+(T-D) := by omega + simp only [coupledVector, ite_eq_right he', zero_mul] + · simp only [coupledVector, ite_eq_right he, mul_zero] + · rw [sphericalCopyCoefficient, ite_eq_right (by tauto)] + apply Finset.sum_eq_zero + intro a _ + have he : j+k ≠ r+a.val := by omega + simp only [coupledVector, ite_eq_right he, mul_zero] + + + +theorem sphericalCopyCoefficient_antisymm {Q r : ℕ} (hrQ : r ≤ Q) + (D T p j k : ℕ) : + sphericalCopyCoefficient Q D T r p k j = -sphericalCopyCoefficient Q D T r p j k := by + by_cases h : Odd r ∧ r ≤ D ∧ D ≤ T ∧ r ≤ j+k ∧ p+j+k=T + · have hs : Odd r ∧ r ≤ D ∧ D ≤ T ∧ r ≤ k+j ∧ p+k+j=T := by + simpa only [Nat.add_comm k j, Nat.add_right_comm p k j] using h + rw [sphericalCopyCoefficient, ite_eq_left hs, sphericalCopyCoefficient, ite_eq_left h, + Nat.add_comm k j] + have hc : coupledCoefficient Q Q r (j+k-r) k = + -coupledCoefficient Q Q r (j+k-r) j := by + have hv := coupledVector_antisymm hrQ h.1 (j+k-r) j k + dsimp only [coupledVector] at hv + rw [ite_eq_left (by omega : j+k=r+(j+k-r)), + ite_eq_left (by omega : k+j=r+(j+k-r))] at hv + exact hv + rw [hc] + ring + · have hs : ¬ (Odd r ∧ r ≤ D ∧ D ≤ T ∧ r ≤ k+j ∧ p+k+j=T) := by + simpa only [Nat.add_comm k j, Nat.add_right_comm p k j] using h + simp only [sphericalCopyCoefficient, ite_eq_right h, ite_eq_right hs, neg_zero] + +theorem sphericalCopyCoefficient_diagonal {Q r : ℕ} (hrQ : r ≤ Q) + (D T p j : ℕ) : sphericalCopyCoefficient Q D T r p j j = 0 := by + have h := sphericalCopyCoefficient_antisymm hrQ D T p j j + linarith + + + +def orderedFourColumn (Q : ℕ) (p : Fin (2*Q-2+1)) (j k : Orbital Q) : FourUncoupled Q → ℂ := + if h : j < k then Pi.single (p,⟨(j,k),h⟩) 1 + else if h : k < j then Pi.single (p,⟨(k,j),h⟩) (-1) else 0 + + +theorem orderedFourColumn_wedgeAnnihilator (Q : ℕ) (p : Fin (2*Q-2+1)) (j k : Orbital Q) : + wedgeAnnihilator Q 4 (wideFourWedgeMatrix Q *ᵥ orderedFourColumn Q p j k) = + annihilator Q k * annihilator Q j * pairAnnihilator Q p.val := by + classical + rw [wedgeAnnihilator_mulVec] + simp only [wideFourWedgeMatrix_annihilator_column] + unfold orderedFourColumn + split_ifs with h hk + · simp [Pi.single_apply, ite_smul, apply_ite] + · simp only [Pi.single_apply, apply_ite, star_neg, star_one, star_zero, + ite_smul, neg_one_smul, zero_smul] + simp only [Finset.sum_ite_eq', Finset.mem_univ, ite_true] + rw [annihilator_swap Q j k, neg_mul, neg_neg] + · have he : j=k := le_antisymm (le_of_not_gt hk) (le_of_not_gt h) + subst k + simp [annihilator_square] + + + +theorem composed_orderedFourColumn_inner {Q D T r : ℕ} + (hr : r ≤ D) (hD : D ≤ T) (hrQ : r ≤ Q) (hor : Odd r) + (p : Fin (2*Q-2+1)) (j k : Orbital Q) : + star (fun b => (composedCoupledVector Q r (D-r) (T-D) b : ℂ)) ⬝ᵥ + orderedFourColumn Q p j k = + (sphericalCopyCoefficient Q D T r p.val j.val k.val : ℂ) := by + classical + unfold orderedFourColumn + split_ifs with h hk + · rw [dotProduct_single] + simp only [Pi.star_apply, Complex.star_def, Complex.conj_ofReal, mul_one, + composedCoupledVector_eq_sphericalCopy_all hr hD hrQ hor] + · rw [dotProduct_single] + change star (composedCoupledVector Q r (D-r) (T-D) (p,⟨(k,j),hk⟩) : ℂ) * (-1) = _ + rw [composedCoupledVector_eq_sphericalCopy_all hr hD hrQ hor] + dsimp only + rw [sphericalCopyCoefficient_antisymm hrQ D T p.val j.val k.val] + simp + · have he : j=k := le_antisymm (le_of_not_gt hk) (le_of_not_gt h) + subst k + simp [sphericalCopyCoefficient_diagonal hrQ] + + + +def rowFourPrewedge {β : Type*} [Fintype β] (Q : ℕ) + (p : β → Fin (2*Q-2+1)) (i j : β → Orbital Q) (a : β → ℝ) : + Matrix (FourUncoupled Q) (FourUncoupled Q) ℂ := + -(∑ b, ∑ c, (a b*a c : ℂ) • Matrix.vecMulVec + (orderedFourColumn Q (p b) (j b) (i c)) (star (orderedFourColumn Q (p c) (j c) (i b)))) + + + +theorem exteriorLift_outer_congruence {ι : Type*} [Fintype ι] + (Q k : ℕ) (W : Matrix (SectorOccupation Q k) ι ℂ) (x y : ι → ℂ) : + exteriorLift Q k (W * Matrix.vecMulVec x (star y) * Wᴴ) = + (wedgeAnnihilator Q k (W *ᵥ x))ᴴ * wedgeAnnihilator Q k (W *ᵥ y) := by + rw [Matrix.mul_vecMulVec, Matrix.vecMulVec_mul, ← Matrix.star_mulVec, exteriorLift_rankOne] + + + +theorem rowFourPrewedge_lift {β : Type*} [Fintype β] (Q : ℕ) + (p : β → Fin (2*Q-2+1)) (i j : β → Orbital Q) (a : β → ℝ) : + exteriorLift Q 4 (wideFourWedgeMatrix Q * rowFourPrewedge Q p i j a * + (wideFourWedgeMatrix Q)ᴴ) = rowFourBody Q (fun b => (p b).val) i j a := by + classical + have hs (c : ℂ) (M : Matrix (SectorOccupation Q 4) (SectorOccupation Q 4) ℂ) : + exteriorLift Q 4 (c • M) = c • exteriorLift Q 4 M := + (exteriorLiftLinear Q 4).map_smul c M + have hn (M : Matrix (SectorOccupation Q 4) (SectorOccupation Q 4) ℂ) : + exteriorLift Q 4 (-M) = -exteriorLift Q 4 M := (exteriorLiftLinear Q 4).map_neg M + simp only [rowFourPrewedge, Matrix.mul_neg, Matrix.neg_mul, Matrix.mul_sum, + Matrix.sum_mul, Matrix.mul_smul, Matrix.smul_mul, hn, exteriorLift_sum, hs, + exteriorLift_outer_congruence, orderedFourColumn_wedgeAnnihilator] + unfold rowFourBody + congr 1 + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro c _ + ext A B + simp [Matrix.smul_apply, Complex.real_smul, Matrix.mul_assoc] + + + +theorem outer_bilinear {ι : Type*} [Fintype ι] (u v x y : ι → ℂ) : + star x ⬝ᵥ (Matrix.vecMulVec u (star v) *ᵥ y) = + (star x ⬝ᵥ u) * star (star y ⬝ᵥ v) := by + rw [Matrix.vecMulVec_mulVec, dotProduct_smul, op_smul_eq_mul, Matrix.star_dotProduct v y] + + + +theorem rowFourPrewedge_coupled_bilinear {β : Type*} [Fintype β] + {Q D T r s : ℕ} (hr : r ≤ D) (hs : s ≤ D) (hD : D ≤ T) + (hrQ : r ≤ Q) (hsQ : s ≤ Q) (hor : Odd r) (hos : Odd s) + (p : β → Fin (2*Q-2+1)) (i j : β → Orbital Q) (a : β → ℝ) : + star (fun b => (composedCoupledVector Q r (D-r) (T-D) b : ℂ)) ⬝ᵥ + (rowFourPrewedge Q p i j a *ᵥ + fun b => (composedCoupledVector Q s (D-s) (T-D) b : ℂ)) = + (-(∑ b, ∑ c, a b*a c * + sphericalCopyCoefficient Q D T r (p b).val (j b).val (i c).val * + sphericalCopyCoefficient Q D T s (p c).val (j c).val (i b).val) : ℝ) := by + classical + simp only [rowFourPrewedge, Matrix.neg_mulVec, dotProduct_neg, + Matrix.sum_mulVec, dotProduct_sum, Matrix.smul_mulVec, dotProduct_smul, + outer_bilinear, composed_orderedFourColumn_inner hr hD hrQ hor, + composed_orderedFourColumn_inner hs hD hsQ hos, Complex.star_def, Complex.conj_ofReal, + Complex.ofReal_neg, Complex.ofReal_sum, Complex.ofReal_mul, smul_eq_mul, mul_assoc] + + +def sourceRowFourP {Q t : ℕ} (hQ : 8 ≤ Q) (b : RowEntry t) : Fin (2*Q-2+1) := + ⟨rowP b, by have := (rowEntry_bounds b).1; omega⟩ + + +def sourceRowFourKernel {Q t : ℕ} (hQ : 8 ≤ Q) (a : RowEntry t → ℝ) : + Matrix (FourUncoupled Q) (FourUncoupled Q) ℂ := + rowFourPrewedge Q (sourceRowFourP hQ) (sourceRowI hQ) (sourceRowJ hQ) a + +theorem sourceRowFourKernel_lift {Q t : ℕ} (hQ : 8 ≤ Q) (a : RowEntry t → ℝ) : + exteriorLift Q 4 (wideFourWedgeMatrix Q * sourceRowFourKernel hQ a * + (wideFourWedgeMatrix Q)ᴴ) = + rowFourBody Q rowP (sourceRowI hQ) (sourceRowJ hQ) a := + rowFourPrewedge_lift Q (sourceRowFourP hQ) (sourceRowI hQ) (sourceRowJ hQ) a + + + +theorem sphericalCopyCoefficient_level (Q D T r p j k : ℕ) (h : p+j+k ≠ T) : + sphericalCopyCoefficient Q D T r p j k = 0 := by + simp [sphericalCopyCoefficient, h] + + + +theorem rowFour_copyWeight_sum {Q D t : ℕ} (hQ : 24 ≤ Q) (hD : D ≤ 23) + (r s : CopyLabel D) (b c : RowEntry t) : + (∑ k : Fin (4*Q-1-2*D), + sphericalCopyCoefficient Q D (D+k.val) r.val.val (rowP b) (rowJ b) (rowI c) * + sphericalCopyCoefficient Q D (D+k.val) s.val.val (rowP c) (rowJ c) (rowI b)) = + sphericalCopyCoefficient Q D (rowFourLevel b c) r.val.val (rowP b) (rowJ b) (rowI c) * + sphericalCopyCoefficient Q D (rowFourLevel b c) s.val.val (rowP c) (rowJ c) (rowI b) := by + classical + have hl := rowFourLevel_le b c + by_cases hd : D ≤ rowFourLevel b c + · let k : Fin (4*Q-1-2*D) := ⟨rowFourLevel b c-D, by omega⟩ + rw [Finset.sum_eq_single k] + · have he : D+k.val = rowFourLevel b c := by dsimp [k]; omega + rw [he] + · intro k' _ hne + have he : rowP b+rowJ b+rowI c ≠ D+k'.val := by + intro he + apply hne + apply Fin.ext + dsimp [k] + dsimp [rowFourLevel] at * + omega + rw [sphericalCopyCoefficient_level _ _ _ _ _ _ _ he, zero_mul] + · simp + · have hz : sphericalCopyCoefficient Q D (rowFourLevel b c) r.val.val + (rowP b) (rowJ b) (rowI c) = 0 := by + simp [sphericalCopyCoefficient, hd] + rw [hz, zero_mul] + apply Finset.sum_eq_zero + intro k _ + have he : rowP b+rowJ b+rowI c ≠ D+k.val := by + dsimp [rowFourLevel] at hd + omega + rw [sphericalCopyCoefficient_level _ _ _ _ _ _ _ he, zero_mul] + + + +theorem sourceRowFourKernel_copyTrace {Q D t : ℕ} (hQ : 24 ≤ Q) (hD : D ≤ 23) + (a : RowEntry t → ℝ) (r s : CopyLabel D) : + (∑ k : Fin (4*Q-1-2*D), + star (fun b => (composedCoupledVector Q r.val.val (D-r.val.val) k.val b : ℂ)) ⬝ᵥ + (sourceRowFourKernel (by omega : 8 ≤ Q) a *ᵥ + fun b => (composedCoupledVector Q s.val.val (D-s.val.val) k.val b : ℂ))) = + (rowFourTrace Q D t a r s : ℂ) := by + classical + have hr : r.val.val ≤ D := by have := r.val.isLt; omega + have hs : s.val.val ≤ D := by have := s.val.isLt; omega + have he (k : Fin (4*Q-1-2*D)) := rowFourPrewedge_coupled_bilinear + hr hs (by omega : D ≤ D+k.val) (by omega : r.val.val ≤ Q) + (by omega : s.val.val ≤ Q) r.property s.property + (sourceRowFourP (by omega : 8 ≤ Q)) + (sourceRowI (by omega : 8 ≤ Q)) (sourceRowJ (by omega : 8 ≤ Q)) a + simp only [Nat.add_sub_cancel_left, sourceRowFourP, sourceRowI, sourceRowJ] at he + simp only [sourceRowFourKernel, he] + rw [← Complex.ofReal_sum] + apply congrArg (fun x : ℝ => (x : ℂ)) + simp only [rowFourTrace, Finset.sum_neg_distrib] + congr 1 + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro b _ + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro c _ + simp only [mul_assoc, ← Finset.mul_sum] + rw [rowFour_copyWeight_sum hQ hD] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/GramCache.lean b/lean/OAI/Analysis/LaughlinFock/GramCache.lean new file mode 100644 index 0000000000000000000000000000000000000000..dd4cb1d464a6561bbaa54003ca9107646a7f70d9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/GramCache.lean @@ -0,0 +1,56 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FastCoupling + +namespace OAI + +/-! Gram Cache. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +def kernelHighestTerm (D : ℕ) (r : CopyLabel D) (A : Occupation 24) + (x y j k : Orbital 24) : ℚ := + if x row.1=A)).map Prod.snd).getD []).getD (r/2) 0 + +def cachedFourGram (D : ℕ) (xs : List (Occupation 24 × List ℚ)) : + Matrix (CopyLabel D) (CopyLabel D) ℚ := fun r s => + ∑ A ∈ highestFourOccupations D, + 2 * highestLookup xs r.val.val A * highestLookup xs s.val.val A / + (2^(2*D) * occupationFactorial A) + +theorem integerFourGram_cached (D : ℕ) (xs : List (Occupation 24 × List ℚ)) + (h : ∀ r A, A ∈ highestFourOccupations D → + kernelHighestEntry D r A = highestLookup xs r.val.val A) : + integerFourGram D = cachedFourGram D xs := by + ext r s + apply Finset.sum_congr rfl + intro A hA + rw [integerHighestEntry_kernel, integerHighestEntry_kernel, h r A hA, h s A hA] + +def boundedMatrixEntriesDecidable {ι κ : Type*} [Fintype ι] {α : Type*} [DecidableEq α] + (s : Finset κ) (A B : ι → κ → α) : Decidable (∀ i, ∀ a∈s, A i a = B i a) := + @Fintype.decidableForallFintype _ _ (fun _ => Finset.decidableDforallFinset) _ + +def boundedEntriesDecidable {κ : Type*} {α : Type*} [DecidableEq α] + (s : Finset κ) (A B : κ → α) : Decidable (∀ a∈s, A a = B a) := + Finset.decidableDforallFinset (p := fun a _ => A a = B a) + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/GramCompression.lean b/lean/OAI/Analysis/LaughlinFock/GramCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..7329b1c1c8ffaaeae3e872bbd331cc6b6733a5be --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/GramCompression.lean @@ -0,0 +1,59 @@ +import Mathlib + +namespace OAI + +/-! Gram Compression. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open scoped BigOperators Polynomial +open Polynomial +open Filter Topology +theorem adjoint_mulVec_mem_gram_range {ι κ : Type*} [Fintype ι] [Fintype κ] + (W : Matrix ι κ ℂ) (x : ι → ℂ) : + ∃ y : κ → ℂ, (Wᴴ * W) *ᵥ y = Wᴴ *ᵥ x := by + classical + have hx : (WithLp.toLp 2 (Wᴴ *ᵥ x)) ∈ W.toEuclideanLin.adjoint.range := by + refine ⟨WithLp.toLp 2 x, ?_⟩ + rw [← Matrix.toEuclideanLin_conjTranspose_eq_adjoint, Matrix.toLpLin_apply] + rw [← LinearMap.range_adjoint_comp_self] at hx + rcases hx with ⟨y, hy⟩ + refine ⟨y.ofLp, ?_⟩ + have := congrArg WithLp.ofLp hy + simpa only [LinearMap.comp_apply, ← Matrix.toEuclideanLin_conjTranspose_eq_adjoint, + Matrix.toLpLin_apply, WithLp.ofLp_toLp, Matrix.mulVec_mulVec] using this + +theorem sandwich_quadratic_form {ι κ : Type*} [Fintype ι] [Fintype κ] + (A : Matrix ι κ ℂ) (C : Matrix ι ι ℂ) (x : κ → ℂ) : + star x ⬝ᵥ (Aᴴ * C * A) *ᵥ x = star (A *ᵥ x) ⬝ᵥ C *ᵥ (A *ᵥ x) := by + rw [← Matrix.mulVec_mulVec, ← Matrix.mulVec_mulVec, + Matrix.dotProduct_mulVec, ← Matrix.star_mulVec] + + +theorem gram_compression_posSemidef_iff {ι κ : Type*} [Fintype ι] [Fintype κ] + (W : Matrix ι κ ℂ) (C : Matrix κ κ ℂ) (hC : C.IsHermitian) : + ((Wᴴ * W) * C * (Wᴴ * W)).PosSemidef ↔ (W * C * Wᴴ).PosSemidef := by + classical + let G := Wᴴ * W + have hg : G.IsHermitian := Matrix.isHermitian_conjTranspose_mul_self _ + constructor + · intro h + have h' : (Gᴴ * C * G).PosSemidef := by rwa [hg.eq] + refine Matrix.posSemidef_iff_dotProduct_mulVec.mpr ⟨?_, ?_⟩ + · change (W * C * Wᴴ)ᴴ = W * C * Wᴴ + simp only [Matrix.conjTranspose_mul, Matrix.conjTranspose_conjTranspose, hC.eq, + Matrix.mul_assoc] + · intro x + obtain ⟨y, hy⟩ := adjoint_mulVec_mem_gram_range W x + have hn := h'.dotProduct_mulVec_nonneg y + rw [sandwich_quadratic_form] at hn + change 0 ≤ star ((Wᴴ * W) *ᵥ y) ⬝ᵥ C *ᵥ ((Wᴴ * W) *ᵥ y) at hn + rw [hy] at hn + rwa [← sandwich_quadratic_form, Matrix.conjTranspose_conjTranspose] at hn + · intro h + have := h.conjTranspose_mul_mul_same W + simpa only [Matrix.mul_assoc] using this +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/HighestTails.lean b/lean/OAI/Analysis/LaughlinFock/HighestTails.lean new file mode 100644 index 0000000000000000000000000000000000000000..3a0a93641d63d2ac42b4752bdffeb81e7c5838d6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/HighestTails.lean @@ -0,0 +1,184 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.BesselComparison +import OAI.Analysis.LaughlinFock.CreationRows +import OAI.Analysis.LaughlinFock.ThreeSpectrum + +namespace OAI + +/-! Highest Tails. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder + + +theorem sum_gram_comparison {ι α β : Type*} [Fintype ι] [Fintype α] [Fintype β] + (A : α → Matrix ι ι ℂ) (B : β → Matrix ι ι ℂ) + (h : ∀ ψ : ι → ℂ, (∑ a, ∑ i, ‖(A a *ᵥ ψ) i‖^2) ≤ + ∑ b, ∑ i, ‖(B b *ᵥ ψ) i‖^2) : + ((∑ b, (B b)ᴴ * B b) - ∑ a, (A a)ᴴ * A a).PosSemidef := by + classical + have hA : (∑ a, (A a)ᴴ * A a).IsHermitian := + (Matrix.posSemidef_sum _ fun a _ => Matrix.posSemidef_conjTranspose_mul_self _).isHermitian + have hB : (∑ b, (B b)ᴴ * B b).IsHermitian := + (Matrix.posSemidef_sum _ fun b _ => Matrix.posSemidef_conjTranspose_mul_self _).isHermitian + have hH := hB.sub hA + apply Matrix.PosSemidef.of_dotProduct_mulVec_nonneg hH + intro ψ + apply Complex.nonneg_iff.mpr + refine ⟨?_, (hH.im_star_dotProduct_mulVec_self ψ).symm⟩ + simp only [Matrix.sub_mulVec, dotProduct_sub, Matrix.sum_mulVec, dotProduct_sum, + gram_quadratic_form, star_dotProduct_self, Complex.sub_re, + Complex.re_sum, Complex.ofReal_re] + exact sub_nonneg.mpr (h ψ) + + + +theorem highestFourAnnihilator_pair_posSemidef {Q D : ℕ} (hD : D ≤ Q) : + ((∑ b : FourHighestShell Q D, + (pairAnnihilator Q b.val.1.val)ᴴ * pairAnnihilator Q b.val.1.val) - + ∑ r : CopyLabel D, (highestFourAnnihilator Q D r)ᴴ * highestFourAnnihilator Q D r).PosSemidef := + sum_gram_comparison _ _ (highestFourAnnihilator_pair_bound hD) + + + +theorem unit_vector_contracts_family {ι κ : Type*} [Fintype ι] [Fintype κ] + (s : ι → ℝ) (hs : ∑ i, s i ^ 2 = 1) (x : ι → κ → ℂ) : + (∑ k, ‖∑ i, (s i : ℂ) * x i k‖^2) ≤ ∑ i, ∑ k, ‖x i k‖^2 := by + classical + let S : Matrix Unit ι ℂ := fun _ i => s i + have hS : S * Sᴴ = 1 := by + ext u v + have hu : u=() := by cases u; rfl + have hv : v=() := by cases v; rfl + subst u v + have hc := congrArg (fun t : ℝ => (t : ℂ)) hs + change (∑ i, (s i : ℂ) * star (s i : ℂ)) = 1 + simpa only [Complex.star_def, Complex.conj_ofReal, Complex.ofReal_sum, + Complex.ofReal_pow, Complex.ofReal_one, Complex.ofReal_mul, pow_two] using hc + have h := row_isometry_contracts_family S hS x + simpa only [S, Fintype.sum_unique] using h + + + +def highestThreeAnnihilator (Q z : ℕ) (hz : z ≤ Q) : FockMatrix Q := + ∑ p : Fin (z+1), (highestCoefficient (2*Q-2) Q z p.val : ℂ) • + (annihilator Q ⟨z-p.val, by omega⟩ * pairAnnihilator Q p.val) + + + +theorem highestThreeAnnihilator_bound {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) + (ψ : Occupation Q → ℂ) : + (∑ A, ‖(highestThreeAnnihilator Q z hz *ᵥ ψ) A‖^2) ≤ + ∑ p : Fin (z+1), ∑ A, ‖(pairAnnihilator Q p.val *ᵥ ψ) A‖^2 := by + have hn : ∑ p : Fin (z+1), highestCoefficient (2*Q-2) Q z p.val ^ 2 = 1 := by + rw [Fin.sum_univ_eq_sum_range (fun p => highestCoefficient (2*Q-2) Q z p ^ 2) (z+1)] + exact highestCoefficient_norm (by omega) + have h := unit_vector_contracts_family _ hn + (fun p A => ((annihilator Q ⟨z-p.val, by omega⟩ * pairAnnihilator Q p.val) *ᵥ ψ) A) + calc + _ ≤ ∑ p : Fin (z+1), ∑ A, + ‖((annihilator Q ⟨z-p.val, by omega⟩ * pairAnnihilator Q p.val) *ᵥ ψ) A‖^2 := by + simpa only [highestThreeAnnihilator, Matrix.sum_mulVec, Matrix.smul_mulVec, + Finset.sum_apply, Pi.smul_apply, smul_eq_mul] using h + _ ≤ _ := by + apply Finset.sum_le_sum + intro p _ + simpa only [Matrix.mulVec_mulVec] using + annihilator_contracts Q ⟨z-p.val, by omega⟩ (pairAnnihilator Q p.val *ᵥ ψ) + + + +theorem highestThreeAnnihilator_pair_posSemidef {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + ((∑ p : Fin (z+1), (pairAnnihilator Q p.val)ᴴ * pairAnnihilator Q p.val) - + (highestThreeAnnihilator Q z hz)ᴴ * highestThreeAnnihilator Q z hz).PosSemidef := by + have h : ∀ ψ : Occupation Q → ℂ, + (∑ _ : Unit, ∑ A, ‖(highestThreeAnnihilator Q z hz *ᵥ ψ) A‖^2) ≤ + ∑ p : Fin (z+1), ∑ A, ‖(pairAnnihilator Q p.val *ᵥ ψ) A‖^2 := by + simpa only [Fintype.sum_unique] using highestThreeAnnihilator_bound hQ hz + simpa only [Fintype.sum_unique] using + sum_gram_comparison (fun _ : Unit => highestThreeAnnihilator Q z hz) + (fun p : Fin (z+1) => pairAnnihilator Q p.val) h + + + +theorem wedgeAnnihilator_mulVec {ι : Type*} [Fintype ι] (Q k : ℕ) + (W : Matrix (SectorOccupation Q k) ι ℂ) (s : ι → ℂ) : + wedgeAnnihilator Q k (W *ᵥ s) = + ∑ i, star (s i) • wedgeAnnihilator Q k (fun A => W A i) := by + classical + simp only [wedgeAnnihilator, Matrix.mulVec, dotProduct, star_sum, star_mul, + Finset.sum_smul, Finset.smul_sum, smul_smul] + rw [Finset.sum_comm] + + + +theorem threeWedgeMatrix_annihilator_column (Q : ℕ) (pj : PairLabel Q × Orbital Q) : + wedgeAnnihilator Q 3 (fun A => threeWedgeMatrix Q A pj) = + annihilator Q pj.2 * pairAnnihilator Q pj.1.val := by + apply wedgeAnnihilator_annihilatorVector + exact orbitalPair_mem Q pj.1.val pj.2 + + + +theorem highestThreeAnnihilator_eq_wedge {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + highestThreeAnnihilator Q z hz = + wedgeAnnihilator Q 3 (threeWedgeMatrix Q *ᵥ threeCoupledColumn Q z 0) := by + classical + rw [wedgeAnnihilator_mulVec] + simp_rw [threeWedgeMatrix_annihilator_column] + let e : Fin (z+1) → PairLabel Q × Orbital Q := + fun p => (⟨p.val, by have := p.isLt; omega⟩, ⟨z-p.val, by omega⟩) + have he : Function.Injective e := by + intro p q h + exact Fin.ext (congrArg (fun b => b.1.val) h) + unfold highestThreeAnnihilator + apply Fintype.sum_of_injective e he + · intro pj hpj + have hn : pj.1.val+pj.2.val ≠ z := by + intro h + apply hpj + refine ⟨⟨pj.1.val, by omega⟩, ?_⟩ + apply Prod.ext + · apply Fin.ext + rfl + · apply Fin.ext + dsimp [e] + omega + simp [threeCoupledColumn, coupledVector, hn] + · intro p + have hp : p.val+(z-p.val) = z := by have := p.isLt; omega + simp only [e, threeCoupledColumn, coupledVector, Nat.add_zero, ite_eq_left hp, + coupledCoefficient, Complex.star_def, Complex.conj_ofReal] + + + +theorem threeSpinProjection_trace {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + (threeSpinProjection Q z).trace = ((3*Q-1-2*z : ℕ) : ℂ) := by + classical + have hz' : z < min (2*Q-2) Q+1 := by omega + let r : Fin (min (2*Q-2) Q+1) := ⟨z,hz'⟩ + unfold threeSpinProjection + rw [Matrix.trace_mul_comm, ← Matrix.mul_assoc, threeCouplingMatrix_gram Q (by omega), + Matrix.one_mul, Matrix.trace_diagonal] + change (∑ c : CoupledIndex (2*Q-2) Q, if c.1.val=z then (1:ℂ) else 0) = _ + rw [Fintype.sum_sigma] + have hs : (∑ a : Fin (min (2*Q-2) Q + 1), + ∑ _ : Fin (2*Q-2+Q-2*a.val+1), if a.val=z then (1:ℂ) else 0) = + ((2*Q-2+Q-2*z+1 : ℕ) : ℂ) := by + rw [Finset.sum_eq_single r] + · simp [r] + · intro a _ ha + have han : a.val ≠ z := by + intro h + apply ha + exact Fin.ext h + simp [han] + · simp + rw [hs] + congr 1 + omega + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/IntegerCompression.lean b/lean/OAI/Analysis/LaughlinFock/IntegerCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..7c751419454be8b79ca193258b71067cba58ae56 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/IntegerCompression.lean @@ -0,0 +1,104 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.IntegerFour + +namespace OAI + +/-! Integer Compression. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +theorem planar_certificate_of_integer (D : ℕ) + (h : ((integerCompression D).map (algebraMap ℚ ℂ)).PosSemidef) : + (planarFourGram D * planarFourComparison certificateRows (3/10^6) D * + planarFourGram D).PosSemidef := by + classical + let d : Matrix (CopyLabel D) (CopyLabel D) ℂ := + Matrix.diagonal (fun r => (Real.sqrt (rationalCopyDiagonal D r.val.val : ℝ) : ℂ)) + let G := (integerFourGram D).map (algebraMap ℚ ℂ) + let Y := (integerRowsFourTrace D).map (algebraMap ℚ ℂ) + let u : CopyLabel D → ℂ := fun r => (rationalCopyDiagonal D r.val.val : ℂ) + let c : CopyLabel D → ℂ := fun r => (if r.val.val=1 then 2 else 0)+3/10^6 + have hd : dᴴ = d := by + ext r s + by_cases hrs : r=s <;> simp [d, Matrix.conjTranspose_apply, hrs, eq_comm] + have hDD : d*d=Matrix.diagonal u := by + rw [Matrix.diagonal_mul_diagonal] + congr 1 + funext r + have hu : 0 ≤ (rationalCopyDiagonal D r.val.val : ℝ) := by + exact_mod_cast (rationalCopyDiagonal_pos D r.val.val).le + change (Real.sqrt (rationalCopyDiagonal D r.val.val : ℝ) : ℂ)* + (Real.sqrt (rationalCopyDiagonal D r.val.val : ℝ) : ℂ) = _ + rw [← Complex.ofReal_mul, Real.mul_self_sqrt hu] + simp [u] + have hc : d*Matrix.diagonal c*d = Matrix.diagonal (fun r => c r*u r) := by + rw [Matrix.diagonal_mul_diagonal, Matrix.diagonal_mul_diagonal] + congr 1 + funext r + have hv := congrFun (congrFun hDD r) r + simp only [d, Matrix.diagonal_mul_diagonal, Matrix.diagonal_apply_eq] at hv + rw [mul_right_comm, hv] + exact mul_comm _ _ + have hG : planarFourGram D = d*G*d := by + ext r s + rw [planarFourGram_rational, rationalFourGram_integer] + simp [d,G,Matrix.diagonal_mul,Matrix.mul_diagonal, Complex.ofReal_mul] + have hE : (Matrix.of (fun r s => ((∑ t : Fin 8, + planarRowFourTrace D (certificateRows t).t.val (certificateRows t).alpha r s : ℝ) : ℂ))) = + d*Y*d := by + ext r s + simp only [Matrix.of_apply, Matrix.diagonal_mul, Matrix.mul_diagonal, d,Y, + Matrix.map_apply, integerRowsFourTrace, Matrix.sum_apply, map_sum, Complex.ofReal_sum, + Finset.mul_sum, Finset.sum_mul] + apply Finset.sum_congr rfl + intro t _ + change ((planarRowFourTrace D t.val (rationalComparisonRow t (certificateEll t) + (certificateAlpha t)).alpha r s : ℝ) : ℂ) = _ + rw [planarRowFourTrace_rational D t (certificateEll t) (certificateAlpha t), + rationalFourTrace_integer] + simp + have hC : planarFourComparison certificateRows (3/10^6) D = Matrix.diagonal c - d*Y*d := by + rw [planarFourComparison, hE] + have hct : (2:ℂ) • targetCopy D + ((3/10^6:ℝ):ℂ) • (1:Matrix (CopyLabel D) (CopyLabel D) ℂ) = + Matrix.diagonal c := by + ext r s + by_cases he : r=s + · subst s + simp [targetCopy, c, Matrix.smul_apply] + · have hf : ¬ (r.val.val=1 ∧ s.val.val=1) := by + intro hh + apply he + apply Subtype.ext + apply Fin.ext + omega + simp [targetCopy, c, Matrix.smul_apply, he, hf] + rw [← hct] + abel + have hM : (integerFourMiddle D).map (algebraMap ℚ ℂ) = + Matrix.diagonal (fun r => c r*u r) - Matrix.diagonal u*Y*Matrix.diagonal u := by + ext r s + simp only [integerFourMiddle, Matrix.map_apply, Matrix.sub_apply, + Matrix.diagonal_mul, Matrix.mul_diagonal] + by_cases hrs : r=s + · subst s + simp only [Matrix.diagonal_apply_eq] + dsimp [c,u,Y] + split_ifs <;> simp + · simp [hrs, c,u,Y] + have hfull : planarFourGram D * planarFourComparison certificateRows (3/10^6) D * + planarFourGram D = d*((integerCompression D).map (algebraMap ℚ ℂ))*d := by + rw [hG, hC, integerCompression, Matrix.map_mul, Matrix.map_mul, hM] + calc + _ = d*(G*(d*Matrix.diagonal c*d-(d*d)*Y*(d*d))*G)*d := by + simp only [Matrix.mul_sub, Matrix.sub_mul, Matrix.mul_assoc] + _ = _ := by rw [hDD, hc] + rw [hfull] + simpa only [hd] using h.mul_mul_conjTranspose_same d + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/IntegerCoupling.lean b/lean/OAI/Analysis/LaughlinFock/IntegerCoupling.lean new file mode 100644 index 0000000000000000000000000000000000000000..354fcccad1b6c26afd3b9891b4697179cb21aa1f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/IntegerCoupling.lean @@ -0,0 +1,40 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.RationalCoupling + +namespace OAI + +/-! Integer Coupling. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators +open Polynomial + + +def integerCoupling (c : ℤ) (z k p : ℕ) : ℤ := + ∑ h ∈ Finset.range (p+1), (-1)^(z-h) * (z.choose h : ℤ) * + (k.choose (p-h) : ℤ) * c^(p-h) + +theorem rationalCoupling_integer (c : ℤ) (z k p : ℕ) : + rationalCoupling (c:ℚ) z k p = (integerCoupling c z k p : ℚ) := by + have h1 : ((X-1)^z : Polynomial ℚ).coeff = fun h => + (-1)^(z-h) * (z.choose h : ℚ) := by + funext h + rw [show (X-1:Polynomial ℚ) = X+C (-1) by simp [sub_eq_add_neg]] + exact coeff_X_add_C_pow (-1) z h + have h2 : ((C (c:ℚ)*X+1)^k : Polynomial ℚ).coeff = fun h => + (k.choose h : ℚ) * (c:ℚ)^h := by + funext h + rw [show ((C (c:ℚ)*X+1)^k : Polynomial ℚ) = ((X+1)^k).comp (C (c:ℚ)*X) by simp] + rw [comp_C_mul_X_coeff, coeff_X_add_one_pow] + unfold rationalCoupling integerCoupling + rw [coeff_mul, Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk] + simp only [h1, h2, Int.cast_sum, Int.cast_mul, Int.cast_pow, Int.cast_neg, Int.cast_one, + Int.cast_natCast] + apply Finset.sum_congr rfl + intro h _ + ring + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/IntegerFour.lean b/lean/OAI/Analysis/LaughlinFock/IntegerFour.lean new file mode 100644 index 0000000000000000000000000000000000000000..052966ef78a416fdfc6010d07bab4aebc4682c95 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/IntegerFour.lean @@ -0,0 +1,87 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.CertificateRows +import OAI.Analysis.LaughlinFock.FastWedge +import OAI.Analysis.LaughlinFock.IntegerCoupling + +namespace OAI + +/-! Integer Four. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +def integerCopyPolynomial (D T r p j k : ℕ) : ℤ := + if r ≤ j+k then + integerCoupling 1 r (j+k-r) j * integerCoupling 1 (D-r) (T-D) p + else 0 + +theorem rationalCopyPolynomial_integer (D T r p j k : ℕ) : + rationalCopyPolynomial D T r p j k = (integerCopyPolynomial D T r p j k : ℚ) := by + simp only [rationalCopyPolynomial, integerCopyPolynomial, apply_ite (fun z:ℤ => (z:ℚ)), + Int.cast_mul, ← rationalCoupling_integer, Int.cast_one, Int.cast_zero] + +def integerFourTrace (D t : ℕ) (a : RowEntry t → ℚ) : + Matrix (CopyLabel D) (CopyLabel D) ℚ := fun r s => + -(∑ b : RowEntry t, ∑ c : RowEntry t, if D ≤ rowFourLevel b c then + a b*a c*rationalFourFactor D b c * + (integerCopyPolynomial D (rowFourLevel b c) r.val.val (rowP b) (rowJ b) (rowI c) : ℚ) * + (integerCopyPolynomial D (rowFourLevel b c) s.val.val (rowP c) (rowJ c) (rowI b) : ℚ) + else 0) + +theorem rationalFourTrace_integer (D t : ℕ) (a : RowEntry t → ℚ) : + rationalFourTrace D t a = integerFourTrace D t a := by + ext r s + simp only [rationalFourTrace, integerFourTrace, rationalCopyPolynomial_integer] + +def integerRowsFourTrace (D : ℕ) : Matrix (CopyLabel D) (CopyLabel D) ℚ := + ∑ t : Fin 8, integerFourTrace D t.val (certificateAlpha t) + +def integerHighestTerm (D : ℕ) (r : CopyLabel D) (A : Occupation 24) + (x y j k : Orbital 24) : ℚ := + if x + ∑ A ∈ highestFourOccupations D, + 2 * integerHighestEntry D r A * integerHighestEntry D s A / + (2^(2*D) * occupationFactorial A) + +theorem rationalFourGram_integer (D : ℕ) : rationalFourGram D = integerFourGram D := by + rw [rationalFourGram_fast] + ext r s + simp only [fastFourGram, integerFourGram, fastHighestEntry, integerHighestEntry, + fastHighestTerm_integer] + + + +def integerFourMiddle (D : ℕ) : Matrix (CopyLabel D) (CopyLabel D) ℚ := + Matrix.diagonal (fun r => ((if r.val.val=1 then 2 else 0)+3/10^6) * + rationalCopyDiagonal D r.val.val) - + Matrix.diagonal (fun r : CopyLabel D => rationalCopyDiagonal D r.val.val) * + integerRowsFourTrace D * Matrix.diagonal (fun r : CopyLabel D => rationalCopyDiagonal D r.val.val) + +def integerCompression (D : ℕ) : Matrix (CopyLabel D) (CopyLabel D) ℚ := + integerFourGram D * integerFourMiddle D * integerFourGram D + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/LDL.lean b/lean/OAI/Analysis/LaughlinFock/LDL.lean new file mode 100644 index 0000000000000000000000000000000000000000..5807b48283389e6bb935ecec7841a16bfa13ea81 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/LDL.lean @@ -0,0 +1,55 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.BesselComparison +import OAI.Analysis.LaughlinFock.PolynomialPositivity + +namespace OAI + +/-! L D L. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def copyMatrixData (D : ℕ) (xs : List (List ℚ)) : Matrix (CopyLabel D) (CopyLabel D) ℚ := + fun r s => ((xs[r.val.val/2]?.getD [])[s.val.val/2]?).getD 0 + +def copyDiagonalData (D : ℕ) (xs : List ℚ) : CopyLabel D → ℚ := + fun r => (xs[r.val.val/2]?).getD 0 + + +def matrixEntriesDecidable {ι : Type*} [Fintype ι] {α : Type*} [DecidableEq α] + (A B : Matrix ι ι α) : Decidable (∀ i j, A i j = B i j) := + @Fintype.decidableForallFintype _ _ (fun _ => + @Fintype.decidableForallFintype _ _ (fun _ => inferInstance) _) _ + + +theorem rational_ldl_posSemidef {ι : Type*} [Fintype ι] [DecidableEq ι] + (M L : Matrix ι ι ℚ) (d : ι → ℚ) + (he : M = L * Matrix.diagonal d * Lᵀ) (hd : ∀ i, 0 ≤ d i) : + (M.map (algebraMap ℚ ℂ)).PosSemidef := by + let Lr := L.map (algebraMap ℚ ℝ) + have hh : (Matrix.diagonal (fun i => (d i : ℝ))).PosSemidef := by + apply Matrix.posSemidef_diagonal_iff.mpr + intro i + exact_mod_cast hd i + have hr : (M.map (algebraMap ℚ ℝ)).PosSemidef := by + have ht : (Lᵀ).map (algebraMap ℚ ℝ) = Lrᴴ := by + ext i j + simp [Lr] + rw [he, Matrix.map_mul, Matrix.map_mul, ht] + have he' : (Matrix.diagonal d).map (algebraMap ℚ ℝ) = + Matrix.diagonal (fun i => (d i : ℝ)) := by + ext i j + by_cases hij : i=j <;> simp [hij] + rw [he'] + exact hh.mul_mul_conjTranspose_same Lr + have hc := real_matrix_posSemidef_complex (M.map (algebraMap ℚ ℝ)) hr + convert hc using 1 + ext i j + simp + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/LadderCalculus.lean b/lean/OAI/Analysis/LaughlinFock/LadderCalculus.lean new file mode 100644 index 0000000000000000000000000000000000000000..09dceb571eb60cb359b8eef93666871003bb28a8 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/LadderCalculus.lean @@ -0,0 +1,451 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FourCoefficients + +namespace OAI + +/-! Ladder Calculus. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators + + + +def spinStep (n p : ℕ) : ℝ := Real.sqrt ((p : ℝ) * ((n : ℝ)+1-p)) + +@[simp] theorem spinStep_zero (n : ℕ) : spinStep n 0 = 0 := by simp [spinStep] + +theorem spinStep_cutoff (n p : ℕ) (hp : n < p) : spinStep n p = 0 := by + apply Real.sqrt_eq_zero_of_nonpos + apply mul_nonpos_of_nonneg_of_nonpos (Nat.cast_nonneg p) + have h : (n : ℝ)+1 ≤ p := by exact_mod_cast hp + linarith + +@[simp] theorem spinStep_last (n : ℕ) : spinStep n (n+1) = 0 := + spinStep_cutoff n (n+1) (by omega) + +theorem spinStep_sq {n p : ℕ} (hp : p ≤ n+1) : + spinStep n p ^ 2 = (p : ℝ)*((n : ℝ)+1-p) := by + apply Real.sq_sqrt + apply mul_nonneg (Nat.cast_nonneg _) + have h : (p : ℝ) ≤ (n : ℝ)+1 := by exact_mod_cast hp + linarith + +theorem spinStep_sq_sub {n p : ℕ} (hp : p ≤ n) : + spinStep n (p+1)^2 - spinStep n p^2 = (n : ℝ)-2*p := by + rw [spinStep_sq (by omega : p+1 ≤ n+1), spinStep_sq (by omega : p ≤ n+1)] + push_cast + ring + +theorem spinStep_pos {n p : ℕ} (hp0 : 0 < p) (hpn : p ≤ n) : + 0 < spinStep n p := by + apply Real.sqrt_pos.mpr + apply mul_pos (by exact_mod_cast hp0) + have h : (p : ℝ) ≤ n := by exact_mod_cast hpn + linarith + +abbrev GridVector := ℕ → ℕ → ℝ + +def GridSupported (n m : ℕ) (f : GridVector) : Prop := + ∀ p q, n < p ∨ m < q → f p q = 0 + +def GridLayer (T : ℕ) (f : GridVector) : Prop := + ∀ p q, p+q ≠ T → f p q = 0 + + +def gridLower (n m : ℕ) (f : GridVector) : GridVector := fun p q => + spinStep n p * f (p-1) q + spinStep m q * f p (q-1) + + +def gridRaise (n m : ℕ) (f : GridVector) : GridVector := fun p q => + spinStep n (p+1) * f (p+1) q + spinStep m (q+1) * f p (q+1) + +theorem gridLower_smul (n m : ℕ) (c : ℝ) (f : GridVector) : + gridLower n m (c • f) = c • gridLower n m f := by + funext p q + simp only [gridLower, Pi.smul_apply, smul_eq_mul] + ring + +theorem gridRaise_smul (n m : ℕ) (c : ℝ) (f : GridVector) : + gridRaise n m (c • f) = c • gridRaise n m f := by + funext p q + simp only [gridRaise, Pi.smul_apply, smul_eq_mul] + ring + +@[simp] theorem gridLower_zero (n m : ℕ) : gridLower n m 0 = 0 := by + funext p q + simp [gridLower] + +@[simp] theorem gridRaise_zero (n m : ℕ) : gridRaise n m 0 = 0 := by + funext p q + simp [gridRaise] + +theorem gridLower_supported {n m : ℕ} {f : GridVector} (hf : GridSupported n m f) : + GridSupported n m (gridLower n m f) := by + intro p q h + rcases h with hp | hq + · simp only [gridLower, spinStep_cutoff n p hp, zero_mul, zero_add, + hf p (q-1) (Or.inl hp), mul_zero] + · simp only [gridLower, spinStep_cutoff m q hq, mul_zero, zero_mul, add_zero, + hf (p-1) q (Or.inr hq)] + +theorem gridRaise_supported {n m : ℕ} {f : GridVector} (hf : GridSupported n m f) : + GridSupported n m (gridRaise n m f) := by + intro p q h + have h1 : n < p+1 ∨ m < q := by omega + have h2 : n < p ∨ m < q+1 := by omega + simp [gridRaise, hf (p+1) q h1, hf p (q+1) h2] + +theorem gridLower_layer {n m T : ℕ} {f : GridVector} (hf : GridLayer T f) : + GridLayer (T+1) (gridLower n m f) := by + intro p q h + unfold gridLower + have h1 : spinStep n p * f (p-1) q = 0 := by + by_cases hp : p = 0 + · simp [hp] + · rw [hf (p-1) q (by omega), mul_zero] + have h2 : spinStep m q * f p (q-1) = 0 := by + by_cases hq : q = 0 + · simp [hq] + · rw [hf p (q-1) (by omega), mul_zero] + rw [h1, h2, zero_add] + + + +theorem grid_commutator_at (n m : ℕ) (f : GridVector) (p q : ℕ) + (hp : p ≤ n) (hq : q ≤ m) : + gridRaise n m (gridLower n m f) p q - gridLower n m (gridRaise n m f) p q = + ((n : ℝ)+m-2*(p+q)) * f p q := by + have hdiag : gridRaise n m (gridLower n m f) p q - + gridLower n m (gridRaise n m f) p q = + (spinStep n (p+1)^2-spinStep n p^2 + + (spinStep m (q+1)^2-spinStep m q^2)) * f p q := by + cases p <;> cases q <;> + simp only [gridRaise, gridLower, Nat.succ_sub_one, + spinStep_zero, zero_mul, zero_add, add_zero, zero_pow (by omega : 2 ≠ 0), sub_zero] <;> ring + rw [hdiag, spinStep_sq_sub hp, spinStep_sq_sub hq] + ring + + +theorem grid_commutator_layer {n m T : ℕ} {f : GridVector} + (hf : GridSupported n m f) (hT : GridLayer T f) : + gridRaise n m (gridLower n m f) = gridLower n m (gridRaise n m f) + + ((n : ℝ)+m-2*T) • f := by + funext p q + simp only [Pi.add_apply, Pi.smul_apply, smul_eq_mul] + by_cases h : n < p ∨ m < q + · rw [gridRaise_supported (gridLower_supported hf) p q h, + gridLower_supported (gridRaise_supported hf) p q h, hf p q h] + ring + · have hp : p ≤ n := by omega + have hq : q ≤ m := by omega + have he := grid_commutator_at n m f p q hp hq + by_cases hl : p+q = T + · have hc : (p : ℝ) + q = T := by exact_mod_cast hl + rw [hc] at he + linarith only [he] + · rw [hT p q hl, mul_zero] at he ⊢ + linarith + + +def gridInner (n m : ℕ) (f g : GridVector) : ℝ := + ∑ p ∈ Finset.range (n+1), ∑ q ∈ Finset.range (m+1), f p q * g p q + +theorem gridInner_smul_left (n m : ℕ) (c : ℝ) (f g : GridVector) : + gridInner n m (c • f) g = c * gridInner n m f g := by + simp only [gridInner, Pi.smul_apply, smul_eq_mul, mul_assoc, Finset.mul_sum] + +theorem gridInner_smul_right (n m : ℕ) (c : ℝ) (f g : GridVector) : + gridInner n m f (c • g) = c * gridInner n m f g := by + simp only [gridInner, Pi.smul_apply, smul_eq_mul, ←mul_assoc, mul_comm _ c, Finset.mul_sum] + +theorem spinStep_sum_adjoint (n : ℕ) (f g : ℕ → ℝ) : + (∑ p ∈ Finset.range (n+1), (spinStep n p * f (p-1)) * g p) = + ∑ p ∈ Finset.range (n+1), f p * (spinStep n (p+1) * g (p+1)) := by + rw [Finset.sum_range_succ', Finset.sum_range_succ] + simp only [spinStep_zero, zero_mul, spinStep_last, mul_zero, add_zero, Nat.add_sub_cancel] + apply Finset.sum_congr rfl + intro p _ + ring + + + +theorem grid_adjoint (n m : ℕ) (f g : GridVector) : + gridInner n m (gridLower n m f) g = gridInner n m f (gridRaise n m g) := by + simp only [gridInner, gridLower, gridRaise, add_mul, mul_add, Finset.sum_add_distrib] + apply congrArg₂ (· + ·) + · rw [Finset.sum_comm, Finset.sum_comm (f := fun p q => f p q * _)] + apply Finset.sum_congr rfl + intro q _ + exact spinStep_sum_adjoint n (fun p => f p q) (fun p => g p q) + · apply Finset.sum_congr rfl + intro p _ + exact spinStep_sum_adjoint m (f p) (g p) + + + +def coupledVector (n m z k : ℕ) : GridVector := fun p q => + if p+q = z+k then coupledCoefficient n m z k p else 0 + +theorem coupledVector_layer (n m z k : ℕ) : + GridLayer (z+k) (coupledVector n m z k) := by + intro p q h + exact ite_eq_right h + +theorem coupledVector_supported {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) (k : ℕ) : + GridSupported n m (coupledVector n m z k) := by + intro p q h + unfold coupledVector + split_ifs with he + · rcases h with hp | hq + · exact coupledCoefficient_left_support hn k p hp + · exact coupledCoefficient_right_support hm k p (by omega) + · rfl + +theorem spinStep_succ {n p : ℕ} (hp : p ≤ n) : + spinStep n (p+1) = Real.sqrt ((p+1 : ℕ) * (n-p : ℕ) : ℝ) := by + unfold spinStep + rw [Nat.cast_sub hp] + congr 2 + push_cast + ring + + + +theorem coupledVector_highest {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) : + gridRaise n m (coupledVector n m z 0) = 0 := by + funext p q + simp only [gridRaise, coupledVector, Nat.add_zero, Pi.zero_apply] + by_cases h : p+q+1 = z + · have h1 : p+1+q = z := by omega + have h2 : p+(q+1) = z := by omega + rw [ite_eq_left h1, ite_eq_left h2, spinStep_succ (by omega : p ≤ n), + spinStep_succ (by omega : q ≤ m)] + have hq1 : q+1 = z-p := by omega + have hmq : m-q = m-z+p+1 := by omega + rw [hq1, hmq] + simp only [coupledCoefficient] + simpa only [mul_comm] using highestCoefficient_raising (m := m) hn (by omega : p < z) + · rw [ite_eq_right (by omega : p+1+q ≠ z), ite_eq_right (by omega : p+(q+1) ≠ z)] + ring + + + +theorem coupledVector_succ_apply (n m z k p q : ℕ) : + coupledVector n m z (k+1) p q = gridLower n m (coupledVector n m z k) p q / + Real.sqrt (((k+1 : ℕ) : ℝ)*((n : ℝ)+m-2*z-k)) := by + by_cases ht : p+q = z+k+1 + · have ht' : (p : ℝ)+q = (z : ℝ)+k+1 := by exact_mod_cast ht + have hr1 : (((z+k+1 : ℕ) : ℝ)-p) = q := by push_cast; linarith + have hr2 : (m : ℝ)+p-z-k = (m : ℝ)+1-q := by linarith + simp only [coupledVector, show z+(k+1) = z+k+1 by omega, ht, ite_true, + coupledCoefficient_lower, hr1, hr2, gridLower, spinStep, + Real.sqrt_mul (Nat.cast_nonneg p), Real.sqrt_mul (Nat.cast_nonneg q)] + by_cases hp : p = 0 + · subst p + have hq : 0+(q-1) = z+k := by omega + simp [hq] + · by_cases hq : q = 0 + · subst q + have hp' : p-1+0 = z+k := by omega + simp [hp'] + · rw [ite_eq_left (by omega : p-1+q = z+k), ite_eq_left (by omega : p+(q-1) = z+k)] + · have hzero := gridLower_layer (n := n) (m := m) (coupledVector_layer n m z k) p q ht + rw [hzero, zero_div] + exact ite_eq_right (by omega) + +theorem coupledVector_succ {n m z : ℕ} (hz : 2*z ≤ n+m) (k : ℕ) : + coupledVector n m z (k+1) = (spinStep (n+m-2*z) (k+1))⁻¹ • + gridLower n m (coupledVector n m z k) := by + funext p q + simp only [Pi.smul_apply, smul_eq_mul, coupledVector_succ_apply] + have hden : Real.sqrt (((k+1 : ℕ) : ℝ)*((n : ℝ)+m-2*z-k)) = + spinStep (n+m-2*z) (k+1) := by + unfold spinStep + rw [Nat.cast_sub hz] + push_cast + congr 2 + ring + rw [hden, div_eq_mul_inv, mul_comm] + + + +theorem coupledVector_lower {n m z k : ℕ} (hz : 2*z ≤ n+m) + (hk : k < n+m-2*z) : + gridLower n m (coupledVector n m z k) = + spinStep (n+m-2*z) (k+1) • coupledVector n m z (k+1) := by + have hpos := spinStep_pos (by omega : 0 < k+1) (by omega : k+1 ≤ n+m-2*z) + rw [coupledVector_succ hz, smul_smul, mul_inv_cancel₀ hpos.ne', one_smul] + + +theorem coupledVector_top_norm {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) : + gridInner n m (coupledVector n m z 0) (coupledVector n m z 0) = 1 := by + have hq : ∀ p, (∑ q ∈ Finset.range (m+1), + coupledVector n m z 0 p q * coupledVector n m z 0 p q) = + if p ≤ z then highestCoefficient n m z p ^ 2 else 0 := by + intro p + by_cases hp : p ≤ z + · rw [ite_eq_left hp] + calc + _ = coupledVector n m z 0 p (z-p) * coupledVector n m z 0 p (z-p) := by + apply Finset.sum_eq_single (z-p) + · intro q _ hne + simp only [coupledVector, Nat.add_zero, ite_eq_right (by omega : p+q ≠ z), mul_zero] + · intro hnot + exact (hnot (Finset.mem_range.mpr (by omega : z-p < m+1))).elim + _ = _ := by simp [coupledVector, coupledCoefficient, show p+(z-p) = z by omega, pow_two] + · rw [ite_eq_right hp] + apply Finset.sum_eq_zero + intro q _ + simp only [coupledVector, Nat.add_zero, ite_eq_right (by omega : p+q ≠ z), mul_zero] + simp only [gridInner, hq] + calc + _ = ∑ p ∈ Finset.range (z+1), if p ≤ z then highestCoefficient n m z p ^ 2 else 0 := by + symm + apply Finset.sum_subset (Finset.range_mono (by omega : z+1 ≤ n+1)) + intro p _ hout + rw [Finset.mem_range] at hout + exact ite_eq_right (by omega) + _ = ∑ p ∈ Finset.range (z+1), highestCoefficient n m z p ^ 2 := by + apply Finset.sum_congr rfl + intro p hp + rw [ite_eq_left (by have := Finset.mem_range.mp hp; omega)] + _ = 1 := highestCoefficient_norm hn + + +theorem coupledVector_commutator {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) (k : ℕ) : + gridRaise n m (gridLower n m (coupledVector n m z k)) = + gridLower n m (gridRaise n m (coupledVector n m z k)) + + (((n+m-2*z : ℕ) : ℝ)-2*k) • coupledVector n m z k := by + have h := grid_commutator_layer (coupledVector_supported hn hm k) (coupledVector_layer n m z k) + convert h using 2 + rw [Nat.cast_sub (by omega : 2*z ≤ n+m)] + push_cast + ring_nf + + + +theorem coupledVector_raise {n m z k : ℕ} (hn : z ≤ n) (hm : z ≤ m) + (hk : k ≤ n+m-2*z) : + gridRaise n m (coupledVector n m z k) = + spinStep (n+m-2*z) k • coupledVector n m z (k-1) := by + have hz : 2*z ≤ n+m := by omega + revert hk + induction k with + | zero => + intro _ + simp only [coupledVector_highest hn hm, spinStep_zero, zero_smul] + | succ k ih => + intro hk + have hprev := ih (by omega : k ≤ n+m-2*z) + have hLR : gridLower n m (gridRaise n m (coupledVector n m z k)) = + spinStep (n+m-2*z) k ^ 2 • coupledVector n m z k := by + rw [hprev, gridLower_smul] + by_cases hk0 : k = 0 + · simp [hk0] + · rw [coupledVector_lower hz (by omega : k-1 < n+m-2*z), + show k-1+1 = k by omega, smul_smul, ← pow_two] + have h := coupledVector_commutator hn hm k + rw [coupledVector_lower hz (by omega : k < n+m-2*z), gridRaise_smul, hLR, ← add_smul] at h + have hsq : spinStep (n+m-2*z) k ^ 2 + (((n+m-2*z : ℕ) : ℝ)-2*k) = + spinStep (n+m-2*z) (k+1)^2 := by + linarith only [spinStep_sq_sub (by omega : k ≤ n+m-2*z)] + rw [hsq] at h + have hpos := spinStep_pos (by omega : 0 < k+1) (by omega : k+1 ≤ n+m-2*z) + funext p q + have he := congrArg (fun f : GridVector => f p q) h + simp only [Pi.smul_apply, smul_eq_mul] at he ⊢ + simp only [Nat.succ_sub_one] + apply mul_left_cancel₀ hpos.ne' + nlinarith only [he] + + + +theorem coupledVector_norm {n m z k : ℕ} (hn : z ≤ n) (hm : z ≤ m) + (hk : k ≤ n+m-2*z) : + gridInner n m (coupledVector n m z k) (coupledVector n m z k) = 1 := by + have hz : 2*z ≤ n+m := by omega + revert hk + induction k with + | zero => exact fun _ => coupledVector_top_norm hn hm + | succ k ih => + intro hk + have hprev := ih (by omega : k ≤ n+m-2*z) + have h := grid_adjoint n m (coupledVector n m z k) (coupledVector n m z (k+1)) + rw [coupledVector_lower hz (by omega : k < n+m-2*z), + coupledVector_raise hn hm (by omega : k+1 ≤ n+m-2*z), + Nat.add_sub_cancel, gridInner_smul_left, gridInner_smul_right, hprev, mul_one] at h + have hpos := spinStep_pos (by omega : 0 < k+1) (by omega : k+1 ≤ n+m-2*z) + apply mul_left_cancel₀ hpos.ne' + simpa using h + +@[simp] theorem gridInner_zero_right (n m : ℕ) (f : GridVector) : + gridInner n m f 0 = 0 := by simp [gridInner] + +@[simp] theorem gridInner_zero_left (n m : ℕ) (g : GridVector) : + gridInner n m 0 g = 0 := by simp [gridInner] + +theorem gridInner_comm (n m : ℕ) (f g : GridVector) : + gridInner n m f g = gridInner n m g f := by + simp only [gridInner, mul_comm] + +theorem gridInner_of_layers {n m T U : ℕ} {f g : GridVector} + (hf : GridLayer T f) (hg : GridLayer U g) (hTU : T ≠ U) : + gridInner n m f g = 0 := by + apply Finset.sum_eq_zero + intro p _ + apply Finset.sum_eq_zero + intro q _ + by_cases h : p+q = T + · rw [hg p q (by omega), mul_zero] + · rw [hf p q h, zero_mul] + + + +theorem coupledVector_orthogonal {n m z r k l : ℕ} + (hzn : z ≤ n) (hzm : z ≤ m) (hrn : r ≤ n) (hrm : r ≤ m) + (hzr : z < r) (hk : k ≤ n+m-2*z) (hl : l ≤ n+m-2*r) : + gridInner n m (coupledVector n m z k) (coupledVector n m r l) = 0 := by + have hz : 2*z ≤ n+m := by omega + induction l generalizing k with + | zero => + by_cases ht : z+k = r + · have h := grid_adjoint n m (coupledVector n m z (k-1)) (coupledVector n m r 0) + rw [coupledVector_lower hz (by omega : k-1 < n+m-2*z), + show k-1+1 = k by omega, coupledVector_highest hrn hrm, + gridInner_smul_left, gridInner_zero_right] at h + exact (mul_eq_zero.mp h).resolve_left (spinStep_pos (by omega : 0 < k) hk).ne' + · exact gridInner_of_layers (coupledVector_layer _ _ _ _) (coupledVector_layer _ _ _ _) (by omega) + | succ l ih => + by_cases ht : z+k = r+(l+1) + · have h := grid_adjoint n m (coupledVector n m z (k-1)) (coupledVector n m r (l+1)) + rw [coupledVector_lower hz (by omega : k-1 < n+m-2*z), + show k-1+1 = k by omega, + coupledVector_raise hrn hrm (by omega : l+1 ≤ n+m-2*r), + Nat.add_sub_cancel, gridInner_smul_left, gridInner_smul_right, + ih (by omega : k-1 ≤ n+m-2*z) (by omega : l ≤ n+m-2*r), mul_zero] at h + exact (mul_eq_zero.mp h).resolve_left (spinStep_pos (by omega : 0 < k) hk).ne' + · exact gridInner_of_layers (coupledVector_layer _ _ _ _) (coupledVector_layer _ _ _ _) (by omega) + + + +theorem coupledVector_gram {n m z r k l : ℕ} + (hzn : z ≤ n) (hzm : z ≤ m) (hrn : r ≤ n) (hrm : r ≤ m) + (hk : k ≤ n+m-2*z) (hl : l ≤ n+m-2*r) : + gridInner n m (coupledVector n m z k) (coupledVector n m r l) = + if z = r ∧ k = l then 1 else 0 := by + rcases lt_trichotomy z r with hzr | rfl | hrz + · rw [ite_eq_right (by omega)] + exact coupledVector_orthogonal hzn hzm hrn hrm hzr hk hl + · by_cases hkl : k = l + · subst l + rw [ite_eq_left ⟨rfl, rfl⟩] + exact coupledVector_norm hzn hzm hk + · rw [ite_eq_right (by tauto)] + exact gridInner_of_layers (coupledVector_layer _ _ _ _) (coupledVector_layer _ _ _ _) (by omega) + · rw [ite_eq_right (by omega), gridInner_comm] + exact coupledVector_orthogonal hrn hrm hzn hzm hrz hl hk + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/LocalEnergy.lean b/lean/OAI/Analysis/LaughlinFock/LocalEnergy.lean new file mode 100644 index 0000000000000000000000000000000000000000..217631b8ff2450d64d806bd83050d490c3474119 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/LocalEnergy.lean @@ -0,0 +1,387 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FermionOperators +import OAI.Analysis.LaughlinFock.SphereScaling + +namespace OAI + +/-! Local Energy. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open scoped BigOperators Polynomial +open Polynomial +open Filter Topology +open Filter Topology +theorem coefficientPairAnnihilator_smul (L : ℕ) (r : ℂ) + (a : Orbital L → Orbital L → ℂ) : + coefficientPairAnnihilator L (fun i j => r * a i j) = + r • coefficientPairAnnihilator L a := by + classical + unfold coefficientPairAnnihilator + simp only [Finset.smul_sum] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + split_ifs <;> simp [smul_smul] + + +def localPairAnnihilator (L Q p : ℕ) : FockMatrix L := + coefficientPairAnnihilator L + (fun i j => (sphericalPairCoefficient Q p i.val j.val : ℂ)) + + +def limitPairAnnihilator (L p : ℕ) : FockMatrix L := + coefficientPairAnnihilator L (fun i j => (limitPairCoefficient p i.val j.val : ℂ)) + +def localDelta (L Q : ℕ) : FockMatrix L := + occupationDiagonal L (fun j => (modeScale Q j.val : ℂ)) + +def localDeltaInv (L Q : ℕ) : FockMatrix L := + occupationDiagonalInv L (fun j => (modeScale Q j.val : ℂ)) + +theorem localDelta_factor_ne_zero {L Q : ℕ} (hQ : 0 < Q) (hL : L ≤ Q) + (j : Orbital L) : (modeScale Q j.val : ℂ) ≠ 0 := by + exact_mod_cast ne_of_gt (modeScale_pos hQ (j.is_le.trans hL)) + +theorem localDelta_inv_mul {L Q : ℕ} (hQ : 0 < Q) (hL : L ≤ Q) : + localDeltaInv L Q * localDelta L Q = 1 := + occupationDiagonal_inv_mul L _ (localDelta_factor_ne_zero hQ hL) + +theorem localDelta_mul_inv {L Q : ℕ} (hQ : 0 < Q) (hL : L ≤ Q) : + localDelta L Q * localDeltaInv L Q = 1 := + occupationDiagonal_mul_inv L _ (localDelta_factor_ne_zero hQ hL) + + +theorem localPair_conjugation {L Q p : ℕ} (hQ : 0 < Q) (hL : L ≤ Q) + (hp : p ≤ 2*Q-2) : + localPairAnnihilator L Q p = (pairScale Q p : ℂ) • + (localDeltaInv L Q * limitPairAnnihilator L p * localDelta L Q) := by + change localPairAnnihilator L Q p = (pairScale Q p : ℂ) • + diagonalConjugate L (fun j => (modeScale Q j.val : ℂ)) (limitPairAnnihilator L p) + rw [limitPairAnnihilator, diagonalConjugate_pair L _ + (localDelta_factor_ne_zero hQ hL), ← coefficientPairAnnihilator_smul] + unfold localPairAnnihilator + congr 1 + funext i j + rw [sphericalPairCoefficient_factorization hQ hp] + push_cast + ring + + +theorem localFour_conjugation {L Q p : ℕ} (hQ : 0 < Q) (hL : L ≤ Q) + (hp : p ≤ 2*Q-2) (j k : Orbital L) : + annihilator L k * annihilator L j * localPairAnnihilator L Q p = + ((pairScale Q p : ℂ) / ((modeScale Q j.val : ℂ) * modeScale Q k.val)) • + (localDeltaInv L Q * + (annihilator L k * annihilator L j * limitPairAnnihilator L p) * + localDelta L Q) := by + let d : Orbital L → ℂ := fun j => modeScale Q j.val + have hd : ∀ j, d j ≠ 0 := localDelta_factor_ne_zero hQ hL + change _ = ((pairScale Q p : ℂ) / (d j * d k)) • + diagonalConjugate L d (annihilator L k * annihilator L j * limitPairAnnihilator L p) + rw [diagonalConjugate_mul L d hd, diagonalConjugate_mul L d hd, + diagonalConjugate_annihilator L d hd, diagonalConjugate_annihilator L d hd] + simp only [Matrix.smul_mul, Matrix.mul_smul, smul_smul] + rw [localPair_conjugation hQ hL hp, Matrix.mul_smul] + congr 1 + field_simp [hd j, hd k] + + + +theorem localDelta_tendsto (L : ℕ) : + Tendsto (fun Q : ℕ => localDelta L Q) atTop (𝓝 1) := by + classical + apply tendsto_pi_nhds.mpr + intro A + apply tendsto_pi_nhds.mpr + intro B + dsimp only [localDelta, occupationDiagonal] + by_cases h : A=B + · subst B + simp only [Matrix.diagonal_apply_eq, Matrix.one_apply_eq] + have ht := tendsto_finsetProd A (fun j _ => + Complex.continuous_ofReal.continuousAt.tendsto.comp (modeScale_tendsto j.val)) + simpa using ht + · simp only [Matrix.diagonal_apply_ne _ h, Matrix.one_apply_ne h] + exact tendsto_const_nhds + +theorem localDeltaInv_tendsto (L : ℕ) : + Tendsto (fun Q : ℕ => localDeltaInv L Q) atTop (𝓝 1) := by + classical + apply tendsto_pi_nhds.mpr + intro A + apply tendsto_pi_nhds.mpr + intro B + dsimp only [localDeltaInv, occupationDiagonalInv] + by_cases h : A=B + · subst B + simp only [Matrix.diagonal_apply_eq, Matrix.one_apply_eq] + have ht : Tendsto (fun Q : ℕ => ∏ j ∈ A, (modeScale Q j.val : ℂ)) atTop (𝓝 1) := by + have ht := tendsto_finsetProd A (fun j _ => + Complex.continuous_ofReal.continuousAt.tendsto.comp (modeScale_tendsto j.val)) + simpa using ht + simpa only [inv_one] using ht.inv₀ (by norm_num : (1:ℂ) ≠ 0) + · simp only [Matrix.diagonal_apply_ne _ h, Matrix.one_apply_ne h] + exact tendsto_const_nhds + +theorem localDelta_posSemidef (L Q : ℕ) : (localDelta L Q).PosSemidef := by + classical + apply Matrix.posSemidef_diagonal_iff.mpr + intro A + rw [← Complex.ofReal_prod] + exact_mod_cast Finset.prod_nonneg (fun j (_ : j ∈ A) => modeScale_nonneg Q j.val) + +theorem localDelta_le_identity {L Q : ℕ} (hQ : 0 < Q) : + (1-localDelta L Q).PosSemidef := by + classical + rw [localDelta, occupationDiagonal, ← Matrix.diagonal_one, Matrix.diagonal_sub] + apply Matrix.posSemidef_diagonal_iff.mpr + intro A + rw [← Complex.ofReal_one, ← Complex.ofReal_prod, ← Complex.ofReal_sub] + exact_mod_cast sub_nonneg.mpr (Finset.prod_le_one₀ + (fun j (_ : j ∈ A) => modeScale_nonneg Q j.val) (fun j _ => modeScale_le_one hQ j.val)) + +theorem localDelta_contraction {L Q : ℕ} (hQ : 0 < Q) : + (1 - (localDelta L Q)ᴴ * localDelta L Q).PosSemidef := by + classical + rw [(localDelta_posSemidef L Q).isHermitian.eq] + rw [localDelta, occupationDiagonal, Matrix.diagonal_mul_diagonal, + ← Matrix.diagonal_one, Matrix.diagonal_sub] + apply Matrix.posSemidef_diagonal_iff.mpr + intro A + rw [← Complex.ofReal_one, ← Complex.ofReal_prod, ← Complex.ofReal_mul, + ← Complex.ofReal_sub] + have h0 := Finset.prod_nonneg (fun j (_ : j ∈ A) => modeScale_nonneg Q j.val) + have h1 := Finset.prod_le_one₀ (fun j (_ : j ∈ A) => modeScale_nonneg Q j.val) + (fun j _ => modeScale_le_one hQ j.val) + have hs : (∏ j ∈ A, modeScale Q j.val) * (∏ j ∈ A, modeScale Q j.val) ≤ (1:ℝ) := by + simpa only [mul_one] using mul_self_le_mul_self h0 h1 + exact_mod_cast sub_nonneg.mpr hs + + +theorem gram_bound_of_scaled_contraction {ι κ : Type*} [Fintype ι] [Fintype κ] + [DecidableEq ι] (D : Matrix ι ι ℂ) (B C : Matrix ι κ ℂ) (r : ℝ) + (hD : (1 - Dᴴ * D).PosSemidef) (hr : 1 ≤ r) + (hDB : D * B = (r:ℂ) • C) : (Bᴴ * B - Cᴴ * C).PosSemidef := by + classical + have hgram : Bᴴ * (Dᴴ * D) * B = (r:ℂ)^2 • (Cᴴ * C) := by + calc + _ = (D * B)ᴴ * (D * B) := by + simp only [Matrix.conjTranspose_mul, Matrix.mul_assoc] + _ = _ := by + rw [hDB] + simp only [Matrix.conjTranspose_smul, Complex.star_def, Complex.conj_ofReal, + Matrix.smul_mul, Matrix.mul_smul, smul_smul, pow_two] + have hs : (0:ℝ) ≤ r^2-1 := by nlinarith + have hs' : (0:ℂ) ≤ (r:ℂ)^2-1 := by exact_mod_cast hs + have h := (hD.conjTranspose_mul_mul_same B).add + ((Matrix.posSemidef_conjTranspose_mul_self C).smul hs') + rw [Matrix.mul_sub, Matrix.mul_one, Matrix.sub_mul, hgram] at h + convert h using 1 + simp only [sub_smul, one_smul] + abel + + +def localHamiltonian (L P Q : ℕ) : FockMatrix L := + ∑ p ∈ Finset.range P, (localPairAnnihilator L Q p)ᴴ * localPairAnnihilator L Q p + +def limitHamiltonian (L P : ℕ) : FockMatrix L := + ∑ p ∈ Finset.range P, (limitPairAnnihilator L p)ᴴ * limitPairAnnihilator L p + +theorem localPair_energy_transfer {L Q p : ℕ} (hQ : 0 < Q) (hL : L ≤ Q) + (hp : p ≤ 2*Q-2) : + ((localPairAnnihilator L Q p)ᴴ * localPairAnnihilator L Q p - + localDelta L Q * ((limitPairAnnihilator L p)ᴴ * limitPairAnnihilator L p) * + localDelta L Q).PosSemidef := by + classical + have hDB : localDelta L Q * localPairAnnihilator L Q p = + (pairScale Q p : ℂ) • (limitPairAnnihilator L p * localDelta L Q) := by + rw [localPair_conjugation hQ hL hp, Matrix.mul_smul] + congr 1 + rw [← Matrix.mul_assoc, ← Matrix.mul_assoc, localDelta_mul_inv hQ hL, + Matrix.one_mul] + have h := gram_bound_of_scaled_contraction (localDelta L Q) + (localPairAnnihilator L Q p) (limitPairAnnihilator L p * localDelta L Q) + (pairScale Q p) (localDelta_contraction hQ) (pairScale_one_le hQ hp) hDB + simpa only [Matrix.conjTranspose_mul, (localDelta_posSemidef L Q).isHermitian.eq, + Matrix.mul_assoc] using h + + +theorem localHamiltonian_energy_transfer {L P Q : ℕ} (hQ : 0 < Q) (hL : L ≤ Q) + (hP : P ≤ 2*Q-1) : + (localHamiltonian L P Q - + localDelta L Q * limitHamiltonian L P * localDelta L Q).PosSemidef := by + classical + unfold localHamiltonian limitHamiltonian + rw [Matrix.mul_sum, Matrix.sum_mul, ← Finset.sum_sub_distrib] + apply Matrix.posSemidef_sum + intro p hp + exact localPair_energy_transfer hQ hL (by have := Finset.mem_range.mp hp; omega) + + +theorem star_dotProduct_self {ι : Type*} [Fintype ι] (x : ι → ℂ) : + star x ⬝ᵥ x = ((∑ i, ‖x i‖^2 : ℝ) : ℂ) := by + simp [dotProduct, RCLike.star_def, RCLike.conj_mul, ← Complex.ofReal_pow, + Complex.ofReal_sum] + +theorem row_isometry_gram_complement {ι κ : Type*} [Fintype ι] [Fintype κ] + [DecidableEq ι] [DecidableEq κ] (S : Matrix ι κ ℂ) (hS : S * Sᴴ = 1) : + (1 - Sᴴ * S).PosSemidef := by + have hsq : (Sᴴ * S) * (Sᴴ * S) = Sᴴ * S := by + calc + _ = Sᴴ * (S * Sᴴ) * S := by simp only [Matrix.mul_assoc] + _ = _ := by rw [hS, Matrix.mul_one] + have heq : (1-Sᴴ*S)ᴴ * (1-Sᴴ*S) = 1-Sᴴ*S := by + rw [Matrix.conjTranspose_sub, Matrix.conjTranspose_one, + (Matrix.isHermitian_conjTranspose_mul_self S).eq] + calc + _ = 1 - Sᴴ*S - Sᴴ*S + (Sᴴ*S)*(Sᴴ*S) := by noncomm_ring + _ = _ := by rw [hsq]; abel + rw [← heq] + exact Matrix.posSemidef_conjTranspose_mul_self _ + + +theorem row_isometry_contracts {ι κ : Type*} [Fintype ι] [Fintype κ] + [DecidableEq ι] [DecidableEq κ] (S : Matrix ι κ ℂ) (hS : S * Sᴴ = 1) + (x : κ → ℂ) : + (∑ i, ‖(S *ᵥ x) i‖^2) ≤ ∑ j, ‖x j‖^2 := by + have h := Complex.re_le_re ((row_isometry_gram_complement S hS).dotProduct_mulVec_nonneg x) + rw [Matrix.sub_mulVec, dotProduct_sub, Matrix.one_mulVec, gram_quadratic_form, + star_dotProduct_self, star_dotProduct_self, Complex.sub_re] at h + simpa only [Complex.ofReal_re, Complex.zero_re, sub_nonneg] using h + + + +theorem row_isometry_contracts_family {ι κ α : Type*} [Fintype ι] [Fintype κ] + [Fintype α] [DecidableEq ι] [DecidableEq κ] + (S : Matrix ι κ ℂ) (hS : S * Sᴴ = 1) (x : κ → α → ℂ) : + (∑ i, ∑ a, ‖(∑ j, S i j * x j a)‖^2) ≤ ∑ j, ∑ a, ‖x j a‖^2 := by + rw [Finset.sum_comm, Finset.sum_comm (f := fun j a => ‖x j a‖^2)] + exact Finset.sum_le_sum fun a _ => row_isometry_contracts S hS (fun j => x j a) + + +theorem twoAnnihilators_contract (L : ℕ) (j k : Orbital L) (B : FockMatrix L) + (ψ : Occupation L → ℂ) : + (∑ A, ‖((annihilator L k * annihilator L j * B) *ᵥ ψ) A‖^2) ≤ + ∑ A, ‖(B *ᵥ ψ) A‖^2 := by + have hk := annihilator_contracts L k (annihilator L j *ᵥ (B *ᵥ ψ)) + have hj := annihilator_contracts L j (B *ᵥ ψ) + simpa only [← Matrix.mulVec_mulVec] using hk.trans hj + +theorem limitHamiltonian_quadratic_form (L P : ℕ) (ψ : Occupation L → ℂ) : + (star ψ ⬝ᵥ (limitHamiltonian L P *ᵥ ψ)).re = + ∑ p ∈ Finset.range P, ∑ A, ‖(limitPairAnnihilator L p *ᵥ ψ) A‖^2 := by + classical + simp only [limitHamiltonian, Matrix.sum_mulVec, dotProduct_sum, Complex.re_sum, + gram_quadratic_form, star_dotProduct_self, Complex.ofReal_re] + + + +theorem finite_annihilator_family_bound {β : Type*} [Fintype β] + (L P : ℕ) (p : β → ℕ) (j k : β → Orbital L) (hp : ∀ b, p b < P) + (ψ : Occupation L → ℂ) : + (∑ b, ∑ A, + ‖((annihilator L (k b) * annihilator L (j b) * limitPairAnnihilator L (p b)) *ᵥ ψ) A‖^2) + ≤ (Fintype.card β : ℝ) * (star ψ ⬝ᵥ (limitHamiltonian L P *ᵥ ψ)).re := by + classical + rw [limitHamiltonian_quadratic_form] + calc + _ ≤ ∑ b : β, ∑ q ∈ Finset.range P, ∑ A, ‖(limitPairAnnihilator L q *ᵥ ψ) A‖^2 := by + apply Finset.sum_le_sum + intro b _ + refine (twoAnnihilators_contract L (j b) (k b) _ ψ).trans ?_ + exact Finset.single_le_sum + (f := fun q => ∑ A : Occupation L, ‖(limitPairAnnihilator L q *ᵥ ψ) A‖^2) + (fun q _ => Finset.sum_nonneg (fun _ _ => sq_nonneg _)) + (Finset.mem_range.mpr (hp b)) + _ = _ := by simp + + + +def entryNormBound {ι κ : Type*} [Fintype ι] [Fintype κ] (R : Matrix ι κ ℂ) : ℝ := + ∑ i, ∑ j, ‖R i j‖ + +theorem entryNormBound_nonneg {ι κ : Type*} [Fintype ι] [Fintype κ] + (R : Matrix ι κ ℂ) : 0 ≤ entryNormBound R := + Finset.sum_nonneg (fun _ _ => Finset.sum_nonneg (fun _ _ => norm_nonneg _)) + +theorem entryNormBound_quadratic_form {ι : Type*} [Fintype ι] + (R : Matrix ι ι ℂ) (x : ι → ℂ) : + |(star x ⬝ᵥ (R *ᵥ x)).re| ≤ entryNormBound R * ∑ i, ‖x i‖^2 := by + classical + have hp (i j : ι) : ‖x i‖ * ‖x j‖ ≤ ∑ k, ‖x k‖^2 := by + have hi := Finset.single_le_sum (f := fun k : ι => ‖x k‖^2) + (fun k _ => sq_nonneg _) (Finset.mem_univ i) + have hj := Finset.single_le_sum (f := fun k : ι => ‖x k‖^2) + (fun k _ => sq_nonneg _) (Finset.mem_univ j) + nlinarith [sq_nonneg (‖x i‖-‖x j‖)] + refine (Complex.abs_re_le_norm _).trans ?_ + calc + ‖star x ⬝ᵥ (R *ᵥ x)‖ = ‖∑ i, ∑ j, star (x i) * (R i j * x j)‖ := by + simp only [dotProduct, Matrix.mulVec, Pi.star_apply, Finset.mul_sum] + _ ≤ ∑ i, ∑ j, ‖R i j‖ * ∑ k, ‖x k‖^2 := by + apply norm_sum_le_of_le + intro i _ + apply norm_sum_le_of_le + intro j _ + calc + _ = ‖R i j‖ * (‖x i‖ * ‖x j‖) := by simp only [norm_mul, norm_star]; ring + _ ≤ _ := mul_le_mul_of_nonneg_left (hp i j) (norm_nonneg _) + _ = _ := by simp only [entryNormBound, Finset.sum_mul] + + + +theorem entryNormBound_lower_bound {ι : Type*} [Fintype ι] [DecidableEq ι] + (R : Matrix ι ι ℂ) (hR : R.IsHermitian) : + (R + entryNormBound R • 1).PosSemidef := by + have hH : (R + entryNormBound R • 1).IsHermitian := + hR.add (Matrix.isHermitian_one.smul (IsSelfAdjoint.all _)) + apply Matrix.PosSemidef.of_dotProduct_mulVec_nonneg hH + intro x + apply Complex.nonneg_iff.mpr + refine ⟨?_, (hH.im_star_dotProduct_mulVec_self x).symm⟩ + have h := (abs_le.mp (entryNormBound_quadratic_form R x)).1 + simp only [Matrix.add_mulVec, dotProduct_add, Matrix.smul_mulVec, Matrix.one_mulVec, + dotProduct_smul, star_dotProduct_self, Complex.add_re, Complex.smul_re, + Complex.ofReal_re, smul_eq_mul] + linarith + +open Filter Topology + +theorem entryNormBound_tendsto_zero {ι κ : Type*} [Fintype ι] [Fintype κ] + {R : ℕ → Matrix ι κ ℂ} (hR : Tendsto R atTop (𝓝 0)) : + Tendsto (fun Q => entryNormBound (R Q)) atTop (𝓝 0) := by + have ht : ∀ i j, Tendsto (fun Q => ‖R Q i j‖) atTop (𝓝 0) := by + intro i j + simpa only [Matrix.zero_apply, norm_zero] using + ((tendsto_pi_nhds.mp (tendsto_pi_nhds.mp hR i) j).norm) + have h := tendsto_finsetSum Finset.univ (fun i _ => + tendsto_finsetSum Finset.univ (fun j _ => ht i j)) + simpa only [entryNormBound, Finset.sum_const_zero] using h + + + +theorem relative_compression_bound {ι κ : Type*} [Fintype ι] [Fintype κ] + [DecidableEq ι] [DecidableEq κ] (A : Matrix κ ι ℂ) (D : Matrix ι ι ℂ) + (hD : D.IsHermitian) (M R : Matrix κ κ ℂ) (hR : R.IsHermitian) + (Hstar HQ : Matrix ι ι ℂ) (C : ℝ) (hC : 0 ≤ C) + (hLimit : (Aᴴ * M * A).PosSemidef) + (hMajorant : (C • Hstar - Aᴴ * A).PosSemidef) + (hEnergy : (HQ - D * Hstar * D).PosSemidef) : + (D * (Aᴴ * (M + R) * A) * D + + (C * entryNormBound R) • HQ).PosSemidef := by + have h1 := (entryNormBound_lower_bound R hR).conjTranspose_mul_mul_same (A * D) + have h2 := hLimit.conjTranspose_mul_mul_same D + have h3 := (hMajorant.conjTranspose_mul_mul_same D).smul (entryNormBound_nonneg R) + have h4 := hEnergy.smul (mul_nonneg hC (entryNormBound_nonneg R)) + convert ((h1.add h2).add h3).add h4 using 1 + simp only [Matrix.conjTranspose_mul, hD.eq, Matrix.mul_add, Matrix.add_mul, + Matrix.mul_sub, Matrix.sub_mul, Matrix.smul_mul, Matrix.mul_smul, + Matrix.mul_one, Matrix.mul_assoc, smul_sub, smul_smul] + rw [mul_comm (entryNormBound R) C] + abel +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Main.lean b/lean/OAI/Analysis/LaughlinFock/Main.lean new file mode 100644 index 0000000000000000000000000000000000000000..71c0c563ac9b81a59a879dc701fe9d7eed48ef8b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Main.lean @@ -0,0 +1,77 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Assembly +import OAI.Analysis.LaughlinFock.Certificate01 +import OAI.Analysis.LaughlinFock.Certificate02 +import OAI.Analysis.LaughlinFock.Certificate03 +import OAI.Analysis.LaughlinFock.Certificate04 +import OAI.Analysis.LaughlinFock.Certificate05 +import OAI.Analysis.LaughlinFock.Certificate06 +import OAI.Analysis.LaughlinFock.Certificate07 +import OAI.Analysis.LaughlinFock.Certificate08 +import OAI.Analysis.LaughlinFock.Certificate09 +import OAI.Analysis.LaughlinFock.Certificate10 +import OAI.Analysis.LaughlinFock.Certificate11 +import OAI.Analysis.LaughlinFock.Certificate12 +import OAI.Analysis.LaughlinFock.Certificate13 +import OAI.Analysis.LaughlinFock.Certificate14 +import OAI.Analysis.LaughlinFock.Certificate15 +import OAI.Analysis.LaughlinFock.Certificate16 +import OAI.Analysis.LaughlinFock.Certificate17 +import OAI.Analysis.LaughlinFock.Certificate18 +import OAI.Analysis.LaughlinFock.Certificate19 +import OAI.Analysis.LaughlinFock.Certificate20 +import OAI.Analysis.LaughlinFock.Certificate21 +import OAI.Analysis.LaughlinFock.Certificate22 +import OAI.Analysis.LaughlinFock.Certificate23 +import OAI.Analysis.LaughlinFock.IntegerCompression +import OAI.Analysis.LaughlinFock.ThreeCertificate + +namespace OAI + +/-! Main. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +theorem certificate_four (D : ℕ) (hD : 1 ≤ D) (hD' : D ≤ 23) : + (planarFourGram D * planarFourComparison certificateRows (3/10^6) D * + planarFourGram D).PosSemidef := by + apply planar_certificate_of_integer D + interval_cases D + · exact integer_certificate_1 + · exact integer_certificate_2 + · exact integer_certificate_3 + · exact integer_certificate_4 + · exact integer_certificate_5 + · exact integer_certificate_6 + · exact integer_certificate_7 + · exact integer_certificate_8 + · exact integer_certificate_9 + · exact integer_certificate_10 + · exact integer_certificate_11 + · exact integer_certificate_12 + · exact integer_certificate_13 + · exact integer_certificate_14 + · exact integer_certificate_15 + · exact integer_certificate_16 + · exact integer_certificate_17 + · exact integer_certificate_18 + · exact integer_certificate_19 + · exact integer_certificate_20 + · exact integer_certificate_21 + · exact integer_certificate_22 + · exact integer_certificate_23 + + + +theorem thm_fock (γ : ℝ) (_hγ : 0 < γ) (hγStar : γ < gammaStar) : + ∃ Qγ : ℤ, 1 ≤ Qγ ∧ ∀ Q : ℤ, Qγ ≤ Q → FockInequality Q.toNat γ := by + exact integer_threshold_of_certificates_le certificateRows certificateEta_le + certificate_three certificate_four γ hγStar + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Model.lean b/lean/OAI/Analysis/LaughlinFock/Model.lean new file mode 100644 index 0000000000000000000000000000000000000000..38d0a57c1cd01db514cdc7e63f8e5b094348a00c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Model.lean @@ -0,0 +1,317 @@ +import Mathlib +import OAI.Analysis.Laughlin.Model + +namespace OAI + +/-! Model. -/ +noncomputable section + +namespace LaughlinFock + +open scoped BigOperators Matrix ComplexConjugate ComplexOrder + +abbrev Orbital (Q : ℕ) := Fin (Q + 1) +abbrev Occupation (Q : ℕ) := Finset (Orbital Q) +abbrev FockSpace (Q : ℕ) := EuclideanSpace ℂ (Occupation Q) +abbrev FockMatrix (Q : ℕ) := Matrix (Occupation Q) (Occupation Q) ℂ + + +def tensorPairCoefficient (Q p : ℕ) (i j : Orbital Q) : ℝ := + _root_.OAI.Laughlin.pairCoefficient Q p i j + + +def pairCoefficient (Q p : ℕ) (i j : Orbital Q) : ℝ := + Real.sqrt 2 * tensorPairCoefficient Q p i j + + + +def annihilator (Q : ℕ) (j : Orbital Q) : FockMatrix Q := fun A B => + if j ∈ B ∧ A = B.erase j then + (-1 : ℂ) ^ (B.filter (fun i => i < j)).card + else 0 + + + +def pairAnnihilator (Q p : ℕ) : FockMatrix Q := + ∑ i : Orbital Q, ∑ j : Orbital Q, + if i < j then + (pairCoefficient Q p i j : ℂ) • (annihilator Q j * annihilator Q i) + else 0 + + + +def hamiltonian (Q : ℕ) : FockMatrix Q := + ∑ p ∈ Finset.range (2 * Q - 1), + (pairAnnihilator Q p)ᴴ * pairAnnihilator Q p + + +abbrev SectorOccupation (Q n : ℕ) := {A : Occupation Q // A.card = n} + + +def sectorHamiltonian (Q n : ℕ) : + Matrix (SectorOccupation Q n) (SectorOccupation Q n) ℂ := + (hamiltonian Q).submatrix Subtype.val Subtype.val + + +def gammaStar : ℝ := 4616733319001 / 10 ^ 14 + + +def FockInequality (Q : ℕ) (γ : ℝ) : Prop := + (hamiltonian Q * hamiltonian Q - γ • hamiltonian Q).PosSemidef + + + + +theorem pairCoefficient_eq (Q p : ℕ) (i j : Orbital Q) : + pairCoefficient Q p i j = + if i.val + j.val = p + 1 then + ((i.val : ℝ) - (j.val : ℝ)) * + Real.sqrt (((Q.descFactorial i.val : ℝ) * (Q.descFactorial j.val : ℝ) * + (p.factorial : ℝ)) / + ((Q : ℝ) * ((2 * Q - 2).descFactorial p : ℝ) * + (i.val.factorial : ℝ) * (j.val.factorial : ℝ))) + else 0 := by + unfold pairCoefficient tensorPairCoefficient Laughlin.pairCoefficient + split_ifs <;> simp [Real.sqrt_ne_zero'.mpr (show (0 : ℝ) < 2 by norm_num), + mul_comm (Real.sqrt 2)] + + +theorem hamiltonian_posSemidef (Q : ℕ) : (hamiltonian Q).PosSemidef := by + unfold hamiltonian + exact Matrix.posSemidef_sum _ (fun p _ => Matrix.posSemidef_conjTranspose_mul_self _) + +theorem hamiltonian_isHermitian (Q : ℕ) : (hamiltonian Q).IsHermitian := + (hamiltonian_posSemidef Q).isHermitian + + +theorem sectorHamiltonian_posSemidef (Q n : ℕ) : + (sectorHamiltonian Q n).PosSemidef := + (hamiltonian_posSemidef Q).submatrix _ + + +theorem gammaStar_gt_one_twenty_fifth : (1 / 25 : ℝ) < gammaStar := by + norm_num [gammaStar] + + + +theorem final_margin_arithmetic : + (1 : ℝ) - 93527408868499 / 10 ^ 14 - 61 / 4096 - + 1222 * (3 / 10 ^ 6) = gammaStar := by + norm_num [gammaStar] + + + +theorem annihilator_card {Q : ℕ} (j : Orbital Q) (A B : Occupation Q) + (h : annihilator Q j A B ≠ 0) : A.card + 1 = B.card := by + by_cases hc : j ∈ B ∧ A = B.erase j + · rcases hc with ⟨hj, rfl⟩ + exact Finset.card_erase_add_one hj + · exact (h (by simp [annihilator, hc])).elim + +theorem annihilator_entry_eq_zero {Q : ℕ} (j : Orbital Q) (A B : Occupation Q) + (h : A.card + 1 ≠ B.card) : annihilator Q j A B = 0 := by + by_contra hh + exact h (annihilator_card j A B hh) + + +theorem pairAnnihilator_entry_eq_zero {Q : ℕ} (p : ℕ) (A B : Occupation Q) + (h : A.card + 2 ≠ B.card) : pairAnnihilator Q p A B = 0 := by + classical + simp only [pairAnnihilator, Matrix.sum_apply] + apply Finset.sum_eq_zero + intro i _ + apply Finset.sum_eq_zero + intro j _ + split_ifs + · simp only [Matrix.smul_apply, smul_eq_mul] + suffices hc : (annihilator Q j * annihilator Q i) A B = 0 by simp [hc] + rw [Matrix.mul_apply] + apply Finset.sum_eq_zero + intro C _ + by_cases hAC : A.card + 1 = C.card + · have hCB : C.card + 1 ≠ B.card := by omega + rw [annihilator_entry_eq_zero i C B hCB, mul_zero] + · rw [annihilator_entry_eq_zero j A C hAC, zero_mul] + · rfl + + +theorem hamiltonian_entry_eq_zero {Q : ℕ} (A B : Occupation Q) + (h : A.card ≠ B.card) : hamiltonian Q A B = 0 := by + classical + simp only [hamiltonian, Matrix.sum_apply, Matrix.mul_apply, Matrix.conjTranspose_apply] + apply Finset.sum_eq_zero + intro p _ + apply Finset.sum_eq_zero + intro C _ + by_cases hCA : C.card + 2 = A.card + · have hCB : C.card + 2 ≠ B.card := by omega + rw [pairAnnihilator_entry_eq_zero p C B hCB, mul_zero] + · rw [pairAnnihilator_entry_eq_zero p C A hCA, star_zero, zero_mul] + + + +theorem sectorHamiltonian_eq_zero_of_le_one (Q n : ℕ) (hn : n ≤ 1) : + sectorHamiltonian Q n = 0 := by + classical + ext A B + change hamiltonian Q A.val B.val = 0 + simp only [hamiltonian, Matrix.sum_apply, Matrix.mul_apply] + apply Finset.sum_eq_zero + intro p _ + apply Finset.sum_eq_zero + intro C _ + have hCB : C.card + 2 ≠ B.val.card := by rw [B.property]; omega + rw [pairAnnihilator_entry_eq_zero p C B.val hCB, mul_zero] + +@[simp] theorem sectorHamiltonian_zero_particles (Q : ℕ) : + sectorHamiltonian Q 0 = 0 := sectorHamiltonian_eq_zero_of_le_one Q 0 (by omega) + +@[simp] theorem sectorHamiltonian_one_particle (Q : ℕ) : + sectorHamiltonian Q 1 = 0 := sectorHamiltonian_eq_zero_of_le_one Q 1 (by omega) + + + +theorem sectorHamiltonian_square (Q n : ℕ) : + (hamiltonian Q * hamiltonian Q).submatrix + (Subtype.val : SectorOccupation Q n → Occupation Q) Subtype.val = + sectorHamiltonian Q n * sectorHamiltonian Q n := by + classical + ext A B + change (∑ C : Occupation Q, hamiltonian Q A.val C * hamiltonian Q C B.val) = + ∑ C : SectorOccupation Q n, hamiltonian Q A.val C.val * hamiltonian Q C.val B.val + let f : Occupation Q → ℂ := fun C => hamiltonian Q A.val C * hamiltonian Q C B.val + change ∑ C, f C = ∑ C : SectorOccupation Q n, f C.val + calc + _ = ∑ C ∈ Finset.univ.filter (fun C : Occupation Q => C.card = n), f C := by + symm + apply Finset.sum_subset (Finset.filter_subset _ _) + intro C _ hC + have hc : A.val.card ≠ C.card := by + rw [A.property] + simpa only [Finset.mem_filter, Finset.mem_univ, true_and, eq_comm] using hC + simp only [f, hamiltonian_entry_eq_zero A.val C hc, zero_mul] + _ = _ := Finset.sum_subtype _ (by intro C; simp) f + + + +theorem sector_inequality_of_fock {Q : ℕ} {γ : ℝ} (h : FockInequality Q γ) + (n : ℕ) : + (sectorHamiltonian Q n * sectorHamiltonian Q n - γ • sectorHamiltonian Q n).PosSemidef := by + have hc := h.submatrix (Subtype.val : SectorOccupation Q n → Occupation Q) + change ((hamiltonian Q * hamiltonian Q - γ • hamiltonian Q).submatrix + (Subtype.val : SectorOccupation Q n → Occupation Q) Subtype.val).PosSemidef at hc + simpa only [Matrix.submatrix_sub, Matrix.submatrix_smul, Pi.sub_apply, Pi.smul_apply, + sectorHamiltonian_square, sectorHamiltonian] using hc + + +theorem gram_quadratic_form {ι κ : Type*} [Fintype ι] [Fintype κ] + (A : Matrix ι κ ℂ) (ψ : κ → ℂ) : + star ψ ⬝ᵥ ((Aᴴ * A) *ᵥ ψ) = star (A *ᵥ ψ) ⬝ᵥ (A *ᵥ ψ) := by + rw [← Matrix.mulVec_mulVec, Matrix.dotProduct_mulVec, Matrix.vecMul_conjTranspose, star_star] + + + +theorem hamiltonian_quadratic_form (Q : ℕ) (ψ : Occupation Q → ℂ) : + (star ψ ⬝ᵥ (hamiltonian Q *ᵥ ψ)).re = + ∑ p ∈ Finset.range (2 * Q - 1), ∑ A : Occupation Q, + ‖(pairAnnihilator Q p *ᵥ ψ) A‖ ^ 2 := by + classical + simp only [hamiltonian, Matrix.sum_mulVec, dotProduct_sum, Complex.re_sum] + apply Finset.sum_congr rfl + intro p _ + rw [gram_quadratic_form] + simp [dotProduct, RCLike.star_def, RCLike.conj_mul, ← Complex.ofReal_pow] + + +theorem occupation_card_le (Q : ℕ) (A : Occupation Q) : A.card ≤ Q + 1 := by + simpa using Finset.card_le_univ A + + + +theorem sector_quadratic_form_decomposition (Q : ℕ) (M : FockMatrix Q) + (hM : ∀ A B : Occupation Q, A.card ≠ B.card → M A B = 0) + (ψ : Occupation Q → ℂ) : + star ψ ⬝ᵥ (M *ᵥ ψ) = + ∑ n ∈ Finset.range (Q + 2), + star (fun A : SectorOccupation Q n => ψ A.val) ⬝ᵥ + (M.submatrix (Subtype.val : SectorOccupation Q n → Occupation Q) + Subtype.val *ᵥ (fun A : SectorOccupation Q n => ψ A.val)) := by + classical + simp only [dotProduct, Matrix.mulVec, Pi.star_apply, Matrix.submatrix_apply] + have hcard : ∀ A ∈ (Finset.univ : Finset (Occupation Q)), + A.card ∈ Finset.range (Q + 2) := by + intro A _ + have := occupation_card_le Q A + simp only [Finset.mem_range] + omega + rw [← Finset.sum_fiberwise_of_maps_to hcard] + apply Finset.sum_congr rfl + intro n _ + rw [Finset.sum_subtype (p := fun A : Occupation Q => A.card = n) _ (by intro A; simp)] + apply Finset.sum_congr rfl + intro A _ + congr 1 + calc + _ = ∑ B ∈ Finset.univ.filter (fun B : Occupation Q => B.card = n), + M A.val B * ψ B := by + symm + apply Finset.sum_subset (Finset.filter_subset _ _) + intro B _ hB + have hAB : A.val.card ≠ B.card := by + rw [A.property] + simpa only [Finset.mem_filter, Finset.mem_univ, true_and, eq_comm] using hB + simp only [hM A.val B hAB, zero_mul] + _ = _ := Finset.sum_subtype _ (by intro B; simp) _ + + + +theorem posSemidef_of_sectors {Q : ℕ} {M : FockMatrix Q} (hHerm : M.IsHermitian) + (hM : ∀ A B : Occupation Q, A.card ≠ B.card → M A B = 0) + (h : ∀ n : ℕ, n ≤ Q + 1 → + (M.submatrix (Subtype.val : SectorOccupation Q n → Occupation Q) + Subtype.val).PosSemidef) : M.PosSemidef := by + apply Matrix.PosSemidef.of_dotProduct_mulVec_nonneg hHerm + intro ψ + rw [sector_quadratic_form_decomposition Q M hM ψ] + apply Finset.sum_nonneg + intro n hn + have hn' : n ≤ Q + 1 := by simpa only [Finset.mem_range, Nat.lt_succ_iff] using hn + exact (h n hn').dotProduct_mulVec_nonneg _ + + +theorem gapMatrix_entry_eq_zero {Q : ℕ} (γ : ℝ) (A B : Occupation Q) + (h : A.card ≠ B.card) : + (hamiltonian Q * hamiltonian Q - γ • hamiltonian Q) A B = 0 := by + classical + simp only [Matrix.sub_apply, Matrix.smul_apply, hamiltonian_entry_eq_zero A B h, + smul_zero, sub_zero, Matrix.mul_apply] + apply Finset.sum_eq_zero + intro C _ + by_cases hAC : A.card = C.card + · have hCB : C.card ≠ B.card := by omega + rw [hamiltonian_entry_eq_zero C B hCB, mul_zero] + · rw [hamiltonian_entry_eq_zero A C hAC, zero_mul] + + + +theorem fock_inequality_iff_sectors (Q : ℕ) (γ : ℝ) : + FockInequality Q γ ↔ ∀ n : ℕ, n ≤ Q + 1 → + (sectorHamiltonian Q n * sectorHamiltonian Q n - + γ • sectorHamiltonian Q n).PosSemidef := by + classical + constructor + · intro h n _ + exact sector_inequality_of_fock h n + · intro h + have hHerm : (hamiltonian Q * hamiltonian Q).IsHermitian := by + simpa only [pow_two] using (hamiltonian_isHermitian Q).pow 2 + apply posSemidef_of_sectors + (hHerm.sub ((hamiltonian_isHermitian Q).smul (show IsSelfAdjoint γ by rfl))) + (gapMatrix_entry_eq_zero γ) + intro n hn + simpa only [Matrix.submatrix_sub, Matrix.submatrix_smul, Pi.sub_apply, Pi.smul_apply, + sectorHamiltonian_square, sectorHamiltonian] using h n hn +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/NormalOrdering.lean b/lean/OAI/Analysis/LaughlinFock/NormalOrdering.lean new file mode 100644 index 0000000000000000000000000000000000000000..a1e01818728779fc381584dfcf2d3d6e1ff33366 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/NormalOrdering.lean @@ -0,0 +1,995 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.GramCompression +import OAI.Analysis.LaughlinFock.PairNormalization +import OAI.Analysis.LaughlinFock.RelativePerturbation + +namespace OAI + +/-! Normal Ordering. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open scoped BigOperators Polynomial +open Polynomial +open Filter Topology +open Filter Topology +open Filter Topology +open scoped Kronecker +open scoped Matrix ComplexOrder Kronecker BigOperators + + + +def annihilatorList (Q : ℕ) : List (Orbital Q) → FockMatrix Q + | [] => 1 + | j :: js => annihilatorList Q js * annihilator Q j + +@[simp] theorem annihilatorList_nil (Q : ℕ) : annihilatorList Q [] = 1 := rfl + +@[simp] theorem annihilatorList_cons (Q : ℕ) (j : Orbital Q) (js : List (Orbital Q)) : + annihilatorList Q (j :: js) = annihilatorList Q js * annihilator Q j := rfl + + +def basisAnnihilator (Q : ℕ) (A : Occupation Q) : FockMatrix Q := + annihilatorList Q (A.sort (· ≤ ·)) + +theorem annihilatorList_entry_eq_zero (Q : ℕ) (js : List (Orbital Q)) + (A B : Occupation Q) (h : A.card + js.length ≠ B.card) : + annihilatorList Q js A B = 0 := by + induction js generalizing A B with + | nil => + have hAB : A ≠ B := by intro hh; subst B; simp at h + simp [hAB] + | cons j js ih => + rw [annihilatorList_cons, Matrix.mul_apply] + apply Finset.sum_eq_zero + intro C _ + by_cases hCB : C.card + 1 = B.card + · have hAC : A.card + js.length ≠ C.card := by simp only [List.length_cons] at h; omega + rw [ih A C hAC, zero_mul] + · rw [annihilator_entry_eq_zero _ _ _ hCB, mul_zero] + +theorem basisAnnihilator_entry_eq_zero (Q : ℕ) (S A B : Occupation Q) + (h : A.card + S.card ≠ B.card) : basisAnnihilator Q S A B = 0 := by + apply annihilatorList_entry_eq_zero + simpa only [Finset.length_sort] using h + +theorem annihilatorList_vacuum (Q : ℕ) (js : List (Orbital Q)) + (hs : js.Pairwise (· ≤ ·)) (hd : js.Nodup) (A : Occupation Q) : + annihilatorList Q js ∅ A = if js.toFinset = A then 1 else 0 := by + induction js generalizing A with + | nil => simp only [annihilatorList, Matrix.one_apply, List.toFinset_nil]; rfl + | cons j js ih => + obtain ⟨hjs, hs⟩ := List.pairwise_cons.mp hs + obtain ⟨hjn, hd⟩ := List.nodup_cons.mp hd + rw [annihilatorList_cons, mul_annihilator_apply] + by_cases hjA : j ∈ A + · rw [ite_eq_left hjA, ih hs hd] + by_cases he : js.toFinset = A.erase j + · have heA : insert j js.toFinset = A := by rw [he, Finset.insert_erase hjA] + have hfilter : A.filter (fun x => x < j) = ∅ := by + apply Finset.filter_eq_empty_iff.mpr + intro x hx + rw [← heA, Finset.mem_insert] at hx + rcases hx with rfl | hx + · exact lt_irrefl _ + · exact not_lt_of_ge (hjs x (List.mem_toFinset.mp hx)) + simp only [ite_eq_left he, one_mul, fermionSign, hfilter, Finset.card_empty, + pow_zero, List.toFinset_cons, ite_eq_left heA] + · have hneA : insert j js.toFinset ≠ A := by + intro h + have hjnot : j ∉ js.toFinset := by simpa using hjn + apply he + rw [← h, Finset.erase_insert hjnot] + simp only [ite_eq_right he, zero_mul, List.toFinset_cons, ite_eq_right hneA] + · have hneA : insert j js.toFinset ≠ A := by + intro h; apply hjA; rw [← h]; exact Finset.mem_insert_self _ _ + simp only [ite_eq_right hjA, List.toFinset_cons, ite_eq_right hneA] + + + +theorem basisAnnihilator_vacuum (Q : ℕ) (S A : Occupation Q) : + basisAnnihilator Q S ∅ A = if S=A then 1 else 0 := by + simpa only [basisAnnihilator, Finset.sort_toFinset] using + annihilatorList_vacuum Q (S.sort (· ≤ ·)) (S.pairwise_sort _) (S.sort_nodup _) A + +theorem basisAnnihilator_same_sector (Q k : ℕ) (S A : SectorOccupation Q k) + (R : Occupation Q) : + basisAnnihilator Q S.val R A.val = if R=∅ then if S=A then 1 else 0 else 0 := by + by_cases hR : R=∅ + · subst R + rw [basisAnnihilator_vacuum] + simp only [Subtype.val_inj, ite_true] + · rw [ite_eq_right hR] + apply basisAnnihilator_entry_eq_zero + rw [S.property, A.property] + have hcard : R.card ≠ 0 := fun h => hR (Finset.card_eq_zero.mp h) + omega + + +def wedgeAnnihilator (Q k : ℕ) (v : SectorOccupation Q k → ℂ) : FockMatrix Q := + ∑ A, star (v A) • basisAnnihilator Q A.val + + +def exteriorLift (Q k : ℕ) (M : Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ) : + FockMatrix Q := + ∑ A, ∑ B, M A B • ((basisAnnihilator Q A.val)ᴴ * basisAnnihilator Q B.val) + + + +theorem exteriorLift_posSemidef (Q k : ℕ) + (M : Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ) (hM : M.PosSemidef) : + (exteriorLift Q k M).PosSemidef := by + let A : SectorOccupation Q k → FockMatrix Q := fun S => basisAnnihilator Q S.val + have hK : (M ⊗ₖ (1 : FockMatrix Q)).PosSemidef := hM.kronecker Matrix.PosSemidef.one + have h := hK.conjTranspose_mul_mul_same (stackFamily A) + simpa only [stackFamily_kronecker, Matrix.mul_one, exteriorLift, A] using h + + + +theorem exteriorLift_rankOne (Q k : ℕ) (v w : SectorOccupation Q k → ℂ) : + exteriorLift Q k (Matrix.vecMulVec v (star w)) = + (wedgeAnnihilator Q k v)ᴴ * wedgeAnnihilator Q k w := by + unfold exteriorLift wedgeAnnihilator + simp only [Matrix.conjTranspose_sum, Matrix.conjTranspose_smul, star_star, + Matrix.sum_mul, Matrix.mul_sum, Matrix.smul_mul, Matrix.mul_smul, + Matrix.vecMulVec_apply, Pi.star_apply, Finset.smul_sum, smul_smul] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro A _ + apply Finset.sum_congr rfl + intro B _ + rw [mul_comm] + +theorem basisAnnihilator_gram_same_sector (Q k : ℕ) (S T A B : SectorOccupation Q k) : + ((basisAnnihilator Q S.val)ᴴ * basisAnnihilator Q T.val) A.val B.val = + (if S=A then (1 : ℂ) else 0) * (if T=B then (1 : ℂ) else 0) := by + classical + rw [Matrix.mul_apply] + simp only [Matrix.conjTranspose_apply, basisAnnihilator_same_sector] + rw [Finset.sum_eq_single ∅] + · simp only [ite_true, apply_ite star, star_one, star_zero] + · intro R _ hR + simp only [ite_eq_right hR, star_zero, zero_mul] + · simp + + +theorem exteriorLift_same_sector (Q k : ℕ) + (M : Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ) : + (exteriorLift Q k M).submatrix Subtype.val Subtype.val = M := by + classical + apply Matrix.ext + intro A B + change exteriorLift Q k M A.val B.val = M A B + simp only [exteriorLift, Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, + basisAnnihilator_gram_same_sector] + simp [mul_ite] + + +theorem exteriorLift_below_sector (Q k n : ℕ) (hn : n < k) + (M : Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ) : + (exteriorLift Q k M).submatrix + (Subtype.val : SectorOccupation Q n → Occupation Q) + (Subtype.val : SectorOccupation Q n → Occupation Q) = 0 := by + classical + ext A B + simp only [Matrix.submatrix_apply, exteriorLift, Matrix.sum_apply, Matrix.smul_apply, + smul_eq_mul, Matrix.mul_apply, Matrix.conjTranspose_apply, Matrix.zero_apply] + apply Finset.sum_eq_zero + intro S _ + apply Finset.sum_eq_zero + intro T _ + suffices hzero : (∑ R, star (basisAnnihilator Q S.val R A.val) * + basisAnnihilator Q T.val R B.val) = 0 by rw [hzero, mul_zero] + apply Finset.sum_eq_zero + intro R _ + have h : basisAnnihilator Q T.val R B.val = 0 := + basisAnnihilator_entry_eq_zero Q _ _ _ (by rw [T.property, B.property]; omega) + rw [h, mul_zero] + + + +theorem annihilator_swap (Q : ℕ) (i j : Orbital Q) : + annihilator Q i * annihilator Q j = -(annihilator Q j * annihilator Q i) := + eq_neg_of_add_eq_zero_left (annihilator_anticommute Q i j) + +theorem annihilatorList_append (Q : ℕ) (is js : List (Orbital Q)) : + annihilatorList Q (is ++ js) = annihilatorList Q js * annihilatorList Q is := by + induction is with + | nil => simp + | cons i is ih => simp only [List.cons_append, annihilatorList_cons, ih, Matrix.mul_assoc] + + + +theorem annihilatorList_perm (Q : ℕ) {is js : List (Orbital Q)} (h : is.Perm js) : + ∃ c : ℂ, annihilatorList Q is = c • annihilatorList Q js := by + induction h with + | nil => exact ⟨1, by simp⟩ + | cons i h ih => + obtain ⟨c, hc⟩ := ih + exact ⟨c, by simp only [annihilatorList_cons, hc, Matrix.smul_mul]⟩ + | swap i j js => + refine ⟨-1, ?_⟩ + simp only [annihilatorList_cons, Matrix.mul_assoc, neg_one_smul] + rw [annihilator_swap Q i j, Matrix.mul_neg] + | trans h₁ h₂ ih₁ ih₂ => + obtain ⟨c, hc⟩ := ih₁ + obtain ⟨d, hd⟩ := ih₂ + exact ⟨c*d, by rw [hc, hd, smul_smul]⟩ + +theorem annihilatorList_mul_of_mem (Q : ℕ) (js : List (Orbital Q)) (i : Orbital Q) + (hi : i ∈ js) : annihilatorList Q js * annihilator Q i = 0 := by + induction js with + | nil => simp at hi + | cons j js ih => + rw [annihilatorList_cons, Matrix.mul_assoc] + rcases List.mem_cons.mp hi with rfl | hi + · rw [annihilator_square, Matrix.mul_zero] + · rw [annihilator_swap Q j i, Matrix.mul_neg, ← Matrix.mul_assoc, + ih hi, Matrix.zero_mul, neg_zero] + +theorem annihilatorList_eq_zero_of_not_nodup (Q : ℕ) (js : List (Orbital Q)) + (h : ¬ js.Nodup) : annihilatorList Q js = 0 := by + induction js with + | nil => simp at h + | cons i js ih => + rw [annihilatorList_cons] + by_cases hi : i ∈ js + · exact annihilatorList_mul_of_mem Q js i hi + · have hjs : ¬ js.Nodup := by intro hj; exact h (List.nodup_cons.mpr ⟨hi,hj⟩) + rw [ih hjs, Matrix.zero_mul] + + + +theorem annihilatorList_expansion (Q : ℕ) (js : List (Orbital Q)) (k : ℕ) + (hk : js.length=k) : + annihilatorList Q js = ∑ S : SectorOccupation Q k, + annihilatorList Q js ∅ S.val • basisAnnihilator Q S.val := by + classical + by_cases hd : js.Nodup + · let T : SectorOccupation Q k := ⟨js.toFinset, by rw [List.toFinset_card_of_nodup hd, hk]⟩ + have hperm : js.Perm (js.toFinset.sort (· ≤ ·)) := by + apply (List.perm_ext_iff_of_nodup hd (js.toFinset.sort_nodup _)).mpr + intro i + simp only [Finset.mem_sort, List.mem_toFinset] + obtain ⟨c, hc⟩ := annihilatorList_perm Q hperm + change annihilatorList Q js = c • basisAnnihilator Q T.val at hc + rw [hc, Finset.sum_eq_single T] + · simp only [Matrix.smul_apply, basisAnnihilator_vacuum, ite_true, smul_eq_mul, mul_one] + · intro S _ hST + have hne : T.val ≠ S.val := by + intro hh; exact hST (Subtype.ext hh.symm) + simp only [Matrix.smul_apply, basisAnnihilator_vacuum, ite_eq_right hne, smul_eq_mul, + mul_zero, zero_smul] + · simp + · rw [annihilatorList_eq_zero_of_not_nodup Q js hd] + simp only [Matrix.zero_apply, zero_smul, Finset.sum_const_zero] + + + +theorem exteriorLift_congruence {α : Type*} [Fintype α] (Q k : ℕ) + (W : Matrix (SectorOccupation Q k) α ℂ) (C : Matrix α α ℂ) : + exteriorLift Q k (W * C * Wᴴ) = + ∑ r, ∑ s, C r s • + ((wedgeAnnihilator Q k (fun A => W A r))ᴴ * + wedgeAnnihilator Q k (fun A => W A s)) := by + classical + have h := quadratic_family_mix (fun A : SectorOccupation Q k => basisAnnihilator Q A.val) + Wᴴ C + simpa only [Matrix.conjTranspose_conjTranspose, Matrix.conjTranspose_apply, + exteriorLift, wedgeAnnihilator] using h.symm + + + +theorem exteriorLift_of_gram_certificate {α : Type*} [Fintype α] (Q k : ℕ) + (W : Matrix (SectorOccupation Q k) α ℂ) (C : Matrix α α ℂ) (hC : C.IsHermitian) + (hG : ((Wᴴ*W) * C * (Wᴴ*W)).PosSemidef) : + (∑ r, ∑ s, C r s • + ((wedgeAnnihilator Q k (fun A => W A r))ᴴ * + wedgeAnnihilator Q k (fun A => W A s))).PosSemidef := by + rw [← exteriorLift_congruence] + apply exteriorLift_posSemidef + exact (gram_compression_posSemidef_iff W C hC).mp hG + + + +def AnnihilationSpace (Q k : ℕ) : Submodule ℂ (FockMatrix Q) := + Submodule.span ℂ (Set.range (fun S : SectorOccupation Q k => basisAnnihilator Q S.val)) + +theorem basisAnnihilator_mem (Q k : ℕ) (S : SectorOccupation Q k) : + basisAnnihilator Q S.val ∈ AnnihilationSpace Q k := + Submodule.subset_span ⟨S,rfl⟩ + +theorem annihilatorList_mem (Q : ℕ) (js : List (Orbital Q)) (k : ℕ) (hk : js.length=k) : + annihilatorList Q js ∈ AnnihilationSpace Q k := by + rw [annihilatorList_expansion Q js k hk] + exact Submodule.sum_mem _ (fun S _ => Submodule.smul_mem _ _ (basisAnnihilator_mem Q k S)) + +theorem annihilationSpace_normal_form (Q k : ℕ) (M : FockMatrix Q) + (hM : M ∈ AnnihilationSpace Q k) : + M = ∑ S : SectorOccupation Q k, M ∅ S.val • basisAnnihilator Q S.val := by + classical + induction hM using Submodule.span_induction with + | mem M hM => + obtain ⟨T,rfl⟩ := hM + rw [Finset.sum_eq_single T] + · simp only [basisAnnihilator_vacuum, ite_true, one_smul] + · intro S _ hST + have hne : T.val ≠ S.val := by intro h; exact hST (Subtype.ext h.symm) + simp only [basisAnnihilator_vacuum, ite_eq_right hne, zero_smul] + · simp + | zero => simp only [Matrix.zero_apply, zero_smul, Finset.sum_const_zero] + | add M N hM hN ihM ihN => + simp only [Matrix.add_apply, add_smul, Finset.sum_add_distrib] + rw [← ihM, ← ihN] + | smul r M hM ihM => + simp only [Matrix.smul_apply, smul_eq_mul, mul_smul, ← Finset.smul_sum] + rw [← ihM] + + +theorem annihilationSpace_ext (Q k : ℕ) {M N : FockMatrix Q} + (hM : M ∈ AnnihilationSpace Q k) (hN : N ∈ AnnihilationSpace Q k) + (h : ∀ S : SectorOccupation Q k, M ∅ S.val = N ∅ S.val) : M=N := by + rw [annihilationSpace_normal_form Q k M hM, annihilationSpace_normal_form Q k N hN] + simp only [h] + + + +theorem annihilationSpace_mul (Q k l : ℕ) {M N : FockMatrix Q} + (hM : M ∈ AnnihilationSpace Q k) (hN : N ∈ AnnihilationSpace Q l) : + N * M ∈ AnnihilationSpace Q (k+l) := by + classical + rw [annihilationSpace_normal_form Q k M hM, annihilationSpace_normal_form Q l N hN] + simp only [Matrix.sum_mul, Matrix.mul_sum, Matrix.smul_mul, Matrix.mul_smul] + apply Submodule.sum_mem + intro T _ + apply Submodule.smul_mem + apply Submodule.sum_mem + intro S _ + apply Submodule.smul_mem + rw [basisAnnihilator, basisAnnihilator, ← annihilatorList_append] + apply annihilatorList_mem + simp only [List.length_append, Finset.length_sort, S.property, T.property] + +theorem annihilator_mem (Q : ℕ) (j : Orbital Q) : + annihilator Q j ∈ AnnihilationSpace Q 1 := by + simpa only [annihilatorList_cons, annihilatorList_nil, Matrix.one_mul] using + annihilatorList_mem Q [j] 1 rfl + +theorem coefficientPairAnnihilator_mem (Q : ℕ) (a : Orbital Q → Orbital Q → ℂ) : + coefficientPairAnnihilator Q a ∈ AnnihilationSpace Q 2 := by + classical + unfold coefficientPairAnnihilator + apply Submodule.sum_mem + intro i _ + apply Submodule.sum_mem + intro j _ + split_ifs + · apply Submodule.smul_mem + exact annihilationSpace_mul Q 1 1 (annihilator_mem Q i) (annihilator_mem Q j) + · exact Submodule.zero_mem _ + +theorem pairAnnihilator_mem (Q p : ℕ) : + pairAnnihilator Q p ∈ AnnihilationSpace Q 2 := + coefficientPairAnnihilator_mem Q _ + +theorem limitPairAnnihilator_mem (L p : ℕ) : + limitPairAnnihilator L p ∈ AnnihilationSpace L 2 := + coefficientPairAnnihilator_mem L _ + +theorem localPairAnnihilator_mem (L Q p : ℕ) : + localPairAnnihilator L Q p ∈ AnnihilationSpace L 2 := + coefficientPairAnnihilator_mem L _ + + + +def annihilatorVector (Q k : ℕ) (M : FockMatrix Q) : SectorOccupation Q k → ℂ := + fun S => star (M ∅ S.val) + +theorem wedgeAnnihilator_mem (Q k : ℕ) (v : SectorOccupation Q k → ℂ) : + wedgeAnnihilator Q k v ∈ AnnihilationSpace Q k := by + exact Submodule.sum_mem _ (fun S _ => + Submodule.smul_mem _ _ (basisAnnihilator_mem Q k S)) + +theorem wedgeAnnihilator_annihilatorVector (Q k : ℕ) (M : FockMatrix Q) + (hM : M ∈ AnnihilationSpace Q k) : + wedgeAnnihilator Q k (annihilatorVector Q k M) = M := by + have h := annihilationSpace_normal_form Q k M hM + simpa only [wedgeAnnihilator, annihilatorVector, star_star] using h.symm + + + +theorem exteriorLift_annihilator_product (Q k : ℕ) {M N : FockMatrix Q} + (hM : M ∈ AnnihilationSpace Q k) (hN : N ∈ AnnihilationSpace Q k) : + exteriorLift Q k (Matrix.vecMulVec (annihilatorVector Q k M) + (star (annihilatorVector Q k N))) = Mᴴ * N := by + rw [exteriorLift_rankOne, wedgeAnnihilator_annihilatorVector Q k M hM, + wedgeAnnihilator_annihilatorVector Q k N hN] + + +def exteriorLiftLinear (Q k : ℕ) : + Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ →ₗ[ℂ] FockMatrix Q where + toFun := exteriorLift Q k + map_add' M N := by + simp only [exteriorLift, Matrix.add_apply, add_smul, Finset.sum_add_distrib] + map_smul' c M := by + simp only [exteriorLift, Matrix.smul_apply, smul_eq_mul, mul_smul, + ← Finset.smul_sum, RingHom.id_apply] + +@[simp] theorem exteriorLift_add (Q k : ℕ) + (M N : Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ) : + exteriorLift Q k (M+N) = exteriorLift Q k M + exteriorLift Q k N := + (exteriorLiftLinear Q k).map_add M N + +@[simp] theorem exteriorLift_sub (Q k : ℕ) + (M N : Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ) : + exteriorLift Q k (M-N) = exteriorLift Q k M - exteriorLift Q k N := + (exteriorLiftLinear Q k).map_sub M N + +@[simp] theorem exteriorLift_sum {α : Type*} (Q k : ℕ) (s : Finset α) + (M : α → Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ) : + exteriorLift Q k (∑ a ∈ s, M a) = ∑ a ∈ s, exteriorLift Q k (M a) := + map_sum (exteriorLiftLinear Q k) M s + + + +def BodySpace (Q k : ℕ) : Submodule ℂ (FockMatrix Q) := + LinearMap.range (exteriorLiftLinear Q k) + +theorem bodySpace_product (Q k : ℕ) {M N : FockMatrix Q} + (hM : M ∈ AnnihilationSpace Q k) (hN : N ∈ AnnihilationSpace Q k) : + Mᴴ*N ∈ BodySpace Q k := + ⟨_, exteriorLift_annihilator_product Q k hM hN⟩ + +theorem bodySpace_reconstruct (Q k : ℕ) {M : FockMatrix Q} (hM : M ∈ BodySpace Q k) : + exteriorLift Q k (M.submatrix + (Subtype.val : SectorOccupation Q k → Occupation Q) Subtype.val) = M := by + obtain ⟨A,rfl⟩ := hM + exact congrArg (exteriorLift Q k) (exteriorLift_same_sector Q k A) + +theorem bodySpace_below_sector (Q k n : ℕ) (hn : n < k) + {M : FockMatrix Q} (hM : M ∈ BodySpace Q k) : + M.submatrix (Subtype.val : SectorOccupation Q n → Occupation Q) + (Subtype.val : SectorOccupation Q n → Occupation Q) = 0 := by + obtain ⟨A,rfl⟩ := hM + exact exteriorLift_below_sector Q k n hn A + + + +theorem bodySpace_two_decomposition (Q k l : ℕ) (hkl : k lhs; unfold coefficientPairAnnihilator + conv_rhs => rhs; unfold coefficientPairAnnihilator + simp only [Matrix.sum_mul, Matrix.mul_sum] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + split_ifs + · simp only [Matrix.smul_mul, Matrix.mul_smul] + congr 1 + rw [Matrix.mul_assoc, annihilator_commutes_coefficientPair, + ← Matrix.mul_assoc, annihilator_commutes_coefficientPair, Matrix.mul_assoc] + · simp + +theorem pairAnnihilators_commute (Q p r : ℕ) : + pairAnnihilator Q p * pairAnnihilator Q r = + pairAnnihilator Q r * pairAnnihilator Q p := + coefficientPairs_commute Q _ _ + + + +theorem annihilationSpace_two_induction (Q : ℕ) (P : FockMatrix Q → Prop) + (hzero : P 0) + (hadd : ∀ M N, P M → P N → P (M+N)) + (hsmul : ∀ (c : ℂ) M, P M → P (c • M)) + (hpair : ∀ i j : Orbital Q, P (annihilator Q j * annihilator Q i)) + {M : FockMatrix Q} (hM : M ∈ AnnihilationSpace Q 2) : P M := by + induction hM using Submodule.span_induction with + | mem M hM => + obtain ⟨S,rfl⟩ := hM + have hlen : (S.val.sort (· ≤ ·)).length = 2 := by rw [Finset.length_sort, S.property] + obtain ⟨i,j,hij⟩ := List.length_eq_two.mp hlen + simpa only [basisAnnihilator, hij, annihilatorList_cons, annihilatorList_nil, + Matrix.one_mul] using hpair i j + | zero => exact hzero + | add M N _ _ ihM ihN => exact hadd M N ihM ihN + | smul c M _ ihM => exact hsmul c M ihM + + + +theorem pair_monomial_commutator_bodies (Q : ℕ) (i j k l : Orbital Q) + {M N : FockMatrix Q} (hM : M ∈ AnnihilationSpace Q 2) + (hN : N ∈ AnnihilationSpace Q 2) : + Mᴴ * ((annihilator Q j * annihilator Q i) * + (annihilator Q l * annihilator Q k)ᴴ - + (annihilator Q l * annihilator Q k)ᴴ * + (annihilator Q j * annihilator Q i)) * N ∈ + BodySpace Q 2 ⊔ BodySpace Q 3 := by + let S := BodySpace Q 2 ⊔ BodySpace Q 3 + have htwo : Mᴴ * N ∈ S := Submodule.mem_sup_left (bodySpace_product Q 2 hM hN) + have hthree (a b : Orbital Q) : Mᴴ * creator Q a * annihilator Q b * N ∈ S := by + have h := bodySpace_product Q 3 + (annihilationSpace_mul Q 2 1 hM (annihilator_mem Q a)) + (annihilationSpace_mul Q 2 1 hN (annihilator_mem Q b)) + apply Submodule.mem_sup_right + simpa only [Matrix.conjTranspose_mul, ← creator_eq_adjoint, Matrix.mul_assoc] using h + have hδtwo (a b c d : Orbital Q) : + Mᴴ * (orbitalDelta Q a b * orbitalDelta Q c d) * N ∈ S := by + classical + by_cases hab : a=b + · by_cases hcd : c=d + · simpa only [orbitalDelta, ite_eq_left hab, ite_eq_left hcd, Matrix.one_mul, + Matrix.mul_one] using htwo + · simp [orbitalDelta, hab, hcd, S] + · simp [orbitalDelta, hab, S] + have hδthree (a b c d : Orbital Q) : + Mᴴ * (orbitalDelta Q a b * creator Q c * annihilator Q d) * N ∈ S := by + classical + by_cases hab : a=b + · simpa only [orbitalDelta, ite_eq_left hab, Matrix.one_mul, Matrix.mul_assoc] using hthree c d + · simp only [orbitalDelta, ite_eq_right hab, Matrix.zero_mul, Matrix.mul_zero] + exact Submodule.zero_mem _ + have hmiddle := pair_normal_order Q i j k l + have heq : Mᴴ * ((annihilator Q j * annihilator Q i) * + (annihilator Q l * annihilator Q k)ᴴ - + (annihilator Q l * annihilator Q k)ᴴ * + (annihilator Q j * annihilator Q i)) * N = + (Mᴴ * (orbitalDelta Q i k * orbitalDelta Q j l) * N - + Mᴴ * (orbitalDelta Q j k * orbitalDelta Q i l) * N) - + Mᴴ * (orbitalDelta Q i k * creator Q l * annihilator Q j) * N + + Mᴴ * (orbitalDelta Q j k * creator Q l * annihilator Q i) * N + + Mᴴ * (orbitalDelta Q i l * creator Q k * annihilator Q j) * N - + Mᴴ * (orbitalDelta Q j l * creator Q k * annihilator Q i) * N := by + rw [Matrix.conjTranspose_mul, ← creator_eq_adjoint, ← creator_eq_adjoint, hmiddle] + noncomm_ring + rw [heq] + exact S.sub_mem (S.add_mem (S.add_mem + (S.sub_mem (S.sub_mem (hδtwo _ _ _ _) (hδtwo _ _ _ _)) (hδthree _ _ _ _)) + (hδthree _ _ _ _)) (hδthree _ _ _ _)) (hδthree _ _ _ _) + + + +theorem pair_commutator_bodies (Q : ℕ) {M N P R : FockMatrix Q} + (hM : M ∈ AnnihilationSpace Q 2) (hN : N ∈ AnnihilationSpace Q 2) + (hP : P ∈ AnnihilationSpace Q 2) (hR : R ∈ AnnihilationSpace Q 2) : + Mᴴ * (P*Rᴴ-Rᴴ*P) * N ∈ BodySpace Q 2 ⊔ BodySpace Q 3 := by + let S := BodySpace Q 2 ⊔ BodySpace Q 3 + refine annihilationSpace_two_induction Q + (fun P => ∀ R, R ∈ AnnihilationSpace Q 2 → Mᴴ * (P*Rᴴ-Rᴴ*P) * N ∈ S) + ?_ ?_ ?_ ?_ hP R hR + · intro R _ + simpa only [Matrix.zero_mul, Matrix.mul_zero, sub_self] using S.zero_mem + · intro P P' hP hP' R hR + have heq : Mᴴ * ((P+P')*Rᴴ-Rᴴ*(P+P')) * N = + Mᴴ*(P*Rᴴ-Rᴴ*P)*N + Mᴴ*(P'*Rᴴ-Rᴴ*P')*N := by noncomm_ring + rw [heq] + exact S.add_mem (hP R hR) (hP' R hR) + · intro c P hP R hR + simpa only [Matrix.smul_mul, Matrix.mul_smul, ← smul_sub] using + S.smul_mem c (hP R hR) + · intro i j R hR + refine annihilationSpace_two_induction Q + (fun R => Mᴴ * ((annihilator Q j * annihilator Q i)*Rᴴ - + Rᴴ*(annihilator Q j * annihilator Q i)) * N ∈ S) ?_ ?_ ?_ ?_ hR + · simpa only [Matrix.conjTranspose_zero, Matrix.zero_mul, Matrix.mul_zero, + sub_self] using S.zero_mem + · intro R R' hR hR' + rw [Matrix.conjTranspose_add] + have heq : Mᴴ * ((annihilator Q j * annihilator Q i)*(Rᴴ+R'ᴴ) - + (Rᴴ+R'ᴴ)*(annihilator Q j * annihilator Q i)) * N = + Mᴴ*((annihilator Q j * annihilator Q i)*Rᴴ-Rᴴ*(annihilator Q j * annihilator Q i))*N + + Mᴴ*((annihilator Q j * annihilator Q i)*R'ᴴ-R'ᴴ*(annihilator Q j * annihilator Q i))*N := + by noncomm_ring + rw [heq] + exact S.add_mem hR hR' + · intro c R hR + simpa only [Matrix.conjTranspose_smul, Matrix.smul_mul, Matrix.mul_smul, + ← smul_sub] using S.smul_mem (star c) hR + · intro k l + exact pair_monomial_commutator_bodies Q i j k l hM hN + + + +def fourBodyTerm (Q : ℕ) : FockMatrix Q := + ∑ p ∈ Finset.range (2*Q-1), ∑ r ∈ Finset.range (2*Q-1), + (pairAnnihilator Q p * pairAnnihilator Q r)ᴴ * + (pairAnnihilator Q p * pairAnnihilator Q r) + +theorem fourBodyTerm_posSemidef (Q : ℕ) : (fourBodyTerm Q).PosSemidef := by + apply Matrix.posSemidef_sum + intro p _ + apply Matrix.posSemidef_sum + intro r _ + exact Matrix.posSemidef_conjTranspose_mul_self _ + +theorem hamiltonian_mem_bodySpace (Q : ℕ) : hamiltonian Q ∈ BodySpace Q 2 := + Submodule.sum_mem _ (fun p _ => bodySpace_product Q 2 + (pairAnnihilator_mem Q p) (pairAnnihilator_mem Q p)) + +theorem fourBodyTerm_mem_bodySpace (Q : ℕ) : fourBodyTerm Q ∈ BodySpace Q 4 := by + apply Submodule.sum_mem + intro p _ + apply Submodule.sum_mem + intro r _ + have h := annihilationSpace_mul Q 2 2 (pairAnnihilator_mem Q r) (pairAnnihilator_mem Q p) + exact bodySpace_product Q 4 h h + +theorem square_remainder_commutators (Q : ℕ) : + hamiltonian Q * hamiltonian Q - fourBodyTerm Q = + ∑ p ∈ Finset.range (2*Q-1), ∑ r ∈ Finset.range (2*Q-1), + (pairAnnihilator Q p)ᴴ * + (pairAnnihilator Q p * (pairAnnihilator Q r)ᴴ - + (pairAnnihilator Q r)ᴴ * pairAnnihilator Q p) * pairAnnihilator Q r := by + classical + have hsquare : hamiltonian Q * hamiltonian Q = + ∑ p ∈ Finset.range (2*Q-1), ∑ r ∈ Finset.range (2*Q-1), + ((pairAnnihilator Q p)ᴴ * pairAnnihilator Q p) * + ((pairAnnihilator Q r)ᴴ * pairAnnihilator Q r) := by + simp only [hamiltonian, Matrix.sum_mul, Matrix.mul_sum] + exact Finset.sum_comm + rw [hsquare, fourBodyTerm, ← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro p _ + rw [← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro r _ + rw [pairAnnihilators_commute Q p r, Matrix.conjTranspose_mul] + have hc := pairAnnihilators_commute Q r p + rw [hc] + noncomm_ring + +theorem square_remainder_mem_bodies (Q : ℕ) : + hamiltonian Q * hamiltonian Q - fourBodyTerm Q ∈ BodySpace Q 2 ⊔ BodySpace Q 3 := by + rw [square_remainder_commutators] + apply Submodule.sum_mem + intro p _ + apply Submodule.sum_mem + intro r _ + exact pair_commutator_bodies Q (pairAnnihilator_mem Q p) (pairAnnihilator_mem Q r) + (pairAnnihilator_mem Q p) (pairAnnihilator_mem Q r) + + + +theorem normal_square_of_pair_projection (Q : ℕ) + (hproj : sectorHamiltonian Q 2 * sectorHamiltonian Q 2 = sectorHamiltonian Q 2) : + hamiltonian Q * hamiltonian Q = hamiltonian Q + + exteriorLift Q 3 (sectorHamiltonian Q 3 * sectorHamiltonian Q 3 - sectorHamiltonian Q 3) + + fourBodyTerm Q := by + obtain ⟨A,hA,B,hB,hAB⟩ := Submodule.mem_sup.mp (square_remainder_mem_bodies Q) + have hF2 := bodySpace_below_sector Q 4 2 (by omega) (fourBodyTerm_mem_bodySpace Q) + have hF3 := bodySpace_below_sector Q 4 3 (by omega) (fourBodyTerm_mem_bodySpace Q) + have hB2 := bodySpace_below_sector Q 3 2 (by omega) hB + have hA2 : A.submatrix (Subtype.val : SectorOccupation Q 2 → Occupation Q) Subtype.val = + sectorHamiltonian Q 2 := by + have h := congrArg (fun X : FockMatrix Q => X.submatrix + (Subtype.val : SectorOccupation Q 2 → Occupation Q) + (Subtype.val : SectorOccupation Q 2 → Occupation Q)) hAB + simp only [Matrix.submatrix_add, Matrix.submatrix_sub, Pi.add_apply, Pi.sub_apply, + hB2, hF2, add_zero, sub_zero, sectorHamiltonian_square, hproj] at h + exact h + have hAH : A=hamiltonian Q := by + rw [← bodySpace_reconstruct Q 2 hA, hA2] + exact bodySpace_reconstruct Q 2 (hamiltonian_mem_bodySpace Q) + have hB3 : B.submatrix (Subtype.val : SectorOccupation Q 3 → Occupation Q) Subtype.val = + sectorHamiltonian Q 3 * sectorHamiltonian Q 3 - sectorHamiltonian Q 3 := by + have h := congrArg (fun X : FockMatrix Q => X.submatrix + (Subtype.val : SectorOccupation Q 3 → Occupation Q) + (Subtype.val : SectorOccupation Q 3 → Occupation Q)) hAB + simp only [hAH, Matrix.submatrix_add, Matrix.submatrix_sub, Pi.add_apply, Pi.sub_apply, + hF3, sub_zero, sectorHamiltonian_square] at h + change sectorHamiltonian Q 3 + _ = _ at h + exact eq_sub_of_add_eq' h + have hBform : B = exteriorLift Q 3 + (sectorHamiltonian Q 3 * sectorHamiltonian Q 3 - sectorHamiltonian Q 3) := by + rw [← hB3] + exact (bodySpace_reconstruct Q 3 hB).symm + rw [hAH,hBform] at hAB + exact (eq_sub_iff_add_eq.mp hAB).symm + + +abbrev IncreasingPair (Q : ℕ) := {ij : Orbital Q × Orbital Q // ij.1 < ij.2} + +theorem sort_pair {Q : ℕ} (i j : Orbital Q) (hij : i S.val.sort (· ≤ ·)) h + simp only [increasingPairSector, sort_pair _ _ ij.property, sort_pair _ _ kl.property, + List.cons.injEq, and_true] at hs + exact Subtype.ext (Prod.ext hs.1 hs.2) + +theorem increasingPairSector_surjective (Q : ℕ) : Function.Surjective (increasingPairSector Q) := by + intro S + have hlen : (S.val.sort (· ≤ ·)).length = 2 := by rw [Finset.length_sort, S.property] + obtain ⟨i,j,hij⟩ := List.length_eq_two.mp hlen + have hlt : i ij.1 < ij.2)) (by intro ij; simp) + (fun ij : Orbital Q × Orbital Q => f ij.1 ij.2)] + simp only [Finset.sum_filter, Fintype.sum_prod_type] + +theorem basisAnnihilator_pair {Q : ℕ} (i j : Orbital Q) (hij : i a i j • basisAnnihilator Q {i,j})] + unfold coefficientPairAnnihilator + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + split_ifs with hij + · rw [basisAnnihilator_pair i j hij] + · rfl + +theorem coefficientPair_vacuum (Q : ℕ) (a : Orbital Q → Orbital Q → ℂ) + (ij : IncreasingPair Q) : + coefficientPairAnnihilator Q a ∅ (increasingPairSector Q ij).val = a ij.val.1 ij.val.2 := by + classical + rw [coefficientPair_basis_expansion] + simp only [Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, basisAnnihilator_vacuum, + Subtype.val_inj, (increasingPairSector_injective Q).eq_iff] + simp + + + +def pairVector (Q p : ℕ) : SectorOccupation Q 2 → ℂ := + annihilatorVector Q 2 (pairAnnihilator Q p) + +theorem pairVector_increasing (Q p : ℕ) (ij : IncreasingPair Q) : + pairVector Q p (increasingPairSector Q ij) = pairCoefficient Q p ij.val.1 ij.val.2 := by + unfold pairVector annihilatorVector + change star (coefficientPairAnnihilator Q + (fun i j => (pairCoefficient Q p i j : ℂ)) ∅ (increasingPairSector Q ij).val) = _ + rw [coefficientPair_vacuum] + simp only [Complex.star_def, Complex.conj_ofReal] + +theorem pairVector_orthonormal (Q p r : ℕ) (hQ : 1 ≤ Q) (hp : p ≤ 2*Q-2) : + (∑ S : SectorOccupation Q 2, star (pairVector Q p S) * pairVector Q r S) = + if p=r then 1 else 0 := by + classical + have hs : (∑ S : SectorOccupation Q 2, star (pairVector Q p S) * pairVector Q r S) = + ∑ i : Orbital Q, ∑ j : Orbital Q, if i star (pairVector Q p S) * pairVector Q r S)] + simp only [increasingPairEquiv_apply, pairVector_increasing, + Complex.star_def, Complex.conj_ofReal] + exact increasingPair_sum Q (fun i j => + (pairCoefficient Q p i j : ℂ) * (pairCoefficient Q r i j : ℂ)) + rw [hs] + by_cases hpr : p=r + · subst r + simp only [ite_true] + have h := congrArg (fun x : ℝ => (x : ℂ)) (pairCoefficient_norm Q p hQ hp) + simpa only [Complex.ofReal_sum, Complex.ofReal_one, Complex.ofReal_pow, + apply_ite (fun x : ℝ => (x : ℂ)), Complex.ofReal_zero, pow_two, Complex.ofReal_mul] using h + · rw [ite_eq_right hpr] + have h := congrArg (fun x : ℝ => (x : ℂ)) (pairCoefficient_orthogonal Q p r hpr) + simpa only [Complex.ofReal_sum, Complex.ofReal_zero, Complex.ofReal_mul, + apply_ite (fun x : ℝ => (x : ℂ))] using h + +abbrev PairLabel (Q : ℕ) := Fin (2*Q-1) + + +def pairWedgeMatrix (Q : ℕ) : Matrix (SectorOccupation Q 2) (PairLabel Q) ℂ := + fun S p => pairVector Q p.val S + +theorem pairWedgeMatrix_gram (Q : ℕ) (hQ : 1 ≤ Q) : + (pairWedgeMatrix Q)ᴴ * pairWedgeMatrix Q = 1 := by + classical + ext p r + simp only [Matrix.mul_apply, Matrix.conjTranspose_apply, pairWedgeMatrix, + pairVector_orthonormal Q p.val r.val hQ (by have := p.isLt; omega), Matrix.one_apply, + Fin.val_inj] + +theorem hamiltonian_exteriorLift (Q : ℕ) : + exteriorLift Q 2 (pairWedgeMatrix Q * (pairWedgeMatrix Q)ᴴ) = hamiltonian Q := by + have h := exteriorLift_congruence Q 2 (pairWedgeMatrix Q) 1 + simp only [Matrix.mul_one, Matrix.one_apply, ite_smul, one_smul, zero_smul, + Finset.sum_ite_eq, Finset.mem_univ, ite_true] at h + rw [h] + simp only [pairWedgeMatrix, pairVector, + wedgeAnnihilator_annihilatorVector Q 2 _ (pairAnnihilator_mem Q _)] + exact Fin.sum_univ_eq_sum_range (fun p => (pairAnnihilator Q p)ᴴ * pairAnnihilator Q p) _ + +theorem sectorHamiltonian_two (Q : ℕ) : + sectorHamiltonian Q 2 = pairWedgeMatrix Q * (pairWedgeMatrix Q)ᴴ := by + rw [sectorHamiltonian, ← hamiltonian_exteriorLift] + exact exteriorLift_same_sector Q 2 _ + + + +theorem sectorHamiltonian_two_projection (Q : ℕ) (hQ : 1 ≤ Q) : + sectorHamiltonian Q 2 * sectorHamiltonian Q 2 = sectorHamiltonian Q 2 := by + rw [sectorHamiltonian_two] + simp only [Matrix.mul_assoc, ← Matrix.mul_assoc (pairWedgeMatrix Q)ᴴ, + pairWedgeMatrix_gram Q hQ, Matrix.one_mul] + + + +theorem normal_square (Q : ℕ) (hQ : 1 ≤ Q) : + hamiltonian Q * hamiltonian Q = hamiltonian Q + + exteriorLift Q 3 (sectorHamiltonian Q 3 * sectorHamiltonian Q 3 - sectorHamiltonian Q 3) + + fourBodyTerm Q := + normal_square_of_pair_projection Q (sectorHamiltonian_two_projection Q hQ) + + +def threeWedgeMatrix (Q : ℕ) : + Matrix (SectorOccupation Q 3) (PairLabel Q × Orbital Q) ℂ := + fun S pj => annihilatorVector Q 3 + (annihilator Q pj.2 * pairAnnihilator Q pj.1.val) S + + +def fourWedgeMatrix (Q : ℕ) : + Matrix (SectorOccupation Q 4) (PairLabel Q × PairLabel Q) ℂ := + fun S pr => annihilatorVector Q 4 + (pairAnnihilator Q pr.2.val * pairAnnihilator Q pr.1.val) S + +theorem basisAnnihilator_singleton (Q : ℕ) (j : Orbital Q) : + basisAnnihilator Q {j} = annihilator Q j := by + simp only [basisAnnihilator, Finset.sort_singleton, annihilatorList_cons, + annihilatorList_nil, Matrix.one_mul] + +theorem annihilator_vacuum (Q : ℕ) (j : Orbital Q) (A : Occupation Q) : + annihilator Q j ∅ A = if {j}=A then 1 else 0 := by + rw [← basisAnnihilator_singleton, basisAnnihilator_vacuum] + +theorem annihilator_mul_vacuum (Q : ℕ) (j : Orbital Q) (M : FockMatrix Q) + (A : Occupation Q) : (annihilator Q j * M) ∅ A = M {j} A := by + classical + simp only [Matrix.mul_apply, annihilator_vacuum, ite_mul, one_mul, zero_mul, + Finset.sum_ite_eq, Finset.mem_univ, ite_true] + +def singletonSectorEquiv (Q : ℕ) : Orbital Q ≃ SectorOccupation Q 1 := + Equiv.ofBijective (fun j => ⟨{j}, Finset.card_singleton j⟩) + ⟨by intro i j h; simpa only [Subtype.mk.injEq, Finset.singleton_inj] using h, + by intro S; obtain ⟨j,hj⟩ := Finset.card_eq_one.mp S.property + exact ⟨j, Subtype.ext hj.symm⟩⟩ + +theorem sum_singleton_support {X : Type*} [AddCommMonoid X] (Q : ℕ) + (f : Occupation Q → X) (hf : ∀ A, A.card ≠ 1 → f A=0) : + ∑ A, f A = ∑ j : Orbital Q, f {j} := by + classical + calc + _ = ∑ A ∈ Finset.univ.filter (fun A : Occupation Q => A.card=1), f A := by + symm + apply Finset.sum_subset (Finset.filter_subset _ _) + intro A _ hA + exact hf A (by simpa only [Finset.mem_filter, Finset.mem_univ, true_and] using hA) + _ = ∑ A : SectorOccupation Q 1, f A.val := Finset.sum_subtype _ (by intro A; simp) _ + _ = _ := (singletonSectorEquiv Q).sum_comp (fun A => f A.val) |>.symm + +theorem threeWedgeMatrix_apply (Q : ℕ) (S : SectorOccupation Q 3) + (pj : PairLabel Q × Orbital Q) : + threeWedgeMatrix Q S pj = star (pairAnnihilator Q pj.1.val {pj.2} S.val) := by + exact congrArg star (annihilator_mul_vacuum Q pj.2 (pairAnnihilator Q pj.1.val) S.val) + + + +theorem sectorHamiltonian_three (Q : ℕ) : + sectorHamiltonian Q 3 = threeWedgeMatrix Q * (threeWedgeMatrix Q)ᴴ := by + classical + ext A B + change hamiltonian Q A.val B.val = _ + simp only [hamiltonian, Matrix.sum_apply, Matrix.mul_apply, Matrix.conjTranspose_apply, + threeWedgeMatrix_apply, star_star, Fintype.sum_prod_type] + rw [Fin.sum_univ_eq_sum_range (fun p => ∑ j : Orbital Q, + star (pairAnnihilator Q p {j} A.val) * pairAnnihilator Q p {j} B.val)] + apply Finset.sum_congr rfl + intro p _ + apply sum_singleton_support + intro C hC + have hc : C.card + 2 ≠ B.val.card := by rw [B.property]; omega + rw [pairAnnihilator_entry_eq_zero p C B.val hc, mul_zero] + + + +theorem fourBodyTerm_exteriorLift (Q : ℕ) : + exteriorLift Q 4 (fourWedgeMatrix Q * (fourWedgeMatrix Q)ᴴ) = fourBodyTerm Q := by + have h := exteriorLift_congruence Q 4 (fourWedgeMatrix Q) 1 + simp only [Matrix.mul_one, Matrix.one_apply, ite_smul, one_smul, zero_smul, + Finset.sum_ite_eq, Finset.mem_univ, ite_true] at h + rw [h] + simp only [fourWedgeMatrix, wedgeAnnihilator_annihilatorVector Q 4 _ + (annihilationSpace_mul Q 2 2 (pairAnnihilator_mem Q _) (pairAnnihilator_mem Q _)), + Fintype.sum_prod_type] + simp_rw [pairAnnihilators_commute Q] + rw [Fin.sum_univ_eq_sum_range (fun p => ∑ r : PairLabel Q, + (pairAnnihilator Q p * pairAnnihilator Q r.val)ᴴ * + (pairAnnihilator Q p * pairAnnihilator Q r.val))] + unfold fourBodyTerm + apply Finset.sum_congr rfl + intro p _ + exact Fin.sum_univ_eq_sum_range (fun r => + (pairAnnihilator Q p * pairAnnihilator Q r)ᴴ * (pairAnnihilator Q p * pairAnnihilator Q r)) _ + + + +theorem normal_ordered_square (Q : ℕ) (hQ : 1 ≤ Q) : + hamiltonian Q * hamiltonian Q = hamiltonian Q + + exteriorLift Q 3 (threeWedgeMatrix Q * + ((threeWedgeMatrix Q)ᴴ * threeWedgeMatrix Q - 1) * (threeWedgeMatrix Q)ᴴ) + + exteriorLift Q 4 (fourWedgeMatrix Q * (fourWedgeMatrix Q)ᴴ) := by + rw [fourBodyTerm_exteriorLift, normal_square Q hQ, sectorHamiltonian_three] + congr 2 + congr 1 + simp only [Matrix.mul_sub, Matrix.sub_mul, Matrix.mul_one, Matrix.mul_assoc] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/NullComponents.lean b/lean/OAI/Analysis/LaughlinFock/NullComponents.lean new file mode 100644 index 0000000000000000000000000000000000000000..c655762633b91303b756fea14f656600e0813169 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/NullComponents.lean @@ -0,0 +1,103 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.ThreeSpectrum + +namespace OAI + +/-! Null Components. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder + +theorem gramShift_zero (Q : ℕ) : gramShift Q 0 = -1 := by + simp [gramShift, fallingRatio] + +theorem gramShift_one {Q : ℕ} (hQ : 2 ≤ Q) : gramShift Q 1 = -1 := by + have hq : (2 : ℝ) ≤ Q := by exact_mod_cast hQ + have h0 : (Q : ℝ) ≠ 0 := by linarith + have h1 : 2 * (Q : ℝ) - 2 ≠ 0 := by linarith + unfold gramShift + rw [fallingRatio_succ (z:=0) hQ (by omega)] + norm_num only [Nat.cast_one, Nat.cast_zero, pow_one, fallingRatio, + Nat.descFactorial_zero, div_one, sub_zero, mul_one] + field_simp (disch := linarith) + +theorem gramShift_three {Q : ℕ} (hQ : 3 ≤ Q) : gramShift Q 3 = -1 := by + have hq : (3 : ℝ) ≤ Q := by exact_mod_cast hQ + have h0 : (Q : ℝ) ≠ 0 := by linarith + have h1 : 2 * (Q : ℝ) - 2 ≠ 0 := by linarith + have h2 : 2 * (Q : ℝ) - 2 - 1 ≠ 0 := by linarith + have h3 : 2 * (Q : ℝ) - 2 - 2 ≠ 0 := by linarith + unfold gramShift + rw [fallingRatio_succ (z:=2) (by omega) (by omega), + fallingRatio_succ (z:=1) (by omega) (by omega), + fallingRatio_succ (z:=0) (by omega) (by omega)] + norm_num only [Nat.cast_ofNat, Nat.cast_zero, Nat.cast_one, + fallingRatio, Nat.descFactorial_zero, div_one, sub_zero, mul_one] + field_simp (disch := linarith) + ring + + + +theorem threeWedgeMatrix_null_column {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) + (hnull : z=0 ∨ z=1 ∨ z=3) (k : ℕ) : + threeWedgeMatrix Q *ᵥ threeCoupledColumn Q z k = 0 := by + have hshift : gramShift Q z = -1 := by + rcases hnull with rfl | rfl | rfl + · exact gramShift_zero Q + · exact gramShift_one hQ + · exact gramShift_three hz + apply (Matrix.conjTranspose_mul_self_mulVec_eq_zero _ _).mp + rw [threeWedgeMatrix_gram_eigenvector hQ hz k, hshift] + simp + + + +theorem threeWedgeMatrix_null_projection {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) + (hnull : z=0 ∨ z=1 ∨ z=3) : + threeWedgeMatrix Q * threeSpinProjection Q z = 0 := by + classical + have hn : threeWedgeMatrix Q * threeCouplingMatrix Q * + Matrix.diagonal (fun c : CoupledIndex (2*Q-2) Q => if c.1.val=z then (1:ℂ) else 0) = 0 := by + ext S c + rw [Matrix.mul_diagonal] + split_ifs with hc + · rw [mul_one] + change (threeWedgeMatrix Q *ᵥ threeCoupledColumn Q c.1.val c.2.val) S = 0 + simpa only [hc, Pi.zero_apply] using congrArg (fun v => v S) + (threeWedgeMatrix_null_column hQ (show c.1.val ≤ Q by omega) + (by simpa only [hc] using hnull) c.2.val) + · simp + unfold threeSpinProjection + rw [← Matrix.mul_assoc, ← Matrix.mul_assoc, hn, Matrix.zero_mul] + + +theorem threeSpinProjection_sum (Q : ℕ) (hQ : 2 ≤ Q) : + (∑ z ∈ Finset.range (Q+1), threeSpinProjection Q z) = 1 := by + classical + have hd : (∑ z ∈ Finset.range (Q+1), Matrix.diagonal + (fun c : CoupledIndex (2*Q-2) Q => if c.1.val=z then (1:ℂ) else 0)) = 1 := by + ext c d + simp only [Matrix.sum_apply, Matrix.diagonal_apply, Matrix.one_apply] + by_cases h : c=d + · subst d + simp only [ite_true] + rw [Finset.sum_ite_eq, ite_eq_left (Finset.mem_range.mpr (by have := coupledIndex_bounds c; omega))] + · simp [h] + simp only [threeSpinProjection, ← Matrix.sum_mul, ← Matrix.mul_sum] + rw [hd, Matrix.mul_one, threeCouplingMatrix_complete Q (by omega)] + + + +theorem normal_ordered_square_spectral (Q : ℕ) (hQ : 2 ≤ Q) : + hamiltonian Q * hamiltonian Q = hamiltonian Q + + exteriorLift Q 3 (threeWedgeMatrix Q * + (∑ z ∈ Finset.range (Q+1), (gramShift Q z : ℂ) • threeSpinProjection Q z) * + (threeWedgeMatrix Q)ᴴ) + + exteriorLift Q 4 (fourWedgeMatrix Q * (fourWedgeMatrix Q)ᴴ) := by + rw [← threeWedgeMatrix_gram_spectral Q hQ] + exact normal_ordered_square Q (by omega) + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/NumericTrace.lean b/lean/OAI/Analysis/LaughlinFock/NumericTrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..b8f988bda4e5f2ea1c602f2459e0b6e1790e70d6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/NumericTrace.lean @@ -0,0 +1,546 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.EntryEnumeration +import OAI.Analysis.LaughlinFock.TableTrace + +namespace OAI + +/-! Numeric Trace. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +structure NumericRowEntry where + p : ℕ + j : ℕ + i : ℕ + a : ℤ + deriving DecidableEq + +def rowToNumeric (t : Fin 8) (b : RowEntry t.val) : NumericRowEntry := + ⟨rowP b, rowJ b, rowI b, certificateAlphaData t b.val.1 b.val.2⟩ + +def numericRowData_0 : List NumericRowEntry := [ + ⟨0, 0, 0, -1458000⟩, + ⟨0, 1, 1, -1303000⟩, + ⟨0, 2, 2, 1475944⟩, + ⟨0, 3, 3, 3608220⟩, + ⟨0, 4, 4, 43844714⟩, + ⟨0, 5, 5, -184490641⟩, + ⟨0, 6, 6, -142169573⟩, + ⟨0, 7, 7, 1489137⟩, + ⟨0, 8, 8, -100397507⟩, + ⟨1, 0, 1, 781353⟩, + ⟨1, 1, 2, -3890972⟩, + ⟨1, 2, 3, -194326⟩, + ⟨1, 3, 4, -13071015⟩, + ⟨1, 4, 5, -49364910⟩, + ⟨1, 5, 6, 44700932⟩, + ⟨1, 6, 7, 51534774⟩, + ⟨1, 7, 8, -41946820⟩, + ⟨2, 0, 2, 2056486⟩, + ⟨2, 1, 3, -760626⟩, + ⟨2, 2, 4, 4305543⟩, + ⟨2, 3, 5, -36416268⟩, + ⟨2, 4, 6, -8021896⟩, + ⟨2, 5, 7, -2613330⟩, + ⟨2, 6, 8, -1141300⟩, + ⟨3, 0, 3, 3923145⟩, + ⟨3, 1, 4, -4779646⟩, + ⟨3, 2, 5, 49466660⟩, + ⟨3, 3, 6, -6088990⟩, + ⟨3, 4, 7, 5250044⟩, + ⟨3, 5, 8, -9079480⟩, + ⟨4, 0, 4, 3991791⟩, + ⟨4, 1, 5, -6855540⟩, + ⟨4, 2, 6, 9257380⟩, + ⟨4, 3, 7, -9310399⟩, + ⟨4, 4, 8, 6494980⟩, + ⟨5, 0, 5, -39241199⟩, + ⟨5, 1, 6, -7152680⟩, + ⟨5, 2, 7, 9042278⟩, + ⟨5, 3, 8, -4542700⟩, + ⟨6, 0, 6, 5245792⟩, + ⟨6, 1, 7, -12421683⟩, + ⟨6, 2, 8, 8099967⟩, + ⟨7, 0, 7, 21052655⟩, + ⟨7, 1, 8, -7572580⟩ +] + +theorem numericRowDataChecked_0 : + rowEntryList_0.map (rowToNumeric ⟨0, by decide⟩) = numericRowData_0 := by + decide +kernel + +def numericRowData_1 : List NumericRowEntry := [ + ⟨0, 1, 0, -2158090⟩, + ⟨0, 2, 1, 10930045⟩, + ⟨0, 3, 2, -20794124⟩, + ⟨0, 4, 3, -10149386⟩, + ⟨0, 5, 4, 597895303⟩, + ⟨0, 6, 5, 834366316⟩, + ⟨0, 7, 6, 765947384⟩, + ⟨0, 8, 7, 1283859555⟩, + ⟨1, 0, 0, -5627000⟩, + ⟨1, 1, 1, -5402022⟩, + ⟨1, 2, 2, 9973000⟩, + ⟨1, 3, 3, 24359402⟩, + ⟨1, 4, 4, 91996112⟩, + ⟨1, 5, 5, -136745470⟩, + ⟨1, 6, 6, -141127842⟩, + ⟨1, 7, 7, -50782825⟩, + ⟨1, 8, 8, -366942013⟩, + ⟨2, 0, 1, -5127489⟩, + ⟨2, 1, 2, 6909968⟩, + ⟨2, 2, 3, -9505204⟩, + ⟨2, 3, 4, 72222049⟩, + ⟨2, 4, 5, 51361561⟩, + ⟨2, 5, 6, -1267754⟩, + ⟨2, 6, 7, -15925422⟩, + ⟨2, 7, 8, -78778293⟩, + ⟨3, 0, 2, -5983211⟩, + ⟨3, 1, 3, -106483⟩, + ⟨3, 2, 4, -96337602⟩, + ⟨3, 3, 5, -7668424⟩, + ⟨3, 4, 6, 10264188⟩, + ⟨3, 5, 7, -19098454⟩, + ⟨3, 6, 8, 2115155⟩, + ⟨4, 0, 3, 10208704⟩, + ⟨4, 1, 4, 618400⟩, + ⟨4, 2, 5, -7918740⟩, + ⟨4, 3, 6, -6479832⟩, + ⟨4, 4, 7, 4936997⟩, + ⟨4, 5, 8, 14394828⟩, + ⟨5, 0, 4, 99243497⟩, + ⟨5, 1, 5, -1336744⟩, + ⟨5, 2, 6, 7033004⟩, + ⟨5, 3, 7, 2815777⟩, + ⟨5, 4, 8, 3603042⟩, + ⟨6, 0, 5, 35489766⟩, + ⟨6, 1, 6, -6585714⟩, + ⟨6, 2, 7, 9964326⟩, + ⟨6, 3, 8, -9564997⟩, + ⟨7, 0, 6, -977099⟩, + ⟨7, 1, 7, -25775399⟩, + ⟨7, 2, 8, 1881084⟩ +] + +theorem numericRowDataChecked_1 : + rowEntryList_1.map (rowToNumeric ⟨1, by decide⟩) = numericRowData_1 := by + decide +kernel + +def numericRowData_2 : List NumericRowEntry := [ + ⟨0, 2, 0, 2286849⟩, + ⟨0, 3, 1, 19304798⟩, + ⟨0, 4, 2, 72232229⟩, + ⟨0, 5, 3, -661988975⟩, + ⟨0, 6, 4, -694800860⟩, + ⟨0, 7, 5, -7185493⟩, + ⟨0, 8, 6, -295108017⟩, + ⟨1, 1, 0, -8424424⟩, + ⟨1, 2, 1, 2832670⟩, + ⟨1, 3, 2, -21562963⟩, + ⟨1, 4, 3, 316632327⟩, + ⟨1, 5, 4, 538338959⟩, + ⟨1, 6, 5, 592775303⟩, + ⟨1, 7, 6, 493483565⟩, + ⟨1, 8, 7, 530121321⟩, + ⟨2, 0, 0, -677288⟩, + ⟨2, 1, 1, 5188364⟩, + ⟨2, 2, 2, -2632251⟩, + ⟨2, 3, 3, -109820524⟩, + ⟨2, 4, 4, -71765788⟩, + ⟨2, 5, 5, -51844671⟩, + ⟨2, 6, 6, -17032491⟩, + ⟨2, 7, 7, -15649485⟩, + ⟨2, 8, 8, -126493796⟩, + ⟨3, 0, 1, 2276756⟩, + ⟨3, 1, 2, -7542800⟩, + ⟨3, 2, 3, 36208527⟩, + ⟨3, 3, 4, 45768030⟩, + ⟨3, 4, 5, 35084799⟩, + ⟨3, 5, 6, 20746753⟩, + ⟨3, 6, 7, -6109724⟩, + ⟨3, 7, 8, -38742315⟩, + ⟨4, 0, 2, 14442833⟩, + ⟨4, 1, 3, -16716287⟩, + ⟨4, 2, 4, -76293178⟩, + ⟨4, 3, 5, -1636292⟩, + ⟨4, 4, 6, -4793945⟩, + ⟨4, 5, 7, -10517615⟩, + ⟨4, 6, 8, 24708653⟩, + ⟨5, 0, 3, 10039299⟩, + ⟨5, 1, 4, 36778073⟩, + ⟨5, 2, 5, -63545981⟩, + ⟨5, 3, 6, -887901⟩, + ⟨5, 4, 7, 3332305⟩, + ⟨5, 5, 8, 4129678⟩, + ⟨6, 0, 4, 57374228⟩, + ⟨6, 1, 5, 40592205⟩, + ⟨6, 2, 6, -31810373⟩, + ⟨6, 3, 7, 4995989⟩, + ⟨6, 4, 8, -3075894⟩, + ⟨7, 0, 5, 88550482⟩, + ⟨7, 1, 6, 31531302⟩, + ⟨7, 2, 7, -4435968⟩, + ⟨7, 3, 8, -7365918⟩ +] + +theorem numericRowDataChecked_2 : + rowEntryList_2.map (rowToNumeric ⟨2, by decide⟩) = numericRowData_2 := by + decide +kernel + +def numericRowData_3 : List NumericRowEntry := [ + ⟨0, 3, 0, 39091021⟩, + ⟨0, 4, 1, -4327630⟩, + ⟨0, 5, 2, 213162965⟩, + ⟨0, 6, 3, 45619843⟩, + ⟨0, 7, 4, -654459233⟩, + ⟨0, 8, 5, -49355411⟩, + ⟨1, 2, 0, -7645272⟩, + ⟨1, 3, 1, 8738979⟩, + ⟨1, 4, 2, -367337826⟩, + ⟨1, 5, 3, -305799567⟩, + ⟨1, 6, 4, -733169191⟩, + ⟨1, 7, 5, 195732122⟩, + ⟨1, 8, 6, 71375471⟩, + ⟨2, 1, 0, -3949210⟩, + ⟨2, 2, 1, 762818⟩, + ⟨2, 3, 2, 68452276⟩, + ⟨2, 4, 3, 199108377⟩, + ⟨2, 5, 4, 46517664⟩, + ⟨2, 6, 5, 68403288⟩, + ⟨2, 7, 6, 47754272⟩, + ⟨2, 8, 7, 127976176⟩, + ⟨3, 0, 0, 11033607⟩, + ⟨3, 1, 1, -2140475⟩, + ⟨3, 2, 2, 18301715⟩, + ⟨3, 3, 3, -133068288⟩, + ⟨3, 4, 4, -15957882⟩, + ⟨3, 5, 5, -12923425⟩, + ⟨3, 6, 6, -63267429⟩, + ⟨3, 7, 7, -35729612⟩, + ⟨3, 8, 8, -80840875⟩, + ⟨4, 0, 1, 8563509⟩, + ⟨4, 1, 2, 21124181⟩, + ⟨4, 2, 3, 91082225⟩, + ⟨4, 3, 4, -17834095⟩, + ⟨4, 4, 5, 23279016⟩, + ⟨4, 5, 6, 25167823⟩, + ⟨4, 6, 7, 5867255⟩, + ⟨4, 7, 8, -14358409⟩, + ⟨5, 0, 2, -78804551⟩, + ⟨5, 1, 3, -37818356⟩, + ⟨5, 2, 4, 61096591⟩, + ⟨5, 3, 5, -30356506⟩, + ⟨5, 4, 6, 14193156⟩, + ⟨5, 5, 7, 7769542⟩, + ⟨5, 6, 8, -14948988⟩, + ⟨6, 0, 3, -10297948⟩, + ⟨6, 1, 4, -16392402⟩, + ⟨6, 2, 5, -224637⟩, + ⟨6, 3, 6, -26277133⟩, + ⟨6, 4, 7, -1390692⟩, + ⟨6, 5, 8, 7844148⟩, + ⟨7, 0, 4, -156393617⟩, + ⟨7, 1, 5, 5235902⟩, + ⟨7, 2, 6, 12966156⟩, + ⟨7, 3, 7, -29134694⟩, + ⟨7, 4, 8, -7754810⟩ +] + +theorem numericRowDataChecked_3 : + rowEntryList_3.map (rowToNumeric ⟨3, by decide⟩) = numericRowData_3 := by + decide +kernel + +def numericRowData_4 : List NumericRowEntry := [ + ⟨0, 4, 0, 19350310⟩, + ⟨0, 5, 1, -256570426⟩, + ⟨0, 6, 2, 437882921⟩, + ⟨0, 7, 3, -166877023⟩, + ⟨0, 8, 4, 644065588⟩, + ⟨1, 3, 0, 7604311⟩, + ⟨1, 4, 1, -56036955⟩, + ⟨1, 5, 2, -106906398⟩, + ⟨1, 6, 3, 395640853⟩, + ⟨1, 7, 4, -375570014⟩, + ⟨1, 8, 5, -1474842820⟩, + ⟨2, 2, 0, 3171752⟩, + ⟨2, 3, 1, -42320168⟩, + ⟨2, 4, 2, -196928392⟩, + ⟨2, 5, 3, 84182344⟩, + ⟨2, 6, 4, 123805380⟩, + ⟨2, 7, 5, -377993673⟩, + ⟨2, 8, 6, 446685144⟩, + ⟨3, 1, 0, 5083588⟩, + ⟨3, 2, 1, 54525539⟩, + ⟨3, 3, 2, 112160315⟩, + ⟨3, 4, 3, -4586199⟩, + ⟨3, 5, 4, 169842096⟩, + ⟨3, 6, 5, 129314466⟩, + ⟨3, 7, 6, 473546⟩, + ⟨3, 8, 7, -43309042⟩, + ⟨4, 0, 0, 8117035⟩, + ⟨4, 1, 1, -12273926⟩, + ⟨4, 2, 2, -13371505⟩, + ⟨4, 3, 3, -33864426⟩, + ⟨4, 4, 4, -63645420⟩, + ⟨4, 5, 5, 39205032⟩, + ⟨4, 6, 6, 47849173⟩, + ⟨4, 7, 7, -57278002⟩, + ⟨4, 8, 8, 30676490⟩, + ⟨5, 0, 1, -32345547⟩, + ⟨5, 1, 2, 6924448⟩, + ⟨5, 2, 3, -21143042⟩, + ⟨5, 3, 4, -30323348⟩, + ⟨5, 4, 5, 13003067⟩, + ⟨5, 5, 6, 19986152⟩, + ⟨5, 6, 7, 9072780⟩, + ⟨5, 7, 8, -25147087⟩, + ⟨6, 0, 2, -62327236⟩, + ⟨6, 1, 3, -2573763⟩, + ⟨6, 2, 4, 19203739⟩, + ⟨6, 3, 5, -59245571⟩, + ⟨6, 4, 6, -6662966⟩, + ⟨6, 5, 7, 28341971⟩, + ⟨6, 6, 8, 18781561⟩, + ⟨7, 0, 3, 135264167⟩, + ⟨7, 1, 4, 9223722⟩, + ⟨7, 2, 5, 1641094⟩, + ⟨7, 3, 6, -16817961⟩, + ⟨7, 4, 7, 11019210⟩, + ⟨7, 5, 8, 24257380⟩ +] + +theorem numericRowDataChecked_4 : + rowEntryList_4.map (rowToNumeric ⟨4, by decide⟩) = numericRowData_4 := by + decide +kernel + +def numericRowData_5 : List NumericRowEntry := [ + ⟨0, 5, 0, 160543938⟩, + ⟨0, 6, 1, -772096646⟩, + ⟨0, 7, 2, 150680285⟩, + ⟨0, 8, 3, -122410154⟩, + ⟨1, 4, 0, 57714191⟩, + ⟨1, 5, 1, -84055787⟩, + ⟨1, 6, 2, -173419469⟩, + ⟨1, 7, 3, 817621606⟩, + ⟨1, 8, 4, -1272768087⟩, + ⟨2, 3, 0, 11295230⟩, + ⟨2, 4, 1, 36541316⟩, + ⟨2, 5, 2, -181828330⟩, + ⟨2, 6, 3, -133076448⟩, + ⟨2, 7, 4, 86288265⟩, + ⟨2, 8, 5, -861124623⟩, + ⟨3, 2, 0, -24815988⟩, + ⟨3, 3, 1, -50599547⟩, + ⟨3, 4, 2, 6698654⟩, + ⟨3, 5, 3, -132907956⟩, + ⟨3, 6, 4, 35137762⟩, + ⟨3, 7, 5, 33919179⟩, + ⟨3, 8, 6, -293036253⟩, + ⟨4, 1, 0, -10241680⟩, + ⟨4, 2, 1, 43618923⟩, + ⟨4, 3, 2, 71239842⟩, + ⟨4, 4, 3, 27177342⟩, + ⟨4, 5, 4, -45431218⟩, + ⟨4, 6, 5, 41533885⟩, + ⟨4, 7, 6, 63934128⟩, + ⟨4, 8, 7, -214411360⟩, + ⟨5, 0, 0, 31688993⟩, + ⟨5, 1, 1, 9888664⟩, + ⟨5, 2, 2, -4845107⟩, + ⟨5, 3, 3, 34212037⟩, + ⟨5, 4, 4, -3172205⟩, + ⟨5, 5, 5, 5715090⟩, + ⟨5, 6, 6, 54142081⟩, + ⟨5, 7, 7, -48900364⟩, + ⟨5, 8, 8, -147596784⟩, + ⟨6, 0, 1, -53903546⟩, + ⟨6, 1, 2, 40649652⟩, + ⟨6, 2, 3, 19129337⟩, + ⟨6, 3, 4, 39646640⟩, + ⟨6, 4, 5, -23829198⟩, + ⟨6, 5, 6, -2574933⟩, + ⟨6, 6, 7, -7391939⟩, + ⟨6, 7, 8, -19892913⟩, + ⟨7, 0, 2, -165809403⟩, + ⟨7, 1, 3, -87926915⟩, + ⟨7, 2, 4, -20371590⟩, + ⟨7, 3, 5, -16611293⟩, + ⟨7, 4, 6, -44679775⟩, + ⟨7, 5, 7, 13277906⟩, + ⟨7, 6, 8, -14870629⟩ +] + +theorem numericRowDataChecked_5 : + rowEntryList_5.map (rowToNumeric ⟨5, by decide⟩) = numericRowData_5 := by + decide +kernel + +def numericRowData_6 : List NumericRowEntry := [ + ⟨0, 6, 0, -67829135⟩, + ⟨0, 7, 1, 720057917⟩, + ⟨0, 8, 2, -875530193⟩, + ⟨1, 5, 0, -51790296⟩, + ⟨1, 6, 1, 175876646⟩, + ⟨1, 7, 2, -200676925⟩, + ⟨1, 8, 3, -10152433⟩, + ⟨2, 4, 0, -7378820⟩, + ⟨2, 5, 1, 52323471⟩, + ⟨2, 6, 2, -211371229⟩, + ⟨2, 7, 3, 182388432⟩, + ⟨2, 8, 4, -61003176⟩, + ⟨3, 3, 0, -656201⟩, + ⟨3, 4, 1, 14264883⟩, + ⟨3, 5, 2, 26191317⟩, + ⟨3, 6, 3, -100136184⟩, + ⟨3, 7, 4, -183883082⟩, + ⟨3, 8, 5, 121658379⟩, + ⟨4, 2, 0, 2431803⟩, + ⟨4, 3, 1, -22478098⟩, + ⟨4, 4, 2, 1654355⟩, + ⟨4, 5, 3, -93663294⟩, + ⟨4, 6, 4, 109018199⟩, + ⟨4, 7, 5, 36347410⟩, + ⟨4, 8, 6, -91971370⟩, + ⟨5, 1, 0, 937204⟩, + ⟨5, 2, 1, -2276330⟩, + ⟨5, 3, 2, 13793516⟩, + ⟨5, 4, 3, 47941518⟩, + ⟨5, 5, 4, 28279597⟩, + ⟨5, 6, 5, -40367840⟩, + ⟨5, 7, 6, 55740134⟩, + ⟨5, 8, 7, 13007596⟩, + ⟨6, 0, 0, -10808966⟩, + ⟨6, 1, 1, -25113301⟩, + ⟨6, 2, 2, -4615426⟩, + ⟨6, 3, 3, 31886801⟩, + ⟨6, 4, 4, -27442867⟩, + ⟨6, 5, 5, 40912313⟩, + ⟨6, 6, 6, -18147728⟩, + ⟨6, 7, 7, -21491028⟩, + ⟨6, 8, 8, 127556721⟩, + ⟨7, 0, 1, 78650298⟩, + ⟨7, 1, 2, 34037298⟩, + ⟨7, 2, 3, 58687256⟩, + ⟨7, 3, 4, 49941189⟩, + ⟨7, 4, 5, 61860018⟩, + ⟨7, 5, 6, 9377295⟩, + ⟨7, 6, 7, 26910871⟩, + ⟨7, 7, 8, 48292819⟩ +] + +theorem numericRowDataChecked_6 : + rowEntryList_6.map (rowToNumeric ⟨6, by decide⟩) = numericRowData_6 := by + decide +kernel + +def numericRowData_7 : List NumericRowEntry := [ + ⟨0, 7, 0, 90151251⟩, + ⟨0, 8, 1, 41493601⟩, + ⟨1, 6, 0, 5671034⟩, + ⟨1, 7, 1, 217565363⟩, + ⟨1, 8, 2, -239274251⟩, + ⟨2, 5, 0, -13713832⟩, + ⟨2, 6, 1, 128996036⟩, + ⟨2, 7, 2, -145424091⟩, + ⟨2, 8, 3, -81564855⟩, + ⟨3, 4, 0, 4354537⟩, + ⟨3, 5, 1, 53285313⟩, + ⟨3, 6, 2, -28885070⟩, + ⟨3, 7, 3, -101829212⟩, + ⟨3, 8, 4, -59154681⟩, + ⟨4, 3, 0, 8355807⟩, + ⟨4, 4, 1, -30008008⟩, + ⟨4, 5, 2, -6707391⟩, + ⟨4, 6, 3, -116951489⟩, + ⟨4, 7, 4, -67400418⟩, + ⟨4, 8, 5, 234283414⟩, + ⟨5, 2, 0, -7051082⟩, + ⟨5, 3, 1, -28653824⟩, + ⟨5, 4, 2, 17782076⟩, + ⟨5, 5, 3, -19218169⟩, + ⟨5, 6, 4, 30912487⟩, + ⟨5, 7, 5, -3984978⟩, + ⟨5, 8, 6, 110000521⟩, + ⟨6, 1, 0, 2562590⟩, + ⟨6, 2, 1, 35701498⟩, + ⟨6, 3, 2, 4486260⟩, + ⟨6, 4, 3, 45335753⟩, + ⟨6, 5, 4, -25079048⟩, + ⟨6, 6, 5, 18952126⟩, + ⟨6, 7, 6, 51942067⟩, + ⟨6, 8, 7, 32561769⟩, + ⟨7, 0, 0, -12496841⟩, + ⟨7, 1, 1, -51081249⟩, + ⟨7, 2, 2, -10849108⟩, + ⟨7, 3, 3, -40398862⟩, + ⟨7, 4, 4, -51858623⟩, + ⟨7, 5, 5, -10716483⟩, + ⟨7, 6, 6, -28108965⟩, + ⟨7, 7, 7, -5754196⟩, + ⟨7, 8, 8, -77199525⟩ +] + +theorem numericRowDataChecked_7 : + rowEntryList_7.map (rowToNumeric ⟨7, by decide⟩) = numericRowData_7 := by + decide +kernel + +def numericRowData (t : Fin 8) : List NumericRowEntry := + ![numericRowData_0, numericRowData_1, numericRowData_2, numericRowData_3, numericRowData_4, numericRowData_5, numericRowData_6, numericRowData_7] t + +theorem sum_table {α β : Type*} [Fintype α] (ls : List α) (hn : ls.Nodup) + (tabs : List β) (g : α → β) (hu : (Finset.univ : Finset α) = ⟨(ls : Multiset α), Multiset.coe_nodup.mpr hn⟩) + (hg : ls.map g = tabs) (f : β → ℤ) : + ∑ x, f (g x) = (tabs.map f).sum := by + rw [hu, Finset.sum_mk, Multiset.map_coe, Multiset.sum_coe, ← hg] + simp only [List.map_map, Function.comp_def] + +theorem numericRow_sum (t : Fin 8) (f : NumericRowEntry → ℤ) : + ∑ b : RowEntry t.val, f (rowToNumeric t b) = ((numericRowData t).map f).sum := by + fin_cases t + · exact sum_table rowEntryList_0 (by decide) numericRowData_0 _ rowEntryChecked_0 numericRowDataChecked_0 f + · exact sum_table rowEntryList_1 (by decide) numericRowData_1 _ rowEntryChecked_1 numericRowDataChecked_1 f + · exact sum_table rowEntryList_2 (by decide) numericRowData_2 _ rowEntryChecked_2 numericRowDataChecked_2 f + · exact sum_table rowEntryList_3 (by decide) numericRowData_3 _ rowEntryChecked_3 numericRowDataChecked_3 f + · exact sum_table rowEntryList_4 (by decide) numericRowData_4 _ rowEntryChecked_4 numericRowDataChecked_4 f + · exact sum_table rowEntryList_5 (by decide) numericRowData_5 _ rowEntryChecked_5 numericRowDataChecked_5 f + · exact sum_table rowEntryList_6 (by decide) numericRowData_6 _ rowEntryChecked_6 numericRowDataChecked_6 f + · exact sum_table rowEntryList_7 (by decide) numericRowData_7 _ rowEntryChecked_7 numericRowDataChecked_7 f + +def numericRowFactor (D t : ℕ) (b c : NumericRowEntry) : ℕ := + 2 * 2^(53+b.p+c.p-(t+2*(b.p+b.j+c.i))) * + t.factorial * b.i.factorial * c.i.factorial * + ((23).factorial / ((b.p+b.j+c.i)-D).factorial) + +def numericRowTerm (D t r s : ℕ) (b c : NumericRowEntry) : ℤ := + if D ≤ b.p+b.j+c.i then + b.a*c.a * (numericRowFactor D t b c : ℤ) * + memoIntegerCopyPolynomial D (b.p+b.j+c.i) r b.p b.j c.i * + memoIntegerCopyPolynomial D (b.p+b.j+c.i) s c.p c.j b.i + else 0 + +def numericFourTrace (D : ℕ) (t : Fin 8) (r s : ℕ) : ℤ := + -(((numericRowData t).map (fun b => ((numericRowData t).map (fun c => + numericRowTerm D t.val r s b c)).sum)).sum) + +theorem memoScaledFourTrace_numeric (D : ℕ) (t : Fin 8) (r s : CopyLabel D) : + memoScaledFourTrace D t r s = numericFourTrace D t r.val.val s.val.val := by + unfold memoScaledFourTrace numericFourTrace + congr 1 + rw [← numericRow_sum] + apply Finset.sum_congr rfl + intro b _ + rw [← numericRow_sum] + rfl + +def numericRowsFourTrace (D r s : ℕ) : ℤ := + ∑ t : Fin 8, numericFourTrace D t r s + +theorem integerRowsFourTrace_numeric {D : ℕ} (hD : D ≤ 23) (r s : CopyLabel D) : + integerRowsFourTrace D r s = (numericRowsFourTrace D r.val.val s.val.val : ℚ) / fourCommonDenominator := by + rw [integerRowsFourTrace_memo hD] + unfold memoScaledRowsFourTrace numericRowsFourTrace + simp only [memoScaledFourTrace_numeric] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/OscillatorLimit.lean b/lean/OAI/Analysis/LaughlinFock/OscillatorLimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..a2b522811559e31903cf8c1bf3e8dc26a38ded36 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/OscillatorLimit.lean @@ -0,0 +1,201 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FiniteCoupling + +namespace OAI + +/-! Oscillator Limit. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators +open Polynomial +open Filter Topology + + + +def monomialWeight (T p : ℕ) : ℝ := + Real.sqrt ((p.factorial : ℝ) * (T-p).factorial) + +def monomialCoefficient (T : ℕ) (P : Polynomial ℝ) (p : ℕ) : ℝ := + monomialWeight T p * P.coeff p + +theorem monomialWeight_left (T p : ℕ) : + monomialWeight (T+1) (p+1) = Real.sqrt (p+1 : ℕ) * monomialWeight T p := by + unfold monomialWeight + rw [Nat.add_sub_add_right, Nat.factorial_succ, Nat.cast_mul, mul_assoc, + Real.sqrt_mul (Nat.cast_nonneg _)] + +theorem monomialWeight_right {T p : ℕ} (hp : p ≤ T) : + monomialWeight (T+1) p = Real.sqrt (((T+1 : ℕ) : ℝ)-p) * monomialWeight T p := by + have hs : T+1-p = (T-p)+1 := by omega + unfold monomialWeight + rw [hs, Nat.factorial_succ, Nat.cast_mul] + have ht : (((T-p+1 : ℕ) : ℝ)) = ((T+1 : ℕ) : ℝ)-p := by + rw [Nat.cast_add, Nat.cast_sub hp, Nat.cast_one, Nat.cast_add, Nat.cast_one] + ring + rw [ht, mul_left_comm, Real.sqrt_mul (sub_nonneg.mpr (by + exact_mod_cast (by omega : p ≤ T+1)))] + + + +theorem monomialCoefficient_linear (P : Polynomial ℝ) (T : ℕ) + (hP : P.natDegree ≤ T) (u v : ℝ) (p : ℕ) : + monomialCoefficient (T+1) ((C v * X + C u) * P) p = + (if p = 0 then 0 else Real.sqrt (p : ℝ) * v * monomialCoefficient T P (p-1)) + + Real.sqrt (((T+1 : ℕ) : ℝ)-p) * u * monomialCoefficient T P p := by + cases p with + | zero => + simp only [monomialCoefficient, Nat.cast_zero, sub_zero, ite_true, zero_add, + add_mul, mul_assoc, coeff_add, coeff_C_mul, coeff_X_mul_zero, mul_zero] + rw [monomialWeight_right (by omega : 0 ≤ T)] + simp only [Nat.cast_zero, sub_zero] + ring + | succ p => + simp only [Nat.add_sub_cancel, Nat.add_one_ne_zero, ite_false, + monomialCoefficient, add_mul, mul_assoc, coeff_add, coeff_C_mul, coeff_X_mul] + by_cases hp : p+1 ≤ T + · have hl := monomialWeight_left T p + have hr := monomialWeight_right hp + calc + _ = monomialWeight (T+1) (p+1) * (v * P.coeff p) + + monomialWeight (T+1) (p+1) * (u * P.coeff (p+1)) := by ring + _ = (Real.sqrt (p+1 : ℕ) * monomialWeight T p) * (v * P.coeff p) + + (Real.sqrt (((T+1 : ℕ) : ℝ)-(p+1 : ℕ)) * monomialWeight T (p+1)) * + (u * P.coeff (p+1)) := by + exact congrArg₂ (· + ·) (congrArg (fun x => x * (v * P.coeff p)) hl) + (congrArg (fun x => x * (u * P.coeff (p+1))) hr) + _ = _ := by ring + · have hc : P.coeff (p+1) = 0 := coeff_eq_zero_of_natDegree_lt (by omega) + simp only [hc, mul_zero, add_zero, monomialWeight_left] + ring + + + +def couplingPolynomial (u v : ℝ) (z k : ℕ) : Polynomial ℝ := + (C u * X - C v)^z * (C v * X + C u)^k + +def polynomialCouplingCoefficient (u v : ℝ) (z k p : ℕ) : ℝ := + monomialCoefficient (z+k) (couplingPolynomial u v z k) p / + Real.sqrt ((z.factorial : ℝ) * k.factorial) + +theorem couplingPolynomial_degree (u v : ℝ) (z k : ℕ) : + (couplingPolynomial u v z k).natDegree ≤ z+k := by + have h1 : (C u * X - C v).natDegree ≤ 1 := by + change _ ≤ max 1 1 + apply natDegree_sub_le_of_le + · exact (natDegree_C_mul_le _ _).trans (by simp) + · simp + have h2 : (C v * X + C u).natDegree ≤ 1 := by + change _ ≤ max 1 1 + apply natDegree_add_le_of_le + · exact (natDegree_C_mul_le _ _).trans (by simp) + · simp + exact natDegree_mul_le.trans (add_le_add + (natDegree_pow_le.trans (by simpa using Nat.mul_le_mul_left z h1)) + (natDegree_pow_le.trans (by simpa using Nat.mul_le_mul_left k h2))) + +theorem polynomialCouplingCoefficient_zero (u v : ℝ) (z k p : ℕ) (hp : z+k < p) : + polynomialCouplingCoefficient u v z k p = 0 := by + have h := coeff_eq_zero_of_natDegree_lt ((couplingPolynomial_degree u v z k).trans_lt hp) + simp only [polynomialCouplingCoefficient, monomialCoefficient, h, mul_zero, zero_div] + +theorem couplingPolynomial_succ (u v : ℝ) (z k : ℕ) : + couplingPolynomial u v z (k+1) = + (C v * X + C u) * couplingPolynomial u v z k := by + unfold couplingPolynomial + rw [pow_succ] + ring + +theorem coefficient_scale_succ (z k : ℕ) : + Real.sqrt ((z.factorial : ℝ) * (k+1).factorial) = + Real.sqrt (k+1 : ℕ) * Real.sqrt ((z.factorial : ℝ) * k.factorial) := by + rw [Nat.factorial_succ, Nat.cast_mul, mul_left_comm, Real.sqrt_mul (Nat.cast_nonneg _)] + + +theorem polynomialCouplingCoefficient_succ (u v : ℝ) (z k p : ℕ) : + polynomialCouplingCoefficient u v z (k+1) p = + ((if p = 0 then 0 else Real.sqrt (p : ℝ) * v * polynomialCouplingCoefficient u v z k (p-1)) + + Real.sqrt (((z+k+1 : ℕ) : ℝ)-p) * u * polynomialCouplingCoefficient u v z k p) / + Real.sqrt (k+1 : ℕ) := by + unfold polynomialCouplingCoefficient + rw [couplingPolynomial_succ, show z+(k+1) = z+k+1 by omega, + monomialCoefficient_linear _ _ (couplingPolynomial_degree u v z k), + coefficient_scale_succ] + split_ifs <;> ring + +theorem coeff_linear_pow (u v : ℝ) (z p : ℕ) : + ((C u * X - C v)^z).coeff p = (-v)^(z-p) * (z.choose p : ℝ) * u^p := by + have h : (C u * X - C v)^z = ((X + C (-v))^z).comp (C u * X) := by simp [sub_eq_add_neg] + rw [h, comp_C_mul_X_coeff, coeff_X_add_C_pow] + +theorem sqrt_nat_pow {a : ℝ} (ha : 0 ≤ a) (n : ℕ) : + Real.sqrt (a^n) = (Real.sqrt a)^n := by + induction n with + | zero => simp + | succ n ih => rw [pow_succ, Real.sqrt_mul (pow_nonneg ha n), ih, pow_succ] + + + +theorem binomial_monomialWeight {z p : ℕ} (hp : p ≤ z) : + (z.choose p : ℝ) * monomialWeight z p / Real.sqrt (z.factorial : ℝ) = + Real.sqrt (z.choose p : ℝ) := by + have hfac : (z.choose p : ℝ) * (p.factorial : ℝ) * (z-p).factorial = + (z.factorial : ℝ) := by exact_mod_cast Nat.choose_mul_factorial_mul_factorial hp + have hfac0 : (z.factorial : ℝ) ≠ 0 := by positivity + have hs := Real.sq_sqrt (by positivity : 0 ≤ ((p.factorial : ℝ) * (z-p).factorial)) + have hsq : ((z.choose p : ℝ) * monomialWeight z p / Real.sqrt (z.factorial : ℝ))^2 = + (Real.sqrt (z.choose p : ℝ))^2 := by + rw [div_pow, mul_pow, monomialWeight, hs, Real.sq_sqrt (by positivity), Real.sq_sqrt (by positivity)] + apply (div_eq_iff hfac0).mpr + nlinarith only [hfac] + have hleft : 0 ≤ ((z.choose p : ℝ) * monomialWeight z p / Real.sqrt (z.factorial : ℝ)) := by + unfold monomialWeight + positivity + nlinarith [Real.sqrt_nonneg (z.choose p : ℝ)] + + +theorem polynomialCouplingCoefficient_top (r : ℝ) (hr : 0 ≤ r) (hr1 : r ≤ 1) (z p : ℕ) : + polynomialCouplingCoefficient (Real.sqrt r) (Real.sqrt (1-r)) z 0 p = + oscillatorCoefficient r z 0 p := by + by_cases hp : p ≤ z + · simp only [polynomialCouplingCoefficient, couplingPolynomial, pow_zero, mul_one, + Nat.factorial_zero, Nat.cast_one, monomialCoefficient, Nat.add_zero, coeff_linear_pow, + oscillatorCoefficient] + rw [neg_pow, Real.sqrt_mul (by positivity : 0 ≤ (z.choose p : ℝ) * (1-r)^(z-p)), + Real.sqrt_mul (Nat.cast_nonneg _), sqrt_nat_pow (by linarith : 0 ≤ 1-r), sqrt_nat_pow hr] + calc + _ = (-1 : ℝ)^(z-p) * ((z.choose p : ℝ) * monomialWeight z p / + Real.sqrt (z.factorial : ℝ)) * (Real.sqrt (1-r))^(z-p) * (Real.sqrt r)^p := by ring + _ = _ := by rw [binomial_monomialWeight hp]; ring + · rw [polynomialCouplingCoefficient_zero _ _ _ _ _ (by omega), + oscillatorCoefficient_zero _ _ _ _ (by omega)] + + + +theorem oscillatorCoefficient_eq_polynomial (r : ℝ) (hr : 0 ≤ r) (hr1 : r ≤ 1) + (z k p : ℕ) : + oscillatorCoefficient r z k p = + polynomialCouplingCoefficient (Real.sqrt r) (Real.sqrt (1-r)) z k p := by + induction k generalizing p with + | zero => exact (polynomialCouplingCoefficient_top r hr hr1 z p).symm + | succ k ih => + rw [oscillatorCoefficient, polynomialCouplingCoefficient_succ, ih p, ih (p-1)] + rw [Real.sqrt_mul (Nat.cast_nonneg p)] + + + +theorem coupledCoefficient_polynomial_limit (n m : ℕ → ℕ) (u : ℝ) + (hu0 : 0 < u) (hu1 : u < 1) + (hn : Tendsto n atTop atTop) (hm : Tendsto m atTop atTop) + (hr : Tendsto (fun Q => (m Q : ℝ) / (n Q + m Q)) atTop (𝓝 (u^2))) + (z k p : ℕ) : + Tendsto (fun Q => coupledCoefficient (n Q) (m Q) z k p) atTop + (𝓝 (polynomialCouplingCoefficient u (Real.sqrt (1-u^2)) z k p)) := by + have h := coupledCoefficient_tendsto n m (u^2) hn hm hr z k p + rw [oscillatorCoefficient_eq_polynomial _ (sq_nonneg _) (by nlinarith) z k p, + Real.sqrt_sq hu0.le] at h + exact h + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/PairDecomposition.lean b/lean/OAI/Analysis/LaughlinFock/PairDecomposition.lean new file mode 100644 index 0000000000000000000000000000000000000000..a9ef0ab599982e93ec560d7e8c8a8ad924569b74 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/PairDecomposition.lean @@ -0,0 +1,190 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.HighestTails + +namespace OAI + +/-! Pair Decomposition. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder + + + +def fourCouplingMatrix (Q : ℕ) : + Matrix (PairLabel Q × PairLabel Q) (CoupledIndex (2*Q-2) (2*Q-2)) ℂ := + fun pq c => coupledVector (2*Q-2) (2*Q-2) c.1.val c.2.val pq.1.val pq.2.val + + +theorem fourCouplingMatrix_complete (Q : ℕ) (hQ : 1 ≤ Q) : + fourCouplingMatrix Q * (fourCouplingMatrix Q)ᴴ = 1 := by + classical + ext pq rs + have hdim : 2*Q-1 = 2*Q-2+1 := by omega + let x : Fin (2*Q-2+1) × Fin (2*Q-2+1) := + (Fin.cast hdim pq.1, Fin.cast hdim pq.2) + let y : Fin (2*Q-2+1) × Fin (2*Q-2+1) := + (Fin.cast hdim rs.1, Fin.cast hdim rs.2) + have h := congrArg (fun t : ℝ => (t : ℂ)) + (coupledVector_resolution (2*Q-2) (2*Q-2) x y) + simpa only [Matrix.mul_apply, Matrix.conjTranspose_apply, + fourCouplingMatrix, Complex.star_def, Complex.conj_ofReal, + Matrix.one_apply, Complex.ofReal_sum, Complex.ofReal_mul, + x, y, Fin.val_cast, Prod.mk.injEq, Fin.cast_inj, ← Prod.ext_iff, + apply_ite, Complex.ofReal_one, Complex.ofReal_zero] using h + + +theorem fourCouplingMatrix_gram (Q : ℕ) (hQ : 1 ≤ Q) : + (fourCouplingMatrix Q)ᴴ * fourCouplingMatrix Q = 1 := by + classical + ext c d + have hc := coupledIndex_bounds c + have hd := coupledIndex_bounds d + have h := coupledVector_gram hc.1 hc.2.1 hd.1 hd.2.1 hc.2.2 hd.2.2 + rw [gridInner_eq_fin_sum] at h + rw [show 2*Q-2+1 = 2*Q-1 by omega] at h + have he : (c.1.val=d.1.val ∧ c.2.val=d.2.val) ↔ c=d := by + constructor + · intro ⟨hz,hk⟩ + rcases c with ⟨z,k⟩ + rcases d with ⟨r,l⟩ + have hr : z=r := Fin.ext hz + subst r + have hl : k=l := Fin.ext hk + subst l + rfl + · rintro rfl + exact ⟨rfl,rfl⟩ + simp only [he] at h + have h' := congrArg (fun t : ℝ => (t : ℂ)) h + simpa only [Matrix.mul_apply, Matrix.conjTranspose_apply, + fourCouplingMatrix, Complex.star_def, Complex.conj_ofReal, + Fintype.sum_prod_type, Matrix.one_apply, Complex.ofReal_sum, + Complex.ofReal_mul, apply_ite, Complex.ofReal_one, Complex.ofReal_zero] using h' + + + +def fourCoupledWedgeMatrix (Q : ℕ) : + Matrix (SectorOccupation Q 4) (CoupledIndex (2*Q-2) (2*Q-2)) ℂ := + fourWedgeMatrix Q * fourCouplingMatrix Q + + +theorem fourCoupledWedgeMatrix_target (Q : ℕ) (hQ : 1 ≤ Q) : + fourCoupledWedgeMatrix Q * (fourCoupledWedgeMatrix Q)ᴴ = + fourWedgeMatrix Q * (fourWedgeMatrix Q)ᴴ := by + unfold fourCoupledWedgeMatrix + rw [Matrix.conjTranspose_mul] + calc + _ = fourWedgeMatrix Q * (fourCouplingMatrix Q * (fourCouplingMatrix Q)ᴴ) * + (fourWedgeMatrix Q)ᴴ := by simp only [Matrix.mul_assoc] + _ = _ := by rw [fourCouplingMatrix_complete Q hQ, Matrix.mul_one] + + + +def retainedFourTarget (Q L : ℕ) : Matrix (SectorOccupation Q 4) (SectorOccupation Q 4) ℂ := + fourCoupledWedgeMatrix Q * Matrix.diagonal + (fun c : CoupledIndex (2*Q-2) (2*Q-2) => if c.1.val+1 ≤ L then (1 : ℂ) else 0) * + (fourCoupledWedgeMatrix Q)ᴴ + +theorem retainedFourTarget_posSemidef (Q L : ℕ) : + (retainedFourTarget Q L).PosSemidef := by + classical + apply Matrix.PosSemidef.mul_mul_conjTranspose_same + apply Matrix.posSemidef_diagonal_iff.mpr + intro c + split_ifs <;> norm_num + + + +theorem discardedFourTarget_posSemidef (Q L : ℕ) (hQ : 1 ≤ Q) : + (fourWedgeMatrix Q * (fourWedgeMatrix Q)ᴴ - retainedFourTarget Q L).PosSemidef := by + classical + rw [← fourCoupledWedgeMatrix_target Q hQ] + have hd : (1 - Matrix.diagonal + (fun c : CoupledIndex (2*Q-2) (2*Q-2) => if c.1.val+1 ≤ L then (1 : ℂ) else 0)).PosSemidef := by + rw [← Matrix.diagonal_one, Matrix.diagonal_sub] + apply Matrix.posSemidef_diagonal_iff.mpr + intro c + split_ifs <;> norm_num + convert hd.mul_mul_conjTranspose_same (fourCoupledWedgeMatrix Q) using 1 + simp only [Matrix.mul_sub, Matrix.sub_mul, Matrix.mul_one, retainedFourTarget] + + + +theorem discardedFourTarget_lift_posSemidef (Q L : ℕ) (hQ : 1 ≤ Q) : + (exteriorLift Q 4 (fourWedgeMatrix Q * (fourWedgeMatrix Q)ᴴ) - + exteriorLift Q 4 (retainedFourTarget Q L)).PosSemidef := by + rw [← exteriorLift_sub] + exact exteriorLift_posSemidef Q 4 _ (discardedFourTarget_posSemidef Q L hQ) + + +theorem fourWedgeMatrix_swap (Q : ℕ) (A : SectorOccupation Q 4) + (p q : PairLabel Q) : fourWedgeMatrix Q A (q,p) = fourWedgeMatrix Q A (p,q) := by + unfold fourWedgeMatrix + rw [pairAnnihilators_commute Q p.val q.val] + + +def fourCoupledAnnihilator (Q z k : ℕ) : FockMatrix Q := + ∑ p : PairLabel Q, ∑ q : PairLabel Q, + (coupledVector (2*Q-2) (2*Q-2) z k p.val q.val : ℂ) • + (pairAnnihilator Q q.val * pairAnnihilator Q p.val) + + + +theorem fourCoupledAnnihilator_odd_zero {Q z : ℕ} (hz : z ≤ 2*Q-2) + (ho : Odd z) (k : ℕ) : fourCoupledAnnihilator Q z k = 0 := by + have h : fourCoupledAnnihilator Q z k = -fourCoupledAnnihilator Q z k := by + unfold fourCoupledAnnihilator + conv_lhs => rw [Finset.sum_comm] + rw [← Finset.sum_neg_distrib] + apply Finset.sum_congr rfl + intro q _ + rw [← Finset.sum_neg_distrib] + apply Finset.sum_congr rfl + intro p _ + rw [coupledVector_antisymm hz ho k p.val q.val, + pairAnnihilators_commute Q p.val q.val, Complex.ofReal_neg, neg_smul, neg_neg] + have h' := eq_neg_iff_add_eq_zero.mp h + have he : (2 : ℂ) • fourCoupledAnnihilator Q z k = 0 := by simpa only [two_smul] using h' + exact (smul_eq_zero.mp he).resolve_left (by norm_num) + + +theorem fourWedgeMatrix_annihilator_column (Q : ℕ) (pq : PairLabel Q × PairLabel Q) : + wedgeAnnihilator Q 4 (fun A => fourWedgeMatrix Q A pq) = + pairAnnihilator Q pq.2.val * pairAnnihilator Q pq.1.val := by + apply wedgeAnnihilator_annihilatorVector + exact annihilationSpace_mul Q 2 2 (pairAnnihilator_mem Q pq.1.val) + (pairAnnihilator_mem Q pq.2.val) + + + +theorem fourCoupledAnnihilator_eq_wedge (Q : ℕ) + (c : CoupledIndex (2*Q-2) (2*Q-2)) : + fourCoupledAnnihilator Q c.1.val c.2.val = + wedgeAnnihilator Q 4 (fun A => fourCoupledWedgeMatrix Q A c) := by + change _ = wedgeAnnihilator Q 4 + (fourWedgeMatrix Q *ᵥ fun pq => fourCouplingMatrix Q pq c) + rw [wedgeAnnihilator_mulVec] + simp only [fourWedgeMatrix_annihilator_column, fourCouplingMatrix, + Complex.star_def, Complex.conj_ofReal, Fintype.sum_prod_type, fourCoupledAnnihilator] + + + +theorem retainedFourTarget_lift (Q L : ℕ) : + exteriorLift Q 4 (retainedFourTarget Q L) = + ∑ c : CoupledIndex (2*Q-2) (2*Q-2), if c.1.val+1 ≤ L then + (fourCoupledAnnihilator Q c.1.val c.2.val)ᴴ * + fourCoupledAnnihilator Q c.1.val c.2.val else 0 := by + classical + unfold retainedFourTarget + rw [exteriorLift_congruence] + apply Finset.sum_congr rfl + intro c _ + simp only [Matrix.diagonal_apply, ite_smul, zero_smul] + rw [Finset.sum_ite_eq, ite_eq_left (Finset.mem_univ c)] + rw [← fourCoupledAnnihilator_eq_wedge] + split_ifs <;> simp + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/PairIdentification.lean b/lean/OAI/Analysis/LaughlinFock/PairIdentification.lean new file mode 100644 index 0000000000000000000000000000000000000000..1cc62ab56d1c1796ab2021ee70d04533b4d5ba8b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/PairIdentification.lean @@ -0,0 +1,212 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LadderCalculus + +namespace OAI + +/-! Pair Identification. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators + + + +theorem spinStep_mul_choose (n p : ℕ) : + spinStep n p * Real.sqrt (n.choose (p-1) : ℝ) = + (p : ℝ) * Real.sqrt (n.choose p : ℝ) := by + rcases p with _ | p + · simp + by_cases hp : p+1 ≤ n + · have hc : ((n.choose (p+1) : ℝ)) * (p+1 : ℕ) = + ((n.choose p : ℝ)) * (n-p : ℕ) := by + exact_mod_cast Nat.choose_succ_right_eq n p + apply (sq_eq_sq₀ (by unfold spinStep; positivity : 0 ≤ spinStep n (p+1) * Real.sqrt (n.choose ((p+1)-1) : ℝ)) + (by positivity : 0 ≤ ((p+1 : ℕ) : ℝ)*Real.sqrt (n.choose (p+1) : ℝ))).mp + rw [mul_pow, mul_pow, spinStep_sq (by omega), Real.sq_sqrt (Nat.cast_nonneg _), + Real.sq_sqrt (Nat.cast_nonneg _)] + simp only [Nat.add_sub_cancel] + rw [Nat.cast_sub (by omega : p ≤ n)] at hc + push_cast at hc ⊢ + have h := congrArg (fun x : ℝ => ((p:ℝ)+1)*x) hc + nlinarith only [h] + · rw [spinStep_cutoff n (p+1) (by omega), Nat.choose_eq_zero_of_lt (by omega : n < p+1)] + simp + + + +def rawPairGrid (Q p : ℕ) : GridVector := fun i j => + if i+j=p+1 then + ((i:ℝ)-j) * Real.sqrt (Q.choose i : ℝ) * Real.sqrt (Q.choose j : ℝ) + else 0 + +theorem rawPairGrid_layer (Q p : ℕ) : GridLayer (p+1) (rawPairGrid Q p) := by + intro i j hij + exact ite_eq_right hij + + + +theorem rawPairGrid_lower (Q p : ℕ) : + gridLower Q Q (rawPairGrid Q p) = ((p+1 : ℕ) : ℝ) • rawPairGrid Q (p+1) := by + funext i j + by_cases ht : i+j=p+2 + · change spinStep Q i * rawPairGrid Q p (i-1) j + + spinStep Q j * rawPairGrid Q p i (j-1) = + ((p+1 : ℕ) : ℝ) * rawPairGrid Q (p+1) i j + conv_rhs => rw [rawPairGrid, ite_eq_left (by omega : i+j=p+1+1)] + have ht' : (i:ℝ)+j = (p:ℝ)+2 := by exact_mod_cast ht + by_cases hi : i=0 + · subst i + simp only [spinStep_zero, zero_mul, zero_add, rawPairGrid, + ite_eq_left (by omega : (j-1)=p+1), Nat.cast_zero, zero_sub, Nat.choose_zero_right, + Nat.cast_one, Real.sqrt_one, mul_one] + rw [show spinStep Q j * (-((j-1:ℕ):ℝ) * Real.sqrt (Q.choose (j-1) : ℝ)) = + -((j-1:ℕ):ℝ) * (spinStep Q j * Real.sqrt (Q.choose (j-1) : ℝ)) by ring, + spinStep_mul_choose] + rw [Nat.cast_sub (by omega : 1 ≤ j)] + push_cast + have he : (j:ℝ)=(p:ℝ)+2 := by exact_mod_cast (show j=p+2 by omega) + rw [he] + ring + · by_cases hj : j=0 + · subst j + simp only [spinStep_zero, zero_mul, add_zero, rawPairGrid, + ite_eq_left (by omega : i-1=p+1), Nat.cast_zero, sub_zero, + Nat.choose_zero_right, Nat.cast_one, Real.sqrt_one, mul_one] + rw [show spinStep Q i * (((i-1:ℕ):ℝ) * Real.sqrt (Q.choose (i-1) : ℝ)) = + ((i-1:ℕ):ℝ) * (spinStep Q i * Real.sqrt (Q.choose (i-1) : ℝ)) by ring, + spinStep_mul_choose] + rw [Nat.cast_sub (by omega : 1 ≤ i)] + push_cast + have he : (i:ℝ)=(p:ℝ)+2 := by exact_mod_cast (show i=p+2 by omega) + rw [he] + ring + · simp only [rawPairGrid, ite_eq_left (by omega : i-1+j=p+1), + ite_eq_left (by omega : i+(j-1)=p+1)] + rw [show spinStep Q i * ((((i-1:ℕ):ℝ)-j) * + Real.sqrt (Q.choose (i-1) : ℝ) * Real.sqrt (Q.choose j : ℝ)) = + (((i-1:ℕ):ℝ)-j) * (spinStep Q i * Real.sqrt (Q.choose (i-1) : ℝ)) * + Real.sqrt (Q.choose j : ℝ) by ring, + show spinStep Q j * (((i:ℝ)-(j-1:ℕ)) * + Real.sqrt (Q.choose i : ℝ) * Real.sqrt (Q.choose (j-1) : ℝ)) = + ((i:ℝ)-(j-1:ℕ)) * Real.sqrt (Q.choose i : ℝ) * + (spinStep Q j * Real.sqrt (Q.choose (j-1) : ℝ)) by ring, + spinStep_mul_choose, spinStep_mul_choose, + Nat.cast_sub (by omega : 1 ≤ i), Nat.cast_sub (by omega : 1 ≤ j)] + push_cast + have he : (p:ℝ)+1=(i:ℝ)+j-1 := by linarith + rw [he] + ring + · have h := gridLower_layer (n := Q) (m := Q) (rawPairGrid_layer Q p) i j (by omega) + simp only [h, Pi.smul_apply, smul_eq_mul, rawPairGrid, + ite_eq_right (by omega : i+j≠p+1+1), mul_zero] + + +def pairTensorNormalizer (Q p : ℕ) : ℝ := + Real.sqrt (2*(Q:ℝ)*((2*Q-2).choose p : ℝ)) + +theorem pairTensorNormalizer_pos {Q p : ℕ} (hQ : 1 ≤ Q) (hp : p ≤ 2*Q-2) : + 0 < pairTensorNormalizer Q p := by + unfold pairTensorNormalizer + apply Real.sqrt_pos.mpr + have hq : 0 < (Q:ℝ) := by exact_mod_cast hQ + have hc : 0 < ((2*Q-2).choose p : ℝ) := by exact_mod_cast Nat.choose_pos hp + positivity + +theorem pairTensorNormalizer_recurrence {Q p : ℕ} (hp : p < 2*Q-2) : + spinStep (2*Q-2) (p+1) * pairTensorNormalizer Q p = + ((p+1 : ℕ):ℝ) * pairTensorNormalizer Q (p+1) := by + apply (sq_eq_sq₀ (by unfold spinStep pairTensorNormalizer; positivity) + (by unfold pairTensorNormalizer; positivity)).mp + rw [mul_pow, mul_pow, spinStep_sq (by omega)] + rw [pairTensorNormalizer, pairTensorNormalizer, + Real.sq_sqrt (by positivity), Real.sq_sqrt (by positivity)] + have hc : (((2*Q-2).choose (p+1) : ℝ)) * (p+1 : ℕ) = + (((2*Q-2).choose p : ℝ)) * ((2*Q-2)-p : ℕ) := by + exact_mod_cast Nat.choose_succ_right_eq (2*Q-2) p + rw [Nat.cast_sub (by omega : p ≤ 2*Q-2)] at hc + have h := congrArg (fun x : ℝ => 2*(Q:ℝ)*((p+1:ℕ):ℝ)*x) hc + push_cast at h ⊢ + nlinarith only [h] + + +def normalizedPairGrid (Q p : ℕ) : GridVector := + (pairTensorNormalizer Q p)⁻¹ • rawPairGrid Q p + +theorem normalizedPairGrid_succ {Q p : ℕ} (hQ : 1 ≤ Q) (hp : p < 2*Q-2) : + normalizedPairGrid Q (p+1) = (spinStep (2*Q-2) (p+1))⁻¹ • + gridLower Q Q (normalizedPairGrid Q p) := by + rw [normalizedPairGrid, normalizedPairGrid, gridLower_smul, + rawPairGrid_lower, smul_smul, smul_smul] + have h1 := (pairTensorNormalizer_pos hQ (by omega : p ≤ 2*Q-2)).ne' + have h2 := (pairTensorNormalizer_pos hQ (by omega : p+1 ≤ 2*Q-2)).ne' + have h3 := (spinStep_pos (by omega : 0 < p+1) (by omega : p+1 ≤ 2*Q-2)).ne' + congr 1 + field_simp [h1, h2, h3] + simpa only [mul_comm] using pairTensorNormalizer_recurrence hp + + +theorem normalizedPairGrid_top {Q : ℕ} (hQ : 1 ≤ Q) : + normalizedPairGrid Q 0 = coupledVector Q Q 1 0 := by + have hpred : Q-1+1 = Q := by omega + have htotal : highestTotal Q Q 1 = 2*Q := by + simp [highestTotal, Finset.sum_range_succ, highestWeight, hpred, two_mul] + funext i j + by_cases ht : i+j=1 + · have hcases : (i=0 ∧ j=1) ∨ (i=1 ∧ j=0) := by omega + rcases hcases with ⟨rfl,rfl⟩ | ⟨rfl,rfl⟩ + all_goals + simp [normalizedPairGrid, rawPairGrid, pairTensorNormalizer, coupledVector, + coupledCoefficient, highestCoefficient, highestWeight, htotal, hpred, + Real.sqrt_div (Nat.cast_nonneg Q)] + ring + · simp [normalizedPairGrid, rawPairGrid, coupledVector, ht] + + + +theorem normalizedPairGrid_eq_coupled {Q p : ℕ} (hQ : 1 ≤ Q) (hp : p ≤ 2*Q-2) : + normalizedPairGrid Q p = coupledVector Q Q 1 p := by + induction p with + | zero => exact normalizedPairGrid_top hQ + | succ p ih => + rw [normalizedPairGrid_succ hQ (by omega), ih (by omega), + coupledVector_succ (by omega : 2*1 ≤ Q+Q)] + simp only [two_mul, mul_one] + + + +theorem sphericalPairCoefficient_eq_normalized {Q p : ℕ} (hQ : 1 ≤ Q) + (hp : p ≤ 2*Q-2) (i j : ℕ) : + sphericalPairCoefficient Q p i j = Real.sqrt 2 * normalizedPairGrid Q p i j := by + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + have hc : ((2*Q-2).choose p : ℝ) ≠ 0 := by + exact_mod_cast (Nat.choose_pos hp).ne' + have hi : (i.factorial : ℝ) ≠ 0 := by exact_mod_cast Nat.factorial_ne_zero i + have hj : (j.factorial : ℝ) ≠ 0 := by exact_mod_cast Nat.factorial_ne_zero j + have hf : (p.factorial : ℝ) ≠ 0 := by exact_mod_cast Nat.factorial_ne_zero p + have hr : ((Q.descFactorial i : ℝ)*(Q.descFactorial j : ℝ)*(p.factorial : ℝ)) / + ((Q : ℝ)*((2*Q-2).descFactorial p : ℝ)*(i.factorial : ℝ)*(j.factorial : ℝ)) = + ((Q.choose i : ℝ)*(Q.choose j : ℝ)) / ((Q : ℝ)*((2*Q-2).choose p : ℝ)) := by + simp only [Nat.descFactorial_eq_factorial_mul_choose, Nat.cast_mul] + field_simp + unfold sphericalPairCoefficient normalizedPairGrid rawPairGrid + simp only [Pi.smul_apply, smul_eq_mul] + split_ifs with hw + · rw [hr, Real.sqrt_div (by positivity), + Real.sqrt_mul (Nat.cast_nonneg (Q.choose i))] + unfold pairTensorNormalizer + rw [mul_assoc (2 : ℝ), Real.sqrt_mul (by norm_num : (0:ℝ) ≤ 2)] + have h2 : Real.sqrt (2 : ℝ) ≠ 0 := by positivity + field_simp + · simp + + + +theorem pairCoefficient_eq_coupled {Q p : ℕ} (hQ : 1 ≤ Q) + (hp : p ≤ 2*Q-2) (i j : Orbital Q) : + pairCoefficient Q p i j = Real.sqrt 2 * coupledVector Q Q 1 p i j := by + rw [pairCoefficient_eq_sphericalPairCoefficient, + sphericalPairCoefficient_eq_normalized hQ hp, normalizedPairGrid_eq_coupled hQ hp] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/PairLie.lean b/lean/OAI/Analysis/LaughlinFock/PairLie.lean new file mode 100644 index 0000000000000000000000000000000000000000..d15d7490b33614a9c73a125d9d57d16a11011b04 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/PairLie.lean @@ -0,0 +1,145 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.CoupledLie + +namespace OAI + +/-! Pair Lie. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + +theorem wedgeAnnihilator_smul (Q k : ℕ) (c : ℂ) (v : SectorOccupation Q k → ℂ) : + wedgeAnnihilator Q k (c • v) = star c • wedgeAnnihilator Q k v := by + unfold wedgeAnnihilator + rw [Finset.smul_sum] + apply Finset.sum_congr rfl + intro S _ + change (star (c * v S)) • basisAnnihilator Q S.val = _ + rw [star_mul, smul_smul, mul_comm] + + +theorem symmetric_sum_upper {ι V : Type*} [Fintype ι] [LinearOrder ι] + [AddCommMonoid V] (f : ι → ι → V) + (hsymm : ∀ i j, f j i = f i j) (hdiag : ∀ i, f i i = 0) : + (∑ i, ∑ j, f i j) = + (∑ i, ∑ j, if i < j then f i j else 0) + ∑ i, ∑ j, if i < j then f i j else 0 := by + have ht (i j : ι) : f i j = + (if i < j then f i j else 0) + (if j < i then f j i else 0) := by + rcases lt_trichotomy i j with h | rfl | h + · simp [h, not_lt.mpr h.le] + · simp [hdiag] + · simp [h, not_lt.mpr h.le, hsymm] + calc + _ = ∑ i, ∑ j, ((if i < j then f i j else 0) + (if j < i then f j i else 0)) := by + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + exact ht i j + _ = _ := by + simp only [Finset.sum_add_distrib] + rw [Finset.sum_comm (f:=fun i j => if j < i then f j i else 0)] + + + +theorem tensorWedge_contraction (Q : ℕ) (s : Orbital Q × Orbital Q → ℂ) + (hs : ∀ i j, s (j,i) = -s (i,j)) : + wedgeAnnihilator Q 2 + (wedgeProductMatrix Q 1 1 (oneParticleMatrix Q) (oneParticleMatrix Q) *ᵥ s) = + (2:ℂ) • coefficientPairAnnihilator Q (fun i j => star (s (i,j))) := by + rw [wedgeAnnihilator_mulVec] + have hc (ij : Orbital Q × Orbital Q) := wedgeProductMatrix_contraction Q 1 1 + (oneParticleMatrix Q) (oneParticleMatrix Q) ij + simp only [oneParticleMatrix_contraction] at hc + simp only [hc, Fintype.sum_prod_type] + have hh := symmetric_sum_upper (fun i j : Orbital Q => star (s (i,j)) • + (annihilator Q j * annihilator Q i)) + (by + intro i j + have ha := eq_neg_of_add_eq_zero_left (annihilator_anticommute Q i j) + rw [hs, star_neg, ha, neg_smul, smul_neg, neg_neg]) + (by intro i; simp only [annihilator_square, smul_zero]) + simpa only [coefficientPairAnnihilator, two_smul ℂ] using hh + + +theorem tensorWedge_intertwines (Q : ℕ) (s : Fin 3) : + sectorOneBody Q 2 (spinGenerator Q s) * + wedgeProductMatrix Q 1 1 (oneParticleMatrix Q) (oneParticleMatrix Q) = + wedgeProductMatrix Q 1 1 (oneParticleMatrix Q) (oneParticleMatrix Q) * + tensorSum (spinGenerator Q s) (spinGenerator Q s) := + wedgeProductMatrix_intertwines Q 1 1 _ (spinGenerator_skew Q s) _ _ _ _ + (oneParticleMatrix_intertwines Q _ (spinGenerator_skew Q s)) + (oneParticleMatrix_intertwines Q _ (spinGenerator_skew Q s)) + + +def pairSpinMatrix (Q : ℕ) : Matrix (SectorOccupation Q 2) (Fin (2*Q-2+1)) ℂ := + fun S p => pairVector Q p.val S + + + +theorem tensorWedge_pairSpinMatrix {Q : ℕ} (hQ : 1 ≤ Q) : + (wedgeProductMatrix Q 1 1 (oneParticleMatrix Q) (oneParticleMatrix Q) * + coupledSpinMatrix Q Q 1) = + (Real.sqrt 2 : ℂ) • + (pairSpinMatrix Q).submatrix id (Fin.cast (by omega)) := by + ext S p + have hv : wedgeAnnihilator Q 2 + (wedgeProductMatrix Q 1 1 (oneParticleMatrix Q) (oneParticleMatrix Q) *ᵥ + (fun ij => coupledSpinMatrix Q Q 1 ij p)) = + wedgeAnnihilator Q 2 ((Real.sqrt 2 : ℂ) • pairVector Q p.val) := by + rw [tensorWedge_contraction] + · rw [wedgeAnnihilator_smul] + simp only [pairVector, wedgeAnnihilator_annihilatorVector Q 2 _ (pairAnnihilator_mem Q _), + Complex.star_def, Complex.conj_ofReal] + unfold coupledSpinMatrix + simp only [Complex.conj_ofReal] + have he (i j : Orbital Q) : + (coupledVector Q Q 1 p.val i.val j.val : ℂ) = + (Real.sqrt 2 : ℂ)⁻¹ * (pairCoefficient Q p.val i j : ℂ) := by + rw [pairCoefficient_eq_coupled hQ (by have := p.isLt; omega)] + push_cast + have hn : (Real.sqrt 2 : ℂ) ≠ 0 := by exact_mod_cast (show Real.sqrt 2 ≠ 0 by positivity) + field_simp + simp_rw [he] + rw [coefficientPairAnnihilator_smul, smul_smul] + congr 1 + have hs : (Real.sqrt 2 : ℂ)^2 = 2 := by exact_mod_cast Real.sq_sqrt (by norm_num : (0:ℝ) ≤ 2) + have hn : (Real.sqrt 2 : ℂ) ≠ 0 := by exact_mod_cast (show Real.sqrt 2 ≠ 0 by positivity) + field_simp + linear_combination -hs + · intro i j + dsimp [coupledSpinMatrix] + rw [coupledVector_antisymm hQ (by decide : Odd 1)] + simp + exact congrFun (wedgeAnnihilator_injective Q 2 hv) S + + +theorem pairSpinMatrix_intertwines {Q : ℕ} (hQ : 1 ≤ Q) (s : Fin 3) : + sectorOneBody Q 2 (spinGenerator Q s) * pairSpinMatrix Q = + pairSpinMatrix Q * spinGenerator (2*Q-2) s := by + have h := coupledSpinMatrix_intertwines hQ hQ s + have he : sectorOneBody Q 2 (spinGenerator Q s) * + (wedgeProductMatrix Q 1 1 (oneParticleMatrix Q) (oneParticleMatrix Q) * coupledSpinMatrix Q Q 1) = + (wedgeProductMatrix Q 1 1 (oneParticleMatrix Q) (oneParticleMatrix Q) * coupledSpinMatrix Q Q 1) * + spinGenerator (Q+Q-2*1) s := by + rw [← Matrix.mul_assoc, tensorWedge_intertwines, Matrix.mul_assoc, h, Matrix.mul_assoc] + rw [tensorWedge_pairSpinMatrix hQ] at he + have hdim : Q+Q-2*1 = 2*Q-2 := by omega + simp only [Matrix.mul_smul, Matrix.smul_mul] at he + have hn : (Real.sqrt 2 : ℂ) ≠ 0 := by exact_mod_cast (show Real.sqrt 2 ≠ 0 by positivity) + have hf := smul_right_injective _ hn he + have hc (n : ℕ) (e : n = 2*Q-2) + (hc : sectorOneBody Q 2 (spinGenerator Q s) * + (pairSpinMatrix Q).submatrix id (Fin.cast (congrArg (·+1) e)) = + (pairSpinMatrix Q).submatrix id (Fin.cast (congrArg (·+1) e)) * spinGenerator n s) : + sectorOneBody Q 2 (spinGenerator Q s) * pairSpinMatrix Q = + pairSpinMatrix Q * spinGenerator (2*Q-2) s := by + subst n + simpa only [Fin.cast_refl, Matrix.submatrix_id_id] using hc + exact hc _ hdim hf + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/PairNormalization.lean b/lean/OAI/Analysis/LaughlinFock/PairNormalization.lean new file mode 100644 index 0000000000000000000000000000000000000000..e31582edb72051e7c8290d203b7f3808fafccf40 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/PairNormalization.lean @@ -0,0 +1,227 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Model + +namespace OAI + +/-! Pair Normalization. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open scoped BigOperators Polynomial +open Polynomial +private def euler (P : ℝ[X]) : ℝ[X] := X * derivative P +private def variance (P : ℝ[X]) : ℝ[X] := euler (euler P) * P - (euler P)^2 +private theorem coeff_euler (P : ℝ[X]) (n : ℕ) : + (euler P).coeff n = (n : ℝ) * P.coeff n := by + cases n with + | zero => simp [euler] + | succ n => simp [euler, coeff_derivative, mul_comm] +private theorem euler_mul (P R : ℝ[X]) : + euler (P * R) = euler P * R + P * euler R := by + simp only [euler, derivative_mul] + ring +private theorem euler_add (P R : ℝ[X]) : euler (P + R) = euler P + euler R := by + simp [euler, mul_add] +private theorem variance_mul (P R : ℝ[X]) : + variance (P * R) = P^2 * variance R + R^2 * variance P := by + simp only [variance, euler_mul, euler_add] + ring +private theorem variance_X_add_one : variance (X + 1) = X := by + simp [variance, euler] + ring +private theorem variance_X_add_one_pow (n : ℕ) : + variance ((X + 1)^(n+1)) = C ((n+1 : ℕ) : ℝ) * X * ((X+1)^n)^2 := by + induction n with + | zero => simp [variance_X_add_one] + | succ n ih => + rw [pow_succ (X + 1) (n + 1), variance_mul, variance_X_add_one, ih] + simp only [pow_succ, Nat.cast_add, Nat.cast_one, map_add, map_one] + ring + +private theorem weighted_antidiagonal (P : ℝ[X]) (n : ℕ) : + (∑ ij ∈ Finset.HasAntidiagonal.antidiagonal n, + ((ij.1 : ℝ) - (ij.2 : ℝ))^2 * P.coeff ij.1 * P.coeff ij.2) = + 2 * (variance P).coeff n := by + have hswap : (∑ ij ∈ Finset.HasAntidiagonal.antidiagonal n, + (ij.2 : ℝ)^2 * P.coeff ij.1 * P.coeff ij.2) = + ∑ ij ∈ Finset.HasAntidiagonal.antidiagonal n, (ij.1 : ℝ)^2 * P.coeff ij.1 * P.coeff ij.2 := by + rw [← Finset.Nat.sum_antidiagonal_swap (f := fun ij => + (ij.1 : ℝ)^2 * P.coeff ij.1 * P.coeff ij.2)] + apply Finset.sum_congr rfl + intro ij _ + dsimp only [Prod.swap] + ring + calc + _ = ∑ ij ∈ Finset.HasAntidiagonal.antidiagonal n, + ((ij.1 : ℝ)^2 * P.coeff ij.1 * P.coeff ij.2 + + (ij.2 : ℝ)^2 * P.coeff ij.1 * P.coeff ij.2 - + 2 * ((ij.1 : ℝ) * P.coeff ij.1 * ((ij.2 : ℝ) * P.coeff ij.2))) := by + apply Finset.sum_congr rfl + intro ij _ + ring + _ = _ := by + simp only [Finset.sum_add_distrib, Finset.sum_sub_distrib, ← Finset.mul_sum, + variance, coeff_sub, pow_two, coeff_mul, coeff_euler] + simp only [pow_two] at hswap + rw [hswap] + have hh : (∑ ij ∈ Finset.HasAntidiagonal.antidiagonal n, + (ij.1 : ℝ) * ((ij.1 : ℝ) * P.coeff ij.1) * P.coeff ij.2) = + ∑ ij ∈ Finset.HasAntidiagonal.antidiagonal n, (ij.1 : ℝ)^2 * P.coeff ij.1 * P.coeff ij.2 := by + apply Finset.sum_congr rfl + intro ij _ + ring + simp only [pow_two] at hh + rw [hh] + ring + + +theorem pair_binomial_identity (Q p : ℕ) (hQ : 1 ≤ Q) : + (∑ ij ∈ Finset.HasAntidiagonal.antidiagonal (p+1), + ((ij.1 : ℝ) - (ij.2 : ℝ))^2 * (Q.choose ij.1 : ℝ) * (Q.choose ij.2 : ℝ)) = + 2 * (Q : ℝ) * ((2*Q-2).choose p : ℝ) := by + obtain ⟨n, rfl⟩ : ∃ n, Q = n+1 := ⟨Q-1, by omega⟩ + have h := weighted_antidiagonal ((X+1)^(n+1)) (p+1) + rw [variance_X_add_one_pow] at h + simp only [coeff_X_add_one_pow, mul_assoc, coeff_C_mul, coeff_X_mul] at h + rw [← pow_mul, coeff_X_add_one_pow] at h + have he : 2*(n+1)-2 = n*2 := by omega + rw [he] + simpa only [mul_assoc] using h + + +theorem pairCoefficient_sq (Q p : ℕ) (i j : Orbital Q) + (hQ : 1 ≤ Q) (hp : p ≤ 2*Q-2) : + pairCoefficient Q p i j ^ 2 = + if i.val + j.val = p+1 then + ((i.val : ℝ) - (j.val : ℝ))^2 * (Q.choose i.val : ℝ) * + (Q.choose j.val : ℝ) / ((Q : ℝ) * ((2*Q-2).choose p : ℝ)) + else 0 := by + rw [pairCoefficient_eq] + split_ifs + · rw [mul_pow, Real.sq_sqrt (by positivity)] + simp only [Nat.descFactorial_eq_factorial_mul_choose, Nat.cast_mul] + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + have hp' : ((2*Q-2).choose p : ℝ) ≠ 0 := by + exact_mod_cast (Nat.ne_of_gt (Nat.choose_pos hp)) + have hi : (i.val.factorial : ℝ) ≠ 0 := by exact_mod_cast Nat.factorial_ne_zero i.val + have hj : (j.val.factorial : ℝ) ≠ 0 := by exact_mod_cast Nat.factorial_ne_zero j.val + have hf : (p.factorial : ℝ) ≠ 0 := by exact_mod_cast Nat.factorial_ne_zero p + field_simp + · simp + +private theorem orbital_sum_eq_antidiagonal (Q p : ℕ) (f : ℕ → ℕ → ℝ) + (hf : ∀ i j, Q < i ∨ Q < j → f i j = 0) : + (∑ i : Orbital Q, ∑ j : Orbital Q, + if i.val + j.val = p+1 then f i.val j.val else 0) = + ∑ ij ∈ Finset.HasAntidiagonal.antidiagonal (p+1), f ij.1 ij.2 := by + classical + have hi (i : Orbital Q) : (∑ j : Orbital Q, + if i.val + j.val = p+1 then f i.val j.val else 0) = + ∑ j ∈ Finset.range (Q+1), if i.val+j=p+1 then f i.val j else 0 := + Fin.sum_univ_eq_sum_range (fun j => if i.val+j=p+1 then f i.val j else 0) _ + simp_rw [hi] + rw [Fin.sum_univ_eq_sum_range + (fun i => ∑ j ∈ Finset.range (Q+1), if i+j=p+1 then f i j else 0) (Q+1)] + rw [← Finset.sum_product (Finset.range (Q+1)) (Finset.range (Q+1)) + (fun ij : ℕ × ℕ => if ij.1+ij.2=p+1 then f ij.1 ij.2 else 0), + ← Finset.sum_filter (fun ij : ℕ × ℕ => ij.1+ij.2=p+1) (fun ij => f ij.1 ij.2)] + have hs : ((Finset.range (Q+1) ×ˢ Finset.range (Q+1)).filter + (fun ij : ℕ × ℕ => ij.1 + ij.2 = p+1)) = + (Finset.HasAntidiagonal.antidiagonal (p+1)).filter + (fun ij : ℕ × ℕ => ij.1 ≤ Q ∧ ij.2 ≤ Q) := by + ext ij + simp only [Finset.mem_filter, Finset.mem_product, Finset.mem_range, + Finset.HasAntidiagonal.mem_antidiagonal, Nat.lt_succ_iff] + tauto + rw [hs] + apply Finset.sum_subset (Finset.filter_subset _ _) + intro ij hij hn + have hn' : ¬ (ij.1 ≤ Q ∧ ij.2 ≤ Q) := by + simpa only [Finset.mem_filter, hij, true_and] using hn + exact hf _ _ (by omega) + + +theorem pairCoefficient_ordered_norm (Q p : ℕ) (hQ : 1 ≤ Q) + (hp : p ≤ 2*Q-2) : + (∑ i : Orbital Q, ∑ j : Orbital Q, pairCoefficient Q p i j ^ 2) = 2 := by + have hsum := orbital_sum_eq_antidiagonal Q p + (fun i j => ((i : ℝ) - (j : ℝ))^2 * (Q.choose i : ℝ) * (Q.choose j : ℝ)) + (by + intro i j hij + rcases hij with hi | hj + · simp [Nat.choose_eq_zero_of_lt hi] + · simp [Nat.choose_eq_zero_of_lt hj]) + rw [pair_binomial_identity Q p hQ] at hsum + have hq : (Q : ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + have hc : ((2*Q-2).choose p : ℝ) ≠ 0 := by + exact_mod_cast (Nat.ne_of_gt (Nat.choose_pos hp)) + calc + _ = (∑ i : Orbital Q, ∑ j : Orbital Q, + if i.val+j.val = p+1 then + ((i.val : ℝ) - (j.val : ℝ))^2 * (Q.choose i.val : ℝ) * (Q.choose j.val : ℝ) + else 0) / ((Q : ℝ) * ((2*Q-2).choose p : ℝ)) := by + simp only [Finset.sum_div, ite_div, zero_div, pairCoefficient_sq Q p _ _ hQ hp] + _ = _ := by rw [hsum]; field_simp + +private theorem sum_eq_twice_upper {ι : Type*} [Fintype ι] [LinearOrder ι] + (f : ι → ι → ℝ) (hsymm : ∀ i j, f j i = f i j) (hdiag : ∀ i, f i i = 0) : + (∑ i, ∑ j, f i j) = 2 * ∑ i, ∑ j, if i < j then f i j else 0 := by + have hterm : ∀ i j, f i j = + (if i < j then f i j else 0) + (if j < i then f j i else 0) := by + intro i j + rcases lt_trichotomy i j with hij | hij | hij + · simp [hij, not_lt.mpr hij.le] + · subst j; simp [hdiag] + · simp [hij, not_lt.mpr hij.le, hsymm] + calc + _ = ∑ i, ∑ j, + ((if i < j then f i j else 0) + (if j < i then f j i else 0)) := by + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + exact hterm i j + _ = (∑ i, ∑ j, if i < j then f i j else 0) + + ∑ i, ∑ j, if j < i then f j i else 0 := by + simp only [Finset.sum_add_distrib] + _ = _ := by + rw [Finset.sum_comm (f := fun i j => if j < i then f j i else 0)] + ring + + + +theorem pairCoefficient_norm (Q p : ℕ) (hQ : 1 ≤ Q) (hp : p ≤ 2*Q-2) : + (∑ i : Orbital Q, ∑ j : Orbital Q, + if i < j then pairCoefficient Q p i j ^ 2 else 0) = 1 := by + have hs := sum_eq_twice_upper (fun i j : Orbital Q => pairCoefficient Q p i j^2) + (by + intro i j + rw [pairCoefficient_sq Q p j i hQ hp, pairCoefficient_sq Q p i j hQ hp] + by_cases h : i.val+j.val = p+1 + · have h' : j.val+i.val=p+1 := by omega + simp only [h, h', ite_true] + ring + · have h' : j.val+i.val≠p+1 := by omega + simp only [h, h', ite_false]) + (by intro i; simp [pairCoefficient_eq]) + rw [pairCoefficient_ordered_norm Q p hQ hp] at hs + linarith + + + +theorem pairCoefficient_orthogonal (Q p r : ℕ) (hpr : p ≠ r) : + (∑ i : Orbital Q, ∑ j : Orbital Q, + if i < j then pairCoefficient Q p i j * pairCoefficient Q r i j else 0) = 0 := by + classical + apply Finset.sum_eq_zero + intro i _ + apply Finset.sum_eq_zero + intro j _ + split_ifs + · rw [pairCoefficient_eq, pairCoefficient_eq] + split_ifs <;> first | omega | simp + · rfl +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/PairOrbit.lean b/lean/OAI/Analysis/LaughlinFock/PairOrbit.lean new file mode 100644 index 0000000000000000000000000000000000000000..34dfd076e54c3a206f1f4005497b4bd186758b49 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/PairOrbit.lean @@ -0,0 +1,86 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PairLie +import OAI.Analysis.LaughlinFock.RowTraces + +namespace OAI + +/-! Pair Orbit. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +theorem fockAverage_spin_column {Q k n : ℕ} + (C : Matrix (SectorOccupation Q k) (Fin (n+1)) ℂ) + (hC : ∀ s, sectorOneBody Q k (spinGenerator Q s) * C = C * spinGenerator n s) + (p : Fin (n+1)) : + fockAverage Q ((wedgeAnnihilator Q k (fun A => C A p))ᴴ * + wedgeAnnihilator Q k (fun A => C A p)) = + (1/(n+1 : ℂ)) • exteriorLift Q k (C*Cᴴ) := by + rw [← exteriorLift_single_congruence Q k C p p, + fockAverage_spin_sandwich C hC, Matrix.trace_single_eq_same] + + +theorem pairSpinMatrix_lift {Q : ℕ} (hQ : 1 ≤ Q) : + exteriorLift Q 2 (pairSpinMatrix Q * (pairSpinMatrix Q)ᴴ) = hamiltonian Q := by + have h := exteriorLift_congruence Q 2 (pairSpinMatrix Q) 1 + simp only [Matrix.mul_one, Matrix.one_apply, ite_smul, one_smul, zero_smul, + Finset.sum_ite_eq, Finset.mem_univ, ite_true] at h + rw [h] + simp only [pairSpinMatrix, pairVector, + wedgeAnnihilator_annihilatorVector Q 2 _ (pairAnnihilator_mem Q _)] + rw [Fin.sum_univ_eq_sum_range (fun p => (pairAnnihilator Q p)ᴴ * pairAnnihilator Q p) (2*Q-2+1)] + have hd : 2*Q-2+1 = 2*Q-1 := by omega + rw [hd] + rfl + + + +theorem fockAverage_pair_energy {Q p : ℕ} (hQ : 1 ≤ Q) (hp : p ≤ 2*Q-2) : + fockAverage Q ((pairAnnihilator Q p)ᴴ * pairAnnihilator Q p) = + (1 / ((2*Q-1 : ℕ) : ℂ)) • hamiltonian Q := by + have h := fockAverage_spin_column (pairSpinMatrix Q) (pairSpinMatrix_intertwines hQ) + (⟨p,by omega⟩ : Fin (2*Q-2+1)) + simp only [pairSpinMatrix, pairVector, + wedgeAnnihilator_annihilatorVector Q 2 _ (pairAnnihilator_mem Q _), + pairSpinMatrix_lift hQ] at h + have hd : ((2*Q-2 : ℕ) : ℂ) + 1 = ((2*Q-1 : ℕ) : ℂ) := by + norm_cast + omega + simpa only [hd] using h + + +theorem fockAverage_hamiltonian {Q : ℕ} (hQ : 1 ≤ Q) : + fockAverage Q (hamiltonian Q) = hamiltonian Q := by + have h := fockAverage_spin_sandwich (pairSpinMatrix Q) (pairSpinMatrix_intertwines hQ) 1 + simp only [Matrix.mul_one, pairSpinMatrix_lift hQ, Matrix.trace_one, Fintype.card_fin] at h + have hm : ((2*Q-2+1 : ℕ) : ℂ) = ((2*Q-2 : ℕ) : ℂ)+1 := by push_cast; rfl + have hn : (((2*Q-2 : ℕ) : ℂ)+1) ≠ 0 := by + rw [← hm]; exact_mod_cast (show 2*Q-2+1 ≠ 0 by omega) + simpa only [hm, div_self hn, one_smul] using h + + + +theorem fockAverage_pair_energy_scaled {Q p : ℕ} (hQ : 1 ≤ Q) (hp : p ≤ 2*Q-2) : + ((2*Q-1 : ℕ) : ℂ) • fockAverage Q ((pairAnnihilator Q p)ᴴ * pairAnnihilator Q p) = + hamiltonian Q := by + rw [fockAverage_pair_energy hQ hp, smul_smul] + have hd : ((2*Q-1 : ℕ) : ℂ) ≠ 0 := by exact_mod_cast (show 2*Q-1 ≠ 0 by omega) + rw [one_div, mul_inv_cancel₀ hd, one_smul] + + + +theorem fockAverage_pair_family {ι : Type*} [Fintype ι] {Q : ℕ} + (hQ : 1 ≤ Q) (p : ι → ℕ) (hp : ∀ i, p i ≤ 2*Q-2) : + fockAverage Q (∑ i, (pairAnnihilator Q (p i))ᴴ * pairAnnihilator Q (p i)) = + ((Fintype.card ι : ℂ) / ((2*Q-1 : ℕ) : ℂ)) • hamiltonian Q := by + rw [map_sum] + simp_rw [fockAverage_pair_energy hQ (hp _)] + rw [← Finset.sum_smul] + simp only [Finset.sum_const, Finset.card_univ, nsmul_eq_mul, mul_one_div] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/PartsTrace.lean b/lean/OAI/Analysis/LaughlinFock/PartsTrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..344495c68b5fdecf46b04b0852d5b261faec1da5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/PartsTrace.lean @@ -0,0 +1,37 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Parts Trace. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +def collectNumericRowParts (D : ℕ) (t : Fin 8) : List (List CollectedFourTerm) := + (numericRowData t).map fun b => (numericRowData t).flatMap fun c => + if D ≤ b.p+b.j+c.i then [collectFourTerm D t.val b c] else [] + +def collectedFourPartsTrace (D r s : ℕ) (ls : Fin 8 → List (List CollectedFourTerm)) : ℤ := + ∑ t : Fin 8, -(directIntegerSum (directIntegerSum (collectedTermValue D r s)) (ls t)) + +theorem collectNumericRowParts_sum (D : ℕ) (t : Fin 8) (r s : ℕ) : + numericFourTrace D t r s = + -(directIntegerSum (directIntegerSum (collectedTermValue D r s)) + (collectNumericRowParts D t)) := by + rw [collectNumericRow_sum] + simp only [collectNumericRow, collectNumericRowParts, List.map_flatMap, + list_flatMap_sum_int, ← directIntegerSum_spec, List.map_map, Function.comp_def] + +theorem integerRowsFourTrace_parts {D : ℕ} (hD : D ≤ 23) + (ls : Fin 8 → List (List CollectedFourTerm)) + (hls : ∀ t, collectNumericRowParts D t = ls t) (r s : CopyLabel D) : + integerRowsFourTrace D r s = + (collectedFourPartsTrace D r.val.val s.val.val ls : ℚ) / fourCommonDenominator := by + rw [integerRowsFourTrace_numeric hD] + simp only [numericRowsFourTrace, collectedFourPartsTrace, collectNumericRowParts_sum, hls] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/PolynomialPositivity.lean b/lean/OAI/Analysis/LaughlinFock/PolynomialPositivity.lean new file mode 100644 index 0000000000000000000000000000000000000000..a74777318fca7ee520ea008f576afbacdbe97d73 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/PolynomialPositivity.lean @@ -0,0 +1,140 @@ +import Mathlib + +namespace OAI + +/-! Polynomial Positivity. -/ +noncomputable section +namespace LaughlinFock +open scoped Matrix ComplexOrder BigOperators +open Polynomial + + + +theorem polynomial_eval_pos_of_nonneg_coeffs (p : ℝ[X]) (hp : p ≠ 0) + (hcoeff : ∀ b, 0 ≤ p.coeff b) {x : ℝ} (hx : 0 < x) : 0 < p.eval x := by + rw [Polynomial.eval_eq_sum, Polynomial.sum] + obtain ⟨b, hb⟩ := Polynomial.support_nonempty.mpr hp + exact Finset.sum_pos' + (fun c _ => mul_nonneg (hcoeff c) (pow_nonneg hx.le c)) + ⟨b, hb, mul_pos (lt_of_le_of_ne (hcoeff b) + (Ne.symm (Polynomial.mem_support_iff.mp hb))) (pow_pos hx b)⟩ + + + +theorem symmetric_posSemidef_of_charpoly_coeffs {ι : Type*} + [Fintype ι] [DecidableEq ι] (M : Matrix ι ι ℝ) (hM : M.IsHermitian) + (hcoeff : ∀ b, 0 ≤ (-M).charpoly.coeff b) : M.PosSemidef := by + apply hM.posSemidef_iff_eigenvalues_nonneg.mpr + intro i + by_contra hi + have hi' : 0 < -hM.eigenvalues i := neg_pos.mpr (lt_of_not_ge hi) + have hspec : -hM.eigenvalues i ∈ spectrum ℝ (-M) := by + rw [← spectrum.neg_eq] + simpa only [Set.mem_neg, neg_neg] using hM.eigenvalues_mem_spectrum_real i + have hz := (Matrix.mem_spectrum_iff_isRoot_charpoly.mp hspec).eq_zero + have hp := polynomial_eval_pos_of_nonneg_coeffs (-M).charpoly + (-M).charpoly_monic.ne_zero hcoeff hi' + exact (ne_of_gt hp) hz + + + +theorem real_matrix_posSemidef_complex {ι : Type*} [Fintype ι] [DecidableEq ι] + (M : Matrix ι ι ℝ) (hM : M.PosSemidef) : + (M.map (algebraMap ℝ ℂ)).PosSemidef := by + have hH : (M.map (algebraMap ℝ ℂ)).IsHermitian := by + apply Matrix.IsHermitian.ext_iff.mpr + intro i j + have h := Matrix.IsHermitian.ext_iff.mp hM.isHermitian i j + simpa using congrArg (algebraMap ℝ ℂ) h + apply Matrix.PosSemidef.of_dotProduct_mulVec_nonneg hH + intro x + have hRe := hM.dotProduct_mulVec_nonneg (fun i => (x i).re) + have hIm := hM.dotProduct_mulVec_nonneg (fun i => (x i).im) + apply Complex.nonneg_iff.mpr + constructor + · have he : (star x ⬝ᵥ (M.map (algebraMap ℝ ℂ) *ᵥ x)).re = + (fun i => (x i).re) ⬝ᵥ (M *ᵥ fun i => (x i).re) + + (fun i => (x i).im) ⬝ᵥ (M *ᵥ fun i => (x i).im) := by + simp [dotProduct, Matrix.mulVec, Matrix.map_apply, Finset.sum_add_distrib, + Complex.mul_re, Complex.mul_im, Finset.mul_sum] + rw [he] + simpa only [star_trivial, Pi.star_apply] using add_nonneg hRe hIm + · exact (hH.im_star_dotProduct_mulVec_self x).symm + + + +theorem rational_posSemidef_of_charpoly_coeffs {ι : Type*} + [Fintype ι] [DecidableEq ι] (M : Matrix ι ι ℚ) (hM : M.IsSymm) + (hcoeff : ∀ b, 0 ≤ (-M).charpoly.coeff b) : + (M.map (algebraMap ℚ ℂ)).PosSemidef := by + let N : Matrix ι ι ℝ := M.map (algebraMap ℚ ℝ) + have hN : N.IsHermitian := by + rw [Matrix.isHermitian_iff_isSymm] + show Nᵀ = N + change (M.map (algebraMap ℚ ℝ))ᵀ = M.map (algebraMap ℚ ℝ) + rw [← Matrix.transpose_map, hM] + have hC (b : ℕ) : 0 ≤ (-N).charpoly.coeff b := by + have hneg : -N = (-M).map (algebraMap ℚ ℝ) := by + ext i j + simp [N] + rw [hneg, Matrix.charpoly_map, Polynomial.coeff_map] + change 0 ≤ ((-M).charpoly.coeff b : ℝ) + exact_mod_cast hcoeff b + have hP := real_matrix_posSemidef_complex N + (symmetric_posSemidef_of_charpoly_coeffs N hN hC) + convert hP using 1 + ext i j + simp [N] + + + +theorem certificate_diagonal_congruence {ι : Type*} [Fintype ι] [DecidableEq ι] + (Y Z : Matrix ι ι ℝ) (u c : ι → ℝ) (hu : ∀ r, 0 ≤ u r) : + let D := Matrix.diagonal (fun r => Real.sqrt (u r)) + let E := D * Y * D + let G := D * Z * D + G * (Matrix.diagonal c - E) * G = + D * (Z * (Matrix.diagonal (fun r => c r * u r) - + Matrix.diagonal u * Y * Matrix.diagonal u) * Z) * D := by + dsimp only + let D := Matrix.diagonal (fun r => Real.sqrt (u r)) + have hDD : D * D = Matrix.diagonal u := by + rw [Matrix.diagonal_mul_diagonal] + congr 1 + funext r + exact Real.mul_self_sqrt (hu r) + have hc : D * Matrix.diagonal c * D = + Matrix.diagonal (fun r => c r * u r) := by + rw [Matrix.diagonal_mul_diagonal, Matrix.diagonal_mul_diagonal] + congr 1 + funext r + rw [mul_right_comm, Real.mul_self_sqrt (hu r)] + exact mul_comm _ _ + change (D * Z * D) * (Matrix.diagonal c - D * Y * D) * (D * Z * D) = _ + calc + _ = D * (Z * (D * Matrix.diagonal c * D - (D * D) * Y * (D * D)) * Z) * D := by + simp only [Matrix.mul_sub, Matrix.sub_mul, Matrix.mul_assoc] + _ = _ := by rw [hDD, hc] + + + +theorem certificate_compression_posSemidef {ι : Type*} [Fintype ι] [DecidableEq ι] + (Y Z : Matrix ι ι ℝ) (u c : ι → ℝ) (hu : ∀ r, 0 ≤ u r) + (hM : (Z * (Matrix.diagonal (fun r => c r * u r) - + Matrix.diagonal u * Y * Matrix.diagonal u) * Z).IsHermitian) + (hcoeff : ∀ b, 0 ≤ (-(Z * (Matrix.diagonal (fun r => c r * u r) - + Matrix.diagonal u * Y * Matrix.diagonal u) * Z)).charpoly.coeff b) : + let D := Matrix.diagonal (fun r => Real.sqrt (u r)) + let E := D * Y * D + let G := D * Z * D + (G * (Matrix.diagonal c - E) * G).PosSemidef := by + dsimp only + rw [certificate_diagonal_congruence Y Z u c hu] + have h := symmetric_posSemidef_of_charpoly_coeffs _ hM hcoeff + simpa only [Matrix.diagonal_conjTranspose, star_trivial] using + h.mul_mul_conjTranspose_same (Matrix.diagonal (fun r => Real.sqrt (u r))) + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/PositiveIntegrals.lean b/lean/OAI/Analysis/LaughlinFock/PositiveIntegrals.lean new file mode 100644 index 0000000000000000000000000000000000000000..8a5748247ac04fefd50da1a4a106e3e939bc3b4d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/PositiveIntegrals.lean @@ -0,0 +1,95 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.NormalOrdering + +namespace OAI + +/-! Positive Integrals. -/ +noncomputable section +namespace LaughlinFock +open scoped Matrix ComplexOrder BigOperators Matrix.Norms.Elementwise +open MeasureTheory + +local instance {ι κ : Type*} [Fintype ι] [Fintype κ] : + ContinuousENorm (Matrix ι κ ℂ) := + inferInstanceAs (ContinuousENorm (ι → κ → ℂ)) + + +def quadraticEvaluation {ι : Type*} [Fintype ι] (x : ι → ℂ) : + Matrix ι ι ℂ →ₗ[ℂ] ℂ where + toFun M := star x ⬝ᵥ (M *ᵥ x) + map_add' M N := by simp only [Matrix.add_mulVec, dotProduct_add] + map_smul' c M := by + simp only [Matrix.smul_mulVec, dotProduct_smul, RingHom.id_apply] + + +theorem matrixIntegral_apply {G ι κ : Type*} [MeasurableSpace G] [Fintype ι] [Fintype κ] + (μ : Measure G) {M : G → Matrix ι κ ℂ} (hM : Integrable M μ) (i : ι) (j : κ) : + (∫ g, M g ∂μ) i j = ∫ g, M g i j ∂μ := by + let L : Matrix ι κ ℂ →ₗ[ℂ] ℂ := + { toFun := fun B => B i j + map_add' _ _ := rfl + map_smul' _ _ := rfl } + exact (L.toContinuousLinearMap.integral_comp_comm hM).symm + + + +theorem matrixIntegral_isHermitian {G ι : Type*} [MeasurableSpace G] [Fintype ι] + (μ : Measure G) {M : G → Matrix ι ι ℂ} (hM : Integrable M μ) + (hH : ∀ᵐ g ∂μ, (M g).IsHermitian) : (∫ g, M g ∂μ).IsHermitian := by + apply Matrix.IsHermitian.ext_iff.mpr + intro i j + simp only [matrixIntegral_apply μ hM, RCLike.star_def, ← integral_conj] + apply integral_congr_ae + filter_upwards [hH] with g hg + exact Matrix.IsHermitian.ext_iff.mp hg i j + +theorem quadraticEvaluation_integral {G ι : Type*} [MeasurableSpace G] [Fintype ι] + (μ : Measure G) {M : G → Matrix ι ι ℂ} (hM : Integrable M μ) (x : ι → ℂ) : + star x ⬝ᵥ ((∫ g, M g ∂μ) *ᵥ x) = ∫ g, star x ⬝ᵥ (M g *ᵥ x) ∂μ := + (LinearMap.toContinuousLinearMap (quadraticEvaluation x)).integral_comp_comm hM |>.symm + + + +theorem matrixIntegral_posSemidef {G ι : Type*} [MeasurableSpace G] [Fintype ι] + (μ : Measure G) {M : G → Matrix ι ι ℂ} (hM : Integrable M μ) + (hP : ∀ᵐ g ∂μ, (M g).PosSemidef) : (∫ g, M g ∂μ).PosSemidef := by + apply Matrix.PosSemidef.of_dotProduct_mulVec_nonneg + (matrixIntegral_isHermitian μ hM (hP.mono (fun _ h => h.isHermitian))) + intro x + rw [quadraticEvaluation_integral μ hM] + apply integral_nonneg_of_ae + exact hP.mono (fun _ h => h.dotProduct_mulVec_nonneg x) + + +theorem exteriorLift_integral {G : Type*} [MeasurableSpace G] (μ : Measure G) + (Q k : ℕ) {M : G → Matrix (SectorOccupation Q k) (SectorOccupation Q k) ℂ} + (hM : Integrable M μ) : + exteriorLift Q k (∫ g, M g ∂μ) = ∫ g, exteriorLift Q k (M g) ∂μ := + (LinearMap.toContinuousLinearMap (exteriorLiftLinear Q k)).integral_comp_comm hM |>.symm + + +theorem matrixIntegral_relative_bound {G ι : Type*} [MeasurableSpace G] [Fintype ι] + (μ : Measure G) {M H : G → Matrix ι ι ℂ} (hM : Integrable M μ) (hH : Integrable H μ) + (r : ℝ) (h : ∀ᵐ g ∂μ, (M g + r • H g).PosSemidef) : + ((∫ g, M g ∂μ) + r • ∫ g, H g ∂μ).PosSemidef := by + have hP := matrixIntegral_posSemidef μ (hM.add (hH.smul r)) h + change (∫ g, M g + r • H g ∂μ).PosSemidef at hP + have hAdd : (∫ g, M g + r • H g ∂μ) = + (∫ g, M g ∂μ) + (∫ g, r • H g ∂μ) := integral_add hM (hH.smul r) + have hS : (∫ g, r • H g ∂μ) = r • ∫ g, H g ∂μ := integral_smul r H + rw [hAdd, hS] at hP + exact hP + + + +theorem conjugationIntegral_posSemidef {G ι : Type*} [MeasurableSpace G] [Fintype ι] + (μ : Measure G) (U : G → Matrix ι ι ℂ) (M : Matrix ι ι ℂ) + (hM : M.PosSemidef) (hI : Integrable (fun g => U g * M * (U g)ᴴ) μ) : + (∫ g, U g * M * (U g)ᴴ ∂μ).PosSemidef := + matrixIntegral_posSemidef μ hI (Filter.Eventually.of_forall + (fun g => hM.mul_mul_conjTranspose_same (U g))) + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/RationalCoupling.lean b/lean/OAI/Analysis/LaughlinFock/RationalCoupling.lean new file mode 100644 index 0000000000000000000000000000000000000000..a71988b7e2a8195e631e149653a2827f2914c3b3 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/RationalCoupling.lean @@ -0,0 +1,97 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.OscillatorLimit + +namespace OAI + +/-! Rational Coupling. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder +open Polynomial + + +def rationalCoupling (c : ℚ) (z k p : ℕ) : ℚ := + (((X-1)^z * (C c*X+1)^k) : Polynomial ℚ).coeff p + + + +def rationalCouplingWeight (c : ℚ) (z k p : ℕ) : ℚ := + c^z * ((p.factorial : ℚ) * (z+k-p).factorial) / + ((1+c)^(z+k) * c^p * (z.factorial : ℚ) * k.factorial) + +theorem couplingPolynomial_rescale (c u v : ℝ) (_hu : u ≠ 0) (hv : v ≠ 0) + (hc : c*u^2 = v^2) (z k : ℕ) : + couplingPolynomial u v z k = + C (v^z*u^k) * (((X-1)^z*(C c*X+1)^k).comp (C (u/v)*X)) := by + have h1 : (C v : Polynomial ℝ) * (C (u/v)*X-1) = C u*X-C v := by + simp only [mul_sub, mul_one, ← mul_assoc, ← C_mul] + congr 2 + field_simp + have h2 : (C u : Polynomial ℝ) * (C c*(C (u/v)*X)+1) = C v*X+C u := by + simp only [mul_add, mul_one, ← mul_assoc, ← C_mul] + congr 2 + congr 1 + field_simp + nlinarith only [hc] + simp only [couplingPolynomial, mul_comp, pow_comp, sub_comp, add_comp, X_comp, + one_comp, C_comp] + rw [show C (v^z*u^k) = (C v)^z*(C u)^k by simp, mul_mul_mul_comm, + ← mul_pow, ← mul_pow, h1, h2] + +theorem polynomialCouplingCoefficient_rescale (c u v : ℝ) + (hu : u ≠ 0) (hv : v ≠ 0) (hc : c*u^2=v^2) (z k p : ℕ) : + polynomialCouplingCoefficient u v z k p = + (((X-1)^z*(C c*X+1)^k : Polynomial ℝ).coeff p) * + (monomialWeight (z+k) p / Real.sqrt ((z.factorial : ℝ)*k.factorial) * + (v^z*u^k*(u/v)^p)) := by + simp only [polynomialCouplingCoefficient, monomialCoefficient, + couplingPolynomial_rescale c u v hu hv hc, coeff_C_mul, comp_C_mul_X_coeff] + ring + +theorem rationalCoupling_real (c : ℚ) (z k p : ℕ) : + (((X-1)^z * (C (c : ℝ)*X+1)^k) : Polynomial ℝ).coeff p = + (rationalCoupling c z k p : ℝ) := by + have h : (((X-1)^z * (C c*X+1)^k) : Polynomial ℚ).map (algebraMap ℚ ℝ) = + ((X-1)^z*(C (c:ℝ)*X+1)^k) := by simp + rw [← h, Polynomial.coeff_map] + rfl + + + +theorem polynomialCouplingCoefficient_rational (c : ℚ) (hc : 0 < c) + (z k p : ℕ) : + polynomialCouplingCoefficient (Real.sqrt (1/(1+(c:ℝ)))) + (Real.sqrt ((c:ℝ)/(1+(c:ℝ)))) z k p = + (rationalCoupling c z k p : ℝ) * Real.sqrt (rationalCouplingWeight c z k p : ℝ) := by + have hcR : (0:ℝ) < c := by exact_mod_cast hc + have hC : (0:ℝ) < 1+(c:ℝ) := by linarith + let u := Real.sqrt (1/(1+(c:ℝ))) + let v := Real.sqrt ((c:ℝ)/(1+(c:ℝ))) + have hu : 0 < u := Real.sqrt_pos.mpr (div_pos zero_lt_one hC) + have hv : 0 < v := Real.sqrt_pos.mpr (div_pos hcR hC) + have hu2 : u^2 = 1/(1+(c:ℝ)) := Real.sq_sqrt (by positivity) + have hv2 : v^2 = (c:ℝ)/(1+(c:ℝ)) := Real.sq_sqrt (by positivity) + have huv2 : (u/v)^2 = 1/(c:ℝ) := by + rw [div_pow, hu2, hv2] + field_simp + rw [polynomialCouplingCoefficient_rescale (c:ℝ) u v hu.ne' hv.ne' + (by rw [hu2, hv2]; ring), rationalCoupling_real] + congr 1 + let f : ℝ := monomialWeight (z+k) p / Real.sqrt ((z.factorial : ℝ)*k.factorial) * + (v^z*u^k*(u/v)^p) + have hf : 0 ≤ f := by dsimp [f, monomialWeight]; positivity + have hs : f^2 = (rationalCouplingWeight c z k p : ℝ) := by + dsimp [f, monomialWeight, rationalCouplingWeight] + push_cast + rw [mul_pow, div_pow, Real.sq_sqrt (by positivity), Real.sq_sqrt (by positivity), + mul_pow, mul_pow, ← pow_mul, mul_comm z 2, pow_mul, hv2, + ← pow_mul, mul_comm k 2, pow_mul, hu2, + ← pow_mul, mul_comm p 2, pow_mul, huv2] + simp only [div_pow, one_pow, pow_add] + field_simp + rw [← hs, Real.sqrt_sq hf] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/RationalFour.lean b/lean/OAI/Analysis/LaughlinFock/RationalFour.lean new file mode 100644 index 0000000000000000000000000000000000000000..2349c24a2b3415ed218279efffe2a7d037158d87 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/RationalFour.lean @@ -0,0 +1,170 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.RationalThree + +namespace OAI + +/-! Rational Four. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +def rationalCopyDiagonal (D r : ℕ) : ℚ := + 2^r / ((r.factorial : ℚ) * (D-r).factorial) + +def rationalCopyPolynomial (D T r p j k : ℕ) : ℚ := + if r ≤ j+k then + rationalCoupling 1 r (j+k-r) j * rationalCoupling 1 (D-r) (T-D) p + else 0 + +def rationalCopyWeight (D T p j k : ℕ) : ℚ := + 2 * (j.factorial : ℚ) * k.factorial * p.factorial / + (2^(j+k+T) * ((T-D).factorial : ℚ)) + +theorem rationalCopyDiagonal_pos (D r : ℕ) : 0 < rationalCopyDiagonal D r := by + unfold rationalCopyDiagonal + positivity + +theorem rationalCopyWeight_pos (D T p j k : ℕ) : 0 < rationalCopyWeight D T p j k := by + unfold rationalCopyWeight + positivity + +theorem couplingWeight_copy {D T r p j k : ℕ} (hr : r ≤ D) + (hD : D ≤ T) (hw : p+j+k=T) (hrjk : r ≤ j+k) : + 2 * rationalCouplingWeight 1 r (j+k-r) j * + rationalCouplingWeight 1 (D-r) (T-D) p = + rationalCopyDiagonal D r * rationalCopyWeight D T p j k := by + have h1 : r+(j+k-r)=j+k := Nat.add_sub_of_le hrjk + have h2 : D-r+(T-D)=T-r := by omega + have h3 : T-r-p=j+k-r := by omega + have hpow : (2:ℚ)^T = 2^r*2^(T-r) := by rw [← pow_add, Nat.add_sub_of_le (hr.trans hD)] + unfold rationalCouplingWeight rationalCopyDiagonal rationalCopyWeight + rw [h1, h2, h3, show j+k-j=k by omega] + norm_num only [one_pow, one_add_one_eq_two, one_mul] + simp only [pow_add] + rw [hpow] + field_simp + + +theorem planarCopyCoefficient_rational {D T : ℕ} (r : CopyLabel D) + (p j k : ℕ) (hD : D ≤ T) (hw : p+j+k=T) : + planarCopyCoefficient D T r.val.val p j k = + (rationalCopyPolynomial D T r.val.val p j k : ℝ) * + (Real.sqrt (rationalCopyDiagonal D r.val.val : ℝ) * + Real.sqrt (rationalCopyWeight D T p j k : ℝ)) := by + have hr : r.val.val ≤ D := Nat.le_of_lt_succ r.val.isLt + have hCoupling (z n a : ℕ) : + polynomialCouplingCoefficient (Real.sqrt (1/2)) (Real.sqrt (1/2)) z n a = + (rationalCoupling 1 z n a : ℝ)*Real.sqrt (rationalCouplingWeight 1 z n a : ℝ) := by + simpa only [Rat.cast_one, show (1:ℝ)+1=2 by norm_num] using + polynomialCouplingCoefficient_rational 1 (by norm_num) z n a + unfold planarCopyCoefficient rationalCopyPolynomial + by_cases hjk : r.val.val ≤ j+k + · rw [ite_eq_left ⟨r.property, hr, hD, hjk, hw⟩, ite_eq_left hjk, hCoupling, hCoupling, + Rat.cast_mul] + have hs : Real.sqrt 2 * Real.sqrt (rationalCouplingWeight 1 r.val.val (j+k-r.val.val) j : ℝ) * + Real.sqrt (rationalCouplingWeight 1 (D-r.val.val) (T-D) p : ℝ) = + Real.sqrt (rationalCopyDiagonal D r.val.val : ℝ) * + Real.sqrt (rationalCopyWeight D T p j k : ℝ) := by + rw [← Real.sqrt_mul (by norm_num : (0:ℝ)≤2), + ← Real.sqrt_mul (mul_nonneg (by norm_num) (by + exact_mod_cast (rationalCouplingWeight_pos (by norm_num : (0:ℚ)<1) r.val.val (j+k-r.val.val) j).le))] + have hc := congrArg (fun q:ℚ => (q:ℝ)) (couplingWeight_copy hr hD hw hjk) + push_cast at hc + rw [hc, Real.sqrt_mul (by exact_mod_cast (rationalCopyDiagonal_pos D r.val.val).le)] + linear_combination ((rationalCoupling 1 r.val.val (j+k-r.val.val) j : ℝ)* + (rationalCoupling 1 (D-r.val.val) (T-D) p : ℝ))*hs + · rw [ite_eq_right (by tauto), ite_eq_right hjk] + simp + + +def rationalFourFactor {t : ℕ} (D : ℕ) (b c : RowEntry t) : ℚ := + 2 * 2^(rowP b) * 2^(rowP c) * (t.factorial : ℚ) * + (rowI b).factorial * (rowI c).factorial / + (2^t * (2^(rowFourLevel b c))^2 * ((rowFourLevel b c-D).factorial : ℚ)) + +theorem rationalFourFactor_pos {t : ℕ} (D : ℕ) (b c : RowEntry t) : + 0 < rationalFourFactor D b c := by + unfold rationalFourFactor + positivity + +theorem row_copy_weight_product {t D : ℕ} (b c : RowEntry t) : + rationalAlphaWeight t b * rationalAlphaWeight t c * + rationalCopyWeight D (rowFourLevel b c) (rowP b) (rowJ b) (rowI c) * + rationalCopyWeight D (rowFourLevel b c) (rowP c) (rowJ c) (rowI b) = + (rationalFourFactor D b c)^2 := by + have h1 : (2:ℚ)^(rowJ b+rowI c) = 2^(rowFourLevel b c)/2^(rowP b) := by + rw [eq_div_iff (by positivity)] + rw [← pow_add] + congr 1 + dsimp [rowFourLevel] + omega + have h2 : (2:ℚ)^(rowJ c+rowI b) = 2^(rowFourLevel b c)/2^(rowP c) := by + rw [eq_div_iff (by positivity)] + rw [← pow_add] + congr 1 + have := rowFourLevel_symm b c + dsimp [rowFourLevel] at * + omega + unfold rationalAlphaWeight rationalCopyWeight rationalFourFactor + rw [pow_add (2:ℚ) (rowJ b+rowI c), pow_add (2:ℚ) (rowJ c+rowI b), h1, h2] + field_simp + + +def rationalFourTrace (D t : ℕ) (a : RowEntry t → ℚ) : + Matrix (CopyLabel D) (CopyLabel D) ℚ := fun r s => + -(∑ b : RowEntry t, ∑ c : RowEntry t, if D ≤ rowFourLevel b c then + a b*a c*rationalFourFactor D b c * + rationalCopyPolynomial D (rowFourLevel b c) r.val.val (rowP b) (rowJ b) (rowI c) * + rationalCopyPolynomial D (rowFourLevel b c) s.val.val (rowP c) (rowJ c) (rowI b) + else 0) + +theorem planarRowFourTrace_rational (D : ℕ) (t : Fin 8) + (ell : ℚ) (a : RowEntry t.val → ℚ) (r s : CopyLabel D) : + planarRowFourTrace D t.val (rationalComparisonRow t ell a).alpha r s = + Real.sqrt (rationalCopyDiagonal D r.val.val : ℝ) * + (rationalFourTrace D t.val a r s : ℝ) * + Real.sqrt (rationalCopyDiagonal D s.val.val : ℝ) := by + classical + unfold planarRowFourTrace rationalFourTrace + push_cast + simp only [mul_neg, neg_mul, Finset.mul_sum, Finset.sum_mul] + congr 1 + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro c _ + by_cases hD : D ≤ rowFourLevel b c + · rw [ite_eq_left hD, + planarCopyCoefficient_rational r _ _ _ hD rfl, + planarCopyCoefficient_rational s _ _ _ hD (rowFourLevel_symm c b)] + have hA : 0 ≤ (rationalAlphaWeight t.val b : ℝ) := by + exact_mod_cast (rationalAlphaWeight_pos t.val b).le + have hB : 0 ≤ (rationalAlphaWeight t.val c : ℝ) := by + exact_mod_cast (rationalAlphaWeight_pos t.val c).le + have hC : 0 ≤ (rationalCopyWeight D (rowFourLevel b c) (rowP b) (rowJ b) (rowI c) : ℝ) := by + exact_mod_cast (rationalCopyWeight_pos _ _ _ _ _).le + have hR : Real.sqrt (rationalAlphaWeight t.val b : ℝ) * + Real.sqrt (rationalAlphaWeight t.val c : ℝ) * + Real.sqrt (rationalCopyWeight D (rowFourLevel b c) (rowP b) (rowJ b) (rowI c) : ℝ) * + Real.sqrt (rationalCopyWeight D (rowFourLevel b c) (rowP c) (rowJ c) (rowI b) : ℝ) = + (rationalFourFactor D b c : ℝ) := by + rw [← Real.sqrt_mul hA, ← Real.sqrt_mul (mul_nonneg hA hB), + ← Real.sqrt_mul (mul_nonneg (mul_nonneg hA hB) hC)] + have hc := congrArg (fun q:ℚ => (q:ℝ)) (row_copy_weight_product (D:=D) b c) + push_cast at hc + rw [hc, Real.sqrt_sq (by exact_mod_cast (rationalFourFactor_pos D b c).le)] + dsimp only [rationalComparisonRow] + push_cast + linear_combination ((a b:ℝ)*(a c:ℝ)* + (rationalCopyPolynomial D (rowFourLevel b c) r.val.val (rowP b) (rowJ b) (rowI c) : ℝ)* + (rationalCopyPolynomial D (rowFourLevel b c) s.val.val (rowP c) (rowJ c) (rowI b) : ℝ)* + Real.sqrt (rationalCopyDiagonal D r.val.val : ℝ)* + Real.sqrt (rationalCopyDiagonal D s.val.val : ℝ))*hR + · simp [planarCopyCoefficient, hD] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/RationalThree.lean b/lean/OAI/Analysis/LaughlinFock/RationalThree.lean new file mode 100644 index 0000000000000000000000000000000000000000..0b7e6a18afe8d9843df75929c1f5f9733703cad3 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/RationalThree.lean @@ -0,0 +1,112 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.RationalCoupling +import OAI.Analysis.LaughlinFock.RelativeTransfer + +namespace OAI + +/-! Rational Three. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + +def rationalAlphaWeight (t : ℕ) (b : RowEntry t) : ℚ := + 2^(rowP b) * (t.factorial : ℚ) * (rowI b).factorial / + (2^t * ((rowP b).factorial : ℚ) * (rowJ b).factorial) + +theorem rationalAlphaWeight_pos (t : ℕ) (b : RowEntry t) : + 0 < rationalAlphaWeight t b := by + unfold rationalAlphaWeight + positivity + +theorem rationalCouplingWeight_pos {c : ℚ} (hc : 0 < c) (z k p : ℕ) : + 0 < rationalCouplingWeight c z k p := by + unfold rationalCouplingWeight + positivity + + + +def rationalComparisonRow (t : Fin 8) (ell : ℚ) (a : RowEntry t.val → ℚ) : ComparisonRow where + t := t + ell := ell + alpha b := (a b : ℝ) * Real.sqrt (rationalAlphaWeight t.val b : ℝ) + +theorem planarThreeCoefficient_rational (z T p : ℕ) (hz : z ≤ T) : + planarThreeCoefficient z T p = (rationalCoupling 2 z (T-z) p : ℝ) * + Real.sqrt (rationalCouplingWeight 2 z (T-z) p : ℝ) := by + rw [planarThreeCoefficient, ite_eq_left hz] + simpa only [Rat.cast_ofNat, show (1:ℝ)+2=3 by norm_num] using + polynomialCouplingCoefficient_rational 2 (by norm_num) z (T-z) p + +theorem rationalAlphaWeight_cancellation {t T z : ℕ} (b : RowEntry t) + (hz : z ≤ T) (hb : rowP b+rowJ b=T) : + rationalAlphaWeight t b * rationalCouplingWeight 2 z (T-z) (rowP b) = + rationalCouplingWeight 2 z (T-z) t := by + have hi : T-t = rowI b := by simp [rowI, hb] + have hj : T-rowP b = rowJ b := by omega + unfold rationalAlphaWeight rationalCouplingWeight + rw [Nat.add_sub_of_le hz, hi, hj] + field_simp + +theorem alpha_mul_planarThree {t T z : ℕ} (a : RowEntry t → ℚ) + (b : RowEntry t) (hz : z ≤ T) (hb : rowP b+rowJ b=T) : + ((a b : ℝ) * Real.sqrt (rationalAlphaWeight t b : ℝ)) * + planarThreeCoefficient z T (rowP b) = + ((a b * rationalCoupling 2 z (T-z) (rowP b) : ℚ) : ℝ) * + Real.sqrt (rationalCouplingWeight 2 z (T-z) t : ℝ) := by + rw [planarThreeCoefficient_rational z T (rowP b) hz, Rat.cast_mul] + rw [mul_mul_mul_comm, ← Real.sqrt_mul (by exact_mod_cast (rationalAlphaWeight_pos t b).le)] + have he : (rationalAlphaWeight t b : ℝ) * (rationalCouplingWeight 2 z (T-z) (rowP b) : ℝ) = + (rationalCouplingWeight 2 z (T-z) t : ℝ) := by + exact_mod_cast rationalAlphaWeight_cancellation b hz hb + rw [he] + + +def rationalThreeTrace (z t : ℕ) (ell : ℚ) (a : RowEntry t → ℚ) : ℚ := + ∑ T ∈ Finset.range 16, if z ≤ T ∧ t ≤ T then + let X := ∑ b : RowEntry t, if rowP b+rowJ b=T then + a b*rationalCoupling 2 z (T-z) (rowP b) else 0 + rationalCouplingWeight 2 z (T-z) t * X * + (X+2*ell*rationalCoupling 2 z (T-z) t) + else 0 + +theorem planarRowThreeTrace_rational (z : ℕ) (t : Fin 8) + (ell : ℚ) (a : RowEntry t.val → ℚ) : + planarRowThreeTrace z t.val (rationalComparisonRow t ell a).ell + (rationalComparisonRow t ell a).alpha = (rationalThreeTrace z t.val ell a : ℝ) := by + classical + unfold planarRowThreeTrace rationalThreeTrace + push_cast + apply Finset.sum_congr rfl + intro T _ + split_ifs with ht + · let X : ℚ := ∑ b : RowEntry t.val, if rowP b+rowJ b=T then + a b*rationalCoupling 2 z (T-z) (rowP b) else 0 + have hX : (∑ b : RowEntry t.val, if rowP b+rowJ b=T then + (rationalComparisonRow t ell a).alpha b*planarThreeCoefficient z T (rowP b) else 0) = + (X : ℝ) * Real.sqrt (rationalCouplingWeight 2 z (T-z) t.val : ℝ) := by + dsimp [X] + rw [Rat.cast_sum, Finset.sum_mul] + apply Finset.sum_congr rfl + intro b _ + split_ifs with hb + · exact alpha_mul_planarThree a b ht.1 hb + · simp + rw [hX, planarThreeCoefficient_rational z T t.val ht.1] + change 2*(ell:ℝ)*((rationalCoupling 2 z (T-z) t.val : ℝ)* + Real.sqrt (rationalCouplingWeight 2 z (T-z) t.val : ℝ))* + ((X:ℝ)*Real.sqrt (rationalCouplingWeight 2 z (T-z) t.val : ℝ))+ + ((X:ℝ)*Real.sqrt (rationalCouplingWeight 2 z (T-z) t.val : ℝ))^2 = _ + have hn : 0 ≤ (rationalCouplingWeight 2 z (T-z) t.val : ℝ) := by + exact_mod_cast (rationalCouplingWeight_pos (by norm_num : (0:ℚ)<2) z (T-z) t.val).le + have hs := Real.sq_sqrt hn + calc + _ = (Real.sqrt (rationalCouplingWeight 2 z (T-z) t.val : ℝ))^2 * + (X:ℝ)*((X:ℝ)+2*(ell:ℝ)*(rationalCoupling 2 z (T-z) t.val : ℝ)) := by ring + _ = _ := by rw [hs]; simp only [Rat.cast_mul, Rat.cast_add, Rat.cast_ofNat]; rfl + · simp + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/RationalWedge.lean b/lean/OAI/Analysis/LaughlinFock/RationalWedge.lean new file mode 100644 index 0000000000000000000000000000000000000000..04204cfd7e3db406472cfe8c906fd014c1289faf --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/RationalWedge.lean @@ -0,0 +1,230 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.RationalFour + +namespace OAI + +/-! Rational Wedge. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + +def rationalWordVacuum {Q : ℕ} : List (Orbital Q) → Occupation Q → ℚ + | [], A => if A=∅ then 1 else 0 + | x::xs, A => if x∈A then + rationalWordVacuum xs (A.erase x) * (-1)^((A.filter (· < x)).card) else 0 + +theorem annihilatorList_vacuum_rational {Q : ℕ} (xs : List (Orbital Q)) + (A : Occupation Q) : + annihilatorList Q xs ∅ A = (rationalWordVacuum xs A : ℂ) := by + induction xs generalizing A with + | nil => by_cases h : A=∅ <;> simp [rationalWordVacuum, h, eq_comm] + | cons x xs ih => + rw [annihilatorList_cons, mul_annihilator_apply] + simp only [rationalWordVacuum] + split_ifs <;> simp [ih, fermionSign] + +theorem rationalWordVacuum_support {Q : ℕ} (xs : List (Orbital Q)) + (A : Occupation Q) (hn : rationalWordVacuum xs A ≠ 0) : + xs.Nodup ∧ xs.toFinset=A := by + induction xs generalizing A with + | nil => simpa [rationalWordVacuum, eq_comm] using hn + | cons x xs ih => + simp only [rationalWordVacuum] at hn + split_ifs at hn with hx + · obtain ⟨hxs,hA⟩ := ih (A.erase x) (fun h => hn (by rw [h, zero_mul])) + refine ⟨List.nodup_cons.mpr ⟨?_,hxs⟩, ?_⟩ + · intro h + have : x ∈ A.erase x := by rw [← hA]; simpa using h + exact Finset.notMem_erase x A this + · rw [List.toFinset_cons, hA, Finset.insert_erase hx] + · simp at hn + +def occupationFactorial {Q : ℕ} (A : Occupation Q) : ℚ := + ∏ a ∈ A, (a.val.factorial : ℚ) + +def factorialMode (Q : ℕ) (a : Orbital Q) : ℂ := + (Real.sqrt (a.val.factorial : ℝ) : ℂ) + +theorem factorialMode_ne_zero (Q : ℕ) (a : Orbital Q) : factorialMode Q a ≠ 0 := by + unfold factorialMode + exact_mod_cast (Real.sqrt_pos.mpr (by positivity : (0:ℝ) (x:ℂ)) + (copy_pair_factorial D r b.val.1.val b.val.2.val.1.val b.val.2.val.2.val + xy.val.1.val xy.val.2.val b.property) + push_cast at hc + dsimp only [factorialMode, planarLocalCopyMatrix] + rw [show (annihilator 24 b.val.2.val.2 * annihilator 24 b.val.2.val.1) * + (annihilator 24 xy.val.2 * annihilator 24 xy.val.1) = + annihilatorList 24 [xy.val.1, xy.val.2, b.val.2.val.1, b.val.2.val.2] by + simp only [annihilatorList_cons, annihilatorList_nil, Matrix.one_mul, Matrix.mul_assoc]] + congr 1 + convert hc using 1 + ring + +end LaughlinFock +end + +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem occupationFactorial_pos {Q : ℕ} (A : Occupation Q) : + 0 < occupationFactorial A := by + unfold occupationFactorial + exact Finset.prod_pos (fun a _ => by positivity) + +theorem factorialMode_prod {Q : ℕ} (A : Occupation Q) : + (∏ a ∈ A, factorialMode Q a) = (Real.sqrt (occupationFactorial A : ℝ) : ℂ) := by + unfold factorialMode occupationFactorial + rw [Rat.cast_prod, Real.sqrt_prod _ (by intro a _; positivity)] + simp + +theorem planarFourWedgeMatrix_rational (D : ℕ) (r : CopyLabel D) + (A : SectorOccupation 24 4) : + planarFourWedgeMatrix D A r = + ((Real.sqrt (rationalCopyDiagonal D r.val.val : ℝ) * Real.sqrt 2 / 2^D * + (rationalHighestEntry D r A.val : ℝ) / Real.sqrt (occupationFactorial A.val : ℝ) : ℝ) : ℂ) := by + classical + have he := congrArg (fun M : FockMatrix 24 => M ∅ A.val) (factorial_conjugate_highest D r) + simp only [diagonalConjugate, occupationDiagonalInv, occupationDiagonal, + Matrix.diagonal_mul, Matrix.mul_diagonal, Finset.prod_empty, inv_one, one_mul, + Matrix.smul_apply, Matrix.sum_apply, smul_eq_mul, + annihilatorList_vacuum_rational] at he + rw [factorialMode_prod] at he + have hsum : (∑ b : FourHighestShell 24 D, ∑ xy : IncreasingPair 24, + (rationalHighestTerm D r b.val.1.val b.val.2.val.1.val b.val.2.val.2.val + xy.val.1.val xy.val.2.val : ℂ) * + (rationalWordVacuum [xy.val.1,xy.val.2,b.val.2.val.1,b.val.2.val.2] A.val : ℂ)) = + (rationalHighestEntry D r A.val : ℂ) := by + unfold rationalHighestEntry + push_cast + rfl + rw [hsum] at he + have hn : (Real.sqrt (occupationFactorial A.val : ℝ) : ℂ) ≠ 0 := by + exact_mod_cast (Real.sqrt_pos.mpr (by exact_mod_cast occupationFactorial_pos A.val)).ne' + have hv : planarHighestFourAnnihilator D r ∅ A.val = + ((Real.sqrt (rationalCopyDiagonal D r.val.val : ℝ) * Real.sqrt 2 / 2^D : ℝ) : ℂ) * + (rationalHighestEntry D r A.val : ℂ) / (Real.sqrt (occupationFactorial A.val : ℝ) : ℂ) := by + apply (eq_div_iff hn).mpr + simpa using he + unfold planarFourWedgeMatrix annihilatorVector + rw [hv] + simp only [map_div₀, map_mul, Complex.star_def, Complex.conj_ofReal] + push_cast + simp + + +def rationalFourGram (D : ℕ) : Matrix (CopyLabel D) (CopyLabel D) ℚ := fun r s => + ∑ A : SectorOccupation 24 4, + 2 * rationalHighestEntry D r A.val * rationalHighestEntry D s A.val / + (2^(2*D) * occupationFactorial A.val) + +theorem planarFourGram_rational (D : ℕ) (r s : CopyLabel D) : + planarFourGram D r s = + ((Real.sqrt (rationalCopyDiagonal D r.val.val : ℝ) * + (rationalFourGram D r s : ℝ) * + Real.sqrt (rationalCopyDiagonal D s.val.val : ℝ) : ℝ) : ℂ) := by + classical + unfold planarFourGram + simp only [Matrix.mul_apply, Matrix.conjTranspose_apply, planarFourWedgeMatrix_rational, + Complex.star_def, Complex.conj_ofReal, ← Complex.ofReal_mul, ← Complex.ofReal_sum] + congr 1 + unfold rationalFourGram + rw [Rat.cast_sum, Finset.mul_sum, Finset.sum_mul] + apply Finset.sum_congr rfl + intro A _ + have hn : 0 < (occupationFactorial A.val : ℝ) := by + exact_mod_cast occupationFactorial_pos A.val + have hn' : Real.sqrt (occupationFactorial A.val : ℝ) ≠ 0 := (Real.sqrt_pos.mpr hn).ne' + have hsq := Real.sq_sqrt hn.le + have hs2 := Real.sq_sqrt (by norm_num : (0:ℝ) ≤ 2) + push_cast + rw [show 2*D=D*2 by omega, pow_mul] + field_simp + rw [hsq, hs2] + ring + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/RectangularOrbit.lean b/lean/OAI/Analysis/LaughlinFock/RectangularOrbit.lean new file mode 100644 index 0000000000000000000000000000000000000000..af069f484567629e43bd0437617734cd43d69667 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/RectangularOrbit.lean @@ -0,0 +1,114 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Rotations + +namespace OAI + +/-! Rectangular Orbit. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder +open NormedSpace MeasureTheory Topology + +section Exponential +open scoped Matrix.Norms.Operator + + + +theorem matrix_exp_intertwiner {ι κ : Type*} + [Fintype ι] [DecidableEq ι] [Fintype κ] [DecidableEq κ] + (X : Matrix ι ι ℂ) (Y : Matrix κ κ ℂ) (C : Matrix κ ι ℂ) + (h : Y*C = C*X) : exp Y * C = C * exp X := by + have hp (n : ℕ) : Y^n*C = C*X^n := by + induction n with + | zero => simp + | succ n ih => + rw [pow_succ, pow_succ, Matrix.mul_assoc, h, ← Matrix.mul_assoc, ih, Matrix.mul_assoc] + have hL := (mulRightLinearMap κ ℂ C).toContinuousLinearMap.hasSum + (exp_series_hasSum_exp' (𝕂:=ℂ) Y) + have hR := (mulLeftLinearMap ι ℂ C).toContinuousLinearMap.hasSum + (exp_series_hasSum_exp' (𝕂:=ℂ) X) + simp only [LinearMap.coe_toContinuousLinearMap', mulRightLinearMap_apply, + mulLeftLinearMap_apply, Matrix.smul_mul, Matrix.mul_smul, hp] at hL hR + exact hL.unique hR + + + +theorem matrix_intertwiner_generator_of_flow {ι κ : Type*} + [Fintype ι] [DecidableEq ι] [Fintype κ] [DecidableEq κ] + (X : Matrix ι ι ℂ) (Y : Matrix κ κ ℂ) (C : Matrix κ ι ℂ) + (h : ∀ t : ℝ, exp ((t:ℂ) • Y) * C = C * exp ((t:ℂ) • X)) : + Y*C = C*X := by + have he : (fun t : ℝ => exp (t • Y) * C) = (fun t : ℝ => C * exp (t • X)) := by + funext t + rw [RCLike.real_smul_eq_coe_smul (K:=ℂ), RCLike.real_smul_eq_coe_smul (K:=ℂ)] + exact h t + have hL := (mulRightLinearMap κ ℂ C).toContinuousLinearMap.restrictScalars ℝ |>.hasFDerivAt + |>.comp_hasDerivAt (0:ℝ) (hasDerivAt_exp_smul_const Y (0:ℝ)) + have hR := (mulLeftLinearMap ι ℂ C).toContinuousLinearMap.restrictScalars ℝ |>.hasFDerivAt + |>.comp_hasDerivAt (0:ℝ) (hasDerivAt_exp_smul_const X (0:ℝ)) + change HasDerivAt (fun t : ℝ => exp (t • Y) * C) ((exp (0 • Y) * Y)*C) 0 at hL + change HasDerivAt (fun t : ℝ => C * exp (t • X)) (C*(exp (0 • X)*X)) 0 at hR + rw [he] at hL + simpa only [zero_smul, exp_zero, Matrix.one_mul] using! hL.unique hR + +end Exponential + +section Groups +variable {J σ : Type*} {I : J → Type*} + [∀ j, Fintype (I j)] [∀ j, DecidableEq (I j)] + + +def intertwinerSubgroup {i j : J} (C : Matrix (I j) (I i) ℂ) : + Subgroup (UnitaryFamily I) where + carrier := {g | (g j).val * C = C * (g i).val} + one_mem' := by simp + mul_mem' := by + intro g h hg hh + change (g j).val * C = C * (g i).val at hg + change (h j).val * C = C * (h i).val at hh + change ((g j).val * (h j).val) * C = C * ((g i).val * (h i).val) + rw [Matrix.mul_assoc, hh, ← Matrix.mul_assoc, hg, Matrix.mul_assoc] + inv_mem' := by + intro g hg + change (g j).val * C = C * (g i).val at hg + have he := congrArg (fun A => ((g j)⁻¹).val * A * ((g i)⁻¹).val) hg + change ((g j)⁻¹).val * C = C * ((g i)⁻¹).val + have hj : ((g j)⁻¹).val * (g j).val = 1 := by + exact congrArg Subtype.val (inv_mul_cancel (g j)) + have hi : (g i).val * ((g i)⁻¹).val = 1 := by + exact congrArg Subtype.val (mul_inv_cancel (g i)) + have heL : ((g j)⁻¹).val * ((g j).val*C) * ((g i)⁻¹).val = C*((g i)⁻¹).val := by + rw [← Matrix.mul_assoc ((g j)⁻¹).val (g j).val C, hj, Matrix.one_mul] + have heR : ((g j)⁻¹).val * (C*(g i).val) * ((g i)⁻¹).val = ((g j)⁻¹).val*C := by + rw [Matrix.mul_assoc ((g j)⁻¹).val (C*(g i).val), Matrix.mul_assoc C, hi, Matrix.mul_one] + rw [heL, heR] at he + exact he.symm + +open scoped Matrix.Norms.Elementwise + +theorem intertwinerSubgroup_isClosed {i j : J} (C : Matrix (I j) (I i) ℂ) : + IsClosed (intertwinerSubgroup C : Set (UnitaryFamily I)) := by + change IsClosed {g : UnitaryFamily I | (g j).val*C = C*(g i).val} + apply isClosed_eq <;> fun_prop + + + +theorem rotationGroup_intertwiner + (X : σ → ∀ j, Matrix (I j) (I j) ℂ) + (hX : ∀ s j, (X s j)ᴴ = -X s j) {i j : J} + (C : Matrix (I j) (I i) ℂ) (hC : ∀ s, X s j*C = C*X s i) + (g : rotationGroup X hX) : (g.val j).val*C = C*(g.val i).val := by + have hle : rotationGroup X hX ≤ intertwinerSubgroup C := by + apply Subgroup.topologicalClosure_minimal + · apply (Subgroup.closure_le _).2 + rintro _ ⟨⟨s,t⟩,rfl⟩ + change exp ((t:ℂ) • X s j)*C = C*exp ((t:ℂ) • X s i) + exact matrix_exp_intertwiner _ _ C (by simp only [Matrix.smul_mul, Matrix.mul_smul, hC s]) + · exact intertwinerSubgroup_isClosed C + exact hle g.property + +end Groups +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/RelativePerturbation.lean b/lean/OAI/Analysis/LaughlinFock/RelativePerturbation.lean new file mode 100644 index 0000000000000000000000000000000000000000..7281fd811f75ff9c127d736ad312473fd71a6216 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/RelativePerturbation.lean @@ -0,0 +1,546 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LocalEnergy + +namespace OAI + +/-! Relative Perturbation. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open scoped BigOperators Polynomial +open Polynomial +open Filter Topology +open Filter Topology +open Filter Topology +open scoped Kronecker + + +def stackFamily {β ι κ : Type*} (A : β → Matrix ι κ ℂ) : Matrix (β × ι) κ ℂ := + fun b j => A b.1 b.2 j + +@[simp] +theorem stackFamily_mulVec {β ι κ : Type*} [Fintype κ] + (A : β → Matrix ι κ ℂ) (x : κ → ℂ) (b : β) (i : ι) : + (stackFamily A *ᵥ x) (b,i) = (A b *ᵥ x) i := rfl + +theorem stackFamily_gram {β ι κ : Type*} [Fintype β] [Fintype ι] + (A : β → Matrix ι κ ℂ) : (stackFamily A)ᴴ * stackFamily A = ∑ b, (A b)ᴴ * A b := by + ext i j + simp only [Matrix.mul_apply, Fintype.sum_prod_type, Matrix.conjTranspose_apply, + stackFamily, Matrix.sum_apply] + + +theorem stackFamily_kronecker {β ι κ : Type*} [Fintype β] [Fintype ι] + (A : β → Matrix ι κ ℂ) (M : Matrix β β ℂ) (D : Matrix ι ι ℂ) : + (stackFamily A)ᴴ * (M ⊗ₖ D) * stackFamily A = + ∑ b, ∑ c, M b c • ((A b)ᴴ * D * A c) := by + ext i j + simp only [Matrix.mul_apply, Fintype.sum_prod_type, Matrix.conjTranspose_apply, + stackFamily, Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, Matrix.kroneckerMap_apply, + Finset.sum_mul, Finset.mul_sum] + conv_lhs => + arg 2 + ext c + rw [Finset.sum_comm] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro c _ + apply Finset.sum_congr rfl + intro x _ + apply Finset.sum_congr rfl + intro y _ + ring + +theorem isHermitian_kronecker {β ι : Type*} (M : Matrix β β ℂ) (D : Matrix ι ι ℂ) + (hM : M.IsHermitian) (hD : D.IsHermitian) : (M ⊗ₖ D).IsHermitian := by + change (M ⊗ₖ D)ᴴ = _ + rw [Matrix.conjTranspose_kronecker, hM.eq, hD.eq] + + +theorem family_gram_majorant {β : Type*} [Fintype β] + (L P : ℕ) (p : β → ℕ) (j k : β → Orbital L) (hp : ∀ b, p b < P) : + ((Fintype.card β : ℝ) • limitHamiltonian L P - + (stackFamily (fun b => annihilator L (k b) * annihilator L (j b) * + limitPairAnnihilator L (p b)))ᴴ * + stackFamily (fun b => annihilator L (k b) * annihilator L (j b) * + limitPairAnnihilator L (p b))).PosSemidef := by + classical + have hH : (limitHamiltonian L P).IsHermitian := + (Matrix.posSemidef_sum _ (fun p _ => Matrix.posSemidef_conjTranspose_mul_self _)).isHermitian + apply Matrix.PosSemidef.of_dotProduct_mulVec_nonneg + ((hH.smul (IsSelfAdjoint.all _)).sub (Matrix.isHermitian_conjTranspose_mul_self _)) + intro ψ + have h := finite_annihilator_family_bound L P p j k hp ψ + rw [Matrix.sub_mulVec, dotProduct_sub, Matrix.smul_mulVec, dotProduct_smul, + gram_quadratic_form, star_dotProduct_self, Fintype.sum_prod_type] + apply Complex.nonneg_iff.mpr + constructor + · simpa only [Complex.sub_re, Complex.smul_re, Complex.ofReal_re, smul_eq_mul, + stackFamily_mulVec, sub_nonneg] using h + · simp only [Complex.sub_im, Complex.smul_im, Complex.ofReal_im, smul_eq_mul, +] + have him : (star ψ ⬝ᵥ (limitHamiltonian L P *ᵥ ψ)).im = 0 := + hH.im_star_dotProduct_mulVec_self ψ + rw [him, mul_zero, sub_self] + + + +def localBlockError {β : Type*} [Fintype β] (L Q : ℕ) + (M Mstar : Matrix β β ℂ) : Matrix (β × Occupation L) (β × Occupation L) ℂ := + M ⊗ₖ ((localDeltaInv L Q)ᴴ * localDeltaInv L Q) - Mstar ⊗ₖ 1 + +theorem localBlockError_hermitian {β : Type*} [Fintype β] (L Q : ℕ) + (M Mstar : Matrix β β ℂ) (hM : M.IsHermitian) (hS : Mstar.IsHermitian) : + (localBlockError L Q M Mstar).IsHermitian := + (isHermitian_kronecker _ _ hM (Matrix.isHermitian_conjTranspose_mul_self _)).sub + (isHermitian_kronecker _ _ hS Matrix.isHermitian_one) + +theorem localBlockError_tendsto {β : Type*} [Fintype β] (L : ℕ) + (M : ℕ → Matrix β β ℂ) (Mstar : Matrix β β ℂ) + (hM : Tendsto M atTop (𝓝 Mstar)) : + Tendsto (fun Q => localBlockError L Q (M Q) Mstar) atTop (𝓝 0) := by + have hD : Tendsto (fun Q => (localDeltaInv L Q)ᴴ * localDeltaInv L Q) + atTop (𝓝 1) := by + have hc := ((continuous_id (X := FockMatrix L)).matrix_conjTranspose.tendsto 1).comp + (localDeltaInv_tendsto L) + simpa using hc.mul (localDeltaInv_tendsto L) + apply tendsto_pi_nhds.mpr + intro a + apply tendsto_pi_nhds.mpr + intro b + have hm := tendsto_pi_nhds.mp (tendsto_pi_nhds.mp hM a.1) b.1 + have hd := tendsto_pi_nhds.mp (tendsto_pi_nhds.mp hD a.2) b.2 + simpa only [localBlockError, Matrix.sub_apply, Matrix.kroneckerMap_apply, Matrix.zero_apply, + sub_self] using (hm.mul hd).sub_const (Mstar a.1 b.1 * (1 : FockMatrix L) a.2 b.2) + + + +theorem local_relative_error {β : Type*} [Fintype β] + (L P : ℕ) (p : β → ℕ) (j k : β → Orbital L) (hp : ∀ b, p b < P) + (M : ℕ → Matrix β β ℂ) (Mstar : Matrix β β ℂ) + (hMH : ∀ Q, (M Q).IsHermitian) (hSH : Mstar.IsHermitian) + (hM : Tendsto M atTop (𝓝 Mstar)) + (hLimit : (∑ b, ∑ c, Mstar b c • + ((annihilator L (k b) * annihilator L (j b) * limitPairAnnihilator L (p b))ᴴ * + (annihilator L (k c) * annihilator L (j c) * limitPairAnnihilator L (p c)))).PosSemidef) : + ∃ ρ : ℕ → ℝ, (∀ Q, 0 ≤ ρ Q) ∧ Tendsto ρ atTop (𝓝 0) ∧ + ∀ Q, 0 < Q → L ≤ Q → P ≤ 2*Q-1 → + (localDelta L Q * + (∑ b, ∑ c, (M Q) b c • + ((annihilator L (k b) * annihilator L (j b) * limitPairAnnihilator L (p b))ᴴ * + ((localDeltaInv L Q)ᴴ * localDeltaInv L Q) * + (annihilator L (k c) * annihilator L (j c) * limitPairAnnihilator L (p c)))) * + localDelta L Q + ρ Q • localHamiltonian L P Q).PosSemidef := by + classical + let A : β → FockMatrix L := fun b => + annihilator L (k b) * annihilator L (j b) * limitPairAnnihilator L (p b) + let C : ℝ := Fintype.card β + let ρ : ℕ → ℝ := fun Q => C * entryNormBound (localBlockError L Q (M Q) Mstar) + have hC : 0 ≤ C := Nat.cast_nonneg _ + refine ⟨ρ, (fun Q => mul_nonneg hC (entryNormBound_nonneg _)), ?_, ?_⟩ + · simpa only [mul_zero] using + (entryNormBound_tendsto_zero (localBlockError_tendsto L M Mstar hM)).const_mul C + · intro Q hQ hL hP + have hLim : ((stackFamily A)ᴴ * (Mstar ⊗ₖ (1 : FockMatrix L)) * stackFamily A).PosSemidef := by + simpa only [stackFamily_kronecker, Matrix.mul_one] using hLimit + have h := relative_compression_bound (stackFamily A) (localDelta L Q) + (localDelta_posSemidef L Q).isHermitian (Mstar ⊗ₖ (1 : FockMatrix L)) + (localBlockError L Q (M Q) Mstar) + (localBlockError_hermitian L Q _ _ (hMH Q) hSH) + (limitHamiltonian L P) (localHamiltonian L P Q) C hC hLim + (family_gram_majorant L P p j k hp) + (localHamiltonian_energy_transfer hQ hL hP) + have heq : (Mstar ⊗ₖ (1 : FockMatrix L)) + localBlockError L Q (M Q) Mstar = + (M Q) ⊗ₖ ((localDeltaInv L Q)ᴴ * localDeltaInv L Q) := by + unfold localBlockError + abel + rw [heq, stackFamily_kronecker] at h + exact h + + + +theorem stackFamily_coupled {α β ι κ : Type*} [Fintype β] [Fintype ι] + (A : β → Matrix ι κ ℂ) (S : Matrix α β ℂ) (D : Matrix ι ι ℂ) : + stackFamily (fun r => D * (∑ b, S r b • A b)) = (S ⊗ₖ D) * stackFamily A := by + ext ⟨r,i⟩ j + simp only [stackFamily, Matrix.mul_apply, Matrix.sum_apply, Matrix.smul_apply, + smul_eq_mul, Fintype.sum_prod_type, Matrix.kroneckerMap_apply, Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro x _ + ring + +theorem stackFamily_mul {β ι κ ν : Type*} [Fintype κ] + (A : β → Matrix ι κ ℂ) (D : Matrix κ ν ℂ) : + stackFamily (fun r => A r * D) = stackFamily A * D := rfl + + + +theorem quadratic_family_change {α β ι : Type*} [Fintype α] [Fintype β] [Fintype ι] + [DecidableEq ι] (A : β → Matrix ι ι ℂ) (S : Matrix α β ℂ) (C : Matrix α α ℂ) + (D J : Matrix ι ι ℂ) (hD : D.IsHermitian) : + (∑ r, ∑ s, C r s • + ((J * (∑ b, S r b • A b) * D)ᴴ * (J * (∑ b, S s b • A b) * D))) = + D * (∑ b, ∑ c, (Sᴴ * C * S) b c • (A b)ᴴ * (Jᴴ * J) * A c) * D := by + let B : α → Matrix ι ι ℂ := fun r => J * (∑ b, S r b • A b) * D + have hB : stackFamily B = (S ⊗ₖ J) * stackFamily A * D := by + rw [show B = (fun r => (J * (∑ b, S r b • A b)) * D) from rfl, + stackFamily_mul, stackFamily_coupled] + have heq : (S ⊗ₖ J)ᴴ * (C ⊗ₖ (1 : Matrix ι ι ℂ)) * (S ⊗ₖ J) = + (Sᴴ * C * S) ⊗ₖ (Jᴴ * J) := by + rw [Matrix.conjTranspose_kronecker, ← Matrix.mul_kronecker_mul, + ← Matrix.mul_kronecker_mul, Matrix.mul_one] + calc + _ = (stackFamily B)ᴴ * (C ⊗ₖ (1 : Matrix ι ι ℂ)) * stackFamily B := by + simp only [stackFamily_kronecker, Matrix.mul_one, B] + _ = D * ((stackFamily A)ᴴ * ((S ⊗ₖ J)ᴴ * (C ⊗ₖ (1 : Matrix ι ι ℂ)) * + (S ⊗ₖ J)) * stackFamily A) * D := by + rw [hB] + simp only [Matrix.conjTranspose_mul, hD.eq, Matrix.mul_assoc] + _ = _ := by + rw [heq, stackFamily_kronecker] + simp only [Matrix.smul_mul] + + +theorem tendsto_matrix_mul {α β ι : Type*} [Fintype β] + {A : ℕ → Matrix α β ℂ} {B : ℕ → Matrix β ι ℂ} + {Astar : Matrix α β ℂ} {Bstar : Matrix β ι ℂ} + (hA : Tendsto A atTop (𝓝 Astar)) (hB : Tendsto B atTop (𝓝 Bstar)) : + Tendsto (fun Q => A Q * B Q) atTop (𝓝 (Astar * Bstar)) := by + apply tendsto_pi_nhds.mpr + intro i + apply tendsto_pi_nhds.mpr + intro j + exact tendsto_finsetSum Finset.univ (fun b _ => + (tendsto_pi_nhds.mp (tendsto_pi_nhds.mp hA i) b).mul + (tendsto_pi_nhds.mp (tendsto_pi_nhds.mp hB b) j)) + +theorem tendsto_matrix_adjoint {α β : Type*} {A : ℕ → Matrix α β ℂ} + {Astar : Matrix α β ℂ} (hA : Tendsto A atTop (𝓝 Astar)) : + Tendsto (fun Q => (A Q)ᴴ) atTop (𝓝 Astarᴴ) := by + apply tendsto_pi_nhds.mpr + intro j + apply tendsto_pi_nhds.mpr + intro i + exact (tendsto_pi_nhds.mp (tendsto_pi_nhds.mp hA i) j).star + +theorem hermitian_congruence {α β : Type*} [Fintype α] (S : Matrix α β ℂ) + (C : Matrix α α ℂ) (hC : C.IsHermitian) : (Sᴴ * C * S).IsHermitian := by + change (Sᴴ * C * S)ᴴ = _ + simp only [Matrix.conjTranspose_mul, Matrix.conjTranspose_conjTranspose, hC.eq, + Matrix.mul_assoc] + + + +theorem quadratic_family_mix {α β ι : Type*} [Fintype α] [Fintype β] [Fintype ι] + [DecidableEq ι] (A : β → Matrix ι ι ℂ) (S : Matrix α β ℂ) (C : Matrix α α ℂ) : + (∑ r, ∑ s, C r s • ((∑ b, S r b • A b)ᴴ * (∑ b, S s b • A b))) = + ∑ b, ∑ c, (Sᴴ * C * S) b c • ((A b)ᴴ * A c) := by + simpa only [Matrix.one_mul, Matrix.mul_one, Matrix.conjTranspose_one, Matrix.smul_mul] + using quadratic_family_change A S C 1 1 Matrix.isHermitian_one + + +def localFourScale (Q p j k : ℕ) : ℝ := + pairScale Q p / (modeScale Q j * modeScale Q k) + +theorem localFourScale_tendsto (p j k : ℕ) : + Tendsto (fun Q => localFourScale Q p j k) atTop (𝓝 1) := by + simpa only [localFourScale, Pi.div_def, mul_one, div_one] using + (pairScale_tendsto p).div ((modeScale_tendsto j).mul (modeScale_tendsto k)) (by norm_num) + + + +theorem local_transfer_of_limitpositive {α β : Type*} [Fintype α] [Fintype β] + (L P : ℕ) (p : β → ℕ) (j k : β → Orbital L) (hp : ∀ b, p b < P) + (S : ℕ → Matrix α β ℂ) (Sstar : Matrix α β ℂ) + (C : ℕ → Matrix α α ℂ) (Cstar : Matrix α α ℂ) + (hS : Tendsto S atTop (𝓝 Sstar)) (hC : Tendsto C atTop (𝓝 Cstar)) + (hCH : ∀ Q, (C Q).IsHermitian) (hCSH : Cstar.IsHermitian) + (hLimit : (∑ r, ∑ s, Cstar r s • + ((∑ b, Sstar r b • (annihilator L (k b) * annihilator L (j b) * + limitPairAnnihilator L (p b)))ᴴ * + (∑ b, Sstar s b • (annihilator L (k b) * annihilator L (j b) * + limitPairAnnihilator L (p b))))).PosSemidef) : + ∃ ρ : ℕ → ℝ, (∀ Q, 0 ≤ ρ Q) ∧ Tendsto ρ atTop (𝓝 0) ∧ + ∀ Q, 0 < Q → L ≤ Q → P ≤ 2*Q-1 → + ((∑ r, ∑ s, (C Q) r s • + ((∑ b, (S Q) r b • (annihilator L (k b) * annihilator L (j b) * + localPairAnnihilator L Q (p b)))ᴴ * + (∑ b, (S Q) s b • (annihilator L (k b) * annihilator L (j b) * + localPairAnnihilator L Q (p b))))) + ρ Q • localHamiltonian L P Q).PosSemidef := by + classical + let A : β → FockMatrix L := fun b => + annihilator L (k b) * annihilator L (j b) * limitPairAnnihilator L (p b) + let B : ℕ → Matrix α β ℂ := fun Q r b => + S Q r b * (localFourScale Q (p b) (j b).val (k b).val : ℂ) + have hB : Tendsto B atTop (𝓝 Sstar) := by + apply tendsto_pi_nhds.mpr + intro r + apply tendsto_pi_nhds.mpr + intro b + have hb := Complex.continuous_ofReal.continuousAt.tendsto.comp + (localFourScale_tendsto (p b) (j b).val (k b).val) + simpa only [B, Function.comp_apply, Complex.ofReal_one, mul_one] using + (tendsto_pi_nhds.mp (tendsto_pi_nhds.mp hS r) b).mul hb + let M : ℕ → Matrix β β ℂ := fun Q => (B Q)ᴴ * C Q * B Q + let Mstar : Matrix β β ℂ := Sstarᴴ * Cstar * Sstar + have hM : Tendsto M atTop (𝓝 Mstar) := + tendsto_matrix_mul (tendsto_matrix_mul (tendsto_matrix_adjoint hB) hC) hB + have hMH : ∀ Q, (M Q).IsHermitian := fun Q => hermitian_congruence _ _ (hCH Q) + have hMS : Mstar.IsHermitian := hermitian_congruence _ _ hCSH + rw [quadratic_family_mix] at hLimit + obtain ⟨ρ, hρ0, hρlim, hρ⟩ := local_relative_error L P p j k hp M Mstar hMH hMS hM hLimit + refine ⟨ρ, hρ0, hρlim, ?_⟩ + intro Q hQ hL hP + have hb (r : α) : + (∑ b, (S Q) r b • (annihilator L (k b) * annihilator L (j b) * + localPairAnnihilator L Q (p b))) = + localDeltaInv L Q * (∑ b, (B Q) r b • A b) * localDelta L Q := by + simp only [Matrix.mul_sum, Matrix.sum_mul, Matrix.mul_smul, Matrix.smul_mul] + apply Finset.sum_congr rfl + intro b _ + rw [localFour_conjugation hQ hL (by have := hp b; omega), smul_smul] + simp only [B, A, localFourScale, Complex.ofReal_div, Complex.ofReal_mul] + simp_rw [hb] + rw [quadratic_family_change _ _ _ _ _ (localDelta_posSemidef L Q).isHermitian] + simpa only [Matrix.smul_mul] using hρ Q hQ hL hP + + +def orbitalMerge (L R : ℕ) : Orbital L ⊕ Fin R ≃ Orbital (L+R) := + finSumFinEquiv.trans (finCongr (by omega)) + +def localOrbital (L R : ℕ) (j : Orbital L) : Orbital (L+R) := + orbitalMerge L R (Sum.inl j) + +def spectatorOrbital (L R : ℕ) (j : Fin R) : Orbital (L+R) := + orbitalMerge L R (Sum.inr j) + +@[simp] theorem localOrbital_val (L R : ℕ) (j : Orbital L) : + (localOrbital L R j).val = j.val := rfl + +@[simp] theorem spectatorOrbital_val (L R : ℕ) (j : Fin R) : + (spectatorOrbital L R j).val = L+1+j.val := rfl + + + +def occupationMerge (L R : ℕ) : Occupation L × Finset (Fin R) ≃ Occupation (L+R) := + Finset.sumEquiv.toEquiv.symm.trans (orbitalMerge L R).finsetCongr + +theorem occupationMerge_apply (L R : ℕ) (A : Occupation L) (S : Finset (Fin R)) : + occupationMerge L R (A,S) = (A.disjSum S).map (orbitalMerge L R).toEmbedding := rfl + +@[simp] theorem localOrbital_mem_occupationMerge (L R : ℕ) (j : Orbital L) + (A : Occupation L) (S : Finset (Fin R)) : + localOrbital L R j ∈ occupationMerge L R (A,S) ↔ j ∈ A := by + simp only [occupationMerge_apply, localOrbital, + Finset.mem_map_equiv, Equiv.symm_apply_apply, Finset.inl_mem_disjSum] + +theorem occupationMerge_erase (L R : ℕ) (j : Orbital L) + (A : Occupation L) (S : Finset (Fin R)) : + (occupationMerge L R (A,S)).erase (localOrbital L R j) = + occupationMerge L R (A.erase j,S) := by + rw [occupationMerge_apply, occupationMerge_apply, localOrbital] + change ((A.disjSum S).map (orbitalMerge L R).toEmbedding).erase + ((orbitalMerge L R).toEmbedding (Sum.inl j)) = _ + rw [← Finset.map_erase] + congr 1 + ext x + cases x <;> simp + + +theorem occupationMerge_lower_count (L R : ℕ) (j : Orbital L) + (A : Occupation L) (S : Finset (Fin R)) : + ((occupationMerge L R (A,S)).filter (fun x => x < localOrbital L R j)).card = + (A.filter (fun x => x < j)).card := by + rw [occupationMerge_apply, Finset.filter_map, Finset.card_map] + have heq : (A.disjSum S).filter (fun x => orbitalMerge L R x < localOrbital L R j) = + (A.filter (fun x => x < j)).disjSum (∅ : Finset (Fin R)) := by + ext x + cases x with + | inl i => simp only [Finset.mem_filter, Finset.inl_mem_disjSum]; rfl + | inr i => + have hn : ¬ orbitalMerge L R (Sum.inr i) < localOrbital L R j := by + change ¬ L+1+i.val < j.val + omega + simp [hn] + change ((A.disjSum S).filter + (fun x => orbitalMerge L R x < localOrbital L R j)).card = _ + rw [heq, Finset.card_disjSum, Finset.card_empty, add_zero] + + + +theorem annihilator_spectator_factorization (L R : ℕ) (j : Orbital L) : + (annihilator (L+R) (localOrbital L R j)).submatrix + (occupationMerge L R) (occupationMerge L R) = + annihilator L j ⊗ₖ (1 : Matrix (Finset (Fin R)) (Finset (Fin R)) ℂ) := by + ext ⟨A,S⟩ ⟨B,T⟩ + simp only [Matrix.submatrix_apply, annihilator, localOrbital_mem_occupationMerge, + occupationMerge_erase, Equiv.apply_eq_iff_eq, Prod.mk.injEq, + occupationMerge_lower_count, Matrix.kroneckerMap_apply, Matrix.one_apply] + by_cases h : S=T <;> by_cases hB : j ∈ B ∧ A=B.erase j <;> simp_all + + +def spectatorExtension (L R : ℕ) (M : FockMatrix L) : FockMatrix (L+R) := + (M ⊗ₖ (1 : Matrix (Finset (Fin R)) (Finset (Fin R)) ℂ)).submatrix + (occupationMerge L R).symm (occupationMerge L R).symm + +theorem spectatorExtension_annihilator (L R : ℕ) (j : Orbital L) : + spectatorExtension L R (annihilator L j) = annihilator (L+R) (localOrbital L R j) := by + ext A B + have h := congrArg (fun M => M ((occupationMerge L R).symm A) ((occupationMerge L R).symm B)) + (annihilator_spectator_factorization L R j) + simpa only [spectatorExtension, Matrix.submatrix_apply, Equiv.apply_symm_apply] using h.symm + +theorem spectatorExtension_mul (L R : ℕ) (A B : FockMatrix L) : + spectatorExtension L R (A*B) = spectatorExtension L R A * spectatorExtension L R B := by + unfold spectatorExtension + rw [Matrix.submatrix_mul_equiv, ← Matrix.mul_kronecker_mul, Matrix.one_mul] + +theorem spectatorExtension_adjoint (L R : ℕ) (M : FockMatrix L) : + spectatorExtension L R Mᴴ = (spectatorExtension L R M)ᴴ := by + simp only [spectatorExtension, Matrix.conjTranspose_submatrix, + Matrix.conjTranspose_kronecker, Matrix.conjTranspose_one] + +theorem spectatorExtension_sum (L R : ℕ) {β : Type*} (s : Finset β) (M : β → FockMatrix L) : + spectatorExtension L R (∑ b ∈ s, M b) = ∑ b ∈ s, spectatorExtension L R (M b) := by + ext A B + simp only [spectatorExtension, Matrix.sum_apply, Matrix.submatrix_apply, + Matrix.kroneckerMap_apply, Finset.sum_mul] + +theorem spectatorExtension_add (L R : ℕ) (M N : FockMatrix L) : + spectatorExtension L R (M+N) = spectatorExtension L R M + spectatorExtension L R N := by + ext A B + simp only [spectatorExtension, Matrix.add_apply, Matrix.submatrix_apply, + Matrix.kroneckerMap_apply, add_mul] + +theorem spectatorExtension_smul (L R : ℕ) (c : ℂ) (M : FockMatrix L) : + spectatorExtension L R (c • M) = c • spectatorExtension L R M := by + ext A B + simp only [spectatorExtension, Matrix.smul_apply, Matrix.submatrix_apply, + Matrix.kroneckerMap_apply, smul_eq_mul, mul_assoc] + +theorem spectatorExtension_real_smul (L R : ℕ) (c : ℝ) (M : FockMatrix L) : + spectatorExtension L R (c • M) = c • spectatorExtension L R M := by + ext A B + simp only [spectatorExtension, Matrix.smul_apply, Matrix.submatrix_apply, + Matrix.kroneckerMap_apply, Algebra.smul_mul_assoc] + +theorem spectatorExtension_posSemidef (L R : ℕ) (M : FockMatrix L) (hM : M.PosSemidef) : + (spectatorExtension L R M).PosSemidef := by + exact (hM.kronecker Matrix.PosSemidef.one).submatrix _ + +@[simp] theorem spectatorExtension_zero (L R : ℕ) : + spectatorExtension L R 0 = 0 := by + simp only [spectatorExtension, Matrix.zero_kronecker, Matrix.submatrix_zero, + Pi.zero_apply] + + + +theorem spectatorExtension_pair {L p : ℕ} (R : ℕ) (hp : p+1 ≤ L) : + spectatorExtension L R (localPairAnnihilator L (L+R) p) = pairAnnihilator (L+R) p := by + classical + let f : Orbital (L+R) → Orbital (L+R) → FockMatrix (L+R) := fun i j => + if i < j then (pairCoefficient (L+R) p i j : ℂ) • + (annihilator (L+R) j * annihilator (L+R) i) else 0 + have hloc (i j : Orbital L) : + f (localOrbital L R i) (localOrbital L R j) = + spectatorExtension L R (if i < j then + (sphericalPairCoefficient (L+R) p i.val j.val : ℂ) • + (annihilator L j * annihilator L i) else 0) := by + unfold f + have he : localOrbital L R i < localOrbital L R j ↔ i < j := Iff.rfl + simp only [he] + split_ifs + · rw [spectatorExtension_smul, spectatorExtension_mul, + spectatorExtension_annihilator, spectatorExtension_annihilator] + rw [pairCoefficient_eq_sphericalPairCoefficient] + rfl + · simp + have hsleft (i : Fin R) (j : Orbital (L+R)) : f (spectatorOrbital L R i) j = 0 := by + have he : (spectatorOrbital L R i).val + j.val ≠ p+1 := by + rw [spectatorOrbital_val]; omega + simp only [f, pairCoefficient_eq_sphericalPairCoefficient, sphericalPairCoefficient, + ite_eq_right he, Complex.ofReal_zero, zero_smul, ite_self] + have hsright (i : Orbital (L+R)) (j : Fin R) : f i (spectatorOrbital L R j) = 0 := by + have he : i.val + (spectatorOrbital L R j).val ≠ p+1 := by + rw [spectatorOrbital_val]; omega + simp only [f, pairCoefficient_eq_sphericalPairCoefficient, sphericalPairCoefficient, + ite_eq_right he, Complex.ofReal_zero, zero_smul, ite_self] + change _ = ∑ i, ∑ j, f i j + rw [← (orbitalMerge L R).sum_comp (fun i => ∑ j, f i j), Fintype.sum_sum_type] + have hright : (∑ i : Fin R, ∑ j, f (orbitalMerge L R (Sum.inr i)) j) = 0 := by + change (∑ i : Fin R, ∑ j, f (spectatorOrbital L R i) j) = 0 + simp only [hsleft, Finset.sum_const_zero] + rw [hright, add_zero] + unfold localPairAnnihilator coefficientPairAnnihilator + rw [spectatorExtension_sum] + apply Finset.sum_congr rfl + intro i _ + change _ = ∑ j, f (localOrbital L R i) j + rw [spectatorExtension_sum, ← (orbitalMerge L R).sum_comp (f (localOrbital L R i)), + Fintype.sum_sum_type] + simp only [localOrbital, spectatorOrbital] at hsright hloc + simp only [hsright, Finset.sum_const_zero, add_zero, hloc, localOrbital] + + + +def partialHamiltonian (Q P : ℕ) : FockMatrix Q := + ∑ p ∈ Finset.range P, (pairAnnihilator Q p)ᴴ * pairAnnihilator Q p + +theorem partialHamiltonian_posSemidef (Q P : ℕ) : + (partialHamiltonian Q P).PosSemidef := by + exact Matrix.posSemidef_sum _ (fun p _ => Matrix.posSemidef_conjTranspose_mul_self _) + +theorem spectatorExtension_localHamiltonian {L P : ℕ} (R : ℕ) (hP : P ≤ L) : + spectatorExtension L R (localHamiltonian L P (L+R)) = partialHamiltonian (L+R) P := by + unfold localHamiltonian partialHamiltonian + rw [spectatorExtension_sum] + apply Finset.sum_congr rfl + intro p hp + rw [spectatorExtension_mul, spectatorExtension_adjoint, + spectatorExtension_pair R (by have := Finset.mem_range.mp hp; omega)] + + + +theorem fock_transfer_of_limitpositive {α β : Type*} [Fintype α] [Fintype β] + (L P : ℕ) (hL : 1 ≤ L) (hP : P ≤ L) + (p : β → ℕ) (j k : β → Orbital L) (hp : ∀ b, p b < P) + (S : ℕ → Matrix α β ℂ) (Sstar : Matrix α β ℂ) + (C : ℕ → Matrix α α ℂ) (Cstar : Matrix α α ℂ) + (hS : Tendsto S atTop (𝓝 Sstar)) (hC : Tendsto C atTop (𝓝 Cstar)) + (hCH : ∀ Q, (C Q).IsHermitian) (hCSH : Cstar.IsHermitian) + (hLimit : (∑ r, ∑ s, Cstar r s • + ((∑ b, Sstar r b • (annihilator L (k b) * annihilator L (j b) * + limitPairAnnihilator L (p b)))ᴴ * + (∑ b, Sstar s b • (annihilator L (k b) * annihilator L (j b) * + limitPairAnnihilator L (p b))))).PosSemidef) : + ∃ ρ : ℕ → ℝ, (∀ Q, 0 ≤ ρ Q) ∧ Tendsto ρ atTop (𝓝 0) ∧ + ∀ R, ((∑ r, ∑ s, C (L+R) r s • + ((∑ b, S (L+R) r b • + (annihilator (L+R) (localOrbital L R (k b)) * + annihilator (L+R) (localOrbital L R (j b)) * pairAnnihilator (L+R) (p b)))ᴴ * + (∑ b, S (L+R) s b • + (annihilator (L+R) (localOrbital L R (k b)) * + annihilator (L+R) (localOrbital L R (j b)) * pairAnnihilator (L+R) (p b))))) + + ρ (L+R) • partialHamiltonian (L+R) P).PosSemidef := by + classical + obtain ⟨ρ, hρ0, hρlim, hρ⟩ := local_transfer_of_limitpositive L P p j k hp + S Sstar C Cstar hS hC hCH hCSH hLimit + refine ⟨ρ, hρ0, hρlim, fun R => ?_⟩ + have h := spectatorExtension_posSemidef L R _ + (hρ (L+R) (by omega) (by omega) (by omega)) + simp only [spectatorExtension_add, spectatorExtension_sum, + spectatorExtension_smul, spectatorExtension_real_smul, spectatorExtension_mul, + spectatorExtension_adjoint, spectatorExtension_annihilator, + spectatorExtension_localHamiltonian R hP] at h + have hb (b : β) : spectatorExtension L R (localPairAnnihilator L (L+R) (p b)) = + pairAnnihilator (L+R) (p b) := spectatorExtension_pair R (by have := hp b; omega) + simpa only [hb] using h +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/RelativeTransfer.lean b/lean/OAI/Analysis/LaughlinFock/RelativeTransfer.lean new file mode 100644 index 0000000000000000000000000000000000000000..885cde1a5208acd7117deab187683b296ee4f6ff --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/RelativeTransfer.lean @@ -0,0 +1,279 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.RowTraces + +namespace OAI + +/-! Relative Transfer. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open Filter Topology + + + +structure ComparisonRow where + t : Fin 8 + ell : ℝ + alpha : RowEntry t.val → ℝ + + +def fourSpinRatio (Q D : ℕ) : ℝ := + (4 * (Q : ℝ) - 1 - 2 * (D : ℝ)) / (2 * (Q : ℝ) - 1) + +theorem fourSpinRatio_tendsto (D : ℕ) : + Tendsto (fun Q => fourSpinRatio Q D) atTop (𝓝 2) := by + have h1 := tendsto_const_div_atTop_nhds_zero_nat (1+2*(D:ℝ)) + have h2 := tendsto_const_div_atTop_nhds_zero_nat (1:ℝ) + have hh : Tendsto (fun Q : ℕ => (4-(1+2*(D:ℝ))/Q)/(2-1/(Q:ℝ))) atTop (𝓝 2) := by + convert ((tendsto_const_nhds (x := (4:ℝ))).sub h1).div + ((tendsto_const_nhds (x := (2:ℝ))).sub h2) (show (2:ℝ)-0 ≠ 0 by norm_num) + using 1; first | rfl | norm_num + apply hh.congr' + filter_upwards [eventually_ge_atTop 1] with Q hQ + have hn : (Q : ℝ) ≠ 0 := by exact_mod_cast (by omega : Q ≠ 0) + have hqr : (1 : ℝ) ≤ Q := by exact_mod_cast hQ + have hd : 2*(Q:ℝ)-1 ≠ 0 := by linarith + have hd' : 2-1/(Q:ℝ) ≠ 0 := by rw [ne_eq, sub_eq_zero, eq_div_iff hn]; linarith + unfold fourSpinRatio + field_simp [hn, hd, hd'] + ring + +theorem fourSpinRatio_eq_dimensions {Q D : ℕ} (hQ : 1 ≤ Q) (hD : D ≤ Q) : + fourSpinRatio Q D = ((4*Q-1-2*D : ℕ) : ℝ) / ((2*Q-1 : ℕ) : ℝ) := by + have h1 : 1 ≤ 4*Q := by omega + have h2 : 2*D ≤ 4*Q-1 := by omega + have h3 : 1 ≤ 2*Q := by omega + simp only [fourSpinRatio, Nat.cast_sub h1, Nat.cast_sub h2, Nat.cast_sub h3, + Nat.cast_mul, Nat.cast_ofNat, Nat.cast_one] + + +def targetCopy (D : ℕ) : Matrix (CopyLabel D) (CopyLabel D) ℂ := fun r s => + if r.val.val=1 ∧ s.val.val=1 then 1 else 0 + +theorem targetCopy_hermitian (D : ℕ) : (targetCopy D).IsHermitian := by + classical + ext r s + simp [targetCopy, Matrix.conjTranspose_apply, and_comm] + + + +def fourComparison {ι : Type*} [Fintype ι] (rows : ι → ComparisonRow) + (ε : ℝ) (Q D : ℕ) : Matrix (CopyLabel D) (CopyLabel D) ℂ := + (fourSpinRatio Q D : ℂ) • targetCopy D - + Matrix.of (fun r s => ((∑ i, rowFourTrace Q D (rows i).t.val (rows i).alpha r s : ℝ) : ℂ)) + + (ε : ℂ) • 1 + + +def planarFourComparison {ι : Type*} [Fintype ι] (rows : ι → ComparisonRow) + (ε : ℝ) (D : ℕ) : Matrix (CopyLabel D) (CopyLabel D) ℂ := + (2 : ℂ) • targetCopy D - + Matrix.of (fun r s => ((∑ i, planarRowFourTrace D (rows i).t.val (rows i).alpha r s : ℝ) : ℂ)) + + (ε : ℂ) • 1 + +theorem fourComparison_hermitian {ι : Type*} [Fintype ι] (rows : ι → ComparisonRow) + (ε : ℝ) (Q D : ℕ) : (fourComparison rows ε Q D).IsHermitian := by + have h : (Matrix.of (fun r s => ((∑ i, rowFourTrace Q D (rows i).t.val (rows i).alpha r s : ℝ) : ℂ))).IsHermitian := by + ext r s + simp only [Matrix.conjTranspose_apply, Matrix.of_apply, Complex.star_def, Complex.conj_ofReal] + apply congrArg (fun x : ℝ => (x : ℂ)) + apply Finset.sum_congr rfl + intro i _ + exact congrFun (congrFun (rowFourTrace_symmetric Q D (rows i).t.val (rows i).alpha) r) s + exact ((targetCopy_hermitian D).smul (show IsSelfAdjoint (fourSpinRatio Q D : ℂ) by simp [IsSelfAdjoint])).sub h |>.add + (Matrix.isHermitian_one.smul (show IsSelfAdjoint (ε : ℂ) by simp [IsSelfAdjoint])) + +theorem planarFourComparison_hermitian {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) (ε : ℝ) (D : ℕ) : + (planarFourComparison rows ε D).IsHermitian := by + have h : (Matrix.of (fun r s => ((∑ i, planarRowFourTrace D (rows i).t.val (rows i).alpha r s : ℝ) : ℂ))).IsHermitian := by + ext r s + simp only [Matrix.conjTranspose_apply, Matrix.of_apply, Complex.star_def, Complex.conj_ofReal] + apply congrArg (fun x : ℝ => (x : ℂ)) + apply Finset.sum_congr rfl + intro i _ + exact congrFun (congrFun (planarRowFourTrace_symmetric D (rows i).t.val (rows i).alpha) r) s + exact ((targetCopy_hermitian D).smul (show IsSelfAdjoint (2 : ℂ) by norm_num)).sub h |>.add + (Matrix.isHermitian_one.smul (show IsSelfAdjoint (ε : ℂ) by simp [IsSelfAdjoint])) + +theorem fourComparison_tendsto {ι : Type*} [Fintype ι] (rows : ι → ComparisonRow) + (ε : ℝ) (D : ℕ) : + Tendsto (fun Q => fourComparison rows ε Q D) atTop (𝓝 (planarFourComparison rows ε D)) := by + apply tendsto_pi_nhds.mpr + intro r + apply tendsto_pi_nhds.mpr + intro s + have hf := Complex.continuous_ofReal.continuousAt.tendsto.comp (fourSpinRatio_tendsto D) + have ht := Complex.continuous_ofReal.continuousAt.tendsto.comp + (tendsto_finsetSum Finset.univ (fun i _ => rowFourTrace_tendsto D (rows i).t.val (rows i).alpha r s)) + simpa only [fourComparison, planarFourComparison, Matrix.add_apply, Matrix.sub_apply, + Matrix.smul_apply, Matrix.of_apply, smul_eq_mul, Function.comp_apply, Complex.ofReal_ofNat] using + ((hf.mul_const (targetCopy D r s)).sub ht).add_const ((ε : ℂ)*(1 : Matrix (CopyLabel D) (CopyLabel D) ℂ) r s) + + + +def localCopyMatrix (D Q : ℕ) : Matrix (CopyLabel D) (FourHighestShell 24 D) ℂ := fun r b => + sphericalCopyCoefficient Q D D r.val.val b.val.1.val b.val.2.val.1.val b.val.2.val.2.val + +def planarLocalCopyMatrix (D : ℕ) : Matrix (CopyLabel D) (FourHighestShell 24 D) ℂ := fun r b => + planarCopyCoefficient D D r.val.val b.val.1.val b.val.2.val.1.val b.val.2.val.2.val + +theorem localCopyMatrix_tendsto (D : ℕ) : Tendsto (localCopyMatrix D) atTop (𝓝 (planarLocalCopyMatrix D)) := by + apply tendsto_pi_nhds.mpr + intro r + apply tendsto_pi_nhds.mpr + intro b + exact Complex.continuous_ofReal.continuousAt.tendsto.comp + (sphericalCopyCoefficient_tendsto D D r.val.val b.val.1.val b.val.2.val.1.val b.val.2.val.2.val) + + + +def planarHighestFourAnnihilator (D : ℕ) (r : CopyLabel D) : FockMatrix 24 := + ∑ b : FourHighestShell 24 D, planarLocalCopyMatrix D r b • + (annihilator 24 b.val.2.val.2 * annihilator 24 b.val.2.val.1 * limitPairAnnihilator 24 b.val.1.val) + +theorem planarHighestFourAnnihilator_mem (D : ℕ) (r : CopyLabel D) : + planarHighestFourAnnihilator D r ∈ AnnihilationSpace 24 4 := by + apply Submodule.sum_mem + intro b _ + apply Submodule.smul_mem + exact annihilationSpace_mul 24 2 2 (limitPairAnnihilator_mem 24 b.val.1.val) + (annihilationSpace_mul 24 1 1 (annihilator_mem 24 b.val.2.val.1) (annihilator_mem 24 b.val.2.val.2)) + + + +def planarFourWedgeMatrix (D : ℕ) : Matrix (SectorOccupation 24 4) (CopyLabel D) ℂ := + fun A r => annihilatorVector 24 4 (planarHighestFourAnnihilator D r) A + +def planarFourGram (D : ℕ) : Matrix (CopyLabel D) (CopyLabel D) ℂ := + (planarFourWedgeMatrix D)ᴴ * planarFourWedgeMatrix D + +theorem planarFourWedgeMatrix_annihilator_column (D : ℕ) (r : CopyLabel D) : + wedgeAnnihilator 24 4 (fun A => planarFourWedgeMatrix D A r) = + planarHighestFourAnnihilator D r := + wedgeAnnihilator_annihilatorVector 24 4 _ (planarHighestFourAnnihilator_mem D r) + + + +theorem planarFourCertificate_lift {ι : Type*} [Fintype ι] (rows : ι → ComparisonRow) + (ε : ℝ) (D : ℕ) + (h : (planarFourGram D * planarFourComparison rows ε D * planarFourGram D).PosSemidef) : + (∑ r, ∑ s, planarFourComparison rows ε D r s • + ((planarHighestFourAnnihilator D r)ᴴ * planarHighestFourAnnihilator D s)).PosSemidef := by + have hh := exteriorLift_of_gram_certificate 24 4 (planarFourWedgeMatrix D) + (planarFourComparison rows ε D) (planarFourComparison_hermitian rows ε D) h + simpa only [planarFourWedgeMatrix_annihilator_column] using hh + + + +def fourShellExtension (D R : ℕ) : FourHighestShell 24 D → FourHighestShell (24+R) D := fun b => + ⟨(⟨b.val.1.val, by have := b.val.1.isLt; omega⟩, + ⟨(localOrbital 24 R b.val.2.val.1, localOrbital 24 R b.val.2.val.2), b.val.2.property⟩), b.property⟩ + +theorem fourShellExtension_injective (D R : ℕ) : Function.Injective (fourShellExtension D R) := by + intro b c he + apply Subtype.ext + apply Prod.ext + · apply Fin.ext + exact congrArg (fun x => x.val.1.val) he + · apply Subtype.ext + apply Prod.ext + · apply Fin.ext + exact congrArg (fun x => x.val.2.val.1.val) he + · apply Fin.ext + exact congrArg (fun x => x.val.2.val.2.val) he + +theorem fourShellExtension_surjective {D : ℕ} (hD : D ≤ 23) (R : ℕ) : + Function.Surjective (fourShellExtension D R) := by + intro b + have hb := b.property + let c : FourHighestShell 24 D := + ⟨(⟨b.val.1.val, by omega⟩, + ⟨(⟨b.val.2.val.1.val, by omega⟩, ⟨b.val.2.val.2.val, by omega⟩), + b.val.2.property⟩), hb⟩ + refine ⟨c, ?_⟩ + apply Subtype.ext + apply Prod.ext + · apply Fin.ext + rfl + · apply Subtype.ext + apply Prod.ext <;> apply Fin.ext <;> rfl + + + +theorem highestFourAnnihilator_local_sum {D : ℕ} (hD : D ≤ 23) (R : ℕ) (r : CopyLabel D) : + highestFourAnnihilator (24+R) D r = + ∑ b : FourHighestShell 24 D, localCopyMatrix D (24+R) r b • + (annihilator (24+R) (localOrbital 24 R b.val.2.val.2) * + annihilator (24+R) (localOrbital 24 R b.val.2.val.1) * pairAnnihilator (24+R) b.val.1.val) := by + classical + unfold highestFourAnnihilator + let e : FourHighestShell 24 D ≃ FourHighestShell (24+R) D := + Equiv.ofBijective (fourShellExtension D R) + ⟨fourShellExtension_injective D R, fourShellExtension_surjective hD R⟩ + rw [← e.sum_comp] + apply Finset.sum_congr rfl + intro b _ + rfl + + + +theorem fourComparison_relative_transfer {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) (ε : ℝ) {D : ℕ} (hD : D ≤ 23) + (hCertificate : (planarFourGram D * planarFourComparison rows ε D * planarFourGram D).PosSemidef) : + ∃ ρ : ℕ → ℝ, (∀ Q, 0 ≤ ρ Q) ∧ Tendsto ρ atTop (𝓝 0) ∧ + ∀ Q, 24 ≤ Q → + ((∑ r, ∑ s, fourComparison rows ε Q D r s • + ((highestFourAnnihilator Q D r)ᴴ * highestFourAnnihilator Q D s)) + + ρ Q • partialHamiltonian Q 24).PosSemidef := by + have hb (b : FourHighestShell 24 D) : b.val.1.val < 24 := by + have := b.property + omega + obtain ⟨ρ, hρ0, hρlim, hρ⟩ := fock_transfer_of_limitpositive 24 24 (by norm_num) le_rfl + (fun b : FourHighestShell 24 D => b.val.1.val) + (fun b => b.val.2.val.1) (fun b => b.val.2.val.2) hb + (localCopyMatrix D) (planarLocalCopyMatrix D) + (fun Q => fourComparison rows ε Q D) (planarFourComparison rows ε D) + (localCopyMatrix_tendsto D) (fourComparison_tendsto rows ε D) + (fun Q => fourComparison_hermitian rows ε Q D) (planarFourComparison_hermitian rows ε D) + (planarFourCertificate_lift rows ε D hCertificate) + refine ⟨ρ, hρ0, hρlim, ?_⟩ + intro Q hQ + obtain ⟨R, rfl⟩ := Nat.exists_eq_add_of_le hQ + simpa only [← highestFourAnnihilator_local_sum hD R] using hρ R + + + +theorem fourComparison_uniform_transfer {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) (ε : ℝ) + (hCertificate : ∀ D, 1 ≤ D → D ≤ 23 → + (planarFourGram D * planarFourComparison rows ε D * planarFourGram D).PosSemidef) : + ∃ ρ : ℕ → ℝ, (∀ Q, 0 ≤ ρ Q) ∧ Tendsto ρ atTop (𝓝 0) ∧ + ∀ D, 1 ≤ D → D ≤ 23 → ∀ Q, 24 ≤ Q → + ((∑ r, ∑ s, fourComparison rows ε Q D r s • + ((highestFourAnnihilator Q D r)ᴴ * highestFourAnnihilator Q D s)) + + ρ Q • partialHamiltonian Q 24).PosSemidef := by + classical + have hh (d : Fin 23) := fourComparison_relative_transfer rows ε + (by omega : d.val+1 ≤ 23) (hCertificate (d.val+1) (by omega) (by omega)) + choose ρ hρpos hρlim hρbound using hh + refine ⟨fun Q => ∑ d, ρ d Q, ?_, ?_, ?_⟩ + · intro Q + exact Finset.sum_nonneg (fun d _ => hρpos d Q) + · simpa only [Finset.sum_const_zero] using + tendsto_finsetSum Finset.univ (fun d _ => hρlim d) + · intro D hD0 hD Q hQ + let d : Fin 23 := ⟨D-1, by omega⟩ + have hd : d.val+1 = D := by dsimp [d]; omega + have hle : ρ d Q ≤ ∑ e, ρ e Q := + Finset.single_le_sum (fun e _ => hρpos e Q) (Finset.mem_univ d) + have h := hρbound d Q hQ + rw [hd] at h + have h' := h.add ((partialHamiltonian_posSemidef Q 24).smul (sub_nonneg.mpr hle)) + convert h' using 1 + simp only [sub_smul] + abel + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Rotations.lean b/lean/OAI/Analysis/LaughlinFock/Rotations.lean new file mode 100644 index 0000000000000000000000000000000000000000..2043237cc02edfd378171045ba023629f1fcbc95 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Rotations.lean @@ -0,0 +1,179 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Flow + +namespace OAI + +/-! Rotations. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder +open NormedSpace MeasureTheory Topology + +private theorem matrix_unitary_isClosed {ι : Type*} [Fintype ι] [DecidableEq ι] : + IsClosed (Matrix.unitaryGroup ι ℂ : Set (Matrix ι ι ℂ)) := + isClosed_unitary + +section UnitaryCompact +open scoped Matrix.Norms.Elementwise + + +theorem unitaryMatrix_compactSpace {ι : Type*} [Fintype ι] [DecidableEq ι] : + CompactSpace (Matrix.unitaryGroup ι ℂ) := by + apply isCompact_iff_compactSpace.mp + apply (isCompact_closedBall (0 : Matrix ι ι ℂ) 1).of_isClosed_subset + matrix_unitary_isClosed + intro U hU + simp only [Metric.mem_closedBall, dist_zero_right] + exact entrywise_sup_norm_bound_of_unitary hU + +end UnitaryCompact + + +def unitaryConjugation {ι : Type*} [Fintype ι] [DecidableEq ι] + (U : Matrix.unitaryGroup ι ℂ) (M : Matrix ι ι ℂ) : Matrix ι ι ℂ := + U.val * M * U.valᴴ + +theorem unitaryConjugation_one {ι : Type*} [Fintype ι] [DecidableEq ι] + (M : Matrix ι ι ℂ) : unitaryConjugation 1 M = M := by + simp [unitaryConjugation] + +theorem unitaryConjugation_mul {ι : Type*} [Fintype ι] [DecidableEq ι] + (U V : Matrix.unitaryGroup ι ℂ) (M : Matrix ι ι ℂ) : + unitaryConjugation (U*V) M = unitaryConjugation U (unitaryConjugation V M) := by + simp [unitaryConjugation, Matrix.conjTranspose_mul, Matrix.mul_assoc] + +theorem unitaryConjugation_inv_cancel {ι : Type*} [Fintype ι] [DecidableEq ι] + (U : Matrix.unitaryGroup ι ℂ) (M : Matrix ι ι ℂ) : + unitaryConjugation U⁻¹ (unitaryConjugation U M) = M := by + rw [← unitaryConjugation_mul, inv_mul_cancel, unitaryConjugation_one] + +section Simultaneous +variable {J : Type*} (I : J → Type*) [∀ j, Fintype (I j)] [∀ j, DecidableEq (I j)] + + + +abbrev UnitaryFamily := ∀ j, Matrix.unitaryGroup (I j) ℂ + + + +def covarianceSubgroup {i j : J} + (L : Matrix (I i) (I i) ℂ →ₗ[ℂ] Matrix (I j) (I j) ℂ) : + Subgroup (UnitaryFamily I) where + carrier := {g | ∀ M, L (unitaryConjugation (g i) M) = unitaryConjugation (g j) (L M)} + one_mem' := by intro M; simp only [Pi.one_apply, unitaryConjugation_one] + mul_mem' := by + intro g h hg hh M + change ∀ M, L (unitaryConjugation (g i) M) = unitaryConjugation (g j) (L M) at hg + change ∀ M, L (unitaryConjugation (h i) M) = unitaryConjugation (h j) (L M) at hh + simp only [Pi.mul_apply, unitaryConjugation_mul, hg, hh] + inv_mem' := by + intro g hg M + have h := congrArg (unitaryConjugation (g j)⁻¹) + (hg (unitaryConjugation (g i)⁻¹ M)) + simpa only [Pi.inv_apply, ← unitaryConjugation_mul, mul_inv_cancel, inv_mul_cancel, + unitaryConjugation_one] using h.symm + +section Closed +open scoped Matrix.Norms.Elementwise + + + +theorem covarianceSubgroup_isClosed {i j : J} + (L : Matrix (I i) (I i) ℂ →ₗ[ℂ] Matrix (I j) (I j) ℂ) : + IsClosed (covarianceSubgroup I L : Set (UnitaryFamily I)) := by + have hL : Continuous L := L.toContinuousLinearMap.continuous + change IsClosed {g : UnitaryFamily I | ∀ M, + L (unitaryConjugation (g i) M) = unitaryConjugation (g j) (L M)} + simp_rw [Set.ofPred_forall] + apply isClosed_iInter + intro M + apply isClosed_eq + · apply hL.comp + unfold unitaryConjugation + fun_prop + · unfold unitaryConjugation + fun_prop + +end Closed + +end Simultaneous + +section Flows +open scoped Matrix.Norms.Operator +variable {J σ : Type*} {I : J → Type*} + [∀ j, Fintype (I j)] [∀ j, DecidableEq (I j)] + + +private theorem rotation_exp_unitary {ι : Type*} [Fintype ι] [DecidableEq ι] + (A : Matrix ι ι ℂ) (hA : Aᴴ = -A) (t : ℝ) : + exp ((t : ℂ) • A) ∈ Matrix.unitaryGroup ι ℂ := by + let B : Matrix ι ι ℂ := (t : ℂ) • A + have hB : Bᴴ = -B := by + dsimp only [B] + rw [Matrix.conjTranspose_smul, hA] + simp + have hstar : (exp B)ᴴ = exp (-B) := by + rw [← Matrix.exp_conjTranspose, hB] + change (exp B) ∈ unitary (Matrix ι ι ℂ) + rw [Unitary.mem_iff] + change (exp B)ᴴ * exp B = 1 ∧ exp B * (exp B)ᴴ = 1 + rw [hstar] + constructor + · simpa only [neg_add_cancel, exp_zero] using! + (exp_add_of_commute (Commute.refl B).neg_left).symm + · simpa only [add_neg_cancel, exp_zero] using! + (exp_add_of_commute (Commute.refl B).neg_right).symm + +def rotationFlow (X : σ → ∀ j, Matrix (I j) (I j) ℂ) + (hX : ∀ s j, (X s j)ᴴ = -X s j) (s : σ) (t : ℝ) : UnitaryFamily I := + fun j => ⟨exp ((t : ℂ) • X s j), rotation_exp_unitary (X s j) (hX s j) t⟩ + +theorem rotationFlow_conjugation + (X : σ → ∀ j, Matrix (I j) (I j) ℂ) + (hX : ∀ s j, (X s j)ᴴ = -X s j) (s : σ) (t : ℝ) (j : J) + (M : Matrix (I j) (I j) ℂ) : + unitaryConjugation (rotationFlow X hX s t j) M = + exp ((t : ℂ) • X s j) * M * exp ((t : ℂ) • (-X s j)) := by + unfold unitaryConjugation rotationFlow + rw [← Matrix.exp_conjTranspose, Matrix.conjTranspose_smul, hX] + simp + + + +def rotationGroup (X : σ → ∀ j, Matrix (I j) (I j) ℂ) + (hX : ∀ s j, (X s j)ᴴ = -X s j) : Subgroup (UnitaryFamily I) := + (Subgroup.closure (Set.range (fun p : σ × ℝ => rotationFlow X hX p.1 p.2))).topologicalClosure + +theorem rotationFlow_mem_group (X : σ → ∀ j, Matrix (I j) (I j) ℂ) + (hX : ∀ s j, (X s j)ᴴ = -X s j) (s : σ) (t : ℝ) : + rotationFlow X hX s t ∈ rotationGroup X hX := + Subgroup.le_topologicalClosure _ (Subgroup.subset_closure ⟨(s,t), rfl⟩) + + + +theorem rotationGroup_covariance (X : σ → ∀ j, Matrix (I j) (I j) ℂ) + (hX : ∀ s j, (X s j)ᴴ = -X s j) {i j : J} + (L : Matrix (I i) (I i) ℂ →ₗ[ℂ] Matrix (I j) (I j) ℂ) + (hL : ∀ s M, L (X s i * M - M * X s i) = X s j * L M - L M * X s j) + (g : rotationGroup X hX) (M : Matrix (I i) (I i) ℂ) : + L (unitaryConjugation (g.val i) M) = unitaryConjugation (g.val j) (L M) := by + have hle : rotationGroup X hX ≤ covarianceSubgroup I L := by + apply Subgroup.topologicalClosure_minimal + · apply (Subgroup.closure_le _).2 + rintro _ ⟨⟨s,t⟩,rfl⟩ M + simp only [rotationFlow_conjugation] + exact matrixExp_conjugation_naturality _ _ L (hL s) M t + · exact covarianceSubgroup_isClosed I L + exact hle g.property M + +instance rotationGroup_compactSpace (X : σ → ∀ j, Matrix (I j) (I j) ℂ) + (hX : ∀ s j, (X s j)ᴴ = -X s j) : CompactSpace (rotationGroup X hX) := by + let (j : J) : CompactSpace (Matrix.unitaryGroup (I j) ℂ) := unitaryMatrix_compactSpace + apply isCompact_iff_compactSpace.mp + exact (Subgroup.isClosed_topologicalClosure _).isCompact + +end Flows +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/RowTraces.lean b/lean/OAI/Analysis/LaughlinFock/RowTraces.lean new file mode 100644 index 0000000000000000000000000000000000000000..8a07d5a69fc23e0b7b472e5f1e7c39361440300e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/RowTraces.lean @@ -0,0 +1,246 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.HighestTails + +namespace OAI + +/-! Row Traces. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open Filter Topology + + + +def rowThreePrewedge {β : Type*} [Fintype β] (Q : ℕ) (t : PairLabel Q) (ℓ : ℝ) + (p : β → PairLabel Q) (i j : β → Orbital Q) (a : β → ℝ) : + Matrix (PairLabel Q × Orbital Q) (PairLabel Q × Orbital Q) ℂ := + (∑ b, (ℓ*a b : ℂ) • + (Matrix.single (t,i b) (p b,j b) 1 + Matrix.single (p b,j b) (t,i b) 1)) + + ∑ b, ∑ c, (a b*a c : ℂ) • + (if i b = i c then Matrix.single (p b,j b) (p c,j c) 1 else 0) + + + +theorem exteriorLift_single_congruence {ι : Type*} [Fintype ι] [DecidableEq ι] + (Q k : ℕ) (W : Matrix (SectorOccupation Q k) ι ℂ) (b c : ι) : + exteriorLift Q k (W * Matrix.single b c (1 : ℂ) * Wᴴ) = + (wedgeAnnihilator Q k (fun A => W A b))ᴴ * + wedgeAnnihilator Q k (fun A => W A c) := by + rw [exteriorLift_congruence] + simp [Matrix.single_apply, ite_smul, ite_and] + + + +theorem rowThreePrewedge_lift {β : Type*} [Fintype β] + (Q : ℕ) (t : PairLabel Q) (ℓ : ℝ) (p : β → PairLabel Q) + (i j : β → Orbital Q) (a : β → ℝ) : + exteriorLift Q 3 (threeWedgeMatrix Q * rowThreePrewedge Q t ℓ p i j a * + (threeWedgeMatrix Q)ᴴ) = rowThreeBody Q t.val ℓ (fun b => (p b).val) i j a := by + classical + have hs (c : ℂ) (M : Matrix (SectorOccupation Q 3) (SectorOccupation Q 3) ℂ) : + exteriorLift Q 3 (c • M) = c • exteriorLift Q 3 M := + (exteriorLiftLinear Q 3).map_smul c M + simp only [rowThreePrewedge, Matrix.mul_add, Matrix.add_mul, Matrix.mul_sum, + Matrix.sum_mul, Matrix.mul_smul, Matrix.smul_mul, exteriorLift_add, exteriorLift_sum, hs] + simp_rw [exteriorLift_single_congruence, threeWedgeMatrix_annihilator_column] + unfold rowThreeBody + apply congrArg₂ (· + ·) + · apply Finset.sum_congr rfl + intro b _ + ext A B + simp [Matrix.smul_apply, Complex.real_smul, Complex.ofReal_mul, mul_add] + · apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro c _ + split_ifs + · rw [exteriorLift_single_congruence, + threeWedgeMatrix_annihilator_column, threeWedgeMatrix_annihilator_column] + ext A B + simp [Matrix.smul_apply, Complex.real_smul, Complex.ofReal_mul] + · simp [exteriorLift] + + +theorem single_bilinear {ι : Type*} [Fintype ι] [DecidableEq ι] + (b c : ι) (x y : ι → ℂ) : + star x ⬝ᵥ (Matrix.single b c 1 *ᵥ y) = star (x b) * y c := by + simp [dotProduct, Matrix.mulVec, Matrix.single_apply, ite_mul, ite_and] + + + +theorem rowThreePrewedge_bilinear {β : Type*} [Fintype β] + (Q : ℕ) (t : PairLabel Q) (ℓ : ℝ) (p : β → PairLabel Q) + (i j : β → Orbital Q) (a : β → ℝ) (x y : PairLabel Q × Orbital Q → ℝ) : + star (fun b => (x b : ℂ)) ⬝ᵥ (rowThreePrewedge Q t ℓ p i j a *ᵥ + fun b => (y b : ℂ)) = + ((∑ b, ℓ*a b * (x (t,i b)*y (p b,j b) + x (p b,j b)*y (t,i b))) + + ∑ b, ∑ c, if i b = i c then a b*a c*x (p b,j b)*y (p c,j c) else 0 : ℝ) := by + classical + simp only [rowThreePrewedge, Matrix.add_mulVec, Matrix.smul_mulVec, + Matrix.sum_mulVec, dotProduct_add, dotProduct_sum, dotProduct_smul] + simp_rw [single_bilinear, Complex.star_def, Complex.conj_ofReal] + simp only [Complex.ofReal_add, Complex.ofReal_sum, Complex.ofReal_mul, smul_eq_mul] + apply congrArg₂ (· + ·) + · apply Finset.sum_congr rfl + intro b _ + ring + · apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro c _ + split_ifs <;> simp [single_bilinear, Matrix.zero_mulVec, dotProduct_zero, mul_assoc] + + + +abbrev RowEntry (t : ℕ) := { b : Fin 8 × Fin 9 // t ≤ b.1.val+b.2.val ∧ b.1.val+b.2.val ≤ t+8 } + +def rowP {t : ℕ} (b : RowEntry t) : ℕ := b.val.1.val +def rowJ {t : ℕ} (b : RowEntry t) : ℕ := b.val.2.val +def rowI {t : ℕ} (b : RowEntry t) : ℕ := rowP b+rowJ b-t + +theorem rowEntry_bounds {t : ℕ} (b : RowEntry t) : + rowP b ≤ 7 ∧ rowJ b ≤ 8 ∧ rowI b ≤ 8 ∧ t+rowI b = rowP b+rowJ b := by + have hp := b.val.1.isLt + have hj := b.val.2.isLt + have ht := b.property + dsimp [rowP, rowJ, rowI] + omega + +theorem rowI_eq_iff {t : ℕ} (b c : RowEntry t) : + rowI b = rowI c ↔ rowP b+rowJ b = rowP c+rowJ c := by + have hb := (rowEntry_bounds b).2.2.2 + have hc := (rowEntry_bounds c).2.2.2 + omega + + +def rowFourLevel {t : ℕ} (b c : RowEntry t) : ℕ := rowP b+rowJ b+rowI c + +theorem rowFourLevel_symm {t : ℕ} (b c : RowEntry t) : + rowFourLevel b c = rowFourLevel c b := by + have hb := (rowEntry_bounds b).2.2.2 + have hc := (rowEntry_bounds c).2.2.2 + dsimp [rowFourLevel] + omega + +theorem rowFourLevel_le {t : ℕ} (b c : RowEntry t) : rowFourLevel b c ≤ 23 := by + have hb := rowEntry_bounds b + have hc := rowEntry_bounds c + dsimp [rowFourLevel] + omega + + +def sphericalThreeCoefficient (Q z T p : ℕ) : ℝ := + if z ≤ T then coupledCoefficient (2*Q-2) Q z (T-z) p else 0 + + +def planarThreeCoefficient (z T p : ℕ) : ℝ := + if z ≤ T then polynomialCouplingCoefficient (Real.sqrt (1/3)) (Real.sqrt (2/3)) + z (T-z) p else 0 + +theorem sphericalThreeCoefficient_tendsto (z T p : ℕ) : + Tendsto (fun Q => sphericalThreeCoefficient Q z T p) atTop + (𝓝 (planarThreeCoefficient z T p)) := by + unfold sphericalThreeCoefficient planarThreeCoefficient + split_ifs + · exact threeCoupling_tendsto z (T-z) p + · exact tendsto_const_nhds + + + +def rowThreeTrace (Q z t : ℕ) (ℓ : ℝ) (a : RowEntry t → ℝ) : ℝ := + ∑ T ∈ Finset.range 16, if z ≤ T ∧ t ≤ T then + let X := ∑ b : RowEntry t, if rowP b+rowJ b=T then + a b*sphericalThreeCoefficient Q z T (rowP b) else 0 + 2*ℓ*sphericalThreeCoefficient Q z T t*X + X^2 + else 0 + + +def planarRowThreeTrace (z t : ℕ) (ℓ : ℝ) (a : RowEntry t → ℝ) : ℝ := + ∑ T ∈ Finset.range 16, if z ≤ T ∧ t ≤ T then + let X := ∑ b : RowEntry t, if rowP b+rowJ b=T then + a b*planarThreeCoefficient z T (rowP b) else 0 + 2*ℓ*planarThreeCoefficient z T t*X + X^2 + else 0 + + + +theorem rowThreeTrace_tendsto (z t : ℕ) (ℓ : ℝ) (a : RowEntry t → ℝ) : + Tendsto (fun Q => rowThreeTrace Q z t ℓ a) atTop (𝓝 (planarRowThreeTrace z t ℓ a)) := by + unfold rowThreeTrace planarRowThreeTrace + apply tendsto_finsetSum + intro T _ + split_ifs + · have hX : Tendsto (fun Q => ∑ b : RowEntry t, if rowP b+rowJ b=T then + a b*sphericalThreeCoefficient Q z T (rowP b) else 0) atTop + (𝓝 (∑ b : RowEntry t, if rowP b+rowJ b=T then + a b*planarThreeCoefficient z T (rowP b) else 0)) := by + apply tendsto_finsetSum + intro b _ + split_ifs + · exact (sphericalThreeCoefficient_tendsto z T (rowP b)).const_mul (a b) + · exact tendsto_const_nhds + exact (((sphericalThreeCoefficient_tendsto z T t).const_mul (2*ℓ)).mul hX).add (hX.pow 2) + · exact tendsto_const_nhds + + + +def rowFourTrace (Q D t : ℕ) (a : RowEntry t → ℝ) : Matrix (CopyLabel D) (CopyLabel D) ℝ := + fun r s => -(∑ b : RowEntry t, ∑ c : RowEntry t, + a b*a c*sphericalCopyCoefficient Q D (rowFourLevel b c) r.val.val (rowP b) (rowJ b) (rowI c) * + sphericalCopyCoefficient Q D (rowFourLevel b c) s.val.val (rowP c) (rowJ c) (rowI b)) + + +def planarRowFourTrace (D t : ℕ) (a : RowEntry t → ℝ) : Matrix (CopyLabel D) (CopyLabel D) ℝ := + fun r s => -(∑ b : RowEntry t, ∑ c : RowEntry t, + a b*a c*planarCopyCoefficient D (rowFourLevel b c) r.val.val (rowP b) (rowJ b) (rowI c) * + planarCopyCoefficient D (rowFourLevel b c) s.val.val (rowP c) (rowJ c) (rowI b)) + + + +theorem rowFourTrace_tendsto (D t : ℕ) (a : RowEntry t → ℝ) (r s : CopyLabel D) : + Tendsto (fun Q => rowFourTrace Q D t a r s) atTop (𝓝 (planarRowFourTrace D t a r s)) := by + unfold rowFourTrace planarRowFourTrace + apply Filter.Tendsto.neg + apply tendsto_finsetSum + intro b _ + apply tendsto_finsetSum + intro c _ + exact ((sphericalCopyCoefficient_tendsto D (rowFourLevel b c) r.val.val + (rowP b) (rowJ b) (rowI c)).const_mul (a b*a c)).mul + (sphericalCopyCoefficient_tendsto D (rowFourLevel b c) s.val.val + (rowP c) (rowJ c) (rowI b)) + + + +theorem rowFourTrace_symmetric (Q D t : ℕ) (a : RowEntry t → ℝ) : + (rowFourTrace Q D t a).IsSymm := by + ext r s + change rowFourTrace Q D t a s r = rowFourTrace Q D t a r s + unfold rowFourTrace + congr 1 + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro c _ + rw [rowFourLevel_symm c b] + ring + +theorem planarRowFourTrace_symmetric (D t : ℕ) (a : RowEntry t → ℝ) : + (planarRowFourTrace D t a).IsSymm := by + ext r s + change planarRowFourTrace D t a s r = planarRowFourTrace D t a r s + unfold planarRowFourTrace + congr 1 + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro c _ + rw [rowFourLevel_symm c b] + ring + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/ScalarAction.lean b/lean/OAI/Analysis/LaughlinFock/ScalarAction.lean new file mode 100644 index 0000000000000000000000000000000000000000..29206ff286bba0683537fa39046284374e9eead9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/ScalarAction.lean @@ -0,0 +1,152 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LadderCalculus + +namespace OAI + +/-! Scalar Action. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators + + + +theorem gridInner_self_eq_zero {n m : ℕ} {f : GridVector} + (hf : GridSupported n m f) (h : gridInner n m f f = 0) : f = 0 := by + funext p q + by_cases hp : p ≤ n + · by_cases hq : q ≤ m + · have hi : f p q * f p q ≤ gridInner n m f f := by + apply le_trans (Finset.single_le_sum (fun a _ => mul_self_nonneg (f p a)) + (Finset.mem_range.mpr (by omega : q < m+1))) + exact Finset.single_le_sum (fun a _ => Finset.sum_nonneg (fun b _ => mul_self_nonneg (f a b))) + (Finset.mem_range.mpr (by omega : p < n+1)) + rw [h] at hi + exact (mul_self_eq_zero.mp (le_antisymm hi (mul_self_nonneg (f p q)))) + · exact hf p q (Or.inr (by omega)) + · exact hf p q (Or.inl (by omega)) + + + +theorem coupledVector_lowest {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) : + gridLower n m (coupledVector n m z (n+m-2*z)) = 0 := by + have hz : 2*z ≤ n+m := by omega + let k := n+m-2*z + have hLR : gridLower n m (gridRaise n m (coupledVector n m z k)) = + spinStep k k ^ 2 • coupledVector n m z k := by + rw [coupledVector_raise hn hm (by rfl : k ≤ n+m-2*z), gridLower_smul] + change spinStep k k • gridLower n m (coupledVector n m z (k-1)) = _ + by_cases hk : k=0 + · simp [hk] + · rw [coupledVector_lower hz (by dsimp [k] at *; omega), + show k-1+1=k by omega, smul_smul, ← pow_two] + have hsq : spinStep k k ^ 2 + (((n+m-2*z : ℕ) : ℝ)-2*k) = 0 := by + rw [spinStep_sq (by omega : k ≤ k+1)] + change (k:ℝ)*((k:ℝ)+1-k) + ((k:ℝ)-2*k) = 0 + ring + have hRL := coupledVector_commutator hn hm k + rw [hLR, ← add_smul, hsq, zero_smul] at hRL + apply gridInner_self_eq_zero (gridLower_supported (coupledVector_supported hn hm k)) + rw [grid_adjoint, hRL, gridInner_zero_right] + + +theorem coupledVector_outside_ladder {n m z k : ℕ} (hz : 2*z ≤ n+m) + (hk : n+m-2*z < k) : coupledVector n m z k = 0 := by + have he : k=(k-1)+1 := by omega + conv_lhs => rw [he, coupledVector_succ hz] + rw [← he, spinStep_cutoff _ _ hk, inv_zero, zero_smul] + + + +theorem coupledVector_lower_all {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) (k : ℕ) : + gridLower n m (coupledVector n m z k) = + spinStep (n+m-2*z) (k+1) • coupledVector n m z (k+1) := by + rcases lt_trichotomy k (n+m-2*z) with hk | rfl | hk + · exact coupledVector_lower (by omega) hk + · rw [coupledVector_lowest hn hm, spinStep_last, zero_smul] + · rw [coupledVector_outside_ladder (by omega) hk, + gridLower_zero, spinStep_cutoff _ _ (by omega), zero_smul] + + +theorem coupledVector_raise_all {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) (k : ℕ) : + gridRaise n m (coupledVector n m z k) = + spinStep (n+m-2*z) k • coupledVector n m z (k-1) := by + by_cases hk : k ≤ n+m-2*z + · exact coupledVector_raise hn hm hk + · rw [coupledVector_outside_ladder (by omega) (by omega), + gridRaise_zero, spinStep_cutoff _ _ (by omega), zero_smul] + + + +theorem grid_highest_eq_of_first {n m z : ℕ} (hz : z ≤ n) {f g : GridVector} + (hf : GridLayer z f) (hg : GridLayer z g) + (hRf : gridRaise n m f = 0) (hRg : gridRaise n m g = 0) + (hfirst : f 0 z = g 0 z) : f = g := by + have hc : ∀ p, p ≤ z → f p (z-p) = g p (z-p) := by + intro p + induction p with + | zero => simpa using fun (_ : 0 ≤ z) => hfirst + | succ p ih => + intro hp + have heF := congrArg (fun h : GridVector => h p (z-(p+1))) hRf + have heG := congrArg (fun h : GridVector => h p (z-(p+1))) hRg + simp only [gridRaise, Pi.zero_apply, + show z-(p+1)+1 = z-p by omega] at heF heG + rw [ih (by omega)] at heF + apply mul_left_cancel₀ (spinStep_pos (by omega : 0 < p+1) (by omega : p+1 ≤ n)).ne' + linarith only [heF, heG] + funext p q + by_cases h : p+q=z + · rw [show q=z-p by omega] + exact hc p (by omega) + · rw [hf p q h, hg p q h] + + + +theorem highestCoefficient_first_ne_zero {n m z : ℕ} (hn : z ≤ n) : + highestCoefficient n m z 0 ≠ 0 := by + have hpos : 0 < highestCoefficient n m z 0 ^ 2 := by + rw [highestCoefficient_sq] + apply div_pos + · simpa [highestWeight] using (show (0:ℝ) < n.descFactorial z by + exact_mod_cast Nat.descFactorial_pos.mpr hn) + · exact_mod_cast highestTotal_pos (m := m) hn + exact fun h => by simp [h] at hpos + + + +theorem grid_highest_unique {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) + {f : GridVector} (hf : GridLayer z f) (hRf : gridRaise n m f = 0) : + f = (f 0 z / highestCoefficient n m z 0) • coupledVector n m z 0 := by + apply grid_highest_eq_of_first (m := m) hn hf + · intro p q hpq + simp [coupledVector_layer n m z 0 p q (by simpa using hpq)] + · exact hRf + · rw [gridRaise_smul, coupledVector_highest hn hm, smul_zero] + · simp only [Pi.smul_apply, smul_eq_mul, coupledVector, zero_add, add_zero, + ite_true, coupledCoefficient] + exact (div_mul_cancel₀ _ (highestCoefficient_first_ne_zero hn)).symm + + + +theorem coupledVector_intertwiner {n m z : ℕ} (hn : z ≤ n) (hm : z ≤ m) + (A : GridVector →ₗ[ℝ] GridVector) + (hL : ∀ f, A (gridLower n m f) = gridLower n m (A f)) + (hR : ∀ f, A (gridRaise n m f) = gridRaise n m (A f)) + (hLayer : ∀ T f, GridLayer T f → GridLayer T (A f)) (k : ℕ) : + A (coupledVector n m z k) = + (A (coupledVector n m z 0) 0 z / highestCoefficient n m z 0) • + coupledVector n m z k := by + induction k with + | zero => + apply grid_highest_unique hn hm + · exact hLayer z _ (by simpa using coupledVector_layer n m z 0) + · rw [← hR, coupledVector_highest hn hm, map_zero] + | succ k ih => + rw [coupledVector_succ (by omega : 2*z ≤ n+m), map_smul, hL, ih, + gridLower_smul] + exact smul_comm _ _ _ + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0801.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0801.lean new file mode 100644 index 0000000000000000000000000000000000000000..6d4b97dd0f5d879e5f1ce9ed1a59bb0c3fb41e24 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0801.lean @@ -0,0 +1,605 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0801. -/ +namespace LaughlinFock + +def collectedFourData_8_0_0 : List CollectedFourTerm := [ + ⟨0, 0, 8, 0, 8, 0, 41940658018787013902275678342080624241881907200000000⟩, + ⟨0, 0, 8, 1, 7, 0, 35046233420828178343039045178545207712415744000000000⟩, + ⟨0, 0, 8, 2, 6, 0, 1907094087379744159052364983198900205649920000000000⟩, + ⟨0, 0, 8, 3, 5, 0, 30343332383216751944681971116542101882404864000000000⟩, + ⟨0, 0, 8, 4, 4, 0, -43412031738016965629236588166396890765590528000000000⟩, + ⟨0, 0, 8, 5, 3, 0, 60726233668553150206446532264453826087485440000000000⟩, + ⟨0, 0, 8, 6, 2, 0, -216558649591462986513861843664125416308526284800000000⟩, + ⟨0, 0, 8, 7, 1, 0, 404917130828636902450377864525641362496815104000000000⟩ +] + +def collectedFourData_8_0_1 : List CollectedFourTerm := [ + ⟨0, 1, 7, 0, 7, 1, -69493449615571622927620712094288167986790400000000⟩, + ⟨0, 1, 8, 0, 8, 1, 9370486522373024539551647613122608605482188800000000⟩, + ⟨0, 1, 7, 1, 6, 1, -4809939206961979278452085678481170541156761600000000⟩, + ⟨0, 1, 8, 1, 7, 1, 7830116966278998007712598742737380941234176000000000⟩, + ⟨0, 1, 7, 2, 5, 1, 487824334990969371778255554827705168953344000000000⟩, + ⟨0, 1, 8, 2, 6, 1, 426087722197497709061253699092621222215680000000000⟩, + ⟨0, 1, 7, 3, 4, 1, -1960027415575781707238044874615807843657318400000000⟩, + ⟨0, 1, 8, 3, 5, 1, 6779383075331177603552916386291899648966656000000000⟩, + ⟨0, 1, 7, 4, 3, 1, 6951803562007991716369381194739755602726092800000000⟩, + ⟨0, 1, 8, 4, 4, 1, -9699224512111815194597955140743338248896512000000000⟩, + ⟨0, 1, 7, 5, 2, 1, -13503210852524472758065276354065815613682483200000000⟩, + ⟨0, 1, 8, 5, 3, 1, 13567606733560486062928640524791381240053760000000000⟩, + ⟨0, 1, 7, 6, 1, 1, 37099634559392832280277725630112527548835430400000000⟩, + ⟨0, 1, 8, 6, 2, 1, -48384074145692090436824756909183027683472179200000000⟩, + ⟨0, 1, 7, 7, 0, 1, -125755230914357467900211309832237170062000128000000000⟩, + ⟨0, 1, 8, 7, 1, 1, 90467596273956427279293957043366031435759616000000000⟩ +] + +def collectedFourData_8_0_2 : List CollectedFourTerm := [ + ⟨0, 2, 6, 0, 6, 2, -2147203936518995075356167686177062395057065164800000⟩, + ⟨0, 2, 7, 0, 7, 2, 39358572524714214670101390748769016044165529600000⟩, + ⟨0, 2, 8, 0, 8, 2, -2653552064423893194743671716174719001460054425600000⟩, + ⟨0, 2, 6, 1, 5, 2, 1350246963975448045719753656718068726016403046400000⟩, + ⟨0, 2, 7, 1, 6, 2, 2724175331112928451326049556653957318955132518400000⟩, + ⟨0, 2, 8, 1, 7, 2, -2217347305387123836434260137903066188781453312000000⟩, + ⟨0, 2, 6, 2, 4, 2, -484622589941828988092109980159342030763746918400000⟩, + ⟨0, 2, 7, 2, 5, 2, -276286032342252992501874756951121442012921856000000⟩, + ⟨0, 2, 8, 2, 6, 2, -120660325604578579950633735543660732387164160000000⟩, + ⟨0, 2, 6, 3, 3, 2, -735701909855200638403433988196913056938196992000000⟩, + ⟨0, 2, 7, 3, 4, 2, 1110088527956477957063602802924003795855317401600000⟩, + ⟨0, 2, 8, 3, 5, 2, -1919798498414543284132445437998697531752579072000000⟩, + ⟨0, 2, 6, 4, 2, 2, 2237044943826591039217729618099007879808811008000000⟩, + ⟨0, 2, 7, 4, 3, 2, -3937249714706187001467801211853021428745188147200000⟩, + ⟨0, 2, 8, 4, 4, 2, 2746644708999301796925495836962641141294956544000000⟩, + ⟨0, 2, 6, 5, 1, 2, -3456888801974118205019534746285539036260990976000000⟩, + ⟨0, 2, 7, 5, 2, 2, 7647729485233453730019146678098739892602064076800000⟩, + ⟨0, 2, 8, 5, 3, 2, -3842100489784765549052791521627530773785477120000000⟩, + ⟨0, 2, 6, 6, 0, 2, 5070580432029788411321584417529292626569514188800000⟩, + ⟨0, 2, 7, 6, 1, 2, -21011889113633343993508145616811513568894228889600000⟩, + ⟨0, 2, 8, 6, 2, 2, 13701493463332572280830560055941526210908415590400000⟩, + ⟨0, 2, 7, 7, 0, 2, 71223207420053882809865495579060421231768502272000000⟩, + ⟨0, 2, 8, 7, 1, 2, -25618784711237211263298204170071725614240366592000000⟩ +] + +def collectedFourData_8_0_3 : List CollectedFourTerm := [ + ⟨0, 3, 5, 0, 5, 3, -3405917384732218558857107050292510092431458304000000⟩, + ⟨0, 3, 6, 0, 6, 3, -3936929951861267302893079633416545652355104768000000⟩, + ⟨0, 3, 7, 0, 7, 3, 36082260375848691665373120557298415218720768000000⟩, + ⟨0, 3, 8, 0, 8, 3, -1621775560233921460288806885582370434692677632000000⟩, + ⟨0, 3, 5, 1, 4, 3, -1822670291060903661322427649845449172535214080000000⟩, + ⟨0, 3, 6, 1, 5, 3, 2475697638437920653253238032359257840365338624000000⟩, + ⟨0, 3, 7, 1, 6, 3, 2497407738681554998862680053742708533674115072000000⟩, + ⟨0, 3, 8, 1, 7, 3, -1355179616273369445097311638311582533565808640000000⟩, + ⟨0, 3, 5, 2, 3, 3, -2689151050611127298840360884173881230510522368000000⟩, + ⟨0, 3, 6, 2, 4, 3, -888562635919743326007141737395121919721734144000000⟩, + ⟨0, 3, 7, 2, 5, 3, -253287248944903420947487134215333223050772480000000⟩, + ⟨0, 3, 8, 2, 6, 3, -73744159678983844195558174507865394590515200000000⟩, + ⟨0, 3, 5, 3, 2, 3, 7305708575586242187609917970437210298982072320000000⟩, + ⟨0, 3, 6, 3, 3, 3, -1348920256380525979051392829720436021101854720000000⟩, + ⟨0, 3, 7, 3, 4, 3, 1017681809491871700646171087512411288033558528000000⟩, + ⟨0, 3, 8, 3, 5, 3, -1173326247125453839825964311365414339571875840000000⟩, + ⟨0, 3, 5, 4, 1, 3, -2024983185372713935683035686785851832045404160000000⟩, + ⟨0, 3, 6, 4, 2, 3, 4101654758182212021353552216048103220083425280000000⟩, + ⟨0, 3, 7, 4, 3, 3, -3609502587563575768060005076911533139035160576000000⟩, + ⟨0, 3, 8, 4, 4, 3, 1678671137235806495656764855042830388355399680000000⟩, + ⟨0, 3, 5, 5, 0, 3, -23182059516497476995309254795177413340395732992000000⟩, + ⟨0, 3, 6, 5, 1, 3, -6338256386959322028672286514042406585929564160000000⟩, + ⟨0, 3, 7, 5, 2, 3, 7011112163607423219748602951784443190752313344000000⟩, + ⟨0, 3, 8, 5, 3, 3, -2348182557951247938506349736874652610225766400000000⟩, + ⟨0, 3, 6, 6, 0, 3, 9296983689654819123302832285820571905695940608000000⟩, + ⟨0, 3, 7, 6, 1, 3, -19262803637263872595502258514929675386453229568000000⟩, + ⟨0, 3, 8, 6, 2, 3, 8373963162604044251532992343383172685536165888000000⟩, + ⟨0, 3, 7, 7, 0, 3, 65294398401257132985451906997727571243444469760000000⟩, + ⟨0, 3, 8, 7, 1, 3, -15657472670165726210557081815186789233841930240000000⟩ +] + +def collectedFourData_8_0_4 : List CollectedFourTerm := [ + ⟨0, 4, 4, 0, 4, 4, 7868486972720448126363840071658653132422234767360000⟩, + ⟨0, 4, 5, 0, 5, 4, -41386465803418885017704581618487431848604257484800000⟩, + ⟨0, 4, 6, 0, 6, 4, -23919490465851726415365256152115625848126360780800000⟩, + ⟨0, 4, 7, 0, 7, 4, 146149291215855130169674444658979554823713587200000⟩, + ⟨0, 4, 8, 0, 8, 4, -4926687231560579698911450472780883313043282329600000⟩, + ⟨0, 4, 4, 1, 3, 4, -4691517032029611061731348003969250659210048307200000⟩, + ⟨0, 4, 5, 1, 4, 4, -22147889437967218631966648955209455956494647296000000⟩, + ⟨0, 4, 6, 1, 5, 4, 15041523924232175116342876972955419190497797734400000⟩, + ⟨0, 4, 7, 1, 6, 4, 10115618231323618109058809443423967611389267148800000⟩, + ⟨0, 4, 8, 1, 7, 4, -4116812631583968628342391189467575360675643392000000⟩, + ⟨0, 4, 4, 2, 2, 4, 3090736001241811397134801433408771911134247649280000⟩, + ⟨0, 4, 5, 2, 3, 4, -32676793188010820192573666412633084684886710681600000⟩, + ⟨0, 4, 6, 2, 4, 4, -5398614087138155805659285109216209871533663846400000⟩, + ⟨0, 4, 7, 2, 5, 4, -1025926633246318336932908970660593457841569792000000⟩, + ⟨0, 4, 8, 2, 6, 4, -224022619899519601034222430426875923330498560000000⟩, + ⟨0, 4, 4, 3, 1, 4, -6862142110944621329792671972843612538518445752320000⟩, + ⟨0, 4, 5, 3, 2, 4, 88774160961339987875043982067967014349658128384000000⟩, + ⟨0, 4, 6, 3, 3, 4, -8195595452856371939776165245015993661765189632000000⟩, + ⟨0, 4, 7, 3, 4, 4, 4122066455683005289729653081671908805838058291200000⟩, + ⟨0, 4, 8, 3, 5, 4, -3564372026505371466219577451348832749252247552000000⟩, + ⟨0, 4, 4, 4, 0, 4, 11462035941234870081455580537616960309924661821440000⟩, + ⟨0, 4, 5, 4, 1, 4, -24606262538724253486161346685878148456138145792000000⟩, + ⟨0, 4, 6, 4, 2, 4, 24920304166491822278520765058213647716469178368000000⟩, + ⟨0, 4, 7, 4, 3, 4, -14620099719897432008757897008842233731361433190400000⟩, + ⟨0, 4, 8, 4, 4, 4, 5099526630316242244196106198804698447430549504000000⟩, + ⟨0, 4, 5, 5, 0, 4, -281693125538855768379121455467704925744393512550400000⟩, + ⟨0, 4, 6, 5, 1, 4, -38509159439405690892051510430939119653429968896000000⟩, + ⟨0, 4, 7, 5, 2, 4, 28398139769312724773511283340127514522191239577600000⟩, + ⟨0, 4, 8, 5, 3, 4, -7133392134706371272185488370806408530016337920000000⟩, + ⟨0, 4, 6, 6, 0, 4, 56485412604494779029957072595596891337234631884800000⟩, + ⟨0, 4, 7, 6, 1, 4, -78022969434050975871965882618129007971786765107200000⟩, + ⟨0, 4, 8, 6, 2, 4, 25438721856684862304114501808358761301274945126400000⟩, + ⟨0, 4, 7, 7, 0, 4, 264471514459130932168502754180728448845824917504000000⟩, + ⟨0, 4, 8, 7, 1, 4, -47564824982001693238229586393115277791825231872000000⟩ +] + +def collectedFourData_8_0_5 : List CollectedFourTerm := [ + ⟨0, 5, 3, 0, 3, 5, -3405917384732218558857107050292510092431458304000000⟩, + ⟨0, 5, 4, 0, 4, 5, -41386465803418885017704581618487431848604257484800000⟩, + ⟨0, 5, 5, 0, 5, 5, 108841735243120329289033773424653365172378796032000000⟩, + ⟨0, 5, 6, 0, 6, 5, 41937040654797953687638076856055035874611560448000000⟩, + ⟨0, 5, 7, 0, 7, 5, -192178072610052707323949566192675504703668224000000⟩, + ⟨0, 5, 8, 0, 8, 5, 5182652607547666857763974124469703548354533785600000⟩, + ⟨0, 5, 3, 1, 2, 5, 366861389663309390041885574967791496206902886400000⟩, + ⟨0, 5, 4, 1, 3, 5, 24676320858814373716735470182516118089153642496000000⟩, + ⟨0, 5, 5, 1, 4, 5, 58246450176521021188532985931447928059739504640000000⟩, + ⟨0, 5, 6, 1, 5, 5, -26371673812248965557915249758164356966712868864000000⟩, + ⟨0, 5, 7, 1, 6, 5, -13301467278987301235585289575287663378506448896000000⟩, + ⟨0, 5, 8, 1, 7, 5, 4330701081080282662847216417112593247881920512000000⟩, + ⟨0, 5, 3, 2, 1, 5, 2871919469078191987793699837854444331626974412800000⟩, + ⟨0, 5, 4, 2, 2, 5, -16256573883424082223985572122140628654458562150400000⟩, + ⟨0, 5, 5, 2, 3, 5, 85936279015877343450450765230599524085760262144000000⟩, + ⟨0, 5, 6, 2, 4, 5, 9465163932948186754279669621833371281558339584000000⟩, + ⟨0, 5, 7, 2, 5, 5, 1349035642775725918114712400049974385720688640000000⟩, + ⟨0, 5, 8, 2, 6, 5, 235661685144996765099596493696094372532060160000000⟩, + ⟨0, 5, 3, 3, 0, 5, -29625483497847203503306262342805725829515968512000000⟩, + ⟨0, 5, 4, 3, 1, 5, 36093318931253215171951014704208489932985571737600000⟩, + ⟨0, 5, 5, 3, 2, 5, -233466026543057028807382176031980446437406146560000000⟩, + ⟨0, 5, 6, 3, 3, 5, 14368994196903619709091557788993320132720721920000000⟩, + ⟨0, 5, 7, 3, 4, 5, -5420284833634361678044974915229203907586555904000000⟩, + ⟨0, 5, 8, 3, 5, 5, 3749558498274415541551711859430149712638902272000000⟩, + ⟨0, 5, 4, 4, 0, 5, -60287722425429081168127310238928620336352277299200000⟩, + ⟨0, 5, 5, 4, 1, 5, 64711694042289864861309043427402748832021217280000000⟩, + ⟨0, 5, 6, 4, 2, 5, -43691725392398946630738432891061073159997358080000000⟩, + ⟨0, 5, 7, 4, 3, 5, 19224606306074588073131675241493238849803911168000000⟩, + ⟨0, 5, 8, 4, 4, 5, -5364471854141947215934731392714480076082642944000000⟩, + ⟨0, 5, 5, 5, 0, 5, 740821135473095045089295831877387724399350644736000000⟩, + ⟨0, 5, 6, 5, 1, 5, 67516496110066584192665781067912242291026165760000000⟩, + ⟨0, 5, 7, 5, 2, 5, -37341951652142838151778659140021603972144955392000000⟩, + ⟨0, 5, 8, 5, 3, 5, 7504006568707101058918335175068766537116549120000000⟩, + ⟨0, 5, 6, 6, 0, 5, -99033507765541980579366786435239797477959794688000000⟩, + ⟨0, 5, 7, 6, 1, 5, 102595802965634236470433753530338478355459866624000000⟩, + ⟨0, 5, 8, 6, 2, 5, -26760387247368635940257367034141031404824585830400000⟩, + ⟨0, 5, 7, 7, 0, 5, -347765120762375667870522780758331704011841863680000000⟩, + ⟨0, 5, 8, 7, 1, 5, 50036049100367639806057020344748488875460001792000000⟩ +] + +def collectedFourData_8_0_6 : List CollectedFourTerm := [ + ⟨0, 6, 2, 0, 2, 6, -2147203936518995075356167686177062395057065164800000⟩, + ⟨0, 6, 3, 0, 3, 6, -3936929951861267302893079633416545652355104768000000⟩, + ⟨0, 6, 4, 0, 4, 6, -23919490465851726415365256152115625848126360780800000⟩, + ⟨0, 6, 5, 0, 5, 6, 41937040654797953687638076856055035874611560448000000⟩, + ⟨0, 6, 6, 0, 6, 6, 12118848814889745837524518584861156144215752704000000⟩, + ⟨0, 6, 7, 0, 7, 6, -44428065903246857233923127567996111354960281600000⟩, + ⟨0, 6, 8, 0, 8, 6, 998445645031918413566783498869878452135342899200000⟩, + ⟨0, 6, 2, 1, 1, 6, 11321175322756401742002052238052035607611100364800000⟩, + ⟨0, 6, 3, 1, 2, 6, 424058316746424901974935338113143683278490828800000⟩, + ⟨0, 6, 4, 1, 3, 6, 14261788487045663189917739850835639032575164416000000⟩, + ⟨0, 6, 5, 1, 4, 6, 22442528535530884214060720582267799709113384960000000⟩, + ⟨0, 6, 6, 1, 5, 6, -7620812602323383445492469103703571934396547072000000⟩, + ⟨0, 6, 7, 1, 6, 6, -3075056674544964840388081838796362230683559526400000⟩, + ⟨0, 6, 8, 1, 7, 6, 834315930811663997763837410944178023336771584000000⟩, + ⟨0, 6, 2, 2, 0, 6, -11967106704851138272289203005738760648266665164800000⟩, + ⟨0, 6, 3, 2, 1, 6, 3319677050251291000582394187989749464687024537600000⟩, + ⟨0, 6, 4, 2, 2, 6, -9395558583305129070345033708642585107159737958400000⟩, + ⟨0, 6, 5, 2, 3, 6, 33111501013474559229063906689872633900371542016000000⟩, + ⟨0, 6, 6, 2, 4, 6, 2735216622835852298017511399230927394813509632000000⟩, + ⟨0, 6, 7, 2, 5, 6, 311872440123191108447720597815436128945176576000000⟩, + ⟨0, 6, 8, 2, 6, 6, 45400570142640234499200065087679608515461120000000⟩, + ⟨0, 6, 3, 3, 0, 6, -34244357729838583042072758087788336616522645504000000⟩, + ⟨0, 6, 4, 3, 1, 6, 20860292883132291067843642014667463470737889689600000⟩, + ⟨0, 6, 5, 3, 2, 6, -89955146569286091591481389059398125280391331840000000⟩, + ⟨0, 6, 6, 3, 3, 6, 4152311788704634486437033522948471183806300160000000⟩, + ⟨0, 6, 7, 3, 4, 6, -1253071011341176766622894803363787624335120793600000⟩, + ⟨0, 6, 8, 3, 5, 6, 722357957765178579393318158174511963417083904000000⟩, + ⟨0, 6, 4, 4, 0, 6, -34843555103558519310425349325607565361669157683200000⟩, + ⟨0, 6, 5, 4, 1, 6, 24933606009041385545297148501728890682521681920000000⟩, + ⟨0, 6, 6, 4, 2, 6, -12625912706875363303947769792583899191013539840000000⟩, + ⟨0, 6, 7, 4, 3, 6, 4444378405559984193194964900996412576283964211200000⟩, + ⟨0, 6, 8, 4, 4, 6, -1033473390221836398028965000414184889917636608000000⟩, + ⟨0, 6, 5, 5, 0, 6, 285440561994646317990626243443666069579370594304000000⟩, + ⟨0, 6, 6, 5, 1, 6, 19510728370276098333844161963756268850490900480000000⟩, + ⟨0, 6, 7, 5, 2, 6, -8632778268744470081351955127820416615325682892800000⟩, + ⟨0, 6, 8, 5, 3, 6, 1445657898795911982893305077885233734185123840000000⟩, + ⟨0, 6, 6, 6, 0, 6, -28618426323830338958514300675041222335056052224000000⟩, + ⟨0, 6, 7, 6, 1, 6, 23718278748703062514454476632549827847254546841600000⟩, + ⟨0, 6, 8, 6, 2, 6, -5155427949693454023528005658222124742635998412800000⟩, + ⟨0, 6, 7, 7, 0, 6, -80396954211482819608299875266601682876248358912000000⟩, + ⟨0, 6, 8, 7, 1, 6, 9639518428479932342807743559286031013111660544000000⟩ +] + +def collectedFourData_8_0_7 : List CollectedFourTerm := [ + ⟨0, 7, 1, 0, 1, 7, -69493449615571622927620712094288167986790400000000⟩, + ⟨0, 7, 2, 0, 2, 7, 39358572524714214670101390748769016044165529600000⟩, + ⟨0, 7, 3, 0, 3, 7, 36082260375848691665373120557298415218720768000000⟩, + ⟨0, 7, 4, 0, 4, 7, 146149291215855130169674444658979554823713587200000⟩, + ⟨0, 7, 5, 0, 5, 7, -192178072610052707323949566192675504703668224000000⟩, + ⟨0, 7, 6, 0, 6, 7, -44428065903246857233923127567996111354960281600000⟩, + ⟨0, 7, 7, 0, 7, 7, 135728859925353368533735675788307031339827200000⟩, + ⟨0, 7, 8, 0, 8, 7, -2614522786296009854766179960244718095512371200000⟩, + ⟨0, 7, 1, 1, 0, 7, 83344459458903659692041790110527003716013260800000⟩, + ⟨0, 7, 2, 1, 1, 7, -207518853904527972989969468441240691917035929600000⟩, + ⟨0, 7, 3, 1, 2, 7, -3886526503260429162614971939303907098676428800000⟩, + ⟨0, 7, 4, 1, 3, 7, -87140245810330095631357851313806797589970944000000⟩, + ⟨0, 7, 5, 1, 4, 7, -102843734586717783611615411750241237970452480000000⟩, + ⟨0, 7, 6, 1, 5, 7, 27938129248408959411129494194152493514804428800000⟩, + ⟨0, 7, 7, 1, 6, 7, 9394375563203040039331209186915206193532108800000⟩, + ⟨0, 7, 8, 1, 7, 7, -2184733864012324371681920207042438731137024000000⟩, + ⟨0, 7, 2, 2, 0, 7, 219358873716237029237039152313022712863365529600000⟩, + ⟨0, 7, 3, 2, 1, 7, -30425090909800718300620355961682673865955737600000⟩, + ⟨0, 7, 4, 2, 2, 7, 57407336058744645451776067462121596634372505600000⟩, + ⟨0, 7, 5, 2, 3, 7, -151734703895166994059812719084350968596267008000000⟩, + ⟨0, 7, 6, 2, 4, 7, -10027386778660222917244859456536392177077452800000⟩, + ⟨0, 7, 7, 2, 5, 7, -952778156767909785574510481192412556296192000000⟩, + ⟨0, 7, 8, 2, 6, 7, -118885615595998257097943325968334921400320000000⟩, + ⟨0, 7, 3, 3, 0, 7, 313852125163563009935204019818664030847893504000000⟩, + ⟨0, 7, 4, 3, 1, 7, -127457439939089963637571230268079840738829926400000⟩, + ⟨0, 7, 5, 3, 2, 7, 412222856432345090297488772799074341402705920000000⟩, + ⟨0, 7, 6, 3, 3, 7, -15222500471557923648193588344265626630488064000000⟩, + ⟨0, 7, 7, 3, 4, 7, 3828163488935897236320514672637086312641331200000⟩, + ⟨0, 7, 8, 3, 5, 7, -1891561498451860606949328781675243235180544000000⟩, + ⟨0, 7, 4, 4, 0, 7, 212895876235143717772732164199210023312477388800000⟩, + ⟨0, 7, 5, 4, 1, 7, -114259191188012251497798564992055906360360960000000⟩, + ⟨0, 7, 6, 4, 2, 7, 46286977451232763142102174865269191329447936000000⟩, + ⟨0, 7, 7, 4, 3, 7, -13577687927653668690449559465637109238752870400000⟩, + ⟨0, 7, 8, 4, 4, 7, 2706246194983603819805484774547677027237888000000⟩, + ⟨0, 7, 5, 5, 0, 7, -1308042155391941459159500652251376037660721152000000⟩, + ⟨0, 7, 6, 5, 1, 7, -71526919684810078072035799354744785120264192000000⟩, + ⟨0, 7, 7, 5, 2, 7, 26373354963431397519900245234564531305945497600000⟩, + ⟨0, 7, 8, 5, 3, 7, -3785589667697827267283463747490441058058240000000⟩, + ⟨0, 7, 6, 6, 0, 7, 104916015554231205385858397123518836527176089600000⟩, + ⟨0, 7, 7, 6, 1, 7, -72459938746015420503370287426690763306775347200000⟩, + ⟨0, 7, 8, 6, 2, 7, 13499967589272180349438103330780771517254860800000⟩, + ⟨0, 7, 7, 7, 0, 7, 245614719316375288684694497266587535937634304000000⟩, + ⟨0, 7, 8, 7, 1, 7, -25241975570312996946912991749374745545539584000000⟩ +] + +def collectedFourData_8_0_8 : List CollectedFourTerm := [ + ⟨0, 8, 0, 0, 0, 8, 41940658018787013902275678342080624241881907200000000⟩, + ⟨0, 8, 1, 0, 1, 8, 9370486522373024539551647613122608605482188800000000⟩, + ⟨0, 8, 2, 0, 2, 8, -2653552064423893194743671716174719001460054425600000⟩, + ⟨0, 8, 3, 0, 3, 8, -1621775560233921460288806885582370434692677632000000⟩, + ⟨0, 8, 4, 0, 4, 8, -4926687231560579698911450472780883313043282329600000⟩, + ⟨0, 8, 5, 0, 5, 8, 5182652607547666857763974124469703548354533785600000⟩, + ⟨0, 8, 6, 0, 6, 8, 998445645031918413566783498869878452135342899200000⟩, + ⟨0, 8, 7, 0, 7, 8, -2614522786296009854766179960244718095512371200000⟩, + ⟨0, 8, 8, 0, 8, 8, 44067733482348023295700216958199414611823820800000⟩, + ⟨0, 8, 1, 1, 0, 8, -11238154651904420327018109773532140601257597337600000⟩, + ⟨0, 8, 2, 1, 1, 8, 13990905865284271695590312132205258116228028825600000⟩, + ⟨0, 8, 3, 1, 2, 8, 174686220639549152597171284925907908659721011200000⟩, + ⟨0, 8, 4, 1, 3, 8, 2937494481274837858591895606912888860355592192000000⟩, + ⟨0, 8, 5, 1, 4, 8, 2773486808285910775750422850954002738721062912000000⟩, + ⟨0, 8, 6, 1, 5, 8, -627862206272054046816285600600411362804996505600000⟩, + ⟨0, 8, 7, 1, 6, 8, -180962316979049160644249531231230614437678284800000⟩, + ⟨0, 8, 8, 1, 7, 8, 36823649101008568082084822578443872492322816000000⟩, + ⟨0, 8, 2, 2, 0, 8, -14789159130045135643318810125341566293671254425600000⟩, + ⟨0, 8, 3, 2, 1, 8, 1367504927391884912398505663349769242738583142400000⟩, + ⟨0, 8, 4, 2, 2, 8, -1935199187116151150954279524134053895964773580800000⟩, + ⟨0, 8, 5, 2, 3, 8, 4091977030040340291669337578197347849150346035200000⟩, + ⟨0, 8, 6, 2, 4, 8, 225348559669626810910312751166532165800925593600000⟩, + ⟨0, 8, 7, 2, 5, 8, 18353209498148125884337306978488424209580032000000⟩, + ⟨0, 8, 8, 2, 6, 8, 2003814864582396412985938290853895083130880000000⟩, + ⟨0, 8, 3, 3, 0, 8, -14106591461172340505456388555327665517096861696000000⟩, + ⟨0, 8, 4, 3, 1, 8, 4296585612501356221063878962727458147616895795200000⟩, + ⟨0, 8, 5, 3, 2, 8, -11116813863123772018170997335911061449550594048000000⟩, + ⟨0, 8, 6, 3, 3, 8, 342099954011560597485877463064966858767597568000000⟩, + ⟨0, 8, 7, 3, 4, 8, -73741285950488900682508349484046240307163955200000⟩, + ⟨0, 8, 8, 3, 5, 8, 31882234270881585181420427570388369980522496000000⟩, + ⟨0, 8, 4, 4, 0, 8, -7176712157641968150376325974143190891766376038400000⟩, + ⟨0, 8, 5, 4, 1, 8, 3081338506024038979848326087762210677246132224000000⟩, + ⟨0, 8, 6, 4, 2, 8, -1040221538306859050172134396354194340610834432000000⟩, + ⟨0, 8, 7, 4, 3, 8, 261544777518872569611045185346223624681842278400000⟩, + ⟨0, 8, 8, 4, 4, 8, -45613729848998065554772310454149589019656192000000⟩, + ⟨0, 8, 5, 5, 0, 8, 35275242359099943226058094279011828058983025868800000⟩, + ⟨0, 8, 6, 5, 1, 8, 1607446554557921267353230018453324542408392704000000⟩, + ⟨0, 8, 7, 5, 2, 8, -508025614750516282062116228630390655554263449600000⟩, + ⟨0, 8, 8, 5, 3, 8, 63806044232636132026785047744585922678620160000000⟩, + ⟨0, 8, 6, 6, 0, 8, -2357810017036273654325773054285191636692710195200000⟩, + ⟨0, 8, 7, 6, 1, 8, 1395783925756548812614297879627730288641258291200000⟩, + ⟨0, 8, 8, 6, 2, 8, -227541705454858560954763467904361019817014067200000⟩, + ⟨0, 8, 7, 7, 0, 8, -4731236088297895887800141305656268027418640384000000⟩, + ⟨0, 8, 8, 7, 1, 8, 425453034041583833987181118585595761426169856000000⟩ +] + +def collectedFourData_8_0_9 : List CollectedFourTerm := [ + ⟨1, 0, 7, 0, 7, 1, 83344459458903659692041790110527003716013260800000⟩, + ⟨1, 0, 8, 0, 8, 1, -11238154651904420327018109773532140601257597337600000⟩, + ⟨1, 0, 7, 1, 6, 1, 5768626905874694390109551037817802065762792243200000⟩, + ⟨1, 0, 8, 1, 7, 1, -9390768045975431972863027115017775611014807552000000⟩, + ⟨1, 0, 7, 2, 5, 1, -585054501332615336219578376870747378169151488000000⟩, + ⟨1, 0, 8, 2, 6, 1, -511012924024837187211262872674009009734287360000000⟩, + ⟨1, 0, 7, 3, 4, 1, 2350688106281479300530419151060146287129971916800000⟩, + ⟨1, 0, 8, 3, 5, 1, -8130608294795459115992144093903813762730688512000000⟩, + ⟨1, 0, 7, 4, 3, 1, -8337394579563515505081143675600141610831681945600000⟩, + ⟨1, 0, 8, 4, 4, 1, 11632414689504379336522940971734811313568743424000000⟩, + ⟨1, 0, 7, 5, 2, 1, 16194588348814358193296358979398905951185954406400000⟩, + ⟨1, 0, 8, 5, 3, 1, -16271819223465366794669964788898419195793899520000000⟩, + ⟨1, 0, 7, 6, 1, 1, -44494107078872245096994384887590658078073998540800000⟩, + ⟨1, 0, 8, 6, 2, 1, 58027692227105068210413406424038198356967056998400000⟩, + ⟨1, 0, 7, 7, 0, 1, 150819995304107368559069543470986967827250937856000000⟩, + ⟨1, 0, 8, 7, 1, 1, -108499044898610401111217453902847549900882706432000000⟩ +] + +def collectedFourData_8_0_10 : List CollectedFourTerm := [ + ⟨1, 1, 6, 0, 6, 2, 11321175322756401742002052238052035607611100364800000⟩, + ⟨1, 1, 7, 0, 7, 2, -207518853904527972989969468441240691917035929600000⟩, + ⟨1, 1, 8, 0, 8, 2, 13990905865284271695590312132205258116228028825600000⟩, + ⟨1, 1, 6, 1, 5, 2, -7119203885667040258099604490668504099078956646400000⟩, + ⟨1, 1, 7, 1, 6, 2, -14363268438980250527273421885319445205576214118400000⟩, + ⟨1, 1, 8, 1, 7, 2, 11691007625677868547991368286733059322976141312000000⟩, + ⟨1, 1, 6, 2, 4, 2, 2555182212917479554040984419084403446370428518400000⟩, + ⟨1, 1, 7, 2, 5, 2, 1456723582784713797733524614488922207715065856000000⟩, + ⟨1, 1, 8, 2, 6, 2, 636183958792878762863194331567849033863004160000000⟩, + ⟨1, 1, 6, 3, 3, 2, 3879002904707915393009336874464775345109204992000000⟩, + ⟨1, 1, 7, 3, 4, 2, -5852963770711995779720207169511603282464315801600000⟩, + ⟨1, 1, 8, 3, 5, 2, 10122175642128742433787988556179188549861507072000000⟩, + ⟨1, 1, 6, 4, 2, 2, -11794863814847770090256930950759558476629803008000000⟩, + ⟨1, 1, 7, 4, 3, 2, 20759227175190605943687800373030649529585840947200000⟩, + ⟨1, 1, 8, 4, 4, 2, -14481738679332591631371908944700072261314412544000000⟩, + ⟨1, 1, 6, 5, 1, 2, 18226514739847634680477401786008326054374014976000000⟩, + ⟨1, 1, 7, 5, 2, 2, -40322805324074330634224684931644032778205187276800000⟩, + ⟨1, 1, 8, 5, 3, 2, 20257551000497049722657551143525928720788357120000000⟩, + ⟨1, 1, 6, 6, 0, 2, -26734735850107876551382393863510792807570525388800000⟩, + ⟨1, 1, 7, 6, 1, 2, 110785601903936951192061997429355488520143739289600000⟩, + ⟨1, 1, 8, 6, 2, 2, -72241395912053662513872946293337568530934425190400000⟩, + ⟨1, 1, 7, 7, 0, 2, -375525773093859789401858020445556044566754230272000000⟩, + ⟨1, 1, 8, 7, 1, 2, 135075550272167608504899833701051425198641774592000000⟩ +] + +def collectedFourData_8_0_11 : List CollectedFourTerm := [ + ⟨1, 2, 5, 0, 5, 3, 366861389663309390041885574967791496206902886400000⟩, + ⟨1, 2, 6, 0, 6, 3, 424058316746424901974935338113143683278490828800000⟩, + ⟨1, 2, 7, 0, 7, 3, -3886526503260429162614971939303907098676428800000⟩, + ⟨1, 2, 8, 0, 8, 3, 174686220639549152597171284925907908659721011200000⟩, + ⟨1, 2, 5, 1, 4, 3, 196325183597841132131711522847202640582934528000000⟩, + ⟨1, 2, 6, 1, 5, 3, -266664681913568113288041601607576666105079398400000⟩, + ⟨1, 2, 7, 1, 6, 3, -269003140732567225229608595996699524150276915200000⟩, + ⟨1, 2, 8, 1, 7, 3, 145970386568412563972252346822830419108429824000000⟩, + ⟨1, 2, 5, 2, 3, 3, 289656377416597615153428543258434155345398988800000⟩, + ⟨1, 2, 6, 2, 4, 3, 95709697738907295879776635161406157147760230400000⟩, + ⟨1, 2, 7, 2, 5, 3, 27282315345775646817013034040900412891987968000000⟩, + ⟨1, 2, 8, 2, 6, 3, 7943200566361371816101034759197305413304320000000⟩, + ⟨1, 2, 5, 3, 2, 3, -786919381112776992173140728405242101956083712000000⟩, + ⟨1, 2, 6, 3, 3, 3, 145296172484716614510834130417908802809495552000000⟩, + ⟨1, 2, 7, 3, 4, 3, -109617504094161364938816282129103455974640844800000⟩, + ⟨1, 2, 8, 3, 5, 3, 126382424740675980332696088803008412431417344000000⟩, + ⟨1, 2, 5, 4, 1, 3, 218116901120629012790540262439844268428230656000000⟩, + ⟨1, 2, 6, 4, 2, 3, -441801310639881455821180741715174632558952448000000⟩, + ⟨1, 2, 7, 4, 3, 3, 388790151282837202112969024380947164405799321600000⟩, + ⟨1, 2, 8, 4, 4, 3, -180814610757927916299447643004613387236671488000000⟩, + ⟨1, 2, 5, 5, 0, 3, 2497007886216964993592666881358479263895073587200000⟩, + ⟨1, 2, 6, 5, 1, 3, 682712257374692902618892833102086182226886656000000⟩, + ⟨1, 2, 7, 5, 2, 3, -755187534188700314615443081191536939258766950400000⟩, + ⟨1, 2, 8, 5, 3, 3, 252929657147532138782105813374962581624586240000000⟩, + ⟨1, 2, 6, 6, 0, 3, -1001405486625462073241069661370076356844244172800000⟩, + ⟨1, 2, 7, 6, 1, 3, 2074853295871614982453160776323075698903010508800000⟩, + ⟨1, 2, 8, 6, 2, 3, -901984227977337026690944715189361189334076620800000⟩, + ⟨1, 2, 7, 7, 0, 3, -7033051900229306208895758728259589498120175616000000⟩, + ⟨1, 2, 8, 7, 1, 3, 1686512482111747571707221555680079376898064384000000⟩ +] + +def collectedFourData_8_0_12 : List CollectedFourTerm := [ + ⟨1, 3, 4, 0, 4, 4, -4691517032029611061731348003969250659210048307200000⟩, + ⟨1, 3, 5, 0, 5, 4, 24676320858814373716735470182516118089153642496000000⟩, + ⟨1, 3, 6, 0, 6, 4, 14261788487045663189917739850835639032575164416000000⟩, + ⟨1, 3, 7, 0, 7, 4, -87140245810330095631357851313806797589970944000000⟩, + ⟨1, 3, 8, 0, 8, 4, 2937494481274837858591895606912888860355592192000000⟩, + ⟨1, 3, 4, 1, 3, 4, 2797276291888437298601440334636560060822585344000000⟩, + ⟨1, 3, 5, 1, 4, 4, 13205486757742841440211723036591235465656401920000000⟩, + ⟨1, 3, 6, 1, 5, 4, -8968378027805022262357304465785995482615513088000000⟩, + ⟨1, 3, 7, 1, 6, 4, -6031349532165016843662355015801281404548939776000000⟩, + ⟨1, 3, 8, 1, 7, 4, 2454613783528090875474421859538119899836579840000000⟩, + ⟨1, 3, 4, 2, 2, 4, -1842824502551059422995435507144946083216071065600000⟩, + ⟨1, 3, 5, 2, 3, 4, 19483254191708822682681122394116802286014431232000000⟩, + ⟨1, 3, 6, 2, 4, 4, 3218876770969204707692224907743347007530467328000000⟩, + ⟨1, 3, 7, 2, 5, 4, 611699846511126776962217481867445959225507840000000⟩, + ⟨1, 3, 8, 2, 6, 4, 133571541830375228261830463824950556046131200000000⟩, + ⟨1, 3, 4, 3, 1, 4, 4091492646720825209216324788758729371351934566400000⟩, + ⟨1, 3, 5, 3, 2, 4, -52930822608996350238002146177535922075787591680000000⟩, + ⟨1, 3, 6, 3, 3, 4, 4886552622887102443883810146878035440844144640000000⟩, + ⟨1, 3, 7, 3, 4, 4, -2457746330525928274370116378240247847425409024000000⟩, + ⟨1, 3, 8, 3, 5, 4, 2125225869829239073860903285182444711486423040000000⟩, + ⟨1, 3, 4, 4, 0, 4, -6834139400175816193384548707098390582063320268800000⟩, + ⟨1, 3, 5, 4, 1, 4, 14671270371958763292716073137177428806693027840000000⟩, + ⟨1, 3, 6, 4, 2, 4, -14858514965556719397457084468033545047491215360000000⟩, + ⟨1, 3, 7, 4, 3, 4, 8717107505377963338885257783687765404793438208000000⟩, + ⟨1, 3, 8, 4, 4, 4, -3040548471944100587246205645960842416572334080000000⟩, + ⟨1, 3, 5, 5, 0, 4, 167957080040037064961583384087769535911619985408000000⟩, + ⟨1, 3, 6, 5, 1, 4, 22960751924159586340801250231234793643620433920000000⟩, + ⟨1, 3, 7, 5, 2, 4, -16932144244197061712179834823785455379286065152000000⟩, + ⟨1, 3, 8, 5, 3, 4, 4253223118008205025322122127521968919307878400000000⟩, + ⟨1, 3, 6, 6, 0, 4, -33678936778309938302813622880657216768359530496000000⟩, + ⟨1, 3, 7, 6, 1, 4, 46520518018068121798541285099490147666801721344000000⟩, + ⟨1, 3, 8, 6, 2, 4, -15167617011690653767294055783079551817826172928000000⟩, + ⟨1, 3, 7, 7, 0, 4, -157688843976403509045057610704798497068107694080000000⟩, + ⟨1, 3, 8, 7, 1, 4, 28360113869695619971077813265617638319917629440000000⟩ +] + +def collectedFourData_8_0_13 : List CollectedFourTerm := [ + ⟨1, 4, 3, 0, 3, 5, -1822670291060903661322427649845449172535214080000000⟩, + ⟨1, 4, 4, 0, 4, 5, -22147889437967218631966648955209455956494647296000000⟩, + ⟨1, 4, 5, 0, 5, 5, 58246450176521021188532985931447928059739504640000000⟩, + ⟨1, 4, 6, 0, 6, 5, 22442528535530884214060720582267799709113384960000000⟩, + ⟨1, 4, 7, 0, 7, 5, -102843734586717783611615411750241237970452480000000⟩, + ⟨1, 4, 8, 0, 8, 5, 2773486808285910775750422850954002738721062912000000⟩, + ⟨1, 4, 3, 1, 2, 5, 196325183597841132131711522847202640582934528000000⟩, + ⟨1, 4, 4, 1, 3, 5, 13205486757742841440211723036591235465656401920000000⟩, + ⟨1, 4, 5, 1, 4, 5, 31170478406906769043964933511583312655469772800000000⟩, + ⟨1, 4, 6, 1, 5, 5, -14112751706370049224985738891105107568786145280000000⟩, + ⟨1, 4, 7, 1, 6, 5, -7118255230032541505859439419563984568629329920000000⟩, + ⟨1, 4, 8, 1, 7, 5, 2317566549128428215781560238400230020863754240000000⟩, + ⟨1, 4, 3, 2, 1, 5, 1536902309513822226246773038884928992476921856000000⟩, + ⟨1, 4, 4, 2, 2, 5, -8699674978782043592332118452642604682269687808000000⟩, + ⟨1, 4, 5, 2, 3, 5, 45988638300125735163667098810065652626101370880000000⟩, + ⟨1, 4, 6, 2, 4, 5, 5065264700177753448080957187541436406096199680000000⟩, + ⟨1, 4, 7, 2, 5, 5, 721933890320386063728838660215300363701452800000000⟩, + ⟨1, 4, 8, 2, 6, 5, 126113908158962949881373353216581496419123200000000⟩, + ⟨1, 4, 3, 3, 0, 5, -15854021847945255875525938933552665178920714240000000⟩, + ⟨1, 4, 4, 3, 1, 5, 19315271831513785614458311359890919635080445952000000⟩, + ⟨1, 4, 5, 3, 2, 5, -124938905582268765080000220232557724813177651200000000⟩, + ⟨1, 4, 6, 3, 3, 5, 7689540255005883638439208761960496835749478400000000⟩, + ⟨1, 4, 7, 3, 4, 5, -2900655247728530978914417264586850020968366080000000⟩, + ⟨1, 4, 8, 3, 5, 5, 2006569187507475552771281403772693183400509440000000⟩, + ⟨1, 4, 4, 4, 0, 5, -32262861416761929980473096610757505464227856384000000⟩, + ⟨1, 4, 5, 4, 1, 5, 34630341517922043241106018066031091841079705600000000⟩, + ⟨1, 4, 6, 4, 2, 5, -23381544777011086264491931308410052963572121600000000⟩, + ⟨1, 4, 7, 4, 3, 5, 10288011954869889508565570721232867323921039360000000⟩, + ⟨1, 4, 8, 4, 4, 5, -2870787036587404469361332871899176334398586880000000⟩, + ⟨1, 4, 5, 5, 0, 5, 396449039154535154141277342128182817144407326720000000⟩, + ⟨1, 4, 6, 5, 1, 5, 36131326076196862719755729424748345132528435200000000⟩, + ⟨1, 4, 7, 5, 2, 5, -19983475286774926566677383362420469644751011840000000⟩, + ⟨1, 4, 8, 5, 3, 5, 4015755020371302847111993212350581013112422400000000⟩, + ⟨1, 4, 6, 6, 0, 5, -52997595664815116258631127736878895996872949760000000⟩, + ⟨1, 4, 7, 6, 1, 5, 54903951250039476813153680830751097596915220480000000⟩, + ⟨1, 4, 8, 6, 2, 5, -14320770971048883178996275485620313310162321408000000⟩, + ⟨1, 4, 7, 7, 0, 5, -186105851164274574021543442142246948111489433600000000⟩, + ⟨1, 4, 8, 7, 1, 5, 26776697692705501586266614621244425357848739840000000⟩ +] + +def collectedFourData_8_0_14 : List CollectedFourTerm := [ + ⟨1, 5, 2, 0, 2, 6, 1350246963975448045719753656718068726016403046400000⟩, + ⟨1, 5, 3, 0, 3, 6, 2475697638437920653253238032359257840365338624000000⟩, + ⟨1, 5, 4, 0, 4, 6, 15041523924232175116342876972955419190497797734400000⟩, + ⟨1, 5, 5, 0, 5, 6, -26371673812248965557915249758164356966712868864000000⟩, + ⟨1, 5, 6, 0, 6, 6, -7620812602323383445492469103703571934396547072000000⟩, + ⟨1, 5, 7, 0, 7, 6, 27938129248408959411129494194152493514804428800000⟩, + ⟨1, 5, 8, 0, 8, 6, -627862206272054046816285600600411362804996505600000⟩, + ⟨1, 5, 2, 1, 1, 6, -7119203885667040258099604490668504099078956646400000⟩, + ⟨1, 5, 3, 1, 2, 6, -266664681913568113288041601607576666105079398400000⟩, + ⟨1, 5, 4, 1, 3, 6, -8968378027805022262357304465785995482615513088000000⟩, + ⟨1, 5, 5, 1, 4, 6, -14112751706370049224985738891105107568786145280000000⟩, + ⟨1, 5, 6, 1, 5, 6, 4792269101366726414897294063290945063140458496000000⟩, + ⟨1, 5, 7, 1, 6, 6, 1933717551574563767910852484398629373686788915200000⟩, + ⟨1, 5, 8, 1, 7, 6, -524650934834402255268635408585939237744934912000000⟩, + ⟨1, 5, 2, 2, 0, 6, 7525391147517827911492667251574624191949203046400000⟩, + ⟨1, 5, 3, 2, 1, 6, -2087544542111602767903728078222827714591378636800000⟩, + ⟨1, 5, 4, 2, 2, 6, 5908299736320357518759890603986550753435267891200000⟩, + ⟨1, 5, 5, 2, 3, 6, -20821824585788934680536152649179606055951269888000000⟩, + ⟨1, 5, 6, 2, 4, 6, -1720012653659093155407092794268243849511960576000000⟩, + ⟨1, 5, 7, 2, 5, 6, -196117754937912592052677600683898219914067968000000⟩, + ⟨1, 5, 8, 2, 6, 6, -28549678470334737838915731481868349116252160000000⟩, + ⟨1, 5, 3, 3, 0, 6, 21534209802616328763117935204527574483019497472000000⟩, + ⟨1, 5, 4, 3, 1, 6, -13117779198351823002632019276445224847343930572800000⟩, + ⟨1, 5, 5, 3, 2, 6, 56567362551531203779821176667804995926748037120000000⟩, + ⟨1, 5, 6, 3, 3, 6, -2611138276538035804089764802079556782396538880000000⟩, + ⟨1, 5, 7, 3, 4, 6, 787980731561079830278309835654047323583728844800000⟩, + ⟨1, 5, 8, 3, 5, 6, -454247322663339780099322887365274754112028672000000⟩, + ⟨1, 5, 4, 4, 0, 6, 21911008867170506726020910694867595022143429017600000⟩, + ⟨1, 5, 5, 4, 1, 6, -15679239983719306246296607431882559355155906560000000⟩, + ⟨1, 5, 6, 4, 2, 6, 7939674480811327294695674285382386033224581120000000⟩, + ⟨1, 5, 7, 4, 3, 6, -2794801344577510623051290852253278847737895321600000⟩, + ⟨1, 5, 8, 4, 4, 6, 649889041167982881167093306440393551714975744000000⟩, + ⟨1, 5, 5, 5, 0, 6, -179496342044503002404731993470793681106079055872000000⟩, + ⟨1, 5, 6, 5, 1, 6, -12269119527427752671754612114349607541685616640000000⟩, + ⟨1, 5, 7, 5, 2, 6, 5428633233107118954103466488370922396078990950400000⟩, + ⟨1, 5, 8, 5, 3, 6, -909087001750211958859843991256870933359493120000000⟩, + ⟨1, 5, 6, 6, 0, 6, 17996401087151748867129235529216533228192530432000000⟩, + ⟨1, 5, 7, 6, 1, 6, -14914994019188911619652660517552498258003938508800000⟩, + ⟨1, 5, 8, 6, 2, 6, 3241937488412467963884955623012280398648862310400000⟩, + ⟨1, 5, 7, 7, 0, 6, 50556792249978933797302455988959658721585135616000000⟩, + ⟨1, 5, 8, 7, 1, 6, -6061711359071583045697825003906888583916552192000000⟩ +] + +def collectedFourData_8_0_15 : List CollectedFourTerm := [ + ⟨1, 6, 1, 0, 1, 7, -4809939206961979278452085678481170541156761600000000⟩, + ⟨1, 6, 2, 0, 2, 7, 2724175331112928451326049556653957318955132518400000⟩, + ⟨1, 6, 3, 0, 3, 7, 2497407738681554998862680053742708533674115072000000⟩, + ⟨1, 6, 4, 0, 4, 7, 10115618231323618109058809443423967611389267148800000⟩, + ⟨1, 6, 5, 0, 5, 7, -13301467278987301235585289575287663378506448896000000⟩, + ⟨1, 6, 6, 0, 6, 7, -3075056674544964840388081838796362230683559526400000⟩, + ⟨1, 6, 7, 0, 7, 7, 9394375563203040039331209186915206193532108800000⟩, + ⟨1, 6, 8, 0, 8, 7, -180962316979049160644249531231230614437678284800000⟩, + ⟨1, 6, 1, 1, 0, 7, 5768626905874694390109551037817802065762792243200000⟩, + ⟨1, 6, 2, 1, 1, 7, -14363268438980250527273421885319445205576214118400000⟩, + ⟨1, 6, 3, 1, 2, 7, -269003140732567225229608595996699524150276915200000⟩, + ⟨1, 6, 4, 1, 3, 7, -6031349532165016843662355015801281404548939776000000⟩, + ⟨1, 6, 5, 1, 4, 7, -7118255230032541505859439419563984568629329920000000⟩, + ⟨1, 6, 6, 1, 5, 7, 1933717551574563767910852484398629373686788915200000⟩, + ⟨1, 6, 7, 1, 6, 7, 650224957839058977837344685672841260874019635200000⟩, + ⟨1, 6, 8, 1, 7, 7, -151214785385121543161334058257857119147524096000000⟩, + ⟨1, 6, 2, 2, 0, 7, 15182766907088891662972856283341563287031932518400000⟩, + ⟨1, 6, 3, 2, 1, 7, -2105850816904065109738236447398552661572085350400000⟩, + ⟨1, 6, 4, 2, 2, 7, 3973407537022390857345439049958721115748984422400000⟩, + ⟨1, 6, 5, 2, 3, 7, -10502208558640811061885898960723578963238060032000000⟩, + ⟨1, 6, 6, 2, 4, 7, -694038374506633856830949113149919441422857011200000⟩, + ⟨1, 6, 7, 2, 5, 7, -65945855863054643396773913761973856808992768000000⟩, + ⟨1, 6, 8, 2, 6, 7, -8228582503276253942970197058546623085281280000000⟩, + ⟨1, 6, 3, 3, 0, 7, 21723049443703208975091605144787043518058070016000000⟩, + ⟨1, 6, 4, 3, 1, 7, -8821875169147734616399231582812668017021393305600000⟩, + ⟨1, 6, 5, 3, 2, 7, 28531708961466071313103732797905959751704903680000000⟩, + ⟨1, 6, 6, 3, 3, 7, -1053614437780581669945629023482410636993888256000000⟩, + ⟨1, 6, 7, 3, 4, 7, 264963586610718778139287809272130404577234124800000⟩, + ⟨1, 6, 8, 3, 5, 7, -130923070650743331551947857336603685920178176000000⟩, + ⟨1, 6, 4, 4, 0, 7, 14735435177972345530246760968986976389604520755200000⟩, + ⟨1, 6, 5, 4, 1, 7, -7908367860441319892219736054358884279480483840000000⟩, + ⟨1, 6, 6, 4, 2, 7, 3203719902322454508784303212652869714909855744000000⟩, + ⟨1, 6, 7, 4, 3, 7, -939769918810908823342908013784049675258141081600000⟩, + ⟨1, 6, 8, 4, 4, 7, 187310886838269355417550409152086729191063552000000⟩, + ⟨1, 6, 5, 5, 0, 7, -90535198387517850297205826014164251227201732608000000⟩, + ⟨1, 6, 6, 5, 1, 7, -4950684377425097363593437863213550303096864768000000⟩, + ⟨1, 6, 7, 5, 2, 7, 1825412823215345983199960300103832097742284390400000⟩, + ⟨1, 6, 8, 5, 3, 7, -262016870149009296673833096839461979773992960000000⟩, + ⟨1, 6, 6, 6, 0, 7, 7261686668946900000883458394711558876276614758400000⟩, + ⟨1, 6, 7, 6, 1, 7, -5015262621679198215014674943741979488659754188800000⟩, + ⟨1, 6, 8, 6, 2, 7, 934390561406326803773640279088403959726158643200000⟩, + ⟨1, 6, 7, 7, 0, 7, 17000046404115719375115235435929946560676233216000000⟩, + ⟨1, 6, 8, 7, 1, 7, -1747105211044519620319488438562593170402574336000000⟩ +] + +def collectedFourData_8_0_16 : List CollectedFourTerm := [ + ⟨1, 7, 0, 0, 0, 8, 35046233420828178343039045178545207712415744000000000⟩, + ⟨1, 7, 1, 0, 1, 8, 7830116966278998007712598742737380941234176000000000⟩, + ⟨1, 7, 2, 0, 2, 8, -2217347305387123836434260137903066188781453312000000⟩, + ⟨1, 7, 3, 0, 3, 8, -1355179616273369445097311638311582533565808640000000⟩, + ⟨1, 7, 4, 0, 4, 8, -4116812631583968628342391189467575360675643392000000⟩, + ⟨1, 7, 5, 0, 5, 8, 4330701081080282662847216417112593247881920512000000⟩, + ⟨1, 7, 6, 0, 6, 8, 834315930811663997763837410944178023336771584000000⟩, + ⟨1, 7, 7, 0, 7, 8, -2184733864012324371681920207042438731137024000000⟩, + ⟨1, 7, 8, 0, 8, 8, 36823649101008568082084822578443872492322816000000⟩, + ⟨1, 7, 1, 1, 0, 8, -9390768045975431972863027115017775611014807552000000⟩, + ⟨1, 7, 2, 1, 1, 8, 11691007625677868547991368286733059322976141312000000⟩, + ⟨1, 7, 3, 1, 2, 8, 145970386568412563972252346822830419108429824000000⟩, + ⟨1, 7, 4, 1, 3, 8, 2454613783528090875474421859538119899836579840000000⟩, + ⟨1, 7, 5, 1, 4, 8, 2317566549128428215781560238400230020863754240000000⟩, + ⟨1, 7, 6, 1, 5, 8, -524650934834402255268635408585939237744934912000000⟩, + ⟨1, 7, 7, 1, 6, 8, -151214785385121543161334058257857119147524096000000⟩, + ⟨1, 7, 8, 1, 7, 8, 30770385176659181861895381076144071974584320000000⟩, + ⟨1, 7, 2, 2, 0, 8, -12358039846136018032915465340028415642605453312000000⟩, + ⟨1, 7, 3, 2, 1, 8, 1142707319185136058828550101936562378320642048000000⟩, + ⟨1, 7, 4, 2, 2, 8, -1617081029036059857977788062576829017165398016000000⟩, + ⟨1, 7, 5, 2, 3, 8, 3419316456199191220025039125959174956519522304000000⟩, + ⟨1, 7, 6, 2, 4, 8, 188304585485794887405499523347473454357020672000000⟩, + ⟨1, 7, 7, 2, 5, 8, 15336212984673210457459622679901758963056640000000⟩, + ⟨1, 7, 8, 2, 6, 8, 1674417302771515183223958260588203317657600000000⟩, + ⟨1, 7, 3, 3, 0, 8, -11787676218600391265912372676353201209784401920000000⟩, + ⟨1, 7, 4, 3, 1, 8, 3590290410342243640787748631075379112264597504000000⟩, + ⟨1, 7, 5, 3, 2, 8, -9289373890328920270246462483773443311361064960000000⟩, + ⟨1, 7, 6, 3, 3, 8, 285863775341178746636259692887450146161295360000000⟩, + ⟨1, 7, 7, 3, 4, 8, -61619307904402184586656218152994187671240704000000⟩, + ⟨1, 7, 8, 3, 5, 8, 26641265946145477395563418115912346024017920000000⟩, + ⟨1, 7, 4, 4, 0, 8, -5996966698952380609402356532592170492093267968000000⟩, + ⟨1, 7, 5, 4, 1, 8, 2574811975585395337768324500421422896098836480000000⟩, + ⟨1, 7, 6, 4, 2, 8, -869224484378499982931677587167140440063344640000000⟩, + ⟨1, 7, 7, 4, 3, 8, 218550679839573990226908371371904285716512768000000⟩, + ⟨1, 7, 8, 4, 4, 8, -38115506503653502794132811437326448029859840000000⟩, + ⟨1, 7, 5, 5, 0, 8, 29476513628840219718078820229365634137929547776000000⟩, + ⟨1, 7, 6, 5, 1, 8, 1343206087451181491505318274539591565395886080000000⟩, + ⟨1, 7, 7, 5, 2, 8, -424513708638786247764674440799368521336225792000000⟩, + ⟨1, 7, 8, 5, 3, 8, 53317273153773150076799966286683825189683200000000⟩, + ⟨1, 7, 6, 6, 0, 8, -1970220881656304562398056829617316339336085504000000⟩, + ⟨1, 7, 7, 6, 1, 8, 1166337667978216169529900430358814973885415424000000⟩, + ⟨1, 7, 8, 6, 2, 8, -190137210502806014532382588558897362128338944000000⟩, + ⟨1, 7, 7, 7, 0, 8, -3953490768915924280555944946380560163070279680000000⟩, + ⟨1, 7, 8, 7, 1, 8, 355514840371408616733285393006992494291845120000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0802.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0802.lean new file mode 100644 index 0000000000000000000000000000000000000000..3a1c1ad4f2e564012c14779a04104b1fabe1c636 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0802.lean @@ -0,0 +1,651 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0802. -/ +namespace LaughlinFock +def collectedFourData_8_0_17 : List CollectedFourTerm := [ + ⟨2, 0, 6, 0, 6, 2, -11967106704851138272289203005738760648266665164800000⟩, + ⟨2, 0, 7, 0, 7, 2, 219358873716237029237039152313022712863365529600000⟩, + ⟨2, 0, 8, 0, 8, 2, -14789159130045135643318810125341566293671254425600000⟩, + ⟨2, 0, 6, 1, 5, 2, 7525391147517827911492667251574624191949203046400000⟩, + ⟨2, 0, 7, 1, 6, 2, 15182766907088891662972856283341563287031932518400000⟩, + ⟨2, 0, 8, 1, 7, 2, -12358039846136018032915465340028415642605453312000000⟩, + ⟨2, 0, 6, 2, 4, 2, -2700968523193595768960315254936405867640546918400000⟩, + ⟨2, 0, 7, 2, 5, 2, -1539837168638892769747931930814133679324921856000000⟩, + ⟨2, 0, 8, 2, 6, 2, -672481531443624922269026381145194356707164160000000⟩, + ⟨2, 0, 6, 3, 3, 2, -4100320006153301588861703014887060606122196992000000⟩, + ⟨2, 0, 7, 3, 4, 2, 6186905509973564113570434308548218279618517401600000⟩, + ⟨2, 0, 8, 3, 5, 2, -10699697914854575675533478747183333493096579072000000⟩, + ⟨2, 0, 6, 4, 2, 2, 12467821565994836931148368532697599146624811008000000⟩, + ⟨2, 0, 7, 4, 3, 2, -21943648043007777210789874529003194229359588147200000⟩, + ⟨2, 0, 8, 4, 4, 2, 15307996485045877499829601209183963700782956544000000⟩, + ⟨2, 0, 6, 5, 1, 2, -19266431313970032605485852938186714483812990976000000⟩, + ⟨2, 0, 7, 5, 2, 2, 42623429122432299131761516359581570050835664076800000⟩, + ⟨2, 0, 8, 5, 3, 2, -21413348657768894659714403866666253600025477120000000⟩, + ⟨2, 0, 6, 6, 0, 2, 28260090275357903689693050285016626312227114188800000⟩, + ⟨2, 0, 7, 6, 1, 2, -117106491291646244182255132571247262208433428889600000⟩, + ⟨2, 0, 8, 6, 2, 2, 76363139757158667915628547227274111948329215590400000⟩, + ⟨2, 0, 7, 7, 0, 2, 396951453264993602044871766249667058959512502272000000⟩, + ⟨2, 0, 8, 7, 1, 2, -142782306363041870537134391822167027262624366592000000⟩ +] + +def collectedFourData_8_0_18 : List CollectedFourTerm := [ + ⟨2, 1, 5, 0, 5, 3, 2871919469078191987793699837854444331626974412800000⟩, + ⟨2, 1, 6, 0, 6, 3, 3319677050251291000582394187989749464687024537600000⟩, + ⟨2, 1, 7, 0, 7, 3, -30425090909800718300620355961682673865955737600000⟩, + ⟨2, 1, 8, 0, 8, 3, 1367504927391884912398505663349769242738583142400000⟩, + ⟨2, 1, 5, 1, 4, 3, 1536902309513822226246773038884928992476921856000000⟩, + ⟨2, 1, 6, 1, 5, 3, -2087544542111602767903728078222827714591378636800000⟩, + ⟨2, 1, 7, 1, 6, 3, -2105850816904065109738236447398552661572085350400000⟩, + ⟨2, 1, 8, 1, 7, 3, 1142707319185136058828550101936562378320642048000000⟩, + ⟨2, 1, 5, 2, 3, 3, 2267531588453186682417090241599062789783656857600000⟩, + ⟨2, 1, 6, 2, 4, 3, 749249040811359270873182002370035092439223500800000⟩, + ⟨2, 1, 7, 2, 5, 3, 213575521465948428268346551983717232448372736000000⟩, + ⟨2, 1, 8, 2, 6, 3, 62182156520374883432928848067157350301040640000000⟩, + ⟨2, 1, 5, 3, 2, 3, -6160280571599138689096542301945860863110938624000000⟩, + ⟨2, 1, 6, 3, 3, 3, 1137429335162150814908120594086764519886946304000000⟩, + ⟨2, 1, 7, 3, 4, 3, -858124220836384038862036715732649725761526169600000⟩, + ⟨2, 1, 8, 3, 5, 3, 989365892374683863369155905456573764849369088000000⟩, + ⟨2, 1, 5, 4, 1, 3, 1707495507876244696878621261782458204434726912000000⟩, + ⟨2, 1, 6, 4, 2, 3, -3458575421783708533242504068913541369294749696000000⟩, + ⟨2, 1, 7, 4, 3, 3, 3043585496636161189901291408651259408142250803200000⟩, + ⟨2, 1, 8, 4, 4, 3, -1415480112001067065273650081903883806390091776000000⟩, + ⟨2, 1, 5, 5, 0, 3, 19547452430057380023428834425657654133563745894400000⟩, + ⟨2, 1, 6, 5, 1, 3, 5344510703435290838564041662681343767097638912000000⟩, + ⟨2, 1, 7, 5, 2, 3, -5911872558276446440565709262521679815985908940800000⟩, + ⟨2, 1, 8, 5, 3, 3, 1980021956892014250211274007638136827915796480000000⟩, + ⟨2, 1, 6, 6, 0, 3, -7839352939596129338545144265299298076438665625600000⟩, + ⟨2, 1, 7, 6, 1, 3, 16242678416945164493103525710934365721044031897600000⟩, + ⟨2, 1, 8, 6, 2, 3, -7061048499835224861972422783730669534683175321600000⟩, + ⟨2, 1, 7, 7, 0, 3, -55057193938678470862854639918911298761845112832000000⟩, + ⟨2, 1, 8, 7, 1, 3, 13202610491840825298491988750972243098015367168000000⟩ +] + +def collectedFourData_8_0_19 : List CollectedFourTerm := [ + ⟨2, 2, 4, 0, 4, 4, 3090736001241811397134801433408771911134247649280000⟩, + ⟨2, 2, 5, 0, 5, 4, -16256573883424082223985572122140628654458562150400000⟩, + ⟨2, 2, 6, 0, 6, 4, -9395558583305129070345033708642585107159737958400000⟩, + ⟨2, 2, 7, 0, 7, 4, 57407336058744645451776067462121596634372505600000⟩, + ⟨2, 2, 8, 0, 8, 4, -1935199187116151150954279524134053895964773580800000⟩, + ⟨2, 2, 4, 1, 3, 4, -1842824502551059422995435507144946083216071065600000⟩, + ⟨2, 2, 5, 1, 4, 4, -8699674978782043592332118452642604682269687808000000⟩, + ⟨2, 2, 6, 1, 5, 4, 5908299736320357518759890603986550753435267891200000⟩, + ⟨2, 2, 7, 1, 6, 4, 3973407537022390857345439049958721115748984422400000⟩, + ⟨2, 2, 8, 1, 7, 4, -1617081029036059857977788062576829017165398016000000⟩, + ⟨2, 2, 4, 2, 2, 4, 1214038869542601862405029200829372867213199933440000⟩, + ⟨2, 2, 5, 2, 3, 4, -12835420769134237783318116880155495080517225676800000⟩, + ⟨2, 2, 6, 2, 4, 4, -2120571715220135933555474476306547502981788467200000⟩, + ⟨2, 2, 7, 2, 5, 4, -402983240742521727143949684631531503501705216000000⟩, + ⟨2, 2, 8, 2, 6, 4, -87995923335254263179428119500783847609466880000000⟩, + ⟨2, 2, 4, 3, 1, 4, -2695444466193378545394505733482308135017628303360000⟩, + ⟨2, 2, 5, 3, 2, 4, 34870426323955098023034703037165292296268152832000000⟩, + ⟨2, 2, 6, 3, 3, 4, -3219223976042136546786432666662795099856961536000000⟩, + ⟨2, 2, 7, 3, 4, 4, 1619144727348503050484806877127392392671500697600000⟩, + ⟨2, 2, 8, 3, 5, 4, -1400082758265091347502591820634323891515293696000000⟩, + ⟨2, 2, 4, 4, 0, 4, 4502279441260098650443517966126812016032213893120000⟩, + ⟨2, 2, 5, 4, 1, 4, -9665322157628072431040839549684904861122953216000000⟩, + ⟨2, 2, 6, 4, 2, 4, 9788677482253363538284604192061680541933502464000000⟩, + ⟨2, 2, 7, 4, 3, 4, -5742764613157823230712236112306867144479683379200000⟩, + ⟨2, 2, 8, 4, 4, 4, 2003090378144255618207735205801107770249838592000000⟩, + ⟨2, 2, 5, 5, 0, 4, -110648856307918138688677292203460482748665508659200000⟩, + ⟨2, 2, 6, 5, 1, 4, -15126370021272538950117100672647280586662084608000000⟩, + ⟨2, 2, 7, 5, 2, 4, 11154768795781039142781781302631157704294190284800000⟩, + ⟨2, 2, 8, 5, 3, 4, -2801991279663958933463160385218335473831772160000000⟩, + ⟨2, 2, 6, 6, 0, 4, 22187429284304991875552292503444226030877173350400000⟩, + ⟨2, 2, 7, 6, 1, 4, -30647366055209496023508019885389789370720557465600000⟩, + ⟨2, 2, 8, 6, 2, 4, 9992311576624403306582778891837807970135257907200000⟩, + ⟨2, 2, 7, 7, 0, 4, 103884219911108095820314563232735978875720302592000000⟩, + ⟨2, 2, 8, 7, 1, 4, -18683428907528740300142610403413531901669933056000000⟩ +] + +def collectedFourData_8_0_20 : List CollectedFourTerm := [ + ⟨2, 3, 3, 0, 3, 5, -2689151050611127298840360884173881230510522368000000⟩, + ⟨2, 3, 4, 0, 4, 5, -32676793188010820192573666412633084684886710681600000⟩, + ⟨2, 3, 5, 0, 5, 5, 85936279015877343450450765230599524085760262144000000⟩, + ⟨2, 3, 6, 0, 6, 5, 33111501013474559229063906689872633900371542016000000⟩, + ⟨2, 3, 7, 0, 7, 5, -151734703895166994059812719084350968596267008000000⟩, + ⟨2, 3, 8, 0, 8, 5, 4091977030040340291669337578197347849150346035200000⟩, + ⟨2, 3, 3, 1, 2, 5, 289656377416597615153428543258434155345398988800000⟩, + ⟨2, 3, 4, 1, 3, 5, 19483254191708822682681122394116802286014431232000000⟩, + ⟨2, 3, 5, 1, 4, 5, 45988638300125735163667098810065652626101370880000000⟩, + ⟨2, 3, 6, 1, 5, 5, -20821824585788934680536152649179606055951269888000000⟩, + ⟨2, 3, 7, 1, 6, 5, -10502208558640811061885898960723578963238060032000000⟩, + ⟨2, 3, 8, 1, 7, 5, 3419316456199191220025039125959174956519522304000000⟩, + ⟨2, 3, 3, 2, 1, 5, 2267531588453186682417090241599062789783656857600000⟩, + ⟨2, 3, 4, 2, 2, 5, -12835420769134237783318116880155495080517225676800000⟩, + ⟨2, 3, 5, 2, 3, 5, 67851215662803526043787983531209999314371739648000000⟩, + ⟨2, 3, 6, 2, 4, 5, 7473245137593189867184614441231036753408688128000000⟩, + ⟨2, 3, 7, 2, 5, 5, 1065134648404698185825294444136991873176698880000000⟩, + ⟨2, 3, 8, 2, 6, 5, 186067304814054411724873406587541385872670720000000⟩, + ⟨2, 3, 3, 3, 0, 5, -23390878601526051087370653897916072257392738304000000⟩, + ⟨2, 3, 4, 3, 1, 5, 28497575120029869906808643682698182988586496819200000⟩, + ⟨2, 3, 5, 3, 2, 5, -184333716776171389644276854147929953980142059520000000⟩, + ⟨2, 3, 6, 3, 3, 5, 11345077251151986305828059971485885750984048640000000⟩, + ⟨2, 3, 7, 3, 4, 5, -4279600180650124769778766665269789396532461568000000⟩, + ⟨2, 3, 8, 3, 5, 5, 2960473797797442828647601152446245968988340224000000⟩, + ⟨2, 3, 4, 4, 0, 5, -47600330185942287117150342336985401249461855846400000⟩, + ⟨2, 3, 5, 4, 1, 5, 51093288639569116191063869874590268140562677760000000⟩, + ⟨2, 3, 6, 4, 2, 5, -34496916974167924397263442974560315925447311360000000⟩, + ⟨2, 3, 7, 4, 3, 5, 15178838593476451247427053709096983540589920256000000⟩, + ⟨2, 3, 8, 4, 4, 5, -4235532895544334085918928514213439237414453248000000⟩, + ⟨2, 3, 5, 5, 0, 5, 584917280643033506538554027679483091212998541312000000⟩, + ⟨2, 3, 6, 5, 1, 5, 53307827506873743862263034097180429130840145920000000⟩, + ⟨2, 3, 7, 5, 2, 5, -29483436376753146375935597251758180102794379264000000⟩, + ⟨2, 3, 8, 5, 3, 5, 5924808170183509865189397522861468526093271040000000⟩, + ⟨2, 3, 6, 6, 0, 5, -78192167152155060917784250424376965750216196096000000⟩, + ⟨2, 3, 7, 6, 1, 5, 81004786719164386128024556970491574334215159808000000⟩, + ⟨2, 3, 8, 6, 2, 5, -21128734303307202259541052098998234808767532236800000⟩, + ⟨2, 3, 7, 7, 0, 5, -274578867959703964340433873481975718566491586560000000⟩, + ⟨2, 3, 8, 7, 1, 5, 39506094484221492183006518496638826540448088064000000⟩ +] + +def collectedFourData_8_0_21 : List CollectedFourTerm := [ + ⟨2, 4, 2, 0, 2, 6, -484622589941828988092109980159342030763746918400000⟩, + ⟨2, 4, 3, 0, 3, 6, -888562635919743326007141737395121919721734144000000⟩, + ⟨2, 4, 4, 0, 4, 6, -5398614087138155805659285109216209871533663846400000⟩, + ⟨2, 4, 5, 0, 5, 6, 9465163932948186754279669621833371281558339584000000⟩, + ⟨2, 4, 6, 0, 6, 6, 2735216622835852298017511399230927394813509632000000⟩, + ⟨2, 4, 7, 0, 7, 6, -10027386778660222917244859456536392177077452800000⟩, + ⟨2, 4, 8, 0, 8, 6, 225348559669626810910312751166532165800925593600000⟩, + ⟨2, 4, 2, 1, 1, 6, 2555182212917479554040984419084403446370428518400000⟩, + ⟨2, 4, 3, 1, 2, 6, 95709697738907295879776635161406157147760230400000⟩, + ⟨2, 4, 4, 1, 3, 6, 3218876770969204707692224907743347007530467328000000⟩, + ⟨2, 4, 5, 1, 4, 6, 5065264700177753448080957187541436406096199680000000⟩, + ⟨2, 4, 6, 1, 5, 6, -1720012653659093155407092794268243849511960576000000⟩, + ⟨2, 4, 7, 1, 6, 6, -694038374506633856830949113149919441422857011200000⟩, + ⟨2, 4, 8, 1, 7, 6, 188304585485794887405499523347473454357020672000000⟩, + ⟨2, 4, 2, 2, 0, 6, -2700968523193595768960315254936405867640546918400000⟩, + ⟨2, 4, 3, 2, 1, 6, 749249040811359270873182002370035092439223500800000⟩, + ⟨2, 4, 4, 2, 2, 6, -2120571715220135933555474476306547502981788467200000⟩, + ⟨2, 4, 5, 2, 3, 6, 7473245137593189867184614441231036753408688128000000⟩, + ⟨2, 4, 6, 2, 4, 6, 617336686686410240707622653503924627943981056000000⟩, + ⟨2, 4, 7, 2, 5, 6, 70389415319815760017576646241548627878084608000000⟩, + ⟨2, 4, 8, 2, 6, 6, 10246880379248663188098483079121204108328960000000⟩, + ⟨2, 4, 3, 3, 0, 6, -7728930192272891188914840162413568094510252032000000⟩, + ⟨2, 4, 4, 3, 1, 6, 4708155099770255149826486163896486248743488716800000⟩, + ⟨2, 4, 5, 3, 2, 6, -20302820504175526249722595395852517151311134720000000⟩, + ⟨2, 4, 6, 3, 3, 6, 937174182229908014655464808060055134173921280000000⟩, + ⟨2, 4, 7, 3, 4, 6, -282817346116492606739843927969728219933625548800000⟩, + ⟨2, 4, 8, 3, 5, 6, 163035740761904236297338850691701376110559232000000⟩, + ⟨2, 4, 4, 4, 0, 6, -7864168665992002995527710224006764827084691865600000⟩, + ⟨2, 4, 5, 4, 1, 6, 5627499333053636013671561477572278598615695360000000⟩, + ⟨2, 4, 6, 4, 2, 6, -2849660627161977883593570298141068780864798720000000⟩, + ⟨2, 4, 7, 4, 3, 6, 1003093435584786203429165990656622934642760089600000⟩, + ⟨2, 4, 8, 4, 4, 6, -233254299923289170011165813122686894802468864000000⟩, + ⟨2, 4, 5, 5, 0, 6, 64423756903387627666398989600278846413767442432000000⟩, + ⟨2, 4, 6, 5, 1, 6, 4403559230514235338383442917997891379097763840000000⟩, + ⟨2, 4, 7, 5, 2, 6, -1948412673728103257867052141516724925798704742400000⟩, + ⟨2, 4, 8, 5, 3, 6, 326284086559627808741435058852353589085470720000000⟩, + ⟨2, 4, 6, 6, 0, 6, -6459160981047028980524546824879624032765345792000000⟩, + ⟨2, 4, 7, 6, 1, 6, 5353200728009673416475754858762779960198089932800000⟩, + ⟨2, 4, 8, 6, 2, 6, -1163576874439486993676859801152231907862668902400000⟩, + ⟨2, 4, 7, 7, 0, 6, -18145542447434295513697360157412893783066935296000000⟩, + ⟨2, 4, 8, 7, 1, 6, 2175633300195660159745716246253686786833252352000000⟩ +] + +def collectedFourData_8_0_22 : List CollectedFourTerm := [ + ⟨2, 5, 1, 0, 1, 7, 487824334990969371778255554827705168953344000000000⟩, + ⟨2, 5, 2, 0, 2, 7, -276286032342252992501874756951121442012921856000000⟩, + ⟨2, 5, 3, 0, 3, 7, -253287248944903420947487134215333223050772480000000⟩, + ⟨2, 5, 4, 0, 4, 7, -1025926633246318336932908970660593457841569792000000⟩, + ⟨2, 5, 5, 0, 5, 7, 1349035642775725918114712400049974385720688640000000⟩, + ⟨2, 5, 6, 0, 6, 7, 311872440123191108447720597815436128945176576000000⟩, + ⟨2, 5, 7, 0, 7, 7, -952778156767909785574510481192412556296192000000⟩, + ⟨2, 5, 8, 0, 8, 7, 18353209498148125884337306978488424209580032000000⟩, + ⟨2, 5, 1, 1, 0, 7, -585054501332615336219578376870747378169151488000000⟩, + ⟨2, 5, 2, 1, 1, 7, 1456723582784713797733524614488922207715065856000000⟩, + ⟨2, 5, 3, 1, 2, 7, 27282315345775646817013034040900412891987968000000⟩, + ⟨2, 5, 4, 1, 3, 7, 611699846511126776962217481867445959225507840000000⟩, + ⟨2, 5, 5, 1, 4, 7, 721933890320386063728838660215300363701452800000000⟩, + ⟨2, 5, 6, 1, 5, 7, -196117754937912592052677600683898219914067968000000⟩, + ⟨2, 5, 7, 1, 6, 7, -65945855863054643396773913761973856808992768000000⟩, + ⟨2, 5, 8, 1, 7, 7, 15336212984673210457459622679901758963056640000000⟩, + ⟨2, 5, 2, 2, 0, 7, -1539837168638892769747931930814133679324921856000000⟩, + ⟨2, 5, 3, 2, 1, 7, 213575521465948428268346551983717232448372736000000⟩, + ⟨2, 5, 4, 2, 2, 7, -402983240742521727143949684631531503501705216000000⟩, + ⟨2, 5, 5, 2, 3, 7, 1065134648404698185825294444136991873176698880000000⟩, + ⟨2, 5, 6, 2, 4, 7, 70389415319815760017576646241548627878084608000000⟩, + ⟨2, 5, 7, 2, 5, 7, 6688232823242674595918133726620364696453120000000⟩, + ⟨2, 5, 8, 2, 6, 7, 834543351768145241765581627621444367155200000000⟩, + ⟨2, 5, 3, 3, 0, 7, -2203153032269547048401770209491025397221949440000000⟩, + ⟨2, 5, 4, 3, 1, 7, 894715131021583574037778990640837183410274304000000⟩, + ⟨2, 5, 5, 3, 2, 7, -2893687706101830509421594748150116338840371200000000⟩, + ⟨2, 5, 6, 3, 3, 7, 106857642130539953295187078765001984484311040000000⟩, + ⟨2, 5, 7, 3, 4, 7, -26872623514265909247016199609418547181125632000000⟩, + ⟨2, 5, 8, 3, 5, 7, 13278226008081730236932906468687201792163840000000⟩, + ⟨2, 5, 4, 4, 0, 7, -1494468756713688886830463944329424439049453568000000⟩, + ⟨2, 5, 5, 4, 1, 7, 802067162678432023935318036824521751239065600000000⟩, + ⟨2, 5, 6, 4, 2, 7, -324921472725827420585614021115999228484648960000000⟩, + ⟨2, 5, 7, 4, 3, 7, 95311523901360753238453002613818410762502144000000⟩, + ⟨2, 5, 8, 4, 4, 7, -18997081850055438473188880609020340789575680000000⟩, + ⟨2, 5, 5, 5, 0, 7, 9182085478906030468560778060173344804406558720000000⟩, + ⟨2, 5, 6, 5, 1, 7, 502098718975902744550684901463693909420933120000000⟩, + ⟨2, 5, 7, 5, 2, 7, -185133482618682294726894591642930171227406336000000⟩, + ⟨2, 5, 8, 5, 3, 7, 26573767346549747759702147794942155974246400000000⟩, + ⟨2, 5, 6, 6, 0, 7, -736480715819535841151016528243688743377043456000000⟩, + ⟨2, 5, 7, 6, 1, 7, 508648248544289689569388641181553537310523392000000⟩, + ⟨2, 5, 8, 6, 2, 7, -94765949137178559320189018411145015211327488000000⟩, + ⟨2, 5, 7, 7, 0, 7, -1724145768807203187291357801308250900466237440000000⟩, + ⟨2, 5, 8, 7, 1, 7, 177191519698096452673665696919473503852298240000000⟩ +] + +def collectedFourData_8_0_23 : List CollectedFourTerm := [ + ⟨2, 6, 0, 0, 0, 8, 1907094087379744159052364983198900205649920000000000⟩, + ⟨2, 6, 1, 0, 1, 8, 426087722197497709061253699092621222215680000000000⟩, + ⟨2, 6, 2, 0, 2, 8, -120660325604578579950633735543660732387164160000000⟩, + ⟨2, 6, 3, 0, 3, 8, -73744159678983844195558174507865394590515200000000⟩, + ⟨2, 6, 4, 0, 4, 8, -224022619899519601034222430426875923330498560000000⟩, + ⟨2, 6, 5, 0, 5, 8, 235661685144996765099596493696094372532060160000000⟩, + ⟨2, 6, 6, 0, 6, 8, 45400570142640234499200065087679608515461120000000⟩, + ⟨2, 6, 7, 0, 7, 8, -118885615595998257097943325968334921400320000000⟩, + ⟨2, 6, 8, 0, 8, 8, 2003814864582396412985938290853895083130880000000⟩, + ⟨2, 6, 1, 1, 0, 8, -511012924024837187211262872674009009734287360000000⟩, + ⟨2, 6, 2, 1, 1, 8, 636183958792878762863194331567849033863004160000000⟩, + ⟨2, 6, 3, 1, 2, 8, 7943200566361371816101034759197305413304320000000⟩, + ⟨2, 6, 4, 1, 3, 8, 133571541830375228261830463824950556046131200000000⟩, + ⟨2, 6, 5, 1, 4, 8, 126113908158962949881373353216581496419123200000000⟩, + ⟨2, 6, 6, 1, 5, 8, -28549678470334737838915731481868349116252160000000⟩, + ⟨2, 6, 7, 1, 6, 8, -8228582503276253942970197058546623085281280000000⟩, + ⟨2, 6, 8, 1, 7, 8, 1674417302771515183223958260588203317657600000000⟩, + ⟨2, 6, 2, 2, 0, 8, -672481531443624922269026381145194356707164160000000⟩, + ⟨2, 6, 3, 2, 1, 8, 62182156520374883432928848067157350301040640000000⟩, + ⟨2, 6, 4, 2, 2, 8, -87995923335254263179428119500783847609466880000000⟩, + ⟨2, 6, 5, 2, 3, 8, 186067304814054411724873406587541385872670720000000⟩, + ⟨2, 6, 6, 2, 4, 8, 10246880379248663188098483079121204108328960000000⟩, + ⟨2, 6, 7, 2, 5, 8, 834543351768145241765581627621444367155200000000⟩, + ⟨2, 6, 8, 2, 6, 8, 91115963863440912975691771762880544768000000000⟩, + ⟨2, 6, 3, 3, 0, 8, -641444327283385322262130523149164038691225600000000⟩, + ⟨2, 6, 4, 3, 1, 8, 195371112533612925472350824813243539359006720000000⟩, + ⟨2, 6, 5, 3, 2, 8, -505495406852409632216806310119843690237132800000000⟩, + ⟨2, 6, 6, 3, 3, 8, 15555712056212475869968840903431862144204800000000⟩, + ⟨2, 6, 7, 3, 4, 8, -3353108345819502563901184489218122679582720000000⟩, + ⟨2, 6, 8, 3, 5, 8, 1449725000576245510460937401008742046105600000000⟩, + ⟨2, 6, 4, 4, 0, 8, -326334062678141131533256132915317260408586240000000⟩, + ⟨2, 6, 5, 4, 1, 8, 140112309239919102282127167319523623069286400000000⟩, + ⟨2, 6, 6, 4, 2, 8, -47300172171391396559735571384617827250995200000000⟩, + ⟨2, 6, 7, 4, 3, 8, 11892767599589470431654677243555261699850240000000⟩, + ⟨2, 6, 8, 4, 4, 8, -2074113249710931257193931635028384756531200000000⟩, + ⟨2, 6, 5, 5, 0, 8, 1604009314870368851047271641939722641269063680000000⟩, + ⟨2, 6, 6, 5, 1, 8, 73092601899644999847665198302614398592614400000000⟩, + ⟨2, 6, 7, 5, 2, 8, -23100559025425371676509587105021038228930560000000⟩, + ⟨2, 6, 8, 5, 3, 8, 2901340499728050716724261887932970827776000000000⟩, + ⟨2, 6, 6, 6, 0, 8, -107212565445215651487521688635383713858846720000000⟩, + ⟨2, 6, 7, 6, 1, 8, 63468037885281321172116282529570324029112320000000⟩, + ⟨2, 6, 8, 6, 2, 8, -10346605456473339546874268338923883116625920000000⟩, + ⟨2, 6, 7, 7, 0, 8, -215135212374322743960018898562710275253862400000000⟩, + ⟨2, 6, 8, 7, 1, 8, 19345880680151136809784323056616951355801600000000⟩ +] + +def collectedFourData_8_0_24 : List CollectedFourTerm := [ + ⟨3, 0, 5, 0, 5, 3, -29625483497847203503306262342805725829515968512000000⟩, + ⟨3, 0, 6, 0, 6, 3, -34244357729838583042072758087788336616522645504000000⟩, + ⟨3, 0, 7, 0, 7, 3, 313852125163563009935204019818664030847893504000000⟩, + ⟨3, 0, 8, 0, 8, 3, -14106591461172340505456388555327665517096861696000000⟩, + ⟨3, 0, 5, 1, 4, 3, -15854021847945255875525938933552665178920714240000000⟩, + ⟨3, 0, 6, 1, 5, 3, 21534209802616328763117935204527574483019497472000000⟩, + ⟨3, 0, 7, 1, 6, 3, 21723049443703208975091605144787043518058070016000000⟩, + ⟨3, 0, 8, 1, 7, 3, -11787676218600391265912372676353201209784401920000000⟩, + ⟨3, 0, 5, 2, 3, 3, -23390878601526051087370653897916072257392738304000000⟩, + ⟨3, 0, 6, 2, 4, 3, -7728930192272891188914840162413568094510252032000000⟩, + ⟨3, 0, 7, 2, 5, 3, -2203153032269547048401770209491025397221949440000000⟩, + ⟨3, 0, 8, 2, 6, 3, -641444327283385322262130523149164038691225600000000⟩, + ⟨3, 0, 5, 3, 2, 3, 63546799407504615809703203543311415375780904960000000⟩, + ⟨3, 0, 6, 3, 3, 3, -11733230810134589558476094080634950139416412160000000⟩, + ⟨3, 0, 7, 3, 4, 3, 8852039626184631764208441549836492858179190784000000⟩, + ⟨3, 0, 8, 3, 5, 3, -10205872146995446185529779799040343303279083520000000⟩, + ⟨3, 0, 5, 4, 1, 3, -17613787759679921541824440947471009385524756480000000⟩, + ⟨3, 0, 6, 4, 2, 3, 35677173467889993804176201248544791409291427840000000⟩, + ⟨3, 0, 7, 4, 3, 3, -31396316253193218720778153477249384298607280128000000⟩, + ⟨3, 0, 8, 4, 4, 3, 14601482789166886884731770806075028294116311040000000⟩, + ⟨3, 0, 5, 5, 0, 3, -201643094671277237833086732856480576593016651776000000⟩, + ⟨3, 0, 6, 5, 1, 3, -55131669029532632533882163451525455067721236480000000⟩, + ⟨3, 0, 7, 5, 2, 3, 60984329401412650819386030624027092320499269632000000⟩, + ⟨3, 0, 8, 5, 3, 3, -20425053153773658133287867011370945262859059200000000⟩, + ⟨3, 0, 6, 6, 0, 3, 80867386306047536723348110631736529521972609024000000⟩, + ⟨3, 0, 7, 6, 1, 3, -167552470249626853027103021393493260042873339904000000⟩, + ⟨3, 0, 8, 6, 2, 3, 72838733140560704580497644261119282095654436864000000⟩, + ⟨3, 0, 7, 7, 0, 3, 567946284020153793252541633666683145674848993280000000⟩, + ⟨3, 0, 8, 7, 1, 3, -136192439748346426668697502342630939906770206720000000⟩ +] + +def collectedFourData_8_0_25 : List CollectedFourTerm := [ + ⟨3, 1, 4, 0, 4, 4, -6862142110944621329792671972843612538518445752320000⟩, + ⟨3, 1, 5, 0, 5, 4, 36093318931253215171951014704208489932985571737600000⟩, + ⟨3, 1, 6, 0, 6, 4, 20860292883132291067843642014667463470737889689600000⟩, + ⟨3, 1, 7, 0, 7, 4, -127457439939089963637571230268079840738829926400000⟩, + ⟨3, 1, 8, 0, 8, 4, 4296585612501356221063878962727458147616895795200000⟩, + ⟨3, 1, 4, 1, 3, 4, 4091492646720825209216324788758729371351934566400000⟩, + ⟨3, 1, 5, 1, 4, 4, 19315271831513785614458311359890919635080445952000000⟩, + ⟨3, 1, 6, 1, 5, 4, -13117779198351823002632019276445224847343930572800000⟩, + ⟨3, 1, 7, 1, 6, 4, -8821875169147734616399231582812668017021393305600000⟩, + ⟨3, 1, 8, 1, 7, 4, 3590290410342243640787748631075379112264597504000000⟩, + ⟨3, 1, 4, 2, 2, 4, -2695444466193378545394505733482308135017628303360000⟩, + ⟨3, 1, 5, 2, 3, 4, 28497575120029869906808643682698182988586496819200000⟩, + ⟨3, 1, 6, 2, 4, 4, 4708155099770255149826486163896486248743488716800000⟩, + ⟨3, 1, 7, 2, 5, 4, 894715131021583574037778990640837183410274304000000⟩, + ⟨3, 1, 8, 2, 6, 4, 195371112533612925472350824813243539359006720000000⟩, + ⟨3, 1, 4, 3, 1, 4, 5984504328983971123261650273155223463476949155840000⟩, + ⟨3, 1, 5, 3, 2, 4, -77420336388505091434648649999674810198243934208000000⟩, + ⟨3, 1, 6, 3, 3, 4, 7147414855777259117979583875708203099052048384000000⟩, + ⟨3, 1, 7, 3, 4, 4, -3594872293456301893274555730152704334883087974400000⟩, + ⟨3, 1, 8, 3, 5, 4, 3108504527865921115513361722378600632155111424000000⟩, + ⟨3, 1, 4, 4, 0, 4, -9996091978317747830737149238888638457532676833280000⟩, + ⟨3, 1, 5, 4, 1, 4, 21459229829741979528591225120870123364159586304000000⟩, + ⟨3, 1, 6, 4, 2, 4, -21733106915128874579725649140269110379587567616000000⟩, + ⟨3, 1, 7, 4, 3, 4, 12750253295447908509277838584003489603817098444800000⟩, + ⟨3, 1, 8, 4, 4, 4, -4447319612664734175709836713030826332308635648000000⟩, + ⟨3, 1, 5, 5, 0, 4, 245665814256977900307014313860575115625475394764800000⟩, + ⟨3, 1, 6, 5, 1, 4, 33584007390796099680236104835843415832528945152000000⟩, + ⟨3, 1, 7, 5, 2, 4, -24766142647131690759860194115351212331034161971200000⟩, + ⟨3, 1, 8, 5, 3, 4, 6221062668230568204982024651741848251966423040000000⟩, + ⟨3, 1, 6, 6, 0, 4, -49261176873166156834580917043409939778363824537600000⟩, + ⟨3, 1, 7, 6, 1, 4, 68044174951367503160821300919825334554367256166400000⟩, + ⟨3, 1, 8, 6, 2, 4, -22185221263829683162702197051223045043668176076800000⟩, + ⟨3, 1, 7, 7, 0, 4, -230646771457745592486329004679360345716868251648000000⟩, + ⟨3, 1, 8, 7, 1, 4, 41481493156219372776263262145673088899443851264000000⟩ +] + +def collectedFourData_8_0_26 : List CollectedFourTerm := [ + ⟨3, 2, 3, 0, 3, 5, 7305708575586242187609917970437210298982072320000000⟩, + ⟨3, 2, 4, 0, 4, 5, 88774160961339987875043982067967014349658128384000000⟩, + ⟨3, 2, 5, 0, 5, 5, -233466026543057028807382176031980446437406146560000000⟩, + ⟨3, 2, 6, 0, 6, 5, -89955146569286091591481389059398125280391331840000000⟩, + ⟨3, 2, 7, 0, 7, 5, 412222856432345090297488772799074341402705920000000⟩, + ⟨3, 2, 8, 0, 8, 5, -11116813863123772018170997335911061449550594048000000⟩, + ⟨3, 2, 3, 1, 2, 5, -786919381112776992173140728405242101956083712000000⟩, + ⟨3, 2, 4, 1, 3, 5, -52930822608996350238002146177535922075787591680000000⟩, + ⟨3, 2, 5, 1, 4, 5, -124938905582268765080000220232557724813177651200000000⟩, + ⟨3, 2, 6, 1, 5, 5, 56567362551531203779821176667804995926748037120000000⟩, + ⟨3, 2, 7, 1, 6, 5, 28531708961466071313103732797905959751704903680000000⟩, + ⟨3, 2, 8, 1, 7, 5, -9289373890328920270246462483773443311361064960000000⟩, + ⟨3, 2, 3, 2, 1, 5, -6160280571599138689096542301945860863110938624000000⟩, + ⟨3, 2, 4, 2, 2, 5, 34870426323955098023034703037165292296268152832000000⟩, + ⟨3, 2, 5, 2, 3, 5, -184333716776171389644276854147929953980142059520000000⟩, + ⟨3, 2, 6, 2, 4, 5, -20302820504175526249722595395852517151311134720000000⟩, + ⟨3, 2, 7, 2, 5, 5, -2893687706101830509421594748150116338840371200000000⟩, + ⟨3, 2, 8, 2, 6, 5, -505495406852409632216806310119843690237132800000000⟩, + ⟨3, 2, 3, 3, 0, 5, 63546799407504615809703203543311415375780904960000000⟩, + ⟨3, 2, 4, 3, 1, 5, -77420336388505091434648649999674810198243934208000000⟩, + ⟨3, 2, 5, 3, 2, 5, 500785708975074888687713089655713250866416844800000000⟩, + ⟨3, 2, 6, 3, 3, 5, -30821559148041744141110377431817121141725593600000000⟩, + ⟨3, 2, 7, 3, 4, 5, 11626536089428949772899547303981532668305080320000000⟩, + ⟨3, 2, 8, 3, 5, 5, -8042820356800694309155959969520578968955125760000000⟩, + ⟨3, 2, 4, 4, 0, 5, 129317444016819290567965731868365109163339022336000000⟩, + ⟨3, 2, 5, 4, 1, 5, -138806883638676429837557845816084143131747942400000000⟩, + ⟨3, 2, 6, 4, 2, 5, 93718953463841681913431418290966213087880806400000000⟩, + ⟨3, 2, 7, 4, 3, 5, -41236869626419589830734436633080544762464829440000000⟩, + ⟨3, 2, 8, 4, 4, 5, 11506816989742446378885525797256400144454123520000000⟩, + ⟨3, 2, 5, 5, 0, 5, -1589064769058351604648253850661005627967280250880000000⟩, + ⟨3, 2, 6, 5, 1, 5, -144823197073416262784624296935294481382296780800000000⟩, + ⟨3, 2, 7, 5, 2, 5, 80098659361825862864840426325380530336809615360000000⟩, + ⟨3, 2, 8, 5, 3, 5, -16096128868542477779874080609700614608886169600000000⟩, + ⟨3, 2, 6, 6, 0, 5, 212427333145660212391853084401592775876846551040000000⟩, + ⟨3, 2, 7, 6, 1, 5, -220068472859954796724568658782384660638775377920000000⟩, + ⟨3, 2, 8, 6, 2, 5, 57401154671425103183222892594234643807293407232000000⟩, + ⟨3, 2, 7, 7, 0, 5, 745957795815187306106181263385688451028772454400000000⟩, + ⟨3, 2, 8, 7, 1, 5, -107327557221341841976198177597822158782186127360000000⟩ +] + +def collectedFourData_8_0_27 : List CollectedFourTerm := [ + ⟨3, 3, 2, 0, 2, 6, -735701909855200638403433988196913056938196992000000⟩, + ⟨3, 3, 3, 0, 3, 6, -1348920256380525979051392829720436021101854720000000⟩, + ⟨3, 3, 4, 0, 4, 6, -8195595452856371939776165245015993661765189632000000⟩, + ⟨3, 3, 5, 0, 5, 6, 14368994196903619709091557788993320132720721920000000⟩, + ⟨3, 3, 6, 0, 6, 6, 4152311788704634486437033522948471183806300160000000⟩, + ⟨3, 3, 7, 0, 7, 6, -15222500471557923648193588344265626630488064000000⟩, + ⟨3, 3, 8, 0, 8, 6, 342099954011560597485877463064966858767597568000000⟩, + ⟨3, 3, 2, 1, 1, 6, 3879002904707915393009336874464775345109204992000000⟩, + ⟨3, 3, 3, 1, 2, 6, 145296172484716614510834130417908802809495552000000⟩, + ⟨3, 3, 4, 1, 3, 6, 4886552622887102443883810146878035440844144640000000⟩, + ⟨3, 3, 5, 1, 4, 6, 7689540255005883638439208761960496835749478400000000⟩, + ⟨3, 3, 6, 1, 5, 6, -2611138276538035804089764802079556782396538880000000⟩, + ⟨3, 3, 7, 1, 6, 6, -1053614437780581669945629023482410636993888256000000⟩, + ⟨3, 3, 8, 1, 7, 6, 285863775341178746636259692887450146161295360000000⟩, + ⟨3, 3, 2, 2, 0, 6, -4100320006153301588861703014887060606122196992000000⟩, + ⟨3, 3, 3, 2, 1, 6, 1137429335162150814908120594086764519886946304000000⟩, + ⟨3, 3, 4, 2, 2, 6, -3219223976042136546786432666662795099856961536000000⟩, + ⟨3, 3, 5, 2, 3, 6, 11345077251151986305828059971485885750984048640000000⟩, + ⟨3, 3, 6, 2, 4, 6, 937174182229908014655464808060055134173921280000000⟩, + ⟨3, 3, 7, 2, 5, 6, 106857642130539953295187078765001984484311040000000⟩, + ⟨3, 3, 8, 2, 6, 6, 15555712056212475869968840903431862144204800000000⟩, + ⟨3, 3, 3, 3, 0, 6, -11733230810134589558476094080634950139416412160000000⟩, + ⟨3, 3, 4, 3, 1, 6, 7147414855777259117979583875708203099052048384000000⟩, + ⟨3, 3, 5, 3, 2, 6, -30821559148041744141110377431817121141725593600000000⟩, + ⟨3, 3, 6, 3, 3, 6, 1422717079317928729606312188946252883715686400000000⟩, + ⟨3, 3, 7, 3, 4, 6, -429342886601836353279285166242094246520684544000000⟩, + ⟨3, 3, 8, 3, 5, 6, 247503332165320337180171193561537761677148160000000⟩, + ⟨3, 3, 4, 4, 0, 6, -11938535320213237947671790378951547356004220928000000⟩, + ⟨3, 3, 5, 4, 1, 6, 8543064423664993699964696904901990418271436800000000⟩, + ⟨3, 3, 6, 4, 2, 6, -4326048371153904691215745905875116405397913600000000⟩, + ⟨3, 3, 7, 4, 3, 6, 1522788602181181941231389044547142092794626048000000⟩, + ⟨3, 3, 8, 4, 4, 6, -354101598846434439764935502640749587275448320000000⟩, + ⟨3, 3, 5, 5, 0, 6, 97801220945062920532608945238432882456956764160000000⟩, + ⟨3, 3, 6, 5, 1, 6, 6685010156952639085089958806062801270027059200000000⟩, + ⟨3, 3, 7, 5, 2, 6, -2957870629637602745316045438428501916738650112000000⟩, + ⟨3, 3, 8, 5, 3, 6, 495329418436915195895960421077858022693273600000000⟩, + ⟨3, 3, 6, 6, 0, 6, -9805603718119893100614657774477201384627240960000000⟩, + ⟨3, 3, 7, 6, 1, 6, 8126653773831927348892757167995690682064830464000000⟩, + ⟨3, 3, 8, 6, 2, 6, -1766417304012241472496891647714687042728230912000000⟩, + ⟨3, 3, 7, 7, 0, 6, -27546611550935826403121678222925237653581332480000000⟩, + ⟨3, 3, 8, 7, 1, 6, 3302812554178805797554610223387647086962933760000000⟩ +] + +def collectedFourData_8_0_28 : List CollectedFourTerm := [ + ⟨3, 4, 1, 0, 1, 7, -1960027415575781707238044874615807843657318400000000⟩, + ⟨3, 4, 2, 0, 2, 7, 1110088527956477957063602802924003795855317401600000⟩, + ⟨3, 4, 3, 0, 3, 7, 1017681809491871700646171087512411288033558528000000⟩, + ⟨3, 4, 4, 0, 4, 7, 4122066455683005289729653081671908805838058291200000⟩, + ⟨3, 4, 5, 0, 5, 7, -5420284833634361678044974915229203907586555904000000⟩, + ⟨3, 4, 6, 0, 6, 7, -1253071011341176766622894803363787624335120793600000⟩, + ⟨3, 4, 7, 0, 7, 7, 3828163488935897236320514672637086312641331200000⟩, + ⟨3, 4, 8, 0, 8, 7, -73741285950488900682508349484046240307163955200000⟩, + ⟨3, 4, 1, 1, 0, 7, 2350688106281479300530419151060146287129971916800000⟩, + ⟨3, 4, 2, 1, 1, 7, -5852963770711995779720207169511603282464315801600000⟩, + ⟨3, 4, 3, 1, 2, 7, -109617504094161364938816282129103455974640844800000⟩, + ⟨3, 4, 4, 1, 3, 7, -2457746330525928274370116378240247847425409024000000⟩, + ⟨3, 4, 5, 1, 4, 7, -2900655247728530978914417264586850020968366080000000⟩, + ⟨3, 4, 6, 1, 5, 7, 787980731561079830278309835654047323583728844800000⟩, + ⟨3, 4, 7, 1, 6, 7, 264963586610718778139287809272130404577234124800000⟩, + ⟨3, 4, 8, 1, 7, 7, -61619307904402184586656218152994187671240704000000⟩, + ⟨3, 4, 2, 2, 0, 7, 6186905509973564113570434308548218279618517401600000⟩, + ⟨3, 4, 3, 2, 1, 7, -858124220836384038862036715732649725761526169600000⟩, + ⟨3, 4, 4, 2, 2, 7, 1619144727348503050484806877127392392671500697600000⟩, + ⟨3, 4, 5, 2, 3, 7, -4279600180650124769778766665269789396532461568000000⟩, + ⟨3, 4, 6, 2, 4, 7, -282817346116492606739843927969728219933625548800000⟩, + ⟨3, 4, 7, 2, 5, 7, -26872623514265909247016199609418547181125632000000⟩, + ⟨3, 4, 8, 2, 6, 7, -3353108345819502563901184489218122679582720000000⟩, + ⟨3, 4, 3, 3, 0, 7, 8852039626184631764208441549836492858179190784000000⟩, + ⟨3, 4, 4, 3, 1, 7, -3594872293456301893274555730152704334883087974400000⟩, + ⟨3, 4, 5, 3, 2, 7, 11626536089428949772899547303981532668305080320000000⟩, + ⟨3, 4, 6, 3, 3, 7, -429342886601836353279285166242094246520684544000000⟩, + ⟨3, 4, 7, 3, 4, 7, 107971404947198135135510568249880563967800115200000⟩, + ⟨3, 4, 8, 3, 5, 7, -53350530384125571083658155692922387640090624000000⟩, + ⟨3, 4, 4, 4, 0, 7, 6004619951840878923190684871901389261734989004800000⟩, + ⟨3, 4, 5, 4, 1, 7, -3222622397490501373090633672228428459446108160000000⟩, + ⟨3, 4, 6, 4, 2, 7, 1305500666471814806764533662320430296602771456000000⟩, + ⟨3, 4, 7, 4, 3, 7, -382951785032273470533779320372598687891088998400000⟩, + ⟨3, 4, 8, 4, 4, 7, 76328298059864199640714677065738797656834048000000⟩, + ⟨3, 4, 5, 5, 0, 7, -36892663977391092456968466661420262921487777792000000⟩, + ⟨3, 4, 6, 5, 1, 7, -2017380405051887322773515754091567025206853632000000⟩, + ⟨3, 4, 7, 5, 2, 7, 743847068392676982499083230581224482075679129600000⟩, + ⟨3, 4, 8, 5, 3, 7, -106770631963930635570201775373144070071255040000000⟩, + ⟨3, 4, 6, 6, 0, 7, 2959102878858819380346031628616828816134347161600000⟩, + ⟨3, 4, 7, 6, 1, 7, -2043695733321438026568119157782115583746323251200000⟩, + ⟨3, 4, 8, 6, 2, 7, 380759722401648067628353430278856034438925516800000⟩, + ⟨3, 4, 7, 7, 0, 7, 6927438286516929932476854646456111390821187584000000⟩, + ⟨3, 4, 8, 7, 1, 7, -711937087808943449760009298571478039175102464000000⟩ +] + +def collectedFourData_8_0_29 : List CollectedFourTerm := [ + ⟨3, 5, 0, 0, 0, 8, 30343332383216751944681971116542101882404864000000000⟩, + ⟨3, 5, 1, 0, 1, 8, 6779383075331177603552916386291899648966656000000000⟩, + ⟨3, 5, 2, 0, 2, 8, -1919798498414543284132445437998697531752579072000000⟩, + ⟨3, 5, 3, 0, 3, 8, -1173326247125453839825964311365414339571875840000000⟩, + ⟨3, 5, 4, 0, 4, 8, -3564372026505371466219577451348832749252247552000000⟩, + ⟨3, 5, 5, 0, 5, 8, 3749558498274415541551711859430149712638902272000000⟩, + ⟨3, 5, 6, 0, 6, 8, 722357957765178579393318158174511963417083904000000⟩, + ⟨3, 5, 7, 0, 7, 8, -1891561498451860606949328781675243235180544000000⟩, + ⟨3, 5, 8, 0, 8, 8, 31882234270881585181420427570388369980522496000000⟩, + ⟨3, 5, 1, 1, 0, 8, -8130608294795459115992144093903813762730688512000000⟩, + ⟨3, 5, 2, 1, 1, 8, 10122175642128742433787988556179188549861507072000000⟩, + ⟨3, 5, 3, 1, 2, 8, 126382424740675980332696088803008412431417344000000⟩, + ⟨3, 5, 4, 1, 3, 8, 2125225869829239073860903285182444711486423040000000⟩, + ⟨3, 5, 5, 1, 4, 8, 2006569187507475552771281403772693183400509440000000⟩, + ⟨3, 5, 6, 1, 5, 8, -454247322663339780099322887365274754112028672000000⟩, + ⟨3, 5, 7, 1, 6, 8, -130923070650743331551947857336603685920178176000000⟩, + ⟨3, 5, 8, 1, 7, 8, 26641265946145477395563418115912346024017920000000⟩, + ⟨3, 5, 2, 2, 0, 8, -10699697914854575675533478747183333493096579072000000⟩, + ⟨3, 5, 3, 2, 1, 8, 989365892374683863369155905456573764849369088000000⟩, + ⟨3, 5, 4, 2, 2, 8, -1400082758265091347502591820634323891515293696000000⟩, + ⟨3, 5, 5, 2, 3, 8, 2960473797797442828647601152446245968988340224000000⟩, + ⟨3, 5, 6, 2, 4, 8, 163035740761904236297338850691701376110559232000000⟩, + ⟨3, 5, 7, 2, 5, 8, 13278226008081730236932906468687201792163840000000⟩, + ⟨3, 5, 8, 2, 6, 8, 1449725000576245510460937401008742046105600000000⟩, + ⟨3, 5, 3, 3, 0, 8, -10205872146995446185529779799040343303279083520000000⟩, + ⟨3, 5, 4, 3, 1, 8, 3108504527865921115513361722378600632155111424000000⟩, + ⟨3, 5, 5, 3, 2, 8, -8042820356800694309155959969520578968955125760000000⟩, + ⟨3, 5, 6, 3, 3, 8, 247503332165320337180171193561537761677148160000000⟩, + ⟨3, 5, 7, 3, 4, 8, -53350530384125571083658155692922387640090624000000⟩, + ⟨3, 5, 8, 3, 5, 8, 23066238759716130004941508654535798182379520000000⟩, + ⟨3, 5, 4, 4, 0, 8, -5192225699474159013289351430267177358336196608000000⟩, + ⟨3, 5, 5, 4, 1, 8, 2229294505384492580020201477498060711793786880000000⟩, + ⟨3, 5, 6, 4, 2, 8, -752582085738552102402852756812774678294691840000000⟩, + ⟨3, 5, 7, 4, 3, 8, 189223071173434863742749511853702142291345408000000⟩, + ⟨3, 5, 8, 4, 4, 8, -33000735597100510174480256552365756294103040000000⟩, + ⟨3, 5, 5, 5, 0, 8, 25521020755593124639808432362321690926048608256000000⟩, + ⟨3, 5, 6, 5, 1, 8, 1162959462184857238617154498702569665703444480000000⟩, + ⟨3, 5, 7, 5, 2, 8, -367547645071706218574319225319015887459581952000000⟩, + ⟨3, 5, 8, 5, 3, 8, 46162556804470063824557261589853062247219200000000⟩, + ⟨3, 5, 6, 6, 0, 8, -1705834300724658903650089234261269994404839424000000⟩, + ⟨3, 5, 7, 6, 1, 8, 1009825252989843248849218163325301262798290944000000⟩, + ⟨3, 5, 8, 6, 2, 8, -164622443371489629280739475857167472671064064000000⟩, + ⟨3, 5, 7, 7, 0, 8, -3422966543500246854166498535218008744347566080000000⟩, + ⟨3, 5, 8, 7, 1, 8, 307807827421043798548498318594747178648862720000000⟩ +] + +def collectedFourData_8_0_30 : List CollectedFourTerm := [ + ⟨4, 0, 4, 0, 4, 4, 11462035941234870081455580537616960309924661821440000⟩, + ⟨4, 0, 5, 0, 5, 4, -60287722425429081168127310238928620336352277299200000⟩, + ⟨4, 0, 6, 0, 6, 4, -34843555103558519310425349325607565361669157683200000⟩, + ⟨4, 0, 7, 0, 7, 4, 212895876235143717772732164199210023312477388800000⟩, + ⟨4, 0, 8, 0, 8, 4, -7176712157641968150376325974143190891766376038400000⟩, + ⟨4, 0, 4, 1, 3, 4, -6834139400175816193384548707098390582063320268800000⟩, + ⟨4, 0, 5, 1, 4, 4, -32262861416761929980473096610757505464227856384000000⟩, + ⟨4, 0, 6, 1, 5, 4, 21911008867170506726020910694867595022143429017600000⟩, + ⟨4, 0, 7, 1, 6, 4, 14735435177972345530246760968986976389604520755200000⟩, + ⟨4, 0, 8, 1, 7, 4, -5996966698952380609402356532592170492093267968000000⟩, + ⟨4, 0, 4, 2, 2, 4, 4502279441260098650443517966126812016032213893120000⟩, + ⟨4, 0, 5, 2, 3, 4, -47600330185942287117150342336985401249461855846400000⟩, + ⟨4, 0, 6, 2, 4, 4, -7864168665992002995527710224006764827084691865600000⟩, + ⟨4, 0, 7, 2, 5, 4, -1494468756713688886830463944329424439049453568000000⟩, + ⟨4, 0, 8, 2, 6, 4, -326334062678141131533256132915317260408586240000000⟩, + ⟨4, 0, 4, 3, 1, 4, -9996091978317747830737149238888638457532676833280000⟩, + ⟨4, 0, 5, 3, 2, 4, 129317444016819290567965731868365109163339022336000000⟩, + ⟨4, 0, 6, 3, 3, 4, -11938535320213237947671790378951547356004220928000000⟩, + ⟨4, 0, 7, 3, 4, 4, 6004619951840878923190684871901389261734989004800000⟩, + ⟨4, 0, 8, 3, 5, 4, -5192225699474159013289351430267177358336196608000000⟩, + ⟨4, 0, 4, 4, 0, 4, 16696763732804053242020884265258354696993384693760000⟩, + ⟨4, 0, 5, 4, 1, 4, -35843976939420018220769778814775517104798957568000000⟩, + ⟨4, 0, 6, 4, 2, 4, 36301441816339203944173952927595044650270851072000000⟩, + ⟨4, 0, 7, 4, 3, 4, -21297119641282765358002953590737838647092550041600000⟩, + ⟨4, 0, 8, 4, 4, 4, 7428487550734331329136486175982922281638690816000000⟩, + ⟨4, 0, 5, 5, 0, 4, -410342768631265189783694012041820252536582019481600000⟩, + ⟨4, 0, 6, 5, 1, 4, -56096346234224607236046084232504342258630262784000000⟩, + ⟨4, 0, 7, 5, 2, 4, 41367609786806997417797503885397341653382358630400000⟩, + ⟨4, 0, 8, 5, 3, 4, -10391222266033412552115115289542884211745095680000000⟩, + ⟨4, 0, 6, 6, 0, 4, 82282379277340960546813966317016116640359854899200000⟩, + ⟨4, 0, 7, 6, 1, 4, -113656168332673271957729932978321194517799947468800000⟩, + ⟨4, 0, 8, 6, 2, 4, 37056621588278276165944576593872722037535512985600000⟩, + ⟨4, 0, 7, 7, 0, 4, 385256023765812671639948123320441938080553762816000000⟩, + ⟨4, 0, 8, 7, 1, 4, -69287746853033921873683826569473356483304357888000000⟩ +] + +def collectedFourData_8_0_31 : List CollectedFourTerm := [ + ⟨4, 1, 3, 0, 3, 5, -2024983185372713935683035686785851832045404160000000⟩, + ⟨4, 1, 4, 0, 4, 5, -24606262538724253486161346685878148456138145792000000⟩, + ⟨4, 1, 5, 0, 5, 5, 64711694042289864861309043427402748832021217280000000⟩, + ⟨4, 1, 6, 0, 6, 5, 24933606009041385545297148501728890682521681920000000⟩, + ⟨4, 1, 7, 0, 7, 5, -114259191188012251497798564992055906360360960000000⟩, + ⟨4, 1, 8, 0, 8, 5, 3081338506024038979848326087762210677246132224000000⟩, + ⟨4, 1, 3, 1, 2, 5, 218116901120629012790540262439844268428230656000000⟩, + ⟨4, 1, 4, 1, 3, 5, 14671270371958763292716073137177428806693027840000000⟩, + ⟨4, 1, 5, 1, 4, 5, 34630341517922043241106018066031091841079705600000000⟩, + ⟨4, 1, 6, 1, 5, 5, -15679239983719306246296607431882559355155906560000000⟩, + ⟨4, 1, 7, 1, 6, 5, -7908367860441319892219736054358884279480483840000000⟩, + ⟨4, 1, 8, 1, 7, 5, 2574811975585395337768324500421422896098836480000000⟩, + ⟨4, 1, 3, 2, 1, 5, 1707495507876244696878621261782458204434726912000000⟩, + ⟨4, 1, 4, 2, 2, 5, -9665322157628072431040839549684904861122953216000000⟩, + ⟨4, 1, 5, 2, 3, 5, 51093288639569116191063869874590268140562677760000000⟩, + ⟨4, 1, 6, 2, 4, 5, 5627499333053636013671561477572278598615695360000000⟩, + ⟨4, 1, 7, 2, 5, 5, 802067162678432023935318036824521751239065600000000⟩, + ⟨4, 1, 8, 2, 6, 5, 140112309239919102282127167319523623069286400000000⟩, + ⟨4, 1, 3, 3, 0, 5, -17613787759679921541824440947471009385524756480000000⟩, + ⟨4, 1, 4, 3, 1, 5, 21459229829741979528591225120870123364159586304000000⟩, + ⟨4, 1, 5, 3, 2, 5, -138806883638676429837557845816084143131747942400000000⟩, + ⟨4, 1, 6, 3, 3, 5, 8543064423664993699964696904901990418271436800000000⟩, + ⟨4, 1, 7, 3, 4, 5, -3222622397490501373090633672228428459446108160000000⟩, + ⟨4, 1, 8, 3, 5, 5, 2229294505384492580020201477498060711793786880000000⟩, + ⟨4, 1, 4, 4, 0, 5, -35843976939420018220769778814775517104798957568000000⟩, + ⟨4, 1, 5, 4, 1, 5, 38474242775246673691272922582846607658791731200000000⟩, + ⟨4, 1, 6, 4, 2, 5, -25976851246051591274802286038736009767891763200000000⟩, + ⟨4, 1, 7, 4, 3, 5, 11429961481074507754038504306357008855696670720000000⟩, + ⟨4, 1, 8, 4, 4, 5, -3189438872398457096084711501610302431832309760000000⟩, + ⟨4, 1, 5, 5, 0, 5, 440454119476442992501627973401096840690469437440000000⟩, + ⟨4, 1, 6, 5, 1, 5, 40141833730625359632952912228631920121374310400000000⟩, + ⟨4, 1, 7, 5, 2, 5, -22201602582481682648653785652425259394720071680000000⟩, + ⟨4, 1, 8, 5, 3, 5, 4461496098723774684566855922070620958674124800000000⟩, + ⟨4, 1, 6, 6, 0, 5, -58880226781973936079809895967849672435323371520000000⟩, + ⟨4, 1, 7, 6, 1, 5, 60998184168097644237033566569038190021139496960000000⟩, + ⟨4, 1, 8, 6, 2, 5, -15910348986413946358080851591576199808382140416000000⟩, + ⟨4, 1, 7, 7, 0, 5, -206763242455538707667069897114182465667412787200000000⟩, + ⟨4, 1, 8, 7, 1, 5, 29748859600918996808820553255423904602317127680000000⟩ +] + +def collectedFourData_8_0_32 : List CollectedFourTerm := [ + ⟨4, 2, 2, 0, 2, 6, 2237044943826591039217729618099007879808811008000000⟩, + ⟨4, 2, 3, 0, 3, 6, 4101654758182212021353552216048103220083425280000000⟩, + ⟨4, 2, 4, 0, 4, 6, 24920304166491822278520765058213647716469178368000000⟩, + ⟨4, 2, 5, 0, 5, 6, -43691725392398946630738432891061073159997358080000000⟩, + ⟨4, 2, 6, 0, 6, 6, -12625912706875363303947769792583899191013539840000000⟩, + ⟨4, 2, 7, 0, 7, 6, 46286977451232763142102174865269191329447936000000⟩, + ⟨4, 2, 8, 0, 8, 6, -1040221538306859050172134396354194340610834432000000⟩, + ⟨4, 2, 2, 1, 1, 6, -11794863814847770090256930950759558476629803008000000⟩, + ⟨4, 2, 3, 1, 2, 6, -441801310639881455821180741715174632558952448000000⟩, + ⟨4, 2, 4, 1, 3, 6, -14858514965556719397457084468033545047491215360000000⟩, + ⟨4, 2, 5, 1, 4, 6, -23381544777011086264491931308410052963572121600000000⟩, + ⟨4, 2, 6, 1, 5, 6, 7939674480811327294695674285382386033224581120000000⟩, + ⟨4, 2, 7, 1, 6, 6, 3203719902322454508784303212652869714909855744000000⟩, + ⟨4, 2, 8, 1, 7, 6, -869224484378499982931677587167140440063344640000000⟩, + ⟨4, 2, 2, 2, 0, 6, 12467821565994836931148368532697599146624811008000000⟩, + ⟨4, 2, 3, 2, 1, 6, -3458575421783708533242504068913541369294749696000000⟩, + ⟨4, 2, 4, 2, 2, 6, 9788677482253363538284604192061680541933502464000000⟩, + ⟨4, 2, 5, 2, 3, 6, -34496916974167924397263442974560315925447311360000000⟩, + ⟨4, 2, 6, 2, 4, 6, -2849660627161977883593570298141068780864798720000000⟩, + ⟨4, 2, 7, 2, 5, 6, -324921472725827420585614021115999228484648960000000⟩, + ⟨4, 2, 8, 2, 6, 6, -47300172171391396559735571384617827250995200000000⟩, + ⟨4, 2, 3, 3, 0, 6, 35677173467889993804176201248544791409291427840000000⟩, + ⟨4, 2, 4, 3, 1, 6, -21733106915128874579725649140269110379587567616000000⟩, + ⟨4, 2, 5, 3, 2, 6, 93718953463841681913431418290966213087880806400000000⟩, + ⟨4, 2, 6, 3, 3, 6, -4326048371153904691215745905875116405397913600000000⟩, + ⟨4, 2, 7, 3, 4, 6, 1305500666471814806764533662320430296602771456000000⟩, + ⟨4, 2, 8, 3, 5, 6, -752582085738552102402852756812774678294691840000000⟩, + ⟨4, 2, 4, 4, 0, 6, 36301441816339203944173952927595044650270851072000000⟩, + ⟨4, 2, 5, 4, 1, 6, -25976851246051591274802286038736009767891763200000000⟩, + ⟨4, 2, 6, 4, 2, 6, 13154192623128871688200119177114820391888486400000000⟩, + ⟨4, 2, 7, 4, 3, 6, -4630335326568127088110388196797768518915325952000000⟩, + ⟨4, 2, 8, 4, 4, 6, 1076714876893870823893985249913835435516231680000000⟩, + ⟨4, 2, 5, 5, 0, 6, -297383660263001443352727922848079500015399075840000000⟩, + ⟨4, 2, 6, 5, 1, 6, -20327075369402880285081789542130847717313740800000000⟩, + ⟨4, 2, 7, 5, 2, 6, 8993981730761440206810604951165708951395237888000000⟩, + ⟨4, 2, 8, 5, 3, 6, -1506145568197527010615338860099208999233126400000000⟩, + ⟨4, 2, 6, 6, 0, 6, 29815847865754003863290338985049985154851799040000000⟩, + ⟨4, 2, 7, 6, 1, 6, -24710673564185918387480627280340400298352705536000000⟩, + ⟨4, 2, 8, 6, 2, 6, 5371135844143887233404316578519915301424857088000000⟩, + ⟨4, 2, 7, 7, 0, 6, 83760837458889668279215620832796124332446187520000000⟩, + ⟨4, 2, 8, 7, 1, 6, -10042844833972068672855793026358833366423306240000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0803.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0803.lean new file mode 100644 index 0000000000000000000000000000000000000000..95ed07c4a0d3554aa2d3b5cf169fd53ce7f4633f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0803.lean @@ -0,0 +1,639 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PartsTrace +import OAI.Analysis.LaughlinFock.Sparse0801 +import OAI.Analysis.LaughlinFock.Sparse0802 + +namespace OAI + +/-! Sparse0803. -/ +namespace LaughlinFock +def collectedFourData_8_0_33 : List CollectedFourTerm := [ + ⟨4, 3, 1, 0, 1, 7, 6951803562007991716369381194739755602726092800000000⟩, + ⟨4, 3, 2, 0, 2, 7, -3937249714706187001467801211853021428745188147200000⟩, + ⟨4, 3, 3, 0, 3, 7, -3609502587563575768060005076911533139035160576000000⟩, + ⟨4, 3, 4, 0, 4, 7, -14620099719897432008757897008842233731361433190400000⟩, + ⟨4, 3, 5, 0, 5, 7, 19224606306074588073131675241493238849803911168000000⟩, + ⟨4, 3, 6, 0, 6, 7, 4444378405559984193194964900996412576283964211200000⟩, + ⟨4, 3, 7, 0, 7, 7, -13577687927653668690449559465637109238752870400000⟩, + ⟨4, 3, 8, 0, 8, 7, 261544777518872569611045185346223624681842278400000⟩, + ⟨4, 3, 1, 1, 0, 7, -8337394579563515505081143675600141610831681945600000⟩, + ⟨4, 3, 2, 1, 1, 7, 20759227175190605943687800373030649529585840947200000⟩, + ⟨4, 3, 3, 1, 2, 7, 388790151282837202112969024380947164405799321600000⟩, + ⟨4, 3, 4, 1, 3, 7, 8717107505377963338885257783687765404793438208000000⟩, + ⟨4, 3, 5, 1, 4, 7, 10288011954869889508565570721232867323921039360000000⟩, + ⟨4, 3, 6, 1, 5, 7, -2794801344577510623051290852253278847737895321600000⟩, + ⟨4, 3, 7, 1, 6, 7, -939769918810908823342908013784049675258141081600000⟩, + ⟨4, 3, 8, 1, 7, 7, 218550679839573990226908371371904285716512768000000⟩, + ⟨4, 3, 2, 2, 0, 7, -21943648043007777210789874529003194229359588147200000⟩, + ⟨4, 3, 3, 2, 1, 7, 3043585496636161189901291408651259408142250803200000⟩, + ⟨4, 3, 4, 2, 2, 7, -5742764613157823230712236112306867144479683379200000⟩, + ⟨4, 3, 5, 2, 3, 7, 15178838593476451247427053709096983540589920256000000⟩, + ⟨4, 3, 6, 2, 4, 7, 1003093435584786203429165990656622934642760089600000⟩, + ⟨4, 3, 7, 2, 5, 7, 95311523901360753238453002613818410762502144000000⟩, + ⟨4, 3, 8, 2, 6, 7, 11892767599589470431654677243555261699850240000000⟩, + ⟨4, 3, 3, 3, 0, 7, -31396316253193218720778153477249384298607280128000000⟩, + ⟨4, 3, 4, 3, 1, 7, 12750253295447908509277838584003489603817098444800000⟩, + ⟨4, 3, 5, 3, 2, 7, -41236869626419589830734436633080544762464829440000000⟩, + ⟨4, 3, 6, 3, 3, 7, 1522788602181181941231389044547142092794626048000000⟩, + ⟨4, 3, 7, 3, 4, 7, -382951785032273470533779320372598687891088998400000⟩, + ⟨4, 3, 8, 3, 5, 7, 189223071173434863742749511853702142291345408000000⟩, + ⟨4, 3, 4, 4, 0, 7, -21297119641282765358002953590737838647092550041600000⟩, + ⟨4, 3, 5, 4, 1, 7, 11429961481074507754038504306357008855696670720000000⟩, + ⟨4, 3, 6, 4, 2, 7, -4630335326568127088110388196797768518915325952000000⟩, + ⟨4, 3, 7, 4, 3, 7, 1358249156164288866068257123413717085473000652800000⟩, + ⟨4, 3, 8, 4, 4, 7, -270720363459148755504033980910703771612348416000000⟩, + ⟨4, 3, 5, 5, 0, 7, 130850492606324080263047987802014822917277220864000000⟩, + ⟨4, 3, 6, 5, 1, 7, 7155222510826456569911878187450760999305478144000000⟩, + ⟨4, 3, 7, 5, 2, 7, -2638268556117286401859672799283282896940643123200000⟩, + ⟨4, 3, 8, 5, 3, 7, 378692896694331638166145289156565231395143680000000⟩, + ⟨4, 3, 6, 6, 0, 7, -10495313366601983945260006403391093252897846067200000⟩, + ⟨4, 3, 7, 6, 1, 7, 7248557426116879508484801284901784117922129510400000⟩, + ⟨4, 3, 8, 6, 2, 7, -1350474372667574506879924872597193830826613145600000⟩, + ⟨4, 3, 7, 7, 0, 7, -24570161505446025948126368092728492575296585728000000⟩, + ⟨4, 3, 8, 7, 1, 7, 2525090589869075110876076777036760287897714688000000⟩ +] + +def collectedFourData_8_0_34 : List CollectedFourTerm := [ + ⟨4, 4, 0, 0, 0, 8, -43412031738016965629236588166396890765590528000000000⟩, + ⟨4, 4, 1, 0, 1, 8, -9699224512111815194597955140743338248896512000000000⟩, + ⟨4, 4, 2, 0, 2, 8, 2746644708999301796925495836962641141294956544000000⟩, + ⟨4, 4, 3, 0, 3, 8, 1678671137235806495656764855042830388355399680000000⟩, + ⟨4, 4, 4, 0, 4, 8, 5099526630316242244196106198804698447430549504000000⟩, + ⟨4, 4, 5, 0, 5, 8, -5364471854141947215934731392714480076082642944000000⟩, + ⟨4, 4, 6, 0, 6, 8, -1033473390221836398028965000414184889917636608000000⟩, + ⟨4, 4, 7, 0, 7, 8, 2706246194983603819805484774547677027237888000000⟩, + ⟨4, 4, 8, 0, 8, 8, -45613729848998065554772310454149589019656192000000⟩, + ⟨4, 4, 1, 1, 0, 8, 11632414689504379336522940971734811313568743424000000⟩, + ⟨4, 4, 2, 1, 1, 8, -14481738679332591631371908944700072261314412544000000⟩, + ⟨4, 4, 3, 1, 2, 8, -180814610757927916299447643004613387236671488000000⟩, + ⟨4, 4, 4, 1, 3, 8, -3040548471944100587246205645960842416572334080000000⟩, + ⟨4, 4, 5, 1, 4, 8, -2870787036587404469361332871899176334398586880000000⟩, + ⟨4, 4, 6, 1, 5, 8, 649889041167982881167093306440393551714975744000000⟩, + ⟨4, 4, 7, 1, 6, 8, 187310886838269355417550409152086729191063552000000⟩, + ⟨4, 4, 8, 1, 7, 8, -38115506503653502794132811437326448029859840000000⟩, + ⟨4, 4, 2, 2, 0, 8, 15307996485045877499829601209183963700782956544000000⟩, + ⟨4, 4, 3, 2, 1, 8, -1415480112001067065273650081903883806390091776000000⟩, + ⟨4, 4, 4, 2, 2, 8, 2003090378144255618207735205801107770249838592000000⟩, + ⟨4, 4, 5, 2, 3, 8, -4235532895544334085918928514213439237414453248000000⟩, + ⟨4, 4, 6, 2, 4, 8, -233254299923289170011165813122686894802468864000000⟩, + ⟨4, 4, 7, 2, 5, 8, -18997081850055438473188880609020340789575680000000⟩, + ⟨4, 4, 8, 2, 6, 8, -2074113249710931257193931635028384756531200000000⟩, + ⟨4, 4, 3, 3, 0, 8, 14601482789166886884731770806075028294116311040000000⟩, + ⟨4, 4, 4, 3, 1, 8, -4447319612664734175709836713030826332308635648000000⟩, + ⟨4, 4, 5, 3, 2, 8, 11506816989742446378885525797256400144454123520000000⟩, + ⟨4, 4, 6, 3, 3, 8, -354101598846434439764935502640749587275448320000000⟩, + ⟨4, 4, 7, 3, 4, 8, 76328298059864199640714677065738797656834048000000⟩, + ⟨4, 4, 8, 3, 5, 8, -33000735597100510174480256552365756294103040000000⟩, + ⟨4, 4, 4, 4, 0, 8, 7428487550734331329136486175982922281638690816000000⟩, + ⟨4, 4, 5, 4, 1, 8, -3189438872398457096084711501610302431832309760000000⟩, + ⟨4, 4, 6, 4, 2, 8, 1076714876893870823893985249913835435516231680000000⟩, + ⟨4, 4, 7, 4, 3, 8, -270720363459148755504033980910703771612348416000000⟩, + ⟨4, 4, 8, 4, 4, 8, 47213963286103581168314876337077572683694080000000⟩, + ⟨4, 4, 5, 5, 0, 8, -36512778129840526698238879765059703007411699712000000⟩, + ⟨4, 4, 6, 5, 1, 8, -1663839437435052242567558081736666841570344960000000⟩, + ⟨4, 4, 7, 5, 2, 8, 525848309327809622470853370911660537548898304000000⟩, + ⟨4, 4, 8, 5, 3, 8, -66044505454915253987942684576840048600678400000000⟩, + ⟨4, 4, 6, 6, 0, 8, 2440527357628552535173656767731690226369691648000000⟩, + ⟨4, 4, 7, 6, 1, 8, -1444751201977199598305342373447502543284338688000000⟩, + ⟨4, 4, 8, 6, 2, 8, 235524386253168179760474670554433864417148928000000⟩, + ⟨4, 4, 7, 7, 0, 8, 4897218616198996707493011638611520138678108160000000⟩, + ⟨4, 4, 8, 7, 1, 8, -440378894593772121464340603053591401794109440000000⟩ +] + +def collectedFourData_8_0_35 : List CollectedFourTerm := [ + ⟨5, 0, 3, 0, 3, 5, -23182059516497476995309254795177413340395732992000000⟩, + ⟨5, 0, 4, 0, 4, 5, -281693125538855768379121455467704925744393512550400000⟩, + ⟨5, 0, 5, 0, 5, 5, 740821135473095045089295831877387724399350644736000000⟩, + ⟨5, 0, 6, 0, 6, 5, 285440561994646317990626243443666069579370594304000000⟩, + ⟨5, 0, 7, 0, 7, 5, -1308042155391941459159500652251376037660721152000000⟩, + ⟨5, 0, 8, 0, 8, 5, 35275242359099943226058094279011828058983025868800000⟩, + ⟨5, 0, 3, 1, 2, 5, 2497007886216964993592666881358479263895073587200000⟩, + ⟨5, 0, 4, 1, 3, 5, 167957080040037064961583384087769535911619985408000000⟩, + ⟨5, 0, 5, 1, 4, 5, 396449039154535154141277342128182817144407326720000000⟩, + ⟨5, 0, 6, 1, 5, 5, -179496342044503002404731993470793681106079055872000000⟩, + ⟨5, 0, 7, 1, 6, 5, -90535198387517850297205826014164251227201732608000000⟩, + ⟨5, 0, 8, 1, 7, 5, 29476513628840219718078820229365634137929547776000000⟩, + ⟨5, 0, 3, 2, 1, 5, 19547452430057380023428834425657654133563745894400000⟩, + ⟨5, 0, 4, 2, 2, 5, -110648856307918138688677292203460482748665508659200000⟩, + ⟨5, 0, 5, 2, 3, 5, 584917280643033506538554027679483091212998541312000000⟩, + ⟨5, 0, 6, 2, 4, 5, 64423756903387627666398989600278846413767442432000000⟩, + ⟨5, 0, 7, 2, 5, 5, 9182085478906030468560778060173344804406558720000000⟩, + ⟨5, 0, 8, 2, 6, 5, 1604009314870368851047271641939722641269063680000000⟩, + ⟨5, 0, 3, 3, 0, 5, -201643094671277237833086732856480576593016651776000000⟩, + ⟨5, 0, 4, 3, 1, 5, 245665814256977900307014313860575115625475394764800000⟩, + ⟨5, 0, 5, 3, 2, 5, -1589064769058351604648253850661005627967280250880000000⟩, + ⟨5, 0, 6, 3, 3, 5, 97801220945062920532608945238432882456956764160000000⟩, + ⟨5, 0, 7, 3, 4, 5, -36892663977391092456968466661420262921487777792000000⟩, + ⟨5, 0, 8, 3, 5, 5, 25521020755593124639808432362321690926048608256000000⟩, + ⟨5, 0, 4, 4, 0, 5, -410342768631265189783694012041820252536582019481600000⟩, + ⟨5, 0, 5, 4, 1, 5, 440454119476442992501627973401096840690469437440000000⟩, + ⟨5, 0, 6, 4, 2, 5, -297383660263001443352727922848079500015399075840000000⟩, + ⟨5, 0, 7, 4, 3, 5, 130850492606324080263047987802014822917277220864000000⟩, + ⟨5, 0, 8, 4, 4, 5, -36512778129840526698238879765059703007411699712000000⟩, + ⟨5, 0, 5, 5, 0, 5, 5042330072538377802744026328545715711324274556928000000⟩, + ⟨5, 0, 6, 5, 1, 5, 459544743564586343833825544419047565978742292480000000⟩, + ⟨5, 0, 7, 5, 2, 5, -254164516597694017588890236185673028393045590016000000⟩, + ⟨5, 0, 8, 5, 3, 5, 51075321928759306612827063088334902602246389760000000⟩, + ⟨5, 0, 6, 6, 0, 5, -674062348499627699210011176316872660102439501824000000⟩, + ⟨5, 0, 7, 6, 1, 5, 698308779054303266828473717727669841681136484352000000⟩, + ⟨5, 0, 8, 6, 2, 5, -182142083843232762236899195510348821637532693299200000⟩, + ⟨5, 0, 7, 7, 0, 5, -2367030910207815308426853487709840466999131504640000000⟩, + ⟨5, 0, 8, 7, 1, 5, 340565708791057432866059358004238111033278857216000000⟩ +] + +def collectedFourData_8_0_36 : List CollectedFourTerm := [ + ⟨5, 1, 2, 0, 2, 6, -3456888801974118205019534746285539036260990976000000⟩, + ⟨5, 1, 3, 0, 3, 6, -6338256386959322028672286514042406585929564160000000⟩, + ⟨5, 1, 4, 0, 4, 6, -38509159439405690892051510430939119653429968896000000⟩, + ⟨5, 1, 5, 0, 5, 6, 67516496110066584192665781067912242291026165760000000⟩, + ⟨5, 1, 6, 0, 6, 6, 19510728370276098333844161963756268850490900480000000⟩, + ⟨5, 1, 7, 0, 7, 6, -71526919684810078072035799354744785120264192000000⟩, + ⟨5, 1, 8, 0, 8, 6, 1607446554557921267353230018453324542408392704000000⟩, + ⟨5, 1, 2, 1, 1, 6, 18226514739847634680477401786008326054374014976000000⟩, + ⟨5, 1, 3, 1, 2, 6, 682712257374692902618892833102086182226886656000000⟩, + ⟨5, 1, 4, 1, 3, 6, 22960751924159586340801250231234793643620433920000000⟩, + ⟨5, 1, 5, 1, 4, 6, 36131326076196862719755729424748345132528435200000000⟩, + ⟨5, 1, 6, 1, 5, 6, -12269119527427752671754612114349607541685616640000000⟩, + ⟨5, 1, 7, 1, 6, 6, -4950684377425097363593437863213550303096864768000000⟩, + ⟨5, 1, 8, 1, 7, 6, 1343206087451181491505318274539591565395886080000000⟩, + ⟨5, 1, 2, 2, 0, 6, -19266431313970032605485852938186714483812990976000000⟩, + ⟨5, 1, 3, 2, 1, 6, 5344510703435290838564041662681343767097638912000000⟩, + ⟨5, 1, 4, 2, 2, 6, -15126370021272538950117100672647280586662084608000000⟩, + ⟨5, 1, 5, 2, 3, 6, 53307827506873743862263034097180429130840145920000000⟩, + ⟨5, 1, 6, 2, 4, 6, 4403559230514235338383442917997891379097763840000000⟩, + ⟨5, 1, 7, 2, 5, 6, 502098718975902744550684901463693909420933120000000⟩, + ⟨5, 1, 8, 2, 6, 6, 73092601899644999847665198302614398592614400000000⟩, + ⟨5, 1, 3, 3, 0, 6, -55131669029532632533882163451525455067721236480000000⟩, + ⟨5, 1, 4, 3, 1, 6, 33584007390796099680236104835843415832528945152000000⟩, + ⟨5, 1, 5, 3, 2, 6, -144823197073416262784624296935294481382296780800000000⟩, + ⟨5, 1, 6, 3, 3, 6, 6685010156952639085089958806062801270027059200000000⟩, + ⟨5, 1, 7, 3, 4, 6, -2017380405051887322773515754091567025206853632000000⟩, + ⟨5, 1, 8, 3, 5, 6, 1162959462184857238617154498702569665703444480000000⟩, + ⟨5, 1, 4, 4, 0, 6, -56096346234224607236046084232504342258630262784000000⟩, + ⟨5, 1, 5, 4, 1, 6, 40141833730625359632952912228631920121374310400000000⟩, + ⟨5, 1, 6, 4, 2, 6, -20327075369402880285081789542130847717313740800000000⟩, + ⟨5, 1, 7, 4, 3, 6, 7155222510826456569911878187450760999305478144000000⟩, + ⟨5, 1, 8, 4, 4, 6, -1663839437435052242567558081736666841570344960000000⟩, + ⟨5, 1, 5, 5, 0, 6, 459544743564586343833825544419047565978742292480000000⟩, + ⟨5, 1, 6, 5, 1, 6, 31411277370750815837202062445791027666721177600000000⟩, + ⟨5, 1, 7, 5, 2, 6, -13898332626722190973785256265186033867566350336000000⟩, + ⟨5, 1, 8, 5, 3, 6, 2327435469373642974208279655335399481199820800000000⟩, + ⟨5, 1, 6, 6, 0, 6, -46074206462826706552583893466960917196313722880000000⟩, + ⟨5, 1, 7, 6, 1, 6, 38185218839257183940113711036069638365503291392000000⟩, + ⟨5, 1, 8, 6, 2, 6, -8299976003943037735650127164456428876895092736000000⟩, + ⟨5, 1, 7, 7, 0, 6, -129434994971676857276546925116679704752359997440000000⟩, + ⟨5, 1, 8, 7, 1, 6, 15519132926822780561014493012877574485080801280000000⟩ +] + +def collectedFourData_8_0_37 : List CollectedFourTerm := [ + ⟨5, 2, 1, 0, 1, 7, -13503210852524472758065276354065815613682483200000000⟩, + ⟨5, 2, 2, 0, 2, 7, 7647729485233453730019146678098739892602064076800000⟩, + ⟨5, 2, 3, 0, 3, 7, 7011112163607423219748602951784443190752313344000000⟩, + ⟨5, 2, 4, 0, 4, 7, 28398139769312724773511283340127514522191239577600000⟩, + ⟨5, 2, 5, 0, 5, 7, -37341951652142838151778659140021603972144955392000000⟩, + ⟨5, 2, 6, 0, 6, 7, -8632778268744470081351955127820416615325682892800000⟩, + ⟨5, 2, 7, 0, 7, 7, 26373354963431397519900245234564531305945497600000⟩, + ⟨5, 2, 8, 0, 8, 7, -508025614750516282062116228630390655554263449600000⟩, + ⟨5, 2, 1, 1, 0, 7, 16194588348814358193296358979398905951185954406400000⟩, + ⟨5, 2, 2, 1, 1, 7, -40322805324074330634224684931644032778205187276800000⟩, + ⟨5, 2, 3, 1, 2, 7, -755187534188700314615443081191536939258766950400000⟩, + ⟨5, 2, 4, 1, 3, 7, -16932144244197061712179834823785455379286065152000000⟩, + ⟨5, 2, 5, 1, 4, 7, -19983475286774926566677383362420469644751011840000000⟩, + ⟨5, 2, 6, 1, 5, 7, 5428633233107118954103466488370922396078990950400000⟩, + ⟨5, 2, 7, 1, 6, 7, 1825412823215345983199960300103832097742284390400000⟩, + ⟨5, 2, 8, 1, 7, 7, -424513708638786247764674440799368521336225792000000⟩, + ⟨5, 2, 2, 2, 0, 7, 42623429122432299131761516359581570050835664076800000⟩, + ⟨5, 2, 3, 2, 1, 7, -5911872558276446440565709262521679815985908940800000⟩, + ⟨5, 2, 4, 2, 2, 7, 11154768795781039142781781302631157704294190284800000⟩, + ⟨5, 2, 5, 2, 3, 7, -29483436376753146375935597251758180102794379264000000⟩, + ⟨5, 2, 6, 2, 4, 7, -1948412673728103257867052141516724925798704742400000⟩, + ⟨5, 2, 7, 2, 5, 7, -185133482618682294726894591642930171227406336000000⟩, + ⟨5, 2, 8, 2, 6, 7, -23100559025425371676509587105021038228930560000000⟩, + ⟨5, 2, 3, 3, 0, 7, 60984329401412650819386030624027092320499269632000000⟩, + ⟨5, 2, 4, 3, 1, 7, -24766142647131690759860194115351212331034161971200000⟩, + ⟨5, 2, 5, 3, 2, 7, 80098659361825862864840426325380530336809615360000000⟩, + ⟨5, 2, 6, 3, 3, 7, -2957870629637602745316045438428501916738650112000000⟩, + ⟨5, 2, 7, 3, 4, 7, 743847068392676982499083230581224482075679129600000⟩, + ⟨5, 2, 8, 3, 5, 7, -367547645071706218574319225319015887459581952000000⟩, + ⟨5, 2, 4, 4, 0, 7, 41367609786806997417797503885397341653382358630400000⟩, + ⟨5, 2, 5, 4, 1, 7, -22201602582481682648653785652425259394720071680000000⟩, + ⟨5, 2, 6, 4, 2, 7, 8993981730761440206810604951165708951395237888000000⟩, + ⟨5, 2, 7, 4, 3, 7, -2638268556117286401859672799283282896940643123200000⟩, + ⟨5, 2, 8, 4, 4, 7, 525848309327809622470853370911660537548898304000000⟩, + ⟨5, 2, 5, 5, 0, 7, -254164516597694017588890236185673028393045590016000000⟩, + ⟨5, 2, 6, 5, 1, 7, -13898332626722190973785256265186033867566350336000000⟩, + ⟨5, 2, 7, 5, 2, 7, 5124583323028605809747762354794385225978531020800000⟩, + ⟨5, 2, 8, 5, 3, 7, -735574586768070347252291957185518761850961920000000⟩, + ⟨5, 2, 6, 6, 0, 7, 20386138372357845068632989881796130953491172556800000⟩, + ⟨5, 2, 7, 6, 1, 7, -14079626736923580827894257161876550014717237657600000⟩, + ⟨5, 2, 8, 6, 2, 7, 2623166785770579816594582749276031808780527206400000⟩, + ⟨5, 2, 7, 7, 0, 7, 47725179304805622319338236615805790576057516032000000⟩, + ⟨5, 2, 8, 7, 1, 7, -4904745991827022828006041366714874999993270272000000⟩ +] + +def collectedFourData_8_0_38 : List CollectedFourTerm := [ + ⟨5, 3, 0, 0, 0, 8, 60726233668553150206446532264453826087485440000000000⟩, + ⟨5, 3, 1, 0, 1, 8, 13567606733560486062928640524791381240053760000000000⟩, + ⟨5, 3, 2, 0, 2, 8, -3842100489784765549052791521627530773785477120000000⟩, + ⟨5, 3, 3, 0, 3, 8, -2348182557951247938506349736874652610225766400000000⟩, + ⟨5, 3, 4, 0, 4, 8, -7133392134706371272185488370806408530016337920000000⟩, + ⟨5, 3, 5, 0, 5, 8, 7504006568707101058918335175068766537116549120000000⟩, + ⟨5, 3, 6, 0, 6, 8, 1445657898795911982893305077885233734185123840000000⟩, + ⟨5, 3, 7, 0, 7, 8, -3785589667697827267283463747490441058058240000000⟩, + ⟨5, 3, 8, 0, 8, 8, 63806044232636132026785047744585922678620160000000⟩, + ⟨5, 3, 1, 1, 0, 8, -16271819223465366794669964788898419195793899520000000⟩, + ⟨5, 3, 2, 1, 1, 8, 20257551000497049722657551143525928720788357120000000⟩, + ⟨5, 3, 3, 1, 2, 8, 252929657147532138782105813374962581624586240000000⟩, + ⟨5, 3, 4, 1, 3, 8, 4253223118008205025322122127521968919307878400000000⟩, + ⟨5, 3, 5, 1, 4, 8, 4015755020371302847111993212350581013112422400000000⟩, + ⟨5, 3, 6, 1, 5, 8, -909087001750211958859843991256870933359493120000000⟩, + ⟨5, 3, 7, 1, 6, 8, -262016870149009296673833096839461979773992960000000⟩, + ⟨5, 3, 8, 1, 7, 8, 53317273153773150076799966286683825189683200000000⟩, + ⟨5, 3, 2, 2, 0, 8, -21413348657768894659714403866666253600025477120000000⟩, + ⟨5, 3, 3, 2, 1, 8, 1980021956892014250211274007638136827915796480000000⟩, + ⟨5, 3, 4, 2, 2, 8, -2801991279663958933463160385218335473831772160000000⟩, + ⟨5, 3, 5, 2, 3, 8, 5924808170183509865189397522861468526093271040000000⟩, + ⟨5, 3, 6, 2, 4, 8, 326284086559627808741435058852353589085470720000000⟩, + ⟨5, 3, 7, 2, 5, 8, 26573767346549747759702147794942155974246400000000⟩, + ⟨5, 3, 8, 2, 6, 8, 2901340499728050716724261887932970827776000000000⟩, + ⟨5, 3, 3, 3, 0, 8, -20425053153773658133287867011370945262859059200000000⟩, + ⟨5, 3, 4, 3, 1, 8, 6221062668230568204982024651741848251966423040000000⟩, + ⟨5, 3, 5, 3, 2, 8, -16096128868542477779874080609700614608886169600000000⟩, + ⟨5, 3, 6, 3, 3, 8, 495329418436915195895960421077858022693273600000000⟩, + ⟨5, 3, 7, 3, 4, 8, -106770631963930635570201775373144070071255040000000⟩, + ⟨5, 3, 8, 3, 5, 8, 46162556804470063824557261589853062247219200000000⟩, + ⟨5, 3, 4, 4, 0, 8, -10391222266033412552115115289542884211745095680000000⟩, + ⟨5, 3, 5, 4, 1, 8, 4461496098723774684566855922070620958674124800000000⟩, + ⟨5, 3, 6, 4, 2, 8, -1506145568197527010615338860099208999233126400000000⟩, + ⟨5, 3, 7, 4, 3, 8, 378692896694331638166145289156565231395143680000000⟩, + ⟨5, 3, 8, 4, 4, 8, -66044505454915253987942684576840048600678400000000⟩, + ⟨5, 3, 5, 5, 0, 8, 51075321928759306612827063088334902602246389760000000⟩, + ⟨5, 3, 6, 5, 1, 8, 2327435469373642974208279655335399481199820800000000⟩, + ⟨5, 3, 7, 5, 2, 8, -735574586768070347252291957185518761850961920000000⟩, + ⟨5, 3, 8, 5, 3, 8, 92385311403589702906252900925703016415232000000000⟩, + ⟨5, 3, 6, 6, 0, 8, -3413893076652807430210214842470569329337303040000000⟩, + ⟨5, 3, 7, 6, 1, 8, 2020967357935459267071393229805163311781642240000000⟩, + ⟨5, 3, 8, 6, 2, 8, -329459560901578477592820389262977473645117440000000⟩, + ⟨5, 3, 7, 7, 0, 8, -6850396770369479919300291600811873950026956800000000⟩, + ⟨5, 3, 8, 7, 1, 8, 616017048388487298244508853758302461571891200000000⟩ +] + +def collectedFourData_8_0_39 : List CollectedFourTerm := [ + ⟨6, 0, 2, 0, 2, 6, 5070580432029788411321584417529292626569514188800000⟩, + ⟨6, 0, 3, 0, 3, 6, 9296983689654819123302832285820571905695940608000000⟩, + ⟨6, 0, 4, 0, 4, 6, 56485412604494779029957072595596891337234631884800000⟩, + ⟨6, 0, 5, 0, 5, 6, -99033507765541980579366786435239797477959794688000000⟩, + ⟨6, 0, 6, 0, 6, 6, -28618426323830338958514300675041222335056052224000000⟩, + ⟨6, 0, 7, 0, 7, 6, 104916015554231205385858397123518836527176089600000⟩, + ⟨6, 0, 8, 0, 8, 6, -2357810017036273654325773054285191636692710195200000⟩, + ⟨6, 0, 2, 1, 1, 6, -26734735850107876551382393863510792807570525388800000⟩, + ⟨6, 0, 3, 1, 2, 6, -1001405486625462073241069661370076356844244172800000⟩, + ⟨6, 0, 4, 1, 3, 6, -33678936778309938302813622880657216768359530496000000⟩, + ⟨6, 0, 5, 1, 4, 6, -52997595664815116258631127736878895996872949760000000⟩, + ⟨6, 0, 6, 1, 5, 6, 17996401087151748867129235529216533228192530432000000⟩, + ⟨6, 0, 7, 1, 6, 6, 7261686668946900000883458394711558876276614758400000⟩, + ⟨6, 0, 8, 1, 7, 6, -1970220881656304562398056829617316339336085504000000⟩, + ⟨6, 0, 2, 2, 0, 6, 28260090275357903689693050285016626312227114188800000⟩, + ⟨6, 0, 3, 2, 1, 6, -7839352939596129338545144265299298076438665625600000⟩, + ⟨6, 0, 4, 2, 2, 6, 22187429284304991875552292503444226030877173350400000⟩, + ⟨6, 0, 5, 2, 3, 6, -78192167152155060917784250424376965750216196096000000⟩, + ⟨6, 0, 6, 2, 4, 6, -6459160981047028980524546824879624032765345792000000⟩, + ⟨6, 0, 7, 2, 5, 6, -736480715819535841151016528243688743377043456000000⟩, + ⟨6, 0, 8, 2, 6, 6, -107212565445215651487521688635383713858846720000000⟩, + ⟨6, 0, 3, 3, 0, 6, 80867386306047536723348110631736529521972609024000000⟩, + ⟨6, 0, 4, 3, 1, 6, -49261176873166156834580917043409939778363824537600000⟩, + ⟨6, 0, 5, 3, 2, 6, 212427333145660212391853084401592775876846551040000000⟩, + ⟨6, 0, 6, 3, 3, 6, -9805603718119893100614657774477201384627240960000000⟩, + ⟨6, 0, 7, 3, 4, 6, 2959102878858819380346031628616828816134347161600000⟩, + ⟨6, 0, 8, 3, 5, 6, -1705834300724658903650089234261269994404839424000000⟩, + ⟨6, 0, 4, 4, 0, 6, 82282379277340960546813966317016116640359854899200000⟩, + ⟨6, 0, 5, 4, 1, 6, -58880226781973936079809895967849672435323371520000000⟩, + ⟨6, 0, 6, 4, 2, 6, 29815847865754003863290338985049985154851799040000000⟩, + ⟨6, 0, 7, 4, 3, 6, -10495313366601983945260006403391093252897846067200000⟩, + ⟨6, 0, 8, 4, 4, 6, 2440527357628552535173656767731690226369691648000000⟩, + ⟨6, 0, 5, 5, 0, 6, -674062348499627699210011176316872660102439501824000000⟩, + ⟨6, 0, 6, 5, 1, 6, -46074206462826706552583893466960917196313722880000000⟩, + ⟨6, 0, 7, 5, 2, 6, 20386138372357845068632989881796130953491172556800000⟩, + ⟨6, 0, 8, 5, 3, 6, -3413893076652807430210214842470569329337303040000000⟩, + ⟨6, 0, 6, 6, 0, 6, 67581858455584378056866004819965619527529529344000000⟩, + ⟨6, 0, 7, 6, 1, 6, -56010255038733627522991937132187046080811735449600000⟩, + ⟨6, 0, 8, 6, 2, 6, 12174443067962317847120674174795522503728745676800000⟩, + ⟨6, 0, 7, 7, 0, 6, 189855847358602002182804668292633659482121961472000000⟩, + ⟨6, 0, 8, 7, 1, 6, -22763535724920876562274654907254085800914059264000000⟩ +] + +def collectedFourData_8_0_40 : List CollectedFourTerm := [ + ⟨6, 1, 1, 0, 1, 7, 37099634559392832280277725630112527548835430400000000⟩, + ⟨6, 1, 2, 0, 2, 7, -21011889113633343993508145616811513568894228889600000⟩, + ⟨6, 1, 3, 0, 3, 7, -19262803637263872595502258514929675386453229568000000⟩, + ⟨6, 1, 4, 0, 4, 7, -78022969434050975871965882618129007971786765107200000⟩, + ⟨6, 1, 5, 0, 5, 7, 102595802965634236470433753530338478355459866624000000⟩, + ⟨6, 1, 6, 0, 6, 7, 23718278748703062514454476632549827847254546841600000⟩, + ⟨6, 1, 7, 0, 7, 7, -72459938746015420503370287426690763306775347200000⟩, + ⟨6, 1, 8, 0, 8, 7, 1395783925756548812614297879627730288641258291200000⟩, + ⟨6, 1, 1, 1, 0, 7, -44494107078872245096994384887590658078073998540800000⟩, + ⟨6, 1, 2, 1, 1, 7, 110785601903936951192061997429355488520143739289600000⟩, + ⟨6, 1, 3, 1, 2, 7, 2074853295871614982453160776323075698903010508800000⟩, + ⟨6, 1, 4, 1, 3, 7, 46520518018068121798541285099490147666801721344000000⟩, + ⟨6, 1, 5, 1, 4, 7, 54903951250039476813153680830751097596915220480000000⟩, + ⟨6, 1, 6, 1, 5, 7, -14914994019188911619652660517552498258003938508800000⟩, + ⟨6, 1, 7, 1, 6, 7, -5015262621679198215014674943741979488659754188800000⟩, + ⟨6, 1, 8, 1, 7, 7, 1166337667978216169529900430358814973885415424000000⟩, + ⟨6, 1, 2, 2, 0, 7, -117106491291646244182255132571247262208433428889600000⟩, + ⟨6, 1, 3, 2, 1, 7, 16242678416945164493103525710934365721044031897600000⟩, + ⟨6, 1, 4, 2, 2, 7, -30647366055209496023508019885389789370720557465600000⟩, + ⟨6, 1, 5, 2, 3, 7, 81004786719164386128024556970491574334215159808000000⟩, + ⟨6, 1, 6, 2, 4, 7, 5353200728009673416475754858762779960198089932800000⟩, + ⟨6, 1, 7, 2, 5, 7, 508648248544289689569388641181553537310523392000000⟩, + ⟨6, 1, 8, 2, 6, 7, 63468037885281321172116282529570324029112320000000⟩, + ⟨6, 1, 3, 3, 0, 7, -167552470249626853027103021393493260042873339904000000⟩, + ⟨6, 1, 4, 3, 1, 7, 68044174951367503160821300919825334554367256166400000⟩, + ⟨6, 1, 5, 3, 2, 7, -220068472859954796724568658782384660638775377920000000⟩, + ⟨6, 1, 6, 3, 3, 7, 8126653773831927348892757167995690682064830464000000⟩, + ⟨6, 1, 7, 3, 4, 7, -2043695733321438026568119157782115583746323251200000⟩, + ⟨6, 1, 8, 3, 5, 7, 1009825252989843248849218163325301262798290944000000⟩, + ⟨6, 1, 4, 4, 0, 7, -113656168332673271957729932978321194517799947468800000⟩, + ⟨6, 1, 5, 4, 1, 7, 60998184168097644237033566569038190021139496960000000⟩, + ⟨6, 1, 6, 4, 2, 7, -24710673564185918387480627280340400298352705536000000⟩, + ⟨6, 1, 7, 4, 3, 7, 7248557426116879508484801284901784117922129510400000⟩, + ⟨6, 1, 8, 4, 4, 7, -1444751201977199598305342373447502543284338688000000⟩, + ⟨6, 1, 5, 5, 0, 7, 698308779054303266828473717727669841681136484352000000⟩, + ⟨6, 1, 6, 5, 1, 7, 38185218839257183940113711036069638365503291392000000⟩, + ⟨6, 1, 7, 5, 2, 7, -14079626736923580827894257161876550014717237657600000⟩, + ⟨6, 1, 8, 5, 3, 7, 2020967357935459267071393229805163311781642240000000⟩, + ⟨6, 1, 6, 6, 0, 7, -56010255038733627522991937132187046080811735449600000⟩, + ⟨6, 1, 7, 6, 1, 7, 38683318536410651446235123491073862010538242867200000⟩, + ⟨6, 1, 8, 6, 2, 7, -7207065801111413121325410793336667292597800140800000⟩, + ⟨6, 1, 7, 7, 0, 7, -131123384713997029745943299911931997689116360704000000⟩, + ⟨6, 1, 8, 7, 1, 7, 13475630788169943105764845527248538174681513984000000⟩ +] + +def collectedFourData_8_0_41 : List CollectedFourTerm := [ + ⟨6, 2, 0, 0, 0, 8, -216558649591462986513861843664125416308526284800000000⟩, + ⟨6, 2, 1, 0, 1, 8, -48384074145692090436824756909183027683472179200000000⟩, + ⟨6, 2, 2, 0, 2, 8, 13701493463332572280830560055941526210908415590400000⟩, + ⟨6, 2, 3, 0, 3, 8, 8373963162604044251532992343383172685536165888000000⟩, + ⟨6, 2, 4, 0, 4, 8, 25438721856684862304114501808358761301274945126400000⟩, + ⟨6, 2, 5, 0, 5, 8, -26760387247368635940257367034141031404824585830400000⟩, + ⟨6, 2, 6, 0, 6, 8, -5155427949693454023528005658222124742635998412800000⟩, + ⟨6, 2, 7, 0, 7, 8, 13499967589272180349438103330780771517254860800000⟩, + ⟨6, 2, 8, 0, 8, 8, -227541705454858560954763467904361019817014067200000⟩, + ⟨6, 2, 1, 1, 0, 8, 58027692227105068210413406424038198356967056998400000⟩, + ⟨6, 2, 2, 1, 1, 8, -72241395912053662513872946293337568530934425190400000⟩, + ⟨6, 2, 3, 1, 2, 8, -901984227977337026690944715189361189334076620800000⟩, + ⟨6, 2, 4, 1, 3, 8, -15167617011690653767294055783079551817826172928000000⟩, + ⟨6, 2, 5, 1, 4, 8, -14320770971048883178996275485620313310162321408000000⟩, + ⟨6, 2, 6, 1, 5, 8, 3241937488412467963884955623012280398648862310400000⟩, + ⟨6, 2, 7, 1, 6, 8, 934390561406326803773640279088403959726158643200000⟩, + ⟨6, 2, 8, 1, 7, 8, -190137210502806014532382588558897362128338944000000⟩, + ⟨6, 2, 2, 2, 0, 8, 76363139757158667915628547227274111948329215590400000⟩, + ⟨6, 2, 3, 2, 1, 8, -7061048499835224861972422783730669534683175321600000⟩, + ⟨6, 2, 4, 2, 2, 8, 9992311576624403306582778891837807970135257907200000⟩, + ⟨6, 2, 5, 2, 3, 8, -21128734303307202259541052098998234808767532236800000⟩, + ⟨6, 2, 6, 2, 4, 8, -1163576874439486993676859801152231907862668902400000⟩, + ⟨6, 2, 7, 2, 5, 8, -94765949137178559320189018411145015211327488000000⟩, + ⟨6, 2, 8, 2, 6, 8, -10346605456473339546874268338923883116625920000000⟩, + ⟨6, 2, 3, 3, 0, 8, 72838733140560704580497644261119282095654436864000000⟩, + ⟨6, 2, 4, 3, 1, 8, -22185221263829683162702197051223045043668176076800000⟩, + ⟨6, 2, 5, 3, 2, 8, 57401154671425103183222892594234643807293407232000000⟩, + ⟨6, 2, 6, 3, 3, 8, -1766417304012241472496891647714687042728230912000000⟩, + ⟨6, 2, 7, 3, 4, 8, 380759722401648067628353430278856034438925516800000⟩, + ⟨6, 2, 8, 3, 5, 8, -164622443371489629280739475857167472671064064000000⟩, + ⟨6, 2, 4, 4, 0, 8, 37056621588278276165944576593872722037535512985600000⟩, + ⟨6, 2, 5, 4, 1, 8, -15910348986413946358080851591576199808382140416000000⟩, + ⟨6, 2, 6, 4, 2, 8, 5371135844143887233404316578519915301424857088000000⟩, + ⟨6, 2, 7, 4, 3, 8, -1350474372667574506879924872597193830826613145600000⟩, + ⟨6, 2, 8, 4, 4, 8, 235524386253168179760474670554433864417148928000000⟩, + ⟨6, 2, 5, 5, 0, 8, -182142083843232762236899195510348821637532693299200000⟩, + ⟨6, 2, 6, 5, 1, 8, -8299976003943037735650127164456428876895092736000000⟩, + ⟨6, 2, 7, 5, 2, 8, 2623166785770579816594582749276031808780527206400000⟩, + ⟨6, 2, 8, 5, 3, 8, -329459560901578477592820389262977473645117440000000⟩, + ⟨6, 2, 6, 6, 0, 8, 12174443067962317847120674174795522503728745676800000⟩, + ⟨6, 2, 7, 6, 1, 8, -7207065801111413121325410793336667292597800140800000⟩, + ⟨6, 2, 8, 6, 2, 8, 1174901081355702959214601267949577061337451724800000⟩, + ⟨6, 2, 7, 7, 0, 8, 24429518910295359655489037381712792921997049856000000⟩, + ⟨6, 2, 8, 7, 1, 8, -2196807080980100070750733989323563481960546304000000⟩ +] + +def collectedFourData_8_0_42 : List CollectedFourTerm := [ + ⟨7, 0, 1, 0, 1, 7, -125755230914357467900211309832237170062000128000000000⟩, + ⟨7, 0, 2, 0, 2, 7, 71223207420053882809865495579060421231768502272000000⟩, + ⟨7, 0, 3, 0, 3, 7, 65294398401257132985451906997727571243444469760000000⟩, + ⟨7, 0, 4, 0, 4, 7, 264471514459130932168502754180728448845824917504000000⟩, + ⟨7, 0, 5, 0, 5, 7, -347765120762375667870522780758331704011841863680000000⟩, + ⟨7, 0, 6, 0, 6, 7, -80396954211482819608299875266601682876248358912000000⟩, + ⟨7, 0, 7, 0, 7, 7, 245614719316375288684694497266587535937634304000000⟩, + ⟨7, 0, 8, 0, 8, 7, -4731236088297895887800141305656268027418640384000000⟩, + ⟨7, 0, 1, 1, 0, 7, 150819995304107368559069543470986967827250937856000000⟩, + ⟨7, 0, 2, 1, 1, 7, -375525773093859789401858020445556044566754230272000000⟩, + ⟨7, 0, 3, 1, 2, 7, -7033051900229306208895758728259589498120175616000000⟩, + ⟨7, 0, 4, 1, 3, 7, -157688843976403509045057610704798497068107694080000000⟩, + ⟨7, 0, 5, 1, 4, 7, -186105851164274574021543442142246948111489433600000000⟩, + ⟨7, 0, 6, 1, 5, 7, 50556792249978933797302455988959658721585135616000000⟩, + ⟨7, 0, 7, 1, 6, 7, 17000046404115719375115235435929946560676233216000000⟩, + ⟨7, 0, 8, 1, 7, 7, -3953490768915924280555944946380560163070279680000000⟩, + ⟨7, 0, 2, 2, 0, 7, 396951453264993602044871766249667058959512502272000000⟩, + ⟨7, 0, 3, 2, 1, 7, -55057193938678470862854639918911298761845112832000000⟩, + ⟨7, 0, 4, 2, 2, 7, 103884219911108095820314563232735978875720302592000000⟩, + ⟨7, 0, 5, 2, 3, 7, -274578867959703964340433873481975718566491586560000000⟩, + ⟨7, 0, 6, 2, 4, 7, -18145542447434295513697360157412893783066935296000000⟩, + ⟨7, 0, 7, 2, 5, 7, -1724145768807203187291357801308250900466237440000000⟩, + ⟨7, 0, 8, 2, 6, 7, -215135212374322743960018898562710275253862400000000⟩, + ⟨7, 0, 3, 3, 0, 7, 567946284020153793252541633666683145674848993280000000⟩, + ⟨7, 0, 4, 3, 1, 7, -230646771457745592486329004679360345716868251648000000⟩, + ⟨7, 0, 5, 3, 2, 7, 745957795815187306106181263385688451028772454400000000⟩, + ⟨7, 0, 6, 3, 3, 7, -27546611550935826403121678222925237653581332480000000⟩, + ⟨7, 0, 7, 3, 4, 7, 6927438286516929932476854646456111390821187584000000⟩, + ⟨7, 0, 8, 3, 5, 7, -3422966543500246854166498535218008744347566080000000⟩, + ⟨7, 0, 4, 4, 0, 7, 385256023765812671639948123320441938080553762816000000⟩, + ⟨7, 0, 5, 4, 1, 7, -206763242455538707667069897114182465667412787200000000⟩, + ⟨7, 0, 6, 4, 2, 7, 83760837458889668279215620832796124332446187520000000⟩, + ⟨7, 0, 7, 4, 3, 7, -24570161505446025948126368092728492575296585728000000⟩, + ⟨7, 0, 8, 4, 4, 7, 4897218616198996707493011638611520138678108160000000⟩, + ⟨7, 0, 5, 5, 0, 7, -2367030910207815308426853487709840466999131504640000000⟩, + ⟨7, 0, 6, 5, 1, 7, -129434994971676857276546925116679704752359997440000000⟩, + ⟨7, 0, 7, 5, 2, 7, 47725179304805622319338236615805790576057516032000000⟩, + ⟨7, 0, 8, 5, 3, 7, -6850396770369479919300291600811873950026956800000000⟩, + ⟨7, 0, 6, 6, 0, 7, 189855847358602002182804668292633659482121961472000000⟩, + ⟨7, 0, 7, 6, 1, 7, -131123384713997029745943299911931997689116360704000000⟩, + ⟨7, 0, 8, 6, 2, 7, 24429518910295359655489037381712792921997049856000000⟩, + ⟨7, 0, 7, 7, 0, 7, 444463987821304591055186634952354641606900449280000000⟩, + ⟨7, 0, 8, 7, 1, 7, -45677837035564326279344884910274489124525178880000000⟩ +] + +def collectedFourData_8_0_43 : List CollectedFourTerm := [ + ⟨7, 1, 0, 0, 0, 8, 404917130828636902450377864525641362496815104000000000⟩, + ⟨7, 1, 1, 0, 1, 8, 90467596273956427279293957043366031435759616000000000⟩, + ⟨7, 1, 2, 0, 2, 8, -25618784711237211263298204170071725614240366592000000⟩, + ⟨7, 1, 3, 0, 3, 8, -15657472670165726210557081815186789233841930240000000⟩, + ⟨7, 1, 4, 0, 4, 8, -47564824982001693238229586393115277791825231872000000⟩, + ⟨7, 1, 5, 0, 5, 8, 50036049100367639806057020344748488875460001792000000⟩, + ⟨7, 1, 6, 0, 6, 8, 9639518428479932342807743559286031013111660544000000⟩, + ⟨7, 1, 7, 0, 7, 8, -25241975570312996946912991749374745545539584000000⟩, + ⟨7, 1, 8, 0, 8, 8, 425453034041583833987181118585595761426169856000000⟩, + ⟨7, 1, 1, 1, 0, 8, -108499044898610401111217453902847549900882706432000000⟩, + ⟨7, 1, 2, 1, 1, 8, 135075550272167608504899833701051425198641774592000000⟩, + ⟨7, 1, 3, 1, 2, 8, 1686512482111747571707221555680079376898064384000000⟩, + ⟨7, 1, 4, 1, 3, 8, 28360113869695619971077813265617638319917629440000000⟩, + ⟨7, 1, 5, 1, 4, 8, 26776697692705501586266614621244425357848739840000000⟩, + ⟨7, 1, 6, 1, 5, 8, -6061711359071583045697825003906888583916552192000000⟩, + ⟨7, 1, 7, 1, 6, 8, -1747105211044519620319488438562593170402574336000000⟩, + ⟨7, 1, 8, 1, 7, 8, 355514840371408616733285393006992494291845120000000⟩, + ⟨7, 1, 2, 2, 0, 8, -142782306363041870537134391822167027262624366592000000⟩, + ⟨7, 1, 3, 2, 1, 8, 13202610491840825298491988750972243098015367168000000⟩, + ⟨7, 1, 4, 2, 2, 8, -18683428907528740300142610403413531901669933056000000⟩, + ⟨7, 1, 5, 2, 3, 8, 39506094484221492183006518496638826540448088064000000⟩, + ⟨7, 1, 6, 2, 4, 8, 2175633300195660159745716246253686786833252352000000⟩, + ⟨7, 1, 7, 2, 5, 8, 177191519698096452673665696919473503852298240000000⟩, + ⟨7, 1, 8, 2, 6, 8, 19345880680151136809784323056616951355801600000000⟩, + ⟨7, 1, 3, 3, 0, 8, -136192439748346426668697502342630939906770206720000000⟩, + ⟨7, 1, 4, 3, 1, 8, 41481493156219372776263262145673088899443851264000000⟩, + ⟨7, 1, 5, 3, 2, 8, -107327557221341841976198177597822158782186127360000000⟩, + ⟨7, 1, 6, 3, 3, 8, 3302812554178805797554610223387647086962933760000000⟩, + ⟨7, 1, 7, 3, 4, 8, -711937087808943449760009298571478039175102464000000⟩, + ⟨7, 1, 8, 3, 5, 8, 307807827421043798548498318594747178648862720000000⟩, + ⟨7, 1, 4, 4, 0, 8, -69287746853033921873683826569473356483304357888000000⟩, + ⟨7, 1, 5, 4, 1, 8, 29748859600918996808820553255423904602317127680000000⟩, + ⟨7, 1, 6, 4, 2, 8, -10042844833972068672855793026358833366423306240000000⟩, + ⟨7, 1, 7, 4, 3, 8, 2525090589869075110876076777036760287897714688000000⟩, + ⟨7, 1, 8, 4, 4, 8, -440378894593772121464340603053591401794109440000000⟩, + ⟨7, 1, 5, 5, 0, 8, 340565708791057432866059358004238111033278857216000000⟩, + ⟨7, 1, 6, 5, 1, 8, 15519132926822780561014493012877574485080801280000000⟩, + ⟨7, 1, 7, 5, 2, 8, -4904745991827022828006041366714874999993270272000000⟩, + ⟨7, 1, 8, 5, 3, 8, 616017048388487298244508853758302461571891200000000⟩, + ⟨7, 1, 6, 6, 0, 8, -22763535724920876562274654907254085800914059264000000⟩, + ⟨7, 1, 7, 6, 1, 8, 13475630788169943105764845527248538174681513984000000⟩, + ⟨7, 1, 8, 6, 2, 8, -2196807080980100070750733989323563481960546304000000⟩, + ⟨7, 1, 7, 7, 0, 8, -45677837035564326279344884910274489124525178880000000⟩, + ⟨7, 1, 8, 7, 1, 8, 4107546948101957994091974249493073330354257920000000⟩ +] + +def collectedFourData_8_0 : List (List CollectedFourTerm) := [ + collectedFourData_8_0_0, + collectedFourData_8_0_1, + collectedFourData_8_0_2, + collectedFourData_8_0_3, + collectedFourData_8_0_4, + collectedFourData_8_0_5, + collectedFourData_8_0_6, + collectedFourData_8_0_7, + collectedFourData_8_0_8, + collectedFourData_8_0_9, + collectedFourData_8_0_10, + collectedFourData_8_0_11, + collectedFourData_8_0_12, + collectedFourData_8_0_13, + collectedFourData_8_0_14, + collectedFourData_8_0_15, + collectedFourData_8_0_16, + collectedFourData_8_0_17, + collectedFourData_8_0_18, + collectedFourData_8_0_19, + collectedFourData_8_0_20, + collectedFourData_8_0_21, + collectedFourData_8_0_22, + collectedFourData_8_0_23, + collectedFourData_8_0_24, + collectedFourData_8_0_25, + collectedFourData_8_0_26, + collectedFourData_8_0_27, + collectedFourData_8_0_28, + collectedFourData_8_0_29, + collectedFourData_8_0_30, + collectedFourData_8_0_31, + collectedFourData_8_0_32, + collectedFourData_8_0_33, + collectedFourData_8_0_34, + collectedFourData_8_0_35, + collectedFourData_8_0_36, + collectedFourData_8_0_37, + collectedFourData_8_0_38, + collectedFourData_8_0_39, + collectedFourData_8_0_40, + collectedFourData_8_0_41, + collectedFourData_8_0_42, + collectedFourData_8_0_43 +] + +theorem collectedFourChecked_8_0 : collectNumericRowParts 8 0 = collectedFourData_8_0 := by + decide +kernel + +def collectedFourData_8_1_0 : List CollectedFourTerm := [ + ⟨0, 1, 7, 0, 8, 0, -49616014343845026366501995332613192783065251840000000⟩, + ⟨0, 1, 7, 1, 7, 0, 3925104368010053562424834998602183650521907200000000⟩, + ⟨0, 1, 8, 1, 8, 0, 56723338964805595530929605258468289423370878976000000⟩, + ⟨0, 1, 7, 2, 6, 0, 2461814341939559416957163790439353649824006144000000⟩, + ⟨0, 1, 8, 2, 7, 0, 24355716481599897326420689829408853411414147072000000⟩, + ⟨0, 1, 7, 3, 5, 0, 5904628205905368950979536067825598024453718016000000⟩, + ⟨0, 1, 8, 3, 6, 0, -1307875901668456584340190112931827130029834240000000⟩, + ⟨0, 1, 7, 4, 4, 0, -3052721622249653170343433728012411263229362176000000⟩, + ⟨0, 1, 8, 4, 5, 0, -17801672832357293491062858431608300349159374848000000⟩, + ⟨0, 1, 7, 5, 3, 0, -3482191028810939789929028837717180443715960832000000⟩, + ⟨0, 1, 8, 5, 4, 0, -8911558357660444078196155392636693360509190144000000⟩, + ⟨0, 1, 7, 6, 2, 0, -24645194989054599446777468671997165785508216832000000⟩, + ⟨0, 1, 8, 6, 3, 0, 47315034882383871532229705755361049959001489408000000⟩, + ⟨0, 1, 7, 7, 1, 0, 127502800345087652396332379978480646857724788736000000⟩, + ⟨0, 1, 8, 7, 2, 0, -18610263040687662023800485001954017403471921152000000⟩ +] + +def collectedFourData_8_1_1 : List CollectedFourTerm := [ + ⟨0, 2, 6, 0, 7, 1, 21416951424401909323492145906381831960398921728000000⟩, + ⟨0, 2, 7, 0, 8, 1, 62822364857219996757787360765219727248698900480000000⟩, + ⟨0, 2, 6, 1, 6, 1, -7892260486510565857625871741907540668818915328000000⟩, + ⟨0, 2, 7, 1, 7, 1, -4969853825842115700655875757301225203590758400000000⟩, + ⟨0, 2, 8, 1, 8, 1, -35910727045418551555128578818961155145896820736000000⟩, + ⟨0, 2, 6, 2, 5, 1, -141792642174968081893700739848204471419011072000000⟩, + ⟨0, 2, 7, 2, 6, 1, -3117078242687373059918210466416218179442311168000000⟩, + ⟨0, 2, 8, 2, 7, 1, -15419252507490914985772015344962506845472161792000000⟩, + ⟨0, 2, 6, 3, 4, 1, 2296007484576031764137743457391674026799136768000000⟩, + ⟨0, 2, 7, 3, 5, 1, -7476269756916410851239883797762933723708260352000000⟩, + ⟨0, 2, 8, 3, 6, 1, 827997352963257182704647005158493880204656640000000⟩, + ⟨0, 2, 6, 4, 3, 1, -2898961470852887156446511397296543261370875904000000⟩, + ⟨0, 2, 7, 4, 4, 1, 3865267980443553140305362160717742965493071872000000⟩, + ⟨0, 2, 8, 4, 5, 1, 11269982086760901650042638425998692431144419328000000⟩, + ⟨0, 2, 6, 5, 2, 1, 6292881550124830021160098114652410106741784576000000⟩, + ⟨0, 2, 7, 5, 3, 1, 4409049743465271188436862225688743231623266304000000⟩, + ⟨0, 2, 8, 5, 4, 1, 5641778949751559741175501095211027290426179584000000⟩, + ⟨0, 2, 6, 6, 1, 1, -11785324770183209000869146212639714800023109632000000⟩, + ⟨0, 2, 7, 6, 2, 1, 31205034343347737977824469504401955190476898304000000⟩, + ⟨0, 2, 8, 6, 3, 1, -29954465548298809544637250661629917386388799488000000⟩, + ⟨0, 2, 6, 7, 0, 1, -3497093571819621481145473944123310757614977024000000⟩, + ⟨0, 2, 7, 7, 1, 1, -161440364558223193846905220371010071612402696192000000⟩, + ⟨0, 2, 8, 7, 2, 1, 11781888874916765337922096164500930113591836672000000⟩ +] + +def collectedFourData_8_1_2 : List CollectedFourTerm := [ + ⟨0, 3, 5, 0, 6, 2, -14794929572197980152859619857313616708724640972800000⟩, + ⟨0, 3, 6, 0, 7, 2, -20372594240050700994801567377050881544023755980800000⟩, + ⟨0, 3, 7, 0, 8, 2, -29879475446218997905796095656164130514916081664000000⟩, + ⟨0, 3, 5, 1, 5, 2, 4849523666454223756207964084230081632956055552000000⟩, + ⟨0, 3, 6, 1, 6, 2, 7507409310611302778425830937078548039027444940800000⟩, + ⟨0, 3, 7, 1, 7, 2, 2363754145486943519029088211117053549079429120000000⟩, + ⟨0, 3, 8, 1, 8, 2, 11386536089476102994661908282860863660473135923200000⟩, + ⟨0, 3, 5, 2, 4, 2, -3642959516180422900475232941873576884500116275200000⟩, + ⟨0, 3, 6, 2, 5, 2, 134878391794083006563091368941999093143778099200000⟩, + ⟨0, 3, 7, 2, 6, 2, 1482539904825262124771643170196387033044641382400000⟩, + ⟨0, 3, 8, 2, 7, 2, 4889120594167682064858859574885146747575101030400000⟩, + ⟨0, 3, 5, 3, 3, 2, 1087807988737193688492212598330254874728044953600000⟩, + ⟨0, 3, 6, 3, 4, 2, -2184047016238363699848399093196376880463006924800000⟩, + ⟨0, 3, 7, 3, 5, 2, 3555851791615901509912074868773947555901446553600000⟩, + ⟨0, 3, 8, 3, 6, 2, -262540541982973496465493130807396209229037568000000⟩, + ⟨0, 3, 5, 4, 2, 2, 2246633371533124706930869652200171113830940672000000⟩, + ⟨0, 3, 6, 4, 3, 2, 2757599090220457522780380015031849610331448934400000⟩, + ⟨0, 3, 7, 4, 4, 2, -1838392744004549363705709780583535480059566489600000⟩, + ⟨0, 3, 8, 4, 5, 2, -3573474232263529065415424924560109835642313113600000⟩, + ⟨0, 3, 5, 5, 1, 2, 758497861931740467105018834400590380638037606400000⟩, + ⟨0, 3, 6, 5, 2, 2, -5986021067187185914555964959350507370209450393600000⟩, + ⟨0, 3, 7, 5, 3, 2, -2097025380219958810461976123883472395642811187200000⟩, + ⟨0, 3, 8, 5, 4, 2, -1788889418444353804145839526674011980196269260800000⟩, + ⟨0, 3, 5, 6, 0, 2, -40275343119487017933557683233992002762974638899200000⟩, + ⟨0, 3, 6, 6, 1, 2, 11210635667623561965297907470635326610106168115200000⟩, + ⟨0, 3, 7, 6, 2, 2, -14841689891483325060198546051474463327306068787200000⟩, + ⟨0, 3, 8, 6, 3, 2, 9497930871053953189329207172782523527919671705600000⟩, + ⟨0, 3, 6, 7, 0, 2, 3326564409022108999185394352579023928281163366400000⟩, + ⟨0, 3, 7, 7, 1, 2, 76784015052749058044330653914098922610958637465600000⟩, + ⟨0, 3, 8, 7, 2, 2, -3735789105766714716417818499139401818525034086400000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0804.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0804.lean new file mode 100644 index 0000000000000000000000000000000000000000..054f5338e72ad6b185df40df1b4ae234e06109a9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0804.lean @@ -0,0 +1,609 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0804. -/ +namespace LaughlinFock +def collectedFourData_8_1_3 : List CollectedFourTerm := [ + ⟨0, 4, 4, 0, 5, 3, -3104786001396462868963317703640604185578344284160000⟩, + ⟨0, 4, 5, 0, 6, 3, -5415933284964979854106066901825516394663798374400000⟩, + ⟨0, 4, 6, 0, 7, 3, -3728865714005033777213188339552623227189801779200000⟩, + ⟨0, 4, 7, 0, 8, 3, -3645961832549412159405178743131148972063719424000000⟩, + ⟨0, 4, 4, 1, 4, 3, -955445675145239113868705870585184478039407329280000⟩, + ⟨0, 4, 5, 1, 5, 3, 1775249859298442972355718991756551441084317696000000⟩, + ⟨0, 4, 6, 1, 6, 3, 1374106844198894983405821108726771136781824819200000⟩, + ⟨0, 4, 7, 1, 7, 3, 288430679162622428033330010471665789483089920000000⟩, + ⟨0, 4, 8, 1, 8, 3, 1042058353615516940043191227898252256113747558400000⟩, + ⟨0, 4, 4, 2, 3, 3, -1500155666734645077142874363038099958985255813120000⟩, + ⟨0, 4, 5, 2, 4, 3, -1333566719813071627596432623237356440266578329600000⟩, + ⟨0, 4, 6, 2, 5, 3, 24687254102001019909206339793288967257640140800000⟩, + ⟨0, 4, 7, 2, 6, 3, 180902905004255623553648718125692957825066598400000⟩, + ⟨0, 4, 8, 2, 7, 3, 447436245487762137769631471479382168321182924800000⟩, + ⟨0, 4, 4, 3, 2, 3, 4002140663716890033209928107200835154509058539520000⟩, + ⟨0, 4, 5, 3, 3, 3, 398210445349035788954293902493201163535305932800000⟩, + ⟨0, 4, 6, 3, 4, 3, -399753607256154813220604001139336335374627635200000⟩, + ⟨0, 4, 7, 3, 5, 3, 433893156450126826238033324992268735251847577600000⟩, + ⟨0, 4, 8, 3, 6, 3, -24026847391188522567101697800356567518806016000000⟩, + ⟨0, 4, 4, 4, 1, 3, -51380224025973260088766160932529677447200768000000⟩, + ⟨0, 4, 5, 4, 2, 3, 822418004534758032008643574593426701949075456000000⟩, + ⟨0, 4, 6, 4, 3, 3, 504732808170283739086013012604739516603406745600000⟩, + ⟨0, 4, 7, 4, 4, 3, -224324881135908361038719868256022793167673753600000⟩, + ⟨0, 4, 8, 4, 5, 3, -327032615177996409650874189687385679161668403200000⟩, + ⟨0, 4, 4, 5, 0, 3, -16491439550391349158149043422409528609774376058880000⟩, + ⟨0, 4, 5, 5, 1, 3, 277660924099998381242309318521965763055792947200000⟩, + ⟨0, 4, 6, 5, 2, 3, -1095641942196290958817106944038420576098215526400000⟩, + ⟨0, 4, 7, 5, 3, 3, -255883826070878567323627506550374283183600435200000⟩, + ⟨0, 4, 8, 5, 4, 3, -163713279221698034852699183645628481593252249600000⟩, + ⟨0, 4, 5, 6, 0, 3, -14743468044221935016231001618805142631441078681600000⟩, + ⟨0, 4, 6, 6, 1, 3, 2051921050438561990169561865982457261761285324800000⟩, + ⟨0, 4, 7, 6, 2, 3, -1811016895938515835043451223470512600719242035200000⟩, + ⟨0, 4, 8, 6, 3, 3, 869219412161003972905096933909116512965440307200000⟩, + ⟨0, 4, 6, 7, 0, 3, 608872479570922296969679743058867423641442713600000⟩, + ⟨0, 4, 7, 7, 1, 3, 9369360875699314758682752375221490548997724569600000⟩, + ⟨0, 4, 8, 7, 2, 3, -341887138847083798848700393910316234636577996800000⟩ +] + +def collectedFourData_8_1_4 : List CollectedFourTerm := [ + ⟨0, 5, 3, 0, 4, 4, -3104786001396462868963317703640604185578344284160000⟩, + ⟨0, 5, 4, 0, 5, 4, 182901405765343498628101457004735384252745179463680000⟩, + ⟨0, 5, 5, 0, 6, 4, 159524973847773745833474195601844208995449543065600000⟩, + ⟨0, 5, 6, 0, 7, 4, 73221877524458163076798068962755728897146565427200000⟩, + ⟨0, 5, 7, 0, 8, 4, 53695451493286540819302853502506395051636031488000000⟩, + ⟨0, 5, 3, 1, 3, 4, 14903508514108932383328563756802301317416736522240000⟩, + ⟨0, 5, 4, 1, 4, 4, 56284831559367464100191026207044215365172660797440000⟩, + ⟨0, 5, 5, 1, 5, 4, -52289545028928347408643401204720060213602811904000000⟩, + ⟨0, 5, 6, 1, 6, 4, -26982651231863422029293311725654759576517686067200000⟩, + ⟨0, 5, 7, 1, 7, 4, -4247827117631350381283743191705138372846551040000000⟩, + ⟨0, 5, 8, 1, 8, 4, -12277428311005821364341776976285414424863980912640000⟩, + ⟨0, 5, 3, 2, 2, 4, -11630900359733156054138291041414913362119056424960000⟩, + ⟨0, 5, 4, 2, 3, 4, 88373427408266631990920164193143976938287409397760000⟩, + ⟨0, 5, 5, 2, 4, 4, 39279877522312806121595545040339586541106390630400000⟩, + ⟨0, 5, 6, 2, 5, 4, -484771304443240629036539977893883250509401292800000⟩, + ⟨0, 5, 7, 2, 6, 4, -2664225136404794150455572807047706706193468620800000⟩, + ⟨0, 5, 8, 2, 7, 4, -5271649527746563706488285160077684695038511022080000⟩, + ⟨0, 5, 3, 3, 1, 4, -260592652825855322224080123890656995796938915840000⟩, + ⟨0, 5, 4, 3, 2, 4, -235764124527496645868403273682078878127035997224960000⟩, + ⟨0, 5, 5, 3, 3, 4, -11729190065277184934865597090416354502227735347200000⟩, + ⟨0, 5, 6, 3, 4, 4, 7849762344761928805855560625513564513745711923200000⟩, + ⟨0, 5, 7, 3, 5, 4, -6390107742610611695180804163186570796519863091200000⟩, + ⟨0, 5, 8, 3, 6, 4, 283081936209528758298868669260556716331342233600000⟩, + ⟨0, 5, 3, 4, 0, 4, 49966910347640854059526039970381105634142417059840000⟩, + ⟨0, 5, 4, 4, 1, 4, 3026783552445158969288452590816980855175512064000000⟩, + ⟨0, 5, 5, 4, 2, 4, -24224118681364790322266373978216020149895430144000000⟩, + ⟨0, 5, 6, 4, 3, 4, -9911186590499585287780124276590181662735309209600000⟩, + ⟨0, 5, 7, 4, 4, 4, 3303716913939249963088378212313898335719338803200000⟩, + ⟨0, 5, 8, 4, 5, 4, 3853065880886401645993591097195809400100193566720000⟩, + ⟨0, 5, 4, 5, 0, 4, 971502536891139963884546044085987280238254741258240000⟩, + ⟨0, 5, 5, 5, 1, 4, -8178433766635170563637053828547570860831853772800000⟩, + ⟨0, 5, 6, 5, 2, 4, 21514574740743261654715358409834037053659440742400000⟩, + ⟨0, 5, 7, 5, 3, 4, 3768497368250829175434015591880891041277437542400000⟩, + ⟨0, 5, 8, 5, 4, 4, 1928853640710497181263164860882336835501723484160000⟩, + ⟨0, 5, 5, 6, 0, 4, 434265200553555221753106278097462804724526245478400000⟩, + ⟨0, 5, 6, 6, 1, 4, -40292550970868001407399200084248993886766943436800000⟩, + ⟨0, 5, 7, 6, 2, 4, 26671527118371456031024987310134397365819696742400000⟩, + ⟨0, 5, 8, 6, 3, 4, -10241057021724966518453366963163332086921816965120000⟩, + ⟨0, 5, 6, 7, 0, 4, -11956125413610172961403532252727527395743603097600000⟩, + ⟨0, 5, 7, 7, 1, 4, -137986102304429724481239459023851856257724134195200000⟩, + ⟨0, 5, 8, 7, 2, 4, 4028080407480417802200739496423288658719963873280000⟩ +] + +def collectedFourData_8_1_5 : List CollectedFourTerm := [ + ⟨0, 6, 2, 0, 3, 5, -14794929572197980152859619857313616708724640972800000⟩, + ⟨0, 6, 3, 0, 4, 5, -5415933284964979854106066901825516394663798374400000⟩, + ⟨0, 6, 4, 0, 5, 5, 159524973847773745833474195601844208995449543065600000⟩, + ⟨0, 6, 5, 0, 6, 5, 92757505697840745199691072324590410957972307968000000⟩, + ⟨0, 6, 6, 0, 7, 5, 31931734062667781477012220877682889411224666112000000⟩, + ⟨0, 6, 7, 0, 8, 5, 18733077439985420740036045894967482963181174784000000⟩, + ⟨0, 6, 2, 1, 2, 5, 14191493002882011866859021215511526182695731200000000⟩, + ⟨0, 6, 3, 1, 3, 5, 25997414246269183217205658411348684090881186201600000⟩, + ⟨0, 6, 4, 1, 4, 5, 49091127785283385885223538702718884738576993484800000⟩, + ⟨0, 6, 5, 1, 5, 5, -30404316352288868496177402108428615672785797120000000⟩, + ⟨0, 6, 6, 1, 6, 5, -11767013802039949947210231192837998237567680512000000⟩, + ⟨0, 6, 7, 1, 7, 5, -1481966761303930357074954374391990357558558720000000⟩, + ⟨0, 6, 8, 1, 8, 5, -3569421135275260943943761498252953256533268889600000⟩, + ⟨0, 6, 2, 2, 1, 5, 19665649758776418284491346056453574562035426918400000⟩, + ⟨0, 6, 3, 2, 2, 5, -20288734993026087043755515275308084937009555046400000⟩, + ⟨0, 6, 4, 2, 3, 5, 77078514717534979614975963074203825631562773299200000⟩, + ⟨0, 6, 5, 2, 4, 5, 22839705753929284953825437949989640724820262912000000⟩, + ⟨0, 6, 6, 2, 5, 5, -211406602753712548164316994737936170208985088000000⟩, + ⟨0, 6, 7, 2, 6, 5, -929485355087605354567389035286573358770447974400000⟩, + ⟨0, 6, 8, 2, 7, 5, -1532628557499667623469750894027444820053799731200000⟩, + ⟨0, 6, 2, 3, 0, 5, -34056230639232602067149877142637895952308476313600000⟩, + ⟨0, 6, 3, 3, 1, 5, -454573172393227294580993429085926153367689625600000⟩, + ⟨0, 6, 4, 3, 2, 5, -205631365391170978470180694269954723122599113523200000⟩, + ⟨0, 6, 5, 3, 3, 5, -6820063267016725719950524096657084105585852416000000⟩, + ⟨0, 6, 6, 3, 4, 5, 3423246331867891234920346574469790800147382272000000⟩, + ⟨0, 6, 7, 3, 5, 5, -2229357978434015354112307904999314694468114841600000⟩, + ⟨0, 6, 8, 3, 6, 5, 82300512821170407236931649490212235199381504000000⟩, + ⟨0, 6, 3, 4, 0, 5, 87161386574447171005665992571268853536984242585600000⟩, + ⟨0, 6, 4, 4, 1, 5, 2639933602621749565366174286475181326996602880000000⟩, + ⟨0, 6, 5, 4, 2, 5, -14085373420941780639046827140795114665090744320000000⟩, + ⟨0, 6, 6, 4, 3, 5, -4322224247085143295613131634833604657299849216000000⟩, + ⟨0, 6, 7, 4, 4, 5, 1152588963635988389553039402043526837161269657600000⟩, + ⟨0, 6, 8, 4, 5, 5, 1120203225175027618179836789424787128310353100800000⟩, + ⟨0, 6, 4, 5, 0, 5, 847335842729595068322022062423275545278924246220800000⟩, + ⟨0, 6, 5, 5, 1, 5, -4755437963161664511920333765092685138765021184000000⟩, + ⟨0, 6, 6, 5, 2, 5, 9382410043546437975126619714928189770725064704000000⟩, + ⟨0, 6, 7, 5, 3, 5, 1314739909406488389428022187725824369332794163200000⟩, + ⟨0, 6, 8, 5, 4, 5, 560776310608377100367147909713497634617321062400000⟩, + ⟨0, 6, 5, 6, 0, 5, 252508154949824489503684858080587403252153188352000000⟩, + ⟨0, 6, 6, 6, 1, 5, -17571401687678376472677402495229233018414563328000000⟩, + ⟨0, 6, 7, 6, 2, 5, 9305067171538596151240504211614280985160659763200000⟩, + ⟨0, 6, 8, 6, 3, 5, -2977386180144552930485111555716461664683216076800000⟩, + ⟨0, 6, 6, 7, 0, 5, -5214012943054877261015773627790696150200221696000000⟩, + ⟨0, 6, 7, 7, 1, 5, -48140098802108393422312425550014828196233058713600000⟩, + ⟨0, 6, 8, 7, 2, 5, 1171085261248076963262749708269295761211208499200000⟩ +] + +def collectedFourData_8_1_6 : List CollectedFourTerm := [ + ⟨0, 7, 1, 0, 2, 6, 21416951424401909323492145906381831960398921728000000⟩, + ⟨0, 7, 2, 0, 3, 6, -20372594240050700994801567377050881544023755980800000⟩, + ⟨0, 7, 3, 0, 4, 6, -3728865714005033777213188339552623227189801779200000⟩, + ⟨0, 7, 4, 0, 5, 6, 73221877524458163076798068962755728897146565427200000⟩, + ⟨0, 7, 5, 0, 6, 6, 31931734062667781477012220877682889411224666112000000⟩, + ⟨0, 7, 6, 0, 7, 6, 8793989295662342851602305114133368176174851686400000⟩, + ⟨0, 7, 7, 0, 8, 6, 4299236253991541172777267718389737326330773504000000⟩, + ⟨0, 7, 1, 1, 1, 6, -21170057903247507399559597241088137633537300889600000⟩, + ⟨0, 7, 2, 1, 2, 6, 19541663054046002709338083340402167616058163200000000⟩, + ⟨0, 7, 3, 1, 3, 6, 17899198814877204946725741727602999697844522188800000⟩, + ⟨0, 7, 4, 1, 4, 6, 22532801350976111982359492640742153026291734937600000⟩, + ⟨0, 7, 5, 1, 5, 6, -10466673686559789721739750432740525981386670080000000⟩, + ⟨0, 7, 6, 1, 6, 6, -3240631818302355889528723980819042658666571366400000⟩, + ⟨0, 7, 7, 1, 7, 6, -340110974708768650099648556217872775716536320000000⟩, + ⟨0, 7, 8, 1, 8, 6, -702155309415438091907522400176662106300271820800000⟩, + ⟨0, 7, 1, 2, 0, 6, -40188373549113520259140166292588135978138756710400000⟩, + ⟨0, 7, 2, 2, 1, 6, 27079568107939466409192711734385257266138211942400000⟩, + ⟨0, 7, 3, 2, 2, 6, -13968777736987637707069927839129954268988257075200000⟩, + ⟨0, 7, 4, 2, 3, 6, 35378996957555400980846982166264138906877716070400000⟩, + ⟨0, 7, 5, 2, 4, 6, 7862559527848864316167975699319018353808375808000000⟩, + ⟨0, 7, 6, 2, 5, 6, -58221310436817773892887810777681481258604953600000⟩, + ⟨0, 7, 7, 2, 6, 6, -213316639988754774993602475225052875478951526400000⟩, + ⟨0, 7, 8, 2, 7, 6, -301489580026013759986931387685935756678371737600000⟩, + ⟨0, 7, 2, 3, 0, 6, -46895374849398029847204020038588586665694566809600000⟩, + ⟨0, 7, 3, 3, 1, 6, -312973263860019127619339285320772688397782220800000⟩, + ⟨0, 7, 4, 3, 2, 6, -94384686539596325012690963415747244747473184358400000⟩, + ⟨0, 7, 5, 3, 3, 6, -2347804039086152365768092324299673991636844544000000⟩, + ⟨0, 7, 6, 3, 4, 6, 942760939314503843771098103781252400318670438400000⟩, + ⟨0, 7, 7, 3, 5, 6, -511637058818258453370424616361414095011420569600000⟩, + ⟨0, 7, 8, 3, 6, 6, 16189667695387183230922707586995962083540992000000⟩, + ⟨0, 7, 3, 4, 0, 6, 60010544606384731989220052767320857360089271500800000⟩, + ⟨0, 7, 4, 4, 1, 6, 1211728109156928514534710792911330638099906560000000⟩, + ⟨0, 7, 5, 4, 2, 6, -4848884140071826540864830482019460693496954880000000⟩, + ⟨0, 7, 6, 4, 3, 6, -1190339168168038245400602983503630351209804595200000⟩, + ⟨0, 7, 7, 4, 4, 6, 264518858382418339150847102043176091931744665600000⟩, + ⟨0, 7, 8, 4, 5, 6, 220359720069928583024522228403215755712554598400000⟩, + ⟨0, 7, 4, 5, 0, 6, 388926697819958950716170850492119222019004406169600000⟩, + ⟨0, 7, 5, 5, 1, 6, -1637057607886146962153528707308643032923897856000000⟩, + ⟨0, 7, 6, 5, 2, 6, 2583912709799416297229749902587896190697524428800000⟩, + ⟨0, 7, 7, 5, 3, 6, 301732456997430123518063632791281115468084019200000⟩, + ⟨0, 7, 8, 5, 4, 6, 110312582619284596056005756910798698378900275200000⟩, + ⟨0, 7, 5, 6, 0, 6, 86925830873224956055070514468987676048666656768000000⟩, + ⟨0, 7, 6, 6, 1, 6, -4839158376052097539115326864586382767199721881600000⟩, + ⟨0, 7, 7, 6, 2, 6, 2135510423093430277294155699032000753019597619200000⟩, + ⟨0, 7, 8, 6, 3, 6, -585693712044272203000634961698763887625004646400000⟩, + ⟨0, 7, 6, 7, 0, 6, -1435937488351947398071658369634785238304633651200000⟩, + ⟨0, 7, 7, 7, 1, 6, -11048139778624661552810998658749971283031202201600000⟩, + ⟨0, 7, 8, 7, 2, 6, 230368931768005307834230667566787019125922201600000⟩ +] + +def collectedFourData_8_1_7 : List CollectedFourTerm := [ + ⟨0, 8, 0, 0, 1, 7, -49616014343845026366501995332613192783065251840000000⟩, + ⟨0, 8, 1, 0, 2, 7, 62822364857219996757787360765219727248698900480000000⟩, + ⟨0, 8, 2, 0, 3, 7, -29879475446218997905796095656164130514916081664000000⟩, + ⟨0, 8, 3, 0, 4, 7, -3645961832549412159405178743131148972063719424000000⟩, + ⟨0, 8, 4, 0, 5, 7, 53695451493286540819302853502506395051636031488000000⟩, + ⟨0, 8, 5, 0, 6, 7, 18733077439985420740036045894967482963181174784000000⟩, + ⟨0, 8, 6, 0, 7, 7, 4299236253991541172777267718389737326330773504000000⟩, + ⟨0, 8, 7, 0, 8, 7, 1801564852622254998081565693763017500021227520000000⟩, + ⟨0, 8, 0, 1, 0, 7, -258737413836138403277256025222872480564117504000000000⟩, + ⟨0, 8, 1, 1, 1, 7, -62098151846717791431873518210703396268079579136000000⟩, + ⟨0, 8, 2, 1, 2, 7, 28660789810154259550871627194194366988025856000000000⟩, + ⟨0, 8, 3, 1, 3, 7, 17501245879450799418731109425887713115332673536000000⟩, + ⟨0, 8, 4, 1, 4, 7, 16523872138420046619115711878192060658775752704000000⟩, + ⟨0, 8, 5, 1, 5, 7, -6140380861389431143440303773837627195192770560000000⟩, + ⟨0, 8, 6, 1, 6, 7, -1584291421181980541807568703054953821245538304000000⟩, + ⟨0, 8, 7, 1, 7, 7, -142521122782572220951304111067461595011481600000000⟩, + ⟨0, 8, 8, 1, 8, 7, -257454108199264279181752420677019919991177216000000⟩, + ⟨0, 8, 1, 2, 0, 7, -117884595995490267041202614138439771858470436864000000⟩, + ⟨0, 8, 2, 2, 1, 7, 39716261995967513999843039410370572880279764992000000⟩, + ⟨0, 8, 3, 2, 2, 7, -13658209863964579790433329704841325271836524544000000⟩, + ⟨0, 8, 4, 2, 3, 7, 25944311717232297589012441741813372206622703616000000⟩, + ⟨0, 8, 5, 2, 4, 7, 4612650732422592315915238905369099148676038656000000⟩, + ⟨0, 8, 6, 2, 5, 7, -28463437942587410353779978490321278018256896000000⟩, + ⟨0, 8, 7, 2, 6, 7, -89388844524749336576953307307507857995333632000000⟩, + ⟨0, 8, 8, 2, 7, 7, -110544960518191432987063775929923476077412352000000⟩, + ⟨0, 8, 2, 3, 0, 7, -68779124781230473254439057220977789110916743168000000⟩, + ⟨0, 8, 3, 3, 1, 7, -306014928442259703174116462300150283764760576000000⟩, + ⟨0, 8, 4, 3, 2, 7, -69214673662295613536964042257261446844840411136000000⟩, + ⟨0, 8, 5, 3, 3, 7, -1377363183339656871315885433764995139851255808000000⟩, + ⟨0, 8, 6, 3, 4, 7, 460900266406653635175821507738273794410676224000000⟩, + ⟨0, 8, 7, 3, 5, 7, -214397927448211678930135753986337401993166848000000⟩, + ⟨0, 8, 8, 3, 6, 7, 5936146038728084662605037176346466152611840000000⟩, + ⟨0, 8, 3, 4, 0, 7, 58676330006634118137776272741177341030407602176000000⟩, + ⟨0, 8, 4, 4, 1, 7, 888590816133530236952723065120314676897382400000000⟩, + ⟨0, 8, 5, 4, 2, 7, -2844647331560976402234397737989505435209564160000000⟩, + ⟨0, 8, 6, 4, 3, 7, -581937177119195252099555041690723934086889472000000⟩, + ⟨0, 8, 7, 4, 4, 7, 110844775668024093912841681009707465811427328000000⟩, + ⟨0, 8, 8, 4, 5, 7, 80797673182695469114686670326395038353850368000000⟩, + ⟨0, 8, 4, 5, 0, 7, 285209767125406079141095927086347846946058665984000000⟩, + ⟨0, 8, 5, 5, 1, 7, -960396541010349080744769438034597285296340992000000⟩, + ⟨0, 8, 6, 5, 2, 7, 1263232285783955104020344665241638422517383168000000⟩, + ⟨0, 8, 7, 5, 3, 7, 126438873629528994684671515914824764511748096000000⟩, + ⟨0, 8, 8, 5, 4, 7, 40447501002377443958332658094442675074760704000000⟩, + ⟨0, 8, 5, 6, 0, 7, 50995925184877123000285728725618903184756965376000000⟩, + ⟨0, 8, 6, 6, 1, 7, -2365784677426429475631818251975164962826878976000000⟩, + ⟨0, 8, 7, 6, 2, 7, 894870691761052192336491268654799145293316096000000⟩, + ⟨0, 8, 8, 6, 3, 7, -214751993313004535794542500295788893808099328000000⟩, + ⟨0, 8, 6, 7, 0, 7, -702006143154314570663218591693074345473605632000000⟩, + ⟨0, 8, 7, 7, 1, 7, -4629645624510304644247449292524881509254955008000000⟩, + ⟨0, 8, 8, 7, 2, 7, 84467677007990660992479388049239065212485632000000⟩ +] + +def collectedFourData_8_1_8 : List CollectedFourTerm := [ + ⟨1, 0, 7, 0, 8, 0, -258737413836138403277256025222872480564117504000000000⟩, + ⟨1, 0, 7, 1, 7, 0, 20468620195443722361685144305505782800056320000000000⟩, + ⟨1, 0, 8, 1, 8, 0, 295800664805416906665190875996275470054824345600000000⟩, + ⟨1, 0, 7, 2, 6, 0, 12837860610163525005183250604749795409421926400000000⟩, + ⟨1, 0, 8, 2, 7, 0, 127010103046640892878211030744856440784237363200000000⟩, + ⟨1, 0, 7, 3, 5, 0, 30791434013066657171074282771946156169206169600000000⟩, + ⟨1, 0, 8, 3, 6, 0, -6820306566165827375208865029231766293970944000000000⟩, + ⟨1, 0, 7, 4, 4, 0, -15919321778423326542936116276453566049786265600000000⟩, + ⟨1, 0, 8, 4, 5, 0, -92832099706383413550139896292239810262518988800000000⟩, + ⟨1, 0, 7, 5, 3, 0, -18158917301057099748324347242084041311335219200000000⟩, + ⟨1, 0, 8, 5, 4, 0, -46471962595216435670439848564579487917172326400000000⟩, + ⟨1, 0, 7, 6, 2, 0, -128519674530172727816742412241684129832448819200000000⟩, + ⟨1, 0, 8, 6, 3, 0, 246738274384454814314376651840670804386565324800000000⟩, + ⟨1, 0, 7, 7, 1, 0, 664901146422816675888551730594099967905339801600000000⟩, + ⟨1, 0, 8, 7, 2, 0, -97048733027769438909336801621800069440418611200000000⟩ +] + +def collectedFourData_8_1_9 : List CollectedFourTerm := [ + ⟨1, 1, 6, 0, 7, 1, -21170057903247507399559597241088137633537300889600000⟩, + ⟨1, 1, 7, 0, 8, 1, -62098151846717791431873518210703396268079579136000000⟩, + ⟨1, 1, 6, 1, 6, 1, 7801278911086053167273113133379205055213312409600000⟩, + ⟨1, 1, 7, 1, 7, 1, 4912561605004055800591572179292560858944634880000000⟩, + ⟨1, 1, 8, 1, 8, 1, 35496750019848228384958853437247912015650042675200000⟩, + ⟨1, 1, 6, 2, 5, 1, 140158063844623773769929228667636265926420070400000⟩, + ⟨1, 1, 7, 2, 6, 1, 3081144724055304144106541398541482997031999897600000⟩, + ⟨1, 1, 8, 2, 7, 1, 15241500152839459957076135345796847342237148774400000⟩, + ⟨1, 1, 6, 3, 4, 1, -2269539227669123825669684102341003300461713817600000⟩, + ⟨1, 1, 7, 3, 5, 1, 7390083701356600742162832733618007750199371366400000⟩, + ⟨1, 1, 8, 3, 6, 1, -818452241806741050494947207280536800668418048000000⟩, + ⟨1, 1, 6, 4, 3, 1, 2865542391216075539056151441544232841104903372800000⟩, + ⟨1, 1, 7, 4, 4, 1, -3820709368763192433718004474851619236689110630400000⟩, + ⟨1, 1, 8, 4, 5, 1, -11140062309402806567286160983836811007507405209600000⟩, + ⟨1, 1, 6, 5, 2, 1, -6220337533316365032452714611423986223229907763200000⟩, + ⟨1, 1, 7, 5, 3, 1, -4358222443419720814672231514900360627898600652800000⟩, + ⟨1, 1, 8, 5, 4, 1, -5576740810434873828267745060034805724126956748800000⟩, + ⟨1, 1, 6, 6, 1, 1, 11649464148715698618494827232988778623226242662400000⟩, + ⟨1, 1, 7, 6, 2, 1, -30845304302684944884754508586398035649802063052800000⟩, + ⟨1, 1, 8, 6, 3, 1, 29609152000774421648573342578852945176246720921600000⟩, + ⟨1, 1, 6, 7, 0, 1, 3456779255900259380966946695385224017919921356800000⟩, + ⟨1, 1, 7, 7, 1, 1, 159579288288665229479155233552843482176290186854400000⟩, + ⟨1, 1, 8, 7, 2, 1, -11646067862274238491111902607308504858687333990400000⟩ +] + +def collectedFourData_8_1_10 : List CollectedFourTerm := [ + ⟨1, 2, 5, 0, 6, 2, 14191493002882011866859021215511526182695731200000000⟩, + ⟨1, 2, 6, 0, 7, 2, 19541663054046002709338083340402167616058163200000000⟩, + ⟨1, 2, 7, 0, 8, 2, 28660789810154259550871627194194366988025856000000000⟩, + ⟨1, 2, 5, 1, 5, 2, -4651727528945001339865245182920579306487808000000000⟩, + ⟨1, 2, 6, 1, 6, 2, -7201206750015198775311795960770875425502003200000000⟩, + ⟨1, 2, 7, 1, 7, 2, -2267344379877823919418495025755388882452480000000000⟩, + ⟨1, 2, 8, 1, 8, 2, -10922116692229513988255837207181355010280652800000000⟩, + ⟨1, 2, 5, 2, 4, 2, 3494375166260175959943251096252497317907660800000000⟩, + ⟨1, 2, 6, 2, 5, 2, -129377145328400448554958143219551538302156800000000⟩, + ⟨1, 2, 7, 2, 6, 2, -1422071972911418549812206307548090785700249600000000⟩, + ⟨1, 2, 8, 2, 7, 2, -4689709428070573517099100355497501939833241600000000⟩, + ⟨1, 2, 5, 3, 3, 2, -1043439874810406310487793209576670011745894400000000⟩, + ⟨1, 2, 6, 3, 4, 2, 2094966914013324262045189704211388431545139200000000⟩, + ⟨1, 2, 7, 3, 5, 2, -3410820279592964412288117803498967205832294400000000⟩, + ⟨1, 2, 8, 3, 6, 2, 251832375838116063965989910759612897820672000000000⟩, + ⟨1, 2, 5, 4, 2, 2, -2155000577499667954487677676769870807564288000000000⟩, + ⟨1, 2, 6, 4, 3, 2, -2645125683271738003936951601318972240796057600000000⟩, + ⟨1, 2, 7, 4, 4, 2, 1763410743915672600994111956027539255092838400000000⟩, + ⟨1, 2, 8, 4, 5, 2, 3427723958784142613498701149674588397266534400000000⟩, + ⟨1, 2, 5, 5, 1, 2, -727561226146891081195664009263106045352345600000000⟩, + ⟨1, 2, 6, 5, 2, 2, 5741870934602275635738888403243397990999654400000000⟩, + ⟨1, 2, 7, 5, 3, 2, 2011494604623272345277664775249957170760908800000000⟩, + ⟨1, 2, 8, 5, 4, 2, 1715926496364601893183522191126678044095283200000000⟩, + ⟨1, 2, 5, 6, 0, 2, 38632644196085781719044358386302038359985356800000000⟩, + ⟨1, 2, 6, 6, 1, 2, -10753390670673098177150047888975377109667020800000000⟩, + ⟨1, 2, 7, 6, 2, 2, 14236346122372185606410743705419360081071308800000000⟩, + ⟨1, 2, 8, 6, 3, 2, -9110541475757389458404709247108472291878502400000000⟩, + ⟨1, 2, 6, 7, 0, 2, -3190884776023985722974041885897247283583385600000000⟩, + ⟨1, 2, 7, 7, 1, 2, -73652247348440006982367673818364125865469542400000000⟩, + ⟨1, 2, 8, 7, 2, 2, 3583418541873795295905218598476882636282265600000000⟩ +] + +def collectedFourData_8_1_11 : List CollectedFourTerm := [ + ⟨1, 3, 4, 0, 5, 3, 14903508514108932383328563756802301317416736522240000⟩, + ⟨1, 3, 5, 0, 6, 3, 25997414246269183217205658411348684090881186201600000⟩, + ⟨1, 3, 6, 0, 7, 3, 17899198814877204946725741727602999697844522188800000⟩, + ⟨1, 3, 7, 0, 8, 3, 17501245879450799418731109425887713115332673536000000⟩, + ⟨1, 3, 4, 1, 4, 3, 4586304095641704426425713145868032597188065361920000⟩, + ⟨1, 3, 5, 1, 5, 3, -8521505630605479058080527416975277654638854144000000⟩, + ⟨1, 3, 6, 1, 6, 3, -6595949943926115502270920729108367005228780748800000⟩, + ⟨1, 3, 7, 1, 7, 3, -1384517026518716127001171326766666786673786880000000⟩, + ⟨1, 3, 8, 1, 8, 3, -5002059896663410097974792264920684227416660377600000⟩, + ⟨1, 3, 4, 2, 3, 3, 7201006040871289506861654102965247004519358791680000⟩, + ⟨1, 3, 5, 2, 4, 3, 6401350351981484718664911559251625062982641254400000⟩, + ⟨1, 3, 6, 2, 5, 3, -118503079289090364358663811184897856006992691200000⟩, + ⟨1, 3, 7, 2, 6, 3, -868365157452179756470785068497432512317462937600000⟩, + ⟨1, 3, 8, 2, 7, 3, -2147771180090516607469621592009172761735017267200000⟩, + ⟨1, 3, 4, 3, 2, 3, -19210965725025442624559552499905755533274282721280000⟩, + ⟨1, 3, 5, 3, 3, 3, -1911478845884114190853477204824151807690486579200000⟩, + ⟨1, 3, 6, 3, 4, 3, 1918886289299232893393867874679621369528634572800000⟩, + ⟨1, 3, 7, 3, 5, 3, -2082762015952005828001103013105092468456973926400000⟩, + ⟨1, 3, 8, 3, 6, 3, 115333013128993710358065449792017245482778624000000⟩, + ⟨1, 3, 4, 4, 1, 3, 246633940594779050427840777393269955417341952000000⟩, + ⟨1, 3, 5, 4, 2, 3, -3947748323790226103219922132873509311856246784000000⟩, + ⟨1, 3, 6, 4, 3, 3, -2422804567056337408875631205921208827849893478400000⟩, + ⟨1, 3, 7, 4, 4, 3, 1076798135018573222400510698131985154556978790400000⟩, + ⟨1, 3, 8, 4, 5, 3, 1569812979865405867358345428584405418759736524800000⟩, + ⟨1, 3, 4, 5, 0, 3, 79161755315382059853810688576024109445831532216320000⟩, + ⟨1, 3, 5, 5, 1, 3, -1332820343978118236518085349837440383588289740800000⟩, + ⟨1, 3, 6, 5, 2, 3, 5259270367295167288896363292680639057032223129600000⟩, + ⟨1, 3, 7, 5, 3, 3, 1228286515964337451471509021396604762993773772800000⟩, + ⟨1, 3, 8, 5, 4, 3, 785851987755631632019298546630444388612204134400000⟩, + ⟨1, 3, 5, 6, 0, 3, 70771190486469997747301658109195025004785722982400000⟩, + ⟨1, 3, 6, 6, 1, 3, -9849575085605219433069233086087533056100610867200000⟩, + ⟨1, 3, 7, 6, 2, 3, 8693193577810219161866366264897216755178196172800000⟩, + ⟨1, 3, 8, 6, 3, 3, -4172403155626081124433017733695338930682776780800000⟩, + ⟨1, 3, 6, 7, 0, 3, -2922692958294202968070740569415265364266608230400000⟩, + ⟨1, 3, 7, 7, 1, 3, -44974548815905048705662816563381297611941504614400000⟩, + ⟨1, 3, 8, 7, 2, 3, 1641117256513040450691821174762639849669473075200000⟩ +] + +def collectedFourData_8_1_12 : List CollectedFourTerm := [ + ⟨1, 4, 3, 0, 4, 4, -955445675145239113868705870585184478039407329280000⟩, + ⟨1, 4, 4, 0, 5, 4, 56284831559367464100191026207044215365172660797440000⟩, + ⟨1, 4, 5, 0, 6, 4, 49091127785283385885223538702718884738576993484800000⟩, + ⟨1, 4, 6, 0, 7, 4, 22532801350976111982359492640742153026291734937600000⟩, + ⟨1, 4, 7, 0, 8, 4, 16523872138420046619115711878192060658775752704000000⟩, + ⟨1, 4, 3, 1, 3, 4, 4586304095641704426425713145868032597188065361920000⟩, + ⟨1, 4, 4, 1, 4, 4, 17320710305150879823911755561452118735532347883520000⟩, + ⟨1, 4, 5, 1, 5, 4, -16091228068772219433811033318287705592018501632000000⟩, + ⟨1, 4, 6, 1, 6, 4, -8303457118088266171611436079016156898407324057600000⟩, + ⟨1, 4, 7, 1, 7, 4, -1307197354819329913310330663170783867903672320000000⟩, + ⟨1, 4, 8, 1, 8, 4, -3778172078971031404426265984529315927394741125120000⟩, + ⟨1, 4, 3, 2, 2, 4, -3579213975376728170985428484406752424786321735680000⟩, + ⟨1, 4, 4, 2, 3, 4, 27195436006543663389506421354746327333299373998080000⟩, + ⟨1, 4, 5, 2, 4, 4, 12087721692267488547226768831907432199611429683200000⟩, + ⟨1, 4, 6, 2, 5, 4, -149180215981547734459442588726284767715550822400000⟩, + ⟨1, 4, 7, 2, 6, 4, -819870478366714046597070279982832430734534246400000⟩, + ⟨1, 4, 8, 2, 7, 4, -1622261482724242047966820733744565342087822704640000⟩, + ⟨1, 4, 3, 3, 1, 4, -80193006218496761527904373500049913383978270720000⟩, + ⟨1, 4, 4, 3, 2, 4, -72552444204812656014238549142183780845019128135680000⟩, + ⟨1, 4, 5, 3, 3, 4, -3609460979206010642678048182883340280793766297600000⟩, + ⟨1, 4, 6, 3, 4, 4, 2415632343049535599912596774915744533038340505600000⟩, + ⟨1, 4, 7, 3, 5, 4, -1966448187940600048160482438332779623433738649600000⟩, + ⟨1, 4, 8, 3, 6, 4, 87113704951479316490578456912832221590375628800000⟩, + ⟨1, 4, 3, 4, 0, 4, 15376476308045279779813932540733329281907393822720000⟩, + ⟨1, 4, 4, 4, 1, 4, 931441733338061424431243758579883482558758912000000⟩, + ⟨1, 4, 5, 4, 2, 4, -7454565119111255380923216365638003849326231552000000⟩, + ⟨1, 4, 6, 4, 3, 4, -3050000985314641229379828542734376792203513036800000⟩, + ⟨1, 4, 7, 4, 4, 4, 1016663317828571738421147315547281261881563545600000⟩, + ⟨1, 4, 8, 4, 5, 4, 1185716223368304551145840855885862570498468085760000⟩, + ⟨1, 4, 4, 5, 0, 4, 298963566844148444247599827493180435516396320849920000⟩, + ⟨1, 4, 5, 5, 1, 4, -2516775445482805588494337214624651855614338662400000⟩, + ⟨1, 4, 6, 5, 2, 4, 6620748540925694686156447161088448872462889779200000⟩, + ⟨1, 4, 7, 5, 3, 4, 1159691685891396022276814397387633409433744179200000⟩, + ⟨1, 4, 8, 5, 4, 4, 593572268161506725411323112589147997841160929280000⟩, + ⟨1, 4, 5, 6, 0, 4, 133637811929180946178410107054336016749981545267200000⟩, + ⟨1, 4, 6, 6, 1, 4, -12399354914757312936078557685745793114197878374400000⟩, + ⟨1, 4, 7, 6, 2, 4, 8207713904695912042089583725603219047594537779200000⟩, + ⟨1, 4, 8, 6, 3, 4, -3151513062710902256503881629992580065348508712960000⟩, + ⟨1, 4, 6, 7, 0, 4, -3679296516020724772600031715979323944553204940800000⟩, + ⟨1, 4, 7, 7, 1, 4, -42462902311984795871544912173955265340806633881600000⟩, + ⟨1, 4, 8, 7, 2, 4, 1239574000505483663042099787814457752500295434240000⟩ +] + +def collectedFourData_8_1_13 : List CollectedFourTerm := [ + ⟨1, 5, 2, 0, 3, 5, 4849523666454223756207964084230081632956055552000000⟩, + ⟨1, 5, 3, 0, 4, 5, 1775249859298442972355718991756551441084317696000000⟩, + ⟨1, 5, 4, 0, 5, 5, -52289545028928347408643401204720060213602811904000000⟩, + ⟨1, 5, 5, 0, 6, 5, -30404316352288868496177402108428615672785797120000000⟩, + ⟨1, 5, 6, 0, 7, 5, -10466673686559789721739750432740525981386670080000000⟩, + ⟨1, 5, 7, 0, 8, 5, -6140380861389431143440303773837627195192770560000000⟩, + ⟨1, 5, 2, 1, 2, 5, -4651727528945001339865245182920579306487808000000000⟩, + ⟨1, 5, 3, 1, 3, 5, -8521505630605479058080527416975277654638854144000000⟩, + ⟨1, 5, 4, 1, 4, 5, -16091228068772219433811033318287705592018501632000000⟩, + ⟨1, 5, 5, 1, 5, 5, 9966012409404185243446409825336386210548940800000000⟩, + ⟨1, 5, 6, 1, 6, 5, 3857024911001895992905203170434058373121966080000000⟩, + ⟨1, 5, 7, 1, 7, 5, 485763237112471758808351657270854365793484800000000⟩, + ⟨1, 5, 8, 1, 8, 5, 1169994908498077808673746411513823077087576064000000⟩, + ⟨1, 5, 2, 2, 1, 5, -6446062041457742508458030387272706216643526656000000⟩, + ⟨1, 5, 3, 2, 2, 5, 6650298673674642913219566024317269944802738176000000⟩, + ⟨1, 5, 4, 2, 3, 5, -25265012548639938213637826456274744944967548928000000⟩, + ⟨1, 5, 5, 2, 4, 5, -7486463051278700991507398796830551620798382080000000⟩, + ⟨1, 5, 6, 2, 5, 5, 69295451410959683668790782475515486713937920000000⟩, + ⟨1, 5, 7, 2, 6, 5, 304669326415069434286305154013693569658781696000000⟩, + ⟨1, 5, 8, 2, 7, 5, 502369303294631261253250584930619693945847808000000⟩, + ⟨1, 5, 2, 3, 0, 5, 11163047155394184462727954876625858711701684224000000⟩, + ⟨1, 5, 3, 3, 1, 5, 149001274179680310139237211314428571029602304000000⟩, + ⟨1, 5, 4, 3, 2, 5, 67402427849585934869558516604525213101051609088000000⟩, + ⟨1, 5, 5, 3, 3, 5, 2235499537778410643403113589603965735471677440000000⟩, + ⟨1, 5, 6, 3, 4, 5, -1122081319920040407834640354510096363400724480000000⟩, + ⟨1, 5, 7, 3, 5, 5, 730745234349104029710863776657653657180831744000000⟩, + ⟨1, 5, 8, 3, 6, 5, -26976693788228079158712394059336241234575360000000⟩, + ⟨1, 5, 3, 4, 0, 5, -28570004671603901107964115888817035785696968704000000⟩, + ⟨1, 5, 4, 4, 1, 5, -865324868314325326954577645979570713867059200000000⟩, + ⟨1, 5, 5, 4, 2, 5, 4616943353624528716289545728441856534826188800000000⟩, + ⟨1, 5, 6, 4, 3, 5, 1416750831808637035093268610755349909539389440000000⟩, + ⟨1, 5, 7, 4, 4, 5, -377798855315286100892820469423075410453725184000000⟩, + ⟨1, 5, 8, 4, 5, 5, -367183366788922442336424152322044471197827072000000⟩, + ⟨1, 5, 4, 5, 0, 5, -277742127983758540241399242383701772972035407872000000⟩, + ⟨1, 5, 5, 5, 1, 5, 1558750843264829256757451946956278668522946560000000⟩, + ⟨1, 5, 6, 5, 2, 5, -3075392777810743087894593104425182299538063360000000⟩, + ⟨1, 5, 7, 5, 3, 5, -430949148813787146848046836135690991921266688000000⟩, + ⟨1, 5, 8, 5, 4, 5, -183812837811176721872705161969385637062639616000000⟩, + ⟨1, 5, 5, 6, 0, 5, -82767833900539619182544882720584857200288071680000000⟩, + ⟨1, 5, 6, 6, 1, 5, 5759603512902054400751272808067899583910379520000000⟩, + ⟨1, 5, 7, 6, 2, 5, -3050041113485257124980998948797866648365170688000000⟩, + ⟨1, 5, 8, 6, 3, 5, 975936024184781587992734614873591654134054912000000⟩, + ⟨1, 5, 6, 7, 0, 5, 1709063841172903789298978944269470740921712640000000⟩, + ⟨1, 5, 7, 7, 1, 5, 15779497111292180326893783949631030379858100224000000⟩, + ⟨1, 5, 8, 7, 2, 5, -383861623818095434565787150855327039438716928000000⟩ +] + +def collectedFourData_8_1_14 : List CollectedFourTerm := [ + ⟨1, 6, 1, 0, 2, 6, -7892260486510565857625871741907540668818915328000000⟩, + ⟨1, 6, 2, 0, 3, 6, 7507409310611302778425830937078548039027444940800000⟩, + ⟨1, 6, 3, 0, 4, 6, 1374106844198894983405821108726771136781824819200000⟩, + ⟨1, 6, 4, 0, 5, 6, -26982651231863422029293311725654759576517686067200000⟩, + ⟨1, 6, 5, 0, 6, 6, -11767013802039949947210231192837998237567680512000000⟩, + ⟨1, 6, 6, 0, 7, 6, -3240631818302355889528723980819042658666571366400000⟩, + ⟨1, 6, 7, 0, 8, 6, -1584291421181980541807568703054953821245538304000000⟩, + ⟨1, 6, 1, 1, 1, 6, 7801278911086053167273113133379205055213312409600000⟩, + ⟨1, 6, 2, 1, 2, 6, -7201206750015198775311795960770875425502003200000000⟩, + ⟨1, 6, 3, 1, 3, 6, -6595949943926115502270920729108367005228780748800000⟩, + ⟨1, 6, 4, 1, 4, 6, -8303457118088266171611436079016156898407324057600000⟩, + ⟨1, 6, 5, 1, 5, 6, 3857024911001895992905203170434058373121966080000000⟩, + ⟨1, 6, 6, 1, 6, 6, 1194190057403597295150966172440484196297107046400000⟩, + ⟨1, 6, 7, 1, 7, 6, 125332702751720862502003102859201270324920320000000⟩, + ⟨1, 6, 8, 1, 8, 6, 258747965295336942871538810304475801500568780800000⟩, + ⟨1, 6, 1, 2, 0, 6, 14809629358238717157615443842012271238195865190400000⟩, + ⟨1, 6, 2, 2, 1, 6, -9978964845881685160141121049123835259642078822400000⟩, + ⟨1, 6, 3, 2, 2, 6, 5147568876346495597605192836671751341972075315200000⟩, + ⟨1, 6, 4, 2, 3, 6, -13037348509945062586365900886312951036636456550400000⟩, + ⟨1, 6, 5, 2, 4, 6, -2897394995899219947180058832744401487064465408000000⟩, + ⟨1, 6, 6, 2, 5, 6, 21454862493166161859356114422498058204453273600000⟩, + ⟨1, 6, 7, 2, 6, 6, 78608316166803085946808798381822469028079206400000⟩, + ⟨1, 6, 8, 2, 7, 6, 111100513438290235897617674861545025110120857600000⟩, + ⟨1, 6, 2, 3, 0, 6, 17281195002492805566883411620270678963398482329600000⟩, + ⟨1, 6, 3, 3, 1, 6, 115332311996671274118849789826145361666559180800000⟩, + ⟨1, 6, 4, 3, 2, 6, 34781258889134548960537211730369608439466190438400000⟩, + ⟨1, 6, 5, 3, 3, 6, 865178273068198991235266212973128064742457344000000⟩, + ⟨1, 6, 6, 3, 4, 6, -347412419355815403560723480078992452866172518400000⟩, + ⟨1, 6, 7, 3, 5, 6, 188540976851871814010727537730618486706248089600000⟩, + ⟨1, 6, 8, 3, 6, 6, -5965978635804327060248068921010290679611392000000⟩, + ⟨1, 6, 3, 4, 0, 6, -22114204799069635956578952974603072006364384460800000⟩, + ⟨1, 6, 4, 4, 1, 6, -446528251700531326847770442408574086346178560000000⟩, + ⟨1, 6, 5, 4, 2, 6, 1786839590005996037739789028702332612646010880000000⟩, + ⟨1, 6, 6, 4, 3, 6, 438646313208454879837682230560706375183446835200000⟩, + ⟨1, 6, 7, 4, 4, 6, -97476605917396307591757931986898026092927385600000⟩, + ⟨1, 6, 8, 4, 5, 6, -81203728628944857174076216116633268543448678400000⟩, + ⟨1, 6, 4, 5, 0, 6, -143321556300313472297615541260879673714665953689600000⟩, + ⟨1, 6, 5, 5, 1, 6, 603264433711164949846171624623026114245165056000000⟩, + ⟨1, 6, 6, 5, 2, 6, -952185573755713420878176618857516731758070988800000⟩, + ⟨1, 6, 7, 5, 3, 6, -111190014893777907015863033522715028272395059200000⟩, + ⟨1, 6, 8, 5, 4, 6, -40650773292559068587995343587197646982558515200000⟩, + ⟨1, 6, 5, 6, 0, 6, -32032630912922378043129225870789074058234298368000000⟩, + ⟨1, 6, 6, 6, 1, 6, 1783255594247076912188675010929216575327803801600000⟩, + ⟨1, 6, 7, 6, 2, 6, -786946946683958592675305208735820305944228659200000⟩, + ⟨1, 6, 8, 6, 3, 6, 215831247368755409105400213167381746754676326400000⟩, + ⟨1, 6, 6, 7, 0, 6, 529150600187990126453302455740995307884983091200000⟩, + ⟨1, 6, 7, 7, 1, 6, 4071298257927482425943203625000638071860468121600000⟩, + ⟨1, 6, 8, 7, 2, 6, -84892176364594343308549423399871662419188121600000⟩ +] + +def collectedFourData_8_1_15 : List CollectedFourTerm := [ + ⟨1, 7, 0, 0, 1, 7, 3925104368010053562424834998602183650521907200000000⟩, + ⟨1, 7, 1, 0, 2, 7, -4969853825842115700655875757301225203590758400000000⟩, + ⟨1, 7, 2, 0, 3, 7, 2363754145486943519029088211117053549079429120000000⟩, + ⟨1, 7, 3, 0, 4, 7, 288430679162622428033330010471665789483089920000000⟩, + ⟨1, 7, 4, 0, 5, 7, -4247827117631350381283743191705138372846551040000000⟩, + ⟨1, 7, 5, 0, 6, 7, -1481966761303930357074954374391990357558558720000000⟩, + ⟨1, 7, 6, 0, 7, 7, -340110974708768650099648556217872775716536320000000⟩, + ⟨1, 7, 7, 0, 8, 7, -142521122782572220951304111067461595011481600000000⟩, + ⟨1, 7, 0, 1, 0, 7, 20468620195443722361685144305505782800056320000000000⟩, + ⟨1, 7, 1, 1, 1, 7, 4912561605004055800591572179292560858944634880000000⟩, + ⟨1, 7, 2, 1, 2, 7, -2267344379877823919418495025755388882452480000000000⟩, + ⟨1, 7, 3, 1, 3, 7, -1384517026518716127001171326766666786673786880000000⟩, + ⟨1, 7, 4, 1, 4, 7, -1307197354819329913310330663170783867903672320000000⟩, + ⟨1, 7, 5, 1, 5, 7, 485763237112471758808351657270854365793484800000000⟩, + ⟨1, 7, 6, 1, 6, 7, 125332702751720862502003102859201270324920320000000⟩, + ⟨1, 7, 7, 1, 7, 7, 11274792805620982657143382313526443900928000000000⟩, + ⟨1, 7, 8, 1, 8, 7, 20367098365699826128471001444651761957601280000000⟩, + ⟨1, 7, 1, 2, 0, 7, 9325806370829530525021734395760933067680645120000000⟩, + ⟨1, 7, 2, 2, 1, 7, -3141938656359291525682618918305206659039887360000000⟩, + ⟨1, 7, 3, 2, 2, 7, 1080495882331906719650674651197745183347179520000000⟩, + ⟨1, 7, 4, 2, 3, 7, -2052444812285806842494918771387270102809313280000000⟩, + ⟨1, 7, 5, 2, 4, 7, -364905077067776828012108056732966438022676480000000⟩, + ⟨1, 7, 6, 2, 5, 7, 2251731947326242405383970112179053191495680000000⟩, + ⟨1, 7, 7, 2, 6, 7, 7071518112357007349224454443022613542338560000000⟩, + ⟨1, 7, 8, 2, 7, 7, 8745170548856841055143741165502353018716160000000⟩, + ⟨1, 7, 2, 3, 0, 7, 5441090879163010019343368311057826560019005440000000⟩, + ⟨1, 7, 3, 3, 1, 7, 24208726722403521950410067765718547515310080000000⟩, + ⟨1, 7, 4, 3, 2, 7, 5475546988509139912138249404146254976259194880000000⟩, + ⟨1, 7, 5, 3, 3, 7, 108962687123484796522127577580612918852976640000000⟩, + ⟨1, 7, 6, 3, 4, 7, -36461647974232618287827577618034558154833920000000⟩, + ⟨1, 7, 7, 3, 5, 7, 16960939983758940445888991683254987616419840000000⟩, + ⟨1, 7, 8, 3, 6, 7, -469606296553475502242541859720624550707200000000⟩, + ⟨1, 7, 3, 4, 0, 7, -4641862556951019865128500520086060664965038080000000⟩, + ⟨1, 7, 4, 4, 1, 7, -70296087662511095546395133055606762504192000000000⟩, + ⟨1, 7, 5, 4, 2, 7, 225038988202067073393863597967640481287372800000000⟩, + ⟨1, 7, 6, 4, 3, 7, 46036832785246664504829870211228420024565760000000⟩, + ⟨1, 7, 7, 4, 4, 7, -8768888813408450516940545478000975795978240000000⟩, + ⟨1, 7, 8, 4, 5, 7, -6391873755449858433065193192440760568381440000000⟩, + ⟨1, 7, 4, 5, 0, 7, -22562838179321335457067848474187291616314654720000000⟩, + ⟨1, 7, 5, 5, 1, 7, 75976611745096807814578279221607378829967360000000⟩, + ⟨1, 7, 6, 5, 2, 7, -99933834434587480801701802304457993030205440000000⟩, + ⟨1, 7, 7, 5, 3, 7, -10002532080271795413786679766833625227591680000000⟩, + ⟨1, 7, 8, 5, 4, 7, -3199786701110088821955785760063009136312320000000⟩, + ⟨1, 7, 5, 6, 0, 7, -4034268599382286147065338641142220228478894080000000⟩, + ⟨1, 7, 6, 6, 1, 7, 187156342441876858463467042891402099902382080000000⟩, + ⟨1, 7, 7, 6, 2, 7, -70792886278484651382744707165613064905031680000000⟩, + ⟨1, 7, 8, 6, 3, 7, 16988950002113711831136370282469869737738240000000⟩, + ⟨1, 7, 6, 7, 0, 7, 55535443854262555746512886573011248412098560000000⟩, + ⟨1, 7, 7, 7, 1, 7, 366249536634904760194748052669460197817712640000000⟩, + ⟨1, 7, 8, 7, 2, 7, -6682206387681265243713370313954003842498560000000⟩ +] + +def collectedFourData_8_1_16 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 1, 8, 56723338964805595530929605258468289423370878976000000⟩, + ⟨1, 8, 1, 0, 2, 8, -35910727045418551555128578818961155145896820736000000⟩, + ⟨1, 8, 2, 0, 3, 8, 11386536089476102994661908282860863660473135923200000⟩, + ⟨1, 8, 3, 0, 4, 8, 1042058353615516940043191227898252256113747558400000⟩, + ⟨1, 8, 4, 0, 5, 8, -12277428311005821364341776976285414424863980912640000⟩, + ⟨1, 8, 5, 0, 6, 8, -3569421135275260943943761498252953256533268889600000⟩, + ⟨1, 8, 6, 0, 7, 8, -702155309415438091907522400176662106300271820800000⟩, + ⟨1, 8, 7, 0, 8, 8, -257454108199264279181752420677019919991177216000000⟩, + ⟨1, 8, 0, 1, 0, 8, 295800664805416906665190875996275470054824345600000000⟩, + ⟨1, 8, 1, 1, 1, 8, 35496750019848228384958853437247912015650042675200000⟩, + ⟨1, 8, 2, 1, 2, 8, -10922116692229513988255837207181355010280652800000000⟩, + ⟨1, 8, 3, 1, 3, 8, -5002059896663410097974792264920684227416660377600000⟩, + ⟨1, 8, 4, 1, 4, 8, -3778172078971031404426265984529315927394741125120000⟩, + ⟨1, 8, 5, 1, 5, 8, 1169994908498077808673746411513823077087576064000000⟩, + ⟨1, 8, 6, 1, 6, 8, 258747965295336942871538810304475801500568780800000⟩, + ⟨1, 8, 7, 1, 7, 8, 20367098365699826128471001444651761957601280000000⟩, + ⟨1, 8, 8, 1, 8, 8, 32703725557602526503054465022711585469733273600000⟩, + ⟨1, 8, 1, 2, 0, 8, 67385580903788089983107912723088080401454648524800000⟩, + ⟨1, 8, 2, 2, 1, 8, -15135160299924153276727205638189618633847183769600000⟩, + ⟨1, 8, 3, 2, 2, 8, 3903675446384491073870400212262447772829378150400000⟩, + ⟨1, 8, 4, 2, 3, 8, -5932149154692052630898414463900593904333336084480000⟩, + ⟨1, 8, 5, 2, 4, 8, -878899533015805814305116731303762037850924646400000⟩, + ⟨1, 8, 6, 2, 5, 8, 4648675461147129149373159307838639171646259200000⟩, + ⟨1, 8, 7, 2, 6, 8, 12774186406104034441665146150049311050275225600000⟩, + ⟨1, 8, 8, 2, 7, 8, 14042238734698390671323264586317211567862579200000⟩, + ⟨1, 8, 2, 3, 0, 8, 26210499844071490070865816100357670627661211238400000⟩, + ⟨1, 8, 3, 3, 1, 8, 87462630482703951018608717035918897941420441600000⟩, + ⟨1, 8, 4, 3, 2, 8, 15825887860627144458849245749156155431682394030080000⟩, + ⟨1, 8, 5, 3, 3, 8, 262444292632274073046841409868026406025507635200000⟩, + ⟨1, 8, 6, 3, 4, 8, -75274665091493821750033822475978251493493964800000⟩, + ⟨1, 8, 7, 3, 5, 8, 30638712300924047224438696462799398951609958400000⟩, + ⟨1, 8, 8, 3, 6, 8, -754053187491406408625857371803468288753664000000⟩, + ⟨1, 8, 3, 4, 0, 8, -16770378476551219548274839815547146438213999001600000⟩, + ⟨1, 8, 4, 4, 1, 8, -203175683218933062779627285538582671363407872000000⟩, + ⟨1, 8, 5, 4, 2, 8, 542022224602837295694381256429831063710203904000000⟩, + ⟨1, 8, 6, 4, 3, 8, 95042527211922578576730115224343728959678054400000⟩, + ⟨1, 8, 7, 4, 4, 8, -15840363907311567561951576930860607274903142400000⟩, + ⟨1, 8, 8, 4, 5, 8, -10263518216670217294020469629547693497699532800000⟩, + ⟨1, 8, 4, 5, 0, 8, -65213018460579345922285744416127014002931290603520000⟩, + ⟨1, 8, 5, 5, 1, 8, 182995010975103397256555961742660598890286284800000⟩, + ⟨1, 8, 6, 5, 2, 8, -206312285272692360795914834610919030971275673600000⟩, + ⟨1, 8, 7, 5, 3, 8, -18068851312584570650899453832217393760095436800000⟩, + ⟨1, 8, 8, 5, 4, 8, -5137940821860169924848299810874403039110758400000⟩, + ⟨1, 8, 5, 6, 0, 8, -9716819553592686998318620540884383056196429414400000⟩, + ⟨1, 8, 6, 6, 1, 8, 386382179078062204482382626003003557266273075200000⟩, + ⟨1, 8, 7, 6, 2, 8, -127882232807584240183504838065062264729029836800000⟩, + ⟨1, 8, 8, 6, 3, 8, 27279386999801867283625454905113086356409548800000⟩, + ⟨1, 8, 6, 7, 0, 8, 114652303697061701111688597921169602202986086400000⟩, + ⟨1, 8, 7, 7, 1, 8, 661603318804778971872592369931968872402282086400000⟩, + ⟨1, 8, 8, 7, 2, 8, -10729709254511066907255967819902033411126067200000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0805.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0805.lean new file mode 100644 index 0000000000000000000000000000000000000000..f44e2b822c607c829c38d07697d8bc0f74199760 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0805.lean @@ -0,0 +1,624 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0805. -/ +namespace LaughlinFock +def collectedFourData_8_1_17 : List CollectedFourTerm := [ + ⟨2, 0, 6, 0, 7, 1, -40188373549113520259140166292588135978138756710400000⟩, + ⟨2, 0, 7, 0, 8, 1, -117884595995490267041202614138439771858470436864000000⟩, + ⟨2, 0, 6, 1, 6, 1, 14809629358238717157615443842012271238195865190400000⟩, + ⟨2, 0, 7, 1, 7, 1, 9325806370829530525021734395760933067680645120000000⟩, + ⟨2, 0, 8, 1, 8, 1, 67385580903788089983107912723088080401454648524800000⟩, + ⟨2, 0, 6, 2, 5, 1, 266070345742614935349689672041983394195282329600000⟩, + ⟨2, 0, 7, 2, 6, 1, 5849119340869625259045855736635678311183705702400000⟩, + ⟨2, 0, 8, 2, 7, 1, 28933841579017134582513124214630940407869577625600000⟩, + ⟨2, 0, 6, 3, 4, 1, -4308400604418837263439216970322730515381511782400000⟩, + ⟨2, 0, 7, 3, 5, 1, 14029033161207138876084459134178374298017307033600000⟩, + ⟨2, 0, 8, 3, 6, 1, -1553716318404258576607531905983230856713469952000000⟩, + ⟨2, 0, 6, 4, 3, 1, 5439828675260531685979615373225876127940293427200000⟩, + ⟨2, 0, 7, 4, 4, 1, -7253078665925541513445260699327938415767951769600000⟩, + ⟨2, 0, 8, 4, 5, 1, -21147839438927678281535154909347805779418572390400000⟩, + ⟨2, 0, 6, 5, 2, 1, -11808434796587942523701657338757881288066911436800000⟩, + ⟨2, 0, 7, 5, 3, 1, -8273471540170603103912907314374112217826276147200000⟩, + ⟨2, 0, 8, 5, 4, 1, -10586657055952715768588410728476413449481696051200000⟩, + ⟨2, 0, 6, 6, 1, 1, 22114867091779377719545541722729155680605411737600000⟩, + ⟨2, 0, 7, 6, 2, 1, -58555466273062096141846519868731181552377213747200000⟩, + ⟨2, 0, 8, 6, 3, 1, 56208805215268963541585606192014808162131928678400000⟩, + ⟨2, 0, 6, 7, 0, 1, 6562208598949343439569416246055305555741979443200000⟩, + ⟨2, 0, 7, 7, 1, 1, 302938805257720086603440041278852945649101019545600000⟩, + ⟨2, 0, 8, 7, 2, 1, -22108419720269437202052445690908211136261888409600000⟩ +] + +def collectedFourData_8_1_18 : List CollectedFourTerm := [ + ⟨2, 1, 5, 0, 6, 2, 19665649758776418284491346056453574562035426918400000⟩, + ⟨2, 1, 6, 0, 7, 2, 27079568107939466409192711734385257266138211942400000⟩, + ⟨2, 1, 7, 0, 8, 2, 39716261995967513999843039410370572880279764992000000⟩, + ⟨2, 1, 5, 1, 5, 2, -6446062041457742508458030387272706216643526656000000⟩, + ⟨2, 1, 6, 1, 6, 2, -9978964845881685160141121049123835259642078822400000⟩, + ⟨2, 1, 7, 1, 7, 2, -3141938656359291525682618918305206659039887360000000⟩, + ⟨2, 1, 8, 1, 8, 2, -15135160299924153276727205638189618633847183769600000⟩, + ⟨2, 1, 5, 2, 4, 2, 4842278267091646557219923170775027852567484825600000⟩, + ⟨2, 1, 6, 2, 5, 2, -179282449443617084267603932815906568538790297600000⟩, + ⟨2, 1, 7, 2, 6, 2, -1970615025872810390816956100382124895273956147200000⟩, + ⟨2, 1, 8, 2, 7, 2, -6498694891660676776256339373363353551425975091200000⟩, + ⟨2, 1, 5, 3, 3, 2, -1445931243329773121922935018307847854752582860800000⟩, + ⟨2, 1, 6, 3, 4, 2, 2903069154094218835727639709220928366097884774400000⟩, + ⟨2, 1, 7, 3, 5, 2, -4726493329136355582883726221279083811360787660800000⟩, + ⟨2, 1, 8, 3, 6, 2, 348972958669478628755829413751485173233352704000000⟩, + ⟨2, 1, 5, 4, 2, 2, -2986259907852045638450879202004241581149782016000000⟩, + ⟨2, 1, 6, 4, 3, 2, -3665443462826801345951711537684318856269738803200000⟩, + ⟨2, 1, 7, 4, 4, 2, 2443620136631603804541478352465196705391627468800000⟩, + ⟨2, 1, 8, 4, 5, 2, 4749917350452570814541741298669330439844187340800000⟩, + ⟨2, 1, 5, 5, 1, 2, -1008207117360028210277236547229472847486464819200000⟩, + ⟨2, 1, 6, 5, 2, 2, 7956712006062732852729444544667196696895999180800000⟩, + ⟨2, 1, 7, 5, 3, 2, 2787398646369089333430986606177558618535729561600000⟩, + ⟨2, 1, 8, 5, 4, 2, 2377819548828139058385151201840013883686151782400000⟩, + ⟨2, 1, 5, 6, 0, 2, 53534610478359265403305225514865882563375372697600000⟩, + ⟨2, 1, 6, 6, 1, 2, -14901350732146725531929241373967193144636840345600000⟩, + ⟨2, 1, 7, 6, 2, 2, 19727804300113483732148567905474622428693502361600000⟩, + ⟨2, 1, 8, 6, 3, 2, -12624796963833618153236512974395595320518823116800000⟩, + ⟨2, 1, 6, 7, 0, 2, -4421720985463332713969215734926226815932642099200000⟩, + ⟨2, 1, 7, 7, 1, 2, -102062503219854667235122268187974315066352520396800000⟩, + ⟨2, 1, 8, 7, 2, 2, 4965668796742120832899948169754358318753854259200000⟩ +] + +def collectedFourData_8_1_19 : List CollectedFourTerm := [ + ⟨2, 2, 4, 0, 5, 3, -11630900359733156054138291041414913362119056424960000⟩, + ⟨2, 2, 5, 0, 6, 3, -20288734993026087043755515275308084937009555046400000⟩, + ⟨2, 2, 6, 0, 7, 3, -13968777736987637707069927839129954268988257075200000⟩, + ⟨2, 2, 7, 0, 8, 3, -13658209863964579790433329704841325271836524544000000⟩, + ⟨2, 2, 4, 1, 4, 3, -3579213975376728170985428484406752424786321735680000⟩, + ⟨2, 2, 5, 1, 5, 3, 6650298673674642913219566024317269944802738176000000⟩, + ⟨2, 2, 6, 1, 6, 3, 5147568876346495597605192836671751341972075315200000⟩, + ⟨2, 2, 7, 1, 7, 3, 1080495882331906719650674651197745183347179520000000⟩, + ⟨2, 2, 8, 1, 8, 3, 3903675446384491073870400212262447772829378150400000⟩, + ⟨2, 2, 4, 2, 3, 3, -5619762868046920405170818399082348383457477918720000⟩, + ⟨2, 2, 5, 2, 4, 3, -4995700713100905882155283780172007798480673177600000⟩, + ⟨2, 2, 6, 2, 5, 3, 92481411758053739386823099576084490129034444800000⟩, + ⟨2, 2, 7, 2, 6, 3, 677683956944024227682201075069254122560972390400000⟩, + ⟨2, 2, 8, 2, 7, 3, 1676149784964433759037818501033149908321619148800000⟩, + ⟨2, 2, 4, 3, 2, 3, 14992498440920244046773722660376817716453043077120000⟩, + ⟨2, 2, 5, 3, 3, 3, 1491744039678237236148673513512634428305493196800000⟩, + ⟨2, 2, 6, 3, 4, 3, -1497524909075536886760928408495104745192764211200000⟩, + ⟨2, 2, 7, 3, 5, 3, 1625415750770488504138106211686032140817504665600000⟩, + ⟨2, 2, 8, 3, 6, 3, -90007449093024823160299677769173602031108096000000⟩, + ⟨2, 2, 4, 4, 1, 3, -192476475299127311027004182503463685464260608000000⟩, + ⟨2, 2, 5, 4, 2, 3, 3080876382620899504612667974121681000633204736000000⟩, + ⟨2, 2, 6, 4, 3, 3, 1890789573734377105332412120876128062200715673600000⟩, + ⟨2, 2, 7, 4, 4, 3, -840347882117227858701475831789872166733453721600000⟩, + ⟨2, 2, 8, 4, 5, 3, -1225103359718647880768010183596642045976064819200000⟩, + ⟨2, 2, 4, 5, 0, 3, -61778908469985496101314865799708767005114137313280000⟩, + ⟨2, 2, 5, 5, 1, 3, 1040151089494084080900233178106444294802060083200000⟩, + ⟨2, 2, 6, 5, 2, 3, -4104405989301009383981336483961402754259641958400000⟩, + ⟨2, 2, 7, 5, 3, 3, -958571471064050275214210384656823117384201011200000⟩, + ⟨2, 2, 8, 5, 4, 3, -613289559195482780012117261550664217817356697600000⟩, + ⟨2, 2, 5, 6, 0, 3, -55230797775475487326629997720482053578785659289600000⟩, + ⟨2, 2, 6, 6, 1, 3, 7686742104916621038241202030067204733103033548800000⟩, + ⟨2, 2, 7, 6, 2, 3, -6784286278339345638965097097750271890105250611200000⟩, + ⟨2, 2, 8, 6, 3, 3, 3256200063077874309745799005607105657625064243200000⟩, + ⟨2, 2, 6, 7, 0, 3, 2280909260247841160379706820665651644608387481600000⟩, + ⟨2, 2, 7, 7, 1, 3, 35098748426019319569278509107039504794593630617600000⟩, + ⟨2, 2, 8, 7, 2, 3, -1280750185170947804390083253902418733402213580800000⟩ +] + +def collectedFourData_8_1_20 : List CollectedFourTerm := [ + ⟨2, 3, 3, 0, 4, 4, -1500155666734645077142874363038099958985255813120000⟩, + ⟨2, 3, 4, 0, 5, 4, 88373427408266631990920164193143976938287409397760000⟩, + ⟨2, 3, 5, 0, 6, 4, 77078514717534979614975963074203825631562773299200000⟩, + ⟨2, 3, 6, 0, 7, 4, 35378996957555400980846982166264138906877716070400000⟩, + ⟨2, 3, 7, 0, 8, 4, 25944311717232297589012441741813372206622703616000000⟩, + ⟨2, 3, 3, 1, 3, 4, 7201006040871289506861654102965247004519358791680000⟩, + ⟨2, 3, 4, 1, 4, 4, 27195436006543663389506421354746327333299373998080000⟩, + ⟨2, 3, 5, 1, 5, 4, -25265012548639938213637826456274744944967548928000000⟩, + ⟨2, 3, 6, 1, 6, 4, -13037348509945062586365900886312951036636456550400000⟩, + ⟨2, 3, 7, 1, 7, 4, -2052444812285806842494918771387270102809313280000000⟩, + ⟨2, 3, 8, 1, 8, 4, -5932149154692052630898414463900593904333336084480000⟩, + ⟨2, 3, 3, 2, 2, 4, -5619762868046920405170818399082348383457477918720000⟩, + ⟨2, 3, 4, 2, 3, 4, 42699850442396104260502636217868329810189950648320000⟩, + ⟨2, 3, 5, 2, 4, 4, 18979063557757864353327247409970789456504736972800000⟩, + ⟨2, 3, 6, 2, 5, 4, -234229482838360029257950621993168278283458969600000⟩, + ⟨2, 3, 7, 2, 6, 4, -1287287572810778391206834763133551621644589465600000⟩, + ⟨2, 3, 8, 2, 7, 4, -2547130432993143507545624915251113038776432066560000⟩, + ⟨2, 3, 3, 3, 1, 4, -125911912985400465998163586092310212998206586880000⟩, + ⟨2, 3, 4, 3, 2, 4, -113915383302932316932708660423294953751833183518720000⟩, + ⟨2, 3, 5, 3, 3, 4, -5667254018382961265363377249868158842259793510400000⟩, + ⟨2, 3, 6, 3, 4, 4, 3792810666731402073255703675720705947585635942400000⟩, + ⟨2, 3, 7, 3, 5, 4, -3087541729707169054441099043944585142246729318400000⟩, + ⟨2, 3, 8, 3, 6, 4, 136778177485963359366079848102775418084602675200000⟩, + ⟨2, 3, 3, 4, 0, 4, 24142773019950784234803989256405466425169155194880000⟩, + ⟨2, 3, 4, 4, 1, 4, 1462466816114715929740228236234603377404674048000000⟩, + ⟨2, 3, 5, 4, 2, 4, -11704493931355358204106499578954159068553412608000000⟩, + ⟨2, 3, 6, 4, 3, 4, -4788839785130099830429577646171845929118937907200000⟩, + ⟨2, 3, 7, 4, 4, 4, 1596274154645093733793169086529965725342656102400000⟩, + ⟨2, 3, 8, 4, 5, 4, 1861705963925967574363967130262868173685564375040000⟩, + ⟨2, 3, 4, 5, 0, 4, 469405954326262490391418343279638265141172822343680000⟩, + ⟨2, 3, 5, 5, 1, 4, -3951616554092112368177295547819349646518098329600000⟩, + ⟨2, 3, 6, 5, 2, 4, 10395309435238176739091550924109506884399844556800000⟩, + ⟨2, 3, 7, 5, 3, 4, 1820844554025087760214935626236794269961342156800000⟩, + ⟨2, 3, 8, 5, 4, 4, 931974286830762557367340110900468566939790213120000⟩, + ⟨2, 3, 5, 6, 0, 4, 209826184858814268689170200883565632951574908108800000⟩, + ⟨2, 3, 6, 6, 1, 4, -19468362276483890492628633284616621011928455577600000⟩, + ⟨2, 3, 7, 6, 2, 4, 12887021047214027688550228692710801530680036556800000⟩, + ⟨2, 3, 8, 6, 3, 4, -4948225004101191920011443696044980403433205923840000⟩, + ⟨2, 3, 6, 7, 0, 4, -5776903555784576407799350215865923049234838323200000⟩, + ⟨2, 3, 7, 7, 1, 4, -66671465669296528850908706940312731852227372646400000⟩, + ⟨2, 3, 8, 7, 2, 4, 1946268646736572212550156900944365359907953704960000⟩ +] + +def collectedFourData_8_1_21 : List CollectedFourTerm := [ + ⟨2, 4, 2, 0, 3, 5, -3642959516180422900475232941873576884500116275200000⟩, + ⟨2, 4, 3, 0, 4, 5, -1333566719813071627596432623237356440266578329600000⟩, + ⟨2, 4, 4, 0, 5, 5, 39279877522312806121595545040339586541106390630400000⟩, + ⟨2, 4, 5, 0, 6, 5, 22839705753929284953825437949989640724820262912000000⟩, + ⟨2, 4, 6, 0, 7, 5, 7862559527848864316167975699319018353808375808000000⟩, + ⟨2, 4, 7, 0, 8, 5, 4612650732422592315915238905369099148676038656000000⟩, + ⟨2, 4, 2, 1, 2, 5, 3494375166260175959943251096252497317907660800000000⟩, + ⟨2, 4, 3, 1, 3, 5, 6401350351981484718664911559251625062982641254400000⟩, + ⟨2, 4, 4, 1, 4, 5, 12087721692267488547226768831907432199611429683200000⟩, + ⟨2, 4, 5, 1, 5, 5, -7486463051278700991507398796830551620798382080000000⟩, + ⟨2, 4, 6, 1, 6, 5, -2897394995899219947180058832744401487064465408000000⟩, + ⟨2, 4, 7, 1, 7, 5, -364905077067776828012108056732966438022676480000000⟩, + ⟨2, 4, 8, 1, 8, 5, -878899533015805814305116731303762037850924646400000⟩, + ⟨2, 4, 2, 2, 1, 5, 4842278267091646557219923170775027852567484825600000⟩, + ⟨2, 4, 3, 2, 2, 5, -4995700713100905882155283780172007798480673177600000⟩, + ⟨2, 4, 4, 2, 3, 5, 18979063557757864353327247409970789456504736972800000⟩, + ⟨2, 4, 5, 2, 4, 5, 5623826934559472119640493323175370763437867008000000⟩, + ⟨2, 4, 6, 2, 5, 5, -52054705061404108835127065932844717668564992000000⟩, + ⟨2, 4, 7, 2, 6, 5, -228867430760178016402759866670372585115064729600000⟩, + ⟨2, 4, 8, 2, 7, 5, -377379544868209594034314502209099931111443660800000⟩, + ⟨2, 4, 2, 3, 0, 5, -8385674895375399043604941074846084720736233062400000⟩, + ⟨2, 4, 3, 3, 1, 5, -111929675372169552815392722294872557476013670400000⟩, + ⟨2, 4, 4, 3, 2, 5, -50632666801241852012280286778828353271631760588800000⟩, + ⟨2, 4, 5, 3, 3, 5, -1679306025641326805841513670944610479079686144000000⟩, + ⟨2, 4, 6, 3, 4, 5, 842906871577298619536921529923176826035765248000000⟩, + ⟨2, 4, 7, 3, 5, 5, -548935418913413393764931916611094384774375014400000⟩, + ⟨2, 4, 8, 3, 6, 5, 20264877565339423230956540043844026038747136000000⟩, + ⟨2, 4, 3, 4, 0, 5, 21461771826311595325163846729760706535233054310400000⟩, + ⟨2, 4, 4, 4, 1, 5, 650031566072984903327656616240612957403217920000000⟩, + ⟨2, 4, 5, 4, 2, 5, -3468245312853592923523641354900544045323386880000000⟩, + ⟨2, 4, 6, 4, 3, 5, -1064262447154411058805853772570252754334777344000000⟩, + ⟨2, 4, 7, 4, 4, 5, 283802292726863146595770273082127290967942758400000⟩, + ⟨2, 4, 8, 4, 5, 5, 275827943573042882463766172603187202503160627200000⟩, + ⟨2, 4, 4, 5, 0, 5, 208639734079785184458096957991285327672080806707200000⟩, + ⟨2, 4, 5, 5, 1, 5, -1170932777811915334753429570693108461528416256000000⟩, + ⟨2, 4, 6, 5, 2, 5, 2310233366509119864288396614573241374852775936000000⟩, + ⟨2, 4, 7, 5, 3, 5, 323728764027026360490799663126541554301062348800000⟩, + ⟨2, 4, 8, 5, 4, 5, 138080102862959331409588638095367700743821721600000⟩, + ⟨2, 4, 5, 6, 0, 5, 62175151392151178149609623325601427217572691968000000⟩, + ⟨2, 4, 6, 6, 1, 5, -4326610997259845669907821358312209049716785152000000⟩, + ⟨2, 4, 7, 6, 2, 5, 2291189210184161221946090080345879165574892748800000⟩, + ⟨2, 4, 8, 6, 3, 5, -733122605644839785966814205671917103109845811200000⟩, + ⟨2, 4, 6, 7, 0, 5, -1283847819328807155677049547364340798968561664000000⟩, + ⟨2, 4, 7, 7, 1, 5, -11853549568127662418107964012991364091957634662400000⟩, + ⟨2, 4, 8, 7, 2, 5, 288356641098124297152544581720653443380333772800000⟩ +] + +def collectedFourData_8_1_22 : List CollectedFourTerm := [ + ⟨2, 5, 1, 0, 2, 6, -141792642174968081893700739848204471419011072000000⟩, + ⟨2, 5, 2, 0, 3, 6, 134878391794083006563091368941999093143778099200000⟩, + ⟨2, 5, 3, 0, 4, 6, 24687254102001019909206339793288967257640140800000⟩, + ⟨2, 5, 4, 0, 5, 6, -484771304443240629036539977893883250509401292800000⟩, + ⟨2, 5, 5, 0, 6, 6, -211406602753712548164316994737936170208985088000000⟩, + ⟨2, 5, 6, 0, 7, 6, -58221310436817773892887810777681481258604953600000⟩, + ⟨2, 5, 7, 0, 8, 6, -28463437942587410353779978490321278018256896000000⟩, + ⟨2, 5, 1, 1, 1, 6, 140158063844623773769929228667636265926420070400000⟩, + ⟨2, 5, 2, 1, 2, 6, -129377145328400448554958143219551538302156800000000⟩, + ⟨2, 5, 3, 1, 3, 6, -118503079289090364358663811184897856006992691200000⟩, + ⟨2, 5, 4, 1, 4, 6, -149180215981547734459442588726284767715550822400000⟩, + ⟨2, 5, 5, 1, 5, 6, 69295451410959683668790782475515486713937920000000⟩, + ⟨2, 5, 6, 1, 6, 6, 21454862493166161859356114422498058204453273600000⟩, + ⟨2, 5, 7, 1, 7, 6, 2251731947326242405383970112179053191495680000000⟩, + ⟨2, 5, 8, 1, 8, 6, 4648675461147129149373159307838639171646259200000⟩, + ⟨2, 5, 1, 2, 0, 6, 266070345742614935349689672041983394195282329600000⟩, + ⟨2, 5, 2, 2, 1, 6, -179282449443617084267603932815906568538790297600000⟩, + ⟨2, 5, 3, 2, 2, 6, 92481411758053739386823099576084490129034444800000⟩, + ⟨2, 5, 4, 2, 3, 6, -234229482838360029257950621993168278283458969600000⟩, + ⟨2, 5, 5, 2, 4, 6, -52054705061404108835127065932844717668564992000000⟩, + ⟨2, 5, 6, 2, 5, 6, 385458848653852077775640493157680442402406400000⟩, + ⟨2, 5, 7, 2, 6, 6, 1412279899436558796405469607956578297289113600000⟩, + ⟨2, 5, 8, 2, 7, 6, 1996035910666673408357627941004343448594022400000⟩, + ⟨2, 5, 2, 3, 0, 6, 310474585010522080095842641953593173182146150400000⟩, + ⟨2, 5, 3, 3, 1, 6, 2072064559210478035216726355827861193175859200000⟩, + ⟨2, 5, 4, 3, 2, 6, 624881376443577745387999234339925534715779481600000⟩, + ⟨2, 5, 5, 3, 3, 6, 15543824674868925494297201576447757156089856000000⟩, + ⟨2, 5, 6, 3, 4, 6, -6241624303842361610343640552004798572501401600000⟩, + ⟨2, 5, 7, 3, 5, 6, 3387334124585677427128176152061370129868390400000⟩, + ⟨2, 5, 8, 3, 6, 6, -107184991597270775924395277962040687198208000000⟩, + ⟨2, 5, 3, 4, 0, 6, -397304616772071484838502581926604432148214579200000⟩, + ⟨2, 5, 4, 4, 1, 6, -8022342993189896459078122507467228645949440000000⟩, + ⟨2, 5, 5, 4, 2, 6, 32102425793323779454216673989721985248133120000000⟩, + ⟨2, 5, 6, 4, 3, 6, 7880735796346570760059393503972912020638924800000⟩, + ⟨2, 5, 7, 4, 4, 6, -1751268287064190190546263512030714962273894400000⟩, + ⟨2, 5, 8, 4, 5, 6, -1458909175189674599599756074874669914233241600000⟩, + ⟨2, 5, 4, 5, 0, 6, -2574920351803403976930240212921915859387442790400000⟩, + ⟨2, 5, 5, 5, 1, 6, 10838271003889710292987877782505026165407744000000⟩, + ⟨2, 5, 6, 5, 2, 6, -17107001039116019533154796220338893395014451200000⟩, + ⟨2, 5, 7, 5, 3, 6, -1997643897107794176162467278434769348381900800000⟩, + ⟨2, 5, 8, 5, 4, 6, -730333288093995363986440731008189946711244800000⟩, + ⟨2, 5, 5, 6, 0, 6, -575499425129465190202359200172512122641580032000000⟩, + ⟨2, 5, 6, 6, 1, 6, 32038035593701046512634147694337422522738278400000⟩, + ⟨2, 5, 7, 6, 2, 6, -14138317787731427817035406515968282660228300800000⟩, + ⟨2, 5, 8, 6, 3, 6, 3877632128417710020890244206296315066947993600000⟩, + ⟨2, 5, 6, 7, 0, 6, 9506739144933927846380305333025212212235468800000⟩, + ⟨2, 5, 7, 7, 1, 6, 73145094242716437985627246654973423573689958400000⟩, + ⟨2, 5, 8, 7, 2, 6, -1525175962868048915631924219643079350969958400000⟩ +] + +def collectedFourData_8_1_23 : List CollectedFourTerm := [ + ⟨2, 6, 0, 0, 1, 7, 2461814341939559416957163790439353649824006144000000⟩, + ⟨2, 6, 1, 0, 2, 7, -3117078242687373059918210466416218179442311168000000⟩, + ⟨2, 6, 2, 0, 3, 7, 1482539904825262124771643170196387033044641382400000⟩, + ⟨2, 6, 3, 0, 4, 7, 180902905004255623553648718125692957825066598400000⟩, + ⟨2, 6, 4, 0, 5, 7, -2664225136404794150455572807047706706193468620800000⟩, + ⟨2, 6, 5, 0, 6, 7, -929485355087605354567389035286573358770447974400000⟩, + ⟨2, 6, 6, 0, 7, 7, -213316639988754774993602475225052875478951526400000⟩, + ⟨2, 6, 7, 0, 8, 7, -89388844524749336576953307307507857995333632000000⟩, + ⟨2, 6, 0, 1, 0, 7, 12837860610163525005183250604749795409421926400000000⟩, + ⟨2, 6, 1, 1, 1, 7, 3081144724055304144106541398541482997031999897600000⟩, + ⟨2, 6, 2, 1, 2, 7, -1422071972911418549812206307548090785700249600000000⟩, + ⟨2, 6, 3, 1, 3, 7, -868365157452179756470785068497432512317462937600000⟩, + ⟨2, 6, 4, 1, 4, 7, -819870478366714046597070279982832430734534246400000⟩, + ⟨2, 6, 5, 1, 5, 7, 304669326415069434286305154013693569658781696000000⟩, + ⟨2, 6, 6, 1, 6, 7, 78608316166803085946808798381822469028079206400000⟩, + ⟨2, 6, 7, 1, 7, 7, 7071518112357007349224454443022613542338560000000⟩, + ⟨2, 6, 8, 1, 8, 7, 12774186406104034441665146150049311050275225600000⟩, + ⟨2, 6, 1, 2, 0, 7, 5849119340869625259045855736635678311183705702400000⟩, + ⟨2, 6, 2, 2, 1, 7, -1970615025872810390816956100382124895273956147200000⟩, + ⟨2, 6, 3, 2, 2, 7, 677683956944024227682201075069254122560972390400000⟩, + ⟨2, 6, 4, 2, 3, 7, -1287287572810778391206834763133551621644589465600000⟩, + ⟨2, 6, 5, 2, 4, 7, -228867430760178016402759866670372585115064729600000⟩, + ⟨2, 6, 6, 2, 5, 7, 1412279899436558796405469607956578297289113600000⟩, + ⟨2, 6, 7, 2, 6, 7, 4435236130322752099494299882880090904933171200000⟩, + ⟨2, 6, 8, 2, 7, 7, 5484946197952430231681256358597490935804723200000⟩, + ⟨2, 6, 2, 3, 0, 7, 3412636787773107988705681625826178609445653708800000⟩, + ⟨2, 6, 3, 3, 1, 7, 15183644830194182436543985184662925010901401600000⟩, + ⟨2, 6, 4, 3, 2, 7, 3434247561959666637602163491388187254904691097600000⟩, + ⟨2, 6, 5, 3, 3, 7, 68341088732084577618476877204409158072061132800000⟩, + ⟨2, 6, 6, 3, 4, 7, -22868642333509393083136735177885639453861478400000⟩, + ⟨2, 6, 7, 3, 5, 7, 10637853516736584578492841141087602408737996800000⟩, + ⟨2, 6, 8, 3, 6, 7, -294535739060252868558392545854459576582144000000⟩, + ⟨2, 6, 3, 4, 0, 7, -2911363047858957223531950221736974751096215961600000⟩, + ⟨2, 6, 4, 4, 1, 7, -44089507071514149764557724886580735078563840000000⟩, + ⟨2, 6, 5, 4, 2, 7, 141143815987824206948008505161854111455379456000000⟩, + ⟨2, 6, 6, 4, 3, 7, 28874171125709863771140605955617543028945715200000⟩, + ⟨2, 6, 7, 4, 4, 7, -5499822226298313764482237277952034214825164800000⟩, + ⟨2, 6, 8, 4, 5, 7, -4008965114731754107292060065628342734081228800000⟩, + ⟨2, 6, 4, 5, 0, 7, -14151348197876110309238147723506469993619809894400000⟩, + ⟨2, 6, 5, 5, 1, 7, 47652315686290516342879973638249901464957747200000⟩, + ⟨2, 6, 6, 5, 2, 7, -62678217899415285687001442706626345433877708800000⟩, + ⟨2, 6, 7, 5, 3, 7, -6273559789037581767545129411988682612251033600000⟩, + ⟨2, 6, 8, 5, 4, 7, -2006897155688602709562878928873853200787046400000⟩, + ⟨2, 6, 5, 6, 0, 7, -2530281838653593856457161626321356448975133081600000⟩, + ⟨2, 6, 6, 6, 1, 7, 117383927867872629892684553926949854114322841600000⟩, + ⟨2, 6, 7, 6, 2, 7, -44401097756293691569663285958542556359399833600000⟩, + ⟨2, 6, 8, 6, 3, 7, 10655421320911617378404586050366117988060364800000⟩, + ⟨2, 6, 6, 7, 0, 7, 34831673083820669648123858690938833816728371200000⟩, + ⟨2, 6, 7, 7, 1, 7, 229710671992561195085549688204206054407195852800000⟩, + ⟨2, 6, 8, 7, 2, 7, -4191060919313557309979043871308459101336371200000⟩ +] + +def collectedFourData_8_1_24 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 1, 8, 24355716481599897326420689829408853411414147072000000⟩, + ⟨2, 7, 1, 0, 2, 8, -15419252507490914985772015344962506845472161792000000⟩, + ⟨2, 7, 2, 0, 3, 8, 4889120594167682064858859574885146747575101030400000⟩, + ⟨2, 7, 3, 0, 4, 8, 447436245487762137769631471479382168321182924800000⟩, + ⟨2, 7, 4, 0, 5, 8, -5271649527746563706488285160077684695038511022080000⟩, + ⟨2, 7, 5, 0, 6, 8, -1532628557499667623469750894027444820053799731200000⟩, + ⟨2, 7, 6, 0, 7, 8, -301489580026013759986931387685935756678371737600000⟩, + ⟨2, 7, 7, 0, 8, 8, -110544960518191432987063775929923476077412352000000⟩, + ⟨2, 7, 0, 1, 0, 8, 127010103046640892878211030744856440784237363200000000⟩, + ⟨2, 7, 1, 1, 1, 8, 15241500152839459957076135345796847342237148774400000⟩, + ⟨2, 7, 2, 1, 2, 8, -4689709428070573517099100355497501939833241600000000⟩, + ⟨2, 7, 3, 1, 3, 8, -2147771180090516607469621592009172761735017267200000⟩, + ⟨2, 7, 4, 1, 4, 8, -1622261482724242047966820733744565342087822704640000⟩, + ⟨2, 7, 5, 1, 5, 8, 502369303294631261253250584930619693945847808000000⟩, + ⟨2, 7, 6, 1, 6, 8, 111100513438290235897617674861545025110120857600000⟩, + ⟨2, 7, 7, 1, 7, 8, 8745170548856841055143741165502353018716160000000⟩, + ⟨2, 7, 8, 1, 8, 8, 14042238734698390671323264586317211567862579200000⟩, + ⟨2, 7, 1, 2, 0, 8, 28933841579017134582513124214630940407869577625600000⟩, + ⟨2, 7, 2, 2, 1, 8, -6498694891660676776256339373363353551425975091200000⟩, + ⟨2, 7, 3, 2, 2, 8, 1676149784964433759037818501033149908321619148800000⟩, + ⟨2, 7, 4, 2, 3, 8, -2547130432993143507545624915251113038776432066560000⟩, + ⟨2, 7, 5, 2, 4, 8, -377379544868209594034314502209099931111443660800000⟩, + ⟨2, 7, 6, 2, 5, 8, 1996035910666673408357627941004343448594022400000⟩, + ⟨2, 7, 7, 2, 6, 8, 5484946197952430231681256358597490935804723200000⟩, + ⟨2, 7, 8, 2, 7, 8, 6029419135595242330204204964109253326825062400000⟩, + ⟨2, 7, 2, 3, 0, 8, 11254194740533666597339226045168580799731911884800000⟩, + ⟨2, 7, 3, 3, 1, 8, 37554471750920401069482365122413554025313075200000⟩, + ⟨2, 7, 4, 3, 2, 8, 6795277655326038394696179553885142693380368629760000⟩, + ⟨2, 7, 5, 3, 3, 8, 112687632643270140793539906323653789655393894400000⟩, + ⟨2, 7, 6, 3, 4, 8, -32321235573832054480575039669401934402001305600000⟩, + ⟨2, 7, 7, 3, 5, 8, 13155568832533214249264329350504078969195724800000⟩, + ⟨2, 7, 8, 3, 6, 8, -323773352940002261560632575546172540715008000000⟩, + ⟨2, 7, 3, 4, 0, 8, -7200820524994752253028725688694791443374617395200000⟩, + ⟨2, 7, 4, 4, 1, 8, -87239034703264092940160944344920942532624384000000⟩, + ⟨2, 7, 5, 4, 2, 8, 232732061794592733710977952653992583168524288000000⟩, + ⟨2, 7, 6, 4, 3, 8, 40809107656807398549008167124581131093855436800000⟩, + ⟨2, 7, 7, 4, 4, 8, -6801493341765776554371913685835574581972172800000⟩, + ⟨2, 7, 8, 4, 5, 8, -4406922165566709649908699358849975327496601600000⟩, + ⟨2, 7, 4, 5, 0, 8, -28000992493066901351599559701204167288077879869440000⟩, + ⟨2, 7, 5, 5, 1, 8, 78573911306988503027438080387159740462504345600000⟩, + ⟨2, 7, 6, 5, 2, 8, -88585820554223338267031810522201067344835379200000⟩, + ⟨2, 7, 7, 5, 3, 8, -7758355339246595859361342128650690567444889600000⟩, + ⟨2, 7, 8, 5, 4, 8, -2206115370502212137640872118139867013893324800000⟩, + ⟨2, 7, 5, 6, 0, 8, -4172182147052503900723054006495617101905841356800000⟩, + ⟨2, 7, 6, 6, 1, 8, 165903752827507676080356881071418949862057574400000⟩, + ⟨2, 7, 7, 6, 2, 8, -54909733138734832717879693432689748470241689600000⟩, + ⟨2, 7, 8, 6, 3, 8, 11713150665747192283575117296657365397510553600000⟩, + ⟨2, 7, 6, 7, 0, 8, 49229101349984199979057890499952589648219340800000⟩, + ⟨2, 7, 7, 7, 1, 8, 284077474108015468081153413131055308714331340800000⟩, + ⟨2, 7, 8, 7, 2, 8, -4607094033992146876691464920452232976426598400000⟩ +] + +def collectedFourData_8_1_25 : List CollectedFourTerm := [ + ⟨3, 0, 5, 0, 6, 2, -34056230639232602067149877142637895952308476313600000⟩, + ⟨3, 0, 6, 0, 7, 2, -46895374849398029847204020038588586665694566809600000⟩, + ⟨3, 0, 7, 0, 8, 2, -68779124781230473254439057220977789110916743168000000⟩, + ⟨3, 0, 5, 1, 5, 2, 11163047155394184462727954876625858711701684224000000⟩, + ⟨3, 0, 6, 1, 6, 2, 17281195002492805566883411620270678963398482329600000⟩, + ⟨3, 0, 7, 1, 7, 2, 5441090879163010019343368311057826560019005440000000⟩, + ⟨3, 0, 8, 1, 8, 2, 26210499844071490070865816100357670627661211238400000⟩, + ⟨3, 0, 5, 2, 4, 2, -8385674895375399043604941074846084720736233062400000⟩, + ⟨3, 0, 6, 2, 5, 2, 310474585010522080095842641953593173182146150400000⟩, + ⟨3, 0, 7, 2, 6, 2, 3412636787773107988705681625826178609445653708800000⟩, + ⟨3, 0, 8, 2, 7, 2, 11254194740533666597339226045168580799731911884800000⟩, + ⟨3, 0, 5, 3, 3, 2, 2504009199560511762310229498551864978501219123200000⟩, + ⟨3, 0, 6, 3, 4, 2, -5027425683168786070885655885019282297761405337600000⟩, + ⟨3, 0, 7, 3, 5, 2, 8185162906200220673502778145469110227444118323200000⟩, + ⟨3, 0, 8, 3, 6, 2, -604338209674421038082027257573823020548489216000000⟩, + ⟨3, 0, 5, 4, 2, 2, 5171492293312891126697351825971697777758961664000000⟩, + ⟨3, 0, 6, 4, 3, 2, 6347676761068476412021903991769493319893961932800000⟩, + ⟨3, 0, 7, 4, 4, 2, -4231769201048605386008856548896215451319874355200000⟩, + ⟨3, 0, 8, 4, 5, 2, -8225727742970351433131124919059718728165045043200000⟩, + ⟨3, 0, 5, 5, 1, 2, 1745975065258424278677144310649601116903099596800000⟩, + ⟨3, 0, 6, 5, 2, 2, -13779133795845830225121792929733614574201156403200000⟩, + ⟨3, 0, 7, 5, 3, 2, -4827111859950913046128997067116442993532757606400000⟩, + ⟨3, 0, 8, 5, 4, 2, -4117818224502214402052130750102573936383990169600000⟩, + ⟨3, 0, 5, 6, 0, 2, -92709219578103521959284112938880820309991515750400000⟩, + ⟨3, 0, 6, 6, 1, 2, 25805597251807343193664540330830945573732247142400000⟩, + ⟨3, 0, 7, 6, 2, 2, -34163867530004855916702469570418479835566728806400000⟩, + ⟨3, 0, 8, 6, 3, 2, 21863147287158466234357203978382083469352317747200000⟩, + ⟨3, 0, 6, 7, 0, 2, 7657369654723452378037196480963062194668096716800000⟩, + ⟨3, 0, 7, 7, 1, 2, 176747994188271165192812221812673514442459394867200000⟩, + ⟨3, 0, 8, 7, 2, 2, -8599357961433170611133403740423731047874481356800000⟩ +] + +def collectedFourData_8_1_26 : List CollectedFourTerm := [ + ⟨3, 1, 4, 0, 5, 3, -260592652825855322224080123890656995796938915840000⟩, + ⟨3, 1, 5, 0, 6, 3, -454573172393227294580993429085926153367689625600000⟩, + ⟨3, 1, 6, 0, 7, 3, -312973263860019127619339285320772688397782220800000⟩, + ⟨3, 1, 7, 0, 8, 3, -306014928442259703174116462300150283764760576000000⟩, + ⟨3, 1, 4, 1, 4, 3, -80193006218496761527904373500049913383978270720000⟩, + ⟨3, 1, 5, 1, 5, 3, 149001274179680310139237211314428571029602304000000⟩, + ⟨3, 1, 6, 1, 6, 3, 115332311996671274118849789826145361666559180800000⟩, + ⟨3, 1, 7, 1, 7, 3, 24208726722403521950410067765718547515310080000000⟩, + ⟨3, 1, 8, 1, 8, 3, 87462630482703951018608717035918897941420441600000⟩, + ⟨3, 1, 4, 2, 3, 3, -125911912985400465998163586092310212998206586880000⟩, + ⟨3, 1, 5, 2, 4, 3, -111929675372169552815392722294872557476013670400000⟩, + ⟨3, 1, 6, 2, 5, 3, 2072064559210478035216726355827861193175859200000⟩, + ⟨3, 1, 7, 2, 6, 3, 15183644830194182436543985184662925010901401600000⟩, + ⟨3, 1, 8, 2, 7, 3, 37554471750920401069482365122413554025313075200000⟩, + ⟨3, 1, 4, 3, 2, 3, 335909931335405394104662311307554194712931860480000⟩, + ⟨3, 1, 5, 3, 3, 3, 33422824081851948809687661987973293751350067200000⟩, + ⟨3, 1, 6, 3, 4, 3, -33552345618903159640332588279385532090076364800000⟩, + ⟨3, 1, 7, 3, 5, 3, 36417765550175236088807344637519354755704422400000⟩, + ⟨3, 1, 8, 3, 6, 3, -2016634930038863394110887170416313561513984000000⟩, + ⟨3, 1, 4, 4, 1, 3, -4312473991989435147333710326578224648159232000000⟩, + ⟨3, 1, 5, 4, 2, 3, 69027652610216728004926716751875910920044544000000⟩, + ⟨3, 1, 6, 4, 3, 3, 42363519221672186584761618975721666667505254400000⟩, + ⟨3, 1, 7, 4, 4, 3, -18828162663629055005680940881748767923398246400000⟩, + ⟨3, 1, 8, 4, 5, 3, -27448686225549874003297568022721287198395596800000⟩, + ⟨3, 1, 4, 5, 0, 3, -1384168821754791497658821600241381171199601541120000⟩, + ⟨3, 1, 5, 5, 1, 3, 23304793555740319763047595717947454435151052800000⟩, + ⟨3, 1, 6, 5, 2, 3, -91960038513374227893369706283350057396312473600000⟩, + ⟨3, 1, 7, 5, 3, 3, -21476985860232618985480956408597331737103564800000⟩, + ⟨3, 1, 8, 5, 4, 3, -13740875447136661741090518911892764827739750400000⟩, + ⟨3, 1, 5, 6, 0, 3, -1237457089721789520141081043030763045428553318400000⟩, + ⟨3, 1, 6, 6, 1, 3, 172222996909448036678652644544535006633210675200000⟩, + ⟨3, 1, 7, 6, 2, 3, -152003293306784060957328308631722623033461964800000⟩, + ⟨3, 1, 8, 6, 3, 3, 72955814797182951596759399485599979072703692800000⟩, + ⟨3, 1, 6, 7, 0, 3, 51104228958993593463267557726260390428829286400000⟩, + ⟨3, 1, 7, 7, 1, 3, 786394490564919007671057556522698006069667430400000⟩, + ⟨3, 1, 8, 7, 2, 3, -28695464498722601862068238645965147931358003200000⟩ +] + +def collectedFourData_8_1_27 : List CollectedFourTerm := [ + ⟨3, 2, 3, 0, 4, 4, 4002140663716890033209928107200835154509058539520000⟩, + ⟨3, 2, 4, 0, 5, 4, -235764124527496645868403273682078878127035997224960000⟩, + ⟨3, 2, 5, 0, 6, 4, -205631365391170978470180694269954723122599113523200000⟩, + ⟨3, 2, 6, 0, 7, 4, -94384686539596325012690963415747244747473184358400000⟩, + ⟨3, 2, 7, 0, 8, 4, -69214673662295613536964042257261446844840411136000000⟩, + ⟨3, 2, 3, 1, 3, 4, -19210965725025442624559552499905755533274282721280000⟩, + ⟨3, 2, 4, 1, 4, 4, -72552444204812656014238549142183780845019128135680000⟩, + ⟨3, 2, 5, 1, 5, 4, 67402427849585934869558516604525213101051609088000000⟩, + ⟨3, 2, 6, 1, 6, 4, 34781258889134548960537211730369608439466190438400000⟩, + ⟨3, 2, 7, 1, 7, 4, 5475546988509139912138249404146254976259194880000000⟩, + ⟨3, 2, 8, 1, 8, 4, 15825887860627144458849245749156155431682394030080000⟩, + ⟨3, 2, 3, 2, 2, 4, 14992498440920244046773722660376817716453043077120000⟩, + ⟨3, 2, 4, 2, 3, 4, -113915383302932316932708660423294953751833183518720000⟩, + ⟨3, 2, 5, 2, 4, 4, -50632666801241852012280286778828353271631760588800000⟩, + ⟨3, 2, 6, 2, 5, 4, 624881376443577745387999234339925534715779481600000⟩, + ⟨3, 2, 7, 2, 6, 4, 3434247561959666637602163491388187254904691097600000⟩, + ⟨3, 2, 8, 2, 7, 4, 6795277655326038394696179553885142693380368629760000⟩, + ⟨3, 2, 3, 3, 1, 4, 335909931335405394104662311307554194712931860480000⟩, + ⟨3, 2, 4, 3, 2, 4, 303905386520267210408310285126708071745583180677120000⟩, + ⟨3, 2, 5, 3, 3, 4, 15119196135127055339124854319036371815438378598400000⟩, + ⟨3, 2, 6, 3, 4, 4, -10118524454295791409498305010468989400661780070400000⟩, + ⟨3, 2, 7, 3, 5, 4, 8236996054069881869827950523478334254650648166400000⟩, + ⟨3, 2, 8, 3, 6, 4, -364899135579166376218220358349169332562637619200000⟩, + ⟨3, 2, 3, 4, 0, 4, -64408498251617223189013129909838635984761630228480000⟩, + ⟨3, 2, 4, 4, 1, 4, -3901593710504300136440993835872233389564100608000000⟩, + ⟨3, 2, 5, 4, 2, 4, 31225446898365561997130453112745481718221242368000000⟩, + ⟨3, 2, 6, 4, 3, 4, 12775747784769415104359394187362369536892547891200000⟩, + ⟨3, 2, 7, 4, 4, 4, -4258567191664293306850385088820379469480355430400000⟩, + ⟨3, 2, 8, 4, 5, 4, -4966690662396637947615727948575547877213696163840000⟩, + ⟨3, 2, 4, 5, 0, 4, -1252289145225266426513523164383585015460881791713280000⟩, + ⟨3, 2, 5, 5, 1, 4, 10542189486890281738330125857331809407542598041600000⟩, + ⟨3, 2, 6, 5, 2, 4, -27732782354009929734789431811595206296226024652800000⟩, + ⟨3, 2, 7, 5, 3, 4, -4857679901868649632431721864219638635160194252800000⟩, + ⟨3, 2, 8, 5, 4, 4, -2486336767292100632818018757749872270041960939520000⟩, + ⟨3, 2, 5, 6, 0, 4, -559777845297822420100497024751568438280307133644800000⟩, + ⟨3, 2, 6, 6, 1, 4, 51938026199830442409365627584931819301665085849600000⟩, + ⟨3, 2, 7, 6, 2, 4, -34380212741184571162652333190030471136692456652800000⟩, + ⟨3, 2, 8, 6, 3, 4, 13200958368033811804915097278256126358413000048640000⟩, + ⟨3, 2, 6, 7, 0, 4, 15411721025792533792918655546721067968587051827200000⟩, + ⟨3, 2, 7, 7, 1, 4, 177867263899016562557519251428341107207096919654400000⟩, + ⟨3, 2, 8, 7, 2, 4, -5192288418025539337908189798401640313068359516160000⟩ +] + +def collectedFourData_8_1_28 : List CollectedFourTerm := [ + ⟨3, 3, 2, 0, 3, 5, 1087807988737193688492212598330254874728044953600000⟩, + ⟨3, 3, 3, 0, 4, 5, 398210445349035788954293902493201163535305932800000⟩, + ⟨3, 3, 4, 0, 5, 5, -11729190065277184934865597090416354502227735347200000⟩, + ⟨3, 3, 5, 0, 6, 5, -6820063267016725719950524096657084105585852416000000⟩, + ⟨3, 3, 6, 0, 7, 5, -2347804039086152365768092324299673991636844544000000⟩, + ⟨3, 3, 7, 0, 8, 5, -1377363183339656871315885433764995139851255808000000⟩, + ⟨3, 3, 2, 1, 2, 5, -1043439874810406310487793209576670011745894400000000⟩, + ⟨3, 3, 3, 1, 3, 5, -1911478845884114190853477204824151807690486579200000⟩, + ⟨3, 3, 4, 1, 4, 5, -3609460979206010642678048182883340280793766297600000⟩, + ⟨3, 3, 5, 1, 5, 5, 2235499537778410643403113589603965735471677440000000⟩, + ⟨3, 3, 6, 1, 6, 5, 865178273068198991235266212973128064742457344000000⟩, + ⟨3, 3, 7, 1, 7, 5, 108962687123484796522127577580612918852976640000000⟩, + ⟨3, 3, 8, 1, 8, 5, 262444292632274073046841409868026406025507635200000⟩, + ⟨3, 3, 2, 2, 1, 5, -1445931243329773121922935018307847854752582860800000⟩, + ⟨3, 3, 3, 2, 2, 5, 1491744039678237236148673513512634428305493196800000⟩, + ⟨3, 3, 4, 2, 3, 5, -5667254018382961265363377249868158842259793510400000⟩, + ⟨3, 3, 5, 2, 4, 5, -1679306025641326805841513670944610479079686144000000⟩, + ⟨3, 3, 6, 2, 5, 5, 15543824674868925494297201576447757156089856000000⟩, + ⟨3, 3, 7, 2, 6, 5, 68341088732084577618476877204409158072061132800000⟩, + ⟨3, 3, 8, 2, 7, 5, 112687632643270140793539906323653789655393894400000⟩, + ⟨3, 3, 2, 3, 0, 5, 2504009199560511762310229498551864978501219123200000⟩, + ⟨3, 3, 3, 3, 1, 5, 33422824081851948809687661987973293751350067200000⟩, + ⟨3, 3, 4, 3, 2, 5, 15119196135127055339124854319036371815438378598400000⟩, + ⟨3, 3, 5, 3, 3, 5, 501450126501122731443400002215655153799790592000000⟩, + ⟨3, 3, 6, 3, 4, 5, -251696683586710870770605976955396948664254464000000⟩, + ⟨3, 3, 7, 3, 5, 5, 163915171536381972139376926947625865439294259200000⟩, + ⟨3, 3, 8, 3, 6, 5, -6051205238061608028246052514999479144808448000000⟩, + ⟨3, 3, 3, 4, 0, 5, -6408604526463347524417112096527538026024481587200000⟩, + ⟨3, 3, 4, 4, 1, 5, -194103043793067861948957581711284288157122560000000⟩, + ⟨3, 3, 5, 4, 2, 5, 1035637355140900038492944399930206543769763840000000⟩, + ⟨3, 3, 6, 4, 3, 5, 317794690549129434333673013172955078503432192000000⟩, + ⟨3, 3, 7, 4, 4, 5, -84744944290213562553931063761459231704953651200000⟩, + ⟨3, 3, 8, 4, 5, 5, -82363759246576162002331807959591540458363289600000⟩, + ⟨3, 3, 4, 5, 0, 5, -62300985913221859567036823782959563770596792729600000⟩, + ⟨3, 3, 5, 5, 1, 5, 349647045024957829416097123769767416570052608000000⟩, + ⟨3, 3, 6, 5, 2, 5, -689848542311217176058410044068255398885326848000000⟩, + ⟨3, 3, 7, 5, 3, 5, -96667210856585359289227985726971432663410278400000⟩, + ⟨3, 3, 8, 5, 4, 5, -41231487287420491289399998668180352431606988800000⟩, + ⟨3, 3, 5, 6, 0, 5, -18565846281004018010696443830474770769116135424000000⟩, + ⟨3, 3, 6, 6, 1, 5, 1291950126284181073523727796816531466785652736000000⟩, + ⟨3, 3, 7, 6, 2, 5, -684161851230232910337001785373550780296357478400000⟩, + ⟨3, 3, 8, 6, 3, 5, 218914490705195852239100803743697168374536601600000⟩, + ⟨3, 3, 6, 7, 0, 5, 383364104922305172304464149685709424874749952000000⟩, + ⟨3, 3, 7, 7, 1, 5, 3539535879504121829588362621157845580102447923200000⟩, + ⟨3, 3, 8, 7, 2, 5, -86104898063991579822416399358914350788535910400000⟩ +] + +def collectedFourData_8_1_29 : List CollectedFourTerm := [ + ⟨3, 4, 1, 0, 2, 6, 2296007484576031764137743457391674026799136768000000⟩, + ⟨3, 4, 2, 0, 3, 6, -2184047016238363699848399093196376880463006924800000⟩, + ⟨3, 4, 3, 0, 4, 6, -399753607256154813220604001139336335374627635200000⟩, + ⟨3, 4, 4, 0, 5, 6, 7849762344761928805855560625513564513745711923200000⟩, + ⟨3, 4, 5, 0, 6, 6, 3423246331867891234920346574469790800147382272000000⟩, + ⟨3, 4, 6, 0, 7, 6, 942760939314503843771098103781252400318670438400000⟩, + ⟨3, 4, 7, 0, 8, 6, 460900266406653635175821507738273794410676224000000⟩, + ⟨3, 4, 1, 1, 1, 6, -2269539227669123825669684102341003300461713817600000⟩, + ⟨3, 4, 2, 1, 2, 6, 2094966914013324262045189704211388431545139200000000⟩, + ⟨3, 4, 3, 1, 3, 6, 1918886289299232893393867874679621369528634572800000⟩, + ⟨3, 4, 4, 1, 4, 6, 2415632343049535599912596774915744533038340505600000⟩, + ⟨3, 4, 5, 1, 5, 6, -1122081319920040407834640354510096363400724480000000⟩, + ⟨3, 4, 6, 1, 6, 6, -347412419355815403560723480078992452866172518400000⟩, + ⟨3, 4, 7, 1, 7, 6, -36461647974232618287827577618034558154833920000000⟩, + ⟨3, 4, 8, 1, 8, 6, -75274665091493821750033822475978251493493964800000⟩, + ⟨3, 4, 1, 2, 0, 6, -4308400604418837263439216970322730515381511782400000⟩, + ⟨3, 4, 2, 2, 1, 6, 2903069154094218835727639709220928366097884774400000⟩, + ⟨3, 4, 3, 2, 2, 6, -1497524909075536886760928408495104745192764211200000⟩, + ⟨3, 4, 4, 2, 3, 6, 3792810666731402073255703675720705947585635942400000⟩, + ⟨3, 4, 5, 2, 4, 6, 842906871577298619536921529923176826035765248000000⟩, + ⟨3, 4, 6, 2, 5, 6, -6241624303842361610343640552004798572501401600000⟩, + ⟨3, 4, 7, 2, 6, 6, -22868642333509393083136735177885639453861478400000⟩, + ⟨3, 4, 8, 2, 7, 6, -32321235573832054480575039669401934402001305600000⟩, + ⟨3, 4, 2, 3, 0, 6, -5027425683168786070885655885019282297761405337600000⟩, + ⟨3, 4, 3, 3, 1, 6, -33552345618903159640332588279385532090076364800000⟩, + ⟨3, 4, 4, 3, 2, 6, -10118524454295791409498305010468989400661780070400000⟩, + ⟨3, 4, 5, 3, 3, 6, -251696683586710870770605976955396948664254464000000⟩, + ⟨3, 4, 6, 3, 4, 6, 101068827674780946354813112370698147196200550400000⟩, + ⟨3, 4, 7, 3, 5, 6, -54850127506697380121695376424565792023615897600000⟩, + ⟨3, 4, 8, 3, 6, 6, 1735615749637244340769371533143878823575552000000⟩, + ⟨3, 4, 3, 4, 0, 6, 6433439420923136302187238438025153291888676044800000⟩, + ⟨3, 4, 4, 4, 1, 6, 129903493394749796816278483213107651265167360000000⟩, + ⟨3, 4, 5, 4, 2, 6, -519825350341981831157491649902451933608673280000000⟩, + ⟨3, 4, 6, 4, 3, 6, -127610488773107267555933574006876280236225331200000⟩, + ⟨3, 4, 7, 4, 4, 6, 28357783823777824693943259315330135258405273600000⟩, + ⟨3, 4, 8, 4, 5, 6, 23623696788291349503321024594133701708113510400000⟩, + ⟨3, 4, 4, 5, 0, 6, 41694944880373128318521808537919144725134809497600000⟩, + ⟨3, 4, 5, 5, 1, 6, -175501005997808277809042857337708576753319936000000⟩, + ⟨3, 4, 6, 5, 2, 6, 277008748987078215962991339813951011818360012800000⟩, + ⟨3, 4, 7, 5, 3, 6, 32347273235922829964546249019451436680033075200000⟩, + ⟨3, 4, 8, 5, 4, 6, 11826076938672534398763888126443286556783411200000⟩, + ⟨3, 4, 5, 6, 0, 6, 9318896715641607207222809589400304568665899008000000⟩, + ⟨3, 4, 6, 6, 1, 6, -518782698353843343744009117154346726902569369600000⟩, + ⟨3, 4, 7, 6, 2, 6, 228937714693890878865270415453350500588794675200000⟩, + ⟨3, 4, 8, 6, 3, 6, -62789382105549685796931256220585636573636198400000⟩, + ⟨3, 4, 6, 7, 0, 6, -153939893466021141315558970329532995969692467200000⟩, + ⟨3, 4, 7, 7, 1, 6, -1184417479392625304554068624652761268454267289600000⟩, + ⟨3, 4, 8, 7, 2, 6, 24696735827232528176984192504491974558587289600000⟩ +] + +def collectedFourData_8_1_30 : List CollectedFourTerm := [ + ⟨3, 5, 0, 0, 1, 7, 5904628205905368950979536067825598024453718016000000⟩, + ⟨3, 5, 1, 0, 2, 7, -7476269756916410851239883797762933723708260352000000⟩, + ⟨3, 5, 2, 0, 3, 7, 3555851791615901509912074868773947555901446553600000⟩, + ⟨3, 5, 3, 0, 4, 7, 433893156450126826238033324992268735251847577600000⟩, + ⟨3, 5, 4, 0, 5, 7, -6390107742610611695180804163186570796519863091200000⟩, + ⟨3, 5, 5, 0, 6, 7, -2229357978434015354112307904999314694468114841600000⟩, + ⟨3, 5, 6, 0, 7, 7, -511637058818258453370424616361414095011420569600000⟩, + ⟨3, 5, 7, 0, 8, 7, -214397927448211678930135753986337401993166848000000⟩, + ⟨3, 5, 0, 1, 0, 7, 30791434013066657171074282771946156169206169600000000⟩, + ⟨3, 5, 1, 1, 1, 7, 7390083701356600742162832733618007750199371366400000⟩, + ⟨3, 5, 2, 1, 2, 7, -3410820279592964412288117803498967205832294400000000⟩, + ⟨3, 5, 3, 1, 3, 7, -2082762015952005828001103013105092468456973926400000⟩, + ⟨3, 5, 4, 1, 4, 7, -1966448187940600048160482438332779623433738649600000⟩, + ⟨3, 5, 5, 1, 5, 7, 730745234349104029710863776657653657180831744000000⟩, + ⟨3, 5, 6, 1, 6, 7, 188540976851871814010727537730618486706248089600000⟩, + ⟨3, 5, 7, 1, 7, 7, 16960939983758940445888991683254987616419840000000⟩, + ⟨3, 5, 8, 1, 8, 7, 30638712300924047224438696462799398951609958400000⟩, + ⟨3, 5, 1, 2, 0, 7, 14029033161207138876084459134178374298017307033600000⟩, + ⟨3, 5, 2, 2, 1, 7, -4726493329136355582883726221279083811360787660800000⟩, + ⟨3, 5, 3, 2, 2, 7, 1625415750770488504138106211686032140817504665600000⟩, + ⟨3, 5, 4, 2, 3, 7, -3087541729707169054441099043944585142246729318400000⟩, + ⟨3, 5, 5, 2, 4, 7, -548935418913413393764931916611094384774375014400000⟩, + ⟨3, 5, 6, 2, 5, 7, 3387334124585677427128176152061370129868390400000⟩, + ⟨3, 5, 7, 2, 6, 7, 10637853516736584578492841141087602408737996800000⟩, + ⟨3, 5, 8, 2, 7, 7, 13155568832533214249264329350504078969195724800000⟩, + ⟨3, 5, 2, 3, 0, 7, 8185162906200220673502778145469110227444118323200000⟩, + ⟨3, 5, 3, 3, 1, 7, 36417765550175236088807344637519354755704422400000⟩, + ⟨3, 5, 4, 3, 2, 7, 8236996054069881869827950523478334254650648166400000⟩, + ⟨3, 5, 5, 3, 3, 7, 163915171536381972139376926947625865439294259200000⟩, + ⟨3, 5, 6, 3, 4, 7, -54850127506697380121695376424565792023615897600000⟩, + ⟨3, 5, 7, 3, 5, 7, 25514746930804331676668274895618977578562355200000⟩, + ⟨3, 5, 8, 3, 6, 7, -706439962947072000796023659648615517782016000000⟩, + ⟨3, 5, 3, 4, 0, 7, -6982864660896784150723625262819837663701788262400000⟩, + ⟨3, 5, 4, 4, 1, 7, -105748082868760111930160034577547444103413760000000⟩, + ⟨3, 5, 5, 4, 2, 7, 338531522370700779732307354548272981694480384000000⟩, + ⟨3, 5, 6, 4, 3, 7, 69254306608954921330109229177787274601745612800000⟩, + ⟨3, 5, 7, 4, 4, 7, -13191248784130924217710631777299482507686707200000⟩, + ⟨3, 5, 8, 4, 5, 7, -9615448285302471502159060366329995500663603200000⟩, + ⟨3, 5, 4, 5, 0, 7, -33941816122061919670312100909174405033100941721600000⟩, + ⟨3, 5, 5, 5, 1, 7, 114293430858924536757737585107801649919610060800000⟩, + ⟨3, 5, 6, 5, 2, 7, -150332852888163272607790920889397939151254323200000⟩, + ⟨3, 5, 7, 5, 3, 7, -15047047801582144530763372800910758081095270400000⟩, + ⟨3, 5, 8, 5, 4, 7, -4813515523877435357488423644995599759677849600000⟩, + ⟨3, 5, 5, 6, 0, 7, -6068846565266664105005155190344546644773987942400000⟩, + ⟨3, 5, 6, 6, 1, 7, 281543753970712173261651828087741869459924582400000⟩, + ⟨3, 5, 7, 6, 2, 7, -106495428886980612373524803596171067827578470400000⟩, + ⟨3, 5, 8, 6, 3, 7, 25556883070106369874162277153090070398579507200000⟩, + ⟨3, 5, 6, 7, 0, 7, 83543294003058406053401875505891841919470796800000⟩, + ⟨3, 5, 7, 7, 1, 7, 550957921536900978388691588189295321231340339200000⟩, + ⟨3, 5, 8, 7, 2, 7, -10052202595159825072264773936937624127982796800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0806.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0806.lean new file mode 100644 index 0000000000000000000000000000000000000000..6ab91fccaa154a153f06ef59eac7cdd22115ccbb --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0806.lean @@ -0,0 +1,647 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0806. -/ +namespace LaughlinFock +def collectedFourData_8_1_31 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 1, 8, -1307875901668456584340190112931827130029834240000000⟩, + ⟨3, 6, 1, 0, 2, 8, 827997352963257182704647005158493880204656640000000⟩, + ⟨3, 6, 2, 0, 3, 8, -262540541982973496465493130807396209229037568000000⟩, + ⟨3, 6, 3, 0, 4, 8, -24026847391188522567101697800356567518806016000000⟩, + ⟨3, 6, 4, 0, 5, 8, 283081936209528758298868669260556716331342233600000⟩, + ⟨3, 6, 5, 0, 6, 8, 82300512821170407236931649490212235199381504000000⟩, + ⟨3, 6, 6, 0, 7, 8, 16189667695387183230922707586995962083540992000000⟩, + ⟨3, 6, 7, 0, 8, 8, 5936146038728084662605037176346466152611840000000⟩, + ⟨3, 6, 0, 1, 0, 8, -6820306566165827375208865029231766293970944000000000⟩, + ⟨3, 6, 1, 1, 1, 8, -818452241806741050494947207280536800668418048000000⟩, + ⟨3, 6, 2, 1, 2, 8, 251832375838116063965989910759612897820672000000000⟩, + ⟨3, 6, 3, 1, 3, 8, 115333013128993710358065449792017245482778624000000⟩, + ⟨3, 6, 4, 1, 4, 8, 87113704951479316490578456912832221590375628800000⟩, + ⟨3, 6, 5, 1, 5, 8, -26976693788228079158712394059336241234575360000000⟩, + ⟨3, 6, 6, 1, 6, 8, -5965978635804327060248068921010290679611392000000⟩, + ⟨3, 6, 7, 1, 7, 8, -469606296553475502242541859720624550707200000000⟩, + ⟨3, 6, 8, 1, 8, 8, -754053187491406408625857371803468288753664000000⟩, + ⟨3, 6, 1, 2, 0, 8, -1553716318404258576607531905983230856713469952000000⟩, + ⟨3, 6, 2, 2, 1, 8, 348972958669478628755829413751485173233352704000000⟩, + ⟨3, 6, 3, 2, 2, 8, -90007449093024823160299677769173602031108096000000⟩, + ⟨3, 6, 4, 2, 3, 8, 136778177485963359366079848102775418084602675200000⟩, + ⟨3, 6, 5, 2, 4, 8, 20264877565339423230956540043844026038747136000000⟩, + ⟨3, 6, 6, 2, 5, 8, -107184991597270775924395277962040687198208000000⟩, + ⟨3, 6, 7, 2, 6, 8, -294535739060252868558392545854459576582144000000⟩, + ⟨3, 6, 8, 2, 7, 8, -323773352940002261560632575546172540715008000000⟩, + ⟨3, 6, 2, 3, 0, 8, -604338209674421038082027257573823020548489216000000⟩, + ⟨3, 6, 3, 3, 1, 8, -2016634930038863394110887170416313561513984000000⟩, + ⟨3, 6, 4, 3, 2, 8, -364899135579166376218220358349169332562637619200000⟩, + ⟨3, 6, 5, 3, 3, 8, -6051205238061608028246052514999479144808448000000⟩, + ⟨3, 6, 6, 3, 4, 8, 1735615749637244340769371533143878823575552000000⟩, + ⟨3, 6, 7, 3, 5, 8, -706439962947072000796023659648615517782016000000⟩, + ⟨3, 6, 8, 3, 6, 8, 17386282445541450956579620107517805199360000000⟩, + ⟨3, 6, 3, 4, 0, 8, 386676353536761077109273598605931499313168384000000⟩, + ⟨3, 6, 4, 4, 1, 8, 4684642772033218909753378947570779585249280000000⟩, + ⟨3, 6, 5, 4, 2, 8, -12497462572974049937143054659634619964456960000000⟩, + ⟨3, 6, 6, 4, 3, 8, -2191405394017218755372812399842007298605056000000⟩, + ⟨3, 6, 7, 4, 4, 8, 365232911286935123305160346446286790066176000000⟩, + ⟨3, 6, 8, 4, 5, 8, 236647002572377488543770172637996092751872000000⟩, + ⟨3, 6, 4, 5, 0, 8, 1503623321126618514781541831575368114671242444800000⟩, + ⟨3, 6, 5, 5, 1, 8, -4219334921880911207888213392014037695332352000000⟩, + ⟨3, 6, 6, 5, 2, 8, 4756963730462356300413964775425793970929664000000⟩, + ⟨3, 6, 7, 5, 3, 8, 416615376207355329847206504211157543288832000000⟩, + ⟨3, 6, 8, 5, 4, 8, 118466033695211103748891306011013221974016000000⟩, + ⟨3, 6, 5, 6, 0, 8, 224041714873127268399529075785108392515731456000000⟩, + ⟨3, 6, 6, 6, 1, 8, -8908853922789796894932650007600879315714048000000⟩, + ⟨3, 6, 7, 6, 2, 8, 2948593887330376023694415997630740359544832000000⟩, + ⟨3, 6, 8, 6, 3, 8, -628983651534782620754814456962435317235712000000⟩, + ⟨3, 6, 6, 7, 0, 8, -2643550041530496998880242108836433400692736000000⟩, + ⟨3, 6, 7, 7, 1, 8, -15254656247678264808027562809750581711732736000000⟩, + ⟨3, 6, 8, 7, 2, 8, 247396017617915621171642688013540553392128000000⟩ +] + +def collectedFourData_8_1_32 : List CollectedFourTerm := [ + ⟨4, 0, 4, 0, 5, 3, 49966910347640854059526039970381105634142417059840000⟩, + ⟨4, 0, 5, 0, 6, 3, 87161386574447171005665992571268853536984242585600000⟩, + ⟨4, 0, 6, 0, 7, 3, 60010544606384731989220052767320857360089271500800000⟩, + ⟨4, 0, 7, 0, 8, 3, 58676330006634118137776272741177341030407602176000000⟩, + ⟨4, 0, 4, 1, 4, 3, 15376476308045279779813932540733329281907393822720000⟩, + ⟨4, 0, 5, 1, 5, 3, -28570004671603901107964115888817035785696968704000000⟩, + ⟨4, 0, 6, 1, 6, 3, -22114204799069635956578952974603072006364384460800000⟩, + ⟨4, 0, 7, 1, 7, 3, -4641862556951019865128500520086060664965038080000000⟩, + ⟨4, 0, 8, 1, 8, 3, -16770378476551219548274839815547146438213999001600000⟩, + ⟨4, 0, 4, 2, 3, 3, 24142773019950784234803989256405466425169155194880000⟩, + ⟨4, 0, 5, 2, 4, 3, 21461771826311595325163846729760706535233054310400000⟩, + ⟨4, 0, 6, 2, 5, 3, -397304616772071484838502581926604432148214579200000⟩, + ⟨4, 0, 7, 2, 6, 3, -2911363047858957223531950221736974751096215961600000⟩, + ⟨4, 0, 8, 2, 7, 3, -7200820524994752253028725688694791443374617395200000⟩, + ⟨4, 0, 4, 3, 2, 3, -64408498251617223189013129909838635984761630228480000⟩, + ⟨4, 0, 5, 3, 3, 3, -6408604526463347524417112096527538026024481587200000⟩, + ⟨4, 0, 6, 3, 4, 3, 6433439420923136302187238438025153291888676044800000⟩, + ⟨4, 0, 7, 3, 5, 3, -6982864660896784150723625262819837663701788262400000⟩, + ⟨4, 0, 8, 3, 6, 3, 386676353536761077109273598605931499313168384000000⟩, + ⟨4, 0, 4, 4, 1, 3, 826888244920194106971558613971815750468370432000000⟩, + ⟨4, 0, 5, 4, 2, 3, -13235593912878674568725663120155191332195794944000000⟩, + ⟨4, 0, 6, 4, 3, 3, -8122923436273616218111854074057374067132360294400000⟩, + ⟨4, 0, 7, 4, 4, 3, 3610175135877850705797452060953808102601680486400000⟩, + ⟨4, 0, 8, 4, 5, 3, 5263103272175199814749019014562454016273206476800000⟩, + ⟨4, 0, 4, 5, 0, 3, 265405178053274738339746301394036398823287417733120000⟩, + ⟨4, 0, 5, 5, 1, 3, -4468539376081823865336308004023046869114211532800000⟩, + ⟨4, 0, 6, 5, 2, 3, 17632726595074096969318199036722497757237582233600000⟩, + ⟨4, 0, 7, 5, 3, 3, 4118069390593807055916068886343796003003223244800000⟩, + ⟨4, 0, 8, 5, 4, 3, 2634721601395261727466689420431718037020108390400000⟩, + ⟨4, 0, 5, 6, 0, 3, 237274177881374333206658989854010928033933190758400000⟩, + ⟨4, 0, 6, 6, 1, 3, -33022615768554037918419052186215127304010674995200000⟩, + ⟨4, 0, 7, 6, 2, 3, 29145621900099352389232484690361865624601021644800000⟩, + ⟨4, 0, 8, 6, 3, 3, -13988792921748275061702695614628484335704788172800000⟩, + ⟨4, 0, 6, 7, 0, 3, -9798896473438834998315850786140611230193575526400000⟩, + ⟨4, 0, 7, 7, 1, 3, -150785920408103658486097423278898851936091924070400000⟩, + ⟨4, 0, 8, 7, 2, 3, 5502164725072873989645360783186405145374307123200000⟩ +] + +def collectedFourData_8_1_33 : List CollectedFourTerm := [ + ⟨4, 1, 3, 0, 4, 4, -51380224025973260088766160932529677447200768000000⟩, + ⟨4, 1, 4, 0, 5, 4, 3026783552445158969288452590816980855175512064000000⟩, + ⟨4, 1, 5, 0, 6, 4, 2639933602621749565366174286475181326996602880000000⟩, + ⟨4, 1, 6, 0, 7, 4, 1211728109156928514534710792911330638099906560000000⟩, + ⟨4, 1, 7, 0, 8, 4, 888590816133530236952723065120314676897382400000000⟩, + ⟨4, 1, 3, 1, 3, 4, 246633940594779050427840777393269955417341952000000⟩, + ⟨4, 1, 4, 1, 4, 4, 931441733338061424431243758579883482558758912000000⟩, + ⟨4, 1, 5, 1, 5, 4, -865324868314325326954577645979570713867059200000000⟩, + ⟨4, 1, 6, 1, 6, 4, -446528251700531326847770442408574086346178560000000⟩, + ⟨4, 1, 7, 1, 7, 4, -70296087662511095546395133055606762504192000000000⟩, + ⟨4, 1, 8, 1, 8, 4, -203175683218933062779627285538582671363407872000000⟩, + ⟨4, 1, 3, 2, 2, 4, -192476475299127311027004182503463685464260608000000⟩, + ⟨4, 1, 4, 2, 3, 4, 1462466816114715929740228236234603377404674048000000⟩, + ⟨4, 1, 5, 2, 4, 4, 650031566072984903327656616240612957403217920000000⟩, + ⟨4, 1, 6, 2, 5, 4, -8022342993189896459078122507467228645949440000000⟩, + ⟨4, 1, 7, 2, 6, 4, -44089507071514149764557724886580735078563840000000⟩, + ⟨4, 1, 8, 2, 7, 4, -87239034703264092940160944344920942532624384000000⟩, + ⟨4, 1, 3, 3, 1, 4, -4312473991989435147333710326578224648159232000000⟩, + ⟨4, 1, 4, 3, 2, 4, -3901593710504300136440993835872233389564100608000000⟩, + ⟨4, 1, 5, 3, 3, 4, -194103043793067861948957581711284288157122560000000⟩, + ⟨4, 1, 6, 3, 4, 4, 129903493394749796816278483213107651265167360000000⟩, + ⟨4, 1, 7, 3, 5, 4, -105748082868760111930160034577547444103413760000000⟩, + ⟨4, 1, 8, 3, 6, 4, 4684642772033218909753378947570779585249280000000⟩, + ⟨4, 1, 3, 4, 0, 4, 826888244920194106971558613971815750468370432000000⟩, + ⟨4, 1, 4, 4, 1, 4, 50089383594494270355102062600715121144627200000000⟩, + ⟨4, 1, 5, 4, 2, 4, -400878077948198534960948523608088270549811200000000⟩, + ⟨4, 1, 6, 4, 3, 4, -164017419285595385704864220420701136439214080000000⟩, + ⟨4, 1, 7, 4, 4, 4, 54672275345304920107026914349114121896591360000000⟩, + ⟨4, 1, 8, 4, 5, 4, 63763295781974745578690367721611314495225856000000⟩, + ⟨4, 1, 4, 5, 0, 4, 16077120279728464865794826922405832222417354752000000⟩, + ⟨4, 1, 5, 5, 1, 4, -135342583650627928791155707408494368328253440000000⟩, + ⟨4, 1, 6, 5, 2, 4, 356038602823427980862421396627465889665515520000000⟩, + ⟨4, 1, 7, 5, 3, 4, 62363795422592580884373202497471849714155520000000⟩, + ⟨4, 1, 8, 5, 4, 4, 31920052502312337633952375102559040483360768000000⟩, + ⟨4, 1, 5, 6, 0, 4, 7186531787082958211688668773515245318905528320000000⟩, + ⟨4, 1, 6, 6, 1, 4, -666790012107113597989530694328925419093360640000000⟩, + ⟨4, 1, 7, 6, 2, 4, 441379546880324856061586478864500765774315520000000⟩, + ⟨4, 1, 8, 6, 3, 4, -169476351607591586515917142236394643496370176000000⟩, + ⟨4, 1, 6, 7, 0, 4, -197858532587309011439601674745699159748116480000000⟩, + ⟨4, 1, 7, 7, 1, 4, -2283492918894780924390663265280074974190632960000000⟩, + ⟨4, 1, 8, 7, 2, 4, 66659561605176627223136082862672341991686144000000⟩ +] + +def collectedFourData_8_1_34 : List CollectedFourTerm := [ + ⟨4, 2, 2, 0, 3, 5, 2246633371533124706930869652200171113830940672000000⟩, + ⟨4, 2, 3, 0, 4, 5, 822418004534758032008643574593426701949075456000000⟩, + ⟨4, 2, 4, 0, 5, 5, -24224118681364790322266373978216020149895430144000000⟩, + ⟨4, 2, 5, 0, 6, 5, -14085373420941780639046827140795114665090744320000000⟩, + ⟨4, 2, 6, 0, 7, 5, -4848884140071826540864830482019460693496954880000000⟩, + ⟨4, 2, 7, 0, 8, 5, -2844647331560976402234397737989505435209564160000000⟩, + ⟨4, 2, 2, 1, 2, 5, -2155000577499667954487677676769870807564288000000000⟩, + ⟨4, 2, 3, 1, 3, 5, -3947748323790226103219922132873509311856246784000000⟩, + ⟨4, 2, 4, 1, 4, 5, -7454565119111255380923216365638003849326231552000000⟩, + ⟨4, 2, 5, 1, 5, 5, 4616943353624528716289545728441856534826188800000000⟩, + ⟨4, 2, 6, 1, 6, 5, 1786839590005996037739789028702332612646010880000000⟩, + ⟨4, 2, 7, 1, 7, 5, 225038988202067073393863597967640481287372800000000⟩, + ⟨4, 2, 8, 1, 8, 5, 542022224602837295694381256429831063710203904000000⟩, + ⟨4, 2, 2, 2, 1, 5, -2986259907852045638450879202004241581149782016000000⟩, + ⟨4, 2, 3, 2, 2, 5, 3080876382620899504612667974121681000633204736000000⟩, + ⟨4, 2, 4, 2, 3, 5, -11704493931355358204106499578954159068553412608000000⟩, + ⟨4, 2, 5, 2, 4, 5, -3468245312853592923523641354900544045323386880000000⟩, + ⟨4, 2, 6, 2, 5, 5, 32102425793323779454216673989721985248133120000000⟩, + ⟨4, 2, 7, 2, 6, 5, 141143815987824206948008505161854111455379456000000⟩, + ⟨4, 2, 8, 2, 7, 5, 232732061794592733710977952653992583168524288000000⟩, + ⟨4, 2, 2, 3, 0, 5, 5171492293312891126697351825971697777758961664000000⟩, + ⟨4, 2, 3, 3, 1, 5, 69027652610216728004926716751875910920044544000000⟩, + ⟨4, 2, 4, 3, 2, 5, 31225446898365561997130453112745481718221242368000000⟩, + ⟨4, 2, 5, 3, 3, 5, 1035637355140900038492944399930206543769763840000000⟩, + ⟨4, 2, 6, 3, 4, 5, -519825350341981831157491649902451933608673280000000⟩, + ⟨4, 2, 7, 3, 5, 5, 338531522370700779732307354548272981694480384000000⟩, + ⟨4, 2, 8, 3, 6, 5, -12497462572974049937143054659634619964456960000000⟩, + ⟨4, 2, 3, 4, 0, 5, -13235593912878674568725663120155191332195794944000000⟩, + ⟨4, 2, 4, 4, 1, 5, -400878077948198534960948523608088270549811200000000⟩, + ⟨4, 2, 5, 4, 2, 5, 2138886151743422317497211561985441536986316800000000⟩, + ⟨4, 2, 6, 4, 3, 5, 656336563507446436669498148859063165612195840000000⟩, + ⟨4, 2, 7, 4, 4, 5, -175022450544906162293142912246484460554420224000000⟩, + ⟨4, 2, 8, 4, 5, 5, -170104625121467596756346540296138010910523392000000⟩, + ⟨4, 2, 4, 5, 0, 5, -128669283073149441978658764294481686461983752192000000⟩, + ⟨4, 2, 5, 5, 1, 5, 722120749014643572684667654756859566526300160000000⟩, + ⟨4, 2, 6, 5, 2, 5, -1424733751274454281803085993253648143965224960000000⟩, + ⟨4, 2, 7, 5, 3, 5, -199645327201124180931565917506803943727955968000000⟩, + ⟨4, 2, 8, 5, 4, 5, -85154766518488842347012461870565968708632576000000⟩, + ⟨4, 2, 5, 6, 0, 5, -38343761268087877660917642951963476792684052480000000⟩, + ⟨4, 2, 6, 6, 1, 5, 2668245037836091492634023432653943075472670720000000⟩, + ⟨4, 2, 7, 6, 2, 5, -1412989114271953286986225466382388742710099968000000⟩, + ⟨4, 2, 8, 6, 3, 5, 452120783651728856662035666947306125768261632000000⟩, + ⟨4, 2, 6, 7, 0, 5, 791756082400361498042949226772597511857111040000000⟩, + ⟨4, 2, 7, 7, 1, 5, 7310149869246789091691995805831153339716337664000000⟩, + ⟨4, 2, 8, 7, 2, 5, -177831142486449023372458705533082006462660608000000⟩ +] + +def collectedFourData_8_1_35 : List CollectedFourTerm := [ + ⟨4, 3, 1, 0, 2, 6, -2898961470852887156446511397296543261370875904000000⟩, + ⟨4, 3, 2, 0, 3, 6, 2757599090220457522780380015031849610331448934400000⟩, + ⟨4, 3, 3, 0, 4, 6, 504732808170283739086013012604739516603406745600000⟩, + ⟨4, 3, 4, 0, 5, 6, -9911186590499585287780124276590181662735309209600000⟩, + ⟨4, 3, 5, 0, 6, 6, -4322224247085143295613131634833604657299849216000000⟩, + ⟨4, 3, 6, 0, 7, 6, -1190339168168038245400602983503630351209804595200000⟩, + ⟨4, 3, 7, 0, 8, 6, -581937177119195252099555041690723934086889472000000⟩, + ⟨4, 3, 1, 1, 1, 6, 2865542391216075539056151441544232841104903372800000⟩, + ⟨4, 3, 2, 1, 2, 6, -2645125683271738003936951601318972240796057600000000⟩, + ⟨4, 3, 3, 1, 3, 6, -2422804567056337408875631205921208827849893478400000⟩, + ⟨4, 3, 4, 1, 4, 6, -3050000985314641229379828542734376792203513036800000⟩, + ⟨4, 3, 5, 1, 5, 6, 1416750831808637035093268610755349909539389440000000⟩, + ⟨4, 3, 6, 1, 6, 6, 438646313208454879837682230560706375183446835200000⟩, + ⟨4, 3, 7, 1, 7, 6, 46036832785246664504829870211228420024565760000000⟩, + ⟨4, 3, 8, 1, 8, 6, 95042527211922578576730115224343728959678054400000⟩, + ⟨4, 3, 1, 2, 0, 6, 5439828675260531685979615373225876127940293427200000⟩, + ⟨4, 3, 2, 2, 1, 6, -3665443462826801345951711537684318856269738803200000⟩, + ⟨4, 3, 3, 2, 2, 6, 1890789573734377105332412120876128062200715673600000⟩, + ⟨4, 3, 4, 2, 3, 6, -4788839785130099830429577646171845929118937907200000⟩, + ⟨4, 3, 5, 2, 4, 6, -1064262447154411058805853772570252754334777344000000⟩, + ⟨4, 3, 6, 2, 5, 6, 7880735796346570760059393503972912020638924800000⟩, + ⟨4, 3, 7, 2, 6, 6, 28874171125709863771140605955617543028945715200000⟩, + ⟨4, 3, 8, 2, 7, 6, 40809107656807398549008167124581131093855436800000⟩, + ⟨4, 3, 2, 3, 0, 6, 6347676761068476412021903991769493319893961932800000⟩, + ⟨4, 3, 3, 3, 1, 6, 42363519221672186584761618975721666667505254400000⟩, + ⟨4, 3, 4, 3, 2, 6, 12775747784769415104359394187362369536892547891200000⟩, + ⟨4, 3, 5, 3, 3, 6, 317794690549129434333673013172955078503432192000000⟩, + ⟨4, 3, 6, 3, 4, 6, -127610488773107267555933574006876280236225331200000⟩, + ⟨4, 3, 7, 3, 5, 6, 69254306608954921330109229177787274601745612800000⟩, + ⟨4, 3, 8, 3, 6, 6, -2191405394017218755372812399842007298605056000000⟩, + ⟨4, 3, 3, 4, 0, 6, -8122923436273616218111854074057374067132360294400000⟩, + ⟨4, 3, 4, 4, 1, 6, -164017419285595385704864220420701136439214080000000⟩, + ⟨4, 3, 5, 4, 2, 6, 656336563507446436669498148859063165612195840000000⟩, + ⟨4, 3, 6, 4, 3, 6, 161122249258805706158441400863687442341403033600000⟩, + ⟨4, 3, 7, 4, 4, 6, -35804814773540373450331139276828191574772940800000⟩, + ⟨4, 3, 8, 4, 5, 6, -29827510253527607217405542735159288315196211200000⟩, + ⟨4, 3, 4, 5, 0, 6, -52644444562799895874561885979072419055956446412800000⟩, + ⟨4, 3, 5, 5, 1, 6, 221589283964165506012151335565622695593771008000000⟩, + ⟨4, 3, 6, 5, 2, 6, -349753951499414665884900412862530151009117798400000⟩, + ⟨4, 3, 7, 5, 3, 6, -40841983063224544042807019878476513065671065600000⟩, + ⟨4, 3, 8, 5, 4, 6, -14931720226027100422987381510577798149413273600000⟩, + ⟨4, 3, 5, 6, 0, 6, -11766129993470382053172251464471023787519770624000000⟩, + ⟨4, 3, 6, 6, 1, 6, 655020100925583479526959187736718162231348428800000⟩, + ⟨4, 3, 7, 6, 2, 6, -289058994180610160565902130145690059638675865600000⟩, + ⟨4, 3, 8, 6, 3, 6, 79278486993373120526806534692924538523693875200000⟩, + ⟨4, 3, 6, 7, 0, 6, 194366012734317552284327043469655554309855641600000⟩, + ⟨4, 3, 7, 7, 1, 6, 1495457075479847799447788681232446513195306188800000⟩, + ⟨4, 3, 8, 7, 2, 6, -31182339822467750497579318322066439252266188800000⟩ +] + +def collectedFourData_8_1_36 : List CollectedFourTerm := [ + ⟨4, 4, 0, 0, 1, 7, -3052721622249653170343433728012411263229362176000000⟩, + ⟨4, 4, 1, 0, 2, 7, 3865267980443553140305362160717742965493071872000000⟩, + ⟨4, 4, 2, 0, 3, 7, -1838392744004549363705709780583535480059566489600000⟩, + ⟨4, 4, 3, 0, 4, 7, -224324881135908361038719868256022793167673753600000⟩, + ⟨4, 4, 4, 0, 5, 7, 3303716913939249963088378212313898335719338803200000⟩, + ⟨4, 4, 5, 0, 6, 7, 1152588963635988389553039402043526837161269657600000⟩, + ⟨4, 4, 6, 0, 7, 7, 264518858382418339150847102043176091931744665600000⟩, + ⟨4, 4, 7, 0, 8, 7, 110844775668024093912841681009707465811427328000000⟩, + ⟨4, 4, 0, 1, 0, 7, -15919321778423326542936116276453566049786265600000000⟩, + ⟨4, 4, 1, 1, 1, 7, -3820709368763192433718004474851619236689110630400000⟩, + ⟨4, 4, 2, 1, 2, 7, 1763410743915672600994111956027539255092838400000000⟩, + ⟨4, 4, 3, 1, 3, 7, 1076798135018573222400510698131985154556978790400000⟩, + ⟨4, 4, 4, 1, 4, 7, 1016663317828571738421147315547281261881563545600000⟩, + ⟨4, 4, 5, 1, 5, 7, -377798855315286100892820469423075410453725184000000⟩, + ⟨4, 4, 6, 1, 6, 7, -97476605917396307591757931986898026092927385600000⟩, + ⟨4, 4, 7, 1, 7, 7, -8768888813408450516940545478000975795978240000000⟩, + ⟨4, 4, 8, 1, 8, 7, -15840363907311567561951576930860607274903142400000⟩, + ⟨4, 4, 1, 2, 0, 7, -7253078665925541513445260699327938415767951769600000⟩, + ⟨4, 4, 2, 2, 1, 7, 2443620136631603804541478352465196705391627468800000⟩, + ⟨4, 4, 3, 2, 2, 7, -840347882117227858701475831789872166733453721600000⟩, + ⟨4, 4, 4, 2, 3, 7, 1596274154645093733793169086529965725342656102400000⟩, + ⟨4, 4, 5, 2, 4, 7, 283802292726863146595770273082127290967942758400000⟩, + ⟨4, 4, 6, 2, 5, 7, -1751268287064190190546263512030714962273894400000⟩, + ⟨4, 4, 7, 2, 6, 7, -5499822226298313764482237277952034214825164800000⟩, + ⟨4, 4, 8, 2, 7, 7, -6801493341765776554371913685835574581972172800000⟩, + ⟨4, 4, 2, 3, 0, 7, -4231769201048605386008856548896215451319874355200000⟩, + ⟨4, 4, 3, 3, 1, 7, -18828162663629055005680940881748767923398246400000⟩, + ⟨4, 4, 4, 3, 2, 7, -4258567191664293306850385088820379469480355430400000⟩, + ⟨4, 4, 5, 3, 3, 7, -84744944290213562553931063761459231704953651200000⟩, + ⟨4, 4, 6, 3, 4, 7, 28357783823777824693943259315330135258405273600000⟩, + ⟨4, 4, 7, 3, 5, 7, -13191248784130924217710631777299482507686707200000⟩, + ⟨4, 4, 8, 3, 6, 7, 365232911286935123305160346446286790066176000000⟩, + ⟨4, 4, 3, 4, 0, 7, 3610175135877850705797452060953808102601680486400000⟩, + ⟨4, 4, 4, 4, 1, 7, 54672275345304920107026914349114121896591360000000⟩, + ⟨4, 4, 5, 4, 2, 7, -175022450544906162293142912246484460554420224000000⟩, + ⟨4, 4, 6, 4, 3, 7, -35804814773540373450331139276828191574772940800000⟩, + ⟨4, 4, 7, 4, 4, 7, 6819940051012298741046237140726910486262579200000⟩, + ⟨4, 4, 8, 4, 5, 7, 4971233727943994409049525637142157034992435200000⟩, + ⟨4, 4, 4, 5, 0, 7, 17548084716089724459013471064442316652981885337600000⟩, + ⟨4, 4, 5, 5, 1, 7, -59090261994004107473760984471775717788273868800000⟩, + ⟨4, 4, 6, 5, 2, 7, 77722819209377200099531192740333323042370355200000⟩, + ⟨4, 4, 7, 5, 3, 7, 7779397207257471500252866460078706885289574400000⟩, + ⟨4, 4, 8, 5, 4, 7, 2488611036352610187988438757406472903694745600000⟩, + ⟨4, 4, 5, 6, 0, 7, 3137623316126197951563842409366271819866596966400000⟩, + ⟨4, 4, 6, 6, 1, 7, -145559495938482150152704013666624256214460006400000⟩, + ⟨4, 4, 7, 6, 2, 7, 55058656886964423648768097646006925309404774400000⟩, + ⟨4, 4, 8, 6, 3, 7, -13213033373954346016659729611409825977283379200000⟩, + ⟨4, 4, 6, 7, 0, 7, -43192291047559906316021904094117932884085964800000⟩, + ⟨4, 4, 7, 7, 1, 7, -284847936461654489897667654650558252833780531200000⟩, + ⟨4, 4, 8, 7, 2, 7, 5197037839366083862316391906102896025717964800000⟩ +] + +def collectedFourData_8_1_37 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 1, 8, -17801672832357293491062858431608300349159374848000000⟩, + ⟨4, 5, 1, 0, 2, 8, 11269982086760901650042638425998692431144419328000000⟩, + ⟨4, 5, 2, 0, 3, 8, -3573474232263529065415424924560109835642313113600000⟩, + ⟨4, 5, 3, 0, 4, 8, -327032615177996409650874189687385679161668403200000⟩, + ⟨4, 5, 4, 0, 5, 8, 3853065880886401645993591097195809400100193566720000⟩, + ⟨4, 5, 5, 0, 6, 8, 1120203225175027618179836789424787128310353100800000⟩, + ⟨4, 5, 6, 0, 7, 8, 220359720069928583024522228403215755712554598400000⟩, + ⟨4, 5, 7, 0, 8, 8, 80797673182695469114686670326395038353850368000000⟩, + ⟨4, 5, 0, 1, 0, 8, -92832099706383413550139896292239810262518988800000000⟩, + ⟨4, 5, 1, 1, 1, 8, -11140062309402806567286160983836811007507405209600000⟩, + ⟨4, 5, 2, 1, 2, 8, 3427723958784142613498701149674588397266534400000000⟩, + ⟨4, 5, 3, 1, 3, 8, 1569812979865405867358345428584405418759736524800000⟩, + ⟨4, 5, 4, 1, 4, 8, 1185716223368304551145840855885862570498468085760000⟩, + ⟨4, 5, 5, 1, 5, 8, -367183366788922442336424152322044471197827072000000⟩, + ⟨4, 5, 6, 1, 6, 8, -81203728628944857174076216116633268543448678400000⟩, + ⟨4, 5, 7, 1, 7, 8, -6391873755449858433065193192440760568381440000000⟩, + ⟨4, 5, 8, 1, 8, 8, -10263518216670217294020469629547693497699532800000⟩, + ⟨4, 5, 1, 2, 0, 8, -21147839438927678281535154909347805779418572390400000⟩, + ⟨4, 5, 2, 2, 1, 8, 4749917350452570814541741298669330439844187340800000⟩, + ⟨4, 5, 3, 2, 2, 8, -1225103359718647880768010183596642045976064819200000⟩, + ⟨4, 5, 4, 2, 3, 8, 1861705963925967574363967130262868173685564375040000⟩, + ⟨4, 5, 5, 2, 4, 8, 275827943573042882463766172603187202503160627200000⟩, + ⟨4, 5, 6, 2, 5, 8, -1458909175189674599599756074874669914233241600000⟩, + ⟨4, 5, 7, 2, 6, 8, -4008965114731754107292060065628342734081228800000⟩, + ⟨4, 5, 8, 2, 7, 8, -4406922165566709649908699358849975327496601600000⟩, + ⟨4, 5, 2, 3, 0, 8, -8225727742970351433131124919059718728165045043200000⟩, + ⟨4, 5, 3, 3, 1, 8, -27448686225549874003297568022721287198395596800000⟩, + ⟨4, 5, 4, 3, 2, 8, -4966690662396637947615727948575547877213696163840000⟩, + ⟨4, 5, 5, 3, 3, 8, -82363759246576162002331807959591540458363289600000⟩, + ⟨4, 5, 6, 3, 4, 8, 23623696788291349503321024594133701708113510400000⟩, + ⟨4, 5, 7, 3, 5, 8, -9615448285302471502159060366329995500663603200000⟩, + ⟨4, 5, 8, 3, 6, 8, 236647002572377488543770172637996092751872000000⟩, + ⟨4, 5, 3, 4, 0, 8, 5263103272175199814749019014562454016273206476800000⟩, + ⟨4, 5, 4, 4, 1, 8, 63763295781974745578690367721611314495225856000000⟩, + ⟨4, 5, 5, 4, 2, 8, -170104625121467596756346540296138010910523392000000⟩, + ⟨4, 5, 6, 4, 3, 8, -29827510253527607217405542735159288315196211200000⟩, + ⟨4, 5, 7, 4, 4, 8, 4971233727943994409049525637142157034992435200000⟩, + ⟨4, 5, 8, 4, 5, 8, 3221033823757532189044814310681023395292774400000⟩, + ⟨4, 5, 4, 5, 0, 8, 20466016991101304388468695902033083199459908648960000⟩, + ⟨4, 5, 5, 5, 1, 8, -57429928752142659351984204472332898733024870400000⟩, + ⟨4, 5, 6, 5, 2, 8, 64747665965136341704674458127478062813334732800000⟩, + ⟨4, 5, 7, 5, 3, 8, 5670607291342877763600118108224587339032166400000⟩, + ⟨4, 5, 8, 5, 4, 8, 1612456939453390661351480662858184327902003200000⟩, + ⟨4, 5, 5, 6, 0, 8, 3049461576502628744201778429406450375145501491200000⟩, + ⟨4, 5, 6, 6, 1, 8, -121259595533835020561131045662009025720064409600000⟩, + ⟨4, 5, 7, 6, 2, 8, 40133703534702792028390394884859894417483366400000⟩, + ⟨4, 5, 8, 6, 3, 8, -8561180129735297737664411619845977105917542400000⟩, + ⟨4, 5, 6, 7, 0, 8, -35981711181662205420782191144438813171069747200000⟩, + ⟨4, 5, 7, 7, 1, 8, -207633154907752879812599819782055070801277747200000⟩, + ⟨4, 5, 8, 7, 2, 8, 3367340097056589314049282413262931498736025600000⟩ +] + +def collectedFourData_8_1_38 : List CollectedFourTerm := [ + ⟨5, 0, 3, 0, 4, 4, -16491439550391349158149043422409528609774376058880000⟩, + ⟨5, 0, 4, 0, 5, 4, 971502536891139963884546044085987280238254741258240000⟩, + ⟨5, 0, 5, 0, 6, 4, 847335842729595068322022062423275545278924246220800000⟩, + ⟨5, 0, 6, 0, 7, 4, 388926697819958950716170850492119222019004406169600000⟩, + ⟨5, 0, 7, 0, 8, 4, 285209767125406079141095927086347846946058665984000000⟩, + ⟨5, 0, 3, 1, 3, 4, 79161755315382059853810688576024109445831532216320000⟩, + ⟨5, 0, 4, 1, 4, 4, 298963566844148444247599827493180435516396320849920000⟩, + ⟨5, 0, 5, 1, 5, 4, -277742127983758540241399242383701772972035407872000000⟩, + ⟨5, 0, 6, 1, 6, 4, -143321556300313472297615541260879673714665953689600000⟩, + ⟨5, 0, 7, 1, 7, 4, -22562838179321335457067848474187291616314654720000000⟩, + ⟨5, 0, 8, 1, 8, 4, -65213018460579345922285744416127014002931290603520000⟩, + ⟨5, 0, 3, 2, 2, 4, -61778908469985496101314865799708767005114137313280000⟩, + ⟨5, 0, 4, 2, 3, 4, 469405954326262490391418343279638265141172822343680000⟩, + ⟨5, 0, 5, 2, 4, 4, 208639734079785184458096957991285327672080806707200000⟩, + ⟨5, 0, 6, 2, 5, 4, -2574920351803403976930240212921915859387442790400000⟩, + ⟨5, 0, 7, 2, 6, 4, -14151348197876110309238147723506469993619809894400000⟩, + ⟨5, 0, 8, 2, 7, 4, -28000992493066901351599559701204167288077879869440000⟩, + ⟨5, 0, 3, 3, 1, 4, -1384168821754791497658821600241381171199601541120000⟩, + ⟨5, 0, 4, 3, 2, 4, -1252289145225266426513523164383585015460881791713280000⟩, + ⟨5, 0, 5, 3, 3, 4, -62300985913221859567036823782959563770596792729600000⟩, + ⟨5, 0, 6, 3, 4, 4, 41694944880373128318521808537919144725134809497600000⟩, + ⟨5, 0, 7, 3, 5, 4, -33941816122061919670312100909174405033100941721600000⟩, + ⟨5, 0, 8, 3, 6, 4, 1503623321126618514781541831575368114671242444800000⟩, + ⟨5, 0, 3, 4, 0, 4, 265405178053274738339746301394036398823287417733120000⟩, + ⟨5, 0, 4, 4, 1, 4, 16077120279728464865794826922405832222417354752000000⟩, + ⟨5, 0, 5, 4, 2, 4, -128669283073149441978658764294481686461983752192000000⟩, + ⟨5, 0, 6, 4, 3, 4, -52644444562799895874561885979072419055956446412800000⟩, + ⟨5, 0, 7, 4, 4, 4, 17548084716089724459013471064442316652981885337600000⟩, + ⟨5, 0, 8, 4, 5, 4, 20466016991101304388468695902033083199459908648960000⟩, + ⟨5, 0, 4, 5, 0, 4, 5160251093951717541148493881918830669301358599864320000⟩, + ⟨5, 0, 5, 5, 1, 4, -43440722168510161381310721457722472890368419430400000⟩, + ⟨5, 0, 6, 5, 2, 4, 114277218664912892459365379330316045079631049523200000⟩, + ⟨5, 0, 7, 5, 3, 4, 20016821293436871064749512512736869420088111923200000⟩, + ⟨5, 0, 8, 5, 4, 4, 10245335170611503793784410209035229063820481658880000⟩, + ⟨5, 0, 5, 6, 0, 4, 2306651183220479307997573623409941553237596517171200000⟩, + ⟨5, 0, 6, 6, 1, 4, -214018669360227335189952119967789866892030010982400000⟩, + ⟨5, 0, 7, 6, 2, 4, 141668983624446569248297184768530547071866057523200000⟩, + ⟨5, 0, 8, 6, 3, 4, -54396590531497285878452986280033004827451756380160000⟩, + ⟨5, 0, 6, 7, 0, 4, -63506379965242574757047459536933280476599995596800000⟩, + ⟨5, 0, 7, 7, 1, 4, -732929568712339695942503287826110365009259895193600000⟩, + ⟨5, 0, 8, 7, 2, 4, 21395627432680018720211591753471455318353421271040000⟩ +] + +def collectedFourData_8_1_39 : List CollectedFourTerm := [ + ⟨5, 1, 2, 0, 3, 5, 758497861931740467105018834400590380638037606400000⟩, + ⟨5, 1, 3, 0, 4, 5, 277660924099998381242309318521965763055792947200000⟩, + ⟨5, 1, 4, 0, 5, 5, -8178433766635170563637053828547570860831853772800000⟩, + ⟨5, 1, 5, 0, 6, 5, -4755437963161664511920333765092685138765021184000000⟩, + ⟨5, 1, 6, 0, 7, 5, -1637057607886146962153528707308643032923897856000000⟩, + ⟨5, 1, 7, 0, 8, 5, -960396541010349080744769438034597285296340992000000⟩, + ⟨5, 1, 2, 1, 2, 5, -727561226146891081195664009263106045352345600000000⟩, + ⟨5, 1, 3, 1, 3, 5, -1332820343978118236518085349837440383588289740800000⟩, + ⟨5, 1, 4, 1, 4, 5, -2516775445482805588494337214624651855614338662400000⟩, + ⟨5, 1, 5, 1, 5, 5, 1558750843264829256757451946956278668522946560000000⟩, + ⟨5, 1, 6, 1, 6, 5, 603264433711164949846171624623026114245165056000000⟩, + ⟨5, 1, 7, 1, 7, 5, 75976611745096807814578279221607378829967360000000⟩, + ⟨5, 1, 8, 1, 8, 5, 182995010975103397256555961742660598890286284800000⟩, + ⟨5, 1, 2, 2, 1, 5, -1008207117360028210277236547229472847486464819200000⟩, + ⟨5, 1, 3, 2, 2, 5, 1040151089494084080900233178106444294802060083200000⟩, + ⟨5, 1, 4, 2, 3, 5, -3951616554092112368177295547819349646518098329600000⟩, + ⟨5, 1, 5, 2, 4, 5, -1170932777811915334753429570693108461528416256000000⟩, + ⟨5, 1, 6, 2, 5, 5, 10838271003889710292987877782505026165407744000000⟩, + ⟨5, 1, 7, 2, 6, 5, 47652315686290516342879973638249901464957747200000⟩, + ⟨5, 1, 8, 2, 7, 5, 78573911306988503027438080387159740462504345600000⟩, + ⟨5, 1, 2, 3, 0, 5, 1745975065258424278677144310649601116903099596800000⟩, + ⟨5, 1, 3, 3, 1, 5, 23304793555740319763047595717947454435151052800000⟩, + ⟨5, 1, 4, 3, 2, 5, 10542189486890281738330125857331809407542598041600000⟩, + ⟨5, 1, 5, 3, 3, 5, 349647045024957829416097123769767416570052608000000⟩, + ⟨5, 1, 6, 3, 4, 5, -175501005997808277809042857337708576753319936000000⟩, + ⟨5, 1, 7, 3, 5, 5, 114293430858924536757737585107801649919610060800000⟩, + ⟨5, 1, 8, 3, 6, 5, -4219334921880911207888213392014037695332352000000⟩, + ⟨5, 1, 3, 4, 0, 5, -4468539376081823865336308004023046869114211532800000⟩, + ⟨5, 1, 4, 4, 1, 5, -135342583650627928791155707408494368328253440000000⟩, + ⟨5, 1, 5, 4, 2, 5, 722120749014643572684667654756859566526300160000000⟩, + ⟨5, 1, 6, 4, 3, 5, 221589283964165506012151335565622695593771008000000⟩, + ⟨5, 1, 7, 4, 4, 5, -59090261994004107473760984471775717788273868800000⟩, + ⟨5, 1, 8, 4, 5, 5, -57429928752142659351984204472332898733024870400000⟩, + ⟨5, 1, 4, 5, 0, 5, -43440722168510161381310721457722472890368419430400000⟩, + ⟨5, 1, 5, 5, 1, 5, 243799033311064817868699661686152969890824192000000⟩, + ⟨5, 1, 6, 5, 2, 5, -481011952308983276247126280940112854963453952000000⟩, + ⟨5, 1, 7, 5, 3, 5, -67403322564988758846782480756209985668094361600000⟩, + ⟨5, 1, 8, 5, 4, 5, -28749554402592040924266948108084830484509491200000⟩, + ⟨5, 1, 5, 6, 0, 5, -12945441525431788879535303270515123825699454976000000⟩, + ⟨5, 1, 6, 6, 1, 5, 900840422808974227270897900287056395961892864000000⟩, + ⟨5, 1, 7, 6, 2, 5, -477046782838771805782009505258124362584267161600000⟩, + ⟨5, 1, 8, 6, 3, 5, 152642906528499897400302625311049429526406758400000⟩, + ⟨5, 1, 6, 7, 0, 5, 267308989210957508477339607359986333277749248000000⟩, + ⟨5, 1, 7, 7, 1, 5, 2468018643576233046566682386710501731322350796800000⟩, + ⟨5, 1, 8, 7, 2, 5, -60038519444231232064443065404120901468395929600000⟩ +] + +def collectedFourData_8_1_40 : List CollectedFourTerm := [ + ⟨5, 2, 1, 0, 2, 6, 6292881550124830021160098114652410106741784576000000⟩, + ⟨5, 2, 2, 0, 3, 6, -5986021067187185914555964959350507370209450393600000⟩, + ⟨5, 2, 3, 0, 4, 6, -1095641942196290958817106944038420576098215526400000⟩, + ⟨5, 2, 4, 0, 5, 6, 21514574740743261654715358409834037053659440742400000⟩, + ⟨5, 2, 5, 0, 6, 6, 9382410043546437975126619714928189770725064704000000⟩, + ⟨5, 2, 6, 0, 7, 6, 2583912709799416297229749902587896190697524428800000⟩, + ⟨5, 2, 7, 0, 8, 6, 1263232285783955104020344665241638422517383168000000⟩, + ⟨5, 2, 1, 1, 1, 6, -6220337533316365032452714611423986223229907763200000⟩, + ⟨5, 2, 2, 1, 2, 6, 5741870934602275635738888403243397990999654400000000⟩, + ⟨5, 2, 3, 1, 3, 6, 5259270367295167288896363292680639057032223129600000⟩, + ⟨5, 2, 4, 1, 4, 6, 6620748540925694686156447161088448872462889779200000⟩, + ⟨5, 2, 5, 1, 5, 6, -3075392777810743087894593104425182299538063360000000⟩, + ⟨5, 2, 6, 1, 6, 6, -952185573755713420878176618857516731758070988800000⟩, + ⟨5, 2, 7, 1, 7, 6, -99933834434587480801701802304457993030205440000000⟩, + ⟨5, 2, 8, 1, 8, 6, -206312285272692360795914834610919030971275673600000⟩, + ⟨5, 2, 1, 2, 0, 6, -11808434796587942523701657338757881288066911436800000⟩, + ⟨5, 2, 2, 2, 1, 6, 7956712006062732852729444544667196696895999180800000⟩, + ⟨5, 2, 3, 2, 2, 6, -4104405989301009383981336483961402754259641958400000⟩, + ⟨5, 2, 4, 2, 3, 6, 10395309435238176739091550924109506884399844556800000⟩, + ⟨5, 2, 5, 2, 4, 6, 2310233366509119864288396614573241374852775936000000⟩, + ⟨5, 2, 6, 2, 5, 6, -17107001039116019533154796220338893395014451200000⟩, + ⟨5, 2, 7, 2, 6, 6, -62678217899415285687001442706626345433877708800000⟩, + ⟨5, 2, 8, 2, 7, 6, -88585820554223338267031810522201067344835379200000⟩, + ⟨5, 2, 2, 3, 0, 6, -13779133795845830225121792929733614574201156403200000⟩, + ⟨5, 2, 3, 3, 1, 6, -91960038513374227893369706283350057396312473600000⟩, + ⟨5, 2, 4, 3, 2, 6, -27732782354009929734789431811595206296226024652800000⟩, + ⟨5, 2, 5, 3, 3, 6, -689848542311217176058410044068255398885326848000000⟩, + ⟨5, 2, 6, 3, 4, 6, 277008748987078215962991339813951011818360012800000⟩, + ⟨5, 2, 7, 3, 5, 6, -150332852888163272607790920889397939151254323200000⟩, + ⟨5, 2, 8, 3, 6, 6, 4756963730462356300413964775425793970929664000000⟩, + ⟨5, 2, 3, 4, 0, 6, 17632726595074096969318199036722497757237582233600000⟩, + ⟨5, 2, 4, 4, 1, 6, 356038602823427980862421396627465889665515520000000⟩, + ⟨5, 2, 5, 4, 2, 6, -1424733751274454281803085993253648143965224960000000⟩, + ⟨5, 2, 6, 4, 3, 6, -349753951499414665884900412862530151009117798400000⟩, + ⟨5, 2, 7, 4, 4, 6, 77722819209377200099531192740333323042370355200000⟩, + ⟨5, 2, 8, 4, 5, 6, 64747665965136341704674458127478062813334732800000⟩, + ⟨5, 2, 4, 5, 0, 6, 114277218664912892459365379330316045079631049523200000⟩, + ⟨5, 2, 5, 5, 1, 6, -481011952308983276247126280940112854963453952000000⟩, + ⟨5, 2, 6, 5, 2, 6, 759223677376570671223318179626825510960077209600000⟩, + ⟨5, 2, 7, 5, 3, 6, 88657184399716063981670494553996100607829606400000⟩, + ⟨5, 2, 8, 5, 4, 6, 32412830479719073390566899300296580743456358400000⟩, + ⟨5, 2, 5, 6, 0, 6, 25541168137876775466243154834455760020235616256000000⟩, + ⟨5, 2, 6, 6, 1, 6, -1421876057863855826461865701206170092633797427200000⟩, + ⟨5, 2, 7, 6, 2, 6, 627470916625063113272267535616095840817800806400000⟩, + ⟨5, 2, 8, 6, 3, 6, -172092707384494267801236965934140592266988748800000⟩, + ⟨5, 2, 6, 7, 0, 6, -421917403113076475589453934617521377740482150400000⟩, + ⟨5, 2, 7, 7, 1, 6, -3246243295714478860843150126812707877947650867200000⟩, + ⟨5, 2, 8, 7, 2, 6, 67688643995947728002972094361818811205890867200000⟩ +] + +def collectedFourData_8_1_41 : List CollectedFourTerm := [ + ⟨5, 3, 0, 0, 1, 7, -3482191028810939789929028837717180443715960832000000⟩, + ⟨5, 3, 1, 0, 2, 7, 4409049743465271188436862225688743231623266304000000⟩, + ⟨5, 3, 2, 0, 3, 7, -2097025380219958810461976123883472395642811187200000⟩, + ⟨5, 3, 3, 0, 4, 7, -255883826070878567323627506550374283183600435200000⟩, + ⟨5, 3, 4, 0, 5, 7, 3768497368250829175434015591880891041277437542400000⟩, + ⟨5, 3, 5, 0, 6, 7, 1314739909406488389428022187725824369332794163200000⟩, + ⟨5, 3, 6, 0, 7, 7, 301732456997430123518063632791281115468084019200000⟩, + ⟨5, 3, 7, 0, 8, 7, 126438873629528994684671515914824764511748096000000⟩, + ⟨5, 3, 0, 1, 0, 7, -18158917301057099748324347242084041311335219200000000⟩, + ⟨5, 3, 1, 1, 1, 7, -4358222443419720814672231514900360627898600652800000⟩, + ⟨5, 3, 2, 1, 2, 7, 2011494604623272345277664775249957170760908800000000⟩, + ⟨5, 3, 3, 1, 3, 7, 1228286515964337451471509021396604762993773772800000⟩, + ⟨5, 3, 4, 1, 4, 7, 1159691685891396022276814397387633409433744179200000⟩, + ⟨5, 3, 5, 1, 5, 7, -430949148813787146848046836135690991921266688000000⟩, + ⟨5, 3, 6, 1, 6, 7, -111190014893777907015863033522715028272395059200000⟩, + ⟨5, 3, 7, 1, 7, 7, -10002532080271795413786679766833625227591680000000⟩, + ⟨5, 3, 8, 1, 8, 7, -18068851312584570650899453832217393760095436800000⟩, + ⟨5, 3, 1, 2, 0, 7, -8273471540170603103912907314374112217826276147200000⟩, + ⟨5, 3, 2, 2, 1, 7, 2787398646369089333430986606177558618535729561600000⟩, + ⟨5, 3, 3, 2, 2, 7, -958571471064050275214210384656823117384201011200000⟩, + ⟨5, 3, 4, 2, 3, 7, 1820844554025087760214935626236794269961342156800000⟩, + ⟨5, 3, 5, 2, 4, 7, 323728764027026360490799663126541554301062348800000⟩, + ⟨5, 3, 6, 2, 5, 7, -1997643897107794176162467278434769348381900800000⟩, + ⟨5, 3, 7, 2, 6, 7, -6273559789037581767545129411988682612251033600000⟩, + ⟨5, 3, 8, 2, 7, 7, -7758355339246595859361342128650690567444889600000⟩, + ⟨5, 3, 2, 3, 0, 7, -4827111859950913046128997067116442993532757606400000⟩, + ⟨5, 3, 3, 3, 1, 7, -21476985860232618985480956408597331737103564800000⟩, + ⟨5, 3, 4, 3, 2, 7, -4857679901868649632431721864219638635160194252800000⟩, + ⟨5, 3, 5, 3, 3, 7, -96667210856585359289227985726971432663410278400000⟩, + ⟨5, 3, 6, 3, 4, 7, 32347273235922829964546249019451436680033075200000⟩, + ⟨5, 3, 7, 3, 5, 7, -15047047801582144530763372800910758081095270400000⟩, + ⟨5, 3, 8, 3, 6, 7, 416615376207355329847206504211157543288832000000⟩, + ⟨5, 3, 3, 4, 0, 7, 4118069390593807055916068886343796003003223244800000⟩, + ⟨5, 3, 4, 4, 1, 7, 62363795422592580884373202497471849714155520000000⟩, + ⟨5, 3, 5, 4, 2, 7, -199645327201124180931565917506803943727955968000000⟩, + ⟨5, 3, 6, 4, 3, 7, -40841983063224544042807019878476513065671065600000⟩, + ⟨5, 3, 7, 4, 4, 7, 7779397207257471500252866460078706885289574400000⟩, + ⟨5, 3, 8, 4, 5, 7, 5670607291342877763600118108224587339032166400000⟩, + ⟨5, 3, 4, 5, 0, 7, 20016821293436871064749512512736869420088111923200000⟩, + ⟨5, 3, 5, 5, 1, 7, -67403322564988758846782480756209985668094361600000⟩, + ⟨5, 3, 6, 5, 2, 7, 88657184399716063981670494553996100607829606400000⟩, + ⟨5, 3, 7, 5, 3, 7, 8873834733972826529393279178561802260499660800000⟩, + ⟨5, 3, 8, 5, 4, 7, 2838719050511006450805427720135834011382579200000⟩, + ⟨5, 3, 5, 6, 0, 7, 3579037041428980932927681134065154492145126604800000⟩, + ⟨5, 3, 6, 6, 1, 7, -166037403221096327711169542736269132142791884800000⟩, + ⟨5, 3, 7, 6, 2, 7, 62804534705289885300095295859155045922426060800000⟩, + ⟨5, 3, 8, 6, 3, 7, -15071897136908548481496781734332318030915174400000⟩, + ⟨5, 3, 6, 7, 0, 7, -49268759818580035728929634368594151749556633600000⟩, + ⟨5, 3, 7, 7, 1, 7, -324921513213878029336693919647504329246926438400000⟩, + ⟨5, 3, 8, 7, 2, 7, 5928178451887539538542017769988798560180633600000⟩ +] + +def collectedFourData_8_1_42 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 1, 8, -8911558357660444078196155392636693360509190144000000⟩, + ⟨5, 4, 1, 0, 2, 8, 5641778949751559741175501095211027290426179584000000⟩, + ⟨5, 4, 2, 0, 3, 8, -1788889418444353804145839526674011980196269260800000⟩, + ⟨5, 4, 3, 0, 4, 8, -163713279221698034852699183645628481593252249600000⟩, + ⟨5, 4, 4, 0, 5, 8, 1928853640710497181263164860882336835501723484160000⟩, + ⟨5, 4, 5, 0, 6, 8, 560776310608377100367147909713497634617321062400000⟩, + ⟨5, 4, 6, 0, 7, 8, 110312582619284596056005756910798698378900275200000⟩, + ⟨5, 4, 7, 0, 8, 8, 40447501002377443958332658094442675074760704000000⟩, + ⟨5, 4, 0, 1, 0, 8, -46471962595216435670439848564579487917172326400000000⟩, + ⟨5, 4, 1, 1, 1, 8, -5576740810434873828267745060034805724126956748800000⟩, + ⟨5, 4, 2, 1, 2, 8, 1715926496364601893183522191126678044095283200000000⟩, + ⟨5, 4, 3, 1, 3, 8, 785851987755631632019298546630444388612204134400000⟩, + ⟨5, 4, 4, 1, 4, 8, 593572268161506725411323112589147997841160929280000⟩, + ⟨5, 4, 5, 1, 5, 8, -183812837811176721872705161969385637062639616000000⟩, + ⟨5, 4, 6, 1, 6, 8, -40650773292559068587995343587197646982558515200000⟩, + ⟨5, 4, 7, 1, 7, 8, -3199786701110088821955785760063009136312320000000⟩, + ⟨5, 4, 8, 1, 8, 8, -5137940821860169924848299810874403039110758400000⟩, + ⟨5, 4, 1, 2, 0, 8, -10586657055952715768588410728476413449481696051200000⟩, + ⟨5, 4, 2, 2, 1, 8, 2377819548828139058385151201840013883686151782400000⟩, + ⟨5, 4, 3, 2, 2, 8, -613289559195482780012117261550664217817356697600000⟩, + ⟨5, 4, 4, 2, 3, 8, 931974286830762557367340110900468566939790213120000⟩, + ⟨5, 4, 5, 2, 4, 8, 138080102862959331409588638095367700743821721600000⟩, + ⟨5, 4, 6, 2, 5, 8, -730333288093995363986440731008189946711244800000⟩, + ⟨5, 4, 7, 2, 6, 8, -2006897155688602709562878928873853200787046400000⟩, + ⟨5, 4, 8, 2, 7, 8, -2206115370502212137640872118139867013893324800000⟩, + ⟨5, 4, 2, 3, 0, 8, -4117818224502214402052130750102573936383990169600000⟩, + ⟨5, 4, 3, 3, 1, 8, -13740875447136661741090518911892764827739750400000⟩, + ⟨5, 4, 4, 3, 2, 8, -2486336767292100632818018757749872270041960939520000⟩, + ⟨5, 4, 5, 3, 3, 8, -41231487287420491289399998668180352431606988800000⟩, + ⟨5, 4, 6, 3, 4, 8, 11826076938672534398763888126443286556783411200000⟩, + ⟨5, 4, 7, 3, 5, 8, -4813515523877435357488423644995599759677849600000⟩, + ⟨5, 4, 8, 3, 6, 8, 118466033695211103748891306011013221974016000000⟩, + ⟨5, 4, 3, 4, 0, 8, 2634721601395261727466689420431718037020108390400000⟩, + ⟨5, 4, 4, 4, 1, 8, 31920052502312337633952375102559040483360768000000⟩, + ⟨5, 4, 5, 4, 2, 8, -85154766518488842347012461870565968708632576000000⟩, + ⟨5, 4, 6, 4, 3, 8, -14931720226027100422987381510577798149413273600000⟩, + ⟨5, 4, 7, 4, 4, 8, 2488611036352610187988438757406472903694745600000⟩, + ⟨5, 4, 8, 4, 5, 8, 1612456939453390661351480662858184327902003200000⟩, + ⟨5, 4, 4, 5, 0, 8, 10245335170611503793784410209035229063820481658880000⟩, + ⟨5, 4, 5, 5, 1, 8, -28749554402592040924266948108084830484509491200000⟩, + ⟨5, 4, 6, 5, 2, 8, 32412830479719073390566899300296580743456358400000⟩, + ⟨5, 4, 7, 5, 3, 8, 2838719050511006450805427720135834011382579200000⟩, + ⟨5, 4, 8, 5, 4, 8, 807199651991954832007323962532359285873049600000⟩, + ⟨5, 4, 5, 6, 0, 8, 1526567477919872953781214218863257799615945113600000⟩, + ⟨5, 4, 6, 6, 1, 8, -60702832379993703315193307627452905175174348800000⟩, + ⟨5, 4, 7, 6, 2, 8, 20091024283316565810380754138463531999376179200000⟩, + ⟨5, 4, 8, 6, 3, 8, -4285746460742945540066176125424088296665907200000⟩, + ⟨5, 4, 6, 7, 0, 8, -18012527363216643636687552994094977763613081600000⟩, + ⟨5, 4, 7, 7, 1, 8, -103941634832335579360274298500430191511837081600000⟩, + ⟨5, 4, 8, 7, 2, 8, 1685698196321479864194383511195507057544396800000⟩ +] + +def collectedFourData_8_1_43 : List CollectedFourTerm := [ + ⟨6, 0, 2, 0, 3, 5, -40275343119487017933557683233992002762974638899200000⟩, + ⟨6, 0, 3, 0, 4, 5, -14743468044221935016231001618805142631441078681600000⟩, + ⟨6, 0, 4, 0, 5, 5, 434265200553555221753106278097462804724526245478400000⟩, + ⟨6, 0, 5, 0, 6, 5, 252508154949824489503684858080587403252153188352000000⟩, + ⟨6, 0, 6, 0, 7, 5, 86925830873224956055070514468987676048666656768000000⟩, + ⟨6, 0, 7, 0, 8, 5, 50995925184877123000285728725618903184756965376000000⟩, + ⟨6, 0, 2, 1, 2, 5, 38632644196085781719044358386302038359985356800000000⟩, + ⟨6, 0, 3, 1, 3, 5, 70771190486469997747301658109195025004785722982400000⟩, + ⟨6, 0, 4, 1, 4, 5, 133637811929180946178410107054336016749981545267200000⟩, + ⟨6, 0, 5, 1, 5, 5, -82767833900539619182544882720584857200288071680000000⟩, + ⟨6, 0, 6, 1, 6, 5, -32032630912922378043129225870789074058234298368000000⟩, + ⟨6, 0, 7, 1, 7, 5, -4034268599382286147065338641142220228478894080000000⟩, + ⟨6, 0, 8, 1, 8, 5, -9716819553592686998318620540884383056196429414400000⟩, + ⟨6, 0, 2, 2, 1, 5, 53534610478359265403305225514865882563375372697600000⟩, + ⟨6, 0, 3, 2, 2, 5, -55230797775475487326629997720482053578785659289600000⟩, + ⟨6, 0, 4, 2, 3, 5, 209826184858814268689170200883565632951574908108800000⟩, + ⟨6, 0, 5, 2, 4, 5, 62175151392151178149609623325601427217572691968000000⟩, + ⟨6, 0, 6, 2, 5, 5, -575499425129465190202359200172512122641580032000000⟩, + ⟨6, 0, 7, 2, 6, 5, -2530281838653593856457161626321356448975133081600000⟩, + ⟨6, 0, 8, 2, 7, 5, -4172182147052503900723054006495617101905841356800000⟩, + ⟨6, 0, 2, 3, 0, 5, -92709219578103521959284112938880820309991515750400000⟩, + ⟨6, 0, 3, 3, 1, 5, -1237457089721789520141081043030763045428553318400000⟩, + ⟨6, 0, 4, 3, 2, 5, -559777845297822420100497024751568438280307133644800000⟩, + ⟨6, 0, 5, 3, 3, 5, -18565846281004018010696443830474770769116135424000000⟩, + ⟨6, 0, 6, 3, 4, 5, 9318896715641607207222809589400304568665899008000000⟩, + ⟨6, 0, 7, 3, 5, 5, -6068846565266664105005155190344546644773987942400000⟩, + ⟨6, 0, 8, 3, 6, 5, 224041714873127268399529075785108392515731456000000⟩, + ⟨6, 0, 3, 4, 0, 5, 237274177881374333206658989854010928033933190758400000⟩, + ⟨6, 0, 4, 4, 1, 5, 7186531787082958211688668773515245318905528320000000⟩, + ⟨6, 0, 5, 4, 2, 5, -38343761268087877660917642951963476792684052480000000⟩, + ⟨6, 0, 6, 4, 3, 5, -11766129993470382053172251464471023787519770624000000⟩, + ⟨6, 0, 7, 4, 4, 5, 3137623316126197951563842409366271819866596966400000⟩, + ⟨6, 0, 8, 4, 5, 5, 3049461576502628744201778429406450375145501491200000⟩, + ⟨6, 0, 4, 5, 0, 5, 2306651183220479307997573623409941553237596517171200000⟩, + ⟨6, 0, 5, 5, 1, 5, -12945441525431788879535303270515123825699454976000000⟩, + ⟨6, 0, 6, 5, 2, 5, 25541168137876775466243154834455760020235616256000000⟩, + ⟨6, 0, 7, 5, 3, 5, 3579037041428980932927681134065154492145126604800000⟩, + ⟨6, 0, 8, 5, 4, 5, 1526567477919872953781214218863257799615945113600000⟩, + ⟨6, 0, 5, 6, 0, 5, 687387698024838318026652974405894388207612592128000000⟩, + ⟨6, 0, 6, 6, 1, 5, -47833565452819025970380244969985224278531899392000000⟩, + ⟨6, 0, 7, 6, 2, 5, 25330622309134474685655539656638224262857805004800000⟩, + ⟨6, 0, 8, 6, 3, 5, -8105158555798767287918626904590290240054440755200000⟩, + ⟨6, 0, 6, 7, 0, 5, -14193792493990482264074196656559210636031033344000000⟩, + ⟨6, 0, 7, 7, 1, 5, -131048883173080131998525763049136134049937909350400000⟩, + ⟨6, 0, 8, 7, 2, 5, 3187974669887751844569762514759664122408520908800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0807.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0807.lean new file mode 100644 index 0000000000000000000000000000000000000000..462f588c794a78a1b776e4058797e9d74a3899c7 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0807.lean @@ -0,0 +1,626 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse0803 +import OAI.Analysis.LaughlinFock.Sparse0804 +import OAI.Analysis.LaughlinFock.Sparse0805 +import OAI.Analysis.LaughlinFock.Sparse0806 + +namespace OAI + +/-! Sparse0807. -/ +namespace LaughlinFock +def collectedFourData_8_1_44 : List CollectedFourTerm := [ + ⟨6, 1, 1, 0, 2, 6, -11785324770183209000869146212639714800023109632000000⟩, + ⟨6, 1, 2, 0, 3, 6, 11210635667623561965297907470635326610106168115200000⟩, + ⟨6, 1, 3, 0, 4, 6, 2051921050438561990169561865982457261761285324800000⟩, + ⟨6, 1, 4, 0, 5, 6, -40292550970868001407399200084248993886766943436800000⟩, + ⟨6, 1, 5, 0, 6, 6, -17571401687678376472677402495229233018414563328000000⟩, + ⟨6, 1, 6, 0, 7, 6, -4839158376052097539115326864586382767199721881600000⟩, + ⟨6, 1, 7, 0, 8, 6, -2365784677426429475631818251975164962826878976000000⟩, + ⟨6, 1, 1, 1, 1, 6, 11649464148715698618494827232988778623226242662400000⟩, + ⟨6, 1, 2, 1, 2, 6, -10753390670673098177150047888975377109667020800000000⟩, + ⟨6, 1, 3, 1, 3, 6, -9849575085605219433069233086087533056100610867200000⟩, + ⟨6, 1, 4, 1, 4, 6, -12399354914757312936078557685745793114197878374400000⟩, + ⟨6, 1, 5, 1, 5, 6, 5759603512902054400751272808067899583910379520000000⟩, + ⟨6, 1, 6, 1, 6, 6, 1783255594247076912188675010929216575327803801600000⟩, + ⟨6, 1, 7, 1, 7, 6, 187156342441876858463467042891402099902382080000000⟩, + ⟨6, 1, 8, 1, 8, 6, 386382179078062204482382626003003557266273075200000⟩, + ⟨6, 1, 1, 2, 0, 6, 22114867091779377719545541722729155680605411737600000⟩, + ⟨6, 1, 2, 2, 1, 6, -14901350732146725531929241373967193144636840345600000⟩, + ⟨6, 1, 3, 2, 2, 6, 7686742104916621038241202030067204733103033548800000⟩, + ⟨6, 1, 4, 2, 3, 6, -19468362276483890492628633284616621011928455577600000⟩, + ⟨6, 1, 5, 2, 4, 6, -4326610997259845669907821358312209049716785152000000⟩, + ⟨6, 1, 6, 2, 5, 6, 32038035593701046512634147694337422522738278400000⟩, + ⟨6, 1, 7, 2, 6, 6, 117383927867872629892684553926949854114322841600000⟩, + ⟨6, 1, 8, 2, 7, 6, 165903752827507676080356881071418949862057574400000⟩, + ⟨6, 1, 2, 3, 0, 6, 25805597251807343193664540330830945573732247142400000⟩, + ⟨6, 1, 3, 3, 1, 6, 172222996909448036678652644544535006633210675200000⟩, + ⟨6, 1, 4, 3, 2, 6, 51938026199830442409365627584931819301665085849600000⟩, + ⟨6, 1, 5, 3, 3, 6, 1291950126284181073523727796816531466785652736000000⟩, + ⟨6, 1, 6, 3, 4, 6, -518782698353843343744009117154346726902569369600000⟩, + ⟨6, 1, 7, 3, 5, 6, 281543753970712173261651828087741869459924582400000⟩, + ⟨6, 1, 8, 3, 6, 6, -8908853922789796894932650007600879315714048000000⟩, + ⟨6, 1, 3, 4, 0, 6, -33022615768554037918419052186215127304010674995200000⟩, + ⟨6, 1, 4, 4, 1, 6, -666790012107113597989530694328925419093360640000000⟩, + ⟨6, 1, 5, 4, 2, 6, 2668245037836091492634023432653943075472670720000000⟩, + ⟨6, 1, 6, 4, 3, 6, 655020100925583479526959187736718162231348428800000⟩, + ⟨6, 1, 7, 4, 4, 6, -145559495938482150152704013666624256214460006400000⟩, + ⟨6, 1, 8, 4, 5, 6, -121259595533835020561131045662009025720064409600000⟩, + ⟨6, 1, 4, 5, 0, 6, -214018669360227335189952119967789866892030010982400000⟩, + ⟨6, 1, 5, 5, 1, 6, 900840422808974227270897900287056395961892864000000⟩, + ⟨6, 1, 6, 5, 2, 6, -1421876057863855826461865701206170092633797427200000⟩, + ⟨6, 1, 7, 5, 3, 6, -166037403221096327711169542736269132142791884800000⟩, + ⟨6, 1, 8, 5, 4, 6, -60702832379993703315193307627452905175174348800000⟩, + ⟨6, 1, 5, 6, 0, 6, -47833565452819025970380244969985224278531899392000000⟩, + ⟨6, 1, 6, 6, 1, 6, 2662893142258643791560897566545758047468676710400000⟩, + ⟨6, 1, 7, 6, 2, 6, -1175129148287278351032007978682344274001710284800000⟩, + ⟨6, 1, 8, 6, 3, 6, 322295665499398914710799397773694647823604121600000⟩, + ⟨6, 1, 6, 7, 0, 6, 790167998916375229805108892179130051023654092800000⟩, + ⟨6, 1, 7, 7, 1, 6, 6079572802743460244458494718402613065401394790400000⟩, + ⟨6, 1, 8, 7, 2, 6, -126767466762461359492292443868353042433074790400000⟩ +] + +def collectedFourData_8_1_45 : List CollectedFourTerm := [ + ⟨6, 2, 0, 0, 1, 7, -24645194989054599446777468671997165785508216832000000⟩, + ⟨6, 2, 1, 0, 2, 7, 31205034343347737977824469504401955190476898304000000⟩, + ⟨6, 2, 2, 0, 3, 7, -14841689891483325060198546051474463327306068787200000⟩, + ⟨6, 2, 3, 0, 4, 7, -1811016895938515835043451223470512600719242035200000⟩, + ⟨6, 2, 4, 0, 5, 7, 26671527118371456031024987310134397365819696742400000⟩, + ⟨6, 2, 5, 0, 6, 7, 9305067171538596151240504211614280985160659763200000⟩, + ⟨6, 2, 6, 0, 7, 7, 2135510423093430277294155699032000753019597619200000⟩, + ⟨6, 2, 7, 0, 8, 7, 894870691761052192336491268654799145293316096000000⟩, + ⟨6, 2, 0, 1, 0, 7, -128519674530172727816742412241684129832448819200000000⟩, + ⟨6, 2, 1, 1, 1, 7, -30845304302684944884754508586398035649802063052800000⟩, + ⟨6, 2, 2, 1, 2, 7, 14236346122372185606410743705419360081071308800000000⟩, + ⟨6, 2, 3, 1, 3, 7, 8693193577810219161866366264897216755178196172800000⟩, + ⟨6, 2, 4, 1, 4, 7, 8207713904695912042089583725603219047594537779200000⟩, + ⟨6, 2, 5, 1, 5, 7, -3050041113485257124980998948797866648365170688000000⟩, + ⟨6, 2, 6, 1, 6, 7, -786946946683958592675305208735820305944228659200000⟩, + ⟨6, 2, 7, 1, 7, 7, -70792886278484651382744707165613064905031680000000⟩, + ⟨6, 2, 8, 1, 8, 7, -127882232807584240183504838065062264729029836800000⟩, + ⟨6, 2, 1, 2, 0, 7, -58555466273062096141846519868731181552377213747200000⟩, + ⟨6, 2, 2, 2, 1, 7, 19727804300113483732148567905474622428693502361600000⟩, + ⟨6, 2, 3, 2, 2, 7, -6784286278339345638965097097750271890105250611200000⟩, + ⟨6, 2, 4, 2, 3, 7, 12887021047214027688550228692710801530680036556800000⟩, + ⟨6, 2, 5, 2, 4, 7, 2291189210184161221946090080345879165574892748800000⟩, + ⟨6, 2, 6, 2, 5, 7, -14138317787731427817035406515968282660228300800000⟩, + ⟨6, 2, 7, 2, 6, 7, -44401097756293691569663285958542556359399833600000⟩, + ⟨6, 2, 8, 2, 7, 7, -54909733138734832717879693432689748470241689600000⟩, + ⟨6, 2, 2, 3, 0, 7, -34163867530004855916702469570418479835566728806400000⟩, + ⟨6, 2, 3, 3, 1, 7, -152003293306784060957328308631722623033461964800000⟩, + ⟨6, 2, 4, 3, 2, 7, -34380212741184571162652333190030471136692456652800000⟩, + ⟨6, 2, 5, 3, 3, 7, -684161851230232910337001785373550780296357478400000⟩, + ⟨6, 2, 6, 3, 4, 7, 228937714693890878865270415453350500588794675200000⟩, + ⟨6, 2, 7, 3, 5, 7, -106495428886980612373524803596171067827578470400000⟩, + ⟨6, 2, 8, 3, 6, 7, 2948593887330376023694415997630740359544832000000⟩, + ⟨6, 2, 3, 4, 0, 7, 29145621900099352389232484690361865624601021644800000⟩, + ⟨6, 2, 4, 4, 1, 7, 441379546880324856061586478864500765774315520000000⟩, + ⟨6, 2, 5, 4, 2, 7, -1412989114271953286986225466382388742710099968000000⟩, + ⟨6, 2, 6, 4, 3, 7, -289058994180610160565902130145690059638675865600000⟩, + ⟨6, 2, 7, 4, 4, 7, 55058656886964423648768097646006925309404774400000⟩, + ⟨6, 2, 8, 4, 5, 7, 40133703534702792028390394884859894417483366400000⟩, + ⟨6, 2, 4, 5, 0, 7, 141668983624446569248297184768530547071866057523200000⟩, + ⟨6, 2, 5, 5, 1, 7, -477046782838771805782009505258124362584267161600000⟩, + ⟨6, 2, 6, 5, 2, 7, 627470916625063113272267535616095840817800806400000⟩, + ⟨6, 2, 7, 5, 3, 7, 62804534705289885300095295859155045922426060800000⟩, + ⟨6, 2, 8, 5, 4, 7, 20091024283316565810380754138463531999376179200000⟩, + ⟨6, 2, 5, 6, 0, 7, 25330622309134474685655539656638224262857805004800000⟩, + ⟨6, 2, 6, 6, 1, 7, -1175129148287278351032007978682344274001710284800000⟩, + ⟨6, 2, 7, 6, 2, 7, 444498877632584072980749085603775414115552460800000⟩, + ⟨6, 2, 8, 6, 3, 7, -106671299971995942332392729361545753939830374400000⟩, + ⟨6, 2, 6, 7, 0, 7, -348699477585073202242011713221236120421505433600000⟩, + ⟨6, 2, 7, 7, 1, 7, -2299630888437819052111287206043332425137153638400000⟩, + ⟨6, 2, 8, 7, 2, 7, 41956662534556365294497561247187831424129433600000⟩ +] + +def collectedFourData_8_1_46 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 1, 8, 47315034882383871532229705755361049959001489408000000⟩, + ⟨6, 3, 1, 0, 2, 8, -29954465548298809544637250661629917386388799488000000⟩, + ⟨6, 3, 2, 0, 3, 8, 9497930871053953189329207172782523527919671705600000⟩, + ⟨6, 3, 3, 0, 4, 8, 869219412161003972905096933909116512965440307200000⟩, + ⟨6, 3, 4, 0, 5, 8, -10241057021724966518453366963163332086921816965120000⟩, + ⟨6, 3, 5, 0, 6, 8, -2977386180144552930485111555716461664683216076800000⟩, + ⟨6, 3, 6, 0, 7, 8, -585693712044272203000634961698763887625004646400000⟩, + ⟨6, 3, 7, 0, 8, 8, -214751993313004535794542500295788893808099328000000⟩, + ⟨6, 3, 0, 1, 0, 8, 246738274384454814314376651840670804386565324800000000⟩, + ⟨6, 3, 1, 1, 1, 8, 29609152000774421648573342578852945176246720921600000⟩, + ⟨6, 3, 2, 1, 2, 8, -9110541475757389458404709247108472291878502400000000⟩, + ⟨6, 3, 3, 1, 3, 8, -4172403155626081124433017733695338930682776780800000⟩, + ⟨6, 3, 4, 1, 4, 8, -3151513062710902256503881629992580065348508712960000⟩, + ⟨6, 3, 5, 1, 5, 8, 975936024184781587992734614873591654134054912000000⟩, + ⟨6, 3, 6, 1, 6, 8, 215831247368755409105400213167381746754676326400000⟩, + ⟨6, 3, 7, 1, 7, 8, 16988950002113711831136370282469869737738240000000⟩, + ⟨6, 3, 8, 1, 8, 8, 27279386999801867283625454905113086356409548800000⟩, + ⟨6, 3, 1, 2, 0, 8, 56208805215268963541585606192014808162131928678400000⟩, + ⟨6, 3, 2, 2, 1, 8, -12624796963833618153236512974395595320518823116800000⟩, + ⟨6, 3, 3, 2, 2, 8, 3256200063077874309745799005607105657625064243200000⟩, + ⟨6, 3, 4, 2, 3, 8, -4948225004101191920011443696044980403433205923840000⟩, + ⟨6, 3, 5, 2, 4, 8, -733122605644839785966814205671917103109845811200000⟩, + ⟨6, 3, 6, 2, 5, 8, 3877632128417710020890244206296315066947993600000⟩, + ⟨6, 3, 7, 2, 6, 8, 10655421320911617378404586050366117988060364800000⟩, + ⟨6, 3, 8, 2, 7, 8, 11713150665747192283575117296657365397510553600000⟩, + ⟨6, 3, 2, 3, 0, 8, 21863147287158466234357203978382083469352317747200000⟩, + ⟨6, 3, 3, 3, 1, 8, 72955814797182951596759399485599979072703692800000⟩, + ⟨6, 3, 4, 3, 2, 8, 13200958368033811804915097278256126358413000048640000⟩, + ⟨6, 3, 5, 3, 3, 8, 218914490705195852239100803743697168374536601600000⟩, + ⟨6, 3, 6, 3, 4, 8, -62789382105549685796931256220585636573636198400000⟩, + ⟨6, 3, 7, 3, 5, 8, 25556883070106369874162277153090070398579507200000⟩, + ⟨6, 3, 8, 3, 6, 8, -628983651534782620754814456962435317235712000000⟩, + ⟨6, 3, 3, 4, 0, 8, -13988792921748275061702695614628484335704788172800000⟩, + ⟨6, 3, 4, 4, 1, 8, -169476351607591586515917142236394643496370176000000⟩, + ⟨6, 3, 5, 4, 2, 8, 452120783651728856662035666947306125768261632000000⟩, + ⟨6, 3, 6, 4, 3, 8, 79278486993373120526806534692924538523693875200000⟩, + ⟨6, 3, 7, 4, 4, 8, -13213033373954346016659729611409825977283379200000⟩, + ⟨6, 3, 8, 4, 5, 8, -8561180129735297737664411619845977105917542400000⟩, + ⟨6, 3, 4, 5, 0, 8, -54396590531497285878452986280033004827451756380160000⟩, + ⟨6, 3, 5, 5, 1, 8, 152642906528499897400302625311049429526406758400000⟩, + ⟨6, 3, 6, 5, 2, 8, -172092707384494267801236965934140592266988748800000⟩, + ⟨6, 3, 7, 5, 3, 8, -15071897136908548481496781734332318030915174400000⟩, + ⟨6, 3, 8, 5, 4, 8, -4285746460742945540066176125424088296665907200000⟩, + ⟨6, 3, 5, 6, 0, 8, -8105158555798767287918626904590290240054440755200000⟩, + ⟨6, 3, 6, 6, 1, 8, 322295665499398914710799397773694647823604121600000⟩, + ⟨6, 3, 7, 6, 2, 8, -106671299971995942332392729361545753939830374400000⟩, + ⟨6, 3, 8, 6, 3, 8, 22754745595397939775276754720679374975559270400000⟩, + ⟨6, 3, 6, 7, 0, 8, 95635726806173842400385859685154644338881331200000⟩, + ⟨6, 3, 7, 7, 1, 8, 551867796904052364404459112235560551622849331200000⟩, + ⟨6, 3, 8, 7, 2, 8, -8950047315973761025588758444355903383247257600000⟩ +] + +def collectedFourData_8_1_47 : List CollectedFourTerm := [ + ⟨7, 0, 1, 0, 2, 6, -3497093571819621481145473944123310757614977024000000⟩, + ⟨7, 0, 2, 0, 3, 6, 3326564409022108999185394352579023928281163366400000⟩, + ⟨7, 0, 3, 0, 4, 6, 608872479570922296969679743058867423641442713600000⟩, + ⟨7, 0, 4, 0, 5, 6, -11956125413610172961403532252727527395743603097600000⟩, + ⟨7, 0, 5, 0, 6, 6, -5214012943054877261015773627790696150200221696000000⟩, + ⟨7, 0, 6, 0, 7, 6, -1435937488351947398071658369634785238304633651200000⟩, + ⟨7, 0, 7, 0, 8, 6, -702006143154314570663218591693074345473605632000000⟩, + ⟨7, 0, 1, 1, 1, 6, 3456779255900259380966946695385224017919921356800000⟩, + ⟨7, 0, 2, 1, 2, 6, -3190884776023985722974041885897247283583385600000000⟩, + ⟨7, 0, 3, 1, 3, 6, -2922692958294202968070740569415265364266608230400000⟩, + ⟨7, 0, 4, 1, 4, 6, -3679296516020724772600031715979323944553204940800000⟩, + ⟨7, 0, 5, 1, 5, 6, 1709063841172903789298978944269470740921712640000000⟩, + ⟨7, 0, 6, 1, 6, 6, 529150600187990126453302455740995307884983091200000⟩, + ⟨7, 0, 7, 1, 7, 6, 55535443854262555746512886573011248412098560000000⟩, + ⟨7, 0, 8, 1, 8, 6, 114652303697061701111688597921169602202986086400000⟩, + ⟨7, 0, 1, 2, 0, 6, 6562208598949343439569416246055305555741979443200000⟩, + ⟨7, 0, 2, 2, 1, 6, -4421720985463332713969215734926226815932642099200000⟩, + ⟨7, 0, 3, 2, 2, 6, 2280909260247841160379706820665651644608387481600000⟩, + ⟨7, 0, 4, 2, 3, 6, -5776903555784576407799350215865923049234838323200000⟩, + ⟨7, 0, 5, 2, 4, 6, -1283847819328807155677049547364340798968561664000000⟩, + ⟨7, 0, 6, 2, 5, 6, 9506739144933927846380305333025212212235468800000⟩, + ⟨7, 0, 7, 2, 6, 6, 34831673083820669648123858690938833816728371200000⟩, + ⟨7, 0, 8, 2, 7, 6, 49229101349984199979057890499952589648219340800000⟩, + ⟨7, 0, 2, 3, 0, 6, 7657369654723452378037196480963062194668096716800000⟩, + ⟨7, 0, 3, 3, 1, 6, 51104228958993593463267557726260390428829286400000⟩, + ⟨7, 0, 4, 3, 2, 6, 15411721025792533792918655546721067968587051827200000⟩, + ⟨7, 0, 5, 3, 3, 6, 383364104922305172304464149685709424874749952000000⟩, + ⟨7, 0, 6, 3, 4, 6, -153939893466021141315558970329532995969692467200000⟩, + ⟨7, 0, 7, 3, 5, 6, 83543294003058406053401875505891841919470796800000⟩, + ⟨7, 0, 8, 3, 6, 6, -2643550041530496998880242108836433400692736000000⟩, + ⟨7, 0, 3, 4, 0, 6, -9798896473438834998315850786140611230193575526400000⟩, + ⟨7, 0, 4, 4, 1, 6, -197858532587309011439601674745699159748116480000000⟩, + ⟨7, 0, 5, 4, 2, 6, 791756082400361498042949226772597511857111040000000⟩, + ⟨7, 0, 6, 4, 3, 6, 194366012734317552284327043469655554309855641600000⟩, + ⟨7, 0, 7, 4, 4, 6, -43192291047559906316021904094117932884085964800000⟩, + ⟨7, 0, 8, 4, 5, 6, -35981711181662205420782191144438813171069747200000⟩, + ⟨7, 0, 4, 5, 0, 6, -63506379965242574757047459536933280476599995596800000⟩, + ⟨7, 0, 5, 5, 1, 6, 267308989210957508477339607359986333277749248000000⟩, + ⟨7, 0, 6, 5, 2, 6, -421917403113076475589453934617521377740482150400000⟩, + ⟨7, 0, 7, 5, 3, 6, -49268759818580035728929634368594151749556633600000⟩, + ⟨7, 0, 8, 5, 4, 6, -18012527363216643636687552994094977763613081600000⟩, + ⟨7, 0, 5, 6, 0, 6, -14193792493990482264074196656559210636031033344000000⟩, + ⟨7, 0, 6, 6, 1, 6, 790167998916375229805108892179130051023654092800000⟩, + ⟨7, 0, 7, 6, 2, 6, -348699477585073202242011713221236120421505433600000⟩, + ⟨7, 0, 8, 6, 3, 6, 95635726806173842400385859685154644338881331200000⟩, + ⟨7, 0, 6, 7, 0, 6, 234468840151027305670225610598740180252334489600000⟩, + ⟨7, 0, 7, 7, 1, 6, 1804009255788463410770692663196875790108904652800000⟩, + ⟨7, 0, 8, 7, 2, 6, -37616077772625483553813437574520815634664652800000⟩ +] + +def collectedFourData_8_1_48 : List CollectedFourTerm := [ + ⟨7, 1, 0, 0, 1, 7, 127502800345087652396332379978480646857724788736000000⟩, + ⟨7, 1, 1, 0, 2, 7, -161440364558223193846905220371010071612402696192000000⟩, + ⟨7, 1, 2, 0, 3, 7, 76784015052749058044330653914098922610958637465600000⟩, + ⟨7, 1, 3, 0, 4, 7, 9369360875699314758682752375221490548997724569600000⟩, + ⟨7, 1, 4, 0, 5, 7, -137986102304429724481239459023851856257724134195200000⟩, + ⟨7, 1, 5, 0, 6, 7, -48140098802108393422312425550014828196233058713600000⟩, + ⟨7, 1, 6, 0, 7, 7, -11048139778624661552810998658749971283031202201600000⟩, + ⟨7, 1, 7, 0, 8, 7, -4629645624510304644247449292524881509254955008000000⟩, + ⟨7, 1, 0, 1, 0, 7, 664901146422816675888551730594099967905339801600000000⟩, + ⟨7, 1, 1, 1, 1, 7, 159579288288665229479155233552843482176290186854400000⟩, + ⟨7, 1, 2, 1, 2, 7, -73652247348440006982367673818364125865469542400000000⟩, + ⟨7, 1, 3, 1, 3, 7, -44974548815905048705662816563381297611941504614400000⟩, + ⟨7, 1, 4, 1, 4, 7, -42462902311984795871544912173955265340806633881600000⟩, + ⟨7, 1, 5, 1, 5, 7, 15779497111292180326893783949631030379858100224000000⟩, + ⟨7, 1, 6, 1, 6, 7, 4071298257927482425943203625000638071860468121600000⟩, + ⟨7, 1, 7, 1, 7, 7, 366249536634904760194748052669460197817712640000000⟩, + ⟨7, 1, 8, 1, 8, 7, 661603318804778971872592369931968872402282086400000⟩, + ⟨7, 1, 1, 2, 0, 7, 302938805257720086603440041278852945649101019545600000⟩, + ⟨7, 1, 2, 2, 1, 7, -102062503219854667235122268187974315066352520396800000⟩, + ⟨7, 1, 3, 2, 2, 7, 35098748426019319569278509107039504794593630617600000⟩, + ⟨7, 1, 4, 2, 3, 7, -66671465669296528850908706940312731852227372646400000⟩, + ⟨7, 1, 5, 2, 4, 7, -11853549568127662418107964012991364091957634662400000⟩, + ⟨7, 1, 6, 2, 5, 7, 73145094242716437985627246654973423573689958400000⟩, + ⟨7, 1, 7, 2, 6, 7, 229710671992561195085549688204206054407195852800000⟩, + ⟨7, 1, 8, 2, 7, 7, 284077474108015468081153413131055308714331340800000⟩, + ⟨7, 1, 2, 3, 0, 7, 176747994188271165192812221812673514442459394867200000⟩, + ⟨7, 1, 3, 3, 1, 7, 786394490564919007671057556522698006069667430400000⟩, + ⟨7, 1, 4, 3, 2, 7, 177867263899016562557519251428341107207096919654400000⟩, + ⟨7, 1, 5, 3, 3, 7, 3539535879504121829588362621157845580102447923200000⟩, + ⟨7, 1, 6, 3, 4, 7, -1184417479392625304554068624652761268454267289600000⟩, + ⟨7, 1, 7, 3, 5, 7, 550957921536900978388691588189295321231340339200000⟩, + ⟨7, 1, 8, 3, 6, 7, -15254656247678264808027562809750581711732736000000⟩, + ⟨7, 1, 3, 4, 0, 7, -150785920408103658486097423278898851936091924070400000⟩, + ⟨7, 1, 4, 4, 1, 7, -2283492918894780924390663265280074974190632960000000⟩, + ⟨7, 1, 5, 4, 2, 7, 7310149869246789091691995805831153339716337664000000⟩, + ⟨7, 1, 6, 4, 3, 7, 1495457075479847799447788681232446513195306188800000⟩, + ⟨7, 1, 7, 4, 4, 7, -284847936461654489897667654650558252833780531200000⟩, + ⟨7, 1, 8, 4, 5, 7, -207633154907752879812599819782055070801277747200000⟩, + ⟨7, 1, 4, 5, 0, 7, -732929568712339695942503287826110365009259895193600000⟩, + ⟨7, 1, 5, 5, 1, 7, 2468018643576233046566682386710501731322350796800000⟩, + ⟨7, 1, 6, 5, 2, 7, -3246243295714478860843150126812707877947650867200000⟩, + ⟨7, 1, 7, 5, 3, 7, -324921513213878029336693919647504329246926438400000⟩, + ⟨7, 1, 8, 5, 4, 7, -103941634832335579360274298500430191511837081600000⟩, + ⟨7, 1, 5, 6, 0, 7, -131048883173080131998525763049136134049937909350400000⟩, + ⟨7, 1, 6, 6, 1, 7, 6079572802743460244458494718402613065401394790400000⟩, + ⟨7, 1, 7, 6, 2, 7, -2299630888437819052111287206043332425137153638400000⟩, + ⟨7, 1, 8, 6, 3, 7, 551867796904052364404459112235560551622849331200000⟩, + ⟨7, 1, 6, 7, 0, 7, 1804009255788463410770692663196875790108904652800000⟩, + ⟨7, 1, 7, 7, 1, 7, 11897222893391740245746720879939517142965367603200000⟩, + ⟨7, 1, 8, 7, 2, 7, -217064298686442335077239975021532612020456652800000⟩ +] + +def collectedFourData_8_1_49 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 1, 8, -18610263040687662023800485001954017403471921152000000⟩, + ⟨7, 2, 1, 0, 2, 8, 11781888874916765337922096164500930113591836672000000⟩, + ⟨7, 2, 2, 0, 3, 8, -3735789105766714716417818499139401818525034086400000⟩, + ⟨7, 2, 3, 0, 4, 8, -341887138847083798848700393910316234636577996800000⟩, + ⟨7, 2, 4, 0, 5, 8, 4028080407480417802200739496423288658719963873280000⟩, + ⟨7, 2, 5, 0, 6, 8, 1171085261248076963262749708269295761211208499200000⟩, + ⟨7, 2, 6, 0, 7, 8, 230368931768005307834230667566787019125922201600000⟩, + ⟨7, 2, 7, 0, 8, 8, 84467677007990660992479388049239065212485632000000⟩, + ⟨7, 2, 0, 1, 0, 8, -97048733027769438909336801621800069440418611200000000⟩, + ⟨7, 2, 1, 1, 1, 8, -11646067862274238491111902607308504858687333990400000⟩, + ⟨7, 2, 2, 1, 2, 8, 3583418541873795295905218598476882636282265600000000⟩, + ⟨7, 2, 3, 1, 3, 8, 1641117256513040450691821174762639849669473075200000⟩, + ⟨7, 2, 4, 1, 4, 8, 1239574000505483663042099787814457752500295434240000⟩, + ⟨7, 2, 5, 1, 5, 8, -383861623818095434565787150855327039438716928000000⟩, + ⟨7, 2, 6, 1, 6, 8, -84892176364594343308549423399871662419188121600000⟩, + ⟨7, 2, 7, 1, 7, 8, -6682206387681265243713370313954003842498560000000⟩, + ⟨7, 2, 8, 1, 8, 8, -10729709254511066907255967819902033411126067200000⟩, + ⟨7, 2, 1, 2, 0, 8, -22108419720269437202052445690908211136261888409600000⟩, + ⟨7, 2, 2, 2, 1, 8, 4965668796742120832899948169754358318753854259200000⟩, + ⟨7, 2, 3, 2, 2, 8, -1280750185170947804390083253902418733402213580800000⟩, + ⟨7, 2, 4, 2, 3, 8, 1946268646736572212550156900944365359907953704960000⟩, + ⟨7, 2, 5, 2, 4, 8, 288356641098124297152544581720653443380333772800000⟩, + ⟨7, 2, 6, 2, 5, 8, -1525175962868048915631924219643079350969958400000⟩, + ⟨7, 2, 7, 2, 6, 8, -4191060919313557309979043871308459101336371200000⟩, + ⟨7, 2, 8, 2, 7, 8, -4607094033992146876691464920452232976426598400000⟩, + ⟨7, 2, 2, 3, 0, 8, -8599357961433170611133403740423731047874481356800000⟩, + ⟨7, 2, 3, 3, 1, 8, -28695464498722601862068238645965147931358003200000⟩, + ⟨7, 2, 4, 3, 2, 8, -5192288418025539337908189798401640313068359516160000⟩, + ⟨7, 2, 5, 3, 3, 8, -86104898063991579822416399358914350788535910400000⟩, + ⟨7, 2, 6, 3, 4, 8, 24696735827232528176984192504491974558587289600000⟩, + ⟨7, 2, 7, 3, 5, 8, -10052202595159825072264773936937624127982796800000⟩, + ⟨7, 2, 8, 3, 6, 8, 247396017617915621171642688013540553392128000000⟩, + ⟨7, 2, 3, 4, 0, 8, 5502164725072873989645360783186405145374307123200000⟩, + ⟨7, 2, 4, 4, 1, 8, 66659561605176627223136082862672341991686144000000⟩, + ⟨7, 2, 5, 4, 2, 8, -177831142486449023372458705533082006462660608000000⟩, + ⟨7, 2, 6, 4, 3, 8, -31182339822467750497579318322066439252266188800000⟩, + ⟨7, 2, 7, 4, 4, 8, 5197037839366083862316391906102896025717964800000⟩, + ⟨7, 2, 8, 4, 5, 8, 3367340097056589314049282413262931498736025600000⟩, + ⟨7, 2, 4, 5, 0, 8, 21395627432680018720211591753471455318353421271040000⟩, + ⟨7, 2, 5, 5, 1, 8, -60038519444231232064443065404120901468395929600000⟩, + ⟨7, 2, 6, 5, 2, 8, 67688643995947728002972094361818811205890867200000⟩, + ⟨7, 2, 7, 5, 3, 8, 5928178451887539538542017769988798560180633600000⟩, + ⟨7, 2, 8, 5, 4, 8, 1685698196321479864194383511195507057544396800000⟩, + ⟨7, 2, 5, 6, 0, 8, 3187974669887751844569762514759664122408520908800000⟩, + ⟨7, 2, 6, 6, 1, 8, -126767466762461359492292443868353042433074790400000⟩, + ⟨7, 2, 7, 6, 2, 8, 41956662534556365294497561247187831424129433600000⟩, + ⟨7, 2, 8, 6, 3, 8, -8950047315973761025588758444355903383247257600000⟩, + ⟨7, 2, 6, 7, 0, 8, -37616077772625483553813437574520815634664652800000⟩, + ⟨7, 2, 7, 7, 1, 8, -217064298686442335077239975021532612020456652800000⟩, + ⟨7, 2, 8, 7, 2, 8, 3520291915474973235236478190122334624835174400000⟩ +] + +def collectedFourData_8_1 : List (List CollectedFourTerm) := [ + collectedFourData_8_1_0, + collectedFourData_8_1_1, + collectedFourData_8_1_2, + collectedFourData_8_1_3, + collectedFourData_8_1_4, + collectedFourData_8_1_5, + collectedFourData_8_1_6, + collectedFourData_8_1_7, + collectedFourData_8_1_8, + collectedFourData_8_1_9, + collectedFourData_8_1_10, + collectedFourData_8_1_11, + collectedFourData_8_1_12, + collectedFourData_8_1_13, + collectedFourData_8_1_14, + collectedFourData_8_1_15, + collectedFourData_8_1_16, + collectedFourData_8_1_17, + collectedFourData_8_1_18, + collectedFourData_8_1_19, + collectedFourData_8_1_20, + collectedFourData_8_1_21, + collectedFourData_8_1_22, + collectedFourData_8_1_23, + collectedFourData_8_1_24, + collectedFourData_8_1_25, + collectedFourData_8_1_26, + collectedFourData_8_1_27, + collectedFourData_8_1_28, + collectedFourData_8_1_29, + collectedFourData_8_1_30, + collectedFourData_8_1_31, + collectedFourData_8_1_32, + collectedFourData_8_1_33, + collectedFourData_8_1_34, + collectedFourData_8_1_35, + collectedFourData_8_1_36, + collectedFourData_8_1_37, + collectedFourData_8_1_38, + collectedFourData_8_1_39, + collectedFourData_8_1_40, + collectedFourData_8_1_41, + collectedFourData_8_1_42, + collectedFourData_8_1_43, + collectedFourData_8_1_44, + collectedFourData_8_1_45, + collectedFourData_8_1_46, + collectedFourData_8_1_47, + collectedFourData_8_1_48, + collectedFourData_8_1_49 +] + +theorem collectedFourChecked_8_1 : collectNumericRowParts 8 1 = collectedFourData_8_1 := by + decide +kernel + +def collectedFourData_8_2_0 : List CollectedFourTerm := [ + ⟨0, 2, 6, 0, 8, 0, -1726454994217044024654949941804794443014655180800000⟩, + ⟨0, 2, 6, 1, 7, 0, 5774002170590175929030573182824596024655347712000000⟩, + ⟨0, 2, 7, 1, 8, 0, 10854693614219411689951937880374519408347211366400000⟩, + ⟨0, 2, 6, 2, 6, 0, -398577164386650389054516441540667261608106393600000⟩, + ⟨0, 2, 7, 2, 7, 0, -640873544096984056035457976155812212137525248000000⟩, + ⟨0, 2, 8, 2, 8, 0, -5180140263325017110748487250693947703482436812800000⟩, + ⟨0, 2, 6, 3, 5, 0, 970989150203599945429938127908966824849021337600000⟩, + ⟨0, 2, 7, 3, 6, 0, -500407581889679029664833372843974560439494246400000⟩, + ⟨0, 2, 8, 3, 7, 0, -3173129942687794115768456799887148465713577984000000⟩, + ⟨0, 2, 6, 4, 4, 0, -448732250456039741774929767429009442118565888000000⟩, + ⟨0, 2, 7, 4, 5, 0, -1722858279489095254577226877916049725485744128000000⟩, + ⟨0, 2, 8, 4, 6, 0, 4047448722554787556807827689899376978314238361600000⟩, + ⟨0, 2, 6, 5, 3, 0, -166222104722589909880777487196863924248825036800000⟩, + ⟨0, 2, 7, 5, 4, 0, 1091709338863023520504214313114530638454587392000000⟩, + ⟨0, 2, 8, 5, 5, 0, 1352939793655494693945723082417182298124530483200000⟩, + ⟨0, 2, 6, 6, 2, 0, -11910307910613112406324392917081895077489200332800000⟩, + ⟨0, 2, 7, 6, 3, 0, 3273510586910224613401431838899951120850039603200000⟩, + ⟨0, 2, 8, 6, 4, 0, -2015411077409025205422546723918192424546153267200000⟩, + ⟨0, 2, 6, 7, 1, 0, 23611638608735021902683199787388232915132769894400000⟩, + ⟨0, 2, 7, 7, 2, 0, -5813138584250275674290364847297037032569490636800000⟩, + ⟨0, 2, 8, 7, 3, 0, -9652707624181153266709213334107120796378647756800000⟩ +] + +def collectedFourData_8_2_1 : List CollectedFourTerm := [ + ⟨0, 3, 5, 0, 7, 1, -59143544215766179464447079991433321947489894400000⟩, + ⟨0, 3, 6, 0, 8, 1, -3643535812754930807966641908435287173958624870400000⟩, + ⟨0, 3, 5, 1, 6, 1, 9758226009821370477764015793874442525160033484800000⟩, + ⟨0, 3, 6, 1, 7, 1, 12185538436819056165754445431098194031129133056000000⟩, + ⟨0, 3, 7, 1, 8, 1, 11453951899228789830098138885054187089157527961600000⟩, + ⟨0, 3, 5, 2, 5, 1, -1706926771282276991856350042546304558256304947200000⟩, + ⟨0, 3, 6, 2, 6, 1, -841163063881467431531208541930554910988618956800000⟩, + ⟨0, 3, 7, 2, 7, 1, -676254439642515181970103681264961705016819712000000⟩, + ⟨0, 3, 8, 2, 8, 1, -3644081200637364034877363830472337710035815628800000⟩, + ⟨0, 3, 5, 3, 4, 1, 2310254131158732226176328831033706188210018713600000⟩, + ⟨0, 3, 6, 3, 5, 1, 2049189671560316817959556874085342642038426828800000⟩, + ⟨0, 3, 7, 3, 6, 1, -528033731460227148388219771310415248581302681600000⟩, + ⟨0, 3, 8, 3, 7, 1, -2232206578110296543063500377358679414579134464000000⟩, + ⟨0, 3, 5, 4, 3, 1, -215492205201573722673144996816986477027760537600000⟩, + ⟨0, 3, 6, 4, 4, 1, -947011089400661685023495279356442710055583744000000⟩, + ⟨0, 3, 7, 4, 5, 1, -1817972626754353211141834259626455491183378432000000⟩, + ⟨0, 3, 8, 4, 6, 1, 2847264948563074406351586774797771697074837913600000⟩, + ⟨0, 3, 5, 5, 2, 1, -16737432655525181264819410200596572184503753113600000⟩, + ⟨0, 3, 6, 5, 3, 1, -350797555370341925405504853324710583330039398400000⟩, + ⟨0, 3, 7, 5, 4, 1, 1151979659646538683390481589699667798364520448000000⟩, + ⟨0, 3, 8, 5, 5, 1, 951754627680599180236430384851275561353556787200000⟩, + ⟨0, 3, 5, 6, 1, 1, 21383234213561752727169599815972852174889680896000000⟩, + ⟨0, 3, 6, 6, 2, 1, -25135687613413499443490401829864666832847660646400000⟩, + ⟨0, 3, 7, 6, 3, 1, 3454232255341483537847423166151990063504608460800000⟩, + ⟨0, 3, 8, 6, 4, 1, -1417784315752941965399798629424245372890592051200000⟩, + ⟨0, 3, 5, 7, 0, 1, 93293561969830618502034198903533688746459057356800000⟩, + ⟨0, 3, 6, 7, 1, 1, 49830346668126167639060868239351700090778759987200000⟩, + ⟨0, 3, 7, 7, 2, 1, -6134066247648923985388261682525286207805666099200000⟩, + ⟨0, 3, 8, 7, 3, 1, -6790405008444555485913203719537395390472834252800000⟩ +] + +def collectedFourData_8_2_2 : List CollectedFourTerm := [ + ⟨0, 4, 4, 0, 6, 2, -8559272824147297575599343845203825995556690329600000⟩, + ⟨0, 4, 5, 0, 7, 2, -110647882191381854540281613936663044833253785600000⟩, + ⟨0, 4, 6, 0, 8, 2, -3408229306473645606136379964855041410303053004800000⟩, + ⟨0, 4, 4, 1, 5, 2, 13263627860070427199849391570154604671229472276480000⟩, + ⟨0, 4, 5, 1, 6, 2, 18256042248542913565935520195102676798915425075200000⟩, + ⟨0, 4, 6, 1, 7, 2, 11398573075675488763578840091296066303606915072000000⟩, + ⟨0, 4, 7, 1, 8, 2, 7142822529923034940161161493108593342381083852800000⟩, + ⟨0, 4, 4, 2, 4, 2, -3536339658139837297169588899668331401812083998720000⟩, + ⟨0, 4, 5, 2, 5, 2, -3193380356258896242198416460440674229166066892800000⟩, + ⟨0, 4, 6, 2, 6, 2, -786839145592559222458635361627248630464879001600000⟩, + ⟨0, 4, 7, 2, 7, 2, -421720423652579657140513291556445566477008896000000⟩, + ⟨0, 4, 8, 2, 8, 2, -1704369736082145387662342615026294730179529932800000⟩, + ⟨0, 4, 4, 3, 3, 2, 4510541974789820955131898220017794039914325606400000⟩, + ⟨0, 4, 5, 3, 4, 2, 4322107008062285383945700403146641889376495206400000⟩, + ⟨0, 4, 6, 3, 5, 2, 1916849086177690019178211873383195142254074265600000⟩, + ⟨0, 4, 7, 3, 6, 2, -329288202606070882606445570540041775457553612800000⟩, + ⟨0, 4, 8, 3, 7, 2, -1044023205561185664546134598241836994431811584000000⟩, + ⟨0, 4, 4, 4, 2, 2, -15037727503635674190827436722869685405053385441280000⟩, + ⟨0, 4, 5, 4, 3, 2, -403150613485700919960651791339356109775726182400000⟩, + ⟨0, 4, 6, 4, 4, 2, -885851303327909305035760817063373862525206528000000⟩, + ⟨0, 4, 7, 4, 5, 2, -1133709653350184134656423442170383303134150656000000⟩, + ⟨0, 4, 8, 4, 6, 2, 1331691568258582733316005627400012641370479001600000⟩, + ⟨0, 4, 4, 5, 1, 2, 14498246222822716620730293819889952921192717352960000⟩, + ⟨0, 4, 5, 5, 2, 2, -31312994532394822478508847418512940115874440806400000⟩, + ⟨0, 4, 6, 5, 3, 2, -328142378803325444847847468100442001695886540800000⟩, + ⟨0, 4, 7, 5, 4, 2, 718388407715453616211712088427191741274128384000000⟩, + ⟨0, 4, 8, 5, 5, 2, 445144247419959916467722905603152823004115763200000⟩, + ⟨0, 4, 4, 6, 0, 2, 45234870483201735282714208769413073589243079557120000⟩, + ⟨0, 4, 5, 6, 1, 2, 40004528161201879155386372231030568568492130304000000⟩, + ⟨0, 4, 6, 6, 2, 2, -23512376868234355048594282937806493153657408716800000⟩, + ⟨0, 4, 7, 6, 3, 2, 2154100889728834183307911649713502959840945766400000⟩, + ⟨0, 4, 8, 6, 4, 2, -663110547492356637637883669868354941649892147200000⟩, + ⟨0, 4, 5, 7, 0, 2, 174536970871969142770894863055070410857159799603200000⟩, + ⟨0, 4, 6, 7, 1, 2, 46612207644978677603840169418033781193883149926400000⟩, + ⟨0, 4, 7, 7, 2, 2, -3825277684001560897936336619218460368011106713600000⟩, + ⟨0, 4, 8, 7, 3, 2, -3175933837618464498189056453694030610344758476800000⟩ +] + +def collectedFourData_8_2_3 : List CollectedFourTerm := [ + ⟨0, 5, 3, 0, 5, 3, 56054215908406102517830530923029842646322380800000000⟩, + ⟨0, 5, 4, 0, 6, 3, 58832577113215882875748524693447845526928097280000000⟩, + ⟨0, 5, 5, 0, 7, 3, 380271793830045178244050113460834518737879040000000⟩, + ⟨0, 5, 6, 0, 8, 3, 7808876509810632866249620661522590168126586880000000⟩, + ⟨0, 5, 3, 1, 4, 3, -53621971034303231715365773267762947162523041792000000⟩, + ⟨0, 5, 4, 1, 5, 3, -91168189741204015002504133714677633766196772864000000⟩, + ⟨0, 5, 5, 1, 6, 3, -62741896153808391724076779130932438589169991680000000⟩, + ⟨0, 5, 6, 1, 7, 3, -26116215058339865987056739186762426208170803200000000⟩, + ⟨0, 5, 7, 1, 8, 3, -12274134319920379816518105871149014565267701760000000⟩, + ⟨0, 5, 3, 2, 3, 3, 37196410187769632769523802109636892288465502208000000⟩, + ⟨0, 5, 4, 2, 4, 3, 24307202248429589155625391508368271571467370496000000⟩, + ⟨0, 5, 5, 2, 5, 3, 10974927422070286440303614986412003746664939520000000⟩, + ⟨0, 5, 6, 2, 6, 3, 1802792350076494411179630781373148033932328960000000⟩, + ⟨0, 5, 7, 2, 7, 3, 724678949208229205076257817817361230803763200000000⟩, + ⟨0, 5, 8, 2, 8, 3, 2343013617806339482434299169599369098410590208000000⟩, + ⟨0, 5, 3, 3, 2, 3, -24527787221028590574115041844627227869045587968000000⟩, + ⟨0, 5, 4, 3, 3, 3, -31003429147108170521651280058869953586549227520000000⟩, + ⟨0, 5, 5, 3, 4, 3, -14854106129554729496903464997266657652779253760000000⟩, + ⟨0, 5, 6, 3, 5, 3, -4391851737637972115132688278226091896062607360000000⟩, + ⟨0, 5, 7, 3, 6, 3, 565844610001197991084733359558651230824693760000000⟩, + ⟨0, 5, 8, 3, 7, 3, 1435228833362591367333249849389565025179402240000000⟩, + ⟨0, 5, 3, 4, 1, 3, 22647346613224357635006903787707141418559471616000000⟩, + ⟨0, 5, 4, 4, 2, 3, 103362549733108977548856438149477521660003221504000000⟩, + ⟨0, 5, 5, 4, 3, 3, 1385537652756190362552578086441792286396252160000000⟩, + ⟨0, 5, 6, 4, 4, 3, 2029647307064471074724779854270264085630156800000000⟩, + ⟨0, 5, 7, 4, 5, 3, 1948152079477812748661857017925675059983155200000000⟩, + ⟨0, 5, 8, 4, 6, 3, -1830689323503311212880944563631214295175397376000000⟩, + ⟨0, 5, 3, 5, 0, 3, -27202629891051365698706557764774500119099736064000000⟩, + ⟨0, 5, 4, 5, 1, 3, -99654398969994735132077029188152817633856585728000000⟩, + ⟨0, 5, 5, 5, 2, 3, 107615693723161233338730787148071970329602293760000000⟩, + ⟨0, 5, 6, 5, 3, 3, 751834188164382750206440314766407103917588480000000⟩, + ⟨0, 5, 7, 5, 4, 3, -1234469395429346446210409764974058592324812800000000⟩, + ⟨0, 5, 8, 5, 5, 3, -611944117237512481395708085232118949428068352000000⟩, + ⟨0, 5, 4, 6, 0, 3, -310924077382055503140003968462607307227178991616000000⟩, + ⟨0, 5, 5, 6, 1, 3, -137486532809298326254136970573352318673721753600000000⟩, + ⟨0, 5, 6, 6, 2, 3, 53871154463529606563868479515073905413932974080000000⟩, + ⟨0, 5, 7, 6, 3, 3, -3701579249439451144151750137699269432185978880000000⟩, + ⟨0, 5, 8, 6, 4, 3, 911584505400256977154233393071790722585198592000000⟩, + ⟨0, 5, 5, 7, 0, 3, -599844169528222518170524771358942643021026426880000000⟩, + ⟨0, 5, 6, 7, 1, 3, -106797090400555819355310251525224734958383267840000000⟩, + ⟨0, 5, 7, 7, 2, 3, 6573307947626555307876198588439467270466437120000000⟩, + ⟨0, 5, 8, 7, 3, 3, 4365987070327423554027516244856668386962178048000000⟩ +] + +def collectedFourData_8_2_4 : List CollectedFourTerm := [ + ⟨0, 6, 2, 0, 4, 4, -8559272824147297575599343845203825995556690329600000⟩, + ⟨0, 6, 3, 0, 5, 4, 58832577113215882875748524693447845526928097280000000⟩, + ⟨0, 6, 4, 0, 6, 4, 30874324738020533338738268338032970592340148224000000⟩, + ⟨0, 6, 5, 0, 7, 4, 133040065300613243436981866511037387964940288000000⟩, + ⟨0, 6, 6, 0, 8, 4, 2048982052401335744532037489861392539899133952000000⟩, + ⟨0, 6, 2, 1, 3, 4, 5110275171322587433170264042617536485012170342400000⟩, + ⟨0, 6, 3, 1, 4, 4, -56279776546926593296535511759854770941850759987200000⟩, + ⟨0, 6, 4, 1, 5, 4, -47843498176711875797623951560910069962659541811200000⟩, + ⟨0, 6, 5, 1, 6, 4, -21950578761877800580745033730207722836900970496000000⟩, + ⟨0, 6, 6, 1, 7, 4, -6852670273881634154138205721537218329475809280000000⟩, + ⟨0, 6, 7, 1, 8, 4, -2576501846193494394085164987784089458015679283200000⟩, + ⟨0, 6, 2, 2, 2, 4, 1247651070030501104467865635761101387616328089600000⟩, + ⟨0, 6, 3, 2, 3, 4, 39040072815978698633386333203276575791542750412800000⟩, + ⟨0, 6, 4, 2, 4, 4, 12756001734321037744454275736126098085371497676800000⟩, + ⟨0, 6, 5, 2, 5, 4, 3839635451779751064670571164556503637393670144000000⟩, + ⟨0, 6, 6, 2, 6, 4, 473037211546676205095712160984454172701097984000000⟩, + ⟨0, 6, 7, 2, 7, 4, 152119620159466846336557281003426350444314624000000⟩, + ⟨0, 6, 8, 2, 8, 4, 409857751443558403130834104030943895259761868800000⟩, + ⟨0, 6, 2, 3, 1, 4, 7150368632038558428341534996031028611262709760000000⟩, + ⟨0, 6, 3, 3, 2, 4, -25743521869178674486962603588047647323475201228800000⟩, + ⟨0, 6, 4, 3, 3, 4, -16270066457194263236385438296010665721505775616000000⟩, + ⟨0, 6, 5, 3, 4, 4, -5196786302644943329816983138871142774181199872000000⟩, + ⟨0, 6, 6, 3, 5, 4, -1152384133098046456986013562319299926340665344000000⟩, + ⟨0, 6, 7, 3, 6, 4, 118778208248920449237374405243543548626940723200000⟩, + ⟨0, 6, 8, 3, 7, 4, 251061136810504831003597379133275408028401664000000⟩, + ⟨0, 6, 2, 4, 0, 4, -27382823365586081810807460601191018998432740147200000⟩, + ⟨0, 6, 3, 4, 1, 4, 23769876082281235964315512743450416656496040345600000⟩, + ⟨0, 6, 4, 4, 2, 4, 54242888596714838094294655921417566357535535923200000⟩, + ⟨0, 6, 5, 4, 3, 4, 484737555585112493364028733598829507459940352000000⟩, + ⟨0, 6, 6, 4, 4, 4, 532562001672716142351124996476585640690974720000000⟩, + ⟨0, 6, 7, 4, 5, 4, 408942683745442331177561410369951991347544064000000⟩, + ⟨0, 6, 8, 4, 6, 4, -320238091669859719229040876504852268658039193600000⟩, + ⟨0, 6, 3, 5, 0, 4, -28550944738262740994494382965524464193411376742400000⟩, + ⟨0, 6, 4, 5, 1, 4, -52296914844492278867060688938341971256716715622400000⟩, + ⟨0, 6, 5, 5, 2, 4, 37649910281536550183186370145090584691838287872000000⟩, + ⟨0, 6, 6, 5, 3, 4, 197274826410067839956322500778192852423278592000000⟩, + ⟨0, 6, 7, 5, 4, 4, -259131323928163601233672039827060197683101696000000⟩, + ⟨0, 6, 8, 5, 5, 4, -107045916418916316125071412739723635046167347200000⟩, + ⟨0, 6, 4, 6, 0, 4, -163167608916567464095159181232008006556097236172800000⟩, + ⟨0, 6, 5, 6, 1, 4, -48100378728270458521324541048013618906314833920000000⟩, + ⟨0, 6, 6, 6, 2, 4, 14135327725984110715755298075004093703055736832000000⟩, + ⟨0, 6, 7, 6, 3, 4, -777010053941966381807074646878694867344136601600000⟩, + ⟨0, 6, 8, 6, 4, 4, 159461290704721376955399625838934411204309811200000⟩, + ⟨0, 6, 5, 7, 0, 4, -209858603186049938820731487152786654320379559936000000⟩, + ⟨0, 6, 6, 7, 1, 4, -28022638237972138344930218938518748572193652736000000⟩, + ⟨0, 6, 7, 7, 2, 4, 1379823588468604205002038758358030937739388518400000⟩, + ⟨0, 6, 8, 7, 3, 4, 763731644526852925036144484276943275879615692800000⟩ +] + +def collectedFourData_8_2_5 : List CollectedFourTerm := [ + ⟨0, 7, 1, 0, 3, 5, -59143544215766179464447079991433321947489894400000⟩, + ⟨0, 7, 2, 0, 4, 5, -110647882191381854540281613936663044833253785600000⟩, + ⟨0, 7, 3, 0, 5, 5, 380271793830045178244050113460834518737879040000000⟩, + ⟨0, 7, 4, 0, 6, 5, 133040065300613243436981866511037387964940288000000⟩, + ⟨0, 7, 5, 0, 7, 5, 429960633763958710244566129594849654996992000000⟩, + ⟨0, 7, 6, 0, 8, 5, 5297541728235422442836622157871468043986534400000⟩, + ⟨0, 7, 1, 1, 2, 5, -17356736226266069562971372202841327641034752000000⟩, + ⟨0, 7, 2, 1, 3, 5, 66061818187034650372577439106760766837384806400000⟩, + ⟨0, 7, 3, 1, 4, 5, -363771444903206876829159764570756052334254489600000⟩, + ⟨0, 7, 4, 1, 5, 5, -206161662664678208756040975883158318045619814400000⟩, + ⟨0, 7, 5, 1, 6, 5, -70940169298753100154634314325857466281099264000000⟩, + ⟨0, 7, 6, 1, 7, 5, -17717239974445542944175759312051524931158016000000⟩, + ⟨0, 7, 7, 1, 8, 5, -5551181714471884377488571096822278782137139200000⟩, + ⟨0, 7, 1, 2, 1, 5, -63581755300726685241850551294589657139694796800000⟩, + ⟨0, 7, 2, 2, 2, 5, 16128700585781290398528934698465153909365145600000⟩, + ⟨0, 7, 3, 2, 3, 5, 252340442140055449826396177323214788131972710400000⟩, + ⟨0, 7, 4, 2, 4, 5, 54966685688155114249517952478501013051513241600000⟩, + ⟨0, 7, 5, 2, 5, 5, 12408984380302885822984650058994334088298496000000⟩, + ⟨0, 7, 6, 2, 6, 5, 1223014308124259174413588111696014800112844800000⟩, + ⟨0, 7, 7, 2, 7, 5, 327748126821339591007477064108326250348544000000⟩, + ⟨0, 7, 8, 2, 8, 5, 756904956909274078286615241368692098229862400000⟩, + ⟨0, 7, 1, 3, 0, 5, -55801845387664121092696924796820257572808294400000⟩, + ⟨0, 7, 2, 3, 1, 5, 92434621757903115787988340506724444521103360000000⟩, + ⟨0, 7, 3, 3, 2, 5, -166396505491453228479154065943163964194448998400000⟩, + ⟨0, 7, 4, 3, 3, 5, -70109086507238070419441785675776561399201792000000⟩, + ⟨0, 7, 5, 3, 4, 5, -16795042359399534359832894972181590413672448000000⟩, + ⟨0, 7, 6, 3, 5, 5, -2979432164810173497175795648104981255212236800000⟩, + ⟨0, 7, 7, 3, 6, 5, 255912650978020326078278844068310170153779200000⟩, + ⟨0, 7, 8, 3, 7, 5, 463647249002481082349915532061460159004672000000⟩, + ⟨0, 7, 2, 4, 0, 5, -353984675576062239885872357184535326201426739200000⟩, + ⟨0, 7, 3, 4, 1, 5, 153639596639333503643167416532732994829208780800000⟩, + ⟨0, 7, 4, 4, 2, 5, 233737174893221857916410508173494532627129958400000⟩, + ⟨0, 7, 5, 4, 3, 5, 1566581210988073944885344070508766998560768000000⟩, + ⟨0, 7, 6, 4, 4, 5, 1376912708155431087063929441706336829046784000000⟩, + ⟨0, 7, 7, 4, 5, 5, 881084231175153329959191853692742935773184000000⟩, + ⟨0, 7, 8, 4, 6, 5, -591399816454277510409405708513649416260812800000⟩, + ⟨0, 7, 3, 5, 0, 5, -184542637835981663127864100637856938237047603200000⟩, + ⟨0, 7, 4, 5, 1, 5, -225351810119554351128101481565543870411623628800000⟩, + ⟨0, 7, 5, 5, 2, 5, 121677475497533616406214931666246327701864448000000⟩, + ⟨0, 7, 6, 5, 3, 5, 510044304005955603426885379461173700093542400000⟩, + ⟨0, 7, 7, 5, 4, 5, -558309348453260424001004944565777649893376000000⟩, + ⟨0, 7, 8, 5, 5, 5, -197687086480616150190987242204035217463705600000⟩, + ⟨0, 7, 4, 6, 0, 5, -703102967575925938263037957996293659268061593600000⟩, + ⟨0, 7, 5, 6, 1, 5, -155451436945425755613165835940348848012001280000000⟩, + ⟨0, 7, 6, 6, 2, 5, 36546190525643831838120020472792517223802470400000⟩, + ⟨0, 7, 7, 6, 3, 5, -1674100878202719194338067308962555897682329600000⟩, + ⟨0, 7, 8, 6, 4, 5, 294485198692589752845406597014071654586777600000⟩, + ⟨0, 7, 5, 7, 0, 5, -678223795386826527642932445697434457655476224000000⟩, + ⟨0, 7, 6, 7, 1, 5, -72451144814530430443237963778280980479161139200000⟩, + ⟨0, 7, 7, 7, 2, 5, 2972888020561758586365761719813238644172390400000⟩, + ⟨0, 7, 8, 7, 3, 5, 1410421702297493559335615382236641869850214400000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0808.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0808.lean new file mode 100644 index 0000000000000000000000000000000000000000..4e6f75f793318bc2a31abb3d7b26d4a61241ec6f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0808.lean @@ -0,0 +1,614 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0808. -/ +namespace LaughlinFock +def collectedFourData_8_2_6 : List CollectedFourTerm := [ + ⟨0, 8, 0, 0, 2, 6, -1726454994217044024654949941804794443014655180800000⟩, + ⟨0, 8, 1, 0, 3, 6, -3643535812754930807966641908435287173958624870400000⟩, + ⟨0, 8, 2, 0, 4, 6, -3408229306473645606136379964855041410303053004800000⟩, + ⟨0, 8, 3, 0, 5, 6, 7808876509810632866249620661522590168126586880000000⟩, + ⟨0, 8, 4, 0, 6, 6, 2048982052401335744532037489861392539899133952000000⟩, + ⟨0, 8, 5, 0, 7, 6, 5297541728235422442836622157871468043986534400000⟩, + ⟨0, 8, 6, 0, 8, 6, 54392476424175363689826551218813722153084518400000⟩, + ⟨0, 8, 0, 1, 1, 6, 12720025579478073882761609540935071463659641241600000⟩, + ⟨0, 8, 1, 1, 2, 6, -1069261081179560630658022687910786211703160832000000⟩, + ⟨0, 8, 2, 1, 3, 6, 2034867910029659493969965515977931631981966131200000⟩, + ⟨0, 8, 3, 1, 4, 6, -7470042051854350032893817160399618703623402291200000⟩, + ⟨0, 8, 4, 1, 5, 6, -3175145364959446178350634178665107335128127897600000⟩, + ⟨0, 8, 5, 1, 6, 6, -874053291293971393162717959402026640295644364800000⟩, + ⟨0, 8, 6, 1, 7, 6, -181911650166931999402965462148832714897227776000000⟩, + ⟨0, 8, 7, 1, 8, 6, -48854334334206176674126554808220764874578329600000⟩, + ⟨0, 8, 0, 2, 0, 6, 2045272337829517057524133401348467902726432358400000⟩, + ⟨0, 8, 1, 2, 1, 6, -3916951639402478871116918825800081472601509068800000⟩, + ⟨0, 8, 2, 2, 2, 6, 496803995911274460069512311401584885733575884800000⟩, + ⟨0, 8, 3, 2, 3, 6, 5181807809767193431843213134174251105018236108800000⟩, + ⟨0, 8, 4, 2, 4, 6, 846555150138640599603796470289025528282637926400000⟩, + ⟨0, 8, 5, 2, 5, 6, 152891003030209276994567238476834544840553267200000⟩, + ⟨0, 8, 6, 2, 6, 6, 12557291727692766333334787379842462948052172800000⟩, + ⟨0, 8, 7, 2, 7, 6, 2884415857509509785474534451229622347497472000000⟩, + ⟨0, 8, 8, 2, 8, 6, 5828637668571409839745837068581039541898444800000⟩, + ⟨0, 8, 1, 3, 0, 6, -3437670582372181359938767456621505466167879270400000⟩, + ⟨0, 8, 2, 3, 1, 6, 2847215695129044302699337914537689966580858880000000⟩, + ⟨0, 8, 3, 3, 2, 6, -3416950150206281789205770727072892018632740044800000⟩, + ⟨0, 8, 4, 3, 3, 6, -1079766908103895051549759196292312126474682368000000⟩, + ⟨0, 8, 5, 3, 4, 6, -206931590335418790150668162363102127197886873600000⟩, + ⟨0, 8, 6, 3, 5, 6, -30591301040274741140848100266380150465940684800000⟩, + ⟨0, 8, 7, 3, 6, 6, 2252212745736544322646862120447344199178649600000⟩, + ⟨0, 8, 8, 3, 7, 6, 3570371412945171793334951220052614073810944000000⟩, + ⟨0, 8, 2, 4, 0, 6, -10903606299975526412867366683522333455242860953600000⟩, + ⟨0, 8, 3, 4, 1, 6, 3154987187164024407357811906015902436653898137600000⟩, + ⟨0, 8, 4, 4, 2, 6, 3599842462892989174373681988054382462897854873600000⟩, + ⟨0, 8, 5, 4, 3, 6, 19301835294146794625969902733628036798323097600000⟩, + ⟨0, 8, 6, 4, 4, 6, 14137442583475100312657411598963152491905024000000⟩, + ⟨0, 8, 7, 4, 5, 6, 7754165837196529537516089676374511863201792000000⟩, + ⟨0, 8, 8, 4, 6, 6, -4554145425929346651943799562220620161325465600000⟩, + ⟨0, 8, 3, 5, 0, 6, -3789580749972598947213920616492591125816043110400000⟩, + ⟨0, 8, 4, 5, 1, 6, -3470697442667236827998566410104169633368191795200000⟩, + ⟨0, 8, 5, 5, 2, 6, 1499187258590742511132225233250514318292261273600000⟩, + ⟨0, 8, 6, 5, 3, 6, 5236876688118084393003602843224518454306406400000⟩, + ⟨0, 8, 7, 5, 4, 6, -4913518053307557152550754749823257031999488000000⟩, + ⟨0, 8, 8, 5, 5, 6, -1522313189169887360748152988227413791159091200000⟩, + ⟨0, 8, 4, 6, 0, 6, -10828657955766577215700590560384070818258642534400000⟩, + ⟨0, 8, 5, 6, 1, 6, -1915315983054960820074335425690499405888618496000000⟩, + ⟨0, 8, 6, 6, 2, 6, 375237781698727521619917528613736114221901414400000⟩, + ⟨0, 8, 7, 6, 3, 6, -14733274502559621133728690904232802265124044800000⟩, + ⟨0, 8, 8, 6, 4, 6, 2267718696076798972511212393591351536726835200000⟩, + ⟨0, 8, 5, 7, 0, 6, -8356390271571628745405561376849023363581791436800000⟩, + ⟨0, 8, 6, 7, 1, 6, -743891674363746096275523006901764702088672051200000⟩, + ⟨0, 8, 7, 7, 2, 6, 26163522068831775827106181992421430631019315200000⟩, + ⟨0, 8, 8, 7, 3, 6, 10861121977785075125476914725785492561644748800000⟩ +] + +def collectedFourData_8_2_7 : List CollectedFourTerm := [ + ⟨1, 1, 6, 0, 8, 0, 12720025579478073882761609540935071463659641241600000⟩, + ⟨1, 1, 6, 1, 7, 0, -42541193110670597193559747456123176073637658624000000⟩, + ⟨1, 1, 7, 1, 8, 0, -79974271494337188950133274497735731823260781772800000⟩, + ⟨1, 1, 6, 2, 6, 0, 2936602311312065481507703935423628105489789747200000⟩, + ⟨1, 1, 7, 2, 7, 0, 4721772592642269611401939546789886117906743296000000⟩, + ⟨1, 1, 8, 2, 8, 0, 38165788784236820138277790932798894625716279705600000⟩, + ⟨1, 1, 6, 3, 5, 0, -7153969764260615603984925181567624215207818035200000⟩, + ⟨1, 1, 7, 3, 6, 0, 3686859641938210498205289655930695504911715532800000⟩, + ⟨1, 1, 8, 3, 7, 0, 23378711969437140148683683013554887818234298368000000⟩, + ⟨1, 1, 6, 4, 4, 0, 3306130610561407548607294081107554928559128576000000⟩, + ⟨1, 1, 7, 4, 5, 0, 12693526016214137270057183455279329149039149056000000⟩, + ⟨1, 1, 8, 4, 6, 0, -29820442151676733888834135510173928406429938483200000⟩, + ⟨1, 1, 6, 5, 3, 0, 1224676826808853386434748426154025183277062553600000⟩, + ⟨1, 1, 7, 5, 4, 0, -8043401514784568687045095815723352665026985984000000⟩, + ⟨1, 1, 8, 5, 5, 0, -9968072634639538711606235683133681816941520486400000⟩, + ⟨1, 1, 6, 6, 2, 0, 87751735081379626613332990045337253886270478745600000⟩, + ⟨1, 1, 7, 6, 3, 0, -24118287786050222011623630609623006872177370726400000⟩, + ⟨1, 1, 8, 6, 4, 0, 14848971182960002831115331849280642751633188454400000⟩, + ⟨1, 1, 6, 7, 1, 0, -173963785955919195502186644317721307080471399628800000⟩, + ⟨1, 1, 7, 7, 2, 0, 42829538989661358836641975564040733696074553753600000⟩, + ⟨1, 1, 8, 7, 3, 0, 71118383219998074142843272846586763715410499993600000⟩ +] + +def collectedFourData_8_2_8 : List CollectedFourTerm := [ + ⟨1, 2, 5, 0, 7, 1, -17356736226266069562971372202841327641034752000000⟩, + ⟨1, 2, 6, 0, 8, 1, -1069261081179560630658022687910786211703160832000000⟩, + ⟨1, 2, 5, 1, 6, 1, 2863726838399521353318257421687014503621853184000000⟩, + ⟨1, 2, 6, 1, 7, 1, 3576065303954409243655141580793429828808212480000000⟩, + ⟨1, 2, 7, 1, 8, 1, 3361368083353000232172757785450688905612361728000000⟩, + ⟨1, 2, 5, 2, 5, 1, -500928345088942921497725806301587878105317376000000⟩, + ⟨1, 2, 6, 2, 6, 1, -246854422011058219751950629109967892925906944000000⟩, + ⟨1, 2, 7, 2, 7, 1, -198459021797810417960473204102816209001512960000000⟩, + ⟨1, 2, 8, 2, 8, 1, -1069421135057662036212558370376533011232456704000000⟩, + ⟨1, 2, 5, 3, 4, 1, 677985604377668807010868633777390315936677888000000⟩, + ⟨1, 2, 6, 3, 5, 1, 601371545761707803493152113843960194954952704000000⟩, + ⟨1, 2, 7, 3, 6, 1, -154960990536698870034781871283799391446499328000000⟩, + ⟨1, 2, 8, 3, 7, 1, -655081146937221897752018499642690943183749120000000⟩, + ⟨1, 2, 5, 4, 3, 1, -63240061347271474894949705056077052335095808000000⟩, + ⟨1, 2, 6, 4, 4, 1, -277917427844888336600621707927181063639531520000000⟩, + ⟨1, 2, 7, 4, 5, 1, -533516747559674409502253237999804160210370560000000⟩, + ⟨1, 2, 8, 4, 6, 1, 835581082158556021009901197553727726459813888000000⟩, + ⟨1, 2, 5, 5, 2, 1, -4911900488192263416940803907186585648798629888000000⟩, + ⟨1, 2, 6, 5, 3, 1, -102947848630263467334743563011362038399107072000000⟩, + ⟨1, 2, 7, 5, 4, 1, 338069139339449263574756439792279409750179840000000⟩, + ⟨1, 2, 8, 5, 5, 1, 279309504423926412478424198819035842216984576000000⟩, + ⟨1, 2, 5, 6, 1, 1, 6275294469253702638864339353430356450271559680000000⟩, + ⟨1, 2, 6, 6, 2, 1, -7376519374291097733174100713346261980819750912000000⟩, + ⟨1, 2, 7, 6, 3, 1, 1013706549298071927316127335811932110679179264000000⟩, + ⟨1, 2, 8, 6, 4, 1, -416074293831397367341429584874307116855197696000000⟩, + ⟨1, 2, 5, 7, 0, 1, 27378672823728080253640283022704798475636178944000000⟩, + ⟨1, 2, 6, 7, 1, 1, 14623610990014083678693612814344328316322840576000000⟩, + ⟨1, 2, 7, 7, 2, 1, -1800152007571141382125808021429584757350465536000000⟩, + ⟨1, 2, 8, 7, 3, 1, -1992766415403117814367366576974490362523418624000000⟩ +] + +def collectedFourData_8_2_9 : List CollectedFourTerm := [ + ⟨1, 3, 4, 0, 6, 2, 5110275171322587433170264042617536485012170342400000⟩, + ⟨1, 3, 5, 0, 7, 2, 66061818187034650372577439106760766837384806400000⟩, + ⟨1, 3, 6, 0, 8, 2, 2034867910029659493969965515977931631981966131200000⟩, + ⟨1, 3, 4, 1, 5, 2, -7918989092596541610381317071075174623376173957120000⟩, + ⟨1, 3, 5, 1, 6, 2, -10899687548940726974782009907315799461649501388800000⟩, + ⟨1, 3, 6, 1, 7, 2, -6805466559355014898293288899378522563666771968000000⟩, + ⟨1, 3, 7, 1, 8, 2, -4264589922271311750947138549827262099963982643200000⟩, + ⟨1, 3, 4, 2, 4, 2, 2111355616726211244703187829597753166083580231680000⟩, + ⟨1, 3, 5, 2, 5, 2, 1906593314929749657631733690374506429770052403200000⟩, + ⟨1, 3, 6, 2, 6, 2, 469778757162927024976186830210098653068420710400000⟩, + ⟨1, 3, 7, 2, 7, 2, 251786273730107373579003741026456435712589824000000⟩, + ⟨1, 3, 8, 2, 8, 2, 1017586251075238615571000870017045640221242163200000⟩, + ⟨1, 3, 4, 3, 3, 2, -2692998708716017666632820688338706873473145241600000⟩, + ⟨1, 3, 5, 3, 4, 2, -2580494463126363203590517241331044141940447641600000⟩, + ⟨1, 3, 6, 3, 5, 2, -1144446087129149546499778458502852561124877926400000⟩, + ⟨1, 3, 7, 3, 6, 2, 196600033736497596302064259959880535394956083200000⟩, + ⟨1, 3, 8, 3, 7, 2, 623329338283531045975023479751915067246903296000000⟩, + ⟨1, 3, 4, 4, 2, 2, 8978207269914885446962102123141742731234451128320000⟩, + ⟨1, 3, 5, 4, 3, 2, 240699252463037516568331181709324136706840985600000⟩, + ⟨1, 3, 6, 4, 4, 2, 528893518630346717165320321907477041939218432000000⟩, + ⟨1, 3, 7, 4, 5, 2, 676876226758358697162272990242419761441931264000000⟩, + ⟨1, 3, 8, 4, 6, 2, -795080434629029485188167089552732999154820710400000⟩, + ⟨1, 3, 4, 5, 1, 2, -8656112408426880860960066970033991860099471114240000⟩, + ⟨1, 3, 5, 5, 2, 2, 18695281922456853947997494914854144754132294041600000⟩, + ⟨1, 3, 6, 5, 3, 2, 195915924811571046608922329789753855338296115200000⟩, + ⟨1, 3, 7, 5, 4, 2, -428910553354161086586137274800373769747562496000000⟩, + ⟨1, 3, 8, 5, 5, 2, -265771361888318333365473179784422186550086860800000⟩, + ⟨1, 3, 4, 6, 0, 2, -27007275063851930678671456290491316210693864161280000⟩, + ⟨1, 3, 5, 6, 1, 2, -23884522809685248831461856039966303737113214976000000⟩, + ⟨1, 3, 6, 6, 2, 2, 14037958387018439462575680033339486533969982259200000⟩, + ⟨1, 3, 7, 6, 3, 2, -1286096204603901439281451954363507871906896281600000⟩, + ⟨1, 3, 8, 6, 4, 2, 395907156637445840420903886869545517629361356800000⟩, + ⟨1, 3, 5, 7, 0, 2, -104206509951239310715733925612251291088019311820800000⟩, + ⟨1, 3, 6, 7, 1, 2, -27829607993877424465484354112200911220219943321600000⟩, + ⟨1, 3, 7, 7, 2, 2, 2283864759727997583584136739730204084727604838400000⟩, + ⟨1, 3, 8, 7, 3, 2, 1896176949793836712176338662231110031831675699200000⟩ +] + +def collectedFourData_8_2_10 : List CollectedFourTerm := [ + ⟨1, 4, 3, 0, 5, 3, -53621971034303231715365773267762947162523041792000000⟩, + ⟨1, 4, 4, 0, 6, 3, -56279776546926593296535511759854770941850759987200000⟩, + ⟨1, 4, 5, 0, 7, 3, -363771444903206876829159764570756052334254489600000⟩, + ⟨1, 4, 6, 0, 8, 3, -7470042051854350032893817160399618703623402291200000⟩, + ⟨1, 4, 3, 1, 4, 3, 51295263540961627288903010645837949323695966126080000⟩, + ⟨1, 4, 4, 1, 5, 3, 87212316688914509647191011557851196039162610319360000⟩, + ⟨1, 4, 5, 1, 6, 3, 60019466576683398643374604548035488688534401843200000⟩, + ⟨1, 4, 6, 1, 7, 3, 24983008051922896523616355422646350285392314368000000⟩, + ⟨1, 4, 7, 1, 8, 3, 11741548147767724729941192448452104947994355302400000⟩, + ⟨1, 4, 3, 2, 3, 3, -35582423147757123186982913556413347610041956433920000⟩, + ⟨1, 4, 4, 2, 4, 3, -23252490000395831093711591959913488893502071767040000⟩, + ⟨1, 4, 5, 2, 5, 3, -10498715052788382021467593775741374324366167244800000⟩, + ⟨1, 4, 6, 2, 6, 3, -1724567503265500919903692684026975274926499430400000⟩, + ⟨1, 4, 7, 2, 7, 3, -693234451572902466397286224615608281116704768000000⟩, + ⟨1, 4, 8, 2, 8, 3, -2241348064742951061005654272971588070214121553920000⟩, + ⟨1, 4, 3, 3, 2, 3, 23463503584648508585848613762688998280477875896320000⟩, + ⟨1, 4, 4, 3, 3, 3, 29658161348770152412230879487286598374213340364800000⟩, + ⟨1, 4, 5, 3, 4, 3, 14209572566690789599509820889230339378724103782400000⟩, + ⟨1, 4, 6, 3, 5, 3, 4201285181606852574472482727677907050237945446400000⟩, + ⟨1, 4, 7, 3, 6, 3, -541292082953758535645958085062016122541729382400000⟩, + ⟨1, 4, 8, 3, 7, 3, -1372952911444159744167457424150054775278901657600000⟩, + ⟨1, 4, 3, 4, 1, 3, -21664657054207881123858452800869761258113298595840000⟩, + ⟨1, 4, 4, 4, 2, 3, -98877551991398420210503264650897370359981366312960000⟩, + ⟨1, 4, 5, 4, 3, 3, -1325417877656680062232143546980587831367722598400000⟩, + ⟨1, 4, 6, 4, 4, 3, -1941579011418149419827718217876104671796396032000000⟩, + ⟨1, 4, 7, 4, 5, 3, -1863619938005610427210120602770120778184654848000000⟩, + ⟨1, 4, 8, 4, 6, 3, 1751254000914166951314214413134451225919739658240000⟩, + ⟨1, 4, 3, 5, 0, 3, 26022282328564007875537317748291710154152723087360000⟩, + ⟨1, 4, 4, 5, 1, 3, 95330301359341630010131821591414713452031870238720000⟩, + ⟨1, 4, 5, 5, 2, 3, -102946148084366012615942156321366897474197153382400000⟩, + ⟨1, 4, 6, 5, 3, 3, -719211399303574107760706822197756217141703475200000⟩, + ⟨1, 4, 7, 5, 4, 3, 1180904613358786313179256121319117940664041472000000⟩, + ⟨1, 4, 8, 5, 5, 3, 585391289439146289938944251570836683792821780480000⟩, + ⟨1, 4, 4, 6, 0, 3, 297432790755490458137540019676460515598603743395840000⟩, + ⟨1, 4, 5, 6, 1, 3, 131520863514592448549622997480799642781078257664000000⟩, + ⟨1, 4, 6, 6, 2, 3, -51533634668051128675404755164720627705896448819200000⟩, + ⟨1, 4, 7, 6, 3, 3, 3540964262508833659580451735536200150502552371200000⟩, + ⟨1, 4, 8, 6, 4, 3, -872030000807875789998861407471104105772042158080000⟩, + ⟨1, 4, 5, 7, 0, 3, 573816369782000034372575589092023658911473283891200000⟩, + ⟨1, 4, 6, 7, 1, 3, 102163064725835807691097951434575498867881122201600000⟩, + ⟨1, 4, 7, 7, 2, 3, -6288085965614730469271160254509386113229835468800000⟩, + ⟨1, 4, 8, 7, 3, 3, -4176542806410589456799768276017795289811800555520000⟩ +] + +def collectedFourData_8_2_11 : List CollectedFourTerm := [ + ⟨1, 5, 2, 0, 4, 4, 13263627860070427199849391570154604671229472276480000⟩, + ⟨1, 5, 3, 0, 5, 4, -91168189741204015002504133714677633766196772864000000⟩, + ⟨1, 5, 4, 0, 6, 4, -47843498176711875797623951560910069962659541811200000⟩, + ⟨1, 5, 5, 0, 7, 4, -206161662664678208756040975883158318045619814400000⟩, + ⟨1, 5, 6, 0, 8, 4, -3175145364959446178350634178665107335128127897600000⟩, + ⟨1, 5, 2, 1, 3, 4, -7918989092596541610381317071075174623376173957120000⟩, + ⟨1, 5, 3, 1, 4, 4, 87212316688914509647191011557851196039162610319360000⟩, + ⟨1, 5, 4, 1, 5, 4, 74139283602410823900909313085095352807465743810560000⟩, + ⟨1, 5, 5, 1, 6, 4, 34015075111210438196198769537331638782881746124800000⟩, + ⟨1, 5, 6, 1, 7, 4, 10619040919470605778345200120391877451751358464000000⟩, + ⟨1, 5, 7, 1, 8, 4, 3992601050440219330425536539684002220696833884160000⟩, + ⟨1, 5, 2, 2, 2, 4, -1933386145306314280692113810300996155079110164480000⟩, + ⟨1, 5, 3, 2, 3, 4, -60497311874479174330532409707953001672173305200640000⟩, + ⟨1, 5, 4, 2, 4, 4, -19766966594303242604360687817470698974122700963840000⟩, + ⟨1, 5, 5, 2, 5, 4, -5949979256072325199579911166669442132913369907200000⟩, + ⟨1, 5, 6, 2, 6, 4, -733028338601366866935933787151649393511445299200000⟩, + ⟨1, 5, 7, 2, 7, 4, -235727739197452334908840528203304230024590131200000⟩, + ⟨1, 5, 8, 2, 8, 4, -635124128229219457204343622619338842964429373440000⟩, + ⟨1, 5, 2, 3, 1, 4, -11080360510313391356982655566158663287452991488000000⟩, + ⟨1, 5, 3, 3, 2, 4, 39892698935483130542789791847751124840342817341440000⟩, + ⟨1, 5, 4, 3, 3, 4, 25212434651928259649672016165993564364363058380800000⟩, + ⟨1, 5, 5, 3, 4, 4, 8053048547784865259918268850445704503569783193600000⟩, + ⟨1, 5, 6, 3, 5, 4, 1785758510949798693650116721786595220837839667200000⟩, + ⟨1, 5, 7, 3, 6, 4, -184061191232863607901292699067912424400260956160000⟩, + ⟨1, 5, 8, 3, 7, 4, -389049579000013762179130113160009057612018483200000⟩, + ⟨1, 5, 2, 4, 0, 4, 42432994757981409829915648893925339493003805327360000⟩, + ⟨1, 5, 3, 4, 1, 4, -36834296220342268759606815333706787210868849377280000⟩, + ⟨1, 5, 4, 4, 2, 4, -84055912597196372956522042612322381055282810716160000⟩, + ⟨1, 5, 5, 4, 3, 4, -751159435991181978604590778692134032950008217600000⟩, + ⟨1, 5, 6, 4, 4, 4, -825269196078560601596838677148683384427380736000000⟩, + ⟨1, 5, 7, 4, 5, 4, -633706120220368309736005950876721021623415603200000⟩, + ⟨1, 5, 8, 4, 6, 4, 496247632456007187227126195629837673943458119680000⟩, + ⟨1, 5, 3, 5, 0, 4, 44243140023928270484474445978687398121279974277120000⟩, + ⟨1, 5, 4, 5, 1, 4, 81040391044696232209128672272771314624880569221120000⟩, + ⟨1, 5, 5, 5, 2, 4, -58343086988711508923773668924061908396905437593600000⟩, + ⟨1, 5, 6, 5, 3, 4, -305701189507743637742374874254499426137119129600000⟩, + ⟨1, 5, 7, 5, 4, 4, 401555309438676814158883227829931375879572684800000⟩, + ⟨1, 5, 8, 5, 5, 4, 165880586878261542540076470645019522970796687360000⟩, + ⟨1, 5, 4, 6, 0, 4, 252847933224101209299763591437499164088756485488640000⟩, + ⟨1, 5, 5, 6, 1, 4, 74537351067996267335715539353075701776904093696000000⟩, + ⟨1, 5, 6, 6, 2, 4, -21904398947146160450234480321260419064079686041600000⟩, + ⟨1, 5, 7, 6, 3, 4, 1204071001212209289421481442138598372387407790080000⟩, + ⟨1, 5, 8, 6, 4, 4, -247104545146291507052010338626009911953782210560000⟩, + ⟨1, 5, 5, 7, 0, 4, 325201272711067765191788266964301228515825339596800000⟩, + ⟨1, 5, 6, 7, 1, 4, 43424465241633452289088176980679811214791724236800000⟩, + ⟨1, 5, 7, 7, 2, 4, -2138203439241087847541870164214002050349840465920000⟩, + ⟨1, 5, 8, 7, 3, 4, -1183494500769455153553100262539230336701316464640000⟩ +] + +def collectedFourData_8_2_12 : List CollectedFourTerm := [ + ⟨1, 6, 1, 0, 3, 5, 9758226009821370477764015793874442525160033484800000⟩, + ⟨1, 6, 2, 0, 4, 5, 18256042248542913565935520195102676798915425075200000⟩, + ⟨1, 6, 3, 0, 5, 5, -62741896153808391724076779130932438589169991680000000⟩, + ⟨1, 6, 4, 0, 6, 5, -21950578761877800580745033730207722836900970496000000⟩, + ⟨1, 6, 5, 0, 7, 5, -70940169298753100154634314325857466281099264000000⟩, + ⟨1, 6, 6, 0, 8, 5, -874053291293971393162717959402026640295644364800000⟩, + ⟨1, 6, 1, 1, 2, 5, 2863726838399521353318257421687014503621853184000000⟩, + ⟨1, 6, 2, 1, 3, 5, -10899687548940726974782009907315799461649501388800000⟩, + ⟨1, 6, 3, 1, 4, 5, 60019466576683398643374604548035488688534401843200000⟩, + ⟨1, 6, 4, 1, 5, 5, 34015075111210438196198769537331638782881746124800000⟩, + ⟨1, 6, 5, 1, 6, 5, 11704577640236979276537518728000263951155724288000000⟩, + ⟨1, 6, 6, 1, 7, 5, 2923207160364826456788225334422123643479785472000000⟩, + ⟨1, 6, 7, 1, 8, 5, 915901921497698417310198231619143917399074406400000⟩, + ⟨1, 6, 1, 2, 1, 5, 10490496410938015516659354848544818364348471705600000⟩, + ⟨1, 6, 2, 2, 2, 5, -2661110483785255070937785346155064167083750195200000⟩, + ⟨1, 6, 3, 2, 3, 5, -41634215508588022480195385733674884929680100556800000⟩, + ⟨1, 6, 4, 2, 4, 5, -9069076753314466066631091808003442212640863027200000⟩, + ⟨1, 6, 5, 2, 5, 5, -2047386164305305251983163939640421127534149632000000⟩, + ⟨1, 6, 6, 2, 6, 5, -201787873726045824208177376340858732178676121600000⟩, + ⟨1, 6, 7, 2, 7, 5, -54075898531722737166497355697754772810498048000000⟩, + ⟨1, 6, 8, 2, 8, 5, -124883446459163452046058376383289105769614540800000⟩, + ⟨1, 6, 1, 3, 0, 5, 9206871625268231934246435333971751588724526284800000⟩, + ⟨1, 6, 2, 3, 1, 5, -15250995560146370501194245768339279194483589120000000⟩, + ⟨1, 6, 3, 3, 2, 5, 27454132642210451369741444497445338727362383052800000⟩, + ⟨1, 6, 4, 3, 3, 5, 11567455426477002729254608304487809241122340864000000⟩, + ⟨1, 6, 5, 3, 4, 5, 2771051707514263496800805552660650794172809216000000⟩, + ⟨1, 6, 6, 3, 5, 5, 491583195269495504976750213122888475256396185600000⟩, + ⟨1, 6, 7, 3, 6, 5, -42223602256666103531437729745497577914525286400000⟩, + ⟨1, 6, 8, 3, 7, 5, -76498199500733539463955815291209179488845824000000⟩, + ⟨1, 6, 2, 4, 0, 5, 58404725555214372568508986634427771317362517606400000⟩, + ⟨1, 6, 3, 4, 1, 5, -25349341638960249307912531322462636990386510233600000⟩, + ⟨1, 6, 4, 4, 2, 5, -38564820721332156185420593313479589541563911372800000⟩, + ⟨1, 6, 5, 4, 3, 5, -258473747596041764167278468340331755031494656000000⟩, + ⟨1, 6, 6, 4, 4, 5, -227179915917080771974849924752023180833456128000000⟩, + ⟨1, 6, 7, 4, 5, 5, -145372063434860645257888061044064022511484928000000⟩, + ⟨1, 6, 8, 4, 6, 5, 97576382133509485536767240024896889429793177600000⟩, + ⟨1, 6, 3, 5, 0, 5, 30448103716653344360105443008135458439419029094400000⟩, + ⟨1, 6, 4, 5, 1, 5, 37181300580271192725378411070684831825190820249600000⟩, + ⟨1, 6, 5, 5, 2, 5, -20075839585766923777639147989312204959662473216000000⟩, + ⟨1, 6, 6, 5, 3, 5, -84153353667049552932810544567051200748113100800000⟩, + ⟨1, 6, 7, 5, 4, 5, 92116711601309479857569739005932383441518592000000⟩, + ⟨1, 6, 8, 5, 5, 5, 32616835779461323546249636696224285196497715200000⟩, + ⟨1, 6, 4, 6, 0, 5, 116006535569659221311448391711398020080070767411200000⟩, + ⟨1, 6, 5, 6, 1, 5, 25648281234735082686072710442773676992243957760000000⟩, + ⟨1, 6, 6, 6, 2, 5, -6029837942179959451055798700555629976529718476800000⟩, + ⟨1, 6, 7, 6, 3, 5, 276213658639479007452283018995265512861283123200000⟩, + ⟨1, 6, 8, 6, 4, 5, -48587773416247178752419912649894786707436339200000⟩, + ⟨1, 6, 5, 7, 0, 5, 111901665150111786938482065547020296856281284608000000⟩, + ⟨1, 6, 6, 7, 1, 5, 11953876879465376894448525182551436073397282406400000⟩, + ⟨1, 6, 7, 7, 2, 5, -490503462232463847990893894764936418617511116800000⟩, + ⟨1, 6, 8, 7, 3, 5, -232708640015980125727133235505701891882142924800000⟩ +] + +def collectedFourData_8_2_13 : List CollectedFourTerm := [ + ⟨1, 7, 0, 0, 2, 6, 5774002170590175929030573182824596024655347712000000⟩, + ⟨1, 7, 1, 0, 3, 6, 12185538436819056165754445431098194031129133056000000⟩, + ⟨1, 7, 2, 0, 4, 6, 11398573075675488763578840091296066303606915072000000⟩, + ⟨1, 7, 3, 0, 5, 6, -26116215058339865987056739186762426208170803200000000⟩, + ⟨1, 7, 4, 0, 6, 6, -6852670273881634154138205721537218329475809280000000⟩, + ⟨1, 7, 5, 0, 7, 6, -17717239974445542944175759312051524931158016000000⟩, + ⟨1, 7, 6, 0, 8, 6, -181911650166931999402965462148832714897227776000000⟩, + ⟨1, 7, 0, 1, 1, 6, -42541193110670597193559747456123176073637658624000000⟩, + ⟨1, 7, 1, 1, 2, 6, 3576065303954409243655141580793429828808212480000000⟩, + ⟨1, 7, 2, 1, 3, 6, -6805466559355014898293288899378522563666771968000000⟩, + ⟨1, 7, 3, 1, 4, 6, 24983008051922896523616355422646350285392314368000000⟩, + ⟨1, 7, 4, 1, 5, 6, 10619040919470605778345200120391877451751358464000000⟩, + ⟨1, 7, 5, 1, 6, 6, 2923207160364826456788225334422123643479785472000000⟩, + ⟨1, 7, 6, 1, 7, 6, 608390178972402828202076718458506186472816640000000⟩, + ⟨1, 7, 7, 1, 8, 6, 163389739919847487641569666526061705448914944000000⟩, + ⟨1, 7, 0, 2, 0, 6, -6840263405436352071555680064313656025993445376000000⟩, + ⟨1, 7, 1, 2, 1, 6, 13099957626328597797164911544720509455965356032000000⟩, + ⟨1, 7, 2, 2, 2, 6, -1661524546170097061433292632248918239736758272000000⟩, + ⟨1, 7, 3, 2, 3, 6, -17330176367989056934299235513531526773192261632000000⟩, + ⟨1, 7, 4, 2, 4, 6, -2831241643018641593503161723272634088235728896000000⟩, + ⟨1, 7, 5, 2, 5, 6, -511332751978564355351630630053357588743979008000000⟩, + ⟨1, 7, 6, 2, 6, 6, -41996941672559411050402125908505344021102592000000⟩, + ⟨1, 7, 7, 2, 7, 6, -9646717393694695256878490547466981689262080000000⟩, + ⟨1, 7, 8, 2, 8, 6, -19493451414977369352821440771041614125596672000000⟩, + ⟨1, 7, 1, 3, 0, 6, 11497037264729071825447094825618128653627949056000000⟩, + ⟨1, 7, 2, 3, 1, 6, -9522304177566507232766966118753219581784883200000000⟩, + ⟨1, 7, 3, 3, 2, 6, 11427739298258924783679070683929083283528220672000000⟩, + ⟨1, 7, 4, 3, 3, 6, 3611201271974509051881392589059110313939435520000000⟩, + ⟨1, 7, 5, 3, 4, 6, 692067534782303188540883400635926893092143104000000⟩, + ⟨1, 7, 6, 3, 5, 6, 102310363837679054565555144799273455842230272000000⟩, + ⟨1, 7, 7, 3, 6, 6, -7532360429940528814032752998789692725919744000000⟩, + ⟨1, 7, 8, 3, 7, 6, -11940845464962549805025289890194094460764160000000⟩, + ⟨1, 7, 2, 4, 0, 6, 36466311982763803986886943726417489163718754304000000⟩, + ⟨1, 7, 3, 4, 1, 6, -10551623371526535006264809471307399155693912064000000⟩, + ⟨1, 7, 4, 4, 2, 6, -12039409231141372287939783280380106187791663104000000⟩, + ⟨1, 7, 5, 4, 3, 6, -64553573222637213853437734181880995684286464000000⟩, + ⟨1, 7, 6, 4, 4, 6, -47281640376961379473623680643882248684175360000000⟩, + ⟨1, 7, 7, 4, 5, 6, -25933239224341052054856518373453679432826880000000⟩, + ⟨1, 7, 8, 4, 6, 6, 15231005535956398120638250146962770948521984000000⟩, + ⟨1, 7, 3, 5, 0, 6, 12673975023537580009467329133615246141246406656000000⟩, + ⟨1, 7, 4, 5, 1, 6, 11607493177955996624653029110676160668581756928000000⟩, + ⟨1, 7, 5, 5, 2, 6, -5013921888621117944014260341069760526867759104000000⟩, + ⟨1, 7, 6, 5, 3, 6, -17514350194816330098075776700560266122756096000000⟩, + ⟨1, 7, 7, 5, 4, 6, 16432900944457048383622836633295963627192320000000⟩, + ⟨1, 7, 8, 5, 5, 6, 5091264868199601676225824822616507828666368000000⟩, + ⟨1, 7, 4, 6, 0, 6, 36215652739636028473273915851250351064550998016000000⟩, + ⟨1, 7, 5, 6, 1, 6, 6405633903327280034046696948090978046511677440000000⟩, + ⟨1, 7, 6, 6, 2, 6, -1254955254132454241882635652194403147071881216000000⟩, + ⟨1, 7, 7, 6, 3, 6, 49274356552954801374452501778044727613980672000000⟩, + ⟨1, 7, 8, 6, 4, 6, -7584218944191748411519230902233627285782528000000⟩, + ⟨1, 7, 5, 7, 0, 6, 27947334699121274676446447058561370877488791552000000⟩, + ⟨1, 7, 6, 7, 1, 6, 2487891174022836054263333114975337657315360768000000⟩, + ⟨1, 7, 7, 7, 2, 6, -87501981645475121880143177019544884612169728000000⟩, + ⟨1, 7, 8, 7, 3, 6, -36324226281505796412932897069222096359391232000000⟩ +] + +def collectedFourData_8_2_14 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 2, 7, 10854693614219411689951937880374519408347211366400000⟩, + ⟨1, 8, 1, 0, 3, 7, 11453951899228789830098138885054187089157527961600000⟩, + ⟨1, 8, 2, 0, 4, 7, 7142822529923034940161161493108593342381083852800000⟩, + ⟨1, 8, 3, 0, 5, 7, -12274134319920379816518105871149014565267701760000000⟩, + ⟨1, 8, 4, 0, 6, 7, -2576501846193494394085164987784089458015679283200000⟩, + ⟨1, 8, 5, 0, 7, 7, -5551181714471884377488571096822278782137139200000⟩, + ⟨1, 8, 6, 0, 8, 7, -48854334334206176674126554808220764874578329600000⟩, + ⟨1, 8, 0, 1, 1, 7, -79974271494337188950133274497735731823260781772800000⟩, + ⟨1, 8, 1, 1, 2, 7, 3361368083353000232172757785450688905612361728000000⟩, + ⟨1, 8, 2, 1, 3, 7, -4264589922271311750947138549827262099963982643200000⟩, + ⟨1, 8, 3, 1, 4, 7, 11741548147767724729941192448452104947994355302400000⟩, + ⟨1, 8, 4, 1, 5, 7, 3992601050440219330425536539684002220696833884160000⟩, + ⟨1, 8, 5, 1, 6, 7, 915901921497698417310198231619143917399074406400000⟩, + ⟨1, 8, 6, 1, 7, 7, 163389739919847487641569666526061705448914944000000⟩, + ⟨1, 8, 7, 1, 8, 7, 38395066241282263490221338660885620472781209600000⟩, + ⟨1, 8, 0, 2, 0, 7, -12859185243253816766501274204152696572516447027200000⟩, + ⟨1, 8, 1, 2, 1, 7, 12313471851234140013906864036228772213550166835200000⟩, + ⟨1, 8, 2, 2, 2, 7, -1041180758645143770616529499672318733737315532800000⟩, + ⟨1, 8, 3, 2, 3, 7, -8144859890816397658157628635776366285503961497600000⟩, + ⟨1, 8, 4, 2, 4, 7, -1064504642527534727951283217803360541706802954240000⟩, + ⟨1, 8, 5, 2, 5, 7, -160211242094598538639414038688708033773148569600000⟩, + ⟨1, 8, 6, 2, 6, 7, -11278731338001674096796502517680187641115443200000⟩, + ⟨1, 8, 7, 2, 7, 7, -2266888689115573841468890801520694182019072000000⟩, + ⟨1, 8, 8, 2, 8, 7, -4071803930440917497366025689149730694207897600000⟩, + ⟨1, 8, 1, 3, 0, 7, 10806786462217545138121587512236255786923825561600000⟩, + ⟨1, 8, 2, 3, 1, 7, -5967073980641352540473046613053516359065927680000000⟩, + ⟨1, 8, 3, 3, 2, 7, 5370824478452544747430585319634456025916610969600000⟩, + ⟨1, 8, 4, 3, 3, 7, 1357757833421671207871811254992998596313140428800000⟩, + ⟨1, 8, 5, 3, 4, 7, 216839228333779134748779677863961946430950604800000⟩, + ⟨1, 8, 6, 3, 5, 7, 27476550931144510344697687378574159937483571200000⟩, + ⟨1, 8, 7, 3, 6, 7, -1770034506466885047398643135340264774277529600000⟩, + ⟨1, 8, 8, 3, 7, 7, -2494211028205369290553447183245745091248128000000⟩, + ⟨1, 8, 2, 4, 0, 7, 22851315957217024880993252700203520400052296089600000⟩, + ⟨1, 8, 3, 4, 1, 7, -4959066322053810909148122859623441849379926835200000⟩, + ⟨1, 8, 4, 4, 2, 7, -4526638357217206443870933368099270633333729525760000⟩, + ⟨1, 8, 5, 4, 3, 7, -20225984171021537159517442106558912949701836800000⟩, + ⟨1, 8, 6, 4, 4, 7, -12697994134658620521911236415652965180768256000000⟩, + ⟨1, 8, 7, 4, 5, 7, -6094069544134467343466146758806714965819392000000⟩, + ⟨1, 8, 8, 4, 6, 7, 3181461655283102341052221809907153415385907200000⟩, + ⟨1, 8, 3, 5, 0, 7, 5956532041825855443424707972110643964779744460800000⟩, + ⟨1, 8, 4, 5, 1, 7, 4364244361306708063694910965436276533126045368320000⟩, + ⟨1, 8, 5, 5, 2, 7, -1570966558338041560955488806731307929981209804800000⟩, + ⟨1, 8, 6, 5, 3, 7, -4703667518153639151064732167221227376187801600000⟩, + ⟨1, 8, 7, 5, 4, 7, 3861578582647683186914325762086824876965888000000⟩, + ⟨1, 8, 8, 5, 5, 7, 1063466487280080505367237725139751932421734400000⟩, + ⟨1, 8, 4, 6, 0, 7, 13616545436370494254871392754625346971420894167040000⟩, + ⟨1, 8, 5, 6, 1, 7, 2007019030336544567337002713611192229825609728000000⟩, + ⟨1, 8, 6, 6, 2, 7, -337031759667916879703418460806791785017350553600000⟩, + ⟨1, 8, 7, 6, 3, 7, 11579014598929819495699772649743882465889484800000⟩, + ⟨1, 8, 8, 6, 4, 7, -1584196243593750382463743815053382917711462400000⟩, + ⟨1, 8, 5, 7, 0, 7, 8756484281623707982957469136036292315025139302400000⟩, + ⟨1, 8, 6, 7, 1, 7, 668149989796127624459238998553969513309457612800000⟩, + ⟨1, 8, 7, 7, 2, 7, -20562150249884662888048924479833350639661875200000⟩, + ⟨1, 8, 8, 7, 3, 7, -7587426371792780004575303904939756828072345600000⟩ +] + +def collectedFourData_8_2_15 : List CollectedFourTerm := [ + ⟨2, 0, 6, 0, 8, 0, 2045272337829517057524133401348467902726432358400000⟩, + ⟨2, 0, 6, 1, 7, 0, -6840263405436352071555680064313656025993445376000000⟩, + ⟨2, 0, 7, 1, 8, 0, -12859185243253816766501274204152696572516447027200000⟩, + ⟨2, 0, 6, 2, 6, 0, 472180770156850178917725362117385884734901452800000⟩, + ⟨2, 0, 7, 2, 7, 0, 759221025847107766790274761043895318902472704000000⟩, + ⟨2, 0, 8, 2, 8, 0, 6136735462056085362705839227772367046877537894400000⟩, + ⟨2, 0, 6, 3, 5, 0, -1150297723309402238346916538477544119210921164800000⟩, + ⟨2, 0, 7, 3, 6, 0, 592815792075291251225831990528014472474473267200000⟩, + ⟨2, 0, 8, 3, 7, 0, 3759098799480211769260824075541440663631429632000000⟩, + ⟨2, 0, 6, 4, 4, 0, 531597789704296601353668094959411744340967424000000⟩, + ⟨2, 0, 7, 4, 5, 0, 2041011432584504436947259460838919380291026944000000⟩, + ⟨2, 0, 8, 4, 6, 0, -4794874432726755382231638381784838850118208716800000⟩, + ⟨2, 0, 6, 5, 3, 0, 196917657201421650285317522492459403356563046400000⟩, + ⟨2, 0, 7, 5, 4, 0, -1293310812738155381759369864299241842478678016000000⟩, + ⟨2, 0, 8, 5, 5, 0, -1602781621288231431586625780791243434668693913600000⟩, + ⟨2, 0, 6, 6, 2, 0, 14109735490473282102062069563883863872503178854400000⟩, + ⟨2, 0, 7, 6, 3, 0, -3878016324448622900701233824017012220287883673600000⟩, + ⟨2, 0, 8, 6, 4, 0, 2387588752552011721508898620851844106604353945600000⟩, + ⟨2, 0, 6, 7, 1, 0, -27971902806058337064536397492970636005480805171200000⟩, + ⟨2, 0, 7, 7, 2, 0, 6886626979655763386019405088304677077874271846400000⟩, + ⟨2, 0, 8, 7, 3, 0, 11435233443688507520527939851963542201409365606400000⟩ +] + +def collectedFourData_8_2_16 : List CollectedFourTerm := [ + ⟨2, 1, 5, 0, 7, 1, -63581755300726685241850551294589657139694796800000⟩, + ⟨2, 1, 6, 0, 8, 1, -3916951639402478871116918825800081472601509068800000⟩, + ⟨2, 1, 5, 1, 6, 1, 10490496410938015516659354848544818364348471705600000⟩, + ⟨2, 1, 6, 1, 7, 1, 13099957626328597797164911544720509455965356032000000⟩, + ⟨2, 1, 7, 1, 8, 1, 12313471851234140013906864036228772213550166835200000⟩, + ⟨2, 1, 5, 2, 5, 1, -1835016851408069596496327955805746302674167398400000⟩, + ⟨2, 1, 6, 2, 6, 1, -904285071259964675917145007255705364064737689600000⟩, + ⟨2, 1, 7, 2, 7, 1, -727001482114736168611996875832132876332171264000000⟩, + ⟨2, 1, 8, 2, 8, 1, -3917537953924962408506415640904355481076210073600000⟩, + ⟨2, 1, 5, 3, 4, 1, 2483618707630143463388349810051856325766492979200000⟩, + ⟨2, 1, 6, 3, 5, 1, 2202963619944714595179067575108928814819416473600000⟩, + ⟨2, 1, 7, 3, 6, 1, -567658092686369464942362512273931340963066675200000⟩, + ⟨2, 1, 8, 3, 7, 1, -2399714361254782487411702535685519705959825408000000⟩, + ⟨2, 1, 5, 4, 3, 1, -231663030040191634445142449719570694476608307200000⟩, + ⟨2, 1, 6, 4, 4, 1, -1018076074942027295546991387650450530467053568000000⟩, + ⟨2, 1, 7, 4, 5, 1, -1954395737191909087880161557062146958089519104000000⟩, + ⟨2, 1, 8, 4, 6, 1, 3060927538860858731437841341875085344756675379200000⟩, + ⟨2, 1, 5, 5, 2, 1, -17993432107883491258051701838270057763977769779200000⟩, + ⟨2, 1, 6, 5, 3, 1, -377121875623145854924689040064590927285243084800000⟩, + ⟨2, 1, 7, 5, 4, 1, 1238425762308904559272896328189609073763680256000000⟩, + ⟨2, 1, 8, 5, 5, 1, 1023175574712861390244685678092773304668939878400000⟩, + ⟨2, 1, 5, 6, 1, 1, 22987860861784124263107767007891027132533440512000000⟩, + ⟨2, 1, 6, 6, 2, 1, -27021903410474539568168625271210600031668980940800000⟩, + ⟨2, 1, 7, 6, 3, 1, 3713442488494841726779054170476998262057965977600000⟩, + ⟨2, 1, 8, 6, 4, 1, -1524176757222157307705485613712009919994422886400000⟩, + ⟨2, 1, 5, 7, 0, 1, 100294436306671174105771666579455255316182702489600000⟩, + ⟨2, 1, 6, 7, 1, 1, 53569682886176950545966531756881526362470770278400000⟩, + ⟨2, 1, 7, 7, 2, 1, -6594374827007619938737506175655114143183562342400000⟩, + ⟨2, 1, 8, 7, 3, 1, -7299966130955305034347331332472666929267055001600000⟩ +] + +def collectedFourData_8_2_17 : List CollectedFourTerm := [ + ⟨2, 2, 4, 0, 6, 2, 1247651070030501104467865635761101387616328089600000⟩, + ⟨2, 2, 5, 0, 7, 2, 16128700585781290398528934698465153909365145600000⟩, + ⟨2, 2, 6, 0, 8, 2, 496803995911274460069512311401584885733575884800000⟩, + ⟨2, 2, 4, 1, 5, 2, -1933386145306314280692113810300996155079110164480000⟩, + ⟨2, 2, 5, 1, 6, 2, -2661110483785255070937785346155064167083750195200000⟩, + ⟨2, 2, 6, 1, 7, 2, -1661524546170097061433292632248918239736758272000000⟩, + ⟨2, 2, 7, 1, 8, 2, -1041180758645143770616529499672318733737315532800000⟩, + ⟨2, 2, 4, 2, 4, 2, 515478131041933919293114853245958393489491230720000⟩, + ⟨2, 2, 5, 2, 5, 2, 465486321134729811116476769748386149368122572800000⟩, + ⟨2, 2, 6, 2, 6, 2, 114694404782948597965928222388301866458519961600000⟩, + ⟨2, 2, 7, 2, 7, 2, 61472504572989237537596867028026804976746496000000⟩, + ⟨2, 2, 8, 2, 8, 2, 248439180364873595625553186832740788315409612800000⟩, + ⟨2, 2, 4, 3, 3, 2, -657483718171426275601540371766185334214649446400000⟩, + ⟨2, 2, 5, 3, 4, 2, -630016304443766162286170281793915082418579046400000⟩, + ⟨2, 2, 6, 3, 5, 2, -279411447980668614320173748586647591694473625600000⟩, + ⟨2, 2, 7, 3, 6, 2, 47999028278528283368450333133127900759641292800000⟩, + ⟨2, 2, 8, 3, 7, 2, 152183099699810538959678364202587389096361984000000⟩, + ⟨2, 2, 4, 4, 2, 2, 2191989576241514409003200559750714727473642209280000⟩, + ⟨2, 2, 5, 4, 3, 2, 58765657390877400849271625739519208762795622400000⟩, + ⟨2, 2, 6, 4, 4, 2, 129127012211471009490220020565937839908323328000000⟩, + ⟨2, 2, 7, 4, 5, 2, 165256335575117059651226062099035244782944256000000⟩, + ⟨2, 2, 8, 4, 6, 2, -194115369871264676511853960853364260724119961600000⟩, + ⟨2, 2, 4, 5, 1, 2, -2113351541084039848618485060883232523075673128960000⟩, + ⟨2, 2, 5, 5, 2, 2, 4564370354451656413032879942067306555523884646400000⟩, + ⟨2, 2, 6, 5, 3, 2, 47832006111700205487286919845979365216931020800000⟩, + ⟨2, 2, 7, 5, 4, 2, -104716613665482232133630839855409356848758784000000⟩, + ⟨2, 2, 8, 5, 5, 2, -64886901962581656455988923503761990870053683200000⟩, + ⟨2, 2, 4, 6, 0, 2, -6593706699223043547481264007372461529235581829120000⟩, + ⟨2, 2, 5, 6, 1, 2, -5831300554596027078640750997259267474355912704000000⟩, + ⟨2, 2, 6, 6, 2, 2, 3427305422004172088391033861481643016178158796800000⟩, + ⟨2, 2, 7, 6, 3, 2, -313994697358134331302246466621984924737365606400000⟩, + ⟨2, 2, 8, 6, 4, 2, 96658980397645114995908927461986375279260467200000⟩, + ⟨2, 2, 5, 7, 0, 2, -25441558289151600071919739548481725189412041523200000⟩, + ⟨2, 2, 6, 7, 1, 2, -6794475645252634754017400725141063476326065766400000⟩, + ⟨2, 2, 7, 7, 2, 2, 557595474950152385586983339654348007018174873600000⟩, + ⟨2, 2, 8, 7, 3, 2, 462943211679376018913808795200965805339364556800000⟩ +] + +def collectedFourData_8_2_18 : List CollectedFourTerm := [ + ⟨2, 3, 3, 0, 5, 3, 37196410187769632769523802109636892288465502208000000⟩, + ⟨2, 3, 4, 0, 6, 3, 39040072815978698633386333203276575791542750412800000⟩, + ⟨2, 3, 5, 0, 7, 3, 252340442140055449826396177323214788131972710400000⟩, + ⟨2, 3, 6, 0, 8, 3, 5181807809767193431843213134174251105018236108800000⟩, + ⟨2, 3, 3, 1, 4, 3, -35582423147757123186982913556413347610041956433920000⟩, + ⟨2, 3, 4, 1, 5, 3, -60497311874479174330532409707953001672173305200640000⟩, + ⟨2, 3, 5, 1, 6, 3, -41634215508588022480195385733674884929680100556800000⟩, + ⟨2, 3, 6, 1, 7, 3, -17330176367989056934299235513531526773192261632000000⟩, + ⟨2, 3, 7, 1, 8, 3, -8144859890816397658157628635776366285503961497600000⟩, + ⟨2, 3, 3, 2, 3, 3, 24682763079187531556921625035538568966958041006080000⟩, + ⟨2, 3, 4, 2, 4, 3, 16129753145188048838278601501809929501939817512960000⟩, + ⟨2, 3, 5, 2, 5, 3, 7282733253095207645742062196138654009146946355200000⟩, + ⟨2, 3, 6, 2, 6, 3, 1196295455214141935332494082922928174844713369600000⟩, + ⟨2, 3, 7, 2, 7, 3, 480881857186924398029910353185559603400671232000000⟩, + ⟨2, 3, 8, 2, 8, 3, 1554775036829747398634991045753700562501715886080000⟩, + ⟨2, 3, 3, 3, 2, 3, -16276128738693049296361920418139222027049558343680000⟩, + ⟨2, 3, 4, 3, 3, 3, -20573229847112135795730416334114018444071613235200000⟩, + ⟨2, 3, 5, 3, 4, 3, -9856875448412489226293805895576934109253573017600000⟩, + ⟨2, 3, 6, 3, 5, 3, -2914341340247925548797909549738028205063379353600000⟩, + ⟨2, 3, 7, 3, 6, 3, 375482697867632638496269494198216741615147417600000⟩, + ⟨2, 3, 8, 3, 7, 3, 952387961082212681614004106838082076501501542400000⟩, + ⟨2, 3, 3, 4, 1, 3, 15028307516897388117618477966848816653650792284160000⟩, + ⟨2, 3, 4, 4, 2, 3, 68589235182752631573779002215855403059683304407040000⟩, + ⟨2, 3, 5, 4, 3, 3, 919413928592480682079480873553550793749666201600000⟩, + ⟨2, 3, 6, 4, 4, 3, 1346831679769344286793407575288419505791827968000000⟩, + ⟨2, 3, 7, 4, 5, 3, 1292753144113574051180688841663413069023281152000000⟩, + ⟨2, 3, 8, 4, 6, 3, -1214807305746076228134529772752975510822988021760000⟩, + ⟨2, 3, 3, 5, 0, 3, -18051098623286430967812298058068440459556568432640000⟩, + ⟨2, 3, 4, 5, 1, 3, -66128583569174287770855449994805348681987160801280000⟩, + ⟨2, 3, 5, 5, 2, 3, 71411532950687449631593544527134938289927723417600000⟩, + ⟨2, 3, 6, 5, 3, 3, 498901508172864128223479151098380547800222924800000⟩, + ⟨2, 3, 7, 5, 4, 3, -819168179458058386548597820041748949162262528000000⟩, + ⟨2, 3, 8, 5, 5, 3, -406073370715825309105287823086346503921881579520000⟩, + ⟨2, 3, 4, 6, 0, 3, -206322741869312150111979621283831857688673947484160000⟩, + ⟨2, 3, 5, 6, 1, 3, -91233199622760087577303107056356230545157390336000000⟩, + ⟨2, 3, 6, 6, 2, 3, 35747776081435557336028902218069007516534885580800000⟩, + ⟨2, 3, 7, 6, 3, 3, -2456290893974282462472398339499269899229646028800000⟩, + ⟨2, 3, 8, 6, 4, 3, 604908491434239073034314144252580803314104401920000⟩, + ⟨2, 3, 5, 7, 0, 3, -398044097431889887496005816384596273027139554508800000⟩, + ⟨2, 3, 6, 7, 1, 3, -70868324835557329170622601411583808391315088998400000⟩, + ⟨2, 3, 7, 7, 2, 3, 4361910246143980631858380759954394333672846131200000⟩, + ⟨2, 3, 8, 7, 3, 3, 2897178085726170930706174642432204416397848084480000⟩ +] + +def collectedFourData_8_2_19 : List CollectedFourTerm := [ + ⟨2, 4, 2, 0, 4, 4, -3536339658139837297169588899668331401812083998720000⟩, + ⟨2, 4, 3, 0, 5, 4, 24307202248429589155625391508368271571467370496000000⟩, + ⟨2, 4, 4, 0, 6, 4, 12756001734321037744454275736126098085371497676800000⟩, + ⟨2, 4, 5, 0, 7, 4, 54966685688155114249517952478501013051513241600000⟩, + ⟨2, 4, 6, 0, 8, 4, 846555150138640599603796470289025528282637926400000⟩, + ⟨2, 4, 2, 1, 3, 4, 2111355616726211244703187829597753166083580231680000⟩, + ⟨2, 4, 3, 1, 4, 4, -23252490000395831093711591959913488893502071767040000⟩, + ⟨2, 4, 4, 1, 5, 4, -19766966594303242604360687817470698974122700963840000⟩, + ⟨2, 4, 5, 1, 6, 4, -9069076753314466066631091808003442212640863027200000⟩, + ⟨2, 4, 6, 1, 7, 4, -2831241643018641593503161723272634088235728896000000⟩, + ⟨2, 4, 7, 1, 8, 4, -1064504642527534727951283217803360541706802954240000⟩, + ⟨2, 4, 2, 2, 2, 4, 515478131041933919293114853245958393489491230720000⟩, + ⟨2, 4, 3, 2, 3, 4, 16129753145188048838278601501809929501939817512960000⟩, + ⟨2, 4, 4, 2, 4, 4, 5270255515762694471670652383316678660771817717760000⟩, + ⟨2, 4, 5, 2, 5, 4, 1586379520772094827861453712273615516609596620800000⟩, + ⟨2, 4, 6, 2, 6, 4, 195439529190967994136008401913792734532783308800000⟩, + ⟨2, 4, 7, 2, 7, 4, 62849573392898931571373970252992045747326156800000⟩, + ⟨2, 4, 8, 2, 8, 4, 169336373592025239143808639344831352264626012160000⟩, + ⟨2, 4, 2, 3, 1, 4, 2954238366191597356364652698442219203573317632000000⟩, + ⟨2, 4, 3, 3, 2, 4, -10636164916876127570437186695640340984697622364160000⟩, + ⟨2, 4, 4, 3, 3, 4, -6722122595604815861849285857467606945152316211200000⟩, + ⟨2, 4, 5, 3, 4, 4, -2147098459704962612047772599151941128280237670400000⟩, + ⟨2, 4, 6, 3, 5, 4, -476117749137375479047100593850915307284909260800000⟩, + ⟨2, 4, 7, 3, 6, 4, 49074272661158630050251654802696903279761162240000⟩, + ⟨2, 4, 8, 3, 7, 4, 103728140574734958588162926270610929745710284800000⟩, + ⟨2, 4, 2, 4, 0, 4, -11313456903298002498068665754520955641566110679040000⟩, + ⟨2, 4, 3, 4, 1, 4, 9820735614560210743510263661203649001135454289920000⟩, + ⟨2, 4, 4, 4, 2, 4, 22410931636091841147861989038927774077256193802240000⟩, + ⟨2, 4, 5, 4, 3, 4, 200273630345013672866866013501261788769314406400000⟩, + ⟨2, 4, 6, 4, 4, 4, 220032725399331210132058029166166501599739904000000⟩, + ⟨2, 4, 7, 4, 5, 4, 168958305237713495665590641517576568234101964800000⟩, + ⟨2, 4, 8, 4, 6, 4, -132309214449180264975094423381003926125433323520000⟩, + ⟨2, 4, 3, 5, 0, 4, -11796076632869333860696678211334626189829136711680000⟩, + ⟨2, 4, 4, 5, 1, 4, -21606935280902708455544269680282174554082304327680000⟩, + ⟨2, 4, 5, 5, 2, 4, 15555395135715706366269691746334914679239239270400000⟩, + ⟨2, 4, 6, 5, 3, 4, 81505848279357222833163274152986070110070374400000⟩, + ⟨2, 4, 7, 5, 4, 4, -107062410125329529588965943834648441915650867200000⟩, + ⟨2, 4, 8, 5, 5, 4, -44226971993014905207646729116250694170485719040000⟩, + ⟨2, 4, 4, 6, 0, 4, -67414148163105556984778663783173011114623458344960000⟩, + ⟨2, 4, 5, 6, 1, 4, -19873099077815000591128632120858590736593977344000000⟩, + ⟨2, 4, 6, 6, 2, 4, 5840136311250379171928042700048194458628810342400000⟩, + ⟨2, 4, 7, 6, 3, 4, -321028611306368985553032136477616205406006149120000⟩, + ⟨2, 4, 8, 6, 4, 4, 65882849845185309285018990927767643237478563840000⟩, + ⟨2, 4, 5, 7, 0, 4, -86704947522524278204385561134346383181999190835200000⟩, + ⟨2, 4, 6, 7, 1, 4, -11577802105696887193656800984013298682775679795200000⟩, + ⟨2, 4, 7, 7, 2, 4, 570086382031462045295020809848195503818151034880000⟩, + ⟨2, 4, 8, 7, 3, 4, 315542518413149271722685187211705203846765608960000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0809.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0809.lean new file mode 100644 index 0000000000000000000000000000000000000000..1c81b3c320814e599a026bc7df270c91bb05e8a5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0809.lean @@ -0,0 +1,625 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0809. -/ +namespace LaughlinFock +def collectedFourData_8_2_20 : List CollectedFourTerm := [ + ⟨2, 5, 1, 0, 3, 5, -1706926771282276991856350042546304558256304947200000⟩, + ⟨2, 5, 2, 0, 4, 5, -3193380356258896242198416460440674229166066892800000⟩, + ⟨2, 5, 3, 0, 5, 5, 10974927422070286440303614986412003746664939520000000⟩, + ⟨2, 5, 4, 0, 6, 5, 3839635451779751064670571164556503637393670144000000⟩, + ⟨2, 5, 5, 0, 7, 5, 12408984380302885822984650058994334088298496000000⟩, + ⟨2, 5, 6, 0, 8, 5, 152891003030209276994567238476834544840553267200000⟩, + ⟨2, 5, 1, 1, 2, 5, -500928345088942921497725806301587878105317376000000⟩, + ⟨2, 5, 2, 1, 3, 5, 1906593314929749657631733690374506429770052403200000⟩, + ⟨2, 5, 3, 1, 4, 5, -10498715052788382021467593775741374324366167244800000⟩, + ⟨2, 5, 4, 1, 5, 5, -5949979256072325199579911166669442132913369907200000⟩, + ⟨2, 5, 5, 1, 6, 5, -2047386164305305251983163939640421127534149632000000⟩, + ⟨2, 5, 6, 1, 7, 5, -511332751978564355351630630053357588743979008000000⟩, + ⟨2, 5, 7, 1, 8, 5, -160211242094598538639414038688708033773148569600000⟩, + ⟨2, 5, 1, 2, 1, 5, -1835016851408069596496327955805746302674167398400000⟩, + ⟨2, 5, 2, 2, 2, 5, 465486321134729811116476769748386149368122572800000⟩, + ⟨2, 5, 3, 2, 3, 5, 7282733253095207645742062196138654009146946355200000⟩, + ⟨2, 5, 4, 2, 4, 5, 1586379520772094827861453712273615516609596620800000⟩, + ⟨2, 5, 5, 2, 5, 5, 358132538792225945161008949759573541674549248000000⟩, + ⟨2, 5, 6, 2, 6, 5, 35297104559419844409397709290310985939576422400000⟩, + ⟨2, 5, 7, 2, 7, 5, 9459055241397424992304470648704038990774272000000⟩, + ⟨2, 5, 8, 2, 8, 5, 21844841248460191353660944846704565174874931200000⟩, + ⟨2, 5, 1, 3, 0, 5, -1610482852222562218934752323217286886228964147200000⟩, + ⟨2, 5, 2, 3, 1, 5, 2667732084102192396765628337767277548724551680000000⟩, + ⟨2, 5, 3, 3, 2, 5, -4802327179362131974738308370565883466989384499200000⟩, + ⟨2, 5, 4, 3, 3, 5, -2023400495458444885867005301939977393480400896000000⟩, + ⟨2, 5, 5, 3, 4, 5, -484717441408199891887018499529710046202036224000000⟩, + ⟨2, 5, 6, 3, 5, 5, -85988633125883622690328167901205680187926118400000⟩, + ⟨2, 5, 7, 3, 6, 5, 7385829862860233549370147277010411003156889600000⟩, + ⟨2, 5, 8, 3, 7, 5, 13381205205871725098419984620410236972302336000000⟩, + ⟨2, 5, 2, 4, 0, 5, -10216261595012440929192265530688970276522793369600000⟩, + ⟨2, 5, 3, 4, 1, 5, 4434153280972621450278952944806711438040524390400000⟩, + ⟨2, 5, 4, 4, 2, 5, 6745829093596526976609704189926918007909724979200000⟩, + ⟨2, 5, 5, 4, 3, 5, 45212701468616435140220884527938627262480384000000⟩, + ⟨2, 5, 6, 4, 4, 5, 39738727099191296447996972718491945656123392000000⟩, + ⟨2, 5, 7, 4, 5, 5, 25428747666201201652434283955508908069486592000000⟩, + ⟨2, 5, 8, 4, 6, 5, -17068239528467930631829835065408624290850406400000⟩, + ⟨2, 5, 3, 5, 0, 5, -5326038084834886784746402358352075832774203801600000⟩, + ⟨2, 5, 4, 5, 1, 5, -6503821215831824483500241481762315764586931814400000⟩, + ⟨2, 5, 5, 5, 2, 5, 3511702640461937213783614005343278555646132224000000⟩, + ⟨2, 5, 6, 5, 3, 5, 14720258797336661687805329461944898007806771200000⟩, + ⟨2, 5, 7, 5, 4, 5, -16113223956537788324142883457202438367346688000000⟩, + ⟨2, 5, 8, 5, 5, 5, -5705396670506027733344571200481592966171852800000⟩, + ⟨2, 5, 4, 6, 0, 5, -20292075732644954376610492498053878270642670796800000⟩, + ⟨2, 5, 5, 6, 1, 5, -4486444342740487398535346723052885390278000640000000⟩, + ⟨2, 5, 6, 6, 2, 5, 1054750299864085331278818430370855559516861235200000⟩, + ⟨2, 5, 7, 6, 3, 5, -48315799208895505394461959622822852563881164800000⟩, + ⟨2, 5, 8, 6, 4, 5, 8499062341630251883477678641353698237533388800000⟩, + ⟨2, 5, 5, 7, 0, 5, -19574044278493536384891190136798605190325338112000000⟩, + ⟨2, 5, 6, 7, 1, 5, -2090994043962014122520504247541480802221660569600000⟩, + ⟨2, 5, 7, 7, 2, 5, 85799764244911578978120500306999972835046195200000⟩, + ⟨2, 5, 8, 7, 3, 5, 40705821647518686725252648955108823785485107200000⟩ +] + +def collectedFourData_8_2_21 : List CollectedFourTerm := [ + ⟨2, 6, 0, 0, 2, 6, -398577164386650389054516441540667261608106393600000⟩, + ⟨2, 6, 1, 0, 3, 6, -841163063881467431531208541930554910988618956800000⟩, + ⟨2, 6, 2, 0, 4, 6, -786839145592559222458635361627248630464879001600000⟩, + ⟨2, 6, 3, 0, 5, 6, 1802792350076494411179630781373148033932328960000000⟩, + ⟨2, 6, 4, 0, 6, 6, 473037211546676205095712160984454172701097984000000⟩, + ⟨2, 6, 5, 0, 7, 6, 1223014308124259174413588111696014800112844800000⟩, + ⟨2, 6, 6, 0, 8, 6, 12557291727692766333334787379842462948052172800000⟩, + ⟨2, 6, 0, 1, 1, 6, 2936602311312065481507703935423628105489789747200000⟩, + ⟨2, 6, 1, 1, 2, 6, -246854422011058219751950629109967892925906944000000⟩, + ⟨2, 6, 2, 1, 3, 6, 469778757162927024976186830210098653068420710400000⟩, + ⟨2, 6, 3, 1, 4, 6, -1724567503265500919903692684026975274926499430400000⟩, + ⟨2, 6, 4, 1, 5, 6, -733028338601366866935933787151649393511445299200000⟩, + ⟨2, 6, 5, 1, 6, 6, -201787873726045824208177376340858732178676121600000⟩, + ⟨2, 6, 6, 1, 7, 6, -41996941672559411050402125908505344021102592000000⟩, + ⟨2, 6, 7, 1, 8, 6, -11278731338001674096796502517680187641115443200000⟩, + ⟨2, 6, 0, 2, 0, 6, 472180770156850178917725362117385884734901452800000⟩, + ⟨2, 6, 1, 2, 1, 6, -904285071259964675917145007255705364064737689600000⟩, + ⟨2, 6, 2, 2, 2, 6, 114694404782948597965928222388301866458519961600000⟩, + ⟨2, 6, 3, 2, 3, 6, 1196295455214141935332494082922928174844713369600000⟩, + ⟨2, 6, 4, 2, 4, 6, 195439529190967994136008401913792734532783308800000⟩, + ⟨2, 6, 5, 2, 5, 6, 35297104559419844409397709290310985939576422400000⟩, + ⟨2, 6, 6, 2, 6, 6, 2899032842422596649926020356594789921692057600000⟩, + ⟨2, 6, 7, 2, 7, 6, 665909217007655984290076928269400171085824000000⟩, + ⟨2, 6, 8, 2, 8, 6, 1345625505418966926307290556028139876227481600000⟩, + ⟨2, 6, 1, 3, 0, 6, -793636090953353363673950169317137626375703756800000⟩, + ⟨2, 6, 2, 3, 1, 6, 657321020219443119016692098003179270003752960000000⟩, + ⟨2, 6, 3, 3, 2, 6, -788852478797106250327468224042622192149174681600000⟩, + ⟨2, 6, 4, 3, 3, 6, -249279844462882477780545142736885249218707456000000⟩, + ⟨2, 6, 5, 3, 4, 6, -47773157582549951863519100796723875022058291200000⟩, + ⟨2, 6, 6, 3, 5, 6, -7062445337047826335518699245018714830641561600000⟩, + ⟨2, 6, 7, 3, 6, 6, 519955963403637110225762185847500117848883200000⟩, + ⟨2, 6, 8, 3, 7, 6, 824272001497620067209918145205593228443648000000⟩, + ⟨2, 6, 2, 4, 0, 6, -2517255587426165434840432779307300118185849651200000⟩, + ⟨2, 6, 3, 4, 1, 6, 728374531017726451560308035534103488746435379200000⟩, + ⟨2, 6, 4, 4, 2, 6, 831075820629334811674969427867469650068714291200000⟩, + ⟨2, 6, 5, 4, 3, 6, 4456108502549256493369758024315482206843699200000⟩, + ⟨2, 6, 6, 4, 4, 6, 3263833575433586337296076224762616383275008000000⟩, + ⟨2, 6, 7, 4, 5, 6, 1790161598145364577865425591173170818187264000000⟩, + ⟨2, 6, 8, 4, 6, 6, -1051390494482334086980942961631932254991155200000⟩, + ⟨2, 6, 3, 5, 0, 6, -874879654898450851845622045234027104280825036800000⟩, + ⟨2, 6, 4, 5, 1, 6, -801260820453450809067706627475343421020202598400000⟩, + ⟨2, 6, 5, 5, 2, 6, 346109112844081013281005186589861919904183091200000⟩, + ⟨2, 6, 6, 5, 3, 6, 1209008904132632619886762729252401456139468800000⟩, + ⟨2, 6, 7, 5, 4, 6, -1134356875452807335055304272802210954346496000000⟩, + ⟨2, 6, 8, 5, 5, 6, -351448069182307628639674252409164897085030400000⟩, + ⟨2, 6, 4, 6, 0, 6, -2499952675615351033004642058428750077031664844800000⟩, + ⟨2, 6, 5, 6, 1, 6, -442178461638197686418918771278986973997432832000000⟩, + ⟨2, 6, 6, 6, 2, 6, 86629081847594011293072403747753187496217804800000⟩, + ⟨2, 6, 7, 6, 3, 6, -3401390011920634794867585373231348933302681600000⟩, + ⟨2, 6, 8, 6, 4, 6, 523535736834419023026493685434959264114278400000⟩, + ⟨2, 6, 5, 7, 0, 6, -1929193839461587008820048633258629484118645145600000⟩, + ⟨2, 6, 6, 7, 1, 6, -171738177463005840483120174066260560755189350400000⟩, + ⟨2, 6, 7, 7, 2, 6, 6040228370558683972170144070742477801678438400000⟩, + ⟨2, 6, 8, 7, 3, 6, 2507447465739658194497771584086905642916249600000⟩ +] + +def collectedFourData_8_2_22 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 2, 7, -640873544096984056035457976155812212137525248000000⟩, + ⟨2, 7, 1, 0, 3, 7, -676254439642515181970103681264961705016819712000000⟩, + ⟨2, 7, 2, 0, 4, 7, -421720423652579657140513291556445566477008896000000⟩, + ⟨2, 7, 3, 0, 5, 7, 724678949208229205076257817817361230803763200000000⟩, + ⟨2, 7, 4, 0, 6, 7, 152119620159466846336557281003426350444314624000000⟩, + ⟨2, 7, 5, 0, 7, 7, 327748126821339591007477064108326250348544000000⟩, + ⟨2, 7, 6, 0, 8, 7, 2884415857509509785474534451229622347497472000000⟩, + ⟨2, 7, 0, 1, 1, 7, 4721772592642269611401939546789886117906743296000000⟩, + ⟨2, 7, 1, 1, 2, 7, -198459021797810417960473204102816209001512960000000⟩, + ⟨2, 7, 2, 1, 3, 7, 251786273730107373579003741026456435712589824000000⟩, + ⟨2, 7, 3, 1, 4, 7, -693234451572902466397286224615608281116704768000000⟩, + ⟨2, 7, 4, 1, 5, 7, -235727739197452334908840528203304230024590131200000⟩, + ⟨2, 7, 5, 1, 6, 7, -54075898531722737166497355697754772810498048000000⟩, + ⟨2, 7, 6, 1, 7, 7, -9646717393694695256878490547466981689262080000000⟩, + ⟨2, 7, 7, 1, 8, 7, -2266888689115573841468890801520694182019072000000⟩, + ⟨2, 7, 0, 2, 0, 7, 759221025847107766790274761043895318902472704000000⟩, + ⟨2, 7, 1, 2, 1, 7, -727001482114736168611996875832132876332171264000000⟩, + ⟨2, 7, 2, 2, 2, 7, 61472504572989237537596867028026804976746496000000⟩, + ⟨2, 7, 3, 2, 3, 7, 480881857186924398029910353185559603400671232000000⟩, + ⟨2, 7, 4, 2, 4, 7, 62849573392898931571373970252992045747326156800000⟩, + ⟨2, 7, 5, 2, 5, 7, 9459055241397424992304470648704038990774272000000⟩, + ⟨2, 7, 6, 2, 6, 7, 665909217007655984290076928269400171085824000000⟩, + ⟨2, 7, 7, 2, 7, 7, 133839704730471823820343134491797136343040000000⟩, + ⟨2, 7, 8, 2, 8, 7, 240403967952747864526154980029423767519232000000⟩, + ⟨2, 7, 1, 3, 0, 7, -638045050969291383682554099531977139224051712000000⟩, + ⟨2, 7, 2, 3, 1, 7, 352302882584634383953950932961180817922457600000000⟩, + ⟨2, 7, 3, 3, 2, 7, -317099629023130432577880539541021875106742272000000⟩, + ⟨2, 7, 4, 3, 3, 7, -80163577679475910920858028111056135537033216000000⟩, + ⟨2, 7, 5, 3, 4, 7, -12802436411423080878363714546908044550209536000000⟩, + ⟨2, 7, 6, 3, 5, 7, -1622247038989333716957561449092086742646784000000⟩, + ⟨2, 7, 7, 3, 6, 7, 104504864683365265159706167588231915241472000000⟩, + ⟨2, 7, 8, 3, 7, 7, 147261076008427526090680715679030533160960000000⟩, + ⟨2, 7, 2, 4, 0, 7, -1349167868321706202870232013298120071076380672000000⟩, + ⟨2, 7, 3, 4, 1, 7, 292788955835965265828460845738495241055371264000000⟩, + ⟨2, 7, 4, 4, 2, 7, 267257913483148941241174918448786610064667443200000⟩, + ⟨2, 7, 5, 4, 3, 7, 1194165272574045292755960734071143348043776000000⟩, + ⟨2, 7, 6, 4, 4, 7, 749704118165162657090496707708214753361920000000⟩, + ⟨2, 7, 7, 4, 5, 7, 359800846115710877716473930350536886845440000000⟩, + ⟨2, 7, 8, 4, 6, 7, -187837140217297846957419882498236092514304000000⟩, + ⟨2, 7, 3, 5, 0, 7, -351680474442087558949711875629035267823763456000000⟩, + ⟨2, 7, 4, 5, 1, 7, -257669985956304927574013020049538917002012262400000⟩, + ⟨2, 7, 5, 5, 2, 7, 92751665010707261621531754043937057497153536000000⟩, + ⟨2, 7, 6, 5, 3, 7, 277709917916440880482904629598725720768512000000⟩, + ⟨2, 7, 7, 5, 4, 7, -227992022624067136203216158887113822044160000000⟩, + ⟨2, 7, 8, 5, 5, 7, -62788279517972115924524402484874479403008000000⟩, + ⟨2, 7, 4, 6, 0, 7, -803936439139366380188266518873395956277890252800000⟩, + ⟨2, 7, 5, 6, 1, 7, -118496702417921799294587941735011441400872960000000⟩, + ⟨2, 7, 6, 6, 2, 7, 19898741131548150617263898544910537328689152000000⟩, + ⟨2, 7, 7, 6, 3, 7, -683638284681378533917375326941725260251136000000⟩, + ⟨2, 7, 8, 6, 4, 7, 93532760781665458439882752338952577875968000000⟩, + ⟨2, 7, 5, 7, 0, 7, -516992861783070949993626718825606020247584768000000⟩, + ⟨2, 7, 6, 7, 1, 7, -39448340705635011865747968357172970935812096000000⟩, + ⟨2, 7, 7, 7, 2, 7, 1214012902919316024252411922565494487384064000000⟩, + ⟨2, 7, 8, 7, 3, 7, 447970343731847502092454605615819592302592000000⟩ +] + +def collectedFourData_8_2_23 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 2, 8, -5180140263325017110748487250693947703482436812800000⟩, + ⟨2, 8, 1, 0, 3, 8, -3644081200637364034877363830472337710035815628800000⟩, + ⟨2, 8, 2, 0, 4, 8, -1704369736082145387662342615026294730179529932800000⟩, + ⟨2, 8, 3, 0, 5, 8, 2343013617806339482434299169599369098410590208000000⟩, + ⟨2, 8, 4, 0, 6, 8, 409857751443558403130834104030943895259761868800000⟩, + ⟨2, 8, 5, 0, 7, 8, 756904956909274078286615241368692098229862400000⟩, + ⟨2, 8, 6, 0, 8, 8, 5828637668571409839745837068581039541898444800000⟩, + ⟨2, 8, 0, 1, 1, 8, 38165788784236820138277790932798894625716279705600000⟩, + ⟨2, 8, 1, 1, 2, 8, -1069421135057662036212558370376533011232456704000000⟩, + ⟨2, 8, 2, 1, 3, 8, 1017586251075238615571000870017045640221242163200000⟩, + ⟨2, 8, 3, 1, 4, 8, -2241348064742951061005654272971588070214121553920000⟩, + ⟨2, 8, 4, 1, 5, 8, -635124128229219457204343622619338842964429373440000⟩, + ⟨2, 8, 5, 1, 6, 8, -124883446459163452046058376383289105769614540800000⟩, + ⟨2, 8, 6, 1, 7, 8, -19493451414977369352821440771041614125596672000000⟩, + ⟨2, 8, 7, 1, 8, 8, -4071803930440917497366025689149730694207897600000⟩, + ⟨2, 8, 0, 2, 0, 8, 6136735462056085362705839227772367046877537894400000⟩, + ⟨2, 8, 1, 2, 1, 8, -3917537953924962408506415640904355481076210073600000⟩, + ⟨2, 8, 2, 2, 2, 8, 248439180364873595625553186832740788315409612800000⟩, + ⟨2, 8, 3, 2, 3, 8, 1554775036829747398634991045753700562501715886080000⟩, + ⟨2, 8, 4, 2, 4, 8, 169336373592025239143808639344831352264626012160000⟩, + ⟨2, 8, 5, 2, 5, 8, 21844841248460191353660944846704565174874931200000⟩, + ⟨2, 8, 6, 2, 6, 8, 1345625505418966926307290556028139876227481600000⟩, + ⟨2, 8, 7, 2, 7, 8, 240403967952747864526154980029423767519232000000⟩, + ⟨2, 8, 8, 2, 8, 8, 388634009103883303697304859658014356972503040000⟩, + ⟨2, 8, 1, 3, 0, 8, -3438185155022423913719790226330626289008692428800000⟩, + ⟨2, 8, 2, 3, 1, 8, 1423820942346431671663851644574926341071175680000000⟩, + ⟨2, 8, 3, 3, 2, 8, -1025238486386677650284291785475929839257706823680000⟩, + ⟨2, 8, 4, 3, 3, 8, -215985706912352691114908628044143308936786739200000⟩, + ⟨2, 8, 5, 3, 4, 8, -29566080741032569119581534777092730766596505600000⟩, + ⟨2, 8, 6, 3, 5, 8, -3278130015325118132781230797673514585921945600000⟩, + ⟨2, 8, 7, 3, 6, 8, 187712489285894646864634549853275184273817600000⟩, + ⟨2, 8, 8, 3, 7, 8, 238060389940634158454405930294029352907571200000⟩, + ⟨2, 8, 2, 4, 0, 8, -5452619210959362777682516158288968852784650649600000⟩, + ⟨2, 8, 3, 4, 1, 8, 946637833783478492711832938012533610378334044160000⟩, + ⟨2, 8, 4, 4, 2, 8, 720076262094739680165772588993129803761414307840000⟩, + ⟨2, 8, 5, 4, 3, 8, 2757817788148403791044566548805288501811609600000⟩, + ⟨2, 8, 6, 4, 4, 8, 1514952725018490695585561507032252891004928000000⟩, + ⟨2, 8, 7, 4, 5, 8, 646277210885684795674299955629764905009152000000⟩, + ⟨2, 8, 8, 4, 6, 8, -303655141314493985256014383899225394910330880000⟩, + ⟨2, 8, 3, 5, 0, 8, -1137044399640260046791899624929422504188591472640000⟩, + ⟨2, 8, 4, 5, 1, 8, -694243391798083673303881413339167085718017146880000⟩, + ⟨2, 8, 5, 5, 2, 8, 214201666655023055158915396596226634165098905600000⟩, + ⟨2, 8, 6, 5, 3, 8, 561177919019364180065109486093580286872780800000⟩, + ⟨2, 8, 7, 5, 4, 8, -409521128358553126930287544019217996054528000000⟩, + ⟨2, 8, 8, 5, 5, 8, -101502737253492279975285335778699496925429760000⟩, + ⟨2, 8, 4, 6, 0, 8, -2166055771791881680979555698520888449271448207360000⟩, + ⟨2, 8, 5, 6, 1, 8, -273657525696309893610329230932490719137366016000000⟩, + ⟨2, 8, 6, 6, 2, 8, 40210066039726881241738205134300111906327756800000⟩, + ⟨2, 8, 7, 6, 3, 8, -1227956656156575990528670296840792722689228800000⟩, + ⟨2, 8, 8, 6, 4, 8, 151203876186760024884410025483675536153640960000⟩, + ⟨2, 8, 5, 7, 0, 8, -1193948729975896933934156746486738655371906252800000⟩, + ⟨2, 8, 6, 7, 1, 8, -79714609805963123409548347705798192756319846400000⟩, + ⟨2, 8, 7, 7, 2, 8, 2180619866095611532993160921425670718042931200000⟩, + ⟨2, 8, 8, 7, 3, 8, 724183182693439389638605053419047820187402240000⟩ +] + +def collectedFourData_8_2_24 : List CollectedFourTerm := [ + ⟨3, 0, 5, 0, 7, 1, -55801845387664121092696924796820257572808294400000⟩, + ⟨3, 0, 6, 0, 8, 1, -3437670582372181359938767456621505466167879270400000⟩, + ⟨3, 0, 5, 1, 6, 1, 9206871625268231934246435333971751588724526284800000⟩, + ⟨3, 0, 6, 1, 7, 1, 11497037264729071825447094825618128653627949056000000⟩, + ⟨3, 0, 7, 1, 8, 1, 10806786462217545138121587512236255786923825561600000⟩, + ⟨3, 0, 5, 2, 5, 1, -1610482852222562218934752323217286886228964147200000⟩, + ⟨3, 0, 6, 2, 6, 1, -793636090953353363673950169317137626375703756800000⟩, + ⟨3, 0, 7, 2, 7, 1, -638045050969291383682554099531977139224051712000000⟩, + ⟨3, 0, 8, 2, 8, 1, -3438185155022423913719790226330626289008692428800000⟩, + ⟨3, 0, 5, 3, 4, 1, 2179721312656234185238431906525611618932988313600000⟩, + ⟨3, 0, 6, 3, 5, 1, 1933407386024129618839970817789462856774503628800000⟩, + ⟨3, 0, 7, 3, 6, 1, -498199034791023836232119991579136245693520281600000⟩, + ⟨3, 0, 8, 3, 7, 1, -2106083563247680215539818801586481250607038464000000⟩, + ⟨3, 0, 5, 4, 3, 1, -203316572862731506452818168984955911371594137600000⟩, + ⟨3, 0, 6, 4, 4, 1, -893503544501006597571175007683149890001567744000000⟩, + ⟨3, 0, 7, 4, 5, 1, -1715254450545914730456723971568141888160530432000000⟩, + ⟨3, 0, 8, 4, 6, 1, 2686390214590454055248819821493693121449007513600000⟩, + ⟨3, 0, 5, 5, 2, 1, -15791742642658219825253879824350174210785122713600000⟩, + ⟨3, 0, 6, 5, 3, 1, -330976968098711294764559818895242423716701798400000⟩, + ⟨3, 0, 7, 5, 4, 1, 1086891083544397543715869724091702739571048448000000⟩, + ⟨3, 0, 8, 5, 5, 1, 897979065763680207251430156292731264824455987200000⟩, + ⟨3, 0, 5, 6, 1, 1, 20175049454599629332396951016473764512342736896000000⟩, + ⟨3, 0, 6, 6, 2, 1, -23715483617270635140119439036266677081909651046400000⟩, + ⟨3, 0, 7, 6, 3, 1, 3259062959474532577319005473385648599493037260800000⟩, + ⟨3, 0, 8, 6, 4, 1, -1337677378482346259153101287393290392658195251200000⟩, + ⟨3, 0, 5, 7, 0, 1, 88022335991781392235533311276839569957948542156800000⟩, + ⟨3, 0, 6, 7, 1, 1, 47014857449940169663205039961217276364924859187200000⟩, + ⟨3, 0, 7, 7, 2, 1, -5787482317600908780201331136543170469989397299200000⟩, + ⟨3, 0, 8, 7, 3, 1, -6406736955406088111312349208804601707671375052800000⟩ +] + +def collectedFourData_8_2_25 : List CollectedFourTerm := [ + ⟨3, 1, 4, 0, 6, 2, 7150368632038558428341534996031028611262709760000000⟩, + ⟨3, 1, 5, 0, 7, 2, 92434621757903115787988340506724444521103360000000⟩, + ⟨3, 1, 6, 0, 8, 2, 2847215695129044302699337914537689966580858880000000⟩, + ⟨3, 1, 4, 1, 5, 2, -11080360510313391356982655566158663287452991488000000⟩, + ⟨3, 1, 5, 1, 6, 2, -15250995560146370501194245768339279194483589120000000⟩, + ⟨3, 1, 6, 1, 7, 2, -9522304177566507232766966118753219581784883200000000⟩, + ⟨3, 1, 7, 1, 8, 2, -5967073980641352540473046613053516359065927680000000⟩, + ⟨3, 1, 4, 2, 4, 2, 2954238366191597356364652698442219203573317632000000⟩, + ⟨3, 1, 5, 2, 5, 2, 2667732084102192396765628337767277548724551680000000⟩, + ⟨3, 1, 6, 2, 6, 2, 657321020219443119016692098003179270003752960000000⟩, + ⟨3, 1, 7, 2, 7, 2, 352302882584634383953950932961180817922457600000000⟩, + ⟨3, 1, 8, 2, 8, 2, 1423820942346431671663851644574926341071175680000000⟩, + ⟨3, 1, 4, 3, 3, 2, -3768081531300346442347100421774354147012771840000000⟩, + ⟨3, 1, 5, 3, 4, 2, -3610664014304440882645405169579301277626531840000000⟩, + ⟨3, 1, 6, 3, 5, 2, -1601325002690539180415702416554777986318991360000000⟩, + ⟨3, 1, 7, 3, 6, 2, 275085522238785842073227190535064573894983680000000⟩, + ⟨3, 1, 8, 3, 7, 2, 872171145088922700202269438216398176675430400000000⟩, + ⟨3, 1, 4, 4, 2, 2, 12562433427263961441541358466261531325385146368000000⟩, + ⟨3, 1, 5, 4, 3, 2, 336789767060899632387554240555361542539837440000000⟩, + ⟨3, 1, 6, 4, 4, 2, 740035222863384631923651331977654060240076800000000⟩, + ⟨3, 1, 7, 4, 5, 2, 947094701816804672151149674708531248994713600000000⟩, + ⟨3, 1, 8, 4, 6, 2, -1112487685912152907905524249719921045363752960000000⟩, + ⟨3, 1, 4, 5, 1, 2, -12111753783426197403028441525698002413185662976000000⟩, + ⟨3, 1, 5, 5, 2, 2, 26158700450343036429447196963378705060425891840000000⟩, + ⟨3, 1, 6, 5, 3, 2, 274128307444337420671134917615571733818900480000000⟩, + ⟨3, 1, 7, 5, 4, 2, -600137656747779281335671027467655399761510400000000⟩, + ⟨3, 1, 8, 5, 5, 2, -371871013914220884190932591310004968929361920000000⟩, + ⟨3, 1, 4, 6, 0, 2, -37788957733057807078383997692324176397097500672000000⟩, + ⟨3, 1, 5, 6, 1, 2, -33419559018655069785344525747831192926185062400000000⟩, + ⟨3, 1, 6, 6, 2, 2, 19642108094625527146397429584324395312170926080000000⟩, + ⟨3, 1, 7, 6, 3, 2, -1799523832060799395001908745356204929020067840000000⟩, + ⟨3, 1, 8, 6, 4, 2, 553958841571991100689973606666135434239672320000000⟩, + ⟨3, 1, 5, 7, 0, 2, -145807209011156374542151346103610906983184465920000000⟩, + ⟨3, 1, 6, 7, 1, 2, -38939577492428779339510138045037508648857763840000000⟩, + ⟨3, 1, 7, 7, 2, 2, 3195615576519115702875977962849907662557020160000000⟩, + ⟨3, 1, 8, 7, 3, 2, 2653157360035344224743823427508884887127982080000000⟩ +] + +def collectedFourData_8_2_26 : List CollectedFourTerm := [ + ⟨3, 2, 3, 0, 5, 3, -24527787221028590574115041844627227869045587968000000⟩, + ⟨3, 2, 4, 0, 6, 3, -25743521869178674486962603588047647323475201228800000⟩, + ⟨3, 2, 5, 0, 7, 3, -166396505491453228479154065943163964194448998400000⟩, + ⟨3, 2, 6, 0, 8, 3, -3416950150206281789205770727072892018632740044800000⟩, + ⟨3, 2, 3, 1, 4, 3, 23463503584648508585848613762688998280477875896320000⟩, + ⟨3, 2, 4, 1, 5, 3, 39892698935483130542789791847751124840342817341440000⟩, + ⟨3, 2, 5, 1, 6, 3, 27454132642210451369741444497445338727362383052800000⟩, + ⟨3, 2, 6, 1, 7, 3, 11427739298258924783679070683929083283528220672000000⟩, + ⟨3, 2, 7, 1, 8, 3, 5370824478452544747430585319634456025916610969600000⟩, + ⟨3, 2, 3, 2, 3, 3, -16276128738693049296361920418139222027049558343680000⟩, + ⟨3, 2, 4, 2, 4, 3, -10636164916876127570437186695640340984697622364160000⟩, + ⟨3, 2, 5, 2, 5, 3, -4802327179362131974738308370565883466989384499200000⟩, + ⟨3, 2, 6, 2, 6, 3, -788852478797106250327468224042622192149174681600000⟩, + ⟨3, 2, 7, 2, 7, 3, -317099629023130432577880539541021875106742272000000⟩, + ⟨3, 2, 8, 2, 8, 3, -1025238486386677650284291785475929839257706823680000⟩, + ⟨3, 2, 3, 3, 2, 3, 10732686849872310209695440849144833993424009953280000⟩, + ⟨3, 2, 4, 3, 3, 3, 13566250119082761633651852991613998452796764979200000⟩, + ⟨3, 2, 5, 3, 4, 3, 6499749369425349368893347853680913037204756889600000⟩, + ⟨3, 2, 6, 3, 5, 3, 1921753844583425934621090051896806414615157145600000⟩, + ⟨3, 2, 7, 3, 6, 3, -247598079276566169308633300273680614392699289600000⟩, + ⟨3, 2, 8, 3, 7, 3, -628016766762472324425679689537040990538720870400000⟩, + ⟨3, 2, 3, 4, 1, 3, -9909857623514563341297986069735935383476486799360000⟩, + ⟨3, 2, 4, 4, 2, 3, -45228616356338795008121241413232743085116321955840000⟩, + ⟨3, 2, 5, 4, 3, 3, -606273269240946414971636801806688335622150553600000⟩, + ⟨3, 2, 6, 4, 4, 3, -888117984965791210041118390799797503475580928000000⟩, + ⟨3, 2, 7, 4, 5, 3, -852457908923676909403115829277383834407534592000000⟩, + ⟨3, 2, 8, 4, 6, 3, 801059429108243123124549668129975014760864808960000⟩, + ⟨3, 2, 3, 5, 0, 3, 11903124626885400117589453956122421966002391613440000⟩, + ⟨3, 2, 4, 5, 1, 3, 43606031303150649080071578865059127335727273082880000⟩, + ⟨3, 2, 5, 5, 2, 3, -47089675495563218921568702586712619322671995289600000⟩, + ⟨3, 2, 6, 5, 3, 3, -328982016676916811180236344100539744671026380800000⟩, + ⟨3, 2, 7, 5, 4, 3, 540169943888593218821672003297358296213618688000000⟩, + ⟨3, 2, 8, 5, 5, 3, 267769959056924005061606881150798382980053073920000⟩, + ⟨3, 2, 4, 6, 0, 3, 136051847097160444413061936231617333797833785999360000⟩, + ⟨3, 2, 5, 6, 1, 3, 60160335272796521086807856408224114744026464256000000⟩, + ⟨3, 2, 6, 6, 2, 3, -23572539417761539301372311404074370406858673356800000⟩, + ⟨3, 2, 7, 6, 3, 3, 1619709539071620963091713567684570156058332364800000⟩, + ⟨3, 2, 8, 6, 4, 3, -398884373282100059919909608492697901104176824320000⟩, + ⟨3, 2, 5, 7, 0, 3, 262475353861054526609727139796176833685524106444800000⟩, + ⟨3, 2, 6, 7, 1, 3, 46731477137243455755544857353286175157928748646400000⟩, + ⟨3, 2, 7, 7, 2, 3, -2876299241097792769521318982653719736384434995200000⟩, + ⟨3, 2, 8, 7, 3, 3, -1910436175679226858380126716700456087437002670080000⟩ +] + +def collectedFourData_8_2_27 : List CollectedFourTerm := [ + ⟨3, 3, 2, 0, 4, 4, 4510541974789820955131898220017794039914325606400000⟩, + ⟨3, 3, 3, 0, 5, 4, -31003429147108170521651280058869953586549227520000000⟩, + ⟨3, 3, 4, 0, 6, 4, -16270066457194263236385438296010665721505775616000000⟩, + ⟨3, 3, 5, 0, 7, 4, -70109086507238070419441785675776561399201792000000⟩, + ⟨3, 3, 6, 0, 8, 4, -1079766908103895051549759196292312126474682368000000⟩, + ⟨3, 3, 2, 1, 3, 4, -2692998708716017666632820688338706873473145241600000⟩, + ⟨3, 3, 3, 1, 4, 4, 29658161348770152412230879487286598374213340364800000⟩, + ⟨3, 3, 4, 1, 5, 4, 25212434651928259649672016165993564364363058380800000⟩, + ⟨3, 3, 5, 1, 6, 4, 11567455426477002729254608304487809241122340864000000⟩, + ⟨3, 3, 6, 1, 7, 4, 3611201271974509051881392589059110313939435520000000⟩, + ⟨3, 3, 7, 1, 8, 4, 1357757833421671207871811254992998596313140428800000⟩, + ⟨3, 3, 2, 2, 2, 4, -657483718171426275601540371766185334214649446400000⟩, + ⟨3, 3, 3, 2, 3, 4, -20573229847112135795730416334114018444071613235200000⟩, + ⟨3, 3, 4, 2, 4, 4, -6722122595604815861849285857467606945152316211200000⟩, + ⟨3, 3, 5, 2, 5, 4, -2023400495458444885867005301939977393480400896000000⟩, + ⟨3, 3, 6, 2, 6, 4, -249279844462882477780545142736885249218707456000000⟩, + ⟨3, 3, 7, 2, 7, 4, -80163577679475910920858028111056135537033216000000⟩, + ⟨3, 3, 8, 2, 8, 4, -215985706912352691114908628044143308936786739200000⟩, + ⟨3, 3, 2, 3, 1, 4, -3768081531300346442347100421774354147012771840000000⟩, + ⟨3, 3, 3, 3, 2, 4, 13566250119082761633651852991613998452796764979200000⟩, + ⟨3, 3, 4, 3, 3, 4, 8573954726709587039150018685871690245885394944000000⟩, + ⟨3, 3, 5, 3, 4, 4, 2738588105985278667241299370980613105435803648000000⟩, + ⟨3, 3, 6, 3, 5, 4, 607280210622138644845426107280714518491037696000000⟩, + ⟨3, 3, 7, 3, 6, 4, -62593412431675327382981407368075605892189388800000⟩, + ⟨3, 3, 8, 3, 7, 4, -132303505109389639160982903286482666390552576000000⟩, + ⟨3, 3, 2, 4, 0, 4, 14430124698243404706200164242964565049626905804800000⟩, + ⟨3, 3, 3, 4, 1, 4, -12526183708294547315924408230670537431942850150400000⟩, + ⟨3, 3, 4, 4, 2, 4, -28584767757266191194349651680639736911997226188800000⟩, + ⟨3, 3, 5, 4, 3, 4, -255445659478845160320148918643690070991699968000000⟩, + ⟨3, 3, 6, 4, 4, 4, -280648054113426659657393738660487736307220480000000⟩, + ⟨3, 3, 7, 4, 5, 4, -215503487061796866245727628565736361794994176000000⟩, + ⟨3, 3, 8, 4, 6, 4, 168758185897339156724317465088922011725882982400000⟩, + ⟨3, 3, 3, 5, 0, 4, 15045698075954036990895477641148718704095762841600000⟩, + ⟨3, 3, 4, 5, 1, 4, 27559283878953954708185014315045073383893604761600000⟩, + ⟨3, 3, 5, 5, 2, 4, -19840645830664899002923851123518876852208795648000000⟩, + ⟨3, 3, 6, 5, 3, 4, -103959343670136242504434055021651571536560128000000⟩, + ⟨3, 3, 7, 5, 4, 4, 136556310048135628918717676071570618831601664000000⟩, + ⟨3, 3, 8, 5, 5, 4, 56410761656667546714340591580891866144230604800000⟩, + ⟨3, 3, 4, 6, 0, 4, 85985616309360667097978759109791308022268769075200000⟩, + ⟨3, 3, 5, 6, 1, 4, 25347804856163755395671067355002626226027233280000000⟩, + ⟨3, 3, 6, 6, 2, 4, -7448996000640212895096416028681710160511500288000000⟩, + ⟨3, 3, 7, 6, 3, 4, 409466614179119301856219886090336883572106854400000⟩, + ⟨3, 3, 8, 6, 4, 4, -84032470965132761892505875567109980837170380800000⟩, + ⟨3, 3, 5, 7, 0, 4, 110590707632425546294751602074336570953982541824000000⟩, + ⟨3, 3, 6, 7, 1, 4, 14767292574216513974204540947571011817280897024000000⟩, + ⟨3, 3, 7, 7, 2, 4, -727135627226929239122236664516426887547427225600000⟩, + ⟨3, 3, 8, 7, 3, 4, -402469194625399173842611672538478644470952755200000⟩ +] + +def collectedFourData_8_2_28 : List CollectedFourTerm := [ + ⟨3, 4, 1, 0, 3, 5, 2310254131158732226176328831033706188210018713600000⟩, + ⟨3, 4, 2, 0, 4, 5, 4322107008062285383945700403146641889376495206400000⟩, + ⟨3, 4, 3, 0, 5, 5, -14854106129554729496903464997266657652779253760000000⟩, + ⟨3, 4, 4, 0, 6, 5, -5196786302644943329816983138871142774181199872000000⟩, + ⟨3, 4, 5, 0, 7, 5, -16795042359399534359832894972181590413672448000000⟩, + ⟨3, 4, 6, 0, 8, 5, -206931590335418790150668162363102127197886873600000⟩, + ⟨3, 4, 1, 1, 2, 5, 677985604377668807010868633777390315936677888000000⟩, + ⟨3, 4, 2, 1, 3, 5, -2580494463126363203590517241331044141940447641600000⟩, + ⟨3, 4, 3, 1, 4, 5, 14209572566690789599509820889230339378724103782400000⟩, + ⟨3, 4, 4, 1, 5, 5, 8053048547784865259918268850445704503569783193600000⟩, + ⟨3, 4, 5, 1, 6, 5, 2771051707514263496800805552660650794172809216000000⟩, + ⟨3, 4, 6, 1, 7, 5, 692067534782303188540883400635926893092143104000000⟩, + ⟨3, 4, 7, 1, 8, 5, 216839228333779134748779677863961946430950604800000⟩, + ⟨3, 4, 1, 2, 1, 5, 2483618707630143463388349810051856325766492979200000⟩, + ⟨3, 4, 2, 2, 2, 5, -630016304443766162286170281793915082418579046400000⟩, + ⟨3, 4, 3, 2, 3, 5, -9856875448412489226293805895576934109253573017600000⟩, + ⟨3, 4, 4, 2, 4, 5, -2147098459704962612047772599151941128280237670400000⟩, + ⟨3, 4, 5, 2, 5, 5, -484717441408199891887018499529710046202036224000000⟩, + ⟨3, 4, 6, 2, 6, 5, -47773157582549951863519100796723875022058291200000⟩, + ⟨3, 4, 7, 2, 7, 5, -12802436411423080878363714546908044550209536000000⟩, + ⟨3, 4, 8, 2, 8, 5, -29566080741032569119581534777092730766596505600000⟩, + ⟨3, 4, 1, 3, 0, 5, 2179721312656234185238431906525611618932988313600000⟩, + ⟨3, 4, 2, 3, 1, 5, -3610664014304440882645405169579301277626531840000000⟩, + ⟨3, 4, 3, 3, 2, 5, 6499749369425349368893347853680913037204756889600000⟩, + ⟨3, 4, 4, 3, 3, 5, 2738588105985278667241299370980613105435803648000000⟩, + ⟨3, 4, 5, 3, 4, 5, 656044822952043428289004853180820512846118912000000⟩, + ⟨3, 4, 6, 3, 5, 5, 116382025435415284995520678098316146978796339200000⟩, + ⟨3, 4, 7, 3, 6, 5, -9996412406075403937762791235161183333698764800000⟩, + ⟨3, 4, 8, 3, 7, 5, -18110902662522946470672767042544621865402368000000⟩, + ⟨3, 4, 2, 4, 0, 5, 13827283602298523314000155136440188950905933004800000⟩, + ⟨3, 4, 3, 4, 1, 5, -6001441366967684994514694017404472087580717875200000⟩, + ⟨3, 4, 4, 4, 2, 5, -9130198081001857879373144173411525477594143129600000⟩, + ⟨3, 4, 5, 4, 3, 5, -61193504083511782145987060049621555968212992000000⟩, + ⟨3, 4, 6, 4, 4, 5, -53784708279505899398122817306981213033988096000000⟩, + ⟨3, 4, 7, 4, 5, 5, -34416748471232009690412529121380864094109696000000⟩, + ⟨3, 4, 8, 4, 6, 5, 23101149706983466985977894062555182811788083200000⟩, + ⟨3, 4, 3, 5, 0, 5, 7208570218249700187337818874997144907164732620800000⟩, + ⟨3, 4, 4, 5, 1, 5, 8802650520798759811085879543496110309006062387200000⟩, + ⟨3, 4, 5, 5, 2, 5, -4752942931719108962856303085462876372611366912000000⟩, + ⟨3, 4, 6, 5, 3, 5, -19923255801258282096057692614198087810390425600000⟩, + ⟨3, 4, 7, 5, 4, 5, 21808575996445730719637507715166044835282944000000⟩, + ⟨3, 4, 8, 5, 5, 5, 7722016228050640395145718190017461675779686400000⟩, + ⟨3, 4, 4, 6, 0, 5, 27464477433857221802701744624253791109831353958400000⟩, + ⟨3, 4, 5, 6, 1, 5, 6072215136237902234528425657233668250607288320000000⟩, + ⟨3, 4, 6, 6, 2, 5, -1427560501480322294523414280594314611956226457600000⟩, + ⟨3, 4, 7, 6, 3, 5, 65393417339593410430480446737249257298224742400000⟩, + ⟨3, 4, 8, 6, 4, 5, -11503126095430973789039408741488111307351654400000⟩, + ⟨3, 4, 5, 7, 0, 5, 26492651834092871256260611348864054574979219456000000⟩, + ⟨3, 4, 6, 7, 1, 5, 2830073152266871521811499774148016026885606604800000⟩, + ⟨3, 4, 7, 7, 2, 5, -116126399289142350665895175650763888150550937600000⟩, + ⟨3, 4, 8, 7, 3, 5, -55093630380373788947352271280014607697680793600000⟩ +] + +def collectedFourData_8_2_29 : List CollectedFourTerm := [ + ⟨3, 5, 0, 0, 2, 6, 970989150203599945429938127908966824849021337600000⟩, + ⟨3, 5, 1, 0, 3, 6, 2049189671560316817959556874085342642038426828800000⟩, + ⟨3, 5, 2, 0, 4, 6, 1916849086177690019178211873383195142254074265600000⟩, + ⟨3, 5, 3, 0, 5, 6, -4391851737637972115132688278226091896062607360000000⟩, + ⟨3, 5, 4, 0, 6, 6, -1152384133098046456986013562319299926340665344000000⟩, + ⟨3, 5, 5, 0, 7, 6, -2979432164810173497175795648104981255212236800000⟩, + ⟨3, 5, 6, 0, 8, 6, -30591301040274741140848100266380150465940684800000⟩, + ⟨3, 5, 0, 1, 1, 6, -7153969764260615603984925181567624215207818035200000⟩, + ⟨3, 5, 1, 1, 2, 6, 601371545761707803493152113843960194954952704000000⟩, + ⟨3, 5, 2, 1, 3, 6, -1144446087129149546499778458502852561124877926400000⟩, + ⟨3, 5, 3, 1, 4, 6, 4201285181606852574472482727677907050237945446400000⟩, + ⟨3, 5, 4, 1, 5, 6, 1785758510949798693650116721786595220837839667200000⟩, + ⟨3, 5, 5, 1, 6, 6, 491583195269495504976750213122888475256396185600000⟩, + ⟨3, 5, 6, 1, 7, 6, 102310363837679054565555144799273455842230272000000⟩, + ⟨3, 5, 7, 1, 8, 6, 27476550931144510344697687378574159937483571200000⟩, + ⟨3, 5, 0, 2, 0, 6, -1150297723309402238346916538477544119210921164800000⟩, + ⟨3, 5, 1, 2, 1, 6, 2202963619944714595179067575108928814819416473600000⟩, + ⟨3, 5, 2, 2, 2, 6, -279411447980668614320173748586647591694473625600000⟩, + ⟨3, 5, 3, 2, 3, 6, -2914341340247925548797909549738028205063379353600000⟩, + ⟨3, 5, 4, 2, 4, 6, -476117749137375479047100593850915307284909260800000⟩, + ⟨3, 5, 5, 2, 5, 6, -85988633125883622690328167901205680187926118400000⟩, + ⟨3, 5, 6, 2, 6, 6, -7062445337047826335518699245018714830641561600000⟩, + ⟨3, 5, 7, 2, 7, 6, -1622247038989333716957561449092086742646784000000⟩, + ⟨3, 5, 8, 2, 8, 6, -3278130015325118132781230797673514585921945600000⟩, + ⟨3, 5, 1, 3, 0, 6, 1933407386024129618839970817789462856774503628800000⟩, + ⟨3, 5, 2, 3, 1, 6, -1601325002690539180415702416554777986318991360000000⟩, + ⟨3, 5, 3, 3, 2, 6, 1921753844583425934621090051896806414615157145600000⟩, + ⟨3, 5, 4, 3, 3, 6, 607280210622138644845426107280714518491037696000000⟩, + ⟨3, 5, 5, 3, 4, 6, 116382025435415284995520678098316146978796339200000⟩, + ⟨3, 5, 6, 3, 5, 6, 17205094543567702712410249342587617626659225600000⟩, + ⟨3, 5, 7, 3, 6, 6, -1266684707904709701885374524080850019234611200000⟩, + ⟨3, 5, 8, 3, 7, 6, -2008040705248193423058033133121699806445568000000⟩, + ⟨3, 5, 2, 4, 0, 6, 6132383091844940357082478808929600097704162099200000⟩, + ⟨3, 5, 3, 4, 1, 6, -1774421191417698011651751398799067988054192947200000⟩, + ⟨3, 5, 4, 4, 2, 6, -2024615750552178643995421104583904910323692339200000⟩, + ⟨3, 5, 5, 4, 3, 6, -10855697201729247331067253451094300113974067200000⟩, + ⟨3, 5, 6, 4, 4, 6, -7951150424518349505548704684983833044451328000000⟩, + ⟨3, 5, 7, 4, 5, 6, -4361081477372527247121193486020189905485824000000⟩, + ⟨3, 5, 8, 4, 6, 6, 2561332795722345975826335599656700292051763200000⟩, + ⟨3, 5, 3, 5, 0, 6, 2131327954895546389060850195526325248352636108800000⟩, + ⟨3, 5, 4, 5, 1, 6, 1951982282629721270174499980853530296429471334400000⟩, + ⟨3, 5, 5, 5, 2, 6, -843169713135357158800874657488300161891513139200000⟩, + ⟨3, 5, 6, 5, 3, 6, -2945313061822889934834963871509510578031820800000⟩, + ⟨3, 5, 7, 5, 4, 6, 2763450385368899585736536022555020111118336000000⟩, + ⟨3, 5, 8, 5, 5, 6, 856176149883449031783201613339187915155046400000⟩, + ⟨3, 5, 4, 6, 0, 6, 6090230803313597628208599275306570946892844236800000⟩, + ⟨3, 5, 5, 6, 1, 6, 1077207946333588289030038210475336442537050112000000⟩, + ⟨3, 5, 6, 6, 2, 6, -211040436035905329006377724981144529704635596800000⟩, + ⟨3, 5, 7, 6, 3, 6, 8286256946677319916660864396739573580405145600000⟩, + ⟨3, 5, 8, 6, 4, 6, -1275405531554567487425295213457479286810214400000⟩, + ⟨3, 5, 5, 7, 0, 6, 4699783264401102417726023802649227411953654169600000⟩, + ⟨3, 5, 6, 7, 1, 6, 418377975188144683013270920932201107592472166400000⟩, + ⟨3, 5, 7, 7, 2, 6, -14714832500727402512723811568150391338460774400000⟩, + ⟨3, 5, 8, 7, 3, 6, -6108489149611369337071274672092269053057433600000⟩ +] + +def collectedFourData_8_2_30 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 2, 7, -500407581889679029664833372843974560439494246400000⟩, + ⟨3, 6, 1, 0, 3, 7, -528033731460227148388219771310415248581302681600000⟩, + ⟨3, 6, 2, 0, 4, 7, -329288202606070882606445570540041775457553612800000⟩, + ⟨3, 6, 3, 0, 5, 7, 565844610001197991084733359558651230824693760000000⟩, + ⟨3, 6, 4, 0, 6, 7, 118778208248920449237374405243543548626940723200000⟩, + ⟨3, 6, 5, 0, 7, 7, 255912650978020326078278844068310170153779200000⟩, + ⟨3, 6, 6, 0, 8, 7, 2252212745736544322646862120447344199178649600000⟩, + ⟨3, 6, 0, 1, 1, 7, 3686859641938210498205289655930695504911715532800000⟩, + ⟨3, 6, 1, 1, 2, 7, -154960990536698870034781871283799391446499328000000⟩, + ⟨3, 6, 2, 1, 3, 7, 196600033736497596302064259959880535394956083200000⟩, + ⟨3, 6, 3, 1, 4, 7, -541292082953758535645958085062016122541729382400000⟩, + ⟨3, 6, 4, 1, 5, 7, -184061191232863607901292699067912424400260956160000⟩, + ⟨3, 6, 5, 1, 6, 7, -42223602256666103531437729745497577914525286400000⟩, + ⟨3, 6, 6, 1, 7, 7, -7532360429940528814032752998789692725919744000000⟩, + ⟨3, 6, 7, 1, 8, 7, -1770034506466885047398643135340264774277529600000⟩, + ⟨3, 6, 0, 2, 0, 7, 592815792075291251225831990528014472474473267200000⟩, + ⟨3, 6, 1, 2, 1, 7, -567658092686369464942362512273931340963066675200000⟩, + ⟨3, 6, 2, 2, 2, 7, 47999028278528283368450333133127900759641292800000⟩, + ⟨3, 6, 3, 2, 3, 7, 375482697867632638496269494198216741615147417600000⟩, + ⟨3, 6, 4, 2, 4, 7, 49074272661158630050251654802696903279761162240000⟩, + ⟨3, 6, 5, 2, 5, 7, 7385829862860233549370147277010411003156889600000⟩, + ⟨3, 6, 6, 2, 6, 7, 519955963403637110225762185847500117848883200000⟩, + ⟨3, 6, 7, 2, 7, 7, 104504864683365265159706167588231915241472000000⟩, + ⟨3, 6, 8, 2, 8, 7, 187712489285894646864634549853275184273817600000⟩, + ⟨3, 6, 1, 3, 0, 7, -498199034791023836232119991579136245693520281600000⟩, + ⟨3, 6, 2, 3, 1, 7, 275085522238785842073227190535064573894983680000000⟩, + ⟨3, 6, 3, 3, 2, 7, -247598079276566169308633300273680614392699289600000⟩, + ⟨3, 6, 4, 3, 3, 7, -62593412431675327382981407368075605892189388800000⟩, + ⟨3, 6, 5, 3, 4, 7, -9996412406075403937762791235161183333698764800000⟩, + ⟨3, 6, 6, 3, 5, 7, -1266684707904709701885374524080850019234611200000⟩, + ⟨3, 6, 7, 3, 6, 7, 81599602782163011921813478854012467517849600000⟩, + ⟨3, 6, 8, 3, 7, 7, 114984554489111157129689334175705992265728000000⟩, + ⟨3, 6, 2, 4, 0, 7, -1053458731084629060780610405673521314361088409600000⟩, + ⟨3, 6, 3, 4, 1, 7, 228615792839948029957347109156471551384826675200000⟩, + ⟨3, 6, 4, 4, 2, 7, 208680616416184773093273828173207530137987317760000⟩, + ⟨3, 6, 5, 4, 3, 7, 932429434682634770695408754986133054344396800000⟩, + ⟨3, 6, 6, 4, 4, 7, 585384789806505485634776851379564845203456000000⟩, + ⟨3, 6, 7, 4, 5, 7, 280940090326737975932806219199801607585792000000⟩, + ⟨3, 6, 8, 4, 6, 7, -146667201339467703979277942267960001508147200000⟩, + ⟨3, 6, 3, 5, 0, 7, -274599532831937788242420685360027102830447820800000⟩, + ⟨3, 6, 4, 5, 1, 7, -201194160354401332352752710381095494214819512320000⟩, + ⟨3, 6, 5, 5, 2, 7, 72422456554433377622759020433495325204597964800000⟩, + ⟨3, 6, 6, 5, 3, 7, 216841761953458384358019961062034297690521600000⟩, + ⟨3, 6, 7, 5, 4, 7, -178020980554287372354049816098154362175488000000⟩, + ⟨3, 6, 8, 5, 5, 7, -49026413110675867991163789792123797530214400000⟩, + ⟨3, 6, 4, 6, 0, 7, -627730530005853370616269668779163050486834135040000⟩, + ⟨3, 6, 5, 6, 1, 7, -92524724830706550058781744923746825381347328000000⟩, + ⟨3, 6, 6, 6, 2, 7, 15537356821800448127451102099961115368331673600000⟩, + ⟨3, 6, 7, 6, 3, 7, -533799193422230927312918227280157196733644800000⟩, + ⟨3, 6, 8, 6, 4, 7, 73032352608919745461419875369873794557542400000⟩, + ⟨3, 6, 5, 7, 0, 7, -403678931985903865447183854427165739505313382400000⟩, + ⟨3, 6, 6, 7, 1, 7, -30802096550703766575889895446790775885319372800000⟩, + ⟨3, 6, 7, 7, 2, 7, 947926883124373124989038703980935250129715200000⟩, + ⟨3, 6, 8, 7, 3, 7, 349784693922735252677557136588393514899865600000⟩ +] + +def collectedFourData_8_2_31 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 2, 8, -3173129942687794115768456799887148465713577984000000⟩, + ⟨3, 7, 1, 0, 3, 8, -2232206578110296543063500377358679414579134464000000⟩, + ⟨3, 7, 2, 0, 4, 8, -1044023205561185664546134598241836994431811584000000⟩, + ⟨3, 7, 3, 0, 5, 8, 1435228833362591367333249849389565025179402240000000⟩, + ⟨3, 7, 4, 0, 6, 8, 251061136810504831003597379133275408028401664000000⟩, + ⟨3, 7, 5, 0, 7, 8, 463647249002481082349915532061460159004672000000⟩, + ⟨3, 7, 6, 0, 8, 8, 3570371412945171793334951220052614073810944000000⟩, + ⟨3, 7, 0, 1, 1, 8, 23378711969437140148683683013554887818234298368000000⟩, + ⟨3, 7, 1, 1, 2, 8, -655081146937221897752018499642690943183749120000000⟩, + ⟨3, 7, 2, 1, 3, 8, 623329338283531045975023479751915067246903296000000⟩, + ⟨3, 7, 3, 1, 4, 8, -1372952911444159744167457424150054775278901657600000⟩, + ⟨3, 7, 4, 1, 5, 8, -389049579000013762179130113160009057612018483200000⟩, + ⟨3, 7, 5, 1, 6, 8, -76498199500733539463955815291209179488845824000000⟩, + ⟨3, 7, 6, 1, 7, 8, -11940845464962549805025289890194094460764160000000⟩, + ⟨3, 7, 7, 1, 8, 8, -2494211028205369290553447183245745091248128000000⟩, + ⟨3, 7, 0, 2, 0, 8, 3759098799480211769260824075541440663631429632000000⟩, + ⟨3, 7, 1, 2, 1, 8, -2399714361254782487411702535685519705959825408000000⟩, + ⟨3, 7, 2, 2, 2, 8, 152183099699810538959678364202587389096361984000000⟩, + ⟨3, 7, 3, 2, 3, 8, 952387961082212681614004106838082076501501542400000⟩, + ⟨3, 7, 4, 2, 4, 8, 103728140574734958588162926270610929745710284800000⟩, + ⟨3, 7, 5, 2, 5, 8, 13381205205871725098419984620410236972302336000000⟩, + ⟨3, 7, 6, 2, 6, 8, 824272001497620067209918145205593228443648000000⟩, + ⟨3, 7, 7, 2, 7, 8, 147261076008427526090680715679030533160960000000⟩, + ⟨3, 7, 8, 2, 8, 8, 238060389940634158454405930294029352907571200000⟩, + ⟨3, 7, 1, 3, 0, 8, -2106083563247680215539818801586481250607038464000000⟩, + ⟨3, 7, 2, 3, 1, 8, 872171145088922700202269438216398176675430400000000⟩, + ⟨3, 7, 3, 3, 2, 8, -628016766762472324425679689537040990538720870400000⟩, + ⟨3, 7, 4, 3, 3, 8, -132303505109389639160982903286482666390552576000000⟩, + ⟨3, 7, 5, 3, 4, 8, -18110902662522946470672767042544621865402368000000⟩, + ⟨3, 7, 6, 3, 5, 8, -2008040705248193423058033133121699806445568000000⟩, + ⟨3, 7, 7, 3, 6, 8, 114984554489111157129689334175705992265728000000⟩, + ⟨3, 7, 8, 3, 7, 8, 145825501451515928363799086072479440961536000000⟩, + ⟨3, 7, 2, 4, 0, 8, -3340038764368160552826654217840392620042354688000000⟩, + ⟨3, 7, 3, 4, 1, 8, 579869405569221206079814948582253806050135244800000⟩, + ⟨3, 7, 4, 4, 2, 8, 441087582984654275565919673422360851487339315200000⟩, + ⟨3, 7, 5, 4, 3, 8, 1689319932513508036707867890568757392703488000000⟩, + ⟨3, 7, 6, 4, 4, 8, 927994534732355527585636426901415096483840000000⟩, + ⟨3, 7, 7, 4, 5, 8, 395881475190366321913912146102317544898560000000⟩, + ⟨3, 7, 8, 4, 6, 8, -186006009910172037882298431546077066192486400000⟩, + ⟨3, 7, 3, 5, 0, 8, -696504234877240009695440157672199819592151859200000⟩, + ⟨3, 7, 4, 5, 1, 8, -425263483621122004552635363053397702959588966400000⟩, + ⟨3, 7, 5, 5, 2, 8, 131210679187363458287378384205988095609274368000000⟩, + ⟨3, 7, 6, 5, 3, 8, 343753328577358816297981795403240281473024000000⟩, + ⟨3, 7, 7, 5, 4, 8, -250854936063781312844278672306883883171840000000⟩, + ⟨3, 7, 8, 5, 5, 8, -62176187993236170426424655539930925944012800000⟩, + ⟨3, 7, 4, 6, 0, 8, -1326832108324572606347262365849804908717198540800000⟩, + ⟨3, 7, 5, 6, 1, 8, -167630767640921017752805241428509255511572480000000⟩, + ⟨3, 7, 6, 6, 2, 8, 24630947824222167339100372809551422427234304000000⟩, + ⟨3, 7, 7, 6, 3, 8, -752193152289694213090083266555610308542464000000⟩, + ⟨3, 7, 8, 6, 4, 8, 92620956690215158275108635311198740204748800000⟩, + ⟨3, 7, 5, 7, 0, 8, -731361367170547106073270027120766813086941184000000⟩, + ⟨3, 7, 6, 7, 1, 8, -48829723209582740413871303135650398383112192000000⟩, + ⟨3, 7, 7, 7, 2, 8, 1335753442762267995006710578336404483342336000000⟩, + ⟨3, 7, 8, 7, 3, 8, 443603304965435257659380751608601858224947200000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0810.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0810.lean new file mode 100644 index 0000000000000000000000000000000000000000..d3c7f703f586c3ce762aeeb5ca9dd5deee022ce1 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0810.lean @@ -0,0 +1,631 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0810. -/ +namespace LaughlinFock +def collectedFourData_8_2_32 : List CollectedFourTerm := [ + ⟨4, 0, 4, 0, 6, 2, -27382823365586081810807460601191018998432740147200000⟩, + ⟨4, 0, 5, 0, 7, 2, -353984675576062239885872357184535326201426739200000⟩, + ⟨4, 0, 6, 0, 8, 2, -10903606299975526412867366683522333455242860953600000⟩, + ⟨4, 0, 4, 1, 5, 2, 42432994757981409829915648893925339493003805327360000⟩, + ⟨4, 0, 5, 1, 6, 2, 58404725555214372568508986634427771317362517606400000⟩, + ⟨4, 0, 6, 1, 7, 2, 36466311982763803986886943726417489163718754304000000⟩, + ⟨4, 0, 7, 1, 8, 2, 22851315957217024880993252700203520400052296089600000⟩, + ⟨4, 0, 4, 2, 4, 2, -11313456903298002498068665754520955641566110679040000⟩, + ⟨4, 0, 5, 2, 5, 2, -10216261595012440929192265530688970276522793369600000⟩, + ⟨4, 0, 6, 2, 6, 2, -2517255587426165434840432779307300118185849651200000⟩, + ⟨4, 0, 7, 2, 7, 2, -1349167868321706202870232013298120071076380672000000⟩, + ⟨4, 0, 8, 2, 8, 2, -5452619210959362777682516158288968852784650649600000⟩, + ⟨4, 0, 4, 3, 3, 2, 14430124698243404706200164242964565049626905804800000⟩, + ⟨4, 0, 5, 3, 4, 2, 13827283602298523314000155136440188950905933004800000⟩, + ⟨4, 0, 6, 3, 5, 2, 6132383091844940357082478808929600097704162099200000⟩, + ⟨4, 0, 7, 3, 6, 2, -1053458731084629060780610405673521314361088409600000⟩, + ⟨4, 0, 8, 3, 7, 2, -3340038764368160552826654217840392620042354688000000⟩, + ⟨4, 0, 4, 4, 2, 2, -48108693870602705101188180230511595496846351400960000⟩, + ⟨4, 0, 5, 4, 3, 2, -1289759336524758503562294419786528613651500236800000⟩, + ⟨4, 0, 6, 4, 4, 2, -2834015256385863619250083506915420619350736896000000⟩, + ⟨4, 0, 7, 4, 5, 2, -3626963624522698858116032643002503183038676992000000⟩, + ⟨4, 0, 8, 4, 6, 2, 4260347314574342981212246517514746892765049651200000⟩, + ⟨4, 0, 4, 5, 1, 2, 46382785499056779158130528505573913477021140254720000⟩, + ⟨4, 0, 5, 5, 2, 2, -100176523864169610188105782484007464852305792204800000⟩, + ⟨4, 0, 6, 5, 3, 2, -1049793011876550395716166287211767712538270105600000⟩, + ⟨4, 0, 7, 5, 4, 2, 2298268004830964437925203795050580643873292288000000⟩, + ⟨4, 0, 8, 5, 5, 2, 1424105359151447355221397764901005726100907622400000⟩, + ⟨4, 0, 4, 6, 0, 2, 144715385740736195306601789399857734943474806947840000⟩, + ⟨4, 0, 5, 6, 1, 2, 127982475961202486480637649901926613889715273728000000⟩, + ⟨4, 0, 6, 6, 2, 2, -75220789886679929498961825082371707938608355737600000⟩, + ⟨4, 0, 7, 6, 3, 2, 6891398999303752322350745794776261680970910924800000⟩, + ⟨4, 0, 8, 6, 4, 2, -2121423088958404026290362617459479459114935910400000⟩, + ⟨4, 0, 5, 7, 0, 2, 558378631262721178978030267937543889944494630502400000⟩, + ⟨4, 0, 6, 7, 1, 2, 149121762426077219174416722063802093692397604044800000⟩, + ⟨4, 0, 7, 7, 2, 2, -12237827359565230260464381775765344549963248435200000⟩, + ⟨4, 0, 8, 7, 3, 2, -10160446697171170052365039387229790115345308057600000⟩ +] + +def collectedFourData_8_2_33 : List CollectedFourTerm := [ + ⟨4, 1, 3, 0, 5, 3, 22647346613224357635006903787707141418559471616000000⟩, + ⟨4, 1, 4, 0, 6, 3, 23769876082281235964315512743450416656496040345600000⟩, + ⟨4, 1, 5, 0, 7, 3, 153639596639333503643167416532732994829208780800000⟩, + ⟨4, 1, 6, 0, 8, 3, 3154987187164024407357811906015902436653898137600000⟩, + ⟨4, 1, 3, 1, 4, 3, -21664657054207881123858452800869761258113298595840000⟩, + ⟨4, 1, 4, 1, 5, 3, -36834296220342268759606815333706787210868849377280000⟩, + ⟨4, 1, 5, 1, 6, 3, -25349341638960249307912531322462636990386510233600000⟩, + ⟨4, 1, 6, 1, 7, 3, -10551623371526535006264809471307399155693912064000000⟩, + ⟨4, 1, 7, 1, 8, 3, -4959066322053810909148122859623441849379926835200000⟩, + ⟨4, 1, 3, 2, 3, 3, 15028307516897388117618477966848816653650792284160000⟩, + ⟨4, 1, 4, 2, 4, 3, 9820735614560210743510263661203649001135454289920000⟩, + ⟨4, 1, 5, 2, 5, 3, 4434153280972621450278952944806711438040524390400000⟩, + ⟨4, 1, 6, 2, 6, 3, 728374531017726451560308035534103488746435379200000⟩, + ⟨4, 1, 7, 2, 7, 3, 292788955835965265828460845738495241055371264000000⟩, + ⟨4, 1, 8, 2, 8, 3, 946637833783478492711832938012533610378334044160000⟩, + ⟨4, 1, 3, 3, 2, 3, -9909857623514563341297986069735935383476486799360000⟩, + ⟨4, 1, 4, 3, 3, 3, -12526183708294547315924408230670537431942850150400000⟩, + ⟨4, 1, 5, 3, 4, 3, -6001441366967684994514694017404472087580717875200000⟩, + ⟨4, 1, 6, 3, 5, 3, -1774421191417698011651751398799067988054192947200000⟩, + ⟨4, 1, 7, 3, 6, 3, 228615792839948029957347109156471551384826675200000⟩, + ⟨4, 1, 8, 3, 7, 3, 579869405569221206079814948582253806050135244800000⟩, + ⟨4, 1, 3, 4, 1, 3, 9150111196945812763541366245785580290722569912320000⟩, + ⟨4, 1, 4, 4, 2, 3, 41761131659702896314446704902405123036795717550080000⟩, + ⟨4, 1, 5, 4, 3, 3, 559792889065049921764946562933240600359809843200000⟩, + ⟨4, 1, 6, 4, 4, 3, 820029775116223371866224595194804506130907136000000⟩, + ⟨4, 1, 7, 4, 5, 3, 787103604683396500103717718008454239804719104000000⟩, + ⟨4, 1, 8, 4, 6, 3, -739645626624333329656095040718746479224181227520000⟩, + ⟨4, 1, 3, 5, 0, 3, -10990562938933376907348871745256459215742204641280000⟩, + ⟨4, 1, 4, 5, 1, 3, -40262943267172964769252419069765673953738159554560000⟩, + ⟨4, 1, 5, 5, 2, 3, 43479511349395792551117747632049794851888378675200000⟩, + ⟨4, 1, 6, 5, 3, 3, 303760371616891661503581156770910853502966169600000⟩, + ⟨4, 1, 7, 5, 4, 3, -498757423123874675823011028699598170416480256000000⟩, + ⟨4, 1, 8, 5, 5, 3, -247241180817645026311027416635403922895315927040000⟩, + ⟨4, 1, 4, 6, 0, 3, -125621333502810035539766081885817328384520560312320000⟩, + ⟨4, 1, 5, 6, 1, 3, -55548099509062599485951584916705584979034243072000000⟩, + ⟨4, 1, 6, 6, 2, 3, 21765333576044934858770645449558339949336041881600000⟩, + ⟨4, 1, 7, 6, 3, 3, -1495533331789991322997342107797381550500845977600000⟩, + ⟨4, 1, 8, 6, 4, 3, 368303613322835063925047601611718450692845731840000⟩, + ⟨4, 1, 5, 7, 0, 3, -242352490371560576847400385026544352640387094937600000⟩, + ⟨4, 1, 6, 7, 1, 3, -43148774528171223053701669603493790126961380556800000⟩, + ⟨4, 1, 7, 7, 2, 3, 2655785672367887210758019553382417391956682342400000⟩, + ⟨4, 1, 8, 7, 3, 3, 1763971199813589550482987241802601745632681000960000⟩ +] + +def collectedFourData_8_2_34 : List CollectedFourTerm := [ + ⟨4, 2, 2, 0, 4, 4, -15037727503635674190827436722869685405053385441280000⟩, + ⟨4, 2, 3, 0, 5, 4, 103362549733108977548856438149477521660003221504000000⟩, + ⟨4, 2, 4, 0, 6, 4, 54242888596714838094294655921417566357535535923200000⟩, + ⟨4, 2, 5, 0, 7, 4, 233737174893221857916410508173494532627129958400000⟩, + ⟨4, 2, 6, 0, 8, 4, 3599842462892989174373681988054382462897854873600000⟩, + ⟨4, 2, 2, 1, 3, 4, 8978207269914885446962102123141742731234451128320000⟩, + ⟨4, 2, 3, 1, 4, 4, -98877551991398420210503264650897370359981366312960000⟩, + ⟨4, 2, 4, 1, 5, 4, -84055912597196372956522042612322381055282810716160000⟩, + ⟨4, 2, 5, 1, 6, 4, -38564820721332156185420593313479589541563911372800000⟩, + ⟨4, 2, 6, 1, 7, 4, -12039409231141372287939783280380106187791663104000000⟩, + ⟨4, 2, 7, 1, 8, 4, -4526638357217206443870933368099270633333729525760000⟩, + ⟨4, 2, 2, 2, 2, 4, 2191989576241514409003200559750714727473642209280000⟩, + ⟨4, 2, 3, 2, 3, 4, 68589235182752631573779002215855403059683304407040000⟩, + ⟨4, 2, 4, 2, 4, 4, 22410931636091841147861989038927774077256193802240000⟩, + ⟨4, 2, 5, 2, 5, 4, 6745829093596526976609704189926918007909724979200000⟩, + ⟨4, 2, 6, 2, 6, 4, 831075820629334811674969427867469650068714291200000⟩, + ⟨4, 2, 7, 2, 7, 4, 267257913483148941241174918448786610064667443200000⟩, + ⟨4, 2, 8, 2, 8, 4, 720076262094739680165772588993129803761414307840000⟩, + ⟨4, 2, 2, 3, 1, 4, 12562433427263961441541358466261531325385146368000000⟩, + ⟨4, 2, 3, 3, 2, 4, -45228616356338795008121241413232743085116321955840000⟩, + ⟨4, 2, 4, 3, 3, 4, -28584767757266191194349651680639736911997226188800000⟩, + ⟨4, 2, 5, 3, 4, 4, -9130198081001857879373144173411525477594143129600000⟩, + ⟨4, 2, 6, 3, 5, 4, -2024615750552178643995421104583904910323692339200000⟩, + ⟨4, 2, 7, 3, 6, 4, 208680616416184773093273828173207530137987317760000⟩, + ⟨4, 2, 8, 3, 7, 4, 441087582984654275565919673422360851487339315200000⟩, + ⟨4, 2, 2, 4, 0, 4, -48108693870602705101188180230511595496846351400960000⟩, + ⟨4, 2, 3, 4, 1, 4, 41761131659702896314446704902405123036795717550080000⟩, + ⟨4, 2, 4, 4, 2, 4, 95298957573387813203782228333142003363490834677760000⟩, + ⟨4, 2, 5, 4, 3, 4, 851632074526560179703765201892699561812138393600000⟩, + ⟨4, 2, 6, 4, 4, 4, 935654514639554830530698372628669944190468096000000⟩, + ⟨4, 2, 7, 4, 5, 4, 718468585955146652207992771621745963350307635200000⟩, + ⟨4, 2, 8, 4, 6, 4, -562624098770376877061925072699782484355165716480000⟩, + ⟨4, 2, 3, 5, 0, 4, -50160958269037092659001187294763585872649854648320000⟩, + ⟨4, 2, 4, 5, 1, 4, -91880089683980915077861002716100381060773519032320000⟩, + ⟨4, 2, 5, 5, 2, 4, 66146868195719806947429980893305901872798341529600000⟩, + ⟨4, 2, 6, 5, 3, 4, 346590784501272072826466559693683875020118425600000⟩, + ⟨4, 2, 7, 5, 4, 4, -455266039177373380730508837381669167848803532800000⟩, + ⟨4, 2, 8, 5, 5, 4, -188068233663879001490800539420476893696056360960000⟩, + ⟨4, 2, 4, 6, 0, 4, -286668048877338895342658921914813891084924527575040000⟩, + ⟨4, 2, 5, 6, 1, 4, -84507224269891703337477849545423062916615110656000000⟩, + ⟨4, 2, 6, 6, 2, 4, 24834259975713696934890411286580034955418114457600000⟩, + ⟨4, 2, 7, 6, 3, 4, -1365123614917437905007155176949053561550804090880000⟩, + ⟨4, 2, 8, 6, 4, 4, 280156443924840356759797947636696301483233116160000⟩, + ⟨4, 2, 5, 7, 0, 4, -368699135293636224902523636819960537506281999564800000⟩, + ⟨4, 2, 6, 7, 1, 4, -49232780215481361604310889104089639524179430604800000⟩, + ⟨4, 2, 7, 7, 2, 4, 2424202564024091001240707349828167847977806725120000⟩, + ⟨4, 2, 8, 7, 3, 4, 1341794868823159855953044792089843634162148311040000⟩ +] + +def collectedFourData_8_2_35 : List CollectedFourTerm := [ + ⟨4, 3, 1, 0, 3, 5, -215492205201573722673144996816986477027760537600000⟩, + ⟨4, 3, 2, 0, 4, 5, -403150613485700919960651791339356109775726182400000⟩, + ⟨4, 3, 3, 0, 5, 5, 1385537652756190362552578086441792286396252160000000⟩, + ⟨4, 3, 4, 0, 6, 5, 484737555585112493364028733598829507459940352000000⟩, + ⟨4, 3, 5, 0, 7, 5, 1566581210988073944885344070508766998560768000000⟩, + ⟨4, 3, 6, 0, 8, 5, 19301835294146794625969902733628036798323097600000⟩, + ⟨4, 3, 1, 1, 2, 5, -63240061347271474894949705056077052335095808000000⟩, + ⟨4, 3, 2, 1, 3, 5, 240699252463037516568331181709324136706840985600000⟩, + ⟨4, 3, 3, 1, 4, 5, -1325417877656680062232143546980587831367722598400000⟩, + ⟨4, 3, 4, 1, 5, 5, -751159435991181978604590778692134032950008217600000⟩, + ⟨4, 3, 5, 1, 6, 5, -258473747596041764167278468340331755031494656000000⟩, + ⟨4, 3, 6, 1, 7, 5, -64553573222637213853437734181880995684286464000000⟩, + ⟨4, 3, 7, 1, 8, 5, -20225984171021537159517442106558912949701836800000⟩, + ⟨4, 3, 1, 2, 1, 5, -231663030040191634445142449719570694476608307200000⟩, + ⟨4, 3, 2, 2, 2, 5, 58765657390877400849271625739519208762795622400000⟩, + ⟨4, 3, 3, 2, 3, 5, 919413928592480682079480873553550793749666201600000⟩, + ⟨4, 3, 4, 2, 4, 5, 200273630345013672866866013501261788769314406400000⟩, + ⟨4, 3, 5, 2, 5, 5, 45212701468616435140220884527938627262480384000000⟩, + ⟨4, 3, 6, 2, 6, 5, 4456108502549256493369758024315482206843699200000⟩, + ⟨4, 3, 7, 2, 7, 5, 1194165272574045292755960734071143348043776000000⟩, + ⟨4, 3, 8, 2, 8, 5, 2757817788148403791044566548805288501811609600000⟩, + ⟨4, 3, 1, 3, 0, 5, -203316572862731506452818168984955911371594137600000⟩, + ⟨4, 3, 2, 3, 1, 5, 336789767060899632387554240555361542539837440000000⟩, + ⟨4, 3, 3, 3, 2, 5, -606273269240946414971636801806688335622150553600000⟩, + ⟨4, 3, 4, 3, 3, 5, -255445659478845160320148918643690070991699968000000⟩, + ⟨4, 3, 5, 3, 4, 5, -61193504083511782145987060049621555968212992000000⟩, + ⟨4, 3, 6, 3, 5, 5, -10855697201729247331067253451094300113974067200000⟩, + ⟨4, 3, 7, 3, 6, 5, 932429434682634770695408754986133054344396800000⟩, + ⟨4, 3, 8, 3, 7, 5, 1689319932513508036707867890568757392703488000000⟩, + ⟨4, 3, 2, 4, 0, 5, -1289759336524758503562294419786528613651500236800000⟩, + ⟨4, 3, 3, 4, 1, 5, 559792889065049921764946562933240600359809843200000⟩, + ⟨4, 3, 4, 4, 2, 5, 851632074526560179703765201892699561812138393600000⟩, + ⟨4, 3, 5, 4, 3, 5, 5707910208282376708569512310030070576054272000000⟩, + ⟨4, 3, 6, 4, 4, 5, 5016844353595371439235161699337362772852736000000⟩, + ⟨4, 3, 7, 4, 5, 5, 3210270646811410696714807920152687029518336000000⟩, + ⟨4, 3, 8, 4, 6, 5, -2154792248137969447191060734388505129726771200000⟩, + ⟨4, 3, 3, 5, 0, 5, -672389531407048301399097331160815727314521292800000⟩, + ⟨4, 3, 4, 5, 1, 5, -821079614905523288806718602548433430087152435200000⟩, + ⟨4, 3, 5, 5, 2, 5, 443337440560997612843674315381896353773780992000000⟩, + ⟨4, 3, 6, 5, 3, 5, 1858369721972898686267088716288294397778329600000⟩, + ⟨4, 3, 7, 5, 4, 5, -2034225616306148860120139025123927763451904000000⟩, + ⟨4, 3, 8, 5, 5, 5, -720281930520932354405323941492727514293862400000⟩, + ⟨4, 3, 4, 6, 0, 5, -2561787782178891843044986127166325471192704614400000⟩, + ⟨4, 3, 5, 6, 1, 5, -566394411990502754377528950673264138644357120000000⟩, + ⟨4, 3, 6, 6, 2, 5, 133157714717889050922042141385631552002169241600000⟩, + ⟨4, 3, 7, 6, 3, 5, -6099663027594257030807656110704072252089958400000⟩, + ⟨4, 3, 8, 6, 4, 5, 1072970274388343451146171435009621382030950400000⟩, + ⟨4, 3, 5, 7, 0, 5, -2471139381753989384043453591696817849154666496000000⟩, + ⟨4, 3, 6, 7, 1, 5, -263979055913591737331485501082118523219397836800000⟩, + ⟨4, 3, 7, 7, 2, 5, 10831853313204348997741098574111240829376921600000⟩, + ⟨4, 3, 8, 7, 3, 5, 5138935904541598648704867465668973190289817600000⟩ +] + +def collectedFourData_8_2_36 : List CollectedFourTerm := [ + ⟨4, 4, 0, 0, 2, 6, -448732250456039741774929767429009442118565888000000⟩, + ⟨4, 4, 1, 0, 3, 6, -947011089400661685023495279356442710055583744000000⟩, + ⟨4, 4, 2, 0, 4, 6, -885851303327909305035760817063373862525206528000000⟩, + ⟨4, 4, 3, 0, 5, 6, 2029647307064471074724779854270264085630156800000000⟩, + ⟨4, 4, 4, 0, 6, 6, 532562001672716142351124996476585640690974720000000⟩, + ⟨4, 4, 5, 0, 7, 6, 1376912708155431087063929441706336829046784000000⟩, + ⟨4, 4, 6, 0, 8, 6, 14137442583475100312657411598963152491905024000000⟩, + ⟨4, 4, 0, 1, 1, 6, 3306130610561407548607294081107554928559128576000000⟩, + ⟨4, 4, 1, 1, 2, 6, -277917427844888336600621707927181063639531520000000⟩, + ⟨4, 4, 2, 1, 3, 6, 528893518630346717165320321907477041939218432000000⟩, + ⟨4, 4, 3, 1, 4, 6, -1941579011418149419827718217876104671796396032000000⟩, + ⟨4, 4, 4, 1, 5, 6, -825269196078560601596838677148683384427380736000000⟩, + ⟨4, 4, 5, 1, 6, 6, -227179915917080771974849924752023180833456128000000⟩, + ⟨4, 4, 6, 1, 7, 6, -47281640376961379473623680643882248684175360000000⟩, + ⟨4, 4, 7, 1, 8, 6, -12697994134658620521911236415652965180768256000000⟩, + ⟨4, 4, 0, 2, 0, 6, 531597789704296601353668094959411744340967424000000⟩, + ⟨4, 4, 1, 2, 1, 6, -1018076074942027295546991387650450530467053568000000⟩, + ⟨4, 4, 2, 2, 2, 6, 129127012211471009490220020565937839908323328000000⟩, + ⟨4, 4, 3, 2, 3, 6, 1346831679769344286793407575288419505791827968000000⟩, + ⟨4, 4, 4, 2, 4, 6, 220032725399331210132058029166166501599739904000000⟩, + ⟨4, 4, 5, 2, 5, 6, 39738727099191296447996972718491945656123392000000⟩, + ⟨4, 4, 6, 2, 6, 6, 3263833575433586337296076224762616383275008000000⟩, + ⟨4, 4, 7, 2, 7, 6, 749704118165162657090496707708214753361920000000⟩, + ⟨4, 4, 8, 2, 8, 6, 1514952725018490695585561507032252891004928000000⟩, + ⟨4, 4, 1, 3, 0, 6, -893503544501006597571175007683149890001567744000000⟩, + ⟨4, 4, 2, 3, 1, 6, 740035222863384631923651331977654060240076800000000⟩, + ⟨4, 4, 3, 3, 2, 6, -888117984965791210041118390799797503475580928000000⟩, + ⟨4, 4, 4, 3, 3, 6, -280648054113426659657393738660487736307220480000000⟩, + ⟨4, 4, 5, 3, 4, 6, -53784708279505899398122817306981213033988096000000⟩, + ⟨4, 4, 6, 3, 5, 6, -7951150424518349505548704684983833044451328000000⟩, + ⟨4, 4, 7, 3, 6, 6, 585384789806505485634776851379564845203456000000⟩, + ⟨4, 4, 8, 3, 7, 6, 927994534732355527585636426901415096483840000000⟩, + ⟨4, 4, 2, 4, 0, 6, -2834015256385863619250083506915420619350736896000000⟩, + ⟨4, 4, 3, 4, 1, 6, 820029775116223371866224595194804506130907136000000⟩, + ⟨4, 4, 4, 4, 2, 6, 935654514639554830530698372628669944190468096000000⟩, + ⟨4, 4, 5, 4, 3, 6, 5016844353595371439235161699337362772852736000000⟩, + ⟨4, 4, 6, 4, 4, 6, 3674539126374871192651465516657456856432640000000⟩, + ⟨4, 4, 7, 4, 5, 6, 2015427160389159704528261353122491919237120000000⟩, + ⟨4, 4, 8, 4, 6, 6, -1183692556554672615910815771151875195273216000000⟩, + ⟨4, 4, 3, 5, 0, 6, -984970418525899463314217650404615054000390144000000⟩, + ⟨4, 4, 4, 5, 1, 6, -902087734297635792410185180371393759487721472000000⟩, + ⟨4, 4, 5, 5, 2, 6, 389661864720390682305579004087314204743172096000000⟩, + ⟨4, 4, 6, 5, 3, 6, 1361144929634100727824966237078511580872704000000⟩, + ⟨4, 4, 7, 5, 4, 6, -1277099038841143896063517812415998386503680000000⟩, + ⟨4, 4, 8, 5, 5, 6, -395672650351889866204308737686261865644032000000⟩, + ⟨4, 4, 4, 6, 0, 6, -2814535027085077340224031534270404555161206784000000⟩, + ⟨4, 4, 5, 6, 1, 6, -497820131013867462561886819486132288943554560000000⟩, + ⟨4, 4, 6, 6, 2, 6, 97530080310123533303112970283565135465283584000000⟩, + ⟨4, 4, 7, 6, 3, 6, -3829405021425666409377579958697893117820928000000⟩, + ⟨4, 4, 8, 6, 4, 6, 589415025181854821668244362101232471375872000000⟩, + ⟨4, 4, 5, 7, 0, 6, -2171954568645931527689714451084586634390274048000000⟩, + ⟨4, 4, 6, 7, 1, 6, -193348906430160928065037942568489713907269632000000⟩, + ⟨4, 4, 7, 7, 2, 6, 6800302456263843083190873564463482821148672000000⟩, + ⟨4, 4, 8, 7, 3, 6, 2822972926542642694652618832248436443578368000000⟩ +] + +def collectedFourData_8_2_37 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 2, 7, -1722858279489095254577226877916049725485744128000000⟩, + ⟨4, 5, 1, 0, 3, 7, -1817972626754353211141834259626455491183378432000000⟩, + ⟨4, 5, 2, 0, 4, 7, -1133709653350184134656423442170383303134150656000000⟩, + ⟨4, 5, 3, 0, 5, 7, 1948152079477812748661857017925675059983155200000000⟩, + ⟨4, 5, 4, 0, 6, 7, 408942683745442331177561410369951991347544064000000⟩, + ⟨4, 5, 5, 0, 7, 7, 881084231175153329959191853692742935773184000000⟩, + ⟨4, 5, 6, 0, 8, 7, 7754165837196529537516089676374511863201792000000⟩, + ⟨4, 5, 0, 1, 1, 7, 12693526016214137270057183455279329149039149056000000⟩, + ⟨4, 5, 1, 1, 2, 7, -533516747559674409502253237999804160210370560000000⟩, + ⟨4, 5, 2, 1, 3, 7, 676876226758358697162272990242419761441931264000000⟩, + ⟨4, 5, 3, 1, 4, 7, -1863619938005610427210120602770120778184654848000000⟩, + ⟨4, 5, 4, 1, 5, 7, -633706120220368309736005950876721021623415603200000⟩, + ⟨4, 5, 5, 1, 6, 7, -145372063434860645257888061044064022511484928000000⟩, + ⟨4, 5, 6, 1, 7, 7, -25933239224341052054856518373453679432826880000000⟩, + ⟨4, 5, 7, 1, 8, 7, -6094069544134467343466146758806714965819392000000⟩, + ⟨4, 5, 0, 2, 0, 7, 2041011432584504436947259460838919380291026944000000⟩, + ⟨4, 5, 1, 2, 1, 7, -1954395737191909087880161557062146958089519104000000⟩, + ⟨4, 5, 2, 2, 2, 7, 165256335575117059651226062099035244782944256000000⟩, + ⟨4, 5, 3, 2, 3, 7, 1292753144113574051180688841663413069023281152000000⟩, + ⟨4, 5, 4, 2, 4, 7, 168958305237713495665590641517576568234101964800000⟩, + ⟨4, 5, 5, 2, 5, 7, 25428747666201201652434283955508908069486592000000⟩, + ⟨4, 5, 6, 2, 6, 7, 1790161598145364577865425591173170818187264000000⟩, + ⟨4, 5, 7, 2, 7, 7, 359800846115710877716473930350536886845440000000⟩, + ⟨4, 5, 8, 2, 8, 7, 646277210885684795674299955629764905009152000000⟩, + ⟨4, 5, 1, 3, 0, 7, -1715254450545914730456723971568141888160530432000000⟩, + ⟨4, 5, 2, 3, 1, 7, 947094701816804672151149674708531248994713600000000⟩, + ⟨4, 5, 3, 3, 2, 7, -852457908923676909403115829277383834407534592000000⟩, + ⟨4, 5, 4, 3, 3, 7, -215503487061796866245727628565736361794994176000000⟩, + ⟨4, 5, 5, 3, 4, 7, -34416748471232009690412529121380864094109696000000⟩, + ⟨4, 5, 6, 3, 5, 7, -4361081477372527247121193486020189905485824000000⟩, + ⟨4, 5, 7, 3, 6, 7, 280940090326737975932806219199801607585792000000⟩, + ⟨4, 5, 8, 3, 7, 7, 395881475190366321913912146102317544898560000000⟩, + ⟨4, 5, 2, 4, 0, 7, -3626963624522698858116032643002503183038676992000000⟩, + ⟨4, 5, 3, 4, 1, 7, 787103604683396500103717718008454239804719104000000⟩, + ⟨4, 5, 4, 4, 2, 7, 718468585955146652207992771621745963350307635200000⟩, + ⟨4, 5, 5, 4, 3, 7, 3210270646811410696714807920152687029518336000000⟩, + ⟨4, 5, 6, 4, 4, 7, 2015427160389159704528261353122491919237120000000⟩, + ⟨4, 5, 7, 4, 5, 7, 967251452969677267497033150155104022691840000000⟩, + ⟨4, 5, 8, 4, 6, 7, -504961977600299331160626363733167040364544000000⟩, + ⟨4, 5, 3, 5, 0, 7, -945421484016685978183403190275993304161058816000000⟩, + ⟨4, 5, 4, 5, 1, 7, -692693391340052928470515917902303176505583206400000⟩, + ⟨4, 5, 5, 5, 2, 7, 249344001592791035727896911446944881569693696000000⟩, + ⟨4, 5, 6, 5, 3, 7, 746566675728109225621215005052754546655232000000⟩, + ⟨4, 5, 7, 5, 4, 7, -612910218331460204022813356721576880373760000000⟩, + ⟨4, 5, 8, 5, 5, 7, -168793529111639468271196585303849448767488000000⟩, + ⟨4, 5, 4, 6, 0, 7, -2161219733771120757204167360881361248804719820800000⟩, + ⟨4, 5, 5, 6, 1, 7, -318554302534881009844796184618543641851330560000000⟩, + ⟨4, 5, 6, 6, 2, 7, 53493721539408562557654526853613199684534272000000⟩, + ⟨4, 5, 7, 6, 3, 7, -1837822593533049065578169632872185563447296000000⟩, + ⟨4, 5, 8, 6, 4, 7, 251443818832033476033029185111574653698048000000⟩, + ⟨4, 5, 5, 7, 0, 7, -1389830241182391310568294939372375835408334848000000⟩, + ⟨4, 5, 6, 7, 1, 7, -106048846957122840866486997677668701994745856000000⟩, + ⟨4, 5, 7, 7, 2, 7, 3263626967389084562569958416638933051899904000000⟩, + ⟨4, 5, 8, 7, 3, 7, 1204277228749504604329185771121293354074112000000⟩ +] + +def collectedFourData_8_2_38 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 2, 8, 4047448722554787556807827689899376978314238361600000⟩, + ⟨4, 6, 1, 0, 3, 8, 2847264948563074406351586774797771697074837913600000⟩, + ⟨4, 6, 2, 0, 4, 8, 1331691568258582733316005627400012641370479001600000⟩, + ⟨4, 6, 3, 0, 5, 8, -1830689323503311212880944563631214295175397376000000⟩, + ⟨4, 6, 4, 0, 6, 8, -320238091669859719229040876504852268658039193600000⟩, + ⟨4, 6, 5, 0, 7, 8, -591399816454277510409405708513649416260812800000⟩, + ⟨4, 6, 6, 0, 8, 8, -4554145425929346651943799562220620161325465600000⟩, + ⟨4, 6, 0, 1, 1, 8, -29820442151676733888834135510173928406429938483200000⟩, + ⟨4, 6, 1, 1, 2, 8, 835581082158556021009901197553727726459813888000000⟩, + ⟨4, 6, 2, 1, 3, 8, -795080434629029485188167089552732999154820710400000⟩, + ⟨4, 6, 3, 1, 4, 8, 1751254000914166951314214413134451225919739658240000⟩, + ⟨4, 6, 4, 1, 5, 8, 496247632456007187227126195629837673943458119680000⟩, + ⟨4, 6, 5, 1, 6, 8, 97576382133509485536767240024896889429793177600000⟩, + ⟨4, 6, 6, 1, 7, 8, 15231005535956398120638250146962770948521984000000⟩, + ⟨4, 6, 7, 1, 8, 8, 3181461655283102341052221809907153415385907200000⟩, + ⟨4, 6, 0, 2, 0, 8, -4794874432726755382231638381784838850118208716800000⟩, + ⟨4, 6, 1, 2, 1, 8, 3060927538860858731437841341875085344756675379200000⟩, + ⟨4, 6, 2, 2, 2, 8, -194115369871264676511853960853364260724119961600000⟩, + ⟨4, 6, 3, 2, 3, 8, -1214807305746076228134529772752975510822988021760000⟩, + ⟨4, 6, 4, 2, 4, 8, -132309214449180264975094423381003926125433323520000⟩, + ⟨4, 6, 5, 2, 5, 8, -17068239528467930631829835065408624290850406400000⟩, + ⟨4, 6, 6, 2, 6, 8, -1051390494482334086980942961631932254991155200000⟩, + ⟨4, 6, 7, 2, 7, 8, -187837140217297846957419882498236092514304000000⟩, + ⟨4, 6, 8, 2, 8, 8, -303655141314493985256014383899225394910330880000⟩, + ⟨4, 6, 1, 3, 0, 8, 2686390214590454055248819821493693121449007513600000⟩, + ⟨4, 6, 2, 3, 1, 8, -1112487685912152907905524249719921045363752960000000⟩, + ⟨4, 6, 3, 3, 2, 8, 801059429108243123124549668129975014760864808960000⟩, + ⟨4, 6, 4, 3, 3, 8, 168758185897339156724317465088922011725882982400000⟩, + ⟨4, 6, 5, 3, 4, 8, 23101149706983466985977894062555182811788083200000⟩, + ⟨4, 6, 6, 3, 5, 8, 2561332795722345975826335599656700292051763200000⟩, + ⟨4, 6, 7, 3, 6, 8, -146667201339467703979277942267960001508147200000⟩, + ⟨4, 6, 8, 3, 7, 8, -186006009910172037882298431546077066192486400000⟩, + ⟨4, 6, 2, 4, 0, 8, 4260347314574342981212246517514746892765049651200000⟩, + ⟨4, 6, 3, 4, 1, 8, -739645626624333329656095040718746479224181227520000⟩, + ⟨4, 6, 4, 4, 2, 8, -562624098770376877061925072699782484355165716480000⟩, + ⟨4, 6, 5, 4, 3, 8, -2154792248137969447191060734388505129726771200000⟩, + ⟨4, 6, 6, 4, 4, 8, -1183692556554672615910815771151875195273216000000⟩, + ⟨4, 6, 7, 4, 5, 8, -504961977600299331160626363733167040364544000000⟩, + ⟨4, 6, 8, 4, 6, 8, 237257786726735459888577478527871746425487360000⟩, + ⟨4, 6, 3, 5, 0, 8, 888417816674724832384500850720338889865775022080000⟩, + ⟨4, 6, 4, 5, 1, 8, 542439854219629729465339767188172638285841039360000⟩, + ⟨4, 6, 5, 5, 2, 8, -167364244595857819838737399922871949006680883200000⟩, + ⟨4, 6, 6, 5, 3, 8, -438470530912411540115637219042571885058457600000⟩, + ⟨4, 6, 7, 5, 4, 8, 319975074723188757664776859582681281724416000000⟩, + ⟨4, 6, 8, 5, 5, 8, 79308108149326589395362091520895480464670720000⟩, + ⟨4, 6, 4, 6, 0, 8, 1692425150838315981042439167496412106875385937920000⟩, + ⟨4, 6, 5, 6, 1, 8, 213819461731347031175648873178500536259837952000000⟩, + ⟨4, 6, 6, 6, 2, 8, -31417716925269464547472934641197418502789529600000⟩, + ⟨4, 6, 7, 6, 3, 8, 959451162838473115886385476677327119817113600000⟩, + ⟨4, 6, 8, 6, 4, 8, -118141576175122980707773286506392645135237120000⟩, + ⟨4, 6, 5, 7, 0, 8, 932879423391330139364084034494459935008070041600000⟩, + ⟨4, 6, 6, 7, 1, 8, 62284181359406437518017310831146647946054860800000⟩, + ⟨4, 6, 7, 7, 2, 8, -1703804654459509783120938661076062989346406400000⟩, + ⟨4, 6, 8, 7, 3, 8, -565832998469199208951309759696917188868833280000⟩ +] + +def collectedFourData_8_2_39 : List CollectedFourTerm := [ + ⟨5, 0, 3, 0, 5, 3, -27202629891051365698706557764774500119099736064000000⟩, + ⟨5, 0, 4, 0, 6, 3, -28550944738262740994494382965524464193411376742400000⟩, + ⟨5, 0, 5, 0, 7, 3, -184542637835981663127864100637856938237047603200000⟩, + ⟨5, 0, 6, 0, 8, 3, -3789580749972598947213920616492591125816043110400000⟩, + ⟨5, 0, 3, 1, 4, 3, 26022282328564007875537317748291710154152723087360000⟩, + ⟨5, 0, 4, 1, 5, 3, 44243140023928270484474445978687398121279974277120000⟩, + ⟨5, 0, 5, 1, 6, 3, 30448103716653344360105443008135458439419029094400000⟩, + ⟨5, 0, 6, 1, 7, 3, 12673975023537580009467329133615246141246406656000000⟩, + ⟨5, 0, 7, 1, 8, 3, 5956532041825855443424707972110643964779744460800000⟩, + ⟨5, 0, 3, 2, 3, 3, -18051098623286430967812298058068440459556568432640000⟩, + ⟨5, 0, 4, 2, 4, 3, -11796076632869333860696678211334626189829136711680000⟩, + ⟨5, 0, 5, 2, 5, 3, -5326038084834886784746402358352075832774203801600000⟩, + ⟨5, 0, 6, 2, 6, 3, -874879654898450851845622045234027104280825036800000⟩, + ⟨5, 0, 7, 2, 7, 3, -351680474442087558949711875629035267823763456000000⟩, + ⟨5, 0, 8, 2, 8, 3, -1137044399640260046791899624929422504188591472640000⟩, + ⟨5, 0, 3, 3, 2, 3, 11903124626885400117589453956122421966002391613440000⟩, + ⟨5, 0, 4, 3, 3, 3, 15045698075954036990895477641148718704095762841600000⟩, + ⟨5, 0, 5, 3, 4, 3, 7208570218249700187337818874997144907164732620800000⟩, + ⟨5, 0, 6, 3, 5, 3, 2131327954895546389060850195526325248352636108800000⟩, + ⟨5, 0, 7, 3, 6, 3, -274599532831937788242420685360027102830447820800000⟩, + ⟨5, 0, 8, 3, 7, 3, -696504234877240009695440157672199819592151859200000⟩, + ⟨5, 0, 3, 4, 1, 3, -10990562938933376907348871745256459215742204641280000⟩, + ⟨5, 0, 4, 4, 2, 3, -50160958269037092659001187294763585872649854648320000⟩, + ⟨5, 0, 5, 4, 3, 3, -672389531407048301399097331160815727314521292800000⟩, + ⟨5, 0, 6, 4, 4, 3, -984970418525899463314217650404615054000390144000000⟩, + ⟨5, 0, 7, 4, 5, 3, -945421484016685978183403190275993304161058816000000⟩, + ⟨5, 0, 8, 4, 6, 3, 888417816674724832384500850720338889865775022080000⟩, + ⟨5, 0, 3, 5, 0, 3, 13201202817619835296267720309334414484286073733120000⟩, + ⟨5, 0, 4, 5, 1, 3, 48361424529165630864675994317958223708182271754240000⟩, + ⟨5, 0, 5, 5, 2, 3, -52224972544498408140832213838478589582335855820800000⟩, + ⟨5, 0, 6, 5, 3, 3, -364858678845737554092154651758377749874894438400000⟩, + ⟨5, 0, 7, 5, 4, 3, 599077402680402880031346530172980065808154624000000⟩, + ⟨5, 0, 8, 5, 5, 3, 296971228041418874298972162035791078212407132160000⟩, + ⟨5, 0, 4, 6, 0, 3, 150888786225485035879599110270145998215200406241280000⟩, + ⟨5, 0, 5, 6, 1, 3, 66721034384398000100945175265619388154131775488000000⟩, + ⟨5, 0, 6, 6, 2, 3, -26143208908133048742549261339088709435896784486400000⟩, + ⟨5, 0, 7, 6, 3, 3, 1796344640685569480707754494220893049103738470400000⟩, + ⟨5, 0, 8, 6, 4, 3, -442384136731838204791251366025592098331673231360000⟩, + ⟨5, 0, 5, 7, 0, 3, 291099227266762975244865063395549704658490910310400000⟩, + ⟨5, 0, 6, 7, 1, 3, 51827711377759287266580684807419925696156480307200000⟩, + ⟨5, 0, 7, 7, 2, 3, -3189969931099801972420762450926159564100966809600000⟩, + ⟨5, 0, 8, 7, 3, 3, -2118776053835085478081861520281581418448777379840000⟩ +] + +def collectedFourData_8_2_40 : List CollectedFourTerm := [ + ⟨5, 1, 2, 0, 4, 4, 14498246222822716620730293819889952921192717352960000⟩, + ⟨5, 1, 3, 0, 5, 4, -99654398969994735132077029188152817633856585728000000⟩, + ⟨5, 1, 4, 0, 6, 4, -52296914844492278867060688938341971256716715622400000⟩, + ⟨5, 1, 5, 0, 7, 4, -225351810119554351128101481565543870411623628800000⟩, + ⟨5, 1, 6, 0, 8, 4, -3470697442667236827998566410104169633368191795200000⟩, + ⟨5, 1, 2, 1, 3, 4, -8656112408426880860960066970033991860099471114240000⟩, + ⟨5, 1, 3, 1, 4, 4, 95330301359341630010131821591414713452031870238720000⟩, + ⟨5, 1, 4, 1, 5, 4, 81040391044696232209128672272771314624880569221120000⟩, + ⟨5, 1, 5, 1, 6, 4, 37181300580271192725378411070684831825190820249600000⟩, + ⟨5, 1, 6, 1, 7, 4, 11607493177955996624653029110676160668581756928000000⟩, + ⟨5, 1, 7, 1, 8, 4, 4364244361306708063694910965436276533126045368320000⟩, + ⟨5, 1, 2, 2, 2, 4, -2113351541084039848618485060883232523075673128960000⟩, + ⟨5, 1, 3, 2, 3, 4, -66128583569174287770855449994805348681987160801280000⟩, + ⟨5, 1, 4, 2, 4, 4, -21606935280902708455544269680282174554082304327680000⟩, + ⟨5, 1, 5, 2, 5, 4, -6503821215831824483500241481762315764586931814400000⟩, + ⟨5, 1, 6, 2, 6, 4, -801260820453450809067706627475343421020202598400000⟩, + ⟨5, 1, 7, 2, 7, 4, -257669985956304927574013020049538917002012262400000⟩, + ⟨5, 1, 8, 2, 8, 4, -694243391798083673303881413339167085718017146880000⟩, + ⟨5, 1, 2, 3, 1, 4, -12111753783426197403028441525698002413185662976000000⟩, + ⟨5, 1, 3, 3, 2, 4, 43606031303150649080071578865059127335727273082880000⟩, + ⟨5, 1, 4, 3, 3, 4, 27559283878953954708185014315045073383893604761600000⟩, + ⟨5, 1, 5, 3, 4, 4, 8802650520798759811085879543496110309006062387200000⟩, + ⟨5, 1, 6, 3, 5, 4, 1951982282629721270174499980853530296429471334400000⟩, + ⟨5, 1, 7, 3, 6, 4, -201194160354401332352752710381095494214819512320000⟩, + ⟨5, 1, 8, 3, 7, 4, -425263483621122004552635363053397702959588966400000⟩, + ⟨5, 1, 2, 4, 0, 4, 46382785499056779158130528505573913477021140254720000⟩, + ⟨5, 1, 3, 4, 1, 4, -40262943267172964769252419069765673953738159554560000⟩, + ⟨5, 1, 4, 4, 2, 4, -91880089683980915077861002716100381060773519032320000⟩, + ⟨5, 1, 5, 4, 3, 4, -821079614905523288806718602548433430087152435200000⟩, + ⟨5, 1, 6, 4, 4, 4, -902087734297635792410185180371393759487721472000000⟩, + ⟨5, 1, 7, 4, 5, 4, -692693391340052928470515917902303176505583206400000⟩, + ⟨5, 1, 8, 4, 6, 4, 542439854219629729465339767188172638285841039360000⟩, + ⟨5, 1, 3, 5, 0, 4, 48361424529165630864675994317958223708182271754240000⟩, + ⟨5, 1, 4, 5, 1, 4, 88583874318199119332540391533983237399835301642240000⟩, + ⟨5, 1, 5, 5, 2, 4, -63773836953641159041991591952890196038461371187200000⟩, + ⟨5, 1, 6, 5, 3, 4, -334156775420078919435577935014665746245694259200000⟩, + ⟨5, 1, 7, 5, 4, 4, 438933285051680456796895977996044614028073369600000⟩, + ⟨5, 1, 8, 5, 5, 4, 181321250680400268029096155025700381524722974720000⟩, + ⟨5, 1, 4, 6, 0, 4, 276383779120548312685353593326111675875801201377280000⟩, + ⟨5, 1, 5, 6, 1, 4, 81475511826901450282752777357487617669586747392000000⟩, + ⟨5, 1, 6, 6, 2, 4, -23943326264054082868884444512138803444075148083200000⟩, + ⟨5, 1, 7, 6, 3, 4, 1316149550447549065089940770855297420370284380160000⟩, + ⟨5, 1, 8, 6, 4, 4, -270105779211037326410964093891398626880646021120000⟩, + ⟨5, 1, 5, 7, 0, 4, 355471985001495927064656611871378500067863927193600000⟩, + ⟨5, 1, 6, 7, 1, 4, 47466545036515040629785876639327132524587096473600000⟩, + ⟨5, 1, 7, 7, 2, 4, -2337233844590015442855816688711457125804372131840000⟩, + ⟨5, 1, 8, 7, 3, 4, -1293657727473447161236632872620671057530223329280000⟩ +] + +def collectedFourData_8_2_41 : List CollectedFourTerm := [ + ⟨5, 2, 1, 0, 3, 5, -16737432655525181264819410200596572184503753113600000⟩, + ⟨5, 2, 2, 0, 4, 5, -31312994532394822478508847418512940115874440806400000⟩, + ⟨5, 2, 3, 0, 5, 5, 107615693723161233338730787148071970329602293760000000⟩, + ⟨5, 2, 4, 0, 6, 5, 37649910281536550183186370145090584691838287872000000⟩, + ⟨5, 2, 5, 0, 7, 5, 121677475497533616406214931666246327701864448000000⟩, + ⟨5, 2, 6, 0, 8, 5, 1499187258590742511132225233250514318292261273600000⟩, + ⟨5, 2, 1, 1, 2, 5, -4911900488192263416940803907186585648798629888000000⟩, + ⟨5, 2, 2, 1, 3, 5, 18695281922456853947997494914854144754132294041600000⟩, + ⟨5, 2, 3, 1, 4, 5, -102946148084366012615942156321366897474197153382400000⟩, + ⟨5, 2, 4, 1, 5, 5, -58343086988711508923773668924061908396905437593600000⟩, + ⟨5, 2, 5, 1, 6, 5, -20075839585766923777639147989312204959662473216000000⟩, + ⟨5, 2, 6, 1, 7, 5, -5013921888621117944014260341069760526867759104000000⟩, + ⟨5, 2, 7, 1, 8, 5, -1570966558338041560955488806731307929981209804800000⟩, + ⟨5, 2, 1, 2, 1, 5, -17993432107883491258051701838270057763977769779200000⟩, + ⟨5, 2, 2, 2, 2, 5, 4564370354451656413032879942067306555523884646400000⟩, + ⟨5, 2, 3, 2, 3, 5, 71411532950687449631593544527134938289927723417600000⟩, + ⟨5, 2, 4, 2, 4, 5, 15555395135715706366269691746334914679239239270400000⟩, + ⟨5, 2, 5, 2, 5, 5, 3511702640461937213783614005343278555646132224000000⟩, + ⟨5, 2, 6, 2, 6, 5, 346109112844081013281005186589861919904183091200000⟩, + ⟨5, 2, 7, 2, 7, 5, 92751665010707261621531754043937057497153536000000⟩, + ⟨5, 2, 8, 2, 8, 5, 214201666655023055158915396596226634165098905600000⟩, + ⟨5, 2, 1, 3, 0, 5, -15791742642658219825253879824350174210785122713600000⟩, + ⟨5, 2, 2, 3, 1, 5, 26158700450343036429447196963378705060425891840000000⟩, + ⟨5, 2, 3, 3, 2, 5, -47089675495563218921568702586712619322671995289600000⟩, + ⟨5, 2, 4, 3, 3, 5, -19840645830664899002923851123518876852208795648000000⟩, + ⟨5, 2, 5, 3, 4, 5, -4752942931719108962856303085462876372611366912000000⟩, + ⟨5, 2, 6, 3, 5, 5, -843169713135357158800874657488300161891513139200000⟩, + ⟨5, 2, 7, 3, 6, 5, 72422456554433377622759020433495325204597964800000⟩, + ⟨5, 2, 8, 3, 7, 5, 131210679187363458287378384205988095609274368000000⟩, + ⟨5, 2, 2, 4, 0, 5, -100176523864169610188105782484007464852305792204800000⟩, + ⟨5, 2, 3, 4, 1, 5, 43479511349395792551117747632049794851888378675200000⟩, + ⟨5, 2, 4, 4, 2, 5, 66146868195719806947429980893305901872798341529600000⟩, + ⟨5, 2, 5, 4, 3, 5, 443337440560997612843674315381896353773780992000000⟩, + ⟨5, 2, 6, 4, 4, 5, 389661864720390682305579004087314204743172096000000⟩, + ⟨5, 2, 7, 4, 5, 5, 249344001592791035727896911446944881569693696000000⟩, + ⟨5, 2, 8, 4, 6, 5, -167364244595857819838737399922871949006680883200000⟩, + ⟨5, 2, 3, 5, 0, 5, -52224972544498408140832213838478589582335855820800000⟩, + ⟨5, 2, 4, 5, 1, 5, -63773836953641159041991591952890196038461371187200000⟩, + ⟨5, 2, 5, 5, 2, 5, 34434333938536378160877745555739432131768614912000000⟩, + ⟨5, 2, 6, 5, 3, 5, 144340896421256233523666167762930267120572825600000⟩, + ⟨5, 2, 7, 5, 4, 5, -157999748655501372185851928882966654242258944000000⟩, + ⟨5, 2, 8, 5, 5, 5, -55944809204624220487939782734306559295645286400000⟩, + ⟨5, 2, 4, 6, 0, 5, -198975876839062954117225618144163636114125907558400000⟩, + ⟨5, 2, 5, 6, 1, 5, -43992256324488123403551592902040931768016568320000000⟩, + ⟨5, 2, 6, 6, 2, 5, 10342454292346840282785862667165342465196136857600000⟩, + ⟨5, 2, 7, 6, 3, 5, -473765160323349540288432296760400798823114342400000⟩, + ⟨5, 2, 8, 6, 4, 5, 83338363409277145604829747052316011029489254400000⟩, + ⟨5, 2, 5, 7, 0, 5, -191935151184862794748892013298784990457501843456000000⟩, + ⟨5, 2, 6, 7, 1, 5, -20503440793554008920441545095300573633859865804800000⟩, + ⟨5, 2, 7, 7, 2, 5, 841317741375830977023446784448741424672381337600000⟩, + ⟨5, 2, 8, 7, 3, 5, 399144802211608003266195987734363698703735193600000⟩ +] + +def collectedFourData_8_2_42 : List CollectedFourTerm := [ + ⟨5, 3, 0, 0, 2, 6, -166222104722589909880777487196863924248825036800000⟩, + ⟨5, 3, 1, 0, 3, 6, -350797555370341925405504853324710583330039398400000⟩, + ⟨5, 3, 2, 0, 4, 6, -328142378803325444847847468100442001695886540800000⟩, + ⟨5, 3, 3, 0, 5, 6, 751834188164382750206440314766407103917588480000000⟩, + ⟨5, 3, 4, 0, 6, 6, 197274826410067839956322500778192852423278592000000⟩, + ⟨5, 3, 5, 0, 7, 6, 510044304005955603426885379461173700093542400000⟩, + ⟨5, 3, 6, 0, 8, 6, 5236876688118084393003602843224518454306406400000⟩, + ⟨5, 3, 0, 1, 1, 6, 1224676826808853386434748426154025183277062553600000⟩, + ⟨5, 3, 1, 1, 2, 6, -102947848630263467334743563011362038399107072000000⟩, + ⟨5, 3, 2, 1, 3, 6, 195915924811571046608922329789753855338296115200000⟩, + ⟨5, 3, 3, 1, 4, 6, -719211399303574107760706822197756217141703475200000⟩, + ⟨5, 3, 4, 1, 5, 6, -305701189507743637742374874254499426137119129600000⟩, + ⟨5, 3, 5, 1, 6, 6, -84153353667049552932810544567051200748113100800000⟩, + ⟨5, 3, 6, 1, 7, 6, -17514350194816330098075776700560266122756096000000⟩, + ⟨5, 3, 7, 1, 8, 6, -4703667518153639151064732167221227376187801600000⟩, + ⟨5, 3, 0, 2, 0, 6, 196917657201421650285317522492459403356563046400000⟩, + ⟨5, 3, 1, 2, 1, 6, -377121875623145854924689040064590927285243084800000⟩, + ⟨5, 3, 2, 2, 2, 6, 47832006111700205487286919845979365216931020800000⟩, + ⟨5, 3, 3, 2, 3, 6, 498901508172864128223479151098380547800222924800000⟩, + ⟨5, 3, 4, 2, 4, 6, 81505848279357222833163274152986070110070374400000⟩, + ⟨5, 3, 5, 2, 5, 6, 14720258797336661687805329461944898007806771200000⟩, + ⟨5, 3, 6, 2, 6, 6, 1209008904132632619886762729252401456139468800000⟩, + ⟨5, 3, 7, 2, 7, 6, 277709917916440880482904629598725720768512000000⟩, + ⟨5, 3, 8, 2, 8, 6, 561177919019364180065109486093580286872780800000⟩, + ⟨5, 3, 1, 3, 0, 6, -330976968098711294764559818895242423716701798400000⟩, + ⟨5, 3, 2, 3, 1, 6, 274128307444337420671134917615571733818900480000000⟩, + ⟨5, 3, 3, 3, 2, 6, -328982016676916811180236344100539744671026380800000⟩, + ⟨5, 3, 4, 3, 3, 6, -103959343670136242504434055021651571536560128000000⟩, + ⟨5, 3, 5, 3, 4, 6, -19923255801258282096057692614198087810390425600000⟩, + ⟨5, 3, 6, 3, 5, 6, -2945313061822889934834963871509510578031820800000⟩, + ⟨5, 3, 7, 3, 6, 6, 216841761953458384358019961062034297690521600000⟩, + ⟨5, 3, 8, 3, 7, 6, 343753328577358816297981795403240281473024000000⟩, + ⟨5, 3, 2, 4, 0, 6, -1049793011876550395716166287211767712538270105600000⟩, + ⟨5, 3, 3, 4, 1, 6, 303760371616891661503581156770910853502966169600000⟩, + ⟨5, 3, 4, 4, 2, 6, 346590784501272072826466559693683875020118425600000⟩, + ⟨5, 3, 5, 4, 3, 6, 1858369721972898686267088716288294397778329600000⟩, + ⟨5, 3, 6, 4, 4, 6, 1361144929634100727824966237078511580872704000000⟩, + ⟨5, 3, 7, 4, 5, 6, 746566675728109225621215005052754546655232000000⟩, + ⟨5, 3, 8, 4, 6, 6, -438470530912411540115637219042571885058457600000⟩, + ⟨5, 3, 3, 5, 0, 6, -364858678845737554092154651758377749874894438400000⟩, + ⟨5, 3, 4, 5, 1, 6, -334156775420078919435577935014665746245694259200000⟩, + ⟨5, 3, 5, 5, 2, 6, 144340896421256233523666167762930267120572825600000⟩, + ⟨5, 3, 6, 5, 3, 6, 504203508453704692205069247506280322852454400000⟩, + ⟨5, 3, 7, 5, 4, 6, -473070723041708032302704152493187712155648000000⟩, + ⟨5, 3, 8, 5, 5, 6, -146567447861872993575300481127910143636275200000⟩, + ⟨5, 3, 4, 6, 0, 6, -1042577027931637620148857704170667988444669542400000⟩, + ⟨5, 3, 5, 6, 1, 6, -184405533291409865518341102748803478339977216000000⟩, + ⟨5, 3, 6, 6, 2, 6, 36127680162137444356732215087051590013970022400000⟩, + ⟨5, 3, 7, 6, 3, 6, -1418511287855355299467458480607440426290380800000⟩, + ⟨5, 3, 8, 6, 4, 6, 218334666031418415527944453828338211042099200000⟩, + ⟨5, 3, 5, 7, 0, 6, -804548501685059486234082848606922089119403212800000⟩, + ⟨5, 3, 6, 7, 1, 6, -71621467233456503230585771945445592499696435200000⟩, + ⟨5, 3, 7, 7, 2, 6, 2519009021262915005244432228054635946128179200000⟩, + ⟨5, 3, 8, 7, 3, 6, 1045702645503917542326728785487617803996364800000⟩ +] + +def collectedFourData_8_2_43 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 2, 7, 1091709338863023520504214313114530638454587392000000⟩, + ⟨5, 4, 1, 0, 3, 7, 1151979659646538683390481589699667798364520448000000⟩, + ⟨5, 4, 2, 0, 4, 7, 718388407715453616211712088427191741274128384000000⟩, + ⟨5, 4, 3, 0, 5, 7, -1234469395429346446210409764974058592324812800000000⟩, + ⟨5, 4, 4, 0, 6, 7, -259131323928163601233672039827060197683101696000000⟩, + ⟨5, 4, 5, 0, 7, 7, -558309348453260424001004944565777649893376000000⟩, + ⟨5, 4, 6, 0, 8, 7, -4913518053307557152550754749823257031999488000000⟩, + ⟨5, 4, 0, 1, 1, 7, -8043401514784568687045095815723352665026985984000000⟩, + ⟨5, 4, 1, 1, 2, 7, 338069139339449263574756439792279409750179840000000⟩, + ⟨5, 4, 2, 1, 3, 7, -428910553354161086586137274800373769747562496000000⟩, + ⟨5, 4, 3, 1, 4, 7, 1180904613358786313179256121319117940664041472000000⟩, + ⟨5, 4, 4, 1, 5, 7, 401555309438676814158883227829931375879572684800000⟩, + ⟨5, 4, 5, 1, 6, 7, 92116711601309479857569739005932383441518592000000⟩, + ⟨5, 4, 6, 1, 7, 7, 16432900944457048383622836633295963627192320000000⟩, + ⟨5, 4, 7, 1, 8, 7, 3861578582647683186914325762086824876965888000000⟩, + ⟨5, 4, 0, 2, 0, 7, -1293310812738155381759369864299241842478678016000000⟩, + ⟨5, 4, 1, 2, 1, 7, 1238425762308904559272896328189609073763680256000000⟩, + ⟨5, 4, 2, 2, 2, 7, -104716613665482232133630839855409356848758784000000⟩, + ⟨5, 4, 3, 2, 3, 7, -819168179458058386548597820041748949162262528000000⟩, + ⟨5, 4, 4, 2, 4, 7, -107062410125329529588965943834648441915650867200000⟩, + ⟨5, 4, 5, 2, 5, 7, -16113223956537788324142883457202438367346688000000⟩, + ⟨5, 4, 6, 2, 6, 7, -1134356875452807335055304272802210954346496000000⟩, + ⟨5, 4, 7, 2, 7, 7, -227992022624067136203216158887113822044160000000⟩, + ⟨5, 4, 8, 2, 8, 7, -409521128358553126930287544019217996054528000000⟩, + ⟨5, 4, 1, 3, 0, 7, 1086891083544397543715869724091702739571048448000000⟩, + ⟨5, 4, 2, 3, 1, 7, -600137656747779281335671027467655399761510400000000⟩, + ⟨5, 4, 3, 3, 2, 7, 540169943888593218821672003297358296213618688000000⟩, + ⟨5, 4, 4, 3, 3, 7, 136556310048135628918717676071570618831601664000000⟩, + ⟨5, 4, 5, 3, 4, 7, 21808575996445730719637507715166044835282944000000⟩, + ⟨5, 4, 6, 3, 5, 7, 2763450385368899585736536022555020111118336000000⟩, + ⟨5, 4, 7, 3, 6, 7, -178020980554287372354049816098154362175488000000⟩, + ⟨5, 4, 8, 3, 7, 7, -250854936063781312844278672306883883171840000000⟩, + ⟨5, 4, 2, 4, 0, 7, 2298268004830964437925203795050580643873292288000000⟩, + ⟨5, 4, 3, 4, 1, 7, -498757423123874675823011028699598170416480256000000⟩, + ⟨5, 4, 4, 4, 2, 7, -455266039177373380730508837381669167848803532800000⟩, + ⟨5, 4, 5, 4, 3, 7, -2034225616306148860120139025123927763451904000000⟩, + ⟨5, 4, 6, 4, 4, 7, -1277099038841143896063517812415998386503680000000⟩, + ⟨5, 4, 7, 4, 5, 7, -612910218331460204022813356721576880373760000000⟩, + ⟨5, 4, 8, 4, 6, 7, 319975074723188757664776859582681281724416000000⟩, + ⟨5, 4, 3, 5, 0, 7, 599077402680402880031346530172980065808154624000000⟩, + ⟨5, 4, 4, 5, 1, 7, 438933285051680456796895977996044614028073369600000⟩, + ⟨5, 4, 5, 5, 2, 7, -157999748655501372185851928882966654242258944000000⟩, + ⟨5, 4, 6, 5, 3, 7, -473070723041708032302704152493187712155648000000⟩, + ⟨5, 4, 7, 5, 4, 7, 388377742500940849264066247465816964464640000000⟩, + ⟨5, 4, 8, 5, 5, 7, 106957997802041956910849035107473326866432000000⟩, + ⟨5, 4, 4, 6, 0, 7, 1369482211498362424339592753205315938299360051200000⟩, + ⟨5, 4, 5, 6, 1, 7, 201855666918497523157267793123307150995619840000000⟩, + ⟨5, 4, 6, 6, 2, 7, -33896923542909461898669036298995453508190208000000⟩, + ⟨5, 4, 7, 6, 3, 7, 1164557823716336273284668160693873718329344000000⟩, + ⟨5, 4, 8, 6, 4, 7, -159330322456769773822723748434074792886272000000⟩, + ⟨5, 4, 5, 7, 0, 7, 880682219655936916527802561311716555171561472000000⟩, + ⟨5, 4, 6, 7, 1, 7, 67199094653960090426127777979377226491101184000000⟩, + ⟨5, 4, 7, 7, 2, 7, -2068035474119462146746136891597191911571456000000⟩, + ⟨5, 4, 8, 7, 3, 7, -763104378844085458638515935606378718035968000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0811.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0811.lean new file mode 100644 index 0000000000000000000000000000000000000000..cb901bb96c089c8fa0551c597b721304713dfa4f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0811.lean @@ -0,0 +1,629 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse0807 +import OAI.Analysis.LaughlinFock.Sparse0808 +import OAI.Analysis.LaughlinFock.Sparse0809 +import OAI.Analysis.LaughlinFock.Sparse0810 + +namespace OAI + +/-! Sparse0811. -/ +namespace LaughlinFock +def collectedFourData_8_2_44 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 2, 8, 1352939793655494693945723082417182298124530483200000⟩, + ⟨5, 5, 1, 0, 3, 8, 951754627680599180236430384851275561353556787200000⟩, + ⟨5, 5, 2, 0, 4, 8, 445144247419959916467722905603152823004115763200000⟩, + ⟨5, 5, 3, 0, 5, 8, -611944117237512481395708085232118949428068352000000⟩, + ⟨5, 5, 4, 0, 6, 8, -107045916418916316125071412739723635046167347200000⟩, + ⟨5, 5, 5, 0, 7, 8, -197687086480616150190987242204035217463705600000⟩, + ⟨5, 5, 6, 0, 8, 8, -1522313189169887360748152988227413791159091200000⟩, + ⟨5, 5, 0, 1, 1, 8, -9968072634639538711606235683133681816941520486400000⟩, + ⟨5, 5, 1, 1, 2, 8, 279309504423926412478424198819035842216984576000000⟩, + ⟨5, 5, 2, 1, 3, 8, -265771361888318333365473179784422186550086860800000⟩, + ⟨5, 5, 3, 1, 4, 8, 585391289439146289938944251570836683792821780480000⟩, + ⟨5, 5, 4, 1, 5, 8, 165880586878261542540076470645019522970796687360000⟩, + ⟨5, 5, 5, 1, 6, 8, 32616835779461323546249636696224285196497715200000⟩, + ⟨5, 5, 6, 1, 7, 8, 5091264868199601676225824822616507828666368000000⟩, + ⟨5, 5, 7, 1, 8, 8, 1063466487280080505367237725139751932421734400000⟩, + ⟨5, 5, 0, 2, 0, 8, -1602781621288231431586625780791243434668693913600000⟩, + ⟨5, 5, 1, 2, 1, 8, 1023175574712861390244685678092773304668939878400000⟩, + ⟨5, 5, 2, 2, 2, 8, -64886901962581656455988923503761990870053683200000⟩, + ⟨5, 5, 3, 2, 3, 8, -406073370715825309105287823086346503921881579520000⟩, + ⟨5, 5, 4, 2, 4, 8, -44226971993014905207646729116250694170485719040000⟩, + ⟨5, 5, 5, 2, 5, 8, -5705396670506027733344571200481592966171852800000⟩, + ⟨5, 5, 6, 2, 6, 8, -351448069182307628639674252409164897085030400000⟩, + ⟨5, 5, 7, 2, 7, 8, -62788279517972115924524402484874479403008000000⟩, + ⟨5, 5, 8, 2, 8, 8, -101502737253492279975285335778699496925429760000⟩, + ⟨5, 5, 1, 3, 0, 8, 897979065763680207251430156292731264824455987200000⟩, + ⟨5, 5, 2, 3, 1, 8, -371871013914220884190932591310004968929361920000000⟩, + ⟨5, 5, 3, 3, 2, 8, 267769959056924005061606881150798382980053073920000⟩, + ⟨5, 5, 4, 3, 3, 8, 56410761656667546714340591580891866144230604800000⟩, + ⟨5, 5, 5, 3, 4, 8, 7722016228050640395145718190017461675779686400000⟩, + ⟨5, 5, 6, 3, 5, 8, 856176149883449031783201613339187915155046400000⟩, + ⟨5, 5, 7, 3, 6, 8, -49026413110675867991163789792123797530214400000⟩, + ⟨5, 5, 8, 3, 7, 8, -62176187993236170426424655539930925944012800000⟩, + ⟨5, 5, 2, 4, 0, 8, 1424105359151447355221397764901005726100907622400000⟩, + ⟨5, 5, 3, 4, 1, 8, -247241180817645026311027416635403922895315927040000⟩, + ⟨5, 5, 4, 4, 2, 8, -188068233663879001490800539420476893696056360960000⟩, + ⟨5, 5, 5, 4, 3, 8, -720281930520932354405323941492727514293862400000⟩, + ⟨5, 5, 6, 4, 4, 8, -395672650351889866204308737686261865644032000000⟩, + ⟨5, 5, 7, 4, 5, 8, -168793529111639468271196585303849448767488000000⟩, + ⟨5, 5, 8, 4, 6, 8, 79308108149326589395362091520895480464670720000⟩, + ⟨5, 5, 3, 5, 0, 8, 296971228041418874298972162035791078212407132160000⟩, + ⟨5, 5, 4, 5, 1, 8, 181321250680400268029096155025700381524722974720000⟩, + ⟨5, 5, 5, 5, 2, 8, -55944809204624220487939782734306559295645286400000⟩, + ⟨5, 5, 6, 5, 3, 8, -146567447861872993575300481127910143636275200000⟩, + ⟨5, 5, 7, 5, 4, 8, 106957997802041956910849035107473326866432000000⟩, + ⟨5, 5, 8, 5, 5, 8, 26510303855567904170337422391081262582333440000⟩, + ⟨5, 5, 4, 6, 0, 8, 565726582672367859466833590349765173900570787840000⟩, + ⟨5, 5, 5, 6, 1, 8, 71473384411832222906800406099842329533743104000000⟩, + ⟨5, 5, 6, 6, 2, 8, -10501993321652374317084701766882304174797619200000⟩, + ⟨5, 5, 7, 6, 3, 8, 320715529029321022094361566577819592635187200000⟩, + ⟨5, 5, 8, 6, 4, 8, -39491158665405962900795585277202004170506240000⟩, + ⟨5, 5, 5, 7, 0, 8, 311833399532695000999754363574818288595841843200000⟩, + ⟨5, 5, 6, 7, 1, 8, 20819719594423124407188906020781304978184601600000⟩, + ⟨5, 5, 7, 7, 2, 8, -569530406843225281616064763060558068763852800000⟩, + ⟨5, 5, 8, 7, 3, 8, -189140871859933898527259012120623943579074560000⟩ +] + +def collectedFourData_8_2_45 : List CollectedFourTerm := [ + ⟨6, 0, 2, 0, 4, 4, 45234870483201735282714208769413073589243079557120000⟩, + ⟨6, 0, 3, 0, 5, 4, -310924077382055503140003968462607307227178991616000000⟩, + ⟨6, 0, 4, 0, 6, 4, -163167608916567464095159181232008006556097236172800000⟩, + ⟨6, 0, 5, 0, 7, 4, -703102967575925938263037957996293659268061593600000⟩, + ⟨6, 0, 6, 0, 8, 4, -10828657955766577215700590560384070818258642534400000⟩, + ⟨6, 0, 2, 1, 3, 4, -27007275063851930678671456290491316210693864161280000⟩, + ⟨6, 0, 3, 1, 4, 4, 297432790755490458137540019676460515598603743395840000⟩, + ⟨6, 0, 4, 1, 5, 4, 252847933224101209299763591437499164088756485488640000⟩, + ⟨6, 0, 5, 1, 6, 4, 116006535569659221311448391711398020080070767411200000⟩, + ⟨6, 0, 6, 1, 7, 4, 36215652739636028473273915851250351064550998016000000⟩, + ⟨6, 0, 7, 1, 8, 4, 13616545436370494254871392754625346971420894167040000⟩, + ⟨6, 0, 2, 2, 2, 4, -6593706699223043547481264007372461529235581829120000⟩, + ⟨6, 0, 3, 2, 3, 4, -206322741869312150111979621283831857688673947484160000⟩, + ⟨6, 0, 4, 2, 4, 4, -67414148163105556984778663783173011114623458344960000⟩, + ⟨6, 0, 5, 2, 5, 4, -20292075732644954376610492498053878270642670796800000⟩, + ⟨6, 0, 6, 2, 6, 4, -2499952675615351033004642058428750077031664844800000⟩, + ⟨6, 0, 7, 2, 7, 4, -803936439139366380188266518873395956277890252800000⟩, + ⟨6, 0, 8, 2, 8, 4, -2166055771791881680979555698520888449271448207360000⟩, + ⟨6, 0, 2, 3, 1, 4, -37788957733057807078383997692324176397097500672000000⟩, + ⟨6, 0, 3, 3, 2, 4, 136051847097160444413061936231617333797833785999360000⟩, + ⟨6, 0, 4, 3, 3, 4, 85985616309360667097978759109791308022268769075200000⟩, + ⟨6, 0, 5, 3, 4, 4, 27464477433857221802701744624253791109831353958400000⟩, + ⟨6, 0, 6, 3, 5, 4, 6090230803313597628208599275306570946892844236800000⟩, + ⟨6, 0, 7, 3, 6, 4, -627730530005853370616269668779163050486834135040000⟩, + ⟨6, 0, 8, 3, 7, 4, -1326832108324572606347262365849804908717198540800000⟩, + ⟨6, 0, 2, 4, 0, 4, 144715385740736195306601789399857734943474806947840000⟩, + ⟨6, 0, 3, 4, 1, 4, -125621333502810035539766081885817328384520560312320000⟩, + ⟨6, 0, 4, 4, 2, 4, -286668048877338895342658921914813891084924527575040000⟩, + ⟨6, 0, 5, 4, 3, 4, -2561787782178891843044986127166325471192704614400000⟩, + ⟨6, 0, 6, 4, 4, 4, -2814535027085077340224031534270404555161206784000000⟩, + ⟨6, 0, 7, 4, 5, 4, -2161219733771120757204167360881361248804719820800000⟩, + ⟨6, 0, 8, 4, 6, 4, 1692425150838315981042439167496412106875385937920000⟩, + ⟨6, 0, 3, 5, 0, 4, 150888786225485035879599110270145998215200406241280000⟩, + ⟨6, 0, 4, 5, 1, 4, 276383779120548312685353593326111675875801201377280000⟩, + ⟨6, 0, 5, 5, 2, 4, -198975876839062954117225618144163636114125907558400000⟩, + ⟨6, 0, 6, 5, 3, 4, -1042577027931637620148857704170667988444669542400000⟩, + ⟨6, 0, 7, 5, 4, 4, 1369482211498362424339592753205315938299360051200000⟩, + ⟨6, 0, 8, 5, 5, 4, 565726582672367859466833590349765173900570787840000⟩, + ⟨6, 0, 4, 6, 0, 4, 862323915598513188933241245353534952478903275356160000⟩, + ⟨6, 0, 5, 6, 1, 4, 254205520336714777963126143979415783059199361024000000⟩, + ⟨6, 0, 6, 6, 2, 4, -74703743186992268727634002199778138264479098470400000⟩, + ⟨6, 0, 7, 6, 3, 4, 4106417668455613870887531399132716344553263595520000⟩, + ⟨6, 0, 8, 6, 4, 4, -842736407672675818660378189076872627749535088640000⟩, + ⟨6, 0, 5, 7, 0, 4, 1109080985025420318268386665675277589295754588979200000⟩, + ⟨6, 0, 6, 7, 1, 4, 148096741082507627113720638788477507674307769139200000⟩, + ⟨6, 0, 7, 7, 2, 4, -7292224771473160790231211832351095031440322068480000⟩, + ⟨6, 0, 8, 7, 3, 4, -4036242649799701108578654264242356513226788700160000⟩ +] + +def collectedFourData_8_2_46 : List CollectedFourTerm := [ + ⟨6, 1, 1, 0, 3, 5, 21383234213561752727169599815972852174889680896000000⟩, + ⟨6, 1, 2, 0, 4, 5, 40004528161201879155386372231030568568492130304000000⟩, + ⟨6, 1, 3, 0, 5, 5, -137486532809298326254136970573352318673721753600000000⟩, + ⟨6, 1, 4, 0, 6, 5, -48100378728270458521324541048013618906314833920000000⟩, + ⟨6, 1, 5, 0, 7, 5, -155451436945425755613165835940348848012001280000000⟩, + ⟨6, 1, 6, 0, 8, 5, -1915315983054960820074335425690499405888618496000000⟩, + ⟨6, 1, 1, 1, 2, 5, 6275294469253702638864339353430356450271559680000000⟩, + ⟨6, 1, 2, 1, 3, 5, -23884522809685248831461856039966303737113214976000000⟩, + ⟨6, 1, 3, 1, 4, 5, 131520863514592448549622997480799642781078257664000000⟩, + ⟨6, 1, 4, 1, 5, 5, 74537351067996267335715539353075701776904093696000000⟩, + ⟨6, 1, 5, 1, 6, 5, 25648281234735082686072710442773676992243957760000000⟩, + ⟨6, 1, 6, 1, 7, 5, 6405633903327280034046696948090978046511677440000000⟩, + ⟨6, 1, 7, 1, 8, 5, 2007019030336544567337002713611192229825609728000000⟩, + ⟨6, 1, 1, 2, 1, 5, 22987860861784124263107767007891027132533440512000000⟩, + ⟨6, 1, 2, 2, 2, 5, -5831300554596027078640750997259267474355912704000000⟩, + ⟨6, 1, 3, 2, 3, 5, -91233199622760087577303107056356230545157390336000000⟩, + ⟨6, 1, 4, 2, 4, 5, -19873099077815000591128632120858590736593977344000000⟩, + ⟨6, 1, 5, 2, 5, 5, -4486444342740487398535346723052885390278000640000000⟩, + ⟨6, 1, 6, 2, 6, 5, -442178461638197686418918771278986973997432832000000⟩, + ⟨6, 1, 7, 2, 7, 5, -118496702417921799294587941735011441400872960000000⟩, + ⟨6, 1, 8, 2, 8, 5, -273657525696309893610329230932490719137366016000000⟩, + ⟨6, 1, 1, 3, 0, 5, 20175049454599629332396951016473764512342736896000000⟩, + ⟨6, 1, 2, 3, 1, 5, -33419559018655069785344525747831192926185062400000000⟩, + ⟨6, 1, 3, 3, 2, 5, 60160335272796521086807856408224114744026464256000000⟩, + ⟨6, 1, 4, 3, 3, 5, 25347804856163755395671067355002626226027233280000000⟩, + ⟨6, 1, 5, 3, 4, 5, 6072215136237902234528425657233668250607288320000000⟩, + ⟨6, 1, 6, 3, 5, 5, 1077207946333588289030038210475336442537050112000000⟩, + ⟨6, 1, 7, 3, 6, 5, -92524724830706550058781744923746825381347328000000⟩, + ⟨6, 1, 8, 3, 7, 5, -167630767640921017752805241428509255511572480000000⟩, + ⟨6, 1, 2, 4, 0, 5, 127982475961202486480637649901926613889715273728000000⟩, + ⟨6, 1, 3, 4, 1, 5, -55548099509062599485951584916705584979034243072000000⟩, + ⟨6, 1, 4, 4, 2, 5, -84507224269891703337477849545423062916615110656000000⟩, + ⟨6, 1, 5, 4, 3, 5, -566394411990502754377528950673264138644357120000000⟩, + ⟨6, 1, 6, 4, 4, 5, -497820131013867462561886819486132288943554560000000⟩, + ⟨6, 1, 7, 4, 5, 5, -318554302534881009844796184618543641851330560000000⟩, + ⟨6, 1, 8, 4, 6, 5, 213819461731347031175648873178500536259837952000000⟩, + ⟨6, 1, 3, 5, 0, 5, 66721034384398000100945175265619388154131775488000000⟩, + ⟨6, 1, 4, 5, 1, 5, 81475511826901450282752777357487617669586747392000000⟩, + ⟨6, 1, 5, 5, 2, 5, -43992256324488123403551592902040931768016568320000000⟩, + ⟨6, 1, 6, 5, 3, 5, -184405533291409865518341102748803478339977216000000⟩, + ⟨6, 1, 7, 5, 4, 5, 201855666918497523157267793123307150995619840000000⟩, + ⟨6, 1, 8, 5, 5, 5, 71473384411832222906800406099842329533743104000000⟩, + ⟨6, 1, 4, 6, 0, 5, 254205520336714777963126143979415783059199361024000000⟩, + ⟨6, 1, 5, 6, 1, 5, 56203166873328100018229759869666357679436595200000000⟩, + ⟨6, 1, 6, 6, 2, 5, -13213204619126829495671857154504306110010228736000000⟩, + ⟨6, 1, 7, 6, 3, 5, 605267940066997181963208748597933364440203264000000⟩, + ⟨6, 1, 8, 6, 4, 5, -106470554978886132742402641716893386050371584000000⟩, + ⟨6, 1, 5, 7, 0, 5, 245210503669836915770328516186948363691921244160000000⟩, + ⟨6, 1, 6, 7, 1, 5, 26194571514988713721183779947474110803741769728000000⟩, + ⟨6, 1, 7, 7, 2, 5, -1074841923616371995726560321129801234866241536000000⟩, + ⟨6, 1, 8, 7, 3, 5, -509935243144898351580160422868938849251229696000000⟩ +] + +def collectedFourData_8_2_47 : List CollectedFourTerm := [ + ⟨6, 2, 0, 0, 2, 6, -11910307910613112406324392917081895077489200332800000⟩, + ⟨6, 2, 1, 0, 3, 6, -25135687613413499443490401829864666832847660646400000⟩, + ⟨6, 2, 2, 0, 4, 6, -23512376868234355048594282937806493153657408716800000⟩, + ⟨6, 2, 3, 0, 5, 6, 53871154463529606563868479515073905413932974080000000⟩, + ⟨6, 2, 4, 0, 6, 6, 14135327725984110715755298075004093703055736832000000⟩, + ⟨6, 2, 5, 0, 7, 6, 36546190525643831838120020472792517223802470400000⟩, + ⟨6, 2, 6, 0, 8, 6, 375237781698727521619917528613736114221901414400000⟩, + ⟨6, 2, 0, 1, 1, 6, 87751735081379626613332990045337253886270478745600000⟩, + ⟨6, 2, 1, 1, 2, 6, -7376519374291097733174100713346261980819750912000000⟩, + ⟨6, 2, 2, 1, 3, 6, 14037958387018439462575680033339486533969982259200000⟩, + ⟨6, 2, 3, 1, 4, 6, -51533634668051128675404755164720627705896448819200000⟩, + ⟨6, 2, 4, 1, 5, 6, -21904398947146160450234480321260419064079686041600000⟩, + ⟨6, 2, 5, 1, 6, 6, -6029837942179959451055798700555629976529718476800000⟩, + ⟨6, 2, 6, 1, 7, 6, -1254955254132454241882635652194403147071881216000000⟩, + ⟨6, 2, 7, 1, 8, 6, -337031759667916879703418460806791785017350553600000⟩, + ⟨6, 2, 0, 2, 0, 6, 14109735490473282102062069563883863872503178854400000⟩, + ⟨6, 2, 1, 2, 1, 6, -27021903410474539568168625271210600031668980940800000⟩, + ⟨6, 2, 2, 2, 2, 6, 3427305422004172088391033861481643016178158796800000⟩, + ⟨6, 2, 3, 2, 3, 6, 35747776081435557336028902218069007516534885580800000⟩, + ⟨6, 2, 4, 2, 4, 6, 5840136311250379171928042700048194458628810342400000⟩, + ⟨6, 2, 5, 2, 5, 6, 1054750299864085331278818430370855559516861235200000⟩, + ⟨6, 2, 6, 2, 6, 6, 86629081847594011293072403747753187496217804800000⟩, + ⟨6, 2, 7, 2, 7, 6, 19898741131548150617263898544910537328689152000000⟩, + ⟨6, 2, 8, 2, 8, 6, 40210066039726881241738205134300111906327756800000⟩, + ⟨6, 2, 1, 3, 0, 6, -23715483617270635140119439036266677081909651046400000⟩, + ⟨6, 2, 2, 3, 1, 6, 19642108094625527146397429584324395312170926080000000⟩, + ⟨6, 2, 3, 3, 2, 6, -23572539417761539301372311404074370406858673356800000⟩, + ⟨6, 2, 4, 3, 3, 6, -7448996000640212895096416028681710160511500288000000⟩, + ⟨6, 2, 5, 3, 4, 6, -1427560501480322294523414280594314611956226457600000⟩, + ⟨6, 2, 6, 3, 5, 6, -211040436035905329006377724981144529704635596800000⟩, + ⟨6, 2, 7, 3, 6, 6, 15537356821800448127451102099961115368331673600000⟩, + ⟨6, 2, 8, 3, 7, 6, 24630947824222167339100372809551422427234304000000⟩, + ⟨6, 2, 2, 4, 0, 6, -75220789886679929498961825082371707938608355737600000⟩, + ⟨6, 2, 3, 4, 1, 6, 21765333576044934858770645449558339949336041881600000⟩, + ⟨6, 2, 4, 4, 2, 6, 24834259975713696934890411286580034955418114457600000⟩, + ⟨6, 2, 5, 4, 3, 6, 133157714717889050922042141385631552002169241600000⟩, + ⟨6, 2, 6, 4, 4, 6, 97530080310123533303112970283565135465283584000000⟩, + ⟨6, 2, 7, 4, 5, 6, 53493721539408562557654526853613199684534272000000⟩, + ⟨6, 2, 8, 4, 6, 6, -31417716925269464547472934641197418502789529600000⟩, + ⟨6, 2, 3, 5, 0, 6, -26143208908133048742549261339088709435896784486400000⟩, + ⟨6, 2, 4, 5, 1, 6, -23943326264054082868884444512138803444075148083200000⟩, + ⟨6, 2, 5, 5, 2, 6, 10342454292346840282785862667165342465196136857600000⟩, + ⟨6, 2, 6, 5, 3, 6, 36127680162137444356732215087051590013970022400000⟩, + ⟨6, 2, 7, 5, 4, 6, -33896923542909461898669036298995453508190208000000⟩, + ⟨6, 2, 8, 5, 5, 6, -10501993321652374317084701766882304174797619200000⟩, + ⟨6, 2, 4, 6, 0, 6, -74703743186992268727634002199778138264479098470400000⟩, + ⟨6, 2, 5, 6, 1, 6, -13213204619126829495671857154504306110010228736000000⟩, + ⟨6, 2, 6, 6, 2, 6, 2588655675761808089537903038819279511088424550400000⟩, + ⟨6, 2, 7, 6, 3, 6, -101640550402329138324174779913832615428017356800000⟩, + ⟨6, 2, 8, 6, 4, 6, 15644327836751731368728957394035408144380723200000⟩, + ⟨6, 2, 5, 7, 0, 6, -57648291724399163384869576061044467878350081228800000⟩, + ⟨6, 2, 6, 7, 1, 6, -5131891027273377205433124670605303853968732979200000⟩, + ⟨6, 2, 7, 7, 2, 6, 180494484310161284611960895071948412774724403200000⟩, + ⟨6, 2, 8, 7, 3, 6, 74927702977170630470416252569144779038575820800000⟩ +] + +def collectedFourData_8_2_48 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 2, 7, 3273510586910224613401431838899951120850039603200000⟩, + ⟨6, 3, 1, 0, 3, 7, 3454232255341483537847423166151990063504608460800000⟩, + ⟨6, 3, 2, 0, 4, 7, 2154100889728834183307911649713502959840945766400000⟩, + ⟨6, 3, 3, 0, 5, 7, -3701579249439451144151750137699269432185978880000000⟩, + ⟨6, 3, 4, 0, 6, 7, -777010053941966381807074646878694867344136601600000⟩, + ⟨6, 3, 5, 0, 7, 7, -1674100878202719194338067308962555897682329600000⟩, + ⟨6, 3, 6, 0, 8, 7, -14733274502559621133728690904232802265124044800000⟩, + ⟨6, 3, 0, 1, 1, 7, -24118287786050222011623630609623006872177370726400000⟩, + ⟨6, 3, 1, 1, 2, 7, 1013706549298071927316127335811932110679179264000000⟩, + ⟨6, 3, 2, 1, 3, 7, -1286096204603901439281451954363507871906896281600000⟩, + ⟨6, 3, 3, 1, 4, 7, 3540964262508833659580451735536200150502552371200000⟩, + ⟨6, 3, 4, 1, 5, 7, 1204071001212209289421481442138598372387407790080000⟩, + ⟨6, 3, 5, 1, 6, 7, 276213658639479007452283018995265512861283123200000⟩, + ⟨6, 3, 6, 1, 7, 7, 49274356552954801374452501778044727613980672000000⟩, + ⟨6, 3, 7, 1, 8, 7, 11579014598929819495699772649743882465889484800000⟩, + ⟨6, 3, 0, 2, 0, 7, -3878016324448622900701233824017012220287883673600000⟩, + ⟨6, 3, 1, 2, 1, 7, 3713442488494841726779054170476998262057965977600000⟩, + ⟨6, 3, 2, 2, 2, 7, -313994697358134331302246466621984924737365606400000⟩, + ⟨6, 3, 3, 2, 3, 7, -2456290893974282462472398339499269899229646028800000⟩, + ⟨6, 3, 4, 2, 4, 7, -321028611306368985553032136477616205406006149120000⟩, + ⟨6, 3, 5, 2, 5, 7, -48315799208895505394461959622822852563881164800000⟩, + ⟨6, 3, 6, 2, 6, 7, -3401390011920634794867585373231348933302681600000⟩, + ⟨6, 3, 7, 2, 7, 7, -683638284681378533917375326941725260251136000000⟩, + ⟨6, 3, 8, 2, 8, 7, -1227956656156575990528670296840792722689228800000⟩, + ⟨6, 3, 1, 3, 0, 7, 3259062959474532577319005473385648599493037260800000⟩, + ⟨6, 3, 2, 3, 1, 7, -1799523832060799395001908745356204929020067840000000⟩, + ⟨6, 3, 3, 3, 2, 7, 1619709539071620963091713567684570156058332364800000⟩, + ⟨6, 3, 4, 3, 3, 7, 409466614179119301856219886090336883572106854400000⟩, + ⟨6, 3, 5, 3, 4, 7, 65393417339593410430480446737249257298224742400000⟩, + ⟨6, 3, 6, 3, 5, 7, 8286256946677319916660864396739573580405145600000⟩, + ⟨6, 3, 7, 3, 6, 7, -533799193422230927312918227280157196733644800000⟩, + ⟨6, 3, 8, 3, 7, 7, -752193152289694213090083266555610308542464000000⟩, + ⟨6, 3, 2, 4, 0, 7, 6891398999303752322350745794776261680970910924800000⟩, + ⟨6, 3, 3, 4, 1, 7, -1495533331789991322997342107797381550500845977600000⟩, + ⟨6, 3, 4, 4, 2, 7, -1365123614917437905007155176949053561550804090880000⟩, + ⟨6, 3, 5, 4, 3, 7, -6099663027594257030807656110704072252089958400000⟩, + ⟨6, 3, 6, 4, 4, 7, -3829405021425666409377579958697893117820928000000⟩, + ⟨6, 3, 7, 4, 5, 7, -1837822593533049065578169632872185563447296000000⟩, + ⟨6, 3, 8, 4, 6, 7, 959451162838473115886385476677327119817113600000⟩, + ⟨6, 3, 3, 5, 0, 7, 1796344640685569480707754494220893049103738470400000⟩, + ⟨6, 3, 4, 5, 1, 7, 1316149550447549065089940770855297420370284380160000⟩, + ⟨6, 3, 5, 5, 2, 7, -473765160323349540288432296760400798823114342400000⟩, + ⟨6, 3, 6, 5, 3, 7, -1418511287855355299467458480607440426290380800000⟩, + ⟨6, 3, 7, 5, 4, 7, 1164557823716336273284668160693873718329344000000⟩, + ⟨6, 3, 8, 5, 5, 7, 320715529029321022094361566577819592635187200000⟩, + ⟨6, 3, 4, 6, 0, 7, 4106417668455613870887531399132716344553263595520000⟩, + ⟨6, 3, 5, 6, 1, 7, 605267940066997181963208748597933364440203264000000⟩, + ⟨6, 3, 6, 6, 2, 7, -101640550402329138324174779913832615428017356800000⟩, + ⟨6, 3, 7, 6, 3, 7, 3491948112283092418989976007284342498158182400000⟩, + ⟨6, 3, 8, 6, 4, 7, -477754910406145155110841172831061316678451200000⟩, + ⟨6, 3, 5, 7, 0, 7, 2640741878007352039904402382426075332693144371200000⟩, + ⟨6, 3, 6, 7, 1, 7, 201497724668746359176569786606814712578860646400000⟩, + ⟨6, 3, 7, 7, 2, 7, -6201042509800644041322799505395672497625497600000⟩, + ⟨6, 3, 8, 7, 3, 7, -2288182553851993539857834496310617668635852800000⟩ +] + +def collectedFourData_8_2_49 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 2, 8, -2015411077409025205422546723918192424546153267200000⟩, + ⟨6, 4, 1, 0, 3, 8, -1417784315752941965399798629424245372890592051200000⟩, + ⟨6, 4, 2, 0, 4, 8, -663110547492356637637883669868354941649892147200000⟩, + ⟨6, 4, 3, 0, 5, 8, 911584505400256977154233393071790722585198592000000⟩, + ⟨6, 4, 4, 0, 6, 8, 159461290704721376955399625838934411204309811200000⟩, + ⟨6, 4, 5, 0, 7, 8, 294485198692589752845406597014071654586777600000⟩, + ⟨6, 4, 6, 0, 8, 8, 2267718696076798972511212393591351536726835200000⟩, + ⟨6, 4, 0, 1, 1, 8, 14848971182960002831115331849280642751633188454400000⟩, + ⟨6, 4, 1, 1, 2, 8, -416074293831397367341429584874307116855197696000000⟩, + ⟨6, 4, 2, 1, 3, 8, 395907156637445840420903886869545517629361356800000⟩, + ⟨6, 4, 3, 1, 4, 8, -872030000807875789998861407471104105772042158080000⟩, + ⟨6, 4, 4, 1, 5, 8, -247104545146291507052010338626009911953782210560000⟩, + ⟨6, 4, 5, 1, 6, 8, -48587773416247178752419912649894786707436339200000⟩, + ⟨6, 4, 6, 1, 7, 8, -7584218944191748411519230902233627285782528000000⟩, + ⟨6, 4, 7, 1, 8, 8, -1584196243593750382463743815053382917711462400000⟩, + ⟨6, 4, 0, 2, 0, 8, 2387588752552011721508898620851844106604353945600000⟩, + ⟨6, 4, 1, 2, 1, 8, -1524176757222157307705485613712009919994422886400000⟩, + ⟨6, 4, 2, 2, 2, 8, 96658980397645114995908927461986375279260467200000⟩, + ⟨6, 4, 3, 2, 3, 8, 604908491434239073034314144252580803314104401920000⟩, + ⟨6, 4, 4, 2, 4, 8, 65882849845185309285018990927767643237478563840000⟩, + ⟨6, 4, 5, 2, 5, 8, 8499062341630251883477678641353698237533388800000⟩, + ⟨6, 4, 6, 2, 6, 8, 523535736834419023026493685434959264114278400000⟩, + ⟨6, 4, 7, 2, 7, 8, 93532760781665458439882752338952577875968000000⟩, + ⟨6, 4, 8, 2, 8, 8, 151203876186760024884410025483675536153640960000⟩, + ⟨6, 4, 1, 3, 0, 8, -1337677378482346259153101287393290392658195251200000⟩, + ⟨6, 4, 2, 3, 1, 8, 553958841571991100689973606666135434239672320000000⟩, + ⟨6, 4, 3, 3, 2, 8, -398884373282100059919909608492697901104176824320000⟩, + ⟨6, 4, 4, 3, 3, 8, -84032470965132761892505875567109980837170380800000⟩, + ⟨6, 4, 5, 3, 4, 8, -11503126095430973789039408741488111307351654400000⟩, + ⟨6, 4, 6, 3, 5, 8, -1275405531554567487425295213457479286810214400000⟩, + ⟨6, 4, 7, 3, 6, 8, 73032352608919745461419875369873794557542400000⟩, + ⟨6, 4, 8, 3, 7, 8, 92620956690215158275108635311198740204748800000⟩, + ⟨6, 4, 2, 4, 0, 8, -2121423088958404026290362617459479459114935910400000⟩, + ⟨6, 4, 3, 4, 1, 8, 368303613322835063925047601611718450692845731840000⟩, + ⟨6, 4, 4, 4, 2, 8, 280156443924840356759797947636696301483233116160000⟩, + ⟨6, 4, 5, 4, 3, 8, 1072970274388343451146171435009621382030950400000⟩, + ⟨6, 4, 6, 4, 4, 8, 589415025181854821668244362101232471375872000000⟩, + ⟨6, 4, 7, 4, 5, 8, 251443818832033476033029185111574653698048000000⟩, + ⟨6, 4, 8, 4, 6, 8, -118141576175122980707773286506392645135237120000⟩, + ⟨6, 4, 3, 5, 0, 8, -442384136731838204791251366025592098331673231360000⟩, + ⟨6, 4, 4, 5, 1, 8, -270105779211037326410964093891398626880646021120000⟩, + ⟨6, 4, 5, 5, 2, 8, 83338363409277145604829747052316011029489254400000⟩, + ⟨6, 4, 6, 5, 3, 8, 218334666031418415527944453828338211042099200000⟩, + ⟨6, 4, 7, 5, 4, 8, -159330322456769773822723748434074792886272000000⟩, + ⟨6, 4, 8, 5, 5, 8, -39491158665405962900795585277202004170506240000⟩, + ⟨6, 4, 4, 6, 0, 8, -842736407672675818660378189076872627749535088640000⟩, + ⟨6, 4, 5, 6, 1, 8, -106470554978886132742402641716893386050371584000000⟩, + ⟨6, 4, 6, 6, 2, 8, 15644327836751731368728957394035408144380723200000⟩, + ⟨6, 4, 7, 6, 3, 8, -477754910406145155110841172831061316678451200000⟩, + ⟨6, 4, 8, 6, 4, 8, 58828130421776326798738175703110015558615040000⟩, + ⟨6, 4, 5, 7, 0, 8, -464523617881209797667100654527351587693867827200000⟩, + ⟨6, 4, 6, 7, 1, 8, -31014161676609421763791711070880146730359193600000⟩, + ⟨6, 4, 7, 7, 2, 8, 848402786477122712410586931140583939165388800000⟩, + ⟨6, 4, 8, 7, 3, 8, 281754302833654110018555844706417529071861760000⟩ +] + +def collectedFourData_8_2_50 : List CollectedFourTerm := [ + ⟨7, 0, 1, 0, 3, 5, 93293561969830618502034198903533688746459057356800000⟩, + ⟨7, 0, 2, 0, 4, 5, 174536970871969142770894863055070410857159799603200000⟩, + ⟨7, 0, 3, 0, 5, 5, -599844169528222518170524771358942643021026426880000000⟩, + ⟨7, 0, 4, 0, 6, 5, -209858603186049938820731487152786654320379559936000000⟩, + ⟨7, 0, 5, 0, 7, 5, -678223795386826527642932445697434457655476224000000⟩, + ⟨7, 0, 6, 0, 8, 5, -8356390271571628745405561376849023363581791436800000⟩, + ⟨7, 0, 1, 1, 2, 5, 27378672823728080253640283022704798475636178944000000⟩, + ⟨7, 0, 2, 1, 3, 5, -104206509951239310715733925612251291088019311820800000⟩, + ⟨7, 0, 3, 1, 4, 5, 573816369782000034372575589092023658911473283891200000⟩, + ⟨7, 0, 4, 1, 5, 5, 325201272711067765191788266964301228515825339596800000⟩, + ⟨7, 0, 5, 1, 6, 5, 111901665150111786938482065547020296856281284608000000⟩, + ⟨7, 0, 6, 1, 7, 5, 27947334699121274676446447058561370877488791552000000⟩, + ⟨7, 0, 7, 1, 8, 5, 8756484281623707982957469136036292315025139302400000⟩, + ⟨7, 0, 1, 2, 1, 5, 100294436306671174105771666579455255316182702489600000⟩, + ⟨7, 0, 2, 2, 2, 5, -25441558289151600071919739548481725189412041523200000⟩, + ⟨7, 0, 3, 2, 3, 5, -398044097431889887496005816384596273027139554508800000⟩, + ⟨7, 0, 4, 2, 4, 5, -86704947522524278204385561134346383181999190835200000⟩, + ⟨7, 0, 5, 2, 5, 5, -19574044278493536384891190136798605190325338112000000⟩, + ⟨7, 0, 6, 2, 6, 5, -1929193839461587008820048633258629484118645145600000⟩, + ⟨7, 0, 7, 2, 7, 5, -516992861783070949993626718825606020247584768000000⟩, + ⟨7, 0, 8, 2, 8, 5, -1193948729975896933934156746486738655371906252800000⟩, + ⟨7, 0, 1, 3, 0, 5, 88022335991781392235533311276839569957948542156800000⟩, + ⟨7, 0, 2, 3, 1, 5, -145807209011156374542151346103610906983184465920000000⟩, + ⟨7, 0, 3, 3, 2, 5, 262475353861054526609727139796176833685524106444800000⟩, + ⟨7, 0, 4, 3, 3, 5, 110590707632425546294751602074336570953982541824000000⟩, + ⟨7, 0, 5, 3, 4, 5, 26492651834092871256260611348864054574979219456000000⟩, + ⟨7, 0, 6, 3, 5, 5, 4699783264401102417726023802649227411953654169600000⟩, + ⟨7, 0, 7, 3, 6, 5, -403678931985903865447183854427165739505313382400000⟩, + ⟨7, 0, 8, 3, 7, 5, -731361367170547106073270027120766813086941184000000⟩, + ⟨7, 0, 2, 4, 0, 5, 558378631262721178978030267937543889944494630502400000⟩, + ⟨7, 0, 3, 4, 1, 5, -242352490371560576847400385026544352640387094937600000⟩, + ⟨7, 0, 4, 4, 2, 5, -368699135293636224902523636819960537506281999564800000⟩, + ⟨7, 0, 5, 4, 3, 5, -2471139381753989384043453591696817849154666496000000⟩, + ⟨7, 0, 6, 4, 4, 5, -2171954568645931527689714451084586634390274048000000⟩, + ⟨7, 0, 7, 4, 5, 5, -1389830241182391310568294939372375835408334848000000⟩, + ⟨7, 0, 8, 4, 6, 5, 932879423391330139364084034494459935008070041600000⟩, + ⟨7, 0, 3, 5, 0, 5, 291099227266762975244865063395549704658490910310400000⟩, + ⟨7, 0, 4, 5, 1, 5, 355471985001495927064656611871378500067863927193600000⟩, + ⟨7, 0, 5, 5, 2, 5, -191935151184862794748892013298784990457501843456000000⟩, + ⟨7, 0, 6, 5, 3, 5, -804548501685059486234082848606922089119403212800000⟩, + ⟨7, 0, 7, 5, 4, 5, 880682219655936916527802561311716555171561472000000⟩, + ⟨7, 0, 8, 5, 5, 5, 311833399532695000999754363574818288595841843200000⟩, + ⟨7, 0, 4, 6, 0, 5, 1109080985025420318268386665675277589295754588979200000⟩, + ⟨7, 0, 5, 6, 1, 5, 245210503669836915770328516186948363691921244160000000⟩, + ⟨7, 0, 6, 6, 2, 5, -57648291724399163384869576061044467878350081228800000⟩, + ⟨7, 0, 7, 6, 3, 5, 2640741878007352039904402382426075332693144371200000⟩, + ⟨7, 0, 8, 6, 4, 5, -464523617881209797667100654527351587693867827200000⟩, + ⟨7, 0, 5, 7, 0, 5, 1069836353626358940237712704037589468915567689728000000⟩, + ⟨7, 0, 6, 7, 1, 5, 114285091604938476467136354131576108969332467302400000⟩, + ⟨7, 0, 7, 7, 2, 5, -4689460472030870129518160279202309108933643468800000⟩, + ⟨7, 0, 8, 7, 3, 5, -2224811959304400678575044991143908439057288396800000⟩ +] + +def collectedFourData_8_2_51 : List CollectedFourTerm := [ + ⟨7, 1, 0, 0, 2, 6, 23611638608735021902683199787388232915132769894400000⟩, + ⟨7, 1, 1, 0, 3, 6, 49830346668126167639060868239351700090778759987200000⟩, + ⟨7, 1, 2, 0, 4, 6, 46612207644978677603840169418033781193883149926400000⟩, + ⟨7, 1, 3, 0, 5, 6, -106797090400555819355310251525224734958383267840000000⟩, + ⟨7, 1, 4, 0, 6, 6, -28022638237972138344930218938518748572193652736000000⟩, + ⟨7, 1, 5, 0, 7, 6, -72451144814530430443237963778280980479161139200000⟩, + ⟨7, 1, 6, 0, 8, 6, -743891674363746096275523006901764702088672051200000⟩, + ⟨7, 1, 0, 1, 1, 6, -173963785955919195502186644317721307080471399628800000⟩, + ⟨7, 1, 1, 1, 2, 6, 14623610990014083678693612814344328316322840576000000⟩, + ⟨7, 1, 2, 1, 3, 6, -27829607993877424465484354112200911220219943321600000⟩, + ⟨7, 1, 3, 1, 4, 6, 102163064725835807691097951434575498867881122201600000⟩, + ⟨7, 1, 4, 1, 5, 6, 43424465241633452289088176980679811214791724236800000⟩, + ⟨7, 1, 5, 1, 6, 6, 11953876879465376894448525182551436073397282406400000⟩, + ⟨7, 1, 6, 1, 7, 6, 2487891174022836054263333114975337657315360768000000⟩, + ⟨7, 1, 7, 1, 8, 6, 668149989796127624459238998553969513309457612800000⟩, + ⟨7, 1, 0, 2, 0, 6, -27971902806058337064536397492970636005480805171200000⟩, + ⟨7, 1, 1, 2, 1, 6, 53569682886176950545966531756881526362470770278400000⟩, + ⟨7, 1, 2, 2, 2, 6, -6794475645252634754017400725141063476326065766400000⟩, + ⟨7, 1, 3, 2, 3, 6, -70868324835557329170622601411583808391315088998400000⟩, + ⟨7, 1, 4, 2, 4, 6, -11577802105696887193656800984013298682775679795200000⟩, + ⟨7, 1, 5, 2, 5, 6, -2090994043962014122520504247541480802221660569600000⟩, + ⟨7, 1, 6, 2, 6, 6, -171738177463005840483120174066260560755189350400000⟩, + ⟨7, 1, 7, 2, 7, 6, -39448340705635011865747968357172970935812096000000⟩, + ⟨7, 1, 8, 2, 8, 6, -79714609805963123409548347705798192756319846400000⟩, + ⟨7, 1, 1, 3, 0, 6, 47014857449940169663205039961217276364924859187200000⟩, + ⟨7, 1, 2, 3, 1, 6, -38939577492428779339510138045037508648857763840000000⟩, + ⟨7, 1, 3, 3, 2, 6, 46731477137243455755544857353286175157928748646400000⟩, + ⟨7, 1, 4, 3, 3, 6, 14767292574216513974204540947571011817280897024000000⟩, + ⟨7, 1, 5, 3, 4, 6, 2830073152266871521811499774148016026885606604800000⟩, + ⟨7, 1, 6, 3, 5, 6, 418377975188144683013270920932201107592472166400000⟩, + ⟨7, 1, 7, 3, 6, 6, -30802096550703766575889895446790775885319372800000⟩, + ⟨7, 1, 8, 3, 7, 6, -48829723209582740413871303135650398383112192000000⟩, + ⟨7, 1, 2, 4, 0, 6, 149121762426077219174416722063802093692397604044800000⟩, + ⟨7, 1, 3, 4, 1, 6, -43148774528171223053701669603493790126961380556800000⟩, + ⟨7, 1, 4, 4, 2, 6, -49232780215481361604310889104089639524179430604800000⟩, + ⟨7, 1, 5, 4, 3, 6, -263979055913591737331485501082118523219397836800000⟩, + ⟨7, 1, 6, 4, 4, 6, -193348906430160928065037942568489713907269632000000⟩, + ⟨7, 1, 7, 4, 5, 6, -106048846957122840866486997677668701994745856000000⟩, + ⟨7, 1, 8, 4, 6, 6, 62284181359406437518017310831146647946054860800000⟩, + ⟨7, 1, 3, 5, 0, 6, 51827711377759287266580684807419925696156480307200000⟩, + ⟨7, 1, 4, 5, 1, 6, 47466545036515040629785876639327132524587096473600000⟩, + ⟨7, 1, 5, 5, 2, 6, -20503440793554008920441545095300573633859865804800000⟩, + ⟨7, 1, 6, 5, 3, 6, -71621467233456503230585771945445592499696435200000⟩, + ⟨7, 1, 7, 5, 4, 6, 67199094653960090426127777979377226491101184000000⟩, + ⟨7, 1, 8, 5, 5, 6, 20819719594423124407188906020781304978184601600000⟩, + ⟨7, 1, 4, 6, 0, 6, 148096741082507627113720638788477507674307769139200000⟩, + ⟨7, 1, 5, 6, 1, 6, 26194571514988713721183779947474110803741769728000000⟩, + ⟨7, 1, 6, 6, 2, 6, -5131891027273377205433124670605303853968732979200000⟩, + ⟨7, 1, 7, 6, 3, 6, 201497724668746359176569786606814712578860646400000⟩, + ⟨7, 1, 8, 6, 4, 6, -31014161676609421763791711070880146730359193600000⟩, + ⟨7, 1, 5, 7, 0, 6, 114285091604938476467136354131576108969332467302400000⟩, + ⟨7, 1, 6, 7, 1, 6, 10173738347050950532672338975245990269982185881600000⟩, + ⟨7, 1, 7, 7, 2, 6, -357822028312460035209753233305621228120807833600000⟩, + ⟨7, 1, 8, 7, 3, 6, -148540731084131975119757126108894096248956518400000⟩ +] + +def collectedFourData_8_2_52 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 2, 7, -5813138584250275674290364847297037032569490636800000⟩, + ⟨7, 2, 1, 0, 3, 7, -6134066247648923985388261682525286207805666099200000⟩, + ⟨7, 2, 2, 0, 4, 7, -3825277684001560897936336619218460368011106713600000⟩, + ⟨7, 2, 3, 0, 5, 7, 6573307947626555307876198588439467270466437120000000⟩, + ⟨7, 2, 4, 0, 6, 7, 1379823588468604205002038758358030937739388518400000⟩, + ⟨7, 2, 5, 0, 7, 7, 2972888020561758586365761719813238644172390400000⟩, + ⟨7, 2, 6, 0, 8, 7, 26163522068831775827106181992421430631019315200000⟩, + ⟨7, 2, 0, 1, 1, 7, 42829538989661358836641975564040733696074553753600000⟩, + ⟨7, 2, 1, 1, 2, 7, -1800152007571141382125808021429584757350465536000000⟩, + ⟨7, 2, 2, 1, 3, 7, 2283864759727997583584136739730204084727604838400000⟩, + ⟨7, 2, 3, 1, 4, 7, -6288085965614730469271160254509386113229835468800000⟩, + ⟨7, 2, 4, 1, 5, 7, -2138203439241087847541870164214002050349840465920000⟩, + ⟨7, 2, 5, 1, 6, 7, -490503462232463847990893894764936418617511116800000⟩, + ⟨7, 2, 6, 1, 7, 7, -87501981645475121880143177019544884612169728000000⟩, + ⟨7, 2, 7, 1, 8, 7, -20562150249884662888048924479833350639661875200000⟩, + ⟨7, 2, 0, 2, 0, 7, 6886626979655763386019405088304677077874271846400000⟩, + ⟨7, 2, 1, 2, 1, 7, -6594374827007619938737506175655114143183562342400000⟩, + ⟨7, 2, 2, 2, 2, 7, 557595474950152385586983339654348007018174873600000⟩, + ⟨7, 2, 3, 2, 3, 7, 4361910246143980631858380759954394333672846131200000⟩, + ⟨7, 2, 4, 2, 4, 7, 570086382031462045295020809848195503818151034880000⟩, + ⟨7, 2, 5, 2, 5, 7, 85799764244911578978120500306999972835046195200000⟩, + ⟨7, 2, 6, 2, 6, 7, 6040228370558683972170144070742477801678438400000⟩, + ⟨7, 2, 7, 2, 7, 7, 1214012902919316024252411922565494487384064000000⟩, + ⟨7, 2, 8, 2, 8, 7, 2180619866095611532993160921425670718042931200000⟩, + ⟨7, 2, 1, 3, 0, 7, -5787482317600908780201331136543170469989397299200000⟩, + ⟨7, 2, 2, 3, 1, 7, 3195615576519115702875977962849907662557020160000000⟩, + ⟨7, 2, 3, 3, 2, 7, -2876299241097792769521318982653719736384434995200000⟩, + ⟨7, 2, 4, 3, 3, 7, -727135627226929239122236664516426887547427225600000⟩, + ⟨7, 2, 5, 3, 4, 7, -116126399289142350665895175650763888150550937600000⟩, + ⟨7, 2, 6, 3, 5, 7, -14714832500727402512723811568150391338460774400000⟩, + ⟨7, 2, 7, 3, 6, 7, 947926883124373124989038703980935250129715200000⟩, + ⟨7, 2, 8, 3, 7, 7, 1335753442762267995006710578336404483342336000000⟩, + ⟨7, 2, 2, 4, 0, 7, -12237827359565230260464381775765344549963248435200000⟩, + ⟨7, 2, 3, 4, 1, 7, 2655785672367887210758019553382417391956682342400000⟩, + ⟨7, 2, 4, 4, 2, 7, 2424202564024091001240707349828167847977806725120000⟩, + ⟨7, 2, 5, 4, 3, 7, 10831853313204348997741098574111240829376921600000⟩, + ⟨7, 2, 6, 4, 4, 7, 6800302456263843083190873564463482821148672000000⟩, + ⟨7, 2, 7, 4, 5, 7, 3263626967389084562569958416638933051899904000000⟩, + ⟨7, 2, 8, 4, 6, 7, -1703804654459509783120938661076062989346406400000⟩, + ⟨7, 2, 3, 5, 0, 7, -3189969931099801972420762450926159564100966809600000⟩, + ⟨7, 2, 4, 5, 1, 7, -2337233844590015442855816688711457125804372131840000⟩, + ⟨7, 2, 5, 5, 2, 7, 841317741375830977023446784448741424672381337600000⟩, + ⟨7, 2, 6, 5, 3, 7, 2519009021262915005244432228054635946128179200000⟩, + ⟨7, 2, 7, 5, 4, 7, -2068035474119462146746136891597191911571456000000⟩, + ⟨7, 2, 8, 5, 5, 7, -569530406843225281616064763060558068763852800000⟩, + ⟨7, 2, 4, 6, 0, 7, -7292224771473160790231211832351095031440322068480000⟩, + ⟨7, 2, 5, 6, 1, 7, -1074841923616371995726560321129801234866241536000000⟩, + ⟨7, 2, 6, 6, 2, 7, 180494484310161284611960895071948412774724403200000⟩, + ⟨7, 2, 7, 6, 3, 7, -6201042509800644041322799505395672497625497600000⟩, + ⟨7, 2, 8, 6, 4, 7, 848402786477122712410586931140583939165388800000⟩, + ⟨7, 2, 5, 7, 0, 7, -4689460472030870129518160279202309108933643468800000⟩, + ⟨7, 2, 6, 7, 1, 7, -357822028312460035209753233305621228120807833600000⟩, + ⟨7, 2, 7, 7, 2, 7, 11011884189542988724234027047037545734366822400000⟩, + ⟨7, 2, 8, 7, 3, 7, 4063381479441095678559771999069660897293107200000⟩ +] + +def collectedFourData_8_2_53 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 2, 8, -9652707624181153266709213334107120796378647756800000⟩, + ⟨7, 3, 1, 0, 3, 8, -6790405008444555485913203719537395390472834252800000⟩, + ⟨7, 3, 2, 0, 4, 8, -3175933837618464498189056453694030610344758476800000⟩, + ⟨7, 3, 3, 0, 5, 8, 4365987070327423554027516244856668386962178048000000⟩, + ⟨7, 3, 4, 0, 6, 8, 763731644526852925036144484276943275879615692800000⟩, + ⟨7, 3, 5, 0, 7, 8, 1410421702297493559335615382236641869850214400000⟩, + ⟨7, 3, 6, 0, 8, 8, 10861121977785075125476914725785492561644748800000⟩, + ⟨7, 3, 0, 1, 1, 8, 71118383219998074142843272846586763715410499993600000⟩, + ⟨7, 3, 1, 1, 2, 8, -1992766415403117814367366576974490362523418624000000⟩, + ⟨7, 3, 2, 1, 3, 8, 1896176949793836712176338662231110031831675699200000⟩, + ⟨7, 3, 3, 1, 4, 8, -4176542806410589456799768276017795289811800555520000⟩, + ⟨7, 3, 4, 1, 5, 8, -1183494500769455153553100262539230336701316464640000⟩, + ⟨7, 3, 5, 1, 6, 8, -232708640015980125727133235505701891882142924800000⟩, + ⟨7, 3, 6, 1, 7, 8, -36324226281505796412932897069222096359391232000000⟩, + ⟨7, 3, 7, 1, 8, 8, -7587426371792780004575303904939756828072345600000⟩, + ⟨7, 3, 0, 2, 0, 8, 11435233443688507520527939851963542201409365606400000⟩, + ⟨7, 3, 1, 2, 1, 8, -7299966130955305034347331332472666929267055001600000⟩, + ⟨7, 3, 2, 2, 2, 8, 462943211679376018913808795200965805339364556800000⟩, + ⟨7, 3, 3, 2, 3, 8, 2897178085726170930706174642432204416397848084480000⟩, + ⟨7, 3, 4, 2, 4, 8, 315542518413149271722685187211705203846765608960000⟩, + ⟨7, 3, 5, 2, 5, 8, 40705821647518686725252648955108823785485107200000⟩, + ⟨7, 3, 6, 2, 6, 8, 2507447465739658194497771584086905642916249600000⟩, + ⟨7, 3, 7, 2, 7, 8, 447970343731847502092454605615819592302592000000⟩, + ⟨7, 3, 8, 2, 8, 8, 724183182693439389638605053419047820187402240000⟩, + ⟨7, 3, 1, 3, 0, 8, -6406736955406088111312349208804601707671375052800000⟩, + ⟨7, 3, 2, 3, 1, 8, 2653157360035344224743823427508884887127982080000000⟩, + ⟨7, 3, 3, 3, 2, 8, -1910436175679226858380126716700456087437002670080000⟩, + ⟨7, 3, 4, 3, 3, 8, -402469194625399173842611672538478644470952755200000⟩, + ⟨7, 3, 5, 3, 4, 8, -55093630380373788947352271280014607697680793600000⟩, + ⟨7, 3, 6, 3, 5, 8, -6108489149611369337071274672092269053057433600000⟩, + ⟨7, 3, 7, 3, 6, 8, 349784693922735252677557136588393514899865600000⟩, + ⟨7, 3, 8, 3, 7, 8, 443603304965435257659380751608601858224947200000⟩, + ⟨7, 3, 2, 4, 0, 8, -10160446697171170052365039387229790115345308057600000⟩, + ⟨7, 3, 3, 4, 1, 8, 1763971199813589550482987241802601745632681000960000⟩, + ⟨7, 3, 4, 4, 2, 8, 1341794868823159855953044792089843634162148311040000⟩, + ⟨7, 3, 5, 4, 3, 8, 5138935904541598648704867465668973190289817600000⟩, + ⟨7, 3, 6, 4, 4, 8, 2822972926542642694652618832248436443578368000000⟩, + ⟨7, 3, 7, 4, 5, 8, 1204277228749504604329185771121293354074112000000⟩, + ⟨7, 3, 8, 4, 6, 8, -565832998469199208951309759696917188868833280000⟩, + ⟨7, 3, 3, 5, 0, 8, -2118776053835085478081861520281581418448777379840000⟩, + ⟨7, 3, 4, 5, 1, 8, -1293657727473447161236632872620671057530223329280000⟩, + ⟨7, 3, 5, 5, 2, 8, 399144802211608003266195987734363698703735193600000⟩, + ⟨7, 3, 6, 5, 3, 8, 1045702645503917542326728785487617803996364800000⟩, + ⟨7, 3, 7, 5, 4, 8, -763104378844085458638515935606378718035968000000⟩, + ⟨7, 3, 8, 5, 5, 8, -189140871859933898527259012120623943579074560000⟩, + ⟨7, 3, 4, 6, 0, 8, -4036242649799701108578654264242356513226788700160000⟩, + ⟨7, 3, 5, 6, 1, 8, -509935243144898351580160422868938849251229696000000⟩, + ⟨7, 3, 6, 6, 2, 8, 74927702977170630470416252569144779038575820800000⟩, + ⟨7, 3, 7, 6, 3, 8, -2288182553851993539857834496310617668635852800000⟩, + ⟨7, 3, 8, 6, 4, 8, 281754302833654110018555844706417529071861760000⟩, + ⟨7, 3, 5, 7, 0, 8, -2224811959304400678575044991143908439057288396800000⟩, + ⟨7, 3, 6, 7, 1, 8, -148540731084131975119757126108894096248956518400000⟩, + ⟨7, 3, 7, 7, 2, 8, 4063381479441095678559771999069660897293107200000⟩, + ⟨7, 3, 8, 7, 3, 8, 1349447731826820959863805989756607732845117440000⟩ +] + +def collectedFourData_8_2 : List (List CollectedFourTerm) := [ + collectedFourData_8_2_0, + collectedFourData_8_2_1, + collectedFourData_8_2_2, + collectedFourData_8_2_3, + collectedFourData_8_2_4, + collectedFourData_8_2_5, + collectedFourData_8_2_6, + collectedFourData_8_2_7, + collectedFourData_8_2_8, + collectedFourData_8_2_9, + collectedFourData_8_2_10, + collectedFourData_8_2_11, + collectedFourData_8_2_12, + collectedFourData_8_2_13, + collectedFourData_8_2_14, + collectedFourData_8_2_15, + collectedFourData_8_2_16, + collectedFourData_8_2_17, + collectedFourData_8_2_18, + collectedFourData_8_2_19, + collectedFourData_8_2_20, + collectedFourData_8_2_21, + collectedFourData_8_2_22, + collectedFourData_8_2_23, + collectedFourData_8_2_24, + collectedFourData_8_2_25, + collectedFourData_8_2_26, + collectedFourData_8_2_27, + collectedFourData_8_2_28, + collectedFourData_8_2_29, + collectedFourData_8_2_30, + collectedFourData_8_2_31, + collectedFourData_8_2_32, + collectedFourData_8_2_33, + collectedFourData_8_2_34, + collectedFourData_8_2_35, + collectedFourData_8_2_36, + collectedFourData_8_2_37, + collectedFourData_8_2_38, + collectedFourData_8_2_39, + collectedFourData_8_2_40, + collectedFourData_8_2_41, + collectedFourData_8_2_42, + collectedFourData_8_2_43, + collectedFourData_8_2_44, + collectedFourData_8_2_45, + collectedFourData_8_2_46, + collectedFourData_8_2_47, + collectedFourData_8_2_48, + collectedFourData_8_2_49, + collectedFourData_8_2_50, + collectedFourData_8_2_51, + collectedFourData_8_2_52, + collectedFourData_8_2_53 +] + +theorem collectedFourChecked_8_2 : collectNumericRowParts 8 2 = collectedFourData_8_2 := by + decide +kernel +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0812.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0812.lean new file mode 100644 index 0000000000000000000000000000000000000000..162dd807f6ffb62bde11479d8f7c18d0f9d58460 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0812.lean @@ -0,0 +1,616 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0812. -/ +namespace LaughlinFock +def collectedFourData_8_3_0 : List CollectedFourTerm := [ + ⟨0, 3, 5, 0, 8, 0, -1233924421118141610547031913806817128691951206400000⟩, + ⟨0, 3, 5, 1, 7, 0, 9786916588865017054720429226741903320988359065600000⟩, + ⟨0, 3, 6, 1, 8, 0, 5353330158817421504047021541366131602343801651200000⟩, + ⟨0, 3, 5, 2, 6, 0, 6840545815572482831601378948729158666493414604800000⟩, + ⟨0, 3, 6, 2, 7, 0, 7163368057073006070752529744462421834697854156800000⟩, + ⟨0, 3, 7, 2, 8, 0, 16797405995879466784452968399240557616302758297600000⟩, + ⟨0, 3, 5, 3, 5, 0, -2584767001452176215213164920975147491141877760000000⟩, + ⟨0, 3, 6, 3, 6, 0, -18980830864796111200183499904601808885068804915200000⟩, + ⟨0, 3, 7, 3, 7, 0, -9379320707929997017185326636937897226967344742400000⟩, + ⟨0, 3, 8, 3, 8, 0, -14147601956134319764730943481667567180002099200000000⟩, + ⟨0, 3, 5, 4, 4, 0, 9311901819073075960709596659711987193588639334400000⟩, + ⟨0, 3, 6, 4, 5, 0, 15101172883068330713250127269105093918048701644800000⟩, + ⟨0, 3, 7, 4, 6, 0, 3080406600564585736283153236436324144488906752000000⟩, + ⟨0, 3, 8, 4, 7, 0, -5025602586695817483885241505999704520898537062400000⟩, + ⟨0, 3, 5, 5, 3, 0, -24285975269925734390125135466046064620093623500800000⟩, + ⟨0, 3, 6, 5, 4, 0, 17032327548740197074077509473128651482769601331200000⟩, + ⟨0, 3, 7, 5, 5, 0, 8158277920480283400211132109624671423423945113600000⟩, + ⟨0, 3, 8, 5, 6, 0, -10464623589045936108490943342022296604931365273600000⟩, + ⟨0, 3, 5, 6, 2, 0, -359430602896809481051247469368588718218359603200000⟩, + ⟨0, 3, 6, 6, 3, 0, -63067119997526996950043467250576475186122666803200000⟩, + ⟨0, 3, 7, 6, 4, 0, -2920545853999776636101952917121280392379446067200000⟩, + ⟨0, 3, 8, 6, 5, 0, 10982155607692975823319547280984841765740819251200000⟩, + ⟨0, 3, 5, 7, 1, 0, 16755417963813713283699379241727163440545818214400000⟩, + ⟨0, 3, 6, 7, 2, 0, 62239523342113057513982808029465441849641323724800000⟩, + ⟨0, 3, 7, 7, 3, 0, -122369596962162963993723629736470570219969760460800000⟩, + ⟨0, 3, 8, 7, 4, 0, -21714156879266828174184540742998235314628067328000000⟩ +] + +def collectedFourData_8_3_1 : List CollectedFourTerm := [ + ⟨0, 4, 4, 0, 7, 1, 362275938816865655492106488600047220902015795200000⟩, + ⟨0, 4, 5, 0, 8, 1, 34150862563576320877188470730578999270965248000000⟩, + ⟨0, 4, 4, 1, 6, 1, 811691679445301338709457617607626733598330060800000⟩, + ⟨0, 4, 5, 1, 7, 1, -270868813054728819672679891979062551659937792000000⟩, + ⟨0, 4, 6, 1, 8, 1, -74081053661923532975638484324387153082580992000000⟩, + ⟨0, 4, 4, 2, 5, 1, -102999420268962813121908018303818945471604326400000⟩, + ⟨0, 4, 5, 2, 6, 1, -189323216243481744033515238575431228311207936000000⟩, + ⟨0, 4, 6, 2, 7, 1, -99128923061484033833405023809776900571660288000000⟩, + ⟨0, 4, 7, 2, 8, 1, -154965164741087765483711719104679252636729344000000⟩, + ⟨0, 4, 4, 3, 4, 1, 70667890576814727162028590728295508613686886400000⟩, + ⟨0, 4, 5, 3, 5, 1, 71537625088472883288485538066143613498163200000000⟩, + ⟨0, 4, 6, 3, 6, 1, 262662661955726337747900341654391446392799232000000⟩, + ⟨0, 4, 7, 3, 7, 1, 86529311669933727644433008272776912495968256000000⟩, + ⟨0, 4, 8, 3, 8, 1, 97889465865808362749470289065181064462336000000000⟩, + ⟨0, 4, 4, 4, 3, 1, 157953025845976131620311301933996164239065088000000⟩, + ⟨0, 4, 5, 4, 4, 1, -257722007755151852645686024627429065734750208000000⟩, + ⟨0, 4, 6, 4, 5, 1, -208974743854710906772499777741790364060090368000000⟩, + ⟨0, 4, 7, 4, 6, 1, -28418418679832124300170838124606094447738880000000⟩, + ⟨0, 4, 8, 4, 7, 1, 34772928612977422324467886913547073373601792000000⟩, + ⟨0, 4, 4, 5, 2, 1, -1082240665121951263506034582291826150088690892800000⟩, + ⟨0, 4, 5, 5, 3, 1, 672153812235990880864542013349593316019142656000000⟩, + ⟨0, 4, 6, 5, 4, 1, -235698664885711667212817402240516262086049792000000⟩, + ⟨0, 4, 7, 5, 5, 1, -75264530860356416313726924766122585184272384000000⟩, + ⟨0, 4, 8, 5, 6, 1, 72406363763597503121606655424841601502937088000000⟩, + ⟨0, 4, 4, 6, 1, 1, 580736952849837534660447693352635519921763123200000⟩, + ⟨0, 4, 5, 6, 2, 1, 9947825742478813833500345807439933550362624000000⟩, + ⟨0, 4, 6, 6, 3, 1, 872742491539482167180145442407388998965133312000000⟩, + ⟨0, 4, 7, 6, 4, 1, 26943616741180055482335902027905518815674368000000⟩, + ⟨0, 4, 8, 6, 5, 1, -75987248568731987331362444459445736225898496000000⟩, + ⟨0, 4, 4, 7, 0, 1, 11081176825915390545926128654327233488202655334400000⟩, + ⟨0, 4, 5, 7, 1, 1, -463733407236530992743422745263392610800631808000000⟩, + ⟨0, 4, 6, 7, 2, 1, -861289950705779503332867090861337217668743168000000⟩, + ⟨0, 4, 7, 7, 3, 1, 1128925785159558141386991383853515734045949952000000⟩, + ⟨0, 4, 8, 7, 4, 1, 150243640245770095790421801811631904380682240000000⟩ +] + +def collectedFourData_8_3_2 : List CollectedFourTerm := [ + ⟨0, 5, 3, 0, 6, 2, 621931153574264275605332046385439123861982412800000⟩, + ⟨0, 5, 4, 0, 7, 2, -8922182957688350798400735876880043435723902156800000⟩, + ⟨0, 5, 5, 0, 8, 2, -420536131864290013354474347665231064770543616000000⟩, + ⟨0, 5, 3, 1, 5, 2, -8337875142043803957136775007134119211320108646400000⟩, + ⟨0, 5, 4, 1, 6, 2, -19990457254477622703162846559326689336552010547200000⟩, + ⟨0, 5, 5, 1, 7, 2, 3335497680992639300978755997516925628594520064000000⟩, + ⟨0, 5, 6, 1, 8, 2, 608159548794595344039823648151235486050942976000000⟩, + ⟨0, 5, 3, 2, 4, 2, 10857705283545978786893971231062193737445461196800000⟩, + ⟨0, 5, 4, 2, 5, 2, 2536684261109800366460027733299325177972758937600000⟩, + ⟨0, 5, 5, 2, 6, 2, 2331339446636884997189868798130922513038835712000000⟩, + ⟨0, 5, 6, 2, 7, 2, 813787036516631272085372783763385506399780864000000⟩, + ⟨0, 5, 7, 2, 8, 2, 954125987778637655475764137923083040429441024000000⟩, + ⟨0, 5, 3, 3, 3, 2, -14512862547114408616331572922606852871551346278400000⟩, + ⟨0, 5, 4, 3, 4, 2, -1740418784143906421935799711899466915179501977600000⟩, + ⟨0, 5, 5, 3, 5, 2, -880919364231534761744449482384095842821734400000000⟩, + ⟨0, 5, 6, 3, 6, 2, -2156297704797442051921177001097717302685597696000000⟩, + ⟨0, 5, 7, 3, 7, 2, -532764025429974799664880251641621841839128576000000⟩, + ⟨0, 5, 8, 3, 8, 2, -482167116556221366555658385687803115392204800000000⟩, + ⟨0, 5, 3, 4, 2, 2, 19867450491440119321812436627136661738498293760000000⟩, + ⟨0, 5, 4, 4, 3, 2, -3890089416152710090212866088743822446445985792000000⟩, + ⟨0, 5, 5, 4, 4, 2, 3173606992675041704997742844735213036881575936000000⟩, + ⟨0, 5, 6, 4, 5, 2, 1715553163054824700257979274463583932833071104000000⟩, + ⟨0, 5, 7, 4, 6, 2, 174973206651342689823095027219750606843412480000000⟩, + ⟨0, 5, 8, 4, 7, 2, -171278518840002606986751797676242951162403225600000⟩, + ⟨0, 5, 3, 5, 1, 2, -16498374199744404250001167485587743037197595443200000⟩, + ⟨0, 5, 4, 5, 2, 2, 26653575862650829427936610448890288381566858035200000⟩, + ⟨0, 5, 5, 5, 3, 2, -8276949482296146844696031022330287754892541952000000⟩, + ⟨0, 5, 6, 5, 4, 2, 1934939996163399871607070670135312305541349376000000⟩, + ⟨0, 5, 7, 5, 5, 2, 463406372469676666507083596664878403749412864000000⟩, + ⟨0, 5, 8, 5, 6, 2, -356646829435903781792769488937191267084166758400000⟩, + ⟨0, 5, 3, 6, 0, 2, -8985023018637271713106250451810931561087578931200000⟩, + ⟨0, 5, 4, 6, 1, 2, -14302471647823008050192749673892936548508028108800000⟩, + ⟨0, 5, 5, 6, 2, 2, -122498228277955278433689458250775557002231808000000⟩, + ⟨0, 5, 6, 6, 3, 2, -7164675090755734405850526794681144834770599936000000⟩, + ⟨0, 5, 7, 6, 4, 2, -165892799071708366515830431501129172624867328000000⟩, + ⟨0, 5, 8, 6, 5, 2, 374284936722938807381769147330600707327577292800000⟩, + ⟨0, 5, 4, 7, 0, 2, -272908787015226981962711952607761427223742618009600000⟩, + ⟨0, 5, 5, 7, 1, 2, 5710445905500897877567021477620803700718043136000000⟩, + ⟨0, 5, 6, 7, 2, 2, 7070656826682957398801858871134510312539029504000000⟩, + ⟨0, 5, 7, 7, 3, 2, -6950835897175948830767079666343603183017787392000000⟩, + ⟨0, 5, 8, 7, 4, 2, -740044315876858287954846645272581718547628032000000⟩ +] + +def collectedFourData_8_3_3 : List CollectedFourTerm := [ + ⟨0, 6, 2, 0, 5, 3, 621931153574264275605332046385439123861982412800000⟩, + ⟨0, 6, 3, 0, 6, 3, 99826445870417118753334958721508390247250001920000⟩, + ⟨0, 6, 4, 0, 7, 3, -716051775950535438376865011097967190332942581760000⟩, + ⟨0, 6, 5, 0, 8, 3, -22500147142675801722521338413564544072600780800000⟩, + ⟨0, 6, 2, 1, 4, 3, -2143513418249200732878973680323487392050540707840000⟩, + ⟨0, 6, 3, 1, 5, 3, -1338316044723016386713887208379920962221464616960000⟩, + ⟨0, 6, 4, 1, 6, 3, -1604338589223531737909170801790499383728448471040000⟩, + ⟨0, 6, 5, 1, 7, 3, 178460738400017433922305165606547245459780403200000⟩, + ⟨0, 6, 6, 1, 8, 3, 24403989866649923372853259749248599947057561600000⟩, + ⟨0, 6, 2, 2, 3, 3, 798874288082152069721421942330758652898238791680000⟩, + ⟨0, 6, 3, 2, 4, 3, 1742775100645313911141060872866356034939671019520000⟩, + ⟨0, 6, 4, 2, 5, 3, 203582159075569421403564869316231398284402360320000⟩, + ⟨0, 6, 5, 2, 6, 3, 124734776905643027132852622594796636566296985600000⟩, + ⟨0, 6, 6, 2, 7, 3, 32655329727414174808776869077396895566292582400000⟩, + ⟨0, 6, 7, 2, 8, 3, 30629437269753708340019888265122457632605470720000⟩, + ⟨0, 6, 2, 3, 2, 3, 427181399821021108683123809741080942264870502400000⟩, + ⟨0, 6, 3, 3, 3, 3, -2329466017513664102421216530293063966544111861760000⟩, + ⟨0, 6, 4, 3, 4, 3, -139677696276114205114270680655582418692284088320000⟩, + ⟨0, 6, 5, 3, 5, 3, -47132252889124561904813286289897635415326720000000⟩, + ⟨0, 6, 6, 3, 6, 3, -86527075734743298287863299065537156343241113600000⟩, + ⟨0, 6, 7, 3, 7, 3, -17102838100532701251365327246474039725947617280000⟩, + ⟨0, 6, 8, 3, 8, 3, -12898809695352989328795099512661020371845120000000⟩, + ⟨0, 6, 2, 4, 1, 3, 986121487483836078164585013194682242626297528320000⟩, + ⟨0, 6, 3, 4, 2, 3, 3188933308242960101074604473544773765183832064000000⟩, + ⟨0, 6, 4, 4, 3, 3, -312199990546285147973570574657253279011333734400000⟩, + ⟨0, 6, 5, 4, 4, 3, 169799022955907880855909167818145374495624396800000⟩, + ⟨0, 6, 6, 4, 5, 3, 68841050164994511844163813234057750340068966400000⟩, + ⟨0, 6, 7, 4, 6, 3, 5617005432890846622156404783433474841667174400000⟩, + ⟨0, 6, 8, 4, 7, 3, -4581998530299025589603663146854548738030960640000⟩, + ⟨0, 6, 2, 5, 0, 3, -7357526528731771603108402268105543094696872509440000⟩, + ⟨0, 6, 3, 5, 1, 3, -2648161375315326334995337993548331437691219476480000⟩, + ⟨0, 6, 4, 5, 2, 3, 2139088653796029487912419465015653305779109232640000⟩, + ⟨0, 6, 5, 5, 3, 3, -442845613333068315314503996932390696389286297600000⟩, + ⟨0, 6, 6, 5, 4, 3, 77644519686553171146194463524782907412027801600000⟩, + ⟨0, 6, 7, 5, 5, 3, 14876312560157557238061859433035478085843025920000⟩, + ⟨0, 6, 8, 5, 6, 3, -9540923516729154316565029612733679174376488960000⟩, + ⟨0, 6, 3, 6, 0, 3, -1442190038012530962520558582714967971220611399680000⟩, + ⟨0, 6, 4, 6, 1, 3, -1147848040381282201807774206687293740528340828160000⟩, + ⟨0, 6, 5, 6, 2, 3, -6554081687945277176978420003863517683148390400000⟩, + ⟨0, 6, 6, 6, 3, 3, -287501295768844644528717131257398883545356697600000⟩, + ⟨0, 6, 7, 6, 4, 3, -5325505381632696905561414924752829726683299840000⟩, + ⟨0, 6, 8, 6, 5, 3, 10012773590012108160629327404191596652338872320000⟩, + ⟨0, 6, 4, 7, 0, 3, -21902355347506824520096779825571805281823458590720000⟩, + ⟨0, 6, 5, 7, 1, 3, 305528736744846598392033932567377591084567756800000⟩, + ⟨0, 6, 6, 7, 2, 3, 283728567430927841383905375350949441727522406400000⟩, + ⟨0, 6, 7, 7, 3, 3, -223136351815099022268451565177202025640503541760000⟩, + ⟨0, 6, 8, 7, 4, 3, -19797473674275854174380675746377818377604300800000⟩ +] + +def collectedFourData_8_3_4 : List CollectedFourTerm := [ + ⟨0, 7, 1, 0, 4, 4, 362275938816865655492106488600047220902015795200000⟩, + ⟨0, 7, 2, 0, 5, 4, -8922182957688350798400735876880043435723902156800000⟩, + ⟨0, 7, 3, 0, 6, 4, -716051775950535438376865011097967190332942581760000⟩, + ⟨0, 7, 4, 0, 7, 4, 3424143715099847150134806032451800234125185515520000⟩, + ⟨0, 7, 5, 0, 8, 4, 80696403544082488200262953361516874958058291200000⟩, + ⟨0, 7, 1, 1, 3, 4, -1463120378371475292096021734593554468598783672320000⟩, + ⟨0, 7, 2, 1, 4, 4, 30750700909527025652039420579586316210833236951040000⟩, + ⟨0, 7, 3, 1, 5, 4, 9599696475731174720342658926345211726573474938880000⟩, + ⟨0, 7, 4, 1, 6, 4, 7671911559592862888949390923344513726639327150080000⟩, + ⟨0, 7, 5, 1, 7, 4, -640046470424553285899186568193575819856891084800000⟩, + ⟨0, 7, 6, 1, 8, 4, -70019603049784634857714514261011424557840465920000⟩, + ⟨0, 7, 1, 2, 2, 4, -255429052018221359581274450376682684013220986880000⟩, + ⟨0, 7, 2, 2, 3, 4, -11460597394902614735856156454706749873819043758080000⟩, + ⟨0, 7, 3, 2, 4, 4, -12500867831349506697443137338969205594718270914560000⟩, + ⟨0, 7, 4, 2, 5, 4, -973525370535807941952151887344622056763964784640000⟩, + ⟨0, 7, 5, 2, 6, 4, -447359203001275392975184704632965728083273318400000⟩, + ⟨0, 7, 6, 2, 7, 4, -93694237600798318918721537049281778145956986880000⟩, + ⟨0, 7, 7, 2, 8, 4, -73234644928467589783664677374191987294176542720000⟩, + ⟨0, 7, 1, 3, 1, 4, 1433472991247459720797695988217451261148004352000000⟩, + ⟨0, 7, 2, 3, 2, 4, -6128315945294502922019412661441771337652004454400000⟩, + ⟨0, 7, 3, 3, 3, 4, 16709182264410217013353408661911878004100070113280000⟩, + ⟨0, 7, 4, 3, 4, 4, 667935646425267610700971117738103620871273840640000⟩, + ⟨0, 7, 5, 3, 5, 4, 169039041165587170179899141441016259757998080000000⟩, + ⟨0, 7, 6, 3, 6, 4, 248262334524443718271302371274189014957366968320000⟩, + ⟨0, 7, 7, 3, 7, 4, 40892696282031660917036665647597698489285345280000⟩, + ⟨0, 7, 8, 3, 8, 4, 26435066549670630514196031636041752337448960000000⟩, + ⟨0, 7, 1, 4, 0, 4, -11469939019894689306054550297820846150412675317760000⟩, + ⟨0, 7, 2, 4, 1, 4, -14146833261646482641628607873523076793313966161920000⟩, + ⟨0, 7, 3, 4, 2, 4, -22874112554495641791214495406466890181107515392000000⟩, + ⟨0, 7, 4, 4, 3, 4, 1492933432172845114365945995339171588618374348800000⟩, + ⟨0, 7, 5, 4, 4, 4, -608981372030767754525227637718589393626936115200000⟩, + ⟨0, 7, 6, 4, 5, 4, -197517825258174745014974579090579881063014727680000⟩, + ⟨0, 7, 7, 4, 6, 4, -13430197715230250620901674594406221620864614400000⟩, + ⟨0, 7, 8, 4, 7, 4, 9390435159500431637107018656273243483270021120000⟩, + ⟨0, 7, 2, 5, 0, 4, 105550586151095428059704312534346382928230628720640000⟩, + ⟨0, 7, 3, 5, 1, 4, 18995173465953111745099056586334590642291149373440000⟩, + ⟨0, 7, 4, 5, 2, 4, -10229074511007209422038452391929646312710240993280000⟩, + ⟨0, 7, 5, 5, 3, 4, 1588258427584759899202921630001043449531754086400000⟩, + ⟨0, 7, 6, 5, 4, 4, -222776622886295285154997834899501508921833553920000⟩, + ⟨0, 7, 7, 5, 5, 4, -35569098400115717441843464663312606643009617920000⟩, + ⟨0, 7, 8, 5, 6, 4, 19553350585590651239692806718126617169420615680000⟩, + ⟨0, 7, 3, 6, 0, 4, 10344781174695426484917500886349006024249222103040000⟩, + ⟨0, 7, 4, 6, 1, 4, 5488983877099905680310116519148255524625391288320000⟩, + ⟨0, 7, 5, 6, 2, 4, 23506104977783524195916796629924695376501145600000⟩, + ⟨0, 7, 6, 6, 3, 4, 824894892844695723106376583526066053757135749120000⟩, + ⟨0, 7, 7, 6, 4, 4, 12733224324484950932920414500507632382341283840000⟩, + ⟨0, 7, 8, 6, 5, 4, -20520369123215529471364061625091874823402946560000⟩, + ⟨0, 7, 4, 7, 0, 4, 104736577616183121875920905810026552635348683325440000⟩, + ⟨0, 7, 5, 7, 1, 4, -1095773733315408502646039141443448518019855155200000⟩, + ⟨0, 7, 6, 7, 2, 4, -814070230890684194377680653117370340159971655680000⟩, + ⟨0, 7, 7, 7, 3, 4, 533516543314013100004387460092461471158249717760000⟩, + ⟨0, 7, 8, 7, 4, 4, 40573320054747314838993027344940131624052326400000⟩ +] + +def collectedFourData_8_3_5 : List CollectedFourTerm := [ + ⟨0, 8, 0, 0, 3, 5, -1233924421118141610547031913806817128691951206400000⟩, + ⟨0, 8, 1, 0, 4, 5, 34150862563576320877188470730578999270965248000000⟩, + ⟨0, 8, 2, 0, 5, 5, -420536131864290013354474347665231064770543616000000⟩, + ⟨0, 8, 3, 0, 6, 5, -22500147142675801722521338413564544072600780800000⟩, + ⟨0, 8, 4, 0, 7, 5, 80696403544082488200262953361516874958058291200000⟩, + ⟨0, 8, 5, 0, 8, 5, 1521410334790115117463179089732353484495257600000⟩, + ⟨0, 8, 0, 1, 2, 5, 482652414061568601503149675918348226469140889600000⟩, + ⟨0, 8, 1, 1, 3, 5, -137924762872509726128625425351356069012360396800000⟩, + ⟨0, 8, 2, 1, 4, 5, 1449396506878928246650571540362221506165263564800000⟩, + ⟨0, 8, 3, 1, 5, 5, 301646599426769065738559399914134053637744230400000⟩, + ⟨0, 8, 4, 1, 6, 5, 180803062802918667696613688093033772650122444800000⟩, + ⟨0, 8, 5, 1, 7, 5, -12067121607444405905781933417567608122009190400000⟩, + ⟨0, 8, 6, 1, 8, 5, -1100095987752104350353345580355900530281676800000⟩, + ⟨0, 8, 0, 2, 1, 5, 498633858974824528608597243272312613456838656000000⟩, + ⟨0, 8, 1, 2, 2, 5, -24078669090492636328794425462212630068540211200000⟩, + ⟨0, 8, 2, 2, 3, 5, -540181177651507606646101284644832228702525849600000⟩, + ⟨0, 8, 3, 2, 4, 5, -392808697727378528518393019405401386851814604800000⟩, + ⟨0, 8, 4, 2, 5, 5, -22942961130610489068514962954881026299946598400000⟩, + ⟨0, 8, 5, 2, 6, 5, -8434290562129016729937689601696561158632243200000⟩, + ⟨0, 8, 6, 2, 7, 5, -1472054258674458616718815374382987419530035200000⟩, + ⟨0, 8, 7, 2, 8, 5, -986235717768203243879017037803147168736870400000⟩, + ⟨0, 8, 0, 3, 0, 5, -2786243343261886170969646488057151358385940070400000⟩, + ⟨0, 8, 1, 3, 1, 5, 135129976538236448919339207625487545773588480000000⟩, + ⟨0, 8, 2, 3, 2, 5, -288850642796515970839860797987304196358012928000000⟩, + ⟨0, 8, 3, 3, 3, 5, 525044518022380861633980730036562354191623782400000⟩, + ⟨0, 8, 4, 3, 4, 5, 15741163032299677495312391184061295155897958400000⟩, + ⟨0, 8, 5, 3, 5, 5, 3186979009192721497045434021850101149859840000000⟩, + ⟨0, 8, 6, 3, 6, 5, 3900513373749428936816202104929338065210572800000⟩, + ⟨0, 8, 7, 3, 7, 5, 550693428070540376842306238343858324347289600000⟩, + ⟨0, 8, 8, 3, 8, 5, 311496095885200529093079525504475516108800000000⟩, + ⟨0, 8, 1, 4, 0, 5, -1081242967336667491513614107666505077256250982400000⟩, + ⟨0, 8, 2, 4, 1, 5, -666793604905327127803262318475426980031784550400000⟩, + ⟨0, 8, 3, 4, 2, 5, -718762127991472298419291311523515363345039360000000⟩, + ⟨0, 8, 4, 4, 3, 5, 35183791549344771056806064746400759653859328000000⟩, + ⟨0, 8, 5, 4, 4, 5, -11481435509032862544296827090588269637376409600000⟩, + ⟨0, 8, 6, 4, 5, 5, -3103253340661542413328297507050239324009267200000⟩, + ⟨0, 8, 7, 4, 6, 5, -180861676825039039255724662694584787140608000000⟩, + ⟨0, 8, 8, 4, 7, 5, 110651656024824724960852660160325844834713600000⟩, + ⟨0, 8, 2, 5, 0, 5, 4974997198162210578924286185833668788834061516800000⟩, + ⟨0, 8, 3, 5, 1, 5, 596876109157391891683783440444130704590320435200000⟩, + ⟨0, 8, 4, 5, 2, 5, -241067429787670615777959902549623733041810636800000⟩, + ⟨0, 8, 5, 5, 3, 5, 29944243856232509657892919301778507371328307200000⟩, + ⟨0, 8, 6, 5, 4, 5, -3500100805026355650465676410071315787861196800000⟩, + ⟨0, 8, 7, 5, 5, 5, -479001643624682229470851874425573688632934400000⟩, + ⟨0, 8, 8, 5, 6, 5, 230405789122629466195465930313698283775590400000⟩, + ⟨0, 8, 3, 6, 0, 5, 325059034006932798251792558775149025572369203200000⟩, + ⟨0, 8, 4, 6, 1, 5, 129358255624647580661901789658747316385035059200000⟩, + ⟨0, 8, 5, 6, 2, 5, 443172551355712826240285473775777657703628800000⟩, + ⟨0, 8, 6, 6, 3, 5, 12960135767842559601626035951751182674611404800000⟩, + ⟨0, 8, 7, 6, 4, 5, 171475681262987336722622243357111635201228800000⟩, + ⟨0, 8, 8, 6, 5, 5, -241800596794203819281710800267996170079436800000⟩, + ⟨0, 8, 4, 7, 0, 5, 2468314952982391414023896556893210464030713446400000⟩, + ⟨0, 8, 5, 7, 1, 5, -20659179458312562029738317309379503728466329600000⟩, + ⟨0, 8, 6, 7, 2, 5, -12790066720522852415747260997766712810222387200000⟩, + ⟨0, 8, 7, 7, 3, 5, 7184756225014121863487475210618857684415283200000⟩, + ⟨0, 8, 8, 7, 4, 5, 478093398040337770221572497363960848187392000000⟩ +] + +def collectedFourData_8_3_6 : List CollectedFourTerm := [ + ⟨1, 2, 5, 0, 8, 0, 482652414061568601503149675918348226469140889600000⟩, + ⟨1, 2, 5, 1, 7, 0, -3828175240712450394579183050511345031722722918400000⟩, + ⟨1, 2, 6, 1, 8, 0, -2093967572244397798516880921253160805787815116800000⟩, + ⟨1, 2, 5, 2, 6, 0, -2675695443642337556899459732101060872086172467200000⟩, + ⟨1, 2, 6, 2, 7, 0, -2801968116025143230132276902386648264060646195200000⟩, + ⟨1, 2, 7, 2, 8, 0, -6570344516349644732078413332800832007345432166400000⟩, + ⟨1, 2, 5, 3, 5, 0, 1011037638680569748087939877636529770347888640000000⟩, + ⟨1, 2, 6, 3, 6, 0, 7424396244209712233796569635909733880748100812800000⟩, + ⟨1, 2, 7, 3, 7, 0, 3668743161625652302894339677044274254602410393600000⟩, + ⟨1, 2, 8, 3, 8, 0, 5533867488515019504675719251946658782301388800000000⟩, + ⟨1, 2, 5, 4, 4, 0, -3642372106070519549555187083693187944899254681600000⟩, + ⟨1, 2, 6, 4, 5, 0, -5906858979717187887661016938233751407466591027200000⟩, + ⟨1, 2, 7, 4, 6, 0, -1204908223395424310928331880113134357109014528000000⟩, + ⟨1, 2, 8, 4, 7, 0, 1965776168352988576412894823036593133850302873600000⟩, + ⟨1, 2, 5, 5, 3, 0, 9499515846560040435488281294815447698344457011200000⟩, + ⟨1, 2, 6, 5, 4, 0, -6662234629441480383176827691691410750257810636800000⟩, + ⟨1, 2, 7, 5, 5, 0, -3191129428605414897282880506293986588004607590400000⟩, + ⟨1, 2, 8, 5, 6, 0, 4093261913822737044603402473747078011054089830400000⟩, + ⟨1, 2, 5, 6, 2, 0, 140592118290801174766739034144671176887946444800000⟩, + ⟨1, 2, 6, 6, 3, 0, 24668851020173313919135175259492419479100247244800000⟩, + ⟨1, 2, 7, 6, 4, 0, 1142378319681165673428916056328415959665396940800000⟩, + ⟨1, 2, 8, 6, 5, 0, -4295695769478013514085594330216626635362061516800000⟩, + ⟨1, 2, 5, 7, 1, 0, -6553920799717254526756664684412203727880559001600000⟩, + ⟨1, 2, 6, 7, 2, 0, -24345134658969556177416925012475234020656100147200000⟩, + ⟨1, 2, 7, 7, 3, 0, 47865153141234636366147788371278705118843974451200000⟩, + ⟨1, 2, 8, 7, 4, 0, 8493543087179332664086936597297041921741422592000000⟩ +] + +def collectedFourData_8_3_7 : List CollectedFourTerm := [ + ⟨1, 3, 4, 0, 7, 1, -1463120378371475292096021734593554468598783672320000⟩, + ⟨1, 3, 5, 0, 8, 1, -137924762872509726128625425351356069012360396800000⟩, + ⟨1, 3, 4, 1, 6, 1, -3278171443098056001854981697447831845492521697280000⟩, + ⟨1, 3, 5, 1, 7, 1, 1093955291482959959984719788765350124036764467200000⟩, + ⟨1, 3, 6, 1, 8, 1, 299190444769734406259274580360450647887393587200000⟩, + ⟨1, 3, 4, 2, 5, 1, 415982776135039444524267838003105341389395722240000⟩, + ⟨1, 3, 5, 2, 6, 1, 764617867499876767649852212915930160460044697600000⟩, + ⟨1, 3, 6, 2, 7, 1, 400351035983632926338626916611697547517152460800000⟩, + ⟨1, 3, 7, 2, 8, 1, 625856332636526884100110940773444490646414950400000⟩, + ⟨1, 3, 4, 3, 4, 1, -285405735575861054461540127864059152732247818240000⟩, + ⟨1, 3, 5, 3, 5, 1, -288918324051750112245051475733244131011461120000000⟩, + ⟨1, 3, 6, 3, 6, 1, -1060813187317396078373524714363544068141822771200000⟩, + ⟨1, 3, 7, 3, 7, 1, -349465105643507313368480912740980032945101209600000⟩, + ⟨1, 3, 8, 3, 8, 1, -395345252030564581580219712528357070051737600000000⟩, + ⟨1, 3, 4, 4, 3, 1, -637923378779813731179022440025534468226600140800000⟩, + ⟨1, 3, 5, 4, 4, 1, 1040859414326136560695690070460083431090736332800000⟩, + ⟨1, 3, 6, 4, 5, 1, 843984304608618419484028595416046849626000588800000⟩, + ⟨1, 3, 7, 4, 6, 1, 114773196440666442271905246420480513653342208000000⟩, + ⟨1, 3, 8, 4, 7, 1, -140437095092375651877658695365298183866626867200000⟩, + ⟨1, 3, 4, 5, 2, 1, 4370835050799982683733453455088369660657643028480000⟩, + ⟨1, 3, 5, 5, 3, 1, -2714621189843062993863493181847716023426980249600000⟩, + ⟨1, 3, 6, 5, 4, 1, 951913949558659894597181278905278207022543667200000⟩, + ⟨1, 3, 7, 5, 5, 1, 303970142841928101376927790622453945162163814400000⟩, + ⟨1, 3, 8, 5, 6, 1, -292426890652130401273747990478819508072795340800000⟩, + ⟨1, 3, 4, 6, 1, 1, -2345416791860080630187619793192634954120555397120000⟩, + ⟨1, 3, 5, 6, 2, 1, -40176188934442991677139227939521457729988198400000⟩, + ⟨1, 3, 6, 6, 3, 1, -3524736775542831679169328356695873679952917299200000⟩, + ⟨1, 3, 7, 6, 4, 1, -108816927919078544181904792585282818962934988800000⟩, + ⟨1, 3, 8, 6, 5, 1, 306888975956784149253537129338581459375069593600000⟩, + ⟨1, 3, 4, 7, 0, 1, -44753443144151072877139207308140461444947813335040000⟩, + ⟨1, 3, 5, 7, 1, 1, 1872875688281342156530906643580499023503346892800000⟩, + ⟨1, 3, 6, 7, 2, 1, 3478483508122848884149687249985935885057445068800000⟩, + ⟨1, 3, 7, 7, 3, 1, -4559381799769338065805047370813499802893103923200000⟩, + ⟨1, 3, 8, 7, 4, 1, -606787556695623103611207301536412848655171584000000⟩ +] + +def collectedFourData_8_3_8 : List CollectedFourTerm := [ + ⟨1, 4, 3, 0, 6, 2, -2143513418249200732878973680323487392050540707840000⟩, + ⟨1, 4, 4, 0, 7, 2, 30750700909527025652039420579586316210833236951040000⟩, + ⟨1, 4, 5, 0, 8, 2, 1449396506878928246650571540362221506165263564800000⟩, + ⟨1, 4, 3, 1, 5, 2, 28736858000992922409245153029014977733220808785920000⟩, + ⟨1, 4, 4, 1, 6, 2, 68898001194585923398354713062605843230472965980160000⟩, + ⟨1, 4, 5, 1, 7, 2, -11495941302598015962329064997874549724072325939200000⟩, + ⟨1, 4, 6, 1, 8, 2, -2096048969063153857231352325534257441577684172800000⟩, + ⟨1, 4, 3, 2, 4, 2, -37421564803308993366833199045856112184440955863040000⟩, + ⟨1, 4, 4, 2, 5, 2, -8742795276135236849510231793312519537749687009280000⟩, + ⟨1, 4, 5, 2, 6, 2, -8035065228105044854107208665732773414126066073600000⟩, + ⟨1, 4, 6, 2, 7, 2, -2804753263035180096424867469705257011421328179200000⟩, + ⟨1, 4, 7, 2, 8, 2, -3288437708498822256522883270209996180985951027200000⟩, + ⟨1, 4, 3, 3, 3, 2, 50019227093166295884455426790961249638627693035520000⟩, + ⟨1, 4, 4, 3, 4, 2, 5998430848407328695032323065506022654366481121280000⟩, + ⟨1, 4, 5, 3, 5, 2, 3036127820215994274827562474802309715271352320000000⟩, + ⟨1, 4, 6, 3, 6, 2, 7431776069441350974956688962779581223512362188800000⟩, + ⟨1, 4, 7, 3, 7, 2, 1836194940077472258313564367885071391226907852800000⟩, + ⟨1, 4, 8, 3, 8, 2, 1661810440330954897022610465164313239161405440000000⟩, + ⟨1, 4, 3, 4, 2, 2, -68474052907720110206340720118761286022807420928000000⟩, + ⟨1, 4, 4, 4, 3, 2, 13407366416348597971013005061815299936435673497600000⟩, + ⟨1, 4, 5, 4, 4, 2, -10937977835574277589666705860392669079405382860800000⟩, + ⟨1, 4, 6, 4, 5, 2, -5912730377943305716392786578423791750648902451200000⟩, + ⟨1, 4, 7, 4, 6, 2, -603052949085719122555909765003634774737158144000000⟩, + ⟨1, 4, 8, 4, 7, 2, 590319043002489663106776696974382370106564935680000⟩, + ⟨1, 4, 3, 5, 1, 2, 56862381427923928651119948173151821748499340328960000⟩, + ⟨1, 4, 4, 5, 2, 2, -91862736216980564885228145969017109952451900866560000⟩, + ⟨1, 4, 5, 5, 3, 2, 28526875001372701586388608045223665919984245145600000⟩, + ⟨1, 4, 6, 5, 4, 2, -6668856868556990184526852178058873858773798092800000⟩, + ⟨1, 4, 7, 5, 5, 2, -1597150700334434526163014311600866345499177779200000⟩, + ⟨1, 4, 8, 5, 6, 2, 1229199180774931532303787635767957070749913579520000⟩, + ⟨1, 4, 3, 6, 0, 2, 30967281978144494975135533022631256444426896015360000⟩, + ⟨1, 4, 4, 6, 1, 2, 49294105489083822885821686203042261759540477296640000⟩, + ⟨1, 4, 5, 6, 2, 2, 422195599169638269059132019044280566496519782400000⟩, + ⟨1, 4, 6, 6, 3, 2, 24693371776232932148213778070810003105330810060800000⟩, + ⟨1, 4, 7, 6, 4, 2, 571756919970184965872813274972664288256616038400000⟩, + ⟨1, 4, 8, 6, 5, 2, -1289989703045760372442293909866533964788625571840000⟩, + ⟨1, 4, 4, 7, 0, 2, 940592288331798241319488324204442487493330080890880000⟩, + ⟨1, 4, 5, 7, 1, 2, -19681306125736253175062411417335405179736739020800000⟩, + ⟨1, 4, 6, 7, 2, 2, -24369333642040270570701527279669478905800241971200000⟩, + ⟨1, 4, 7, 7, 3, 2, 23956365472317131477142110094063146121620461977600000⟩, + ⟨1, 4, 8, 7, 4, 2, 2550595692247594765886422651681762316438313369600000⟩ +] + +def collectedFourData_8_3_9 : List CollectedFourTerm := [ + ⟨1, 5, 2, 0, 5, 3, -8337875142043803957136775007134119211320108646400000⟩, + ⟨1, 5, 3, 0, 6, 3, -1338316044723016386713887208379920962221464616960000⟩, + ⟨1, 5, 4, 0, 7, 3, 9599696475731174720342658926345211726573474938880000⟩, + ⟨1, 5, 5, 0, 8, 3, 301646599426769065738559399914134053637744230400000⟩, + ⟨1, 5, 2, 1, 4, 3, 28736858000992922409245153029014977733220808785920000⟩, + ⟨1, 5, 3, 1, 5, 3, 17942037502647742386619404245184210815523728916480000⟩, + ⟨1, 5, 4, 1, 6, 3, 21508449553671058081606371004677834435244610027520000⟩, + ⟨1, 5, 5, 1, 7, 3, -2392521014560510613151037423971206565820209561600000⟩, + ⟨1, 5, 6, 1, 8, 3, -327170329555668760543595311621688414805216460800000⟩, + ⟨1, 5, 2, 2, 3, 3, -10710050509509879871746364431330680679360721059840000⟩, + ⟨1, 5, 3, 2, 4, 3, -23364388656739498845097423541908012456438671605760000⟩, + ⟨1, 5, 4, 2, 5, 3, -2729309528497686822098474529748607318406369116160000⟩, + ⟨1, 5, 5, 2, 6, 3, -1672247787770213832335879957513366624914951372800000⟩, + ⟨1, 5, 6, 2, 7, 3, -437791322117679479352275472034555671369429811200000⟩, + ⟨1, 5, 7, 2, 8, 3, -410631341039220420246618148285290185940648591360000⟩, + ⟨1, 5, 2, 3, 2, 3, -5726976618298407231833708907161865254843134771200000⟩, + ⟨1, 5, 3, 3, 3, 3, 31229818107742847738597069112090602507005203578880000⟩, + ⟨1, 5, 4, 3, 4, 3, 1872578958274505081768613700194995400089964380160000⟩, + ⟨1, 5, 5, 3, 5, 3, 631875148067861173461583292309784292082319360000000⟩, + ⟨1, 5, 6, 3, 6, 3, 1160018998463484737226317863892375387270597836800000⟩, + ⟨1, 5, 7, 3, 7, 3, 229287965134557894555133617219378138804010352640000⟩, + ⟨1, 5, 8, 3, 8, 3, 172926961614240805208433622303068910056898560000000⟩, + ⟨1, 5, 2, 4, 1, 3, -13220366579602345067329944637013464360134283100160000⟩, + ⟨1, 5, 3, 4, 2, 3, -42752204335844589807417368039002447794753503232000000⟩, + ⟨1, 5, 4, 4, 3, 3, 4185486650028939893933822138499215182787719987200000⟩, + ⟨1, 5, 5, 4, 4, 3, -2276398351346351194484584829023597922676532838400000⟩, + ⟨1, 5, 6, 4, 5, 3, -922912572596122274218333700273529205569041203200000⟩, + ⟨1, 5, 7, 4, 6, 3, -75303978105083283838519180745566589516198707200000⟩, + ⟨1, 5, 8, 4, 7, 3, 61428232734605351702885952146831299532103352320000⟩, + ⟨1, 5, 2, 5, 0, 3, 98638148609024753345751113946117394076000814366720000⟩, + ⟨1, 5, 3, 5, 1, 3, 35502384430281852644923451641239911641890674442240000⟩, + ⟨1, 5, 4, 5, 2, 3, -28677537715569898989913209754981332536780988088320000⟩, + ⟨1, 5, 5, 5, 3, 3, 5936977766674984725598235446873168907252583628800000⟩, + ⟨1, 5, 6, 5, 4, 3, -1040935651622954312183106839875617584023653580800000⟩, + ⟨1, 5, 7, 5, 5, 3, -199438211107076473506365751141980681270156328960000⟩, + ⟨1, 5, 8, 5, 6, 3, 127909702810502554613428502282050237561810452480000⟩, + ⟨1, 5, 3, 6, 0, 3, 19334616699840265075567228199026063724863385763840000⟩, + ⟨1, 5, 4, 6, 1, 3, 15388541943486943267982047620757613315564324782080000⟩, + ⟨1, 5, 5, 6, 2, 3, 87866823314420213169737704074325816272696115200000⟩, + ⟨1, 5, 6, 6, 3, 3, 3854365380347829096524975669205820990416538828800000⟩, + ⟨1, 5, 7, 6, 4, 3, 71396003697752684802660130851250536414361681920000⟩, + ⟨1, 5, 8, 6, 5, 3, -134235526777009653464945715297749895427034972160000⟩, + ⟨1, 5, 4, 7, 0, 3, 293632346851685634595041375690582432850105451151360000⟩, + ⟨1, 5, 5, 7, 1, 3, -4096048967228189683586016410815410551902332518400000⟩, + ⟨1, 5, 6, 7, 2, 3, -3803786570063734603533946600881235488652079923200000⟩, + ⟨1, 5, 7, 7, 3, 3, 2991461402750419157374822460115027476635063418880000⟩, + ⟨1, 5, 8, 7, 4, 3, 265413402553246631957096088051409500829541990400000⟩ +] + +def collectedFourData_8_3_10 : List CollectedFourTerm := [ + ⟨1, 6, 1, 0, 4, 4, 811691679445301338709457617607626733598330060800000⟩, + ⟨1, 6, 2, 0, 5, 4, -19990457254477622703162846559326689336552010547200000⟩, + ⟨1, 6, 3, 0, 6, 4, -1604338589223531737909170801790499383728448471040000⟩, + ⟨1, 6, 4, 0, 7, 4, 7671911559592862888949390923344513726639327150080000⟩, + ⟨1, 6, 5, 0, 8, 4, 180803062802918667696613688093033772650122444800000⟩, + ⟨1, 6, 1, 1, 3, 4, -3278171443098056001854981697447831845492521697280000⟩, + ⟨1, 6, 2, 1, 4, 4, 68898001194585923398354713062605843230472965980160000⟩, + ⟨1, 6, 3, 1, 5, 4, 21508449553671058081606371004677834435244610027520000⟩, + ⟨1, 6, 4, 1, 6, 4, 17189181259729427863889415960646215356391956152320000⟩, + ⟨1, 6, 5, 1, 7, 4, -1434046092596191271577945096422989314726769459200000⟩, + ⟨1, 6, 6, 1, 8, 4, -156881324713931367098188530040048220955664711680000⟩, + ⟨1, 6, 1, 2, 2, 4, -572297561049448198290215236467271564038525419520000⟩, + ⟨1, 6, 2, 2, 3, 4, -25677861955986668980716593909728754479126617784320000⟩, + ⟨1, 6, 3, 2, 4, 4, -28008623585904677010228585991433160023253178122240000⟩, + ⟨1, 6, 4, 2, 5, 4, -2181217018092595372804326102168627183408969154560000⟩, + ⟨1, 6, 5, 2, 6, 4, -1002323654133090523106190948860294969020750233600000⟩, + ⟨1, 6, 6, 2, 7, 4, -209925156279792554888744503579181526847869419520000⟩, + ⟨1, 6, 7, 2, 8, 4, -164084736429646598541942478870069951639458938880000⟩, + ⟨1, 6, 1, 3, 1, 4, 3211745454321522649531732230433165187594846208000000⟩, + ⟨1, 6, 2, 3, 2, 4, -13730702287468441793941682742779550289370913177600000⟩, + ⟨1, 6, 3, 3, 3, 4, 37437496563118048026116715586916699850597854085120000⟩, + ⟨1, 6, 4, 3, 4, 4, 1496532748983848459499490130369697699989091778560000⟩, + ⟨1, 6, 5, 3, 5, 4, 378737775585142497640570311862051353730744320000000⟩, + ⟨1, 6, 6, 3, 6, 4, 556240284439711680712135901865957170405997281280000⟩, + ⟨1, 6, 7, 3, 7, 4, 91621490045983844102723783469601369944615813120000⟩, + ⟨1, 6, 8, 3, 8, 4, 59228674236621786618000142202920492691619840000000⟩, + ⟨1, 6, 1, 4, 0, 4, -25698792187520478494697517832167611378273657815040000⟩, + ⟨1, 6, 2, 4, 1, 4, -31696465645716523969823462959952295553861869895680000⟩, + ⟨1, 6, 3, 4, 2, 4, -51250234547222021100558061817832268377115066368000000⟩, + ⟨1, 6, 4, 4, 3, 4, 3344968613753267118069623454613284382336824115200000⟩, + ⟨1, 6, 5, 4, 4, 4, -1364443673043475946176001878598232783696219340800000⟩, + ⟨1, 6, 6, 4, 5, 4, -442545469146480339866364739749667393323631902720000⟩, + ⟨1, 6, 7, 4, 6, 4, -30090819098721191779576371116536949005457817600000⟩, + ⟨1, 6, 8, 4, 7, 4, 21039592389794850453362183519356845866593812480000⟩, + ⟨1, 6, 2, 5, 0, 4, 236489712287318097181867126382241435305007183298560000⟩, + ⟨1, 6, 3, 5, 1, 4, 42559338338305661835125713727278574360107690229760000⟩, + ⟨1, 6, 4, 5, 2, 4, -22918592651022699612898607272251818673649609605120000⟩, + ⟨1, 6, 5, 5, 3, 4, 3558547538899953144149003384307869807527172505600000⟩, + ⟨1, 6, 6, 5, 4, 4, -499138672477884345789966331546946294207144263680000⟩, + ⟨1, 6, 7, 5, 5, 4, -79693786209024985558484626148862021456290119680000⟩, + ⟨1, 6, 8, 5, 6, 4, 43809953339528709885490215675659226113082654720000⟩, + ⟨1, 6, 3, 6, 0, 4, 23177837403734742656910267248338396321327255388160000⟩, + ⟨1, 6, 4, 6, 1, 4, 12298256837597037228472480752547233181293902561280000⟩, + ⟨1, 6, 5, 6, 2, 4, 52666235270677644814735903614254351271749222400000⟩, + ⟨1, 6, 6, 6, 3, 4, 1848205329687746194425106771119996640174779924480000⟩, + ⟨1, 6, 7, 6, 4, 4, 28529226286594853394524439589415495107199631360000⟩, + ⟨1, 6, 8, 6, 5, 4, -45976591575076179148829111952165720809527050240000⟩, + ⟨1, 6, 4, 7, 0, 4, 234665898216354411103932986740289038856534894837760000⟩, + ⟨1, 6, 5, 7, 1, 4, -2455118672224180538742641214098136872665271500800000⟩, + ⟨1, 6, 6, 7, 2, 4, -1823952302921536260848720803064639597933462814720000⟩, + ⟨1, 6, 7, 7, 3, 4, 1195362133264155335076826246155304105879315415040000⟩, + ⟨1, 6, 8, 7, 4, 4, 90905916643162904326927917641985911890221465600000⟩ +] + +def collectedFourData_8_3_11 : List CollectedFourTerm := [ + ⟨1, 7, 0, 0, 3, 5, 9786916588865017054720429226741903320988359065600000⟩, + ⟨1, 7, 1, 0, 4, 5, -270868813054728819672679891979062551659937792000000⟩, + ⟨1, 7, 2, 0, 5, 5, 3335497680992639300978755997516925628594520064000000⟩, + ⟨1, 7, 3, 0, 6, 5, 178460738400017433922305165606547245459780403200000⟩, + ⟨1, 7, 4, 0, 7, 5, -640046470424553285899186568193575819856891084800000⟩, + ⟨1, 7, 5, 0, 8, 5, -12067121607444405905781933417567608122009190400000⟩, + ⟨1, 7, 0, 1, 2, 5, -3828175240712450394579183050511345031722722918400000⟩, + ⟨1, 7, 1, 1, 3, 5, 1093955291482959959984719788765350124036764467200000⟩, + ⟨1, 7, 2, 1, 4, 5, -11495941302598015962329064997874549724072325939200000⟩, + ⟨1, 7, 3, 1, 5, 5, -2392521014560510613151037423971206565820209561600000⟩, + ⟨1, 7, 4, 1, 6, 5, -1434046092596191271577945096422989314726769459200000⟩, + ⟨1, 7, 5, 1, 7, 5, 95710815523637096851165109215004612814805401600000⟩, + ⟨1, 7, 6, 1, 8, 5, 8725451484393692698054597508766847307297587200000⟩, + ⟨1, 7, 0, 2, 1, 5, -3954932654423287025700604372194974596778164224000000⟩, + ⟨1, 7, 1, 2, 2, 5, 190980842850966583340141675549605245857090764800000⟩, + ⟨1, 7, 2, 2, 3, 5, 4284466729136894852237486482301161607505798758400000⟩, + ⟨1, 7, 3, 2, 4, 5, 3115576524982696502482476813665127485626594099200000⟩, + ⟨1, 7, 4, 2, 5, 5, 181972933709655874645162496485350047443687833600000⟩, + ⟨1, 7, 5, 2, 6, 5, 66896883476062443581888312651976607617830092800000⟩, + ⟨1, 7, 6, 2, 7, 5, 11675652088055297209522109361188647312608460800000⟩, + ⟨1, 7, 7, 2, 8, 5, 7822364596698972886750898136918126914804121600000⟩, + ⟨1, 7, 0, 3, 0, 5, 22099190785181522729750693584428823524620736921600000⟩, + ⟨1, 7, 1, 3, 1, 5, -1071788341652721088057674970889625804912721920000000⟩, + ⟨1, 7, 2, 3, 2, 5, 2291029417448315248732345726982939293633216512000000⟩, + ⟨1, 7, 3, 3, 3, 5, -4164409760744889736195588994169878847579330969600000⟩, + ⟨1, 7, 4, 3, 4, 5, -124851609200862309345297089283702242047269273600000⟩, + ⟨1, 7, 5, 3, 5, 5, -25277640347833346401338630591394109309583360000000⟩, + ⟨1, 7, 6, 3, 6, 5, -30937064206935884784395338617631448740606771200000⟩, + ⟨1, 7, 7, 3, 7, 5, -4367845027071144586194379352038266097788518400000⟩, + ⟨1, 7, 8, 3, 8, 5, -2470642655263301037242347796141100446515200000000⟩, + ⟨1, 7, 1, 4, 0, 5, 8575918064764271399639511914213479332393359769600000⟩, + ⟨1, 7, 2, 4, 1, 5, 5288697817718478236523964195854234813592082841600000⟩, + ⟨1, 7, 3, 4, 2, 5, 5700888055617912729926416138674671961180733440000000⟩, + ⟨1, 7, 4, 4, 3, 5, -279061527011047268902403977358527621194842112000000⟩, + ⟨1, 7, 5, 4, 4, 5, 91065424854395492868230272231262677335696998400000⟩, + ⟨1, 7, 6, 4, 5, 5, 24613567151584355375087394316390286102416588800000⟩, + ⟨1, 7, 7, 4, 6, 5, 1434510991852265758109654435942001102815232000000⟩, + ⟨1, 7, 8, 4, 7, 5, -877637648952129204015910559534209443456614400000⟩, + ⟨1, 7, 2, 5, 0, 5, -39459371882865851398692597757458055858704560947200000⟩, + ⟨1, 7, 3, 5, 1, 5, -4734144647948730360886310349501104357324410060800000⟩, + ⟨1, 7, 4, 5, 2, 5, 1912035119206150631113851835088601068273349427200000⟩, + ⟨1, 7, 5, 5, 3, 5, -237503863220421851647628874723051769208556748800000⟩, + ⟨1, 7, 6, 5, 4, 5, 27761177301581658691580428006509795268047667200000⟩, + ⟨1, 7, 7, 5, 5, 5, 3799219021725776910256943236841653254330777600000⟩, + ⟨1, 7, 8, 5, 6, 5, -1827471927082393605765568979620260512111001600000⟩, + ⟨1, 7, 3, 6, 0, 5, -2578217594072800622133254967033691185005513932800000⟩, + ⟨1, 7, 4, 6, 1, 5, -1026009726537611305277964430100856341682506956800000⟩, + ⟨1, 7, 5, 6, 2, 5, -3515039268501184127617875886715169412428595200000⟩, + ⟨1, 7, 6, 6, 3, 5, -102793789935126811232014202750111780080661299200000⟩, + ⟨1, 7, 7, 6, 4, 5, -1360065625428593897266801287367979334578995200000⟩, + ⟨1, 7, 8, 6, 5, 5, 1917850260081753177924656355380084224504627200000⟩, + ⟨1, 7, 4, 7, 0, 5, -19577530152127542818009471414966104183281392025600000⟩, + ⟨1, 7, 5, 7, 1, 5, 163859036009418635186213238166497317511128678400000⟩, + ⟨1, 7, 6, 7, 2, 5, 101444881078166641255486155744127668567461068800000⟩, + ⟨1, 7, 7, 7, 3, 5, -56986156268649998773467729542230980420226252800000⟩, + ⟨1, 7, 8, 7, 4, 5, -3792015238719254241939826824089762443296768000000⟩ +] + +def collectedFourData_8_3_12 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 3, 6, 5353330158817421504047021541366131602343801651200000⟩, + ⟨1, 8, 1, 0, 4, 6, -74081053661923532975638484324387153082580992000000⟩, + ⟨1, 8, 2, 0, 5, 6, 608159548794595344039823648151235486050942976000000⟩, + ⟨1, 8, 3, 0, 6, 6, 24403989866649923372853259749248599947057561600000⟩, + ⟨1, 8, 4, 0, 7, 6, -70019603049784634857714514261011424557840465920000⟩, + ⟨1, 8, 5, 0, 8, 6, -1100095987752104350353345580355900530281676800000⟩, + ⟨1, 8, 0, 1, 2, 6, -2093967572244397798516880921253160805787815116800000⟩, + ⟨1, 8, 1, 1, 3, 6, 299190444769734406259274580360450647887393587200000⟩, + ⟨1, 8, 2, 1, 4, 6, -2096048969063153857231352325534257441577684172800000⟩, + ⟨1, 8, 3, 1, 5, 6, -327170329555668760543595311621688414805216460800000⟩, + ⟨1, 8, 4, 1, 6, 6, -156881324713931367098188530040048220955664711680000⟩, + ⟨1, 8, 5, 1, 7, 6, 8725451484393692698054597508766847307297587200000⟩, + ⟨1, 8, 6, 1, 8, 6, 681817289389433591450901102590677136651059200000⟩, + ⟨1, 8, 0, 2, 1, 6, -2163302411211346889915977169425023775694389248000000⟩, + ⟨1, 8, 1, 2, 2, 6, 52232155884196371295522581491819179865328844800000⟩, + ⟨1, 8, 2, 2, 3, 6, 781184579340470476164167886378860628667898265600000⟩, + ⟨1, 8, 3, 2, 4, 6, 426046079524921878397799694999591796489165209600000⟩, + ⟨1, 8, 4, 2, 5, 6, 19907417934362044009386611143230293445904957440000⟩, + ⟨1, 8, 5, 2, 6, 6, 6098636899435538403947060596586810428725657600000⟩, + ⟨1, 8, 6, 2, 7, 6, 912349518276544210883966170905270821899468800000⟩, + ⟨1, 8, 7, 2, 8, 6, 534842868136043194095724692351040556000870400000⟩, + ⟨1, 8, 0, 3, 0, 6, 12088001715511910242304235585551605666281632563200000⟩, + ⟨1, 8, 1, 3, 1, 6, -293127912205074415781441176319126342121553920000000⟩, + ⟨1, 8, 2, 3, 2, 6, 417722196219865023061348431092584540230647808000000⟩, + ⟨1, 8, 3, 3, 3, 6, -569470991283236743897916343123201100249615564800000⟩, + ⟨1, 8, 4, 3, 4, 6, -13658477189277313821287261243537685883587133440000⟩, + ⟨1, 8, 5, 3, 5, 6, -2304429476316627437500651769559524699013120000000⟩, + ⟨1, 8, 6, 3, 6, 6, -2417459462924927982462484485415298026124083200000⟩, + ⟨1, 8, 7, 3, 7, 6, -298645087808655675729534755226973602683289600000⟩, + ⟨1, 8, 8, 3, 8, 6, -150156994663782320263849448870212376985600000000⟩, + ⟨1, 8, 1, 4, 0, 6, 2345463987497508361661886774084654390165739929600000⟩, + ⟨1, 8, 2, 4, 1, 6, 964285508835204191816679296171510001727596134400000⟩, + ⟨1, 8, 3, 4, 2, 6, 779579954602449049858932481276449657685278720000000⟩, + ⟨1, 8, 4, 4, 3, 6, -30528685416887353350983550236437294890142924800000⟩, + ⟨1, 8, 5, 4, 4, 6, 8301955658046747078830367732084101299883212800000⟩, + ⟨1, 8, 6, 4, 5, 6, 1923333785938089874028638453735121818012876800000⟩, + ⟨1, 8, 7, 4, 6, 6, 98082614760595444288759219679141044420608000000⟩, + ⟨1, 8, 8, 4, 7, 6, -53339737938101338990141764331548792009523200000⟩, + ⟨1, 8, 2, 5, 0, 6, -7194606650981148034040352735643750134327332044800000⟩, + ⟨1, 8, 3, 5, 1, 6, -647380589431565964477193181367190087207904870400000⟩, + ⟨1, 8, 4, 5, 2, 6, 209172218347298376593544154219607185343517818880000⟩, + ⟨1, 8, 5, 5, 3, 6, -21651977621840203725019694220856879312640409600000⟩, + ⟨1, 8, 6, 5, 4, 6, 2169291834569077820048942178388759857541939200000⟩, + ⟨1, 8, 7, 5, 5, 6, 259766106928117577780469703527224526136934400000⟩, + ⟨1, 8, 8, 5, 6, 6, -111067333763764726209924978915303347768524800000⟩, + ⟨1, 8, 3, 6, 0, 6, -352563799768324982754722736634765002697762406400000⟩, + ⟨1, 8, 4, 6, 1, 6, -112243090302065809304115392648267307229611294720000⟩, + ⟨1, 8, 5, 6, 2, 6, -320447636301576857638178059799808765748838400000⟩, + ⟨1, 8, 6, 6, 3, 6, -8032430567632125732258015078652157206147891200000⟩, + ⟨1, 8, 7, 6, 4, 6, -92992520479605539291422061413062167809228800000⟩, + ⟨1, 8, 8, 6, 5, 6, 116560211836194871461550521481255978637721600000⟩, + ⟨1, 8, 4, 7, 0, 6, -2141736503972717907857903831499219328624219914240000⟩, + ⟨1, 8, 5, 7, 1, 6, 14938166195299072477476566902709155804269772800000⟩, + ⟨1, 8, 6, 7, 2, 6, 7927025204696927389762928532588097801342156800000⟩, + ⟨1, 8, 7, 7, 3, 6, -3896346032711830697178898827517198433727283200000⟩, + ⟨1, 8, 8, 7, 4, 6, -230465385494879074479152254518415174139904000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0813.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0813.lean new file mode 100644 index 0000000000000000000000000000000000000000..73e65252e6281b11e01ddf404160aff3cf552f81 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0813.lean @@ -0,0 +1,616 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0813. -/ +namespace LaughlinFock +def collectedFourData_8_3_13 : List CollectedFourTerm := [ + ⟨2, 1, 5, 0, 8, 0, 498633858974824528608597243272312613456838656000000⟩, + ⟨2, 1, 5, 1, 7, 0, -3954932654423287025700604372194974596778164224000000⟩, + ⟨2, 1, 6, 1, 8, 0, -2163302411211346889915977169425023775694389248000000⟩, + ⟨2, 1, 5, 2, 6, 0, -2764292284953826601089644781404986142193876992000000⟩, + ⟨2, 1, 6, 2, 7, 0, -2894746060960985010309820047128310200320131072000000⟩, + ⟨2, 1, 7, 2, 8, 0, -6787899833364510895719966724017241969083285504000000⟩, + ⟨2, 1, 5, 3, 5, 0, 1044514819892266188788671755343945835898470400000000⟩, + ⟨2, 1, 6, 3, 6, 0, 7670230671085459785036229128755937039045623808000000⟩, + ⟨2, 1, 7, 3, 7, 0, 3790221507180815105365343494902475236726276096000000⟩, + ⟨2, 1, 8, 3, 8, 0, 5717103282739554636659205121016038233735168000000000⟩, + ⟨2, 1, 5, 4, 4, 0, -3762977260982933376418482006341167394404171776000000⟩, + ⟨2, 1, 6, 4, 5, 0, -6102445158599698108276530829156140787634798592000000⟩, + ⟨2, 1, 7, 4, 6, 0, -1244804790441842655947696182493334791604142080000000⟩, + ⟨2, 1, 8, 4, 7, 0, 2030866371221666414446881252644600210465488896000000⟩, + ⟨2, 1, 5, 5, 3, 0, 9814061023961836096409565381662840564672888832000000⟩, + ⟨2, 1, 6, 5, 4, 0, -6882832584880325708240533414194978608746856448000000⟩, + ⟨2, 1, 7, 5, 5, 0, -3296793168573411270782393229243191026614534144000000⟩, + ⟨2, 1, 8, 5, 6, 0, 4228796799561321392860372550079761178421100544000000⟩, + ⟨2, 1, 5, 6, 2, 0, 145247363200476034704992434810553989047779328000000⟩, + ⟨2, 1, 6, 6, 3, 0, 25485678766531433561183389024364354317559267328000000⟩, + ⟨2, 1, 7, 6, 4, 0, 1180204414929398532625708955498965528517541888000000⟩, + ⟨2, 1, 8, 6, 5, 0, -4437933585562492936801194250468735206448693248000000⟩, + ⟨2, 1, 5, 7, 1, 0, -6770932299452885064027202103032441248443006976000000⟩, + ⟨2, 1, 6, 7, 2, 0, -25151243604295350368545865844542174286726561792000000⟩, + ⟨2, 1, 7, 7, 3, 0, 49450050027492870962224629107698869325352927232000000⟩, + ⟨2, 1, 8, 7, 4, 0, 8774778790164559835239026388966004329933701120000000⟩ +] + +def collectedFourData_8_3_14 : List CollectedFourTerm := [ + ⟨2, 2, 4, 0, 7, 1, -255429052018221359581274450376682684013220986880000⟩, + ⟨2, 2, 5, 0, 8, 1, -24078669090492636328794425462212630068540211200000⟩, + ⟨2, 2, 4, 1, 6, 1, -572297561049448198290215236467271564038525419520000⟩, + ⟨2, 2, 5, 1, 7, 1, 190980842850966583340141675549605245857090764800000⟩, + ⟨2, 2, 6, 1, 8, 1, 52232155884196371295522581491819179865328844800000⟩, + ⟨2, 2, 4, 2, 5, 1, 72621561243202099236790234568558365984853852160000⟩, + ⟨2, 2, 5, 2, 6, 1, 133485678922107719024184625080825577711494758400000⟩, + ⟨2, 2, 6, 2, 7, 1, 69892598796029353452795505579290647065735987200000⟩, + ⟨2, 2, 7, 2, 8, 1, 109260927609307715392262283184092187306072473600000⟩, + ⟨2, 2, 4, 3, 4, 1, -49825644941018207697316383814861181098823516160000⟩, + ⟨2, 2, 5, 3, 5, 1, -50438866626526489449750520424841808529326080000000⟩, + ⟨2, 2, 6, 3, 6, 1, -185194951017294226639687628397177738720234700800000⟩, + ⟨2, 2, 7, 3, 7, 1, -61009020151385868250539993950151134765540966400000⟩, + ⟨2, 2, 8, 3, 8, 1, -69018697599216387404491998589642172950118400000000⟩, + ⟨2, 2, 4, 4, 3, 1, -111367571876316432569644472118630369058829107200000⟩, + ⟨2, 2, 5, 4, 4, 1, 181711455472643849803681850744399299446256435200000⟩, + ⟨2, 2, 6, 4, 5, 1, 147341335703618714615052336227854083580703539200000⟩, + ⟨2, 2, 7, 4, 6, 1, 20036908238931869308982254394701739062198272000000⟩, + ⟨2, 2, 8, 4, 7, 1, -24517267750426179079732735524634177521372364800000⟩, + ⟨2, 2, 4, 5, 2, 1, 763052903956203851923705388856890482927935160320000⟩, + ⟨2, 2, 5, 5, 3, 1, -473913922162693291024720883753287664739444326400000⟩, + ⟨2, 2, 6, 5, 4, 1, 166183508433751316595870668372579110517263564800000⟩, + ⟨2, 2, 7, 5, 5, 1, 53066587394796099277992384095908474786519449600000⟩, + ⟨2, 2, 8, 5, 6, 1, -51051386179890536054346370348543494499545907200000⟩, + ⟨2, 2, 4, 6, 1, 1, -409458850131834161898880808708573257913157550080000⟩, + ⟨2, 2, 5, 6, 2, 1, -7013890316155682265667875292610241846942105600000⟩, + ⟨2, 2, 6, 6, 3, 1, -615342514874113274752253946003997256154139852800000⟩, + ⟨2, 2, 7, 6, 4, 1, -18997073072581054815614558650460258434233139200000⟩, + ⟨2, 2, 8, 6, 5, 1, 53576152285387611336583984451226632236459622400000⟩, + ⟨2, 2, 4, 7, 0, 1, -7812979523657176223902946978218185561153585807360000⟩, + ⟨2, 2, 5, 7, 1, 1, 326963432864044383482462457923926606096839475200000⟩, + ⟨2, 2, 6, 7, 2, 1, 607267698594825628968623480765835835048407859200000⟩, + ⟨2, 2, 7, 7, 3, 1, -795969072756999856546462607430275846330174668800000⟩, + ⟨2, 2, 8, 7, 4, 1, -105931933335333984588015128848210615081107456000000⟩ +] + +def collectedFourData_8_3_15 : List CollectedFourTerm := [ + ⟨2, 3, 3, 0, 6, 2, 798874288082152069721421942330758652898238791680000⟩, + ⟨2, 3, 4, 0, 7, 2, -11460597394902614735856156454706749873819043758080000⟩, + ⟨2, 3, 5, 0, 8, 2, -540181177651507606646101284644832228702525849600000⟩, + ⟨2, 3, 3, 1, 5, 2, -10710050509509879871746364431330680679360721059840000⟩, + ⟨2, 3, 4, 1, 6, 2, -25677861955986668980716593909728754479126617784320000⟩, + ⟨2, 3, 5, 1, 7, 2, 4284466729136894852237486482301161607505798758400000⟩, + ⟨2, 3, 6, 1, 8, 2, 781184579340470476164167886378860628667898265600000⟩, + ⟨2, 3, 3, 2, 4, 2, 13946787403636416834614986734580822871948478382080000⟩, + ⟨2, 3, 4, 2, 5, 2, 3258386111608911444627784406497813495816975810560000⟩, + ⟨2, 3, 5, 2, 6, 2, 2994619468740741593792338615170720523560891187200000⟩, + ⟨2, 3, 6, 2, 7, 2, 1045314317688506958551998624283718015997339238400000⟩, + ⟨2, 3, 7, 2, 8, 2, 1225580540300627394568656296932498514540652134400000⟩, + ⟨2, 3, 3, 3, 3, 2, -18641858779270376581258511528255594160173654999040000⟩, + ⟨2, 3, 4, 3, 4, 2, -2235578342003323252939774339499599164061840834560000⟩, + ⟨2, 3, 5, 3, 5, 2, -1131546194323606737493547201057430715383152640000000⟩, + ⟨2, 3, 6, 3, 6, 2, -2769777303988261327329815257992742740717836697600000⟩, + ⟨2, 3, 7, 3, 7, 2, -684338578450598182657200147170438380892297625600000⟩, + ⟨2, 3, 8, 3, 8, 2, -619346546256393731445142868580683303752826880000000⟩, + ⟨2, 3, 3, 4, 2, 2, 25519859032855818744867575514034867342783021056000000⟩, + ⟨2, 3, 4, 4, 3, 2, -4996843131341584955777585628117579006261539635200000⟩, + ⟨2, 3, 5, 4, 4, 2, 4076517171322362364438232928216962073489938841600000⟩, + ⟨2, 3, 6, 4, 5, 2, 2203638302931315737959949440520514420869588582400000⟩, + ⟨2, 3, 7, 4, 6, 2, 224754130893286187389125347875957367937957888000000⟩, + ⟨2, 3, 8, 4, 7, 2, -220008282292509081850623768496189591583572623360000⟩, + ⟨2, 3, 3, 5, 1, 2, -21192260377353694422042833135590475739523102801920000⟩, + ⟨2, 3, 4, 5, 2, 2, 34236677676858410514791609676698237219858672517120000⟩, + ⟨2, 3, 5, 5, 3, 2, -10631791135016215552259030580572286945949070131200000⟩, + ⟨2, 3, 6, 5, 4, 2, 2485442002757204828889704458063010247302814105600000⟩, + ⟨2, 3, 7, 5, 5, 2, 595248258222587752173607499107116210358478438400000⟩, + ⟨2, 3, 8, 5, 6, 2, -458114986401533868338197150918923712273097687040000⟩, + ⟨2, 3, 3, 6, 0, 2, -11541315829194094146561376142473653188989519134720000⟩, + ⟨2, 3, 4, 6, 1, 2, -18371610410259687393671146465357700143999384289280000⟩, + ⟨2, 3, 5, 6, 2, 2, -157349707189400362018791744512890701102238924800000⟩, + ⟨2, 3, 6, 6, 3, 2, -9203068023804915270004360746153236482250873241600000⟩, + ⟨2, 3, 7, 6, 4, 2, -213090293024759247390854843219400488938949836800000⟩, + ⟨2, 3, 8, 6, 5, 2, 480771240749088712929240762650471536906658119680000⟩, + ⟨2, 3, 4, 7, 0, 2, -350552969866815909076111420919771968052209133813760000⟩, + ⟨2, 3, 5, 7, 1, 2, 7335101933985903785172662853212368823324875161600000⟩, + ⟨2, 3, 6, 7, 2, 2, 9082301001046517895057932089843992046906795622400000⟩, + ⟨2, 3, 7, 7, 3, 2, -8928390300147976829381134364208909102355788595200000⟩, + ⟨2, 3, 8, 7, 4, 2, -950591351788222415464574497729900858351760179200000⟩ +] + +def collectedFourData_8_3_16 : List CollectedFourTerm := [ + ⟨2, 4, 2, 0, 5, 3, 10857705283545978786893971231062193737445461196800000⟩, + ⟨2, 4, 3, 0, 6, 3, 1742775100645313911141060872866356034939671019520000⟩, + ⟨2, 4, 4, 0, 7, 3, -12500867831349506697443137338969205594718270914560000⟩, + ⟨2, 4, 5, 0, 8, 3, -392808697727378528518393019405401386851814604800000⟩, + ⟨2, 4, 2, 1, 4, 3, -37421564803308993366833199045856112184440955863040000⟩, + ⟨2, 4, 3, 1, 5, 3, -23364388656739498845097423541908012456438671605760000⟩, + ⟨2, 4, 4, 1, 6, 3, -28008623585904677010228585991433160023253178122240000⟩, + ⟨2, 4, 5, 1, 7, 3, 3115576524982696502482476813665127485626594099200000⟩, + ⟨2, 4, 6, 1, 8, 3, 426046079524921878397799694999591796489165209600000⟩, + ⟨2, 4, 2, 2, 3, 3, 13946787403636416834614986734580822871948478382080000⟩, + ⟨2, 4, 3, 2, 4, 3, 30425455148146836498566542498151384521072831365120000⟩, + ⟨2, 4, 4, 2, 5, 3, 3554147547565426548836905304016231135985973329920000⟩, + ⟨2, 4, 5, 2, 6, 3, 2177625993595783771004143882305205386329299353600000⟩, + ⟨2, 4, 6, 2, 7, 3, 570098384812528947367911613123436944843761254400000⟩, + ⟨2, 4, 7, 2, 8, 3, 534730252640630267606376821611584962752224952320000⟩, + ⟨2, 4, 2, 3, 2, 3, 7457754311250181499540661641260222367708636774400000⟩, + ⟨2, 4, 3, 3, 3, 3, -40667934611155872216066170478686066564129158594560000⟩, + ⟨2, 4, 4, 3, 4, 3, -2438500229703643938182561019687710137499170897920000⟩, + ⟨2, 4, 5, 3, 5, 3, -822837235727194630784099973445140500258488320000000⟩, + ⟨2, 4, 6, 3, 6, 3, -1510594029541120571916333887848296175214631321600000⟩, + ⟨2, 4, 7, 3, 7, 3, -298582205667900170685394015241948554927464775680000⟩, + ⟨2, 4, 8, 3, 8, 3, -225188066839563489716938449746039390569758720000000⟩, + ⟨2, 4, 2, 4, 1, 3, 17215758405633479734456399672898196195900307537920000⟩, + ⟨2, 4, 3, 4, 2, 3, 55672557695167561834942785984111286066278825984000000⟩, + ⟨2, 4, 4, 4, 3, 3, -5450403099115109115322687630903335784112612966400000⟩, + ⟨2, 4, 5, 4, 4, 3, 2964359862171078556208923846028278235493354700800000⟩, + ⟨2, 4, 6, 4, 5, 3, 1201830507775104747046037293479011735703021158400000⟩, + ⟨2, 4, 7, 4, 6, 3, 98061962672083627214016847588403639459669606400000⟩, + ⟨2, 4, 8, 4, 7, 3, -79992760236743849366377998488501756071080099840000⟩, + ⟨2, 4, 2, 5, 0, 3, -128448067291264190648758009155411915844484742512640000⟩, + ⟨2, 4, 3, 5, 1, 3, -46231734157710493636401164332095114278826022010880000⟩, + ⟨2, 4, 4, 5, 2, 3, 37344317043479726169367391976555027539955642531840000⟩, + ⟨2, 4, 5, 5, 3, 3, -7731220936671508728549998332017169834448624025600000⟩, + ⟨2, 4, 6, 5, 4, 3, 1355521920383123688621375514931537486628362649600000⟩, + ⟨2, 4, 7, 5, 5, 3, 259711411071509920448880059259637015856566763520000⟩, + ⟨2, 4, 8, 5, 6, 3, -166565921456334189011023756583146627106875637760000⟩, + ⟨2, 4, 3, 6, 0, 3, -25177826043306930767799113077859345228936333230080000⟩, + ⟨2, 4, 4, 6, 1, 3, -20039188680500067515000644634043971014881139752960000⟩, + ⟨2, 4, 5, 6, 2, 3, -114421486949194858344717667791500179902195302400000⟩, + ⟨2, 4, 6, 6, 3, 3, -5019212046471236153728525360927407044722006425600000⟩, + ⟨2, 4, 7, 6, 4, 3, -92972940151648649119573304931462657864672215040000⟩, + ⟨2, 4, 8, 6, 5, 3, 174803503710065312255577966636159778672261201920000⟩, + ⟨2, 4, 4, 7, 0, 3, -382372418574027519263516423236787136389215231672320000⟩, + ⟨2, 4, 5, 7, 1, 3, 5333936015529616734525691904938646571582278860800000⟩, + ⟨2, 4, 6, 7, 2, 3, 4953347565856997982396636762445968851880797798400000⟩, + ⟨2, 4, 7, 7, 3, 3, -3895525625513912480422893997731856527993140674560000⟩, + ⟨2, 4, 8, 7, 4, 3, -345625288713535640615826874110421734328683724800000⟩ +] + +def collectedFourData_8_3_17 : List CollectedFourTerm := [ + ⟨2, 5, 1, 0, 4, 4, -102999420268962813121908018303818945471604326400000⟩, + ⟨2, 5, 2, 0, 5, 4, 2536684261109800366460027733299325177972758937600000⟩, + ⟨2, 5, 3, 0, 6, 4, 203582159075569421403564869316231398284402360320000⟩, + ⟨2, 5, 4, 0, 7, 4, -973525370535807941952151887344622056763964784640000⟩, + ⟨2, 5, 5, 0, 8, 4, -22942961130610489068514962954881026299946598400000⟩, + ⟨2, 5, 1, 1, 3, 4, 415982776135039444524267838003105341389395722240000⟩, + ⟨2, 5, 2, 1, 4, 4, -8742795276135236849510231793312519537749687009280000⟩, + ⟨2, 5, 3, 1, 5, 4, -2729309528497686822098474529748607318406369116160000⟩, + ⟨2, 5, 4, 1, 6, 4, -2181217018092595372804326102168627183408969154560000⟩, + ⟨2, 5, 5, 1, 7, 4, 181972933709655874645162496485350047443687833600000⟩, + ⟨2, 5, 6, 1, 8, 4, 19907417934362044009386611143230293445904957440000⟩, + ⟨2, 5, 1, 2, 2, 4, 72621561243202099236790234568558365984853852160000⟩, + ⟨2, 5, 2, 2, 3, 4, 3258386111608911444627784406497813495816975810560000⟩, + ⟨2, 5, 3, 2, 4, 4, 3554147547565426548836905304016231135985973329920000⟩, + ⟨2, 5, 4, 2, 5, 4, 276785008438013518328721969898241047772245524480000⟩, + ⟨2, 5, 5, 2, 6, 4, 127189618807141928132214783364851959006547148800000⟩, + ⟨2, 5, 6, 2, 7, 4, 26638402171950730695709700653101130270805852160000⟩, + ⟨2, 5, 7, 2, 8, 4, 20821493129988491591477607900207071485797335040000⟩, + ⟨2, 5, 1, 3, 1, 4, -407553666279618502352772423666287288531288064000000⟩, + ⟨2, 5, 2, 3, 2, 4, 1742354161448904597995134341162509504390941900800000⟩, + ⟨2, 5, 3, 3, 3, 4, -4750622114246151269099796640133924666343382056960000⟩, + ⟨2, 5, 4, 3, 4, 4, -189902162929885044953873109640401661093981716480000⟩, + ⟨2, 5, 5, 3, 5, 4, -48059838861333337443430141448958182487490560000000⟩, + ⟨2, 5, 6, 3, 6, 4, -70583976993192929243646896792032737478563594240000⟩, + ⟨2, 5, 7, 3, 7, 4, -11626286923827984499689339630878381361290280960000⟩, + ⟨2, 5, 8, 3, 8, 4, -7515808359450359841909469889188716053790720000000⟩, + ⟨2, 5, 1, 4, 0, 4, 3261042048300970169204954811448920629227888312320000⟩, + ⟨2, 5, 2, 4, 1, 4, 4022115377990519793339744930137159406642989629440000⟩, + ⟨2, 5, 3, 4, 2, 4, 6503386175671601866196448323298818672604217344000000⟩, + ⟨2, 5, 4, 4, 3, 4, -424458987025602549359199880694986848769513881600000⟩, + ⟨2, 5, 5, 4, 4, 4, 173140751435536716261983082297852266478462566400000⟩, + ⟨2, 5, 6, 4, 5, 4, 56156700775710416431040021334236538901113077760000⟩, + ⟨2, 5, 7, 4, 6, 4, 3818367245928355516187792713560356459171020800000⟩, + ⟨2, 5, 8, 4, 7, 4, -2669814011553122892529590003625177567293603840000⟩, + ⟨2, 5, 2, 5, 0, 4, -30009305111780494076504210002175726051194809876480000⟩, + ⟨2, 5, 3, 5, 1, 4, -5400556993354678774394930484540047609508743086080000⟩, + ⟨2, 5, 4, 5, 2, 4, 2908249297379827290003372438923355208060722216960000⟩, + ⟨2, 5, 5, 5, 3, 4, -451561033318365255681527690833087284657310924800000⟩, + ⟨2, 5, 6, 5, 4, 4, 63338081689066150157740243567363560807270973440000⟩, + ⟨2, 5, 7, 5, 5, 4, 10112723816730204217799545230367917891586621440000⟩, + ⟨2, 5, 8, 5, 6, 4, -5559253482880936945444321945295295036008693760000⟩, + ⟨2, 5, 3, 6, 0, 4, -2941146097868602621193936912191963828371880673280000⟩, + ⟨2, 5, 4, 6, 1, 4, -1560584340912496267698663003130635742322349834240000⟩, + ⟨2, 5, 5, 6, 2, 4, -6683069246608131775147728522226650745877299200000⟩, + ⟨2, 5, 6, 6, 3, 4, -234527570402024169042165302723651701804200099840000⟩, + ⟨2, 5, 7, 6, 4, 4, -3620209301947569409898314509532433306489978880000⟩, + ⟨2, 5, 8, 6, 5, 4, 5834188520217359968277877686241262347139153920000⟩, + ⟨2, 5, 4, 7, 0, 4, -29777872664282680696141318779722757805875218350080000⟩, + ⟨2, 5, 5, 7, 1, 4, 311541692904143221087884382937660003415647846400000⟩, + ⟨2, 5, 6, 7, 2, 4, 231449988408828930581664741956597232678217973760000⟩, + ⟨2, 5, 7, 7, 3, 4, -151685190147345406173542329072127440813629112320000⟩, + ⟨2, 5, 8, 7, 4, 4, -11535484409133225241441382457353074843110604800000⟩ +] + +def collectedFourData_8_3_18 : List CollectedFourTerm := [ + ⟨2, 6, 0, 0, 3, 5, 6840545815572482831601378948729158666493414604800000⟩, + ⟨2, 6, 1, 0, 4, 5, -189323216243481744033515238575431228311207936000000⟩, + ⟨2, 6, 2, 0, 5, 5, 2331339446636884997189868798130922513038835712000000⟩, + ⟨2, 6, 3, 0, 6, 5, 124734776905643027132852622594796636566296985600000⟩, + ⟨2, 6, 4, 0, 7, 5, -447359203001275392975184704632965728083273318400000⟩, + ⟨2, 6, 5, 0, 8, 5, -8434290562129016729937689601696561158632243200000⟩, + ⟨2, 6, 0, 1, 2, 5, -2675695443642337556899459732101060872086172467200000⟩, + ⟨2, 6, 1, 1, 3, 5, 764617867499876767649852212915930160460044697600000⟩, + ⟨2, 6, 2, 1, 4, 5, -8035065228105044854107208665732773414126066073600000⟩, + ⟨2, 6, 3, 1, 5, 5, -1672247787770213832335879957513366624914951372800000⟩, + ⟨2, 6, 4, 1, 6, 5, -1002323654133090523106190948860294969020750233600000⟩, + ⟨2, 6, 5, 1, 7, 5, 66896883476062443581888312651976607617830092800000⟩, + ⟨2, 6, 6, 1, 8, 5, 6098636899435538403947060596586810428725657600000⟩, + ⟨2, 6, 0, 2, 1, 5, -2764292284953826601089644781404986142193876992000000⟩, + ⟨2, 6, 1, 2, 2, 5, 133485678922107719024184625080825577711494758400000⟩, + ⟨2, 6, 2, 2, 3, 5, 2994619468740741593792338615170720523560891187200000⟩, + ⟨2, 6, 3, 2, 4, 5, 2177625993595783771004143882305205386329299353600000⟩, + ⟨2, 6, 4, 2, 5, 5, 127189618807141928132214783364851959006547148800000⟩, + ⟨2, 6, 5, 2, 6, 5, 46757443182632439189676366295841820589319782400000⟩, + ⟨2, 6, 6, 2, 7, 5, 8160673722906328629580148208896269611329126400000⟩, + ⟨2, 6, 7, 2, 8, 5, 5467426121799299674241646136327833484315852800000⟩, + ⟨2, 6, 0, 3, 0, 5, 15446185290380879144218166310539842111922818252800000⟩, + ⟨2, 6, 1, 3, 1, 5, -749124322160196848732703175252498311398031360000000⟩, + ⟨2, 6, 2, 3, 2, 5, 1601310438540990559268859095885992260267933696000000⟩, + ⟨2, 6, 3, 3, 3, 5, -2910705890311083299380271351657164823830777036800000⟩, + ⟨2, 6, 4, 3, 4, 5, -87264783053136616937014030265658675779390668800000⟩, + ⟨2, 6, 5, 3, 5, 5, -17667756268163940611592919161922145621114880000000⟩, + ⟨2, 6, 6, 3, 6, 5, -21623399278545878375975633200557299083090329600000⟩, + ⟨2, 6, 7, 3, 7, 5, -3052896563662813604188023412924802428777267200000⟩, + ⟨2, 6, 8, 3, 8, 5, -1726850752612392325478257902865887107481600000000⟩, + ⟨2, 6, 1, 4, 0, 5, 5994120814247066801428787755618118933546847436800000⟩, + ⟨2, 6, 2, 4, 1, 5, 3696524783707894095530020788214881050273041612800000⟩, + ⟨2, 6, 3, 4, 2, 5, 3984624327775817016115759087735343966343659520000000⟩, + ⟨2, 6, 4, 4, 3, 5, -195049497310987570209294345213309894311018496000000⟩, + ⟨2, 6, 5, 4, 4, 5, 63649996939772338079158017422949754986509107200000⟩, + ⟨2, 6, 6, 4, 5, 5, 17203603633103863422238390268855388597544550400000⟩, + ⟨2, 6, 7, 4, 6, 5, 1002648594540207233889928684901482371219456000000⟩, + ⟨2, 6, 8, 4, 7, 5, -613423083012561342951271805923196136534835200000⟩, + ⟨2, 6, 2, 5, 0, 5, -27580049218520965082981858111889856717775280537600000⟩, + ⟨2, 6, 3, 5, 1, 5, -3308920952558779412916702779059481076612621926400000⟩, + ⟨2, 6, 4, 5, 2, 5, 1336413130239017722307864907987806767764052377600000⟩, + ⟨2, 6, 5, 5, 3, 5, -166002851151627768075247581843483313465353830400000⟩, + ⟨2, 6, 6, 5, 4, 5, 19403619464966032044529504381427545148070297600000⟩, + ⟨2, 6, 7, 5, 5, 5, 2655456552176822310402947986527544190749900800000⟩, + ⟨2, 6, 8, 5, 6, 5, -1277307855888181394615858457783754170354892800000⟩, + ⟨2, 6, 3, 6, 0, 5, -1802040041378888989129338861277313325515302502400000⟩, + ⟨2, 6, 4, 6, 1, 5, -717127450497404498041302806352293522743649894400000⟩, + ⟨2, 6, 5, 6, 2, 5, -2456829680869610418084307267942796913908121600000⟩, + ⟨2, 6, 6, 6, 3, 5, -71847514303696974022742187721300933170796953600000⟩, + ⟨2, 6, 7, 6, 4, 5, -950615154267752043170342998668380577831321600000⟩, + ⟨2, 6, 8, 6, 5, 5, 1340477611347278666651307351361512860653977600000⟩, + ⟨2, 6, 4, 7, 0, 5, -13683675624021121317150318943823578785775406284800000⟩, + ⟨2, 6, 5, 7, 1, 5, 114528946164029567055012848220339714714186547200000⟩, + ⟨2, 6, 6, 7, 2, 5, 70904697150481853701986647765239261257164390400000⟩, + ⟨2, 6, 7, 7, 3, 5, -39830360182346270555439641762871542527977062400000⟩, + ⟨2, 6, 8, 7, 4, 5, -2650421482422817641108817620833205479276544000000⟩ +] + +def collectedFourData_8_3_19 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 3, 6, 7163368057073006070752529744462421834697854156800000⟩, + ⟨2, 7, 1, 0, 4, 6, -99128923061484033833405023809776900571660288000000⟩, + ⟨2, 7, 2, 0, 5, 6, 813787036516631272085372783763385506399780864000000⟩, + ⟨2, 7, 3, 0, 6, 6, 32655329727414174808776869077396895566292582400000⟩, + ⟨2, 7, 4, 0, 7, 6, -93694237600798318918721537049281778145956986880000⟩, + ⟨2, 7, 5, 0, 8, 6, -1472054258674458616718815374382987419530035200000⟩, + ⟨2, 7, 0, 1, 2, 6, -2801968116025143230132276902386648264060646195200000⟩, + ⟨2, 7, 1, 1, 3, 6, 400351035983632926338626916611697547517152460800000⟩, + ⟨2, 7, 2, 1, 4, 6, -2804753263035180096424867469705257011421328179200000⟩, + ⟨2, 7, 3, 1, 5, 6, -437791322117679479352275472034555671369429811200000⟩, + ⟨2, 7, 4, 1, 6, 6, -209925156279792554888744503579181526847869419520000⟩, + ⟨2, 7, 5, 1, 7, 6, 11675652088055297209522109361188647312608460800000⟩, + ⟨2, 7, 6, 1, 8, 6, 912349518276544210883966170905270821899468800000⟩, + ⟨2, 7, 0, 2, 1, 6, -2894746060960985010309820047128310200320131072000000⟩, + ⟨2, 7, 1, 2, 2, 6, 69892598796029353452795505579290647065735987200000⟩, + ⟨2, 7, 2, 2, 3, 6, 1045314317688506958551998624283718015997339238400000⟩, + ⟨2, 7, 3, 2, 4, 6, 570098384812528947367911613123436944843761254400000⟩, + ⟨2, 7, 4, 2, 5, 6, 26638402171950730695709700653101130270805852160000⟩, + ⟨2, 7, 5, 2, 6, 6, 8160673722906328629580148208896269611329126400000⟩, + ⟨2, 7, 6, 2, 7, 6, 1220828008402131972385254899801888216265523200000⟩, + ⟨2, 7, 7, 2, 8, 6, 715680931961310341324291394046223812499865600000⟩, + ⟨2, 7, 0, 3, 0, 6, 16175128899927606248667203132137948260246277324800000⟩, + ⟨2, 7, 1, 3, 1, 6, -392238673990207180039989774244530537501818880000000⟩, + ⟨2, 7, 2, 3, 2, 6, 558960076879094951669261998009611434078502912000000⟩, + ⟨2, 7, 3, 3, 3, 6, -762017321436640789620721025651814608747574067200000⟩, + ⟨2, 7, 4, 3, 4, 6, -18276604712073825128274425357107819125575516160000⟩, + ⟨2, 7, 5, 3, 5, 6, -3083590215939640798253201713536205250887680000000⟩, + ⟨2, 7, 6, 3, 6, 6, -3234837266194458498352318092928652615142604800000⟩, + ⟨2, 7, 7, 3, 7, 6, -399621285992730670544562883082405695350374400000⟩, + ⟨2, 7, 8, 3, 8, 6, -200927233555539254393739225858088265318400000000⟩, + ⟨2, 7, 1, 4, 0, 6, 3138499085355545005792707498710338087267231334400000⟩, + ⟨2, 7, 2, 4, 1, 6, 1290324304117719773829692199050927377368062361600000⟩, + ⟨2, 7, 3, 4, 2, 6, 1043167146254852841338308600177517123422126080000000⟩, + ⟨2, 7, 4, 4, 3, 6, -40850872905636505439886482164621817798669107200000⟩, + ⟨2, 7, 5, 4, 4, 6, 11108966233688415134035916135333588211282739200000⟩, + ⟨2, 7, 6, 4, 5, 6, 2573640593152157805159964170585338014806835200000⟩, + ⟨2, 7, 7, 4, 6, 6, 131245757068242386198089097557491541082112000000⟩, + ⟨2, 7, 8, 4, 7, 6, -71374670267459545190235876200345611586764800000⟩, + ⟨2, 7, 2, 5, 0, 6, -9627206605584790048946318365139075271803220787200000⟩, + ⟨2, 7, 3, 5, 1, 6, -866269274923182684246979497467810119255955865600000⟩, + ⟨2, 7, 4, 5, 2, 6, 279896352902533620857130063200929889823039160320000⟩, + ⟨2, 7, 5, 5, 3, 6, -28972822573493637028889201534785738584254054400000⟩, + ⟨2, 7, 6, 5, 4, 6, 2902760594473435979365634955993477366467788800000⟩, + ⟨2, 7, 7, 5, 5, 6, 347596762664484869243376523848044082993561600000⟩, + ⟨2, 7, 8, 5, 6, 6, -148620796264016372779782750371361080947507200000⟩, + ⟨2, 7, 3, 6, 0, 6, -471770689723087871766600008841719099686492569600000⟩, + ⟨2, 7, 4, 6, 1, 6, -150194092993247296943479565407341615108933550080000⟩, + ⟨2, 7, 5, 6, 2, 6, -428795589613764518305142466999967911877017600000⟩, + ⟨2, 7, 6, 6, 3, 6, -10748310834903462231624318843263577444109516800000⟩, + ⟨2, 7, 7, 6, 4, 6, -124434628724163610101550331976655540794163200000⟩, + ⟨2, 7, 8, 6, 5, 6, 155970895390750397619930834349457137886822400000⟩, + ⟨2, 7, 4, 7, 0, 6, -2865888410404808440454768471349376807804977807360000⟩, + ⟨2, 7, 5, 7, 1, 6, 19988974970729566980710497854316661901046579200000⟩, + ⟨2, 7, 6, 7, 2, 6, 10607266403214424970589375295660686746792755200000⟩, + ⟨2, 7, 7, 7, 3, 6, -5213756649038201393614082554207940111027404800000⟩, + ⟨2, 7, 8, 7, 4, 6, -308389046021351226664008846727908169875456000000⟩ +] + +def collectedFourData_8_3_20 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 3, 7, 16797405995879466784452968399240557616302758297600000⟩, + ⟨2, 8, 1, 0, 4, 7, -154965164741087765483711719104679252636729344000000⟩, + ⟨2, 8, 2, 0, 5, 7, 954125987778637655475764137923083040429441024000000⟩, + ⟨2, 8, 3, 0, 6, 7, 30629437269753708340019888265122457632605470720000⟩, + ⟨2, 8, 4, 0, 7, 7, -73234644928467589783664677374191987294176542720000⟩, + ⟨2, 8, 5, 0, 8, 7, -986235717768203243879017037803147168736870400000⟩, + ⟨2, 8, 0, 1, 2, 7, -6570344516349644732078413332800832007345432166400000⟩, + ⟨2, 8, 1, 1, 3, 7, 625856332636526884100110940773444490646414950400000⟩, + ⟨2, 8, 2, 1, 4, 7, -3288437708498822256522883270209996180985951027200000⟩, + ⟨2, 8, 3, 1, 5, 7, -410631341039220420246618148285290185940648591360000⟩, + ⟨2, 8, 4, 1, 6, 7, -164084736429646598541942478870069951639458938880000⟩, + ⟨2, 8, 5, 1, 7, 7, 7822364596698972886750898136918126914804121600000⟩, + ⟨2, 8, 6, 1, 8, 7, 534842868136043194095724692351040556000870400000⟩, + ⟨2, 8, 0, 2, 1, 7, -6787899833364510895719966724017241969083285504000000⟩, + ⟨2, 8, 1, 2, 2, 7, 109260927609307715392262283184092187306072473600000⟩, + ⟨2, 8, 2, 2, 3, 7, 1225580540300627394568656296932498514540652134400000⟩, + ⟨2, 8, 3, 2, 4, 7, 534730252640630267606376821611584962752224952320000⟩, + ⟨2, 8, 4, 2, 5, 7, 20821493129988491591477607900207071485797335040000⟩, + ⟨2, 8, 5, 2, 6, 7, 5467426121799299674241646136327833484315852800000⟩, + ⟨2, 8, 6, 2, 7, 7, 715680931961310341324291394046223812499865600000⟩, + ⟨2, 8, 7, 2, 8, 7, 372933919782595425891695395008740576565657600000⟩, + ⟨2, 8, 0, 3, 0, 7, 37929114489586272176254033027306073422669912473600000⟩, + ⟨2, 8, 1, 3, 1, 7, -613174529244283517442568504147698991434301440000000⟩, + ⟨2, 8, 2, 3, 2, 7, 655353687819762103939044933419422373948424192000000⟩, + ⟨2, 8, 3, 3, 3, 7, -714742798196744368534151845702956153974198108160000⟩, + ⟨2, 8, 4, 3, 4, 7, -14285624077432908504381985841497639362798551040000⟩, + ⟨2, 8, 5, 3, 5, 7, -2065920323248616773877488044708392714895360000000⟩, + ⟨2, 8, 6, 3, 6, 7, -1896345212822678262866215267531687543072358400000⟩, + ⟨2, 8, 7, 3, 7, 7, -208238512384856051958999470117766878881382400000⟩, + ⟨2, 8, 8, 3, 8, 7, -94230989969273105957103487655318661365760000000⟩, + ⟨2, 8, 1, 4, 0, 7, 4906318083373256029779457707644665452704248627200000⟩, + ⟨2, 8, 2, 4, 1, 7, 1512842913412447965728807179074182626353453465600000⟩, + ⟨2, 8, 3, 4, 2, 7, 978450468416418866714668164882108283852161024000000⟩, + ⟨2, 8, 4, 4, 3, 7, -31930450034813623310844916861263147912973516800000⟩, + ⟨2, 8, 5, 4, 4, 7, 7442700717438252143988521035650439313778278400000⟩, + ⟨2, 8, 6, 4, 5, 7, 1508734633841956716962985125668222079179161600000⟩, + ⟨2, 8, 7, 4, 6, 7, 68390804410784454929804411872472519933952000000⟩, + ⟨2, 8, 8, 4, 7, 7, -33473341164447334050563612308291229287710720000⟩, + ⟨2, 8, 2, 5, 0, 7, -11287434672615221366463583843796600451566351155200000⟩, + ⟨2, 8, 3, 5, 1, 7, -812527101592849426911384105545912368945094983680000⟩, + ⟨2, 8, 4, 5, 2, 7, 218776635004236963484915578828261068634146734080000⟩, + ⟨2, 8, 5, 5, 3, 7, -19410991339592584655511246931558342064917708800000⟩, + ⟨2, 8, 6, 5, 4, 7, 1701673285029203441958686225208169988515430400000⟩, + ⟨2, 8, 7, 5, 5, 7, 181129072209534126443872792243893912050073600000⟩, + ⟨2, 8, 8, 5, 6, 7, -69700281610201969222894658263780880893870080000⟩, + ⟨2, 8, 3, 6, 0, 7, -442502674669088236948387398274970873295148154880000⟩, + ⟨2, 8, 4, 6, 1, 7, -117396878958327609758261540458633588836422123520000⟩, + ⟨2, 8, 5, 6, 2, 7, -287281208288731215592471674899902596592435200000⟩, + ⟨2, 8, 6, 6, 3, 7, -6300937611516323462999515885693504034596454400000⟩, + ⟨2, 8, 7, 6, 4, 7, -64841595988340479624791870921412179079987200000⟩, + ⟨2, 8, 8, 6, 5, 7, 73147336072796707907696586261293442646671360000⟩, + ⟨2, 8, 4, 7, 0, 7, -2240077143643017925141052292924190833755648163840000⟩, + ⟨2, 8, 5, 7, 1, 7, 13392061441716051667205790920923532679865958400000⟩, + ⟨2, 8, 6, 7, 2, 7, 6218253720235616767454193035319350973274521600000⟩, + ⟨2, 8, 7, 7, 3, 7, -2716834579607745556430246198270849167707340800000⟩, + ⟨2, 8, 8, 7, 4, 7, -144628503503678063812586035884315543758438400000⟩ +] + +def collectedFourData_8_3_21 : List CollectedFourTerm := [ + ⟨3, 0, 5, 0, 8, 0, -2786243343261886170969646488057151358385940070400000⟩, + ⟨3, 0, 5, 1, 7, 0, 22099190785181522729750693584428823524620736921600000⟩, + ⟨3, 0, 6, 1, 8, 0, 12088001715511910242304235585551605666281632563200000⟩, + ⟨3, 0, 5, 2, 6, 0, 15446185290380879144218166310539842111922818252800000⟩, + ⟨3, 0, 6, 2, 7, 0, 16175128899927606248667203132137948260246277324800000⟩, + ⟨3, 0, 7, 2, 8, 0, 37929114489586272176254033027306073422669912473600000⟩, + ⟨3, 0, 5, 3, 5, 0, -5836491869699027130227063235667512329093775360000000⟩, + ⟨3, 0, 6, 3, 6, 0, -42859362163117801627360526773023165749895836467200000⟩, + ⟨3, 0, 7, 3, 7, 0, -21178825412262600273100084089101574790537700966400000⟩, + ⟨3, 0, 8, 3, 8, 0, -31945766773687967576262321951822469085213491200000000⟩, + ⟨3, 0, 5, 4, 4, 0, 21026591266416382305617882054659007219707045478400000⟩, + ⟨3, 0, 6, 4, 5, 0, 34098962384396747321801924178401755838475455692800000⟩, + ⟨3, 0, 7, 4, 6, 0, 6955662955098689723546274942599525581058998272000000⟩, + ⟨3, 0, 8, 4, 7, 0, -11347981702454909767830026824275350966088656486400000⟩, + ⟨3, 0, 5, 5, 3, 0, -54838558806653726940931100378087156314431868108800000⟩, + ⟨3, 0, 6, 5, 4, 0, 38459575352216598204057372063068621492561589043200000⟩, + ⟨3, 0, 7, 5, 5, 0, 18421669236289673434020226531853346473644759449600000⟩, + ⟨3, 0, 8, 5, 6, 0, -23629476259412587656525713543300003543268301209600000⟩, + ⟨3, 0, 5, 6, 2, 0, -811606535656657802372245316745765440397194035200000⟩, + ⟨3, 0, 6, 6, 3, 0, -142407703635994333580998715906700180719030973235200000⟩, + ⟨3, 0, 7, 6, 4, 0, -6594691948007786952513920865872452742806713139200000⟩, + ⟨3, 0, 8, 6, 5, 0, 24798081173296644647886647957607516467860026163200000⟩, + ⟨3, 0, 5, 7, 1, 0, 37834304083991202702639761022803783534382573158400000⟩, + ⟨3, 0, 6, 7, 2, 0, 140538962218296017630787041055502971989459258572800000⟩, + ⟨3, 0, 7, 7, 3, 0, -276314715162625200229361519541938766730712894668800000⟩, + ⟨3, 0, 8, 7, 4, 0, -49031305340871322897497052949060712464916676608000000⟩ +] + +def collectedFourData_8_3_22 : List CollectedFourTerm := [ + ⟨3, 1, 4, 0, 7, 1, 1433472991247459720797695988217451261148004352000000⟩, + ⟨3, 1, 5, 0, 8, 1, 135129976538236448919339207625487545773588480000000⟩, + ⟨3, 1, 4, 1, 6, 1, 3211745454321522649531732230433165187594846208000000⟩, + ⟨3, 1, 5, 1, 7, 1, -1071788341652721088057674970889625804912721920000000⟩, + ⟨3, 1, 6, 1, 8, 1, -293127912205074415781441176319126342121553920000000⟩, + ⟨3, 1, 4, 2, 5, 1, -407553666279618502352772423666287288531288064000000⟩, + ⟨3, 1, 5, 2, 6, 1, -749124322160196848732703175252498311398031360000000⟩, + ⟨3, 1, 6, 2, 7, 1, -392238673990207180039989774244530537501818880000000⟩, + ⟨3, 1, 7, 2, 8, 1, -613174529244283517442568504147698991434301440000000⟩, + ⟨3, 1, 4, 3, 4, 1, 279622524259065591322997849149115481314033664000000⟩, + ⟨3, 1, 5, 3, 5, 1, 283063936725180285480821756189191314604032000000000⟩, + ⟨3, 1, 6, 3, 6, 1, 1039317799996179586130860510353581117087416320000000⟩, + ⟨3, 1, 7, 3, 7, 1, 342383851478433037352486683718658317415874560000000⟩, + ⟨3, 1, 8, 3, 8, 1, 387334322849441667159479746626755871375360000000000⟩, + ⟨3, 1, 4, 4, 3, 1, 624997059356120112541942511734451308729466880000000⟩, + ⟨3, 1, 5, 4, 4, 1, -1019768352746808136170189768652858455050158080000000⟩, + ⟨3, 1, 6, 4, 5, 1, -826882547449596805963294388405401995108679680000000⟩, + ⟨3, 1, 7, 4, 6, 1, -112447533127764926782387911600143690681548800000000⟩, + ⟨3, 1, 8, 4, 7, 1, 137591401063146060176060153462795427297361920000000⟩, + ⟨3, 1, 4, 5, 2, 1, -4282268285739600900729645320937504506829078528000000⟩, + ⟨3, 1, 5, 5, 3, 1, 2659614488754043355311855340728242947028418560000000⟩, + ⟨3, 1, 6, 5, 4, 1, -932625200807358634407017844059254688757841920000000⟩, + ⟨3, 1, 7, 5, 5, 1, -297810758670813170643746603639897570767011840000000⟩, + ⟨3, 1, 8, 5, 6, 1, 286501408811541403482684066374413389272186880000000⟩, + ⟨3, 1, 4, 6, 1, 1, 2297891324630351480144692178266593982395973632000000⟩, + ⟨3, 1, 5, 6, 2, 1, 39362093905684800299954760813063948195594240000000⟩, + ⟨3, 1, 6, 6, 3, 1, 3453314603287199860976879845711312598461317120000000⟩, + ⟨3, 1, 7, 6, 4, 1, 106611957203508394679864849616406329352519680000000⟩, + ⟨3, 1, 8, 6, 5, 1, -300670447113374480874008227698453171362856960000000⟩, + ⟨3, 1, 4, 7, 0, 1, 43846598653676484503141405769663460324770054144000000⟩, + ⟨3, 1, 5, 7, 1, 1, -1834925379211464338111119112618519233120174080000000⟩, + ⟨3, 1, 6, 7, 2, 1, -3407998571480377726185313783870470961684807680000000⟩, + ⟨3, 1, 7, 7, 3, 1, 4466994488880805822466930643061174991081963520000000⟩, + ⟨3, 1, 8, 7, 4, 1, 594492146241827043045737470592916308518502400000000⟩ +] + +def collectedFourData_8_3_23 : List CollectedFourTerm := [ + ⟨3, 2, 3, 0, 6, 2, 427181399821021108683123809741080942264870502400000⟩, + ⟨3, 2, 4, 0, 7, 2, -6128315945294502922019412661441771337652004454400000⟩, + ⟨3, 2, 5, 0, 8, 2, -288850642796515970839860797987304196358012928000000⟩, + ⟨3, 2, 3, 1, 5, 2, -5726976618298407231833708907161865254843134771200000⟩, + ⟨3, 2, 4, 1, 6, 2, -13730702287468441793941682742779550289370913177600000⟩, + ⟨3, 2, 5, 1, 7, 2, 2291029417448315248732345726982939293633216512000000⟩, + ⟨3, 2, 6, 1, 8, 2, 417722196219865023061348431092584540230647808000000⟩, + ⟨3, 2, 3, 2, 4, 2, 7457754311250181499540661641260222367708636774400000⟩, + ⟨3, 2, 4, 2, 5, 2, 1742354161448904597995134341162509504390941900800000⟩, + ⟨3, 2, 5, 2, 6, 2, 1601310438540990559268859095885992260267933696000000⟩, + ⟨3, 2, 6, 2, 7, 2, 558960076879094951669261998009611434078502912000000⟩, + ⟨3, 2, 7, 2, 8, 2, 655353687819762103939044933419422373948424192000000⟩, + ⟨3, 2, 3, 3, 3, 2, -9968346018135447830335623005854424226161963827200000⟩, + ⟨3, 2, 4, 3, 4, 2, -1195428992763289601303444231009496499865046220800000⟩, + ⟨3, 2, 5, 3, 5, 2, -605070778299475923391845004914103822791475200000000⟩, + ⟨3, 2, 6, 3, 6, 2, -1481080770230679317611352757779292823190765568000000⟩, + ⟨3, 2, 7, 3, 7, 2, -365935812749542163317112196283186249998532608000000⟩, + ⟨3, 2, 8, 3, 8, 2, -331182676112006414533113344983477841716838400000000⟩, + ⟨3, 2, 3, 4, 2, 2, 13646213512593878712235195212467285738473390080000000⟩, + ⟨3, 2, 4, 4, 3, 2, -2671957872942639789184773799308117014621454336000000⟩, + ⟨3, 2, 5, 4, 4, 2, 2179832719138456378592135465469177329759551488000000⟩, + ⟨3, 2, 6, 4, 5, 2, 1178349721588004033968357051409536962193784832000000⟩, + ⟨3, 2, 7, 4, 6, 2, 120182594036219313293026698370164553773219840000000⟩, + ⟨3, 2, 8, 4, 7, 2, -117644850264936343415134619723769023870848204800000⟩, + ⟨3, 2, 3, 5, 1, 2, -11332120195159610748642386992074105576830376345600000⟩, + ⟨3, 2, 4, 5, 2, 2, 18307350872854095445846660370918076664105245081600000⟩, + ⟨3, 2, 5, 5, 3, 2, -5685129046478843082325338133736226172610543616000000⟩, + ⟨3, 2, 6, 5, 4, 2, 1329038385326780864816332401444143817459499008000000⟩, + ⟨3, 2, 7, 5, 5, 2, 318296618106203148096112829631002929803558912000000⟩, + ⟨3, 2, 8, 5, 6, 2, -244967454941885304768338393012092976682447667200000⟩, + ⟨3, 2, 3, 6, 0, 2, -6171478448164352950179027974682746726309796249600000⟩, + ⟨3, 2, 4, 6, 1, 2, -9823836327066929802832622434124294160531220070400000⟩, + ⟨3, 2, 5, 6, 2, 2, -84139481244242527350434663485191914954686464000000⟩, + ⟨3, 2, 6, 6, 3, 2, -4921149096555701811018463699681333617767743488000000⟩, + ⟨3, 2, 7, 6, 4, 2, -113945599477382802855581279634037302701850624000000⟩, + ⟨3, 2, 8, 6, 5, 2, 257082415444775222192693186839005168625149542400000⟩, + ⟨3, 2, 4, 7, 0, 2, -187450905121286331673673042921719781071432502476800000⟩, + ⟨3, 2, 5, 7, 1, 2, 3922293105104608211819028525233539602960089088000000⟩, + ⟨3, 2, 6, 7, 2, 2, 4856571444472294018616712805800033205755052032000000⟩, + ⟨3, 2, 7, 7, 3, 2, -4774270900271387024675034837715480924322267136000000⟩, + ⟨3, 2, 8, 7, 4, 2, -508308942186021309340955589372098963891552256000000⟩ +] + +def collectedFourData_8_3_24 : List CollectedFourTerm := [ + ⟨3, 3, 2, 0, 5, 3, -14512862547114408616331572922606852871551346278400000⟩, + ⟨3, 3, 3, 0, 6, 3, -2329466017513664102421216530293063966544111861760000⟩, + ⟨3, 3, 4, 0, 7, 3, 16709182264410217013353408661911878004100070113280000⟩, + ⟨3, 3, 5, 0, 8, 3, 525044518022380861633980730036562354191623782400000⟩, + ⟨3, 3, 2, 1, 4, 3, 50019227093166295884455426790961249638627693035520000⟩, + ⟨3, 3, 3, 1, 5, 3, 31229818107742847738597069112090602507005203578880000⟩, + ⟨3, 3, 4, 1, 6, 3, 37437496563118048026116715586916699850597854085120000⟩, + ⟨3, 3, 5, 1, 7, 3, -4164409760744889736195588994169878847579330969600000⟩, + ⟨3, 3, 6, 1, 8, 3, -569470991283236743897916343123201100249615564800000⟩, + ⟨3, 3, 2, 2, 3, 3, -18641858779270376581258511528255594160173654999040000⟩, + ⟨3, 3, 3, 2, 4, 3, -40667934611155872216066170478686066564129158594560000⟩, + ⟨3, 3, 4, 2, 5, 3, -4750622114246151269099796640133924666343382056960000⟩, + ⟨3, 3, 5, 2, 6, 3, -2910705890311083299380271351657164823830777036800000⟩, + ⟨3, 3, 6, 2, 7, 3, -762017321436640789620721025651814608747574067200000⟩, + ⟨3, 3, 7, 2, 8, 3, -714742798196744368534151845702956153974198108160000⟩, + ⟨3, 3, 2, 3, 2, 3, -9968346018135447830335623005854424226161963827200000⟩, + ⟨3, 3, 3, 3, 3, 3, 54358460620694604094318858320209152899103881953280000⟩, + ⟨3, 3, 4, 3, 4, 3, 3259401294344041046706249093129596276476697640960000⟩, + ⟨3, 3, 5, 3, 5, 3, 1099838629701353294253734799788863813488476160000000⟩, + ⟨3, 3, 6, 3, 6, 3, 2019123096704849742273650592735802128031599820800000⟩, + ⟨3, 3, 7, 3, 7, 3, 399097451690758066578114573388260806206779555840000⟩, + ⟨3, 3, 8, 3, 8, 3, 300995779121541272409031832036675146859151360000000⟩, + ⟨3, 3, 2, 4, 1, 3, -23011302007240576359545211049722161776011729960960000⟩, + ⟨3, 3, 3, 4, 2, 3, -74414266769671607804929022236528843166834491392000000⟩, + ⟨3, 3, 4, 4, 3, 3, 7285236515278730687550977431784126152371811123200000⟩, + ⟨3, 3, 5, 4, 4, 3, -3962287250978108134428048363965706820911523430400000⟩, + ⟨3, 3, 6, 4, 5, 3, -1606416872513644945336370652324745287858074419200000⟩, + ⟨3, 3, 7, 4, 6, 3, -131073716609061342167431072091414827371803443200000⟩, + ⟨3, 3, 8, 4, 7, 3, 106921665652449959247207414279023693366474833920000⟩, + ⟨3, 3, 2, 5, 0, 3, 171689053659026342275250805792053536514193563320320000⟩, + ⟨3, 3, 3, 5, 1, 3, 61795267565639966899341431715638567133192325693440000⟩, + ⟨3, 3, 4, 5, 2, 3, -49915974509752231309348846667010033962908039249920000⟩, + ⟨3, 3, 5, 5, 3, 3, 10333872935869836203679215369671567123218746572800000⟩, + ⟨3, 3, 6, 5, 4, 3, -1811847236260225990763728840771557598035758284800000⟩, + ⟨3, 3, 7, 5, 5, 3, -347141123503307655299190761853464811291814133760000⟩, + ⟨3, 3, 8, 5, 6, 3, 222638970206028622166563533545834199854748794880000⟩, + ⟨3, 3, 3, 6, 0, 3, 33653734289086863842052748038714149876431627223040000⟩, + ⟨3, 3, 4, 6, 1, 3, 26785216883397356687866026855802433060582436372480000⟩, + ⟨3, 3, 5, 6, 2, 3, 152940540304275623504621243498636623322755891200000⟩, + ⟨3, 3, 6, 6, 3, 3, 6708888537953416557861447351792658605421677772800000⟩, + ⟨3, 3, 7, 6, 4, 3, 124271516474732211953636958004350497196626411520000⟩, + ⟨3, 3, 8, 6, 5, 3, -233649666835464581884821234525907472415153192960000⟩, + ⟨3, 3, 4, 7, 0, 3, 511094951249240942316386329641998767934664773468160000⟩, + ⟨3, 3, 5, 7, 1, 3, -7129561745039662617103089678699399416203601510400000⟩, + ⟨3, 3, 6, 7, 2, 3, -6620851321163227344643310421203903114745426739200000⟩, + ⟨3, 3, 7, 7, 3, 3, 5206922316957718498722010277685644851011680993280000⟩, + ⟨3, 3, 8, 7, 4, 3, 461977202080411816362014219444572572103370342400000⟩ +] + +def collectedFourData_8_3_25 : List CollectedFourTerm := [ + ⟨3, 4, 1, 0, 4, 4, 70667890576814727162028590728295508613686886400000⟩, + ⟨3, 4, 2, 0, 5, 4, -1740418784143906421935799711899466915179501977600000⟩, + ⟨3, 4, 3, 0, 6, 4, -139677696276114205114270680655582418692284088320000⟩, + ⟨3, 4, 4, 0, 7, 4, 667935646425267610700971117738103620871273840640000⟩, + ⟨3, 4, 5, 0, 8, 4, 15741163032299677495312391184061295155897958400000⟩, + ⟨3, 4, 1, 1, 3, 4, -285405735575861054461540127864059152732247818240000⟩, + ⟨3, 4, 2, 1, 4, 4, 5998430848407328695032323065506022654366481121280000⟩, + ⟨3, 4, 3, 1, 5, 4, 1872578958274505081768613700194995400089964380160000⟩, + ⟨3, 4, 4, 1, 6, 4, 1496532748983848459499490130369697699989091778560000⟩, + ⟨3, 4, 5, 1, 7, 4, -124851609200862309345297089283702242047269273600000⟩, + ⟨3, 4, 6, 1, 8, 4, -13658477189277313821287261243537685883587133440000⟩, + ⟨3, 4, 1, 2, 2, 4, -49825644941018207697316383814861181098823516160000⟩, + ⟨3, 4, 2, 2, 3, 4, -2235578342003323252939774339499599164061840834560000⟩, + ⟨3, 4, 3, 2, 4, 4, -2438500229703643938182561019687710137499170897920000⟩, + ⟨3, 4, 4, 2, 5, 4, -189902162929885044953873109640401661093981716480000⟩, + ⟨3, 4, 5, 2, 6, 4, -87264783053136616937014030265658675779390668800000⟩, + ⟨3, 4, 6, 2, 7, 4, -18276604712073825128274425357107819125575516160000⟩, + ⟨3, 4, 7, 2, 8, 4, -14285624077432908504381985841497639362798551040000⟩, + ⟨3, 4, 1, 3, 1, 4, 279622524259065591322997849149115481314033664000000⟩, + ⟨3, 4, 2, 3, 2, 4, -1195428992763289601303444231009496499865046220800000⟩, + ⟨3, 4, 3, 3, 3, 4, 3259401294344041046706249093129596276476697640960000⟩, + ⟨3, 4, 4, 3, 4, 4, 130291852470488622168929313673816128872754708480000⟩, + ⟨3, 4, 5, 3, 5, 4, 32973849997634092786277482570310654424514560000000⟩, + ⟨3, 4, 6, 3, 6, 4, 48427658617942963262491703309669073873524490240000⟩, + ⟨3, 4, 7, 3, 7, 4, 7976794141192901042660762951788841594215464960000⟩, + ⟨3, 4, 8, 3, 8, 4, 5156595263886098287941972975006939579678720000000⟩, + ⟨3, 4, 1, 4, 0, 4, -2237400579866830047428551128295441681189510840320000⟩, + ⟨3, 4, 2, 4, 1, 4, -2759572905138061618088992409645808251523500605440000⟩, + ⟨3, 4, 3, 4, 2, 4, -4461972518301808677741973937569195182149074944000000⟩, + ⟨3, 4, 4, 4, 3, 4, 291221262907531060096796232525548923704154521600000⟩, + ⟨3, 4, 5, 4, 4, 4, -118791849943265660321043082185099205407041126400000⟩, + ⟨3, 4, 6, 4, 5, 4, -38529106039722686486466637607994642545780981760000⟩, + ⟨3, 4, 7, 4, 6, 4, -2619781334814649238679478228462029746523340800000⟩, + ⟨3, 4, 8, 4, 7, 4, 1831759090839616187540538526880032318386339840000⟩, + ⟨3, 4, 2, 5, 0, 4, 20589380837171442416994677794565951531413646868480000⟩, + ⟨3, 4, 3, 5, 1, 4, 3705321541263497153670438914150672055540991918080000⟩, + ⟨3, 4, 4, 5, 2, 4, -1995349513430863298477481456609304777398901800960000⟩, + ⟨3, 4, 5, 5, 3, 4, 309815973798363614435395916271586147759344844800000⟩, + ⟨3, 4, 6, 5, 4, 4, -43456250670733522406090735489178766778239549440000⟩, + ⟨3, 4, 7, 5, 5, 4, -6938338664898143842457241293968418117454397440000⟩, + ⟨3, 4, 8, 5, 6, 4, 3814203184747325739522987533210299353802997760000⟩, + ⟨3, 4, 3, 6, 0, 4, 2017920004519040858711372280439693623541660385280000⟩, + ⟨3, 4, 4, 6, 1, 4, 1070716739487579933737673317461698668315006730240000⟩, + ⟨3, 4, 5, 6, 2, 4, 4585253052913468187407604316748462255452979200000⟩, + ⟨3, 4, 6, 6, 3, 4, 160909339481113851749861167807494050711171235840000⟩, + ⟨3, 4, 7, 6, 4, 4, 2483825191900508281325860857587622881399930880000⟩, + ⟨3, 4, 8, 6, 5, 4, -4002836082714009229926168060695012030986321920000⟩, + ⟨3, 4, 4, 7, 0, 4, 20430595061164233577709363067380157429261092782080000⟩, + ⟨3, 4, 5, 7, 1, 4, -213748720204202637227027161663233634888738406400000⟩, + ⟨3, 4, 6, 7, 2, 4, -158797810824269242428355702285644771870124277760000⟩, + ⟨3, 4, 7, 7, 3, 4, 104071191774329020690267680223073075615571640320000⟩, + ⟨3, 4, 8, 7, 4, 4, 7914494546148651431952519850150274127416524800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0814.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0814.lean new file mode 100644 index 0000000000000000000000000000000000000000..20d050edb8d3dddfad5502e58d0f3fea5697cc00 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0814.lean @@ -0,0 +1,667 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0814. -/ +namespace LaughlinFock +def collectedFourData_8_3_26 : List CollectedFourTerm := [ + ⟨3, 5, 0, 0, 3, 5, -2584767001452176215213164920975147491141877760000000⟩, + ⟨3, 5, 1, 0, 4, 5, 71537625088472883288485538066143613498163200000000⟩, + ⟨3, 5, 2, 0, 5, 5, -880919364231534761744449482384095842821734400000000⟩, + ⟨3, 5, 3, 0, 6, 5, -47132252889124561904813286289897635415326720000000⟩, + ⟨3, 5, 4, 0, 7, 5, 169039041165587170179899141441016259757998080000000⟩, + ⟨3, 5, 5, 0, 8, 5, 3186979009192721497045434021850101149859840000000⟩, + ⟨3, 5, 0, 1, 2, 5, 1011037638680569748087939877636529770347888640000000⟩, + ⟨3, 5, 1, 1, 3, 5, -288918324051750112245051475733244131011461120000000⟩, + ⟨3, 5, 2, 1, 4, 5, 3036127820215994274827562474802309715271352320000000⟩, + ⟨3, 5, 3, 1, 5, 5, 631875148067861173461583292309784292082319360000000⟩, + ⟨3, 5, 4, 1, 6, 5, 378737775585142497640570311862051353730744320000000⟩, + ⟨3, 5, 5, 1, 7, 5, -25277640347833346401338630591394109309583360000000⟩, + ⟨3, 5, 6, 1, 8, 5, -2304429476316627437500651769559524699013120000000⟩, + ⟨3, 5, 0, 2, 1, 5, 1044514819892266188788671755343945835898470400000000⟩, + ⟨3, 5, 1, 2, 2, 5, -50438866626526489449750520424841808529326080000000⟩, + ⟨3, 5, 2, 2, 3, 5, -1131546194323606737493547201057430715383152640000000⟩, + ⟨3, 5, 3, 2, 4, 5, -822837235727194630784099973445140500258488320000000⟩, + ⟨3, 5, 4, 2, 5, 5, -48059838861333337443430141448958182487490560000000⟩, + ⟨3, 5, 5, 2, 6, 5, -17667756268163940611592919161922145621114880000000⟩, + ⟨3, 5, 6, 2, 7, 5, -3083590215939640798253201713536205250887680000000⟩, + ⟨3, 5, 7, 2, 8, 5, -2065920323248616773877488044708392714895360000000⟩, + ⟨3, 5, 0, 3, 0, 5, -5836491869699027130227063235667512329093775360000000⟩, + ⟨3, 5, 1, 3, 1, 5, 283063936725180285480821756189191314604032000000000⟩, + ⟨3, 5, 2, 3, 2, 5, -605070778299475923391845004914103822791475200000000⟩, + ⟨3, 5, 3, 3, 3, 5, 1099838629701353294253734799788863813488476160000000⟩, + ⟨3, 5, 4, 3, 4, 5, 32973849997634092786277482570310654424514560000000⟩, + ⟨3, 5, 5, 3, 5, 5, 6675934146612852124838654578129744429056000000000⟩, + ⟨3, 5, 6, 3, 6, 5, 8170612465919526214910689600035372945899520000000⟩, + ⟨3, 5, 7, 3, 7, 5, 1153566763435526575936045836719945825648640000000⟩, + ⟨3, 5, 8, 3, 8, 5, 652507411268879539500903966439290961920000000000⟩, + ⟨3, 5, 1, 4, 0, 5, -2264937053431142060839380452022981371268956160000000⟩, + ⟨3, 5, 2, 4, 1, 5, -1396767968314335745133335079007778080408207360000000⟩, + ⟨3, 5, 3, 4, 2, 5, -1505629192947163242255132644747022616756224000000000⟩, + ⟨3, 5, 4, 4, 3, 5, 73701356279430589346291358780540474045235200000000⟩, + ⟨3, 5, 5, 4, 4, 5, -24050772579861287610637743066215894105456640000000⟩, + ⟨3, 5, 6, 4, 5, 5, -6500549543236731431610163790965207707156480000000⟩, + ⟨3, 5, 7, 4, 6, 5, -378860557489452193340002942977622356787200000000⟩, + ⟨3, 5, 8, 4, 7, 5, 231787899043145720525306907424186423050240000000⟩, + ⟨3, 5, 2, 5, 0, 5, 10421390783784086612255680448274655205256069120000000⟩, + ⟨3, 5, 3, 5, 1, 5, 1250308077626968570118238749355638408274247680000000⟩, + ⟨3, 5, 4, 5, 2, 5, -504976744909080323972628890251951680383877120000000⟩, + ⟨3, 5, 5, 5, 3, 5, 62725797527283340199607260995571392425492480000000⟩, + ⟨3, 5, 6, 5, 4, 5, -7331846997881991949716619182415625186181120000000⟩, + ⟨3, 5, 7, 5, 5, 5, -1003390176004865434738143525579931999272960000000⟩, + ⟨3, 5, 8, 5, 6, 5, 482643240116811947393916227821797491343360000000⟩, + ⟨3, 5, 3, 6, 0, 5, 680918417891168285195262136326042191533178880000000⟩, + ⟨3, 5, 4, 6, 1, 5, 270973606471794739606652350401149983292129280000000⟩, + ⟨3, 5, 5, 6, 2, 5, 928337074045105697765031080208122165329920000000⟩, + ⟨3, 5, 6, 6, 3, 5, 27148284525160693050598882245314099879608320000000⟩, + ⟨3, 5, 7, 6, 4, 5, 359199214226156013100092205145633241169920000000⟩, + ⟨3, 5, 8, 6, 5, 5, -506512548765951274230214539022427089797120000000⟩, + ⟨3, 5, 4, 7, 0, 5, 5170510389832873523801761125768785666255093760000000⟩, + ⟨3, 5, 5, 7, 1, 5, -43275880132541985631390392169801655663984640000000⟩, + ⟨3, 5, 6, 7, 2, 5, -26792031861742258652203876322304483372564480000000⟩, + ⟨3, 5, 7, 7, 3, 5, 15050290346848191027101871253596410877050880000000⟩, + ⟨3, 5, 8, 7, 4, 5, 1001487625755069027487296264516301278412800000000⟩ +] + +def collectedFourData_8_3_27 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 3, 6, -18980830864796111200183499904601808885068804915200000⟩, + ⟨3, 6, 1, 0, 4, 6, 262662661955726337747900341654391446392799232000000⟩, + ⟨3, 6, 2, 0, 5, 6, -2156297704797442051921177001097717302685597696000000⟩, + ⟨3, 6, 3, 0, 6, 6, -86527075734743298287863299065537156343241113600000⟩, + ⟨3, 6, 4, 0, 7, 6, 248262334524443718271302371274189014957366968320000⟩, + ⟨3, 6, 5, 0, 8, 6, 3900513373749428936816202104929338065210572800000⟩, + ⟨3, 6, 0, 1, 2, 6, 7424396244209712233796569635909733880748100812800000⟩, + ⟨3, 6, 1, 1, 3, 6, -1060813187317396078373524714363544068141822771200000⟩, + ⟨3, 6, 2, 1, 4, 6, 7431776069441350974956688962779581223512362188800000⟩, + ⟨3, 6, 3, 1, 5, 6, 1160018998463484737226317863892375387270597836800000⟩, + ⟨3, 6, 4, 1, 6, 6, 556240284439711680712135901865957170405997281280000⟩, + ⟨3, 6, 5, 1, 7, 6, -30937064206935884784395338617631448740606771200000⟩, + ⟨3, 6, 6, 1, 8, 6, -2417459462924927982462484485415298026124083200000⟩, + ⟨3, 6, 0, 2, 1, 6, 7670230671085459785036229128755937039045623808000000⟩, + ⟨3, 6, 1, 2, 2, 6, -185194951017294226639687628397177738720234700800000⟩, + ⟨3, 6, 2, 2, 3, 6, -2769777303988261327329815257992742740717836697600000⟩, + ⟨3, 6, 3, 2, 4, 6, -1510594029541120571916333887848296175214631321600000⟩, + ⟨3, 6, 4, 2, 5, 6, -70583976993192929243646896792032737478563594240000⟩, + ⟨3, 6, 5, 2, 6, 6, -21623399278545878375975633200557299083090329600000⟩, + ⟨3, 6, 6, 2, 7, 6, -3234837266194458498352318092928652615142604800000⟩, + ⟨3, 6, 7, 2, 8, 6, -1896345212822678262866215267531687543072358400000⟩, + ⟨3, 6, 0, 3, 0, 6, -42859362163117801627360526773023165749895836467200000⟩, + ⟨3, 6, 1, 3, 1, 6, 1039317799996179586130860510353581117087416320000000⟩, + ⟨3, 6, 2, 3, 2, 6, -1481080770230679317611352757779292823190765568000000⟩, + ⟨3, 6, 3, 3, 3, 6, 2019123096704849742273650592735802128031599820800000⟩, + ⟨3, 6, 4, 3, 4, 6, 48427658617942963262491703309669073873524490240000⟩, + ⟨3, 6, 5, 3, 5, 6, 8170612465919526214910689600035372945899520000000⟩, + ⟨3, 6, 6, 3, 6, 6, 8571372926196508795608983503288624372462387200000⟩, + ⟨3, 6, 7, 3, 7, 6, 1058879563212010946991319375215327478127001600000⟩, + ⟨3, 6, 8, 3, 8, 6, 532398420109576681812627549488831633817600000000⟩, + ⟨3, 6, 1, 4, 0, 6, -8316104915149659632976698310568901835721644441600000⟩, + ⟨3, 6, 2, 4, 1, 6, -3418982129923046190827329931668036536366425702400000⟩, + ⟨3, 6, 3, 4, 2, 6, -2764087927497314503917877937363193475230597120000000⟩, + ⟨3, 6, 4, 4, 3, 6, 108242868874448816127953192477103500580146380800000⟩, + ⟨3, 6, 5, 4, 4, 6, -29435512385291067262637479115676695206350028800000⟩, + ⟨3, 6, 6, 4, 5, 6, -6819395068938420007104447820084107293805772800000⟩, + ⟨3, 6, 7, 4, 6, 6, -347762881480688191564439801967567194554368000000⟩, + ⟨3, 6, 8, 4, 7, 6, 189122007075928527847541672952658801144627200000⟩, + ⟨3, 6, 2, 5, 0, 6, 25509282620292764923800648535814032297862941900800000⟩, + ⟨3, 6, 3, 5, 1, 6, 2295360291371793540465874710455238706413856358400000⟩, + ⟨3, 6, 4, 5, 2, 6, -741643496716691221999631589707004413693373972480000⟩, + ⟨3, 6, 5, 5, 3, 6, 76769508499600034220059663226307700642650521600000⟩, + ⟨3, 6, 6, 5, 4, 6, -7691466841536016011742814323218473679008563200000⟩, + ⟨3, 6, 7, 5, 5, 6, -921029787764543757946078957829068603942502400000⟩, + ⟨3, 6, 8, 5, 6, 6, 393801655087826325556064923135874035403980800000⟩, + ⟨3, 6, 3, 6, 0, 6, 1250054387441462476393922228813071859931571814400000⟩, + ⟨3, 6, 4, 6, 1, 6, 397970431406416198274931734583236520186080133120000⟩, + ⟨3, 6, 5, 6, 2, 6, 1136182937576851096571624057667775266973286400000⟩, + ⟨3, 6, 6, 6, 3, 6, 28479881030002321827604162705675442575323955200000⟩, + ⟨3, 6, 7, 6, 4, 6, 329715382864485162143546798002050333199564800000⟩, + ⟨3, 6, 8, 6, 5, 6, -413277268689206613311610866860876474456473600000⟩, + ⟨3, 6, 4, 7, 0, 6, 7593766334756776493842175710375617552375129047040000⟩, + ⟨3, 6, 5, 7, 1, 6, -52964939126007824269746831971499083907779788800000⟩, + ⟨3, 6, 6, 7, 2, 6, -28106154525796310060075479306754650425576652800000⟩, + ⟨3, 6, 7, 7, 3, 6, 13814930677460744243286967976330557492769587200000⟩, + ⟨3, 6, 8, 7, 4, 6, 817140802545731247542757496783944793718784000000⟩ +] + +def collectedFourData_8_3_28 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 3, 7, -9379320707929997017185326636937897226967344742400000⟩, + ⟨3, 7, 1, 0, 4, 7, 86529311669933727644433008272776912495968256000000⟩, + ⟨3, 7, 2, 0, 5, 7, -532764025429974799664880251641621841839128576000000⟩, + ⟨3, 7, 3, 0, 6, 7, -17102838100532701251365327246474039725947617280000⟩, + ⟨3, 7, 4, 0, 7, 7, 40892696282031660917036665647597698489285345280000⟩, + ⟨3, 7, 5, 0, 8, 7, 550693428070540376842306238343858324347289600000⟩, + ⟨3, 7, 0, 1, 2, 7, 3668743161625652302894339677044274254602410393600000⟩, + ⟨3, 7, 1, 1, 3, 7, -349465105643507313368480912740980032945101209600000⟩, + ⟨3, 7, 2, 1, 4, 7, 1836194940077472258313564367885071391226907852800000⟩, + ⟨3, 7, 3, 1, 5, 7, 229287965134557894555133617219378138804010352640000⟩, + ⟨3, 7, 4, 1, 6, 7, 91621490045983844102723783469601369944615813120000⟩, + ⟨3, 7, 5, 1, 7, 7, -4367845027071144586194379352038266097788518400000⟩, + ⟨3, 7, 6, 1, 8, 7, -298645087808655675729534755226973602683289600000⟩, + ⟨3, 7, 0, 2, 1, 7, 3790221507180815105365343494902475236726276096000000⟩, + ⟨3, 7, 1, 2, 2, 7, -61009020151385868250539993950151134765540966400000⟩, + ⟨3, 7, 2, 2, 3, 7, -684338578450598182657200147170438380892297625600000⟩, + ⟨3, 7, 3, 2, 4, 7, -298582205667900170685394015241948554927464775680000⟩, + ⟨3, 7, 4, 2, 5, 7, -11626286923827984499689339630878381361290280960000⟩, + ⟨3, 7, 5, 2, 6, 7, -3052896563662813604188023412924802428777267200000⟩, + ⟨3, 7, 6, 2, 7, 7, -399621285992730670544562883082405695350374400000⟩, + ⟨3, 7, 7, 2, 8, 7, -208238512384856051958999470117766878881382400000⟩, + ⟨3, 7, 0, 3, 0, 7, -21178825412262600273100084089101574790537700966400000⟩, + ⟨3, 7, 1, 3, 1, 7, 342383851478433037352486683718658317415874560000000⟩, + ⟨3, 7, 2, 3, 2, 7, -365935812749542163317112196283186249998532608000000⟩, + ⟨3, 7, 3, 3, 3, 7, 399097451690758066578114573388260806206779555840000⟩, + ⟨3, 7, 4, 3, 4, 7, 7976794141192901042660762951788841594215464960000⟩, + ⟨3, 7, 5, 3, 5, 7, 1153566763435526575936045836719945825648640000000⟩, + ⟨3, 7, 6, 3, 6, 7, 1058879563212010946991319375215327478127001600000⟩, + ⟨3, 7, 7, 3, 7, 7, 116276036423655937529292811116866078087577600000⟩, + ⟨3, 7, 8, 3, 8, 7, 52616616861219857012795823150260803338240000000⟩, + ⟨3, 7, 1, 4, 0, 7, -2739585553290951420843836894525639373611650252800000⟩, + ⟨3, 7, 2, 4, 1, 7, -844739888355100746027597788687404825359836774400000⟩, + ⟨3, 7, 3, 4, 2, 7, -546346307421107824587520230952826012304408576000000⟩, + ⟨3, 7, 4, 4, 3, 7, 17829296457948192688780516017687387452945203200000⟩, + ⟨3, 7, 5, 4, 4, 7, -4155848645863436067395512568802311522589081600000⟩, + ⟨3, 7, 6, 4, 5, 7, -842445910841017515914544546195798437029478400000⟩, + ⟨3, 7, 7, 4, 6, 7, -38187996896628903652714218810407909326848000000⟩, + ⟨3, 7, 8, 4, 7, 7, 18690814642708677903628347968354203761377280000⟩, + ⟨3, 7, 2, 5, 0, 7, 6302667792291104005449477766366782846418078924800000⟩, + ⟨3, 7, 3, 5, 1, 7, 453698164561458563943434479150595922297429688320000⟩, + ⟨3, 7, 4, 5, 2, 7, -122160304014194095960082468541475760566614097920000⟩, + ⟨3, 7, 5, 5, 3, 7, 10838692181254162303123833212531215455957811200000⟩, + ⟨3, 7, 6, 5, 4, 7, -950178824297091790744683273806095486392729600000⟩, + ⟨3, 7, 7, 5, 5, 7, -101138691188376140237203440806528534603366400000⟩, + ⟨3, 7, 8, 5, 6, 7, 38919181617416847991613183638765460961361920000⟩, + ⟨3, 7, 3, 6, 0, 7, 247084252226582408587203695882492669794052997120000⟩, + ⟨3, 7, 4, 6, 1, 7, 65551965471948617460645153752824747307544084480000⟩, + ⟨3, 7, 5, 6, 2, 7, 160411827073932109135802949217105199549644800000⟩, + ⟨3, 7, 6, 6, 3, 7, 3518311972310924011348316248856587964881305600000⟩, + ⟨3, 7, 7, 6, 4, 7, 36206193035868830162384585218050891762892800000⟩, + ⟨3, 7, 8, 6, 5, 7, -40843944840399515116303066296347928444272640000⟩, + ⟨3, 7, 4, 7, 0, 7, 1250812294820143664463530207339398606566362972160000⟩, + ⟨3, 7, 5, 7, 1, 7, -7477847426737850648720993722420968482773401600000⟩, + ⟨3, 7, 6, 7, 2, 7, -3472143014205630518008797901963607763478118400000⟩, + ⟨3, 7, 7, 7, 3, 7, 1517023690371368197874216865624934935900979200000⟩, + ⟨3, 7, 8, 7, 4, 7, 80757535907731104466427247814697499072921600000⟩ +] + +def collectedFourData_8_3_29 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 3, 8, -14147601956134319764730943481667567180002099200000000⟩, + ⟨3, 8, 1, 0, 4, 8, 97889465865808362749470289065181064462336000000000⟩, + ⟨3, 8, 2, 0, 5, 8, -482167116556221366555658385687803115392204800000000⟩, + ⟨3, 8, 3, 0, 6, 8, -12898809695352989328795099512661020371845120000000⟩, + ⟨3, 8, 4, 0, 7, 8, 26435066549670630514196031636041752337448960000000⟩, + ⟨3, 8, 5, 0, 8, 8, 311496095885200529093079525504475516108800000000⟩, + ⟨3, 8, 0, 1, 2, 8, 5533867488515019504675719251946658782301388800000000⟩, + ⟨3, 8, 1, 1, 3, 8, -395345252030564581580219712528357070051737600000000⟩, + ⟨3, 8, 2, 1, 4, 8, 1661810440330954897022610465164313239161405440000000⟩, + ⟨3, 8, 3, 1, 5, 8, 172926961614240805208433622303068910056898560000000⟩, + ⟨3, 8, 4, 1, 6, 8, 59228674236621786618000142202920492691619840000000⟩, + ⟨3, 8, 5, 1, 7, 8, -2470642655263301037242347796141100446515200000000⟩, + ⟨3, 8, 6, 1, 8, 8, -150156994663782320263849448870212376985600000000⟩, + ⟨3, 8, 0, 2, 1, 8, 5717103282739554636659205121016038233735168000000000⟩, + ⟨3, 8, 1, 2, 2, 8, -69018697599216387404491998589642172950118400000000⟩, + ⟨3, 8, 2, 2, 3, 8, -619346546256393731445142868580683303752826880000000⟩, + ⟨3, 8, 3, 2, 4, 8, -225188066839563489716938449746039390569758720000000⟩, + ⟨3, 8, 4, 2, 5, 8, -7515808359450359841909469889188716053790720000000⟩, + ⟨3, 8, 5, 2, 6, 8, -1726850752612392325478257902865887107481600000000⟩, + ⟨3, 8, 6, 2, 7, 8, -200927233555539254393739225858088265318400000000⟩, + ⟨3, 8, 7, 2, 8, 8, -94230989969273105957103487655318661365760000000⟩, + ⟨3, 8, 0, 3, 0, 8, -31945766773687967576262321951822469085213491200000000⟩, + ⟨3, 8, 1, 3, 1, 8, 387334322849441667159479746626755871375360000000000⟩, + ⟨3, 8, 2, 3, 2, 8, -331182676112006414533113344983477841716838400000000⟩, + ⟨3, 8, 3, 3, 3, 8, 300995779121541272409031832036675146859151360000000⟩, + ⟨3, 8, 4, 3, 4, 8, 5156595263886098287941972975006939579678720000000⟩, + ⟨3, 8, 5, 3, 5, 8, 652507411268879539500903966439290961920000000000⟩, + ⟨3, 8, 6, 3, 6, 8, 532398420109576681812627549488831633817600000000⟩, + ⟨3, 8, 7, 3, 7, 8, 52616616861219857012795823150260803338240000000⟩, + ⟨3, 8, 8, 3, 8, 8, 21645266455992590369575600916696924160000000000⟩, + ⟨3, 8, 1, 4, 0, 8, -3099256903005266925981578150229218790526156800000000⟩, + ⟨3, 8, 2, 4, 1, 8, -764514450613442485991997667207300292668293120000000⟩, + ⟨3, 8, 3, 4, 2, 8, -412049567782799227421423342543140766613504000000000⟩, + ⟨3, 8, 4, 4, 3, 8, 11525741299841012240408156987713831462502400000000⟩, + ⟨3, 8, 5, 4, 4, 8, -2350728304152626273934994082327822126284800000000⟩, + ⟨3, 8, 6, 4, 5, 8, -423576851931108707856218697632194127462400000000⟩, + ⟨3, 8, 7, 4, 6, 8, -17280630327699976823572075585790489395200000000⟩, + ⟨3, 8, 8, 4, 7, 8, 7688971419201539159387565619068555755520000000⟩, + ⟨3, 8, 2, 5, 0, 8, 5704099772067282482849693984095167853929431040000000⟩, + ⟨3, 8, 3, 5, 1, 8, 342175155340266047720032091772163951196897280000000⟩, + ⟨3, 8, 4, 5, 2, 8, -78970477859201118966587409177997984860733440000000⟩, + ⟨3, 8, 5, 5, 3, 8, 6130834556699391795638208373596979042713600000000⟩, + ⟨3, 8, 6, 5, 4, 8, -477744327544510078886182372278330300825600000000⟩, + ⟨3, 8, 7, 5, 5, 8, -45766745477242333367058302831894577807360000000⟩, + ⟨3, 8, 8, 5, 6, 8, 16010456517569151077283674784395459297280000000⟩, + ⟨3, 8, 3, 6, 0, 8, 186348764424660980270343271368061172035092480000000⟩, + ⟨3, 8, 4, 6, 1, 8, 42376040889093931311163510886695217513103360000000⟩, + ⟨3, 8, 5, 6, 2, 8, 90735889190493877971119615308804286054400000000⟩, + ⟨3, 8, 6, 6, 3, 8, 1768986578444238161369142431551262923161600000000⟩, + ⟨3, 8, 7, 6, 4, 8, 16383834929069717384860277550952973598720000000⟩, + ⟨3, 8, 8, 6, 5, 8, -16802259854831246273603615574869158133760000000⟩, + ⟨3, 8, 4, 7, 0, 8, 808587089163051976214640654370133461035909120000000⟩, + ⟨3, 8, 5, 7, 1, 8, -4229794946373796628843344026447993687244800000000⟩, + ⟨3, 8, 6, 7, 2, 8, -1745773097697852296250544102639583782502400000000⟩, + ⟨3, 8, 7, 7, 3, 8, 686475534776870681177981061517696649134080000000⟩, + ⟨3, 8, 8, 7, 4, 8, 33221793557399451645992414752029435494400000000⟩ +] + +def collectedFourData_8_3_30 : List CollectedFourTerm := [ + ⟨4, 0, 4, 0, 7, 1, -11469939019894689306054550297820846150412675317760000⟩, + ⟨4, 0, 5, 0, 8, 1, -1081242967336667491513614107666505077256250982400000⟩, + ⟨4, 0, 4, 1, 6, 1, -25698792187520478494697517832167611378273657815040000⟩, + ⟨4, 0, 5, 1, 7, 1, 8575918064764271399639511914213479332393359769600000⟩, + ⟨4, 0, 6, 1, 8, 1, 2345463987497508361661886774084654390165739929600000⟩, + ⟨4, 0, 4, 2, 5, 1, 3261042048300970169204954811448920629227888312320000⟩, + ⟨4, 0, 5, 2, 6, 1, 5994120814247066801428787755618118933546847436800000⟩, + ⟨4, 0, 6, 2, 7, 1, 3138499085355545005792707498710338087267231334400000⟩, + ⟨4, 0, 7, 2, 8, 1, 4906318083373256029779457707644665452704248627200000⟩, + ⟨4, 0, 4, 3, 4, 1, -2237400579866830047428551128295441681189510840320000⟩, + ⟨4, 0, 5, 3, 5, 1, -2264937053431142060839380452022981371268956160000000⟩, + ⟨4, 0, 6, 3, 6, 1, -8316104915149659632976698310568901835721644441600000⟩, + ⟨4, 0, 7, 3, 7, 1, -2739585553290951420843836894525639373611650252800000⟩, + ⟨4, 0, 8, 3, 8, 1, -3099256903005266925981578150229218790526156800000000⟩, + ⟨4, 0, 4, 4, 3, 1, -5000916098314316951923229728654228049724073574400000⟩, + ⟨4, 0, 5, 4, 4, 1, 8159679946425411364642563557683851720340694630400000⟩, + ⟨4, 0, 6, 4, 5, 1, 6616303518637264433584064438742947835159144038400000⟩, + ⟨4, 0, 7, 4, 6, 1, 899749319162721452374187899862446322843910144000000⟩, + ⟨4, 0, 8, 4, 7, 1, -1100938064052942318534187700132007901816002969600000⟩, + ⟨4, 0, 4, 5, 2, 1, 34264584267833676141796960275318523488264404336640000⟩, + ⟨4, 0, 5, 5, 3, 1, -21280914386737195304409788497435732751902624972800000⟩, + ⟨4, 0, 6, 5, 4, 1, 7462403719492750844529561868988915133762345369600000⟩, + ⟨4, 0, 7, 5, 5, 1, 2382933799436421003867141484006770092004291379200000⟩, + ⟨4, 0, 8, 5, 6, 1, -2292441998033440346275099075255619830881347174400000⟩, + ⟨4, 0, 4, 6, 1, 1, -18386585257472230765024018286422950015855136604160000⟩, + ⟨4, 0, 5, 6, 2, 1, -314955928399235626234238002140198262487069491200000⟩, + ⟨4, 0, 6, 6, 3, 1, -27631708555420049843398553452544352855078312345600000⟩, + ⟨4, 0, 7, 6, 4, 1, -853055938536875197716931763719494176822683238400000⟩, + ⟨4, 0, 8, 6, 5, 1, 2405815606245722456309835269246081378240220364800000⟩, + ⟨4, 0, 4, 7, 0, 1, -350838708408317273624790718491143292458273309982720000⟩, + ⟨4, 0, 5, 7, 1, 1, 14682161668980752181262207239963749186043012710400000⟩, + ⟨4, 0, 6, 7, 2, 1, 27269112172633978889346962946073962942455768678400000⟩, + ⟨4, 0, 7, 7, 3, 1, -35742671611190208330345332474549022611060922777600000⟩, + ⟨4, 0, 8, 7, 4, 1, -4756830932172720596657807487646129148198387712000000⟩ +] + +def collectedFourData_8_3_31 : List CollectedFourTerm := [ + ⟨4, 1, 3, 0, 6, 2, 986121487483836078164585013194682242626297528320000⟩, + ⟨4, 1, 4, 0, 7, 2, -14146833261646482641628607873523076793313966161920000⟩, + ⟨4, 1, 5, 0, 8, 2, -666793604905327127803262318475426980031784550400000⟩, + ⟨4, 1, 3, 1, 5, 2, -13220366579602345067329944637013464360134283100160000⟩, + ⟨4, 1, 4, 1, 6, 2, -31696465645716523969823462959952295553861869895680000⟩, + ⟨4, 1, 5, 1, 7, 2, 5288697817718478236523964195854234813592082841600000⟩, + ⟨4, 1, 6, 1, 8, 2, 964285508835204191816679296171510001727596134400000⟩, + ⟨4, 1, 3, 2, 4, 2, 17215758405633479734456399672898196195900307537920000⟩, + ⟨4, 1, 4, 2, 5, 2, 4022115377990519793339744930137159406642989629440000⟩, + ⟨4, 1, 5, 2, 6, 2, 3696524783707894095530020788214881050273041612800000⟩, + ⟨4, 1, 6, 2, 7, 2, 1290324304117719773829692199050927377368062361600000⟩, + ⟨4, 1, 7, 2, 8, 2, 1512842913412447965728807179074182626353453465600000⟩, + ⟨4, 1, 3, 3, 3, 2, -23011302007240576359545211049722161776011729960960000⟩, + ⟨4, 1, 4, 3, 4, 2, -2759572905138061618088992409645808251523500605440000⟩, + ⟨4, 1, 5, 3, 5, 2, -1396767968314335745133335079007778080408207360000000⟩, + ⟨4, 1, 6, 3, 6, 2, -3418982129923046190827329931668036536366425702400000⟩, + ⟨4, 1, 7, 3, 7, 2, -844739888355100746027597788687404825359836774400000⟩, + ⟨4, 1, 8, 3, 8, 2, -764514450613442485991997667207300292668293120000000⟩, + ⟨4, 1, 3, 4, 2, 2, 31501428604333405192825172748946467641773522944000000⟩, + ⟨4, 1, 4, 4, 3, 2, -6168047282171679050246493749972867415544745164800000⟩, + ⟨4, 1, 5, 4, 4, 2, 5032007209029636468711789550770531814634579558400000⟩, + ⟨4, 1, 6, 4, 5, 2, 2720146478089578451230141287480584624508869017600000⟩, + ⟨4, 1, 7, 4, 6, 2, 277433985773531860778905366431917558948954112000000⟩, + ⟨4, 1, 8, 4, 7, 2, -271575763333044282656511900268479414354460016640000⟩, + ⟨4, 1, 3, 5, 1, 2, -26159489219049355903954059725290113152573327278080000⟩, + ⟨4, 1, 4, 5, 2, 2, 42261372059249955404653667912630110087981962362880000⟩, + ⟨4, 1, 5, 5, 3, 2, -13123764082893487735071641496247345992128318668800000⟩, + ⟨4, 1, 6, 5, 4, 2, 3068001813774355368960421185038752421840840294400000⟩, + ⟨4, 1, 7, 5, 5, 2, 734767793353061450596525277499673566187723161600000⟩, + ⟨4, 1, 8, 5, 6, 2, -565492016163701561210689083863079195394399272960000⟩, + ⟨4, 1, 3, 6, 0, 2, -14246471194270363129080063736241304098957458145280000⟩, + ⟨4, 1, 4, 6, 1, 2, -22677710442692067302909113053405341121780614430720000⟩, + ⟨4, 1, 5, 6, 2, 2, -194230718929836286451628414073247761888916275200000⟩, + ⟨4, 1, 6, 6, 3, 2, -11360164251670307579151114694333086671179245158400000⟩, + ⟨4, 1, 7, 6, 4, 2, -263036274744059748915182627551682204976493363200000⟩, + ⟨4, 1, 8, 6, 5, 2, 593458643167880966118603393862702270467350200320000⟩, + ⟨4, 1, 4, 7, 0, 2, -432718665807644739643328758370368841022091548426240000⟩, + ⟨4, 1, 5, 7, 1, 2, 9054367799660498242984496022498039975335323238400000⟩, + ⟨4, 1, 6, 7, 2, 2, 11211090789301897481681559453279405918448621977600000⟩, + ⟨4, 1, 7, 7, 3, 2, -11021105141279462458057827049892039685617536204800000⟩, + ⟨4, 1, 8, 7, 4, 2, -1173399334287092746048699434217820009016380620800000⟩ +] + +def collectedFourData_8_3_32 : List CollectedFourTerm := [ + ⟨4, 2, 2, 0, 5, 3, 19867450491440119321812436627136661738498293760000000⟩, + ⟨4, 2, 3, 0, 6, 3, 3188933308242960101074604473544773765183832064000000⟩, + ⟨4, 2, 4, 0, 7, 3, -22874112554495641791214495406466890181107515392000000⟩, + ⟨4, 2, 5, 0, 8, 3, -718762127991472298419291311523515363345039360000000⟩, + ⟨4, 2, 2, 1, 4, 3, -68474052907720110206340720118761286022807420928000000⟩, + ⟨4, 2, 3, 1, 5, 3, -42752204335844589807417368039002447794753503232000000⟩, + ⟨4, 2, 4, 1, 6, 3, -51250234547222021100558061817832268377115066368000000⟩, + ⟨4, 2, 5, 1, 7, 3, 5700888055617912729926416138674671961180733440000000⟩, + ⟨4, 2, 6, 1, 8, 3, 779579954602449049858932481276449657685278720000000⟩, + ⟨4, 2, 2, 2, 3, 3, 25519859032855818744867575514034867342783021056000000⟩, + ⟨4, 2, 3, 2, 4, 3, 55672557695167561834942785984111286066278825984000000⟩, + ⟨4, 2, 4, 2, 5, 3, 6503386175671601866196448323298818672604217344000000⟩, + ⟨4, 2, 5, 2, 6, 3, 3984624327775817016115759087735343966343659520000000⟩, + ⟨4, 2, 6, 2, 7, 3, 1043167146254852841338308600177517123422126080000000⟩, + ⟨4, 2, 7, 2, 8, 3, 978450468416418866714668164882108283852161024000000⟩, + ⟨4, 2, 2, 3, 2, 3, 13646213512593878712235195212467285738473390080000000⟩, + ⟨4, 2, 3, 3, 3, 3, -74414266769671607804929022236528843166834491392000000⟩, + ⟨4, 2, 4, 3, 4, 3, -4461972518301808677741973937569195182149074944000000⟩, + ⟨4, 2, 5, 3, 5, 3, -1505629192947163242255132644747022616756224000000000⟩, + ⟨4, 2, 6, 3, 6, 3, -2764087927497314503917877937363193475230597120000000⟩, + ⟨4, 2, 7, 3, 7, 3, -546346307421107824587520230952826012304408576000000⟩, + ⟨4, 2, 8, 3, 8, 3, -412049567782799227421423342543140766613504000000000⟩, + ⟨4, 2, 2, 4, 1, 3, 31501428604333405192825172748946467641773522944000000⟩, + ⟨4, 2, 3, 4, 2, 3, 101869755611874296574707586414240533586955468800000000⟩, + ⟨4, 2, 4, 4, 3, 3, -9973158314967323938186126290460487920889364480000000⟩, + ⟨4, 2, 5, 4, 4, 3, 5424191508471492699662683680090727566079426560000000⟩, + ⟨4, 2, 6, 4, 5, 3, 2199111827847129505134085927947599707247738880000000⟩, + ⟨4, 2, 7, 4, 6, 3, 179433972243976900132598753810095849057812480000000⟩, + ⟨4, 2, 8, 4, 7, 3, -146370910074851477602161325304346724886642688000000⟩, + ⟨4, 2, 2, 5, 0, 3, -235034526263815922664330149412955901631972507648000000⟩, + ⟨4, 2, 3, 5, 1, 3, -84594918127282463183389999506808534131032457216000000⟩, + ⟨4, 2, 4, 5, 2, 3, 68332704804791918963745235162492028012973785088000000⟩, + ⟨4, 2, 5, 5, 3, 3, -14146603281862422274744469878862255337945169920000000⟩, + ⟨4, 2, 6, 5, 4, 3, 2480336677040318760869454818779124636288286720000000⟩, + ⟨4, 2, 7, 5, 5, 3, 475220450986504855374457591113800141047332864000000⟩, + ⟨4, 2, 8, 5, 6, 3, -304782650815704419682846257693143514461765632000000⟩, + ⟨4, 2, 3, 6, 0, 3, -46070435633902869134473464612853077507525574656000000⟩, + ⟨4, 2, 4, 6, 1, 3, -36667746876662256393491261087483740131554230272000000⟩, + ⟨4, 2, 5, 6, 2, 3, -209368661955215066749234808523614704034119680000000⟩, + ⟨4, 2, 6, 6, 3, 3, -9184164078428575355863327354472811500320849920000000⟩, + ⟨4, 2, 7, 6, 4, 3, -170122068822930466256676436346243561268707328000000⟩, + ⟨4, 2, 8, 6, 5, 3, 319855795031838435116324811631550752823967744000000⟩, + ⟨4, 2, 4, 7, 0, 3, -699665803862260474671066946669918849947899265024000000⟩, + ⟨4, 2, 5, 7, 1, 3, 9760046616262098215542871676690939391833538560000000⟩, + ⟨4, 2, 6, 7, 2, 3, 9063645122205770539874301900223420239320186880000000⟩, + ⟨4, 2, 7, 7, 3, 3, -7128040454396831674685111340193636271775547392000000⟩, + ⟨4, 2, 8, 7, 4, 3, -632425833339924492761846618010895789703823360000000⟩ +] + +def collectedFourData_8_3_33 : List CollectedFourTerm := [ + ⟨4, 3, 1, 0, 4, 4, 157953025845976131620311301933996164239065088000000⟩, + ⟨4, 3, 2, 0, 5, 4, -3890089416152710090212866088743822446445985792000000⟩, + ⟨4, 3, 3, 0, 6, 4, -312199990546285147973570574657253279011333734400000⟩, + ⟨4, 3, 4, 0, 7, 4, 1492933432172845114365945995339171588618374348800000⟩, + ⟨4, 3, 5, 0, 8, 4, 35183791549344771056806064746400759653859328000000⟩, + ⟨4, 3, 1, 1, 3, 4, -637923378779813731179022440025534468226600140800000⟩, + ⟨4, 3, 2, 1, 4, 4, 13407366416348597971013005061815299936435673497600000⟩, + ⟨4, 3, 3, 1, 5, 4, 4185486650028939893933822138499215182787719987200000⟩, + ⟨4, 3, 4, 1, 6, 4, 3344968613753267118069623454613284382336824115200000⟩, + ⟨4, 3, 5, 1, 7, 4, -279061527011047268902403977358527621194842112000000⟩, + ⟨4, 3, 6, 1, 8, 4, -30528685416887353350983550236437294890142924800000⟩, + ⟨4, 3, 1, 2, 2, 4, -111367571876316432569644472118630369058829107200000⟩, + ⟨4, 3, 2, 2, 3, 4, -4996843131341584955777585628117579006261539635200000⟩, + ⟨4, 3, 3, 2, 4, 4, -5450403099115109115322687630903335784112612966400000⟩, + ⟨4, 3, 4, 2, 5, 4, -424458987025602549359199880694986848769513881600000⟩, + ⟨4, 3, 5, 2, 6, 4, -195049497310987570209294345213309894311018496000000⟩, + ⟨4, 3, 6, 2, 7, 4, -40850872905636505439886482164621817798669107200000⟩, + ⟨4, 3, 7, 2, 8, 4, -31930450034813623310844916861263147912973516800000⟩, + ⟨4, 3, 1, 3, 1, 4, 624997059356120112541942511734451308729466880000000⟩, + ⟨4, 3, 2, 3, 2, 4, -2671957872942639789184773799308117014621454336000000⟩, + ⟨4, 3, 3, 3, 3, 4, 7285236515278730687550977431784126152371811123200000⟩, + ⟨4, 3, 4, 3, 4, 4, 291221262907531060096796232525548923704154521600000⟩, + ⟨4, 3, 5, 3, 5, 4, 73701356279430589346291358780540474045235200000000⟩, + ⟨4, 3, 6, 3, 6, 4, 108242868874448816127953192477103500580146380800000⟩, + ⟨4, 3, 7, 3, 7, 4, 17829296457948192688780516017687387452945203200000⟩, + ⟨4, 3, 8, 3, 8, 4, 11525741299841012240408156987713831462502400000000⟩, + ⟨4, 3, 1, 4, 0, 4, -5000916098314316951923229728654228049724073574400000⟩, + ⟨4, 3, 2, 4, 1, 4, -6168047282171679050246493749972867415544745164800000⟩, + ⟨4, 3, 3, 4, 2, 4, -9973158314967323938186126290460487920889364480000000⟩, + ⟨4, 3, 4, 4, 3, 4, 650921929202495060587234973476145447433142272000000⟩, + ⟨4, 3, 5, 4, 4, 4, -265517082669735795314592854713660223036325888000000⟩, + ⟨4, 3, 6, 4, 5, 4, -86118162470118298212113891985358610203095859200000⟩, + ⟨4, 3, 7, 4, 6, 4, -5855592766547748869716857071235837236084736000000⟩, + ⟨4, 3, 8, 4, 7, 4, 4094248302268101099147841855145758061022412800000⟩, + ⟨4, 3, 2, 5, 0, 4, 46020264323460348353461029262239144690583181721600000⟩, + ⟨4, 3, 3, 5, 1, 4, 8281933200463523702053719445557991938073401753600000⟩, + ⟨4, 3, 4, 5, 2, 4, -4459896718214834775324289233108594146025878323200000⟩, + ⟨4, 3, 5, 5, 3, 4, 692483815739147280871511912846518499112124416000000⟩, + ⟨4, 3, 6, 5, 4, 4, -97131048193698306363570147383454220140989644800000⟩, + ⟨4, 3, 7, 5, 5, 4, -15508197252237692020789159197261352816921804800000⟩, + ⟨4, 3, 8, 5, 6, 4, 8525299528607412717376681235152401008374579200000⟩, + ⟨4, 3, 3, 6, 0, 4, 4510345052431519920142308462956191536337492377600000⟩, + ⟨4, 3, 4, 6, 1, 4, 2393207826716822678394459994450027003847167180800000⟩, + ⟨4, 3, 5, 6, 2, 4, 10248708261497211025085286268854747386609664000000⟩, + ⟨4, 3, 6, 6, 3, 4, 359655804785802418882774080356000954552470732800000⟩, + ⟨4, 3, 7, 6, 4, 4, 5551710989684833518314288636925518974392729600000⟩, + ⟨4, 3, 8, 6, 5, 4, -8946921523614411791913253172369692993939046400000⟩, + ⟨4, 3, 4, 7, 0, 4, 45665354992264481242192248737413790715885492633600000⟩, + ⟨4, 3, 5, 7, 1, 4, -477759514984528552292508362786799232103743488000000⟩, + ⟨4, 3, 6, 7, 2, 4, -354936230764464353733825865908007841865872179200000⟩, + ⟨4, 3, 7, 7, 3, 4, 232614268092294743907393147101589850391209574400000⟩, + ⟨4, 3, 8, 7, 4, 4, 17690047791178921332959759258398546005590016000000⟩ +] + +def collectedFourData_8_3_34 : List CollectedFourTerm := [ + ⟨4, 4, 0, 0, 3, 5, 9311901819073075960709596659711987193588639334400000⟩, + ⟨4, 4, 1, 0, 4, 5, -257722007755151852645686024627429065734750208000000⟩, + ⟨4, 4, 2, 0, 5, 5, 3173606992675041704997742844735213036881575936000000⟩, + ⟨4, 4, 3, 0, 6, 5, 169799022955907880855909167818145374495624396800000⟩, + ⟨4, 4, 4, 0, 7, 5, -608981372030767754525227637718589393626936115200000⟩, + ⟨4, 4, 5, 0, 8, 5, -11481435509032862544296827090588269637376409600000⟩, + ⟨4, 4, 0, 1, 2, 5, -3642372106070519549555187083693187944899254681600000⟩, + ⟨4, 4, 1, 1, 3, 5, 1040859414326136560695690070460083431090736332800000⟩, + ⟨4, 4, 2, 1, 4, 5, -10937977835574277589666705860392669079405382860800000⟩, + ⟨4, 4, 3, 1, 5, 5, -2276398351346351194484584829023597922676532838400000⟩, + ⟨4, 4, 4, 1, 6, 5, -1364443673043475946176001878598232783696219340800000⟩, + ⟨4, 4, 5, 1, 7, 5, 91065424854395492868230272231262677335696998400000⟩, + ⟨4, 4, 6, 1, 8, 5, 8301955658046747078830367732084101299883212800000⟩, + ⟨4, 4, 0, 2, 1, 5, -3762977260982933376418482006341167394404171776000000⟩, + ⟨4, 4, 1, 2, 2, 5, 181711455472643849803681850744399299446256435200000⟩, + ⟨4, 4, 2, 2, 3, 5, 4076517171322362364438232928216962073489938841600000⟩, + ⟨4, 4, 3, 2, 4, 5, 2964359862171078556208923846028278235493354700800000⟩, + ⟨4, 4, 4, 2, 5, 5, 173140751435536716261983082297852266478462566400000⟩, + ⟨4, 4, 5, 2, 6, 5, 63649996939772338079158017422949754986509107200000⟩, + ⟨4, 4, 6, 2, 7, 5, 11108966233688415134035916135333588211282739200000⟩, + ⟨4, 4, 7, 2, 8, 5, 7442700717438252143988521035650439313778278400000⟩, + ⟨4, 4, 0, 3, 0, 5, 21026591266416382305617882054659007219707045478400000⟩, + ⟨4, 4, 1, 3, 1, 5, -1019768352746808136170189768652858455050158080000000⟩, + ⟨4, 4, 2, 3, 2, 5, 2179832719138456378592135465469177329759551488000000⟩, + ⟨4, 4, 3, 3, 3, 5, -3962287250978108134428048363965706820911523430400000⟩, + ⟨4, 4, 4, 3, 4, 5, -118791849943265660321043082185099205407041126400000⟩, + ⟨4, 4, 5, 3, 5, 5, -24050772579861287610637743066215894105456640000000⟩, + ⟨4, 4, 6, 3, 6, 5, -29435512385291067262637479115676695206350028800000⟩, + ⟨4, 4, 7, 3, 7, 5, -4155848645863436067395512568802311522589081600000⟩, + ⟨4, 4, 8, 3, 8, 5, -2350728304152626273934994082327822126284800000000⟩, + ⟨4, 4, 1, 4, 0, 5, 8159679946425411364642563557683851720340694630400000⟩, + ⟨4, 4, 2, 4, 1, 5, 5032007209029636468711789550770531814634579558400000⟩, + ⟨4, 4, 3, 4, 2, 5, 5424191508471492699662683680090727566079426560000000⟩, + ⟨4, 4, 4, 4, 3, 5, -265517082669735795314592854713660223036325888000000⟩, + ⟨4, 4, 5, 4, 4, 5, 86645501436183084912650909653180771867400601600000⟩, + ⟨4, 4, 6, 4, 5, 5, 23418930635771950978034988194306033525666611200000⟩, + ⟨4, 4, 7, 4, 6, 5, 1364886008092417828864565229360352768032768000000⟩, + ⟨4, 4, 8, 4, 7, 5, -835040898280722628628269658057079223064985600000⟩, + ⟨4, 4, 2, 5, 0, 5, -37544183960205950480168497321147121744837659852800000⟩, + ⟨4, 4, 3, 5, 1, 5, -4504369661139743276303240315639220438301881139200000⟩, + ⟨4, 4, 4, 5, 2, 5, 1819233171448961773994743885345785223171591372800000⟩, + ⟨4, 4, 5, 5, 3, 5, -225976448851661121264695794254554403869766451200000⟩, + ⟨4, 4, 6, 5, 4, 5, 26413769348798303345951150474949211584253132800000⟩, + ⟨4, 4, 7, 5, 5, 5, 3614821297211858084542789383197046648235622400000⟩, + ⟨4, 4, 8, 5, 6, 5, -1738774312377888553904887314333973996791398400000⟩, + ⟨4, 4, 3, 6, 0, 5, -2453082018858498079224829392475774400884585267200000⟩, + ⟨4, 4, 4, 6, 1, 5, -976211634397942231570824881395756446833128243200000⟩, + ⟨4, 4, 5, 6, 2, 5, -3344434404979980192551637473295532603264204800000⟩, + ⟨4, 4, 6, 6, 3, 5, -97804622200967340483808307684810002940087500800000⟩, + ⟨4, 4, 7, 6, 4, 5, -1294053899048915198169719876125791506713804800000⟩, + ⟨4, 4, 8, 6, 5, 5, 1824766070437729931194795797141346753236172800000⟩, + ⟨4, 4, 4, 7, 0, 5, -18627321177332742688034724242985056024285046374400000⟩, + ⟨4, 4, 5, 7, 1, 5, 155906024296117632003111720239346374359488921600000⟩, + ⟨4, 4, 6, 7, 2, 5, 96521183568908060679083520377755467347342131200000⟩, + ⟨4, 4, 7, 7, 3, 5, -54220293736207636673863297777858564018352947200000⟩, + ⟨4, 4, 8, 7, 4, 5, -3607967154799020224434499296961170853855232000000⟩ +] + +def collectedFourData_8_3_35 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 3, 6, 15101172883068330713250127269105093918048701644800000⟩, + ⟨4, 5, 1, 0, 4, 6, -208974743854710906772499777741790364060090368000000⟩, + ⟨4, 5, 2, 0, 5, 6, 1715553163054824700257979274463583932833071104000000⟩, + ⟨4, 5, 3, 0, 6, 6, 68841050164994511844163813234057750340068966400000⟩, + ⟨4, 5, 4, 0, 7, 6, -197517825258174745014974579090579881063014727680000⟩, + ⟨4, 5, 5, 0, 8, 6, -3103253340661542413328297507050239324009267200000⟩, + ⟨4, 5, 0, 1, 2, 6, -5906858979717187887661016938233751407466591027200000⟩, + ⟨4, 5, 1, 1, 3, 6, 843984304608618419484028595416046849626000588800000⟩, + ⟨4, 5, 2, 1, 4, 6, -5912730377943305716392786578423791750648902451200000⟩, + ⟨4, 5, 3, 1, 5, 6, -922912572596122274218333700273529205569041203200000⟩, + ⟨4, 5, 4, 1, 6, 6, -442545469146480339866364739749667393323631902720000⟩, + ⟨4, 5, 5, 1, 7, 6, 24613567151584355375087394316390286102416588800000⟩, + ⟨4, 5, 6, 1, 8, 6, 1923333785938089874028638453735121818012876800000⟩, + ⟨4, 5, 0, 2, 1, 6, -6102445158599698108276530829156140787634798592000000⟩, + ⟨4, 5, 1, 2, 2, 6, 147341335703618714615052336227854083580703539200000⟩, + ⟨4, 5, 2, 2, 3, 6, 2203638302931315737959949440520514420869588582400000⟩, + ⟨4, 5, 3, 2, 4, 6, 1201830507775104747046037293479011735703021158400000⟩, + ⟨4, 5, 4, 2, 5, 6, 56156700775710416431040021334236538901113077760000⟩, + ⟨4, 5, 5, 2, 6, 6, 17203603633103863422238390268855388597544550400000⟩, + ⟨4, 5, 6, 2, 7, 6, 2573640593152157805159964170585338014806835200000⟩, + ⟨4, 5, 7, 2, 8, 6, 1508734633841956716962985125668222079179161600000⟩, + ⟨4, 5, 0, 3, 0, 6, 34098962384396747321801924178401755838475455692800000⟩, + ⟨4, 5, 1, 3, 1, 6, -826882547449596805963294388405401995108679680000000⟩, + ⟨4, 5, 2, 3, 2, 6, 1178349721588004033968357051409536962193784832000000⟩, + ⟨4, 5, 3, 3, 3, 6, -1606416872513644945336370652324745287858074419200000⟩, + ⟨4, 5, 4, 3, 4, 6, -38529106039722686486466637607994642545780981760000⟩, + ⟨4, 5, 5, 3, 5, 6, -6500549543236731431610163790965207707156480000000⟩, + ⟨4, 5, 6, 3, 6, 6, -6819395068938420007104447820084107293805772800000⟩, + ⟨4, 5, 7, 3, 7, 6, -842445910841017515914544546195798437029478400000⟩, + ⟨4, 5, 8, 3, 8, 6, -423576851931108707856218697632194127462400000000⟩, + ⟨4, 5, 1, 4, 0, 6, 6616303518637264433584064438742947835159144038400000⟩, + ⟨4, 5, 2, 4, 1, 6, 2720146478089578451230141287480584624508869017600000⟩, + ⟨4, 5, 3, 4, 2, 6, 2199111827847129505134085927947599707247738880000000⟩, + ⟨4, 5, 4, 4, 3, 6, -86118162470118298212113891985358610203095859200000⟩, + ⟨4, 5, 5, 4, 4, 6, 23418930635771950978034988194306033525666611200000⟩, + ⟨4, 5, 6, 4, 5, 6, 5425519284563150262940619421997143505974067200000⟩, + ⟨4, 5, 7, 4, 6, 6, 276680585426537194153532429145327934636032000000⟩, + ⟨4, 5, 8, 4, 7, 6, -150465706437722220370848317860250148195532800000⟩, + ⟨4, 5, 2, 5, 0, 6, -20295217301923380378956862926564527406002156339200000⟩, + ⟨4, 5, 3, 5, 1, 6, -1826191531648100542191732565991063021883595161600000⟩, + ⟨4, 5, 4, 5, 2, 6, 590052497769958877922491015557294384257454571520000⟩, + ⟨4, 5, 5, 5, 3, 6, -61077917413553480481857565399704203352761958400000⟩, + ⟨4, 5, 6, 5, 4, 6, 6119340682490748884665728155592582587272396800000⟩, + ⟨4, 5, 7, 5, 5, 6, 732772456304036093382007312314412614392217600000⟩, + ⟨4, 5, 8, 5, 6, 6, -313309091550328761307351957102359341118259200000⟩, + ⟨4, 5, 3, 6, 0, 6, -994544841185190264868323096566256632841476505600000⟩, + ⟨4, 5, 4, 6, 1, 6, -316625775226944149809418910734427836705019002880000⟩, + ⟨4, 5, 5, 6, 2, 6, -903948572607691622679042042499446618036633600000⟩, + ⟨4, 5, 6, 6, 3, 6, -22658629128873124442789609201272921464294604800000⟩, + ⟨4, 5, 7, 6, 4, 6, -262321972853064585474307369257326907437875200000⟩, + ⟨4, 5, 8, 6, 5, 6, 328803914200255997576764693315769311061606400000⟩, + ⟨4, 5, 4, 7, 0, 6, -6041610036548736597075265006062844945821031464960000⟩, + ⟨4, 5, 5, 7, 1, 6, 42138972112463732889670371206942200494764851200000⟩, + ⟨4, 5, 6, 7, 2, 6, 22361291852586279921224522331468969486267187200000⟩, + ⟨4, 5, 7, 7, 3, 6, -10991176203717780299348511482423465017658572800000⟩, + ⟨4, 5, 8, 7, 4, 6, -650118249140451509218915964199569159356416000000⟩ +] + +def collectedFourData_8_3_36 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 3, 7, 3080406600564585736283153236436324144488906752000000⟩, + ⟨4, 6, 1, 0, 4, 7, -28418418679832124300170838124606094447738880000000⟩, + ⟨4, 6, 2, 0, 5, 7, 174973206651342689823095027219750606843412480000000⟩, + ⟨4, 6, 3, 0, 6, 7, 5617005432890846622156404783433474841667174400000⟩, + ⟨4, 6, 4, 0, 7, 7, -13430197715230250620901674594406221620864614400000⟩, + ⟨4, 6, 5, 0, 8, 7, -180861676825039039255724662694584787140608000000⟩, + ⟨4, 6, 0, 1, 2, 7, -1204908223395424310928331880113134357109014528000000⟩, + ⟨4, 6, 1, 1, 3, 7, 114773196440666442271905246420480513653342208000000⟩, + ⟨4, 6, 2, 1, 4, 7, -603052949085719122555909765003634774737158144000000⟩, + ⟨4, 6, 3, 1, 5, 7, -75303978105083283838519180745566589516198707200000⟩, + ⟨4, 6, 4, 1, 6, 7, -30090819098721191779576371116536949005457817600000⟩, + ⟨4, 6, 5, 1, 7, 7, 1434510991852265758109654435942001102815232000000⟩, + ⟨4, 6, 6, 1, 8, 7, 98082614760595444288759219679141044420608000000⟩, + ⟨4, 6, 0, 2, 1, 7, -1244804790441842655947696182493334791604142080000000⟩, + ⟨4, 6, 1, 2, 2, 7, 20036908238931869308982254394701739062198272000000⟩, + ⟨4, 6, 2, 2, 3, 7, 224754130893286187389125347875957367937957888000000⟩, + ⟨4, 6, 3, 2, 4, 7, 98061962672083627214016847588403639459669606400000⟩, + ⟨4, 6, 4, 2, 5, 7, 3818367245928355516187792713560356459171020800000⟩, + ⟨4, 6, 5, 2, 6, 7, 1002648594540207233889928684901482371219456000000⟩, + ⟨4, 6, 6, 2, 7, 7, 131245757068242386198089097557491541082112000000⟩, + ⟨4, 6, 7, 2, 8, 7, 68390804410784454929804411872472519933952000000⟩, + ⟨4, 6, 0, 3, 0, 7, 6955662955098689723546274942599525581058998272000000⟩, + ⟨4, 6, 1, 3, 1, 7, -112447533127764926782387911600143690681548800000000⟩, + ⟨4, 6, 2, 3, 2, 7, 120182594036219313293026698370164553773219840000000⟩, + ⟨4, 6, 3, 3, 3, 7, -131073716609061342167431072091414827371803443200000⟩, + ⟨4, 6, 4, 3, 4, 7, -2619781334814649238679478228462029746523340800000⟩, + ⟨4, 6, 5, 3, 5, 7, -378860557489452193340002942977622356787200000000⟩, + ⟨4, 6, 6, 3, 6, 7, -347762881480688191564439801967567194554368000000⟩, + ⟨4, 6, 7, 3, 7, 7, -38187996896628903652714218810407909326848000000⟩, + ⟨4, 6, 8, 3, 8, 7, -17280630327699976823572075585790489395200000000⟩, + ⟨4, 6, 1, 4, 0, 7, 899749319162721452374187899862446322843910144000000⟩, + ⟨4, 6, 2, 4, 1, 7, 277433985773531860778905366431917558948954112000000⟩, + ⟨4, 6, 3, 4, 2, 7, 179433972243976900132598753810095849057812480000000⟩, + ⟨4, 6, 4, 4, 3, 7, -5855592766547748869716857071235837236084736000000⟩, + ⟨4, 6, 5, 4, 4, 7, 1364886008092417828864565229360352768032768000000⟩, + ⟨4, 6, 6, 4, 5, 7, 276680585426537194153532429145327934636032000000⟩, + ⟨4, 6, 7, 4, 6, 7, 12541905897647610508667475251982017495040000000⟩, + ⟨4, 6, 8, 4, 7, 7, -6138537170037318287892571727846697231974400000⟩, + ⟨4, 6, 2, 5, 0, 7, -2069955818028975037931756755270913016886984704000000⟩, + ⟨4, 6, 3, 5, 1, 7, -149005974344979764492821006003016751375817113600000⟩, + ⟨4, 6, 4, 5, 2, 7, 40120539485780051599344189013993007456295321600000⟩, + ⟨4, 6, 5, 5, 3, 7, -3559701174136701514912326841690295239704576000000⟩, + ⟨4, 6, 6, 5, 4, 7, 312062804250504220124511660616699827191808000000⟩, + ⟨4, 6, 7, 5, 5, 7, 33216509127972386080623157849534362550272000000⟩, + ⟨4, 6, 8, 5, 6, 7, -12782045488806152636811864051054617926041600000⟩, + ⟨4, 6, 3, 6, 0, 7, -81148729759375879575480070742723684170570137600000⟩, + ⟨4, 6, 4, 6, 1, 7, -21528926604359313251935541957860038489302630400000⟩, + ⟨4, 6, 5, 6, 2, 7, -52683308985200485075941240717016830050304000000⟩, + ⟨4, 6, 6, 6, 3, 7, -1155502808768319704126843876876416123404288000000⟩, + ⟨4, 6, 7, 6, 4, 7, -11891031289154025692436949471689487417344000000⟩, + ⟨4, 6, 8, 6, 5, 7, 13414186506394654219234440454745428800307200000⟩, + ⟨4, 6, 4, 7, 0, 7, -410798454281841180701428827531803209694497996800000⟩, + ⟨4, 6, 5, 7, 1, 7, 2455914590047313578885854905048677239226368000000⟩, + ⟨4, 6, 6, 7, 2, 7, 1140339752965302656235937268744227475423232000000⟩, + ⟨4, 6, 7, 7, 3, 7, -498229022607346640977712731720805007753216000000⟩, + ⟨4, 6, 8, 7, 4, 7, -26522821257746367989451864289879384915968000000⟩ +] + +def collectedFourData_8_3_37 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 3, 8, -5025602586695817483885241505999704520898537062400000⟩, + ⟨4, 7, 1, 0, 4, 8, 34772928612977422324467886913547073373601792000000⟩, + ⟨4, 7, 2, 0, 5, 8, -171278518840002606986751797676242951162403225600000⟩, + ⟨4, 7, 3, 0, 6, 8, -4581998530299025589603663146854548738030960640000⟩, + ⟨4, 7, 4, 0, 7, 8, 9390435159500431637107018656273243483270021120000⟩, + ⟨4, 7, 5, 0, 8, 8, 110651656024824724960852660160325844834713600000⟩, + ⟨4, 7, 0, 1, 2, 8, 1965776168352988576412894823036593133850302873600000⟩, + ⟨4, 7, 1, 1, 3, 8, -140437095092375651877658695365298183866626867200000⟩, + ⟨4, 7, 2, 1, 4, 8, 590319043002489663106776696974382370106564935680000⟩, + ⟨4, 7, 3, 1, 5, 8, 61428232734605351702885952146831299532103352320000⟩, + ⟨4, 7, 4, 1, 6, 8, 21039592389794850453362183519356845866593812480000⟩, + ⟨4, 7, 5, 1, 7, 8, -877637648952129204015910559534209443456614400000⟩, + ⟨4, 7, 6, 1, 8, 8, -53339737938101338990141764331548792009523200000⟩, + ⟨4, 7, 0, 2, 1, 8, 2030866371221666414446881252644600210465488896000000⟩, + ⟨4, 7, 1, 2, 2, 8, -24517267750426179079732735524634177521372364800000⟩, + ⟨4, 7, 2, 2, 3, 8, -220008282292509081850623768496189591583572623360000⟩, + ⟨4, 7, 3, 2, 4, 8, -79992760236743849366377998488501756071080099840000⟩, + ⟨4, 7, 4, 2, 5, 8, -2669814011553122892529590003625177567293603840000⟩, + ⟨4, 7, 5, 2, 6, 8, -613423083012561342951271805923196136534835200000⟩, + ⟨4, 7, 6, 2, 7, 8, -71374670267459545190235876200345611586764800000⟩, + ⟨4, 7, 7, 2, 8, 8, -33473341164447334050563612308291229287710720000⟩, + ⟨4, 7, 0, 3, 0, 8, -11347981702454909767830026824275350966088656486400000⟩, + ⟨4, 7, 1, 3, 1, 8, 137591401063146060176060153462795427297361920000000⟩, + ⟨4, 7, 2, 3, 2, 8, -117644850264936343415134619723769023870848204800000⟩, + ⟨4, 7, 3, 3, 3, 8, 106921665652449959247207414279023693366474833920000⟩, + ⟨4, 7, 4, 3, 4, 8, 1831759090839616187540538526880032318386339840000⟩, + ⟨4, 7, 5, 3, 5, 8, 231787899043145720525306907424186423050240000000⟩, + ⟨4, 7, 6, 3, 6, 8, 189122007075928527847541672952658801144627200000⟩, + ⟨4, 7, 7, 3, 7, 8, 18690814642708677903628347968354203761377280000⟩, + ⟨4, 7, 8, 3, 8, 8, 7688971419201539159387565619068555755520000000⟩, + ⟨4, 7, 1, 4, 0, 8, -1100938064052942318534187700132007901816002969600000⟩, + ⟨4, 7, 2, 4, 1, 8, -271575763333044282656511900268479414354460016640000⟩, + ⟨4, 7, 3, 4, 2, 8, -146370910074851477602161325304346724886642688000000⟩, + ⟨4, 7, 4, 4, 3, 8, 4094248302268101099147841855145758061022412800000⟩, + ⟨4, 7, 5, 4, 4, 8, -835040898280722628628269658057079223064985600000⟩, + ⟨4, 7, 6, 4, 5, 8, -150465706437722220370848317860250148195532800000⟩, + ⟨4, 7, 7, 4, 6, 8, -6138537170037318287892571727846697231974400000⟩, + ⟨4, 7, 8, 4, 7, 8, 2731326112593564893502274849769365375549440000⟩, + ⟨4, 7, 2, 5, 0, 8, 2026247180133783000426242089746750390081033338880000⟩, + ⟨4, 7, 3, 5, 1, 8, 121549669768271906556620973407085582048464732160000⟩, + ⟨4, 7, 4, 5, 2, 8, -28052403441399021952197309967959868514689351680000⟩, + ⟨4, 7, 5, 5, 3, 8, 2177834667831676919702262298752462198354739200000⟩, + ⟨4, 7, 6, 5, 4, 8, -169707427147814553399380473053081830110003200000⟩, + ⟨4, 7, 7, 5, 5, 8, -16257559066775207828924915493707869763665920000⟩, + ⟨4, 7, 8, 5, 6, 8, 5687337821515998112351693659360733597532160000⟩, + ⟨4, 7, 3, 6, 0, 8, 66196012258747373554838916840041918029690306560000⟩, + ⟨4, 7, 4, 6, 1, 8, 15053091072711281395298899354741585649514577920000⟩, + ⟨4, 7, 5, 6, 2, 8, 32231788880953849445727192451256205233356800000⟩, + ⟨4, 7, 6, 6, 3, 8, 628390843340400638027387680092961327231795200000⟩, + ⟨4, 7, 7, 6, 4, 8, 5819971713568636948232791219295959740579840000⟩, + ⟨4, 7, 8, 6, 5, 8, -5968607319501370067459725449600625771806720000⟩, + ⟨4, 7, 4, 7, 0, 8, 287231530789902211294671966464341550438169968640000⟩, + ⟨4, 7, 5, 7, 1, 8, -1502535093198039701568146818288325320350105600000⟩, + ⟨4, 7, 6, 7, 2, 8, -620144800707382786026362992687477060062412800000⟩, + ⟨4, 7, 7, 7, 3, 8, 243854275372947979112350129201972374153461760000⟩, + ⟨4, 7, 8, 7, 4, 8, 11801260182072653298442954802438054137036800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0815.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0815.lean new file mode 100644 index 0000000000000000000000000000000000000000..8e70e890b4e2f56e7c1ed99c87c55da9c51b4710 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0815.lean @@ -0,0 +1,617 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0815. -/ +namespace LaughlinFock +def collectedFourData_8_3_38 : List CollectedFourTerm := [ + ⟨5, 0, 3, 0, 6, 2, -7357526528731771603108402268105543094696872509440000⟩, + ⟨5, 0, 4, 0, 7, 2, 105550586151095428059704312534346382928230628720640000⟩, + ⟨5, 0, 5, 0, 8, 2, 4974997198162210578924286185833668788834061516800000⟩, + ⟨5, 0, 3, 1, 5, 2, 98638148609024753345751113946117394076000814366720000⟩, + ⟨5, 0, 4, 1, 6, 2, 236489712287318097181867126382241435305007183298560000⟩, + ⟨5, 0, 5, 1, 7, 2, -39459371882865851398692597757458055858704560947200000⟩, + ⟨5, 0, 6, 1, 8, 2, -7194606650981148034040352735643750134327332044800000⟩, + ⟨5, 0, 3, 2, 4, 2, -128448067291264190648758009155411915844484742512640000⟩, + ⟨5, 0, 4, 2, 5, 2, -30009305111780494076504210002175726051194809876480000⟩, + ⟨5, 0, 5, 2, 6, 2, -27580049218520965082981858111889856717775280537600000⟩, + ⟨5, 0, 6, 2, 7, 2, -9627206605584790048946318365139075271803220787200000⟩, + ⟨5, 0, 7, 2, 8, 2, -11287434672615221366463583843796600451566351155200000⟩, + ⟨5, 0, 3, 3, 3, 2, 171689053659026342275250805792053536514193563320320000⟩, + ⟨5, 0, 4, 3, 4, 2, 20589380837171442416994677794565951531413646868480000⟩, + ⟨5, 0, 5, 3, 5, 2, 10421390783784086612255680448274655205256069120000000⟩, + ⟨5, 0, 6, 3, 6, 2, 25509282620292764923800648535814032297862941900800000⟩, + ⟨5, 0, 7, 3, 7, 2, 6302667792291104005449477766366782846418078924800000⟩, + ⟨5, 0, 8, 3, 8, 2, 5704099772067282482849693984095167853929431040000000⟩, + ⟨5, 0, 3, 4, 2, 2, -235034526263815922664330149412955901631972507648000000⟩, + ⟨5, 0, 4, 4, 3, 2, 46020264323460348353461029262239144690583181721600000⟩, + ⟨5, 0, 5, 4, 4, 2, -37544183960205950480168497321147121744837659852800000⟩, + ⟨5, 0, 6, 4, 5, 2, -20295217301923380378956862926564527406002156339200000⟩, + ⟨5, 0, 7, 4, 6, 2, -2069955818028975037931756755270913016886984704000000⟩, + ⟨5, 0, 8, 4, 7, 2, 2026247180133783000426242089746750390081033338880000⟩, + ⟨5, 0, 3, 5, 1, 2, 195177915044045981129426868788775357655545135759360000⟩, + ⟨5, 0, 4, 5, 2, 2, -315315273029817168526794540376066940021389614120960000⟩, + ⟨5, 0, 5, 5, 3, 2, 97917390121051138672436830658167555547012372889600000⟩, + ⟨5, 0, 6, 5, 4, 2, -22890592104060620401365177495673494011751746764800000⟩, + ⟨5, 0, 7, 5, 5, 2, -5482157726678141234414518286272227835009774387200000⟩, + ⟨5, 0, 8, 5, 6, 2, 4219178431378262099648490008150498376291786424320000⟩, + ⟨5, 0, 3, 6, 0, 2, 106293992254555074963058635578428190628815579381760000⟩, + ⟨5, 0, 4, 6, 1, 2, 169200101925311054195903135651209098057222444810240000⟩, + ⟨5, 0, 5, 6, 2, 2, 1449169991080170072139408423918008559708038758400000⟩, + ⟨5, 0, 6, 6, 3, 2, 84759039239356033619187466215747833212219215052800000⟩, + ⟨5, 0, 7, 6, 4, 2, 1962533413997756261455410181082101640566564454400000⟩, + ⟨5, 0, 8, 6, 5, 2, -4427839537250137854473293255764699996734556733440000⟩, + ⟨5, 0, 4, 7, 0, 2, 3228546485971739787223412159625446138824156596142080000⟩, + ⟨5, 0, 5, 7, 1, 2, -67555318621924657478998320362265778600964574412800000⟩, + ⟨5, 0, 6, 7, 2, 2, -83646790933212666042952956869238060490968740659200000⟩, + ⟨5, 0, 7, 7, 3, 2, 82229293735205128618108639828677550708287445401600000⟩, + ⟨5, 0, 8, 7, 4, 2, 8754820618341913369112372503103371629825726873600000⟩ +] + +def collectedFourData_8_3_39 : List CollectedFourTerm := [ + ⟨5, 1, 2, 0, 5, 3, -16498374199744404250001167485587743037197595443200000⟩, + ⟨5, 1, 3, 0, 6, 3, -2648161375315326334995337993548331437691219476480000⟩, + ⟨5, 1, 4, 0, 7, 3, 18995173465953111745099056586334590642291149373440000⟩, + ⟨5, 1, 5, 0, 8, 3, 596876109157391891683783440444130704590320435200000⟩, + ⟨5, 1, 2, 1, 4, 3, 56862381427923928651119948173151821748499340328960000⟩, + ⟨5, 1, 3, 1, 5, 3, 35502384430281852644923451641239911641890674442240000⟩, + ⟨5, 1, 4, 1, 6, 3, 42559338338305661835125713727278574360107690229760000⟩, + ⟨5, 1, 5, 1, 7, 3, -4734144647948730360886310349501104357324410060800000⟩, + ⟨5, 1, 6, 1, 8, 3, -647380589431565964477193181367190087207904870400000⟩, + ⟨5, 1, 2, 2, 3, 3, -21192260377353694422042833135590475739523102801920000⟩, + ⟨5, 1, 3, 2, 4, 3, -46231734157710493636401164332095114278826022010880000⟩, + ⟨5, 1, 4, 2, 5, 3, -5400556993354678774394930484540047609508743086080000⟩, + ⟨5, 1, 5, 2, 6, 3, -3308920952558779412916702779059481076612621926400000⟩, + ⟨5, 1, 6, 2, 7, 3, -866269274923182684246979497467810119255955865600000⟩, + ⟨5, 1, 7, 2, 8, 3, -812527101592849426911384105545912368945094983680000⟩, + ⟨5, 1, 2, 3, 2, 3, -11332120195159610748642386992074105576830376345600000⟩, + ⟨5, 1, 3, 3, 3, 3, 61795267565639966899341431715638567133192325693440000⟩, + ⟨5, 1, 4, 3, 4, 3, 3705321541263497153670438914150672055540991918080000⟩, + ⟨5, 1, 5, 3, 5, 3, 1250308077626968570118238749355638408274247680000000⟩, + ⟨5, 1, 6, 3, 6, 3, 2295360291371793540465874710455238706413856358400000⟩, + ⟨5, 1, 7, 3, 7, 3, 453698164561458563943434479150595922297429688320000⟩, + ⟨5, 1, 8, 3, 8, 3, 342175155340266047720032091772163951196897280000000⟩, + ⟨5, 1, 2, 4, 1, 3, -26159489219049355903954059725290113152573327278080000⟩, + ⟨5, 1, 3, 4, 2, 3, -84594918127282463183389999506808534131032457216000000⟩, + ⟨5, 1, 4, 4, 3, 3, 8281933200463523702053719445557991938073401753600000⟩, + ⟨5, 1, 5, 4, 4, 3, -4504369661139743276303240315639220438301881139200000⟩, + ⟨5, 1, 6, 4, 5, 3, -1826191531648100542191732565991063021883595161600000⟩, + ⟨5, 1, 7, 4, 6, 3, -149005974344979764492821006003016751375817113600000⟩, + ⟨5, 1, 8, 4, 7, 3, 121549669768271906556620973407085582048464732160000⟩, + ⟨5, 1, 2, 5, 0, 3, 195177915044045981129426868788775357655545135759360000⟩, + ⟨5, 1, 3, 5, 1, 3, 70249507618603333531352276213900342632287169413120000⟩, + ⟨5, 1, 4, 5, 2, 3, -56745002809286472685401973802876277178266455900160000⟩, + ⟨5, 1, 5, 5, 3, 3, 11747655024989594371648610272972353218936202854400000⟩, + ⟨5, 1, 6, 5, 4, 3, -2059726921518832049876689153399676410266019430400000⟩, + ⟨5, 1, 7, 5, 5, 3, -394633666313887079861734833281556972218854932480000⟩, + ⟨5, 1, 8, 5, 6, 3, 253098313994239823068426070327268359748704010240000⟩, + ⟨5, 1, 3, 6, 0, 3, 38257917741425934079869686039889338690950838353920000⟩, + ⟨5, 1, 4, 6, 1, 3, 30449715190850932858794975522291143601434960855040000⟩, + ⟨5, 1, 5, 6, 2, 3, 173864408627830061263574198288148873921272217600000⟩, + ⟨5, 1, 6, 6, 3, 3, 7626734781246808219295609022199248594114340454400000⟩, + ⟨5, 1, 7, 6, 4, 3, 141273161963315791552983622140402878009793576960000⟩, + ⟨5, 1, 8, 6, 5, 3, -265615389285386852894998406943065503776720814080000⟩, + ⟨5, 1, 4, 7, 0, 3, 581018095495342622467542765649302167540159144263680000⟩, + ⟨5, 1, 5, 7, 1, 3, -8104960490598366906877056513088362694143324979200000⟩, + ⟨5, 1, 6, 7, 2, 3, -7526653150803932063172118259388717966611290521600000⟩, + ⟨5, 1, 7, 7, 3, 3, 5919283844609223051925174831051394395789527613440000⟩, + ⟨5, 1, 8, 7, 4, 3, 525180523616895249987293099555529497746027315200000⟩ +] + +def collectedFourData_8_3_40 : List CollectedFourTerm := [ + ⟨5, 2, 1, 0, 4, 4, -1082240665121951263506034582291826150088690892800000⟩, + ⟨5, 2, 2, 0, 5, 4, 26653575862650829427936610448890288381566858035200000⟩, + ⟨5, 2, 3, 0, 6, 4, 2139088653796029487912419465015653305779109232640000⟩, + ⟨5, 2, 4, 0, 7, 4, -10229074511007209422038452391929646312710240993280000⟩, + ⟨5, 2, 5, 0, 8, 4, -241067429787670615777959902549623733041810636800000⟩, + ⟨5, 2, 1, 1, 3, 4, 4370835050799982683733453455088369660657643028480000⟩, + ⟨5, 2, 2, 1, 4, 4, -91862736216980564885228145969017109952451900866560000⟩, + ⟨5, 2, 3, 1, 5, 4, -28677537715569898989913209754981332536780988088320000⟩, + ⟨5, 2, 4, 1, 6, 4, -22918592651022699612898607272251818673649609605120000⟩, + ⟨5, 2, 5, 1, 7, 4, 1912035119206150631113851835088601068273349427200000⟩, + ⟨5, 2, 6, 1, 8, 4, 209172218347298376593544154219607185343517818880000⟩, + ⟨5, 2, 1, 2, 2, 4, 763052903956203851923705388856890482927935160320000⟩, + ⟨5, 2, 2, 2, 3, 4, 34236677676858410514791609676698237219858672517120000⟩, + ⟨5, 2, 3, 2, 4, 4, 37344317043479726169367391976555027539955642531840000⟩, + ⟨5, 2, 4, 2, 5, 4, 2908249297379827290003372438923355208060722216960000⟩, + ⟨5, 2, 5, 2, 6, 4, 1336413130239017722307864907987806767764052377600000⟩, + ⟨5, 2, 6, 2, 7, 4, 279896352902533620857130063200929889823039160320000⟩, + ⟨5, 2, 7, 2, 8, 4, 218776635004236963484915578828261068634146734080000⟩, + ⟨5, 2, 1, 3, 1, 4, -4282268285739600900729645320937504506829078528000000⟩, + ⟨5, 2, 2, 3, 2, 4, 18307350872854095445846660370918076664105245081600000⟩, + ⟨5, 2, 3, 3, 3, 4, -49915974509752231309348846667010033962908039249920000⟩, + ⟨5, 2, 4, 3, 4, 4, -1995349513430863298477481456609304777398901800960000⟩, + ⟨5, 2, 5, 3, 5, 4, -504976744909080323972628890251951680383877120000000⟩, + ⟨5, 2, 6, 3, 6, 4, -741643496716691221999631589707004413693373972480000⟩, + ⟨5, 2, 7, 3, 7, 4, -122160304014194095960082468541475760566614097920000⟩, + ⟨5, 2, 8, 3, 8, 4, -78970477859201118966587409177997984860733440000000⟩, + ⟨5, 2, 1, 4, 0, 4, 34264584267833676141796960275318523488264404336640000⟩, + ⟨5, 2, 2, 4, 1, 4, 42261372059249955404653667912630110087981962362880000⟩, + ⟨5, 2, 3, 4, 2, 4, 68332704804791918963745235162492028012973785088000000⟩, + ⟨5, 2, 4, 4, 3, 4, -4459896718214834775324289233108594146025878323200000⟩, + ⟨5, 2, 5, 4, 4, 4, 1819233171448961773994743885345785223171591372800000⟩, + ⟨5, 2, 6, 4, 5, 4, 590052497769958877922491015557294384257454571520000⟩, + ⟨5, 2, 7, 4, 6, 4, 40120539485780051599344189013993007456295321600000⟩, + ⟨5, 2, 8, 4, 7, 4, -28052403441399021952197309967959868514689351680000⟩, + ⟨5, 2, 2, 5, 0, 4, -315315273029817168526794540376066940021389614120960000⟩, + ⟨5, 2, 3, 5, 1, 4, -56745002809286472685401973802876277178266455900160000⟩, + ⟨5, 2, 4, 5, 2, 4, 30557702613450697711385409984744326541350975569920000⟩, + ⟨5, 2, 5, 5, 3, 4, -4744664695835033300895715413741082630118021529600000⟩, + ⟨5, 2, 6, 5, 4, 4, 665509062825074577800302464969108065778275450880000⟩, + ⟨5, 2, 7, 5, 5, 4, 106256917961611183990902679021163136471143546880000⟩, + ⟨5, 2, 8, 5, 6, 4, -58412466508877506188204300398924763726631403520000⟩, + ⟨5, 2, 3, 6, 0, 4, -30903357522462690489120673850517571563151750594560000⟩, + ⟨5, 2, 4, 6, 1, 4, -16397449914550369727355479372154916724734930452480000⟩, + ⟨5, 2, 5, 6, 2, 4, -70220679763230615250207703310555936759113318400000⟩, + ⟨5, 2, 6, 6, 3, 4, -2464239828909065808306115329419488313357295943680000⟩, + ⟨5, 2, 7, 6, 4, 4, -38038444416381037823510427897371403510098165760000⟩, + ⟨5, 2, 8, 6, 5, 4, 61301277697283384321559477680445644552892579840000⟩, + ⟨5, 2, 4, 7, 0, 4, -312883554431238722714148574904421757215945428828160000⟩, + ⟨5, 2, 5, 7, 1, 4, 3273446472430264870433570731261069640254409932800000⟩, + ⟨5, 2, 6, 7, 2, 4, 2431902905316821061472968692227152399857897963520000⟩, + ⟨5, 2, 7, 7, 3, 4, -1593794223749428521039025639895791800941165936640000⟩, + ⟨5, 2, 8, 7, 4, 4, -121206219285936512562147642576630805241108889600000⟩ +] + +def collectedFourData_8_3_41 : List CollectedFourTerm := [ + ⟨5, 3, 0, 0, 3, 5, -24285975269925734390125135466046064620093623500800000⟩, + ⟨5, 3, 1, 0, 4, 5, 672153812235990880864542013349593316019142656000000⟩, + ⟨5, 3, 2, 0, 5, 5, -8276949482296146844696031022330287754892541952000000⟩, + ⟨5, 3, 3, 0, 6, 5, -442845613333068315314503996932390696389286297600000⟩, + ⟨5, 3, 4, 0, 7, 5, 1588258427584759899202921630001043449531754086400000⟩, + ⟨5, 3, 5, 0, 8, 5, 29944243856232509657892919301778507371328307200000⟩, + ⟨5, 3, 0, 1, 2, 5, 9499515846560040435488281294815447698344457011200000⟩, + ⟨5, 3, 1, 1, 3, 5, -2714621189843062993863493181847716023426980249600000⟩, + ⟨5, 3, 2, 1, 4, 5, 28526875001372701586388608045223665919984245145600000⟩, + ⟨5, 3, 3, 1, 5, 5, 5936977766674984725598235446873168907252583628800000⟩, + ⟨5, 3, 4, 1, 6, 5, 3558547538899953144149003384307869807527172505600000⟩, + ⟨5, 3, 5, 1, 7, 5, -237503863220421851647628874723051769208556748800000⟩, + ⟨5, 3, 6, 1, 8, 5, -21651977621840203725019694220856879312640409600000⟩, + ⟨5, 3, 0, 2, 1, 5, 9814061023961836096409565381662840564672888832000000⟩, + ⟨5, 3, 1, 2, 2, 5, -473913922162693291024720883753287664739444326400000⟩, + ⟨5, 3, 2, 2, 3, 5, -10631791135016215552259030580572286945949070131200000⟩, + ⟨5, 3, 3, 2, 4, 5, -7731220936671508728549998332017169834448624025600000⟩, + ⟨5, 3, 4, 2, 5, 5, -451561033318365255681527690833087284657310924800000⟩, + ⟨5, 3, 5, 2, 6, 5, -166002851151627768075247581843483313465353830400000⟩, + ⟨5, 3, 6, 2, 7, 5, -28972822573493637028889201534785738584254054400000⟩, + ⟨5, 3, 7, 2, 8, 5, -19410991339592584655511246931558342064917708800000⟩, + ⟨5, 3, 0, 3, 0, 5, -54838558806653726940931100378087156314431868108800000⟩, + ⟨5, 3, 1, 3, 1, 5, 2659614488754043355311855340728242947028418560000000⟩, + ⟨5, 3, 2, 3, 2, 5, -5685129046478843082325338133736226172610543616000000⟩, + ⟨5, 3, 3, 3, 3, 5, 10333872935869836203679215369671567123218746572800000⟩, + ⟨5, 3, 4, 3, 4, 5, 309815973798363614435395916271586147759344844800000⟩, + ⟨5, 3, 5, 3, 5, 5, 62725797527283340199607260995571392425492480000000⟩, + ⟨5, 3, 6, 3, 6, 5, 76769508499600034220059663226307700642650521600000⟩, + ⟨5, 3, 7, 3, 7, 5, 10838692181254162303123833212531215455957811200000⟩, + ⟨5, 3, 8, 3, 8, 5, 6130834556699391795638208373596979042713600000000⟩, + ⟨5, 3, 1, 4, 0, 5, -21280914386737195304409788497435732751902624972800000⟩, + ⟨5, 3, 2, 4, 1, 5, -13123764082893487735071641496247345992128318668800000⟩, + ⟨5, 3, 3, 4, 2, 5, -14146603281862422274744469878862255337945169920000000⟩, + ⟨5, 3, 4, 4, 3, 5, 692483815739147280871511912846518499112124416000000⟩, + ⟨5, 3, 5, 4, 4, 5, -225976448851661121264695794254554403869766451200000⟩, + ⟨5, 3, 6, 4, 5, 5, -61077917413553480481857565399704203352761958400000⟩, + ⟨5, 3, 7, 4, 6, 5, -3559701174136701514912326841690295239704576000000⟩, + ⟨5, 3, 8, 4, 7, 5, 2177834667831676919702262298752462198354739200000⟩, + ⟨5, 3, 2, 5, 0, 5, 97917390121051138672436830658167555547012372889600000⟩, + ⟨5, 3, 3, 5, 1, 5, 11747655024989594371648610272972353218936202854400000⟩, + ⟨5, 3, 4, 5, 2, 5, -4744664695835033300895715413741082630118021529600000⟩, + ⟨5, 3, 5, 5, 3, 5, 589359569616185146110854983429123145789236838400000⟩, + ⟨5, 3, 6, 5, 4, 5, -68888628945434101536867896400749807565117849600000⟩, + ⟨5, 3, 7, 5, 5, 5, -9427661753206368620956460802961555227200716800000⟩, + ⟨5, 3, 8, 5, 6, 5, 4534823365931381992601838083439881448377548800000⟩, + ⟨5, 3, 3, 6, 0, 5, 6397778928797515332518952588173589506970510950400000⟩, + ⟨5, 3, 4, 6, 1, 5, 2546016063296742417319798649310569566413678182400000⟩, + ⟨5, 3, 5, 6, 2, 5, 8722477194171884120452079097150899784096153600000⟩, + ⟨5, 3, 6, 6, 3, 5, 255080077325553475043856647126646672961673625600000⟩, + ⟨5, 3, 7, 6, 4, 5, 3374966961730838494782622292792087657683353600000⟩, + ⟨5, 3, 8, 6, 5, 5, -4759094814474922074257297283072108852255129600000⟩, + ⟨5, 3, 4, 7, 0, 5, 48581124484267588235325946310662040965266328780800000⟩, + ⟨5, 3, 5, 7, 1, 5, -406611874142896819402353858437662455262032691200000⟩, + ⟨5, 3, 6, 7, 2, 5, -251732795590385689623046176938789518514218598400000⟩, + ⟨5, 3, 7, 7, 3, 5, 141409643098741762962485290802098350357636710400000⟩, + ⟨5, 3, 8, 7, 4, 5, 9409785755760414120353474091447642356711424000000⟩ +] + +def collectedFourData_8_3_42 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 3, 6, 17032327548740197074077509473128651482769601331200000⟩, + ⟨5, 4, 1, 0, 4, 6, -235698664885711667212817402240516262086049792000000⟩, + ⟨5, 4, 2, 0, 5, 6, 1934939996163399871607070670135312305541349376000000⟩, + ⟨5, 4, 3, 0, 6, 6, 77644519686553171146194463524782907412027801600000⟩, + ⟨5, 4, 4, 0, 7, 6, -222776622886295285154997834899501508921833553920000⟩, + ⟨5, 4, 5, 0, 8, 6, -3500100805026355650465676410071315787861196800000⟩, + ⟨5, 4, 0, 1, 2, 6, -6662234629441480383176827691691410750257810636800000⟩, + ⟨5, 4, 1, 1, 3, 6, 951913949558659894597181278905278207022543667200000⟩, + ⟨5, 4, 2, 1, 4, 6, -6668856868556990184526852178058873858773798092800000⟩, + ⟨5, 4, 3, 1, 5, 6, -1040935651622954312183106839875617584023653580800000⟩, + ⟨5, 4, 4, 1, 6, 6, -499138672477884345789966331546946294207144263680000⟩, + ⟨5, 4, 5, 1, 7, 6, 27761177301581658691580428006509795268047667200000⟩, + ⟨5, 4, 6, 1, 8, 6, 2169291834569077820048942178388759857541939200000⟩, + ⟨5, 4, 0, 2, 1, 6, -6882832584880325708240533414194978608746856448000000⟩, + ⟨5, 4, 1, 2, 2, 6, 166183508433751316595870668372579110517263564800000⟩, + ⟨5, 4, 2, 2, 3, 6, 2485442002757204828889704458063010247302814105600000⟩, + ⟨5, 4, 3, 2, 4, 6, 1355521920383123688621375514931537486628362649600000⟩, + ⟨5, 4, 4, 2, 5, 6, 63338081689066150157740243567363560807270973440000⟩, + ⟨5, 4, 5, 2, 6, 6, 19403619464966032044529504381427545148070297600000⟩, + ⟨5, 4, 6, 2, 7, 6, 2902760594473435979365634955993477366467788800000⟩, + ⟨5, 4, 7, 2, 8, 6, 1701673285029203441958686225208169988515430400000⟩, + ⟨5, 4, 0, 3, 0, 6, 38459575352216598204057372063068621492561589043200000⟩, + ⟨5, 4, 1, 3, 1, 6, -932625200807358634407017844059254688757841920000000⟩, + ⟨5, 4, 2, 3, 2, 6, 1329038385326780864816332401444143817459499008000000⟩, + ⟨5, 4, 3, 3, 3, 6, -1811847236260225990763728840771557598035758284800000⟩, + ⟨5, 4, 4, 3, 4, 6, -43456250670733522406090735489178766778239549440000⟩, + ⟨5, 4, 5, 3, 5, 6, -7331846997881991949716619182415625186181120000000⟩, + ⟨5, 4, 6, 3, 6, 6, -7691466841536016011742814323218473679008563200000⟩, + ⟨5, 4, 7, 3, 7, 6, -950178824297091790744683273806095486392729600000⟩, + ⟨5, 4, 8, 3, 8, 6, -477744327544510078886182372278330300825600000000⟩, + ⟨5, 4, 1, 4, 0, 6, 7462403719492750844529561868988915133762345369600000⟩, + ⟨5, 4, 2, 4, 1, 6, 3068001813774355368960421185038752421840840294400000⟩, + ⟨5, 4, 3, 4, 2, 6, 2480336677040318760869454818779124636288286720000000⟩, + ⟨5, 4, 4, 4, 3, 6, -97131048193698306363570147383454220140989644800000⟩, + ⟨5, 4, 5, 4, 4, 6, 26413769348798303345951150474949211584253132800000⟩, + ⟨5, 4, 6, 4, 5, 6, 6119340682490748884665728155592582587272396800000⟩, + ⟨5, 4, 7, 4, 6, 6, 312062804250504220124511660616699827191808000000⟩, + ⟨5, 4, 8, 4, 7, 6, -169707427147814553399380473053081830110003200000⟩, + ⟨5, 4, 2, 5, 0, 6, -22890592104060620401365177495673494011751746764800000⟩, + ⟨5, 4, 3, 5, 1, 6, -2059726921518832049876689153399676410266019430400000⟩, + ⟨5, 4, 4, 5, 2, 6, 665509062825074577800302464969108065778275450880000⟩, + ⟨5, 4, 5, 5, 3, 6, -68888628945434101536867896400749807565117849600000⟩, + ⟨5, 4, 6, 5, 4, 6, 6901888727025588782699774038137330916864819200000⟩, + ⟨5, 4, 7, 5, 5, 6, 826480207273101666600356922155657188501094400000⟩, + ⟨5, 4, 8, 5, 6, 6, -353375404189078885410312228758053018455244800000⟩, + ⟨5, 4, 3, 6, 0, 6, -1121728333828208368992219086090040026581067366400000⟩, + ⟨5, 4, 4, 6, 1, 6, -357116229037128377892076948364092425244476702720000⟩, + ⟨5, 4, 5, 6, 2, 6, -1019546514372601396678352485215211165738598400000⟩, + ⟨5, 4, 6, 6, 3, 6, -25556239645537904444411103699569245454283571200000⟩, + ⟨5, 4, 7, 6, 4, 6, -295867996443817229619914164512269888441548800000⟩, + ⟨5, 4, 8, 6, 5, 6, 370851721871601577422301743581307854231961600000⟩, + ⟨5, 4, 4, 7, 0, 6, -6814217800236589404272143837978430166156957450240000⟩, + ⟨5, 4, 5, 7, 1, 6, 47527750403509060378040831510777784364223692800000⟩, + ⟨5, 4, 6, 7, 2, 6, 25220878549987106503538852484461829938793676800000⟩, + ⟨5, 4, 7, 7, 3, 6, -12396739955049289385290108074729188699091763200000⟩, + ⟨5, 4, 8, 7, 4, 6, -733256088816048506124626864292147970965504000000⟩ +] + +def collectedFourData_8_3_43 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 3, 7, 8158277920480283400211132109624671423423945113600000⟩, + ⟨5, 5, 1, 0, 4, 7, -75264530860356416313726924766122585184272384000000⟩, + ⟨5, 5, 2, 0, 5, 7, 463406372469676666507083596664878403749412864000000⟩, + ⟨5, 5, 3, 0, 6, 7, 14876312560157557238061859433035478085843025920000⟩, + ⟨5, 5, 4, 0, 7, 7, -35569098400115717441843464663312606643009617920000⟩, + ⟨5, 5, 5, 0, 8, 7, -479001643624682229470851874425573688632934400000⟩, + ⟨5, 5, 0, 1, 2, 7, -3191129428605414897282880506293986588004607590400000⟩, + ⟨5, 5, 1, 1, 3, 7, 303970142841928101376927790622453945162163814400000⟩, + ⟨5, 5, 2, 1, 4, 7, -1597150700334434526163014311600866345499177779200000⟩, + ⟨5, 5, 3, 1, 5, 7, -199438211107076473506365751141980681270156328960000⟩, + ⟨5, 5, 4, 1, 6, 7, -79693786209024985558484626148862021456290119680000⟩, + ⟨5, 5, 5, 1, 7, 7, 3799219021725776910256943236841653254330777600000⟩, + ⟨5, 5, 6, 1, 8, 7, 259766106928117577780469703527224526136934400000⟩, + ⟨5, 5, 0, 2, 1, 7, -3296793168573411270782393229243191026614534144000000⟩, + ⟨5, 5, 1, 2, 2, 7, 53066587394796099277992384095908474786519449600000⟩, + ⟨5, 5, 2, 2, 3, 7, 595248258222587752173607499107116210358478438400000⟩, + ⟨5, 5, 3, 2, 4, 7, 259711411071509920448880059259637015856566763520000⟩, + ⟨5, 5, 4, 2, 5, 7, 10112723816730204217799545230367917891586621440000⟩, + ⟨5, 5, 5, 2, 6, 7, 2655456552176822310402947986527544190749900800000⟩, + ⟨5, 5, 6, 2, 7, 7, 347596762664484869243376523848044082993561600000⟩, + ⟨5, 5, 7, 2, 8, 7, 181129072209534126443872792243893912050073600000⟩, + ⟨5, 5, 0, 3, 0, 7, 18421669236289673434020226531853346473644759449600000⟩, + ⟨5, 5, 1, 3, 1, 7, -297810758670813170643746603639897570767011840000000⟩, + ⟨5, 5, 2, 3, 2, 7, 318296618106203148096112829631002929803558912000000⟩, + ⟨5, 5, 3, 3, 3, 7, -347141123503307655299190761853464811291814133760000⟩, + ⟨5, 5, 4, 3, 4, 7, -6938338664898143842457241293968418117454397440000⟩, + ⟨5, 5, 5, 3, 5, 7, -1003390176004865434738143525579931999272960000000⟩, + ⟨5, 5, 6, 3, 6, 7, -921029787764543757946078957829068603942502400000⟩, + ⟨5, 5, 7, 3, 7, 7, -101138691188376140237203440806528534603366400000⟩, + ⟨5, 5, 8, 3, 8, 7, -45766745477242333367058302831894577807360000000⟩, + ⟨5, 5, 1, 4, 0, 7, 2382933799436421003867141484006770092004291379200000⟩, + ⟨5, 5, 2, 4, 1, 7, 734767793353061450596525277499673566187723161600000⟩, + ⟨5, 5, 3, 4, 2, 7, 475220450986504855374457591113800141047332864000000⟩, + ⟨5, 5, 4, 4, 3, 7, -15508197252237692020789159197261352816921804800000⟩, + ⟨5, 5, 5, 4, 4, 7, 3614821297211858084542789383197046648235622400000⟩, + ⟨5, 5, 6, 4, 5, 7, 732772456304036093382007312314412614392217600000⟩, + ⟨5, 5, 7, 4, 6, 7, 33216509127972386080623157849534362550272000000⟩, + ⟨5, 5, 8, 4, 7, 7, -16257559066775207828924915493707869763665920000⟩, + ⟨5, 5, 2, 5, 0, 7, -5482157726678141234414518286272227835009774387200000⟩, + ⟨5, 5, 3, 5, 1, 7, -394633666313887079861734833281556972218854932480000⟩, + ⟨5, 5, 4, 5, 2, 7, 106256917961611183990902679021163136471143546880000⟩, + ⟨5, 5, 5, 5, 3, 7, -9427661753206368620956460802961555227200716800000⟩, + ⟨5, 5, 6, 5, 4, 7, 826480207273101666600356922155657188501094400000⟩, + ⟨5, 5, 7, 5, 5, 7, 87971994659569024524625914873168768113049600000⟩, + ⟨5, 5, 8, 5, 6, 7, -33852504883864748598832170697526866744442880000⟩, + ⟨5, 5, 3, 6, 0, 7, -214917696303338031208336634354076261746925895680000⟩, + ⟨5, 5, 4, 6, 1, 7, -57018111354453511020765170265944057029821726720000⟩, + ⟨5, 5, 5, 6, 2, 7, -139528683126774802601181867596677620380467200000⟩, + ⟨5, 5, 6, 6, 3, 7, -3060282058251577001729458436299136096953958400000⟩, + ⟨5, 5, 7, 6, 4, 7, -31492705540971492490600105593559265260339200000⟩, + ⟨5, 5, 8, 6, 5, 7, 35526693643711253228918529349634099207208960000⟩, + ⟨5, 5, 4, 7, 0, 7, -1087975840176656678732845507999601644536059658240000⟩, + ⟨5, 5, 5, 7, 1, 7, 6504347111480712816580824556178897918912102400000⟩, + ⟨5, 5, 6, 7, 2, 7, 3020123585879101395912288291159515864865177600000⟩, + ⟨5, 5, 7, 7, 3, 7, -1319530620968998018881149748234745816075468800000⟩, + ⟨5, 5, 8, 7, 4, 7, -70244151215705890213226395163843417761382400000⟩ +] + +def collectedFourData_8_3_44 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 3, 8, -10464623589045936108490943342022296604931365273600000⟩, + ⟨5, 6, 1, 0, 4, 8, 72406363763597503121606655424841601502937088000000⟩, + ⟨5, 6, 2, 0, 5, 8, -356646829435903781792769488937191267084166758400000⟩, + ⟨5, 6, 3, 0, 6, 8, -9540923516729154316565029612733679174376488960000⟩, + ⟨5, 6, 4, 0, 7, 8, 19553350585590651239692806718126617169420615680000⟩, + ⟨5, 6, 5, 0, 8, 8, 230405789122629466195465930313698283775590400000⟩, + ⟨5, 6, 0, 1, 2, 8, 4093261913822737044603402473747078011054089830400000⟩, + ⟨5, 6, 1, 1, 3, 8, -292426890652130401273747990478819508072795340800000⟩, + ⟨5, 6, 2, 1, 4, 8, 1229199180774931532303787635767957070749913579520000⟩, + ⟨5, 6, 3, 1, 5, 8, 127909702810502554613428502282050237561810452480000⟩, + ⟨5, 6, 4, 1, 6, 8, 43809953339528709885490215675659226113082654720000⟩, + ⟨5, 6, 5, 1, 7, 8, -1827471927082393605765568979620260512111001600000⟩, + ⟨5, 6, 6, 1, 8, 8, -111067333763764726209924978915303347768524800000⟩, + ⟨5, 6, 0, 2, 1, 8, 4228796799561321392860372550079761178421100544000000⟩, + ⟨5, 6, 1, 2, 2, 8, -51051386179890536054346370348543494499545907200000⟩, + ⟨5, 6, 2, 2, 3, 8, -458114986401533868338197150918923712273097687040000⟩, + ⟨5, 6, 3, 2, 4, 8, -166565921456334189011023756583146627106875637760000⟩, + ⟨5, 6, 4, 2, 5, 8, -5559253482880936945444321945295295036008693760000⟩, + ⟨5, 6, 5, 2, 6, 8, -1277307855888181394615858457783754170354892800000⟩, + ⟨5, 6, 6, 2, 7, 8, -148620796264016372779782750371361080947507200000⟩, + ⟨5, 6, 7, 2, 8, 8, -69700281610201969222894658263780880893870080000⟩, + ⟨5, 6, 0, 3, 0, 8, -23629476259412587656525713543300003543268301209600000⟩, + ⟨5, 6, 1, 3, 1, 8, 286501408811541403482684066374413389272186880000000⟩, + ⟨5, 6, 2, 3, 2, 8, -244967454941885304768338393012092976682447667200000⟩, + ⟨5, 6, 3, 3, 3, 8, 222638970206028622166563533545834199854748794880000⟩, + ⟨5, 6, 4, 3, 4, 8, 3814203184747325739522987533210299353802997760000⟩, + ⟨5, 6, 5, 3, 5, 8, 482643240116811947393916227821797491343360000000⟩, + ⟨5, 6, 6, 3, 6, 8, 393801655087826325556064923135874035403980800000⟩, + ⟨5, 6, 7, 3, 7, 8, 38919181617416847991613183638765460961361920000⟩, + ⟨5, 6, 8, 3, 8, 8, 16010456517569151077283674784395459297280000000⟩, + ⟨5, 6, 1, 4, 0, 8, -2292441998033440346275099075255619830881347174400000⟩, + ⟨5, 6, 2, 4, 1, 8, -565492016163701561210689083863079195394399272960000⟩, + ⟨5, 6, 3, 4, 2, 8, -304782650815704419682846257693143514461765632000000⟩, + ⟨5, 6, 4, 4, 3, 8, 8525299528607412717376681235152401008374579200000⟩, + ⟨5, 6, 5, 4, 4, 8, -1738774312377888553904887314333973996791398400000⟩, + ⟨5, 6, 6, 4, 5, 8, -313309091550328761307351957102359341118259200000⟩, + ⟨5, 6, 7, 4, 6, 8, -12782045488806152636811864051054617926041600000⟩, + ⟨5, 6, 8, 4, 7, 8, 5687337821515998112351693659360733597532160000⟩, + ⟨5, 6, 2, 5, 0, 8, 4219178431378262099648490008150498376291786424320000⟩, + ⟨5, 6, 3, 5, 1, 8, 253098313994239823068426070327268359748704010240000⟩, + ⟨5, 6, 4, 5, 2, 8, -58412466508877506188204300398924763726631403520000⟩, + ⟨5, 6, 5, 5, 3, 8, 4534823365931381992601838083439881448377548800000⟩, + ⟨5, 6, 6, 5, 4, 8, -353375404189078885410312228758053018455244800000⟩, + ⟨5, 6, 7, 5, 5, 8, -33852504883864748598832170697526866744442880000⟩, + ⟨5, 6, 8, 5, 6, 8, 11842530024850078806024834686553321363210240000⟩, + ⟨5, 6, 3, 6, 0, 8, 137837471115896946841785090503381614512140451840000⟩, + ⟨5, 6, 4, 6, 1, 8, 31344486399414875707043378255521166304089210880000⟩, + ⟨5, 6, 5, 6, 2, 8, 67115043902136026897963757854720477311795200000⟩, + ⟨5, 6, 6, 6, 3, 8, 1308474661281139024952383248179866970672332800000⟩, + ⟨5, 6, 7, 6, 4, 8, 12118708598769820655685266681532845402357760000⟩, + ⟨5, 6, 8, 6, 5, 8, -12428206940746449989273132730704963127214080000⟩, + ⟨5, 6, 4, 7, 0, 8, 598091432971421649545923324876989402572610600960000⟩, + ⟨5, 6, 5, 7, 1, 8, -3128672414582475972409729792323140503103078400000⟩, + ⟨5, 6, 6, 7, 2, 8, -1291304236289279234170675603589392434934579200000⟩, + ⟨5, 6, 7, 7, 3, 8, 507768602537912781893143276979884693011824640000⟩, + ⟨5, 6, 8, 7, 4, 8, 24573321019993497787475499552379214443315200000⟩ +] + +def collectedFourData_8_3_45 : List CollectedFourTerm := [ + ⟨6, 0, 2, 0, 5, 3, -8985023018637271713106250451810931561087578931200000⟩, + ⟨6, 0, 3, 0, 6, 3, -1442190038012530962520558582714967971220611399680000⟩, + ⟨6, 0, 4, 0, 7, 3, 10344781174695426484917500886349006024249222103040000⟩, + ⟨6, 0, 5, 0, 8, 3, 325059034006932798251792558775149025572369203200000⟩, + ⟨6, 0, 2, 1, 4, 3, 30967281978144494975135533022631256444426896015360000⟩, + ⟨6, 0, 3, 1, 5, 3, 19334616699840265075567228199026063724863385763840000⟩, + ⟨6, 0, 4, 1, 6, 3, 23177837403734742656910267248338396321327255388160000⟩, + ⟨6, 0, 5, 1, 7, 3, -2578217594072800622133254967033691185005513932800000⟩, + ⟨6, 0, 6, 1, 8, 3, -352563799768324982754722736634765002697762406400000⟩, + ⟨6, 0, 2, 2, 3, 3, -11541315829194094146561376142473653188989519134720000⟩, + ⟨6, 0, 3, 2, 4, 3, -25177826043306930767799113077859345228936333230080000⟩, + ⟨6, 0, 4, 2, 5, 3, -2941146097868602621193936912191963828371880673280000⟩, + ⟨6, 0, 5, 2, 6, 3, -1802040041378888989129338861277313325515302502400000⟩, + ⟨6, 0, 6, 2, 7, 3, -471770689723087871766600008841719099686492569600000⟩, + ⟨6, 0, 7, 2, 8, 3, -442502674669088236948387398274970873295148154880000⟩, + ⟨6, 0, 2, 3, 2, 3, -6171478448164352950179027974682746726309796249600000⟩, + ⟨6, 0, 3, 3, 3, 3, 33653734289086863842052748038714149876431627223040000⟩, + ⟨6, 0, 4, 3, 4, 3, 2017920004519040858711372280439693623541660385280000⟩, + ⟨6, 0, 5, 3, 5, 3, 680918417891168285195262136326042191533178880000000⟩, + ⟨6, 0, 6, 3, 6, 3, 1250054387441462476393922228813071859931571814400000⟩, + ⟨6, 0, 7, 3, 7, 3, 247084252226582408587203695882492669794052997120000⟩, + ⟨6, 0, 8, 3, 8, 3, 186348764424660980270343271368061172035092480000000⟩, + ⟨6, 0, 2, 4, 1, 3, -14246471194270363129080063736241304098957458145280000⟩, + ⟨6, 0, 3, 4, 2, 3, -46070435633902869134473464612853077507525574656000000⟩, + ⟨6, 0, 4, 4, 3, 3, 4510345052431519920142308462956191536337492377600000⟩, + ⟨6, 0, 5, 4, 4, 3, -2453082018858498079224829392475774400884585267200000⟩, + ⟨6, 0, 6, 4, 5, 3, -994544841185190264868323096566256632841476505600000⟩, + ⟨6, 0, 7, 4, 6, 3, -81148729759375879575480070742723684170570137600000⟩, + ⟨6, 0, 8, 4, 7, 3, 66196012258747373554838916840041918029690306560000⟩, + ⟨6, 0, 2, 5, 0, 3, 106293992254555074963058635578428190628815579381760000⟩, + ⟨6, 0, 3, 5, 1, 3, 38257917741425934079869686039889338690950838353920000⟩, + ⟨6, 0, 4, 5, 2, 3, -30903357522462690489120673850517571563151750594560000⟩, + ⟨6, 0, 5, 5, 3, 3, 6397778928797515332518952588173589506970510950400000⟩, + ⟨6, 0, 6, 5, 4, 3, -1121728333828208368992219086090040026581067366400000⟩, + ⟨6, 0, 7, 5, 5, 3, -214917696303338031208336634354076261746925895680000⟩, + ⟨6, 0, 8, 5, 6, 3, 137837471115896946841785090503381614512140451840000⟩, + ⟨6, 0, 3, 6, 0, 3, 20835281548964302679150086461458363530863150366720000⟩, + ⟨6, 0, 4, 6, 1, 3, 16582930450503611649927987382097045025865743728640000⟩, + ⟨6, 0, 5, 6, 2, 3, 94686645770648799420530146160401373338376601600000⟩, + ⟨6, 0, 6, 6, 3, 3, 4153523658567866155169663024957441706945832550400000⟩, + ⟨6, 0, 7, 6, 4, 3, 76937436185422969152411838613688947070845583360000⟩, + ⟨6, 0, 8, 6, 5, 3, -144654276714760999711163703402788186693597921280000⟩, + ⟨6, 0, 4, 7, 0, 3, 316422751664301460822590336207776983093387072634880000⟩, + ⟨6, 0, 5, 7, 1, 3, -4413965624218909531230853629113083521104294707200000⟩, + ⟨6, 0, 6, 7, 2, 3, -4099019151494319350216026782604486001815034265600000⟩, + ⟨6, 0, 7, 7, 3, 3, 3223645006093118342274145935961681931141161943040000⟩, + ⟨6, 0, 8, 7, 4, 3, 286013581490404247388022102281847782079935283200000⟩ +] + +def collectedFourData_8_3_46 : List CollectedFourTerm := [ + ⟨6, 1, 1, 0, 4, 4, 580736952849837534660447693352635519921763123200000⟩, + ⟨6, 1, 2, 0, 5, 4, -14302471647823008050192749673892936548508028108800000⟩, + ⟨6, 1, 3, 0, 6, 4, -1147848040381282201807774206687293740528340828160000⟩, + ⟨6, 1, 4, 0, 7, 4, 5488983877099905680310116519148255524625391288320000⟩, + ⟨6, 1, 5, 0, 8, 4, 129358255624647580661901789658747316385035059200000⟩, + ⟨6, 1, 1, 1, 3, 4, -2345416791860080630187619793192634954120555397120000⟩, + ⟨6, 1, 2, 1, 4, 4, 49294105489083822885821686203042261759540477296640000⟩, + ⟨6, 1, 3, 1, 5, 4, 15388541943486943267982047620757613315564324782080000⟩, + ⟨6, 1, 4, 1, 6, 4, 12298256837597037228472480752547233181293902561280000⟩, + ⟨6, 1, 5, 1, 7, 4, -1026009726537611305277964430100856341682506956800000⟩, + ⟨6, 1, 6, 1, 8, 4, -112243090302065809304115392648267307229611294720000⟩, + ⟨6, 1, 1, 2, 2, 4, -409458850131834161898880808708573257913157550080000⟩, + ⟨6, 1, 2, 2, 3, 4, -18371610410259687393671146465357700143999384289280000⟩, + ⟨6, 1, 3, 2, 4, 4, -20039188680500067515000644634043971014881139752960000⟩, + ⟨6, 1, 4, 2, 5, 4, -1560584340912496267698663003130635742322349834240000⟩, + ⟨6, 1, 5, 2, 6, 4, -717127450497404498041302806352293522743649894400000⟩, + ⟨6, 1, 6, 2, 7, 4, -150194092993247296943479565407341615108933550080000⟩, + ⟨6, 1, 7, 2, 8, 4, -117396878958327609758261540458633588836422123520000⟩, + ⟨6, 1, 1, 3, 1, 4, 2297891324630351480144692178266593982395973632000000⟩, + ⟨6, 1, 2, 3, 2, 4, -9823836327066929802832622434124294160531220070400000⟩, + ⟨6, 1, 3, 3, 3, 4, 26785216883397356687866026855802433060582436372480000⟩, + ⟨6, 1, 4, 3, 4, 4, 1070716739487579933737673317461698668315006730240000⟩, + ⟨6, 1, 5, 3, 5, 4, 270973606471794739606652350401149983292129280000000⟩, + ⟨6, 1, 6, 3, 6, 4, 397970431406416198274931734583236520186080133120000⟩, + ⟨6, 1, 7, 3, 7, 4, 65551965471948617460645153752824747307544084480000⟩, + ⟨6, 1, 8, 3, 8, 4, 42376040889093931311163510886695217513103360000000⟩, + ⟨6, 1, 1, 4, 0, 4, -18386585257472230765024018286422950015855136604160000⟩, + ⟨6, 1, 2, 4, 1, 4, -22677710442692067302909113053405341121780614430720000⟩, + ⟨6, 1, 3, 4, 2, 4, -36667746876662256393491261087483740131554230272000000⟩, + ⟨6, 1, 4, 4, 3, 4, 2393207826716822678394459994450027003847167180800000⟩, + ⟨6, 1, 5, 4, 4, 4, -976211634397942231570824881395756446833128243200000⟩, + ⟨6, 1, 6, 4, 5, 4, -316625775226944149809418910734427836705019002880000⟩, + ⟨6, 1, 7, 4, 6, 4, -21528926604359313251935541957860038489302630400000⟩, + ⟨6, 1, 8, 4, 7, 4, 15053091072711281395298899354741585649514577920000⟩, + ⟨6, 1, 2, 5, 0, 4, 169200101925311054195903135651209098057222444810240000⟩, + ⟨6, 1, 3, 5, 1, 4, 30449715190850932858794975522291143601434960855040000⟩, + ⟨6, 1, 4, 5, 2, 4, -16397449914550369727355479372154916724734930452480000⟩, + ⟨6, 1, 5, 5, 3, 4, 2546016063296742417319798649310569566413678182400000⟩, + ⟨6, 1, 6, 5, 4, 4, -357116229037128377892076948364092425244476702720000⟩, + ⟨6, 1, 7, 5, 5, 4, -57018111354453511020765170265944057029821726720000⟩, + ⟨6, 1, 8, 5, 6, 4, 31344486399414875707043378255521166304089210880000⟩, + ⟨6, 1, 3, 6, 0, 4, 16582930450503611649927987382097045025865743728640000⟩, + ⟨6, 1, 4, 6, 1, 4, 8798971804308207959407797884208335002795109253120000⟩, + ⟨6, 1, 5, 6, 2, 4, 37680845773936587194815345954845950696069529600000⟩, + ⟨6, 1, 6, 6, 3, 4, 1322326147456856575654402110199787712111622225920000⟩, + ⟨6, 1, 7, 6, 4, 4, 20411661669567565796925985126919005665692221440000⟩, + ⟨6, 1, 8, 6, 5, 4, -32894640132294894938393542286111922174516264960000⟩, + ⟨6, 1, 4, 7, 0, 4, 167895226868737946465682660676121619349602608087040000⟩, + ⟨6, 1, 5, 7, 1, 4, -1756551376215370796142292316187180410541912883200000⟩, + ⟨6, 1, 6, 7, 2, 4, -1304973956694941234993998762922853010038985850880000⟩, + ⟨6, 1, 7, 7, 3, 4, 855239717743943506999831331914379881173127004160000⟩, + ⟨6, 1, 8, 7, 4, 4, 65039997777788428830563529820131796390930022400000⟩ +] + +def collectedFourData_8_3_47 : List CollectedFourTerm := [ + ⟨6, 2, 0, 0, 3, 5, -359430602896809481051247469368588718218359603200000⟩, + ⟨6, 2, 1, 0, 4, 5, 9947825742478813833500345807439933550362624000000⟩, + ⟨6, 2, 2, 0, 5, 5, -122498228277955278433689458250775557002231808000000⟩, + ⟨6, 2, 3, 0, 6, 5, -6554081687945277176978420003863517683148390400000⟩, + ⟨6, 2, 4, 0, 7, 5, 23506104977783524195916796629924695376501145600000⟩, + ⟨6, 2, 5, 0, 8, 5, 443172551355712826240285473775777657703628800000⟩, + ⟨6, 2, 0, 1, 2, 5, 140592118290801174766739034144671176887946444800000⟩, + ⟨6, 2, 1, 1, 3, 5, -40176188934442991677139227939521457729988198400000⟩, + ⟨6, 2, 2, 1, 4, 5, 422195599169638269059132019044280566496519782400000⟩, + ⟨6, 2, 3, 1, 5, 5, 87866823314420213169737704074325816272696115200000⟩, + ⟨6, 2, 4, 1, 6, 5, 52666235270677644814735903614254351271749222400000⟩, + ⟨6, 2, 5, 1, 7, 5, -3515039268501184127617875886715169412428595200000⟩, + ⟨6, 2, 6, 1, 8, 5, -320447636301576857638178059799808765748838400000⟩, + ⟨6, 2, 0, 2, 1, 5, 145247363200476034704992434810553989047779328000000⟩, + ⟨6, 2, 1, 2, 2, 5, -7013890316155682265667875292610241846942105600000⟩, + ⟨6, 2, 2, 2, 3, 5, -157349707189400362018791744512890701102238924800000⟩, + ⟨6, 2, 3, 2, 4, 5, -114421486949194858344717667791500179902195302400000⟩, + ⟨6, 2, 4, 2, 5, 5, -6683069246608131775147728522226650745877299200000⟩, + ⟨6, 2, 5, 2, 6, 5, -2456829680869610418084307267942796913908121600000⟩, + ⟨6, 2, 6, 2, 7, 5, -428795589613764518305142466999967911877017600000⟩, + ⟨6, 2, 7, 2, 8, 5, -287281208288731215592471674899902596592435200000⟩, + ⟨6, 2, 0, 3, 0, 5, -811606535656657802372245316745765440397194035200000⟩, + ⟨6, 2, 1, 3, 1, 5, 39362093905684800299954760813063948195594240000000⟩, + ⟨6, 2, 2, 3, 2, 5, -84139481244242527350434663485191914954686464000000⟩, + ⟨6, 2, 3, 3, 3, 5, 152940540304275623504621243498636623322755891200000⟩, + ⟨6, 2, 4, 3, 4, 5, 4585253052913468187407604316748462255452979200000⟩, + ⟨6, 2, 5, 3, 5, 5, 928337074045105697765031080208122165329920000000⟩, + ⟨6, 2, 6, 3, 6, 5, 1136182937576851096571624057667775266973286400000⟩, + ⟨6, 2, 7, 3, 7, 5, 160411827073932109135802949217105199549644800000⟩, + ⟨6, 2, 8, 3, 8, 5, 90735889190493877971119615308804286054400000000⟩, + ⟨6, 2, 1, 4, 0, 5, -314955928399235626234238002140198262487069491200000⟩, + ⟨6, 2, 2, 4, 1, 5, -194230718929836286451628414073247761888916275200000⟩, + ⟨6, 2, 3, 4, 2, 5, -209368661955215066749234808523614704034119680000000⟩, + ⟨6, 2, 4, 4, 3, 5, 10248708261497211025085286268854747386609664000000⟩, + ⟨6, 2, 5, 4, 4, 5, -3344434404979980192551637473295532603264204800000⟩, + ⟨6, 2, 6, 4, 5, 5, -903948572607691622679042042499446618036633600000⟩, + ⟨6, 2, 7, 4, 6, 5, -52683308985200485075941240717016830050304000000⟩, + ⟨6, 2, 8, 4, 7, 5, 32231788880953849445727192451256205233356800000⟩, + ⟨6, 2, 2, 5, 0, 5, 1449169991080170072139408423918008559708038758400000⟩, + ⟨6, 2, 3, 5, 1, 5, 173864408627830061263574198288148873921272217600000⟩, + ⟨6, 2, 4, 5, 2, 5, -70220679763230615250207703310555936759113318400000⟩, + ⟨6, 2, 5, 5, 3, 5, 8722477194171884120452079097150899784096153600000⟩, + ⟨6, 2, 6, 5, 4, 5, -1019546514372601396678352485215211165738598400000⟩, + ⟨6, 2, 7, 5, 5, 5, -139528683126774802601181867596677620380467200000⟩, + ⟨6, 2, 8, 5, 6, 5, 67115043902136026897963757854720477311795200000⟩, + ⟨6, 2, 3, 6, 0, 5, 94686645770648799420530146160401373338376601600000⟩, + ⟨6, 2, 4, 6, 1, 5, 37680845773936587194815345954845950696069529600000⟩, + ⟨6, 2, 5, 6, 2, 5, 129092004822108943181141709269616646579814400000⟩, + ⟨6, 2, 6, 6, 3, 5, 3775165912057227928235668863906045621593702400000⟩, + ⟨6, 2, 7, 6, 4, 5, 49949256570063126958845917510133491328614400000⟩, + ⟨6, 2, 8, 6, 5, 5, -70434244431108314639038925611364451247718400000⟩, + ⟨6, 2, 4, 7, 0, 5, 718996979479286464550229502788508591622140723200000⟩, + ⟨6, 2, 5, 7, 1, 5, -6017825079858526064896043286263655044009164800000⟩, + ⟨6, 2, 6, 7, 2, 5, -3725626394752905367953230457352296148343193600000⟩, + ⟨6, 2, 7, 7, 3, 5, 2092852055949525509069048214567972159199641600000⟩, + ⟨6, 2, 8, 7, 4, 5, 139264119712377448626916639186375667613696000000⟩ +] + +def collectedFourData_8_3_48 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 3, 6, -63067119997526996950043467250576475186122666803200000⟩, + ⟨6, 3, 1, 0, 4, 6, 872742491539482167180145442407388998965133312000000⟩, + ⟨6, 3, 2, 0, 5, 6, -7164675090755734405850526794681144834770599936000000⟩, + ⟨6, 3, 3, 0, 6, 6, -287501295768844644528717131257398883545356697600000⟩, + ⟨6, 3, 4, 0, 7, 6, 824894892844695723106376583526066053757135749120000⟩, + ⟨6, 3, 5, 0, 8, 6, 12960135767842559601626035951751182674611404800000⟩, + ⟨6, 3, 0, 1, 2, 6, 24668851020173313919135175259492419479100247244800000⟩, + ⟨6, 3, 1, 1, 3, 6, -3524736775542831679169328356695873679952917299200000⟩, + ⟨6, 3, 2, 1, 4, 6, 24693371776232932148213778070810003105330810060800000⟩, + ⟨6, 3, 3, 1, 5, 6, 3854365380347829096524975669205820990416538828800000⟩, + ⟨6, 3, 4, 1, 6, 6, 1848205329687746194425106771119996640174779924480000⟩, + ⟨6, 3, 5, 1, 7, 6, -102793789935126811232014202750111780080661299200000⟩, + ⟨6, 3, 6, 1, 8, 6, -8032430567632125732258015078652157206147891200000⟩, + ⟨6, 3, 0, 2, 1, 6, 25485678766531433561183389024364354317559267328000000⟩, + ⟨6, 3, 1, 2, 2, 6, -615342514874113274752253946003997256154139852800000⟩, + ⟨6, 3, 2, 2, 3, 6, -9203068023804915270004360746153236482250873241600000⟩, + ⟨6, 3, 3, 2, 4, 6, -5019212046471236153728525360927407044722006425600000⟩, + ⟨6, 3, 4, 2, 5, 6, -234527570402024169042165302723651701804200099840000⟩, + ⟨6, 3, 5, 2, 6, 6, -71847514303696974022742187721300933170796953600000⟩, + ⟨6, 3, 6, 2, 7, 6, -10748310834903462231624318843263577444109516800000⟩, + ⟨6, 3, 7, 2, 8, 6, -6300937611516323462999515885693504034596454400000⟩, + ⟨6, 3, 0, 3, 0, 6, -142407703635994333580998715906700180719030973235200000⟩, + ⟨6, 3, 1, 3, 1, 6, 3453314603287199860976879845711312598461317120000000⟩, + ⟨6, 3, 2, 3, 2, 6, -4921149096555701811018463699681333617767743488000000⟩, + ⟨6, 3, 3, 3, 3, 6, 6708888537953416557861447351792658605421677772800000⟩, + ⟨6, 3, 4, 3, 4, 6, 160909339481113851749861167807494050711171235840000⟩, + ⟨6, 3, 5, 3, 5, 6, 27148284525160693050598882245314099879608320000000⟩, + ⟨6, 3, 6, 3, 6, 6, 28479881030002321827604162705675442575323955200000⟩, + ⟨6, 3, 7, 3, 7, 6, 3518311972310924011348316248856587964881305600000⟩, + ⟨6, 3, 8, 3, 8, 6, 1768986578444238161369142431551262923161600000000⟩, + ⟨6, 3, 1, 4, 0, 6, -27631708555420049843398553452544352855078312345600000⟩, + ⟨6, 3, 2, 4, 1, 6, -11360164251670307579151114694333086671179245158400000⟩, + ⟨6, 3, 3, 4, 2, 6, -9184164078428575355863327354472811500320849920000000⟩, + ⟨6, 3, 4, 4, 3, 6, 359655804785802418882774080356000954552470732800000⟩, + ⟨6, 3, 5, 4, 4, 6, -97804622200967340483808307684810002940087500800000⟩, + ⟨6, 3, 6, 4, 5, 6, -22658629128873124442789609201272921464294604800000⟩, + ⟨6, 3, 7, 4, 6, 6, -1155502808768319704126843876876416123404288000000⟩, + ⟨6, 3, 8, 4, 7, 6, 628390843340400638027387680092961327231795200000⟩, + ⟨6, 3, 2, 5, 0, 6, 84759039239356033619187466215747833212219215052800000⟩, + ⟨6, 3, 3, 5, 1, 6, 7626734781246808219295609022199248594114340454400000⟩, + ⟨6, 3, 4, 5, 2, 6, -2464239828909065808306115329419488313357295943680000⟩, + ⟨6, 3, 5, 5, 3, 6, 255080077325553475043856647126646672961673625600000⟩, + ⟨6, 3, 6, 5, 4, 6, -25556239645537904444411103699569245454283571200000⟩, + ⟨6, 3, 7, 5, 5, 6, -3060282058251577001729458436299136096953958400000⟩, + ⟨6, 3, 8, 5, 6, 6, 1308474661281139024952383248179866970672332800000⟩, + ⟨6, 3, 3, 6, 0, 6, 4153523658567866155169663024957441706945832550400000⟩, + ⟨6, 3, 4, 6, 1, 6, 1322326147456856575654402110199787712111622225920000⟩, + ⟨6, 3, 5, 6, 2, 6, 3775165912057227928235668863906045621593702400000⟩, + ⟨6, 3, 6, 6, 3, 6, 94629370401575572286682634727663545093403443200000⟩, + ⟨6, 3, 7, 6, 4, 6, 1095536847900172783335013572664571007388876800000⟩, + ⟨6, 3, 8, 6, 5, 6, -1373185783190022511263262389593677797890457600000⟩, + ⟨6, 3, 4, 7, 0, 6, 25231612676952792069987801420020982029270793584640000⟩, + ⟨6, 3, 5, 7, 1, 6, -175985245077812326766338537960027885719571660800000⟩, + ⟨6, 3, 6, 7, 2, 6, -93387598929351350168863837951416011875732684800000⟩, + ⟨6, 3, 7, 7, 3, 6, 45902515911928847781671167915583092361999155200000⟩, + ⟨6, 3, 8, 7, 4, 6, 2715092791043671911995913338566520806047744000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0816.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0816.lean new file mode 100644 index 0000000000000000000000000000000000000000..22b44c5dc31f69ea8b7714898076c4cd3f7d1d8e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0816.lean @@ -0,0 +1,660 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PartsTrace +import OAI.Analysis.LaughlinFock.Sparse0812 +import OAI.Analysis.LaughlinFock.Sparse0813 +import OAI.Analysis.LaughlinFock.Sparse0814 +import OAI.Analysis.LaughlinFock.Sparse0815 + +namespace OAI + +/-! Sparse0816. -/ +namespace LaughlinFock +def collectedFourData_8_3_49 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 3, 7, -2920545853999776636101952917121280392379446067200000⟩, + ⟨6, 4, 1, 0, 4, 7, 26943616741180055482335902027905518815674368000000⟩, + ⟨6, 4, 2, 0, 5, 7, -165892799071708366515830431501129172624867328000000⟩, + ⟨6, 4, 3, 0, 6, 7, -5325505381632696905561414924752829726683299840000⟩, + ⟨6, 4, 4, 0, 7, 7, 12733224324484950932920414500507632382341283840000⟩, + ⟨6, 4, 5, 0, 8, 7, 171475681262987336722622243357111635201228800000⟩, + ⟨6, 4, 0, 1, 2, 7, 1142378319681165673428916056328415959665396940800000⟩, + ⟨6, 4, 1, 1, 3, 7, -108816927919078544181904792585282818962934988800000⟩, + ⟨6, 4, 2, 1, 4, 7, 571756919970184965872813274972664288256616038400000⟩, + ⟨6, 4, 3, 1, 5, 7, 71396003697752684802660130851250536414361681920000⟩, + ⟨6, 4, 4, 1, 6, 7, 28529226286594853394524439589415495107199631360000⟩, + ⟨6, 4, 5, 1, 7, 7, -1360065625428593897266801287367979334578995200000⟩, + ⟨6, 4, 6, 1, 8, 7, -92992520479605539291422061413062167809228800000⟩, + ⟨6, 4, 0, 2, 1, 7, 1180204414929398532625708955498965528517541888000000⟩, + ⟨6, 4, 1, 2, 2, 7, -18997073072581054815614558650460258434233139200000⟩, + ⟨6, 4, 2, 2, 3, 7, -213090293024759247390854843219400488938949836800000⟩, + ⟨6, 4, 3, 2, 4, 7, -92972940151648649119573304931462657864672215040000⟩, + ⟨6, 4, 4, 2, 5, 7, -3620209301947569409898314509532433306489978880000⟩, + ⟨6, 4, 5, 2, 6, 7, -950615154267752043170342998668380577831321600000⟩, + ⟨6, 4, 6, 2, 7, 7, -124434628724163610101550331976655540794163200000⟩, + ⟨6, 4, 7, 2, 8, 7, -64841595988340479624791870921412179079987200000⟩, + ⟨6, 4, 0, 3, 0, 7, -6594691948007786952513920865872452742806713139200000⟩, + ⟨6, 4, 1, 3, 1, 7, 106611957203508394679864849616406329352519680000000⟩, + ⟨6, 4, 2, 3, 2, 7, -113945599477382802855581279634037302701850624000000⟩, + ⟨6, 4, 3, 3, 3, 7, 124271516474732211953636958004350497196626411520000⟩, + ⟨6, 4, 4, 3, 4, 7, 2483825191900508281325860857587622881399930880000⟩, + ⟨6, 4, 5, 3, 5, 7, 359199214226156013100092205145633241169920000000⟩, + ⟨6, 4, 6, 3, 6, 7, 329715382864485162143546798002050333199564800000⟩, + ⟨6, 4, 7, 3, 7, 7, 36206193035868830162384585218050891762892800000⟩, + ⟨6, 4, 8, 3, 8, 7, 16383834929069717384860277550952973598720000000⟩, + ⟨6, 4, 1, 4, 0, 7, -853055938536875197716931763719494176822683238400000⟩, + ⟨6, 4, 2, 4, 1, 7, -263036274744059748915182627551682204976493363200000⟩, + ⟨6, 4, 3, 4, 2, 7, -170122068822930466256676436346243561268707328000000⟩, + ⟨6, 4, 4, 4, 3, 7, 5551710989684833518314288636925518974392729600000⟩, + ⟨6, 4, 5, 4, 4, 7, -1294053899048915198169719876125791506713804800000⟩, + ⟨6, 4, 6, 4, 5, 7, -262321972853064585474307369257326907437875200000⟩, + ⟨6, 4, 7, 4, 6, 7, -11891031289154025692436949471689487417344000000⟩, + ⟨6, 4, 8, 4, 7, 7, 5819971713568636948232791219295959740579840000⟩, + ⟨6, 4, 2, 5, 0, 7, 1962533413997756261455410181082101640566564454400000⟩, + ⟨6, 4, 3, 5, 1, 7, 141273161963315791552983622140402878009793576960000⟩, + ⟨6, 4, 4, 5, 2, 7, -38038444416381037823510427897371403510098165760000⟩, + ⟨6, 4, 5, 5, 3, 7, 3374966961730838494782622292792087657683353600000⟩, + ⟨6, 4, 6, 5, 4, 7, -295867996443817229619914164512269888441548800000⟩, + ⟨6, 4, 7, 5, 5, 7, -31492705540971492490600105593559265260339200000⟩, + ⟨6, 4, 8, 5, 6, 7, 12118708598769820655685266681532845402357760000⟩, + ⟨6, 4, 3, 6, 0, 7, 76937436185422969152411838613688947070845583360000⟩, + ⟨6, 4, 4, 6, 1, 7, 20411661669567565796925985126919005665692221440000⟩, + ⟨6, 4, 5, 6, 2, 7, 49949256570063126958845917510133491328614400000⟩, + ⟨6, 4, 6, 6, 3, 7, 1095536847900172783335013572664571007388876800000⟩, + ⟨6, 4, 7, 6, 4, 7, 11273934462078904222343515756300209645158400000⟩, + ⟨6, 4, 8, 6, 5, 7, -12718044033164397637706615761469941135441920000⟩, + ⟨6, 4, 4, 7, 0, 7, 389479662283041916720532145964583758024125972480000⟩, + ⟨6, 4, 5, 7, 1, 7, -2328462473890825345513653202127369645378764800000⟩, + ⟨6, 4, 6, 7, 2, 7, -1081160693871885698921262547575959931007795200000⟩, + ⟨6, 4, 7, 7, 3, 7, 472372934810473459793090482211712126261657600000⟩, + ⟨6, 4, 8, 7, 4, 7, 25146393221755530988161784039058088709324800000⟩ +] + +def collectedFourData_8_3_50 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 3, 8, 10982155607692975823319547280984841765740819251200000⟩, + ⟨6, 5, 1, 0, 4, 8, -75987248568731987331362444459445736225898496000000⟩, + ⟨6, 5, 2, 0, 5, 8, 374284936722938807381769147330600707327577292800000⟩, + ⟨6, 5, 3, 0, 6, 8, 10012773590012108160629327404191596652338872320000⟩, + ⟨6, 5, 4, 0, 7, 8, -20520369123215529471364061625091874823402946560000⟩, + ⟨6, 5, 5, 0, 8, 8, -241800596794203819281710800267996170079436800000⟩, + ⟨6, 5, 0, 1, 2, 8, -4295695769478013514085594330216626635362061516800000⟩, + ⟨6, 5, 1, 1, 3, 8, 306888975956784149253537129338581459375069593600000⟩, + ⟨6, 5, 2, 1, 4, 8, -1289989703045760372442293909866533964788625571840000⟩, + ⟨6, 5, 3, 1, 5, 8, -134235526777009653464945715297749895427034972160000⟩, + ⟨6, 5, 4, 1, 6, 8, -45976591575076179148829111952165720809527050240000⟩, + ⟨6, 5, 5, 1, 7, 8, 1917850260081753177924656355380084224504627200000⟩, + ⟨6, 5, 6, 1, 8, 8, 116560211836194871461550521481255978637721600000⟩, + ⟨6, 5, 0, 2, 1, 8, -4437933585562492936801194250468735206448693248000000⟩, + ⟨6, 5, 1, 2, 2, 8, 53576152285387611336583984451226632236459622400000⟩, + ⟨6, 5, 2, 2, 3, 8, 480771240749088712929240762650471536906658119680000⟩, + ⟨6, 5, 3, 2, 4, 8, 174803503710065312255577966636159778672261201920000⟩, + ⟨6, 5, 4, 2, 5, 8, 5834188520217359968277877686241262347139153920000⟩, + ⟨6, 5, 5, 2, 6, 8, 1340477611347278666651307351361512860653977600000⟩, + ⟨6, 5, 6, 2, 7, 8, 155970895390750397619930834349457137886822400000⟩, + ⟨6, 5, 7, 2, 8, 8, 73147336072796707907696586261293442646671360000⟩, + ⟨6, 5, 0, 3, 0, 8, 24798081173296644647886647957607516467860026163200000⟩, + ⟨6, 5, 1, 3, 1, 8, -300670447113374480874008227698453171362856960000000⟩, + ⟨6, 5, 2, 3, 2, 8, 257082415444775222192693186839005168625149542400000⟩, + ⟨6, 5, 3, 3, 3, 8, -233649666835464581884821234525907472415153192960000⟩, + ⟨6, 5, 4, 3, 4, 8, -4002836082714009229926168060695012030986321920000⟩, + ⟨6, 5, 5, 3, 5, 8, -506512548765951274230214539022427089797120000000⟩, + ⟨6, 5, 6, 3, 6, 8, -413277268689206613311610866860876474456473600000⟩, + ⟨6, 5, 7, 3, 7, 8, -40843944840399515116303066296347928444272640000⟩, + ⟨6, 5, 8, 3, 8, 8, -16802259854831246273603615574869158133760000000⟩, + ⟨6, 5, 1, 4, 0, 8, 2405815606245722456309835269246081378240220364800000⟩, + ⟨6, 5, 2, 4, 1, 8, 593458643167880966118603393862702270467350200320000⟩, + ⟨6, 5, 3, 4, 2, 8, 319855795031838435116324811631550752823967744000000⟩, + ⟨6, 5, 4, 4, 3, 8, -8946921523614411791913253172369692993939046400000⟩, + ⟨6, 5, 5, 4, 4, 8, 1824766070437729931194795797141346753236172800000⟩, + ⟨6, 5, 6, 4, 5, 8, 328803914200255997576764693315769311061606400000⟩, + ⟨6, 5, 7, 4, 6, 8, 13414186506394654219234440454745428800307200000⟩, + ⟨6, 5, 8, 4, 7, 8, -5968607319501370067459725449600625771806720000⟩, + ⟨6, 5, 2, 5, 0, 8, -4427839537250137854473293255764699996734556733440000⟩, + ⟨6, 5, 3, 5, 1, 8, -265615389285386852894998406943065503776720814080000⟩, + ⟨6, 5, 4, 5, 2, 8, 61301277697283384321559477680445644552892579840000⟩, + ⟨6, 5, 5, 5, 3, 8, -4759094814474922074257297283072108852255129600000⟩, + ⟨6, 5, 6, 5, 4, 8, 370851721871601577422301743581307854231961600000⟩, + ⟨6, 5, 7, 5, 5, 8, 35526693643711253228918529349634099207208960000⟩, + ⟨6, 5, 8, 5, 6, 8, -12428206940746449989273132730704963127214080000⟩, + ⟨6, 5, 3, 6, 0, 8, -144654276714760999711163703402788186693597921280000⟩, + ⟨6, 5, 4, 6, 1, 8, -32894640132294894938393542286111922174516264960000⟩, + ⟨6, 5, 5, 6, 2, 8, -70434244431108314639038925611364451247718400000⟩, + ⟨6, 5, 6, 6, 3, 8, -1373185783190022511263262389593677797890457600000⟩, + ⟨6, 5, 7, 6, 4, 8, -12718044033164397637706615761469941135441920000⟩, + ⟨6, 5, 8, 6, 5, 8, 13042848735692661495274043375149391397519360000⟩, + ⟨6, 5, 4, 7, 0, 8, -627670276778590121209857865560824139829550776320000⟩, + ⟨6, 5, 5, 7, 1, 8, 3283402122404847703941676470807519269014732800000⟩, + ⟨6, 5, 6, 7, 2, 8, 1355166188170072399036167089644399405459046400000⟩, + ⟨6, 5, 7, 7, 3, 8, -532880495731291438893594141601452694312058880000⟩, + ⟨6, 5, 8, 7, 4, 8, -25788604142613527508702310131334149203558400000⟩ +] + +def collectedFourData_8_3_51 : List CollectedFourTerm := [ + ⟨7, 0, 1, 0, 4, 4, 11081176825915390545926128654327233488202655334400000⟩, + ⟨7, 0, 2, 0, 5, 4, -272908787015226981962711952607761427223742618009600000⟩, + ⟨7, 0, 3, 0, 6, 4, -21902355347506824520096779825571805281823458590720000⟩, + ⟨7, 0, 4, 0, 7, 4, 104736577616183121875920905810026552635348683325440000⟩, + ⟨7, 0, 5, 0, 8, 4, 2468314952982391414023896556893210464030713446400000⟩, + ⟨7, 0, 1, 1, 3, 4, -44753443144151072877139207308140461444947813335040000⟩, + ⟨7, 0, 2, 1, 4, 4, 940592288331798241319488324204442487493330080890880000⟩, + ⟨7, 0, 3, 1, 5, 4, 293632346851685634595041375690582432850105451151360000⟩, + ⟨7, 0, 4, 1, 6, 4, 234665898216354411103932986740289038856534894837760000⟩, + ⟨7, 0, 5, 1, 7, 4, -19577530152127542818009471414966104183281392025600000⟩, + ⟨7, 0, 6, 1, 8, 4, -2141736503972717907857903831499219328624219914240000⟩, + ⟨7, 0, 1, 2, 2, 4, -7812979523657176223902946978218185561153585807360000⟩, + ⟨7, 0, 2, 2, 3, 4, -350552969866815909076111420919771968052209133813760000⟩, + ⟨7, 0, 3, 2, 4, 4, -382372418574027519263516423236787136389215231672320000⟩, + ⟨7, 0, 4, 2, 5, 4, -29777872664282680696141318779722757805875218350080000⟩, + ⟨7, 0, 5, 2, 6, 4, -13683675624021121317150318943823578785775406284800000⟩, + ⟨7, 0, 6, 2, 7, 4, -2865888410404808440454768471349376807804977807360000⟩, + ⟨7, 0, 7, 2, 8, 4, -2240077143643017925141052292924190833755648163840000⟩, + ⟨7, 0, 1, 3, 1, 4, 43846598653676484503141405769663460324770054144000000⟩, + ⟨7, 0, 2, 3, 2, 4, -187450905121286331673673042921719781071432502476800000⟩, + ⟨7, 0, 3, 3, 3, 4, 511094951249240942316386329641998767934664773468160000⟩, + ⟨7, 0, 4, 3, 4, 4, 20430595061164233577709363067380157429261092782080000⟩, + ⟨7, 0, 5, 3, 5, 4, 5170510389832873523801761125768785666255093760000000⟩, + ⟨7, 0, 6, 3, 6, 4, 7593766334756776493842175710375617552375129047040000⟩, + ⟨7, 0, 7, 3, 7, 4, 1250812294820143664463530207339398606566362972160000⟩, + ⟨7, 0, 8, 3, 8, 4, 808587089163051976214640654370133461035909120000000⟩, + ⟨7, 0, 1, 4, 0, 4, -350838708408317273624790718491143292458273309982720000⟩, + ⟨7, 0, 2, 4, 1, 4, -432718665807644739643328758370368841022091548426240000⟩, + ⟨7, 0, 3, 4, 2, 4, -699665803862260474671066946669918849947899265024000000⟩, + ⟨7, 0, 4, 4, 3, 4, 45665354992264481242192248737413790715885492633600000⟩, + ⟨7, 0, 5, 4, 4, 4, -18627321177332742688034724242985056024285046374400000⟩, + ⟨7, 0, 6, 4, 5, 4, -6041610036548736597075265006062844945821031464960000⟩, + ⟨7, 0, 7, 4, 6, 4, -410798454281841180701428827531803209694497996800000⟩, + ⟨7, 0, 8, 4, 7, 4, 287231530789902211294671966464341550438169968640000⟩, + ⟨7, 0, 2, 5, 0, 4, 3228546485971739787223412159625446138824156596142080000⟩, + ⟨7, 0, 3, 5, 1, 4, 581018095495342622467542765649302167540159144263680000⟩, + ⟨7, 0, 4, 5, 2, 4, -312883554431238722714148574904421757215945428828160000⟩, + ⟨7, 0, 5, 5, 3, 4, 48581124484267588235325946310662040965266328780800000⟩, + ⟨7, 0, 6, 5, 4, 4, -6814217800236589404272143837978430166156957450240000⟩, + ⟨7, 0, 7, 5, 5, 4, -1087975840176656678732845507999601644536059658240000⟩, + ⟨7, 0, 8, 5, 6, 4, 598091432971421649545923324876989402572610600960000⟩, + ⟨7, 0, 3, 6, 0, 4, 316422751664301460822590336207776983093387072634880000⟩, + ⟨7, 0, 4, 6, 1, 4, 167895226868737946465682660676121619349602608087040000⟩, + ⟨7, 0, 5, 6, 2, 4, 718996979479286464550229502788508591622140723200000⟩, + ⟨7, 0, 6, 6, 3, 4, 25231612676952792069987801420020982029270793584640000⟩, + ⟨7, 0, 7, 6, 4, 4, 389479662283041916720532145964583758024125972480000⟩, + ⟨7, 0, 8, 6, 5, 4, -627670276778590121209857865560824139829550776320000⟩, + ⟨7, 0, 4, 7, 0, 4, 3203647861617536182058062958353794103143827169607680000⟩, + ⟨7, 0, 5, 7, 1, 4, -33517165229677701877353025139307929787982833254400000⟩, + ⟨7, 0, 6, 7, 2, 4, -24900511490423822615277302231488768296352701480960000⟩, + ⟨7, 0, 7, 7, 3, 4, 16319027908177752705597195626122078256584426782720000⟩, + ⟨7, 0, 8, 7, 4, 4, 1241043320208996173417283272684231518271098060800000⟩ +] + +def collectedFourData_8_3_52 : List CollectedFourTerm := [ + ⟨7, 1, 0, 0, 3, 5, 16755417963813713283699379241727163440545818214400000⟩, + ⟨7, 1, 1, 0, 4, 5, -463733407236530992743422745263392610800631808000000⟩, + ⟨7, 1, 2, 0, 5, 5, 5710445905500897877567021477620803700718043136000000⟩, + ⟨7, 1, 3, 0, 6, 5, 305528736744846598392033932567377591084567756800000⟩, + ⟨7, 1, 4, 0, 7, 5, -1095773733315408502646039141443448518019855155200000⟩, + ⟨7, 1, 5, 0, 8, 5, -20659179458312562029738317309379503728466329600000⟩, + ⟨7, 1, 0, 1, 2, 5, -6553920799717254526756664684412203727880559001600000⟩, + ⟨7, 1, 1, 1, 3, 5, 1872875688281342156530906643580499023503346892800000⟩, + ⟨7, 1, 2, 1, 4, 5, -19681306125736253175062411417335405179736739020800000⟩, + ⟨7, 1, 3, 1, 5, 5, -4096048967228189683586016410815410551902332518400000⟩, + ⟨7, 1, 4, 1, 6, 5, -2455118672224180538742641214098136872665271500800000⟩, + ⟨7, 1, 5, 1, 7, 5, 163859036009418635186213238166497317511128678400000⟩, + ⟨7, 1, 6, 1, 8, 5, 14938166195299072477476566902709155804269772800000⟩, + ⟨7, 1, 0, 2, 1, 5, -6770932299452885064027202103032441248443006976000000⟩, + ⟨7, 1, 1, 2, 2, 5, 326963432864044383482462457923926606096839475200000⟩, + ⟨7, 1, 2, 2, 3, 5, 7335101933985903785172662853212368823324875161600000⟩, + ⟨7, 1, 3, 2, 4, 5, 5333936015529616734525691904938646571582278860800000⟩, + ⟨7, 1, 4, 2, 5, 5, 311541692904143221087884382937660003415647846400000⟩, + ⟨7, 1, 5, 2, 6, 5, 114528946164029567055012848220339714714186547200000⟩, + ⟨7, 1, 6, 2, 7, 5, 19988974970729566980710497854316661901046579200000⟩, + ⟨7, 1, 7, 2, 8, 5, 13392061441716051667205790920923532679865958400000⟩, + ⟨7, 1, 0, 3, 0, 5, 37834304083991202702639761022803783534382573158400000⟩, + ⟨7, 1, 1, 3, 1, 5, -1834925379211464338111119112618519233120174080000000⟩, + ⟨7, 1, 2, 3, 2, 5, 3922293105104608211819028525233539602960089088000000⟩, + ⟨7, 1, 3, 3, 3, 5, -7129561745039662617103089678699399416203601510400000⟩, + ⟨7, 1, 4, 3, 4, 5, -213748720204202637227027161663233634888738406400000⟩, + ⟨7, 1, 5, 3, 5, 5, -43275880132541985631390392169801655663984640000000⟩, + ⟨7, 1, 6, 3, 6, 5, -52964939126007824269746831971499083907779788800000⟩, + ⟨7, 1, 7, 3, 7, 5, -7477847426737850648720993722420968482773401600000⟩, + ⟨7, 1, 8, 3, 8, 5, -4229794946373796628843344026447993687244800000000⟩, + ⟨7, 1, 1, 4, 0, 5, 14682161668980752181262207239963749186043012710400000⟩, + ⟨7, 1, 2, 4, 1, 5, 9054367799660498242984496022498039975335323238400000⟩, + ⟨7, 1, 3, 4, 2, 5, 9760046616262098215542871676690939391833538560000000⟩, + ⟨7, 1, 4, 4, 3, 5, -477759514984528552292508362786799232103743488000000⟩, + ⟨7, 1, 5, 4, 4, 5, 155906024296117632003111720239346374359488921600000⟩, + ⟨7, 1, 6, 4, 5, 5, 42138972112463732889670371206942200494764851200000⟩, + ⟨7, 1, 7, 4, 6, 5, 2455914590047313578885854905048677239226368000000⟩, + ⟨7, 1, 8, 4, 7, 5, -1502535093198039701568146818288325320350105600000⟩, + ⟨7, 1, 2, 5, 0, 5, -67555318621924657478998320362265778600964574412800000⟩, + ⟨7, 1, 3, 5, 1, 5, -8104960490598366906877056513088362694143324979200000⟩, + ⟨7, 1, 4, 5, 2, 5, 3273446472430264870433570731261069640254409932800000⟩, + ⟨7, 1, 5, 5, 3, 5, -406611874142896819402353858437662455262032691200000⟩, + ⟨7, 1, 6, 5, 4, 5, 47527750403509060378040831510777784364223692800000⟩, + ⟨7, 1, 7, 5, 5, 5, 6504347111480712816580824556178897918912102400000⟩, + ⟨7, 1, 8, 5, 6, 5, -3128672414582475972409729792323140503103078400000⟩, + ⟨7, 1, 3, 6, 0, 5, -4413965624218909531230853629113083521104294707200000⟩, + ⟨7, 1, 4, 6, 1, 5, -1756551376215370796142292316187180410541912883200000⟩, + ⟨7, 1, 5, 6, 2, 5, -6017825079858526064896043286263655044009164800000⟩, + ⟨7, 1, 6, 6, 3, 5, -175985245077812326766338537960027885719571660800000⟩, + ⟨7, 1, 7, 6, 4, 5, -2328462473890825345513653202127369645378764800000⟩, + ⟨7, 1, 8, 6, 5, 5, 3283402122404847703941676470807519269014732800000⟩, + ⟨7, 1, 4, 7, 0, 5, -33517165229677701877353025139307929787982833254400000⟩, + ⟨7, 1, 5, 7, 1, 5, 280530298849089120138190261040117558302841241600000⟩, + ⟨7, 1, 6, 7, 2, 5, 173675883238643026054274721066536697941144371200000⟩, + ⟨7, 1, 7, 7, 3, 5, -97561561679066516308405540358470550837998387200000⟩, + ⟨7, 1, 8, 7, 4, 5, -6492014075421916318510041399673453000261632000000⟩ +] + +def collectedFourData_8_3_53 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 3, 6, 62239523342113057513982808029465441849641323724800000⟩, + ⟨7, 2, 1, 0, 4, 6, -861289950705779503332867090861337217668743168000000⟩, + ⟨7, 2, 2, 0, 5, 6, 7070656826682957398801858871134510312539029504000000⟩, + ⟨7, 2, 3, 0, 6, 6, 283728567430927841383905375350949441727522406400000⟩, + ⟨7, 2, 4, 0, 7, 6, -814070230890684194377680653117370340159971655680000⟩, + ⟨7, 2, 5, 0, 8, 6, -12790066720522852415747260997766712810222387200000⟩, + ⟨7, 2, 0, 1, 2, 6, -24345134658969556177416925012475234020656100147200000⟩, + ⟨7, 2, 1, 1, 3, 6, 3478483508122848884149687249985935885057445068800000⟩, + ⟨7, 2, 2, 1, 4, 6, -24369333642040270570701527279669478905800241971200000⟩, + ⟨7, 2, 3, 1, 5, 6, -3803786570063734603533946600881235488652079923200000⟩, + ⟨7, 2, 4, 1, 6, 6, -1823952302921536260848720803064639597933462814720000⟩, + ⟨7, 2, 5, 1, 7, 6, 101444881078166641255486155744127668567461068800000⟩, + ⟨7, 2, 6, 1, 8, 6, 7927025204696927389762928532588097801342156800000⟩, + ⟨7, 2, 0, 2, 1, 6, -25151243604295350368545865844542174286726561792000000⟩, + ⟨7, 2, 1, 2, 2, 6, 607267698594825628968623480765835835048407859200000⟩, + ⟨7, 2, 2, 2, 3, 6, 9082301001046517895057932089843992046906795622400000⟩, + ⟨7, 2, 3, 2, 4, 6, 4953347565856997982396636762445968851880797798400000⟩, + ⟨7, 2, 4, 2, 5, 6, 231449988408828930581664741956597232678217973760000⟩, + ⟨7, 2, 5, 2, 6, 6, 70904697150481853701986647765239261257164390400000⟩, + ⟨7, 2, 6, 2, 7, 6, 10607266403214424970589375295660686746792755200000⟩, + ⟨7, 2, 7, 2, 8, 6, 6218253720235616767454193035319350973274521600000⟩, + ⟨7, 2, 0, 3, 0, 6, 140538962218296017630787041055502971989459258572800000⟩, + ⟨7, 2, 1, 3, 1, 6, -3407998571480377726185313783870470961684807680000000⟩, + ⟨7, 2, 2, 3, 2, 6, 4856571444472294018616712805800033205755052032000000⟩, + ⟨7, 2, 3, 3, 3, 6, -6620851321163227344643310421203903114745426739200000⟩, + ⟨7, 2, 4, 3, 4, 6, -158797810824269242428355702285644771870124277760000⟩, + ⟨7, 2, 5, 3, 5, 6, -26792031861742258652203876322304483372564480000000⟩, + ⟨7, 2, 6, 3, 6, 6, -28106154525796310060075479306754650425576652800000⟩, + ⟨7, 2, 7, 3, 7, 6, -3472143014205630518008797901963607763478118400000⟩, + ⟨7, 2, 8, 3, 8, 6, -1745773097697852296250544102639583782502400000000⟩, + ⟨7, 2, 1, 4, 0, 6, 27269112172633978889346962946073962942455768678400000⟩, + ⟨7, 2, 2, 4, 1, 6, 11211090789301897481681559453279405918448621977600000⟩, + ⟨7, 2, 3, 4, 2, 6, 9063645122205770539874301900223420239320186880000000⟩, + ⟨7, 2, 4, 4, 3, 6, -354936230764464353733825865908007841865872179200000⟩, + ⟨7, 2, 5, 4, 4, 6, 96521183568908060679083520377755467347342131200000⟩, + ⟨7, 2, 6, 4, 5, 6, 22361291852586279921224522331468969486267187200000⟩, + ⟨7, 2, 7, 4, 6, 6, 1140339752965302656235937268744227475423232000000⟩, + ⟨7, 2, 8, 4, 7, 6, -620144800707382786026362992687477060062412800000⟩, + ⟨7, 2, 2, 5, 0, 6, -83646790933212666042952956869238060490968740659200000⟩, + ⟨7, 2, 3, 5, 1, 6, -7526653150803932063172118259388717966611290521600000⟩, + ⟨7, 2, 4, 5, 2, 6, 2431902905316821061472968692227152399857897963520000⟩, + ⟨7, 2, 5, 5, 3, 6, -251732795590385689623046176938789518514218598400000⟩, + ⟨7, 2, 6, 5, 4, 6, 25220878549987106503538852484461829938793676800000⟩, + ⟨7, 2, 7, 5, 5, 6, 3020123585879101395912288291159515864865177600000⟩, + ⟨7, 2, 8, 5, 6, 6, -1291304236289279234170675603589392434934579200000⟩, + ⟨7, 2, 3, 6, 0, 6, -4099019151494319350216026782604486001815034265600000⟩, + ⟨7, 2, 4, 6, 1, 6, -1304973956694941234993998762922853010038985850880000⟩, + ⟨7, 2, 5, 6, 2, 6, -3725626394752905367953230457352296148343193600000⟩, + ⟨7, 2, 6, 6, 3, 6, -93387598929351350168863837951416011875732684800000⟩, + ⟨7, 2, 7, 6, 4, 6, -1081160693871885698921262547575959931007795200000⟩, + ⟨7, 2, 8, 6, 5, 6, 1355166188170072399036167089644399405459046400000⟩, + ⟨7, 2, 4, 7, 0, 6, -24900511490423822615277302231488768296352701480960000⟩, + ⟨7, 2, 5, 7, 1, 6, 173675883238643026054274721066536697941144371200000⟩, + ⟨7, 2, 6, 7, 2, 6, 92162122571241130841794260099591567381312307200000⟩, + ⟨7, 2, 7, 7, 3, 6, -45300161330884286443075985793095860688309452800000⟩, + ⟨7, 2, 8, 7, 4, 6, -2679464055926318356249693123700696354390016000000⟩ +] + +def collectedFourData_8_3_54 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 3, 7, -122369596962162963993723629736470570219969760460800000⟩, + ⟨7, 3, 1, 0, 4, 7, 1128925785159558141386991383853515734045949952000000⟩, + ⟨7, 3, 2, 0, 5, 7, -6950835897175948830767079666343603183017787392000000⟩, + ⟨7, 3, 3, 0, 6, 7, -223136351815099022268451565177202025640503541760000⟩, + ⟨7, 3, 4, 0, 7, 7, 533516543314013100004387460092461471158249717760000⟩, + ⟨7, 3, 5, 0, 8, 7, 7184756225014121863487475210618857684415283200000⟩, + ⟨7, 3, 0, 1, 2, 7, 47865153141234636366147788371278705118843974451200000⟩, + ⟨7, 3, 1, 1, 3, 7, -4559381799769338065805047370813499802893103923200000⟩, + ⟨7, 3, 2, 1, 4, 7, 23956365472317131477142110094063146121620461977600000⟩, + ⟨7, 3, 3, 1, 5, 7, 2991461402750419157374822460115027476635063418880000⟩, + ⟨7, 3, 4, 1, 6, 7, 1195362133264155335076826246155304105879315415040000⟩, + ⟨7, 3, 5, 1, 7, 7, -56986156268649998773467729542230980420226252800000⟩, + ⟨7, 3, 6, 1, 8, 7, -3896346032711830697178898827517198433727283200000⟩, + ⟨7, 3, 0, 2, 1, 7, 49450050027492870962224629107698869325352927232000000⟩, + ⟨7, 3, 1, 2, 2, 7, -795969072756999856546462607430275846330174668800000⟩, + ⟨7, 3, 2, 2, 3, 7, -8928390300147976829381134364208909102355788595200000⟩, + ⟨7, 3, 3, 2, 4, 7, -3895525625513912480422893997731856527993140674560000⟩, + ⟨7, 3, 4, 2, 5, 7, -151685190147345406173542329072127440813629112320000⟩, + ⟨7, 3, 5, 2, 6, 7, -39830360182346270555439641762871542527977062400000⟩, + ⟨7, 3, 6, 2, 7, 7, -5213756649038201393614082554207940111027404800000⟩, + ⟨7, 3, 7, 2, 8, 7, -2716834579607745556430246198270849167707340800000⟩, + ⟨7, 3, 0, 3, 0, 7, -276314715162625200229361519541938766730712894668800000⟩, + ⟨7, 3, 1, 3, 1, 7, 4466994488880805822466930643061174991081963520000000⟩, + ⟨7, 3, 2, 3, 2, 7, -4774270900271387024675034837715480924322267136000000⟩, + ⟨7, 3, 3, 3, 3, 7, 5206922316957718498722010277685644851011680993280000⟩, + ⟨7, 3, 4, 3, 4, 7, 104071191774329020690267680223073075615571640320000⟩, + ⟨7, 3, 5, 3, 5, 7, 15050290346848191027101871253596410877050880000000⟩, + ⟨7, 3, 6, 3, 6, 7, 13814930677460744243286967976330557492769587200000⟩, + ⟨7, 3, 7, 3, 7, 7, 1517023690371368197874216865624934935900979200000⟩, + ⟨7, 3, 8, 3, 8, 7, 686475534776870681177981061517696649134080000000⟩, + ⟨7, 3, 1, 4, 0, 7, -35742671611190208330345332474549022611060922777600000⟩, + ⟨7, 3, 2, 4, 1, 7, -11021105141279462458057827049892039685617536204800000⟩, + ⟨7, 3, 3, 4, 2, 7, -7128040454396831674685111340193636271775547392000000⟩, + ⟨7, 3, 4, 4, 3, 7, 232614268092294743907393147101589850391209574400000⟩, + ⟨7, 3, 5, 4, 4, 7, -54220293736207636673863297777858564018352947200000⟩, + ⟨7, 3, 6, 4, 5, 7, -10991176203717780299348511482423465017658572800000⟩, + ⟨7, 3, 7, 4, 6, 7, -498229022607346640977712731720805007753216000000⟩, + ⟨7, 3, 8, 4, 7, 7, 243854275372947979112350129201972374153461760000⟩, + ⟨7, 3, 2, 5, 0, 7, 82229293735205128618108639828677550708287445401600000⟩, + ⟨7, 3, 3, 5, 1, 7, 5919283844609223051925174831051394395789527613440000⟩, + ⟨7, 3, 4, 5, 2, 7, -1593794223749428521039025639895791800941165936640000⟩, + ⟨7, 3, 5, 5, 3, 7, 141409643098741762962485290802098350357636710400000⟩, + ⟨7, 3, 6, 5, 4, 7, -12396739955049289385290108074729188699091763200000⟩, + ⟨7, 3, 7, 5, 5, 7, -1319530620968998018881149748234745816075468800000⟩, + ⟨7, 3, 8, 5, 6, 7, 507768602537912781893143276979884693011824640000⟩, + ⟨7, 3, 3, 6, 0, 7, 3223645006093118342274145935961681931141161943040000⟩, + ⟨7, 3, 4, 6, 1, 7, 855239717743943506999831331914379881173127004160000⟩, + ⟨7, 3, 5, 6, 2, 7, 2092852055949525509069048214567972159199641600000⟩, + ⟨7, 3, 6, 6, 3, 7, 45902515911928847781671167915583092361999155200000⟩, + ⟨7, 3, 7, 6, 4, 7, 472372934810473459793090482211712126261657600000⟩, + ⟨7, 3, 8, 6, 5, 7, -532880495731291438893594141601452694312058880000⟩, + ⟨7, 3, 4, 7, 0, 7, 16319027908177752705597195626122078256584426782720000⟩, + ⟨7, 3, 5, 7, 1, 7, -97561561679066516308405540358470550837998387200000⟩, + ⟨7, 3, 6, 7, 2, 7, -45300161330884286443075985793095860688309452800000⟩, + ⟨7, 3, 7, 7, 3, 7, 19792219858293701619327636189106827413579366400000⟩, + ⟨7, 3, 8, 7, 4, 7, 1053622903877381243506989614482633771922227200000⟩ +] + +def collectedFourData_8_3_55 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 3, 8, -21714156879266828174184540742998235314628067328000000⟩, + ⟨7, 4, 1, 0, 4, 8, 150243640245770095790421801811631904380682240000000⟩, + ⟨7, 4, 2, 0, 5, 8, -740044315876858287954846645272581718547628032000000⟩, + ⟨7, 4, 3, 0, 6, 8, -19797473674275854174380675746377818377604300800000⟩, + ⟨7, 4, 4, 0, 7, 8, 40573320054747314838993027344940131624052326400000⟩, + ⟨7, 4, 5, 0, 8, 8, 478093398040337770221572497363960848187392000000⟩, + ⟨7, 4, 0, 1, 2, 8, 8493543087179332664086936597297041921741422592000000⟩, + ⟨7, 4, 1, 1, 3, 8, -606787556695623103611207301536412848655171584000000⟩, + ⟨7, 4, 2, 1, 4, 8, 2550595692247594765886422651681762316438313369600000⟩, + ⟨7, 4, 3, 1, 5, 8, 265413402553246631957096088051409500829541990400000⟩, + ⟨7, 4, 4, 1, 6, 8, 90905916643162904326927917641985911890221465600000⟩, + ⟨7, 4, 5, 1, 7, 8, -3792015238719254241939826824089762443296768000000⟩, + ⟨7, 4, 6, 1, 8, 8, -230465385494879074479152254518415174139904000000⟩, + ⟨7, 4, 0, 2, 1, 8, 8774778790164559835239026388966004329933701120000000⟩, + ⟨7, 4, 1, 2, 2, 8, -105931933335333984588015128848210615081107456000000⟩, + ⟨7, 4, 2, 2, 3, 8, -950591351788222415464574497729900858351760179200000⟩, + ⟨7, 4, 3, 2, 4, 8, -345625288713535640615826874110421734328683724800000⟩, + ⟨7, 4, 4, 2, 5, 8, -11535484409133225241441382457353074843110604800000⟩, + ⟨7, 4, 5, 2, 6, 8, -2650421482422817641108817620833205479276544000000⟩, + ⟨7, 4, 6, 2, 7, 8, -308389046021351226664008846727908169875456000000⟩, + ⟨7, 4, 7, 2, 8, 8, -144628503503678063812586035884315543758438400000⟩, + ⟨7, 4, 0, 3, 0, 8, -49031305340871322897497052949060712464916676608000000⟩, + ⟨7, 4, 1, 3, 1, 8, 594492146241827043045737470592916308518502400000000⟩, + ⟨7, 4, 2, 3, 2, 8, -508308942186021309340955589372098963891552256000000⟩, + ⟨7, 4, 3, 3, 3, 8, 461977202080411816362014219444572572103370342400000⟩, + ⟨7, 4, 4, 3, 4, 8, 7914494546148651431952519850150274127416524800000⟩, + ⟨7, 4, 5, 3, 5, 8, 1001487625755069027487296264516301278412800000000⟩, + ⟨7, 4, 6, 3, 6, 8, 817140802545731247542757496783944793718784000000⟩, + ⟨7, 4, 7, 3, 7, 8, 80757535907731104466427247814697499072921600000⟩, + ⟨7, 4, 8, 3, 8, 8, 33221793557399451645992414752029435494400000000⟩, + ⟨7, 4, 1, 4, 0, 8, -4756830932172720596657807487646129148198387712000000⟩, + ⟨7, 4, 2, 4, 1, 8, -1173399334287092746048699434217820009016380620800000⟩, + ⟨7, 4, 3, 4, 2, 8, -632425833339924492761846618010895789703823360000000⟩, + ⟨7, 4, 4, 4, 3, 8, 17690047791178921332959759258398546005590016000000⟩, + ⟨7, 4, 5, 4, 4, 8, -3607967154799020224434499296961170853855232000000⟩, + ⟨7, 4, 6, 4, 5, 8, -650118249140451509218915964199569159356416000000⟩, + ⟨7, 4, 7, 4, 6, 8, -26522821257746367989451864289879384915968000000⟩, + ⟨7, 4, 8, 4, 7, 8, 11801260182072653298442954802438054137036800000⟩, + ⟨7, 4, 2, 5, 0, 8, 8754820618341913369112372503103371629825726873600000⟩, + ⟨7, 4, 3, 5, 1, 8, 525180523616895249987293099555529497746027315200000⟩, + ⟨7, 4, 4, 5, 2, 8, -121206219285936512562147642576630805241108889600000⟩, + ⟨7, 4, 5, 5, 3, 8, 9409785755760414120353474091447642356711424000000⟩, + ⟨7, 4, 6, 5, 4, 8, -733256088816048506124626864292147970965504000000⟩, + ⟨7, 4, 7, 5, 5, 8, -70244151215705890213226395163843417761382400000⟩, + ⟨7, 4, 8, 5, 6, 8, 24573321019993497787475499552379214443315200000⟩, + ⟨7, 4, 3, 6, 0, 8, 286013581490404247388022102281847782079935283200000⟩, + ⟨7, 4, 4, 6, 1, 8, 65039997777788428830563529820131796390930022400000⟩, + ⟨7, 4, 5, 6, 2, 8, 139264119712377448626916639186375667613696000000⟩, + ⟨7, 4, 6, 6, 3, 8, 2715092791043671911995913338566520806047744000000⟩, + ⟨7, 4, 7, 6, 4, 8, 25146393221755530988161784039058088709324800000⟩, + ⟨7, 4, 8, 6, 5, 8, -25788604142613527508702310131334149203558400000⟩, + ⟨7, 4, 4, 7, 0, 8, 1241043320208996173417283272684231518271098060800000⟩, + ⟨7, 4, 5, 7, 1, 8, -6492014075421916318510041399673453000261632000000⟩, + ⟨7, 4, 6, 7, 2, 8, -2679464055926318356249693123700696354390016000000⟩, + ⟨7, 4, 7, 7, 3, 8, 1053622903877381243506989614482633771922227200000⟩, + ⟨7, 4, 8, 7, 4, 8, 50989788895156187583344873561684805943296000000⟩ +] + +def collectedFourData_8_3 : List (List CollectedFourTerm) := [ + collectedFourData_8_3_0, + collectedFourData_8_3_1, + collectedFourData_8_3_2, + collectedFourData_8_3_3, + collectedFourData_8_3_4, + collectedFourData_8_3_5, + collectedFourData_8_3_6, + collectedFourData_8_3_7, + collectedFourData_8_3_8, + collectedFourData_8_3_9, + collectedFourData_8_3_10, + collectedFourData_8_3_11, + collectedFourData_8_3_12, + collectedFourData_8_3_13, + collectedFourData_8_3_14, + collectedFourData_8_3_15, + collectedFourData_8_3_16, + collectedFourData_8_3_17, + collectedFourData_8_3_18, + collectedFourData_8_3_19, + collectedFourData_8_3_20, + collectedFourData_8_3_21, + collectedFourData_8_3_22, + collectedFourData_8_3_23, + collectedFourData_8_3_24, + collectedFourData_8_3_25, + collectedFourData_8_3_26, + collectedFourData_8_3_27, + collectedFourData_8_3_28, + collectedFourData_8_3_29, + collectedFourData_8_3_30, + collectedFourData_8_3_31, + collectedFourData_8_3_32, + collectedFourData_8_3_33, + collectedFourData_8_3_34, + collectedFourData_8_3_35, + collectedFourData_8_3_36, + collectedFourData_8_3_37, + collectedFourData_8_3_38, + collectedFourData_8_3_39, + collectedFourData_8_3_40, + collectedFourData_8_3_41, + collectedFourData_8_3_42, + collectedFourData_8_3_43, + collectedFourData_8_3_44, + collectedFourData_8_3_45, + collectedFourData_8_3_46, + collectedFourData_8_3_47, + collectedFourData_8_3_48, + collectedFourData_8_3_49, + collectedFourData_8_3_50, + collectedFourData_8_3_51, + collectedFourData_8_3_52, + collectedFourData_8_3_53, + collectedFourData_8_3_54, + collectedFourData_8_3_55 +] + +theorem collectedFourChecked_8_3 : collectNumericRowParts 8 3 = collectedFourData_8_3 := by + decide +kernel + +def collectedFourData_8_4_0 : List CollectedFourTerm := [ + ⟨0, 4, 4, 0, 8, 0, 3188267756893289755659608583063857779664800972800000⟩, + ⟨0, 4, 4, 1, 7, 0, -3718310024326781545233358360315978344748076236800000⟩, + ⟨0, 4, 5, 1, 8, 0, -18251999086355370931237084206484977768443412480000000⟩, + ⟨0, 4, 4, 2, 6, 0, 2451456550626464195752343106258193547066867712000000⟩, + ⟨0, 4, 5, 2, 7, 0, -9355763313468361111966814054150593710070431744000000⟩, + ⟨0, 4, 6, 2, 8, 0, 8291965146675613845677179745412329459284967424000000⟩, + ⟨0, 4, 4, 3, 5, 0, 6726048881095939321466195573698692402664754380800000⟩, + ⟨0, 4, 5, 3, 6, 0, 6401353373465336945410484524876050553368477696000000⟩, + ⟨0, 4, 6, 3, 7, 0, 17581184331250784710068825390445610907205632000000⟩, + ⟨0, 4, 7, 3, 8, 0, -937953538178475979241245847302114882621538304000000⟩, + ⟨0, 4, 4, 4, 4, 0, -5040943512353746722593803047392846958487928832000000⟩, + ⟨0, 4, 5, 4, 5, 0, 3881472376803017318040818402069113566589353984000000⟩, + ⟨0, 4, 6, 4, 6, 0, 3552960559738264514863764314403350818672607232000000⟩, + ⟨0, 4, 7, 4, 7, 0, -2480964812645535936626445725779952872244379648000000⟩, + ⟨0, 4, 8, 4, 8, 0, 664367554802912440142044375451778734232698880000000⟩, + ⟨0, 4, 4, 5, 3, 0, -4803433911613591707716638603360738008578496921600000⟩, + ⟨0, 4, 5, 5, 4, 0, 2574722825081172232617745110726481352545271808000000⟩, + ⟨0, 4, 6, 5, 5, 0, 2968076785650361598110523368077486261729755136000000⟩, + ⟨0, 4, 7, 5, 6, 0, 785964843287451455974518254039023247362621440000000⟩, + ⟨0, 4, 8, 5, 7, 0, -1089232092759380684402569020598285145041010688000000⟩, + ⟨0, 4, 4, 6, 2, 0, 6084017578954440255578283354216964140247390617600000⟩, + ⟨0, 4, 5, 6, 3, 0, -23462299154294470723066048005051210234077380608000000⟩, + ⟨0, 4, 6, 6, 4, 0, -1978989723302179150435369594277655481392562176000000⟩, + ⟨0, 4, 7, 6, 5, 0, 4910466868032178412600674345667949568947388416000000⟩, + ⟨0, 4, 8, 6, 6, 0, 1627025746029189515774021747892863212902678528000000⟩, + ⟨0, 4, 4, 7, 1, 0, 5844412568967825232686513277078469449476577689600000⟩, + ⟨0, 4, 5, 7, 2, 0, 1299804786025869516450414596723238967783194624000000⟩, + ⟨0, 4, 6, 7, 3, 0, -9990317220858350520484474588988577476606164992000000⟩, + ⟨0, 4, 7, 7, 4, 0, 3818327639731821099239250280548782339071672320000000⟩, + ⟨0, 4, 8, 7, 5, 0, 4202779714765299985038138168270612037348884480000000⟩ +] + +def collectedFourData_8_4_1 : List CollectedFourTerm := [ + ⟨0, 5, 3, 0, 7, 1, 2738292973182149077686094497665222490090236805120000⟩, + ⟨0, 5, 4, 0, 8, 1, -10568502734428748029760526900472787977712141598720000⟩, + ⟨0, 5, 3, 1, 6, 1, -12984178986386778789418956656422078363827060080640000⟩, + ⟨0, 5, 4, 1, 7, 1, 12325492291100151680637946161029617335830650552320000⟩, + ⟨0, 5, 5, 1, 8, 1, 30250957096668014021581019902625091721076146176000000⟩, + ⟨0, 5, 3, 2, 5, 1, -5525408277236643856405648631902091314208377405440000⟩, + ⟨0, 5, 4, 2, 6, 1, -8126113373826084512055957517874752192101797068800000⟩, + ⟨0, 5, 5, 2, 7, 1, 15506290202145010519335085456875141124003253452800000⟩, + ⟨0, 5, 6, 2, 8, 1, -9162097101888439720935100720001440610086236979200000⟩, + ⟨0, 5, 3, 3, 4, 1, 602041252632604737582591650096622144024194580480000⟩, + ⟨0, 5, 4, 3, 5, 1, -22295575971646042086389478294445772514686580817920000⟩, + ⟨0, 5, 5, 3, 6, 1, -10609635982618228056278599408832829342755271475200000⟩, + ⟨0, 5, 6, 3, 7, 1, -19426096849152713599492053872979497142819225600000⟩, + ⟨0, 5, 7, 3, 8, 1, 777284507517769889812791125223040890995893862400000⟩, + ⟨0, 5, 3, 4, 3, 1, 8890927519160920981891581164670330897664353239040000⟩, + ⟨0, 5, 4, 4, 4, 1, 16709771373256256092434641522922383846719409356800000⟩, + ⟨0, 5, 5, 4, 5, 1, -6433172267159949061378798729887995006425025740800000⟩, + ⟨0, 5, 6, 4, 6, 1, -3925796728722713723446288208087560592803076505600000⟩, + ⟨0, 5, 7, 4, 7, 1, 2055981916024456915220467342413512014444678348800000⟩, + ⟨0, 5, 8, 4, 8, 1, -440450480008748156510008950555745133540042342400000⟩, + ⟨0, 5, 3, 5, 2, 1, 11101989678288074753064761234165535380591723151360000⟩, + ⟨0, 5, 4, 5, 3, 1, 15922472107236855273105772643336328753071354019840000⟩, + ⟨0, 5, 5, 5, 4, 1, -4267358843753664956156425647822376554326497689600000⟩, + ⟨0, 5, 6, 5, 5, 1, -3279537146498014598048893340858602313439038668800000⟩, + ⟨0, 5, 7, 5, 6, 1, -651331085468671627591826673524766577382129664000000⟩, + ⟨0, 5, 8, 5, 7, 1, 722119547573516438995909339719376057883940618240000⟩, + ⟨0, 5, 3, 6, 1, 1, 2702911932952670683875311704751812992449988526080000⟩, + ⟨0, 5, 4, 6, 2, 1, -20167364011530427302783121259299662200372975370240000⟩, + ⟨0, 5, 5, 6, 3, 1, 38886535208975799889391849295905589894766500249600000⟩, + ⟨0, 5, 6, 6, 4, 1, 2186658492625623014805795799788501360538602700800000⟩, + ⟨0, 5, 7, 6, 5, 1, -4069316512855290810034047208918413566279260569600000⟩, + ⟨0, 5, 8, 6, 6, 1, -1078656333597955181330103961099683976365673021440000⟩, + ⟨0, 5, 3, 7, 0, 1, -284103183614965985974399639445126786082110114365440000⟩, + ⟨0, 5, 4, 7, 1, 1, -19373118861401048616842932179829146691709215703040000⟩, + ⟨0, 5, 5, 7, 2, 1, -2154303133047327076776140026683678621065596108800000⟩, + ⟨0, 5, 6, 7, 3, 1, 11038668739806421183510855776483573270518012313600000⟩, + ⟨0, 5, 7, 7, 4, 1, -3164257927694594638237070621869302735062433792000000⟩, + ⟨0, 5, 8, 7, 5, 1, -2786283480216832462061405569419948863101757030400000⟩ +] + +def collectedFourData_8_4_2 : List CollectedFourTerm := [ + ⟨0, 6, 2, 0, 6, 2, 8175259124647403038077759061729331461475385999360000⟩, + ⟨0, 6, 3, 0, 7, 2, -2336691224207528312703200991137761341355075829760000⟩, + ⟨0, 6, 4, 0, 8, 2, 4509255918634351347302723083211177153260714721280000⟩, + ⟨0, 6, 2, 1, 5, 2, -3991877571916932009573171113478264558733083279360000⟩, + ⟨0, 6, 3, 1, 6, 2, 11079901744688731062269071949637899971455583518720000⟩, + ⟨0, 6, 4, 1, 7, 2, -5258909465261125537380527060855004004364247367680000⟩, + ⟨0, 6, 5, 1, 8, 2, -8604770278898439985596036721395558615368073216000000⟩, + ⟨0, 6, 2, 2, 4, 2, -14706585312105750269849578015305017881191650426880000⟩, + ⟨0, 6, 3, 2, 5, 2, 4715044430245361599235154997631998184144366469120000⟩, + ⟨0, 6, 4, 2, 6, 2, 3467163300913850094449235541841936804155175731200000⟩, + ⟨0, 6, 5, 2, 7, 2, -4410705573414332686822197113266869871475215564800000⟩, + ⟨0, 6, 6, 2, 8, 2, 1954592888981554230813553875215256657519339110400000⟩, + ⟨0, 6, 2, 3, 3, 2, 16752233889973105184118536577637678843537077043200000⟩, + ⟨0, 6, 3, 3, 4, 2, -513745068703405244241017299660481595526128599040000⟩, + ⟨0, 6, 4, 3, 5, 2, 9512838330636148695170696621166709354912630702080000⟩, + ⟨0, 6, 5, 3, 6, 2, 3017870809225413824017936176666358079074546483200000⟩, + ⟨0, 6, 6, 3, 7, 2, 4144259806436092621808058982112393373627187200000⟩, + ⟨0, 6, 7, 3, 8, 2, -132657382187893915239113771076461447607264215040000⟩, + ⟨0, 6, 2, 4, 2, 2, -3994328639696577632382129676446880714355166412800000⟩, + ⟨0, 6, 3, 4, 3, 2, -7586972070758980515940043818016708004191058001920000⟩, + ⟨0, 6, 4, 4, 4, 2, -7129546857987863631718145519668293623876891443200000⟩, + ⟨0, 6, 5, 4, 5, 2, 1829891508774404932915479949167670410726919372800000⟩, + ⟨0, 6, 6, 4, 6, 2, 837508518433719677940125719694812398283338547200000⟩, + ⟨0, 6, 7, 4, 7, 2, -350889765803314331120683253993246996734389780480000⟩, + ⟨0, 6, 8, 4, 8, 2, 62642236204210440426328235834129954246964019200000⟩, + ⟨0, 6, 2, 5, 1, 2, 4136934617380719312208038373214271732128164085760000⟩, + ⟨0, 6, 3, 5, 2, 2, -9473756864792812193285190537478332810622434017280000⟩, + ⟨0, 6, 4, 5, 3, 2, -6793630412277036389456874179086021024702173020160000⟩, + ⟨0, 6, 5, 5, 4, 2, 1213834075754595748210611898808490327700773273600000⟩, + ⟨0, 6, 6, 5, 5, 2, 699638948857532957098439278477390370093767065600000⟩, + ⟨0, 6, 7, 5, 6, 2, 111161197605495882943162459233995329901061734400000⟩, + ⟨0, 6, 8, 5, 7, 2, -102702086431780800978807760410489174527752273920000⟩, + ⟨0, 6, 2, 6, 0, 2, -74473431012568162667045254375332732029031300464640000⟩, + ⟨0, 6, 3, 6, 1, 2, -2306499215164945771665805881037539091079327907840000⟩, + ⟨0, 6, 4, 6, 2, 2, 8604795572034499786542842399263247996685134069760000⟩, + ⟨0, 6, 5, 6, 3, 2, -11061127796594185199062641176009202923065678233600000⟩, + ⟨0, 6, 6, 6, 4, 2, -466490050562357470014874255490439961095281049600000⟩, + ⟨0, 6, 7, 6, 5, 2, 694501010464319371790014762376818980332670812160000⟩, + ⟨0, 6, 8, 6, 6, 2, 153409856270490769146528793527694676622594539520000⟩, + ⟨0, 6, 3, 7, 0, 2, 242436226665345766027833514493948215810688412549120000⟩, + ⟨0, 6, 4, 7, 1, 2, 8265915530645068696271129219223111117942250536960000⟩, + ⟨0, 6, 5, 7, 2, 2, 612783374481239712081448453188227246955744460800000⟩, + ⟨0, 6, 6, 7, 3, 2, -2354930665185971532428298343032894101078094643200000⟩, + ⟨0, 6, 7, 7, 4, 2, 540036716537359569298991137188748621348287283200000⟩, + ⟨0, 6, 8, 7, 5, 2, 396273896434772101603229318962660270337635123200000⟩ +] + +def collectedFourData_8_4_3 : List CollectedFourTerm := [ + ⟨0, 7, 1, 0, 5, 3, 2738292973182149077686094497665222490090236805120000⟩, + ⟨0, 7, 2, 0, 6, 3, -2336691224207528312703200991137761341355075829760000⟩, + ⟨0, 7, 3, 0, 7, 3, 333942068015120637987947979339880724244285358080000⟩, + ⟨0, 7, 4, 0, 8, 3, -429618950385387820580194259231945771448438620160000⟩, + ⟨0, 7, 1, 1, 4, 3, 1196128505590307549082739422909276985354302259200000⟩, + ⟨0, 7, 2, 1, 5, 3, 1140977325389848929020535427699716047102552309760000⟩, + ⟨0, 7, 3, 1, 6, 3, -1583454957032477096759521438318764670895007989760000⟩, + ⟨0, 7, 4, 1, 7, 3, 501042124333788841302706102852560732153666600960000⟩, + ⟨0, 7, 5, 1, 8, 3, 614864033373711176386188693403549313336868864000000⟩, + ⟨0, 7, 1, 2, 3, 3, 1806677729229604094257076540927095370500685168640000⟩, + ⟨0, 7, 2, 2, 4, 3, 4203505762068304325713717840459601679078213550080000⟩, + ⟨0, 7, 3, 2, 5, 3, -673838148364386455973652038385050338471140392960000⟩, + ⟨0, 7, 4, 2, 6, 3, -330333670350753691093353497023222761428248166400000⟩, + ⟨0, 7, 5, 2, 7, 3, 315172181358992098159133094183797126509835059200000⟩, + ⟨0, 7, 6, 2, 8, 3, -111734196578842340353994100655744294896040673280000⟩, + ⟨0, 7, 1, 3, 2, 3, -4655467198785232515899932295084718698704341565440000⟩, + ⟨0, 7, 2, 3, 3, 3, -4788202712566668037262125136400531509950493491200000⟩, + ⟨0, 7, 3, 3, 4, 3, 73420522531199672938541768444686678651903672320000⟩, + ⟨0, 7, 4, 3, 5, 3, -906334812780269517771064385139868953608988917760000⟩, + ⟨0, 7, 5, 3, 6, 3, -215645526587918403976396076329592063129341132800000⟩, + ⟨0, 7, 6, 3, 7, 3, -236906387256633163986633459155852686566359040000⟩, + ⟨0, 7, 7, 3, 8, 3, 6319460053366914490516758267086932054313533440000⟩, + ⟨0, 7, 1, 4, 1, 3, 2095930125269086612530307766233360885757163601920000⟩, + ⟨0, 7, 2, 4, 2, 3, 1141677901173846819057002337627268416426265804800000⟩, + ⟨0, 7, 3, 4, 3, 3, 1084272118213424238874697877438038394057114255360000⟩, + ⟨0, 7, 4, 4, 4, 3, 679266932975457641216778867816948258780374630400000⟩, + ⟨0, 7, 5, 4, 5, 3, -130757061171117419164589604649120994428138291200000⟩, + ⟨0, 7, 6, 4, 6, 3, -47876129071505769919432511623947110363210711040000⟩, + ⟨0, 7, 7, 4, 7, 3, 16715495372798605654756706973833400811813601280000⟩, + ⟨0, 7, 8, 4, 8, 3, -2557814312870074814521476070420446088632729600000⟩, + ⟨0, 7, 1, 5, 0, 3, 11046833160898497949664982301044700366976298516480000⟩, + ⟨0, 7, 2, 5, 1, 3, -1182438216106181205260832153565131753170046812160000⟩, + ⟨0, 7, 3, 5, 2, 3, 1353916994477650006313160008085375382601324298240000⟩, + ⟨0, 7, 4, 5, 3, 3, 647262523949326676259675214582897633450807787520000⟩, + ⟨0, 7, 5, 5, 4, 3, -86735948953243464576906487756777333157422694400000⟩, + ⟨0, 7, 6, 5, 5, 3, -39994822597863214333372321024564992489207889920000⟩, + ⟨0, 7, 7, 5, 6, 3, -5295436531058458827260195140817104696403558400000⟩, + ⟨0, 7, 8, 5, 7, 3, 4193542289589779734075210176345539164986408960000⟩, + ⟨0, 7, 2, 6, 0, 3, 21286348240515043809717778858803534419183523594240000⟩, + ⟨0, 7, 3, 6, 1, 3, 329627256613100415086776788495225994523411742720000⟩, + ⟨0, 7, 4, 6, 2, 3, -819821120966201932361050570380220549294687518720000⟩, + ⟨0, 7, 5, 6, 3, 3, 790385963859412761754914941337267926523602534400000⟩, + ⟨0, 7, 6, 6, 4, 3, 26666878461205965986246120846850530281751838720000⟩, + ⟨0, 7, 7, 6, 5, 3, -33084260523367576285747579051928801890806005760000⟩, + ⟨0, 7, 8, 6, 6, 3, -6264047228850809881247664074558973840992501760000⟩, + ⟨0, 7, 3, 7, 0, 3, -34647134399139523673366269552201914182429269032960000⟩, + ⟨0, 7, 4, 7, 1, 3, -787534355629455078509568796902372881175014277120000⟩, + ⟨0, 7, 5, 7, 2, 3, -43787160494204676560191153554379360125006643200000⟩, + ⟨0, 7, 6, 7, 3, 3, 134619483861181926764751252461327039972235018240000⟩, + ⟨0, 7, 7, 7, 4, 3, -25725974696798414639805578840286328222069555200000⟩, + ⟨0, 7, 8, 7, 5, 3, -16180697011093067141456395617906878014134681600000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0817.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0817.lean new file mode 100644 index 0000000000000000000000000000000000000000..bc1c44252aa5da7a7c8549f3a3d144d10f7600db --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0817.lean @@ -0,0 +1,656 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0817. -/ +namespace LaughlinFock +def collectedFourData_8_4_4 : List CollectedFourTerm := [ + ⟨0, 8, 0, 0, 4, 4, 3188267756893289755659608583063857779664800972800000⟩, + ⟨0, 8, 1, 0, 5, 4, -10568502734428748029760526900472787977712141598720000⟩, + ⟨0, 8, 2, 0, 6, 4, 4509255918634351347302723083211177153260714721280000⟩, + ⟨0, 8, 3, 0, 7, 4, -429618950385387820580194259231945771448438620160000⟩, + ⟨0, 8, 4, 0, 8, 4, 414530977544924853540234410711005405567506186240000⟩, + ⟨0, 8, 0, 1, 3, 4, 2505859552088723034943592511322754768925213327360000⟩, + ⟨0, 8, 1, 1, 4, 4, -4616484615000488825239969837350491039303152435200000⟩, + ⟨0, 8, 2, 1, 5, 4, -2201813703171947104128234041891582351963880161280000⟩, + ⟨0, 8, 3, 1, 6, 4, 2037126561101698417404761728380427182783615467520000⟩, + ⟨0, 8, 4, 1, 7, 4, -483445810304590012882519620638431159663397437440000⟩, + ⟨0, 8, 5, 1, 8, 4, -474616286982649387940414464244018434798308556800000⟩, + ⟨0, 8, 0, 2, 2, 4, 2090384006139809764100497582219604138717651927040000⟩, + ⟨0, 8, 1, 2, 3, 4, -6972912945617263006752531925819504491841286307840000⟩, + ⟨0, 8, 2, 2, 4, 4, -8111762067771039161286300033593311242379056906240000⟩, + ⟨0, 8, 3, 2, 5, 4, 866897781853686354064266659826232272166500433920000⟩, + ⟨0, 8, 4, 2, 6, 4, 318732539995419774322692529923844305237678489600000⟩, + ⟨0, 8, 5, 2, 7, 4, -243282811089243705873415268051308269513253847040000⟩, + ⟨0, 8, 6, 2, 8, 4, 71873436823454199462989519920679488301857505280000⟩, + ⟨0, 8, 0, 3, 1, 4, 6700808290814832457937518635126953787266716139520000⟩, + ⟨0, 8, 1, 3, 2, 4, 17967879369470317468869331656245622613339684208640000⟩, + ⟨0, 8, 2, 3, 3, 4, 9240087521013740874979644549703491925514492313600000⟩, + ⟨0, 8, 3, 3, 4, 4, -94456047463814847049713552547988129681390960640000⟩, + ⟨0, 8, 4, 3, 5, 4, 874504850374449395830990214574010227652967792640000⟩, + ⟨0, 8, 5, 3, 6, 4, 166457742815099596489181230207002906493043343360000⟩, + ⟨0, 8, 6, 3, 7, 4, 152390913246935485004179298160666337125335040000⟩, + ⟨0, 8, 7, 3, 8, 4, -3484299551801665145168775261310844745044459520000⟩, + ⟨0, 8, 0, 4, 0, 4, 21398545839998903758610991517989936766955343052800000⟩, + ⟨0, 8, 1, 4, 1, 4, -8089289012174839236689048793014818607480721899520000⟩, + ⟨0, 8, 2, 4, 2, 4, -2203165647094925530094930492921368681952732774400000⟩, + ⟨0, 8, 3, 4, 3, 4, -1394924131984174941216612240968372923405141278720000⟩, + ⟨0, 8, 4, 4, 4, 4, -655411465177855424798921713995486749330610585600000⟩, + ⟨0, 8, 5, 4, 5, 4, 100931958126227730214583073545150247508314685440000⟩, + ⟨0, 8, 6, 4, 6, 4, 30796497791473722687147102755416814249878487040000⟩, + ⟨0, 8, 7, 4, 7, 4, -9216260969092545606910787809848718793103114240000⟩, + ⟨0, 8, 8, 4, 8, 4, 1233992665525229844718320975742773480338227200000⟩, + ⟨0, 8, 1, 5, 0, 4, -42635498688827818376576451922515108363003368570880000⟩, + ⟨0, 8, 2, 5, 1, 4, 2281823318870263728281114393906801893580451348480000⟩, + ⟨0, 8, 3, 5, 2, 4, -1741824267705287791825579072771434507185663508480000⟩, + ⟨0, 8, 4, 5, 3, 4, -624531032768044957197722417677237894866303713280000⟩, + ⟨0, 8, 5, 5, 4, 4, 66951865462399501841403832159785825116388065280000⟩, + ⟨0, 8, 6, 5, 5, 4, 25726818138656570956040157351491917026605137920000⟩, + ⟨0, 8, 7, 5, 6, 4, 2919693609255555594675528571176042728993587200000⟩, + ⟨0, 8, 8, 5, 7, 4, -2023133736442784399396939354595549512434974720000⟩, + ⟨0, 8, 2, 6, 0, 4, -41077567628648574088452073341304954164270040350720000⟩, + ⟨0, 8, 3, 6, 1, 4, -424067913474509923685757032604241678327810621440000⟩, + ⟨0, 8, 4, 6, 2, 4, 791029470141488525494693574306020745065613230080000⟩, + ⟨0, 8, 5, 6, 3, 4, -610102447189580353113541824847118675421199073280000⟩, + ⟨0, 8, 6, 6, 4, 4, -17153568585493797701196614842881280240747806720000⟩, + ⟨0, 8, 7, 6, 5, 4, 18241348650007227829437412826926882150762414080000⟩, + ⟨0, 8, 8, 6, 6, 4, 3022028728986230350029964083047626430553784320000⟩, + ⟨0, 8, 3, 7, 0, 4, 44573795697239925012977103781198650602789189713920000⟩, + ⟨0, 8, 4, 7, 1, 4, 759876597613869968275757757860079048014356807680000⟩, + ⟨0, 8, 5, 7, 2, 4, 33799504285919944294655031934983203234607267840000⟩, + ⟨0, 8, 6, 7, 3, 4, -86594482841923508383688081782076780436510474240000⟩, + ⟨0, 8, 7, 7, 4, 4, 14184281781789004368850355100328129547835801600000⟩, + ⟨0, 8, 8, 7, 5, 4, 7806220074032824467381582409346894267626291200000⟩ +] + +def collectedFourData_8_4_5 : List CollectedFourTerm := [ + ⟨1, 3, 4, 0, 8, 0, 2505859552088723034943592511322754768925213327360000⟩, + ⟨1, 3, 4, 1, 7, 0, -2922453006633838165798379927380259810073284444160000⟩, + ⟨1, 3, 5, 1, 8, 0, -14345390582823954456697221185531393324378750976000000⟩, + ⟨1, 3, 4, 2, 6, 0, 1926753422963340491688835575108962081753687654400000⟩, + ⟨1, 3, 5, 2, 7, 0, -7353281045937135534852048959105250035376114892800000⟩, + ⟨1, 3, 6, 2, 8, 0, 6517175360651274713266638145540425599679253708800000⟩, + ⟨1, 3, 4, 3, 5, 0, 5286423575958787578861313036248853617662975016960000⟩, + ⟨1, 3, 5, 3, 6, 0, 5031225016315456429658372086839407209448944435200000⟩, + ⟨1, 3, 6, 3, 7, 0, 13818155203007909013282803187509125582317158400000⟩, + ⟨1, 3, 7, 3, 8, 0, -737196500506659051165586230953797900414274764800000⟩, + ⟨1, 3, 4, 4, 4, 0, -3961993601277729617131095578843227570798224998400000⟩, + ⟨1, 3, 5, 4, 5, 0, 3050692530622954301483365778001136214837349580800000⟩, + ⟨1, 3, 6, 4, 6, 0, 2792494494091706228095383120727767055648319078400000⟩, + ⟨1, 3, 7, 4, 7, 0, -1949945816414660852852877718594842067738401177600000⟩, + ⟨1, 3, 8, 4, 8, 0, 522168120823996091081640511881834554411974656000000⟩, + ⟨1, 3, 4, 5, 3, 0, -3775319912896099666878558515554603208605087825920000⟩, + ⟨1, 3, 5, 5, 4, 0, 2023636117531536590513503705180289115828623769600000⟩, + ⟨1, 3, 6, 5, 5, 0, 2332797660602407594967670498677145496110445363200000⟩, + ⟨1, 3, 7, 5, 6, 0, 617739054663624848246156767399565062179913728000000⟩, + ⟨1, 3, 8, 5, 7, 0, -856095802550261870904392129283175960444246425600000⟩, + ⟨1, 3, 4, 6, 2, 0, 4781810916707444845517901415697108397569731461120000⟩, + ⟨1, 3, 5, 6, 3, 0, -18440492120724902180749466294993617523058514329600000⟩, + ⟨1, 3, 6, 6, 4, 0, -1555412117097216244869083316477215365682901811200000⟩, + ⟨1, 3, 7, 6, 5, 0, 3859443824901269556601609641828021489536021299200000⟩, + ⟨1, 3, 8, 6, 6, 0, 1278781557278717721409638097967518510181095833600000⟩, + ⟨1, 3, 4, 7, 1, 0, 4593490314805322711935427645813824491475194347520000⟩, + ⟨1, 3, 5, 7, 2, 0, 1021598086255896246469288468497206508664966348800000⟩, + ⟨1, 3, 6, 7, 3, 0, -7852016751779437570227641360398496828186060390400000⟩, + ⟨1, 3, 7, 7, 4, 0, 3001063122235946011715277175417881323617910784000000⟩, + ⟨1, 3, 8, 7, 5, 0, 3303228115267055989751621497795132593983717376000000⟩ +] + +def collectedFourData_8_4_6 : List CollectedFourTerm := [ + ⟨1, 4, 3, 0, 7, 1, 1196128505590307549082739422909276985354302259200000⟩, + ⟨1, 4, 4, 0, 8, 1, -4616484615000488825239969837350491039303152435200000⟩, + ⟨1, 4, 3, 1, 6, 1, -5671689172563493624301224415497322098067924582400000⟩, + ⟨1, 4, 4, 1, 7, 1, 5383964688659994665332807767314845712694588211200000⟩, + ⟨1, 4, 5, 1, 8, 1, 13214083540032912068101758860840077076107100160000000⟩, + ⟨1, 4, 3, 2, 5, 1, -2413583356548952653899633733559837916628674150400000⟩, + ⟨1, 4, 4, 2, 6, 1, -3549611360539195391352522047190732607856836608000000⟩, + ⟨1, 4, 5, 2, 7, 1, 6773386160059935028883701613124084096772866048000000⟩, + ⟨1, 4, 6, 2, 8, 1, -4002144993937476735235672072097571583737987072000000⟩, + ⟨1, 4, 3, 3, 4, 1, 262980882932446027218292860299028857961106636800000⟩, + ⟨1, 4, 4, 3, 5, 1, -9739050652877744657313803638922394776284377907200000⟩, + ⟨1, 4, 5, 3, 6, 1, -4634452250738816076716662134207095718839058432000000⟩, + ⟨1, 4, 6, 3, 7, 1, -8485618018669169611174315513181770975543296000000⟩, + ⟨1, 4, 7, 3, 8, 1, 339529833184830374922434238063921734860406784000000⟩, + ⟨1, 4, 3, 4, 3, 1, 3883693947637458159895750016048060990065370726400000⟩, + ⟨1, 4, 4, 4, 4, 1, 7299085253913473457928746997996823625427058688000000⟩, + ⟨1, 4, 5, 4, 5, 1, -2810108635373977539833651617983365948928688128000000⟩, + ⟨1, 4, 6, 4, 6, 1, -1714848418473467525821873930502288435992068096000000⟩, + ⟨1, 4, 7, 4, 7, 1, 898084536906652453059014241538466043981201408000000⟩, + ⟨1, 4, 8, 4, 8, 1, -192395547006486398807977413670346519513923584000000⟩, + ⟨1, 4, 3, 5, 2, 1, 4849519920995830766357507917648143661523376537600000⟩, + ⟨1, 4, 4, 5, 3, 1, 6955180820115151021190110912119457635394545254400000⟩, + ⟨1, 4, 5, 5, 4, 1, -1864048006033837697515571003400589614080065536000000⟩, + ⟨1, 4, 6, 5, 5, 1, -1432552288774994290419184352459181396074692608000000⟩, + ⟨1, 4, 7, 5, 6, 1, -284511440352124651382384575158378043791114240000000⟩, + ⟨1, 4, 8, 5, 7, 1, 315432929842019281550197191113011511184221798400000⟩, + ⟨1, 4, 3, 6, 1, 1, 1180673522799793178362186354324021980821245132800000⟩, + ⟨1, 4, 4, 6, 2, 1, -8809414921287537916757632391871372597226006118400000⟩, + ⟨1, 4, 5, 6, 3, 1, 16986236937621894851520073762214848761887195136000000⟩, + ⟨1, 4, 6, 6, 4, 1, 955166076324243767110062115825751953640521728000000⟩, + ⟨1, 4, 7, 6, 5, 1, -1777540068562920440673013903122542577724686336000000⟩, + ⟨1, 4, 8, 6, 6, 1, -471173684111929584497099255028439961336964710400000⟩, + ⟨1, 4, 3, 7, 0, 1, -124100642180705474469439153112703602721366107750400000⟩, + ⟨1, 4, 4, 7, 1, 1, -8462476418431653524205004302632586351567332966400000⟩, + ⟨1, 4, 5, 7, 2, 1, -941032757399187389364868605308174513637163008000000⟩, + ⟨1, 4, 6, 7, 3, 1, 4821860360729487447407087885945982360408293376000000⟩, + ⟨1, 4, 7, 7, 4, 1, -1382196552167047136493681510818492644558110720000000⟩, + ⟨1, 4, 8, 7, 5, 1, -1217091497506840721534088197135667152409329664000000⟩ +] + +def collectedFourData_8_4_7 : List CollectedFourTerm := [ + ⟨1, 5, 2, 0, 6, 2, -3991877571916932009573171113478264558733083279360000⟩, + ⟨1, 5, 3, 0, 7, 2, 1140977325389848929020535427699716047102552309760000⟩, + ⟨1, 5, 4, 0, 8, 2, -2201813703171947104128234041891582351963880161280000⟩, + ⟨1, 5, 2, 1, 5, 2, 1949184277368174203598907851350569186804220559360000⟩, + ⟨1, 5, 3, 1, 6, 2, -5410178515359761515146648932391794701819938078720000⟩, + ⟨1, 5, 4, 1, 7, 2, 2567860226451595542485962833053885097209160007680000⟩, + ⟨1, 5, 5, 1, 8, 2, 4201602538110809883262125078224408321999241216000000⟩, + ⟨1, 5, 2, 2, 4, 2, 7181043092552730808321004999581832665283564666880000⟩, + ⟨1, 5, 3, 2, 5, 2, -2302297679463474049410344441218959784044260229120000⟩, + ⟨1, 5, 4, 2, 6, 2, -1692972810777837219686983706916030867876033331200000⟩, + ⟨1, 5, 5, 2, 7, 2, 2153692792655189532371933546252008630837365964800000⟩, + ⟨1, 5, 6, 2, 8, 2, -954403450311467394536438905221446460118558310400000⟩, + ⟨1, 5, 2, 3, 3, 2, -8179907905705018315200466795764759202578510643200000⟩, + ⟨1, 5, 3, 3, 4, 2, 250855341240146632693707655989573113873474519040000⟩, + ⟨1, 5, 4, 3, 5, 2, -4645000898240759226108748694127321100274714542080000⟩, + ⟨1, 5, 5, 3, 6, 2, -1473588863008585630519092312537542381161100083200000⟩, + ⟨1, 5, 6, 3, 7, 2, -2023590631351707272418947955036512633172787200000⟩, + ⟨1, 5, 7, 3, 8, 2, 64774953384478302976931872517499151100978135040000⟩, + ⟨1, 5, 2, 4, 2, 2, 1950381103346119898589703813900709114468420812800000⟩, + ⟨1, 5, 3, 4, 3, 2, 3704624304410556049576236697052332655585966161920000⟩, + ⟨1, 5, 4, 4, 4, 2, 3481269249867363648933845897805981915129525043200000⟩, + ⟨1, 5, 5, 4, 5, 2, -893513313956618216545721817758399129990253772800000⟩, + ⟨1, 5, 6, 4, 6, 2, -408945015693204314357348047195154491016164147200000⟩, + ⟨1, 5, 7, 4, 7, 2, 171335117941701643128901800594945573340556820480000⟩, + ⟨1, 5, 8, 4, 8, 2, -30587426520146606128866743623103577828045619200000⟩, + ⟨1, 5, 2, 5, 1, 2, -2020013832444864394778250824384710236620728565760000⟩, + ⟨1, 5, 3, 5, 2, 2, 4625917903488053912358913432503993750552607457280000⟩, + ⟨1, 5, 4, 5, 3, 2, 3317245418301176165360236074725981102620708700160000⟩, + ⟨1, 5, 5, 5, 4, 2, -592700114963300719314017106767021830259186073600000⟩, + ⟨1, 5, 6, 5, 5, 2, -341625015892616024682463807186198654715795865600000⟩, + ⟨1, 5, 7, 5, 6, 2, -54278633230227263644672440857898999301432934400000⟩, + ⟨1, 5, 8, 5, 7, 2, 50148154225482378008523479270078218313316433920000⟩, + ⟨1, 5, 2, 6, 0, 2, 36364452114610585600856907813769527826471075184640000⟩, + ⟨1, 5, 3, 6, 1, 2, 1126234942070788498801129384577846127099736227840000⟩, + ⟨1, 5, 4, 6, 2, 2, -4201614888435248671920977496114362939980130549760000⟩, + ⟨1, 5, 5, 6, 3, 2, 5401011429498347606833014364100434505670171033600000⟩, + ⟨1, 5, 6, 6, 4, 2, 227781302337934808412786727881604953831741849600000⟩, + ⟨1, 5, 7, 6, 5, 2, -339116224339339745839017505834769179706822492160000⟩, + ⟨1, 5, 8, 6, 6, 2, -74908128931458744067823223090866113599787499520000⟩, + ⟨1, 5, 3, 7, 0, 2, -118378600737906684744100575588463275784384146309120000⟩, + ⟨1, 5, 4, 7, 1, 2, -4036143969878756293310204058950703710926232616960000⟩, + ⟨1, 5, 5, 7, 2, 2, -299214516841475332138769288757096744485702860800000⟩, + ⟨1, 5, 6, 7, 3, 2, 1149883418059944003444928006785700161444328243200000⟩, + ⟨1, 5, 7, 7, 4, 2, -263693226586273475528343465630498802833240883200000⟩, + ⟨1, 5, 8, 7, 5, 2, -193495625691537429628552567631616333350908723200000⟩ +] + +def collectedFourData_8_4_8 : List CollectedFourTerm := [ + ⟨1, 6, 1, 0, 5, 3, -12984178986386778789418956656422078363827060080640000⟩, + ⟨1, 6, 2, 0, 6, 3, 11079901744688731062269071949637899971455583518720000⟩, + ⟨1, 6, 3, 0, 7, 3, -1583454957032477096759521438318764670895007989760000⟩, + ⟨1, 6, 4, 0, 8, 3, 2037126561101698417404761728380427182783615467520000⟩, + ⟨1, 6, 1, 1, 4, 3, -5671689172563493624301224415497322098067924582400000⟩, + ⟨1, 6, 2, 1, 5, 3, -5410178515359761515146648932391794701819938078720000⟩, + ⟨1, 6, 3, 1, 6, 3, 7508277156734844044586061410362323401456715038720000⟩, + ⟨1, 6, 4, 1, 7, 3, -2375794221357271862344815124618958013214092165120000⟩, + ⟨1, 6, 5, 1, 8, 3, -2915504199077131878138372016345662201274564608000000⟩, + ⟨1, 6, 1, 2, 3, 3, -8566733814379030439728807529586447898189580206080000⟩, + ⟨1, 6, 2, 2, 4, 3, -19931786598267863008186155864019155235658017013760000⟩, + ⟨1, 6, 3, 2, 5, 3, 3195142087390022678713086078864794446394944389120000⟩, + ⟨1, 6, 4, 2, 6, 3, 1566344997803478307940247474246958661774396620800000⟩, + ⟨1, 6, 5, 2, 7, 3, -1494453681316478577592304569376298544243566182400000⟩, + ⟨1, 6, 6, 2, 8, 3, 529810659957936393558153874070566709265338204160000⟩, + ⟨1, 6, 1, 3, 2, 3, 22074854650791678569121948872129218331279024455680000⟩, + ⟨1, 6, 2, 3, 3, 3, 22704247373070531844641343746385596011623376486400000⟩, + ⟨1, 6, 3, 3, 4, 3, -348138499114399442692906642319288268458337239040000⟩, + ⟨1, 6, 4, 3, 5, 3, 4297572811230952191433119849635120553583674654720000⟩, + ⟨1, 6, 5, 3, 6, 3, 1022527590091036281772835023607688794862098841600000⟩, + ⟨1, 6, 6, 3, 7, 3, 1123340331105531225922702880177365302776954880000⟩, + ⟨1, 6, 7, 3, 8, 3, -29965018803259830096634821338885888719642951680000⟩, + ⟨1, 6, 1, 4, 1, 3, -9938283505810842298072053370524131388631013130240000⟩, + ⟨1, 6, 2, 4, 2, 3, -5413500439442408518793495740655038798658902425600000⟩, + ⟨1, 6, 3, 4, 3, 3, -5141299119820420117624716116213014716489840721920000⟩, + ⟨1, 6, 4, 4, 4, 3, -3220883785505975729641034514086120255881268428800000⟩, + ⟨1, 6, 5, 4, 5, 3, 620011482557596616299138780517567070162282086400000⟩, + ⟨1, 6, 6, 4, 6, 3, 227014506894560802482029178754355534865765498880000⟩, + ⟨1, 6, 7, 4, 7, 3, -79259957167519621181863569733006267460521820160000⟩, + ⟨1, 6, 8, 4, 8, 3, 12128402321265346132056701171140059936797491200000⟩, + ⟨1, 6, 1, 5, 0, 3, -52380830100577333228484123447183355425988343234560000⟩, + ⟨1, 6, 2, 5, 1, 3, 5606773850945889304628399569739876266627584491520000⟩, + ⟨1, 6, 3, 5, 2, 3, -6419875725927034759401167058503731975103478497280000⟩, + ⟨1, 6, 4, 5, 3, 3, -3069128301626576056201970374322121732842261053440000⟩, + ⟨1, 6, 5, 5, 4, 3, 411276330470321266959353258804544237602655436800000⟩, + ⟨1, 6, 6, 5, 5, 3, 189643672253217006348168752468082170693670666240000⟩, + ⟨1, 6, 7, 5, 6, 3, 25109400784976007671021351554903210600484044800000⟩, + ⟨1, 6, 8, 5, 7, 3, -19884542745526728075339998369022073673739141120000⟩, + ⟨1, 6, 2, 6, 0, 3, -100933595575137040792118058301679997215921437409280000⟩, + ⟨1, 6, 3, 6, 1, 3, -1562995391863587345989344951591709529729757347840000⟩, + ⟨1, 6, 4, 6, 2, 3, 3887350358670819729203514753991830168867270819840000⟩, + ⟨1, 6, 5, 6, 3, 3, -3747777510874762394818132923345853828412787916800000⟩, + ⟨1, 6, 6, 6, 4, 3, -126446485580448733094758066480956172907933859840000⟩, + ⟨1, 6, 7, 6, 5, 3, 156875821716203246437776444739070428831253790720000⟩, + ⟨1, 6, 8, 6, 6, 3, 29702267505752671908075140083436987119011102720000⟩, + ⟨1, 6, 3, 7, 0, 3, 164286509445715646690848796686181216875724270469120000⟩, + ⟨1, 6, 4, 7, 1, 3, 3734256024306509341153668201147602740158545264640000⟩, + ⟨1, 6, 5, 7, 2, 3, 207625821900898121736784983697949021123798630400000⟩, + ⟨1, 6, 6, 7, 3, 3, -638325953660591741181645071132624167277722337280000⟩, + ⟨1, 6, 7, 7, 4, 3, 121984996979455237970542738727183953443579494400000⟩, + ⟨1, 6, 8, 7, 5, 3, 76724100808095210881513388749440230511293235200000⟩ +] + +def collectedFourData_8_4_9 : List CollectedFourTerm := [ + ⟨1, 7, 0, 0, 4, 4, -3718310024326781545233358360315978344748076236800000⟩, + ⟨1, 7, 1, 0, 5, 4, 12325492291100151680637946161029617335830650552320000⟩, + ⟨1, 7, 2, 0, 6, 4, -5258909465261125537380527060855004004364247367680000⟩, + ⟨1, 7, 3, 0, 7, 4, 501042124333788841302706102852560732153666600960000⟩, + ⟨1, 7, 4, 0, 8, 4, -483445810304590012882519620638431159663397437440000⟩, + ⟨1, 7, 0, 1, 3, 4, -2922453006633838165798379927380259810073284444160000⟩, + ⟨1, 7, 1, 1, 4, 4, 5383964688659994665332807767314845712694588211200000⟩, + ⟨1, 7, 2, 1, 5, 4, 2567860226451595542485962833053885097209160007680000⟩, + ⟨1, 7, 3, 1, 6, 4, -2375794221357271862344815124618958013214092165120000⟩, + ⟨1, 7, 4, 1, 7, 4, 563817577362435377940260563271858205760306544640000⟩, + ⟨1, 7, 5, 1, 8, 4, 553520165858330715181364080274161466218433740800000⟩, + ⟨1, 7, 0, 2, 2, 4, -2437905595575165053098786499244492712914966282240000⟩, + ⟨1, 7, 1, 2, 3, 4, 8132143872919528518849327220740997773890986967040000⟩, + ⟨1, 7, 2, 2, 4, 4, 9460324072949657812175625696135904635869661757440000⟩, + ⟨1, 7, 3, 2, 5, 4, -1011017567569090277021679929686512896027677163520000⟩, + ⟨1, 7, 4, 2, 6, 4, -371721100268860706708803308961116626687203737600000⟩, + ⟨1, 7, 5, 2, 7, 4, 283728025434411545875947200737088904987137802240000⟩, + ⟨1, 7, 6, 2, 8, 4, -83822232322130550532296926500171514554016071680000⟩, + ⟨1, 7, 0, 3, 1, 4, -7814802437768628923038342128969296604187192197120000⟩, + ⟨1, 7, 1, 3, 2, 4, -20954998472429731191810544159384002588042948771840000⟩, + ⟨1, 7, 2, 3, 3, 4, -10776231068033263576902908072297643569537718681600000⟩, + ⟨1, 7, 3, 3, 4, 4, 110159150649637274518907467624050852213125283840000⟩, + ⟨1, 7, 4, 3, 5, 4, -1019889293940044704995282364073219279759962275840000⟩, + ⟨1, 7, 5, 3, 6, 4, -194130964188309824324401400800756038807752540160000⟩, + ⟨1, 7, 6, 3, 7, 4, -177725556179301247065279969805533626750730240000⟩, + ⟨1, 7, 7, 3, 8, 4, 4063556432238218272249468348411024310922117120000⟩, + ⟨1, 7, 0, 4, 0, 4, -24956005445544872192756190864727155096584768716800000⟩, + ⟨1, 7, 1, 4, 1, 4, 9434114922943377445500334257383918876966906757120000⟩, + ⟨1, 7, 2, 4, 2, 4, 2569436927978708406531759826160764660446815846400000⟩, + ⟨1, 7, 3, 4, 3, 4, 1626827098168872920598180557887726156238888632320000⟩, + ⟨1, 7, 4, 4, 4, 4, 764372131468721394820761562905264096745724313600000⟩, + ⟨1, 7, 5, 4, 5, 4, -117711666739489775081351459924653226741874032640000⟩, + ⟨1, 7, 6, 4, 6, 4, -35916345546766752923442806268703588938405642240000⟩, + ⟨1, 7, 7, 4, 7, 4, 10748443406014546831783607338126913419283005440000⟩, + ⟨1, 7, 8, 4, 8, 4, -1439141141219325290622661352049155268358963200000⟩, + ⟨1, 7, 1, 5, 0, 4, 49723553432449632416257194354589011711349783265280000⟩, + ⟨1, 7, 2, 5, 1, 4, -2661171258892445011715888565234691911120196730880000⟩, + ⟨1, 7, 3, 5, 2, 4, 2031398592925957360261768302761347580842349690880000⟩, + ⟨1, 7, 4, 5, 3, 4, 728357897364108524075898956971301760206037319680000⟩, + ⟨1, 7, 5, 5, 4, 4, -78082460909367812335811560309303196543279431680000⟩, + ⟨1, 7, 6, 5, 5, 4, -30003843175396299220234058774343404909777387520000⟩, + ⟨1, 7, 7, 5, 6, 4, -3405086035131625583045640348460866268771123200000⟩, + ⟨1, 7, 8, 5, 7, 4, 2359475121405458001524186710508127612378808320000⟩, + ⟨1, 7, 2, 6, 0, 4, 47906619874799123009441027372892117359153979064320000⟩, + ⟨1, 7, 3, 6, 1, 4, 494568240154362914609866411107725580236897648640000⟩, + ⟨1, 7, 4, 6, 2, 4, -922536321488585499465875586036812920079756820480000⟩, + ⟨1, 7, 5, 6, 3, 4, 711530592230383076678140570824653059363889479680000⟩, + ⟨1, 7, 6, 6, 4, 4, 20005310371601054393086377573376984147631800320000⟩, + ⟨1, 7, 7, 6, 5, 4, -21273931399241580520532324256183389528763924480000⟩, + ⟨1, 7, 8, 6, 6, 4, -3524434135902819693475002148662208051984465920000⟩, + ⟨1, 7, 3, 7, 0, 4, -51984087912628980259950671510753746848746852843520000⟩, + ⟨1, 7, 4, 7, 1, 4, -886204354715853909522972051660423435334535086080000⟩, + ⟨1, 7, 5, 7, 2, 4, -39418595044876123646037150082895249260192727040000⟩, + ⟨1, 7, 6, 7, 3, 4, 100990618779228962099402988897235482724207165440000⟩, + ⟨1, 7, 7, 7, 4, 4, -16542386386171718014082718013294034330163609600000⟩, + ⟨1, 7, 8, 7, 5, 4, -9103986417270251431827913305067206326039347200000⟩ +] + +def collectedFourData_8_4_10 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 4, 5, -18251999086355370931237084206484977768443412480000000⟩, + ⟨1, 8, 1, 0, 5, 5, 30250957096668014021581019902625091721076146176000000⟩, + ⟨1, 8, 2, 0, 6, 5, -8604770278898439985596036721395558615368073216000000⟩, + ⟨1, 8, 3, 0, 7, 5, 614864033373711176386188693403549313336868864000000⟩, + ⟨1, 8, 4, 0, 8, 5, -474616286982649387940414464244018434798308556800000⟩, + ⟨1, 8, 0, 1, 3, 5, -14345390582823954456697221185531393324378750976000000⟩, + ⟨1, 8, 1, 1, 4, 5, 13214083540032912068101758860840077076107100160000000⟩, + ⟨1, 8, 2, 1, 5, 5, 4201602538110809883262125078224408321999241216000000⟩, + ⟨1, 8, 3, 1, 6, 5, -2915504199077131878138372016345662201274564608000000⟩, + ⟨1, 8, 4, 1, 7, 5, 553520165858330715181364080274161466218433740800000⟩, + ⟨1, 8, 5, 1, 8, 5, 452842352907115671464111599929191603613204480000000⟩, + ⟨1, 8, 0, 2, 2, 5, -11966901740829127897567136507081724521625944064000000⟩, + ⟨1, 8, 1, 2, 3, 5, 19959051500219009553652366588664237126867484672000000⟩, + ⟨1, 8, 2, 2, 4, 5, 15479238794543999286712812195910051071082364928000000⟩, + ⟨1, 8, 3, 2, 5, 5, -1240690770728651716352509798476165747906183168000000⟩, + ⟨1, 8, 4, 2, 6, 5, -364932086786639256874754377364605388898435072000000⟩, + ⟨1, 8, 5, 2, 7, 5, 232121744695916654349079492198553977664569344000000⟩, + ⟨1, 8, 6, 2, 8, 5, -58779518412181068604392524112145632265764864000000⟩, + ⟨1, 8, 0, 3, 1, 5, -38360375014728808955137428362471321715848773632000000⟩, + ⟨1, 8, 1, 3, 2, 5, -51430705141728176218915043384161840726448013312000000⟩, + ⟨1, 8, 2, 3, 3, 5, -17632361504848678613670743124019547570354257920000000⟩, + ⟨1, 8, 3, 3, 4, 5, 135184042203076972360954075720713903544467456000000⟩, + ⟨1, 8, 4, 3, 5, 5, -1001262312146640415521372220444370599458688204800000⟩, + ⟨1, 8, 5, 3, 6, 5, -158821174037697686742274081001388473472516096000000⟩, + ⟨1, 8, 6, 3, 7, 5, -124628303402965630365068340948496445079552000000⟩, + ⟨1, 8, 7, 3, 8, 5, 2493337961443718632288398380058462287560704000000⟩, + ⟨1, 8, 0, 4, 0, 5, -122501078611279772395860536230777319036792340480000000⟩, + ⟨1, 8, 1, 4, 1, 5, 23154532008840523228057334482617109208226594816000000⟩, + ⟨1, 8, 2, 4, 2, 5, 4204182379906683220818190641432185714434375680000000⟩, + ⟨1, 8, 3, 4, 3, 5, 1996393960910539251707819301623201546096345088000000⟩, + ⟨1, 8, 4, 4, 4, 5, 750411845915326325634043681921053935158689792000000⟩, + ⟨1, 8, 5, 4, 5, 5, -96301510620250436870022431959468898814787584000000⟩, + ⟨1, 8, 6, 4, 6, 5, -25185985100602649628091920121245203171377152000000⟩, + ⟨1, 8, 7, 4, 7, 5, 6595085467013989305404268558504958988648448000000⟩, + ⟨1, 8, 8, 4, 8, 5, -784920587364218515192470072512080018145280000000⟩, + ⟨1, 8, 1, 5, 0, 5, 122038539804615989957527889805138533326472085504000000⟩, + ⟨1, 8, 2, 5, 1, 5, -4354280579812081409688449961419274121490989056000000⟩, + ⟨1, 8, 3, 5, 2, 5, 2492872099121236523631435254365747611583905792000000⟩, + ⟨1, 8, 4, 5, 3, 5, 715055366026740610895879930216296066632489369600000⟩, + ⟨1, 8, 5, 5, 4, 5, -63880319995470376731240621064761042700075008000000⟩, + ⟨1, 8, 6, 5, 5, 5, -21039900793703575485820354116258814331191296000000⟩, + ⟨1, 8, 7, 5, 6, 5, -2089310291354617498364755798997060749885440000000⟩, + ⟨1, 8, 8, 5, 7, 5, 1286879059406020942327878232376493188579328000000⟩, + ⟨1, 8, 2, 6, 0, 5, 78386110577526016130921831522041899403060445184000000⟩, + ⟨1, 8, 3, 6, 1, 5, 606919474733160070227473766034438154172235776000000⟩, + ⟨1, 8, 4, 6, 2, 5, -905687368012726939805263874900091059228481945600000⟩, + ⟨1, 8, 5, 6, 3, 5, 582112825196449404287075369737985038963703808000000⟩, + ⟨1, 8, 6, 6, 4, 5, 14028527715772394560038821038146065044340736000000⟩, + ⟨1, 8, 7, 6, 5, 5, -13053368799325922121939792715629944704598016000000⟩, + ⟨1, 8, 8, 6, 6, 5, -1922258236419733712744424594542603028922368000000⟩, + ⟨1, 8, 3, 7, 0, 5, -63793330765776370378298809546179015112988295168000000⟩, + ⟨1, 8, 4, 7, 1, 5, -870018958439404509160897064756110016388897177600000⟩, + ⟨1, 8, 5, 7, 2, 5, -32248887085684158185566096301942598191284224000000⟩, + ⟨1, 8, 6, 7, 3, 5, 70818681053236416511008776183315368626880512000000⟩, + ⟨1, 8, 7, 7, 4, 5, -10150162951420717656178547588662527598264320000000⟩, + ⟨1, 8, 8, 7, 5, 5, -4965396486369085100951124378976363877498880000000⟩ +] + +def collectedFourData_8_4_11 : List CollectedFourTerm := [ + ⟨2, 2, 4, 0, 8, 0, 2090384006139809764100497582219604138717651927040000⟩, + ⟨2, 2, 4, 1, 7, 0, -2437905595575165053098786499244492712914966282240000⟩, + ⟨2, 2, 5, 1, 8, 0, -11966901740829127897567136507081724521625944064000000⟩, + ⟨2, 2, 4, 2, 6, 0, 1607294605070944923529573583464169390422464921600000⟩, + ⟨2, 2, 5, 2, 7, 0, -6134095216256463342158955884402938020342477619200000⟩, + ⟨2, 2, 6, 2, 8, 0, 5436617198980000127389026059400815136738587443200000⟩, + ⟨2, 2, 4, 3, 5, 0, 4409926040608922076129849856311340753824975421440000⟩, + ⟨2, 2, 5, 3, 6, 0, 4197039812797919906663943908442740833557204172800000⟩, + ⟨2, 2, 6, 3, 7, 0, 11527082835368185606479734344265626191239577600000⟩, + ⟨2, 2, 7, 3, 8, 0, -614968134489764255789262290613882151383544627200000⟩, + ⟨2, 2, 4, 4, 4, 0, -3305088686888224710587135813984242552450685337600000⟩, + ⟨2, 2, 5, 4, 5, 0, 2544882800134927819663995429199742038873158451200000⟩, + ⟨2, 2, 6, 4, 6, 0, 2329494413530524307165761001604099730872834457600000⟩, + ⟨2, 2, 7, 4, 7, 0, -1626641662368841408342667891859927222343591526400000⟩, + ⟨2, 2, 8, 4, 8, 0, 435591806163569914455201912926031697447747584000000⟩, + ⟨2, 2, 4, 5, 3, 0, -3149365796419433637214838196077815290852676730880000⟩, + ⟨2, 2, 5, 5, 4, 0, 1688113992984475843777138100720234183927424614400000⟩, + ⟨2, 2, 6, 5, 5, 0, 1946016054738162995741204913770684439807708364800000⟩, + ⟨2, 2, 7, 5, 6, 0, 515316925388101943667071012564611122585403392000000⟩, + ⟨2, 2, 8, 5, 7, 0, -714153740932057668226548741848715003605444198400000⟩, + ⟨2, 2, 4, 6, 2, 0, 3988978972240528196088007145168085564677349703680000⟩, + ⟨2, 2, 5, 6, 3, 0, -15383028854262654418420414741080052187764516454400000⟩, + ⟨2, 2, 6, 6, 4, 0, -1297522285247757441560715953675024809094597836800000⟩, + ⟨2, 2, 7, 6, 5, 0, 3219541828449218218110823869430724444457585868800000⟩, + ⟨2, 2, 8, 6, 6, 0, 1066757517377152904534404880732698273309419110400000⟩, + ⟨2, 2, 4, 7, 1, 0, 3831882229163013433360791400158486274032040673280000⟩, + ⟨2, 2, 5, 7, 2, 0, 852215479687327735946480526252267099089220403200000⟩, + ⟨2, 2, 6, 7, 3, 0, -6550139739547720936780376799456690582958217625600000⟩, + ⟨2, 2, 7, 7, 4, 0, 2503482027517839876498989536773552771302424576000000⟩, + ⟨2, 2, 8, 7, 5, 0, 2755547578486601973434985757125059034338033664000000⟩ +] + +def collectedFourData_8_4_12 : List CollectedFourTerm := [ + ⟨2, 3, 3, 0, 7, 1, 1806677729229604094257076540927095370500685168640000⟩, + ⟨2, 3, 4, 0, 8, 1, -6972912945617263006752531925819504491841286307840000⟩, + ⟨2, 3, 3, 1, 6, 1, -8566733814379030439728807529586447898189580206080000⟩, + ⟨2, 3, 4, 1, 7, 1, 8132143872919528518849327220740997773890986967040000⟩, + ⟨2, 3, 5, 1, 8, 1, 19959051500219009553652366588664237126867484672000000⟩, + ⟨2, 3, 3, 2, 5, 1, -3645567577008978326430419166877271567825035591680000⟩, + ⟨2, 3, 4, 2, 6, 1, -5361467235781363193159388487858261820528236953600000⟩, + ⟨2, 3, 5, 2, 7, 1, 10230778607531809695635428610611773741865736601600000⟩, + ⟨2, 3, 6, 2, 8, 1, -6044991149279720746113530318843246989984294502400000⟩, + ⟨2, 3, 3, 3, 4, 1, 397216270815908841685303083333326427382150594560000⟩, + ⟨2, 3, 4, 3, 5, 1, -14710230410995595223138823253983271785366542090240000⟩, + ⟨2, 3, 5, 3, 6, 1, -7000051942124436293433504012446173694246938214400000⟩, + ⟨2, 3, 6, 3, 7, 1, -12816998358811837451388702680324395293160243200000⟩, + ⟨2, 3, 7, 3, 8, 1, 512838700153996466018555216778540609786662092800000⟩, + ⟨2, 3, 3, 4, 3, 1, 5866078209445906988335072923400518003657151610880000⟩, + ⟨2, 3, 4, 4, 4, 1, 11024814399424124819169260891664125550520801689600000⟩, + ⟨2, 3, 5, 4, 5, 1, -4244494353673481091682687916448274827357821337600000⟩, + ⟨2, 3, 6, 4, 6, 1, -2590171902250272136854189982795359633500484403200000⟩, + ⟨2, 3, 7, 4, 7, 1, 1356500847702796560986213352110244442924489113600000⟩, + ⟨2, 3, 8, 4, 8, 1, -290601510084422020692187999391992706386152652800000⟩, + ⟨2, 3, 3, 5, 2, 1, 7324898284565615149210676530735819055257532497920000⟩, + ⟨2, 3, 4, 5, 3, 1, 10505368137067796441192675574164537783995575828480000⟩, + ⟨2, 3, 5, 5, 4, 1, -2815528601631442145405372132723540162627449651200000⟩, + ⟨2, 3, 6, 5, 5, 1, -2163781152267901514976346313572668958345632153600000⟩, + ⟨2, 3, 7, 5, 6, 1, -429736838970778994092164624623560841974775808000000⟩, + ⟨2, 3, 8, 5, 7, 1, 476441826064477252714521892241673522026674913280000⟩, + ⟨2, 3, 3, 6, 1, 1, 1783333938756632214350037091141020659100690677760000⟩, + ⟨2, 3, 4, 6, 2, 1, -13306073445660827964101654635097082727111097057280000⟩, + ⟨2, 3, 5, 6, 3, 1, 25656654644705948444010370548839581012125233971200000⟩, + ⟨2, 3, 6, 6, 4, 1, 1442718963510519752440178208547601539176962457600000⟩, + ⟨2, 3, 7, 6, 5, 1, -2684863741376179759229100919080336412871177011200000⟩, + ⟨2, 3, 8, 6, 6, 1, -711678551013194447131805644524347332637679943680000⟩, + ⟨2, 3, 3, 7, 0, 1, -187446303104633077870358081573395249665991696711680000⟩, + ⟨2, 3, 4, 7, 1, 1, -12782044410659568267481623458238724665636689018880000⟩, + ⟨2, 3, 5, 7, 2, 1, -1421371464121733715952362246469946027240167833600000⟩, + ⟨2, 3, 6, 7, 3, 1, 7283120238728621543699479164205079038199542579200000⟩, + ⟨2, 3, 7, 7, 4, 1, -2087721943375766898123980236839508007687553024000000⟩, + ⟨2, 3, 8, 7, 5, 1, -1838341024984711624126037192049373585058090188800000⟩ +] + +def collectedFourData_8_4_13 : List CollectedFourTerm := [ + ⟨2, 4, 2, 0, 6, 2, -14706585312105750269849578015305017881191650426880000⟩, + ⟨2, 4, 3, 0, 7, 2, 4203505762068304325713717840459601679078213550080000⟩, + ⟨2, 4, 4, 0, 8, 2, -8111762067771039161286300033593311242379056906240000⟩, + ⟨2, 4, 2, 1, 5, 2, 7181043092552730808321004999581832665283564666880000⟩, + ⟨2, 4, 3, 1, 6, 2, -19931786598267863008186155864019155235658017013760000⟩, + ⟨2, 4, 4, 1, 7, 2, 9460324072949657812175625696135904635869661757440000⟩, + ⟨2, 4, 5, 1, 8, 2, 15479238794543999286712812195910051071082364928000000⟩, + ⟨2, 4, 2, 2, 4, 2, 26455877207631978271151100505539639997736461271040000⟩, + ⟨2, 4, 3, 2, 5, 2, -8481957832347384246995351559321796066583469096960000⟩, + ⟨2, 4, 4, 2, 6, 2, -6237127422929350831008419996213383558824827289600000⟩, + ⟨2, 4, 5, 2, 7, 2, 7934478505572246201115798872846986883627378278400000⟩, + ⟨2, 4, 6, 2, 8, 2, -3516143847426029135627420521856883725616493363200000⟩, + ⟨2, 4, 2, 3, 3, 2, -30135822377601327156172207462070631919167052185600000⟩, + ⟨2, 4, 3, 3, 4, 2, 924183021768881638320402062599018668303392440320000⟩, + ⟨2, 4, 4, 3, 5, 2, -17112774816884361649838025549539012389974457712640000⟩, + ⟨2, 4, 5, 3, 6, 2, -5428889022364948642501844920592678854522935705600000⟩, + ⟨2, 4, 6, 3, 7, 2, -7455165575747047423900099433095271512906137600000⟩, + ⟨2, 4, 7, 3, 8, 2, 238639176897163254235466931519292225853136568320000⟩, + ⟨2, 4, 2, 4, 2, 2, 7185452351862742790538568885797347574501762662400000⟩, + ⟨2, 4, 3, 4, 3, 2, 13648307694955531298864275160816979535941976719360000⟩, + ⟨2, 4, 4, 4, 4, 2, 12825439231343780503460509202278582924990847385600000⟩, + ⟨2, 4, 5, 4, 5, 2, -3291816831169786173924909378210995101774538342400000⟩, + ⟨2, 4, 6, 4, 6, 2, -1506605514047484622086978635618831421247429017600000⟩, + ⟨2, 4, 7, 4, 7, 2, 631220392803612265098155871214878553582432419840000⟩, + ⟨2, 4, 8, 4, 8, 2, -112687974391029931608304165368550563851639193600000⟩, + ⟨2, 4, 2, 5, 1, 2, -7441988193094384751822507974101893813383546798080000⟩, + ⟨2, 4, 3, 5, 2, 2, 17042470634131993637464985942753623087635486474240000⟩, + ⟨2, 4, 4, 5, 3, 2, 12221154548587784127814640073013764791916067553280000⟩, + ⟨2, 4, 5, 5, 4, 2, -2183582699661024023406957026016757718501346508800000⟩, + ⟨2, 4, 6, 5, 5, 2, -1258590062059846379150290109809445561260887244800000⟩, + ⟨2, 4, 7, 5, 6, 2, -199969396817324643640231955899611367148303155200000⟩, + ⟨2, 4, 8, 5, 7, 2, 184752186176775876885398216613786524669297295360000⟩, + ⟨2, 4, 2, 6, 0, 2, 133971272344079207093949693784610881258317278085120000⟩, + ⟨2, 4, 3, 6, 1, 2, 4149192944583420147426542936913183374360413470720000⟩, + ⟨2, 4, 4, 6, 2, 2, -15479284294711957596429984468805837829737367470080000⟩, + ⟨2, 4, 5, 6, 3, 2, 19898013886591351826682510269127224615741738188800000⟩, + ⟨2, 4, 6, 6, 4, 2, 839175324138698273634813934347802643903859916800000⟩, + ⟨2, 4, 7, 6, 5, 2, -1249347354500849209974624872945241542060440289280000⟩, + ⟨2, 4, 8, 6, 6, 2, -275971085999938912610561741375694533053026140160000⟩, + ⟨2, 4, 3, 7, 0, 2, -436121839789719168589080287541079190625640733736960000⟩, + ⟨2, 4, 4, 7, 1, 2, -14869668359207461312118267094192721544338923847680000⟩, + ⟨2, 4, 5, 7, 2, 2, -1102344382880595342212423187130834591957804646400000⟩, + ⟨2, 4, 6, 7, 3, 2, 4236316941592373773709074604348245301228312985600000⟩, + ⟨2, 4, 7, 7, 4, 2, -971479426197232551190210881678407973297822105600000⟩, + ⟨2, 4, 8, 7, 5, 2, -712862525336759620777121579405667617530812825600000⟩ +] + +def collectedFourData_8_4_14 : List CollectedFourTerm := [ + ⟨2, 5, 1, 0, 5, 3, -5525408277236643856405648631902091314208377405440000⟩, + ⟨2, 5, 2, 0, 6, 3, 4715044430245361599235154997631998184144366469120000⟩, + ⟨2, 5, 3, 0, 7, 3, -673838148364386455973652038385050338471140392960000⟩, + ⟨2, 5, 4, 0, 8, 3, 866897781853686354064266659826232272166500433920000⟩, + ⟨2, 5, 1, 1, 4, 3, -2413583356548952653899633733559837916628674150400000⟩, + ⟨2, 5, 2, 1, 5, 3, -2302297679463474049410344441218959784044260229120000⟩, + ⟨2, 5, 3, 1, 6, 3, 3195142087390022678713086078864794446394944389120000⟩, + ⟨2, 5, 4, 1, 7, 3, -1011017567569090277021679929686512896027677163520000⟩, + ⟨2, 5, 5, 1, 8, 3, -1240690770728651716352509798476165747906183168000000⟩, + ⟨2, 5, 1, 2, 3, 3, -3645567577008978326430419166877271567825035591680000⟩, + ⟨2, 5, 2, 2, 4, 3, -8481957832347384246995351559321796066583469096960000⟩, + ⟨2, 5, 3, 2, 5, 3, 1359690478321483910597202607854084550645273067520000⟩, + ⟨2, 5, 4, 2, 6, 3, 666557017193427471027941820367011568541289676800000⟩, + ⟨2, 5, 5, 2, 7, 3, -635963717794583627022490900412690342158427750400000⟩, + ⟨2, 5, 6, 2, 8, 3, 225460555416637052961929052518452269105398415360000⟩, + ⟨2, 5, 1, 3, 2, 3, 9393938941704510770748195095535262482182732513280000⟩, + ⟨2, 5, 2, 3, 3, 3, 9661776574022904798501949220499132833967007334400000⟩, + ⟨2, 5, 3, 3, 4, 3, -148150094561099681170602234666637334595596451840000⟩, + ⟨2, 5, 4, 3, 5, 3, 1828829101023554212318800900852430388038069125120000⟩, + ⟨2, 5, 5, 3, 6, 3, 435135900076196669147721849707924773754476953600000⟩, + ⟨2, 5, 6, 3, 7, 3, 478036691434389006149305270398260651470356480000⟩, + ⟨2, 5, 7, 3, 8, 3, -12751592772763976113338658545095354250197729280000⟩, + ⟨2, 5, 1, 4, 1, 3, -4229229587955085746749475002389714738881799127040000⟩, + ⟨2, 5, 2, 4, 2, 3, -2303711321931115147593742162932589074576939417600000⟩, + ⟨2, 5, 3, 4, 3, 3, -2187876240938242161591964391995626306773786296320000⟩, + ⟨2, 5, 4, 4, 4, 3, -1370644839932575228414506345130494504347684044800000⟩, + ⟨2, 5, 5, 4, 5, 3, 263845452322961189078874560637297630856504934400000⟩, + ⟨2, 5, 6, 4, 6, 3, 96605864472687754535087073750377588708584980480000⟩, + ⟨2, 5, 7, 4, 7, 3, -33729019281542204020479783913174010680427151360000⟩, + ⟨2, 5, 8, 4, 8, 3, 5161233116536415330030979614201344358036275200000⟩, + ⟨2, 5, 1, 5, 0, 3, -22290625576688642234035831878914966637910960373760000⟩, + ⟨2, 5, 2, 5, 1, 3, 2385958686882780423224639669601027042546989137920000⟩, + ⟨2, 5, 3, 5, 2, 3, -2731973620516076275954577821721708250446828666880000⟩, + ⟨2, 5, 4, 5, 3, 3, -1306065400014008083767616401984623253878200074240000⟩, + ⟨2, 5, 5, 5, 4, 3, 175018354490860763995411313351936240887057612800000⟩, + ⟨2, 5, 6, 5, 5, 3, 80702731954950916734838430298900110366516183040000⟩, + ⟨2, 5, 7, 5, 6, 3, 10685287924574969559620064048035994712984780800000⟩, + ⟨2, 5, 8, 5, 7, 3, -8461853243889530710483680307202528195924459520000⟩, + ⟨2, 5, 2, 6, 0, 3, -42952220931861473946949127988883803683184055418880000⟩, + ⟨2, 5, 3, 6, 1, 3, -665131594730816693664959098900520463592209776640000⟩, + ⟨2, 5, 4, 6, 2, 3, 1654259223539538416705400870367730303448530288640000⟩, + ⟨2, 5, 5, 6, 3, 3, -1594864095876989673959902635185281525804223692800000⟩, + ⟨2, 5, 6, 6, 4, 3, -53809213411661383329123032445159155476086128640000⟩, + ⟨2, 5, 7, 6, 5, 3, 66758396100192879048017173626513322071419781120000⟩, + ⟨2, 5, 8, 6, 6, 3, 12639779142065965596756600968869517385132933120000⟩, + ⟨2, 5, 3, 7, 0, 3, 69912009075152225980624377304242477939308384747520000⟩, + ⟨2, 5, 4, 7, 1, 3, 1589110036734467008118655802063335904532433469440000⟩, + ⟨2, 5, 5, 7, 2, 3, 88355023147946451288233932463466489345107558400000⟩, + ⟨2, 5, 6, 7, 3, 3, -271639162678602319157936967970246678608221306880000⟩, + ⟨2, 5, 7, 7, 4, 3, 51910630061064304577455203789250356914316902400000⟩, + ⟨2, 5, 8, 7, 5, 3, 32649887383180568702191648203281511438562099200000⟩ +] + +def collectedFourData_8_4_15 : List CollectedFourTerm := [ + ⟨2, 6, 0, 0, 4, 4, 2451456550626464195752343106258193547066867712000000⟩, + ⟨2, 6, 1, 0, 5, 4, -8126113373826084512055957517874752192101797068800000⟩, + ⟨2, 6, 2, 0, 6, 4, 3467163300913850094449235541841936804155175731200000⟩, + ⟨2, 6, 3, 0, 7, 4, -330333670350753691093353497023222761428248166400000⟩, + ⟨2, 6, 4, 0, 8, 4, 318732539995419774322692529923844305237678489600000⟩, + ⟨2, 6, 0, 1, 3, 4, 1926753422963340491688835575108962081753687654400000⟩, + ⟨2, 6, 1, 1, 4, 4, -3549611360539195391352522047190732607856836608000000⟩, + ⟨2, 6, 2, 1, 5, 4, -1692972810777837219686983706916030867876033331200000⟩, + ⟨2, 6, 3, 1, 6, 4, 1566344997803478307940247474246958661774396620800000⟩, + ⟨2, 6, 4, 1, 7, 4, -371721100268860706708803308961116626687203737600000⟩, + ⟨2, 6, 5, 1, 8, 4, -364932086786639256874754377364605388898435072000000⟩, + ⟨2, 6, 0, 2, 2, 4, 1607294605070944923529573583464169390422464921600000⟩, + ⟨2, 6, 1, 2, 3, 4, -5361467235781363193159388487858261820528236953600000⟩, + ⟨2, 6, 2, 2, 4, 4, -6237127422929350831008419996213383558824827289600000⟩, + ⟨2, 6, 3, 2, 5, 4, 666557017193427471027941820367011568541289676800000⟩, + ⟨2, 6, 4, 2, 6, 4, 245073197312309400511149130298716814976221184000000⟩, + ⟨2, 6, 5, 2, 7, 4, -187059960572661621028983831745372366046861721600000⟩, + ⟨2, 6, 6, 2, 8, 4, 55263428592516202415777651823853032231351091200000⟩, + ⟨2, 6, 0, 3, 1, 4, 5152246182427500486744145137460589568868535500800000⟩, + ⟨2, 6, 1, 3, 2, 4, 13815488202306707017882196035274088768618469785600000⟩, + ⟨2, 6, 2, 3, 3, 4, 7104695969394745395081641192983405939491078144000000⟩, + ⟨2, 6, 3, 3, 4, 4, -72627180010465849565815742755401728624531865600000⟩, + ⟨2, 6, 4, 3, 5, 4, 672406086148181850955379154904434200937077145600000⟩, + ⟨2, 6, 5, 3, 6, 4, 127989226483347998907153214306773200865224294400000⟩, + ⟨2, 6, 6, 3, 7, 4, 117173252380525453916514599422533326969241600000⟩, + ⟨2, 6, 7, 3, 8, 4, -2679075163038425446387148914785296256388300800000⟩, + ⟨2, 6, 0, 4, 0, 4, 16453324931674402572914745304240790815912230912000000⟩, + ⟨2, 6, 1, 4, 1, 4, -6219847908298001464640881435558025580029725900800000⟩, + ⟨2, 6, 2, 4, 2, 4, -1694012319388398383582662738067088656748773376000000⟩, + ⟨2, 6, 3, 4, 3, 4, -1072556059191107925386011095539176533455064268800000⟩, + ⟨2, 6, 4, 4, 4, 4, -503945355967076809278572581595292778075521024000000⟩, + ⟨2, 6, 5, 4, 5, 4, 77606502584713233309735150525230505250101657600000⟩, + ⟨2, 6, 6, 4, 6, 4, 23679402736496240176687521908302455349287321600000⟩, + ⟨2, 6, 7, 4, 7, 4, -7086375752512154796451697468411793941043609600000⟩, + ⟨2, 6, 8, 4, 8, 4, 948815982216792371230941910616748261900288000000⟩, + ⟨2, 6, 1, 5, 0, 4, -32782401140548622564713274073066692373092971315200000⟩, + ⟨2, 6, 2, 5, 1, 4, 1754492140856897770356022277415021856559412019200000⟩, + ⟨2, 6, 3, 5, 2, 4, -1339287298525720228830649532075389205903258419200000⟩, + ⟨2, 6, 4, 5, 3, 4, -480201415969084550953824653367750831763567411200000⟩, + ⟨2, 6, 5, 5, 4, 4, 51479236274807751643366490022742868834333491200000⟩, + ⟨2, 6, 6, 5, 5, 4, 19781330070671432653591888384890703736261836800000⟩, + ⟨2, 6, 7, 5, 6, 4, 2244950101432561414909375915642349250674688000000⟩, + ⟨2, 6, 8, 5, 7, 4, -1555585926016707297365558661908555522428108800000⟩, + ⟨2, 6, 2, 6, 0, 4, -31584509183499712774463352026241958116787539148800000⟩, + ⟨2, 6, 3, 6, 1, 4, -326065482470824517429030224848718547572595097600000⟩, + ⟨2, 6, 4, 6, 2, 4, 608221932466080710180778830559195375802200883200000⟩, + ⟨2, 6, 5, 6, 3, 4, -469107287956740999848333637543081836041941811200000⟩, + ⟨2, 6, 6, 6, 4, 4, -13189365286090224165429396332452757560413388800000⟩, + ⟨2, 6, 7, 6, 5, 4, 14025758515305940202910353789959396973032243200000⟩, + ⟨2, 6, 8, 6, 6, 4, 2323635493862511799049836611907686322982092800000⟩, + ⟨2, 6, 3, 7, 0, 4, 34272756173640836513085901834772366651363740876800000⟩, + ⟨2, 6, 4, 7, 1, 4, 584268513477495491921658972407729837411873587200000⟩, + ⟨2, 6, 5, 7, 2, 4, 25988412049301707781839126592944014081235353600000⟩, + ⟨2, 6, 6, 7, 3, 4, -66582429205317641571471064319623876511898009600000⟩, + ⟨2, 6, 7, 7, 4, 4, 10906283016762974554120586714724850062065664000000⟩, + ⟨2, 6, 8, 7, 5, 4, 6002196426176782266823883875568944674766848000000⟩ +] + +def collectedFourData_8_4_16 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 4, 5, -9355763313468361111966814054150593710070431744000000⟩, + ⟨2, 7, 1, 0, 5, 5, 15506290202145010519335085456875141124003253452800000⟩, + ⟨2, 7, 2, 0, 6, 5, -4410705573414332686822197113266869871475215564800000⟩, + ⟨2, 7, 3, 0, 7, 5, 315172181358992098159133094183797126509835059200000⟩, + ⟨2, 7, 4, 0, 8, 5, -243282811089243705873415268051308269513253847040000⟩, + ⟨2, 7, 0, 1, 3, 5, -7353281045937135534852048959105250035376114892800000⟩, + ⟨2, 7, 1, 1, 4, 5, 6773386160059935028883701613124084096772866048000000⟩, + ⟨2, 7, 2, 1, 5, 5, 2153692792655189532371933546252008630837365964800000⟩, + ⟨2, 7, 3, 1, 6, 5, -1494453681316478577592304569376298544243566182400000⟩, + ⟨2, 7, 4, 1, 7, 5, 283728025434411545875947200737088904987137802240000⟩, + ⟨2, 7, 5, 1, 8, 5, 232121744695916654349079492198553977664569344000000⟩, + ⟨2, 7, 0, 2, 2, 5, -6134095216256463342158955884402938020342477619200000⟩, + ⟨2, 7, 1, 2, 3, 5, 10230778607531809695635428610611773741865736601600000⟩, + ⟨2, 7, 2, 2, 4, 5, 7934478505572246201115798872846986883627378278400000⟩, + ⟨2, 7, 3, 2, 5, 5, -635963717794583627022490900412690342158427750400000⟩, + ⟨2, 7, 4, 2, 6, 5, -187059960572661621028983831745372366046861721600000⟩, + ⟨2, 7, 5, 2, 7, 5, 118982917597656683549884972047538277070353203200000⟩, + ⟨2, 7, 6, 2, 8, 5, -30129700277879713395952680737722263110103859200000⟩, + ⟨2, 7, 0, 3, 1, 5, -19663083893203984402714438093823327224169339289600000⟩, + ⟨2, 7, 1, 3, 2, 5, -26362783718880387398270616151128137441291639193600000⟩, + ⟨2, 7, 2, 3, 3, 5, -9038144266629794947746299102012298924052709376000000⟩, + ⟨2, 7, 3, 3, 4, 5, 69293774157341155424869631688606343261637836800000⟩, + ⟨2, 7, 4, 3, 5, 5, -513235463294700279007589019697615417841748541440000⟩, + ⟨2, 7, 5, 3, 6, 5, -81409894140016342996219196090895092383796428800000⟩, + ⟨2, 7, 6, 3, 7, 5, -63883024718587134206548889177408715463065600000⟩, + ⟨2, 7, 7, 3, 8, 5, 1278056157979524338189784995482499097506611200000⟩, + ⟨2, 7, 0, 4, 0, 5, -62792633930630493083344751389332585919643910144000000⟩, + ⟨2, 7, 1, 4, 1, 5, 11868744902073968595806309062377231171332132044800000⟩, + ⟨2, 7, 2, 4, 2, 5, 2155015189676698684249672037280796957898440704000000⟩, + ⟨2, 7, 3, 4, 3, 5, 1023328419552658711338080271687323011720308326400000⟩, + ⟨2, 7, 4, 4, 4, 5, 384652419978210620193419967521397124856650137600000⟩, + ⟨2, 7, 5, 4, 5, 5, -49363038855621198755748633130616910339322675200000⟩, + ⟨2, 7, 6, 4, 6, 5, -12910044226001073180740099298516542502312345600000⟩, + ⟨2, 7, 7, 4, 7, 5, 3380564417604227357505768950087447063455334400000⟩, + ⟨2, 7, 8, 4, 8, 5, -402341201120155089248368940971509713731584000000⟩, + ⟨2, 7, 1, 5, 0, 5, 62555541896055744297656181514154258805566944051200000⟩, + ⟨2, 7, 2, 5, 1, 5, -2231953788317236818257222809131049935444954316800000⟩, + ⟨2, 7, 3, 5, 2, 5, 1277817362349238362728304172860126511777814937600000⟩, + ⟨2, 7, 4, 5, 3, 5, 366529097931679390391984246008590169197646970880000⟩, + ⟨2, 7, 5, 5, 4, 5, -32744312085410147046497302272618037219059302400000⟩, + ⟨2, 7, 6, 5, 5, 5, -10784809435581250307226630524011146147318988800000⟩, + ⟨2, 7, 7, 5, 6, 5, -1070956254261497525162668572656371217989632000000⟩, + ⟨2, 7, 8, 5, 7, 5, 659639299558263509470705309943114045482598400000⟩, + ⟨2, 7, 2, 6, 0, 5, 40179812312993746805350270441569899652437979955200000⟩, + ⟨2, 7, 3, 6, 1, 5, 311099892623971780046663893762590812744240332800000⟩, + ⟨2, 7, 4, 6, 2, 5, -464244854003945134604976544968633237150294343680000⟩, + ⟨2, 7, 5, 6, 3, 5, 298384291414067916586709308365611479190627942400000⟩, + ⟨2, 7, 6, 6, 4, 5, 7190860810600966212459566351346517368687820800000⟩, + ⟨2, 7, 7, 6, 5, 5, -6691005645578971224857678235080816690253004800000⟩, + ⟨2, 7, 8, 6, 6, 5, -985327305914263481666733764568476895569510400000⟩, + ⟨2, 7, 3, 7, 0, 5, -32699722413890468593665549406665137425398261350400000⟩, + ⟨2, 7, 4, 7, 1, 5, -445961640414189843430894730168033600064486113280000⟩, + ⟨2, 7, 5, 7, 2, 5, -16530405971912343405482550778452445156815667200000⟩, + ⟨2, 7, 6, 7, 3, 5, 36300835594573178468406622808478394334419353600000⟩, + ⟨2, 7, 7, 7, 4, 5, -5202855956617855230369403495951984855351296000000⟩, + ⟨2, 7, 8, 7, 5, 5, -2545204723285624309386530149008176698097664000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0818.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0818.lean new file mode 100644 index 0000000000000000000000000000000000000000..7effb7c7a1775aa0e8ae619a9b25aad42175c6a9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0818.lean @@ -0,0 +1,656 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0818. -/ +namespace LaughlinFock +def collectedFourData_8_4_17 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 4, 6, 8291965146675613845677179745412329459284967424000000⟩, + ⟨2, 8, 1, 0, 5, 6, -9162097101888439720935100720001440610086236979200000⟩, + ⟨2, 8, 2, 0, 6, 6, 1954592888981554230813553875215256657519339110400000⟩, + ⟨2, 8, 3, 0, 7, 6, -111734196578842340353994100655744294896040673280000⟩, + ⟨2, 8, 4, 0, 8, 6, 71873436823454199462989519920679488301857505280000⟩, + ⟨2, 8, 0, 1, 3, 6, 6517175360651274713266638145540425599679253708800000⟩, + ⟨2, 8, 1, 1, 4, 6, -4002144993937476735235672072097571583737987072000000⟩, + ⟨2, 8, 2, 1, 5, 6, -954403450311467394536438905221446460118558310400000⟩, + ⟨2, 8, 3, 1, 6, 6, 529810659957936393558153874070566709265338204160000⟩, + ⟨2, 8, 4, 1, 7, 6, -83822232322130550532296926500171514554016071680000⟩, + ⟨2, 8, 5, 1, 8, 6, -58779518412181068604392524112145632265764864000000⟩, + ⟨2, 8, 0, 2, 2, 6, 5436617198980000127389026059400815136738587443200000⟩, + ⟨2, 8, 1, 2, 3, 6, -6044991149279720746113530318843246989984294502400000⟩, + ⟨2, 8, 2, 2, 4, 6, -3516143847426029135627420521856883725616493363200000⟩, + ⟨2, 8, 3, 2, 5, 6, 225460555416637052961929052518452269105398415360000⟩, + ⟨2, 8, 4, 2, 6, 6, 55263428592516202415777651823853032231351091200000⟩, + ⟨2, 8, 5, 2, 7, 6, -30129700277879713395952680737722263110103859200000⟩, + ⟨2, 8, 6, 2, 8, 6, 6675949791940138403263954340967647292476620800000⟩, + ⟨2, 8, 0, 3, 1, 6, 17427290628856443308047617977229790361505339801600000⟩, + ⟨2, 8, 1, 3, 2, 6, 15576800199125213087590880822012327485988300390400000⟩, + ⟨2, 8, 2, 3, 3, 6, 4005230505437888987090791950090492422073090048000000⟩, + ⟨2, 8, 3, 3, 4, 6, -24565886970104454103985179094824759883590533120000⟩, + ⟨2, 8, 4, 3, 5, 6, 151625988213101591098156475198758273511671726080000⟩, + ⟨2, 8, 5, 3, 6, 6, 20615192160499822704866636595089466010160332800000⟩, + ⟨2, 8, 6, 3, 7, 6, 14154799471791185337975030225531142825574400000⟩, + ⟨2, 8, 7, 3, 8, 6, -251718807194236898446625943937488189495705600000⟩, + ⟨2, 8, 0, 4, 0, 6, 55652790111865776812337387210687967399010893824000000⟩, + ⟨2, 8, 1, 4, 1, 6, -7012805245661051793410863466538074154600706867200000⟩, + ⟨2, 8, 2, 4, 2, 6, -954989467167870557074121270336923891025313792000000⟩, + ⟨2, 8, 3, 4, 3, 6, -362788296549480952865238687877887577074444533760000⟩, + ⟨2, 8, 4, 4, 4, 6, -113638490456899451689649780225799307094340403200000⟩, + ⟨2, 8, 5, 4, 5, 6, 12500059635068897630348998130539448816055091200000⟩, + ⟨2, 8, 6, 4, 6, 6, 2860526532611594426357019976693578532808294400000⟩, + ⟨2, 8, 7, 4, 7, 6, -665817098513013308292510266567583572636467200000⟩, + ⟨2, 8, 8, 4, 8, 6, 71318589514918720878923494109511053790412800000⟩, + ⟨2, 8, 1, 5, 0, 6, -36961771103292637881832654778510185715169283276800000⟩, + ⟨2, 8, 2, 5, 1, 6, 989084610289062740984023097196908195952879206400000⟩, + ⟨2, 8, 3, 5, 2, 6, -453009195611591400641473262699156212679536803840000⟩, + ⟨2, 8, 4, 5, 3, 6, -108284287928942603398467267052693845595819868160000⟩, + ⟨2, 8, 5, 5, 4, 6, 8291747495005050652863604655355424737224294400000⟩, + ⟨2, 8, 6, 5, 5, 6, 2389630352892756711491093378823258574631731200000⟩, + ⟨2, 8, 7, 5, 6, 6, 210929566120232227486221369813459655458816000000⟩, + ⟨2, 8, 8, 5, 7, 6, -116926987099824580443916860939166247320289280000⟩, + ⟨2, 8, 2, 6, 0, 6, -17805581016553071573681564164664861545494845849600000⟩, + ⟨2, 8, 3, 6, 1, 6, -110290497112466249472445842847435897957798379520000⟩, + ⟨2, 8, 4, 6, 2, 6, 137152612777999599624993809820949313230743797760000⟩, + ⟨2, 8, 5, 6, 3, 6, -75558991571664419450092357891379064109164134400000⟩, + ⟨2, 8, 6, 6, 4, 6, -1593305784314303185019003606689721152123699200000⟩, + ⟨2, 8, 7, 6, 5, 6, 1317823125000761465544163743159946337216102400000⟩, + ⟨2, 8, 8, 6, 6, 6, 174658109765283624851405779337978045980999680000⟩, + ⟨2, 8, 3, 7, 0, 6, 11592638653934843690351113436141031496030208655360000⟩, + ⟨2, 8, 4, 7, 1, 6, 131751173231204196542376164715559427393936424960000⟩, + ⟨2, 8, 5, 7, 2, 6, 4185946919620676751449652429930832596251443200000⟩, + ⟨2, 8, 6, 7, 3, 6, -8043311204551355269657803121362789315536486400000⟩, + ⟨2, 8, 7, 7, 4, 6, 1024725468616112884226640734355808371867648000000⟩, + ⟨2, 8, 8, 7, 5, 6, 451160384236240608094076261669355586899148800000⟩ +] + +def collectedFourData_8_4_18 : List CollectedFourTerm := [ + ⟨3, 1, 4, 0, 8, 0, 6700808290814832457937518635126953787266716139520000⟩, + ⟨3, 1, 4, 1, 7, 0, -7814802437768628923038342128969296604187192197120000⟩, + ⟨3, 1, 5, 1, 8, 0, -38360375014728808955137428362471321715848773632000000⟩, + ⟨3, 1, 4, 2, 6, 0, 5152246182427500486744145137460589568868535500800000⟩, + ⟨3, 1, 5, 2, 7, 0, -19663083893203984402714438093823327224169339289600000⟩, + ⟨3, 1, 6, 2, 8, 0, 17427290628856443308047617977229790361505339801600000⟩, + ⟨3, 1, 4, 3, 5, 0, 14136191670046730613962750663573984422524585246720000⟩, + ⟨3, 1, 5, 3, 6, 0, 13453776479284478775438902717256970903514146406400000⟩, + ⟨3, 1, 6, 3, 7, 0, 36950518184828879389607447086466158841089228800000⟩, + ⟨3, 1, 7, 3, 8, 0, -1971304584264186918497552336637444502714947993600000⟩, + ⟨3, 1, 4, 4, 4, 0, -10594592003158340551243752082975294177304956108800000⟩, + ⟨3, 1, 5, 4, 5, 0, 8157722081784652422326872464136324802135300505600000⟩, + ⟨3, 1, 6, 4, 6, 0, 7467286122427485504299312580947427253245758668800000⟩, + ⟨3, 1, 7, 4, 7, 0, -5214263936851490127446210411813044467776303923200000⟩, + ⟨3, 1, 8, 4, 8, 0, 1396306696558526678180066399975672514600763392000000⟩, + ⟨3, 1, 4, 5, 3, 0, -10095416142427450699135181360663020865941080637440000⟩, + ⟨3, 1, 5, 5, 4, 0, 5411315914591030815596764137400511675946447667200000⟩, + ⟨3, 1, 6, 5, 5, 0, 6238031134637429753142137471773131171663603302400000⟩, + ⟨3, 1, 7, 5, 6, 0, 1651868707326329664868248333804979914849386496000000⟩, + ⟨3, 1, 8, 5, 7, 0, -2289247953533137002832796804716904353019147059200000⟩, + ⟨3, 1, 4, 6, 2, 0, 12786829257479325149819178843169792442515681443840000⟩, + ⟨3, 1, 5, 6, 3, 0, -49310905068986086459237039549610221947424289587200000⟩, + ⟨3, 1, 6, 6, 4, 0, -4159258806500682749993541041992508884184884838400000⟩, + ⟨3, 1, 7, 6, 5, 0, 10320368177967573973608003962952713589934679654400000⟩, + ⟨3, 1, 8, 6, 6, 0, 3419533251179969921769574821003770881088107315200000⟩, + ⟨3, 1, 4, 7, 1, 0, 12283249458082690660349055558157686301346381168640000⟩, + ⟨3, 1, 5, 7, 2, 0, 2731810296613822915867758289733692922854480281600000⟩, + ⟨3, 1, 6, 7, 3, 0, -20996731004371035050385706154325078863189429452800000⟩, + ⟨3, 1, 7, 7, 4, 0, 8025010274009670732195799180558626012096626688000000⟩, + ⟨3, 1, 8, 7, 5, 0, 8833016328782040936952455535673573852087058432000000⟩ +] + +def collectedFourData_8_4_19 : List CollectedFourTerm := [ + ⟨3, 2, 3, 0, 7, 1, -4655467198785232515899932295084718698704341565440000⟩, + ⟨3, 2, 4, 0, 8, 1, 17967879369470317468869331656245622613339684208640000⟩, + ⟨3, 2, 3, 1, 6, 1, 22074854650791678569121948872129218331279024455680000⟩, + ⟨3, 2, 4, 1, 7, 1, -20954998472429731191810544159384002588042948771840000⟩, + ⟨3, 2, 5, 1, 8, 1, -51430705141728176218915043384161840726448013312000000⟩, + ⟨3, 2, 3, 2, 5, 1, 9393938941704510770748195095535262482182732513280000⟩, + ⟨3, 2, 4, 2, 6, 1, 13815488202306707017882196035274088768618469785600000⟩, + ⟨3, 2, 5, 2, 7, 1, -26362783718880387398270616151128137441291639193600000⟩, + ⟨3, 2, 6, 2, 8, 1, 15576800199125213087590880822012327485988300390400000⟩, + ⟨3, 2, 3, 3, 4, 1, -1023551289579351356438699345291424179410446581760000⟩, + ⟨3, 2, 4, 3, 5, 1, 37905484778497398978542316266285700523712619479040000⟩, + ⟨3, 2, 5, 3, 6, 1, 18037811436492014586077445010959801916024317542400000⟩, + ⟨3, 2, 6, 3, 7, 1, 33026983440913128540385534960798470753170227200000⟩, + ⟨3, 2, 7, 3, 8, 1, -1321488447113727918743465630671020511166516428800000⟩, + ⟨3, 2, 3, 4, 3, 1, -15115775352602237773859336463537619086418095636480000⟩, + ⟨3, 2, 4, 4, 4, 1, -28408863948912570260518884629645470812205586841600000⟩, + ⟨3, 2, 5, 4, 5, 1, 10937260098613180672170629172035855367200676249600000⟩, + ⟨3, 2, 6, 4, 6, 1, 6674383668460456071850020690859153050406433587200000⟩, + ⟨3, 2, 7, 4, 7, 1, -3495446420484526162330908260704818831164021145600000⟩, + ⟨3, 2, 8, 4, 8, 1, 748825192355902092908076534865366063753514188800000⟩, + ⟨3, 2, 3, 5, 2, 1, -18874879092451407417724691565166782919878188728320000⟩, + ⟨3, 2, 4, 5, 3, 1, -27070349062274397421972069606786811307470440366080000⟩, + ⟨3, 2, 5, 5, 4, 1, 7255085309390580033876249689383584930731340595200000⟩, + ⟨3, 2, 6, 5, 5, 1, 5575655257580660006028419121503146708792088985600000⟩, + ⟨3, 2, 7, 5, 6, 1, 1107350650074826257908668596699915133038624768000000⟩, + ⟨3, 2, 8, 5, 7, 1, -1227700578518963864108408988441499903806280826880000⟩, + ⟨3, 2, 3, 6, 1, 1, -4595314660740399769310901935193465037643537448960000⟩, + ⟨3, 2, 4, 6, 2, 1, 34287237545854915128357494694752476078229296250880000⟩, + ⟨3, 2, 5, 6, 3, 1, -66112352079483490491619824182418367489481323315200000⟩, + ⟨3, 2, 6, 6, 4, 1, -3717614216981956294310896028442627216454031769600000⟩, + ⟨3, 2, 7, 6, 5, 1, 6918386649131109457450970048051355902610191155200000⟩, + ⟨3, 2, 8, 6, 6, 1, 1833861178846616267764754941943162273612987105280000⟩, + ⟨3, 2, 3, 7, 0, 1, 483013711587226778878110621904683556458366008033280000⟩, + ⟨3, 2, 4, 7, 1, 1, 32936913719867572609434428126821729680583274004480000⟩, + ⟨3, 2, 5, 7, 2, 1, 3662605743930727896769003838171183745592826265600000⟩, + ⟨3, 2, 6, 7, 3, 1, -18767224960850191539751267312906292862326616883200000⟩, + ⟨3, 2, 7, 7, 4, 1, 5379665045029649677126428762712937747032571904000000⟩, + ⟨3, 2, 8, 7, 5, 1, 4737057530258569297978097905024318870267940044800000⟩ +] + +def collectedFourData_8_4_20 : List CollectedFourTerm := [ + ⟨3, 3, 2, 0, 6, 2, 16752233889973105184118536577637678843537077043200000⟩, + ⟨3, 3, 3, 0, 7, 2, -4788202712566668037262125136400531509950493491200000⟩, + ⟨3, 3, 4, 0, 8, 2, 9240087521013740874979644549703491925514492313600000⟩, + ⟨3, 3, 2, 1, 5, 2, -8179907905705018315200466795764759202578510643200000⟩, + ⟨3, 3, 3, 1, 6, 2, 22704247373070531844641343746385596011623376486400000⟩, + ⟨3, 3, 4, 1, 7, 2, -10776231068033263576902908072297643569537718681600000⟩, + ⟨3, 3, 5, 1, 8, 2, -17632361504848678613670743124019547570354257920000000⟩, + ⟨3, 3, 2, 2, 4, 2, -30135822377601327156172207462070631919167052185600000⟩, + ⟨3, 3, 3, 2, 5, 2, 9661776574022904798501949220499132833967007334400000⟩, + ⟨3, 3, 4, 2, 6, 2, 7104695969394745395081641192983405939491078144000000⟩, + ⟨3, 3, 5, 2, 7, 2, -9038144266629794947746299102012298924052709376000000⟩, + ⟨3, 3, 6, 2, 8, 2, 4005230505437888987090791950090492422073090048000000⟩, + ⟨3, 3, 2, 3, 3, 2, 34327638552553801366075532503116083213667139584000000⟩, + ⟨3, 3, 3, 3, 4, 2, -1052734527373276086586157330404197405194767564800000⟩, + ⟨3, 3, 4, 3, 5, 2, 19493118229349248139087558736724400150979123609600000⟩, + ⟨3, 3, 5, 3, 6, 2, 6184033664871388222190219421228248763815952384000000⟩, + ⟨3, 3, 6, 3, 7, 2, 8492160128468882225825250032481726432804864000000⟩, + ⟨3, 3, 7, 3, 8, 2, -271833278891817216498421976768969348297313484800000⟩, + ⟨3, 3, 2, 4, 2, 2, -8184930481760253931802631139954969318193627136000000⟩, + ⟨3, 3, 3, 4, 3, 2, -15546752550370048230251900338310872736926688870400000⟩, + ⟨3, 3, 4, 4, 4, 2, -14609425178273697523097525746190671974009667584000000⟩, + ⟨3, 3, 5, 4, 5, 2, 3749700172297197610287323345499102507052302336000000⟩, + ⟨3, 3, 6, 4, 6, 2, 1716170505635396648858347263296379855059288064000000⟩, + ⟨3, 3, 7, 4, 7, 2, -719021542523709682159722996514999332920465817600000⟩, + ⟨3, 3, 8, 4, 8, 2, 128362584755273381845476621812346107360968704000000⟩, + ⟨3, 3, 2, 5, 1, 2, 8477149805435338328417461698110856988114236211200000⟩, + ⟨3, 3, 3, 5, 2, 2, -19413034913751737311256455339459820835793639833600000⟩, + ⟨3, 3, 4, 5, 3, 2, -13921086034494088317419362183192425177545913139200000⟩, + ⟨3, 3, 5, 5, 4, 2, 2487313494364295095527837075209579134590124032000000⟩, + ⟨3, 3, 6, 5, 5, 2, 1433656735657516756010539821577500151693443072000000⟩, + ⟨3, 3, 7, 5, 6, 2, 227784630845826735719765211374564205215612928000000⟩, + ⟨3, 3, 8, 5, 7, 2, -210450744944140183055650836531895613606225510400000⟩, + ⟨3, 3, 2, 6, 0, 2, -152606335271987720821968954573452248514378386636800000⟩, + ⟨3, 3, 3, 6, 1, 2, -4726335120435594147467649003757749415036374220800000⟩, + ⟨3, 3, 4, 6, 2, 2, 17632413333974168623508893867029295042659562291200000⟩, + ⟨3, 3, 5, 6, 3, 2, -22665776963176140666974376724469920903811039232000000⟩, + ⟨3, 3, 6, 6, 4, 2, -955902475409675838523445881209844684032049152000000⟩, + ⟨3, 3, 7, 6, 5, 2, 1423128391006533127617830421896435015917712179200000⟩, + ⟨3, 3, 8, 6, 6, 2, 314357961513698222033500149025199293467092582400000⟩, + ⟨3, 3, 3, 7, 0, 2, 496785277454501692274919409395248781196739896934400000⟩, + ⟨3, 3, 4, 7, 1, 2, 16938001373760691765740900931530384091292840755200000⟩, + ⟨3, 3, 5, 7, 2, 2, 1255677680264287954680279739265817536832208896000000⟩, + ⟨3, 3, 6, 7, 3, 2, -4825577843634017425551806932767719574768451584000000⟩, + ⟨3, 3, 7, 7, 4, 2, 1106609741253570537149845588598295841298448384000000⟩, + ⟨3, 3, 8, 7, 5, 2, 812019887853107947437487847251981753525469184000000⟩ +] + +def collectedFourData_8_4_21 : List CollectedFourTerm := [ + ⟨3, 4, 1, 0, 5, 3, 602041252632604737582591650096622144024194580480000⟩, + ⟨3, 4, 2, 0, 6, 3, -513745068703405244241017299660481595526128599040000⟩, + ⟨3, 4, 3, 0, 7, 3, 73420522531199672938541768444686678651903672320000⟩, + ⟨3, 4, 4, 0, 8, 3, -94456047463814847049713552547988129681390960640000⟩, + ⟨3, 4, 1, 1, 4, 3, 262980882932446027218292860299028857961106636800000⟩, + ⟨3, 4, 2, 1, 5, 3, 250855341240146632693707655989573113873474519040000⟩, + ⟨3, 4, 3, 1, 6, 3, -348138499114399442692906642319288268458337239040000⟩, + ⟨3, 4, 4, 1, 7, 3, 110159150649637274518907467624050852213125283840000⟩, + ⟨3, 4, 5, 1, 8, 3, 135184042203076972360954075720713903544467456000000⟩, + ⟨3, 4, 1, 2, 3, 3, 397216270815908841685303083333326427382150594560000⟩, + ⟨3, 4, 2, 2, 4, 3, 924183021768881638320402062599018668303392440320000⟩, + ⟨3, 4, 3, 2, 5, 3, -148150094561099681170602234666637334595596451840000⟩, + ⟨3, 4, 4, 2, 6, 3, -72627180010465849565815742755401728624531865600000⟩, + ⟨3, 4, 5, 2, 7, 3, 69293774157341155424869631688606343261637836800000⟩, + ⟨3, 4, 6, 2, 8, 3, -24565886970104454103985179094824759883590533120000⟩, + ⟨3, 4, 1, 3, 2, 3, -1023551289579351356438699345291424179410446581760000⟩, + ⟨3, 4, 2, 3, 3, 3, -1052734527373276086586157330404197405194767564800000⟩, + ⟨3, 4, 3, 3, 4, 3, 16142240361613613341176026127899158457383649280000⟩, + ⟨3, 4, 4, 3, 5, 3, -199266824746175357269269488924863279957844951040000⟩, + ⟨3, 4, 5, 3, 6, 3, -47411838040374667824612077786967654154842931200000⟩, + ⟨3, 4, 6, 3, 7, 3, -52086252105778936866213601317521702686556160000⟩, + ⟨3, 4, 7, 3, 8, 3, 1389396855541522447676620705188673971038453760000⟩, + ⟨3, 4, 1, 4, 1, 3, 460811319462666097695181676254695577156772167680000⟩, + ⟨3, 4, 2, 4, 2, 3, 251009369872836003682180023732750351575757619200000⟩, + ⟨3, 4, 3, 4, 3, 3, 238388131086364743259011782865203881053719101440000⟩, + ⟨3, 4, 4, 4, 4, 3, 149343667462002164728969309420301453362829721600000⟩, + ⟨3, 4, 5, 4, 5, 3, -28748255087744106588249560528279273319746764800000⟩, + ⟨3, 4, 6, 4, 6, 3, -10526048527201288364245638076956088249519964160000⟩, + ⟨3, 4, 7, 4, 7, 3, 3675069786604886519589437055894160766266245120000⟩, + ⟨3, 4, 8, 4, 8, 3, -562361203860662075415071565972802831279718400000⟩, + ⟨3, 4, 1, 5, 0, 3, 2428757382407500421349467249979352940797671505920000⟩, + ⟨3, 4, 2, 5, 1, 3, -259970935088790606595901374000338137923599728640000⟩, + ⟨3, 4, 3, 5, 2, 3, 297672269292886605787707903486324321320655912960000⟩, + ⟨3, 4, 4, 5, 3, 3, 142307176228755138007726621990128409404065710080000⟩, + ⟨3, 4, 5, 5, 4, 3, -19069770790597875131036773456518070725613977600000⟩, + ⟨3, 4, 6, 5, 5, 3, -8793264026695762697660195211442090214613319680000⟩, + ⟨3, 4, 7, 5, 6, 3, -1164254984261255562552641159933456614529433600000⟩, + ⟨3, 4, 8, 5, 7, 3, 921992452129223720710118125036098486628515840000⟩, + ⟨3, 4, 2, 6, 0, 3, 4680017764425332702877081774617511519232941096960000⟩, + ⟨3, 4, 3, 6, 1, 3, 72471867844945652491442665327030286769067130880000⟩, + ⟨3, 4, 4, 6, 2, 3, -180245919423146676627485990798251337595098234880000⟩, + ⟨3, 4, 5, 6, 3, 3, 173774304066585605307574507680235250953853337600000⟩, + ⟨3, 4, 6, 6, 4, 3, 5862981452247231903227610822453612688315514880000⟩, + ⟨3, 4, 7, 6, 5, 3, -7273907446347858446353960247738926613177303040000⟩, + ⟨3, 4, 8, 6, 6, 3, -1377213788714740215688922290090387879011287040000⟩, + ⟨3, 4, 3, 7, 0, 3, -7617520987737145063105240656362325764718031011840000⟩, + ⟨3, 4, 4, 7, 1, 3, -173147349314995929744288686491482562234920468480000⟩, + ⟨3, 4, 5, 7, 2, 3, -9627047657548924200819287541578019019476172800000⟩, + ⟨3, 4, 6, 7, 3, 3, 29597447565428762057749576670570668528458792960000⟩, + ⟨3, 4, 7, 7, 4, 3, -5656114295782095413946194659608342519663820800000⟩, + ⟨3, 4, 8, 7, 5, 3, -3557488987639862843482301580916812306343526400000⟩ +] + +def collectedFourData_8_4_22 : List CollectedFourTerm := [ + ⟨3, 5, 0, 0, 4, 4, 6726048881095939321466195573698692402664754380800000⟩, + ⟨3, 5, 1, 0, 5, 4, -22295575971646042086389478294445772514686580817920000⟩, + ⟨3, 5, 2, 0, 6, 4, 9512838330636148695170696621166709354912630702080000⟩, + ⟨3, 5, 3, 0, 7, 4, -906334812780269517771064385139868953608988917760000⟩, + ⟨3, 5, 4, 0, 8, 4, 874504850374449395830990214574010227652967792640000⟩, + ⟨3, 5, 0, 1, 3, 4, 5286423575958787578861313036248853617662975016960000⟩, + ⟨3, 5, 1, 1, 4, 4, -9739050652877744657313803638922394776284377907200000⟩, + ⟨3, 5, 2, 1, 5, 4, -4645000898240759226108748694127321100274714542080000⟩, + ⟨3, 5, 3, 1, 6, 4, 4297572811230952191433119849635120553583674654720000⟩, + ⟨3, 5, 4, 1, 7, 4, -1019889293940044704995282364073219279759962275840000⟩, + ⟨3, 5, 5, 1, 8, 4, -1001262312146640415521372220444370599458688204800000⟩, + ⟨3, 5, 0, 2, 2, 4, 4409926040608922076129849856311340753824975421440000⟩, + ⟨3, 5, 1, 2, 3, 4, -14710230410995595223138823253983271785366542090240000⟩, + ⟨3, 5, 2, 2, 4, 4, -17112774816884361649838025549539012389974457712640000⟩, + ⟨3, 5, 3, 2, 5, 4, 1828829101023554212318800900852430388038069125120000⟩, + ⟨3, 5, 4, 2, 6, 4, 672406086148181850955379154904434200937077145600000⟩, + ⟨3, 5, 5, 2, 7, 4, -513235463294700279007589019697615417841748541440000⟩, + ⟨3, 5, 6, 2, 8, 4, 151625988213101591098156475198758273511671726080000⟩, + ⟨3, 5, 0, 3, 1, 4, 14136191670046730613962750663573984422524585246720000⟩, + ⟨3, 5, 1, 3, 2, 4, 37905484778497398978542316266285700523712619479040000⟩, + ⟨3, 5, 2, 3, 3, 4, 19493118229349248139087558736724400150979123609600000⟩, + ⟨3, 5, 3, 3, 4, 4, -199266824746175357269269488924863279957844951040000⟩, + ⟨3, 5, 4, 3, 5, 4, 1844877161793191413094022216864530190549689303040000⟩, + ⟨3, 5, 5, 3, 6, 4, 351163390336519030623654825194180534506314792960000⟩, + ⟨3, 5, 6, 3, 7, 4, 321487657151012866719237057073342852827709440000⟩, + ⟨3, 5, 7, 3, 8, 4, -7350564911346952876427971048612913367188766720000⟩, + ⟨3, 5, 0, 4, 0, 4, 45142904008931394137017844810595688182081965260800000⟩, + ⟨3, 5, 1, 4, 1, 4, -17065365100394641353480393021735630456994104606720000⟩, + ⟨3, 5, 2, 4, 2, 4, -4647852992733385569362033034338464549441005158400000⟩, + ⟨3, 5, 3, 4, 3, 4, -2942766609504656980331092777157664595125385297920000⟩, + ⟨3, 5, 4, 4, 4, 4, -1382672312413473990885775967833959221513787801600000⟩, + ⟨3, 5, 5, 4, 5, 4, 212928566791154198698997332265861950342000803840000⟩, + ⟨3, 5, 6, 4, 6, 4, 64969056963350980833434202260871196687403581440000⟩, + ⟨3, 5, 7, 4, 7, 4, -19442853143381032974589790214172483846290800640000⟩, + ⟨3, 5, 8, 4, 8, 4, 2603261589084395891788761912501592055296819200000⟩, + ⟨3, 5, 1, 5, 0, 4, -89944907428474734236974162311720285183621652807680000⟩, + ⟨3, 5, 2, 5, 1, 4, 4813791171573686916917398740165585275920349921280000⟩, + ⟨3, 5, 3, 5, 2, 4, -3674595755496021797666581946101265272096979681280000⟩, + ⟨3, 5, 4, 5, 3, 4, -1317526184893696725218506309571559169277904814080000⟩, + ⟨3, 5, 5, 5, 4, 4, 141243318980040779102762887390285244661843886080000⟩, + ⟨3, 5, 6, 5, 5, 4, 54273934797836156218879797499719185926843269120000⟩, + ⟨3, 5, 7, 5, 6, 4, 6159458185786737754965641324546894215721779200000⟩, + ⟨3, 5, 8, 5, 7, 4, -4268053200640852576892244284529548397033553920000⟩, + ⟨3, 5, 2, 6, 0, 4, -86658257352900816313682506904349086763425118289920000⟩, + ⟨3, 5, 3, 6, 1, 4, -894624207382524004826527322732786588657217699840000⟩, + ⟨3, 5, 4, 6, 2, 4, 1668775425481664798771620675847892792700179578880000⟩, + ⟨3, 5, 5, 6, 3, 4, -1287087282240052067904911193804684567550969774080000⟩, + ⟨3, 5, 6, 6, 4, 4, -36187594514862008700532713733740636554573905920000⟩, + ⟨3, 5, 7, 6, 5, 4, 38482402367803547233778690195664319867131002880000⟩, + ⟨3, 5, 8, 6, 6, 4, 6375346897163986569490842136649312067146219520000⟩, + ⟨3, 5, 3, 7, 0, 4, 94033986959663620830950011956959938816037219205120000⟩, + ⟨3, 5, 4, 7, 1, 4, 1603054551519846442513655346333656941043625492480000⟩, + ⟨3, 5, 5, 7, 2, 4, 71304274081870390221282273764758044637648650240000⟩, + ⟨3, 5, 6, 7, 3, 4, -182681872677952486237276269696773001600187760640000⟩, + ⟨3, 5, 7, 7, 4, 4, 29923513293787826239320227996208607377594777600000⟩, + ⟨3, 5, 8, 7, 5, 4, 16468195834875252864342400956844246285103923200000⟩ +] + +def collectedFourData_8_4_23 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 4, 5, 6401353373465336945410484524876050553368477696000000⟩, + ⟨3, 6, 1, 0, 5, 5, -10609635982618228056278599408832829342755271475200000⟩, + ⟨3, 6, 2, 0, 6, 5, 3017870809225413824017936176666358079074546483200000⟩, + ⟨3, 6, 3, 0, 7, 5, -215645526587918403976396076329592063129341132800000⟩, + ⟨3, 6, 4, 0, 8, 5, 166457742815099596489181230207002906493043343360000⟩, + ⟨3, 6, 0, 1, 3, 5, 5031225016315456429658372086839407209448944435200000⟩, + ⟨3, 6, 1, 1, 4, 5, -4634452250738816076716662134207095718839058432000000⟩, + ⟨3, 6, 2, 1, 5, 5, -1473588863008585630519092312537542381161100083200000⟩, + ⟨3, 6, 3, 1, 6, 5, 1022527590091036281772835023607688794862098841600000⟩, + ⟨3, 6, 4, 1, 7, 5, -194130964188309824324401400800756038807752540160000⟩, + ⟨3, 6, 5, 1, 8, 5, -158821174037697686742274081001388473472516096000000⟩, + ⟨3, 6, 0, 2, 2, 5, 4197039812797919906663943908442740833557204172800000⟩, + ⟨3, 6, 1, 2, 3, 5, -7000051942124436293433504012446173694246938214400000⟩, + ⟨3, 6, 2, 2, 4, 5, -5428889022364948642501844920592678854522935705600000⟩, + ⟨3, 6, 3, 2, 5, 5, 435135900076196669147721849707924773754476953600000⟩, + ⟨3, 6, 4, 2, 6, 5, 127989226483347998907153214306773200865224294400000⟩, + ⟨3, 6, 5, 2, 7, 5, -81409894140016342996219196090895092383796428800000⟩, + ⟨3, 6, 6, 2, 8, 5, 20615192160499822704866636595089466010160332800000⟩, + ⟨3, 6, 0, 3, 1, 5, 13453776479284478775438902717256970903514146406400000⟩, + ⟨3, 6, 1, 3, 2, 5, 18037811436492014586077445010959801916024317542400000⟩, + ⟨3, 6, 2, 3, 3, 5, 6184033664871388222190219421228248763815952384000000⟩, + ⟨3, 6, 3, 3, 4, 5, -47411838040374667824612077786967654154842931200000⟩, + ⟨3, 6, 4, 3, 5, 5, 351163390336519030623654825194180534506314792960000⟩, + ⟨3, 6, 5, 3, 6, 5, 55701868786744177201235457512239292606526259200000⟩, + ⟨3, 6, 6, 3, 7, 5, 43709722241561940294118115076861550028390400000⟩, + ⟨3, 6, 7, 3, 8, 5, -874465163797246038702957090742795491921100800000⟩, + ⟨3, 6, 0, 4, 0, 5, 42963660534460656204631340587620372389660983296000000⟩, + ⟨3, 6, 1, 4, 1, 5, -8120773011467403802113178205669449602027434803200000⟩, + ⟨3, 6, 2, 4, 2, 5, -1474493666855270368489204580818993500269838336000000⟩, + ⟨3, 6, 3, 4, 3, 5, -700176630295481269269456771031091275594570137600000⟩, + ⟨3, 6, 4, 4, 4, 5, -263184946405650752708979442699649699029608038400000⟩, + ⟨3, 6, 5, 4, 5, 5, 33774930458965150008632546204103442816617676800000⟩, + ⟨3, 6, 6, 4, 6, 5, 8833245603672906418168155029275536502711910400000⟩, + ⟨3, 6, 7, 4, 7, 5, -2313032802753244285538343408726520511437209600000⟩, + ⟨3, 6, 8, 4, 8, 5, 275287875374842357233504122555597907296256000000⟩, + ⟨3, 6, 1, 5, 0, 5, -42801438613651483420908763010442925689222778060800000⟩, + ⟨3, 6, 2, 5, 1, 5, 1527136208297965441069548368899823603245331251200000⟩, + ⟨3, 6, 3, 5, 2, 5, -874301776250737743871839660125628359726491238400000⟩, + ⟨3, 6, 4, 5, 3, 5, -250784698041741163491617350182543765184362577920000⟩, + ⟨3, 6, 5, 5, 4, 5, 22404148716331342171958924898852409653696921600000⟩, + ⟨3, 6, 6, 5, 5, 5, 7379128131988340360878726492291322252309299200000⟩, + ⟨3, 6, 7, 5, 6, 5, 732764308090340849841325516620701984882688000000⟩, + ⟨3, 6, 8, 5, 7, 5, -451335087690692016500975664736368659634585600000⟩, + ⟨3, 6, 2, 6, 0, 5, -27491629328065558544272650643584691827519573196800000⟩, + ⟨3, 6, 3, 6, 1, 5, -212859205647742413592217965528699004051993395200000⟩, + ⟨3, 6, 4, 6, 2, 5, 317643281763439077324136390267801089950739333120000⟩, + ⟨3, 6, 5, 6, 3, 5, -204159000867713346731826682763170912625334681600000⟩, + ⟨3, 6, 6, 6, 4, 5, -4920094658849970141422189197944290853204787200000⟩, + ⟨3, 6, 7, 6, 5, 5, 4578086268978528245216615501229822315803443200000⟩, + ⟨3, 6, 8, 6, 6, 5, 674175699229344634639080145287735068432793600000⟩, + ⟨3, 6, 3, 7, 0, 5, 22373639795290843022547795418361508325997779353600000⟩, + ⟨3, 6, 4, 7, 1, 5, 305133633211077469150600094483027790057198059520000⟩, + ⟨3, 6, 5, 7, 2, 5, 11310351329722154827118482092865412865510604800000⟩, + ⟨3, 6, 6, 7, 3, 5, -24837575364739097479891946759340619100218982400000⟩, + ⟨3, 6, 7, 7, 4, 5, 3559871964867290861667551751944610370289664000000⟩, + ⟨3, 6, 8, 7, 5, 5, 1741467189332337174040148200109649980030976000000⟩ +] + +def collectedFourData_8_4_24 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 4, 6, 17581184331250784710068825390445610907205632000000⟩, + ⟨3, 7, 1, 0, 5, 6, -19426096849152713599492053872979497142819225600000⟩, + ⟨3, 7, 2, 0, 6, 6, 4144259806436092621808058982112393373627187200000⟩, + ⟨3, 7, 3, 0, 7, 6, -236906387256633163986633459155852686566359040000⟩, + ⟨3, 7, 4, 0, 8, 6, 152390913246935485004179298160666337125335040000⟩, + ⟨3, 7, 0, 1, 3, 6, 13818155203007909013282803187509125582317158400000⟩, + ⟨3, 7, 1, 1, 4, 6, -8485618018669169611174315513181770975543296000000⟩, + ⟨3, 7, 2, 1, 5, 6, -2023590631351707272418947955036512633172787200000⟩, + ⟨3, 7, 3, 1, 6, 6, 1123340331105531225922702880177365302776954880000⟩, + ⟨3, 7, 4, 1, 7, 6, -177725556179301247065279969805533626750730240000⟩, + ⟨3, 7, 5, 1, 8, 6, -124628303402965630365068340948496445079552000000⟩, + ⟨3, 7, 0, 2, 2, 6, 11527082835368185606479734344265626191239577600000⟩, + ⟨3, 7, 1, 2, 3, 6, -12816998358811837451388702680324395293160243200000⟩, + ⟨3, 7, 2, 2, 4, 6, -7455165575747047423900099433095271512906137600000⟩, + ⟨3, 7, 3, 2, 5, 6, 478036691434389006149305270398260651470356480000⟩, + ⟨3, 7, 4, 2, 6, 6, 117173252380525453916514599422533326969241600000⟩, + ⟨3, 7, 5, 2, 7, 6, -63883024718587134206548889177408715463065600000⟩, + ⟨3, 7, 6, 2, 8, 6, 14154799471791185337975030225531142825574400000⟩, + ⟨3, 7, 0, 3, 1, 6, 36950518184828879389607447086466158841089228800000⟩, + ⟨3, 7, 1, 3, 2, 6, 33026983440913128540385534960798470753170227200000⟩, + ⟨3, 7, 2, 3, 3, 6, 8492160128468882225825250032481726432804864000000⟩, + ⟨3, 7, 3, 3, 4, 6, -52086252105778936866213601317521702686556160000⟩, + ⟨3, 7, 4, 3, 5, 6, 321487657151012866719237057073342852827709440000⟩, + ⟨3, 7, 5, 3, 6, 6, 43709722241561940294118115076861550028390400000⟩, + ⟨3, 7, 6, 3, 7, 6, 30011961493256326662418500594590495539200000⟩, + ⟨3, 7, 7, 3, 8, 6, -533711209664058611771543175601209527500800000⟩, + ⟨3, 7, 0, 4, 0, 6, 117998802961369994191591562597713991625080832000000⟩, + ⟨3, 7, 1, 4, 1, 6, -14869023147372944342033191733483031903181209600000⟩, + ⟨3, 7, 2, 4, 2, 6, -2024833143855245075355458121450168313184256000000⟩, + ⟨3, 7, 3, 4, 3, 6, -769208239787891881649515165831537708687687680000⟩, + ⟨3, 7, 4, 4, 4, 6, -240943999704198390577443940364429754472857600000⟩, + ⟨3, 7, 5, 4, 5, 6, 26503470372627105759582846877595883641241600000⟩, + ⟨3, 7, 6, 4, 6, 6, 6065081481250650656175220288424623944499200000⟩, + ⟨3, 7, 7, 4, 7, 6, -1411710364526667133074320764480194714009600000⟩, + ⟨3, 7, 8, 4, 8, 6, 151214488523180885538161998696704009830400000⟩, + ⟨3, 7, 1, 5, 0, 6, -78368842545969317029224174689563369068193382400000⟩, + ⟨3, 7, 2, 5, 1, 6, 2097123968214821600344157412072818291716915200000⟩, + ⟨3, 7, 3, 5, 2, 6, -960500681191612055977250488805755437837189120000⟩, + ⟨3, 7, 4, 5, 3, 6, -229591658018512718072086052827111527158906880000⟩, + ⟨3, 7, 5, 5, 4, 6, 17580722851484228973869560927797231432499200000⟩, + ⟨3, 7, 6, 5, 5, 6, 5066655608725386084027729855140375140761600000⟩, + ⟨3, 7, 7, 5, 6, 6, 447227106876746679523284905977014386688000000⟩, + ⟨3, 7, 8, 5, 7, 6, -247916492307492235608780639592072127447040000⟩, + ⟨3, 7, 2, 6, 0, 6, -37752595004881742077505089284636636697382092800000⟩, + ⟨3, 7, 3, 6, 1, 6, -233845358177481463644462906503252231438991360000⟩, + ⟨3, 7, 4, 6, 2, 6, 290800229391871597162485075462779498586439680000⟩, + ⟨3, 7, 5, 6, 3, 6, -160205275252204936427943686929650789069619200000⟩, + ⟨3, 7, 6, 6, 4, 6, -3378234495029013170194033056686974540185600000⟩, + ⟨3, 7, 7, 6, 5, 6, 2794137561698763767091285059251578549043200000⟩, + ⟨3, 7, 8, 6, 6, 6, 370321916266420534522562054055606343434240000⟩, + ⟨3, 7, 3, 7, 0, 6, 24579495144419799599115426875404841763974676480000⟩, + ⟨3, 7, 4, 7, 1, 6, 279347732589664197365185099132799028591329280000⟩, + ⟨3, 7, 5, 7, 2, 6, 8875327270784241675796485005035341191577600000⟩, + ⟨3, 7, 6, 7, 3, 6, -17053971455430700791452218240366925787955200000⟩, + ⟨3, 7, 7, 7, 4, 6, 2172692122311933400113207316298191601664000000⟩, + ⟨3, 7, 8, 7, 5, 6, 956580706492154102176800567195387455078400000⟩ +] + +def collectedFourData_8_4_25 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 4, 7, -937953538178475979241245847302114882621538304000000⟩, + ⟨3, 8, 1, 0, 5, 7, 777284507517769889812791125223040890995893862400000⟩, + ⟨3, 8, 2, 0, 6, 7, -132657382187893915239113771076461447607264215040000⟩, + ⟨3, 8, 3, 0, 7, 7, 6319460053366914490516758267086932054313533440000⟩, + ⟨3, 8, 4, 0, 8, 7, -3484299551801665145168775261310844745044459520000⟩, + ⟨3, 8, 0, 1, 3, 7, -737196500506659051165586230953797900414274764800000⟩, + ⟨3, 8, 1, 1, 4, 7, 339529833184830374922434238063921734860406784000000⟩, + ⟨3, 8, 2, 1, 5, 7, 64774953384478302976931872517499151100978135040000⟩, + ⟨3, 8, 3, 1, 6, 7, -29965018803259830096634821338885888719642951680000⟩, + ⟨3, 8, 4, 1, 7, 7, 4063556432238218272249468348411024310922117120000⟩, + ⟨3, 8, 5, 1, 8, 7, 2493337961443718632288398380058462287560704000000⟩, + ⟨3, 8, 0, 2, 2, 7, -614968134489764255789262290613882151383544627200000⟩, + ⟨3, 8, 1, 2, 3, 7, 512838700153996466018555216778540609786662092800000⟩, + ⟨3, 8, 2, 2, 4, 7, 238639176897163254235466931519292225853136568320000⟩, + ⟨3, 8, 3, 2, 5, 7, -12751592772763976113338658545095354250197729280000⟩, + ⟨3, 8, 4, 2, 6, 7, -2679075163038425446387148914785296256388300800000⟩, + ⟨3, 8, 5, 2, 7, 7, 1278056157979524338189784995482499097506611200000⟩, + ⟨3, 8, 6, 2, 8, 7, -251718807194236898446625943937488189495705600000⟩, + ⟨3, 8, 0, 3, 1, 7, -1971304584264186918497552336637444502714947993600000⟩, + ⟨3, 8, 1, 3, 2, 7, -1321488447113727918743465630671020511166516428800000⟩, + ⟨3, 8, 2, 3, 3, 7, -271833278891817216498421976768969348297313484800000⟩, + ⟨3, 8, 3, 3, 4, 7, 1389396855541522447676620705188673971038453760000⟩, + ⟨3, 8, 4, 3, 5, 7, -7350564911346952876427971048612913367188766720000⟩, + ⟨3, 8, 5, 3, 6, 7, -874465163797246038702957090742795491921100800000⟩, + ⟨3, 8, 6, 3, 7, 7, -533711209664058611771543175601209527500800000⟩, + ⟨3, 8, 7, 3, 8, 7, 8542023814290514657167846660012074367713280000⟩, + ⟨3, 8, 0, 4, 0, 7, -6295218379669184231289703150931160959186632704000000⟩, + ⟨3, 8, 1, 4, 1, 7, 594945110390520304945222462978291185660356198400000⟩, + ⟨3, 8, 2, 4, 2, 7, 64814726097520827567125358991300220324885299200000⟩, + ⟨3, 8, 3, 4, 3, 7, 20518571915051473717858206240474809632271892480000⟩, + ⟨3, 8, 4, 4, 4, 7, 5508996909929085914489259684322422500936908800000⟩, + ⟨3, 8, 5, 4, 5, 7, -530233558394870879476433382746184035283763200000⟩, + ⟨3, 8, 6, 4, 6, 7, -107857061418551998736327224330103743630540800000⟩, + ⟨3, 8, 7, 4, 7, 7, 22594360647320701626893027803656562786959360000⟩, + ⟨3, 8, 8, 4, 8, 7, -2200164601519594746943378171887136171622400000⟩, + ⟨3, 8, 1, 5, 0, 7, 3135724466736521448485191388919906723482409369600000⟩, + ⟨3, 8, 2, 5, 1, 7, -67128748857593202770447463889306525784227184640000⟩, + ⟨3, 8, 3, 5, 2, 7, 25621283395144730401074697358639476127375032320000⟩, + ⟨3, 8, 4, 5, 3, 7, 5249434458306798117035163368238561759791677440000⟩, + ⟨3, 8, 5, 5, 4, 7, -351723344363392867639082054410019356960358400000⟩, + ⟨3, 8, 6, 5, 5, 7, -90101771405098928946924279222111178221158400000⟩, + ⟨3, 8, 7, 5, 6, 7, -7157849653826902527306819284529484451020800000⟩, + ⟨3, 8, 8, 5, 7, 7, 3607174787515363153093989238165563758346240000⟩, + ⟨3, 8, 2, 6, 0, 7, 1208457157142906392269689340559792118850083880960000⟩, + ⟨3, 8, 3, 6, 1, 7, 6237807333016496561966931371357443644677160960000⟩, + ⟨3, 8, 4, 6, 2, 7, -6648920774508813008724150852077035146014883840000⟩, + ⟨3, 8, 5, 6, 3, 7, 3205097746683738834938686116033188927530598400000⟩, + ⟨3, 8, 6, 6, 4, 7, 60076100633273117327414729661961264850534400000⟩, + ⟨3, 8, 7, 6, 5, 7, -44720045523229288145145496807896895318917120000⟩, + ⟨3, 8, 8, 6, 6, 7, -5388168682072943995221959315601847945789440000⟩, + ⟨3, 8, 3, 7, 0, 7, -655656183422458093237660851828884224263617249280000⟩, + ⟨3, 8, 4, 7, 1, 7, -6387068354146448016446707815141800747351408640000⟩, + ⟨3, 8, 5, 7, 2, 7, -177561515323945605979048396812830790333235200000⟩, + ⟨3, 8, 6, 7, 3, 7, 303275603532259534135664253511246413614284800000⟩, + ⟨3, 8, 7, 7, 4, 7, -34773839323314769055537366111943699883622400000⟩, + ⟨3, 8, 8, 7, 5, 7, -13918210017276262629162427070156091319910400000⟩ +] + +def collectedFourData_8_4_26 : List CollectedFourTerm := [ + ⟨4, 0, 4, 0, 8, 0, 21398545839998903758610991517989936766955343052800000⟩, + ⟨4, 0, 4, 1, 7, 0, -24956005445544872192756190864727155096584768716800000⟩, + ⟨4, 0, 5, 1, 8, 0, -122501078611279772395860536230777319036792340480000000⟩, + ⟨4, 0, 4, 2, 6, 0, 16453324931674402572914745304240790815912230912000000⟩, + ⟨4, 0, 5, 2, 7, 0, -62792633930630493083344751389332585919643910144000000⟩, + ⟨4, 0, 6, 2, 8, 0, 55652790111865776812337387210687967399010893824000000⟩, + ⟨4, 0, 4, 3, 5, 0, 45142904008931394137017844810595688182081965260800000⟩, + ⟨4, 0, 5, 3, 6, 0, 42963660534460656204631340587620372389660983296000000⟩, + ⟨4, 0, 6, 3, 7, 0, 117998802961369994191591562597713991625080832000000⟩, + ⟨4, 0, 7, 3, 8, 0, -6295218379669184231289703150931160959186632704000000⟩, + ⟨4, 0, 4, 4, 4, 0, -33833062042146751780972348344843589595569324032000000⟩, + ⟨4, 0, 5, 4, 5, 0, 26051094486067276173781984390525271989114896384000000⟩, + ⟨4, 0, 6, 4, 6, 0, 23846237268149261820741637872892374509716242432000000⟩, + ⟨4, 0, 7, 4, 7, 0, -16651374137582091690607244540686969676337512448000000⟩, + ⟨4, 0, 8, 4, 8, 0, 4459004280716667281149194337120369687532666880000000⟩, + ⟨4, 0, 4, 5, 3, 0, -32238980093449194657653113051588509365658294681600000⟩, + ⟨4, 0, 5, 5, 4, 0, 17280645353160959470467504601090710848938180608000000⟩, + ⟨4, 0, 6, 5, 5, 0, 19920700517406890415311425643932599486813044736000000⟩, + ⟨4, 0, 7, 5, 6, 0, 5275123048041097866811331726405328340191805440000000⟩, + ⟨4, 0, 8, 5, 7, 0, -7310547496180590052454648493062489613677887488000000⟩, + ⟨4, 0, 4, 6, 2, 0, 40833812898285106510386962256291704283917293977600000⟩, + ⟨4, 0, 5, 6, 3, 0, -157470803033856196962717326156474682017901969408000000⟩, + ⟨4, 0, 6, 6, 4, 0, -13282291683127849623373814877126023726053195776000000⟩, + ⟨4, 0, 7, 6, 5, 0, 32957348122408435462852317869751002463014486016000000⟩, + ⟨4, 0, 8, 6, 6, 0, 10920031711260474748917851233107932182455779328000000⟩, + ⟨4, 0, 4, 7, 1, 0, 39225667290499636471022591202320280568389540249600000⟩, + ⟨4, 0, 5, 7, 2, 0, 8723838277600302027583922776318036054087041024000000⟩, + ⟨4, 0, 6, 7, 3, 0, -67051539364741928138239188681054431047625736192000000⟩, + ⟨4, 0, 7, 7, 4, 0, 25627288942178668952601559686412701773668024320000000⟩, + ⟨4, 0, 8, 7, 5, 0, 28207597742498146449584771590068332654997012480000000⟩ +] + +def collectedFourData_8_4_27 : List CollectedFourTerm := [ + ⟨4, 1, 3, 0, 7, 1, 2095930125269086612530307766233360885757163601920000⟩, + ⟨4, 1, 4, 0, 8, 1, -8089289012174839236689048793014818607480721899520000⟩, + ⟨4, 1, 3, 1, 6, 1, -9938283505810842298072053370524131388631013130240000⟩, + ⟨4, 1, 4, 1, 7, 1, 9434114922943377445500334257383918876966906757120000⟩, + ⟨4, 1, 5, 1, 8, 1, 23154532008840523228057334482617109208226594816000000⟩, + ⟨4, 1, 3, 2, 5, 1, -4229229587955085746749475002389714738881799127040000⟩, + ⟨4, 1, 4, 2, 6, 1, -6219847908298001464640881435558025580029725900800000⟩, + ⟨4, 1, 5, 2, 7, 1, 11868744902073968595806309062377231171332132044800000⟩, + ⟨4, 1, 6, 2, 8, 1, -7012805245661051793410863466538074154600706867200000⟩, + ⟨4, 1, 3, 3, 4, 1, 460811319462666097695181676254695577156772167680000⟩, + ⟨4, 1, 4, 3, 5, 1, -17065365100394641353480393021735630456994104606720000⟩, + ⟨4, 1, 5, 3, 6, 1, -8120773011467403802113178205669449602027434803200000⟩, + ⟨4, 1, 6, 3, 7, 1, -14869023147372944342033191733483031903181209600000⟩, + ⟨4, 1, 7, 3, 8, 1, 594945110390520304945222462978291185660356198400000⟩, + ⟨4, 1, 3, 4, 3, 1, 6805248018197996130611537106036216712424734064640000⟩, + ⟨4, 1, 4, 4, 4, 1, 12789907270903664715626543794342167437690850508800000⟩, + ⟨4, 1, 5, 4, 5, 1, -4924045632749485784811868135077375690819816652800000⟩, + ⟨4, 1, 6, 4, 6, 1, -3004863142839988129310847786688513834346977689600000⟩, + ⟨4, 1, 7, 4, 7, 1, 1573679104831662764911450229026792533939506380800000⟩, + ⟨4, 1, 8, 4, 8, 1, -337127341296419204644592552905306375033611878400000⟩, + ⟨4, 1, 3, 5, 2, 1, 8497627845171626207711727623405291645687310581760000⟩, + ⟨4, 1, 4, 5, 3, 1, 12187296715563888168143590709687451957654391357440000⟩, + ⟨4, 1, 5, 5, 4, 1, -3266299860369911590708881643334772245149620633600000⟩, + ⟨4, 1, 6, 5, 5, 1, -2510206456943266895358975550679641386795191500800000⟩, + ⟨4, 1, 7, 5, 6, 1, -498538489828420107958140977365436132568858624000000⟩, + ⟨4, 1, 8, 5, 7, 1, 552721030447730266902658877039833577741447331840000⟩, + ⟨4, 1, 3, 6, 1, 1, 2068848951411292678058224471502111535499868897280000⟩, + ⟨4, 1, 4, 6, 2, 1, -15436400046673351913925707050004016638916915363840000⟩, + ⟨4, 1, 5, 6, 3, 1, 29764331797234557571850700720189617698477021593600000⟩, + ⟨4, 1, 6, 6, 4, 1, 1673700898061162674305930615258978061650808012800000⟩, + ⟨4, 1, 7, 6, 5, 1, -3114715317929207514249546620639505702027106713600000⟩, + ⟨4, 1, 8, 6, 6, 1, -825619583639003859125199571728934947431424983040000⟩, + ⟨4, 1, 3, 7, 0, 1, -217456797740485024060680731393487555451283350487040000⟩, + ⟨4, 1, 4, 7, 1, 1, -14828473008438827757679757101747440783354117488640000⟩, + ⟨4, 1, 5, 7, 2, 1, -1648935625127179516045807165828441773892750540800000⟩, + ⟨4, 1, 6, 7, 3, 1, 8449161058080623395386632066299452208130398617600000⟩, + ⟨4, 1, 7, 7, 4, 1, -2421970030135074426058353289375467050392092672000000⟩, + ⟨4, 1, 8, 7, 5, 1, -2132662772362009678776586630607118547294774886400000⟩ +] + +def collectedFourData_8_4_28 : List CollectedFourTerm := [ + ⟨4, 2, 2, 0, 6, 2, -3994328639696577632382129676446880714355166412800000⟩, + ⟨4, 2, 3, 0, 7, 2, 1141677901173846819057002337627268416426265804800000⟩, + ⟨4, 2, 4, 0, 8, 2, -2203165647094925530094930492921368681952732774400000⟩, + ⟨4, 2, 2, 1, 5, 2, 1950381103346119898589703813900709114468420812800000⟩, + ⟨4, 2, 3, 1, 6, 2, -5413500439442408518793495740655038798658902425600000⟩, + ⟨4, 2, 4, 1, 7, 2, 2569436927978708406531759826160764660446815846400000⟩, + ⟨4, 2, 5, 1, 8, 2, 4204182379906683220818190641432185714434375680000000⟩, + ⟨4, 2, 2, 2, 4, 2, 7185452351862742790538568885797347574501762662400000⟩, + ⟨4, 2, 3, 2, 5, 2, -2303711321931115147593742162932589074576939417600000⟩, + ⟨4, 2, 4, 2, 6, 2, -1694012319388398383582662738067088656748773376000000⟩, + ⟨4, 2, 5, 2, 7, 2, 2155015189676698684249672037280796957898440704000000⟩, + ⟨4, 2, 6, 2, 8, 2, -954989467167870557074121270336923891025313792000000⟩, + ⟨4, 2, 2, 3, 3, 2, -8184930481760253931802631139954969318193627136000000⟩, + ⟨4, 2, 3, 3, 4, 2, 251009369872836003682180023732750351575757619200000⟩, + ⟨4, 2, 4, 3, 5, 2, -4647852992733385569362033034338464549441005158400000⟩, + ⟨4, 2, 5, 3, 6, 2, -1474493666855270368489204580818993500269838336000000⟩, + ⟨4, 2, 6, 3, 7, 2, -2024833143855245075355458121450168313184256000000⟩, + ⟨4, 2, 7, 3, 8, 2, 64814726097520827567125358991300220324885299200000⟩, + ⟨4, 2, 2, 4, 2, 2, 1951578664191691049554711776639778017974943744000000⟩, + ⟨4, 2, 3, 4, 3, 2, 3706898994729746466226569292948678440430180761600000⟩, + ⟨4, 2, 4, 4, 4, 2, 3483406797108453873343458085024409948453339136000000⟩, + ⟨4, 2, 5, 4, 5, 2, -894061943431111785517809851924149404690284544000000⟩, + ⟨4, 2, 6, 4, 6, 2, -409196113562203074540092629427865991885357056000000⟩, + ⟨4, 2, 7, 4, 7, 2, 171440320062644200554307409827001576362239590400000⟩, + ⟨4, 2, 8, 4, 8, 2, -30606207621083478621002444152317065734127616000000⟩, + ⟨4, 2, 2, 5, 1, 2, -2021254148744636703902369232532876084929940684800000⟩, + ⟨4, 2, 3, 5, 2, 2, 4628758280759213706133978829390122372693386854400000⟩, + ⟨4, 2, 4, 5, 3, 2, 3319282252651802456275458722264972761955617996800000⟩, + ⟨4, 2, 5, 5, 4, 2, -593064040992745851174293707901056865720598528000000⟩, + ⟨4, 2, 6, 5, 5, 2, -341834778355038742367631782719630399858802688000000⟩, + ⟨4, 2, 7, 5, 6, 2, -54311961058207199682178480378216522356621312000000⟩, + ⟨4, 2, 8, 5, 7, 2, 50178945882494983692396913096052286529575321600000⟩, + ⟨4, 2, 2, 6, 0, 2, 36386780388786535931350798826192483647558464307200000⟩, + ⟨4, 2, 3, 6, 1, 2, 1126926465828491107943739387536345009229083443200000⟩, + ⟨4, 2, 4, 6, 2, 2, -4204194737814391224206035653295937227162701004800000⟩, + ⟨4, 2, 5, 6, 3, 2, 5404327724864085497783261633014015157052899328000000⟩, + ⟨4, 2, 6, 6, 4, 2, 227921163193110816837407227642448119760683008000000⟩, + ⟨4, 2, 7, 6, 5, 2, -339324446369213794533431144082294888303742156800000⟩, + ⟨4, 2, 8, 6, 6, 2, -74954123553776098870836042323725597214874009600000⟩, + ⟨4, 2, 3, 7, 0, 2, -118451286828309222397646551854381223055875217817600000⟩, + ⟨4, 2, 4, 7, 1, 2, -4038622217836102880935441123011524861153299660800000⟩, + ⟨4, 2, 5, 7, 2, 2, -299398238673675759691779288155379654966902784000000⟩, + ⟨4, 2, 6, 7, 3, 2, 1150589462307438815161193407142949377997275136000000⟩, + ⟨4, 2, 7, 7, 4, 2, -263855137857286237210582834707089683787022336000000⟩, + ⟨4, 2, 8, 7, 5, 2, -193614434669290509476548919053394425241665536000000⟩ +] + +def collectedFourData_8_4_29 : List CollectedFourTerm := [ + ⟨4, 3, 1, 0, 5, 3, 8890927519160920981891581164670330897664353239040000⟩, + ⟨4, 3, 2, 0, 6, 3, -7586972070758980515940043818016708004191058001920000⟩, + ⟨4, 3, 3, 0, 7, 3, 1084272118213424238874697877438038394057114255360000⟩, + ⟨4, 3, 4, 0, 8, 3, -1394924131984174941216612240968372923405141278720000⟩, + ⟨4, 3, 1, 1, 4, 3, 3883693947637458159895750016048060990065370726400000⟩, + ⟨4, 3, 2, 1, 5, 3, 3704624304410556049576236697052332655585966161920000⟩, + ⟨4, 3, 3, 1, 6, 3, -5141299119820420117624716116213014716489840721920000⟩, + ⟨4, 3, 4, 1, 7, 3, 1626827098168872920598180557887726156238888632320000⟩, + ⟨4, 3, 5, 1, 8, 3, 1996393960910539251707819301623201546096345088000000⟩, + ⟨4, 3, 1, 2, 3, 3, 5866078209445906988335072923400518003657151610880000⟩, + ⟨4, 3, 2, 2, 4, 3, 13648307694955531298864275160816979535941976719360000⟩, + ⟨4, 3, 3, 2, 5, 3, -2187876240938242161591964391995626306773786296320000⟩, + ⟨4, 3, 4, 2, 6, 3, -1072556059191107925386011095539176533455064268800000⟩, + ⟨4, 3, 5, 2, 7, 3, 1023328419552658711338080271687323011720308326400000⟩, + ⟨4, 3, 6, 2, 8, 3, -362788296549480952865238687877887577074444533760000⟩, + ⟨4, 3, 1, 3, 2, 3, -15115775352602237773859336463537619086418095636480000⟩, + ⟨4, 3, 2, 3, 3, 3, -15546752550370048230251900338310872736926688870400000⟩, + ⟨4, 3, 3, 3, 4, 3, 238388131086364743259011782865203881053719101440000⟩, + ⟨4, 3, 4, 3, 5, 3, -2942766609504656980331092777157664595125385297920000⟩, + ⟨4, 3, 5, 3, 6, 3, -700176630295481269269456771031091275594570137600000⟩, + ⟨4, 3, 6, 3, 7, 3, -769208239787891881649515165831537708687687680000⟩, + ⟨4, 3, 7, 3, 8, 3, 20518571915051473717858206240474809632271892480000⟩, + ⟨4, 3, 1, 4, 1, 3, 6805248018197996130611537106036216712424734064640000⟩, + ⟨4, 3, 2, 4, 2, 3, 3706898994729746466226569292948678440430180761600000⟩, + ⟨4, 3, 3, 4, 3, 3, 3520508911389365553960394371882582855587588997120000⟩, + ⟨4, 3, 4, 4, 4, 3, 2205502890448312478069089995935589129515748556800000⟩, + ⟨4, 3, 5, 4, 5, 3, -424553385951213108935695861449725299172730470400000⟩, + ⟨4, 3, 6, 4, 6, 3, -155448375189047408067402856474331687646060871680000⟩, + ⟨4, 3, 7, 4, 7, 3, 54273322563332716605203586482394536783653109760000⟩, + ⟨4, 3, 8, 4, 8, 3, -8304933725470833325767203006494092163232563200000⟩, + ⟨4, 3, 1, 5, 0, 3, 35867817619118795265429107557848797747993546588160000⟩, + ⟨4, 3, 2, 5, 1, 3, -3839243126373344430349408729596240741708563742720000⟩, + ⟨4, 3, 3, 5, 2, 3, 4396015321498709841456511593686960374533932974080000⟩, + ⟨4, 3, 4, 5, 3, 3, 2101588194785109605223168736731518301217058979840000⟩, + ⟨4, 3, 5, 5, 4, 3, -281621814393646345538968159906284233959460044800000⟩, + ⟨4, 3, 6, 5, 5, 3, -129858664628595785044859175924740735130811760640000⟩, + ⟨4, 3, 7, 5, 6, 3, -17193683379045023412700708218339721606909132800000⟩, + ⟨4, 3, 8, 5, 7, 3, 13615957426918735592342357013528503464042168320000⟩, + ⟨4, 3, 2, 6, 0, 3, 69114364754807679231520883787416724458407282606080000⟩, + ⟨4, 3, 3, 6, 1, 3, 1070262413696807104453241463447173987020560138240000⟩, + ⟨4, 3, 4, 6, 2, 3, -2661866438899451732381184899052162085156017930240000⟩, + ⟨4, 3, 5, 6, 3, 3, 2566293813576073477667918097240768801579781324800000⟩, + ⟨4, 3, 6, 6, 4, 3, 86584337718009584185810771775834195295983370240000⟩, + ⟨4, 3, 7, 6, 5, 3, -107420851318355798610146945920356507692480593920000⟩, + ⟨4, 3, 8, 6, 6, 3, -20338652742329739788186926870166983002732625920000⟩, + ⟨4, 3, 3, 7, 0, 3, -112495325995523289085708122311994490447181717176320000⟩, + ⟨4, 3, 4, 7, 1, 3, -2557034964236759178189460660703127299576341463040000⟩, + ⟨4, 3, 5, 7, 2, 3, -142171956776205692329641126486003223284311654400000⟩, + ⟨4, 3, 6, 7, 3, 3, 437094235495817983901818593432978718172727214080000⟩, + ⟨4, 3, 7, 7, 4, 3, -83529329633125332010460198971698308006176358400000⟩, + ⟨4, 3, 8, 7, 5, 3, -52536892781035035729263376576829920596144947200000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0819.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0819.lean new file mode 100644 index 0000000000000000000000000000000000000000..71ec4ca1c92d53a51ebfa8486fad6c0b1065ae67 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0819.lean @@ -0,0 +1,624 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0819. -/ +namespace LaughlinFock +def collectedFourData_8_4_30 : List CollectedFourTerm := [ + ⟨4, 4, 0, 0, 4, 4, -5040943512353746722593803047392846958487928832000000⟩, + ⟨4, 4, 1, 0, 5, 4, 16709771373256256092434641522922383846719409356800000⟩, + ⟨4, 4, 2, 0, 6, 4, -7129546857987863631718145519668293623876891443200000⟩, + ⟨4, 4, 3, 0, 7, 4, 679266932975457641216778867816948258780374630400000⟩, + ⟨4, 4, 4, 0, 8, 4, -655411465177855424798921713995486749330610585600000⟩, + ⟨4, 4, 0, 1, 3, 4, -3961993601277729617131095578843227570798224998400000⟩, + ⟨4, 4, 1, 1, 4, 4, 7299085253913473457928746997996823625427058688000000⟩, + ⟨4, 4, 2, 1, 5, 4, 3481269249867363648933845897805981915129525043200000⟩, + ⟨4, 4, 3, 1, 6, 4, -3220883785505975729641034514086120255881268428800000⟩, + ⟨4, 4, 4, 1, 7, 4, 764372131468721394820761562905264096745724313600000⟩, + ⟨4, 4, 5, 1, 8, 4, 750411845915326325634043681921053935158689792000000⟩, + ⟨4, 4, 0, 2, 2, 4, -3305088686888224710587135813984242552450685337600000⟩, + ⟨4, 4, 1, 2, 3, 4, 11024814399424124819169260891664125550520801689600000⟩, + ⟨4, 4, 2, 2, 4, 4, 12825439231343780503460509202278582924990847385600000⟩, + ⟨4, 4, 3, 2, 5, 4, -1370644839932575228414506345130494504347684044800000⟩, + ⟨4, 4, 4, 2, 6, 4, -503945355967076809278572581595292778075521024000000⟩, + ⟨4, 4, 5, 2, 7, 4, 384652419978210620193419967521397124856650137600000⟩, + ⟨4, 4, 6, 2, 8, 4, -113638490456899451689649780225799307094340403200000⟩, + ⟨4, 4, 0, 3, 1, 4, -10594592003158340551243752082975294177304956108800000⟩, + ⟨4, 4, 1, 3, 2, 4, -28408863948912570260518884629645470812205586841600000⟩, + ⟨4, 4, 2, 3, 3, 4, -14609425178273697523097525746190671974009667584000000⟩, + ⟨4, 4, 3, 3, 4, 4, 149343667462002164728969309420301453362829721600000⟩, + ⟨4, 4, 4, 3, 5, 4, -1382672312413473990885775967833959221513787801600000⟩, + ⟨4, 4, 5, 3, 6, 4, -263184946405650752708979442699649699029608038400000⟩, + ⟨4, 4, 6, 3, 7, 4, -240943999704198390577443940364429754472857600000⟩, + ⟨4, 4, 7, 3, 8, 4, 5508996909929085914489259684322422500936908800000⟩, + ⟨4, 4, 0, 4, 0, 4, -33833062042146751780972348344843589595569324032000000⟩, + ⟨4, 4, 1, 4, 1, 4, 12789907270903664715626543794342167437690850508800000⟩, + ⟨4, 4, 2, 4, 2, 4, 3483406797108453873343458085024409948453339136000000⟩, + ⟨4, 4, 3, 4, 3, 4, 2205502890448312478069089995935589129515748556800000⟩, + ⟨4, 4, 4, 4, 4, 4, 1036265591610771993876022155292982546754699264000000⟩, + ⟨4, 4, 5, 4, 5, 4, -159582675703920437498146970477099334567041433600000⟩, + ⟨4, 4, 6, 4, 6, 4, -48692085352460532311799423922065786082531737600000⟩, + ⟨4, 4, 7, 4, 7, 4, 14571753216102632926781785899449777007466905600000⟩, + ⟨4, 4, 8, 4, 8, 4, -1951055493417177234778947890529649104519168000000⟩, + ⟨4, 4, 1, 5, 0, 4, 67410630756068794863443042877633922664630530867200000⟩, + ⟨4, 4, 2, 5, 1, 4, -3607771784765295934356732716314447090099106611200000⟩, + ⟨4, 4, 3, 5, 2, 4, 2753983796676197585805166087022764848286217011200000⟩, + ⟨4, 4, 4, 5, 3, 4, 987440797934535421997576217445313479686959923200000⟩, + ⟨4, 4, 5, 5, 4, 4, -105857035097808343146242932945992474283946803200000⟩, + ⟨4, 4, 6, 5, 5, 4, -40676457210712911288332388943016547209497804800000⟩, + ⟨4, 4, 7, 5, 6, 4, -4616303171468573431225734845737459481837568000000⟩, + ⟨4, 4, 8, 5, 7, 4, 3198759847348225511941270228218128091630796800000⟩, + ⟨4, 4, 2, 6, 0, 4, 64947398973378904516430071595209204833113132236800000⟩, + ⟨4, 4, 3, 6, 1, 4, 670490234894744126889088304666279556576549273600000⟩, + ⟨4, 4, 4, 6, 2, 4, -1250690086166379604936520354706679937656632115200000⟩, + ⟨4, 4, 5, 6, 3, 4, 964627881827678983467992446259030473449878323200000⟩, + ⟨4, 4, 6, 6, 4, 4, 27121363971957679865056055235254409302428876800000⟩, + ⟨4, 4, 7, 6, 5, 4, -28841243943525652688408684317613906707297075200000⟩, + ⟨4, 4, 8, 6, 6, 4, -4778104374261828870618787393447415524412620800000⟩, + ⟨4, 4, 3, 7, 0, 4, -70475255961541056423450668084144901616393047244800000⟩, + ⟨4, 4, 4, 7, 1, 4, -1201434539696121804446966437021020467724759859200000⟩, + ⟨4, 4, 5, 7, 2, 4, -53440113830622478554402711237301345472584089600000⟩, + ⟨4, 4, 6, 7, 3, 4, 136913813321931810434271464017782615347665305600000⟩, + ⟨4, 4, 7, 7, 4, 4, -22426649415098004818411525318369307267170304000000⟩, + ⟨4, 4, 8, 7, 5, 4, -12342349337856571390372798186696352703971328000000⟩ +] + +def collectedFourData_8_4_31 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 4, 5, 3881472376803017318040818402069113566589353984000000⟩, + ⟨4, 5, 1, 0, 5, 5, -6433172267159949061378798729887995006425025740800000⟩, + ⟨4, 5, 2, 0, 6, 5, 1829891508774404932915479949167670410726919372800000⟩, + ⟨4, 5, 3, 0, 7, 5, -130757061171117419164589604649120994428138291200000⟩, + ⟨4, 5, 4, 0, 8, 5, 100931958126227730214583073545150247508314685440000⟩, + ⟨4, 5, 0, 1, 3, 5, 3050692530622954301483365778001136214837349580800000⟩, + ⟨4, 5, 1, 1, 4, 5, -2810108635373977539833651617983365948928688128000000⟩, + ⟨4, 5, 2, 1, 5, 5, -893513313956618216545721817758399129990253772800000⟩, + ⟨4, 5, 3, 1, 6, 5, 620011482557596616299138780517567070162282086400000⟩, + ⟨4, 5, 4, 1, 7, 5, -117711666739489775081351459924653226741874032640000⟩, + ⟨4, 5, 5, 1, 8, 5, -96301510620250436870022431959468898814787584000000⟩, + ⟨4, 5, 0, 2, 2, 5, 2544882800134927819663995429199742038873158451200000⟩, + ⟨4, 5, 1, 2, 3, 5, -4244494353673481091682687916448274827357821337600000⟩, + ⟨4, 5, 2, 2, 4, 5, -3291816831169786173924909378210995101774538342400000⟩, + ⟨4, 5, 3, 2, 5, 5, 263845452322961189078874560637297630856504934400000⟩, + ⟨4, 5, 4, 2, 6, 5, 77606502584713233309735150525230505250101657600000⟩, + ⟨4, 5, 5, 2, 7, 5, -49363038855621198755748633130616910339322675200000⟩, + ⟨4, 5, 6, 2, 8, 5, 12500059635068897630348998130539448816055091200000⟩, + ⟨4, 5, 0, 3, 1, 5, 8157722081784652422326872464136324802135300505600000⟩, + ⟨4, 5, 1, 3, 2, 5, 10937260098613180672170629172035855367200676249600000⟩, + ⟨4, 5, 2, 3, 3, 5, 3749700172297197610287323345499102507052302336000000⟩, + ⟨4, 5, 3, 3, 4, 5, -28748255087744106588249560528279273319746764800000⟩, + ⟨4, 5, 4, 3, 5, 5, 212928566791154198698997332265861950342000803840000⟩, + ⟨4, 5, 5, 3, 6, 5, 33774930458965150008632546204103442816617676800000⟩, + ⟨4, 5, 6, 3, 7, 5, 26503470372627105759582846877595883641241600000⟩, + ⟨4, 5, 7, 3, 8, 5, -530233558394870879476433382746184035283763200000⟩, + ⟨4, 5, 0, 4, 0, 5, 26051094486067276173781984390525271989114896384000000⟩, + ⟨4, 5, 1, 4, 1, 5, -4924045632749485784811868135077375690819816652800000⟩, + ⟨4, 5, 2, 4, 2, 5, -894061943431111785517809851924149404690284544000000⟩, + ⟨4, 5, 3, 4, 3, 5, -424553385951213108935695861449725299172730470400000⟩, + ⟨4, 5, 4, 4, 4, 5, -159582675703920437498146970477099334567041433600000⟩, + ⟨4, 5, 5, 4, 5, 5, 20479491125787943832567645605455371202409267200000⟩, + ⟨4, 5, 6, 4, 6, 5, 5356054697791592994047362022184097259559321600000⟩, + ⟨4, 5, 7, 4, 7, 5, -1402511688815861178568341929604570549741158400000⟩, + ⟨4, 5, 8, 4, 8, 5, 166921308916555501382110808808105625780224000000⟩, + ⟨4, 5, 1, 5, 0, 5, -25952730926395227033055954047783505301249143603200000⟩, + ⟨4, 5, 2, 5, 1, 5, 925981845135259664638382499731551907883044044800000⟩, + ⟨4, 5, 3, 5, 2, 5, -530134488055915001375070872180601725768014233600000⟩, + ⟨4, 5, 4, 5, 3, 5, -152063762330144867943948203686072278339739975680000⟩, + ⟨4, 5, 5, 5, 4, 5, 13584796728875316895398217139064789298210406400000⟩, + ⟨4, 5, 6, 5, 5, 5, 4474347897731768191737218638006501797317836800000⟩, + ⟨4, 5, 7, 5, 6, 5, 444312984243227233508992904189561486180352000000⟩, + ⟨4, 5, 8, 5, 7, 5, -273667859489693699219471377118946690229862400000⟩, + ⟨4, 5, 2, 6, 0, 5, -16669599943117713076680573157322684034561815347200000⟩, + ⟨4, 5, 3, 6, 1, 5, -129067570350780740224997569715480112986377420800000⟩, + ⟨4, 5, 4, 6, 2, 5, 192603587383961287928038020940574897492962836480000⟩, + ⟨4, 5, 5, 6, 3, 5, -123792185200791526687329173461288763330553446400000⟩, + ⟨4, 5, 6, 6, 4, 5, -2983308434235689649656078740880548617309388800000⟩, + ⟨4, 5, 7, 6, 5, 5, 2775931018793578858634752552083557662379212800000⟩, + ⟨4, 5, 8, 6, 6, 5, 408787673637516033821822309447889651656294400000⟩, + ⟨4, 5, 3, 7, 0, 5, 13566297588559828256275102909311264858627794534400000⟩, + ⟨4, 5, 4, 7, 1, 5, 185018339004957959344290058366867137139656622080000⟩, + ⟨4, 5, 5, 7, 2, 5, 6858052305037545159195639538769243080438579200000⟩, + ⟨4, 5, 6, 7, 3, 5, -15060309447158185509582247808876158847130009600000⟩, + ⟨4, 5, 7, 7, 4, 5, 2158534905113013635844638445889642567827456000000⟩, + ⟨4, 5, 8, 7, 5, 5, 1055941829195263235948151067182866160943104000000⟩ +] + +def collectedFourData_8_4_32 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 4, 6, 3552960559738264514863764314403350818672607232000000⟩, + ⟨4, 6, 1, 0, 5, 6, -3925796728722713723446288208087560592803076505600000⟩, + ⟨4, 6, 2, 0, 6, 6, 837508518433719677940125719694812398283338547200000⟩, + ⟨4, 6, 3, 0, 7, 6, -47876129071505769919432511623947110363210711040000⟩, + ⟨4, 6, 4, 0, 8, 6, 30796497791473722687147102755416814249878487040000⟩, + ⟨4, 6, 0, 1, 3, 6, 2792494494091706228095383120727767055648319078400000⟩, + ⟨4, 6, 1, 1, 4, 6, -1714848418473467525821873930502288435992068096000000⟩, + ⟨4, 6, 2, 1, 5, 6, -408945015693204314357348047195154491016164147200000⟩, + ⟨4, 6, 3, 1, 6, 6, 227014506894560802482029178754355534865765498880000⟩, + ⟨4, 6, 4, 1, 7, 6, -35916345546766752923442806268703588938405642240000⟩, + ⟨4, 6, 5, 1, 8, 6, -25185985100602649628091920121245203171377152000000⟩, + ⟨4, 6, 0, 2, 2, 6, 2329494413530524307165761001604099730872834457600000⟩, + ⟨4, 6, 1, 2, 3, 6, -2590171902250272136854189982795359633500484403200000⟩, + ⟨4, 6, 2, 2, 4, 6, -1506605514047484622086978635618831421247429017600000⟩, + ⟨4, 6, 3, 2, 5, 6, 96605864472687754535087073750377588708584980480000⟩, + ⟨4, 6, 4, 2, 6, 6, 23679402736496240176687521908302455349287321600000⟩, + ⟨4, 6, 5, 2, 7, 6, -12910044226001073180740099298516542502312345600000⟩, + ⟨4, 6, 6, 2, 8, 6, 2860526532611594426357019976693578532808294400000⟩, + ⟨4, 6, 0, 3, 1, 6, 7467286122427485504299312580947427253245758668800000⟩, + ⟨4, 6, 1, 3, 2, 6, 6674383668460456071850020690859153050406433587200000⟩, + ⟨4, 6, 2, 3, 3, 6, 1716170505635396648858347263296379855059288064000000⟩, + ⟨4, 6, 3, 3, 4, 6, -10526048527201288364245638076956088249519964160000⟩, + ⟨4, 6, 4, 3, 5, 6, 64969056963350980833434202260871196687403581440000⟩, + ⟨4, 6, 5, 3, 6, 6, 8833245603672906418168155029275536502711910400000⟩, + ⟨4, 6, 6, 3, 7, 6, 6065081481250650656175220288424623944499200000⟩, + ⟨4, 6, 7, 3, 8, 6, -107857061418551998736327224330103743630540800000⟩, + ⟨4, 6, 0, 4, 0, 6, 23846237268149261820741637872892374509716242432000000⟩, + ⟨4, 6, 1, 4, 1, 6, -3004863142839988129310847786688513834346977689600000⟩, + ⟨4, 6, 2, 4, 2, 6, -409196113562203074540092629427865991885357056000000⟩, + ⟨4, 6, 3, 4, 3, 6, -155448375189047408067402856474331687646060871680000⟩, + ⟨4, 6, 4, 4, 4, 6, -48692085352460532311799423922065786082531737600000⟩, + ⟨4, 6, 5, 4, 5, 6, 5356054697791592994047362022184097259559321600000⟩, + ⟨4, 6, 6, 4, 6, 6, 1225685078347018619563428405662553283441459200000⟩, + ⟨4, 6, 7, 4, 7, 6, -285290862801626700527033049026304063150489600000⟩, + ⟨4, 6, 8, 4, 8, 6, 30558755523020769692527068448110066165350400000⟩, + ⟨4, 6, 1, 5, 0, 6, -15837465863049614201041476817471328829751846502400000⟩, + ⟨4, 6, 2, 5, 1, 6, 423805279983602437435875068312284639878394675200000⟩, + ⟨4, 6, 3, 5, 2, 6, -194106436379803826514598973291723107536595845120000⟩, + ⟨4, 6, 4, 5, 3, 6, -46397904169329493860074721410851737965565050880000⟩, + ⟨4, 6, 5, 5, 4, 6, 3552867299842981163149079921562890345329459200000⟩, + ⟨4, 6, 6, 5, 5, 6, 1023914385311337476090750983582911689234841600000⟩, + ⟨4, 6, 7, 5, 6, 6, 90379592298255888744431235801307139801088000000⟩, + ⟨4, 6, 8, 5, 7, 6, -50101148061537274848911426315043136906199040000⟩, + ⟨4, 6, 2, 6, 0, 6, -7629376869776208947844223900364588324982934732800000⟩, + ⟨4, 6, 3, 6, 1, 6, -47257529357998062524937877652253175339926159360000⟩, + ⟨4, 6, 4, 6, 2, 6, 58767471310543638195292780366581456875217223680000⟩, + ⟨4, 6, 5, 6, 3, 6, -32375692883290631256919832540681156364022579200000⟩, + ⟨4, 6, 6, 6, 4, 6, -682703377442575340937914083519378694445465600000⟩, + ⟨4, 6, 7, 6, 5, 6, 564663925259731140703047246064559863313203200000⟩, + ⟨4, 6, 8, 6, 6, 6, 74837914108126645551319382394707418273546240000⟩, + ⟨4, 6, 3, 7, 0, 6, 4967240840036672152835858427819454577177505300480000⟩, + ⟨4, 6, 4, 7, 1, 6, 56453049899441997996532062293536216939002593280000⟩, + ⟨4, 6, 5, 7, 2, 6, 1793604296145983814113078449814133840386457600000⟩, + ⟨4, 6, 6, 7, 3, 6, -3446416738850989731436583190723066462417715200000⟩, + ⟨4, 6, 7, 7, 4, 6, 439076758060424377891461764907391845924864000000⟩, + ⟨4, 6, 8, 7, 5, 6, 193314253370972639522738686109608017552998400000⟩ +] + +def collectedFourData_8_4_33 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 4, 7, -2480964812645535936626445725779952872244379648000000⟩, + ⟨4, 7, 1, 0, 5, 7, 2055981916024456915220467342413512014444678348800000⟩, + ⟨4, 7, 2, 0, 6, 7, -350889765803314331120683253993246996734389780480000⟩, + ⟨4, 7, 3, 0, 7, 7, 16715495372798605654756706973833400811813601280000⟩, + ⟨4, 7, 4, 0, 8, 7, -9216260969092545606910787809848718793103114240000⟩, + ⟨4, 7, 0, 1, 3, 7, -1949945816414660852852877718594842067738401177600000⟩, + ⟨4, 7, 1, 1, 4, 7, 898084536906652453059014241538466043981201408000000⟩, + ⟨4, 7, 2, 1, 5, 7, 171335117941701643128901800594945573340556820480000⟩, + ⟨4, 7, 3, 1, 6, 7, -79259957167519621181863569733006267460521820160000⟩, + ⟨4, 7, 4, 1, 7, 7, 10748443406014546831783607338126913419283005440000⟩, + ⟨4, 7, 5, 1, 8, 7, 6595085467013989305404268558504958988648448000000⟩, + ⟨4, 7, 0, 2, 2, 7, -1626641662368841408342667891859927222343591526400000⟩, + ⟨4, 7, 1, 2, 3, 7, 1356500847702796560986213352110244442924489113600000⟩, + ⟨4, 7, 2, 2, 4, 7, 631220392803612265098155871214878553582432419840000⟩, + ⟨4, 7, 3, 2, 5, 7, -33729019281542204020479783913174010680427151360000⟩, + ⟨4, 7, 4, 2, 6, 7, -7086375752512154796451697468411793941043609600000⟩, + ⟨4, 7, 5, 2, 7, 7, 3380564417604227357505768950087447063455334400000⟩, + ⟨4, 7, 6, 2, 8, 7, -665817098513013308292510266567583572636467200000⟩, + ⟨4, 7, 0, 3, 1, 7, -5214263936851490127446210411813044467776303923200000⟩, + ⟨4, 7, 1, 3, 2, 7, -3495446420484526162330908260704818831164021145600000⟩, + ⟨4, 7, 2, 3, 3, 7, -719021542523709682159722996514999332920465817600000⟩, + ⟨4, 7, 3, 3, 4, 7, 3675069786604886519589437055894160766266245120000⟩, + ⟨4, 7, 4, 3, 5, 7, -19442853143381032974589790214172483846290800640000⟩, + ⟨4, 7, 5, 3, 6, 7, -2313032802753244285538343408726520511437209600000⟩, + ⟨4, 7, 6, 3, 7, 7, -1411710364526667133074320764480194714009600000⟩, + ⟨4, 7, 7, 3, 8, 7, 22594360647320701626893027803656562786959360000⟩, + ⟨4, 7, 0, 4, 0, 7, -16651374137582091690607244540686969676337512448000000⟩, + ⟨4, 7, 1, 4, 1, 7, 1573679104831662764911450229026792533939506380800000⟩, + ⟨4, 7, 2, 4, 2, 7, 171440320062644200554307409827001576362239590400000⟩, + ⟨4, 7, 3, 4, 3, 7, 54273322563332716605203586482394536783653109760000⟩, + ⟨4, 7, 4, 4, 4, 7, 14571753216102632926781785899449777007466905600000⟩, + ⟨4, 7, 5, 4, 5, 7, -1402511688815861178568341929604570549741158400000⟩, + ⟨4, 7, 6, 4, 6, 7, -285290862801626700527033049026304063150489600000⟩, + ⟨4, 7, 7, 4, 7, 7, 59763955727580233357578405928438509936312320000⟩, + ⟨4, 7, 8, 4, 8, 7, -5819617642254407333905576060357452811468800000⟩, + ⟨4, 7, 1, 5, 0, 7, 8294250991614333514898698952746966564046320435200000⟩, + ⟨4, 7, 2, 5, 1, 7, -177561101966777338712414621295323362843353415680000⟩, + ⟨4, 7, 3, 5, 2, 7, 67770417159061918672882088569751629736013987840000⟩, + ⟨4, 7, 4, 5, 3, 7, 13885189028275698139946680024753033186671329280000⟩, + ⟨4, 7, 5, 5, 4, 7, -930337384137617516426111535353804295556300800000⟩, + ⟨4, 7, 6, 5, 5, 7, -238326649790350904664193992521591334685900800000⟩, + ⟨4, 7, 7, 5, 6, 7, -18933105321867735177004610242494783396249600000⟩, + ⟨4, 7, 8, 5, 7, 7, 9541276147075917574609192314696115295354880000⟩, + ⟨4, 7, 2, 6, 0, 7, 3196469294506477729165011342802847225439867371520000⟩, + ⟨4, 7, 3, 6, 1, 7, 16499517163004139233065234692675695749386731520000⟩, + ⟨4, 7, 4, 6, 2, 7, -17586946274182529391037000077423560800421806080000⟩, + ⟨4, 7, 5, 6, 3, 7, 8477749064259915347704792603425456857599180800000⟩, + ⟨4, 7, 6, 6, 4, 7, 158906263141300557090405996069240074718412800000⟩, + ⟨4, 7, 7, 6, 5, 7, -118288225212629649616180383599974896044605440000⟩, + ⟨4, 7, 8, 6, 6, 7, -14252152543485558988084353199175418280673280000⟩, + ⟨4, 7, 3, 7, 0, 7, -1734264922571315316066465970148983404211061391360000⟩, + ⟨4, 7, 4, 7, 1, 7, -16894324929327088684110378757817256428364103680000⟩, + ⟨4, 7, 5, 7, 2, 7, -469664918002480270385992192149718556894822400000⟩, + ⟨4, 7, 6, 7, 3, 7, 802189096017038135396374982570414700075417600000⟩, + ⟨4, 7, 7, 7, 4, 7, -91979685826738074169020287598817977355468800000⟩, + ⟨4, 7, 8, 7, 5, 7, -36814818540939779061642174216148892830924800000⟩ +] + +def collectedFourData_8_4_34 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 4, 8, 664367554802912440142044375451778734232698880000000⟩, + ⟨4, 8, 1, 0, 5, 8, -440450480008748156510008950555745133540042342400000⟩, + ⟨4, 8, 2, 0, 6, 8, 62642236204210440426328235834129954246964019200000⟩, + ⟨4, 8, 3, 0, 7, 8, -2557814312870074814521476070420446088632729600000⟩, + ⟨4, 8, 4, 0, 8, 8, 1233992665525229844718320975742773480338227200000⟩, + ⟨4, 8, 0, 1, 3, 8, 522168120823996091081640511881834554411974656000000⟩, + ⟨4, 8, 1, 1, 4, 8, -192395547006486398807977413670346519513923584000000⟩, + ⟨4, 8, 2, 1, 5, 8, -30587426520146606128866743623103577828045619200000⟩, + ⟨4, 8, 3, 1, 6, 8, 12128402321265346132056701171140059936797491200000⟩, + ⟨4, 8, 4, 1, 7, 8, -1439141141219325290622661352049155268358963200000⟩, + ⟨4, 8, 5, 1, 8, 8, -784920587364218515192470072512080018145280000000⟩, + ⟨4, 8, 0, 2, 2, 8, 435591806163569914455201912926031697447747584000000⟩, + ⟨4, 8, 1, 2, 3, 8, -290601510084422020692187999391992706386152652800000⟩, + ⟨4, 8, 2, 2, 4, 8, -112687974391029931608304165368550563851639193600000⟩, + ⟨4, 8, 3, 2, 5, 8, 5161233116536415330030979614201344358036275200000⟩, + ⟨4, 8, 4, 2, 6, 8, 948815982216792371230941910616748261900288000000⟩, + ⟨4, 8, 5, 2, 7, 8, -402341201120155089248368940971509713731584000000⟩, + ⟨4, 8, 6, 2, 8, 8, 71318589514918720878923494109511053790412800000⟩, + ⟨4, 8, 0, 3, 1, 8, 1396306696558526678180066399975672514600763392000000⟩, + ⟨4, 8, 1, 3, 2, 8, 748825192355902092908076534865366063753514188800000⟩, + ⟨4, 8, 2, 3, 3, 8, 128362584755273381845476621812346107360968704000000⟩, + ⟨4, 8, 3, 3, 4, 8, -562361203860662075415071565972802831279718400000⟩, + ⟨4, 8, 4, 3, 5, 8, 2603261589084395891788761912501592055296819200000⟩, + ⟨4, 8, 5, 3, 6, 8, 275287875374842357233504122555597907296256000000⟩, + ⟨4, 8, 6, 3, 7, 8, 151214488523180885538161998696704009830400000⟩, + ⟨4, 8, 7, 3, 8, 8, -2200164601519594746943378171887136171622400000⟩, + ⟨4, 8, 0, 4, 0, 8, 4459004280716667281149194337120369687532666880000000⟩, + ⟨4, 8, 1, 4, 1, 8, -337127341296419204644592552905306375033611878400000⟩, + ⟨4, 8, 2, 4, 2, 8, -30606207621083478621002444152317065734127616000000⟩, + ⟨4, 8, 3, 4, 3, 8, -8304933725470833325767203006494092163232563200000⟩, + ⟨4, 8, 4, 4, 4, 8, -1951055493417177234778947890529649104519168000000⟩, + ⟨4, 8, 5, 4, 5, 8, 166921308916555501382110808808105625780224000000⟩, + ⟨4, 8, 6, 4, 6, 8, 30558755523020769692527068448110066165350400000⟩, + ⟨4, 8, 7, 4, 7, 8, -5819617642254407333905576060357452811468800000⟩, + ⟨4, 8, 8, 4, 8, 8, 519470640771888027898508822985232613376000000⟩, + ⟨4, 8, 1, 5, 0, 8, -1776867200093656799875489996574620688286587289600000⟩, + ⟨4, 8, 2, 5, 1, 8, 31698913944151574765928462414010031210181427200000⟩, + ⟨4, 8, 3, 5, 2, 8, -10370266577962744667911728690681534856613068800000⟩, + ⟨4, 8, 4, 5, 3, 8, -1859129366864128619714654721687639239845478400000⟩, + ⟨4, 8, 5, 5, 4, 8, 110725019358212414859917953815519783026688000000⟩, + ⟨4, 8, 6, 5, 5, 8, 25528212695083887959018194697673537434419200000⟩, + ⟨4, 8, 7, 5, 6, 8, 1843643587717774854329305424057560203264000000⟩, + ⟨4, 8, 8, 5, 7, 8, -851673277968660390535046776334400985497600000⟩, + ⟨4, 8, 2, 6, 0, 8, -570646408303109798848274414363464906258042060800000⟩, + ⟨4, 8, 3, 6, 1, 8, -2524765208194462046163318842209610064356966400000⟩, + ⟨4, 8, 4, 6, 2, 8, 2354768683754443900814018541119342329095782400000⟩, + ⟨4, 8, 5, 6, 3, 8, -1008987648200743418097395666261213328703488000000⟩, + ⟨4, 8, 6, 6, 4, 8, -17021146764831200385021351248802576806707200000⟩, + ⟨4, 8, 7, 6, 5, 8, 11518518711449661758784054893600875059609600000⟩, + ⟨4, 8, 8, 6, 6, 8, 1272175470839891015060138271091034003865600000⟩, + ⟨4, 8, 3, 7, 0, 8, 265378174103058815195802309029143199859553075200000⟩, + ⟨4, 8, 4, 7, 1, 8, 2262031546383431560458521200077795523716710400000⟩, + ⟨4, 8, 5, 7, 2, 8, 55897632433531641343422192471645842571264000000⟩, + ⟨4, 8, 6, 7, 3, 8, -85925992258164697120914040224627600811622400000⟩, + ⟨4, 8, 7, 7, 4, 8, 8956679588049344016971215271098520174592000000⟩, + ⟨4, 8, 8, 7, 5, 8, 3286163894773406269148714198398975082496000000⟩ +] + +def collectedFourData_8_4_35 : List CollectedFourTerm := [ + ⟨5, 0, 3, 0, 7, 1, 11046833160898497949664982301044700366976298516480000⟩, + ⟨5, 0, 4, 0, 8, 1, -42635498688827818376576451922515108363003368570880000⟩, + ⟨5, 0, 3, 1, 6, 1, -52380830100577333228484123447183355425988343234560000⟩, + ⟨5, 0, 4, 1, 7, 1, 49723553432449632416257194354589011711349783265280000⟩, + ⟨5, 0, 5, 1, 8, 1, 122038539804615989957527889805138533326472085504000000⟩, + ⟨5, 0, 3, 2, 5, 1, -22290625576688642234035831878914966637910960373760000⟩, + ⟨5, 0, 4, 2, 6, 1, -32782401140548622564713274073066692373092971315200000⟩, + ⟨5, 0, 5, 2, 7, 1, 62555541896055744297656181514154258805566944051200000⟩, + ⟨5, 0, 6, 2, 8, 1, -36961771103292637881832654778510185715169283276800000⟩, + ⟨5, 0, 3, 3, 4, 1, 2428757382407500421349467249979352940797671505920000⟩, + ⟨5, 0, 4, 3, 5, 1, -89944907428474734236974162311720285183621652807680000⟩, + ⟨5, 0, 5, 3, 6, 1, -42801438613651483420908763010442925689222778060800000⟩, + ⟨5, 0, 6, 3, 7, 1, -78368842545969317029224174689563369068193382400000⟩, + ⟨5, 0, 7, 3, 8, 1, 3135724466736521448485191388919906723482409369600000⟩, + ⟨5, 0, 3, 4, 3, 1, 35867817619118795265429107557848797747993546588160000⟩, + ⟨5, 0, 4, 4, 4, 1, 67410630756068794863443042877633922664630530867200000⟩, + ⟨5, 0, 5, 4, 5, 1, -25952730926395227033055954047783505301249143603200000⟩, + ⟨5, 0, 6, 4, 6, 1, -15837465863049614201041476817471328829751846502400000⟩, + ⟨5, 0, 7, 4, 7, 1, 8294250991614333514898698952746966564046320435200000⟩, + ⟨5, 0, 8, 4, 8, 1, -1776867200093656799875489996574620688286587289600000⟩, + ⟨5, 0, 3, 5, 2, 1, 44787693987157419487126034211719080101067295293440000⟩, + ⟨5, 0, 4, 5, 3, 1, 64234504707982983805741115931277218488453022351360000⟩, + ⟨5, 0, 5, 5, 4, 1, -17215397200486366423118225498821177900173518438400000⟩, + ⟨5, 0, 6, 5, 5, 1, -13230322707300323579819175306476382930731217715200000⟩, + ⟨5, 0, 7, 5, 6, 1, -2627602635709908066531462388806914853732089856000000⟩, + ⟨5, 0, 8, 5, 7, 1, 2913177750661930077046659256746237163400551464960000⟩, + ⟨5, 0, 3, 6, 1, 1, 10904098817896520420424266592371782145460739768320000⟩, + ⟨5, 0, 4, 6, 2, 1, -81359265685726816012973177758141326643629612072960000⟩, + ⟨5, 0, 5, 6, 3, 1, 156876225760371188805359054165362758122889176678400000⟩, + ⟨5, 0, 6, 6, 4, 1, 8821426992826834080050371999081335843982619443200000⟩, + ⟨5, 0, 7, 6, 5, 1, -16416453986719347065464119621804189098367673958400000⟩, + ⟨5, 0, 8, 6, 6, 1, -4351519969521704849534781557545342313793595637760000⟩, + ⟨5, 0, 3, 7, 0, 1, -1146130271892522758985328646967959105955925076213760000⟩, + ⟨5, 0, 4, 7, 1, 1, -78155118522417277057224427503173088706530807644160000⟩, + ⟨5, 0, 5, 7, 2, 1, -8690898863578868898785426901749392547129799475200000⟩, + ⟨5, 0, 6, 7, 3, 1, 44532244387772345022249260859515699780548716134400000⟩, + ⟨5, 0, 7, 7, 4, 1, -12765262792414662789488626713913505772384288768000000⟩, + ⟨5, 0, 8, 7, 5, 1, -11240436668525732529155379519132540233026476441600000⟩ +] + +def collectedFourData_8_4_36 : List CollectedFourTerm := [ + ⟨5, 1, 2, 0, 6, 2, 4136934617380719312208038373214271732128164085760000⟩, + ⟨5, 1, 3, 0, 7, 2, -1182438216106181205260832153565131753170046812160000⟩, + ⟨5, 1, 4, 0, 8, 2, 2281823318870263728281114393906801893580451348480000⟩, + ⟨5, 1, 2, 1, 5, 2, -2020013832444864394778250824384710236620728565760000⟩, + ⟨5, 1, 3, 1, 6, 2, 5606773850945889304628399569739876266627584491520000⟩, + ⟨5, 1, 4, 1, 7, 2, -2661171258892445011715888565234691911120196730880000⟩, + ⟨5, 1, 5, 1, 8, 2, -4354280579812081409688449961419274121490989056000000⟩, + ⟨5, 1, 2, 2, 4, 2, -7441988193094384751822507974101893813383546798080000⟩, + ⟨5, 1, 3, 2, 5, 2, 2385958686882780423224639669601027042546989137920000⟩, + ⟨5, 1, 4, 2, 6, 2, 1754492140856897770356022277415021856559412019200000⟩, + ⟨5, 1, 5, 2, 7, 2, -2231953788317236818257222809131049935444954316800000⟩, + ⟨5, 1, 6, 2, 8, 2, 989084610289062740984023097196908195952879206400000⟩, + ⟨5, 1, 2, 3, 3, 2, 8477149805435338328417461698110856988114236211200000⟩, + ⟨5, 1, 3, 3, 4, 2, -259970935088790606595901374000338137923599728640000⟩, + ⟨5, 1, 4, 3, 5, 2, 4813791171573686916917398740165585275920349921280000⟩, + ⟨5, 1, 5, 3, 6, 2, 1527136208297965441069548368899823603245331251200000⟩, + ⟨5, 1, 6, 3, 7, 2, 2097123968214821600344157412072818291716915200000⟩, + ⟨5, 1, 7, 3, 8, 2, -67128748857593202770447463889306525784227184640000⟩, + ⟨5, 1, 2, 4, 2, 2, -2021254148744636703902369232532876084929940684800000⟩, + ⟨5, 1, 3, 4, 3, 2, -3839243126373344430349408729596240741708563742720000⟩, + ⟨5, 1, 4, 4, 4, 2, -3607771784765295934356732716314447090099106611200000⟩, + ⟨5, 1, 5, 4, 5, 2, 925981845135259664638382499731551907883044044800000⟩, + ⟨5, 1, 6, 4, 6, 2, 423805279983602437435875068312284639878394675200000⟩, + ⟨5, 1, 7, 4, 7, 2, -177561101966777338712414621295323362843353415680000⟩, + ⟨5, 1, 8, 4, 8, 2, 31698913944151574765928462414010031210181427200000⟩, + ⟨5, 1, 2, 5, 1, 2, 2093417195411661160813738293105197768021020508160000⟩, + ⟨5, 1, 3, 5, 2, 2, -4794014738009906263956378498488057115986865684480000⟩, + ⟨5, 1, 4, 5, 3, 2, -3437787647061459157327718547533766185867343298560000⟩, + ⟨5, 1, 5, 5, 4, 2, 614237681177120604400497283901558936219261337600000⟩, + ⟨5, 1, 6, 5, 5, 2, 354039002686831633314284841173731645471693209600000⟩, + ⟨5, 1, 7, 5, 6, 2, 56251012900280219380669777126506050261247590400000⟩, + ⟨5, 1, 8, 5, 7, 2, -51970440344321843328608173888299494089131294720000⟩, + ⟨5, 1, 2, 6, 0, 2, -37685865381581527458093935758230788682107049738240000⟩, + ⟨5, 1, 3, 6, 1, 2, -1167160123329896461979232751219443006073932349440000⟩, + ⟨5, 1, 4, 6, 2, 2, 4354293378923223030417448921029270219134242652160000⟩, + ⟨5, 1, 5, 6, 3, 2, -5597273651063162612877804024034786095689996697600000⟩, + ⟨5, 1, 6, 6, 4, 2, -236058430614984597384984084085418148216019353600000⟩, + ⟨5, 1, 7, 6, 5, 2, 351439046541493978595442804497827084494239170560000⟩, + ⟨5, 1, 8, 6, 6, 2, 77630144240861114777126866661073239576747704320000⟩, + ⟨5, 1, 3, 7, 0, 2, 122680248210760439967369248367325346133708814417920000⟩, + ⟨5, 1, 4, 7, 1, 2, 4182809569910158493256765549331194551662396047360000⟩, + ⟨5, 1, 5, 7, 2, 2, 310087388814865157937901785671686521610882252800000⟩, + ⟨5, 1, 6, 7, 3, 2, -1191667938814040766355813405552206955697877811200000⟩, + ⟨5, 1, 7, 7, 4, 2, 273275324150214948979990792154187243204064051200000⟩, + ⟨5, 1, 8, 7, 5, 2, 200526879347822003546178266312047734503453491200000⟩ +] + +def collectedFourData_8_4_37 : List CollectedFourTerm := [ + ⟨5, 2, 1, 0, 5, 3, 11101989678288074753064761234165535380591723151360000⟩, + ⟨5, 2, 2, 0, 6, 3, -9473756864792812193285190537478332810622434017280000⟩, + ⟨5, 2, 3, 0, 7, 3, 1353916994477650006313160008085375382601324298240000⟩, + ⟨5, 2, 4, 0, 8, 3, -1741824267705287791825579072771434507185663508480000⟩, + ⟨5, 2, 1, 1, 4, 3, 4849519920995830766357507917648143661523376537600000⟩, + ⟨5, 2, 2, 1, 5, 3, 4625917903488053912358913432503993750552607457280000⟩, + ⟨5, 2, 3, 1, 6, 3, -6419875725927034759401167058503731975103478497280000⟩, + ⟨5, 2, 4, 1, 7, 3, 2031398592925957360261768302761347580842349690880000⟩, + ⟨5, 2, 5, 1, 8, 3, 2492872099121236523631435254365747611583905792000000⟩, + ⟨5, 2, 1, 2, 3, 3, 7324898284565615149210676530735819055257532497920000⟩, + ⟨5, 2, 2, 2, 4, 3, 17042470634131993637464985942753623087635486474240000⟩, + ⟨5, 2, 3, 2, 5, 3, -2731973620516076275954577821721708250446828666880000⟩, + ⟨5, 2, 4, 2, 6, 3, -1339287298525720228830649532075389205903258419200000⟩, + ⟨5, 2, 5, 2, 7, 3, 1277817362349238362728304172860126511777814937600000⟩, + ⟨5, 2, 6, 2, 8, 3, -453009195611591400641473262699156212679536803840000⟩, + ⟨5, 2, 1, 3, 2, 3, -18874879092451407417724691565166782919878188728320000⟩, + ⟨5, 2, 2, 3, 3, 3, -19413034913751737311256455339459820835793639833600000⟩, + ⟨5, 2, 3, 3, 4, 3, 297672269292886605787707903486324321320655912960000⟩, + ⟨5, 2, 4, 3, 5, 3, -3674595755496021797666581946101265272096979681280000⟩, + ⟨5, 2, 5, 3, 6, 3, -874301776250737743871839660125628359726491238400000⟩, + ⟨5, 2, 6, 3, 7, 3, -960500681191612055977250488805755437837189120000⟩, + ⟨5, 2, 7, 3, 8, 3, 25621283395144730401074697358639476127375032320000⟩, + ⟨5, 2, 1, 4, 1, 3, 8497627845171626207711727623405291645687310581760000⟩, + ⟨5, 2, 2, 4, 2, 3, 4628758280759213706133978829390122372693386854400000⟩, + ⟨5, 2, 3, 4, 3, 3, 4396015321498709841456511593686960374533932974080000⟩, + ⟨5, 2, 4, 4, 4, 3, 2753983796676197585805166087022764848286217011200000⟩, + ⟨5, 2, 5, 4, 5, 3, -530134488055915001375070872180601725768014233600000⟩, + ⟨5, 2, 6, 4, 6, 3, -194106436379803826514598973291723107536595845120000⟩, + ⟨5, 2, 7, 4, 7, 3, 67770417159061918672882088569751629736013987840000⟩, + ⟨5, 2, 8, 4, 8, 3, -10370266577962744667911728690681534856613068800000⟩, + ⟨5, 2, 1, 5, 0, 3, 44787693987157419487126034211719080101067295293440000⟩, + ⟨5, 2, 2, 5, 1, 3, -4794014738009906263956378498488057115986865684480000⟩, + ⟨5, 2, 3, 5, 2, 3, 5489249194720780155773398657270041314216084766720000⟩, + ⟨5, 2, 4, 5, 3, 3, 2624226819556649408901061897449638400272954818560000⟩, + ⟨5, 2, 5, 5, 4, 3, -351657627378126486884904911222253324036420403200000⟩, + ⟨5, 2, 6, 5, 5, 3, -162152885763149511775361521890976814547609845760000⟩, + ⟨5, 2, 7, 5, 6, 3, -21469536782808652944875806091625583980262195200000⟩, + ⟨5, 2, 8, 5, 7, 3, 17002075260189247395824121319288135398331514880000⟩, + ⟨5, 2, 2, 6, 0, 3, 86302240399067650750352229197357184009351431454720000⟩, + ⟨5, 2, 3, 6, 1, 3, 1336423252165146273281187243380712514594705244160000⟩, + ⟨5, 2, 4, 6, 2, 3, -3323839235665269610930842432139592335465025372160000⟩, + ⟨5, 2, 5, 6, 3, 3, 3204498897148239969188838717214439653227311923200000⟩, + ⟨5, 2, 6, 6, 4, 3, 108116776520237537458519624794991474308714332160000⟩, + ⟨5, 2, 7, 6, 5, 3, -134135069710010854514875196984931993066437345280000⟩, + ⟨5, 2, 8, 6, 6, 3, -25396620580812021806642008263590179773905633280000⟩, + ⟨5, 2, 3, 7, 0, 3, -140471502592545978078427694583315046609286206586880000⟩, + ⟨5, 2, 4, 7, 1, 3, -3192937488107803584111849449720126366606017167360000⟩, + ⟨5, 2, 5, 7, 2, 3, -177528339227808057550698197702856594234644889600000⟩, + ⟨5, 2, 6, 7, 3, 3, 545794089588051512108398022003053778229232926720000⟩, + ⟨5, 2, 7, 7, 4, 3, -104302026242229145473252930741361104865827225600000⟩, + ⟨5, 2, 8, 7, 5, 3, -65602159069161282337714284602120894535224524800000⟩ +] + +def collectedFourData_8_4_38 : List CollectedFourTerm := [ + ⟨5, 3, 0, 0, 4, 4, -4803433911613591707716638603360738008578496921600000⟩, + ⟨5, 3, 1, 0, 5, 4, 15922472107236855273105772643336328753071354019840000⟩, + ⟨5, 3, 2, 0, 6, 4, -6793630412277036389456874179086021024702173020160000⟩, + ⟨5, 3, 3, 0, 7, 4, 647262523949326676259675214582897633450807787520000⟩, + ⟨5, 3, 4, 0, 8, 4, -624531032768044957197722417677237894866303713280000⟩, + ⟨5, 3, 0, 1, 3, 4, -3775319912896099666878558515554603208605087825920000⟩, + ⟨5, 3, 1, 1, 4, 4, 6955180820115151021190110912119457635394545254400000⟩, + ⟨5, 3, 2, 1, 5, 4, 3317245418301176165360236074725981102620708700160000⟩, + ⟨5, 3, 3, 1, 6, 4, -3069128301626576056201970374322121732842261053440000⟩, + ⟨5, 3, 4, 1, 7, 4, 728357897364108524075898956971301760206037319680000⟩, + ⟨5, 3, 5, 1, 8, 4, 715055366026740610895879930216296066632489369600000⟩, + ⟨5, 3, 0, 2, 2, 4, -3149365796419433637214838196077815290852676730880000⟩, + ⟨5, 3, 1, 2, 3, 4, 10505368137067796441192675574164537783995575828480000⟩, + ⟨5, 3, 2, 2, 4, 4, 12221154548587784127814640073013764791916067553280000⟩, + ⟨5, 3, 3, 2, 5, 4, -1306065400014008083767616401984623253878200074240000⟩, + ⟨5, 3, 4, 2, 6, 4, -480201415969084550953824653367750831763567411200000⟩, + ⟨5, 3, 5, 2, 7, 4, 366529097931679390391984246008590169197646970880000⟩, + ⟨5, 3, 6, 2, 8, 4, -108284287928942603398467267052693845595819868160000⟩, + ⟨5, 3, 0, 3, 1, 4, -10095416142427450699135181360663020865941080637440000⟩, + ⟨5, 3, 1, 3, 2, 4, -27070349062274397421972069606786811307470440366080000⟩, + ⟨5, 3, 2, 3, 3, 4, -13921086034494088317419362183192425177545913139200000⟩, + ⟨5, 3, 3, 3, 4, 4, 142307176228755138007726621990128409404065710080000⟩, + ⟨5, 3, 4, 3, 5, 4, -1317526184893696725218506309571559169277904814080000⟩, + ⟨5, 3, 5, 3, 6, 4, -250784698041741163491617350182543765184362577920000⟩, + ⟨5, 3, 6, 3, 7, 4, -229591658018512718072086052827111527158906880000⟩, + ⟨5, 3, 7, 3, 8, 4, 5249434458306798117035163368238561759791677440000⟩, + ⟨5, 3, 0, 4, 0, 4, -32238980093449194657653113051588509365658294681600000⟩, + ⟨5, 3, 1, 4, 1, 4, 12187296715563888168143590709687451957654391357440000⟩, + ⟨5, 3, 2, 4, 2, 4, 3319282252651802456275458722264972761955617996800000⟩, + ⟨5, 3, 3, 4, 3, 4, 2101588194785109605223168736731518301217058979840000⟩, + ⟨5, 3, 4, 4, 4, 4, 987440797934535421997576217445313479686959923200000⟩, + ⟨5, 3, 5, 4, 5, 4, -152063762330144867943948203686072278339739975680000⟩, + ⟨5, 3, 6, 4, 6, 4, -46397904169329493860074721410851737965565050880000⟩, + ⟨5, 3, 7, 4, 7, 4, 13885189028275698139946680024753033186671329280000⟩, + ⟨5, 3, 8, 4, 8, 4, -1859129366864128619714654721687639239845478400000⟩, + ⟨5, 3, 1, 5, 0, 4, 64234504707982983805741115931277218488453022351360000⟩, + ⟨5, 3, 2, 5, 1, 4, -3437787647061459157327718547533766185867343298560000⟩, + ⟨5, 3, 3, 5, 2, 4, 2624226819556649408901061897449638400272954818560000⟩, + ⟨5, 3, 4, 5, 3, 4, 940916438140139504761202260841955685535223644160000⟩, + ⟨5, 3, 5, 5, 4, 4, -100869464401965025182548543108427754992996188160000⟩, + ⟨5, 3, 6, 5, 5, 4, -38759941168038703714712900616900412654737162240000⟩, + ⟨5, 3, 7, 5, 6, 4, -4398800967671993466886133339461764900087398400000⟩, + ⟨5, 3, 8, 5, 7, 4, 3048046757160754674289942393099070381846691840000⟩, + ⟨5, 3, 2, 6, 0, 4, 61887330801324313910112645297853132274334003363840000⟩, + ⟨5, 3, 3, 6, 1, 4, 638899349656741035902158617701811657754992967680000⟩, + ⟨5, 3, 4, 6, 2, 4, -1191762446472129955638367210864633894290598133760000⟩, + ⟨5, 3, 5, 6, 3, 4, 919178377679449231318960007154760835548745564160000⟩, + ⟨5, 3, 6, 6, 4, 4, 25843511063524601387521295402115071966277795840000⟩, + ⟨5, 3, 7, 6, 5, 4, -27482356997641643763141231553979815758145781760000⟩, + ⟨5, 3, 8, 6, 6, 4, -4552978728746347497124552417739372311389143040000⟩, + ⟨5, 3, 3, 7, 0, 4, -67154736724524217774536799950350524331197716234240000⟩, + ⟨5, 3, 4, 7, 1, 4, -1144827629275612156432727156615778070376176680960000⟩, + ⟨5, 3, 5, 7, 2, 4, -50922224060916825557210254720361631037500948480000⟩, + ⟨5, 3, 6, 7, 3, 4, 130462968344555643440437496677080626808257249280000⟩, + ⟨5, 3, 7, 7, 4, 4, -21369993149169673299802860581004047008609075200000⟩, + ⟨5, 3, 8, 7, 5, 4, -11760825967034058015710107943319801279440486400000⟩ +] + +def collectedFourData_8_4_39 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 4, 5, 2574722825081172232617745110726481352545271808000000⟩, + ⟨5, 4, 1, 0, 5, 5, -4267358843753664956156425647822376554326497689600000⟩, + ⟨5, 4, 2, 0, 6, 5, 1213834075754595748210611898808490327700773273600000⟩, + ⟨5, 4, 3, 0, 7, 5, -86735948953243464576906487756777333157422694400000⟩, + ⟨5, 4, 4, 0, 8, 5, 66951865462399501841403832159785825116388065280000⟩, + ⟨5, 4, 0, 1, 3, 5, 2023636117531536590513503705180289115828623769600000⟩, + ⟨5, 4, 1, 1, 4, 5, -1864048006033837697515571003400589614080065536000000⟩, + ⟨5, 4, 2, 1, 5, 5, -592700114963300719314017106767021830259186073600000⟩, + ⟨5, 4, 3, 1, 6, 5, 411276330470321266959353258804544237602655436800000⟩, + ⟨5, 4, 4, 1, 7, 5, -78082460909367812335811560309303196543279431680000⟩, + ⟨5, 4, 5, 1, 8, 5, -63880319995470376731240621064761042700075008000000⟩, + ⟨5, 4, 0, 2, 2, 5, 1688113992984475843777138100720234183927424614400000⟩, + ⟨5, 4, 1, 2, 3, 5, -2815528601631442145405372132723540162627449651200000⟩, + ⟨5, 4, 2, 2, 4, 5, -2183582699661024023406957026016757718501346508800000⟩, + ⟨5, 4, 3, 2, 5, 5, 175018354490860763995411313351936240887057612800000⟩, + ⟨5, 4, 4, 2, 6, 5, 51479236274807751643366490022742868834333491200000⟩, + ⟨5, 4, 5, 2, 7, 5, -32744312085410147046497302272618037219059302400000⟩, + ⟨5, 4, 6, 2, 8, 5, 8291747495005050652863604655355424737224294400000⟩, + ⟨5, 4, 0, 3, 1, 5, 5411315914591030815596764137400511675946447667200000⟩, + ⟨5, 4, 1, 3, 2, 5, 7255085309390580033876249689383584930731340595200000⟩, + ⟨5, 4, 2, 3, 3, 5, 2487313494364295095527837075209579134590124032000000⟩, + ⟨5, 4, 3, 3, 4, 5, -19069770790597875131036773456518070725613977600000⟩, + ⟨5, 4, 4, 3, 5, 5, 141243318980040779102762887390285244661843886080000⟩, + ⟨5, 4, 5, 3, 6, 5, 22404148716331342171958924898852409653696921600000⟩, + ⟨5, 4, 6, 3, 7, 5, 17580722851484228973869560927797231432499200000⟩, + ⟨5, 4, 7, 3, 8, 5, -351723344363392867639082054410019356960358400000⟩, + ⟨5, 4, 0, 4, 0, 5, 17280645353160959470467504601090710848938180608000000⟩, + ⟨5, 4, 1, 4, 1, 5, -3266299860369911590708881643334772245149620633600000⟩, + ⟨5, 4, 2, 4, 2, 5, -593064040992745851174293707901056865720598528000000⟩, + ⟨5, 4, 3, 4, 3, 5, -281621814393646345538968159906284233959460044800000⟩, + ⟨5, 4, 4, 4, 4, 5, -105857035097808343146242932945992474283946803200000⟩, + ⟨5, 4, 5, 4, 5, 5, 13584796728875316895398217139064789298210406400000⟩, + ⟨5, 4, 6, 4, 6, 5, 3552867299842981163149079921562890345329459200000⟩, + ⟨5, 4, 7, 4, 7, 5, -930337384137617516426111535353804295556300800000⟩, + ⟨5, 4, 8, 4, 8, 5, 110725019358212414859917953815519783026688000000⟩, + ⟨5, 4, 1, 5, 0, 5, -17215397200486366423118225498821177900173518438400000⟩, + ⟨5, 4, 2, 5, 1, 5, 614237681177120604400497283901558936219261337600000⟩, + ⟨5, 4, 3, 5, 2, 5, -351657627378126486884904911222253324036420403200000⟩, + ⟨5, 4, 4, 5, 3, 5, -100869464401965025182548543108427754992996188160000⟩, + ⟨5, 4, 5, 5, 4, 5, 9011293348616401090405691245950661261315276800000⟩, + ⟨5, 4, 6, 5, 5, 5, 2967998878078473693153873734557711331858841600000⟩, + ⟨5, 4, 7, 5, 6, 5, 294729079832641280004162722565891475636224000000⟩, + ⟨5, 4, 8, 5, 7, 5, -181533917007953110734797207728841072364748800000⟩, + ⟨5, 4, 2, 6, 0, 5, -11057556332235913595114710293467858978981963366400000⟩, + ⟨5, 4, 3, 6, 1, 5, -85615247797701859672260360550021173115197849600000⟩, + ⟨5, 4, 4, 6, 2, 5, 127761015534638683745217683527854200482179317760000⟩, + ⟨5, 4, 5, 6, 3, 5, -82115891564241073673789083685571775374871756800000⟩, + ⟨5, 4, 6, 6, 4, 5, -1978937777784839778000156654632773296429465600000⟩, + ⟨5, 4, 7, 6, 5, 5, 1841376740860773436869594493031582776531353600000⟩, + ⟨5, 4, 8, 6, 6, 5, 271163839839883548691373166171405861833932800000⟩, + ⟨5, 4, 3, 7, 0, 5, 8999022191130050873308218881783812894808132812800000⟩, + ⟨5, 4, 4, 7, 1, 5, 122729442399648171568235408984146931155426344960000⟩, + ⟨5, 4, 5, 7, 2, 5, 4549197338336958236409375563344295462594150400000⟩, + ⟨5, 4, 6, 7, 3, 5, -9990054989988573190274509163487987368145715200000⟩, + ⟨5, 4, 7, 7, 4, 5, 1431835280380495997493456212594286208745472000000⟩, + ⟨5, 4, 8, 7, 5, 5, 700444899681681878982811025518372740661248000000⟩ +] + +def collectedFourData_8_4_40 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 4, 6, 2968076785650361598110523368077486261729755136000000⟩, + ⟨5, 5, 1, 0, 5, 6, -3279537146498014598048893340858602313439038668800000⟩, + ⟨5, 5, 2, 0, 6, 6, 699638948857532957098439278477390370093767065600000⟩, + ⟨5, 5, 3, 0, 7, 6, -39994822597863214333372321024564992489207889920000⟩, + ⟨5, 5, 4, 0, 8, 6, 25726818138656570956040157351491917026605137920000⟩, + ⟨5, 5, 0, 1, 3, 6, 2332797660602407594967670498677145496110445363200000⟩, + ⟨5, 5, 1, 1, 4, 6, -1432552288774994290419184352459181396074692608000000⟩, + ⟨5, 5, 2, 1, 5, 6, -341625015892616024682463807186198654715795865600000⟩, + ⟨5, 5, 3, 1, 6, 6, 189643672253217006348168752468082170693670666240000⟩, + ⟨5, 5, 4, 1, 7, 6, -30003843175396299220234058774343404909777387520000⟩, + ⟨5, 5, 5, 1, 8, 6, -21039900793703575485820354116258814331191296000000⟩, + ⟨5, 5, 0, 2, 2, 6, 1946016054738162995741204913770684439807708364800000⟩, + ⟨5, 5, 1, 2, 3, 6, -2163781152267901514976346313572668958345632153600000⟩, + ⟨5, 5, 2, 2, 4, 6, -1258590062059846379150290109809445561260887244800000⟩, + ⟨5, 5, 3, 2, 5, 6, 80702731954950916734838430298900110366516183040000⟩, + ⟨5, 5, 4, 2, 6, 6, 19781330070671432653591888384890703736261836800000⟩, + ⟨5, 5, 5, 2, 7, 6, -10784809435581250307226630524011146147318988800000⟩, + ⟨5, 5, 6, 2, 8, 6, 2389630352892756711491093378823258574631731200000⟩, + ⟨5, 5, 0, 3, 1, 6, 6238031134637429753142137471773131171663603302400000⟩, + ⟨5, 5, 1, 3, 2, 6, 5575655257580660006028419121503146708792088985600000⟩, + ⟨5, 5, 2, 3, 3, 6, 1433656735657516756010539821577500151693443072000000⟩, + ⟨5, 5, 3, 3, 4, 6, -8793264026695762697660195211442090214613319680000⟩, + ⟨5, 5, 4, 3, 5, 6, 54273934797836156218879797499719185926843269120000⟩, + ⟨5, 5, 5, 3, 6, 6, 7379128131988340360878726492291322252309299200000⟩, + ⟨5, 5, 6, 3, 7, 6, 5066655608725386084027729855140375140761600000⟩, + ⟨5, 5, 7, 3, 8, 6, -90101771405098928946924279222111178221158400000⟩, + ⟨5, 5, 0, 4, 0, 6, 19920700517406890415311425643932599486813044736000000⟩, + ⟨5, 5, 1, 4, 1, 6, -2510206456943266895358975550679641386795191500800000⟩, + ⟨5, 5, 2, 4, 2, 6, -341834778355038742367631782719630399858802688000000⟩, + ⟨5, 5, 3, 4, 3, 6, -129858664628595785044859175924740735130811760640000⟩, + ⟨5, 5, 4, 4, 4, 6, -40676457210712911288332388943016547209497804800000⟩, + ⟨5, 5, 5, 4, 5, 6, 4474347897731768191737218638006501797317836800000⟩, + ⟨5, 5, 6, 4, 6, 6, 1023914385311337476090750983582911689234841600000⟩, + ⟨5, 5, 7, 4, 7, 6, -238326649790350904664193992521591334685900800000⟩, + ⟨5, 5, 8, 4, 8, 6, 25528212695083887959018194697673537434419200000⟩, + ⟨5, 5, 1, 5, 0, 6, -13230322707300323579819175306476382930731217715200000⟩, + ⟨5, 5, 2, 5, 1, 6, 354039002686831633314284841173731645471693209600000⟩, + ⟨5, 5, 3, 5, 2, 6, -162152885763149511775361521890976814547609845760000⟩, + ⟨5, 5, 4, 5, 3, 6, -38759941168038703714712900616900412654737162240000⟩, + ⟨5, 5, 5, 5, 4, 6, 2967998878078473693153873734557711331858841600000⟩, + ⟨5, 5, 6, 5, 5, 6, 855358922914674329708733521979056048622796800000⟩, + ⟨5, 5, 7, 5, 6, 6, 75501420656568987194043743755937695924224000000⟩, + ⟨5, 5, 8, 5, 7, 6, -41853561838253268402198750681406845663313920000⟩, + ⟨5, 5, 2, 6, 0, 6, -6373438712708013491283317736535154648567670374400000⟩, + ⟨5, 5, 3, 6, 1, 6, -39478055969469386370749279755172993473739489280000⟩, + ⟨5, 5, 4, 6, 2, 6, 49093246157803578156058295632783986360204656640000⟩, + ⟨5, 5, 5, 6, 3, 6, -27046048176037015999283867454620366150408601600000⟩, + ⟨5, 5, 6, 6, 4, 6, -570317630044752582680456083793088650988748800000⟩, + ⟨5, 5, 7, 6, 5, 6, 471709679879216556458540636555105988614553600000⟩, + ⟨5, 5, 8, 6, 6, 6, 62518193437866254166557611229215872012779520000⟩, + ⟨5, 5, 3, 7, 0, 6, 4149540074583132929831188413178244386232771543040000⟩, + ⟨5, 5, 4, 7, 1, 6, 47159821807320786386104740822671415836084797440000⟩, + ⟨5, 5, 5, 7, 2, 6, 1498343475680411308191417690161944938204364800000⟩, + ⟨5, 5, 6, 7, 3, 6, -2879072070818034247861743817826744726559129600000⟩, + ⟨5, 5, 7, 7, 4, 6, 366796509785565857158876887407328831209472000000⟩, + ⟨5, 5, 8, 7, 5, 6, 161491110897100418489684778329059710153523200000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0820.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0820.lean new file mode 100644 index 0000000000000000000000000000000000000000..dac322f7011a72f34940142bcaeca75eac91e817 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0820.lean @@ -0,0 +1,637 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0820. -/ +namespace LaughlinFock +def collectedFourData_8_4_41 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 4, 7, 785964843287451455974518254039023247362621440000000⟩, + ⟨5, 6, 1, 0, 5, 7, -651331085468671627591826673524766577382129664000000⟩, + ⟨5, 6, 2, 0, 6, 7, 111161197605495882943162459233995329901061734400000⟩, + ⟨5, 6, 3, 0, 7, 7, -5295436531058458827260195140817104696403558400000⟩, + ⟨5, 6, 4, 0, 8, 7, 2919693609255555594675528571176042728993587200000⟩, + ⟨5, 6, 0, 1, 3, 7, 617739054663624848246156767399565062179913728000000⟩, + ⟨5, 6, 1, 1, 4, 7, -284511440352124651382384575158378043791114240000000⟩, + ⟨5, 6, 2, 1, 5, 7, -54278633230227263644672440857898999301432934400000⟩, + ⟨5, 6, 3, 1, 6, 7, 25109400784976007671021351554903210600484044800000⟩, + ⟨5, 6, 4, 1, 7, 7, -3405086035131625583045640348460866268771123200000⟩, + ⟨5, 6, 5, 1, 8, 7, -2089310291354617498364755798997060749885440000000⟩, + ⟨5, 6, 0, 2, 2, 7, 515316925388101943667071012564611122585403392000000⟩, + ⟨5, 6, 1, 2, 3, 7, -429736838970778994092164624623560841974775808000000⟩, + ⟨5, 6, 2, 2, 4, 7, -199969396817324643640231955899611367148303155200000⟩, + ⟨5, 6, 3, 2, 5, 7, 10685287924574969559620064048035994712984780800000⟩, + ⟨5, 6, 4, 2, 6, 7, 2244950101432561414909375915642349250674688000000⟩, + ⟨5, 6, 5, 2, 7, 7, -1070956254261497525162668572656371217989632000000⟩, + ⟨5, 6, 6, 2, 8, 7, 210929566120232227486221369813459655458816000000⟩, + ⟨5, 6, 0, 3, 1, 7, 1651868707326329664868248333804979914849386496000000⟩, + ⟨5, 6, 1, 3, 2, 7, 1107350650074826257908668596699915133038624768000000⟩, + ⟨5, 6, 2, 3, 3, 7, 227784630845826735719765211374564205215612928000000⟩, + ⟨5, 6, 3, 3, 4, 7, -1164254984261255562552641159933456614529433600000⟩, + ⟨5, 6, 4, 3, 5, 7, 6159458185786737754965641324546894215721779200000⟩, + ⟨5, 6, 5, 3, 6, 7, 732764308090340849841325516620701984882688000000⟩, + ⟨5, 6, 6, 3, 7, 7, 447227106876746679523284905977014386688000000⟩, + ⟨5, 6, 7, 3, 8, 7, -7157849653826902527306819284529484451020800000⟩, + ⟨5, 6, 0, 4, 0, 7, 5275123048041097866811331726405328340191805440000000⟩, + ⟨5, 6, 1, 4, 1, 7, -498538489828420107958140977365436132568858624000000⟩, + ⟨5, 6, 2, 4, 2, 7, -54311961058207199682178480378216522356621312000000⟩, + ⟨5, 6, 3, 4, 3, 7, -17193683379045023412700708218339721606909132800000⟩, + ⟨5, 6, 4, 4, 4, 7, -4616303171468573431225734845737459481837568000000⟩, + ⟨5, 6, 5, 4, 5, 7, 444312984243227233508992904189561486180352000000⟩, + ⟨5, 6, 6, 4, 6, 7, 90379592298255888744431235801307139801088000000⟩, + ⟨5, 6, 7, 4, 7, 7, -18933105321867735177004610242494783396249600000⟩, + ⟨5, 6, 8, 4, 8, 7, 1843643587717774854329305424057560203264000000⟩, + ⟨5, 6, 1, 5, 0, 7, -2627602635709908066531462388806914853732089856000000⟩, + ⟨5, 6, 2, 5, 1, 7, 56251012900280219380669777126506050261247590400000⟩, + ⟨5, 6, 3, 5, 2, 7, -21469536782808652944875806091625583980262195200000⟩, + ⟨5, 6, 4, 5, 3, 7, -4398800967671993466886133339461764900087398400000⟩, + ⟨5, 6, 5, 5, 4, 7, 294729079832641280004162722565891475636224000000⟩, + ⟨5, 6, 6, 5, 5, 7, 75501420656568987194043743755937695924224000000⟩, + ⟨5, 6, 7, 5, 6, 7, 5997971064079195721918648199911087013888000000⟩, + ⟨5, 6, 8, 5, 7, 7, -3022657787597669466632679954476366718566400000⟩, + ⟨5, 6, 2, 6, 0, 7, -1012635276133147277435191667850244366066620825600000⟩, + ⟨5, 6, 3, 6, 1, 7, -5227015052870059760498265984033947234441625600000⟩, + ⟨5, 6, 4, 6, 2, 7, 5571510487306375282029309386959654561932902400000⟩, + ⟨5, 6, 5, 6, 3, 7, -2685734469412395871222920388756102786842624000000⟩, + ⟨5, 6, 6, 6, 4, 7, -50341196122837136265985455044925623107584000000⟩, + ⟨5, 6, 7, 6, 5, 7, 37473480445237668466322867222853906019123200000⟩, + ⟨5, 6, 8, 6, 6, 7, 4515054297930465866316774038955295663718400000⟩, + ⟨5, 6, 3, 7, 0, 7, 549411765592192904120556129896021640212171980800000⟩, + ⟨5, 6, 4, 7, 1, 7, 5352089387904983964748734154042218434160230400000⟩, + ⟨5, 6, 5, 7, 2, 7, 148788935576158642808547066327213142966272000000⟩, + ⟨5, 6, 6, 7, 3, 7, -254131950571930328647340841755101970300928000000⟩, + ⟨5, 6, 7, 7, 4, 7, 29138986166979520848482245764117392523264000000⟩, + ⟨5, 6, 8, 7, 5, 7, 11662863148119852667866657967042612690944000000⟩ +] + +def collectedFourData_8_4_42 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 4, 8, -1089232092759380684402569020598285145041010688000000⟩, + ⟨5, 7, 1, 0, 5, 8, 722119547573516438995909339719376057883940618240000⟩, + ⟨5, 7, 2, 0, 6, 8, -102702086431780800978807760410489174527752273920000⟩, + ⟨5, 7, 3, 0, 7, 8, 4193542289589779734075210176345539164986408960000⟩, + ⟨5, 7, 4, 0, 8, 8, -2023133736442784399396939354595549512434974720000⟩, + ⟨5, 7, 0, 1, 3, 8, -856095802550261870904392129283175960444246425600000⟩, + ⟨5, 7, 1, 1, 4, 8, 315432929842019281550197191113011511184221798400000⟩, + ⟨5, 7, 2, 1, 5, 8, 50148154225482378008523479270078218313316433920000⟩, + ⟨5, 7, 3, 1, 6, 8, -19884542745526728075339998369022073673739141120000⟩, + ⟨5, 7, 4, 1, 7, 8, 2359475121405458001524186710508127612378808320000⟩, + ⟨5, 7, 5, 1, 8, 8, 1286879059406020942327878232376493188579328000000⟩, + ⟨5, 7, 0, 2, 2, 8, -714153740932057668226548741848715003605444198400000⟩, + ⟨5, 7, 1, 2, 3, 8, 476441826064477252714521892241673522026674913280000⟩, + ⟨5, 7, 2, 2, 4, 8, 184752186176775876885398216613786524669297295360000⟩, + ⟨5, 7, 3, 2, 5, 8, -8461853243889530710483680307202528195924459520000⟩, + ⟨5, 7, 4, 2, 6, 8, -1555585926016707297365558661908555522428108800000⟩, + ⟨5, 7, 5, 2, 7, 8, 659639299558263509470705309943114045482598400000⟩, + ⟨5, 7, 6, 2, 8, 8, -116926987099824580443916860939166247320289280000⟩, + ⟨5, 7, 0, 3, 1, 8, -2289247953533137002832796804716904353019147059200000⟩, + ⟨5, 7, 1, 3, 2, 8, -1227700578518963864108408988441499903806280826880000⟩, + ⟨5, 7, 2, 3, 3, 8, -210450744944140183055650836531895613606225510400000⟩, + ⟨5, 7, 3, 3, 4, 8, 921992452129223720710118125036098486628515840000⟩, + ⟨5, 7, 4, 3, 5, 8, -4268053200640852576892244284529548397033553920000⟩, + ⟨5, 7, 5, 3, 6, 8, -451335087690692016500975664736368659634585600000⟩, + ⟨5, 7, 6, 3, 7, 8, -247916492307492235608780639592072127447040000⟩, + ⟨5, 7, 7, 3, 8, 8, 3607174787515363153093989238165563758346240000⟩, + ⟨5, 7, 0, 4, 0, 8, -7310547496180590052454648493062489613677887488000000⟩, + ⟨5, 7, 1, 4, 1, 8, 552721030447730266902658877039833577741447331840000⟩, + ⟨5, 7, 2, 4, 2, 8, 50178945882494983692396913096052286529575321600000⟩, + ⟨5, 7, 3, 4, 3, 8, 13615957426918735592342357013528503464042168320000⟩, + ⟨5, 7, 4, 4, 4, 8, 3198759847348225511941270228218128091630796800000⟩, + ⟨5, 7, 5, 4, 5, 8, -273667859489693699219471377118946690229862400000⟩, + ⟨5, 7, 6, 4, 6, 8, -50101148061537274848911426315043136906199040000⟩, + ⟨5, 7, 7, 4, 7, 8, 9541276147075917574609192314696115295354880000⟩, + ⟨5, 7, 8, 4, 8, 8, -851673277968660390535046776334400985497600000⟩, + ⟨5, 7, 1, 5, 0, 8, 2913177750661930077046659256746237163400551464960000⟩, + ⟨5, 7, 2, 5, 1, 8, -51970440344321843328608173888299494089131294720000⟩, + ⟨5, 7, 3, 5, 2, 8, 17002075260189247395824121319288135398331514880000⟩, + ⟨5, 7, 4, 5, 3, 8, 3048046757160754674289942393099070381846691840000⟩, + ⟨5, 7, 5, 5, 4, 8, -181533917007953110734797207728841072364748800000⟩, + ⟨5, 7, 6, 5, 5, 8, -41853561838253268402198750681406845663313920000⟩, + ⟨5, 7, 7, 5, 6, 8, -3022657787597669466632679954476366718566400000⟩, + ⟨5, 7, 8, 5, 7, 8, 1396320245024974246678078087392053176565760000⟩, + ⟨5, 7, 2, 6, 0, 8, 935576063352477710597924110474966439714441134080000⟩, + ⟨5, 7, 3, 6, 1, 8, 4139358208519895854647451200172140719127920640000⟩, + ⟨5, 7, 4, 6, 2, 8, -3860648526298053487239869689990033340356362240000⟩, + ⟨5, 7, 5, 6, 3, 8, 1654237507043960257485297913346259386420428800000⟩, + ⟨5, 7, 6, 6, 4, 8, 27906208209282009538677040085824489358622720000⟩, + ⟨5, 7, 7, 6, 5, 8, -18884637202493019271025833960936009849896960000⟩, + ⟨5, 7, 8, 6, 6, 8, -2085734531198106590828064575520590329282560000⟩, + ⟨5, 7, 3, 7, 0, 8, -435088110280593835334209533095654006199964139520000⟩, + ⟨5, 7, 4, 7, 1, 8, -3708605782059726442588196531591504165118935040000⟩, + ⟨5, 7, 5, 7, 2, 8, -91644293457305050357184590011127285835366400000⟩, + ⟨5, 7, 6, 7, 3, 8, 140875856584465439092169598871983712622346240000⟩, + ⟨5, 7, 7, 7, 4, 8, -14684496227032559089237694854792257680179200000⟩, + ⟨5, 7, 8, 7, 5, 8, -5387673058953334800469553843042296371609600000⟩ +] + +def collectedFourData_8_4_43 : List CollectedFourTerm := [ + ⟨6, 0, 2, 0, 6, 2, -74473431012568162667045254375332732029031300464640000⟩, + ⟨6, 0, 3, 0, 7, 2, 21286348240515043809717778858803534419183523594240000⟩, + ⟨6, 0, 4, 0, 8, 2, -41077567628648574088452073341304954164270040350720000⟩, + ⟨6, 0, 2, 1, 5, 2, 36364452114610585600856907813769527826471075184640000⟩, + ⟨6, 0, 3, 1, 6, 2, -100933595575137040792118058301679997215921437409280000⟩, + ⟨6, 0, 4, 1, 7, 2, 47906619874799123009441027372892117359153979064320000⟩, + ⟨6, 0, 5, 1, 8, 2, 78386110577526016130921831522041899403060445184000000⟩, + ⟨6, 0, 2, 2, 4, 2, 133971272344079207093949693784610881258317278085120000⟩, + ⟨6, 0, 3, 2, 5, 2, -42952220931861473946949127988883803683184055418880000⟩, + ⟨6, 0, 4, 2, 6, 2, -31584509183499712774463352026241958116787539148800000⟩, + ⟨6, 0, 5, 2, 7, 2, 40179812312993746805350270441569899652437979955200000⟩, + ⟨6, 0, 6, 2, 8, 2, -17805581016553071573681564164664861545494845849600000⟩, + ⟨6, 0, 2, 3, 3, 2, -152606335271987720821968954573452248514378386636800000⟩, + ⟨6, 0, 3, 3, 4, 2, 4680017764425332702877081774617511519232941096960000⟩, + ⟨6, 0, 4, 3, 5, 2, -86658257352900816313682506904349086763425118289920000⟩, + ⟨6, 0, 5, 3, 6, 2, -27491629328065558544272650643584691827519573196800000⟩, + ⟨6, 0, 6, 3, 7, 2, -37752595004881742077505089284636636697382092800000⟩, + ⟨6, 0, 7, 3, 8, 2, 1208457157142906392269689340559792118850083880960000⟩, + ⟨6, 0, 2, 4, 2, 2, 36386780388786535931350798826192483647558464307200000⟩, + ⟨6, 0, 3, 4, 3, 2, 69114364754807679231520883787416724458407282606080000⟩, + ⟨6, 0, 4, 4, 4, 2, 64947398973378904516430071595209204833113132236800000⟩, + ⟨6, 0, 5, 4, 5, 2, -16669599943117713076680573157322684034561815347200000⟩, + ⟨6, 0, 6, 4, 6, 2, -7629376869776208947844223900364588324982934732800000⟩, + ⟨6, 0, 7, 4, 7, 2, 3196469294506477729165011342802847225439867371520000⟩, + ⟨6, 0, 8, 4, 8, 2, -570646408303109798848274414363464906258042060800000⟩, + ⟨6, 0, 2, 5, 1, 2, -37685865381581527458093935758230788682107049738240000⟩, + ⟨6, 0, 3, 5, 2, 2, 86302240399067650750352229197357184009351431454720000⟩, + ⟨6, 0, 4, 5, 3, 2, 61887330801324313910112645297853132274334003363840000⟩, + ⟨6, 0, 5, 5, 4, 2, -11057556332235913595114710293467858978981963366400000⟩, + ⟨6, 0, 6, 5, 5, 2, -6373438712708013491283317736535154648567670374400000⟩, + ⟨6, 0, 7, 5, 6, 2, -1012635276133147277435191667850244366066620825600000⟩, + ⟨6, 0, 8, 5, 7, 2, 935576063352477710597924110474966439714441134080000⟩, + ⟨6, 0, 2, 6, 0, 2, 678423991486992729274911399196611573559600726671360000⟩, + ⟨6, 0, 3, 6, 1, 2, 21011310780750050441954266039454267554069122908160000⟩, + ⟨6, 0, 4, 6, 2, 2, -78386340988158232308904194939130653549785241354240000⟩, + ⟨6, 0, 5, 6, 3, 2, 100762572209769034897572060781672643132156962406400000⟩, + ⟨6, 0, 6, 6, 4, 2, 4249542928109148956733846760069741611906917990400000⟩, + ⟨6, 0, 7, 6, 5, 2, -6326634092250148747307254585618356923891806371840000⟩, + ⟨6, 0, 8, 6, 6, 2, -1397504124751660072813623156770111875021516308480000⟩, + ⟨6, 0, 3, 7, 0, 2, -2208499733919770552485932580368255068781614601338880000⟩, + ⟨6, 0, 4, 7, 1, 2, -75299275612106249395365185785158616248797406167040000⟩, + ⟨6, 0, 5, 7, 2, 2, -5582218210978798889665393671923198600223601459200000⟩, + ⟨6, 0, 6, 7, 3, 2, 21452502453941824375973259413549242697359609036800000⟩, + ⟨6, 0, 7, 7, 4, 2, -4919524450551710858628397637016257958863752396800000⟩, + ⟨6, 0, 8, 7, 5, 2, -3609901073256735584126125202327130997781220556800000⟩ +] + +def collectedFourData_8_4_44 : List CollectedFourTerm := [ + ⟨6, 1, 1, 0, 5, 3, 2702911932952670683875311704751812992449988526080000⟩, + ⟨6, 1, 2, 0, 6, 3, -2306499215164945771665805881037539091079327907840000⟩, + ⟨6, 1, 3, 0, 7, 3, 329627256613100415086776788495225994523411742720000⟩, + ⟨6, 1, 4, 0, 8, 3, -424067913474509923685757032604241678327810621440000⟩, + ⟨6, 1, 1, 1, 4, 3, 1180673522799793178362186354324021980821245132800000⟩, + ⟨6, 1, 2, 1, 5, 3, 1126234942070788498801129384577846127099736227840000⟩, + ⟨6, 1, 3, 1, 6, 3, -1562995391863587345989344951591709529729757347840000⟩, + ⟨6, 1, 4, 1, 7, 3, 494568240154362914609866411107725580236897648640000⟩, + ⟨6, 1, 5, 1, 8, 3, 606919474733160070227473766034438154172235776000000⟩, + ⟨6, 1, 1, 2, 3, 3, 1783333938756632214350037091141020659100690677760000⟩, + ⟨6, 1, 2, 2, 4, 3, 4149192944583420147426542936913183374360413470720000⟩, + ⟨6, 1, 3, 2, 5, 3, -665131594730816693664959098900520463592209776640000⟩, + ⟨6, 1, 4, 2, 6, 3, -326065482470824517429030224848718547572595097600000⟩, + ⟨6, 1, 5, 2, 7, 3, 311099892623971780046663893762590812744240332800000⟩, + ⟨6, 1, 6, 2, 8, 3, -110290497112466249472445842847435897957798379520000⟩, + ⟨6, 1, 1, 3, 2, 3, -4595314660740399769310901935193465037643537448960000⟩, + ⟨6, 1, 2, 3, 3, 3, -4726335120435594147467649003757749415036374220800000⟩, + ⟨6, 1, 3, 3, 4, 3, 72471867844945652491442665327030286769067130880000⟩, + ⟨6, 1, 4, 3, 5, 3, -894624207382524004826527322732786588657217699840000⟩, + ⟨6, 1, 5, 3, 6, 3, -212859205647742413592217965528699004051993395200000⟩, + ⟨6, 1, 6, 3, 7, 3, -233845358177481463644462906503252231438991360000⟩, + ⟨6, 1, 7, 3, 8, 3, 6237807333016496561966931371357443644677160960000⟩, + ⟨6, 1, 1, 4, 1, 3, 2068848951411292678058224471502111535499868897280000⟩, + ⟨6, 1, 2, 4, 2, 3, 1126926465828491107943739387536345009229083443200000⟩, + ⟨6, 1, 3, 4, 3, 3, 1070262413696807104453241463447173987020560138240000⟩, + ⟨6, 1, 4, 4, 4, 3, 670490234894744126889088304666279556576549273600000⟩, + ⟨6, 1, 5, 4, 5, 3, -129067570350780740224997569715480112986377420800000⟩, + ⟨6, 1, 6, 4, 6, 3, -47257529357998062524937877652253175339926159360000⟩, + ⟨6, 1, 7, 4, 7, 3, 16499517163004139233065234692675695749386731520000⟩, + ⟨6, 1, 8, 4, 8, 3, -2524765208194462046163318842209610064356966400000⟩, + ⟨6, 1, 1, 5, 0, 3, 10904098817896520420424266592371782145460739768320000⟩, + ⟨6, 1, 2, 5, 1, 3, -1167160123329896461979232751219443006073932349440000⟩, + ⟨6, 1, 3, 5, 2, 3, 1336423252165146273281187243380712514594705244160000⟩, + ⟨6, 1, 4, 5, 3, 3, 638899349656741035902158617701811657754992967680000⟩, + ⟨6, 1, 5, 5, 4, 3, -85615247797701859672260360550021173115197849600000⟩, + ⟨6, 1, 6, 5, 5, 3, -39478055969469386370749279755172993473739489280000⟩, + ⟨6, 1, 7, 5, 6, 3, -5227015052870059760498265984033947234441625600000⟩, + ⟨6, 1, 8, 5, 7, 3, 4139358208519895854647451200172140719127920640000⟩, + ⟨6, 1, 2, 6, 0, 3, 21011310780750050441954266039454267554069122908160000⟩, + ⟨6, 1, 3, 6, 1, 3, 325368196190720651054754403182406087421177364480000⟩, + ⟨6, 1, 4, 6, 2, 3, -809228344975481892306527869610332665290403348480000⟩, + ⟨6, 1, 5, 6, 3, 3, 780173514768683290495225152873837912747776409600000⟩, + ⟨6, 1, 6, 6, 4, 3, 26322320041463865523404990168513276556062228480000⟩, + ⟨6, 1, 7, 6, 5, 3, -32656784148851112999611761790713892662243491840000⟩, + ⟨6, 1, 8, 6, 6, 3, -6183110488635693168573221877393295805345955840000⟩, + ⟨6, 1, 3, 7, 0, 3, -34199464384273456409637581810019266319979527536640000⟩, + ⟨6, 1, 4, 7, 1, 3, -777358751707044319928463082583861073320953774080000⟩, + ⟨6, 1, 5, 7, 2, 3, -43221393681758845262271876054003704532880588800000⟩, + ⟨6, 1, 6, 7, 3, 3, 132880087302518930242738657786769349596581724160000⟩, + ⟨6, 1, 7, 7, 4, 3, -25393573542281986872151687801942386657774796800000⟩, + ⟨6, 1, 8, 7, 5, 3, -15971628844356620917024383745764538506962534400000⟩ +] + +def collectedFourData_8_4_45 : List CollectedFourTerm := [ + ⟨6, 2, 0, 0, 4, 4, 6084017578954440255578283354216964140247390617600000⟩, + ⟨6, 2, 1, 0, 5, 4, -20167364011530427302783121259299662200372975370240000⟩, + ⟨6, 2, 2, 0, 6, 4, 8604795572034499786542842399263247996685134069760000⟩, + ⟨6, 2, 3, 0, 7, 4, -819821120966201932361050570380220549294687518720000⟩, + ⟨6, 2, 4, 0, 8, 4, 791029470141488525494693574306020745065613230080000⟩, + ⟨6, 2, 0, 1, 3, 4, 4781810916707444845517901415697108397569731461120000⟩, + ⟨6, 2, 1, 1, 4, 4, -8809414921287537916757632391871372597226006118400000⟩, + ⟨6, 2, 2, 1, 5, 4, -4201614888435248671920977496114362939980130549760000⟩, + ⟨6, 2, 3, 1, 6, 4, 3887350358670819729203514753991830168867270819840000⟩, + ⟨6, 2, 4, 1, 7, 4, -922536321488585499465875586036812920079756820480000⟩, + ⟨6, 2, 5, 1, 8, 4, -905687368012726939805263874900091059228481945600000⟩, + ⟨6, 2, 0, 2, 2, 4, 3988978972240528196088007145168085564677349703680000⟩, + ⟨6, 2, 1, 2, 3, 4, -13306073445660827964101654635097082727111097057280000⟩, + ⟨6, 2, 2, 2, 4, 4, -15479284294711957596429984468805837829737367470080000⟩, + ⟨6, 2, 3, 2, 5, 4, 1654259223539538416705400870367730303448530288640000⟩, + ⟨6, 2, 4, 2, 6, 4, 608221932466080710180778830559195375802200883200000⟩, + ⟨6, 2, 5, 2, 7, 4, -464244854003945134604976544968633237150294343680000⟩, + ⟨6, 2, 6, 2, 8, 4, 137152612777999599624993809820949313230743797760000⟩, + ⟨6, 2, 0, 3, 1, 4, 12786829257479325149819178843169792442515681443840000⟩, + ⟨6, 2, 1, 3, 2, 4, 34287237545854915128357494694752476078229296250880000⟩, + ⟨6, 2, 2, 3, 3, 4, 17632413333974168623508893867029295042659562291200000⟩, + ⟨6, 2, 3, 3, 4, 4, -180245919423146676627485990798251337595098234880000⟩, + ⟨6, 2, 4, 3, 5, 4, 1668775425481664798771620675847892792700179578880000⟩, + ⟨6, 2, 5, 3, 6, 4, 317643281763439077324136390267801089950739333120000⟩, + ⟨6, 2, 6, 3, 7, 4, 290800229391871597162485075462779498586439680000⟩, + ⟨6, 2, 7, 3, 8, 4, -6648920774508813008724150852077035146014883840000⟩, + ⟨6, 2, 0, 4, 0, 4, 40833812898285106510386962256291704283917293977600000⟩, + ⟨6, 2, 1, 4, 1, 4, -15436400046673351913925707050004016638916915363840000⟩, + ⟨6, 2, 2, 4, 2, 4, -4204194737814391224206035653295937227162701004800000⟩, + ⟨6, 2, 3, 4, 3, 4, -2661866438899451732381184899052162085156017930240000⟩, + ⟨6, 2, 4, 4, 4, 4, -1250690086166379604936520354706679937656632115200000⟩, + ⟨6, 2, 5, 4, 5, 4, 192603587383961287928038020940574897492962836480000⟩, + ⟨6, 2, 6, 4, 6, 4, 58767471310543638195292780366581456875217223680000⟩, + ⟨6, 2, 7, 4, 7, 4, -17586946274182529391037000077423560800421806080000⟩, + ⟨6, 2, 8, 4, 8, 4, 2354768683754443900814018541119342329095782400000⟩, + ⟨6, 2, 1, 5, 0, 4, -81359265685726816012973177758141326643629612072960000⟩, + ⟨6, 2, 2, 5, 1, 4, 4354293378923223030417448921029270219134242652160000⟩, + ⟨6, 2, 3, 5, 2, 4, -3323839235665269610930842432139592335465025372160000⟩, + ⟨6, 2, 4, 5, 3, 4, -1191762446472129955638367210864633894290598133760000⟩, + ⟨6, 2, 5, 5, 4, 4, 127761015534638683745217683527854200482179317760000⟩, + ⟨6, 2, 6, 5, 5, 4, 49093246157803578156058295632783986360204656640000⟩, + ⟨6, 2, 7, 5, 6, 4, 5571510487306375282029309386959654561932902400000⟩, + ⟨6, 2, 8, 5, 7, 4, -3860648526298053487239869689990033340356362240000⟩, + ⟨6, 2, 2, 6, 0, 4, -78386340988158232308904194939130653549785241354240000⟩, + ⟨6, 2, 3, 6, 1, 4, -809228344975481892306527869610332665290403348480000⟩, + ⟨6, 2, 4, 6, 2, 4, 1509483383698413146342599260715036719329952399360000⟩, + ⟨6, 2, 5, 6, 3, 4, -1164229072554888642375501130603267138793515253760000⟩, + ⟨6, 2, 6, 6, 4, 4, -32733327553905912046717058673344242199549706240000⟩, + ⟨6, 2, 7, 6, 5, 4, 34809085783504759590421349971064724982710927360000⟩, + ⟨6, 2, 8, 6, 6, 4, 5766791660300614202500538866756129691994685440000⟩, + ⟨6, 2, 3, 7, 0, 4, 85058024375901894297513952096697530086022856048640000⟩, + ⟨6, 2, 4, 7, 1, 4, 1450035859668108872236750597187456038523696578560000⟩, + ⟨6, 2, 5, 7, 2, 4, 64497963758181769289406651255879973943409377280000⟩, + ⟨6, 2, 6, 7, 3, 4, -165244074846491795537037910985292497331242926080000⟩, + ⟨6, 2, 7, 7, 4, 4, 27067180765688701179347536825484446948078387200000⟩, + ⟨6, 2, 8, 7, 5, 4, 14896233245441410641368150548899828429383270400000⟩ +] + +def collectedFourData_8_4_46 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 4, 5, -23462299154294470723066048005051210234077380608000000⟩, + ⟨6, 3, 1, 0, 5, 5, 38886535208975799889391849295905589894766500249600000⟩, + ⟨6, 3, 2, 0, 6, 5, -11061127796594185199062641176009202923065678233600000⟩, + ⟨6, 3, 3, 0, 7, 5, 790385963859412761754914941337267926523602534400000⟩, + ⟨6, 3, 4, 0, 8, 5, -610102447189580353113541824847118675421199073280000⟩, + ⟨6, 3, 0, 1, 3, 5, -18440492120724902180749466294993617523058514329600000⟩, + ⟨6, 3, 1, 1, 4, 5, 16986236937621894851520073762214848761887195136000000⟩, + ⟨6, 3, 2, 1, 5, 5, 5401011429498347606833014364100434505670171033600000⟩, + ⟨6, 3, 3, 1, 6, 5, -3747777510874762394818132923345853828412787916800000⟩, + ⟨6, 3, 4, 1, 7, 5, 711530592230383076678140570824653059363889479680000⟩, + ⟨6, 3, 5, 1, 8, 5, 582112825196449404287075369737985038963703808000000⟩, + ⟨6, 3, 0, 2, 2, 5, -15383028854262654418420414741080052187764516454400000⟩, + ⟨6, 3, 1, 2, 3, 5, 25656654644705948444010370548839581012125233971200000⟩, + ⟨6, 3, 2, 2, 4, 5, 19898013886591351826682510269127224615741738188800000⟩, + ⟨6, 3, 3, 2, 5, 5, -1594864095876989673959902635185281525804223692800000⟩, + ⟨6, 3, 4, 2, 6, 5, -469107287956740999848333637543081836041941811200000⟩, + ⟨6, 3, 5, 2, 7, 5, 298384291414067916586709308365611479190627942400000⟩, + ⟨6, 3, 6, 2, 8, 5, -75558991571664419450092357891379064109164134400000⟩, + ⟨6, 3, 0, 3, 1, 5, -49310905068986086459237039549610221947424289587200000⟩, + ⟨6, 3, 1, 3, 2, 5, -66112352079483490491619824182418367489481323315200000⟩, + ⟨6, 3, 2, 3, 3, 5, -22665776963176140666974376724469920903811039232000000⟩, + ⟨6, 3, 3, 3, 4, 5, 173774304066585605307574507680235250953853337600000⟩, + ⟨6, 3, 4, 3, 5, 5, -1287087282240052067904911193804684567550969774080000⟩, + ⟨6, 3, 5, 3, 6, 5, -204159000867713346731826682763170912625334681600000⟩, + ⟨6, 3, 6, 3, 7, 5, -160205275252204936427943686929650789069619200000⟩, + ⟨6, 3, 7, 3, 8, 5, 3205097746683738834938686116033188927530598400000⟩, + ⟨6, 3, 0, 4, 0, 5, -157470803033856196962717326156474682017901969408000000⟩, + ⟨6, 3, 1, 4, 1, 5, 29764331797234557571850700720189617698477021593600000⟩, + ⟨6, 3, 2, 4, 2, 5, 5404327724864085497783261633014015157052899328000000⟩, + ⟨6, 3, 3, 4, 3, 5, 2566293813576073477667918097240768801579781324800000⟩, + ⟨6, 3, 4, 4, 4, 5, 964627881827678983467992446259030473449878323200000⟩, + ⟨6, 3, 5, 4, 5, 5, -123792185200791526687329173461288763330553446400000⟩, + ⟨6, 3, 6, 4, 6, 5, -32375692883290631256919832540681156364022579200000⟩, + ⟨6, 3, 7, 4, 7, 5, 8477749064259915347704792603425456857599180800000⟩, + ⟨6, 3, 8, 4, 8, 5, -1008987648200743418097395666261213328703488000000⟩, + ⟨6, 3, 1, 5, 0, 5, 156876225760371188805359054165362758122889176678400000⟩, + ⟨6, 3, 2, 5, 1, 5, -5597273651063162612877804024034786095689996697600000⟩, + ⟨6, 3, 3, 5, 2, 5, 3204498897148239969188838717214439653227311923200000⟩, + ⟨6, 3, 4, 5, 3, 5, 919178377679449231318960007154760835548745564160000⟩, + ⟨6, 3, 5, 5, 4, 5, -82115891564241073673789083685571775374871756800000⟩, + ⟨6, 3, 6, 5, 5, 5, -27046048176037015999283867454620366150408601600000⟩, + ⟨6, 3, 7, 5, 6, 5, -2685734469412395871222920388756102786842624000000⟩, + ⟨6, 3, 8, 5, 7, 5, 1654237507043960257485297913346259386420428800000⟩, + ⟨6, 3, 2, 6, 0, 5, 100762572209769034897572060781672643132156962406400000⟩, + ⟨6, 3, 3, 6, 1, 5, 780173514768683290495225152873837912747776409600000⟩, + ⟨6, 3, 4, 6, 2, 5, -1164229072554888642375501130603267138793515253760000⟩, + ⟨6, 3, 5, 6, 3, 5, 748285444333639993004220003868085013107756236800000⟩, + ⟨6, 3, 6, 6, 4, 5, 18033176114271186604073103536753052070025625600000⟩, + ⟨6, 3, 7, 6, 5, 5, -16779643823786427274268690344841204406524313600000⟩, + ⟨6, 3, 8, 6, 6, 5, -2470994962321804450554120193936218917752012800000⟩, + ⟨6, 3, 3, 7, 0, 5, -82004069986745588444356102547847133835436018892800000⟩, + ⟨6, 3, 4, 7, 1, 5, -1118378593831557758437462833604458837934300200960000⟩, + ⟨6, 3, 5, 7, 2, 5, -41454803532344066383604182767616202281215590400000⟩, + ⟨6, 3, 6, 7, 3, 5, 91034909256911819670406211416980034520560435200000⟩, + ⟨6, 3, 7, 7, 4, 5, -13047675408284458218159512994687465314844672000000⟩, + ⟨6, 3, 8, 7, 5, 5, -6382841530491069708506391360120126122754048000000⟩ +] + +def collectedFourData_8_4_47 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 4, 6, -1978989723302179150435369594277655481392562176000000⟩, + ⟨6, 4, 1, 0, 5, 6, 2186658492625623014805795799788501360538602700800000⟩, + ⟨6, 4, 2, 0, 6, 6, -466490050562357470014874255490439961095281049600000⟩, + ⟨6, 4, 3, 0, 7, 6, 26666878461205965986246120846850530281751838720000⟩, + ⟨6, 4, 4, 0, 8, 6, -17153568585493797701196614842881280240747806720000⟩, + ⟨6, 4, 0, 1, 3, 6, -1555412117097216244869083316477215365682901811200000⟩, + ⟨6, 4, 1, 1, 4, 6, 955166076324243767110062115825751953640521728000000⟩, + ⟨6, 4, 2, 1, 5, 6, 227781302337934808412786727881604953831741849600000⟩, + ⟨6, 4, 3, 1, 6, 6, -126446485580448733094758066480956172907933859840000⟩, + ⟨6, 4, 4, 1, 7, 6, 20005310371601054393086377573376984147631800320000⟩, + ⟨6, 4, 5, 1, 8, 6, 14028527715772394560038821038146065044340736000000⟩, + ⟨6, 4, 0, 2, 2, 6, -1297522285247757441560715953675024809094597836800000⟩, + ⟨6, 4, 1, 2, 3, 6, 1442718963510519752440178208547601539176962457600000⟩, + ⟨6, 4, 2, 2, 4, 6, 839175324138698273634813934347802643903859916800000⟩, + ⟨6, 4, 3, 2, 5, 6, -53809213411661383329123032445159155476086128640000⟩, + ⟨6, 4, 4, 2, 6, 6, -13189365286090224165429396332452757560413388800000⟩, + ⟨6, 4, 5, 2, 7, 6, 7190860810600966212459566351346517368687820800000⟩, + ⟨6, 4, 6, 2, 8, 6, -1593305784314303185019003606689721152123699200000⟩, + ⟨6, 4, 0, 3, 1, 6, -4159258806500682749993541041992508884184884838400000⟩, + ⟨6, 4, 1, 3, 2, 6, -3717614216981956294310896028442627216454031769600000⟩, + ⟨6, 4, 2, 3, 3, 6, -955902475409675838523445881209844684032049152000000⟩, + ⟨6, 4, 3, 3, 4, 6, 5862981452247231903227610822453612688315514880000⟩, + ⟨6, 4, 4, 3, 5, 6, -36187594514862008700532713733740636554573905920000⟩, + ⟨6, 4, 5, 3, 6, 6, -4920094658849970141422189197944290853204787200000⟩, + ⟨6, 4, 6, 3, 7, 6, -3378234495029013170194033056686974540185600000⟩, + ⟨6, 4, 7, 3, 8, 6, 60076100633273117327414729661961264850534400000⟩, + ⟨6, 4, 0, 4, 0, 6, -13282291683127849623373814877126023726053195776000000⟩, + ⟨6, 4, 1, 4, 1, 6, 1673700898061162674305930615258978061650808012800000⟩, + ⟨6, 4, 2, 4, 2, 6, 227921163193110816837407227642448119760683008000000⟩, + ⟨6, 4, 3, 4, 3, 6, 86584337718009584185810771775834195295983370240000⟩, + ⟨6, 4, 4, 4, 4, 6, 27121363971957679865056055235254409302428876800000⟩, + ⟨6, 4, 5, 4, 5, 6, -2983308434235689649656078740880548617309388800000⟩, + ⟨6, 4, 6, 4, 6, 6, -682703377442575340937914083519378694445465600000⟩, + ⟨6, 4, 7, 4, 7, 6, 158906263141300557090405996069240074718412800000⟩, + ⟨6, 4, 8, 4, 8, 6, -17021146764831200385021351248802576806707200000⟩, + ⟨6, 4, 1, 5, 0, 6, 8821426992826834080050371999081335843982619443200000⟩, + ⟨6, 4, 2, 5, 1, 6, -236058430614984597384984084085418148216019353600000⟩, + ⟨6, 4, 3, 5, 2, 6, 108116776520237537458519624794991474308714332160000⟩, + ⟨6, 4, 4, 5, 3, 6, 25843511063524601387521295402115071966277795840000⟩, + ⟨6, 4, 5, 5, 4, 6, -1978937777784839778000156654632773296429465600000⟩, + ⟨6, 4, 6, 5, 5, 6, -570317630044752582680456083793088650988748800000⟩, + ⟨6, 4, 7, 5, 6, 6, -50341196122837136265985455044925623107584000000⟩, + ⟨6, 4, 8, 5, 7, 6, 27906208209282009538677040085824489358622720000⟩, + ⟨6, 4, 2, 6, 0, 6, 4249542928109148956733846760069741611906917990400000⟩, + ⟨6, 4, 3, 6, 1, 6, 26322320041463865523404990168513276556062228480000⟩, + ⟨6, 4, 4, 6, 2, 6, -32733327553905912046717058673344242199549706240000⟩, + ⟨6, 4, 5, 6, 3, 6, 18033176114271186604073103536753052070025625600000⟩, + ⟨6, 4, 6, 6, 4, 6, 380263992607357828241481176647360704203980800000⟩, + ⟨6, 4, 7, 6, 5, 6, -314516326995422032447300177741571096680857600000⟩, + ⟨6, 4, 8, 6, 6, 6, -41684522088886941724363119089806137958072320000⟩, + ⟨6, 4, 3, 7, 0, 6, -2766740134127357670945922370309261561220971888640000⟩, + ⟨6, 4, 4, 7, 1, 6, -31444200891520984207853393743855412776575959040000⟩, + ⟨6, 4, 5, 7, 2, 6, -999032893853745074338966056232092462533836800000⟩, + ⟨6, 4, 6, 7, 3, 6, 1919645094204242455510032322268918399474073600000⟩, + ⟨6, 4, 7, 7, 4, 6, -244564603893725275081511768646696988311552000000⟩, + ⟨6, 4, 8, 7, 5, 6, -107675532659774586622031197273398267032371200000⟩ +] + +def collectedFourData_8_4_48 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 4, 7, 4910466868032178412600674345667949568947388416000000⟩, + ⟨6, 5, 1, 0, 5, 7, -4069316512855290810034047208918413566279260569600000⟩, + ⟨6, 5, 2, 0, 6, 7, 694501010464319371790014762376818980332670812160000⟩, + ⟨6, 5, 3, 0, 7, 7, -33084260523367576285747579051928801890806005760000⟩, + ⟨6, 5, 4, 0, 8, 7, 18241348650007227829437412826926882150762414080000⟩, + ⟨6, 5, 0, 1, 3, 7, 3859443824901269556601609641828021489536021299200000⟩, + ⟨6, 5, 1, 1, 4, 7, -1777540068562920440673013903122542577724686336000000⟩, + ⟨6, 5, 2, 1, 5, 7, -339116224339339745839017505834769179706822492160000⟩, + ⟨6, 5, 3, 1, 6, 7, 156875821716203246437776444739070428831253790720000⟩, + ⟨6, 5, 4, 1, 7, 7, -21273931399241580520532324256183389528763924480000⟩, + ⟨6, 5, 5, 1, 8, 7, -13053368799325922121939792715629944704598016000000⟩, + ⟨6, 5, 0, 2, 2, 7, 3219541828449218218110823869430724444457585868800000⟩, + ⟨6, 5, 1, 2, 3, 7, -2684863741376179759229100919080336412871177011200000⟩, + ⟨6, 5, 2, 2, 4, 7, -1249347354500849209974624872945241542060440289280000⟩, + ⟨6, 5, 3, 2, 5, 7, 66758396100192879048017173626513322071419781120000⟩, + ⟨6, 5, 4, 2, 6, 7, 14025758515305940202910353789959396973032243200000⟩, + ⟨6, 5, 5, 2, 7, 7, -6691005645578971224857678235080816690253004800000⟩, + ⟨6, 5, 6, 2, 8, 7, 1317823125000761465544163743159946337216102400000⟩, + ⟨6, 5, 0, 3, 1, 7, 10320368177967573973608003962952713589934679654400000⟩, + ⟨6, 5, 1, 3, 2, 7, 6918386649131109457450970048051355902610191155200000⟩, + ⟨6, 5, 2, 3, 3, 7, 1423128391006533127617830421896435015917712179200000⟩, + ⟨6, 5, 3, 3, 4, 7, -7273907446347858446353960247738926613177303040000⟩, + ⟨6, 5, 4, 3, 5, 7, 38482402367803547233778690195664319867131002880000⟩, + ⟨6, 5, 5, 3, 6, 7, 4578086268978528245216615501229822315803443200000⟩, + ⟨6, 5, 6, 3, 7, 7, 2794137561698763767091285059251578549043200000⟩, + ⟨6, 5, 7, 3, 8, 7, -44720045523229288145145496807896895318917120000⟩, + ⟨6, 5, 0, 4, 0, 7, 32957348122408435462852317869751002463014486016000000⟩, + ⟨6, 5, 1, 4, 1, 7, -3114715317929207514249546620639505702027106713600000⟩, + ⟨6, 5, 2, 4, 2, 7, -339324446369213794533431144082294888303742156800000⟩, + ⟨6, 5, 3, 4, 3, 7, -107420851318355798610146945920356507692480593920000⟩, + ⟨6, 5, 4, 4, 4, 7, -28841243943525652688408684317613906707297075200000⟩, + ⟨6, 5, 5, 4, 5, 7, 2775931018793578858634752552083557662379212800000⟩, + ⟨6, 5, 6, 4, 6, 7, 564663925259731140703047246064559863313203200000⟩, + ⟨6, 5, 7, 4, 7, 7, -118288225212629649616180383599974896044605440000⟩, + ⟨6, 5, 8, 4, 8, 7, 11518518711449661758784054893600875059609600000⟩, + ⟨6, 5, 1, 5, 0, 7, -16416453986719347065464119621804189098367673958400000⟩, + ⟨6, 5, 2, 5, 1, 7, 351439046541493978595442804497827084494239170560000⟩, + ⟨6, 5, 3, 5, 2, 7, -134135069710010854514875196984931993066437345280000⟩, + ⟨6, 5, 4, 5, 3, 7, -27482356997641643763141231553979815758145781760000⟩, + ⟨6, 5, 5, 5, 4, 7, 1841376740860773436869594493031582776531353600000⟩, + ⟨6, 5, 6, 5, 5, 7, 471709679879216556458540636555105988614553600000⟩, + ⟨6, 5, 7, 5, 6, 7, 37473480445237668466322867222853906019123200000⟩, + ⟨6, 5, 8, 5, 7, 7, -18884637202493019271025833960936009849896960000⟩, + ⟨6, 5, 2, 6, 0, 7, -6326634092250148747307254585618356923891806371840000⟩, + ⟨6, 5, 3, 6, 1, 7, -32656784148851112999611761790713892662243491840000⟩, + ⟨6, 5, 4, 6, 2, 7, 34809085783504759590421349971064724982710927360000⟩, + ⟨6, 5, 5, 6, 3, 7, -16779643823786427274268690344841204406524313600000⟩, + ⟨6, 5, 6, 6, 4, 7, -314516326995422032447300177741571096680857600000⟩, + ⟨6, 5, 7, 6, 5, 7, 234122792803968152601548186877004830191124480000⟩, + ⟨6, 5, 8, 6, 6, 7, 28208672088460344811543956014721807427829760000⟩, + ⟨6, 5, 3, 7, 0, 7, 3432555915049792701904065201048692537957673861120000⟩, + ⟨6, 5, 4, 7, 1, 7, 33438210167426258827916833799689640360867266560000⟩, + ⟨6, 5, 5, 7, 2, 7, 929587556894437327010949126063004152810700800000⟩, + ⟨6, 5, 6, 7, 3, 7, -1587738349939728019095228444674882261955379200000⟩, + ⟨6, 5, 7, 7, 4, 7, 182051433169091444404378636638712275507609600000⟩, + ⟨6, 5, 8, 7, 5, 7, 72865985755409382534779737185039356107161600000⟩ +] + +def collectedFourData_8_4_49 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 4, 8, 1627025746029189515774021747892863212902678528000000⟩, + ⟨6, 6, 1, 0, 5, 8, -1078656333597955181330103961099683976365673021440000⟩, + ⟨6, 6, 2, 0, 6, 8, 153409856270490769146528793527694676622594539520000⟩, + ⟨6, 6, 3, 0, 7, 8, -6264047228850809881247664074558973840992501760000⟩, + ⟨6, 6, 4, 0, 8, 8, 3022028728986230350029964083047626430553784320000⟩, + ⟨6, 6, 0, 1, 3, 8, 1278781557278717721409638097967518510181095833600000⟩, + ⟨6, 6, 1, 1, 4, 8, -471173684111929584497099255028439961336964710400000⟩, + ⟨6, 6, 2, 1, 5, 8, -74908128931458744067823223090866113599787499520000⟩, + ⟨6, 6, 3, 1, 6, 8, 29702267505752671908075140083436987119011102720000⟩, + ⟨6, 6, 4, 1, 7, 8, -3524434135902819693475002148662208051984465920000⟩, + ⟨6, 6, 5, 1, 8, 8, -1922258236419733712744424594542603028922368000000⟩, + ⟨6, 6, 0, 2, 2, 8, 1066757517377152904534404880732698273309419110400000⟩, + ⟨6, 6, 1, 2, 3, 8, -711678551013194447131805644524347332637679943680000⟩, + ⟨6, 6, 2, 2, 4, 8, -275971085999938912610561741375694533053026140160000⟩, + ⟨6, 6, 3, 2, 5, 8, 12639779142065965596756600968869517385132933120000⟩, + ⟨6, 6, 4, 2, 6, 8, 2323635493862511799049836611907686322982092800000⟩, + ⟨6, 6, 5, 2, 7, 8, -985327305914263481666733764568476895569510400000⟩, + ⟨6, 6, 6, 2, 8, 8, 174658109765283624851405779337978045980999680000⟩, + ⟨6, 6, 0, 3, 1, 8, 3419533251179969921769574821003770881088107315200000⟩, + ⟨6, 6, 1, 3, 2, 8, 1833861178846616267764754941943162273612987105280000⟩, + ⟨6, 6, 2, 3, 3, 8, 314357961513698222033500149025199293467092582400000⟩, + ⟨6, 6, 3, 3, 4, 8, -1377213788714740215688922290090387879011287040000⟩, + ⟨6, 6, 4, 3, 5, 8, 6375346897163986569490842136649312067146219520000⟩, + ⟨6, 6, 5, 3, 6, 8, 674175699229344634639080145287735068432793600000⟩, + ⟨6, 6, 6, 3, 7, 8, 370321916266420534522562054055606343434240000⟩, + ⟨6, 6, 7, 3, 8, 8, -5388168682072943995221959315601847945789440000⟩, + ⟨6, 6, 0, 4, 0, 8, 10920031711260474748917851233107932182455779328000000⟩, + ⟨6, 6, 1, 4, 1, 8, -825619583639003859125199571728934947431424983040000⟩, + ⟨6, 6, 2, 4, 2, 8, -74954123553776098870836042323725597214874009600000⟩, + ⟨6, 6, 3, 4, 3, 8, -20338652742329739788186926870166983002732625920000⟩, + ⟨6, 6, 4, 4, 4, 8, -4778104374261828870618787393447415524412620800000⟩, + ⟨6, 6, 5, 4, 5, 8, 408787673637516033821822309447889651656294400000⟩, + ⟨6, 6, 6, 4, 6, 8, 74837914108126645551319382394707418273546240000⟩, + ⟨6, 6, 7, 4, 7, 8, -14252152543485558988084353199175418280673280000⟩, + ⟨6, 6, 8, 4, 8, 8, 1272175470839891015060138271091034003865600000⟩, + ⟨6, 6, 1, 5, 0, 8, -4351519969521704849534781557545342313793595637760000⟩, + ⟨6, 6, 2, 5, 1, 8, 77630144240861114777126866661073239576747704320000⟩, + ⟨6, 6, 3, 5, 2, 8, -25396620580812021806642008263590179773905633280000⟩, + ⟨6, 6, 4, 5, 3, 8, -4552978728746347497124552417739372311389143040000⟩, + ⟨6, 6, 5, 5, 4, 8, 271163839839883548691373166171405861833932800000⟩, + ⟨6, 6, 6, 5, 5, 8, 62518193437866254166557611229215872012779520000⟩, + ⟨6, 6, 7, 5, 6, 8, 4515054297930465866316774038955295663718400000⟩, + ⟨6, 6, 8, 5, 7, 8, -2085734531198106590828064575520590329282560000⟩, + ⟨6, 6, 2, 6, 0, 8, -1397504124751660072813623156770111875021516308480000⟩, + ⟨6, 6, 3, 6, 1, 8, -6183110488635693168573221877393295805345955840000⟩, + ⟨6, 6, 4, 6, 2, 8, 5766791660300614202500538866756129691994685440000⟩, + ⟨6, 6, 5, 6, 3, 8, -2470994962321804450554120193936218917752012800000⟩, + ⟨6, 6, 6, 6, 4, 8, -41684522088886941724363119089806137958072320000⟩, + ⟨6, 6, 7, 6, 5, 8, 28208672088460344811543956014721807427829760000⟩, + ⟨6, 6, 8, 6, 6, 8, 3115537821736858986501246473365211169423360000⟩, + ⟨6, 6, 3, 7, 0, 8, 649906995876675515899985690797311398520155013120000⟩, + ⟨6, 6, 4, 7, 1, 8, 5539679861982221465634028389695733947946762240000⟩, + ⟨6, 6, 5, 7, 2, 8, 136892427172202943338251000249371054204518400000⟩, + ⟨6, 6, 6, 7, 3, 8, -210431410514338244958660058205524424329789440000⟩, + ⟨6, 6, 7, 7, 4, 8, 21934768161599143274179010031234785162035200000⟩, + ⟨6, 6, 8, 7, 5, 8, 8047763958090943393041249998131657546137600000⟩ +] + +def collectedFourData_8_4_50 : List CollectedFourTerm := [ + ⟨7, 0, 1, 0, 5, 3, -284103183614965985974399639445126786082110114365440000⟩, + ⟨7, 0, 2, 0, 6, 3, 242436226665345766027833514493948215810688412549120000⟩, + ⟨7, 0, 3, 0, 7, 3, -34647134399139523673366269552201914182429269032960000⟩, + ⟨7, 0, 4, 0, 8, 3, 44573795697239925012977103781198650602789189713920000⟩, + ⟨7, 0, 1, 1, 4, 3, -124100642180705474469439153112703602721366107750400000⟩, + ⟨7, 0, 2, 1, 5, 3, -118378600737906684744100575588463275784384146309120000⟩, + ⟨7, 0, 3, 1, 6, 3, 164286509445715646690848796686181216875724270469120000⟩, + ⟨7, 0, 4, 1, 7, 3, -51984087912628980259950671510753746848746852843520000⟩, + ⟨7, 0, 5, 1, 8, 3, -63793330765776370378298809546179015112988295168000000⟩, + ⟨7, 0, 1, 2, 3, 3, -187446303104633077870358081573395249665991696711680000⟩, + ⟨7, 0, 2, 2, 4, 3, -436121839789719168589080287541079190625640733736960000⟩, + ⟨7, 0, 3, 2, 5, 3, 69912009075152225980624377304242477939308384747520000⟩, + ⟨7, 0, 4, 2, 6, 3, 34272756173640836513085901834772366651363740876800000⟩, + ⟨7, 0, 5, 2, 7, 3, -32699722413890468593665549406665137425398261350400000⟩, + ⟨7, 0, 6, 2, 8, 3, 11592638653934843690351113436141031496030208655360000⟩, + ⟨7, 0, 1, 3, 2, 3, 483013711587226778878110621904683556458366008033280000⟩, + ⟨7, 0, 2, 3, 3, 3, 496785277454501692274919409395248781196739896934400000⟩, + ⟨7, 0, 3, 3, 4, 3, -7617520987737145063105240656362325764718031011840000⟩, + ⟨7, 0, 4, 3, 5, 3, 94033986959663620830950011956959938816037219205120000⟩, + ⟨7, 0, 5, 3, 6, 3, 22373639795290843022547795418361508325997779353600000⟩, + ⟨7, 0, 6, 3, 7, 3, 24579495144419799599115426875404841763974676480000⟩, + ⟨7, 0, 7, 3, 8, 3, -655656183422458093237660851828884224263617249280000⟩, + ⟨7, 0, 1, 4, 1, 3, -217456797740485024060680731393487555451283350487040000⟩, + ⟨7, 0, 2, 4, 2, 3, -118451286828309222397646551854381223055875217817600000⟩, + ⟨7, 0, 3, 4, 3, 3, -112495325995523289085708122311994490447181717176320000⟩, + ⟨7, 0, 4, 4, 4, 3, -70475255961541056423450668084144901616393047244800000⟩, + ⟨7, 0, 5, 4, 5, 3, 13566297588559828256275102909311264858627794534400000⟩, + ⟨7, 0, 6, 4, 6, 3, 4967240840036672152835858427819454577177505300480000⟩, + ⟨7, 0, 7, 4, 7, 3, -1734264922571315316066465970148983404211061391360000⟩, + ⟨7, 0, 8, 4, 8, 3, 265378174103058815195802309029143199859553075200000⟩, + ⟨7, 0, 1, 5, 0, 3, -1146130271892522758985328646967959105955925076213760000⟩, + ⟨7, 0, 2, 5, 1, 3, 122680248210760439967369248367325346133708814417920000⟩, + ⟨7, 0, 3, 5, 2, 3, -140471502592545978078427694583315046609286206586880000⟩, + ⟨7, 0, 4, 5, 3, 3, -67154736724524217774536799950350524331197716234240000⟩, + ⟨7, 0, 5, 5, 4, 3, 8999022191130050873308218881783812894808132812800000⟩, + ⟨7, 0, 6, 5, 5, 3, 4149540074583132929831188413178244386232771543040000⟩, + ⟨7, 0, 7, 5, 6, 3, 549411765592192904120556129896021640212171980800000⟩, + ⟨7, 0, 8, 5, 7, 3, -435088110280593835334209533095654006199964139520000⟩, + ⟨7, 0, 2, 6, 0, 3, -2208499733919770552485932580368255068781614601338880000⟩, + ⟨7, 0, 3, 6, 1, 3, -34199464384273456409637581810019266319979527536640000⟩, + ⟨7, 0, 4, 6, 2, 3, 85058024375901894297513952096697530086022856048640000⟩, + ⟨7, 0, 5, 6, 3, 3, -82004069986745588444356102547847133835436018892800000⟩, + ⟨7, 0, 6, 6, 4, 3, -2766740134127357670945922370309261561220971888640000⟩, + ⟨7, 0, 7, 6, 5, 3, 3432555915049792701904065201048692537957673861120000⟩, + ⟨7, 0, 8, 6, 6, 3, 649906995876675515899985690797311398520155013120000⟩, + ⟨7, 0, 3, 7, 0, 3, 3594707097572633518673194288228254359646312616427520000⟩, + ⟨7, 0, 4, 7, 1, 3, 81708210126428251526815062968857797494551546429440000⟩, + ⟨7, 0, 5, 7, 2, 3, 4543002454338004936183402933348609105464813158400000⟩, + ⟨7, 0, 6, 7, 3, 3, -13967031400997294701194439693340388912509359226880000⟩, + ⟨7, 0, 7, 7, 4, 3, 2669119551683672687319332470141033120186918502400000⟩, + ⟨7, 0, 8, 7, 5, 3, 1678778559848028726247194777498301187237294899200000⟩ +] + +def collectedFourData_8_4_51 : List CollectedFourTerm := [ + ⟨7, 1, 0, 0, 4, 4, 5844412568967825232686513277078469449476577689600000⟩, + ⟨7, 1, 1, 0, 5, 4, -19373118861401048616842932179829146691709215703040000⟩, + ⟨7, 1, 2, 0, 6, 4, 8265915530645068696271129219223111117942250536960000⟩, + ⟨7, 1, 3, 0, 7, 4, -787534355629455078509568796902372881175014277120000⟩, + ⟨7, 1, 4, 0, 8, 4, 759876597613869968275757757860079048014356807680000⟩, + ⟨7, 1, 0, 1, 3, 4, 4593490314805322711935427645813824491475194347520000⟩, + ⟨7, 1, 1, 1, 4, 4, -8462476418431653524205004302632586351567332966400000⟩, + ⟨7, 1, 2, 1, 5, 4, -4036143969878756293310204058950703710926232616960000⟩, + ⟨7, 1, 3, 1, 6, 4, 3734256024306509341153668201147602740158545264640000⟩, + ⟨7, 1, 4, 1, 7, 4, -886204354715853909522972051660423435334535086080000⟩, + ⟨7, 1, 5, 1, 8, 4, -870018958439404509160897064756110016388897177600000⟩, + ⟨7, 1, 0, 2, 2, 4, 3831882229163013433360791400158486274032040673280000⟩, + ⟨7, 1, 1, 2, 3, 4, -12782044410659568267481623458238724665636689018880000⟩, + ⟨7, 1, 2, 2, 4, 4, -14869668359207461312118267094192721544338923847680000⟩, + ⟨7, 1, 3, 2, 5, 4, 1589110036734467008118655802063335904532433469440000⟩, + ⟨7, 1, 4, 2, 6, 4, 584268513477495491921658972407729837411873587200000⟩, + ⟨7, 1, 5, 2, 7, 4, -445961640414189843430894730168033600064486113280000⟩, + ⟨7, 1, 6, 2, 8, 4, 131751173231204196542376164715559427393936424960000⟩, + ⟨7, 1, 0, 3, 1, 4, 12283249458082690660349055558157686301346381168640000⟩, + ⟨7, 1, 1, 3, 2, 4, 32936913719867572609434428126821729680583274004480000⟩, + ⟨7, 1, 2, 3, 3, 4, 16938001373760691765740900931530384091292840755200000⟩, + ⟨7, 1, 3, 3, 4, 4, -173147349314995929744288686491482562234920468480000⟩, + ⟨7, 1, 4, 3, 5, 4, 1603054551519846442513655346333656941043625492480000⟩, + ⟨7, 1, 5, 3, 6, 4, 305133633211077469150600094483027790057198059520000⟩, + ⟨7, 1, 6, 3, 7, 4, 279347732589664197365185099132799028591329280000⟩, + ⟨7, 1, 7, 3, 8, 4, -6387068354146448016446707815141800747351408640000⟩, + ⟨7, 1, 0, 4, 0, 4, 39225667290499636471022591202320280568389540249600000⟩, + ⟨7, 1, 1, 4, 1, 4, -14828473008438827757679757101747440783354117488640000⟩, + ⟨7, 1, 2, 4, 2, 4, -4038622217836102880935441123011524861153299660800000⟩, + ⟨7, 1, 3, 4, 3, 4, -2557034964236759178189460660703127299576341463040000⟩, + ⟨7, 1, 4, 4, 4, 4, -1201434539696121804446966437021020467724759859200000⟩, + ⟨7, 1, 5, 4, 5, 4, 185018339004957959344290058366867137139656622080000⟩, + ⟨7, 1, 6, 4, 6, 4, 56453049899441997996532062293536216939002593280000⟩, + ⟨7, 1, 7, 4, 7, 4, -16894324929327088684110378757817256428364103680000⟩, + ⟨7, 1, 8, 4, 8, 4, 2262031546383431560458521200077795523716710400000⟩, + ⟨7, 1, 1, 5, 0, 4, -78155118522417277057224427503173088706530807644160000⟩, + ⟨7, 1, 2, 5, 1, 4, 4182809569910158493256765549331194551662396047360000⟩, + ⟨7, 1, 3, 5, 2, 4, -3192937488107803584111849449720126366606017167360000⟩, + ⟨7, 1, 4, 5, 3, 4, -1144827629275612156432727156615778070376176680960000⟩, + ⟨7, 1, 5, 5, 4, 4, 122729442399648171568235408984146931155426344960000⟩, + ⟨7, 1, 6, 5, 5, 4, 47159821807320786386104740822671415836084797440000⟩, + ⟨7, 1, 7, 5, 6, 4, 5352089387904983964748734154042218434160230400000⟩, + ⟨7, 1, 8, 5, 7, 4, -3708605782059726442588196531591504165118935040000⟩, + ⟨7, 1, 2, 6, 0, 4, -75299275612106249395365185785158616248797406167040000⟩, + ⟨7, 1, 3, 6, 1, 4, -777358751707044319928463082583861073320953774080000⟩, + ⟨7, 1, 4, 6, 2, 4, 1450035859668108872236750597187456038523696578560000⟩, + ⟨7, 1, 5, 6, 3, 4, -1118378593831557758437462833604458837934300200960000⟩, + ⟨7, 1, 6, 6, 4, 4, -31444200891520984207853393743855412776575959040000⟩, + ⟨7, 1, 7, 6, 5, 4, 33438210167426258827916833799689640360867266560000⟩, + ⟨7, 1, 8, 6, 6, 4, 5539679861982221465634028389695733947946762240000⟩, + ⟨7, 1, 3, 7, 0, 4, 81708210126428251526815062968857797494551546429440000⟩, + ⟨7, 1, 4, 7, 1, 4, 1392929539357897803468929221730317870552590581760000⟩, + ⟨7, 1, 5, 7, 2, 4, 61957860109590519366423850702739476413551738880000⟩, + ⟨7, 1, 6, 7, 3, 4, -158736317810946399273024736942017810601271623680000⟩, + ⟨7, 1, 7, 7, 4, 4, 26001202235300085907163581119596663334449971200000⟩, + ⟨7, 1, 8, 7, 5, 4, 14309579431704350808331806667149498676307558400000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0821.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0821.lean new file mode 100644 index 0000000000000000000000000000000000000000..e76fe6912f9171688edc685f9373046bb9bd9fa0 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0821.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse0816 +import OAI.Analysis.LaughlinFock.Sparse0817 +import OAI.Analysis.LaughlinFock.Sparse0818 +import OAI.Analysis.LaughlinFock.Sparse0819 +import OAI.Analysis.LaughlinFock.Sparse0820 + +namespace OAI + +/-! Sparse0821. -/ +namespace LaughlinFock +def collectedFourData_8_4_52 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 4, 5, 1299804786025869516450414596723238967783194624000000⟩, + ⟨7, 2, 1, 0, 5, 5, -2154303133047327076776140026683678621065596108800000⟩, + ⟨7, 2, 2, 0, 6, 5, 612783374481239712081448453188227246955744460800000⟩, + ⟨7, 2, 3, 0, 7, 5, -43787160494204676560191153554379360125006643200000⟩, + ⟨7, 2, 4, 0, 8, 5, 33799504285919944294655031934983203234607267840000⟩, + ⟨7, 2, 0, 1, 3, 5, 1021598086255896246469288468497206508664966348800000⟩, + ⟨7, 2, 1, 1, 4, 5, -941032757399187389364868605308174513637163008000000⟩, + ⟨7, 2, 2, 1, 5, 5, -299214516841475332138769288757096744485702860800000⟩, + ⟨7, 2, 3, 1, 6, 5, 207625821900898121736784983697949021123798630400000⟩, + ⟨7, 2, 4, 1, 7, 5, -39418595044876123646037150082895249260192727040000⟩, + ⟨7, 2, 5, 1, 8, 5, -32248887085684158185566096301942598191284224000000⟩, + ⟨7, 2, 0, 2, 2, 5, 852215479687327735946480526252267099089220403200000⟩, + ⟨7, 2, 1, 2, 3, 5, -1421371464121733715952362246469946027240167833600000⟩, + ⟨7, 2, 2, 2, 4, 5, -1102344382880595342212423187130834591957804646400000⟩, + ⟨7, 2, 3, 2, 5, 5, 88355023147946451288233932463466489345107558400000⟩, + ⟨7, 2, 4, 2, 6, 5, 25988412049301707781839126592944014081235353600000⟩, + ⟨7, 2, 5, 2, 7, 5, -16530405971912343405482550778452445156815667200000⟩, + ⟨7, 2, 6, 2, 8, 5, 4185946919620676751449652429930832596251443200000⟩, + ⟨7, 2, 0, 3, 1, 5, 2731810296613822915867758289733692922854480281600000⟩, + ⟨7, 2, 1, 3, 2, 5, 3662605743930727896769003838171183745592826265600000⟩, + ⟨7, 2, 2, 3, 3, 5, 1255677680264287954680279739265817536832208896000000⟩, + ⟨7, 2, 3, 3, 4, 5, -9627047657548924200819287541578019019476172800000⟩, + ⟨7, 2, 4, 3, 5, 5, 71304274081870390221282273764758044637648650240000⟩, + ⟨7, 2, 5, 3, 6, 5, 11310351329722154827118482092865412865510604800000⟩, + ⟨7, 2, 6, 3, 7, 5, 8875327270784241675796485005035341191577600000⟩, + ⟨7, 2, 7, 3, 8, 5, -177561515323945605979048396812830790333235200000⟩, + ⟨7, 2, 0, 4, 0, 5, 8723838277600302027583922776318036054087041024000000⟩, + ⟨7, 2, 1, 4, 1, 5, -1648935625127179516045807165828441773892750540800000⟩, + ⟨7, 2, 2, 4, 2, 5, -299398238673675759691779288155379654966902784000000⟩, + ⟨7, 2, 3, 4, 3, 5, -142171956776205692329641126486003223284311654400000⟩, + ⟨7, 2, 4, 4, 4, 5, -53440113830622478554402711237301345472584089600000⟩, + ⟨7, 2, 5, 4, 5, 5, 6858052305037545159195639538769243080438579200000⟩, + ⟨7, 2, 6, 4, 6, 5, 1793604296145983814113078449814133840386457600000⟩, + ⟨7, 2, 7, 4, 7, 5, -469664918002480270385992192149718556894822400000⟩, + ⟨7, 2, 8, 4, 8, 5, 55897632433531641343422192471645842571264000000⟩, + ⟨7, 2, 1, 5, 0, 5, -8690898863578868898785426901749392547129799475200000⟩, + ⟨7, 2, 2, 5, 1, 5, 310087388814865157937901785671686521610882252800000⟩, + ⟨7, 2, 3, 5, 2, 5, -177528339227808057550698197702856594234644889600000⟩, + ⟨7, 2, 4, 5, 3, 5, -50922224060916825557210254720361631037500948480000⟩, + ⟨7, 2, 5, 5, 4, 5, 4549197338336958236409375563344295462594150400000⟩, + ⟨7, 2, 6, 5, 5, 5, 1498343475680411308191417690161944938204364800000⟩, + ⟨7, 2, 7, 5, 6, 5, 148788935576158642808547066327213142966272000000⟩, + ⟨7, 2, 8, 5, 7, 5, -91644293457305050357184590011127285835366400000⟩, + ⟨7, 2, 2, 6, 0, 5, -5582218210978798889665393671923198600223601459200000⟩, + ⟨7, 2, 3, 6, 1, 5, -43221393681758845262271876054003704532880588800000⟩, + ⟨7, 2, 4, 6, 2, 5, 64497963758181769289406651255879973943409377280000⟩, + ⟨7, 2, 5, 6, 3, 5, -41454803532344066383604182767616202281215590400000⟩, + ⟨7, 2, 6, 6, 4, 5, -999032893853745074338966056232092462533836800000⟩, + ⟨7, 2, 7, 6, 5, 5, 929587556894437327010949126063004152810700800000⟩, + ⟨7, 2, 8, 6, 6, 5, 136892427172202943338251000249371054204518400000⟩, + ⟨7, 2, 3, 7, 0, 5, 4543002454338004936183402933348609105464813158400000⟩, + ⟨7, 2, 4, 7, 1, 5, 61957860109590519366423850702739476413551738880000⟩, + ⟨7, 2, 5, 7, 2, 5, 2296584477111669774529965209208240861295411200000⟩, + ⟨7, 2, 6, 7, 3, 5, -5043308414465697217778038163194930901129625600000⟩, + ⟨7, 2, 7, 7, 4, 5, 722837554438733476805287869316125966729216000000⟩, + ⟨7, 2, 8, 7, 5, 5, 353607628784258372738498471818086731218944000000⟩ +] + +def collectedFourData_8_4_53 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 4, 6, -9990317220858350520484474588988577476606164992000000⟩, + ⟨7, 3, 1, 0, 5, 6, 11038668739806421183510855776483573270518012313600000⟩, + ⟨7, 3, 2, 0, 6, 6, -2354930665185971532428298343032894101078094643200000⟩, + ⟨7, 3, 3, 0, 7, 6, 134619483861181926764751252461327039972235018240000⟩, + ⟨7, 3, 4, 0, 8, 6, -86594482841923508383688081782076780436510474240000⟩, + ⟨7, 3, 0, 1, 3, 6, -7852016751779437570227641360398496828186060390400000⟩, + ⟨7, 3, 1, 1, 4, 6, 4821860360729487447407087885945982360408293376000000⟩, + ⟨7, 3, 2, 1, 5, 6, 1149883418059944003444928006785700161444328243200000⟩, + ⟨7, 3, 3, 1, 6, 6, -638325953660591741181645071132624167277722337280000⟩, + ⟨7, 3, 4, 1, 7, 6, 100990618779228962099402988897235482724207165440000⟩, + ⟨7, 3, 5, 1, 8, 6, 70818681053236416511008776183315368626880512000000⟩, + ⟨7, 3, 0, 2, 2, 6, -6550139739547720936780376799456690582958217625600000⟩, + ⟨7, 3, 1, 2, 3, 6, 7283120238728621543699479164205079038199542579200000⟩, + ⟨7, 3, 2, 2, 4, 6, 4236316941592373773709074604348245301228312985600000⟩, + ⟨7, 3, 3, 2, 5, 6, -271639162678602319157936967970246678608221306880000⟩, + ⟨7, 3, 4, 2, 6, 6, -66582429205317641571471064319623876511898009600000⟩, + ⟨7, 3, 5, 2, 7, 6, 36300835594573178468406622808478394334419353600000⟩, + ⟨7, 3, 6, 2, 8, 6, -8043311204551355269657803121362789315536486400000⟩, + ⟨7, 3, 0, 3, 1, 6, -20996731004371035050385706154325078863189429452800000⟩, + ⟨7, 3, 1, 3, 2, 6, -18767224960850191539751267312906292862326616883200000⟩, + ⟨7, 3, 2, 3, 3, 6, -4825577843634017425551806932767719574768451584000000⟩, + ⟨7, 3, 3, 3, 4, 6, 29597447565428762057749576670570668528458792960000⟩, + ⟨7, 3, 4, 3, 5, 6, -182681872677952486237276269696773001600187760640000⟩, + ⟨7, 3, 5, 3, 6, 6, -24837575364739097479891946759340619100218982400000⟩, + ⟨7, 3, 6, 3, 7, 6, -17053971455430700791452218240366925787955200000⟩, + ⟨7, 3, 7, 3, 8, 6, 303275603532259534135664253511246413614284800000⟩, + ⟨7, 3, 0, 4, 0, 6, -67051539364741928138239188681054431047625736192000000⟩, + ⟨7, 3, 1, 4, 1, 6, 8449161058080623395386632066299452208130398617600000⟩, + ⟨7, 3, 2, 4, 2, 6, 1150589462307438815161193407142949377997275136000000⟩, + ⟨7, 3, 3, 4, 3, 6, 437094235495817983901818593432978718172727214080000⟩, + ⟨7, 3, 4, 4, 4, 6, 136913813321931810434271464017782615347665305600000⟩, + ⟨7, 3, 5, 4, 5, 6, -15060309447158185509582247808876158847130009600000⟩, + ⟨7, 3, 6, 4, 6, 6, -3446416738850989731436583190723066462417715200000⟩, + ⟨7, 3, 7, 4, 7, 6, 802189096017038135396374982570414700075417600000⟩, + ⟨7, 3, 8, 4, 8, 6, -85925992258164697120914040224627600811622400000⟩, + ⟨7, 3, 1, 5, 0, 6, 44532244387772345022249260859515699780548716134400000⟩, + ⟨7, 3, 2, 5, 1, 6, -1191667938814040766355813405552206955697877811200000⟩, + ⟨7, 3, 3, 5, 2, 6, 545794089588051512108398022003053778229232926720000⟩, + ⟨7, 3, 4, 5, 3, 6, 130462968344555643440437496677080626808257249280000⟩, + ⟨7, 3, 5, 5, 4, 6, -9990054989988573190274509163487987368145715200000⟩, + ⟨7, 3, 6, 5, 5, 6, -2879072070818034247861743817826744726559129600000⟩, + ⟨7, 3, 7, 5, 6, 6, -254131950571930328647340841755101970300928000000⟩, + ⟨7, 3, 8, 5, 7, 6, 140875856584465439092169598871983712622346240000⟩, + ⟨7, 3, 2, 6, 0, 6, 21452502453941824375973259413549242697359609036800000⟩, + ⟨7, 3, 3, 6, 1, 6, 132880087302518930242738657786769349596581724160000⟩, + ⟨7, 3, 4, 6, 2, 6, -165244074846491795537037910985292497331242926080000⟩, + ⟨7, 3, 5, 6, 3, 6, 91034909256911819670406211416980034520560435200000⟩, + ⟨7, 3, 6, 6, 4, 6, 1919645094204242455510032322268918399474073600000⟩, + ⟨7, 3, 7, 6, 5, 6, -1587738349939728019095228444674882261955379200000⟩, + ⟨7, 3, 8, 6, 6, 6, -210431410514338244958660058205524424329789440000⟩, + ⟨7, 3, 3, 7, 0, 6, -13967031400997294701194439693340388912509359226880000⟩, + ⟨7, 3, 4, 7, 1, 6, -158736317810946399273024736942017810601271623680000⟩, + ⟨7, 3, 5, 7, 2, 6, -5043308414465697217778038163194930901129625600000⟩, + ⟨7, 3, 6, 7, 3, 6, 9690734225018790626070119134529007398368051200000⟩, + ⟨7, 3, 7, 7, 4, 6, -1234608722381329822495008002784697604112384000000⟩, + ⟨7, 3, 8, 7, 5, 6, -543566606501163375770022664539281272759910400000⟩ +] + +def collectedFourData_8_4_54 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 4, 7, 3818327639731821099239250280548782339071672320000000⟩, + ⟨7, 4, 1, 0, 5, 7, -3164257927694594638237070621869302735062433792000000⟩, + ⟨7, 4, 2, 0, 6, 7, 540036716537359569298991137188748621348287283200000⟩, + ⟨7, 4, 3, 0, 7, 7, -25725974696798414639805578840286328222069555200000⟩, + ⟨7, 4, 4, 0, 8, 7, 14184281781789004368850355100328129547835801600000⟩, + ⟨7, 4, 0, 1, 3, 7, 3001063122235946011715277175417881323617910784000000⟩, + ⟨7, 4, 1, 1, 4, 7, -1382196552167047136493681510818492644558110720000000⟩, + ⟨7, 4, 2, 1, 5, 7, -263693226586273475528343465630498802833240883200000⟩, + ⟨7, 4, 3, 1, 6, 7, 121984996979455237970542738727183953443579494400000⟩, + ⟨7, 4, 4, 1, 7, 7, -16542386386171718014082718013294034330163609600000⟩, + ⟨7, 4, 5, 1, 8, 7, -10150162951420717656178547588662527598264320000000⟩, + ⟨7, 4, 0, 2, 2, 7, 2503482027517839876498989536773552771302424576000000⟩, + ⟨7, 4, 1, 2, 3, 7, -2087721943375766898123980236839508007687553024000000⟩, + ⟨7, 4, 2, 2, 4, 7, -971479426197232551190210881678407973297822105600000⟩, + ⟨7, 4, 3, 2, 5, 7, 51910630061064304577455203789250356914316902400000⟩, + ⟨7, 4, 4, 2, 6, 7, 10906283016762974554120586714724850062065664000000⟩, + ⟨7, 4, 5, 2, 7, 7, -5202855956617855230369403495951984855351296000000⟩, + ⟨7, 4, 6, 2, 8, 7, 1024725468616112884226640734355808371867648000000⟩, + ⟨7, 4, 0, 3, 1, 7, 8025010274009670732195799180558626012096626688000000⟩, + ⟨7, 4, 1, 3, 2, 7, 5379665045029649677126428762712937747032571904000000⟩, + ⟨7, 4, 2, 3, 3, 7, 1106609741253570537149845588598295841298448384000000⟩, + ⟨7, 4, 3, 3, 4, 7, -5656114295782095413946194659608342519663820800000⟩, + ⟨7, 4, 4, 3, 5, 7, 29923513293787826239320227996208607377594777600000⟩, + ⟨7, 4, 5, 3, 6, 7, 3559871964867290861667551751944610370289664000000⟩, + ⟨7, 4, 6, 3, 7, 7, 2172692122311933400113207316298191601664000000⟩, + ⟨7, 4, 7, 3, 8, 7, -34773839323314769055537366111943699883622400000⟩, + ⟨7, 4, 0, 4, 0, 7, 25627288942178668952601559686412701773668024320000000⟩, + ⟨7, 4, 1, 4, 1, 7, -2421970030135074426058353289375467050392092672000000⟩, + ⟨7, 4, 2, 4, 2, 7, -263855137857286237210582834707089683787022336000000⟩, + ⟨7, 4, 3, 4, 3, 7, -83529329633125332010460198971698308006176358400000⟩, + ⟨7, 4, 4, 4, 4, 7, -22426649415098004818411525318369307267170304000000⟩, + ⟨7, 4, 5, 4, 5, 7, 2158534905113013635844638445889642567827456000000⟩, + ⟨7, 4, 6, 4, 6, 7, 439076758060424377891461764907391845924864000000⟩, + ⟨7, 4, 7, 4, 7, 7, -91979685826738074169020287598817977355468800000⟩, + ⟨7, 4, 8, 4, 8, 7, 8956679588049344016971215271098520174592000000⟩, + ⟨7, 4, 1, 5, 0, 7, -12765262792414662789488626713913505772384288768000000⟩, + ⟨7, 4, 2, 5, 1, 7, 273275324150214948979990792154187243204064051200000⟩, + ⟨7, 4, 3, 5, 2, 7, -104302026242229145473252930741361104865827225600000⟩, + ⟨7, 4, 4, 5, 3, 7, -21369993149169673299802860581004047008609075200000⟩, + ⟨7, 4, 5, 5, 4, 7, 1431835280380495997493456212594286208745472000000⟩, + ⟨7, 4, 6, 5, 5, 7, 366796509785565857158876887407328831209472000000⟩, + ⟨7, 4, 7, 5, 6, 7, 29138986166979520848482245764117392523264000000⟩, + ⟨7, 4, 8, 5, 7, 7, -14684496227032559089237694854792257680179200000⟩, + ⟨7, 4, 2, 6, 0, 7, -4919524450551710858628397637016257958863752396800000⟩, + ⟨7, 4, 3, 6, 1, 7, -25393573542281986872151687801942386657774796800000⟩, + ⟨7, 4, 4, 6, 2, 7, 27067180765688701179347536825484446948078387200000⟩, + ⟨7, 4, 5, 6, 3, 7, -13047675408284458218159512994687465314844672000000⟩, + ⟨7, 4, 6, 6, 4, 7, -244564603893725275081511768646696988311552000000⟩, + ⟨7, 4, 7, 6, 5, 7, 182051433169091444404378636638712275507609600000⟩, + ⟨7, 4, 8, 6, 6, 7, 21934768161599143274179010031234785162035200000⟩, + ⟨7, 4, 3, 7, 0, 7, 2669119551683672687319332470141033120186918502400000⟩, + ⟨7, 4, 4, 7, 1, 7, 26001202235300085907163581119596663334449971200000⟩, + ⟨7, 4, 5, 7, 2, 7, 722837554438733476805287869316125966729216000000⟩, + ⟨7, 4, 6, 7, 3, 7, -1234608722381329822495008002784697604112384000000⟩, + ⟨7, 4, 7, 7, 4, 7, 141561288937257337190499074085967041134592000000⟩, + ⟨7, 4, 8, 7, 5, 7, 56659827850071868475277899888244012613632000000⟩ +] + +def collectedFourData_8_4_55 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 4, 8, 4202779714765299985038138168270612037348884480000000⟩, + ⟨7, 5, 1, 0, 5, 8, -2786283480216832462061405569419948863101757030400000⟩, + ⟨7, 5, 2, 0, 6, 8, 396273896434772101603229318962660270337635123200000⟩, + ⟨7, 5, 3, 0, 7, 8, -16180697011093067141456395617906878014134681600000⟩, + ⟨7, 5, 4, 0, 8, 8, 7806220074032824467381582409346894267626291200000⟩, + ⟨7, 5, 0, 1, 3, 8, 3303228115267055989751621497795132593983717376000000⟩, + ⟨7, 5, 1, 1, 4, 8, -1217091497506840721534088197135667152409329664000000⟩, + ⟨7, 5, 2, 1, 5, 8, -193495625691537429628552567631616333350908723200000⟩, + ⟨7, 5, 3, 1, 6, 8, 76724100808095210881513388749440230511293235200000⟩, + ⟨7, 5, 4, 1, 7, 8, -9103986417270251431827913305067206326039347200000⟩, + ⟨7, 5, 5, 1, 8, 8, -4965396486369085100951124378976363877498880000000⟩, + ⟨7, 5, 0, 2, 2, 8, 2755547578486601973434985757125059034338033664000000⟩, + ⟨7, 5, 1, 2, 3, 8, -1838341024984711624126037192049373585058090188800000⟩, + ⟨7, 5, 2, 2, 4, 8, -712862525336759620777121579405667617530812825600000⟩, + ⟨7, 5, 3, 2, 5, 8, 32649887383180568702191648203281511438562099200000⟩, + ⟨7, 5, 4, 2, 6, 8, 6002196426176782266823883875568944674766848000000⟩, + ⟨7, 5, 5, 2, 7, 8, -2545204723285624309386530149008176698097664000000⟩, + ⟨7, 5, 6, 2, 8, 8, 451160384236240608094076261669355586899148800000⟩, + ⟨7, 5, 0, 3, 1, 8, 8833016328782040936952455535673573852087058432000000⟩, + ⟨7, 5, 1, 3, 2, 8, 4737057530258569297978097905024318870267940044800000⟩, + ⟨7, 5, 2, 3, 3, 8, 812019887853107947437487847251981753525469184000000⟩, + ⟨7, 5, 3, 3, 4, 8, -3557488987639862843482301580916812306343526400000⟩, + ⟨7, 5, 4, 3, 5, 8, 16468195834875252864342400956844246285103923200000⟩, + ⟨7, 5, 5, 3, 6, 8, 1741467189332337174040148200109649980030976000000⟩, + ⟨7, 5, 6, 3, 7, 8, 956580706492154102176800567195387455078400000⟩, + ⟨7, 5, 7, 3, 8, 8, -13918210017276262629162427070156091319910400000⟩, + ⟨7, 5, 0, 4, 0, 8, 28207597742498146449584771590068332654997012480000000⟩, + ⟨7, 5, 1, 4, 1, 8, -2132662772362009678776586630607118547294774886400000⟩, + ⟨7, 5, 2, 4, 2, 8, -193614434669290509476548919053394425241665536000000⟩, + ⟨7, 5, 3, 4, 3, 8, -52536892781035035729263376576829920596144947200000⟩, + ⟨7, 5, 4, 4, 4, 8, -12342349337856571390372798186696352703971328000000⟩, + ⟨7, 5, 5, 4, 5, 8, 1055941829195263235948151067182866160943104000000⟩, + ⟨7, 5, 6, 4, 6, 8, 193314253370972639522738686109608017552998400000⟩, + ⟨7, 5, 7, 4, 7, 8, -36814818540939779061642174216148892830924800000⟩, + ⟨7, 5, 8, 4, 8, 8, 3286163894773406269148714198398975082496000000⟩, + ⟨7, 5, 1, 5, 0, 8, -11240436668525732529155379519132540233026476441600000⟩, + ⟨7, 5, 2, 5, 1, 8, 200526879347822003546178266312047734503453491200000⟩, + ⟨7, 5, 3, 5, 2, 8, -65602159069161282337714284602120894535224524800000⟩, + ⟨7, 5, 4, 5, 3, 8, -11760825967034058015710107943319801279440486400000⟩, + ⟨7, 5, 5, 5, 4, 8, 700444899681681878982811025518372740661248000000⟩, + ⟨7, 5, 6, 5, 5, 8, 161491110897100418489684778329059710153523200000⟩, + ⟨7, 5, 7, 5, 6, 8, 11662863148119852667866657967042612690944000000⟩, + ⟨7, 5, 8, 5, 7, 8, -5387673058953334800469553843042296371609600000⟩, + ⟨7, 5, 2, 6, 0, 8, -3609901073256735584126125202327130997781220556800000⟩, + ⟨7, 5, 3, 6, 1, 8, -15971628844356620917024383745764538506962534400000⟩, + ⟨7, 5, 4, 6, 2, 8, 14896233245441410641368150548899828429383270400000⟩, + ⟨7, 5, 5, 6, 3, 8, -6382841530491069708506391360120126122754048000000⟩, + ⟨7, 5, 6, 6, 4, 8, -107675532659774586622031197273398267032371200000⟩, + ⟨7, 5, 7, 6, 5, 8, 72865985755409382534779737185039356107161600000⟩, + ⟨7, 5, 8, 6, 6, 8, 8047763958090943393041249998131657546137600000⟩, + ⟨7, 5, 3, 7, 0, 8, 1678778559848028726247194777498301187237294899200000⟩, + ⟨7, 5, 4, 7, 1, 8, 14309579431704350808331806667149498676307558400000⟩, + ⟨7, 5, 5, 7, 2, 8, 353607628784258372738498471818086731218944000000⟩, + ⟨7, 5, 6, 7, 3, 8, -543566606501163375770022664539281272759910400000⟩, + ⟨7, 5, 7, 7, 4, 8, 56659827850071868475277899888244012613632000000⟩, + ⟨7, 5, 8, 7, 5, 8, 20788226120471678413044683227307773526016000000⟩ +] + +def collectedFourData_8_4 : List (List CollectedFourTerm) := [ + collectedFourData_8_4_0, + collectedFourData_8_4_1, + collectedFourData_8_4_2, + collectedFourData_8_4_3, + collectedFourData_8_4_4, + collectedFourData_8_4_5, + collectedFourData_8_4_6, + collectedFourData_8_4_7, + collectedFourData_8_4_8, + collectedFourData_8_4_9, + collectedFourData_8_4_10, + collectedFourData_8_4_11, + collectedFourData_8_4_12, + collectedFourData_8_4_13, + collectedFourData_8_4_14, + collectedFourData_8_4_15, + collectedFourData_8_4_16, + collectedFourData_8_4_17, + collectedFourData_8_4_18, + collectedFourData_8_4_19, + collectedFourData_8_4_20, + collectedFourData_8_4_21, + collectedFourData_8_4_22, + collectedFourData_8_4_23, + collectedFourData_8_4_24, + collectedFourData_8_4_25, + collectedFourData_8_4_26, + collectedFourData_8_4_27, + collectedFourData_8_4_28, + collectedFourData_8_4_29, + collectedFourData_8_4_30, + collectedFourData_8_4_31, + collectedFourData_8_4_32, + collectedFourData_8_4_33, + collectedFourData_8_4_34, + collectedFourData_8_4_35, + collectedFourData_8_4_36, + collectedFourData_8_4_37, + collectedFourData_8_4_38, + collectedFourData_8_4_39, + collectedFourData_8_4_40, + collectedFourData_8_4_41, + collectedFourData_8_4_42, + collectedFourData_8_4_43, + collectedFourData_8_4_44, + collectedFourData_8_4_45, + collectedFourData_8_4_46, + collectedFourData_8_4_47, + collectedFourData_8_4_48, + collectedFourData_8_4_49, + collectedFourData_8_4_50, + collectedFourData_8_4_51, + collectedFourData_8_4_52, + collectedFourData_8_4_53, + collectedFourData_8_4_54, + collectedFourData_8_4_55 +] + +theorem collectedFourChecked_8_4 : collectNumericRowParts 8 4 = collectedFourData_8_4 := by + decide +kernel + +def collectedFourData_8_5_0 : List CollectedFourTerm := [ + ⟨0, 5, 3, 0, 8, 0, -3142158857000482201351096466105449464145851187200000⟩, + ⟨0, 5, 3, 1, 7, 0, 41975226515405880467123648296007570682849892761600000⟩, + ⟨0, 5, 4, 1, 8, 0, -65341630359759375672236861404773549337354646323200000⟩, + ⟨0, 5, 3, 2, 6, 0, -13663812227255726045178399779308033813339806105600000⟩, + ⟨0, 5, 4, 2, 7, 0, 8859769464057849753802834686667269164821905408000000⟩, + ⟨0, 5, 5, 2, 8, 0, -55260741709806425585753961125881915156690108416000000⟩, + ⟨0, 5, 3, 3, 5, 0, -27293024146426962612657421845504651108660176486400000⟩, + ⟨0, 5, 4, 3, 6, 0, 7215638668895064210200137878434780838470929612800000⟩, + ⟨0, 5, 5, 3, 7, 0, 4353374505069030420219138147644932022952001536000000⟩, + ⟨0, 5, 6, 3, 8, 0, -18804944436761841739802011152381248001986789376000000⟩, + ⟨0, 5, 3, 4, 4, 0, 11161887877377388016491718258514953999755090329600000⟩, + ⟨0, 5, 4, 4, 5, 0, -18658857862137120813647738156188093428078634598400000⟩, + ⟨0, 5, 5, 4, 6, 0, 10661375739988814383442674636871230136443207680000000⟩, + ⟨0, 5, 6, 4, 7, 0, 8205658599196048929196787645750918160687562752000000⟩, + ⟨0, 5, 7, 4, 8, 0, -12039447206159242430300086195060570866560532480000000⟩, + ⟨0, 5, 3, 5, 3, 0, 28102153702204333432134111956488546326047568691200000⟩, + ⟨0, 5, 4, 5, 4, 0, -2605685024978229081626533685174394880322961408000000⟩, + ⟨0, 5, 5, 5, 5, 0, 2934024682634560826403279894979070637889290240000000⟩, + ⟨0, 5, 6, 5, 6, 0, 13897786563571149856131164928253827654623428608000000⟩, + ⟨0, 5, 7, 5, 7, 0, -5491624611121071167179937146705630871634837504000000⟩, + ⟨0, 5, 8, 5, 8, 0, -6630184851276123334467490443841173136007076249600000⟩, + ⟨0, 5, 3, 6, 2, 0, 31426107050875943872249410744610076232004298342400000⟩, + ⟨0, 5, 4, 6, 3, 0, 65132396007636868510564604408594382165091811328000000⟩, + ⟨0, 5, 5, 6, 4, 0, -24466965559382655942568668023382126995812909056000000⟩, + ⟨0, 5, 6, 6, 5, 0, -1321924410312043662026858143934416307500351488000000⟩, + ⟨0, 5, 7, 6, 6, 0, -1660263884183180300353301967743310637100433408000000⟩, + ⟨0, 5, 8, 6, 7, 0, -1787216317942996108503714941751899458900485734400000⟩, + ⟨0, 5, 3, 7, 1, 0, -288896645340428661212884147248952421194206806016000000⟩, + ⟨0, 5, 4, 7, 2, 0, -66933816695952804786540942159238575060613595136000000⟩, + ⟨0, 5, 5, 7, 3, 0, -34111759340605101101614860655917279506482593792000000⟩, + ⟨0, 5, 6, 7, 4, 0, -45875589943310983710672134636440897977109708800000000⟩, + ⟨0, 5, 7, 7, 5, 0, 5964558903794837811606105060474852611261988864000000⟩, + ⟨0, 5, 8, 7, 6, 0, -2672009957201978239989536979380456436783277670400000⟩ +] + +def collectedFourData_8_5_1 : List CollectedFourTerm := [ + ⟨0, 6, 2, 0, 7, 1, -6200455941958884784349150515918734915935404032000000⟩, + ⟨0, 6, 3, 0, 8, 1, 3777860355414456583290423351117857551229229465600000⟩, + ⟨0, 6, 2, 1, 6, 1, 14272335322599165765236098313348731139887045017600000⟩, + ⟨0, 6, 3, 1, 7, 1, -50467386080368770506524952248011788079529249996800000⟩, + ⟨0, 6, 4, 1, 8, 1, 39280565707923200534974478457256126538461269196800000⟩, + ⟨0, 6, 2, 2, 5, 1, 29928760731105889506397367783798444115691044864000000⟩, + ⟨0, 6, 3, 2, 6, 1, 16428187391662735754895159824176720251085180108800000⟩, + ⟨0, 6, 4, 2, 7, 1, -5326110699623771643812467094575270914416443392000000⟩, + ⟨0, 6, 5, 2, 8, 1, 22146913933728351312777491670487848257329299456000000⟩, + ⟨0, 6, 2, 3, 4, 1, -2205183458336392257087624940452487055997822566400000⟩, + ⟨0, 6, 3, 3, 5, 1, 32814774362039865244242657972425703327391757107200000⟩, + ⟨0, 6, 4, 3, 6, 1, -4337730284622910834112407785740444786467484467200000⟩, + ⟨0, 6, 5, 3, 7, 1, -1744707137507380474830493209906242205700325376000000⟩, + ⟨0, 6, 6, 3, 8, 1, 5652360153206227377175998353021026436867162112000000⟩, + ⟨0, 6, 2, 4, 3, 1, -46904026138056441561228802357337634210195072614400000⟩, + ⟨0, 6, 3, 4, 4, 1, -13420089697113229781017717956713440223534304460800000⟩, + ⟨0, 6, 4, 4, 5, 1, 11216899368030639509660440788395768547294943641600000⟩, + ⟨0, 6, 5, 4, 6, 1, -4272772380953603110078525159675988888392826880000000⟩, + ⟨0, 6, 6, 4, 7, 1, -2466443751157209558842363147673987565668532224000000⟩, + ⟨0, 6, 7, 4, 8, 1, 2895038244162673280860839891917055296387678208000000⟩, + ⟨0, 6, 2, 5, 2, 1, 6379998017673319135194056126714965843839339724800000⟩, + ⟨0, 6, 3, 5, 3, 1, -33787601838395867444114296710152495069226703257600000⟩, + ⟨0, 6, 4, 5, 4, 1, 1566425283150613959138951483587915206876987392000000⟩, + ⟨0, 6, 5, 5, 5, 1, -1175872601692046270093860873106989502001315840000000⟩, + ⟨0, 6, 6, 5, 6, 1, -4177374480092932014926910140161135735625220096000000⟩, + ⟨0, 6, 7, 5, 7, 1, 1320531001095050175020290940372419276679046758400000⟩, + ⟨0, 6, 8, 5, 8, 1, 1328593579480171041614551018770227337758559436800000⟩, + ⟨0, 6, 2, 6, 1, 1, -107054271114801085932913074579955103053020502425600000⟩, + ⟨0, 6, 3, 6, 2, 1, -37784036185187925977385739895376495680165196595200000⟩, + ⟨0, 6, 4, 6, 3, 1, -39154783053409510051813624559116439547619049472000000⟩, + ⟨0, 6, 5, 6, 4, 1, 9805655221000861087131817462093975082495901696000000⟩, + ⟨0, 6, 6, 6, 5, 1, 397341927147171669001484945062807383526342656000000⟩, + ⟨0, 6, 7, 6, 6, 1, 399231572497233112444288324458507530767486156800000⟩, + ⟨0, 6, 8, 6, 7, 1, 358132416881896664577158306517810027896714035200000⟩, + ⟨0, 6, 2, 7, 0, 1, 873345965281341770024895413471034458254393265356800000⟩, + ⟨0, 6, 3, 7, 1, 1, 347344368287509705792719096745786644740249223168000000⟩, + ⟨0, 6, 4, 7, 2, 1, 40237719357958537766450116122438162160721854464000000⟩, + ⟨0, 6, 5, 7, 3, 1, 13671010827391258133878038991103218297992118272000000⟩, + ⟨0, 6, 6, 7, 4, 1, 13789211527447139057490678018646384014104985600000000⟩, + ⟨0, 6, 7, 7, 5, 1, -1434254068344028955629284984374888346297984614400000⟩, + ⟨0, 6, 8, 7, 6, 1, 535432322488317534517379435630632358099759923200000⟩ +] + +def collectedFourData_8_5_2 : List CollectedFourTerm := [ + ⟨0, 7, 1, 0, 6, 2, -6200455941958884784349150515918734915935404032000000⟩, + ⟨0, 7, 2, 0, 7, 2, 605032072930613544970569357483345429512847360000000⟩, + ⟨0, 7, 3, 0, 8, 2, -184319242284356332733741479145440376776556544000000⟩, + ⟨0, 7, 1, 1, 5, 2, -1350049133512698570097902301720412580067934208000000⟩, + ⟨0, 7, 2, 1, 6, 2, -1392675104319005964356966256102222539991810048000000⟩, + ⟨0, 7, 3, 1, 7, 2, 2462269509002309292839090433097739072157253632000000⟩, + ⟨0, 7, 4, 1, 8, 2, -1277648091184492857457231436124667365543641088000000⟩, + ⟨0, 7, 1, 2, 4, 2, 1173805487139480556233340577592663304398962688000000⟩, + ⟨0, 7, 2, 2, 5, 2, -2920407840147413226816727229321863899088158720000000⟩, + ⟨0, 7, 3, 2, 6, 2, -801520111191218556150577044284783131216576512000000⟩, + ⟨0, 7, 4, 2, 7, 2, 173238217071782510170490804153319206651166720000000⟩, + ⟨0, 7, 5, 2, 8, 2, -540266448619674985673593475643435683382558720000000⟩, + ⟨0, 7, 1, 3, 3, 2, -3250787460165476358909189779749974725929992192000000⟩, + ⟨0, 7, 2, 3, 4, 2, 215178808055211530584576970174073763918774272000000⟩, + ⟨0, 7, 3, 3, 5, 2, -1601010566066770634684274458188304032179683328000000⟩, + ⟨0, 7, 4, 3, 6, 2, 141089944056069055465034215244168874952753152000000⟩, + ⟨0, 7, 5, 3, 7, 2, 42561538455566979556419100731211666025349120000000⟩, + ⟨0, 7, 6, 3, 8, 2, -110309925994388791188672243888071348324401152000000⟩, + ⟨0, 7, 1, 4, 2, 2, 5604629144775682697617048350069264723744915456000000⟩, + ⟨0, 7, 2, 4, 3, 2, 4576831192535574076649855625335993600481165312000000⟩, + ⟨0, 7, 3, 4, 4, 2, 654757066606459892805387646952425317300436992000000⟩, + ⟨0, 7, 4, 4, 5, 2, -364843270668124935326618741980024760073977856000000⟩, + ⟨0, 7, 5, 4, 6, 2, 104232832029135878477109480838174841870745600000000⟩, + ⟨0, 7, 6, 4, 7, 2, 48134446547102008280332764088320302518370304000000⟩, + ⟨0, 7, 7, 4, 8, 2, -47082316915492640317508947389537799781744640000000⟩, + ⟨0, 7, 1, 5, 1, 2, 2541204167617530656011318381501044194977775616000000⟩, + ⟨0, 7, 2, 5, 2, 2, -622551544928256795061245420485486195930824704000000⟩, + ⟨0, 7, 3, 5, 3, 2, 1648474158271376964802073431381134490283802624000000⟩, + ⟨0, 7, 4, 5, 4, 2, -50949884171266518122748837876314231506206720000000⟩, + ⟨0, 7, 5, 5, 5, 2, 28685013020159042079773833959594420653260800000000⟩, + ⟨0, 7, 6, 5, 6, 2, 81524506093001448227351977654992931878076416000000⟩, + ⟨0, 7, 7, 5, 7, 2, -21475937050452432658859708744958739136643072000000⟩, + ⟨0, 7, 8, 5, 8, 2, -18520336822226779366096112833682944768868352000000⟩, + ⟨0, 7, 1, 6, 0, 2, -27704433226685278036085820470366287055969845248000000⟩, + ⟨0, 7, 2, 6, 1, 2, 10446210435970146246873369372163993453763493888000000⟩, + ⟨0, 7, 3, 6, 2, 2, 1843457477224434628884331030487082491285864448000000⟩, + ⟨0, 7, 4, 6, 3, 2, 1273556857630513783356434395444553465745899520000000⟩, + ⟨0, 7, 5, 6, 4, 2, -239205631018915819421658271223130151735787520000000⟩, + ⟨0, 7, 6, 6, 5, 2, -7754417162043346582426342640176830848434176000000⟩, + ⟨0, 7, 7, 6, 6, 2, -6492745806341413107513832682329381319737344000000⟩, + ⟨0, 7, 8, 6, 7, 2, -4992296432898616384486333011681857375305728000000⟩, + ⟨0, 7, 2, 7, 0, 2, -85219913617001182446371939036378297785399640064000000⟩, + ⟨0, 7, 3, 7, 1, 2, -16946695947280065120601839922575477739691704320000000⟩, + ⟨0, 7, 4, 7, 2, 2, -1308780675756492771336290054637382181050122240000000⟩, + ⟨0, 7, 5, 7, 3, 2, -333499669112246179560743596084172310592880640000000⟩, + ⟨0, 7, 6, 7, 4, 2, -269106508057673939904322126623105737136537600000000⟩, + ⟨0, 7, 7, 7, 5, 2, 23325427468623722990337599933034454478487552000000⟩, + ⟨0, 7, 8, 7, 6, 2, -7463822730402401987785058305656247233282048000000⟩ +] + +def collectedFourData_8_5_3 : List CollectedFourTerm := [ + ⟨0, 8, 0, 0, 5, 3, -3142158857000482201351096466105449464145851187200000⟩, + ⟨0, 8, 1, 0, 6, 3, 3777860355414456583290423351117857551229229465600000⟩, + ⟨0, 8, 2, 0, 7, 3, -184319242284356332733741479145440376776556544000000⟩, + ⟨0, 8, 3, 0, 8, 3, 37434470662819907861225069122979733080270438400000⟩, + ⟨0, 8, 0, 1, 4, 3, -2259159189495744359539475598315458494789897420800000⟩, + ⟨0, 8, 1, 1, 5, 3, 822568073558143287895612965378401206582797926400000⟩, + ⟨0, 8, 2, 1, 6, 3, 424269772564279689668396442131455271826043699200000⟩, + ⟨0, 8, 3, 1, 7, 3, -500076685192221840587944463231239801667793715200000⟩, + ⟨0, 8, 4, 1, 8, 3, 194613755707614403271021506533263909676751257600000⟩, + ⟨0, 8, 0, 2, 3, 3, -884278968823040993928202890771204477391208448000000⟩, + ⟨0, 8, 1, 2, 4, 3, -715185021285907614100920103968313759634974310400000⟩, + ⟨0, 8, 2, 2, 5, 3, 889684009064089495341757491492540004788338688000000⟩, + ⟨0, 8, 3, 2, 6, 3, 162785397314941013859327687062320599786533683200000⟩, + ⟨0, 8, 4, 2, 7, 3, -26387970434937365218942310857046979923410944000000⟩, + ⟨0, 8, 5, 2, 8, 3, 65835519732957270182611186745739375684039475200000⟩, + ⟨0, 8, 0, 3, 2, 3, 3885579360307839579863421249313829121936693657600000⟩, + ⟨0, 8, 1, 3, 3, 3, 1980664193826641752987624722874763382435191193600000⟩, + ⟨0, 8, 2, 3, 4, 3, -65552879972589522813403666935911131925761228800000⟩, + ⟨0, 8, 3, 3, 5, 3, 325158579882996252088287093771253581014158540800000⟩, + ⟨0, 8, 4, 3, 6, 3, -21491085139001592487003251499492608951346790400000⟩, + ⟨0, 8, 5, 3, 7, 3, -5186442748787151674968076091423439348511539200000⟩, + ⟨0, 8, 6, 3, 8, 3, 11201743337475880691093075339836572275677593600000⟩, + ⟨0, 8, 0, 4, 1, 3, 3207195330919534170333706168835386077842767872000000⟩, + ⟨0, 8, 1, 4, 2, 3, -3414830530375355414630578520395474790383406284800000⟩, + ⟨0, 8, 2, 4, 3, 3, -1394303038160275761692505006150469382187044044800000⟩, + ⟨0, 8, 3, 4, 4, 3, -132978434033166669536646738312752749578761011200000⟩, + ⟨0, 8, 4, 4, 5, 3, 55573611888346312472843710739589823999456051200000⟩, + ⟨0, 8, 5, 4, 6, 3, -12701552516186164007429628591684404637597696000000⟩, + ⟨0, 8, 6, 4, 7, 3, -4887952838799983925654913002800065908257587200000⟩, + ⟨0, 8, 7, 4, 8, 3, 4098095370061844440412985642081667006857216000000⟩, + ⟨0, 8, 0, 5, 0, 3, -19846898241527132635849904009553387251516728934400000⟩, + ⟨0, 8, 1, 5, 1, 3, -1548323957096496104494027746343393087563025612800000⟩, + ⟨0, 8, 2, 5, 2, 3, 189656440010398091980796022900631426356058521600000⟩, + ⟨0, 8, 3, 5, 3, 3, -334798237836853753053152222692360028470797926400000⟩, + ⟨0, 8, 4, 5, 4, 3, 7760782002378699781190862346093408177618944000000⟩, + ⟨0, 8, 5, 5, 5, 3, -3495484025620544962611660145351181287292928000000⟩, + ⟨0, 8, 6, 5, 6, 3, -8278643873034091354198379865149780261653708800000⟩, + ⟨0, 8, 7, 5, 7, 3, 1869288598353547084889264339581328474033356800000⟩, + ⟨0, 8, 8, 5, 8, 3, 1410526235984926639412287466040579929092915200000⟩, + ⟨0, 8, 1, 6, 0, 3, 16879965108381274600373646298488333932983379558400000⟩, + ⟨0, 8, 2, 6, 1, 3, -3182372767404954656515676130122491850701091635200000⟩, + ⟨0, 8, 3, 6, 2, 3, -374398538069354155197980627706044063377312972800000⟩, + ⟨0, 8, 4, 6, 3, 3, -193990571332424893027375526313791675122581504000000⟩, + ⟨0, 8, 5, 6, 4, 3, 29149000611486096905552089892646337478079283200000⟩, + ⟨0, 8, 6, 6, 5, 3, 787444919375126787348277095640624494595276800000⟩, + ⟨0, 8, 7, 6, 6, 3, 565135559826299881331323576775848360515993600000⟩, + ⟨0, 8, 8, 6, 7, 3, 380217982211124802681486687310689791167692800000⟩, + ⟨0, 8, 2, 7, 0, 3, 25961714441583578173753335909343612124261882265600000⟩, + ⟨0, 8, 3, 7, 1, 3, 3441803386384835701204871953895316010882301952000000⟩, + ⟨0, 8, 4, 7, 2, 3, 199355929433107755237142567344863289853083648000000⟩, + ⟨0, 8, 5, 7, 3, 3, 40639436527790378939695670158021000725685862400000⟩, + ⟨0, 8, 6, 7, 4, 3, 27327205657447246553750227497862339158343680000000⟩, + ⟨0, 8, 7, 7, 5, 3, -2030270228320603336182419608174119835454668800000⟩, + ⟨0, 8, 8, 7, 6, 3, 568451744859110037164953538522616131538124800000⟩ +] + +def collectedFourData_8_5_4 : List CollectedFourTerm := [ + ⟨1, 4, 3, 0, 8, 0, -2259159189495744359539475598315458494789897420800000⟩, + ⟨1, 4, 3, 1, 7, 0, 30179479469083403545299149923338811731851241062400000⟩, + ⟨1, 4, 4, 1, 8, 0, -46979529489734471588559533357847855185961733324800000⟩, + ⟨1, 4, 3, 2, 6, 0, -9824050393879990396337491035473936254604043878400000⟩, + ⟨1, 4, 4, 2, 7, 0, 6370024722635150207169825091094251419532787712000000⟩, + ⟨1, 4, 5, 2, 8, 0, -39731540680675649295253876124873975556760141824000000⟩, + ⟨1, 4, 3, 3, 5, 0, -19623223750179812927932158509267761022201600409600000⟩, + ⟨1, 4, 4, 3, 6, 0, 5187922428109312913263095685896526623816233779200000⟩, + ⟨1, 4, 5, 3, 7, 0, 3130002799359319189707899166003587216786325504000000⟩, + ⟨1, 4, 6, 3, 8, 0, -13520437688125731108984078537212179908095115264000000⟩, + ⟨1, 4, 3, 4, 4, 0, 8025209010078513846656909306536624652848359014400000⟩, + ⟨1, 4, 4, 4, 5, 0, -13415403906402662912491170693274354040499181977600000⟩, + ⟨1, 4, 5, 4, 6, 0, 7665349230196169365043951538590536112296427520000000⟩, + ⟨1, 4, 6, 4, 7, 0, 5899730049910613433999717619650127545162006528000000⟩, + ⟨1, 4, 7, 4, 8, 0, -8656159357330463564904498131573040690726174720000000⟩, + ⟨1, 4, 3, 5, 3, 0, 20204974245497553706822286557741764774374198476800000⟩, + ⟨1, 4, 4, 5, 4, 0, -1873443558079823407081846413585406064131571712000000⟩, + ⟨1, 4, 5, 5, 5, 0, 2109514230705932063733938541924666427425423360000000⟩, + ⟨1, 4, 6, 5, 6, 0, 9992273993019642820601255884501135206238912512000000⟩, + ⟨1, 4, 7, 5, 7, 0, -3948385415917008656748108718411576535527981056000000⟩, + ⟨1, 4, 8, 5, 8, 0, -4766991013660780837019378791699057986675041894400000⟩, + ⟨1, 4, 3, 6, 2, 0, 22594840606447575017728568379229344183378090393600000⟩, + ⟨1, 4, 4, 6, 3, 0, 46829093521704839305245036367266115196490350592000000⟩, + ⟨1, 4, 5, 6, 4, 0, -17591335320111961463866585070525285650120310784000000⟩, + ⟨1, 4, 6, 6, 5, 0, -950441341538684039388114897853525858380152832000000⟩, + ⟨1, 4, 7, 6, 6, 0, -1193701713261200143751648065927139137224179712000000⟩, + ⟨1, 4, 8, 6, 7, 0, -1284978370619995686395086787491446733837801881600000⟩, + ⟨1, 4, 3, 7, 1, 0, -207711812431519647600953794159430231326640308224000000⟩, + ⟨1, 4, 4, 7, 2, 0, -48124284594902725040121267800198691222039035904000000⟩, + ⟨1, 4, 5, 7, 3, 0, -24525779278314661255573667021099172858679001088000000⟩, + ⟨1, 4, 6, 7, 4, 0, -32983774949209596269846330999869525388899123200000000⟩, + ⟨1, 4, 7, 7, 5, 0, 4288417190867286365842810760332940061595140096000000⟩, + ⟨1, 4, 8, 7, 6, 0, -1921130065015058964364010744890619594240792985600000⟩ +] + +def collectedFourData_8_5_5 : List CollectedFourTerm := [ + ⟨1, 5, 2, 0, 7, 1, -1350049133512698570097902301720412580067934208000000⟩, + ⟨1, 5, 3, 0, 8, 1, 822568073558143287895612965378401206582797926400000⟩, + ⟨1, 5, 2, 1, 6, 1, 3107570494145034179931866935056988193197287014400000⟩, + ⟨1, 5, 3, 1, 7, 1, -10988458185371374492794632594075664543948944179200000⟩, + ⟨1, 5, 4, 1, 8, 1, 8552708735338028541380558753623207882091868979200000⟩, + ⟨1, 5, 2, 2, 5, 1, 6516504249100962738271685961437589432346607616000000⟩, + ⟨1, 5, 3, 2, 6, 1, 3576972461527021042002432844429053115673817907200000⟩, + ⟨1, 5, 4, 2, 7, 1, -1159674579148467715086902740013010825718530048000000⟩, + ⟨1, 5, 5, 2, 8, 1, 4822132798957405168699554791872002923339710464000000⟩, + ⟨1, 5, 2, 3, 4, 1, -480143080610784474020902928078674584992848281600000⟩, + ⟨1, 5, 3, 3, 5, 1, 7144887103236254178673802540631854505458977996800000⟩, + ⟨1, 5, 4, 3, 6, 1, -944470707797149965581238602855789284847045836800000⟩, + ⟨1, 5, 5, 3, 7, 1, -379881799221544822305343360750269040315858944000000⟩, + ⟨1, 5, 6, 3, 8, 1, 1230710128185662434517231095636403540855881728000000⟩, + ⟨1, 5, 2, 4, 3, 1, -10212594112221813344980119675881793866142685593600000⟩, + ⟨1, 5, 3, 4, 4, 1, -2922007774403527605416594294584152749879014195200000⟩, + ⟨1, 5, 4, 4, 5, 1, 2442298665495350549930513370564510372740884070400000⟩, + ⟨1, 5, 5, 4, 6, 1, -930327173453150630324841649670541143672094720000000⟩, + ⟨1, 5, 6, 4, 7, 1, -537028289576979745596298428467811902036115456000000⟩, + ⟨1, 5, 7, 4, 8, 1, 630347817903075461997616123813813385378660352000000⟩, + ⟨1, 5, 2, 5, 2, 1, 1389141520591376196214938059588975804674159411200000⟩, + ⟨1, 5, 3, 5, 3, 1, -7356704573403914140465533709683745635795625574400000⟩, + ⟨1, 5, 4, 5, 4, 1, 341063804988793322302841370736377467448066048000000⟩, + ⟨1, 5, 5, 5, 5, 1, -256027266687446485483513004555948136553512960000000⟩, + ⟨1, 5, 6, 5, 6, 1, -909555821378162633935796631629259974979354624000000⟩, + ⟨1, 5, 7, 5, 7, 1, 287524296679673192793064654659758165547653529600000⟩, + ⟨1, 5, 8, 5, 8, 1, 289279792898757982164633924687151745622815539200000⟩, + ⟨1, 5, 2, 6, 1, 1, -23309338427733495494411557608055768219948312166400000⟩, + ⟨1, 5, 3, 6, 2, 1, -8226863603244946257484202487995703599257406668800000⟩, + ⟨1, 5, 4, 6, 3, 1, -8525321593920249721404967713430684559178989568000000⟩, + ⟨1, 5, 5, 6, 4, 1, 2135023046459099127744534949104420131149185024000000⟩, + ⟨1, 5, 6, 6, 5, 1, 86514786892241413679248960824798192561291264000000⟩, + ⟨1, 5, 7, 6, 6, 1, 86926226646249372747473763193296398140519219200000⟩, + ⟨1, 5, 8, 6, 7, 1, 77977549331874471563778982347610797447630028800000⟩, + ⟨1, 5, 2, 7, 0, 1, 190156977925786401863000952790042823454232884019200000⟩, + ⟨1, 5, 3, 7, 1, 1, 75628625995674822787782094696202670352568942592000000⟩, + ⟨1, 5, 4, 7, 2, 1, 8761113482983164274303004048829731813789270016000000⟩, + ⟨1, 5, 5, 7, 3, 1, 2976641797720989865207288905678958258991136768000000⟩, + ⟨1, 5, 6, 7, 4, 1, 3002378091016966739616732348869502751368806400000000⟩, + ⟨1, 5, 7, 7, 5, 1, -312285657753288933769588294802446125339613593600000⟩, + ⟨1, 5, 8, 7, 6, 1, 116581740084371066338651064777578749300100300800000⟩ +] + +def collectedFourData_8_5_6 : List CollectedFourTerm := [ + ⟨1, 6, 1, 0, 6, 2, 14272335322599165765236098313348731139887045017600000⟩, + ⟨1, 6, 2, 0, 7, 2, -1392675104319005964356966256102222539991810048000000⟩, + ⟨1, 6, 3, 0, 8, 2, 424269772564279689668396442131455271826043699200000⟩, + ⟨1, 6, 1, 1, 5, 2, 3107570494145034179931866935056988193197287014400000⟩, + ⟨1, 6, 2, 1, 6, 2, 3205687818821441981565378836178408377780954726400000⟩, + ⟨1, 6, 3, 1, 7, 2, -5667701926447394194110006698630679322036902297600000⟩, + ⟨1, 6, 4, 1, 8, 2, 2940916305568154883361493056146625052298077798400000⟩, + ⟨1, 6, 1, 2, 4, 2, -2701889292139513102166093766842463412445144678400000⟩, + ⟨1, 6, 2, 2, 5, 2, 6722254034783665076265729075662935830923575296000000⟩, + ⟨1, 6, 3, 2, 6, 2, 1844955258421525808377383345982609143535081881600000⟩, + ⟨1, 6, 4, 2, 7, 2, -398763243845673079225375963758651125526429696000000⟩, + ⟨1, 6, 5, 2, 8, 2, 1243596275891564964429118087584570862045495296000000⟩, + ⟨1, 6, 1, 3, 3, 2, 7482728549043500445915470770770941530064132505600000⟩, + ⟨1, 6, 2, 3, 4, 2, -495302947336311532947453580370075749533194649600000⟩, + ⟨1, 6, 3, 3, 5, 2, 3685238612744710192335246235952877143431997030400000⟩, + ⟨1, 6, 4, 3, 6, 2, -324763696583706379717529491989950399159835033600000⟩, + ⟨1, 6, 5, 3, 7, 2, -97969012983848626097409571401650041327190016000000⟩, + ⟨1, 6, 6, 3, 8, 2, 253913626343037526740693639517709017613441433600000⟩, + ⟨1, 6, 1, 4, 2, 2, -12900849108812384016040799102767001026209565900800000⟩, + ⟨1, 6, 2, 4, 3, 2, -10535042923659933613515308409091885601130125721600000⟩, + ⟨1, 6, 3, 4, 4, 2, -1507133103907918764290991964524742792839797145600000⟩, + ⟨1, 6, 4, 4, 5, 2, 839803644750068019980205954609442137687510220800000⟩, + ⟨1, 6, 5, 4, 6, 2, -239925248121994679985491862081651305695150080000000⟩, + ⟨1, 6, 6, 4, 7, 2, -110796845928547503939336338413466313322345267200000⟩, + ⟨1, 6, 7, 4, 8, 2, 108375032590022663645352051982680831717015552000000⟩, + ⟨1, 6, 1, 5, 1, 2, -5849395325590460111708767895014938513536502988800000⟩, + ⟨1, 6, 2, 5, 2, 2, 1433001780512798160624171945245189021312955187200000⟩, + ⟨1, 6, 3, 5, 3, 2, -3794491272533021173072605544502710224135861043200000⟩, + ⟨1, 6, 4, 5, 4, 2, 117277477389859524493545791805178782412701696000000⟩, + ⟨1, 6, 5, 5, 5, 2, -66027745118932677530083433613986486487613440000000⟩, + ⟨1, 6, 6, 5, 6, 2, -187654762627182126285709789320198583975988428800000⟩, + ⟨1, 6, 7, 5, 7, 2, 49433747746984777490402395191187765114542489600000⟩, + ⟨1, 6, 8, 5, 8, 2, 42630487159109308497107561093096971460778393600000⟩, + ⟨1, 6, 1, 6, 0, 2, 63770626649899388591352423104326511417838954086400000⟩, + ⟨1, 6, 2, 6, 1, 2, -24045299182546691652263899378230445020344116838400000⟩, + ⟨1, 6, 3, 6, 2, 2, -4243307833195843068206736531289314418246444646400000⟩, + ⟨1, 6, 4, 6, 3, 2, -2931499021143904771707246115061840783905652736000000⟩, + ⟨1, 6, 5, 6, 4, 2, 550608376047474430510983762673042613795291136000000⟩, + ⟨1, 6, 6, 6, 5, 2, 17849274795916985680075413611960238485589196800000⟩, + ⟨1, 6, 7, 6, 6, 2, 14945134064323075760238823200054433021113139200000⟩, + ⟨1, 6, 8, 6, 7, 2, 11491369245603327392595782635306782210549350400000⟩, + ⟨1, 6, 2, 7, 0, 2, 196160926662518781832964314398384580770707747635200000⟩, + ⟨1, 6, 3, 7, 1, 2, 39008248656840022402402438245932976063041765376000000⟩, + ⟨1, 6, 4, 7, 2, 2, 3012577920557452485671603842602179912093663232000000⟩, + ⟨1, 6, 5, 7, 3, 2, 767656306584785579038462897492762791197540352000000⟩, + ⟨1, 6, 6, 7, 4, 2, 619434821639818852656742108019370418168135680000000⟩, + ⟨1, 6, 7, 7, 5, 2, -53690942326087851529978705722799378224748953600000⟩, + ⟨1, 6, 8, 7, 6, 2, 17180378635685679902267629736709697512564326400000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0822.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0822.lean new file mode 100644 index 0000000000000000000000000000000000000000..0b0f3e46efd90a4d863f6e08bffeb6c0e3577da5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0822.lean @@ -0,0 +1,613 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0822. -/ +namespace LaughlinFock +def collectedFourData_8_5_7 : List CollectedFourTerm := [ + ⟨1, 7, 0, 0, 5, 3, 41975226515405880467123648296007570682849892761600000⟩, + ⟨1, 7, 1, 0, 6, 3, -50467386080368770506524952248011788079529249996800000⟩, + ⟨1, 7, 2, 0, 7, 3, 2462269509002309292839090433097739072157253632000000⟩, + ⟨1, 7, 3, 0, 8, 3, -500076685192221840587944463231239801667793715200000⟩, + ⟨1, 7, 0, 1, 4, 3, 30179479469083403545299149923338811731851241062400000⟩, + ⟨1, 7, 1, 1, 5, 3, -10988458185371374492794632594075664543948944179200000⟩, + ⟨1, 7, 2, 1, 6, 3, -5667701926447394194110006698630679322036902297600000⟩, + ⟨1, 7, 3, 1, 7, 3, 6680385394662943402714633236486807066850728345600000⟩, + ⟨1, 7, 4, 1, 8, 3, -2599791051506255842651488820645822081912327372800000⟩, + ⟨1, 7, 0, 2, 3, 3, 11812836876932916974508724108723771123741753344000000⟩, + ⟨1, 7, 1, 2, 4, 3, 9553957847172187506745927980521283704367297331200000⟩, + ⟨1, 7, 2, 2, 5, 3, -11885041306679499972021230837707497626941784064000000⟩, + ⟨1, 7, 3, 2, 6, 3, -2174604861390667959570278158071102351269796249600000⟩, + ⟨1, 7, 4, 2, 7, 3, 352509560049961330164165201920912347556216832000000⟩, + ⟨1, 7, 5, 2, 8, 3, -879478403007404342879635161321949517426825625600000⟩, + ⟨1, 7, 0, 3, 2, 3, -51906374316224591167139545343901770839818554572800000⟩, + ⟨1, 7, 1, 3, 3, 3, -26459142255522921990023752834134478314873343180800000⟩, + ⟨1, 7, 2, 3, 4, 3, 875702697034657461855145521447979858899920486400000⟩, + ⟨1, 7, 3, 3, 5, 3, -4343703060591112200126897110158442404084344422400000⟩, + ⟨1, 7, 4, 3, 6, 3, 287093430926215733472259705158724906365694771200000⟩, + ⟨1, 7, 5, 3, 7, 3, 69284246626965366037412033197831534566545817600000⟩, + ⟨1, 7, 6, 3, 8, 3, -149640974679058561709119492731561697105202380800000⟩, + ⟨1, 7, 0, 4, 1, 3, -42844030687554416198514420522586639578867695616000000⟩, + ⟨1, 7, 1, 4, 2, 3, 45617771585571730870153949917501972152502871654400000⟩, + ⟨1, 7, 2, 4, 3, 3, 18626106610588594695794586146698037058553144934400000⟩, + ⟨1, 7, 3, 4, 4, 3, 1776421926526827008357891323851036628734286233600000⟩, + ⟨1, 7, 4, 4, 5, 3, -742392429362851789047243681466210387737811353600000⟩, + ⟨1, 7, 5, 4, 6, 3, 169676508486011257051992743365334237957849088000000⟩, + ⟨1, 7, 6, 4, 7, 3, 65296802912475740698245581345150049967511961600000⟩, + ⟨1, 7, 7, 4, 8, 3, -54745316601940220918154169202887429768347648000000⟩, + ⟨1, 7, 0, 5, 0, 3, 265129195317505933017592832882750557234411025203200000⟩, + ⟨1, 7, 1, 5, 1, 3, 20683629242219762944324876568227267874241537638400000⟩, + ⟨1, 7, 2, 5, 2, 3, -2533567649454053373132332884777304425763753164800000⟩, + ⟨1, 7, 3, 5, 3, 3, 4472476570957313419578668672865112977612944179200000⟩, + ⟨1, 7, 4, 5, 4, 3, -103674128938695205551152585984620527806840832000000⟩, + ⟨1, 7, 5, 5, 5, 3, 46695199203412735171066863004979575111286784000000⟩, + ⟨1, 7, 6, 5, 6, 3, 110592101680914376854233745804156520676877926400000⟩, + ⟨1, 7, 7, 5, 7, 3, -24971306642802134263204646266305900645344870400000⟩, + ⟨1, 7, 8, 5, 8, 3, -18842827799581572468382931274112594005825945600000⟩, + ⟨1, 7, 1, 6, 0, 3, -225494760526788681257349106621432515517465441075200000⟩, + ⟨1, 7, 2, 6, 1, 3, 42512432963303084785229916166703242015235742105600000⟩, + ⟨1, 7, 3, 6, 2, 3, 5001485971177153878194551879771409208509359718400000⟩, + ⟨1, 7, 4, 6, 3, 3, 2591466104710150122209975812787190993373888512000000⟩, + ⟨1, 7, 5, 6, 4, 3, -389393394493372577549230598217887480786033049600000⟩, + ⟨1, 7, 6, 6, 5, 3, -10519257734387486847297305095632883496150630400000⟩, + ⟨1, 7, 7, 6, 6, 3, -7549488811735150500860021807490470742117580800000⟩, + ⟨1, 7, 8, 6, 7, 3, -5079226307411381775320211618173211480843878400000⟩, + ⟨1, 7, 2, 7, 0, 3, -346815324752241686905332208863245030324528008396800000⟩, + ⟨1, 7, 3, 7, 1, 3, -45978094469388673427618815706550720174653177856000000⟩, + ⟨1, 7, 4, 7, 2, 3, -2663140431776929753851096646173164342234578944000000⟩, + ⟨1, 7, 5, 7, 3, 3, -542890933064050115646820458797027645191303987200000⟩, + ⟨1, 7, 6, 7, 4, 3, -365056542239695304811972155997247864087511040000000⟩, + ⟨1, 7, 7, 7, 5, 3, 27121815477717287776934384528283733512840806400000⟩, + ⟨1, 7, 8, 7, 6, 3, -7593788805546438448521664290729415613507174400000⟩ +] + +def collectedFourData_8_5_8 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 5, 4, -65341630359759375672236861404773549337354646323200000⟩, + ⟨1, 8, 1, 0, 6, 4, 39280565707923200534974478457256126538461269196800000⟩, + ⟨1, 8, 2, 0, 7, 4, -1277648091184492857457231436124667365543641088000000⟩, + ⟨1, 8, 3, 0, 8, 4, 194613755707614403271021506533263909676751257600000⟩, + ⟨1, 8, 0, 1, 4, 4, -46979529489734471588559533357847855185961733324800000⟩, + ⟨1, 8, 1, 1, 5, 4, 8552708735338028541380558753623207882091868979200000⟩, + ⟨1, 8, 2, 1, 6, 4, 2940916305568154883361493056146625052298077798400000⟩, + ⟨1, 8, 3, 1, 7, 4, -2599791051506255842651488820645822081912327372800000⟩, + ⟨1, 8, 4, 1, 8, 4, 809404022335812812995577427036650270648036229120000⟩, + ⟨1, 8, 0, 2, 3, 4, -18388704118830444856144489592501221383563378688000000⟩, + ⟨1, 8, 1, 2, 4, 4, -7436185983338595538879579431519968616871310131200000⟩, + ⟨1, 8, 2, 2, 5, 4, 6167034227411079244199105104003484965064933376000000⟩, + ⟨1, 8, 3, 2, 6, 4, 846286243264069460804603625318715143398149324800000⟩, + ⟨1, 8, 4, 2, 7, 4, -109748302907249959981370634180831159174089932800000⟩, + ⟨1, 8, 5, 2, 8, 4, 228176464585246677120876156562345475005690675200000⟩, + ⟨1, 8, 0, 3, 2, 4, 80801163101317439943187235672692844650326235545600000⟩, + ⟨1, 8, 1, 3, 3, 4, 20594093664534823096328966739207090049406258380800000⟩, + ⟨1, 8, 2, 3, 4, 4, -454393751464187518231854323265833883808668057600000⟩, + ⟨1, 8, 3, 3, 5, 4, 1690429470782782544324627348504226356496905011200000⟩, + ⟨1, 8, 4, 3, 6, 4, -89382020775567967865269414737568549634027028480000⟩, + ⟨1, 8, 5, 3, 7, 4, -17975466359075747391369629878230112638546739200000⟩, + ⟨1, 8, 6, 3, 8, 4, 33277401477901608147971056712992870995119308800000⟩, + ⟨1, 8, 0, 4, 1, 4, 66694072878460514916217871143740467089067999232000000⟩, + ⟨1, 8, 1, 4, 2, 4, -35505937861780947543162581390977082933928945254400000⟩, + ⟨1, 8, 2, 4, 3, 4, -9664908520456792501063473753525687363693025689600000⟩, + ⟨1, 8, 3, 4, 4, 4, -691326256711715420839675789955757774740442316800000⟩, + ⟨1, 8, 4, 4, 5, 4, 231132197385556736476503506949297998453475901440000⟩, + ⟨1, 8, 5, 4, 6, 4, -44021758461737579110755964927982101327773696000000⟩, + ⟨1, 8, 6, 4, 7, 4, -14520808424311585684507264568276782308497817600000⟩, + ⟨1, 8, 7, 4, 8, 4, 10652557884407961001576758954226031800614912000000⟩, + ⟨1, 8, 0, 5, 0, 4, -412719008714786071807833032305030747963655612006400000⟩, + ⟨1, 8, 1, 5, 1, 4, -16098805993904536884414145885629730235831707238400000⟩, + ⟨1, 8, 2, 5, 2, 4, 1314644014140987245436342885980111593331176243200000⟩, + ⟨1, 8, 3, 5, 3, 4, -1740543977677633545711538618748707165877934489600000⟩, + ⟨1, 8, 4, 5, 4, 4, 32277308180795417249629838551196133776739532800000⟩, + ⟨1, 8, 5, 5, 5, 4, -12114846062057128583087775564470370516860928000000⟩, + ⟨1, 8, 6, 5, 6, 4, -24593650073543201883320681666107077527234150400000⟩, + ⟨1, 8, 7, 5, 7, 4, 4859014541753937081271328970647005768030617600000⟩, + ⟨1, 8, 8, 5, 8, 4, 3259121024003078916113293314697018754256076800000⟩, + ⟨1, 8, 1, 6, 0, 4, 175510610824173806200254067849155943155666989875200000⟩, + ⟨1, 8, 2, 6, 1, 4, -22059294739502847084048268270553040496351405670400000⟩, + ⟨1, 8, 3, 6, 2, 4, -1946417415152212623786237985569730191183524659200000⟩, + ⟨1, 8, 4, 6, 3, 4, -806812181188196110494664967930757744369126604800000⟩, + ⟨1, 8, 5, 6, 4, 4, 101026253498118001402552910034776783630578483200000⟩, + ⟨1, 8, 6, 6, 5, 4, 2339289513634277096036429512362263853819494400000⟩, + ⟨1, 8, 7, 6, 6, 4, 1469009068838753671224030405988612157158195200000⟩, + ⟨1, 8, 8, 6, 7, 4, 878520645639056208844984617723776629682995200000⟩, + ⟨1, 8, 2, 7, 0, 4, 179959153960678806884070455763028038937939751731200000⟩, + ⟨1, 8, 3, 7, 1, 4, 17893195003737799321908493276788515262513020928000000⟩, + ⟨1, 8, 4, 7, 2, 4, 829126854743385265565607169437235798928365977600000⟩, + ⟨1, 8, 5, 7, 3, 4, 140850455609082023647813689456969331698460262400000⟩, + ⟨1, 8, 6, 7, 4, 4, 81181863084623120631535703970321299606077440000000⟩, + ⟨1, 8, 7, 7, 5, 4, -5277468964283525717316547301556094901000601600000⟩, + ⟨1, 8, 8, 7, 6, 4, 1313448119954968162971434576814075116991283200000⟩ +] + +def collectedFourData_8_5_9 : List CollectedFourTerm := [ + ⟨2, 3, 3, 0, 8, 0, -884278968823040993928202890771204477391208448000000⟩, + ⟨2, 3, 3, 1, 7, 0, 11812836876932916974508724108723771123741753344000000⟩, + ⟨2, 3, 4, 1, 8, 0, -18388704118830444856144489592501221383563378688000000⟩, + ⟨2, 3, 3, 2, 6, 0, -3845324929893415084841893352316634534514786304000000⟩, + ⟨2, 3, 4, 2, 7, 0, 2493351915748077545591198652119390236673310720000000⟩, + ⟨2, 3, 5, 2, 8, 0, -15551699936072499541377282381796195494726205440000000⟩, + ⟨2, 3, 3, 3, 5, 0, -7680912502082669005200719343311474030045822976000000⟩, + ⟨2, 3, 4, 3, 6, 0, 2030654022254358706934892885675518675021463552000000⟩, + ⟨2, 3, 5, 3, 7, 0, 1225144142431360179376484854368614417159946240000000⟩, + ⟨2, 3, 6, 3, 8, 0, -5292163010239488648264349175954840322142371840000000⟩, + ⟨2, 3, 3, 4, 4, 0, 3141223328138104957797104760819455266299838464000000⟩, + ⟨2, 3, 4, 4, 5, 0, -5251050739521465360540448221817517358559789056000000⟩, + ⟨2, 3, 5, 4, 6, 0, 3000367191680419746232790224408897326887731200000000⟩, + ⟨2, 3, 6, 4, 7, 0, 2309269408338474611144306967726558279295303680000000⟩, + ⟨2, 3, 7, 4, 8, 0, -3388189599944310818537376169084229436781363200000000⟩, + ⟨2, 3, 3, 5, 3, 0, 7908620992260684501526160032134956677551095808000000⟩, + ⟨2, 3, 4, 5, 4, 0, -733302347789297219547722121449204274136350720000000⟩, + ⟨2, 3, 5, 5, 5, 0, 825705013316276581759570870079552877074841600000000⟩, + ⟨2, 3, 6, 5, 6, 0, 3911170927586085722887111889146770069619998720000000⟩, + ⟨2, 3, 7, 5, 7, 0, -1545475060074160051553384506055503459500687360000000⟩, + ⟨2, 3, 8, 5, 8, 0, -1865893256902159870307335605184622643080331264000000⟩, + ⟨2, 3, 3, 6, 2, 0, 8844061297269672991431111194614948871081558016000000⟩, + ⟨2, 3, 4, 6, 3, 0, 18329820546879576015049154622184177972826603520000000⟩, + ⟨2, 3, 5, 6, 4, 0, -6885591741129602959712621378896199800628183040000000⟩, + ⟨2, 3, 6, 6, 5, 0, -372021278239453798190390194941208857327697920000000⟩, + ⟨2, 3, 7, 6, 6, 0, -467238132218791932809312974124585746924830720000000⟩, + ⟨2, 3, 8, 6, 7, 0, -502965596145256333120579516905192828274999296000000⟩, + ⟨2, 3, 3, 7, 1, 0, -81302454542969290487731910663130360149641789440000000⟩, + ⟨2, 3, 4, 7, 2, 0, -18836783593999718611837734940955449347004170240000000⟩, + ⟨2, 3, 5, 7, 3, 0, -9599868353965079793071806237281572923669217280000000⟩, + ⟨2, 3, 6, 7, 4, 0, -12910492822105423190461298272366193585160192000000000⟩, + ⟨2, 3, 7, 7, 5, 0, 1678570128681173023045881086141723257350389760000000⟩, + ⟨2, 3, 8, 7, 6, 0, -751967776669001371466969192585957694857281536000000⟩ +] + +def collectedFourData_8_5_10 : List CollectedFourTerm := [ + ⟨2, 4, 2, 0, 7, 1, 1173805487139480556233340577592663304398962688000000⟩, + ⟨2, 4, 3, 0, 8, 1, -715185021285907614100920103968313759634974310400000⟩, + ⟨2, 4, 2, 1, 6, 1, -2701889292139513102166093766842463412445144678400000⟩, + ⟨2, 4, 3, 1, 7, 1, 9553957847172187506745927980521283704367297331200000⟩, + ⟨2, 4, 4, 1, 8, 1, -7436185983338595538879579431519968616871310131200000⟩, + ⟨2, 4, 2, 2, 5, 1, -5665800047336205306683071578870703327675416576000000⟩, + ⟨2, 4, 3, 2, 6, 1, -3110012664326293641970425458917203867965010739200000⟩, + ⟨2, 4, 4, 2, 7, 1, 1008283587989751846420484540441725272145788928000000⟩, + ⟨2, 4, 5, 2, 8, 1, -4192622178426977616888739396589293498011746304000000⟩, + ⟨2, 4, 2, 3, 4, 1, 417462274996298552843044691265531089998420377600000⟩, + ⟨2, 4, 3, 3, 5, 1, -6212149971867626118335906594005988788136627404800000⟩, + ⟨2, 4, 4, 3, 6, 1, 821173742299487857788855476621779739853245644800000⟩, + ⟨2, 4, 5, 3, 7, 1, 330289712664352862701134431914308959767363584000000⟩, + ⟨2, 4, 6, 3, 8, 1, -1070045723286911767039274735734162905165201408000000⟩, + ⟨2, 4, 2, 4, 3, 1, 8879379801284514617225237967118533035912960409600000⟩, + ⟨2, 4, 3, 4, 4, 1, 2540551061378701117729135859787895727526720307200000⟩, + ⟨2, 4, 4, 4, 5, 1, -2123466104772629181992779797922131688936597094400000⟩, + ⟨2, 4, 5, 4, 6, 1, 808876591174820322086787941693355148097617920000000⟩, + ⟨2, 4, 6, 4, 7, 1, 466921341902894162645433307404419651459874816000000⟩, + ⟨2, 4, 7, 4, 8, 1, -548058369946776843067351972493593572091625472000000⟩, + ⟨2, 4, 2, 5, 2, 1, -1207794515626865392641390783858048821670130483200000⟩, + ⟨2, 4, 3, 5, 3, 1, 6396315497834732598330664714238081176760116838400000⟩, + ⟨2, 4, 4, 5, 4, 1, -296539256107562784438815003325139808239484928000000⟩, + ⟨2, 4, 5, 5, 5, 1, 222603906061631550939912358195833453737410560000000⟩, + ⟨2, 4, 6, 5, 6, 1, 790816858061634621445880184980015322249560064000000⟩, + ⟨2, 4, 7, 5, 7, 1, -249989121692470475937136800690548423771396505600000⟩, + ⟨2, 4, 8, 5, 8, 1, -251515444730249719363171324927655797851370291200000⟩, + ⟨2, 4, 2, 6, 1, 1, 20266395251019488346373318962754342473716622950400000⟩, + ⟨2, 4, 3, 6, 2, 1, 7152878661764768357894206811051265556833160396800000⟩, + ⟨2, 4, 4, 6, 3, 1, 7412374126365946079804615693771758714799259648000000⟩, + ⟨2, 4, 5, 6, 4, 1, -1856304118785887336995308100518255405998014464000000⟩, + ⟨2, 4, 6, 6, 5, 1, -75220619051536604982121193396727613545775104000000⟩, + ⟨2, 4, 7, 6, 6, 1, -75578346951131836868465153566533444416254771200000⟩, + ⟨2, 4, 8, 6, 7, 1, -67797884541646464811401074577351063158705356800000⟩, + ⟨2, 4, 2, 7, 0, 1, -165332726466321360098119277003546144071516107571200000⟩, + ⟨2, 4, 3, 7, 1, 1, -65755603981288482439224475084288147284780122112000000⟩, + ⟨2, 4, 4, 7, 2, 1, -7617384304391758973768617518210058764970622976000000⟩, + ⟨2, 4, 5, 7, 3, 1, -2588052826138687405242828775268239610738638848000000⟩, + ⟨2, 4, 6, 7, 4, 1, -2610429346770085990482124345524544141157990400000000⟩, + ⟨2, 4, 7, 7, 5, 1, 271517983698868489998852716001037297741568409600000⟩, + ⟨2, 4, 8, 7, 6, 1, -101362448828249500449924086054276662546975948800000⟩ +] + +def collectedFourData_8_5_11 : List CollectedFourTerm := [ + ⟨2, 5, 1, 0, 6, 2, 29928760731105889506397367783798444115691044864000000⟩, + ⟨2, 5, 2, 0, 7, 2, -2920407840147413226816727229321863899088158720000000⟩, + ⟨2, 5, 3, 0, 8, 2, 889684009064089495341757491492540004788338688000000⟩, + ⟨2, 5, 1, 1, 5, 2, 6516504249100962738271685961437589432346607616000000⟩, + ⟨2, 5, 2, 1, 6, 2, 6722254034783665076265729075662935830923575296000000⟩, + ⟨2, 5, 3, 1, 7, 2, -11885041306679499972021230837707497626941784064000000⟩, + ⟨2, 5, 4, 1, 8, 2, 6167034227411079244199105104003484965064933376000000⟩, + ⟨2, 5, 1, 2, 4, 2, -5665800047336205306683071578870703327675416576000000⟩, + ⟨2, 5, 2, 2, 5, 2, 14096412957883935535481545662675685681334845440000000⟩, + ⟨2, 5, 3, 2, 6, 2, 3868828978636815844352050502124764660785741824000000⟩, + ⟨2, 5, 4, 2, 7, 2, -836197401732806755641810956212489120320061440000000⟩, + ⟨2, 5, 5, 2, 8, 2, 2607792946702916251792420668042712708483645440000000⟩, + ⟨2, 5, 1, 3, 3, 2, 15691110620525574131876339344725973194384605184000000⟩, + ⟨2, 5, 2, 3, 4, 2, -1038638951872692845064304311428974050325561344000000⟩, + ⟨2, 5, 3, 3, 5, 2, 7727861081236356116466907452266476605177593856000000⟩, + ⟨2, 5, 4, 3, 6, 2, -681022043660415500803825656440927723773231104000000⟩, + ⟨2, 5, 5, 3, 7, 2, -205438779455627472323610905462728481298186240000000⟩, + ⟨2, 5, 6, 3, 8, 2, 532451066866068199235354220985730686311727104000000⟩, + ⟨2, 5, 1, 4, 2, 2, -27052785509767003945276659943199597453547405312000000⟩, + ⟨2, 5, 2, 4, 3, 2, -22091744050806697105690641429194254716632039424000000⟩, + ⟨2, 5, 3, 4, 4, 2, -3160423647373679165015719232227071640977014784000000⟩, + ⟨2, 5, 4, 4, 5, 2, 1761049034844157381884354423697268570547290112000000⟩, + ⟨2, 5, 5, 4, 6, 2, -503117757682188831181883154202219135578931200000000⟩, + ⟨2, 5, 6, 4, 7, 2, -232338451739292224069235821752348108765790208000000⟩, + ⟨2, 5, 7, 4, 8, 2, 227259964560719484071146312575597201881825280000000⟩, + ⟨2, 5, 1, 5, 1, 2, -12266048208946131948352566028306563376330309632000000⟩, + ⟨2, 5, 2, 5, 2, 2, 3004971957764080492869747426533570579433259008000000⟩, + ⟨2, 5, 3, 5, 3, 2, -7956961409958579791919819970221088389199822848000000⟩, + ⟨2, 5, 4, 5, 4, 2, 245928187687057400380525062067435385326141440000000⟩, + ⟨2, 5, 5, 5, 5, 2, -138458671311479798588514828109605473196441600000000⟩, + ⟨2, 5, 6, 5, 6, 2, -393507745143043179637226473767412398116831232000000⟩, + ⟨2, 5, 7, 5, 7, 2, 103661438364518399332677676986932788350418944000000⟩, + ⟨2, 5, 8, 5, 8, 2, 89395156517602874813137360764618612097941504000000⟩, + ⟨2, 5, 1, 6, 0, 2, 133725545507289040258642050559076563033780125696000000⟩, + ⟨2, 5, 2, 6, 1, 2, -50422442415768555837938652011807050028575358976000000⟩, + ⟨2, 5, 3, 6, 2, 2, -8898119472225101877507271092316962261194244096000000⟩, + ⟨2, 5, 4, 6, 3, 2, -6147286397367886004985516476246186135692247040000000⟩, + ⟨2, 5, 5, 6, 4, 2, 1154613170920553059904862518336458226443223040000000⟩, + ⟨2, 5, 6, 6, 5, 2, 37429520994008767548954111157173456576970752000000⟩, + ⟨2, 5, 7, 6, 6, 2, 31339604304081653553531589047030855172620288000000⟩, + ⟨2, 5, 8, 6, 7, 2, 24097138474589757419208168854684144454598656000000⟩, + ⟨2, 5, 2, 7, 0, 2, 411344976570055853351992909592558180642196553728000000⟩, + ⟨2, 5, 3, 7, 1, 2, 81799405227079369624772906370577369597099376640000000⟩, + ⟨2, 5, 4, 7, 2, 2, 6317306994981448761373114977326302709132820480000000⟩, + ⟨2, 5, 5, 7, 3, 2, 1609757716883328310094718539566860805110497280000000⟩, + ⟨2, 5, 6, 7, 4, 2, 1298940653112207643550003958803976395371315200000000⟩, + ⟨2, 5, 7, 7, 5, 2, -112588678025289876501512906802154420939259904000000⟩, + ⟨2, 5, 8, 7, 6, 2, 36026861045162185124023027980604230699319296000000⟩ +] + +def collectedFourData_8_5_12 : List CollectedFourTerm := [ + ⟨2, 6, 0, 0, 5, 3, -13663812227255726045178399779308033813339806105600000⟩, + ⟨2, 6, 1, 0, 6, 3, 16428187391662735754895159824176720251085180108800000⟩, + ⟨2, 6, 2, 0, 7, 3, -801520111191218556150577044284783131216576512000000⟩, + ⟨2, 6, 3, 0, 8, 3, 162785397314941013859327687062320599786533683200000⟩, + ⟨2, 6, 0, 1, 4, 3, -9824050393879990396337491035473936254604043878400000⟩, + ⟨2, 6, 1, 1, 5, 3, 3576972461527021042002432844429053115673817907200000⟩, + ⟨2, 6, 2, 1, 6, 3, 1844955258421525808377383345982609143535081881600000⟩, + ⟨2, 6, 3, 1, 7, 3, -2174604861390667959570278158071102351269796249600000⟩, + ⟨2, 6, 4, 1, 8, 3, 846286243264069460804603625318715143398149324800000⟩, + ⟨2, 6, 0, 2, 3, 3, -3845324929893415084841893352316634534514786304000000⟩, + ⟨2, 6, 1, 2, 4, 3, -3110012664326293641970425458917203867965010739200000⟩, + ⟨2, 6, 2, 2, 5, 3, 3868828978636815844352050502124764660785741824000000⟩, + ⟨2, 6, 3, 2, 6, 3, 707879265013949331488239129649626290211887513600000⟩, + ⟨2, 6, 4, 2, 7, 3, -114749218448347991321556054762177583971827712000000⟩, + ⟨2, 6, 5, 2, 8, 3, 286288574338232171546102559341202209410488729600000⟩, + ⟨2, 6, 0, 3, 2, 3, 16896608093210289657573224684821712317306424524800000⟩, + ⟨2, 6, 1, 3, 3, 3, 8613002989775930263304349280604870729104411852800000⟩, + ⟨2, 6, 2, 3, 4, 3, -285059503247501871716384795529498217291343462400000⟩, + ⟨2, 6, 3, 3, 5, 3, 1413965996564415622750440419944945125014529638400000⟩, + ⟨2, 6, 4, 3, 6, 3, -93454903225231403418179798189066903763497779200000⟩, + ⟨2, 6, 5, 3, 7, 3, -22553468195586142402598466778837793879202201600000⟩, + ⟨2, 6, 6, 3, 8, 3, 48711260170752027255596842190782439141199052800000⟩, + ⟨2, 6, 0, 4, 1, 3, 13946626116684933872483702344637242297659949056000000⟩, + ⟨2, 6, 1, 4, 2, 3, -14849536665211887743123160246308499550707803750400000⟩, + ⟨2, 6, 2, 4, 3, 3, -6063186416838523152794433521935528940326512230400000⟩, + ⟨2, 6, 3, 4, 4, 3, -578262409889170944885070686715961455817628057600000⟩, + ⟨2, 6, 4, 4, 5, 3, 241664229019161265258571196123617874209773977600000⟩, + ⟨2, 6, 5, 4, 6, 3, -55233244553863308197592189384570267141931008000000⟩, + ⟨2, 6, 6, 4, 7, 3, -21255472051085515121016901789426613260753305600000⟩, + ⟨2, 6, 7, 4, 8, 3, 17820743054144864435305188238656331440979968000000⟩, + ⟨2, 6, 0, 5, 0, 3, -86305086154858588179009485985364346222465463091200000⟩, + ⟨2, 6, 1, 5, 1, 3, -6732952972633498846244472487039718628591560294400000⟩, + ⟨2, 6, 2, 5, 2, 3, 824729143855463531130975260112578150228872396800000⟩, + ⟨2, 6, 3, 5, 3, 3, -1455884461610519694364003593989572771097817907200000⟩, + ⟨2, 6, 4, 5, 4, 3, 33748092583198119912152293218258917850611712000000⟩, + ⟨2, 6, 5, 5, 5, 3, -15200261840053664811128414576669805294649344000000⟩, + ⟨2, 6, 6, 5, 6, 3, -36000037084516366520516926391869476618790502400000⟩, + ⟨2, 6, 7, 5, 7, 3, 8128681447644896983229602722158130785314406400000⟩, + ⟨2, 6, 8, 5, 8, 3, 6133733686690201164637502981512497756477849600000⟩, + ⟨2, 6, 1, 6, 0, 3, 73403250484835271215502083992515040843402523443200000⟩, + ⟨2, 6, 2, 6, 1, 3, -13838684137205857719619117077986423263555328409600000⟩, + ⟨2, 6, 3, 6, 2, 3, -1628088061474456722856112041422012493693609574400000⟩, + ⟨2, 6, 4, 6, 3, 3, -843576299345550435002740109418371601338990592000000⟩, + ⟨2, 6, 5, 6, 4, 3, 126755676302029577630452571831257590339836313600000⟩, + ⟨2, 6, 6, 6, 5, 3, 3424237922814417908826748304151650433918566400000⟩, + ⟨2, 6, 7, 6, 6, 3, 2457516161287583550965683867564947006082252800000⟩, + ⟨2, 6, 8, 6, 7, 3, 1653394163310461150977822434782437079148134400000⟩, + ⟨2, 6, 2, 7, 0, 3, 112895626023842632482707954798138654836967394508800000⟩, + ⟨2, 6, 3, 7, 1, 3, 14966829283605524952772583879576147533177552896000000⟩, + ⟨2, 6, 4, 7, 2, 3, 866907788603766764911098160430553748318715904000000⟩, + ⟨2, 6, 5, 7, 3, 3, 176722328503558517469676771605369714214384435200000⟩, + ⟨2, 6, 6, 7, 4, 3, 118833522998707584952579059890977596128624640000000⟩, + ⟨2, 6, 7, 7, 5, 3, -8828716953172198351980058173976764484052582400000⟩, + ⟨2, 6, 8, 7, 6, 3, 2471936733786075432502437893889780498196070400000⟩ +] + +def collectedFourData_8_5_13 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 5, 4, 8859769464057849753802834686667269164821905408000000⟩, + ⟨2, 7, 1, 0, 6, 4, -5326110699623771643812467094575270914416443392000000⟩, + ⟨2, 7, 2, 0, 7, 4, 173238217071782510170490804153319206651166720000000⟩, + ⟨2, 7, 3, 0, 8, 4, -26387970434937365218942310857046979923410944000000⟩, + ⟨2, 7, 0, 1, 4, 4, 6370024722635150207169825091094251419532787712000000⟩, + ⟨2, 7, 1, 1, 5, 4, -1159674579148467715086902740013010825718530048000000⟩, + ⟨2, 7, 2, 1, 6, 4, -398763243845673079225375963758651125526429696000000⟩, + ⟨2, 7, 3, 1, 7, 4, 352509560049961330164165201920912347556216832000000⟩, + ⟨2, 7, 4, 1, 8, 4, -109748302907249959981370634180831159174089932800000⟩, + ⟨2, 7, 0, 2, 3, 4, 2493351915748077545591198652119390236673310720000000⟩, + ⟨2, 7, 1, 2, 4, 4, 1008283587989751846420484540441725272145788928000000⟩, + ⟨2, 7, 2, 2, 5, 4, -836197401732806755641810956212489120320061440000000⟩, + ⟨2, 7, 3, 2, 6, 4, -114749218448347991321556054762177583971827712000000⟩, + ⟨2, 7, 4, 2, 7, 4, 14880936662832990984809166330729373454303232000000⟩, + ⟨2, 7, 5, 2, 8, 4, -30938788368434131497477747223926357557772288000000⟩, + ⟨2, 7, 0, 3, 2, 4, -10955950648367727508773285476543808790188785664000000⟩, + ⟨2, 7, 1, 3, 3, 4, -2792383985284825761135153931886551577344868352000000⟩, + ⟨2, 7, 2, 3, 4, 4, 61611928899166294987222722983559438683602944000000⟩, + ⟨2, 7, 3, 3, 5, 4, -229207862184109739737774695908100715082416128000000⟩, + ⟨2, 7, 4, 3, 6, 4, 12119441984276770032920933152325684398601011200000⟩, + ⟨2, 7, 5, 3, 7, 4, 2437320389367231590525511559097785094504448000000⟩, + ⟨2, 7, 6, 3, 8, 4, -4512132676118183670012596338740158552604672000000⟩, + ⟨2, 7, 0, 4, 1, 4, -9043149169509171867108670619876927375230894080000000⟩, + ⟨2, 7, 1, 4, 2, 4, 4814303260089342220528996907743333670071566336000000⟩, + ⟨2, 7, 2, 4, 3, 4, 1310479412757201905521658173166890843870593024000000⟩, + ⟨2, 7, 3, 4, 4, 4, 93737961927071053028375415383567462345736192000000⟩, + ⟨2, 7, 4, 4, 5, 4, -31339560602979239924358192807312849060338073600000⟩, + ⟨2, 7, 5, 4, 6, 4, 5968976121747157833581625702776479930122240000000⟩, + ⟨2, 7, 6, 4, 7, 4, 1968898149048626402454682601564282598457344000000⟩, + ⟨2, 7, 7, 4, 8, 4, -1444396268332321105743941856837865077473280000000⟩, + ⟨2, 7, 0, 5, 0, 4, 55961188150876020483476069065345844130103689216000000⟩, + ⟨2, 7, 1, 5, 1, 4, 2182861201461948760166552148832873516992823296000000⟩, + ⟨2, 7, 2, 5, 2, 4, -178254549641078885403938000491862825744990208000000⟩, + ⟨2, 7, 3, 5, 3, 4, 236002963185549651458611497842061170939265024000000⟩, + ⟨2, 7, 4, 5, 4, 4, -4376528529020452842987774662538074869727232000000⟩, + ⟨2, 7, 5, 5, 5, 4, 1642670111097768208445899690707037527736320000000⟩, + ⟨2, 7, 6, 5, 6, 4, 3334689825332123200943321671429822743576576000000⟩, + ⟨2, 7, 7, 5, 7, 4, -658841054706170186465504883642429125689344000000⟩, + ⟨2, 7, 8, 5, 8, 4, -441909097908186370687178651048790397550592000000⟩, + ⟨2, 7, 1, 6, 0, 4, -23797746426538392293090494614037173057028620288000000⟩, + ⟨2, 7, 2, 6, 1, 4, 2991052792157771374798516998518320729870565376000000⟩, + ⟨2, 7, 3, 6, 2, 4, 263917650724800327614770257280825512582709248000000⟩, + ⟨2, 7, 4, 6, 3, 4, 109396871286567826797393501647446202659110912000000⟩, + ⟨2, 7, 5, 6, 4, 4, -13698300928255098693865754001423164724215808000000⟩, + ⟨2, 7, 6, 6, 5, 4, -317187766610297819552764885464221730471936000000⟩, + ⟨2, 7, 7, 6, 6, 4, -199185138461696233671047426317191991001088000000⟩, + ⟨2, 7, 8, 6, 7, 4, -119119929314937288333677990175869226713088000000⟩, + ⟨2, 7, 2, 7, 0, 4, -24400931049011841649509390575332583156301692928000000⟩, + ⟨2, 7, 3, 7, 1, 4, -2426165093152910296698318102342938071998136320000000⟩, + ⟨2, 7, 4, 7, 2, 4, -112422551274596398318117927987143353768607744000000⟩, + ⟨2, 7, 5, 7, 3, 4, -19098124101484021673555387166917040701177856000000⟩, + ⟨2, 7, 6, 7, 4, 4, -11007570328937195073120842919363103791513600000000⟩, + ⟨2, 7, 7, 7, 5, 4, 715579916200982500325882734741615546466304000000⟩, + ⟨2, 7, 8, 7, 6, 4, -178092396558378008597951802973349958647808000000⟩ +] + +def collectedFourData_8_5_14 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 5, 5, -55260741709806425585753961125881915156690108416000000⟩, + ⟨2, 8, 1, 0, 6, 5, 22146913933728351312777491670487848257329299456000000⟩, + ⟨2, 8, 2, 0, 7, 5, -540266448619674985673593475643435683382558720000000⟩, + ⟨2, 8, 3, 0, 8, 5, 65835519732957270182611186745739375684039475200000⟩, + ⟨2, 8, 0, 1, 4, 5, -39731540680675649295253876124873975556760141824000000⟩, + ⟨2, 8, 1, 1, 5, 5, 4822132798957405168699554791872002923339710464000000⟩, + ⟨2, 8, 2, 1, 6, 5, 1243596275891564964429118087584570862045495296000000⟩, + ⟨2, 8, 3, 1, 7, 5, -879478403007404342879635161321949517426825625600000⟩, + ⟨2, 8, 4, 1, 8, 5, 228176464585246677120876156562345475005690675200000⟩, + ⟨2, 8, 0, 2, 3, 5, -15551699936072499541377282381796195494726205440000000⟩, + ⟨2, 8, 1, 2, 4, 5, -4192622178426977616888739396589293498011746304000000⟩, + ⟨2, 8, 2, 2, 5, 5, 2607792946702916251792420668042712708483645440000000⟩, + ⟨2, 8, 3, 2, 6, 5, 286288574338232171546102559341202209410488729600000⟩, + ⟨2, 8, 4, 2, 7, 5, -30938788368434131497477747223926357557772288000000⟩, + ⟨2, 8, 5, 2, 8, 5, 55135275077763691658787865072906001329422336000000⟩, + ⟨2, 8, 0, 3, 2, 5, 68335182018104264499053873725327559658861232128000000⟩, + ⟨2, 8, 1, 3, 3, 5, 11611228395307834014172328269100740435809140736000000⟩, + ⟨2, 8, 2, 3, 4, 5, -192145004616203390986809435885672927376441344000000⟩, + ⟨2, 8, 3, 3, 5, 5, 571852191928785033000487823786939252172285542400000⟩, + ⟨2, 8, 4, 3, 6, 5, -25197395781649030148771137819273224635862220800000⟩, + ⟨2, 8, 5, 3, 7, 5, -4343490395296490266717718785834200235769856000000⟩, + ⟨2, 8, 6, 3, 8, 5, 7035843296681644688816378716606190831271936000000⟩, + ⟨2, 8, 0, 4, 1, 5, 56404529770982971432341930327755861358972764160000000⟩, + ⟨2, 8, 1, 4, 2, 5, -20018727729335046148178508218685375832022581248000000⟩, + ⟨2, 8, 2, 4, 3, 5, -4086904554242568794795052348308919794924519424000000⟩, + ⟨2, 8, 3, 4, 4, 5, -233867453254615253978257610912222338134677913600000⟩, + ⟨2, 8, 4, 4, 5, 5, 65157728644663111337449095043414914700306022400000⟩, + ⟨2, 8, 5, 4, 6, 5, -10637169642393111439488146780508885646049280000000⟩, + ⟨2, 8, 6, 4, 7, 5, -3070135529735880473364546641019027295567872000000⟩, + ⟨2, 8, 7, 4, 8, 5, 2002018711528343156412814950373718155591680000000⟩, + ⟨2, 8, 0, 5, 0, 5, -349044834261756076120066903821002647283152453632000000⟩, + ⟨2, 8, 1, 5, 1, 5, -9076724440118671191575797494854157830379798528000000⟩, + ⟨2, 8, 2, 5, 2, 5, 555910549719988142748634161714114566981419008000000⟩, + ⟨2, 8, 3, 5, 3, 5, -588805333784493530667461636245410193865913139200000⟩, + ⟨2, 8, 4, 5, 4, 5, 9099191335580901445354720912047570878988288000000⟩, + ⟨2, 8, 5, 5, 5, 5, -2927363132610611661139058519751693214679040000000⟩, + ⟨2, 8, 6, 5, 6, 5, -5199837136495799213691367676628985958105088000000⟩, + ⟨2, 8, 7, 5, 7, 5, 913192693974302263326864633832057721585664000000⟩, + ⟨2, 8, 8, 5, 8, 5, 551260946862903485589458437393019470400716800000⟩, + ⟨2, 8, 1, 6, 0, 5, 98955254903445205142773748354794107657240182784000000⟩, + ⟨2, 8, 2, 6, 1, 5, -9327996425773967611802299577280947824650878976000000⟩, + ⟨2, 8, 3, 6, 2, 5, -658449869989387777316954765032544908196865638400000⟩, + ⟨2, 8, 4, 6, 3, 5, -227445807047712988586461651942684476894609408000000⟩, + ⟨2, 8, 5, 6, 4, 5, 24411414590103925633504120145352044656459776000000⟩, + ⟨2, 8, 6, 6, 5, 5, 494596143705246119250863462218428756000768000000⟩, + ⟨2, 8, 7, 6, 6, 5, 276082390270293689350619984527882325065728000000⟩, + ⟨2, 8, 8, 6, 7, 5, 148596544708472265442150154330941020123955200000⟩, + ⟨2, 8, 2, 7, 0, 5, 76097552743807764093738123363816562172759113728000000⟩, + ⟨2, 8, 3, 7, 1, 5, 6053055132053761193938588638368548620028870656000000⟩, + ⟨2, 8, 4, 7, 2, 5, 233736464345786651335804311492679917524484096000000⟩, + ⟨2, 8, 5, 7, 3, 5, 34034310370050323065706832134396247992696832000000⟩, + ⟨2, 8, 6, 7, 4, 5, 17164286928334106501219059329031394348236800000000⟩, + ⟨2, 8, 7, 7, 5, 5, -991836113978828613058287736487726939111424000000⟩, + ⟨2, 8, 8, 7, 6, 5, 222161941495607427246048470362100023374643200000⟩ +] + +def collectedFourData_8_5_15 : List CollectedFourTerm := [ + ⟨3, 2, 3, 0, 8, 0, 3885579360307839579863421249313829121936693657600000⟩, + ⟨3, 2, 3, 1, 7, 0, -51906374316224591167139545343901770839818554572800000⟩, + ⟨3, 2, 4, 1, 8, 0, 80801163101317439943187235672692844650326235545600000⟩, + ⟨3, 2, 3, 2, 6, 0, 16896608093210289657573224684821712317306424524800000⟩, + ⟨3, 2, 4, 2, 7, 0, -10955950648367727508773285476543808790188785664000000⟩, + ⟨3, 2, 5, 2, 8, 0, 68335182018104264499053873725327559658861232128000000⟩, + ⟨3, 2, 3, 3, 5, 0, 33750429602714329684483271047156263270766293811200000⟩, + ⟨3, 2, 4, 3, 6, 0, -8922825980244031970839339904049593205823792742400000⟩, + ⟨3, 2, 5, 3, 7, 0, -5383363125292167584915879646221154054033113088000000⟩, + ⟨3, 2, 6, 3, 8, 0, 23254108815163042704126309951777025518949367808000000⟩, + ⟨3, 2, 3, 4, 4, 0, -13802739814310160125191511492769686328659725516800000⟩, + ⟨3, 2, 4, 4, 5, 0, 23073458820998919035661502525799802033214272307200000⟩, + ⟨3, 2, 5, 4, 6, 0, -13183808780225811472183561984208998516591165440000000⟩, + ⟨3, 2, 6, 4, 7, 0, -10147080126052269123950869168563837573965807616000000⟩, + ⟨3, 2, 7, 4, 8, 0, 14887925691454325045367594031016669637079203840000000⟩, + ⟨3, 2, 3, 5, 3, 0, -34750995533599446750824758600496085390138644889600000⟩, + ⟨3, 2, 4, 5, 4, 0, 3222178258098511730833216781458721225954033664000000⟩, + ⟨3, 2, 5, 5, 5, 0, -3628201586332736891170260295194297635878993920000000⟩, + ⟨3, 2, 6, 5, 6, 0, -17185939693999178815506703979595559592225931264000000⟩, + ⟨3, 2, 7, 5, 7, 0, 6790918032673904816356669366034919374802911232000000⟩, + ⟨3, 2, 8, 5, 8, 0, 8198856450477753266755683007824423813452188876800000⟩, + ⟨3, 2, 3, 6, 2, 0, -38861381135985480192838668753488018536209265459200000⟩, + ⟨3, 2, 4, 6, 3, 0, -80542424852529252761483854780162439253300609024000000⟩, + ⟨3, 2, 5, 6, 4, 0, 30255738399443186813016272459654482024357429248000000⟩, + ⟨3, 2, 6, 6, 5, 0, 1634685717162899132190693734076897895649378304000000⟩, + ⟨3, 2, 7, 6, 6, 0, 2053074772675537192087760418180069002695409664000000⟩, + ⟨3, 2, 8, 6, 7, 0, 2210063575217773771697310075946229047865062195200000⟩, + ⟨3, 2, 3, 7, 1, 0, 357248278487267881594632290308973798658228092928000000⟩, + ⟨3, 2, 4, 7, 2, 0, 82770053487586156116297213645393876801067941888000000⟩, + ⟨3, 2, 5, 7, 3, 0, 42182446550194581706421635809577080997004967936000000⟩, + ⟨3, 2, 6, 7, 4, 0, 56729546002596550336630470099583663478302310400000000⟩, + ⟨3, 2, 7, 7, 5, 0, -7375746429335293848081058727112235988771930112000000⟩, + ⟨3, 2, 8, 7, 6, 0, 3304195367815373039116131301369306357477618483200000⟩ +] + +def collectedFourData_8_5_16 : List CollectedFourTerm := [ + ⟨3, 3, 2, 0, 7, 1, -3250787460165476358909189779749974725929992192000000⟩, + ⟨3, 3, 3, 0, 8, 1, 1980664193826641752987624722874763382435191193600000⟩, + ⟨3, 3, 2, 1, 6, 1, 7482728549043500445915470770770941530064132505600000⟩, + ⟨3, 3, 3, 1, 7, 1, -26459142255522921990023752834134478314873343180800000⟩, + ⟨3, 3, 4, 1, 8, 1, 20594093664534823096328966739207090049406258380800000⟩, + ⟨3, 3, 2, 2, 5, 1, 15691110620525574131876339344725973194384605184000000⟩, + ⟨3, 3, 3, 2, 6, 1, 8613002989775930263304349280604870729104411852800000⟩, + ⟨3, 3, 4, 2, 7, 1, -2792383985284825761135153931886551577344868352000000⟩, + ⟨3, 3, 5, 2, 8, 1, 11611228395307834014172328269100740435809140736000000⟩, + ⟨3, 3, 2, 3, 4, 1, -1156138000306400210140960630908352061996688998400000⟩, + ⟨3, 3, 3, 3, 5, 1, 17204195627358611033776959072356121381440795443200000⟩, + ⟨3, 3, 4, 3, 6, 1, -2274193921677523816390001321546883816135799603200000⟩, + ⟨3, 3, 5, 3, 7, 1, -914718552532504187907769859244608277505376256000000⟩, + ⟨3, 3, 6, 3, 8, 1, 2963430702255227285254687205939345776466460672000000⟩, + ⟨3, 3, 2, 4, 3, 1, -24590936767901104478365006783192957085712541286400000⟩, + ⟨3, 3, 3, 4, 4, 1, -7035911505547937682676121637585413721612405964800000⟩, + ⟨3, 3, 4, 4, 5, 1, 5880818467038766453174002547998621874184100249600000⟩, + ⟨3, 3, 5, 4, 6, 1, -2240137661837362732310219179558075215674081280000000⟩, + ⟨3, 3, 6, 4, 7, 1, -1293112069905668565346866378505655360730169344000000⟩, + ⟨3, 3, 7, 4, 8, 1, 1517816449132008402176763436638806065438261248000000⟩, + ⟨3, 3, 2, 5, 2, 1, 3344918139226502400604921131641355373210553548800000⟩, + ⟨3, 3, 3, 5, 3, 1, -17714231565142150345196357501154657795755841945600000⟩, + ⟨3, 3, 4, 5, 4, 1, 821248584848978080957056302244591738764132352000000⟩, + ⟨3, 3, 5, 5, 5, 1, -616488842774524626232234741869226058884055040000000⟩, + ⟨3, 3, 6, 5, 6, 1, -2190122259301334956008591610453492116096024576000000⟩, + ⟨3, 3, 7, 5, 7, 1, 692330638150354486044975643021233139189442150400000⟩, + ⟨3, 3, 8, 5, 8, 1, 696557702894672594531275092814346978811759820800000⟩, + ⟨3, 3, 2, 6, 1, 1, -56126627679448512390646742575000834751157868953600000⟩, + ⟨3, 3, 3, 6, 2, 1, -19809490168950866436741399163812744508296344371200000⟩, + ⟨3, 3, 4, 6, 3, 1, -20528148082495859090818699721375207853058424832000000⟩, + ⟨3, 3, 5, 6, 4, 1, 5140928559048069820200177301313077436718514176000000⟩, + ⟨3, 3, 6, 6, 5, 1, 208319221402279100512596507743388800108199936000000⟩, + ⟨3, 3, 7, 6, 6, 1, 209309928451186710561942287779237433474600140800000⟩, + ⟨3, 3, 8, 6, 7, 1, 187762380827533072624332129085180197440009011200000⟩, + ⟨3, 3, 2, 7, 0, 1, 457879571905443776430422536963198166350410075340800000⟩, + ⟨3, 3, 3, 7, 1, 1, 182106401103046955820759902055950424449910571008000000⟩, + ⟨3, 3, 4, 7, 2, 1, 21095912097261801660666897122024462630239862784000000⟩, + ⟨3, 3, 5, 7, 3, 1, 7167464938300927195938567785962483003668037632000000⟩, + ⟨3, 3, 6, 7, 4, 1, 7229435438070827239470072915885865244924313600000000⟩, + ⟨3, 3, 7, 7, 5, 1, -751953595623985190162060827222103265018013286400000⟩, + ⟨3, 3, 8, 7, 6, 1, 280717530453479317807954970134924343586796339200000⟩ +] + +def collectedFourData_8_5_17 : List CollectedFourTerm := [ + ⟨3, 4, 1, 0, 6, 2, -2205183458336392257087624940452487055997822566400000⟩, + ⟨3, 4, 2, 0, 7, 2, 215178808055211530584576970174073763918774272000000⟩, + ⟨3, 4, 3, 0, 8, 2, -65552879972589522813403666935911131925761228800000⟩, + ⟨3, 4, 1, 1, 5, 2, -480143080610784474020902928078674584992848281600000⟩, + ⟨3, 4, 2, 1, 6, 2, -495302947336311532947453580370075749533194649600000⟩, + ⟨3, 4, 3, 1, 7, 2, 875702697034657461855145521447979858899920486400000⟩, + ⟨3, 4, 4, 1, 8, 2, -454393751464187518231854323265833883808668057600000⟩, + ⟨3, 4, 1, 2, 4, 2, 417462274996298552843044691265531089998420377600000⟩, + ⟨3, 4, 2, 2, 5, 2, -1038638951872692845064304311428974050325561344000000⟩, + ⟨3, 4, 3, 2, 6, 2, -285059503247501871716384795529498217291343462400000⟩, + ⟨3, 4, 4, 2, 7, 2, 61611928899166294987222722983559438683602944000000⟩, + ⟨3, 4, 5, 2, 8, 2, -192145004616203390986809435885672927376441344000000⟩, + ⟨3, 4, 1, 3, 3, 2, -1156138000306400210140960630908352061996688998400000⟩, + ⟨3, 4, 2, 3, 4, 2, 76528041252073551105720239887491049806259814400000⟩, + ⟨3, 4, 3, 3, 5, 2, -569397162073349536290582611331849581164599705600000⟩, + ⟨3, 4, 4, 3, 6, 2, 50178440695726754308545317980104049358693990400000⟩, + ⟨3, 4, 5, 3, 7, 2, 15136951450365922515929673734797300202471424000000⟩, + ⟨3, 4, 6, 3, 8, 2, -39231570447428684045887706209730340753663590400000⟩, + ⟨3, 4, 1, 4, 2, 2, 1993278493688445359928711650545916098779493171200000⟩, + ⟨3, 4, 2, 4, 3, 2, 1627743593673356454341554343838914553464645222400000⟩, + ⟨3, 4, 3, 4, 4, 2, 232863432306442955654371435934486142573241958400000⟩, + ⟨3, 4, 4, 4, 5, 2, -129755997445007103379205630912602045007737651200000⟩, + ⟨3, 4, 5, 4, 6, 2, 37070260503067095680324912167749789281157120000000⟩, + ⟨3, 4, 6, 4, 7, 2, 17118948395964664185501597185924257987480780800000⟩, + ⟨3, 4, 7, 4, 8, 2, -16744759968312108623019532009338418262704128000000⟩, + ⟨3, 4, 1, 5, 1, 2, 903775697648983990122548118170362935050974003200000⟩, + ⟨3, 4, 2, 5, 2, 2, -221409583696492057644525526662856208338963660800000⟩, + ⟨3, 4, 3, 5, 3, 2, 586277522063417514283531831621633159394544844800000⟩, + ⟨3, 4, 4, 5, 4, 2, -18120254837765465956692290240121265081810944000000⟩, + ⟨3, 4, 5, 5, 5, 2, 10201784643958720830072510783943526747996160000000⟩, + ⟨3, 4, 6, 5, 6, 2, 28994076237002526145949046195474293035578163200000⟩, + ⟨3, 4, 7, 5, 7, 2, -7637886887551952259182478898191775400617574400000⟩, + ⟨3, 4, 8, 5, 8, 2, -6586731812223832972326389779143387880253030400000⟩, + ⟨3, 4, 1, 6, 0, 2, -9853042815875653245945927200076692727392737689600000⟩, + ⟨3, 4, 2, 6, 1, 2, 3715180088583090430825945583435753305352542617600000⟩, + ⟨3, 4, 3, 6, 2, 2, 655623065944658542397343599114982670948997529600000⟩, + ⟨3, 4, 4, 6, 3, 2, 452938709989515704828177764000498929320853504000000⟩, + ⟨3, 4, 5, 6, 4, 2, -85073147136528685457804588843824163642671104000000⟩, + ⟨3, 4, 6, 6, 5, 2, -2757847586507567954640199934954521152926515200000⟩, + ⟨3, 4, 7, 6, 6, 2, -2309135938607078279858574217738780597341388800000⟩, + ⟨3, 4, 8, 6, 7, 2, -1775503223632583293210782688606394426956185600000⟩, + ⟨3, 4, 2, 7, 0, 2, -30308342739340023881644193859271855238307171532800000⟩, + ⟨3, 4, 3, 7, 1, 2, -6027068642405681531084441333766785177657278464000000⟩, + ⟨3, 4, 4, 7, 2, 2, -465466011497333354721643894934598441813147648000000⟩, + ⟨3, 4, 5, 7, 3, 2, -118608689517539700416642739048900799997411328000000⟩, + ⟨3, 4, 6, 7, 4, 2, -95707352113201525640111287593721965072875520000000⟩, + ⟨3, 4, 7, 7, 5, 2, 8295655560481913158267091153527933963232870400000⟩, + ⟨3, 4, 8, 7, 6, 2, -2654498084513231266324420979661271182449049600000⟩ +] + +def collectedFourData_8_5_18 : List CollectedFourTerm := [ + ⟨3, 5, 0, 0, 5, 3, -27293024146426962612657421845504651108660176486400000⟩, + ⟨3, 5, 1, 0, 6, 3, 32814774362039865244242657972425703327391757107200000⟩, + ⟨3, 5, 2, 0, 7, 3, -1601010566066770634684274458188304032179683328000000⟩, + ⟨3, 5, 3, 0, 8, 3, 325158579882996252088287093771253581014158540800000⟩, + ⟨3, 5, 0, 1, 4, 3, -19623223750179812927932158509267761022201600409600000⟩, + ⟨3, 5, 1, 1, 5, 3, 7144887103236254178673802540631854505458977996800000⟩, + ⟨3, 5, 2, 1, 6, 3, 3685238612744710192335246235952877143431997030400000⟩, + ⟨3, 5, 3, 1, 7, 3, -4343703060591112200126897110158442404084344422400000⟩, + ⟨3, 5, 4, 1, 8, 3, 1690429470782782544324627348504226356496905011200000⟩, + ⟨3, 5, 0, 2, 3, 3, -7680912502082669005200719343311474030045822976000000⟩, + ⟨3, 5, 1, 2, 4, 3, -6212149971867626118335906594005988788136627404800000⟩, + ⟨3, 5, 2, 2, 5, 3, 7727861081236356116466907452266476605177593856000000⟩, + ⟨3, 5, 3, 2, 6, 3, 1413965996564415622750440419944945125014529638400000⟩, + ⟨3, 5, 4, 2, 7, 3, -229207862184109739737774695908100715082416128000000⟩, + ⟨3, 5, 5, 2, 8, 3, 571852191928785033000487823786939252172285542400000⟩, + ⟨3, 5, 0, 3, 2, 3, 33750429602714329684483271047156263270766293811200000⟩, + ⟨3, 5, 1, 3, 3, 3, 17204195627358611033776959072356121381440795443200000⟩, + ⟨3, 5, 2, 3, 4, 3, -569397162073349536290582611331849581164599705600000⟩, + ⟨3, 5, 3, 3, 5, 3, 2824351465360414530364202902600230043679037849600000⟩, + ⟨3, 5, 4, 3, 6, 3, -186673154453946853996609380764376634495913164800000⟩, + ⟨3, 5, 5, 3, 7, 3, -45049825173968611014539421856363873493739110400000⟩, + ⟨3, 5, 6, 3, 8, 3, 97299170826664428635751772629691108481512243200000⟩, + ⟨3, 5, 0, 4, 1, 3, 27857935767338966801803629774340587077568036864000000⟩, + ⟨3, 5, 1, 4, 2, 3, -29661470461254996929884276511457823411570055577600000⟩, + ⟨3, 5, 2, 4, 3, 3, -12111019276814062459746203138489724571513100697600000⟩, + ⟨3, 5, 3, 4, 4, 3, -1155060509730525672270173605579475485662275174400000⟩, + ⟨3, 5, 4, 4, 5, 3, 482716501679585084806148555411776169232983654400000⟩, + ⟨3, 5, 5, 4, 6, 3, -110326624240858971467889224285098624577175552000000⟩, + ⟨3, 5, 6, 4, 7, 3, -42457119747063032459980432574897604427933286400000⟩, + ⟨3, 5, 7, 4, 8, 3, 35596359375741547595161343726202448659873792000000⟩, + ⟨3, 5, 0, 5, 0, 3, -172391625500045724453329455966925434795257023692800000⟩, + ⟨3, 5, 1, 5, 1, 3, -13448856366181974871807686278952763959272905113600000⟩, + ⟨3, 5, 2, 5, 2, 3, 1647369860119194304842886851144856103120220979200000⟩, + ⟨3, 5, 3, 5, 3, 3, -2908082247052681187818665518541763337714977996800000⟩, + ⟨3, 5, 4, 5, 4, 3, 67410726263622877288805617239670458446512128000000⟩, + ⟨3, 5, 5, 5, 5, 3, -30362032684045361961512583126742143112052736000000⟩, + ⟨3, 5, 6, 5, 6, 3, -71908912760089140984417268939216459342125465600000⟩, + ⟨3, 5, 7, 5, 7, 3, 16236778970559903610766839471009521857042841600000⟩, + ⟨3, 5, 8, 5, 8, 3, 12251935172575977411431811017629984612574822400000⟩, + ⟨3, 5, 1, 6, 0, 3, 146620624946278471363437916485199445325639371980800000⟩, + ⟨3, 5, 2, 6, 1, 3, -27642325145402950651965071225223386060168783462400000⟩, + ⟨3, 5, 3, 6, 2, 3, -3252053382707846083256810905148099744040065433600000⟩, + ⟨3, 5, 4, 6, 3, 3, -1685016445224946881827279344606674779633614848000000⟩, + ⟨3, 5, 5, 6, 4, 3, 253190374433504414160599998536715125452596838400000⟩, + ⟨3, 5, 6, 6, 5, 3, 6839804789183282853957110054985269417449881600000⟩, + ⟨3, 5, 7, 6, 6, 3, 4908809255770022625462183495914044892853043200000⟩, + ⟨3, 5, 8, 6, 7, 3, 3302601504782027019444789826940331573746073600000⟩, + ⟨3, 5, 2, 7, 0, 3, 225505371110736763111319587026563877313149350707200000⟩, + ⟨3, 5, 3, 7, 1, 3, 29895758682782916354665562703822932138811981824000000⟩, + ⟨3, 5, 4, 7, 2, 3, 1731620342373531560221183213699616909480165376000000⟩, + ⟨3, 5, 5, 7, 3, 3, 352997150344266797431879631995415557537844428800000⟩, + ⟨3, 5, 6, 7, 4, 3, 237366128768889529689635836666025458437980160000000⟩, + ⟨3, 5, 7, 7, 5, 3, -17635077310579624111822372726154280268568985600000⟩, + ⟨3, 5, 8, 7, 6, 3, 4937613884146102652149462021917441248565657600000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0823.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0823.lean new file mode 100644 index 0000000000000000000000000000000000000000..82d74d376288fcd91facf74c4667e4f8fb3b9560 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0823.lean @@ -0,0 +1,632 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0823. -/ +namespace LaughlinFock +def collectedFourData_8_5_19 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 5, 4, 7215638668895064210200137878434780838470929612800000⟩, + ⟨3, 6, 1, 0, 6, 4, -4337730284622910834112407785740444786467484467200000⟩, + ⟨3, 6, 2, 0, 7, 4, 141089944056069055465034215244168874952753152000000⟩, + ⟨3, 6, 3, 0, 8, 4, -21491085139001592487003251499492608951346790400000⟩, + ⟨3, 6, 0, 1, 4, 4, 5187922428109312913263095685896526623816233779200000⟩, + ⟨3, 6, 1, 1, 5, 4, -944470707797149965581238602855789284847045836800000⟩, + ⟨3, 6, 2, 1, 6, 4, -324763696583706379717529491989950399159835033600000⟩, + ⟨3, 6, 3, 1, 7, 4, 287093430926215733472259705158724906365694771200000⟩, + ⟨3, 6, 4, 1, 8, 4, -89382020775567967865269414737568549634027028480000⟩, + ⟨3, 6, 0, 2, 3, 4, 2030654022254358706934892885675518675021463552000000⟩, + ⟨3, 6, 1, 2, 4, 4, 821173742299487857788855476621779739853245644800000⟩, + ⟨3, 6, 2, 2, 5, 4, -681022043660415500803825656440927723773231104000000⟩, + ⟨3, 6, 3, 2, 6, 4, -93454903225231403418179798189066903763497779200000⟩, + ⟨3, 6, 4, 2, 7, 4, 12119441984276770032920933152325684398601011200000⟩, + ⟨3, 6, 5, 2, 8, 4, -25197395781649030148771137819273224635862220800000⟩, + ⟨3, 6, 0, 3, 2, 4, -8922825980244031970839339904049593205823792742400000⟩, + ⟨3, 6, 1, 3, 3, 4, -2274193921677523816390001321546883816135799603200000⟩, + ⟨3, 6, 2, 3, 4, 4, 50178440695726754308545317980104049358693990400000⟩, + ⟨3, 6, 3, 3, 5, 4, -186673154453946853996609380764376634495913164800000⟩, + ⟨3, 6, 4, 3, 6, 4, 9870405159179521978927445439407772189767761920000⟩, + ⟨3, 6, 5, 3, 7, 4, 1985020414058229452794464695560326943132876800000⟩, + ⟨3, 6, 6, 3, 8, 4, -3674804310548226266206398915373326165816115200000⟩, + ⟨3, 6, 0, 4, 1, 4, -7364988118574662218172079282799994724709040128000000⟩, + ⟨3, 6, 1, 4, 2, 4, 3920900302001515633243973730217456929643010457600000⟩, + ⟨3, 6, 2, 4, 3, 4, 1067290290547905311160596652026622548313007718400000⟩, + ⟨3, 6, 3, 4, 4, 4, 76342761012948493480554617534584388800688947200000⟩, + ⟨3, 6, 4, 4, 5, 4, -25523795655227533509985307541262319964924149760000⟩, + ⟨3, 6, 5, 4, 6, 4, 4861297474219342714396372937090407159824384000000⟩, + ⟨3, 6, 6, 4, 7, 4, 1603524524766169790442972819984422902589030400000⟩, + ⟨3, 6, 7, 4, 8, 4, -1176355841906178920649464024045609809870848000000⟩, + ⟨3, 6, 0, 5, 0, 4, 45576322817076034597647943147626962223256672665600000⟩, + ⟨3, 6, 1, 5, 1, 4, 1777781889020575569364557040665450566567696793600000⟩, + ⟨3, 6, 2, 5, 2, 4, -145175382555331603864067664914550290417241292800000⟩, + ⟨3, 6, 3, 5, 3, 4, 192207270634276989858021682592363144951522918400000⟩, + ⟨3, 6, 4, 5, 4, 4, -3564364582806961413098937497512395010159411200000⟩, + ⟨3, 6, 5, 5, 5, 4, 1337835484541656690849871954383078542016512000000⟩, + ⟨3, 6, 6, 5, 6, 4, 2715862636161283715449015283367751368415641600000⟩, + ⟨3, 6, 7, 5, 7, 4, -536578181890536052463693222045091942000230400000⟩, + ⟨3, 6, 8, 5, 8, 4, -359902860671321889363515650524053238919987200000⟩, + ⟨3, 6, 1, 6, 0, 4, -19381535833918007558901504027467003677282979020800000⟩, + ⟨3, 6, 2, 6, 1, 4, 2435995233888993758724505313599505250125453721600000⟩, + ⟨3, 6, 3, 6, 2, 4, 214941755956436519131537179128874917688036556800000⟩, + ⟨3, 6, 4, 6, 3, 4, 89095805247957044793148525613177471509934899200000⟩, + ⟨3, 6, 5, 6, 4, 4, -11156271083244210164419593418700789113474252800000⟩, + ⟨3, 6, 6, 6, 5, 4, -258326395888576309479950697522984908331417600000⟩, + ⟨3, 6, 7, 6, 6, 4, -162221826785000912349544883227076791684300800000⟩, + ⟨3, 6, 8, 6, 7, 4, -97014529744573946002834888462249902263500800000⟩, + ⟨3, 6, 2, 7, 0, 4, -19872785894549819191801999560451919569627172044800000⟩, + ⟨3, 6, 3, 7, 1, 4, -1975935235594661489896334971630680031742656512000000⟩, + ⟨3, 6, 4, 7, 2, 4, -91560001817618302793762930371711199074477670400000⟩, + ⟨3, 6, 5, 7, 3, 4, -15554034823261526938065816669021801513851289600000⟩, + ⟨3, 6, 6, 7, 4, 4, -8964866460496265011862106063668470622453760000000⟩, + ⟨3, 6, 7, 7, 5, 4, 582787863157291834819388012338874088318566400000⟩, + ⟨3, 6, 8, 7, 6, 4, -145043320648014085626794886659233748405452800000⟩ +] + +def collectedFourData_8_5_20 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 5, 5, 4353374505069030420219138147644932022952001536000000⟩, + ⟨3, 7, 1, 0, 6, 5, -1744707137507380474830493209906242205700325376000000⟩, + ⟨3, 7, 2, 0, 7, 5, 42561538455566979556419100731211666025349120000000⟩, + ⟨3, 7, 3, 0, 8, 5, -5186442748787151674968076091423439348511539200000⟩, + ⟨3, 7, 0, 1, 4, 5, 3130002799359319189707899166003587216786325504000000⟩, + ⟨3, 7, 1, 1, 5, 5, -379881799221544822305343360750269040315858944000000⟩, + ⟨3, 7, 2, 1, 6, 5, -97969012983848626097409571401650041327190016000000⟩, + ⟨3, 7, 3, 1, 7, 5, 69284246626965366037412033197831534566545817600000⟩, + ⟨3, 7, 4, 1, 8, 5, -17975466359075747391369629878230112638546739200000⟩, + ⟨3, 7, 0, 2, 3, 5, 1225144142431360179376484854368614417159946240000000⟩, + ⟨3, 7, 1, 2, 4, 5, 330289712664352862701134431914308959767363584000000⟩, + ⟨3, 7, 2, 2, 5, 5, -205438779455627472323610905462728481298186240000000⟩, + ⟨3, 7, 3, 2, 6, 5, -22553468195586142402598466778837793879202201600000⟩, + ⟨3, 7, 4, 2, 7, 5, 2437320389367231590525511559097785094504448000000⟩, + ⟨3, 7, 5, 2, 8, 5, -4343490395296490266717718785834200235769856000000⟩, + ⟨3, 7, 0, 3, 2, 5, -5383363125292167584915879646221154054033113088000000⟩, + ⟨3, 7, 1, 3, 3, 5, -914718552532504187907769859244608277505376256000000⟩, + ⟨3, 7, 2, 3, 4, 5, 15136951450365922515929673734797300202471424000000⟩, + ⟨3, 7, 3, 3, 5, 5, -45049825173968611014539421856363873493739110400000⟩, + ⟨3, 7, 4, 3, 6, 5, 1985020414058229452794464695560326943132876800000⟩, + ⟨3, 7, 5, 3, 7, 5, 342174928617370197829207923992606357323776000000⟩, + ⟨3, 7, 6, 3, 8, 5, -554275239197508842374286742048846649491456000000⟩, + ⟨3, 7, 0, 4, 1, 5, -4443480747415116973064402372785662940529295360000000⟩, + ⟨3, 7, 1, 4, 2, 5, 1577051198090242000369155265050551010730180608000000⟩, + ⟨3, 7, 2, 4, 3, 5, 321961405884149013285078596380260741471535104000000⟩, + ⟨3, 7, 3, 4, 4, 5, 18423795574632935274500870967764726836730265600000⟩, + ⟨3, 7, 4, 4, 5, 5, -5133047185277746884615248676185173404313190400000⟩, + ⟨3, 7, 5, 4, 6, 5, 837983380144729493544968854122185757818880000000⟩, + ⟨3, 7, 6, 4, 7, 5, 241861569872613322075814779646762299686912000000⟩, + ⟨3, 7, 7, 4, 8, 5, -157716616675306090035684110720411400929280000000⟩, + ⟨3, 7, 0, 5, 0, 5, 27497330574763595397165120437347830321352015872000000⟩, + ⟨3, 7, 1, 5, 1, 5, 715053391332557423315493249565829122372927488000000⟩, + ⟨3, 7, 2, 5, 2, 5, -43793961850143675874818119413352319909101568000000⟩, + ⟨3, 7, 3, 5, 3, 5, 46385373218600865605608447955020225438757683200000⟩, + ⟨3, 7, 4, 5, 4, 5, -716823306228505476393387248690448404840448000000⟩, + ⟨3, 7, 5, 5, 5, 5, 230614132823420784319305359876889079971840000000⟩, + ⟨3, 7, 6, 5, 6, 5, 409636890858359409093930300906963361333248000000⟩, + ⟨3, 7, 7, 5, 7, 5, -71940217759646108435315423616028737798144000000⟩, + ⟨3, 7, 8, 5, 8, 5, -43427671751414572632497494502590993190092800000⟩, + ⟨3, 7, 1, 6, 0, 5, -7795575493747286866118246689474159527711473664000000⟩, + ⟨3, 7, 2, 6, 1, 5, 734848294953905692614075238151486007511351296000000⟩, + ⟨3, 7, 3, 6, 2, 5, 51871885685695395843363146776588762267149926400000⟩, + ⟨3, 7, 4, 6, 3, 5, 17917906040530996174961657666777953723219968000000⟩, + ⟨3, 7, 5, 6, 4, 5, -1923101764853254421841133785458372662788096000000⟩, + ⟨3, 7, 6, 6, 5, 5, -38963686980874930475482138616181741846528000000⟩, + ⟨3, 7, 7, 6, 6, 5, -21749437338585892536147054329855043698688000000⟩, + ⟨3, 7, 8, 6, 7, 5, -11706256363193492350218872395729447629619200000⟩, + ⟨3, 7, 2, 7, 0, 5, -5994873318072932846295526694052914325973106688000000⟩, + ⟨3, 7, 3, 7, 1, 5, -476852374295654448056484625761744287302680576000000⟩, + ⟨3, 7, 4, 7, 2, 5, -18413476426563302028514252693693947042594816000000⟩, + ⟨3, 7, 5, 7, 3, 5, -2681181874840648116210094251803872510083072000000⟩, + ⟨3, 7, 6, 7, 4, 5, -1352181798497996799749884730895764344012800000000⟩, + ⟨3, 7, 7, 7, 5, 5, 78135651426407510673738565637164555567104000000⟩, + ⟨3, 7, 8, 7, 6, 5, -17501649492554426790530167220379820700467200000⟩ +] + +def collectedFourData_8_5_21 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 5, 6, -18804944436761841739802011152381248001986789376000000⟩, + ⟨3, 8, 1, 0, 6, 6, 5652360153206227377175998353021026436867162112000000⟩, + ⟨3, 8, 2, 0, 7, 6, -110309925994388791188672243888071348324401152000000⟩, + ⟨3, 8, 3, 0, 8, 6, 11201743337475880691093075339836572275677593600000⟩, + ⟨3, 8, 0, 1, 4, 6, -13520437688125731108984078537212179908095115264000000⟩, + ⟨3, 8, 1, 1, 5, 6, 1230710128185662434517231095636403540855881728000000⟩, + ⟨3, 8, 2, 1, 6, 6, 253913626343037526740693639517709017613441433600000⟩, + ⟨3, 8, 3, 1, 7, 6, -149640974679058561709119492731561697105202380800000⟩, + ⟨3, 8, 4, 1, 8, 6, 33277401477901608147971056712992870995119308800000⟩, + ⟨3, 8, 0, 2, 3, 6, -5292163010239488648264349175954840322142371840000000⟩, + ⟨3, 8, 1, 2, 4, 6, -1070045723286911767039274735734162905165201408000000⟩, + ⟨3, 8, 2, 2, 5, 6, 532451066866068199235354220985730686311727104000000⟩, + ⟨3, 8, 3, 2, 6, 6, 48711260170752027255596842190782439141199052800000⟩, + ⟨3, 8, 4, 2, 7, 6, -4512132676118183670012596338740158552604672000000⟩, + ⟨3, 8, 5, 2, 8, 6, 7035843296681644688816378716606190831271936000000⟩, + ⟨3, 8, 0, 3, 2, 6, 23254108815163042704126309951777025518949367808000000⟩, + ⟨3, 8, 1, 3, 3, 6, 2963430702255227285254687205939345776466460672000000⟩, + ⟨3, 8, 2, 3, 4, 6, -39231570447428684045887706209730340753663590400000⟩, + ⟨3, 8, 3, 3, 5, 6, 97299170826664428635751772629691108481512243200000⟩, + ⟨3, 8, 4, 3, 6, 6, -3674804310548226266206398915373326165816115200000⟩, + ⟨3, 8, 5, 3, 7, 6, -554275239197508842374286742048846649491456000000⟩, + ⟨3, 8, 6, 3, 8, 6, 798087021431723126827099846361118022828032000000⟩, + ⟨3, 8, 0, 4, 1, 6, 19194169595027127769565035742837700172720373760000000⟩, + ⟨3, 8, 1, 4, 2, 6, -5109202089003155909795921162098683061097988096000000⟩, + ⟨3, 8, 2, 4, 3, 6, -834451482368454545554065321219339986181449318400000⟩, + ⟨3, 8, 3, 4, 4, 6, -39791942054585233351544723957132477600681164800000⟩, + ⟨3, 8, 4, 4, 5, 6, 9502644803607934222637682053813736482380185600000⟩, + ⟨3, 8, 5, 4, 6, 6, -1357415168756108427368289338682487634657280000000⟩, + ⟨3, 8, 6, 4, 7, 6, -348250411073571362183122341835513805144064000000⟩, + ⟨3, 8, 7, 4, 8, 6, 204382982204709381020708850723420314271744000000⟩, + ⟨3, 8, 0, 5, 0, 6, -118778150838070997473041928804558174227164823552000000⟩, + ⟨3, 8, 1, 5, 1, 6, -2316571767086055918051262886178249363639238656000000⟩, + ⟨3, 8, 2, 5, 2, 6, 113504089983348803548604747503428564662668492800000⟩, + ⟨3, 8, 3, 5, 3, 6, -100183704048271241762839213869862824523176345600000⟩, + ⟨3, 8, 4, 5, 4, 6, 1327031881875986991179605539059868654108672000000⟩, + ⟨3, 8, 5, 5, 5, 6, -373562446990275420282414549788005540823040000000⟩, + ⟨3, 8, 6, 5, 6, 6, -589825889691608764902492974161408039059456000000⟩, + ⟨3, 8, 7, 5, 7, 6, 93226424432136536479479019566844934828851200000⟩, + ⟨3, 8, 8, 5, 8, 6, 51161249322109076671865730464201509856870400000⟩, + ⟨3, 8, 1, 6, 0, 6, 25255470872389738621364519887257172206963130368000000⟩, + ⟨3, 8, 2, 6, 1, 6, -1904561347520215614997624643403020804451572121600000⟩, + ⟨3, 8, 3, 6, 2, 6, -112033541682867047705450885542517103794533171200000⟩, + ⟨3, 8, 4, 6, 3, 6, -33170841915487669229435674017985944147197952000000⟩, + ⟨3, 8, 5, 6, 4, 6, 3115154272179712677995577401223512510693376000000⟩, + ⟨3, 8, 6, 6, 5, 6, 56102836077589379390004271961262696431616000000⟩, + ⟨3, 8, 7, 6, 6, 6, 28184822615654268640110068073028011845222400000⟩, + ⟨3, 8, 8, 6, 7, 6, 13790900508184850948293758538882666305945600000⟩, + ⟨3, 8, 2, 7, 0, 6, 15537362042322157225554304304535879814306647244800000⟩, + ⟨3, 8, 3, 7, 1, 6, 1029911668836030005629377019158753936049963008000000⟩, + ⟨3, 8, 4, 7, 2, 6, 34088275397719930243656435070818726627508224000000⟩, + ⟨3, 8, 5, 7, 3, 6, 4343137385939632206673442296790880230572032000000⟩, + ⟨3, 8, 6, 7, 4, 6, 1946972672926694413823604824100686109081600000000⟩, + ⟨3, 8, 7, 7, 5, 6, -101255009089585698015670668691196471358259200000⟩, + ⟨3, 8, 8, 7, 6, 6, 20618334281472842300408659731966475213209600000⟩ +] + +def collectedFourData_8_5_22 : List CollectedFourTerm := [ + ⟨4, 1, 3, 0, 8, 0, 3207195330919534170333706168835386077842767872000000⟩, + ⟨4, 1, 3, 1, 7, 0, -42844030687554416198514420522586639578867695616000000⟩, + ⟨4, 1, 4, 1, 8, 0, 66694072878460514916217871143740467089067999232000000⟩, + ⟨4, 1, 3, 2, 6, 0, 13946626116684933872483702344637242297659949056000000⟩, + ⟨4, 1, 4, 2, 7, 0, -9043149169509171867108670619876927375230894080000000⟩, + ⟨4, 1, 5, 2, 8, 0, 56404529770982971432341930327755861358972764160000000⟩, + ⟨4, 1, 3, 3, 5, 0, 27857935767338966801803629774340587077568036864000000⟩, + ⟨4, 1, 4, 3, 6, 0, -7364988118574662218172079282799994724709040128000000⟩, + ⟨4, 1, 5, 3, 7, 0, -4443480747415116973064402372785662940529295360000000⟩, + ⟨4, 1, 6, 3, 8, 0, 19194169595027127769565035742837700172720373760000000⟩, + ⟨4, 1, 3, 4, 4, 0, -11392916880957879311593106784647819871488311296000000⟩, + ⟨4, 1, 4, 4, 5, 0, 19045059317231150265639530224501504150270377984000000⟩, + ⟨4, 1, 5, 4, 6, 0, -10882045132215818998496690367712429255478476800000000⟩, + ⟨4, 1, 6, 4, 7, 0, -8375499503415862680251548940650429392900587520000000⟩, + ⟨4, 1, 7, 4, 8, 0, 12288639952248037171088282315060984482155724800000000⟩, + ⟨4, 1, 3, 5, 3, 0, -28683812704660784152457432979378354617069862912000000⟩, + ⟨4, 1, 4, 5, 4, 0, 2659617551588303929179844836025078349121454080000000⟩, + ⟨4, 1, 5, 5, 5, 0, -2994753190782673231753709057248539466688102400000000⟩, + ⟨4, 1, 6, 5, 6, 0, -14185443259018138604128814054370452690782126080000000⟩, + ⟨4, 1, 7, 5, 7, 0, 5605290379482427012745474692583870774158295040000000⟩, + ⟨4, 1, 8, 5, 8, 0, 6767416564815311490081824954748950143089770496000000⟩, + ⟨4, 1, 3, 6, 2, 0, -32076565313684046976601692183218590344412135424000000⟩, + ⟨4, 1, 4, 6, 3, 0, -66480507789063389087892367277490144728611553280000000⟩, + ⟨4, 1, 5, 6, 4, 0, 24973383356794764529958065528125990023787970560000000⟩, + ⟨4, 1, 6, 6, 5, 0, 1349285631162694049027972144604573764293754880000000⟩, + ⟨4, 1, 7, 6, 6, 0, 1694628062990326699824433677165418447456174080000000⟩, + ⟨4, 1, 8, 6, 7, 0, 1824208161048141164648927671839378316506169344000000⟩, + ⟨4, 1, 3, 7, 1, 0, 294876234532147720056127818486341206664187740160000000⟩, + ⟨4, 1, 4, 7, 2, 0, 68319214322858423639885613020747556789273231360000000⟩, + ⟨4, 1, 5, 7, 3, 0, 34817805294247953663664274744026262335830097920000000⟩, + ⟨4, 1, 6, 7, 4, 0, 46825123924453303060241772603170505608921088000000000⟩, + ⟨4, 1, 7, 7, 5, 0, -6088013476666308212110258720651448177802608640000000⟩, + ⟨4, 1, 8, 7, 6, 0, 2727315278734608490885384021511293246535368704000000⟩ +] + +def collectedFourData_8_5_23 : List CollectedFourTerm := [ + ⟨4, 2, 2, 0, 7, 1, 5604629144775682697617048350069264723744915456000000⟩, + ⟨4, 2, 3, 0, 8, 1, -3414830530375355414630578520395474790383406284800000⟩, + ⟨4, 2, 2, 1, 6, 1, -12900849108812384016040799102767001026209565900800000⟩, + ⟨4, 2, 3, 1, 7, 1, 45617771585571730870153949917501972152502871654400000⟩, + ⟨4, 2, 4, 1, 8, 1, -35505937861780947543162581390977082933928945254400000⟩, + ⟨4, 2, 2, 2, 5, 1, -27052785509767003945276659943199597453547405312000000⟩, + ⟨4, 2, 3, 2, 6, 1, -14849536665211887743123160246308499550707803750400000⟩, + ⟨4, 2, 4, 2, 7, 1, 4814303260089342220528996907743333670071566336000000⟩, + ⟨4, 2, 5, 2, 8, 1, -20018727729335046148178508218685375832022581248000000⟩, + ⟨4, 2, 2, 3, 4, 1, 1993278493688445359928711650545916098779493171200000⟩, + ⟨4, 2, 3, 3, 5, 1, -29661470461254996929884276511457823411570055577600000⟩, + ⟨4, 2, 4, 3, 6, 1, 3920900302001515633243973730217456929643010457600000⟩, + ⟨4, 2, 5, 3, 7, 1, 1577051198090242000369155265050551010730180608000000⟩, + ⟨4, 2, 6, 3, 8, 1, -5109202089003155909795921162098683061097988096000000⟩, + ⟨4, 2, 2, 4, 3, 1, 42396829259240093507428372699485680741924418355200000⟩, + ⟨4, 2, 3, 4, 4, 1, 12130499199738273016137799954947109192347313766400000⟩, + ⟨4, 2, 4, 4, 5, 1, -10139022307482001447008208304432278480127577292800000⟩, + ⟨4, 2, 5, 4, 6, 1, 3862184465053964358365068466176855569900503040000000⟩, + ⟨4, 2, 6, 4, 7, 1, 2229433232182334534156419734561142859410440192000000⟩, + ⟨4, 2, 7, 4, 8, 1, -2616842353265435017823431373089702189637566464000000⟩, + ⟨4, 2, 2, 5, 2, 1, -5766918298941454466827586747451993735821682278400000⟩, + ⟨4, 2, 3, 5, 3, 1, 30540815025245381740731526221898288120422255820800000⟩, + ⟨4, 2, 4, 5, 4, 1, -1415901165533617980491153612670547197570318336000000⟩, + ⟨4, 2, 5, 5, 5, 1, 1062878265030360688139268413747603215975710720000000⟩, + ⟨4, 2, 6, 5, 6, 1, 3775953732907963118458240141747390256007610368000000⟩, + ⟨4, 2, 7, 5, 7, 1, -1193635855910772274285394970426065500679385907200000⟩, + ⟨4, 2, 8, 5, 8, 1, -1200923668649428857972578662227424848845891174400000⟩, + ⟨4, 2, 2, 6, 1, 1, 96766994811219687181474813779648388391559285964800000⟩, + ⟨4, 2, 3, 6, 2, 1, 34153215891388309618167429879900406583721040281600000⟩, + ⟨4, 2, 4, 6, 3, 1, 35392242169400628250733978709603334806596222976000000⟩, + ⟨4, 2, 5, 6, 4, 1, -8863390297372374135520832954979732273305223168000000⟩, + ⟨4, 2, 6, 6, 5, 1, -359159740215301299427372644317459199031246848000000⟩, + ⟨4, 2, 7, 6, 6, 1, -360867801929049775351729824027333628478776934400000⟩, + ⟨4, 2, 8, 6, 7, 1, -323718029792355310009164748648541674622523801600000⟩, + ⟨4, 2, 2, 7, 0, 1, -789422632191411332791094572339250177547230930534400000⟩, + ⟨4, 2, 3, 7, 1, 1, -313966648259555376309204031777835610105282822144000000⟩, + ⟨4, 2, 4, 7, 2, 1, -36371114760581988509814189214559831517258842112000000⟩, + ⟨4, 2, 5, 7, 3, 1, -12357308307481404692743605036075837873639653376000000⟩, + ⟨4, 2, 6, 7, 4, 1, -12464150625960453041397689640281207770762444800000000⟩, + ⟨4, 2, 7, 7, 5, 1, 1296430815362665083259314109824628517518914355200000⟩, + ⟨4, 2, 8, 7, 6, 1, -483980473010972586199545091966240905426999705600000⟩ +] + +def collectedFourData_8_5_24 : List CollectedFourTerm := [ + ⟨4, 3, 1, 0, 6, 2, -46904026138056441561228802357337634210195072614400000⟩, + ⟨4, 3, 2, 0, 7, 2, 4576831192535574076649855625335993600481165312000000⟩, + ⟨4, 3, 3, 0, 8, 2, -1394303038160275761692505006150469382187044044800000⟩, + ⟨4, 3, 1, 1, 5, 2, -10212594112221813344980119675881793866142685593600000⟩, + ⟨4, 3, 2, 1, 6, 2, -10535042923659933613515308409091885601130125721600000⟩, + ⟨4, 3, 3, 1, 7, 2, 18626106610588594695794586146698037058553144934400000⟩, + ⟨4, 3, 4, 1, 8, 2, -9664908520456792501063473753525687363693025689600000⟩, + ⟨4, 3, 1, 2, 4, 2, 8879379801284514617225237967118533035912960409600000⟩, + ⟨4, 3, 2, 2, 5, 2, -22091744050806697105690641429194254716632039424000000⟩, + ⟨4, 3, 3, 2, 6, 2, -6063186416838523152794433521935528940326512230400000⟩, + ⟨4, 3, 4, 2, 7, 2, 1310479412757201905521658173166890843870593024000000⟩, + ⟨4, 3, 5, 2, 8, 2, -4086904554242568794795052348308919794924519424000000⟩, + ⟨4, 3, 1, 3, 3, 2, -24590936767901104478365006783192957085712541286400000⟩, + ⟨4, 3, 2, 3, 4, 2, 1627743593673356454341554343838914553464645222400000⟩, + ⟨4, 3, 3, 3, 5, 2, -12111019276814062459746203138489724571513100697600000⟩, + ⟨4, 3, 4, 3, 6, 2, 1067290290547905311160596652026622548313007718400000⟩, + ⟨4, 3, 5, 3, 7, 2, 321961405884149013285078596380260741471535104000000⟩, + ⟨4, 3, 6, 3, 8, 2, -834451482368454545554065321219339986181449318400000⟩, + ⟨4, 3, 1, 4, 2, 2, 42396829259240093507428372699485680741924418355200000⟩, + ⟨4, 3, 2, 4, 3, 2, 34621939401498305007833676881802805829446297190400000⟩, + ⟨4, 3, 3, 4, 4, 2, 4952981337769853986436805873324973986746361446400000⟩, + ⟨4, 3, 4, 4, 5, 2, -2759896766286095604762471753795340226627056435200000⟩, + ⟨4, 3, 5, 4, 6, 2, 788480641375816816830733234316736611242475520000000⟩, + ⟨4, 3, 6, 4, 7, 2, 364118277771825836700385622028810194703404236800000⟩, + ⟨4, 3, 7, 4, 8, 2, -356159328268180331448899741129848307306201088000000⟩, + ⟨4, 3, 1, 5, 1, 2, 19223216456307010607462301702955245807795909427200000⟩, + ⟨4, 3, 2, 5, 2, 2, -4709359151800905119401865116314012800418368716800000⟩, + ⟨4, 3, 3, 5, 3, 2, 12470062803646636383247007797893651487964056780800000⟩, + ⟨4, 3, 4, 5, 4, 2, -385415963159807157620363016010195775231361024000000⟩, + ⟨4, 3, 5, 5, 5, 2, 216990913742864022072635641963723751801487360000000⟩, + ⟨4, 3, 6, 5, 6, 2, 616701029806887925914154990246186696884564787200000⟩, + ⟨4, 3, 7, 5, 7, 2, -162457071251350747698180215271759420695406182400000⟩, + ⟨4, 3, 8, 5, 8, 2, -140099110537489928449184681070731477677139558400000⟩, + ⟨4, 3, 1, 6, 0, 2, -209573210803906763623848908833615224127715121561600000⟩, + ⟨4, 3, 2, 6, 1, 2, 79021499695970374395737499761761357617304279449600000⟩, + ⟨4, 3, 3, 6, 2, 2, 13945035414414016697783482837197653531931810201600000⟩, + ⟨4, 3, 4, 6, 3, 2, 9633959937425315733124302600286216199847542784000000⟩, + ⟨4, 3, 5, 6, 4, 2, -1809497120003229299641897185944817001650192384000000⟩, + ⟨4, 3, 6, 6, 5, 2, -58659135498827218988420960454016691747369779200000⟩, + ⟨4, 3, 7, 6, 6, 2, -49115084738781837885269670479169196386995404800000⟩, + ⟨4, 3, 8, 6, 7, 2, -37764771586075620523220286174701586069690777600000⟩, + ⟨4, 3, 2, 7, 0, 2, -644655343605575235145615543287322259732738919628800000⟩, + ⟨4, 3, 3, 7, 1, 2, -128195132278256274223679470316220255861624274944000000⟩, + ⟨4, 3, 4, 7, 2, 2, -9900414356508101959498091722726802527258411008000000⟩, + ⟨4, 3, 5, 7, 3, 2, -2522794669214616693565293236608704753369612288000000⟩, + ⟨4, 3, 6, 7, 4, 2, -2035685569901906502637836493896628481996881920000000⟩, + ⟨4, 3, 7, 7, 5, 2, 176447743506427690474136615378829167210948198400000⟩, + ⟨4, 3, 8, 7, 6, 2, -56460902184237383307873991202577166265588121600000⟩ +] + +def collectedFourData_8_5_25 : List CollectedFourTerm := [ + ⟨4, 4, 0, 0, 5, 3, 11161887877377388016491718258514953999755090329600000⟩, + ⟨4, 4, 1, 0, 6, 3, -13420089697113229781017717956713440223534304460800000⟩, + ⟨4, 4, 2, 0, 7, 3, 654757066606459892805387646952425317300436992000000⟩, + ⟨4, 4, 3, 0, 8, 3, -132978434033166669536646738312752749578761011200000⟩, + ⟨4, 4, 0, 1, 4, 3, 8025209010078513846656909306536624652848359014400000⟩, + ⟨4, 4, 1, 1, 5, 3, -2922007774403527605416594294584152749879014195200000⟩, + ⟨4, 4, 2, 1, 6, 3, -1507133103907918764290991964524742792839797145600000⟩, + ⟨4, 4, 3, 1, 7, 3, 1776421926526827008357891323851036628734286233600000⟩, + ⟨4, 4, 4, 1, 8, 3, -691326256711715420839675789955757774740442316800000⟩, + ⟨4, 4, 0, 2, 3, 3, 3141223328138104957797104760819455266299838464000000⟩, + ⟨4, 4, 1, 2, 4, 3, 2540551061378701117729135859787895727526720307200000⟩, + ⟨4, 4, 2, 2, 5, 3, -3160423647373679165015719232227071640977014784000000⟩, + ⟨4, 4, 3, 2, 6, 3, -578262409889170944885070686715961455817628057600000⟩, + ⟨4, 4, 4, 2, 7, 3, 93737961927071053028375415383567462345736192000000⟩, + ⟨4, 4, 5, 2, 8, 3, -233867453254615253978257610912222338134677913600000⟩, + ⟨4, 4, 0, 3, 2, 3, -13802739814310160125191511492769686328659725516800000⟩, + ⟨4, 4, 1, 3, 3, 3, -7035911505547937682676121637585413721612405964800000⟩, + ⟨4, 4, 2, 3, 4, 3, 232863432306442955654371435934486142573241958400000⟩, + ⟨4, 4, 3, 3, 5, 3, -1155060509730525672270173605579475485662275174400000⟩, + ⟨4, 4, 4, 3, 6, 3, 76342761012948493480554617534584388800688947200000⟩, + ⟨4, 4, 5, 3, 7, 3, 18423795574632935274500870967764726836730265600000⟩, + ⟨4, 4, 6, 3, 8, 3, -39791942054585233351544723957132477600681164800000⟩, + ⟨4, 4, 0, 4, 1, 3, -11392916880957879311593106784647819871488311296000000⟩, + ⟨4, 4, 1, 4, 2, 3, 12130499199738273016137799954947109192347313766400000⟩, + ⟨4, 4, 2, 4, 3, 3, 4952981337769853986436805873324973986746361446400000⟩, + ⟨4, 4, 3, 4, 4, 3, 472379162969609193825333142256833946862590361600000⟩, + ⟨4, 4, 4, 4, 5, 3, -197414087914942552692266262724434521868573081600000⟩, + ⟨4, 4, 5, 4, 6, 3, 45119712753679164870326761574917769766371328000000⟩, + ⟨4, 4, 6, 4, 7, 3, 17363470155253693446643473012193984993925529600000⟩, + ⟨4, 4, 7, 4, 8, 3, -14557660230805664374267818604125674891378688000000⟩, + ⟨4, 4, 0, 5, 0, 3, 70502117482728628662469200316150723586922066739200000⟩, + ⟨4, 4, 1, 5, 1, 3, 5500109699566890718363370936677510381190932070400000⟩, + ⟨4, 4, 2, 5, 2, 3, -673716388941403995215566963062269136924888268800000⟩, + ⟨4, 4, 3, 5, 3, 3, 1189303457383382055146707798004460222263014195200000⟩, + ⟨4, 4, 4, 5, 4, 3, -27568618422434562082978735016338976975880192000000⟩, + ⟨4, 4, 5, 5, 5, 3, 12417004533114311765381724912523680210223104000000⟩, + ⟨4, 4, 6, 5, 6, 3, 29408218646129905647179237165712832534570598400000⟩, + ⟨4, 4, 7, 5, 7, 3, -6640272085161168710123647956225056395650662400000⟩, + ⟨4, 4, 8, 5, 8, 3, -5010610987756464467706614007448856128231833600000⟩, + ⟨4, 4, 1, 6, 0, 3, -59962683775209689380541802209127394357418341171200000⟩, + ⟨4, 4, 2, 6, 1, 3, 11304739712524293394107689275460003152185104793600000⟩, + ⟨4, 4, 3, 6, 2, 3, 1329975565708166019617829707629232781126952550400000⟩, + ⟨4, 4, 4, 6, 3, 3, 689112519456738140480522560709781075391414272000000⟩, + ⟨4, 4, 5, 6, 4, 3, -103545966760445939325893614456486058983528857600000⟩, + ⟨4, 4, 6, 6, 5, 3, -2797239827672498082879680029026606532421222400000⟩, + ⟨4, 4, 7, 6, 6, 3, -2007530504145701830519817322827710940892364800000⟩, + ⟨4, 4, 8, 6, 7, 3, -1350647971520618130049215462238817438033510400000⟩, + ⟨4, 4, 2, 7, 0, 3, -92223773172968108591622859476067626509665094860800000⟩, + ⟨4, 4, 3, 7, 1, 3, -12226314850127720413187895135852371910366068736000000⟩, + ⟨4, 4, 4, 7, 2, 3, -708171875863361542629166486367055016900952064000000⟩, + ⟨4, 4, 5, 7, 3, 3, -144363431184383822636636056032244616557441843200000⟩, + ⟨4, 4, 6, 7, 4, 3, -97074406302180280443021589896826246649610240000000⟩, + ⟨4, 4, 7, 7, 5, 3, 7212126974040029066709036843966921282315878400000⟩, + ⟨4, 4, 8, 7, 6, 3, -2019310585039574451729179620904888441398886400000⟩ +] + +def collectedFourData_8_5_26 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 5, 4, -18658857862137120813647738156188093428078634598400000⟩, + ⟨4, 5, 1, 0, 6, 4, 11216899368030639509660440788395768547294943641600000⟩, + ⟨4, 5, 2, 0, 7, 4, -364843270668124935326618741980024760073977856000000⟩, + ⟨4, 5, 3, 0, 8, 4, 55573611888346312472843710739589823999456051200000⟩, + ⟨4, 5, 0, 1, 4, 4, -13415403906402662912491170693274354040499181977600000⟩, + ⟨4, 5, 1, 1, 5, 4, 2442298665495350549930513370564510372740884070400000⟩, + ⟨4, 5, 2, 1, 6, 4, 839803644750068019980205954609442137687510220800000⟩, + ⟨4, 5, 3, 1, 7, 4, -742392429362851789047243681466210387737811353600000⟩, + ⟨4, 5, 4, 1, 8, 4, 231132197385556736476503506949297998453475901440000⟩, + ⟨4, 5, 0, 2, 3, 4, -5251050739521465360540448221817517358559789056000000⟩, + ⟨4, 5, 1, 2, 4, 4, -2123466104772629181992779797922131688936597094400000⟩, + ⟨4, 5, 2, 2, 5, 4, 1761049034844157381884354423697268570547290112000000⟩, + ⟨4, 5, 3, 2, 6, 4, 241664229019161265258571196123617874209773977600000⟩, + ⟨4, 5, 4, 2, 7, 4, -31339560602979239924358192807312849060338073600000⟩, + ⟨4, 5, 5, 2, 8, 4, 65157728644663111337449095043414914700306022400000⟩, + ⟨4, 5, 0, 3, 2, 4, 23073458820998919035661502525799802033214272307200000⟩, + ⟨4, 5, 1, 3, 3, 4, 5880818467038766453174002547998621874184100249600000⟩, + ⟨4, 5, 2, 3, 4, 4, -129755997445007103379205630912602045007737651200000⟩, + ⟨4, 5, 3, 3, 5, 4, 482716501679585084806148555411776169232983654400000⟩, + ⟨4, 5, 4, 3, 6, 4, -25523795655227533509985307541262319964924149760000⟩, + ⟨4, 5, 5, 3, 7, 4, -5133047185277746884615248676185173404313190400000⟩, + ⟨4, 5, 6, 3, 8, 4, 9502644803607934222637682053813736482380185600000⟩, + ⟨4, 5, 0, 4, 1, 4, 19045059317231150265639530224501504150270377984000000⟩, + ⟨4, 5, 1, 4, 2, 4, -10139022307482001447008208304432278480127577292800000⟩, + ⟨4, 5, 2, 4, 3, 4, -2759896766286095604762471753795340226627056435200000⟩, + ⟨4, 5, 3, 4, 4, 4, -197414087914942552692266262724434521868573081600000⟩, + ⟨4, 5, 4, 4, 5, 4, 66001763265406312131913676443259673368623841280000⟩, + ⟨4, 5, 5, 4, 6, 4, -12570787252421388628817814709670728226045952000000⟩, + ⟨4, 5, 6, 4, 7, 4, -4146540252221997449617253071085578728190771200000⟩, + ⟨4, 5, 7, 4, 8, 4, 3041928435807217892308024720502878994694144000000⟩, + ⟨4, 5, 0, 5, 0, 4, -117855420475609997607775133338967160369663757516800000⟩, + ⟨4, 5, 1, 5, 1, 4, -4597150869002162128440354988340290412232887500800000⟩, + ⟨4, 5, 2, 5, 2, 4, 375407770882201726873675133406839377869825638400000⟩, + ⟨4, 5, 3, 5, 3, 4, -497027125026963083114033962127722031554442035200000⟩, + ⟨4, 5, 4, 5, 4, 4, 9217059663218284412996245180205846656293273600000⟩, + ⟨4, 5, 5, 5, 5, 4, -3459497252349061684871059120479198234279936000000⟩, + ⟨4, 5, 6, 5, 6, 4, -7022925790293528861423455553259885281725644800000⟩, + ⟨4, 5, 7, 5, 7, 4, 1387532897258089205359037030067707661464371200000⟩, + ⟨4, 5, 8, 5, 8, 4, 930669706396352226635592828329253123234201600000⟩, + ⟨4, 5, 1, 6, 0, 4, 50118546516738362308567180231895897744964216422400000⟩, + ⟨4, 5, 2, 6, 1, 4, -6299219086165582387020118290077637142091975884800000⟩, + ⟨4, 5, 3, 6, 2, 4, -555816034735488617848002741899667171757680230400000⟩, + ⟨4, 5, 4, 6, 3, 4, -230392075118812664086762018224771935153789337600000⟩, + ⟨4, 5, 5, 6, 4, 4, 28848905268922013827605889759078044127356518400000⟩, + ⟨4, 5, 6, 6, 5, 4, 668004001323033266923437341764611381972172800000⟩, + ⟨4, 5, 7, 6, 6, 4, 419488024139250278896593686910046759708262400000⟩, + ⟨4, 5, 8, 6, 7, 4, 250869036564891256191844001660331132085862400000⟩, + ⟨4, 5, 2, 7, 0, 4, 51388865815792015869612894234231271558285256294400000⟩, + ⟨4, 5, 3, 7, 1, 4, 5109553900568990465794901308579484374124199936000000⟩, + ⟨4, 5, 4, 7, 2, 4, 236764219796161938544262023861168649169744691200000⟩, + ⟨4, 5, 5, 7, 3, 4, 40221044631993688234107830512276980607274188800000⟩, + ⟨4, 5, 6, 7, 4, 4, 23182170936651810888791376440972203555553280000000⟩, + ⟨4, 5, 7, 7, 5, 4, -1507026113891550272171551928387133966070579200000⟩, + ⟨4, 5, 8, 7, 6, 4, 375066273133947984005446057554885831190118400000⟩ +] + +def collectedFourData_8_5_27 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 5, 5, 10661375739988814383442674636871230136443207680000000⟩, + ⟨4, 6, 1, 0, 6, 5, -4272772380953603110078525159675988888392826880000000⟩, + ⟨4, 6, 2, 0, 7, 5, 104232832029135878477109480838174841870745600000000⟩, + ⟨4, 6, 3, 0, 8, 5, -12701552516186164007429628591684404637597696000000⟩, + ⟨4, 6, 0, 1, 4, 5, 7665349230196169365043951538590536112296427520000000⟩, + ⟨4, 6, 1, 1, 5, 5, -930327173453150630324841649670541143672094720000000⟩, + ⟨4, 6, 2, 1, 6, 5, -239925248121994679985491862081651305695150080000000⟩, + ⟨4, 6, 3, 1, 7, 5, 169676508486011257051992743365334237957849088000000⟩, + ⟨4, 6, 4, 1, 8, 5, -44021758461737579110755964927982101327773696000000⟩, + ⟨4, 6, 0, 2, 3, 5, 3000367191680419746232790224408897326887731200000000⟩, + ⟨4, 6, 1, 2, 4, 5, 808876591174820322086787941693355148097617920000000⟩, + ⟨4, 6, 2, 2, 5, 5, -503117757682188831181883154202219135578931200000000⟩, + ⟨4, 6, 3, 2, 6, 5, -55233244553863308197592189384570267141931008000000⟩, + ⟨4, 6, 4, 2, 7, 5, 5968976121747157833581625702776479930122240000000⟩, + ⟨4, 6, 5, 2, 8, 5, -10637169642393111439488146780508885646049280000000⟩, + ⟨4, 6, 0, 3, 2, 5, -13183808780225811472183561984208998516591165440000000⟩, + ⟨4, 6, 1, 3, 3, 5, -2240137661837362732310219179558075215674081280000000⟩, + ⟨4, 6, 2, 3, 4, 5, 37070260503067095680324912167749789281157120000000⟩, + ⟨4, 6, 3, 3, 5, 5, -110326624240858971467889224285098624577175552000000⟩, + ⟨4, 6, 4, 3, 6, 5, 4861297474219342714396372937090407159824384000000⟩, + ⟨4, 6, 5, 3, 7, 5, 837983380144729493544968854122185757818880000000⟩, + ⟨4, 6, 6, 3, 8, 5, -1357415168756108427368289338682487634657280000000⟩, + ⟨4, 6, 0, 4, 1, 5, -10882045132215818998496690367712429255478476800000000⟩, + ⟨4, 6, 1, 4, 2, 5, 3862184465053964358365068466176855569900503040000000⟩, + ⟨4, 6, 2, 4, 3, 5, 788480641375816816830733234316736611242475520000000⟩, + ⟨4, 6, 3, 4, 4, 5, 45119712753679164870326761574917769766371328000000⟩, + ⟨4, 6, 4, 4, 5, 5, -12570787252421388628817814709670728226045952000000⟩, + ⟨4, 6, 5, 4, 6, 5, 2052213901925071838619972418300138645094400000000⟩, + ⟨4, 6, 6, 4, 7, 5, 592316849945488737717670132236925072834560000000⟩, + ⟨4, 6, 7, 4, 8, 5, -386246602229449332092722512593175340646400000000⟩, + ⟨4, 6, 0, 5, 0, 5, 67340719885891994815817059620219846097486479360000000⟩, + ⟨4, 6, 1, 5, 1, 5, 1751159444305325714156112997059477571570237440000000⟩, + ⟨4, 6, 2, 5, 2, 5, -107251026045073477000252286037373883347107840000000⟩, + ⟨4, 6, 3, 5, 3, 5, 113597369614603479227123783414232709821628416000000⟩, + ⟨4, 6, 4, 5, 4, 5, -1755493950264216606091389225404039681802240000000⟩, + ⟨4, 6, 5, 5, 5, 5, 564771975882003757374424192107381207859200000000⟩, + ⟨4, 6, 6, 5, 6, 5, 1003197130252984660152019323102437824266240000000⟩, + ⟨4, 6, 7, 5, 7, 5, -176180958348319639956493094552460821790720000000⟩, + ⟨4, 6, 8, 5, 8, 5, -106353984826165836563573558160635109310464000000⟩, + ⟨4, 6, 1, 6, 0, 5, -19091295580362840253849637952749413675114168320000000⟩, + ⟨4, 6, 2, 6, 1, 5, 1799636988563997928008714498822712213351956480000000⟩, + ⟨4, 6, 3, 6, 2, 5, 127033790222506194267716382608019984463429632000000⟩, + ⟨4, 6, 4, 6, 3, 5, 43880793749649408322430054627284690497699840000000⟩, + ⟨4, 6, 5, 6, 4, 5, -4709659248810952118416022918175155269140480000000⟩, + ⟨4, 6, 6, 6, 5, 5, -95421725522286760640737823568108862832640000000⟩, + ⟨4, 6, 7, 6, 6, 5, -53264180081453771225930326770288364093440000000⟩, + ⟨4, 6, 8, 6, 7, 5, -28668518513929641045991730573072029188096000000⟩, + ⟨4, 6, 2, 7, 0, 5, -14681391845151064207701553255473779452611133440000000⟩, + ⟨4, 6, 3, 7, 1, 5, -1167807255946417090184671389048439210644602880000000⟩, + ⟨4, 6, 4, 7, 2, 5, -45094441251133533136080781450566632032174080000000⟩, + ⟨4, 6, 5, 7, 3, 5, -6566190747347739294287558699081901916815360000000⟩, + ⟨4, 6, 6, 7, 4, 5, -3311481290152038869288654726948469080064000000000⟩, + ⟨4, 6, 7, 7, 5, 5, 191353520717261199715908814021645062635520000000⟩, + ⟨4, 6, 8, 7, 6, 5, -42861385137539084808556189072974032142336000000⟩ +] + +def collectedFourData_8_5_28 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 5, 6, 8205658599196048929196787645750918160687562752000000⟩, + ⟨4, 7, 1, 0, 6, 6, -2466443751157209558842363147673987565668532224000000⟩, + ⟨4, 7, 2, 0, 7, 6, 48134446547102008280332764088320302518370304000000⟩, + ⟨4, 7, 3, 0, 8, 6, -4887952838799983925654913002800065908257587200000⟩, + ⟨4, 7, 0, 1, 4, 6, 5899730049910613433999717619650127545162006528000000⟩, + ⟨4, 7, 1, 1, 5, 6, -537028289576979745596298428467811902036115456000000⟩, + ⟨4, 7, 2, 1, 6, 6, -110796845928547503939336338413466313322345267200000⟩, + ⟨4, 7, 3, 1, 7, 6, 65296802912475740698245581345150049967511961600000⟩, + ⟨4, 7, 4, 1, 8, 6, -14520808424311585684507264568276782308497817600000⟩, + ⟨4, 7, 0, 2, 3, 6, 2309269408338474611144306967726558279295303680000000⟩, + ⟨4, 7, 1, 2, 4, 6, 466921341902894162645433307404419651459874816000000⟩, + ⟨4, 7, 2, 2, 5, 6, -232338451739292224069235821752348108765790208000000⟩, + ⟨4, 7, 3, 2, 6, 6, -21255472051085515121016901789426613260753305600000⟩, + ⟨4, 7, 4, 2, 7, 6, 1968898149048626402454682601564282598457344000000⟩, + ⟨4, 7, 5, 2, 8, 6, -3070135529735880473364546641019027295567872000000⟩, + ⟨4, 7, 0, 3, 2, 6, -10147080126052269123950869168563837573965807616000000⟩, + ⟨4, 7, 1, 3, 3, 6, -1293112069905668565346866378505655360730169344000000⟩, + ⟨4, 7, 2, 3, 4, 6, 17118948395964664185501597185924257987480780800000⟩, + ⟨4, 7, 3, 3, 5, 6, -42457119747063032459980432574897604427933286400000⟩, + ⟨4, 7, 4, 3, 6, 6, 1603524524766169790442972819984422902589030400000⟩, + ⟨4, 7, 5, 3, 7, 6, 241861569872613322075814779646762299686912000000⟩, + ⟨4, 7, 6, 3, 8, 6, -348250411073571362183122341835513805144064000000⟩, + ⟨4, 7, 0, 4, 1, 6, -8375499503415862680251548940650429392900587520000000⟩, + ⟨4, 7, 1, 4, 2, 6, 2229433232182334534156419734561142859410440192000000⟩, + ⟨4, 7, 2, 4, 3, 6, 364118277771825836700385622028810194703404236800000⟩, + ⟨4, 7, 3, 4, 4, 6, 17363470155253693446643473012193984993925529600000⟩, + ⟨4, 7, 4, 4, 5, 6, -4146540252221997449617253071085578728190771200000⟩, + ⟨4, 7, 5, 4, 6, 6, 592316849945488737717670132236925072834560000000⟩, + ⟨4, 7, 6, 4, 7, 6, 151961309426314080578624537917303321264128000000⟩, + ⟨4, 7, 7, 4, 8, 6, -89183830406796880309405064040892216639488000000⟩, + ⟨4, 7, 0, 5, 0, 6, 51829610988675441639155406655827729919040815104000000⟩, + ⟨4, 7, 1, 5, 1, 6, 1010851008104216279887027847892728997123981312000000⟩, + ⟨4, 7, 2, 5, 2, 6, -49528240572465552750043866744992008152652185600000⟩, + ⟨4, 7, 3, 5, 3, 6, 43715804393228381538063878689952981111223091200000⟩, + ⟨4, 7, 4, 5, 4, 6, -579058907062534903627857755359454737465344000000⟩, + ⟨4, 7, 5, 5, 5, 6, 163006379295120754056254520666483673006080000000⟩, + ⟨4, 7, 6, 5, 6, 6, 257374325143702921298259252101043990822912000000⟩, + ⟨4, 7, 7, 5, 7, 6, -40679950631409040278410064233937420838502400000⟩, + ⟨4, 7, 8, 5, 8, 6, -22324540593956031357668756502368727387340800000⟩, + ⟨4, 7, 1, 6, 0, 6, -11020387347470193149820699823993761050432372736000000⟩, + ⟨4, 7, 2, 6, 1, 6, 831067608390487764780809244426716633579598643200000⟩, + ⟨4, 7, 3, 6, 2, 6, 48886557351972127728389996946818985951127142400000⟩, + ⟨4, 7, 4, 6, 3, 6, 14474310473063234445168815002778428615163904000000⟩, + ⟨4, 7, 5, 6, 4, 6, -1359317626664333503869857556523775271370752000000⟩, + ⟨4, 7, 6, 6, 5, 6, -24480833795998731347149016706258391007232000000⟩, + ⟨4, 7, 7, 6, 6, 6, -12298628844169221717308697816783005732044800000⟩, + ⟨4, 7, 8, 6, 7, 6, -6017748243085508660180244251389723882291200000⟩, + ⟨4, 7, 2, 7, 0, 6, -6779827979824504630795383275373425694468577689600000⟩, + ⟨4, 7, 3, 7, 1, 6, -449408588800487790783683757402905547443798016000000⟩, + ⟨4, 7, 4, 7, 2, 6, -14874638480837228889553141452715842179432448000000⟩, + ⟨4, 7, 5, 7, 3, 6, -1895155965936063520266090175563650316632064000000⟩, + ⟨4, 7, 6, 7, 4, 6, -849574063338828013681183128187697312563200000000⟩, + ⟨4, 7, 7, 7, 5, 6, 44183275246661958129141342371372375369318400000⟩, + ⟨4, 7, 8, 7, 6, 6, -8996942935237932681033439938313641472819200000⟩ +] + +def collectedFourData_8_5_29 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 5, 7, -12039447206159242430300086195060570866560532480000000⟩, + ⟨4, 8, 1, 0, 6, 7, 2895038244162673280860839891917055296387678208000000⟩, + ⟨4, 8, 2, 0, 7, 7, -47082316915492640317508947389537799781744640000000⟩, + ⟨4, 8, 3, 0, 8, 7, 4098095370061844440412985642081667006857216000000⟩, + ⟨4, 8, 0, 1, 4, 7, -8656159357330463564904498131573040690726174720000000⟩, + ⟨4, 8, 1, 1, 5, 7, 630347817903075461997616123813813385378660352000000⟩, + ⟨4, 8, 2, 1, 6, 7, 108375032590022663645352051982680831717015552000000⟩, + ⟨4, 8, 3, 1, 7, 7, -54745316601940220918154169202887429768347648000000⟩, + ⟨4, 8, 4, 1, 8, 7, 10652557884407961001576758954226031800614912000000⟩, + ⟨4, 8, 0, 2, 3, 7, -3388189599944310818537376169084229436781363200000000⟩, + ⟨4, 8, 1, 2, 4, 7, -548058369946776843067351972493593572091625472000000⟩, + ⟨4, 8, 2, 2, 5, 7, 227259964560719484071146312575597201881825280000000⟩, + ⟨4, 8, 3, 2, 6, 7, 17820743054144864435305188238656331440979968000000⟩, + ⟨4, 8, 4, 2, 7, 7, -1444396268332321105743941856837865077473280000000⟩, + ⟨4, 8, 5, 2, 8, 7, 2002018711528343156412814950373718155591680000000⟩, + ⟨4, 8, 0, 3, 2, 7, 14887925691454325045367594031016669637079203840000000⟩, + ⟨4, 8, 1, 3, 3, 7, 1517816449132008402176763436638806065438261248000000⟩, + ⟨4, 8, 2, 3, 4, 7, -16744759968312108623019532009338418262704128000000⟩, + ⟨4, 8, 3, 3, 5, 7, 35596359375741547595161343726202448659873792000000⟩, + ⟨4, 8, 4, 3, 6, 7, -1176355841906178920649464024045609809870848000000⟩, + ⟨4, 8, 5, 3, 7, 7, -157716616675306090035684110720411400929280000000⟩, + ⟨4, 8, 6, 3, 8, 7, 204382982204709381020708850723420314271744000000⟩, + ⟨4, 8, 0, 4, 1, 7, 12288639952248037171088282315060984482155724800000000⟩, + ⟨4, 8, 1, 4, 2, 7, -2616842353265435017823431373089702189637566464000000⟩, + ⟨4, 8, 2, 4, 3, 7, -356159328268180331448899741129848307306201088000000⟩, + ⟨4, 8, 3, 4, 4, 7, -14557660230805664374267818604125674891378688000000⟩, + ⟨4, 8, 4, 4, 5, 7, 3041928435807217892308024720502878994694144000000⟩, + ⟨4, 8, 5, 4, 6, 7, -386246602229449332092722512593175340646400000000⟩, + ⟨4, 8, 6, 4, 7, 7, -89183830406796880309405064040892216639488000000⟩, + ⟨4, 8, 7, 4, 8, 7, 47582420432336056622172306927609635143680000000⟩, + ⟨4, 8, 0, 5, 0, 7, -76045067884626034825996590532801519248432168960000000⟩, + ⟨4, 8, 1, 5, 1, 7, -1186506818263770047925755717331338364928917504000000⟩, + ⟨4, 8, 2, 5, 2, 7, 48445645191280980133711814746765326702084096000000⟩, + ⟨4, 8, 3, 5, 3, 7, -36651649778683428966823352923448948174094336000000⟩, + ⟨4, 8, 4, 5, 4, 7, 424801315857736221558883918036396702433280000000⟩, + ⟨4, 8, 5, 5, 5, 7, -106295574995476757512561009137292620595200000000⟩, + ⟨4, 8, 6, 5, 6, 7, -151049160153558664138161516463075048292352000000⟩, + ⟨4, 8, 7, 5, 7, 7, 21704052239977121913212399562036571275264000000⟩, + ⟨4, 8, 8, 5, 8, 7, 10918283792968014948266633503585666596864000000⟩, + ⟨4, 8, 1, 6, 0, 7, 12935402569567490393401611763516850162066522112000000⟩, + ⟨4, 8, 2, 6, 1, 7, -812902013491567999077955858454510356987379712000000⟩, + ⟨4, 8, 3, 6, 2, 7, -40986846835364449595440677065945540273897472000000⟩, + ⟨4, 8, 4, 6, 3, 7, -10618446690133808622775204944307525496340480000000⟩, + ⟨4, 8, 5, 6, 4, 7, 886403644768871447051508820967773049978880000000⟩, + ⟨4, 8, 6, 6, 5, 7, 14367436933267610150606093181782769795072000000⟩, + ⟨4, 8, 7, 6, 6, 7, 6561711082998247071454492715277172604928000000⟩, + ⟨4, 8, 8, 6, 7, 7, 2943105719740109420657399162433171357696000000⟩, + ⟨4, 8, 2, 7, 0, 7, 6631633528106702387563879334105731825177460736000000⟩, + ⟨4, 8, 3, 7, 1, 7, 376787444103379950240836553814681911275028480000000⟩, + ⟨4, 8, 4, 7, 2, 7, 10912129875735396210202990078927532992757760000000⟩, + ⟨4, 8, 5, 7, 3, 7, 1235820916803296601615094147707381649244160000000⟩, + ⟨4, 8, 6, 7, 4, 7, 498602371017099735268293471706711012147200000000⟩, + ⟨4, 8, 7, 7, 5, 7, -23573187754717381401428782773000443265024000000⟩, + ⟨4, 8, 8, 7, 6, 7, 4400143233525742923019983956040468135936000000⟩ +] + +def collectedFourData_8_5_30 : List CollectedFourTerm := [ + ⟨5, 0, 3, 0, 8, 0, -19846898241527132635849904009553387251516728934400000⟩, + ⟨5, 0, 3, 1, 7, 0, 265129195317505933017592832882750557234411025203200000⟩, + ⟨5, 0, 4, 1, 8, 0, -412719008714786071807833032305030747963655612006400000⟩, + ⟨5, 0, 3, 2, 6, 0, -86305086154858588179009485985364346222465463091200000⟩, + ⟨5, 0, 4, 2, 7, 0, 55961188150876020483476069065345844130103689216000000⟩, + ⟨5, 0, 5, 2, 8, 0, -349044834261756076120066903821002647283152453632000000⟩, + ⟨5, 0, 3, 3, 5, 0, -172391625500045724453329455966925434795257023692800000⟩, + ⟨5, 0, 4, 3, 6, 0, 45576322817076034597647943147626962223256672665600000⟩, + ⟨5, 0, 5, 3, 7, 0, 27497330574763595397165120437347830321352015872000000⟩, + ⟨5, 0, 6, 3, 8, 0, -118778150838070997473041928804558174227164823552000000⟩, + ⟨5, 0, 3, 4, 4, 0, 70502117482728628662469200316150723586922066739200000⟩, + ⟨5, 0, 4, 4, 5, 0, -117855420475609997607775133338967160369663757516800000⟩, + ⟨5, 0, 5, 4, 6, 0, 67340719885891994815817059620219846097486479360000000⟩, + ⟨5, 0, 6, 4, 7, 0, 51829610988675441639155406655827729919040815104000000⟩, + ⟨5, 0, 7, 4, 8, 0, -76045067884626034825996590532801519248432168960000000⟩, + ⟨5, 0, 3, 5, 3, 0, 177502351178968031881826912475587955064373143142400000⟩, + ⟨5, 0, 4, 5, 4, 0, -16458354874387581352600862114396242731614601216000000⟩, + ⟨5, 0, 5, 5, 5, 0, 18532255040079322252273194249221917970509332480000000⟩, + ⟨5, 0, 6, 5, 6, 0, 87782944231204837702265206424580126448986095616000000⟩, + ⟨5, 0, 7, 5, 7, 0, -34686888791367426678025921199445292740098654208000000⟩, + ⟨5, 0, 8, 5, 8, 0, -41878405915927162751037431440596620445419254579200000⟩, + ⟨5, 0, 3, 6, 2, 0, 198497522611402927811297011307162228637087616204800000⟩, + ⟨5, 0, 4, 6, 3, 0, 411397416432474987182278222207648404143452717056000000⟩, + ⟨5, 0, 5, 6, 4, 0, -154541319467076845913266071350467072000274726912000000⟩, + ⟨5, 0, 6, 6, 5, 0, -8349704915778503835462358928333891663220965376000000⟩, + ⟨5, 0, 7, 6, 6, 0, -10486767176030499265442696906105093114315145216000000⟩, + ⟨5, 0, 8, 6, 7, 0, -11288640075846427154445699621629333585137552588800000⟩, + ⟨5, 0, 3, 7, 1, 0, -1824765259597172998145732740550170888680958328832000000⟩, + ⟨5, 0, 4, 7, 2, 0, -422775775935698113339875823461615317381988483072000000⟩, + ⟨5, 0, 5, 7, 3, 0, -215460976762559725340409299394928374832309469184000000⟩, + ⟨5, 0, 6, 7, 4, 0, -289765160455341945755555750683376541748533657600000000⟩, + ⟨5, 0, 7, 7, 5, 0, 37674095743273428630733337465515949872725884928000000⟩, + ⟨5, 0, 8, 7, 6, 0, -16877284737780141016983053182677689814641069260800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0824.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0824.lean new file mode 100644 index 0000000000000000000000000000000000000000..34e0fad135bd3f96fd0f160bf240df2d9e2cce10 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0824.lean @@ -0,0 +1,655 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0824. -/ +namespace LaughlinFock +def collectedFourData_8_5_31 : List CollectedFourTerm := [ + ⟨5, 1, 2, 0, 7, 1, 2541204167617530656011318381501044194977775616000000⟩, + ⟨5, 1, 3, 0, 8, 1, -1548323957096496104494027746343393087563025612800000⟩, + ⟨5, 1, 2, 1, 6, 1, -5849395325590460111708767895014938513536502988800000⟩, + ⟨5, 1, 3, 1, 7, 1, 20683629242219762944324876568227267874241537638400000⟩, + ⟨5, 1, 4, 1, 8, 1, -16098805993904536884414145885629730235831707238400000⟩, + ⟨5, 1, 2, 2, 5, 1, -12266048208946131948352566028306563376330309632000000⟩, + ⟨5, 1, 3, 2, 6, 1, -6732952972633498846244472487039718628591560294400000⟩, + ⟨5, 1, 4, 2, 7, 1, 2182861201461948760166552148832873516992823296000000⟩, + ⟨5, 1, 5, 2, 8, 1, -9076724440118671191575797494854157830379798528000000⟩, + ⟨5, 1, 2, 3, 4, 1, 903775697648983990122548118170362935050974003200000⟩, + ⟨5, 1, 3, 3, 5, 1, -13448856366181974871807686278952763959272905113600000⟩, + ⟨5, 1, 4, 3, 6, 1, 1777781889020575569364557040665450566567696793600000⟩, + ⟨5, 1, 5, 3, 7, 1, 715053391332557423315493249565829122372927488000000⟩, + ⟨5, 1, 6, 3, 8, 1, -2316571767086055918051262886178249363639238656000000⟩, + ⟨5, 1, 2, 4, 3, 1, 19223216456307010607462301702955245807795909427200000⟩, + ⟨5, 1, 3, 4, 4, 1, 5500109699566890718363370936677510381190932070400000⟩, + ⟨5, 1, 4, 4, 5, 1, -4597150869002162128440354988340290412232887500800000⟩, + ⟨5, 1, 5, 4, 6, 1, 1751159444305325714156112997059477571570237440000000⟩, + ⟨5, 1, 6, 4, 7, 1, 1010851008104216279887027847892728997123981312000000⟩, + ⟨5, 1, 7, 4, 8, 1, -1186506818263770047925755717331338364928917504000000⟩, + ⟨5, 1, 2, 5, 2, 1, -2614787961348041486203460423651708327766156902400000⟩, + ⟨5, 1, 3, 5, 3, 1, 13847561438910497518970341244580551124476284108800000⟩, + ⟨5, 1, 4, 5, 4, 1, -641986088614353404068943795246167996074295296000000⟩, + ⟨5, 1, 5, 5, 5, 1, 481921391584482113133238551046435924523089920000000⟩, + ⟨5, 1, 6, 5, 6, 1, 1712061425463099591102959364359010657761230848000000⟩, + ⟨5, 1, 7, 5, 7, 1, -541208407069291509142676951002815845692027699200000⟩, + ⟨5, 1, 8, 5, 8, 1, -544512786293303746559471521309065605103904358400000⟩, + ⟨5, 1, 2, 6, 1, 1, 43875283118654484739236292373817343034610470092800000⟩, + ⟨5, 1, 3, 6, 2, 1, 15485466088623943665093519609638022202877647257600000⟩, + ⟨5, 1, 4, 6, 3, 1, 16047255042029987496959338901715704955940110336000000⟩, + ⟨5, 1, 5, 6, 4, 1, -4018764450079406623976294971424292124804251648000000⟩, + ⟨5, 1, 6, 6, 5, 1, -162847211670788029718234009695602220757680128000000⟩, + ⟨5, 1, 7, 6, 6, 1, -163621666756647112434607248261743146107823718400000⟩, + ⟨5, 1, 8, 6, 7, 1, -146777527146123778860677835627894008769517977600000⟩, + ⟨5, 1, 2, 7, 0, 1, -357933420948355389506674266949990444179692873318400000⟩, + ⟨5, 1, 3, 7, 1, 1, -142356137121722510467086900687407572881437097984000000⟩, + ⟨5, 1, 4, 7, 2, 1, -16491087282133753225654527030628705883947794432000000⟩, + ⟨5, 1, 5, 7, 3, 1, -5602947592130704247537920564909951547904884736000000⟩, + ⟨5, 1, 6, 7, 4, 1, -5651391144412831899318552327806063857159372800000000⟩, + ⟨5, 1, 7, 7, 5, 1, 587816839602730821798758401371572165344965427200000⟩, + ⟨5, 1, 8, 7, 6, 1, -219442386514980033694932741338123165343783321600000⟩ +] + +def collectedFourData_8_5_32 : List CollectedFourTerm := [ + ⟨5, 2, 1, 0, 6, 2, 6379998017673319135194056126714965843839339724800000⟩, + ⟨5, 2, 2, 0, 7, 2, -622551544928256795061245420485486195930824704000000⟩, + ⟨5, 2, 3, 0, 8, 2, 189656440010398091980796022900631426356058521600000⟩, + ⟨5, 2, 1, 1, 5, 2, 1389141520591376196214938059588975804674159411200000⟩, + ⟨5, 2, 2, 1, 6, 2, 1433001780512798160624171945245189021312955187200000⟩, + ⟨5, 2, 3, 1, 7, 2, -2533567649454053373132332884777304425763753164800000⟩, + ⟨5, 2, 4, 1, 8, 2, 1314644014140987245436342885980111593331176243200000⟩, + ⟨5, 2, 1, 2, 4, 2, -1207794515626865392641390783858048821670130483200000⟩, + ⟨5, 2, 2, 2, 5, 2, 3004971957764080492869747426533570579433259008000000⟩, + ⟨5, 2, 3, 2, 6, 2, 824729143855463531130975260112578150228872396800000⟩, + ⟨5, 2, 4, 2, 7, 2, -178254549641078885403938000491862825744990208000000⟩, + ⟨5, 2, 5, 2, 8, 2, 555910549719988142748634161714114566981419008000000⟩, + ⟨5, 2, 1, 3, 3, 2, 3344918139226502400604921131641355373210553548800000⟩, + ⟨5, 2, 2, 3, 4, 2, -221409583696492057644525526662856208338963660800000⟩, + ⟨5, 2, 3, 3, 5, 2, 1647369860119194304842886851144856103120220979200000⟩, + ⟨5, 2, 4, 3, 6, 2, -145175382555331603864067664914550290417241292800000⟩, + ⟨5, 2, 5, 3, 7, 2, -43793961850143675874818119413352319909101568000000⟩, + ⟨5, 2, 6, 3, 8, 2, 113504089983348803548604747503428564662668492800000⟩, + ⟨5, 2, 1, 4, 2, 2, -5766918298941454466827586747451993735821682278400000⟩, + ⟨5, 2, 2, 4, 3, 2, -4709359151800905119401865116314012800418368716800000⟩, + ⟨5, 2, 3, 4, 4, 2, -673716388941403995215566963062269136924888268800000⟩, + ⟨5, 2, 4, 4, 5, 2, 375407770882201726873675133406839377869825638400000⟩, + ⟨5, 2, 5, 4, 6, 2, -107251026045073477000252286037373883347107840000000⟩, + ⟨5, 2, 6, 4, 7, 2, -49528240572465552750043866744992008152652185600000⟩, + ⟨5, 2, 7, 4, 8, 2, 48445645191280980133711814746765326702084096000000⟩, + ⟨5, 2, 1, 5, 1, 2, -2614787961348041486203460423651708327766156902400000⟩, + ⟨5, 2, 2, 5, 2, 2, 640578315485445012647552264029693878810024345600000⟩, + ⟨5, 2, 3, 5, 3, 2, -1696207820909764046554869119744232899334478233600000⟩, + ⟨5, 2, 4, 5, 4, 2, 52425202768342012269946477180904236759646208000000⟩, + ⟨5, 2, 5, 5, 5, 2, -29515623999052290806379987685203785149317120000000⟩, + ⟨5, 2, 6, 5, 6, 2, -83885151694316260220289476282856744358930022400000⟩, + ⟨5, 2, 7, 5, 7, 2, 22097800079888393551678198507927866306251980800000⟩, + ⟨5, 2, 8, 5, 8, 2, 19056616693758703584958648351538134450490572800000⟩, + ⟨5, 2, 1, 6, 0, 2, 28506650272427170396623162503142860921217692467200000⟩, + ⟨5, 2, 2, 6, 1, 2, -10748693724712189361043460210319059554374202163200000⟩, + ⟨5, 2, 3, 6, 2, 2, -1896837129471041027871668698504025640908567347200000⟩, + ⟨5, 2, 4, 6, 3, 2, -1310434313724024240137160618597805090960048128000000⟩, + ⟨5, 2, 5, 6, 4, 2, 246132133830602440199124909594873454896611328000000⟩, + ⟨5, 2, 6, 6, 5, 2, 7978956158249656154805377430300293234845286400000⟩, + ⟨5, 2, 7, 6, 6, 2, 6680751506255868849646951135189660516063641600000⟩, + ⟨5, 2, 8, 6, 7, 2, 5136854715795020756121224162373910867948339200000⟩, + ⟨5, 2, 2, 7, 0, 2, 87687564435945206358842510854816553127305124249600000⟩, + ⟨5, 2, 3, 7, 1, 2, 17437409048922523495632372890030019303438286848000000⟩, + ⟨5, 2, 4, 7, 2, 2, 1346678082234317711167240395969033452163956736000000⟩, + ⟨5, 2, 5, 7, 3, 2, 343156575540255236509650238071709694737514496000000⟩, + ⟨5, 2, 6, 7, 4, 2, 276898828734929437639013855798108365667696640000000⟩, + ⟨5, 2, 7, 7, 5, 2, -24000844841772595399918844124563691476405452800000⟩, + ⟨5, 2, 8, 7, 6, 2, 7679947195816740736922561672541189698695987200000⟩ +] + +def collectedFourData_8_5_33 : List CollectedFourTerm := [ + ⟨5, 3, 0, 0, 5, 3, 28102153702204333432134111956488546326047568691200000⟩, + ⟨5, 3, 1, 0, 6, 3, -33787601838395867444114296710152495069226703257600000⟩, + ⟨5, 3, 2, 0, 7, 3, 1648474158271376964802073431381134490283802624000000⟩, + ⟨5, 3, 3, 0, 8, 3, -334798237836853753053152222692360028470797926400000⟩, + ⟨5, 3, 0, 1, 4, 3, 20204974245497553706822286557741764774374198476800000⟩, + ⟨5, 3, 1, 1, 5, 3, -7356704573403914140465533709683745635795625574400000⟩, + ⟨5, 3, 2, 1, 6, 3, -3794491272533021173072605544502710224135861043200000⟩, + ⟨5, 3, 3, 1, 7, 3, 4472476570957313419578668672865112977612944179200000⟩, + ⟨5, 3, 4, 1, 8, 3, -1740543977677633545711538618748707165877934489600000⟩, + ⟨5, 3, 0, 2, 3, 3, 7908620992260684501526160032134956677551095808000000⟩, + ⟨5, 3, 1, 2, 4, 3, 6396315497834732598330664714238081176760116838400000⟩, + ⟨5, 3, 2, 2, 5, 3, -7956961409958579791919819970221088389199822848000000⟩, + ⟨5, 3, 3, 2, 6, 3, -1455884461610519694364003593989572771097817907200000⟩, + ⟨5, 3, 4, 2, 7, 3, 236002963185549651458611497842061170939265024000000⟩, + ⟨5, 3, 5, 2, 8, 3, -588805333784493530667461636245410193865913139200000⟩, + ⟨5, 3, 0, 3, 2, 3, -34750995533599446750824758600496085390138644889600000⟩, + ⟨5, 3, 1, 3, 3, 3, -17714231565142150345196357501154657795755841945600000⟩, + ⟨5, 3, 2, 3, 4, 3, 586277522063417514283531831621633159394544844800000⟩, + ⟨5, 3, 3, 3, 5, 3, -2908082247052681187818665518541763337714977996800000⟩, + ⟨5, 3, 4, 3, 6, 3, 192207270634276989858021682592363144951522918400000⟩, + ⟨5, 3, 5, 3, 7, 3, 46385373218600865605608447955020225438757683200000⟩, + ⟨5, 3, 6, 3, 8, 3, -100183704048271241762839213869862824523176345600000⟩, + ⟨5, 3, 0, 4, 1, 3, -28683812704660784152457432979378354617069862912000000⟩, + ⟨5, 3, 1, 4, 2, 3, 30540815025245381740731526221898288120422255820800000⟩, + ⟨5, 3, 2, 4, 3, 3, 12470062803646636383247007797893651487964056780800000⟩, + ⟨5, 3, 3, 4, 4, 3, 1189303457383382055146707798004460222263014195200000⟩, + ⟨5, 3, 4, 4, 5, 3, -497027125026963083114033962127722031554442035200000⟩, + ⟨5, 3, 5, 4, 6, 3, 113597369614603479227123783414232709821628416000000⟩, + ⟨5, 3, 6, 4, 7, 3, 43715804393228381538063878689952981111223091200000⟩, + ⟨5, 3, 7, 4, 8, 3, -36651649778683428966823352923448948174094336000000⟩, + ⟨5, 3, 0, 5, 0, 3, 177502351178968031881826912475587955064373143142400000⟩, + ⟨5, 3, 1, 5, 1, 3, 13847561438910497518970341244580551124476284108800000⟩, + ⟨5, 3, 2, 5, 2, 3, -1696207820909764046554869119744232899334478233600000⟩, + ⟨5, 3, 3, 5, 3, 3, 2994295313222918566194972827991576165843625574400000⟩, + ⟨5, 3, 4, 5, 4, 3, -69409186042344602210301916397283051804033024000000⟩, + ⟨5, 3, 5, 5, 5, 3, 31262146130116371155558545190407649926053888000000⟩, + ⟨5, 3, 6, 5, 6, 3, 74040725868297660514983769019438513011870924800000⟩, + ⟨5, 3, 7, 5, 7, 3, -16718134854217977230738202319663638168521932800000⟩, + ⟨5, 3, 8, 5, 8, 3, -12615156294955607458475077037891236123587379200000⟩, + ⟨5, 3, 1, 6, 0, 3, -150967343012188136414929996997156539699105785446400000⟩, + ⟨5, 3, 2, 6, 1, 3, 28461810085787674821037896014742046507908936499200000⟩, + ⟨5, 3, 3, 6, 2, 3, 3348463824247691850461896959394373017753406668800000⟩, + ⟨5, 3, 4, 6, 3, 3, 1734970477452662233225812563004710056869494784000000⟩, + ⟨5, 3, 5, 6, 4, 3, -260696461486862594047440503626074686768755507200000⟩, + ⟨5, 3, 6, 6, 5, 3, -7042577782787229766171296641240290288258252800000⟩, + ⟨5, 3, 7, 6, 6, 3, -5054335916033393141736356666654346943502745600000⟩, + ⟨5, 3, 8, 6, 7, 3, -3400510496989612429950991617582508622531788800000⟩, + ⟨5, 3, 2, 7, 0, 3, -232190707985585369677183232888707530902090652057600000⟩, + ⟨5, 3, 3, 7, 1, 3, -30782048960212446493232454913354026625208942592000000⟩, + ⟨5, 3, 4, 7, 2, 3, -1782955994695635212656640307999927426254635008000000⟩, + ⟨5, 3, 5, 7, 3, 3, -363462111131183701647205256828223011265341030400000⟩, + ⟨5, 3, 6, 7, 4, 3, -244403089909471274651290845539570847873761280000000⟩, + ⟨5, 3, 7, 7, 5, 3, 18157887175615298502062860800747883121659084800000⟩, + ⟨5, 3, 8, 7, 6, 3, -5083994487015365049813437029275638275296460800000⟩ +] + +def collectedFourData_8_5_34 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 5, 4, -2605685024978229081626533685174394880322961408000000⟩, + ⟨5, 4, 1, 0, 6, 4, 1566425283150613959138951483587915206876987392000000⟩, + ⟨5, 4, 2, 0, 7, 4, -50949884171266518122748837876314231506206720000000⟩, + ⟨5, 4, 3, 0, 8, 4, 7760782002378699781190862346093408177618944000000⟩, + ⟨5, 4, 0, 1, 4, 4, -1873443558079823407081846413585406064131571712000000⟩, + ⟨5, 4, 1, 1, 5, 4, 341063804988793322302841370736377467448066048000000⟩, + ⟨5, 4, 2, 1, 6, 4, 117277477389859524493545791805178782412701696000000⟩, + ⟨5, 4, 3, 1, 7, 4, -103674128938695205551152585984620527806840832000000⟩, + ⟨5, 4, 4, 1, 8, 4, 32277308180795417249629838551196133776739532800000⟩, + ⟨5, 4, 0, 2, 3, 4, -733302347789297219547722121449204274136350720000000⟩, + ⟨5, 4, 1, 2, 4, 4, -296539256107562784438815003325139808239484928000000⟩, + ⟨5, 4, 2, 2, 5, 4, 245928187687057400380525062067435385326141440000000⟩, + ⟨5, 4, 3, 2, 6, 4, 33748092583198119912152293218258917850611712000000⟩, + ⟨5, 4, 4, 2, 7, 4, -4376528529020452842987774662538074869727232000000⟩, + ⟨5, 4, 5, 2, 8, 4, 9099191335580901445354720912047570878988288000000⟩, + ⟨5, 4, 0, 3, 2, 4, 3222178258098511730833216781458721225954033664000000⟩, + ⟨5, 4, 1, 3, 3, 4, 821248584848978080957056302244591738764132352000000⟩, + ⟨5, 4, 2, 3, 4, 4, -18120254837765465956692290240121265081810944000000⟩, + ⟨5, 4, 3, 3, 5, 4, 67410726263622877288805617239670458446512128000000⟩, + ⟨5, 4, 4, 3, 6, 4, -3564364582806961413098937497512395010159411200000⟩, + ⟨5, 4, 5, 3, 7, 4, -716823306228505476393387248690448404840448000000⟩, + ⟨5, 4, 6, 3, 8, 4, 1327031881875986991179605539059868654108672000000⟩, + ⟨5, 4, 0, 4, 1, 4, 2659617551588303929179844836025078349121454080000000⟩, + ⟨5, 4, 1, 4, 2, 4, -1415901165533617980491153612670547197570318336000000⟩, + ⟨5, 4, 2, 4, 3, 4, -385415963159807157620363016010195775231361024000000⟩, + ⟨5, 4, 3, 4, 4, 4, -27568618422434562082978735016338976975880192000000⟩, + ⟨5, 4, 4, 4, 5, 4, 9217059663218284412996245180205846656293273600000⟩, + ⟨5, 4, 5, 4, 6, 4, -1755493950264216606091389225404039681802240000000⟩, + ⟨5, 4, 6, 4, 7, 4, -579058907062534903627857755359454737465344000000⟩, + ⟨5, 4, 7, 4, 8, 4, 424801315857736221558883918036396702433280000000⟩, + ⟨5, 4, 0, 5, 0, 4, -16458354874387581352600862114396242731614601216000000⟩, + ⟨5, 4, 1, 5, 1, 4, -641986088614353404068943795246167996074295296000000⟩, + ⟨5, 4, 2, 5, 2, 4, 52425202768342012269946477180904236759646208000000⟩, + ⟨5, 4, 3, 5, 3, 4, -69409186042344602210301916397283051804033024000000⟩, + ⟨5, 4, 4, 5, 4, 4, 1287150291632478702478491945422853853151232000000⟩, + ⟨5, 4, 5, 5, 5, 4, -483114253348345414030343544708826209976320000000⟩, + ⟨5, 4, 6, 5, 6, 4, -980742374399827172665799663276858410008576000000⟩, + ⟨5, 4, 7, 5, 7, 4, 193767149027199617130492255874184688697344000000⟩, + ⟨5, 4, 8, 5, 8, 4, 129966803706607228320163494097393488494592000000⟩, + ⟨5, 4, 1, 6, 0, 4, 6998989278831574209920955760751178905485836288000000⟩, + ⟨5, 4, 2, 6, 1, 4, -879677682479474412331060740672888449978597376000000⟩, + ⟨5, 4, 3, 6, 2, 4, -77618980167693970739702533965425875246645248000000⟩, + ⟨5, 4, 4, 6, 3, 4, -32173951077088583761031760496613260800294912000000⟩, + ⟨5, 4, 5, 6, 4, 4, 4028711778698108286421048254669120558071808000000⟩, + ⟨5, 4, 6, 6, 5, 4, 93285882540808513850580125442923808423936000000⟩, + ⟨5, 4, 7, 6, 6, 4, 58580952314096022297582643572729433817088000000⟩, + ⟨5, 4, 8, 6, 7, 4, 35033531882694884708926293866341453529088000000⟩, + ⟨5, 4, 2, 7, 0, 4, 7176387702622655272049513229176449145323388928000000⟩, + ⟨5, 4, 3, 7, 1, 4, 713542499835881767490667536387969313480376320000000⟩, + ⟨5, 4, 4, 7, 2, 4, 33063812722717840506050298427064777120415744000000⟩, + ⟨5, 4, 5, 7, 3, 4, 5616816123522531919997303637784820088569856000000⟩, + ⟨5, 4, 6, 7, 4, 4, 3237359762447995902750326804046249826713600000000⟩, + ⟨5, 4, 7, 7, 5, 4, -210454219986677232872513252230627332194304000000⟩, + ⟨5, 4, 8, 7, 6, 4, 52377513055752784994758274409719616503808000000⟩ +] + +def collectedFourData_8_5_35 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 5, 5, 2934024682634560826403279894979070637889290240000000⟩, + ⟨5, 5, 1, 0, 6, 5, -1175872601692046270093860873106989502001315840000000⟩, + ⟨5, 5, 2, 0, 7, 5, 28685013020159042079773833959594420653260800000000⟩, + ⟨5, 5, 3, 0, 8, 5, -3495484025620544962611660145351181287292928000000⟩, + ⟨5, 5, 0, 1, 4, 5, 2109514230705932063733938541924666427425423360000000⟩, + ⟨5, 5, 1, 1, 5, 5, -256027266687446485483513004555948136553512960000000⟩, + ⟨5, 5, 2, 1, 6, 5, -66027745118932677530083433613986486487613440000000⟩, + ⟨5, 5, 3, 1, 7, 5, 46695199203412735171066863004979575111286784000000⟩, + ⟨5, 5, 4, 1, 8, 5, -12114846062057128583087775564470370516860928000000⟩, + ⟨5, 5, 0, 2, 3, 5, 825705013316276581759570870079552877074841600000000⟩, + ⟨5, 5, 1, 2, 4, 5, 222603906061631550939912358195833453737410560000000⟩, + ⟨5, 5, 2, 2, 5, 5, -138458671311479798588514828109605473196441600000000⟩, + ⟨5, 5, 3, 2, 6, 5, -15200261840053664811128414576669805294649344000000⟩, + ⟨5, 5, 4, 2, 7, 5, 1642670111097768208445899690707037527736320000000⟩, + ⟨5, 5, 5, 2, 8, 5, -2927363132610611661139058519751693214679040000000⟩, + ⟨5, 5, 0, 3, 2, 5, -3628201586332736891170260295194297635878993920000000⟩, + ⟨5, 5, 1, 3, 3, 5, -616488842774524626232234741869226058884055040000000⟩, + ⟨5, 5, 2, 3, 4, 5, 10201784643958720830072510783943526747996160000000⟩, + ⟨5, 5, 3, 3, 5, 5, -30362032684045361961512583126742143112052736000000⟩, + ⟨5, 5, 4, 3, 6, 5, 1337835484541656690849871954383078542016512000000⟩, + ⟨5, 5, 5, 3, 7, 5, 230614132823420784319305359876889079971840000000⟩, + ⟨5, 5, 6, 3, 8, 5, -373562446990275420282414549788005540823040000000⟩, + ⟨5, 5, 0, 4, 1, 5, -2994753190782673231753709057248539466688102400000000⟩, + ⟨5, 5, 1, 4, 2, 5, 1062878265030360688139268413747603215975710720000000⟩, + ⟨5, 5, 2, 4, 3, 5, 216990913742864022072635641963723751801487360000000⟩, + ⟨5, 5, 3, 4, 4, 5, 12417004533114311765381724912523680210223104000000⟩, + ⟨5, 5, 4, 4, 5, 5, -3459497252349061684871059120479198234279936000000⟩, + ⟨5, 5, 5, 4, 6, 5, 564771975882003757374424192107381207859200000000⟩, + ⟨5, 5, 6, 4, 7, 5, 163006379295120754056254520666483673006080000000⟩, + ⟨5, 5, 7, 4, 8, 5, -106295574995476757512561009137292620595200000000⟩, + ⟨5, 5, 0, 5, 0, 5, 18532255040079322252273194249221917970509332480000000⟩, + ⟨5, 5, 1, 5, 1, 5, 481921391584482113133238551046435924523089920000000⟩, + ⟨5, 5, 2, 5, 2, 5, -29515623999052290806379987685203785149317120000000⟩, + ⟨5, 5, 3, 5, 3, 5, 31262146130116371155558545190407649926053888000000⟩, + ⟨5, 5, 4, 5, 4, 5, -483114253348345414030343544708826209976320000000⟩, + ⟨5, 5, 5, 5, 5, 5, 155425993578182289171022549711926696345600000000⟩, + ⟨5, 5, 6, 5, 6, 5, 276081175027933462106335784060148063928320000000⟩, + ⟨5, 5, 7, 5, 7, 5, -48485232395038320692560020318148582440960000000⟩, + ⟨5, 5, 8, 5, 8, 5, -29268757071011879138496849331973838077952000000⟩, + ⟨5, 5, 1, 6, 0, 5, -5253949754923040053025308244936809865029877760000000⟩, + ⟨5, 5, 2, 6, 1, 5, 495262475781989521008368186365262693023088640000000⟩, + ⟨5, 5, 3, 6, 2, 5, 34959866825014945064613301697121226825138176000000⟩, + ⟨5, 5, 4, 6, 3, 5, 12076052387138060261371493704470384208773120000000⟩, + ⟨5, 5, 5, 6, 4, 5, -1296104444661845832261452470407410630000640000000⟩, + ⟨5, 5, 6, 6, 5, 5, -26260184873876635564926051492455535083520000000⟩, + ⟨5, 5, 7, 6, 6, 5, -14658372696978172564189559980801570897920000000⟩, + ⟨5, 5, 8, 6, 7, 5, -7889614153541097937047636140026786480128000000⟩, + ⟨5, 5, 2, 7, 0, 5, -4040338423448921069762343204582265406273617920000000⟩, + ⟨5, 5, 3, 7, 1, 5, -321382098996364479168925016710420633579683840000000⟩, + ⟨5, 5, 4, 7, 2, 5, -12410049782241210707386699474913981827645440000000⟩, + ⟨5, 5, 5, 7, 3, 5, -1807024364720978611241875584021864885780480000000⟩, + ⟨5, 5, 6, 7, 4, 5, -911324024060596104673709080835367370752000000000⟩, + ⟨5, 5, 7, 7, 5, 5, 52660741595254684693444559974438388367360000000⟩, + ⟨5, 5, 8, 7, 6, 5, -11795509790894747659581153586237509992448000000⟩ +] + +def collectedFourData_8_5_36 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 5, 6, 13897786563571149856131164928253827654623428608000000⟩, + ⟨5, 6, 1, 0, 6, 6, -4177374480092932014926910140161135735625220096000000⟩, + ⟨5, 6, 2, 0, 7, 6, 81524506093001448227351977654992931878076416000000⟩, + ⟨5, 6, 3, 0, 8, 6, -8278643873034091354198379865149780261653708800000⟩, + ⟨5, 6, 0, 1, 4, 6, 9992273993019642820601255884501135206238912512000000⟩, + ⟨5, 6, 1, 1, 5, 6, -909555821378162633935796631629259974979354624000000⟩, + ⟨5, 6, 2, 1, 6, 6, -187654762627182126285709789320198583975988428800000⟩, + ⟨5, 6, 3, 1, 7, 6, 110592101680914376854233745804156520676877926400000⟩, + ⟨5, 6, 4, 1, 8, 6, -24593650073543201883320681666107077527234150400000⟩, + ⟨5, 6, 0, 2, 3, 6, 3911170927586085722887111889146770069619998720000000⟩, + ⟨5, 6, 1, 2, 4, 6, 790816858061634621445880184980015322249560064000000⟩, + ⟨5, 6, 2, 2, 5, 6, -393507745143043179637226473767412398116831232000000⟩, + ⟨5, 6, 3, 2, 6, 6, -36000037084516366520516926391869476618790502400000⟩, + ⟨5, 6, 4, 2, 7, 6, 3334689825332123200943321671429822743576576000000⟩, + ⟨5, 6, 5, 2, 8, 6, -5199837136495799213691367676628985958105088000000⟩, + ⟨5, 6, 0, 3, 2, 6, -17185939693999178815506703979595559592225931264000000⟩, + ⟨5, 6, 1, 3, 3, 6, -2190122259301334956008591610453492116096024576000000⟩, + ⟨5, 6, 2, 3, 4, 6, 28994076237002526145949046195474293035578163200000⟩, + ⟨5, 6, 3, 3, 5, 6, -71908912760089140984417268939216459342125465600000⟩, + ⟨5, 6, 4, 3, 6, 6, 2715862636161283715449015283367751368415641600000⟩, + ⟨5, 6, 5, 3, 7, 6, 409636890858359409093930300906963361333248000000⟩, + ⟨5, 6, 6, 3, 8, 6, -589825889691608764902492974161408039059456000000⟩, + ⟨5, 6, 0, 4, 1, 6, -14185443259018138604128814054370452690782126080000000⟩, + ⟨5, 6, 1, 4, 2, 6, 3775953732907963118458240141747390256007610368000000⟩, + ⟨5, 6, 2, 4, 3, 6, 616701029806887925914154990246186696884564787200000⟩, + ⟨5, 6, 3, 4, 4, 6, 29408218646129905647179237165712832534570598400000⟩, + ⟨5, 6, 4, 4, 5, 6, -7022925790293528861423455553259885281725644800000⟩, + ⟨5, 6, 5, 4, 6, 6, 1003197130252984660152019323102437824266240000000⟩, + ⟨5, 6, 6, 4, 7, 6, 257374325143702921298259252101043990822912000000⟩, + ⟨5, 6, 7, 4, 8, 6, -151049160153558664138161516463075048292352000000⟩, + ⟨5, 6, 0, 5, 0, 6, 87782944231204837702265206424580126448986095616000000⟩, + ⟨5, 6, 1, 5, 1, 6, 1712061425463099591102959364359010657761230848000000⟩, + ⟨5, 6, 2, 5, 2, 6, -83885151694316260220289476282856744358930022400000⟩, + ⟨5, 6, 3, 5, 3, 6, 74040725868297660514983769019438513011870924800000⟩, + ⟨5, 6, 4, 5, 4, 6, -980742374399827172665799663276858410008576000000⟩, + ⟨5, 6, 5, 5, 5, 6, 276081175027933462106335784060148063928320000000⟩, + ⟨5, 6, 6, 5, 6, 6, 435910584695882618587274001336317402677248000000⟩, + ⟨5, 6, 7, 5, 7, 6, -68898951188064984725714574506092983327129600000⟩, + ⟨5, 6, 8, 5, 8, 6, -37810700573745388697737201818738321732403200000⟩, + ⟨5, 6, 1, 6, 0, 6, -18665045511158182765963038249222886227122847744000000⟩, + ⟨5, 6, 2, 6, 1, 6, 1407565291887740087430973371758510276055190732800000⟩, + ⟨5, 6, 3, 6, 2, 6, 82798343568918948866021515591310676191713689600000⟩, + ⟨5, 6, 4, 6, 3, 6, 24514897272134155249675730012441708976930816000000⟩, + ⟨5, 6, 5, 6, 4, 6, -2302253502154220493240656736063478309060608000000⟩, + ⟨5, 6, 6, 6, 5, 6, -41462778262354678192985792551377099030528000000⟩, + ⟨5, 6, 7, 6, 6, 6, -20829981729631047127927876617032726426419200000⟩, + ⟨5, 6, 8, 6, 7, 6, -10192159430554626468219923445535279467724800000⟩, + ⟨5, 6, 2, 7, 0, 6, -11482881119446086619196518507965364576408987238400000⟩, + ⟨5, 6, 3, 7, 1, 6, -761155801387693996799995754120317767845412864000000⟩, + ⟨5, 6, 4, 7, 2, 6, -25192926115304370596990897829634864098312192000000⟩, + ⟨5, 6, 5, 7, 3, 6, -3209793924626408979423064809413569419411456000000⟩, + ⟨5, 6, 6, 7, 4, 6, -1438909364738343088429882866383090142412800000000⟩, + ⟨5, 6, 7, 7, 5, 6, 74832473424837098478814914598337064311193600000⟩, + ⟨5, 6, 8, 7, 6, 6, -15237971593263300798880362264385999916236800000⟩ +] + +def collectedFourData_8_5_37 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 5, 7, -5491624611121071167179937146705630871634837504000000⟩, + ⟨5, 7, 1, 0, 6, 7, 1320531001095050175020290940372419276679046758400000⟩, + ⟨5, 7, 2, 0, 7, 7, -21475937050452432658859708744958739136643072000000⟩, + ⟨5, 7, 3, 0, 8, 7, 1869288598353547084889264339581328474033356800000⟩, + ⟨5, 7, 0, 1, 4, 7, -3948385415917008656748108718411576535527981056000000⟩, + ⟨5, 7, 1, 1, 5, 7, 287524296679673192793064654659758165547653529600000⟩, + ⟨5, 7, 2, 1, 6, 7, 49433747746984777490402395191187765114542489600000⟩, + ⟨5, 7, 3, 1, 7, 7, -24971306642802134263204646266305900645344870400000⟩, + ⟨5, 7, 4, 1, 8, 7, 4859014541753937081271328970647005768030617600000⟩, + ⟨5, 7, 0, 2, 3, 7, -1545475060074160051553384506055503459500687360000000⟩, + ⟨5, 7, 1, 2, 4, 7, -249989121692470475937136800690548423771396505600000⟩, + ⟨5, 7, 2, 2, 5, 7, 103661438364518399332677676986932788350418944000000⟩, + ⟨5, 7, 3, 2, 6, 7, 8128681447644896983229602722158130785314406400000⟩, + ⟨5, 7, 4, 2, 7, 7, -658841054706170186465504883642429125689344000000⟩, + ⟨5, 7, 5, 2, 8, 7, 913192693974302263326864633832057721585664000000⟩, + ⟨5, 7, 0, 3, 2, 7, 6790918032673904816356669366034919374802911232000000⟩, + ⟨5, 7, 1, 3, 3, 7, 692330638150354486044975643021233139189442150400000⟩, + ⟨5, 7, 2, 3, 4, 7, -7637886887551952259182478898191775400617574400000⟩, + ⟨5, 7, 3, 3, 5, 7, 16236778970559903610766839471009521857042841600000⟩, + ⟨5, 7, 4, 3, 6, 7, -536578181890536052463693222045091942000230400000⟩, + ⟨5, 7, 5, 3, 7, 7, -71940217759646108435315423616028737798144000000⟩, + ⟨5, 7, 6, 3, 8, 7, 93226424432136536479479019566844934828851200000⟩, + ⟨5, 7, 0, 4, 1, 7, 5605290379482427012745474692583870774158295040000000⟩, + ⟨5, 7, 1, 4, 2, 7, -1193635855910772274285394970426065500679385907200000⟩, + ⟨5, 7, 2, 4, 3, 7, -162457071251350747698180215271759420695406182400000⟩, + ⟨5, 7, 3, 4, 4, 7, -6640272085161168710123647956225056395650662400000⟩, + ⟨5, 7, 4, 4, 5, 7, 1387532897258089205359037030067707661464371200000⟩, + ⟨5, 7, 5, 4, 6, 7, -176180958348319639956493094552460821790720000000⟩, + ⟨5, 7, 6, 4, 7, 7, -40679950631409040278410064233937420838502400000⟩, + ⟨5, 7, 7, 4, 8, 7, 21704052239977121913212399562036571275264000000⟩, + ⟨5, 7, 0, 5, 0, 7, -34686888791367426678025921199445292740098654208000000⟩, + ⟨5, 7, 1, 5, 1, 7, -541208407069291509142676951002815845692027699200000⟩, + ⟨5, 7, 2, 5, 2, 7, 22097800079888393551678198507927866306251980800000⟩, + ⟨5, 7, 3, 5, 3, 7, -16718134854217977230738202319663638168521932800000⟩, + ⟨5, 7, 4, 5, 4, 7, 193767149027199617130492255874184688697344000000⟩, + ⟨5, 7, 5, 5, 5, 7, -48485232395038320692560020318148582440960000000⟩, + ⟨5, 7, 6, 5, 6, 7, -68898951188064984725714574506092983327129600000⟩, + ⟨5, 7, 7, 5, 7, 7, 9899998347194818532268651697345037284147200000⟩, + ⟨5, 7, 8, 5, 8, 7, 4980221679778875254815598831889638699827200000⟩, + ⟨5, 7, 1, 6, 0, 7, 5900302056181963519132960244481970480095009177600000⟩, + ⟨5, 7, 2, 6, 1, 7, -370793826932216521416250574170678586232117657600000⟩, + ⟨5, 7, 3, 6, 2, 7, -18695574054113267672726872763935538896542105600000⟩, + ⟨5, 7, 4, 6, 3, 7, -4843455199968308119122477577225737710075904000000⟩, + ⟨5, 7, 5, 6, 4, 7, 404320562866860315890216899837162866868224000000⟩, + ⟨5, 7, 6, 6, 5, 7, 6553504401854732377750253318733630642585600000⟩, + ⟨5, 7, 7, 6, 6, 7, 2993032276101867859576644662973100877414400000⟩, + ⟨5, 7, 8, 6, 7, 7, 1342456304421308050748579164240898477260800000⟩, + ⟨5, 7, 2, 7, 0, 7, 3024926416576267018608927928910556798273768652800000⟩, + ⟨5, 7, 3, 7, 1, 7, 171866296331359804789063370019606554480738304000000⟩, + ⟨5, 7, 4, 7, 2, 7, 4977414656935487395473325002443388195176448000000⟩, + ⟨5, 7, 5, 7, 3, 7, 563702339936605226690797462570646705799168000000⟩, + ⟨5, 7, 6, 7, 4, 7, 227430462956806274433623185126775649730560000000⟩, + ⟨5, 7, 7, 7, 5, 7, -10752578238821139585670251778419306214195200000⟩, + ⟨5, 7, 8, 7, 6, 7, 2007063485549887210324128299214546193612800000⟩ +] + +def collectedFourData_8_5_38 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 5, 8, -6630184851276123334467490443841173136007076249600000⟩, + ⟨5, 8, 1, 0, 6, 8, 1328593579480171041614551018770227337758559436800000⟩, + ⟨5, 8, 2, 0, 7, 8, -18520336822226779366096112833682944768868352000000⟩, + ⟨5, 8, 3, 0, 8, 8, 1410526235984926639412287466040579929092915200000⟩, + ⟨5, 8, 0, 1, 4, 8, -4766991013660780837019378791699057986675041894400000⟩, + ⟨5, 8, 1, 1, 5, 8, 289279792898757982164633924687151745622815539200000⟩, + ⟨5, 8, 2, 1, 6, 8, 42630487159109308497107561093096971460778393600000⟩, + ⟨5, 8, 3, 1, 7, 8, -18842827799581572468382931274112594005825945600000⟩, + ⟨5, 8, 4, 1, 8, 8, 3259121024003078916113293314697018754256076800000⟩, + ⟨5, 8, 0, 2, 3, 8, -1865893256902159870307335605184622643080331264000000⟩, + ⟨5, 8, 1, 2, 4, 8, -251515444730249719363171324927655797851370291200000⟩, + ⟨5, 8, 2, 2, 5, 8, 89395156517602874813137360764618612097941504000000⟩, + ⟨5, 8, 3, 2, 6, 8, 6133733686690201164637502981512497756477849600000⟩, + ⟨5, 8, 4, 2, 7, 8, -441909097908186370687178651048790397550592000000⟩, + ⟨5, 8, 5, 2, 8, 8, 551260946862903485589458437393019470400716800000⟩, + ⟨5, 8, 0, 3, 2, 8, 8198856450477753266755683007824423813452188876800000⟩, + ⟨5, 8, 1, 3, 3, 8, 696557702894672594531275092814346978811759820800000⟩, + ⟨5, 8, 2, 3, 4, 8, -6586731812223832972326389779143387880253030400000⟩, + ⟨5, 8, 3, 3, 5, 8, 12251935172575977411431811017629984612574822400000⟩, + ⟨5, 8, 4, 3, 6, 8, -359902860671321889363515650524053238919987200000⟩, + ⟨5, 8, 5, 3, 7, 8, -43427671751414572632497494502590993190092800000⟩, + ⟨5, 8, 6, 3, 8, 8, 51161249322109076671865730464201509856870400000⟩, + ⟨5, 8, 0, 4, 1, 8, 6767416564815311490081824954748950143089770496000000⟩, + ⟨5, 8, 1, 4, 2, 8, -1200923668649428857972578662227424848845891174400000⟩, + ⟨5, 8, 2, 4, 3, 8, -140099110537489928449184681070731477677139558400000⟩, + ⟨5, 8, 3, 4, 4, 8, -5010610987756464467706614007448856128231833600000⟩, + ⟨5, 8, 4, 4, 5, 8, 930669706396352226635592828329253123234201600000⟩, + ⟨5, 8, 5, 4, 6, 8, -106353984826165836563573558160635109310464000000⟩, + ⟨5, 8, 6, 4, 7, 8, -22324540593956031357668756502368727387340800000⟩, + ⟨5, 8, 7, 4, 8, 8, 10918283792968014948266633503585666596864000000⟩, + ⟨5, 8, 0, 5, 0, 8, -41878405915927162751037431440596620445419254579200000⟩, + ⟨5, 8, 1, 5, 1, 8, -544512786293303746559471521309065605103904358400000⟩, + ⟨5, 8, 2, 5, 2, 8, 19056616693758703584958648351538134450490572800000⟩, + ⟨5, 8, 3, 5, 3, 8, -12615156294955607458475077037891236123587379200000⟩, + ⟨5, 8, 4, 5, 4, 8, 129966803706607228320163494097393488494592000000⟩, + ⟨5, 8, 5, 5, 5, 8, -29268757071011879138496849331973838077952000000⟩, + ⟨5, 8, 6, 5, 6, 8, -37810700573745388697737201818738321732403200000⟩, + ⟨5, 8, 7, 5, 7, 8, 4980221679778875254815598831889638699827200000⟩, + ⟨5, 8, 8, 5, 8, 8, 2312597866716649888797627828955872283852800000⟩, + ⟨5, 8, 1, 6, 0, 8, 5936326691563039859507981034561028276769469235200000⟩, + ⟨5, 8, 2, 6, 1, 8, -319763768642749013674918423836831190783465881600000⟩, + ⟨5, 8, 3, 6, 2, 8, -14107290721910374124340111917848283933206118400000⟩, + ⟨5, 8, 4, 6, 3, 8, -3248684797172012781398003465489452653084672000000⟩, + ⟨5, 8, 5, 6, 4, 8, 244073499265643105653038130670828392336588800000⟩, + ⟨5, 8, 6, 6, 5, 8, 3596463928324289380588475950554221327155200000⟩, + ⟨5, 8, 7, 6, 6, 8, 1505653203865843590538768292759516636774400000⟩, + ⟨5, 8, 8, 6, 7, 8, 623378191852471689211207813414119486259200000⟩, + ⟨5, 8, 2, 7, 0, 8, 2608624525478561746913703464427491244234296524800000⟩, + ⟨5, 8, 3, 7, 1, 8, 129686726956161847454415430256796986146553856000000⟩, + ⟨5, 8, 4, 7, 2, 8, 3338536366623825063480776853601227179556864000000⟩, + ⟨5, 8, 5, 7, 3, 8, 340286434301052218495357899056897926470041600000⟩, + ⟨5, 8, 6, 7, 4, 8, 124810392435954936737835487807778869739520000000⟩, + ⟨5, 8, 7, 7, 5, 8, -5409114363505842731082130073595396961075200000⟩, + ⟨5, 8, 8, 7, 6, 8, 931992797407692802282217193146382758707200000⟩ +] + +def collectedFourData_8_5_39 : List CollectedFourTerm := [ + ⟨6, 0, 2, 0, 7, 1, -27704433226685278036085820470366287055969845248000000⟩, + ⟨6, 0, 3, 0, 8, 1, 16879965108381274600373646298488333932983379558400000⟩, + ⟨6, 0, 2, 1, 6, 1, 63770626649899388591352423104326511417838954086400000⟩, + ⟨6, 0, 3, 1, 7, 1, -225494760526788681257349106621432515517465441075200000⟩, + ⟨6, 0, 4, 1, 8, 1, 175510610824173806200254067849155943155666989875200000⟩, + ⟨6, 0, 2, 2, 5, 1, 133725545507289040258642050559076563033780125696000000⟩, + ⟨6, 0, 3, 2, 6, 1, 73403250484835271215502083992515040843402523443200000⟩, + ⟨6, 0, 4, 2, 7, 1, -23797746426538392293090494614037173057028620288000000⟩, + ⟨6, 0, 5, 2, 8, 1, 98955254903445205142773748354794107657240182784000000⟩, + ⟨6, 0, 2, 3, 4, 1, -9853042815875653245945927200076692727392737689600000⟩, + ⟨6, 0, 3, 3, 5, 1, 146620624946278471363437916485199445325639371980800000⟩, + ⟨6, 0, 4, 3, 6, 1, -19381535833918007558901504027467003677282979020800000⟩, + ⟨6, 0, 5, 3, 7, 1, -7795575493747286866118246689474159527711473664000000⟩, + ⟨6, 0, 6, 3, 8, 1, 25255470872389738621364519887257172206963130368000000⟩, + ⟨6, 0, 2, 4, 3, 1, -209573210803906763623848908833615224127715121561600000⟩, + ⟨6, 0, 3, 4, 4, 1, -59962683775209689380541802209127394357418341171200000⟩, + ⟨6, 0, 4, 4, 5, 1, 50118546516738362308567180231895897744964216422400000⟩, + ⟨6, 0, 5, 4, 6, 1, -19091295580362840253849637952749413675114168320000000⟩, + ⟨6, 0, 6, 4, 7, 1, -11020387347470193149820699823993761050432372736000000⟩, + ⟨6, 0, 7, 4, 8, 1, 12935402569567490393401611763516850162066522112000000⟩, + ⟨6, 0, 2, 5, 2, 1, 28506650272427170396623162503142860921217692467200000⟩, + ⟨6, 0, 3, 5, 3, 1, -150967343012188136414929996997156539699105785446400000⟩, + ⟨6, 0, 4, 5, 4, 1, 6998989278831574209920955760751178905485836288000000⟩, + ⟨6, 0, 5, 5, 5, 1, -5253949754923040053025308244936809865029877760000000⟩, + ⟨6, 0, 6, 5, 6, 1, -18665045511158182765963038249222886227122847744000000⟩, + ⟨6, 0, 7, 5, 7, 1, 5900302056181963519132960244481970480095009177600000⟩, + ⟨6, 0, 8, 5, 8, 1, 5936326691563039859507981034561028276769469235200000⟩, + ⟨6, 0, 2, 6, 1, 1, -478332228064259332958976357340387406400683664998400000⟩, + ⟨6, 0, 3, 6, 2, 1, -168823924776811270774854344040817884632714104012800000⟩, + ⟨6, 0, 4, 6, 3, 1, -174948597774541710472066314442117151723416977408000000⟩, + ⟨6, 0, 5, 6, 4, 1, 43812926477837653015252802380935992175853830144000000⟩, + ⟨6, 0, 6, 6, 5, 1, 1775374745318085317928932357372308393593667584000000⟩, + ⟨6, 0, 7, 6, 6, 1, 1783817923354175737164499430582390445546091315200000⟩, + ⟨6, 0, 8, 6, 7, 1, 1600181619334488831961602761292854845676244172800000⟩, + ⟨6, 0, 2, 7, 0, 1, 3902221901973216677727331751904016479354644280115200000⟩, + ⟨6, 0, 3, 7, 1, 1, 1551979233134643252556280653726551074151755415552000000⟩, + ⟨6, 0, 4, 7, 2, 1, 179787296221716451312678270371758582663108100096000000⟩, + ⟨6, 0, 5, 7, 3, 1, 61083831601115510531969877410127305189105860608000000⟩, + ⟨6, 0, 6, 7, 4, 1, 61611967504781177169167635598762632081204838400000000⟩, + ⟨6, 0, 7, 7, 5, 1, -6408431321582050432383419283174957366736689561600000⟩, + ⟨6, 0, 8, 7, 6, 1, 2392380361161023558967390739461998829523225804800000⟩ +] + +def collectedFourData_8_5_40 : List CollectedFourTerm := [ + ⟨6, 1, 1, 0, 6, 2, -107054271114801085932913074579955103053020502425600000⟩, + ⟨6, 1, 2, 0, 7, 2, 10446210435970146246873369372163993453763493888000000⟩, + ⟨6, 1, 3, 0, 8, 2, -3182372767404954656515676130122491850701091635200000⟩, + ⟨6, 1, 1, 1, 5, 2, -23309338427733495494411557608055768219948312166400000⟩, + ⟨6, 1, 2, 1, 6, 2, -24045299182546691652263899378230445020344116838400000⟩, + ⟨6, 1, 3, 1, 7, 2, 42512432963303084785229916166703242015235742105600000⟩, + ⟨6, 1, 4, 1, 8, 2, -22059294739502847084048268270553040496351405670400000⟩, + ⟨6, 1, 1, 2, 4, 2, 20266395251019488346373318962754342473716622950400000⟩, + ⟨6, 1, 2, 2, 5, 2, -50422442415768555837938652011807050028575358976000000⟩, + ⟨6, 1, 3, 2, 6, 2, -13838684137205857719619117077986423263555328409600000⟩, + ⟨6, 1, 4, 2, 7, 2, 2991052792157771374798516998518320729870565376000000⟩, + ⟨6, 1, 5, 2, 8, 2, -9327996425773967611802299577280947824650878976000000⟩, + ⟨6, 1, 1, 3, 3, 2, -56126627679448512390646742575000834751157868953600000⟩, + ⟨6, 1, 2, 3, 4, 2, 3715180088583090430825945583435753305352542617600000⟩, + ⟨6, 1, 3, 3, 5, 2, -27642325145402950651965071225223386060168783462400000⟩, + ⟨6, 1, 4, 3, 6, 2, 2435995233888993758724505313599505250125453721600000⟩, + ⟨6, 1, 5, 3, 7, 2, 734848294953905692614075238151486007511351296000000⟩, + ⟨6, 1, 6, 3, 8, 2, -1904561347520215614997624643403020804451572121600000⟩, + ⟨6, 1, 1, 4, 2, 2, 96766994811219687181474813779648388391559285964800000⟩, + ⟨6, 1, 2, 4, 3, 2, 79021499695970374395737499761761357617304279449600000⟩, + ⟨6, 1, 3, 4, 4, 2, 11304739712524293394107689275460003152185104793600000⟩, + ⟨6, 1, 4, 4, 5, 2, -6299219086165582387020118290077637142091975884800000⟩, + ⟨6, 1, 5, 4, 6, 2, 1799636988563997928008714498822712213351956480000000⟩, + ⟨6, 1, 6, 4, 7, 2, 831067608390487764780809244426716633579598643200000⟩, + ⟨6, 1, 7, 4, 8, 2, -812902013491567999077955858454510356987379712000000⟩, + ⟨6, 1, 1, 5, 1, 2, 43875283118654484739236292373817343034610470092800000⟩, + ⟨6, 1, 2, 5, 2, 2, -10748693724712189361043460210319059554374202163200000⟩, + ⟨6, 1, 3, 5, 3, 2, 28461810085787674821037896014742046507908936499200000⟩, + ⟨6, 1, 4, 5, 4, 2, -879677682479474412331060740672888449978597376000000⟩, + ⟨6, 1, 5, 5, 5, 2, 495262475781989521008368186365262693023088640000000⟩, + ⟨6, 1, 6, 5, 6, 2, 1407565291887740087430973371758510276055190732800000⟩, + ⟨6, 1, 7, 5, 7, 2, -370793826932216521416250574170678586232117657600000⟩, + ⟨6, 1, 8, 5, 8, 2, -319763768642749013674918423836831190783465881600000⟩, + ⟨6, 1, 1, 6, 0, 2, -478332228064259332958976357340387406400683664998400000⟩, + ⟨6, 1, 2, 6, 1, 2, 180359550104521653571126092540501821673942967910400000⟩, + ⟨6, 1, 3, 6, 2, 2, 31828303983246092134066650438672071804404000358400000⟩, + ⟨6, 1, 4, 6, 3, 2, 21988657349255820109293772630451919807490031616000000⟩, + ⟨6, 1, 5, 6, 4, 2, -4130016359280162912581801920809206866054742016000000⟩, + ⟨6, 1, 6, 6, 5, 2, -133884263507949546547680668464230480562932940800000⟩, + ⟨6, 1, 7, 6, 6, 2, -112100815865481151064688101421274970388116275200000⟩, + ⟨6, 1, 8, 6, 7, 2, -86194734841408661178836559033470662530721382400000⟩, + ⟨6, 1, 2, 7, 0, 2, -1471368528723410620056537529121447847679923270451200000⟩, + ⟨6, 1, 3, 7, 1, 2, -292593996219423659811549869967352446184593555456000000⟩, + ⟨6, 1, 4, 7, 2, 2, -22596815879959884236358386263289298918196641792000000⟩, + ⟨6, 1, 5, 7, 3, 2, -5758054621796004651825017205742680248797888512000000⟩, + ⟨6, 1, 6, 7, 4, 2, -4646271393916576820524960485442854955599790080000000⟩, + ⟨6, 1, 7, 7, 5, 2, 402726292948350187578314304268516138178681241600000⟩, + ⟨6, 1, 8, 7, 6, 2, -128866991333040267936343070622521779980494438400000⟩ +] + +def collectedFourData_8_5_41 : List CollectedFourTerm := [ + ⟨6, 2, 0, 0, 5, 3, 31426107050875943872249410744610076232004298342400000⟩, + ⟨6, 2, 1, 0, 6, 3, -37784036185187925977385739895376495680165196595200000⟩, + ⟨6, 2, 2, 0, 7, 3, 1843457477224434628884331030487082491285864448000000⟩, + ⟨6, 2, 3, 0, 8, 3, -374398538069354155197980627706044063377312972800000⟩, + ⟨6, 2, 0, 1, 4, 3, 22594840606447575017728568379229344183378090393600000⟩, + ⟨6, 2, 1, 1, 5, 3, -8226863603244946257484202487995703599257406668800000⟩, + ⟨6, 2, 2, 1, 6, 3, -4243307833195843068206736531289314418246444646400000⟩, + ⟨6, 2, 3, 1, 7, 3, 5001485971177153878194551879771409208509359718400000⟩, + ⟨6, 2, 4, 1, 8, 3, -1946417415152212623786237985569730191183524659200000⟩, + ⟨6, 2, 0, 2, 3, 3, 8844061297269672991431111194614948871081558016000000⟩, + ⟨6, 2, 1, 2, 4, 3, 7152878661764768357894206811051265556833160396800000⟩, + ⟨6, 2, 2, 2, 5, 3, -8898119472225101877507271092316962261194244096000000⟩, + ⟨6, 2, 3, 2, 6, 3, -1628088061474456722856112041422012493693609574400000⟩, + ⟨6, 2, 4, 2, 7, 3, 263917650724800327614770257280825512582709248000000⟩, + ⟨6, 2, 5, 2, 8, 3, -658449869989387777316954765032544908196865638400000⟩, + ⟨6, 2, 0, 3, 2, 3, -38861381135985480192838668753488018536209265459200000⟩, + ⟨6, 2, 1, 3, 3, 3, -19809490168950866436741399163812744508296344371200000⟩, + ⟨6, 2, 2, 3, 4, 3, 655623065944658542397343599114982670948997529600000⟩, + ⟨6, 2, 3, 3, 5, 3, -3252053382707846083256810905148099744040065433600000⟩, + ⟨6, 2, 4, 3, 6, 3, 214941755956436519131537179128874917688036556800000⟩, + ⟨6, 2, 5, 3, 7, 3, 51871885685695395843363146776588762267149926400000⟩, + ⟨6, 2, 6, 3, 8, 3, -112033541682867047705450885542517103794533171200000⟩, + ⟨6, 2, 0, 4, 1, 3, -32076565313684046976601692183218590344412135424000000⟩, + ⟨6, 2, 1, 4, 2, 3, 34153215891388309618167429879900406583721040281600000⟩, + ⟨6, 2, 2, 4, 3, 3, 13945035414414016697783482837197653531931810201600000⟩, + ⟨6, 2, 3, 4, 4, 3, 1329975565708166019617829707629232781126952550400000⟩, + ⟨6, 2, 4, 4, 5, 3, -555816034735488617848002741899667171757680230400000⟩, + ⟨6, 2, 5, 4, 6, 3, 127033790222506194267716382608019984463429632000000⟩, + ⟨6, 2, 6, 4, 7, 3, 48886557351972127728389996946818985951127142400000⟩, + ⟨6, 2, 7, 4, 8, 3, -40986846835364449595440677065945540273897472000000⟩, + ⟨6, 2, 0, 5, 0, 3, 198497522611402927811297011307162228637087616204800000⟩, + ⟨6, 2, 1, 5, 1, 3, 15485466088623943665093519609638022202877647257600000⟩, + ⟨6, 2, 2, 5, 2, 3, -1896837129471041027871668698504025640908567347200000⟩, + ⟨6, 2, 3, 5, 3, 3, 3348463824247691850461896959394373017753406668800000⟩, + ⟨6, 2, 4, 5, 4, 3, -77618980167693970739702533965425875246645248000000⟩, + ⟨6, 2, 5, 5, 5, 3, 34959866825014945064613301697121226825138176000000⟩, + ⟨6, 2, 6, 5, 6, 3, 82798343568918948866021515591310676191713689600000⟩, + ⟨6, 2, 7, 5, 7, 3, -18695574054113267672726872763935538896542105600000⟩, + ⟨6, 2, 8, 5, 8, 3, -14107290721910374124340111917848283933206118400000⟩, + ⟨6, 2, 1, 6, 0, 3, -168823924776811270774854344040817884632714104012800000⟩, + ⟨6, 2, 2, 6, 1, 3, 31828303983246092134066650438672071804404000358400000⟩, + ⟨6, 2, 3, 6, 2, 3, 3744523772515671538624796447842627865760340377600000⟩, + ⟨6, 2, 4, 6, 3, 3, 1940184675249993293679015114858599694905376768000000⟩, + ⟨6, 2, 5, 6, 4, 3, -291531922901271013721146354501657102169564774400000⟩, + ⟨6, 2, 6, 6, 5, 3, -7875581553688236540462173192274614393870745600000⟩, + ⟨6, 2, 7, 6, 6, 3, -5652168273348148235766466160937898272305971200000⟩, + ⟨6, 2, 8, 6, 7, 3, -3802726582398574026558045177895191259486617600000⟩, + ⟨6, 2, 2, 7, 0, 3, -259654477827488242154328271811325929120444134195200000⟩, + ⟨6, 2, 3, 7, 1, 3, -34422983238934500191468391629230085049925238784000000⟩, + ⟨6, 2, 4, 7, 2, 3, -1993845971738135230706989925184192201847996416000000⟩, + ⟨6, 2, 5, 7, 3, 3, -406452805517535494172232098663907623720242380800000⟩, + ⟨6, 2, 6, 7, 4, 3, -273311353587018247678388753603966790071746560000000⟩, + ⟨6, 2, 7, 7, 5, 3, 20305621848259033941858279847037234776218009600000⟩, + ⟨6, 2, 8, 7, 6, 3, -5685334892409887328012829172451353917233561600000⟩ +] + +def collectedFourData_8_5_42 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 5, 4, 65132396007636868510564604408594382165091811328000000⟩, + ⟨6, 3, 1, 0, 6, 4, -39154783053409510051813624559116439547619049472000000⟩, + ⟨6, 3, 2, 0, 7, 4, 1273556857630513783356434395444553465745899520000000⟩, + ⟨6, 3, 3, 0, 8, 4, -193990571332424893027375526313791675122581504000000⟩, + ⟨6, 3, 0, 1, 4, 4, 46829093521704839305245036367266115196490350592000000⟩, + ⟨6, 3, 1, 1, 5, 4, -8525321593920249721404967713430684559178989568000000⟩, + ⟨6, 3, 2, 1, 6, 4, -2931499021143904771707246115061840783905652736000000⟩, + ⟨6, 3, 3, 1, 7, 4, 2591466104710150122209975812787190993373888512000000⟩, + ⟨6, 3, 4, 1, 8, 4, -806812181188196110494664967930757744369126604800000⟩, + ⟨6, 3, 0, 2, 3, 4, 18329820546879576015049154622184177972826603520000000⟩, + ⟨6, 3, 1, 2, 4, 4, 7412374126365946079804615693771758714799259648000000⟩, + ⟨6, 3, 2, 2, 5, 4, -6147286397367886004985516476246186135692247040000000⟩, + ⟨6, 3, 3, 2, 6, 4, -843576299345550435002740109418371601338990592000000⟩, + ⟨6, 3, 4, 2, 7, 4, 109396871286567826797393501647446202659110912000000⟩, + ⟨6, 3, 5, 2, 8, 4, -227445807047712988586461651942684476894609408000000⟩, + ⟨6, 3, 0, 3, 2, 4, -80542424852529252761483854780162439253300609024000000⟩, + ⟨6, 3, 1, 3, 3, 4, -20528148082495859090818699721375207853058424832000000⟩, + ⟨6, 3, 2, 3, 4, 4, 452938709989515704828177764000498929320853504000000⟩, + ⟨6, 3, 3, 3, 5, 4, -1685016445224946881827279344606674779633614848000000⟩, + ⟨6, 3, 4, 3, 6, 4, 89095805247957044793148525613177471509934899200000⟩, + ⟨6, 3, 5, 3, 7, 4, 17917906040530996174961657666777953723219968000000⟩, + ⟨6, 3, 6, 3, 8, 4, -33170841915487669229435674017985944147197952000000⟩, + ⟨6, 3, 0, 4, 1, 4, -66480507789063389087892367277490144728611553280000000⟩, + ⟨6, 3, 1, 4, 2, 4, 35392242169400628250733978709603334806596222976000000⟩, + ⟨6, 3, 2, 4, 3, 4, 9633959937425315733124302600286216199847542784000000⟩, + ⟨6, 3, 3, 4, 4, 4, 689112519456738140480522560709781075391414272000000⟩, + ⟨6, 3, 4, 4, 5, 4, -230392075118812664086762018224771935153789337600000⟩, + ⟨6, 3, 5, 4, 6, 4, 43880793749649408322430054627284690497699840000000⟩, + ⟨6, 3, 6, 4, 7, 4, 14474310473063234445168815002778428615163904000000⟩, + ⟨6, 3, 7, 4, 8, 4, -10618446690133808622775204944307525496340480000000⟩, + ⟨6, 3, 0, 5, 0, 4, 411397416432474987182278222207648404143452717056000000⟩, + ⟨6, 3, 1, 5, 1, 4, 16047255042029987496959338901715704955940110336000000⟩, + ⟨6, 3, 2, 5, 2, 4, -1310434313724024240137160618597805090960048128000000⟩, + ⟨6, 3, 3, 5, 3, 4, 1734970477452662233225812563004710056869494784000000⟩, + ⟨6, 3, 4, 5, 4, 4, -32173951077088583761031760496613260800294912000000⟩, + ⟨6, 3, 5, 5, 5, 4, 12076052387138060261371493704470384208773120000000⟩, + ⟨6, 3, 6, 5, 6, 4, 24514897272134155249675730012441708976930816000000⟩, + ⟨6, 3, 7, 5, 7, 4, -4843455199968308119122477577225737710075904000000⟩, + ⟨6, 3, 8, 5, 8, 4, -3248684797172012781398003465489452653084672000000⟩, + ⟨6, 3, 1, 6, 0, 4, -174948597774541710472066314442117151723416977408000000⟩, + ⟨6, 3, 2, 6, 1, 4, 21988657349255820109293772630451919807490031616000000⟩, + ⟨6, 3, 3, 6, 2, 4, 1940184675249993293679015114858599694905376768000000⟩, + ⟨6, 3, 4, 6, 3, 4, 804228639530511633695471911163022043137441792000000⟩, + ⟨6, 3, 5, 6, 4, 4, -100702751274777996953382387692784635219017728000000⟩, + ⟨6, 3, 6, 6, 5, 4, -2331798734430921367042145147990398338072576000000⟩, + ⟨6, 3, 7, 6, 6, 4, -1464305066825209544442576655655178451550208000000⟩, + ⟨6, 3, 8, 6, 7, 4, -875707482008083540563302535273128770142208000000⟩, + ⟨6, 3, 2, 7, 0, 4, -179382895964357580556773041573540282385876123648000000⟩, + ⟨6, 3, 3, 7, 1, 4, -17835898131232542359819872407275519521975173120000000⟩, + ⟨6, 3, 4, 7, 2, 4, -826471857931636854566961469154990598131810304000000⟩, + ⟨6, 3, 5, 7, 3, 4, -140399429920508513743999456717296113912119296000000⟩, + ⟨6, 3, 6, 7, 4, 4, -80921905773593580665699232352494375508377600000000⟩, + ⟨6, 3, 7, 7, 5, 4, 5260569664503143427295965302631373958283264000000⟩, + ⟨6, 3, 8, 7, 6, 4, -1309242248982477863621413617684459949129728000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0825.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0825.lean new file mode 100644 index 0000000000000000000000000000000000000000..8e92fa82f2f0e97197dce49c3cd81ce85192ffc4 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0825.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0825. -/ +namespace LaughlinFock +def collectedFourData_8_5_43 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 5, 5, -24466965559382655942568668023382126995812909056000000⟩, + ⟨6, 4, 1, 0, 6, 5, 9805655221000861087131817462093975082495901696000000⟩, + ⟨6, 4, 2, 0, 7, 5, -239205631018915819421658271223130151735787520000000⟩, + ⟨6, 4, 3, 0, 8, 5, 29149000611486096905552089892646337478079283200000⟩, + ⟨6, 4, 0, 1, 4, 5, -17591335320111961463866585070525285650120310784000000⟩, + ⟨6, 4, 1, 1, 5, 5, 2135023046459099127744534949104420131149185024000000⟩, + ⟨6, 4, 2, 1, 6, 5, 550608376047474430510983762673042613795291136000000⟩, + ⟨6, 4, 3, 1, 7, 5, -389393394493372577549230598217887480786033049600000⟩, + ⟨6, 4, 4, 1, 8, 5, 101026253498118001402552910034776783630578483200000⟩, + ⟨6, 4, 0, 2, 3, 5, -6885591741129602959712621378896199800628183040000000⟩, + ⟨6, 4, 1, 2, 4, 5, -1856304118785887336995308100518255405998014464000000⟩, + ⟨6, 4, 2, 2, 5, 5, 1154613170920553059904862518336458226443223040000000⟩, + ⟨6, 4, 3, 2, 6, 5, 126755676302029577630452571831257590339836313600000⟩, + ⟨6, 4, 4, 2, 7, 5, -13698300928255098693865754001423164724215808000000⟩, + ⟨6, 4, 5, 2, 8, 5, 24411414590103925633504120145352044656459776000000⟩, + ⟨6, 4, 0, 3, 2, 5, 30255738399443186813016272459654482024357429248000000⟩, + ⟨6, 4, 1, 3, 3, 5, 5140928559048069820200177301313077436718514176000000⟩, + ⟨6, 4, 2, 3, 4, 5, -85073147136528685457804588843824163642671104000000⟩, + ⟨6, 4, 3, 3, 5, 5, 253190374433504414160599998536715125452596838400000⟩, + ⟨6, 4, 4, 3, 6, 5, -11156271083244210164419593418700789113474252800000⟩, + ⟨6, 4, 5, 3, 7, 5, -1923101764853254421841133785458372662788096000000⟩, + ⟨6, 4, 6, 3, 8, 5, 3115154272179712677995577401223512510693376000000⟩, + ⟨6, 4, 0, 4, 1, 5, 24973383356794764529958065528125990023787970560000000⟩, + ⟨6, 4, 1, 4, 2, 5, -8863390297372374135520832954979732273305223168000000⟩, + ⟨6, 4, 2, 4, 3, 5, -1809497120003229299641897185944817001650192384000000⟩, + ⟨6, 4, 3, 4, 4, 5, -103545966760445939325893614456486058983528857600000⟩, + ⟨6, 4, 4, 4, 5, 5, 28848905268922013827605889759078044127356518400000⟩, + ⟨6, 4, 5, 4, 6, 5, -4709659248810952118416022918175155269140480000000⟩, + ⟨6, 4, 6, 4, 7, 5, -1359317626664333503869857556523775271370752000000⟩, + ⟨6, 4, 7, 4, 8, 5, 886403644768871447051508820967773049978880000000⟩, + ⟨6, 4, 0, 5, 0, 5, -154541319467076845913266071350467072000274726912000000⟩, + ⟨6, 4, 1, 5, 1, 5, -4018764450079406623976294971424292124804251648000000⟩, + ⟨6, 4, 2, 5, 2, 5, 246132133830602440199124909594873454896611328000000⟩, + ⟨6, 4, 3, 5, 3, 5, -260696461486862594047440503626074686768755507200000⟩, + ⟨6, 4, 4, 5, 4, 5, 4028711778698108286421048254669120558071808000000⟩, + ⟨6, 4, 5, 5, 5, 5, -1296104444661845832261452470407410630000640000000⟩, + ⟨6, 4, 6, 5, 6, 5, -2302253502154220493240656736063478309060608000000⟩, + ⟨6, 4, 7, 5, 7, 5, 404320562866860315890216899837162866868224000000⟩, + ⟨6, 4, 8, 5, 8, 5, 244073499265643105653038130670828392336588800000⟩, + ⟨6, 4, 1, 6, 0, 5, 43812926477837653015252802380935992175853830144000000⟩, + ⟨6, 4, 2, 6, 1, 5, -4130016359280162912581801920809206866054742016000000⟩, + ⟨6, 4, 3, 6, 2, 5, -291531922901271013721146354501657102169564774400000⟩, + ⟨6, 4, 4, 6, 3, 5, -100702751274777996953382387692784635219017728000000⟩, + ⟨6, 4, 5, 6, 4, 5, 10808274039613432993157741587596110846754816000000⟩, + ⟨6, 4, 6, 6, 5, 5, 218984878585013141158044662943862109503488000000⟩, + ⟨6, 4, 7, 6, 6, 5, 122236838038976420567389396952767789006848000000⟩, + ⟨6, 4, 8, 6, 7, 5, 65791852029743441968297842033162739462963200000⟩, + ⟨6, 4, 2, 7, 0, 5, 33692566269077891357000043451964994306176974848000000⟩, + ⟨6, 4, 3, 7, 1, 5, 2680019971912942912284212381728344414823120896000000⟩, + ⟨6, 4, 4, 7, 2, 5, 103487970775922231742995376924675309029031936000000⟩, + ⟨6, 4, 5, 7, 3, 5, 15068858540376586923757168892536304657498112000000⟩, + ⟨6, 4, 6, 7, 4, 5, 7599572574184031599256893270840520264908800000000⟩, + ⟨6, 4, 7, 7, 5, 5, -439140324404395990959953289153370216464384000000⟩, + ⟨6, 4, 8, 7, 6, 5, 98363293777760118962324619865956161893171200000⟩ +] + +def collectedFourData_8_5_44 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 5, 6, -1321924410312043662026858143934416307500351488000000⟩, + ⟨6, 5, 1, 0, 6, 6, 397341927147171669001484945062807383526342656000000⟩, + ⟨6, 5, 2, 0, 7, 6, -7754417162043346582426342640176830848434176000000⟩, + ⟨6, 5, 3, 0, 8, 6, 787444919375126787348277095640624494595276800000⟩, + ⟨6, 5, 0, 1, 4, 6, -950441341538684039388114897853525858380152832000000⟩, + ⟨6, 5, 1, 1, 5, 6, 86514786892241413679248960824798192561291264000000⟩, + ⟨6, 5, 2, 1, 6, 6, 17849274795916985680075413611960238485589196800000⟩, + ⟨6, 5, 3, 1, 7, 6, -10519257734387486847297305095632883496150630400000⟩, + ⟨6, 5, 4, 1, 8, 6, 2339289513634277096036429512362263853819494400000⟩, + ⟨6, 5, 0, 2, 3, 6, -372021278239453798190390194941208857327697920000000⟩, + ⟨6, 5, 1, 2, 4, 6, -75220619051536604982121193396727613545775104000000⟩, + ⟨6, 5, 2, 2, 5, 6, 37429520994008767548954111157173456576970752000000⟩, + ⟨6, 5, 3, 2, 6, 6, 3424237922814417908826748304151650433918566400000⟩, + ⟨6, 5, 4, 2, 7, 6, -317187766610297819552764885464221730471936000000⟩, + ⟨6, 5, 5, 2, 8, 6, 494596143705246119250863462218428756000768000000⟩, + ⟨6, 5, 0, 3, 2, 6, 1634685717162899132190693734076897895649378304000000⟩, + ⟨6, 5, 1, 3, 3, 6, 208319221402279100512596507743388800108199936000000⟩, + ⟨6, 5, 2, 3, 4, 6, -2757847586507567954640199934954521152926515200000⟩, + ⟨6, 5, 3, 3, 5, 6, 6839804789183282853957110054985269417449881600000⟩, + ⟨6, 5, 4, 3, 6, 6, -258326395888576309479950697522984908331417600000⟩, + ⟨6, 5, 5, 3, 7, 6, -38963686980874930475482138616181741846528000000⟩, + ⟨6, 5, 6, 3, 8, 6, 56102836077589379390004271961262696431616000000⟩, + ⟨6, 5, 0, 4, 1, 6, 1349285631162694049027972144604573764293754880000000⟩, + ⟨6, 5, 1, 4, 2, 6, -359159740215301299427372644317459199031246848000000⟩, + ⟨6, 5, 2, 4, 3, 6, -58659135498827218988420960454016691747369779200000⟩, + ⟨6, 5, 3, 4, 4, 6, -2797239827672498082879680029026606532421222400000⟩, + ⟨6, 5, 4, 4, 5, 6, 668004001323033266923437341764611381972172800000⟩, + ⟨6, 5, 5, 4, 6, 6, -95421725522286760640737823568108862832640000000⟩, + ⟨6, 5, 6, 4, 7, 6, -24480833795998731347149016706258391007232000000⟩, + ⟨6, 5, 7, 4, 8, 6, 14367436933267610150606093181782769795072000000⟩, + ⟨6, 5, 0, 5, 0, 6, -8349704915778503835462358928333891663220965376000000⟩, + ⟨6, 5, 1, 5, 1, 6, -162847211670788029718234009695602220757680128000000⟩, + ⟨6, 5, 2, 5, 2, 6, 7978956158249656154805377430300293234845286400000⟩, + ⟨6, 5, 3, 5, 3, 6, -7042577782787229766171296641240290288258252800000⟩, + ⟨6, 5, 4, 5, 4, 6, 93285882540808513850580125442923808423936000000⟩, + ⟨6, 5, 5, 5, 5, 6, -26260184873876635564926051492455535083520000000⟩, + ⟨6, 5, 6, 5, 6, 6, -41462778262354678192985792551377099030528000000⟩, + ⟨6, 5, 7, 5, 7, 6, 6553504401854732377750253318733630642585600000⟩, + ⟨6, 5, 8, 5, 8, 6, 3596463928324289380588475950554221327155200000⟩, + ⟨6, 5, 1, 6, 0, 6, 1775374745318085317928932357372308393593667584000000⟩, + ⟨6, 5, 2, 6, 1, 6, -133884263507949546547680668464230480562932940800000⟩, + ⟨6, 5, 3, 6, 2, 6, -7875581553688236540462173192274614393870745600000⟩, + ⟨6, 5, 4, 6, 3, 6, -2331798734430921367042145147990398338072576000000⟩, + ⟨6, 5, 5, 6, 4, 6, 218984878585013141158044662943862109503488000000⟩, + ⟨6, 5, 6, 6, 5, 6, 3943840873771354247853882298011230404608000000⟩, + ⟨6, 5, 7, 6, 6, 6, 1981298330406770329875451633309991514931200000⟩, + ⟨6, 5, 8, 6, 7, 6, 969453969048449245816500187252961103052800000⟩, + ⟨6, 5, 2, 7, 0, 6, 1092224346882369377587372343197180769790748262400000⟩, + ⟨6, 5, 3, 7, 1, 6, 72399329871883537918027327658288280087035904000000⟩, + ⟨6, 5, 4, 7, 2, 6, 2396291225705160054502580479725379950477312000000⟩, + ⟨6, 5, 5, 7, 3, 6, 305307965525745238813881961385921259503616000000⟩, + ⟨6, 5, 6, 7, 4, 6, 136865637184274316449713987860363529420800000000⟩, + ⟨6, 5, 7, 7, 5, 6, -7117886927664862549237822036852992481689600000⟩, + ⟨6, 5, 8, 7, 6, 6, 1449399623503804773073403212799383751884800000⟩ +] + +def collectedFourData_8_5_45 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 5, 7, -1660263884183180300353301967743310637100433408000000⟩, + ⟨6, 6, 1, 0, 6, 7, 399231572497233112444288324458507530767486156800000⟩, + ⟨6, 6, 2, 0, 7, 7, -6492745806341413107513832682329381319737344000000⟩, + ⟨6, 6, 3, 0, 8, 7, 565135559826299881331323576775848360515993600000⟩, + ⟨6, 6, 0, 1, 4, 7, -1193701713261200143751648065927139137224179712000000⟩, + ⟨6, 6, 1, 1, 5, 7, 86926226646249372747473763193296398140519219200000⟩, + ⟨6, 6, 2, 1, 6, 7, 14945134064323075760238823200054433021113139200000⟩, + ⟨6, 6, 3, 1, 7, 7, -7549488811735150500860021807490470742117580800000⟩, + ⟨6, 6, 4, 1, 8, 7, 1469009068838753671224030405988612157158195200000⟩, + ⟨6, 6, 0, 2, 3, 7, -467238132218791932809312974124585746924830720000000⟩, + ⟨6, 6, 1, 2, 4, 7, -75578346951131836868465153566533444416254771200000⟩, + ⟨6, 6, 2, 2, 5, 7, 31339604304081653553531589047030855172620288000000⟩, + ⟨6, 6, 3, 2, 6, 7, 2457516161287583550965683867564947006082252800000⟩, + ⟨6, 6, 4, 2, 7, 7, -199185138461696233671047426317191991001088000000⟩, + ⟨6, 6, 5, 2, 8, 7, 276082390270293689350619984527882325065728000000⟩, + ⟨6, 6, 0, 3, 2, 7, 2053074772675537192087760418180069002695409664000000⟩, + ⟨6, 6, 1, 3, 3, 7, 209309928451186710561942287779237433474600140800000⟩, + ⟨6, 6, 2, 3, 4, 7, -2309135938607078279858574217738780597341388800000⟩, + ⟨6, 6, 3, 3, 5, 7, 4908809255770022625462183495914044892853043200000⟩, + ⟨6, 6, 4, 3, 6, 7, -162221826785000912349544883227076791684300800000⟩, + ⟨6, 6, 5, 3, 7, 7, -21749437338585892536147054329855043698688000000⟩, + ⟨6, 6, 6, 3, 8, 7, 28184822615654268640110068073028011845222400000⟩, + ⟨6, 6, 0, 4, 1, 7, 1694628062990326699824433677165418447456174080000000⟩, + ⟨6, 6, 1, 4, 2, 7, -360867801929049775351729824027333628478776934400000⟩, + ⟨6, 6, 2, 4, 3, 7, -49115084738781837885269670479169196386995404800000⟩, + ⟨6, 6, 3, 4, 4, 7, -2007530504145701830519817322827710940892364800000⟩, + ⟨6, 6, 4, 4, 5, 7, 419488024139250278896593686910046759708262400000⟩, + ⟨6, 6, 5, 4, 6, 7, -53264180081453771225930326770288364093440000000⟩, + ⟨6, 6, 6, 4, 7, 7, -12298628844169221717308697816783005732044800000⟩, + ⟨6, 6, 7, 4, 8, 7, 6561711082998247071454492715277172604928000000⟩, + ⟨6, 6, 0, 5, 0, 7, -10486767176030499265442696906105093114315145216000000⟩, + ⟨6, 6, 1, 5, 1, 7, -163621666756647112434607248261743146107823718400000⟩, + ⟨6, 6, 2, 5, 2, 7, 6680751506255868849646951135189660516063641600000⟩, + ⟨6, 6, 3, 5, 3, 7, -5054335916033393141736356666654346943502745600000⟩, + ⟨6, 6, 4, 5, 4, 7, 58580952314096022297582643572729433817088000000⟩, + ⟨6, 6, 5, 5, 5, 7, -14658372696978172564189559980801570897920000000⟩, + ⟨6, 6, 6, 5, 6, 7, -20829981729631047127927876617032726426419200000⟩, + ⟨6, 6, 7, 5, 7, 7, 2993032276101867859576644662973100877414400000⟩, + ⟨6, 6, 8, 5, 8, 7, 1505653203865843590538768292759516636774400000⟩, + ⟨6, 6, 1, 6, 0, 7, 1783817923354175737164499430582390445546091315200000⟩, + ⟨6, 6, 2, 6, 1, 7, -112100815865481151064688101421274970388116275200000⟩, + ⟨6, 6, 3, 6, 2, 7, -5652168273348148235766466160937898272305971200000⟩, + ⟨6, 6, 4, 6, 3, 7, -1464305066825209544442576655655178451550208000000⟩, + ⟨6, 6, 5, 6, 4, 7, 122236838038976420567389396952767789006848000000⟩, + ⟨6, 6, 6, 6, 5, 7, 1981298330406770329875451633309991514931200000⟩, + ⟨6, 6, 7, 6, 6, 7, 904873101148129081577025609599663525068800000⟩, + ⟨6, 6, 8, 6, 7, 7, 405860173656283597862069146100413602201600000⟩, + ⟨6, 6, 2, 7, 0, 7, 914515546379996461755133769797835137132108185600000⟩, + ⟨6, 6, 3, 7, 1, 7, 51959743229614219806325543847459313583915008000000⟩, + ⟨6, 6, 4, 7, 2, 7, 1504804566353454946167995581596749524893696000000⟩, + ⟨6, 6, 5, 7, 3, 7, 170422179719097784334674756395555813851136000000⟩, + ⟨6, 6, 6, 7, 4, 7, 68758265640659509832303176043549813637120000000⟩, + ⟨6, 6, 7, 7, 5, 7, -3250789807376210767173830250454455838310400000⟩, + ⟨6, 6, 8, 7, 6, 7, 606788565185819382268652503935049374105600000⟩ +] + +def collectedFourData_8_5_46 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 5, 8, -1787216317942996108503714941751899458900485734400000⟩, + ⟨6, 7, 1, 0, 6, 8, 358132416881896664577158306517810027896714035200000⟩, + ⟨6, 7, 2, 0, 7, 8, -4992296432898616384486333011681857375305728000000⟩, + ⟨6, 7, 3, 0, 8, 8, 380217982211124802681486687310689791167692800000⟩, + ⟨6, 7, 0, 1, 4, 8, -1284978370619995686395086787491446733837801881600000⟩, + ⟨6, 7, 1, 1, 5, 8, 77977549331874471563778982347610797447630028800000⟩, + ⟨6, 7, 2, 1, 6, 8, 11491369245603327392595782635306782210549350400000⟩, + ⟨6, 7, 3, 1, 7, 8, -5079226307411381775320211618173211480843878400000⟩, + ⟨6, 7, 4, 1, 8, 8, 878520645639056208844984617723776629682995200000⟩, + ⟨6, 7, 0, 2, 3, 8, -502965596145256333120579516905192828274999296000000⟩, + ⟨6, 7, 1, 2, 4, 8, -67797884541646464811401074577351063158705356800000⟩, + ⟨6, 7, 2, 2, 5, 8, 24097138474589757419208168854684144454598656000000⟩, + ⟨6, 7, 3, 2, 6, 8, 1653394163310461150977822434782437079148134400000⟩, + ⟨6, 7, 4, 2, 7, 8, -119119929314937288333677990175869226713088000000⟩, + ⟨6, 7, 5, 2, 8, 8, 148596544708472265442150154330941020123955200000⟩, + ⟨6, 7, 0, 3, 2, 8, 2210063575217773771697310075946229047865062195200000⟩, + ⟨6, 7, 1, 3, 3, 8, 187762380827533072624332129085180197440009011200000⟩, + ⟨6, 7, 2, 3, 4, 8, -1775503223632583293210782688606394426956185600000⟩, + ⟨6, 7, 3, 3, 5, 8, 3302601504782027019444789826940331573746073600000⟩, + ⟨6, 7, 4, 3, 6, 8, -97014529744573946002834888462249902263500800000⟩, + ⟨6, 7, 5, 3, 7, 8, -11706256363193492350218872395729447629619200000⟩, + ⟨6, 7, 6, 3, 8, 8, 13790900508184850948293758538882666305945600000⟩, + ⟨6, 7, 0, 4, 1, 8, 1824208161048141164648927671839378316506169344000000⟩, + ⟨6, 7, 1, 4, 2, 8, -323718029792355310009164748648541674622523801600000⟩, + ⟨6, 7, 2, 4, 3, 8, -37764771586075620523220286174701586069690777600000⟩, + ⟨6, 7, 3, 4, 4, 8, -1350647971520618130049215462238817438033510400000⟩, + ⟨6, 7, 4, 4, 5, 8, 250869036564891256191844001660331132085862400000⟩, + ⟨6, 7, 5, 4, 6, 8, -28668518513929641045991730573072029188096000000⟩, + ⟨6, 7, 6, 4, 7, 8, -6017748243085508660180244251389723882291200000⟩, + ⟨6, 7, 7, 4, 8, 8, 2943105719740109420657399162433171357696000000⟩, + ⟨6, 7, 0, 5, 0, 8, -11288640075846427154445699621629333585137552588800000⟩, + ⟨6, 7, 1, 5, 1, 8, -146777527146123778860677835627894008769517977600000⟩, + ⟨6, 7, 2, 5, 2, 8, 5136854715795020756121224162373910867948339200000⟩, + ⟨6, 7, 3, 5, 3, 8, -3400510496989612429950991617582508622531788800000⟩, + ⟨6, 7, 4, 5, 4, 8, 35033531882694884708926293866341453529088000000⟩, + ⟨6, 7, 5, 5, 5, 8, -7889614153541097937047636140026786480128000000⟩, + ⟨6, 7, 6, 5, 6, 8, -10192159430554626468219923445535279467724800000⟩, + ⟨6, 7, 7, 5, 7, 8, 1342456304421308050748579164240898477260800000⟩, + ⟨6, 7, 8, 5, 8, 8, 623378191852471689211207813414119486259200000⟩, + ⟨6, 7, 1, 6, 0, 8, 1600181619334488831961602761292854845676244172800000⟩, + ⟨6, 7, 2, 6, 1, 8, -86194734841408661178836559033470662530721382400000⟩, + ⟨6, 7, 3, 6, 2, 8, -3802726582398574026558045177895191259486617600000⟩, + ⟨6, 7, 4, 6, 3, 8, -875707482008083540563302535273128770142208000000⟩, + ⟨6, 7, 5, 6, 4, 8, 65791852029743441968297842033162739462963200000⟩, + ⟨6, 7, 6, 6, 5, 8, 969453969048449245816500187252961103052800000⟩, + ⟨6, 7, 7, 6, 6, 8, 405860173656283597862069146100413602201600000⟩, + ⟨6, 7, 8, 6, 7, 8, 168036291856041092988063962927096188108800000⟩, + ⟨6, 7, 2, 7, 0, 8, 703174409748810139338568806833280027697820467200000⟩, + ⟨6, 7, 3, 7, 1, 8, 34958035082846824702223289905233031419920384000000⟩, + ⟨6, 7, 4, 7, 2, 8, 899927650030421471988747005776263376797696000000⟩, + ⟨6, 7, 5, 7, 3, 8, 91726774109536798457412806363066183083622400000⟩, + ⟨6, 7, 6, 7, 4, 8, 33643582345592430095851751990378134241280000000⟩, + ⟨6, 7, 7, 7, 5, 8, -1458067561150547893253544188452193225932800000⟩, + ⟨6, 7, 8, 7, 6, 8, 251225685723042020299390101485750373580800000⟩ +] + +def collectedFourData_8_5_47 : List CollectedFourTerm := [ + ⟨7, 0, 1, 0, 6, 2, 873345965281341770024895413471034458254393265356800000⟩, + ⟨7, 0, 2, 0, 7, 2, -85219913617001182446371939036378297785399640064000000⟩, + ⟨7, 0, 3, 0, 8, 2, 25961714441583578173753335909343612124261882265600000⟩, + ⟨7, 0, 1, 1, 5, 2, 190156977925786401863000952790042823454232884019200000⟩, + ⟨7, 0, 2, 1, 6, 2, 196160926662518781832964314398384580770707747635200000⟩, + ⟨7, 0, 3, 1, 7, 2, -346815324752241686905332208863245030324528008396800000⟩, + ⟨7, 0, 4, 1, 8, 2, 179959153960678806884070455763028038937939751731200000⟩, + ⟨7, 0, 1, 2, 4, 2, -165332726466321360098119277003546144071516107571200000⟩, + ⟨7, 0, 2, 2, 5, 2, 411344976570055853351992909592558180642196553728000000⟩, + ⟨7, 0, 3, 2, 6, 2, 112895626023842632482707954798138654836967394508800000⟩, + ⟨7, 0, 4, 2, 7, 2, -24400931049011841649509390575332583156301692928000000⟩, + ⟨7, 0, 5, 2, 8, 2, 76097552743807764093738123363816562172759113728000000⟩, + ⟨7, 0, 1, 3, 3, 2, 457879571905443776430422536963198166350410075340800000⟩, + ⟨7, 0, 2, 3, 4, 2, -30308342739340023881644193859271855238307171532800000⟩, + ⟨7, 0, 3, 3, 5, 2, 225505371110736763111319587026563877313149350707200000⟩, + ⟨7, 0, 4, 3, 6, 2, -19872785894549819191801999560451919569627172044800000⟩, + ⟨7, 0, 5, 3, 7, 2, -5994873318072932846295526694052914325973106688000000⟩, + ⟨7, 0, 6, 3, 8, 2, 15537362042322157225554304304535879814306647244800000⟩, + ⟨7, 0, 1, 4, 2, 2, -789422632191411332791094572339250177547230930534400000⟩, + ⟨7, 0, 2, 4, 3, 2, -644655343605575235145615543287322259732738919628800000⟩, + ⟨7, 0, 3, 4, 4, 2, -92223773172968108591622859476067626509665094860800000⟩, + ⟨7, 0, 4, 4, 5, 2, 51388865815792015869612894234231271558285256294400000⟩, + ⟨7, 0, 5, 4, 6, 2, -14681391845151064207701553255473779452611133440000000⟩, + ⟨7, 0, 6, 4, 7, 2, -6779827979824504630795383275373425694468577689600000⟩, + ⟨7, 0, 7, 4, 8, 2, 6631633528106702387563879334105731825177460736000000⟩, + ⟨7, 0, 1, 5, 1, 2, -357933420948355389506674266949990444179692873318400000⟩, + ⟨7, 0, 2, 5, 2, 2, 87687564435945206358842510854816553127305124249600000⟩, + ⟨7, 0, 3, 5, 3, 2, -232190707985585369677183232888707530902090652057600000⟩, + ⟨7, 0, 4, 5, 4, 2, 7176387702622655272049513229176449145323388928000000⟩, + ⟨7, 0, 5, 5, 5, 2, -4040338423448921069762343204582265406273617920000000⟩, + ⟨7, 0, 6, 5, 6, 2, -11482881119446086619196518507965364576408987238400000⟩, + ⟨7, 0, 7, 5, 7, 2, 3024926416576267018608927928910556798273768652800000⟩, + ⟨7, 0, 8, 5, 8, 2, 2608624525478561746913703464427491244234296524800000⟩, + ⟨7, 0, 1, 6, 0, 2, 3902221901973216677727331751904016479354644280115200000⟩, + ⟨7, 0, 2, 6, 1, 2, -1471368528723410620056537529121447847679923270451200000⟩, + ⟨7, 0, 3, 6, 2, 2, -259654477827488242154328271811325929120444134195200000⟩, + ⟨7, 0, 4, 6, 3, 2, -179382895964357580556773041573540282385876123648000000⟩, + ⟨7, 0, 5, 6, 4, 2, 33692566269077891357000043451964994306176974848000000⟩, + ⟨7, 0, 6, 6, 5, 2, 1092224346882369377587372343197180769790748262400000⟩, + ⟨7, 0, 7, 6, 6, 2, 914515546379996461755133769797835137132108185600000⟩, + ⟨7, 0, 8, 6, 7, 2, 703174409748810139338568806833280027697820467200000⟩, + ⟨7, 0, 2, 7, 0, 2, 12003386269610232679750090551856256093874703407513600000⟩, + ⟨7, 0, 3, 7, 1, 2, 2386974227209959585259336362535863214398838407168000000⟩, + ⟨7, 0, 4, 7, 2, 2, 184344237473770652165961712063827728213502590976000000⟩, + ⟨7, 0, 5, 7, 3, 2, 46974060160780039106082825178868541539940827136000000⟩, + ⟨7, 0, 6, 7, 4, 2, 37904161442822951321447073873590355499407114240000000⟩, + ⟨7, 0, 7, 7, 5, 2, -3285430645564643674553391529015943977442790604800000⟩, + ⟨7, 0, 8, 7, 6, 2, 1051293570697115980303353472404003591128560435200000⟩ +] + +def collectedFourData_8_5_48 : List CollectedFourTerm := [ + ⟨7, 1, 0, 0, 5, 3, -288896645340428661212884147248952421194206806016000000⟩, + ⟨7, 1, 1, 0, 6, 3, 347344368287509705792719096745786644740249223168000000⟩, + ⟨7, 1, 2, 0, 7, 3, -16946695947280065120601839922575477739691704320000000⟩, + ⟨7, 1, 3, 0, 8, 3, 3441803386384835701204871953895316010882301952000000⟩, + ⟨7, 1, 0, 1, 4, 3, -207711812431519647600953794159430231326640308224000000⟩, + ⟨7, 1, 1, 1, 5, 3, 75628625995674822787782094696202670352568942592000000⟩, + ⟨7, 1, 2, 1, 6, 3, 39008248656840022402402438245932976063041765376000000⟩, + ⟨7, 1, 3, 1, 7, 3, -45978094469388673427618815706550720174653177856000000⟩, + ⟨7, 1, 4, 1, 8, 3, 17893195003737799321908493276788515262513020928000000⟩, + ⟨7, 1, 0, 2, 3, 3, -81302454542969290487731910663130360149641789440000000⟩, + ⟨7, 1, 1, 2, 4, 3, -65755603981288482439224475084288147284780122112000000⟩, + ⟨7, 1, 2, 2, 5, 3, 81799405227079369624772906370577369597099376640000000⟩, + ⟨7, 1, 3, 2, 6, 3, 14966829283605524952772583879576147533177552896000000⟩, + ⟨7, 1, 4, 2, 7, 3, -2426165093152910296698318102342938071998136320000000⟩, + ⟨7, 1, 5, 2, 8, 3, 6053055132053761193938588638368548620028870656000000⟩, + ⟨7, 1, 0, 3, 2, 3, 357248278487267881594632290308973798658228092928000000⟩, + ⟨7, 1, 1, 3, 3, 3, 182106401103046955820759902055950424449910571008000000⟩, + ⟨7, 1, 2, 3, 4, 3, -6027068642405681531084441333766785177657278464000000⟩, + ⟨7, 1, 3, 3, 5, 3, 29895758682782916354665562703822932138811981824000000⟩, + ⟨7, 1, 4, 3, 6, 3, -1975935235594661489896334971630680031742656512000000⟩, + ⟨7, 1, 5, 3, 7, 3, -476852374295654448056484625761744287302680576000000⟩, + ⟨7, 1, 6, 3, 8, 3, 1029911668836030005629377019158753936049963008000000⟩, + ⟨7, 1, 0, 4, 1, 3, 294876234532147720056127818486341206664187740160000000⟩, + ⟨7, 1, 1, 4, 2, 3, -313966648259555376309204031777835610105282822144000000⟩, + ⟨7, 1, 2, 4, 3, 3, -128195132278256274223679470316220255861624274944000000⟩, + ⟨7, 1, 3, 4, 4, 3, -12226314850127720413187895135852371910366068736000000⟩, + ⟨7, 1, 4, 4, 5, 3, 5109553900568990465794901308579484374124199936000000⟩, + ⟨7, 1, 5, 4, 6, 3, -1167807255946417090184671389048439210644602880000000⟩, + ⟨7, 1, 6, 4, 7, 3, -449408588800487790783683757402905547443798016000000⟩, + ⟨7, 1, 7, 4, 8, 3, 376787444103379950240836553814681911275028480000000⟩, + ⟨7, 1, 0, 5, 0, 3, -1824765259597172998145732740550170888680958328832000000⟩, + ⟨7, 1, 1, 5, 1, 3, -142356137121722510467086900687407572881437097984000000⟩, + ⟨7, 1, 2, 5, 2, 3, 17437409048922523495632372890030019303438286848000000⟩, + ⟨7, 1, 3, 5, 3, 3, -30782048960212446493232454913354026625208942592000000⟩, + ⟨7, 1, 4, 5, 4, 3, 713542499835881767490667536387969313480376320000000⟩, + ⟨7, 1, 5, 5, 5, 3, -321382098996364479168925016710420633579683840000000⟩, + ⟨7, 1, 6, 5, 6, 3, -761155801387693996799995754120317767845412864000000⟩, + ⟨7, 1, 7, 5, 7, 3, 171866296331359804789063370019606554480738304000000⟩, + ⟨7, 1, 8, 5, 8, 3, 129686726956161847454415430256796986146553856000000⟩, + ⟨7, 1, 1, 6, 0, 3, 1551979233134643252556280653726551074151755415552000000⟩, + ⟨7, 1, 2, 6, 1, 3, -292593996219423659811549869967352446184593555456000000⟩, + ⟨7, 1, 3, 6, 2, 3, -34422983238934500191468391629230085049925238784000000⟩, + ⟨7, 1, 4, 6, 3, 3, -17835898131232542359819872407275519521975173120000000⟩, + ⟨7, 1, 5, 6, 4, 3, 2680019971912942912284212381728344414823120896000000⟩, + ⟨7, 1, 6, 6, 5, 3, 72399329871883537918027327658288280087035904000000⟩, + ⟨7, 1, 7, 6, 6, 3, 51959743229614219806325543847459313583915008000000⟩, + ⟨7, 1, 8, 6, 7, 3, 34958035082846824702223289905233031419920384000000⟩, + ⟨7, 1, 2, 7, 0, 3, 2386974227209959585259336362535863214398838407168000000⟩, + ⟨7, 1, 3, 7, 1, 3, 316446588953523950035772279611156957883856322560000000⟩, + ⟨7, 1, 4, 7, 2, 3, 18329200356511197297520441305156245307984445440000000⟩, + ⟨7, 1, 5, 7, 3, 3, 3736474639163069206796330379823725119035932672000000⟩, + ⟨7, 1, 6, 7, 4, 3, 2512520340394515352734560039910628540180070400000000⟩, + ⟨7, 1, 7, 7, 5, 3, -186667283479193761434375683188252258194161664000000⟩, + ⟨7, 1, 8, 7, 6, 3, 52264640204880943678263512170406171161657344000000⟩ +] + +def collectedFourData_8_5_49 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 5, 4, -66933816695952804786540942159238575060613595136000000⟩, + ⟨7, 2, 1, 0, 6, 4, 40237719357958537766450116122438162160721854464000000⟩, + ⟨7, 2, 2, 0, 7, 4, -1308780675756492771336290054637382181050122240000000⟩, + ⟨7, 2, 3, 0, 8, 4, 199355929433107755237142567344863289853083648000000⟩, + ⟨7, 2, 0, 1, 4, 4, -48124284594902725040121267800198691222039035904000000⟩, + ⟨7, 2, 1, 1, 5, 4, 8761113482983164274303004048829731813789270016000000⟩, + ⟨7, 2, 2, 1, 6, 4, 3012577920557452485671603842602179912093663232000000⟩, + ⟨7, 2, 3, 1, 7, 4, -2663140431776929753851096646173164342234578944000000⟩, + ⟨7, 2, 4, 1, 8, 4, 829126854743385265565607169437235798928365977600000⟩, + ⟨7, 2, 0, 2, 3, 4, -18836783593999718611837734940955449347004170240000000⟩, + ⟨7, 2, 1, 2, 4, 4, -7617384304391758973768617518210058764970622976000000⟩, + ⟨7, 2, 2, 2, 5, 4, 6317306994981448761373114977326302709132820480000000⟩, + ⟨7, 2, 3, 2, 6, 4, 866907788603766764911098160430553748318715904000000⟩, + ⟨7, 2, 4, 2, 7, 4, -112422551274596398318117927987143353768607744000000⟩, + ⟨7, 2, 5, 2, 8, 4, 233736464345786651335804311492679917524484096000000⟩, + ⟨7, 2, 0, 3, 2, 4, 82770053487586156116297213645393876801067941888000000⟩, + ⟨7, 2, 1, 3, 3, 4, 21095912097261801660666897122024462630239862784000000⟩, + ⟨7, 2, 2, 3, 4, 4, -465466011497333354721643894934598441813147648000000⟩, + ⟨7, 2, 3, 3, 5, 4, 1731620342373531560221183213699616909480165376000000⟩, + ⟨7, 2, 4, 3, 6, 4, -91560001817618302793762930371711199074477670400000⟩, + ⟨7, 2, 5, 3, 7, 4, -18413476426563302028514252693693947042594816000000⟩, + ⟨7, 2, 6, 3, 8, 4, 34088275397719930243656435070818726627508224000000⟩, + ⟨7, 2, 0, 4, 1, 4, 68319214322858423639885613020747556789273231360000000⟩, + ⟨7, 2, 1, 4, 2, 4, -36371114760581988509814189214559831517258842112000000⟩, + ⟨7, 2, 2, 4, 3, 4, -9900414356508101959498091722726802527258411008000000⟩, + ⟨7, 2, 3, 4, 4, 4, -708171875863361542629166486367055016900952064000000⟩, + ⟨7, 2, 4, 4, 5, 4, 236764219796161938544262023861168649169744691200000⟩, + ⟨7, 2, 5, 4, 6, 4, -45094441251133533136080781450566632032174080000000⟩, + ⟨7, 2, 6, 4, 7, 4, -14874638480837228889553141452715842179432448000000⟩, + ⟨7, 2, 7, 4, 8, 4, 10912129875735396210202990078927532992757760000000⟩, + ⟨7, 2, 0, 5, 0, 4, -422775775935698113339875823461615317381988483072000000⟩, + ⟨7, 2, 1, 5, 1, 4, -16491087282133753225654527030628705883947794432000000⟩, + ⟨7, 2, 2, 5, 2, 4, 1346678082234317711167240395969033452163956736000000⟩, + ⟨7, 2, 3, 5, 3, 4, -1782955994695635212656640307999927426254635008000000⟩, + ⟨7, 2, 4, 5, 4, 4, 33063812722717840506050298427064777120415744000000⟩, + ⟨7, 2, 5, 5, 5, 4, -12410049782241210707386699474913981827645440000000⟩, + ⟨7, 2, 6, 5, 6, 4, -25192926115304370596990897829634864098312192000000⟩, + ⟨7, 2, 7, 5, 7, 4, 4977414656935487395473325002443388195176448000000⟩, + ⟨7, 2, 8, 5, 8, 4, 3338536366623825063480776853601227179556864000000⟩, + ⟨7, 2, 1, 6, 0, 4, 179787296221716451312678270371758582663108100096000000⟩, + ⟨7, 2, 2, 6, 1, 4, -22596815879959884236358386263289298918196641792000000⟩, + ⟨7, 2, 3, 6, 2, 4, -1993845971738135230706989925184192201847996416000000⟩, + ⟨7, 2, 4, 6, 3, 4, -826471857931636854566961469154990598131810304000000⟩, + ⟨7, 2, 5, 6, 4, 4, 103487970775922231742995376924675309029031936000000⟩, + ⟨7, 2, 6, 6, 5, 4, 2396291225705160054502580479725379950477312000000⟩, + ⟨7, 2, 7, 6, 6, 4, 1504804566353454946167995581596749524893696000000⟩, + ⟨7, 2, 8, 6, 7, 4, 899927650030421471988747005776263376797696000000⟩, + ⟨7, 2, 2, 7, 0, 4, 184344237473770652165961712063827728213502590976000000⟩, + ⟨7, 2, 3, 7, 1, 4, 18329200356511197297520441305156245307984445440000000⟩, + ⟨7, 2, 4, 7, 2, 4, 849330275469575935318996343469364108484149248000000⟩, + ⟨7, 2, 5, 7, 3, 4, 144282573381972950721782319635030980744445952000000⟩, + ⟨7, 2, 6, 7, 4, 4, 83160030027174118762828417480005917029171200000000⟩, + ⟨7, 2, 7, 7, 5, 4, -5406065602113853361196218080494703783968768000000⟩, + ⟨7, 2, 8, 7, 6, 4, 1345453047569678349629191953713331947175936000000⟩ +] + +def collectedFourData_8_5_50 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 5, 5, -34111759340605101101614860655917279506482593792000000⟩, + ⟨7, 3, 1, 0, 6, 5, 13671010827391258133878038991103218297992118272000000⟩, + ⟨7, 3, 2, 0, 7, 5, -333499669112246179560743596084172310592880640000000⟩, + ⟨7, 3, 3, 0, 8, 5, 40639436527790378939695670158021000725685862400000⟩, + ⟨7, 3, 0, 1, 4, 5, -24525779278314661255573667021099172858679001088000000⟩, + ⟨7, 3, 1, 1, 5, 5, 2976641797720989865207288905678958258991136768000000⟩, + ⟨7, 3, 2, 1, 6, 5, 767656306584785579038462897492762791197540352000000⟩, + ⟨7, 3, 3, 1, 7, 5, -542890933064050115646820458797027645191303987200000⟩, + ⟨7, 3, 4, 1, 8, 5, 140850455609082023647813689456969331698460262400000⟩, + ⟨7, 3, 0, 2, 3, 5, -9599868353965079793071806237281572923669217280000000⟩, + ⟨7, 3, 1, 2, 4, 5, -2588052826138687405242828775268239610738638848000000⟩, + ⟨7, 3, 2, 2, 5, 5, 1609757716883328310094718539566860805110497280000000⟩, + ⟨7, 3, 3, 2, 6, 5, 176722328503558517469676771605369714214384435200000⟩, + ⟨7, 3, 4, 2, 7, 5, -19098124101484021673555387166917040701177856000000⟩, + ⟨7, 3, 5, 2, 8, 5, 34034310370050323065706832134396247992696832000000⟩, + ⟨7, 3, 0, 3, 2, 5, 42182446550194581706421635809577080997004967936000000⟩, + ⟨7, 3, 1, 3, 3, 5, 7167464938300927195938567785962483003668037632000000⟩, + ⟨7, 3, 2, 3, 4, 5, -118608689517539700416642739048900799997411328000000⟩, + ⟨7, 3, 3, 3, 5, 5, 352997150344266797431879631995415557537844428800000⟩, + ⟨7, 3, 4, 3, 6, 5, -15554034823261526938065816669021801513851289600000⟩, + ⟨7, 3, 5, 3, 7, 5, -2681181874840648116210094251803872510083072000000⟩, + ⟨7, 3, 6, 3, 8, 5, 4343137385939632206673442296790880230572032000000⟩, + ⟨7, 3, 0, 4, 1, 5, 34817805294247953663664274744026262335830097920000000⟩, + ⟨7, 3, 1, 4, 2, 5, -12357308307481404692743605036075837873639653376000000⟩, + ⟨7, 3, 2, 4, 3, 5, -2522794669214616693565293236608704753369612288000000⟩, + ⟨7, 3, 3, 4, 4, 5, -144363431184383822636636056032244616557441843200000⟩, + ⟨7, 3, 4, 4, 5, 5, 40221044631993688234107830512276980607274188800000⟩, + ⟨7, 3, 5, 4, 6, 5, -6566190747347739294287558699081901916815360000000⟩, + ⟨7, 3, 6, 4, 7, 5, -1895155965936063520266090175563650316632064000000⟩, + ⟨7, 3, 7, 4, 8, 5, 1235820916803296601615094147707381649244160000000⟩, + ⟨7, 3, 0, 5, 0, 5, -215460976762559725340409299394928374832309469184000000⟩, + ⟨7, 3, 1, 5, 1, 5, -5602947592130704247537920564909951547904884736000000⟩, + ⟨7, 3, 2, 5, 2, 5, 343156575540255236509650238071709694737514496000000⟩, + ⟨7, 3, 3, 5, 3, 5, -363462111131183701647205256828223011265341030400000⟩, + ⟨7, 3, 4, 5, 4, 5, 5616816123522531919997303637784820088569856000000⟩, + ⟨7, 3, 5, 5, 5, 5, -1807024364720978611241875584021864885780480000000⟩, + ⟨7, 3, 6, 5, 6, 5, -3209793924626408979423064809413569419411456000000⟩, + ⟨7, 3, 7, 5, 7, 5, 563702339936605226690797462570646705799168000000⟩, + ⟨7, 3, 8, 5, 8, 5, 340286434301052218495357899056897926470041600000⟩, + ⟨7, 3, 1, 6, 0, 5, 61083831601115510531969877410127305189105860608000000⟩, + ⟨7, 3, 2, 6, 1, 5, -5758054621796004651825017205742680248797888512000000⟩, + ⟨7, 3, 3, 6, 2, 5, -406452805517535494172232098663907623720242380800000⟩, + ⟨7, 3, 4, 6, 3, 5, -140399429920508513743999456717296113912119296000000⟩, + ⟨7, 3, 5, 6, 4, 5, 15068858540376586923757168892536304657498112000000⟩, + ⟨7, 3, 6, 6, 5, 5, 305307965525745238813881961385921259503616000000⟩, + ⟨7, 3, 7, 6, 6, 5, 170422179719097784334674756395555813851136000000⟩, + ⟨7, 3, 8, 6, 7, 5, 91726774109536798457412806363066183083622400000⟩, + ⟨7, 3, 2, 7, 0, 5, 46974060160780039106082825178868541539940827136000000⟩, + ⟨7, 3, 3, 7, 1, 5, 3736474639163069206796330379823725119035932672000000⟩, + ⟨7, 3, 4, 7, 2, 5, 144282573381972950721782319635030980744445952000000⟩, + ⟨7, 3, 5, 7, 3, 5, 21008950816535899842747455732618955098947584000000⟩, + ⟨7, 3, 6, 7, 4, 5, 10595297978936192885426931816308735056281600000000⟩, + ⟨7, 3, 7, 7, 5, 5, -612247931868833545624249322401899938316288000000⟩, + ⟨7, 3, 8, 7, 6, 5, 137137766314036269269157125783840356722278400000⟩ +] + +def collectedFourData_8_5_51 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 5, 6, -45875589943310983710672134636440897977109708800000000⟩, + ⟨7, 4, 1, 0, 6, 6, 13789211527447139057490678018646384014104985600000000⟩, + ⟨7, 4, 2, 0, 7, 6, -269106508057673939904322126623105737136537600000000⟩, + ⟨7, 4, 3, 0, 8, 6, 27327205657447246553750227497862339158343680000000⟩, + ⟨7, 4, 0, 1, 4, 6, -32983774949209596269846330999869525388899123200000000⟩, + ⟨7, 4, 1, 1, 5, 6, 3002378091016966739616732348869502751368806400000000⟩, + ⟨7, 4, 2, 1, 6, 6, 619434821639818852656742108019370418168135680000000⟩, + ⟨7, 4, 3, 1, 7, 6, -365056542239695304811972155997247864087511040000000⟩, + ⟨7, 4, 4, 1, 8, 6, 81181863084623120631535703970321299606077440000000⟩, + ⟨7, 4, 0, 2, 3, 6, -12910492822105423190461298272366193585160192000000000⟩, + ⟨7, 4, 1, 2, 4, 6, -2610429346770085990482124345524544141157990400000000⟩, + ⟨7, 4, 2, 2, 5, 6, 1298940653112207643550003958803976395371315200000000⟩, + ⟨7, 4, 3, 2, 6, 6, 118833522998707584952579059890977596128624640000000⟩, + ⟨7, 4, 4, 2, 7, 6, -11007570328937195073120842919363103791513600000000⟩, + ⟨7, 4, 5, 2, 8, 6, 17164286928334106501219059329031394348236800000000⟩, + ⟨7, 4, 0, 3, 2, 6, 56729546002596550336630470099583663478302310400000000⟩, + ⟨7, 4, 1, 3, 3, 6, 7229435438070827239470072915885865244924313600000000⟩, + ⟨7, 4, 2, 3, 4, 6, -95707352113201525640111287593721965072875520000000⟩, + ⟨7, 4, 3, 3, 5, 6, 237366128768889529689635836666025458437980160000000⟩, + ⟨7, 4, 4, 3, 6, 6, -8964866460496265011862106063668470622453760000000⟩, + ⟨7, 4, 5, 3, 7, 6, -1352181798497996799749884730895764344012800000000⟩, + ⟨7, 4, 6, 3, 8, 6, 1946972672926694413823604824100686109081600000000⟩, + ⟨7, 4, 0, 4, 1, 6, 46825123924453303060241772603170505608921088000000000⟩, + ⟨7, 4, 1, 4, 2, 6, -12464150625960453041397689640281207770762444800000000⟩, + ⟨7, 4, 2, 4, 3, 6, -2035685569901906502637836493896628481996881920000000⟩, + ⟨7, 4, 3, 4, 4, 6, -97074406302180280443021589896826246649610240000000⟩, + ⟨7, 4, 4, 4, 5, 6, 23182170936651810888791376440972203555553280000000⟩, + ⟨7, 4, 5, 4, 6, 6, -3311481290152038869288654726948469080064000000000⟩, + ⟨7, 4, 6, 4, 7, 6, -849574063338828013681183128187697312563200000000⟩, + ⟨7, 4, 7, 4, 8, 6, 498602371017099735268293471706711012147200000000⟩, + ⟨7, 4, 0, 5, 0, 6, -289765160455341945755555750683376541748533657600000000⟩, + ⟨7, 4, 1, 5, 1, 6, -5651391144412831899318552327806063857159372800000000⟩, + ⟨7, 4, 2, 5, 2, 6, 276898828734929437639013855798108365667696640000000⟩, + ⟨7, 4, 3, 5, 3, 6, -244403089909471274651290845539570847873761280000000⟩, + ⟨7, 4, 4, 5, 4, 6, 3237359762447995902750326804046249826713600000000⟩, + ⟨7, 4, 5, 5, 5, 6, -911324024060596104673709080835367370752000000000⟩, + ⟨7, 4, 6, 5, 6, 6, -1438909364738343088429882866383090142412800000000⟩, + ⟨7, 4, 7, 5, 7, 6, 227430462956806274433623185126775649730560000000⟩, + ⟨7, 4, 8, 5, 8, 6, 124810392435954936737835487807778869739520000000⟩, + ⟨7, 4, 1, 6, 0, 6, 61611967504781177169167635598762632081204838400000000⟩, + ⟨7, 4, 2, 6, 1, 6, -4646271393916576820524960485442854955599790080000000⟩, + ⟨7, 4, 3, 6, 2, 6, -273311353587018247678388753603966790071746560000000⟩, + ⟨7, 4, 4, 6, 3, 6, -80921905773593580665699232352494375508377600000000⟩, + ⟨7, 4, 5, 6, 4, 6, 7599572574184031599256893270840520264908800000000⟩, + ⟨7, 4, 6, 6, 5, 6, 136865637184274316449713987860363529420800000000⟩, + ⟨7, 4, 7, 6, 6, 6, 68758265640659509832303176043549813637120000000⟩, + ⟨7, 4, 8, 6, 7, 6, 33643582345592430095851751990378134241280000000⟩, + ⟨7, 4, 2, 7, 0, 6, 37904161442822951321447073873590355499407114240000000⟩, + ⟨7, 4, 3, 7, 1, 6, 2512520340394515352734560039910628540180070400000000⟩, + ⟨7, 4, 4, 7, 2, 6, 83160030027174118762828417480005917029171200000000⟩, + ⟨7, 4, 5, 7, 3, 6, 10595297978936192885426931816308735056281600000000⟩, + ⟨7, 4, 6, 7, 4, 6, 4749735915167509210726663405963397038080000000000⟩, + ⟨7, 4, 7, 7, 5, 6, -247016591424714611297359822641314094120960000000⟩, + ⟨7, 4, 8, 7, 6, 6, 50299443956976518538420777575302802964480000000⟩ +] + +def collectedFourData_8_5_52 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 5, 7, 5964558903794837811606105060474852611261988864000000⟩, + ⟨7, 5, 1, 0, 6, 7, -1434254068344028955629284984374888346297984614400000⟩, + ⟨7, 5, 2, 0, 7, 7, 23325427468623722990337599933034454478487552000000⟩, + ⟨7, 5, 3, 0, 8, 7, -2030270228320603336182419608174119835454668800000⟩, + ⟨7, 5, 0, 1, 4, 7, 4288417190867286365842810760332940061595140096000000⟩, + ⟨7, 5, 1, 1, 5, 7, -312285657753288933769588294802446125339613593600000⟩, + ⟨7, 5, 2, 1, 6, 7, -53690942326087851529978705722799378224748953600000⟩, + ⟨7, 5, 3, 1, 7, 7, 27121815477717287776934384528283733512840806400000⟩, + ⟨7, 5, 4, 1, 8, 7, -5277468964283525717316547301556094901000601600000⟩, + ⟨7, 5, 0, 2, 3, 7, 1678570128681173023045881086141723257350389760000000⟩, + ⟨7, 5, 1, 2, 4, 7, 271517983698868489998852716001037297741568409600000⟩, + ⟨7, 5, 2, 2, 5, 7, -112588678025289876501512906802154420939259904000000⟩, + ⟨7, 5, 3, 2, 6, 7, -8828716953172198351980058173976764484052582400000⟩, + ⟨7, 5, 4, 2, 7, 7, 715579916200982500325882734741615546466304000000⟩, + ⟨7, 5, 5, 2, 8, 7, -991836113978828613058287736487726939111424000000⟩, + ⟨7, 5, 0, 3, 2, 7, -7375746429335293848081058727112235988771930112000000⟩, + ⟨7, 5, 1, 3, 3, 7, -751953595623985190162060827222103265018013286400000⟩, + ⟨7, 5, 2, 3, 4, 7, 8295655560481913158267091153527933963232870400000⟩, + ⟨7, 5, 3, 3, 5, 7, -17635077310579624111822372726154280268568985600000⟩, + ⟨7, 5, 4, 3, 6, 7, 582787863157291834819388012338874088318566400000⟩, + ⟨7, 5, 5, 3, 7, 7, 78135651426407510673738565637164555567104000000⟩, + ⟨7, 5, 6, 3, 8, 7, -101255009089585698015670668691196471358259200000⟩, + ⟨7, 5, 0, 4, 1, 7, -6088013476666308212110258720651448177802608640000000⟩, + ⟨7, 5, 1, 4, 2, 7, 1296430815362665083259314109824628517518914355200000⟩, + ⟨7, 5, 2, 4, 3, 7, 176447743506427690474136615378829167210948198400000⟩, + ⟨7, 5, 3, 4, 4, 7, 7212126974040029066709036843966921282315878400000⟩, + ⟨7, 5, 4, 4, 5, 7, -1507026113891550272171551928387133966070579200000⟩, + ⟨7, 5, 5, 4, 6, 7, 191353520717261199715908814021645062635520000000⟩, + ⟨7, 5, 6, 4, 7, 7, 44183275246661958129141342371372375369318400000⟩, + ⟨7, 5, 7, 4, 8, 7, -23573187754717381401428782773000443265024000000⟩, + ⟨7, 5, 0, 5, 0, 7, 37674095743273428630733337465515949872725884928000000⟩, + ⟨7, 5, 1, 5, 1, 7, 587816839602730821798758401371572165344965427200000⟩, + ⟨7, 5, 2, 5, 2, 7, -24000844841772595399918844124563691476405452800000⟩, + ⟨7, 5, 3, 5, 3, 7, 18157887175615298502062860800747883121659084800000⟩, + ⟨7, 5, 4, 5, 4, 7, -210454219986677232872513252230627332194304000000⟩, + ⟨7, 5, 5, 5, 5, 7, 52660741595254684693444559974438388367360000000⟩, + ⟨7, 5, 6, 5, 6, 7, 74832473424837098478814914598337064311193600000⟩, + ⟨7, 5, 7, 5, 7, 7, -10752578238821139585670251778419306214195200000⟩, + ⟨7, 5, 8, 5, 8, 7, -5409114363505842731082130073595396961075200000⟩, + ⟨7, 5, 1, 6, 0, 7, -6408431321582050432383419283174957366736689561600000⟩, + ⟨7, 5, 2, 6, 1, 7, 402726292948350187578314304268516138178681241600000⟩, + ⟨7, 5, 3, 6, 2, 7, 20305621848259033941858279847037234776218009600000⟩, + ⟨7, 5, 4, 6, 3, 7, 5260569664503143427295965302631373958283264000000⟩, + ⟨7, 5, 5, 6, 4, 7, -439140324404395990959953289153370216464384000000⟩, + ⟨7, 5, 6, 6, 5, 7, -7117886927664862549237822036852992481689600000⟩, + ⟨7, 5, 7, 6, 6, 7, -3250789807376210767173830250454455838310400000⟩, + ⟨7, 5, 8, 6, 7, 7, -1458067561150547893253544188452193225932800000⟩, + ⟨7, 5, 2, 7, 0, 7, -3285430645564643674553391529015943977442790604800000⟩, + ⟨7, 5, 3, 7, 1, 7, -186667283479193761434375683188252258194161664000000⟩, + ⟨7, 5, 4, 7, 2, 7, -5406065602113853361196218080494703783968768000000⟩, + ⟨7, 5, 5, 7, 3, 7, -612247931868833545624249322401899938316288000000⟩, + ⟨7, 5, 6, 7, 4, 7, -247016591424714611297359822641314094120960000000⟩, + ⟨7, 5, 7, 7, 5, 7, 11678581624685872868464418801478400160563200000⟩, + ⟨7, 5, 8, 7, 6, 7, -2179910177941723353166533082568515701964800000⟩ +] + +def collectedFourData_8_5_53 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 5, 8, -2672009957201978239989536979380456436783277670400000⟩, + ⟨7, 6, 1, 0, 6, 8, 535432322488317534517379435630632358099759923200000⟩, + ⟨7, 6, 2, 0, 7, 8, -7463822730402401987785058305656247233282048000000⟩, + ⟨7, 6, 3, 0, 8, 8, 568451744859110037164953538522616131538124800000⟩, + ⟨7, 6, 0, 1, 4, 8, -1921130065015058964364010744890619594240792985600000⟩, + ⟨7, 6, 1, 1, 5, 8, 116581740084371066338651064777578749300100300800000⟩, + ⟨7, 6, 2, 1, 6, 8, 17180378635685679902267629736709697512564326400000⟩, + ⟨7, 6, 3, 1, 7, 8, -7593788805546438448521664290729415613507174400000⟩, + ⟨7, 6, 4, 1, 8, 8, 1313448119954968162971434576814075116991283200000⟩, + ⟨7, 6, 0, 2, 3, 8, -751967776669001371466969192585957694857281536000000⟩, + ⟨7, 6, 1, 2, 4, 8, -101362448828249500449924086054276662546975948800000⟩, + ⟨7, 6, 2, 2, 5, 8, 36026861045162185124023027980604230699319296000000⟩, + ⟨7, 6, 3, 2, 6, 8, 2471936733786075432502437893889780498196070400000⟩, + ⟨7, 6, 4, 2, 7, 8, -178092396558378008597951802973349958647808000000⟩, + ⟨7, 6, 5, 2, 8, 8, 222161941495607427246048470362100023374643200000⟩, + ⟨7, 6, 0, 3, 2, 8, 3304195367815373039116131301369306357477618483200000⟩, + ⟨7, 6, 1, 3, 3, 8, 280717530453479317807954970134924343586796339200000⟩, + ⟨7, 6, 2, 3, 4, 8, -2654498084513231266324420979661271182449049600000⟩, + ⟨7, 6, 3, 3, 5, 8, 4937613884146102652149462021917441248565657600000⟩, + ⟨7, 6, 4, 3, 6, 8, -145043320648014085626794886659233748405452800000⟩, + ⟨7, 6, 5, 3, 7, 8, -17501649492554426790530167220379820700467200000⟩, + ⟨7, 6, 6, 3, 8, 8, 20618334281472842300408659731966475213209600000⟩, + ⟨7, 6, 0, 4, 1, 8, 2727315278734608490885384021511293246535368704000000⟩, + ⟨7, 6, 1, 4, 2, 8, -483980473010972586199545091966240905426999705600000⟩, + ⟨7, 6, 2, 4, 3, 8, -56460902184237383307873991202577166265588121600000⟩, + ⟨7, 6, 3, 4, 4, 8, -2019310585039574451729179620904888441398886400000⟩, + ⟨7, 6, 4, 4, 5, 8, 375066273133947984005446057554885831190118400000⟩, + ⟨7, 6, 5, 4, 6, 8, -42861385137539084808556189072974032142336000000⟩, + ⟨7, 6, 6, 4, 7, 8, -8996942935237932681033439938313641472819200000⟩, + ⟨7, 6, 7, 4, 8, 8, 4400143233525742923019983956040468135936000000⟩, + ⟨7, 6, 0, 5, 0, 8, -16877284737780141016983053182677689814641069260800000⟩, + ⟨7, 6, 1, 5, 1, 8, -219442386514980033694932741338123165343783321600000⟩, + ⟨7, 6, 2, 5, 2, 8, 7679947195816740736922561672541189698695987200000⟩, + ⟨7, 6, 3, 5, 3, 8, -5083994487015365049813437029275638275296460800000⟩, + ⟨7, 6, 4, 5, 4, 8, 52377513055752784994758274409719616503808000000⟩, + ⟨7, 6, 5, 5, 5, 8, -11795509790894747659581153586237509992448000000⟩, + ⟨7, 6, 6, 5, 6, 8, -15237971593263300798880362264385999916236800000⟩, + ⟨7, 6, 7, 5, 7, 8, 2007063485549887210324128299214546193612800000⟩, + ⟨7, 6, 8, 5, 8, 8, 931992797407692802282217193146382758707200000⟩, + ⟨7, 6, 1, 6, 0, 8, 2392380361161023558967390739461998829523225804800000⟩, + ⟨7, 6, 2, 6, 1, 8, -128866991333040267936343070622521779980494438400000⟩, + ⟨7, 6, 3, 6, 2, 8, -5685334892409887328012829172451353917233561600000⟩, + ⟨7, 6, 4, 6, 3, 8, -1309242248982477863621413617684459949129728000000⟩, + ⟨7, 6, 5, 6, 4, 8, 98363293777760118962324619865956161893171200000⟩, + ⟨7, 6, 6, 6, 5, 8, 1449399623503804773073403212799383751884800000⟩, + ⟨7, 6, 7, 6, 6, 8, 606788565185819382268652503935049374105600000⟩, + ⟨7, 6, 8, 6, 7, 8, 251225685723042020299390101485750373580800000⟩, + ⟨7, 6, 2, 7, 0, 8, 1051293570697115980303353472404003591128560435200000⟩, + ⟨7, 6, 3, 7, 1, 8, 52264640204880943678263512170406171161657344000000⟩, + ⟨7, 6, 4, 7, 2, 8, 1345453047569678349629191953713331947175936000000⟩, + ⟨7, 6, 5, 7, 3, 8, 137137766314036269269157125783840356722278400000⟩, + ⟨7, 6, 6, 7, 4, 8, 50299443956976518538420777575302802964480000000⟩, + ⟨7, 6, 7, 7, 5, 8, -2179910177941723353166533082568515701964800000⟩, + ⟨7, 6, 8, 7, 6, 8, 375599487883745797840939547211305110732800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0826.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0826.lean new file mode 100644 index 0000000000000000000000000000000000000000..32b038c59f1c9a41cf3030447015dcb5752c7fcf --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0826.lean @@ -0,0 +1,643 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse0821 +import OAI.Analysis.LaughlinFock.Sparse0822 +import OAI.Analysis.LaughlinFock.Sparse0823 +import OAI.Analysis.LaughlinFock.Sparse0824 +import OAI.Analysis.LaughlinFock.Sparse0825 + +namespace OAI + +/-! Sparse0826. -/ +namespace LaughlinFock +def collectedFourData_8_5 : List (List CollectedFourTerm) := [ + collectedFourData_8_5_0, + collectedFourData_8_5_1, + collectedFourData_8_5_2, + collectedFourData_8_5_3, + collectedFourData_8_5_4, + collectedFourData_8_5_5, + collectedFourData_8_5_6, + collectedFourData_8_5_7, + collectedFourData_8_5_8, + collectedFourData_8_5_9, + collectedFourData_8_5_10, + collectedFourData_8_5_11, + collectedFourData_8_5_12, + collectedFourData_8_5_13, + collectedFourData_8_5_14, + collectedFourData_8_5_15, + collectedFourData_8_5_16, + collectedFourData_8_5_17, + collectedFourData_8_5_18, + collectedFourData_8_5_19, + collectedFourData_8_5_20, + collectedFourData_8_5_21, + collectedFourData_8_5_22, + collectedFourData_8_5_23, + collectedFourData_8_5_24, + collectedFourData_8_5_25, + collectedFourData_8_5_26, + collectedFourData_8_5_27, + collectedFourData_8_5_28, + collectedFourData_8_5_29, + collectedFourData_8_5_30, + collectedFourData_8_5_31, + collectedFourData_8_5_32, + collectedFourData_8_5_33, + collectedFourData_8_5_34, + collectedFourData_8_5_35, + collectedFourData_8_5_36, + collectedFourData_8_5_37, + collectedFourData_8_5_38, + collectedFourData_8_5_39, + collectedFourData_8_5_40, + collectedFourData_8_5_41, + collectedFourData_8_5_42, + collectedFourData_8_5_43, + collectedFourData_8_5_44, + collectedFourData_8_5_45, + collectedFourData_8_5_46, + collectedFourData_8_5_47, + collectedFourData_8_5_48, + collectedFourData_8_5_49, + collectedFourData_8_5_50, + collectedFourData_8_5_51, + collectedFourData_8_5_52, + collectedFourData_8_5_53 +] + +theorem collectedFourChecked_8_5 : collectNumericRowParts 8 5 = collectedFourData_8_5 := by + decide +kernel + +def collectedFourData_8_6_0 : List CollectedFourTerm := [ + ⟨0, 6, 2, 0, 8, 0, 9495201555716022741973022191007139348137115648000000⟩, + ⟨0, 6, 2, 1, 7, 0, 4352717623425940759279365083525052978796953600000000⟩, + ⟨0, 6, 3, 1, 8, 0, 165156036399368390338922433258186650714898432000000⟩, + ⟨0, 6, 2, 2, 6, 0, 9169357897560970587625583280632569991975141376000000⟩, + ⟨0, 6, 3, 2, 7, 0, -5934055514420184108435881560919498683167277056000000⟩, + ⟨0, 6, 4, 2, 8, 0, 992377172637640278412276628311402172701999104000000⟩, + ⟨0, 6, 2, 3, 5, 0, -2272376997736744081553104174011758252912541696000000⟩, + ⟨0, 6, 3, 3, 6, 0, 6515914066942515402470386808155049321608249344000000⟩, + ⟨0, 6, 4, 3, 7, 0, 5982684344534958756960047229359634890417504256000000⟩, + ⟨0, 6, 5, 3, 8, 0, -1649244707353412641126890785434279350034759680000000⟩, + ⟨0, 6, 2, 4, 4, 0, -287065995810044317743761083552783720230420480000000⟩, + ⟨0, 6, 3, 4, 5, 0, 12189439432418804799693828275020905174383198208000000⟩, + ⟨0, 6, 4, 4, 6, 0, -7093871446277985445371891949252050485545795584000000⟩, + ⟨0, 6, 5, 4, 7, 0, -985477105009010586376824261375400696243814400000000⟩, + ⟨0, 6, 6, 4, 8, 0, 935097708316554391085704561562299277298892800000000⟩, + ⟨0, 6, 2, 5, 3, 0, -4786940416369859259358060883138938244255711232000000⟩, + ⟨0, 6, 3, 5, 4, 0, -12478318987141663282587692522020924777511780352000000⟩, + ⟨0, 6, 4, 5, 5, 0, -3680336448606137372843273983133631461933973504000000⟩, + ⟨0, 6, 5, 5, 6, 0, 2188963785791996618695297491145605986333491200000000⟩, + ⟨0, 6, 6, 5, 7, 0, -1133449932618327990056157209485817403062353920000000⟩, + ⟨0, 6, 7, 5, 8, 0, -92576214176382343134479701873655491715923968000000⟩, + ⟨0, 6, 2, 6, 2, 0, 3203500725727113238130428457780078289673519104000000⟩, + ⟨0, 6, 3, 6, 3, 0, -16599127059660804895701488488490053494613475328000000⟩, + ⟨0, 6, 4, 6, 4, 0, 7142887055593512404484928110092692723794444288000000⟩, + ⟨0, 6, 5, 6, 5, 0, -4436976144871121098329940991931386999529799680000000⟩, + ⟨0, 6, 6, 6, 6, 0, 738051368113888788940688436916482263513825280000000⟩, + ⟨0, 6, 7, 6, 7, 0, 305907103971960672057882338657870775633051648000000⟩, + ⟨0, 6, 8, 6, 8, 0, -605221662938744783306159099245346119653261312000000⟩, + ⟨0, 6, 2, 7, 1, 0, -47249596828024117369010078933186641150328438784000000⟩, + ⟨0, 6, 3, 7, 2, 0, -61100968963731478117236442407946085459753435136000000⟩, + ⟨0, 6, 4, 7, 3, 0, -25997595109071447248294155446481009060601659392000000⟩, + ⟨0, 6, 5, 7, 4, 0, -13417546164515223513413671805835737253764136960000000⟩, + ⟨0, 6, 6, 7, 5, 0, -762731886212701531683698695071332846429798400000000⟩, + ⟨0, 6, 7, 7, 6, 0, -766108220879245168060176195275560906414620672000000⟩, + ⟨0, 6, 8, 7, 7, 0, -458272366897543719509669160671800849267163136000000⟩ +] + +def collectedFourData_8_6_1 : List CollectedFourTerm := [ + ⟨0, 7, 1, 0, 7, 1, 41449724252682616652945269918804631069545149235200000⟩, + ⟨0, 7, 2, 0, 8, 1, -25199698675591391439348750463393705710489855590400000⟩, + ⟨0, 7, 1, 1, 6, 1, 20248478093427240574104430254834767247699030835200000⟩, + ⟨0, 7, 2, 1, 7, 1, -11551852995078270225958572386060874376575713280000000⟩, + ⟨0, 7, 3, 1, 8, 1, -219157135701541423281985335867215104009096396800000⟩, + ⟨0, 7, 1, 2, 5, 1, 12047883336546860380646291235396535295274280550400000⟩, + ⟨0, 7, 2, 2, 6, 1, -24334929038772394273581490730208762026739420364800000⟩, + ⟨0, 7, 3, 2, 7, 1, 7874314726768521432340326551441358544683034214400000⟩, + ⟨0, 7, 4, 2, 8, 1, -877903278347631214163898714283681925946566246400000⟩, + ⟨0, 7, 1, 3, 4, 1, 6569198981217839594290478506552328479601747558400000⟩, + ⟨0, 7, 2, 3, 5, 1, 6030753037131586808991469213129845239437905100800000⟩, + ⟨0, 7, 3, 3, 6, 1, -8646423676185805331741373709218766072185461145600000⟩, + ⟨0, 7, 4, 3, 7, 1, -5292562489548619404991626951302366776797010329600000⟩, + ⟨0, 7, 5, 3, 8, 1, 1094249274850855839097846293895592514542370816000000⟩, + ⟨0, 7, 1, 4, 3, 1, -20703022728095948315698294383091243256979967180800000⟩, + ⟨0, 7, 2, 4, 4, 1, 761856033489558871391544155651846382607663104000000⟩, + ⟨0, 7, 3, 4, 5, 1, -16175022663758624622916723443154730101085778739200000⟩, + ⟨0, 7, 4, 4, 6, 1, 6275570590072520216608494524916052151484442214400000⟩, + ⟨0, 7, 5, 4, 7, 1, 653849366761770614000757800023023458482913280000000⟩, + ⟨0, 7, 6, 4, 8, 1, -496338710527483308951511614497182872332402688000000⟩, + ⟨0, 7, 1, 5, 2, 1, -4193140516305841359840454334976392554491150336000000⟩, + ⟨0, 7, 2, 5, 3, 1, 12704254392358068401862002503320307319820622233600000⟩, + ⟨0, 7, 3, 5, 4, 1, 16558357219104253369837821622011809021500902604800000⟩, + ⟨0, 7, 4, 5, 5, 1, 3255797818349633027785405479709537554825373286400000⟩, + ⟨0, 7, 5, 5, 6, 1, -1452344836759509096394177783235801796512317440000000⟩, + ⟨0, 7, 6, 5, 7, 1, 601621705410914947199778733199892878105719603200000⟩, + ⟨0, 7, 7, 5, 8, 1, 40948625262329958820419809895559242684196454400000⟩, + ⟨0, 7, 1, 6, 1, 1, -92520504427112063828990209408141151867343627878400000⟩, + ⟨0, 7, 2, 6, 2, 1, -8501899882974526612610205369811385687578194739200000⟩, + ⟨0, 7, 3, 6, 3, 1, 22026546657637779657189746070810180600397509427200000⟩, + ⟨0, 7, 4, 6, 4, 1, -6318932091419770846120769480607523349684079820800000⟩, + ⟨0, 7, 5, 6, 5, 1, 2943867521543830032918569477355700770954018816000000⟩, + ⟨0, 7, 6, 6, 6, 1, -391748863348387813094096476707294086555290828800000⟩, + ⟨0, 7, 7, 6, 7, 1, -135309868491340058570159944423264800072951398400000⟩, + ⟨0, 7, 8, 6, 8, 1, 229460314371939699901845431314392406144371916800000⟩, + ⟨0, 7, 1, 7, 0, 1, 579514835130808418976469959805977336108051490406400000⟩, + ⟨0, 7, 2, 7, 1, 1, 125397612217363722751635111477670896875406046003200000⟩, + ⟨0, 7, 3, 7, 2, 1, 81079163914419181153549198505841410450785724006400000⟩, + ⟨0, 7, 4, 7, 3, 1, 22998689011301920762346533651637211114165711667200000⟩, + ⟨0, 7, 5, 7, 4, 1, 8902341838864828474756892889603882434798026752000000⟩, + ⟨0, 7, 6, 7, 5, 1, 404848987987093513610982644278658496687243264000000⟩, + ⟨0, 7, 7, 7, 6, 1, 338867588465048478212770344326167034318133657600000⟩, + ⟨0, 7, 8, 7, 7, 1, 173746790334116265128422973187636025308374630400000⟩ +] + +def collectedFourData_8_6_2 : List CollectedFourTerm := [ + ⟨0, 8, 0, 0, 6, 2, 9495201555716022741973022191007139348137115648000000⟩, + ⟨0, 8, 1, 0, 7, 2, -25199698675591391439348750463393705710489855590400000⟩, + ⟨0, 8, 2, 0, 8, 2, 7660181397943846000387618572466834843401348710400000⟩, + ⟨0, 8, 0, 1, 5, 2, 14499943104101012337825462267411438608299170201600000⟩, + ⟨0, 8, 1, 1, 6, 2, -12310227770952085769027856285045556239254578790400000⟩, + ⟨0, 8, 2, 1, 7, 2, 3511521727455885323263400245057074989660897280000000⟩, + ⟨0, 8, 3, 1, 8, 2, 44412790690858124570270114937386965402858291200000⟩, + ⟨0, 8, 0, 2, 4, 2, 4131757430982925135573400757857065402047135744000000⟩, + ⟨0, 8, 1, 2, 5, 2, -7324609155632932664922911214974487238783323340800000⟩, + ⟨0, 8, 2, 2, 6, 2, 7397309513214372046624166684999933257994521804800000⟩, + ⟨0, 8, 3, 2, 7, 2, -1595751334650484287821892561101321584110049689600000⟩, + ⟨0, 8, 4, 2, 8, 2, 133432118545652050310999944006803395332748083200000⟩, + ⟨0, 8, 0, 3, 3, 2, 734877218300060567106502435540252824676230758400000⟩, + ⟨0, 8, 1, 3, 4, 2, -3993798218234894065495140125585281161727102156800000⟩, + ⟨0, 8, 2, 3, 5, 2, -1833222802595459264033255249773585760235867340800000⟩, + ⟨0, 8, 3, 3, 6, 2, 1752221317027457863494785598317695727430952550400000⟩, + ⟨0, 8, 4, 3, 7, 2, 804414156927300201904429638410906255171046604800000⟩, + ⟨0, 8, 5, 3, 8, 2, -133051558240179707519348657002370385173702246400000⟩, + ⟨0, 8, 0, 4, 2, 2, -5446735448723004650316881389251444114855454310400000⟩, + ⟨0, 8, 1, 4, 3, 2, 12586571897113959620112997529196455002239506841600000⟩, + ⟨0, 8, 2, 4, 4, 2, -231588301541904976427854772536957990342754304000000⟩, + ⟨0, 8, 3, 4, 5, 2, 3277912415152748220186300907216441168177712332800000⟩, + ⟨0, 8, 4, 4, 6, 2, -953821109419056201635311826041486751854441267200000⟩, + ⟨0, 8, 5, 4, 7, 2, -79502613436838416248926817757690612691238912000000⟩, + ⟨0, 8, 6, 4, 8, 2, 50292196035195063493135139882835762474909696000000⟩, + ⟨0, 8, 0, 5, 1, 2, -4198286003829253315581552046388634630534620774400000⟩, + ⟨0, 8, 1, 5, 2, 2, 2549254052238531899100343780477847050515382272000000⟩, + ⟨0, 8, 2, 5, 3, 2, -3861827652143694627618906039713230390237436313600000⟩, + ⟨0, 8, 3, 5, 4, 2, -3355596207271312741734868054004877175473517363200000⟩, + ⟨0, 8, 4, 5, 5, 2, -494847224259571807870305386530690176294007603200000⟩, + ⟨0, 8, 5, 5, 6, 2, 176592983037863951956416039049363540490059776000000⟩, + ⟨0, 8, 6, 5, 7, 2, -60960138924885897758092779898309869698442854400000⟩, + ⟨0, 8, 7, 5, 8, 2, -3556435921192753609699685200945766778431078400000⟩, + ⟨0, 8, 0, 6, 0, 2, 96839387526443055927008989070992386946430612275200000⟩, + ⟨0, 8, 1, 6, 1, 2, 56248596942742023678648142020373229550684654796800000⟩, + ⟨0, 8, 2, 6, 2, 2, 2584399764820363991367047680555048631123784499200000⟩, + ⟨0, 8, 3, 6, 3, 2, -4463739696253051578569712056231126078392683724800000⟩, + ⟨0, 8, 4, 6, 4, 2, 960411604215901846149670659871519521741629030400000⟩, + ⟨0, 8, 5, 6, 5, 2, -357949664666168953001094700524367101104121446400000⟩, + ⟨0, 8, 6, 6, 6, 2, 39694487280961387841287843633759300794030489600000⟩, + ⟨0, 8, 7, 6, 7, 2, 11751820084596609738364722619723290962716262400000⟩, + ⟨0, 8, 8, 6, 8, 2, -17437784220618554705043331564297819100754739200000⟩, + ⟨0, 8, 1, 7, 0, 2, -352320781057699192905682339971848111515388136652800000⟩, + ⟨0, 8, 2, 7, 1, 2, -38118251683082188141519170400851837148749574963200000⟩, + ⟨0, 8, 3, 7, 2, 2, -16430913484947271993369595481862385087228254617600000⟩, + ⟨0, 8, 4, 7, 3, 2, -3495560244776141713182491079550709636313749913600000⟩, + ⟨0, 8, 5, 7, 4, 2, -1082450297999195275206702304714082448132852940800000⟩, + ⟨0, 8, 6, 7, 5, 2, -41021875257037444841268206099147278660927488000000⟩, + ⟨0, 8, 7, 7, 6, 2, -29431045765869222422163965480865367519238553600000⟩, + ⟨0, 8, 8, 7, 7, 2, -13203847676946602138075593811973599414294937600000⟩ +] + +def collectedFourData_8_6_3 : List CollectedFourTerm := [ + ⟨1, 5, 2, 0, 8, 0, 14499943104101012337825462267411438608299170201600000⟩, + ⟨1, 5, 2, 1, 7, 0, 6646952939076873264019747984927928601406341120000000⟩, + ⟨1, 5, 3, 1, 8, 0, 252206666392253510197242914552330088354309734400000⟩, + ⟨1, 5, 2, 2, 6, 0, 14002353402991807127731258706943907426362143539200000⟩, + ⟨1, 5, 3, 2, 7, 0, -9061784189707080986670120533336091311582950195200000⟩, + ⟨1, 5, 4, 2, 8, 0, 1515440452382195077690264415553272165398531276800000⟩, + ⟨1, 5, 2, 3, 5, 0, -3470104029378446476131043242432753046276748083200000⟩, + ⟨1, 5, 3, 3, 6, 0, 9950329404540296369060300239088858151019924684800000⟩, + ⟨1, 5, 4, 3, 7, 0, 9136044358461345448994828142287687479035376435200000⟩, + ⟨1, 5, 5, 3, 8, 0, -2518530468367807352816852148779836749650067456000000⟩, + ⟨1, 5, 2, 4, 4, 0, -438373064746792215146704691736947566697250816000000⟩, + ⟨1, 5, 3, 4, 5, 0, 18614262920470440808138392911438486873501702553600000⟩, + ⟨1, 5, 4, 4, 6, 0, -10832917211422052323076274351184949454341721292800000⟩, + ⟨1, 5, 5, 4, 7, 0, -1504903489323275047974275244306546712620564480000000⟩, + ⟨1, 5, 6, 4, 8, 0, 1427970063384591698373520482366808953465077760000000⟩, + ⟨1, 5, 2, 5, 3, 0, -7310046371611793560996900317947059793574651494400000⟩, + ⟨1, 5, 3, 5, 4, 0, -19055405436807853596763344886307343073771152998400000⟩, + ⟨1, 5, 4, 5, 5, 0, -5620172336058852643667519015113189368210967756800000⟩, + ⟨1, 5, 5, 5, 6, 0, 3342725287575850681664408395433269586338775040000000⟩, + ⟨1, 5, 6, 5, 7, 0, -1730870001850480966036009113246232348578545664000000⟩, + ⟨1, 5, 7, 5, 8, 0, -141371389588094784346233268816663297209768345600000⟩, + ⟨1, 5, 2, 6, 2, 0, 4892005502403119539362941203223474913114115276800000⟩, + ⟨1, 5, 3, 6, 3, 0, -25348213677247771039587316466869066325019957657600000⟩, + ⟨1, 5, 4, 6, 4, 0, 10907768023394562325111359723529458059648276889600000⟩, + ⟨1, 5, 5, 6, 5, 0, -6775622537065060420845784031733860217919635456000000⟩, + ⟨1, 5, 6, 6, 6, 0, 1127064315882054579947681201940197046774398976000000⟩, + ⟨1, 5, 7, 6, 7, 0, 467144965455054643000729861946886694037461401600000⟩, + ⟨1, 5, 8, 6, 8, 0, -924222579845956230928843140134688498070742630400000⟩, + ⟨1, 5, 2, 7, 1, 0, -72153967630695279651724092159898555935330454732800000⟩, + ⟨1, 5, 3, 7, 2, 0, -93306136618680645601899480342613259567645274931200000⟩, + ⟨1, 5, 4, 7, 3, 0, -39700436869406119896340703906758168672716875366400000⟩, + ⟨1, 5, 5, 7, 4, 0, -20489681534458846401796338203961685778557304832000000⟩, + ⟨1, 5, 6, 7, 5, 0, -1164753469304720789541312410737895131085537280000000⟩, + ⟨1, 5, 7, 7, 6, 0, -1169909406256455651702067878809750438635005542400000⟩, + ⟨1, 5, 8, 7, 7, 0, -699819083060528220103256239174040029748212531200000⟩ +] + +def collectedFourData_8_6_4 : List CollectedFourTerm := [ + ⟨1, 6, 1, 0, 7, 1, 20248478093427240574104430254834767247699030835200000⟩, + ⟨1, 6, 2, 0, 8, 1, -12310227770952085769027856285045556239254578790400000⟩, + ⟨1, 6, 1, 1, 6, 1, 9891522138979433559116333268400864336905712435200000⟩, + ⟨1, 6, 2, 1, 7, 1, -5643160395553072364381088656813153926281953280000000⟩, + ⟨1, 6, 3, 1, 8, 1, -107059782454010466929986947406924473420270796800000⟩, + ⟨1, 6, 1, 2, 5, 1, 5885474661425467044974808643957286307438683750400000⟩, + ⟨1, 6, 2, 2, 6, 1, -11887781799050180187733756970299954205142338764800000⟩, + ⟨1, 6, 3, 2, 7, 1, 3846657417398978387731920637745734574076749414400000⟩, + ⟨1, 6, 4, 2, 8, 1, -428861846978861285104248635466155897196537446400000⟩, + ⟨1, 6, 1, 3, 4, 1, 3209099313946465845773931291883879269902214758400000⟩, + ⟨1, 6, 2, 3, 5, 1, 2946064731693011712621061974428749578518711500800000⟩, + ⟨1, 6, 3, 3, 6, 1, -4223838000138395852275838937578061118754625945600000⟩, + ⟨1, 6, 4, 3, 7, 1, -2585453523753760032279300683748375758959647129600000⟩, + ⟨1, 6, 5, 3, 8, 1, 534548368416038609322157823018247810308898816000000⟩, + ⟨1, 6, 1, 4, 3, 1, -10113570349034257909435263285963501116557413580800000⟩, + ⟨1, 6, 2, 4, 4, 1, 372171962120117319173619026695455903112495104000000⟩, + ⟨1, 6, 3, 4, 5, 1, -7901610878547850623109274296033121983475692339200000⟩, + ⟨1, 6, 4, 4, 6, 1, 3065659806135277177889276682035560992142157414400000⟩, + ⟨1, 6, 5, 4, 7, 1, 319409955505798838711508600290518265789153280000000⟩, + ⟨1, 6, 6, 4, 8, 1, -242464906298748896887342020260877153953906688000000⟩, + ⟨1, 6, 1, 5, 2, 1, -2048378256257905122309260585636497936493838336000000⟩, + ⟨1, 6, 2, 5, 3, 1, 6206116479540645343832999353377235390078491033600000⟩, + ⟨1, 6, 3, 5, 4, 1, 8088872470423634567221274315426259643761741004800000⟩, + ⟨1, 6, 4, 5, 5, 1, 1590479840097225713185851752870413948531664486400000⟩, + ⟨1, 6, 5, 5, 6, 1, -709480536757100799935510416568971207051837440000000⟩, + ⟨1, 6, 6, 5, 7, 1, 293896380305951896657680039194197227222545203200000⟩, + ⟨1, 6, 7, 5, 8, 1, 20003687757382058761958039762483633375831654400000⟩, + ⟨1, 6, 1, 6, 1, 1, -45196908806069335259821094634368170928686655078400000⟩, + ⟨1, 6, 2, 6, 2, 1, -4153237123689183030157903883761106309296108339200000⟩, + ⟨1, 6, 3, 6, 3, 1, 10760120978179156577466149363998376999032927027200000⟩, + ⟨1, 6, 4, 6, 4, 1, -3086842200613356146195398465949825114162646220800000⟩, + ⟨1, 6, 5, 6, 5, 1, 1438099724296098721136032147245437759904546816000000⟩, + ⟨1, 6, 6, 6, 6, 1, -191372039757815142734593586098147179121921228800000⟩, + ⟨1, 6, 7, 6, 7, 1, -66099810248896880184606835476847392004138598400000⟩, + ⟨1, 6, 8, 6, 8, 1, 112092956772093517396832131963070153759706316800000⟩, + ⟨1, 6, 1, 7, 0, 1, 283097020680489389017145656772023533286694741606400000⟩, + ⟨1, 6, 2, 7, 1, 1, 61257604235739705142722496925282362347134071603200000⟩, + ⟨1, 6, 3, 7, 2, 1, 39607734525477834915195145418269454783297775206400000⟩, + ⟨1, 6, 4, 7, 3, 1, 11235019267776033402155541964205874010419049267200000⟩, + ⟨1, 6, 5, 7, 4, 1, 4348855799512078636045433514217660108612042752000000⟩, + ⟨1, 6, 6, 7, 5, 1, 197771541601324545848316743776435821833355264000000⟩, + ⟨1, 6, 7, 7, 6, 1, 165539169809144712384201512857892479867394457600000⟩, + ⟨1, 6, 8, 7, 7, 1, 84876513446430415637895949399274094225417830400000⟩ +] + +def collectedFourData_8_6_5 : List CollectedFourTerm := [ + ⟨1, 7, 0, 0, 6, 2, 4352717623425940759279365083525052978796953600000000⟩, + ⟨1, 7, 1, 0, 7, 2, -11551852995078270225958572386060874376575713280000000⟩, + ⟨1, 7, 2, 0, 8, 2, 3511521727455885323263400245057074989660897280000000⟩, + ⟨1, 7, 0, 1, 5, 2, 6646952939076873264019747984927928601406341120000000⟩, + ⟨1, 7, 1, 1, 6, 2, -5643160395553072364381088656813153926281953280000000⟩, + ⟨1, 7, 2, 1, 7, 2, 1609724914047676114409295137174784464388096000000000⟩, + ⟨1, 7, 3, 1, 8, 2, 20359371584824451736591916904986470871203840000000⟩, + ⟨1, 7, 0, 2, 4, 2, 1894048618139553169497783786605347771043020800000000⟩, + ⟨1, 7, 1, 2, 5, 2, -3357691268516340831500679462390839678399938560000000⟩, + ⟨1, 7, 2, 2, 6, 2, 3391018010009637778699641946061888082526863360000000⟩, + ⟨1, 7, 3, 2, 7, 2, -731512113374495896204717972169779481117982720000000⟩, + ⟨1, 7, 4, 2, 8, 2, 61166930529777687692734458190084335458058240000000⟩, + ⟨1, 7, 0, 3, 3, 2, 336876789858484941868107697044843433694330880000000⟩, + ⟨1, 7, 1, 3, 4, 2, -1830806411734694953608100920961769844517109760000000⟩, + ⟨1, 7, 2, 3, 5, 2, -840371966166422735963731090344408343180738560000000⟩, + ⟨1, 7, 3, 3, 6, 2, 803239885116150151119239190885745619663585280000000⟩, + ⟨1, 7, 4, 3, 7, 2, 368753381046764318886396379742354707694223360000000⟩, + ⟨1, 7, 5, 3, 8, 2, -60992476987250341810615928102242858020372480000000⟩, + ⟨1, 7, 0, 4, 2, 2, -2496850776540216357761386837254869762734817280000000⟩, + ⟨1, 7, 1, 4, 3, 2, 5769839954803810612019509181430919106521989120000000⟩, + ⟨1, 7, 2, 4, 4, 2, -106162936677621234957774620342056389496012800000000⟩, + ⟨1, 7, 3, 4, 5, 2, 1502635521085169288105201400369994374536232960000000⟩, + ⟨1, 7, 4, 4, 6, 2, -437243372686987928802026702158838019171287040000000⟩, + ⟨1, 7, 5, 4, 7, 2, -36444979559873191248596193958210524571238400000000⟩, + ⟨1, 7, 6, 4, 8, 2, 23054563583371789251320813058773270868787200000000⟩, + ⟨1, 7, 0, 5, 1, 2, -1924546137311778076891428120964249950439342080000000⟩, + ⟨1, 7, 1, 5, 2, 2, 1168609531315199196164939696852166414591590400000000⟩, + ⟨1, 7, 2, 5, 3, 2, -1770309474894753963121365789183192581296619520000000⟩, + ⟨1, 7, 3, 5, 4, 2, -1538246730497093620447359001263895159756554240000000⟩, + ⟨1, 7, 4, 5, 5, 2, -226844077116130413608942630217014852179722240000000⟩, + ⟨1, 7, 5, 5, 6, 2, 80952403688528640946506580926344360833843200000000⟩, + ⟨1, 7, 6, 5, 7, 2, -27944880313268437877752213474366468474798080000000⟩, + ⟨1, 7, 7, 5, 8, 2, -1630314134979247087318170875676022674554880000000⟩, + ⟨1, 7, 0, 6, 0, 2, 44392370846975345031956398502239565622426992640000000⟩, + ⟨1, 7, 1, 6, 1, 2, 25785051298702317579830847244377755133683957760000000⟩, + ⟨1, 7, 2, 6, 2, 2, 1184720759881033190521313466255685033855549440000000⟩, + ⟨1, 7, 3, 6, 3, 2, -2046233387280788870872819148065381385880207360000000⟩, + ⟨1, 7, 4, 6, 4, 2, 440264536869864906160098576487898305297121280000000⟩, + ⟨1, 7, 5, 6, 5, 2, -164088545624806195618496976574343855713812480000000⟩, + ⟨1, 7, 6, 6, 6, 2, 18196443048298032494516228523266113504542720000000⟩, + ⟨1, 7, 7, 6, 7, 2, 5387179417877796723156723993878334202183680000000⟩, + ⟨1, 7, 8, 6, 8, 2, -7993695578256895490416006178963895814717440000000⟩, + ⟨1, 7, 1, 7, 0, 2, -161508195882988404506785860238985648747273256960000000⟩, + ⟨1, 7, 2, 7, 1, 2, -17473877189605974076353828141695997592196874240000000⟩, + ⟨1, 7, 3, 7, 2, 2, -7532133601931081160939542400895903112437432320000000⟩, + ⟨1, 7, 4, 7, 3, 2, -1602407973322568059890298434708959925916139520000000⟩, + ⟨1, 7, 5, 7, 4, 2, -496208580822322732399497633088331586270658560000000⟩, + ⟨1, 7, 6, 7, 5, 2, -18804934084816556499046553612670490745241600000000⟩, + ⟨1, 7, 7, 7, 6, 2, -13491554742599049368982564461957300638187520000000⟩, + ⟨1, 7, 8, 7, 7, 2, -6052806793330170182417536761604040105656320000000⟩ +] + +def collectedFourData_8_6_6 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 6, 3, 165156036399368390338922433258186650714898432000000⟩, + ⟨1, 8, 1, 0, 7, 3, -219157135701541423281985335867215104009096396800000⟩, + ⟨1, 8, 2, 0, 8, 3, 44412790690858124570270114937386965402858291200000⟩, + ⟨1, 8, 0, 1, 5, 3, 252206666392253510197242914552330088354309734400000⟩, + ⟨1, 8, 1, 1, 6, 3, -107059782454010466929986947406924473420270796800000⟩, + ⟨1, 8, 2, 1, 7, 3, 20359371584824451736591916904986470871203840000000⟩, + ⟨1, 8, 3, 1, 8, 3, 193124928230756410164138594334627515806515200000⟩, + ⟨1, 8, 0, 2, 4, 3, 71866265993478316714529685744874843061354496000000⟩, + ⟨1, 8, 1, 2, 5, 3, -63700776082558744042772240187304207338543513600000⟩, + ⟨1, 8, 2, 2, 6, 3, 42888691797046642137003222943274286033823334400000⟩, + ⟨1, 8, 3, 2, 7, 3, -6938977650011617082089800711095910884022681600000⟩, + ⟨1, 8, 4, 2, 8, 3, 464173818703288242429027034547793036060917760000⟩, + ⟨1, 8, 0, 3, 3, 3, 12782183495785631010484357747030722227050905600000⟩, + ⟨1, 8, 1, 3, 4, 3, -34733327145934138214840257899549233004517785600000⟩, + ⟨1, 8, 2, 3, 5, 3, -10628800597755414176976837676701684347594342400000⟩, + ⟨1, 8, 3, 3, 6, 3, 7619372951607488903349828551951485321504358400000⟩, + ⟨1, 8, 4, 3, 7, 3, 2798336675679636271797148967259300065590640640000⟩, + ⟨1, 8, 5, 3, 8, 3, -385708294636454184667330896907328636426649600000⟩, + ⟨1, 8, 0, 4, 2, 3, -94738508998316018561961632555581449598245273600000⟩, + ⟨1, 8, 1, 4, 3, 3, 109463096395864986812541592021657915497853747200000⟩, + ⟨1, 8, 2, 4, 4, 3, -1342720521682789622282263720807916227264512000000⟩, + ⟨1, 8, 3, 4, 5, 3, 14253700118272132394343938181447502401424588800000⟩, + ⟨1, 8, 4, 4, 6, 3, -3318082569208199885690404881785904144800808960000⟩, + ⟨1, 8, 5, 4, 7, 3, -230473192899471415714312447243085590560768000000⟩, + ⟨1, 8, 6, 4, 8, 3, 124966274660709712068017526937560759140352000000⟩, + ⟨1, 8, 0, 5, 1, 3, -73023439470432239667723651856356092075940249600000⟩, + ⟨1, 8, 1, 5, 2, 3, 22170392727961177625526216868229737479143424000000⟩, + ⟨1, 8, 2, 5, 3, 3, -22390402301029592293775351903531618555186380800000⟩, + ⟨1, 8, 3, 5, 4, 3, -14591500930700676917935920778458906269791027200000⟩, + ⟨1, 8, 4, 5, 5, 3, -1721438048521284081436177767415475456452853760000⟩, + ⟨1, 8, 5, 5, 6, 3, 511932210589695287456732162226542151204864000000⟩, + ⟨1, 8, 6, 5, 7, 3, -151474027081879151865905967603793361947852800000⟩, + ⟨1, 8, 7, 5, 8, 3, -7732416960898295751574427169061111804723200000⟩, + ⟨1, 8, 0, 6, 0, 3, 1684388616435610782438564603461337943802432716800000⟩, + ⟨1, 8, 1, 6, 1, 3, 489183682388318187630356905723801675912288665600000⟩, + ⟨1, 8, 2, 6, 2, 3, 14984032342534246821780668153748373380897177600000⟩, + ⟨1, 8, 3, 6, 3, 3, -19410160790843847516364251820915817930607820800000⟩, + ⟨1, 8, 4, 6, 4, 3, 3341009096721508847249145414592706302936350720000⟩, + ⟨1, 8, 5, 6, 5, 3, -1037674090782540169355348226616983687895449600000⟩, + ⟨1, 8, 6, 6, 6, 3, 98633040334871695031560346577224005268275200000⟩, + ⟨1, 8, 7, 6, 7, 3, 25550853426619365968833450604439603983155200000⟩, + ⟨1, 8, 8, 6, 8, 3, -33700710225589957695456118858507258901299200000⟩, + ⟨1, 8, 1, 7, 0, 3, -3064068908868537606899824477995537703577950617600000⟩, + ⟨1, 8, 2, 7, 1, 3, -221004940425640551610404540160861945042934169600000⟩, + ⟨1, 8, 3, 7, 2, 3, -71448313384175184912267181387217410824182169600000⟩, + ⟨1, 8, 4, 7, 3, 3, -12160097321470686988035302669991273396940308480000⟩, + ⟨1, 8, 5, 7, 4, 3, -3137956924309880449049404256112075112395571200000⟩, + ⟨1, 8, 6, 7, 5, 3, -101931339941505699386829654947095281401856000000⟩, + ⟨1, 8, 7, 7, 6, 3, -63989095403315441559060553985686139358412800000⟩, + ⟨1, 8, 8, 7, 7, 3, -25518095578763975834786776472191969630617600000⟩ +] + +def collectedFourData_8_6_7 : List CollectedFourTerm := [ + ⟨2, 4, 2, 0, 8, 0, 4131757430982925135573400757857065402047135744000000⟩, + ⟨2, 4, 2, 1, 7, 0, 1894048618139553169497783786605347771043020800000000⟩, + ⟨2, 4, 3, 1, 8, 0, 71866265993478316714529685744874843061354496000000⟩, + ⟨2, 4, 2, 2, 6, 0, 3989969292203466312308621150648447461887049728000000⟩, + ⟨2, 4, 3, 2, 7, 0, -2582154557089011552514054709932185646968864768000000⟩, + ⟨2, 4, 4, 2, 8, 0, 431824615130478832681801118679560963292659712000000⟩, + ⟨2, 4, 2, 3, 5, 0, -988805818528562510127583147936734975715442688000000⟩, + ⟨2, 4, 3, 3, 6, 0, 2835345432928594563504696888011362140193554432000000⟩, + ⟨2, 4, 4, 3, 7, 0, 2603314985228188115625059095737751107815866368000000⟩, + ⟨2, 4, 5, 3, 8, 0, -717655021342289460987519552792655790384087040000000⟩, + ⟨2, 4, 2, 4, 4, 0, -124914363787954613465379982129564327807549440000000⟩, + ⟨2, 4, 3, 4, 5, 0, 5304132477745471778879492651780964361042919424000000⟩, + ⟨2, 4, 4, 4, 6, 0, -3086838745929749778706098714246025113765937152000000⟩, + ⟨2, 4, 5, 4, 7, 0, -428822108492616778614029997364526860940083200000000⟩, + ⟨2, 4, 6, 4, 8, 0, 406899935968834505822963452678388138272358400000000⟩, + ⟨2, 4, 2, 5, 3, 0, -2082997029705199389621374166468333131211472896000000⟩, + ⟨2, 4, 3, 5, 4, 0, -5429835996505079881253017148771744777037152256000000⟩, + ⟨2, 4, 4, 5, 5, 0, -1601467581369211833203145340551732084093222912000000⟩, + ⟨2, 4, 5, 5, 6, 0, 952509257968729837994321173850441723255193600000000⟩, + ⟨2, 4, 6, 5, 7, 0, -493211245097126533580955967697252171655413760000000⟩, + ⟨2, 4, 7, 5, 8, 0, -40283764237239561505100220651751883044552704000000⟩, + ⟨2, 4, 2, 6, 2, 0, 1393976510242080351092878782124336233119219712000000⟩, + ⟨2, 4, 3, 6, 3, 0, -7222971115899758437462017305020338326716022784000000⟩, + ⟨2, 4, 4, 6, 4, 0, 3108167477798708251282371637928991010968305664000000⟩, + ⟨2, 4, 5, 6, 5, 0, -1930713008048705075350227313975515507893207040000000⟩, + ⟨2, 4, 6, 6, 6, 0, 321156871368984721601496504538238776340643840000000⟩, + ⟨2, 4, 7, 6, 7, 0, 133112914203041677957069236288239266896543744000000⟩, + ⟨2, 4, 8, 6, 8, 0, -263357137662195974160965071112497298078171136000000⟩, + ⟨2, 4, 2, 7, 1, 0, -20560266326059497454879762251650489215459786752000000⟩, + ⟨2, 4, 3, 7, 2, 0, -26587574900311561122578172696355377924966187008000000⟩, + ⟨2, 4, 4, 7, 3, 0, -11312635771794440627005364588040404718506213376000000⟩, + ⟨2, 4, 5, 7, 4, 0, -5838532836348169356147447246339606410302586880000000⟩, + ⟨2, 4, 6, 7, 5, 0, -331896392110794649881252922076405794288435200000000⟩, + ⟨2, 4, 7, 7, 6, 0, -333365575862831913217574678681850466025865216000000⟩, + ⟨2, 4, 8, 7, 7, 0, -199413382247079137800730438101461712144171008000000⟩ +] + +def collectedFourData_8_6_8 : List CollectedFourTerm := [ + ⟨2, 5, 1, 0, 7, 1, 12047883336546860380646291235396535295274280550400000⟩, + ⟨2, 5, 2, 0, 8, 1, -7324609155632932664922911214974487238783323340800000⟩, + ⟨2, 5, 1, 1, 6, 1, 5885474661425467044974808643957286307438683750400000⟩, + ⟨2, 5, 2, 1, 7, 1, -3357691268516340831500679462390839678399938560000000⟩, + ⟨2, 5, 3, 1, 8, 1, -63700776082558744042772240187304207338543513600000⟩, + ⟨2, 5, 1, 2, 5, 1, 3501868721880564445028080599315595264944557260800000⟩, + ⟨2, 5, 2, 2, 6, 1, -7073252991382720939511909825213945860146698649600000⟩, + ⟨2, 5, 3, 2, 7, 1, 2288768547771946266249788562187960399931690188800000⟩, + ⟨2, 5, 4, 2, 8, 1, -255173622237541260187266539692859273293647052800000⟩, + ⟨2, 5, 1, 3, 4, 1, 1909420252298850425358268050061390098901814476800000⟩, + ⟨2, 5, 2, 3, 5, 1, 1752914170911151890490207212710042470765402521600000⟩, + ⟨2, 5, 3, 3, 6, 1, -2513191718574612246847999849292514836601844531200000⟩, + ⟨2, 5, 4, 3, 7, 1, -1538349809922775923187949049544512127221576499200000⟩, + ⟨2, 5, 5, 3, 8, 1, 318057305378838212661256395691312214056108032000000⟩, + ⟨2, 5, 1, 4, 3, 1, -6017593772673534742422329624371799286309558681600000⟩, + ⟨2, 5, 2, 4, 4, 1, 221443031919144706300330506738773182862327808000000⟩, + ⟨2, 5, 3, 4, 5, 1, -4701473641440523993055792563380296360005101158400000⟩, + ⟨2, 5, 4, 4, 6, 1, 1824073469790694069686220985627209385617706188800000⟩, + ⟨2, 5, 5, 4, 7, 1, 190049536696520308548018337961158573094338560000000⟩, + ⟨2, 5, 6, 4, 8, 1, -144267084707088458379708133212881694360600576000000⟩, + ⟨2, 5, 1, 5, 2, 1, -1218788994740564556682529063966734006534275072000000⟩, + ⟨2, 5, 2, 5, 3, 1, 3692651219194469400665406941060867489967321907200000⟩, + ⟨2, 5, 3, 5, 4, 1, 4812894648092270317602029973055669359408159129600000⟩, + ⟨2, 5, 4, 5, 5, 1, 946338558098405251420751244046515089831677132800000⟩, + ⟨2, 5, 5, 5, 6, 1, -422142281358658587900322833669963031385210880000000⟩, + ⟨2, 5, 6, 5, 7, 1, 174868910474258705071770796198335985857488486400000⟩, + ⟨2, 5, 7, 5, 8, 1, 11902232616676522106881744796624780744510668800000⟩, + ⟨2, 5, 1, 6, 1, 1, -26892247504014984314137153949247117151758503116800000⟩, + ⟨2, 5, 2, 6, 2, 1, -2471184061554987593886219655141270056996333158400000⟩, + ⟨2, 5, 3, 6, 3, 1, 6402292638196531584818934058235765116375557734400000⟩, + ⟨2, 5, 4, 6, 4, 1, -1836677035168945881855476047303860477484439961600000⟩, + ⟨2, 5, 5, 6, 5, 1, 855672096672970632479519368494943808658604032000000⟩, + ⟨2, 5, 6, 6, 6, 1, -113866731032372400872761335225740057386785177600000⟩, + ⟨2, 5, 7, 6, 7, 1, -39329513989750051207250681849761857375358156800000⟩, + ⟨2, 5, 8, 6, 8, 1, 66695524463991526956923451322103041028102553600000⟩, + ⟨2, 5, 1, 7, 0, 1, 168443270765602237059334634740384200358743559372800000⟩, + ⟨2, 5, 2, 7, 1, 1, 36448392116349587717107039088266452989804701286400000⟩, + ⟨2, 5, 3, 7, 2, 1, 23566678077537801765084838502476385495089466572800000⟩, + ⟨2, 5, 4, 7, 3, 1, 6684858032167846983080594309871125093138458214400000⟩, + ⟨2, 5, 5, 7, 4, 1, 2587577549198340530815476150979088222785634304000000⟩, + ⟨2, 5, 6, 7, 5, 1, 117674446914369727476865479249595994763952128000000⟩, + ⟨2, 5, 7, 7, 6, 1, 98496123821611413868309823422219051089474355200000⟩, + ⟨2, 5, 8, 7, 7, 1, 50501688437877214307889351146830324365577420800000⟩ +] + +def collectedFourData_8_6_9 : List CollectedFourTerm := [ + ⟨2, 6, 0, 0, 6, 2, 9169357897560970587625583280632569991975141376000000⟩, + ⟨2, 6, 1, 0, 7, 2, -24334929038772394273581490730208762026739420364800000⟩, + ⟨2, 6, 2, 0, 8, 2, 7397309513214372046624166684999933257994521804800000⟩, + ⟨2, 6, 0, 1, 5, 2, 14002353402991807127731258706943907426362143539200000⟩, + ⟨2, 6, 1, 1, 6, 2, -11887781799050180187733756970299954205142338764800000⟩, + ⟨2, 6, 2, 1, 7, 2, 3391018010009637778699641946061888082526863360000000⟩, + ⟨2, 6, 3, 1, 8, 2, 42888691797046642137003222943274286033823334400000⟩, + ⟨2, 6, 0, 2, 4, 2, 3989969292203466312308621150648447461887049728000000⟩, + ⟨2, 6, 1, 2, 5, 2, -7073252991382720939511909825213945860146698649600000⟩, + ⟨2, 6, 2, 2, 6, 2, 7143458515092070890846801046000211474878405017600000⟩, + ⟨2, 6, 3, 2, 7, 2, -1540990469455863297050696520049966737161138995200000⟩, + ⟨2, 6, 4, 2, 8, 2, 128853173131257925587522898293236669830555238400000⟩, + ⟨2, 6, 0, 3, 3, 2, 709658682421635653831704664885892831899339980800000⟩, + ⟨2, 6, 1, 3, 4, 2, -3856744379648457283110574631534952551726815641600000⟩, + ⟨2, 6, 2, 3, 5, 2, -1770312708406740757405928359641823540758026649600000⟩, + ⟨2, 6, 3, 3, 6, 2, 1692090923745412833992840116744719406176455884800000⟩, + ⟨2, 6, 4, 3, 7, 2, 776809345167710543266152938782495475444062617600000⟩, + ⟨2, 6, 5, 3, 8, 2, -128485672386591752680882208753664234751839436800000⟩, + ⟨2, 6, 0, 4, 2, 2, -5259821648820958358475226033436428308677709004800000⟩, + ⟨2, 6, 1, 4, 3, 2, 12154642716198545527302711337198707326665831219200000⟩, + ⟨2, 6, 2, 4, 4, 2, -223640963202899159726735743102589990703464448000000⟩, + ⟨2, 6, 3, 4, 5, 2, 3165425390396306362576080944919070946186860953600000⟩, + ⟨2, 6, 4, 4, 6, 2, -921089149207898923297223950647345680866502246400000⟩, + ⟨2, 6, 5, 4, 7, 2, -76774348824113938544432271340308141749305344000000⟩, + ⟨2, 6, 6, 4, 8, 2, 48566335553287345398387683382253893873303552000000⟩, + ⟨2, 6, 0, 5, 1, 2, -4054214826251630956451995280407791549402631372800000⟩, + ⟨2, 6, 1, 5, 2, 2, 2461772152978800531981396370654272745755377664000000⟩, + ⟨2, 6, 2, 5, 3, 2, -3729302603364575083434069592387927232314815283200000⟩, + ⟨2, 6, 3, 5, 4, 2, -3240443333785411147614682673669252937226282598400000⟩, + ⟨2, 6, 4, 5, 5, 2, -477865717460114173553342310178043300359333478400000⟩, + ⟨2, 6, 5, 5, 6, 2, 170532900662579238131766462606394492308160512000000⟩, + ⟨2, 6, 6, 5, 7, 2, -58868190212436778380281012573291128891952332800000⟩, + ⟨2, 6, 7, 5, 8, 2, -3434390898371951297749973914775175257967820800000⟩, + ⟨2, 6, 0, 6, 0, 2, 93516182631849173611800840837402070397865059942400000⟩, + ⟨2, 6, 1, 6, 1, 2, 54318332641730034202957333476735199553888295321600000⟩, + ⟨2, 6, 2, 6, 2, 2, 2495711781888903064169247939759034815218083430400000⟩, + ⟨2, 6, 3, 6, 3, 2, -4310559033036541811928901003653635173921692057600000⟩, + ⟨2, 6, 4, 6, 4, 2, 927453480197577855839974694383996250866109644800000⟩, + ⟨2, 6, 5, 6, 5, 2, -345666025663268045936981753844427012730309836800000⟩, + ⟨2, 6, 6, 6, 6, 2, 38332304828243321813385679329176620635468595200000⟩, + ⟨2, 6, 7, 6, 7, 2, 11348536802627750701141244915924957259418828800000⟩, + ⟨2, 6, 8, 6, 8, 2, -16839377607844306738642611225173921764894310400000⟩, + ⟨2, 6, 1, 7, 0, 2, -340230306572217999187983034108546663141000976793600000⟩, + ⟨2, 6, 2, 7, 1, 2, -36810160380542812944348718649790643896339293798400000⟩, + ⟨2, 6, 3, 7, 2, 2, -15867059318677216110288094876627970474839847731200000⟩, + ⟨2, 6, 4, 7, 3, 2, -3375604272196122441632569218620517698810098483200000⟩, + ⟨2, 6, 5, 7, 4, 2, -1045304212915961180707945706149042426771773849600000⟩, + ⟨2, 6, 6, 7, 5, 2, -39614141274804422947495407011289928833171456000000⟩, + ⟨2, 6, 7, 7, 6, 2, -28421070405219132387577885498251863102010163200000⟩, + ⟨2, 6, 8, 7, 7, 2, -12750735649410086129601088281105821892555571200000⟩ +] + +def collectedFourData_8_6_10 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 6, 3, -5934055514420184108435881560919498683167277056000000⟩, + ⟨2, 7, 1, 0, 7, 3, 7874314726768521432340326551441358544683034214400000⟩, + ⟨2, 7, 2, 0, 8, 3, -1595751334650484287821892561101321584110049689600000⟩, + ⟨2, 7, 0, 1, 5, 3, -9061784189707080986670120533336091311582950195200000⟩, + ⟨2, 7, 1, 1, 6, 3, 3846657417398978387731920637745734574076749414400000⟩, + ⟨2, 7, 2, 1, 7, 3, -731512113374495896204717972169779481117982720000000⟩, + ⟨2, 7, 3, 1, 8, 3, -6938977650011617082089800711095910884022681600000⟩, + ⟨2, 7, 0, 2, 4, 3, -2582154557089011552514054709932185646968864768000000⟩, + ⟨2, 7, 1, 2, 5, 3, 2288768547771946266249788562187960399931690188800000⟩, + ⟨2, 7, 2, 2, 6, 3, -1540990469455863297050696520049966737161138995200000⟩, + ⟨2, 7, 3, 2, 7, 3, 249317430268914578680159531195974046368713932800000⟩, + ⟨2, 7, 4, 2, 8, 3, -16677762851278115458760695513436395178903470080000⟩, + ⟨2, 7, 0, 3, 3, 3, -459263785406438013062054695659254502407326924800000⟩, + ⟨2, 7, 1, 3, 4, 3, 1247968260670119693333803585559126194577525964800000⟩, + ⟨2, 7, 2, 3, 5, 3, 381892749268135571295939785896078928059249459200000⟩, + ⟨2, 7, 3, 3, 6, 3, -273764029857060229905358602624466853976814387200000⟩, + ⟨2, 7, 4, 3, 7, 3, -100544221958480571887232907069437065259248517120000⟩, + ⟨2, 7, 5, 3, 8, 3, 13858496986512866183172629440072408122576076800000⟩, + ⟨2, 7, 0, 4, 2, 3, 3403954127295545662010096891252107438780632268800000⟩, + ⟨2, 7, 1, 4, 3, 3, -3933008474620155824409801848209960557837130137600000⟩, + ⟨2, 7, 2, 4, 4, 3, 48243941243236178085378025434620768022429696000000⟩, + ⟨2, 7, 3, 4, 5, 3, -512135369870427862306660197337749769599477350400000⟩, + ⟨2, 7, 4, 4, 6, 3, 119218689164344164338469839462930002428485959680000⟩, + ⟨2, 7, 5, 4, 7, 3, 8280900602046450371246696670787998050156544000000⟩, + ⟨2, 7, 6, 4, 8, 3, -4490037587689212308272744885222974387388416000000⟩, + ⟨2, 7, 0, 5, 1, 3, 2623731793996384227356007741473334887780764876800000⟩, + ⟨2, 7, 1, 5, 2, 3, -796582093470016841084932029492511289578094592000000⟩, + ⟨2, 7, 2, 5, 3, 3, 804487036266869099074275061738077398925469286400000⟩, + ⟨2, 7, 3, 5, 4, 3, 524272551274563865509070637010722314736212377600000⟩, + ⟨2, 7, 4, 5, 5, 3, 61851259979738240526129011848129263406499758080000⟩, + ⟨2, 7, 5, 5, 6, 3, -18393721619191836840887824014690597168218112000000⟩, + ⟨2, 7, 6, 5, 7, 3, 5442460991998563127146461087839470309762662400000⟩, + ⟨2, 7, 7, 5, 8, 3, 277825700513058391737610344764305284110745600000⟩, + ⟨2, 7, 0, 6, 0, 3, -60520074080831753249937809854251724722976220774400000⟩, + ⟨2, 7, 1, 6, 1, 3, -17576367121219390339041408426007049295201357004800000⟩, + ⟨2, 7, 2, 6, 2, 3, -538376202825885811632651899790818761077738700800000⟩, + ⟨2, 7, 3, 6, 3, 3, 697406974566567305660972149330112463950472806400000⟩, + ⟨2, 7, 4, 6, 4, 3, -120042439176652993292129905315810234104293621760000⟩, + ⟨2, 7, 5, 6, 5, 3, 37283624594193954191224195001661635078966476800000⟩, + ⟨2, 7, 6, 6, 6, 3, -3543884617622200191419826582573153299044761600000⟩, + ⟨2, 7, 7, 6, 7, 3, -918042028495619369246700554417486253627801600000⟩, + ⟨2, 7, 8, 6, 8, 3, 1210866340183031724320776122020951787936153600000⟩, + ⟨2, 7, 1, 7, 0, 3, 110091979691662770540911989789408041353725398220800000⟩, + ⟨2, 7, 2, 7, 1, 3, 7940706340733495666277582716501677563368492236800000⟩, + ⟨2, 7, 3, 7, 2, 3, 2567137522047045390884819191276449379832876236800000⟩, + ⟨2, 7, 4, 7, 3, 3, 436912232453134836489058655127322053452853411840000⟩, + ⟨2, 7, 5, 7, 4, 3, 112746775695721759938642635278934181789931929600000⟩, + ⟨2, 7, 6, 7, 5, 3, 3662392505045873482785303230644664452251648000000⟩, + ⟨2, 7, 7, 7, 6, 3, 2299127859441990109630802751320918917015142400000⟩, + ⟨2, 7, 8, 7, 7, 3, 916865039195411395592101167296072762838220800000⟩ +] + +def collectedFourData_8_6_11 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 6, 4, 992377172637640278412276628311402172701999104000000⟩, + ⟨2, 8, 1, 0, 7, 4, -877903278347631214163898714283681925946566246400000⟩, + ⟨2, 8, 2, 0, 8, 4, 133432118545652050310999944006803395332748083200000⟩, + ⟨2, 8, 0, 1, 5, 4, 1515440452382195077690264415553272165398531276800000⟩, + ⟨2, 8, 1, 1, 6, 4, -428861846978861285104248635466155897196537446400000⟩, + ⟨2, 8, 2, 1, 7, 4, 61166930529777687692734458190084335458058240000000⟩, + ⟨2, 8, 3, 1, 8, 4, 464173818703288242429027034547793036060917760000⟩, + ⟨2, 8, 0, 2, 4, 4, 431824615130478832681801118679560963292659712000000⟩, + ⟨2, 8, 1, 2, 5, 4, -255173622237541260187266539692859273293647052800000⟩, + ⟨2, 8, 2, 2, 6, 4, 128853173131257925587522898293236669830555238400000⟩, + ⟨2, 8, 3, 2, 7, 4, -16677762851278115458760695513436395178903470080000⟩, + ⟨2, 8, 4, 2, 8, 4, 929697579452097325886599586433357041620746240000⟩, + ⟨2, 8, 0, 3, 3, 4, 76804623035454270597366672687136041717674803200000⟩, + ⟨2, 8, 1, 3, 4, 4, -139135336258740337935299257135807885107580108800000⟩, + ⟨2, 8, 2, 3, 5, 4, -31932768900507825857654671383463646091175526400000⟩, + ⟨2, 8, 3, 3, 6, 4, 18313086101688181679764705887722543060531281920000⟩, + ⟨2, 8, 4, 3, 7, 4, 5604811665464484263835257182455257097421455360000⟩, + ⟨2, 8, 5, 3, 8, 4, -662175713584192665743914028272142802694963200000⟩, + ⟨2, 8, 0, 4, 2, 4, -569257629023688783167011530737062234459157299200000⟩, + ⟨2, 8, 1, 4, 3, 4, 438489081710227651031245662684494355911776665600000⟩, + ⟨2, 8, 2, 4, 4, 4, -4034019052527952240564328542668549292818432000000⟩, + ⟨2, 8, 3, 4, 5, 4, 34258624586487818569104161156875870985980477440000⟩, + ⟨2, 8, 4, 4, 6, 4, -6645815013075847542158996124864673813144535040000⟩, + ⟨2, 8, 5, 4, 7, 4, -395671426029558068347877595678948936646656000000⟩, + ⟨2, 8, 6, 4, 8, 4, 187721988591099661780447040794476555534336000000⟩, + ⟨2, 8, 0, 5, 1, 4, -438777752105345064825774024172926568792011571200000⟩, + ⟨2, 8, 1, 5, 2, 4, 88810525816680976199316814023908520835940352000000⟩, + ⟨2, 8, 2, 5, 3, 4, -67268882852047051180018695845275430445436108800000⟩, + ⟨2, 8, 3, 5, 4, 4, -35070525434827186639655047493359893847851663360000⟩, + ⟨2, 8, 4, 5, 5, 4, -3447882500908581308074937476003151638419210240000⟩, + ⟨2, 8, 5, 5, 6, 4, 878874220668434717839658293229283849535488000000⟩, + ⟨2, 8, 6, 5, 7, 4, -227541435966744136898184655372374895912550400000⟩, + ⟨2, 8, 7, 5, 8, 4, -10324881243760624863317592228459845989171200000⟩, + ⟨2, 8, 0, 6, 0, 4, 10121027661134829181201931171801104994365184409600000⟩, + ⟨2, 8, 1, 6, 1, 4, 1959580084436421939057411838304143845767302348800000⟩, + ⟨2, 8, 2, 6, 2, 4, 45017463409081790783378069709039551458679193600000⟩, + ⟨2, 8, 3, 6, 3, 4, -46652125846568853734190861794001423004902359040000⟩, + ⟨2, 8, 4, 6, 4, 4, 6691734744597780229766819886950311349484257280000⟩, + ⟨2, 8, 5, 6, 5, 4, -1781456585421368614041414348929357707424563200000⟩, + ⟨2, 8, 6, 6, 6, 4, 148164699017547738296539395455044952889753600000⟩, + ⟨2, 8, 7, 6, 7, 4, 34117343728439046574794381294500989580083200000⟩, + ⟨2, 8, 8, 6, 8, 4, -40499658696918539489567949259107396464148480000⟩, + ⟨2, 8, 1, 7, 0, 4, -12274097904993831560462981763436732439472164044800000⟩, + ⟨2, 8, 2, 7, 1, 4, -663978933801132471528085513818812177591146905600000⟩, + ⟨2, 8, 3, 7, 2, 4, -171725301167828220882051796852571117200059924480000⟩, + ⟨2, 8, 4, 7, 3, 4, -24355559469630084308264743468905354000617963520000⟩, + ⟨2, 8, 5, 7, 4, 4, -5387177031050989468585506000124136149902950400000⟩, + ⟨2, 8, 6, 7, 5, 4, -153119342682869758527287535971843501457408000000⟩, + ⟨2, 8, 7, 7, 6, 4, -85442858846834336052913192104270595149004800000⟩, + ⟨2, 8, 8, 7, 7, 4, -30666242777000560955373842853349257841213440000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0827.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0827.lean new file mode 100644 index 0000000000000000000000000000000000000000..e6bccf4d649e8ab9eeda84a5754d2d5e9ac18f77 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0827.lean @@ -0,0 +1,654 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0827. -/ +namespace LaughlinFock +def collectedFourData_8_6_12 : List CollectedFourTerm := [ + ⟨3, 3, 2, 0, 8, 0, 734877218300060567106502435540252824676230758400000⟩, + ⟨3, 3, 2, 1, 7, 0, 336876789858484941868107697044843433694330880000000⟩, + ⟨3, 3, 3, 1, 8, 0, 12782183495785631010484357747030722227050905600000⟩, + ⟨3, 3, 2, 2, 6, 0, 709658682421635653831704664885892831899339980800000⟩, + ⟨3, 3, 3, 2, 7, 0, -459263785406438013062054695659254502407326924800000⟩, + ⟨3, 3, 4, 2, 8, 0, 76804623035454270597366672687136041717674803200000⟩, + ⟨3, 3, 2, 3, 5, 0, -175869682936908949590376290317214250462661836800000⟩, + ⟨3, 3, 3, 3, 6, 0, 504296488715858817850644304268146898218726195200000⟩, + ⟨3, 3, 4, 3, 7, 0, 463027393708403855809270155304563064202644684800000⟩, + ⟨3, 3, 5, 3, 8, 0, -127642615664789678184173436419940728275206144000000⟩, + ⟨3, 3, 2, 4, 4, 0, -22217354653459389254811964420707441426038784000000⟩, + ⟨3, 3, 3, 4, 5, 0, 943396650420814256689416995560623675514709606400000⟩, + ⟨3, 3, 4, 4, 6, 0, -549027262331334206427781320695438003821294387200000⟩, + ⟨3, 3, 5, 4, 7, 0, -76270595139863453165493967409585784902123520000000⟩, + ⟨3, 3, 6, 4, 8, 0, 72371502457760230377088596987326150989578240000000⟩, + ⟨3, 3, 2, 5, 3, 0, -370483284289244498353106688985687865819765145600000⟩, + ⟨3, 3, 3, 5, 4, 0, -965754364720275036701833384210800018007366041600000⟩, + ⟨3, 3, 4, 5, 5, 0, -284838125435247959473123663570973989151126323200000⟩, + ⟨3, 3, 5, 5, 6, 0, 169413951712696200319756153043937569758248960000000⟩, + ⟨3, 3, 6, 5, 7, 0, -87722891260114633088314090046621159560052736000000⟩, + ⟨3, 3, 7, 5, 8, 0, -7164898012484607972333860940340118719719014400000⟩, + ⟨3, 3, 2, 6, 2, 0, 247933620822126944001208363860013270552490803200000⟩, + ⟨3, 3, 3, 6, 3, 0, -1284682610288511546946805374727029804312716902400000⟩, + ⟨3, 3, 4, 6, 4, 0, 552820805250430327125405837567698312301536870400000⟩, + ⟨3, 3, 5, 6, 5, 0, -343397943463743069799749692676619636146438144000000⟩, + ⟨3, 3, 6, 6, 6, 0, 57121182018046013671460642155384417365786624000000⟩, + ⟨3, 3, 7, 6, 7, 0, 23675554468858205544275857094109598872659558400000⟩, + ⟨3, 3, 8, 6, 8, 0, -46840881629060110001436392439195383407155609600000⟩, + ⟨3, 3, 2, 7, 1, 0, -3656863109122208778473944307977509323624624947200000⟩, + ⟨3, 3, 3, 7, 2, 0, -4728884357433667366922331619831109947048643788800000⟩, + ⟨3, 3, 4, 7, 3, 0, -2012073178661976775116223799479239666149464473600000⟩, + ⟨3, 3, 5, 7, 4, 0, -1038445465736934924465784781440744201931194368000000⟩, + ⟨3, 3, 6, 7, 5, 0, -59031320563313798153831655662954119660830720000000⟩, + ⟨3, 3, 7, 7, 6, 0, -59292630595885565520038629950509419570239897600000⟩, + ⟨3, 3, 8, 7, 7, 0, -35467801313466266233348181474169928788266188800000⟩ +] + +def collectedFourData_8_6_13 : List CollectedFourTerm := [ + ⟨3, 4, 1, 0, 7, 1, 6569198981217839594290478506552328479601747558400000⟩, + ⟨3, 4, 2, 0, 8, 1, -3993798218234894065495140125585281161727102156800000⟩, + ⟨3, 4, 1, 1, 6, 1, 3209099313946465845773931291883879269902214758400000⟩, + ⟨3, 4, 2, 1, 7, 1, -1830806411734694953608100920961769844517109760000000⟩, + ⟨3, 4, 3, 1, 8, 1, -34733327145934138214840257899549233004517785600000⟩, + ⟨3, 4, 1, 2, 5, 1, 1909420252298850425358268050061390098901814476800000⟩, + ⟨3, 4, 2, 2, 6, 1, -3856744379648457283110574631534952551726815641600000⟩, + ⟨3, 4, 3, 2, 7, 1, 1247968260670119693333803585559126194577525964800000⟩, + ⟨3, 4, 4, 2, 8, 1, -139135336258740337935299257135807885107580108800000⟩, + ⟨3, 4, 1, 3, 4, 1, 1041125750119810757670718244849003713006456012800000⟩, + ⟨3, 4, 2, 3, 5, 1, 955789632422879021656327751462240292525676953600000⟩, + ⟨3, 4, 3, 3, 6, 1, -1370336682061317012843197525415519812127503155200000⟩, + ⟨3, 4, 4, 3, 7, 1, -838796801214530954167512327372687824433394483200000⟩, + ⟨3, 4, 5, 3, 8, 1, 173423137334463066471333337864312283486748672000000⟩, + ⟨3, 4, 1, 4, 3, 1, -3281138252801178664048861310408771058735356313600000⟩, + ⟨3, 4, 2, 4, 4, 1, 120743478256320751176602085131520078898003968000000⟩, + ⟨3, 4, 3, 4, 5, 1, -2563513854909702998091762428715404300330100326400000⟩, + ⟨3, 4, 4, 4, 6, 1, 994589775206934776665247956203701528223861964800000⟩, + ⟨3, 4, 5, 4, 7, 1, 103625938928251480432610499898616649099509760000000⟩, + ⟨3, 4, 6, 4, 8, 1, -78662712727819839377127946822571134965252096000000⟩, + ⟨3, 4, 1, 5, 2, 1, -664553863854397914657578632028634969393856512000000⟩, + ⟨3, 4, 2, 5, 3, 1, 2013445843515100909401524687137868610547168051200000⟩, + ⟨3, 4, 3, 5, 4, 1, 2624266996597469968495239856244715718444685721600000⟩, + ⟨3, 4, 4, 5, 5, 1, 515998214631535182293338309625062309577411788800000⟩, + ⟨3, 4, 5, 5, 6, 1, -230176253136354267985903339039968631172628480000000⟩, + ⟨3, 4, 6, 5, 7, 1, 95348588332481801124406177510131452592154214400000⟩, + ⟨3, 4, 7, 5, 8, 1, 6489781831013253562692031052745384273956044800000⟩, + ⟨3, 4, 1, 6, 1, 1, -14663200163147272148210570626669551959086517452800000⟩, + ⟨3, 4, 2, 6, 2, 1, -1347431691202087724388102566547642293625972326400000⟩, + ⟨3, 4, 3, 6, 3, 1, 3490898201903878053627087183319637789342328422400000⟩, + ⟨3, 4, 4, 6, 4, 1, -1001461963999746814885434061669648604147063193600000⟩, + ⟨3, 4, 5, 6, 5, 1, 466561644788611800419599215343120471579164672000000⟩, + ⟨3, 4, 6, 6, 6, 1, -62086691296502921638323204281266451418552729600000⟩, + ⟨3, 4, 7, 6, 7, 1, -21444713234358923922131990374150693226073292800000⟩, + ⟨3, 4, 8, 6, 8, 1, 36366236219400538050385039366596883230857625600000⟩, + ⟨3, 4, 1, 7, 0, 1, 91844959964855402509121484789085035783120538828800000⟩, + ⟨3, 4, 2, 7, 1, 1, 19873759868791933007761240116143962418875623014400000⟩, + ⟨3, 4, 3, 7, 2, 1, 12849908427319038916822957189201796239792590028800000⟩, + ⟨3, 4, 4, 7, 3, 1, 3644969107668127505361701153227290465190438502400000⟩, + ⟨3, 4, 5, 7, 4, 1, 1410896115540235144806836759090658528548880384000000⟩, + ⟨3, 4, 6, 7, 5, 1, 64162877012620022138797759354856816076914688000000⟩, + ⟨3, 4, 7, 7, 6, 1, 53705752138224915938624065627015240031089459200000⟩, + ⟨3, 4, 8, 7, 7, 1, 27536425359425074474434907846822715485637836800000⟩ +] + +def collectedFourData_8_6_14 : List CollectedFourTerm := [ + ⟨3, 5, 0, 0, 6, 2, -2272376997736744081553104174011758252912541696000000⟩, + ⟨3, 5, 1, 0, 7, 2, 6030753037131586808991469213129845239437905100800000⟩, + ⟨3, 5, 2, 0, 8, 2, -1833222802595459264033255249773585760235867340800000⟩, + ⟨3, 5, 0, 1, 5, 2, -3470104029378446476131043242432753046276748083200000⟩, + ⟨3, 5, 1, 1, 6, 2, 2946064731693011712621061974428749578518711500800000⟩, + ⟨3, 5, 2, 1, 7, 2, -840371966166422735963731090344408343180738560000000⟩, + ⟨3, 5, 3, 1, 8, 2, -10628800597755414176976837676701684347594342400000⟩, + ⟨3, 5, 0, 2, 4, 2, -988805818528562510127583147936734975715442688000000⟩, + ⟨3, 5, 1, 2, 5, 2, 1752914170911151890490207212710042470765402521600000⟩, + ⟨3, 5, 2, 2, 6, 2, -1770312708406740757405928359641823540758026649600000⟩, + ⟨3, 5, 3, 2, 7, 2, 381892749268135571295939785896078928059249459200000⟩, + ⟨3, 5, 4, 2, 8, 2, -31932768900507825857654671383463646091175526400000⟩, + ⟨3, 5, 0, 3, 3, 2, -175869682936908949590376290317214250462661836800000⟩, + ⟨3, 5, 1, 3, 4, 2, 955789632422879021656327751462240292525676953600000⟩, + ⟨3, 5, 2, 3, 5, 2, 438724054871342136294611480417412975481690521600000⟩, + ⟨3, 5, 3, 3, 6, 2, -419338904223705250168885106193690665849507020800000⟩, + ⟨3, 5, 4, 3, 7, 2, -192511155885363423826485174007612294750116249600000⟩, + ⟨3, 5, 5, 3, 8, 2, 31841693794904992902800274384811330059947212800000⟩, + ⟨3, 5, 0, 4, 2, 2, 1303504330456747229402959867242727657890958540800000⟩, + ⟨3, 5, 1, 4, 3, 2, -3012198981931425878632871719661196042749293363200000⟩, + ⟨3, 5, 2, 4, 4, 2, 55423355289593052528795858236983595979767808000000⟩, + ⟨3, 5, 3, 4, 5, 2, -784464945697206648416157646942904670314142105600000⟩, + ⟨3, 5, 4, 4, 6, 2, 228266997417745814441342702429922342327445094400000⟩, + ⟨3, 5, 5, 4, 7, 2, 19026442879990496800638313965653531950055424000000⟩, + ⟨3, 5, 6, 4, 8, 2, -12035850820591285443277269342652532042760192000000⟩, + ⟨3, 5, 0, 5, 1, 2, 1004727334016271326571578042645192338265918668800000⟩, + ⟨3, 5, 1, 5, 2, 2, -610083549643743226878747915559080700510470144000000⟩, + ⟨3, 5, 2, 5, 3, 2, 924206640002522316606515688985211786931417907200000⟩, + ⟨3, 5, 3, 5, 4, 2, 803056111063351136994240098405057358417258086400000⟩, + ⟨3, 5, 4, 5, 5, 2, 118426074812956546472354616014324811627390566400000⟩, + ⟨3, 5, 5, 5, 6, 2, -42261960450474769804433347852585219865444352000000⟩, + ⟨3, 5, 6, 5, 7, 2, 14588886466381183836677096194468866811546828800000⟩, + ⟨3, 5, 7, 5, 8, 2, 851120761768145468349724678410301516598476800000⟩, + ⟨3, 5, 0, 6, 0, 2, -23175452927329632002610069161673304953407825510400000⟩, + ⟨3, 5, 1, 6, 1, 2, -13461327502911938447691931228387603656069454233600000⟩, + ⟨3, 5, 2, 6, 2, 2, -618494567395330032697383941897085572222445158400000⟩, + ⟨3, 5, 3, 6, 3, 2, 1068255302442070194709273584706370014459566489600000⟩, + ⟨3, 5, 4, 6, 4, 2, -229844224472082567627830545401137498549963980800000⟩, + ⟨3, 5, 5, 6, 5, 2, 85663961903507583306014189264664365212945612800000⟩, + ⟨3, 5, 6, 6, 6, 2, -9499623499820322232666766304044267255051059200000⟩, + ⟨3, 5, 7, 6, 7, 2, -2812427465081256178063501796336046319652044800000⟩, + ⟨3, 5, 8, 6, 8, 2, 4173183636167928270285307186308582849537638400000⟩, + ⟨3, 5, 1, 7, 0, 2, 84316866156274702928828655644129864652659726745600000⟩, + ⟨3, 5, 2, 7, 1, 2, 9122401226589238840042328075790094761885853286400000⟩, + ⟨3, 5, 3, 7, 2, 2, 3932220883981130542814438139448383164514513715200000⟩, + ⟨3, 5, 4, 7, 3, 2, 836552088739030126371764796138194207629325107200000⟩, + ⟨3, 5, 5, 7, 4, 2, 259050336523495670677262234289591223846541721600000⟩, + ⟨3, 5, 6, 7, 5, 2, 9817291943845269068477872748487610912997376000000⟩, + ⟨3, 5, 7, 7, 6, 2, 7043392499387064176345582598418988161774387200000⟩, + ⟨3, 5, 8, 7, 7, 2, 3159924469918282292030247756334214168130355200000⟩ +] + +def collectedFourData_8_6_15 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 6, 3, 6515914066942515402470386808155049321608249344000000⟩, + ⟨3, 6, 1, 0, 7, 3, -8646423676185805331741373709218766072185461145600000⟩, + ⟨3, 6, 2, 0, 8, 3, 1752221317027457863494785598317695727430952550400000⟩, + ⟨3, 6, 0, 1, 5, 3, 9950329404540296369060300239088858151019924684800000⟩, + ⟨3, 6, 1, 1, 6, 3, -4223838000138395852275838937578061118754625945600000⟩, + ⟨3, 6, 2, 1, 7, 3, 803239885116150151119239190885745619663585280000000⟩, + ⟨3, 6, 3, 1, 8, 3, 7619372951607488903349828551951485321504358400000⟩, + ⟨3, 6, 0, 2, 4, 3, 2835345432928594563504696888011362140193554432000000⟩, + ⟨3, 6, 1, 2, 5, 3, -2513191718574612246847999849292514836601844531200000⟩, + ⟨3, 6, 2, 2, 6, 3, 1692090923745412833992840116744719406176455884800000⟩, + ⟨3, 6, 3, 2, 7, 3, -273764029857060229905358602624466853976814387200000⟩, + ⟨3, 6, 4, 2, 8, 3, 18313086101688181679764705887722543060531281920000⟩, + ⟨3, 6, 0, 3, 3, 3, 504296488715858817850644304268146898218726195200000⟩, + ⟨3, 6, 1, 3, 4, 3, -1370336682061317012843197525415519812127503155200000⟩, + ⟨3, 6, 2, 3, 5, 3, -419338904223705250168885106193690665849507020800000⟩, + ⟨3, 6, 3, 3, 6, 3, 300607719094246907949570964219775690507865292800000⟩, + ⟨3, 6, 4, 3, 7, 3, 110402996503322654881151471636754361079436410880000⟩, + ⟨3, 6, 5, 3, 8, 3, -15217379622024470131806957201922845995905843200000⟩, + ⟨3, 6, 0, 4, 2, 3, -3737725831410472159675618815125830139024454451200000⟩, + ⟨3, 6, 1, 4, 3, 3, 4318656133719305769806405367593627660029683302400000⟩, + ⟨3, 6, 2, 4, 4, 3, -52974458130303863615804117055821448115912704000000⟩, + ⟨3, 6, 3, 4, 5, 3, 562352349520206638748518765116520340221696409600000⟩, + ⟨3, 6, 4, 4, 6, 3, -130908572034870868120882295023079313520271032320000⟩, + ⟨3, 6, 5, 4, 7, 3, -9092876968998057189526444607169103770157056000000⟩, + ⟨3, 6, 6, 4, 8, 3, 4930304242626123333482732106735219306921984000000⟩, + ⟨3, 6, 0, 5, 1, 3, -2880999488939869018943252110480321399072437043200000⟩, + ⟨3, 6, 1, 5, 2, 3, 874690244420970787028636918516362234149470208000000⟩, + ⟨3, 6, 2, 5, 3, 3, -883370299375498520748463227632939771367102873600000⟩, + ⟨3, 6, 3, 5, 4, 3, -575679631486487714926652266813751649351657062400000⟩, + ⟨3, 6, 4, 5, 5, 3, -67916030441699336777682386546998243575642193920000⟩, + ⟨3, 6, 5, 5, 6, 3, 20197301685275431340921028027640221624434688000000⟩, + ⟨3, 6, 6, 5, 7, 3, -5976116679456848941335856458711519175743897600000⟩, + ⟨3, 6, 7, 5, 8, 3, -305067653265471458384832533717071602017894400000⟩, + ⟨3, 6, 0, 6, 0, 3, 66454316289662486012033597790043656816757938585600000⟩, + ⟨3, 6, 1, 6, 1, 3, 19299802216644695704802954364625408628123448115200000⟩, + ⟨3, 6, 2, 6, 2, 3, 591166204086827410157641697861660315934208819200000⟩, + ⟨3, 6, 3, 6, 3, 3, -765790597158937184876410898298589665279187353600000⟩, + ⟨3, 6, 4, 6, 4, 3, 131813094124326181393472212652242678541702922240000⟩, + ⟨3, 6, 5, 6, 5, 3, -40939437349306573660110167249403951189275443200000⟩, + ⟨3, 6, 6, 6, 6, 3, 3891377081908202169892561781776121330034278400000⟩, + ⟨3, 6, 7, 6, 7, 3, 1008059825693008692051824296730084464027238400000⟩, + ⟨3, 6, 8, 6, 8, 3, -1329596765654245642337914421869655418627686400000⟩, + ⟨3, 6, 1, 7, 0, 3, -120886951156294895466117528082683279826390037299200000⟩, + ⟨3, 6, 2, 7, 1, 3, -8719325260997430111155016870530822051193893683200000⟩, + ⟨3, 6, 3, 7, 2, 3, -2818855915829212171942946220891791316739109683200000⟩, + ⟨3, 6, 4, 7, 3, 3, -479753274053892643404909489836746494665985884160000⟩, + ⟨3, 6, 5, 7, 4, 3, -123802060828874521669441707098356375492126310400000⟩, + ⟨3, 6, 6, 7, 5, 3, -4021505155167894809391310045361084722839552000000⟩, + ⟨3, 6, 7, 7, 6, 3, -2524566803366227293890768646708666037803417600000⟩, + ⟨3, 6, 8, 7, 7, 3, -1006767427750449956877829087701947288597299200000⟩ +] + +def collectedFourData_8_6_16 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 6, 4, 5982684344534958756960047229359634890417504256000000⟩, + ⟨3, 7, 1, 0, 7, 4, -5292562489548619404991626951302366776797010329600000⟩, + ⟨3, 7, 2, 0, 8, 4, 804414156927300201904429638410906255171046604800000⟩, + ⟨3, 7, 0, 1, 5, 4, 9136044358461345448994828142287687479035376435200000⟩, + ⟨3, 7, 1, 1, 6, 4, -2585453523753760032279300683748375758959647129600000⟩, + ⟨3, 7, 2, 1, 7, 4, 368753381046764318886396379742354707694223360000000⟩, + ⟨3, 7, 3, 1, 8, 4, 2798336675679636271797148967259300065590640640000⟩, + ⟨3, 7, 0, 2, 4, 4, 2603314985228188115625059095737751107815866368000000⟩, + ⟨3, 7, 1, 2, 5, 4, -1538349809922775923187949049544512127221576499200000⟩, + ⟨3, 7, 2, 2, 6, 4, 776809345167710543266152938782495475444062617600000⟩, + ⟨3, 7, 3, 2, 7, 4, -100544221958480571887232907069437065259248517120000⟩, + ⟨3, 7, 4, 2, 8, 4, 5604811665464484263835257182455257097421455360000⟩, + ⟨3, 7, 0, 3, 3, 4, 463027393708403855809270155304563064202644684800000⟩, + ⟨3, 7, 1, 3, 4, 4, -838796801214530954167512327372687824433394483200000⟩, + ⟨3, 7, 2, 3, 5, 4, -192511155885363423826485174007612294750116249600000⟩, + ⟨3, 7, 3, 3, 6, 4, 110402996503322654881151471636754361079436410880000⟩, + ⟨3, 7, 4, 3, 7, 4, 33789389689322481438491931337230999322928087040000⟩, + ⟨3, 7, 5, 3, 8, 4, -3992018744709639834450151718714342128798924800000⟩, + ⟨3, 7, 0, 4, 2, 4, -3431849098377715430999192599462976658728602828800000⟩, + ⟨3, 7, 1, 4, 3, 4, 2643492652521124191738670483437033369431860838400000⟩, + ⟨3, 7, 2, 4, 4, 4, -24319647102490524399705817011444169675112448000000⟩, + ⟨3, 7, 3, 4, 5, 4, 206532901632674194994165652376886759087312732160000⟩, + ⟨3, 7, 4, 4, 6, 4, -40065223719048894956364932260778456967083458560000⟩, + ⟨3, 7, 5, 4, 7, 4, -2385360436894307296583193650514032678928384000000⟩, + ⟨3, 7, 6, 4, 8, 4, 1131708218644230706196221954052624329211904000000⟩, + ⟨3, 7, 0, 5, 1, 4, -2645232942303293821739809763362492419383545036800000⟩, + ⟨3, 7, 1, 5, 2, 4, 535406654932584654749746867511852841805283328000000⟩, + ⟨3, 7, 2, 5, 3, 4, -405539852598211010521602173947462712078578483200000⟩, + ⟨3, 7, 3, 5, 4, 4, -211427559257420079790238906575467212262384599040000⟩, + ⟨3, 7, 4, 5, 5, 4, -20786041062548537839289252416784351194628751360000⟩, + ⟨3, 7, 5, 5, 6, 4, 5298415950896060756972940188748875858706432000000⟩, + ⟨3, 7, 6, 5, 7, 4, -1371765316883519684229821563224188639615385600000⟩, + ⟨3, 7, 7, 5, 8, 4, -62244988175261464095333908640705677151436800000⟩, + ⟨3, 7, 0, 6, 0, 4, 61016028389627582910861807202387583143850174054400000⟩, + ⟨3, 7, 1, 6, 1, 4, 11813602142681538390928795699773127344419713843200000⟩, + ⟨3, 7, 2, 6, 2, 4, 271394063662658694338365393608655260248073830400000⟩, + ⟨3, 7, 3, 6, 3, 4, -281248854404529362531886026488753004418233794560000⟩, + ⟨3, 7, 4, 6, 4, 4, 40342057232007811495197921568913554002589777920000⟩, + ⟨3, 7, 5, 6, 5, 4, -10739759758622322529830372966815816131333324800000⟩, + ⟨3, 7, 6, 6, 6, 4, 893231575318276877915244739739139430573670400000⟩, + ⟨3, 7, 7, 6, 7, 4, 205681170253782948393202817791519301094604800000⟩, + ⟨3, 7, 8, 6, 8, 4, -244157847163153765773784019316774085035294720000⟩, + ⟨3, 7, 1, 7, 0, 4, -73996112974183801129528155503593493983969620787200000⟩, + ⟨3, 7, 2, 7, 1, 4, -4002889709559587978005001373717223273574852198400000⟩, + ⟨3, 7, 3, 7, 2, 4, -1035269954997702168895876597929546378205955358720000⟩, + ⟨3, 7, 4, 7, 3, 4, -146830890873939589719838819572334648934824673280000⟩, + ⟨3, 7, 5, 7, 4, 4, -32477348908826177923360745146525437883160985600000⟩, + ⟨3, 7, 6, 7, 5, 4, -923101336439933547151493004714654472077312000000⟩, + ⟨3, 7, 7, 7, 6, 4, -515104204399025508338562334609966615442227200000⟩, + ⟨3, 7, 8, 7, 7, 4, -184875726312843182597673494444208463974236160000⟩ +] + +def collectedFourData_8_6_17 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 6, 5, -1649244707353412641126890785434279350034759680000000⟩, + ⟨3, 8, 1, 0, 7, 5, 1094249274850855839097846293895592514542370816000000⟩, + ⟨3, 8, 2, 0, 8, 5, -133051558240179707519348657002370385173702246400000⟩, + ⟨3, 8, 0, 1, 5, 5, -2518530468367807352816852148779836749650067456000000⟩, + ⟨3, 8, 1, 1, 6, 5, 534548368416038609322157823018247810308898816000000⟩, + ⟨3, 8, 2, 1, 7, 5, -60992476987250341810615928102242858020372480000000⟩, + ⟨3, 8, 3, 1, 8, 5, -385708294636454184667330896907328636426649600000⟩, + ⟨3, 8, 0, 2, 4, 5, -717655021342289460987519552792655790384087040000000⟩, + ⟨3, 8, 1, 2, 5, 5, 318057305378838212661256395691312214056108032000000⟩, + ⟨3, 8, 2, 2, 6, 5, -128485672386591752680882208753664234751839436800000⟩, + ⟨3, 8, 3, 2, 7, 5, 13858496986512866183172629440072408122576076800000⟩, + ⟨3, 8, 4, 2, 8, 5, -662175713584192665743914028272142802694963200000⟩, + ⟨3, 8, 0, 3, 3, 5, -127642615664789678184173436419940728275206144000000⟩, + ⟨3, 8, 1, 3, 4, 5, 173423137334463066471333337864312283486748672000000⟩, + ⟨3, 8, 2, 3, 5, 5, 31841693794904992902800274384811330059947212800000⟩, + ⟨3, 8, 3, 3, 6, 5, -15217379622024470131806957201922845995905843200000⟩, + ⟨3, 8, 4, 3, 7, 5, -3992018744709639834450151718714342128798924800000⟩, + ⟨3, 8, 5, 3, 8, 5, 412679455860529497974895447425910784917504000000⟩, + ⟨3, 8, 0, 4, 2, 5, 946056759137771913719447288883501009117118464000000⟩, + ⟨3, 8, 1, 4, 3, 5, -546548089664881175053892129249307156717502464000000⟩, + ⟨3, 8, 2, 4, 4, 5, 4022513670318300491243884217802758673137664000000⟩, + ⟨3, 8, 3, 4, 5, 5, -28467429944150594377545958484879289784624742400000⟩, + ⟨3, 8, 4, 4, 6, 5, 4733471825564525970805880833028371520893747200000⟩, + ⟨3, 8, 5, 4, 7, 5, 246589334890604920520726230204382781112320000000⟩, + ⟨3, 8, 6, 4, 8, 5, -103992549296165965557712387149604627415040000000⟩, + ⟨3, 8, 0, 5, 1, 5, 729210531355505679222799607477063462581960704000000⟩, + ⟨3, 8, 1, 5, 2, 5, -110696537842913485403473752145228244849786880000000⟩, + ⟨3, 8, 2, 5, 3, 5, 67077025997145960714333231815915975231510937600000⟩, + ⟨3, 8, 3, 5, 4, 5, 29142084306392955068648735854412577013078425600000⟩, + ⟨3, 8, 4, 5, 5, 5, 2455749166023538729536782664847850516722483200000⟩, + ⟨3, 8, 5, 5, 6, 5, -547729745617107625263719926382302970511360000000⟩, + ⟨3, 8, 6, 5, 7, 5, 126051370829202535667920858266628842848256000000⟩, + ⟨3, 8, 7, 5, 8, 5, 5147716880689218069967024473846339285811200000⟩, + ⟨3, 8, 0, 6, 0, 5, -16820269312259859752041492315510656691372818432000000⟩, + ⟨3, 8, 1, 6, 1, 5, -2442488984028657598763397910867503944168374272000000⟩, + ⟨3, 8, 2, 6, 2, 5, -44889069587464630899897048843413935344530227200000⟩, + ⟨3, 8, 3, 6, 3, 5, 38765891518210799502675054181272224843327078400000⟩, + ⟨3, 8, 4, 6, 4, 5, -4766178085815359548725315872027818286540390400000⟩, + ⟨3, 8, 5, 6, 5, 5, 1110234820198330419436661321115508622229504000000⟩, + ⟨3, 8, 6, 6, 6, 5, -82078955599048329313730249064321650786304000000⟩, + ⟨3, 8, 7, 6, 7, 5, -17010019010271328359178326578426474083123200000⟩, + ⟨3, 8, 8, 6, 8, 5, 18356431844259304739642959950215084035276800000⟩, + ⟨3, 8, 1, 7, 0, 5, 15298863853507044787358354617125532300593856512000000⟩, + ⟨3, 8, 2, 7, 1, 5, 662085206648864354622868623959667192009798451200000⟩, + ⟨3, 8, 3, 7, 2, 5, 142696271074509221064738578796298409807236300800000⟩, + ⟨3, 8, 4, 7, 3, 5, 17347210886629526741928655562820100852128153600000⟩, + ⟨3, 8, 5, 7, 4, 5, 3357382700982732671032284055125856289292288000000⟩, + ⟨3, 8, 6, 7, 5, 5, 84823684809930797203043388781187165061120000000⟩, + ⟨3, 8, 7, 7, 6, 5, 42599584095554609344186756682640423439564800000⟩, + ⟨3, 8, 8, 7, 7, 5, 13899445416767193205874578564934827140710400000⟩ +] + +def collectedFourData_8_6_18 : List CollectedFourTerm := [ + ⟨4, 2, 2, 0, 8, 0, -5446735448723004650316881389251444114855454310400000⟩, + ⟨4, 2, 2, 1, 7, 0, -2496850776540216357761386837254869762734817280000000⟩, + ⟨4, 2, 3, 1, 8, 0, -94738508998316018561961632555581449598245273600000⟩, + ⟨4, 2, 2, 2, 6, 0, -5259821648820958358475226033436428308677709004800000⟩, + ⟨4, 2, 3, 2, 7, 0, 3403954127295545662010096891252107438780632268800000⟩, + ⟨4, 2, 4, 2, 8, 0, -569257629023688783167011530737062234459157299200000⟩, + ⟨4, 2, 2, 3, 5, 0, 1303504330456747229402959867242727657890958540800000⟩, + ⟨4, 2, 3, 3, 6, 0, -3737725831410472159675618815125830139024454451200000⟩, + ⟨4, 2, 4, 3, 7, 0, -3431849098377715430999192599462976658728602828800000⟩, + ⟨4, 2, 5, 3, 8, 0, 946056759137771913719447288883501009117118464000000⟩, + ⟨4, 2, 2, 4, 4, 0, 164669757279694798295094032207112205504610304000000⟩, + ⟨4, 2, 3, 4, 5, 0, -6992231967593122753120139463534226055698474598400000⟩, + ⟨4, 2, 4, 4, 6, 0, 4069259704325734088164138424083865230338372403200000⟩, + ⟨4, 2, 5, 4, 7, 0, 565299541064111042190449957950484502408069120000000⟩, + ⟨4, 2, 6, 4, 8, 0, -536400391926524651781070682365832103135805440000000⟩, + ⟨4, 2, 2, 5, 3, 0, 2745934133548829211868253494266124889063266713600000⟩, + ⟨4, 2, 3, 5, 4, 0, 7157942037241208090437620574256900297897646489600000⟩, + ⟨4, 2, 4, 5, 5, 0, 2111152552183895768493557749661720295274394419200000⟩, + ⟨4, 2, 5, 5, 6, 0, -1255655983507461152988745741748965679573237760000000⟩, + ⟨4, 2, 6, 5, 7, 0, 650181240610790124026209862885437467122466816000000⟩, + ⟨4, 2, 7, 5, 8, 0, 53104522795466959425375456716164473150662246400000⟩, + ⟨4, 2, 2, 6, 2, 0, -1837625126801424468426504997279406314130453299200000⟩, + ⟨4, 2, 3, 6, 3, 0, 9521762465303872579895130152734650691532252774400000⟩, + ⟨4, 2, 4, 6, 4, 0, -4097376543682232184329323765171468677889287782400000⟩, + ⟨4, 2, 5, 6, 5, 0, 2545184018643558264520293940119206343909310464000000⟩, + ⟨4, 2, 6, 6, 6, 0, -423368637947916416416003645149551104930873344000000⟩, + ⟨4, 2, 7, 6, 7, 0, -175477588068389992752789654721730094490347110400000⟩, + ⟨4, 2, 8, 6, 8, 0, 347173492476217691475090782985130016429939097600000⟩, + ⟨4, 2, 2, 7, 1, 0, 27103801058982582087254585683266654899088339763200000⟩, + ⟨4, 2, 3, 7, 2, 0, 35049368004804212745435702780398544539135823052800000⟩, + ⟨4, 2, 4, 7, 3, 0, 14913008642442578135839349175770879525819881881600000⟩, + ⟨4, 2, 5, 7, 4, 0, 7696711217799044988107817052585857298263441408000000⟩, + ⟨4, 2, 6, 7, 5, 0, 437526131291565188995086206013519690014392320000000⟩, + ⟨4, 2, 7, 7, 6, 0, 439462899206085653293202846169203210721008025600000⟩, + ⟨4, 2, 8, 7, 7, 0, 262878921664219367617711060341056643732917452800000⟩ +] + +def collectedFourData_8_6_19 : List CollectedFourTerm := [ + ⟨4, 3, 1, 0, 7, 1, -20703022728095948315698294383091243256979967180800000⟩, + ⟨4, 3, 2, 0, 8, 1, 12586571897113959620112997529196455002239506841600000⟩, + ⟨4, 3, 1, 1, 6, 1, -10113570349034257909435263285963501116557413580800000⟩, + ⟨4, 3, 2, 1, 7, 1, 5769839954803810612019509181430919106521989120000000⟩, + ⟨4, 3, 3, 1, 8, 1, 109463096395864986812541592021657915497853747200000⟩, + ⟨4, 3, 1, 2, 5, 1, -6017593772673534742422329624371799286309558681600000⟩, + ⟨4, 3, 2, 2, 6, 1, 12154642716198545527302711337198707326665831219200000⟩, + ⟨4, 3, 3, 2, 7, 1, -3933008474620155824409801848209960557837130137600000⟩, + ⟨4, 3, 4, 2, 8, 1, 438489081710227651031245662684494355911776665600000⟩, + ⟨4, 3, 1, 3, 4, 1, -3281138252801178664048861310408771058735356313600000⟩, + ⟨4, 3, 2, 3, 5, 1, -3012198981931425878632871719661196042749293363200000⟩, + ⟨4, 3, 3, 3, 6, 1, 4318656133719305769806405367593627660029683302400000⟩, + ⟨4, 3, 4, 3, 7, 1, 2643492652521124191738670483437033369431860838400000⟩, + ⟨4, 3, 5, 3, 8, 1, -546548089664881175053892129249307156717502464000000⟩, + ⟨4, 3, 1, 4, 3, 1, 10340603171861089716052964657863198165427237683200000⟩, + ⟨4, 3, 2, 4, 4, 1, -380526603282543146604325738471272596128137216000000⟩, + ⟨4, 3, 3, 4, 5, 1, 8078988892515709402173217805625587251215649996800000⟩, + ⟨4, 3, 4, 4, 6, 1, -3134478766758823074747904592536302038252362137600000⟩, + ⟨4, 3, 5, 4, 7, 1, -326580177428900292530867755809857690790789120000000⟩, + ⟨4, 3, 6, 4, 8, 1, 247907839922946676234686389957287779187556352000000⟩, + ⟨4, 3, 1, 5, 2, 1, 2094360939097476517216256023052638517716844544000000⟩, + ⟨4, 3, 2, 5, 3, 1, -6345433465977267773092368618362218623034353254400000⟩, + ⟨4, 3, 3, 5, 4, 1, -8270454195479009046746883801595096419836048179200000⟩, + ⟨4, 3, 4, 5, 5, 1, -1626183465551407847935033644637182632453052825600000⟩, + ⟨4, 3, 5, 5, 6, 1, 725407194054347112206303812441734125463797760000000⟩, + ⟨4, 3, 6, 5, 7, 1, -300493864926783137147484805851983613780610252800000⟩, + ⟨4, 3, 7, 5, 8, 1, -20452737256398857653587571355846930782067097600000⟩, + ⟨4, 3, 1, 6, 1, 1, 46211504189812194292816524493358915394180061593600000⟩, + ⟨4, 3, 2, 6, 2, 1, 4246470385091313496702743306749788995124513996800000⟩, + ⟨4, 3, 3, 6, 3, 1, -11001667786608436601895567059498880369834118348800000⟩, + ⟨4, 3, 4, 6, 4, 1, 3156136670740135881967296277263319292500456243200000⟩, + ⟨4, 3, 5, 6, 5, 1, -1470382669749146254306914719623815433461694464000000⟩, + ⟨4, 3, 6, 6, 6, 1, 195668023559469745370158246865162070954029875200000⟩, + ⟨4, 3, 7, 6, 7, 1, 67583640982378454712348814717262798314379673600000⟩, + ⟨4, 3, 8, 6, 8, 1, -114609257100928874852921520998976671278379827200000⟩, + ⟨4, 3, 1, 7, 0, 1, -289452077650562755184108923850908943966310865305600000⟩, + ⟨4, 3, 2, 7, 1, 1, -62632735502867035328350315376889578324589595852800000⟩, + ⟨4, 3, 3, 7, 2, 1, -40496862248404453655618525626699148903512119705600000⟩, + ⟨4, 3, 4, 7, 3, 1, -11487226752457306735991573708519873783895215308800000⟩, + ⟨4, 3, 5, 7, 4, 1, -4446480374628060886025110439509698507763089408000000⟩, + ⟨4, 3, 6, 7, 5, 1, -202211183568995286452481332929108256653049856000000⟩, + ⟨4, 3, 7, 7, 6, 1, -169255248672804285392337775546070726680667750400000⟩, + ⟨4, 3, 8, 7, 7, 1, -86781849917569186889741241228806431474031001600000⟩ +] + +def collectedFourData_8_6_20 : List CollectedFourTerm := [ + ⟨4, 4, 0, 0, 6, 2, -287065995810044317743761083552783720230420480000000⟩, + ⟨4, 4, 1, 0, 7, 2, 761856033489558871391544155651846382607663104000000⟩, + ⟨4, 4, 2, 0, 8, 2, -231588301541904976427854772536957990342754304000000⟩, + ⟨4, 4, 0, 1, 5, 2, -438373064746792215146704691736947566697250816000000⟩, + ⟨4, 4, 1, 1, 6, 2, 372171962120117319173619026695455903112495104000000⟩, + ⟨4, 4, 2, 1, 7, 2, -106162936677621234957774620342056389496012800000000⟩, + ⟨4, 4, 3, 1, 8, 2, -1342720521682789622282263720807916227264512000000⟩, + ⟨4, 4, 0, 2, 4, 2, -124914363787954613465379982129564327807549440000000⟩, + ⟨4, 4, 1, 2, 5, 2, 221443031919144706300330506738773182862327808000000⟩, + ⟨4, 4, 2, 2, 6, 2, -223640963202899159726735743102589990703464448000000⟩, + ⟨4, 4, 3, 2, 7, 2, 48243941243236178085378025434620768022429696000000⟩, + ⟨4, 4, 4, 2, 8, 2, -4034019052527952240564328542668549292818432000000⟩, + ⟨4, 4, 0, 3, 3, 2, -22217354653459389254811964420707441426038784000000⟩, + ⟨4, 4, 1, 3, 4, 2, 120743478256320751176602085131520078898003968000000⟩, + ⟨4, 4, 2, 3, 5, 2, 55423355289593052528795858236983595979767808000000⟩, + ⟨4, 4, 3, 3, 6, 2, -52974458130303863615804117055821448115912704000000⟩, + ⟨4, 4, 4, 3, 7, 2, -24319647102490524399705817011444169675112448000000⟩, + ⟨4, 4, 5, 3, 8, 2, 4022513670318300491243884217802758673137664000000⟩, + ⟨4, 4, 0, 4, 2, 2, 164669757279694798295094032207112205504610304000000⟩, + ⟨4, 4, 1, 4, 3, 2, -380526603282543146604325738471272596128137216000000⟩, + ⟨4, 4, 2, 4, 4, 2, 7001549783855062684803217192449314169815040000000⟩, + ⟨4, 4, 3, 4, 5, 2, -99100286193237423291124496260209370598473728000000⟩, + ⟨4, 4, 4, 4, 6, 2, 28836629216700700988049398697931392807862272000000⟩, + ⟨4, 4, 5, 4, 7, 2, 2403582142182974482315646662643863907205120000000⟩, + ⟨4, 4, 6, 4, 8, 2, -1520471077059568713517763686596128758824960000000⟩, + ⟨4, 4, 0, 5, 1, 2, 126925705085123329267506707871183963049426944000000⟩, + ⟨4, 4, 1, 5, 2, 2, -77070944601287123217438130953456288761118720000000⟩, + ⟨4, 4, 2, 5, 3, 2, 116753645944674932313603952229750802204327936000000⟩, + ⟨4, 4, 3, 5, 4, 2, 101448880376516405818165316237965327683551232000000⟩, + ⟨4, 4, 4, 5, 5, 2, 14960589343192534185224226851698853000773632000000⟩, + ⟨4, 4, 5, 5, 6, 2, -5338890410210772356335752889911081707765760000000⟩, + ⟨4, 4, 6, 5, 7, 2, 1842992261144412355142426589300609981087744000000⟩, + ⟨4, 4, 7, 5, 8, 2, 107520815989126495341315503176222437801984000000⟩, + ⟨4, 4, 0, 6, 0, 2, -2927720391272604837067031105611072586857316352000000⟩, + ⟨4, 4, 1, 6, 1, 2, -1700549419571370155279429811592840027589050368000000⟩, + ⟨4, 4, 2, 6, 2, 2, -78133495924874737398129358000374933557870592000000⟩, + ⟨4, 4, 3, 6, 3, 2, 134951098554650843786760345134756435903643648000000⟩, + ⟨4, 4, 4, 6, 4, 2, -29035877957302579031664547600802115175317504000000⟩, + ⟨4, 4, 5, 6, 5, 2, 10821800499369870402486526666905968562929664000000⟩, + ⟨4, 4, 6, 6, 6, 2, -1200073263596882064939569718386223476637696000000⟩, + ⟨4, 4, 7, 6, 7, 2, -355289765611595748656720432521779634765824000000⟩, + ⟨4, 4, 8, 6, 8, 2, 527192062500147890507976316746923079892992000000⟩, + ⟨4, 4, 1, 7, 0, 2, 10651623903445850864530587034485090019524476928000000⟩, + ⟨4, 4, 2, 7, 1, 2, 1152419336623205333371989324845613698600927232000000⟩, + ⟨4, 4, 3, 7, 2, 2, 496751597525134243471435957816640524806782976000000⟩, + ⟨4, 4, 4, 7, 3, 2, 105680377261354072780208872223966612932263936000000⟩, + ⟨4, 4, 5, 7, 4, 2, 32725442518169489549783400629159403410423808000000⟩, + ⟨4, 4, 6, 7, 5, 2, 1240203844179362199295416200019588289658880000000⟩, + ⟨4, 4, 7, 7, 6, 2, 889781265930498000956438830441970150670336000000⟩, + ⟨4, 4, 8, 7, 7, 2, 399188543778204043823508418987123776946176000000⟩ +] + +def collectedFourData_8_6_21 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 6, 3, 12189439432418804799693828275020905174383198208000000⟩, + ⟨4, 5, 1, 0, 7, 3, -16175022663758624622916723443154730101085778739200000⟩, + ⟨4, 5, 2, 0, 8, 3, 3277912415152748220186300907216441168177712332800000⟩, + ⟨4, 5, 0, 1, 5, 3, 18614262920470440808138392911438486873501702553600000⟩, + ⟨4, 5, 1, 1, 6, 3, -7901610878547850623109274296033121983475692339200000⟩, + ⟨4, 5, 2, 1, 7, 3, 1502635521085169288105201400369994374536232960000000⟩, + ⟨4, 5, 3, 1, 8, 3, 14253700118272132394343938181447502401424588800000⟩, + ⟨4, 5, 0, 2, 4, 3, 5304132477745471778879492651780964361042919424000000⟩, + ⟨4, 5, 1, 2, 5, 3, -4701473641440523993055792563380296360005101158400000⟩, + ⟨4, 5, 2, 2, 6, 3, 3165425390396306362576080944919070946186860953600000⟩, + ⟨4, 5, 3, 2, 7, 3, -512135369870427862306660197337749769599477350400000⟩, + ⟨4, 5, 4, 2, 8, 3, 34258624586487818569104161156875870985980477440000⟩, + ⟨4, 5, 0, 3, 3, 3, 943396650420814256689416995560623675514709606400000⟩, + ⟨4, 5, 1, 3, 4, 3, -2563513854909702998091762428715404300330100326400000⟩, + ⟨4, 5, 2, 3, 5, 3, -784464945697206648416157646942904670314142105600000⟩, + ⟨4, 5, 3, 3, 6, 3, 562352349520206638748518765116520340221696409600000⟩, + ⟨4, 5, 4, 3, 7, 3, 206532901632674194994165652376886759087312732160000⟩, + ⟨4, 5, 5, 3, 8, 3, -28467429944150594377545958484879289784624742400000⟩, + ⟨4, 5, 0, 4, 2, 3, -6992231967593122753120139463534226055698474598400000⟩, + ⟨4, 5, 1, 4, 3, 3, 8078988892515709402173217805625587251215649996800000⟩, + ⟨4, 5, 2, 4, 4, 3, -99100286193237423291124496260209370598473728000000⟩, + ⟨4, 5, 3, 4, 5, 3, 1052002809388100376300624860272797870611182387200000⟩, + ⟨4, 5, 4, 4, 6, 3, -244893056232745764964269577880886983421843210240000⟩, + ⟨4, 5, 5, 4, 7, 3, -17010210991325451666331305415353041097326592000000⟩, + ⟨4, 5, 6, 4, 8, 3, 9223210179180343478322544850248741775474688000000⟩, + ⟨4, 5, 0, 5, 1, 3, -5389538354016460228657672669852065151909783142400000⟩, + ⟨4, 5, 1, 5, 2, 3, 1636299012994808082378585669257220342002221056000000⟩, + ⟨4, 5, 2, 5, 3, 3, -1652536950305103185186853362376440506058224435200000⟩, + ⟨4, 5, 3, 5, 4, 3, -1076934399132496518352710938182802411887578316800000⟩, + ⟨4, 5, 4, 5, 5, 3, -127051758364865088931551016758800021888371261440000⟩, + ⟨4, 5, 5, 5, 6, 3, 37783461086446996954896952712619969705148416000000⟩, + ⟨4, 5, 6, 5, 7, 3, -11179630602385858896039598957237992646980403200000⟩, + ⟨4, 5, 7, 5, 8, 3, -570695629817367780967314167799863239822540800000⟩, + ⟨4, 5, 0, 6, 0, 3, 124317303008224211701855752915182174332968448819200000⟩, + ⟨4, 5, 1, 6, 1, 3, 36104492441202748995098441672642385657637267046400000⟩, + ⟨4, 5, 2, 6, 2, 3, 1105905413296926059112733528840600945997276774400000⟩, + ⟨4, 5, 3, 6, 3, 3, -1432578454240539029819862670863209718564991795200000⟩, + ⟨4, 5, 4, 6, 4, 3, 246585162223006933832312154704787347590537543680000⟩, + ⟨4, 5, 5, 6, 5, 3, -76586153046189223764699375152344403397731942400000⟩, + ⟨4, 5, 6, 6, 6, 3, 7279670167731377118386795378175399500238028800000⟩, + ⟨4, 5, 7, 6, 7, 3, 1885795924148118663443485770158230511340748800000⟩, + ⟨4, 5, 8, 6, 8, 3, -2487300949333613750380480363470163096161484800000⟩, + ⟨4, 5, 1, 7, 0, 3, -226145427049940084490182551221676678777043052134400000⟩, + ⟨4, 5, 2, 7, 1, 3, -16311400989724733863346840233486195596242347622400000⟩, + ⟨4, 5, 3, 7, 2, 3, -5273285236991870060658007960710322100678059622400000⟩, + ⟨4, 5, 4, 7, 3, 3, -897483210567966490587881770888517160457595781120000⟩, + ⟨4, 5, 5, 7, 4, 3, -231598775947378981652312403432813859064040652800000⟩, + ⟨4, 5, 6, 7, 5, 3, -7523103130652674978968486233184372485259264000000⟩, + ⟨4, 5, 7, 7, 6, 3, -4722753220281115100182277120579228772021043200000⟩, + ⟨4, 5, 8, 7, 7, 3, -1883378211716439143383682923710759204972134400000⟩ +] + +def collectedFourData_8_6_22 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 6, 4, -7093871446277985445371891949252050485545795584000000⟩, + ⟨4, 6, 1, 0, 7, 4, 6275570590072520216608494524916052151484442214400000⟩, + ⟨4, 6, 2, 0, 8, 4, -953821109419056201635311826041486751854441267200000⟩, + ⟨4, 6, 0, 1, 5, 4, -10832917211422052323076274351184949454341721292800000⟩, + ⟨4, 6, 1, 1, 6, 4, 3065659806135277177889276682035560992142157414400000⟩, + ⟨4, 6, 2, 1, 7, 4, -437243372686987928802026702158838019171287040000000⟩, + ⟨4, 6, 3, 1, 8, 4, -3318082569208199885690404881785904144800808960000⟩, + ⟨4, 6, 0, 2, 4, 4, -3086838745929749778706098714246025113765937152000000⟩, + ⟨4, 6, 1, 2, 5, 4, 1824073469790694069686220985627209385617706188800000⟩, + ⟨4, 6, 2, 2, 6, 4, -921089149207898923297223950647345680866502246400000⟩, + ⟨4, 6, 3, 2, 7, 4, 119218689164344164338469839462930002428485959680000⟩, + ⟨4, 6, 4, 2, 8, 4, -6645815013075847542158996124864673813144535040000⟩, + ⟨4, 6, 0, 3, 3, 4, -549027262331334206427781320695438003821294387200000⟩, + ⟨4, 6, 1, 3, 4, 4, 994589775206934776665247956203701528223861964800000⟩, + ⟨4, 6, 2, 3, 5, 4, 228266997417745814441342702429922342327445094400000⟩, + ⟨4, 6, 3, 3, 6, 4, -130908572034870868120882295023079313520271032320000⟩, + ⟨4, 6, 4, 3, 7, 4, -40065223719048894956364932260778456967083458560000⟩, + ⟨4, 6, 5, 3, 8, 4, 4733471825564525970805880833028371520893747200000⟩, + ⟨4, 6, 0, 4, 2, 4, 4069259704325734088164138424083865230338372403200000⟩, + ⟨4, 6, 1, 4, 3, 4, -3134478766758823074747904592536302038252362137600000⟩, + ⟨4, 6, 2, 4, 4, 4, 28836629216700700988049398697931392807862272000000⟩, + ⟨4, 6, 3, 4, 5, 4, -244893056232745764964269577880886983421843210240000⟩, + ⟨4, 6, 4, 4, 6, 4, 47506692675324992878715057667209055333871779840000⟩, + ⟨4, 6, 5, 4, 7, 4, 2828402656379998403834221415184625488101376000000⟩, + ⟨4, 6, 6, 4, 8, 4, -1341904763050384954174416741993457077190656000000⟩, + ⟨4, 6, 0, 5, 1, 4, 3136542287292922403964287557507820188834411315200000⟩, + ⟨4, 6, 1, 5, 2, 4, -634849803674324378311803575296109165351534592000000⟩, + ⟨4, 6, 2, 5, 3, 4, 480862337873828273000504957799620799160437964800000⟩, + ⟨4, 6, 3, 5, 4, 4, 250696817548552013992979989040935185808946626560000⟩, + ⟨4, 6, 4, 5, 5, 4, 24646712860502174368848850798946553861022679040000⟩, + ⟨4, 6, 5, 5, 6, 4, -6282511237434675800351950062617750874882048000000⟩, + ⟨4, 6, 6, 5, 7, 4, 1626548594582568599277489257158150946448998400000⟩, + ⟨4, 6, 7, 5, 8, 4, 73805990565715025048106024497025463300915200000⟩, + ⟨4, 6, 0, 6, 0, 4, -72348771326011050539878723145281226190295243161600000⟩, + ⟨4, 6, 1, 6, 1, 4, -14007788158539591433739567671899376275260493004800000⟩, + ⟨4, 6, 2, 6, 2, 4, -321801132741449204211838170247132439123696025600000⟩, + ⟨4, 6, 3, 6, 3, 4, 333486291881870987411928354355841678763192483840000⟩, + ⟨4, 6, 4, 6, 4, 4, -47834943547317928499131579249756212418188410880000⟩, + ⟨4, 6, 5, 6, 5, 4, 12734496875331688462772568020591987242775347200000⟩, + ⟨4, 6, 6, 6, 6, 4, -1059134930435105465696543591439094005733785600000⟩, + ⟨4, 6, 7, 6, 7, 4, -243883129490724872348364435585831563113267200000⟩, + ⟨4, 6, 8, 6, 8, 4, 289506228413599057522059318114930456086446080000⟩, + ⟨4, 6, 1, 7, 0, 4, 87739697221803705618935897896182757500765654220800000⟩, + ⟨4, 6, 2, 7, 1, 4, 4746361896760239906618020060759886725914401177600000⟩, + ⟨4, 6, 3, 7, 2, 4, 1227554647715340550920527699579521677138151342080000⟩, + ⟨4, 6, 4, 7, 3, 4, 174102360114264672875732446991092673247361105920000⟩, + ⟨4, 6, 5, 7, 4, 4, 38509492529985386271243250786629673149687398400000⟩, + ⟨4, 6, 6, 7, 5, 4, 1094552517813189872357450997423353383354368000000⟩, + ⟨4, 6, 7, 7, 6, 4, 610776500482079566994962026668814783794380800000⟩, + ⟨4, 6, 8, 7, 7, 4, 219213409980185935063090860684444180928266240000⟩ +] + +def collectedFourData_8_6_23 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 6, 5, -985477105009010586376824261375400696243814400000000⟩, + ⟨4, 7, 1, 0, 7, 5, 653849366761770614000757800023023458482913280000000⟩, + ⟨4, 7, 2, 0, 8, 5, -79502613436838416248926817757690612691238912000000⟩, + ⟨4, 7, 0, 1, 5, 5, -1504903489323275047974275244306546712620564480000000⟩, + ⟨4, 7, 1, 1, 6, 5, 319409955505798838711508600290518265789153280000000⟩, + ⟨4, 7, 2, 1, 7, 5, -36444979559873191248596193958210524571238400000000⟩, + ⟨4, 7, 3, 1, 8, 5, -230473192899471415714312447243085590560768000000⟩, + ⟨4, 7, 0, 2, 4, 5, -428822108492616778614029997364526860940083200000000⟩, + ⟨4, 7, 1, 2, 5, 5, 190049536696520308548018337961158573094338560000000⟩, + ⟨4, 7, 2, 2, 6, 5, -76774348824113938544432271340308141749305344000000⟩, + ⟨4, 7, 3, 2, 7, 5, 8280900602046450371246696670787998050156544000000⟩, + ⟨4, 7, 4, 2, 8, 5, -395671426029558068347877595678948936646656000000⟩, + ⟨4, 7, 0, 3, 3, 5, -76270595139863453165493967409585784902123520000000⟩, + ⟨4, 7, 1, 3, 4, 5, 103625938928251480432610499898616649099509760000000⟩, + ⟨4, 7, 2, 3, 5, 5, 19026442879990496800638313965653531950055424000000⟩, + ⟨4, 7, 3, 3, 6, 5, -9092876968998057189526444607169103770157056000000⟩, + ⟨4, 7, 4, 3, 7, 5, -2385360436894307296583193650514032678928384000000⟩, + ⟨4, 7, 5, 3, 8, 5, 246589334890604920520726230204382781112320000000⟩, + ⟨4, 7, 0, 4, 2, 5, 565299541064111042190449957950484502408069120000000⟩, + ⟨4, 7, 1, 4, 3, 5, -326580177428900292530867755809857690790789120000000⟩, + ⟨4, 7, 2, 4, 4, 5, 2403582142182974482315646662643863907205120000000⟩, + ⟨4, 7, 3, 4, 5, 5, -17010210991325451666331305415353041097326592000000⟩, + ⟨4, 7, 4, 4, 6, 5, 2828402656379998403834221415184625488101376000000⟩, + ⟨4, 7, 5, 4, 7, 5, 147345110637979521232717555557650241945600000000⟩, + ⟨4, 7, 6, 4, 8, 5, -62138914841417635166288888294416790323200000000⟩, + ⟨4, 7, 0, 5, 1, 5, 435726899821613120129433562168502857834168320000000⟩, + ⟨4, 7, 1, 5, 2, 5, -66144765031874903552497208490029125887590400000000⟩, + ⟨4, 7, 2, 5, 3, 5, 40080694573432103084782394699474706584567808000000⟩, + ⟨4, 7, 3, 5, 4, 5, 17413338813909896974572606266306314106830848000000⟩, + ⟨4, 7, 4, 5, 5, 5, 1467389628701458069786587401433606317408256000000⟩, + ⟨4, 7, 5, 5, 6, 5, -327286255115082765809115150044657142988800000000⟩, + ⟨4, 7, 6, 5, 7, 5, 75319774835912691832948773433337425428480000000⟩, + ⟨4, 7, 7, 5, 8, 5, 3075927487515382590598221352775498858496000000⟩, + ⟨4, 7, 0, 6, 0, 5, -10050655450589673711663550246772812880082370560000000⟩, + ⟨4, 7, 1, 6, 1, 5, -1459466240676658522498786817789913533786357760000000⟩, + ⟨4, 7, 2, 6, 2, 5, -26822672309551449798903320783216947312459776000000⟩, + ⟨4, 7, 3, 6, 3, 5, 23163875182455462372246901154238063257321472000000⟩, + ⟨4, 7, 4, 6, 4, 5, -2847945705706732420213062897708059099922432000000⟩, + ⟨4, 7, 5, 6, 5, 5, 663401247620190584172361824247667302072320000000⟩, + ⟨4, 7, 6, 6, 6, 5, -49044833180465198132899206098135097016320000000⟩, + ⟨4, 7, 7, 6, 7, 5, -10164037038075711712642199502920620179456000000⟩, + ⟨4, 7, 8, 6, 8, 5, 10968562294921734830722114404040304492544000000⟩, + ⟨4, 7, 1, 7, 0, 5, 9141566435265432803020940007659558639983656960000000⟩, + ⟨4, 7, 2, 7, 1, 5, 395617345205643398090365830884494143909789696000000⟩, + ⟨4, 7, 3, 7, 2, 5, 85265641591629742277277747820828103974846464000000⟩, + ⟨4, 7, 4, 7, 3, 5, 10365520100391719449012961688246774386393088000000⟩, + ⟨4, 7, 5, 7, 4, 5, 2006144855169026825754526152088909554647040000000⟩, + ⟨4, 7, 6, 7, 5, 5, 50684897741360284893585032886542244249600000000⟩, + ⟨4, 7, 7, 7, 6, 5, 25454630608724493414843003320209804099584000000⟩, + ⟨4, 7, 8, 7, 7, 5, 8305368614780870062441613095582964908032000000⟩ +] + +def collectedFourData_8_6_24 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 6, 6, 935097708316554391085704561562299277298892800000000⟩, + ⟨4, 8, 1, 0, 7, 6, -496338710527483308951511614497182872332402688000000⟩, + ⟨4, 8, 2, 0, 8, 6, 50292196035195063493135139882835762474909696000000⟩, + ⟨4, 8, 0, 1, 5, 6, 1427970063384591698373520482366808953465077760000000⟩, + ⟨4, 8, 1, 1, 6, 6, -242464906298748896887342020260877153953906688000000⟩, + ⟨4, 8, 2, 1, 7, 6, 23054563583371789251320813058773270868787200000000⟩, + ⟨4, 8, 3, 1, 8, 6, 124966274660709712068017526937560759140352000000⟩, + ⟨4, 8, 0, 2, 4, 6, 406899935968834505822963452678388138272358400000000⟩, + ⟨4, 8, 1, 2, 5, 6, -144267084707088458379708133212881694360600576000000⟩, + ⟨4, 8, 2, 2, 6, 6, 48566335553287345398387683382253893873303552000000⟩, + ⟨4, 8, 3, 2, 7, 6, -4490037587689212308272744885222974387388416000000⟩, + ⟨4, 8, 4, 2, 8, 6, 187721988591099661780447040794476555534336000000⟩, + ⟨4, 8, 0, 3, 3, 6, 72371502457760230377088596987326150989578240000000⟩, + ⟨4, 8, 1, 3, 4, 6, -78662712727819839377127946822571134965252096000000⟩, + ⟨4, 8, 2, 3, 5, 6, -12035850820591285443277269342652532042760192000000⟩, + ⟨4, 8, 3, 3, 6, 6, 4930304242626123333482732106735219306921984000000⟩, + ⟨4, 8, 4, 3, 7, 6, 1131708218644230706196221954052624329211904000000⟩, + ⟨4, 8, 5, 3, 8, 6, -103992549296165965557712387149604627415040000000⟩, + ⟨4, 8, 0, 4, 2, 6, -536400391926524651781070682365832103135805440000000⟩, + ⟨4, 8, 1, 4, 3, 6, 247907839922946676234686389957287779187556352000000⟩, + ⟨4, 8, 2, 4, 4, 6, -1520471077059568713517763686596128758824960000000⟩, + ⟨4, 8, 3, 4, 5, 6, 9223210179180343478322544850248741775474688000000⟩, + ⟨4, 8, 4, 4, 6, 6, -1341904763050384954174416741993457077190656000000⟩, + ⟨4, 8, 5, 4, 7, 6, -62138914841417635166288888294416790323200000000⟩, + ⟨4, 8, 6, 4, 8, 6, 23584903827859451258303274726649610895360000000⟩, + ⟨4, 8, 0, 5, 1, 6, -413451741703671399161713812998822117077155840000000⟩, + ⟨4, 8, 1, 5, 2, 6, 50210658682224911334873944410374302167203840000000⟩, + ⟨4, 8, 2, 5, 3, 6, -25354463980171600415880134185568016021848064000000⟩, + ⟨4, 8, 3, 5, 4, 6, -9441792572935939282942214134472088037097472000000⟩, + ⟨4, 8, 4, 5, 5, 6, -696186990053750148613553470528859915943936000000⟩, + ⟨4, 8, 5, 5, 6, 6, 138024347379467888885129544935767906713600000000⟩, + ⟨4, 8, 6, 5, 7, 6, -28587715932512449174222220369279324258304000000⟩, + ⟨4, 8, 7, 5, 8, 6, -1061338339628529364008457939311529033728000000⟩, + ⟨4, 8, 0, 6, 0, 6, 9536847513915361498054624407140017122280734720000000⟩, + ⟨4, 8, 1, 6, 1, 6, 1107884520166212761814852119890347509359312896000000⟩, + ⟨4, 8, 2, 6, 2, 6, 16967632077295953986070554339235833114001408000000⟩, + ⟨4, 8, 3, 6, 3, 6, -12559825946958387160926405234197995620139008000000⟩, + ⟨4, 8, 4, 6, 4, 6, 1351176749454766853971220473128518934331392000000⟩, + ⟨4, 8, 5, 6, 5, 6, -279771981934605371182487890754605720535040000000⟩, + ⟨4, 8, 6, 6, 6, 6, 18615028549608520289083247156088312692736000000⟩, + ⟨4, 8, 7, 6, 7, 6, 3507066482450751723950830239587141419008000000⟩, + ⟨4, 8, 8, 6, 8, 6, -3469276425728463166833038967000400920576000000⟩, + ⟨4, 8, 1, 7, 0, 6, -6939386236851909133581534347500359186923913216000000⟩, + ⟨4, 8, 2, 7, 1, 6, -250261774046114668513013233044907726385184768000000⟩, + ⟨4, 8, 3, 7, 2, 6, -46232403223176215679986282797017971394871296000000⟩, + ⟨4, 8, 4, 7, 3, 6, -4917807852723708379675645566418463886409728000000⟩, + ⟨4, 8, 5, 7, 4, 6, -846038689544165497768135583381068846202880000000⟩, + ⟨4, 8, 6, 7, 5, 6, -19237517130860814010901958431441242030080000000⟩, + ⟨4, 8, 7, 7, 6, 6, -8783033896531700902931995893395946995712000000⟩, + ⟨4, 8, 8, 7, 7, 6, -2626927647170729872619330721950705123328000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0828.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0828.lean new file mode 100644 index 0000000000000000000000000000000000000000..4a080602d23649771d1cbb1e0ca10c7ecd4ffacc --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0828.lean @@ -0,0 +1,654 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0828. -/ +namespace LaughlinFock +def collectedFourData_8_6_25 : List CollectedFourTerm := [ + ⟨5, 1, 2, 0, 8, 0, -4198286003829253315581552046388634630534620774400000⟩, + ⟨5, 1, 2, 1, 7, 0, -1924546137311778076891428120964249950439342080000000⟩, + ⟨5, 1, 3, 1, 8, 0, -73023439470432239667723651856356092075940249600000⟩, + ⟨5, 1, 2, 2, 6, 0, -4054214826251630956451995280407791549402631372800000⟩, + ⟨5, 1, 3, 2, 7, 0, 2623731793996384227356007741473334887780764876800000⟩, + ⟨5, 1, 4, 2, 8, 0, -438777752105345064825774024172926568792011571200000⟩, + ⟨5, 1, 2, 3, 5, 0, 1004727334016271326571578042645192338265918668800000⟩, + ⟨5, 1, 3, 3, 6, 0, -2880999488939869018943252110480321399072437043200000⟩, + ⟨5, 1, 4, 3, 7, 0, -2645232942303293821739809763362492419383545036800000⟩, + ⟨5, 1, 5, 3, 8, 0, 729210531355505679222799607477063462581960704000000⟩, + ⟨5, 1, 2, 4, 4, 0, 126925705085123329267506707871183963049426944000000⟩, + ⟨5, 1, 3, 4, 5, 0, -5389538354016460228657672669852065151909783142400000⟩, + ⟨5, 1, 4, 4, 6, 0, 3136542287292922403964287557507820188834411315200000⟩, + ⟨5, 1, 5, 4, 7, 0, 435726899821613120129433562168502857834168320000000⟩, + ⟨5, 1, 6, 4, 8, 0, -413451741703671399161713812998822117077155840000000⟩, + ⟨5, 1, 2, 5, 3, 0, 2116536951141598996859346458442718682828872089600000⟩, + ⟨5, 1, 3, 5, 4, 0, 5517265920858399456856085589725700631828208025600000⟩, + ⟨5, 1, 4, 5, 5, 0, 1627254030459667867681087898332194596036227891200000⟩, + ⟨5, 1, 5, 5, 6, 0, -967846334894007962343713256501532098413199360000000⟩, + ⟨5, 1, 6, 5, 7, 0, 501152814948739636720458020929889087181029376000000⟩, + ⟨5, 1, 7, 5, 8, 0, 40932403802448484717964061674581542086010470400000⟩, + ⟨5, 1, 2, 6, 2, 0, -1416421987586002827948805219395032175902667571200000⟩, + ⟨5, 1, 3, 6, 3, 0, 7339273674333529975387015773616140424785061478400000⟩, + ⟨5, 1, 4, 6, 4, 0, -3158214449316135173846055416506815009926833766400000⟩, + ⟨5, 1, 5, 6, 5, 0, 1961800888483826510405224076009019367388872704000000⟩, + ⟨5, 1, 6, 6, 6, 0, -326328062724932124132377729815071281469456384000000⟩, + ⟨5, 1, 7, 6, 7, 0, -135256266603871592203715083470021487329961574400000⟩, + ⟨5, 1, 8, 6, 8, 0, 267597651489599383931363668995223537365653913600000⟩, + ⟨5, 1, 2, 7, 1, 0, 20891322831399345968816838140836442785904276275200000⟩, + ⟨5, 1, 3, 7, 2, 0, 27015681690971289534451040967217029945481809100800000⟩, + ⟨5, 1, 4, 7, 3, 0, 11494789135248006519624477315744056056445770137600000⟩, + ⟨5, 1, 5, 7, 4, 0, 5932543499753998295943050134366703062182002688000000⟩, + ⟨5, 1, 6, 7, 5, 0, 337240508668654542647534173303260755546603520000000⟩, + ⟨5, 1, 7, 7, 6, 0, 338733348867108313139676923041185429823527321600000⟩, + ⟨5, 1, 8, 7, 7, 0, 202624288973566566213455018022331291418807500800000⟩ +] + +def collectedFourData_8_6_26 : List CollectedFourTerm := [ + ⟨5, 2, 1, 0, 7, 1, -4193140516305841359840454334976392554491150336000000⟩, + ⟨5, 2, 2, 0, 8, 1, 2549254052238531899100343780477847050515382272000000⟩, + ⟨5, 2, 1, 1, 6, 1, -2048378256257905122309260585636497936493838336000000⟩, + ⟨5, 2, 2, 1, 7, 1, 1168609531315199196164939696852166414591590400000000⟩, + ⟨5, 2, 3, 1, 8, 1, 22170392727961177625526216868229737479143424000000⟩, + ⟨5, 2, 1, 2, 5, 1, -1218788994740564556682529063966734006534275072000000⟩, + ⟨5, 2, 2, 2, 6, 1, 2461772152978800531981396370654272745755377664000000⟩, + ⟨5, 2, 3, 2, 7, 1, -796582093470016841084932029492511289578094592000000⟩, + ⟨5, 2, 4, 2, 8, 1, 88810525816680976199316814023908520835940352000000⟩, + ⟨5, 2, 1, 3, 4, 1, -664553863854397914657578632028634969393856512000000⟩, + ⟨5, 2, 2, 3, 5, 1, -610083549643743226878747915559080700510470144000000⟩, + ⟨5, 2, 3, 3, 6, 1, 874690244420970787028636918516362234149470208000000⟩, + ⟨5, 2, 4, 3, 7, 1, 535406654932584654749746867511852841805283328000000⟩, + ⟨5, 2, 5, 3, 8, 1, -110696537842913485403473752145228244849786880000000⟩, + ⟨5, 2, 1, 4, 3, 1, 2094360939097476517216256023052638517716844544000000⟩, + ⟨5, 2, 2, 4, 4, 1, -77070944601287123217438130953456288761118720000000⟩, + ⟨5, 2, 3, 4, 5, 1, 1636299012994808082378585669257220342002221056000000⟩, + ⟨5, 2, 4, 4, 6, 1, -634849803674324378311803575296109165351534592000000⟩, + ⟨5, 2, 5, 4, 7, 1, -66144765031874903552497208490029125887590400000000⟩, + ⟨5, 2, 6, 4, 8, 1, 50210658682224911334873944410374302167203840000000⟩, + ⟨5, 2, 1, 5, 2, 1, 424186836136737078060152604811618192698900480000000⟩, + ⟨5, 2, 2, 5, 3, 1, -1285188859093686125038101662964230258109186048000000⟩, + ⟨5, 2, 3, 5, 4, 1, -1675077935757263151302332964656081295967780864000000⟩, + ⟨5, 2, 4, 5, 5, 1, -329363294718141741929406583804106374278807552000000⟩, + ⟨5, 2, 5, 5, 6, 1, 146922231413149988217737600163100333650739200000000⟩, + ⟨5, 2, 6, 5, 7, 1, -60861305929779668954458165286497626227736576000000⟩, + ⟨5, 2, 7, 5, 8, 1, -4142448297792670148745769887154602132897792000000⟩, + ⟨5, 2, 1, 6, 1, 1, 9359567106825069650872332632411131927553114112000000⟩, + ⟨5, 2, 2, 6, 2, 1, 860069916208649828997929955768833037677101056000000⟩, + ⟨5, 2, 3, 6, 3, 1, -2228251378981476323307509039648202116768464896000000⟩, + ⟨5, 2, 4, 6, 4, 1, 639236343547029069114176433862225496578719744000000⟩, + ⟨5, 2, 5, 6, 5, 1, -297807775607177626244574535062644516066426880000000⟩, + ⟨5, 2, 6, 6, 6, 1, 39630131701456926246913980185207340672221184000000⟩, + ⟨5, 2, 7, 6, 7, 1, 13688228379235427109122931789455391260147712000000⟩, + ⟨5, 2, 8, 6, 8, 1, -23212683761460371397433256665719721137537024000000⟩, + ⟨5, 2, 1, 7, 0, 1, -58624928845697310912003557118537302970992689152000000⟩, + ⟨5, 2, 2, 7, 1, 1, -12685483870320462036332760307555830909502488576000000⟩, + ⟨5, 2, 3, 7, 2, 1, -8202137248615119481185117925887152340338737152000000⟩, + ⟨5, 2, 4, 7, 3, 1, -2326595326118886130164544969944969924990468096000000⟩, + ⟨5, 2, 5, 7, 4, 1, -900579459274276127516264022584927960023695360000000⟩, + ⟨5, 2, 6, 7, 5, 1, -40955367619948186044066257971338766995947520000000⟩, + ⟨5, 2, 7, 7, 6, 1, -34280551691817037096923436191868829583802368000000⟩, + ⟨5, 2, 8, 7, 7, 1, -17576587522917665648821771276766294386409472000000⟩ +] + +def collectedFourData_8_6_27 : List CollectedFourTerm := [ + ⟨5, 3, 0, 0, 6, 2, -4786940416369859259358060883138938244255711232000000⟩, + ⟨5, 3, 1, 0, 7, 2, 12704254392358068401862002503320307319820622233600000⟩, + ⟨5, 3, 2, 0, 8, 2, -3861827652143694627618906039713230390237436313600000⟩, + ⟨5, 3, 0, 1, 5, 2, -7310046371611793560996900317947059793574651494400000⟩, + ⟨5, 3, 1, 1, 6, 2, 6206116479540645343832999353377235390078491033600000⟩, + ⟨5, 3, 2, 1, 7, 2, -1770309474894753963121365789183192581296619520000000⟩, + ⟨5, 3, 3, 1, 8, 2, -22390402301029592293775351903531618555186380800000⟩, + ⟨5, 3, 0, 2, 4, 2, -2082997029705199389621374166468333131211472896000000⟩, + ⟨5, 3, 1, 2, 5, 2, 3692651219194469400665406941060867489967321907200000⟩, + ⟨5, 3, 2, 2, 6, 2, -3729302603364575083434069592387927232314815283200000⟩, + ⟨5, 3, 3, 2, 7, 2, 804487036266869099074275061738077398925469286400000⟩, + ⟨5, 3, 4, 2, 8, 2, -67268882852047051180018695845275430445436108800000⟩, + ⟨5, 3, 0, 3, 3, 2, -370483284289244498353106688985687865819765145600000⟩, + ⟨5, 3, 1, 3, 4, 2, 2013445843515100909401524687137868610547168051200000⟩, + ⟨5, 3, 2, 3, 5, 2, 924206640002522316606515688985211786931417907200000⟩, + ⟨5, 3, 3, 3, 6, 2, -883370299375498520748463227632939771367102873600000⟩, + ⟨5, 3, 4, 3, 7, 2, -405539852598211010521602173947462712078578483200000⟩, + ⟨5, 3, 5, 3, 8, 2, 67077025997145960714333231815915975231510937600000⟩, + ⟨5, 3, 0, 4, 2, 2, 2745934133548829211868253494266124889063266713600000⟩, + ⟨5, 3, 1, 4, 3, 2, -6345433465977267773092368618362218623034353254400000⟩, + ⟨5, 3, 2, 4, 4, 2, 116753645944674932313603952229750802204327936000000⟩, + ⟨5, 3, 3, 4, 5, 2, -1652536950305103185186853362376440506058224435200000⟩, + ⟨5, 3, 4, 4, 6, 2, 480862337873828273000504957799620799160437964800000⟩, + ⟨5, 3, 5, 4, 7, 2, 40080694573432103084782394699474706584567808000000⟩, + ⟨5, 3, 6, 4, 8, 2, -25354463980171600415880134185568016021848064000000⟩, + ⟨5, 3, 0, 5, 1, 2, 2116536951141598996859346458442718682828872089600000⟩, + ⟨5, 3, 1, 5, 2, 2, -1285188859093686125038101662964230258109186048000000⟩, + ⟨5, 3, 2, 5, 3, 2, 1946913792258866801462338050472000708697024102400000⟩, + ⟨5, 3, 3, 5, 4, 2, 1691700698647587812670625567273571337286503628800000⟩, + ⟨5, 3, 4, 5, 5, 2, 249473817257790149471470557004437083996867788800000⟩, + ⟨5, 3, 5, 5, 6, 2, -89028135189229460266357473286005414936182784000000⟩, + ⟨5, 3, 6, 5, 7, 2, 30732633856665141558196086617858189546854809600000⟩, + ⟨5, 3, 7, 5, 8, 2, 1792952656085389338460440297408083531504025600000⟩, + ⟨5, 3, 0, 6, 0, 2, -48820909732850488778722204880746900760692575436800000⟩, + ⟨5, 3, 1, 6, 1, 2, -28357342441795633196949021917403247073318613811200000⟩, + ⟨5, 3, 2, 6, 2, 2, -1302907327841599279836426486029781578959080652800000⟩, + ⟨5, 3, 3, 6, 3, 2, 2250363600474086019247597291732167587657888563200000⟩, + ⟨5, 3, 4, 6, 4, 2, -484184890399098670738178255530917594475895193600000⟩, + ⟨5, 3, 5, 6, 5, 2, 180457856187899570907845468916156626441443737600000⟩, + ⟨5, 3, 6, 6, 6, 2, -20011702158963233783386267087385558365136486400000⟩, + ⟨5, 3, 7, 6, 7, 2, -5924599093422869631522196618641207891433881600000⟩, + ⟨5, 3, 8, 6, 8, 2, 8791138720732599629569251403320026781764812800000⟩, + ⟨5, 3, 1, 7, 0, 2, 177620093315114106746758083663497424610499179315200000⟩, + ⟨5, 3, 2, 7, 1, 2, 19217053846872731351072615858249493103319502028800000⟩, + ⟨5, 3, 3, 7, 2, 2, 8283531779440929654724829226035713187521128038400000⟩, + ⟨5, 3, 4, 7, 3, 2, 1762262603420092524952595497777972755481126502400000⟩, + ⟨5, 3, 5, 7, 4, 2, 545709856689103783428309078901106833167168307200000⟩, + ⟨5, 3, 6, 7, 5, 2, 20680895657763345068956193902311645791649792000000⟩, + ⟨5, 3, 7, 7, 6, 2, 14837458862351283810500955732865802496796262400000⟩, + ⟨5, 3, 8, 7, 7, 2, 6656628795659163758376242769458303219426918400000⟩ +] + +def collectedFourData_8_6_28 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 6, 3, -12478318987141663282587692522020924777511780352000000⟩, + ⟨5, 4, 1, 0, 7, 3, 16558357219104253369837821622011809021500902604800000⟩, + ⟨5, 4, 2, 0, 8, 3, -3355596207271312741734868054004877175473517363200000⟩, + ⟨5, 4, 0, 1, 5, 3, -19055405436807853596763344886307343073771152998400000⟩, + ⟨5, 4, 1, 1, 6, 3, 8088872470423634567221274315426259643761741004800000⟩, + ⟨5, 4, 2, 1, 7, 3, -1538246730497093620447359001263895159756554240000000⟩, + ⟨5, 4, 3, 1, 8, 3, -14591500930700676917935920778458906269791027200000⟩, + ⟨5, 4, 0, 2, 4, 3, -5429835996505079881253017148771744777037152256000000⟩, + ⟨5, 4, 1, 2, 5, 3, 4812894648092270317602029973055669359408159129600000⟩, + ⟨5, 4, 2, 2, 6, 3, -3240443333785411147614682673669252937226282598400000⟩, + ⟨5, 4, 3, 2, 7, 3, 524272551274563865509070637010722314736212377600000⟩, + ⟨5, 4, 4, 2, 8, 3, -35070525434827186639655047493359893847851663360000⟩, + ⟨5, 4, 0, 3, 3, 3, -965754364720275036701833384210800018007366041600000⟩, + ⟨5, 4, 1, 3, 4, 3, 2624266996597469968495239856244715718444685721600000⟩, + ⟨5, 4, 2, 3, 5, 3, 803056111063351136994240098405057358417258086400000⟩, + ⟨5, 4, 3, 3, 6, 3, -575679631486487714926652266813751649351657062400000⟩, + ⟨5, 4, 4, 3, 7, 3, -211427559257420079790238906575467212262384599040000⟩, + ⟨5, 4, 5, 3, 8, 3, 29142084306392955068648735854412577013078425600000⟩, + ⟨5, 4, 0, 4, 2, 3, 7157942037241208090437620574256900297897646489600000⟩, + ⟨5, 4, 1, 4, 3, 3, -8270454195479009046746883801595096419836048179200000⟩, + ⟨5, 4, 2, 4, 4, 3, 101448880376516405818165316237965327683551232000000⟩, + ⟨5, 4, 3, 4, 5, 3, -1076934399132496518352710938182802411887578316800000⟩, + ⟨5, 4, 4, 4, 6, 3, 250696817548552013992979989040935185808946626560000⟩, + ⟨5, 4, 5, 4, 7, 3, 17413338813909896974572606266306314106830848000000⟩, + ⟨5, 4, 6, 4, 8, 3, -9441792572935939282942214134472088037097472000000⟩, + ⟨5, 4, 0, 5, 1, 3, 5517265920858399456856085589725700631828208025600000⟩, + ⟨5, 4, 1, 5, 2, 3, -1675077935757263151302332964656081295967780864000000⟩, + ⟨5, 4, 2, 5, 3, 3, 1691700698647587812670625567273571337286503628800000⟩, + ⟨5, 4, 3, 5, 4, 3, 1102456846773502674794756242326640981043262259200000⟩, + ⟨5, 4, 4, 5, 5, 3, 130062779141225381814642432666532375164207759360000⟩, + ⟨5, 4, 5, 5, 6, 3, -38678897621905081846878830603955037173448704000000⟩, + ⟨5, 4, 6, 5, 7, 3, 11444578529506606872270423504883491600649420800000⟩, + ⟨5, 4, 7, 5, 8, 3, 584220640572616935378432229539827286225715200000⟩, + ⟨5, 4, 0, 6, 0, 3, -127263519471784436565733599157568784289460178124800000⟩, + ⟨5, 4, 1, 6, 1, 3, -36960138819178952484801438933397645390702549401600000⟩, + ⟨5, 4, 2, 6, 2, 3, -1132114449826460726602721841111314948700084633600000⟩, + ⟨5, 4, 3, 6, 3, 3, 1466529369560395307639115980540181391877131468800000⟩, + ⟨5, 4, 4, 6, 4, 3, -252429025040422066139305374982826192524982353920000⟩, + ⟨5, 4, 5, 6, 5, 3, 78401181039279603011215105427636827671075225600000⟩, + ⟨5, 4, 6, 6, 6, 3, -7452192283144704163104250456643404454638387200000⟩, + ⟨5, 4, 7, 6, 7, 3, -1930487715750711598283353456110238252086067200000⟩, + ⟨5, 4, 8, 6, 8, 3, 2546247908682232158499856009632788839084851200000⟩, + ⟨5, 4, 1, 7, 0, 3, 231504885180151564165736208309734109623986264473600000⟩, + ⟨5, 4, 2, 7, 1, 3, 16697967597725233612963731155916909113377397145600000⟩, + ⟨5, 4, 3, 7, 2, 3, 5398257701856610004911784983614545945297525145600000⟩, + ⟨5, 4, 4, 7, 3, 3, 918752814611494567592631634350244428546079457280000⟩, + ⟨5, 4, 5, 7, 4, 3, 237087473901125802850922685482266028674331443200000⟩, + ⟨5, 4, 6, 7, 5, 3, 7701394404387306072160291611801754288521216000000⟩, + ⟨5, 4, 7, 7, 6, 3, 4834678535214980686787728004894580508773580800000⟩, + ⟨5, 4, 8, 7, 7, 3, 1928012705549550245124486349868754118744473600000⟩ +] + +def collectedFourData_8_6_29 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 6, 4, -3680336448606137372843273983133631461933973504000000⟩, + ⟨5, 5, 1, 0, 7, 4, 3255797818349633027785405479709537554825373286400000⟩, + ⟨5, 5, 2, 0, 8, 4, -494847224259571807870305386530690176294007603200000⟩, + ⟨5, 5, 0, 1, 5, 4, -5620172336058852643667519015113189368210967756800000⟩, + ⟨5, 5, 1, 1, 6, 4, 1590479840097225713185851752870413948531664486400000⟩, + ⟨5, 5, 2, 1, 7, 4, -226844077116130413608942630217014852179722240000000⟩, + ⟨5, 5, 3, 1, 8, 4, -1721438048521284081436177767415475456452853760000⟩, + ⟨5, 5, 0, 2, 4, 4, -1601467581369211833203145340551732084093222912000000⟩, + ⟨5, 5, 1, 2, 5, 4, 946338558098405251420751244046515089831677132800000⟩, + ⟨5, 5, 2, 2, 6, 4, -477865717460114173553342310178043300359333478400000⟩, + ⟨5, 5, 3, 2, 7, 4, 61851259979738240526129011848129263406499758080000⟩, + ⟨5, 5, 4, 2, 8, 4, -3447882500908581308074937476003151638419210240000⟩, + ⟨5, 5, 0, 3, 3, 4, -284838125435247959473123663570973989151126323200000⟩, + ⟨5, 5, 1, 3, 4, 4, 515998214631535182293338309625062309577411788800000⟩, + ⟨5, 5, 2, 3, 5, 4, 118426074812956546472354616014324811627390566400000⟩, + ⟨5, 5, 3, 3, 6, 4, -67916030441699336777682386546998243575642193920000⟩, + ⟨5, 5, 4, 3, 7, 4, -20786041062548537839289252416784351194628751360000⟩, + ⟨5, 5, 5, 3, 8, 4, 2455749166023538729536782664847850516722483200000⟩, + ⟨5, 5, 0, 4, 2, 4, 2111152552183895768493557749661720295274394419200000⟩, + ⟨5, 5, 1, 4, 3, 4, -1626183465551407847935033644637182632453052825600000⟩, + ⟨5, 5, 2, 4, 4, 4, 14960589343192534185224226851698853000773632000000⟩, + ⟨5, 5, 3, 4, 5, 4, -127051758364865088931551016758800021888371261440000⟩, + ⟨5, 5, 4, 4, 6, 4, 24646712860502174368848850798946553861022679040000⟩, + ⟨5, 5, 5, 4, 7, 4, 1467389628701458069786587401433606317408256000000⟩, + ⟨5, 5, 6, 4, 8, 4, -696186990053750148613553470528859915943936000000⟩, + ⟨5, 5, 0, 5, 1, 4, 1627254030459667867681087898332194596036227891200000⟩, + ⟨5, 5, 1, 5, 2, 4, -329363294718141741929406583804106374278807552000000⟩, + ⟨5, 5, 2, 5, 3, 4, 249473817257790149471470557004437083996867788800000⟩, + ⟨5, 5, 3, 5, 4, 4, 130062779141225381814642432666532375164207759360000⟩, + ⟨5, 5, 4, 5, 5, 4, 12786839508690080429135962051754983912888074240000⟩, + ⟨5, 5, 5, 5, 6, 4, -3259398661367061208919908976572888711692288000000⟩, + ⟨5, 5, 6, 5, 7, 4, 843861652047864471003082473675094816613990400000⟩, + ⟨5, 5, 7, 5, 8, 4, 38290921855794424290669927248532289565491200000⟩, + ⟨5, 5, 0, 6, 0, 4, -37534909130992856097620961788648251808441538969600000⟩, + ⟨5, 5, 1, 6, 1, 4, -7267311469434048425085561663251152876149198028800000⟩, + ⟨5, 5, 2, 6, 2, 4, -166952058125115214774030271474330552535456153600000⟩, + ⟨5, 5, 3, 6, 3, 4, 173014377891964315609385674295654017752146903040000⟩, + ⟨5, 5, 4, 6, 4, 4, -24817011076029635177338710413968002451274465280000⟩, + ⟨5, 5, 5, 6, 5, 4, 6606721500364161969998380293870550928012083200000⟩, + ⟨5, 5, 6, 6, 6, 4, -549484568192652260241348823948746915682713600000⟩, + ⟨5, 5, 7, 6, 7, 4, -126527803254143184440025281421128146039603200000⟩, + ⟨5, 5, 8, 6, 8, 4, 150197298132333495369954811423458444422676480000⟩, + ⟨5, 5, 1, 7, 0, 4, 45519799466410711995162252888386024804360965324800000⟩, + ⟨5, 5, 2, 7, 1, 4, 2462436600269560317768141450515158673177287065600000⟩, + ⟨5, 5, 3, 7, 2, 4, 636861570844090012857220332018985976501612052480000⟩, + ⟨5, 5, 4, 7, 3, 4, 90325186545785422491937234823186968793862635520000⟩, + ⟨5, 5, 5, 7, 4, 4, 19978919839292100938855022200757877956044390400000⟩, + ⟨5, 5, 6, 7, 5, 4, 567859391973487488538499047381629778526208000000⟩, + ⟨5, 5, 7, 7, 6, 4, 316873943050618839824202693799726677806284800000⟩, + ⟨5, 5, 8, 7, 7, 4, 113729027778847020370468220898406615681597440000⟩ +] + +def collectedFourData_8_6_30 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 6, 5, 2188963785791996618695297491145605986333491200000000⟩, + ⟨5, 6, 1, 0, 7, 5, -1452344836759509096394177783235801796512317440000000⟩, + ⟨5, 6, 2, 0, 8, 5, 176592983037863951956416039049363540490059776000000⟩, + ⟨5, 6, 0, 1, 5, 5, 3342725287575850681664408395433269586338775040000000⟩, + ⟨5, 6, 1, 1, 6, 5, -709480536757100799935510416568971207051837440000000⟩, + ⟨5, 6, 2, 1, 7, 5, 80952403688528640946506580926344360833843200000000⟩, + ⟨5, 6, 3, 1, 8, 5, 511932210589695287456732162226542151204864000000⟩, + ⟨5, 6, 0, 2, 4, 5, 952509257968729837994321173850441723255193600000000⟩, + ⟨5, 6, 1, 2, 5, 5, -422142281358658587900322833669963031385210880000000⟩, + ⟨5, 6, 2, 2, 6, 5, 170532900662579238131766462606394492308160512000000⟩, + ⟨5, 6, 3, 2, 7, 5, -18393721619191836840887824014690597168218112000000⟩, + ⟨5, 6, 4, 2, 8, 5, 878874220668434717839658293229283849535488000000⟩, + ⟨5, 6, 0, 3, 3, 5, 169413951712696200319756153043937569758248960000000⟩, + ⟨5, 6, 1, 3, 4, 5, -230176253136354267985903339039968631172628480000000⟩, + ⟨5, 6, 2, 3, 5, 5, -42261960450474769804433347852585219865444352000000⟩, + ⟨5, 6, 3, 3, 6, 5, 20197301685275431340921028027640221624434688000000⟩, + ⟨5, 6, 4, 3, 7, 5, 5298415950896060756972940188748875858706432000000⟩, + ⟨5, 6, 5, 3, 8, 5, -547729745617107625263719926382302970511360000000⟩, + ⟨5, 6, 0, 4, 2, 5, -1255655983507461152988745741748965679573237760000000⟩, + ⟨5, 6, 1, 4, 3, 5, 725407194054347112206303812441734125463797760000000⟩, + ⟨5, 6, 2, 4, 4, 5, -5338890410210772356335752889911081707765760000000⟩, + ⟨5, 6, 3, 4, 5, 5, 37783461086446996954896952712619969705148416000000⟩, + ⟨5, 6, 4, 4, 6, 5, -6282511237434675800351950062617750874882048000000⟩, + ⟨5, 6, 5, 4, 7, 5, -327286255115082765809115150044657142988800000000⟩, + ⟨5, 6, 6, 4, 8, 5, 138024347379467888885129544935767906713600000000⟩, + ⟨5, 6, 0, 5, 1, 5, -967846334894007962343713256501532098413199360000000⟩, + ⟨5, 6, 1, 5, 2, 5, 146922231413149988217737600163100333650739200000000⟩, + ⟨5, 6, 2, 5, 3, 5, -89028135189229460266357473286005414936182784000000⟩, + ⟨5, 6, 3, 5, 4, 5, -38678897621905081846878830603955037173448704000000⟩, + ⟨5, 6, 4, 5, 5, 5, -3259398661367061208919908976572888711692288000000⟩, + ⟨5, 6, 5, 5, 6, 5, 726975549602287628028507721379801884262400000000⟩, + ⟨5, 6, 6, 5, 7, 5, -167301968388512402830451072808390796247040000000⟩, + ⟨5, 6, 7, 5, 8, 5, -6832318928233013684114191567070385143808000000⟩, + ⟨5, 6, 0, 6, 0, 5, 22324740669254390012638607823428707943322746880000000⟩, + ⟨5, 6, 1, 6, 1, 5, 3241799054680201036105044428455968837709332480000000⟩, + ⟨5, 6, 2, 6, 2, 5, 59579119621695377868748360823815309778485248000000⟩, + ⟨5, 6, 3, 6, 3, 5, -51452117614175695719110844282445294422982656000000⟩, + ⟨5, 6, 4, 6, 4, 5, 6325920695678534523476291101050407523188736000000⟩, + ⟨5, 6, 5, 6, 5, 5, -1473561688149567425650214666923335336591360000000⟩, + ⟨5, 6, 6, 6, 6, 5, 108939480345681315053654380760364597903360000000⟩, + ⟨5, 6, 7, 6, 7, 5, 22576586387151889958710471353088383909888000000⟩, + ⟨5, 6, 8, 6, 8, 5, -24363615880825258480261311533558752346112000000⟩, + ⟨5, 6, 1, 7, 0, 5, -20305451816685994898844282048090900432766894080000000⟩, + ⟨5, 6, 2, 7, 1, 5, -878754095132840540284339016321235437809041408000000⟩, + ⟨5, 6, 3, 7, 2, 5, -189393950065121821636831001691264250672054272000000⟩, + ⟨5, 6, 4, 7, 3, 5, -23024125071326780534989612484481049348276224000000⟩, + ⟨5, 6, 5, 7, 4, 5, -4456093819630419215991818453273053935697920000000⟩, + ⟨5, 6, 6, 7, 5, 5, -112582428428303054492116914738006117580800000000⟩, + ⟨5, 6, 7, 7, 6, 5, -56540394799634579424032467961249406124032000000⟩, + ⟨5, 6, 8, 7, 7, 5, -18448070516303406363283273651927212097536000000⟩ +] + +def collectedFourData_8_6_31 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 6, 6, -1133449932618327990056157209485817403062353920000000⟩, + ⟨5, 7, 1, 0, 7, 6, 601621705410914947199778733199892878105719603200000⟩, + ⟨5, 7, 2, 0, 8, 6, -60960138924885897758092779898309869698442854400000⟩, + ⟨5, 7, 0, 1, 5, 6, -1730870001850480966036009113246232348578545664000000⟩, + ⟨5, 7, 1, 1, 6, 6, 293896380305951896657680039194197227222545203200000⟩, + ⟨5, 7, 2, 1, 7, 6, -27944880313268437877752213474366468474798080000000⟩, + ⟨5, 7, 3, 1, 8, 6, -151474027081879151865905967603793361947852800000⟩, + ⟨5, 7, 0, 2, 4, 6, -493211245097126533580955967697252171655413760000000⟩, + ⟨5, 7, 1, 2, 5, 6, 174868910474258705071770796198335985857488486400000⟩, + ⟨5, 7, 2, 2, 6, 6, -58868190212436778380281012573291128891952332800000⟩, + ⟨5, 7, 3, 2, 7, 6, 5442460991998563127146461087839470309762662400000⟩, + ⟨5, 7, 4, 2, 8, 6, -227541435966744136898184655372374895912550400000⟩, + ⟨5, 7, 0, 3, 3, 6, -87722891260114633088314090046621159560052736000000⟩, + ⟨5, 7, 1, 3, 4, 6, 95348588332481801124406177510131452592154214400000⟩, + ⟨5, 7, 2, 3, 5, 6, 14588886466381183836677096194468866811546828800000⟩, + ⟨5, 7, 3, 3, 6, 6, -5976116679456848941335856458711519175743897600000⟩, + ⟨5, 7, 4, 3, 7, 6, -1371765316883519684229821563224188639615385600000⟩, + ⟨5, 7, 5, 3, 8, 6, 126051370829202535667920858266628842848256000000⟩, + ⟨5, 7, 0, 4, 2, 6, 650181240610790124026209862885437467122466816000000⟩, + ⟨5, 7, 1, 4, 3, 6, -300493864926783137147484805851983613780610252800000⟩, + ⟨5, 7, 2, 4, 4, 6, 1842992261144412355142426589300609981087744000000⟩, + ⟨5, 7, 3, 4, 5, 6, -11179630602385858896039598957237992646980403200000⟩, + ⟨5, 7, 4, 4, 6, 6, 1626548594582568599277489257158150946448998400000⟩, + ⟨5, 7, 5, 4, 7, 6, 75319774835912691832948773433337425428480000000⟩, + ⟨5, 7, 6, 4, 8, 6, -28587715932512449174222220369279324258304000000⟩, + ⟨5, 7, 0, 5, 1, 6, 501152814948739636720458020929889087181029376000000⟩, + ⟨5, 7, 1, 5, 2, 6, -60861305929779668954458165286497626227736576000000⟩, + ⟨5, 7, 2, 5, 3, 6, 30732633856665141558196086617858189546854809600000⟩, + ⟨5, 7, 3, 5, 4, 6, 11444578529506606872270423504883491600649420800000⟩, + ⟨5, 7, 4, 5, 5, 6, 843861652047864471003082473675094816613990400000⟩, + ⟨5, 7, 5, 5, 6, 6, -167301968388512402830451072808390796247040000000⟩, + ⟨5, 7, 6, 5, 7, 6, 34651720787288019600867876800381662632345600000⟩, + ⟨5, 7, 7, 5, 8, 6, 1286468631928212811721000191050508350259200000⟩, + ⟨5, 7, 0, 6, 0, 6, -11559796453248638452596835379828638219876958208000000⟩, + ⟨5, 7, 1, 6, 1, 6, -1342888153358820285401205621985886161709983334400000⟩, + ⟨5, 7, 2, 6, 2, 6, -20566793463034742938838615371789868855407411200000⟩, + ⟨5, 7, 3, 6, 3, 6, 15224006803424530759385608627826195443168051200000⟩, + ⟨5, 7, 4, 6, 4, 6, -1637787347786449878459226198668717115362508800000⟩, + ⟨5, 7, 5, 6, 5, 6, 339117004834884652187558225653028414816256000000⟩, + ⟨5, 7, 6, 6, 6, 6, -22563634439043466862681700482127894046310400000⟩, + ⟨5, 7, 7, 6, 7, 6, -4250982793421769176511131387209723360051200000⟩, + ⟨5, 7, 8, 6, 8, 6, 4205176738220722047161805845619651536486400000⟩, + ⟨5, 7, 1, 7, 0, 6, 8411363638921137159567344151887105435686561382400000⟩, + ⟨5, 7, 2, 7, 1, 6, 303347113790044745495928534144840610427908915200000⟩, + ⟨5, 7, 3, 7, 2, 6, 56039185907568282773548692843602884809877094400000⟩, + ⟨5, 7, 4, 7, 3, 6, 5960969564704141518388675963153991880356659200000⟩, + ⟨5, 7, 5, 7, 4, 6, 1025499781603257269382256203160373723922432000000⟩, + ⟨5, 7, 6, 7, 5, 6, 23318164831109448697279438673816963776512000000⟩, + ⟨5, 7, 7, 7, 6, 6, 10646084456917824396382275135954586750156800000⟩, + ⟨5, 7, 8, 7, 7, 6, 3184149568753867730307908329121313403699200000⟩ +] + +def collectedFourData_8_6_32 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 6, 7, -92576214176382343134479701873655491715923968000000⟩, + ⟨5, 8, 1, 0, 7, 7, 40948625262329958820419809895559242684196454400000⟩, + ⟨5, 8, 2, 0, 8, 7, -3556435921192753609699685200945766778431078400000⟩, + ⟨5, 8, 0, 1, 5, 7, -141371389588094784346233268816663297209768345600000⟩, + ⟨5, 8, 1, 1, 6, 7, 20003687757382058761958039762483633375831654400000⟩, + ⟨5, 8, 2, 1, 7, 7, -1630314134979247087318170875676022674554880000000⟩, + ⟨5, 8, 3, 1, 8, 7, -7732416960898295751574427169061111804723200000⟩, + ⟨5, 8, 0, 2, 4, 7, -40283764237239561505100220651751883044552704000000⟩, + ⟨5, 8, 1, 2, 5, 7, 11902232616676522106881744796624780744510668800000⟩, + ⟨5, 8, 2, 2, 6, 7, -3434390898371951297749973914775175257967820800000⟩, + ⟨5, 8, 3, 2, 7, 7, 277825700513058391737610344764305284110745600000⟩, + ⟨5, 8, 4, 2, 8, 7, -10324881243760624863317592228459845989171200000⟩, + ⟨5, 8, 0, 3, 3, 7, -7164898012484607972333860940340118719719014400000⟩, + ⟨5, 8, 1, 3, 4, 7, 6489781831013253562692031052745384273956044800000⟩, + ⟨5, 8, 2, 3, 5, 7, 851120761768145468349724678410301516598476800000⟩, + ⟨5, 8, 3, 3, 6, 7, -305067653265471458384832533717071602017894400000⟩, + ⟨5, 8, 4, 3, 7, 7, -62244988175261464095333908640705677151436800000⟩, + ⟨5, 8, 5, 3, 8, 7, 5147716880689218069967024473846339285811200000⟩, + ⟨5, 8, 0, 4, 2, 7, 53104522795466959425375456716164473150662246400000⟩, + ⟨5, 8, 1, 4, 3, 7, -20452737256398857653587571355846930782067097600000⟩, + ⟨5, 8, 2, 4, 4, 7, 107520815989126495341315503176222437801984000000⟩, + ⟨5, 8, 3, 4, 5, 7, -570695629817367780967314167799863239822540800000⟩, + ⟨5, 8, 4, 4, 6, 7, 73805990565715025048106024497025463300915200000⟩, + ⟨5, 8, 5, 4, 7, 7, 3075927487515382590598221352775498858496000000⟩, + ⟨5, 8, 6, 4, 8, 7, -1061338339628529364008457939311529033728000000⟩, + ⟨5, 8, 0, 5, 1, 7, 40932403802448484717964061674581542086010470400000⟩, + ⟨5, 8, 1, 5, 2, 7, -4142448297792670148745769887154602132897792000000⟩, + ⟨5, 8, 2, 5, 3, 7, 1792952656085389338460440297408083531504025600000⟩, + ⟨5, 8, 3, 5, 4, 7, 584220640572616935378432229539827286225715200000⟩, + ⟨5, 8, 4, 5, 5, 7, 38290921855794424290669927248532289565491200000⟩, + ⟨5, 8, 5, 5, 6, 7, -6832318928233013684114191567070385143808000000⟩, + ⟨5, 8, 6, 5, 7, 7, 1286468631928212811721000191050508350259200000⟩, + ⟨5, 8, 7, 5, 8, 7, 43780935301021258158975962756534186803200000⟩, + ⟨5, 8, 0, 6, 0, 7, -944163620724914507552236507446521680733877043200000⟩, + ⟨5, 8, 1, 6, 1, 7, -91401994420321272433405781809183692082171084800000⟩, + ⟨5, 8, 2, 6, 2, 7, -1199873956091480108893644828498404807226163200000⟩, + ⟨5, 8, 3, 6, 3, 7, 777152167189681489336317143538208124751052800000⟩, + ⟨5, 8, 4, 6, 4, 7, -74315958307040907630361504400585875940966400000⟩, + ⟨5, 8, 5, 6, 5, 7, 13848943639674235370421748259700994159411200000⟩, + ⟨5, 8, 6, 6, 6, 7, -837690229189808608397960555858464918732800000⟩, + ⟨5, 8, 7, 6, 7, 7, -144668900605528690726523312521027466035200000⟩, + ⟨5, 8, 8, 6, 8, 7, 132101570599716554780251135319857535385600000⟩, + ⟨5, 8, 1, 7, 0, 7, 572508894705049354732502102707666866972445900800000⟩, + ⟨5, 8, 2, 7, 1, 7, 17697377189418538495681845764078590772851507200000⟩, + ⟨5, 8, 3, 7, 2, 7, 2860677569180780356307408466595038241593753600000⟩, + ⟨5, 8, 4, 7, 3, 7, 270483934461224477653841781880442079254937600000⟩, + ⟨5, 8, 5, 7, 4, 7, 41879612273754051214387512871079773628006400000⟩, + ⟨5, 8, 6, 7, 5, 7, 865702681650336208971960956285966352384000000⟩, + ⟨5, 8, 7, 7, 6, 7, 362306179295583671748076931615002774732800000⟩, + ⟨5, 8, 8, 7, 7, 7, 100026987030935563658872241668024487116800000⟩ +] + +def collectedFourData_8_6_33 : List CollectedFourTerm := [ + ⟨6, 0, 2, 0, 8, 0, 96839387526443055927008989070992386946430612275200000⟩, + ⟨6, 0, 2, 1, 7, 0, 44392370846975345031956398502239565622426992640000000⟩, + ⟨6, 0, 3, 1, 8, 0, 1684388616435610782438564603461337943802432716800000⟩, + ⟨6, 0, 2, 2, 6, 0, 93516182631849173611800840837402070397865059942400000⟩, + ⟨6, 0, 3, 2, 7, 0, -60520074080831753249937809854251724722976220774400000⟩, + ⟨6, 0, 4, 2, 8, 0, 10121027661134829181201931171801104994365184409600000⟩, + ⟨6, 0, 2, 3, 5, 0, -23175452927329632002610069161673304953407825510400000⟩, + ⟨6, 0, 3, 3, 6, 0, 66454316289662486012033597790043656816757938585600000⟩, + ⟨6, 0, 4, 3, 7, 0, 61016028389627582910861807202387583143850174054400000⟩, + ⟨6, 0, 5, 3, 8, 0, -16820269312259859752041492315510656691372818432000000⟩, + ⟨6, 0, 2, 4, 4, 0, -2927720391272604837067031105611072586857316352000000⟩, + ⟨6, 0, 3, 4, 5, 0, 124317303008224211701855752915182174332968448819200000⟩, + ⟨6, 0, 4, 4, 6, 0, -72348771326011050539878723145281226190295243161600000⟩, + ⟨6, 0, 5, 4, 7, 0, -10050655450589673711663550246772812880082370560000000⟩, + ⟨6, 0, 6, 4, 8, 0, 9536847513915361498054624407140017122280734720000000⟩, + ⟨6, 0, 2, 5, 3, 0, -48820909732850488778722204880746900760692575436800000⟩, + ⟨6, 0, 3, 5, 4, 0, -127263519471784436565733599157568784289460178124800000⟩, + ⟨6, 0, 4, 5, 5, 0, -37534909130992856097620961788648251808441538969600000⟩, + ⟨6, 0, 5, 5, 6, 0, 22324740669254390012638607823428707943322746880000000⟩, + ⟨6, 0, 6, 5, 7, 0, -11559796453248638452596835379828638219876958208000000⟩, + ⟨6, 0, 7, 5, 8, 0, -944163620724914507552236507446521680733877043200000⟩, + ⟨6, 0, 2, 6, 2, 0, 32671770725412026929467832738792073781669632409600000⟩, + ⟨6, 0, 3, 6, 3, 0, -169290697885553621546513011763672709255887270707200000⟩, + ⟨6, 0, 4, 6, 4, 0, 72848670307354275793756966959462405646132130611200000⟩, + ⟨6, 0, 5, 6, 5, 0, -45251704223181873532056442908828613696586514432000000⟩, + ⟨6, 0, 6, 6, 6, 0, 7527216987634834426772933919889995708468559872000000⟩, + ⟨6, 0, 7, 6, 7, 0, 3119876541304099232388725210124208338459898675200000⟩, + ⟨6, 0, 8, 6, 8, 0, -6172517224917796113834461295096105816417946828800000⟩, + ⟨6, 0, 2, 7, 1, 0, -481887824165537626811618951032655263173833234841600000⟩, + ⟨6, 0, 3, 7, 2, 0, -623154798452697973021961345617935884400183371366400000⟩, + ⟨6, 0, 4, 7, 3, 0, -265143522520315969710755199665491753377528073420800000⟩, + ⟨6, 0, 5, 7, 4, 0, -136842482495512131712853054060087504814791983104000000⟩, + ⟨6, 0, 6, 7, 5, 0, -7778927943163264811551693896041957131718492160000000⟩, + ⟨6, 0, 7, 7, 6, 0, -7813362407695042434825547292023486691601599692800000⟩, + ⟨6, 0, 8, 7, 7, 0, -4673814986469233833696791802708409630522238566400000⟩ +] + +def collectedFourData_8_6_34 : List CollectedFourTerm := [ + ⟨6, 1, 1, 0, 7, 1, -92520504427112063828990209408141151867343627878400000⟩, + ⟨6, 1, 2, 0, 8, 1, 56248596942742023678648142020373229550684654796800000⟩, + ⟨6, 1, 1, 1, 6, 1, -45196908806069335259821094634368170928686655078400000⟩, + ⟨6, 1, 2, 1, 7, 1, 25785051298702317579830847244377755133683957760000000⟩, + ⟨6, 1, 3, 1, 8, 1, 489183682388318187630356905723801675912288665600000⟩, + ⟨6, 1, 1, 2, 5, 1, -26892247504014984314137153949247117151758503116800000⟩, + ⟨6, 1, 2, 2, 6, 1, 54318332641730034202957333476735199553888295321600000⟩, + ⟨6, 1, 3, 2, 7, 1, -17576367121219390339041408426007049295201357004800000⟩, + ⟨6, 1, 4, 2, 8, 1, 1959580084436421939057411838304143845767302348800000⟩, + ⟨6, 1, 1, 3, 4, 1, -14663200163147272148210570626669551959086517452800000⟩, + ⟨6, 1, 2, 3, 5, 1, -13461327502911938447691931228387603656069454233600000⟩, + ⟨6, 1, 3, 3, 6, 1, 19299802216644695704802954364625408628123448115200000⟩, + ⟨6, 1, 4, 3, 7, 1, 11813602142681538390928795699773127344419713843200000⟩, + ⟨6, 1, 5, 3, 8, 1, -2442488984028657598763397910867503944168374272000000⟩, + ⟨6, 1, 1, 4, 3, 1, 46211504189812194292816524493358915394180061593600000⟩, + ⟨6, 1, 2, 4, 4, 1, -1700549419571370155279429811592840027589050368000000⟩, + ⟨6, 1, 3, 4, 5, 1, 36104492441202748995098441672642385657637267046400000⟩, + ⟨6, 1, 4, 4, 6, 1, -14007788158539591433739567671899376275260493004800000⟩, + ⟨6, 1, 5, 4, 7, 1, -1459466240676658522498786817789913533786357760000000⟩, + ⟨6, 1, 6, 4, 8, 1, 1107884520166212761814852119890347509359312896000000⟩, + ⟨6, 1, 1, 5, 2, 1, 9359567106825069650872332632411131927553114112000000⟩, + ⟨6, 1, 2, 5, 3, 1, -28357342441795633196949021917403247073318613811200000⟩, + ⟨6, 1, 3, 5, 4, 1, -36960138819178952484801438933397645390702549401600000⟩, + ⟨6, 1, 4, 5, 5, 1, -7267311469434048425085561663251152876149198028800000⟩, + ⟨6, 1, 5, 5, 6, 1, 3241799054680201036105044428455968837709332480000000⟩, + ⟨6, 1, 6, 5, 7, 1, -1342888153358820285401205621985886161709983334400000⟩, + ⟨6, 1, 7, 5, 8, 1, -91401994420321272433405781809183692082171084800000⟩, + ⟨6, 1, 1, 6, 1, 1, 206516301224688097497570037709702118627221490892800000⟩, + ⟨6, 1, 2, 6, 2, 1, 18977208653220404738525207993691064559118739046400000⟩, + ⟨6, 1, 3, 6, 3, 1, -49165760310699141452772480328340999650528355942400000⟩, + ⟨6, 1, 4, 6, 4, 1, 14104575967136530000847079422305782927304792473600000⟩, + ⟨6, 1, 5, 6, 5, 1, -6571047527347537034037683390337293439857590272000000⟩, + ⟨6, 1, 6, 6, 6, 1, 874428071578663838172453998760414960670054809600000⟩, + ⟨6, 1, 7, 6, 7, 1, 302027034256440349909691505213270366589078732800000⟩, + ⟨6, 1, 8, 6, 8, 1, -512181550407336815378729799331797883929860505600000⟩, + ⟨6, 1, 1, 7, 0, 1, -1293543101576290892641866375251848342936862117068800000⟩, + ⟨6, 1, 2, 7, 1, 1, -279901749540710467794649761470878261003843692134400000⟩, + ⟨6, 1, 3, 7, 2, 1, -180977926370766390358134104627448347784179928268800000⟩, + ⟨6, 1, 4, 7, 3, 1, -51335692742279677526147261037076331781624850022400000⟩, + ⟨6, 1, 5, 7, 4, 1, -19871040697238219368395901116838150815910723584000000⟩, + ⟨6, 1, 6, 7, 5, 1, -903669041488195824444289888002073362419417088000000⟩, + ⟨6, 1, 7, 7, 6, 1, -756391044429112202135195184389517925657293619200000⟩, + ⟨6, 1, 8, 7, 7, 1, -387822620635738874114228989141808312134454476800000⟩ +] + +def collectedFourData_8_6_35 : List CollectedFourTerm := [ + ⟨6, 2, 0, 0, 6, 2, 3203500725727113238130428457780078289673519104000000⟩, + ⟨6, 2, 1, 0, 7, 2, -8501899882974526612610205369811385687578194739200000⟩, + ⟨6, 2, 2, 0, 8, 2, 2584399764820363991367047680555048631123784499200000⟩, + ⟨6, 2, 0, 1, 5, 2, 4892005502403119539362941203223474913114115276800000⟩, + ⟨6, 2, 1, 1, 6, 2, -4153237123689183030157903883761106309296108339200000⟩, + ⟨6, 2, 2, 1, 7, 2, 1184720759881033190521313466255685033855549440000000⟩, + ⟨6, 2, 3, 1, 8, 2, 14984032342534246821780668153748373380897177600000⟩, + ⟨6, 2, 0, 2, 4, 2, 1393976510242080351092878782124336233119219712000000⟩, + ⟨6, 2, 1, 2, 5, 2, -2471184061554987593886219655141270056996333158400000⟩, + ⟨6, 2, 2, 2, 6, 2, 2495711781888903064169247939759034815218083430400000⟩, + ⟨6, 2, 3, 2, 7, 2, -538376202825885811632651899790818761077738700800000⟩, + ⟨6, 2, 4, 2, 8, 2, 45017463409081790783378069709039551458679193600000⟩, + ⟨6, 2, 0, 3, 3, 2, 247933620822126944001208363860013270552490803200000⟩, + ⟨6, 2, 1, 3, 4, 2, -1347431691202087724388102566547642293625972326400000⟩, + ⟨6, 2, 2, 3, 5, 2, -618494567395330032697383941897085572222445158400000⟩, + ⟨6, 2, 3, 3, 6, 2, 591166204086827410157641697861660315934208819200000⟩, + ⟨6, 2, 4, 3, 7, 2, 271394063662658694338365393608655260248073830400000⟩, + ⟨6, 2, 5, 3, 8, 2, -44889069587464630899897048843413935344530227200000⟩, + ⟨6, 2, 0, 4, 2, 2, -1837625126801424468426504997279406314130453299200000⟩, + ⟨6, 2, 1, 4, 3, 2, 4246470385091313496702743306749788995124513996800000⟩, + ⟨6, 2, 2, 4, 4, 2, -78133495924874737398129358000374933557870592000000⟩, + ⟨6, 2, 3, 4, 5, 2, 1105905413296926059112733528840600945997276774400000⟩, + ⟨6, 2, 4, 4, 6, 2, -321801132741449204211838170247132439123696025600000⟩, + ⟨6, 2, 5, 4, 7, 2, -26822672309551449798903320783216947312459776000000⟩, + ⟨6, 2, 6, 4, 8, 2, 16967632077295953986070554339235833114001408000000⟩, + ⟨6, 2, 0, 5, 1, 2, -1416421987586002827948805219395032175902667571200000⟩, + ⟨6, 2, 1, 5, 2, 2, 860069916208649828997929955768833037677101056000000⟩, + ⟨6, 2, 2, 5, 3, 2, -1302907327841599279836426486029781578959080652800000⟩, + ⟨6, 2, 3, 5, 4, 2, -1132114449826460726602721841111314948700084633600000⟩, + ⟨6, 2, 4, 5, 5, 2, -166952058125115214774030271474330552535456153600000⟩, + ⟨6, 2, 5, 5, 6, 2, 59579119621695377868748360823815309778485248000000⟩, + ⟨6, 2, 6, 5, 7, 2, -20566793463034742938838615371789868855407411200000⟩, + ⟨6, 2, 7, 5, 8, 2, -1199873956091480108893644828498404807226163200000⟩, + ⟨6, 2, 0, 6, 0, 2, 32671770725412026929467832738792073781669632409600000⟩, + ⟨6, 2, 1, 6, 1, 2, 18977208653220404738525207993691064559118739046400000⟩, + ⟨6, 2, 2, 6, 2, 2, 871927412345139730542715657227713466798283161600000⟩, + ⟨6, 2, 3, 6, 3, 2, -1505981023414437470398680217254285465784575590400000⟩, + ⟨6, 2, 4, 6, 4, 2, 324024640556497760468096330654496050086359859200000⟩, + ⟨6, 2, 5, 6, 5, 2, -120765420702581207714829718719697155351851827200000⟩, + ⟨6, 2, 6, 6, 6, 2, 13392166355370891982569106405946616961617100800000⟩, + ⟨6, 2, 7, 6, 7, 2, 3964840972433764022449093595974908148658995200000⟩, + ⟨6, 2, 8, 6, 8, 2, -5883177316251487927792202035712973824694681600000⟩, + ⟨6, 2, 1, 7, 0, 2, -118866342245009008761183540882640983557830764134400000⟩, + ⟨6, 2, 2, 7, 1, 2, -12860374391599128600533131526461712148792449433600000⟩, + ⟨6, 2, 3, 7, 2, 2, -5543478246831037451595082741108954029448023244800000⟩, + ⟨6, 2, 4, 7, 3, 2, -1179335658675102702178597252205659192759733452800000⟩, + ⟨6, 2, 5, 7, 4, 2, -365198178770251691988233726454693626567353958400000⟩, + ⟨6, 2, 6, 7, 5, 2, -13840001856253045949739313775801707133927424000000⟩, + ⟨6, 2, 7, 7, 6, 2, -9929476053419090017710521974863824329428172800000⟩, + ⟨6, 2, 8, 7, 7, 2, -4454727513396003100104053043541597167078604800000⟩ +] + +def collectedFourData_8_6_36 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 6, 3, -16599127059660804895701488488490053494613475328000000⟩, + ⟨6, 3, 1, 0, 7, 3, 22026546657637779657189746070810180600397509427200000⟩, + ⟨6, 3, 2, 0, 8, 3, -4463739696253051578569712056231126078392683724800000⟩, + ⟨6, 3, 0, 1, 5, 3, -25348213677247771039587316466869066325019957657600000⟩, + ⟨6, 3, 1, 1, 6, 3, 10760120978179156577466149363998376999032927027200000⟩, + ⟨6, 3, 2, 1, 7, 3, -2046233387280788870872819148065381385880207360000000⟩, + ⟨6, 3, 3, 1, 8, 3, -19410160790843847516364251820915817930607820800000⟩, + ⟨6, 3, 0, 2, 4, 3, -7222971115899758437462017305020338326716022784000000⟩, + ⟨6, 3, 1, 2, 5, 3, 6402292638196531584818934058235765116375557734400000⟩, + ⟨6, 3, 2, 2, 6, 3, -4310559033036541811928901003653635173921692057600000⟩, + ⟨6, 3, 3, 2, 7, 3, 697406974566567305660972149330112463950472806400000⟩, + ⟨6, 3, 4, 2, 8, 3, -46652125846568853734190861794001423004902359040000⟩, + ⟨6, 3, 0, 3, 3, 3, -1284682610288511546946805374727029804312716902400000⟩, + ⟨6, 3, 1, 3, 4, 3, 3490898201903878053627087183319637789342328422400000⟩, + ⟨6, 3, 2, 3, 5, 3, 1068255302442070194709273584706370014459566489600000⟩, + ⟨6, 3, 3, 3, 6, 3, -765790597158937184876410898298589665279187353600000⟩, + ⟨6, 3, 4, 3, 7, 3, -281248854404529362531886026488753004418233794560000⟩, + ⟨6, 3, 5, 3, 8, 3, 38765891518210799502675054181272224843327078400000⟩, + ⟨6, 3, 0, 4, 2, 3, 9521762465303872579895130152734650691532252774400000⟩, + ⟨6, 3, 1, 4, 3, 3, -11001667786608436601895567059498880369834118348800000⟩, + ⟨6, 3, 2, 4, 4, 3, 134951098554650843786760345134756435903643648000000⟩, + ⟨6, 3, 3, 4, 5, 3, -1432578454240539029819862670863209718564991795200000⟩, + ⟨6, 3, 4, 4, 6, 3, 333486291881870987411928354355841678763192483840000⟩, + ⟨6, 3, 5, 4, 7, 3, 23163875182455462372246901154238063257321472000000⟩, + ⟨6, 3, 6, 4, 8, 3, -12559825946958387160926405234197995620139008000000⟩, + ⟨6, 3, 0, 5, 1, 3, 7339273674333529975387015773616140424785061478400000⟩, + ⟨6, 3, 1, 5, 2, 3, -2228251378981476323307509039648202116768464896000000⟩, + ⟨6, 3, 2, 5, 3, 3, 2250363600474086019247597291732167587657888563200000⟩, + ⟨6, 3, 3, 5, 4, 3, 1466529369560395307639115980540181391877131468800000⟩, + ⟨6, 3, 4, 5, 5, 3, 173014377891964315609385674295654017752146903040000⟩, + ⟨6, 3, 5, 5, 6, 3, -51452117614175695719110844282445294422982656000000⟩, + ⟨6, 3, 6, 5, 7, 3, 15224006803424530759385608627826195443168051200000⟩, + ⟨6, 3, 7, 5, 8, 3, 777152167189681489336317143538208124751052800000⟩, + ⟨6, 3, 0, 6, 0, 3, -169290697885553621546513011763672709255887270707200000⟩, + ⟨6, 3, 1, 6, 1, 3, -49165760310699141452772480328340999650528355942400000⟩, + ⟨6, 3, 2, 6, 2, 3, -1505981023414437470398680217254285465784575590400000⟩, + ⟨6, 3, 3, 6, 3, 3, 1950832268925142614634032701567966060093846323200000⟩, + ⟨6, 3, 4, 6, 4, 3, -335790539135116888830798756531145184790844538880000⟩, + ⟨6, 3, 5, 6, 5, 3, 104292186074061396411253262150150332086642278400000⟩, + ⟨6, 3, 6, 6, 6, 3, -9913185158065743177042361343883494294342860800000⟩, + ⟨6, 3, 7, 6, 7, 3, -2568007029943753818677716181938561111346380800000⟩, + ⟨6, 3, 8, 6, 8, 3, 3387114290407596566879061572802714373246156800000⟩, + ⟨6, 3, 1, 7, 0, 3, 307956464969146036485184365370618340307548661350400000⟩, + ⟨6, 3, 2, 7, 1, 3, 22212261609785179388566107380505659142180333158400000⟩, + ⟨6, 3, 3, 7, 2, 3, 7180964486181645469016275635131340115807725158400000⟩, + ⟨6, 3, 4, 7, 3, 3, 1222159388766397409001829854066406841535871057920000⟩, + ⟨6, 3, 5, 7, 4, 3, 315382633477642161913713468078278451066096844800000⟩, + ⟨6, 3, 6, 7, 5, 3, 10244683148965435581287470235193294899380224000000⟩, + ⟨6, 3, 7, 7, 6, 3, 6431270380356816460356704271825540220138291200000⟩, + ⟨6, 3, 8, 7, 7, 3, 2564714678718771662832441662171871099381350400000⟩ +] + +def collectedFourData_8_6_37 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 6, 4, 7142887055593512404484928110092692723794444288000000⟩, + ⟨6, 4, 1, 0, 7, 4, -6318932091419770846120769480607523349684079820800000⟩, + ⟨6, 4, 2, 0, 8, 4, 960411604215901846149670659871519521741629030400000⟩, + ⟨6, 4, 0, 1, 5, 4, 10907768023394562325111359723529458059648276889600000⟩, + ⟨6, 4, 1, 1, 6, 4, -3086842200613356146195398465949825114162646220800000⟩, + ⟨6, 4, 2, 1, 7, 4, 440264536869864906160098576487898305297121280000000⟩, + ⟨6, 4, 3, 1, 8, 4, 3341009096721508847249145414592706302936350720000⟩, + ⟨6, 4, 0, 2, 4, 4, 3108167477798708251282371637928991010968305664000000⟩, + ⟨6, 4, 1, 2, 5, 4, -1836677035168945881855476047303860477484439961600000⟩, + ⟨6, 4, 2, 2, 6, 4, 927453480197577855839974694383996250866109644800000⟩, + ⟨6, 4, 3, 2, 7, 4, -120042439176652993292129905315810234104293621760000⟩, + ⟨6, 4, 4, 2, 8, 4, 6691734744597780229766819886950311349484257280000⟩, + ⟨6, 4, 0, 3, 3, 4, 552820805250430327125405837567698312301536870400000⟩, + ⟨6, 4, 1, 3, 4, 4, -1001461963999746814885434061669648604147063193600000⟩, + ⟨6, 4, 2, 3, 5, 4, -229844224472082567627830545401137498549963980800000⟩, + ⟨6, 4, 3, 3, 6, 4, 131813094124326181393472212652242678541702922240000⟩, + ⟨6, 4, 4, 3, 7, 4, 40342057232007811495197921568913554002589777920000⟩, + ⟨6, 4, 5, 3, 8, 4, -4766178085815359548725315872027818286540390400000⟩, + ⟨6, 4, 0, 4, 2, 4, -4097376543682232184329323765171468677889287782400000⟩, + ⟨6, 4, 1, 4, 3, 4, 3156136670740135881967296277263319292500456243200000⟩, + ⟨6, 4, 2, 4, 4, 4, -29035877957302579031664547600802115175317504000000⟩, + ⟨6, 4, 3, 4, 5, 4, 246585162223006933832312154704787347590537543680000⟩, + ⟨6, 4, 4, 4, 6, 4, -47834943547317928499131579249756212418188410880000⟩, + ⟨6, 4, 5, 4, 7, 4, -2847945705706732420213062897708059099922432000000⟩, + ⟨6, 4, 6, 4, 8, 4, 1351176749454766853971220473128518934331392000000⟩, + ⟨6, 4, 0, 5, 1, 4, -3158214449316135173846055416506815009926833766400000⟩, + ⟨6, 4, 1, 5, 2, 4, 639236343547029069114176433862225496578719744000000⟩, + ⟨6, 4, 2, 5, 3, 4, -484184890399098670738178255530917594475895193600000⟩, + ⟨6, 4, 3, 5, 4, 4, -252429025040422066139305374982826192524982353920000⟩, + ⟨6, 4, 4, 5, 5, 4, -24817011076029635177338710413968002451274465280000⟩, + ⟨6, 4, 5, 5, 6, 4, 6325920695678534523476291101050407523188736000000⟩, + ⟨6, 4, 6, 5, 7, 4, -1637787347786449878459226198668717115362508800000⟩, + ⟨6, 4, 7, 5, 8, 4, -74315958307040907630361504400585875940966400000⟩, + ⟨6, 4, 0, 6, 0, 4, 72848670307354275793756966959462405646132130611200000⟩, + ⟨6, 4, 1, 6, 1, 4, 14104575967136530000847079422305782927304792473600000⟩, + ⟨6, 4, 2, 6, 2, 4, 324024640556497760468096330654496050086359859200000⟩, + ⟨6, 4, 3, 6, 3, 4, -335790539135116888830798756531145184790844538880000⟩, + ⟨6, 4, 4, 6, 4, 4, 48165462492058013855729814243253808286306140160000⟩, + ⟨6, 4, 5, 6, 5, 4, -12822486787243407217516115284111753384191590400000⟩, + ⟨6, 4, 6, 6, 6, 4, 1066453098568794057076041336531908599952179200000⟩, + ⟨6, 4, 7, 6, 7, 4, 245568257320330173696894144190073903933030400000⟩, + ⟨6, 4, 8, 6, 8, 4, -291506592290192573330007898337734499562946560000⟩, + ⟨6, 4, 1, 7, 0, 4, -88345940900316234114548545330143390895194085785600000⟩, + ⟨6, 4, 2, 7, 1, 4, -4779157221874817236539038562938119730058441523200000⟩, + ⟨6, 4, 3, 7, 2, 4, -1236036523864568505616893165860381506002286018560000⟩, + ⟨6, 4, 4, 7, 3, 4, -175305332754648431516548280910826876404435517440000⟩, + ⟨6, 4, 5, 7, 4, 4, -38775576607640801968682474968610461029551308800000⟩, + ⟨6, 4, 6, 7, 5, 4, -1102115406285972510437546457039028120190976000000⟩, + ⟨6, 4, 7, 7, 6, 4, -614996704154143857777739753999155211114905600000⟩, + ⟨6, 4, 8, 7, 7, 4, -220728080628178979592463790332061186449735680000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0829.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0829.lean new file mode 100644 index 0000000000000000000000000000000000000000..c808e42e5485e4d580368edeb2eed6463bae9f5b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0829.lean @@ -0,0 +1,638 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0829. -/ +namespace LaughlinFock +def collectedFourData_8_6_38 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 6, 5, -4436976144871121098329940991931386999529799680000000⟩, + ⟨6, 5, 1, 0, 7, 5, 2943867521543830032918569477355700770954018816000000⟩, + ⟨6, 5, 2, 0, 8, 5, -357949664666168953001094700524367101104121446400000⟩, + ⟨6, 5, 0, 1, 5, 5, -6775622537065060420845784031733860217919635456000000⟩, + ⟨6, 5, 1, 1, 6, 5, 1438099724296098721136032147245437759904546816000000⟩, + ⟨6, 5, 2, 1, 7, 5, -164088545624806195618496976574343855713812480000000⟩, + ⟨6, 5, 3, 1, 8, 5, -1037674090782540169355348226616983687895449600000⟩, + ⟨6, 5, 0, 2, 4, 5, -1930713008048705075350227313975515507893207040000000⟩, + ⟨6, 5, 1, 2, 5, 5, 855672096672970632479519368494943808658604032000000⟩, + ⟨6, 5, 2, 2, 6, 5, -345666025663268045936981753844427012730309836800000⟩, + ⟨6, 5, 3, 2, 7, 5, 37283624594193954191224195001661635078966476800000⟩, + ⟨6, 5, 4, 2, 8, 5, -1781456585421368614041414348929357707424563200000⟩, + ⟨6, 5, 0, 3, 3, 5, -343397943463743069799749692676619636146438144000000⟩, + ⟨6, 5, 1, 3, 4, 5, 466561644788611800419599215343120471579164672000000⟩, + ⟨6, 5, 2, 3, 5, 5, 85663961903507583306014189264664365212945612800000⟩, + ⟨6, 5, 3, 3, 6, 5, -40939437349306573660110167249403951189275443200000⟩, + ⟨6, 5, 4, 3, 7, 5, -10739759758622322529830372966815816131333324800000⟩, + ⟨6, 5, 5, 3, 8, 5, 1110234820198330419436661321115508622229504000000⟩, + ⟨6, 5, 0, 4, 2, 5, 2545184018643558264520293940119206343909310464000000⟩, + ⟨6, 5, 1, 4, 3, 5, -1470382669749146254306914719623815433461694464000000⟩, + ⟨6, 5, 2, 4, 4, 5, 10821800499369870402486526666905968562929664000000⟩, + ⟨6, 5, 3, 4, 5, 5, -76586153046189223764699375152344403397731942400000⟩, + ⟨6, 5, 4, 4, 6, 5, 12734496875331688462772568020591987242775347200000⟩, + ⟨6, 5, 5, 4, 7, 5, 663401247620190584172361824247667302072320000000⟩, + ⟨6, 5, 6, 4, 8, 5, -279771981934605371182487890754605720535040000000⟩, + ⟨6, 5, 0, 5, 1, 5, 1961800888483826510405224076009019367388872704000000⟩, + ⟨6, 5, 1, 5, 2, 5, -297807775607177626244574535062644516066426880000000⟩, + ⟨6, 5, 2, 5, 3, 5, 180457856187899570907845468916156626441443737600000⟩, + ⟨6, 5, 3, 5, 4, 5, 78401181039279603011215105427636827671075225600000⟩, + ⟨6, 5, 4, 5, 5, 5, 6606721500364161969998380293870550928012083200000⟩, + ⟨6, 5, 5, 5, 6, 5, -1473561688149567425650214666923335336591360000000⟩, + ⟨6, 5, 6, 5, 7, 5, 339117004834884652187558225653028414816256000000⟩, + ⟨6, 5, 7, 5, 8, 5, 13848943639674235370421748259700994159411200000⟩, + ⟨6, 5, 0, 6, 0, 5, -45251704223181873532056442908828613696586514432000000⟩, + ⟨6, 5, 1, 6, 1, 5, -6571047527347537034037683390337293439857590272000000⟩, + ⟨6, 5, 2, 6, 2, 5, -120765420702581207714829718719697155351851827200000⟩, + ⟨6, 5, 3, 6, 3, 5, 104292186074061396411253262150150332086642278400000⟩, + ⟨6, 5, 4, 6, 4, 5, -12822486787243407217516115284111753384191590400000⟩, + ⟨6, 5, 5, 6, 5, 5, 2986873561249920398654265919125632795541504000000⟩, + ⟨6, 5, 6, 6, 6, 5, -220817666635612019851779031005335654498304000000⟩, + ⟨6, 5, 7, 6, 7, 5, -45762189343928102198795867223764535292723200000⟩, + ⟨6, 5, 8, 6, 8, 5, 49384454492888084834380789224861458025676800000⟩, + ⟨6, 5, 1, 7, 0, 5, 41158655024924595718667167002830766816217792512000000⟩, + ⟨6, 5, 2, 7, 1, 5, 1781213093893879323897537586050999646170592051200000⟩, + ⟨6, 5, 3, 7, 2, 5, 383896912263357878446615041542799039493098700800000⟩, + ⟨6, 5, 4, 7, 3, 5, 46669339328993999705201094619568266892908953600000⟩, + ⟨6, 5, 5, 7, 4, 5, 9032393365911342062685141538387144671756288000000⟩, + ⟨6, 5, 6, 7, 5, 5, 228201833447557888865866652679738092421120000000⟩, + ⟨6, 5, 7, 7, 6, 5, 114605999686196843775608308564099915893964800000⟩, + ⟨6, 5, 8, 7, 7, 5, 37393788481577243870409563618578509751910400000⟩ +] + +def collectedFourData_8_6_39 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 6, 6, 738051368113888788940688436916482263513825280000000⟩, + ⟨6, 6, 1, 0, 7, 6, -391748863348387813094096476707294086555290828800000⟩, + ⟨6, 6, 2, 0, 8, 6, 39694487280961387841287843633759300794030489600000⟩, + ⟨6, 6, 0, 1, 5, 6, 1127064315882054579947681201940197046774398976000000⟩, + ⟨6, 6, 1, 1, 6, 6, -191372039757815142734593586098147179121921228800000⟩, + ⟨6, 6, 2, 1, 7, 6, 18196443048298032494516228523266113504542720000000⟩, + ⟨6, 6, 3, 1, 8, 6, 98633040334871695031560346577224005268275200000⟩, + ⟨6, 6, 0, 2, 4, 6, 321156871368984721601496504538238776340643840000000⟩, + ⟨6, 6, 1, 2, 5, 6, -113866731032372400872761335225740057386785177600000⟩, + ⟨6, 6, 2, 2, 6, 6, 38332304828243321813385679329176620635468595200000⟩, + ⟨6, 6, 3, 2, 7, 6, -3543884617622200191419826582573153299044761600000⟩, + ⟨6, 6, 4, 2, 8, 6, 148164699017547738296539395455044952889753600000⟩, + ⟨6, 6, 0, 3, 3, 6, 57121182018046013671460642155384417365786624000000⟩, + ⟨6, 6, 1, 3, 4, 6, -62086691296502921638323204281266451418552729600000⟩, + ⟨6, 6, 2, 3, 5, 6, -9499623499820322232666766304044267255051059200000⟩, + ⟨6, 6, 3, 3, 6, 6, 3891377081908202169892561781776121330034278400000⟩, + ⟨6, 6, 4, 3, 7, 6, 893231575318276877915244739739139430573670400000⟩, + ⟨6, 6, 5, 3, 8, 6, -82078955599048329313730249064321650786304000000⟩, + ⟨6, 6, 0, 4, 2, 6, -423368637947916416416003645149551104930873344000000⟩, + ⟨6, 6, 1, 4, 3, 6, 195668023559469745370158246865162070954029875200000⟩, + ⟨6, 6, 2, 4, 4, 6, -1200073263596882064939569718386223476637696000000⟩, + ⟨6, 6, 3, 4, 5, 6, 7279670167731377118386795378175399500238028800000⟩, + ⟨6, 6, 4, 4, 6, 6, -1059134930435105465696543591439094005733785600000⟩, + ⟨6, 6, 5, 4, 7, 6, -49044833180465198132899206098135097016320000000⟩, + ⟨6, 6, 6, 4, 8, 6, 18615028549608520289083247156088312692736000000⟩, + ⟨6, 6, 0, 5, 1, 6, -326328062724932124132377729815071281469456384000000⟩, + ⟨6, 6, 1, 5, 2, 6, 39630131701456926246913980185207340672221184000000⟩, + ⟨6, 6, 2, 5, 3, 6, -20011702158963233783386267087385558365136486400000⟩, + ⟨6, 6, 3, 5, 4, 6, -7452192283144704163104250456643404454638387200000⟩, + ⟨6, 6, 4, 5, 5, 6, -549484568192652260241348823948746915682713600000⟩, + ⟨6, 6, 5, 5, 6, 6, 108939480345681315053654380760364597903360000000⟩, + ⟨6, 6, 6, 5, 7, 6, -22563634439043466862681700482127894046310400000⟩, + ⟨6, 6, 7, 5, 8, 6, -837690229189808608397960555858464918732800000⟩, + ⟨6, 6, 0, 6, 0, 6, 7527216987634834426772933919889995708468559872000000⟩, + ⟨6, 6, 1, 6, 1, 6, 874428071578663838172453998760414960670054809600000⟩, + ⟨6, 6, 2, 6, 2, 6, 13392166355370891982569106405946616961617100800000⟩, + ⟨6, 6, 3, 6, 3, 6, -9913185158065743177042361343883494294342860800000⟩, + ⟨6, 6, 4, 6, 4, 6, 1066453098568794057076041336531908599952179200000⟩, + ⟨6, 6, 5, 6, 5, 6, -220817666635612019851779031005335654498304000000⟩, + ⟨6, 6, 6, 6, 6, 6, 14692418948658911254176778653855618013593600000⟩, + ⟨6, 6, 7, 6, 7, 6, 2768047865392589701851380600819680070860800000⟩, + ⟨6, 6, 8, 6, 8, 6, -2738221032520548575484071296818749217177600000⟩, + ⟨6, 6, 1, 7, 0, 6, -5477099837192031530549272068518453011044473241600000⟩, + ⟨6, 6, 2, 7, 1, 6, -197525930262269593721799669340560968202898636800000⟩, + ⟨6, 6, 3, 7, 2, 6, -36490185086099087497760492376328040171018649600000⟩, + ⟨6, 6, 4, 7, 3, 6, -3881513965378309307588843961496636041776332800000⟩, + ⟨6, 6, 5, 7, 4, 6, -667759108745426296921780403372091022245888000000⟩, + ⟨6, 6, 6, 7, 5, 6, -15183735037814592020470621511068164292608000000⟩, + ⟨6, 6, 7, 7, 6, 6, -6932249032238508629968837648953870857011200000⟩, + ⟨6, 6, 8, 7, 7, 6, -2073374286651786323929729935913970879692800000⟩ +] + +def collectedFourData_8_6_40 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 6, 7, 305907103971960672057882338657870775633051648000000⟩, + ⟨6, 7, 1, 0, 7, 7, -135309868491340058570159944423264800072951398400000⟩, + ⟨6, 7, 2, 0, 8, 7, 11751820084596609738364722619723290962716262400000⟩, + ⟨6, 7, 0, 1, 5, 7, 467144965455054643000729861946886694037461401600000⟩, + ⟨6, 7, 1, 1, 6, 7, -66099810248896880184606835476847392004138598400000⟩, + ⟨6, 7, 2, 1, 7, 7, 5387179417877796723156723993878334202183680000000⟩, + ⟨6, 7, 3, 1, 8, 7, 25550853426619365968833450604439603983155200000⟩, + ⟨6, 7, 0, 2, 4, 7, 133112914203041677957069236288239266896543744000000⟩, + ⟨6, 7, 1, 2, 5, 7, -39329513989750051207250681849761857375358156800000⟩, + ⟨6, 7, 2, 2, 6, 7, 11348536802627750701141244915924957259418828800000⟩, + ⟨6, 7, 3, 2, 7, 7, -918042028495619369246700554417486253627801600000⟩, + ⟨6, 7, 4, 2, 8, 7, 34117343728439046574794381294500989580083200000⟩, + ⟨6, 7, 0, 3, 3, 7, 23675554468858205544275857094109598872659558400000⟩, + ⟨6, 7, 1, 3, 4, 7, -21444713234358923922131990374150693226073292800000⟩, + ⟨6, 7, 2, 3, 5, 7, -2812427465081256178063501796336046319652044800000⟩, + ⟨6, 7, 3, 3, 6, 7, 1008059825693008692051824296730084464027238400000⟩, + ⟨6, 7, 4, 3, 7, 7, 205681170253782948393202817791519301094604800000⟩, + ⟨6, 7, 5, 3, 8, 7, -17010019010271328359178326578426474083123200000⟩, + ⟨6, 7, 0, 4, 2, 7, -175477588068389992752789654721730094490347110400000⟩, + ⟨6, 7, 1, 4, 3, 7, 67583640982378454712348814717262798314379673600000⟩, + ⟨6, 7, 2, 4, 4, 7, -355289765611595748656720432521779634765824000000⟩, + ⟨6, 7, 3, 4, 5, 7, 1885795924148118663443485770158230511340748800000⟩, + ⟨6, 7, 4, 4, 6, 7, -243883129490724872348364435585831563113267200000⟩, + ⟨6, 7, 5, 4, 7, 7, -10164037038075711712642199502920620179456000000⟩, + ⟨6, 7, 6, 4, 8, 7, 3507066482450751723950830239587141419008000000⟩, + ⟨6, 7, 0, 5, 1, 7, -135256266603871592203715083470021487329961574400000⟩, + ⟨6, 7, 1, 5, 2, 7, 13688228379235427109122931789455391260147712000000⟩, + ⟨6, 7, 2, 5, 3, 7, -5924599093422869631522196618641207891433881600000⟩, + ⟨6, 7, 3, 5, 4, 7, -1930487715750711598283353456110238252086067200000⟩, + ⟨6, 7, 4, 5, 5, 7, -126527803254143184440025281421128146039603200000⟩, + ⟨6, 7, 5, 5, 6, 7, 22576586387151889958710471353088383909888000000⟩, + ⟨6, 7, 6, 5, 7, 7, -4250982793421769176511131387209723360051200000⟩, + ⟨6, 7, 7, 5, 8, 7, -144668900605528690726523312521027466035200000⟩, + ⟨6, 7, 0, 6, 0, 7, 3119876541304099232388725210124208338459898675200000⟩, + ⟨6, 7, 1, 6, 1, 7, 302027034256440349909691505213270366589078732800000⟩, + ⟨6, 7, 2, 6, 2, 7, 3964840972433764022449093595974908148658995200000⟩, + ⟨6, 7, 3, 6, 3, 7, -2568007029943753818677716181938561111346380800000⟩, + ⟨6, 7, 4, 6, 4, 7, 245568257320330173696894144190073903933030400000⟩, + ⟨6, 7, 5, 6, 5, 7, -45762189343928102198795867223764535292723200000⟩, + ⟨6, 7, 6, 6, 6, 7, 2768047865392589701851380600819680070860800000⟩, + ⟨6, 7, 7, 6, 7, 7, 478041198949080836644534908993506849587200000⟩, + ⟨6, 7, 8, 6, 8, 7, -436513949634119213242156505505067538841600000⟩, + ⟨6, 7, 1, 7, 0, 7, -1891787642598258344422464412232566948231957708800000⟩, + ⟨6, 7, 2, 7, 1, 7, -58478880909947559030858035013924846451241779200000⟩, + ⟨6, 7, 3, 7, 2, 7, -9452769249327252737439338054938211720468889600000⟩, + ⟨6, 7, 4, 7, 3, 7, -893782034598297819757638235683591860885913600000⟩, + ⟨6, 7, 5, 7, 4, 7, -138386204492266208108221694764003403130470400000⟩, + ⟨6, 7, 6, 7, 5, 7, -2860611687359057227243260649615575220224000000⟩, + ⟨6, 7, 7, 7, 6, 7, -1197197736432528957061816846632092486860800000⟩, + ⟨6, 7, 8, 7, 7, 7, -330527297901545076398222360859036667084800000⟩ +] + +def collectedFourData_8_6_41 : List CollectedFourTerm := [ + ⟨6, 8, 0, 0, 6, 8, -605221662938744783306159099245346119653261312000000⟩, + ⟨6, 8, 1, 0, 7, 8, 229460314371939699901845431314392406144371916800000⟩, + ⟨6, 8, 2, 0, 8, 8, -17437784220618554705043331564297819100754739200000⟩, + ⟨6, 8, 0, 1, 5, 8, -924222579845956230928843140134688498070742630400000⟩, + ⟨6, 8, 1, 1, 6, 8, 112092956772093517396832131963070153759706316800000⟩, + ⟨6, 8, 2, 1, 7, 8, -7993695578256895490416006178963895814717440000000⟩, + ⟨6, 8, 3, 1, 8, 8, -33700710225589957695456118858507258901299200000⟩, + ⟨6, 8, 0, 2, 4, 8, -263357137662195974160965071112497298078171136000000⟩, + ⟨6, 8, 1, 2, 5, 8, 66695524463991526956923451322103041028102553600000⟩, + ⟨6, 8, 2, 2, 6, 8, -16839377607844306738642611225173921764894310400000⟩, + ⟨6, 8, 3, 2, 7, 8, 1210866340183031724320776122020951787936153600000⟩, + ⟨6, 8, 4, 2, 8, 8, -40499658696918539489567949259107396464148480000⟩, + ⟨6, 8, 0, 3, 3, 8, -46840881629060110001436392439195383407155609600000⟩, + ⟨6, 8, 1, 3, 4, 8, 36366236219400538050385039366596883230857625600000⟩, + ⟨6, 8, 2, 3, 5, 8, 4173183636167928270285307186308582849537638400000⟩, + ⟨6, 8, 3, 3, 6, 8, -1329596765654245642337914421869655418627686400000⟩, + ⟨6, 8, 4, 3, 7, 8, -244157847163153765773784019316774085035294720000⟩, + ⟨6, 8, 5, 3, 8, 8, 18356431844259304739642959950215084035276800000⟩, + ⟨6, 8, 0, 4, 2, 8, 347173492476217691475090782985130016429939097600000⟩, + ⟨6, 8, 1, 4, 3, 8, -114609257100928874852921520998976671278379827200000⟩, + ⟨6, 8, 2, 4, 4, 8, 527192062500147890507976316746923079892992000000⟩, + ⟨6, 8, 3, 4, 5, 8, -2487300949333613750380480363470163096161484800000⟩, + ⟨6, 8, 4, 4, 6, 8, 289506228413599057522059318114930456086446080000⟩, + ⟨6, 8, 5, 4, 7, 8, 10968562294921734830722114404040304492544000000⟩, + ⟨6, 8, 6, 4, 8, 8, -3469276425728463166833038967000400920576000000⟩, + ⟨6, 8, 0, 5, 1, 8, 267597651489599383931363668995223537365653913600000⟩, + ⟨6, 8, 1, 5, 2, 8, -23212683761460371397433256665719721137537024000000⟩, + ⟨6, 8, 2, 5, 3, 8, 8791138720732599629569251403320026781764812800000⟩, + ⟨6, 8, 3, 5, 4, 8, 2546247908682232158499856009632788839084851200000⟩, + ⟨6, 8, 4, 5, 5, 8, 150197298132333495369954811423458444422676480000⟩, + ⟨6, 8, 5, 5, 6, 8, -24363615880825258480261311533558752346112000000⟩, + ⟨6, 8, 6, 5, 7, 8, 4205176738220722047161805845619651536486400000⟩, + ⟨6, 8, 7, 5, 8, 8, 132101570599716554780251135319857535385600000⟩, + ⟨6, 8, 0, 6, 0, 8, -6172517224917796113834461295096105816417946828800000⟩, + ⟨6, 8, 1, 6, 1, 8, -512181550407336815378729799331797883929860505600000⟩, + ⟨6, 8, 2, 6, 2, 8, -5883177316251487927792202035712973824694681600000⟩, + ⟨6, 8, 3, 6, 3, 8, 3387114290407596566879061572802714373246156800000⟩, + ⟨6, 8, 4, 6, 4, 8, -291506592290192573330007898337734499562946560000⟩, + ⟨6, 8, 5, 6, 5, 8, 49384454492888084834380789224861458025676800000⟩, + ⟨6, 8, 6, 6, 6, 8, -2738221032520548575484071296818749217177600000⟩, + ⟨6, 8, 7, 6, 7, 8, -436513949634119213242156505505067538841600000⟩, + ⟨6, 8, 8, 6, 8, 8, 370123144851007436779593145375063120281600000⟩, + ⟨6, 8, 1, 7, 0, 8, 3208119201027301183218254070138059862927055257600000⟩, + ⟨6, 8, 2, 7, 1, 8, 86773121051054501812688866754994720980179353600000⟩, + ⟨6, 8, 3, 7, 2, 8, 12467882460984967671429480026098292890376601600000⟩, + ⟨6, 8, 4, 7, 3, 8, 1060981406957986579978708771381472968877015040000⟩, + ⟨6, 8, 5, 7, 4, 8, 149340040679207640977928705243535648594329600000⟩, + ⟨6, 8, 6, 7, 5, 8, 2829787441948631537142710575263412912128000000⟩, + ⟨6, 8, 7, 7, 6, 8, 1093197643993975471641576706470966617702400000⟩, + ⟨6, 8, 8, 7, 7, 8, 280256342462746186648225845555227315404800000⟩ +] + +def collectedFourData_8_6_42 : List CollectedFourTerm := [ + ⟨7, 0, 1, 0, 7, 1, 579514835130808418976469959805977336108051490406400000⟩, + ⟨7, 0, 2, 0, 8, 1, -352320781057699192905682339971848111515388136652800000⟩, + ⟨7, 0, 1, 1, 6, 1, 283097020680489389017145656772023533286694741606400000⟩, + ⟨7, 0, 2, 1, 7, 1, -161508195882988404506785860238985648747273256960000000⟩, + ⟨7, 0, 3, 1, 8, 1, -3064068908868537606899824477995537703577950617600000⟩, + ⟨7, 0, 1, 2, 5, 1, 168443270765602237059334634740384200358743559372800000⟩, + ⟨7, 0, 2, 2, 6, 1, -340230306572217999187983034108546663141000976793600000⟩, + ⟨7, 0, 3, 2, 7, 1, 110091979691662770540911989789408041353725398220800000⟩, + ⟨7, 0, 4, 2, 8, 1, -12274097904993831560462981763436732439472164044800000⟩, + ⟨7, 0, 1, 3, 4, 1, 91844959964855402509121484789085035783120538828800000⟩, + ⟨7, 0, 2, 3, 5, 1, 84316866156274702928828655644129864652659726745600000⟩, + ⟨7, 0, 3, 3, 6, 1, -120886951156294895466117528082683279826390037299200000⟩, + ⟨7, 0, 4, 3, 7, 1, -73996112974183801129528155503593493983969620787200000⟩, + ⟨7, 0, 5, 3, 8, 1, 15298863853507044787358354617125532300593856512000000⟩, + ⟨7, 0, 1, 4, 3, 1, -289452077650562755184108923850908943966310865305600000⟩, + ⟨7, 0, 2, 4, 4, 1, 10651623903445850864530587034485090019524476928000000⟩, + ⟨7, 0, 3, 4, 5, 1, -226145427049940084490182551221676678777043052134400000⟩, + ⟨7, 0, 4, 4, 6, 1, 87739697221803705618935897896182757500765654220800000⟩, + ⟨7, 0, 5, 4, 7, 1, 9141566435265432803020940007659558639983656960000000⟩, + ⟨7, 0, 6, 4, 8, 1, -6939386236851909133581534347500359186923913216000000⟩, + ⟨7, 0, 1, 5, 2, 1, -58624928845697310912003557118537302970992689152000000⟩, + ⟨7, 0, 2, 5, 3, 1, 177620093315114106746758083663497424610499179315200000⟩, + ⟨7, 0, 3, 5, 4, 1, 231504885180151564165736208309734109623986264473600000⟩, + ⟨7, 0, 4, 5, 5, 1, 45519799466410711995162252888386024804360965324800000⟩, + ⟨7, 0, 5, 5, 6, 1, -20305451816685994898844282048090900432766894080000000⟩, + ⟨7, 0, 6, 5, 7, 1, 8411363638921137159567344151887105435686561382400000⟩, + ⟨7, 0, 7, 5, 8, 1, 572508894705049354732502102707666866972445900800000⟩, + ⟨7, 0, 1, 6, 1, 1, -1293543101576290892641866375251848342936862117068800000⟩, + ⟨7, 0, 2, 6, 2, 1, -118866342245009008761183540882640983557830764134400000⟩, + ⟨7, 0, 3, 6, 3, 1, 307956464969146036485184365370618340307548661350400000⟩, + ⟨7, 0, 4, 6, 4, 1, -88345940900316234114548545330143390895194085785600000⟩, + ⟨7, 0, 5, 6, 5, 1, 41158655024924595718667167002830766816217792512000000⟩, + ⟨7, 0, 6, 6, 6, 1, -5477099837192031530549272068518453011044473241600000⟩, + ⟨7, 0, 7, 6, 7, 1, -1891787642598258344422464412232566948231957708800000⟩, + ⟨7, 0, 8, 6, 8, 1, 3208119201027301183218254070138059862927055257600000⟩, + ⟨7, 0, 1, 7, 0, 1, 8102284157293344147865610951721376430982960041164800000⟩, + ⟨7, 0, 2, 7, 1, 1, 1753202895318161592836290740537334661793293166182400000⟩, + ⟨7, 0, 3, 7, 2, 1, 1133579997347448277711605818200641288282523356364800000⟩, + ⟨7, 0, 4, 7, 3, 1, 321548133574055743350934620060488467316316989030400000⟩, + ⟨7, 0, 5, 7, 4, 1, 124464981517795189912605228983466042910115364864000000⟩, + ⟨7, 0, 6, 7, 5, 1, 5660254652020534064788940656566788617087746048000000⟩, + ⟨7, 0, 7, 7, 6, 1, 4737758771647018014347802189795800474759410483200000⟩, + ⟨7, 0, 8, 7, 7, 1, 2429180033651634398780836978479411209880521932800000⟩ +] + +def collectedFourData_8_6_43 : List CollectedFourTerm := [ + ⟨7, 1, 0, 0, 6, 2, -47249596828024117369010078933186641150328438784000000⟩, + ⟨7, 1, 1, 0, 7, 2, 125397612217363722751635111477670896875406046003200000⟩, + ⟨7, 1, 2, 0, 8, 2, -38118251683082188141519170400851837148749574963200000⟩, + ⟨7, 1, 0, 1, 5, 2, -72153967630695279651724092159898555935330454732800000⟩, + ⟨7, 1, 1, 1, 6, 2, 61257604235739705142722496925282362347134071603200000⟩, + ⟨7, 1, 2, 1, 7, 2, -17473877189605974076353828141695997592196874240000000⟩, + ⟨7, 1, 3, 1, 8, 2, -221004940425640551610404540160861945042934169600000⟩, + ⟨7, 1, 0, 2, 4, 2, -20560266326059497454879762251650489215459786752000000⟩, + ⟨7, 1, 1, 2, 5, 2, 36448392116349587717107039088266452989804701286400000⟩, + ⟨7, 1, 2, 2, 6, 2, -36810160380542812944348718649790643896339293798400000⟩, + ⟨7, 1, 3, 2, 7, 2, 7940706340733495666277582716501677563368492236800000⟩, + ⟨7, 1, 4, 2, 8, 2, -663978933801132471528085513818812177591146905600000⟩, + ⟨7, 1, 0, 3, 3, 2, -3656863109122208778473944307977509323624624947200000⟩, + ⟨7, 1, 1, 3, 4, 2, 19873759868791933007761240116143962418875623014400000⟩, + ⟨7, 1, 2, 3, 5, 2, 9122401226589238840042328075790094761885853286400000⟩, + ⟨7, 1, 3, 3, 6, 2, -8719325260997430111155016870530822051193893683200000⟩, + ⟨7, 1, 4, 3, 7, 2, -4002889709559587978005001373717223273574852198400000⟩, + ⟨7, 1, 5, 3, 8, 2, 662085206648864354622868623959667192009798451200000⟩, + ⟨7, 1, 0, 4, 2, 2, 27103801058982582087254585683266654899088339763200000⟩, + ⟨7, 1, 1, 4, 3, 2, -62632735502867035328350315376889578324589595852800000⟩, + ⟨7, 1, 2, 4, 4, 2, 1152419336623205333371989324845613698600927232000000⟩, + ⟨7, 1, 3, 4, 5, 2, -16311400989724733863346840233486195596242347622400000⟩, + ⟨7, 1, 4, 4, 6, 2, 4746361896760239906618020060759886725914401177600000⟩, + ⟨7, 1, 5, 4, 7, 2, 395617345205643398090365830884494143909789696000000⟩, + ⟨7, 1, 6, 4, 8, 2, -250261774046114668513013233044907726385184768000000⟩, + ⟨7, 1, 0, 5, 1, 2, 20891322831399345968816838140836442785904276275200000⟩, + ⟨7, 1, 1, 5, 2, 2, -12685483870320462036332760307555830909502488576000000⟩, + ⟨7, 1, 2, 5, 3, 2, 19217053846872731351072615858249493103319502028800000⟩, + ⟨7, 1, 3, 5, 4, 2, 16697967597725233612963731155916909113377397145600000⟩, + ⟨7, 1, 4, 5, 5, 2, 2462436600269560317768141450515158673177287065600000⟩, + ⟨7, 1, 5, 5, 6, 2, -878754095132840540284339016321235437809041408000000⟩, + ⟨7, 1, 6, 5, 7, 2, 303347113790044745495928534144840610427908915200000⟩, + ⟨7, 1, 7, 5, 8, 2, 17697377189418538495681845764078590772851507200000⟩, + ⟨7, 1, 0, 6, 0, 2, -481887824165537626811618951032655263173833234841600000⟩, + ⟨7, 1, 1, 6, 1, 2, -279901749540710467794649761470878261003843692134400000⟩, + ⟨7, 1, 2, 6, 2, 2, -12860374391599128600533131526461712148792449433600000⟩, + ⟨7, 1, 3, 6, 3, 2, 22212261609785179388566107380505659142180333158400000⟩, + ⟨7, 1, 4, 6, 4, 2, -4779157221874817236539038562938119730058441523200000⟩, + ⟨7, 1, 5, 6, 5, 2, 1781213093893879323897537586050999646170592051200000⟩, + ⟨7, 1, 6, 6, 6, 2, -197525930262269593721799669340560968202898636800000⟩, + ⟨7, 1, 7, 6, 7, 2, -58478880909947559030858035013924846451241779200000⟩, + ⟨7, 1, 8, 6, 8, 2, 86773121051054501812688866754994720980179353600000⟩, + ⟨7, 1, 1, 7, 0, 2, 1753202895318161592836290740537334661793293166182400000⟩, + ⟨7, 1, 2, 7, 1, 2, 189682337257028164558014431014329850375098177945600000⟩, + ⟨7, 1, 3, 7, 2, 2, 81762775979467800973995642696376160626829741260800000⟩, + ⟨7, 1, 4, 7, 3, 2, 17394450374180305720277245868660955339941530828800000⟩, + ⟨7, 1, 5, 7, 4, 2, 5386440705521150322942117950104233267383658086400000⟩, + ⟨7, 1, 6, 7, 5, 2, 204131218874200599640843573400361264432021504000000⟩, + ⟨7, 1, 7, 7, 6, 2, 146453452146817860722558790540239838368287948800000⟩, + ⟨7, 1, 8, 7, 7, 2, 65704395599564915363030621420788598136687820800000⟩ +] + +def collectedFourData_8_6_44 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 6, 3, -61100968963731478117236442407946085459753435136000000⟩, + ⟨7, 2, 1, 0, 7, 3, 81079163914419181153549198505841410450785724006400000⟩, + ⟨7, 2, 2, 0, 8, 3, -16430913484947271993369595481862385087228254617600000⟩, + ⟨7, 2, 0, 1, 5, 3, -93306136618680645601899480342613259567645274931200000⟩, + ⟨7, 2, 1, 1, 6, 3, 39607734525477834915195145418269454783297775206400000⟩, + ⟨7, 2, 2, 1, 7, 3, -7532133601931081160939542400895903112437432320000000⟩, + ⟨7, 2, 3, 1, 8, 3, -71448313384175184912267181387217410824182169600000⟩, + ⟨7, 2, 0, 2, 4, 3, -26587574900311561122578172696355377924966187008000000⟩, + ⟨7, 2, 1, 2, 5, 3, 23566678077537801765084838502476385495089466572800000⟩, + ⟨7, 2, 2, 2, 6, 3, -15867059318677216110288094876627970474839847731200000⟩, + ⟨7, 2, 3, 2, 7, 3, 2567137522047045390884819191276449379832876236800000⟩, + ⟨7, 2, 4, 2, 8, 3, -171725301167828220882051796852571117200059924480000⟩, + ⟨7, 2, 0, 3, 3, 3, -4728884357433667366922331619831109947048643788800000⟩, + ⟨7, 2, 1, 3, 4, 3, 12849908427319038916822957189201796239792590028800000⟩, + ⟨7, 2, 2, 3, 5, 3, 3932220883981130542814438139448383164514513715200000⟩, + ⟨7, 2, 3, 3, 6, 3, -2818855915829212171942946220891791316739109683200000⟩, + ⟨7, 2, 4, 3, 7, 3, -1035269954997702168895876597929546378205955358720000⟩, + ⟨7, 2, 5, 3, 8, 3, 142696271074509221064738578796298409807236300800000⟩, + ⟨7, 2, 0, 4, 2, 3, 35049368004804212745435702780398544539135823052800000⟩, + ⟨7, 2, 1, 4, 3, 3, -40496862248404453655618525626699148903512119705600000⟩, + ⟨7, 2, 2, 4, 4, 3, 496751597525134243471435957816640524806782976000000⟩, + ⟨7, 2, 3, 4, 5, 3, -5273285236991870060658007960710322100678059622400000⟩, + ⟨7, 2, 4, 4, 6, 3, 1227554647715340550920527699579521677138151342080000⟩, + ⟨7, 2, 5, 4, 7, 3, 85265641591629742277277747820828103974846464000000⟩, + ⟨7, 2, 6, 4, 8, 3, -46232403223176215679986282797017971394871296000000⟩, + ⟨7, 2, 0, 5, 1, 3, 27015681690971289534451040967217029945481809100800000⟩, + ⟨7, 2, 1, 5, 2, 3, -8202137248615119481185117925887152340338737152000000⟩, + ⟨7, 2, 2, 5, 3, 3, 8283531779440929654724829226035713187521128038400000⟩, + ⟨7, 2, 3, 5, 4, 3, 5398257701856610004911784983614545945297525145600000⟩, + ⟨7, 2, 4, 5, 5, 3, 636861570844090012857220332018985976501612052480000⟩, + ⟨7, 2, 5, 5, 6, 3, -189393950065121821636831001691264250672054272000000⟩, + ⟨7, 2, 6, 5, 7, 3, 56039185907568282773548692843602884809877094400000⟩, + ⟨7, 2, 7, 5, 8, 3, 2860677569180780356307408466595038241593753600000⟩, + ⟨7, 2, 0, 6, 0, 3, -623154798452697973021961345617935884400183371366400000⟩, + ⟨7, 2, 1, 6, 1, 3, -180977926370766390358134104627448347784179928268800000⟩, + ⟨7, 2, 2, 6, 2, 3, -5543478246831037451595082741108954029448023244800000⟩, + ⟨7, 2, 3, 6, 3, 3, 7180964486181645469016275635131340115807725158400000⟩, + ⟨7, 2, 4, 6, 4, 3, -1236036523864568505616893165860381506002286018560000⟩, + ⟨7, 2, 5, 6, 5, 3, 383896912263357878446615041542799039493098700800000⟩, + ⟨7, 2, 6, 6, 6, 3, -36490185086099087497760492376328040171018649600000⟩, + ⟨7, 2, 7, 6, 7, 3, -9452769249327252737439338054938211720468889600000⟩, + ⟨7, 2, 8, 6, 8, 3, 12467882460984967671429480026098292890376601600000⟩, + ⟨7, 2, 1, 7, 0, 3, 1133579997347448277711605818200641288282523356364800000⟩, + ⟨7, 2, 2, 7, 1, 3, 81762775979467800973995642696376160626829741260800000⟩, + ⟨7, 2, 3, 7, 2, 3, 26432949553481435164436735837220895943715245260800000⟩, + ⟨7, 2, 4, 7, 3, 3, 4498737952504993457313393909538800038885499863040000⟩, + ⟨7, 2, 5, 7, 4, 3, 1160915536736128270291118397970229468738460057600000⟩, + ⟨7, 2, 6, 7, 5, 3, 37710420847937719002324916524876177277452288000000⟩, + ⟨7, 2, 7, 7, 6, 3, 23673344417159805961969515531954369849615974400000⟩, + ⟨7, 2, 8, 7, 7, 3, 9440650187325238714425645202411249419996364800000⟩ +] + +def collectedFourData_8_6_45 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 6, 4, -25997595109071447248294155446481009060601659392000000⟩, + ⟨7, 3, 1, 0, 7, 4, 22998689011301920762346533651637211114165711667200000⟩, + ⟨7, 3, 2, 0, 8, 4, -3495560244776141713182491079550709636313749913600000⟩, + ⟨7, 3, 0, 1, 5, 4, -39700436869406119896340703906758168672716875366400000⟩, + ⟨7, 3, 1, 1, 6, 4, 11235019267776033402155541964205874010419049267200000⟩, + ⟨7, 3, 2, 1, 7, 4, -1602407973322568059890298434708959925916139520000000⟩, + ⟨7, 3, 3, 1, 8, 4, -12160097321470686988035302669991273396940308480000⟩, + ⟨7, 3, 0, 2, 4, 4, -11312635771794440627005364588040404718506213376000000⟩, + ⟨7, 3, 1, 2, 5, 4, 6684858032167846983080594309871125093138458214400000⟩, + ⟨7, 3, 2, 2, 6, 4, -3375604272196122441632569218620517698810098483200000⟩, + ⟨7, 3, 3, 2, 7, 4, 436912232453134836489058655127322053452853411840000⟩, + ⟨7, 3, 4, 2, 8, 4, -24355559469630084308264743468905354000617963520000⟩, + ⟨7, 3, 0, 3, 3, 4, -2012073178661976775116223799479239666149464473600000⟩, + ⟨7, 3, 1, 3, 4, 4, 3644969107668127505361701153227290465190438502400000⟩, + ⟨7, 3, 2, 3, 5, 4, 836552088739030126371764796138194207629325107200000⟩, + ⟨7, 3, 3, 3, 6, 4, -479753274053892643404909489836746494665985884160000⟩, + ⟨7, 3, 4, 3, 7, 4, -146830890873939589719838819572334648934824673280000⟩, + ⟨7, 3, 5, 3, 8, 4, 17347210886629526741928655562820100852128153600000⟩, + ⟨7, 3, 0, 4, 2, 4, 14913008642442578135839349175770879525819881881600000⟩, + ⟨7, 3, 1, 4, 3, 4, -11487226752457306735991573708519873783895215308800000⟩, + ⟨7, 3, 2, 4, 4, 4, 105680377261354072780208872223966612932263936000000⟩, + ⟨7, 3, 3, 4, 5, 4, -897483210567966490587881770888517160457595781120000⟩, + ⟨7, 3, 4, 4, 6, 4, 174102360114264672875732446991092673247361105920000⟩, + ⟨7, 3, 5, 4, 7, 4, 10365520100391719449012961688246774386393088000000⟩, + ⟨7, 3, 6, 4, 8, 4, -4917807852723708379675645566418463886409728000000⟩, + ⟨7, 3, 0, 5, 1, 4, 11494789135248006519624477315744056056445770137600000⟩, + ⟨7, 3, 1, 5, 2, 4, -2326595326118886130164544969944969924990468096000000⟩, + ⟨7, 3, 2, 5, 3, 4, 1762262603420092524952595497777972755481126502400000⟩, + ⟨7, 3, 3, 5, 4, 4, 918752814611494567592631634350244428546079457280000⟩, + ⟨7, 3, 4, 5, 5, 4, 90325186545785422491937234823186968793862635520000⟩, + ⟨7, 3, 5, 5, 6, 4, -23024125071326780534989612484481049348276224000000⟩, + ⟨7, 3, 6, 5, 7, 4, 5960969564704141518388675963153991880356659200000⟩, + ⟨7, 3, 7, 5, 8, 4, 270483934461224477653841781880442079254937600000⟩, + ⟨7, 3, 0, 6, 0, 4, -265143522520315969710755199665491753377528073420800000⟩, + ⟨7, 3, 1, 6, 1, 4, -51335692742279677526147261037076331781624850022400000⟩, + ⟨7, 3, 2, 6, 2, 4, -1179335658675102702178597252205659192759733452800000⟩, + ⟨7, 3, 3, 6, 3, 4, 1222159388766397409001829854066406841535871057920000⟩, + ⟨7, 3, 4, 6, 4, 4, -175305332754648431516548280910826876404435517440000⟩, + ⟨7, 3, 5, 6, 5, 4, 46669339328993999705201094619568266892908953600000⟩, + ⟨7, 3, 6, 6, 6, 4, -3881513965378309307588843961496636041776332800000⟩, + ⟨7, 3, 7, 6, 7, 4, -893782034598297819757638235683591860885913600000⟩, + ⟨7, 3, 8, 6, 8, 4, 1060981406957986579978708771381472968877015040000⟩, + ⟨7, 3, 1, 7, 0, 4, 321548133574055743350934620060488467316316989030400000⟩, + ⟨7, 3, 2, 7, 1, 4, 17394450374180305720277245868660955339941530828800000⟩, + ⟨7, 3, 3, 7, 2, 4, 4498737952504993457313393909538800038885499863040000⟩, + ⟨7, 3, 4, 7, 3, 4, 638049716584479890306030658137336538547051560960000⟩, + ⟨7, 3, 5, 7, 4, 4, 141129452687736170949598200756148699890135859200000⟩, + ⟨7, 3, 6, 7, 5, 4, 4011312214947479153148683795119983908880384000000⟩, + ⟨7, 3, 7, 7, 6, 4, 2238371569307185253965427230856405508843110400000⟩, + ⟨7, 3, 8, 7, 7, 4, 803372533362430765390101342445732107512709120000⟩ +] + +def collectedFourData_8_6_46 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 6, 5, -13417546164515223513413671805835737253764136960000000⟩, + ⟨7, 4, 1, 0, 7, 5, 8902341838864828474756892889603882434798026752000000⟩, + ⟨7, 4, 2, 0, 8, 5, -1082450297999195275206702304714082448132852940800000⟩, + ⟨7, 4, 0, 1, 5, 5, -20489681534458846401796338203961685778557304832000000⟩, + ⟨7, 4, 1, 1, 6, 5, 4348855799512078636045433514217660108612042752000000⟩, + ⟨7, 4, 2, 1, 7, 5, -496208580822322732399497633088331586270658560000000⟩, + ⟨7, 4, 3, 1, 8, 5, -3137956924309880449049404256112075112395571200000⟩, + ⟨7, 4, 0, 2, 4, 5, -5838532836348169356147447246339606410302586880000000⟩, + ⟨7, 4, 1, 2, 5, 5, 2587577549198340530815476150979088222785634304000000⟩, + ⟨7, 4, 2, 2, 6, 5, -1045304212915961180707945706149042426771773849600000⟩, + ⟨7, 4, 3, 2, 7, 5, 112746775695721759938642635278934181789931929600000⟩, + ⟨7, 4, 4, 2, 8, 5, -5387177031050989468585506000124136149902950400000⟩, + ⟨7, 4, 0, 3, 3, 5, -1038445465736934924465784781440744201931194368000000⟩, + ⟨7, 4, 1, 3, 4, 5, 1410896115540235144806836759090658528548880384000000⟩, + ⟨7, 4, 2, 3, 5, 5, 259050336523495670677262234289591223846541721600000⟩, + ⟨7, 4, 3, 3, 6, 5, -123802060828874521669441707098356375492126310400000⟩, + ⟨7, 4, 4, 3, 7, 5, -32477348908826177923360745146525437883160985600000⟩, + ⟨7, 4, 5, 3, 8, 5, 3357382700982732671032284055125856289292288000000⟩, + ⟨7, 4, 0, 4, 2, 5, 7696711217799044988107817052585857298263441408000000⟩, + ⟨7, 4, 1, 4, 3, 5, -4446480374628060886025110439509698507763089408000000⟩, + ⟨7, 4, 2, 4, 4, 5, 32725442518169489549783400629159403410423808000000⟩, + ⟨7, 4, 3, 4, 5, 5, -231598775947378981652312403432813859064040652800000⟩, + ⟨7, 4, 4, 4, 6, 5, 38509492529985386271243250786629673149687398400000⟩, + ⟨7, 4, 5, 4, 7, 5, 2006144855169026825754526152088909554647040000000⟩, + ⟨7, 4, 6, 4, 8, 5, -846038689544165497768135583381068846202880000000⟩, + ⟨7, 4, 0, 5, 1, 5, 5932543499753998295943050134366703062182002688000000⟩, + ⟨7, 4, 1, 5, 2, 5, -900579459274276127516264022584927960023695360000000⟩, + ⟨7, 4, 2, 5, 3, 5, 545709856689103783428309078901106833167168307200000⟩, + ⟨7, 4, 3, 5, 4, 5, 237087473901125802850922685482266028674331443200000⟩, + ⟨7, 4, 4, 5, 5, 5, 19978919839292100938855022200757877956044390400000⟩, + ⟨7, 4, 5, 5, 6, 5, -4456093819630419215991818453273053935697920000000⟩, + ⟨7, 4, 6, 5, 7, 5, 1025499781603257269382256203160373723922432000000⟩, + ⟨7, 4, 7, 5, 8, 5, 41879612273754051214387512871079773628006400000⟩, + ⟨7, 4, 0, 6, 0, 5, -136842482495512131712853054060087504814791983104000000⟩, + ⟨7, 4, 1, 6, 1, 5, -19871040697238219368395901116838150815910723584000000⟩, + ⟨7, 4, 2, 6, 2, 5, -365198178770251691988233726454693626567353958400000⟩, + ⟨7, 4, 3, 6, 3, 5, 315382633477642161913713468078278451066096844800000⟩, + ⟨7, 4, 4, 6, 4, 5, -38775576607640801968682474968610461029551308800000⟩, + ⟨7, 4, 5, 6, 5, 5, 9032393365911342062685141538387144671756288000000⟩, + ⟨7, 4, 6, 6, 6, 5, -667759108745426296921780403372091022245888000000⟩, + ⟨7, 4, 7, 6, 7, 5, -138386204492266208108221694764003403130470400000⟩, + ⟨7, 4, 8, 6, 8, 5, 149340040679207640977928705243535648594329600000⟩, + ⟨7, 4, 1, 7, 0, 5, 124464981517795189912605228983466042910115364864000000⟩, + ⟨7, 4, 2, 7, 1, 5, 5386440705521150322942117950104233267383658086400000⟩, + ⟨7, 4, 3, 7, 2, 5, 1160915536736128270291118397970229468738460057600000⟩, + ⟨7, 4, 4, 7, 3, 5, 141129452687736170949598200756148699890135859200000⟩, + ⟨7, 4, 5, 7, 4, 5, 27314222796367255324912086192593240101748736000000⟩, + ⟨7, 4, 6, 7, 5, 5, 690089046038483967468889413334726229360640000000⟩, + ⟨7, 4, 7, 7, 6, 5, 346571908730563882198609398042333854407065600000⟩, + ⟨7, 4, 8, 7, 7, 5, 113079914526395072027041114630571571334348800000⟩ +] + +def collectedFourData_8_6_47 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 6, 6, -762731886212701531683698695071332846429798400000000⟩, + ⟨7, 5, 1, 0, 7, 6, 404848987987093513610982644278658496687243264000000⟩, + ⟨7, 5, 2, 0, 8, 6, -41021875257037444841268206099147278660927488000000⟩, + ⟨7, 5, 0, 1, 5, 6, -1164753469304720789541312410737895131085537280000000⟩, + ⟨7, 5, 1, 1, 6, 6, 197771541601324545848316743776435821833355264000000⟩, + ⟨7, 5, 2, 1, 7, 6, -18804934084816556499046553612670490745241600000000⟩, + ⟨7, 5, 3, 1, 8, 6, -101931339941505699386829654947095281401856000000⟩, + ⟨7, 5, 0, 2, 4, 6, -331896392110794649881252922076405794288435200000000⟩, + ⟨7, 5, 1, 2, 5, 6, 117674446914369727476865479249595994763952128000000⟩, + ⟨7, 5, 2, 2, 6, 6, -39614141274804422947495407011289928833171456000000⟩, + ⟨7, 5, 3, 2, 7, 6, 3662392505045873482785303230644664452251648000000⟩, + ⟨7, 5, 4, 2, 8, 6, -153119342682869758527287535971843501457408000000⟩, + ⟨7, 5, 0, 3, 3, 6, -59031320563313798153831655662954119660830720000000⟩, + ⟨7, 5, 1, 3, 4, 6, 64162877012620022138797759354856816076914688000000⟩, + ⟨7, 5, 2, 3, 5, 6, 9817291943845269068477872748487610912997376000000⟩, + ⟨7, 5, 3, 3, 6, 6, -4021505155167894809391310045361084722839552000000⟩, + ⟨7, 5, 4, 3, 7, 6, -923101336439933547151493004714654472077312000000⟩, + ⟨7, 5, 5, 3, 8, 6, 84823684809930797203043388781187165061120000000⟩, + ⟨7, 5, 0, 4, 2, 6, 437526131291565188995086206013519690014392320000000⟩, + ⟨7, 5, 1, 4, 3, 6, -202211183568995286452481332929108256653049856000000⟩, + ⟨7, 5, 2, 4, 4, 6, 1240203844179362199295416200019588289658880000000⟩, + ⟨7, 5, 3, 4, 5, 6, -7523103130652674978968486233184372485259264000000⟩, + ⟨7, 5, 4, 4, 6, 6, 1094552517813189872357450997423353383354368000000⟩, + ⟨7, 5, 5, 4, 7, 6, 50684897741360284893585032886542244249600000000⟩, + ⟨7, 5, 6, 4, 8, 6, -19237517130860814010901958431441242030080000000⟩, + ⟨7, 5, 0, 5, 1, 6, 337240508668654542647534173303260755546603520000000⟩, + ⟨7, 5, 1, 5, 2, 6, -40955367619948186044066257971338766995947520000000⟩, + ⟨7, 5, 2, 5, 3, 6, 20680895657763345068956193902311645791649792000000⟩, + ⟨7, 5, 3, 5, 4, 6, 7701394404387306072160291611801754288521216000000⟩, + ⟨7, 5, 4, 5, 5, 6, 567859391973487488538499047381629778526208000000⟩, + ⟨7, 5, 5, 5, 6, 6, -112582428428303054492116914738006117580800000000⟩, + ⟨7, 5, 6, 5, 7, 6, 23318164831109448697279438673816963776512000000⟩, + ⟨7, 5, 7, 5, 8, 6, 865702681650336208971960956285966352384000000⟩, + ⟨7, 5, 0, 6, 0, 6, -7778927943163264811551693896041957131718492160000000⟩, + ⟨7, 5, 1, 6, 1, 6, -903669041488195824444289888002073362419417088000000⟩, + ⟨7, 5, 2, 6, 2, 6, -13840001856253045949739313775801707133927424000000⟩, + ⟨7, 5, 3, 6, 3, 6, 10244683148965435581287470235193294899380224000000⟩, + ⟨7, 5, 4, 6, 4, 6, -1102115406285972510437546457039028120190976000000⟩, + ⟨7, 5, 5, 6, 5, 6, 228201833447557888865866652679738092421120000000⟩, + ⟨7, 5, 6, 6, 6, 6, -15183735037814592020470621511068164292608000000⟩, + ⟨7, 5, 7, 6, 7, 6, -2860611687359057227243260649615575220224000000⟩, + ⟨7, 5, 8, 6, 8, 6, 2829787441948631537142710575263412912128000000⟩, + ⟨7, 5, 1, 7, 0, 6, 5660254652020534064788940656566788617087746048000000⟩, + ⟨7, 5, 2, 7, 1, 6, 204131218874200599640843573400361264432021504000000⟩, + ⟨7, 5, 3, 7, 2, 6, 37710420847937719002324916524876177277452288000000⟩, + ⟨7, 5, 4, 7, 3, 6, 4011312214947479153148683795119983908880384000000⟩, + ⟨7, 5, 5, 7, 4, 6, 690089046038483967468889413334726229360640000000⟩, + ⟨7, 5, 6, 7, 5, 6, 15691480790479511780273437726489171722240000000⟩, + ⟨7, 5, 7, 7, 6, 6, 7164064194566394843835397074647238311936000000⟩, + ⟨7, 5, 8, 7, 7, 6, 2142708148518466073158539391751562461184000000⟩ +] + +def collectedFourData_8_6_48 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 6, 7, -766108220879245168060176195275560906414620672000000⟩, + ⟨7, 6, 1, 0, 7, 7, 338867588465048478212770344326167034318133657600000⟩, + ⟨7, 6, 2, 0, 8, 7, -29431045765869222422163965480865367519238553600000⟩, + ⟨7, 6, 0, 1, 5, 7, -1169909406256455651702067878809750438635005542400000⟩, + ⟨7, 6, 1, 1, 6, 7, 165539169809144712384201512857892479867394457600000⟩, + ⟨7, 6, 2, 1, 7, 7, -13491554742599049368982564461957300638187520000000⟩, + ⟨7, 6, 3, 1, 8, 7, -63989095403315441559060553985686139358412800000⟩, + ⟨7, 6, 0, 2, 4, 7, -333365575862831913217574678681850466025865216000000⟩, + ⟨7, 6, 1, 2, 5, 7, 98496123821611413868309823422219051089474355200000⟩, + ⟨7, 6, 2, 2, 6, 7, -28421070405219132387577885498251863102010163200000⟩, + ⟨7, 6, 3, 2, 7, 7, 2299127859441990109630802751320918917015142400000⟩, + ⟨7, 6, 4, 2, 8, 7, -85442858846834336052913192104270595149004800000⟩, + ⟨7, 6, 0, 3, 3, 7, -59292630595885565520038629950509419570239897600000⟩, + ⟨7, 6, 1, 3, 4, 7, 53705752138224915938624065627015240031089459200000⟩, + ⟨7, 6, 2, 3, 5, 7, 7043392499387064176345582598418988161774387200000⟩, + ⟨7, 6, 3, 3, 6, 7, -2524566803366227293890768646708666037803417600000⟩, + ⟨7, 6, 4, 3, 7, 7, -515104204399025508338562334609966615442227200000⟩, + ⟨7, 6, 5, 3, 8, 7, 42599584095554609344186756682640423439564800000⟩, + ⟨7, 6, 0, 4, 2, 7, 439462899206085653293202846169203210721008025600000⟩, + ⟨7, 6, 1, 4, 3, 7, -169255248672804285392337775546070726680667750400000⟩, + ⟨7, 6, 2, 4, 4, 7, 889781265930498000956438830441970150670336000000⟩, + ⟨7, 6, 3, 4, 5, 7, -4722753220281115100182277120579228772021043200000⟩, + ⟨7, 6, 4, 4, 6, 7, 610776500482079566994962026668814783794380800000⟩, + ⟨7, 6, 5, 4, 7, 7, 25454630608724493414843003320209804099584000000⟩, + ⟨7, 6, 6, 4, 8, 7, -8783033896531700902931995893395946995712000000⟩, + ⟨7, 6, 0, 5, 1, 7, 338733348867108313139676923041185429823527321600000⟩, + ⟨7, 6, 1, 5, 2, 7, -34280551691817037096923436191868829583802368000000⟩, + ⟨7, 6, 2, 5, 3, 7, 14837458862351283810500955732865802496796262400000⟩, + ⟨7, 6, 3, 5, 4, 7, 4834678535214980686787728004894580508773580800000⟩, + ⟨7, 6, 4, 5, 5, 7, 316873943050618839824202693799726677806284800000⟩, + ⟨7, 6, 5, 5, 6, 7, -56540394799634579424032467961249406124032000000⟩, + ⟨7, 6, 6, 5, 7, 7, 10646084456917824396382275135954586750156800000⟩, + ⟨7, 6, 7, 5, 8, 7, 362306179295583671748076931615002774732800000⟩, + ⟨7, 6, 0, 6, 0, 7, -7813362407695042434825547292023486691601599692800000⟩, + ⟨7, 6, 1, 6, 1, 7, -756391044429112202135195184389517925657293619200000⟩, + ⟨7, 6, 2, 6, 2, 7, -9929476053419090017710521974863824329428172800000⟩, + ⟨7, 6, 3, 6, 3, 7, 6431270380356816460356704271825540220138291200000⟩, + ⟨7, 6, 4, 6, 4, 7, -614996704154143857777739753999155211114905600000⟩, + ⟨7, 6, 5, 6, 5, 7, 114605999686196843775608308564099915893964800000⟩, + ⟨7, 6, 6, 6, 6, 7, -6932249032238508629968837648953870857011200000⟩, + ⟨7, 6, 7, 6, 7, 7, -1197197736432528957061816846632092486860800000⟩, + ⟨7, 6, 8, 6, 8, 7, 1093197643993975471641576706470966617702400000⟩, + ⟨7, 6, 1, 7, 0, 7, 4737758771647018014347802189795800474759410483200000⟩, + ⟨7, 6, 2, 7, 1, 7, 146453452146817860722558790540239838368287948800000⟩, + ⟨7, 6, 3, 7, 2, 7, 23673344417159805961969515531954369849615974400000⟩, + ⟨7, 6, 4, 7, 3, 7, 2238371569307185253965427230856405508843110400000⟩, + ⟨7, 6, 5, 7, 4, 7, 346571908730563882198609398042333854407065600000⟩, + ⟨7, 6, 6, 7, 5, 7, 7164064194566394843835397074647238311936000000⟩, + ⟨7, 6, 7, 7, 6, 7, 2998240367713241727408767247927183881011200000⟩, + ⟨7, 6, 8, 7, 7, 7, 827766589463012216226948900014739632947200000⟩ +] + +def collectedFourData_8_6_49 : List CollectedFourTerm := [ + ⟨7, 7, 0, 0, 6, 8, -458272366897543719509669160671800849267163136000000⟩, + ⟨7, 7, 1, 0, 7, 8, 173746790334116265128422973187636025308374630400000⟩, + ⟨7, 7, 2, 0, 8, 8, -13203847676946602138075593811973599414294937600000⟩, + ⟨7, 7, 0, 1, 5, 8, -699819083060528220103256239174040029748212531200000⟩, + ⟨7, 7, 1, 1, 6, 8, 84876513446430415637895949399274094225417830400000⟩, + ⟨7, 7, 2, 1, 7, 8, -6052806793330170182417536761604040105656320000000⟩, + ⟨7, 7, 3, 1, 8, 8, -25518095578763975834786776472191969630617600000⟩, + ⟨7, 7, 0, 2, 4, 8, -199413382247079137800730438101461712144171008000000⟩, + ⟨7, 7, 1, 2, 5, 8, 50501688437877214307889351146830324365577420800000⟩, + ⟨7, 7, 2, 2, 6, 8, -12750735649410086129601088281105821892555571200000⟩, + ⟨7, 7, 3, 2, 7, 8, 916865039195411395592101167296072762838220800000⟩, + ⟨7, 7, 4, 2, 8, 8, -30666242777000560955373842853349257841213440000⟩, + ⟨7, 7, 0, 3, 3, 8, -35467801313466266233348181474169928788266188800000⟩, + ⟨7, 7, 1, 3, 4, 8, 27536425359425074474434907846822715485637836800000⟩, + ⟨7, 7, 2, 3, 5, 8, 3159924469918282292030247756334214168130355200000⟩, + ⟨7, 7, 3, 3, 6, 8, -1006767427750449956877829087701947288597299200000⟩, + ⟨7, 7, 4, 3, 7, 8, -184875726312843182597673494444208463974236160000⟩, + ⟨7, 7, 5, 3, 8, 8, 13899445416767193205874578564934827140710400000⟩, + ⟨7, 7, 0, 4, 2, 8, 262878921664219367617711060341056643732917452800000⟩, + ⟨7, 7, 1, 4, 3, 8, -86781849917569186889741241228806431474031001600000⟩, + ⟨7, 7, 2, 4, 4, 8, 399188543778204043823508418987123776946176000000⟩, + ⟨7, 7, 3, 4, 5, 8, -1883378211716439143383682923710759204972134400000⟩, + ⟨7, 7, 4, 4, 6, 8, 219213409980185935063090860684444180928266240000⟩, + ⟨7, 7, 5, 4, 7, 8, 8305368614780870062441613095582964908032000000⟩, + ⟨7, 7, 6, 4, 8, 8, -2626927647170729872619330721950705123328000000⟩, + ⟨7, 7, 0, 5, 1, 8, 202624288973566566213455018022331291418807500800000⟩, + ⟨7, 7, 1, 5, 2, 8, -17576587522917665648821771276766294386409472000000⟩, + ⟨7, 7, 2, 5, 3, 8, 6656628795659163758376242769458303219426918400000⟩, + ⟨7, 7, 3, 5, 4, 8, 1928012705549550245124486349868754118744473600000⟩, + ⟨7, 7, 4, 5, 5, 8, 113729027778847020370468220898406615681597440000⟩, + ⟨7, 7, 5, 5, 6, 8, -18448070516303406363283273651927212097536000000⟩, + ⟨7, 7, 6, 5, 7, 8, 3184149568753867730307908329121313403699200000⟩, + ⟨7, 7, 7, 5, 8, 8, 100026987030935563658872241668024487116800000⟩, + ⟨7, 7, 0, 6, 0, 8, -4673814986469233833696791802708409630522238566400000⟩, + ⟨7, 7, 1, 6, 1, 8, -387822620635738874114228989141808312134454476800000⟩, + ⟨7, 7, 2, 6, 2, 8, -4454727513396003100104053043541597167078604800000⟩, + ⟨7, 7, 3, 6, 3, 8, 2564714678718771662832441662171871099381350400000⟩, + ⟨7, 7, 4, 6, 4, 8, -220728080628178979592463790332061186449735680000⟩, + ⟨7, 7, 5, 6, 5, 8, 37393788481577243870409563618578509751910400000⟩, + ⟨7, 7, 6, 6, 6, 8, -2073374286651786323929729935913970879692800000⟩, + ⟨7, 7, 7, 6, 7, 8, -330527297901545076398222360859036667084800000⟩, + ⟨7, 7, 8, 6, 8, 8, 280256342462746186648225845555227315404800000⟩, + ⟨7, 7, 1, 7, 0, 8, 2429180033651634398780836978479411209880521932800000⟩, + ⟨7, 7, 2, 7, 1, 8, 65704395599564915363030621420788598136687820800000⟩, + ⟨7, 7, 3, 7, 2, 8, 9440650187325238714425645202411249419996364800000⟩, + ⟨7, 7, 4, 7, 3, 8, 803372533362430765390101342445732107512709120000⟩, + ⟨7, 7, 5, 7, 4, 8, 113079914526395072027041114630571571334348800000⟩, + ⟨7, 7, 6, 7, 5, 8, 2142708148518466073158539391751562461184000000⟩, + ⟨7, 7, 7, 7, 6, 8, 827766589463012216226948900014739632947200000⟩, + ⟨7, 7, 8, 7, 7, 8, 212209418900873374359364214615089505894400000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0830.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0830.lean new file mode 100644 index 0000000000000000000000000000000000000000..dee77774a36da1133436a5fdace478f49dad5033 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0830.lean @@ -0,0 +1,647 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse0826 +import OAI.Analysis.LaughlinFock.Sparse0827 +import OAI.Analysis.LaughlinFock.Sparse0828 +import OAI.Analysis.LaughlinFock.Sparse0829 + +namespace OAI + +/-! Sparse0830. -/ +namespace LaughlinFock +def collectedFourData_8_6 : List (List CollectedFourTerm) := [ + collectedFourData_8_6_0, + collectedFourData_8_6_1, + collectedFourData_8_6_2, + collectedFourData_8_6_3, + collectedFourData_8_6_4, + collectedFourData_8_6_5, + collectedFourData_8_6_6, + collectedFourData_8_6_7, + collectedFourData_8_6_8, + collectedFourData_8_6_9, + collectedFourData_8_6_10, + collectedFourData_8_6_11, + collectedFourData_8_6_12, + collectedFourData_8_6_13, + collectedFourData_8_6_14, + collectedFourData_8_6_15, + collectedFourData_8_6_16, + collectedFourData_8_6_17, + collectedFourData_8_6_18, + collectedFourData_8_6_19, + collectedFourData_8_6_20, + collectedFourData_8_6_21, + collectedFourData_8_6_22, + collectedFourData_8_6_23, + collectedFourData_8_6_24, + collectedFourData_8_6_25, + collectedFourData_8_6_26, + collectedFourData_8_6_27, + collectedFourData_8_6_28, + collectedFourData_8_6_29, + collectedFourData_8_6_30, + collectedFourData_8_6_31, + collectedFourData_8_6_32, + collectedFourData_8_6_33, + collectedFourData_8_6_34, + collectedFourData_8_6_35, + collectedFourData_8_6_36, + collectedFourData_8_6_37, + collectedFourData_8_6_38, + collectedFourData_8_6_39, + collectedFourData_8_6_40, + collectedFourData_8_6_41, + collectedFourData_8_6_42, + collectedFourData_8_6_43, + collectedFourData_8_6_44, + collectedFourData_8_6_45, + collectedFourData_8_6_46, + collectedFourData_8_6_47, + collectedFourData_8_6_48, + collectedFourData_8_6_49 +] + +theorem collectedFourChecked_8_6 : collectNumericRowParts 8 6 = collectedFourData_8_6 := by + decide +kernel + +def collectedFourData_8_7_0 : List CollectedFourTerm := [ + ⟨0, 7, 1, 0, 8, 0, 1046665030905692811215467036853956733702032588800000⟩, + ⟨0, 7, 1, 1, 7, 0, 10976056640078226772295976774233958376096451788800000⟩, + ⟨0, 7, 2, 1, 8, 0, -6035629236369518737109976906039557613786287308800000⟩, + ⟨0, 7, 1, 2, 6, 0, 13015562568951473985638565295195886186216502067200000⟩, + ⟨0, 7, 2, 2, 7, 0, -7336567906022294078368560924608599661039163801600000⟩, + ⟨0, 7, 3, 2, 8, 0, -1543088803248120465996647458091296483776135168000000⟩, + ⟨0, 7, 1, 3, 5, 0, 10752862597384982793364417130235694866544931635200000⟩, + ⟨0, 7, 2, 3, 6, 0, -2914472781888764028984184857054862028480446464000000⟩, + ⟨0, 7, 3, 3, 7, 0, -3852922116536077886327669075099557156113245798400000⟩, + ⟨0, 7, 4, 3, 8, 0, -746080534406755867385963619198910383434131046400000⟩, + ⟨0, 7, 1, 4, 4, 0, -12111104117760529725823015289764733987424986726400000⟩, + ⟨0, 7, 2, 4, 5, 0, -1353537208459987034764482873162230043137959526400000⟩, + ⟨0, 7, 3, 4, 6, 0, -8850210458859798129951032916411963055317555609600000⟩, + ⟨0, 7, 4, 4, 7, 0, -1700157587889916183835612781575117782749963878400000⟩, + ⟨0, 7, 5, 4, 8, 0, 1846792719579529442434517696766430345036824576000000⟩, + ⟨0, 7, 1, 5, 3, 0, -23129122455311628343374270978748585316459112038400000⟩, + ⟨0, 7, 2, 5, 4, 0, 7176770076371970088279236010326260972876778700800000⟩, + ⟨0, 7, 3, 5, 5, 0, -2908639158650389611837826405308409192102703923200000⟩, + ⟨0, 7, 4, 5, 6, 0, 1559518498345170246982978362166082352270488371200000⟩, + ⟨0, 7, 5, 5, 7, 0, -62825005256962783361640952203512759665557504000000⟩, + ⟨0, 7, 6, 5, 8, 0, 520262594430406771183477260651564570245490278400000⟩, + ⟨0, 7, 1, 6, 2, 0, 57635889651591577353006694575861892721780824473600000⟩, + ⟨0, 7, 2, 6, 3, 0, 3621270826063786312491702919691299435698978816000000⟩, + ⟨0, 7, 3, 6, 4, 0, 13722987498205669519926229597412732498720115916800000⟩, + ⟨0, 7, 4, 6, 5, 0, -2530449217941373995062769910924641118946171289600000⟩, + ⟨0, 7, 5, 6, 6, 0, 597577911637465023686716911822826356275675136000000⟩, + ⟨0, 7, 6, 6, 7, 0, 491334300816593684062020854714679588881537433600000⟩, + ⟨0, 7, 7, 6, 8, 0, 89836463088422662270228173318245196595042713600000⟩, + ⟨0, 7, 1, 7, 1, 0, -164929394874661707980527644206780944134757259673600000⟩, + ⟨0, 7, 2, 7, 2, 0, -17514614975153126476461120880040940221136214425600000⟩, + ⟨0, 7, 3, 7, 3, 0, -24457212750728375044442561687954870287859082854400000⟩, + ⟨0, 7, 4, 7, 4, 0, -10464959596063339414794696046387769200627364659200000⟩, + ⟨0, 7, 5, 7, 5, 0, -675801071736057061823385841922095458734309376000000⟩, + ⟨0, 7, 6, 7, 6, 0, -531780865207120205074642179120250010462060544000000⟩, + ⟨0, 7, 7, 7, 7, 0, -31751138370740811381881486475452438549417164800000⟩, + ⟨0, 7, 8, 7, 8, 0, -121708590711417473777686720746234693833195520000000⟩ +] + +def collectedFourData_8_7_1 : List CollectedFourTerm := [ + ⟨0, 8, 0, 0, 7, 1, 1046665030905692811215467036853956733702032588800000⟩, + ⟨0, 8, 1, 0, 8, 1, 120436213284088221186034662613473816296502067200000⟩, + ⟨0, 8, 0, 1, 6, 1, 131682542638864428535961079272833200536577638400000⟩, + ⟨0, 8, 1, 1, 7, 1, 1262977800432316104180204649005178390448386867200000⟩, + ⟨0, 8, 2, 1, 8, 1, -347249744928458478961741300265511420694206873600000⟩, + ⟨0, 8, 0, 2, 5, 1, -636875838544513555629599892960019875098945126400000⟩, + ⟨0, 8, 1, 2, 6, 1, 1497656865645179593575374673866991924084001996800000⟩, + ⟨0, 8, 2, 2, 7, 1, -422097056370707722614531158793764708134630195200000⟩, + ⟨0, 8, 3, 2, 8, 1, -59186007218713854024424424389208307520241664000000⟩, + ⟨0, 8, 0, 3, 4, 1, 404452876970945892437744757131405148736507084800000⟩, + ⟨0, 8, 1, 3, 5, 1, 1237295615076146085370819124849318393679760588800000⟩, + ⟨0, 8, 2, 3, 6, 1, -167679274269100826179636433676439609417924608000000⟩, + ⟨0, 8, 3, 3, 7, 1, -147780915604102855544588852370464295158494003200000⟩, + ⟨0, 8, 4, 3, 8, 1, -21462242387893138932787859632388467274966630400000⟩, + ⟨0, 8, 0, 4, 3, 1, 1552188065258817864977403892010514579000498585600000⟩, + ⟨0, 8, 1, 4, 4, 1, -1393583883632997045132350944997971397938092441600000⟩, + ⟨0, 8, 2, 4, 5, 1, -77873479629379361698611621748775263362927820800000⟩, + ⟨0, 8, 3, 4, 6, 1, -339454617908329948877372677253497335128575180800000⟩, + ⟨0, 8, 4, 4, 7, 1, -48907849174651646026186013734003874780833382400000⟩, + ⟨0, 8, 5, 4, 8, 1, 42500841300548276613560440740342721883720908800000⟩, + ⟨0, 8, 0, 5, 2, 1, -2619640527255183368649037247912806784246690611200000⟩, + ⟨0, 8, 1, 5, 3, 1, -2661390074999738598026396199588160120028764569600000⟩, + ⟨0, 8, 2, 5, 4, 1, 412903357849296587169646425091358067552524697600000⟩, + ⟨0, 8, 3, 5, 5, 1, -111562431065631177475418177658946567624300953600000⟩, + ⟨0, 8, 4, 5, 6, 1, 44862132807822638052870141224768553723573043200000⟩, + ⟨0, 8, 5, 5, 7, 1, -1445812272175411190166051259783754552652595200000⟩, + ⟨0, 8, 6, 5, 8, 1, 9977476864833948537952763797498966627162521600000⟩, + ⟨0, 8, 0, 6, 1, 1, 1904123259022901832276616939394231846188351488000000⟩, + ⟨0, 8, 1, 6, 2, 1, 6631967338099306923778284383041111674929440358400000⟩, + ⟨0, 8, 2, 6, 3, 1, 208343707245991447472803284726750244925079552000000⟩, + ⟨0, 8, 3, 6, 4, 1, 526352621716562264711557284573376353388619366400000⟩, + ⟨0, 8, 4, 6, 5, 1, -72792563216913522047873845255009688979347865600000⟩, + ⟨0, 8, 5, 6, 6, 1, 13752254770096440671861658658030457902124236800000⟩, + ⟨0, 8, 6, 6, 7, 1, 9422696676212195373745447987557545422513766400000⟩, + ⟨0, 8, 7, 6, 8, 1, 1476739809603116587287371246567660025230131200000⟩, + ⟨0, 8, 0, 7, 0, 1, -18571465285052247574968722979108130211194365542400000⟩, + ⟨0, 8, 1, 7, 1, 1, -18977868937450069109197746568669718156021229158400000⟩, + ⟨0, 8, 2, 7, 2, 1, -1007673822307286595386254875444251512938902323200000⟩, + ⟨0, 8, 3, 7, 3, 1, -938069647947199732030023745037368638152323891200000⟩, + ⟨0, 8, 4, 7, 4, 1, -301041897050445101702654557911439566775202611200000⟩, + ⟨0, 8, 5, 7, 5, 1, -15552429786020567277836169236167616824659148800000⟩, + ⟨0, 8, 6, 7, 6, 1, -10198371623419026906794938152598951434387456000000⟩, + ⟨0, 8, 7, 7, 7, 1, -521928050374598201596641907109815995963801600000⟩, + ⟨0, 8, 8, 7, 8, 1, -1750574605604981705051192070272368099983360000000⟩ +] + +def collectedFourData_8_7_2 : List CollectedFourTerm := [ + ⟨1, 6, 1, 0, 8, 0, 131682542638864428535961079272833200536577638400000⟩, + ⟨1, 6, 1, 1, 7, 0, 1380914622955357251457347881947663752451483238400000⟩, + ⟨1, 6, 2, 1, 8, 0, -759351827759896028992159870823426212304938598400000⟩, + ⟨1, 6, 1, 2, 6, 0, 1637508011012540543062942421071359447295170969600000⟩, + ⟨1, 6, 2, 2, 7, 0, -923024929257193213578961284398079076465429708800000⟩, + ⟨1, 6, 3, 2, 8, 0, -194138383464903922381794382883257326369767424000000⟩, + ⟨1, 6, 1, 3, 5, 0, 1352834236035139401683612442288772090401757593600000⟩, + ⟨1, 6, 2, 3, 6, 0, -366674317989569884645223565153705131142807552000000⟩, + ⟨1, 6, 3, 3, 7, 0, -484742076895373529980462422327076570845623091200000⟩, + ⟨1, 6, 4, 3, 8, 0, -93865543304748646330937566406928142292955955200000⟩, + ⟨1, 6, 1, 4, 4, 0, -1523716697605449045474765462561926255324902195200000⟩, + ⟨1, 6, 2, 4, 5, 0, -170290604829026146596868952292646368056652595200000⟩, + ⟨1, 6, 3, 4, 6, 0, -1113458634519658888107691949922944507857128652800000⟩, + ⟨1, 6, 4, 4, 7, 0, -213899449632300786057467144746489796353012531200000⟩, + ⟨1, 6, 5, 4, 8, 0, 232347841821695345570904892533640305120903168000000⟩, + ⟨1, 6, 1, 5, 3, 0, -2909910586470635331075753245968744344580207411200000⟩, + ⟨1, 6, 2, 5, 4, 0, 902920517726105409621316267892601447539697254400000⟩, + ⟨1, 6, 3, 5, 5, 0, -365940380848131627191265843456831653158689177600000⟩, + ⟨1, 6, 4, 5, 6, 0, 196205428757597700034775284773544998649567641600000⟩, + ⟨1, 6, 5, 5, 7, 0, -7904110856152504887114658802427395699638272000000⟩, + ⟨1, 6, 6, 5, 8, 0, 65455039818427975740718668083305573453607731200000⟩, + ⟨1, 6, 1, 6, 2, 0, 7251260214557066751797619916939996161108659404800000⟩, + ⟨1, 6, 2, 6, 3, 0, 455597670581760830958964107452455176779071488000000⟩, + ⟨1, 6, 3, 6, 4, 0, 1726510232983883736461190661430398076963939942400000⟩, + ⟨1, 6, 4, 6, 5, 0, -318359720825592135880994048524753388576754892800000⟩, + ⟨1, 6, 5, 6, 6, 0, 75182199180908977583420932346734716804661248000000⟩, + ⟨1, 6, 6, 6, 7, 0, 61815526559850634718335264716315655955860684800000⟩, + ⟨1, 6, 7, 6, 8, 0, 11302464047097691946725867589916446755179724800000⟩, + ⟨1, 6, 1, 7, 1, 0, -20750021670439876302008135377656772943512653004800000⟩, + ⟨1, 6, 2, 7, 2, 0, -2203540736689334138121083115947489034534440140800000⟩, + ⟨1, 6, 3, 7, 3, 0, -3076999675902759012002734790213603577570734899200000⟩, + ⟨1, 6, 4, 7, 4, 0, -1316612715177994900477661131928842924673571225600000⟩, + ⟨1, 6, 5, 7, 5, 0, -85023575658459107207298168378358469983469568000000⟩, + ⟨1, 6, 6, 7, 6, 0, -66904171238599799908828072405229915175124992000000⟩, + ⟨1, 6, 7, 7, 7, 0, -3994659713356074149969075720820134695560806400000⟩, + ⟨1, 6, 8, 7, 8, 0, -15312345604977410285462812594811409121935360000000⟩ +] + +def collectedFourData_8_7_3 : List CollectedFourTerm := [ + ⟨1, 7, 0, 0, 7, 1, 10976056640078226772295976774233958376096451788800000⟩, + ⟨1, 7, 1, 0, 8, 1, 1262977800432316104180204649005178390448386867200000⟩, + ⟨1, 7, 0, 1, 6, 1, 1380914622955357251457347881947663752451483238400000⟩, + ⟨1, 7, 1, 1, 7, 1, 13244462615428263752606675032861053703083471667200000⟩, + ⟨1, 7, 2, 1, 8, 1, -3641502062306786919059597122185562473788709273600000⟩, + ⟨1, 7, 0, 2, 5, 1, -6678722485371490577015699083654266045172442726400000⟩, + ⟨1, 7, 1, 2, 6, 1, 15705470326546771752898422037695822624862293196800000⟩, + ⟨1, 7, 2, 2, 7, 1, -4426402967075549226857113733646595814226866995200000⟩, + ⟨1, 7, 3, 2, 8, 1, -620665588655952036746722019055620586328817664000000⟩, + ⟨1, 7, 0, 3, 4, 1, 4241373844346658827782958292129959985151790284800000⟩, + ⟨1, 7, 1, 3, 5, 1, 12975141378177806052780584288415183662826179788800000⟩, + ⟨1, 7, 2, 3, 6, 1, -1758401358027879090627612864973565835878596608000000⟩, + ⟨1, 7, 3, 3, 7, 1, -1549733345528579313031666562356613727244202803200000⟩, + ⟨1, 7, 4, 3, 8, 1, -225067983659261464297659934740956488191600230400000⟩, + ⟨1, 7, 0, 4, 3, 1, 16277322368926350727896278009849297205949208985600000⟩, + ⟨1, 7, 1, 4, 4, 1, -14614088736890430931851266241841805027045906841600000⟩, + ⟨1, 7, 2, 4, 5, 1, -816635406680612092099055663151095754691235020800000⟩, + ⟨1, 7, 3, 4, 6, 1, -3559756945040856109416824488814021744547122380800000⟩, + ⟨1, 7, 4, 4, 7, 1, -512881683092886335232011682165716996223034982400000⟩, + ⟨1, 7, 5, 4, 8, 1, 445693347528896221875449566891658934641020108800000⟩, + ⟨1, 7, 0, 5, 2, 1, -27471370452604745644114648349882710848041071411200000⟩, + ⟨1, 7, 1, 5, 3, 1, -27909185213976263616393475839574324099572930969600000⟩, + ⟨1, 7, 2, 5, 4, 1, 4329991457449119023544149231909451586525043097600000⟩, + ⟨1, 7, 3, 5, 5, 1, -1169921155406903534429647568991045158157523353600000⟩, + ⟨1, 7, 4, 5, 6, 1, 470455490680991581694261988369148051616641843200000⟩, + ⟨1, 7, 5, 5, 7, 1, -15161791902597132278913993153376100606489395200000⟩, + ⟨1, 7, 6, 5, 8, 1, 104630753832221018772654238057387266357696921600000⟩, + ⟨1, 7, 0, 6, 1, 1, 19967959302739748350721706743709954299802943488000000⟩, + ⟨1, 7, 1, 6, 2, 1, 69547416784468498693099004509807211260336825958400000⟩, + ⟨1, 7, 2, 6, 3, 1, 2184836852108346034576072550038150357085847552000000⟩, + ⟨1, 7, 3, 6, 4, 1, 5519699252410777856280637147568895091106276966400000⟩, + ⟨1, 7, 4, 6, 5, 1, -763353387428979141335753265719791856643578265600000⟩, + ⟨1, 7, 5, 6, 6, 1, 144215697313159860952128288490386237556575436800000⟩, + ⟨1, 7, 6, 6, 7, 1, 98812943364399717995835023381584878749771366400000⟩, + ⟨1, 7, 7, 6, 8, 1, 15486119545654904535496840130855620723290931200000⟩, + ⟨1, 7, 0, 7, 0, 1, -194753286714464272098916646381021582853210007142400000⟩, + ⟨1, 7, 1, 7, 1, 1, -199015117745155383362253585606832805748647814758400000⟩, + ⟨1, 7, 2, 7, 2, 1, -10567167739231998961490214704987806031867491123200000⟩, + ⟨1, 7, 3, 7, 3, 1, -9837250012353216320396720592540259705318224691200000⟩, + ⟨1, 7, 4, 7, 4, 1, -3156934468521482040737315469708539935977583411200000⟩, + ⟨1, 7, 5, 7, 5, 1, -163093583125146310886266439704581932202118348800000⟩, + ⟨1, 7, 6, 7, 6, 1, -106947209727979978892822914344442665375891456000000⟩, + ⟨1, 7, 7, 7, 7, 1, -5473300123536240863236747087887570810018201600000⟩, + ⟨1, 7, 8, 7, 8, 1, -18357741451605016362297479862089061614223360000000⟩ +] + +def collectedFourData_8_7_4 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 7, 2, -6035629236369518737109976906039557613786287308800000⟩, + ⟨1, 8, 1, 0, 8, 2, -347249744928458478961741300265511420694206873600000⟩, + ⟨1, 8, 0, 1, 6, 2, -759351827759896028992159870823426212304938598400000⟩, + ⟨1, 8, 1, 1, 7, 2, -3641502062306786919059597122185562473788709273600000⟩, + ⟨1, 8, 2, 1, 8, 2, 667475792453700279698307435217913450627019571200000⟩, + ⟨1, 8, 0, 2, 5, 2, 3672566024041524166162858408401067156340893286400000⟩, + ⟨1, 8, 1, 2, 6, 2, -4318144438491346882778770961983918511413945958400000⟩, + ⟨1, 8, 2, 2, 7, 2, 811345641885085434968697179247310237942048358400000⟩, + ⟨1, 8, 3, 2, 8, 2, 85324527189977742622395498114480051182370816000000⟩, + ⟨1, 8, 0, 3, 4, 2, -2332291169474980664478070748590701384087424204800000⟩, + ⟨1, 8, 1, 3, 5, 2, -3567453467860371561191866709216152949803607654400000⟩, + ⟨1, 8, 2, 3, 6, 2, 322309398654527257729962580015179239245479936000000⟩, + ⟨1, 8, 3, 3, 7, 2, 213045909737178048775476818424920620569251020800000⟩, + ⟨1, 8, 4, 3, 8, 2, 24752549060003648688778563496732355662530478080000⟩, + ⟨1, 8, 0, 4, 3, 2, -8950744880540562526445642743450990431390243225600000⟩, + ⟨1, 8, 1, 4, 4, 2, 4018074256340833455973807482189022383970241740800000⟩, + ⟨1, 8, 2, 4, 5, 2, 149686683103124779531614875056947626763721113600000⟩, + ⟨1, 8, 3, 4, 6, 2, 489369128558562771995262824969658044341498675200000⟩, + ⟨1, 8, 4, 4, 7, 2, 56405752681169999146773425728364671792557588480000⟩, + ⟨1, 8, 5, 4, 8, 2, -40847089366295921050776363088593629421030604800000⟩, + ⟨1, 8, 0, 5, 2, 2, 15106245540082893417738201834192172345040515891200000⟩, + ⟨1, 8, 1, 5, 3, 2, 7673497858313096014956089601450878187072179404800000⟩, + ⟨1, 8, 2, 5, 4, 2, -793673717583388434374683125225038178669507379200000⟩, + ⟨1, 8, 3, 5, 5, 2, 160832131278314648038614167104521570791876198400000⟩, + ⟨1, 8, 4, 5, 6, 2, -51739800678443351595078968642999764424211824640000⟩, + ⟨1, 8, 5, 5, 7, 2, 1389554213075648512421632116288502302454579200000⟩, + ⟨1, 8, 6, 5, 8, 2, -8219351026139363636167116918053670537186508800000⟩, + ⟨1, 8, 0, 6, 1, 2, -10980191056794126587483095115978659425511538688000000⟩, + ⟨1, 8, 1, 6, 2, 2, -19121731775945108112045554756951066963627684659200000⟩, + ⟨1, 8, 2, 6, 3, 2, -400473673855139545866046902214576046063222784000000⟩, + ⟨1, 8, 3, 6, 4, 2, -758807540728489497595795555981562563696105881600000⟩, + ⟨1, 8, 4, 6, 5, 2, 83952154656797001155802314992532691140864901120000⟩, + ⟨1, 8, 5, 6, 6, 2, -13217140235173463009897337949442304568511692800000⟩, + ⟨1, 8, 6, 6, 7, 2, -7762328356540230883582015218898413483668275200000⟩, + ⟨1, 8, 7, 6, 8, 2, -1064458745893940154437493496832840482317926400000⟩, + ⟨1, 8, 0, 7, 0, 2, 107092981543187298551581665309130111515122624102400000⟩, + ⟨1, 8, 1, 7, 1, 2, 54718260962509992034693831720055664464540939059200000⟩, + ⟨1, 8, 2, 7, 2, 2, 1936928371878217173401317077116072050194540134400000⟩, + ⟨1, 8, 3, 7, 3, 2, 1352352573583574389150297181401725942662745292800000⟩, + ⟨1, 8, 4, 7, 4, 2, 347193652516995866068705360404828815276365578240000⟩, + ⟨1, 8, 5, 7, 5, 2, 14947268569114875913836120958720231850429644800000⟩, + ⟨1, 8, 6, 7, 6, 2, 8401322037973454964683093586455958449553408000000⟩, + ⟨1, 8, 7, 7, 7, 2, 376214465361997185159295696096949976642355200000⟩, + ⟨1, 8, 8, 7, 8, 2, 1121638618113542640907789611199622063063040000000⟩ +] + +def collectedFourData_8_7_5 : List CollectedFourTerm := [ + ⟨2, 5, 1, 0, 8, 0, -636875838544513555629599892960019875098945126400000⟩, + ⟨2, 5, 1, 1, 7, 0, -6678722485371490577015699083654266045172442726400000⟩, + ⟨2, 5, 2, 1, 8, 0, 3672566024041524166162858408401067156340893286400000⟩, + ⟨2, 5, 1, 2, 6, 0, -7919723197455748246529277654920031680931142041600000⟩, + ⟨2, 5, 2, 2, 7, 0, 4464162553652484722384663463043768588713118924800000⟩, + ⟨2, 5, 3, 2, 8, 0, 938940297515151659356994870919365528968495104000000⟩, + ⟨2, 5, 1, 3, 5, 0, -6542913139591209592913595011653224415180200345600000⟩, + ⟨2, 5, 2, 3, 6, 0, 1773401462810323179259364544440737384410120192000000⟩, + ⟨2, 5, 3, 3, 7, 0, 2344430100709759161168501173544922193629229875200000⟩, + ⟨2, 5, 4, 3, 8, 0, 453975868058646002831192402723544305845351219200000⟩, + ⟨2, 5, 1, 4, 4, 0, 7369377368062307682937994655992732987287614259200000⟩, + ⟨2, 5, 2, 4, 5, 0, 823601743810265746259617747930048427478692659200000⟩, + ⟨2, 5, 3, 4, 6, 0, 5385185365755875450161535024828161469698591948800000⟩, + ⟨2, 5, 4, 4, 7, 0, 1034513676747427278150702947142635243202360115200000⟩, + ⟨2, 5, 5, 4, 8, 0, -1123738375860664536428924172976003139059580928000000⟩, + ⟨2, 5, 1, 5, 3, 0, 14073632751233643058263187732138455594702156595200000⟩, + ⟨2, 5, 2, 5, 4, 0, -4366928602243905291993634641141679028733109862400000⟩, + ⟨2, 5, 3, 5, 5, 0, 1769851813608345373766989104457948424820070809600000⟩, + ⟨2, 5, 4, 5, 6, 0, -948937455663169567265264998635717633123129753600000⟩, + ⟨2, 5, 5, 5, 7, 0, 38227825257493296073015748293454243731341312000000⟩, + ⟨2, 5, 6, 5, 8, 0, -316569930500586582061857281532156089703019315200000⟩, + ⟨2, 5, 1, 6, 2, 0, -35070346737727041610732101955576024207962459340800000⟩, + ⟨2, 5, 2, 6, 3, 0, -2203474679908323702503505591267101654434971648000000⟩, + ⟨2, 5, 3, 6, 4, 0, -8350177862245876243859953317446292482325636710400000⟩, + ⟨2, 5, 4, 6, 5, 0, 1539730400829574237076739224087993763526134988800000⟩, + ⟨2, 5, 5, 6, 6, 0, -363614836009631868146373536637758001389764608000000⟩, + ⟨2, 5, 6, 6, 7, 0, -298967611985161630002788606097258653271510220800000⟩, + ⟨2, 5, 7, 6, 8, 0, -54663785520572733277617978725699420894842060800000⟩, + ⟨2, 5, 1, 7, 1, 0, 100356411611981811326301634305998355082857204940800000⟩, + ⟨2, 5, 2, 7, 2, 0, 10657311336209151474689564375787690724988603596800000⟩, + ⟨2, 5, 3, 7, 3, 0, 14881750530638640299843551794450396022102504243200000⟩, + ⟨2, 5, 4, 7, 4, 0, 6367729618625059261505878651477662741349112217600000⟩, + ⟨2, 5, 5, 7, 5, 0, 411212146715889051312644662348531323610595328000000⟩, + ⟨2, 5, 6, 7, 6, 0, 323578580013940869049024746403974646629138432000000⟩, + ⟨2, 5, 7, 7, 7, 0, 19319966061262675227205024561872219222206054400000⟩, + ⟨2, 5, 8, 7, 8, 0, 74057371249263738658561755818331449390530560000000⟩ +] + +def collectedFourData_8_7_6 : List CollectedFourTerm := [ + ⟨2, 6, 0, 0, 7, 1, 13015562568951473985638565295195886186216502067200000⟩, + ⟨2, 6, 1, 0, 8, 1, 1497656865645179593575374673866991924084001996800000⟩, + ⟨2, 6, 0, 1, 6, 1, 1637508011012540543062942421071359447295170969600000⟩, + ⟨2, 6, 1, 1, 7, 1, 15705470326546771752898422037695822624862293196800000⟩, + ⟨2, 6, 2, 1, 8, 1, -4318144438491346882778770961983918511413945958400000⟩, + ⟨2, 6, 0, 2, 5, 1, -7919723197455748246529277654920031680931142041600000⟩, + ⟨2, 6, 1, 2, 6, 1, 18623767935341427713571005817849817320106701619200000⟩, + ⟨2, 6, 2, 2, 7, 1, -5248890987223773876059788157010734148242689228800000⟩, + ⟨2, 6, 3, 2, 8, 1, -735993997520868067096263631376760271867478016000000⟩, + ⟨2, 6, 0, 3, 4, 1, 5029480847232102829055636839013706744517047091200000⟩, + ⟨2, 6, 1, 3, 5, 1, 15386105409844248819932813946762650953006134067200000⟩, + ⟨2, 6, 2, 3, 6, 1, -2085137098616319548790004884409778385664868352000000⟩, + ⟨2, 6, 3, 3, 7, 1, -1837695630165221254384027378638850607830322380800000⟩, + ⟨2, 6, 4, 3, 8, 1, -266888785257214895754832589391557458759621017600000⟩, + ⟨2, 6, 0, 4, 3, 1, 19301878142116112663065163386549984033564419686400000⟩, + ⟨2, 6, 1, 4, 4, 1, -17329592273482544705800430988440105584028968550400000⟩, + ⟨2, 6, 2, 4, 5, 1, -968377768101321145815339180527946642054394675200000⟩, + ⟨2, 6, 3, 4, 6, 1, -4221209927002399698716312952487158043299230515200000⟩, + ⟨2, 6, 4, 4, 7, 1, -608182324095316192803140703100515017278724505600000⟩, + ⟨2, 6, 5, 4, 8, 1, 528509449390599992493377540495182995031012147200000⟩, + ⟨2, 6, 0, 5, 2, 1, -32575938035444898118999358980398095484817558732800000⟩, + ⟨2, 6, 1, 5, 3, 1, -33095104946394889195719844427321454989360391782400000⟩, + ⟨2, 6, 2, 5, 4, 1, 5134564861087736890631675795827518423469287014400000⟩, + ⟨2, 6, 3, 5, 5, 1, -1387308985208555674147580718323084772453541478400000⟩, + ⟨2, 6, 4, 5, 6, 1, 557872747531810516988680412746565760613928140800000⟩, + ⟨2, 6, 5, 5, 7, 1, -17979066402145346719988250167529258739354828800000⟩, + ⟨2, 6, 6, 5, 8, 1, 124072621688851460216615288234122982866708070400000⟩, + ⟨2, 6, 0, 6, 1, 1, 23678287403337740639171851165417833889448067072000000⟩, + ⟨2, 6, 1, 6, 2, 1, 82470306445206562574769331617471236694951434649600000⟩, + ⟨2, 6, 2, 6, 3, 1, 2590810314127942148370669640124039825549426688000000⟩, + ⟨2, 6, 3, 6, 4, 1, 6545337122188459632122415511431702514637576601600000⟩, + ⟨2, 6, 4, 6, 5, 1, -905195199159624877963648251784525427901884006400000⟩, + ⟨2, 6, 5, 6, 6, 1, 171013005249125732363342550796785136738448179200000⟩, + ⟨2, 6, 6, 6, 7, 1, 117173780088332048893100530218054651983010201600000⟩, + ⟨2, 6, 7, 6, 8, 1, 18363658689656438640350244238151974233361612800000⟩, + ⟨2, 6, 0, 7, 0, 1, -230941190617160461928727573033447698368325851545600000⟩, + ⟨2, 6, 1, 7, 1, 1, -235994929884113057626650475333870920035498301849600000⟩, + ⟨2, 6, 2, 7, 2, 1, -12530696350852589990515671832674361924492512460800000⟩, + ⟨2, 6, 3, 7, 3, 1, -11665149628937175419615694101429782022762319052800000⟩, + ⟨2, 6, 4, 7, 4, 1, -3743537360319969351925786209580425971470486732800000⟩, + ⟨2, 6, 5, 7, 5, 1, -193398668152709271322310781259092976957862707200000⟩, + ⟨2, 6, 6, 7, 6, 1, -126819507718883134578161918176292082510987264000000⟩, + ⟨2, 6, 7, 7, 7, 1, -6490316381606068183737119073241821568460390400000⟩, + ⟨2, 6, 8, 7, 8, 1, -21768868394459764704839664712616186310819840000000⟩ +] + +def collectedFourData_8_7_7 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 7, 2, -7336567906022294078368560924608599661039163801600000⟩, + ⟨2, 7, 1, 0, 8, 2, -422097056370707722614531158793764708134630195200000⟩, + ⟨2, 7, 0, 1, 6, 2, -923024929257193213578961284398079076465429708800000⟩, + ⟨2, 7, 1, 1, 7, 2, -4426402967075549226857113733646595814226866995200000⟩, + ⟨2, 7, 2, 1, 8, 2, 811345641885085434968697179247310237942048358400000⟩, + ⟨2, 7, 0, 2, 5, 2, 4464162553652484722384663463043768588713118924800000⟩, + ⟨2, 7, 1, 2, 6, 2, -5248890987223773876059788157010734148242689228800000⟩, + ⟨2, 7, 2, 2, 7, 2, 986225654994946161905757262166117118450126028800000⟩, + ⟨2, 7, 3, 2, 8, 2, 103715646416189575961467091214845975055040512000000⟩, + ⟨2, 7, 0, 3, 4, 2, -2835000605796283615776938974077008226291390873600000⟩, + ⟨2, 7, 1, 3, 5, 2, -4336393703711915489047570712328092212832029900800000⟩, + ⟨2, 7, 2, 3, 6, 2, 391780988754124232867016950041333173533540352000000⟩, + ⟨2, 7, 3, 3, 7, 2, 258966500869307217251114742062372043479423385600000⟩, + ⟨2, 7, 4, 3, 8, 2, 30087791995503394698738097788868090887992770560000⟩, + ⟨2, 7, 0, 4, 3, 2, -10880016822416172929840420287238566982576190259200000⟩, + ⟨2, 7, 1, 4, 4, 2, 4884142726238158334198521619497931437407574425600000⟩, + ⟨2, 7, 2, 4, 5, 2, 181950625561268440229788862381478580883501875200000⟩, + ⟨2, 7, 3, 4, 6, 2, 594849302728283382099909719306191652683933286400000⟩, + ⟨2, 7, 4, 4, 7, 2, 68563627524049463578847863738613857885995663360000⟩, + ⟨2, 7, 5, 4, 8, 2, -49651400568708501407591220055221746588555673600000⟩, + ⟨2, 7, 0, 5, 2, 2, 18362293618374831648094564740373416800229418598400000⟩, + ⟨2, 7, 1, 5, 3, 2, 9327467925795565703145481669112371322451237273600000⟩, + ⟨2, 7, 2, 5, 4, 2, -964744668076758328407442779113665244099405414400000⟩, + ⟨2, 7, 3, 5, 5, 2, 195498398987708674954752219877575973875272908800000⟩, + ⟨2, 7, 4, 5, 6, 2, -62891961427005429854696392618742283762118164480000⟩, + ⟨2, 7, 5, 5, 7, 2, 1689063135604561973151202627713265654195814400000⟩, + ⟨2, 7, 6, 5, 8, 2, -9990976016773607588123284539285228205218201600000⟩, + ⟨2, 7, 0, 6, 1, 2, -13346896264576460700099828837058912138051977216000000⟩, + ⟨2, 7, 1, 6, 2, 2, -23243290493991624807894192936960315422035830374400000⟩, + ⟨2, 7, 2, 6, 3, 2, -486793039755992249543998601988482316462194688000000⟩, + ⟨2, 7, 3, 6, 4, 2, -922363324872646350826234571729645481871225651200000⟩, + ⟨2, 7, 4, 6, 5, 2, 102047468354261995910362298310859519915028643840000⟩, + ⟨2, 7, 5, 6, 6, 2, -16066004564106875716739319139002976954849689600000⟩, + ⟨2, 7, 6, 6, 7, 2, -9435445231366637784815729187312075650000486400000⟩, + ⟨2, 7, 7, 6, 8, 2, -1293895560275946527714527110527469218483404800000⟩, + ⟨2, 7, 0, 7, 0, 2, 130176142466727772848482390943490868708771679436800000⟩, + ⟨2, 7, 1, 7, 1, 2, 66512408487897017135058054710584478846884931174400000⟩, + ⟨2, 7, 2, 7, 2, 2, 2354420056778275696221704308186355408464301260800000⟩, + ⟨2, 7, 3, 7, 3, 2, 1643842936738746018041550404729576197004564889600000⟩, + ⟨2, 7, 4, 7, 4, 2, 422028873622962346030281549883105662482440519680000⟩, + ⟨2, 7, 5, 7, 5, 2, 18169050246834971844483276333715809982060953600000⟩, + ⟨2, 7, 6, 7, 6, 2, 10212169637681216023269265090110240646496256000000⟩, + ⟨2, 7, 7, 7, 7, 2, 457304924517928396702821707339593329043046400000⟩, + ⟨2, 7, 8, 7, 8, 2, 1363400163519124950421470290407039728353280000000⟩ +] + +def collectedFourData_8_7_8 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 7, 3, -1543088803248120465996647458091296483776135168000000⟩, + ⟨2, 8, 1, 0, 8, 3, -59186007218713854024424424389208307520241664000000⟩, + ⟨2, 8, 0, 1, 6, 3, -194138383464903922381794382883257326369767424000000⟩, + ⟨2, 8, 1, 1, 7, 3, -620665588655952036746722019055620586328817664000000⟩, + ⟨2, 8, 2, 1, 8, 3, 85324527189977742622395498114480051182370816000000⟩, + ⟨2, 8, 0, 2, 5, 3, 938940297515151659356994870919365528968495104000000⟩, + ⟨2, 8, 1, 2, 6, 3, -735993997520868067096263631376760271867478016000000⟩, + ⟨2, 8, 2, 2, 7, 3, 103715646416189575961467091214845975055040512000000⟩, + ⟨2, 8, 3, 2, 8, 3, 8725739596853769313719020133545843311509504000000⟩, + ⟨2, 8, 0, 3, 4, 3, -596281224142272701208740252065010160897097728000000⟩, + ⟨2, 8, 1, 3, 5, 3, -608044584005987269049560697019050911183405056000000⟩, + ⟨2, 8, 2, 3, 6, 3, 41201339973675820121403326941712993463828480000000⟩, + ⟨2, 8, 3, 3, 7, 3, 21787206935261933793563137201950717384012595200000⟩, + ⟨2, 8, 4, 3, 8, 3, 2109439342639070579277629479152844118006169600000⟩, + ⟨2, 8, 0, 4, 3, 3, -2288376847713808027199631216538785343881609216000000⟩, + ⟨2, 8, 1, 4, 4, 3, 684849378334639341145931517475866413516193792000000⟩, + ⟨2, 8, 2, 4, 5, 3, 19134694631335387644891951620605610922344448000000⟩, + ⟨2, 8, 3, 4, 6, 3, 50045487776729721961839938647063872058215628800000⟩, + ⟨2, 8, 4, 4, 7, 3, 4806960025345029928394487156275053852203417600000⟩, + ⟨2, 8, 5, 4, 8, 3, -2983743168062082290785846010605472430686208000000⟩, + ⟨2, 8, 0, 5, 2, 3, 3862112372899846282242476418513431830129016832000000⟩, + ⟨2, 8, 1, 5, 3, 3, 1307887784708013193323027641008786751883313152000000⟩, + ⟨2, 8, 2, 5, 4, 3, -101456615298317287479119584800090568582496256000000⟩, + ⟨2, 8, 3, 5, 5, 3, 16447548466537712298569392166847997070121369600000⟩, + ⟨2, 8, 4, 5, 6, 3, -4409322485002924111720064261026380300209356800000⟩, + ⟨2, 8, 5, 5, 7, 3, 101502284599435626825646300882832229138432000000⟩, + ⟨2, 8, 6, 5, 8, 3, -525346572896459305583807610990934508961792000000⟩, + ⟨2, 8, 0, 6, 1, 3, -2807231725760505149255602940178070620528967680000000⟩, + ⟨2, 8, 1, 6, 2, 3, -3259149852388118500720579890448124355394142208000000⟩, + ⟨2, 8, 2, 6, 3, 3, -51193207693885563657030262215194031811461120000000⟩, + ⟨2, 8, 3, 6, 4, 3, -77599691701585358100764356545762042545858150400000⟩, + ⟨2, 8, 4, 6, 5, 3, 7154494573592064199699290074290374683551334400000⟩, + ⟨2, 8, 5, 6, 6, 3, -965467858049085103349945081636760676466688000000⟩, + ⟨2, 8, 6, 6, 7, 3, -496135593532475601882060341245130223648768000000⟩, + ⟨2, 8, 7, 6, 8, 3, -60476226825817176399374849317860500570112000000⟩, + ⟨2, 8, 0, 7, 0, 3, 27379743561775107941518961911611190421816868864000000⟩, + ⟨2, 8, 1, 7, 1, 3, 9326300265504306053309842674297496524143198208000000⟩, + ⟨2, 8, 2, 7, 2, 3, 247600736086359426228527224922746025454600192000000⟩, + ⟨2, 8, 3, 7, 3, 3, 138298761081343109626230817633536932391891763200000⟩, + ⟨2, 8, 4, 7, 4, 3, 29588223352613433582008551307869942530755788800000⟩, + ⟨2, 8, 5, 7, 5, 3, 1091847942318390419692537873407337832644608000000⟩, + ⟨2, 8, 6, 7, 6, 3, 536977399604008175364171328027720647966720000000⟩, + ⟨2, 8, 7, 7, 7, 3, 21374272540058243958955495350724687036416000000⟩, + ⟨2, 8, 8, 7, 8, 3, 57352362947422712259557503332026029178880000000⟩ +] + +def collectedFourData_8_7_9 : List CollectedFourTerm := [ + ⟨3, 4, 1, 0, 8, 0, 404452876970945892437744757131405148736507084800000⟩, + ⟨3, 4, 1, 1, 7, 0, 4241373844346658827782958292129959985151790284800000⟩, + ⟨3, 4, 2, 1, 8, 0, -2332291169474980664478070748590701384087424204800000⟩, + ⟨3, 4, 1, 2, 6, 0, 5029480847232102829055636839013706744517047091200000⟩, + ⟨3, 4, 2, 2, 7, 0, -2835000605796283615776938974077008226291390873600000⟩, + ⟨3, 4, 3, 2, 8, 0, -596281224142272701208740252065010160897097728000000⟩, + ⟨3, 4, 1, 3, 5, 0, 4155127079599062763361427685749598928323687219200000⟩, + ⟨3, 4, 2, 3, 6, 0, -1126212175511800970879989707509226487198777344000000⟩, + ⟨3, 4, 3, 3, 7, 0, -1488848283609478740646261613055313037855450726400000⟩, + ⟨3, 4, 4, 3, 8, 0, -288300850494375633189983962437132735903852134400000⟩, + ⟨3, 4, 1, 4, 4, 0, -4679979515016654296295560049929535016072013414400000⟩, + ⟨3, 4, 2, 4, 5, 0, -523034592619527958621648141703656467316762214400000⟩, + ⟨3, 4, 3, 4, 6, 0, -3419903193657687014850416753305735079994694041600000⟩, + ⟨3, 4, 4, 4, 7, 0, -656975830300781245900712150964318280117282406400000⟩, + ⟨3, 4, 5, 4, 8, 0, 713638658546374283784079924767695241002090496000000⟩, + ⟨3, 4, 1, 5, 3, 0, -8937568221582223603439243927961636690603697766400000⟩, + ⟨3, 4, 2, 5, 4, 0, 2773251440564441597138142834086514049864748236800000⟩, + ⟨3, 4, 3, 5, 5, 0, -1123957943611186638256496569880541246235292467200000⟩, + ⟨3, 4, 4, 5, 6, 0, 602629995958989641688856222150626018313057075200000⟩, + ⟨3, 4, 5, 5, 7, 0, -24276873088906016203480074355079362520285184000000⟩, + ⟨3, 4, 6, 5, 8, 0, 201040157915341648241263830729615235535496806400000⟩, + ⟨3, 4, 1, 6, 2, 0, 22271692182354530607414840002900451708387301785600000⟩, + ⟨3, 4, 2, 6, 3, 0, 1399333464523110997790917626361394982379585536000000⟩, + ⟨3, 4, 3, 6, 4, 0, 5302844377520531271100475715189252154628820172800000⟩, + ⟨3, 4, 4, 6, 5, 0, -977817578695321877881752203270750305099815321600000⟩, + ⟨3, 4, 5, 6, 6, 0, 230916385318541794331811120496440792638816256000000⟩, + ⟨3, 4, 6, 6, 7, 0, 189861670784800305097430548723207110053697945600000⟩, + ⟨3, 4, 7, 6, 8, 0, 34714655482056106309092711683542714999740825600000⟩, + ⟨3, 4, 1, 7, 1, 0, -63732107488498392097467657434616255930135320985600000⟩, + ⟨3, 4, 2, 7, 2, 0, -6768007152784457303420411098553548476679559577600000⟩, + ⟨3, 4, 3, 7, 3, 0, -9450769604066258477624611487197837065948915302400000⟩, + ⟨3, 4, 4, 7, 4, 0, -4043875443464483111856704137161602545623446323200000⟩, + ⟨3, 4, 5, 7, 5, 0, -261143421871256314330788032119568993454391296000000⟩, + ⟨3, 4, 6, 7, 6, 0, -205491054444617088802915636144838954685825024000000⟩, + ⟨3, 4, 7, 7, 7, 0, -12269292354246805122863935629455190624357580800000⟩, + ⟨3, 4, 8, 7, 8, 0, -47030700569710227272295231922906679130193920000000⟩ +] + +def collectedFourData_8_7_10 : List CollectedFourTerm := [ + ⟨3, 5, 0, 0, 7, 1, 10752862597384982793364417130235694866544931635200000⟩, + ⟨3, 5, 1, 0, 8, 1, 1237295615076146085370819124849318393679760588800000⟩, + ⟨3, 5, 0, 1, 6, 1, 1352834236035139401683612442288772090401757593600000⟩, + ⟨3, 5, 1, 1, 7, 1, 12975141378177806052780584288415183662826179788800000⟩, + ⟨3, 5, 2, 1, 8, 1, -3567453467860371561191866709216152949803607654400000⟩, + ⟨3, 5, 0, 2, 5, 1, -6542913139591209592913595011653224415180200345600000⟩, + ⟨3, 5, 1, 2, 6, 1, 15386105409844248819932813946762650953006134067200000⟩, + ⟨3, 5, 2, 2, 7, 1, -4336393703711915489047570712328092212832029900800000⟩, + ⟨3, 5, 3, 2, 8, 1, -608044584005987269049560697019050911183405056000000⟩, + ⟨3, 5, 0, 3, 4, 1, 4155127079599062763361427685749598928323687219200000⟩, + ⟨3, 5, 1, 3, 5, 1, 12711296688443109672300327587182806031972643635200000⟩, + ⟨3, 5, 2, 3, 6, 1, -1722644918293186219540795525488920629170143232000000⟩, + ⟨3, 5, 3, 3, 7, 1, -1518220092469912118138351492775183705621449932800000⟩, + ⟨3, 5, 4, 3, 8, 1, -220491309649553591376383469463040224701028761600000⟩, + ⟨3, 5, 0, 4, 3, 1, 15946329052941061624477992028351257078527321702400000⟩, + ⟨3, 5, 1, 4, 4, 1, -14316916660212705988656409267551917762775770726400000⟩, + ⟨3, 5, 2, 4, 5, 1, -800029428431743638514426729137554925628371763200000⟩, + ⟨3, 5, 3, 4, 6, 1, -3487370607249202908796428967464276883944977203200000⟩, + ⟨3, 5, 4, 4, 7, 1, -502452424204513775407543527116616407606466969600000⟩, + ⟨3, 5, 5, 4, 8, 1, 436630338535918729437659195550102033871876915200000⟩, + ⟨3, 5, 0, 5, 2, 1, -26912750318735166257728913314357557196755881164800000⟩, + ⟨3, 5, 1, 5, 3, 1, -27341662279242439548983507843932963656704616038400000⟩, + ⟨3, 5, 2, 5, 4, 1, 4241942686391721070854543351939797796698613350400000⟩, + ⟨3, 5, 3, 5, 5, 1, -1146131242429034941428430355311234637097231974400000⟩, + ⟨3, 5, 4, 5, 6, 1, 460888952686925989794502727977934860407590092800000⟩, + ⟨3, 5, 5, 5, 7, 1, -14853482485091226702006521603487086821559500800000⟩, + ⟨3, 5, 6, 5, 8, 1, 102503126242127915746951998341103449450899046400000⟩, + ⟨3, 5, 0, 6, 1, 1, 19561918252911411241677103165227558691512778752000000⟩, + ⟨3, 5, 1, 6, 2, 1, 68133195847021981922772723621332846472702040473600000⟩, + ⟨3, 5, 2, 6, 3, 1, 2140409004691209572080549386705291020397969408000000⟩, + ⟨3, 5, 3, 6, 4, 1, 5407458214395538735554754021165322423013841305600000⟩, + ⟨3, 5, 4, 6, 5, 1, -747830879288693004254484218697096180261086822400000⟩, + ⟨3, 5, 5, 6, 6, 1, 141283124572452871735297936526128530102367027200000⟩, + ⟨3, 5, 6, 6, 7, 1, 96803618793370377260277444388058566110058905600000⟩, + ⟨3, 5, 7, 6, 8, 1, 15171215045763316252855354312691817732951244800000⟩, + ⟨3, 5, 0, 7, 0, 1, -190793050828756604351731124835768132854653491609600000⟩, + ⟨3, 5, 1, 7, 1, 1, -194968219105399765974562314763906256401390475673600000⟩, + ⟨3, 5, 2, 7, 2, 1, -10352288300752715757952354520558089121775275212800000⟩, + ⟨3, 5, 3, 7, 3, 1, -9637213180252317979292458256731853102907182284800000⟩, + ⟨3, 5, 4, 7, 4, 1, -3092739376454069442378410309423408895497129164800000⟩, + ⟨3, 5, 5, 7, 5, 1, -159777135574929532259599882009789872508973875200000⟩, + ⟨3, 5, 6, 7, 6, 1, -104772477866011384046227292979826338167783424000000⟩, + ⟨3, 5, 7, 7, 7, 1, -5362002594605415407800188519528776635672166400000⟩, + ⟨3, 5, 8, 7, 8, 1, -17984443584833816570979501246484946815549440000000⟩ +] + +def collectedFourData_8_7_11 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 7, 2, -2914472781888764028984184857054862028480446464000000⟩, + ⟨3, 6, 1, 0, 8, 2, -167679274269100826179636433676439609417924608000000⟩, + ⟨3, 6, 0, 1, 6, 2, -366674317989569884645223565153705131142807552000000⟩, + ⟨3, 6, 1, 1, 7, 2, -1758401358027879090627612864973565835878596608000000⟩, + ⟨3, 6, 2, 1, 8, 2, 322309398654527257729962580015179239245479936000000⟩, + ⟨3, 6, 0, 2, 5, 2, 1773401462810323179259364544440737384410120192000000⟩, + ⟨3, 6, 1, 2, 6, 2, -2085137098616319548790004884409778385664868352000000⟩, + ⟨3, 6, 2, 2, 7, 2, 391780988754124232867016950041333173533540352000000⟩, + ⟨3, 6, 3, 2, 8, 2, 41201339973675820121403326941712993463828480000000⟩, + ⟨3, 6, 0, 3, 4, 2, -1126212175511800970879989707509226487198777344000000⟩, + ⟨3, 6, 1, 3, 5, 2, -1722644918293186219540795525488920629170143232000000⟩, + ⟨3, 6, 2, 3, 6, 2, 155636128883653689195968022837844819134382080000000⟩, + ⟨3, 6, 3, 3, 7, 2, 102875190126029391124798667677469764510285824000000⟩, + ⟨3, 6, 4, 3, 8, 2, 11952462235924242306052012610459432420533862400000⟩, + ⟨3, 6, 0, 4, 3, 2, -4322118094128829372714396115101810937108103168000000⟩, + ⟨3, 6, 1, 4, 4, 2, 1940239798884217060767568296173308924787687424000000⟩, + ⟨3, 6, 2, 4, 5, 2, 72280411309306766577324074525030044881911808000000⟩, + ⟨3, 6, 3, 4, 6, 2, 236305602883330472002642797826939104899629056000000⟩, + ⟨3, 6, 4, 4, 7, 2, 27237098982260036116539605029270191388124774400000⟩, + ⟨3, 6, 5, 4, 8, 2, -19724162223234180267330959939512140608569344000000⟩, + ⟨3, 6, 0, 5, 2, 2, 7294474153217300129363392330163754923024449536000000⟩, + ⟨3, 6, 1, 5, 3, 2, 3705363562621267765393238156063532602930233344000000⟩, + ⟨3, 6, 2, 5, 4, 2, -383247604683654920547269890732103782342066176000000⟩, + ⟨3, 6, 3, 5, 5, 2, 77662303416397414038850890308390147485335552000000⟩, + ⟨3, 6, 4, 5, 6, 2, -24984013250684190031939001489648014075310899200000⟩, + ⟨3, 6, 5, 5, 7, 2, 670985207070777082097224296704479567282176000000⟩, + ⟨3, 6, 6, 5, 8, 2, -3968944067359882336627048162840798732222464000000⟩, + ⟨3, 6, 0, 6, 1, 2, -5302093074592841535102083779866504666430832640000000⟩, + ⟨3, 6, 1, 6, 2, 2, -9233464253859873354680419705392613362631704576000000⟩, + ⟨3, 6, 2, 6, 3, 2, -193379940451057989388235099208417275302379520000000⟩, + ⟨3, 6, 3, 6, 4, 2, -366411493737707199130580688186400021149646848000000⟩, + ⟨3, 6, 4, 6, 5, 2, 40538651422419997113277864147970627410172313600000⟩, + ⟨3, 6, 5, 6, 6, 2, -6382266696850752088377370776654065103273984000000⟩, + ⟨3, 6, 6, 6, 7, 2, -3748257858997950045003853930591904707117056000000⟩, + ⟨3, 6, 7, 6, 8, 2, -514003746893077499371009382544240009019392000000⟩, + ⟨3, 6, 0, 7, 0, 2, 51712848423187384952229314689958760505694748672000000⟩, + ⟨3, 6, 1, 7, 1, 2, 26422246298125384091104291164234437778342936576000000⟩, + ⟨3, 6, 2, 7, 2, 2, 935300164942333632529463972530719810631237632000000⟩, + ⟨3, 6, 3, 7, 3, 2, 653021352517228392967592231319391771488681984000000⟩, + ⟨3, 6, 4, 7, 4, 2, 167652188475710272412139810976463299718361907200000⟩, + ⟨3, 6, 5, 7, 5, 2, 7217707665964993931795366019908276840300544000000⟩, + ⟨3, 6, 6, 7, 6, 2, 4056813871867991425399445693992897074954240000000⟩, + ⟨3, 6, 7, 7, 7, 2, 181665701538338348544310642643434739859456000000⟩, + ⟨3, 6, 8, 7, 8, 2, 541614651196428940122042074051233657651200000000⟩ +] + +def collectedFourData_8_7_12 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 7, 3, -3852922116536077886327669075099557156113245798400000⟩, + ⟨3, 7, 1, 0, 8, 3, -147780915604102855544588852370464295158494003200000⟩, + ⟨3, 7, 0, 1, 6, 3, -484742076895373529980462422327076570845623091200000⟩, + ⟨3, 7, 1, 1, 7, 3, -1549733345528579313031666562356613727244202803200000⟩, + ⟨3, 7, 2, 1, 8, 3, 213045909737178048775476818424920620569251020800000⟩, + ⟨3, 7, 0, 2, 5, 3, 2344430100709759161168501173544922193629229875200000⟩, + ⟨3, 7, 1, 2, 6, 3, -1837695630165221254384027378638850607830322380800000⟩, + ⟨3, 7, 2, 2, 7, 3, 258966500869307217251114742062372043479423385600000⟩, + ⟨3, 7, 3, 2, 8, 3, 21787206935261933793563137201950717384012595200000⟩, + ⟨3, 7, 0, 3, 4, 3, -1488848283609478740646261613055313037855450726400000⟩, + ⟨3, 7, 1, 3, 5, 3, -1518220092469912118138351492775183705621449932800000⟩, + ⟨3, 7, 2, 3, 6, 3, 102875190126029391124798667677469764510285824000000⟩, + ⟨3, 7, 3, 3, 7, 3, 54400246623344275712736936356290375653796085760000⟩, + ⟨3, 7, 4, 3, 8, 3, 5267036789870700009219032856494492489330196480000⟩, + ⟨3, 7, 0, 4, 3, 3, -5713823954244535172140329642485010952440564940800000⟩, + ⟨3, 7, 1, 4, 4, 3, 1709993171311496757104254851689044402901719449600000⟩, + ⟨3, 7, 2, 4, 5, 3, 47777216698773338874785794903169810649474662400000⟩, + ⟨3, 7, 3, 4, 6, 3, 124958049259329144258351345626958086429674045440000⟩, + ⟨3, 7, 4, 4, 7, 3, 12002447659506889964429583115610506241381498880000⟩, + ⟨3, 7, 5, 4, 8, 3, -7450076766865959775196745216142391242024550400000⟩, + ⟨3, 7, 0, 5, 2, 3, 9643267546735453691222303199725052528512571801600000⟩, + ⟨3, 7, 1, 5, 3, 3, 3265651180309034658657520230696018279449336217600000⟩, + ⟨3, 7, 2, 5, 4, 3, -253325949957608440791716328655531849529740492800000⟩, + ⟨3, 7, 3, 5, 5, 3, 41067709853204388376489602823890364677991956480000⟩, + ⟨3, 7, 4, 5, 6, 3, -11009590689561811395171464677762956047249571840000⟩, + ⟨3, 7, 5, 5, 7, 3, 253439981152673305785478910239311042025881600000⟩, + ⟨3, 7, 6, 5, 8, 3, -1311732302961784427316552674232287918397849600000⟩, + ⟨3, 7, 0, 6, 1, 3, -7009347212977754697673169013375088350707318784000000⟩, + ⟨3, 7, 1, 6, 2, 3, -8137736804867695163339604598754667803621877350400000⟩, + ⟨3, 7, 2, 6, 3, 3, -127823778984728267226643874044196674816966656000000⟩, + ⟨3, 7, 3, 6, 4, 3, -193757849686985311655090934073063471563952619520000⟩, + ⟨3, 7, 4, 6, 5, 3, 17863981850691842875434262593231124194624798720000⟩, + ⟨3, 7, 5, 6, 6, 3, -2410666486110131462749819586054484125967974400000⟩, + ⟨3, 7, 6, 6, 7, 3, -1238795717458561949233549706805528177829478400000⟩, + ⟨3, 7, 7, 6, 8, 3, -151002451298570305281933945659720042387865600000⟩, + ⟨3, 7, 0, 7, 0, 3, 68364192191787322196546980302175027983205741363200000⟩, + ⟨3, 7, 1, 7, 1, 3, 23286740518614157237584037177965601106659010150400000⟩, + ⟨3, 7, 2, 7, 2, 3, 618231659856293358741900766805261620294031769600000⟩, + ⟨3, 7, 3, 7, 3, 3, 345316714202199875298465219848395993552949084160000⟩, + ⟨3, 7, 4, 7, 4, 3, 73878522029534021295575604393386481135585853440000⟩, + ⟨3, 7, 5, 7, 5, 3, 2726223582205918211848483367725596190074470400000⟩, + ⟨3, 7, 6, 7, 6, 3, 1340773191185965193927982324398328366759936000000⟩, + ⟨3, 7, 7, 7, 7, 3, 53369195098241011191503949455533477252300800000⟩, + ⟨3, 7, 8, 7, 8, 3, 143202508611682132464858302831227614265344000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0831.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0831.lean new file mode 100644 index 0000000000000000000000000000000000000000..22310bb9d21a6e0ec304c0055a07593f7c46dd9a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0831.lean @@ -0,0 +1,651 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0831. -/ +namespace LaughlinFock +def collectedFourData_8_7_13 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 7, 4, -746080534406755867385963619198910383434131046400000⟩, + ⟨3, 8, 1, 0, 8, 4, -21462242387893138932787859632388467274966630400000⟩, + ⟨3, 8, 0, 1, 6, 4, -93865543304748646330937566406928142292955955200000⟩, + ⟨3, 8, 1, 1, 7, 4, -225067983659261464297659934740956488191600230400000⟩, + ⟨3, 8, 2, 1, 8, 4, 24752549060003648688778563496732355662530478080000⟩, + ⟨3, 8, 0, 2, 5, 4, 453975868058646002831192402723544305845351219200000⟩, + ⟨3, 8, 1, 2, 6, 4, -266888785257214895754832589391557458759621017600000⟩, + ⟨3, 8, 2, 2, 7, 4, 30087791995503394698738097788868090887992770560000⟩, + ⟨3, 8, 3, 2, 8, 4, 2109439342639070579277629479152844118006169600000⟩, + ⟨3, 8, 0, 3, 4, 4, -288300850494375633189983962437132735903852134400000⟩, + ⟨3, 8, 1, 3, 5, 4, -220491309649553591376383469463040224701028761600000⟩, + ⟨3, 8, 2, 3, 6, 4, 11952462235924242306052012610459432420533862400000⟩, + ⟨3, 8, 3, 3, 7, 4, 5267036789870700009219032856494492489330196480000⟩, + ⟨3, 8, 4, 3, 8, 4, 437104266476619541428205925475702368706232320000⟩, + ⟨3, 8, 0, 4, 3, 4, -1106425902302291782771991751692513245194407116800000⟩, + ⟨3, 8, 1, 4, 4, 4, 248342539862505128437595784140919535075275571200000⟩, + ⟨3, 8, 2, 4, 5, 4, 5550953321496409011675063616967665502115594240000⟩, + ⟨3, 8, 3, 4, 6, 4, 12098449611751065765892003950830027378125701120000⟩, + ⟨3, 8, 4, 4, 7, 4, 996066913795293539634822690266529828616273920000⟩, + ⟨3, 8, 5, 4, 8, 4, -540987828926569740445152388465869701146214400000⟩, + ⟨3, 8, 0, 5, 2, 4, 1867324069131191792307194540158131866365958553600000⟩, + ⟨3, 8, 1, 5, 3, 4, 474270963199770284608579455318453631191298867200000⟩, + ⟨3, 8, 2, 5, 4, 4, -29432449617236144060392742436441805018135265280000⟩, + ⟨3, 8, 3, 5, 5, 4, 3976179375990952416501973184381075412001751040000⟩, + ⟨3, 8, 4, 5, 6, 4, -913671055388028371134002200406802517521858560000⟩, + ⟨3, 8, 5, 5, 7, 4, 18403561393724133037771444415471464061337600000⟩, + ⟨3, 8, 6, 5, 8, 4, -84668026672716920245154492890734549742387200000⟩, + ⟨3, 8, 0, 6, 1, 4, -1357291260068993886342122714404350180420747264000000⟩, + ⟨3, 8, 1, 6, 2, 4, -1181844618305373301407353532072568162425294028800000⟩, + ⟨3, 8, 2, 6, 3, 4, -14851091787013150056537554409610150376216985600000⟩, + ⟨3, 8, 3, 6, 4, 4, -18759652501091019543983256708765948801145896960000⟩, + ⟨3, 8, 4, 6, 5, 4, 1482507716333986466053763685601085403672084480000⟩, + ⟨3, 8, 5, 6, 6, 4, -175050710133202932900812588558336601253478400000⟩, + ⟨3, 8, 6, 6, 7, 4, -79960208810139169130071140209991508348108800000⟩, + ⟨3, 8, 7, 6, 8, 4, -8772042581243741889140237693847688477409280000⟩, + ⟨3, 8, 0, 7, 0, 4, 13238054521224125301034952266573719489297462067200000⟩, + ⟨3, 8, 1, 7, 1, 4, 3381936479358190048335847207466103544132455628800000⟩, + ⟨3, 8, 2, 7, 2, 4, 71828694152910737399786028382544372964482088960000⟩, + ⟨3, 8, 3, 7, 3, 4, 33433595447704638235376062600659120227541319680000⟩, + ⟨3, 8, 4, 7, 4, 4, 6131078720049911482300638262080539607391272960000⟩, + ⟨3, 8, 5, 7, 5, 4, 197964910034937184987235605279471938463334400000⟩, + ⟨3, 8, 6, 7, 6, 4, 86542520952694991911132459463838586109952000000⟩, + ⟨3, 8, 7, 7, 7, 4, 3100326172869933117179425919825645446103040000⟩, + ⟨3, 8, 8, 7, 8, 4, 7562661716475380382594513979118349975552000000⟩ +] + +def collectedFourData_8_7_14 : List CollectedFourTerm := [ + ⟨4, 3, 1, 0, 8, 0, 1552188065258817864977403892010514579000498585600000⟩, + ⟨4, 3, 1, 1, 7, 0, 16277322368926350727896278009849297205949208985600000⟩, + ⟨4, 3, 2, 1, 8, 0, -8950744880540562526445642743450990431390243225600000⟩, + ⟨4, 3, 1, 2, 6, 0, 19301878142116112663065163386549984033564419686400000⟩, + ⟨4, 3, 2, 2, 7, 0, -10880016822416172929840420287238566982576190259200000⟩, + ⟨4, 3, 3, 2, 8, 0, -2288376847713808027199631216538785343881609216000000⟩, + ⟨4, 3, 1, 3, 5, 0, 15946329052941061624477992028351257078527321702400000⟩, + ⟨4, 3, 2, 3, 6, 0, -4322118094128829372714396115101810937108103168000000⟩, + ⟨4, 3, 3, 3, 7, 0, -5713823954244535172140329642485010952440564940800000⟩, + ⟨4, 3, 4, 3, 8, 0, -1106425902302291782771991751692513245194407116800000⟩, + ⟨4, 3, 1, 4, 4, 0, -17960580236857679742101865127852425272326147276800000⟩, + ⟨4, 3, 2, 4, 5, 0, -2007274762048135107519572296197921678102940876800000⟩, + ⟨4, 3, 3, 4, 6, 0, -13124725335845007982477226056496630673509135155200000⟩, + ⟨4, 3, 4, 4, 7, 0, -2521307427934625444664216607190480841123613900800000⟩, + ⟨4, 3, 5, 4, 8, 0, 2738765062073145349350804241155090090465165312000000⟩, + ⟨4, 3, 1, 5, 3, 0, -34300131154643671674477841611160653631283055820800000⟩, + ⟨4, 3, 2, 5, 4, 0, 10643039110623446326651064790612610573045176729600000⟩, + ⟨4, 3, 3, 5, 5, 0, -4313466921021435156137197517937643294376224358400000⟩, + ⟨4, 3, 4, 5, 6, 0, 2312741831631742874593205497181333371700536934400000⟩, + ⟨4, 3, 5, 5, 7, 0, -93168511873658445219389445838532373431451648000000⟩, + ⟨4, 3, 6, 5, 8, 0, 771541387196901600223348661709538392896490700800000⟩, + ⟨4, 3, 1, 6, 2, 0, 85473133625532755069552134704615262053396067123200000⟩, + ⟨4, 3, 2, 6, 3, 0, 5370288670504562270164811569530321466338312192000000⟩, + ⟨4, 3, 3, 6, 4, 0, 20350978379376130155183089584177771128555149721600000⟩, + ⟨4, 3, 4, 6, 5, 0, -3752617083646514618871071818820305485797995315200000⟩, + ⟨4, 3, 5, 6, 6, 0, 886198807753553939199647486436332243917996032000000⟩, + ⟨4, 3, 6, 6, 7, 0, 728641174836879274621042770349736393392206643200000⟩, + ⟨4, 3, 7, 6, 8, 0, 133226086391987385795670604674769328079582003200000⟩, + ⟨4, 3, 1, 7, 1, 0, -244587743715185924095611053145612749927175369523200000⟩, + ⟨4, 3, 2, 7, 2, 0, -25973903330382283042776485766533356008355607347200000⟩, + ⟨4, 3, 3, 7, 3, 0, -36269668537915315015646931941103312402910072012800000⟩, + ⟨4, 3, 4, 7, 4, 0, -15519373351347632245372599395170544506540287590400000⟩, + ⟨4, 3, 5, 7, 5, 0, -1002202545288188668544738030381149331140902912000000⟩, + ⟨4, 3, 6, 7, 6, 0, -788622804750866777771792543229509062128304128000000⟩, + ⟨4, 3, 7, 7, 7, 0, -47086447509189580418429023972078357816383897600000⟩, + ⟨4, 3, 8, 7, 8, 0, -180491959092454010616253992085977034905354240000000⟩ +] + +def collectedFourData_8_7_15 : List CollectedFourTerm := [ + ⟨4, 4, 0, 0, 7, 1, -12111104117760529725823015289764733987424986726400000⟩, + ⟨4, 4, 1, 0, 8, 1, -1393583883632997045132350944997971397938092441600000⟩, + ⟨4, 4, 0, 1, 6, 1, -1523716697605449045474765462561926255324902195200000⟩, + ⟨4, 4, 1, 1, 7, 1, -14614088736890430931851266241841805027045906841600000⟩, + ⟨4, 4, 2, 1, 8, 1, 4018074256340833455973807482189022383970241740800000⟩, + ⟨4, 4, 0, 2, 5, 1, 7369377368062307682937994655992732987287614259200000⟩, + ⟨4, 4, 1, 2, 6, 1, -17329592273482544705800430988440105584028968550400000⟩, + ⟨4, 4, 2, 2, 7, 1, 4884142726238158334198521619497931437407574425600000⟩, + ⟨4, 4, 3, 2, 8, 1, 684849378334639341145931517475866413516193792000000⟩, + ⟨4, 4, 0, 3, 4, 1, -4679979515016654296295560049929535016072013414400000⟩, + ⟨4, 4, 1, 3, 5, 1, -14316916660212705988656409267551917762775770726400000⟩, + ⟨4, 4, 2, 3, 6, 1, 1940239798884217060767568296173308924787687424000000⟩, + ⟨4, 4, 3, 3, 7, 1, 1709993171311496757104254851689044402901719449600000⟩, + ⟨4, 4, 4, 3, 8, 1, 248342539862505128437595784140919535075275571200000⟩, + ⟨4, 4, 0, 4, 3, 1, -17960580236857679742101865127852425272326147276800000⟩, + ⟨4, 4, 1, 4, 4, 1, 16125349575219579286669459501982172409899044044800000⟩, + ⟨4, 4, 2, 4, 5, 1, 901084675569614860233251342762069589745886822400000⟩, + ⟨4, 4, 3, 4, 6, 1, 3927875776249974880725069995445077349836940902400000⟩, + ⟨4, 4, 4, 4, 7, 1, 565919406916064958032235615170868644137874227200000⟩, + ⟨4, 4, 5, 4, 8, 1, -491783043174713359394740259528588158363395686400000⟩, + ⟨4, 4, 0, 5, 2, 1, 30312218560735766680896077032278973052882622873600000⟩, + ⟨4, 4, 1, 5, 3, 1, 30795308283496631048237006518055101782890958028800000⟩, + ⟨4, 4, 2, 5, 4, 1, -4777761184166611052016217066843776175311736012800000⟩, + ⟨4, 4, 3, 5, 5, 1, 1290904136825110512334378875831033271021259980800000⟩, + ⟨4, 4, 4, 5, 6, 1, -519105869917322118279059605680976036101724569600000⟩, + ⟨4, 4, 5, 5, 7, 1, 16729691396970021048900484691892992323721625600000⟩, + ⟨4, 4, 6, 5, 8, 1, -115450748400362570179811519239300294246190284800000⟩, + ⟨4, 4, 0, 6, 1, 1, -22032870462024372525747815169969027038853464064000000⟩, + ⟨4, 4, 1, 6, 2, 1, -76739400443908527278967818866363608584437314355200000⟩, + ⟨4, 4, 2, 6, 3, 1, -2410773510368451973573645054525530011709997056000000⟩, + ⟨4, 4, 3, 6, 4, 1, -6090498121208260202612939257958798687825244979200000⟩, + ⟨4, 4, 4, 6, 5, 1, 842292697364548988619531857513390669359271116800000⟩, + ⟨4, 4, 5, 6, 6, 1, -159129219431822136604726122624429629993543270400000⟩, + ⟨4, 4, 6, 6, 7, 1, -109031311017368280366089756605780529291408179200000⟩, + ⟨4, 4, 7, 6, 8, 1, -17087558159336924988024880141291112170625433600000⟩, + ⟨4, 4, 0, 7, 0, 1, 214892962930094257434110686669729379908024742707200000⟩, + ⟨4, 4, 1, 7, 1, 1, 219595515134182997876461520942321087739241640755200000⟩, + ⟨4, 4, 2, 7, 2, 1, 11659931514235222770911013249438670007660288409600000⟩, + ⟨4, 4, 3, 7, 3, 1, 10854532100082324746451312830147980993068898713600000⟩, + ⟨4, 4, 4, 7, 4, 1, 3483396933430745821440398617625090408058558873600000⟩, + ⟨4, 4, 5, 7, 5, 1, 179959290566598342154144101063977256643618406400000⟩, + ⟨4, 4, 6, 7, 6, 1, 118006751841097097076271691509327254748397568000000⟩, + ⟨4, 4, 7, 7, 7, 1, 6039300801515046459447139570918075887570124800000⟩, + ⟨4, 4, 8, 7, 8, 1, 20256138008206570779925246614973632825262080000000⟩ +] + +def collectedFourData_8_7_16 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 7, 2, -1353537208459987034764482873162230043137959526400000⟩, + ⟨4, 5, 1, 0, 8, 2, -77873479629379361698611621748775263362927820800000⟩, + ⟨4, 5, 0, 1, 6, 2, -170290604829026146596868952292646368056652595200000⟩, + ⟨4, 5, 1, 1, 7, 2, -816635406680612092099055663151095754691235020800000⟩, + ⟨4, 5, 2, 1, 8, 2, 149686683103124779531614875056947626763721113600000⟩, + ⟨4, 5, 0, 2, 5, 2, 823601743810265746259617747930048427478692659200000⟩, + ⟨4, 5, 1, 2, 6, 2, -968377768101321145815339180527946642054394675200000⟩, + ⟨4, 5, 2, 2, 7, 2, 181950625561268440229788862381478580883501875200000⟩, + ⟨4, 5, 3, 2, 8, 2, 19134694631335387644891951620605610922344448000000⟩, + ⟨4, 5, 0, 3, 4, 2, -523034592619527958621648141703656467316762214400000⟩, + ⟨4, 5, 1, 3, 5, 2, -800029428431743638514426729137554925628371763200000⟩, + ⟨4, 5, 2, 3, 6, 2, 72280411309306766577324074525030044881911808000000⟩, + ⟨4, 5, 3, 3, 7, 2, 47777216698773338874785794903169810649474662400000⟩, + ⟨4, 5, 4, 3, 8, 2, 5550953321496409011675063616967665502115594240000⟩, + ⟨4, 5, 0, 4, 3, 2, -2007274762048135107519572296197921678102940876800000⟩, + ⟨4, 5, 1, 4, 4, 2, 901084675569614860233251342762069589745886822400000⟩, + ⟨4, 5, 2, 4, 5, 2, 33568413044686574924682149051569949303950540800000⟩, + ⟨4, 5, 3, 4, 6, 2, 109744866398400617200254545227637039463766425600000⟩, + ⟨4, 5, 4, 4, 7, 2, 12649432567047275696943278857685414526257725440000⟩, + ⟨4, 5, 5, 4, 8, 2, -9160280254031645526043265584583611970381414400000⟩, + ⟨4, 5, 0, 5, 2, 2, 3387694077599420041702571843849393357668850073600000⟩, + ⟨4, 5, 1, 5, 3, 2, 1720842096740899559404821734469546655701427814400000⟩, + ⟨4, 5, 2, 5, 4, 2, -177987557892482508173563238009635865223600537600000⟩, + ⟨4, 5, 3, 5, 5, 2, 36067867238986318353908237854122098352665395200000⟩, + ⟨4, 5, 4, 5, 6, 2, -11603056223960674498106971604406822124828753920000⟩, + ⟨4, 5, 5, 5, 7, 2, 311618433954957807854727952724155136842137600000⟩, + ⟨4, 5, 6, 5, 8, 2, -1843253952087571090930451835775707509057126400000⟩, + ⟨4, 5, 0, 6, 1, 2, -2462393988983675925103861671536373261416792064000000⟩, + ⟨4, 5, 1, 6, 2, 2, -4288198369272529358614900708786446862340692377600000⟩, + ⟨4, 5, 2, 6, 3, 2, -89809363256655587021305027844117750561636352000000⟩, + ⟨4, 5, 3, 6, 4, 2, -170168544192058639849836938786387973043440844800000⟩, + ⟨4, 5, 4, 6, 5, 2, 18826929323894807030595800978520796699148943360000⟩, + ⟨4, 5, 5, 6, 6, 2, -2964047392099549206618753657234861219800678400000⟩, + ⟨4, 5, 6, 6, 7, 2, -1740763032883224388953078169404939389475225600000⟩, + ⟨4, 5, 7, 6, 8, 2, -238713224920480094497511274398351296246579200000⟩, + ⟨4, 5, 0, 7, 0, 2, 24016441303278908940993969222688204015919117107200000⟩, + ⟨4, 5, 1, 7, 1, 2, 12270999310012370967023178591318323953829255577600000⟩, + ⟨4, 5, 2, 7, 2, 2, 434371383460917638477277976766322344474129203200000⟩, + ⟨4, 5, 3, 7, 3, 2, 303275674435401061374287230324981486529701478400000⟩, + ⟨4, 5, 4, 7, 4, 2, 77860900466038877509020047996091485903357214720000⟩, + ⟨4, 5, 5, 7, 5, 2, 3352042244614578161879396649108940840658534400000⟩, + ⟨4, 5, 6, 7, 6, 2, 1884062379135139286475775440591053572276224000000⟩, + ⟨4, 5, 7, 7, 7, 2, 84369045427754670075646159463749984557465600000⟩, + ⟨4, 5, 8, 7, 8, 2, 251536259867334003699082183918029499269120000000⟩ +] + +def collectedFourData_8_7_17 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 7, 3, -8850210458859798129951032916411963055317555609600000⟩, + ⟨4, 6, 1, 0, 8, 3, -339454617908329948877372677253497335128575180800000⟩, + ⟨4, 6, 0, 1, 6, 3, -1113458634519658888107691949922944507857128652800000⟩, + ⟨4, 6, 1, 1, 7, 3, -3559756945040856109416824488814021744547122380800000⟩, + ⟨4, 6, 2, 1, 8, 3, 489369128558562771995262824969658044341498675200000⟩, + ⟨4, 6, 0, 2, 5, 3, 5385185365755875450161535024828161469698591948800000⟩, + ⟨4, 6, 1, 2, 6, 3, -4221209927002399698716312952487158043299230515200000⟩, + ⟨4, 6, 2, 2, 7, 3, 594849302728283382099909719306191652683933286400000⟩, + ⟨4, 6, 3, 2, 8, 3, 50045487776729721961839938647063872058215628800000⟩, + ⟨4, 6, 0, 3, 4, 3, -3419903193657687014850416753305735079994694041600000⟩, + ⟨4, 6, 1, 3, 5, 3, -3487370607249202908796428967464276883944977203200000⟩, + ⟨4, 6, 2, 3, 6, 3, 236305602883330472002642797826939104899629056000000⟩, + ⟨4, 6, 3, 3, 7, 3, 124958049259329144258351345626958086429674045440000⟩, + ⟨4, 6, 4, 3, 8, 3, 12098449611751065765892003950830027378125701120000⟩, + ⟨4, 6, 0, 4, 3, 3, -13124725335845007982477226056496630673509135155200000⟩, + ⟨4, 6, 1, 4, 4, 3, 3927875776249974880725069995445077349836940902400000⟩, + ⟨4, 6, 2, 4, 5, 3, 109744866398400617200254545227637039463766425600000⟩, + ⟨4, 6, 3, 4, 6, 3, 287030207469618650532422671722656299226612367360000⟩, + ⟨4, 6, 4, 4, 7, 3, 27569772913962955681110382765603800390272286720000⟩, + ⟨4, 6, 5, 4, 8, 3, -17112919837762858444261841503427906164595097600000⟩, + ⟨4, 6, 0, 5, 2, 3, 22150706585377256936427919902145747407193138790400000⟩, + ⟨4, 6, 1, 5, 3, 3, 7501241747638174465743754003075715525576648294400000⟩, + ⟨4, 6, 2, 5, 4, 3, -581892886490799791901749441051902039454593843200000⟩, + ⟨4, 6, 3, 5, 5, 3, 94333044964586873989847857081965495752715141120000⟩, + ⟨4, 6, 4, 5, 6, 3, -25289167992870073475624464311386066677357608960000⟩, + ⟨4, 6, 5, 5, 7, 3, 582154817577044187323458284850221028894310400000⟩, + ⟨4, 6, 6, 5, 8, 3, -3013065563166290609647123844941430047270502400000⟩, + ⟨4, 6, 0, 6, 1, 3, -16100558520982142840693335650341230139771191296000000⟩, + ⟨4, 6, 1, 6, 2, 3, -18692483575722443916204811061399668797082278297600000⟩, + ⟨4, 6, 2, 6, 3, 3, -293612824616002706817487727238766277179736064000000⟩, + ⟨4, 6, 3, 6, 4, 3, -445064212543078819449018994082869025656673402880000⟩, + ⟨4, 6, 4, 6, 5, 3, 41033790517938736566793397790319369174835527680000⟩, + ⟨4, 6, 5, 6, 6, 3, -5537331174338807464293044614161122127878553600000⟩, + ⟨4, 6, 6, 6, 7, 3, -2845529310854376753138501100576521280133529600000⟩, + ⟨4, 6, 7, 6, 8, 3, -346854525831306261584480094858228821026406400000⟩, + ⟨4, 6, 0, 7, 0, 3, 157033407488446456842048821998014468800025251020800000⟩, + ⟨4, 6, 1, 7, 1, 3, 53489935238005335942609079810898174095736281497600000⟩, + ⟨4, 6, 2, 7, 2, 3, 1420085881979230759944925457502649034108986982400000⟩, + ⟨4, 6, 3, 7, 3, 3, 793196826516436609403789295275745936394986455040000⟩, + ⟨4, 6, 4, 7, 4, 3, 169699892334889241147722444240882286730789519360000⟩, + ⟨4, 6, 5, 7, 5, 3, 6262169784558404311090958304719926887815577600000⟩, + ⟨4, 6, 6, 7, 6, 3, 3079772847903022274827213464129832048656384000000⟩, + ⟨4, 6, 7, 7, 7, 3, 122589710965666463955589699313501109170995200000⟩, + ⟨4, 6, 8, 7, 8, 3, 328937959584162316535660095064370824871936000000⟩ +] + +def collectedFourData_8_7_18 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 7, 4, -1700157587889916183835612781575117782749963878400000⟩, + ⟨4, 7, 1, 0, 8, 4, -48907849174651646026186013734003874780833382400000⟩, + ⟨4, 7, 0, 1, 6, 4, -213899449632300786057467144746489796353012531200000⟩, + ⟨4, 7, 1, 1, 7, 4, -512881683092886335232011682165716996223034982400000⟩, + ⟨4, 7, 2, 1, 8, 4, 56405752681169999146773425728364671792557588480000⟩, + ⟨4, 7, 0, 2, 5, 4, 1034513676747427278150702947142635243202360115200000⟩, + ⟨4, 7, 1, 2, 6, 4, -608182324095316192803140703100515017278724505600000⟩, + ⟨4, 7, 2, 2, 7, 4, 68563627524049463578847863738613857885995663360000⟩, + ⟨4, 7, 3, 2, 8, 4, 4806960025345029928394487156275053852203417600000⟩, + ⟨4, 7, 0, 3, 4, 4, -656975830300781245900712150964318280117282406400000⟩, + ⟨4, 7, 1, 3, 5, 4, -502452424204513775407543527116616407606466969600000⟩, + ⟨4, 7, 2, 3, 6, 4, 27237098982260036116539605029270191388124774400000⟩, + ⟨4, 7, 3, 3, 7, 4, 12002447659506889964429583115610506241381498880000⟩, + ⟨4, 7, 4, 3, 8, 4, 996066913795293539634822690266529828616273920000⟩, + ⟨4, 7, 0, 4, 3, 4, -2521307427934625444664216607190480841123613900800000⟩, + ⟨4, 7, 1, 4, 4, 4, 565919406916064958032235615170868644137874227200000⟩, + ⟨4, 7, 2, 4, 5, 4, 12649432567047275696943278857685414526257725440000⟩, + ⟨4, 7, 3, 4, 6, 4, 27569772913962955681110382765603800390272286720000⟩, + ⟨4, 7, 4, 4, 7, 4, 2269822952667862447067768539901301871890923520000⟩, + ⟨4, 7, 5, 4, 8, 4, -1232795281325692274873556567950996019766886400000⟩, + ⟨4, 7, 0, 5, 2, 4, 4255231223405742772568551131700832733496973721600000⟩, + ⟨4, 7, 1, 5, 3, 4, 1080761847567976393502898669157766157370078003200000⟩, + ⟨4, 7, 2, 5, 4, 4, -67070242740913643482539888411620919429751111680000⟩, + ⟨4, 7, 3, 5, 5, 4, 9060860356419447417537188323340820790105866240000⟩, + ⟨4, 7, 4, 5, 6, 4, -2082060455964736397117613813870055684162191360000⟩, + ⟨4, 7, 5, 5, 7, 4, 41937770930610517312515137798360956246425600000⟩, + ⟨4, 7, 6, 5, 8, 4, -192940281056583488978533255733845880419123200000⟩, + ⟨4, 7, 0, 6, 1, 4, -3092975795994805441648939395282947200027459584000000⟩, + ⟨4, 7, 1, 6, 2, 4, -2693170512907765056188727189162511094631943372800000⟩, + ⟨4, 7, 2, 6, 3, 4, -33842454300482265648845432871338359593212313600000⟩, + ⟨4, 7, 3, 6, 4, 4, -42749226222968903282925011029038571380812021760000⟩, + ⟨4, 7, 4, 6, 5, 4, 3378317255032991063492219081791134583624826880000⟩, + ⟨4, 7, 5, 6, 6, 4, -398903039783942486524125487499253163386470400000⟩, + ⟨4, 7, 6, 6, 7, 4, -182212173443067426482766130372338088987852800000⟩, + ⟨4, 7, 7, 6, 8, 4, -19989604430108486704954479635675500699975680000⟩, + ⟨4, 7, 0, 7, 0, 4, 30166688186089480119895553671470770720355857203200000⟩, + ⟨4, 7, 1, 7, 1, 4, 7706708192989507659800457927153663450769312972800000⟩, + ⟨4, 7, 2, 7, 2, 4, 163682194830882094265162597142341267679357173760000⟩, + ⟨4, 7, 3, 7, 3, 4, 76187996294602273575040629717150931093637038080000⟩, + ⟨4, 7, 4, 7, 4, 4, 13971413978963694006567717625965117425068277760000⟩, + ⟨4, 7, 5, 7, 5, 4, 451119588851714401836872536268749905749606400000⟩, + ⟨4, 7, 6, 7, 6, 4, 197211851653308744284055783217925783027712000000⟩, + ⟨4, 7, 7, 7, 7, 4, 7064978678112514941292178990747426739978240000⟩, + ⟨4, 7, 8, 7, 8, 4, 17233684714926892243603516911854196621312000000⟩ +] + +def collectedFourData_8_7_19 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 7, 5, 1846792719579529442434517696766430345036824576000000⟩, + ⟨4, 8, 1, 0, 8, 5, 42500841300548276613560440740342721883720908800000⟩, + ⟨4, 8, 0, 1, 6, 5, 232347841821695345570904892533640305120903168000000⟩, + ⟨4, 8, 1, 1, 7, 5, 445693347528896221875449566891658934641020108800000⟩, + ⟨4, 8, 2, 1, 8, 5, -40847089366295921050776363088593629421030604800000⟩, + ⟨4, 8, 0, 2, 5, 5, -1123738375860664536428924172976003139059580928000000⟩, + ⟨4, 8, 1, 2, 6, 5, 528509449390599992493377540495182995031012147200000⟩, + ⟨4, 8, 2, 2, 7, 5, -49651400568708501407591220055221746588555673600000⟩, + ⟨4, 8, 3, 2, 8, 5, -2983743168062082290785846010605472430686208000000⟩, + ⟨4, 8, 0, 3, 4, 5, 713638658546374283784079924767695241002090496000000⟩, + ⟨4, 8, 1, 3, 5, 5, 436630338535918729437659195550102033871876915200000⟩, + ⟨4, 8, 2, 3, 6, 5, -19724162223234180267330959939512140608569344000000⟩, + ⟨4, 8, 3, 3, 7, 5, -7450076766865959775196745216142391242024550400000⟩, + ⟨4, 8, 4, 3, 8, 5, -540987828926569740445152388465869701146214400000⟩, + ⟨4, 8, 0, 4, 3, 5, 2738765062073145349350804241155090090465165312000000⟩, + ⟨4, 8, 1, 4, 4, 5, -491783043174713359394740259528588158363395686400000⟩, + ⟨4, 8, 2, 4, 5, 5, -9160280254031645526043265584583611970381414400000⟩, + ⟨4, 8, 3, 4, 6, 5, -17112919837762858444261841503427906164595097600000⟩, + ⟨4, 8, 4, 4, 7, 5, -1232795281325692274873556567950996019766886400000⟩, + ⟨4, 8, 5, 4, 8, 5, 595165051235030158102619983136706816638976000000⟩, + ⟨4, 8, 0, 5, 2, 5, -4622236255914680139498475125223049059236839424000000⟩, + ⟨4, 8, 1, 5, 3, 5, -939180285829878334512949604801924076948317798400000⟩, + ⟨4, 8, 2, 5, 4, 5, 48569943114540371106786924428067550083730636800000⟩, + ⟨4, 8, 3, 5, 5, 5, -5624194926249792262241332391485696774452019200000⟩, + ⟨4, 8, 4, 5, 6, 5, 1130816966376730934013769589694526259409715200000⟩, + ⟨4, 8, 5, 5, 7, 5, -20246585919568920140249128990071381295104000000⟩, + ⟨4, 8, 6, 5, 8, 5, 83832395045487527566079308042756664013619200000⟩, + ⟨4, 8, 0, 6, 1, 5, 3359738663383690667241537503363408137562357760000000⟩, + ⟨4, 8, 1, 6, 2, 5, 2340360790671069222722761282398934454914095513600000⟩, + ⟨4, 8, 2, 6, 3, 5, 24507531403761617629070296132427094253633536000000⟩, + ⟨4, 8, 3, 6, 4, 5, 26535005702188777536744970001179077153443020800000⟩, + ⟨4, 8, 4, 6, 5, 5, -1834845121259665789893654315221504461740441600000⟩, + ⟨4, 8, 5, 6, 6, 5, 192581162263629079097520319565169778753536000000⟩, + ⟨4, 8, 6, 6, 7, 5, 79171041021218094130693041820602022546636800000⟩, + ⟨4, 8, 7, 6, 8, 5, 7895878955682138647207219983479810608332800000⟩, + ⟨4, 8, 0, 7, 0, 5, -32768503645029836424633985752749738907295285248000000⟩, + ⟨4, 8, 1, 7, 1, 5, -6697116871572490547155070469803776201555810713600000⟩, + ⟨4, 8, 2, 7, 2, 5, -118532967332611750505983862875840387174996377600000⟩, + ⟨4, 8, 3, 7, 3, 5, -47290889092850736223821405250367116443805286400000⟩, + ⟨4, 8, 4, 7, 4, 5, -7588209999581666202328910509314002778272563200000⟩, + ⟨4, 8, 5, 7, 5, 5, -217790104552747543410615974880571111243776000000⟩, + ⟨4, 8, 6, 7, 6, 5, -85688388992258766494077185579805229187072000000⟩, + ⟨4, 8, 7, 7, 7, 5, -2790661349097485426863951795743013365350400000⟩, + ⟨4, 8, 8, 7, 8, 5, -6240018315509385199030392147870807490560000000⟩ +] + +def collectedFourData_8_7_20 : List CollectedFourTerm := [ + ⟨5, 2, 1, 0, 8, 0, -2619640527255183368649037247912806784246690611200000⟩, + ⟨5, 2, 1, 1, 7, 0, -27471370452604745644114648349882710848041071411200000⟩, + ⟨5, 2, 2, 1, 8, 0, 15106245540082893417738201834192172345040515891200000⟩, + ⟨5, 2, 1, 2, 6, 0, -32575938035444898118999358980398095484817558732800000⟩, + ⟨5, 2, 2, 2, 7, 0, 18362293618374831648094564740373416800229418598400000⟩, + ⟨5, 2, 3, 2, 8, 0, 3862112372899846282242476418513431830129016832000000⟩, + ⟨5, 2, 1, 3, 5, 0, -26912750318735166257728913314357557196755881164800000⟩, + ⟨5, 2, 2, 3, 6, 0, 7294474153217300129363392330163754923024449536000000⟩, + ⟨5, 2, 3, 3, 7, 0, 9643267546735453691222303199725052528512571801600000⟩, + ⟨5, 2, 4, 3, 8, 0, 1867324069131191792307194540158131866365958553600000⟩, + ⟨5, 2, 1, 4, 4, 0, 30312218560735766680896077032278973052882622873600000⟩, + ⟨5, 2, 2, 4, 5, 0, 3387694077599420041702571843849393357668850073600000⟩, + ⟨5, 2, 3, 4, 6, 0, 22150706585377256936427919902145747407193138790400000⟩, + ⟨5, 2, 4, 4, 7, 0, 4255231223405742772568551131700832733496973721600000⟩, + ⟨5, 2, 5, 4, 8, 0, -4622236255914680139498475125223049059236839424000000⟩, + ⟨5, 2, 1, 5, 3, 0, 57888612645588202254508886666076869398198065561600000⟩, + ⟨5, 2, 2, 5, 4, 0, -17962344390724436591657859791620928387792712499200000⟩, + ⟨5, 2, 3, 5, 5, 0, 7279873497415548981350618306328710980374940876800000⟩, + ⟨5, 2, 4, 5, 6, 0, -3903233356075747755225176599573530234290228428800000⟩, + ⟨5, 2, 5, 5, 7, 0, 157241261565552994997233175094171161377898496000000⟩, + ⟨5, 2, 6, 5, 8, 0, -1302136726594834784744561411795225856811047321600000⟩, + ⟨5, 2, 1, 6, 2, 0, -144253708586277483355306747768896048266788365926400000⟩, + ⟨5, 2, 2, 6, 3, 0, -9063480231029426587052151848721972191438045184000000⟩, + ⟨5, 2, 3, 6, 4, 0, -34346513109555594706021498503108883870743999283200000⟩, + ⟨5, 2, 4, 6, 5, 0, 6333322627339868810243863895466019558712043110400000⟩, + ⟨5, 2, 5, 6, 6, 0, -1495644995575542761272424984913238525281828864000000⟩, + ⟨5, 2, 6, 6, 7, 0, -1229733686369532563270906448471861542085092966400000⟩, + ⟨5, 2, 7, 6, 8, 0, -224846758592913215973252775836345158133507686400000⟩, + ⟨5, 2, 1, 7, 1, 0, 412792740935916924850928073335363882861824730726400000⟩, + ⟨5, 2, 2, 7, 2, 0, 43836369663061525734576327292303316472031503974400000⟩, + ⟨5, 2, 3, 7, 3, 0, 61212617039541721160184240771750382991023118745600000⟩, + ⟨5, 2, 4, 7, 4, 0, 26192173679685747999676469044461633280966184140800000⟩, + ⟨5, 2, 5, 7, 5, 0, 1691425454761157583792868485530117004406554624000000⟩, + ⟨5, 2, 6, 7, 6, 0, 1330965175085626372448450881955462402807955456000000⟩, + ⟨5, 2, 7, 7, 7, 0, 79468183617929778673906029473177207512970035200000⟩, + ⟨5, 2, 8, 7, 8, 0, 304617759577629978788183458767196303896084480000000⟩ +] + +def collectedFourData_8_7_21 : List CollectedFourTerm := [ + ⟨5, 3, 0, 0, 7, 1, -23129122455311628343374270978748585316459112038400000⟩, + ⟨5, 3, 1, 0, 8, 1, -2661390074999738598026396199588160120028764569600000⟩, + ⟨5, 3, 0, 1, 6, 1, -2909910586470635331075753245968744344580207411200000⟩, + ⟨5, 3, 1, 1, 7, 1, -27909185213976263616393475839574324099572930969600000⟩, + ⟨5, 3, 2, 1, 8, 1, 7673497858313096014956089601450878187072179404800000⟩, + ⟨5, 3, 0, 2, 5, 1, 14073632751233643058263187732138455594702156595200000⟩, + ⟨5, 3, 1, 2, 6, 1, -33095104946394889195719844427321454989360391782400000⟩, + ⟨5, 3, 2, 2, 7, 1, 9327467925795565703145481669112371322451237273600000⟩, + ⟨5, 3, 3, 2, 8, 1, 1307887784708013193323027641008786751883313152000000⟩, + ⟨5, 3, 0, 3, 4, 1, -8937568221582223603439243927961636690603697766400000⟩, + ⟨5, 3, 1, 3, 5, 1, -27341662279242439548983507843932963656704616038400000⟩, + ⟨5, 3, 2, 3, 6, 1, 3705363562621267765393238156063532602930233344000000⟩, + ⟨5, 3, 3, 3, 7, 1, 3265651180309034658657520230696018279449336217600000⟩, + ⟨5, 3, 4, 3, 8, 1, 474270963199770284608579455318453631191298867200000⟩, + ⟨5, 3, 0, 4, 3, 1, -34300131154643671674477841611160653631283055820800000⟩, + ⟨5, 3, 1, 4, 4, 1, 30795308283496631048237006518055101782890958028800000⟩, + ⟨5, 3, 2, 4, 5, 1, 1720842096740899559404821734469546655701427814400000⟩, + ⟨5, 3, 3, 4, 6, 1, 7501241747638174465743754003075715525576648294400000⟩, + ⟨5, 3, 4, 4, 7, 1, 1080761847567976393502898669157766157370078003200000⟩, + ⟨5, 3, 5, 4, 8, 1, -939180285829878334512949604801924076948317798400000⟩, + ⟨5, 3, 0, 5, 2, 1, 57888612645588202254508886666076869398198065561600000⟩, + ⟨5, 3, 1, 5, 3, 1, 58811190904844771478941134316893257878966422732800000⟩, + ⟨5, 3, 2, 5, 4, 1, -9124306290850206368975076851428311937451871436800000⟩, + ⟨5, 3, 3, 5, 5, 1, 2465297925637625489901170478052410615592176844800000⟩, + ⟨5, 3, 4, 5, 6, 1, -991359921923364091910089921776352997951510937600000⟩, + ⟨5, 3, 5, 5, 7, 1, 31949447151779825999212602307770381084760473600000⟩, + ⟨5, 3, 6, 5, 8, 1, -220481507824995955887506270023356732941323468800000⟩, + ⟨5, 3, 0, 6, 1, 1, -42077167696945765547863981125626371881968861184000000⟩, + ⟨5, 3, 1, 6, 2, 1, -146552698478704538651865380965018561737477272371200000⟩, + ⟨5, 3, 2, 6, 3, 1, -4603963040129807883497756760851632701661249536000000⟩, + ⟨5, 3, 3, 6, 4, 1, -11631299301002062862145031527600366998860804915200000⟩, + ⟨5, 3, 4, 6, 5, 1, 1608564400993831417219168217202672958702406860800000⟩, + ⟨5, 3, 5, 6, 6, 1, -303896256416408013592623668047730773613504102400000⟩, + ⟨5, 3, 6, 6, 7, 1, -208222018361294201787242355706175009613624115200000⟩, + ⟨5, 3, 7, 6, 8, 1, -32632881468666910866463846796471839177152921600000⟩, + ⟨5, 3, 0, 7, 0, 1, 410390795592792774243975089073128198280517464883200000⟩, + ⟨5, 3, 1, 7, 1, 1, 419371471898049081094919873645300454436614910771200000⟩, + ⟨5, 3, 2, 7, 2, 1, 22267497759994569974686523231470995955051501977600000⟩, + ⟨5, 3, 3, 7, 3, 1, 20729390128002453131554786469265280209918728601600000⟩, + ⟨5, 3, 4, 7, 4, 1, 6652400429422993152780325070512687049176881561600000⟩, + ⟨5, 3, 5, 7, 5, 1, 343676383921263229120481835550391552272918118400000⟩, + ⟨5, 3, 6, 7, 6, 1, 225362823021539596132765868676825033901867008000000⟩, + ⟨5, 3, 7, 7, 7, 1, 11533525467579925638570975758772262717410508800000⟩, + ⟨5, 3, 8, 7, 8, 1, 38684061494975716800096877450982433730068480000000⟩ +] + +def collectedFourData_8_7_22 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 7, 2, 7176770076371970088279236010326260972876778700800000⟩, + ⟨5, 4, 1, 0, 8, 2, 412903357849296587169646425091358067552524697600000⟩, + ⟨5, 4, 0, 1, 6, 2, 902920517726105409621316267892601447539697254400000⟩, + ⟨5, 4, 1, 1, 7, 2, 4329991457449119023544149231909451586525043097600000⟩, + ⟨5, 4, 2, 1, 8, 2, -793673717583388434374683125225038178669507379200000⟩, + ⟨5, 4, 0, 2, 5, 2, -4366928602243905291993634641141679028733109862400000⟩, + ⟨5, 4, 1, 2, 6, 2, 5134564861087736890631675795827518423469287014400000⟩, + ⟨5, 4, 2, 2, 7, 2, -964744668076758328407442779113665244099405414400000⟩, + ⟨5, 4, 3, 2, 8, 2, -101456615298317287479119584800090568582496256000000⟩, + ⟨5, 4, 0, 3, 4, 2, 2773251440564441597138142834086514049864748236800000⟩, + ⟨5, 4, 1, 3, 5, 2, 4241942686391721070854543351939797796698613350400000⟩, + ⟨5, 4, 2, 3, 6, 2, -383247604683654920547269890732103782342066176000000⟩, + ⟨5, 4, 3, 3, 7, 2, -253325949957608440791716328655531849529740492800000⟩, + ⟨5, 4, 4, 3, 8, 2, -29432449617236144060392742436441805018135265280000⟩, + ⟨5, 4, 0, 4, 3, 2, 10643039110623446326651064790612610573045176729600000⟩, + ⟨5, 4, 1, 4, 4, 2, -4777761184166611052016217066843776175311736012800000⟩, + ⟨5, 4, 2, 4, 5, 2, -177987557892482508173563238009635865223600537600000⟩, + ⟨5, 4, 3, 4, 6, 2, -581892886490799791901749441051902039454593843200000⟩, + ⟨5, 4, 4, 4, 7, 2, -67070242740913643482539888411620919429751111680000⟩, + ⟨5, 4, 5, 4, 8, 2, 48569943114540371106786924428067550083730636800000⟩, + ⟨5, 4, 0, 5, 2, 2, -17962344390724436591657859791620928387792712499200000⟩, + ⟨5, 4, 1, 5, 3, 2, -9124306290850206368975076851428311937451871436800000⟩, + ⟨5, 4, 2, 5, 4, 2, 943731558663725967075103475880095163002073907200000⟩, + ⟨5, 4, 3, 5, 5, 2, -191240247184505831232856764291235166158218854400000⟩, + ⟨5, 4, 4, 5, 6, 2, 61522111237213317349950234062515230122170122240000⟩, + ⟨5, 4, 5, 5, 7, 2, -1652273641297500120707491009444755398669107200000⟩, + ⟨5, 4, 6, 5, 8, 2, 9773362508111290304778178358203107551005900800000⟩, + ⟨5, 4, 0, 6, 1, 2, 13056187436829279241233193692375120549519556608000000⟩, + ⟨5, 4, 1, 6, 2, 2, 22737028244060971476725128782888746422000366387200000⟩, + ⟨5, 4, 2, 6, 3, 2, 476190197631674418335671686444466408305721344000000⟩, + ⟨5, 4, 3, 6, 4, 2, 902273323750634286942994387268283212397910425600000⟩, + ⟨5, 4, 4, 6, 5, 2, -99824771832781501666859396829834782103746641920000⟩, + ⟨5, 4, 5, 6, 6, 2, 15716070822147086268814321562058407526845644800000⟩, + ⟨5, 4, 6, 6, 7, 2, 9229931742079743139893647602264280403227443200000⟩, + ⟨5, 4, 7, 6, 8, 2, 1265713213301884740830503929831535696832102400000⟩, + ⟨5, 4, 0, 7, 0, 2, -127340775125363828643904694466001033222777366118400000⟩, + ⟨5, 4, 1, 7, 1, 2, -65063701318914475531782672419841150378623316787200000⟩, + ⟨5, 4, 2, 7, 2, 2, -2303138419372653384048576042751936832052029030400000⟩, + ⟨5, 4, 3, 7, 3, 2, -1608038383854932197582708381088362223721303244800000⟩, + ⟨5, 4, 4, 7, 4, 2, -412836660190389598226817306159771066063220899840000⟩, + ⟨5, 4, 5, 7, 5, 2, -17773310054221386402695096811442934609923276800000⟩, + ⟨5, 4, 6, 7, 6, 2, -9989738309432642606550896181100400898736128000000⟩, + ⟨5, 4, 7, 7, 7, 2, -447344363208820255935598731814656837628723200000⟩, + ⟨5, 4, 8, 7, 8, 2, -1333703936364134183070991544902146997616640000000⟩ +] + +def collectedFourData_8_7_23 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 7, 3, -2908639158650389611837826405308409192102703923200000⟩, + ⟨5, 5, 1, 0, 8, 3, -111562431065631177475418177658946567624300953600000⟩, + ⟨5, 5, 0, 1, 6, 3, -365940380848131627191265843456831653158689177600000⟩, + ⟨5, 5, 1, 1, 7, 3, -1169921155406903534429647568991045158157523353600000⟩, + ⟨5, 5, 2, 1, 8, 3, 160832131278314648038614167104521570791876198400000⟩, + ⟨5, 5, 0, 2, 5, 3, 1769851813608345373766989104457948424820070809600000⟩, + ⟨5, 5, 1, 2, 6, 3, -1387308985208555674147580718323084772453541478400000⟩, + ⟨5, 5, 2, 2, 7, 3, 195498398987708674954752219877575973875272908800000⟩, + ⟨5, 5, 3, 2, 8, 3, 16447548466537712298569392166847997070121369600000⟩, + ⟨5, 5, 0, 3, 4, 3, -1123957943611186638256496569880541246235292467200000⟩, + ⟨5, 5, 1, 3, 5, 3, -1146131242429034941428430355311234637097231974400000⟩, + ⟨5, 5, 2, 3, 6, 3, 77662303416397414038850890308390147485335552000000⟩, + ⟨5, 5, 3, 3, 7, 3, 41067709853204388376489602823890364677991956480000⟩, + ⟨5, 5, 4, 3, 8, 3, 3976179375990952416501973184381075412001751040000⟩, + ⟨5, 5, 0, 4, 3, 3, -4313466921021435156137197517937643294376224358400000⟩, + ⟨5, 5, 1, 4, 4, 3, 1290904136825110512334378875831033271021259980800000⟩, + ⟨5, 5, 2, 4, 5, 3, 36067867238986318353908237854122098352665395200000⟩, + ⟨5, 5, 3, 4, 6, 3, 94333044964586873989847857081965495752715141120000⟩, + ⟨5, 5, 4, 4, 7, 3, 9060860356419447417537188323340820790105866240000⟩, + ⟨5, 5, 5, 4, 8, 3, -5624194926249792262241332391485696774452019200000⟩, + ⟨5, 5, 0, 5, 2, 3, 7279873497415548981350618306328710980374940876800000⟩, + ⟨5, 5, 1, 5, 3, 3, 2465297925637625489901170478052410615592176844800000⟩, + ⟨5, 5, 2, 5, 4, 3, -191240247184505831232856764291235166158218854400000⟩, + ⟨5, 5, 3, 5, 5, 3, 31002741665204956210837134389782070231606231040000⟩, + ⟨5, 5, 4, 5, 6, 3, -8311335041768777601403062695006577533198008320000⟩, + ⟨5, 5, 5, 5, 7, 3, 191326331353674440390406298849289339456716800000⟩, + ⟨5, 5, 6, 5, 8, 3, -990249952285942217277993893964260647423180800000⟩, + ⟨5, 5, 0, 6, 1, 3, -5291480378682906159400580213253764875007557632000000⟩, + ⟨5, 5, 1, 6, 2, 3, -6143321670542531087819598390766075863922586419200000⟩, + ⟨5, 5, 2, 6, 3, 3, -96496435099474451737436729813683922679103488000000⟩, + ⟨5, 5, 3, 6, 4, 3, -146271233066640280783286716640171668783717416960000⟩, + ⟨5, 5, 4, 6, 5, 3, 13485836351931255376955744562065117456954818560000⟩, + ⟨5, 5, 5, 6, 6, 3, -1819854834296494764718133634356519193752371200000⟩, + ⟨5, 5, 6, 6, 7, 3, -935188831848954857368032219881622599840563200000⟩, + ⟨5, 5, 7, 6, 8, 3, -113994425429519913609458127380002361887948800000⟩, + ⟨5, 5, 0, 7, 0, 3, 51609339728181306952692163969092513663406414233600000⟩, + ⟨5, 5, 1, 7, 1, 3, 17579572932210239222295589528412573722140160819200000⟩, + ⟨5, 5, 2, 7, 2, 3, 466714031736541827776472484838362803319131340800000⟩, + ⟨5, 5, 3, 7, 3, 3, 260685704690028530330366497804917849429041479680000⟩, + ⟨5, 5, 4, 7, 4, 3, 55772205006705062689004051902483302209153925120000⟩, + ⟨5, 5, 5, 7, 5, 3, 2058074476099008956112984779049047466128179200000⟩, + ⟨5, 5, 6, 7, 6, 3, 1012173433253365037334305921538503032700928000000⟩, + ⟨5, 5, 7, 7, 7, 3, 40289350792264496981837167307310611457638400000⟩, + ⟨5, 5, 8, 7, 8, 3, 108106110522519317776515187993940708032512000000⟩ +] + +def collectedFourData_8_7_24 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 7, 4, 1559518498345170246982978362166082352270488371200000⟩, + ⟨5, 6, 1, 0, 8, 4, 44862132807822638052870141224768553723573043200000⟩, + ⟨5, 6, 0, 1, 6, 4, 196205428757597700034775284773544998649567641600000⟩, + ⟨5, 6, 1, 1, 7, 4, 470455490680991581694261988369148051616641843200000⟩, + ⟨5, 6, 2, 1, 8, 4, -51739800678443351595078968642999764424211824640000⟩, + ⟨5, 6, 0, 2, 5, 4, -948937455663169567265264998635717633123129753600000⟩, + ⟨5, 6, 1, 2, 6, 4, 557872747531810516988680412746565760613928140800000⟩, + ⟨5, 6, 2, 2, 7, 4, -62891961427005429854696392618742283762118164480000⟩, + ⟨5, 6, 3, 2, 8, 4, -4409322485002924111720064261026380300209356800000⟩, + ⟨5, 6, 0, 3, 4, 4, 602629995958989641688856222150626018313057075200000⟩, + ⟨5, 6, 1, 3, 5, 4, 460888952686925989794502727977934860407590092800000⟩, + ⟨5, 6, 2, 3, 6, 4, -24984013250684190031939001489648014075310899200000⟩, + ⟨5, 6, 3, 3, 7, 4, -11009590689561811395171464677762956047249571840000⟩, + ⟨5, 6, 4, 3, 8, 4, -913671055388028371134002200406802517521858560000⟩, + ⟨5, 6, 0, 4, 3, 4, 2312741831631742874593205497181333371700536934400000⟩, + ⟨5, 6, 1, 4, 4, 4, -519105869917322118279059605680976036101724569600000⟩, + ⟨5, 6, 2, 4, 5, 4, -11603056223960674498106971604406822124828753920000⟩, + ⟨5, 6, 3, 4, 6, 4, -25289167992870073475624464311386066677357608960000⟩, + ⟨5, 6, 4, 4, 7, 4, -2082060455964736397117613813870055684162191360000⟩, + ⟨5, 6, 5, 4, 8, 4, 1130816966376730934013769589694526259409715200000⟩, + ⟨5, 6, 0, 5, 2, 4, -3903233356075747755225176599573530234290228428800000⟩, + ⟨5, 6, 1, 5, 3, 4, -991359921923364091910089921776352997951510937600000⟩, + ⟨5, 6, 2, 5, 4, 4, 61522111237213317349950234062515230122170122240000⟩, + ⟨5, 6, 3, 5, 5, 4, -8311335041768777601403062695006577533198008320000⟩, + ⟨5, 6, 4, 5, 6, 4, 1909829899815279671836013672564419883150868480000⟩, + ⟨5, 6, 5, 5, 7, 4, -38468627856327998395689449121666921450700800000⟩, + ⟨5, 6, 6, 5, 8, 4, 176980027926176462806612046439836211059097600000⟩, + ⟨5, 6, 0, 6, 1, 4, 2837121101682309308007617923689196308620378112000000⟩, + ⟨5, 6, 1, 6, 2, 4, 2470388194596793732005884556429091140062832230400000⟩, + ⟨5, 6, 2, 6, 3, 4, 31042965597387011178490940772640897079495884800000⟩, + ⟨5, 6, 3, 6, 4, 4, 39212958586624353698746400219951498232783175680000⟩, + ⟨5, 6, 4, 6, 5, 4, -3098858770522254648964325324125449326784675840000⟩, + ⟨5, 6, 5, 6, 6, 4, 365905298438404489521851461475782714667827200000⟩, + ⟨5, 6, 6, 6, 7, 4, 167139362334535286154218323369306295264870400000⟩, + ⟨5, 6, 7, 6, 8, 4, 18336040203218650776218574410905987307274240000⟩, + ⟨5, 6, 0, 7, 0, 4, -27671263296484144506137328235179267605520816537600000⟩, + ⟨5, 6, 1, 7, 1, 4, -7069199981180581006781948392877461633080125030400000⟩, + ⟨5, 6, 2, 7, 2, 4, -150142205938280974385191894122937385542672711680000⟩, + ⟨5, 6, 3, 7, 3, 4, -69885633202243373388541506986002426111658557440000⟩, + ⟨5, 6, 4, 7, 4, 4, -12815681736464407815690474968043003972346183680000⟩, + ⟨5, 6, 5, 7, 5, 4, -413802431487115298735835685709390109946675200000⟩, + ⟨5, 6, 6, 7, 6, 4, -180898249042871961555704260053667588079616000000⟩, + ⟨5, 6, 7, 7, 7, 4, -6480555107015220667029104960540539952824320000⟩, + ⟨5, 6, 8, 7, 8, 4, -15808093496164260062327641638423459004416000000⟩ +] + +def collectedFourData_8_7_25 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 7, 5, -62825005256962783361640952203512759665557504000000⟩, + ⟨5, 7, 1, 0, 8, 5, -1445812272175411190166051259783754552652595200000⟩, + ⟨5, 7, 0, 1, 6, 5, -7904110856152504887114658802427395699638272000000⟩, + ⟨5, 7, 1, 1, 7, 5, -15161791902597132278913993153376100606489395200000⟩, + ⟨5, 7, 2, 1, 8, 5, 1389554213075648512421632116288502302454579200000⟩, + ⟨5, 7, 0, 2, 5, 5, 38227825257493296073015748293454243731341312000000⟩, + ⟨5, 7, 1, 2, 6, 5, -17979066402145346719988250167529258739354828800000⟩, + ⟨5, 7, 2, 2, 7, 5, 1689063135604561973151202627713265654195814400000⟩, + ⟨5, 7, 3, 2, 8, 5, 101502284599435626825646300882832229138432000000⟩, + ⟨5, 7, 0, 3, 4, 5, -24276873088906016203480074355079362520285184000000⟩, + ⟨5, 7, 1, 3, 5, 5, -14853482485091226702006521603487086821559500800000⟩, + ⟨5, 7, 2, 3, 6, 5, 670985207070777082097224296704479567282176000000⟩, + ⟨5, 7, 3, 3, 7, 5, 253439981152673305785478910239311042025881600000⟩, + ⟨5, 7, 4, 3, 8, 5, 18403561393724133037771444415471464061337600000⟩, + ⟨5, 7, 0, 4, 3, 5, -93168511873658445219389445838532373431451648000000⟩, + ⟨5, 7, 1, 4, 4, 5, 16729691396970021048900484691892992323721625600000⟩, + ⟨5, 7, 2, 4, 5, 5, 311618433954957807854727952724155136842137600000⟩, + ⟨5, 7, 3, 4, 6, 5, 582154817577044187323458284850221028894310400000⟩, + ⟨5, 7, 4, 4, 7, 5, 41937770930610517312515137798360956246425600000⟩, + ⟨5, 7, 5, 4, 8, 5, -20246585919568920140249128990071381295104000000⟩, + ⟨5, 7, 0, 5, 2, 5, 157241261565552994997233175094171161377898496000000⟩, + ⟨5, 7, 1, 5, 3, 5, 31949447151779825999212602307770381084760473600000⟩, + ⟨5, 7, 2, 5, 4, 5, -1652273641297500120707491009444755398669107200000⟩, + ⟨5, 7, 3, 5, 5, 5, 191326331353674440390406298849289339456716800000⟩, + ⟨5, 7, 4, 5, 6, 5, -38468627856327998395689449121666921450700800000⟩, + ⟨5, 7, 5, 5, 7, 5, 688757245654546559088896438435856777216000000⟩, + ⟨5, 7, 6, 5, 8, 5, -2851847207105978032445946760922720423116800000⟩, + ⟨5, 7, 0, 6, 1, 5, -114293064376579495019334553807365189182423040000000⟩, + ⟨5, 7, 1, 6, 2, 5, -79615420517022311182705437352142572297283174400000⟩, + ⟨5, 7, 2, 6, 3, 5, -833707959183992115602833844150888608825344000000⟩, + ⟨5, 7, 3, 6, 4, 5, -902679469687912524023769749789958212891443200000⟩, + ⟨5, 7, 4, 6, 5, 5, 62418566613743305448663427670238409680486400000⟩, + ⟨5, 7, 5, 6, 6, 5, -6551310498104591222696441738041013305344000000⟩, + ⟨5, 7, 6, 6, 7, 5, -2693275220128486247112148505810821133107200000⟩, + ⟨5, 7, 7, 6, 8, 5, -268605475665949596432554402466812343091200000⟩, + ⟨5, 7, 0, 7, 0, 5, 1114733338471529252137029992887342413845102592000000⟩, + ⟨5, 7, 1, 7, 1, 5, 227825460974759401752792610497111097075983974400000⟩, + ⟨5, 7, 2, 7, 2, 5, 4032306504592565893783966814784768967075430400000⟩, + ⟨5, 7, 3, 7, 3, 5, 1608762220235105000951807675568509949680025600000⟩, + ⟨5, 7, 4, 7, 4, 5, 258139058087252809280167456869866990783692800000⟩, + ⟨5, 7, 5, 7, 5, 5, 7408879360622590210721016950415691874304000000⟩, + ⟨5, 7, 6, 7, 6, 5, 2914985223747792532902348049592969330688000000⟩, + ⟨5, 7, 7, 7, 7, 5, 94933942541948780730790075468990749081600000⟩, + ⟨5, 7, 8, 7, 8, 5, 212275681682715779544357621838632714240000000⟩ +] + +def collectedFourData_8_7_26 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 7, 6, 520262594430406771183477260651564570245490278400000⟩, + ⟨5, 8, 1, 0, 8, 6, 9977476864833948537952763797498966627162521600000⟩, + ⟨5, 8, 0, 1, 6, 6, 65455039818427975740718668083305573453607731200000⟩, + ⟨5, 8, 1, 1, 7, 6, 104630753832221018772654238057387266357696921600000⟩, + ⟨5, 8, 2, 1, 8, 6, -8219351026139363636167116918053670537186508800000⟩, + ⟨5, 8, 0, 2, 5, 6, -316569930500586582061857281532156089703019315200000⟩, + ⟨5, 8, 1, 2, 6, 6, 124072621688851460216615288234122982866708070400000⟩, + ⟨5, 8, 2, 2, 7, 6, -9990976016773607588123284539285228205218201600000⟩, + ⟨5, 8, 3, 2, 8, 6, -525346572896459305583807610990934508961792000000⟩, + ⟨5, 8, 0, 3, 4, 6, 201040157915341648241263830729615235535496806400000⟩, + ⟨5, 8, 1, 3, 5, 6, 102503126242127915746951998341103449450899046400000⟩, + ⟨5, 8, 2, 3, 6, 6, -3968944067359882336627048162840798732222464000000⟩, + ⟨5, 8, 3, 3, 7, 6, -1311732302961784427316552674232287918397849600000⟩, + ⟨5, 8, 4, 3, 8, 6, -84668026672716920245154492890734549742387200000⟩, + ⟨5, 8, 0, 4, 3, 6, 771541387196901600223348661709538392896490700800000⟩, + ⟨5, 8, 1, 4, 4, 6, -115450748400362570179811519239300294246190284800000⟩, + ⟨5, 8, 2, 4, 5, 6, -1843253952087571090930451835775707509057126400000⟩, + ⟨5, 8, 3, 4, 6, 6, -3013065563166290609647123844941430047270502400000⟩, + ⟨5, 8, 4, 4, 7, 6, -192940281056583488978533255733845880419123200000⟩, + ⟨5, 8, 5, 4, 8, 6, 83832395045487527566079308042756664013619200000⟩, + ⟨5, 8, 0, 5, 2, 6, -1302136726594834784744561411795225856811047321600000⟩, + ⟨5, 8, 1, 5, 3, 6, -220481507824995955887506270023356732941323468800000⟩, + ⟨5, 8, 2, 5, 4, 6, 9773362508111290304778178358203107551005900800000⟩, + ⟨5, 8, 3, 5, 5, 6, -990249952285942217277993893964260647423180800000⟩, + ⟨5, 8, 4, 5, 6, 6, 176980027926176462806612046439836211059097600000⟩, + ⟨5, 8, 5, 5, 7, 6, -2851847207105978032445946760922720423116800000⟩, + ⟨5, 8, 6, 5, 8, 6, 10734792191417567052050648301962623608422400000⟩, + ⟨5, 8, 0, 6, 1, 6, 946476740507246312279041891230970744179523584000000⟩, + ⟨5, 8, 1, 6, 2, 6, 549421962712626242774848712983393096460088115200000⟩, + ⟨5, 8, 2, 6, 3, 6, 4931465289614031257398084502762475346722816000000⟩, + ⟨5, 8, 3, 6, 4, 6, 4672008789713240812357042287667666106921779200000⟩, + ⟨5, 8, 4, 6, 5, 6, -287164899763769894489384709165773782568140800000⟩, + ⟨5, 8, 5, 6, 6, 6, 27126156080068994621374407187341698609971200000⟩, + ⟨5, 8, 6, 6, 7, 6, 10137902805709221918950861359901719501209600000⟩, + ⟨5, 8, 7, 6, 8, 6, 926816354654507426619441990400983485644800000⟩, + ⟨5, 8, 0, 7, 0, 6, -9231261603547439514231721927466146098800964403200000⟩, + ⟨5, 8, 1, 7, 1, 6, -1572211904575677835765686809289304086072734515200000⟩, + ⟨5, 8, 2, 7, 2, 6, -23851493014347765589550145450150634775484825600000⟩, + ⟨5, 8, 3, 7, 3, 6, -8326489618840663577427733299484419941833113600000⟩, + ⟨5, 8, 4, 7, 4, 6, -1187602996388230686992168054751720008948121600000⟩, + ⟨5, 8, 5, 7, 5, 6, -30676979510098869085932656975605283369779200000⟩, + ⟨5, 8, 6, 7, 6, 6, -10972453411955374016864696535289203523584000000⟩, + ⟨5, 8, 7, 7, 7, 6, -327567151568918016476554859374954571366400000⟩, + ⟨5, 8, 8, 7, 8, 6, -676109385935290341863497625309848535040000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0832.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0832.lean new file mode 100644 index 0000000000000000000000000000000000000000..e3af75552fb8eabdafc072e929f1875fae1a0896 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0832.lean @@ -0,0 +1,651 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0832. -/ +namespace LaughlinFock +def collectedFourData_8_7_27 : List CollectedFourTerm := [ + ⟨6, 1, 1, 0, 8, 0, 1904123259022901832276616939394231846188351488000000⟩, + ⟨6, 1, 1, 1, 7, 0, 19967959302739748350721706743709954299802943488000000⟩, + ⟨6, 1, 2, 1, 8, 0, -10980191056794126587483095115978659425511538688000000⟩, + ⟨6, 1, 1, 2, 6, 0, 23678287403337740639171851165417833889448067072000000⟩, + ⟨6, 1, 2, 2, 7, 0, -13346896264576460700099828837058912138051977216000000⟩, + ⟨6, 1, 3, 2, 8, 0, -2807231725760505149255602940178070620528967680000000⟩, + ⟨6, 1, 1, 3, 5, 0, 19561918252911411241677103165227558691512778752000000⟩, + ⟨6, 1, 2, 3, 6, 0, -5302093074592841535102083779866504666430832640000000⟩, + ⟨6, 1, 3, 3, 7, 0, -7009347212977754697673169013375088350707318784000000⟩, + ⟨6, 1, 4, 3, 8, 0, -1357291260068993886342122714404350180420747264000000⟩, + ⟨6, 1, 1, 4, 4, 0, -22032870462024372525747815169969027038853464064000000⟩, + ⟨6, 1, 2, 4, 5, 0, -2462393988983675925103861671536373261416792064000000⟩, + ⟨6, 1, 3, 4, 6, 0, -16100558520982142840693335650341230139771191296000000⟩, + ⟨6, 1, 4, 4, 7, 0, -3092975795994805441648939395282947200027459584000000⟩, + ⟨6, 1, 5, 4, 8, 0, 3359738663383690667241537503363408137562357760000000⟩, + ⟨6, 1, 1, 5, 3, 0, -42077167696945765547863981125626371881968861184000000⟩, + ⟨6, 1, 2, 5, 4, 0, 13056187436829279241233193692375120549519556608000000⟩, + ⟨6, 1, 3, 5, 5, 0, -5291480378682906159400580213253764875007557632000000⟩, + ⟨6, 1, 4, 5, 6, 0, 2837121101682309308007617923689196308620378112000000⟩, + ⟨6, 1, 5, 5, 7, 0, -114293064376579495019334553807365189182423040000000⟩, + ⟨6, 1, 6, 5, 8, 0, 946476740507246312279041891230970744179523584000000⟩, + ⟨6, 1, 1, 6, 2, 0, 104852875370364099033730005909758339025979047936000000⟩, + ⟨6, 1, 2, 6, 3, 0, 6587920493686982587272130378292704217042780160000000⟩, + ⟨6, 1, 3, 6, 4, 0, 24965255269876615089061120505783876777586720768000000⟩, + ⟨6, 1, 4, 6, 5, 0, -4603466313849384935373839980837626639701508096000000⟩, + ⟨6, 1, 5, 6, 6, 0, 1087130998962125280803457835858047293309583360000000⟩, + ⟨6, 1, 6, 6, 7, 0, 893849553119280261188961397921484296773697536000000⟩, + ⟨6, 1, 7, 6, 8, 0, 163433088738044310964160629767306560548110336000000⟩, + ⟨6, 1, 1, 7, 1, 0, -300044319437774614577944142884303467916805799936000000⟩, + ⟨6, 1, 2, 7, 2, 0, -31863093503908998713152946046006430150170771456000000⟩, + ⟨6, 1, 3, 7, 3, 0, -44493267926641391839685464885894055394325561344000000⟩, + ⟨6, 1, 4, 7, 4, 0, -19038156796311800363828111149082349866154196992000000⟩, + ⟨6, 1, 5, 7, 5, 0, -1229436831429954952346821906860428664514805760000000⟩, + ⟨6, 1, 6, 7, 6, 0, -967431111430182002073632315037677451151933440000000⟩, + ⟨6, 1, 7, 7, 7, 0, -57762588112709700874834486981620460576309248000000⟩, + ⟨6, 1, 8, 7, 8, 0, -221415783993446341240340432745564319462195200000000⟩ +] + +def collectedFourData_8_7_28 : List CollectedFourTerm := [ + ⟨6, 2, 0, 0, 7, 1, 57635889651591577353006694575861892721780824473600000⟩, + ⟨6, 2, 1, 0, 8, 1, 6631967338099306923778284383041111674929440358400000⟩, + ⟨6, 2, 0, 1, 6, 1, 7251260214557066751797619916939996161108659404800000⟩, + ⟨6, 2, 1, 1, 7, 1, 69547416784468498693099004509807211260336825958400000⟩, + ⟨6, 2, 2, 1, 8, 1, -19121731775945108112045554756951066963627684659200000⟩, + ⟨6, 2, 0, 2, 5, 1, -35070346737727041610732101955576024207962459340800000⟩, + ⟨6, 2, 1, 2, 6, 1, 82470306445206562574769331617471236694951434649600000⟩, + ⟨6, 2, 2, 2, 7, 1, -23243290493991624807894192936960315422035830374400000⟩, + ⟨6, 2, 3, 2, 8, 1, -3259149852388118500720579890448124355394142208000000⟩, + ⟨6, 2, 0, 3, 4, 1, 22271692182354530607414840002900451708387301785600000⟩, + ⟨6, 2, 1, 3, 5, 1, 68133195847021981922772723621332846472702040473600000⟩, + ⟨6, 2, 2, 3, 6, 1, -9233464253859873354680419705392613362631704576000000⟩, + ⟨6, 2, 3, 3, 7, 1, -8137736804867695163339604598754667803621877350400000⟩, + ⟨6, 2, 4, 3, 8, 1, -1181844618305373301407353532072568162425294028800000⟩, + ⟨6, 2, 0, 4, 3, 1, 85473133625532755069552134704615262053396067123200000⟩, + ⟨6, 2, 1, 4, 4, 1, -76739400443908527278967818866363608584437314355200000⟩, + ⟨6, 2, 2, 4, 5, 1, -4288198369272529358614900708786446862340692377600000⟩, + ⟨6, 2, 3, 4, 6, 1, -18692483575722443916204811061399668797082278297600000⟩, + ⟨6, 2, 4, 4, 7, 1, -2693170512907765056188727189162511094631943372800000⟩, + ⟨6, 2, 5, 4, 8, 1, 2340360790671069222722761282398934454914095513600000⟩, + ⟨6, 2, 0, 5, 2, 1, -144253708586277483355306747768896048266788365926400000⟩, + ⟨6, 2, 1, 5, 3, 1, -146552698478704538651865380965018561737477272371200000⟩, + ⟨6, 2, 2, 5, 4, 1, 22737028244060971476725128782888746422000366387200000⟩, + ⟨6, 2, 3, 5, 5, 1, -6143321670542531087819598390766075863922586419200000⟩, + ⟨6, 2, 4, 5, 6, 1, 2470388194596793732005884556429091140062832230400000⟩, + ⟨6, 2, 5, 5, 7, 1, -79615420517022311182705437352142572297283174400000⟩, + ⟨6, 2, 6, 5, 8, 1, 549421962712626242774848712983393096460088115200000⟩, + ⟨6, 2, 0, 6, 1, 1, 104852875370364099033730005909758339025979047936000000⟩, + ⟨6, 2, 1, 6, 2, 1, 365197390172569855197721225257183700984093527244800000⟩, + ⟨6, 2, 2, 6, 3, 1, 11472700974869410511705480985855922280746450944000000⟩, + ⟨6, 2, 3, 6, 4, 1, 28984250669797270009667478853263107026070588620800000⟩, + ⟨6, 2, 4, 6, 5, 1, -4008411494741677086743277244121049548553663283200000⟩, + ⟨6, 2, 5, 6, 6, 1, 757284723369409811720838845074132103184619929600000⟩, + ⟨6, 2, 6, 6, 7, 1, 518872313313693015111618567054735569910025420800000⟩, + ⟨6, 2, 7, 6, 8, 1, 81318483179616708818008883803889196320843366400000⟩, + ⟨6, 2, 0, 7, 0, 1, -1022660442674213399515940919759548200244092914892800000⟩, + ⟨6, 2, 1, 7, 1, 1, -1045039556690601259546517747795752977575900400844800000⟩, + ⟨6, 2, 2, 7, 2, 1, -55488791076782674449464822550408301464214988390400000⟩, + ⟨6, 2, 3, 7, 3, 1, -51655952112786015888929655324392406604008810086400000⟩, + ⟨6, 2, 4, 7, 4, 1, -16577240135644312689154541463244735199100429926400000⟩, + ⟨6, 2, 5, 7, 5, 1, -856413561639257038217197398220819176015632793600000⟩, + ⟨6, 2, 6, 7, 6, 1, -561585802675262460483790812356070281872146432000000⟩, + ⟨6, 2, 7, 7, 7, 1, -28740606239066295655727515734713553057428275200000⟩, + ⟨6, 2, 8, 7, 8, 1, -96397531030744975845962135463838575671377920000000⟩ +] + +def collectedFourData_8_7_29 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 7, 2, 3621270826063786312491702919691299435698978816000000⟩, + ⟨6, 3, 1, 0, 8, 2, 208343707245991447472803284726750244925079552000000⟩, + ⟨6, 3, 0, 1, 6, 2, 455597670581760830958964107452455176779071488000000⟩, + ⟨6, 3, 1, 1, 7, 2, 2184836852108346034576072550038150357085847552000000⟩, + ⟨6, 3, 2, 1, 8, 2, -400473673855139545866046902214576046063222784000000⟩, + ⟨6, 3, 0, 2, 5, 2, -2203474679908323702503505591267101654434971648000000⟩, + ⟨6, 3, 1, 2, 6, 2, 2590810314127942148370669640124039825549426688000000⟩, + ⟨6, 3, 2, 2, 7, 2, -486793039755992249543998601988482316462194688000000⟩, + ⟨6, 3, 3, 2, 8, 2, -51193207693885563657030262215194031811461120000000⟩, + ⟨6, 3, 0, 3, 4, 2, 1399333464523110997790917626361394982379585536000000⟩, + ⟨6, 3, 1, 3, 5, 2, 2140409004691209572080549386705291020397969408000000⟩, + ⟨6, 3, 2, 3, 6, 2, -193379940451057989388235099208417275302379520000000⟩, + ⟨6, 3, 3, 3, 7, 2, -127823778984728267226643874044196674816966656000000⟩, + ⟨6, 3, 4, 3, 8, 2, -14851091787013150056537554409610150376216985600000⟩, + ⟨6, 3, 0, 4, 3, 2, 5370288670504562270164811569530321466338312192000000⟩, + ⟨6, 3, 1, 4, 4, 2, -2410773510368451973573645054525530011709997056000000⟩, + ⟨6, 3, 2, 4, 5, 2, -89809363256655587021305027844117750561636352000000⟩, + ⟨6, 3, 3, 4, 6, 2, -293612824616002706817487727238766277179736064000000⟩, + ⟨6, 3, 4, 4, 7, 2, -33842454300482265648845432871338359593212313600000⟩, + ⟨6, 3, 5, 4, 8, 2, 24507531403761617629070296132427094253633536000000⟩, + ⟨6, 3, 0, 5, 2, 2, -9063480231029426587052151848721972191438045184000000⟩, + ⟨6, 3, 1, 5, 3, 2, -4603963040129807883497756760851632701661249536000000⟩, + ⟨6, 3, 2, 5, 4, 2, 476190197631674418335671686444466408305721344000000⟩, + ⟨6, 3, 3, 5, 5, 2, -96496435099474451737436729813683922679103488000000⟩, + ⟨6, 3, 4, 5, 6, 2, 31042965597387011178490940772640897079495884800000⟩, + ⟨6, 3, 5, 5, 7, 2, -833707959183992115602833844150888608825344000000⟩, + ⟨6, 3, 6, 5, 8, 2, 4931465289614031257398084502762475346722816000000⟩, + ⟨6, 3, 0, 6, 1, 2, 6587920493686982587272130378292704217042780160000000⟩, + ⟨6, 3, 1, 6, 2, 2, 11472700974869410511705480985855922280746450944000000⟩, + ⟨6, 3, 2, 6, 3, 2, 240277123551499349794994741899466841658490880000000⟩, + ⟨6, 3, 3, 6, 4, 2, 455271107986437643854505851828122683139162112000000⟩, + ⟨6, 3, 4, 6, 5, 2, -50369808438849810299760797065743571173664358400000⟩, + ⟨6, 3, 5, 6, 6, 2, 7930050449291251172734942562499468717981696000000⟩, + ⟨6, 3, 6, 6, 7, 2, 4657259768457031502821073927716218354008064000000⟩, + ⟨6, 3, 7, 6, 8, 2, 638656426877009572717860002425591402856448000000⟩, + ⟨6, 3, 0, 7, 0, 2, -64253895418500599130495660303672281606041632768000000⟩, + ⟨6, 3, 1, 7, 1, 2, -32829989105770693477996082343842930296507858944000000⟩, + ⟨6, 3, 2, 7, 2, 2, -1162122776361405717838768067075666995480363008000000⟩, + ⟨6, 3, 3, 7, 3, 2, -811387633249686720574965634129724325752733696000000⟩, + ⟨6, 3, 4, 7, 4, 2, -208310052790881923903715337616635374051577036800000⟩, + ⟨6, 3, 5, 7, 5, 2, -8968096859315103249244340764408382893326336000000⟩, + ⟨6, 3, 6, 7, 6, 2, -5040644679291134198286524419468624983490560000000⟩, + ⟨6, 3, 7, 7, 7, 2, -225722027381864970253601341777059369713664000000⟩, + ⟨6, 3, 8, 7, 8, 2, -672963339213369757293137936001702612172800000000⟩ +] + +def collectedFourData_8_7_30 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 7, 3, 13722987498205669519926229597412732498720115916800000⟩, + ⟨6, 4, 1, 0, 8, 3, 526352621716562264711557284573376353388619366400000⟩, + ⟨6, 4, 0, 1, 6, 3, 1726510232983883736461190661430398076963939942400000⟩, + ⟨6, 4, 1, 1, 7, 3, 5519699252410777856280637147568895091106276966400000⟩, + ⟨6, 4, 2, 1, 8, 3, -758807540728489497595795555981562563696105881600000⟩, + ⟨6, 4, 0, 2, 5, 3, -8350177862245876243859953317446292482325636710400000⟩, + ⟨6, 4, 1, 2, 6, 3, 6545337122188459632122415511431702514637576601600000⟩, + ⟨6, 4, 2, 2, 7, 3, -922363324872646350826234571729645481871225651200000⟩, + ⟨6, 4, 3, 2, 8, 3, -77599691701585358100764356545762042545858150400000⟩, + ⟨6, 4, 0, 3, 4, 3, 5302844377520531271100475715189252154628820172800000⟩, + ⟨6, 4, 1, 3, 5, 3, 5407458214395538735554754021165322423013841305600000⟩, + ⟨6, 4, 2, 3, 6, 3, -366411493737707199130580688186400021149646848000000⟩, + ⟨6, 4, 3, 3, 7, 3, -193757849686985311655090934073063471563952619520000⟩, + ⟨6, 4, 4, 3, 8, 3, -18759652501091019543983256708765948801145896960000⟩, + ⟨6, 4, 0, 4, 3, 3, 20350978379376130155183089584177771128555149721600000⟩, + ⟨6, 4, 1, 4, 4, 3, -6090498121208260202612939257958798687825244979200000⟩, + ⟨6, 4, 2, 4, 5, 3, -170168544192058639849836938786387973043440844800000⟩, + ⟨6, 4, 3, 4, 6, 3, -445064212543078819449018994082869025656673402880000⟩, + ⟨6, 4, 4, 4, 7, 3, -42749226222968903282925011029038571380812021760000⟩, + ⟨6, 4, 5, 4, 8, 3, 26535005702188777536744970001179077153443020800000⟩, + ⟨6, 4, 0, 5, 2, 3, -34346513109555594706021498503108883870743999283200000⟩, + ⟨6, 4, 1, 5, 3, 3, -11631299301002062862145031527600366998860804915200000⟩, + ⟨6, 4, 2, 5, 4, 3, 902273323750634286942994387268283212397910425600000⟩, + ⟨6, 4, 3, 5, 5, 3, -146271233066640280783286716640171668783717416960000⟩, + ⟨6, 4, 4, 5, 6, 3, 39212958586624353698746400219951498232783175680000⟩, + ⟨6, 4, 5, 5, 7, 3, -902679469687912524023769749789958212891443200000⟩, + ⟨6, 4, 6, 5, 8, 3, 4672008789713240812357042287667666106921779200000⟩, + ⟨6, 4, 0, 6, 1, 3, 24965255269876615089061120505783876777586720768000000⟩, + ⟨6, 4, 1, 6, 2, 3, 28984250669797270009667478853263107026070588620800000⟩, + ⟨6, 4, 2, 6, 3, 3, 455271107986437643854505851828122683139162112000000⟩, + ⟨6, 4, 3, 6, 4, 3, 690109083057250283254532012261918672229016535040000⟩, + ⟨6, 4, 4, 6, 5, 3, -63626305487226849420419554786606084580117053440000⟩, + ⟨6, 4, 5, 6, 6, 3, 8586092594307169993047144196533964094885068800000⟩, + ⟨6, 4, 6, 6, 7, 3, 4412229894436119353699859629353340729347276800000⟩, + ⟨6, 4, 7, 6, 8, 3, 537826794493235407803910156762834609058611200000⟩, + ⟨6, 4, 0, 7, 0, 3, -243493360726499477783178473530779944082427242086400000⟩, + ⟨6, 4, 1, 7, 1, 3, -82940594007698563734443686060779143357646294220800000⟩, + ⟨6, 4, 2, 7, 2, 3, -2201961286160197818870538164580430214310605619200000⟩, + ⟨6, 4, 3, 7, 3, 3, -1229917659529175231418820798584797314146442936320000⟩, + ⟨6, 4, 4, 7, 4, 3, -263133799109513925693774834954377087180215418880000⟩, + ⟨6, 4, 5, 7, 5, 3, -9710015153267626440284307837622532178758860800000⟩, + ⟨6, 4, 6, 7, 6, 3, -4775443983569563130746105072268534372892672000000⟩, + ⟨6, 4, 7, 7, 7, 3, -190085544158598828622832414811620084652441600000⟩, + ⟨6, 4, 8, 7, 8, 3, -510045668184064436986125136441651796901888000000⟩ +] + +def collectedFourData_8_7_31 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 7, 4, -2530449217941373995062769910924641118946171289600000⟩, + ⟨6, 5, 1, 0, 8, 4, -72792563216913522047873845255009688979347865600000⟩, + ⟨6, 5, 0, 1, 6, 4, -318359720825592135880994048524753388576754892800000⟩, + ⟨6, 5, 1, 1, 7, 4, -763353387428979141335753265719791856643578265600000⟩, + ⟨6, 5, 2, 1, 8, 4, 83952154656797001155802314992532691140864901120000⟩, + ⟨6, 5, 0, 2, 5, 4, 1539730400829574237076739224087993763526134988800000⟩, + ⟨6, 5, 1, 2, 6, 4, -905195199159624877963648251784525427901884006400000⟩, + ⟨6, 5, 2, 2, 7, 4, 102047468354261995910362298310859519915028643840000⟩, + ⟨6, 5, 3, 2, 8, 4, 7154494573592064199699290074290374683551334400000⟩, + ⟨6, 5, 0, 3, 4, 4, -977817578695321877881752203270750305099815321600000⟩, + ⟨6, 5, 1, 3, 5, 4, -747830879288693004254484218697096180261086822400000⟩, + ⟨6, 5, 2, 3, 6, 4, 40538651422419997113277864147970627410172313600000⟩, + ⟨6, 5, 3, 3, 7, 4, 17863981850691842875434262593231124194624798720000⟩, + ⟨6, 5, 4, 3, 8, 4, 1482507716333986466053763685601085403672084480000⟩, + ⟨6, 5, 0, 4, 3, 4, -3752617083646514618871071818820305485797995315200000⟩, + ⟨6, 5, 1, 4, 4, 4, 842292697364548988619531857513390669359271116800000⟩, + ⟨6, 5, 2, 4, 5, 4, 18826929323894807030595800978520796699148943360000⟩, + ⟨6, 5, 3, 4, 6, 4, 41033790517938736566793397790319369174835527680000⟩, + ⟨6, 5, 4, 4, 7, 4, 3378317255032991063492219081791134583624826880000⟩, + ⟨6, 5, 5, 4, 8, 4, -1834845121259665789893654315221504461740441600000⟩, + ⟨6, 5, 0, 5, 2, 4, 6333322627339868810243863895466019558712043110400000⟩, + ⟨6, 5, 1, 5, 3, 4, 1608564400993831417219168217202672958702406860800000⟩, + ⟨6, 5, 2, 5, 4, 4, -99824771832781501666859396829834782103746641920000⟩, + ⟨6, 5, 3, 5, 5, 4, 13485836351931255376955744562065117456954818560000⟩, + ⟨6, 5, 4, 5, 6, 4, -3098858770522254648964325324125449326784675840000⟩, + ⟨6, 5, 5, 5, 7, 4, 62418566613743305448663427670238409680486400000⟩, + ⟨6, 5, 6, 5, 8, 4, -287164899763769894489384709165773782568140800000⟩, + ⟨6, 5, 0, 6, 1, 4, -4603466313849384935373839980837626639701508096000000⟩, + ⟨6, 5, 1, 6, 2, 4, -4008411494741677086743277244121049548553663283200000⟩, + ⟨6, 5, 2, 6, 3, 4, -50369808438849810299760797065743571173664358400000⟩, + ⟨6, 5, 3, 6, 4, 4, -63626305487226849420419554786606084580117053440000⟩, + ⟨6, 5, 4, 6, 5, 4, 5028157576007948464942304065755544139040030720000⟩, + ⟨6, 5, 5, 6, 6, 4, -593711954847959741067356363221199610288537600000⟩, + ⟨6, 5, 6, 6, 7, 4, -271197596665528884761383109308439292228403200000⟩, + ⟨6, 5, 7, 6, 8, 4, -29751759047174062527678402979526233471057920000⟩, + ⟨6, 5, 0, 7, 0, 4, 44898939411323591745196971657558069713621011660800000⟩, + ⟨6, 5, 1, 7, 1, 4, 11470368311008227046692995570268850798978085683200000⟩, + ⟨6, 5, 2, 7, 2, 4, 243618288593346345384180703540291959881402941440000⟩, + ⟨6, 5, 3, 7, 3, 4, 113395285833162195516210332976074695806308843520000⟩, + ⟨6, 5, 4, 7, 4, 4, 20794515654564722269112580612899179718969917440000⟩, + ⟨6, 5, 5, 7, 5, 4, 671429059834757129604639217932786101492121600000⟩, + ⟨6, 5, 6, 7, 6, 4, 293522541286447769906682811492353366294528000000⟩, + ⟨6, 5, 7, 7, 7, 4, 10515242762284371091786625948435291370946560000⟩, + ⟨6, 5, 8, 7, 8, 4, 25649954051176231403678255740265774972928000000⟩ +] + +def collectedFourData_8_7_32 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 7, 5, 597577911637465023686716911822826356275675136000000⟩, + ⟨6, 6, 1, 0, 8, 5, 13752254770096440671861658658030457902124236800000⟩, + ⟨6, 6, 0, 1, 6, 5, 75182199180908977583420932346734716804661248000000⟩, + ⟨6, 6, 1, 1, 7, 5, 144215697313159860952128288490386237556575436800000⟩, + ⟨6, 6, 2, 1, 8, 5, -13217140235173463009897337949442304568511692800000⟩, + ⟨6, 6, 0, 2, 5, 5, -363614836009631868146373536637758001389764608000000⟩, + ⟨6, 6, 1, 2, 6, 5, 171013005249125732363342550796785136738448179200000⟩, + ⟨6, 6, 2, 2, 7, 5, -16066004564106875716739319139002976954849689600000⟩, + ⟨6, 6, 3, 2, 8, 5, -965467858049085103349945081636760676466688000000⟩, + ⟨6, 6, 0, 3, 4, 5, 230916385318541794331811120496440792638816256000000⟩, + ⟨6, 6, 1, 3, 5, 5, 141283124572452871735297936526128530102367027200000⟩, + ⟨6, 6, 2, 3, 6, 5, -6382266696850752088377370776654065103273984000000⟩, + ⟨6, 6, 3, 3, 7, 5, -2410666486110131462749819586054484125967974400000⟩, + ⟨6, 6, 4, 3, 8, 5, -175050710133202932900812588558336601253478400000⟩, + ⟨6, 6, 0, 4, 3, 5, 886198807753553939199647486436332243917996032000000⟩, + ⟨6, 6, 1, 4, 4, 5, -159129219431822136604726122624429629993543270400000⟩, + ⟨6, 6, 2, 4, 5, 5, -2964047392099549206618753657234861219800678400000⟩, + ⟨6, 6, 3, 4, 6, 5, -5537331174338807464293044614161122127878553600000⟩, + ⟨6, 6, 4, 4, 7, 5, -398903039783942486524125487499253163386470400000⟩, + ⟨6, 6, 5, 4, 8, 5, 192581162263629079097520319565169778753536000000⟩, + ⟨6, 6, 0, 5, 2, 5, -1495644995575542761272424984913238525281828864000000⟩, + ⟨6, 6, 1, 5, 3, 5, -303896256416408013592623668047730773613504102400000⟩, + ⟨6, 6, 2, 5, 4, 5, 15716070822147086268814321562058407526845644800000⟩, + ⟨6, 6, 3, 5, 5, 5, -1819854834296494764718133634356519193752371200000⟩, + ⟨6, 6, 4, 5, 6, 5, 365905298438404489521851461475782714667827200000⟩, + ⟨6, 6, 5, 5, 7, 5, -6551310498104591222696441738041013305344000000⟩, + ⟨6, 6, 6, 5, 8, 5, 27126156080068994621374407187341698609971200000⟩, + ⟨6, 6, 0, 6, 1, 5, 1087130998962125280803457835858047293309583360000000⟩, + ⟨6, 6, 1, 6, 2, 5, 757284723369409811720838845074132103184619929600000⟩, + ⟨6, 6, 2, 6, 3, 5, 7930050449291251172734942562499468717981696000000⟩, + ⟨6, 6, 3, 6, 4, 5, 8586092594307169993047144196533964094885068800000⟩, + ⟨6, 6, 4, 6, 5, 5, -593711954847959741067356363221199610288537600000⟩, + ⟨6, 6, 5, 6, 6, 5, 62314653694550370933559494466976870301696000000⟩, + ⟨6, 6, 6, 6, 7, 5, 25617853511137480580588688124671410621644800000⟩, + ⟨6, 6, 7, 6, 8, 5, 2554917401858183739653730353043724881100800000⟩, + ⟨6, 6, 0, 7, 0, 5, -10603103297992144397879617749949945637008048128000000⟩, + ⟨6, 6, 1, 7, 1, 5, -2167026689934912063104763140981040371004447129600000⟩, + ⟨6, 6, 2, 7, 2, 5, -38354430536709556480510735995842187507636633600000⟩, + ⟨6, 6, 3, 7, 3, 5, -15302199561420645033056031423582023388128870400000⟩, + ⟨6, 6, 4, 7, 4, 5, -2455363093292326449647502668118762418549555200000⟩, + ⟨6, 6, 5, 7, 5, 5, -70471663914490252202120696321241394446336000000⟩, + ⟨6, 6, 6, 7, 6, 5, -27726711288547317603973947124295393083392000000⟩, + ⟨6, 6, 7, 7, 7, 5, -902991203831877404571019257741358556774400000⟩, + ⟨6, 6, 8, 7, 8, 5, -2019120540182014292732802157575835484160000000⟩ +] + +def collectedFourData_8_7_33 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 7, 6, 491334300816593684062020854714679588881537433600000⟩, + ⟨6, 7, 1, 0, 8, 6, 9422696676212195373745447987557545422513766400000⟩, + ⟨6, 7, 0, 1, 6, 6, 61815526559850634718335264716315655955860684800000⟩, + ⟨6, 7, 1, 1, 7, 6, 98812943364399717995835023381584878749771366400000⟩, + ⟨6, 7, 2, 1, 8, 6, -7762328356540230883582015218898413483668275200000⟩, + ⟨6, 7, 0, 2, 5, 6, -298967611985161630002788606097258653271510220800000⟩, + ⟨6, 7, 1, 2, 6, 6, 117173780088332048893100530218054651983010201600000⟩, + ⟨6, 7, 2, 2, 7, 6, -9435445231366637784815729187312075650000486400000⟩, + ⟨6, 7, 3, 2, 8, 6, -496135593532475601882060341245130223648768000000⟩, + ⟨6, 7, 0, 3, 4, 6, 189861670784800305097430548723207110053697945600000⟩, + ⟨6, 7, 1, 3, 5, 6, 96803618793370377260277444388058566110058905600000⟩, + ⟨6, 7, 2, 3, 6, 6, -3748257858997950045003853930591904707117056000000⟩, + ⟨6, 7, 3, 3, 7, 6, -1238795717458561949233549706805528177829478400000⟩, + ⟨6, 7, 4, 3, 8, 6, -79960208810139169130071140209991508348108800000⟩, + ⟨6, 7, 0, 4, 3, 6, 728641174836879274621042770349736393392206643200000⟩, + ⟨6, 7, 1, 4, 4, 6, -109031311017368280366089756605780529291408179200000⟩, + ⟨6, 7, 2, 4, 5, 6, -1740763032883224388953078169404939389475225600000⟩, + ⟨6, 7, 3, 4, 6, 6, -2845529310854376753138501100576521280133529600000⟩, + ⟨6, 7, 4, 4, 7, 6, -182212173443067426482766130372338088987852800000⟩, + ⟨6, 7, 5, 4, 8, 6, 79171041021218094130693041820602022546636800000⟩, + ⟨6, 7, 0, 5, 2, 6, -1229733686369532563270906448471861542085092966400000⟩, + ⟨6, 7, 1, 5, 3, 6, -208222018361294201787242355706175009613624115200000⟩, + ⟨6, 7, 2, 5, 4, 6, 9229931742079743139893647602264280403227443200000⟩, + ⟨6, 7, 3, 5, 5, 6, -935188831848954857368032219881622599840563200000⟩, + ⟨6, 7, 4, 5, 6, 6, 167139362334535286154218323369306295264870400000⟩, + ⟨6, 7, 5, 5, 7, 6, -2693275220128486247112148505810821133107200000⟩, + ⟨6, 7, 6, 5, 8, 6, 10137902805709221918950861359901719501209600000⟩, + ⟨6, 7, 0, 6, 1, 6, 893849553119280261188961397921484296773697536000000⟩, + ⟨6, 7, 1, 6, 2, 6, 518872313313693015111618567054735569910025420800000⟩, + ⟨6, 7, 2, 6, 3, 6, 4657259768457031502821073927716218354008064000000⟩, + ⟨6, 7, 3, 6, 4, 6, 4412229894436119353699859629353340729347276800000⟩, + ⟨6, 7, 4, 6, 5, 6, -271197596665528884761383109308439292228403200000⟩, + ⟨6, 7, 5, 6, 6, 6, 25617853511137480580588688124671410621644800000⟩, + ⟨6, 7, 6, 6, 7, 6, 9574202412616507287852104090738374370918400000⟩, + ⟨6, 7, 7, 6, 8, 6, 875282348711060861347459242816154317619200000⟩, + ⟨6, 7, 0, 7, 0, 6, -8717973412252993618578798438269500576196512972800000⟩, + ⟨6, 7, 1, 7, 1, 6, -1484791805407311929290885823152078620103331020800000⟩, + ⟨6, 7, 2, 7, 2, 6, -22525272370324202401781499831832058897262182400000⟩, + ⟨6, 7, 3, 7, 3, 6, -7863509694770013132268910084524977951237734400000⟩, + ⟨6, 7, 4, 7, 4, 6, -1121568404349616423274999244324915680536166400000⟩, + ⟨6, 7, 5, 7, 5, 6, -28971239601150300636953216360037185539276800000⟩, + ⟨6, 7, 6, 7, 6, 6, -10362349288839543554417259484992069697536000000⟩, + ⟨6, 7, 7, 7, 7, 6, -309353351768068348136865941477303884185600000⟩, + ⟨6, 7, 8, 7, 8, 6, -638515503459837405706954760844906332160000000⟩ +] + +def collectedFourData_8_7_34 : List CollectedFourTerm := [ + ⟨6, 8, 0, 0, 7, 7, 89836463088422662270228173318245196595042713600000⟩, + ⟨6, 8, 1, 0, 8, 7, 1476739809603116587287371246567660025230131200000⟩, + ⟨6, 8, 0, 1, 6, 7, 11302464047097691946725867589916446755179724800000⟩, + ⟨6, 8, 1, 1, 7, 7, 15486119545654904535496840130855620723290931200000⟩, + ⟨6, 8, 2, 1, 8, 7, -1064458745893940154437493496832840482317926400000⟩, + ⟨6, 8, 0, 2, 5, 7, -54663785520572733277617978725699420894842060800000⟩, + ⟨6, 8, 1, 2, 6, 7, 18363658689656438640350244238151974233361612800000⟩, + ⟨6, 8, 2, 2, 7, 7, -1293895560275946527714527110527469218483404800000⟩, + ⟨6, 8, 3, 2, 8, 7, -60476226825817176399374849317860500570112000000⟩, + ⟨6, 8, 0, 3, 4, 7, 34714655482056106309092711683542714999740825600000⟩, + ⟨6, 8, 1, 3, 5, 7, 15171215045763316252855354312691817732951244800000⟩, + ⟨6, 8, 2, 3, 6, 7, -514003746893077499371009382544240009019392000000⟩, + ⟨6, 8, 3, 3, 7, 7, -151002451298570305281933945659720042387865600000⟩, + ⟨6, 8, 4, 3, 8, 7, -8772042581243741889140237693847688477409280000⟩, + ⟨6, 8, 0, 4, 3, 7, 133226086391987385795670604674769328079582003200000⟩, + ⟨6, 8, 1, 4, 4, 7, -17087558159336924988024880141291112170625433600000⟩, + ⟨6, 8, 2, 4, 5, 7, -238713224920480094497511274398351296246579200000⟩, + ⟨6, 8, 3, 4, 6, 7, -346854525831306261584480094858228821026406400000⟩, + ⟨6, 8, 4, 4, 7, 7, -19989604430108486704954479635675500699975680000⟩, + ⟨6, 8, 5, 4, 8, 7, 7895878955682138647207219983479810608332800000⟩, + ⟨6, 8, 0, 5, 2, 7, -224846758592913215973252775836345158133507686400000⟩, + ⟨6, 8, 1, 5, 3, 7, -32632881468666910866463846796471839177152921600000⟩, + ⟨6, 8, 2, 5, 4, 7, 1265713213301884740830503929831535696832102400000⟩, + ⟨6, 8, 3, 5, 5, 7, -113994425429519913609458127380002361887948800000⟩, + ⟨6, 8, 4, 5, 6, 7, 18336040203218650776218574410905987307274240000⟩, + ⟨6, 8, 5, 5, 7, 7, -268605475665949596432554402466812343091200000⟩, + ⟨6, 8, 6, 5, 8, 7, 926816354654507426619441990400983485644800000⟩, + ⟨6, 8, 0, 6, 1, 7, 163433088738044310964160629767306560548110336000000⟩, + ⟨6, 8, 1, 6, 2, 7, 81318483179616708818008883803889196320843366400000⟩, + ⟨6, 8, 2, 6, 3, 7, 638656426877009572717860002425591402856448000000⟩, + ⟨6, 8, 3, 6, 4, 7, 537826794493235407803910156762834609058611200000⟩, + ⟨6, 8, 4, 6, 5, 7, -29751759047174062527678402979526233471057920000⟩, + ⟨6, 8, 5, 6, 6, 7, 2554917401858183739653730353043724881100800000⟩, + ⟨6, 8, 6, 6, 7, 7, 875282348711060861347459242816154317619200000⟩, + ⟨6, 8, 7, 6, 8, 7, 73863797119153581603549176687137023590400000⟩, + ⟨6, 8, 0, 7, 0, 7, -1594010219425058558000828918135087614816734412800000⟩, + ⟨6, 8, 1, 7, 1, 7, -232698901743580217709251722591501970347288166400000⟩, + ⟨6, 8, 2, 7, 2, 7, -3088921529328563021960348573286213056515276800000⟩, + ⟨6, 8, 3, 7, 3, 7, -958519005987816157961858027745127431772569600000⟩, + ⟨6, 8, 4, 7, 4, 7, -123041772240655939093166643754366406586531840000⟩, + ⟨6, 8, 5, 7, 5, 7, -2889356993871547124251456244537111661772800000⟩, + ⟨6, 8, 6, 7, 6, 7, -947335457598828512715352074658322055168000000⟩, + ⟨6, 8, 7, 7, 7, 7, -26105876859936268367287800505950221107200000⟩, + ⟨6, 8, 8, 7, 8, 7, -50034575844319803402772608702889328640000000⟩ +] + +def collectedFourData_8_7_35 : List CollectedFourTerm := [ + ⟨7, 0, 1, 0, 8, 0, -18571465285052247574968722979108130211194365542400000⟩, + ⟨7, 0, 1, 1, 7, 0, -194753286714464272098916646381021582853210007142400000⟩, + ⟨7, 0, 2, 1, 8, 0, 107092981543187298551581665309130111515122624102400000⟩, + ⟨7, 0, 1, 2, 6, 0, -230941190617160461928727573033447698368325851545600000⟩, + ⟨7, 0, 2, 2, 7, 0, 130176142466727772848482390943490868708771679436800000⟩, + ⟨7, 0, 3, 2, 8, 0, 27379743561775107941518961911611190421816868864000000⟩, + ⟨7, 0, 1, 3, 5, 0, -190793050828756604351731124835768132854653491609600000⟩, + ⟨7, 0, 2, 3, 6, 0, 51712848423187384952229314689958760505694748672000000⟩, + ⟨7, 0, 3, 3, 7, 0, 68364192191787322196546980302175027983205741363200000⟩, + ⟨7, 0, 4, 3, 8, 0, 13238054521224125301034952266573719489297462067200000⟩, + ⟨7, 0, 1, 4, 4, 0, 214892962930094257434110686669729379908024742707200000⟩, + ⟨7, 0, 2, 4, 5, 0, 24016441303278908940993969222688204015919117107200000⟩, + ⟨7, 0, 3, 4, 6, 0, 157033407488446456842048821998014468800025251020800000⟩, + ⟨7, 0, 4, 4, 7, 0, 30166688186089480119895553671470770720355857203200000⟩, + ⟨7, 0, 5, 4, 8, 0, -32768503645029836424633985752749738907295285248000000⟩, + ⟨7, 0, 1, 5, 3, 0, 410390795592792774243975089073128198280517464883200000⟩, + ⟨7, 0, 2, 5, 4, 0, -127340775125363828643904694466001033222777366118400000⟩, + ⟨7, 0, 3, 5, 5, 0, 51609339728181306952692163969092513663406414233600000⟩, + ⟨7, 0, 4, 5, 6, 0, -27671263296484144506137328235179267605520816537600000⟩, + ⟨7, 0, 5, 5, 7, 0, 1114733338471529252137029992887342413845102592000000⟩, + ⟨7, 0, 6, 5, 8, 0, -9231261603547439514231721927466146098800964403200000⟩, + ⟨7, 0, 1, 6, 2, 0, -1022660442674213399515940919759548200244092914892800000⟩, + ⟨7, 0, 2, 6, 3, 0, -64253895418500599130495660303672281606041632768000000⟩, + ⟨7, 0, 3, 6, 4, 0, -243493360726499477783178473530779944082427242086400000⟩, + ⟨7, 0, 4, 6, 5, 0, 44898939411323591745196971657558069713621011660800000⟩, + ⟨7, 0, 5, 6, 6, 0, -10603103297992144397879617749949945637008048128000000⟩, + ⟨7, 0, 6, 6, 7, 0, -8717973412252993618578798438269500576196512972800000⟩, + ⟨7, 0, 7, 6, 8, 0, -1594010219425058558000828918135087614816734412800000⟩, + ⟨7, 0, 1, 7, 1, 0, 2926419093937835355805532730952998204398614924492800000⟩, + ⟨7, 0, 2, 7, 2, 0, 310769973570866689862581977935230405616419523788800000⟩, + ⟨7, 0, 3, 7, 3, 0, 433955720462217629694369169231208389253121913651200000⟩, + ⟨7, 0, 4, 7, 4, 0, 185684653742173313382555973730022689687933131161600000⟩, + ⟨7, 0, 5, 7, 5, 0, 11991053271825730746347102131321503800673435648000000⟩, + ⟨7, 0, 6, 7, 6, 0, 9435635648306024046746341266833761246497472512000000⟩, + ⟨7, 0, 7, 7, 7, 0, 563375240981212922075218809974190813332530790400000⟩, + ⟨7, 0, 8, 7, 8, 0, 2159532229077959383680009032964704268409896960000000⟩ +] + +def collectedFourData_8_7_36 : List CollectedFourTerm := [ + ⟨7, 1, 0, 0, 7, 1, -164929394874661707980527644206780944134757259673600000⟩, + ⟨7, 1, 1, 0, 8, 1, -18977868937450069109197746568669718156021229158400000⟩, + ⟨7, 1, 0, 1, 6, 1, -20750021670439876302008135377656772943512653004800000⟩, + ⟨7, 1, 1, 1, 7, 1, -199015117745155383362253585606832805748647814758400000⟩, + ⟨7, 1, 2, 1, 8, 1, 54718260962509992034693831720055664464540939059200000⟩, + ⟨7, 1, 0, 2, 5, 1, 100356411611981811326301634305998355082857204940800000⟩, + ⟨7, 1, 1, 2, 6, 1, -235994929884113057626650475333870920035498301849600000⟩, + ⟨7, 1, 2, 2, 7, 1, 66512408487897017135058054710584478846884931174400000⟩, + ⟨7, 1, 3, 2, 8, 1, 9326300265504306053309842674297496524143198208000000⟩, + ⟨7, 1, 0, 3, 4, 1, -63732107488498392097467657434616255930135320985600000⟩, + ⟨7, 1, 1, 3, 5, 1, -194968219105399765974562314763906256401390475673600000⟩, + ⟨7, 1, 2, 3, 6, 1, 26422246298125384091104291164234437778342936576000000⟩, + ⟨7, 1, 3, 3, 7, 1, 23286740518614157237584037177965601106659010150400000⟩, + ⟨7, 1, 4, 3, 8, 1, 3381936479358190048335847207466103544132455628800000⟩, + ⟨7, 1, 0, 4, 3, 1, -244587743715185924095611053145612749927175369523200000⟩, + ⟨7, 1, 1, 4, 4, 1, 219595515134182997876461520942321087739241640755200000⟩, + ⟨7, 1, 2, 4, 5, 1, 12270999310012370967023178591318323953829255577600000⟩, + ⟨7, 1, 3, 4, 6, 1, 53489935238005335942609079810898174095736281497600000⟩, + ⟨7, 1, 4, 4, 7, 1, 7706708192989507659800457927153663450769312972800000⟩, + ⟨7, 1, 5, 4, 8, 1, -6697116871572490547155070469803776201555810713600000⟩, + ⟨7, 1, 0, 5, 2, 1, 412792740935916924850928073335363882861824730726400000⟩, + ⟨7, 1, 1, 5, 3, 1, 419371471898049081094919873645300454436614910771200000⟩, + ⟨7, 1, 2, 5, 4, 1, -65063701318914475531782672419841150378623316787200000⟩, + ⟨7, 1, 3, 5, 5, 1, 17579572932210239222295589528412573722140160819200000⟩, + ⟨7, 1, 4, 5, 6, 1, -7069199981180581006781948392877461633080125030400000⟩, + ⟨7, 1, 5, 5, 7, 1, 227825460974759401752792610497111097075983974400000⟩, + ⟨7, 1, 6, 5, 8, 1, -1572211904575677835765686809289304086072734515200000⟩, + ⟨7, 1, 0, 6, 1, 1, -300044319437774614577944142884303467916805799936000000⟩, + ⟨7, 1, 1, 6, 2, 1, -1045039556690601259546517747795752977575900400844800000⟩, + ⟨7, 1, 2, 6, 3, 1, -32829989105770693477996082343842930296507858944000000⟩, + ⟨7, 1, 3, 6, 4, 1, -82940594007698563734443686060779143357646294220800000⟩, + ⟨7, 1, 4, 6, 5, 1, 11470368311008227046692995570268850798978085683200000⟩, + ⟨7, 1, 5, 6, 6, 1, -2167026689934912063104763140981040371004447129600000⟩, + ⟨7, 1, 6, 6, 7, 1, -1484791805407311929290885823152078620103331020800000⟩, + ⟨7, 1, 7, 6, 8, 1, -232698901743580217709251722591501970347288166400000⟩, + ⟨7, 1, 0, 7, 0, 1, 2926419093937835355805532730952998204398614924492800000⟩, + ⟨7, 1, 1, 7, 1, 1, 2990458597012496164648850317601466414100942474444800000⟩, + ⟨7, 1, 2, 7, 2, 1, 158785312241078170582032749294621839047797401190400000⟩, + ⟨7, 1, 3, 7, 3, 1, 147817357815366658359286328383725763857226294886400000⟩, + ⟨7, 1, 4, 7, 4, 1, 47437008447188457577245791309083370487384794726400000⟩, + ⟨7, 1, 5, 7, 5, 1, 2450691250494404293297450789357344126794307993600000⟩, + ⟨7, 1, 6, 7, 6, 1, 1607019639417928507331831227354813107831570432000000⟩, + ⟨7, 1, 7, 7, 7, 1, 82243387305972369893153251294739562323194675200000⟩, + ⟨7, 1, 8, 7, 8, 1, 275848721281482965599178918834165937780817920000000⟩ +] + +def collectedFourData_8_7_37 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 7, 2, -17514614975153126476461120880040940221136214425600000⟩, + ⟨7, 2, 1, 0, 8, 2, -1007673822307286595386254875444251512938902323200000⟩, + ⟨7, 2, 0, 1, 6, 2, -2203540736689334138121083115947489034534440140800000⟩, + ⟨7, 2, 1, 1, 7, 2, -10567167739231998961490214704987806031867491123200000⟩, + ⟨7, 2, 2, 1, 8, 2, 1936928371878217173401317077116072050194540134400000⟩, + ⟨7, 2, 0, 2, 5, 2, 10657311336209151474689564375787690724988603596800000⟩, + ⟨7, 2, 1, 2, 6, 2, -12530696350852589990515671832674361924492512460800000⟩, + ⟨7, 2, 2, 2, 7, 2, 2354420056778275696221704308186355408464301260800000⟩, + ⟨7, 2, 3, 2, 8, 2, 247600736086359426228527224922746025454600192000000⟩, + ⟨7, 2, 0, 3, 4, 2, -6768007152784457303420411098553548476679559577600000⟩, + ⟨7, 2, 1, 3, 5, 2, -10352288300752715757952354520558089121775275212800000⟩, + ⟨7, 2, 2, 3, 6, 2, 935300164942333632529463972530719810631237632000000⟩, + ⟨7, 2, 3, 3, 7, 2, 618231659856293358741900766805261620294031769600000⟩, + ⟨7, 2, 4, 3, 8, 2, 71828694152910737399786028382544372964482088960000⟩, + ⟨7, 2, 0, 4, 3, 2, -25973903330382283042776485766533356008355607347200000⟩, + ⟨7, 2, 1, 4, 4, 2, 11659931514235222770911013249438670007660288409600000⟩, + ⟨7, 2, 2, 4, 5, 2, 434371383460917638477277976766322344474129203200000⟩, + ⟨7, 2, 3, 4, 6, 2, 1420085881979230759944925457502649034108986982400000⟩, + ⟨7, 2, 4, 4, 7, 2, 163682194830882094265162597142341267679357173760000⟩, + ⟨7, 2, 5, 4, 8, 2, -118532967332611750505983862875840387174996377600000⟩, + ⟨7, 2, 0, 5, 2, 2, 43836369663061525734576327292303316472031503974400000⟩, + ⟨7, 2, 1, 5, 3, 2, 22267497759994569974686523231470995955051501977600000⟩, + ⟨7, 2, 2, 5, 4, 2, -2303138419372653384048576042751936832052029030400000⟩, + ⟨7, 2, 3, 5, 5, 2, 466714031736541827776472484838362803319131340800000⟩, + ⟨7, 2, 4, 5, 6, 2, -150142205938280974385191894122937385542672711680000⟩, + ⟨7, 2, 5, 5, 7, 2, 4032306504592565893783966814784768967075430400000⟩, + ⟨7, 2, 6, 5, 8, 2, -23851493014347765589550145450150634775484825600000⟩, + ⟨7, 2, 0, 6, 1, 2, -31863093503908998713152946046006430150170771456000000⟩, + ⟨7, 2, 1, 6, 2, 2, -55488791076782674449464822550408301464214988390400000⟩, + ⟨7, 2, 2, 6, 3, 2, -1162122776361405717838768067075666995480363008000000⟩, + ⟨7, 2, 3, 6, 4, 2, -2201961286160197818870538164580430214310605619200000⟩, + ⟨7, 2, 4, 6, 5, 2, 243618288593346345384180703540291959881402941440000⟩, + ⟨7, 2, 5, 6, 6, 2, -38354430536709556480510735995842187507636633600000⟩, + ⟨7, 2, 6, 6, 7, 2, -22525272370324202401781499831832058897262182400000⟩, + ⟨7, 2, 7, 6, 8, 2, -3088921529328563021960348573286213056515276800000⟩, + ⟨7, 2, 0, 7, 0, 2, 310769973570866689862581977935230405616419523788800000⟩, + ⟨7, 2, 1, 7, 1, 2, 158785312241078170582032749294621839047797401190400000⟩, + ⟨7, 2, 2, 7, 2, 2, 5620715477928045928969931010086421832886176972800000⟩, + ⟨7, 2, 3, 7, 3, 2, 3924352161038478464326019562380185375042279833600000⟩, + ⟨7, 2, 4, 7, 4, 2, 1007511049388122582141556351642276537564009594880000⟩, + ⟨7, 2, 5, 7, 5, 2, 43375039066469781591884006429350551289960857600000⟩, + ⟨7, 2, 6, 7, 6, 2, 24379549341881602207497522823667114726916096000000⟩, + ⟨7, 2, 7, 7, 7, 2, 1091725692690486197277067466390369271703142400000⟩, + ⟨7, 2, 8, 7, 8, 2, 3254850118881421736951064417389790080532480000000⟩ +] + +def collectedFourData_8_7_38 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 7, 3, -24457212750728375044442561687954870287859082854400000⟩, + ⟨7, 3, 1, 0, 8, 3, -938069647947199732030023745037368638152323891200000⟩, + ⟨7, 3, 0, 1, 6, 3, -3076999675902759012002734790213603577570734899200000⟩, + ⟨7, 3, 1, 1, 7, 3, -9837250012353216320396720592540259705318224691200000⟩, + ⟨7, 3, 2, 1, 8, 3, 1352352573583574389150297181401725942662745292800000⟩, + ⟨7, 3, 0, 2, 5, 3, 14881750530638640299843551794450396022102504243200000⟩, + ⟨7, 3, 1, 2, 6, 3, -11665149628937175419615694101429782022762319052800000⟩, + ⟨7, 3, 2, 2, 7, 3, 1643842936738746018041550404729576197004564889600000⟩, + ⟨7, 3, 3, 2, 8, 3, 138298761081343109626230817633536932391891763200000⟩, + ⟨7, 3, 0, 3, 4, 3, -9450769604066258477624611487197837065948915302400000⟩, + ⟨7, 3, 1, 3, 5, 3, -9637213180252317979292458256731853102907182284800000⟩, + ⟨7, 3, 2, 3, 6, 3, 653021352517228392967592231319391771488681984000000⟩, + ⟨7, 3, 3, 3, 7, 3, 345316714202199875298465219848395993552949084160000⟩, + ⟨7, 3, 4, 3, 8, 3, 33433595447704638235376062600659120227541319680000⟩, + ⟨7, 3, 0, 4, 3, 3, -36269668537915315015646931941103312402910072012800000⟩, + ⟨7, 3, 1, 4, 4, 3, 10854532100082324746451312830147980993068898713600000⟩, + ⟨7, 3, 2, 4, 5, 3, 303275674435401061374287230324981486529701478400000⟩, + ⟨7, 3, 3, 4, 6, 3, 793196826516436609403789295275745936394986455040000⟩, + ⟨7, 3, 4, 4, 7, 3, 76187996294602273575040629717150931093637038080000⟩, + ⟨7, 3, 5, 4, 8, 3, -47290889092850736223821405250367116443805286400000⟩, + ⟨7, 3, 0, 5, 2, 3, 61212617039541721160184240771750382991023118745600000⟩, + ⟨7, 3, 1, 5, 3, 3, 20729390128002453131554786469265280209918728601600000⟩, + ⟨7, 3, 2, 5, 4, 3, -1608038383854932197582708381088362223721303244800000⟩, + ⟨7, 3, 3, 5, 5, 3, 260685704690028530330366497804917849429041479680000⟩, + ⟨7, 3, 4, 5, 6, 3, -69885633202243373388541506986002426111658557440000⟩, + ⟨7, 3, 5, 5, 7, 3, 1608762220235105000951807675568509949680025600000⟩, + ⟨7, 3, 6, 5, 8, 3, -8326489618840663577427733299484419941833113600000⟩, + ⟨7, 3, 0, 6, 1, 3, -44493267926641391839685464885894055394325561344000000⟩, + ⟨7, 3, 1, 6, 2, 3, -51655952112786015888929655324392406604008810086400000⟩, + ⟨7, 3, 2, 6, 3, 3, -811387633249686720574965634129724325752733696000000⟩, + ⟨7, 3, 3, 6, 4, 3, -1229917659529175231418820798584797314146442936320000⟩, + ⟨7, 3, 4, 6, 5, 3, 113395285833162195516210332976074695806308843520000⟩, + ⟨7, 3, 5, 6, 6, 3, -15302199561420645033056031423582023388128870400000⟩, + ⟨7, 3, 6, 6, 7, 3, -7863509694770013132268910084524977951237734400000⟩, + ⟨7, 3, 7, 6, 8, 3, -958519005987816157961858027745127431772569600000⟩, + ⟨7, 3, 0, 7, 0, 3, 433955720462217629694369169231208389253121913651200000⟩, + ⟨7, 3, 1, 7, 1, 3, 147817357815366658359286328383725763857226294886400000⟩, + ⟨7, 3, 2, 7, 2, 3, 3924352161038478464326019562380185375042279833600000⟩, + ⟨7, 3, 3, 7, 3, 3, 2191968612440699293024073324413825088211187138560000⟩, + ⟨7, 3, 4, 7, 4, 3, 468959059211434117844301111151485947126784983040000⟩, + ⟨7, 3, 5, 7, 5, 3, 17305262899008986996580689554119949682108006400000⟩, + ⟨7, 3, 6, 7, 6, 3, 8510832608469392724955946175729188707762176000000⟩, + ⟨7, 3, 7, 7, 7, 3, 338771903343400525007071428816960238701772800000⟩, + ⟨7, 3, 8, 7, 8, 3, 909007271266270124107574227424322785378304000000⟩ +] + +def collectedFourData_8_7_39 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 7, 4, -10464959596063339414794696046387769200627364659200000⟩, + ⟨7, 4, 1, 0, 8, 4, -301041897050445101702654557911439566775202611200000⟩, + ⟨7, 4, 0, 1, 6, 4, -1316612715177994900477661131928842924673571225600000⟩, + ⟨7, 4, 1, 1, 7, 4, -3156934468521482040737315469708539935977583411200000⟩, + ⟨7, 4, 2, 1, 8, 4, 347193652516995866068705360404828815276365578240000⟩, + ⟨7, 4, 0, 2, 5, 4, 6367729618625059261505878651477662741349112217600000⟩, + ⟨7, 4, 1, 2, 6, 4, -3743537360319969351925786209580425971470486732800000⟩, + ⟨7, 4, 2, 2, 7, 4, 422028873622962346030281549883105662482440519680000⟩, + ⟨7, 4, 3, 2, 8, 4, 29588223352613433582008551307869942530755788800000⟩, + ⟨7, 4, 0, 3, 4, 4, -4043875443464483111856704137161602545623446323200000⟩, + ⟨7, 4, 1, 3, 5, 4, -3092739376454069442378410309423408895497129164800000⟩, + ⟨7, 4, 2, 3, 6, 4, 167652188475710272412139810976463299718361907200000⟩, + ⟨7, 4, 3, 3, 7, 4, 73878522029534021295575604393386481135585853440000⟩, + ⟨7, 4, 4, 3, 8, 4, 6131078720049911482300638262080539607391272960000⟩, + ⟨7, 4, 0, 4, 3, 4, -15519373351347632245372599395170544506540287590400000⟩, + ⟨7, 4, 1, 4, 4, 4, 3483396933430745821440398617625090408058558873600000⟩, + ⟨7, 4, 2, 4, 5, 4, 77860900466038877509020047996091485903357214720000⟩, + ⟨7, 4, 3, 4, 6, 4, 169699892334889241147722444240882286730789519360000⟩, + ⟨7, 4, 4, 4, 7, 4, 13971413978963694006567717625965117425068277760000⟩, + ⟨7, 4, 5, 4, 8, 4, -7588209999581666202328910509314002778272563200000⟩, + ⟨7, 4, 0, 5, 2, 4, 26192173679685747999676469044461633280966184140800000⟩, + ⟨7, 4, 1, 5, 3, 4, 6652400429422993152780325070512687049176881561600000⟩, + ⟨7, 4, 2, 5, 4, 4, -412836660190389598226817306159771066063220899840000⟩, + ⟨7, 4, 3, 5, 5, 4, 55772205006705062689004051902483302209153925120000⟩, + ⟨7, 4, 4, 5, 6, 4, -12815681736464407815690474968043003972346183680000⟩, + ⟨7, 4, 5, 5, 7, 4, 258139058087252809280167456869866990783692800000⟩, + ⟨7, 4, 6, 5, 8, 4, -1187602996388230686992168054751720008948121600000⟩, + ⟨7, 4, 0, 6, 1, 4, -19038156796311800363828111149082349866154196992000000⟩, + ⟨7, 4, 1, 6, 2, 4, -16577240135644312689154541463244735199100429926400000⟩, + ⟨7, 4, 2, 6, 3, 4, -208310052790881923903715337616635374051577036800000⟩, + ⟨7, 4, 3, 6, 4, 4, -263133799109513925693774834954377087180215418880000⟩, + ⟨7, 4, 4, 6, 5, 4, 20794515654564722269112580612899179718969917440000⟩, + ⟨7, 4, 5, 6, 6, 4, -2455363093292326449647502668118762418549555200000⟩, + ⟨7, 4, 6, 6, 7, 4, -1121568404349616423274999244324915680536166400000⟩, + ⟨7, 4, 7, 6, 8, 4, -123041772240655939093166643754366406586531840000⟩, + ⟨7, 4, 0, 7, 0, 4, 185684653742173313382555973730022689687933131161600000⟩, + ⟨7, 4, 1, 7, 1, 4, 47437008447188457577245791309083370487384794726400000⟩, + ⟨7, 4, 2, 7, 2, 4, 1007511049388122582141556351642276537564009594880000⟩, + ⟨7, 4, 3, 7, 3, 4, 468959059211434117844301111151485947126784983040000⟩, + ⟨7, 4, 4, 7, 4, 4, 85998076784866009367948405582336897162548346880000⟩, + ⟨7, 4, 5, 7, 5, 4, 2776770991085077254984250140100309531439923200000⟩, + ⟨7, 4, 6, 7, 6, 4, 1213895743616410791093936986903332264083456000000⟩, + ⟨7, 4, 7, 7, 7, 4, 43486978466071265483527208170096665160581120000⟩, + ⟨7, 4, 8, 7, 8, 4, 106078292693348718095209313984488465760256000000⟩ +] + +def collectedFourData_8_7_40 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 7, 5, -675801071736057061823385841922095458734309376000000⟩, + ⟨7, 5, 1, 0, 8, 5, -15552429786020567277836169236167616824659148800000⟩, + ⟨7, 5, 0, 1, 6, 5, -85023575658459107207298168378358469983469568000000⟩, + ⟨7, 5, 1, 1, 7, 5, -163093583125146310886266439704581932202118348800000⟩, + ⟨7, 5, 2, 1, 8, 5, 14947268569114875913836120958720231850429644800000⟩, + ⟨7, 5, 0, 2, 5, 5, 411212146715889051312644662348531323610595328000000⟩, + ⟨7, 5, 1, 2, 6, 5, -193398668152709271322310781259092976957862707200000⟩, + ⟨7, 5, 2, 2, 7, 5, 18169050246834971844483276333715809982060953600000⟩, + ⟨7, 5, 3, 2, 8, 5, 1091847942318390419692537873407337832644608000000⟩, + ⟨7, 5, 0, 3, 4, 5, -261143421871256314330788032119568993454391296000000⟩, + ⟨7, 5, 1, 3, 5, 5, -159777135574929532259599882009789872508973875200000⟩, + ⟨7, 5, 2, 3, 6, 5, 7217707665964993931795366019908276840300544000000⟩, + ⟨7, 5, 3, 3, 7, 5, 2726223582205918211848483367725596190074470400000⟩, + ⟨7, 5, 4, 3, 8, 5, 197964910034937184987235605279471938463334400000⟩, + ⟨7, 5, 0, 4, 3, 5, -1002202545288188668544738030381149331140902912000000⟩, + ⟨7, 5, 1, 4, 4, 5, 179959290566598342154144101063977256643618406400000⟩, + ⟨7, 5, 2, 4, 5, 5, 3352042244614578161879396649108940840658534400000⟩, + ⟨7, 5, 3, 4, 6, 5, 6262169784558404311090958304719926887815577600000⟩, + ⟨7, 5, 4, 4, 7, 5, 451119588851714401836872536268749905749606400000⟩, + ⟨7, 5, 5, 4, 8, 5, -217790104552747543410615974880571111243776000000⟩, + ⟨7, 5, 0, 5, 2, 5, 1691425454761157583792868485530117004406554624000000⟩, + ⟨7, 5, 1, 5, 3, 5, 343676383921263229120481835550391552272918118400000⟩, + ⟨7, 5, 2, 5, 4, 5, -17773310054221386402695096811442934609923276800000⟩, + ⟨7, 5, 3, 5, 5, 5, 2058074476099008956112984779049047466128179200000⟩, + ⟨7, 5, 4, 5, 6, 5, -413802431487115298735835685709390109946675200000⟩, + ⟨7, 5, 5, 5, 7, 5, 7408879360622590210721016950415691874304000000⟩, + ⟨7, 5, 6, 5, 8, 5, -30676979510098869085932656975605283369779200000⟩, + ⟨7, 5, 0, 6, 1, 5, -1229436831429954952346821906860428664514805760000000⟩, + ⟨7, 5, 1, 6, 2, 5, -856413561639257038217197398220819176015632793600000⟩, + ⟨7, 5, 2, 6, 3, 5, -8968096859315103249244340764408382893326336000000⟩, + ⟨7, 5, 3, 6, 4, 5, -9710015153267626440284307837622532178758860800000⟩, + ⟨7, 5, 4, 6, 5, 5, 671429059834757129604639217932786101492121600000⟩, + ⟨7, 5, 5, 6, 6, 5, -70471663914490252202120696321241394446336000000⟩, + ⟨7, 5, 6, 6, 7, 5, -28971239601150300636953216360037185539276800000⟩, + ⟨7, 5, 7, 6, 8, 5, -2889356993871547124251456244537111661772800000⟩, + ⟨7, 5, 0, 7, 0, 5, 11991053271825730746347102131321503800673435648000000⟩, + ⟨7, 5, 1, 7, 1, 5, 2450691250494404293297450789357344126794307993600000⟩, + ⟨7, 5, 2, 7, 2, 5, 43375039066469781591884006429350551289960857600000⟩, + ⟨7, 5, 3, 7, 3, 5, 17305262899008986996580689554119949682108006400000⟩, + ⟨7, 5, 4, 7, 4, 5, 2776770991085077254984250140100309531439923200000⟩, + ⟨7, 5, 5, 7, 5, 5, 79696429658746279060168659291812004888576000000⟩, + ⟨7, 5, 6, 7, 6, 5, 31356147607885830201697428225246124572672000000⟩, + ⟨7, 5, 7, 7, 7, 5, 1021193071955499774977166167875613255270400000⟩, + ⟨7, 5, 8, 7, 8, 5, 2283424133399215800256720313491453378560000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0833.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0833.lean new file mode 100644 index 0000000000000000000000000000000000000000..2cb94f99b6328a8bca5dcb79cee42a401195a65c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0833.lean @@ -0,0 +1,219 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse0811 +import OAI.Analysis.LaughlinFock.Sparse0830 +import OAI.Analysis.LaughlinFock.Sparse0831 +import OAI.Analysis.LaughlinFock.Sparse0832 + +namespace OAI + +/-! Sparse0833. -/ +namespace LaughlinFock +def collectedFourData_8_7_41 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 7, 6, -531780865207120205074642179120250010462060544000000⟩, + ⟨7, 6, 1, 0, 8, 6, -10198371623419026906794938152598951434387456000000⟩, + ⟨7, 6, 0, 1, 6, 6, -66904171238599799908828072405229915175124992000000⟩, + ⟨7, 6, 1, 1, 7, 6, -106947209727979978892822914344442665375891456000000⟩, + ⟨7, 6, 2, 1, 8, 6, 8401322037973454964683093586455958449553408000000⟩, + ⟨7, 6, 0, 2, 5, 6, 323578580013940869049024746403974646629138432000000⟩, + ⟨7, 6, 1, 2, 6, 6, -126819507718883134578161918176292082510987264000000⟩, + ⟨7, 6, 2, 2, 7, 6, 10212169637681216023269265090110240646496256000000⟩, + ⟨7, 6, 3, 2, 8, 6, 536977399604008175364171328027720647966720000000⟩, + ⟨7, 6, 0, 3, 4, 6, -205491054444617088802915636144838954685825024000000⟩, + ⟨7, 6, 1, 3, 5, 6, -104772477866011384046227292979826338167783424000000⟩, + ⟨7, 6, 2, 3, 6, 6, 4056813871867991425399445693992897074954240000000⟩, + ⟨7, 6, 3, 3, 7, 6, 1340773191185965193927982324398328366759936000000⟩, + ⟨7, 6, 4, 3, 8, 6, 86542520952694991911132459463838586109952000000⟩, + ⟨7, 6, 0, 4, 3, 6, -788622804750866777771792543229509062128304128000000⟩, + ⟨7, 6, 1, 4, 4, 6, 118006751841097097076271691509327254748397568000000⟩, + ⟨7, 6, 2, 4, 5, 6, 1884062379135139286475775440591053572276224000000⟩, + ⟨7, 6, 3, 4, 6, 6, 3079772847903022274827213464129832048656384000000⟩, + ⟨7, 6, 4, 4, 7, 6, 197211851653308744284055783217925783027712000000⟩, + ⟨7, 6, 5, 4, 8, 6, -85688388992258766494077185579805229187072000000⟩, + ⟨7, 6, 0, 5, 2, 6, 1330965175085626372448450881955462402807955456000000⟩, + ⟨7, 6, 1, 5, 3, 6, 225362823021539596132765868676825033901867008000000⟩, + ⟨7, 6, 2, 5, 4, 6, -9989738309432642606550896181100400898736128000000⟩, + ⟨7, 6, 3, 5, 5, 6, 1012173433253365037334305921538503032700928000000⟩, + ⟨7, 6, 4, 5, 6, 6, -180898249042871961555704260053667588079616000000⟩, + ⟨7, 6, 5, 5, 7, 6, 2914985223747792532902348049592969330688000000⟩, + ⟨7, 6, 6, 5, 8, 6, -10972453411955374016864696535289203523584000000⟩, + ⟨7, 6, 0, 6, 1, 6, -967431111430182002073632315037677451151933440000000⟩, + ⟨7, 6, 1, 6, 2, 6, -561585802675262460483790812356070281872146432000000⟩, + ⟨7, 6, 2, 6, 3, 6, -5040644679291134198286524419468624983490560000000⟩, + ⟨7, 6, 3, 6, 4, 6, -4775443983569563130746105072268534372892672000000⟩, + ⟨7, 6, 4, 6, 5, 6, 293522541286447769906682811492353366294528000000⟩, + ⟨7, 6, 5, 6, 6, 6, -27726711288547317603973947124295393083392000000⟩, + ⟨7, 6, 6, 6, 7, 6, -10362349288839543554417259484992069697536000000⟩, + ⟨7, 6, 7, 6, 8, 6, -947335457598828512715352074658322055168000000⟩, + ⟨7, 6, 0, 7, 0, 6, 9435635648306024046746341266833761246497472512000000⟩, + ⟨7, 6, 1, 7, 1, 6, 1607019639417928507331831227354813107831570432000000⟩, + ⟨7, 6, 2, 7, 2, 6, 24379549341881602207497522823667114726916096000000⟩, + ⟨7, 6, 3, 7, 3, 6, 8510832608469392724955946175729188707762176000000⟩, + ⟨7, 6, 4, 7, 4, 6, 1213895743616410791093936986903332264083456000000⟩, + ⟨7, 6, 5, 7, 5, 6, 31356147607885830201697428225246124572672000000⟩, + ⟨7, 6, 6, 7, 6, 6, 11215376295200790541781494458414991933440000000⟩, + ⟨7, 6, 7, 7, 7, 6, 334819272305097959054535891252752154624000000⟩, + ⟨7, 6, 8, 7, 8, 6, 691078001909702536200863613270255206400000000⟩ +] + +def collectedFourData_8_7_42 : List CollectedFourTerm := [ + ⟨7, 7, 0, 0, 7, 7, -31751138370740811381881486475452438549417164800000⟩, + ⟨7, 7, 1, 0, 8, 7, -521928050374598201596641907109815995963801600000⟩, + ⟨7, 7, 0, 1, 6, 7, -3994659713356074149969075720820134695560806400000⟩, + ⟨7, 7, 1, 1, 7, 7, -5473300123536240863236747087887570810018201600000⟩, + ⟨7, 7, 2, 1, 8, 7, 376214465361997185159295696096949976642355200000⟩, + ⟨7, 7, 0, 2, 5, 7, 19319966061262675227205024561872219222206054400000⟩, + ⟨7, 7, 1, 2, 6, 7, -6490316381606068183737119073241821568460390400000⟩, + ⟨7, 7, 2, 2, 7, 7, 457304924517928396702821707339593329043046400000⟩, + ⟨7, 7, 3, 2, 8, 7, 21374272540058243958955495350724687036416000000⟩, + ⟨7, 7, 0, 3, 4, 7, -12269292354246805122863935629455190624357580800000⟩, + ⟨7, 7, 1, 3, 5, 7, -5362002594605415407800188519528776635672166400000⟩, + ⟨7, 7, 2, 3, 6, 7, 181665701538338348544310642643434739859456000000⟩, + ⟨7, 7, 3, 3, 7, 7, 53369195098241011191503949455533477252300800000⟩, + ⟨7, 7, 4, 3, 8, 7, 3100326172869933117179425919825645446103040000⟩, + ⟨7, 7, 0, 4, 3, 7, -47086447509189580418429023972078357816383897600000⟩, + ⟨7, 7, 1, 4, 4, 7, 6039300801515046459447139570918075887570124800000⟩, + ⟨7, 7, 2, 4, 5, 7, 84369045427754670075646159463749984557465600000⟩, + ⟨7, 7, 3, 4, 6, 7, 122589710965666463955589699313501109170995200000⟩, + ⟨7, 7, 4, 4, 7, 7, 7064978678112514941292178990747426739978240000⟩, + ⟨7, 7, 5, 4, 8, 7, -2790661349097485426863951795743013365350400000⟩, + ⟨7, 7, 0, 5, 2, 7, 79468183617929778673906029473177207512970035200000⟩, + ⟨7, 7, 1, 5, 3, 7, 11533525467579925638570975758772262717410508800000⟩, + ⟨7, 7, 2, 5, 4, 7, -447344363208820255935598731814656837628723200000⟩, + ⟨7, 7, 3, 5, 5, 7, 40289350792264496981837167307310611457638400000⟩, + ⟨7, 7, 4, 5, 6, 7, -6480555107015220667029104960540539952824320000⟩, + ⟨7, 7, 5, 5, 7, 7, 94933942541948780730790075468990749081600000⟩, + ⟨7, 7, 6, 5, 8, 7, -327567151568918016476554859374954571366400000⟩, + ⟨7, 7, 0, 6, 1, 7, -57762588112709700874834486981620460576309248000000⟩, + ⟨7, 7, 1, 6, 2, 7, -28740606239066295655727515734713553057428275200000⟩, + ⟨7, 7, 2, 6, 3, 7, -225722027381864970253601341777059369713664000000⟩, + ⟨7, 7, 3, 6, 4, 7, -190085544158598828622832414811620084652441600000⟩, + ⟨7, 7, 4, 6, 5, 7, 10515242762284371091786625948435291370946560000⟩, + ⟨7, 7, 5, 6, 6, 7, -902991203831877404571019257741358556774400000⟩, + ⟨7, 7, 6, 6, 7, 7, -309353351768068348136865941477303884185600000⟩, + ⟨7, 7, 7, 6, 8, 7, -26105876859936268367287800505950221107200000⟩, + ⟨7, 7, 0, 7, 0, 7, 563375240981212922075218809974190813332530790400000⟩, + ⟨7, 7, 1, 7, 1, 7, 82243387305972369893153251294739562323194675200000⟩, + ⟨7, 7, 2, 7, 2, 7, 1091725692690486197277067466390369271703142400000⟩, + ⟨7, 7, 3, 7, 3, 7, 338771903343400525007071428816960238701772800000⟩, + ⟨7, 7, 4, 7, 4, 7, 43486978466071265483527208170096665160581120000⟩, + ⟨7, 7, 5, 7, 5, 7, 1021193071955499774977166167875613255270400000⟩, + ⟨7, 7, 6, 7, 6, 7, 334819272305097959054535891252752154624000000⟩, + ⟨7, 7, 7, 7, 7, 7, 9226668993563453858663145268313692569600000⟩, + ⟨7, 7, 8, 7, 8, 7, 17683852261532942848468738532463083520000000⟩ +] + +def collectedFourData_8_7_43 : List CollectedFourTerm := [ + ⟨7, 8, 0, 0, 7, 8, -121708590711417473777686720746234693833195520000000⟩, + ⟨7, 8, 1, 0, 8, 8, -1750574605604981705051192070272368099983360000000⟩, + ⟨7, 8, 0, 1, 6, 8, -15312345604977410285462812594811409121935360000000⟩, + ⟨7, 8, 1, 1, 7, 8, -18357741451605016362297479862089061614223360000000⟩, + ⟨7, 8, 2, 1, 8, 8, 1121638618113542640907789611199622063063040000000⟩, + ⟨7, 8, 0, 2, 5, 8, 74057371249263738658561755818331449390530560000000⟩, + ⟨7, 8, 1, 2, 6, 8, -21768868394459764704839664712616186310819840000000⟩, + ⟨7, 8, 2, 2, 7, 8, 1363400163519124950421470290407039728353280000000⟩, + ⟨7, 8, 3, 2, 8, 8, 57352362947422712259557503332026029178880000000⟩, + ⟨7, 8, 0, 3, 4, 8, -47030700569710227272295231922906679130193920000000⟩, + ⟨7, 8, 1, 3, 5, 8, -17984443584833816570979501246484946815549440000000⟩, + ⟨7, 8, 2, 3, 6, 8, 541614651196428940122042074051233657651200000000⟩, + ⟨7, 8, 3, 3, 7, 8, 143202508611682132464858302831227614265344000000⟩, + ⟨7, 8, 4, 3, 8, 8, 7562661716475380382594513979118349975552000000⟩, + ⟨7, 8, 0, 4, 3, 8, -180491959092454010616253992085977034905354240000000⟩, + ⟨7, 8, 1, 4, 4, 8, 20256138008206570779925246614973632825262080000000⟩, + ⟨7, 8, 2, 4, 5, 8, 251536259867334003699082183918029499269120000000⟩, + ⟨7, 8, 3, 4, 6, 8, 328937959584162316535660095064370824871936000000⟩, + ⟨7, 8, 4, 4, 7, 8, 17233684714926892243603516911854196621312000000⟩, + ⟨7, 8, 5, 4, 8, 8, -6240018315509385199030392147870807490560000000⟩, + ⟨7, 8, 0, 5, 2, 8, 304617759577629978788183458767196303896084480000000⟩, + ⟨7, 8, 1, 5, 3, 8, 38684061494975716800096877450982433730068480000000⟩, + ⟨7, 8, 2, 5, 4, 8, -1333703936364134183070991544902146997616640000000⟩, + ⟨7, 8, 3, 5, 5, 8, 108106110522519317776515187993940708032512000000⟩, + ⟨7, 8, 4, 5, 6, 8, -15808093496164260062327641638423459004416000000⟩, + ⟨7, 8, 5, 5, 7, 8, 212275681682715779544357621838632714240000000⟩, + ⟨7, 8, 6, 5, 8, 8, -676109385935290341863497625309848535040000000⟩, + ⟨7, 8, 0, 6, 1, 8, -221415783993446341240340432745564319462195200000000⟩, + ⟨7, 8, 1, 6, 2, 8, -96397531030744975845962135463838575671377920000000⟩, + ⟨7, 8, 2, 6, 3, 8, -672963339213369757293137936001702612172800000000⟩, + ⟨7, 8, 3, 6, 4, 8, -510045668184064436986125136441651796901888000000⟩, + ⟨7, 8, 4, 6, 5, 8, 25649954051176231403678255740265774972928000000⟩, + ⟨7, 8, 5, 6, 6, 8, -2019120540182014292732802157575835484160000000⟩, + ⟨7, 8, 6, 6, 7, 8, -638515503459837405706954760844906332160000000⟩, + ⟨7, 8, 7, 6, 8, 8, -50034575844319803402772608702889328640000000⟩, + ⟨7, 8, 0, 7, 0, 8, 2159532229077959383680009032964704268409896960000000⟩, + ⟨7, 8, 1, 7, 1, 8, 275848721281482965599178918834165937780817920000000⟩, + ⟨7, 8, 2, 7, 2, 8, 3254850118881421736951064417389790080532480000000⟩, + ⟨7, 8, 3, 7, 3, 8, 909007271266270124107574227424322785378304000000⟩, + ⟨7, 8, 4, 7, 4, 8, 106078292693348718095209313984488465760256000000⟩, + ⟨7, 8, 5, 7, 5, 8, 2283424133399215800256720313491453378560000000⟩, + ⟨7, 8, 6, 7, 6, 8, 691078001909702536200863613270255206400000000⟩, + ⟨7, 8, 7, 7, 7, 8, 17683852261532942848468738532463083520000000⟩, + ⟨7, 8, 8, 7, 8, 8, 31633379531748517887443843114493542400000000⟩ +] + +def collectedFourData_8_7 : List (List CollectedFourTerm) := [ + collectedFourData_8_7_0, + collectedFourData_8_7_1, + collectedFourData_8_7_2, + collectedFourData_8_7_3, + collectedFourData_8_7_4, + collectedFourData_8_7_5, + collectedFourData_8_7_6, + collectedFourData_8_7_7, + collectedFourData_8_7_8, + collectedFourData_8_7_9, + collectedFourData_8_7_10, + collectedFourData_8_7_11, + collectedFourData_8_7_12, + collectedFourData_8_7_13, + collectedFourData_8_7_14, + collectedFourData_8_7_15, + collectedFourData_8_7_16, + collectedFourData_8_7_17, + collectedFourData_8_7_18, + collectedFourData_8_7_19, + collectedFourData_8_7_20, + collectedFourData_8_7_21, + collectedFourData_8_7_22, + collectedFourData_8_7_23, + collectedFourData_8_7_24, + collectedFourData_8_7_25, + collectedFourData_8_7_26, + collectedFourData_8_7_27, + collectedFourData_8_7_28, + collectedFourData_8_7_29, + collectedFourData_8_7_30, + collectedFourData_8_7_31, + collectedFourData_8_7_32, + collectedFourData_8_7_33, + collectedFourData_8_7_34, + collectedFourData_8_7_35, + collectedFourData_8_7_36, + collectedFourData_8_7_37, + collectedFourData_8_7_38, + collectedFourData_8_7_39, + collectedFourData_8_7_40, + collectedFourData_8_7_41, + collectedFourData_8_7_42, + collectedFourData_8_7_43 +] + +theorem collectedFourChecked_8_7 : collectNumericRowParts 8 7 = collectedFourData_8_7 := by + decide +kernel + +def collectedFourData_8 : Fin 8 → List (List CollectedFourTerm) := + ![collectedFourData_8_0, collectedFourData_8_1, collectedFourData_8_2, collectedFourData_8_3, collectedFourData_8_4, collectedFourData_8_5, collectedFourData_8_6, collectedFourData_8_7] + +theorem collectedFourChecked_8 (t : Fin 8) : + collectNumericRowParts 8 t = collectedFourData_8 t := by + fin_cases t + · exact collectedFourChecked_8_0 + · exact collectedFourChecked_8_1 + · exact collectedFourChecked_8_2 + · exact collectedFourChecked_8_3 + · exact collectedFourChecked_8_4 + · exact collectedFourChecked_8_5 + · exact collectedFourChecked_8_6 + · exact collectedFourChecked_8_7 + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0901.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0901.lean new file mode 100644 index 0000000000000000000000000000000000000000..6b869f61b71687fe5c32f0b60785e538a207ad50 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0901.lean @@ -0,0 +1,640 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0901. -/ +namespace LaughlinFock + +def collectedFourData_9_0_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_9_0_1 : List CollectedFourTerm := [ + ⟨0, 1, 8, 0, 8, 1, 9370486522373024539551647613122608605482188800000000⟩, + ⟨0, 1, 8, 1, 7, 1, 7830116966278998007712598742737380941234176000000000⟩, + ⟨0, 1, 8, 2, 6, 1, 426087722197497709061253699092621222215680000000000⟩, + ⟨0, 1, 8, 3, 5, 1, 6779383075331177603552916386291899648966656000000000⟩, + ⟨0, 1, 8, 4, 4, 1, -9699224512111815194597955140743338248896512000000000⟩, + ⟨0, 1, 8, 5, 3, 1, 13567606733560486062928640524791381240053760000000000⟩, + ⟨0, 1, 8, 6, 2, 1, -48384074145692090436824756909183027683472179200000000⟩, + ⟨0, 1, 8, 7, 1, 1, 90467596273956427279293957043366031435759616000000000⟩ +] + +def collectedFourData_9_0_2 : List CollectedFourTerm := [ + ⟨0, 2, 7, 0, 7, 2, 39358572524714214670101390748769016044165529600000⟩, + ⟨0, 2, 8, 0, 8, 2, -5307104128847786389487343432349438002920108851200000⟩, + ⟨0, 2, 7, 1, 6, 2, 2724175331112928451326049556653957318955132518400000⟩, + ⟨0, 2, 8, 1, 7, 2, -4434694610774247672868520275806132377562906624000000⟩, + ⟨0, 2, 7, 2, 5, 2, -276286032342252992501874756951121442012921856000000⟩, + ⟨0, 2, 8, 2, 6, 2, -241320651209157159901267471087321464774328320000000⟩, + ⟨0, 2, 7, 3, 4, 2, 1110088527956477957063602802924003795855317401600000⟩, + ⟨0, 2, 8, 3, 5, 2, -3839596996829086568264890875997395063505158144000000⟩, + ⟨0, 2, 7, 4, 3, 2, -3937249714706187001467801211853021428745188147200000⟩, + ⟨0, 2, 8, 4, 4, 2, 5493289417998603593850991673925282282589913088000000⟩, + ⟨0, 2, 7, 5, 2, 2, 7647729485233453730019146678098739892602064076800000⟩, + ⟨0, 2, 8, 5, 3, 2, -7684200979569531098105583043255061547570954240000000⟩, + ⟨0, 2, 7, 6, 1, 2, -21011889113633343993508145616811513568894228889600000⟩, + ⟨0, 2, 8, 6, 2, 2, 27402986926665144561661120111883052421816831180800000⟩, + ⟨0, 2, 7, 7, 0, 2, 71223207420053882809865495579060421231768502272000000⟩, + ⟨0, 2, 8, 7, 1, 2, -51237569422474422526596408340143451228480733184000000⟩ +] + +def collectedFourData_9_0_3 : List CollectedFourTerm := [ + ⟨0, 3, 6, 0, 6, 3, -3936929951861267302893079633416545652355104768000000⟩, + ⟨0, 3, 7, 0, 7, 3, 72164520751697383330746241114596830437441536000000⟩, + ⟨0, 3, 8, 0, 8, 3, -4865326680701764380866420656747111304078032896000000⟩, + ⟨0, 3, 6, 1, 5, 3, 2475697638437920653253238032359257840365338624000000⟩, + ⟨0, 3, 7, 1, 6, 3, 4994815477363109997725360107485417067348230144000000⟩, + ⟨0, 3, 8, 1, 7, 3, -4065538848820108335291934914934747600697425920000000⟩, + ⟨0, 3, 6, 2, 4, 3, -888562635919743326007141737395121919721734144000000⟩, + ⟨0, 3, 7, 2, 5, 3, -506574497889806841894974268430666446101544960000000⟩, + ⟨0, 3, 8, 2, 6, 3, -221232479036951532586674523523596183771545600000000⟩, + ⟨0, 3, 6, 3, 3, 3, -1348920256380525979051392829720436021101854720000000⟩, + ⟨0, 3, 7, 3, 4, 3, 2035363618983743401292342175024822576067117056000000⟩, + ⟨0, 3, 8, 3, 5, 3, -3519978741376361519477892934096243018715627520000000⟩, + ⟨0, 3, 6, 4, 2, 3, 4101654758182212021353552216048103220083425280000000⟩, + ⟨0, 3, 7, 4, 3, 3, -7219005175127151536120010153823066278070321152000000⟩, + ⟨0, 3, 8, 4, 4, 3, 5036013411707419486970294565128491165066199040000000⟩, + ⟨0, 3, 6, 5, 1, 3, -6338256386959322028672286514042406585929564160000000⟩, + ⟨0, 3, 7, 5, 2, 3, 14022224327214846439497205903568886381504626688000000⟩, + ⟨0, 3, 8, 5, 3, 3, -7044547673853743815519049210623957830677299200000000⟩, + ⟨0, 3, 6, 6, 0, 3, 9296983689654819123302832285820571905695940608000000⟩, + ⟨0, 3, 7, 6, 1, 3, -38525607274527745191004517029859350772906459136000000⟩, + ⟨0, 3, 8, 6, 2, 3, 25121889487812132754598977030149518056608497664000000⟩, + ⟨0, 3, 7, 7, 0, 3, 130588796802514265970903813995455142486888939520000000⟩, + ⟨0, 3, 8, 7, 1, 3, -46972418010497178631671245445560367701525790720000000⟩ +] + +def collectedFourData_9_0_4 : List CollectedFourTerm := [ + ⟨0, 4, 5, 0, 5, 4, -41386465803418885017704581618487431848604257484800000⟩, + ⟨0, 4, 6, 0, 6, 4, -47838980931703452830730512304231251696252721561600000⟩, + ⟨0, 4, 7, 0, 7, 4, 438447873647565390509023333976938664471140761600000⟩, + ⟨0, 4, 8, 0, 8, 4, -19706748926242318795645801891123533252173129318400000⟩, + ⟨0, 4, 5, 1, 4, 4, -22147889437967218631966648955209455956494647296000000⟩, + ⟨0, 4, 6, 1, 5, 4, 30083047848464350232685753945910838380995595468800000⟩, + ⟨0, 4, 7, 1, 6, 4, 30346854693970854327176428330271902834167801446400000⟩, + ⟨0, 4, 8, 1, 7, 4, -16467250526335874513369564757870301442702573568000000⟩, + ⟨0, 4, 5, 2, 3, 4, -32676793188010820192573666412633084684886710681600000⟩, + ⟨0, 4, 6, 2, 4, 4, -10797228174276311611318570218432419743067327692800000⟩, + ⟨0, 4, 7, 2, 5, 4, -3077779899738955010798726911981780373524709376000000⟩, + ⟨0, 4, 8, 2, 6, 4, -896090479598078404136889721707503693321994240000000⟩, + ⟨0, 4, 5, 3, 2, 4, 88774160961339987875043982067967014349658128384000000⟩, + ⟨0, 4, 6, 3, 3, 4, -16391190905712743879552330490031987323530379264000000⟩, + ⟨0, 4, 7, 3, 4, 4, 12366199367049015869188959245015726417514174873600000⟩, + ⟨0, 4, 8, 3, 5, 4, -14257488106021485864878309805395330997008990208000000⟩, + ⟨0, 4, 5, 4, 1, 4, -24606262538724253486161346685878148456138145792000000⟩, + ⟨0, 4, 6, 4, 2, 4, 49840608332983644557041530116427295432938356736000000⟩, + ⟨0, 4, 7, 4, 3, 4, -43860299159692296026273691026526701194084299571200000⟩, + ⟨0, 4, 8, 4, 4, 4, 20398106521264968976784424795218793789722198016000000⟩, + ⟨0, 4, 5, 5, 0, 4, -281693125538855768379121455467704925744393512550400000⟩, + ⟨0, 4, 6, 5, 1, 4, -77018318878811381784103020861878239306859937792000000⟩, + ⟨0, 4, 7, 5, 2, 4, 85194419307938174320533850020382543566573718732800000⟩, + ⟨0, 4, 8, 5, 3, 4, -28533568538825485088741953483225634120065351680000000⟩, + ⟨0, 4, 6, 6, 0, 4, 112970825208989558059914145191193782674469263769600000⟩, + ⟨0, 4, 7, 6, 1, 4, -234068908302152927615897647854387023915360295321600000⟩, + ⟨0, 4, 8, 6, 2, 4, 101754887426739449216458007233435045205099780505600000⟩, + ⟨0, 4, 7, 7, 0, 4, 793414543377392796505508262542185346537474752512000000⟩, + ⟨0, 4, 8, 7, 1, 4, -190259299928006772952918345572461111167300927488000000⟩ +] + +def collectedFourData_9_0_5 : List CollectedFourTerm := [ + ⟨0, 5, 4, 0, 4, 5, -41386465803418885017704581618487431848604257484800000⟩, + ⟨0, 5, 5, 0, 5, 5, 217683470486240658578067546849306730344757592064000000⟩, + ⟨0, 5, 6, 0, 6, 5, 125811121964393861062914230568165107623834681344000000⟩, + ⟨0, 5, 7, 0, 7, 5, -768712290440210829295798264770702018814672896000000⟩, + ⟨0, 5, 8, 0, 8, 5, 25913263037738334288819870622348517741772668928000000⟩, + ⟨0, 5, 4, 1, 3, 5, 24676320858814373716735470182516118089153642496000000⟩, + ⟨0, 5, 5, 1, 4, 5, 116492900353042042377065971862895856119479009280000000⟩, + ⟨0, 5, 6, 1, 5, 5, -79115021436746896673745749274493070900138606592000000⟩, + ⟨0, 5, 7, 1, 6, 5, -53205869115949204942341158301150653514025795584000000⟩, + ⟨0, 5, 8, 1, 7, 5, 21653505405401413314236082085562966239409602560000000⟩, + ⟨0, 5, 4, 2, 2, 5, -16256573883424082223985572122140628654458562150400000⟩, + ⟨0, 5, 5, 2, 3, 5, 171872558031754686900901530461199048171520524288000000⟩, + ⟨0, 5, 6, 2, 4, 5, 28395491798844560262839008865500113844675018752000000⟩, + ⟨0, 5, 7, 2, 5, 5, 5396142571102903672458849600199897542882754560000000⟩, + ⟨0, 5, 8, 2, 6, 5, 1178308425724983825497982468480471862660300800000000⟩, + ⟨0, 5, 4, 3, 1, 5, 36093318931253215171951014704208489932985571737600000⟩, + ⟨0, 5, 5, 3, 2, 5, -466932053086114057614764352063960892874812293120000000⟩, + ⟨0, 5, 6, 3, 3, 5, 43106982590710859127274673366979960398162165760000000⟩, + ⟨0, 5, 7, 3, 4, 5, -21681139334537446712179899660916815630346223616000000⟩, + ⟨0, 5, 8, 3, 5, 5, 18747792491372077707758559297150748563194511360000000⟩, + ⟨0, 5, 4, 4, 0, 5, -60287722425429081168127310238928620336352277299200000⟩, + ⟨0, 5, 5, 4, 1, 5, 129423388084579729722618086854805497664042434560000000⟩, + ⟨0, 5, 6, 4, 2, 5, -131075176177196839892215298673183219479992074240000000⟩, + ⟨0, 5, 7, 4, 3, 5, 76898425224298352292526700965972955399215644672000000⟩, + ⟨0, 5, 8, 4, 4, 5, -26822359270709736079673656963572400380413214720000000⟩, + ⟨0, 5, 5, 5, 0, 5, 1481642270946190090178591663754775448798701289472000000⟩, + ⟨0, 5, 6, 5, 1, 5, 202549488330199752577997343203736726873078497280000000⟩, + ⟨0, 5, 7, 5, 2, 5, -149367806608571352607114636560086415888579821568000000⟩, + ⟨0, 5, 8, 5, 3, 5, 37520032843535505294591675875343832685582745600000000⟩, + ⟨0, 5, 6, 6, 0, 5, -297100523296625941738100359305719392433879384064000000⟩, + ⟨0, 5, 7, 6, 1, 5, 410383211862536945881735014121353913421839466496000000⟩, + ⟨0, 5, 8, 6, 2, 5, -133801936236843179701286835170705157024122929152000000⟩, + ⟨0, 5, 7, 7, 0, 5, -1391060483049502671482091123033326816047367454720000000⟩, + ⟨0, 5, 8, 7, 1, 5, 250180245501838199030285101723742444377300008960000000⟩ +] + +def collectedFourData_9_0_6 : List CollectedFourTerm := [ + ⟨0, 6, 3, 0, 3, 6, -3936929951861267302893079633416545652355104768000000⟩, + ⟨0, 6, 4, 0, 4, 6, -47838980931703452830730512304231251696252721561600000⟩, + ⟨0, 6, 5, 0, 5, 6, 125811121964393861062914230568165107623834681344000000⟩, + ⟨0, 6, 6, 0, 6, 6, 48475395259558983350098074339444624576863010816000000⟩, + ⟨0, 6, 7, 0, 7, 6, -222140329516234286169615637839980556774801408000000⟩, + ⟨0, 6, 8, 0, 8, 6, 5990673870191510481400700993219270712812057395200000⟩, + ⟨0, 6, 3, 1, 2, 6, 424058316746424901974935338113143683278490828800000⟩, + ⟨0, 6, 4, 1, 3, 6, 28523576974091326379835479701671278065150328832000000⟩, + ⟨0, 6, 5, 1, 4, 6, 67327585606592652642182161746803399127340154880000000⟩, + ⟨0, 6, 6, 1, 5, 6, -30483250409293533781969876414814287737586188288000000⟩, + ⟨0, 6, 7, 1, 6, 6, -15375283372724824201940409193981811153417797632000000⟩, + ⟨0, 6, 8, 1, 7, 6, 5005895584869983986583024465665068140020629504000000⟩, + ⟨0, 6, 3, 2, 1, 6, 3319677050251291000582394187989749464687024537600000⟩, + ⟨0, 6, 4, 2, 2, 6, -18791117166610258140690067417285170214319475916800000⟩, + ⟨0, 6, 5, 2, 3, 6, 99334503040423677687191720069617901701114626048000000⟩, + ⟨0, 6, 6, 2, 4, 6, 10940866491343409192070045596923709579254038528000000⟩, + ⟨0, 6, 7, 2, 5, 6, 1559362200615955542238602989077180644725882880000000⟩, + ⟨0, 6, 8, 2, 6, 6, 272403420855841406995200390526077651092766720000000⟩, + ⟨0, 6, 3, 3, 0, 6, -34244357729838583042072758087788336616522645504000000⟩, + ⟨0, 6, 4, 3, 1, 6, 41720585766264582135687284029334926941475779379200000⟩, + ⟨0, 6, 5, 3, 2, 6, -269865439707858274774444167178194375841173995520000000⟩, + ⟨0, 6, 6, 3, 3, 6, 16609247154818537945748134091793884735225200640000000⟩, + ⟨0, 6, 7, 3, 4, 6, -6265355056705883833114474016818938121675603968000000⟩, + ⟨0, 6, 8, 3, 5, 6, 4334147746591071476359908949047071780502503424000000⟩, + ⟨0, 6, 4, 4, 0, 6, -69687110207117038620850698651215130723338315366400000⟩, + ⟨0, 6, 5, 4, 1, 6, 74800818027124156635891445505186672047565045760000000⟩, + ⟨0, 6, 6, 4, 2, 6, -50503650827501453215791079170335596764054159360000000⟩, + ⟨0, 6, 7, 4, 3, 6, 22221892027799920965974824504982062881419821056000000⟩, + ⟨0, 6, 8, 4, 4, 6, -6200840341331018388173790002485109339505819648000000⟩, + ⟨0, 6, 5, 5, 0, 6, 856321685983938953971878730330998208738111782912000000⟩, + ⟨0, 6, 6, 5, 1, 6, 78042913481104393335376647855025075401963601920000000⟩, + ⟨0, 6, 7, 5, 2, 6, -43163891343722350406759775639102083076628414464000000⟩, + ⟨0, 6, 8, 5, 3, 6, 8673947392775471897359830467311402405110743040000000⟩, + ⟨0, 6, 6, 6, 0, 6, -114473705295321355834057202700164889340224208896000000⟩, + ⟨0, 6, 7, 6, 1, 6, 118591393743515312572272383162749139236272734208000000⟩, + ⟨0, 6, 8, 6, 2, 6, -30932567698160724141168033949332748455815990476800000⟩, + ⟨0, 6, 7, 7, 0, 6, -401984771057414098041499376333008414381241794560000000⟩, + ⟨0, 6, 8, 7, 1, 6, 57837110570879594056846461355716186078669963264000000⟩ +] + +def collectedFourData_9_0_7 : List CollectedFourTerm := [ + ⟨0, 7, 2, 0, 2, 7, 39358572524714214670101390748769016044165529600000⟩, + ⟨0, 7, 3, 0, 3, 7, 72164520751697383330746241114596830437441536000000⟩, + ⟨0, 7, 4, 0, 4, 7, 438447873647565390509023333976938664471140761600000⟩, + ⟨0, 7, 5, 0, 5, 7, -768712290440210829295798264770702018814672896000000⟩, + ⟨0, 7, 6, 0, 6, 7, -222140329516234286169615637839980556774801408000000⟩, + ⟨0, 7, 7, 0, 7, 7, 814373159552120211202414054729842188038963200000⟩, + ⟨0, 7, 8, 0, 8, 7, -18301659504072068983363259721713026668586598400000⟩, + ⟨0, 7, 2, 1, 1, 7, -207518853904527972989969468441240691917035929600000⟩, + ⟨0, 7, 3, 1, 2, 7, -7773053006520858325229943878607814197352857600000⟩, + ⟨0, 7, 4, 1, 3, 7, -261420737430990286894073553941420392769912832000000⟩, + ⟨0, 7, 5, 1, 4, 7, -411374938346871134446461647000964951881809920000000⟩, + ⟨0, 7, 6, 1, 5, 7, 139690646242044797055647470970762467574022144000000⟩, + ⟨0, 7, 7, 1, 6, 7, 56366253379218240235987255121491237161192652800000⟩, + ⟨0, 7, 8, 1, 7, 7, -15293137048086270601773441449297071117959168000000⟩, + ⟨0, 7, 2, 2, 0, 7, 219358873716237029237039152313022712863365529600000⟩, + ⟨0, 7, 3, 2, 1, 7, -60850181819601436601240711923365347731911475200000⟩, + ⟨0, 7, 4, 2, 2, 7, 172222008176233936355328202386364789903117516800000⟩, + ⟨0, 7, 5, 2, 3, 7, -606938815580667976239250876337403874385068032000000⟩, + ⟨0, 7, 6, 2, 4, 7, -50136933893301114586224297282681960885387264000000⟩, + ⟨0, 7, 7, 2, 5, 7, -5716668940607458713447062887154475337777152000000⟩, + ⟨0, 7, 8, 2, 6, 7, -832199309171987799685603281778344449802240000000⟩, + ⟨0, 7, 3, 3, 0, 7, 627704250327126019870408039637328061695787008000000⟩, + ⟨0, 7, 4, 3, 1, 7, -382372319817269890912713690804239522216489779200000⟩, + ⟨0, 7, 5, 3, 2, 7, 1648891425729380361189955091196297365610823680000000⟩, + ⟨0, 7, 6, 3, 3, 7, -76112502357789618240967941721328133152440320000000⟩, + ⟨0, 7, 7, 3, 4, 7, 22968980933615383417923088035822517875847987200000⟩, + ⟨0, 7, 8, 3, 5, 7, -13240930489163024248645301471726702646263808000000⟩, + ⟨0, 7, 4, 4, 0, 7, 638687628705431153318196492597630069937432166400000⟩, + ⟨0, 7, 5, 4, 1, 7, -457036764752049005991194259968223625441443840000000⟩, + ⟨0, 7, 6, 4, 2, 7, 231434887256163815710510874326345956647239680000000⟩, + ⟨0, 7, 7, 4, 3, 7, -81466127565922012142697356793822655432517222400000⟩, + ⟨0, 7, 8, 4, 4, 7, 18943723364885226738638393421833739190665216000000⟩, + ⟨0, 7, 5, 5, 0, 7, -5232168621567765836638002609005504150642884608000000⟩, + ⟨0, 7, 6, 5, 1, 7, -357634598424050390360178996773723925601320960000000⟩, + ⟨0, 7, 7, 5, 2, 7, 158240129780588385119401471407387187835672985600000⟩, + ⟨0, 7, 8, 5, 3, 7, -26499127673884790870984246232433087406407680000000⟩, + ⟨0, 7, 6, 6, 0, 7, 524580077771156026929291985617594182635880448000000⟩, + ⟨0, 7, 7, 6, 1, 7, -434759632476092523020221724560144579840652083200000⟩, + ⟨0, 7, 8, 6, 2, 7, 94499773124905262446066723315465400620784025600000⟩, + ⟨0, 7, 7, 7, 0, 7, 1473688315898251732108166983599525215625805824000000⟩, + ⟨0, 7, 8, 7, 1, 7, -176693828992190978628390942245623218818777088000000⟩ +] + +def collectedFourData_9_0_8 : List CollectedFourTerm := [ + ⟨0, 8, 1, 0, 1, 8, 9370486522373024539551647613122608605482188800000000⟩, + ⟨0, 8, 2, 0, 2, 8, -5307104128847786389487343432349438002920108851200000⟩, + ⟨0, 8, 3, 0, 3, 8, -4865326680701764380866420656747111304078032896000000⟩, + ⟨0, 8, 4, 0, 4, 8, -19706748926242318795645801891123533252173129318400000⟩, + ⟨0, 8, 5, 0, 5, 8, 25913263037738334288819870622348517741772668928000000⟩, + ⟨0, 8, 6, 0, 6, 8, 5990673870191510481400700993219270712812057395200000⟩, + ⟨0, 8, 7, 0, 7, 8, -18301659504072068983363259721713026668586598400000⟩, + ⟨0, 8, 8, 0, 8, 8, 352541867858784186365601735665595316894590566400000⟩, + ⟨0, 8, 1, 1, 0, 8, -11238154651904420327018109773532140601257597337600000⟩, + ⟨0, 8, 2, 1, 1, 8, 27981811730568543391180624264410516232456057651200000⟩, + ⟨0, 8, 3, 1, 2, 8, 524058661918647457791513854777723725979163033600000⟩, + ⟨0, 8, 4, 1, 3, 8, 11749977925099351434367582427651555441422368768000000⟩, + ⟨0, 8, 5, 1, 4, 8, 13867434041429553878752114254770013693605314560000000⟩, + ⟨0, 8, 6, 1, 5, 8, -3767173237632324280897713603602468176829979033600000⟩, + ⟨0, 8, 7, 1, 6, 8, -1266736218853344124509746718618614301063747993600000⟩, + ⟨0, 8, 8, 1, 7, 8, 294589192808068544656678580627550979938582528000000⟩, + ⟨0, 8, 2, 2, 0, 8, -29578318260090271286637620250683132587342508851200000⟩, + ⟨0, 8, 3, 2, 1, 8, 4102514782175654737195516990049307728215749427200000⟩, + ⟨0, 8, 4, 2, 2, 8, -7740796748464604603817118096536215583859094323200000⟩, + ⟨0, 8, 5, 2, 3, 8, 20459885150201701458346687890986739245751730176000000⟩, + ⟨0, 8, 6, 2, 4, 8, 1352091358017760865461876506999192994805553561600000⟩, + ⟨0, 8, 7, 2, 5, 8, 128472466487036881190361148849418969467060224000000⟩, + ⟨0, 8, 8, 2, 6, 8, 16030518916659171303887506326831160665047040000000⟩, + ⟨0, 8, 3, 3, 0, 8, -42319774383517021516369165665982996551290585088000000⟩, + ⟨0, 8, 4, 3, 1, 8, 17186342450005424884255515850909832590467583180800000⟩, + ⟨0, 8, 5, 3, 2, 8, -55584069315618860090854986679555307247752970240000000⟩, + ⟨0, 8, 6, 3, 3, 8, 2052599724069363584915264778389801152605585408000000⟩, + ⟨0, 8, 7, 3, 4, 8, -516189001653422304777558446388323682150147686400000⟩, + ⟨0, 8, 8, 3, 5, 8, 255057874167052681451363420563106959844179968000000⟩, + ⟨0, 8, 4, 4, 0, 8, -28706848630567872601505303896572763567065504153600000⟩, + ⟨0, 8, 5, 4, 1, 8, 15406692530120194899241630438811053386230661120000000⟩, + ⟨0, 8, 6, 4, 2, 8, -6241329229841154301032806378125166043665006592000000⟩, + ⟨0, 8, 7, 4, 3, 8, 1830813442632107987277316297423565372772895948800000⟩, + ⟨0, 8, 8, 4, 4, 8, -364909838791984524438178483633196712157249536000000⟩, + ⟨0, 8, 5, 5, 0, 8, 176376211795499716130290471395059140294915129344000000⟩, + ⟨0, 8, 6, 5, 1, 8, 9644679327347527604119380110719947254450356224000000⟩, + ⟨0, 8, 7, 5, 2, 8, -3556179303253613974434813600412734588879844147200000⟩, + ⟨0, 8, 8, 5, 3, 8, 510448353861089056214280381956687381428961280000000⟩, + ⟨0, 8, 6, 6, 0, 8, -14146860102217641925954638325711149820156261171200000⟩, + ⟨0, 8, 7, 6, 1, 8, 9770487480295841688300085157394112020488808038400000⟩, + ⟨0, 8, 8, 6, 2, 8, -1820333643638868487638107743234888158536112537600000⟩, + ⟨0, 8, 7, 7, 0, 8, -33118652618085271214600989139593876191930482688000000⟩, + ⟨0, 8, 8, 7, 1, 8, 3403624272332670671897448948684766091409358848000000⟩ +] + +def collectedFourData_9_0_9 : List CollectedFourTerm := [ + ⟨1, 0, 8, 0, 8, 1, -11238154651904420327018109773532140601257597337600000⟩, + ⟨1, 0, 8, 1, 7, 1, -9390768045975431972863027115017775611014807552000000⟩, + ⟨1, 0, 8, 2, 6, 1, -511012924024837187211262872674009009734287360000000⟩, + ⟨1, 0, 8, 3, 5, 1, -8130608294795459115992144093903813762730688512000000⟩, + ⟨1, 0, 8, 4, 4, 1, 11632414689504379336522940971734811313568743424000000⟩, + ⟨1, 0, 8, 5, 3, 1, -16271819223465366794669964788898419195793899520000000⟩, + ⟨1, 0, 8, 6, 2, 1, 58027692227105068210413406424038198356967056998400000⟩, + ⟨1, 0, 8, 7, 1, 1, -108499044898610401111217453902847549900882706432000000⟩ +] + +def collectedFourData_9_0_10 : List CollectedFourTerm := [ + ⟨1, 1, 7, 0, 7, 2, -207518853904527972989969468441240691917035929600000⟩, + ⟨1, 1, 8, 0, 8, 2, 27981811730568543391180624264410516232456057651200000⟩, + ⟨1, 1, 7, 1, 6, 2, -14363268438980250527273421885319445205576214118400000⟩, + ⟨1, 1, 8, 1, 7, 2, 23382015251355737095982736573466118645952282624000000⟩, + ⟨1, 1, 7, 2, 5, 2, 1456723582784713797733524614488922207715065856000000⟩, + ⟨1, 1, 8, 2, 6, 2, 1272367917585757525726388663135698067726008320000000⟩, + ⟨1, 1, 7, 3, 4, 2, -5852963770711995779720207169511603282464315801600000⟩, + ⟨1, 1, 8, 3, 5, 2, 20244351284257484867575977112358377099723014144000000⟩, + ⟨1, 1, 7, 4, 3, 2, 20759227175190605943687800373030649529585840947200000⟩, + ⟨1, 1, 8, 4, 4, 2, -28963477358665183262743817889400144522628825088000000⟩, + ⟨1, 1, 7, 5, 2, 2, -40322805324074330634224684931644032778205187276800000⟩, + ⟨1, 1, 8, 5, 3, 2, 40515102000994099445315102287051857441576714240000000⟩, + ⟨1, 1, 7, 6, 1, 2, 110785601903936951192061997429355488520143739289600000⟩, + ⟨1, 1, 8, 6, 2, 2, -144482791824107325027745892586675137061868850380800000⟩, + ⟨1, 1, 7, 7, 0, 2, -375525773093859789401858020445556044566754230272000000⟩, + ⟨1, 1, 8, 7, 1, 2, 270151100544335217009799667402102850397283549184000000⟩ +] + +def collectedFourData_9_0_11 : List CollectedFourTerm := [ + ⟨1, 2, 6, 0, 6, 3, 424058316746424901974935338113143683278490828800000⟩, + ⟨1, 2, 7, 0, 7, 3, -7773053006520858325229943878607814197352857600000⟩, + ⟨1, 2, 8, 0, 8, 3, 524058661918647457791513854777723725979163033600000⟩, + ⟨1, 2, 6, 1, 5, 3, -266664681913568113288041601607576666105079398400000⟩, + ⟨1, 2, 7, 1, 6, 3, -538006281465134450459217191993399048300553830400000⟩, + ⟨1, 2, 8, 1, 7, 3, 437911159705237691916757040468491257325289472000000⟩, + ⟨1, 2, 6, 2, 4, 3, 95709697738907295879776635161406157147760230400000⟩, + ⟨1, 2, 7, 2, 5, 3, 54564630691551293634026068081800825783975936000000⟩, + ⟨1, 2, 8, 2, 6, 3, 23829601699084115448303104277591916239912960000000⟩, + ⟨1, 2, 6, 3, 3, 3, 145296172484716614510834130417908802809495552000000⟩, + ⟨1, 2, 7, 3, 4, 3, -219235008188322729877632564258206911949281689600000⟩, + ⟨1, 2, 8, 3, 5, 3, 379147274222027940998088266409025237294252032000000⟩, + ⟨1, 2, 6, 4, 2, 3, -441801310639881455821180741715174632558952448000000⟩, + ⟨1, 2, 7, 4, 3, 3, 777580302565674404225938048761894328811598643200000⟩, + ⟨1, 2, 8, 4, 4, 3, -542443832273783748898342929013840161710014464000000⟩, + ⟨1, 2, 6, 5, 1, 3, 682712257374692902618892833102086182226886656000000⟩, + ⟨1, 2, 7, 5, 2, 3, -1510375068377400629230886162383073878517533900800000⟩, + ⟨1, 2, 8, 5, 3, 3, 758788971442596416346317440124887744873758720000000⟩, + ⟨1, 2, 6, 6, 0, 3, -1001405486625462073241069661370076356844244172800000⟩, + ⟨1, 2, 7, 6, 1, 3, 4149706591743229964906321552646151397806021017600000⟩, + ⟨1, 2, 8, 6, 2, 3, -2705952683932011080072834145568083568002229862400000⟩, + ⟨1, 2, 7, 7, 0, 3, -14066103800458612417791517456519178996240351232000000⟩, + ⟨1, 2, 8, 7, 1, 3, 5059537446335242715121664667040238130694193152000000⟩ +] + +def collectedFourData_9_0_12 : List CollectedFourTerm := [ + ⟨1, 3, 5, 0, 5, 4, 24676320858814373716735470182516118089153642496000000⟩, + ⟨1, 3, 6, 0, 6, 4, 28523576974091326379835479701671278065150328832000000⟩, + ⟨1, 3, 7, 0, 7, 4, -261420737430990286894073553941420392769912832000000⟩, + ⟨1, 3, 8, 0, 8, 4, 11749977925099351434367582427651555441422368768000000⟩, + ⟨1, 3, 5, 1, 4, 4, 13205486757742841440211723036591235465656401920000000⟩, + ⟨1, 3, 6, 1, 5, 4, -17936756055610044524714608931571990965231026176000000⟩, + ⟨1, 3, 7, 1, 6, 4, -18094048596495050530987065047403844213646819328000000⟩, + ⟨1, 3, 8, 1, 7, 4, 9818455134112363501897687438152479599346319360000000⟩, + ⟨1, 3, 5, 2, 3, 4, 19483254191708822682681122394116802286014431232000000⟩, + ⟨1, 3, 6, 2, 4, 4, 6437753541938409415384449815486694015060934656000000⟩, + ⟨1, 3, 7, 2, 5, 4, 1835099539533380330886652445602337877676523520000000⟩, + ⟨1, 3, 8, 2, 6, 4, 534286167321500913047321855299802224184524800000000⟩, + ⟨1, 3, 5, 3, 2, 4, -52930822608996350238002146177535922075787591680000000⟩, + ⟨1, 3, 6, 3, 3, 4, 9773105245774204887767620293756070881688289280000000⟩, + ⟨1, 3, 7, 3, 4, 4, -7373238991577784823110349134720743542276227072000000⟩, + ⟨1, 3, 8, 3, 5, 4, 8500903479316956295443613140729778845945692160000000⟩, + ⟨1, 3, 5, 4, 1, 4, 14671270371958763292716073137177428806693027840000000⟩, + ⟨1, 3, 6, 4, 2, 4, -29717029931113438794914168936067090094982430720000000⟩, + ⟨1, 3, 7, 4, 3, 4, 26151322516133890016655773351063296214380314624000000⟩, + ⟨1, 3, 8, 4, 4, 4, -12162193887776402348984822583843369666289336320000000⟩, + ⟨1, 3, 5, 5, 0, 4, 167957080040037064961583384087769535911619985408000000⟩, + ⟨1, 3, 6, 5, 1, 4, 45921503848319172681602500462469587287240867840000000⟩, + ⟨1, 3, 7, 5, 2, 4, -50796432732591185136539504471356366137858195456000000⟩, + ⟨1, 3, 8, 5, 3, 4, 17012892472032820101288488510087875677231513600000000⟩, + ⟨1, 3, 6, 6, 0, 4, -67357873556619876605627245761314433536719060992000000⟩, + ⟨1, 3, 7, 6, 1, 4, 139561554054204365395623855298470443000405164032000000⟩, + ⟨1, 3, 8, 6, 2, 4, -60670468046762615069176223132318207271304691712000000⟩, + ⟨1, 3, 7, 7, 0, 4, -473066531929210527135172832114395491204323082240000000⟩, + ⟨1, 3, 8, 7, 1, 4, 113440455478782479884311253062470553279670517760000000⟩ +] + +def collectedFourData_9_0_13 : List CollectedFourTerm := [ + ⟨1, 4, 4, 0, 4, 5, -22147889437967218631966648955209455956494647296000000⟩, + ⟨1, 4, 5, 0, 5, 5, 116492900353042042377065971862895856119479009280000000⟩, + ⟨1, 4, 6, 0, 6, 5, 67327585606592652642182161746803399127340154880000000⟩, + ⟨1, 4, 7, 0, 7, 5, -411374938346871134446461647000964951881809920000000⟩, + ⟨1, 4, 8, 0, 8, 5, 13867434041429553878752114254770013693605314560000000⟩, + ⟨1, 4, 4, 1, 3, 5, 13205486757742841440211723036591235465656401920000000⟩, + ⟨1, 4, 5, 1, 4, 5, 62340956813813538087929867023166625310939545600000000⟩, + ⟨1, 4, 6, 1, 5, 5, -42338255119110147674957216673315322706358435840000000⟩, + ⟨1, 4, 7, 1, 6, 5, -28473020920130166023437757678255938274517319680000000⟩, + ⟨1, 4, 8, 1, 7, 5, 11587832745642141078907801192001150104318771200000000⟩, + ⟨1, 4, 4, 2, 2, 5, -8699674978782043592332118452642604682269687808000000⟩, + ⟨1, 4, 5, 2, 3, 5, 91977276600251470327334197620131305252202741760000000⟩, + ⟨1, 4, 6, 2, 4, 5, 15195794100533260344242871562624309218288599040000000⟩, + ⟨1, 4, 7, 2, 5, 5, 2887735561281544254915354640861201454805811200000000⟩, + ⟨1, 4, 8, 2, 6, 5, 630569540794814749406866766082907482095616000000000⟩, + ⟨1, 4, 4, 3, 1, 5, 19315271831513785614458311359890919635080445952000000⟩, + ⟨1, 4, 5, 3, 2, 5, -249877811164537530160000440465115449626355302400000000⟩, + ⟨1, 4, 6, 3, 3, 5, 23068620765017650915317626285881490507248435200000000⟩, + ⟨1, 4, 7, 3, 4, 5, -11602620990914123915657669058347400083873464320000000⟩, + ⟨1, 4, 8, 3, 5, 5, 10032845937537377763856407018863465917002547200000000⟩, + ⟨1, 4, 4, 4, 0, 5, -32262861416761929980473096610757505464227856384000000⟩, + ⟨1, 4, 5, 4, 1, 5, 69260683035844086482212036132062183682159411200000000⟩, + ⟨1, 4, 6, 4, 2, 5, -70144634331033258793475793925230158890716364800000000⟩, + ⟨1, 4, 7, 4, 3, 5, 41152047819479558034262282884931469295684157440000000⟩, + ⟨1, 4, 8, 4, 4, 5, -14353935182937022346806664359495881671992934400000000⟩, + ⟨1, 4, 5, 5, 0, 5, 792898078309070308282554684256365634288814653440000000⟩, + ⟨1, 4, 6, 5, 1, 5, 108393978228590588159267188274245035397585305600000000⟩, + ⟨1, 4, 7, 5, 2, 5, -79933901147099706266709533449681878579004047360000000⟩, + ⟨1, 4, 8, 5, 3, 5, 20078775101856514235559966061752905065562112000000000⟩, + ⟨1, 4, 6, 6, 0, 5, -158992786994445348775893383210636687990618849280000000⟩, + ⟨1, 4, 7, 6, 1, 5, 219615805000157907252614723323004390387660881920000000⟩, + ⟨1, 4, 8, 6, 2, 5, -71603854855244415894981377428101566550811607040000000⟩, + ⟨1, 4, 7, 7, 0, 5, -744423404657098296086173768568987792445957734400000000⟩, + ⟨1, 4, 8, 7, 1, 5, 133883488463527507931333073106222126789243699200000000⟩ +] + +def collectedFourData_9_0_14 : List CollectedFourTerm := [ + ⟨1, 5, 3, 0, 3, 6, 2475697638437920653253238032359257840365338624000000⟩, + ⟨1, 5, 4, 0, 4, 6, 30083047848464350232685753945910838380995595468800000⟩, + ⟨1, 5, 5, 0, 5, 6, -79115021436746896673745749274493070900138606592000000⟩, + ⟨1, 5, 6, 0, 6, 6, -30483250409293533781969876414814287737586188288000000⟩, + ⟨1, 5, 7, 0, 7, 6, 139690646242044797055647470970762467574022144000000⟩, + ⟨1, 5, 8, 0, 8, 6, -3767173237632324280897713603602468176829979033600000⟩, + ⟨1, 5, 3, 1, 2, 6, -266664681913568113288041601607576666105079398400000⟩, + ⟨1, 5, 4, 1, 3, 6, -17936756055610044524714608931571990965231026176000000⟩, + ⟨1, 5, 5, 1, 4, 6, -42338255119110147674957216673315322706358435840000000⟩, + ⟨1, 5, 6, 1, 5, 6, 19169076405466905659589176253163780252561833984000000⟩, + ⟨1, 5, 7, 1, 6, 6, 9668587757872818839554262421993146868433944576000000⟩, + ⟨1, 5, 8, 1, 7, 6, -3147905609006413531611812451515635426469609472000000⟩, + ⟨1, 5, 3, 2, 1, 6, -2087544542111602767903728078222827714591378636800000⟩, + ⟨1, 5, 4, 2, 2, 6, 11816599472640715037519781207973101506870535782400000⟩, + ⟨1, 5, 5, 2, 3, 6, -62465473757366804041608457947538818167853809664000000⟩, + ⟨1, 5, 6, 2, 4, 6, -6880050614636372621628371177072975398047842304000000⟩, + ⟨1, 5, 7, 2, 5, 6, -980588774689562960263388003419491099570339840000000⟩, + ⟨1, 5, 8, 2, 6, 6, -171298070822008427033494388891210094697512960000000⟩, + ⟨1, 5, 3, 3, 0, 6, 21534209802616328763117935204527574483019497472000000⟩, + ⟨1, 5, 4, 3, 1, 6, -26235558396703646005264038552890449694687861145600000⟩, + ⟨1, 5, 5, 3, 2, 6, 169702087654593611339463530003414987780244111360000000⟩, + ⟨1, 5, 6, 3, 3, 6, -10444553106152143216359059208318227129586155520000000⟩, + ⟨1, 5, 7, 3, 4, 6, 3939903657805399151391549178270236617918644224000000⟩, + ⟨1, 5, 8, 3, 5, 6, -2725483935980038680595937324191648524672172032000000⟩, + ⟨1, 5, 4, 4, 0, 6, 43822017734341013452041821389735190044286858035200000⟩, + ⟨1, 5, 5, 4, 1, 6, -47037719951157918738889822295647678065467719680000000⟩, + ⟨1, 5, 6, 4, 2, 6, 31758697923245309178782697141529544132898324480000000⟩, + ⟨1, 5, 7, 4, 3, 6, -13974006722887553115256454261266394238689476608000000⟩, + ⟨1, 5, 8, 4, 4, 6, 3899334247007897287002559838642361310289854464000000⟩, + ⟨1, 5, 5, 5, 0, 6, -538489026133509007214195980412381043318237167616000000⟩, + ⟨1, 5, 6, 5, 1, 6, -49076478109711010687018448457398430166742466560000000⟩, + ⟨1, 5, 7, 5, 2, 6, 27143166165535594770517332441854611980394954752000000⟩, + ⟨1, 5, 8, 5, 3, 6, -5454522010501271753159063947541225600156958720000000⟩, + ⟨1, 5, 6, 6, 0, 6, 71985604348606995468516942116866132912770121728000000⟩, + ⟨1, 5, 7, 6, 1, 6, -74574970095944558098263302587762491290019692544000000⟩, + ⟨1, 5, 8, 6, 2, 6, 19451624930474807783309733738073682391893173862400000⟩, + ⟨1, 5, 7, 7, 0, 6, 252783961249894668986512279944798293607925678080000000⟩, + ⟨1, 5, 8, 7, 1, 6, -36370268154429498274186950023441331503499313152000000⟩ +] + +def collectedFourData_9_0_15 : List CollectedFourTerm := [ + ⟨1, 6, 2, 0, 2, 7, 2724175331112928451326049556653957318955132518400000⟩, + ⟨1, 6, 3, 0, 3, 7, 4994815477363109997725360107485417067348230144000000⟩, + ⟨1, 6, 4, 0, 4, 7, 30346854693970854327176428330271902834167801446400000⟩, + ⟨1, 6, 5, 0, 5, 7, -53205869115949204942341158301150653514025795584000000⟩, + ⟨1, 6, 6, 0, 6, 7, -15375283372724824201940409193981811153417797632000000⟩, + ⟨1, 6, 7, 0, 7, 7, 56366253379218240235987255121491237161192652800000⟩, + ⟨1, 6, 8, 0, 8, 7, -1266736218853344124509746718618614301063747993600000⟩, + ⟨1, 6, 2, 1, 1, 7, -14363268438980250527273421885319445205576214118400000⟩, + ⟨1, 6, 3, 1, 2, 7, -538006281465134450459217191993399048300553830400000⟩, + ⟨1, 6, 4, 1, 3, 7, -18094048596495050530987065047403844213646819328000000⟩, + ⟨1, 6, 5, 1, 4, 7, -28473020920130166023437757678255938274517319680000000⟩, + ⟨1, 6, 6, 1, 5, 7, 9668587757872818839554262421993146868433944576000000⟩, + ⟨1, 6, 7, 1, 6, 7, 3901349747034353867024068114037047565244117811200000⟩, + ⟨1, 6, 8, 1, 7, 7, -1058503497695850802129338407804999834032668672000000⟩, + ⟨1, 6, 2, 2, 0, 7, 15182766907088891662972856283341563287031932518400000⟩, + ⟨1, 6, 3, 2, 1, 7, -4211701633808130219476472894797105323144170700800000⟩, + ⟨1, 6, 4, 2, 2, 7, 11920222611067172572036317149876163347246953267200000⟩, + ⟨1, 6, 5, 2, 3, 7, -42008834234563244247543595842894315852952240128000000⟩, + ⟨1, 6, 6, 2, 4, 7, -3470191872533169284154745565749597207114285056000000⟩, + ⟨1, 6, 7, 2, 5, 7, -395675135178327860380643482571843140853956608000000⟩, + ⟨1, 6, 8, 2, 6, 7, -57600077522933777600791379409826361596968960000000⟩, + ⟨1, 6, 3, 3, 0, 7, 43446098887406417950183210289574087036116140032000000⟩, + ⟨1, 6, 4, 3, 1, 7, -26465625507443203849197694748438004051064179916800000⟩, + ⟨1, 6, 5, 3, 2, 7, 114126835845864285252414931191623839006819614720000000⟩, + ⟨1, 6, 6, 3, 3, 7, -5268072188902908349728145117412053184969441280000000⟩, + ⟨1, 6, 7, 3, 4, 7, 1589781519664312668835726855632782427463404748800000⟩, + ⟨1, 6, 8, 3, 5, 7, -916461494555203320863635001356225801441247232000000⟩, + ⟨1, 6, 4, 4, 0, 7, 44206305533917036590740282906960929168813562265600000⟩, + ⟨1, 6, 5, 4, 1, 7, -31633471441765279568878944217435537117921935360000000⟩, + ⟨1, 6, 6, 4, 2, 7, 16018599511612272543921516063264348574549278720000000⟩, + ⟨1, 6, 7, 4, 3, 7, -5638619512865452940057448082704298051548846489600000⟩, + ⟨1, 6, 8, 4, 4, 7, 1311176207867885487922852864064607104337444864000000⟩, + ⟨1, 6, 5, 5, 0, 7, -362140793550071401188823304056657004908806930432000000⟩, + ⟨1, 6, 6, 5, 1, 7, -24753421887125486817967189316067751515484323840000000⟩, + ⟨1, 6, 7, 5, 2, 7, 10952476939292075899199761800622992586453706342400000⟩, + ⟨1, 6, 8, 5, 3, 7, -1834118091043065076716831677876233858417950720000000⟩, + ⟨1, 6, 6, 6, 0, 7, 36308433344734500004417291973557794381383073792000000⟩, + ⟨1, 6, 7, 6, 1, 7, -30091575730075189290088049662451876931958525132800000⟩, + ⟨1, 6, 8, 6, 2, 7, 6540733929844287626415481953618827718083110502400000⟩, + ⟨1, 6, 7, 7, 0, 7, 102000278424694316250691412615579679364057399296000000⟩, + ⟨1, 6, 8, 7, 1, 7, -12229736477311637342236419069938152192818020352000000⟩ +] + +def collectedFourData_9_0_16 : List CollectedFourTerm := [ + ⟨1, 7, 1, 0, 1, 8, 7830116966278998007712598742737380941234176000000000⟩, + ⟨1, 7, 2, 0, 2, 8, -4434694610774247672868520275806132377562906624000000⟩, + ⟨1, 7, 3, 0, 3, 8, -4065538848820108335291934914934747600697425920000000⟩, + ⟨1, 7, 4, 0, 4, 8, -16467250526335874513369564757870301442702573568000000⟩, + ⟨1, 7, 5, 0, 5, 8, 21653505405401413314236082085562966239409602560000000⟩, + ⟨1, 7, 6, 0, 6, 8, 5005895584869983986583024465665068140020629504000000⟩, + ⟨1, 7, 7, 0, 7, 8, -15293137048086270601773441449297071117959168000000⟩, + ⟨1, 7, 8, 0, 8, 8, 294589192808068544656678580627550979938582528000000⟩, + ⟨1, 7, 1, 1, 0, 8, -9390768045975431972863027115017775611014807552000000⟩, + ⟨1, 7, 2, 1, 1, 8, 23382015251355737095982736573466118645952282624000000⟩, + ⟨1, 7, 3, 1, 2, 8, 437911159705237691916757040468491257325289472000000⟩, + ⟨1, 7, 4, 1, 3, 8, 9818455134112363501897687438152479599346319360000000⟩, + ⟨1, 7, 5, 1, 4, 8, 11587832745642141078907801192001150104318771200000000⟩, + ⟨1, 7, 6, 1, 5, 8, -3147905609006413531611812451515635426469609472000000⟩, + ⟨1, 7, 7, 1, 6, 8, -1058503497695850802129338407804999834032668672000000⟩, + ⟨1, 7, 8, 1, 7, 8, 246163081413273454895163048609152575796674560000000⟩, + ⟨1, 7, 2, 2, 0, 8, -24716079692272036065830930680056831285210906624000000⟩, + ⟨1, 7, 3, 2, 1, 8, 3428121957555408176485650305809687134961926144000000⟩, + ⟨1, 7, 4, 2, 2, 8, -6468324116144239431911152250307316068661592064000000⟩, + ⟨1, 7, 5, 2, 3, 8, 17096582280995956100125195629795874782597611520000000⟩, + ⟨1, 7, 6, 2, 4, 8, 1129827512914769324432997140084840726142124032000000⟩, + ⟨1, 7, 7, 2, 5, 8, 107353490892712473202217358759312312741396480000000⟩, + ⟨1, 7, 8, 2, 6, 8, 13395338422172121465791666084705626541260800000000⟩, + ⟨1, 7, 3, 3, 0, 8, -35363028655801173797737118029059603629353205760000000⟩, + ⟨1, 7, 4, 3, 1, 8, 14361161641368974563150994524301516449058390016000000⟩, + ⟨1, 7, 5, 3, 2, 8, -46446869451644601351232312418867216556805324800000000⟩, + ⟨1, 7, 6, 3, 3, 8, 1715182652047072479817558157324700876967772160000000⟩, + ⟨1, 7, 7, 3, 4, 8, -431335155330815292106593527070959313698684928000000⟩, + ⟨1, 7, 8, 3, 5, 8, 213130127569163819164507344927298768192143360000000⟩, + ⟨1, 7, 4, 4, 0, 8, -23987866795809522437609426130368681968373071872000000⟩, + ⟨1, 7, 5, 4, 1, 8, 12874059877926976688841622502107114480494182400000000⟩, + ⟨1, 7, 6, 4, 2, 8, -5215346906270999897590065523002842640380067840000000⟩, + ⟨1, 7, 7, 4, 3, 8, 1529854758877017931588358599603330000015589376000000⟩, + ⟨1, 7, 8, 4, 4, 8, -304924052029228022353062491498611584238878720000000⟩, + ⟨1, 7, 5, 5, 0, 8, 147382568144201098590394101146828170689647738880000000⟩, + ⟨1, 7, 6, 5, 1, 8, 8059236524707088949031909647237549392375316480000000⟩, + ⟨1, 7, 7, 5, 2, 8, -2971595960471503734352721085595579649353580544000000⟩, + ⟨1, 7, 8, 5, 3, 8, 426538185230185200614399730293470601517465600000000⟩, + ⟨1, 7, 6, 6, 0, 8, -11821325289937827374388340977703898036016513024000000⟩, + ⟨1, 7, 7, 6, 1, 8, 8164363675847513186709303012511704817197907968000000⟩, + ⟨1, 7, 8, 6, 2, 8, -1521097684022448116259060708471178897026711552000000⟩, + ⟨1, 7, 7, 7, 0, 8, -27674435382411469963891614624663921141491957760000000⟩, + ⟨1, 7, 8, 7, 1, 8, 2844118722971268933866283144055939954334760960000000⟩ +] + +def collectedFourData_9_0_17 : List CollectedFourTerm := [ + ⟨2, 0, 7, 0, 7, 2, 219358873716237029237039152313022712863365529600000⟩, + ⟨2, 0, 8, 0, 8, 2, -29578318260090271286637620250683132587342508851200000⟩, + ⟨2, 0, 7, 1, 6, 2, 15182766907088891662972856283341563287031932518400000⟩, + ⟨2, 0, 8, 1, 7, 2, -24716079692272036065830930680056831285210906624000000⟩, + ⟨2, 0, 7, 2, 5, 2, -1539837168638892769747931930814133679324921856000000⟩, + ⟨2, 0, 8, 2, 6, 2, -1344963062887249844538052762290388713414328320000000⟩, + ⟨2, 0, 7, 3, 4, 2, 6186905509973564113570434308548218279618517401600000⟩, + ⟨2, 0, 8, 3, 5, 2, -21399395829709151351066957494366666986193158144000000⟩, + ⟨2, 0, 7, 4, 3, 2, -21943648043007777210789874529003194229359588147200000⟩, + ⟨2, 0, 8, 4, 4, 2, 30615992970091754999659202418367927401565913088000000⟩, + ⟨2, 0, 7, 5, 2, 2, 42623429122432299131761516359581570050835664076800000⟩, + ⟨2, 0, 8, 5, 3, 2, -42826697315537789319428807733332507200050954240000000⟩, + ⟨2, 0, 7, 6, 1, 2, -117106491291646244182255132571247262208433428889600000⟩, + ⟨2, 0, 8, 6, 2, 2, 152726279514317335831257094454548223896658431180800000⟩, + ⟨2, 0, 7, 7, 0, 2, 396951453264993602044871766249667058959512502272000000⟩, + ⟨2, 0, 8, 7, 1, 2, -285564612726083741074268783644334054525248733184000000⟩ +] + +def collectedFourData_9_0_18 : List CollectedFourTerm := [ + ⟨2, 1, 6, 0, 6, 3, 3319677050251291000582394187989749464687024537600000⟩, + ⟨2, 1, 7, 0, 7, 3, -60850181819601436601240711923365347731911475200000⟩, + ⟨2, 1, 8, 0, 8, 3, 4102514782175654737195516990049307728215749427200000⟩, + ⟨2, 1, 6, 1, 5, 3, -2087544542111602767903728078222827714591378636800000⟩, + ⟨2, 1, 7, 1, 6, 3, -4211701633808130219476472894797105323144170700800000⟩, + ⟨2, 1, 8, 1, 7, 3, 3428121957555408176485650305809687134961926144000000⟩, + ⟨2, 1, 6, 2, 4, 3, 749249040811359270873182002370035092439223500800000⟩, + ⟨2, 1, 7, 2, 5, 3, 427151042931896856536693103967434464896745472000000⟩, + ⟨2, 1, 8, 2, 6, 3, 186546469561124650298786544201472050903121920000000⟩, + ⟨2, 1, 6, 3, 3, 3, 1137429335162150814908120594086764519886946304000000⟩, + ⟨2, 1, 7, 3, 4, 3, -1716248441672768077724073431465299451523052339200000⟩, + ⟨2, 1, 8, 3, 5, 3, 2968097677124051590107467716369721294548107264000000⟩, + ⟨2, 1, 6, 4, 2, 3, -3458575421783708533242504068913541369294749696000000⟩, + ⟨2, 1, 7, 4, 3, 3, 6087170993272322379802582817302518816284501606400000⟩, + ⟨2, 1, 8, 4, 4, 3, -4246440336003201195820950245711651419170275328000000⟩, + ⟨2, 1, 6, 5, 1, 3, 5344510703435290838564041662681343767097638912000000⟩, + ⟨2, 1, 7, 5, 2, 3, -11823745116552892881131418525043359631971817881600000⟩, + ⟨2, 1, 8, 5, 3, 3, 5940065870676042750633822022914410483747389440000000⟩, + ⟨2, 1, 6, 6, 0, 3, -7839352939596129338545144265299298076438665625600000⟩, + ⟨2, 1, 7, 6, 1, 3, 32485356833890328986207051421868731442088063795200000⟩, + ⟨2, 1, 8, 6, 2, 3, -21183145499505674585917268351192008604049525964800000⟩, + ⟨2, 1, 7, 7, 0, 3, -110114387877356941725709279837822597523690225664000000⟩, + ⟨2, 1, 8, 7, 1, 3, 39607831475522475895475966252916729294046101504000000⟩ +] + +def collectedFourData_9_0_19 : List CollectedFourTerm := [ + ⟨2, 2, 5, 0, 5, 4, -16256573883424082223985572122140628654458562150400000⟩, + ⟨2, 2, 6, 0, 6, 4, -18791117166610258140690067417285170214319475916800000⟩, + ⟨2, 2, 7, 0, 7, 4, 172222008176233936355328202386364789903117516800000⟩, + ⟨2, 2, 8, 0, 8, 4, -7740796748464604603817118096536215583859094323200000⟩, + ⟨2, 2, 5, 1, 4, 4, -8699674978782043592332118452642604682269687808000000⟩, + ⟨2, 2, 6, 1, 5, 4, 11816599472640715037519781207973101506870535782400000⟩, + ⟨2, 2, 7, 1, 6, 4, 11920222611067172572036317149876163347246953267200000⟩, + ⟨2, 2, 8, 1, 7, 4, -6468324116144239431911152250307316068661592064000000⟩, + ⟨2, 2, 5, 2, 3, 4, -12835420769134237783318116880155495080517225676800000⟩, + ⟨2, 2, 6, 2, 4, 4, -4241143430440271867110948952613095005963576934400000⟩, + ⟨2, 2, 7, 2, 5, 4, -1208949722227565181431849053894594510505115648000000⟩, + ⟨2, 2, 8, 2, 6, 4, -351983693341017052717712478003135390437867520000000⟩, + ⟨2, 2, 5, 3, 2, 4, 34870426323955098023034703037165292296268152832000000⟩, + ⟨2, 2, 6, 3, 3, 4, -6438447952084273093572865333325590199713923072000000⟩, + ⟨2, 2, 7, 3, 4, 4, 4857434182045509151454420631382177178014502092800000⟩, + ⟨2, 2, 8, 3, 5, 4, -5600331033060365390010367282537295566061174784000000⟩, + ⟨2, 2, 5, 4, 1, 4, -9665322157628072431040839549684904861122953216000000⟩, + ⟨2, 2, 6, 4, 2, 4, 19577354964506727076569208384123361083867004928000000⟩, + ⟨2, 2, 7, 4, 3, 4, -17228293839473469692136708336920601433439050137600000⟩, + ⟨2, 2, 8, 4, 4, 4, 8012361512577022472830940823204431080999354368000000⟩, + ⟨2, 2, 5, 5, 0, 4, -110648856307918138688677292203460482748665508659200000⟩, + ⟨2, 2, 6, 5, 1, 4, -30252740042545077900234201345294561173324169216000000⟩, + ⟨2, 2, 7, 5, 2, 4, 33464306387343117428345343907893473112882570854400000⟩, + ⟨2, 2, 8, 5, 3, 4, -11207965118655835733852641540873341895327088640000000⟩, + ⟨2, 2, 6, 6, 0, 4, 44374858568609983751104585006888452061754346700800000⟩, + ⟨2, 2, 7, 6, 1, 4, -91942098165628488070524059656169368112161672396800000⟩, + ⟨2, 2, 8, 6, 2, 4, 39969246306497613226331115567351231880541031628800000⟩, + ⟨2, 2, 7, 7, 0, 4, 311652659733324287460943689698207936627160907776000000⟩, + ⟨2, 2, 8, 7, 1, 4, -74733715630114961200570441613654127606679732224000000⟩ +] + +def collectedFourData_9_0_20 : List CollectedFourTerm := [ + ⟨2, 3, 4, 0, 4, 5, -32676793188010820192573666412633084684886710681600000⟩, + ⟨2, 3, 5, 0, 5, 5, 171872558031754686900901530461199048171520524288000000⟩, + ⟨2, 3, 6, 0, 6, 5, 99334503040423677687191720069617901701114626048000000⟩, + ⟨2, 3, 7, 0, 7, 5, -606938815580667976239250876337403874385068032000000⟩, + ⟨2, 3, 8, 0, 8, 5, 20459885150201701458346687890986739245751730176000000⟩, + ⟨2, 3, 4, 1, 3, 5, 19483254191708822682681122394116802286014431232000000⟩, + ⟨2, 3, 5, 1, 4, 5, 91977276600251470327334197620131305252202741760000000⟩, + ⟨2, 3, 6, 1, 5, 5, -62465473757366804041608457947538818167853809664000000⟩, + ⟨2, 3, 7, 1, 6, 5, -42008834234563244247543595842894315852952240128000000⟩, + ⟨2, 3, 8, 1, 7, 5, 17096582280995956100125195629795874782597611520000000⟩, + ⟨2, 3, 4, 2, 2, 5, -12835420769134237783318116880155495080517225676800000⟩, + ⟨2, 3, 5, 2, 3, 5, 135702431325607052087575967062419998628743479296000000⟩, + ⟨2, 3, 6, 2, 4, 5, 22419735412779569601553843323693110260226064384000000⟩, + ⟨2, 3, 7, 2, 5, 5, 4260538593618792743301177776547967492706795520000000⟩, + ⟨2, 3, 8, 2, 6, 5, 930336524070272058624367032937706929363353600000000⟩, + ⟨2, 3, 4, 3, 1, 5, 28497575120029869906808643682698182988586496819200000⟩, + ⟨2, 3, 5, 3, 2, 5, -368667433552342779288553708295859907960284119040000000⟩, + ⟨2, 3, 6, 3, 3, 5, 34035231753455958917484179914457657252952145920000000⟩, + ⟨2, 3, 7, 3, 4, 5, -17118400722600499079115066661079157586129846272000000⟩, + ⟨2, 3, 8, 3, 5, 5, 14802368988987214143238005762231229844941701120000000⟩, + ⟨2, 3, 4, 4, 0, 5, -47600330185942287117150342336985401249461855846400000⟩, + ⟨2, 3, 5, 4, 1, 5, 102186577279138232382127739749180536281125355520000000⟩, + ⟨2, 3, 6, 4, 2, 5, -103490750922503773191790328923680947776341934080000000⟩, + ⟨2, 3, 7, 4, 3, 5, 60715354373905804989708214836387934162359681024000000⟩, + ⟨2, 3, 8, 4, 4, 5, -21177664477721670429594642571067196187072266240000000⟩, + ⟨2, 3, 5, 5, 0, 5, 1169834561286067013077108055358966182425997082624000000⟩, + ⟨2, 3, 6, 5, 1, 5, 159923482520621231586789102291541287392520437760000000⟩, + ⟨2, 3, 7, 5, 2, 5, -117933745507012585503742389007032720411177517056000000⟩, + ⟨2, 3, 8, 5, 3, 5, 29624040850917549325946987614307342630466355200000000⟩, + ⟨2, 3, 6, 6, 0, 5, -234576501456465182753352751273130897250648588288000000⟩, + ⟨2, 3, 7, 6, 1, 5, 324019146876657544512098227881966297336860639232000000⟩, + ⟨2, 3, 8, 6, 2, 5, -105643671516536011297705260494991174043837661184000000⟩, + ⟨2, 3, 7, 7, 0, 5, -1098315471838815857361735493927902874265966346240000000⟩, + ⟨2, 3, 8, 7, 1, 5, 197530472421107460915032592483194132702240440320000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0902.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0902.lean new file mode 100644 index 0000000000000000000000000000000000000000..f415323acace4778e7e154a87a1f1ad2fafbff9d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0902.lean @@ -0,0 +1,644 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0902. -/ +namespace LaughlinFock +def collectedFourData_9_0_21 : List CollectedFourTerm := [ + ⟨2, 4, 3, 0, 3, 6, -888562635919743326007141737395121919721734144000000⟩, + ⟨2, 4, 4, 0, 4, 6, -10797228174276311611318570218432419743067327692800000⟩, + ⟨2, 4, 5, 0, 5, 6, 28395491798844560262839008865500113844675018752000000⟩, + ⟨2, 4, 6, 0, 6, 6, 10940866491343409192070045596923709579254038528000000⟩, + ⟨2, 4, 7, 0, 7, 6, -50136933893301114586224297282681960885387264000000⟩, + ⟨2, 4, 8, 0, 8, 6, 1352091358017760865461876506999192994805553561600000⟩, + ⟨2, 4, 3, 1, 2, 6, 95709697738907295879776635161406157147760230400000⟩, + ⟨2, 4, 4, 1, 3, 6, 6437753541938409415384449815486694015060934656000000⟩, + ⟨2, 4, 5, 1, 4, 6, 15195794100533260344242871562624309218288599040000000⟩, + ⟨2, 4, 6, 1, 5, 6, -6880050614636372621628371177072975398047842304000000⟩, + ⟨2, 4, 7, 1, 6, 6, -3470191872533169284154745565749597207114285056000000⟩, + ⟨2, 4, 8, 1, 7, 6, 1129827512914769324432997140084840726142124032000000⟩, + ⟨2, 4, 3, 2, 1, 6, 749249040811359270873182002370035092439223500800000⟩, + ⟨2, 4, 4, 2, 2, 6, -4241143430440271867110948952613095005963576934400000⟩, + ⟨2, 4, 5, 2, 3, 6, 22419735412779569601553843323693110260226064384000000⟩, + ⟨2, 4, 6, 2, 4, 6, 2469346746745640962830490614015698511775924224000000⟩, + ⟨2, 4, 7, 2, 5, 6, 351947076599078800087883231207743139390423040000000⟩, + ⟨2, 4, 8, 2, 6, 6, 61481282275491979128590898474727224649973760000000⟩, + ⟨2, 4, 3, 3, 0, 6, -7728930192272891188914840162413568094510252032000000⟩, + ⟨2, 4, 4, 3, 1, 6, 9416310199540510299652972327792972497486977433600000⟩, + ⟨2, 4, 5, 3, 2, 6, -60908461512526578749167786187557551453933404160000000⟩, + ⟨2, 4, 6, 3, 3, 6, 3748696728919632058621859232240220536695685120000000⟩, + ⟨2, 4, 7, 3, 4, 6, -1414086730582463033699219639848641099668127744000000⟩, + ⟨2, 4, 8, 3, 5, 6, 978214444571425417784033104150208256663355392000000⟩, + ⟨2, 4, 4, 4, 0, 6, -15728337331984005991055420448013529654169383731200000⟩, + ⟨2, 4, 5, 4, 1, 6, 16882497999160908041014684432716835795847086080000000⟩, + ⟨2, 4, 6, 4, 2, 6, -11398642508647911534374281192564275123459194880000000⟩, + ⟨2, 4, 7, 4, 3, 6, 5015467177923931017145829953283114673213800448000000⟩, + ⟨2, 4, 8, 4, 4, 6, -1399525799539735020066994878736121368814813184000000⟩, + ⟨2, 4, 5, 5, 0, 6, 193271270710162882999196968800836539241302327296000000⟩, + ⟨2, 4, 6, 5, 1, 6, 17614236922056941353533771671991565516391055360000000⟩, + ⟨2, 4, 7, 5, 2, 6, -9742063368640516289335260707583624628993523712000000⟩, + ⟨2, 4, 8, 5, 3, 6, 1957704519357766852448610353114121534512824320000000⟩, + ⟨2, 4, 6, 6, 0, 6, -25836643924188115922098187299518496131061383168000000⟩, + ⟨2, 4, 7, 6, 1, 6, 26766003640048367082378774293813899800990449664000000⟩, + ⟨2, 4, 8, 6, 2, 6, -6981461246636921962061158806913391447176013414400000⟩, + ⟨2, 4, 7, 7, 0, 6, -90727712237171477568486800787064468915334676480000000⟩, + ⟨2, 4, 8, 7, 1, 6, 13053799801173960958474297477522120720999514112000000⟩ +] + +def collectedFourData_9_0_22 : List CollectedFourTerm := [ + ⟨2, 5, 2, 0, 2, 7, -276286032342252992501874756951121442012921856000000⟩, + ⟨2, 5, 3, 0, 3, 7, -506574497889806841894974268430666446101544960000000⟩, + ⟨2, 5, 4, 0, 4, 7, -3077779899738955010798726911981780373524709376000000⟩, + ⟨2, 5, 5, 0, 5, 7, 5396142571102903672458849600199897542882754560000000⟩, + ⟨2, 5, 6, 0, 6, 7, 1559362200615955542238602989077180644725882880000000⟩, + ⟨2, 5, 7, 0, 7, 7, -5716668940607458713447062887154475337777152000000⟩, + ⟨2, 5, 8, 0, 8, 7, 128472466487036881190361148849418969467060224000000⟩, + ⟨2, 5, 2, 1, 1, 7, 1456723582784713797733524614488922207715065856000000⟩, + ⟨2, 5, 3, 1, 2, 7, 54564630691551293634026068081800825783975936000000⟩, + ⟨2, 5, 4, 1, 3, 7, 1835099539533380330886652445602337877676523520000000⟩, + ⟨2, 5, 5, 1, 4, 7, 2887735561281544254915354640861201454805811200000000⟩, + ⟨2, 5, 6, 1, 5, 7, -980588774689562960263388003419491099570339840000000⟩, + ⟨2, 5, 7, 1, 6, 7, -395675135178327860380643482571843140853956608000000⟩, + ⟨2, 5, 8, 1, 7, 7, 107353490892712473202217358759312312741396480000000⟩, + ⟨2, 5, 2, 2, 0, 7, -1539837168638892769747931930814133679324921856000000⟩, + ⟨2, 5, 3, 2, 1, 7, 427151042931896856536693103967434464896745472000000⟩, + ⟨2, 5, 4, 2, 2, 7, -1208949722227565181431849053894594510505115648000000⟩, + ⟨2, 5, 5, 2, 3, 7, 4260538593618792743301177776547967492706795520000000⟩, + ⟨2, 5, 6, 2, 4, 7, 351947076599078800087883231207743139390423040000000⟩, + ⟨2, 5, 7, 2, 5, 7, 40129396939456047575508802359722188178718720000000⟩, + ⟨2, 5, 8, 2, 6, 7, 5841803462377016692359071393350110570086400000000⟩, + ⟨2, 5, 3, 3, 0, 7, -4406306064539094096803540418982050794443898880000000⟩, + ⟨2, 5, 4, 3, 1, 7, 2684145393064750722113336971922511550230822912000000⟩, + ⟨2, 5, 5, 3, 2, 7, -11574750824407322037686378992600465355361484800000000⟩, + ⟨2, 5, 6, 3, 3, 7, 534288210652699766475935393825009922421555200000000⟩, + ⟨2, 5, 7, 3, 4, 7, -161235741085595455482097197656511283086753792000000⟩, + ⟨2, 5, 8, 3, 5, 7, 92947582056572111658530345280810412545146880000000⟩, + ⟨2, 5, 4, 4, 0, 7, -4483406270141066660491391832988273317148360704000000⟩, + ⟨2, 5, 5, 4, 1, 7, 3208268650713728095741272147298087004956262400000000⟩, + ⟨2, 5, 6, 4, 2, 7, -1624607363629137102928070105579996142423244800000000⟩, + ⟨2, 5, 7, 4, 3, 7, 571869143408164519430718015682910464575012864000000⟩, + ⟨2, 5, 8, 4, 4, 7, -132979572950388069312322164263142385527029760000000⟩, + ⟨2, 5, 5, 5, 0, 7, 36728341915624121874243112240693379217626234880000000⟩, + ⟨2, 5, 6, 5, 1, 7, 2510493594879513722753424507318469547104665600000000⟩, + ⟨2, 5, 7, 5, 2, 7, -1110800895712093768361367549857581027364438016000000⟩, + ⟨2, 5, 8, 5, 3, 7, 186016371425848234317915034564595091819724800000000⟩, + ⟨2, 5, 6, 6, 0, 7, -3682403579097679205755082641218443716885217280000000⟩, + ⟨2, 5, 7, 6, 1, 7, 3051889491265738137416331847089321223863140352000000⟩, + ⟨2, 5, 8, 6, 2, 7, -663361643960249915241323128878015106479292416000000⟩, + ⟨2, 5, 7, 7, 0, 7, -10344874612843219123748146807849505402797424640000000⟩, + ⟨2, 5, 8, 7, 1, 7, 1240340637886675168715659878436314526966087680000000⟩ +] + +def collectedFourData_9_0_23 : List CollectedFourTerm := [ + ⟨2, 6, 1, 0, 1, 8, 426087722197497709061253699092621222215680000000000⟩, + ⟨2, 6, 2, 0, 2, 8, -241320651209157159901267471087321464774328320000000⟩, + ⟨2, 6, 3, 0, 3, 8, -221232479036951532586674523523596183771545600000000⟩, + ⟨2, 6, 4, 0, 4, 8, -896090479598078404136889721707503693321994240000000⟩, + ⟨2, 6, 5, 0, 5, 8, 1178308425724983825497982468480471862660300800000000⟩, + ⟨2, 6, 6, 0, 6, 8, 272403420855841406995200390526077651092766720000000⟩, + ⟨2, 6, 7, 0, 7, 8, -832199309171987799685603281778344449802240000000⟩, + ⟨2, 6, 8, 0, 8, 8, 16030518916659171303887506326831160665047040000000⟩, + ⟨2, 6, 1, 1, 0, 8, -511012924024837187211262872674009009734287360000000⟩, + ⟨2, 6, 2, 1, 1, 8, 1272367917585757525726388663135698067726008320000000⟩, + ⟨2, 6, 3, 1, 2, 8, 23829601699084115448303104277591916239912960000000⟩, + ⟨2, 6, 4, 1, 3, 8, 534286167321500913047321855299802224184524800000000⟩, + ⟨2, 6, 5, 1, 4, 8, 630569540794814749406866766082907482095616000000000⟩, + ⟨2, 6, 6, 1, 5, 8, -171298070822008427033494388891210094697512960000000⟩, + ⟨2, 6, 7, 1, 6, 8, -57600077522933777600791379409826361596968960000000⟩, + ⟨2, 6, 8, 1, 7, 8, 13395338422172121465791666084705626541260800000000⟩, + ⟨2, 6, 2, 2, 0, 8, -1344963062887249844538052762290388713414328320000000⟩, + ⟨2, 6, 3, 2, 1, 8, 186546469561124650298786544201472050903121920000000⟩, + ⟨2, 6, 4, 2, 2, 8, -351983693341017052717712478003135390437867520000000⟩, + ⟨2, 6, 5, 2, 3, 8, 930336524070272058624367032937706929363353600000000⟩, + ⟨2, 6, 6, 2, 4, 8, 61481282275491979128590898474727224649973760000000⟩, + ⟨2, 6, 7, 2, 5, 8, 5841803462377016692359071393350110570086400000000⟩, + ⟨2, 6, 8, 2, 6, 8, 728927710907527303805534174103044358144000000000⟩, + ⟨2, 6, 3, 3, 0, 8, -1924332981850155966786391569447492116073676800000000⟩, + ⟨2, 6, 4, 3, 1, 8, 781484450134451701889403299252974157436026880000000⟩, + ⟨2, 6, 5, 3, 2, 8, -2527477034262048161084031550599218451185664000000000⟩, + ⟨2, 6, 6, 3, 3, 8, 93334272337274855219813045420591172865228800000000⟩, + ⟨2, 6, 7, 3, 4, 8, -23471758420736517947308291424526858757079040000000⟩, + ⟨2, 6, 8, 3, 5, 8, 11597800004609964083687499208069936368844800000000⟩, + ⟨2, 6, 4, 4, 0, 8, -1305336250712564526133024531661269041634344960000000⟩, + ⟨2, 6, 5, 4, 1, 8, 700561546199595511410635836597618115346432000000000⟩, + ⟨2, 6, 6, 4, 2, 8, -283801033028348379358413428307706963505971200000000⟩, + ⟨2, 6, 7, 4, 3, 8, 83249373197126293021582740704886831898951680000000⟩, + ⟨2, 6, 8, 4, 4, 8, -16592905997687450057551453080227078052249600000000⟩, + ⟨2, 6, 5, 5, 0, 8, 8020046574351844255236358209698613206345318400000000⟩, + ⟨2, 6, 6, 5, 1, 8, 438555611397869999085991189815686391555686400000000⟩, + ⟨2, 6, 7, 5, 2, 8, -161703913177977601735567109735147267602513920000000⟩, + ⟨2, 6, 8, 5, 3, 8, 23210723997824405733794095103463766622208000000000⟩, + ⟨2, 6, 6, 6, 0, 8, -643275392671293908925130131812302283153080320000000⟩, + ⟨2, 6, 7, 6, 1, 8, 444276265196969248204813977706992268203786240000000⟩, + ⟨2, 6, 8, 6, 2, 8, -82772843651786716374994146711391064933007360000000⟩, + ⟨2, 6, 7, 7, 0, 8, -1505946486620259207720132289938971926777036800000000⟩, + ⟨2, 6, 8, 7, 1, 8, 154767045441209094478274584452935610846412800000000⟩ +] + +def collectedFourData_9_0_24 : List CollectedFourTerm := [ + ⟨3, 0, 6, 0, 6, 3, -34244357729838583042072758087788336616522645504000000⟩, + ⟨3, 0, 7, 0, 7, 3, 627704250327126019870408039637328061695787008000000⟩, + ⟨3, 0, 8, 0, 8, 3, -42319774383517021516369165665982996551290585088000000⟩, + ⟨3, 0, 6, 1, 5, 3, 21534209802616328763117935204527574483019497472000000⟩, + ⟨3, 0, 7, 1, 6, 3, 43446098887406417950183210289574087036116140032000000⟩, + ⟨3, 0, 8, 1, 7, 3, -35363028655801173797737118029059603629353205760000000⟩, + ⟨3, 0, 6, 2, 4, 3, -7728930192272891188914840162413568094510252032000000⟩, + ⟨3, 0, 7, 2, 5, 3, -4406306064539094096803540418982050794443898880000000⟩, + ⟨3, 0, 8, 2, 6, 3, -1924332981850155966786391569447492116073676800000000⟩, + ⟨3, 0, 6, 3, 3, 3, -11733230810134589558476094080634950139416412160000000⟩, + ⟨3, 0, 7, 3, 4, 3, 17704079252369263528416883099672985716358381568000000⟩, + ⟨3, 0, 8, 3, 5, 3, -30617616440986338556589339397121029909837250560000000⟩, + ⟨3, 0, 6, 4, 2, 3, 35677173467889993804176201248544791409291427840000000⟩, + ⟨3, 0, 7, 4, 3, 3, -62792632506386437441556306954498768597214560256000000⟩, + ⟨3, 0, 8, 4, 4, 3, 43804448367500660654195312418225084882348933120000000⟩, + ⟨3, 0, 6, 5, 1, 3, -55131669029532632533882163451525455067721236480000000⟩, + ⟨3, 0, 7, 5, 2, 3, 121968658802825301638772061248054184640998539264000000⟩, + ⟨3, 0, 8, 5, 3, 3, -61275159461320974399863601034112835788577177600000000⟩, + ⟨3, 0, 6, 6, 0, 3, 80867386306047536723348110631736529521972609024000000⟩, + ⟨3, 0, 7, 6, 1, 3, -335104940499253706054206042786986520085746679808000000⟩, + ⟨3, 0, 8, 6, 2, 3, 218516199421682113741492932783357846286963310592000000⟩, + ⟨3, 0, 7, 7, 0, 3, 1135892568040307586505083267333366291349697986560000000⟩, + ⟨3, 0, 8, 7, 1, 3, -408577319245039280006092507027892819720310620160000000⟩ +] + +def collectedFourData_9_0_25 : List CollectedFourTerm := [ + ⟨3, 1, 5, 0, 5, 4, 36093318931253215171951014704208489932985571737600000⟩, + ⟨3, 1, 6, 0, 6, 4, 41720585766264582135687284029334926941475779379200000⟩, + ⟨3, 1, 7, 0, 7, 4, -382372319817269890912713690804239522216489779200000⟩, + ⟨3, 1, 8, 0, 8, 4, 17186342450005424884255515850909832590467583180800000⟩, + ⟨3, 1, 5, 1, 4, 4, 19315271831513785614458311359890919635080445952000000⟩, + ⟨3, 1, 6, 1, 5, 4, -26235558396703646005264038552890449694687861145600000⟩, + ⟨3, 1, 7, 1, 6, 4, -26465625507443203849197694748438004051064179916800000⟩, + ⟨3, 1, 8, 1, 7, 4, 14361161641368974563150994524301516449058390016000000⟩, + ⟨3, 1, 5, 2, 3, 4, 28497575120029869906808643682698182988586496819200000⟩, + ⟨3, 1, 6, 2, 4, 4, 9416310199540510299652972327792972497486977433600000⟩, + ⟨3, 1, 7, 2, 5, 4, 2684145393064750722113336971922511550230822912000000⟩, + ⟨3, 1, 8, 2, 6, 4, 781484450134451701889403299252974157436026880000000⟩, + ⟨3, 1, 5, 3, 2, 4, -77420336388505091434648649999674810198243934208000000⟩, + ⟨3, 1, 6, 3, 3, 4, 14294829711554518235959167751416406198104096768000000⟩, + ⟨3, 1, 7, 3, 4, 4, -10784616880368905679823667190458113004649263923200000⟩, + ⟨3, 1, 8, 3, 5, 4, 12434018111463684462053446889514402528620445696000000⟩, + ⟨3, 1, 5, 4, 1, 4, 21459229829741979528591225120870123364159586304000000⟩, + ⟨3, 1, 6, 4, 2, 4, -43466213830257749159451298280538220759175135232000000⟩, + ⟨3, 1, 7, 4, 3, 4, 38250759886343725527833515752010468811451295334400000⟩, + ⟨3, 1, 8, 4, 4, 4, -17789278450658936702839346852123305329234542592000000⟩, + ⟨3, 1, 5, 5, 0, 4, 245665814256977900307014313860575115625475394764800000⟩, + ⟨3, 1, 6, 5, 1, 4, 67168014781592199360472209671686831665057890304000000⟩, + ⟨3, 1, 7, 5, 2, 4, -74298427941395072279580582346053636993102485913600000⟩, + ⟨3, 1, 8, 5, 3, 4, 24884250672922272819928098606967393007865692160000000⟩, + ⟨3, 1, 6, 6, 0, 4, -98522353746332313669161834086819879556727649075200000⟩, + ⟨3, 1, 7, 6, 1, 4, 204132524854102509482463902759476003663101768499200000⟩, + ⟨3, 1, 8, 6, 2, 4, -88740885055318732650808788204892180174672704307200000⟩, + ⟨3, 1, 7, 7, 0, 4, -691940314373236777458987014038081037150604754944000000⟩, + ⟨3, 1, 8, 7, 1, 4, 165925972624877491105053048582692355597775405056000000⟩ +] + +def collectedFourData_9_0_26 : List CollectedFourTerm := [ + ⟨3, 2, 4, 0, 4, 5, 88774160961339987875043982067967014349658128384000000⟩, + ⟨3, 2, 5, 0, 5, 5, -466932053086114057614764352063960892874812293120000000⟩, + ⟨3, 2, 6, 0, 6, 5, -269865439707858274774444167178194375841173995520000000⟩, + ⟨3, 2, 7, 0, 7, 5, 1648891425729380361189955091196297365610823680000000⟩, + ⟨3, 2, 8, 0, 8, 5, -55584069315618860090854986679555307247752970240000000⟩, + ⟨3, 2, 4, 1, 3, 5, -52930822608996350238002146177535922075787591680000000⟩, + ⟨3, 2, 5, 1, 4, 5, -249877811164537530160000440465115449626355302400000000⟩, + ⟨3, 2, 6, 1, 5, 5, 169702087654593611339463530003414987780244111360000000⟩, + ⟨3, 2, 7, 1, 6, 5, 114126835845864285252414931191623839006819614720000000⟩, + ⟨3, 2, 8, 1, 7, 5, -46446869451644601351232312418867216556805324800000000⟩, + ⟨3, 2, 4, 2, 2, 5, 34870426323955098023034703037165292296268152832000000⟩, + ⟨3, 2, 5, 2, 3, 5, -368667433552342779288553708295859907960284119040000000⟩, + ⟨3, 2, 6, 2, 4, 5, -60908461512526578749167786187557551453933404160000000⟩, + ⟨3, 2, 7, 2, 5, 5, -11574750824407322037686378992600465355361484800000000⟩, + ⟨3, 2, 8, 2, 6, 5, -2527477034262048161084031550599218451185664000000000⟩, + ⟨3, 2, 4, 3, 1, 5, -77420336388505091434648649999674810198243934208000000⟩, + ⟨3, 2, 5, 3, 2, 5, 1001571417950149777375426179311426501732833689600000000⟩, + ⟨3, 2, 6, 3, 3, 5, -92464677444125232423331132295451363425176780800000000⟩, + ⟨3, 2, 7, 3, 4, 5, 46506144357715799091598189215926130673220321280000000⟩, + ⟨3, 2, 8, 3, 5, 5, -40214101784003471545779799847602894844775628800000000⟩, + ⟨3, 2, 4, 4, 0, 5, 129317444016819290567965731868365109163339022336000000⟩, + ⟨3, 2, 5, 4, 1, 5, -277613767277352859675115691632168286263495884800000000⟩, + ⟨3, 2, 6, 4, 2, 5, 281156860391525045740294254872898639263642419200000000⟩, + ⟨3, 2, 7, 4, 3, 5, -164947478505678359322937746532322179049859317760000000⟩, + ⟨3, 2, 8, 4, 4, 5, 57534084948712231894427628986282000722270617600000000⟩, + ⟨3, 2, 5, 5, 0, 5, -3178129538116703209296507701322011255934560501760000000⟩, + ⟨3, 2, 6, 5, 1, 5, -434469591220248788353872890805883444146890342400000000⟩, + ⟨3, 2, 7, 5, 2, 5, 320394637447303451459361705301522121347238461440000000⟩, + ⟨3, 2, 8, 5, 3, 5, -80480644342712388899370403048503073044430848000000000⟩, + ⟨3, 2, 6, 6, 0, 5, 637281999436980637175559253204778327630539653120000000⟩, + ⟨3, 2, 7, 6, 1, 5, -880273891439819186898274635129538642555101511680000000⟩, + ⟨3, 2, 8, 6, 2, 5, 287005773357125515916114462971173219036467036160000000⟩, + ⟨3, 2, 7, 7, 0, 5, 2983831183260749224424725053542753804115089817600000000⟩, + ⟨3, 2, 8, 7, 1, 5, -536637786106709209880990887989110793910930636800000000⟩ +] + +def collectedFourData_9_0_27 : List CollectedFourTerm := [ + ⟨3, 3, 3, 0, 3, 6, -1348920256380525979051392829720436021101854720000000⟩, + ⟨3, 3, 4, 0, 4, 6, -16391190905712743879552330490031987323530379264000000⟩, + ⟨3, 3, 5, 0, 5, 6, 43106982590710859127274673366979960398162165760000000⟩, + ⟨3, 3, 6, 0, 6, 6, 16609247154818537945748134091793884735225200640000000⟩, + ⟨3, 3, 7, 0, 7, 6, -76112502357789618240967941721328133152440320000000⟩, + ⟨3, 3, 8, 0, 8, 6, 2052599724069363584915264778389801152605585408000000⟩, + ⟨3, 3, 3, 1, 2, 6, 145296172484716614510834130417908802809495552000000⟩, + ⟨3, 3, 4, 1, 3, 6, 9773105245774204887767620293756070881688289280000000⟩, + ⟨3, 3, 5, 1, 4, 6, 23068620765017650915317626285881490507248435200000000⟩, + ⟨3, 3, 6, 1, 5, 6, -10444553106152143216359059208318227129586155520000000⟩, + ⟨3, 3, 7, 1, 6, 6, -5268072188902908349728145117412053184969441280000000⟩, + ⟨3, 3, 8, 1, 7, 6, 1715182652047072479817558157324700876967772160000000⟩, + ⟨3, 3, 3, 2, 1, 6, 1137429335162150814908120594086764519886946304000000⟩, + ⟨3, 3, 4, 2, 2, 6, -6438447952084273093572865333325590199713923072000000⟩, + ⟨3, 3, 5, 2, 3, 6, 34035231753455958917484179914457657252952145920000000⟩, + ⟨3, 3, 6, 2, 4, 6, 3748696728919632058621859232240220536695685120000000⟩, + ⟨3, 3, 7, 2, 5, 6, 534288210652699766475935393825009922421555200000000⟩, + ⟨3, 3, 8, 2, 6, 6, 93334272337274855219813045420591172865228800000000⟩, + ⟨3, 3, 3, 3, 0, 6, -11733230810134589558476094080634950139416412160000000⟩, + ⟨3, 3, 4, 3, 1, 6, 14294829711554518235959167751416406198104096768000000⟩, + ⟨3, 3, 5, 3, 2, 6, -92464677444125232423331132295451363425176780800000000⟩, + ⟨3, 3, 6, 3, 3, 6, 5690868317271714918425248755785011534862745600000000⟩, + ⟨3, 3, 7, 3, 4, 6, -2146714433009181766396425831210471232603422720000000⟩, + ⟨3, 3, 8, 3, 5, 6, 1485019992991922023081027161369226570062888960000000⟩, + ⟨3, 3, 4, 4, 0, 6, -23877070640426475895343580757903094712008441856000000⟩, + ⟨3, 3, 5, 4, 1, 6, 25629193270994981099894090714705971254814310400000000⟩, + ⟨3, 3, 6, 4, 2, 6, -17304193484615618764862983623500465621591654400000000⟩, + ⟨3, 3, 7, 4, 3, 6, 7613943010905909706156945222735710463973130240000000⟩, + ⟨3, 3, 8, 4, 4, 6, -2124609593078606638589613015844497523652689920000000⟩, + ⟨3, 3, 5, 5, 0, 6, 293403662835188761597826835715298647370870292480000000⟩, + ⟨3, 3, 6, 5, 1, 6, 26740040627810556340359835224251205080108236800000000⟩, + ⟨3, 3, 7, 5, 2, 6, -14789353148188013726580227192142509583693250560000000⟩, + ⟨3, 3, 8, 5, 3, 6, 2971976510621491175375762526467148136159641600000000⟩, + ⟨3, 3, 6, 6, 0, 6, -39222414872479572402458631097908805538508963840000000⟩, + ⟨3, 3, 7, 6, 1, 6, 40633268869159636744463785839978453410324152320000000⟩, + ⟨3, 3, 8, 6, 2, 6, -10598503824073448834981349886288122256369385472000000⟩, + ⟨3, 3, 7, 7, 0, 6, -137733057754679132015608391114626188267906662400000000⟩, + ⟨3, 3, 8, 7, 1, 6, 19816875325072834785327661340325882521777602560000000⟩ +] + +def collectedFourData_9_0_28 : List CollectedFourTerm := [ + ⟨3, 4, 2, 0, 2, 7, 1110088527956477957063602802924003795855317401600000⟩, + ⟨3, 4, 3, 0, 3, 7, 2035363618983743401292342175024822576067117056000000⟩, + ⟨3, 4, 4, 0, 4, 7, 12366199367049015869188959245015726417514174873600000⟩, + ⟨3, 4, 5, 0, 5, 7, -21681139334537446712179899660916815630346223616000000⟩, + ⟨3, 4, 6, 0, 6, 7, -6265355056705883833114474016818938121675603968000000⟩, + ⟨3, 4, 7, 0, 7, 7, 22968980933615383417923088035822517875847987200000⟩, + ⟨3, 4, 8, 0, 8, 7, -516189001653422304777558446388323682150147686400000⟩, + ⟨3, 4, 2, 1, 1, 7, -5852963770711995779720207169511603282464315801600000⟩, + ⟨3, 4, 3, 1, 2, 7, -219235008188322729877632564258206911949281689600000⟩, + ⟨3, 4, 4, 1, 3, 7, -7373238991577784823110349134720743542276227072000000⟩, + ⟨3, 4, 5, 1, 4, 7, -11602620990914123915657669058347400083873464320000000⟩, + ⟨3, 4, 6, 1, 5, 7, 3939903657805399151391549178270236617918644224000000⟩, + ⟨3, 4, 7, 1, 6, 7, 1589781519664312668835726855632782427463404748800000⟩, + ⟨3, 4, 8, 1, 7, 7, -431335155330815292106593527070959313698684928000000⟩, + ⟨3, 4, 2, 2, 0, 7, 6186905509973564113570434308548218279618517401600000⟩, + ⟨3, 4, 3, 2, 1, 7, -1716248441672768077724073431465299451523052339200000⟩, + ⟨3, 4, 4, 2, 2, 7, 4857434182045509151454420631382177178014502092800000⟩, + ⟨3, 4, 5, 2, 3, 7, -17118400722600499079115066661079157586129846272000000⟩, + ⟨3, 4, 6, 2, 4, 7, -1414086730582463033699219639848641099668127744000000⟩, + ⟨3, 4, 7, 2, 5, 7, -161235741085595455482097197656511283086753792000000⟩, + ⟨3, 4, 8, 2, 6, 7, -23471758420736517947308291424526858757079040000000⟩, + ⟨3, 4, 3, 3, 0, 7, 17704079252369263528416883099672985716358381568000000⟩, + ⟨3, 4, 4, 3, 1, 7, -10784616880368905679823667190458113004649263923200000⟩, + ⟨3, 4, 5, 3, 2, 7, 46506144357715799091598189215926130673220321280000000⟩, + ⟨3, 4, 6, 3, 3, 7, -2146714433009181766396425831210471232603422720000000⟩, + ⟨3, 4, 7, 3, 4, 7, 647828429683188810813063409499283383806800691200000⟩, + ⟨3, 4, 8, 3, 5, 7, -373453712688878997585607089850456713480634368000000⟩, + ⟨3, 4, 4, 4, 0, 7, 18013859855522636769572054615704167785204967014400000⟩, + ⟨3, 4, 5, 4, 1, 7, -12890489589962005492362534688913713837784432640000000⟩, + ⟨3, 4, 6, 4, 2, 7, 6527503332359074033822668311602151483013857280000000⟩, + ⟨3, 4, 7, 4, 3, 7, -2297710710193640823202675922235592127346533990400000⟩, + ⟨3, 4, 8, 4, 4, 7, 534298086419049397485002739460171583597838336000000⟩, + ⟨3, 4, 5, 5, 0, 7, -147570655909564369827873866645681051685951111168000000⟩, + ⟨3, 4, 6, 5, 1, 7, -10086902025259436613867578770457835126034268160000000⟩, + ⟨3, 4, 7, 5, 2, 7, 4463082410356061894994499383487346892454074777600000⟩, + ⟨3, 4, 8, 5, 3, 7, -747394423747514448991412427612008490498785280000000⟩, + ⟨3, 4, 6, 6, 0, 7, 14795514394294096901730158143084144080671735808000000⟩, + ⟨3, 4, 7, 6, 1, 7, -12262174399928628159408714946692693502477939507200000⟩, + ⟨3, 4, 8, 6, 2, 7, 2665318056811536473398474011951992241072478617600000⟩, + ⟨3, 4, 7, 7, 0, 7, 41564629719101579594861127878736668344927125504000000⟩, + ⟨3, 4, 8, 7, 1, 7, -4983559614662604148320065090000346274225717248000000⟩ +] + +def collectedFourData_9_0_29 : List CollectedFourTerm := [ + ⟨3, 5, 1, 0, 1, 8, 6779383075331177603552916386291899648966656000000000⟩, + ⟨3, 5, 2, 0, 2, 8, -3839596996829086568264890875997395063505158144000000⟩, + ⟨3, 5, 3, 0, 3, 8, -3519978741376361519477892934096243018715627520000000⟩, + ⟨3, 5, 4, 0, 4, 8, -14257488106021485864878309805395330997008990208000000⟩, + ⟨3, 5, 5, 0, 5, 8, 18747792491372077707758559297150748563194511360000000⟩, + ⟨3, 5, 6, 0, 6, 8, 4334147746591071476359908949047071780502503424000000⟩, + ⟨3, 5, 7, 0, 7, 8, -13240930489163024248645301471726702646263808000000⟩, + ⟨3, 5, 8, 0, 8, 8, 255057874167052681451363420563106959844179968000000⟩, + ⟨3, 5, 1, 1, 0, 8, -8130608294795459115992144093903813762730688512000000⟩, + ⟨3, 5, 2, 1, 1, 8, 20244351284257484867575977112358377099723014144000000⟩, + ⟨3, 5, 3, 1, 2, 8, 379147274222027940998088266409025237294252032000000⟩, + ⟨3, 5, 4, 1, 3, 8, 8500903479316956295443613140729778845945692160000000⟩, + ⟨3, 5, 5, 1, 4, 8, 10032845937537377763856407018863465917002547200000000⟩, + ⟨3, 5, 6, 1, 5, 8, -2725483935980038680595937324191648524672172032000000⟩, + ⟨3, 5, 7, 1, 6, 8, -916461494555203320863635001356225801441247232000000⟩, + ⟨3, 5, 8, 1, 7, 8, 213130127569163819164507344927298768192143360000000⟩, + ⟨3, 5, 2, 2, 0, 8, -21399395829709151351066957494366666986193158144000000⟩, + ⟨3, 5, 3, 2, 1, 8, 2968097677124051590107467716369721294548107264000000⟩, + ⟨3, 5, 4, 2, 2, 8, -5600331033060365390010367282537295566061174784000000⟩, + ⟨3, 5, 5, 2, 3, 8, 14802368988987214143238005762231229844941701120000000⟩, + ⟨3, 5, 6, 2, 4, 8, 978214444571425417784033104150208256663355392000000⟩, + ⟨3, 5, 7, 2, 5, 8, 92947582056572111658530345280810412545146880000000⟩, + ⟨3, 5, 8, 2, 6, 8, 11597800004609964083687499208069936368844800000000⟩, + ⟨3, 5, 3, 3, 0, 8, -30617616440986338556589339397121029909837250560000000⟩, + ⟨3, 5, 4, 3, 1, 8, 12434018111463684462053446889514402528620445696000000⟩, + ⟨3, 5, 5, 3, 2, 8, -40214101784003471545779799847602894844775628800000000⟩, + ⟨3, 5, 6, 3, 3, 8, 1485019992991922023081027161369226570062888960000000⟩, + ⟨3, 5, 7, 3, 4, 8, -373453712688878997585607089850456713480634368000000⟩, + ⟨3, 5, 8, 3, 5, 8, 184529910077729040039532069236286385459036160000000⟩, + ⟨3, 5, 4, 4, 0, 8, -20768902797896636053157405721068709433344786432000000⟩, + ⟨3, 5, 5, 4, 1, 8, 11146472526922462900101007387490303558968934400000000⟩, + ⟨3, 5, 6, 4, 2, 8, -4515492514431312614417116540876648069768151040000000⟩, + ⟨3, 5, 7, 4, 3, 8, 1324561498214044046199246582975914996039417856000000⟩, + ⟨3, 5, 8, 4, 4, 8, -264005884776804081395842052418926050352824320000000⟩, + ⟨3, 5, 5, 5, 0, 8, 127605103777965623199042161811608454630243041280000000⟩, + ⟨3, 5, 6, 5, 1, 8, 6977756773109143431702926992215417994220666880000000⟩, + ⟨3, 5, 7, 5, 2, 8, -2572833515501943530020234577233111212217073664000000⟩, + ⟨3, 5, 8, 5, 3, 8, 369300454435760510596458092718824497977753600000000⟩, + ⟨3, 5, 6, 6, 0, 8, -10235005804347953421900535405567619966429036544000000⟩, + ⟨3, 5, 7, 6, 1, 8, 7068776770928902741944527143277108839588036608000000⟩, + ⟨3, 5, 8, 6, 2, 8, -1316979546971917034245915806857339781368512512000000⟩, + ⟨3, 5, 7, 7, 0, 8, -23960765804501727979165489746526061210432962560000000⟩, + ⟨3, 5, 8, 7, 1, 8, 2462462619368350388387986548757977429190901760000000⟩ +] + +def collectedFourData_9_0_30 : List CollectedFourTerm := [ + ⟨4, 0, 5, 0, 5, 4, -60287722425429081168127310238928620336352277299200000⟩, + ⟨4, 0, 6, 0, 6, 4, -69687110207117038620850698651215130723338315366400000⟩, + ⟨4, 0, 7, 0, 7, 4, 638687628705431153318196492597630069937432166400000⟩, + ⟨4, 0, 8, 0, 8, 4, -28706848630567872601505303896572763567065504153600000⟩, + ⟨4, 0, 5, 1, 4, 4, -32262861416761929980473096610757505464227856384000000⟩, + ⟨4, 0, 6, 1, 5, 4, 43822017734341013452041821389735190044286858035200000⟩, + ⟨4, 0, 7, 1, 6, 4, 44206305533917036590740282906960929168813562265600000⟩, + ⟨4, 0, 8, 1, 7, 4, -23987866795809522437609426130368681968373071872000000⟩, + ⟨4, 0, 5, 2, 3, 4, -47600330185942287117150342336985401249461855846400000⟩, + ⟨4, 0, 6, 2, 4, 4, -15728337331984005991055420448013529654169383731200000⟩, + ⟨4, 0, 7, 2, 5, 4, -4483406270141066660491391832988273317148360704000000⟩, + ⟨4, 0, 8, 2, 6, 4, -1305336250712564526133024531661269041634344960000000⟩, + ⟨4, 0, 5, 3, 2, 4, 129317444016819290567965731868365109163339022336000000⟩, + ⟨4, 0, 6, 3, 3, 4, -23877070640426475895343580757903094712008441856000000⟩, + ⟨4, 0, 7, 3, 4, 4, 18013859855522636769572054615704167785204967014400000⟩, + ⟨4, 0, 8, 3, 5, 4, -20768902797896636053157405721068709433344786432000000⟩, + ⟨4, 0, 5, 4, 1, 4, -35843976939420018220769778814775517104798957568000000⟩, + ⟨4, 0, 6, 4, 2, 4, 72602883632678407888347905855190089300541702144000000⟩, + ⟨4, 0, 7, 4, 3, 4, -63891358923848296074008860772213515941277650124800000⟩, + ⟨4, 0, 8, 4, 4, 4, 29713950202937325316545944703931689126554763264000000⟩, + ⟨4, 0, 5, 5, 0, 4, -410342768631265189783694012041820252536582019481600000⟩, + ⟨4, 0, 6, 5, 1, 4, -112192692468449214472092168465008684517260525568000000⟩, + ⟨4, 0, 7, 5, 2, 4, 124102829360420992253392511656192024960147075891200000⟩, + ⟨4, 0, 8, 5, 3, 4, -41564889064133650208460461158171536846980382720000000⟩, + ⟨4, 0, 6, 6, 0, 4, 164564758554681921093627932634032233280719709798400000⟩, + ⟨4, 0, 7, 6, 1, 4, -340968504998019815873189798934963583553399842406400000⟩, + ⟨4, 0, 8, 6, 2, 4, 148226486353113104663778306375490888150142051942400000⟩, + ⟨4, 0, 7, 7, 0, 4, 1155768071297438014919844369961325814241661288448000000⟩, + ⟨4, 0, 8, 7, 1, 4, -277150987412135687494735306277893425933217431552000000⟩ +] + +def collectedFourData_9_0_31 : List CollectedFourTerm := [ + ⟨4, 1, 4, 0, 4, 5, -24606262538724253486161346685878148456138145792000000⟩, + ⟨4, 1, 5, 0, 5, 5, 129423388084579729722618086854805497664042434560000000⟩, + ⟨4, 1, 6, 0, 6, 5, 74800818027124156635891445505186672047565045760000000⟩, + ⟨4, 1, 7, 0, 7, 5, -457036764752049005991194259968223625441443840000000⟩, + ⟨4, 1, 8, 0, 8, 5, 15406692530120194899241630438811053386230661120000000⟩, + ⟨4, 1, 4, 1, 3, 5, 14671270371958763292716073137177428806693027840000000⟩, + ⟨4, 1, 5, 1, 4, 5, 69260683035844086482212036132062183682159411200000000⟩, + ⟨4, 1, 6, 1, 5, 5, -47037719951157918738889822295647678065467719680000000⟩, + ⟨4, 1, 7, 1, 6, 5, -31633471441765279568878944217435537117921935360000000⟩, + ⟨4, 1, 8, 1, 7, 5, 12874059877926976688841622502107114480494182400000000⟩, + ⟨4, 1, 4, 2, 2, 5, -9665322157628072431040839549684904861122953216000000⟩, + ⟨4, 1, 5, 2, 3, 5, 102186577279138232382127739749180536281125355520000000⟩, + ⟨4, 1, 6, 2, 4, 5, 16882497999160908041014684432716835795847086080000000⟩, + ⟨4, 1, 7, 2, 5, 5, 3208268650713728095741272147298087004956262400000000⟩, + ⟨4, 1, 8, 2, 6, 5, 700561546199595511410635836597618115346432000000000⟩, + ⟨4, 1, 4, 3, 1, 5, 21459229829741979528591225120870123364159586304000000⟩, + ⟨4, 1, 5, 3, 2, 5, -277613767277352859675115691632168286263495884800000000⟩, + ⟨4, 1, 6, 3, 3, 5, 25629193270994981099894090714705971254814310400000000⟩, + ⟨4, 1, 7, 3, 4, 5, -12890489589962005492362534688913713837784432640000000⟩, + ⟨4, 1, 8, 3, 5, 5, 11146472526922462900101007387490303558968934400000000⟩, + ⟨4, 1, 4, 4, 0, 5, -35843976939420018220769778814775517104798957568000000⟩, + ⟨4, 1, 5, 4, 1, 5, 76948485550493347382545845165693215317583462400000000⟩, + ⟨4, 1, 6, 4, 2, 5, -77930553738154773824406858116208029303675289600000000⟩, + ⟨4, 1, 7, 4, 3, 5, 45719845924298031016154017225428035422786682880000000⟩, + ⟨4, 1, 8, 4, 4, 5, -15947194361992285480423557508051512159161548800000000⟩, + ⟨4, 1, 5, 5, 0, 5, 880908238952885985003255946802193681380938874880000000⟩, + ⟨4, 1, 6, 5, 1, 5, 120425501191876078898858736685895760364122931200000000⟩, + ⟨4, 1, 7, 5, 2, 5, -88806410329926730594615142609701037578880286720000000⟩, + ⟨4, 1, 8, 5, 3, 5, 22307480493618873422834279610353104793370624000000000⟩, + ⟨4, 1, 6, 6, 0, 5, -176640680345921808239429687903549017305970114560000000⟩, + ⟨4, 1, 7, 6, 1, 5, 243992736672390576948134266276152760084557987840000000⟩, + ⟨4, 1, 8, 6, 2, 5, -79551744932069731790404257957880999041910702080000000⟩, + ⟨4, 1, 7, 7, 0, 5, -827052969822154830668279588456729862669651148800000000⟩, + ⟨4, 1, 8, 7, 1, 5, 148744298004594984044102766277119523011585638400000000⟩ +] + +def collectedFourData_9_0_32 : List CollectedFourTerm := [ + ⟨4, 2, 3, 0, 3, 6, 4101654758182212021353552216048103220083425280000000⟩, + ⟨4, 2, 4, 0, 4, 6, 49840608332983644557041530116427295432938356736000000⟩, + ⟨4, 2, 5, 0, 5, 6, -131075176177196839892215298673183219479992074240000000⟩, + ⟨4, 2, 6, 0, 6, 6, -50503650827501453215791079170335596764054159360000000⟩, + ⟨4, 2, 7, 0, 7, 6, 231434887256163815710510874326345956647239680000000⟩, + ⟨4, 2, 8, 0, 8, 6, -6241329229841154301032806378125166043665006592000000⟩, + ⟨4, 2, 3, 1, 2, 6, -441801310639881455821180741715174632558952448000000⟩, + ⟨4, 2, 4, 1, 3, 6, -29717029931113438794914168936067090094982430720000000⟩, + ⟨4, 2, 5, 1, 4, 6, -70144634331033258793475793925230158890716364800000000⟩, + ⟨4, 2, 6, 1, 5, 6, 31758697923245309178782697141529544132898324480000000⟩, + ⟨4, 2, 7, 1, 6, 6, 16018599511612272543921516063264348574549278720000000⟩, + ⟨4, 2, 8, 1, 7, 6, -5215346906270999897590065523002842640380067840000000⟩, + ⟨4, 2, 3, 2, 1, 6, -3458575421783708533242504068913541369294749696000000⟩, + ⟨4, 2, 4, 2, 2, 6, 19577354964506727076569208384123361083867004928000000⟩, + ⟨4, 2, 5, 2, 3, 6, -103490750922503773191790328923680947776341934080000000⟩, + ⟨4, 2, 6, 2, 4, 6, -11398642508647911534374281192564275123459194880000000⟩, + ⟨4, 2, 7, 2, 5, 6, -1624607363629137102928070105579996142423244800000000⟩, + ⟨4, 2, 8, 2, 6, 6, -283801033028348379358413428307706963505971200000000⟩, + ⟨4, 2, 3, 3, 0, 6, 35677173467889993804176201248544791409291427840000000⟩, + ⟨4, 2, 4, 3, 1, 6, -43466213830257749159451298280538220759175135232000000⟩, + ⟨4, 2, 5, 3, 2, 6, 281156860391525045740294254872898639263642419200000000⟩, + ⟨4, 2, 6, 3, 3, 6, -17304193484615618764862983623500465621591654400000000⟩, + ⟨4, 2, 7, 3, 4, 6, 6527503332359074033822668311602151483013857280000000⟩, + ⟨4, 2, 8, 3, 5, 6, -4515492514431312614417116540876648069768151040000000⟩, + ⟨4, 2, 4, 4, 0, 6, 72602883632678407888347905855190089300541702144000000⟩, + ⟨4, 2, 5, 4, 1, 6, -77930553738154773824406858116208029303675289600000000⟩, + ⟨4, 2, 6, 4, 2, 6, 52616770492515486752800476708459281567553945600000000⟩, + ⟨4, 2, 7, 4, 3, 6, -23151676632840635440551940983988842594576629760000000⟩, + ⟨4, 2, 8, 4, 4, 6, 6460289261363224943363911499483012613097390080000000⟩, + ⟨4, 2, 5, 5, 0, 6, -892150980789004330058183768544238500046197227520000000⟩, + ⟨4, 2, 6, 5, 1, 6, -81308301477611521140327158168523390869254963200000000⟩, + ⟨4, 2, 7, 5, 2, 6, 44969908653807201034053024755828544756976189440000000⟩, + ⟨4, 2, 8, 5, 3, 6, -9036873409185162063692033160595253995398758400000000⟩, + ⟨4, 2, 6, 6, 0, 6, 119263391463016015453161355940199940619407196160000000⟩, + ⟨4, 2, 7, 6, 1, 6, -123553367820929591937403136401702001491763527680000000⟩, + ⟨4, 2, 8, 6, 2, 6, 32226815064863323400425899471119491808549142528000000⟩, + ⟨4, 2, 7, 7, 0, 6, 418804187294448341396078104163980621662230937600000000⟩, + ⟨4, 2, 8, 7, 1, 6, -60257069003832412037134758158153000198539837440000000⟩ +] + +def collectedFourData_9_0_33 : List CollectedFourTerm := [ + ⟨4, 3, 2, 0, 2, 7, -3937249714706187001467801211853021428745188147200000⟩, + ⟨4, 3, 3, 0, 3, 7, -7219005175127151536120010153823066278070321152000000⟩, + ⟨4, 3, 4, 0, 4, 7, -43860299159692296026273691026526701194084299571200000⟩, + ⟨4, 3, 5, 0, 5, 7, 76898425224298352292526700965972955399215644672000000⟩, + ⟨4, 3, 6, 0, 6, 7, 22221892027799920965974824504982062881419821056000000⟩, + ⟨4, 3, 7, 0, 7, 7, -81466127565922012142697356793822655432517222400000⟩, + ⟨4, 3, 8, 0, 8, 7, 1830813442632107987277316297423565372772895948800000⟩, + ⟨4, 3, 2, 1, 1, 7, 20759227175190605943687800373030649529585840947200000⟩, + ⟨4, 3, 3, 1, 2, 7, 777580302565674404225938048761894328811598643200000⟩, + ⟨4, 3, 4, 1, 3, 7, 26151322516133890016655773351063296214380314624000000⟩, + ⟨4, 3, 5, 1, 4, 7, 41152047819479558034262282884931469295684157440000000⟩, + ⟨4, 3, 6, 1, 5, 7, -13974006722887553115256454261266394238689476608000000⟩, + ⟨4, 3, 7, 1, 6, 7, -5638619512865452940057448082704298051548846489600000⟩, + ⟨4, 3, 8, 1, 7, 7, 1529854758877017931588358599603330000015589376000000⟩, + ⟨4, 3, 2, 2, 0, 7, -21943648043007777210789874529003194229359588147200000⟩, + ⟨4, 3, 3, 2, 1, 7, 6087170993272322379802582817302518816284501606400000⟩, + ⟨4, 3, 4, 2, 2, 7, -17228293839473469692136708336920601433439050137600000⟩, + ⟨4, 3, 5, 2, 3, 7, 60715354373905804989708214836387934162359681024000000⟩, + ⟨4, 3, 6, 2, 4, 7, 5015467177923931017145829953283114673213800448000000⟩, + ⟨4, 3, 7, 2, 5, 7, 571869143408164519430718015682910464575012864000000⟩, + ⟨4, 3, 8, 2, 6, 7, 83249373197126293021582740704886831898951680000000⟩, + ⟨4, 3, 3, 3, 0, 7, -62792632506386437441556306954498768597214560256000000⟩, + ⟨4, 3, 4, 3, 1, 7, 38250759886343725527833515752010468811451295334400000⟩, + ⟨4, 3, 5, 3, 2, 7, -164947478505678359322937746532322179049859317760000000⟩, + ⟨4, 3, 6, 3, 3, 7, 7613943010905909706156945222735710463973130240000000⟩, + ⟨4, 3, 7, 3, 4, 7, -2297710710193640823202675922235592127346533990400000⟩, + ⟨4, 3, 8, 3, 5, 7, 1324561498214044046199246582975914996039417856000000⟩, + ⟨4, 3, 4, 4, 0, 7, -63891358923848296074008860772213515941277650124800000⟩, + ⟨4, 3, 5, 4, 1, 7, 45719845924298031016154017225428035422786682880000000⟩, + ⟨4, 3, 6, 4, 2, 7, -23151676632840635440551940983988842594576629760000000⟩, + ⟨4, 3, 7, 4, 3, 7, 8149494936985733196409542740482302512838003916800000⟩, + ⟨4, 3, 8, 4, 4, 7, -1895042544214041288528237866374926401286438912000000⟩, + ⟨4, 3, 5, 5, 0, 7, 523401970425296321052191951208059291669108883456000000⟩, + ⟨4, 3, 6, 5, 1, 7, 35776112554132282849559390937253804996527390720000000⟩, + ⟨4, 3, 7, 5, 2, 7, -15829611336703718411158036795699697381643858739200000⟩, + ⟨4, 3, 8, 5, 3, 7, 2650850276860321467163017024095956619766005760000000⟩, + ⟨4, 3, 6, 6, 0, 7, -52476566833009919726300032016955466264489230336000000⟩, + ⟨4, 3, 7, 6, 1, 7, 43491344556701277050908807709410704707532777062400000⟩, + ⟨4, 3, 8, 6, 2, 7, -9453320608673021548159474108180356815786292019200000⟩, + ⟨4, 3, 7, 7, 0, 7, -147420969032676155688758208556370955451779514368000000⟩, + ⟨4, 3, 8, 7, 1, 7, 17675634129083525776132537439257322015284002816000000⟩ +] + +def collectedFourData_9_0_34 : List CollectedFourTerm := [ + ⟨4, 4, 1, 0, 1, 8, -9699224512111815194597955140743338248896512000000000⟩, + ⟨4, 4, 2, 0, 2, 8, 5493289417998603593850991673925282282589913088000000⟩, + ⟨4, 4, 3, 0, 3, 8, 5036013411707419486970294565128491165066199040000000⟩, + ⟨4, 4, 4, 0, 4, 8, 20398106521264968976784424795218793789722198016000000⟩, + ⟨4, 4, 5, 0, 5, 8, -26822359270709736079673656963572400380413214720000000⟩, + ⟨4, 4, 6, 0, 6, 8, -6200840341331018388173790002485109339505819648000000⟩, + ⟨4, 4, 7, 0, 7, 8, 18943723364885226738638393421833739190665216000000⟩, + ⟨4, 4, 8, 0, 8, 8, -364909838791984524438178483633196712157249536000000⟩, + ⟨4, 4, 1, 1, 0, 8, 11632414689504379336522940971734811313568743424000000⟩, + ⟨4, 4, 2, 1, 1, 8, -28963477358665183262743817889400144522628825088000000⟩, + ⟨4, 4, 3, 1, 2, 8, -542443832273783748898342929013840161710014464000000⟩, + ⟨4, 4, 4, 1, 3, 8, -12162193887776402348984822583843369666289336320000000⟩, + ⟨4, 4, 5, 1, 4, 8, -14353935182937022346806664359495881671992934400000000⟩, + ⟨4, 4, 6, 1, 5, 8, 3899334247007897287002559838642361310289854464000000⟩, + ⟨4, 4, 7, 1, 6, 8, 1311176207867885487922852864064607104337444864000000⟩, + ⟨4, 4, 8, 1, 7, 8, -304924052029228022353062491498611584238878720000000⟩, + ⟨4, 4, 2, 2, 0, 8, 30615992970091754999659202418367927401565913088000000⟩, + ⟨4, 4, 3, 2, 1, 8, -4246440336003201195820950245711651419170275328000000⟩, + ⟨4, 4, 4, 2, 2, 8, 8012361512577022472830940823204431080999354368000000⟩, + ⟨4, 4, 5, 2, 3, 8, -21177664477721670429594642571067196187072266240000000⟩, + ⟨4, 4, 6, 2, 4, 8, -1399525799539735020066994878736121368814813184000000⟩, + ⟨4, 4, 7, 2, 5, 8, -132979572950388069312322164263142385527029760000000⟩, + ⟨4, 4, 8, 2, 6, 8, -16592905997687450057551453080227078052249600000000⟩, + ⟨4, 4, 3, 3, 0, 8, 43804448367500660654195312418225084882348933120000000⟩, + ⟨4, 4, 4, 3, 1, 8, -17789278450658936702839346852123305329234542592000000⟩, + ⟨4, 4, 5, 3, 2, 8, 57534084948712231894427628986282000722270617600000000⟩, + ⟨4, 4, 6, 3, 3, 8, -2124609593078606638589613015844497523652689920000000⟩, + ⟨4, 4, 7, 3, 4, 8, 534298086419049397485002739460171583597838336000000⟩, + ⟨4, 4, 8, 3, 5, 8, -264005884776804081395842052418926050352824320000000⟩, + ⟨4, 4, 4, 4, 0, 8, 29713950202937325316545944703931689126554763264000000⟩, + ⟨4, 4, 5, 4, 1, 8, -15947194361992285480423557508051512159161548800000000⟩, + ⟨4, 4, 6, 4, 2, 8, 6460289261363224943363911499483012613097390080000000⟩, + ⟨4, 4, 7, 4, 3, 8, -1895042544214041288528237866374926401286438912000000⟩, + ⟨4, 4, 8, 4, 4, 8, 377711706288828649346519010696620581469552640000000⟩, + ⟨4, 4, 5, 5, 0, 8, -182563890649202633491194398825298515037058498560000000⟩, + ⟨4, 4, 6, 5, 1, 8, -9983036624610313455405348490420001049422069760000000⟩, + ⟨4, 4, 7, 5, 2, 8, 3680938165294667357295973596381623762842288128000000⟩, + ⟨4, 4, 8, 5, 3, 8, -528356043639322031903541476614720388805427200000000⟩, + ⟨4, 4, 6, 6, 0, 8, 14643164145771315211041940606390141358218149888000000⟩, + ⟨4, 4, 7, 6, 1, 8, -10113258413840397188137396614132517802990370816000000⟩, + ⟨4, 4, 8, 6, 2, 8, 1884195090025345438083797364435470915337191424000000⟩, + ⟨4, 4, 7, 7, 0, 8, 34280530313392976952451081470280640970746757120000000⟩, + ⟨4, 4, 8, 7, 1, 8, -3523031156750176971714724824428731214352875520000000⟩ +] + +def collectedFourData_9_0_35 : List CollectedFourTerm := [ + ⟨5, 0, 4, 0, 4, 5, -281693125538855768379121455467704925744393512550400000⟩, + ⟨5, 0, 5, 0, 5, 5, 1481642270946190090178591663754775448798701289472000000⟩, + ⟨5, 0, 6, 0, 6, 5, 856321685983938953971878730330998208738111782912000000⟩, + ⟨5, 0, 7, 0, 7, 5, -5232168621567765836638002609005504150642884608000000⟩, + ⟨5, 0, 8, 0, 8, 5, 176376211795499716130290471395059140294915129344000000⟩, + ⟨5, 0, 4, 1, 3, 5, 167957080040037064961583384087769535911619985408000000⟩, + ⟨5, 0, 5, 1, 4, 5, 792898078309070308282554684256365634288814653440000000⟩, + ⟨5, 0, 6, 1, 5, 5, -538489026133509007214195980412381043318237167616000000⟩, + ⟨5, 0, 7, 1, 6, 5, -362140793550071401188823304056657004908806930432000000⟩, + ⟨5, 0, 8, 1, 7, 5, 147382568144201098590394101146828170689647738880000000⟩, + ⟨5, 0, 4, 2, 2, 5, -110648856307918138688677292203460482748665508659200000⟩, + ⟨5, 0, 5, 2, 3, 5, 1169834561286067013077108055358966182425997082624000000⟩, + ⟨5, 0, 6, 2, 4, 5, 193271270710162882999196968800836539241302327296000000⟩, + ⟨5, 0, 7, 2, 5, 5, 36728341915624121874243112240693379217626234880000000⟩, + ⟨5, 0, 8, 2, 6, 5, 8020046574351844255236358209698613206345318400000000⟩, + ⟨5, 0, 4, 3, 1, 5, 245665814256977900307014313860575115625475394764800000⟩, + ⟨5, 0, 5, 3, 2, 5, -3178129538116703209296507701322011255934560501760000000⟩, + ⟨5, 0, 6, 3, 3, 5, 293403662835188761597826835715298647370870292480000000⟩, + ⟨5, 0, 7, 3, 4, 5, -147570655909564369827873866645681051685951111168000000⟩, + ⟨5, 0, 8, 3, 5, 5, 127605103777965623199042161811608454630243041280000000⟩, + ⟨5, 0, 4, 4, 0, 5, -410342768631265189783694012041820252536582019481600000⟩, + ⟨5, 0, 5, 4, 1, 5, 880908238952885985003255946802193681380938874880000000⟩, + ⟨5, 0, 6, 4, 2, 5, -892150980789004330058183768544238500046197227520000000⟩, + ⟨5, 0, 7, 4, 3, 5, 523401970425296321052191951208059291669108883456000000⟩, + ⟨5, 0, 8, 4, 4, 5, -182563890649202633491194398825298515037058498560000000⟩, + ⟨5, 0, 5, 5, 0, 5, 10084660145076755605488052657091431422648549113856000000⟩, + ⟨5, 0, 6, 5, 1, 5, 1378634230693759031501476633257142697936226877440000000⟩, + ⟨5, 0, 7, 5, 2, 5, -1016658066390776070355560944742692113572182360064000000⟩, + ⟨5, 0, 8, 5, 3, 5, 255376609643796533064135315441674513011231948800000000⟩, + ⟨5, 0, 6, 6, 0, 5, -2022187045498883097630033528950617980307318505472000000⟩, + ⟨5, 0, 7, 6, 1, 5, 2793235116217213067313894870910679366724545937408000000⟩, + ⟨5, 0, 8, 6, 2, 5, -910710419216163811184495977551744108187663466496000000⟩, + ⟨5, 0, 7, 7, 0, 5, -9468123640831261233707413950839361867996526018560000000⟩, + ⟨5, 0, 8, 7, 1, 5, 1702828543955287164330296790021190555166394286080000000⟩ +] + +def collectedFourData_9_0_36 : List CollectedFourTerm := [ + ⟨5, 1, 3, 0, 3, 6, -6338256386959322028672286514042406585929564160000000⟩, + ⟨5, 1, 4, 0, 4, 6, -77018318878811381784103020861878239306859937792000000⟩, + ⟨5, 1, 5, 0, 5, 6, 202549488330199752577997343203736726873078497280000000⟩, + ⟨5, 1, 6, 0, 6, 6, 78042913481104393335376647855025075401963601920000000⟩, + ⟨5, 1, 7, 0, 7, 6, -357634598424050390360178996773723925601320960000000⟩, + ⟨5, 1, 8, 0, 8, 6, 9644679327347527604119380110719947254450356224000000⟩, + ⟨5, 1, 3, 1, 2, 6, 682712257374692902618892833102086182226886656000000⟩, + ⟨5, 1, 4, 1, 3, 6, 45921503848319172681602500462469587287240867840000000⟩, + ⟨5, 1, 5, 1, 4, 6, 108393978228590588159267188274245035397585305600000000⟩, + ⟨5, 1, 6, 1, 5, 6, -49076478109711010687018448457398430166742466560000000⟩, + ⟨5, 1, 7, 1, 6, 6, -24753421887125486817967189316067751515484323840000000⟩, + ⟨5, 1, 8, 1, 7, 6, 8059236524707088949031909647237549392375316480000000⟩, + ⟨5, 1, 3, 2, 1, 6, 5344510703435290838564041662681343767097638912000000⟩, + ⟨5, 1, 4, 2, 2, 6, -30252740042545077900234201345294561173324169216000000⟩, + ⟨5, 1, 5, 2, 3, 6, 159923482520621231586789102291541287392520437760000000⟩, + ⟨5, 1, 6, 2, 4, 6, 17614236922056941353533771671991565516391055360000000⟩, + ⟨5, 1, 7, 2, 5, 6, 2510493594879513722753424507318469547104665600000000⟩, + ⟨5, 1, 8, 2, 6, 6, 438555611397869999085991189815686391555686400000000⟩, + ⟨5, 1, 3, 3, 0, 6, -55131669029532632533882163451525455067721236480000000⟩, + ⟨5, 1, 4, 3, 1, 6, 67168014781592199360472209671686831665057890304000000⟩, + ⟨5, 1, 5, 3, 2, 6, -434469591220248788353872890805883444146890342400000000⟩, + ⟨5, 1, 6, 3, 3, 6, 26740040627810556340359835224251205080108236800000000⟩, + ⟨5, 1, 7, 3, 4, 6, -10086902025259436613867578770457835126034268160000000⟩, + ⟨5, 1, 8, 3, 5, 6, 6977756773109143431702926992215417994220666880000000⟩, + ⟨5, 1, 4, 4, 0, 6, -112192692468449214472092168465008684517260525568000000⟩, + ⟨5, 1, 5, 4, 1, 6, 120425501191876078898858736685895760364122931200000000⟩, + ⟨5, 1, 6, 4, 2, 6, -81308301477611521140327158168523390869254963200000000⟩, + ⟨5, 1, 7, 4, 3, 6, 35776112554132282849559390937253804996527390720000000⟩, + ⟨5, 1, 8, 4, 4, 6, -9983036624610313455405348490420001049422069760000000⟩, + ⟨5, 1, 5, 5, 0, 6, 1378634230693759031501476633257142697936226877440000000⟩, + ⟨5, 1, 6, 5, 1, 6, 125645109483003263348808249783164110666884710400000000⟩, + ⟨5, 1, 7, 5, 2, 6, -69491663133610954868926281325930169337831751680000000⟩, + ⟨5, 1, 8, 5, 3, 6, 13964612816241857845249677932012396887198924800000000⟩, + ⟨5, 1, 6, 6, 0, 6, -184296825851306826210335573867843668785254891520000000⟩, + ⟨5, 1, 7, 6, 1, 6, 190926094196285919700568555180348191827516456960000000⟩, + ⟨5, 1, 8, 6, 2, 6, -49799856023658226413900762986738573261370556416000000⟩, + ⟨5, 1, 7, 7, 0, 6, -647174974858384286382734625583398523761799987200000000⟩, + ⟨5, 1, 8, 7, 1, 6, 93114797560936683366086958077265446910484807680000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0903.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0903.lean new file mode 100644 index 0000000000000000000000000000000000000000..db651a011c601215cc5fe8ac65cba0c1b0e179ba --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0903.lean @@ -0,0 +1,641 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PartsTrace +import OAI.Analysis.LaughlinFock.Sparse0901 +import OAI.Analysis.LaughlinFock.Sparse0902 + +namespace OAI + +/-! Sparse0903. -/ +namespace LaughlinFock +def collectedFourData_9_0_37 : List CollectedFourTerm := [ + ⟨5, 2, 2, 0, 2, 7, 7647729485233453730019146678098739892602064076800000⟩, + ⟨5, 2, 3, 0, 3, 7, 14022224327214846439497205903568886381504626688000000⟩, + ⟨5, 2, 4, 0, 4, 7, 85194419307938174320533850020382543566573718732800000⟩, + ⟨5, 2, 5, 0, 5, 7, -149367806608571352607114636560086415888579821568000000⟩, + ⟨5, 2, 6, 0, 6, 7, -43163891343722350406759775639102083076628414464000000⟩, + ⟨5, 2, 7, 0, 7, 7, 158240129780588385119401471407387187835672985600000⟩, + ⟨5, 2, 8, 0, 8, 7, -3556179303253613974434813600412734588879844147200000⟩, + ⟨5, 2, 2, 1, 1, 7, -40322805324074330634224684931644032778205187276800000⟩, + ⟨5, 2, 3, 1, 2, 7, -1510375068377400629230886162383073878517533900800000⟩, + ⟨5, 2, 4, 1, 3, 7, -50796432732591185136539504471356366137858195456000000⟩, + ⟨5, 2, 5, 1, 4, 7, -79933901147099706266709533449681878579004047360000000⟩, + ⟨5, 2, 6, 1, 5, 7, 27143166165535594770517332441854611980394954752000000⟩, + ⟨5, 2, 7, 1, 6, 7, 10952476939292075899199761800622992586453706342400000⟩, + ⟨5, 2, 8, 1, 7, 7, -2971595960471503734352721085595579649353580544000000⟩, + ⟨5, 2, 2, 2, 0, 7, 42623429122432299131761516359581570050835664076800000⟩, + ⟨5, 2, 3, 2, 1, 7, -11823745116552892881131418525043359631971817881600000⟩, + ⟨5, 2, 4, 2, 2, 7, 33464306387343117428345343907893473112882570854400000⟩, + ⟨5, 2, 5, 2, 3, 7, -117933745507012585503742389007032720411177517056000000⟩, + ⟨5, 2, 6, 2, 4, 7, -9742063368640516289335260707583624628993523712000000⟩, + ⟨5, 2, 7, 2, 5, 7, -1110800895712093768361367549857581027364438016000000⟩, + ⟨5, 2, 8, 2, 6, 7, -161703913177977601735567109735147267602513920000000⟩, + ⟨5, 2, 3, 3, 0, 7, 121968658802825301638772061248054184640998539264000000⟩, + ⟨5, 2, 4, 3, 1, 7, -74298427941395072279580582346053636993102485913600000⟩, + ⟨5, 2, 5, 3, 2, 7, 320394637447303451459361705301522121347238461440000000⟩, + ⟨5, 2, 6, 3, 3, 7, -14789353148188013726580227192142509583693250560000000⟩, + ⟨5, 2, 7, 3, 4, 7, 4463082410356061894994499383487346892454074777600000⟩, + ⟨5, 2, 8, 3, 5, 7, -2572833515501943530020234577233111212217073664000000⟩, + ⟨5, 2, 4, 4, 0, 7, 124102829360420992253392511656192024960147075891200000⟩, + ⟨5, 2, 5, 4, 1, 7, -88806410329926730594615142609701037578880286720000000⟩, + ⟨5, 2, 6, 4, 2, 7, 44969908653807201034053024755828544756976189440000000⟩, + ⟨5, 2, 7, 4, 3, 7, -15829611336703718411158036795699697381643858739200000⟩, + ⟨5, 2, 8, 4, 4, 7, 3680938165294667357295973596381623762842288128000000⟩, + ⟨5, 2, 5, 5, 0, 7, -1016658066390776070355560944742692113572182360064000000⟩, + ⟨5, 2, 6, 5, 1, 7, -69491663133610954868926281325930169337831751680000000⟩, + ⟨5, 2, 7, 5, 2, 7, 30747499938171634858486574128766311355871186124800000⟩, + ⟨5, 2, 8, 5, 3, 7, -5149022107376492430766043700298631332956733440000000⟩, + ⟨5, 2, 6, 6, 0, 7, 101930691861789225343164949408980654767455862784000000⟩, + ⟨5, 2, 7, 6, 1, 7, -84477760421541484967365542971259300088303425945600000⟩, + ⟨5, 2, 8, 6, 2, 7, 18362167500394058716162079244932222661463690444800000⟩, + ⟨5, 2, 7, 7, 0, 7, 286351075828833733916029419694834743456345096192000000⟩, + ⟨5, 2, 8, 7, 1, 7, -34333221942789159796042289567004124999952891904000000⟩ +] + +def collectedFourData_9_0_38 : List CollectedFourTerm := [ + ⟨5, 3, 1, 0, 1, 8, 13567606733560486062928640524791381240053760000000000⟩, + ⟨5, 3, 2, 0, 2, 8, -7684200979569531098105583043255061547570954240000000⟩, + ⟨5, 3, 3, 0, 3, 8, -7044547673853743815519049210623957830677299200000000⟩, + ⟨5, 3, 4, 0, 4, 8, -28533568538825485088741953483225634120065351680000000⟩, + ⟨5, 3, 5, 0, 5, 8, 37520032843535505294591675875343832685582745600000000⟩, + ⟨5, 3, 6, 0, 6, 8, 8673947392775471897359830467311402405110743040000000⟩, + ⟨5, 3, 7, 0, 7, 8, -26499127673884790870984246232433087406407680000000⟩, + ⟨5, 3, 8, 0, 8, 8, 510448353861089056214280381956687381428961280000000⟩, + ⟨5, 3, 1, 1, 0, 8, -16271819223465366794669964788898419195793899520000000⟩, + ⟨5, 3, 2, 1, 1, 8, 40515102000994099445315102287051857441576714240000000⟩, + ⟨5, 3, 3, 1, 2, 8, 758788971442596416346317440124887744873758720000000⟩, + ⟨5, 3, 4, 1, 3, 8, 17012892472032820101288488510087875677231513600000000⟩, + ⟨5, 3, 5, 1, 4, 8, 20078775101856514235559966061752905065562112000000000⟩, + ⟨5, 3, 6, 1, 5, 8, -5454522010501271753159063947541225600156958720000000⟩, + ⟨5, 3, 7, 1, 6, 8, -1834118091043065076716831677876233858417950720000000⟩, + ⟨5, 3, 8, 1, 7, 8, 426538185230185200614399730293470601517465600000000⟩, + ⟨5, 3, 2, 2, 0, 8, -42826697315537789319428807733332507200050954240000000⟩, + ⟨5, 3, 3, 2, 1, 8, 5940065870676042750633822022914410483747389440000000⟩, + ⟨5, 3, 4, 2, 2, 8, -11207965118655835733852641540873341895327088640000000⟩, + ⟨5, 3, 5, 2, 3, 8, 29624040850917549325946987614307342630466355200000000⟩, + ⟨5, 3, 6, 2, 4, 8, 1957704519357766852448610353114121534512824320000000⟩, + ⟨5, 3, 7, 2, 5, 8, 186016371425848234317915034564595091819724800000000⟩, + ⟨5, 3, 8, 2, 6, 8, 23210723997824405733794095103463766622208000000000⟩, + ⟨5, 3, 3, 3, 0, 8, -61275159461320974399863601034112835788577177600000000⟩, + ⟨5, 3, 4, 3, 1, 8, 24884250672922272819928098606967393007865692160000000⟩, + ⟨5, 3, 5, 3, 2, 8, -80480644342712388899370403048503073044430848000000000⟩, + ⟨5, 3, 6, 3, 3, 8, 2971976510621491175375762526467148136159641600000000⟩, + ⟨5, 3, 7, 3, 4, 8, -747394423747514448991412427612008490498785280000000⟩, + ⟨5, 3, 8, 3, 5, 8, 369300454435760510596458092718824497977753600000000⟩, + ⟨5, 3, 4, 4, 0, 8, -41564889064133650208460461158171536846980382720000000⟩, + ⟨5, 3, 5, 4, 1, 8, 22307480493618873422834279610353104793370624000000000⟩, + ⟨5, 3, 6, 4, 2, 8, -9036873409185162063692033160595253995398758400000000⟩, + ⟨5, 3, 7, 4, 3, 8, 2650850276860321467163017024095956619766005760000000⟩, + ⟨5, 3, 8, 4, 4, 8, -528356043639322031903541476614720388805427200000000⟩, + ⟨5, 3, 5, 5, 0, 8, 255376609643796533064135315441674513011231948800000000⟩, + ⟨5, 3, 6, 5, 1, 8, 13964612816241857845249677932012396887198924800000000⟩, + ⟨5, 3, 7, 5, 2, 8, -5149022107376492430766043700298631332956733440000000⟩, + ⟨5, 3, 8, 5, 3, 8, 739082491228717623250023207405624131321856000000000⟩, + ⟨5, 3, 6, 6, 0, 8, -20483358459916844581261289054823415976023818240000000⟩, + ⟨5, 3, 7, 6, 1, 8, 14146771505548214869499752608636143182471495680000000⟩, + ⟨5, 3, 8, 6, 2, 8, -2635676487212627820742563114103819789160939520000000⟩, + ⟨5, 3, 7, 7, 0, 8, -47952777392586359435102041205683117650188697600000000⟩, + ⟨5, 3, 8, 7, 1, 8, 4928136387107898385956070830066419692575129600000000⟩ +] + +def collectedFourData_9_0_39 : List CollectedFourTerm := [ + ⟨6, 0, 3, 0, 3, 6, 9296983689654819123302832285820571905695940608000000⟩, + ⟨6, 0, 4, 0, 4, 6, 112970825208989558059914145191193782674469263769600000⟩, + ⟨6, 0, 5, 0, 5, 6, -297100523296625941738100359305719392433879384064000000⟩, + ⟨6, 0, 6, 0, 6, 6, -114473705295321355834057202700164889340224208896000000⟩, + ⟨6, 0, 7, 0, 7, 6, 524580077771156026929291985617594182635880448000000⟩, + ⟨6, 0, 8, 0, 8, 6, -14146860102217641925954638325711149820156261171200000⟩, + ⟨6, 0, 3, 1, 2, 6, -1001405486625462073241069661370076356844244172800000⟩, + ⟨6, 0, 4, 1, 3, 6, -67357873556619876605627245761314433536719060992000000⟩, + ⟨6, 0, 5, 1, 4, 6, -158992786994445348775893383210636687990618849280000000⟩, + ⟨6, 0, 6, 1, 5, 6, 71985604348606995468516942116866132912770121728000000⟩, + ⟨6, 0, 7, 1, 6, 6, 36308433344734500004417291973557794381383073792000000⟩, + ⟨6, 0, 8, 1, 7, 6, -11821325289937827374388340977703898036016513024000000⟩, + ⟨6, 0, 3, 2, 1, 6, -7839352939596129338545144265299298076438665625600000⟩, + ⟨6, 0, 4, 2, 2, 6, 44374858568609983751104585006888452061754346700800000⟩, + ⟨6, 0, 5, 2, 3, 6, -234576501456465182753352751273130897250648588288000000⟩, + ⟨6, 0, 6, 2, 4, 6, -25836643924188115922098187299518496131061383168000000⟩, + ⟨6, 0, 7, 2, 5, 6, -3682403579097679205755082641218443716885217280000000⟩, + ⟨6, 0, 8, 2, 6, 6, -643275392671293908925130131812302283153080320000000⟩, + ⟨6, 0, 3, 3, 0, 6, 80867386306047536723348110631736529521972609024000000⟩, + ⟨6, 0, 4, 3, 1, 6, -98522353746332313669161834086819879556727649075200000⟩, + ⟨6, 0, 5, 3, 2, 6, 637281999436980637175559253204778327630539653120000000⟩, + ⟨6, 0, 6, 3, 3, 6, -39222414872479572402458631097908805538508963840000000⟩, + ⟨6, 0, 7, 3, 4, 6, 14795514394294096901730158143084144080671735808000000⟩, + ⟨6, 0, 8, 3, 5, 6, -10235005804347953421900535405567619966429036544000000⟩, + ⟨6, 0, 4, 4, 0, 6, 164564758554681921093627932634032233280719709798400000⟩, + ⟨6, 0, 5, 4, 1, 6, -176640680345921808239429687903549017305970114560000000⟩, + ⟨6, 0, 6, 4, 2, 6, 119263391463016015453161355940199940619407196160000000⟩, + ⟨6, 0, 7, 4, 3, 6, -52476566833009919726300032016955466264489230336000000⟩, + ⟨6, 0, 8, 4, 4, 6, 14643164145771315211041940606390141358218149888000000⟩, + ⟨6, 0, 5, 5, 0, 6, -2022187045498883097630033528950617980307318505472000000⟩, + ⟨6, 0, 6, 5, 1, 6, -184296825851306826210335573867843668785254891520000000⟩, + ⟨6, 0, 7, 5, 2, 6, 101930691861789225343164949408980654767455862784000000⟩, + ⟨6, 0, 8, 5, 3, 6, -20483358459916844581261289054823415976023818240000000⟩, + ⟨6, 0, 6, 6, 0, 6, 270327433822337512227464019279862478110118117376000000⟩, + ⟨6, 0, 7, 6, 1, 6, -280051275193668137614959685660935230404058677248000000⟩, + ⟨6, 0, 8, 6, 2, 6, 73046658407773907082724045048773135022372474060800000⟩, + ⟨6, 0, 7, 7, 0, 6, 949279236793010010914023341463168297410609807360000000⟩, + ⟨6, 0, 8, 7, 1, 6, -136581214349525259373647929443524514805484355584000000⟩ +] + +def collectedFourData_9_0_40 : List CollectedFourTerm := [ + ⟨6, 1, 2, 0, 2, 7, -21011889113633343993508145616811513568894228889600000⟩, + ⟨6, 1, 3, 0, 3, 7, -38525607274527745191004517029859350772906459136000000⟩, + ⟨6, 1, 4, 0, 4, 7, -234068908302152927615897647854387023915360295321600000⟩, + ⟨6, 1, 5, 0, 5, 7, 410383211862536945881735014121353913421839466496000000⟩, + ⟨6, 1, 6, 0, 6, 7, 118591393743515312572272383162749139236272734208000000⟩, + ⟨6, 1, 7, 0, 7, 7, -434759632476092523020221724560144579840652083200000⟩, + ⟨6, 1, 8, 0, 8, 7, 9770487480295841688300085157394112020488808038400000⟩, + ⟨6, 1, 2, 1, 1, 7, 110785601903936951192061997429355488520143739289600000⟩, + ⟨6, 1, 3, 1, 2, 7, 4149706591743229964906321552646151397806021017600000⟩, + ⟨6, 1, 4, 1, 3, 7, 139561554054204365395623855298470443000405164032000000⟩, + ⟨6, 1, 5, 1, 4, 7, 219615805000157907252614723323004390387660881920000000⟩, + ⟨6, 1, 6, 1, 5, 7, -74574970095944558098263302587762491290019692544000000⟩, + ⟨6, 1, 7, 1, 6, 7, -30091575730075189290088049662451876931958525132800000⟩, + ⟨6, 1, 8, 1, 7, 7, 8164363675847513186709303012511704817197907968000000⟩, + ⟨6, 1, 2, 2, 0, 7, -117106491291646244182255132571247262208433428889600000⟩, + ⟨6, 1, 3, 2, 1, 7, 32485356833890328986207051421868731442088063795200000⟩, + ⟨6, 1, 4, 2, 2, 7, -91942098165628488070524059656169368112161672396800000⟩, + ⟨6, 1, 5, 2, 3, 7, 324019146876657544512098227881966297336860639232000000⟩, + ⟨6, 1, 6, 2, 4, 7, 26766003640048367082378774293813899800990449664000000⟩, + ⟨6, 1, 7, 2, 5, 7, 3051889491265738137416331847089321223863140352000000⟩, + ⟨6, 1, 8, 2, 6, 7, 444276265196969248204813977706992268203786240000000⟩, + ⟨6, 1, 3, 3, 0, 7, -335104940499253706054206042786986520085746679808000000⟩, + ⟨6, 1, 4, 3, 1, 7, 204132524854102509482463902759476003663101768499200000⟩, + ⟨6, 1, 5, 3, 2, 7, -880273891439819186898274635129538642555101511680000000⟩, + ⟨6, 1, 6, 3, 3, 7, 40633268869159636744463785839978453410324152320000000⟩, + ⟨6, 1, 7, 3, 4, 7, -12262174399928628159408714946692693502477939507200000⟩, + ⟨6, 1, 8, 3, 5, 7, 7068776770928902741944527143277108839588036608000000⟩, + ⟨6, 1, 4, 4, 0, 7, -340968504998019815873189798934963583553399842406400000⟩, + ⟨6, 1, 5, 4, 1, 7, 243992736672390576948134266276152760084557987840000000⟩, + ⟨6, 1, 6, 4, 2, 7, -123553367820929591937403136401702001491763527680000000⟩, + ⟨6, 1, 7, 4, 3, 7, 43491344556701277050908807709410704707532777062400000⟩, + ⟨6, 1, 8, 4, 4, 7, -10113258413840397188137396614132517802990370816000000⟩, + ⟨6, 1, 5, 5, 0, 7, 2793235116217213067313894870910679366724545937408000000⟩, + ⟨6, 1, 6, 5, 1, 7, 190926094196285919700568555180348191827516456960000000⟩, + ⟨6, 1, 7, 5, 2, 7, -84477760421541484967365542971259300088303425945600000⟩, + ⟨6, 1, 8, 5, 3, 7, 14146771505548214869499752608636143182471495680000000⟩, + ⟨6, 1, 6, 6, 0, 7, -280051275193668137614959685660935230404058677248000000⟩, + ⟨6, 1, 7, 6, 1, 7, 232099911218463908677410740946443172063229457203200000⟩, + ⟨6, 1, 8, 6, 2, 7, -50449460607779891849277875553356671048184600985600000⟩, + ⟨6, 1, 7, 7, 0, 7, -786740308283982178475659799471591986134698164224000000⟩, + ⟨6, 1, 8, 7, 1, 7, 94329415517189601740353918690739767222770597888000000⟩ +] + +def collectedFourData_9_0_41 : List CollectedFourTerm := [ + ⟨6, 2, 1, 0, 1, 8, -48384074145692090436824756909183027683472179200000000⟩, + ⟨6, 2, 2, 0, 2, 8, 27402986926665144561661120111883052421816831180800000⟩, + ⟨6, 2, 3, 0, 3, 8, 25121889487812132754598977030149518056608497664000000⟩, + ⟨6, 2, 4, 0, 4, 8, 101754887426739449216458007233435045205099780505600000⟩, + ⟨6, 2, 5, 0, 5, 8, -133801936236843179701286835170705157024122929152000000⟩, + ⟨6, 2, 6, 0, 6, 8, -30932567698160724141168033949332748455815990476800000⟩, + ⟨6, 2, 7, 0, 7, 8, 94499773124905262446066723315465400620784025600000⟩, + ⟨6, 2, 8, 0, 8, 8, -1820333643638868487638107743234888158536112537600000⟩, + ⟨6, 2, 1, 1, 0, 8, 58027692227105068210413406424038198356967056998400000⟩, + ⟨6, 2, 2, 1, 1, 8, -144482791824107325027745892586675137061868850380800000⟩, + ⟨6, 2, 3, 1, 2, 8, -2705952683932011080072834145568083568002229862400000⟩, + ⟨6, 2, 4, 1, 3, 8, -60670468046762615069176223132318207271304691712000000⟩, + ⟨6, 2, 5, 1, 4, 8, -71603854855244415894981377428101566550811607040000000⟩, + ⟨6, 2, 6, 1, 5, 8, 19451624930474807783309733738073682391893173862400000⟩, + ⟨6, 2, 7, 1, 6, 8, 6540733929844287626415481953618827718083110502400000⟩, + ⟨6, 2, 8, 1, 7, 8, -1521097684022448116259060708471178897026711552000000⟩, + ⟨6, 2, 2, 2, 0, 8, 152726279514317335831257094454548223896658431180800000⟩, + ⟨6, 2, 3, 2, 1, 8, -21183145499505674585917268351192008604049525964800000⟩, + ⟨6, 2, 4, 2, 2, 8, 39969246306497613226331115567351231880541031628800000⟩, + ⟨6, 2, 5, 2, 3, 8, -105643671516536011297705260494991174043837661184000000⟩, + ⟨6, 2, 6, 2, 4, 8, -6981461246636921962061158806913391447176013414400000⟩, + ⟨6, 2, 7, 2, 5, 8, -663361643960249915241323128878015106479292416000000⟩, + ⟨6, 2, 8, 2, 6, 8, -82772843651786716374994146711391064933007360000000⟩, + ⟨6, 2, 3, 3, 0, 8, 218516199421682113741492932783357846286963310592000000⟩, + ⟨6, 2, 4, 3, 1, 8, -88740885055318732650808788204892180174672704307200000⟩, + ⟨6, 2, 5, 3, 2, 8, 287005773357125515916114462971173219036467036160000000⟩, + ⟨6, 2, 6, 3, 3, 8, -10598503824073448834981349886288122256369385472000000⟩, + ⟨6, 2, 7, 3, 4, 8, 2665318056811536473398474011951992241072478617600000⟩, + ⟨6, 2, 8, 3, 5, 8, -1316979546971917034245915806857339781368512512000000⟩, + ⟨6, 2, 4, 4, 0, 8, 148226486353113104663778306375490888150142051942400000⟩, + ⟨6, 2, 5, 4, 1, 8, -79551744932069731790404257957880999041910702080000000⟩, + ⟨6, 2, 6, 4, 2, 8, 32226815064863323400425899471119491808549142528000000⟩, + ⟨6, 2, 7, 4, 3, 8, -9453320608673021548159474108180356815786292019200000⟩, + ⟨6, 2, 8, 4, 4, 8, 1884195090025345438083797364435470915337191424000000⟩, + ⟨6, 2, 5, 5, 0, 8, -910710419216163811184495977551744108187663466496000000⟩, + ⟨6, 2, 6, 5, 1, 8, -49799856023658226413900762986738573261370556416000000⟩, + ⟨6, 2, 7, 5, 2, 8, 18362167500394058716162079244932222661463690444800000⟩, + ⟨6, 2, 8, 5, 3, 8, -2635676487212627820742563114103819789160939520000000⟩, + ⟨6, 2, 6, 6, 0, 8, 73046658407773907082724045048773135022372474060800000⟩, + ⟨6, 2, 7, 6, 1, 8, -50449460607779891849277875553356671048184600985600000⟩, + ⟨6, 2, 8, 6, 2, 8, 9399208650845623673716810143596616490699613798400000⟩, + ⟨6, 2, 7, 7, 0, 8, 171006632372067517588423261671989550453979348992000000⟩, + ⟨6, 2, 8, 7, 1, 8, -17574456647840800566005871914588507855684370432000000⟩ +] + +def collectedFourData_9_0_42 : List CollectedFourTerm := [ + ⟨7, 0, 2, 0, 2, 7, 71223207420053882809865495579060421231768502272000000⟩, + ⟨7, 0, 3, 0, 3, 7, 130588796802514265970903813995455142486888939520000000⟩, + ⟨7, 0, 4, 0, 4, 7, 793414543377392796505508262542185346537474752512000000⟩, + ⟨7, 0, 5, 0, 5, 7, -1391060483049502671482091123033326816047367454720000000⟩, + ⟨7, 0, 6, 0, 6, 7, -401984771057414098041499376333008414381241794560000000⟩, + ⟨7, 0, 7, 0, 7, 7, 1473688315898251732108166983599525215625805824000000⟩, + ⟨7, 0, 8, 0, 8, 7, -33118652618085271214600989139593876191930482688000000⟩, + ⟨7, 0, 2, 1, 1, 7, -375525773093859789401858020445556044566754230272000000⟩, + ⟨7, 0, 3, 1, 2, 7, -14066103800458612417791517456519178996240351232000000⟩, + ⟨7, 0, 4, 1, 3, 7, -473066531929210527135172832114395491204323082240000000⟩, + ⟨7, 0, 5, 1, 4, 7, -744423404657098296086173768568987792445957734400000000⟩, + ⟨7, 0, 6, 1, 5, 7, 252783961249894668986512279944798293607925678080000000⟩, + ⟨7, 0, 7, 1, 6, 7, 102000278424694316250691412615579679364057399296000000⟩, + ⟨7, 0, 8, 1, 7, 7, -27674435382411469963891614624663921141491957760000000⟩, + ⟨7, 0, 2, 2, 0, 7, 396951453264993602044871766249667058959512502272000000⟩, + ⟨7, 0, 3, 2, 1, 7, -110114387877356941725709279837822597523690225664000000⟩, + ⟨7, 0, 4, 2, 2, 7, 311652659733324287460943689698207936627160907776000000⟩, + ⟨7, 0, 5, 2, 3, 7, -1098315471838815857361735493927902874265966346240000000⟩, + ⟨7, 0, 6, 2, 4, 7, -90727712237171477568486800787064468915334676480000000⟩, + ⟨7, 0, 7, 2, 5, 7, -10344874612843219123748146807849505402797424640000000⟩, + ⟨7, 0, 8, 2, 6, 7, -1505946486620259207720132289938971926777036800000000⟩, + ⟨7, 0, 3, 3, 0, 7, 1135892568040307586505083267333366291349697986560000000⟩, + ⟨7, 0, 4, 3, 1, 7, -691940314373236777458987014038081037150604754944000000⟩, + ⟨7, 0, 5, 3, 2, 7, 2983831183260749224424725053542753804115089817600000000⟩, + ⟨7, 0, 6, 3, 3, 7, -137733057754679132015608391114626188267906662400000000⟩, + ⟨7, 0, 7, 3, 4, 7, 41564629719101579594861127878736668344927125504000000⟩, + ⟨7, 0, 8, 3, 5, 7, -23960765804501727979165489746526061210432962560000000⟩, + ⟨7, 0, 4, 4, 0, 7, 1155768071297438014919844369961325814241661288448000000⟩, + ⟨7, 0, 5, 4, 1, 7, -827052969822154830668279588456729862669651148800000000⟩, + ⟨7, 0, 6, 4, 2, 7, 418804187294448341396078104163980621662230937600000000⟩, + ⟨7, 0, 7, 4, 3, 7, -147420969032676155688758208556370955451779514368000000⟩, + ⟨7, 0, 8, 4, 4, 7, 34280530313392976952451081470280640970746757120000000⟩, + ⟨7, 0, 5, 5, 0, 7, -9468123640831261233707413950839361867996526018560000000⟩, + ⟨7, 0, 6, 5, 1, 7, -647174974858384286382734625583398523761799987200000000⟩, + ⟨7, 0, 7, 5, 2, 7, 286351075828833733916029419694834743456345096192000000⟩, + ⟨7, 0, 8, 5, 3, 7, -47952777392586359435102041205683117650188697600000000⟩, + ⟨7, 0, 6, 6, 0, 7, 949279236793010010914023341463168297410609807360000000⟩, + ⟨7, 0, 7, 6, 1, 7, -786740308283982178475659799471591986134698164224000000⟩, + ⟨7, 0, 8, 6, 2, 7, 171006632372067517588423261671989550453979348992000000⟩, + ⟨7, 0, 7, 7, 0, 7, 2666783926927827546331119809714127849641402695680000000⟩, + ⟨7, 0, 8, 7, 1, 7, -319744859248950283955414194371921423871676252160000000⟩ +] + +def collectedFourData_9_0_43 : List CollectedFourTerm := [ + ⟨7, 1, 1, 0, 1, 8, 90467596273956427279293957043366031435759616000000000⟩, + ⟨7, 1, 2, 0, 2, 8, -51237569422474422526596408340143451228480733184000000⟩, + ⟨7, 1, 3, 0, 3, 8, -46972418010497178631671245445560367701525790720000000⟩, + ⟨7, 1, 4, 0, 4, 8, -190259299928006772952918345572461111167300927488000000⟩, + ⟨7, 1, 5, 0, 5, 8, 250180245501838199030285101723742444377300008960000000⟩, + ⟨7, 1, 6, 0, 6, 8, 57837110570879594056846461355716186078669963264000000⟩, + ⟨7, 1, 7, 0, 7, 8, -176693828992190978628390942245623218818777088000000⟩, + ⟨7, 1, 8, 0, 8, 8, 3403624272332670671897448948684766091409358848000000⟩, + ⟨7, 1, 1, 1, 0, 8, -108499044898610401111217453902847549900882706432000000⟩, + ⟨7, 1, 2, 1, 1, 8, 270151100544335217009799667402102850397283549184000000⟩, + ⟨7, 1, 3, 1, 2, 8, 5059537446335242715121664667040238130694193152000000⟩, + ⟨7, 1, 4, 1, 3, 8, 113440455478782479884311253062470553279670517760000000⟩, + ⟨7, 1, 5, 1, 4, 8, 133883488463527507931333073106222126789243699200000000⟩, + ⟨7, 1, 6, 1, 5, 8, -36370268154429498274186950023441331503499313152000000⟩, + ⟨7, 1, 7, 1, 6, 8, -12229736477311637342236419069938152192818020352000000⟩, + ⟨7, 1, 8, 1, 7, 8, 2844118722971268933866283144055939954334760960000000⟩, + ⟨7, 1, 2, 2, 0, 8, -285564612726083741074268783644334054525248733184000000⟩, + ⟨7, 1, 3, 2, 1, 8, 39607831475522475895475966252916729294046101504000000⟩, + ⟨7, 1, 4, 2, 2, 8, -74733715630114961200570441613654127606679732224000000⟩, + ⟨7, 1, 5, 2, 3, 8, 197530472421107460915032592483194132702240440320000000⟩, + ⟨7, 1, 6, 2, 4, 8, 13053799801173960958474297477522120720999514112000000⟩, + ⟨7, 1, 7, 2, 5, 8, 1240340637886675168715659878436314526966087680000000⟩, + ⟨7, 1, 8, 2, 6, 8, 154767045441209094478274584452935610846412800000000⟩, + ⟨7, 1, 3, 3, 0, 8, -408577319245039280006092507027892819720310620160000000⟩, + ⟨7, 1, 4, 3, 1, 8, 165925972624877491105053048582692355597775405056000000⟩, + ⟨7, 1, 5, 3, 2, 8, -536637786106709209880990887989110793910930636800000000⟩, + ⟨7, 1, 6, 3, 3, 8, 19816875325072834785327661340325882521777602560000000⟩, + ⟨7, 1, 7, 3, 4, 8, -4983559614662604148320065090000346274225717248000000⟩, + ⟨7, 1, 8, 3, 5, 8, 2462462619368350388387986548757977429190901760000000⟩, + ⟨7, 1, 4, 4, 0, 8, -277150987412135687494735306277893425933217431552000000⟩, + ⟨7, 1, 5, 4, 1, 8, 148744298004594984044102766277119523011585638400000000⟩, + ⟨7, 1, 6, 4, 2, 8, -60257069003832412037134758158153000198539837440000000⟩, + ⟨7, 1, 7, 4, 3, 8, 17675634129083525776132537439257322015284002816000000⟩, + ⟨7, 1, 8, 4, 4, 8, -3523031156750176971714724824428731214352875520000000⟩, + ⟨7, 1, 5, 5, 0, 8, 1702828543955287164330296790021190555166394286080000000⟩, + ⟨7, 1, 6, 5, 1, 8, 93114797560936683366086958077265446910484807680000000⟩, + ⟨7, 1, 7, 5, 2, 8, -34333221942789159796042289567004124999952891904000000⟩, + ⟨7, 1, 8, 5, 3, 8, 4928136387107898385956070830066419692575129600000000⟩, + ⟨7, 1, 6, 6, 0, 8, -136581214349525259373647929443524514805484355584000000⟩, + ⟨7, 1, 7, 6, 1, 8, 94329415517189601740353918690739767222770597888000000⟩, + ⟨7, 1, 8, 6, 2, 8, -17574456647840800566005871914588507855684370432000000⟩, + ⟨7, 1, 7, 7, 0, 8, -319744859248950283955414194371921423871676252160000000⟩, + ⟨7, 1, 8, 7, 1, 8, 32860375584815663952735793995944586642834063360000000⟩ +] + +def collectedFourData_9_0 : List (List CollectedFourTerm) := [ + collectedFourData_9_0_0, + collectedFourData_9_0_1, + collectedFourData_9_0_2, + collectedFourData_9_0_3, + collectedFourData_9_0_4, + collectedFourData_9_0_5, + collectedFourData_9_0_6, + collectedFourData_9_0_7, + collectedFourData_9_0_8, + collectedFourData_9_0_9, + collectedFourData_9_0_10, + collectedFourData_9_0_11, + collectedFourData_9_0_12, + collectedFourData_9_0_13, + collectedFourData_9_0_14, + collectedFourData_9_0_15, + collectedFourData_9_0_16, + collectedFourData_9_0_17, + collectedFourData_9_0_18, + collectedFourData_9_0_19, + collectedFourData_9_0_20, + collectedFourData_9_0_21, + collectedFourData_9_0_22, + collectedFourData_9_0_23, + collectedFourData_9_0_24, + collectedFourData_9_0_25, + collectedFourData_9_0_26, + collectedFourData_9_0_27, + collectedFourData_9_0_28, + collectedFourData_9_0_29, + collectedFourData_9_0_30, + collectedFourData_9_0_31, + collectedFourData_9_0_32, + collectedFourData_9_0_33, + collectedFourData_9_0_34, + collectedFourData_9_0_35, + collectedFourData_9_0_36, + collectedFourData_9_0_37, + collectedFourData_9_0_38, + collectedFourData_9_0_39, + collectedFourData_9_0_40, + collectedFourData_9_0_41, + collectedFourData_9_0_42, + collectedFourData_9_0_43 +] + +theorem collectedFourChecked_9_0 : collectNumericRowParts 9 0 = collectedFourData_9_0 := by + decide +kernel + +def collectedFourData_9_1_0 : List CollectedFourTerm := [ + ⟨0, 1, 8, 1, 8, 0, 56723338964805595530929605258468289423370878976000000⟩, + ⟨0, 1, 8, 2, 7, 0, 24355716481599897326420689829408853411414147072000000⟩, + ⟨0, 1, 8, 3, 6, 0, -1307875901668456584340190112931827130029834240000000⟩, + ⟨0, 1, 8, 4, 5, 0, -17801672832357293491062858431608300349159374848000000⟩, + ⟨0, 1, 8, 5, 4, 0, -8911558357660444078196155392636693360509190144000000⟩, + ⟨0, 1, 8, 6, 3, 0, 47315034882383871532229705755361049959001489408000000⟩, + ⟨0, 1, 8, 7, 2, 0, -18610263040687662023800485001954017403471921152000000⟩ +] + +def collectedFourData_9_1_1 : List CollectedFourTerm := [ + ⟨0, 2, 7, 0, 8, 1, 62822364857219996757787360765219727248698900480000000⟩, + ⟨0, 2, 7, 1, 7, 1, -4969853825842115700655875757301225203590758400000000⟩, + ⟨0, 2, 8, 1, 8, 1, -71821454090837103110257157637922310291793641472000000⟩, + ⟨0, 2, 7, 2, 6, 1, -3117078242687373059918210466416218179442311168000000⟩, + ⟨0, 2, 8, 2, 7, 1, -30838505014981829971544030689925013690944323584000000⟩, + ⟨0, 2, 7, 3, 5, 1, -7476269756916410851239883797762933723708260352000000⟩, + ⟨0, 2, 8, 3, 6, 1, 1655994705926514365409294010316987760409313280000000⟩, + ⟨0, 2, 7, 4, 4, 1, 3865267980443553140305362160717742965493071872000000⟩, + ⟨0, 2, 8, 4, 5, 1, 22539964173521803300085276851997384862288838656000000⟩, + ⟨0, 2, 7, 5, 3, 1, 4409049743465271188436862225688743231623266304000000⟩, + ⟨0, 2, 8, 5, 4, 1, 11283557899503119482351002190422054580852359168000000⟩, + ⟨0, 2, 7, 6, 2, 1, 31205034343347737977824469504401955190476898304000000⟩, + ⟨0, 2, 8, 6, 3, 1, -59908931096597619089274501323259834772777598976000000⟩, + ⟨0, 2, 7, 7, 1, 1, -161440364558223193846905220371010071612402696192000000⟩, + ⟨0, 2, 8, 7, 2, 1, 23563777749833530675844192329001860227183673344000000⟩ +] + +def collectedFourData_9_1_2 : List CollectedFourTerm := [ + ⟨0, 3, 6, 0, 7, 2, -20372594240050700994801567377050881544023755980800000⟩, + ⟨0, 3, 7, 0, 8, 2, -59758950892437995811592191312328261029832163328000000⟩, + ⟨0, 3, 6, 1, 6, 2, 7507409310611302778425830937078548039027444940800000⟩, + ⟨0, 3, 7, 1, 7, 2, 4727508290973887038058176422234107098158858240000000⟩, + ⟨0, 3, 8, 1, 8, 2, 34159608268428308983985724848582590981419407769600000⟩, + ⟨0, 3, 6, 2, 5, 2, 134878391794083006563091368941999093143778099200000⟩, + ⟨0, 3, 7, 2, 6, 2, 2965079809650524249543286340392774066089282764800000⟩, + ⟨0, 3, 8, 2, 7, 2, 14667361782503046194576578724655440242725303091200000⟩, + ⟨0, 3, 6, 3, 4, 2, -2184047016238363699848399093196376880463006924800000⟩, + ⟨0, 3, 7, 3, 5, 2, 7111703583231803019824149737547895111802893107200000⟩, + ⟨0, 3, 8, 3, 6, 2, -787621625948920489396479392422188627687112704000000⟩, + ⟨0, 3, 6, 4, 3, 2, 2757599090220457522780380015031849610331448934400000⟩, + ⟨0, 3, 7, 4, 4, 2, -3676785488009098727411419561167070960119132979200000⟩, + ⟨0, 3, 8, 4, 5, 2, -10720422696790587196246274773680329506926939340800000⟩, + ⟨0, 3, 6, 5, 2, 2, -5986021067187185914555964959350507370209450393600000⟩, + ⟨0, 3, 7, 5, 3, 2, -4194050760439917620923952247766944791285622374400000⟩, + ⟨0, 3, 8, 5, 4, 2, -5366668255333061412437518580022035940588807782400000⟩, + ⟨0, 3, 6, 6, 1, 2, 11210635667623561965297907470635326610106168115200000⟩, + ⟨0, 3, 7, 6, 2, 2, -29683379782966650120397092102948926654612137574400000⟩, + ⟨0, 3, 8, 6, 3, 2, 28493792613161859567987621518347570583759015116800000⟩, + ⟨0, 3, 6, 7, 0, 2, 3326564409022108999185394352579023928281163366400000⟩, + ⟨0, 3, 7, 7, 1, 2, 153568030105498116088661307828197845221917274931200000⟩, + ⟨0, 3, 8, 7, 2, 2, -11207367317300144149253455497418205455575102259200000⟩ +] + +def collectedFourData_9_1_3 : List CollectedFourTerm := [ + ⟨0, 4, 5, 0, 6, 3, -5415933284964979854106066901825516394663798374400000⟩, + ⟨0, 4, 6, 0, 7, 3, -7457731428010067554426376679105246454379603558400000⟩, + ⟨0, 4, 7, 0, 8, 3, -10937885497648236478215536229393446916191158272000000⟩, + ⟨0, 4, 5, 1, 5, 3, 1775249859298442972355718991756551441084317696000000⟩, + ⟨0, 4, 6, 1, 6, 3, 2748213688397789966811642217453542273563649638400000⟩, + ⟨0, 4, 7, 1, 7, 3, 865292037487867284099990031414997368449269760000000⟩, + ⟨0, 4, 8, 1, 8, 3, 4168233414462067760172764911593009024454990233600000⟩, + ⟨0, 4, 5, 2, 4, 3, -1333566719813071627596432623237356440266578329600000⟩, + ⟨0, 4, 6, 2, 5, 3, 49374508204002039818412679586577934515280281600000⟩, + ⟨0, 4, 7, 2, 6, 3, 542708715012766870660946154377078873475199795200000⟩, + ⟨0, 4, 8, 2, 7, 3, 1789744981951048551078525885917528673284731699200000⟩, + ⟨0, 4, 5, 3, 3, 3, 398210445349035788954293902493201163535305932800000⟩, + ⟨0, 4, 6, 3, 4, 3, -799507214512309626441208002278672670749255270400000⟩, + ⟨0, 4, 7, 3, 5, 3, 1301679469350380478714099974976806205755542732800000⟩, + ⟨0, 4, 8, 3, 6, 3, -96107389564754090268406791201426270075224064000000⟩, + ⟨0, 4, 5, 4, 2, 3, 822418004534758032008643574593426701949075456000000⟩, + ⟨0, 4, 6, 4, 3, 3, 1009465616340567478172026025209479033206813491200000⟩, + ⟨0, 4, 7, 4, 4, 3, -672974643407725083116159604768068379503021260800000⟩, + ⟨0, 4, 8, 4, 5, 3, -1308130460711985638603496758749542716646673612800000⟩, + ⟨0, 4, 5, 5, 1, 3, 277660924099998381242309318521965763055792947200000⟩, + ⟨0, 4, 6, 5, 2, 3, -2191283884392581917634213888076841152196431052800000⟩, + ⟨0, 4, 7, 5, 3, 3, -767651478212635701970882519651122849550801305600000⟩, + ⟨0, 4, 8, 5, 4, 3, -654853116886792139410796734582513926373008998400000⟩, + ⟨0, 4, 5, 6, 0, 3, -14743468044221935016231001618805142631441078681600000⟩, + ⟨0, 4, 6, 6, 1, 3, 4103842100877123980339123731964914523522570649600000⟩, + ⟨0, 4, 7, 6, 2, 3, -5433050687815547505130353670411537802157726105600000⟩, + ⟨0, 4, 8, 6, 3, 3, 3476877648644015891620387735636466051861761228800000⟩, + ⟨0, 4, 6, 7, 0, 3, 1217744959141844593939359486117734847282885427200000⟩, + ⟨0, 4, 7, 7, 1, 3, 28108082627097944276048257125664471646993173708800000⟩, + ⟨0, 4, 8, 7, 2, 3, -1367548555388335195394801575641264938546311987200000⟩ +] + +def collectedFourData_9_1_4 : List CollectedFourTerm := [ + ⟨0, 5, 4, 0, 5, 4, 182901405765343498628101457004735384252745179463680000⟩, + ⟨0, 5, 5, 0, 6, 4, 319049947695547491666948391203688417990899086131200000⟩, + ⟨0, 5, 6, 0, 7, 4, 219665632573374489230394206888267186691439696281600000⟩, + ⟨0, 5, 7, 0, 8, 4, 214781805973146163277211414010025580206544125952000000⟩, + ⟨0, 5, 4, 1, 4, 4, 56284831559367464100191026207044215365172660797440000⟩, + ⟨0, 5, 5, 1, 5, 4, -104579090057856694817286802409440120427205623808000000⟩, + ⟨0, 5, 6, 1, 6, 4, -80947953695590266087879935176964278729553058201600000⟩, + ⟨0, 5, 7, 1, 7, 4, -16991308470525401525134972766820553491386204160000000⟩, + ⟨0, 5, 8, 1, 8, 4, -61387141555029106821708884881427072124319904563200000⟩, + ⟨0, 5, 4, 2, 3, 4, 88373427408266631990920164193143976938287409397760000⟩, + ⟨0, 5, 5, 2, 4, 4, 78559755044625612243191090080679173082212781260800000⟩, + ⟨0, 5, 6, 2, 5, 4, -1454313913329721887109619933681649751528203878400000⟩, + ⟨0, 5, 7, 2, 6, 4, -10656900545619176601822291228190826824773874483200000⟩, + ⟨0, 5, 8, 2, 7, 4, -26358247638732818532441425800388423475192555110400000⟩, + ⟨0, 5, 4, 3, 2, 4, -235764124527496645868403273682078878127035997224960000⟩, + ⟨0, 5, 5, 3, 3, 4, -23458380130554369869731194180832709004455470694400000⟩, + ⟨0, 5, 6, 3, 4, 4, 23549287034285786417566681876540693541237135769600000⟩, + ⟨0, 5, 7, 3, 5, 4, -25560430970442446780723216652746283186079452364800000⟩, + ⟨0, 5, 8, 3, 6, 4, 1415409681047643791494343346302783581656711168000000⟩, + ⟨0, 5, 4, 4, 1, 4, 3026783552445158969288452590816980855175512064000000⟩, + ⟨0, 5, 5, 4, 2, 4, -48448237362729580644532747956432040299790860288000000⟩, + ⟨0, 5, 6, 4, 3, 4, -29733559771498755863340372829770544988205927628800000⟩, + ⟨0, 5, 7, 4, 4, 4, 13214867655756999852353512849255593342877355212800000⟩, + ⟨0, 5, 8, 4, 5, 4, 19265329404432008229967955485979047000500967833600000⟩, + ⟨0, 5, 4, 5, 0, 4, 971502536891139963884546044085987280238254741258240000⟩, + ⟨0, 5, 5, 5, 1, 4, -16356867533270341127274107657095141721663707545600000⟩, + ⟨0, 5, 6, 5, 2, 4, 64543724222229784964146075229502111160978322227200000⟩, + ⟨0, 5, 7, 5, 3, 4, 15073989473003316701736062367523564165109750169600000⟩, + ⟨0, 5, 8, 5, 4, 4, 9644268203552485906315824304411684177508617420800000⟩, + ⟨0, 5, 5, 6, 0, 4, 868530401107110443506212556194925609449052490956800000⟩, + ⟨0, 5, 6, 6, 1, 4, -120877652912604004222197600252746981660300830310400000⟩, + ⟨0, 5, 7, 6, 2, 4, 106686108473485824124099949240537589463278786969600000⟩, + ⟨0, 5, 8, 6, 3, 4, -51205285108624832592266834815816660434609084825600000⟩, + ⟨0, 5, 6, 7, 0, 4, -35868376240830518884210596758182582187230809292800000⟩, + ⟨0, 5, 7, 7, 1, 4, -551944409217718897924957836095407425030896536780800000⟩, + ⟨0, 5, 8, 7, 2, 4, 20140402037402089011003697482116443293599819366400000⟩ +] + +def collectedFourData_9_1_5 : List CollectedFourTerm := [ + ⟨0, 6, 3, 0, 4, 5, -5415933284964979854106066901825516394663798374400000⟩, + ⟨0, 6, 4, 0, 5, 5, 319049947695547491666948391203688417990899086131200000⟩, + ⟨0, 6, 5, 0, 6, 5, 278272517093522235599073216973771232873916923904000000⟩, + ⟨0, 6, 6, 0, 7, 5, 127726936250671125908048883510731557644898664448000000⟩, + ⟨0, 6, 7, 0, 8, 5, 93665387199927103700180229474837414815905873920000000⟩, + ⟨0, 6, 3, 1, 3, 5, 25997414246269183217205658411348684090881186201600000⟩, + ⟨0, 6, 4, 1, 4, 5, 98182255570566771770447077405437769477153986969600000⟩, + ⟨0, 6, 5, 1, 5, 5, -91212949056866605488532206325285847018357391360000000⟩, + ⟨0, 6, 6, 1, 6, 5, -47068055208159799788840924771351992950270722048000000⟩, + ⟨0, 6, 7, 1, 7, 5, -7409833806519651785374771871959951787792793600000000⟩, + ⟨0, 6, 8, 1, 8, 5, -21416526811651565663662568989517719539199613337600000⟩, + ⟨0, 6, 3, 2, 2, 5, -20288734993026087043755515275308084937009555046400000⟩, + ⟨0, 6, 4, 2, 3, 5, 154157029435069959229951926148407651263125546598400000⟩, + ⟨0, 6, 5, 2, 4, 5, 68519117261787854861476313849968922174460788736000000⟩, + ⟨0, 6, 6, 2, 5, 5, -845626411014850192657267978951744680835940352000000⟩, + ⟨0, 6, 7, 2, 6, 5, -4647426775438026772836945176432866793852239872000000⟩, + ⟨0, 6, 8, 2, 7, 5, -9195771344998005740818505364164668920322798387200000⟩, + ⟨0, 6, 3, 3, 1, 5, -454573172393227294580993429085926153367689625600000⟩, + ⟨0, 6, 4, 3, 2, 5, -411262730782341956940361388539909446245198227046400000⟩, + ⟨0, 6, 5, 3, 3, 5, -20460189801050177159851572289971252316757557248000000⟩, + ⟨0, 6, 6, 3, 4, 5, 13692985327471564939681386297879163200589529088000000⟩, + ⟨0, 6, 7, 3, 5, 5, -11146789892170076770561539524996573472340574208000000⟩, + ⟨0, 6, 8, 3, 6, 5, 493803076927022443421589896941273411196289024000000⟩, + ⟨0, 6, 3, 4, 0, 5, 87161386574447171005665992571268853536984242585600000⟩, + ⟨0, 6, 4, 4, 1, 5, 5279867205243499130732348572950362653993205760000000⟩, + ⟨0, 6, 5, 4, 2, 5, -42256120262825341917140481422385343995272232960000000⟩, + ⟨0, 6, 6, 4, 3, 5, -17288896988340573182452526539334418629199396864000000⟩, + ⟨0, 6, 7, 4, 4, 5, 5762944818179941947765197010217634185806348288000000⟩, + ⟨0, 6, 8, 4, 5, 5, 6721219351050165709079020736548722769862118604800000⟩, + ⟨0, 6, 4, 5, 0, 5, 1694671685459190136644044124846551090557848492441600000⟩, + ⟨0, 6, 5, 5, 1, 5, -14266313889484993535761001295278055416295063552000000⟩, + ⟨0, 6, 6, 5, 2, 5, 37529640174185751900506478859712759082900258816000000⟩, + ⟨0, 6, 7, 5, 3, 5, 6573699547032441947140110938629121846663970816000000⟩, + ⟨0, 6, 8, 5, 4, 5, 3364657863650262602202887458280985807703926374400000⟩, + ⟨0, 6, 5, 6, 0, 5, 757524464849473468511054574241762209756459565056000000⟩, + ⟨0, 6, 6, 6, 1, 5, -70285606750713505890709609980916932073658253312000000⟩, + ⟨0, 6, 7, 6, 2, 5, 46525335857692980756202521058071404925803298816000000⟩, + ⟨0, 6, 8, 6, 3, 5, -17864317080867317582910669334298769988099296460800000⟩, + ⟨0, 6, 6, 7, 0, 5, -20856051772219509044063094511162784600800886784000000⟩, + ⟨0, 6, 7, 7, 1, 5, -240700494010541967111562127750074140981165293568000000⟩, + ⟨0, 6, 8, 7, 2, 5, 7026511567488461779576498249615774567267250995200000⟩ +] + +def collectedFourData_9_1_6 : List CollectedFourTerm := [ + ⟨0, 7, 2, 0, 3, 6, -20372594240050700994801567377050881544023755980800000⟩, + ⟨0, 7, 3, 0, 4, 6, -7457731428010067554426376679105246454379603558400000⟩, + ⟨0, 7, 4, 0, 5, 6, 219665632573374489230394206888267186691439696281600000⟩, + ⟨0, 7, 5, 0, 6, 6, 127726936250671125908048883510731557644898664448000000⟩, + ⟨0, 7, 6, 0, 7, 6, 43969946478311714258011525570666840880874258432000000⟩, + ⟨0, 7, 7, 0, 8, 6, 25795417523949247036663606310338423957984641024000000⟩, + ⟨0, 7, 2, 1, 2, 6, 19541663054046002709338083340402167616058163200000000⟩, + ⟨0, 7, 3, 1, 3, 6, 35798397629754409893451483455205999395689044377600000⟩, + ⟨0, 7, 4, 1, 4, 6, 67598404052928335947078477922226459078875204812800000⟩, + ⟨0, 7, 5, 1, 5, 6, -41866694746239158886959001730962103925546680320000000⟩, + ⟨0, 7, 6, 1, 6, 6, -16203159091511779447643619904095213293332856832000000⟩, + ⟨0, 7, 7, 1, 7, 6, -2040665848252611900597891337307236654299217920000000⟩, + ⟨0, 7, 8, 1, 8, 6, -4915087165908066643352656801236634744101902745600000⟩, + ⟨0, 7, 2, 2, 1, 6, 27079568107939466409192711734385257266138211942400000⟩, + ⟨0, 7, 3, 2, 2, 6, -27937555473975275414139855678259908537976514150400000⟩, + ⟨0, 7, 4, 2, 3, 6, 106136990872666202942540946498792416720633148211200000⟩, + ⟨0, 7, 5, 2, 4, 6, 31450238111395457264671902797276073415233503232000000⟩, + ⟨0, 7, 6, 2, 5, 6, -291106552184088869464439053888407406293024768000000⟩, + ⟨0, 7, 7, 2, 6, 6, -1279899839932528649961614851350317252873709158400000⟩, + ⟨0, 7, 8, 2, 7, 6, -2110427060182096319908519713801550296748602163200000⟩, + ⟨0, 7, 2, 3, 0, 6, -46895374849398029847204020038588586665694566809600000⟩, + ⟨0, 7, 3, 3, 1, 6, -625946527720038255238678570641545376795564441600000⟩, + ⟨0, 7, 4, 3, 2, 6, -283154059618788975038072890247241734242419553075200000⟩, + ⟨0, 7, 5, 3, 3, 6, -9391216156344609463072369297198695966547378176000000⟩, + ⟨0, 7, 6, 3, 4, 6, 4713804696572519218855490518906262001593352192000000⟩, + ⟨0, 7, 7, 3, 5, 6, -3069822352909550720222547698168484570068523417600000⟩, + ⟨0, 7, 8, 3, 6, 6, 113327673867710282616458953108971734584786944000000⟩, + ⟨0, 7, 3, 4, 0, 6, 120021089212769463978440105534641714720178543001600000⟩, + ⟨0, 7, 4, 4, 1, 6, 3635184327470785543604132378733991914299719680000000⟩, + ⟨0, 7, 5, 4, 2, 6, -19395536560287306163459321928077842773987819520000000⟩, + ⟨0, 7, 6, 4, 3, 6, -5951695840840191227003014917518151756049022976000000⟩, + ⟨0, 7, 7, 4, 4, 6, 1587113150294510034905082612259056551590467993600000⟩, + ⟨0, 7, 8, 4, 5, 6, 1542518040489500081171655598822510289987882188800000⟩, + ⟨0, 7, 4, 5, 0, 6, 1166780093459876852148512551476357666057013218508800000⟩, + ⟨0, 7, 5, 5, 1, 6, -6548230431544587848614114829234572131695591424000000⟩, + ⟨0, 7, 6, 5, 2, 6, 12919563548997081486148749512939480953487622144000000⟩, + ⟨0, 7, 7, 5, 3, 6, 1810394741984580741108381796747686692808504115200000⟩, + ⟨0, 7, 8, 5, 4, 6, 772188078334992172392040298375590888652301926400000⟩, + ⟨0, 7, 5, 6, 0, 6, 347703323492899824220282057875950704194666627072000000⟩, + ⟨0, 7, 6, 6, 1, 6, -24195791880260487695576634322931913835998609408000000⟩, + ⟨0, 7, 7, 6, 2, 6, 12813062538560581663764934194192004518117585715200000⟩, + ⟨0, 7, 8, 6, 3, 6, -4099855984309905421004444731891347213375032524800000⟩, + ⟨0, 7, 6, 7, 0, 6, -7179687441759736990358291848173926191523168256000000⟩, + ⟨0, 7, 7, 7, 1, 6, -66288838671747969316865991952499827698187213209600000⟩, + ⟨0, 7, 8, 7, 2, 6, 1612582522376037154839614672967509133881455411200000⟩ +] + +def collectedFourData_9_1_7 : List CollectedFourTerm := [ + ⟨0, 8, 1, 0, 2, 7, 62822364857219996757787360765219727248698900480000000⟩, + ⟨0, 8, 2, 0, 3, 7, -59758950892437995811592191312328261029832163328000000⟩, + ⟨0, 8, 3, 0, 4, 7, -10937885497648236478215536229393446916191158272000000⟩, + ⟨0, 8, 4, 0, 5, 7, 214781805973146163277211414010025580206544125952000000⟩, + ⟨0, 8, 5, 0, 6, 7, 93665387199927103700180229474837414815905873920000000⟩, + ⟨0, 8, 6, 0, 7, 7, 25795417523949247036663606310338423957984641024000000⟩, + ⟨0, 8, 7, 0, 8, 7, 12610953968355784986570959856341122500148592640000000⟩, + ⟨0, 8, 1, 1, 1, 7, -62098151846717791431873518210703396268079579136000000⟩, + ⟨0, 8, 2, 1, 2, 7, 57321579620308519101743254388388733976051712000000000⟩, + ⟨0, 8, 3, 1, 3, 7, 52503737638352398256193328277663139345998020608000000⟩, + ⟨0, 8, 4, 1, 4, 7, 66095488553680186476462847512768242635103010816000000⟩, + ⟨0, 8, 5, 1, 5, 7, -30701904306947155717201518869188135975963852800000000⟩, + ⟨0, 8, 6, 1, 6, 7, -9505748527091883250845412218329722927473229824000000⟩, + ⟨0, 8, 7, 1, 7, 7, -997647859478005546659128777472231165080371200000000⟩, + ⟨0, 8, 8, 1, 8, 7, -2059632865594114233454019365416159359929417728000000⟩, + ⟨0, 8, 1, 2, 0, 7, -117884595995490267041202614138439771858470436864000000⟩, + ⟨0, 8, 2, 2, 1, 7, 79432523991935027999686078820741145760559529984000000⟩, + ⟨0, 8, 3, 2, 2, 7, -40974629591893739371299989114523975815509573632000000⟩, + ⟨0, 8, 4, 2, 3, 7, 103777246868929190356049766967253488826490814464000000⟩, + ⟨0, 8, 5, 2, 4, 7, 23063253662112961579576194526845495743380193280000000⟩, + ⟨0, 8, 6, 2, 5, 7, -170780627655524462122679870941927668109541376000000⟩, + ⟨0, 8, 7, 2, 6, 7, -625721911673245356038673151152555005967335424000000⟩, + ⟨0, 8, 8, 2, 7, 7, -884359684145531463896510207439387808619298816000000⟩, + ⟨0, 8, 2, 3, 0, 7, -137558249562460946508878114441955578221833486336000000⟩, + ⟨0, 8, 3, 3, 1, 7, -918044785326779109522349386900450851294281728000000⟩, + ⟨0, 8, 4, 3, 2, 7, -276858694649182454147856169029045787379361644544000000⟩, + ⟨0, 8, 5, 3, 3, 7, -6886815916698284356579427168824975699256279040000000⟩, + ⟨0, 8, 6, 3, 4, 7, 2765401598439921811054929046429642766464057344000000⟩, + ⟨0, 8, 7, 3, 5, 7, -1500785492137481752510950277904361813952167936000000⟩, + ⟨0, 8, 8, 3, 6, 7, 47489168309824677300840297410771729220894720000000⟩, + ⟨0, 8, 3, 4, 0, 7, 176028990019902354413328818223532023091222806528000000⟩, + ⟨0, 8, 4, 4, 1, 7, 3554363264534120947810892260481258707589529600000000⟩, + ⟨0, 8, 5, 4, 2, 7, -14223236657804882011171988689947527176047820800000000⟩, + ⟨0, 8, 6, 4, 3, 7, -3491623062715171512597330250144343604521336832000000⟩, + ⟨0, 8, 7, 4, 4, 7, 775913429676168657389891767067952260679991296000000⟩, + ⟨0, 8, 8, 4, 5, 7, 646381385461563752917493362611160306830802944000000⟩, + ⟨0, 8, 4, 5, 0, 7, 1140839068501624316564383708345391387784234663936000000⟩, + ⟨0, 8, 5, 5, 1, 7, -4801982705051745403723847190172986426481704960000000⟩, + ⟨0, 8, 6, 5, 2, 7, 7579393714703730624122067991449830535104299008000000⟩, + ⟨0, 8, 7, 5, 3, 7, 885072115406702962792700611403773351582236672000000⟩, + ⟨0, 8, 8, 5, 4, 7, 323580008019019551666661264755541400598085632000000⟩, + ⟨0, 8, 5, 6, 0, 7, 254979625924385615001428643628094515923784826880000000⟩, + ⟨0, 8, 6, 6, 1, 7, -14194708064558576853790909511850989776961273856000000⟩, + ⟨0, 8, 7, 6, 2, 7, 6264094842327365346355438880583594017053212672000000⟩, + ⟨0, 8, 8, 6, 3, 7, -1718015946504036286356340002366311150464794624000000⟩, + ⟨0, 8, 6, 7, 0, 7, -4212036858925887423979311550158446072841633792000000⟩, + ⟨0, 8, 7, 7, 1, 7, -32407519371572132509732145047674170564784685056000000⟩, + ⟨0, 8, 8, 7, 2, 7, 675741416063925287939835104393912521699885056000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0904.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0904.lean new file mode 100644 index 0000000000000000000000000000000000000000..f4266e9d7d1207540180f8d5b1f3fa19ad8b10cc --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0904.lean @@ -0,0 +1,643 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0904. -/ +namespace LaughlinFock +def collectedFourData_9_1_8 : List CollectedFourTerm := [ + ⟨1, 0, 8, 1, 8, 0, 295800664805416906665190875996275470054824345600000000⟩, + ⟨1, 0, 8, 2, 7, 0, 127010103046640892878211030744856440784237363200000000⟩, + ⟨1, 0, 8, 3, 6, 0, -6820306566165827375208865029231766293970944000000000⟩, + ⟨1, 0, 8, 4, 5, 0, -92832099706383413550139896292239810262518988800000000⟩, + ⟨1, 0, 8, 5, 4, 0, -46471962595216435670439848564579487917172326400000000⟩, + ⟨1, 0, 8, 6, 3, 0, 246738274384454814314376651840670804386565324800000000⟩, + ⟨1, 0, 8, 7, 2, 0, -97048733027769438909336801621800069440418611200000000⟩ +] + +def collectedFourData_9_1_9 : List CollectedFourTerm := [ + ⟨1, 1, 7, 0, 8, 1, -62098151846717791431873518210703396268079579136000000⟩, + ⟨1, 1, 7, 1, 7, 1, 4912561605004055800591572179292560858944634880000000⟩, + ⟨1, 1, 8, 1, 8, 1, 70993500039696456769917706874495824031300085350400000⟩, + ⟨1, 1, 7, 2, 6, 1, 3081144724055304144106541398541482997031999897600000⟩, + ⟨1, 1, 8, 2, 7, 1, 30483000305678919914152270691593694684474297548800000⟩, + ⟨1, 1, 7, 3, 5, 1, 7390083701356600742162832733618007750199371366400000⟩, + ⟨1, 1, 8, 3, 6, 1, -1636904483613482100989894414561073601336836096000000⟩, + ⟨1, 1, 7, 4, 4, 1, -3820709368763192433718004474851619236689110630400000⟩, + ⟨1, 1, 8, 4, 5, 1, -22280124618805613134572321967673622015014810419200000⟩, + ⟨1, 1, 7, 5, 3, 1, -4358222443419720814672231514900360627898600652800000⟩, + ⟨1, 1, 8, 5, 4, 1, -11153481620869747656535490120069611448253913497600000⟩, + ⟨1, 1, 7, 6, 2, 1, -30845304302684944884754508586398035649802063052800000⟩, + ⟨1, 1, 8, 6, 3, 1, 59218304001548843297146685157705890352493441843200000⟩, + ⟨1, 1, 7, 7, 1, 1, 159579288288665229479155233552843482176290186854400000⟩, + ⟨1, 1, 8, 7, 2, 1, -23292135724548476982223805214617009717374667980800000⟩ +] + +def collectedFourData_9_1_10 : List CollectedFourTerm := [ + ⟨1, 2, 6, 0, 7, 2, 19541663054046002709338083340402167616058163200000000⟩, + ⟨1, 2, 7, 0, 8, 2, 57321579620308519101743254388388733976051712000000000⟩, + ⟨1, 2, 6, 1, 6, 2, -7201206750015198775311795960770875425502003200000000⟩, + ⟨1, 2, 7, 1, 7, 2, -4534688759755647838836990051510777764904960000000000⟩, + ⟨1, 2, 8, 1, 8, 2, -32766350076688541964767511621544065030841958400000000⟩, + ⟨1, 2, 6, 2, 5, 2, -129377145328400448554958143219551538302156800000000⟩, + ⟨1, 2, 7, 2, 6, 2, -2844143945822837099624412615096181571400499200000000⟩, + ⟨1, 2, 8, 2, 7, 2, -14069128284211720551297301066492505819499724800000000⟩, + ⟨1, 2, 6, 3, 4, 2, 2094966914013324262045189704211388431545139200000000⟩, + ⟨1, 2, 7, 3, 5, 2, -6821640559185928824576235606997934411664588800000000⟩, + ⟨1, 2, 8, 3, 6, 2, 755497127514348191897969732278838693462016000000000⟩, + ⟨1, 2, 6, 4, 3, 2, -2645125683271738003936951601318972240796057600000000⟩, + ⟨1, 2, 7, 4, 4, 2, 3526821487831345201988223912055078510185676800000000⟩, + ⟨1, 2, 8, 4, 5, 2, 10283171876352427840496103449023765191799603200000000⟩, + ⟨1, 2, 6, 5, 2, 2, 5741870934602275635738888403243397990999654400000000⟩, + ⟨1, 2, 7, 5, 3, 2, 4022989209246544690555329550499914341521817600000000⟩, + ⟨1, 2, 8, 5, 4, 2, 5147779489093805679550566573380034132285849600000000⟩, + ⟨1, 2, 6, 6, 1, 2, -10753390670673098177150047888975377109667020800000000⟩, + ⟨1, 2, 7, 6, 2, 2, 28472692244744371212821487410838720162142617600000000⟩, + ⟨1, 2, 8, 6, 3, 2, -27331624427272168375214127741325416875635507200000000⟩, + ⟨1, 2, 6, 7, 0, 2, -3190884776023985722974041885897247283583385600000000⟩, + ⟨1, 2, 7, 7, 1, 2, -147304494696880013964735347636728251730939084800000000⟩, + ⟨1, 2, 8, 7, 2, 2, 10750255625621385887715655795430647908846796800000000⟩ +] + +def collectedFourData_9_1_11 : List CollectedFourTerm := [ + ⟨1, 3, 5, 0, 6, 3, 25997414246269183217205658411348684090881186201600000⟩, + ⟨1, 3, 6, 0, 7, 3, 35798397629754409893451483455205999395689044377600000⟩, + ⟨1, 3, 7, 0, 8, 3, 52503737638352398256193328277663139345998020608000000⟩, + ⟨1, 3, 5, 1, 5, 3, -8521505630605479058080527416975277654638854144000000⟩, + ⟨1, 3, 6, 1, 6, 3, -13191899887852231004541841458216734010457561497600000⟩, + ⟨1, 3, 7, 1, 7, 3, -4153551079556148381003513980300000360021360640000000⟩, + ⟨1, 3, 8, 1, 8, 3, -20008239586653640391899169059682736909666641510400000⟩, + ⟨1, 3, 5, 2, 4, 3, 6401350351981484718664911559251625062982641254400000⟩, + ⟨1, 3, 6, 2, 5, 3, -237006158578180728717327622369795712013985382400000⟩, + ⟨1, 3, 7, 2, 6, 3, -2605095472356539269412355205492297536952388812800000⟩, + ⟨1, 3, 8, 2, 7, 3, -8591084720362066429878486368036691046940069068800000⟩, + ⟨1, 3, 5, 3, 3, 3, -1911478845884114190853477204824151807690486579200000⟩, + ⟨1, 3, 6, 3, 4, 3, 3837772578598465786787735749359242739057269145600000⟩, + ⟨1, 3, 7, 3, 5, 3, -6248286047856017484003309039315277405370921779200000⟩, + ⟨1, 3, 8, 3, 6, 3, 461332052515974841432261799168068981931114496000000⟩, + ⟨1, 3, 5, 4, 2, 3, -3947748323790226103219922132873509311856246784000000⟩, + ⟨1, 3, 6, 4, 3, 3, -4845609134112674817751262411842417655699786956800000⟩, + ⟨1, 3, 7, 4, 4, 3, 3230394405055719667201532094395955463670936371200000⟩, + ⟨1, 3, 8, 4, 5, 3, 6279251919461623469433381714337621675038946099200000⟩, + ⟨1, 3, 5, 5, 1, 3, -1332820343978118236518085349837440383588289740800000⟩, + ⟨1, 3, 6, 5, 2, 3, 10518540734590334577792726585361278114064446259200000⟩, + ⟨1, 3, 7, 5, 3, 3, 3684859547893012354414527064189814288981321318400000⟩, + ⟨1, 3, 8, 5, 4, 3, 3143407951022526528077194186521777554448816537600000⟩, + ⟨1, 3, 5, 6, 0, 3, 70771190486469997747301658109195025004785722982400000⟩, + ⟨1, 3, 6, 6, 1, 3, -19699150171210438866138466172175066112201221734400000⟩, + ⟨1, 3, 7, 6, 2, 3, 26079580733430657485599098794691650265534588518400000⟩, + ⟨1, 3, 8, 6, 3, 3, -16689612622504324497732070934781355722731107123200000⟩, + ⟨1, 3, 6, 7, 0, 3, -5845385916588405936141481138830530728533216460800000⟩, + ⟨1, 3, 7, 7, 1, 3, -134923646447715146116988449690143892835824513843200000⟩, + ⟨1, 3, 8, 7, 2, 3, 6564469026052161802767284699050559398677892300800000⟩ +] + +def collectedFourData_9_1_12 : List CollectedFourTerm := [ + ⟨1, 4, 4, 0, 5, 4, 56284831559367464100191026207044215365172660797440000⟩, + ⟨1, 4, 5, 0, 6, 4, 98182255570566771770447077405437769477153986969600000⟩, + ⟨1, 4, 6, 0, 7, 4, 67598404052928335947078477922226459078875204812800000⟩, + ⟨1, 4, 7, 0, 8, 4, 66095488553680186476462847512768242635103010816000000⟩, + ⟨1, 4, 4, 1, 4, 4, 17320710305150879823911755561452118735532347883520000⟩, + ⟨1, 4, 5, 1, 5, 4, -32182456137544438867622066636575411184037003264000000⟩, + ⟨1, 4, 6, 1, 6, 4, -24910371354264798514834308237048470695221972172800000⟩, + ⟨1, 4, 7, 1, 7, 4, -5228789419277319653241322652683135471614689280000000⟩, + ⟨1, 4, 8, 1, 8, 4, -18890860394855157022131329922646579636973705625600000⟩, + ⟨1, 4, 4, 2, 3, 4, 27195436006543663389506421354746327333299373998080000⟩, + ⟨1, 4, 5, 2, 4, 4, 24175443384534977094453537663814864399222859366400000⟩, + ⟨1, 4, 6, 2, 5, 4, -447540647944643203378327766178854303146652467200000⟩, + ⟨1, 4, 7, 2, 6, 4, -3279481913466856186388281119931329722938136985600000⟩, + ⟨1, 4, 8, 2, 7, 4, -8111307413621210239834103668722826710439113523200000⟩, + ⟨1, 4, 4, 3, 2, 4, -72552444204812656014238549142183780845019128135680000⟩, + ⟨1, 4, 5, 3, 3, 4, -7218921958412021285356096365766680561587532595200000⟩, + ⟨1, 4, 6, 3, 4, 4, 7246897029148606799737790324747233599115021516800000⟩, + ⟨1, 4, 7, 3, 5, 4, -7865792751762400192641929753331118493734954598400000⟩, + ⟨1, 4, 8, 3, 6, 4, 435568524757396582452892284564161107951878144000000⟩, + ⟨1, 4, 4, 4, 1, 4, 931441733338061424431243758579883482558758912000000⟩, + ⟨1, 4, 5, 4, 2, 4, -14909130238222510761846432731276007698652463104000000⟩, + ⟨1, 4, 6, 4, 3, 4, -9150002955943923688139485628203130376610539110400000⟩, + ⟨1, 4, 7, 4, 4, 4, 4066653271314286953684589262189125047526254182400000⟩, + ⟨1, 4, 8, 4, 5, 4, 5928581116841522755729204279429312852492340428800000⟩, + ⟨1, 4, 4, 5, 0, 4, 298963566844148444247599827493180435516396320849920000⟩, + ⟨1, 4, 5, 5, 1, 4, -5033550890965611176988674429249303711228677324800000⟩, + ⟨1, 4, 6, 5, 2, 4, 19862245622777084058469341483265346617388669337600000⟩, + ⟨1, 4, 7, 5, 3, 4, 4638766743565584089107257589550533637734976716800000⟩, + ⟨1, 4, 8, 5, 4, 4, 2967861340807533627056615562945739989205804646400000⟩, + ⟨1, 4, 5, 6, 0, 4, 267275623858361892356820214108672033499963090534400000⟩, + ⟨1, 4, 6, 6, 1, 4, -37198064744271938808235673057237379342593635123200000⟩, + ⟨1, 4, 7, 6, 2, 4, 32830855618783648168358334902412876190378151116800000⟩, + ⟨1, 4, 8, 6, 3, 4, -15757565313554511282519408149962900326742543564800000⟩, + ⟨1, 4, 6, 7, 0, 4, -11037889548062174317800095147937971833659614822400000⟩, + ⟨1, 4, 7, 7, 1, 4, -169851609247939183486179648695821061363226535526400000⟩, + ⟨1, 4, 8, 7, 2, 4, 6197870002527418315210498939072288762501477171200000⟩ +] + +def collectedFourData_9_1_13 : List CollectedFourTerm := [ + ⟨1, 5, 3, 0, 4, 5, 1775249859298442972355718991756551441084317696000000⟩, + ⟨1, 5, 4, 0, 5, 5, -104579090057856694817286802409440120427205623808000000⟩, + ⟨1, 5, 5, 0, 6, 5, -91212949056866605488532206325285847018357391360000000⟩, + ⟨1, 5, 6, 0, 7, 5, -41866694746239158886959001730962103925546680320000000⟩, + ⟨1, 5, 7, 0, 8, 5, -30701904306947155717201518869188135975963852800000000⟩, + ⟨1, 5, 3, 1, 3, 5, -8521505630605479058080527416975277654638854144000000⟩, + ⟨1, 5, 4, 1, 4, 5, -32182456137544438867622066636575411184037003264000000⟩, + ⟨1, 5, 5, 1, 5, 5, 29898037228212555730339229476009158631646822400000000⟩, + ⟨1, 5, 6, 1, 6, 5, 15428099644007583971620812681736233492487864320000000⟩, + ⟨1, 5, 7, 1, 7, 5, 2428816185562358794041758286354271828967424000000000⟩, + ⟨1, 5, 8, 1, 8, 5, 7019969450988466852042478469082938462525456384000000⟩, + ⟨1, 5, 3, 2, 2, 5, 6650298673674642913219566024317269944802738176000000⟩, + ⟨1, 5, 4, 2, 3, 5, -50530025097279876427275652912549489889935097856000000⟩, + ⟨1, 5, 5, 2, 4, 5, -22459389153836102974522196390491654862395146240000000⟩, + ⟨1, 5, 6, 2, 5, 5, 277181805643838734675163129902061946855751680000000⟩, + ⟨1, 5, 7, 2, 6, 5, 1523346632075347171431525770068467848293908480000000⟩, + ⟨1, 5, 8, 2, 7, 5, 3014215819767787567519503509583718163675086848000000⟩, + ⟨1, 5, 3, 3, 1, 5, 149001274179680310139237211314428571029602304000000⟩, + ⟨1, 5, 4, 3, 2, 5, 134804855699171869739117033209050426202103218176000000⟩, + ⟨1, 5, 5, 3, 3, 5, 6706498613335231930209340768811897206415032320000000⟩, + ⟨1, 5, 6, 3, 4, 5, -4488325279680161631338561418040385453602897920000000⟩, + ⟨1, 5, 7, 3, 5, 5, 3653726171745520148554318883288268285904158720000000⟩, + ⟨1, 5, 8, 3, 6, 5, -161860162729368474952274364356017447407452160000000⟩, + ⟨1, 5, 3, 4, 0, 5, -28570004671603901107964115888817035785696968704000000⟩, + ⟨1, 5, 4, 4, 1, 5, -1730649736628650653909155291959141427734118400000000⟩, + ⟨1, 5, 5, 4, 2, 5, 13850830060873586148868637185325569604478566400000000⟩, + ⟨1, 5, 6, 4, 3, 5, 5667003327234548140373074443021399638157557760000000⟩, + ⟨1, 5, 7, 4, 4, 5, -1888994276576430504464102347115377052268625920000000⟩, + ⟨1, 5, 8, 4, 5, 5, -2203100200733534654018544913932266827186962432000000⟩, + ⟨1, 5, 4, 5, 0, 5, -555484255967517080482798484767403545944070815744000000⟩, + ⟨1, 5, 5, 5, 1, 5, 4676252529794487770272355840868836005568839680000000⟩, + ⟨1, 5, 6, 5, 2, 5, -12301571111242972351578372417700729198152253440000000⟩, + ⟨1, 5, 7, 5, 3, 5, -2154745744068935734240234180678454959606333440000000⟩, + ⟨1, 5, 8, 5, 4, 5, -1102877026867060331236230971816313822375837696000000⟩, + ⟨1, 5, 5, 6, 0, 5, -248303501701618857547634648161754571600864215040000000⟩, + ⟨1, 5, 6, 6, 1, 5, 23038414051608217603005091232271598335641518080000000⟩, + ⟨1, 5, 7, 6, 2, 5, -15250205567426285624904994743989333241825853440000000⟩, + ⟨1, 5, 8, 6, 3, 5, 5855616145108689527956407689241549924804329472000000⟩, + ⟨1, 5, 6, 7, 0, 5, 6836255364691615157195915777077882963686850560000000⟩, + ⟨1, 5, 7, 7, 1, 5, 78897485556460901634468919748155151899290501120000000⟩, + ⟨1, 5, 8, 7, 2, 5, -2303169742908572607394722905131962236632301568000000⟩ +] + +def collectedFourData_9_1_14 : List CollectedFourTerm := [ + ⟨1, 6, 2, 0, 3, 6, 7507409310611302778425830937078548039027444940800000⟩, + ⟨1, 6, 3, 0, 4, 6, 2748213688397789966811642217453542273563649638400000⟩, + ⟨1, 6, 4, 0, 5, 6, -80947953695590266087879935176964278729553058201600000⟩, + ⟨1, 6, 5, 0, 6, 6, -47068055208159799788840924771351992950270722048000000⟩, + ⟨1, 6, 6, 0, 7, 6, -16203159091511779447643619904095213293332856832000000⟩, + ⟨1, 6, 7, 0, 8, 6, -9505748527091883250845412218329722927473229824000000⟩, + ⟨1, 6, 2, 1, 2, 6, -7201206750015198775311795960770875425502003200000000⟩, + ⟨1, 6, 3, 1, 3, 6, -13191899887852231004541841458216734010457561497600000⟩, + ⟨1, 6, 4, 1, 4, 6, -24910371354264798514834308237048470695221972172800000⟩, + ⟨1, 6, 5, 1, 5, 6, 15428099644007583971620812681736233492487864320000000⟩, + ⟨1, 6, 6, 1, 6, 6, 5970950287017986475754830862202420981485535232000000⟩, + ⟨1, 6, 7, 1, 7, 6, 751996216510325175012018617155207621949521920000000⟩, + ⟨1, 6, 8, 1, 8, 6, 1811235757067358600100771672131330610503981465600000⟩, + ⟨1, 6, 2, 2, 1, 6, -9978964845881685160141121049123835259642078822400000⟩, + ⟨1, 6, 3, 2, 2, 6, 10295137752692991195210385673343502683944150630400000⟩, + ⟨1, 6, 4, 2, 3, 6, -39112045529835187759097702658938853109909369651200000⟩, + ⟨1, 6, 5, 2, 4, 6, -11589579983596879788720235330977605948257861632000000⟩, + ⟨1, 6, 6, 2, 5, 6, 107274312465830809296780572112490291022266368000000⟩, + ⟨1, 6, 7, 2, 6, 6, 471649897000818515680852790290934814168475238400000⟩, + ⟨1, 6, 8, 2, 7, 6, 777703594068031651283323724030815175770846003200000⟩, + ⟨1, 6, 2, 3, 0, 6, 17281195002492805566883411620270678963398482329600000⟩, + ⟨1, 6, 3, 3, 1, 6, 230664623993342548237699579652290723333118361600000⟩, + ⟨1, 6, 4, 3, 2, 6, 104343776667403646881611635191108825318398571315200000⟩, + ⟨1, 6, 5, 3, 3, 6, 3460713092272795964941064851892512258969829376000000⟩, + ⟨1, 6, 6, 3, 4, 6, -1737062096779077017803617400394962264330862592000000⟩, + ⟨1, 6, 7, 3, 5, 6, 1131245861111230884064365226383710920237488537600000⟩, + ⟨1, 6, 8, 3, 6, 6, -41761850450630289421736482447072034757279744000000⟩, + ⟨1, 6, 3, 4, 0, 6, -44228409598139271913157905949206144012728768921600000⟩, + ⟨1, 6, 4, 4, 1, 6, -1339584755101593980543311327225722259038535680000000⟩, + ⟨1, 6, 5, 4, 2, 6, 7147358360023984150959156114809330450584043520000000⟩, + ⟨1, 6, 6, 4, 3, 6, 2193231566042274399188411152803531875917234176000000⟩, + ⟨1, 6, 7, 4, 4, 6, -584859635504377845550547591921388156557564313600000⟩, + ⟨1, 6, 8, 4, 5, 6, -568426100402614000218533512816432879804140748800000⟩, + ⟨1, 6, 4, 5, 0, 6, -429964668900940416892846623782639021143997861068800000⟩, + ⟨1, 6, 5, 5, 1, 6, 2413057734844659799384686498492104456980660224000000⟩, + ⟨1, 6, 6, 5, 2, 6, -4760927868778567104390883094287583658790354944000000⟩, + ⟨1, 6, 7, 5, 3, 6, -667140089362667442095178201136290169634370355200000⟩, + ⟨1, 6, 8, 5, 4, 6, -284555413047913480115967405110383528877909606400000⟩, + ⟨1, 6, 5, 6, 0, 6, -128130523651689512172516903483156296232937193472000000⟩, + ⟨1, 6, 6, 6, 1, 6, 8916277971235384560943375054646082876639019008000000⟩, + ⟨1, 6, 7, 6, 2, 6, -4721681680103751556051831252414921835665371955200000⟩, + ⟨1, 6, 8, 6, 3, 6, 1510818731581287863737801492171672227282734284800000⟩, + ⟨1, 6, 6, 7, 0, 6, 2645753000939950632266512278704976539424915456000000⟩, + ⟨1, 6, 7, 7, 1, 6, 24427789547564894555659221750003828431162808729600000⟩, + ⟨1, 6, 8, 7, 2, 6, -594245234552160403159845963799101636934316851200000⟩ +] + +def collectedFourData_9_1_15 : List CollectedFourTerm := [ + ⟨1, 7, 1, 0, 2, 7, -4969853825842115700655875757301225203590758400000000⟩, + ⟨1, 7, 2, 0, 3, 7, 4727508290973887038058176422234107098158858240000000⟩, + ⟨1, 7, 3, 0, 4, 7, 865292037487867284099990031414997368449269760000000⟩, + ⟨1, 7, 4, 0, 5, 7, -16991308470525401525134972766820553491386204160000000⟩, + ⟨1, 7, 5, 0, 6, 7, -7409833806519651785374771871959951787792793600000000⟩, + ⟨1, 7, 6, 0, 7, 7, -2040665848252611900597891337307236654299217920000000⟩, + ⟨1, 7, 7, 0, 8, 7, -997647859478005546659128777472231165080371200000000⟩, + ⟨1, 7, 1, 1, 1, 7, 4912561605004055800591572179292560858944634880000000⟩, + ⟨1, 7, 2, 1, 2, 7, -4534688759755647838836990051510777764904960000000000⟩, + ⟨1, 7, 3, 1, 3, 7, -4153551079556148381003513980300000360021360640000000⟩, + ⟨1, 7, 4, 1, 4, 7, -5228789419277319653241322652683135471614689280000000⟩, + ⟨1, 7, 5, 1, 5, 7, 2428816185562358794041758286354271828967424000000000⟩, + ⟨1, 7, 6, 1, 6, 7, 751996216510325175012018617155207621949521920000000⟩, + ⟨1, 7, 7, 1, 7, 7, 78923549639346878600003676194685107306496000000000⟩, + ⟨1, 7, 8, 1, 8, 7, 162936786925598609027768011557214095660810240000000⟩, + ⟨1, 7, 1, 2, 0, 7, 9325806370829530525021734395760933067680645120000000⟩, + ⟨1, 7, 2, 2, 1, 7, -6283877312718583051365237836610413318079774720000000⟩, + ⟨1, 7, 3, 2, 2, 7, 3241487646995720158952023953593235550041538560000000⟩, + ⟨1, 7, 4, 2, 3, 7, -8209779249143227369979675085549080411237253120000000⟩, + ⟨1, 7, 5, 2, 4, 7, -1824525385338884140060540283664832190113382400000000⟩, + ⟨1, 7, 6, 2, 5, 7, 13510391683957454432303820673074319148974080000000⟩, + ⟨1, 7, 7, 2, 6, 7, 49500626786499051444571181101158294796369920000000⟩, + ⟨1, 7, 8, 2, 7, 7, 69961364390854728441149929324018824149729280000000⟩, + ⟨1, 7, 2, 3, 0, 7, 10882181758326020038686736622115653120038010880000000⟩, + ⟨1, 7, 3, 3, 1, 7, 72626180167210565851230203297155642545930240000000⟩, + ⟨1, 7, 4, 3, 2, 7, 21902187954036559648552997616585019905036779520000000⟩, + ⟨1, 7, 5, 3, 3, 7, 544813435617423982610637887903064594264883200000000⟩, + ⟨1, 7, 6, 3, 4, 7, -218769887845395709726965465708207348929003520000000⟩, + ⟨1, 7, 7, 3, 5, 7, 118726579886312583121222941782784913314938880000000⟩, + ⟨1, 7, 8, 3, 6, 7, -3756850372427804017940334877764996405657600000000⟩, + ⟨1, 7, 3, 4, 0, 7, -13925587670853059595385501560258181994895114240000000⟩, + ⟨1, 7, 4, 4, 1, 7, -281184350650044382185580532222427050016768000000000⟩, + ⟨1, 7, 5, 4, 2, 7, 1125194941010335366969317989838202406436864000000000⟩, + ⟨1, 7, 6, 4, 3, 7, 276220996711479987028979221267370520147394560000000⟩, + ⟨1, 7, 7, 4, 4, 7, -61382221693859153618583818346006830571847680000000⟩, + ⟨1, 7, 8, 4, 5, 7, -51134990043598867464521545539526084547051520000000⟩, + ⟨1, 7, 4, 5, 0, 7, -90251352717285341828271393896749166465258618880000000⟩, + ⟨1, 7, 5, 5, 1, 7, 379883058725484039072891396108036894149836800000000⟩, + ⟨1, 7, 6, 5, 2, 7, -599603006607524884810210813826747958181232640000000⟩, + ⟨1, 7, 7, 5, 3, 7, -70017724561902567896506758367835376593141760000000⟩, + ⟨1, 7, 8, 5, 4, 7, -25598293608880710575646286080504073090498560000000⟩, + ⟨1, 7, 5, 6, 0, 7, -20171342996911430735326693205711101142394470400000000⟩, + ⟨1, 7, 6, 6, 1, 7, 1122938054651261150780802257348412599414292480000000⟩, + ⟨1, 7, 7, 6, 2, 7, -495550203949392559679212950159291454335221760000000⟩, + ⟨1, 7, 8, 6, 3, 7, 135911600016909694649090962259758957901905920000000⟩, + ⟨1, 7, 6, 7, 0, 7, 333212663125575334479077319438067490472591360000000⟩, + ⟨1, 7, 7, 7, 1, 7, 2563746756444333321363236368686221384723988480000000⟩, + ⟨1, 7, 8, 7, 2, 7, -53457651101450121949706962511632030739988480000000⟩ +] + +def collectedFourData_9_1_16 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 1, 8, 56723338964805595530929605258468289423370878976000000⟩, + ⟨1, 8, 1, 0, 2, 8, -71821454090837103110257157637922310291793641472000000⟩, + ⟨1, 8, 2, 0, 3, 8, 34159608268428308983985724848582590981419407769600000⟩, + ⟨1, 8, 3, 0, 4, 8, 4168233414462067760172764911593009024454990233600000⟩, + ⟨1, 8, 4, 0, 5, 8, -61387141555029106821708884881427072124319904563200000⟩, + ⟨1, 8, 5, 0, 6, 8, -21416526811651565663662568989517719539199613337600000⟩, + ⟨1, 8, 6, 0, 7, 8, -4915087165908066643352656801236634744101902745600000⟩, + ⟨1, 8, 7, 0, 8, 8, -2059632865594114233454019365416159359929417728000000⟩, + ⟨1, 8, 0, 1, 0, 8, 295800664805416906665190875996275470054824345600000000⟩, + ⟨1, 8, 1, 1, 1, 8, 70993500039696456769917706874495824031300085350400000⟩, + ⟨1, 8, 2, 1, 2, 8, -32766350076688541964767511621544065030841958400000000⟩, + ⟨1, 8, 3, 1, 3, 8, -20008239586653640391899169059682736909666641510400000⟩, + ⟨1, 8, 4, 1, 4, 8, -18890860394855157022131329922646579636973705625600000⟩, + ⟨1, 8, 5, 1, 5, 8, 7019969450988466852042478469082938462525456384000000⟩, + ⟨1, 8, 6, 1, 6, 8, 1811235757067358600100771672131330610503981465600000⟩, + ⟨1, 8, 7, 1, 7, 8, 162936786925598609027768011557214095660810240000000⟩, + ⟨1, 8, 8, 1, 8, 8, 294333530018422738527490185204404269227599462400000⟩, + ⟨1, 8, 1, 2, 0, 8, 134771161807576179966215825446176160802909297049600000⟩, + ⟨1, 8, 2, 2, 1, 8, -45405480899772459830181616914568855901541551308800000⟩, + ⟨1, 8, 3, 2, 2, 8, 15614701785537964295481600849049791091317512601600000⟩, + ⟨1, 8, 4, 2, 3, 8, -29660745773460263154492072319502969521666680422400000⟩, + ⟨1, 8, 5, 2, 4, 8, -5273397198094834885830700387822572227105547878400000⟩, + ⟨1, 8, 6, 2, 5, 8, 32540728228029904045612115154870474201523814400000⟩, + ⟨1, 8, 7, 2, 6, 8, 102193491248832275533321169200394488402201804800000⟩, + ⟨1, 8, 8, 2, 7, 8, 126380148612285516041909381276854904110763212800000⟩, + ⟨1, 8, 2, 3, 0, 8, 78631499532214470212597448301073011882983633715200000⟩, + ⟨1, 8, 3, 3, 1, 8, 349850521930815804074434868143675591765681766400000⟩, + ⟨1, 8, 4, 3, 2, 8, 79129439303135722294246228745780777158411970150400000⟩, + ⟨1, 8, 5, 3, 3, 8, 1574665755793644438281048459208158436153045811200000⟩, + ⟨1, 8, 6, 3, 4, 8, -526922655640456752250236757331847760454457753600000⟩, + ⟨1, 8, 7, 3, 5, 8, 245109698407392377795509571702395191612879667200000⟩, + ⟨1, 8, 8, 3, 6, 8, -6786478687422657677632716346231214598782976000000⟩, + ⟨1, 8, 3, 4, 0, 8, -67081513906204878193099359262188585752855996006400000⟩, + ⟨1, 8, 4, 4, 1, 8, -1015878416094665313898136427692913356817039360000000⟩, + ⟨1, 8, 5, 4, 2, 8, 3252133347617023774166287538578986382261223424000000⟩, + ⟨1, 8, 6, 4, 3, 8, 665297690483458050037110806570406102717746380800000⟩, + ⟨1, 8, 7, 4, 4, 8, -126722911258492540495612615446884858199225139200000⟩, + ⟨1, 8, 8, 4, 5, 8, -92371663950031955646184226665929241479295795200000⟩, + ⟨1, 8, 4, 5, 0, 8, -326065092302896729611428722080635070014656453017600000⟩, + ⟨1, 8, 5, 5, 1, 8, 1097970065850620383539335770455963593341717708800000⟩, + ⟨1, 8, 6, 5, 2, 8, -1444185996908846525571403842276433216798929715200000⟩, + ⟨1, 8, 7, 5, 3, 8, -144550810500676565207195630657739150080763494400000⟩, + ⟨1, 8, 8, 5, 4, 8, -46241467396741529323634698297869627351996825600000⟩, + ⟨1, 8, 5, 6, 0, 8, -58300917321556121989911723245306298337178576486400000⟩, + ⟨1, 8, 6, 6, 1, 8, 2704675253546435431376678382021024900863911526400000⟩, + ⟨1, 8, 7, 6, 2, 8, -1023057862460673921468038704520498117832238694400000⟩, + ⟨1, 8, 8, 6, 3, 8, 245514482998216805552629094146017777207685939200000⟩, + ⟨1, 8, 6, 7, 0, 8, 802566125879431907781820185448187215420902604800000⟩, + ⟨1, 8, 7, 7, 1, 8, 5292826550438231774980738959455750979218256691200000⟩, + ⟨1, 8, 8, 7, 2, 8, -96567383290599602165303710379118300700134604800000⟩ +] + +def collectedFourData_9_1_17 : List CollectedFourTerm := [ + ⟨2, 0, 7, 0, 8, 1, -117884595995490267041202614138439771858470436864000000⟩, + ⟨2, 0, 7, 1, 7, 1, 9325806370829530525021734395760933067680645120000000⟩, + ⟨2, 0, 8, 1, 8, 1, 134771161807576179966215825446176160802909297049600000⟩, + ⟨2, 0, 7, 2, 6, 1, 5849119340869625259045855736635678311183705702400000⟩, + ⟨2, 0, 8, 2, 7, 1, 57867683158034269165026248429261880815739155251200000⟩, + ⟨2, 0, 7, 3, 5, 1, 14029033161207138876084459134178374298017307033600000⟩, + ⟨2, 0, 8, 3, 6, 1, -3107432636808517153215063811966461713426939904000000⟩, + ⟨2, 0, 7, 4, 4, 1, -7253078665925541513445260699327938415767951769600000⟩, + ⟨2, 0, 8, 4, 5, 1, -42295678877855356563070309818695611558837144780800000⟩, + ⟨2, 0, 7, 5, 3, 1, -8273471540170603103912907314374112217826276147200000⟩, + ⟨2, 0, 8, 5, 4, 1, -21173314111905431537176821456952826898963392102400000⟩, + ⟨2, 0, 7, 6, 2, 1, -58555466273062096141846519868731181552377213747200000⟩, + ⟨2, 0, 8, 6, 3, 1, 112417610430537927083171212384029616324263857356800000⟩, + ⟨2, 0, 7, 7, 1, 1, 302938805257720086603440041278852945649101019545600000⟩, + ⟨2, 0, 8, 7, 2, 1, -44216839440538874404104891381816422272523776819200000⟩ +] + +def collectedFourData_9_1_18 : List CollectedFourTerm := [ + ⟨2, 1, 6, 0, 7, 2, 27079568107939466409192711734385257266138211942400000⟩, + ⟨2, 1, 7, 0, 8, 2, 79432523991935027999686078820741145760559529984000000⟩, + ⟨2, 1, 6, 1, 6, 2, -9978964845881685160141121049123835259642078822400000⟩, + ⟨2, 1, 7, 1, 7, 2, -6283877312718583051365237836610413318079774720000000⟩, + ⟨2, 1, 8, 1, 8, 2, -45405480899772459830181616914568855901541551308800000⟩, + ⟨2, 1, 6, 2, 5, 2, -179282449443617084267603932815906568538790297600000⟩, + ⟨2, 1, 7, 2, 6, 2, -3941230051745620781633912200764249790547912294400000⟩, + ⟨2, 1, 8, 2, 7, 2, -19496084674982030328769018120090060654277925273600000⟩, + ⟨2, 1, 6, 3, 4, 2, 2903069154094218835727639709220928366097884774400000⟩, + ⟨2, 1, 7, 3, 5, 2, -9452986658272711165767452442558167622721575321600000⟩, + ⟨2, 1, 8, 3, 6, 2, 1046918876008435886267488241254455519700058112000000⟩, + ⟨2, 1, 6, 4, 3, 2, -3665443462826801345951711537684318856269738803200000⟩, + ⟨2, 1, 7, 4, 4, 2, 4887240273263207609082956704930393410783254937600000⟩, + ⟨2, 1, 8, 4, 5, 2, 14249752051357712443625223896007991319532562022400000⟩, + ⟨2, 1, 6, 5, 2, 2, 7956712006062732852729444544667196696895999180800000⟩, + ⟨2, 1, 7, 5, 3, 2, 5574797292738178666861973212355117237071459123200000⟩, + ⟨2, 1, 8, 5, 4, 2, 7133458646484417175155453605520041651058455347200000⟩, + ⟨2, 1, 6, 6, 1, 2, -14901350732146725531929241373967193144636840345600000⟩, + ⟨2, 1, 7, 6, 2, 2, 39455608600226967464297135810949244857387004723200000⟩, + ⟨2, 1, 8, 6, 3, 2, -37874390891500854459709538923186785961556469350400000⟩, + ⟨2, 1, 6, 7, 0, 2, -4421720985463332713969215734926226815932642099200000⟩, + ⟨2, 1, 7, 7, 1, 2, -204125006439709334470244536375948630132705040793600000⟩, + ⟨2, 1, 8, 7, 2, 2, 14897006390226362498699844509263074956261562777600000⟩ +] + +def collectedFourData_9_1_19 : List CollectedFourTerm := [ + ⟨2, 2, 5, 0, 6, 3, -20288734993026087043755515275308084937009555046400000⟩, + ⟨2, 2, 6, 0, 7, 3, -27937555473975275414139855678259908537976514150400000⟩, + ⟨2, 2, 7, 0, 8, 3, -40974629591893739371299989114523975815509573632000000⟩, + ⟨2, 2, 5, 1, 5, 3, 6650298673674642913219566024317269944802738176000000⟩, + ⟨2, 2, 6, 1, 6, 3, 10295137752692991195210385673343502683944150630400000⟩, + ⟨2, 2, 7, 1, 7, 3, 3241487646995720158952023953593235550041538560000000⟩, + ⟨2, 2, 8, 1, 8, 3, 15614701785537964295481600849049791091317512601600000⟩, + ⟨2, 2, 5, 2, 4, 3, -4995700713100905882155283780172007798480673177600000⟩, + ⟨2, 2, 6, 2, 5, 3, 184962823516107478773646199152168980258068889600000⟩, + ⟨2, 2, 7, 2, 6, 3, 2033051870832072683046603225207762367682917171200000⟩, + ⟨2, 2, 8, 2, 7, 3, 6704599139857735036151274004132599633286476595200000⟩, + ⟨2, 2, 5, 3, 3, 3, 1491744039678237236148673513512634428305493196800000⟩, + ⟨2, 2, 6, 3, 4, 3, -2995049818151073773521856816990209490385528422400000⟩, + ⟨2, 2, 7, 3, 5, 3, 4876247252311465512414318635058096422452513996800000⟩, + ⟨2, 2, 8, 3, 6, 3, -360029796372099292641198711076694408124432384000000⟩, + ⟨2, 2, 5, 4, 2, 3, 3080876382620899504612667974121681000633204736000000⟩, + ⟨2, 2, 6, 4, 3, 3, 3781579147468754210664824241752256124401431347200000⟩, + ⟨2, 2, 7, 4, 4, 3, -2521043646351683576104427495369616500200361164800000⟩, + ⟨2, 2, 8, 4, 5, 3, -4900413438874591523072040734386568183904259276800000⟩, + ⟨2, 2, 5, 5, 1, 3, 1040151089494084080900233178106444294802060083200000⟩, + ⟨2, 2, 6, 5, 2, 3, -8208811978602018767962672967922805508519283916800000⟩, + ⟨2, 2, 7, 5, 3, 3, -2875714413192150825642631153970469352152603033600000⟩, + ⟨2, 2, 8, 5, 4, 3, -2453158236781931120048469046202656871269426790400000⟩, + ⟨2, 2, 5, 6, 0, 3, -55230797775475487326629997720482053578785659289600000⟩, + ⟨2, 2, 6, 6, 1, 3, 15373484209833242076482404060134409466206067097600000⟩, + ⟨2, 2, 7, 6, 2, 3, -20352858835018036916895291293250815670315751833600000⟩, + ⟨2, 2, 8, 6, 3, 3, 13024800252311497238983196022428422630500256972800000⟩, + ⟨2, 2, 6, 7, 0, 3, 4561818520495682320759413641331303289216774963200000⟩, + ⟨2, 2, 7, 7, 1, 3, 105296245278057958707835527321118514383780891852800000⟩, + ⟨2, 2, 8, 7, 2, 3, -5123000740683791217560333015609674933608854323200000⟩ +] + +def collectedFourData_9_1_20 : List CollectedFourTerm := [ + ⟨2, 3, 4, 0, 5, 4, 88373427408266631990920164193143976938287409397760000⟩, + ⟨2, 3, 5, 0, 6, 4, 154157029435069959229951926148407651263125546598400000⟩, + ⟨2, 3, 6, 0, 7, 4, 106136990872666202942540946498792416720633148211200000⟩, + ⟨2, 3, 7, 0, 8, 4, 103777246868929190356049766967253488826490814464000000⟩, + ⟨2, 3, 4, 1, 4, 4, 27195436006543663389506421354746327333299373998080000⟩, + ⟨2, 3, 5, 1, 5, 4, -50530025097279876427275652912549489889935097856000000⟩, + ⟨2, 3, 6, 1, 6, 4, -39112045529835187759097702658938853109909369651200000⟩, + ⟨2, 3, 7, 1, 7, 4, -8209779249143227369979675085549080411237253120000000⟩, + ⟨2, 3, 8, 1, 8, 4, -29660745773460263154492072319502969521666680422400000⟩, + ⟨2, 3, 4, 2, 3, 4, 42699850442396104260502636217868329810189950648320000⟩, + ⟨2, 3, 5, 2, 4, 4, 37958127115515728706654494819941578913009473945600000⟩, + ⟨2, 3, 6, 2, 5, 4, -702688448515080087773851865979504834850376908800000⟩, + ⟨2, 3, 7, 2, 6, 4, -5149150291243113564827339052534206486578357862400000⟩, + ⟨2, 3, 8, 2, 7, 4, -12735652164965717537728124576255565193882160332800000⟩, + ⟨2, 3, 4, 3, 2, 4, -113915383302932316932708660423294953751833183518720000⟩, + ⟨2, 3, 5, 3, 3, 4, -11334508036765922530726754499736317684519587020800000⟩, + ⟨2, 3, 6, 3, 4, 4, 11378432000194206219767111027162117842756907827200000⟩, + ⟨2, 3, 7, 3, 5, 4, -12350166918828676217764396175778340568986917273600000⟩, + ⟨2, 3, 8, 3, 6, 4, 683890887429816796830399240513877090423013376000000⟩, + ⟨2, 3, 4, 4, 1, 4, 1462466816114715929740228236234603377404674048000000⟩, + ⟨2, 3, 5, 4, 2, 4, -23408987862710716408212999157908318137106825216000000⟩, + ⟨2, 3, 6, 4, 3, 4, -14366519355390299491288732938515537787356813721600000⟩, + ⟨2, 3, 7, 4, 4, 4, 6385096618580374935172676346119862901370624409600000⟩, + ⟨2, 3, 8, 4, 5, 4, 9308529819629837871819835651314340868427821875200000⟩, + ⟨2, 3, 4, 5, 0, 4, 469405954326262490391418343279638265141172822343680000⟩, + ⟨2, 3, 5, 5, 1, 4, -7903233108184224736354591095638699293036196659200000⟩, + ⟨2, 3, 6, 5, 2, 4, 31185928305714530217274652772328520653199533670400000⟩, + ⟨2, 3, 7, 5, 3, 4, 7283378216100351040859742504947177079845368627200000⟩, + ⟨2, 3, 8, 5, 4, 4, 4659871434153812786836700554502342834698951065600000⟩, + ⟨2, 3, 5, 6, 0, 4, 419652369717628537378340401767131265903149816217600000⟩, + ⟨2, 3, 6, 6, 1, 4, -58405086829451671477885899853849863035785366732800000⟩, + ⟨2, 3, 7, 6, 2, 4, 51548084188856110754200914770843206122720146227200000⟩, + ⟨2, 3, 8, 6, 3, 4, -24741125020505959600057218480224902017166029619200000⟩, + ⟨2, 3, 6, 7, 0, 4, -17330710667353729223398050647597769147704514969600000⟩, + ⟨2, 3, 7, 7, 1, 4, -266685862677186115403634827761250927408909490585600000⟩, + ⟨2, 3, 8, 7, 2, 4, 9731343233682861062750784504721826799539768524800000⟩ +] + +def collectedFourData_9_1_21 : List CollectedFourTerm := [ + ⟨2, 4, 3, 0, 4, 5, -1333566719813071627596432623237356440266578329600000⟩, + ⟨2, 4, 4, 0, 5, 5, 78559755044625612243191090080679173082212781260800000⟩, + ⟨2, 4, 5, 0, 6, 5, 68519117261787854861476313849968922174460788736000000⟩, + ⟨2, 4, 6, 0, 7, 5, 31450238111395457264671902797276073415233503232000000⟩, + ⟨2, 4, 7, 0, 8, 5, 23063253662112961579576194526845495743380193280000000⟩, + ⟨2, 4, 3, 1, 3, 5, 6401350351981484718664911559251625062982641254400000⟩, + ⟨2, 4, 4, 1, 4, 5, 24175443384534977094453537663814864399222859366400000⟩, + ⟨2, 4, 5, 1, 5, 5, -22459389153836102974522196390491654862395146240000000⟩, + ⟨2, 4, 6, 1, 6, 5, -11589579983596879788720235330977605948257861632000000⟩, + ⟨2, 4, 7, 1, 7, 5, -1824525385338884140060540283664832190113382400000000⟩, + ⟨2, 4, 8, 1, 8, 5, -5273397198094834885830700387822572227105547878400000⟩, + ⟨2, 4, 3, 2, 2, 5, -4995700713100905882155283780172007798480673177600000⟩, + ⟨2, 4, 4, 2, 3, 5, 37958127115515728706654494819941578913009473945600000⟩, + ⟨2, 4, 5, 2, 4, 5, 16871480803678416358921479969526112290313601024000000⟩, + ⟨2, 4, 6, 2, 5, 5, -208218820245616435340508263731378870674259968000000⟩, + ⟨2, 4, 7, 2, 6, 5, -1144337153800890082013799333351862925575323648000000⟩, + ⟨2, 4, 8, 2, 7, 5, -2264277269209257564205887013254599586668661964800000⟩, + ⟨2, 4, 3, 3, 1, 5, -111929675372169552815392722294872557476013670400000⟩, + ⟨2, 4, 4, 3, 2, 5, -101265333602483704024560573557656706543263521177600000⟩, + ⟨2, 4, 5, 3, 3, 5, -5037918076923980417524541012833831437239058432000000⟩, + ⟨2, 4, 6, 3, 4, 5, 3371627486309194478147686119692707304143060992000000⟩, + ⟨2, 4, 7, 3, 5, 5, -2744677094567066968824659583055471923871875072000000⟩, + ⟨2, 4, 8, 3, 6, 5, 121589265392036539385739240263064156232482816000000⟩, + ⟨2, 4, 3, 4, 0, 5, 21461771826311595325163846729760706535233054310400000⟩, + ⟨2, 4, 4, 4, 1, 5, 1300063132145969806655313232481225914806435840000000⟩, + ⟨2, 4, 5, 4, 2, 5, -10404735938560778770570924064701632135970160640000000⟩, + ⟨2, 4, 6, 4, 3, 5, -4257049788617644235223415090281011017339109376000000⟩, + ⟨2, 4, 7, 4, 4, 5, 1419011463634315732978851365410636454839713792000000⟩, + ⟨2, 4, 8, 4, 5, 5, 1654967661438257294782597035619123215018963763200000⟩, + ⟨2, 4, 4, 5, 0, 5, 417279468159570368916193915982570655344161613414400000⟩, + ⟨2, 4, 5, 5, 1, 5, -3512798333435746004260288712079325384585248768000000⟩, + ⟨2, 4, 6, 5, 2, 5, 9240933466036479457153586458292965499411103744000000⟩, + ⟨2, 4, 7, 5, 3, 5, 1618643820135131802453998315632707771505311744000000⟩, + ⟨2, 4, 8, 5, 4, 5, 828480617177755988457531828572206204462930329600000⟩, + ⟨2, 4, 5, 6, 0, 5, 186525454176453534448828869976804281652718075904000000⟩, + ⟨2, 4, 6, 6, 1, 5, -17306443989039382679631285433248836198867140608000000⟩, + ⟨2, 4, 7, 6, 2, 5, 11455946050920806109730450401729395827874463744000000⟩, + ⟨2, 4, 8, 6, 3, 5, -4398735633869038715800885234031502618659074867200000⟩, + ⟨2, 4, 6, 7, 0, 5, -5135391277315228622708198189457363195874246656000000⟩, + ⟨2, 4, 7, 7, 1, 5, -59267747840638312090539820064956820459788173312000000⟩, + ⟨2, 4, 8, 7, 2, 5, 1730139846588745782915267490323920660282002636800000⟩ +] + +def collectedFourData_9_1_22 : List CollectedFourTerm := [ + ⟨2, 5, 2, 0, 3, 6, 134878391794083006563091368941999093143778099200000⟩, + ⟨2, 5, 3, 0, 4, 6, 49374508204002039818412679586577934515280281600000⟩, + ⟨2, 5, 4, 0, 5, 6, -1454313913329721887109619933681649751528203878400000⟩, + ⟨2, 5, 5, 0, 6, 6, -845626411014850192657267978951744680835940352000000⟩, + ⟨2, 5, 6, 0, 7, 6, -291106552184088869464439053888407406293024768000000⟩, + ⟨2, 5, 7, 0, 8, 6, -170780627655524462122679870941927668109541376000000⟩, + ⟨2, 5, 2, 1, 2, 6, -129377145328400448554958143219551538302156800000000⟩, + ⟨2, 5, 3, 1, 3, 6, -237006158578180728717327622369795712013985382400000⟩, + ⟨2, 5, 4, 1, 4, 6, -447540647944643203378327766178854303146652467200000⟩, + ⟨2, 5, 5, 1, 5, 6, 277181805643838734675163129902061946855751680000000⟩, + ⟨2, 5, 6, 1, 6, 6, 107274312465830809296780572112490291022266368000000⟩, + ⟨2, 5, 7, 1, 7, 6, 13510391683957454432303820673074319148974080000000⟩, + ⟨2, 5, 8, 1, 8, 6, 32540728228029904045612115154870474201523814400000⟩, + ⟨2, 5, 2, 2, 1, 6, -179282449443617084267603932815906568538790297600000⟩, + ⟨2, 5, 3, 2, 2, 6, 184962823516107478773646199152168980258068889600000⟩, + ⟨2, 5, 4, 2, 3, 6, -702688448515080087773851865979504834850376908800000⟩, + ⟨2, 5, 5, 2, 4, 6, -208218820245616435340508263731378870674259968000000⟩, + ⟨2, 5, 6, 2, 5, 6, 1927294243269260388878202465788402212012032000000⟩, + ⟨2, 5, 7, 2, 6, 6, 8473679396619352778432817647739469783734681600000⟩, + ⟨2, 5, 8, 2, 7, 6, 13972251374666713858503395587030404140158156800000⟩, + ⟨2, 5, 2, 3, 0, 6, 310474585010522080095842641953593173182146150400000⟩, + ⟨2, 5, 3, 3, 1, 6, 4144129118420956070433452711655722386351718400000⟩, + ⟨2, 5, 4, 3, 2, 6, 1874644129330733236163997703019776604147338444800000⟩, + ⟨2, 5, 5, 3, 3, 6, 62175298699475701977188806305791028624359424000000⟩, + ⟨2, 5, 6, 3, 4, 6, -31208121519211808051718202760023992862507008000000⟩, + ⟨2, 5, 7, 3, 5, 6, 20324004747514064562769056912368220779210342400000⟩, + ⟨2, 5, 8, 3, 6, 6, -750294941180895431470766945734284810387456000000⟩, + ⟨2, 5, 3, 4, 0, 6, -794609233544142969677005163853208864296429158400000⟩, + ⟨2, 5, 4, 4, 1, 6, -24067028979569689377234367522401685937848320000000⟩, + ⟨2, 5, 5, 4, 2, 6, 128409703173295117816866695958887940992532480000000⟩, + ⟨2, 5, 6, 4, 3, 6, 39403678981732853800296967519864560103194624000000⟩, + ⟨2, 5, 7, 4, 4, 6, -10507609722385141143277581072184289773643366400000⟩, + ⟨2, 5, 8, 4, 5, 6, -10212364226327722197198292524122689399632691200000⟩, + ⟨2, 5, 4, 5, 0, 6, -7724761055410211930790720638765747578162328371200000⟩, + ⟨2, 5, 5, 5, 1, 6, 43353084015558841171951511130020104661630976000000⟩, + ⟨2, 5, 6, 5, 2, 6, -85535005195580097665773981101694466975072256000000⟩, + ⟨2, 5, 7, 5, 3, 6, -11985863382646765056974803670608616090291404800000⟩, + ⟨2, 5, 8, 5, 4, 6, -5112333016657967547905085117057329626978713600000⟩, + ⟨2, 5, 5, 6, 0, 6, -2301997700517860760809436800690048490566320128000000⟩, + ⟨2, 5, 6, 6, 1, 6, 160190177968505232563170738471687112613691392000000⟩, + ⟨2, 5, 7, 6, 2, 6, -84829906726388566902212439095809695961369804800000⟩, + ⟨2, 5, 8, 6, 3, 6, 27143424898923970146231709444074205468635955200000⟩, + ⟨2, 5, 6, 7, 0, 6, 47533695724669639231901526665126061061177344000000⟩, + ⟨2, 5, 7, 7, 1, 6, 438870565456298627913763479929840541442139750400000⟩, + ⟨2, 5, 8, 7, 2, 6, -10676231740076342409423469537501555456789708800000⟩ +] + +def collectedFourData_9_1_23 : List CollectedFourTerm := [ + ⟨2, 6, 1, 0, 2, 7, -3117078242687373059918210466416218179442311168000000⟩, + ⟨2, 6, 2, 0, 3, 7, 2965079809650524249543286340392774066089282764800000⟩, + ⟨2, 6, 3, 0, 4, 7, 542708715012766870660946154377078873475199795200000⟩, + ⟨2, 6, 4, 0, 5, 7, -10656900545619176601822291228190826824773874483200000⟩, + ⟨2, 6, 5, 0, 6, 7, -4647426775438026772836945176432866793852239872000000⟩, + ⟨2, 6, 6, 0, 7, 7, -1279899839932528649961614851350317252873709158400000⟩, + ⟨2, 6, 7, 0, 8, 7, -625721911673245356038673151152555005967335424000000⟩, + ⟨2, 6, 1, 1, 1, 7, 3081144724055304144106541398541482997031999897600000⟩, + ⟨2, 6, 2, 1, 2, 7, -2844143945822837099624412615096181571400499200000000⟩, + ⟨2, 6, 3, 1, 3, 7, -2605095472356539269412355205492297536952388812800000⟩, + ⟨2, 6, 4, 1, 4, 7, -3279481913466856186388281119931329722938136985600000⟩, + ⟨2, 6, 5, 1, 5, 7, 1523346632075347171431525770068467848293908480000000⟩, + ⟨2, 6, 6, 1, 6, 7, 471649897000818515680852790290934814168475238400000⟩, + ⟨2, 6, 7, 1, 7, 7, 49500626786499051444571181101158294796369920000000⟩, + ⟨2, 6, 8, 1, 8, 7, 102193491248832275533321169200394488402201804800000⟩, + ⟨2, 6, 1, 2, 0, 7, 5849119340869625259045855736635678311183705702400000⟩, + ⟨2, 6, 2, 2, 1, 7, -3941230051745620781633912200764249790547912294400000⟩, + ⟨2, 6, 3, 2, 2, 7, 2033051870832072683046603225207762367682917171200000⟩, + ⟨2, 6, 4, 2, 3, 7, -5149150291243113564827339052534206486578357862400000⟩, + ⟨2, 6, 5, 2, 4, 7, -1144337153800890082013799333351862925575323648000000⟩, + ⟨2, 6, 6, 2, 5, 7, 8473679396619352778432817647739469783734681600000⟩, + ⟨2, 6, 7, 2, 6, 7, 31046652912259264696460099180160636334532198400000⟩, + ⟨2, 6, 8, 2, 7, 7, 43879569583619441853450050868779927486437785600000⟩, + ⟨2, 6, 2, 3, 0, 7, 6825273575546215977411363251652357218891307417600000⟩, + ⟨2, 6, 3, 3, 1, 7, 45550934490582547309631955553988775032704204800000⟩, + ⟨2, 6, 4, 3, 2, 7, 13736990247838666550408653965552749019618764390400000⟩, + ⟨2, 6, 5, 3, 3, 7, 341705443660422888092384386022045790360305664000000⟩, + ⟨2, 6, 6, 3, 4, 7, -137211854001056358498820411067313836723168870400000⟩, + ⟨2, 6, 7, 3, 5, 7, 74464974617156092049449887987613216861165977600000⟩, + ⟨2, 6, 8, 3, 6, 7, -2356285912482022948467140366835676612657152000000⟩, + ⟨2, 6, 3, 4, 0, 7, -8734089143576871670595850665210924253288647884800000⟩, + ⟨2, 6, 4, 4, 1, 7, -176358028286056599058230899546322940314255360000000⟩, + ⟨2, 6, 5, 4, 2, 7, 705719079939121034740042525809270557276897280000000⟩, + ⟨2, 6, 6, 4, 3, 7, 173245026754259182626843635733705258173674291200000⟩, + ⟨2, 6, 7, 4, 4, 7, -38498755584088196351375660945664239503776153600000⟩, + ⟨2, 6, 8, 4, 5, 7, -32071720917854032858336480525026741872649830400000⟩, + ⟨2, 6, 4, 5, 0, 7, -56605392791504441236952590894025879974479239577600000⟩, + ⟨2, 6, 5, 5, 1, 7, 238261578431452581714399868191249507324788736000000⟩, + ⟨2, 6, 6, 5, 2, 7, -376069307396491714122008656239758072603266252800000⟩, + ⟨2, 6, 7, 5, 3, 7, -43914918523263072372815905883920778285757235200000⟩, + ⟨2, 6, 8, 5, 4, 7, -16055177245508821676503031430990825606296371200000⟩, + ⟨2, 6, 5, 6, 0, 7, -12651409193267969282285808131606782244875665408000000⟩, + ⟨2, 6, 6, 6, 1, 7, 704303567207235779356107323561699124685937049600000⟩, + ⟨2, 6, 7, 6, 2, 7, -310807684294055840987643001709797894515798835200000⟩, + ⟨2, 6, 8, 6, 3, 7, 85243370567292939027236688402928943904482918400000⟩, + ⟨2, 6, 6, 7, 0, 7, 208990038502924017888743152145633002900370227200000⟩, + ⟨2, 6, 7, 7, 1, 7, 1607974703947928365598847817429442380850370969600000⟩, + ⟨2, 6, 8, 7, 2, 7, -33528487354508458479832350970467672810690969600000⟩ +] + +def collectedFourData_9_1_24 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 1, 8, 24355716481599897326420689829408853411414147072000000⟩, + ⟨2, 7, 1, 0, 2, 8, -30838505014981829971544030689925013690944323584000000⟩, + ⟨2, 7, 2, 0, 3, 8, 14667361782503046194576578724655440242725303091200000⟩, + ⟨2, 7, 3, 0, 4, 8, 1789744981951048551078525885917528673284731699200000⟩, + ⟨2, 7, 4, 0, 5, 8, -26358247638732818532441425800388423475192555110400000⟩, + ⟨2, 7, 5, 0, 6, 8, -9195771344998005740818505364164668920322798387200000⟩, + ⟨2, 7, 6, 0, 7, 8, -2110427060182096319908519713801550296748602163200000⟩, + ⟨2, 7, 7, 0, 8, 8, -884359684145531463896510207439387808619298816000000⟩, + ⟨2, 7, 0, 1, 0, 8, 127010103046640892878211030744856440784237363200000000⟩, + ⟨2, 7, 1, 1, 1, 8, 30483000305678919914152270691593694684474297548800000⟩, + ⟨2, 7, 2, 1, 2, 8, -14069128284211720551297301066492505819499724800000000⟩, + ⟨2, 7, 3, 1, 3, 8, -8591084720362066429878486368036691046940069068800000⟩, + ⟨2, 7, 4, 1, 4, 8, -8111307413621210239834103668722826710439113523200000⟩, + ⟨2, 7, 5, 1, 5, 8, 3014215819767787567519503509583718163675086848000000⟩, + ⟨2, 7, 6, 1, 6, 8, 777703594068031651283323724030815175770846003200000⟩, + ⟨2, 7, 7, 1, 7, 8, 69961364390854728441149929324018824149729280000000⟩, + ⟨2, 7, 8, 1, 8, 8, 126380148612285516041909381276854904110763212800000⟩, + ⟨2, 7, 1, 2, 0, 8, 57867683158034269165026248429261880815739155251200000⟩, + ⟨2, 7, 2, 2, 1, 8, -19496084674982030328769018120090060654277925273600000⟩, + ⟨2, 7, 3, 2, 2, 8, 6704599139857735036151274004132599633286476595200000⟩, + ⟨2, 7, 4, 2, 3, 8, -12735652164965717537728124576255565193882160332800000⟩, + ⟨2, 7, 5, 2, 4, 8, -2264277269209257564205887013254599586668661964800000⟩, + ⟨2, 7, 6, 2, 5, 8, 13972251374666713858503395587030404140158156800000⟩, + ⟨2, 7, 7, 2, 6, 8, 43879569583619441853450050868779927486437785600000⟩, + ⟨2, 7, 8, 2, 7, 8, 54264772220357180971837844676983279941425561600000⟩, + ⟨2, 7, 2, 3, 0, 8, 33762584221600999792017678135505742399195735654400000⟩, + ⟨2, 7, 3, 3, 1, 8, 150217887003681604277929460489654216101252300800000⟩, + ⟨2, 7, 4, 3, 2, 8, 33976388276630191973480897769425713466901843148800000⟩, + ⟨2, 7, 5, 3, 3, 8, 676125795859620844761239437941922737932363366400000⟩, + ⟨2, 7, 6, 3, 4, 8, -226248649016824381364025277685813540814009139200000⟩, + ⟨2, 7, 7, 3, 5, 8, 105244550660265713994114634804032631753565798400000⟩, + ⟨2, 7, 8, 3, 6, 8, -2913960176460020354045693179915552866435072000000⟩, + ⟨2, 7, 3, 4, 0, 8, -28803282099979009012114902754779165773498469580800000⟩, + ⟨2, 7, 4, 4, 1, 8, -436195173516320464700804721724604712663121920000000⟩, + ⟨2, 7, 5, 4, 2, 8, 1396392370767556402265867715923955499011145728000000⟩, + ⟨2, 7, 6, 4, 3, 8, 285663753597651789843057169872067917656988057600000⟩, + ⟨2, 7, 7, 4, 4, 8, -54411946734126212434975309486684596655777382400000⟩, + ⟨2, 7, 8, 4, 5, 8, -39662299490100386849178294229649777947469414400000⟩, + ⟨2, 7, 4, 5, 0, 8, -140004962465334506757997798506020836440389399347200000⟩, + ⟨2, 7, 5, 5, 1, 8, 471443467841931018164628482322958442775026073600000⟩, + ⟨2, 7, 6, 5, 2, 8, -620100743879563367869222673655407471413847654400000⟩, + ⟨2, 7, 7, 5, 3, 8, -62066842713972766874890737029205524539559116800000⟩, + ⟨2, 7, 8, 5, 4, 8, -19855038334519909238767849063258803125039923200000⟩, + ⟨2, 7, 5, 6, 0, 8, -25033092882315023404338324038973702611435048140800000⟩, + ⟨2, 7, 6, 6, 1, 8, 1161326269792553732562498167499932649034403020800000⟩, + ⟨2, 7, 7, 6, 2, 8, -439277865109878661743037547461517987761933516800000⟩, + ⟨2, 7, 8, 6, 3, 8, 105418355991724730552176055669916288577594982400000⟩, + ⟨2, 7, 6, 7, 0, 8, 344603709449889399853405233499668127537535385600000⟩, + ⟨2, 7, 7, 7, 1, 8, 2272619792864123744649227305048442469714650726400000⟩, + ⟨2, 7, 8, 7, 2, 8, -41463846305929321890223184284070096787839385600000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0905.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0905.lean new file mode 100644 index 0000000000000000000000000000000000000000..aa162cb6b701f175449eb6b85ef039bf55b67c13 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0905.lean @@ -0,0 +1,610 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0905. -/ +namespace LaughlinFock +def collectedFourData_9_1_25 : List CollectedFourTerm := [ + ⟨3, 0, 6, 0, 7, 2, -46895374849398029847204020038588586665694566809600000⟩, + ⟨3, 0, 7, 0, 8, 2, -137558249562460946508878114441955578221833486336000000⟩, + ⟨3, 0, 6, 1, 6, 2, 17281195002492805566883411620270678963398482329600000⟩, + ⟨3, 0, 7, 1, 7, 2, 10882181758326020038686736622115653120038010880000000⟩, + ⟨3, 0, 8, 1, 8, 2, 78631499532214470212597448301073011882983633715200000⟩, + ⟨3, 0, 6, 2, 5, 2, 310474585010522080095842641953593173182146150400000⟩, + ⟨3, 0, 7, 2, 6, 2, 6825273575546215977411363251652357218891307417600000⟩, + ⟨3, 0, 8, 2, 7, 2, 33762584221600999792017678135505742399195735654400000⟩, + ⟨3, 0, 6, 3, 4, 2, -5027425683168786070885655885019282297761405337600000⟩, + ⟨3, 0, 7, 3, 5, 2, 16370325812400441347005556290938220454888236646400000⟩, + ⟨3, 0, 8, 3, 6, 2, -1813014629023263114246081772721469061645467648000000⟩, + ⟨3, 0, 6, 4, 3, 2, 6347676761068476412021903991769493319893961932800000⟩, + ⟨3, 0, 7, 4, 4, 2, -8463538402097210772017713097792430902639748710400000⟩, + ⟨3, 0, 8, 4, 5, 2, -24677183228911054299393374757179156184495135129600000⟩, + ⟨3, 0, 6, 5, 2, 2, -13779133795845830225121792929733614574201156403200000⟩, + ⟨3, 0, 7, 5, 3, 2, -9654223719901826092257994134232885987065515212800000⟩, + ⟨3, 0, 8, 5, 4, 2, -12353454673506643206156392250307721809151970508800000⟩, + ⟨3, 0, 6, 6, 1, 2, 25805597251807343193664540330830945573732247142400000⟩, + ⟨3, 0, 7, 6, 2, 2, -68327735060009711833404939140836959671133457612800000⟩, + ⟨3, 0, 8, 6, 3, 2, 65589441861475398703071611935146250408056953241600000⟩, + ⟨3, 0, 6, 7, 0, 2, 7657369654723452378037196480963062194668096716800000⟩, + ⟨3, 0, 7, 7, 1, 2, 353495988376542330385624443625347028884918789734400000⟩, + ⟨3, 0, 8, 7, 2, 2, -25798073884299511833400211221271193143623444070400000⟩ +] + +def collectedFourData_9_1_26 : List CollectedFourTerm := [ + ⟨3, 1, 5, 0, 6, 3, -454573172393227294580993429085926153367689625600000⟩, + ⟨3, 1, 6, 0, 7, 3, -625946527720038255238678570641545376795564441600000⟩, + ⟨3, 1, 7, 0, 8, 3, -918044785326779109522349386900450851294281728000000⟩, + ⟨3, 1, 5, 1, 5, 3, 149001274179680310139237211314428571029602304000000⟩, + ⟨3, 1, 6, 1, 6, 3, 230664623993342548237699579652290723333118361600000⟩, + ⟨3, 1, 7, 1, 7, 3, 72626180167210565851230203297155642545930240000000⟩, + ⟨3, 1, 8, 1, 8, 3, 349850521930815804074434868143675591765681766400000⟩, + ⟨3, 1, 5, 2, 4, 3, -111929675372169552815392722294872557476013670400000⟩, + ⟨3, 1, 6, 2, 5, 3, 4144129118420956070433452711655722386351718400000⟩, + ⟨3, 1, 7, 2, 6, 3, 45550934490582547309631955553988775032704204800000⟩, + ⟨3, 1, 8, 2, 7, 3, 150217887003681604277929460489654216101252300800000⟩, + ⟨3, 1, 5, 3, 3, 3, 33422824081851948809687661987973293751350067200000⟩, + ⟨3, 1, 6, 3, 4, 3, -67104691237806319280665176558771064180152729600000⟩, + ⟨3, 1, 7, 3, 5, 3, 109253296650525708266422033912558064267113267200000⟩, + ⟨3, 1, 8, 3, 6, 3, -8066539720155453576443548681665254246055936000000⟩, + ⟨3, 1, 5, 4, 2, 3, 69027652610216728004926716751875910920044544000000⟩, + ⟨3, 1, 6, 4, 3, 3, 84727038443344373169523237951443333335010508800000⟩, + ⟨3, 1, 7, 4, 4, 3, -56484487990887165017042822645246303770194739200000⟩, + ⟨3, 1, 8, 4, 5, 3, -109794744902199496013190272090885148793582387200000⟩, + ⟨3, 1, 5, 5, 1, 3, 23304793555740319763047595717947454435151052800000⟩, + ⟨3, 1, 6, 5, 2, 3, -183920077026748455786739412566700114792624947200000⟩, + ⟨3, 1, 7, 5, 3, 3, -64430957580697856956442869225791995211310694400000⟩, + ⟨3, 1, 8, 5, 4, 3, -54963501788546646964362075647571059310959001600000⟩, + ⟨3, 1, 5, 6, 0, 3, -1237457089721789520141081043030763045428553318400000⟩, + ⟨3, 1, 6, 6, 1, 3, 344445993818896073357305289089070013266421350400000⟩, + ⟨3, 1, 7, 6, 2, 3, -456009879920352182871984925895167869100385894400000⟩, + ⟨3, 1, 8, 6, 3, 3, 291823259188731806387037597942399916290814771200000⟩, + ⟨3, 1, 6, 7, 0, 3, 102208457917987186926535115452520780857658572800000⟩, + ⟨3, 1, 7, 7, 1, 3, 2359183471694757023013172669568094018209002291200000⟩, + ⟨3, 1, 8, 7, 2, 3, -114781857994890407448272954583860591725432012800000⟩ +] + +def collectedFourData_9_1_27 : List CollectedFourTerm := [ + ⟨3, 2, 4, 0, 5, 4, -235764124527496645868403273682078878127035997224960000⟩, + ⟨3, 2, 5, 0, 6, 4, -411262730782341956940361388539909446245198227046400000⟩, + ⟨3, 2, 6, 0, 7, 4, -283154059618788975038072890247241734242419553075200000⟩, + ⟨3, 2, 7, 0, 8, 4, -276858694649182454147856169029045787379361644544000000⟩, + ⟨3, 2, 4, 1, 4, 4, -72552444204812656014238549142183780845019128135680000⟩, + ⟨3, 2, 5, 1, 5, 4, 134804855699171869739117033209050426202103218176000000⟩, + ⟨3, 2, 6, 1, 6, 4, 104343776667403646881611635191108825318398571315200000⟩, + ⟨3, 2, 7, 1, 7, 4, 21902187954036559648552997616585019905036779520000000⟩, + ⟨3, 2, 8, 1, 8, 4, 79129439303135722294246228745780777158411970150400000⟩, + ⟨3, 2, 4, 2, 3, 4, -113915383302932316932708660423294953751833183518720000⟩, + ⟨3, 2, 5, 2, 4, 4, -101265333602483704024560573557656706543263521177600000⟩, + ⟨3, 2, 6, 2, 5, 4, 1874644129330733236163997703019776604147338444800000⟩, + ⟨3, 2, 7, 2, 6, 4, 13736990247838666550408653965552749019618764390400000⟩, + ⟨3, 2, 8, 2, 7, 4, 33976388276630191973480897769425713466901843148800000⟩, + ⟨3, 2, 4, 3, 2, 4, 303905386520267210408310285126708071745583180677120000⟩, + ⟨3, 2, 5, 3, 3, 4, 30238392270254110678249708638072743630876757196800000⟩, + ⟨3, 2, 6, 3, 4, 4, -30355573362887374228494915031406968201985340211200000⟩, + ⟨3, 2, 7, 3, 5, 4, 32947984216279527479311802093913337018602592665600000⟩, + ⟨3, 2, 8, 3, 6, 4, -1824495677895831881091101791745846662813188096000000⟩, + ⟨3, 2, 4, 4, 1, 4, -3901593710504300136440993835872233389564100608000000⟩, + ⟨3, 2, 5, 4, 2, 4, 62450893796731123994260906225490963436442484736000000⟩, + ⟨3, 2, 6, 4, 3, 4, 38327243354308245313078182562087108610677643673600000⟩, + ⟨3, 2, 7, 4, 4, 4, -17034268766657173227401540355281517877921421721600000⟩, + ⟨3, 2, 8, 4, 5, 4, -24833453311983189738078639742877739386068480819200000⟩, + ⟨3, 2, 4, 5, 0, 4, -1252289145225266426513523164383585015460881791713280000⟩, + ⟨3, 2, 5, 5, 1, 4, 21084378973780563476660251714663618815085196083200000⟩, + ⟨3, 2, 6, 5, 2, 4, -83198347062029789204368295434785618888678073958400000⟩, + ⟨3, 2, 7, 5, 3, 4, -19430719607474598529726887456878554540640777011200000⟩, + ⟨3, 2, 8, 5, 4, 4, -12431683836460503164090093788749361350209804697600000⟩, + ⟨3, 2, 5, 6, 0, 4, -1119555690595644840200994049503136876560614267289600000⟩, + ⟨3, 2, 6, 6, 1, 4, 155814078599491327228096882754795457904995257548800000⟩, + ⟨3, 2, 7, 6, 2, 4, -137520850964738284650609332760121884546769826611200000⟩, + ⟨3, 2, 8, 6, 3, 4, 66004791840169059024575486391280631792065000243200000⟩, + ⟨3, 2, 6, 7, 0, 4, 46235163077377601378755966640163203905761155481600000⟩, + ⟨3, 2, 7, 7, 1, 4, 711469055596066250230077005713364428828387678617600000⟩, + ⟨3, 2, 8, 7, 2, 4, -25961442090127696689540948992008201565341797580800000⟩ +] + +def collectedFourData_9_1_28 : List CollectedFourTerm := [ + ⟨3, 3, 3, 0, 4, 5, 398210445349035788954293902493201163535305932800000⟩, + ⟨3, 3, 4, 0, 5, 5, -23458380130554369869731194180832709004455470694400000⟩, + ⟨3, 3, 5, 0, 6, 5, -20460189801050177159851572289971252316757557248000000⟩, + ⟨3, 3, 6, 0, 7, 5, -9391216156344609463072369297198695966547378176000000⟩, + ⟨3, 3, 7, 0, 8, 5, -6886815916698284356579427168824975699256279040000000⟩, + ⟨3, 3, 3, 1, 3, 5, -1911478845884114190853477204824151807690486579200000⟩, + ⟨3, 3, 4, 1, 4, 5, -7218921958412021285356096365766680561587532595200000⟩, + ⟨3, 3, 5, 1, 5, 5, 6706498613335231930209340768811897206415032320000000⟩, + ⟨3, 3, 6, 1, 6, 5, 3460713092272795964941064851892512258969829376000000⟩, + ⟨3, 3, 7, 1, 7, 5, 544813435617423982610637887903064594264883200000000⟩, + ⟨3, 3, 8, 1, 8, 5, 1574665755793644438281048459208158436153045811200000⟩, + ⟨3, 3, 3, 2, 2, 5, 1491744039678237236148673513512634428305493196800000⟩, + ⟨3, 3, 4, 2, 3, 5, -11334508036765922530726754499736317684519587020800000⟩, + ⟨3, 3, 5, 2, 4, 5, -5037918076923980417524541012833831437239058432000000⟩, + ⟨3, 3, 6, 2, 5, 5, 62175298699475701977188806305791028624359424000000⟩, + ⟨3, 3, 7, 2, 6, 5, 341705443660422888092384386022045790360305664000000⟩, + ⟨3, 3, 8, 2, 7, 5, 676125795859620844761239437941922737932363366400000⟩, + ⟨3, 3, 3, 3, 1, 5, 33422824081851948809687661987973293751350067200000⟩, + ⟨3, 3, 4, 3, 2, 5, 30238392270254110678249708638072743630876757196800000⟩, + ⟨3, 3, 5, 3, 3, 5, 1504350379503368194330200006646965461399371776000000⟩, + ⟨3, 3, 6, 3, 4, 5, -1006786734346843483082423907821587794657017856000000⟩, + ⟨3, 3, 7, 3, 5, 5, 819575857681909860696884634738129327196471296000000⟩, + ⟨3, 3, 8, 3, 6, 5, -36307231428369648169476315089996874868850688000000⟩, + ⟨3, 3, 3, 4, 0, 5, -6408604526463347524417112096527538026024481587200000⟩, + ⟨3, 3, 4, 4, 1, 5, -388206087586135723897915163422568576314245120000000⟩, + ⟨3, 3, 5, 4, 2, 5, 3106912065422700115478833199790619631309291520000000⟩, + ⟨3, 3, 6, 4, 3, 5, 1271178762196517737334692052691820314013728768000000⟩, + ⟨3, 3, 7, 4, 4, 5, -423724721451067812769655318807296158524768256000000⟩, + ⟨3, 3, 8, 4, 5, 5, -494182555479456972013990847757549242750179737600000⟩, + ⟨3, 3, 4, 5, 0, 5, -124601971826443719134073647565919127541193585459200000⟩, + ⟨3, 3, 5, 5, 1, 5, 1048941135074873488248291371309302249710157824000000⟩, + ⟨3, 3, 6, 5, 2, 5, -2759394169244868704233640176273021595541307392000000⟩, + ⟨3, 3, 7, 5, 3, 5, -483336054282926796446139928634857163317051392000000⟩, + ⟨3, 3, 8, 5, 4, 5, -247388923724522947736399992009082114589641932800000⟩, + ⟨3, 3, 5, 6, 0, 5, -55697538843012054032089331491424312307348406272000000⟩, + ⟨3, 3, 6, 6, 1, 5, 5167800505136724294094911187266125867142610944000000⟩, + ⟨3, 3, 7, 6, 2, 5, -3420809256151164551685008926867753901481787392000000⟩, + ⟨3, 3, 8, 6, 3, 5, 1313486944231175113434604822462183010247219609600000⟩, + ⟨3, 3, 6, 7, 0, 5, 1533456419689220689217856598742837699498999808000000⟩, + ⟨3, 3, 7, 7, 1, 5, 17697679397520609147941813105789227900512239616000000⟩, + ⟨3, 3, 8, 7, 2, 5, -516629388383949478934498396153486104731215462400000⟩ +] + +def collectedFourData_9_1_29 : List CollectedFourTerm := [ + ⟨3, 4, 2, 0, 3, 6, -2184047016238363699848399093196376880463006924800000⟩, + ⟨3, 4, 3, 0, 4, 6, -799507214512309626441208002278672670749255270400000⟩, + ⟨3, 4, 4, 0, 5, 6, 23549287034285786417566681876540693541237135769600000⟩, + ⟨3, 4, 5, 0, 6, 6, 13692985327471564939681386297879163200589529088000000⟩, + ⟨3, 4, 6, 0, 7, 6, 4713804696572519218855490518906262001593352192000000⟩, + ⟨3, 4, 7, 0, 8, 6, 2765401598439921811054929046429642766464057344000000⟩, + ⟨3, 4, 2, 1, 2, 6, 2094966914013324262045189704211388431545139200000000⟩, + ⟨3, 4, 3, 1, 3, 6, 3837772578598465786787735749359242739057269145600000⟩, + ⟨3, 4, 4, 1, 4, 6, 7246897029148606799737790324747233599115021516800000⟩, + ⟨3, 4, 5, 1, 5, 6, -4488325279680161631338561418040385453602897920000000⟩, + ⟨3, 4, 6, 1, 6, 6, -1737062096779077017803617400394962264330862592000000⟩, + ⟨3, 4, 7, 1, 7, 6, -218769887845395709726965465708207348929003520000000⟩, + ⟨3, 4, 8, 1, 8, 6, -526922655640456752250236757331847760454457753600000⟩, + ⟨3, 4, 2, 2, 1, 6, 2903069154094218835727639709220928366097884774400000⟩, + ⟨3, 4, 3, 2, 2, 6, -2995049818151073773521856816990209490385528422400000⟩, + ⟨3, 4, 4, 2, 3, 6, 11378432000194206219767111027162117842756907827200000⟩, + ⟨3, 4, 5, 2, 4, 6, 3371627486309194478147686119692707304143060992000000⟩, + ⟨3, 4, 6, 2, 5, 6, -31208121519211808051718202760023992862507008000000⟩, + ⟨3, 4, 7, 2, 6, 6, -137211854001056358498820411067313836723168870400000⟩, + ⟨3, 4, 8, 2, 7, 6, -226248649016824381364025277685813540814009139200000⟩, + ⟨3, 4, 2, 3, 0, 6, -5027425683168786070885655885019282297761405337600000⟩, + ⟨3, 4, 3, 3, 1, 6, -67104691237806319280665176558771064180152729600000⟩, + ⟨3, 4, 4, 3, 2, 6, -30355573362887374228494915031406968201985340211200000⟩, + ⟨3, 4, 5, 3, 3, 6, -1006786734346843483082423907821587794657017856000000⟩, + ⟨3, 4, 6, 3, 4, 6, 505344138373904731774065561853490735981002752000000⟩, + ⟨3, 4, 7, 3, 5, 6, -329100765040184280730172258547394752141695385600000⟩, + ⟨3, 4, 8, 3, 6, 6, 12149310247460710385385600732007151765028864000000⟩, + ⟨3, 4, 3, 4, 0, 6, 12866878841846272604374476876050306583777352089600000⟩, + ⟨3, 4, 4, 4, 1, 6, 389710480184249390448835449639322953795502080000000⟩, + ⟨3, 4, 5, 4, 2, 6, -2079301401367927324629966599609807734434693120000000⟩, + ⟨3, 4, 6, 4, 3, 6, -638052443865536337779667870034381401181126656000000⟩, + ⟨3, 4, 7, 4, 4, 6, 170146702942666948163659555891980811550431641600000⟩, + ⟨3, 4, 8, 4, 5, 6, 165365877518039446523247172158935911956794572800000⟩, + ⟨3, 4, 4, 5, 0, 6, 125084834641119384955565425613757434175404428492800000⟩, + ⟨3, 4, 5, 5, 1, 6, -702004023991233111236171429350834307013279744000000⟩, + ⟨3, 4, 6, 5, 2, 6, 1385043744935391079814956699069755059091800064000000⟩, + ⟨3, 4, 7, 5, 3, 6, 194083639415536979787277494116708620080198451200000⟩, + ⟨3, 4, 8, 5, 4, 6, 82782538570707740791347216885103005897483878400000⟩, + ⟨3, 4, 5, 6, 0, 6, 37275586862566428828891238357601218274663596032000000⟩, + ⟨3, 4, 6, 6, 1, 6, -2593913491769216718720045585771733634512846848000000⟩, + ⟨3, 4, 7, 6, 2, 6, 1373626288163345273191622492720103003532768051200000⟩, + ⟨3, 4, 8, 6, 3, 6, -439525674738847800578518793544099456015453388800000⟩, + ⟨3, 4, 6, 7, 0, 6, -769699467330105706577794851647664979848462336000000⟩, + ⟨3, 4, 7, 7, 1, 6, -7106504876355751827324411747916567610725603737600000⟩, + ⟨3, 4, 8, 7, 2, 6, 172877150790627697238889347531443821910111027200000⟩ +] + +def collectedFourData_9_1_30 : List CollectedFourTerm := [ + ⟨3, 5, 1, 0, 2, 7, -7476269756916410851239883797762933723708260352000000⟩, + ⟨3, 5, 2, 0, 3, 7, 7111703583231803019824149737547895111802893107200000⟩, + ⟨3, 5, 3, 0, 4, 7, 1301679469350380478714099974976806205755542732800000⟩, + ⟨3, 5, 4, 0, 5, 7, -25560430970442446780723216652746283186079452364800000⟩, + ⟨3, 5, 5, 0, 6, 7, -11146789892170076770561539524996573472340574208000000⟩, + ⟨3, 5, 6, 0, 7, 7, -3069822352909550720222547698168484570068523417600000⟩, + ⟨3, 5, 7, 0, 8, 7, -1500785492137481752510950277904361813952167936000000⟩, + ⟨3, 5, 1, 1, 1, 7, 7390083701356600742162832733618007750199371366400000⟩, + ⟨3, 5, 2, 1, 2, 7, -6821640559185928824576235606997934411664588800000000⟩, + ⟨3, 5, 3, 1, 3, 7, -6248286047856017484003309039315277405370921779200000⟩, + ⟨3, 5, 4, 1, 4, 7, -7865792751762400192641929753331118493734954598400000⟩, + ⟨3, 5, 5, 1, 5, 7, 3653726171745520148554318883288268285904158720000000⟩, + ⟨3, 5, 6, 1, 6, 7, 1131245861111230884064365226383710920237488537600000⟩, + ⟨3, 5, 7, 1, 7, 7, 118726579886312583121222941782784913314938880000000⟩, + ⟨3, 5, 8, 1, 8, 7, 245109698407392377795509571702395191612879667200000⟩, + ⟨3, 5, 1, 2, 0, 7, 14029033161207138876084459134178374298017307033600000⟩, + ⟨3, 5, 2, 2, 1, 7, -9452986658272711165767452442558167622721575321600000⟩, + ⟨3, 5, 3, 2, 2, 7, 4876247252311465512414318635058096422452513996800000⟩, + ⟨3, 5, 4, 2, 3, 7, -12350166918828676217764396175778340568986917273600000⟩, + ⟨3, 5, 5, 2, 4, 7, -2744677094567066968824659583055471923871875072000000⟩, + ⟨3, 5, 6, 2, 5, 7, 20324004747514064562769056912368220779210342400000⟩, + ⟨3, 5, 7, 2, 6, 7, 74464974617156092049449887987613216861165977600000⟩, + ⟨3, 5, 8, 2, 7, 7, 105244550660265713994114634804032631753565798400000⟩, + ⟨3, 5, 2, 3, 0, 7, 16370325812400441347005556290938220454888236646400000⟩, + ⟨3, 5, 3, 3, 1, 7, 109253296650525708266422033912558064267113267200000⟩, + ⟨3, 5, 4, 3, 2, 7, 32947984216279527479311802093913337018602592665600000⟩, + ⟨3, 5, 5, 3, 3, 7, 819575857681909860696884634738129327196471296000000⟩, + ⟨3, 5, 6, 3, 4, 7, -329100765040184280730172258547394752141695385600000⟩, + ⟨3, 5, 7, 3, 5, 7, 178603228515630321736677924269332843049936486400000⟩, + ⟨3, 5, 8, 3, 6, 7, -5651519703576576006368189277188924142256128000000⟩, + ⟨3, 5, 3, 4, 0, 7, -20948593982690352452170875788459512991105364787200000⟩, + ⟨3, 5, 4, 4, 1, 7, -422992331475040447720640138310189776413655040000000⟩, + ⟨3, 5, 5, 4, 2, 7, 1692657611853503898661536772741364908472401920000000⟩, + ⟨3, 5, 6, 4, 3, 7, 415525839653729527980655375066723647610473676800000⟩, + ⟨3, 5, 7, 4, 4, 7, -92338741488916469523974422441096377553806950400000⟩, + ⟨3, 5, 8, 4, 5, 7, -76923586282419772017272482930639964005308825600000⟩, + ⟨3, 5, 4, 5, 0, 7, -135767264488247678681248403636697620132403766886400000⟩, + ⟨3, 5, 5, 5, 1, 7, 571467154294622683788687925539008249598050304000000⟩, + ⟨3, 5, 6, 5, 2, 7, -901997117328979635646745525336387634907525939200000⟩, + ⟨3, 5, 7, 5, 3, 7, -105329334611075011715343609606375306567666892800000⟩, + ⟨3, 5, 8, 5, 4, 7, -38508124191019482859907389159964798077422796800000⟩, + ⟨3, 5, 5, 6, 0, 7, -30344232826333320525025775951722733223869939712000000⟩, + ⟨3, 5, 6, 6, 1, 7, 1689262523824273039569910968526451216759547494400000⟩, + ⟨3, 5, 7, 6, 2, 7, -745468002208864286614673625173197474793049292800000⟩, + ⟨3, 5, 8, 6, 3, 7, 204455064560850958993298217224720563188636057600000⟩, + ⟨3, 5, 6, 7, 0, 7, 501259764018350436320411253035351051516824780800000⟩, + ⟨3, 5, 7, 7, 1, 7, 3856705450758306848720841117325067248619382374400000⟩, + ⟨3, 5, 8, 7, 2, 7, -80417620761278600578118191495500993023862374400000⟩ +] + +def collectedFourData_9_1_31 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 1, 8, -1307875901668456584340190112931827130029834240000000⟩, + ⟨3, 6, 1, 0, 2, 8, 1655994705926514365409294010316987760409313280000000⟩, + ⟨3, 6, 2, 0, 3, 8, -787621625948920489396479392422188627687112704000000⟩, + ⟨3, 6, 3, 0, 4, 8, -96107389564754090268406791201426270075224064000000⟩, + ⟨3, 6, 4, 0, 5, 8, 1415409681047643791494343346302783581656711168000000⟩, + ⟨3, 6, 5, 0, 6, 8, 493803076927022443421589896941273411196289024000000⟩, + ⟨3, 6, 6, 0, 7, 8, 113327673867710282616458953108971734584786944000000⟩, + ⟨3, 6, 7, 0, 8, 8, 47489168309824677300840297410771729220894720000000⟩, + ⟨3, 6, 0, 1, 0, 8, -6820306566165827375208865029231766293970944000000000⟩, + ⟨3, 6, 1, 1, 1, 8, -1636904483613482100989894414561073601336836096000000⟩, + ⟨3, 6, 2, 1, 2, 8, 755497127514348191897969732278838693462016000000000⟩, + ⟨3, 6, 3, 1, 3, 8, 461332052515974841432261799168068981931114496000000⟩, + ⟨3, 6, 4, 1, 4, 8, 435568524757396582452892284564161107951878144000000⟩, + ⟨3, 6, 5, 1, 5, 8, -161860162729368474952274364356017447407452160000000⟩, + ⟨3, 6, 6, 1, 6, 8, -41761850450630289421736482447072034757279744000000⟩, + ⟨3, 6, 7, 1, 7, 8, -3756850372427804017940334877764996405657600000000⟩, + ⟨3, 6, 8, 1, 8, 8, -6786478687422657677632716346231214598782976000000⟩, + ⟨3, 6, 1, 2, 0, 8, -3107432636808517153215063811966461713426939904000000⟩, + ⟨3, 6, 2, 2, 1, 8, 1046918876008435886267488241254455519700058112000000⟩, + ⟨3, 6, 3, 2, 2, 8, -360029796372099292641198711076694408124432384000000⟩, + ⟨3, 6, 4, 2, 3, 8, 683890887429816796830399240513877090423013376000000⟩, + ⟨3, 6, 5, 2, 4, 8, 121589265392036539385739240263064156232482816000000⟩, + ⟨3, 6, 6, 2, 5, 8, -750294941180895431470766945734284810387456000000⟩, + ⟨3, 6, 7, 2, 6, 8, -2356285912482022948467140366835676612657152000000⟩, + ⟨3, 6, 8, 2, 7, 8, -2913960176460020354045693179915552866435072000000⟩, + ⟨3, 6, 2, 3, 0, 8, -1813014629023263114246081772721469061645467648000000⟩, + ⟨3, 6, 3, 3, 1, 8, -8066539720155453576443548681665254246055936000000⟩, + ⟨3, 6, 4, 3, 2, 8, -1824495677895831881091101791745846662813188096000000⟩, + ⟨3, 6, 5, 3, 3, 8, -36307231428369648169476315089996874868850688000000⟩, + ⟨3, 6, 6, 3, 4, 8, 12149310247460710385385600732007151765028864000000⟩, + ⟨3, 6, 7, 3, 5, 8, -5651519703576576006368189277188924142256128000000⟩, + ⟨3, 6, 8, 3, 6, 8, 156476542009873058609216580967660246794240000000⟩, + ⟨3, 6, 3, 4, 0, 8, 1546705414147044308437094394423725997252673536000000⟩, + ⟨3, 6, 4, 4, 1, 8, 23423213860166094548766894737853897926246400000000⟩, + ⟨3, 6, 5, 4, 2, 8, -74984775437844299622858327957807719786741760000000⟩, + ⟨3, 6, 6, 4, 3, 8, -15339837758120531287609686798894051090235392000000⟩, + ⟨3, 6, 7, 4, 4, 8, 2921863290295480986441282771570294320529408000000⟩, + ⟨3, 6, 8, 4, 5, 8, 2129823023151397396893931553741964834766848000000⟩, + ⟨3, 6, 4, 5, 0, 8, 7518116605633092573907709157876840573356212224000000⟩, + ⟨3, 6, 5, 5, 1, 8, -25316009531285467247329280352084226171994112000000⟩, + ⟨3, 6, 6, 5, 2, 8, 33298746113236494102897753427980557796507648000000⟩, + ⟨3, 6, 7, 5, 3, 8, 3332923009658842638777652033689260346310656000000⟩, + ⟨3, 6, 8, 5, 4, 8, 1066194303256899933740021754099118997766144000000⟩, + ⟨3, 6, 5, 6, 0, 8, 1344250289238763610397174454710650355094388736000000⟩, + ⟨3, 6, 6, 6, 1, 8, -62361977459528578264528550053206155209998336000000⟩, + ⟨3, 6, 7, 6, 2, 8, 23588751098643008189555327981045922876358656000000⟩, + ⟨3, 6, 8, 6, 3, 8, -5660852863813043586793330112661917855121408000000⟩, + ⟨3, 6, 6, 7, 0, 8, -18504850290713478992161694761855033804849152000000⟩, + ⟨3, 6, 7, 7, 1, 8, -122037249981426118464220502478004653693861888000000⟩, + ⟨3, 6, 8, 7, 2, 8, 2226564158561240590544784192121864980529152000000⟩ +] + +def collectedFourData_9_1_32 : List CollectedFourTerm := [ + ⟨4, 0, 5, 0, 6, 3, 87161386574447171005665992571268853536984242585600000⟩, + ⟨4, 0, 6, 0, 7, 3, 120021089212769463978440105534641714720178543001600000⟩, + ⟨4, 0, 7, 0, 8, 3, 176028990019902354413328818223532023091222806528000000⟩, + ⟨4, 0, 5, 1, 5, 3, -28570004671603901107964115888817035785696968704000000⟩, + ⟨4, 0, 6, 1, 6, 3, -44228409598139271913157905949206144012728768921600000⟩, + ⟨4, 0, 7, 1, 7, 3, -13925587670853059595385501560258181994895114240000000⟩, + ⟨4, 0, 8, 1, 8, 3, -67081513906204878193099359262188585752855996006400000⟩, + ⟨4, 0, 5, 2, 4, 3, 21461771826311595325163846729760706535233054310400000⟩, + ⟨4, 0, 6, 2, 5, 3, -794609233544142969677005163853208864296429158400000⟩, + ⟨4, 0, 7, 2, 6, 3, -8734089143576871670595850665210924253288647884800000⟩, + ⟨4, 0, 8, 2, 7, 3, -28803282099979009012114902754779165773498469580800000⟩, + ⟨4, 0, 5, 3, 3, 3, -6408604526463347524417112096527538026024481587200000⟩, + ⟨4, 0, 6, 3, 4, 3, 12866878841846272604374476876050306583777352089600000⟩, + ⟨4, 0, 7, 3, 5, 3, -20948593982690352452170875788459512991105364787200000⟩, + ⟨4, 0, 8, 3, 6, 3, 1546705414147044308437094394423725997252673536000000⟩, + ⟨4, 0, 5, 4, 2, 3, -13235593912878674568725663120155191332195794944000000⟩, + ⟨4, 0, 6, 4, 3, 3, -16245846872547232436223708148114748134264720588800000⟩, + ⟨4, 0, 7, 4, 4, 3, 10830525407633552117392356182861424307805041459200000⟩, + ⟨4, 0, 8, 4, 5, 3, 21052413088700799258996076058249816065092825907200000⟩, + ⟨4, 0, 5, 5, 1, 3, -4468539376081823865336308004023046869114211532800000⟩, + ⟨4, 0, 6, 5, 2, 3, 35265453190148193938636398073444995514475164467200000⟩, + ⟨4, 0, 7, 5, 3, 3, 12354208171781421167748206659031388009009669734400000⟩, + ⟨4, 0, 8, 5, 4, 3, 10538886405581046909866757681726872148080433561600000⟩, + ⟨4, 0, 5, 6, 0, 3, 237274177881374333206658989854010928033933190758400000⟩, + ⟨4, 0, 6, 6, 1, 3, -66045231537108075836838104372430254608021349990400000⟩, + ⟨4, 0, 7, 6, 2, 3, 87436865700298057167697454071085596873803064934400000⟩, + ⟨4, 0, 8, 6, 3, 3, -55955171686993100246810782458513937342819152691200000⟩, + ⟨4, 0, 6, 7, 0, 3, -19597792946877669996631701572281222460387151052800000⟩, + ⟨4, 0, 7, 7, 1, 3, -452357761224310975458292269836696555808275772211200000⟩, + ⟨4, 0, 8, 7, 2, 3, 22008658900291495958581443132745620581497228492800000⟩ +] + +def collectedFourData_9_1_33 : List CollectedFourTerm := [ + ⟨4, 1, 4, 0, 5, 4, 3026783552445158969288452590816980855175512064000000⟩, + ⟨4, 1, 5, 0, 6, 4, 5279867205243499130732348572950362653993205760000000⟩, + ⟨4, 1, 6, 0, 7, 4, 3635184327470785543604132378733991914299719680000000⟩, + ⟨4, 1, 7, 0, 8, 4, 3554363264534120947810892260481258707589529600000000⟩, + ⟨4, 1, 4, 1, 4, 4, 931441733338061424431243758579883482558758912000000⟩, + ⟨4, 1, 5, 1, 5, 4, -1730649736628650653909155291959141427734118400000000⟩, + ⟨4, 1, 6, 1, 6, 4, -1339584755101593980543311327225722259038535680000000⟩, + ⟨4, 1, 7, 1, 7, 4, -281184350650044382185580532222427050016768000000000⟩, + ⟨4, 1, 8, 1, 8, 4, -1015878416094665313898136427692913356817039360000000⟩, + ⟨4, 1, 4, 2, 3, 4, 1462466816114715929740228236234603377404674048000000⟩, + ⟨4, 1, 5, 2, 4, 4, 1300063132145969806655313232481225914806435840000000⟩, + ⟨4, 1, 6, 2, 5, 4, -24067028979569689377234367522401685937848320000000⟩, + ⟨4, 1, 7, 2, 6, 4, -176358028286056599058230899546322940314255360000000⟩, + ⟨4, 1, 8, 2, 7, 4, -436195173516320464700804721724604712663121920000000⟩, + ⟨4, 1, 4, 3, 2, 4, -3901593710504300136440993835872233389564100608000000⟩, + ⟨4, 1, 5, 3, 3, 4, -388206087586135723897915163422568576314245120000000⟩, + ⟨4, 1, 6, 3, 4, 4, 389710480184249390448835449639322953795502080000000⟩, + ⟨4, 1, 7, 3, 5, 4, -422992331475040447720640138310189776413655040000000⟩, + ⟨4, 1, 8, 3, 6, 4, 23423213860166094548766894737853897926246400000000⟩, + ⟨4, 1, 4, 4, 1, 4, 50089383594494270355102062600715121144627200000000⟩, + ⟨4, 1, 5, 4, 2, 4, -801756155896397069921897047216176541099622400000000⟩, + ⟨4, 1, 6, 4, 3, 4, -492052257856786157114592661262103409317642240000000⟩, + ⟨4, 1, 7, 4, 4, 4, 218689101381219680428107657396456487586365440000000⟩, + ⟨4, 1, 8, 4, 5, 4, 318816478909873727893451838608056572476129280000000⟩, + ⟨4, 1, 4, 5, 0, 4, 16077120279728464865794826922405832222417354752000000⟩, + ⟨4, 1, 5, 5, 1, 4, -270685167301255857582311414816988736656506880000000⟩, + ⟨4, 1, 6, 5, 2, 4, 1068115808470283942587264189882397668996546560000000⟩, + ⟨4, 1, 7, 5, 3, 4, 249455181690370323537492809989887398856622080000000⟩, + ⟨4, 1, 8, 5, 4, 4, 159600262511561688169761875512795202416803840000000⟩, + ⟨4, 1, 5, 6, 0, 4, 14373063574165916423377337547030490637811056640000000⟩, + ⟨4, 1, 6, 6, 1, 4, -2000370036321340793968592082986776257280081920000000⟩, + ⟨4, 1, 7, 6, 2, 4, 1765518187521299424246345915458003063097262080000000⟩, + ⟨4, 1, 8, 6, 3, 4, -847381758037957932579585711181973217481850880000000⟩, + ⟨4, 1, 6, 7, 0, 4, -593575597761927034318805024237097479244349440000000⟩, + ⟨4, 1, 7, 7, 1, 4, -9133971675579123697562653061120299896762531840000000⟩, + ⟨4, 1, 8, 7, 2, 4, 333297808025883136115680414313361709958430720000000⟩ +] + +def collectedFourData_9_1_34 : List CollectedFourTerm := [ + ⟨4, 2, 3, 0, 4, 5, 822418004534758032008643574593426701949075456000000⟩, + ⟨4, 2, 4, 0, 5, 5, -48448237362729580644532747956432040299790860288000000⟩, + ⟨4, 2, 5, 0, 6, 5, -42256120262825341917140481422385343995272232960000000⟩, + ⟨4, 2, 6, 0, 7, 5, -19395536560287306163459321928077842773987819520000000⟩, + ⟨4, 2, 7, 0, 8, 5, -14223236657804882011171988689947527176047820800000000⟩, + ⟨4, 2, 3, 1, 3, 5, -3947748323790226103219922132873509311856246784000000⟩, + ⟨4, 2, 4, 1, 4, 5, -14909130238222510761846432731276007698652463104000000⟩, + ⟨4, 2, 5, 1, 5, 5, 13850830060873586148868637185325569604478566400000000⟩, + ⟨4, 2, 6, 1, 6, 5, 7147358360023984150959156114809330450584043520000000⟩, + ⟨4, 2, 7, 1, 7, 5, 1125194941010335366969317989838202406436864000000000⟩, + ⟨4, 2, 8, 1, 8, 5, 3252133347617023774166287538578986382261223424000000⟩, + ⟨4, 2, 3, 2, 2, 5, 3080876382620899504612667974121681000633204736000000⟩, + ⟨4, 2, 4, 2, 3, 5, -23408987862710716408212999157908318137106825216000000⟩, + ⟨4, 2, 5, 2, 4, 5, -10404735938560778770570924064701632135970160640000000⟩, + ⟨4, 2, 6, 2, 5, 5, 128409703173295117816866695958887940992532480000000⟩, + ⟨4, 2, 7, 2, 6, 5, 705719079939121034740042525809270557276897280000000⟩, + ⟨4, 2, 8, 2, 7, 5, 1396392370767556402265867715923955499011145728000000⟩, + ⟨4, 2, 3, 3, 1, 5, 69027652610216728004926716751875910920044544000000⟩, + ⟨4, 2, 4, 3, 2, 5, 62450893796731123994260906225490963436442484736000000⟩, + ⟨4, 2, 5, 3, 3, 5, 3106912065422700115478833199790619631309291520000000⟩, + ⟨4, 2, 6, 3, 4, 5, -2079301401367927324629966599609807734434693120000000⟩, + ⟨4, 2, 7, 3, 5, 5, 1692657611853503898661536772741364908472401920000000⟩, + ⟨4, 2, 8, 3, 6, 5, -74984775437844299622858327957807719786741760000000⟩, + ⟨4, 2, 3, 4, 0, 5, -13235593912878674568725663120155191332195794944000000⟩, + ⟨4, 2, 4, 4, 1, 5, -801756155896397069921897047216176541099622400000000⟩, + ⟨4, 2, 5, 4, 2, 5, 6416658455230266952491634685956324610958950400000000⟩, + ⟨4, 2, 6, 4, 3, 5, 2625346254029785746677992595436252662448783360000000⟩, + ⟨4, 2, 7, 4, 4, 5, -875112252724530811465714561232422302772101120000000⟩, + ⟨4, 2, 8, 4, 5, 5, -1020627750728805580538079241776828065463140352000000⟩, + ⟨4, 2, 4, 5, 0, 5, -257338566146298883957317528588963372923967504384000000⟩, + ⟨4, 2, 5, 5, 1, 5, 2166362247043930718054002964270578699578900480000000⟩, + ⟨4, 2, 6, 5, 2, 5, -5698935005097817127212343973014592575860899840000000⟩, + ⟨4, 2, 7, 5, 3, 5, -998226636005620904657829587534019718639779840000000⟩, + ⟨4, 2, 8, 5, 4, 5, -510928599110933054082074771223395812251795456000000⟩, + ⟨4, 2, 5, 6, 0, 5, -115031283804263632982752928855890430378052157440000000⟩, + ⟨4, 2, 6, 6, 1, 5, 10672980151344365970536093730615772301890682880000000⟩, + ⟨4, 2, 7, 6, 2, 5, -7064945571359766434931127331911943713550499840000000⟩, + ⟨4, 2, 8, 6, 3, 5, 2712724701910373139972214001683836754609569792000000⟩, + ⟨4, 2, 6, 7, 0, 5, 3167024329601445992171796907090390047428444160000000⟩, + ⟨4, 2, 7, 7, 1, 5, 36550749346233945458459979029155766698581688320000000⟩, + ⟨4, 2, 8, 7, 2, 5, -1066986854918694140234752233198492038775963648000000⟩ +] + +def collectedFourData_9_1_35 : List CollectedFourTerm := [ + ⟨4, 3, 2, 0, 3, 6, 2757599090220457522780380015031849610331448934400000⟩, + ⟨4, 3, 3, 0, 4, 6, 1009465616340567478172026025209479033206813491200000⟩, + ⟨4, 3, 4, 0, 5, 6, -29733559771498755863340372829770544988205927628800000⟩, + ⟨4, 3, 5, 0, 6, 6, -17288896988340573182452526539334418629199396864000000⟩, + ⟨4, 3, 6, 0, 7, 6, -5951695840840191227003014917518151756049022976000000⟩, + ⟨4, 3, 7, 0, 8, 6, -3491623062715171512597330250144343604521336832000000⟩, + ⟨4, 3, 2, 1, 2, 6, -2645125683271738003936951601318972240796057600000000⟩, + ⟨4, 3, 3, 1, 3, 6, -4845609134112674817751262411842417655699786956800000⟩, + ⟨4, 3, 4, 1, 4, 6, -9150002955943923688139485628203130376610539110400000⟩, + ⟨4, 3, 5, 1, 5, 6, 5667003327234548140373074443021399638157557760000000⟩, + ⟨4, 3, 6, 1, 6, 6, 2193231566042274399188411152803531875917234176000000⟩, + ⟨4, 3, 7, 1, 7, 6, 276220996711479987028979221267370520147394560000000⟩, + ⟨4, 3, 8, 1, 8, 6, 665297690483458050037110806570406102717746380800000⟩, + ⟨4, 3, 2, 2, 1, 6, -3665443462826801345951711537684318856269738803200000⟩, + ⟨4, 3, 3, 2, 2, 6, 3781579147468754210664824241752256124401431347200000⟩, + ⟨4, 3, 4, 2, 3, 6, -14366519355390299491288732938515537787356813721600000⟩, + ⟨4, 3, 5, 2, 4, 6, -4257049788617644235223415090281011017339109376000000⟩, + ⟨4, 3, 6, 2, 5, 6, 39403678981732853800296967519864560103194624000000⟩, + ⟨4, 3, 7, 2, 6, 6, 173245026754259182626843635733705258173674291200000⟩, + ⟨4, 3, 8, 2, 7, 6, 285663753597651789843057169872067917656988057600000⟩, + ⟨4, 3, 2, 3, 0, 6, 6347676761068476412021903991769493319893961932800000⟩, + ⟨4, 3, 3, 3, 1, 6, 84727038443344373169523237951443333335010508800000⟩, + ⟨4, 3, 4, 3, 2, 6, 38327243354308245313078182562087108610677643673600000⟩, + ⟨4, 3, 5, 3, 3, 6, 1271178762196517737334692052691820314013728768000000⟩, + ⟨4, 3, 6, 3, 4, 6, -638052443865536337779667870034381401181126656000000⟩, + ⟨4, 3, 7, 3, 5, 6, 415525839653729527980655375066723647610473676800000⟩, + ⟨4, 3, 8, 3, 6, 6, -15339837758120531287609686798894051090235392000000⟩, + ⟨4, 3, 3, 4, 0, 6, -16245846872547232436223708148114748134264720588800000⟩, + ⟨4, 3, 4, 4, 1, 6, -492052257856786157114592661262103409317642240000000⟩, + ⟨4, 3, 5, 4, 2, 6, 2625346254029785746677992595436252662448783360000000⟩, + ⟨4, 3, 6, 4, 3, 6, 805611246294028530792207004318437211707015168000000⟩, + ⟨4, 3, 7, 4, 4, 6, -214828888641242240701986835660969149448637644800000⟩, + ⟨4, 3, 8, 4, 5, 6, -208792571774693250521838799146115018206373478400000⟩, + ⟨4, 3, 4, 5, 0, 6, -157933333688399687623685657937217257167869339238400000⟩, + ⟨4, 3, 5, 5, 1, 6, 886357135856662024048605342262490782375084032000000⟩, + ⟨4, 3, 6, 5, 2, 6, -1748769757497073329424502064312650755045588992000000⟩, + ⟨4, 3, 7, 5, 3, 6, -245051898379347264256842119270859078394026393600000⟩, + ⟨4, 3, 8, 5, 4, 6, -104522041582189702960911670574044587045892915200000⟩, + ⟨4, 3, 5, 6, 0, 6, -47064519973881528212689005857884095150079082496000000⟩, + ⟨4, 3, 6, 6, 1, 6, 3275100504627917397634795938683590811156742144000000⟩, + ⟨4, 3, 7, 6, 2, 6, -1734353965083660963395412780874140357832055193600000⟩, + ⟨4, 3, 8, 6, 3, 6, 554949408953611843687645742850471769665857126400000⟩, + ⟨4, 3, 6, 7, 0, 6, 971830063671587761421635217348277771549278208000000⟩, + ⟨4, 3, 7, 7, 1, 6, 8972742452879086796686732087394679079171837132800000⟩, + ⟨4, 3, 8, 7, 2, 6, -218276378757274253483055228254465074765863321600000⟩ +] + +def collectedFourData_9_1_36 : List CollectedFourTerm := [ + ⟨4, 4, 1, 0, 2, 7, 3865267980443553140305362160717742965493071872000000⟩, + ⟨4, 4, 2, 0, 3, 7, -3676785488009098727411419561167070960119132979200000⟩, + ⟨4, 4, 3, 0, 4, 7, -672974643407725083116159604768068379503021260800000⟩, + ⟨4, 4, 4, 0, 5, 7, 13214867655756999852353512849255593342877355212800000⟩, + ⟨4, 4, 5, 0, 6, 7, 5762944818179941947765197010217634185806348288000000⟩, + ⟨4, 4, 6, 0, 7, 7, 1587113150294510034905082612259056551590467993600000⟩, + ⟨4, 4, 7, 0, 8, 7, 775913429676168657389891767067952260679991296000000⟩, + ⟨4, 4, 1, 1, 1, 7, -3820709368763192433718004474851619236689110630400000⟩, + ⟨4, 4, 2, 1, 2, 7, 3526821487831345201988223912055078510185676800000000⟩, + ⟨4, 4, 3, 1, 3, 7, 3230394405055719667201532094395955463670936371200000⟩, + ⟨4, 4, 4, 1, 4, 7, 4066653271314286953684589262189125047526254182400000⟩, + ⟨4, 4, 5, 1, 5, 7, -1888994276576430504464102347115377052268625920000000⟩, + ⟨4, 4, 6, 1, 6, 7, -584859635504377845550547591921388156557564313600000⟩, + ⟨4, 4, 7, 1, 7, 7, -61382221693859153618583818346006830571847680000000⟩, + ⟨4, 4, 8, 1, 8, 7, -126722911258492540495612615446884858199225139200000⟩, + ⟨4, 4, 1, 2, 0, 7, -7253078665925541513445260699327938415767951769600000⟩, + ⟨4, 4, 2, 2, 1, 7, 4887240273263207609082956704930393410783254937600000⟩, + ⟨4, 4, 3, 2, 2, 7, -2521043646351683576104427495369616500200361164800000⟩, + ⟨4, 4, 4, 2, 3, 7, 6385096618580374935172676346119862901370624409600000⟩, + ⟨4, 4, 5, 2, 4, 7, 1419011463634315732978851365410636454839713792000000⟩, + ⟨4, 4, 6, 2, 5, 7, -10507609722385141143277581072184289773643366400000⟩, + ⟨4, 4, 7, 2, 6, 7, -38498755584088196351375660945664239503776153600000⟩, + ⟨4, 4, 8, 2, 7, 7, -54411946734126212434975309486684596655777382400000⟩, + ⟨4, 4, 2, 3, 0, 7, -8463538402097210772017713097792430902639748710400000⟩, + ⟨4, 4, 3, 3, 1, 7, -56484487990887165017042822645246303770194739200000⟩, + ⟨4, 4, 4, 3, 2, 7, -17034268766657173227401540355281517877921421721600000⟩, + ⟨4, 4, 5, 3, 3, 7, -423724721451067812769655318807296158524768256000000⟩, + ⟨4, 4, 6, 3, 4, 7, 170146702942666948163659555891980811550431641600000⟩, + ⟨4, 4, 7, 3, 5, 7, -92338741488916469523974422441096377553806950400000⟩, + ⟨4, 4, 8, 3, 6, 7, 2921863290295480986441282771570294320529408000000⟩, + ⟨4, 4, 3, 4, 0, 7, 10830525407633552117392356182861424307805041459200000⟩, + ⟨4, 4, 4, 4, 1, 7, 218689101381219680428107657396456487586365440000000⟩, + ⟨4, 4, 5, 4, 2, 7, -875112252724530811465714561232422302772101120000000⟩, + ⟨4, 4, 6, 4, 3, 7, -214828888641242240701986835660969149448637644800000⟩, + ⟨4, 4, 7, 4, 4, 7, 47739580357086091187323659985088373403838054400000⟩, + ⟨4, 4, 8, 4, 5, 7, 39769869823551955272396205097137256279939481600000⟩, + ⟨4, 4, 4, 5, 0, 7, 70192338864358897836053884257769266611927541350400000⟩, + ⟨4, 4, 5, 5, 1, 7, -295451309970020537368804922358878588941369344000000⟩, + ⟨4, 4, 6, 5, 2, 7, 466336915256263200597187156441999938254222131200000⟩, + ⟨4, 4, 7, 5, 3, 7, 54455780450802300501770065220550948197027020800000⟩, + ⟨4, 4, 8, 5, 4, 7, 19908888290820881503907510059251783229557964800000⟩, + ⟨4, 4, 5, 6, 0, 7, 15688116580630989757819212046831359099332984832000000⟩, + ⟨4, 4, 6, 6, 1, 7, -873356975630892900916224081999745537286760038400000⟩, + ⟨4, 4, 7, 6, 2, 7, 385410598208750965541376683522048477165833420800000⟩, + ⟨4, 4, 8, 6, 3, 7, -105704266991634768133277836891278607818267033600000⟩, + ⟨4, 4, 6, 7, 0, 7, -259153746285359437896131424564707597304515788800000⟩, + ⟨4, 4, 7, 7, 1, 7, -1993935555231581429283673582553907769836463718400000⟩, + ⟨4, 4, 8, 7, 2, 7, 41576302714928670898531135248823168205743718400000⟩ +] + +def collectedFourData_9_1_37 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 1, 8, -17801672832357293491062858431608300349159374848000000⟩, + ⟨4, 5, 1, 0, 2, 8, 22539964173521803300085276851997384862288838656000000⟩, + ⟨4, 5, 2, 0, 3, 8, -10720422696790587196246274773680329506926939340800000⟩, + ⟨4, 5, 3, 0, 4, 8, -1308130460711985638603496758749542716646673612800000⟩, + ⟨4, 5, 4, 0, 5, 8, 19265329404432008229967955485979047000500967833600000⟩, + ⟨4, 5, 5, 0, 6, 8, 6721219351050165709079020736548722769862118604800000⟩, + ⟨4, 5, 6, 0, 7, 8, 1542518040489500081171655598822510289987882188800000⟩, + ⟨4, 5, 7, 0, 8, 8, 646381385461563752917493362611160306830802944000000⟩, + ⟨4, 5, 0, 1, 0, 8, -92832099706383413550139896292239810262518988800000000⟩, + ⟨4, 5, 1, 1, 1, 8, -22280124618805613134572321967673622015014810419200000⟩, + ⟨4, 5, 2, 1, 2, 8, 10283171876352427840496103449023765191799603200000000⟩, + ⟨4, 5, 3, 1, 3, 8, 6279251919461623469433381714337621675038946099200000⟩, + ⟨4, 5, 4, 1, 4, 8, 5928581116841522755729204279429312852492340428800000⟩, + ⟨4, 5, 5, 1, 5, 8, -2203100200733534654018544913932266827186962432000000⟩, + ⟨4, 5, 6, 1, 6, 8, -568426100402614000218533512816432879804140748800000⟩, + ⟨4, 5, 7, 1, 7, 8, -51134990043598867464521545539526084547051520000000⟩, + ⟨4, 5, 8, 1, 8, 8, -92371663950031955646184226665929241479295795200000⟩, + ⟨4, 5, 1, 2, 0, 8, -42295678877855356563070309818695611558837144780800000⟩, + ⟨4, 5, 2, 2, 1, 8, 14249752051357712443625223896007991319532562022400000⟩, + ⟨4, 5, 3, 2, 2, 8, -4900413438874591523072040734386568183904259276800000⟩, + ⟨4, 5, 4, 2, 3, 8, 9308529819629837871819835651314340868427821875200000⟩, + ⟨4, 5, 5, 2, 4, 8, 1654967661438257294782597035619123215018963763200000⟩, + ⟨4, 5, 6, 2, 5, 8, -10212364226327722197198292524122689399632691200000⟩, + ⟨4, 5, 7, 2, 6, 8, -32071720917854032858336480525026741872649830400000⟩, + ⟨4, 5, 8, 2, 7, 8, -39662299490100386849178294229649777947469414400000⟩, + ⟨4, 5, 2, 3, 0, 8, -24677183228911054299393374757179156184495135129600000⟩, + ⟨4, 5, 3, 3, 1, 8, -109794744902199496013190272090885148793582387200000⟩, + ⟨4, 5, 4, 3, 2, 8, -24833453311983189738078639742877739386068480819200000⟩, + ⟨4, 5, 5, 3, 3, 8, -494182555479456972013990847757549242750179737600000⟩, + ⟨4, 5, 6, 3, 4, 8, 165365877518039446523247172158935911956794572800000⟩, + ⟨4, 5, 7, 3, 5, 8, -76923586282419772017272482930639964005308825600000⟩, + ⟨4, 5, 8, 3, 6, 8, 2129823023151397396893931553741964834766848000000⟩, + ⟨4, 5, 3, 4, 0, 8, 21052413088700799258996076058249816065092825907200000⟩, + ⟨4, 5, 4, 4, 1, 8, 318816478909873727893451838608056572476129280000000⟩, + ⟨4, 5, 5, 4, 2, 8, -1020627750728805580538079241776828065463140352000000⟩, + ⟨4, 5, 6, 4, 3, 8, -208792571774693250521838799146115018206373478400000⟩, + ⟨4, 5, 7, 4, 4, 8, 39769869823551955272396205097137256279939481600000⟩, + ⟨4, 5, 8, 4, 5, 8, 28989304413817789701403328796129210557634969600000⟩, + ⟨4, 5, 4, 5, 0, 8, 102330084955506521942343479510165415997299543244800000⟩, + ⟨4, 5, 5, 5, 1, 8, -344579572512855956111905226833997392398149222400000⟩, + ⟨4, 5, 6, 5, 2, 8, 453233661755954391932721206892346439693343129600000⟩, + ⟨4, 5, 7, 5, 3, 8, 45364858330743022108800944865796698712257331200000⟩, + ⟨4, 5, 8, 5, 4, 8, 14512112455080515952163325965723658951118028800000⟩, + ⟨4, 5, 5, 6, 0, 8, 18296769459015772465210670576438702250873008947200000⟩, + ⟨4, 5, 6, 6, 1, 8, -848817168736845143927917319634063180040450867200000⟩, + ⟨4, 5, 7, 6, 2, 8, 321069628277622336227123159078879155339866931200000⟩, + ⟨4, 5, 8, 6, 3, 8, -77050621167617679638979704578613793953257881600000⟩, + ⟨4, 5, 6, 7, 0, 8, -251871978271635437945475338011071692197488230400000⟩, + ⟨4, 5, 7, 7, 1, 8, -1661065239262023038500798558256440566410221977600000⟩, + ⟨4, 5, 8, 7, 2, 8, 30306060873509303826443541719366383488624230400000⟩ +] + +def collectedFourData_9_1_38 : List CollectedFourTerm := [ + ⟨5, 0, 4, 0, 5, 4, 971502536891139963884546044085987280238254741258240000⟩, + ⟨5, 0, 5, 0, 6, 4, 1694671685459190136644044124846551090557848492441600000⟩, + ⟨5, 0, 6, 0, 7, 4, 1166780093459876852148512551476357666057013218508800000⟩, + ⟨5, 0, 7, 0, 8, 4, 1140839068501624316564383708345391387784234663936000000⟩, + ⟨5, 0, 4, 1, 4, 4, 298963566844148444247599827493180435516396320849920000⟩, + ⟨5, 0, 5, 1, 5, 4, -555484255967517080482798484767403545944070815744000000⟩, + ⟨5, 0, 6, 1, 6, 4, -429964668900940416892846623782639021143997861068800000⟩, + ⟨5, 0, 7, 1, 7, 4, -90251352717285341828271393896749166465258618880000000⟩, + ⟨5, 0, 8, 1, 8, 4, -326065092302896729611428722080635070014656453017600000⟩, + ⟨5, 0, 4, 2, 3, 4, 469405954326262490391418343279638265141172822343680000⟩, + ⟨5, 0, 5, 2, 4, 4, 417279468159570368916193915982570655344161613414400000⟩, + ⟨5, 0, 6, 2, 5, 4, -7724761055410211930790720638765747578162328371200000⟩, + ⟨5, 0, 7, 2, 6, 4, -56605392791504441236952590894025879974479239577600000⟩, + ⟨5, 0, 8, 2, 7, 4, -140004962465334506757997798506020836440389399347200000⟩, + ⟨5, 0, 4, 3, 2, 4, -1252289145225266426513523164383585015460881791713280000⟩, + ⟨5, 0, 5, 3, 3, 4, -124601971826443719134073647565919127541193585459200000⟩, + ⟨5, 0, 6, 3, 4, 4, 125084834641119384955565425613757434175404428492800000⟩, + ⟨5, 0, 7, 3, 5, 4, -135767264488247678681248403636697620132403766886400000⟩, + ⟨5, 0, 8, 3, 6, 4, 7518116605633092573907709157876840573356212224000000⟩, + ⟨5, 0, 4, 4, 1, 4, 16077120279728464865794826922405832222417354752000000⟩, + ⟨5, 0, 5, 4, 2, 4, -257338566146298883957317528588963372923967504384000000⟩, + ⟨5, 0, 6, 4, 3, 4, -157933333688399687623685657937217257167869339238400000⟩, + ⟨5, 0, 7, 4, 4, 4, 70192338864358897836053884257769266611927541350400000⟩, + ⟨5, 0, 8, 4, 5, 4, 102330084955506521942343479510165415997299543244800000⟩, + ⟨5, 0, 4, 5, 0, 4, 5160251093951717541148493881918830669301358599864320000⟩, + ⟨5, 0, 5, 5, 1, 4, -86881444337020322762621442915444945780736838860800000⟩, + ⟨5, 0, 6, 5, 2, 4, 342831655994738677378096137990948135238893148569600000⟩, + ⟨5, 0, 7, 5, 3, 4, 80067285173747484258998050050947477680352447692800000⟩, + ⟨5, 0, 8, 5, 4, 4, 51226675853057518968922051045176145319102408294400000⟩, + ⟨5, 0, 5, 6, 0, 4, 4613302366440958615995147246819883106475193034342400000⟩, + ⟨5, 0, 6, 6, 1, 4, -642056008080682005569856359903369600676090032947200000⟩, + ⟨5, 0, 7, 6, 2, 4, 566675934497786276993188739074122188287464230092800000⟩, + ⟨5, 0, 8, 6, 3, 4, -271982952657486429392264931400165024137258781900800000⟩, + ⟨5, 0, 6, 7, 0, 4, -190519139895727724271142378610799841429799986790400000⟩, + ⟨5, 0, 7, 7, 1, 4, -2931718274849358783770013151304441460037039580774400000⟩, + ⟨5, 0, 8, 7, 2, 4, 106978137163400093601057958767357276591767106355200000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0906.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0906.lean new file mode 100644 index 0000000000000000000000000000000000000000..dcc8b7312f127f5e9c3e8a17716482bb9a739bfd --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0906.lean @@ -0,0 +1,611 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse0903 +import OAI.Analysis.LaughlinFock.Sparse0904 +import OAI.Analysis.LaughlinFock.Sparse0905 + +namespace OAI + +/-! Sparse0906. -/ +namespace LaughlinFock +def collectedFourData_9_1_39 : List CollectedFourTerm := [ + ⟨5, 1, 3, 0, 4, 5, 277660924099998381242309318521965763055792947200000⟩, + ⟨5, 1, 4, 0, 5, 5, -16356867533270341127274107657095141721663707545600000⟩, + ⟨5, 1, 5, 0, 6, 5, -14266313889484993535761001295278055416295063552000000⟩, + ⟨5, 1, 6, 0, 7, 5, -6548230431544587848614114829234572131695591424000000⟩, + ⟨5, 1, 7, 0, 8, 5, -4801982705051745403723847190172986426481704960000000⟩, + ⟨5, 1, 3, 1, 3, 5, -1332820343978118236518085349837440383588289740800000⟩, + ⟨5, 1, 4, 1, 4, 5, -5033550890965611176988674429249303711228677324800000⟩, + ⟨5, 1, 5, 1, 5, 5, 4676252529794487770272355840868836005568839680000000⟩, + ⟨5, 1, 6, 1, 6, 5, 2413057734844659799384686498492104456980660224000000⟩, + ⟨5, 1, 7, 1, 7, 5, 379883058725484039072891396108036894149836800000000⟩, + ⟨5, 1, 8, 1, 8, 5, 1097970065850620383539335770455963593341717708800000⟩, + ⟨5, 1, 3, 2, 2, 5, 1040151089494084080900233178106444294802060083200000⟩, + ⟨5, 1, 4, 2, 3, 5, -7903233108184224736354591095638699293036196659200000⟩, + ⟨5, 1, 5, 2, 4, 5, -3512798333435746004260288712079325384585248768000000⟩, + ⟨5, 1, 6, 2, 5, 5, 43353084015558841171951511130020104661630976000000⟩, + ⟨5, 1, 7, 2, 6, 5, 238261578431452581714399868191249507324788736000000⟩, + ⟨5, 1, 8, 2, 7, 5, 471443467841931018164628482322958442775026073600000⟩, + ⟨5, 1, 3, 3, 1, 5, 23304793555740319763047595717947454435151052800000⟩, + ⟨5, 1, 4, 3, 2, 5, 21084378973780563476660251714663618815085196083200000⟩, + ⟨5, 1, 5, 3, 3, 5, 1048941135074873488248291371309302249710157824000000⟩, + ⟨5, 1, 6, 3, 4, 5, -702004023991233111236171429350834307013279744000000⟩, + ⟨5, 1, 7, 3, 5, 5, 571467154294622683788687925539008249598050304000000⟩, + ⟨5, 1, 8, 3, 6, 5, -25316009531285467247329280352084226171994112000000⟩, + ⟨5, 1, 3, 4, 0, 5, -4468539376081823865336308004023046869114211532800000⟩, + ⟨5, 1, 4, 4, 1, 5, -270685167301255857582311414816988736656506880000000⟩, + ⟨5, 1, 5, 4, 2, 5, 2166362247043930718054002964270578699578900480000000⟩, + ⟨5, 1, 6, 4, 3, 5, 886357135856662024048605342262490782375084032000000⟩, + ⟨5, 1, 7, 4, 4, 5, -295451309970020537368804922358878588941369344000000⟩, + ⟨5, 1, 8, 4, 5, 5, -344579572512855956111905226833997392398149222400000⟩, + ⟨5, 1, 4, 5, 0, 5, -86881444337020322762621442915444945780736838860800000⟩, + ⟨5, 1, 5, 5, 1, 5, 731397099933194453606098985058458909672472576000000⟩, + ⟨5, 1, 6, 5, 2, 5, -1924047809235933104988505123760451419853815808000000⟩, + ⟨5, 1, 7, 5, 3, 5, -337016612824943794233912403781049928340471808000000⟩, + ⟨5, 1, 8, 5, 4, 5, -172497326415552245545601688648508982907056947200000⟩, + ⟨5, 1, 5, 6, 0, 5, -38836324576295366638605909811545371477098364928000000⟩, + ⟨5, 1, 6, 6, 1, 5, 3603361691235896909083591601148225583847571456000000⟩, + ⟨5, 1, 7, 6, 2, 5, -2385233914193859028910047526290621812921335808000000⟩, + ⟨5, 1, 8, 6, 3, 5, 915857439170999384401815751866296577158440550400000⟩, + ⟨5, 1, 6, 7, 0, 5, 1069235956843830033909358429439945333110996992000000⟩, + ⟨5, 1, 7, 7, 1, 5, 12340093217881165232833411933552508656611753984000000⟩, + ⟨5, 1, 8, 7, 2, 5, -360231116665387392386658392424725408810375577600000⟩ +] + +def collectedFourData_9_1_40 : List CollectedFourTerm := [ + ⟨5, 2, 2, 0, 3, 6, -5986021067187185914555964959350507370209450393600000⟩, + ⟨5, 2, 3, 0, 4, 6, -2191283884392581917634213888076841152196431052800000⟩, + ⟨5, 2, 4, 0, 5, 6, 64543724222229784964146075229502111160978322227200000⟩, + ⟨5, 2, 5, 0, 6, 6, 37529640174185751900506478859712759082900258816000000⟩, + ⟨5, 2, 6, 0, 7, 6, 12919563548997081486148749512939480953487622144000000⟩, + ⟨5, 2, 7, 0, 8, 6, 7579393714703730624122067991449830535104299008000000⟩, + ⟨5, 2, 2, 1, 2, 6, 5741870934602275635738888403243397990999654400000000⟩, + ⟨5, 2, 3, 1, 3, 6, 10518540734590334577792726585361278114064446259200000⟩, + ⟨5, 2, 4, 1, 4, 6, 19862245622777084058469341483265346617388669337600000⟩, + ⟨5, 2, 5, 1, 5, 6, -12301571111242972351578372417700729198152253440000000⟩, + ⟨5, 2, 6, 1, 6, 6, -4760927868778567104390883094287583658790354944000000⟩, + ⟨5, 2, 7, 1, 7, 6, -599603006607524884810210813826747958181232640000000⟩, + ⟨5, 2, 8, 1, 8, 6, -1444185996908846525571403842276433216798929715200000⟩, + ⟨5, 2, 2, 2, 1, 6, 7956712006062732852729444544667196696895999180800000⟩, + ⟨5, 2, 3, 2, 2, 6, -8208811978602018767962672967922805508519283916800000⟩, + ⟨5, 2, 4, 2, 3, 6, 31185928305714530217274652772328520653199533670400000⟩, + ⟨5, 2, 5, 2, 4, 6, 9240933466036479457153586458292965499411103744000000⟩, + ⟨5, 2, 6, 2, 5, 6, -85535005195580097665773981101694466975072256000000⟩, + ⟨5, 2, 7, 2, 6, 6, -376069307396491714122008656239758072603266252800000⟩, + ⟨5, 2, 8, 2, 7, 6, -620100743879563367869222673655407471413847654400000⟩, + ⟨5, 2, 2, 3, 0, 6, -13779133795845830225121792929733614574201156403200000⟩, + ⟨5, 2, 3, 3, 1, 6, -183920077026748455786739412566700114792624947200000⟩, + ⟨5, 2, 4, 3, 2, 6, -83198347062029789204368295434785618888678073958400000⟩, + ⟨5, 2, 5, 3, 3, 6, -2759394169244868704233640176273021595541307392000000⟩, + ⟨5, 2, 6, 3, 4, 6, 1385043744935391079814956699069755059091800064000000⟩, + ⟨5, 2, 7, 3, 5, 6, -901997117328979635646745525336387634907525939200000⟩, + ⟨5, 2, 8, 3, 6, 6, 33298746113236494102897753427980557796507648000000⟩, + ⟨5, 2, 3, 4, 0, 6, 35265453190148193938636398073444995514475164467200000⟩, + ⟨5, 2, 4, 4, 1, 6, 1068115808470283942587264189882397668996546560000000⟩, + ⟨5, 2, 5, 4, 2, 6, -5698935005097817127212343973014592575860899840000000⟩, + ⟨5, 2, 6, 4, 3, 6, -1748769757497073329424502064312650755045588992000000⟩, + ⟨5, 2, 7, 4, 4, 6, 466336915256263200597187156441999938254222131200000⟩, + ⟨5, 2, 8, 4, 5, 6, 453233661755954391932721206892346439693343129600000⟩, + ⟨5, 2, 4, 5, 0, 6, 342831655994738677378096137990948135238893148569600000⟩, + ⟨5, 2, 5, 5, 1, 6, -1924047809235933104988505123760451419853815808000000⟩, + ⟨5, 2, 6, 5, 2, 6, 3796118386882853356116590898134127554800386048000000⟩, + ⟨5, 2, 7, 5, 3, 6, 531943106398296383890022967323976603646977638400000⟩, + ⟨5, 2, 8, 5, 4, 6, 226889813358033513733968295102076065204194508800000⟩, + ⟨5, 2, 5, 6, 0, 6, 102164672551507101864972619337823040080942465024000000⟩, + ⟨5, 2, 6, 6, 1, 6, -7109380289319279132309328506030850463168987136000000⟩, + ⟨5, 2, 7, 6, 2, 6, 3764825499750378679633605213696575044906804838400000⟩, + ⟨5, 2, 8, 6, 3, 6, -1204648951691459874608658761538984145868921241600000⟩, + ⟨5, 2, 6, 7, 0, 6, -2109587015565382377947269673087606888702410752000000⟩, + ⟨5, 2, 7, 7, 1, 6, -19477459774286873165058900760876247267685905203200000⟩, + ⟨5, 2, 8, 7, 2, 6, 473820507971634096020804660532731678441236070400000⟩ +] + +def collectedFourData_9_1_41 : List CollectedFourTerm := [ + ⟨5, 3, 1, 0, 2, 7, 4409049743465271188436862225688743231623266304000000⟩, + ⟨5, 3, 2, 0, 3, 7, -4194050760439917620923952247766944791285622374400000⟩, + ⟨5, 3, 3, 0, 4, 7, -767651478212635701970882519651122849550801305600000⟩, + ⟨5, 3, 4, 0, 5, 7, 15073989473003316701736062367523564165109750169600000⟩, + ⟨5, 3, 5, 0, 6, 7, 6573699547032441947140110938629121846663970816000000⟩, + ⟨5, 3, 6, 0, 7, 7, 1810394741984580741108381796747686692808504115200000⟩, + ⟨5, 3, 7, 0, 8, 7, 885072115406702962792700611403773351582236672000000⟩, + ⟨5, 3, 1, 1, 1, 7, -4358222443419720814672231514900360627898600652800000⟩, + ⟨5, 3, 2, 1, 2, 7, 4022989209246544690555329550499914341521817600000000⟩, + ⟨5, 3, 3, 1, 3, 7, 3684859547893012354414527064189814288981321318400000⟩, + ⟨5, 3, 4, 1, 4, 7, 4638766743565584089107257589550533637734976716800000⟩, + ⟨5, 3, 5, 1, 5, 7, -2154745744068935734240234180678454959606333440000000⟩, + ⟨5, 3, 6, 1, 6, 7, -667140089362667442095178201136290169634370355200000⟩, + ⟨5, 3, 7, 1, 7, 7, -70017724561902567896506758367835376593141760000000⟩, + ⟨5, 3, 8, 1, 8, 7, -144550810500676565207195630657739150080763494400000⟩, + ⟨5, 3, 1, 2, 0, 7, -8273471540170603103912907314374112217826276147200000⟩, + ⟨5, 3, 2, 2, 1, 7, 5574797292738178666861973212355117237071459123200000⟩, + ⟨5, 3, 3, 2, 2, 7, -2875714413192150825642631153970469352152603033600000⟩, + ⟨5, 3, 4, 2, 3, 7, 7283378216100351040859742504947177079845368627200000⟩, + ⟨5, 3, 5, 2, 4, 7, 1618643820135131802453998315632707771505311744000000⟩, + ⟨5, 3, 6, 2, 5, 7, -11985863382646765056974803670608616090291404800000⟩, + ⟨5, 3, 7, 2, 6, 7, -43914918523263072372815905883920778285757235200000⟩, + ⟨5, 3, 8, 2, 7, 7, -62066842713972766874890737029205524539559116800000⟩, + ⟨5, 3, 2, 3, 0, 7, -9654223719901826092257994134232885987065515212800000⟩, + ⟨5, 3, 3, 3, 1, 7, -64430957580697856956442869225791995211310694400000⟩, + ⟨5, 3, 4, 3, 2, 7, -19430719607474598529726887456878554540640777011200000⟩, + ⟨5, 3, 5, 3, 3, 7, -483336054282926796446139928634857163317051392000000⟩, + ⟨5, 3, 6, 3, 4, 7, 194083639415536979787277494116708620080198451200000⟩, + ⟨5, 3, 7, 3, 5, 7, -105329334611075011715343609606375306567666892800000⟩, + ⟨5, 3, 8, 3, 6, 7, 3332923009658842638777652033689260346310656000000⟩, + ⟨5, 3, 3, 4, 0, 7, 12354208171781421167748206659031388009009669734400000⟩, + ⟨5, 3, 4, 4, 1, 7, 249455181690370323537492809989887398856622080000000⟩, + ⟨5, 3, 5, 4, 2, 7, -998226636005620904657829587534019718639779840000000⟩, + ⟨5, 3, 6, 4, 3, 7, -245051898379347264256842119270859078394026393600000⟩, + ⟨5, 3, 7, 4, 4, 7, 54455780450802300501770065220550948197027020800000⟩, + ⟨5, 3, 8, 4, 5, 7, 45364858330743022108800944865796698712257331200000⟩, + ⟨5, 3, 4, 5, 0, 7, 80067285173747484258998050050947477680352447692800000⟩, + ⟨5, 3, 5, 5, 1, 7, -337016612824943794233912403781049928340471808000000⟩, + ⟨5, 3, 6, 5, 2, 7, 531943106398296383890022967323976603646977638400000⟩, + ⟨5, 3, 7, 5, 3, 7, 62116843137809785705752954249932615823497625600000⟩, + ⟨5, 3, 8, 5, 4, 7, 22709752404088051606443421761086672091060633600000⟩, + ⟨5, 3, 5, 6, 0, 7, 17895185207144904664638405670325772460725633024000000⟩, + ⟨5, 3, 6, 6, 1, 7, -996224419326577966267017256417614792856751308800000⟩, + ⟨5, 3, 7, 6, 2, 7, 439631742937029197100667071014085321456982425600000⟩, + ⟨5, 3, 8, 6, 3, 7, -120575177095268387851974253874658544247321395200000⟩, + ⟨5, 3, 6, 7, 0, 7, -295612558911480214373577806211564910497339801600000⟩, + ⟨5, 3, 7, 7, 1, 7, -2274450592497146205356857437532530304728485068800000⟩, + ⟨5, 3, 8, 7, 2, 7, 47425427615100316308336142159910388481445068800000⟩ +] + +def collectedFourData_9_1_42 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 1, 8, -8911558357660444078196155392636693360509190144000000⟩, + ⟨5, 4, 1, 0, 2, 8, 11283557899503119482351002190422054580852359168000000⟩, + ⟨5, 4, 2, 0, 3, 8, -5366668255333061412437518580022035940588807782400000⟩, + ⟨5, 4, 3, 0, 4, 8, -654853116886792139410796734582513926373008998400000⟩, + ⟨5, 4, 4, 0, 5, 8, 9644268203552485906315824304411684177508617420800000⟩, + ⟨5, 4, 5, 0, 6, 8, 3364657863650262602202887458280985807703926374400000⟩, + ⟨5, 4, 6, 0, 7, 8, 772188078334992172392040298375590888652301926400000⟩, + ⟨5, 4, 7, 0, 8, 8, 323580008019019551666661264755541400598085632000000⟩, + ⟨5, 4, 0, 1, 0, 8, -46471962595216435670439848564579487917172326400000000⟩, + ⟨5, 4, 1, 1, 1, 8, -11153481620869747656535490120069611448253913497600000⟩, + ⟨5, 4, 2, 1, 2, 8, 5147779489093805679550566573380034132285849600000000⟩, + ⟨5, 4, 3, 1, 3, 8, 3143407951022526528077194186521777554448816537600000⟩, + ⟨5, 4, 4, 1, 4, 8, 2967861340807533627056615562945739989205804646400000⟩, + ⟨5, 4, 5, 1, 5, 8, -1102877026867060331236230971816313822375837696000000⟩, + ⟨5, 4, 6, 1, 6, 8, -284555413047913480115967405110383528877909606400000⟩, + ⟨5, 4, 7, 1, 7, 8, -25598293608880710575646286080504073090498560000000⟩, + ⟨5, 4, 8, 1, 8, 8, -46241467396741529323634698297869627351996825600000⟩, + ⟨5, 4, 1, 2, 0, 8, -21173314111905431537176821456952826898963392102400000⟩, + ⟨5, 4, 2, 2, 1, 8, 7133458646484417175155453605520041651058455347200000⟩, + ⟨5, 4, 3, 2, 2, 8, -2453158236781931120048469046202656871269426790400000⟩, + ⟨5, 4, 4, 2, 3, 8, 4659871434153812786836700554502342834698951065600000⟩, + ⟨5, 4, 5, 2, 4, 8, 828480617177755988457531828572206204462930329600000⟩, + ⟨5, 4, 6, 2, 5, 8, -5112333016657967547905085117057329626978713600000⟩, + ⟨5, 4, 7, 2, 6, 8, -16055177245508821676503031430990825606296371200000⟩, + ⟨5, 4, 8, 2, 7, 8, -19855038334519909238767849063258803125039923200000⟩, + ⟨5, 4, 2, 3, 0, 8, -12353454673506643206156392250307721809151970508800000⟩, + ⟨5, 4, 3, 3, 1, 8, -54963501788546646964362075647571059310959001600000⟩, + ⟨5, 4, 4, 3, 2, 8, -12431683836460503164090093788749361350209804697600000⟩, + ⟨5, 4, 5, 3, 3, 8, -247388923724522947736399992009082114589641932800000⟩, + ⟨5, 4, 6, 3, 4, 8, 82782538570707740791347216885103005897483878400000⟩, + ⟨5, 4, 7, 3, 5, 8, -38508124191019482859907389159964798077422796800000⟩, + ⟨5, 4, 8, 3, 6, 8, 1066194303256899933740021754099118997766144000000⟩, + ⟨5, 4, 3, 4, 0, 8, 10538886405581046909866757681726872148080433561600000⟩, + ⟨5, 4, 4, 4, 1, 8, 159600262511561688169761875512795202416803840000000⟩, + ⟨5, 4, 5, 4, 2, 8, -510928599110933054082074771223395812251795456000000⟩, + ⟨5, 4, 6, 4, 3, 8, -104522041582189702960911670574044587045892915200000⟩, + ⟨5, 4, 7, 4, 4, 8, 19908888290820881503907510059251783229557964800000⟩, + ⟨5, 4, 8, 4, 5, 8, 14512112455080515952163325965723658951118028800000⟩, + ⟨5, 4, 4, 5, 0, 8, 51226675853057518968922051045176145319102408294400000⟩, + ⟨5, 4, 5, 5, 1, 8, -172497326415552245545601688648508982907056947200000⟩, + ⟨5, 4, 6, 5, 2, 8, 226889813358033513733968295102076065204194508800000⟩, + ⟨5, 4, 7, 5, 3, 8, 22709752404088051606443421761086672091060633600000⟩, + ⟨5, 4, 8, 5, 4, 8, 7264796867927593488065915662791233572857446400000⟩, + ⟨5, 4, 5, 6, 0, 8, 9159404867519237722687285313179546797695670681600000⟩, + ⟨5, 4, 6, 6, 1, 8, -424919826659955923206353153392170336226220441600000⟩, + ⟨5, 4, 7, 6, 2, 8, 160728194266532526483046033107708255995009433600000⟩, + ⟨5, 4, 8, 6, 3, 8, -38571718146686509860595585128816794669993164800000⟩, + ⟨5, 4, 6, 7, 0, 8, -126087691542516505456812870958664844345291571200000⟩, + ⟨5, 4, 7, 7, 1, 8, -831533078658684634882194388003441532094696652800000⟩, + ⟨5, 4, 8, 7, 2, 8, 15171283766893318777749451600759563517899571200000⟩ +] + +def collectedFourData_9_1_43 : List CollectedFourTerm := [ + ⟨6, 0, 3, 0, 4, 5, -14743468044221935016231001618805142631441078681600000⟩, + ⟨6, 0, 4, 0, 5, 5, 868530401107110443506212556194925609449052490956800000⟩, + ⟨6, 0, 5, 0, 6, 5, 757524464849473468511054574241762209756459565056000000⟩, + ⟨6, 0, 6, 0, 7, 5, 347703323492899824220282057875950704194666627072000000⟩, + ⟨6, 0, 7, 0, 8, 5, 254979625924385615001428643628094515923784826880000000⟩, + ⟨6, 0, 3, 1, 3, 5, 70771190486469997747301658109195025004785722982400000⟩, + ⟨6, 0, 4, 1, 4, 5, 267275623858361892356820214108672033499963090534400000⟩, + ⟨6, 0, 5, 1, 5, 5, -248303501701618857547634648161754571600864215040000000⟩, + ⟨6, 0, 6, 1, 6, 5, -128130523651689512172516903483156296232937193472000000⟩, + ⟨6, 0, 7, 1, 7, 5, -20171342996911430735326693205711101142394470400000000⟩, + ⟨6, 0, 8, 1, 8, 5, -58300917321556121989911723245306298337178576486400000⟩, + ⟨6, 0, 3, 2, 2, 5, -55230797775475487326629997720482053578785659289600000⟩, + ⟨6, 0, 4, 2, 3, 5, 419652369717628537378340401767131265903149816217600000⟩, + ⟨6, 0, 5, 2, 4, 5, 186525454176453534448828869976804281652718075904000000⟩, + ⟨6, 0, 6, 2, 5, 5, -2301997700517860760809436800690048490566320128000000⟩, + ⟨6, 0, 7, 2, 6, 5, -12651409193267969282285808131606782244875665408000000⟩, + ⟨6, 0, 8, 2, 7, 5, -25033092882315023404338324038973702611435048140800000⟩, + ⟨6, 0, 3, 3, 1, 5, -1237457089721789520141081043030763045428553318400000⟩, + ⟨6, 0, 4, 3, 2, 5, -1119555690595644840200994049503136876560614267289600000⟩, + ⟨6, 0, 5, 3, 3, 5, -55697538843012054032089331491424312307348406272000000⟩, + ⟨6, 0, 6, 3, 4, 5, 37275586862566428828891238357601218274663596032000000⟩, + ⟨6, 0, 7, 3, 5, 5, -30344232826333320525025775951722733223869939712000000⟩, + ⟨6, 0, 8, 3, 6, 5, 1344250289238763610397174454710650355094388736000000⟩, + ⟨6, 0, 3, 4, 0, 5, 237274177881374333206658989854010928033933190758400000⟩, + ⟨6, 0, 4, 4, 1, 5, 14373063574165916423377337547030490637811056640000000⟩, + ⟨6, 0, 5, 4, 2, 5, -115031283804263632982752928855890430378052157440000000⟩, + ⟨6, 0, 6, 4, 3, 5, -47064519973881528212689005857884095150079082496000000⟩, + ⟨6, 0, 7, 4, 4, 5, 15688116580630989757819212046831359099332984832000000⟩, + ⟨6, 0, 8, 4, 5, 5, 18296769459015772465210670576438702250873008947200000⟩, + ⟨6, 0, 4, 5, 0, 5, 4613302366440958615995147246819883106475193034342400000⟩, + ⟨6, 0, 5, 5, 1, 5, -38836324576295366638605909811545371477098364928000000⟩, + ⟨6, 0, 6, 5, 2, 5, 102164672551507101864972619337823040080942465024000000⟩, + ⟨6, 0, 7, 5, 3, 5, 17895185207144904664638405670325772460725633024000000⟩, + ⟨6, 0, 8, 5, 4, 5, 9159404867519237722687285313179546797695670681600000⟩, + ⟨6, 0, 5, 6, 0, 5, 2062163094074514954079958923217683164622837776384000000⟩, + ⟨6, 0, 6, 6, 1, 5, -191334261811276103881520979879940897114127597568000000⟩, + ⟨6, 0, 7, 6, 2, 5, 126653111545672373428277698283191121314289025024000000⟩, + ⟨6, 0, 8, 6, 3, 5, -48630951334792603727511761427541741440326644531200000⟩, + ⟨6, 0, 6, 7, 0, 5, -56775169975961929056296786626236842544124133376000000⟩, + ⟨6, 0, 7, 7, 1, 5, -655244415865400659992628815245680670249689546752000000⟩, + ⟨6, 0, 8, 7, 2, 5, 19127848019326511067418575088557984734451125452800000⟩ +] + +def collectedFourData_9_1_44 : List CollectedFourTerm := [ + ⟨6, 1, 2, 0, 3, 6, 11210635667623561965297907470635326610106168115200000⟩, + ⟨6, 1, 3, 0, 4, 6, 4103842100877123980339123731964914523522570649600000⟩, + ⟨6, 1, 4, 0, 5, 6, -120877652912604004222197600252746981660300830310400000⟩, + ⟨6, 1, 5, 0, 6, 6, -70285606750713505890709609980916932073658253312000000⟩, + ⟨6, 1, 6, 0, 7, 6, -24195791880260487695576634322931913835998609408000000⟩, + ⟨6, 1, 7, 0, 8, 6, -14194708064558576853790909511850989776961273856000000⟩, + ⟨6, 1, 2, 1, 2, 6, -10753390670673098177150047888975377109667020800000000⟩, + ⟨6, 1, 3, 1, 3, 6, -19699150171210438866138466172175066112201221734400000⟩, + ⟨6, 1, 4, 1, 4, 6, -37198064744271938808235673057237379342593635123200000⟩, + ⟨6, 1, 5, 1, 5, 6, 23038414051608217603005091232271598335641518080000000⟩, + ⟨6, 1, 6, 1, 6, 6, 8916277971235384560943375054646082876639019008000000⟩, + ⟨6, 1, 7, 1, 7, 6, 1122938054651261150780802257348412599414292480000000⟩, + ⟨6, 1, 8, 1, 8, 6, 2704675253546435431376678382021024900863911526400000⟩, + ⟨6, 1, 2, 2, 1, 6, -14901350732146725531929241373967193144636840345600000⟩, + ⟨6, 1, 3, 2, 2, 6, 15373484209833242076482404060134409466206067097600000⟩, + ⟨6, 1, 4, 2, 3, 6, -58405086829451671477885899853849863035785366732800000⟩, + ⟨6, 1, 5, 2, 4, 6, -17306443989039382679631285433248836198867140608000000⟩, + ⟨6, 1, 6, 2, 5, 6, 160190177968505232563170738471687112613691392000000⟩, + ⟨6, 1, 7, 2, 6, 6, 704303567207235779356107323561699124685937049600000⟩, + ⟨6, 1, 8, 2, 7, 6, 1161326269792553732562498167499932649034403020800000⟩, + ⟨6, 1, 2, 3, 0, 6, 25805597251807343193664540330830945573732247142400000⟩, + ⟨6, 1, 3, 3, 1, 6, 344445993818896073357305289089070013266421350400000⟩, + ⟨6, 1, 4, 3, 2, 6, 155814078599491327228096882754795457904995257548800000⟩, + ⟨6, 1, 5, 3, 3, 6, 5167800505136724294094911187266125867142610944000000⟩, + ⟨6, 1, 6, 3, 4, 6, -2593913491769216718720045585771733634512846848000000⟩, + ⟨6, 1, 7, 3, 5, 6, 1689262523824273039569910968526451216759547494400000⟩, + ⟨6, 1, 8, 3, 6, 6, -62361977459528578264528550053206155209998336000000⟩, + ⟨6, 1, 3, 4, 0, 6, -66045231537108075836838104372430254608021349990400000⟩, + ⟨6, 1, 4, 4, 1, 6, -2000370036321340793968592082986776257280081920000000⟩, + ⟨6, 1, 5, 4, 2, 6, 10672980151344365970536093730615772301890682880000000⟩, + ⟨6, 1, 6, 4, 3, 6, 3275100504627917397634795938683590811156742144000000⟩, + ⟨6, 1, 7, 4, 4, 6, -873356975630892900916224081999745537286760038400000⟩, + ⟨6, 1, 8, 4, 5, 6, -848817168736845143927917319634063180040450867200000⟩, + ⟨6, 1, 4, 5, 0, 6, -642056008080682005569856359903369600676090032947200000⟩, + ⟨6, 1, 5, 5, 1, 6, 3603361691235896909083591601148225583847571456000000⟩, + ⟨6, 1, 6, 5, 2, 6, -7109380289319279132309328506030850463168987136000000⟩, + ⟨6, 1, 7, 5, 3, 6, -996224419326577966267017256417614792856751308800000⟩, + ⟨6, 1, 8, 5, 4, 6, -424919826659955923206353153392170336226220441600000⟩, + ⟨6, 1, 5, 6, 0, 6, -191334261811276103881520979879940897114127597568000000⟩, + ⟨6, 1, 6, 6, 1, 6, 13314465711293218957804487832728790237343383552000000⟩, + ⟨6, 1, 7, 6, 2, 6, -7050774889723670106192047872094065644010261708800000⟩, + ⟨6, 1, 8, 6, 3, 6, 2256069658495792402975595784415862534765228851200000⟩, + ⟨6, 1, 6, 7, 0, 6, 3950839994581876149025544460895650255118270464000000⟩, + ⟨6, 1, 7, 7, 1, 6, 36477436816460761466750968310415678392408368742400000⟩, + ⟨6, 1, 8, 7, 2, 6, -887372267337229516446047107078471297031523532800000⟩ +] + +def collectedFourData_9_1_45 : List CollectedFourTerm := [ + ⟨6, 2, 1, 0, 2, 7, 31205034343347737977824469504401955190476898304000000⟩, + ⟨6, 2, 2, 0, 3, 7, -29683379782966650120397092102948926654612137574400000⟩, + ⟨6, 2, 3, 0, 4, 7, -5433050687815547505130353670411537802157726105600000⟩, + ⟨6, 2, 4, 0, 5, 7, 106686108473485824124099949240537589463278786969600000⟩, + ⟨6, 2, 5, 0, 6, 7, 46525335857692980756202521058071404925803298816000000⟩, + ⟨6, 2, 6, 0, 7, 7, 12813062538560581663764934194192004518117585715200000⟩, + ⟨6, 2, 7, 0, 8, 7, 6264094842327365346355438880583594017053212672000000⟩, + ⟨6, 2, 1, 1, 1, 7, -30845304302684944884754508586398035649802063052800000⟩, + ⟨6, 2, 2, 1, 2, 7, 28472692244744371212821487410838720162142617600000000⟩, + ⟨6, 2, 3, 1, 3, 7, 26079580733430657485599098794691650265534588518400000⟩, + ⟨6, 2, 4, 1, 4, 7, 32830855618783648168358334902412876190378151116800000⟩, + ⟨6, 2, 5, 1, 5, 7, -15250205567426285624904994743989333241825853440000000⟩, + ⟨6, 2, 6, 1, 6, 7, -4721681680103751556051831252414921835665371955200000⟩, + ⟨6, 2, 7, 1, 7, 7, -495550203949392559679212950159291454335221760000000⟩, + ⟨6, 2, 8, 1, 8, 7, -1023057862460673921468038704520498117832238694400000⟩, + ⟨6, 2, 1, 2, 0, 7, -58555466273062096141846519868731181552377213747200000⟩, + ⟨6, 2, 2, 2, 1, 7, 39455608600226967464297135810949244857387004723200000⟩, + ⟨6, 2, 3, 2, 2, 7, -20352858835018036916895291293250815670315751833600000⟩, + ⟨6, 2, 4, 2, 3, 7, 51548084188856110754200914770843206122720146227200000⟩, + ⟨6, 2, 5, 2, 4, 7, 11455946050920806109730450401729395827874463744000000⟩, + ⟨6, 2, 6, 2, 5, 7, -84829906726388566902212439095809695961369804800000⟩, + ⟨6, 2, 7, 2, 6, 7, -310807684294055840987643001709797894515798835200000⟩, + ⟨6, 2, 8, 2, 7, 7, -439277865109878661743037547461517987761933516800000⟩, + ⟨6, 2, 2, 3, 0, 7, -68327735060009711833404939140836959671133457612800000⟩, + ⟨6, 2, 3, 3, 1, 7, -456009879920352182871984925895167869100385894400000⟩, + ⟨6, 2, 4, 3, 2, 7, -137520850964738284650609332760121884546769826611200000⟩, + ⟨6, 2, 5, 3, 3, 7, -3420809256151164551685008926867753901481787392000000⟩, + ⟨6, 2, 6, 3, 4, 7, 1373626288163345273191622492720103003532768051200000⟩, + ⟨6, 2, 7, 3, 5, 7, -745468002208864286614673625173197474793049292800000⟩, + ⟨6, 2, 8, 3, 6, 7, 23588751098643008189555327981045922876358656000000⟩, + ⟨6, 2, 3, 4, 0, 7, 87436865700298057167697454071085596873803064934400000⟩, + ⟨6, 2, 4, 4, 1, 7, 1765518187521299424246345915458003063097262080000000⟩, + ⟨6, 2, 5, 4, 2, 7, -7064945571359766434931127331911943713550499840000000⟩, + ⟨6, 2, 6, 4, 3, 7, -1734353965083660963395412780874140357832055193600000⟩, + ⟨6, 2, 7, 4, 4, 7, 385410598208750965541376683522048477165833420800000⟩, + ⟨6, 2, 8, 4, 5, 7, 321069628277622336227123159078879155339866931200000⟩, + ⟨6, 2, 4, 5, 0, 7, 566675934497786276993188739074122188287464230092800000⟩, + ⟨6, 2, 5, 5, 1, 7, -2385233914193859028910047526290621812921335808000000⟩, + ⟨6, 2, 6, 5, 2, 7, 3764825499750378679633605213696575044906804838400000⟩, + ⟨6, 2, 7, 5, 3, 7, 439631742937029197100667071014085321456982425600000⟩, + ⟨6, 2, 8, 5, 4, 7, 160728194266532526483046033107708255995009433600000⟩, + ⟨6, 2, 5, 6, 0, 7, 126653111545672373428277698283191121314289025024000000⟩, + ⟨6, 2, 6, 6, 1, 7, -7050774889723670106192047872094065644010261708800000⟩, + ⟨6, 2, 7, 6, 2, 7, 3111492143428088510865243599226427898808867225600000⟩, + ⟨6, 2, 8, 6, 3, 7, -853370399775967538659141834892366031518642995200000⟩, + ⟨6, 2, 6, 7, 0, 7, -2092196865510439213452070279327416722529032601600000⟩, + ⟨6, 2, 7, 7, 1, 7, -16097416219064733364779010442303326975960075468800000⟩, + ⟨6, 2, 8, 7, 2, 7, 335653300276450922355980489977502651393035468800000⟩ +] + +def collectedFourData_9_1_46 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 1, 8, 47315034882383871532229705755361049959001489408000000⟩, + ⟨6, 3, 1, 0, 2, 8, -59908931096597619089274501323259834772777598976000000⟩, + ⟨6, 3, 2, 0, 3, 8, 28493792613161859567987621518347570583759015116800000⟩, + ⟨6, 3, 3, 0, 4, 8, 3476877648644015891620387735636466051861761228800000⟩, + ⟨6, 3, 4, 0, 5, 8, -51205285108624832592266834815816660434609084825600000⟩, + ⟨6, 3, 5, 0, 6, 8, -17864317080867317582910669334298769988099296460800000⟩, + ⟨6, 3, 6, 0, 7, 8, -4099855984309905421004444731891347213375032524800000⟩, + ⟨6, 3, 7, 0, 8, 8, -1718015946504036286356340002366311150464794624000000⟩, + ⟨6, 3, 0, 1, 0, 8, 246738274384454814314376651840670804386565324800000000⟩, + ⟨6, 3, 1, 1, 1, 8, 59218304001548843297146685157705890352493441843200000⟩, + ⟨6, 3, 2, 1, 2, 8, -27331624427272168375214127741325416875635507200000000⟩, + ⟨6, 3, 3, 1, 3, 8, -16689612622504324497732070934781355722731107123200000⟩, + ⟨6, 3, 4, 1, 4, 8, -15757565313554511282519408149962900326742543564800000⟩, + ⟨6, 3, 5, 1, 5, 8, 5855616145108689527956407689241549924804329472000000⟩, + ⟨6, 3, 6, 1, 6, 8, 1510818731581287863737801492171672227282734284800000⟩, + ⟨6, 3, 7, 1, 7, 8, 135911600016909694649090962259758957901905920000000⟩, + ⟨6, 3, 8, 1, 8, 8, 245514482998216805552629094146017777207685939200000⟩, + ⟨6, 3, 1, 2, 0, 8, 112417610430537927083171212384029616324263857356800000⟩, + ⟨6, 3, 2, 2, 1, 8, -37874390891500854459709538923186785961556469350400000⟩, + ⟨6, 3, 3, 2, 2, 8, 13024800252311497238983196022428422630500256972800000⟩, + ⟨6, 3, 4, 2, 3, 8, -24741125020505959600057218480224902017166029619200000⟩, + ⟨6, 3, 5, 2, 4, 8, -4398735633869038715800885234031502618659074867200000⟩, + ⟨6, 3, 6, 2, 5, 8, 27143424898923970146231709444074205468635955200000⟩, + ⟨6, 3, 7, 2, 6, 8, 85243370567292939027236688402928943904482918400000⟩, + ⟨6, 3, 8, 2, 7, 8, 105418355991724730552176055669916288577594982400000⟩, + ⟨6, 3, 2, 3, 0, 8, 65589441861475398703071611935146250408056953241600000⟩, + ⟨6, 3, 3, 3, 1, 8, 291823259188731806387037597942399916290814771200000⟩, + ⟨6, 3, 4, 3, 2, 8, 66004791840169059024575486391280631792065000243200000⟩, + ⟨6, 3, 5, 3, 3, 8, 1313486944231175113434604822462183010247219609600000⟩, + ⟨6, 3, 6, 3, 4, 8, -439525674738847800578518793544099456015453388800000⟩, + ⟨6, 3, 7, 3, 5, 8, 204455064560850958993298217224720563188636057600000⟩, + ⟨6, 3, 8, 3, 6, 8, -5660852863813043586793330112661917855121408000000⟩, + ⟨6, 3, 3, 4, 0, 8, -55955171686993100246810782458513937342819152691200000⟩, + ⟨6, 3, 4, 4, 1, 8, -847381758037957932579585711181973217481850880000000⟩, + ⟨6, 3, 5, 4, 2, 8, 2712724701910373139972214001683836754609569792000000⟩, + ⟨6, 3, 6, 4, 3, 8, 554949408953611843687645742850471769665857126400000⟩, + ⟨6, 3, 7, 4, 4, 8, -105704266991634768133277836891278607818267033600000⟩, + ⟨6, 3, 8, 4, 5, 8, -77050621167617679638979704578613793953257881600000⟩, + ⟨6, 3, 4, 5, 0, 8, -271982952657486429392264931400165024137258781900800000⟩, + ⟨6, 3, 5, 5, 1, 8, 915857439170999384401815751866296577158440550400000⟩, + ⟨6, 3, 6, 5, 2, 8, -1204648951691459874608658761538984145868921241600000⟩, + ⟨6, 3, 7, 5, 3, 8, -120575177095268387851974253874658544247321395200000⟩, + ⟨6, 3, 8, 5, 4, 8, -38571718146686509860595585128816794669993164800000⟩, + ⟨6, 3, 5, 6, 0, 8, -48630951334792603727511761427541741440326644531200000⟩, + ⟨6, 3, 6, 6, 1, 8, 2256069658495792402975595784415862534765228851200000⟩, + ⟨6, 3, 7, 6, 2, 8, -853370399775967538659141834892366031518642995200000⟩, + ⟨6, 3, 8, 6, 3, 8, 204792710358581457977490792486114374780033433600000⟩, + ⟨6, 3, 6, 7, 0, 8, 669450087643216896802701017796082510372169318400000⟩, + ⟨6, 3, 7, 7, 1, 8, 4414942375232418915235672897884484412982794649600000⟩, + ⟨6, 3, 8, 7, 2, 8, -80550425843763849230298825999203130449225318400000⟩ +] + +def collectedFourData_9_1_47 : List CollectedFourTerm := [ + ⟨7, 0, 2, 0, 3, 6, 3326564409022108999185394352579023928281163366400000⟩, + ⟨7, 0, 3, 0, 4, 6, 1217744959141844593939359486117734847282885427200000⟩, + ⟨7, 0, 4, 0, 5, 6, -35868376240830518884210596758182582187230809292800000⟩, + ⟨7, 0, 5, 0, 6, 6, -20856051772219509044063094511162784600800886784000000⟩, + ⟨7, 0, 6, 0, 7, 6, -7179687441759736990358291848173926191523168256000000⟩, + ⟨7, 0, 7, 0, 8, 6, -4212036858925887423979311550158446072841633792000000⟩, + ⟨7, 0, 2, 1, 2, 6, -3190884776023985722974041885897247283583385600000000⟩, + ⟨7, 0, 3, 1, 3, 6, -5845385916588405936141481138830530728533216460800000⟩, + ⟨7, 0, 4, 1, 4, 6, -11037889548062174317800095147937971833659614822400000⟩, + ⟨7, 0, 5, 1, 5, 6, 6836255364691615157195915777077882963686850560000000⟩, + ⟨7, 0, 6, 1, 6, 6, 2645753000939950632266512278704976539424915456000000⟩, + ⟨7, 0, 7, 1, 7, 6, 333212663125575334479077319438067490472591360000000⟩, + ⟨7, 0, 8, 1, 8, 6, 802566125879431907781820185448187215420902604800000⟩, + ⟨7, 0, 2, 2, 1, 6, -4421720985463332713969215734926226815932642099200000⟩, + ⟨7, 0, 3, 2, 2, 6, 4561818520495682320759413641331303289216774963200000⟩, + ⟨7, 0, 4, 2, 3, 6, -17330710667353729223398050647597769147704514969600000⟩, + ⟨7, 0, 5, 2, 4, 6, -5135391277315228622708198189457363195874246656000000⟩, + ⟨7, 0, 6, 2, 5, 6, 47533695724669639231901526665126061061177344000000⟩, + ⟨7, 0, 7, 2, 6, 6, 208990038502924017888743152145633002900370227200000⟩, + ⟨7, 0, 8, 2, 7, 6, 344603709449889399853405233499668127537535385600000⟩, + ⟨7, 0, 2, 3, 0, 6, 7657369654723452378037196480963062194668096716800000⟩, + ⟨7, 0, 3, 3, 1, 6, 102208457917987186926535115452520780857658572800000⟩, + ⟨7, 0, 4, 3, 2, 6, 46235163077377601378755966640163203905761155481600000⟩, + ⟨7, 0, 5, 3, 3, 6, 1533456419689220689217856598742837699498999808000000⟩, + ⟨7, 0, 6, 3, 4, 6, -769699467330105706577794851647664979848462336000000⟩, + ⟨7, 0, 7, 3, 5, 6, 501259764018350436320411253035351051516824780800000⟩, + ⟨7, 0, 8, 3, 6, 6, -18504850290713478992161694761855033804849152000000⟩, + ⟨7, 0, 3, 4, 0, 6, -19597792946877669996631701572281222460387151052800000⟩, + ⟨7, 0, 4, 4, 1, 6, -593575597761927034318805024237097479244349440000000⟩, + ⟨7, 0, 5, 4, 2, 6, 3167024329601445992171796907090390047428444160000000⟩, + ⟨7, 0, 6, 4, 3, 6, 971830063671587761421635217348277771549278208000000⟩, + ⟨7, 0, 7, 4, 4, 6, -259153746285359437896131424564707597304515788800000⟩, + ⟨7, 0, 8, 4, 5, 6, -251871978271635437945475338011071692197488230400000⟩, + ⟨7, 0, 4, 5, 0, 6, -190519139895727724271142378610799841429799986790400000⟩, + ⟨7, 0, 5, 5, 1, 6, 1069235956843830033909358429439945333110996992000000⟩, + ⟨7, 0, 6, 5, 2, 6, -2109587015565382377947269673087606888702410752000000⟩, + ⟨7, 0, 7, 5, 3, 6, -295612558911480214373577806211564910497339801600000⟩, + ⟨7, 0, 8, 5, 4, 6, -126087691542516505456812870958664844345291571200000⟩, + ⟨7, 0, 5, 6, 0, 6, -56775169975961929056296786626236842544124133376000000⟩, + ⟨7, 0, 6, 6, 1, 6, 3950839994581876149025544460895650255118270464000000⟩, + ⟨7, 0, 7, 6, 2, 6, -2092196865510439213452070279327416722529032601600000⟩, + ⟨7, 0, 8, 6, 3, 6, 669450087643216896802701017796082510372169318400000⟩, + ⟨7, 0, 6, 7, 0, 6, 1172344200755136528351128052993700901261672448000000⟩, + ⟨7, 0, 7, 7, 1, 6, 10824055534730780464624155979181254740653427916800000⟩, + ⟨7, 0, 8, 7, 2, 6, -263312544408378384876694063021645709442652569600000⟩ +] + +def collectedFourData_9_1_48 : List CollectedFourTerm := [ + ⟨7, 1, 1, 0, 2, 7, -161440364558223193846905220371010071612402696192000000⟩, + ⟨7, 1, 2, 0, 3, 7, 153568030105498116088661307828197845221917274931200000⟩, + ⟨7, 1, 3, 0, 4, 7, 28108082627097944276048257125664471646993173708800000⟩, + ⟨7, 1, 4, 0, 5, 7, -551944409217718897924957836095407425030896536780800000⟩, + ⟨7, 1, 5, 0, 6, 7, -240700494010541967111562127750074140981165293568000000⟩, + ⟨7, 1, 6, 0, 7, 7, -66288838671747969316865991952499827698187213209600000⟩, + ⟨7, 1, 7, 0, 8, 7, -32407519371572132509732145047674170564784685056000000⟩, + ⟨7, 1, 1, 1, 1, 7, 159579288288665229479155233552843482176290186854400000⟩, + ⟨7, 1, 2, 1, 2, 7, -147304494696880013964735347636728251730939084800000000⟩, + ⟨7, 1, 3, 1, 3, 7, -134923646447715146116988449690143892835824513843200000⟩, + ⟨7, 1, 4, 1, 4, 7, -169851609247939183486179648695821061363226535526400000⟩, + ⟨7, 1, 5, 1, 5, 7, 78897485556460901634468919748155151899290501120000000⟩, + ⟨7, 1, 6, 1, 6, 7, 24427789547564894555659221750003828431162808729600000⟩, + ⟨7, 1, 7, 1, 7, 7, 2563746756444333321363236368686221384723988480000000⟩, + ⟨7, 1, 8, 1, 8, 7, 5292826550438231774980738959455750979218256691200000⟩, + ⟨7, 1, 1, 2, 0, 7, 302938805257720086603440041278852945649101019545600000⟩, + ⟨7, 1, 2, 2, 1, 7, -204125006439709334470244536375948630132705040793600000⟩, + ⟨7, 1, 3, 2, 2, 7, 105296245278057958707835527321118514383780891852800000⟩, + ⟨7, 1, 4, 2, 3, 7, -266685862677186115403634827761250927408909490585600000⟩, + ⟨7, 1, 5, 2, 4, 7, -59267747840638312090539820064956820459788173312000000⟩, + ⟨7, 1, 6, 2, 5, 7, 438870565456298627913763479929840541442139750400000⟩, + ⟨7, 1, 7, 2, 6, 7, 1607974703947928365598847817429442380850370969600000⟩, + ⟨7, 1, 8, 2, 7, 7, 2272619792864123744649227305048442469714650726400000⟩, + ⟨7, 1, 2, 3, 0, 7, 353495988376542330385624443625347028884918789734400000⟩, + ⟨7, 1, 3, 3, 1, 7, 2359183471694757023013172669568094018209002291200000⟩, + ⟨7, 1, 4, 3, 2, 7, 711469055596066250230077005713364428828387678617600000⟩, + ⟨7, 1, 5, 3, 3, 7, 17697679397520609147941813105789227900512239616000000⟩, + ⟨7, 1, 6, 3, 4, 7, -7106504876355751827324411747916567610725603737600000⟩, + ⟨7, 1, 7, 3, 5, 7, 3856705450758306848720841117325067248619382374400000⟩, + ⟨7, 1, 8, 3, 6, 7, -122037249981426118464220502478004653693861888000000⟩, + ⟨7, 1, 3, 4, 0, 7, -452357761224310975458292269836696555808275772211200000⟩, + ⟨7, 1, 4, 4, 1, 7, -9133971675579123697562653061120299896762531840000000⟩, + ⟨7, 1, 5, 4, 2, 7, 36550749346233945458459979029155766698581688320000000⟩, + ⟨7, 1, 6, 4, 3, 7, 8972742452879086796686732087394679079171837132800000⟩, + ⟨7, 1, 7, 4, 4, 7, -1993935555231581429283673582553907769836463718400000⟩, + ⟨7, 1, 8, 4, 5, 7, -1661065239262023038500798558256440566410221977600000⟩, + ⟨7, 1, 4, 5, 0, 7, -2931718274849358783770013151304441460037039580774400000⟩, + ⟨7, 1, 5, 5, 1, 7, 12340093217881165232833411933552508656611753984000000⟩, + ⟨7, 1, 6, 5, 2, 7, -19477459774286873165058900760876247267685905203200000⟩, + ⟨7, 1, 7, 5, 3, 7, -2274450592497146205356857437532530304728485068800000⟩, + ⟨7, 1, 8, 5, 4, 7, -831533078658684634882194388003441532094696652800000⟩, + ⟨7, 1, 5, 6, 0, 7, -655244415865400659992628815245680670249689546752000000⟩, + ⟨7, 1, 6, 6, 1, 7, 36477436816460761466750968310415678392408368742400000⟩, + ⟨7, 1, 7, 6, 2, 7, -16097416219064733364779010442303326975960075468800000⟩, + ⟨7, 1, 8, 6, 3, 7, 4414942375232418915235672897884484412982794649600000⟩, + ⟨7, 1, 6, 7, 0, 7, 10824055534730780464624155979181254740653427916800000⟩, + ⟨7, 1, 7, 7, 1, 7, 83280560253742181720227046159576620000757573222400000⟩, + ⟨7, 1, 8, 7, 2, 7, -1736514389491538680617919800172260896163653222400000⟩ +] + +def collectedFourData_9_1_49 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 1, 8, -18610263040687662023800485001954017403471921152000000⟩, + ⟨7, 2, 1, 0, 2, 8, 23563777749833530675844192329001860227183673344000000⟩, + ⟨7, 2, 2, 0, 3, 8, -11207367317300144149253455497418205455575102259200000⟩, + ⟨7, 2, 3, 0, 4, 8, -1367548555388335195394801575641264938546311987200000⟩, + ⟨7, 2, 4, 0, 5, 8, 20140402037402089011003697482116443293599819366400000⟩, + ⟨7, 2, 5, 0, 6, 8, 7026511567488461779576498249615774567267250995200000⟩, + ⟨7, 2, 6, 0, 7, 8, 1612582522376037154839614672967509133881455411200000⟩, + ⟨7, 2, 7, 0, 8, 8, 675741416063925287939835104393912521699885056000000⟩, + ⟨7, 2, 0, 1, 0, 8, -97048733027769438909336801621800069440418611200000000⟩, + ⟨7, 2, 1, 1, 1, 8, -23292135724548476982223805214617009717374667980800000⟩, + ⟨7, 2, 2, 1, 2, 8, 10750255625621385887715655795430647908846796800000000⟩, + ⟨7, 2, 3, 1, 3, 8, 6564469026052161802767284699050559398677892300800000⟩, + ⟨7, 2, 4, 1, 4, 8, 6197870002527418315210498939072288762501477171200000⟩, + ⟨7, 2, 5, 1, 5, 8, -2303169742908572607394722905131962236632301568000000⟩, + ⟨7, 2, 6, 1, 6, 8, -594245234552160403159845963799101636934316851200000⟩, + ⟨7, 2, 7, 1, 7, 8, -53457651101450121949706962511632030739988480000000⟩, + ⟨7, 2, 8, 1, 8, 8, -96567383290599602165303710379118300700134604800000⟩, + ⟨7, 2, 1, 2, 0, 8, -44216839440538874404104891381816422272523776819200000⟩, + ⟨7, 2, 2, 2, 1, 8, 14897006390226362498699844509263074956261562777600000⟩, + ⟨7, 2, 3, 2, 2, 8, -5123000740683791217560333015609674933608854323200000⟩, + ⟨7, 2, 4, 2, 3, 8, 9731343233682861062750784504721826799539768524800000⟩, + ⟨7, 2, 5, 2, 4, 8, 1730139846588745782915267490323920660282002636800000⟩, + ⟨7, 2, 6, 2, 5, 8, -10676231740076342409423469537501555456789708800000⟩, + ⟨7, 2, 7, 2, 6, 8, -33528487354508458479832350970467672810690969600000⟩, + ⟨7, 2, 8, 2, 7, 8, -41463846305929321890223184284070096787839385600000⟩, + ⟨7, 2, 2, 3, 0, 8, -25798073884299511833400211221271193143623444070400000⟩, + ⟨7, 2, 3, 3, 1, 8, -114781857994890407448272954583860591725432012800000⟩, + ⟨7, 2, 4, 3, 2, 8, -25961442090127696689540948992008201565341797580800000⟩, + ⟨7, 2, 5, 3, 3, 8, -516629388383949478934498396153486104731215462400000⟩, + ⟨7, 2, 6, 3, 4, 8, 172877150790627697238889347531443821910111027200000⟩, + ⟨7, 2, 7, 3, 5, 8, -80417620761278600578118191495500993023862374400000⟩, + ⟨7, 2, 8, 3, 6, 8, 2226564158561240590544784192121864980529152000000⟩, + ⟨7, 2, 3, 4, 0, 8, 22008658900291495958581443132745620581497228492800000⟩, + ⟨7, 2, 4, 4, 1, 8, 333297808025883136115680414313361709958430720000000⟩, + ⟨7, 2, 5, 4, 2, 8, -1066986854918694140234752233198492038775963648000000⟩, + ⟨7, 2, 6, 4, 3, 8, -218276378757274253483055228254465074765863321600000⟩, + ⟨7, 2, 7, 4, 4, 8, 41576302714928670898531135248823168205743718400000⟩, + ⟨7, 2, 8, 4, 5, 8, 30306060873509303826443541719366383488624230400000⟩, + ⟨7, 2, 4, 5, 0, 8, 106978137163400093601057958767357276591767106355200000⟩, + ⟨7, 2, 5, 5, 1, 8, -360231116665387392386658392424725408810375577600000⟩, + ⟨7, 2, 6, 5, 2, 8, 473820507971634096020804660532731678441236070400000⟩, + ⟨7, 2, 7, 5, 3, 8, 47425427615100316308336142159910388481445068800000⟩, + ⟨7, 2, 8, 5, 4, 8, 15171283766893318777749451600759563517899571200000⟩, + ⟨7, 2, 5, 6, 0, 8, 19127848019326511067418575088557984734451125452800000⟩, + ⟨7, 2, 6, 6, 1, 8, -887372267337229516446047107078471297031523532800000⟩, + ⟨7, 2, 7, 6, 2, 8, 335653300276450922355980489977502651393035468800000⟩, + ⟨7, 2, 8, 6, 3, 8, -80550425843763849230298825999203130449225318400000⟩, + ⟨7, 2, 6, 7, 0, 8, -263312544408378384876694063021645709442652569600000⟩, + ⟨7, 2, 7, 7, 1, 8, -1736514389491538680617919800172260896163653222400000⟩, + ⟨7, 2, 8, 7, 2, 8, 31682627239274759117128303711101011623516569600000⟩ +] + +def collectedFourData_9_1 : List (List CollectedFourTerm) := [ + collectedFourData_9_1_0, + collectedFourData_9_1_1, + collectedFourData_9_1_2, + collectedFourData_9_1_3, + collectedFourData_9_1_4, + collectedFourData_9_1_5, + collectedFourData_9_1_6, + collectedFourData_9_1_7, + collectedFourData_9_1_8, + collectedFourData_9_1_9, + collectedFourData_9_1_10, + collectedFourData_9_1_11, + collectedFourData_9_1_12, + collectedFourData_9_1_13, + collectedFourData_9_1_14, + collectedFourData_9_1_15, + collectedFourData_9_1_16, + collectedFourData_9_1_17, + collectedFourData_9_1_18, + collectedFourData_9_1_19, + collectedFourData_9_1_20, + collectedFourData_9_1_21, + collectedFourData_9_1_22, + collectedFourData_9_1_23, + collectedFourData_9_1_24, + collectedFourData_9_1_25, + collectedFourData_9_1_26, + collectedFourData_9_1_27, + collectedFourData_9_1_28, + collectedFourData_9_1_29, + collectedFourData_9_1_30, + collectedFourData_9_1_31, + collectedFourData_9_1_32, + collectedFourData_9_1_33, + collectedFourData_9_1_34, + collectedFourData_9_1_35, + collectedFourData_9_1_36, + collectedFourData_9_1_37, + collectedFourData_9_1_38, + collectedFourData_9_1_39, + collectedFourData_9_1_40, + collectedFourData_9_1_41, + collectedFourData_9_1_42, + collectedFourData_9_1_43, + collectedFourData_9_1_44, + collectedFourData_9_1_45, + collectedFourData_9_1_46, + collectedFourData_9_1_47, + collectedFourData_9_1_48, + collectedFourData_9_1_49 +] + +theorem collectedFourChecked_9_1 : collectNumericRowParts 9 1 = collectedFourData_9_1 := by + decide +kernel +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0907.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0907.lean new file mode 100644 index 0000000000000000000000000000000000000000..36edd9ab7c42a63939b33e5cd54e2334df4ceb15 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0907.lean @@ -0,0 +1,626 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0907. -/ +namespace LaughlinFock +def collectedFourData_9_2_0 : List CollectedFourTerm := [ + ⟨0, 2, 7, 1, 8, 0, 10854693614219411689951937880374519408347211366400000⟩, + ⟨0, 2, 7, 2, 7, 0, -640873544096984056035457976155812212137525248000000⟩, + ⟨0, 2, 8, 2, 8, 0, -10360280526650034221496974501387895406964873625600000⟩, + ⟨0, 2, 7, 3, 6, 0, -500407581889679029664833372843974560439494246400000⟩, + ⟨0, 2, 8, 3, 7, 0, -6346259885375588231536913599774296931427155968000000⟩, + ⟨0, 2, 7, 4, 5, 0, -1722858279489095254577226877916049725485744128000000⟩, + ⟨0, 2, 8, 4, 6, 0, 8094897445109575113615655379798753956628476723200000⟩, + ⟨0, 2, 7, 5, 4, 0, 1091709338863023520504214313114530638454587392000000⟩, + ⟨0, 2, 8, 5, 5, 0, 2705879587310989387891446164834364596249060966400000⟩, + ⟨0, 2, 7, 6, 3, 0, 3273510586910224613401431838899951120850039603200000⟩, + ⟨0, 2, 8, 6, 4, 0, -4030822154818050410845093447836384849092306534400000⟩, + ⟨0, 2, 7, 7, 2, 0, -5813138584250275674290364847297037032569490636800000⟩, + ⟨0, 2, 8, 7, 3, 0, -19305415248362306533418426668214241592757295513600000⟩ +] + +def collectedFourData_9_2_1 : List CollectedFourTerm := [ + ⟨0, 3, 6, 0, 8, 1, -3643535812754930807966641908435287173958624870400000⟩, + ⟨0, 3, 6, 1, 7, 1, 12185538436819056165754445431098194031129133056000000⟩, + ⟨0, 3, 7, 1, 8, 1, 22907903798457579660196277770108374178315055923200000⟩, + ⟨0, 3, 6, 2, 6, 1, -841163063881467431531208541930554910988618956800000⟩, + ⟨0, 3, 7, 2, 7, 1, -1352508879285030363940207362529923410033639424000000⟩, + ⟨0, 3, 8, 2, 8, 1, -10932243601912092104632091491417013130107446886400000⟩, + ⟨0, 3, 6, 3, 5, 1, 2049189671560316817959556874085342642038426828800000⟩, + ⟨0, 3, 7, 3, 6, 1, -1056067462920454296776439542620830497162605363200000⟩, + ⟨0, 3, 8, 3, 7, 1, -6696619734330889629190501132076038243737403392000000⟩, + ⟨0, 3, 6, 4, 4, 1, -947011089400661685023495279356442710055583744000000⟩, + ⟨0, 3, 7, 4, 5, 1, -3635945253508706422283668519252910982366756864000000⟩, + ⟨0, 3, 8, 4, 6, 1, 8541794845689223219054760324393315091224513740800000⟩, + ⟨0, 3, 6, 5, 3, 1, -350797555370341925405504853324710583330039398400000⟩, + ⟨0, 3, 7, 5, 4, 1, 2303959319293077366780963179399335596729040896000000⟩, + ⟨0, 3, 8, 5, 5, 1, 2855263883041797540709291154553826684060670361600000⟩, + ⟨0, 3, 6, 6, 2, 1, -25135687613413499443490401829864666832847660646400000⟩, + ⟨0, 3, 7, 6, 3, 1, 6908464510682967075694846332303980127009216921600000⟩, + ⟨0, 3, 8, 6, 4, 1, -4253352947258825896199395888272736118671776153600000⟩, + ⟨0, 3, 6, 7, 1, 1, 49830346668126167639060868239351700090778759987200000⟩, + ⟨0, 3, 7, 7, 2, 1, -12268132495297847970776523365050572415611332198400000⟩, + ⟨0, 3, 8, 7, 3, 1, -20371215025333666457739611158612186171418502758400000⟩ +] + +def collectedFourData_9_2_2 : List CollectedFourTerm := [ + ⟨0, 4, 5, 0, 7, 2, -110647882191381854540281613936663044833253785600000⟩, + ⟨0, 4, 6, 0, 8, 2, -6816458612947291212272759929710082820606106009600000⟩, + ⟨0, 4, 5, 1, 6, 2, 18256042248542913565935520195102676798915425075200000⟩, + ⟨0, 4, 6, 1, 7, 2, 22797146151350977527157680182592132607213830144000000⟩, + ⟨0, 4, 7, 1, 8, 2, 21428467589769104820483484479325780027143251558400000⟩, + ⟨0, 4, 5, 2, 5, 2, -3193380356258896242198416460440674229166066892800000⟩, + ⟨0, 4, 6, 2, 6, 2, -1573678291185118444917270723254497260929758003200000⟩, + ⟨0, 4, 7, 2, 7, 2, -1265161270957738971421539874669336699431026688000000⟩, + ⟨0, 4, 8, 2, 8, 2, -6817478944328581550649370460105178920718119731200000⟩, + ⟨0, 4, 5, 3, 4, 2, 4322107008062285383945700403146641889376495206400000⟩, + ⟨0, 4, 6, 3, 5, 2, 3833698172355380038356423746766390284508148531200000⟩, + ⟨0, 4, 7, 3, 6, 2, -987864607818212647819336711620125326372660838400000⟩, + ⟨0, 4, 8, 3, 7, 2, -4176092822244742658184538392967347977727246336000000⟩, + ⟨0, 4, 5, 4, 3, 2, -403150613485700919960651791339356109775726182400000⟩, + ⟨0, 4, 6, 4, 4, 2, -1771702606655818610071521634126747725050413056000000⟩, + ⟨0, 4, 7, 4, 5, 2, -3401128960050552403969270326511149909402451968000000⟩, + ⟨0, 4, 8, 4, 6, 2, 5326766273034330933264022509600050565481916006400000⟩, + ⟨0, 4, 5, 5, 2, 2, -31312994532394822478508847418512940115874440806400000⟩, + ⟨0, 4, 6, 5, 3, 2, -656284757606650889695694936200884003391773081600000⟩, + ⟨0, 4, 7, 5, 4, 2, 2155165223146360848635136265281575223822385152000000⟩, + ⟨0, 4, 8, 5, 5, 2, 1780576989679839665870891622412611292016463052800000⟩, + ⟨0, 4, 5, 6, 1, 2, 40004528161201879155386372231030568568492130304000000⟩, + ⟨0, 4, 6, 6, 2, 2, -47024753736468710097188565875612986307314817433600000⟩, + ⟨0, 4, 7, 6, 3, 2, 6462302669186502549923734949140508879522837299200000⟩, + ⟨0, 4, 8, 6, 4, 2, -2652442189969426550551534679473419766599568588800000⟩, + ⟨0, 4, 5, 7, 0, 2, 174536970871969142770894863055070410857159799603200000⟩, + ⟨0, 4, 6, 7, 1, 2, 93224415289957355207680338836067562387766299852800000⟩, + ⟨0, 4, 7, 7, 2, 2, -11475833052004682693809009857655381104033320140800000⟩, + ⟨0, 4, 8, 7, 3, 2, -12703735350473857992756225814776122441379033907200000⟩ +] + +def collectedFourData_9_2_3 : List CollectedFourTerm := [ + ⟨0, 5, 4, 0, 6, 3, 58832577113215882875748524693447845526928097280000000⟩, + ⟨0, 5, 5, 0, 7, 3, 760543587660090356488100226921669037475758080000000⟩, + ⟨0, 5, 6, 0, 8, 3, 23426629529431898598748861984567770504379760640000000⟩, + ⟨0, 5, 4, 1, 5, 3, -91168189741204015002504133714677633766196772864000000⟩, + ⟨0, 5, 5, 1, 6, 3, -125483792307616783448153558261864877178339983360000000⟩, + ⟨0, 5, 6, 1, 7, 3, -78348645175019597961170217560287278624512409600000000⟩, + ⟨0, 5, 7, 1, 8, 3, -49096537279681519266072423484596058261070807040000000⟩, + ⟨0, 5, 4, 2, 4, 3, 24307202248429589155625391508368271571467370496000000⟩, + ⟨0, 5, 5, 2, 5, 3, 21949854844140572880607229972824007493329879040000000⟩, + ⟨0, 5, 6, 2, 6, 3, 5408377050229483233538892344119444101796986880000000⟩, + ⟨0, 5, 7, 2, 7, 3, 2898715796832916820305031271269444923215052800000000⟩, + ⟨0, 5, 8, 2, 8, 3, 11715068089031697412171495847996845492052951040000000⟩, + ⟨0, 5, 4, 3, 3, 3, -31003429147108170521651280058869953586549227520000000⟩, + ⟨0, 5, 5, 3, 4, 3, -29708212259109458993806929994533315305558507520000000⟩, + ⟨0, 5, 6, 3, 5, 3, -13175555212913916345398064834678275688187822080000000⟩, + ⟨0, 5, 7, 3, 6, 3, 2263378440004791964338933438234604923298775040000000⟩, + ⟨0, 5, 8, 3, 7, 3, 7176144166812956836666249246947825125897011200000000⟩, + ⟨0, 5, 4, 4, 2, 3, 103362549733108977548856438149477521660003221504000000⟩, + ⟨0, 5, 5, 4, 3, 3, 2771075305512380725105156172883584572792504320000000⟩, + ⟨0, 5, 6, 4, 4, 3, 6088941921193413224174339562810792256890470400000000⟩, + ⟨0, 5, 7, 4, 5, 3, 7792608317911250994647428071702700239932620800000000⟩, + ⟨0, 5, 8, 4, 6, 3, -9153446617516556064404722818156071475876986880000000⟩, + ⟨0, 5, 4, 5, 1, 3, -99654398969994735132077029188152817633856585728000000⟩, + ⟨0, 5, 5, 5, 2, 3, 215231387446322466677461574296143940659204587520000000⟩, + ⟨0, 5, 6, 5, 3, 3, 2255502564493148250619320944299221311752765440000000⟩, + ⟨0, 5, 7, 5, 4, 3, -4937877581717385784841639059896234369299251200000000⟩, + ⟨0, 5, 8, 5, 5, 3, -3059720586187562406978540426160594747140341760000000⟩, + ⟨0, 5, 4, 6, 0, 3, -310924077382055503140003968462607307227178991616000000⟩, + ⟨0, 5, 5, 6, 1, 3, -274973065618596652508273941146704637347443507200000000⟩, + ⟨0, 5, 6, 6, 2, 3, 161613463390588819691605438545221716241798922240000000⟩, + ⟨0, 5, 7, 6, 3, 3, -14806316997757804576607000550797077728743915520000000⟩, + ⟨0, 5, 8, 6, 4, 3, 4557922527001284885771166965358953612925992960000000⟩, + ⟨0, 5, 5, 7, 0, 3, -1199688339056445036341049542717885286042052853760000000⟩, + ⟨0, 5, 6, 7, 1, 3, -320391271201667458065930754575674204875149803520000000⟩, + ⟨0, 5, 7, 7, 2, 3, 26293231790506221231504794353757869081865748480000000⟩, + ⟨0, 5, 8, 7, 3, 3, 21829935351637117770137581224283341934810890240000000⟩ +] + +def collectedFourData_9_2_4 : List CollectedFourTerm := [ + ⟨0, 6, 3, 0, 5, 4, 58832577113215882875748524693447845526928097280000000⟩, + ⟨0, 6, 4, 0, 6, 4, 61748649476041066677476536676065941184680296448000000⟩, + ⟨0, 6, 5, 0, 7, 4, 399120195901839730310945599533112163894820864000000⟩, + ⟨0, 6, 6, 0, 8, 4, 8195928209605342978128149959445570159596535808000000⟩, + ⟨0, 6, 3, 1, 4, 4, -56279776546926593296535511759854770941850759987200000⟩, + ⟨0, 6, 4, 1, 5, 4, -95686996353423751595247903121820139925319083622400000⟩, + ⟨0, 6, 5, 1, 6, 4, -65851736285633401742235101190623168510702911488000000⟩, + ⟨0, 6, 6, 1, 7, 4, -27410681095526536616552822886148873317903237120000000⟩, + ⟨0, 6, 7, 1, 8, 4, -12882509230967471970425824938920447290078396416000000⟩, + ⟨0, 6, 3, 2, 3, 4, 39040072815978698633386333203276575791542750412800000⟩, + ⟨0, 6, 4, 2, 4, 4, 25512003468642075488908551472252196170742995353600000⟩, + ⟨0, 6, 5, 2, 5, 4, 11518906355339253194011713493669510912181010432000000⟩, + ⟨0, 6, 6, 2, 6, 4, 1892148846186704820382848643937816690804391936000000⟩, + ⟨0, 6, 7, 2, 7, 4, 760598100797334231682786405017131752221573120000000⟩, + ⟨0, 6, 8, 2, 8, 4, 2459146508661350418785004624185663371558571212800000⟩, + ⟨0, 6, 3, 3, 2, 4, -25743521869178674486962603588047647323475201228800000⟩, + ⟨0, 6, 4, 3, 3, 4, -32540132914388526472770876592021331443011551232000000⟩, + ⟨0, 6, 5, 3, 4, 4, -15590358907934829989450949416613428322543599616000000⟩, + ⟨0, 6, 6, 3, 5, 4, -4609536532392185827944054249277199705362661376000000⟩, + ⟨0, 6, 7, 3, 6, 4, 593891041244602246186872026217717743134703616000000⟩, + ⟨0, 6, 8, 3, 7, 4, 1506366820863028986021584274799652448170409984000000⟩, + ⟨0, 6, 3, 4, 1, 4, 23769876082281235964315512743450416656496040345600000⟩, + ⟨0, 6, 4, 4, 2, 4, 108485777193429676188589311842835132715071071846400000⟩, + ⟨0, 6, 5, 4, 3, 4, 1454212666755337480092086200796488522379821056000000⟩, + ⟨0, 6, 6, 4, 4, 4, 2130248006690864569404499985906342562763898880000000⟩, + ⟨0, 6, 7, 4, 5, 4, 2044713418727211655887807051849759956737720320000000⟩, + ⟨0, 6, 8, 4, 6, 4, -1921428550019158315374245259029113611948235161600000⟩, + ⟨0, 6, 3, 5, 0, 4, -28550944738262740994494382965524464193411376742400000⟩, + ⟨0, 6, 4, 5, 1, 4, -104593829688984557734121377876683942513433431244800000⟩, + ⟨0, 6, 5, 5, 2, 4, 112949730844609650549559110435271754075514863616000000⟩, + ⟨0, 6, 6, 5, 3, 4, 789099305640271359825290003112771409693114368000000⟩, + ⟨0, 6, 7, 5, 4, 4, -1295656619640818006168360199135300988415508480000000⟩, + ⟨0, 6, 8, 5, 5, 4, -642275498513497896750428476438341810277004083200000⟩, + ⟨0, 6, 4, 6, 0, 4, -326335217833134928190318362464016013112194472345600000⟩, + ⟨0, 6, 5, 6, 1, 4, -144301136184811375563973623144040856718944501760000000⟩, + ⟨0, 6, 6, 6, 2, 4, 56541310903936442863021192300016374812222947328000000⟩, + ⟨0, 6, 7, 6, 3, 4, -3885050269709831909035373234393474336720683008000000⟩, + ⟨0, 6, 8, 6, 4, 4, 956767744228328261732397755033606467225858867200000⟩, + ⟨0, 6, 5, 7, 0, 4, -629575809558149816462194461458359962961138679808000000⟩, + ⟨0, 6, 6, 7, 1, 4, -112090552951888553379720875754074994288774610944000000⟩, + ⟨0, 6, 7, 7, 2, 4, 6899117942343021025010193791790154688696942592000000⟩, + ⟨0, 6, 8, 7, 3, 4, 4582389867161117550216866905661659655277694156800000⟩ +] + +def collectedFourData_9_2_5 : List CollectedFourTerm := [ + ⟨0, 7, 2, 0, 4, 5, -110647882191381854540281613936663044833253785600000⟩, + ⟨0, 7, 3, 0, 5, 5, 760543587660090356488100226921669037475758080000000⟩, + ⟨0, 7, 4, 0, 6, 5, 399120195901839730310945599533112163894820864000000⟩, + ⟨0, 7, 5, 0, 7, 5, 1719842535055834840978264518379398619987968000000⟩, + ⟨0, 7, 6, 0, 8, 5, 26487708641177112214183110789357340219932672000000⟩, + ⟨0, 7, 2, 1, 3, 5, 66061818187034650372577439106760766837384806400000⟩, + ⟨0, 7, 3, 1, 4, 5, -727542889806413753658319529141512104668508979200000⟩, + ⟨0, 7, 4, 1, 5, 5, -618484987994034626268122927649474954136859443200000⟩, + ⟨0, 7, 5, 1, 6, 5, -283760677195012400618537257303429865124397056000000⟩, + ⟨0, 7, 6, 1, 7, 5, -88586199872227714720878796560257624655790080000000⟩, + ⟨0, 7, 7, 1, 8, 5, -33307090286831306264931426580933672692822835200000⟩, + ⟨0, 7, 2, 2, 2, 5, 16128700585781290398528934698465153909365145600000⟩, + ⟨0, 7, 3, 2, 3, 5, 504680884280110899652792354646429576263945420800000⟩, + ⟨0, 7, 4, 2, 4, 5, 164900057064465342748553857435503039154539724800000⟩, + ⟨0, 7, 5, 2, 5, 5, 49635937521211543291938600235977336353193984000000⟩, + ⟨0, 7, 6, 2, 6, 5, 6115071540621295872067940558480074000564224000000⟩, + ⟨0, 7, 7, 2, 7, 5, 1966488760928037546044862384649957502091264000000⟩, + ⟨0, 7, 8, 2, 8, 5, 5298334698364918548006306689580844687609036800000⟩, + ⟨0, 7, 2, 3, 1, 5, 92434621757903115787988340506724444521103360000000⟩, + ⟨0, 7, 3, 3, 2, 5, -332793010982906456958308131886327928388897996800000⟩, + ⟨0, 7, 4, 3, 3, 5, -210327259521714211258325357027329684197605376000000⟩, + ⟨0, 7, 5, 3, 4, 5, -67180169437598137439331579888726361654689792000000⟩, + ⟨0, 7, 6, 3, 5, 5, -14897160824050867485878978240524906276061184000000⟩, + ⟨0, 7, 7, 3, 6, 5, 1535475905868121956469673064409861020922675200000⟩, + ⟨0, 7, 8, 3, 7, 5, 3245530743017367576449408724430221113032704000000⟩, + ⟨0, 7, 2, 4, 0, 5, -353984675576062239885872357184535326201426739200000⟩, + ⟨0, 7, 3, 4, 1, 5, 307279193278667007286334833065465989658417561600000⟩, + ⟨0, 7, 4, 4, 2, 5, 701211524679665573749231524520483597881389875200000⟩, + ⟨0, 7, 5, 4, 3, 5, 6266324843952295779541376282035067994243072000000⟩, + ⟨0, 7, 6, 4, 4, 5, 6884563540777155435319647208531684145233920000000⟩, + ⟨0, 7, 7, 4, 5, 5, 5286505387050919979755151122156457614639104000000⟩, + ⟨0, 7, 8, 4, 6, 5, -4139798715179942572865839959595545913825689600000⟩, + ⟨0, 7, 3, 5, 0, 5, -369085275671963326255728201275713876474095206400000⟩, + ⟨0, 7, 4, 5, 1, 5, -676055430358663053384304444696631611234870886400000⟩, + ⟨0, 7, 5, 5, 2, 5, 486709901990134465624859726664985310807457792000000⟩, + ⟨0, 7, 6, 5, 3, 5, 2550221520029778017134426897305868500467712000000⟩, + ⟨0, 7, 7, 5, 4, 5, -3349856090719562544006029667394665899360256000000⟩, + ⟨0, 7, 8, 5, 5, 5, -1383809605364313051336910695428246522245939200000⟩, + ⟨0, 7, 4, 6, 0, 5, -2109308902727777814789113873988880977804184780800000⟩, + ⟨0, 7, 5, 6, 1, 5, -621805747781703022452663343761395392048005120000000⟩, + ⟨0, 7, 6, 6, 2, 5, 182730952628219159190600102363962586119012352000000⟩, + ⟨0, 7, 7, 6, 3, 5, -10044605269216315166028403853775335386093977600000⟩, + ⟨0, 7, 8, 6, 4, 5, 2061396390848128269917846179098501582107443200000⟩, + ⟨0, 7, 5, 7, 0, 5, -2712895181547306110571729782789737830621904896000000⟩, + ⟨0, 7, 6, 7, 1, 5, -362255724072652152216189818891404902395805696000000⟩, + ⟨0, 7, 7, 7, 2, 5, 17837328123370551518194570318879431865034342400000⟩, + ⟨0, 7, 8, 7, 3, 5, 9872951916082454915349307675656493088951500800000⟩ +] + +def collectedFourData_9_2_6 : List CollectedFourTerm := [ + ⟨0, 8, 1, 0, 3, 6, -3643535812754930807966641908435287173958624870400000⟩, + ⟨0, 8, 2, 0, 4, 6, -6816458612947291212272759929710082820606106009600000⟩, + ⟨0, 8, 3, 0, 5, 6, 23426629529431898598748861984567770504379760640000000⟩, + ⟨0, 8, 4, 0, 6, 6, 8195928209605342978128149959445570159596535808000000⟩, + ⟨0, 8, 5, 0, 7, 6, 26487708641177112214183110789357340219932672000000⟩, + ⟨0, 8, 6, 0, 8, 6, 326354858545052182138959307312882332918507110400000⟩, + ⟨0, 8, 1, 1, 2, 6, -1069261081179560630658022687910786211703160832000000⟩, + ⟨0, 8, 2, 1, 3, 6, 4069735820059318987939931031955863263963932262400000⟩, + ⟨0, 8, 3, 1, 4, 6, -22410126155563050098681451481198856110870206873600000⟩, + ⟨0, 8, 4, 1, 5, 6, -12700581459837784713402536714660429340512511590400000⟩, + ⟨0, 8, 5, 1, 6, 6, -4370266456469856965813589797010133201478221824000000⟩, + ⟨0, 8, 6, 1, 7, 6, -1091469901001591996417792772892996289383366656000000⟩, + ⟨0, 8, 7, 1, 8, 6, -341980340339443236718885883657545354122048307200000⟩, + ⟨0, 8, 1, 2, 1, 6, -3916951639402478871116918825800081472601509068800000⟩, + ⟨0, 8, 2, 2, 2, 6, 993607991822548920139024622803169771467151769600000⟩, + ⟨0, 8, 3, 2, 3, 6, 15545423429301580295529639402522753315054708326400000⟩, + ⟨0, 8, 4, 2, 4, 6, 3386220600554562398415185881156102113130551705600000⟩, + ⟨0, 8, 5, 2, 5, 6, 764455015151046384972836192384172724202766336000000⟩, + ⟨0, 8, 6, 2, 6, 6, 75343750366156598000008724279054777688313036800000⟩, + ⟨0, 8, 7, 2, 7, 6, 20190911002566568498321741158607356432482304000000⟩, + ⟨0, 8, 8, 2, 8, 6, 46629101348571278717966696548648316335187558400000⟩, + ⟨0, 8, 1, 3, 0, 6, -3437670582372181359938767456621505466167879270400000⟩, + ⟨0, 8, 2, 3, 1, 6, 5694431390258088605398675829075379933161717760000000⟩, + ⟨0, 8, 3, 3, 2, 6, -10250850450618845367617312181218676055898220134400000⟩, + ⟨0, 8, 4, 3, 3, 6, -4319067632415580206199036785169248505898729472000000⟩, + ⟨0, 8, 5, 3, 4, 6, -1034657951677093950753340811815510635989434368000000⟩, + ⟨0, 8, 6, 3, 5, 6, -183547806241648446845088601598280902795644108800000⟩, + ⟨0, 8, 7, 3, 6, 6, 15765489220155810258528034843131409394250547200000⟩, + ⟨0, 8, 8, 3, 7, 6, 28562971303561374346679609760420912590487552000000⟩, + ⟨0, 8, 2, 4, 0, 6, -21807212599951052825734733367044666910485721907200000⟩, + ⟨0, 8, 3, 4, 1, 6, 9464961561492073222073435718047707309961694412800000⟩, + ⟨0, 8, 4, 4, 2, 6, 14399369851571956697494727952217529851591419494400000⟩, + ⟨0, 8, 5, 4, 3, 6, 96509176470733973129849513668140183991615488000000⟩, + ⟨0, 8, 6, 4, 4, 6, 84824655500850601875944469593778914951430144000000⟩, + ⟨0, 8, 7, 4, 5, 6, 54279160860375706762612627734621583042412544000000⟩, + ⟨0, 8, 8, 4, 6, 6, -36433163407434773215550396497764961290603724800000⟩, + ⟨0, 8, 3, 5, 0, 6, -11368742249917796841641761849477773377448129331200000⟩, + ⟨0, 8, 4, 5, 1, 6, -13882789770668947311994265640416678533472767180800000⟩, + ⟨0, 8, 5, 5, 2, 6, 7495936292953712555661126166252571591461306368000000⟩, + ⟨0, 8, 6, 5, 3, 6, 31421260128708506358021617059347110725838438400000⟩, + ⟨0, 8, 7, 5, 4, 6, -34394626373152900067855283248762799223996416000000⟩, + ⟨0, 8, 8, 5, 5, 6, -12178505513359098885985223905819310329272729600000⟩, + ⟨0, 8, 4, 6, 0, 6, -43314631823066308862802362241536283273034570137600000⟩, + ⟨0, 8, 5, 6, 1, 6, -9576579915274804100371677128452497029443092480000000⟩, + ⟨0, 8, 6, 6, 2, 6, 2251426690192365129719505171682416685331408486400000⟩, + ⟨0, 8, 7, 6, 3, 6, -103132921517917347936100836329629615855868313600000⟩, + ⟨0, 8, 8, 6, 4, 6, 18141749568614391780089699148730812293814681600000⟩, + ⟨0, 8, 5, 7, 0, 6, -41781951357858143727027806884245116817908957184000000⟩, + ⟨0, 8, 6, 7, 1, 6, -4463350046182476577653138041410588212532032307200000⟩, + ⟨0, 8, 7, 7, 2, 6, 183144654481822430789743273946950014417135206400000⟩, + ⟨0, 8, 8, 7, 3, 6, 86888975822280601003815317806283940493157990400000⟩ +] + +def collectedFourData_9_2_7 : List CollectedFourTerm := [ + ⟨1, 1, 7, 1, 8, 0, -79974271494337188950133274497735731823260781772800000⟩, + ⟨1, 1, 7, 2, 7, 0, 4721772592642269611401939546789886117906743296000000⟩, + ⟨1, 1, 8, 2, 8, 0, 76331577568473640276555581865597789251432559411200000⟩, + ⟨1, 1, 7, 3, 6, 0, 3686859641938210498205289655930695504911715532800000⟩, + ⟨1, 1, 8, 3, 7, 0, 46757423938874280297367366027109775636468596736000000⟩, + ⟨1, 1, 7, 4, 5, 0, 12693526016214137270057183455279329149039149056000000⟩, + ⟨1, 1, 8, 4, 6, 0, -59640884303353467777668271020347856812859876966400000⟩, + ⟨1, 1, 7, 5, 4, 0, -8043401514784568687045095815723352665026985984000000⟩, + ⟨1, 1, 8, 5, 5, 0, -19936145269279077423212471366267363633883040972800000⟩, + ⟨1, 1, 7, 6, 3, 0, -24118287786050222011623630609623006872177370726400000⟩, + ⟨1, 1, 8, 6, 4, 0, 29697942365920005662230663698561285503266376908800000⟩, + ⟨1, 1, 7, 7, 2, 0, 42829538989661358836641975564040733696074553753600000⟩, + ⟨1, 1, 8, 7, 3, 0, 142236766439996148285686545693173527430820999987200000⟩ +] + +def collectedFourData_9_2_8 : List CollectedFourTerm := [ + ⟨1, 2, 6, 0, 8, 1, -1069261081179560630658022687910786211703160832000000⟩, + ⟨1, 2, 6, 1, 7, 1, 3576065303954409243655141580793429828808212480000000⟩, + ⟨1, 2, 7, 1, 8, 1, 6722736166706000464345515570901377811224723456000000⟩, + ⟨1, 2, 6, 2, 6, 1, -246854422011058219751950629109967892925906944000000⟩, + ⟨1, 2, 7, 2, 7, 1, -396918043595620835920946408205632418003025920000000⟩, + ⟨1, 2, 8, 2, 8, 1, -3208263405172986108637675111129599033697370112000000⟩, + ⟨1, 2, 6, 3, 5, 1, 601371545761707803493152113843960194954952704000000⟩, + ⟨1, 2, 7, 3, 6, 1, -309921981073397740069563742567598782892998656000000⟩, + ⟨1, 2, 8, 3, 7, 1, -1965243440811665693256055498928072829551247360000000⟩, + ⟨1, 2, 6, 4, 4, 1, -277917427844888336600621707927181063639531520000000⟩, + ⟨1, 2, 7, 4, 5, 1, -1067033495119348819004506475999608320420741120000000⟩, + ⟨1, 2, 8, 4, 6, 1, 2506743246475668063029703592661183179379441664000000⟩, + ⟨1, 2, 6, 5, 3, 1, -102947848630263467334743563011362038399107072000000⟩, + ⟨1, 2, 7, 5, 4, 1, 676138278678898527149512879584558819500359680000000⟩, + ⟨1, 2, 8, 5, 5, 1, 837928513271779237435272596457107526650953728000000⟩, + ⟨1, 2, 6, 6, 2, 1, -7376519374291097733174100713346261980819750912000000⟩, + ⟨1, 2, 7, 6, 3, 1, 2027413098596143854632254671623864221358358528000000⟩, + ⟨1, 2, 8, 6, 4, 1, -1248222881494192102024288754622921350565593088000000⟩, + ⟨1, 2, 6, 7, 1, 1, 14623610990014083678693612814344328316322840576000000⟩, + ⟨1, 2, 7, 7, 2, 1, -3600304015142282764251616042859169514700931072000000⟩, + ⟨1, 2, 8, 7, 3, 1, -5978299246209353443102099730923471087570255872000000⟩ +] + +def collectedFourData_9_2_9 : List CollectedFourTerm := [ + ⟨1, 3, 5, 0, 7, 2, 66061818187034650372577439106760766837384806400000⟩, + ⟨1, 3, 6, 0, 8, 2, 4069735820059318987939931031955863263963932262400000⟩, + ⟨1, 3, 5, 1, 6, 2, -10899687548940726974782009907315799461649501388800000⟩, + ⟨1, 3, 6, 1, 7, 2, -13610933118710029796586577798757045127333543936000000⟩, + ⟨1, 3, 7, 1, 8, 2, -12793769766813935252841415649481786299891947929600000⟩, + ⟨1, 3, 5, 2, 5, 2, 1906593314929749657631733690374506429770052403200000⟩, + ⟨1, 3, 6, 2, 6, 2, 939557514325854049952373660420197306136841420800000⟩, + ⟨1, 3, 7, 2, 7, 2, 755358821190322120737011223079369307137769472000000⟩, + ⟨1, 3, 8, 2, 8, 2, 4070345004300954462284003480068182560884968652800000⟩, + ⟨1, 3, 5, 3, 4, 2, -2580494463126363203590517241331044141940447641600000⟩, + ⟨1, 3, 6, 3, 5, 2, -2288892174258299092999556917005705122249755852800000⟩, + ⟨1, 3, 7, 3, 6, 2, 589800101209492788906192779879641606184868249600000⟩, + ⟨1, 3, 8, 3, 7, 2, 2493317353134124183900093919007660268987613184000000⟩, + ⟨1, 3, 5, 4, 3, 2, 240699252463037516568331181709324136706840985600000⟩, + ⟨1, 3, 6, 4, 4, 2, 1057787037260693434330640643814954083878436864000000⟩, + ⟨1, 3, 7, 4, 5, 2, 2030628680275076091486818970727259284325793792000000⟩, + ⟨1, 3, 8, 4, 6, 2, -3180321738516117940752668358210931996619282841600000⟩, + ⟨1, 3, 5, 5, 2, 2, 18695281922456853947997494914854144754132294041600000⟩, + ⟨1, 3, 6, 5, 3, 2, 391831849623142093217844659579507710676592230400000⟩, + ⟨1, 3, 7, 5, 4, 2, -1286731660062483259758411824401121309242687488000000⟩, + ⟨1, 3, 8, 5, 5, 2, -1063085447553273333461892719137688746200347443200000⟩, + ⟨1, 3, 5, 6, 1, 2, -23884522809685248831461856039966303737113214976000000⟩, + ⟨1, 3, 6, 6, 2, 2, 28075916774036878925151360066678973067939964518400000⟩, + ⟨1, 3, 7, 6, 3, 2, -3858288613811704317844355863090523615720688844800000⟩, + ⟨1, 3, 8, 6, 4, 2, 1583628626549783361683615547478182070517445427200000⟩, + ⟨1, 3, 5, 7, 0, 2, -104206509951239310715733925612251291088019311820800000⟩, + ⟨1, 3, 6, 7, 1, 2, -55659215987754848930968708224401822440439886643200000⟩, + ⟨1, 3, 7, 7, 2, 2, 6851594279183992750752410219190612254182814515200000⟩, + ⟨1, 3, 8, 7, 3, 2, 7584707799175346848705354648924440127326702796800000⟩ +] + +def collectedFourData_9_2_10 : List CollectedFourTerm := [ + ⟨1, 4, 4, 0, 6, 3, -56279776546926593296535511759854770941850759987200000⟩, + ⟨1, 4, 5, 0, 7, 3, -727542889806413753658319529141512104668508979200000⟩, + ⟨1, 4, 6, 0, 8, 3, -22410126155563050098681451481198856110870206873600000⟩, + ⟨1, 4, 4, 1, 5, 3, 87212316688914509647191011557851196039162610319360000⟩, + ⟨1, 4, 5, 1, 6, 3, 120038933153366797286749209096070977377068803686400000⟩, + ⟨1, 4, 6, 1, 7, 3, 74949024155768689570849066267939050856176943104000000⟩, + ⟨1, 4, 7, 1, 8, 3, 46966192591070898919764769793808419791977421209600000⟩, + ⟨1, 4, 4, 2, 4, 3, -23252490000395831093711591959913488893502071767040000⟩, + ⟨1, 4, 5, 2, 5, 3, -20997430105576764042935187551482748648732334489600000⟩, + ⟨1, 4, 6, 2, 6, 3, -5173702509796502759711078052080925824779498291200000⟩, + ⟨1, 4, 7, 2, 7, 3, -2772937806291609865589144898462433124466819072000000⟩, + ⟨1, 4, 8, 2, 8, 3, -11206740323714755305028271364857940351070607769600000⟩, + ⟨1, 4, 4, 3, 3, 3, 29658161348770152412230879487286598374213340364800000⟩, + ⟨1, 4, 5, 3, 4, 3, 28419145133381579199019641778460678757448207564800000⟩, + ⟨1, 4, 6, 3, 5, 3, 12603855544820557723417448183033721150713836339200000⟩, + ⟨1, 4, 7, 3, 6, 3, -2165168331815034142583832340248064490166917529600000⟩, + ⟨1, 4, 8, 3, 7, 3, -6864764557220798720837287120750273876394508288000000⟩, + ⟨1, 4, 4, 4, 2, 3, -98877551991398420210503264650897370359981366312960000⟩, + ⟨1, 4, 5, 4, 3, 3, -2650835755313360124464287093961175662735445196800000⟩, + ⟨1, 4, 6, 4, 4, 3, -5824737034254448259483154653628314015389188096000000⟩, + ⟨1, 4, 7, 4, 5, 3, -7454479752022441708840482411080483112738619392000000⟩, + ⟨1, 4, 8, 4, 6, 3, 8756270004570834756571072065672256129598698291200000⟩, + ⟨1, 4, 4, 5, 1, 3, 95330301359341630010131821591414713452031870238720000⟩, + ⟨1, 4, 5, 5, 2, 3, -205892296168732025231884312642733794948394306764800000⟩, + ⟨1, 4, 6, 5, 3, 3, -2157634197910722323282120466593268651425110425600000⟩, + ⟨1, 4, 7, 5, 4, 3, 4723618453435145252717024485276471762656165888000000⟩, + ⟨1, 4, 8, 5, 5, 3, 2926956447195731449694721257854183418964108902400000⟩, + ⟨1, 4, 4, 6, 0, 3, 297432790755490458137540019676460515598603743395840000⟩, + ⟨1, 4, 5, 6, 1, 3, 263041727029184897099245994961599285562156515328000000⟩, + ⟨1, 4, 6, 6, 2, 3, -154600904004153386026214265494161883117689346457600000⟩, + ⟨1, 4, 7, 6, 3, 3, 14163857050035334638321806942144800602010209484800000⟩, + ⟨1, 4, 8, 6, 4, 3, -4360150004039378949994307037355520528860210790400000⟩, + ⟨1, 4, 5, 7, 0, 3, 1147632739564000068745151178184047317822946567782400000⟩, + ⟨1, 4, 6, 7, 1, 3, 306489194177507423073293854303726496603643366604800000⟩, + ⟨1, 4, 7, 7, 2, 3, -25152343862458921877084641018037544452919341875200000⟩, + ⟨1, 4, 8, 7, 3, 3, -20882714032052947283998841380088976449059002777600000⟩ +] + +def collectedFourData_9_2_11 : List CollectedFourTerm := [ + ⟨1, 5, 3, 0, 5, 4, -91168189741204015002504133714677633766196772864000000⟩, + ⟨1, 5, 4, 0, 6, 4, -95686996353423751595247903121820139925319083622400000⟩, + ⟨1, 5, 5, 0, 7, 4, -618484987994034626268122927649474954136859443200000⟩, + ⟨1, 5, 6, 0, 8, 4, -12700581459837784713402536714660429340512511590400000⟩, + ⟨1, 5, 3, 1, 4, 4, 87212316688914509647191011557851196039162610319360000⟩, + ⟨1, 5, 4, 1, 5, 4, 148278567204821647801818626170190705614931487621120000⟩, + ⟨1, 5, 5, 1, 6, 4, 102045225333631314588596308611994916348645238374400000⟩, + ⟨1, 5, 6, 1, 7, 4, 42476163677882423113380800481567509807005433856000000⟩, + ⟨1, 5, 7, 1, 8, 4, 19963005252201096652127682698420011103484169420800000⟩, + ⟨1, 5, 3, 2, 3, 4, -60497311874479174330532409707953001672173305200640000⟩, + ⟨1, 5, 4, 2, 4, 4, -39533933188606485208721375634941397948245401927680000⟩, + ⟨1, 5, 5, 2, 5, 4, -17849937768216975598739733500008326398740109721600000⟩, + ⟨1, 5, 6, 2, 6, 4, -2932113354405467467743735148606597574045781196800000⟩, + ⟨1, 5, 7, 2, 7, 4, -1178638695987261674544202641016521150122950656000000⟩, + ⟨1, 5, 8, 2, 8, 4, -3810744769375316743226061735716033057786576240640000⟩, + ⟨1, 5, 3, 3, 2, 4, 39892698935483130542789791847751124840342817341440000⟩, + ⟨1, 5, 4, 3, 3, 4, 50424869303856519299344032331987128728726116761600000⟩, + ⟨1, 5, 5, 3, 4, 4, 24159145643354595779754806551337113510709349580800000⟩, + ⟨1, 5, 6, 3, 5, 4, 7143034043799194774600466887146380883351358668800000⟩, + ⟨1, 5, 7, 3, 6, 4, -920305956164318039506463495339562122001304780800000⟩, + ⟨1, 5, 8, 3, 7, 4, -2334297474000082573074780678960054345672110899200000⟩, + ⟨1, 5, 3, 4, 1, 4, -36834296220342268759606815333706787210868849377280000⟩, + ⟨1, 5, 4, 4, 2, 4, -168111825194392745913044085224644762110565621432320000⟩, + ⟨1, 5, 5, 4, 3, 4, -2253478307973545935813772336076402098850024652800000⟩, + ⟨1, 5, 6, 4, 4, 4, -3301076784314242406387354708594733537709522944000000⟩, + ⟨1, 5, 7, 4, 5, 4, -3168530601101841548680029754383605108117078016000000⟩, + ⟨1, 5, 8, 4, 6, 4, 2977485794736043123362757173779026043660748718080000⟩, + ⟨1, 5, 3, 5, 0, 4, 44243140023928270484474445978687398121279974277120000⟩, + ⟨1, 5, 4, 5, 1, 4, 162080782089392464418257344545542629249761138442240000⟩, + ⟨1, 5, 5, 5, 2, 4, -175029260966134526771321006772185725190716312780800000⟩, + ⟨1, 5, 6, 5, 3, 4, -1222804758030974550969499497017997704548476518400000⟩, + ⟨1, 5, 7, 5, 4, 4, 2007776547193384070794416139149656879397863424000000⟩, + ⟨1, 5, 8, 5, 5, 4, 995283521269569255240458823870117137824780124160000⟩, + ⟨1, 5, 4, 6, 0, 4, 505695866448202418599527182874998328177512970977280000⟩, + ⟨1, 5, 5, 6, 1, 4, 223612053203988802007146618059227105330712281088000000⟩, + ⟨1, 5, 6, 6, 2, 4, -87617595788584641800937921285041676256318744166400000⟩, + ⟨1, 5, 7, 6, 3, 4, 6020355006061046447107407210692991861937038950400000⟩, + ⟨1, 5, 8, 6, 4, 4, -1482627270877749042312062031756059471722693263360000⟩, + ⟨1, 5, 5, 7, 0, 4, 975603818133203295575364800892903685547476018790400000⟩, + ⟨1, 5, 6, 7, 1, 4, 173697860966533809156352707922719244859166896947200000⟩, + ⟨1, 5, 7, 7, 2, 4, -10691017196205439237709350821070010251749202329600000⟩, + ⟨1, 5, 8, 7, 3, 4, -7100967004616730921318601575235382020207898787840000⟩ +] + +def collectedFourData_9_2_12 : List CollectedFourTerm := [ + ⟨1, 6, 2, 0, 4, 5, 18256042248542913565935520195102676798915425075200000⟩, + ⟨1, 6, 3, 0, 5, 5, -125483792307616783448153558261864877178339983360000000⟩, + ⟨1, 6, 4, 0, 6, 5, -65851736285633401742235101190623168510702911488000000⟩, + ⟨1, 6, 5, 0, 7, 5, -283760677195012400618537257303429865124397056000000⟩, + ⟨1, 6, 6, 0, 8, 5, -4370266456469856965813589797010133201478221824000000⟩, + ⟨1, 6, 2, 1, 3, 5, -10899687548940726974782009907315799461649501388800000⟩, + ⟨1, 6, 3, 1, 4, 5, 120038933153366797286749209096070977377068803686400000⟩, + ⟨1, 6, 4, 1, 5, 5, 102045225333631314588596308611994916348645238374400000⟩, + ⟨1, 6, 5, 1, 6, 5, 46818310560947917106150074912001055804622897152000000⟩, + ⟨1, 6, 6, 1, 7, 5, 14616035801824132283941126672110618217398927360000000⟩, + ⟨1, 6, 7, 1, 8, 5, 5495411528986190503861189389714863504394446438400000⟩, + ⟨1, 6, 2, 2, 2, 5, -2661110483785255070937785346155064167083750195200000⟩, + ⟨1, 6, 3, 2, 3, 5, -83268431017176044960390771467349769859360201113600000⟩, + ⟨1, 6, 4, 2, 4, 5, -27207230259943398199893275424010326637922589081600000⟩, + ⟨1, 6, 5, 2, 5, 5, -8189544657221221007932655758561684510136598528000000⟩, + ⟨1, 6, 6, 2, 6, 5, -1008939368630229121040886881704293660893380608000000⟩, + ⟨1, 6, 7, 2, 7, 5, -324455391190336422998984134186528636862988288000000⟩, + ⟨1, 6, 8, 2, 8, 5, -874184125214144164322408634683023740387301785600000⟩, + ⟨1, 6, 2, 3, 1, 5, -15250995560146370501194245768339279194483589120000000⟩, + ⟨1, 6, 3, 3, 2, 5, 54908265284420902739482888994890677454724766105600000⟩, + ⟨1, 6, 4, 3, 3, 5, 34702366279431008187763824913463427723367022592000000⟩, + ⟨1, 6, 5, 3, 4, 5, 11084206830057053987203222210642603176691236864000000⟩, + ⟨1, 6, 6, 3, 5, 5, 2457915976347477524883751065614442376281980928000000⟩, + ⟨1, 6, 7, 3, 6, 5, -253341613539996621188626378472985467487151718400000⟩, + ⟨1, 6, 8, 3, 7, 5, -535487396505134776247690707038464256421920768000000⟩, + ⟨1, 6, 2, 4, 0, 5, 58404725555214372568508986634427771317362517606400000⟩, + ⟨1, 6, 3, 4, 1, 5, -50698683277920498615825062644925273980773020467200000⟩, + ⟨1, 6, 4, 4, 2, 5, -115694462163996468556261779940438768624691734118400000⟩, + ⟨1, 6, 5, 4, 3, 5, -1033894990384167056669113873361327020125978624000000⟩, + ⟨1, 6, 6, 4, 4, 5, -1135899579585403859874249623760115904167280640000000⟩, + ⟨1, 6, 7, 4, 5, 5, -872232380609163871547328366264384135068909568000000⟩, + ⟨1, 6, 8, 4, 6, 5, 683034674934566398757370680174278226008552243200000⟩, + ⟨1, 6, 3, 5, 0, 5, 60896207433306688720210886016270916878838058188800000⟩, + ⟨1, 6, 4, 5, 1, 5, 111543901740813578176135233212054495475572460748800000⟩, + ⟨1, 6, 5, 5, 2, 5, -80303358343067695110556591957248819838649892864000000⟩, + ⟨1, 6, 6, 5, 3, 5, -420766768335247764664052722835256003740565504000000⟩, + ⟨1, 6, 7, 5, 4, 5, 552700269607856879145418434035594300649111552000000⟩, + ⟨1, 6, 8, 5, 5, 5, 228317850456229264823747456873569996375484006400000⟩, + ⟨1, 6, 4, 6, 0, 5, 348019606708977663934345175134194060240212302233600000⟩, + ⟨1, 6, 5, 6, 1, 5, 102593124938940330744290841771094707968975831040000000⟩, + ⟨1, 6, 6, 6, 2, 5, -30149189710899797255278993502778149882648592384000000⟩, + ⟨1, 6, 7, 6, 3, 5, 1657281951836874044713698113971593077167698739200000⟩, + ⟨1, 6, 8, 6, 4, 5, -340114413913730251266939388549263506952054374400000⟩, + ⟨1, 6, 5, 7, 0, 5, 447606660600447147753928262188081187425125138432000000⟩, + ⟨1, 6, 6, 7, 1, 5, 59769384397326884472242625912757180366986412032000000⟩, + ⟨1, 6, 7, 7, 2, 5, -2943020773394783087945363368589618511705066700800000⟩, + ⟨1, 6, 8, 7, 3, 5, -1628960480111860880089932648539913243175000473600000⟩ +] + +def collectedFourData_9_2_13 : List CollectedFourTerm := [ + ⟨1, 7, 1, 0, 3, 6, 12185538436819056165754445431098194031129133056000000⟩, + ⟨1, 7, 2, 0, 4, 6, 22797146151350977527157680182592132607213830144000000⟩, + ⟨1, 7, 3, 0, 5, 6, -78348645175019597961170217560287278624512409600000000⟩, + ⟨1, 7, 4, 0, 6, 6, -27410681095526536616552822886148873317903237120000000⟩, + ⟨1, 7, 5, 0, 7, 6, -88586199872227714720878796560257624655790080000000⟩, + ⟨1, 7, 6, 0, 8, 6, -1091469901001591996417792772892996289383366656000000⟩, + ⟨1, 7, 1, 1, 2, 6, 3576065303954409243655141580793429828808212480000000⟩, + ⟨1, 7, 2, 1, 3, 6, -13610933118710029796586577798757045127333543936000000⟩, + ⟨1, 7, 3, 1, 4, 6, 74949024155768689570849066267939050856176943104000000⟩, + ⟨1, 7, 4, 1, 5, 6, 42476163677882423113380800481567509807005433856000000⟩, + ⟨1, 7, 5, 1, 6, 6, 14616035801824132283941126672110618217398927360000000⟩, + ⟨1, 7, 6, 1, 7, 6, 3650341073834416969212460310751037118836899840000000⟩, + ⟨1, 7, 7, 1, 8, 6, 1143728179438932413490987665682431938142404608000000⟩, + ⟨1, 7, 1, 2, 1, 6, 13099957626328597797164911544720509455965356032000000⟩, + ⟨1, 7, 2, 2, 2, 6, -3323049092340194122866585264497836479473516544000000⟩, + ⟨1, 7, 3, 2, 3, 6, -51990529103967170802897706540594580319576784896000000⟩, + ⟨1, 7, 4, 2, 4, 6, -11324966572074566374012646893090536352942915584000000⟩, + ⟨1, 7, 5, 2, 5, 6, -2556663759892821776758153150266787943719895040000000⟩, + ⟨1, 7, 6, 2, 6, 6, -251981650035356466302412755451032064126615552000000⟩, + ⟨1, 7, 7, 2, 7, 6, -67527021755862866798149433832268871824834560000000⟩, + ⟨1, 7, 8, 2, 8, 6, -155947611319818954822571526168332913004773376000000⟩, + ⟨1, 7, 1, 3, 0, 6, 11497037264729071825447094825618128653627949056000000⟩, + ⟨1, 7, 2, 3, 1, 6, -19044608355133014465533932237506439163569766400000000⟩, + ⟨1, 7, 3, 3, 2, 6, 34283217894776774351037212051787249850584662016000000⟩, + ⟨1, 7, 4, 3, 3, 6, 14444805087898036207525570356236441255757742080000000⟩, + ⟨1, 7, 5, 3, 4, 6, 3460337673911515942704417003179634465460715520000000⟩, + ⟨1, 7, 6, 3, 5, 6, 613862183026074327393330868795640735053381632000000⟩, + ⟨1, 7, 7, 3, 6, 6, -52726523009583701698229270991527849081438208000000⟩, + ⟨1, 7, 8, 3, 7, 6, -95526763719700398440202319121552755686113280000000⟩, + ⟨1, 7, 2, 4, 0, 6, 72932623965527607973773887452834978327437508608000000⟩, + ⟨1, 7, 3, 4, 1, 6, -31654870114579605018794428413922197467081736192000000⟩, + ⟨1, 7, 4, 4, 2, 6, -48157636924565489151759133121520424751166652416000000⟩, + ⟨1, 7, 5, 4, 3, 6, -322767866113186069267188670909404978421432320000000⟩, + ⟨1, 7, 6, 4, 4, 6, -283689842261768276841742083863293492105052160000000⟩, + ⟨1, 7, 7, 4, 5, 6, -181532674570387364383995628614175756029788160000000⟩, + ⟨1, 7, 8, 4, 6, 6, 121848044287651184965106001175702167588175872000000⟩, + ⟨1, 7, 3, 5, 0, 6, 38021925070612740028401987400845738423739219968000000⟩, + ⟨1, 7, 4, 5, 1, 6, 46429972711823986498612116442704642674327027712000000⟩, + ⟨1, 7, 5, 5, 2, 6, -25069609443105589720071301705348802634338795520000000⟩, + ⟨1, 7, 6, 5, 3, 6, -105086101168897980588454660203361596736536576000000⟩, + ⟨1, 7, 7, 5, 4, 6, 115030306611199338685359856433071745390346240000000⟩, + ⟨1, 7, 8, 5, 5, 6, 40730118945596813409806598580932062629330944000000⟩, + ⟨1, 7, 4, 6, 0, 6, 144862610958544113893095663405001404258203992064000000⟩, + ⟨1, 7, 5, 6, 1, 6, 32028169516636400170233484740454890232558387200000000⟩, + ⟨1, 7, 6, 6, 2, 6, -7529731524794725451295813913166418882431287296000000⟩, + ⟨1, 7, 7, 6, 3, 6, 344920495870683609621167512446313093297864704000000⟩, + ⟨1, 7, 8, 6, 4, 6, -60673751553533987292153847217869018286260224000000⟩, + ⟨1, 7, 5, 7, 0, 6, 139736673495606373382232235292806854387443957760000000⟩, + ⟨1, 7, 6, 7, 1, 6, 14927347044137016325579998689852025943892164608000000⟩, + ⟨1, 7, 7, 7, 2, 6, -612513871518325853161002239136814192285188096000000⟩, + ⟨1, 7, 8, 7, 3, 6, -290593810252046371303463176553776770875129856000000⟩ +] + +def collectedFourData_9_2_14 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 2, 7, 10854693614219411689951937880374519408347211366400000⟩, + ⟨1, 8, 1, 0, 3, 7, 22907903798457579660196277770108374178315055923200000⟩, + ⟨1, 8, 2, 0, 4, 7, 21428467589769104820483484479325780027143251558400000⟩, + ⟨1, 8, 3, 0, 5, 7, -49096537279681519266072423484596058261070807040000000⟩, + ⟨1, 8, 4, 0, 6, 7, -12882509230967471970425824938920447290078396416000000⟩, + ⟨1, 8, 5, 0, 7, 7, -33307090286831306264931426580933672692822835200000⟩, + ⟨1, 8, 6, 0, 8, 7, -341980340339443236718885883657545354122048307200000⟩, + ⟨1, 8, 0, 1, 1, 7, -79974271494337188950133274497735731823260781772800000⟩, + ⟨1, 8, 1, 1, 2, 7, 6722736166706000464345515570901377811224723456000000⟩, + ⟨1, 8, 2, 1, 3, 7, -12793769766813935252841415649481786299891947929600000⟩, + ⟨1, 8, 3, 1, 4, 7, 46966192591070898919764769793808419791977421209600000⟩, + ⟨1, 8, 4, 1, 5, 7, 19963005252201096652127682698420011103484169420800000⟩, + ⟨1, 8, 5, 1, 6, 7, 5495411528986190503861189389714863504394446438400000⟩, + ⟨1, 8, 6, 1, 7, 7, 1143728179438932413490987665682431938142404608000000⟩, + ⟨1, 8, 7, 1, 8, 7, 307160529930258107921770709287084963782249676800000⟩, + ⟨1, 8, 0, 2, 0, 7, -12859185243253816766501274204152696572516447027200000⟩, + ⟨1, 8, 1, 2, 1, 7, 24626943702468280027813728072457544427100333670400000⟩, + ⟨1, 8, 2, 2, 2, 7, -3123542275935431311849588499016956201211946598400000⟩, + ⟨1, 8, 3, 2, 3, 7, -32579439563265590632630514543105465142015845990400000⟩, + ⟨1, 8, 4, 2, 4, 7, -5322523212637673639756416089016802708534014771200000⟩, + ⟨1, 8, 5, 2, 5, 7, -961267452567591231836484232132248202638891417600000⟩, + ⟨1, 8, 6, 2, 6, 7, -78951119366011718677575517623761313487808102400000⟩, + ⟨1, 8, 7, 2, 7, 7, -18135109512924590731751126412165553456152576000000⟩, + ⟨1, 8, 8, 2, 8, 7, -36646235373968257476294231202347576247871078400000⟩, + ⟨1, 8, 1, 3, 0, 7, 21613572924435090276243175024472511573847651123200000⟩, + ⟨1, 8, 2, 3, 1, 7, -17901221941924057621419139839160549077197783040000000⟩, + ⟨1, 8, 3, 3, 2, 7, 21483297913810178989722341278537824103666443878400000⟩, + ⟨1, 8, 4, 3, 3, 7, 6788789167108356039359056274964992981565702144000000⟩, + ⟨1, 8, 5, 3, 4, 7, 1301035370002674808492678067183771678585703628800000⟩, + ⟨1, 8, 6, 3, 5, 7, 192335856518011572412883811650019119562384998400000⟩, + ⟨1, 8, 7, 3, 6, 7, -14160276051735080379189145082722118194220236800000⟩, + ⟨1, 8, 8, 3, 7, 7, -22447899253848323614981024649211705821233152000000⟩, + ⟨1, 8, 2, 4, 0, 7, 68553947871651074642979758100610561200156888268800000⟩, + ⟨1, 8, 3, 4, 1, 7, -19836265288215243636592491438493767397519707340800000⟩, + ⟨1, 8, 4, 4, 2, 7, -22633191786086032219354666840496353166668647628800000⟩, + ⟨1, 8, 5, 4, 3, 7, -121355905026129222957104652639353477698211020800000⟩, + ⟨1, 8, 6, 4, 4, 7, -88885958942610343653378654909570756265377792000000⟩, + ⟨1, 8, 7, 4, 5, 7, -48752556353075738747729174070453719726555136000000⟩, + ⟨1, 8, 8, 4, 6, 7, 28633154897547921069469996289164380738473164800000⟩, + ⟨1, 8, 3, 5, 0, 7, 23826128167303421773698831888442575859118977843200000⟩, + ⟨1, 8, 4, 5, 1, 7, 21821221806533540318474554827181382665630226841600000⟩, + ⟨1, 8, 5, 5, 2, 7, -9425799350028249365732932840387847579887258828800000⟩, + ⟨1, 8, 6, 5, 3, 7, -32925672627075474057453125170548591633314611200000⟩, + ⟨1, 8, 7, 5, 4, 7, 30892628661181465495314606096694599015727104000000⟩, + ⟨1, 8, 8, 5, 5, 7, 9571198385520724548305139526257767391795609600000⟩, + ⟨1, 8, 4, 6, 0, 7, 68082727181852471274356963773126734857104470835200000⟩, + ⟨1, 8, 5, 6, 1, 7, 12042114182019267404022016281667153378953658368000000⟩, + ⟨1, 8, 6, 6, 2, 7, -2359222317675418157923929225647542495121453875200000⟩, + ⟨1, 8, 7, 6, 3, 7, 92632116791438555965598181197951059727115878400000⟩, + ⟨1, 8, 8, 6, 4, 7, -14257766192343753442173694335480446259403161600000⟩, + ⟨1, 8, 5, 7, 0, 7, 52538905689742247897744814816217753890150835814400000⟩, + ⟨1, 8, 6, 7, 1, 7, 4677049928572893371214672989877786593166203289600000⟩, + ⟨1, 8, 7, 7, 2, 7, -164497201999077303104391395838666805117295001600000⟩, + ⟨1, 8, 8, 7, 3, 7, -68286837346135020041177735144457811452651110400000⟩ +] + +def collectedFourData_9_2_15 : List CollectedFourTerm := [ + ⟨2, 0, 7, 1, 8, 0, -12859185243253816766501274204152696572516447027200000⟩, + ⟨2, 0, 7, 2, 7, 0, 759221025847107766790274761043895318902472704000000⟩, + ⟨2, 0, 8, 2, 8, 0, 12273470924112170725411678455544734093755075788800000⟩, + ⟨2, 0, 7, 3, 6, 0, 592815792075291251225831990528014472474473267200000⟩, + ⟨2, 0, 8, 3, 7, 0, 7518197598960423538521648151082881327262859264000000⟩, + ⟨2, 0, 7, 4, 5, 0, 2041011432584504436947259460838919380291026944000000⟩, + ⟨2, 0, 8, 4, 6, 0, -9589748865453510764463276763569677700236417433600000⟩, + ⟨2, 0, 7, 5, 4, 0, -1293310812738155381759369864299241842478678016000000⟩, + ⟨2, 0, 8, 5, 5, 0, -3205563242576462863173251561582486869337387827200000⟩, + ⟨2, 0, 7, 6, 3, 0, -3878016324448622900701233824017012220287883673600000⟩, + ⟨2, 0, 8, 6, 4, 0, 4775177505104023443017797241703688213208707891200000⟩, + ⟨2, 0, 7, 7, 2, 0, 6886626979655763386019405088304677077874271846400000⟩, + ⟨2, 0, 8, 7, 3, 0, 22870466887377015041055879703927084402818731212800000⟩ +] + +def collectedFourData_9_2_16 : List CollectedFourTerm := [ + ⟨2, 1, 6, 0, 8, 1, -3916951639402478871116918825800081472601509068800000⟩, + ⟨2, 1, 6, 1, 7, 1, 13099957626328597797164911544720509455965356032000000⟩, + ⟨2, 1, 7, 1, 8, 1, 24626943702468280027813728072457544427100333670400000⟩, + ⟨2, 1, 6, 2, 6, 1, -904285071259964675917145007255705364064737689600000⟩, + ⟨2, 1, 7, 2, 7, 1, -1454002964229472337223993751664265752664342528000000⟩, + ⟨2, 1, 8, 2, 8, 1, -11752613861774887225519246922713066443228630220800000⟩, + ⟨2, 1, 6, 3, 5, 1, 2202963619944714595179067575108928814819416473600000⟩, + ⟨2, 1, 7, 3, 6, 1, -1135316185372738929884725024547862681926133350400000⟩, + ⟨2, 1, 8, 3, 7, 1, -7199143083764347462235107607056559117879476224000000⟩, + ⟨2, 1, 6, 4, 4, 1, -1018076074942027295546991387650450530467053568000000⟩, + ⟨2, 1, 7, 4, 5, 1, -3908791474383818175760323114124293916179038208000000⟩, + ⟨2, 1, 8, 4, 6, 1, 9182782616582576194313524025625256034270026137600000⟩, + ⟨2, 1, 6, 5, 3, 1, -377121875623145854924689040064590927285243084800000⟩, + ⟨2, 1, 7, 5, 4, 1, 2476851524617809118545792656379218147527360512000000⟩, + ⟨2, 1, 8, 5, 5, 1, 3069526724138584170734057034278319914006819635200000⟩, + ⟨2, 1, 6, 6, 2, 1, -27021903410474539568168625271210600031668980940800000⟩, + ⟨2, 1, 7, 6, 3, 1, 7426884976989683453558108340953996524115931955200000⟩, + ⟨2, 1, 8, 6, 4, 1, -4572530271666471923116456841136029759983268659200000⟩, + ⟨2, 1, 6, 7, 1, 1, 53569682886176950545966531756881526362470770278400000⟩, + ⟨2, 1, 7, 7, 2, 1, -13188749654015239877475012351310228286367124684800000⟩, + ⟨2, 1, 8, 7, 3, 1, -21899898392865915103041993997418000787801165004800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0908.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0908.lean new file mode 100644 index 0000000000000000000000000000000000000000..2008fffa81ffb66f577025fc0a065fa587bee4fe --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0908.lean @@ -0,0 +1,644 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0908. -/ +namespace LaughlinFock +def collectedFourData_9_2_17 : List CollectedFourTerm := [ + ⟨2, 2, 5, 0, 7, 2, 16128700585781290398528934698465153909365145600000⟩, + ⟨2, 2, 6, 0, 8, 2, 993607991822548920139024622803169771467151769600000⟩, + ⟨2, 2, 5, 1, 6, 2, -2661110483785255070937785346155064167083750195200000⟩, + ⟨2, 2, 6, 1, 7, 2, -3323049092340194122866585264497836479473516544000000⟩, + ⟨2, 2, 7, 1, 8, 2, -3123542275935431311849588499016956201211946598400000⟩, + ⟨2, 2, 5, 2, 5, 2, 465486321134729811116476769748386149368122572800000⟩, + ⟨2, 2, 6, 2, 6, 2, 229388809565897195931856444776603732917039923200000⟩, + ⟨2, 2, 7, 2, 7, 2, 184417513718967712612790601084080414930239488000000⟩, + ⟨2, 2, 8, 2, 8, 2, 993756721459494382502212747330963153261638451200000⟩, + ⟨2, 2, 5, 3, 4, 2, -630016304443766162286170281793915082418579046400000⟩, + ⟨2, 2, 6, 3, 5, 2, -558822895961337228640347497173295183388947251200000⟩, + ⟨2, 2, 7, 3, 6, 2, 143997084835584850105350999399383702278923878400000⟩, + ⟨2, 2, 8, 3, 7, 2, 608732398799242155838713456810349556385447936000000⟩, + ⟨2, 2, 5, 4, 3, 2, 58765657390877400849271625739519208762795622400000⟩, + ⟨2, 2, 6, 4, 4, 2, 258254024422942018980440041131875679816646656000000⟩, + ⟨2, 2, 7, 4, 5, 2, 495769006725351178953678186297105734348832768000000⟩, + ⟨2, 2, 8, 4, 6, 2, -776461479485058706047415843413457042896479846400000⟩, + ⟨2, 2, 5, 5, 2, 2, 4564370354451656413032879942067306555523884646400000⟩, + ⟨2, 2, 6, 5, 3, 2, 95664012223400410974573839691958730433862041600000⟩, + ⟨2, 2, 7, 5, 4, 2, -314149840996446696400892519566228070546276352000000⟩, + ⟨2, 2, 8, 5, 5, 2, -259547607850326625823955694015047963480214732800000⟩, + ⟨2, 2, 5, 6, 1, 2, -5831300554596027078640750997259267474355912704000000⟩, + ⟨2, 2, 6, 6, 2, 2, 6854610844008344176782067722963286032356317593600000⟩, + ⟨2, 2, 7, 6, 3, 2, -941984092074402993906739399865954774212096819200000⟩, + ⟨2, 2, 8, 6, 4, 2, 386635921590580459983635709847945501117041868800000⟩, + ⟨2, 2, 5, 7, 0, 2, -25441558289151600071919739548481725189412041523200000⟩, + ⟨2, 2, 6, 7, 1, 2, -13588951290505269508034801450282126952652131532800000⟩, + ⟨2, 2, 7, 7, 2, 2, 1672786424850457156760950018963044021054524620800000⟩, + ⟨2, 2, 8, 7, 3, 2, 1851772846717504075655235180803863221357458227200000⟩ +] + +def collectedFourData_9_2_18 : List CollectedFourTerm := [ + ⟨2, 3, 4, 0, 6, 3, 39040072815978698633386333203276575791542750412800000⟩, + ⟨2, 3, 5, 0, 7, 3, 504680884280110899652792354646429576263945420800000⟩, + ⟨2, 3, 6, 0, 8, 3, 15545423429301580295529639402522753315054708326400000⟩, + ⟨2, 3, 4, 1, 5, 3, -60497311874479174330532409707953001672173305200640000⟩, + ⟨2, 3, 5, 1, 6, 3, -83268431017176044960390771467349769859360201113600000⟩, + ⟨2, 3, 6, 1, 7, 3, -51990529103967170802897706540594580319576784896000000⟩, + ⟨2, 3, 7, 1, 8, 3, -32579439563265590632630514543105465142015845990400000⟩, + ⟨2, 3, 4, 2, 4, 3, 16129753145188048838278601501809929501939817512960000⟩, + ⟨2, 3, 5, 2, 5, 3, 14565466506190415291484124392277308018293892710400000⟩, + ⟨2, 3, 6, 2, 6, 3, 3588886365642425805997482248768784524534140108800000⟩, + ⟨2, 3, 7, 2, 7, 3, 1923527428747697592119641412742238413602684928000000⟩, + ⟨2, 3, 8, 2, 8, 3, 7773875184148736993174955228768502812508579430400000⟩, + ⟨2, 3, 4, 3, 3, 3, -20573229847112135795730416334114018444071613235200000⟩, + ⟨2, 3, 5, 3, 4, 3, -19713750896824978452587611791153868218507146035200000⟩, + ⟨2, 3, 6, 3, 5, 3, -8743024020743776646393728649214084615190138060800000⟩, + ⟨2, 3, 7, 3, 6, 3, 1501930791470530553985077976792866966460589670400000⟩, + ⟨2, 3, 8, 3, 7, 3, 4761939805411063408070020534190410382507507712000000⟩, + ⟨2, 3, 4, 4, 2, 3, 68589235182752631573779002215855403059683304407040000⟩, + ⟨2, 3, 5, 4, 3, 3, 1838827857184961364158961747107101587499332403200000⟩, + ⟨2, 3, 6, 4, 4, 3, 4040495039308032860380222725865258517375483904000000⟩, + ⟨2, 3, 7, 4, 5, 3, 5171012576454296204722755366653652276093124608000000⟩, + ⟨2, 3, 8, 4, 6, 3, -6074036528730381140672648863764877554114940108800000⟩, + ⟨2, 3, 4, 5, 1, 3, -66128583569174287770855449994805348681987160801280000⟩, + ⟨2, 3, 5, 5, 2, 3, 142823065901374899263187089054269876579855446835200000⟩, + ⟨2, 3, 6, 5, 3, 3, 1496704524518592384670437453295141643400668774400000⟩, + ⟨2, 3, 7, 5, 4, 3, -3276672717832233546194391280166995796649050112000000⟩, + ⟨2, 3, 8, 5, 5, 3, -2030366853579126545526439115431732519609407897600000⟩, + ⟨2, 3, 4, 6, 0, 3, -206322741869312150111979621283831857688673947484160000⟩, + ⟨2, 3, 5, 6, 1, 3, -182466399245520175154606214112712461090314780672000000⟩, + ⟨2, 3, 6, 6, 2, 3, 107243328244306672008086706654207022549604656742400000⟩, + ⟨2, 3, 7, 6, 3, 3, -9825163575897129849889593357997079596918584115200000⟩, + ⟨2, 3, 8, 6, 4, 3, 3024542457171195365171570721262904016570522009600000⟩, + ⟨2, 3, 5, 7, 0, 3, -796088194863779774992011632769192546054279109017600000⟩, + ⟨2, 3, 6, 7, 1, 3, -212604974506671987511867804234751425173945266995200000⟩, + ⟨2, 3, 7, 7, 2, 3, 17447640984575922527433523039817577334691384524800000⟩, + ⟨2, 3, 8, 7, 3, 3, 14485890428630854653530873212161022081989240422400000⟩ +] + +def collectedFourData_9_2_19 : List CollectedFourTerm := [ + ⟨2, 4, 3, 0, 5, 4, 24307202248429589155625391508368271571467370496000000⟩, + ⟨2, 4, 4, 0, 6, 4, 25512003468642075488908551472252196170742995353600000⟩, + ⟨2, 4, 5, 0, 7, 4, 164900057064465342748553857435503039154539724800000⟩, + ⟨2, 4, 6, 0, 8, 4, 3386220600554562398415185881156102113130551705600000⟩, + ⟨2, 4, 3, 1, 4, 4, -23252490000395831093711591959913488893502071767040000⟩, + ⟨2, 4, 4, 1, 5, 4, -39533933188606485208721375634941397948245401927680000⟩, + ⟨2, 4, 5, 1, 6, 4, -27207230259943398199893275424010326637922589081600000⟩, + ⟨2, 4, 6, 1, 7, 4, -11324966572074566374012646893090536352942915584000000⟩, + ⟨2, 4, 7, 1, 8, 4, -5322523212637673639756416089016802708534014771200000⟩, + ⟨2, 4, 3, 2, 3, 4, 16129753145188048838278601501809929501939817512960000⟩, + ⟨2, 4, 4, 2, 4, 4, 10540511031525388943341304766633357321543635435520000⟩, + ⟨2, 4, 5, 2, 5, 4, 4759138562316284483584361136820846549828789862400000⟩, + ⟨2, 4, 6, 2, 6, 4, 781758116763871976544033607655170938131133235200000⟩, + ⟨2, 4, 7, 2, 7, 4, 314247866964494657856869851264960228736630784000000⟩, + ⟨2, 4, 8, 2, 8, 4, 1016018241552151434862851836068988113587756072960000⟩, + ⟨2, 4, 3, 3, 2, 4, -10636164916876127570437186695640340984697622364160000⟩, + ⟨2, 4, 4, 3, 3, 4, -13444245191209631723698571714935213890304632422400000⟩, + ⟨2, 4, 5, 3, 4, 4, -6441295379114887836143317797455823384840713011200000⟩, + ⟨2, 4, 6, 3, 5, 4, -1904470996549501916188402375403661229139637043200000⟩, + ⟨2, 4, 7, 3, 6, 4, 245371363305793150251258274013484516398805811200000⟩, + ⟨2, 4, 8, 3, 7, 4, 622368843448409751528977557623665578474261708800000⟩, + ⟨2, 4, 3, 4, 1, 4, 9820735614560210743510263661203649001135454289920000⟩, + ⟨2, 4, 4, 4, 2, 4, 44821863272183682295723978077855548154512387604480000⟩, + ⟨2, 4, 5, 4, 3, 4, 600820891035041018600598040503785366307943219200000⟩, + ⟨2, 4, 6, 4, 4, 4, 880130901597324840528232116664666006398959616000000⟩, + ⟨2, 4, 7, 4, 5, 4, 844791526188567478327953207587882841170509824000000⟩, + ⟨2, 4, 8, 4, 6, 4, -793855286695081589850566540286023556752599941120000⟩, + ⟨2, 4, 3, 5, 0, 4, -11796076632869333860696678211334626189829136711680000⟩, + ⟨2, 4, 4, 5, 1, 4, -43213870561805416911088539360564349108164608655360000⟩, + ⟨2, 4, 5, 5, 2, 4, 46666185407147119098809075239004744037717717811200000⟩, + ⟨2, 4, 6, 5, 3, 4, 326023393117428891332653096611944280440281497600000⟩, + ⟨2, 4, 7, 5, 4, 4, -535312050626647647944829719173242209578254336000000⟩, + ⟨2, 4, 8, 5, 5, 4, -265361831958089431245880374697504165022914314240000⟩, + ⟨2, 4, 4, 6, 0, 4, -134828296326211113969557327566346022229246916689920000⟩, + ⟨2, 4, 5, 6, 1, 4, -59619297233445001773385896362575772209781932032000000⟩, + ⟨2, 4, 6, 6, 2, 4, 23360545245001516687712170800192777834515241369600000⟩, + ⟨2, 4, 7, 6, 3, 4, -1605143056531844927765160682388081027030030745600000⟩, + ⟨2, 4, 8, 6, 4, 4, 395297099071111855710113945566605859424871383040000⟩, + ⟨2, 4, 5, 7, 0, 4, -260114842567572834613156683403039149545997572505600000⟩, + ⟨2, 4, 6, 7, 1, 4, -46311208422787548774627203936053194731102719180800000⟩, + ⟨2, 4, 7, 7, 2, 4, 2850431910157310226475104049240977519090755174400000⟩, + ⟨2, 4, 8, 7, 3, 4, 1893255110478895630336111123270231223080593653760000⟩ +] + +def collectedFourData_9_2_20 : List CollectedFourTerm := [ + ⟨2, 5, 2, 0, 4, 5, -3193380356258896242198416460440674229166066892800000⟩, + ⟨2, 5, 3, 0, 5, 5, 21949854844140572880607229972824007493329879040000000⟩, + ⟨2, 5, 4, 0, 6, 5, 11518906355339253194011713493669510912181010432000000⟩, + ⟨2, 5, 5, 0, 7, 5, 49635937521211543291938600235977336353193984000000⟩, + ⟨2, 5, 6, 0, 8, 5, 764455015151046384972836192384172724202766336000000⟩, + ⟨2, 5, 2, 1, 3, 5, 1906593314929749657631733690374506429770052403200000⟩, + ⟨2, 5, 3, 1, 4, 5, -20997430105576764042935187551482748648732334489600000⟩, + ⟨2, 5, 4, 1, 5, 5, -17849937768216975598739733500008326398740109721600000⟩, + ⟨2, 5, 5, 1, 6, 5, -8189544657221221007932655758561684510136598528000000⟩, + ⟨2, 5, 6, 1, 7, 5, -2556663759892821776758153150266787943719895040000000⟩, + ⟨2, 5, 7, 1, 8, 5, -961267452567591231836484232132248202638891417600000⟩, + ⟨2, 5, 2, 2, 2, 5, 465486321134729811116476769748386149368122572800000⟩, + ⟨2, 5, 3, 2, 3, 5, 14565466506190415291484124392277308018293892710400000⟩, + ⟨2, 5, 4, 2, 4, 5, 4759138562316284483584361136820846549828789862400000⟩, + ⟨2, 5, 5, 2, 5, 5, 1432530155168903780644035799038294166698196992000000⟩, + ⟨2, 5, 6, 2, 6, 5, 176485522797099222046988546451554929697882112000000⟩, + ⟨2, 5, 7, 2, 7, 5, 56754331448384549953826823892224233944645632000000⟩, + ⟨2, 5, 8, 2, 8, 5, 152913888739221339475626613926931956224124518400000⟩, + ⟨2, 5, 2, 3, 1, 5, 2667732084102192396765628337767277548724551680000000⟩, + ⟨2, 5, 3, 3, 2, 5, -9604654358724263949476616741131766933978768998400000⟩, + ⟨2, 5, 4, 3, 3, 5, -6070201486375334657601015905819932180441202688000000⟩, + ⟨2, 5, 5, 3, 4, 5, -1938869765632799567548073998118840184808144896000000⟩, + ⟨2, 5, 6, 3, 5, 5, -429943165629418113451640839506028400939630592000000⟩, + ⟨2, 5, 7, 3, 6, 5, 44314979177161401296220883662062466018941337600000⟩, + ⟨2, 5, 8, 3, 7, 5, 93668436441102075688939892342871658806116352000000⟩, + ⟨2, 5, 2, 4, 0, 5, -10216261595012440929192265530688970276522793369600000⟩, + ⟨2, 5, 3, 4, 1, 5, 8868306561945242900557905889613422876081048780800000⟩, + ⟨2, 5, 4, 4, 2, 5, 20237487280789580929829112569780754023729174937600000⟩, + ⟨2, 5, 5, 4, 3, 5, 180850805874465740560883538111754509049921536000000⟩, + ⟨2, 5, 6, 4, 4, 5, 198693635495956482239984863592459728280616960000000⟩, + ⟨2, 5, 7, 4, 5, 5, 152572485997207209914605703733053448416919552000000⟩, + ⟨2, 5, 8, 4, 6, 5, -119477676699275514422808845457860370035952844800000⟩, + ⟨2, 5, 3, 5, 0, 5, -10652076169669773569492804716704151665548407603200000⟩, + ⟨2, 5, 4, 5, 1, 5, -19511463647495473450500724445286947293760795443200000⟩, + ⟨2, 5, 5, 5, 2, 5, 14046810561847748855134456021373114222584528896000000⟩, + ⟨2, 5, 6, 5, 3, 5, 73601293986683308439026647309724490039033856000000⟩, + ⟨2, 5, 7, 5, 4, 5, -96679343739226729944857300743214630204080128000000⟩, + ⟨2, 5, 8, 5, 5, 5, -39937776693542194133411998403371150763202969600000⟩, + ⟨2, 5, 4, 6, 0, 5, -60876227197934863129831477494161634811928012390400000⟩, + ⟨2, 5, 5, 6, 1, 5, -17945777370961949594141386892211541561112002560000000⟩, + ⟨2, 5, 6, 6, 2, 5, 5273751499320426656394092151854277797584306176000000⟩, + ⟨2, 5, 7, 6, 3, 5, -289894795253373032366771757736937115383286988800000⟩, + ⟨2, 5, 8, 6, 4, 5, 59493436391411763184343750489475887662733721600000⟩, + ⟨2, 5, 5, 7, 0, 5, -78296177113974145539564760547194420761301352448000000⟩, + ⟨2, 5, 6, 7, 1, 5, -10454970219810070612602521237707404011108302848000000⟩, + ⟨2, 5, 7, 7, 2, 5, 514798585469469473868723001841999837010277171200000⟩, + ⟨2, 5, 8, 7, 3, 5, 284940751532630807076768542685761766498395750400000⟩ +] + +def collectedFourData_9_2_21 : List CollectedFourTerm := [ + ⟨2, 6, 1, 0, 3, 6, -841163063881467431531208541930554910988618956800000⟩, + ⟨2, 6, 2, 0, 4, 6, -1573678291185118444917270723254497260929758003200000⟩, + ⟨2, 6, 3, 0, 5, 6, 5408377050229483233538892344119444101796986880000000⟩, + ⟨2, 6, 4, 0, 6, 6, 1892148846186704820382848643937816690804391936000000⟩, + ⟨2, 6, 5, 0, 7, 6, 6115071540621295872067940558480074000564224000000⟩, + ⟨2, 6, 6, 0, 8, 6, 75343750366156598000008724279054777688313036800000⟩, + ⟨2, 6, 1, 1, 2, 6, -246854422011058219751950629109967892925906944000000⟩, + ⟨2, 6, 2, 1, 3, 6, 939557514325854049952373660420197306136841420800000⟩, + ⟨2, 6, 3, 1, 4, 6, -5173702509796502759711078052080925824779498291200000⟩, + ⟨2, 6, 4, 1, 5, 6, -2932113354405467467743735148606597574045781196800000⟩, + ⟨2, 6, 5, 1, 6, 6, -1008939368630229121040886881704293660893380608000000⟩, + ⟨2, 6, 6, 1, 7, 6, -251981650035356466302412755451032064126615552000000⟩, + ⟨2, 6, 7, 1, 8, 6, -78951119366011718677575517623761313487808102400000⟩, + ⟨2, 6, 1, 2, 1, 6, -904285071259964675917145007255705364064737689600000⟩, + ⟨2, 6, 2, 2, 2, 6, 229388809565897195931856444776603732917039923200000⟩, + ⟨2, 6, 3, 2, 3, 6, 3588886365642425805997482248768784524534140108800000⟩, + ⟨2, 6, 4, 2, 4, 6, 781758116763871976544033607655170938131133235200000⟩, + ⟨2, 6, 5, 2, 5, 6, 176485522797099222046988546451554929697882112000000⟩, + ⟨2, 6, 6, 2, 6, 6, 17394197054535579899556122139568739530152345600000⟩, + ⟨2, 6, 7, 2, 7, 6, 4661364519053591890030538497885801197600768000000⟩, + ⟨2, 6, 8, 2, 8, 6, 10765004043351735410458324448225119009819852800000⟩, + ⟨2, 6, 1, 3, 0, 6, -793636090953353363673950169317137626375703756800000⟩, + ⟨2, 6, 2, 3, 1, 6, 1314642040438886238033384196006358540007505920000000⟩, + ⟨2, 6, 3, 3, 2, 6, -2366557436391318750982404672127866576447524044800000⟩, + ⟨2, 6, 4, 3, 3, 6, -997119377851529911122180570947540996874829824000000⟩, + ⟨2, 6, 5, 3, 4, 6, -238865787912749759317595503983619375110291456000000⟩, + ⟨2, 6, 6, 3, 5, 6, -42374672022286958013112195470112288983849369600000⟩, + ⟨2, 6, 7, 3, 6, 6, 3639691743825459771580335300932500824942182400000⟩, + ⟨2, 6, 8, 3, 7, 6, 6594176011980960537679345161644745827549184000000⟩, + ⟨2, 6, 2, 4, 0, 6, -5034511174852330869680865558614600236371699302400000⟩, + ⟨2, 6, 3, 4, 1, 6, 2185123593053179354680924106602310466239306137600000⟩, + ⟨2, 6, 4, 4, 2, 6, 3324303282517339246699877711469878600274857164800000⟩, + ⟨2, 6, 5, 4, 3, 6, 22280542512746282466848790121577411034218496000000⟩, + ⟨2, 6, 6, 4, 4, 6, 19583001452601518023776457348575698299650048000000⟩, + ⟨2, 6, 7, 4, 5, 6, 12531131187017552045057979138212195727310848000000⟩, + ⟨2, 6, 8, 4, 6, 6, -8411123955858672695847543693055458039929241600000⟩, + ⟨2, 6, 3, 5, 0, 6, -2624638964695352555536866135702081312842475110400000⟩, + ⟨2, 6, 4, 5, 1, 6, -3205043281813803236270826509901373684080810393600000⟩, + ⟨2, 6, 5, 5, 2, 6, 1730545564220405066405025932949309599520915456000000⟩, + ⟨2, 6, 6, 5, 3, 6, 7254053424795795719320576375514408736836812800000⟩, + ⟨2, 6, 7, 5, 4, 6, -7940498128169651345387129909615476680425472000000⟩, + ⟨2, 6, 8, 5, 5, 6, -2811584553458461029117394019273319176680243200000⟩, + ⟨2, 6, 4, 6, 0, 6, -9999810702461404132018568233715000308126659379200000⟩, + ⟨2, 6, 5, 6, 1, 6, -2210892308190988432094593856394934869987164160000000⟩, + ⟨2, 6, 6, 6, 2, 6, 519774491085564067758434422486519124977306828800000⟩, + ⟨2, 6, 7, 6, 3, 6, -23809730083444443564073097612619442533118771200000⟩, + ⟨2, 6, 8, 6, 4, 6, 4188285894675352184211949483479674112914227200000⟩, + ⟨2, 6, 5, 7, 0, 6, -9645969197307935044100243166293147420593225728000000⟩, + ⟨2, 6, 6, 7, 1, 6, -1030429064778035042898721044397563364531136102400000⟩, + ⟨2, 6, 7, 7, 2, 6, 42281598593910787805191008495197344611749068800000⟩, + ⟨2, 6, 8, 7, 3, 6, 20059579725917265555982172672695245143329996800000⟩ +] + +def collectedFourData_9_2_22 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 2, 7, -640873544096984056035457976155812212137525248000000⟩, + ⟨2, 7, 1, 0, 3, 7, -1352508879285030363940207362529923410033639424000000⟩, + ⟨2, 7, 2, 0, 4, 7, -1265161270957738971421539874669336699431026688000000⟩, + ⟨2, 7, 3, 0, 5, 7, 2898715796832916820305031271269444923215052800000000⟩, + ⟨2, 7, 4, 0, 6, 7, 760598100797334231682786405017131752221573120000000⟩, + ⟨2, 7, 5, 0, 7, 7, 1966488760928037546044862384649957502091264000000⟩, + ⟨2, 7, 6, 0, 8, 7, 20190911002566568498321741158607356432482304000000⟩, + ⟨2, 7, 0, 1, 1, 7, 4721772592642269611401939546789886117906743296000000⟩, + ⟨2, 7, 1, 1, 2, 7, -396918043595620835920946408205632418003025920000000⟩, + ⟨2, 7, 2, 1, 3, 7, 755358821190322120737011223079369307137769472000000⟩, + ⟨2, 7, 3, 1, 4, 7, -2772937806291609865589144898462433124466819072000000⟩, + ⟨2, 7, 4, 1, 5, 7, -1178638695987261674544202641016521150122950656000000⟩, + ⟨2, 7, 5, 1, 6, 7, -324455391190336422998984134186528636862988288000000⟩, + ⟨2, 7, 6, 1, 7, 7, -67527021755862866798149433832268871824834560000000⟩, + ⟨2, 7, 7, 1, 8, 7, -18135109512924590731751126412165553456152576000000⟩, + ⟨2, 7, 0, 2, 0, 7, 759221025847107766790274761043895318902472704000000⟩, + ⟨2, 7, 1, 2, 1, 7, -1454002964229472337223993751664265752664342528000000⟩, + ⟨2, 7, 2, 2, 2, 7, 184417513718967712612790601084080414930239488000000⟩, + ⟨2, 7, 3, 2, 3, 7, 1923527428747697592119641412742238413602684928000000⟩, + ⟨2, 7, 4, 2, 4, 7, 314247866964494657856869851264960228736630784000000⟩, + ⟨2, 7, 5, 2, 5, 7, 56754331448384549953826823892224233944645632000000⟩, + ⟨2, 7, 6, 2, 6, 7, 4661364519053591890030538497885801197600768000000⟩, + ⟨2, 7, 7, 2, 7, 7, 1070717637843774590562745075934377090744320000000⟩, + ⟨2, 7, 8, 2, 8, 7, 2163635711574730780735394820264813907673088000000⟩, + ⟨2, 7, 1, 3, 0, 7, -1276090101938582767365108199063954278448103424000000⟩, + ⟨2, 7, 2, 3, 1, 7, 1056908647753903151861852798883542453767372800000000⟩, + ⟨2, 7, 3, 3, 2, 7, -1268398516092521730311522158164087500426969088000000⟩, + ⟨2, 7, 4, 3, 3, 7, -400817888397379554604290140555280677685166080000000⟩, + ⟨2, 7, 5, 3, 4, 7, -76814618468538485270182287281448267301257216000000⟩, + ⟨2, 7, 6, 3, 5, 7, -11355729272925336018702930143644607198527488000000⟩, + ⟨2, 7, 7, 3, 6, 7, 836038917466922121277649340705855321931776000000⟩, + ⟨2, 7, 8, 3, 7, 7, 1325349684075847734816126441111274798448640000000⟩, + ⟨2, 7, 2, 4, 0, 7, -4047503604965118608610696039894360213229142016000000⟩, + ⟨2, 7, 3, 4, 1, 7, 1171155823343861063313843382953980964221485056000000⟩, + ⟨2, 7, 4, 4, 2, 7, 1336289567415744706205874592243933050323337216000000⟩, + ⟨2, 7, 5, 4, 3, 7, 7164991635444271756535764404426860088262656000000⟩, + ⟨2, 7, 6, 4, 4, 7, 5247928827156138599633476953957503273533440000000⟩, + ⟨2, 7, 7, 4, 5, 7, 2878406768925687021731791442804295094763520000000⟩, + ⟨2, 7, 8, 4, 6, 7, -1690534261955680622616778942484124832628736000000⟩, + ⟨2, 7, 3, 5, 0, 7, -1406721897768350235798847502516141071295053824000000⟩, + ⟨2, 7, 4, 5, 1, 7, -1288349929781524637870065100247694585010061312000000⟩, + ⟨2, 7, 5, 5, 2, 7, 556509990064243569729190524263622344982921216000000⟩, + ⟨2, 7, 6, 5, 3, 7, 1943969425415086163380332407191080045379584000000⟩, + ⟨2, 7, 7, 5, 4, 7, -1823936180992537089625729271096910576353280000000⟩, + ⟨2, 7, 8, 5, 5, 7, -565094515661749043320719622363870314627072000000⟩, + ⟨2, 7, 4, 6, 0, 7, -4019682195696831900941332594366979781389451264000000⟩, + ⟨2, 7, 5, 6, 1, 7, -710980214507530795767527650410068648405237760000000⟩, + ⟨2, 7, 6, 6, 2, 7, 139291187920837054320847289814373761300824064000000⟩, + ⟨2, 7, 7, 6, 3, 7, -5469106277451028271339002615533802082009088000000⟩, + ⟨2, 7, 8, 6, 4, 7, 841794847034989125958944771050573200883712000000⟩, + ⟨2, 7, 5, 7, 0, 7, -3101957170698425699961760312953636121485508608000000⟩, + ⟨2, 7, 6, 7, 1, 7, -276138384939445083060235778500210796550684672000000⟩, + ⟨2, 7, 7, 7, 2, 7, 9712103223354528194019295380523955899072512000000⟩, + ⟨2, 7, 8, 7, 3, 7, 4031733093586627518832091450542376330723328000000⟩ +] + +def collectedFourData_9_2_23 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 2, 8, -10360280526650034221496974501387895406964873625600000⟩, + ⟨2, 8, 1, 0, 3, 8, -10932243601912092104632091491417013130107446886400000⟩, + ⟨2, 8, 2, 0, 4, 8, -6817478944328581550649370460105178920718119731200000⟩, + ⟨2, 8, 3, 0, 5, 8, 11715068089031697412171495847996845492052951040000000⟩, + ⟨2, 8, 4, 0, 6, 8, 2459146508661350418785004624185663371558571212800000⟩, + ⟨2, 8, 5, 0, 7, 8, 5298334698364918548006306689580844687609036800000⟩, + ⟨2, 8, 6, 0, 8, 8, 46629101348571278717966696548648316335187558400000⟩, + ⟨2, 8, 0, 1, 1, 8, 76331577568473640276555581865597789251432559411200000⟩, + ⟨2, 8, 1, 1, 2, 8, -3208263405172986108637675111129599033697370112000000⟩, + ⟨2, 8, 2, 1, 3, 8, 4070345004300954462284003480068182560884968652800000⟩, + ⟨2, 8, 3, 1, 4, 8, -11206740323714755305028271364857940351070607769600000⟩, + ⟨2, 8, 4, 1, 5, 8, -3810744769375316743226061735716033057786576240640000⟩, + ⟨2, 8, 5, 1, 6, 8, -874184125214144164322408634683023740387301785600000⟩, + ⟨2, 8, 6, 1, 7, 8, -155947611319818954822571526168332913004773376000000⟩, + ⟨2, 8, 7, 1, 8, 8, -36646235373968257476294231202347576247871078400000⟩, + ⟨2, 8, 0, 2, 0, 8, 12273470924112170725411678455544734093755075788800000⟩, + ⟨2, 8, 1, 2, 1, 8, -11752613861774887225519246922713066443228630220800000⟩, + ⟨2, 8, 2, 2, 2, 8, 993756721459494382502212747330963153261638451200000⟩, + ⟨2, 8, 3, 2, 3, 8, 7773875184148736993174955228768502812508579430400000⟩, + ⟨2, 8, 4, 2, 4, 8, 1016018241552151434862851836068988113587756072960000⟩, + ⟨2, 8, 5, 2, 5, 8, 152913888739221339475626613926931956224124518400000⟩, + ⟨2, 8, 6, 2, 6, 8, 10765004043351735410458324448225119009819852800000⟩, + ⟨2, 8, 7, 2, 7, 8, 2163635711574730780735394820264813907673088000000⟩, + ⟨2, 8, 8, 2, 8, 8, 3886340091038833036973048596580143569725030400000⟩, + ⟨2, 8, 1, 3, 0, 8, -10314555465067271741159370678991878867026077286400000⟩, + ⟨2, 8, 2, 3, 1, 8, 5695283769385726686655406578299705364284702720000000⟩, + ⟨2, 8, 3, 3, 2, 8, -5126192431933388251421458927379649196288534118400000⟩, + ⟨2, 8, 4, 3, 3, 8, -1295914241474116146689451768264859853620720435200000⟩, + ⟨2, 8, 5, 3, 4, 8, -206962565187227983837070743439649115366175539200000⟩, + ⟨2, 8, 6, 3, 5, 8, -26225040122600945062249846381388116687375564800000⟩, + ⟨2, 8, 7, 3, 6, 8, 1689412403573051821781710948679476658464358400000⟩, + ⟨2, 8, 8, 3, 7, 8, 2380603899406341584544059302940293529075712000000⟩, + ⟨2, 8, 2, 4, 0, 8, -21810476843837451110730064633155875411138602598400000⟩, + ⟨2, 8, 3, 4, 1, 8, 4733189168917392463559164690062668051891670220800000⟩, + ⟨2, 8, 4, 4, 2, 8, 4320457572568438080994635533958778822568485847040000⟩, + ⟨2, 8, 5, 4, 3, 8, 19304724517038826537311965841637019512681267200000⟩, + ⟨2, 8, 6, 4, 4, 8, 12119621800147925564684492056258023128039424000000⟩, + ⟨2, 8, 7, 4, 5, 8, 5816494897971163161068699600667884145082368000000⟩, + ⟨2, 8, 8, 4, 6, 8, -3036551413144939852560143838992253949103308800000⟩, + ⟨2, 8, 3, 5, 0, 8, -5685221998201300233959498124647112520942957363200000⟩, + ⟨2, 8, 4, 5, 1, 8, -4165460350788502039823288480035002514308102881280000⟩, + ⟨2, 8, 5, 5, 2, 8, 1499411666585161386112407776173586439155692339200000⟩, + ⟨2, 8, 6, 5, 3, 8, 4489423352154913440520875888748642294982246400000⟩, + ⟨2, 8, 7, 5, 4, 8, -3685690155226978142372587896172961964490752000000⟩, + ⟨2, 8, 8, 5, 5, 8, -1015027372534922799752853357786994969254297600000⟩, + ⟨2, 8, 4, 6, 0, 8, -12996334630751290085877334191125330695628689244160000⟩, + ⟨2, 8, 5, 6, 1, 8, -1915602679874169255272304616527435033961562112000000⟩, + ⟨2, 8, 6, 6, 2, 8, 321680528317815049933905641074400895250622054400000⟩, + ⟨2, 8, 7, 6, 3, 8, -11051609905409183914758032671567134504203059200000⟩, + ⟨2, 8, 8, 6, 4, 8, 1512038761867600248844100254836755361536409600000⟩, + ⟨2, 8, 5, 7, 0, 8, -8357641109831278537539097225407170587603343769600000⟩, + ⟨2, 8, 6, 7, 1, 8, -637716878447704987276386781646385542050558771200000⟩, + ⟨2, 8, 7, 7, 2, 8, 19625578794860503796938448292831036462386380800000⟩, + ⟨2, 8, 8, 7, 3, 8, 7241831826934393896386050534190478201874022400000⟩ +] + +def collectedFourData_9_2_24 : List CollectedFourTerm := [ + ⟨3, 0, 6, 0, 8, 1, -3437670582372181359938767456621505466167879270400000⟩, + ⟨3, 0, 6, 1, 7, 1, 11497037264729071825447094825618128653627949056000000⟩, + ⟨3, 0, 7, 1, 8, 1, 21613572924435090276243175024472511573847651123200000⟩, + ⟨3, 0, 6, 2, 6, 1, -793636090953353363673950169317137626375703756800000⟩, + ⟨3, 0, 7, 2, 7, 1, -1276090101938582767365108199063954278448103424000000⟩, + ⟨3, 0, 8, 2, 8, 1, -10314555465067271741159370678991878867026077286400000⟩, + ⟨3, 0, 6, 3, 5, 1, 1933407386024129618839970817789462856774503628800000⟩, + ⟨3, 0, 7, 3, 6, 1, -996398069582047672464239983158272491387040563200000⟩, + ⟨3, 0, 8, 3, 7, 1, -6318250689743040646619456404759443751821115392000000⟩, + ⟨3, 0, 6, 4, 4, 1, -893503544501006597571175007683149890001567744000000⟩, + ⟨3, 0, 7, 4, 5, 1, -3430508901091829460913447943136283776321060864000000⟩, + ⟨3, 0, 8, 4, 6, 1, 8059170643771362165746459464481079364347022540800000⟩, + ⟨3, 0, 6, 5, 3, 1, -330976968098711294764559818895242423716701798400000⟩, + ⟨3, 0, 7, 5, 4, 1, 2173782167088795087431739448183405479142096896000000⟩, + ⟨3, 0, 8, 5, 5, 1, 2693937197291040621754290468878193794473367961600000⟩, + ⟨3, 0, 6, 6, 2, 1, -23715483617270635140119439036266677081909651046400000⟩, + ⟨3, 0, 7, 6, 3, 1, 6518125918949065154638010946771297198986074521600000⟩, + ⟨3, 0, 8, 6, 4, 1, -4013032135447038777459303862179871177974585753600000⟩, + ⟨3, 0, 6, 7, 1, 1, 47014857449940169663205039961217276364924859187200000⟩, + ⟨3, 0, 7, 7, 2, 1, -11574964635201817560402662273086340939978794598400000⟩, + ⟨3, 0, 8, 7, 3, 1, -19220210866218264333937047626413805123014125158400000⟩ +] + +def collectedFourData_9_2_25 : List CollectedFourTerm := [ + ⟨3, 1, 5, 0, 7, 2, 92434621757903115787988340506724444521103360000000⟩, + ⟨3, 1, 6, 0, 8, 2, 5694431390258088605398675829075379933161717760000000⟩, + ⟨3, 1, 5, 1, 6, 2, -15250995560146370501194245768339279194483589120000000⟩, + ⟨3, 1, 6, 1, 7, 2, -19044608355133014465533932237506439163569766400000000⟩, + ⟨3, 1, 7, 1, 8, 2, -17901221941924057621419139839160549077197783040000000⟩, + ⟨3, 1, 5, 2, 5, 2, 2667732084102192396765628337767277548724551680000000⟩, + ⟨3, 1, 6, 2, 6, 2, 1314642040438886238033384196006358540007505920000000⟩, + ⟨3, 1, 7, 2, 7, 2, 1056908647753903151861852798883542453767372800000000⟩, + ⟨3, 1, 8, 2, 8, 2, 5695283769385726686655406578299705364284702720000000⟩, + ⟨3, 1, 5, 3, 4, 2, -3610664014304440882645405169579301277626531840000000⟩, + ⟨3, 1, 6, 3, 5, 2, -3202650005381078360831404833109555972637982720000000⟩, + ⟨3, 1, 7, 3, 6, 2, 825256566716357526219681571605193721684951040000000⟩, + ⟨3, 1, 8, 3, 7, 2, 3488684580355690800809077752865592706701721600000000⟩, + ⟨3, 1, 5, 4, 3, 2, 336789767060899632387554240555361542539837440000000⟩, + ⟨3, 1, 6, 4, 4, 2, 1480070445726769263847302663955308120480153600000000⟩, + ⟨3, 1, 7, 4, 5, 2, 2841284105450414016453449024125593746984140800000000⟩, + ⟨3, 1, 8, 4, 6, 2, -4449950743648611631622096998879684181455011840000000⟩, + ⟨3, 1, 5, 5, 2, 2, 26158700450343036429447196963378705060425891840000000⟩, + ⟨3, 1, 6, 5, 3, 2, 548256614888674841342269835231143467637800960000000⟩, + ⟨3, 1, 7, 5, 4, 2, -1800412970243337844007013082402966199284531200000000⟩, + ⟨3, 1, 8, 5, 5, 2, -1487484055656883536763730365240019875717447680000000⟩, + ⟨3, 1, 5, 6, 1, 2, -33419559018655069785344525747831192926185062400000000⟩, + ⟨3, 1, 6, 6, 2, 2, 39284216189251054292794859168648790624341852160000000⟩, + ⟨3, 1, 7, 6, 3, 2, -5398571496182398185005726236068614787060203520000000⟩, + ⟨3, 1, 8, 6, 4, 2, 2215835366287964402759894426664541736958689280000000⟩, + ⟨3, 1, 5, 7, 0, 2, -145807209011156374542151346103610906983184465920000000⟩, + ⟨3, 1, 6, 7, 1, 2, -77879154984857558679020276090075017297715527680000000⟩, + ⟨3, 1, 7, 7, 2, 2, 9586846729557347108627933888549722987671060480000000⟩, + ⟨3, 1, 8, 7, 3, 2, 10612629440141376898975293710035539548511928320000000⟩ +] + +def collectedFourData_9_2_26 : List CollectedFourTerm := [ + ⟨3, 2, 4, 0, 6, 3, -25743521869178674486962603588047647323475201228800000⟩, + ⟨3, 2, 5, 0, 7, 3, -332793010982906456958308131886327928388897996800000⟩, + ⟨3, 2, 6, 0, 8, 3, -10250850450618845367617312181218676055898220134400000⟩, + ⟨3, 2, 4, 1, 5, 3, 39892698935483130542789791847751124840342817341440000⟩, + ⟨3, 2, 5, 1, 6, 3, 54908265284420902739482888994890677454724766105600000⟩, + ⟨3, 2, 6, 1, 7, 3, 34283217894776774351037212051787249850584662016000000⟩, + ⟨3, 2, 7, 1, 8, 3, 21483297913810178989722341278537824103666443878400000⟩, + ⟨3, 2, 4, 2, 4, 3, -10636164916876127570437186695640340984697622364160000⟩, + ⟨3, 2, 5, 2, 5, 3, -9604654358724263949476616741131766933978768998400000⟩, + ⟨3, 2, 6, 2, 6, 3, -2366557436391318750982404672127866576447524044800000⟩, + ⟨3, 2, 7, 2, 7, 3, -1268398516092521730311522158164087500426969088000000⟩, + ⟨3, 2, 8, 2, 8, 3, -5126192431933388251421458927379649196288534118400000⟩, + ⟨3, 2, 4, 3, 3, 3, 13566250119082761633651852991613998452796764979200000⟩, + ⟨3, 2, 5, 3, 4, 3, 12999498738850698737786695707361826074409513779200000⟩, + ⟨3, 2, 6, 3, 5, 3, 5765261533750277803863270155690419243845471436800000⟩, + ⟨3, 2, 7, 3, 6, 3, -990392317106264677234533201094722457570797158400000⟩, + ⟨3, 2, 8, 3, 7, 3, -3140083833812361622128398447685204952693604352000000⟩, + ⟨3, 2, 4, 4, 2, 3, -45228616356338795008121241413232743085116321955840000⟩, + ⟨3, 2, 5, 4, 3, 3, -1212546538481892829943273603613376671244301107200000⟩, + ⟨3, 2, 6, 4, 4, 3, -2664353954897373630123355172399392510426742784000000⟩, + ⟨3, 2, 7, 4, 5, 3, -3409831635694707637612463317109535337630138368000000⟩, + ⟨3, 2, 8, 4, 6, 3, 4005297145541215615622748340649875073804324044800000⟩, + ⟨3, 2, 4, 5, 1, 3, 43606031303150649080071578865059127335727273082880000⟩, + ⟨3, 2, 5, 5, 2, 3, -94179350991126437843137405173425238645343990579200000⟩, + ⟨3, 2, 6, 5, 3, 3, -986946050030750433540709032301619234013079142400000⟩, + ⟨3, 2, 7, 5, 4, 3, 2160679775554372875286688013189433184854474752000000⟩, + ⟨3, 2, 8, 5, 5, 3, 1338849795284620025308034405753991914900265369600000⟩, + ⟨3, 2, 4, 6, 0, 3, 136051847097160444413061936231617333797833785999360000⟩, + ⟨3, 2, 5, 6, 1, 3, 120320670545593042173615712816448229488052928512000000⟩, + ⟨3, 2, 6, 6, 2, 3, -70717618253284617904116934212223111220576020070400000⟩, + ⟨3, 2, 7, 6, 3, 3, 6478838156286483852366854270738280624233329459200000⟩, + ⟨3, 2, 8, 6, 4, 3, -1994421866410500299599548042463489505520884121600000⟩, + ⟨3, 2, 5, 7, 0, 3, 524950707722109053219454279592353667371048212889600000⟩, + ⟨3, 2, 6, 7, 1, 3, 140194431411730367266634572059858525473786245939200000⟩, + ⟨3, 2, 7, 7, 2, 3, -11505196964391171078085275930614878945537739980800000⟩, + ⟨3, 2, 8, 7, 3, 3, -9552180878396134291900633583502280437185013350400000⟩ +] + +def collectedFourData_9_2_27 : List CollectedFourTerm := [ + ⟨3, 3, 3, 0, 5, 4, -31003429147108170521651280058869953586549227520000000⟩, + ⟨3, 3, 4, 0, 6, 4, -32540132914388526472770876592021331443011551232000000⟩, + ⟨3, 3, 5, 0, 7, 4, -210327259521714211258325357027329684197605376000000⟩, + ⟨3, 3, 6, 0, 8, 4, -4319067632415580206199036785169248505898729472000000⟩, + ⟨3, 3, 3, 1, 4, 4, 29658161348770152412230879487286598374213340364800000⟩, + ⟨3, 3, 4, 1, 5, 4, 50424869303856519299344032331987128728726116761600000⟩, + ⟨3, 3, 5, 1, 6, 4, 34702366279431008187763824913463427723367022592000000⟩, + ⟨3, 3, 6, 1, 7, 4, 14444805087898036207525570356236441255757742080000000⟩, + ⟨3, 3, 7, 1, 8, 4, 6788789167108356039359056274964992981565702144000000⟩, + ⟨3, 3, 3, 2, 3, 4, -20573229847112135795730416334114018444071613235200000⟩, + ⟨3, 3, 4, 2, 4, 4, -13444245191209631723698571714935213890304632422400000⟩, + ⟨3, 3, 5, 2, 5, 4, -6070201486375334657601015905819932180441202688000000⟩, + ⟨3, 3, 6, 2, 6, 4, -997119377851529911122180570947540996874829824000000⟩, + ⟨3, 3, 7, 2, 7, 4, -400817888397379554604290140555280677685166080000000⟩, + ⟨3, 3, 8, 2, 8, 4, -1295914241474116146689451768264859853620720435200000⟩, + ⟨3, 3, 3, 3, 2, 4, 13566250119082761633651852991613998452796764979200000⟩, + ⟨3, 3, 4, 3, 3, 4, 17147909453419174078300037371743380491770789888000000⟩, + ⟨3, 3, 5, 3, 4, 4, 8215764317955836001723898112941839316307410944000000⟩, + ⟨3, 3, 6, 3, 5, 4, 2429120842488554579381704429122858073964150784000000⟩, + ⟨3, 3, 7, 3, 6, 4, -312967062158376636914907036840378029460946944000000⟩, + ⟨3, 3, 8, 3, 7, 4, -793821030656337834965897419718895998343315456000000⟩, + ⟨3, 3, 3, 4, 1, 4, -12526183708294547315924408230670537431942850150400000⟩, + ⟨3, 3, 4, 4, 2, 4, -57169535514532382388699303361279473823994452377600000⟩, + ⟨3, 3, 5, 4, 3, 4, -766336978436535480960446755931070212975099904000000⟩, + ⟨3, 3, 6, 4, 4, 4, -1122592216453706638629574954641950945228881920000000⟩, + ⟨3, 3, 7, 4, 5, 4, -1077517435308984331228638142828681808974970880000000⟩, + ⟨3, 3, 8, 4, 6, 4, 1012549115384034940345904790533532070355297894400000⟩, + ⟨3, 3, 3, 5, 0, 4, 15045698075954036990895477641148718704095762841600000⟩, + ⟨3, 3, 4, 5, 1, 4, 55118567757907909416370028630090146767787209523200000⟩, + ⟨3, 3, 5, 5, 2, 4, -59521937491994697008771553370556630556626386944000000⟩, + ⟨3, 3, 6, 5, 3, 4, -415837374680544970017736220086606286146240512000000⟩, + ⟨3, 3, 7, 5, 4, 4, 682781550240678144593588380357853094158008320000000⟩, + ⟨3, 3, 8, 5, 5, 4, 338464569940005280286043549485351196865383628800000⟩, + ⟨3, 3, 4, 6, 0, 4, 171971232618721334195957518219582616044537538150400000⟩, + ⟨3, 3, 5, 6, 1, 4, 76043414568491266187013202065007878678081699840000000⟩, + ⟨3, 3, 6, 6, 2, 4, -29795984002560851580385664114726840642046001152000000⟩, + ⟨3, 3, 7, 6, 3, 4, 2047333070895596509281099430451684417860534272000000⟩, + ⟨3, 3, 8, 6, 4, 4, -504194825790796571355035253402659885023022284800000⟩, + ⟨3, 3, 5, 7, 0, 4, 331772122897276638884254806223009712861947625472000000⟩, + ⟨3, 3, 6, 7, 1, 4, 59069170296866055896818163790284047269123588096000000⟩, + ⟨3, 3, 7, 7, 2, 4, -3635678136134646195611183322582134437737136128000000⟩, + ⟨3, 3, 8, 7, 3, 4, -2414815167752395043055670035230871866825716531200000⟩ +] + +def collectedFourData_9_2_28 : List CollectedFourTerm := [ + ⟨3, 4, 2, 0, 4, 5, 4322107008062285383945700403146641889376495206400000⟩, + ⟨3, 4, 3, 0, 5, 5, -29708212259109458993806929994533315305558507520000000⟩, + ⟨3, 4, 4, 0, 6, 5, -15590358907934829989450949416613428322543599616000000⟩, + ⟨3, 4, 5, 0, 7, 5, -67180169437598137439331579888726361654689792000000⟩, + ⟨3, 4, 6, 0, 8, 5, -1034657951677093950753340811815510635989434368000000⟩, + ⟨3, 4, 2, 1, 3, 5, -2580494463126363203590517241331044141940447641600000⟩, + ⟨3, 4, 3, 1, 4, 5, 28419145133381579199019641778460678757448207564800000⟩, + ⟨3, 4, 4, 1, 5, 5, 24159145643354595779754806551337113510709349580800000⟩, + ⟨3, 4, 5, 1, 6, 5, 11084206830057053987203222210642603176691236864000000⟩, + ⟨3, 4, 6, 1, 7, 5, 3460337673911515942704417003179634465460715520000000⟩, + ⟨3, 4, 7, 1, 8, 5, 1301035370002674808492678067183771678585703628800000⟩, + ⟨3, 4, 2, 2, 2, 5, -630016304443766162286170281793915082418579046400000⟩, + ⟨3, 4, 3, 2, 3, 5, -19713750896824978452587611791153868218507146035200000⟩, + ⟨3, 4, 4, 2, 4, 5, -6441295379114887836143317797455823384840713011200000⟩, + ⟨3, 4, 5, 2, 5, 5, -1938869765632799567548073998118840184808144896000000⟩, + ⟨3, 4, 6, 2, 6, 5, -238865787912749759317595503983619375110291456000000⟩, + ⟨3, 4, 7, 2, 7, 5, -76814618468538485270182287281448267301257216000000⟩, + ⟨3, 4, 8, 2, 8, 5, -206962565187227983837070743439649115366175539200000⟩, + ⟨3, 4, 2, 3, 1, 5, -3610664014304440882645405169579301277626531840000000⟩, + ⟨3, 4, 3, 3, 2, 5, 12999498738850698737786695707361826074409513779200000⟩, + ⟨3, 4, 4, 3, 3, 5, 8215764317955836001723898112941839316307410944000000⟩, + ⟨3, 4, 5, 3, 4, 5, 2624179291808173713156019412723282051384475648000000⟩, + ⟨3, 4, 6, 3, 5, 5, 581910127177076424977603390491580734893981696000000⟩, + ⟨3, 4, 7, 3, 6, 5, -59978474436452423626576747410967100002192588800000⟩, + ⟨3, 4, 8, 3, 7, 5, -126776318637660625294709369297812353057816576000000⟩, + ⟨3, 4, 2, 4, 0, 5, 13827283602298523314000155136440188950905933004800000⟩, + ⟨3, 4, 3, 4, 1, 5, -12002882733935369989029388034808944175161435750400000⟩, + ⟨3, 4, 4, 4, 2, 5, -27390594243005573638119432520234576432782429388800000⟩, + ⟨3, 4, 5, 4, 3, 5, -244774016334047128583948240198486223872851968000000⟩, + ⟨3, 4, 6, 4, 4, 5, -268923541397529496990614086534906065169940480000000⟩, + ⟨3, 4, 7, 4, 5, 5, -206500490827392058142475174728285184564658176000000⟩, + ⟨3, 4, 8, 4, 6, 5, 161708047948884268901845258437886279682516582400000⟩, + ⟨3, 4, 3, 5, 0, 5, 14417140436499400374675637749994289814329465241600000⟩, + ⟨3, 4, 4, 5, 1, 5, 26407951562396279433257638630488330927018187161600000⟩, + ⟨3, 4, 5, 5, 2, 5, -19011771726876435851425212341851505490445467648000000⟩, + ⟨3, 4, 6, 5, 3, 5, -99616279006291410480288463070990439051952128000000⟩, + ⟨3, 4, 7, 5, 4, 5, 130851455978674384317825046290996269011697664000000⟩, + ⟨3, 4, 8, 5, 5, 5, 54054113596354482766020027330122231730457804800000⟩, + ⟨3, 4, 4, 6, 0, 5, 82393432301571665408105233872761373329494061875200000⟩, + ⟨3, 4, 5, 6, 1, 5, 24288860544951608938113702628934673002429153280000000⟩, + ⟨3, 4, 6, 6, 2, 5, -7137802507401611472617071402971573059781132288000000⟩, + ⟨3, 4, 7, 6, 3, 5, 392360504037560462582882680423495543789348454400000⟩, + ⟨3, 4, 8, 6, 4, 5, -80521882668016816523275861190416779151461580800000⟩, + ⟨3, 4, 5, 7, 0, 5, 105970607336371485025042445395456218299916877824000000⟩, + ⟨3, 4, 6, 7, 1, 5, 14150365761334357609057498870740080134428033024000000⟩, + ⟨3, 4, 7, 7, 2, 5, -696758395734854103995371053904583328903305625600000⟩, + ⟨3, 4, 8, 7, 3, 5, -385655412662616522631465898960102253883765555200000⟩ +] + +def collectedFourData_9_2_29 : List CollectedFourTerm := [ + ⟨3, 5, 1, 0, 3, 6, 2049189671560316817959556874085342642038426828800000⟩, + ⟨3, 5, 2, 0, 4, 6, 3833698172355380038356423746766390284508148531200000⟩, + ⟨3, 5, 3, 0, 5, 6, -13175555212913916345398064834678275688187822080000000⟩, + ⟨3, 5, 4, 0, 6, 6, -4609536532392185827944054249277199705362661376000000⟩, + ⟨3, 5, 5, 0, 7, 6, -14897160824050867485878978240524906276061184000000⟩, + ⟨3, 5, 6, 0, 8, 6, -183547806241648446845088601598280902795644108800000⟩, + ⟨3, 5, 1, 1, 2, 6, 601371545761707803493152113843960194954952704000000⟩, + ⟨3, 5, 2, 1, 3, 6, -2288892174258299092999556917005705122249755852800000⟩, + ⟨3, 5, 3, 1, 4, 6, 12603855544820557723417448183033721150713836339200000⟩, + ⟨3, 5, 4, 1, 5, 6, 7143034043799194774600466887146380883351358668800000⟩, + ⟨3, 5, 5, 1, 6, 6, 2457915976347477524883751065614442376281980928000000⟩, + ⟨3, 5, 6, 1, 7, 6, 613862183026074327393330868795640735053381632000000⟩, + ⟨3, 5, 7, 1, 8, 6, 192335856518011572412883811650019119562384998400000⟩, + ⟨3, 5, 1, 2, 1, 6, 2202963619944714595179067575108928814819416473600000⟩, + ⟨3, 5, 2, 2, 2, 6, -558822895961337228640347497173295183388947251200000⟩, + ⟨3, 5, 3, 2, 3, 6, -8743024020743776646393728649214084615190138060800000⟩, + ⟨3, 5, 4, 2, 4, 6, -1904470996549501916188402375403661229139637043200000⟩, + ⟨3, 5, 5, 2, 5, 6, -429943165629418113451640839506028400939630592000000⟩, + ⟨3, 5, 6, 2, 6, 6, -42374672022286958013112195470112288983849369600000⟩, + ⟨3, 5, 7, 2, 7, 6, -11355729272925336018702930143644607198527488000000⟩, + ⟨3, 5, 8, 2, 8, 6, -26225040122600945062249846381388116687375564800000⟩, + ⟨3, 5, 1, 3, 0, 6, 1933407386024129618839970817789462856774503628800000⟩, + ⟨3, 5, 2, 3, 1, 6, -3202650005381078360831404833109555972637982720000000⟩, + ⟨3, 5, 3, 3, 2, 6, 5765261533750277803863270155690419243845471436800000⟩, + ⟨3, 5, 4, 3, 3, 6, 2429120842488554579381704429122858073964150784000000⟩, + ⟨3, 5, 5, 3, 4, 6, 581910127177076424977603390491580734893981696000000⟩, + ⟨3, 5, 6, 3, 5, 6, 103230567261406216274461496055525705759955353600000⟩, + ⟨3, 5, 7, 3, 6, 6, -8866792955332967913197621668565950134642278400000⟩, + ⟨3, 5, 8, 3, 7, 6, -16064325641985547384464265064973598451564544000000⟩, + ⟨3, 5, 2, 4, 0, 6, 12264766183689880714164957617859200195408324198400000⟩, + ⟨3, 5, 3, 4, 1, 6, -5323263574253094034955254196397203964162578841600000⟩, + ⟨3, 5, 4, 4, 2, 6, -8098463002208714575981684418335619641294769356800000⟩, + ⟨3, 5, 5, 4, 3, 6, -54278486008646236655336267255471500569870336000000⟩, + ⟨3, 5, 6, 4, 4, 6, -47706902547110097033292228109902998266707968000000⟩, + ⟨3, 5, 7, 4, 5, 6, -30527570341607690729848354402141329338400768000000⟩, + ⟨3, 5, 8, 4, 6, 6, 20490662365778767806610684797253602336414105600000⟩, + ⟨3, 5, 3, 5, 0, 6, 6393983864686639167182550586578975745057908326400000⟩, + ⟨3, 5, 4, 5, 1, 6, 7807929130518885080697999923414121185717885337600000⟩, + ⟨3, 5, 5, 5, 2, 6, -4215848565676785794004373287441500809457565696000000⟩, + ⟨3, 5, 6, 5, 3, 6, -17671878370937339609009783229057063468190924800000⟩, + ⟨3, 5, 7, 5, 4, 6, 19344152697582297100155752157885140777828352000000⟩, + ⟨3, 5, 8, 5, 5, 6, 6849409199067592254265612906713503321240371200000⟩, + ⟨3, 5, 4, 6, 0, 6, 24360923213254390512834397101226283787571376947200000⟩, + ⟨3, 5, 5, 6, 1, 6, 5386039731667941445150191052376682212685250560000000⟩, + ⟨3, 5, 6, 6, 2, 6, -1266242616215431974038266349886867178227813580800000⟩, + ⟨3, 5, 7, 6, 3, 6, 58003798626741239416626050777177015062836019200000⟩, + ⟨3, 5, 8, 6, 4, 6, -10203244252436539899402361707659834294481715200000⟩, + ⟨3, 5, 5, 7, 0, 6, 23498916322005512088630119013246137059768270848000000⟩, + ⟨3, 5, 6, 7, 1, 6, 2510267851128868098079625525593206645554832998400000⟩, + ⟨3, 5, 7, 7, 2, 6, -103003827505091817589066680977052739369225420800000⟩, + ⟨3, 5, 8, 7, 3, 6, -48867913196890954696570197376738152424459468800000⟩ +] + +def collectedFourData_9_2_30 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 2, 7, -500407581889679029664833372843974560439494246400000⟩, + ⟨3, 6, 1, 0, 3, 7, -1056067462920454296776439542620830497162605363200000⟩, + ⟨3, 6, 2, 0, 4, 7, -987864607818212647819336711620125326372660838400000⟩, + ⟨3, 6, 3, 0, 5, 7, 2263378440004791964338933438234604923298775040000000⟩, + ⟨3, 6, 4, 0, 6, 7, 593891041244602246186872026217717743134703616000000⟩, + ⟨3, 6, 5, 0, 7, 7, 1535475905868121956469673064409861020922675200000⟩, + ⟨3, 6, 6, 0, 8, 7, 15765489220155810258528034843131409394250547200000⟩, + ⟨3, 6, 0, 1, 1, 7, 3686859641938210498205289655930695504911715532800000⟩, + ⟨3, 6, 1, 1, 2, 7, -309921981073397740069563742567598782892998656000000⟩, + ⟨3, 6, 2, 1, 3, 7, 589800101209492788906192779879641606184868249600000⟩, + ⟨3, 6, 3, 1, 4, 7, -2165168331815034142583832340248064490166917529600000⟩, + ⟨3, 6, 4, 1, 5, 7, -920305956164318039506463495339562122001304780800000⟩, + ⟨3, 6, 5, 1, 6, 7, -253341613539996621188626378472985467487151718400000⟩, + ⟨3, 6, 6, 1, 7, 7, -52726523009583701698229270991527849081438208000000⟩, + ⟨3, 6, 7, 1, 8, 7, -14160276051735080379189145082722118194220236800000⟩, + ⟨3, 6, 0, 2, 0, 7, 592815792075291251225831990528014472474473267200000⟩, + ⟨3, 6, 1, 2, 1, 7, -1135316185372738929884725024547862681926133350400000⟩, + ⟨3, 6, 2, 2, 2, 7, 143997084835584850105350999399383702278923878400000⟩, + ⟨3, 6, 3, 2, 3, 7, 1501930791470530553985077976792866966460589670400000⟩, + ⟨3, 6, 4, 2, 4, 7, 245371363305793150251258274013484516398805811200000⟩, + ⟨3, 6, 5, 2, 5, 7, 44314979177161401296220883662062466018941337600000⟩, + ⟨3, 6, 6, 2, 6, 7, 3639691743825459771580335300932500824942182400000⟩, + ⟨3, 6, 7, 2, 7, 7, 836038917466922121277649340705855321931776000000⟩, + ⟨3, 6, 8, 2, 8, 7, 1689412403573051821781710948679476658464358400000⟩, + ⟨3, 6, 1, 3, 0, 7, -996398069582047672464239983158272491387040563200000⟩, + ⟨3, 6, 2, 3, 1, 7, 825256566716357526219681571605193721684951040000000⟩, + ⟨3, 6, 3, 3, 2, 7, -990392317106264677234533201094722457570797158400000⟩, + ⟨3, 6, 4, 3, 3, 7, -312967062158376636914907036840378029460946944000000⟩, + ⟨3, 6, 5, 3, 4, 7, -59978474436452423626576747410967100002192588800000⟩, + ⟨3, 6, 6, 3, 5, 7, -8866792955332967913197621668565950134642278400000⟩, + ⟨3, 6, 7, 3, 6, 7, 652796822257304095374507830832099740142796800000⟩, + ⟨3, 6, 8, 3, 7, 7, 1034860990402000414167204007581353930391552000000⟩, + ⟨3, 6, 2, 4, 0, 7, -3160376193253887182341831217020563943083265228800000⟩, + ⟨3, 6, 3, 4, 1, 7, 914463171359792119829388436625886205539306700800000⟩, + ⟨3, 6, 4, 4, 2, 7, 1043403082080923865466369140866037650689936588800000⟩, + ⟨3, 6, 5, 4, 3, 7, 5594576608095808624172452529916798326066380800000⟩, + ⟨3, 6, 6, 4, 4, 7, 4097693528645538399443437959656953916424192000000⟩, + ⟨3, 6, 7, 4, 5, 7, 2247520722613903807462449753598412860686336000000⟩, + ⟨3, 6, 8, 4, 6, 7, -1320004812055209335813501480411640013573324800000⟩, + ⟨3, 6, 3, 5, 0, 7, -1098398131327751152969682741440108411321791283200000⟩, + ⟨3, 6, 4, 5, 1, 7, -1005970801772006661763763551905477471074097561600000⟩, + ⟨3, 6, 5, 5, 2, 7, 434534739326600265736554122600971951227587788800000⟩, + ⟨3, 6, 6, 5, 3, 7, 1517892333674208690506139727434240083833651200000⟩, + ⟨3, 6, 7, 5, 4, 7, -1424167844434298978832398528785234897403904000000⟩, + ⟨3, 6, 8, 5, 5, 7, -441237717996082811920474108129114177771929600000⟩, + ⟨3, 6, 4, 6, 0, 7, -3138652650029266853081348343895815252434170675200000⟩, + ⟨3, 6, 5, 6, 1, 7, -555148348984239300352690469542480952288083968000000⟩, + ⟨3, 6, 6, 6, 2, 7, 108761497752603136892157714699727807578321715200000⟩, + ⟨3, 6, 7, 6, 3, 7, -4270393547377847418503345818241257573869158400000⟩, + ⟨3, 6, 8, 6, 4, 7, 657291173480277709152778878328864151017881600000⟩, + ⟨3, 6, 5, 7, 0, 7, -2422073591915423192683103126562994437031880294400000⟩, + ⟨3, 6, 6, 7, 1, 7, -215614675854926366031229268127535431197235609600000⟩, + ⟨3, 6, 7, 7, 2, 7, 7583415064994984999912309631847482001037721600000⟩, + ⟨3, 6, 8, 7, 3, 7, 3148062245304617274098014229295541634098790400000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0909.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0909.lean new file mode 100644 index 0000000000000000000000000000000000000000..44c49ccd997ae784a0867961494cbb34abfc03b8 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0909.lean @@ -0,0 +1,645 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0909. -/ +namespace LaughlinFock +def collectedFourData_9_2_31 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 2, 8, -6346259885375588231536913599774296931427155968000000⟩, + ⟨3, 7, 1, 0, 3, 8, -6696619734330889629190501132076038243737403392000000⟩, + ⟨3, 7, 2, 0, 4, 8, -4176092822244742658184538392967347977727246336000000⟩, + ⟨3, 7, 3, 0, 5, 8, 7176144166812956836666249246947825125897011200000000⟩, + ⟨3, 7, 4, 0, 6, 8, 1506366820863028986021584274799652448170409984000000⟩, + ⟨3, 7, 5, 0, 7, 8, 3245530743017367576449408724430221113032704000000⟩, + ⟨3, 7, 6, 0, 8, 8, 28562971303561374346679609760420912590487552000000⟩, + ⟨3, 7, 0, 1, 1, 8, 46757423938874280297367366027109775636468596736000000⟩, + ⟨3, 7, 1, 1, 2, 8, -1965243440811665693256055498928072829551247360000000⟩, + ⟨3, 7, 2, 1, 3, 8, 2493317353134124183900093919007660268987613184000000⟩, + ⟨3, 7, 3, 1, 4, 8, -6864764557220798720837287120750273876394508288000000⟩, + ⟨3, 7, 4, 1, 5, 8, -2334297474000082573074780678960054345672110899200000⟩, + ⟨3, 7, 5, 1, 6, 8, -535487396505134776247690707038464256421920768000000⟩, + ⟨3, 7, 6, 1, 7, 8, -95526763719700398440202319121552755686113280000000⟩, + ⟨3, 7, 7, 1, 8, 8, -22447899253848323614981024649211705821233152000000⟩, + ⟨3, 7, 0, 2, 0, 8, 7518197598960423538521648151082881327262859264000000⟩, + ⟨3, 7, 1, 2, 1, 8, -7199143083764347462235107607056559117879476224000000⟩, + ⟨3, 7, 2, 2, 2, 8, 608732398799242155838713456810349556385447936000000⟩, + ⟨3, 7, 3, 2, 3, 8, 4761939805411063408070020534190410382507507712000000⟩, + ⟨3, 7, 4, 2, 4, 8, 622368843448409751528977557623665578474261708800000⟩, + ⟨3, 7, 5, 2, 5, 8, 93668436441102075688939892342871658806116352000000⟩, + ⟨3, 7, 6, 2, 6, 8, 6594176011980960537679345161644745827549184000000⟩, + ⟨3, 7, 7, 2, 7, 8, 1325349684075847734816126441111274798448640000000⟩, + ⟨3, 7, 8, 2, 8, 8, 2380603899406341584544059302940293529075712000000⟩, + ⟨3, 7, 1, 3, 0, 8, -6318250689743040646619456404759443751821115392000000⟩, + ⟨3, 7, 2, 3, 1, 8, 3488684580355690800809077752865592706701721600000000⟩, + ⟨3, 7, 3, 3, 2, 8, -3140083833812361622128398447685204952693604352000000⟩, + ⟨3, 7, 4, 3, 3, 8, -793821030656337834965897419718895998343315456000000⟩, + ⟨3, 7, 5, 3, 4, 8, -126776318637660625294709369297812353057816576000000⟩, + ⟨3, 7, 6, 3, 5, 8, -16064325641985547384464265064973598451564544000000⟩, + ⟨3, 7, 7, 3, 6, 8, 1034860990402000414167204007581353930391552000000⟩, + ⟨3, 7, 8, 3, 7, 8, 1458255014515159283637990860724794409615360000000⟩, + ⟨3, 7, 2, 4, 0, 8, -13360155057472642211306616871361570480169418752000000⟩, + ⟨3, 7, 3, 4, 1, 8, 2899347027846106030399074742911269030250676224000000⟩, + ⟨3, 7, 4, 4, 2, 8, 2646525497907925653395518040534165108924035891200000⟩, + ⟨3, 7, 5, 4, 3, 8, 11825239527594556256955075233981301748924416000000⟩, + ⟨3, 7, 6, 4, 4, 8, 7423956277858844220685091415211320771870720000000⟩, + ⟨3, 7, 7, 4, 5, 8, 3562933276713296897225209314920857904087040000000⟩, + ⟨3, 7, 8, 4, 6, 8, -1860060099101720378822984315460770661924864000000⟩, + ⟨3, 7, 3, 5, 0, 8, -3482521174386200048477200788360999097960759296000000⟩, + ⟨3, 7, 4, 5, 1, 8, -2551580901726732027315812178320386217757533798400000⟩, + ⟨3, 7, 5, 5, 2, 8, 918474754311544208011648689441916669264920576000000⟩, + ⟨3, 7, 6, 5, 3, 8, 2750026628618870530383854363225922251784192000000⟩, + ⟨3, 7, 7, 5, 4, 8, -2257694424574031815598508050761954948546560000000⟩, + ⟨3, 7, 8, 5, 5, 8, -621761879932361704264246555399309259440128000000⟩, + ⟨3, 7, 4, 6, 0, 8, -7960992649947435638083574195098829452303191244800000⟩, + ⟨3, 7, 5, 6, 1, 8, -1173415373486447124269636689999564788581007360000000⟩, + ⟨3, 7, 6, 6, 2, 8, 197047582593777338712802982476411379417874432000000⟩, + ⟨3, 7, 7, 6, 3, 8, -6769738370607247917810749399000492776882176000000⟩, + ⟨3, 7, 8, 6, 4, 8, 926209566902151582751086353111987402047488000000⟩, + ⟨3, 7, 5, 7, 0, 8, -5119529570193829742512890189845367691608588288000000⟩, + ⟨3, 7, 6, 7, 1, 8, -390637785676661923310970425085203187064897536000000⟩, + ⟨3, 7, 7, 7, 2, 8, 12021780984860411955060395205027640350081024000000⟩, + ⟨3, 7, 8, 7, 3, 8, 4436033049654352576593807516086018582249472000000⟩ +] + +def collectedFourData_9_2_32 : List CollectedFourTerm := [ + ⟨4, 0, 5, 0, 7, 2, -353984675576062239885872357184535326201426739200000⟩, + ⟨4, 0, 6, 0, 8, 2, -21807212599951052825734733367044666910485721907200000⟩, + ⟨4, 0, 5, 1, 6, 2, 58404725555214372568508986634427771317362517606400000⟩, + ⟨4, 0, 6, 1, 7, 2, 72932623965527607973773887452834978327437508608000000⟩, + ⟨4, 0, 7, 1, 8, 2, 68553947871651074642979758100610561200156888268800000⟩, + ⟨4, 0, 5, 2, 5, 2, -10216261595012440929192265530688970276522793369600000⟩, + ⟨4, 0, 6, 2, 6, 2, -5034511174852330869680865558614600236371699302400000⟩, + ⟨4, 0, 7, 2, 7, 2, -4047503604965118608610696039894360213229142016000000⟩, + ⟨4, 0, 8, 2, 8, 2, -21810476843837451110730064633155875411138602598400000⟩, + ⟨4, 0, 5, 3, 4, 2, 13827283602298523314000155136440188950905933004800000⟩, + ⟨4, 0, 6, 3, 5, 2, 12264766183689880714164957617859200195408324198400000⟩, + ⟨4, 0, 7, 3, 6, 2, -3160376193253887182341831217020563943083265228800000⟩, + ⟨4, 0, 8, 3, 7, 2, -13360155057472642211306616871361570480169418752000000⟩, + ⟨4, 0, 5, 4, 3, 2, -1289759336524758503562294419786528613651500236800000⟩, + ⟨4, 0, 6, 4, 4, 2, -5668030512771727238500167013830841238701473792000000⟩, + ⟨4, 0, 7, 4, 5, 2, -10880890873568096574348097929007509549116030976000000⟩, + ⟨4, 0, 8, 4, 6, 2, 17041389258297371924848986070058987571060198604800000⟩, + ⟨4, 0, 5, 5, 2, 2, -100176523864169610188105782484007464852305792204800000⟩, + ⟨4, 0, 6, 5, 3, 2, -2099586023753100791432332574423535425076540211200000⟩, + ⟨4, 0, 7, 5, 4, 2, 6894804014492893313775611385151741931619876864000000⟩, + ⟨4, 0, 8, 5, 5, 2, 5696421436605789420885591059604022904403630489600000⟩, + ⟨4, 0, 5, 6, 1, 2, 127982475961202486480637649901926613889715273728000000⟩, + ⟨4, 0, 6, 6, 2, 2, -150441579773359858997923650164743415877216711475200000⟩, + ⟨4, 0, 7, 6, 3, 2, 20674196997911256967052237384328785042912732774400000⟩, + ⟨4, 0, 8, 6, 4, 2, -8485692355833616105161450469837917836459743641600000⟩, + ⟨4, 0, 5, 7, 0, 2, 558378631262721178978030267937543889944494630502400000⟩, + ⟨4, 0, 6, 7, 1, 2, 298243524852154438348833444127604187384795208089600000⟩, + ⟨4, 0, 7, 7, 2, 2, -36713482078695690781393145327296033649889745305600000⟩, + ⟨4, 0, 8, 7, 3, 2, -40641786788684680209460157548919160461381232230400000⟩ +] + +def collectedFourData_9_2_33 : List CollectedFourTerm := [ + ⟨4, 1, 4, 0, 6, 3, 23769876082281235964315512743450416656496040345600000⟩, + ⟨4, 1, 5, 0, 7, 3, 307279193278667007286334833065465989658417561600000⟩, + ⟨4, 1, 6, 0, 8, 3, 9464961561492073222073435718047707309961694412800000⟩, + ⟨4, 1, 4, 1, 5, 3, -36834296220342268759606815333706787210868849377280000⟩, + ⟨4, 1, 5, 1, 6, 3, -50698683277920498615825062644925273980773020467200000⟩, + ⟨4, 1, 6, 1, 7, 3, -31654870114579605018794428413922197467081736192000000⟩, + ⟨4, 1, 7, 1, 8, 3, -19836265288215243636592491438493767397519707340800000⟩, + ⟨4, 1, 4, 2, 4, 3, 9820735614560210743510263661203649001135454289920000⟩, + ⟨4, 1, 5, 2, 5, 3, 8868306561945242900557905889613422876081048780800000⟩, + ⟨4, 1, 6, 2, 6, 3, 2185123593053179354680924106602310466239306137600000⟩, + ⟨4, 1, 7, 2, 7, 3, 1171155823343861063313843382953980964221485056000000⟩, + ⟨4, 1, 8, 2, 8, 3, 4733189168917392463559164690062668051891670220800000⟩, + ⟨4, 1, 4, 3, 3, 3, -12526183708294547315924408230670537431942850150400000⟩, + ⟨4, 1, 5, 3, 4, 3, -12002882733935369989029388034808944175161435750400000⟩, + ⟨4, 1, 6, 3, 5, 3, -5323263574253094034955254196397203964162578841600000⟩, + ⟨4, 1, 7, 3, 6, 3, 914463171359792119829388436625886205539306700800000⟩, + ⟨4, 1, 8, 3, 7, 3, 2899347027846106030399074742911269030250676224000000⟩, + ⟨4, 1, 4, 4, 2, 3, 41761131659702896314446704902405123036795717550080000⟩, + ⟨4, 1, 5, 4, 3, 3, 1119585778130099843529893125866481200719619686400000⟩, + ⟨4, 1, 6, 4, 4, 3, 2460089325348670115598673785584413518392721408000000⟩, + ⟨4, 1, 7, 4, 5, 3, 3148414418733586000414870872033816959218876416000000⟩, + ⟨4, 1, 8, 4, 6, 3, -3698228133121666648280475203593732396120906137600000⟩, + ⟨4, 1, 4, 5, 1, 3, -40262943267172964769252419069765673953738159554560000⟩, + ⟨4, 1, 5, 5, 2, 3, 86959022698791585102235495264099589703776757350400000⟩, + ⟨4, 1, 6, 5, 3, 3, 911281114850674984510743470312732560508898508800000⟩, + ⟨4, 1, 7, 5, 4, 3, -1995029692495498703292044114798392681665921024000000⟩, + ⟨4, 1, 8, 5, 5, 3, -1236205904088225131555137083177019614476579635200000⟩, + ⟨4, 1, 4, 6, 0, 3, -125621333502810035539766081885817328384520560312320000⟩, + ⟨4, 1, 5, 6, 1, 3, -111096199018125198971903169833411169958068486144000000⟩, + ⟨4, 1, 6, 6, 2, 3, 65296000728134804576311936348675019848008125644800000⟩, + ⟨4, 1, 7, 6, 3, 3, -5982133327159965291989368431189526202003383910400000⟩, + ⟨4, 1, 8, 6, 4, 3, 1841518066614175319625238008058592253464228659200000⟩, + ⟨4, 1, 5, 7, 0, 3, -484704980743121153694800770053088705280774189875200000⟩, + ⟨4, 1, 6, 7, 1, 3, -129446323584513669161105008810481370380884141670400000⟩, + ⟨4, 1, 7, 7, 2, 3, 10623142689471548843032078213529669567826729369600000⟩, + ⟨4, 1, 8, 7, 3, 3, 8819855999067947752414936209013008728163405004800000⟩ +] + +def collectedFourData_9_2_34 : List CollectedFourTerm := [ + ⟨4, 2, 3, 0, 5, 4, 103362549733108977548856438149477521660003221504000000⟩, + ⟨4, 2, 4, 0, 6, 4, 108485777193429676188589311842835132715071071846400000⟩, + ⟨4, 2, 5, 0, 7, 4, 701211524679665573749231524520483597881389875200000⟩, + ⟨4, 2, 6, 0, 8, 4, 14399369851571956697494727952217529851591419494400000⟩, + ⟨4, 2, 3, 1, 4, 4, -98877551991398420210503264650897370359981366312960000⟩, + ⟨4, 2, 4, 1, 5, 4, -168111825194392745913044085224644762110565621432320000⟩, + ⟨4, 2, 5, 1, 6, 4, -115694462163996468556261779940438768624691734118400000⟩, + ⟨4, 2, 6, 1, 7, 4, -48157636924565489151759133121520424751166652416000000⟩, + ⟨4, 2, 7, 1, 8, 4, -22633191786086032219354666840496353166668647628800000⟩, + ⟨4, 2, 3, 2, 3, 4, 68589235182752631573779002215855403059683304407040000⟩, + ⟨4, 2, 4, 2, 4, 4, 44821863272183682295723978077855548154512387604480000⟩, + ⟨4, 2, 5, 2, 5, 4, 20237487280789580929829112569780754023729174937600000⟩, + ⟨4, 2, 6, 2, 6, 4, 3324303282517339246699877711469878600274857164800000⟩, + ⟨4, 2, 7, 2, 7, 4, 1336289567415744706205874592243933050323337216000000⟩, + ⟨4, 2, 8, 2, 8, 4, 4320457572568438080994635533958778822568485847040000⟩, + ⟨4, 2, 3, 3, 2, 4, -45228616356338795008121241413232743085116321955840000⟩, + ⟨4, 2, 4, 3, 3, 4, -57169535514532382388699303361279473823994452377600000⟩, + ⟨4, 2, 5, 3, 4, 4, -27390594243005573638119432520234576432782429388800000⟩, + ⟨4, 2, 6, 3, 5, 4, -8098463002208714575981684418335619641294769356800000⟩, + ⟨4, 2, 7, 3, 6, 4, 1043403082080923865466369140866037650689936588800000⟩, + ⟨4, 2, 8, 3, 7, 4, 2646525497907925653395518040534165108924035891200000⟩, + ⟨4, 2, 3, 4, 1, 4, 41761131659702896314446704902405123036795717550080000⟩, + ⟨4, 2, 4, 4, 2, 4, 190597915146775626407564456666284006726981669355520000⟩, + ⟨4, 2, 5, 4, 3, 4, 2554896223579680539111295605678098685436415180800000⟩, + ⟨4, 2, 6, 4, 4, 4, 3742618058558219322122793490514679776761872384000000⟩, + ⟨4, 2, 7, 4, 5, 4, 3592342929775733261039963858108729816751538176000000⟩, + ⟨4, 2, 8, 4, 6, 4, -3375744592622261262371550436198694906130994298880000⟩, + ⟨4, 2, 3, 5, 0, 4, -50160958269037092659001187294763585872649854648320000⟩, + ⟨4, 2, 4, 5, 1, 4, -183760179367961830155722005432200762121547038064640000⟩, + ⟨4, 2, 5, 5, 2, 4, 198440604587159420842289942679917705618395024588800000⟩, + ⟨4, 2, 6, 5, 3, 4, 1386363138005088291305866238774735500080473702400000⟩, + ⟨4, 2, 7, 5, 4, 4, -2276330195886866903652544186908345839244017664000000⟩, + ⟨4, 2, 8, 5, 5, 4, -1128409401983274008944803236522861362176338165760000⟩, + ⟨4, 2, 4, 6, 0, 4, -573336097754677790685317843829627782169849055150080000⟩, + ⟨4, 2, 5, 6, 1, 4, -253521672809675110012433548636269188749845331968000000⟩, + ⟨4, 2, 6, 6, 2, 4, 99337039902854787739561645146320139821672457830400000⟩, + ⟨4, 2, 7, 6, 3, 4, -6825618074587189525035775884745267807754020454400000⟩, + ⟨4, 2, 8, 6, 4, 4, 1680938663549042140558787685820177808899398696960000⟩, + ⟨4, 2, 5, 7, 0, 4, -1106097405880908674707570910459881612518845998694400000⟩, + ⟨4, 2, 6, 7, 1, 4, -196931120861925446417243556416358558096717722419200000⟩, + ⟨4, 2, 7, 7, 2, 4, 12121012820120455006203536749140839239889033625600000⟩, + ⟨4, 2, 8, 7, 3, 4, 8050769212938959135718268752539061804972889866240000⟩ +] + +def collectedFourData_9_2_35 : List CollectedFourTerm := [ + ⟨4, 3, 2, 0, 4, 5, -403150613485700919960651791339356109775726182400000⟩, + ⟨4, 3, 3, 0, 5, 5, 2771075305512380725105156172883584572792504320000000⟩, + ⟨4, 3, 4, 0, 6, 5, 1454212666755337480092086200796488522379821056000000⟩, + ⟨4, 3, 5, 0, 7, 5, 6266324843952295779541376282035067994243072000000⟩, + ⟨4, 3, 6, 0, 8, 5, 96509176470733973129849513668140183991615488000000⟩, + ⟨4, 3, 2, 1, 3, 5, 240699252463037516568331181709324136706840985600000⟩, + ⟨4, 3, 3, 1, 4, 5, -2650835755313360124464287093961175662735445196800000⟩, + ⟨4, 3, 4, 1, 5, 5, -2253478307973545935813772336076402098850024652800000⟩, + ⟨4, 3, 5, 1, 6, 5, -1033894990384167056669113873361327020125978624000000⟩, + ⟨4, 3, 6, 1, 7, 5, -322767866113186069267188670909404978421432320000000⟩, + ⟨4, 3, 7, 1, 8, 5, -121355905026129222957104652639353477698211020800000⟩, + ⟨4, 3, 2, 2, 2, 5, 58765657390877400849271625739519208762795622400000⟩, + ⟨4, 3, 3, 2, 3, 5, 1838827857184961364158961747107101587499332403200000⟩, + ⟨4, 3, 4, 2, 4, 5, 600820891035041018600598040503785366307943219200000⟩, + ⟨4, 3, 5, 2, 5, 5, 180850805874465740560883538111754509049921536000000⟩, + ⟨4, 3, 6, 2, 6, 5, 22280542512746282466848790121577411034218496000000⟩, + ⟨4, 3, 7, 2, 7, 5, 7164991635444271756535764404426860088262656000000⟩, + ⟨4, 3, 8, 2, 8, 5, 19304724517038826537311965841637019512681267200000⟩, + ⟨4, 3, 2, 3, 1, 5, 336789767060899632387554240555361542539837440000000⟩, + ⟨4, 3, 3, 3, 2, 5, -1212546538481892829943273603613376671244301107200000⟩, + ⟨4, 3, 4, 3, 3, 5, -766336978436535480960446755931070212975099904000000⟩, + ⟨4, 3, 5, 3, 4, 5, -244774016334047128583948240198486223872851968000000⟩, + ⟨4, 3, 6, 3, 5, 5, -54278486008646236655336267255471500569870336000000⟩, + ⟨4, 3, 7, 3, 6, 5, 5594576608095808624172452529916798326066380800000⟩, + ⟨4, 3, 8, 3, 7, 5, 11825239527594556256955075233981301748924416000000⟩, + ⟨4, 3, 2, 4, 0, 5, -1289759336524758503562294419786528613651500236800000⟩, + ⟨4, 3, 3, 4, 1, 5, 1119585778130099843529893125866481200719619686400000⟩, + ⟨4, 3, 4, 4, 2, 5, 2554896223579680539111295605678098685436415180800000⟩, + ⟨4, 3, 5, 4, 3, 5, 22831640833129506834278049240120282304217088000000⟩, + ⟨4, 3, 6, 4, 4, 5, 25084221767976857196175808496686813864263680000000⟩, + ⟨4, 3, 7, 4, 5, 5, 19261623880868464180288847520916122177110016000000⟩, + ⟨4, 3, 8, 4, 6, 5, -15083545736965786130337425140719535908087398400000⟩, + ⟨4, 3, 3, 5, 0, 5, -1344779062814096602798194662321631454629042585600000⟩, + ⟨4, 3, 4, 5, 1, 5, -2463238844716569866420155807645300290261457305600000⟩, + ⟨4, 3, 5, 5, 2, 5, 1773349762243990451374697261527585415095123968000000⟩, + ⟨4, 3, 6, 5, 3, 5, 9291848609864493431335443581441471988891648000000⟩, + ⟨4, 3, 7, 5, 4, 5, -12205353697836893160720834150743566580711424000000⟩, + ⟨4, 3, 8, 5, 5, 5, -5041973513646526480837267590449092600057036800000⟩, + ⟨4, 3, 4, 6, 0, 5, -7685363346536675529134958381498976413578113843200000⟩, + ⟨4, 3, 5, 6, 1, 5, -2265577647962011017510115802693056554577428480000000⟩, + ⟨4, 3, 6, 6, 2, 5, 665788573589445254610210706928157760010846208000000⟩, + ⟨4, 3, 7, 6, 3, 5, -36597978165565542184845936664224433512539750400000⟩, + ⟨4, 3, 8, 6, 4, 5, 7510791920718404158023200045067349674216652800000⟩, + ⟨4, 3, 5, 7, 0, 5, -9884557527015957536173814366787271396618665984000000⟩, + ⟨4, 3, 6, 7, 1, 5, -1319895279567958686657427505410592616096989184000000⟩, + ⟨4, 3, 7, 7, 2, 5, 64991119879226093986446591444667444976261529600000⟩, + ⟨4, 3, 8, 7, 3, 5, 35972551331791190540934072259682812332028723200000⟩ +] + +def collectedFourData_9_2_36 : List CollectedFourTerm := [ + ⟨4, 4, 1, 0, 3, 6, -947011089400661685023495279356442710055583744000000⟩, + ⟨4, 4, 2, 0, 4, 6, -1771702606655818610071521634126747725050413056000000⟩, + ⟨4, 4, 3, 0, 5, 6, 6088941921193413224174339562810792256890470400000000⟩, + ⟨4, 4, 4, 0, 6, 6, 2130248006690864569404499985906342562763898880000000⟩, + ⟨4, 4, 5, 0, 7, 6, 6884563540777155435319647208531684145233920000000⟩, + ⟨4, 4, 6, 0, 8, 6, 84824655500850601875944469593778914951430144000000⟩, + ⟨4, 4, 1, 1, 2, 6, -277917427844888336600621707927181063639531520000000⟩, + ⟨4, 4, 2, 1, 3, 6, 1057787037260693434330640643814954083878436864000000⟩, + ⟨4, 4, 3, 1, 4, 6, -5824737034254448259483154653628314015389188096000000⟩, + ⟨4, 4, 4, 1, 5, 6, -3301076784314242406387354708594733537709522944000000⟩, + ⟨4, 4, 5, 1, 6, 6, -1135899579585403859874249623760115904167280640000000⟩, + ⟨4, 4, 6, 1, 7, 6, -283689842261768276841742083863293492105052160000000⟩, + ⟨4, 4, 7, 1, 8, 6, -88885958942610343653378654909570756265377792000000⟩, + ⟨4, 4, 1, 2, 1, 6, -1018076074942027295546991387650450530467053568000000⟩, + ⟨4, 4, 2, 2, 2, 6, 258254024422942018980440041131875679816646656000000⟩, + ⟨4, 4, 3, 2, 3, 6, 4040495039308032860380222725865258517375483904000000⟩, + ⟨4, 4, 4, 2, 4, 6, 880130901597324840528232116664666006398959616000000⟩, + ⟨4, 4, 5, 2, 5, 6, 198693635495956482239984863592459728280616960000000⟩, + ⟨4, 4, 6, 2, 6, 6, 19583001452601518023776457348575698299650048000000⟩, + ⟨4, 4, 7, 2, 7, 6, 5247928827156138599633476953957503273533440000000⟩, + ⟨4, 4, 8, 2, 8, 6, 12119621800147925564684492056258023128039424000000⟩, + ⟨4, 4, 1, 3, 0, 6, -893503544501006597571175007683149890001567744000000⟩, + ⟨4, 4, 2, 3, 1, 6, 1480070445726769263847302663955308120480153600000000⟩, + ⟨4, 4, 3, 3, 2, 6, -2664353954897373630123355172399392510426742784000000⟩, + ⟨4, 4, 4, 3, 3, 6, -1122592216453706638629574954641950945228881920000000⟩, + ⟨4, 4, 5, 3, 4, 6, -268923541397529496990614086534906065169940480000000⟩, + ⟨4, 4, 6, 3, 5, 6, -47706902547110097033292228109902998266707968000000⟩, + ⟨4, 4, 7, 3, 6, 6, 4097693528645538399443437959656953916424192000000⟩, + ⟨4, 4, 8, 3, 7, 6, 7423956277858844220685091415211320771870720000000⟩, + ⟨4, 4, 2, 4, 0, 6, -5668030512771727238500167013830841238701473792000000⟩, + ⟨4, 4, 3, 4, 1, 6, 2460089325348670115598673785584413518392721408000000⟩, + ⟨4, 4, 4, 4, 2, 6, 3742618058558219322122793490514679776761872384000000⟩, + ⟨4, 4, 5, 4, 3, 6, 25084221767976857196175808496686813864263680000000⟩, + ⟨4, 4, 6, 4, 4, 6, 22047234758249227155908793099944741138595840000000⟩, + ⟨4, 4, 7, 4, 5, 6, 14107990122724117931697829471857443434659840000000⟩, + ⟨4, 4, 8, 4, 6, 6, -9469540452437380927286526169215001562185728000000⟩, + ⟨4, 4, 3, 5, 0, 6, -2954911255577698389942652951213845162001170432000000⟩, + ⟨4, 4, 4, 5, 1, 6, -3608350937190543169640740721485575037950885888000000⟩, + ⟨4, 4, 5, 5, 2, 6, 1948309323601953411527895020436571023715860480000000⟩, + ⟨4, 4, 6, 5, 3, 6, 8166869577804604366949797422471069485236224000000⟩, + ⟨4, 4, 7, 5, 4, 6, -8939693271888007272444624686911988705525760000000⟩, + ⟨4, 4, 8, 5, 5, 6, -3165381202815118929634469901490094925152256000000⟩, + ⟨4, 4, 4, 6, 0, 6, -11258140108340309360896126137081618220644827136000000⟩, + ⟨4, 4, 5, 6, 1, 6, -2489100655069337312809434097430661444717772800000000⟩, + ⟨4, 4, 6, 6, 2, 6, 585180481860741199818677821701390812791701504000000⟩, + ⟨4, 4, 7, 6, 3, 6, -26805835149979664865643059710885251824746496000000⟩, + ⟨4, 4, 8, 6, 4, 6, 4715320201454838573345954896809859771006976000000⟩, + ⟨4, 4, 5, 7, 0, 6, -10859772843229657638448572255422933171951370240000000⟩, + ⟨4, 4, 6, 7, 1, 6, -1160093438580965568390227655410938283443617792000000⟩, + ⟨4, 4, 7, 7, 2, 6, 47602117193846901582336114951244379748040704000000⟩, + ⟨4, 4, 8, 7, 3, 6, 22583783412341141557220950657987491548626944000000⟩ +] + +def collectedFourData_9_2_37 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 2, 7, -1722858279489095254577226877916049725485744128000000⟩, + ⟨4, 5, 1, 0, 3, 7, -3635945253508706422283668519252910982366756864000000⟩, + ⟨4, 5, 2, 0, 4, 7, -3401128960050552403969270326511149909402451968000000⟩, + ⟨4, 5, 3, 0, 5, 7, 7792608317911250994647428071702700239932620800000000⟩, + ⟨4, 5, 4, 0, 6, 7, 2044713418727211655887807051849759956737720320000000⟩, + ⟨4, 5, 5, 0, 7, 7, 5286505387050919979755151122156457614639104000000⟩, + ⟨4, 5, 6, 0, 8, 7, 54279160860375706762612627734621583042412544000000⟩, + ⟨4, 5, 0, 1, 1, 7, 12693526016214137270057183455279329149039149056000000⟩, + ⟨4, 5, 1, 1, 2, 7, -1067033495119348819004506475999608320420741120000000⟩, + ⟨4, 5, 2, 1, 3, 7, 2030628680275076091486818970727259284325793792000000⟩, + ⟨4, 5, 3, 1, 4, 7, -7454479752022441708840482411080483112738619392000000⟩, + ⟨4, 5, 4, 1, 5, 7, -3168530601101841548680029754383605108117078016000000⟩, + ⟨4, 5, 5, 1, 6, 7, -872232380609163871547328366264384135068909568000000⟩, + ⟨4, 5, 6, 1, 7, 7, -181532674570387364383995628614175756029788160000000⟩, + ⟨4, 5, 7, 1, 8, 7, -48752556353075738747729174070453719726555136000000⟩, + ⟨4, 5, 0, 2, 0, 7, 2041011432584504436947259460838919380291026944000000⟩, + ⟨4, 5, 1, 2, 1, 7, -3908791474383818175760323114124293916179038208000000⟩, + ⟨4, 5, 2, 2, 2, 7, 495769006725351178953678186297105734348832768000000⟩, + ⟨4, 5, 3, 2, 3, 7, 5171012576454296204722755366653652276093124608000000⟩, + ⟨4, 5, 4, 2, 4, 7, 844791526188567478327953207587882841170509824000000⟩, + ⟨4, 5, 5, 2, 5, 7, 152572485997207209914605703733053448416919552000000⟩, + ⟨4, 5, 6, 2, 6, 7, 12531131187017552045057979138212195727310848000000⟩, + ⟨4, 5, 7, 2, 7, 7, 2878406768925687021731791442804295094763520000000⟩, + ⟨4, 5, 8, 2, 8, 7, 5816494897971163161068699600667884145082368000000⟩, + ⟨4, 5, 1, 3, 0, 7, -3430508901091829460913447943136283776321060864000000⟩, + ⟨4, 5, 2, 3, 1, 7, 2841284105450414016453449024125593746984140800000000⟩, + ⟨4, 5, 3, 3, 2, 7, -3409831635694707637612463317109535337630138368000000⟩, + ⟨4, 5, 4, 3, 3, 7, -1077517435308984331228638142828681808974970880000000⟩, + ⟨4, 5, 5, 3, 4, 7, -206500490827392058142475174728285184564658176000000⟩, + ⟨4, 5, 6, 3, 5, 7, -30527570341607690729848354402141329338400768000000⟩, + ⟨4, 5, 7, 3, 6, 7, 2247520722613903807462449753598412860686336000000⟩, + ⟨4, 5, 8, 3, 7, 7, 3562933276713296897225209314920857904087040000000⟩, + ⟨4, 5, 2, 4, 0, 7, -10880890873568096574348097929007509549116030976000000⟩, + ⟨4, 5, 3, 4, 1, 7, 3148414418733586000414870872033816959218876416000000⟩, + ⟨4, 5, 4, 4, 2, 7, 3592342929775733261039963858108729816751538176000000⟩, + ⟨4, 5, 5, 4, 3, 7, 19261623880868464180288847520916122177110016000000⟩, + ⟨4, 5, 6, 4, 4, 7, 14107990122724117931697829471857443434659840000000⟩, + ⟨4, 5, 7, 4, 5, 7, 7738011623757418139976265201240832181534720000000⟩, + ⟨4, 5, 8, 4, 6, 7, -4544657798402693980445637273598503363280896000000⟩, + ⟨4, 5, 3, 5, 0, 7, -3781685936066743912733612761103973216644235264000000⟩, + ⟨4, 5, 4, 5, 1, 7, -3463466956700264642352579589511515882527916032000000⟩, + ⟨4, 5, 5, 5, 2, 7, 1496064009556746214367381468681669289418162176000000⟩, + ⟨4, 5, 6, 5, 3, 7, 5225966730096764579348505035369281826586624000000⟩, + ⟨4, 5, 7, 5, 4, 7, -4903281746651681632182506853772615042990080000000⟩, + ⟨4, 5, 8, 5, 5, 7, -1519141762004755214440769267734645038907392000000⟩, + ⟨4, 5, 4, 6, 0, 7, -10806098668855603786020836804406806244023599104000000⟩, + ⟨4, 5, 5, 6, 1, 7, -1911325815209286059068777107711261851107983360000000⟩, + ⟨4, 5, 6, 6, 2, 7, 374456050775859937903581687975292397791739904000000⟩, + ⟨4, 5, 7, 6, 3, 7, -14702580748264392524625357062977484507578368000000⟩, + ⟨4, 5, 8, 6, 4, 7, 2262994369488301284297262666004171883282432000000⟩, + ⟨4, 5, 5, 7, 0, 7, -8338981447094347863409769636234255012450009088000000⟩, + ⟨4, 5, 6, 7, 1, 7, -742341928699859886065408983743680913963220992000000⟩, + ⟨4, 5, 7, 7, 2, 7, 26109015739112676500559667333111464415199232000000⟩, + ⟨4, 5, 8, 7, 3, 7, 10838495058745541438962671940091640186667008000000⟩ +] + +def collectedFourData_9_2_38 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 2, 8, 8094897445109575113615655379798753956628476723200000⟩, + ⟨4, 6, 1, 0, 3, 8, 8541794845689223219054760324393315091224513740800000⟩, + ⟨4, 6, 2, 0, 4, 8, 5326766273034330933264022509600050565481916006400000⟩, + ⟨4, 6, 3, 0, 5, 8, -9153446617516556064404722818156071475876986880000000⟩, + ⟨4, 6, 4, 0, 6, 8, -1921428550019158315374245259029113611948235161600000⟩, + ⟨4, 6, 5, 0, 7, 8, -4139798715179942572865839959595545913825689600000⟩, + ⟨4, 6, 6, 0, 8, 8, -36433163407434773215550396497764961290603724800000⟩, + ⟨4, 6, 0, 1, 1, 8, -59640884303353467777668271020347856812859876966400000⟩, + ⟨4, 6, 1, 1, 2, 8, 2506743246475668063029703592661183179379441664000000⟩, + ⟨4, 6, 2, 1, 3, 8, -3180321738516117940752668358210931996619282841600000⟩, + ⟨4, 6, 3, 1, 4, 8, 8756270004570834756571072065672256129598698291200000⟩, + ⟨4, 6, 4, 1, 5, 8, 2977485794736043123362757173779026043660748718080000⟩, + ⟨4, 6, 5, 1, 6, 8, 683034674934566398757370680174278226008552243200000⟩, + ⟨4, 6, 6, 1, 7, 8, 121848044287651184965106001175702167588175872000000⟩, + ⟨4, 6, 7, 1, 8, 8, 28633154897547921069469996289164380738473164800000⟩, + ⟨4, 6, 0, 2, 0, 8, -9589748865453510764463276763569677700236417433600000⟩, + ⟨4, 6, 1, 2, 1, 8, 9182782616582576194313524025625256034270026137600000⟩, + ⟨4, 6, 2, 2, 2, 8, -776461479485058706047415843413457042896479846400000⟩, + ⟨4, 6, 3, 2, 3, 8, -6074036528730381140672648863764877554114940108800000⟩, + ⟨4, 6, 4, 2, 4, 8, -793855286695081589850566540286023556752599941120000⟩, + ⟨4, 6, 5, 2, 5, 8, -119477676699275514422808845457860370035952844800000⟩, + ⟨4, 6, 6, 2, 6, 8, -8411123955858672695847543693055458039929241600000⟩, + ⟨4, 6, 7, 2, 7, 8, -1690534261955680622616778942484124832628736000000⟩, + ⟨4, 6, 8, 2, 8, 8, -3036551413144939852560143838992253949103308800000⟩, + ⟨4, 6, 1, 3, 0, 8, 8059170643771362165746459464481079364347022540800000⟩, + ⟨4, 6, 2, 3, 1, 8, -4449950743648611631622096998879684181455011840000000⟩, + ⟨4, 6, 3, 3, 2, 8, 4005297145541215615622748340649875073804324044800000⟩, + ⟨4, 6, 4, 3, 3, 8, 1012549115384034940345904790533532070355297894400000⟩, + ⟨4, 6, 5, 3, 4, 8, 161708047948884268901845258437886279682516582400000⟩, + ⟨4, 6, 6, 3, 5, 8, 20490662365778767806610684797253602336414105600000⟩, + ⟨4, 6, 7, 3, 6, 8, -1320004812055209335813501480411640013573324800000⟩, + ⟨4, 6, 8, 3, 7, 8, -1860060099101720378822984315460770661924864000000⟩, + ⟨4, 6, 2, 4, 0, 8, 17041389258297371924848986070058987571060198604800000⟩, + ⟨4, 6, 3, 4, 1, 8, -3698228133121666648280475203593732396120906137600000⟩, + ⟨4, 6, 4, 4, 2, 8, -3375744592622261262371550436198694906130994298880000⟩, + ⟨4, 6, 5, 4, 3, 8, -15083545736965786130337425140719535908087398400000⟩, + ⟨4, 6, 6, 4, 4, 8, -9469540452437380927286526169215001562185728000000⟩, + ⟨4, 6, 7, 4, 5, 8, -4544657798402693980445637273598503363280896000000⟩, + ⟨4, 6, 8, 4, 6, 8, 2372577867267354598885774785278717464254873600000⟩, + ⟨4, 6, 3, 5, 0, 8, 4442089083373624161922504253601694449328875110400000⟩, + ⟨4, 6, 4, 5, 1, 8, 3254639125317778376792038603129035829715046236160000⟩, + ⟨4, 6, 5, 5, 2, 8, -1171549712171004738871161799460103643046766182400000⟩, + ⟨4, 6, 6, 5, 3, 8, -3507764247299292320925097752340575080467660800000⟩, + ⟨4, 6, 7, 5, 4, 8, 2879775672508698818982991736244131535519744000000⟩, + ⟨4, 6, 8, 5, 5, 8, 793081081493265893953620915208954804646707200000⟩, + ⟨4, 6, 4, 6, 0, 8, 10154550905029895886254635004978472641252315627520000⟩, + ⟨4, 6, 5, 6, 1, 8, 1496736232119429218229542112249503753818865664000000⟩, + ⟨4, 6, 6, 6, 2, 8, -251341735402155716379783477129579348022316236800000⟩, + ⟨4, 6, 7, 6, 3, 8, 8635060465546258042977469290095944078354022400000⟩, + ⟨4, 6, 8, 6, 4, 8, -1181415761751229807077732865063926451352371200000⟩, + ⟨4, 6, 5, 7, 0, 8, 6530155963739310975548588241461219545056490291200000⟩, + ⟨4, 6, 6, 7, 1, 8, 498273450875251500144138486649173183568438886400000⟩, + ⟨4, 6, 7, 7, 2, 8, -15334241890135588048088447949684566904117657600000⟩, + ⟨4, 6, 8, 7, 3, 8, -5658329984691992089513097596969171888688332800000⟩ +] + +def collectedFourData_9_2_39 : List CollectedFourTerm := [ + ⟨5, 0, 4, 0, 6, 3, -28550944738262740994494382965524464193411376742400000⟩, + ⟨5, 0, 5, 0, 7, 3, -369085275671963326255728201275713876474095206400000⟩, + ⟨5, 0, 6, 0, 8, 3, -11368742249917796841641761849477773377448129331200000⟩, + ⟨5, 0, 4, 1, 5, 3, 44243140023928270484474445978687398121279974277120000⟩, + ⟨5, 0, 5, 1, 6, 3, 60896207433306688720210886016270916878838058188800000⟩, + ⟨5, 0, 6, 1, 7, 3, 38021925070612740028401987400845738423739219968000000⟩, + ⟨5, 0, 7, 1, 8, 3, 23826128167303421773698831888442575859118977843200000⟩, + ⟨5, 0, 4, 2, 4, 3, -11796076632869333860696678211334626189829136711680000⟩, + ⟨5, 0, 5, 2, 5, 3, -10652076169669773569492804716704151665548407603200000⟩, + ⟨5, 0, 6, 2, 6, 3, -2624638964695352555536866135702081312842475110400000⟩, + ⟨5, 0, 7, 2, 7, 3, -1406721897768350235798847502516141071295053824000000⟩, + ⟨5, 0, 8, 2, 8, 3, -5685221998201300233959498124647112520942957363200000⟩, + ⟨5, 0, 4, 3, 3, 3, 15045698075954036990895477641148718704095762841600000⟩, + ⟨5, 0, 5, 3, 4, 3, 14417140436499400374675637749994289814329465241600000⟩, + ⟨5, 0, 6, 3, 5, 3, 6393983864686639167182550586578975745057908326400000⟩, + ⟨5, 0, 7, 3, 6, 3, -1098398131327751152969682741440108411321791283200000⟩, + ⟨5, 0, 8, 3, 7, 3, -3482521174386200048477200788360999097960759296000000⟩, + ⟨5, 0, 4, 4, 2, 3, -50160958269037092659001187294763585872649854648320000⟩, + ⟨5, 0, 5, 4, 3, 3, -1344779062814096602798194662321631454629042585600000⟩, + ⟨5, 0, 6, 4, 4, 3, -2954911255577698389942652951213845162001170432000000⟩, + ⟨5, 0, 7, 4, 5, 3, -3781685936066743912733612761103973216644235264000000⟩, + ⟨5, 0, 8, 4, 6, 3, 4442089083373624161922504253601694449328875110400000⟩, + ⟨5, 0, 4, 5, 1, 3, 48361424529165630864675994317958223708182271754240000⟩, + ⟨5, 0, 5, 5, 2, 3, -104449945088996816281664427676957179164671711641600000⟩, + ⟨5, 0, 6, 5, 3, 3, -1094576036537212662276463955275133249624683315200000⟩, + ⟨5, 0, 7, 5, 4, 3, 2396309610721611520125386120691920263232618496000000⟩, + ⟨5, 0, 8, 5, 5, 3, 1484856140207094371494860810178955391062035660800000⟩, + ⟨5, 0, 4, 6, 0, 3, 150888786225485035879599110270145998215200406241280000⟩, + ⟨5, 0, 5, 6, 1, 3, 133442068768796000201890350531238776308263550976000000⟩, + ⟨5, 0, 6, 6, 2, 3, -78429626724399146227647784017266128307690353459200000⟩, + ⟨5, 0, 7, 6, 3, 3, 7185378562742277922831017976883572196414953881600000⟩, + ⟨5, 0, 8, 6, 4, 3, -2211920683659191023956256830127960491658366156800000⟩, + ⟨5, 0, 5, 7, 0, 3, 582198454533525950489730126791099409316981820620800000⟩, + ⟨5, 0, 6, 7, 1, 3, 155483134133277861799742054422259777088469440921600000⟩, + ⟨5, 0, 7, 7, 2, 3, -12759879724399207889683049803704638256403867238400000⟩, + ⟨5, 0, 8, 7, 3, 3, -10593880269175427390409307601407907092243886899200000⟩ +] + +def collectedFourData_9_2_40 : List CollectedFourTerm := [ + ⟨5, 1, 3, 0, 5, 4, -99654398969994735132077029188152817633856585728000000⟩, + ⟨5, 1, 4, 0, 6, 4, -104593829688984557734121377876683942513433431244800000⟩, + ⟨5, 1, 5, 0, 7, 4, -676055430358663053384304444696631611234870886400000⟩, + ⟨5, 1, 6, 0, 8, 4, -13882789770668947311994265640416678533472767180800000⟩, + ⟨5, 1, 3, 1, 4, 4, 95330301359341630010131821591414713452031870238720000⟩, + ⟨5, 1, 4, 1, 5, 4, 162080782089392464418257344545542629249761138442240000⟩, + ⟨5, 1, 5, 1, 6, 4, 111543901740813578176135233212054495475572460748800000⟩, + ⟨5, 1, 6, 1, 7, 4, 46429972711823986498612116442704642674327027712000000⟩, + ⟨5, 1, 7, 1, 8, 4, 21821221806533540318474554827181382665630226841600000⟩, + ⟨5, 1, 3, 2, 3, 4, -66128583569174287770855449994805348681987160801280000⟩, + ⟨5, 1, 4, 2, 4, 4, -43213870561805416911088539360564349108164608655360000⟩, + ⟨5, 1, 5, 2, 5, 4, -19511463647495473450500724445286947293760795443200000⟩, + ⟨5, 1, 6, 2, 6, 4, -3205043281813803236270826509901373684080810393600000⟩, + ⟨5, 1, 7, 2, 7, 4, -1288349929781524637870065100247694585010061312000000⟩, + ⟨5, 1, 8, 2, 8, 4, -4165460350788502039823288480035002514308102881280000⟩, + ⟨5, 1, 3, 3, 2, 4, 43606031303150649080071578865059127335727273082880000⟩, + ⟨5, 1, 4, 3, 3, 4, 55118567757907909416370028630090146767787209523200000⟩, + ⟨5, 1, 5, 3, 4, 4, 26407951562396279433257638630488330927018187161600000⟩, + ⟨5, 1, 6, 3, 5, 4, 7807929130518885080697999923414121185717885337600000⟩, + ⟨5, 1, 7, 3, 6, 4, -1005970801772006661763763551905477471074097561600000⟩, + ⟨5, 1, 8, 3, 7, 4, -2551580901726732027315812178320386217757533798400000⟩, + ⟨5, 1, 3, 4, 1, 4, -40262943267172964769252419069765673953738159554560000⟩, + ⟨5, 1, 4, 4, 2, 4, -183760179367961830155722005432200762121547038064640000⟩, + ⟨5, 1, 5, 4, 3, 4, -2463238844716569866420155807645300290261457305600000⟩, + ⟨5, 1, 6, 4, 4, 4, -3608350937190543169640740721485575037950885888000000⟩, + ⟨5, 1, 7, 4, 5, 4, -3463466956700264642352579589511515882527916032000000⟩, + ⟨5, 1, 8, 4, 6, 4, 3254639125317778376792038603129035829715046236160000⟩, + ⟨5, 1, 3, 5, 0, 4, 48361424529165630864675994317958223708182271754240000⟩, + ⟨5, 1, 4, 5, 1, 4, 177167748636398238665080783067966474799670603284480000⟩, + ⟨5, 1, 5, 5, 2, 4, -191321510860923477125974775858670588115384113561600000⟩, + ⟨5, 1, 6, 5, 3, 4, -1336627101680315677742311740058662984982777036800000⟩, + ⟨5, 1, 7, 5, 4, 4, 2194666425258402283984479889980223070140366848000000⟩, + ⟨5, 1, 8, 5, 5, 4, 1087927504082401608174576930154202289148337848320000⟩, + ⟨5, 1, 4, 6, 0, 4, 552767558241096625370707186652223351751602402754560000⟩, + ⟨5, 1, 5, 6, 1, 4, 244426535480704350848258332072462853008760242176000000⟩, + ⟨5, 1, 6, 6, 2, 4, -95773305056216331475537778048555213776300592332800000⟩, + ⟨5, 1, 7, 6, 3, 4, 6580747752237745325449703854276487101851421900800000⟩, + ⟨5, 1, 8, 6, 4, 4, -1620634675266223958465784563348391761283876126720000⟩, + ⟨5, 1, 5, 7, 0, 4, 1066415955004487781193969835614135500203591781580800000⟩, + ⟨5, 1, 6, 7, 1, 4, 189866180146060162519143506557308530098348385894400000⟩, + ⟨5, 1, 7, 7, 2, 4, -11686169222950077214279083443557285629021860659200000⟩, + ⟨5, 1, 8, 7, 3, 4, -7761946364840682967419797235724026345181339975680000⟩ +] + +def collectedFourData_9_2_41 : List CollectedFourTerm := [ + ⟨5, 2, 2, 0, 4, 5, -31312994532394822478508847418512940115874440806400000⟩, + ⟨5, 2, 3, 0, 5, 5, 215231387446322466677461574296143940659204587520000000⟩, + ⟨5, 2, 4, 0, 6, 5, 112949730844609650549559110435271754075514863616000000⟩, + ⟨5, 2, 5, 0, 7, 5, 486709901990134465624859726664985310807457792000000⟩, + ⟨5, 2, 6, 0, 8, 5, 7495936292953712555661126166252571591461306368000000⟩, + ⟨5, 2, 2, 1, 3, 5, 18695281922456853947997494914854144754132294041600000⟩, + ⟨5, 2, 3, 1, 4, 5, -205892296168732025231884312642733794948394306764800000⟩, + ⟨5, 2, 4, 1, 5, 5, -175029260966134526771321006772185725190716312780800000⟩, + ⟨5, 2, 5, 1, 6, 5, -80303358343067695110556591957248819838649892864000000⟩, + ⟨5, 2, 6, 1, 7, 5, -25069609443105589720071301705348802634338795520000000⟩, + ⟨5, 2, 7, 1, 8, 5, -9425799350028249365732932840387847579887258828800000⟩, + ⟨5, 2, 2, 2, 2, 5, 4564370354451656413032879942067306555523884646400000⟩, + ⟨5, 2, 3, 2, 3, 5, 142823065901374899263187089054269876579855446835200000⟩, + ⟨5, 2, 4, 2, 4, 5, 46666185407147119098809075239004744037717717811200000⟩, + ⟨5, 2, 5, 2, 5, 5, 14046810561847748855134456021373114222584528896000000⟩, + ⟨5, 2, 6, 2, 6, 5, 1730545564220405066405025932949309599520915456000000⟩, + ⟨5, 2, 7, 2, 7, 5, 556509990064243569729190524263622344982921216000000⟩, + ⟨5, 2, 8, 2, 8, 5, 1499411666585161386112407776173586439155692339200000⟩, + ⟨5, 2, 2, 3, 1, 5, 26158700450343036429447196963378705060425891840000000⟩, + ⟨5, 2, 3, 3, 2, 5, -94179350991126437843137405173425238645343990579200000⟩, + ⟨5, 2, 4, 3, 3, 5, -59521937491994697008771553370556630556626386944000000⟩, + ⟨5, 2, 5, 3, 4, 5, -19011771726876435851425212341851505490445467648000000⟩, + ⟨5, 2, 6, 3, 5, 5, -4215848565676785794004373287441500809457565696000000⟩, + ⟨5, 2, 7, 3, 6, 5, 434534739326600265736554122600971951227587788800000⟩, + ⟨5, 2, 8, 3, 7, 5, 918474754311544208011648689441916669264920576000000⟩, + ⟨5, 2, 2, 4, 0, 5, -100176523864169610188105782484007464852305792204800000⟩, + ⟨5, 2, 3, 4, 1, 5, 86959022698791585102235495264099589703776757350400000⟩, + ⟨5, 2, 4, 4, 2, 5, 198440604587159420842289942679917705618395024588800000⟩, + ⟨5, 2, 5, 4, 3, 5, 1773349762243990451374697261527585415095123968000000⟩, + ⟨5, 2, 6, 4, 4, 5, 1948309323601953411527895020436571023715860480000000⟩, + ⟨5, 2, 7, 4, 5, 5, 1496064009556746214367381468681669289418162176000000⟩, + ⟨5, 2, 8, 4, 6, 5, -1171549712171004738871161799460103643046766182400000⟩, + ⟨5, 2, 3, 5, 0, 5, -104449945088996816281664427676957179164671711641600000⟩, + ⟨5, 2, 4, 5, 1, 5, -191321510860923477125974775858670588115384113561600000⟩, + ⟨5, 2, 5, 5, 2, 5, 137737335754145512643510982222957728527074459648000000⟩, + ⟨5, 2, 6, 5, 3, 5, 721704482106281167618330838814651335602864128000000⟩, + ⟨5, 2, 7, 5, 4, 5, -947998491933008233115111573297799925453553664000000⟩, + ⟨5, 2, 8, 5, 5, 5, -391613664432369543415578479140145915069517004800000⟩, + ⟨5, 2, 4, 6, 0, 5, -596927630517188862351676854432490908342377722675200000⟩, + ⟨5, 2, 5, 6, 1, 5, -175969025297952493614206371608163727072066273280000000⟩, + ⟨5, 2, 6, 6, 2, 5, 51712271461734201413929313335826712325980684288000000⟩, + ⟨5, 2, 7, 6, 3, 5, -2842590961940097241730593780562404792938686054400000⟩, + ⟨5, 2, 8, 6, 4, 5, 583368543864940019233808229366212077206424780800000⟩, + ⟨5, 2, 5, 7, 0, 5, -767740604739451178995568053195139961830007373824000000⟩, + ⟨5, 2, 6, 7, 1, 5, -102517203967770044602207725476502868169299329024000000⟩, + ⟨5, 2, 7, 7, 2, 5, 5047906448254985862140680706692448548034288025600000⟩, + ⟨5, 2, 8, 7, 3, 5, 2794013615481256022863371914140545890926146355200000⟩ +] + +def collectedFourData_9_2_42 : List CollectedFourTerm := [ + ⟨5, 3, 1, 0, 3, 6, -350797555370341925405504853324710583330039398400000⟩, + ⟨5, 3, 2, 0, 4, 6, -656284757606650889695694936200884003391773081600000⟩, + ⟨5, 3, 3, 0, 5, 6, 2255502564493148250619320944299221311752765440000000⟩, + ⟨5, 3, 4, 0, 6, 6, 789099305640271359825290003112771409693114368000000⟩, + ⟨5, 3, 5, 0, 7, 6, 2550221520029778017134426897305868500467712000000⟩, + ⟨5, 3, 6, 0, 8, 6, 31421260128708506358021617059347110725838438400000⟩, + ⟨5, 3, 1, 1, 2, 6, -102947848630263467334743563011362038399107072000000⟩, + ⟨5, 3, 2, 1, 3, 6, 391831849623142093217844659579507710676592230400000⟩, + ⟨5, 3, 3, 1, 4, 6, -2157634197910722323282120466593268651425110425600000⟩, + ⟨5, 3, 4, 1, 5, 6, -1222804758030974550969499497017997704548476518400000⟩, + ⟨5, 3, 5, 1, 6, 6, -420766768335247764664052722835256003740565504000000⟩, + ⟨5, 3, 6, 1, 7, 6, -105086101168897980588454660203361596736536576000000⟩, + ⟨5, 3, 7, 1, 8, 6, -32925672627075474057453125170548591633314611200000⟩, + ⟨5, 3, 1, 2, 1, 6, -377121875623145854924689040064590927285243084800000⟩, + ⟨5, 3, 2, 2, 2, 6, 95664012223400410974573839691958730433862041600000⟩, + ⟨5, 3, 3, 2, 3, 6, 1496704524518592384670437453295141643400668774400000⟩, + ⟨5, 3, 4, 2, 4, 6, 326023393117428891332653096611944280440281497600000⟩, + ⟨5, 3, 5, 2, 5, 6, 73601293986683308439026647309724490039033856000000⟩, + ⟨5, 3, 6, 2, 6, 6, 7254053424795795719320576375514408736836812800000⟩, + ⟨5, 3, 7, 2, 7, 6, 1943969425415086163380332407191080045379584000000⟩, + ⟨5, 3, 8, 2, 8, 6, 4489423352154913440520875888748642294982246400000⟩, + ⟨5, 3, 1, 3, 0, 6, -330976968098711294764559818895242423716701798400000⟩, + ⟨5, 3, 2, 3, 1, 6, 548256614888674841342269835231143467637800960000000⟩, + ⟨5, 3, 3, 3, 2, 6, -986946050030750433540709032301619234013079142400000⟩, + ⟨5, 3, 4, 3, 3, 6, -415837374680544970017736220086606286146240512000000⟩, + ⟨5, 3, 5, 3, 4, 6, -99616279006291410480288463070990439051952128000000⟩, + ⟨5, 3, 6, 3, 5, 6, -17671878370937339609009783229057063468190924800000⟩, + ⟨5, 3, 7, 3, 6, 6, 1517892333674208690506139727434240083833651200000⟩, + ⟨5, 3, 8, 3, 7, 6, 2750026628618870530383854363225922251784192000000⟩, + ⟨5, 3, 2, 4, 0, 6, -2099586023753100791432332574423535425076540211200000⟩, + ⟨5, 3, 3, 4, 1, 6, 911281114850674984510743470312732560508898508800000⟩, + ⟨5, 3, 4, 4, 2, 6, 1386363138005088291305866238774735500080473702400000⟩, + ⟨5, 3, 5, 4, 3, 6, 9291848609864493431335443581441471988891648000000⟩, + ⟨5, 3, 6, 4, 4, 6, 8166869577804604366949797422471069485236224000000⟩, + ⟨5, 3, 7, 4, 5, 6, 5225966730096764579348505035369281826586624000000⟩, + ⟨5, 3, 8, 4, 6, 6, -3507764247299292320925097752340575080467660800000⟩, + ⟨5, 3, 3, 5, 0, 6, -1094576036537212662276463955275133249624683315200000⟩, + ⟨5, 3, 4, 5, 1, 6, -1336627101680315677742311740058662984982777036800000⟩, + ⟨5, 3, 5, 5, 2, 6, 721704482106281167618330838814651335602864128000000⟩, + ⟨5, 3, 6, 5, 3, 6, 3025221050722228153230415485037681937114726400000⟩, + ⟨5, 3, 7, 5, 4, 6, -3311495061291956226118929067452313985089536000000⟩, + ⟨5, 3, 8, 5, 5, 6, -1172539582894983948602403849023281149090201600000⟩, + ⟨5, 3, 4, 6, 0, 6, -4170308111726550480595430816682671953778678169600000⟩, + ⟨5, 3, 5, 6, 1, 6, -922027666457049327591705513744017391699886080000000⟩, + ⟨5, 3, 6, 6, 2, 6, 216766080972824666140393290522309540083820134400000⟩, + ⟨5, 3, 7, 6, 3, 6, -9929579014987487096272209364252082984032665600000⟩, + ⟨5, 3, 8, 6, 4, 6, 1746677328251347324223555630626705688336793600000⟩, + ⟨5, 3, 5, 7, 0, 6, -4022742508425297431170414243034610445597016064000000⟩, + ⟨5, 3, 6, 7, 1, 6, -429728803400739019383514631672673554998178611200000⟩, + ⟨5, 3, 7, 7, 2, 6, 17633063148840405036711025596382451622897254400000⟩, + ⟨5, 3, 8, 7, 3, 6, 8365621164031340338613830283900942431970918400000⟩ +] + +def collectedFourData_9_2_43 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 2, 7, 1091709338863023520504214313114530638454587392000000⟩, + ⟨5, 4, 1, 0, 3, 7, 2303959319293077366780963179399335596729040896000000⟩, + ⟨5, 4, 2, 0, 4, 7, 2155165223146360848635136265281575223822385152000000⟩, + ⟨5, 4, 3, 0, 5, 7, -4937877581717385784841639059896234369299251200000000⟩, + ⟨5, 4, 4, 0, 6, 7, -1295656619640818006168360199135300988415508480000000⟩, + ⟨5, 4, 5, 0, 7, 7, -3349856090719562544006029667394665899360256000000⟩, + ⟨5, 4, 6, 0, 8, 7, -34394626373152900067855283248762799223996416000000⟩, + ⟨5, 4, 0, 1, 1, 7, -8043401514784568687045095815723352665026985984000000⟩, + ⟨5, 4, 1, 1, 2, 7, 676138278678898527149512879584558819500359680000000⟩, + ⟨5, 4, 2, 1, 3, 7, -1286731660062483259758411824401121309242687488000000⟩, + ⟨5, 4, 3, 1, 4, 7, 4723618453435145252717024485276471762656165888000000⟩, + ⟨5, 4, 4, 1, 5, 7, 2007776547193384070794416139149656879397863424000000⟩, + ⟨5, 4, 5, 1, 6, 7, 552700269607856879145418434035594300649111552000000⟩, + ⟨5, 4, 6, 1, 7, 7, 115030306611199338685359856433071745390346240000000⟩, + ⟨5, 4, 7, 1, 8, 7, 30892628661181465495314606096694599015727104000000⟩, + ⟨5, 4, 0, 2, 0, 7, -1293310812738155381759369864299241842478678016000000⟩, + ⟨5, 4, 1, 2, 1, 7, 2476851524617809118545792656379218147527360512000000⟩, + ⟨5, 4, 2, 2, 2, 7, -314149840996446696400892519566228070546276352000000⟩, + ⟨5, 4, 3, 2, 3, 7, -3276672717832233546194391280166995796649050112000000⟩, + ⟨5, 4, 4, 2, 4, 7, -535312050626647647944829719173242209578254336000000⟩, + ⟨5, 4, 5, 2, 5, 7, -96679343739226729944857300743214630204080128000000⟩, + ⟨5, 4, 6, 2, 6, 7, -7940498128169651345387129909615476680425472000000⟩, + ⟨5, 4, 7, 2, 7, 7, -1823936180992537089625729271096910576353280000000⟩, + ⟨5, 4, 8, 2, 8, 7, -3685690155226978142372587896172961964490752000000⟩, + ⟨5, 4, 1, 3, 0, 7, 2173782167088795087431739448183405479142096896000000⟩, + ⟨5, 4, 2, 3, 1, 7, -1800412970243337844007013082402966199284531200000000⟩, + ⟨5, 4, 3, 3, 2, 7, 2160679775554372875286688013189433184854474752000000⟩, + ⟨5, 4, 4, 3, 3, 7, 682781550240678144593588380357853094158008320000000⟩, + ⟨5, 4, 5, 3, 4, 7, 130851455978674384317825046290996269011697664000000⟩, + ⟨5, 4, 6, 3, 5, 7, 19344152697582297100155752157885140777828352000000⟩, + ⟨5, 4, 7, 3, 6, 7, -1424167844434298978832398528785234897403904000000⟩, + ⟨5, 4, 8, 3, 7, 7, -2257694424574031815598508050761954948546560000000⟩, + ⟨5, 4, 2, 4, 0, 7, 6894804014492893313775611385151741931619876864000000⟩, + ⟨5, 4, 3, 4, 1, 7, -1995029692495498703292044114798392681665921024000000⟩, + ⟨5, 4, 4, 4, 2, 7, -2276330195886866903652544186908345839244017664000000⟩, + ⟨5, 4, 5, 4, 3, 7, -12205353697836893160720834150743566580711424000000⟩, + ⟨5, 4, 6, 4, 4, 7, -8939693271888007272444624686911988705525760000000⟩, + ⟨5, 4, 7, 4, 5, 7, -4903281746651681632182506853772615042990080000000⟩, + ⟨5, 4, 8, 4, 6, 7, 2879775672508698818982991736244131535519744000000⟩, + ⟨5, 4, 3, 5, 0, 7, 2396309610721611520125386120691920263232618496000000⟩, + ⟨5, 4, 4, 5, 1, 7, 2194666425258402283984479889980223070140366848000000⟩, + ⟨5, 4, 5, 5, 2, 7, -947998491933008233115111573297799925453553664000000⟩, + ⟨5, 4, 6, 5, 3, 7, -3311495061291956226118929067452313985089536000000⟩, + ⟨5, 4, 7, 5, 4, 7, 3107021940007526794112529979726535715717120000000⟩, + ⟨5, 4, 8, 5, 5, 7, 962621980218377612197641315967259941797888000000⟩, + ⟨5, 4, 4, 6, 0, 7, 6847411057491812121697963766026579691496800256000000⟩, + ⟨5, 4, 5, 6, 1, 7, 1211134001510985138943606758739842905973719040000000⟩, + ⟨5, 4, 6, 6, 2, 7, -237278464800366233290683254092968174557331456000000⟩, + ⟨5, 4, 7, 6, 3, 7, 9316462589730690186277345285550989746634752000000⟩, + ⟨5, 4, 8, 6, 4, 7, -1433972902110927964404513735906673135976448000000⟩, + ⟨5, 4, 5, 7, 0, 7, 5284093317935621499166815367870299331029368832000000⟩, + ⟨5, 4, 6, 7, 1, 7, 470393662577720632982894445855640585437708288000000⟩, + ⟨5, 4, 7, 7, 2, 7, -16544283792955697173969095132777535292571648000000⟩, + ⟨5, 4, 8, 7, 3, 7, -6867939409596769127746643420457408462323712000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0910.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0910.lean new file mode 100644 index 0000000000000000000000000000000000000000..13ad85466a48bdb6371810f77f88259847b1528a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0910.lean @@ -0,0 +1,631 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PartsTrace +import OAI.Analysis.LaughlinFock.Sparse0907 +import OAI.Analysis.LaughlinFock.Sparse0908 +import OAI.Analysis.LaughlinFock.Sparse0909 + +namespace OAI + +/-! Sparse0910. -/ +namespace LaughlinFock +def collectedFourData_9_2_44 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 2, 8, 2705879587310989387891446164834364596249060966400000⟩, + ⟨5, 5, 1, 0, 3, 8, 2855263883041797540709291154553826684060670361600000⟩, + ⟨5, 5, 2, 0, 4, 8, 1780576989679839665870891622412611292016463052800000⟩, + ⟨5, 5, 3, 0, 5, 8, -3059720586187562406978540426160594747140341760000000⟩, + ⟨5, 5, 4, 0, 6, 8, -642275498513497896750428476438341810277004083200000⟩, + ⟨5, 5, 5, 0, 7, 8, -1383809605364313051336910695428246522245939200000⟩, + ⟨5, 5, 6, 0, 8, 8, -12178505513359098885985223905819310329272729600000⟩, + ⟨5, 5, 0, 1, 1, 8, -19936145269279077423212471366267363633883040972800000⟩, + ⟨5, 5, 1, 1, 2, 8, 837928513271779237435272596457107526650953728000000⟩, + ⟨5, 5, 2, 1, 3, 8, -1063085447553273333461892719137688746200347443200000⟩, + ⟨5, 5, 3, 1, 4, 8, 2926956447195731449694721257854183418964108902400000⟩, + ⟨5, 5, 4, 1, 5, 8, 995283521269569255240458823870117137824780124160000⟩, + ⟨5, 5, 5, 1, 6, 8, 228317850456229264823747456873569996375484006400000⟩, + ⟨5, 5, 6, 1, 7, 8, 40730118945596813409806598580932062629330944000000⟩, + ⟨5, 5, 7, 1, 8, 8, 9571198385520724548305139526257767391795609600000⟩, + ⟨5, 5, 0, 2, 0, 8, -3205563242576462863173251561582486869337387827200000⟩, + ⟨5, 5, 1, 2, 1, 8, 3069526724138584170734057034278319914006819635200000⟩, + ⟨5, 5, 2, 2, 2, 8, -259547607850326625823955694015047963480214732800000⟩, + ⟨5, 5, 3, 2, 3, 8, -2030366853579126545526439115431732519609407897600000⟩, + ⟨5, 5, 4, 2, 4, 8, -265361831958089431245880374697504165022914314240000⟩, + ⟨5, 5, 5, 2, 5, 8, -39937776693542194133411998403371150763202969600000⟩, + ⟨5, 5, 6, 2, 6, 8, -2811584553458461029117394019273319176680243200000⟩, + ⟨5, 5, 7, 2, 7, 8, -565094515661749043320719622363870314627072000000⟩, + ⟨5, 5, 8, 2, 8, 8, -1015027372534922799752853357786994969254297600000⟩, + ⟨5, 5, 1, 3, 0, 8, 2693937197291040621754290468878193794473367961600000⟩, + ⟨5, 5, 2, 3, 1, 8, -1487484055656883536763730365240019875717447680000000⟩, + ⟨5, 5, 3, 3, 2, 8, 1338849795284620025308034405753991914900265369600000⟩, + ⟨5, 5, 4, 3, 3, 8, 338464569940005280286043549485351196865383628800000⟩, + ⟨5, 5, 5, 3, 4, 8, 54054113596354482766020027330122231730457804800000⟩, + ⟨5, 5, 6, 3, 5, 8, 6849409199067592254265612906713503321240371200000⟩, + ⟨5, 5, 7, 3, 6, 8, -441237717996082811920474108129114177771929600000⟩, + ⟨5, 5, 8, 3, 7, 8, -621761879932361704264246555399309259440128000000⟩, + ⟨5, 5, 2, 4, 0, 8, 5696421436605789420885591059604022904403630489600000⟩, + ⟨5, 5, 3, 4, 1, 8, -1236205904088225131555137083177019614476579635200000⟩, + ⟨5, 5, 4, 4, 2, 8, -1128409401983274008944803236522861362176338165760000⟩, + ⟨5, 5, 5, 4, 3, 8, -5041973513646526480837267590449092600057036800000⟩, + ⟨5, 5, 6, 4, 4, 8, -3165381202815118929634469901490094925152256000000⟩, + ⟨5, 5, 7, 4, 5, 8, -1519141762004755214440769267734645038907392000000⟩, + ⟨5, 5, 8, 4, 6, 8, 793081081493265893953620915208954804646707200000⟩, + ⟨5, 5, 3, 5, 0, 8, 1484856140207094371494860810178955391062035660800000⟩, + ⟨5, 5, 4, 5, 1, 8, 1087927504082401608174576930154202289148337848320000⟩, + ⟨5, 5, 5, 5, 2, 8, -391613664432369543415578479140145915069517004800000⟩, + ⟨5, 5, 6, 5, 3, 8, -1172539582894983948602403849023281149090201600000⟩, + ⟨5, 5, 7, 5, 4, 8, 962621980218377612197641315967259941797888000000⟩, + ⟨5, 5, 8, 5, 5, 8, 265103038555679041703374223910812625823334400000⟩, + ⟨5, 5, 4, 6, 0, 8, 3394359496034207156801001542098591043403424727040000⟩, + ⟨5, 5, 5, 6, 1, 8, 500313690882825560347602842698896306736201728000000⟩, + ⟨5, 5, 6, 6, 2, 8, -84015946573218994536677614135058433398380953600000⟩, + ⟨5, 5, 7, 6, 3, 8, 2886439761263889198849254099200376333716684800000⟩, + ⟨5, 5, 8, 6, 4, 8, -394911586654059629007955852772020041705062400000⟩, + ⟨5, 5, 5, 7, 0, 8, 2182833796728865006998280545023728020170892902400000⟩, + ⟨5, 5, 6, 7, 1, 8, 166557756755384995257511248166250439825476812800000⟩, + ⟨5, 5, 7, 7, 2, 8, -5125773661589027534544582867545022618874675200000⟩, + ⟨5, 5, 8, 7, 3, 8, -1891408718599338985272590121206239435790745600000⟩ +] + +def collectedFourData_9_2_45 : List CollectedFourTerm := [ + ⟨6, 0, 3, 0, 5, 4, -310924077382055503140003968462607307227178991616000000⟩, + ⟨6, 0, 4, 0, 6, 4, -326335217833134928190318362464016013112194472345600000⟩, + ⟨6, 0, 5, 0, 7, 4, -2109308902727777814789113873988880977804184780800000⟩, + ⟨6, 0, 6, 0, 8, 4, -43314631823066308862802362241536283273034570137600000⟩, + ⟨6, 0, 3, 1, 4, 4, 297432790755490458137540019676460515598603743395840000⟩, + ⟨6, 0, 4, 1, 5, 4, 505695866448202418599527182874998328177512970977280000⟩, + ⟨6, 0, 5, 1, 6, 4, 348019606708977663934345175134194060240212302233600000⟩, + ⟨6, 0, 6, 1, 7, 4, 144862610958544113893095663405001404258203992064000000⟩, + ⟨6, 0, 7, 1, 8, 4, 68082727181852471274356963773126734857104470835200000⟩, + ⟨6, 0, 3, 2, 3, 4, -206322741869312150111979621283831857688673947484160000⟩, + ⟨6, 0, 4, 2, 4, 4, -134828296326211113969557327566346022229246916689920000⟩, + ⟨6, 0, 5, 2, 5, 4, -60876227197934863129831477494161634811928012390400000⟩, + ⟨6, 0, 6, 2, 6, 4, -9999810702461404132018568233715000308126659379200000⟩, + ⟨6, 0, 7, 2, 7, 4, -4019682195696831900941332594366979781389451264000000⟩, + ⟨6, 0, 8, 2, 8, 4, -12996334630751290085877334191125330695628689244160000⟩, + ⟨6, 0, 3, 3, 2, 4, 136051847097160444413061936231617333797833785999360000⟩, + ⟨6, 0, 4, 3, 3, 4, 171971232618721334195957518219582616044537538150400000⟩, + ⟨6, 0, 5, 3, 4, 4, 82393432301571665408105233872761373329494061875200000⟩, + ⟨6, 0, 6, 3, 5, 4, 24360923213254390512834397101226283787571376947200000⟩, + ⟨6, 0, 7, 3, 6, 4, -3138652650029266853081348343895815252434170675200000⟩, + ⟨6, 0, 8, 3, 7, 4, -7960992649947435638083574195098829452303191244800000⟩, + ⟨6, 0, 3, 4, 1, 4, -125621333502810035539766081885817328384520560312320000⟩, + ⟨6, 0, 4, 4, 2, 4, -573336097754677790685317843829627782169849055150080000⟩, + ⟨6, 0, 5, 4, 3, 4, -7685363346536675529134958381498976413578113843200000⟩, + ⟨6, 0, 6, 4, 4, 4, -11258140108340309360896126137081618220644827136000000⟩, + ⟨6, 0, 7, 4, 5, 4, -10806098668855603786020836804406806244023599104000000⟩, + ⟨6, 0, 8, 4, 6, 4, 10154550905029895886254635004978472641252315627520000⟩, + ⟨6, 0, 3, 5, 0, 4, 150888786225485035879599110270145998215200406241280000⟩, + ⟨6, 0, 4, 5, 1, 4, 552767558241096625370707186652223351751602402754560000⟩, + ⟨6, 0, 5, 5, 2, 4, -596927630517188862351676854432490908342377722675200000⟩, + ⟨6, 0, 6, 5, 3, 4, -4170308111726550480595430816682671953778678169600000⟩, + ⟨6, 0, 7, 5, 4, 4, 6847411057491812121697963766026579691496800256000000⟩, + ⟨6, 0, 8, 5, 5, 4, 3394359496034207156801001542098591043403424727040000⟩, + ⟨6, 0, 4, 6, 0, 4, 1724647831197026377866482490707069904957806550712320000⟩, + ⟨6, 0, 5, 6, 1, 4, 762616561010144333889378431938247349177598083072000000⟩, + ⟨6, 0, 6, 6, 2, 4, -298814972747969074910536008799112553057916393881600000⟩, + ⟨6, 0, 7, 6, 3, 4, 20532088342278069354437656995663581722766317977600000⟩, + ⟨6, 0, 8, 6, 4, 4, -5056418446036054911962269134461235766497210531840000⟩, + ⟨6, 0, 5, 7, 0, 4, 3327242955076260954805159997025832767887263766937600000⟩, + ⟨6, 0, 6, 7, 1, 4, 592386964330030508454882555153910030697231076556800000⟩, + ⟨6, 0, 7, 7, 2, 4, -36461123857365803951156059161755475157201610342400000⟩, + ⟨6, 0, 8, 7, 3, 4, -24217455898798206651471925585454139079360732200960000⟩ +] + +def collectedFourData_9_2_46 : List CollectedFourTerm := [ + ⟨6, 1, 2, 0, 4, 5, 40004528161201879155386372231030568568492130304000000⟩, + ⟨6, 1, 3, 0, 5, 5, -274973065618596652508273941146704637347443507200000000⟩, + ⟨6, 1, 4, 0, 6, 5, -144301136184811375563973623144040856718944501760000000⟩, + ⟨6, 1, 5, 0, 7, 5, -621805747781703022452663343761395392048005120000000⟩, + ⟨6, 1, 6, 0, 8, 5, -9576579915274804100371677128452497029443092480000000⟩, + ⟨6, 1, 2, 1, 3, 5, -23884522809685248831461856039966303737113214976000000⟩, + ⟨6, 1, 3, 1, 4, 5, 263041727029184897099245994961599285562156515328000000⟩, + ⟨6, 1, 4, 1, 5, 5, 223612053203988802007146618059227105330712281088000000⟩, + ⟨6, 1, 5, 1, 6, 5, 102593124938940330744290841771094707968975831040000000⟩, + ⟨6, 1, 6, 1, 7, 5, 32028169516636400170233484740454890232558387200000000⟩, + ⟨6, 1, 7, 1, 8, 5, 12042114182019267404022016281667153378953658368000000⟩, + ⟨6, 1, 2, 2, 2, 5, -5831300554596027078640750997259267474355912704000000⟩, + ⟨6, 1, 3, 2, 3, 5, -182466399245520175154606214112712461090314780672000000⟩, + ⟨6, 1, 4, 2, 4, 5, -59619297233445001773385896362575772209781932032000000⟩, + ⟨6, 1, 5, 2, 5, 5, -17945777370961949594141386892211541561112002560000000⟩, + ⟨6, 1, 6, 2, 6, 5, -2210892308190988432094593856394934869987164160000000⟩, + ⟨6, 1, 7, 2, 7, 5, -710980214507530795767527650410068648405237760000000⟩, + ⟨6, 1, 8, 2, 8, 5, -1915602679874169255272304616527435033961562112000000⟩, + ⟨6, 1, 2, 3, 1, 5, -33419559018655069785344525747831192926185062400000000⟩, + ⟨6, 1, 3, 3, 2, 5, 120320670545593042173615712816448229488052928512000000⟩, + ⟨6, 1, 4, 3, 3, 5, 76043414568491266187013202065007878678081699840000000⟩, + ⟨6, 1, 5, 3, 4, 5, 24288860544951608938113702628934673002429153280000000⟩, + ⟨6, 1, 6, 3, 5, 5, 5386039731667941445150191052376682212685250560000000⟩, + ⟨6, 1, 7, 3, 6, 5, -555148348984239300352690469542480952288083968000000⟩, + ⟨6, 1, 8, 3, 7, 5, -1173415373486447124269636689999564788581007360000000⟩, + ⟨6, 1, 2, 4, 0, 5, 127982475961202486480637649901926613889715273728000000⟩, + ⟨6, 1, 3, 4, 1, 5, -111096199018125198971903169833411169958068486144000000⟩, + ⟨6, 1, 4, 4, 2, 5, -253521672809675110012433548636269188749845331968000000⟩, + ⟨6, 1, 5, 4, 3, 5, -2265577647962011017510115802693056554577428480000000⟩, + ⟨6, 1, 6, 4, 4, 5, -2489100655069337312809434097430661444717772800000000⟩, + ⟨6, 1, 7, 4, 5, 5, -1911325815209286059068777107711261851107983360000000⟩, + ⟨6, 1, 8, 4, 6, 5, 1496736232119429218229542112249503753818865664000000⟩, + ⟨6, 1, 3, 5, 0, 5, 133442068768796000201890350531238776308263550976000000⟩, + ⟨6, 1, 4, 5, 1, 5, 244426535480704350848258332072462853008760242176000000⟩, + ⟨6, 1, 5, 5, 2, 5, -175969025297952493614206371608163727072066273280000000⟩, + ⟨6, 1, 6, 5, 3, 5, -922027666457049327591705513744017391699886080000000⟩, + ⟨6, 1, 7, 5, 4, 5, 1211134001510985138943606758739842905973719040000000⟩, + ⟨6, 1, 8, 5, 5, 5, 500313690882825560347602842698896306736201728000000⟩, + ⟨6, 1, 4, 6, 0, 5, 762616561010144333889378431938247349177598083072000000⟩, + ⟨6, 1, 5, 6, 1, 5, 224812667493312400072919039478665430717746380800000000⟩, + ⟨6, 1, 6, 6, 2, 5, -66066023095634147478359285772521530550051143680000000⟩, + ⟨6, 1, 7, 6, 3, 5, 3631607640401983091779252491587600186641219584000000⟩, + ⟨6, 1, 8, 6, 4, 5, -745293884852202929196818492018253702352601088000000⟩, + ⟨6, 1, 5, 7, 0, 5, 980842014679347663081314064747793454767684976640000000⟩, + ⟨6, 1, 6, 7, 1, 5, 130972857574943568605918899737370554018708848640000000⟩, + ⟨6, 1, 7, 7, 2, 5, -6449051541698231974359361926778807409197449216000000⟩, + ⟨6, 1, 8, 7, 3, 5, -3569546702014288461061122960082571944758607872000000⟩ +] + +def collectedFourData_9_2_47 : List CollectedFourTerm := [ + ⟨6, 2, 1, 0, 3, 6, -25135687613413499443490401829864666832847660646400000⟩, + ⟨6, 2, 2, 0, 4, 6, -47024753736468710097188565875612986307314817433600000⟩, + ⟨6, 2, 3, 0, 5, 6, 161613463390588819691605438545221716241798922240000000⟩, + ⟨6, 2, 4, 0, 6, 6, 56541310903936442863021192300016374812222947328000000⟩, + ⟨6, 2, 5, 0, 7, 6, 182730952628219159190600102363962586119012352000000⟩, + ⟨6, 2, 6, 0, 8, 6, 2251426690192365129719505171682416685331408486400000⟩, + ⟨6, 2, 1, 1, 2, 6, -7376519374291097733174100713346261980819750912000000⟩, + ⟨6, 2, 2, 1, 3, 6, 28075916774036878925151360066678973067939964518400000⟩, + ⟨6, 2, 3, 1, 4, 6, -154600904004153386026214265494161883117689346457600000⟩, + ⟨6, 2, 4, 1, 5, 6, -87617595788584641800937921285041676256318744166400000⟩, + ⟨6, 2, 5, 1, 6, 6, -30149189710899797255278993502778149882648592384000000⟩, + ⟨6, 2, 6, 1, 7, 6, -7529731524794725451295813913166418882431287296000000⟩, + ⟨6, 2, 7, 1, 8, 6, -2359222317675418157923929225647542495121453875200000⟩, + ⟨6, 2, 1, 2, 1, 6, -27021903410474539568168625271210600031668980940800000⟩, + ⟨6, 2, 2, 2, 2, 6, 6854610844008344176782067722963286032356317593600000⟩, + ⟨6, 2, 3, 2, 3, 6, 107243328244306672008086706654207022549604656742400000⟩, + ⟨6, 2, 4, 2, 4, 6, 23360545245001516687712170800192777834515241369600000⟩, + ⟨6, 2, 5, 2, 5, 6, 5273751499320426656394092151854277797584306176000000⟩, + ⟨6, 2, 6, 2, 6, 6, 519774491085564067758434422486519124977306828800000⟩, + ⟨6, 2, 7, 2, 7, 6, 139291187920837054320847289814373761300824064000000⟩, + ⟨6, 2, 8, 2, 8, 6, 321680528317815049933905641074400895250622054400000⟩, + ⟨6, 2, 1, 3, 0, 6, -23715483617270635140119439036266677081909651046400000⟩, + ⟨6, 2, 2, 3, 1, 6, 39284216189251054292794859168648790624341852160000000⟩, + ⟨6, 2, 3, 3, 2, 6, -70717618253284617904116934212223111220576020070400000⟩, + ⟨6, 2, 4, 3, 3, 6, -29795984002560851580385664114726840642046001152000000⟩, + ⟨6, 2, 5, 3, 4, 6, -7137802507401611472617071402971573059781132288000000⟩, + ⟨6, 2, 6, 3, 5, 6, -1266242616215431974038266349886867178227813580800000⟩, + ⟨6, 2, 7, 3, 6, 6, 108761497752603136892157714699727807578321715200000⟩, + ⟨6, 2, 8, 3, 7, 6, 197047582593777338712802982476411379417874432000000⟩, + ⟨6, 2, 2, 4, 0, 6, -150441579773359858997923650164743415877216711475200000⟩, + ⟨6, 2, 3, 4, 1, 6, 65296000728134804576311936348675019848008125644800000⟩, + ⟨6, 2, 4, 4, 2, 6, 99337039902854787739561645146320139821672457830400000⟩, + ⟨6, 2, 5, 4, 3, 6, 665788573589445254610210706928157760010846208000000⟩, + ⟨6, 2, 6, 4, 4, 6, 585180481860741199818677821701390812791701504000000⟩, + ⟨6, 2, 7, 4, 5, 6, 374456050775859937903581687975292397791739904000000⟩, + ⟨6, 2, 8, 4, 6, 6, -251341735402155716379783477129579348022316236800000⟩, + ⟨6, 2, 3, 5, 0, 6, -78429626724399146227647784017266128307690353459200000⟩, + ⟨6, 2, 4, 5, 1, 6, -95773305056216331475537778048555213776300592332800000⟩, + ⟨6, 2, 5, 5, 2, 6, 51712271461734201413929313335826712325980684288000000⟩, + ⟨6, 2, 6, 5, 3, 6, 216766080972824666140393290522309540083820134400000⟩, + ⟨6, 2, 7, 5, 4, 6, -237278464800366233290683254092968174557331456000000⟩, + ⟨6, 2, 8, 5, 5, 6, -84015946573218994536677614135058433398380953600000⟩, + ⟨6, 2, 4, 6, 0, 6, -298814972747969074910536008799112553057916393881600000⟩, + ⟨6, 2, 5, 6, 1, 6, -66066023095634147478359285772521530550051143680000000⟩, + ⟨6, 2, 6, 6, 2, 6, 15531934054570848537227418232915677066530547302400000⟩, + ⟨6, 2, 7, 6, 3, 6, -711483852816303968269223459396828307996121497600000⟩, + ⟨6, 2, 8, 6, 4, 6, 125154622694013850949831659152283265155045785600000⟩, + ⟨6, 2, 5, 7, 0, 6, -288241458621995816924347880305222339391750406144000000⟩, + ⟨6, 2, 6, 7, 1, 6, -30791346163640263232598748023631823123812397875200000⟩, + ⟨6, 2, 7, 7, 2, 6, 1263461390171128992283726265503638889423070822400000⟩, + ⟨6, 2, 8, 7, 3, 6, 599421623817365043763330020553158232308606566400000⟩ +] + +def collectedFourData_9_2_48 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 2, 7, 3273510586910224613401431838899951120850039603200000⟩, + ⟨6, 3, 1, 0, 3, 7, 6908464510682967075694846332303980127009216921600000⟩, + ⟨6, 3, 2, 0, 4, 7, 6462302669186502549923734949140508879522837299200000⟩, + ⟨6, 3, 3, 0, 5, 7, -14806316997757804576607000550797077728743915520000000⟩, + ⟨6, 3, 4, 0, 6, 7, -3885050269709831909035373234393474336720683008000000⟩, + ⟨6, 3, 5, 0, 7, 7, -10044605269216315166028403853775335386093977600000⟩, + ⟨6, 3, 6, 0, 8, 7, -103132921517917347936100836329629615855868313600000⟩, + ⟨6, 3, 0, 1, 1, 7, -24118287786050222011623630609623006872177370726400000⟩, + ⟨6, 3, 1, 1, 2, 7, 2027413098596143854632254671623864221358358528000000⟩, + ⟨6, 3, 2, 1, 3, 7, -3858288613811704317844355863090523615720688844800000⟩, + ⟨6, 3, 3, 1, 4, 7, 14163857050035334638321806942144800602010209484800000⟩, + ⟨6, 3, 4, 1, 5, 7, 6020355006061046447107407210692991861937038950400000⟩, + ⟨6, 3, 5, 1, 6, 7, 1657281951836874044713698113971593077167698739200000⟩, + ⟨6, 3, 6, 1, 7, 7, 344920495870683609621167512446313093297864704000000⟩, + ⟨6, 3, 7, 1, 8, 7, 92632116791438555965598181197951059727115878400000⟩, + ⟨6, 3, 0, 2, 0, 7, -3878016324448622900701233824017012220287883673600000⟩, + ⟨6, 3, 1, 2, 1, 7, 7426884976989683453558108340953996524115931955200000⟩, + ⟨6, 3, 2, 2, 2, 7, -941984092074402993906739399865954774212096819200000⟩, + ⟨6, 3, 3, 2, 3, 7, -9825163575897129849889593357997079596918584115200000⟩, + ⟨6, 3, 4, 2, 4, 7, -1605143056531844927765160682388081027030030745600000⟩, + ⟨6, 3, 5, 2, 5, 7, -289894795253373032366771757736937115383286988800000⟩, + ⟨6, 3, 6, 2, 6, 7, -23809730083444443564073097612619442533118771200000⟩, + ⟨6, 3, 7, 2, 7, 7, -5469106277451028271339002615533802082009088000000⟩, + ⟨6, 3, 8, 2, 8, 7, -11051609905409183914758032671567134504203059200000⟩, + ⟨6, 3, 1, 3, 0, 7, 6518125918949065154638010946771297198986074521600000⟩, + ⟨6, 3, 2, 3, 1, 7, -5398571496182398185005726236068614787060203520000000⟩, + ⟨6, 3, 3, 3, 2, 7, 6478838156286483852366854270738280624233329459200000⟩, + ⟨6, 3, 4, 3, 3, 7, 2047333070895596509281099430451684417860534272000000⟩, + ⟨6, 3, 5, 3, 4, 7, 392360504037560462582882680423495543789348454400000⟩, + ⟨6, 3, 6, 3, 5, 7, 58003798626741239416626050777177015062836019200000⟩, + ⟨6, 3, 7, 3, 6, 7, -4270393547377847418503345818241257573869158400000⟩, + ⟨6, 3, 8, 3, 7, 7, -6769738370607247917810749399000492776882176000000⟩, + ⟨6, 3, 2, 4, 0, 7, 20674196997911256967052237384328785042912732774400000⟩, + ⟨6, 3, 3, 4, 1, 7, -5982133327159965291989368431189526202003383910400000⟩, + ⟨6, 3, 4, 4, 2, 7, -6825618074587189525035775884745267807754020454400000⟩, + ⟨6, 3, 5, 4, 3, 7, -36597978165565542184845936664224433512539750400000⟩, + ⟨6, 3, 6, 4, 4, 7, -26805835149979664865643059710885251824746496000000⟩, + ⟨6, 3, 7, 4, 5, 7, -14702580748264392524625357062977484507578368000000⟩, + ⟨6, 3, 8, 4, 6, 7, 8635060465546258042977469290095944078354022400000⟩, + ⟨6, 3, 3, 5, 0, 7, 7185378562742277922831017976883572196414953881600000⟩, + ⟨6, 3, 4, 5, 1, 7, 6580747752237745325449703854276487101851421900800000⟩, + ⟨6, 3, 5, 5, 2, 7, -2842590961940097241730593780562404792938686054400000⟩, + ⟨6, 3, 6, 5, 3, 7, -9929579014987487096272209364252082984032665600000⟩, + ⟨6, 3, 7, 5, 4, 7, 9316462589730690186277345285550989746634752000000⟩, + ⟨6, 3, 8, 5, 5, 7, 2886439761263889198849254099200376333716684800000⟩, + ⟨6, 3, 4, 6, 0, 7, 20532088342278069354437656995663581722766317977600000⟩, + ⟨6, 3, 5, 6, 1, 7, 3631607640401983091779252491587600186641219584000000⟩, + ⟨6, 3, 6, 6, 2, 7, -711483852816303968269223459396828307996121497600000⟩, + ⟨6, 3, 7, 6, 3, 7, 27935584898264739351919808058274739985265459200000⟩, + ⟨6, 3, 8, 6, 4, 7, -4299794193655306395997570555479551850106060800000⟩, + ⟨6, 3, 5, 7, 0, 7, 15844451268044112239426414294556451996158866227200000⟩, + ⟨6, 3, 6, 7, 1, 7, 1410484072681224514235988506247702988052024524800000⟩, + ⟨6, 3, 7, 7, 2, 7, -49608340078405152330582396043165379981003980800000⟩, + ⟨6, 3, 8, 7, 3, 7, -20593642984667941858720510466795559017722675200000⟩ +] + +def collectedFourData_9_2_49 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 2, 8, -4030822154818050410845093447836384849092306534400000⟩, + ⟨6, 4, 1, 0, 3, 8, -4253352947258825896199395888272736118671776153600000⟩, + ⟨6, 4, 2, 0, 4, 8, -2652442189969426550551534679473419766599568588800000⟩, + ⟨6, 4, 3, 0, 5, 8, 4557922527001284885771166965358953612925992960000000⟩, + ⟨6, 4, 4, 0, 6, 8, 956767744228328261732397755033606467225858867200000⟩, + ⟨6, 4, 5, 0, 7, 8, 2061396390848128269917846179098501582107443200000⟩, + ⟨6, 4, 6, 0, 8, 8, 18141749568614391780089699148730812293814681600000⟩, + ⟨6, 4, 0, 1, 1, 8, 29697942365920005662230663698561285503266376908800000⟩, + ⟨6, 4, 1, 1, 2, 8, -1248222881494192102024288754622921350565593088000000⟩, + ⟨6, 4, 2, 1, 3, 8, 1583628626549783361683615547478182070517445427200000⟩, + ⟨6, 4, 3, 1, 4, 8, -4360150004039378949994307037355520528860210790400000⟩, + ⟨6, 4, 4, 1, 5, 8, -1482627270877749042312062031756059471722693263360000⟩, + ⟨6, 4, 5, 1, 6, 8, -340114413913730251266939388549263506952054374400000⟩, + ⟨6, 4, 6, 1, 7, 8, -60673751553533987292153847217869018286260224000000⟩, + ⟨6, 4, 7, 1, 8, 8, -14257766192343753442173694335480446259403161600000⟩, + ⟨6, 4, 0, 2, 0, 8, 4775177505104023443017797241703688213208707891200000⟩, + ⟨6, 4, 1, 2, 1, 8, -4572530271666471923116456841136029759983268659200000⟩, + ⟨6, 4, 2, 2, 2, 8, 386635921590580459983635709847945501117041868800000⟩, + ⟨6, 4, 3, 2, 3, 8, 3024542457171195365171570721262904016570522009600000⟩, + ⟨6, 4, 4, 2, 4, 8, 395297099071111855710113945566605859424871383040000⟩, + ⟨6, 4, 5, 2, 5, 8, 59493436391411763184343750489475887662733721600000⟩, + ⟨6, 4, 6, 2, 6, 8, 4188285894675352184211949483479674112914227200000⟩, + ⟨6, 4, 7, 2, 7, 8, 841794847034989125958944771050573200883712000000⟩, + ⟨6, 4, 8, 2, 8, 8, 1512038761867600248844100254836755361536409600000⟩, + ⟨6, 4, 1, 3, 0, 8, -4013032135447038777459303862179871177974585753600000⟩, + ⟨6, 4, 2, 3, 1, 8, 2215835366287964402759894426664541736958689280000000⟩, + ⟨6, 4, 3, 3, 2, 8, -1994421866410500299599548042463489505520884121600000⟩, + ⟨6, 4, 4, 3, 3, 8, -504194825790796571355035253402659885023022284800000⟩, + ⟨6, 4, 5, 3, 4, 8, -80521882668016816523275861190416779151461580800000⟩, + ⟨6, 4, 6, 3, 5, 8, -10203244252436539899402361707659834294481715200000⟩, + ⟨6, 4, 7, 3, 6, 8, 657291173480277709152778878328864151017881600000⟩, + ⟨6, 4, 8, 3, 7, 8, 926209566902151582751086353111987402047488000000⟩, + ⟨6, 4, 2, 4, 0, 8, -8485692355833616105161450469837917836459743641600000⟩, + ⟨6, 4, 3, 4, 1, 8, 1841518066614175319625238008058592253464228659200000⟩, + ⟨6, 4, 4, 4, 2, 8, 1680938663549042140558787685820177808899398696960000⟩, + ⟨6, 4, 5, 4, 3, 8, 7510791920718404158023200045067349674216652800000⟩, + ⟨6, 4, 6, 4, 4, 8, 4715320201454838573345954896809859771006976000000⟩, + ⟨6, 4, 7, 4, 5, 8, 2262994369488301284297262666004171883282432000000⟩, + ⟨6, 4, 8, 4, 6, 8, -1181415761751229807077732865063926451352371200000⟩, + ⟨6, 4, 3, 5, 0, 8, -2211920683659191023956256830127960491658366156800000⟩, + ⟨6, 4, 4, 5, 1, 8, -1620634675266223958465784563348391761283876126720000⟩, + ⟨6, 4, 5, 5, 2, 8, 583368543864940019233808229366212077206424780800000⟩, + ⟨6, 4, 6, 5, 3, 8, 1746677328251347324223555630626705688336793600000⟩, + ⟨6, 4, 7, 5, 4, 8, -1433972902110927964404513735906673135976448000000⟩, + ⟨6, 4, 8, 5, 5, 8, -394911586654059629007955852772020041705062400000⟩, + ⟨6, 4, 4, 6, 0, 8, -5056418446036054911962269134461235766497210531840000⟩, + ⟨6, 4, 5, 6, 1, 8, -745293884852202929196818492018253702352601088000000⟩, + ⟨6, 4, 6, 6, 2, 8, 125154622694013850949831659152283265155045785600000⟩, + ⟨6, 4, 7, 6, 3, 8, -4299794193655306395997570555479551850106060800000⟩, + ⟨6, 4, 8, 6, 4, 8, 588281304217763267987381757031100155586150400000⟩, + ⟨6, 4, 5, 7, 0, 8, -3251665325168468583669704581691461113857074790400000⟩, + ⟨6, 4, 6, 7, 1, 8, -248113293412875374110333688567041173842873548800000⟩, + ⟨6, 4, 7, 7, 2, 8, 7635625078294104411695282380265255452488499200000⟩, + ⟨6, 4, 8, 7, 3, 8, 2817543028336541100185558447064175290718617600000⟩ +] + +def collectedFourData_9_2_50 : List CollectedFourTerm := [ + ⟨7, 0, 2, 0, 4, 5, 174536970871969142770894863055070410857159799603200000⟩, + ⟨7, 0, 3, 0, 5, 5, -1199688339056445036341049542717885286042052853760000000⟩, + ⟨7, 0, 4, 0, 6, 5, -629575809558149816462194461458359962961138679808000000⟩, + ⟨7, 0, 5, 0, 7, 5, -2712895181547306110571729782789737830621904896000000⟩, + ⟨7, 0, 6, 0, 8, 5, -41781951357858143727027806884245116817908957184000000⟩, + ⟨7, 0, 2, 1, 3, 5, -104206509951239310715733925612251291088019311820800000⟩, + ⟨7, 0, 3, 1, 4, 5, 1147632739564000068745151178184047317822946567782400000⟩, + ⟨7, 0, 4, 1, 5, 5, 975603818133203295575364800892903685547476018790400000⟩, + ⟨7, 0, 5, 1, 6, 5, 447606660600447147753928262188081187425125138432000000⟩, + ⟨7, 0, 6, 1, 7, 5, 139736673495606373382232235292806854387443957760000000⟩, + ⟨7, 0, 7, 1, 8, 5, 52538905689742247897744814816217753890150835814400000⟩, + ⟨7, 0, 2, 2, 2, 5, -25441558289151600071919739548481725189412041523200000⟩, + ⟨7, 0, 3, 2, 3, 5, -796088194863779774992011632769192546054279109017600000⟩, + ⟨7, 0, 4, 2, 4, 5, -260114842567572834613156683403039149545997572505600000⟩, + ⟨7, 0, 5, 2, 5, 5, -78296177113974145539564760547194420761301352448000000⟩, + ⟨7, 0, 6, 2, 6, 5, -9645969197307935044100243166293147420593225728000000⟩, + ⟨7, 0, 7, 2, 7, 5, -3101957170698425699961760312953636121485508608000000⟩, + ⟨7, 0, 8, 2, 8, 5, -8357641109831278537539097225407170587603343769600000⟩, + ⟨7, 0, 2, 3, 1, 5, -145807209011156374542151346103610906983184465920000000⟩, + ⟨7, 0, 3, 3, 2, 5, 524950707722109053219454279592353667371048212889600000⟩, + ⟨7, 0, 4, 3, 3, 5, 331772122897276638884254806223009712861947625472000000⟩, + ⟨7, 0, 5, 3, 4, 5, 105970607336371485025042445395456218299916877824000000⟩, + ⟨7, 0, 6, 3, 5, 5, 23498916322005512088630119013246137059768270848000000⟩, + ⟨7, 0, 7, 3, 6, 5, -2422073591915423192683103126562994437031880294400000⟩, + ⟨7, 0, 8, 3, 7, 5, -5119529570193829742512890189845367691608588288000000⟩, + ⟨7, 0, 2, 4, 0, 5, 558378631262721178978030267937543889944494630502400000⟩, + ⟨7, 0, 3, 4, 1, 5, -484704980743121153694800770053088705280774189875200000⟩, + ⟨7, 0, 4, 4, 2, 5, -1106097405880908674707570910459881612518845998694400000⟩, + ⟨7, 0, 5, 4, 3, 5, -9884557527015957536173814366787271396618665984000000⟩, + ⟨7, 0, 6, 4, 4, 5, -10859772843229657638448572255422933171951370240000000⟩, + ⟨7, 0, 7, 4, 5, 5, -8338981447094347863409769636234255012450009088000000⟩, + ⟨7, 0, 8, 4, 6, 5, 6530155963739310975548588241461219545056490291200000⟩, + ⟨7, 0, 3, 5, 0, 5, 582198454533525950489730126791099409316981820620800000⟩, + ⟨7, 0, 4, 5, 1, 5, 1066415955004487781193969835614135500203591781580800000⟩, + ⟨7, 0, 5, 5, 2, 5, -767740604739451178995568053195139961830007373824000000⟩, + ⟨7, 0, 6, 5, 3, 5, -4022742508425297431170414243034610445597016064000000⟩, + ⟨7, 0, 7, 5, 4, 5, 5284093317935621499166815367870299331029368832000000⟩, + ⟨7, 0, 8, 5, 5, 5, 2182833796728865006998280545023728020170892902400000⟩, + ⟨7, 0, 4, 6, 0, 5, 3327242955076260954805159997025832767887263766937600000⟩, + ⟨7, 0, 5, 6, 1, 5, 980842014679347663081314064747793454767684976640000000⟩, + ⟨7, 0, 6, 6, 2, 5, -288241458621995816924347880305222339391750406144000000⟩, + ⟨7, 0, 7, 6, 3, 5, 15844451268044112239426414294556451996158866227200000⟩, + ⟨7, 0, 8, 6, 4, 5, -3251665325168468583669704581691461113857074790400000⟩, + ⟨7, 0, 5, 7, 0, 5, 4279345414505435760950850816150357875662270758912000000⟩, + ⟨7, 0, 6, 7, 1, 5, 571425458024692382335681770657880544846662336512000000⟩, + ⟨7, 0, 7, 7, 2, 5, -28136762832185220777108961675213854653601860812800000⟩, + ⟨7, 0, 8, 7, 3, 5, -15573683715130804750025314938007359073401018777600000⟩ +] + +def collectedFourData_9_2_51 : List CollectedFourTerm := [ + ⟨7, 1, 1, 0, 3, 6, 49830346668126167639060868239351700090778759987200000⟩, + ⟨7, 1, 2, 0, 4, 6, 93224415289957355207680338836067562387766299852800000⟩, + ⟨7, 1, 3, 0, 5, 6, -320391271201667458065930754575674204875149803520000000⟩, + ⟨7, 1, 4, 0, 6, 6, -112090552951888553379720875754074994288774610944000000⟩, + ⟨7, 1, 5, 0, 7, 6, -362255724072652152216189818891404902395805696000000⟩, + ⟨7, 1, 6, 0, 8, 6, -4463350046182476577653138041410588212532032307200000⟩, + ⟨7, 1, 1, 1, 2, 6, 14623610990014083678693612814344328316322840576000000⟩, + ⟨7, 1, 2, 1, 3, 6, -55659215987754848930968708224401822440439886643200000⟩, + ⟨7, 1, 3, 1, 4, 6, 306489194177507423073293854303726496603643366604800000⟩, + ⟨7, 1, 4, 1, 5, 6, 173697860966533809156352707922719244859166896947200000⟩, + ⟨7, 1, 5, 1, 6, 6, 59769384397326884472242625912757180366986412032000000⟩, + ⟨7, 1, 6, 1, 7, 6, 14927347044137016325579998689852025943892164608000000⟩, + ⟨7, 1, 7, 1, 8, 6, 4677049928572893371214672989877786593166203289600000⟩, + ⟨7, 1, 1, 2, 1, 6, 53569682886176950545966531756881526362470770278400000⟩, + ⟨7, 1, 2, 2, 2, 6, -13588951290505269508034801450282126952652131532800000⟩, + ⟨7, 1, 3, 2, 3, 6, -212604974506671987511867804234751425173945266995200000⟩, + ⟨7, 1, 4, 2, 4, 6, -46311208422787548774627203936053194731102719180800000⟩, + ⟨7, 1, 5, 2, 5, 6, -10454970219810070612602521237707404011108302848000000⟩, + ⟨7, 1, 6, 2, 6, 6, -1030429064778035042898721044397563364531136102400000⟩, + ⟨7, 1, 7, 2, 7, 6, -276138384939445083060235778500210796550684672000000⟩, + ⟨7, 1, 8, 2, 8, 6, -637716878447704987276386781646385542050558771200000⟩, + ⟨7, 1, 1, 3, 0, 6, 47014857449940169663205039961217276364924859187200000⟩, + ⟨7, 1, 2, 3, 1, 6, -77879154984857558679020276090075017297715527680000000⟩, + ⟨7, 1, 3, 3, 2, 6, 140194431411730367266634572059858525473786245939200000⟩, + ⟨7, 1, 4, 3, 3, 6, 59069170296866055896818163790284047269123588096000000⟩, + ⟨7, 1, 5, 3, 4, 6, 14150365761334357609057498870740080134428033024000000⟩, + ⟨7, 1, 6, 3, 5, 6, 2510267851128868098079625525593206645554832998400000⟩, + ⟨7, 1, 7, 3, 6, 6, -215614675854926366031229268127535431197235609600000⟩, + ⟨7, 1, 8, 3, 7, 6, -390637785676661923310970425085203187064897536000000⟩, + ⟨7, 1, 2, 4, 0, 6, 298243524852154438348833444127604187384795208089600000⟩, + ⟨7, 1, 3, 4, 1, 6, -129446323584513669161105008810481370380884141670400000⟩, + ⟨7, 1, 4, 4, 2, 6, -196931120861925446417243556416358558096717722419200000⟩, + ⟨7, 1, 5, 4, 3, 6, -1319895279567958686657427505410592616096989184000000⟩, + ⟨7, 1, 6, 4, 4, 6, -1160093438580965568390227655410938283443617792000000⟩, + ⟨7, 1, 7, 4, 5, 6, -742341928699859886065408983743680913963220992000000⟩, + ⟨7, 1, 8, 4, 6, 6, 498273450875251500144138486649173183568438886400000⟩, + ⟨7, 1, 3, 5, 0, 6, 155483134133277861799742054422259777088469440921600000⟩, + ⟨7, 1, 4, 5, 1, 6, 189866180146060162519143506557308530098348385894400000⟩, + ⟨7, 1, 5, 5, 2, 6, -102517203967770044602207725476502868169299329024000000⟩, + ⟨7, 1, 6, 5, 3, 6, -429728803400739019383514631672673554998178611200000⟩, + ⟨7, 1, 7, 5, 4, 6, 470393662577720632982894445855640585437708288000000⟩, + ⟨7, 1, 8, 5, 5, 6, 166557756755384995257511248166250439825476812800000⟩, + ⟨7, 1, 4, 6, 0, 6, 592386964330030508454882555153910030697231076556800000⟩, + ⟨7, 1, 5, 6, 1, 6, 130972857574943568605918899737370554018708848640000000⟩, + ⟨7, 1, 6, 6, 2, 6, -30791346163640263232598748023631823123812397875200000⟩, + ⟨7, 1, 7, 6, 3, 6, 1410484072681224514235988506247702988052024524800000⟩, + ⟨7, 1, 8, 6, 4, 6, -248113293412875374110333688567041173842873548800000⟩, + ⟨7, 1, 5, 7, 0, 6, 571425458024692382335681770657880544846662336512000000⟩, + ⟨7, 1, 6, 7, 1, 6, 61042430082305703196034033851475941619893115289600000⟩, + ⟨7, 1, 7, 7, 2, 6, -2504754198187220246468272633139348596845654835200000⟩, + ⟨7, 1, 8, 7, 3, 6, -1188325848673055800958057008871152769991652147200000⟩ +] + +def collectedFourData_9_2_52 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 2, 7, -5813138584250275674290364847297037032569490636800000⟩, + ⟨7, 2, 1, 0, 3, 7, -12268132495297847970776523365050572415611332198400000⟩, + ⟨7, 2, 2, 0, 4, 7, -11475833052004682693809009857655381104033320140800000⟩, + ⟨7, 2, 3, 0, 5, 7, 26293231790506221231504794353757869081865748480000000⟩, + ⟨7, 2, 4, 0, 6, 7, 6899117942343021025010193791790154688696942592000000⟩, + ⟨7, 2, 5, 0, 7, 7, 17837328123370551518194570318879431865034342400000⟩, + ⟨7, 2, 6, 0, 8, 7, 183144654481822430789743273946950014417135206400000⟩, + ⟨7, 2, 0, 1, 1, 7, 42829538989661358836641975564040733696074553753600000⟩, + ⟨7, 2, 1, 1, 2, 7, -3600304015142282764251616042859169514700931072000000⟩, + ⟨7, 2, 2, 1, 3, 7, 6851594279183992750752410219190612254182814515200000⟩, + ⟨7, 2, 3, 1, 4, 7, -25152343862458921877084641018037544452919341875200000⟩, + ⟨7, 2, 4, 1, 5, 7, -10691017196205439237709350821070010251749202329600000⟩, + ⟨7, 2, 5, 1, 6, 7, -2943020773394783087945363368589618511705066700800000⟩, + ⟨7, 2, 6, 1, 7, 7, -612513871518325853161002239136814192285188096000000⟩, + ⟨7, 2, 7, 1, 8, 7, -164497201999077303104391395838666805117295001600000⟩, + ⟨7, 2, 0, 2, 0, 7, 6886626979655763386019405088304677077874271846400000⟩, + ⟨7, 2, 1, 2, 1, 7, -13188749654015239877475012351310228286367124684800000⟩, + ⟨7, 2, 2, 2, 2, 7, 1672786424850457156760950018963044021054524620800000⟩, + ⟨7, 2, 3, 2, 3, 7, 17447640984575922527433523039817577334691384524800000⟩, + ⟨7, 2, 4, 2, 4, 7, 2850431910157310226475104049240977519090755174400000⟩, + ⟨7, 2, 5, 2, 5, 7, 514798585469469473868723001841999837010277171200000⟩, + ⟨7, 2, 6, 2, 6, 7, 42281598593910787805191008495197344611749068800000⟩, + ⟨7, 2, 7, 2, 7, 7, 9712103223354528194019295380523955899072512000000⟩, + ⟨7, 2, 8, 2, 8, 7, 19625578794860503796938448292831036462386380800000⟩, + ⟨7, 2, 1, 3, 0, 7, -11574964635201817560402662273086340939978794598400000⟩, + ⟨7, 2, 2, 3, 1, 7, 9586846729557347108627933888549722987671060480000000⟩, + ⟨7, 2, 3, 3, 2, 7, -11505196964391171078085275930614878945537739980800000⟩, + ⟨7, 2, 4, 3, 3, 7, -3635678136134646195611183322582134437737136128000000⟩, + ⟨7, 2, 5, 3, 4, 7, -696758395734854103995371053904583328903305625600000⟩, + ⟨7, 2, 6, 3, 5, 7, -103003827505091817589066680977052739369225420800000⟩, + ⟨7, 2, 7, 3, 6, 7, 7583415064994984999912309631847482001037721600000⟩, + ⟨7, 2, 8, 3, 7, 7, 12021780984860411955060395205027640350081024000000⟩, + ⟨7, 2, 2, 4, 0, 7, -36713482078695690781393145327296033649889745305600000⟩, + ⟨7, 2, 3, 4, 1, 7, 10623142689471548843032078213529669567826729369600000⟩, + ⟨7, 2, 4, 4, 2, 7, 12121012820120455006203536749140839239889033625600000⟩, + ⟨7, 2, 5, 4, 3, 7, 64991119879226093986446591444667444976261529600000⟩, + ⟨7, 2, 6, 4, 4, 7, 47602117193846901582336114951244379748040704000000⟩, + ⟨7, 2, 7, 4, 5, 7, 26109015739112676500559667333111464415199232000000⟩, + ⟨7, 2, 8, 4, 6, 7, -15334241890135588048088447949684566904117657600000⟩, + ⟨7, 2, 3, 5, 0, 7, -12759879724399207889683049803704638256403867238400000⟩, + ⟨7, 2, 4, 5, 1, 7, -11686169222950077214279083443557285629021860659200000⟩, + ⟨7, 2, 5, 5, 2, 7, 5047906448254985862140680706692448548034288025600000⟩, + ⟨7, 2, 6, 5, 3, 7, 17633063148840405036711025596382451622897254400000⟩, + ⟨7, 2, 7, 5, 4, 7, -16544283792955697173969095132777535292571648000000⟩, + ⟨7, 2, 8, 5, 5, 7, -5125773661589027534544582867545022618874675200000⟩, + ⟨7, 2, 4, 6, 0, 7, -36461123857365803951156059161755475157201610342400000⟩, + ⟨7, 2, 5, 6, 1, 7, -6449051541698231974359361926778807409197449216000000⟩, + ⟨7, 2, 6, 6, 2, 7, 1263461390171128992283726265503638889423070822400000⟩, + ⟨7, 2, 7, 6, 3, 7, -49608340078405152330582396043165379981003980800000⟩, + ⟨7, 2, 8, 6, 4, 7, 7635625078294104411695282380265255452488499200000⟩, + ⟨7, 2, 5, 7, 0, 7, -28136762832185220777108961675213854653601860812800000⟩, + ⟨7, 2, 6, 7, 1, 7, -2504754198187220246468272633139348596845654835200000⟩, + ⟨7, 2, 7, 7, 2, 7, 88095073516343909793872216376300365874934579200000⟩, + ⟨7, 2, 8, 7, 3, 7, 36570433314969861107037947991626948075637964800000⟩ +] + +def collectedFourData_9_2_53 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 2, 8, -19305415248362306533418426668214241592757295513600000⟩, + ⟨7, 3, 1, 0, 3, 8, -20371215025333666457739611158612186171418502758400000⟩, + ⟨7, 3, 2, 0, 4, 8, -12703735350473857992756225814776122441379033907200000⟩, + ⟨7, 3, 3, 0, 5, 8, 21829935351637117770137581224283341934810890240000000⟩, + ⟨7, 3, 4, 0, 6, 8, 4582389867161117550216866905661659655277694156800000⟩, + ⟨7, 3, 5, 0, 7, 8, 9872951916082454915349307675656493088951500800000⟩, + ⟨7, 3, 6, 0, 8, 8, 86888975822280601003815317806283940493157990400000⟩, + ⟨7, 3, 0, 1, 1, 8, 142236766439996148285686545693173527430820999987200000⟩, + ⟨7, 3, 1, 1, 2, 8, -5978299246209353443102099730923471087570255872000000⟩, + ⟨7, 3, 2, 1, 3, 8, 7584707799175346848705354648924440127326702796800000⟩, + ⟨7, 3, 3, 1, 4, 8, -20882714032052947283998841380088976449059002777600000⟩, + ⟨7, 3, 4, 1, 5, 8, -7100967004616730921318601575235382020207898787840000⟩, + ⟨7, 3, 5, 1, 6, 8, -1628960480111860880089932648539913243175000473600000⟩, + ⟨7, 3, 6, 1, 7, 8, -290593810252046371303463176553776770875129856000000⟩, + ⟨7, 3, 7, 1, 8, 8, -68286837346135020041177735144457811452651110400000⟩, + ⟨7, 3, 0, 2, 0, 8, 22870466887377015041055879703927084402818731212800000⟩, + ⟨7, 3, 1, 2, 1, 8, -21899898392865915103041993997418000787801165004800000⟩, + ⟨7, 3, 2, 2, 2, 8, 1851772846717504075655235180803863221357458227200000⟩, + ⟨7, 3, 3, 2, 3, 8, 14485890428630854653530873212161022081989240422400000⟩, + ⟨7, 3, 4, 2, 4, 8, 1893255110478895630336111123270231223080593653760000⟩, + ⟨7, 3, 5, 2, 5, 8, 284940751532630807076768542685761766498395750400000⟩, + ⟨7, 3, 6, 2, 6, 8, 20059579725917265555982172672695245143329996800000⟩, + ⟨7, 3, 7, 2, 7, 8, 4031733093586627518832091450542376330723328000000⟩, + ⟨7, 3, 8, 2, 8, 8, 7241831826934393896386050534190478201874022400000⟩, + ⟨7, 3, 1, 3, 0, 8, -19220210866218264333937047626413805123014125158400000⟩, + ⟨7, 3, 2, 3, 1, 8, 10612629440141376898975293710035539548511928320000000⟩, + ⟨7, 3, 3, 3, 2, 8, -9552180878396134291900633583502280437185013350400000⟩, + ⟨7, 3, 4, 3, 3, 8, -2414815167752395043055670035230871866825716531200000⟩, + ⟨7, 3, 5, 3, 4, 8, -385655412662616522631465898960102253883765555200000⟩, + ⟨7, 3, 6, 3, 5, 8, -48867913196890954696570197376738152424459468800000⟩, + ⟨7, 3, 7, 3, 6, 8, 3148062245304617274098014229295541634098790400000⟩, + ⟨7, 3, 8, 3, 7, 8, 4436033049654352576593807516086018582249472000000⟩, + ⟨7, 3, 2, 4, 0, 8, -40641786788684680209460157548919160461381232230400000⟩, + ⟨7, 3, 3, 4, 1, 8, 8819855999067947752414936209013008728163405004800000⟩, + ⟨7, 3, 4, 4, 2, 8, 8050769212938959135718268752539061804972889866240000⟩, + ⟨7, 3, 5, 4, 3, 8, 35972551331791190540934072259682812332028723200000⟩, + ⟨7, 3, 6, 4, 4, 8, 22583783412341141557220950657987491548626944000000⟩, + ⟨7, 3, 7, 4, 5, 8, 10838495058745541438962671940091640186667008000000⟩, + ⟨7, 3, 8, 4, 6, 8, -5658329984691992089513097596969171888688332800000⟩, + ⟨7, 3, 3, 5, 0, 8, -10593880269175427390409307601407907092243886899200000⟩, + ⟨7, 3, 4, 5, 1, 8, -7761946364840682967419797235724026345181339975680000⟩, + ⟨7, 3, 5, 5, 2, 8, 2794013615481256022863371914140545890926146355200000⟩, + ⟨7, 3, 6, 5, 3, 8, 8365621164031340338613830283900942431970918400000⟩, + ⟨7, 3, 7, 5, 4, 8, -6867939409596769127746643420457408462323712000000⟩, + ⟨7, 3, 8, 5, 5, 8, -1891408718599338985272590121206239435790745600000⟩, + ⟨7, 3, 4, 6, 0, 8, -24217455898798206651471925585454139079360732200960000⟩, + ⟨7, 3, 5, 6, 1, 8, -3569546702014288461061122960082571944758607872000000⟩, + ⟨7, 3, 6, 6, 2, 8, 599421623817365043763330020553158232308606566400000⟩, + ⟨7, 3, 7, 6, 3, 8, -20593642984667941858720510466795559017722675200000⟩, + ⟨7, 3, 8, 6, 4, 8, 2817543028336541100185558447064175290718617600000⟩, + ⟨7, 3, 5, 7, 0, 8, -15573683715130804750025314938007359073401018777600000⟩, + ⟨7, 3, 6, 7, 1, 8, -1188325848673055800958057008871152769991652147200000⟩, + ⟨7, 3, 7, 7, 2, 8, 36570433314969861107037947991626948075637964800000⟩, + ⟨7, 3, 8, 7, 3, 8, 13494477318268209598638059897566077328451174400000⟩ +] + +def collectedFourData_9_2 : List (List CollectedFourTerm) := [ + collectedFourData_9_2_0, + collectedFourData_9_2_1, + collectedFourData_9_2_2, + collectedFourData_9_2_3, + collectedFourData_9_2_4, + collectedFourData_9_2_5, + collectedFourData_9_2_6, + collectedFourData_9_2_7, + collectedFourData_9_2_8, + collectedFourData_9_2_9, + collectedFourData_9_2_10, + collectedFourData_9_2_11, + collectedFourData_9_2_12, + collectedFourData_9_2_13, + collectedFourData_9_2_14, + collectedFourData_9_2_15, + collectedFourData_9_2_16, + collectedFourData_9_2_17, + collectedFourData_9_2_18, + collectedFourData_9_2_19, + collectedFourData_9_2_20, + collectedFourData_9_2_21, + collectedFourData_9_2_22, + collectedFourData_9_2_23, + collectedFourData_9_2_24, + collectedFourData_9_2_25, + collectedFourData_9_2_26, + collectedFourData_9_2_27, + collectedFourData_9_2_28, + collectedFourData_9_2_29, + collectedFourData_9_2_30, + collectedFourData_9_2_31, + collectedFourData_9_2_32, + collectedFourData_9_2_33, + collectedFourData_9_2_34, + collectedFourData_9_2_35, + collectedFourData_9_2_36, + collectedFourData_9_2_37, + collectedFourData_9_2_38, + collectedFourData_9_2_39, + collectedFourData_9_2_40, + collectedFourData_9_2_41, + collectedFourData_9_2_42, + collectedFourData_9_2_43, + collectedFourData_9_2_44, + collectedFourData_9_2_45, + collectedFourData_9_2_46, + collectedFourData_9_2_47, + collectedFourData_9_2_48, + collectedFourData_9_2_49, + collectedFourData_9_2_50, + collectedFourData_9_2_51, + collectedFourData_9_2_52, + collectedFourData_9_2_53 +] + +theorem collectedFourChecked_9_2 : collectNumericRowParts 9 2 = collectedFourData_9_2 := by + decide +kernel + +def collectedFourData_9_3_0 : List CollectedFourTerm := [ + ⟨0, 3, 6, 1, 8, 0, 5353330158817421504047021541366131602343801651200000⟩, + ⟨0, 3, 6, 2, 7, 0, 7163368057073006070752529744462421834697854156800000⟩, + ⟨0, 3, 7, 2, 8, 0, 33594811991758933568905936798481115232605516595200000⟩, + ⟨0, 3, 6, 3, 6, 0, -18980830864796111200183499904601808885068804915200000⟩, + ⟨0, 3, 7, 3, 7, 0, -18758641415859994034370653273875794453934689484800000⟩, + ⟨0, 3, 8, 3, 8, 0, -42442805868402959294192830445002701540006297600000000⟩, + ⟨0, 3, 6, 4, 5, 0, 15101172883068330713250127269105093918048701644800000⟩, + ⟨0, 3, 7, 4, 6, 0, 6160813201129171472566306472872648288977813504000000⟩, + ⟨0, 3, 8, 4, 7, 0, -15076807760087452451655724517999113562695611187200000⟩, + ⟨0, 3, 6, 5, 4, 0, 17032327548740197074077509473128651482769601331200000⟩, + ⟨0, 3, 7, 5, 5, 0, 16316555840960566800422264219249342846847890227200000⟩, + ⟨0, 3, 8, 5, 6, 0, -31393870767137808325472830026066889814794095820800000⟩, + ⟨0, 3, 6, 6, 3, 0, -63067119997526996950043467250576475186122666803200000⟩, + ⟨0, 3, 7, 6, 4, 0, -5841091707999553272203905834242560784758892134400000⟩, + ⟨0, 3, 8, 6, 5, 0, 32946466823078927469958641842954525297222457753600000⟩, + ⟨0, 3, 6, 7, 2, 0, 62239523342113057513982808029465441849641323724800000⟩, + ⟨0, 3, 7, 7, 3, 0, -244739193924325927987447259472941140439939520921600000⟩, + ⟨0, 3, 8, 7, 4, 0, -65142470637800484522553622228994705943884201984000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0911.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0911.lean new file mode 100644 index 0000000000000000000000000000000000000000..4661ebb6f160b26fe199c6e250a0eb96e2d2b6c7 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0911.lean @@ -0,0 +1,650 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0911. -/ +namespace LaughlinFock +def collectedFourData_9_3_1 : List CollectedFourTerm := [ + ⟨0, 4, 5, 0, 8, 1, 34150862563576320877188470730578999270965248000000⟩, + ⟨0, 4, 5, 1, 7, 1, -270868813054728819672679891979062551659937792000000⟩, + ⟨0, 4, 6, 1, 8, 1, -148162107323847065951276968648774306165161984000000⟩, + ⟨0, 4, 5, 2, 6, 1, -189323216243481744033515238575431228311207936000000⟩, + ⟨0, 4, 6, 2, 7, 1, -198257846122968067666810047619553801143320576000000⟩, + ⟨0, 4, 7, 2, 8, 1, -464895494223263296451135157314037757910188032000000⟩, + ⟨0, 4, 5, 3, 5, 1, 71537625088472883288485538066143613498163200000000⟩, + ⟨0, 4, 6, 3, 6, 1, 525325323911452675495800683308782892785598464000000⟩, + ⟨0, 4, 7, 3, 7, 1, 259587935009801182933299024818330737487904768000000⟩, + ⟨0, 4, 8, 3, 8, 1, 391557863463233450997881156260724257849344000000000⟩, + ⟨0, 4, 5, 4, 4, 1, -257722007755151852645686024627429065734750208000000⟩, + ⟨0, 4, 6, 4, 5, 1, -417949487709421813544999555483580728120180736000000⟩, + ⟨0, 4, 7, 4, 6, 1, -85255256039496372900512514373818283343216640000000⟩, + ⟨0, 4, 8, 4, 7, 1, 139091714451909689297871547654188293494407168000000⟩, + ⟨0, 4, 5, 5, 3, 1, 672153812235990880864542013349593316019142656000000⟩, + ⟨0, 4, 6, 5, 4, 1, -471397329771423334425634804481032524172099584000000⟩, + ⟨0, 4, 7, 5, 5, 1, -225793592581069248941180774298367755552817152000000⟩, + ⟨0, 4, 8, 5, 6, 1, 289625455054390012486426621699366406011748352000000⟩, + ⟨0, 4, 5, 6, 2, 1, 9947825742478813833500345807439933550362624000000⟩, + ⟨0, 4, 6, 6, 3, 1, 1745484983078964334360290884814777997930266624000000⟩, + ⟨0, 4, 7, 6, 4, 1, 80830850223540166447007706083716556447023104000000⟩, + ⟨0, 4, 8, 6, 5, 1, -303948994274927949325449777837782944903593984000000⟩, + ⟨0, 4, 5, 7, 1, 1, -463733407236530992743422745263392610800631808000000⟩, + ⟨0, 4, 6, 7, 2, 1, -1722579901411559006665734181722674435337486336000000⟩, + ⟨0, 4, 7, 7, 3, 1, 3386777355478674424160974151560547202137849856000000⟩, + ⟨0, 4, 8, 7, 4, 1, 600974560983080383161687207246527617522728960000000⟩ +] + +def collectedFourData_9_3_2 : List CollectedFourTerm := [ + ⟨0, 5, 4, 0, 7, 2, -8922182957688350798400735876880043435723902156800000⟩, + ⟨0, 5, 5, 0, 8, 2, -841072263728580026708948695330462129541087232000000⟩, + ⟨0, 5, 4, 1, 6, 2, -19990457254477622703162846559326689336552010547200000⟩, + ⟨0, 5, 5, 1, 7, 2, 6670995361985278601957511995033851257189040128000000⟩, + ⟨0, 5, 6, 1, 8, 2, 1824478646383786032119470944453706458152828928000000⟩, + ⟨0, 5, 4, 2, 5, 2, 2536684261109800366460027733299325177972758937600000⟩, + ⟨0, 5, 5, 2, 6, 2, 4662678893273769994379737596261845026077671424000000⟩, + ⟨0, 5, 6, 2, 7, 2, 2441361109549893816256118351290156519199342592000000⟩, + ⟨0, 5, 7, 2, 8, 2, 3816503951114550621903056551692332161717764096000000⟩, + ⟨0, 5, 4, 3, 4, 2, -1740418784143906421935799711899466915179501977600000⟩, + ⟨0, 5, 5, 3, 5, 2, -1761838728463069523488898964768191685643468800000000⟩, + ⟨0, 5, 6, 3, 6, 2, -6468893114392326155763531003293151908056793088000000⟩, + ⟨0, 5, 7, 3, 7, 2, -2131056101719899198659521006566487367356514304000000⟩, + ⟨0, 5, 8, 3, 8, 2, -2410835582781106832778291928439015576961024000000000⟩, + ⟨0, 5, 4, 4, 3, 2, -3890089416152710090212866088743822446445985792000000⟩, + ⟨0, 5, 5, 4, 4, 2, 6347213985350083409995485689470426073763151872000000⟩, + ⟨0, 5, 6, 4, 5, 2, 5146659489164474100773937823390751798499213312000000⟩, + ⟨0, 5, 7, 4, 6, 2, 699892826605370759292380108879002427373649920000000⟩, + ⟨0, 5, 8, 4, 7, 2, -856392594200013034933758988381214755812016128000000⟩, + ⟨0, 5, 4, 5, 2, 2, 26653575862650829427936610448890288381566858035200000⟩, + ⟨0, 5, 5, 5, 3, 2, -16553898964592293689392062044660575509785083904000000⟩, + ⟨0, 5, 6, 5, 4, 2, 5804819988490199614821212010405936916624048128000000⟩, + ⟨0, 5, 7, 5, 5, 2, 1853625489878706666028334386659513614997651456000000⟩, + ⟨0, 5, 8, 5, 6, 2, -1783234147179518908963847444685956335420833792000000⟩, + ⟨0, 5, 4, 6, 1, 2, -14302471647823008050192749673892936548508028108800000⟩, + ⟨0, 5, 5, 6, 2, 2, -244996456555910556867378916501551114004463616000000⟩, + ⟨0, 5, 6, 6, 3, 2, -21494025272267203217551580384043434504311799808000000⟩, + ⟨0, 5, 7, 6, 4, 2, -663571196286833466063321726004516690499469312000000⟩, + ⟨0, 5, 8, 6, 5, 2, 1871424683614694036908845736653003536637886464000000⟩, + ⟨0, 5, 4, 7, 0, 2, -272908787015226981962711952607761427223742618009600000⟩, + ⟨0, 5, 5, 7, 1, 2, 11420891811001795755134042955241607401436086272000000⟩, + ⟨0, 5, 6, 7, 2, 2, 21211970480048872196405576613403530937617088512000000⟩, + ⟨0, 5, 7, 7, 3, 2, -27803343588703795323068318665374412732071149568000000⟩, + ⟨0, 5, 8, 7, 4, 2, -3700221579384291439774233226362908592738140160000000⟩ +] + +def collectedFourData_9_3_3 : List CollectedFourTerm := [ + ⟨0, 6, 3, 0, 6, 3, 99826445870417118753334958721508390247250001920000⟩, + ⟨0, 6, 4, 0, 7, 3, -1432103551901070876753730022195934380665885163520000⟩, + ⟨0, 6, 5, 0, 8, 3, -67500441428027405167564015240693632217802342400000⟩, + ⟨0, 6, 3, 1, 5, 3, -1338316044723016386713887208379920962221464616960000⟩, + ⟨0, 6, 4, 1, 6, 3, -3208677178447063475818341603580998767456896942080000⟩, + ⟨0, 6, 5, 1, 7, 3, 535382215200052301766915496819641736379341209600000⟩, + ⟨0, 6, 6, 1, 8, 3, 97615959466599693491413038996994399788230246400000⟩, + ⟨0, 6, 3, 2, 4, 3, 1742775100645313911141060872866356034939671019520000⟩, + ⟨0, 6, 4, 2, 5, 3, 407164318151138842807129738632462796568804720640000⟩, + ⟨0, 6, 5, 2, 6, 3, 374204330716929081398557867784389909698890956800000⟩, + ⟨0, 6, 6, 2, 7, 3, 130621318909656699235107476309587582265170329600000⟩, + ⟨0, 6, 7, 2, 8, 3, 153147186348768541700099441325612288163027353600000⟩, + ⟨0, 6, 3, 3, 3, 3, -2329466017513664102421216530293063966544111861760000⟩, + ⟨0, 6, 4, 3, 4, 3, -279355392552228410228541361311164837384568176640000⟩, + ⟨0, 6, 5, 3, 5, 3, -141396758667373685714439858869692906245980160000000⟩, + ⟨0, 6, 6, 3, 6, 3, -346108302938973193151453196262148625372964454400000⟩, + ⟨0, 6, 7, 3, 7, 3, -85514190502663506256826636232370198629738086400000⟩, + ⟨0, 6, 8, 3, 8, 3, -77392858172117935972770597075966122231070720000000⟩, + ⟨0, 6, 3, 4, 2, 3, 3188933308242960101074604473544773765183832064000000⟩, + ⟨0, 6, 4, 4, 3, 3, -624399981092570295947141149314506558022667468800000⟩, + ⟨0, 6, 5, 4, 4, 3, 509397068867723642567727503454436123486873190400000⟩, + ⟨0, 6, 6, 4, 5, 3, 275364200659978047376655252936231001360275865600000⟩, + ⟨0, 6, 7, 4, 6, 3, 28085027164454233110782023917167374208335872000000⟩, + ⟨0, 6, 8, 4, 7, 3, -27491991181794153537621978881127292428185763840000⟩, + ⟨0, 6, 3, 5, 1, 3, -2648161375315326334995337993548331437691219476480000⟩, + ⟨0, 6, 4, 5, 2, 3, 4278177307592058975824838930031306611558218465280000⟩, + ⟨0, 6, 5, 5, 3, 3, -1328536839999204945943511990797172089167858892800000⟩, + ⟨0, 6, 6, 5, 4, 3, 310578078746212684584777854099131629648111206400000⟩, + ⟨0, 6, 7, 5, 5, 3, 74381562800787786190309297165177390429215129600000⟩, + ⟨0, 6, 8, 5, 6, 3, -57245541100374925899390177676402075046258933760000⟩, + ⟨0, 6, 3, 6, 0, 3, -1442190038012530962520558582714967971220611399680000⟩, + ⟨0, 6, 4, 6, 1, 3, -2295696080762564403615548413374587481056681656320000⟩, + ⟨0, 6, 5, 6, 2, 3, -19662245063835831530935260011590553049445171200000⟩, + ⟨0, 6, 6, 6, 3, 3, -1150005183075378578114868525029595534181426790400000⟩, + ⟨0, 6, 7, 6, 4, 3, -26627526908163484527807074623764148633416499200000⟩, + ⟨0, 6, 8, 6, 5, 3, 60076641540072648963775964425149579914033233920000⟩, + ⟨0, 6, 4, 7, 0, 3, -43804710695013649040193559651143610563646917181440000⟩, + ⟨0, 6, 5, 7, 1, 3, 916586210234539795176101797702132773253703270400000⟩, + ⟨0, 6, 6, 7, 2, 3, 1134914269723711365535621501403797766910089625600000⟩, + ⟨0, 6, 7, 7, 3, 3, -1115681759075495111342257825886010128202517708800000⟩, + ⟨0, 6, 8, 7, 4, 3, -118784842045655125046284054478266910265625804800000⟩ +] + +def collectedFourData_9_3_4 : List CollectedFourTerm := [ + ⟨0, 7, 2, 0, 5, 4, -8922182957688350798400735876880043435723902156800000⟩, + ⟨0, 7, 3, 0, 6, 4, -1432103551901070876753730022195934380665885163520000⟩, + ⟨0, 7, 4, 0, 7, 4, 10272431145299541450404418097355400702375556546560000⟩, + ⟨0, 7, 5, 0, 8, 4, 322785614176329952801051813446067499832233164800000⟩, + ⟨0, 7, 2, 1, 4, 4, 30750700909527025652039420579586316210833236951040000⟩, + ⟨0, 7, 3, 1, 5, 4, 19199392951462349440685317852690423453146949877760000⟩, + ⟨0, 7, 4, 1, 6, 4, 23015734678778588666848172770033541179917981450240000⟩, + ⟨0, 7, 5, 1, 7, 4, -2560185881698213143596746272774303279427564339200000⟩, + ⟨0, 7, 6, 1, 8, 4, -350098015248923174288572571305057122789202329600000⟩, + ⟨0, 7, 2, 2, 3, 4, -11460597394902614735856156454706749873819043758080000⟩, + ⟨0, 7, 3, 2, 4, 4, -25001735662699013394886274677938411189436541829120000⟩, + ⟨0, 7, 4, 2, 5, 4, -2920576111607423825856455662033866170291894353920000⟩, + ⟨0, 7, 5, 2, 6, 4, -1789436812005101571900738818531862912333093273600000⟩, + ⟨0, 7, 6, 2, 7, 4, -468471188003991594593607685246408890729784934400000⟩, + ⟨0, 7, 7, 2, 8, 4, -439407869570805538701988064245151923765059256320000⟩, + ⟨0, 7, 2, 3, 2, 4, -6128315945294502922019412661441771337652004454400000⟩, + ⟨0, 7, 3, 3, 3, 4, 33418364528820434026706817323823756008200140226560000⟩, + ⟨0, 7, 4, 3, 4, 4, 2003806939275802832102913353214310862613821521920000⟩, + ⟨0, 7, 5, 3, 5, 4, 676156164662348680719596565764065039031992320000000⟩, + ⟨0, 7, 6, 3, 6, 4, 1241311672622218591356511856370945074786834841600000⟩, + ⟨0, 7, 7, 3, 7, 4, 245356177692189965502219993885586190935712071680000⟩, + ⟨0, 7, 8, 3, 8, 4, 185045465847694413599372221452292266362142720000000⟩, + ⟨0, 7, 2, 4, 1, 4, -14146833261646482641628607873523076793313966161920000⟩, + ⟨0, 7, 3, 4, 2, 4, -45748225108991283582428990812933780362215030784000000⟩, + ⟨0, 7, 4, 4, 3, 4, 4478800296518535343097837986017514765855123046400000⟩, + ⟨0, 7, 5, 4, 4, 4, -2435925488123071018100910550874357574507744460800000⟩, + ⟨0, 7, 6, 4, 5, 4, -987589126290873725074872895452899405315073638400000⟩, + ⟨0, 7, 7, 4, 6, 4, -80581186291381503725410047566437329725187686400000⟩, + ⟨0, 7, 8, 4, 7, 4, 65733046116503021459749130593912704382890147840000⟩, + ⟨0, 7, 2, 5, 0, 4, 105550586151095428059704312534346382928230628720640000⟩, + ⟨0, 7, 3, 5, 1, 4, 37990346931906223490198113172669181284582298746880000⟩, + ⟨0, 7, 4, 5, 2, 4, -30687223533021628266115357175788938938130722979840000⟩, + ⟨0, 7, 5, 5, 3, 4, 6353033710339039596811686520004173798127016345600000⟩, + ⟨0, 7, 6, 5, 4, 4, -1113883114431476425774989174497507544609167769600000⟩, + ⟨0, 7, 7, 5, 5, 4, -213414590400694304651060787979875639858057707520000⟩, + ⟨0, 7, 8, 5, 6, 4, 136873454099134558677849647026886320185944309760000⟩, + ⟨0, 7, 3, 6, 0, 4, 20689562349390852969835001772698012048498444206080000⟩, + ⟨0, 7, 4, 6, 1, 4, 16466951631299717040930349557444766573876173864960000⟩, + ⟨0, 7, 5, 6, 2, 4, 94024419911134096783667186519698781506004582400000⟩, + ⟨0, 7, 6, 6, 3, 4, 4124474464223478615531882917630330268785678745600000⟩, + ⟨0, 7, 7, 6, 4, 4, 76399345946909705597522487003045794294047703040000⟩, + ⟨0, 7, 8, 6, 5, 4, -143642583862508706299548431375643123763820625920000⟩, + ⟨0, 7, 4, 7, 0, 4, 314209732848549365627762717430079657906046049976320000⟩, + ⟨0, 7, 5, 7, 1, 4, -4383094933261634010584156565773794072079420620800000⟩, + ⟨0, 7, 6, 7, 2, 4, -4070351154453420971888403265586851700799858278400000⟩, + ⟨0, 7, 7, 7, 3, 4, 3201099259884078600026324760554768826949498306560000⟩, + ⟨0, 7, 8, 7, 4, 4, 284013240383231203872951191414580921368366284800000⟩ +] + +def collectedFourData_9_3_5 : List CollectedFourTerm := [ + ⟨0, 8, 1, 0, 4, 5, 34150862563576320877188470730578999270965248000000⟩, + ⟨0, 8, 2, 0, 5, 5, -841072263728580026708948695330462129541087232000000⟩, + ⟨0, 8, 3, 0, 6, 5, -67500441428027405167564015240693632217802342400000⟩, + ⟨0, 8, 4, 0, 7, 5, 322785614176329952801051813446067499832233164800000⟩, + ⟨0, 8, 5, 0, 8, 5, 7607051673950575587315895448661767422476288000000⟩, + ⟨0, 8, 1, 1, 3, 5, -137924762872509726128625425351356069012360396800000⟩, + ⟨0, 8, 2, 1, 4, 5, 2898793013757856493301143080724443012330527129600000⟩, + ⟨0, 8, 3, 1, 5, 5, 904939798280307197215678199742402160913232691200000⟩, + ⟨0, 8, 4, 1, 6, 5, 723212251211674670786454752372135090600489779200000⟩, + ⟨0, 8, 5, 1, 7, 5, -60335608037222029528909667087838040610045952000000⟩, + ⟨0, 8, 6, 1, 8, 5, -6600575926512626102120073482135403181690060800000⟩, + ⟨0, 8, 1, 2, 2, 5, -24078669090492636328794425462212630068540211200000⟩, + ⟨0, 8, 2, 2, 3, 5, -1080362355303015213292202569289664457405051699200000⟩, + ⟨0, 8, 3, 2, 4, 5, -1178426093182135585555179058216204160555443814400000⟩, + ⟨0, 8, 4, 2, 5, 5, -91771844522441956274059851819524105199786393600000⟩, + ⟨0, 8, 5, 2, 6, 5, -42171452810645083649688448008482805793161216000000⟩, + ⟨0, 8, 6, 2, 7, 5, -8832325552046751700312892246297924517180211200000⟩, + ⟨0, 8, 7, 2, 8, 5, -6903650024377422707153119264622030181158092800000⟩, + ⟨0, 8, 1, 3, 1, 5, 135129976538236448919339207625487545773588480000000⟩, + ⟨0, 8, 2, 3, 2, 5, -577701285593031941679721595974608392716025856000000⟩, + ⟨0, 8, 3, 3, 3, 5, 1575133554067142584901942190109687062574871347200000⟩, + ⟨0, 8, 4, 3, 4, 5, 62964652129198709981249564736245180623591833600000⟩, + ⟨0, 8, 5, 3, 5, 5, 15934895045963607485227170109250505749299200000000⟩, + ⟨0, 8, 6, 3, 6, 5, 23403080242496573620897212629576028391263436800000⟩, + ⟨0, 8, 7, 3, 7, 5, 3854853996493782637896143668407008270431027200000⟩, + ⟨0, 8, 8, 3, 8, 5, 2491968767081604232744636204035804128870400000000⟩, + ⟨0, 8, 1, 4, 0, 5, -1081242967336667491513614107666505077256250982400000⟩, + ⟨0, 8, 2, 4, 1, 5, -1333587209810654255606524636950853960063569100800000⟩, + ⟨0, 8, 3, 4, 2, 5, -2156286383974416895257873934570546090035118080000000⟩, + ⟨0, 8, 4, 4, 3, 5, 140735166197379084227224258985603038615437312000000⟩, + ⟨0, 8, 5, 4, 4, 5, -57407177545164312721484135452941348186882048000000⟩, + ⟨0, 8, 6, 4, 5, 5, -18619520043969254479969785042301435944055603200000⟩, + ⟨0, 8, 7, 4, 6, 5, -1266031737775273274790072638862093509984256000000⟩, + ⟨0, 8, 8, 4, 7, 5, 885213248198597799686821281282606758677708800000⟩, + ⟨0, 8, 2, 5, 0, 5, 9949994396324421157848572371667337577668123033600000⟩, + ⟨0, 8, 3, 5, 1, 5, 1790628327472175675051350321332392113770961305600000⟩, + ⟨0, 8, 4, 5, 2, 5, -964269719150682463111839610198494932167242547200000⟩, + ⟨0, 8, 5, 5, 3, 5, 149721219281162548289464596508892536856641536000000⟩, + ⟨0, 8, 6, 5, 4, 5, -21000604830158133902794058460427894727167180800000⟩, + ⟨0, 8, 7, 5, 5, 5, -3353011505372775606295963120979015820430540800000⟩, + ⟨0, 8, 8, 5, 6, 5, 1843246312981035729563727442509586270204723200000⟩, + ⟨0, 8, 3, 6, 0, 5, 975177102020798394755377676325447076717107609600000⟩, + ⟨0, 8, 4, 6, 1, 5, 517433022498590322647607158634989265540140236800000⟩, + ⟨0, 8, 5, 6, 2, 5, 2215862756778564131201427368878888288518144000000⟩, + ⟨0, 8, 6, 6, 3, 5, 77760814607055357609756215710507096047668428800000⟩, + ⟨0, 8, 7, 6, 4, 5, 1200329768840911357058355703499781446408601600000⟩, + ⟨0, 8, 8, 6, 5, 5, -1934404774353630554253686402143969360635494400000⟩, + ⟨0, 8, 4, 7, 0, 5, 9873259811929565656095586227572841856122853785600000⟩, + ⟨0, 8, 5, 7, 1, 5, -103295897291562810148691586546897518642331648000000⟩, + ⟨0, 8, 6, 7, 2, 5, -76740400323137114494483565986600276861334323200000⟩, + ⟨0, 8, 7, 7, 3, 5, 50293293575098853044412326474332003790906982400000⟩, + ⟨0, 8, 8, 7, 4, 5, 3824747184322702161772579978911686785499136000000⟩ +] + +def collectedFourData_9_3_6 : List CollectedFourTerm := [ + ⟨1, 2, 6, 1, 8, 0, -2093967572244397798516880921253160805787815116800000⟩, + ⟨1, 2, 6, 2, 7, 0, -2801968116025143230132276902386648264060646195200000⟩, + ⟨1, 2, 7, 2, 8, 0, -13140689032699289464156826665601664014690864332800000⟩, + ⟨1, 2, 6, 3, 6, 0, 7424396244209712233796569635909733880748100812800000⟩, + ⟨1, 2, 7, 3, 7, 0, 7337486323251304605788679354088548509204820787200000⟩, + ⟨1, 2, 8, 3, 8, 0, 16601602465545058514027157755839976346904166400000000⟩, + ⟨1, 2, 6, 4, 5, 0, -5906858979717187887661016938233751407466591027200000⟩, + ⟨1, 2, 7, 4, 6, 0, -2409816446790848621856663760226268714218029056000000⟩, + ⟨1, 2, 8, 4, 7, 0, 5897328505058965729238684469109779401550908620800000⟩, + ⟨1, 2, 6, 5, 4, 0, -6662234629441480383176827691691410750257810636800000⟩, + ⟨1, 2, 7, 5, 5, 0, -6382258857210829794565761012587973176009215180800000⟩, + ⟨1, 2, 8, 5, 6, 0, 12279785741468211133810207421241234033162269491200000⟩, + ⟨1, 2, 6, 6, 3, 0, 24668851020173313919135175259492419479100247244800000⟩, + ⟨1, 2, 7, 6, 4, 0, 2284756639362331346857832112656831919330793881600000⟩, + ⟨1, 2, 8, 6, 5, 0, -12887087308434040542256782990649879906086184550400000⟩, + ⟨1, 2, 6, 7, 2, 0, -24345134658969556177416925012475234020656100147200000⟩, + ⟨1, 2, 7, 7, 3, 0, 95730306282469272732295576742557410237687948902400000⟩, + ⟨1, 2, 8, 7, 4, 0, 25480629261537997992260809791891125765224267776000000⟩ +] + +def collectedFourData_9_3_7 : List CollectedFourTerm := [ + ⟨1, 3, 5, 0, 8, 1, -137924762872509726128625425351356069012360396800000⟩, + ⟨1, 3, 5, 1, 7, 1, 1093955291482959959984719788765350124036764467200000⟩, + ⟨1, 3, 6, 1, 8, 1, 598380889539468812518549160720901295774787174400000⟩, + ⟨1, 3, 5, 2, 6, 1, 764617867499876767649852212915930160460044697600000⟩, + ⟨1, 3, 6, 2, 7, 1, 800702071967265852677253833223395095034304921600000⟩, + ⟨1, 3, 7, 2, 8, 1, 1877568997909580652300332822320333471939244851200000⟩, + ⟨1, 3, 5, 3, 5, 1, -288918324051750112245051475733244131011461120000000⟩, + ⟨1, 3, 6, 3, 6, 1, -2121626374634792156747049428727088136283645542400000⟩, + ⟨1, 3, 7, 3, 7, 1, -1048395316930521940105442738222940098835303628800000⟩, + ⟨1, 3, 8, 3, 8, 1, -1581381008122258326320878850113428280206950400000000⟩, + ⟨1, 3, 5, 4, 4, 1, 1040859414326136560695690070460083431090736332800000⟩, + ⟨1, 3, 6, 4, 5, 1, 1687968609217236838968057190832093699252001177600000⟩, + ⟨1, 3, 7, 4, 6, 1, 344319589321999326815715739261441540960026624000000⟩, + ⟨1, 3, 8, 4, 7, 1, -561748380369502607510634781461192735466507468800000⟩, + ⟨1, 3, 5, 5, 3, 1, -2714621189843062993863493181847716023426980249600000⟩, + ⟨1, 3, 6, 5, 4, 1, 1903827899117319789194362557810556414045087334400000⟩, + ⟨1, 3, 7, 5, 5, 1, 911910428525784304130783371867361835486491443200000⟩, + ⟨1, 3, 8, 5, 6, 1, -1169707562608521605094991961915278032291181363200000⟩, + ⟨1, 3, 5, 6, 2, 1, -40176188934442991677139227939521457729988198400000⟩, + ⟨1, 3, 6, 6, 3, 1, -7049473551085663358338656713391747359905834598400000⟩, + ⟨1, 3, 7, 6, 4, 1, -326450783757235632545714377755848456888804966400000⟩, + ⟨1, 3, 8, 6, 5, 1, 1227555903827136597014148517354325837500278374400000⟩, + ⟨1, 3, 5, 7, 1, 1, 1872875688281342156530906643580499023503346892800000⟩, + ⟨1, 3, 6, 7, 2, 1, 6956967016245697768299374499971871770114890137600000⟩, + ⟨1, 3, 7, 7, 3, 1, -13678145399308014197415142112440499408679311769600000⟩, + ⟨1, 3, 8, 7, 4, 1, -2427150226782492414444829206145651394620686336000000⟩ +] + +def collectedFourData_9_3_8 : List CollectedFourTerm := [ + ⟨1, 4, 4, 0, 7, 2, 30750700909527025652039420579586316210833236951040000⟩, + ⟨1, 4, 5, 0, 8, 2, 2898793013757856493301143080724443012330527129600000⟩, + ⟨1, 4, 4, 1, 6, 2, 68898001194585923398354713062605843230472965980160000⟩, + ⟨1, 4, 5, 1, 7, 2, -22991882605196031924658129995749099448144651878400000⟩, + ⟨1, 4, 6, 1, 8, 2, -6288146907189461571694056976602772324733052518400000⟩, + ⟨1, 4, 4, 2, 5, 2, -8742795276135236849510231793312519537749687009280000⟩, + ⟨1, 4, 5, 2, 6, 2, -16070130456210089708214417331465546828252132147200000⟩, + ⟨1, 4, 6, 2, 7, 2, -8414259789105540289274602409115771034263984537600000⟩, + ⟨1, 4, 7, 2, 8, 2, -13153750833995289026091533080839984723943804108800000⟩, + ⟨1, 4, 4, 3, 4, 2, 5998430848407328695032323065506022654366481121280000⟩, + ⟨1, 4, 5, 3, 5, 2, 6072255640431988549655124949604619430542704640000000⟩, + ⟨1, 4, 6, 3, 6, 2, 22295328208324052924870066888338743670537086566400000⟩, + ⟨1, 4, 7, 3, 7, 2, 7344779760309889033254257471540285564907631411200000⟩, + ⟨1, 4, 8, 3, 8, 2, 8309052201654774485113052325821566195807027200000000⟩, + ⟨1, 4, 4, 4, 3, 2, 13407366416348597971013005061815299936435673497600000⟩, + ⟨1, 4, 5, 4, 4, 2, -21875955671148555179333411720785338158810765721600000⟩, + ⟨1, 4, 6, 4, 5, 2, -17738191133829917149178359735271375251946707353600000⟩, + ⟨1, 4, 7, 4, 6, 2, -2412211796342876490223639060014539098948632576000000⟩, + ⟨1, 4, 8, 4, 7, 2, 2951595215012448315533883484871911850532824678400000⟩, + ⟨1, 4, 4, 5, 2, 2, -91862736216980564885228145969017109952451900866560000⟩, + ⟨1, 4, 5, 5, 3, 2, 57053750002745403172777216090447331839968490291200000⟩, + ⟨1, 4, 6, 5, 4, 2, -20006570605670970553580556534176621576321394278400000⟩, + ⟨1, 4, 7, 5, 5, 2, -6388602801337738104652057246403465381996711116800000⟩, + ⟨1, 4, 8, 5, 6, 2, 6145995903874657661518938178839785353749567897600000⟩, + ⟨1, 4, 4, 6, 1, 2, 49294105489083822885821686203042261759540477296640000⟩, + ⟨1, 4, 5, 6, 2, 2, 844391198339276538118264038088561132993039564800000⟩, + ⟨1, 4, 6, 6, 3, 2, 74080115328698796444641334212430009315992430182400000⟩, + ⟨1, 4, 7, 6, 4, 2, 2287027679880739863491253099890657153026464153600000⟩, + ⟨1, 4, 8, 6, 5, 2, -6449948515228801862211469549332669823943127859200000⟩, + ⟨1, 4, 4, 7, 0, 2, 940592288331798241319488324204442487493330080890880000⟩, + ⟨1, 4, 5, 7, 1, 2, -39362612251472506350124822834670810359473478041600000⟩, + ⟨1, 4, 6, 7, 2, 2, -73108000926120811712104581839008436717400725913600000⟩, + ⟨1, 4, 7, 7, 3, 2, 95825461889268525908568440376252584486481847910400000⟩, + ⟨1, 4, 8, 7, 4, 2, 12752978461237973829432113258408811582191566848000000⟩ +] + +def collectedFourData_9_3_9 : List CollectedFourTerm := [ + ⟨1, 5, 3, 0, 6, 3, -1338316044723016386713887208379920962221464616960000⟩, + ⟨1, 5, 4, 0, 7, 3, 19199392951462349440685317852690423453146949877760000⟩, + ⟨1, 5, 5, 0, 8, 3, 904939798280307197215678199742402160913232691200000⟩, + ⟨1, 5, 3, 1, 5, 3, 17942037502647742386619404245184210815523728916480000⟩, + ⟨1, 5, 4, 1, 6, 3, 43016899107342116163212742009355668870489220055040000⟩, + ⟨1, 5, 5, 1, 7, 3, -7177563043681531839453112271913619697460628684800000⟩, + ⟨1, 5, 6, 1, 8, 3, -1308681318222675042174381246486753659220865843200000⟩, + ⟨1, 5, 3, 2, 4, 3, -23364388656739498845097423541908012456438671605760000⟩, + ⟨1, 5, 4, 2, 5, 3, -5458619056995373644196949059497214636812738232320000⟩, + ⟨1, 5, 5, 2, 6, 3, -5016743363310641497007639872540099874744854118400000⟩, + ⟨1, 5, 6, 2, 7, 3, -1751165288470717917409101888138222685477719244800000⟩, + ⟨1, 5, 7, 2, 8, 3, -2053156705196102101233090741426450929703242956800000⟩, + ⟨1, 5, 3, 3, 3, 3, 31229818107742847738597069112090602507005203578880000⟩, + ⟨1, 5, 4, 3, 4, 3, 3745157916549010163537227400389990800179928760320000⟩, + ⟨1, 5, 5, 3, 5, 3, 1895625444203583520384749876929352876246958080000000⟩, + ⟨1, 5, 6, 3, 6, 3, 4640075993853938948905271455569501549082391347200000⟩, + ⟨1, 5, 7, 3, 7, 3, 1146439825672789472775668086096890694020051763200000⟩, + ⟨1, 5, 8, 3, 8, 3, 1037561769685444831250601733818413460341391360000000⟩, + ⟨1, 5, 3, 4, 2, 3, -42752204335844589807417368039002447794753503232000000⟩, + ⟨1, 5, 4, 4, 3, 3, 8370973300057879787867644276998430365575439974400000⟩, + ⟨1, 5, 5, 4, 4, 3, -6829195054039053583453754487070793768029598515200000⟩, + ⟨1, 5, 6, 4, 5, 3, -3691650290384489096873334801094116822276164812800000⟩, + ⟨1, 5, 7, 4, 6, 3, -376519890525416419192595903727832947580993536000000⟩, + ⟨1, 5, 8, 4, 7, 3, 368569396407632110217315712880987797192620113920000⟩, + ⟨1, 5, 3, 5, 1, 3, 35502384430281852644923451641239911641890674442240000⟩, + ⟨1, 5, 4, 5, 2, 3, -57355075431139797979826419509962665073561976176640000⟩, + ⟨1, 5, 5, 5, 3, 3, 17810933300024954176794706340619506721757750886400000⟩, + ⟨1, 5, 6, 5, 4, 3, -4163742606491817248732427359502470336094614323200000⟩, + ⟨1, 5, 7, 5, 5, 3, -997191055535382367531828755709903406350781644800000⟩, + ⟨1, 5, 8, 5, 6, 3, 767458216863015327680571013692301425370862714880000⟩, + ⟨1, 5, 3, 6, 0, 3, 19334616699840265075567228199026063724863385763840000⟩, + ⟨1, 5, 4, 6, 1, 3, 30777083886973886535964095241515226631128649564160000⟩, + ⟨1, 5, 5, 6, 2, 3, 263600469943260639509213112222977448818088345600000⟩, + ⟨1, 5, 6, 6, 3, 3, 15417461521391316386099902676823283961666155315200000⟩, + ⟨1, 5, 7, 6, 4, 3, 356980018488763424013300654256252682071808409600000⟩, + ⟨1, 5, 8, 6, 5, 3, -805413160662057920789674291786499372562209832960000⟩, + ⟨1, 5, 4, 7, 0, 3, 587264693703371269190082751381164865700210902302720000⟩, + ⟨1, 5, 5, 7, 1, 3, -12288146901684569050758049232446231655706997555200000⟩, + ⟨1, 5, 6, 7, 2, 3, -15215146280254938414135786403524941954608319692800000⟩, + ⟨1, 5, 7, 7, 3, 3, 14957307013752095786874112300575137383175317094400000⟩, + ⟨1, 5, 8, 7, 4, 3, 1592480415319479791742576528308457004977251942400000⟩ +] + +def collectedFourData_9_3_10 : List CollectedFourTerm := [ + ⟨1, 6, 2, 0, 5, 4, -19990457254477622703162846559326689336552010547200000⟩, + ⟨1, 6, 3, 0, 6, 4, -3208677178447063475818341603580998767456896942080000⟩, + ⟨1, 6, 4, 0, 7, 4, 23015734678778588666848172770033541179917981450240000⟩, + ⟨1, 6, 5, 0, 8, 4, 723212251211674670786454752372135090600489779200000⟩, + ⟨1, 6, 2, 1, 4, 4, 68898001194585923398354713062605843230472965980160000⟩, + ⟨1, 6, 3, 1, 5, 4, 43016899107342116163212742009355668870489220055040000⟩, + ⟨1, 6, 4, 1, 6, 4, 51567543779188283591668247881938646069175868456960000⟩, + ⟨1, 6, 5, 1, 7, 4, -5736184370384765086311780385691957258907077836800000⟩, + ⟨1, 6, 6, 1, 8, 4, -784406623569656835490942650200241104778323558400000⟩, + ⟨1, 6, 2, 2, 3, 4, -25677861955986668980716593909728754479126617784320000⟩, + ⟨1, 6, 3, 2, 4, 4, -56017247171809354020457171982866320046506356244480000⟩, + ⟨1, 6, 4, 2, 5, 4, -6543651054277786118412978306505881550226907463680000⟩, + ⟨1, 6, 5, 2, 6, 4, -4009294616532362092424763795441179876083000934400000⟩, + ⟨1, 6, 6, 2, 7, 4, -1049625781398962774443722517895907634239347097600000⟩, + ⟨1, 6, 7, 2, 8, 4, -984508418577879591251654873220419709836753633280000⟩, + ⟨1, 6, 2, 3, 2, 4, -13730702287468441793941682742779550289370913177600000⟩, + ⟨1, 6, 3, 3, 3, 4, 74874993126236096052233431173833399701195708170240000⟩, + ⟨1, 6, 4, 3, 4, 4, 4489598246951545378498470391109093099967275335680000⟩, + ⟨1, 6, 5, 3, 5, 4, 1514951102340569990562281247448205414922977280000000⟩, + ⟨1, 6, 6, 3, 6, 4, 2781201422198558403560679509329785852029986406400000⟩, + ⟨1, 6, 7, 3, 7, 4, 549728940275903064616342700817608219667694878720000⟩, + ⟨1, 6, 8, 3, 8, 4, 414600719656352506326000995420443448841338880000000⟩, + ⟨1, 6, 2, 4, 1, 4, -31696465645716523969823462959952295553861869895680000⟩, + ⟨1, 6, 3, 4, 2, 4, -102500469094444042201116123635664536754230132736000000⟩, + ⟨1, 6, 4, 4, 3, 4, 10034905841259801354208870363839853147010472345600000⟩, + ⟨1, 6, 5, 4, 4, 4, -5457774692173903784704007514392931134784877363200000⟩, + ⟨1, 6, 6, 4, 5, 4, -2212727345732401699331823698748336966618159513600000⟩, + ⟨1, 6, 7, 4, 6, 4, -180544914592327150677458226699221694032746905600000⟩, + ⟨1, 6, 8, 4, 7, 4, 147277146728563953173535284635497921066156687360000⟩, + ⟨1, 6, 2, 5, 0, 4, 236489712287318097181867126382241435305007183298560000⟩, + ⟨1, 6, 3, 5, 1, 4, 85118676676611323670251427454557148720215380459520000⟩, + ⟨1, 6, 4, 5, 2, 4, -68755777953068098838695821816755456020948828815360000⟩, + ⟨1, 6, 5, 5, 3, 4, 14234190155599812576596013537231479230108690022400000⟩, + ⟨1, 6, 6, 5, 4, 4, -2495693362389421728949831657734731471035721318400000⟩, + ⟨1, 6, 7, 5, 5, 4, -478162717254149913350907756893172128737740718080000⟩, + ⟨1, 6, 8, 5, 6, 4, 306669673376700969198431509729614582791578583040000⟩, + ⟨1, 6, 3, 6, 0, 4, 46355674807469485313820534496676792642654510776320000⟩, + ⟨1, 6, 4, 6, 1, 4, 36894770512791111685417442257641699543881707683840000⟩, + ⟨1, 6, 5, 6, 2, 4, 210664941082710579258943614457017405086996889600000⟩, + ⟨1, 6, 6, 6, 3, 4, 9241026648438730972125533855599983200873899622400000⟩, + ⟨1, 6, 7, 6, 4, 4, 171175357719569120367146637536492970643197788160000⟩, + ⟨1, 6, 8, 6, 5, 4, -321836141025533254041803783665160045666689351680000⟩, + ⟨1, 6, 4, 7, 0, 4, 703997694649063233311798960220867116569604684513280000⟩, + ⟨1, 6, 5, 7, 1, 4, -9820474688896722154970564856392547490661086003200000⟩, + ⟨1, 6, 6, 7, 2, 4, -9119761514607681304243604015323197989667314073600000⟩, + ⟨1, 6, 7, 7, 3, 4, 7172172799584932010460957476931824635275892490240000⟩, + ⟨1, 6, 8, 7, 4, 4, 636341416502140330288495423493901383231550259200000⟩ +] + +def collectedFourData_9_3_11 : List CollectedFourTerm := [ + ⟨1, 7, 1, 0, 4, 5, -270868813054728819672679891979062551659937792000000⟩, + ⟨1, 7, 2, 0, 5, 5, 6670995361985278601957511995033851257189040128000000⟩, + ⟨1, 7, 3, 0, 6, 5, 535382215200052301766915496819641736379341209600000⟩, + ⟨1, 7, 4, 0, 7, 5, -2560185881698213143596746272774303279427564339200000⟩, + ⟨1, 7, 5, 0, 8, 5, -60335608037222029528909667087838040610045952000000⟩, + ⟨1, 7, 1, 1, 3, 5, 1093955291482959959984719788765350124036764467200000⟩, + ⟨1, 7, 2, 1, 4, 5, -22991882605196031924658129995749099448144651878400000⟩, + ⟨1, 7, 3, 1, 5, 5, -7177563043681531839453112271913619697460628684800000⟩, + ⟨1, 7, 4, 1, 6, 5, -5736184370384765086311780385691957258907077836800000⟩, + ⟨1, 7, 5, 1, 7, 5, 478554077618185484255825546075023064074027008000000⟩, + ⟨1, 7, 6, 1, 8, 5, 52352708906362156188327585052601083843785523200000⟩, + ⟨1, 7, 1, 2, 2, 5, 190980842850966583340141675549605245857090764800000⟩, + ⟨1, 7, 2, 2, 3, 5, 8568933458273789704474972964602323215011597516800000⟩, + ⟨1, 7, 3, 2, 4, 5, 9346729574948089507447430440995382456879782297600000⟩, + ⟨1, 7, 4, 2, 5, 5, 727891734838623498580649985941400189774751334400000⟩, + ⟨1, 7, 5, 2, 6, 5, 334484417380312217909441563259883038089150464000000⟩, + ⟨1, 7, 6, 2, 7, 5, 70053912528331783257132656167131883875650764800000⟩, + ⟨1, 7, 7, 2, 8, 5, 54756552176892810207256286958426888403628851200000⟩, + ⟨1, 7, 1, 3, 1, 5, -1071788341652721088057674970889625804912721920000000⟩, + ⟨1, 7, 2, 3, 2, 5, 4582058834896630497464691453965878587266433024000000⟩, + ⟨1, 7, 3, 3, 3, 5, -12493229282234669208586766982509636542737992908800000⟩, + ⟨1, 7, 4, 3, 4, 5, -499406436803449237381188357134808968189077094400000⟩, + ⟨1, 7, 5, 3, 5, 5, -126388201739166732006693152956970546547916800000000⟩, + ⟨1, 7, 6, 3, 6, 5, -185622385241615308706372031705788692443640627200000⟩, + ⟨1, 7, 7, 3, 7, 5, -30574915189498012103360655464267862684519628800000⟩, + ⟨1, 7, 8, 3, 8, 5, -19765141242106408297938782369128803572121600000000⟩, + ⟨1, 7, 1, 4, 0, 5, 8575918064764271399639511914213479332393359769600000⟩, + ⟨1, 7, 2, 4, 1, 5, 10577395635436956473047928391708469627184165683200000⟩, + ⟨1, 7, 3, 4, 2, 5, 17102664166853738189779248416024015883542200320000000⟩, + ⟨1, 7, 4, 4, 3, 5, -1116246108044189075609615909434110484779368448000000⟩, + ⟨1, 7, 5, 4, 4, 5, 455327124271977464341151361156313386678484992000000⟩, + ⟨1, 7, 6, 4, 5, 5, 147681402909506132250524365898341716614499532800000⟩, + ⟨1, 7, 7, 4, 6, 5, 10041576942965860306767581051594007719706624000000⟩, + ⟨1, 7, 8, 4, 7, 5, -7021101191617033632127284476273675547652915200000⟩, + ⟨1, 7, 2, 5, 0, 5, -78918743765731702797385195514916111717409121894400000⟩, + ⟨1, 7, 3, 5, 1, 5, -14202433943846191082658931048503313071973230182400000⟩, + ⟨1, 7, 4, 5, 2, 5, 7648140476824602524455407340354404273093397708800000⟩, + ⟨1, 7, 5, 5, 3, 5, -1187519316102109258238144373615258846042783744000000⟩, + ⟨1, 7, 6, 5, 4, 5, 166567063809489952149482568039058771608286003200000⟩, + ⟨1, 7, 7, 5, 5, 5, 26594533152080438371798602657891572780315443200000⟩, + ⟨1, 7, 8, 5, 6, 5, -14619775416659148846124551836962084096888012800000⟩, + ⟨1, 7, 3, 6, 0, 5, -7734652782218401866399764901101073555016541798400000⟩, + ⟨1, 7, 4, 6, 1, 5, -4104038906150445221111857720403425366730027827200000⟩, + ⟨1, 7, 5, 6, 2, 5, -17575196342505920638089379433575847062142976000000⟩, + ⟨1, 7, 6, 6, 3, 5, -616762739610760867392085216500670680483967795200000⟩, + ⟨1, 7, 7, 6, 4, 5, -9520459378000157280867609011575855342052966400000⟩, + ⟨1, 7, 8, 6, 5, 5, 15342802080654025423397250843040673796037017600000⟩, + ⟨1, 7, 4, 7, 0, 5, -78310120608510171272037885659864416733125568102400000⟩, + ⟨1, 7, 5, 7, 1, 5, 819295180047093175931066190832486587555643392000000⟩, + ⟨1, 7, 6, 7, 2, 5, 608669286468999847532916934464766011404766412800000⟩, + ⟨1, 7, 7, 7, 3, 5, -398903093880549991414274106795616862941583769600000⟩, + ⟨1, 7, 8, 7, 4, 5, -30336121909754033935518614592718099546374144000000⟩ +] + +def collectedFourData_9_3_12 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 3, 6, 5353330158817421504047021541366131602343801651200000⟩, + ⟨1, 8, 1, 0, 4, 6, -148162107323847065951276968648774306165161984000000⟩, + ⟨1, 8, 2, 0, 5, 6, 1824478646383786032119470944453706458152828928000000⟩, + ⟨1, 8, 3, 0, 6, 6, 97615959466599693491413038996994399788230246400000⟩, + ⟨1, 8, 4, 0, 7, 6, -350098015248923174288572571305057122789202329600000⟩, + ⟨1, 8, 5, 0, 8, 6, -6600575926512626102120073482135403181690060800000⟩, + ⟨1, 8, 0, 1, 2, 6, -2093967572244397798516880921253160805787815116800000⟩, + ⟨1, 8, 1, 1, 3, 6, 598380889539468812518549160720901295774787174400000⟩, + ⟨1, 8, 2, 1, 4, 6, -6288146907189461571694056976602772324733052518400000⟩, + ⟨1, 8, 3, 1, 5, 6, -1308681318222675042174381246486753659220865843200000⟩, + ⟨1, 8, 4, 1, 6, 6, -784406623569656835490942650200241104778323558400000⟩, + ⟨1, 8, 5, 1, 7, 6, 52352708906362156188327585052601083843785523200000⟩, + ⟨1, 8, 6, 1, 8, 6, 4772721025726035140156307718134739956557414400000⟩, + ⟨1, 8, 0, 2, 1, 6, -2163302411211346889915977169425023775694389248000000⟩, + ⟨1, 8, 1, 2, 2, 6, 104464311768392742591045162983638359730657689600000⟩, + ⟨1, 8, 2, 2, 3, 6, 2343553738021411428492503659136581886003694796800000⟩, + ⟨1, 8, 3, 2, 4, 6, 1704184318099687513591198779998367185956660838400000⟩, + ⟨1, 8, 4, 2, 5, 6, 99537089671810220046933055716151467229524787200000⟩, + ⟨1, 8, 5, 2, 6, 6, 36591821396613230423682363579520862572353945600000⟩, + ⟨1, 8, 6, 2, 7, 6, 6386446627935809476187763196336895753296281600000⟩, + ⟨1, 8, 7, 2, 8, 6, 4278742945088345552765797538808324448006963200000⟩, + ⟨1, 8, 0, 3, 0, 6, 12088001715511910242304235585551605666281632563200000⟩, + ⟨1, 8, 1, 3, 1, 6, -586255824410148831562882352638252684243107840000000⟩, + ⟨1, 8, 2, 3, 2, 6, 1253166588659595069184045293277753620691943424000000⟩, + ⟨1, 8, 3, 3, 3, 6, -2277883965132946975591665372492804400998462259200000⟩, + ⟨1, 8, 4, 3, 4, 6, -68292385946386569106436306217688429417935667200000⟩, + ⟨1, 8, 5, 3, 5, 6, -13826576857899764625003910617357148194078720000000⟩, + ⟨1, 8, 6, 3, 6, 6, -16922216240474495877237391397907086182868582400000⟩, + ⟨1, 8, 7, 3, 7, 6, -2389160702469245405836278041815788821466316800000⟩, + ⟨1, 8, 8, 3, 8, 6, -1351412951974040882374645039831911392870400000000⟩, + ⟨1, 8, 1, 4, 0, 6, 4690927974995016723323773548169308780331479859200000⟩, + ⟨1, 8, 2, 4, 1, 6, 2892856526505612575450037888514530005182788403200000⟩, + ⟨1, 8, 3, 4, 2, 6, 3118319818409796199435729925105798630741114880000000⟩, + ⟨1, 8, 4, 4, 3, 6, -152643427084436766754917751182186474450714624000000⟩, + ⟨1, 8, 5, 4, 4, 6, 49811733948280482472982206392504607799299276800000⟩, + ⟨1, 8, 6, 4, 5, 6, 13463336501566629118200469176145852726090137600000⟩, + ⟨1, 8, 7, 4, 6, 6, 784660918084763554310073757433128355364864000000⟩, + ⟨1, 8, 8, 4, 7, 6, -480057641442912050911275878983939128085708800000⟩, + ⟨1, 8, 2, 5, 0, 6, -21583819952943444102121058206931250402981996134400000⟩, + ⟨1, 8, 3, 5, 1, 6, -2589522357726263857908772725468760348831619481600000⟩, + ⟨1, 8, 4, 5, 2, 6, 1045861091736491882967720771098035926717589094400000⟩, + ⟨1, 8, 5, 5, 3, 6, -129911865731041222350118165325141275875842457600000⟩, + ⟨1, 8, 6, 5, 4, 6, 15185042841983544740342595248721319002793574400000⟩, + ⟨1, 8, 7, 5, 5, 6, 2078128855424940622243757628217796209095475200000⟩, + ⟨1, 8, 8, 5, 6, 6, -999606003873882535889324810237730129916723200000⟩, + ⟨1, 8, 3, 6, 0, 6, -1410255199073299931018890946539060010791049625600000⟩, + ⟨1, 8, 4, 6, 1, 6, -561215451510329046520576963241336536148056473600000⟩, + ⟨1, 8, 5, 6, 2, 6, -1922685817809461145829068358798852594493030400000⟩, + ⟨1, 8, 6, 6, 3, 6, -56227013973424880125806105550565100443035238400000⟩, + ⟨1, 8, 7, 6, 4, 6, -743940163836844314331376491304497342473830400000⟩, + ⟨1, 8, 8, 6, 5, 6, 1049041906525753843153954693331303807739494400000⟩, + ⟨1, 8, 4, 7, 0, 6, -10708682519863589539289519157496096643121099571200000⟩, + ⟨1, 8, 5, 7, 1, 6, 89628997171794434864859401416254934825618636800000⟩, + ⟨1, 8, 6, 7, 2, 6, 55489176432878491728340499728116684609395097600000⟩, + ⟨1, 8, 7, 7, 3, 6, -31170768261694645577431190620137587469818265600000⟩, + ⟨1, 8, 8, 7, 4, 6, -2074188469453911670312370290665736567259136000000⟩ +] + +def collectedFourData_9_3_13 : List CollectedFourTerm := [ + ⟨2, 1, 6, 1, 8, 0, -2163302411211346889915977169425023775694389248000000⟩, + ⟨2, 1, 6, 2, 7, 0, -2894746060960985010309820047128310200320131072000000⟩, + ⟨2, 1, 7, 2, 8, 0, -13575799666729021791439933448034483938166571008000000⟩, + ⟨2, 1, 6, 3, 6, 0, 7670230671085459785036229128755937039045623808000000⟩, + ⟨2, 1, 7, 3, 7, 0, 7580443014361630210730686989804950473452552192000000⟩, + ⟨2, 1, 8, 3, 8, 0, 17151309848218663909977615363048114701205504000000000⟩, + ⟨2, 1, 6, 4, 5, 0, -6102445158599698108276530829156140787634798592000000⟩, + ⟨2, 1, 7, 4, 6, 0, -2489609580883685311895392364986669583208284160000000⟩, + ⟨2, 1, 8, 4, 7, 0, 6092599113664999243340643757933800631396466688000000⟩, + ⟨2, 1, 6, 5, 4, 0, -6882832584880325708240533414194978608746856448000000⟩, + ⟨2, 1, 7, 5, 5, 0, -6593586337146822541564786458486382053229068288000000⟩, + ⟨2, 1, 8, 5, 6, 0, 12686390398683964178581117650239283535263301632000000⟩, + ⟨2, 1, 6, 6, 3, 0, 25485678766531433561183389024364354317559267328000000⟩, + ⟨2, 1, 7, 6, 4, 0, 2360408829858797065251417910997931057035083776000000⟩, + ⟨2, 1, 8, 6, 5, 0, -13313800756687478810403582751406205619346079744000000⟩, + ⟨2, 1, 6, 7, 2, 0, -25151243604295350368545865844542174286726561792000000⟩, + ⟨2, 1, 7, 7, 3, 0, 98900100054985741924449258215397738650705854464000000⟩, + ⟨2, 1, 8, 7, 4, 0, 26324336370493679505717079166898012989801103360000000⟩ +] + +def collectedFourData_9_3_14 : List CollectedFourTerm := [ + ⟨2, 2, 5, 0, 8, 1, -24078669090492636328794425462212630068540211200000⟩, + ⟨2, 2, 5, 1, 7, 1, 190980842850966583340141675549605245857090764800000⟩, + ⟨2, 2, 6, 1, 8, 1, 104464311768392742591045162983638359730657689600000⟩, + ⟨2, 2, 5, 2, 6, 1, 133485678922107719024184625080825577711494758400000⟩, + ⟨2, 2, 6, 2, 7, 1, 139785197592058706905591011158581294131471974400000⟩, + ⟨2, 2, 7, 2, 8, 1, 327782782827923146176786849552276561918217420800000⟩, + ⟨2, 2, 5, 3, 5, 1, -50438866626526489449750520424841808529326080000000⟩, + ⟨2, 2, 6, 3, 6, 1, -370389902034588453279375256794355477440469401600000⟩, + ⟨2, 2, 7, 3, 7, 1, -183027060454157604751619981850453404296622899200000⟩, + ⟨2, 2, 8, 3, 8, 1, -276074790396865549617967994358568691800473600000000⟩, + ⟨2, 2, 5, 4, 4, 1, 181711455472643849803681850744399299446256435200000⟩, + ⟨2, 2, 6, 4, 5, 1, 294682671407237429230104672455708167161407078400000⟩, + ⟨2, 2, 7, 4, 6, 1, 60110724716795607926946763184105217186594816000000⟩, + ⟨2, 2, 8, 4, 7, 1, -98069071001704716318930942098536710085489459200000⟩, + ⟨2, 2, 5, 5, 3, 1, -473913922162693291024720883753287664739444326400000⟩, + ⟨2, 2, 6, 5, 4, 1, 332367016867502633191741336745158221034527129600000⟩, + ⟨2, 2, 7, 5, 5, 1, 159199762184388297833977152287725424359558348800000⟩, + ⟨2, 2, 8, 5, 6, 1, -204205544719562144217385481394173977998183628800000⟩, + ⟨2, 2, 5, 6, 2, 1, -7013890316155682265667875292610241846942105600000⟩, + ⟨2, 2, 6, 6, 3, 1, -1230685029748226549504507892007994512308279705600000⟩, + ⟨2, 2, 7, 6, 4, 1, -56991219217743164446843675951380775302699417600000⟩, + ⟨2, 2, 8, 6, 5, 1, 214304609141550445346335937804906528945838489600000⟩, + ⟨2, 2, 5, 7, 1, 1, 326963432864044383482462457923926606096839475200000⟩, + ⟨2, 2, 6, 7, 2, 1, 1214535397189651257937246961531671670096815718400000⟩, + ⟨2, 2, 7, 7, 3, 1, -2387907218270999569639387822290827538990524006400000⟩, + ⟨2, 2, 8, 7, 4, 1, -423727733341335938352060515392842460324429824000000⟩ +] + +def collectedFourData_9_3_15 : List CollectedFourTerm := [ + ⟨2, 3, 4, 0, 7, 2, -11460597394902614735856156454706749873819043758080000⟩, + ⟨2, 3, 5, 0, 8, 2, -1080362355303015213292202569289664457405051699200000⟩, + ⟨2, 3, 4, 1, 6, 2, -25677861955986668980716593909728754479126617784320000⟩, + ⟨2, 3, 5, 1, 7, 2, 8568933458273789704474972964602323215011597516800000⟩, + ⟨2, 3, 6, 1, 8, 2, 2343553738021411428492503659136581886003694796800000⟩, + ⟨2, 3, 4, 2, 5, 2, 3258386111608911444627784406497813495816975810560000⟩, + ⟨2, 3, 5, 2, 6, 2, 5989238937481483187584677230341441047121782374400000⟩, + ⟨2, 3, 6, 2, 7, 2, 3135942953065520875655995872851154047992017715200000⟩, + ⟨2, 3, 7, 2, 8, 2, 4902322161202509578274625187729994058162608537600000⟩, + ⟨2, 3, 4, 3, 4, 2, -2235578342003323252939774339499599164061840834560000⟩, + ⟨2, 3, 5, 3, 5, 2, -2263092388647213474987094402114861430766305280000000⟩, + ⟨2, 3, 6, 3, 6, 2, -8309331911964783981989445773978228222153510092800000⟩, + ⟨2, 3, 7, 3, 7, 2, -2737354313802392730628800588681753523569190502400000⟩, + ⟨2, 3, 8, 3, 8, 2, -3096732731281968657225714342903416518764134400000000⟩, + ⟨2, 3, 4, 4, 3, 2, -4996843131341584955777585628117579006261539635200000⟩, + ⟨2, 3, 5, 4, 4, 2, 8153034342644724728876465856433924146979877683200000⟩, + ⟨2, 3, 6, 4, 5, 2, 6610914908793947213879848321561543262608765747200000⟩, + ⟨2, 3, 7, 4, 6, 2, 899016523573144749556501391503829471751831552000000⟩, + ⟨2, 3, 8, 4, 7, 2, -1100041411462545409253118842480947957917863116800000⟩, + ⟨2, 3, 4, 5, 2, 2, 34236677676858410514791609676698237219858672517120000⟩, + ⟨2, 3, 5, 5, 3, 2, -21263582270032431104518061161144573891898140262400000⟩, + ⟨2, 3, 6, 5, 4, 2, 7456326008271614486669113374189030741908442316800000⟩, + ⟨2, 3, 7, 5, 5, 2, 2380993032890351008694429996428464841433913753600000⟩, + ⟨2, 3, 8, 5, 6, 2, -2290574932007669341690985754594618561365488435200000⟩, + ⟨2, 3, 4, 6, 1, 2, -18371610410259687393671146465357700143999384289280000⟩, + ⟨2, 3, 5, 6, 2, 2, -314699414378800724037583489025781402204477849600000⟩, + ⟨2, 3, 6, 6, 3, 2, -27609204071414745810013082238459709446752619724800000⟩, + ⟨2, 3, 7, 6, 4, 2, -852361172099036989563419372877601955755799347200000⟩, + ⟨2, 3, 8, 6, 5, 2, 2403856203745443564646203813252357684533290598400000⟩, + ⟨2, 3, 4, 7, 0, 2, -350552969866815909076111420919771968052209133813760000⟩, + ⟨2, 3, 5, 7, 1, 2, 14670203867971807570345325706424737646649750323200000⟩, + ⟨2, 3, 6, 7, 2, 2, 27246903003139553685173796269531976140720386867200000⟩, + ⟨2, 3, 7, 7, 3, 2, -35713561200591907317524537456835636409423154380800000⟩, + ⟨2, 3, 8, 7, 4, 2, -4752956758941112077322872488649504291758800896000000⟩ +] + +def collectedFourData_9_3_16 : List CollectedFourTerm := [ + ⟨2, 4, 3, 0, 6, 3, 1742775100645313911141060872866356034939671019520000⟩, + ⟨2, 4, 4, 0, 7, 3, -25001735662699013394886274677938411189436541829120000⟩, + ⟨2, 4, 5, 0, 8, 3, -1178426093182135585555179058216204160555443814400000⟩, + ⟨2, 4, 3, 1, 5, 3, -23364388656739498845097423541908012456438671605760000⟩, + ⟨2, 4, 4, 1, 6, 3, -56017247171809354020457171982866320046506356244480000⟩, + ⟨2, 4, 5, 1, 7, 3, 9346729574948089507447430440995382456879782297600000⟩, + ⟨2, 4, 6, 1, 8, 3, 1704184318099687513591198779998367185956660838400000⟩, + ⟨2, 4, 3, 2, 4, 3, 30425455148146836498566542498151384521072831365120000⟩, + ⟨2, 4, 4, 2, 5, 3, 7108295095130853097673810608032462271971946659840000⟩, + ⟨2, 4, 5, 2, 6, 3, 6532877980787351313012431646915616158987898060800000⟩, + ⟨2, 4, 6, 2, 7, 3, 2280393539250115789471646452493747779375045017600000⟩, + ⟨2, 4, 7, 2, 8, 3, 2673651263203151338031884108057924813761124761600000⟩, + ⟨2, 4, 3, 3, 3, 3, -40667934611155872216066170478686066564129158594560000⟩, + ⟨2, 4, 4, 3, 4, 3, -4877000459407287876365122039375420274998341795840000⟩, + ⟨2, 4, 5, 3, 5, 3, -2468511707181583892352299920335421500775464960000000⟩, + ⟨2, 4, 6, 3, 6, 3, -6042376118164482287665335551393184700858525286400000⟩, + ⟨2, 4, 7, 3, 7, 3, -1492911028339500853426970076209742774637323878400000⟩, + ⟨2, 4, 8, 3, 8, 3, -1351128401037380938301630698476236343418552320000000⟩, + ⟨2, 4, 3, 4, 2, 3, 55672557695167561834942785984111286066278825984000000⟩, + ⟨2, 4, 4, 4, 3, 3, -10900806198230218230645375261806671568225225932800000⟩, + ⟨2, 4, 5, 4, 4, 3, 8893079586513235668626771538084834706480064102400000⟩, + ⟨2, 4, 6, 4, 5, 3, 4807322031100418988184149173916046942812084633600000⟩, + ⟨2, 4, 7, 4, 6, 3, 490309813360418136070084237942018197298348032000000⟩, + ⟨2, 4, 8, 4, 7, 3, -479956561420463096198267990931010536426480599040000⟩, + ⟨2, 4, 3, 5, 1, 3, -46231734157710493636401164332095114278826022010880000⟩, + ⟨2, 4, 4, 5, 2, 3, 74688634086959452338734783953110055079911285063680000⟩, + ⟨2, 4, 5, 5, 3, 3, -23193662810014526185649994996051509503345872076800000⟩, + ⟨2, 4, 6, 5, 4, 3, 5422087681532494754485502059726149946513450598400000⟩, + ⟨2, 4, 7, 5, 5, 3, 1298557055357549602244400296298185079282833817600000⟩, + ⟨2, 4, 8, 5, 6, 3, -999395528738005134066142539498879762641253826560000⟩, + ⟨2, 4, 3, 6, 0, 3, -25177826043306930767799113077859345228936333230080000⟩, + ⟨2, 4, 4, 6, 1, 3, -40078377361000135030001289268087942029762279505920000⟩, + ⟨2, 4, 5, 6, 2, 3, -343264460847584575034153003374500539706585907200000⟩, + ⟨2, 4, 6, 6, 3, 3, -20076848185884944614914101443709628178888025702400000⟩, + ⟨2, 4, 7, 6, 4, 3, -464864700758243245597866524657313289323361075200000⟩, + ⟨2, 4, 8, 6, 5, 3, 1048821022260391873533467799816958672033567211520000⟩, + ⟨2, 4, 4, 7, 0, 3, -764744837148055038527032846473574272778430463344640000⟩, + ⟨2, 4, 5, 7, 1, 3, 16001808046588850203577075714815939714746836582400000⟩, + ⟨2, 4, 6, 7, 2, 3, 19813390263427991929586547049783875407523191193600000⟩, + ⟨2, 4, 7, 7, 3, 3, -19477628127569562402114469988659282639965703372800000⟩, + ⟨2, 4, 8, 7, 4, 3, -2073751732281213843694961244662530405972102348800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0912.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0912.lean new file mode 100644 index 0000000000000000000000000000000000000000..0e1523e2d9154d212467106c4b0147205d8ee9ef --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0912.lean @@ -0,0 +1,645 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0912. -/ +namespace LaughlinFock +def collectedFourData_9_3_17 : List CollectedFourTerm := [ + ⟨2, 5, 2, 0, 5, 4, 2536684261109800366460027733299325177972758937600000⟩, + ⟨2, 5, 3, 0, 6, 4, 407164318151138842807129738632462796568804720640000⟩, + ⟨2, 5, 4, 0, 7, 4, -2920576111607423825856455662033866170291894353920000⟩, + ⟨2, 5, 5, 0, 8, 4, -91771844522441956274059851819524105199786393600000⟩, + ⟨2, 5, 2, 1, 4, 4, -8742795276135236849510231793312519537749687009280000⟩, + ⟨2, 5, 3, 1, 5, 4, -5458619056995373644196949059497214636812738232320000⟩, + ⟨2, 5, 4, 1, 6, 4, -6543651054277786118412978306505881550226907463680000⟩, + ⟨2, 5, 5, 1, 7, 4, 727891734838623498580649985941400189774751334400000⟩, + ⟨2, 5, 6, 1, 8, 4, 99537089671810220046933055716151467229524787200000⟩, + ⟨2, 5, 2, 2, 3, 4, 3258386111608911444627784406497813495816975810560000⟩, + ⟨2, 5, 3, 2, 4, 4, 7108295095130853097673810608032462271971946659840000⟩, + ⟨2, 5, 4, 2, 5, 4, 830355025314040554986165909694723143316736573440000⟩, + ⟨2, 5, 5, 2, 6, 4, 508758475228567712528859133459407836026188595200000⟩, + ⟨2, 5, 6, 2, 7, 4, 133192010859753653478548503265505651354029260800000⟩, + ⟨2, 5, 7, 2, 8, 4, 124928958779930949548865647401242428914784010240000⟩, + ⟨2, 5, 2, 3, 2, 4, 1742354161448904597995134341162509504390941900800000⟩, + ⟨2, 5, 3, 3, 3, 4, -9501244228492302538199593280267849332686764113920000⟩, + ⟨2, 5, 4, 3, 4, 4, -569706488789655134861619328921204983281945149440000⟩, + ⟨2, 5, 5, 3, 5, 4, -192239355445333349773720565795832729949962240000000⟩, + ⟨2, 5, 6, 3, 6, 4, -352919884965964646218234483960163687392817971200000⟩, + ⟨2, 5, 7, 3, 7, 4, -69757721542967906998136037785270288167741685760000⟩, + ⟨2, 5, 8, 3, 8, 4, -52610658516152518893366289224321012376535040000000⟩, + ⟨2, 5, 2, 4, 1, 4, 4022115377990519793339744930137159406642989629440000⟩, + ⟨2, 5, 3, 4, 2, 4, 13006772351343203732392896646597637345208434688000000⟩, + ⟨2, 5, 4, 4, 3, 4, -1273376961076807648077599642084960546308541644800000⟩, + ⟨2, 5, 5, 4, 4, 4, 692563005742146865047932329191409065913850265600000⟩, + ⟨2, 5, 6, 4, 5, 4, 280783503878552082155200106671182694505565388800000⟩, + ⟨2, 5, 7, 4, 6, 4, 22910203475570133097126756281362138755026124800000⟩, + ⟨2, 5, 8, 4, 7, 4, -18688698080871860247707130025376242971055226880000⟩, + ⟨2, 5, 2, 5, 0, 4, -30009305111780494076504210002175726051194809876480000⟩, + ⟨2, 5, 3, 5, 1, 4, -10801113986709357548789860969080095219017486172160000⟩, + ⟨2, 5, 4, 5, 2, 4, 8724747892139481870010117316770065624182166650880000⟩, + ⟨2, 5, 5, 5, 3, 4, -1806244133273461022726110763332349138629243699200000⟩, + ⟨2, 5, 6, 5, 4, 4, 316690408445330750788701217836817804036354867200000⟩, + ⟨2, 5, 7, 5, 5, 4, 60676342900381225306797271382207507349519728640000⟩, + ⟨2, 5, 8, 5, 6, 4, -38914774380166558618110253617067065252060856320000⟩, + ⟨2, 5, 3, 6, 0, 4, -5882292195737205242387873824383927656743761346560000⟩, + ⟨2, 5, 4, 6, 1, 4, -4681753022737488803095989009391907226967049502720000⟩, + ⟨2, 5, 5, 6, 2, 4, -26732276986432527100590914088906602983509196800000⟩, + ⟨2, 5, 6, 6, 3, 4, -1172637852010120845210826513618258509021000499200000⟩, + ⟨2, 5, 7, 6, 4, 4, -21721255811685416459389887057194599838939873280000⟩, + ⟨2, 5, 8, 6, 5, 4, 40839319641521519777945143803688836429974077440000⟩, + ⟨2, 5, 4, 7, 0, 4, -89333617992848042088423956339168273417625655050240000⟩, + ⟨2, 5, 5, 7, 1, 4, 1246166771616572884351537531750640013662591385600000⟩, + ⟨2, 5, 6, 7, 2, 4, 1157249942044144652908323709782986163391089868800000⟩, + ⟨2, 5, 7, 7, 3, 4, -910111140884072437041253974432764644881774673920000⟩, + ⟨2, 5, 8, 7, 4, 4, -80748390863932576690089677201471523901774233600000⟩ +] + +def collectedFourData_9_3_18 : List CollectedFourTerm := [ + ⟨2, 6, 1, 0, 4, 5, -189323216243481744033515238575431228311207936000000⟩, + ⟨2, 6, 2, 0, 5, 5, 4662678893273769994379737596261845026077671424000000⟩, + ⟨2, 6, 3, 0, 6, 5, 374204330716929081398557867784389909698890956800000⟩, + ⟨2, 6, 4, 0, 7, 5, -1789436812005101571900738818531862912333093273600000⟩, + ⟨2, 6, 5, 0, 8, 5, -42171452810645083649688448008482805793161216000000⟩, + ⟨2, 6, 1, 1, 3, 5, 764617867499876767649852212915930160460044697600000⟩, + ⟨2, 6, 2, 1, 4, 5, -16070130456210089708214417331465546828252132147200000⟩, + ⟨2, 6, 3, 1, 5, 5, -5016743363310641497007639872540099874744854118400000⟩, + ⟨2, 6, 4, 1, 6, 5, -4009294616532362092424763795441179876083000934400000⟩, + ⟨2, 6, 5, 1, 7, 5, 334484417380312217909441563259883038089150464000000⟩, + ⟨2, 6, 6, 1, 8, 5, 36591821396613230423682363579520862572353945600000⟩, + ⟨2, 6, 1, 2, 2, 5, 133485678922107719024184625080825577711494758400000⟩, + ⟨2, 6, 2, 2, 3, 5, 5989238937481483187584677230341441047121782374400000⟩, + ⟨2, 6, 3, 2, 4, 5, 6532877980787351313012431646915616158987898060800000⟩, + ⟨2, 6, 4, 2, 5, 5, 508758475228567712528859133459407836026188595200000⟩, + ⟨2, 6, 5, 2, 6, 5, 233787215913162195948381831479209102946598912000000⟩, + ⟨2, 6, 6, 2, 7, 5, 48964042337437971777480889253377617667974758400000⟩, + ⟨2, 6, 7, 2, 8, 5, 38271982852595097719691522954294834390210969600000⟩, + ⟨2, 6, 1, 3, 1, 5, -749124322160196848732703175252498311398031360000000⟩, + ⟨2, 6, 2, 3, 2, 5, 3202620877081981118537718191771984520535867392000000⟩, + ⟨2, 6, 3, 3, 3, 5, -8732117670933249898140814054971494471492331110400000⟩, + ⟨2, 6, 4, 3, 4, 5, -349059132212546467748056121062634703117562675200000⟩, + ⟨2, 6, 5, 3, 5, 5, -88338781340819703057964595809610728105574400000000⟩, + ⟨2, 6, 6, 3, 6, 5, -129740395671275270255853799203343794498541977600000⟩, + ⟨2, 6, 7, 3, 7, 5, -21370275945639695229316163890473617001440870400000⟩, + ⟨2, 6, 8, 3, 8, 5, -13814806020899138603826063222927096859852800000000⟩, + ⟨2, 6, 1, 4, 0, 5, 5994120814247066801428787755618118933546847436800000⟩, + ⟨2, 6, 2, 4, 1, 5, 7393049567415788191060041576429762100546083225600000⟩, + ⟨2, 6, 3, 4, 2, 5, 11953872983327451048347277263206031899030978560000000⟩, + ⟨2, 6, 4, 4, 3, 5, -780197989243950280837177380853239577244073984000000⟩, + ⟨2, 6, 5, 4, 4, 5, 318249984698861690395790087114748774932545536000000⟩, + ⟨2, 6, 6, 4, 5, 5, 103221621798623180533430341613132331585267302400000⟩, + ⟨2, 6, 7, 4, 6, 5, 7018540161781450637229500794310376598536192000000⟩, + ⟨2, 6, 8, 4, 7, 5, -4907384664100490743610174447385569092278681600000⟩, + ⟨2, 6, 2, 5, 0, 5, -55160098437041930165963716223779713435550561075200000⟩, + ⟨2, 6, 3, 5, 1, 5, -9926762857676338238750108337178443229837865779200000⟩, + ⟨2, 6, 4, 5, 2, 5, 5345652520956070889231459631951227071056209510400000⟩, + ⟨2, 6, 5, 5, 3, 5, -830014255758138840376237909217416567326769152000000⟩, + ⟨2, 6, 6, 5, 4, 5, 116421716789796192267177026288565270888421785600000⟩, + ⟨2, 6, 7, 5, 5, 5, 18588195865237756172820635905692809335249305600000⟩, + ⟨2, 6, 8, 5, 6, 5, -10218462847105451156926867662270033362839142400000⟩, + ⟨2, 6, 3, 6, 0, 5, -5406120124136666967388016583831939976545907507200000⟩, + ⟨2, 6, 4, 6, 1, 5, -2868509801989617992165211225409174090974599577600000⟩, + ⟨2, 6, 5, 6, 2, 5, -12284148404348052090421536339713984569540608000000⟩, + ⟨2, 6, 6, 6, 3, 5, -431085085822181844136453126327805599024781721600000⟩, + ⟨2, 6, 7, 6, 4, 5, -6654306079874264302192400990678664044819251200000⟩, + ⟨2, 6, 8, 6, 5, 5, 10723820890778229333210458810892102885231820800000⟩, + ⟨2, 6, 4, 7, 0, 5, -54734702496084485268601275775294315143101625139200000⟩, + ⟨2, 6, 5, 7, 1, 5, 572644730820147835275064241101698573570932736000000⟩, + ⟨2, 6, 6, 7, 2, 5, 425428182902891122211919886591435567542986342400000⟩, + ⟨2, 6, 7, 7, 3, 5, -278812521276423893888077492340100797695839436800000⟩, + ⟨2, 6, 8, 7, 4, 5, -21203371859382541128870540966665643834212352000000⟩ +] + +def collectedFourData_9_3_19 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 3, 6, 7163368057073006070752529744462421834697854156800000⟩, + ⟨2, 7, 1, 0, 4, 6, -198257846122968067666810047619553801143320576000000⟩, + ⟨2, 7, 2, 0, 5, 6, 2441361109549893816256118351290156519199342592000000⟩, + ⟨2, 7, 3, 0, 6, 6, 130621318909656699235107476309587582265170329600000⟩, + ⟨2, 7, 4, 0, 7, 6, -468471188003991594593607685246408890729784934400000⟩, + ⟨2, 7, 5, 0, 8, 6, -8832325552046751700312892246297924517180211200000⟩, + ⟨2, 7, 0, 1, 2, 6, -2801968116025143230132276902386648264060646195200000⟩, + ⟨2, 7, 1, 1, 3, 6, 800702071967265852677253833223395095034304921600000⟩, + ⟨2, 7, 2, 1, 4, 6, -8414259789105540289274602409115771034263984537600000⟩, + ⟨2, 7, 3, 1, 5, 6, -1751165288470717917409101888138222685477719244800000⟩, + ⟨2, 7, 4, 1, 6, 6, -1049625781398962774443722517895907634239347097600000⟩, + ⟨2, 7, 5, 1, 7, 6, 70053912528331783257132656167131883875650764800000⟩, + ⟨2, 7, 6, 1, 8, 6, 6386446627935809476187763196336895753296281600000⟩, + ⟨2, 7, 0, 2, 1, 6, -2894746060960985010309820047128310200320131072000000⟩, + ⟨2, 7, 1, 2, 2, 6, 139785197592058706905591011158581294131471974400000⟩, + ⟨2, 7, 2, 2, 3, 6, 3135942953065520875655995872851154047992017715200000⟩, + ⟨2, 7, 3, 2, 4, 6, 2280393539250115789471646452493747779375045017600000⟩, + ⟨2, 7, 4, 2, 5, 6, 133192010859753653478548503265505651354029260800000⟩, + ⟨2, 7, 5, 2, 6, 6, 48964042337437971777480889253377617667974758400000⟩, + ⟨2, 7, 6, 2, 7, 6, 8545796058814923806696784298613217513858662400000⟩, + ⟨2, 7, 7, 2, 8, 6, 5725447455690482730594331152369790499998924800000⟩, + ⟨2, 7, 0, 3, 0, 6, 16175128899927606248667203132137948260246277324800000⟩, + ⟨2, 7, 1, 3, 1, 6, -784477347980414360079979548489061075003637760000000⟩, + ⟨2, 7, 2, 3, 2, 6, 1676880230637284855007785994028834302235508736000000⟩, + ⟨2, 7, 3, 3, 3, 6, -3048069285746563158482884102607258434990296268800000⟩, + ⟨2, 7, 4, 3, 4, 6, -91383023560369125641372126785539095627877580800000⟩, + ⟨2, 7, 5, 3, 5, 6, -18501541295637844789519210281217231505326080000000⟩, + ⟨2, 7, 6, 3, 6, 6, -22643860863361209488466226650500568305998233600000⟩, + ⟨2, 7, 7, 3, 7, 6, -3196970287941845364356503064659245562802995200000⟩, + ⟨2, 7, 8, 3, 8, 6, -1808345101999853289543653032722794387865600000000⟩, + ⟨2, 7, 1, 4, 0, 6, 6276998170711090011585414997420676174534462668800000⟩, + ⟨2, 7, 2, 4, 1, 6, 3870972912353159321489076597152782132104187084800000⟩, + ⟨2, 7, 3, 4, 2, 6, 4172668585019411365353234400710068493688504320000000⟩, + ⟨2, 7, 4, 4, 3, 6, -204254364528182527199432410823109088993345536000000⟩, + ⟨2, 7, 5, 4, 4, 6, 66653797402130490804215496812001529267696435200000⟩, + ⟨2, 7, 6, 4, 5, 6, 18015484152065104636119749194097366103647846400000⟩, + ⟨2, 7, 7, 4, 6, 6, 1049966056545939089584712780459932328656896000000⟩, + ⟨2, 7, 8, 4, 7, 6, -642372032407135906712122885803110504280883200000⟩, + ⟨2, 7, 2, 5, 0, 6, -28881619816754370146838955095417225815409662361600000⟩, + ⟨2, 7, 3, 5, 1, 6, -3465077099692730736987917989871240477023823462400000⟩, + ⟨2, 7, 4, 5, 2, 6, 1399481764512668104285650316004649449115195801600000⟩, + ⟨2, 7, 5, 5, 3, 6, -173836935440961822173335209208714431505524326400000⟩, + ⟨2, 7, 6, 5, 4, 6, 20319324161314051855559444691954341565274521600000⟩, + ⟨2, 7, 7, 5, 5, 6, 2780774101315878953947012190784352663948492800000⟩, + ⟨2, 7, 8, 5, 6, 6, -1337587166376147355018044753342249728527564800000⟩, + ⟨2, 7, 3, 6, 0, 6, -1887082758892351487066400035366876398745970278400000⟩, + ⟨2, 7, 4, 6, 1, 6, -750970464966236484717397827036708075544667750400000⟩, + ⟨2, 7, 5, 6, 2, 6, -2572773537682587109830854801999807471262105600000⟩, + ⟨2, 7, 6, 6, 3, 6, -75238175844324235621370231902845042108766617600000⟩, + ⟨2, 7, 7, 6, 4, 6, -995477029793308880812402655813244326353305600000⟩, + ⟨2, 7, 8, 6, 5, 6, 1403738058516753578579377509145114240981401600000⟩, + ⟨2, 7, 4, 7, 0, 6, -14329442052024042202273842356746884039024889036800000⟩, + ⟨2, 7, 5, 7, 1, 6, 119933849824377401884262987125899971406279475200000⟩, + ⟨2, 7, 6, 7, 2, 6, 74250864822500974794125627069624807227549286400000⟩, + ⟨2, 7, 7, 7, 3, 6, -41710053192305611148912660433663520888219238400000⟩, + ⟨2, 7, 8, 7, 4, 6, -2775501414192161039976079620551173528879104000000⟩ +] + +def collectedFourData_9_3_20 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 3, 7, 33594811991758933568905936798481115232605516595200000⟩, + ⟨2, 8, 1, 0, 4, 7, -464895494223263296451135157314037757910188032000000⟩, + ⟨2, 8, 2, 0, 5, 7, 3816503951114550621903056551692332161717764096000000⟩, + ⟨2, 8, 3, 0, 6, 7, 153147186348768541700099441325612288163027353600000⟩, + ⟨2, 8, 4, 0, 7, 7, -439407869570805538701988064245151923765059256320000⟩, + ⟨2, 8, 5, 0, 8, 7, -6903650024377422707153119264622030181158092800000⟩, + ⟨2, 8, 0, 1, 2, 7, -13140689032699289464156826665601664014690864332800000⟩, + ⟨2, 8, 1, 1, 3, 7, 1877568997909580652300332822320333471939244851200000⟩, + ⟨2, 8, 2, 1, 4, 7, -13153750833995289026091533080839984723943804108800000⟩, + ⟨2, 8, 3, 1, 5, 7, -2053156705196102101233090741426450929703242956800000⟩, + ⟨2, 8, 4, 1, 6, 7, -984508418577879591251654873220419709836753633280000⟩, + ⟨2, 8, 5, 1, 7, 7, 54756552176892810207256286958426888403628851200000⟩, + ⟨2, 8, 6, 1, 8, 7, 4278742945088345552765797538808324448006963200000⟩, + ⟨2, 8, 0, 2, 1, 7, -13575799666729021791439933448034483938166571008000000⟩, + ⟨2, 8, 1, 2, 2, 7, 327782782827923146176786849552276561918217420800000⟩, + ⟨2, 8, 2, 2, 3, 7, 4902322161202509578274625187729994058162608537600000⟩, + ⟨2, 8, 3, 2, 4, 7, 2673651263203151338031884108057924813761124761600000⟩, + ⟨2, 8, 4, 2, 5, 7, 124928958779930949548865647401242428914784010240000⟩, + ⟨2, 8, 5, 2, 6, 7, 38271982852595097719691522954294834390210969600000⟩, + ⟨2, 8, 6, 2, 7, 7, 5725447455690482730594331152369790499998924800000⟩, + ⟨2, 8, 7, 2, 8, 7, 3356405278043358833025258555078665189090918400000⟩, + ⟨2, 8, 0, 3, 0, 7, 75858228979172544352508066054612146845339824947200000⟩, + ⟨2, 8, 1, 3, 1, 7, -1839523587732850552327705512443096974302904320000000⟩, + ⟨2, 8, 2, 3, 2, 7, 2621414751279048415756179733677689495793696768000000⟩, + ⟨2, 8, 3, 3, 3, 7, -3573713990983721842670759228514780769870990540800000⟩, + ⟨2, 8, 4, 3, 4, 7, -85713744464597451026291915048985836176791306240000⟩, + ⟨2, 8, 5, 3, 5, 7, -14461442262740317417142416312958749004267520000000⟩, + ⟨2, 8, 6, 3, 6, 7, -15170761702581426102929722140253500344578867200000⟩, + ⟨2, 8, 7, 3, 7, 7, -1874146611463704467630995231059901909932441600000⟩, + ⟨2, 8, 8, 3, 8, 7, -942309899692731059571034876553186613657600000000⟩, + ⟨2, 8, 1, 4, 0, 7, 14718954250119768089338373122933996358112745881600000⟩, + ⟨2, 8, 2, 4, 1, 7, 6051371653649791862915228716296730505413813862400000⟩, + ⟨2, 8, 3, 4, 2, 7, 4892252342082094333573340824410541419260805120000000⟩, + ⟨2, 8, 4, 4, 3, 7, -191582700208881739865069501167578887477841100800000⟩, + ⟨2, 8, 5, 4, 4, 7, 52098905022067765007919647249553075196447948800000⟩, + ⟨2, 8, 6, 4, 5, 7, 12069877070735653735703881005345776633433292800000⟩, + ⟨2, 8, 7, 4, 6, 7, 615517239697060094368239706852252679405568000000⟩, + ⟨2, 8, 8, 4, 7, 7, -334733411644473340505636123082912292877107200000⟩, + ⟨2, 8, 2, 5, 0, 7, -45149738690460885465854335375186401806265404620800000⟩, + ⟨2, 8, 3, 5, 1, 7, -4062635507964247134556920527729561844725474918400000⟩, + ⟨2, 8, 4, 5, 2, 7, 1312659810025421780909493472969566411804880404480000⟩, + ⟨2, 8, 5, 5, 3, 7, -135876939377148092588578728520908394454423961600000⟩, + ⟨2, 8, 6, 5, 4, 7, 13613386280233627535669489801665359908123443200000⟩, + ⟨2, 8, 7, 5, 5, 7, 1630161649885807137994855130195045208450662400000⟩, + ⟨2, 8, 8, 5, 6, 7, -697002816102019692228946582637808808938700800000⟩, + ⟨2, 8, 3, 6, 0, 7, -2212513373345441184741936991374854366475740774400000⟩, + ⟨2, 8, 4, 6, 1, 7, -704381273749965658549569242751801533018532741120000⟩, + ⟨2, 8, 5, 6, 2, 7, -2010968458021118509147301724299318176147046400000⟩, + ⟨2, 8, 6, 6, 3, 7, -50407500892130587703996127085548032276771635200000⟩, + ⟨2, 8, 7, 6, 4, 7, -583574363895064316623126838292709611719884800000⟩, + ⟨2, 8, 8, 6, 5, 7, 731473360727967079076965862612934426466713600000⟩, + ⟨2, 8, 4, 7, 0, 7, -13440462861858107550846313757545145002533888983040000⟩, + ⟨2, 8, 5, 7, 1, 7, 93744430092012361670440536446464728759061708800000⟩, + ⟨2, 8, 6, 7, 2, 7, 49746029761884934139633544282554807786196172800000⟩, + ⟨2, 8, 7, 7, 3, 7, -24451511216469710007872215784437642509366067200000⟩, + ⟨2, 8, 8, 7, 4, 7, -1446285035036780638125860358843155437584384000000⟩ +] + +def collectedFourData_9_3_21 : List CollectedFourTerm := [ + ⟨3, 0, 6, 1, 8, 0, 12088001715511910242304235585551605666281632563200000⟩, + ⟨3, 0, 6, 2, 7, 0, 16175128899927606248667203132137948260246277324800000⟩, + ⟨3, 0, 7, 2, 8, 0, 75858228979172544352508066054612146845339824947200000⟩, + ⟨3, 0, 6, 3, 6, 0, -42859362163117801627360526773023165749895836467200000⟩, + ⟨3, 0, 7, 3, 7, 0, -42357650824525200546200168178203149581075401932800000⟩, + ⟨3, 0, 8, 3, 8, 0, -95837300321063902728786965855467407255640473600000000⟩, + ⟨3, 0, 6, 4, 5, 0, 34098962384396747321801924178401755838475455692800000⟩, + ⟨3, 0, 7, 4, 6, 0, 13911325910197379447092549885199051162117996544000000⟩, + ⟨3, 0, 8, 4, 7, 0, -34043945107364729303490080472826052898265969459200000⟩, + ⟨3, 0, 6, 5, 4, 0, 38459575352216598204057372063068621492561589043200000⟩, + ⟨3, 0, 7, 5, 5, 0, 36843338472579346868040453063706692947289518899200000⟩, + ⟨3, 0, 8, 5, 6, 0, -70888428778237762969577140629900010629804903628800000⟩, + ⟨3, 0, 6, 6, 3, 0, -142407703635994333580998715906700180719030973235200000⟩, + ⟨3, 0, 7, 6, 4, 0, -13189383896015573905027841731744905485613426278400000⟩, + ⟨3, 0, 8, 6, 5, 0, 74394243519889933943659943872822549403580078489600000⟩, + ⟨3, 0, 6, 7, 2, 0, 140538962218296017630787041055502971989459258572800000⟩, + ⟨3, 0, 7, 7, 3, 0, -552629430325250400458723039083877533461425789337600000⟩, + ⟨3, 0, 8, 7, 4, 0, -147093916022613968692491158847182137394750029824000000⟩ +] + +def collectedFourData_9_3_22 : List CollectedFourTerm := [ + ⟨3, 1, 5, 0, 8, 1, 135129976538236448919339207625487545773588480000000⟩, + ⟨3, 1, 5, 1, 7, 1, -1071788341652721088057674970889625804912721920000000⟩, + ⟨3, 1, 6, 1, 8, 1, -586255824410148831562882352638252684243107840000000⟩, + ⟨3, 1, 5, 2, 6, 1, -749124322160196848732703175252498311398031360000000⟩, + ⟨3, 1, 6, 2, 7, 1, -784477347980414360079979548489061075003637760000000⟩, + ⟨3, 1, 7, 2, 8, 1, -1839523587732850552327705512443096974302904320000000⟩, + ⟨3, 1, 5, 3, 5, 1, 283063936725180285480821756189191314604032000000000⟩, + ⟨3, 1, 6, 3, 6, 1, 2078635599992359172261721020707162234174832640000000⟩, + ⟨3, 1, 7, 3, 7, 1, 1027151554435299112057460051155974952247623680000000⟩, + ⟨3, 1, 8, 3, 8, 1, 1549337291397766668637918986507023485501440000000000⟩, + ⟨3, 1, 5, 4, 4, 1, -1019768352746808136170189768652858455050158080000000⟩, + ⟨3, 1, 6, 4, 5, 1, -1653765094899193611926588776810803990217359360000000⟩, + ⟨3, 1, 7, 4, 6, 1, -337342599383294780347163734800431072044646400000000⟩, + ⟨3, 1, 8, 4, 7, 1, 550365604252584240704240613851181709189447680000000⟩, + ⟨3, 1, 5, 5, 3, 1, 2659614488754043355311855340728242947028418560000000⟩, + ⟨3, 1, 6, 5, 4, 1, -1865250401614717268814035688118509377515683840000000⟩, + ⟨3, 1, 7, 5, 5, 1, -893432276012439511931239810919692712301035520000000⟩, + ⟨3, 1, 8, 5, 6, 1, 1146005635246165613930736265497653557088747520000000⟩, + ⟨3, 1, 5, 6, 2, 1, 39362093905684800299954760813063948195594240000000⟩, + ⟨3, 1, 6, 6, 3, 1, 6906629206574399721953759691422625196922634240000000⟩, + ⟨3, 1, 7, 6, 4, 1, 319835871610525184039594548849218988057559040000000⟩, + ⟨3, 1, 8, 6, 5, 1, -1202681788453497923496032910793812685451427840000000⟩, + ⟨3, 1, 5, 7, 1, 1, -1834925379211464338111119112618519233120174080000000⟩, + ⟨3, 1, 6, 7, 2, 1, -6815997142960755452370627567740941923369615360000000⟩, + ⟨3, 1, 7, 7, 3, 1, 13400983466642417467400791929183524973245890560000000⟩, + ⟨3, 1, 8, 7, 4, 1, 2377968584967308172182949882371665234074009600000000⟩ +] + +def collectedFourData_9_3_23 : List CollectedFourTerm := [ + ⟨3, 2, 4, 0, 7, 2, -6128315945294502922019412661441771337652004454400000⟩, + ⟨3, 2, 5, 0, 8, 2, -577701285593031941679721595974608392716025856000000⟩, + ⟨3, 2, 4, 1, 6, 2, -13730702287468441793941682742779550289370913177600000⟩, + ⟨3, 2, 5, 1, 7, 2, 4582058834896630497464691453965878587266433024000000⟩, + ⟨3, 2, 6, 1, 8, 2, 1253166588659595069184045293277753620691943424000000⟩, + ⟨3, 2, 4, 2, 5, 2, 1742354161448904597995134341162509504390941900800000⟩, + ⟨3, 2, 5, 2, 6, 2, 3202620877081981118537718191771984520535867392000000⟩, + ⟨3, 2, 6, 2, 7, 2, 1676880230637284855007785994028834302235508736000000⟩, + ⟨3, 2, 7, 2, 8, 2, 2621414751279048415756179733677689495793696768000000⟩, + ⟨3, 2, 4, 3, 4, 2, -1195428992763289601303444231009496499865046220800000⟩, + ⟨3, 2, 5, 3, 5, 2, -1210141556598951846783690009828207645582950400000000⟩, + ⟨3, 2, 6, 3, 6, 2, -4443242310692037952834058273337878469572296704000000⟩, + ⟨3, 2, 7, 3, 7, 2, -1463743250998168653268448785132744999994130432000000⟩, + ⟨3, 2, 8, 3, 8, 2, -1655913380560032072665566724917389208584192000000000⟩, + ⟨3, 2, 4, 4, 3, 2, -2671957872942639789184773799308117014621454336000000⟩, + ⟨3, 2, 5, 4, 4, 2, 4359665438276912757184270930938354659519102976000000⟩, + ⟨3, 2, 6, 4, 5, 2, 3535049164764012101905071154228610886581354496000000⟩, + ⟨3, 2, 7, 4, 6, 2, 480730376144877253172106793480658215092879360000000⟩, + ⟨3, 2, 8, 4, 7, 2, -588224251324681717075673098618845119354241024000000⟩, + ⟨3, 2, 4, 5, 2, 2, 18307350872854095445846660370918076664105245081600000⟩, + ⟨3, 2, 5, 5, 3, 2, -11370258092957686164650676267472452345221087232000000⟩, + ⟨3, 2, 6, 5, 4, 2, 3987115155980342594448997204332431452378497024000000⟩, + ⟨3, 2, 7, 5, 5, 2, 1273186472424812592384451318524011719214235648000000⟩, + ⟨3, 2, 8, 5, 6, 2, -1224837274709426523841691965060464883412238336000000⟩, + ⟨3, 2, 4, 6, 1, 2, -9823836327066929802832622434124294160531220070400000⟩, + ⟨3, 2, 5, 6, 2, 2, -168278962488485054700869326970383829909372928000000⟩, + ⟨3, 2, 6, 6, 3, 2, -14763447289667105433055391099044000853303230464000000⟩, + ⟨3, 2, 7, 6, 4, 2, -455782397909531211422325118536149210807402496000000⟩, + ⟨3, 2, 8, 6, 5, 2, 1285412077223876110963465934195025843125747712000000⟩, + ⟨3, 2, 4, 7, 0, 2, -187450905121286331673673042921719781071432502476800000⟩, + ⟨3, 2, 5, 7, 1, 2, 7844586210209216423638057050467079205920178176000000⟩, + ⟨3, 2, 6, 7, 2, 2, 14569714333416882055850138417400099617265156096000000⟩, + ⟨3, 2, 7, 7, 3, 2, -19097083601085548098700139350861923697289068544000000⟩, + ⟨3, 2, 8, 7, 4, 2, -2541544710930106546704777946860494819457761280000000⟩ +] + +def collectedFourData_9_3_24 : List CollectedFourTerm := [ + ⟨3, 3, 3, 0, 6, 3, -2329466017513664102421216530293063966544111861760000⟩, + ⟨3, 3, 4, 0, 7, 3, 33418364528820434026706817323823756008200140226560000⟩, + ⟨3, 3, 5, 0, 8, 3, 1575133554067142584901942190109687062574871347200000⟩, + ⟨3, 3, 3, 1, 5, 3, 31229818107742847738597069112090602507005203578880000⟩, + ⟨3, 3, 4, 1, 6, 3, 74874993126236096052233431173833399701195708170240000⟩, + ⟨3, 3, 5, 1, 7, 3, -12493229282234669208586766982509636542737992908800000⟩, + ⟨3, 3, 6, 1, 8, 3, -2277883965132946975591665372492804400998462259200000⟩, + ⟨3, 3, 3, 2, 4, 3, -40667934611155872216066170478686066564129158594560000⟩, + ⟨3, 3, 4, 2, 5, 3, -9501244228492302538199593280267849332686764113920000⟩, + ⟨3, 3, 5, 2, 6, 3, -8732117670933249898140814054971494471492331110400000⟩, + ⟨3, 3, 6, 2, 7, 3, -3048069285746563158482884102607258434990296268800000⟩, + ⟨3, 3, 7, 2, 8, 3, -3573713990983721842670759228514780769870990540800000⟩, + ⟨3, 3, 3, 3, 3, 3, 54358460620694604094318858320209152899103881953280000⟩, + ⟨3, 3, 4, 3, 4, 3, 6518802588688082093412498186259192552953395281920000⟩, + ⟨3, 3, 5, 3, 5, 3, 3299515889104059882761204399366591440465428480000000⟩, + ⟨3, 3, 6, 3, 6, 3, 8076492386819398969094602370943208512126399283200000⟩, + ⟨3, 3, 7, 3, 7, 3, 1995487258453790332890572866941304031033897779200000⟩, + ⟨3, 3, 8, 3, 8, 3, 1805974674729247634454190992220050881154908160000000⟩, + ⟨3, 3, 3, 4, 2, 3, -74414266769671607804929022236528843166834491392000000⟩, + ⟨3, 3, 4, 4, 3, 3, 14570473030557461375101954863568252304743622246400000⟩, + ⟨3, 3, 5, 4, 4, 3, -11886861752934324403284145091897120462734570291200000⟩, + ⟨3, 3, 6, 4, 5, 3, -6425667490054579781345482609298981151432297676800000⟩, + ⟨3, 3, 7, 4, 6, 3, -655368583045306710837155360457074136859017216000000⟩, + ⟨3, 3, 8, 4, 7, 3, 641529993914699755483244485674142160198849003520000⟩, + ⟨3, 3, 3, 5, 1, 3, 61795267565639966899341431715638567133192325693440000⟩, + ⟨3, 3, 4, 5, 2, 3, -99831949019504462618697693334020067925816078499840000⟩, + ⟨3, 3, 5, 5, 3, 3, 31001618807609508611037646109014701369656239718400000⟩, + ⟨3, 3, 6, 5, 4, 3, -7247388945040903963054915363086230392143033139200000⟩, + ⟨3, 3, 7, 5, 5, 3, -1735705617516538276495953809267324056459070668800000⟩, + ⟨3, 3, 8, 5, 6, 3, 1335833821236171732999381201275005199128492769280000⟩, + ⟨3, 3, 3, 6, 0, 3, 33653734289086863842052748038714149876431627223040000⟩, + ⟨3, 3, 4, 6, 1, 3, 53570433766794713375732053711604866121164872744960000⟩, + ⟨3, 3, 5, 6, 2, 3, 458821620912826870513863730495909869968267673600000⟩, + ⟨3, 3, 6, 6, 3, 3, 26835554151813666231445789407170634421686711091200000⟩, + ⟨3, 3, 7, 6, 4, 3, 621357582373661059768184790021752485983132057600000⟩, + ⟨3, 3, 8, 6, 5, 3, -1401898001012787491308927407155444834490919157760000⟩, + ⟨3, 3, 4, 7, 0, 3, 1022189902498481884632772659283997535869329546936320000⟩, + ⟨3, 3, 5, 7, 1, 3, -21388685235118987851309269036098198248610804531200000⟩, + ⟨3, 3, 6, 7, 2, 3, -26483405284652909378573241684815612458981706956800000⟩, + ⟨3, 3, 7, 7, 3, 3, 26034611584788592493610051388428224255058404966400000⟩, + ⟨3, 3, 8, 7, 4, 3, 2771863212482470898172085316667435432620222054400000⟩ +] + +def collectedFourData_9_3_25 : List CollectedFourTerm := [ + ⟨3, 4, 2, 0, 5, 4, -1740418784143906421935799711899466915179501977600000⟩, + ⟨3, 4, 3, 0, 6, 4, -279355392552228410228541361311164837384568176640000⟩, + ⟨3, 4, 4, 0, 7, 4, 2003806939275802832102913353214310862613821521920000⟩, + ⟨3, 4, 5, 0, 8, 4, 62964652129198709981249564736245180623591833600000⟩, + ⟨3, 4, 2, 1, 4, 4, 5998430848407328695032323065506022654366481121280000⟩, + ⟨3, 4, 3, 1, 5, 4, 3745157916549010163537227400389990800179928760320000⟩, + ⟨3, 4, 4, 1, 6, 4, 4489598246951545378498470391109093099967275335680000⟩, + ⟨3, 4, 5, 1, 7, 4, -499406436803449237381188357134808968189077094400000⟩, + ⟨3, 4, 6, 1, 8, 4, -68292385946386569106436306217688429417935667200000⟩, + ⟨3, 4, 2, 2, 3, 4, -2235578342003323252939774339499599164061840834560000⟩, + ⟨3, 4, 3, 2, 4, 4, -4877000459407287876365122039375420274998341795840000⟩, + ⟨3, 4, 4, 2, 5, 4, -569706488789655134861619328921204983281945149440000⟩, + ⟨3, 4, 5, 2, 6, 4, -349059132212546467748056121062634703117562675200000⟩, + ⟨3, 4, 6, 2, 7, 4, -91383023560369125641372126785539095627877580800000⟩, + ⟨3, 4, 7, 2, 8, 4, -85713744464597451026291915048985836176791306240000⟩, + ⟨3, 4, 2, 3, 2, 4, -1195428992763289601303444231009496499865046220800000⟩, + ⟨3, 4, 3, 3, 3, 4, 6518802588688082093412498186259192552953395281920000⟩, + ⟨3, 4, 4, 3, 4, 4, 390875557411465866506787941021448386618264125440000⟩, + ⟨3, 4, 5, 3, 5, 4, 131895399990536371145109930281242617698058240000000⟩, + ⟨3, 4, 6, 3, 6, 4, 242138293089714816312458516548345369367622451200000⟩, + ⟨3, 4, 7, 3, 7, 4, 47860764847157406255964577710733049565292789760000⟩, + ⟨3, 4, 8, 3, 8, 4, 36096166847202688015593810825048577057751040000000⟩, + ⟨3, 4, 2, 4, 1, 4, -2759572905138061618088992409645808251523500605440000⟩, + ⟨3, 4, 3, 4, 2, 4, -8923945036603617355483947875138390364298149888000000⟩, + ⟨3, 4, 4, 4, 3, 4, 873663788722593180290388697576646771112463564800000⟩, + ⟨3, 4, 5, 4, 4, 4, -475167399773062641284172328740396821628164505600000⟩, + ⟨3, 4, 6, 4, 5, 4, -192645530198613432432333188039973212728904908800000⟩, + ⟨3, 4, 7, 4, 6, 4, -15718688008887895432076869370772178479140044800000⟩, + ⟨3, 4, 8, 4, 7, 4, 12822313635877313312783769688160226228704378880000⟩, + ⟨3, 4, 2, 5, 0, 4, 20589380837171442416994677794565951531413646868480000⟩, + ⟨3, 4, 3, 5, 1, 4, 7410643082526994307340877828301344111081983836160000⟩, + ⟨3, 4, 4, 5, 2, 4, -5986048540292589895432444369827914332196705402880000⟩, + ⟨3, 4, 5, 5, 3, 4, 1239263895193454457741583665086344591037379379200000⟩, + ⟨3, 4, 6, 5, 4, 4, -217281253353667612030453677445893833891197747200000⟩, + ⟨3, 4, 7, 5, 5, 4, -41630031989388863054743447763810508704726384640000⟩, + ⟨3, 4, 8, 5, 6, 4, 26699422293231280176660912732472095476620984320000⟩, + ⟨3, 4, 3, 6, 0, 4, 4035840009038081717422744560879387247083320770560000⟩, + ⟨3, 4, 4, 6, 1, 4, 3212150218462739801213019952385096004945020190720000⟩, + ⟨3, 4, 5, 6, 2, 4, 18341012211653872749630417266993849021811916800000⟩, + ⟨3, 4, 6, 6, 3, 4, 804546697405569258749305839037470253555856179200000⟩, + ⟨3, 4, 7, 6, 4, 4, 14902951151403049687955165145525737288399585280000⟩, + ⟨3, 4, 8, 6, 5, 4, -28019852578998064609483176424865084216904253440000⟩, + ⟨3, 4, 4, 7, 0, 4, 61291785183492700733128089202140472287783278346240000⟩, + ⟨3, 4, 5, 7, 1, 4, -854994880816810548908108646652934539554953625600000⟩, + ⟨3, 4, 6, 7, 2, 4, -793989054121346212141778511428223859350621388800000⟩, + ⟨3, 4, 7, 7, 3, 4, 624427150645974124141606081338438453693429841920000⟩, + ⟨3, 4, 8, 7, 4, 4, 55401461823040560023667638951051918891915673600000⟩ +] + +def collectedFourData_9_3_26 : List CollectedFourTerm := [ + ⟨3, 5, 1, 0, 4, 5, 71537625088472883288485538066143613498163200000000⟩, + ⟨3, 5, 2, 0, 5, 5, -1761838728463069523488898964768191685643468800000000⟩, + ⟨3, 5, 3, 0, 6, 5, -141396758667373685714439858869692906245980160000000⟩, + ⟨3, 5, 4, 0, 7, 5, 676156164662348680719596565764065039031992320000000⟩, + ⟨3, 5, 5, 0, 8, 5, 15934895045963607485227170109250505749299200000000⟩, + ⟨3, 5, 1, 1, 3, 5, -288918324051750112245051475733244131011461120000000⟩, + ⟨3, 5, 2, 1, 4, 5, 6072255640431988549655124949604619430542704640000000⟩, + ⟨3, 5, 3, 1, 5, 5, 1895625444203583520384749876929352876246958080000000⟩, + ⟨3, 5, 4, 1, 6, 5, 1514951102340569990562281247448205414922977280000000⟩, + ⟨3, 5, 5, 1, 7, 5, -126388201739166732006693152956970546547916800000000⟩, + ⟨3, 5, 6, 1, 8, 5, -13826576857899764625003910617357148194078720000000⟩, + ⟨3, 5, 1, 2, 2, 5, -50438866626526489449750520424841808529326080000000⟩, + ⟨3, 5, 2, 2, 3, 5, -2263092388647213474987094402114861430766305280000000⟩, + ⟨3, 5, 3, 2, 4, 5, -2468511707181583892352299920335421500775464960000000⟩, + ⟨3, 5, 4, 2, 5, 5, -192239355445333349773720565795832729949962240000000⟩, + ⟨3, 5, 5, 2, 6, 5, -88338781340819703057964595809610728105574400000000⟩, + ⟨3, 5, 6, 2, 7, 5, -18501541295637844789519210281217231505326080000000⟩, + ⟨3, 5, 7, 2, 8, 5, -14461442262740317417142416312958749004267520000000⟩, + ⟨3, 5, 1, 3, 1, 5, 283063936725180285480821756189191314604032000000000⟩, + ⟨3, 5, 2, 3, 2, 5, -1210141556598951846783690009828207645582950400000000⟩, + ⟨3, 5, 3, 3, 3, 5, 3299515889104059882761204399366591440465428480000000⟩, + ⟨3, 5, 4, 3, 4, 5, 131895399990536371145109930281242617698058240000000⟩, + ⟨3, 5, 5, 3, 5, 5, 33379670733064260624193272890648722145280000000000⟩, + ⟨3, 5, 6, 3, 6, 5, 49023674795517157289464137600212237675397120000000⟩, + ⟨3, 5, 7, 3, 7, 5, 8074967344048686031552320857039620779540480000000⟩, + ⟨3, 5, 8, 3, 8, 5, 5220059290151036316007231731514327695360000000000⟩, + ⟨3, 5, 1, 4, 0, 5, -2264937053431142060839380452022981371268956160000000⟩, + ⟨3, 5, 2, 4, 1, 5, -2793535936628671490266670158015556160816414720000000⟩, + ⟨3, 5, 3, 4, 2, 5, -4516887578841489726765397934241067850268672000000000⟩, + ⟨3, 5, 4, 4, 3, 5, 294805425117722357385165435122161896180940800000000⟩, + ⟨3, 5, 5, 4, 4, 5, -120253862899306438053188715331079470527283200000000⟩, + ⟨3, 5, 6, 4, 5, 5, -39003297259420388589660982745791246242938880000000⟩, + ⟨3, 5, 7, 4, 6, 5, -2652023902426165353380020600843356497510400000000⟩, + ⟨3, 5, 8, 4, 7, 5, 1854303192345165764202455259393491384401920000000⟩, + ⟨3, 5, 2, 5, 0, 5, 20842781567568173224511360896549310410512138240000000⟩, + ⟨3, 5, 3, 5, 1, 5, 3750924232880905710354716248066915224822743040000000⟩, + ⟨3, 5, 4, 5, 2, 5, -2019906979636321295890515561007806721535508480000000⟩, + ⟨3, 5, 5, 5, 3, 5, 313628987636416700998036304977856962127462400000000⟩, + ⟨3, 5, 6, 5, 4, 5, -43991081987291951698299715094493751117086720000000⟩, + ⟨3, 5, 7, 5, 5, 5, -7023731232034058043167004679059523994910720000000⟩, + ⟨3, 5, 8, 5, 6, 5, 3861145920934495579151329822574379930746880000000⟩, + ⟨3, 5, 3, 6, 0, 5, 2042755253673504855585786408978126574599536640000000⟩, + ⟨3, 5, 4, 6, 1, 5, 1083894425887178958426609401604599933168517120000000⟩, + ⟨3, 5, 5, 6, 2, 5, 4641685370225528488825155401040610826649600000000⟩, + ⟨3, 5, 6, 6, 3, 5, 162889707150964158303593293471884599277649920000000⟩, + ⟨3, 5, 7, 6, 4, 5, 2514394499583092091700645436019432688189440000000⟩, + ⟨3, 5, 8, 6, 5, 5, -4052100390127610193841716312179416718376960000000⟩, + ⟨3, 5, 4, 7, 0, 5, 20682041559331494095207044503075142665020375040000000⟩, + ⟨3, 5, 5, 7, 1, 5, -216379400662709928156951960849008278319923200000000⟩, + ⟨3, 5, 6, 7, 2, 5, -160752191170453551913223257933826900235386880000000⟩, + ⟨3, 5, 7, 7, 3, 5, 105352032427937337189713098775174876139356160000000⟩, + ⟨3, 5, 8, 7, 4, 5, 8011901006040552219898370116130410227302400000000⟩ +] + +def collectedFourData_9_3_27 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 3, 6, -18980830864796111200183499904601808885068804915200000⟩, + ⟨3, 6, 1, 0, 4, 6, 525325323911452675495800683308782892785598464000000⟩, + ⟨3, 6, 2, 0, 5, 6, -6468893114392326155763531003293151908056793088000000⟩, + ⟨3, 6, 3, 0, 6, 6, -346108302938973193151453196262148625372964454400000⟩, + ⟨3, 6, 4, 0, 7, 6, 1241311672622218591356511856370945074786834841600000⟩, + ⟨3, 6, 5, 0, 8, 6, 23403080242496573620897212629576028391263436800000⟩, + ⟨3, 6, 0, 1, 2, 6, 7424396244209712233796569635909733880748100812800000⟩, + ⟨3, 6, 1, 1, 3, 6, -2121626374634792156747049428727088136283645542400000⟩, + ⟨3, 6, 2, 1, 4, 6, 22295328208324052924870066888338743670537086566400000⟩, + ⟨3, 6, 3, 1, 5, 6, 4640075993853938948905271455569501549082391347200000⟩, + ⟨3, 6, 4, 1, 6, 6, 2781201422198558403560679509329785852029986406400000⟩, + ⟨3, 6, 5, 1, 7, 6, -185622385241615308706372031705788692443640627200000⟩, + ⟨3, 6, 6, 1, 8, 6, -16922216240474495877237391397907086182868582400000⟩, + ⟨3, 6, 0, 2, 1, 6, 7670230671085459785036229128755937039045623808000000⟩, + ⟨3, 6, 1, 2, 2, 6, -370389902034588453279375256794355477440469401600000⟩, + ⟨3, 6, 2, 2, 3, 6, -8309331911964783981989445773978228222153510092800000⟩, + ⟨3, 6, 3, 2, 4, 6, -6042376118164482287665335551393184700858525286400000⟩, + ⟨3, 6, 4, 2, 5, 6, -352919884965964646218234483960163687392817971200000⟩, + ⟨3, 6, 5, 2, 6, 6, -129740395671275270255853799203343794498541977600000⟩, + ⟨3, 6, 6, 2, 7, 6, -22643860863361209488466226650500568305998233600000⟩, + ⟨3, 6, 7, 2, 8, 6, -15170761702581426102929722140253500344578867200000⟩, + ⟨3, 6, 0, 3, 0, 6, -42859362163117801627360526773023165749895836467200000⟩, + ⟨3, 6, 1, 3, 1, 6, 2078635599992359172261721020707162234174832640000000⟩, + ⟨3, 6, 2, 3, 2, 6, -4443242310692037952834058273337878469572296704000000⟩, + ⟨3, 6, 3, 3, 3, 6, 8076492386819398969094602370943208512126399283200000⟩, + ⟨3, 6, 4, 3, 4, 6, 242138293089714816312458516548345369367622451200000⟩, + ⟨3, 6, 5, 3, 5, 6, 49023674795517157289464137600212237675397120000000⟩, + ⟨3, 6, 6, 3, 6, 6, 59999610483375561569262884523020370607236710400000⟩, + ⟨3, 6, 7, 3, 7, 6, 8471036505696087575930555001722619825016012800000⟩, + ⟨3, 6, 8, 3, 8, 6, 4791585780986190136313647945399484704358400000000⟩, + ⟨3, 6, 1, 4, 0, 6, -16632209830299319265953396621137803671443288883200000⟩, + ⟨3, 6, 2, 4, 1, 6, -10256946389769138572481989795004109609099277107200000⟩, + ⟨3, 6, 3, 4, 2, 6, -11056351709989258015671511749452773900922388480000000⟩, + ⟨3, 6, 4, 4, 3, 6, 541214344372244080639765962385517502900731904000000⟩, + ⟨3, 6, 5, 4, 4, 6, -176613074311746403575824874694060171238100172800000⟩, + ⟨3, 6, 6, 4, 5, 6, -47735765482568940049731134740588751056640409600000⟩, + ⟨3, 6, 7, 4, 6, 6, -2782103051845505532515518415740537556434944000000⟩, + ⟨3, 6, 8, 4, 7, 6, 1702098063683356750627875056573929210301644800000⟩, + ⟨3, 6, 2, 5, 0, 6, 76527847860878294771401945607442096893588825702400000⟩, + ⟨3, 6, 3, 5, 1, 6, 9181441165487174161863498841820954825655425433600000⟩, + ⟨3, 6, 4, 5, 2, 6, -3708217483583456109998157948535022068466869862400000⟩, + ⟨3, 6, 5, 5, 3, 6, 460617050997600205320357979357846203855903129600000⟩, + ⟨3, 6, 6, 5, 4, 6, -53840267890752112082199700262529315753059942400000⟩, + ⟨3, 6, 7, 5, 5, 6, -7368238302116350063568631662632548831540019200000⟩, + ⟨3, 6, 8, 5, 6, 6, 3544214895790436930004584308222866318635827200000⟩, + ⟨3, 6, 3, 6, 0, 6, 5000217549765849905575688915252287439726287257600000⟩, + ⟨3, 6, 4, 6, 1, 6, 1989852157032080991374658672916182600930400665600000⟩, + ⟨3, 6, 5, 6, 2, 6, 6817097625461106579429744346006651601839718400000⟩, + ⟨3, 6, 6, 6, 3, 6, 199359167210016252793229138939728098027267686400000⟩, + ⟨3, 6, 7, 6, 4, 6, 2637723062915881297148374384016402665596518400000⟩, + ⟨3, 6, 8, 6, 5, 6, -3719495418202859519804497801747888270108262400000⟩, + ⟨3, 6, 4, 7, 0, 6, 37968831673783882469210878551878087761875645235200000⟩, + ⟨3, 6, 5, 7, 1, 6, -317789634756046945618480991828994503446678732800000⟩, + ⟨3, 6, 6, 7, 2, 6, -196743081680574170420528355147282552979036569600000⟩, + ⟨3, 6, 7, 7, 3, 6, 110519445419685953946295743810644459942156697600000⟩, + ⟨3, 6, 8, 7, 4, 6, 7354267222911581227884817471055503143469056000000⟩ +] + +def collectedFourData_9_3_28 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 3, 7, -18758641415859994034370653273875794453934689484800000⟩, + ⟨3, 7, 1, 0, 4, 7, 259587935009801182933299024818330737487904768000000⟩, + ⟨3, 7, 2, 0, 5, 7, -2131056101719899198659521006566487367356514304000000⟩, + ⟨3, 7, 3, 0, 6, 7, -85514190502663506256826636232370198629738086400000⟩, + ⟨3, 7, 4, 0, 7, 7, 245356177692189965502219993885586190935712071680000⟩, + ⟨3, 7, 5, 0, 8, 7, 3854853996493782637896143668407008270431027200000⟩, + ⟨3, 7, 0, 1, 2, 7, 7337486323251304605788679354088548509204820787200000⟩, + ⟨3, 7, 1, 1, 3, 7, -1048395316930521940105442738222940098835303628800000⟩, + ⟨3, 7, 2, 1, 4, 7, 7344779760309889033254257471540285564907631411200000⟩, + ⟨3, 7, 3, 1, 5, 7, 1146439825672789472775668086096890694020051763200000⟩, + ⟨3, 7, 4, 1, 6, 7, 549728940275903064616342700817608219667694878720000⟩, + ⟨3, 7, 5, 1, 7, 7, -30574915189498012103360655464267862684519628800000⟩, + ⟨3, 7, 6, 1, 8, 7, -2389160702469245405836278041815788821466316800000⟩, + ⟨3, 7, 0, 2, 1, 7, 7580443014361630210730686989804950473452552192000000⟩, + ⟨3, 7, 1, 2, 2, 7, -183027060454157604751619981850453404296622899200000⟩, + ⟨3, 7, 2, 2, 3, 7, -2737354313802392730628800588681753523569190502400000⟩, + ⟨3, 7, 3, 2, 4, 7, -1492911028339500853426970076209742774637323878400000⟩, + ⟨3, 7, 4, 2, 5, 7, -69757721542967906998136037785270288167741685760000⟩, + ⟨3, 7, 5, 2, 6, 7, -21370275945639695229316163890473617001440870400000⟩, + ⟨3, 7, 6, 2, 7, 7, -3196970287941845364356503064659245562802995200000⟩, + ⟨3, 7, 7, 2, 8, 7, -1874146611463704467630995231059901909932441600000⟩, + ⟨3, 7, 0, 3, 0, 7, -42357650824525200546200168178203149581075401932800000⟩, + ⟨3, 7, 1, 3, 1, 7, 1027151554435299112057460051155974952247623680000000⟩, + ⟨3, 7, 2, 3, 2, 7, -1463743250998168653268448785132744999994130432000000⟩, + ⟨3, 7, 3, 3, 3, 7, 1995487258453790332890572866941304031033897779200000⟩, + ⟨3, 7, 4, 3, 4, 7, 47860764847157406255964577710733049565292789760000⟩, + ⟨3, 7, 5, 3, 5, 7, 8074967344048686031552320857039620779540480000000⟩, + ⟨3, 7, 6, 3, 6, 7, 8471036505696087575930555001722619825016012800000⟩, + ⟨3, 7, 7, 3, 7, 7, 1046484327812903437763635300051794702788198400000⟩, + ⟨3, 7, 8, 3, 8, 7, 526166168612198570127958231502608033382400000000⟩, + ⟨3, 7, 1, 4, 0, 7, -8218756659872854262531510683576918120834950758400000⟩, + ⟨3, 7, 2, 4, 1, 7, -3378959553420402984110391154749619301439347097600000⟩, + ⟨3, 7, 3, 4, 2, 7, -2731731537105539122937601154764130061522042880000000⟩, + ⟨3, 7, 4, 4, 3, 7, 106975778747689156132683096106124324717671219200000⟩, + ⟨3, 7, 5, 4, 4, 7, -29090940521044052471768587981616180658123571200000⟩, + ⟨3, 7, 6, 4, 5, 7, -6739567286728140127316356369566387496235827200000⟩, + ⟨3, 7, 7, 4, 6, 7, -343691972069660132874427969293671183941632000000⟩, + ⟨3, 7, 8, 4, 7, 7, 186908146427086779036283479683542037613772800000⟩, + ⟨3, 7, 2, 5, 0, 7, 25210671169164416021797911065467131385672315699200000⟩, + ⟨3, 7, 3, 5, 1, 7, 2268490822807292819717172395752979611487148441600000⟩, + ⟨3, 7, 4, 5, 2, 7, -732961824085164575760494811248854563399684587520000⟩, + ⟨3, 7, 5, 5, 3, 7, 75870845268779136121866832487718508191704678400000⟩, + ⟨3, 7, 6, 5, 4, 7, -7601430594376734325957466190448763891141836800000⟩, + ⟨3, 7, 7, 5, 5, 7, -910248220695385262134830967258756811430297600000⟩, + ⟨3, 7, 8, 5, 6, 7, 389191816174168479916131836387654609613619200000⟩, + ⟨3, 7, 3, 6, 0, 7, 1235421261132912042936018479412463348970264985600000⟩, + ⟨3, 7, 4, 6, 1, 7, 393311792831691704763870922516948483845264506880000⟩, + ⟨3, 7, 5, 6, 2, 7, 1122882789517524763950620644519736396847513600000⟩, + ⟨3, 7, 6, 6, 3, 7, 28146495778487392090786529990852703719050444800000⟩, + ⟨3, 7, 7, 6, 4, 7, 325855737322819471461461266962458025866035200000⟩, + ⟨3, 7, 8, 6, 5, 7, -408439448403995151163030662963479284442726400000⟩, + ⟨3, 7, 4, 7, 0, 7, 7504873768920861986781181244036391639398177832960000⟩, + ⟨3, 7, 5, 7, 1, 7, -52344931987164954541046956056946779379413811200000⟩, + ⟨3, 7, 6, 7, 2, 7, -27777144113645044144070383215708862107824947200000⟩, + ⟨3, 7, 7, 7, 3, 7, 13653213213342313780867951790624414423108812800000⟩, + ⟨3, 7, 8, 7, 4, 7, 807575359077311044664272478146974990729216000000⟩ +] + +def collectedFourData_9_3_29 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 3, 8, -42442805868402959294192830445002701540006297600000000⟩, + ⟨3, 8, 1, 0, 4, 8, 391557863463233450997881156260724257849344000000000⟩, + ⟨3, 8, 2, 0, 5, 8, -2410835582781106832778291928439015576961024000000000⟩, + ⟨3, 8, 3, 0, 6, 8, -77392858172117935972770597075966122231070720000000⟩, + ⟨3, 8, 4, 0, 7, 8, 185045465847694413599372221452292266362142720000000⟩, + ⟨3, 8, 5, 0, 8, 8, 2491968767081604232744636204035804128870400000000⟩, + ⟨3, 8, 0, 1, 2, 8, 16601602465545058514027157755839976346904166400000000⟩, + ⟨3, 8, 1, 1, 3, 8, -1581381008122258326320878850113428280206950400000000⟩, + ⟨3, 8, 2, 1, 4, 8, 8309052201654774485113052325821566195807027200000000⟩, + ⟨3, 8, 3, 1, 5, 8, 1037561769685444831250601733818413460341391360000000⟩, + ⟨3, 8, 4, 1, 6, 8, 414600719656352506326000995420443448841338880000000⟩, + ⟨3, 8, 5, 1, 7, 8, -19765141242106408297938782369128803572121600000000⟩, + ⟨3, 8, 6, 1, 8, 8, -1351412951974040882374645039831911392870400000000⟩, + ⟨3, 8, 0, 2, 1, 8, 17151309848218663909977615363048114701205504000000000⟩, + ⟨3, 8, 1, 2, 2, 8, -276074790396865549617967994358568691800473600000000⟩, + ⟨3, 8, 2, 2, 3, 8, -3096732731281968657225714342903416518764134400000000⟩, + ⟨3, 8, 3, 2, 4, 8, -1351128401037380938301630698476236343418552320000000⟩, + ⟨3, 8, 4, 2, 5, 8, -52610658516152518893366289224321012376535040000000⟩, + ⟨3, 8, 5, 2, 6, 8, -13814806020899138603826063222927096859852800000000⟩, + ⟨3, 8, 6, 2, 7, 8, -1808345101999853289543653032722794387865600000000⟩, + ⟨3, 8, 7, 2, 8, 8, -942309899692731059571034876553186613657600000000⟩, + ⟨3, 8, 0, 3, 0, 8, -95837300321063902728786965855467407255640473600000000⟩, + ⟨3, 8, 1, 3, 1, 8, 1549337291397766668637918986507023485501440000000000⟩, + ⟨3, 8, 2, 3, 2, 8, -1655913380560032072665566724917389208584192000000000⟩, + ⟨3, 8, 3, 3, 3, 8, 1805974674729247634454190992220050881154908160000000⟩, + ⟨3, 8, 4, 3, 4, 8, 36096166847202688015593810825048577057751040000000⟩, + ⟨3, 8, 5, 3, 5, 8, 5220059290151036316007231731514327695360000000000⟩, + ⟨3, 8, 6, 3, 6, 8, 4791585780986190136313647945399484704358400000000⟩, + ⟨3, 8, 7, 3, 7, 8, 526166168612198570127958231502608033382400000000⟩, + ⟨3, 8, 8, 3, 8, 8, 238097931015918494065331610083666165760000000000⟩, + ⟨3, 8, 1, 4, 0, 8, -12397027612021067703926312600916875162104627200000000⟩, + ⟨3, 8, 2, 4, 1, 8, -3822572253067212429959988336036501463341465600000000⟩, + ⟨3, 8, 3, 4, 2, 8, -2472297406696795364528540055258844599681024000000000⟩, + ⟨3, 8, 4, 4, 3, 8, 80680189098887085682857098913996820237516800000000⟩, + ⟨3, 8, 5, 4, 4, 8, -18805826433221010191479952658622577010278400000000⟩, + ⟨3, 8, 6, 4, 5, 8, -3812191667379978370705968278689747147161600000000⟩, + ⟨3, 8, 7, 4, 6, 8, -172806303276999768235720755857904893952000000000⟩, + ⟨3, 8, 8, 4, 7, 8, 84578685611216930753263221809754113310720000000⟩, + ⟨3, 8, 2, 5, 0, 8, 28520498860336412414248469920475839269647155200000000⟩, + ⟨3, 8, 3, 5, 1, 8, 2053050932041596286320192550632983707181383680000000⟩, + ⟨3, 8, 4, 5, 2, 8, -552793345014407832766111864245985894025134080000000⟩, + ⟨3, 8, 5, 5, 3, 8, 49046676453595134365105666988775832341708800000000⟩, + ⟨3, 8, 6, 5, 4, 8, -4299698947900590709975641350504972707430400000000⟩, + ⟨3, 8, 7, 5, 5, 8, -457667454772423333670583028318945778073600000000⟩, + ⟨3, 8, 8, 5, 6, 8, 176115021693260661850120422628350052270080000000⟩, + ⟨3, 8, 3, 6, 0, 8, 1118092586547965881622059628208367032210554880000000⟩, + ⟨3, 8, 4, 6, 1, 8, 296632286223657519178144576206866522591723520000000⟩, + ⟨3, 8, 5, 6, 2, 8, 725887113523951023768956922470434288435200000000⟩, + ⟨3, 8, 6, 6, 3, 8, 15920879205998143452322281883961366308454400000000⟩, + ⟨3, 8, 7, 6, 4, 8, 163838349290697173848602775509529735987200000000⟩, + ⟨3, 8, 8, 6, 5, 8, -184824858403143709009639771323560739471360000000⟩, + ⟨3, 8, 4, 7, 0, 8, 5660109624141363833502484580590934227251363840000000⟩, + ⟨3, 8, 5, 7, 1, 8, -33838359570990373030746752211583949497958400000000⟩, + ⟨3, 8, 6, 7, 2, 8, -15711957879280670666254896923756254042521600000000⟩, + ⟨3, 8, 7, 7, 3, 8, 6864755347768706811779810615176966491340800000000⟩, + ⟨3, 8, 8, 7, 4, 8, 365439729131393968105916562272323790438400000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0913.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0913.lean new file mode 100644 index 0000000000000000000000000000000000000000..aadd1daad5ee0135efd39c31dd35a30726d966f6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0913.lean @@ -0,0 +1,646 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0913. -/ +namespace LaughlinFock +def collectedFourData_9_3_30 : List CollectedFourTerm := [ + ⟨4, 0, 5, 0, 8, 1, -1081242967336667491513614107666505077256250982400000⟩, + ⟨4, 0, 5, 1, 7, 1, 8575918064764271399639511914213479332393359769600000⟩, + ⟨4, 0, 6, 1, 8, 1, 4690927974995016723323773548169308780331479859200000⟩, + ⟨4, 0, 5, 2, 6, 1, 5994120814247066801428787755618118933546847436800000⟩, + ⟨4, 0, 6, 2, 7, 1, 6276998170711090011585414997420676174534462668800000⟩, + ⟨4, 0, 7, 2, 8, 1, 14718954250119768089338373122933996358112745881600000⟩, + ⟨4, 0, 5, 3, 5, 1, -2264937053431142060839380452022981371268956160000000⟩, + ⟨4, 0, 6, 3, 6, 1, -16632209830299319265953396621137803671443288883200000⟩, + ⟨4, 0, 7, 3, 7, 1, -8218756659872854262531510683576918120834950758400000⟩, + ⟨4, 0, 8, 3, 8, 1, -12397027612021067703926312600916875162104627200000000⟩, + ⟨4, 0, 5, 4, 4, 1, 8159679946425411364642563557683851720340694630400000⟩, + ⟨4, 0, 6, 4, 5, 1, 13232607037274528867168128877485895670318288076800000⟩, + ⟨4, 0, 7, 4, 6, 1, 2699247957488164357122563699587338968531730432000000⟩, + ⟨4, 0, 8, 4, 7, 1, -4403752256211769274136750800528031607264011878400000⟩, + ⟨4, 0, 5, 5, 3, 1, -21280914386737195304409788497435732751902624972800000⟩, + ⟨4, 0, 6, 5, 4, 1, 14924807438985501689059123737977830267524690739200000⟩, + ⟨4, 0, 7, 5, 5, 1, 7148801398309263011601424452020310276012874137600000⟩, + ⟨4, 0, 8, 5, 6, 1, -9169767992133761385100396301022479323525388697600000⟩, + ⟨4, 0, 5, 6, 2, 1, -314955928399235626234238002140198262487069491200000⟩, + ⟨4, 0, 6, 6, 3, 1, -55263417110840099686797106905088705710156624691200000⟩, + ⟨4, 0, 7, 6, 4, 1, -2559167815610625593150795291158482530468049715200000⟩, + ⟨4, 0, 8, 6, 5, 1, 9623262424982889825239341076984325512960881459200000⟩, + ⟨4, 0, 5, 7, 1, 1, 14682161668980752181262207239963749186043012710400000⟩, + ⟨4, 0, 6, 7, 2, 1, 54538224345267957778693925892147925884911537356800000⟩, + ⟨4, 0, 7, 7, 3, 1, -107228014833570624991035997423647067833182768332800000⟩, + ⟨4, 0, 8, 7, 4, 1, -19027323728690882386631229950584516592793550848000000⟩ +] + +def collectedFourData_9_3_31 : List CollectedFourTerm := [ + ⟨4, 1, 4, 0, 7, 2, -14146833261646482641628607873523076793313966161920000⟩, + ⟨4, 1, 5, 0, 8, 2, -1333587209810654255606524636950853960063569100800000⟩, + ⟨4, 1, 4, 1, 6, 2, -31696465645716523969823462959952295553861869895680000⟩, + ⟨4, 1, 5, 1, 7, 2, 10577395635436956473047928391708469627184165683200000⟩, + ⟨4, 1, 6, 1, 8, 2, 2892856526505612575450037888514530005182788403200000⟩, + ⟨4, 1, 4, 2, 5, 2, 4022115377990519793339744930137159406642989629440000⟩, + ⟨4, 1, 5, 2, 6, 2, 7393049567415788191060041576429762100546083225600000⟩, + ⟨4, 1, 6, 2, 7, 2, 3870972912353159321489076597152782132104187084800000⟩, + ⟨4, 1, 7, 2, 8, 2, 6051371653649791862915228716296730505413813862400000⟩, + ⟨4, 1, 4, 3, 4, 2, -2759572905138061618088992409645808251523500605440000⟩, + ⟨4, 1, 5, 3, 5, 2, -2793535936628671490266670158015556160816414720000000⟩, + ⟨4, 1, 6, 3, 6, 2, -10256946389769138572481989795004109609099277107200000⟩, + ⟨4, 1, 7, 3, 7, 2, -3378959553420402984110391154749619301439347097600000⟩, + ⟨4, 1, 8, 3, 8, 2, -3822572253067212429959988336036501463341465600000000⟩, + ⟨4, 1, 4, 4, 3, 2, -6168047282171679050246493749972867415544745164800000⟩, + ⟨4, 1, 5, 4, 4, 2, 10064014418059272937423579101541063629269159116800000⟩, + ⟨4, 1, 6, 4, 5, 2, 8160439434268735353690423862441753873526607052800000⟩, + ⟨4, 1, 7, 4, 6, 2, 1109735943094127443115621465727670235795816448000000⟩, + ⟨4, 1, 8, 4, 7, 2, -1357878816665221413282559501342397071772300083200000⟩, + ⟨4, 1, 4, 5, 2, 2, 42261372059249955404653667912630110087981962362880000⟩, + ⟨4, 1, 5, 5, 3, 2, -26247528165786975470143282992494691984256637337600000⟩, + ⟨4, 1, 6, 5, 4, 2, 9204005441323066106881263555116257265522520883200000⟩, + ⟨4, 1, 7, 5, 5, 2, 2939071173412245802386101109998694264750892646400000⟩, + ⟨4, 1, 8, 5, 6, 2, -2827460080818507806053445419315395976971996364800000⟩, + ⟨4, 1, 4, 6, 1, 2, -22677710442692067302909113053405341121780614430720000⟩, + ⟨4, 1, 5, 6, 2, 2, -388461437859672572903256828146495523777832550400000⟩, + ⟨4, 1, 6, 6, 3, 2, -34080492755010922737453344082999260013537735475200000⟩, + ⟨4, 1, 7, 6, 4, 2, -1052145098976238995660730510206728819905973452800000⟩, + ⟨4, 1, 8, 6, 5, 2, 2967293215839404830593016969313511352336751001600000⟩, + ⟨4, 1, 4, 7, 0, 2, -432718665807644739643328758370368841022091548426240000⟩, + ⟨4, 1, 5, 7, 1, 2, 18108735599320996485968992044996079950670646476800000⟩, + ⟨4, 1, 6, 7, 2, 2, 33633272367905692445044678359838217755345865932800000⟩, + ⟨4, 1, 7, 7, 3, 2, -44084420565117849832231308199568158742470144819200000⟩, + ⟨4, 1, 8, 7, 4, 2, -5866996671435463730243497171089100045081903104000000⟩ +] + +def collectedFourData_9_3_32 : List CollectedFourTerm := [ + ⟨4, 2, 3, 0, 6, 3, 3188933308242960101074604473544773765183832064000000⟩, + ⟨4, 2, 4, 0, 7, 3, -45748225108991283582428990812933780362215030784000000⟩, + ⟨4, 2, 5, 0, 8, 3, -2156286383974416895257873934570546090035118080000000⟩, + ⟨4, 2, 3, 1, 5, 3, -42752204335844589807417368039002447794753503232000000⟩, + ⟨4, 2, 4, 1, 6, 3, -102500469094444042201116123635664536754230132736000000⟩, + ⟨4, 2, 5, 1, 7, 3, 17102664166853738189779248416024015883542200320000000⟩, + ⟨4, 2, 6, 1, 8, 3, 3118319818409796199435729925105798630741114880000000⟩, + ⟨4, 2, 3, 2, 4, 3, 55672557695167561834942785984111286066278825984000000⟩, + ⟨4, 2, 4, 2, 5, 3, 13006772351343203732392896646597637345208434688000000⟩, + ⟨4, 2, 5, 2, 6, 3, 11953872983327451048347277263206031899030978560000000⟩, + ⟨4, 2, 6, 2, 7, 3, 4172668585019411365353234400710068493688504320000000⟩, + ⟨4, 2, 7, 2, 8, 3, 4892252342082094333573340824410541419260805120000000⟩, + ⟨4, 2, 3, 3, 3, 3, -74414266769671607804929022236528843166834491392000000⟩, + ⟨4, 2, 4, 3, 4, 3, -8923945036603617355483947875138390364298149888000000⟩, + ⟨4, 2, 5, 3, 5, 3, -4516887578841489726765397934241067850268672000000000⟩, + ⟨4, 2, 6, 3, 6, 3, -11056351709989258015671511749452773900922388480000000⟩, + ⟨4, 2, 7, 3, 7, 3, -2731731537105539122937601154764130061522042880000000⟩, + ⟨4, 2, 8, 3, 8, 3, -2472297406696795364528540055258844599681024000000000⟩, + ⟨4, 2, 3, 4, 2, 3, 101869755611874296574707586414240533586955468800000000⟩, + ⟨4, 2, 4, 4, 3, 3, -19946316629934647876372252580920975841778728960000000⟩, + ⟨4, 2, 5, 4, 4, 3, 16272574525414478098988051040272182698238279680000000⟩, + ⟨4, 2, 6, 4, 5, 3, 8796447311388518020536343711790398828990955520000000⟩, + ⟨4, 2, 7, 4, 6, 3, 897169861219884500662993769050479245289062400000000⟩, + ⟨4, 2, 8, 4, 7, 3, -878225460449108865612967951826080349319856128000000⟩, + ⟨4, 2, 3, 5, 1, 3, -84594918127282463183389999506808534131032457216000000⟩, + ⟨4, 2, 4, 5, 2, 3, 136665409609583837927490470324984056025947570176000000⟩, + ⟨4, 2, 5, 5, 3, 3, -42439809845587266824233409636586766013835509760000000⟩, + ⟨4, 2, 6, 5, 4, 3, 9921346708161275043477819275116498545153146880000000⟩, + ⟨4, 2, 7, 5, 5, 3, 2376102254932524276872287955569000705236664320000000⟩, + ⟨4, 2, 8, 5, 6, 3, -1828695904894226518097077546158861086770593792000000⟩, + ⟨4, 2, 3, 6, 0, 3, -46070435633902869134473464612853077507525574656000000⟩, + ⟨4, 2, 4, 6, 1, 3, -73335493753324512786982522174967480263108460544000000⟩, + ⟨4, 2, 5, 6, 2, 3, -628105985865645200247704425570844112102359040000000⟩, + ⟨4, 2, 6, 6, 3, 3, -36736656313714301423453309417891246001283399680000000⟩, + ⟨4, 2, 7, 6, 4, 3, -850610344114652331283382181731217806343536640000000⟩, + ⟨4, 2, 8, 6, 5, 3, 1919134770191030610697948869789304516943806464000000⟩, + ⟨4, 2, 4, 7, 0, 3, -1399331607724520949342133893339837699895798530048000000⟩, + ⟨4, 2, 5, 7, 1, 3, 29280139848786294646628615030072818175500615680000000⟩, + ⟨4, 2, 6, 7, 2, 3, 36254580488823082159497207600893680957280747520000000⟩, + ⟨4, 2, 7, 7, 3, 3, -35640202271984158373425556700968181358877736960000000⟩, + ⟨4, 2, 8, 7, 4, 3, -3794555000039546956571079708065374738222940160000000⟩ +] + +def collectedFourData_9_3_33 : List CollectedFourTerm := [ + ⟨4, 3, 2, 0, 5, 4, -3890089416152710090212866088743822446445985792000000⟩, + ⟨4, 3, 3, 0, 6, 4, -624399981092570295947141149314506558022667468800000⟩, + ⟨4, 3, 4, 0, 7, 4, 4478800296518535343097837986017514765855123046400000⟩, + ⟨4, 3, 5, 0, 8, 4, 140735166197379084227224258985603038615437312000000⟩, + ⟨4, 3, 2, 1, 4, 4, 13407366416348597971013005061815299936435673497600000⟩, + ⟨4, 3, 3, 1, 5, 4, 8370973300057879787867644276998430365575439974400000⟩, + ⟨4, 3, 4, 1, 6, 4, 10034905841259801354208870363839853147010472345600000⟩, + ⟨4, 3, 5, 1, 7, 4, -1116246108044189075609615909434110484779368448000000⟩, + ⟨4, 3, 6, 1, 8, 4, -152643427084436766754917751182186474450714624000000⟩, + ⟨4, 3, 2, 2, 3, 4, -4996843131341584955777585628117579006261539635200000⟩, + ⟨4, 3, 3, 2, 4, 4, -10900806198230218230645375261806671568225225932800000⟩, + ⟨4, 3, 4, 2, 5, 4, -1273376961076807648077599642084960546308541644800000⟩, + ⟨4, 3, 5, 2, 6, 4, -780197989243950280837177380853239577244073984000000⟩, + ⟨4, 3, 6, 2, 7, 4, -204254364528182527199432410823109088993345536000000⟩, + ⟨4, 3, 7, 2, 8, 4, -191582700208881739865069501167578887477841100800000⟩, + ⟨4, 3, 2, 3, 2, 4, -2671957872942639789184773799308117014621454336000000⟩, + ⟨4, 3, 3, 3, 3, 4, 14570473030557461375101954863568252304743622246400000⟩, + ⟨4, 3, 4, 3, 4, 4, 873663788722593180290388697576646771112463564800000⟩, + ⟨4, 3, 5, 3, 5, 4, 294805425117722357385165435122161896180940800000000⟩, + ⟨4, 3, 6, 3, 6, 4, 541214344372244080639765962385517502900731904000000⟩, + ⟨4, 3, 7, 3, 7, 4, 106975778747689156132683096106124324717671219200000⟩, + ⟨4, 3, 8, 3, 8, 4, 80680189098887085682857098913996820237516800000000⟩, + ⟨4, 3, 2, 4, 1, 4, -6168047282171679050246493749972867415544745164800000⟩, + ⟨4, 3, 3, 4, 2, 4, -19946316629934647876372252580920975841778728960000000⟩, + ⟨4, 3, 4, 4, 3, 4, 1952765787607485181761704920428436342299426816000000⟩, + ⟨4, 3, 5, 4, 4, 4, -1062068330678943181258371418854640892145303552000000⟩, + ⟨4, 3, 6, 4, 5, 4, -430590812350591491060569459926793051015479296000000⟩, + ⟨4, 3, 7, 4, 6, 4, -35133556599286493218301142427415023416508416000000⟩, + ⟨4, 3, 8, 4, 7, 4, 28659738115876707694034892986020306427156889600000⟩, + ⟨4, 3, 2, 5, 0, 4, 46020264323460348353461029262239144690583181721600000⟩, + ⟨4, 3, 3, 5, 1, 4, 16563866400927047404107438891115983876146803507200000⟩, + ⟨4, 3, 4, 5, 2, 4, -13379690154644504325972867699325782438077634969600000⟩, + ⟨4, 3, 5, 5, 3, 4, 2769935262956589123486047651386073996448497664000000⟩, + ⟨4, 3, 6, 5, 4, 4, -485655240968491531817850736917271100704948224000000⟩, + ⟨4, 3, 7, 5, 5, 4, -93049183513426152124734955183568116901530828800000⟩, + ⟨4, 3, 8, 5, 6, 4, 59677096700251889021636768646066807058622054400000⟩, + ⟨4, 3, 3, 6, 0, 4, 9020690104863039840284616925912383072674984755200000⟩, + ⟨4, 3, 4, 6, 1, 4, 7179623480150468035183379983350081011541501542400000⟩, + ⟨4, 3, 5, 6, 2, 4, 40994833045988844100341145075418989546438656000000⟩, + ⟨4, 3, 6, 6, 3, 4, 1798279023929012094413870401780004772762353664000000⟩, + ⟨4, 3, 7, 6, 4, 4, 33310265938109001109885731821553113846356377600000⟩, + ⟨4, 3, 8, 6, 5, 4, -62628450665300882543392772206587850957573324800000⟩, + ⟨4, 3, 4, 7, 0, 4, 136996064976793443726576746212241372147656477900800000⟩, + ⟨4, 3, 5, 7, 1, 4, -1911038059938114209170033451147196928414973952000000⟩, + ⟨4, 3, 6, 7, 2, 4, -1774681153822321768669129329540039209329360896000000⟩, + ⟨4, 3, 7, 7, 3, 4, 1395685608553768463444358882609539102347257446400000⟩, + ⟨4, 3, 8, 7, 4, 4, 123830334538252449330718314808789822039130112000000⟩ +] + +def collectedFourData_9_3_34 : List CollectedFourTerm := [ + ⟨4, 4, 1, 0, 4, 5, -257722007755151852645686024627429065734750208000000⟩, + ⟨4, 4, 2, 0, 5, 5, 6347213985350083409995485689470426073763151872000000⟩, + ⟨4, 4, 3, 0, 6, 5, 509397068867723642567727503454436123486873190400000⟩, + ⟨4, 4, 4, 0, 7, 5, -2435925488123071018100910550874357574507744460800000⟩, + ⟨4, 4, 5, 0, 8, 5, -57407177545164312721484135452941348186882048000000⟩, + ⟨4, 4, 1, 1, 3, 5, 1040859414326136560695690070460083431090736332800000⟩, + ⟨4, 4, 2, 1, 4, 5, -21875955671148555179333411720785338158810765721600000⟩, + ⟨4, 4, 3, 1, 5, 5, -6829195054039053583453754487070793768029598515200000⟩, + ⟨4, 4, 4, 1, 6, 5, -5457774692173903784704007514392931134784877363200000⟩, + ⟨4, 4, 5, 1, 7, 5, 455327124271977464341151361156313386678484992000000⟩, + ⟨4, 4, 6, 1, 8, 5, 49811733948280482472982206392504607799299276800000⟩, + ⟨4, 4, 1, 2, 2, 5, 181711455472643849803681850744399299446256435200000⟩, + ⟨4, 4, 2, 2, 3, 5, 8153034342644724728876465856433924146979877683200000⟩, + ⟨4, 4, 3, 2, 4, 5, 8893079586513235668626771538084834706480064102400000⟩, + ⟨4, 4, 4, 2, 5, 5, 692563005742146865047932329191409065913850265600000⟩, + ⟨4, 4, 5, 2, 6, 5, 318249984698861690395790087114748774932545536000000⟩, + ⟨4, 4, 6, 2, 7, 5, 66653797402130490804215496812001529267696435200000⟩, + ⟨4, 4, 7, 2, 8, 5, 52098905022067765007919647249553075196447948800000⟩, + ⟨4, 4, 1, 3, 1, 5, -1019768352746808136170189768652858455050158080000000⟩, + ⟨4, 4, 2, 3, 2, 5, 4359665438276912757184270930938354659519102976000000⟩, + ⟨4, 4, 3, 3, 3, 5, -11886861752934324403284145091897120462734570291200000⟩, + ⟨4, 4, 4, 3, 4, 5, -475167399773062641284172328740396821628164505600000⟩, + ⟨4, 4, 5, 3, 5, 5, -120253862899306438053188715331079470527283200000000⟩, + ⟨4, 4, 6, 3, 6, 5, -176613074311746403575824874694060171238100172800000⟩, + ⟨4, 4, 7, 3, 7, 5, -29090940521044052471768587981616180658123571200000⟩, + ⟨4, 4, 8, 3, 8, 5, -18805826433221010191479952658622577010278400000000⟩, + ⟨4, 4, 1, 4, 0, 5, 8159679946425411364642563557683851720340694630400000⟩, + ⟨4, 4, 2, 4, 1, 5, 10064014418059272937423579101541063629269159116800000⟩, + ⟨4, 4, 3, 4, 2, 5, 16272574525414478098988051040272182698238279680000000⟩, + ⟨4, 4, 4, 4, 3, 5, -1062068330678943181258371418854640892145303552000000⟩, + ⟨4, 4, 5, 4, 4, 5, 433227507180915424563254548265903859337003008000000⟩, + ⟨4, 4, 6, 4, 5, 5, 140513583814631705868209929165836201153999667200000⟩, + ⟨4, 4, 7, 4, 6, 5, 9554202056646924802051956605522469376229376000000⟩, + ⟨4, 4, 8, 4, 7, 5, -6680327186245781029026157264456633784519884800000⟩, + ⟨4, 4, 2, 5, 0, 5, -75088367920411900960336994642294243489675319705600000⟩, + ⟨4, 4, 3, 5, 1, 5, -13513108983419229828909720946917661314905643417600000⟩, + ⟨4, 4, 4, 5, 2, 5, 7276932685795847095978975541383140892686365491200000⟩, + ⟨4, 4, 5, 5, 3, 5, -1129882244258305606323478971272772019348832256000000⟩, + ⟨4, 4, 6, 5, 4, 5, 158482616092789820075706902849695269505518796800000⟩, + ⟨4, 4, 7, 5, 5, 5, 25303749080483006591799525682379326537649356800000⟩, + ⟨4, 4, 8, 5, 6, 5, -13910194499023108431239098514671791974331187200000⟩, + ⟨4, 4, 3, 6, 0, 5, -7359246056575494237674488177427323202653755801600000⟩, + ⟨4, 4, 4, 6, 1, 5, -3904846537591768926283299525583025787332512972800000⟩, + ⟨4, 4, 5, 6, 2, 5, -16722172024899900962758187366477663016321024000000⟩, + ⟨4, 4, 6, 6, 3, 5, -586827733205804042902849846108860017640525004800000⟩, + ⟨4, 4, 7, 6, 4, 5, -9058377293342406387188039132880540546996633600000⟩, + ⟨4, 4, 8, 6, 5, 5, 14598128563501839449558366377130774025889382400000⟩, + ⟨4, 4, 4, 7, 0, 5, -74509284709330970752138896971940224097140185497600000⟩, + ⟨4, 4, 5, 7, 1, 5, 779530121480588160015558601196731871797444608000000⟩, + ⟨4, 4, 6, 7, 2, 5, 579127101413448364074501122266532804084052787200000⟩, + ⟨4, 4, 7, 7, 3, 5, -379542056153453456717043084445009948128470630400000⟩, + ⟨4, 4, 8, 7, 4, 5, -28863737238392161795475994375689366830841856000000⟩ +] + +def collectedFourData_9_3_35 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 3, 6, 15101172883068330713250127269105093918048701644800000⟩, + ⟨4, 5, 1, 0, 4, 6, -417949487709421813544999555483580728120180736000000⟩, + ⟨4, 5, 2, 0, 5, 6, 5146659489164474100773937823390751798499213312000000⟩, + ⟨4, 5, 3, 0, 6, 6, 275364200659978047376655252936231001360275865600000⟩, + ⟨4, 5, 4, 0, 7, 6, -987589126290873725074872895452899405315073638400000⟩, + ⟨4, 5, 5, 0, 8, 6, -18619520043969254479969785042301435944055603200000⟩, + ⟨4, 5, 0, 1, 2, 6, -5906858979717187887661016938233751407466591027200000⟩, + ⟨4, 5, 1, 1, 3, 6, 1687968609217236838968057190832093699252001177600000⟩, + ⟨4, 5, 2, 1, 4, 6, -17738191133829917149178359735271375251946707353600000⟩, + ⟨4, 5, 3, 1, 5, 6, -3691650290384489096873334801094116822276164812800000⟩, + ⟨4, 5, 4, 1, 6, 6, -2212727345732401699331823698748336966618159513600000⟩, + ⟨4, 5, 5, 1, 7, 6, 147681402909506132250524365898341716614499532800000⟩, + ⟨4, 5, 6, 1, 8, 6, 13463336501566629118200469176145852726090137600000⟩, + ⟨4, 5, 0, 2, 1, 6, -6102445158599698108276530829156140787634798592000000⟩, + ⟨4, 5, 1, 2, 2, 6, 294682671407237429230104672455708167161407078400000⟩, + ⟨4, 5, 2, 2, 3, 6, 6610914908793947213879848321561543262608765747200000⟩, + ⟨4, 5, 3, 2, 4, 6, 4807322031100418988184149173916046942812084633600000⟩, + ⟨4, 5, 4, 2, 5, 6, 280783503878552082155200106671182694505565388800000⟩, + ⟨4, 5, 5, 2, 6, 6, 103221621798623180533430341613132331585267302400000⟩, + ⟨4, 5, 6, 2, 7, 6, 18015484152065104636119749194097366103647846400000⟩, + ⟨4, 5, 7, 2, 8, 6, 12069877070735653735703881005345776633433292800000⟩, + ⟨4, 5, 0, 3, 0, 6, 34098962384396747321801924178401755838475455692800000⟩, + ⟨4, 5, 1, 3, 1, 6, -1653765094899193611926588776810803990217359360000000⟩, + ⟨4, 5, 2, 3, 2, 6, 3535049164764012101905071154228610886581354496000000⟩, + ⟨4, 5, 3, 3, 3, 6, -6425667490054579781345482609298981151432297676800000⟩, + ⟨4, 5, 4, 3, 4, 6, -192645530198613432432333188039973212728904908800000⟩, + ⟨4, 5, 5, 3, 5, 6, -39003297259420388589660982745791246242938880000000⟩, + ⟨4, 5, 6, 3, 6, 6, -47735765482568940049731134740588751056640409600000⟩, + ⟨4, 5, 7, 3, 7, 6, -6739567286728140127316356369566387496235827200000⟩, + ⟨4, 5, 8, 3, 8, 6, -3812191667379978370705968278689747147161600000000⟩, + ⟨4, 5, 1, 4, 0, 6, 13232607037274528867168128877485895670318288076800000⟩, + ⟨4, 5, 2, 4, 1, 6, 8160439434268735353690423862441753873526607052800000⟩, + ⟨4, 5, 3, 4, 2, 6, 8796447311388518020536343711790398828990955520000000⟩, + ⟨4, 5, 4, 4, 3, 6, -430590812350591491060569459926793051015479296000000⟩, + ⟨4, 5, 5, 4, 4, 6, 140513583814631705868209929165836201153999667200000⟩, + ⟨4, 5, 6, 4, 5, 6, 37978634991942051840584335953980004541818470400000⟩, + ⟨4, 5, 7, 4, 6, 6, 2213444683412297553228259433162623477088256000000⟩, + ⟨4, 5, 8, 4, 7, 6, -1354191357939499983337634860742251333759795200000⟩, + ⟨4, 5, 2, 5, 0, 6, -60885651905770141136870588779693582218006469017600000⟩, + ⟨4, 5, 3, 5, 1, 6, -7304766126592402168766930263964252087534380646400000⟩, + ⟨4, 5, 4, 5, 2, 6, 2950262488849794389612455077786471921287272857600000⟩, + ⟨4, 5, 5, 5, 3, 6, -366467504481320882891145392398225220116571750400000⟩, + ⟨4, 5, 6, 5, 4, 6, 42835384777435242192660097089148078110906777600000⟩, + ⟨4, 5, 7, 5, 5, 6, 5862179650432288747056058498515300915137740800000⟩, + ⟨4, 5, 8, 5, 6, 6, -2819781823952958851766167613921234070064332800000⟩, + ⟨4, 5, 3, 6, 0, 6, -3978179364740761059473292386265026531365906022400000⟩, + ⟨4, 5, 4, 6, 1, 6, -1583128876134720749047094553672139183525095014400000⟩, + ⟨4, 5, 5, 6, 2, 6, -5423691435646149736074252254996679708219801600000⟩, + ⟨4, 5, 6, 6, 3, 6, -158610403902111871099527264408910450250062233600000⟩, + ⟨4, 5, 7, 6, 4, 6, -2098575782824516683794458954058615259503001600000⟩, + ⟨4, 5, 8, 6, 5, 6, 2959235227802303978190882239841923799554457600000⟩, + ⟨4, 5, 4, 7, 0, 6, -30208050182743682985376325030314224729105157324800000⟩, + ⟨4, 5, 5, 7, 1, 6, 252833832674782397338022227241653202968589107200000⟩, + ⟨4, 5, 6, 7, 2, 6, 156529042968103959448571656320282786403870310400000⟩, + ⟨4, 5, 7, 7, 3, 6, -87929409629742242394788091859387720141268582400000⟩, + ⟨4, 5, 8, 7, 4, 6, -5851064242264063582970243677796122434207744000000⟩ +] + +def collectedFourData_9_3_36 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 3, 7, 6160813201129171472566306472872648288977813504000000⟩, + ⟨4, 6, 1, 0, 4, 7, -85255256039496372900512514373818283343216640000000⟩, + ⟨4, 6, 2, 0, 5, 7, 699892826605370759292380108879002427373649920000000⟩, + ⟨4, 6, 3, 0, 6, 7, 28085027164454233110782023917167374208335872000000⟩, + ⟨4, 6, 4, 0, 7, 7, -80581186291381503725410047566437329725187686400000⟩, + ⟨4, 6, 5, 0, 8, 7, -1266031737775273274790072638862093509984256000000⟩, + ⟨4, 6, 0, 1, 2, 7, -2409816446790848621856663760226268714218029056000000⟩, + ⟨4, 6, 1, 1, 3, 7, 344319589321999326815715739261441540960026624000000⟩, + ⟨4, 6, 2, 1, 4, 7, -2412211796342876490223639060014539098948632576000000⟩, + ⟨4, 6, 3, 1, 5, 7, -376519890525416419192595903727832947580993536000000⟩, + ⟨4, 6, 4, 1, 6, 7, -180544914592327150677458226699221694032746905600000⟩, + ⟨4, 6, 5, 1, 7, 7, 10041576942965860306767581051594007719706624000000⟩, + ⟨4, 6, 6, 1, 8, 7, 784660918084763554310073757433128355364864000000⟩, + ⟨4, 6, 0, 2, 1, 7, -2489609580883685311895392364986669583208284160000000⟩, + ⟨4, 6, 1, 2, 2, 7, 60110724716795607926946763184105217186594816000000⟩, + ⟨4, 6, 2, 2, 3, 7, 899016523573144749556501391503829471751831552000000⟩, + ⟨4, 6, 3, 2, 4, 7, 490309813360418136070084237942018197298348032000000⟩, + ⟨4, 6, 4, 2, 5, 7, 22910203475570133097126756281362138755026124800000⟩, + ⟨4, 6, 5, 2, 6, 7, 7018540161781450637229500794310376598536192000000⟩, + ⟨4, 6, 6, 2, 7, 7, 1049966056545939089584712780459932328656896000000⟩, + ⟨4, 6, 7, 2, 8, 7, 615517239697060094368239706852252679405568000000⟩, + ⟨4, 6, 0, 3, 0, 7, 13911325910197379447092549885199051162117996544000000⟩, + ⟨4, 6, 1, 3, 1, 7, -337342599383294780347163734800431072044646400000000⟩, + ⟨4, 6, 2, 3, 2, 7, 480730376144877253172106793480658215092879360000000⟩, + ⟨4, 6, 3, 3, 3, 7, -655368583045306710837155360457074136859017216000000⟩, + ⟨4, 6, 4, 3, 4, 7, -15718688008887895432076869370772178479140044800000⟩, + ⟨4, 6, 5, 3, 5, 7, -2652023902426165353380020600843356497510400000000⟩, + ⟨4, 6, 6, 3, 6, 7, -2782103051845505532515518415740537556434944000000⟩, + ⟨4, 6, 7, 3, 7, 7, -343691972069660132874427969293671183941632000000⟩, + ⟨4, 6, 8, 3, 8, 7, -172806303276999768235720755857904893952000000000⟩, + ⟨4, 6, 1, 4, 0, 7, 2699247957488164357122563699587338968531730432000000⟩, + ⟨4, 6, 2, 4, 1, 7, 1109735943094127443115621465727670235795816448000000⟩, + ⟨4, 6, 3, 4, 2, 7, 897169861219884500662993769050479245289062400000000⟩, + ⟨4, 6, 4, 4, 3, 7, -35133556599286493218301142427415023416508416000000⟩, + ⟨4, 6, 5, 4, 4, 7, 9554202056646924802051956605522469376229376000000⟩, + ⟨4, 6, 6, 4, 5, 7, 2213444683412297553228259433162623477088256000000⟩, + ⟨4, 6, 7, 4, 6, 7, 112877153078828494578007277267838157455360000000⟩, + ⟨4, 6, 8, 4, 7, 7, -61385371700373182878925717278466972319744000000⟩, + ⟨4, 6, 2, 5, 0, 7, -8279823272115900151727027021083652067547938816000000⟩, + ⟨4, 6, 3, 5, 1, 7, -745029871724898822464105030015083756879085568000000⟩, + ⟨4, 6, 4, 5, 2, 7, 240723236914680309596065134083958044737771929600000⟩, + ⟨4, 6, 5, 5, 3, 7, -24917908218956910604386287891832066677932032000000⟩, + ⟨4, 6, 6, 5, 4, 7, 2496502434004033760996093284933598617534464000000⟩, + ⟨4, 6, 7, 5, 5, 7, 298948582151751474725608420645809262952448000000⟩, + ⟨4, 6, 8, 5, 6, 7, -127820454888061526368118640510546179260416000000⟩, + ⟨4, 6, 3, 6, 0, 7, -405743648796879397877400353713618420852850688000000⟩, + ⟨4, 6, 4, 6, 1, 7, -129173559626155879511613251747160230935815782400000⟩, + ⟨4, 6, 5, 6, 2, 7, -368783162896403395531588685019117810352128000000⟩, + ⟨4, 6, 6, 6, 3, 7, -9244022470146557633014751015011328987234304000000⟩, + ⟨4, 6, 7, 6, 4, 7, -107019281602386231231932545245205386756096000000⟩, + ⟨4, 6, 8, 6, 5, 7, 134141865063946542192344404547454288003072000000⟩, + ⟨4, 6, 4, 7, 0, 7, -2464790725691047084208572965190819258166987980800000⟩, + ⟨4, 6, 5, 7, 1, 7, 17191402130331195052200984335340740674584576000000⟩, + ⟨4, 6, 6, 7, 2, 7, 9122718023722421249887498149953819803385856000000⟩, + ⟨4, 6, 7, 7, 3, 7, -4484061203466119768799414585487245069778944000000⟩, + ⟨4, 6, 8, 7, 4, 7, -265228212577463679894518642898793849159680000000⟩ +] + +def collectedFourData_9_3_37 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 3, 8, -15076807760087452451655724517999113562695611187200000⟩, + ⟨4, 7, 1, 0, 4, 8, 139091714451909689297871547654188293494407168000000⟩, + ⟨4, 7, 2, 0, 5, 8, -856392594200013034933758988381214755812016128000000⟩, + ⟨4, 7, 3, 0, 6, 8, -27491991181794153537621978881127292428185763840000⟩, + ⟨4, 7, 4, 0, 7, 8, 65733046116503021459749130593912704382890147840000⟩, + ⟨4, 7, 5, 0, 8, 8, 885213248198597799686821281282606758677708800000⟩, + ⟨4, 7, 0, 1, 2, 8, 5897328505058965729238684469109779401550908620800000⟩, + ⟨4, 7, 1, 1, 3, 8, -561748380369502607510634781461192735466507468800000⟩, + ⟨4, 7, 2, 1, 4, 8, 2951595215012448315533883484871911850532824678400000⟩, + ⟨4, 7, 3, 1, 5, 8, 368569396407632110217315712880987797192620113920000⟩, + ⟨4, 7, 4, 1, 6, 8, 147277146728563953173535284635497921066156687360000⟩, + ⟨4, 7, 5, 1, 7, 8, -7021101191617033632127284476273675547652915200000⟩, + ⟨4, 7, 6, 1, 8, 8, -480057641442912050911275878983939128085708800000⟩, + ⟨4, 7, 0, 2, 1, 8, 6092599113664999243340643757933800631396466688000000⟩, + ⟨4, 7, 1, 2, 2, 8, -98069071001704716318930942098536710085489459200000⟩, + ⟨4, 7, 2, 2, 3, 8, -1100041411462545409253118842480947957917863116800000⟩, + ⟨4, 7, 3, 2, 4, 8, -479956561420463096198267990931010536426480599040000⟩, + ⟨4, 7, 4, 2, 5, 8, -18688698080871860247707130025376242971055226880000⟩, + ⟨4, 7, 5, 2, 6, 8, -4907384664100490743610174447385569092278681600000⟩, + ⟨4, 7, 6, 2, 7, 8, -642372032407135906712122885803110504280883200000⟩, + ⟨4, 7, 7, 2, 8, 8, -334733411644473340505636123082912292877107200000⟩, + ⟨4, 7, 0, 3, 0, 8, -34043945107364729303490080472826052898265969459200000⟩, + ⟨4, 7, 1, 3, 1, 8, 550365604252584240704240613851181709189447680000000⟩, + ⟨4, 7, 2, 3, 2, 8, -588224251324681717075673098618845119354241024000000⟩, + ⟨4, 7, 3, 3, 3, 8, 641529993914699755483244485674142160198849003520000⟩, + ⟨4, 7, 4, 3, 4, 8, 12822313635877313312783769688160226228704378880000⟩, + ⟨4, 7, 5, 3, 5, 8, 1854303192345165764202455259393491384401920000000⟩, + ⟨4, 7, 6, 3, 6, 8, 1702098063683356750627875056573929210301644800000⟩, + ⟨4, 7, 7, 3, 7, 8, 186908146427086779036283479683542037613772800000⟩, + ⟨4, 7, 8, 3, 8, 8, 84578685611216930753263221809754113310720000000⟩, + ⟨4, 7, 1, 4, 0, 8, -4403752256211769274136750800528031607264011878400000⟩, + ⟨4, 7, 2, 4, 1, 8, -1357878816665221413282559501342397071772300083200000⟩, + ⟨4, 7, 3, 4, 2, 8, -878225460449108865612967951826080349319856128000000⟩, + ⟨4, 7, 4, 4, 3, 8, 28659738115876707694034892986020306427156889600000⟩, + ⟨4, 7, 5, 4, 4, 8, -6680327186245781029026157264456633784519884800000⟩, + ⟨4, 7, 6, 4, 5, 8, -1354191357939499983337634860742251333759795200000⟩, + ⟨4, 7, 7, 4, 6, 8, -61385371700373182878925717278466972319744000000⟩, + ⟨4, 7, 8, 4, 7, 8, 30044587238529213828525023347463019131043840000⟩, + ⟨4, 7, 2, 5, 0, 8, 10131235900668915002131210448733751950405166694400000⟩, + ⟨4, 7, 3, 5, 1, 8, 729298018609631439339725840442513492290788392960000⟩, + ⟨4, 7, 4, 5, 2, 8, -196366824089793153665381169775719079602825461760000⟩, + ⟨4, 7, 5, 5, 3, 8, 17422677342653415357618098390019697586837913600000⟩, + ⟨4, 7, 6, 5, 4, 8, -1527366844330330980594424257477736470990028800000⟩, + ⟨4, 7, 7, 5, 5, 8, -162575590667752078289249154937078697636659200000⟩, + ⟨4, 7, 8, 5, 6, 8, 62560716036675979235868630252968069572853760000⟩, + ⟨4, 7, 3, 6, 0, 8, 397176073552484241329033501040251508178141839360000⟩, + ⟨4, 7, 4, 6, 1, 8, 105371637508978969767092295483191099546602045440000⟩, + ⟨4, 7, 5, 6, 2, 8, 257854311047630795565817539610049641866854400000⟩, + ⟨4, 7, 6, 6, 3, 8, 5655517590063605742246489120836651945086156800000⟩, + ⟨4, 7, 7, 6, 4, 8, 58199717135686369482327912192959597405798400000⟩, + ⟨4, 7, 8, 6, 5, 8, -65654680514515070742056979945606883489873920000⟩, + ⟨4, 7, 4, 7, 0, 8, 2010620715529315479062703765250390853067189780480000⟩, + ⟨4, 7, 5, 7, 1, 8, -12020280745584317612545174546306602562800844800000⟩, + ⟨4, 7, 6, 7, 2, 8, -5581303206366445074237266934187293540561715200000⟩, + ⟨4, 7, 7, 7, 3, 8, 2438542753729479791123501292019723741534617600000⟩, + ⟨4, 7, 8, 7, 4, 8, 129813862002799186282872502826818595507404800000⟩ +] + +def collectedFourData_9_3_38 : List CollectedFourTerm := [ + ⟨5, 0, 4, 0, 7, 2, 105550586151095428059704312534346382928230628720640000⟩, + ⟨5, 0, 5, 0, 8, 2, 9949994396324421157848572371667337577668123033600000⟩, + ⟨5, 0, 4, 1, 6, 2, 236489712287318097181867126382241435305007183298560000⟩, + ⟨5, 0, 5, 1, 7, 2, -78918743765731702797385195514916111717409121894400000⟩, + ⟨5, 0, 6, 1, 8, 2, -21583819952943444102121058206931250402981996134400000⟩, + ⟨5, 0, 4, 2, 5, 2, -30009305111780494076504210002175726051194809876480000⟩, + ⟨5, 0, 5, 2, 6, 2, -55160098437041930165963716223779713435550561075200000⟩, + ⟨5, 0, 6, 2, 7, 2, -28881619816754370146838955095417225815409662361600000⟩, + ⟨5, 0, 7, 2, 8, 2, -45149738690460885465854335375186401806265404620800000⟩, + ⟨5, 0, 4, 3, 4, 2, 20589380837171442416994677794565951531413646868480000⟩, + ⟨5, 0, 5, 3, 5, 2, 20842781567568173224511360896549310410512138240000000⟩, + ⟨5, 0, 6, 3, 6, 2, 76527847860878294771401945607442096893588825702400000⟩, + ⟨5, 0, 7, 3, 7, 2, 25210671169164416021797911065467131385672315699200000⟩, + ⟨5, 0, 8, 3, 8, 2, 28520498860336412414248469920475839269647155200000000⟩, + ⟨5, 0, 4, 4, 3, 2, 46020264323460348353461029262239144690583181721600000⟩, + ⟨5, 0, 5, 4, 4, 2, -75088367920411900960336994642294243489675319705600000⟩, + ⟨5, 0, 6, 4, 5, 2, -60885651905770141136870588779693582218006469017600000⟩, + ⟨5, 0, 7, 4, 6, 2, -8279823272115900151727027021083652067547938816000000⟩, + ⟨5, 0, 8, 4, 7, 2, 10131235900668915002131210448733751950405166694400000⟩, + ⟨5, 0, 4, 5, 2, 2, -315315273029817168526794540376066940021389614120960000⟩, + ⟨5, 0, 5, 5, 3, 2, 195834780242102277344873661316335111094024745779200000⟩, + ⟨5, 0, 6, 5, 4, 2, -68671776312181861204095532487020482035255240294400000⟩, + ⟨5, 0, 7, 5, 5, 2, -21928630906712564937658073145088911340039097548800000⟩, + ⟨5, 0, 8, 5, 6, 2, 21095892156891310498242450040752491881458932121600000⟩, + ⟨5, 0, 4, 6, 1, 2, 169200101925311054195903135651209098057222444810240000⟩, + ⟨5, 0, 5, 6, 2, 2, 2898339982160340144278816847836017119416077516800000⟩, + ⟨5, 0, 6, 6, 3, 2, 254277117718068100857562398647243499636657645158400000⟩, + ⟨5, 0, 7, 6, 4, 2, 7850133655991025045821640724328406562266257817600000⟩, + ⟨5, 0, 8, 6, 5, 2, -22139197686250689272366466278823499983672783667200000⟩, + ⟨5, 0, 4, 7, 0, 2, 3228546485971739787223412159625446138824156596142080000⟩, + ⟨5, 0, 5, 7, 1, 2, -135110637243849314957996640724531557201929148825600000⟩, + ⟨5, 0, 6, 7, 2, 2, -250940372799637998128858870607714181472906221977600000⟩, + ⟨5, 0, 7, 7, 3, 2, 328917174940820514472434559314710202833149781606400000⟩, + ⟨5, 0, 8, 7, 4, 2, 43774103091709566845561862515516858149128634368000000⟩ +] + +def collectedFourData_9_3_39 : List CollectedFourTerm := [ + ⟨5, 1, 3, 0, 6, 3, -2648161375315326334995337993548331437691219476480000⟩, + ⟨5, 1, 4, 0, 7, 3, 37990346931906223490198113172669181284582298746880000⟩, + ⟨5, 1, 5, 0, 8, 3, 1790628327472175675051350321332392113770961305600000⟩, + ⟨5, 1, 3, 1, 5, 3, 35502384430281852644923451641239911641890674442240000⟩, + ⟨5, 1, 4, 1, 6, 3, 85118676676611323670251427454557148720215380459520000⟩, + ⟨5, 1, 5, 1, 7, 3, -14202433943846191082658931048503313071973230182400000⟩, + ⟨5, 1, 6, 1, 8, 3, -2589522357726263857908772725468760348831619481600000⟩, + ⟨5, 1, 3, 2, 4, 3, -46231734157710493636401164332095114278826022010880000⟩, + ⟨5, 1, 4, 2, 5, 3, -10801113986709357548789860969080095219017486172160000⟩, + ⟨5, 1, 5, 2, 6, 3, -9926762857676338238750108337178443229837865779200000⟩, + ⟨5, 1, 6, 2, 7, 3, -3465077099692730736987917989871240477023823462400000⟩, + ⟨5, 1, 7, 2, 8, 3, -4062635507964247134556920527729561844725474918400000⟩, + ⟨5, 1, 3, 3, 3, 3, 61795267565639966899341431715638567133192325693440000⟩, + ⟨5, 1, 4, 3, 4, 3, 7410643082526994307340877828301344111081983836160000⟩, + ⟨5, 1, 5, 3, 5, 3, 3750924232880905710354716248066915224822743040000000⟩, + ⟨5, 1, 6, 3, 6, 3, 9181441165487174161863498841820954825655425433600000⟩, + ⟨5, 1, 7, 3, 7, 3, 2268490822807292819717172395752979611487148441600000⟩, + ⟨5, 1, 8, 3, 8, 3, 2053050932041596286320192550632983707181383680000000⟩, + ⟨5, 1, 3, 4, 2, 3, -84594918127282463183389999506808534131032457216000000⟩, + ⟨5, 1, 4, 4, 3, 3, 16563866400927047404107438891115983876146803507200000⟩, + ⟨5, 1, 5, 4, 4, 3, -13513108983419229828909720946917661314905643417600000⟩, + ⟨5, 1, 6, 4, 5, 3, -7304766126592402168766930263964252087534380646400000⟩, + ⟨5, 1, 7, 4, 6, 3, -745029871724898822464105030015083756879085568000000⟩, + ⟨5, 1, 8, 4, 7, 3, 729298018609631439339725840442513492290788392960000⟩, + ⟨5, 1, 3, 5, 1, 3, 70249507618603333531352276213900342632287169413120000⟩, + ⟨5, 1, 4, 5, 2, 3, -113490005618572945370803947605752554356532911800320000⟩, + ⟨5, 1, 5, 5, 3, 3, 35242965074968783114945830818917059656808608563200000⟩, + ⟨5, 1, 6, 5, 4, 3, -8238907686075328199506756613598705641064077721600000⟩, + ⟨5, 1, 7, 5, 5, 3, -1973168331569435399308674166407784861094274662400000⟩, + ⟨5, 1, 8, 5, 6, 3, 1518589883965438938410556421963610158492224061440000⟩, + ⟨5, 1, 3, 6, 0, 3, 38257917741425934079869686039889338690950838353920000⟩, + ⟨5, 1, 4, 6, 1, 3, 60899430381701865717589951044582287202869921710080000⟩, + ⟨5, 1, 5, 6, 2, 3, 521593225883490183790722594864446621763816652800000⟩, + ⟨5, 1, 6, 6, 3, 3, 30506939124987232877182436088796994376457361817600000⟩, + ⟨5, 1, 7, 6, 4, 3, 706365809816578957764918110702014390048967884800000⟩, + ⟨5, 1, 8, 6, 5, 3, -1593692335712321117369990441658393022660324884480000⟩, + ⟨5, 1, 4, 7, 0, 3, 1162036190990685244935085531298604335080318288527360000⟩, + ⟨5, 1, 5, 7, 1, 3, -24314881471795100720631169539265088082429974937600000⟩, + ⟨5, 1, 6, 7, 2, 3, -30106612603215728252688473037554871866445162086400000⟩, + ⟨5, 1, 7, 7, 3, 3, 29596419223046115259625874155256971978947638067200000⟩, + ⟨5, 1, 8, 7, 4, 3, 3151083141701371499923758597333176986476163891200000⟩ +] + +def collectedFourData_9_3_40 : List CollectedFourTerm := [ + ⟨5, 2, 2, 0, 5, 4, 26653575862650829427936610448890288381566858035200000⟩, + ⟨5, 2, 3, 0, 6, 4, 4278177307592058975824838930031306611558218465280000⟩, + ⟨5, 2, 4, 0, 7, 4, -30687223533021628266115357175788938938130722979840000⟩, + ⟨5, 2, 5, 0, 8, 4, -964269719150682463111839610198494932167242547200000⟩, + ⟨5, 2, 2, 1, 4, 4, -91862736216980564885228145969017109952451900866560000⟩, + ⟨5, 2, 3, 1, 5, 4, -57355075431139797979826419509962665073561976176640000⟩, + ⟨5, 2, 4, 1, 6, 4, -68755777953068098838695821816755456020948828815360000⟩, + ⟨5, 2, 5, 1, 7, 4, 7648140476824602524455407340354404273093397708800000⟩, + ⟨5, 2, 6, 1, 8, 4, 1045861091736491882967720771098035926717589094400000⟩, + ⟨5, 2, 2, 2, 3, 4, 34236677676858410514791609676698237219858672517120000⟩, + ⟨5, 2, 3, 2, 4, 4, 74688634086959452338734783953110055079911285063680000⟩, + ⟨5, 2, 4, 2, 5, 4, 8724747892139481870010117316770065624182166650880000⟩, + ⟨5, 2, 5, 2, 6, 4, 5345652520956070889231459631951227071056209510400000⟩, + ⟨5, 2, 6, 2, 7, 4, 1399481764512668104285650316004649449115195801600000⟩, + ⟨5, 2, 7, 2, 8, 4, 1312659810025421780909493472969566411804880404480000⟩, + ⟨5, 2, 2, 3, 2, 4, 18307350872854095445846660370918076664105245081600000⟩, + ⟨5, 2, 3, 3, 3, 4, -99831949019504462618697693334020067925816078499840000⟩, + ⟨5, 2, 4, 3, 4, 4, -5986048540292589895432444369827914332196705402880000⟩, + ⟨5, 2, 5, 3, 5, 4, -2019906979636321295890515561007806721535508480000000⟩, + ⟨5, 2, 6, 3, 6, 4, -3708217483583456109998157948535022068466869862400000⟩, + ⟨5, 2, 7, 3, 7, 4, -732961824085164575760494811248854563399684587520000⟩, + ⟨5, 2, 8, 3, 8, 4, -552793345014407832766111864245985894025134080000000⟩, + ⟨5, 2, 2, 4, 1, 4, 42261372059249955404653667912630110087981962362880000⟩, + ⟨5, 2, 3, 4, 2, 4, 136665409609583837927490470324984056025947570176000000⟩, + ⟨5, 2, 4, 4, 3, 4, -13379690154644504325972867699325782438077634969600000⟩, + ⟨5, 2, 5, 4, 4, 4, 7276932685795847095978975541383140892686365491200000⟩, + ⟨5, 2, 6, 4, 5, 4, 2950262488849794389612455077786471921287272857600000⟩, + ⟨5, 2, 7, 4, 6, 4, 240723236914680309596065134083958044737771929600000⟩, + ⟨5, 2, 8, 4, 7, 4, -196366824089793153665381169775719079602825461760000⟩, + ⟨5, 2, 2, 5, 0, 4, -315315273029817168526794540376066940021389614120960000⟩, + ⟨5, 2, 3, 5, 1, 4, -113490005618572945370803947605752554356532911800320000⟩, + ⟨5, 2, 4, 5, 2, 4, 91673107840352093134156229954232979624052926709760000⟩, + ⟨5, 2, 5, 5, 3, 4, -18978658783340133203582861654964330520472086118400000⟩, + ⟨5, 2, 6, 5, 4, 4, 3327545314125372889001512324845540328891377254400000⟩, + ⟨5, 2, 7, 5, 5, 4, 637541507769667103945416074126978818826861281280000⟩, + ⟨5, 2, 8, 5, 6, 4, -408887265562142543317430102792473346086419824640000⟩, + ⟨5, 2, 3, 6, 0, 4, -61806715044925380978241347701035143126303501189120000⟩, + ⟨5, 2, 4, 6, 1, 4, -49192349743651109182066438116464750174204791357440000⟩, + ⟨5, 2, 5, 6, 2, 4, -280882719052922461000830813242223747036453273600000⟩, + ⟨5, 2, 6, 6, 3, 4, -12321199144545329041530576647097441566786479718400000⟩, + ⟨5, 2, 7, 6, 4, 4, -228230666498286226941062567384228421060588994560000⟩, + ⟨5, 2, 8, 6, 5, 4, 429108943880983690250916343763119511870248058880000⟩, + ⟨5, 2, 4, 7, 0, 4, -938650663293716168142445724713265271647836286484480000⟩, + ⟨5, 2, 5, 7, 1, 4, 13093785889721059481734282925044278561017639731200000⟩, + ⟨5, 2, 6, 7, 2, 4, 12159514526584105307364843461135761999289489817600000⟩, + ⟨5, 2, 7, 7, 3, 4, -9562765342496571126234153839374750805646995619840000⟩, + ⟨5, 2, 8, 7, 4, 4, -848443535001555587935033498036415636687762227200000⟩ +] + +def collectedFourData_9_3_41 : List CollectedFourTerm := [ + ⟨5, 3, 1, 0, 4, 5, 672153812235990880864542013349593316019142656000000⟩, + ⟨5, 3, 2, 0, 5, 5, -16553898964592293689392062044660575509785083904000000⟩, + ⟨5, 3, 3, 0, 6, 5, -1328536839999204945943511990797172089167858892800000⟩, + ⟨5, 3, 4, 0, 7, 5, 6353033710339039596811686520004173798127016345600000⟩, + ⟨5, 3, 5, 0, 8, 5, 149721219281162548289464596508892536856641536000000⟩, + ⟨5, 3, 1, 1, 3, 5, -2714621189843062993863493181847716023426980249600000⟩, + ⟨5, 3, 2, 1, 4, 5, 57053750002745403172777216090447331839968490291200000⟩, + ⟨5, 3, 3, 1, 5, 5, 17810933300024954176794706340619506721757750886400000⟩, + ⟨5, 3, 4, 1, 6, 5, 14234190155599812576596013537231479230108690022400000⟩, + ⟨5, 3, 5, 1, 7, 5, -1187519316102109258238144373615258846042783744000000⟩, + ⟨5, 3, 6, 1, 8, 5, -129911865731041222350118165325141275875842457600000⟩, + ⟨5, 3, 1, 2, 2, 5, -473913922162693291024720883753287664739444326400000⟩, + ⟨5, 3, 2, 2, 3, 5, -21263582270032431104518061161144573891898140262400000⟩, + ⟨5, 3, 3, 2, 4, 5, -23193662810014526185649994996051509503345872076800000⟩, + ⟨5, 3, 4, 2, 5, 5, -1806244133273461022726110763332349138629243699200000⟩, + ⟨5, 3, 5, 2, 6, 5, -830014255758138840376237909217416567326769152000000⟩, + ⟨5, 3, 6, 2, 7, 5, -173836935440961822173335209208714431505524326400000⟩, + ⟨5, 3, 7, 2, 8, 5, -135876939377148092588578728520908394454423961600000⟩, + ⟨5, 3, 1, 3, 1, 5, 2659614488754043355311855340728242947028418560000000⟩, + ⟨5, 3, 2, 3, 2, 5, -11370258092957686164650676267472452345221087232000000⟩, + ⟨5, 3, 3, 3, 3, 5, 31001618807609508611037646109014701369656239718400000⟩, + ⟨5, 3, 4, 3, 4, 5, 1239263895193454457741583665086344591037379379200000⟩, + ⟨5, 3, 5, 3, 5, 5, 313628987636416700998036304977856962127462400000000⟩, + ⟨5, 3, 6, 3, 6, 5, 460617050997600205320357979357846203855903129600000⟩, + ⟨5, 3, 7, 3, 7, 5, 75870845268779136121866832487718508191704678400000⟩, + ⟨5, 3, 8, 3, 8, 5, 49046676453595134365105666988775832341708800000000⟩, + ⟨5, 3, 1, 4, 0, 5, -21280914386737195304409788497435732751902624972800000⟩, + ⟨5, 3, 2, 4, 1, 5, -26247528165786975470143282992494691984256637337600000⟩, + ⟨5, 3, 3, 4, 2, 5, -42439809845587266824233409636586766013835509760000000⟩, + ⟨5, 3, 4, 4, 3, 5, 2769935262956589123486047651386073996448497664000000⟩, + ⟨5, 3, 5, 4, 4, 5, -1129882244258305606323478971272772019348832256000000⟩, + ⟨5, 3, 6, 4, 5, 5, -366467504481320882891145392398225220116571750400000⟩, + ⟨5, 3, 7, 4, 6, 5, -24917908218956910604386287891832066677932032000000⟩, + ⟨5, 3, 8, 4, 7, 5, 17422677342653415357618098390019697586837913600000⟩, + ⟨5, 3, 2, 5, 0, 5, 195834780242102277344873661316335111094024745779200000⟩, + ⟨5, 3, 3, 5, 1, 5, 35242965074968783114945830818917059656808608563200000⟩, + ⟨5, 3, 4, 5, 2, 5, -18978658783340133203582861654964330520472086118400000⟩, + ⟨5, 3, 5, 5, 3, 5, 2946797848080925730554274917145615728946184192000000⟩, + ⟨5, 3, 6, 5, 4, 5, -413331773672604609221207378404498845390707097600000⟩, + ⟨5, 3, 7, 5, 5, 5, -65993632272444580346695225620730886590405017600000⟩, + ⟨5, 3, 8, 5, 6, 5, 36278586927451055940814704667519051587020390400000⟩, + ⟨5, 3, 3, 6, 0, 5, 19193336786392545997556857764520768520911532851200000⟩, + ⟨5, 3, 4, 6, 1, 5, 10184064253186969669279194597242278265654712729600000⟩, + ⟨5, 3, 5, 6, 2, 5, 43612385970859420602260395485754498920480768000000⟩, + ⟨5, 3, 6, 6, 3, 5, 1530480463953320850263139882759880037770041753600000⟩, + ⟨5, 3, 7, 6, 4, 5, 23624768732115869463478356049544613603783475200000⟩, + ⟨5, 3, 8, 6, 5, 5, -38072758515799376594058378264576870818041036800000⟩, + ⟨5, 3, 4, 7, 0, 5, 194324497937070352941303785242648163861065315123200000⟩, + ⟨5, 3, 5, 7, 1, 5, -2033059370714484097011769292188312276310163456000000⟩, + ⟨5, 3, 6, 7, 2, 5, -1510396773542314137738277061632737111085311590400000⟩, + ⟨5, 3, 7, 7, 3, 5, 989867501691192340737397035614688452503456972800000⟩, + ⟨5, 3, 8, 7, 4, 5, 75278286046083312962827792731581138853691392000000⟩ +] + +def collectedFourData_9_3_42 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 3, 6, 17032327548740197074077509473128651482769601331200000⟩, + ⟨5, 4, 1, 0, 4, 6, -471397329771423334425634804481032524172099584000000⟩, + ⟨5, 4, 2, 0, 5, 6, 5804819988490199614821212010405936916624048128000000⟩, + ⟨5, 4, 3, 0, 6, 6, 310578078746212684584777854099131629648111206400000⟩, + ⟨5, 4, 4, 0, 7, 6, -1113883114431476425774989174497507544609167769600000⟩, + ⟨5, 4, 5, 0, 8, 6, -21000604830158133902794058460427894727167180800000⟩, + ⟨5, 4, 0, 1, 2, 6, -6662234629441480383176827691691410750257810636800000⟩, + ⟨5, 4, 1, 1, 3, 6, 1903827899117319789194362557810556414045087334400000⟩, + ⟨5, 4, 2, 1, 4, 6, -20006570605670970553580556534176621576321394278400000⟩, + ⟨5, 4, 3, 1, 5, 6, -4163742606491817248732427359502470336094614323200000⟩, + ⟨5, 4, 4, 1, 6, 6, -2495693362389421728949831657734731471035721318400000⟩, + ⟨5, 4, 5, 1, 7, 6, 166567063809489952149482568039058771608286003200000⟩, + ⟨5, 4, 6, 1, 8, 6, 15185042841983544740342595248721319002793574400000⟩, + ⟨5, 4, 0, 2, 1, 6, -6882832584880325708240533414194978608746856448000000⟩, + ⟨5, 4, 1, 2, 2, 6, 332367016867502633191741336745158221034527129600000⟩, + ⟨5, 4, 2, 2, 3, 6, 7456326008271614486669113374189030741908442316800000⟩, + ⟨5, 4, 3, 2, 4, 6, 5422087681532494754485502059726149946513450598400000⟩, + ⟨5, 4, 4, 2, 5, 6, 316690408445330750788701217836817804036354867200000⟩, + ⟨5, 4, 5, 2, 6, 6, 116421716789796192267177026288565270888421785600000⟩, + ⟨5, 4, 6, 2, 7, 6, 20319324161314051855559444691954341565274521600000⟩, + ⟨5, 4, 7, 2, 8, 6, 13613386280233627535669489801665359908123443200000⟩, + ⟨5, 4, 0, 3, 0, 6, 38459575352216598204057372063068621492561589043200000⟩, + ⟨5, 4, 1, 3, 1, 6, -1865250401614717268814035688118509377515683840000000⟩, + ⟨5, 4, 2, 3, 2, 6, 3987115155980342594448997204332431452378497024000000⟩, + ⟨5, 4, 3, 3, 3, 6, -7247388945040903963054915363086230392143033139200000⟩, + ⟨5, 4, 4, 3, 4, 6, -217281253353667612030453677445893833891197747200000⟩, + ⟨5, 4, 5, 3, 5, 6, -43991081987291951698299715094493751117086720000000⟩, + ⟨5, 4, 6, 3, 6, 6, -53840267890752112082199700262529315753059942400000⟩, + ⟨5, 4, 7, 3, 7, 6, -7601430594376734325957466190448763891141836800000⟩, + ⟨5, 4, 8, 3, 8, 6, -4299698947900590709975641350504972707430400000000⟩, + ⟨5, 4, 1, 4, 0, 6, 14924807438985501689059123737977830267524690739200000⟩, + ⟨5, 4, 2, 4, 1, 6, 9204005441323066106881263555116257265522520883200000⟩, + ⟨5, 4, 3, 4, 2, 6, 9921346708161275043477819275116498545153146880000000⟩, + ⟨5, 4, 4, 4, 3, 6, -485655240968491531817850736917271100704948224000000⟩, + ⟨5, 4, 5, 4, 4, 6, 158482616092789820075706902849695269505518796800000⟩, + ⟨5, 4, 6, 4, 5, 6, 42835384777435242192660097089148078110906777600000⟩, + ⟨5, 4, 7, 4, 6, 6, 2496502434004033760996093284933598617534464000000⟩, + ⟨5, 4, 8, 4, 7, 6, -1527366844330330980594424257477736470990028800000⟩, + ⟨5, 4, 2, 5, 0, 6, -68671776312181861204095532487020482035255240294400000⟩, + ⟨5, 4, 3, 5, 1, 6, -8238907686075328199506756613598705641064077721600000⟩, + ⟨5, 4, 4, 5, 2, 6, 3327545314125372889001512324845540328891377254400000⟩, + ⟨5, 4, 5, 5, 3, 6, -413331773672604609221207378404498845390707097600000⟩, + ⟨5, 4, 6, 5, 4, 6, 48313221089179121478898418266961316418053734400000⟩, + ⟨5, 4, 7, 5, 5, 6, 6611841658184813332802855377245257508008755200000⟩, + ⟨5, 4, 8, 5, 6, 6, -3180378637701709968692810058822477166097203200000⟩, + ⟨5, 4, 3, 6, 0, 6, -4486913335312833475968876344360160106324269465600000⟩, + ⟨5, 4, 4, 6, 1, 6, -1785581145185641889460384741820462126222383513600000⟩, + ⟨5, 4, 5, 6, 2, 6, -6117279086235608380070114911291266994431590400000⟩, + ⟨5, 4, 6, 6, 3, 6, -178893677518765331110877725896984718179984998400000⟩, + ⟨5, 4, 7, 6, 4, 6, -2366943971550537836959313316098159107532390400000⟩, + ⟨5, 4, 8, 6, 5, 6, 3337665496844414196800715692231770688087654400000⟩, + ⟨5, 4, 4, 7, 0, 6, -34071089001182947021360719189892150830784787251200000⟩, + ⟨5, 4, 5, 7, 1, 6, 285166502421054362268244989064666706185342156800000⟩, + ⟨5, 4, 6, 7, 2, 6, 176546149849909745524771967391232809571555737600000⟩, + ⟨5, 4, 7, 7, 3, 6, -99173919640394315082320864597833509592734105600000⟩, + ⟨5, 4, 8, 7, 4, 6, -6599304799344436555121641778629331738689536000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0914.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0914.lean new file mode 100644 index 0000000000000000000000000000000000000000..088859aad84856287b959bcb1605f79c0cb5ada2 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0914.lean @@ -0,0 +1,617 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0914. -/ +namespace LaughlinFock +def collectedFourData_9_3_43 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 3, 7, 16316555840960566800422264219249342846847890227200000⟩, + ⟨5, 5, 1, 0, 4, 7, -225793592581069248941180774298367755552817152000000⟩, + ⟨5, 5, 2, 0, 5, 7, 1853625489878706666028334386659513614997651456000000⟩, + ⟨5, 5, 3, 0, 6, 7, 74381562800787786190309297165177390429215129600000⟩, + ⟨5, 5, 4, 0, 7, 7, -213414590400694304651060787979875639858057707520000⟩, + ⟨5, 5, 5, 0, 8, 7, -3353011505372775606295963120979015820430540800000⟩, + ⟨5, 5, 0, 1, 2, 7, -6382258857210829794565761012587973176009215180800000⟩, + ⟨5, 5, 1, 1, 3, 7, 911910428525784304130783371867361835486491443200000⟩, + ⟨5, 5, 2, 1, 4, 7, -6388602801337738104652057246403465381996711116800000⟩, + ⟨5, 5, 3, 1, 5, 7, -997191055535382367531828755709903406350781644800000⟩, + ⟨5, 5, 4, 1, 6, 7, -478162717254149913350907756893172128737740718080000⟩, + ⟨5, 5, 5, 1, 7, 7, 26594533152080438371798602657891572780315443200000⟩, + ⟨5, 5, 6, 1, 8, 7, 2078128855424940622243757628217796209095475200000⟩, + ⟨5, 5, 0, 2, 1, 7, -6593586337146822541564786458486382053229068288000000⟩, + ⟨5, 5, 1, 2, 2, 7, 159199762184388297833977152287725424359558348800000⟩, + ⟨5, 5, 2, 2, 3, 7, 2380993032890351008694429996428464841433913753600000⟩, + ⟨5, 5, 3, 2, 4, 7, 1298557055357549602244400296298185079282833817600000⟩, + ⟨5, 5, 4, 2, 5, 7, 60676342900381225306797271382207507349519728640000⟩, + ⟨5, 5, 5, 2, 6, 7, 18588195865237756172820635905692809335249305600000⟩, + ⟨5, 5, 6, 2, 7, 7, 2780774101315878953947012190784352663948492800000⟩, + ⟨5, 5, 7, 2, 8, 7, 1630161649885807137994855130195045208450662400000⟩, + ⟨5, 5, 0, 3, 0, 7, 36843338472579346868040453063706692947289518899200000⟩, + ⟨5, 5, 1, 3, 1, 7, -893432276012439511931239810919692712301035520000000⟩, + ⟨5, 5, 2, 3, 2, 7, 1273186472424812592384451318524011719214235648000000⟩, + ⟨5, 5, 3, 3, 3, 7, -1735705617516538276495953809267324056459070668800000⟩, + ⟨5, 5, 4, 3, 4, 7, -41630031989388863054743447763810508704726384640000⟩, + ⟨5, 5, 5, 3, 5, 7, -7023731232034058043167004679059523994910720000000⟩, + ⟨5, 5, 6, 3, 6, 7, -7368238302116350063568631662632548831540019200000⟩, + ⟨5, 5, 7, 3, 7, 7, -910248220695385262134830967258756811430297600000⟩, + ⟨5, 5, 8, 3, 8, 7, -457667454772423333670583028318945778073600000000⟩, + ⟨5, 5, 1, 4, 0, 7, 7148801398309263011601424452020310276012874137600000⟩, + ⟨5, 5, 2, 4, 1, 7, 2939071173412245802386101109998694264750892646400000⟩, + ⟨5, 5, 3, 4, 2, 7, 2376102254932524276872287955569000705236664320000000⟩, + ⟨5, 5, 4, 4, 3, 7, -93049183513426152124734955183568116901530828800000⟩, + ⟨5, 5, 5, 4, 4, 7, 25303749080483006591799525682379326537649356800000⟩, + ⟨5, 5, 6, 4, 5, 7, 5862179650432288747056058498515300915137740800000⟩, + ⟨5, 5, 7, 4, 6, 7, 298948582151751474725608420645809262952448000000⟩, + ⟨5, 5, 8, 4, 7, 7, -162575590667752078289249154937078697636659200000⟩, + ⟨5, 5, 2, 5, 0, 7, -21928630906712564937658073145088911340039097548800000⟩, + ⟨5, 5, 3, 5, 1, 7, -1973168331569435399308674166407784861094274662400000⟩, + ⟨5, 5, 4, 5, 2, 7, 637541507769667103945416074126978818826861281280000⟩, + ⟨5, 5, 5, 5, 3, 7, -65993632272444580346695225620730886590405017600000⟩, + ⟨5, 5, 6, 5, 4, 7, 6611841658184813332802855377245257508008755200000⟩, + ⟨5, 5, 7, 5, 5, 7, 791747951936121220721633233858518913017446400000⟩, + ⟨5, 5, 8, 5, 6, 7, -338525048838647485988321706975268667444428800000⟩, + ⟨5, 5, 3, 6, 0, 7, -1074588481516690156041683171770381308734629478400000⟩, + ⟨5, 5, 4, 6, 1, 7, -342108668126721066124591021595664342178930360320000⟩, + ⟨5, 5, 5, 6, 2, 7, -976700781887423618208273073176743342663270400000⟩, + ⟨5, 5, 6, 6, 3, 7, -24482256466012616013835667490393088775631667200000⟩, + ⟨5, 5, 7, 6, 4, 7, -283434349868743432415400950342033387343052800000⟩, + ⟨5, 5, 8, 6, 5, 7, 355266936437112532289185293496340992072089600000⟩, + ⟨5, 5, 4, 7, 0, 7, -6527855041059940072397073047997609867216357949440000⟩, + ⟨5, 5, 5, 7, 1, 7, 45530429780364989716065771893252285432384716800000⟩, + ⟨5, 5, 6, 7, 2, 7, 24160988687032811167298306329276126918921420800000⟩, + ⟨5, 5, 7, 7, 3, 7, -11875775588720982169930347734112712344679219200000⟩, + ⟨5, 5, 8, 7, 4, 7, -702441512157058902132263951638434177613824000000⟩ +] + +def collectedFourData_9_3_44 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 3, 8, -31393870767137808325472830026066889814794095820800000⟩, + ⟨5, 6, 1, 0, 4, 8, 289625455054390012486426621699366406011748352000000⟩, + ⟨5, 6, 2, 0, 5, 8, -1783234147179518908963847444685956335420833792000000⟩, + ⟨5, 6, 3, 0, 6, 8, -57245541100374925899390177676402075046258933760000⟩, + ⟨5, 6, 4, 0, 7, 8, 136873454099134558677849647026886320185944309760000⟩, + ⟨5, 6, 5, 0, 8, 8, 1843246312981035729563727442509586270204723200000⟩, + ⟨5, 6, 0, 1, 2, 8, 12279785741468211133810207421241234033162269491200000⟩, + ⟨5, 6, 1, 1, 3, 8, -1169707562608521605094991961915278032291181363200000⟩, + ⟨5, 6, 2, 1, 4, 8, 6145995903874657661518938178839785353749567897600000⟩, + ⟨5, 6, 3, 1, 5, 8, 767458216863015327680571013692301425370862714880000⟩, + ⟨5, 6, 4, 1, 6, 8, 306669673376700969198431509729614582791578583040000⟩, + ⟨5, 6, 5, 1, 7, 8, -14619775416659148846124551836962084096888012800000⟩, + ⟨5, 6, 6, 1, 8, 8, -999606003873882535889324810237730129916723200000⟩, + ⟨5, 6, 0, 2, 1, 8, 12686390398683964178581117650239283535263301632000000⟩, + ⟨5, 6, 1, 2, 2, 8, -204205544719562144217385481394173977998183628800000⟩, + ⟨5, 6, 2, 2, 3, 8, -2290574932007669341690985754594618561365488435200000⟩, + ⟨5, 6, 3, 2, 4, 8, -999395528738005134066142539498879762641253826560000⟩, + ⟨5, 6, 4, 2, 5, 8, -38914774380166558618110253617067065252060856320000⟩, + ⟨5, 6, 5, 2, 6, 8, -10218462847105451156926867662270033362839142400000⟩, + ⟨5, 6, 6, 2, 7, 8, -1337587166376147355018044753342249728527564800000⟩, + ⟨5, 6, 7, 2, 8, 8, -697002816102019692228946582637808808938700800000⟩, + ⟨5, 6, 0, 3, 0, 8, -70888428778237762969577140629900010629804903628800000⟩, + ⟨5, 6, 1, 3, 1, 8, 1146005635246165613930736265497653557088747520000000⟩, + ⟨5, 6, 2, 3, 2, 8, -1224837274709426523841691965060464883412238336000000⟩, + ⟨5, 6, 3, 3, 3, 8, 1335833821236171732999381201275005199128492769280000⟩, + ⟨5, 6, 4, 3, 4, 8, 26699422293231280176660912732472095476620984320000⟩, + ⟨5, 6, 5, 3, 5, 8, 3861145920934495579151329822574379930746880000000⟩, + ⟨5, 6, 6, 3, 6, 8, 3544214895790436930004584308222866318635827200000⟩, + ⟨5, 6, 7, 3, 7, 8, 389191816174168479916131836387654609613619200000⟩, + ⟨5, 6, 8, 3, 8, 8, 176115021693260661850120422628350052270080000000⟩, + ⟨5, 6, 1, 4, 0, 8, -9169767992133761385100396301022479323525388697600000⟩, + ⟨5, 6, 2, 4, 1, 8, -2827460080818507806053445419315395976971996364800000⟩, + ⟨5, 6, 3, 4, 2, 8, -1828695904894226518097077546158861086770593792000000⟩, + ⟨5, 6, 4, 4, 3, 8, 59677096700251889021636768646066807058622054400000⟩, + ⟨5, 6, 5, 4, 4, 8, -13910194499023108431239098514671791974331187200000⟩, + ⟨5, 6, 6, 4, 5, 8, -2819781823952958851766167613921234070064332800000⟩, + ⟨5, 6, 7, 4, 6, 8, -127820454888061526368118640510546179260416000000⟩, + ⟨5, 6, 8, 4, 7, 8, 62560716036675979235868630252968069572853760000⟩, + ⟨5, 6, 2, 5, 0, 8, 21095892156891310498242450040752491881458932121600000⟩, + ⟨5, 6, 3, 5, 1, 8, 1518589883965438938410556421963610158492224061440000⟩, + ⟨5, 6, 4, 5, 2, 8, -408887265562142543317430102792473346086419824640000⟩, + ⟨5, 6, 5, 5, 3, 8, 36278586927451055940814704667519051587020390400000⟩, + ⟨5, 6, 6, 5, 4, 8, -3180378637701709968692810058822477166097203200000⟩, + ⟨5, 6, 7, 5, 5, 8, -338525048838647485988321706975268667444428800000⟩, + ⟨5, 6, 8, 5, 6, 8, 130267830273350866866273181552086534995312640000⟩, + ⟨5, 6, 3, 6, 0, 8, 827024826695381681050710543020289687072842711040000⟩, + ⟨5, 6, 4, 6, 1, 8, 219411404795904129949303647788648164128624476160000⟩, + ⟨5, 6, 5, 6, 2, 8, 536920351217088215183710062837763818494361600000⟩, + ⟨5, 6, 6, 6, 3, 8, 11776271951530251224571449233618802736050995200000⟩, + ⟨5, 6, 7, 6, 4, 8, 121187085987698206556852666815328454023577600000⟩, + ⟨5, 6, 8, 6, 5, 8, -136710276348210949882004460037754594399354880000⟩, + ⟨5, 6, 4, 7, 0, 8, 4186640030799951546821463274138925818008274206720000⟩, + ⟨5, 6, 5, 7, 1, 8, -25029379316659807779277838338585124024824627200000⟩, + ⟨5, 6, 6, 7, 2, 8, -11621738126603513107536080432304531914411212800000⟩, + ⟨5, 6, 7, 7, 3, 8, 5077686025379127818931432769798846930118246400000⟩, + ⟨5, 6, 8, 7, 4, 8, 270306531219928475662230495076171358876467200000⟩ +] + +def collectedFourData_9_3_45 : List CollectedFourTerm := [ + ⟨6, 0, 3, 0, 6, 3, -1442190038012530962520558582714967971220611399680000⟩, + ⟨6, 0, 4, 0, 7, 3, 20689562349390852969835001772698012048498444206080000⟩, + ⟨6, 0, 5, 0, 8, 3, 975177102020798394755377676325447076717107609600000⟩, + ⟨6, 0, 3, 1, 5, 3, 19334616699840265075567228199026063724863385763840000⟩, + ⟨6, 0, 4, 1, 6, 3, 46355674807469485313820534496676792642654510776320000⟩, + ⟨6, 0, 5, 1, 7, 3, -7734652782218401866399764901101073555016541798400000⟩, + ⟨6, 0, 6, 1, 8, 3, -1410255199073299931018890946539060010791049625600000⟩, + ⟨6, 0, 3, 2, 4, 3, -25177826043306930767799113077859345228936333230080000⟩, + ⟨6, 0, 4, 2, 5, 3, -5882292195737205242387873824383927656743761346560000⟩, + ⟨6, 0, 5, 2, 6, 3, -5406120124136666967388016583831939976545907507200000⟩, + ⟨6, 0, 6, 2, 7, 3, -1887082758892351487066400035366876398745970278400000⟩, + ⟨6, 0, 7, 2, 8, 3, -2212513373345441184741936991374854366475740774400000⟩, + ⟨6, 0, 3, 3, 3, 3, 33653734289086863842052748038714149876431627223040000⟩, + ⟨6, 0, 4, 3, 4, 3, 4035840009038081717422744560879387247083320770560000⟩, + ⟨6, 0, 5, 3, 5, 3, 2042755253673504855585786408978126574599536640000000⟩, + ⟨6, 0, 6, 3, 6, 3, 5000217549765849905575688915252287439726287257600000⟩, + ⟨6, 0, 7, 3, 7, 3, 1235421261132912042936018479412463348970264985600000⟩, + ⟨6, 0, 8, 3, 8, 3, 1118092586547965881622059628208367032210554880000000⟩, + ⟨6, 0, 3, 4, 2, 3, -46070435633902869134473464612853077507525574656000000⟩, + ⟨6, 0, 4, 4, 3, 3, 9020690104863039840284616925912383072674984755200000⟩, + ⟨6, 0, 5, 4, 4, 3, -7359246056575494237674488177427323202653755801600000⟩, + ⟨6, 0, 6, 4, 5, 3, -3978179364740761059473292386265026531365906022400000⟩, + ⟨6, 0, 7, 4, 6, 3, -405743648796879397877400353713618420852850688000000⟩, + ⟨6, 0, 8, 4, 7, 3, 397176073552484241329033501040251508178141839360000⟩, + ⟨6, 0, 3, 5, 1, 3, 38257917741425934079869686039889338690950838353920000⟩, + ⟨6, 0, 4, 5, 2, 3, -61806715044925380978241347701035143126303501189120000⟩, + ⟨6, 0, 5, 5, 3, 3, 19193336786392545997556857764520768520911532851200000⟩, + ⟨6, 0, 6, 5, 4, 3, -4486913335312833475968876344360160106324269465600000⟩, + ⟨6, 0, 7, 5, 5, 3, -1074588481516690156041683171770381308734629478400000⟩, + ⟨6, 0, 8, 5, 6, 3, 827024826695381681050710543020289687072842711040000⟩, + ⟨6, 0, 3, 6, 0, 3, 20835281548964302679150086461458363530863150366720000⟩, + ⟨6, 0, 4, 6, 1, 3, 33165860901007223299855974764194090051731487457280000⟩, + ⟨6, 0, 5, 6, 2, 3, 284059937311946398261590438481204120015129804800000⟩, + ⟨6, 0, 6, 6, 3, 3, 16614094634271464620678652099829766827783330201600000⟩, + ⟨6, 0, 7, 6, 4, 3, 384687180927114845762059193068444735354227916800000⟩, + ⟨6, 0, 8, 6, 5, 3, -867925660288565998266982220416729120161587527680000⟩, + ⟨6, 0, 4, 7, 0, 3, 632845503328602921645180672415553966186774145269760000⟩, + ⟨6, 0, 5, 7, 1, 3, -13241896872656728593692560887339250563312884121600000⟩, + ⟨6, 0, 6, 7, 2, 3, -16396076605977277400864107130417944007260137062400000⟩, + ⟨6, 0, 7, 7, 3, 3, 16118225030465591711370729679808409655705809715200000⟩, + ⟨6, 0, 8, 7, 4, 3, 1716081488942425484328132613691086692479611699200000⟩ +] + +def collectedFourData_9_3_46 : List CollectedFourTerm := [ + ⟨6, 1, 2, 0, 5, 4, -14302471647823008050192749673892936548508028108800000⟩, + ⟨6, 1, 3, 0, 6, 4, -2295696080762564403615548413374587481056681656320000⟩, + ⟨6, 1, 4, 0, 7, 4, 16466951631299717040930349557444766573876173864960000⟩, + ⟨6, 1, 5, 0, 8, 4, 517433022498590322647607158634989265540140236800000⟩, + ⟨6, 1, 2, 1, 4, 4, 49294105489083822885821686203042261759540477296640000⟩, + ⟨6, 1, 3, 1, 5, 4, 30777083886973886535964095241515226631128649564160000⟩, + ⟨6, 1, 4, 1, 6, 4, 36894770512791111685417442257641699543881707683840000⟩, + ⟨6, 1, 5, 1, 7, 4, -4104038906150445221111857720403425366730027827200000⟩, + ⟨6, 1, 6, 1, 8, 4, -561215451510329046520576963241336536148056473600000⟩, + ⟨6, 1, 2, 2, 3, 4, -18371610410259687393671146465357700143999384289280000⟩, + ⟨6, 1, 3, 2, 4, 4, -40078377361000135030001289268087942029762279505920000⟩, + ⟨6, 1, 4, 2, 5, 4, -4681753022737488803095989009391907226967049502720000⟩, + ⟨6, 1, 5, 2, 6, 4, -2868509801989617992165211225409174090974599577600000⟩, + ⟨6, 1, 6, 2, 7, 4, -750970464966236484717397827036708075544667750400000⟩, + ⟨6, 1, 7, 2, 8, 4, -704381273749965658549569242751801533018532741120000⟩, + ⟨6, 1, 2, 3, 2, 4, -9823836327066929802832622434124294160531220070400000⟩, + ⟨6, 1, 3, 3, 3, 4, 53570433766794713375732053711604866121164872744960000⟩, + ⟨6, 1, 4, 3, 4, 4, 3212150218462739801213019952385096004945020190720000⟩, + ⟨6, 1, 5, 3, 5, 4, 1083894425887178958426609401604599933168517120000000⟩, + ⟨6, 1, 6, 3, 6, 4, 1989852157032080991374658672916182600930400665600000⟩, + ⟨6, 1, 7, 3, 7, 4, 393311792831691704763870922516948483845264506880000⟩, + ⟨6, 1, 8, 3, 8, 4, 296632286223657519178144576206866522591723520000000⟩, + ⟨6, 1, 2, 4, 1, 4, -22677710442692067302909113053405341121780614430720000⟩, + ⟨6, 1, 3, 4, 2, 4, -73335493753324512786982522174967480263108460544000000⟩, + ⟨6, 1, 4, 4, 3, 4, 7179623480150468035183379983350081011541501542400000⟩, + ⟨6, 1, 5, 4, 4, 4, -3904846537591768926283299525583025787332512972800000⟩, + ⟨6, 1, 6, 4, 5, 4, -1583128876134720749047094553672139183525095014400000⟩, + ⟨6, 1, 7, 4, 6, 4, -129173559626155879511613251747160230935815782400000⟩, + ⟨6, 1, 8, 4, 7, 4, 105371637508978969767092295483191099546602045440000⟩, + ⟨6, 1, 2, 5, 0, 4, 169200101925311054195903135651209098057222444810240000⟩, + ⟨6, 1, 3, 5, 1, 4, 60899430381701865717589951044582287202869921710080000⟩, + ⟨6, 1, 4, 5, 2, 4, -49192349743651109182066438116464750174204791357440000⟩, + ⟨6, 1, 5, 5, 3, 4, 10184064253186969669279194597242278265654712729600000⟩, + ⟨6, 1, 6, 5, 4, 4, -1785581145185641889460384741820462126222383513600000⟩, + ⟨6, 1, 7, 5, 5, 4, -342108668126721066124591021595664342178930360320000⟩, + ⟨6, 1, 8, 5, 6, 4, 219411404795904129949303647788648164128624476160000⟩, + ⟨6, 1, 3, 6, 0, 4, 33165860901007223299855974764194090051731487457280000⟩, + ⟨6, 1, 4, 6, 1, 4, 26396915412924623878223393652625005008385327759360000⟩, + ⟨6, 1, 5, 6, 2, 4, 150723383095746348779261383819383802784278118400000⟩, + ⟨6, 1, 6, 6, 3, 4, 6611630737284282878272010550998938560558111129600000⟩, + ⟨6, 1, 7, 6, 4, 4, 122469970017405394781555910761514033994153328640000⟩, + ⟨6, 1, 8, 6, 5, 4, -230262480926064264568754796002783455221613854720000⟩, + ⟨6, 1, 4, 7, 0, 4, 503685680606213839397047982028364858048807824261120000⟩, + ⟨6, 1, 5, 7, 1, 4, -7026205504861483184569169264748721642167651532800000⟩, + ⟨6, 1, 6, 7, 2, 4, -6524869783474706174969993814614265050194929254400000⟩, + ⟨6, 1, 7, 7, 3, 4, 5131438306463661041998987991486279287038762024960000⟩, + ⟨6, 1, 8, 7, 4, 4, 455279984444519001813944708740922574736510156800000⟩ +] + +def collectedFourData_9_3_47 : List CollectedFourTerm := [ + ⟨6, 2, 1, 0, 4, 5, 9947825742478813833500345807439933550362624000000⟩, + ⟨6, 2, 2, 0, 5, 5, -244996456555910556867378916501551114004463616000000⟩, + ⟨6, 2, 3, 0, 6, 5, -19662245063835831530935260011590553049445171200000⟩, + ⟨6, 2, 4, 0, 7, 5, 94024419911134096783667186519698781506004582400000⟩, + ⟨6, 2, 5, 0, 8, 5, 2215862756778564131201427368878888288518144000000⟩, + ⟨6, 2, 1, 1, 3, 5, -40176188934442991677139227939521457729988198400000⟩, + ⟨6, 2, 2, 1, 4, 5, 844391198339276538118264038088561132993039564800000⟩, + ⟨6, 2, 3, 1, 5, 5, 263600469943260639509213112222977448818088345600000⟩, + ⟨6, 2, 4, 1, 6, 5, 210664941082710579258943614457017405086996889600000⟩, + ⟨6, 2, 5, 1, 7, 5, -17575196342505920638089379433575847062142976000000⟩, + ⟨6, 2, 6, 1, 8, 5, -1922685817809461145829068358798852594493030400000⟩, + ⟨6, 2, 1, 2, 2, 5, -7013890316155682265667875292610241846942105600000⟩, + ⟨6, 2, 2, 2, 3, 5, -314699414378800724037583489025781402204477849600000⟩, + ⟨6, 2, 3, 2, 4, 5, -343264460847584575034153003374500539706585907200000⟩, + ⟨6, 2, 4, 2, 5, 5, -26732276986432527100590914088906602983509196800000⟩, + ⟨6, 2, 5, 2, 6, 5, -12284148404348052090421536339713984569540608000000⟩, + ⟨6, 2, 6, 2, 7, 5, -2572773537682587109830854801999807471262105600000⟩, + ⟨6, 2, 7, 2, 8, 5, -2010968458021118509147301724299318176147046400000⟩, + ⟨6, 2, 1, 3, 1, 5, 39362093905684800299954760813063948195594240000000⟩, + ⟨6, 2, 2, 3, 2, 5, -168278962488485054700869326970383829909372928000000⟩, + ⟨6, 2, 3, 3, 3, 5, 458821620912826870513863730495909869968267673600000⟩, + ⟨6, 2, 4, 3, 4, 5, 18341012211653872749630417266993849021811916800000⟩, + ⟨6, 2, 5, 3, 5, 5, 4641685370225528488825155401040610826649600000000⟩, + ⟨6, 2, 6, 3, 6, 5, 6817097625461106579429744346006651601839718400000⟩, + ⟨6, 2, 7, 3, 7, 5, 1122882789517524763950620644519736396847513600000⟩, + ⟨6, 2, 8, 3, 8, 5, 725887113523951023768956922470434288435200000000⟩, + ⟨6, 2, 1, 4, 0, 5, -314955928399235626234238002140198262487069491200000⟩, + ⟨6, 2, 2, 4, 1, 5, -388461437859672572903256828146495523777832550400000⟩, + ⟨6, 2, 3, 4, 2, 5, -628105985865645200247704425570844112102359040000000⟩, + ⟨6, 2, 4, 4, 3, 5, 40994833045988844100341145075418989546438656000000⟩, + ⟨6, 2, 5, 4, 4, 5, -16722172024899900962758187366477663016321024000000⟩, + ⟨6, 2, 6, 4, 5, 5, -5423691435646149736074252254996679708219801600000⟩, + ⟨6, 2, 7, 4, 6, 5, -368783162896403395531588685019117810352128000000⟩, + ⟨6, 2, 8, 4, 7, 5, 257854311047630795565817539610049641866854400000⟩, + ⟨6, 2, 2, 5, 0, 5, 2898339982160340144278816847836017119416077516800000⟩, + ⟨6, 2, 3, 5, 1, 5, 521593225883490183790722594864446621763816652800000⟩, + ⟨6, 2, 4, 5, 2, 5, -280882719052922461000830813242223747036453273600000⟩, + ⟨6, 2, 5, 5, 3, 5, 43612385970859420602260395485754498920480768000000⟩, + ⟨6, 2, 6, 5, 4, 5, -6117279086235608380070114911291266994431590400000⟩, + ⟨6, 2, 7, 5, 5, 5, -976700781887423618208273073176743342663270400000⟩, + ⟨6, 2, 8, 5, 6, 5, 536920351217088215183710062837763818494361600000⟩, + ⟨6, 2, 3, 6, 0, 5, 284059937311946398261590438481204120015129804800000⟩, + ⟨6, 2, 4, 6, 1, 5, 150723383095746348779261383819383802784278118400000⟩, + ⟨6, 2, 5, 6, 2, 5, 645460024110544715905708546348083232899072000000⟩, + ⟨6, 2, 6, 6, 3, 5, 22650995472343367569414013183436273729562214400000⟩, + ⟨6, 2, 7, 6, 4, 5, 349644795990441888711921422570934439300300800000⟩, + ⟨6, 2, 8, 6, 5, 5, -563473955448866517112311404890915609981747200000⟩, + ⟨6, 2, 4, 7, 0, 5, 2875987917917145858200918011154034366488562892800000⟩, + ⟨6, 2, 5, 7, 1, 5, -30089125399292630324480216431318275220045824000000⟩, + ⟨6, 2, 6, 7, 2, 5, -22353758368517432207719382744113776890059161600000⟩, + ⟨6, 2, 7, 7, 3, 5, 14649964391646678563483337501975805114397491200000⟩, + ⟨6, 2, 8, 7, 4, 5, 1114112957699019589015333113491005340909568000000⟩ +] + +def collectedFourData_9_3_48 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 3, 6, -63067119997526996950043467250576475186122666803200000⟩, + ⟨6, 3, 1, 0, 4, 6, 1745484983078964334360290884814777997930266624000000⟩, + ⟨6, 3, 2, 0, 5, 6, -21494025272267203217551580384043434504311799808000000⟩, + ⟨6, 3, 3, 0, 6, 6, -1150005183075378578114868525029595534181426790400000⟩, + ⟨6, 3, 4, 0, 7, 6, 4124474464223478615531882917630330268785678745600000⟩, + ⟨6, 3, 5, 0, 8, 6, 77760814607055357609756215710507096047668428800000⟩, + ⟨6, 3, 0, 1, 2, 6, 24668851020173313919135175259492419479100247244800000⟩, + ⟨6, 3, 1, 1, 3, 6, -7049473551085663358338656713391747359905834598400000⟩, + ⟨6, 3, 2, 1, 4, 6, 74080115328698796444641334212430009315992430182400000⟩, + ⟨6, 3, 3, 1, 5, 6, 15417461521391316386099902676823283961666155315200000⟩, + ⟨6, 3, 4, 1, 6, 6, 9241026648438730972125533855599983200873899622400000⟩, + ⟨6, 3, 5, 1, 7, 6, -616762739610760867392085216500670680483967795200000⟩, + ⟨6, 3, 6, 1, 8, 6, -56227013973424880125806105550565100443035238400000⟩, + ⟨6, 3, 0, 2, 1, 6, 25485678766531433561183389024364354317559267328000000⟩, + ⟨6, 3, 1, 2, 2, 6, -1230685029748226549504507892007994512308279705600000⟩, + ⟨6, 3, 2, 2, 3, 6, -27609204071414745810013082238459709446752619724800000⟩, + ⟨6, 3, 3, 2, 4, 6, -20076848185884944614914101443709628178888025702400000⟩, + ⟨6, 3, 4, 2, 5, 6, -1172637852010120845210826513618258509021000499200000⟩, + ⟨6, 3, 5, 2, 6, 6, -431085085822181844136453126327805599024781721600000⟩, + ⟨6, 3, 6, 2, 7, 6, -75238175844324235621370231902845042108766617600000⟩, + ⟨6, 3, 7, 2, 8, 6, -50407500892130587703996127085548032276771635200000⟩, + ⟨6, 3, 0, 3, 0, 6, -142407703635994333580998715906700180719030973235200000⟩, + ⟨6, 3, 1, 3, 1, 6, 6906629206574399721953759691422625196922634240000000⟩, + ⟨6, 3, 2, 3, 2, 6, -14763447289667105433055391099044000853303230464000000⟩, + ⟨6, 3, 3, 3, 3, 6, 26835554151813666231445789407170634421686711091200000⟩, + ⟨6, 3, 4, 3, 4, 6, 804546697405569258749305839037470253555856179200000⟩, + ⟨6, 3, 5, 3, 5, 6, 162889707150964158303593293471884599277649920000000⟩, + ⟨6, 3, 6, 3, 6, 6, 199359167210016252793229138939728098027267686400000⟩, + ⟨6, 3, 7, 3, 7, 6, 28146495778487392090786529990852703719050444800000⟩, + ⟨6, 3, 8, 3, 8, 6, 15920879205998143452322281883961366308454400000000⟩, + ⟨6, 3, 1, 4, 0, 6, -55263417110840099686797106905088705710156624691200000⟩, + ⟨6, 3, 2, 4, 1, 6, -34080492755010922737453344082999260013537735475200000⟩, + ⟨6, 3, 3, 4, 2, 6, -36736656313714301423453309417891246001283399680000000⟩, + ⟨6, 3, 4, 4, 3, 6, 1798279023929012094413870401780004772762353664000000⟩, + ⟨6, 3, 5, 4, 4, 6, -586827733205804042902849846108860017640525004800000⟩, + ⟨6, 3, 6, 4, 5, 6, -158610403902111871099527264408910450250062233600000⟩, + ⟨6, 3, 7, 4, 6, 6, -9244022470146557633014751015011328987234304000000⟩, + ⟨6, 3, 8, 4, 7, 6, 5655517590063605742246489120836651945086156800000⟩, + ⟨6, 3, 2, 5, 0, 6, 254277117718068100857562398647243499636657645158400000⟩, + ⟨6, 3, 3, 5, 1, 6, 30506939124987232877182436088796994376457361817600000⟩, + ⟨6, 3, 4, 5, 2, 6, -12321199144545329041530576647097441566786479718400000⟩, + ⟨6, 3, 5, 5, 3, 6, 1530480463953320850263139882759880037770041753600000⟩, + ⟨6, 3, 6, 5, 4, 6, -178893677518765331110877725896984718179984998400000⟩, + ⟨6, 3, 7, 5, 5, 6, -24482256466012616013835667490393088775631667200000⟩, + ⟨6, 3, 8, 5, 6, 6, 11776271951530251224571449233618802736050995200000⟩, + ⟨6, 3, 3, 6, 0, 6, 16614094634271464620678652099829766827783330201600000⟩, + ⟨6, 3, 4, 6, 1, 6, 6611630737284282878272010550998938560558111129600000⟩, + ⟨6, 3, 5, 6, 2, 6, 22650995472343367569414013183436273729562214400000⟩, + ⟨6, 3, 6, 6, 3, 6, 662405592811029006006778443093644815653824102400000⟩, + ⟨6, 3, 7, 6, 4, 6, 8764294783201382266680108581316568059111014400000⟩, + ⟨6, 3, 8, 6, 5, 6, -12358672048710202601369361506343100181014118400000⟩, + ⟨6, 3, 4, 7, 0, 6, 126158063384763960349939007100104910146353967923200000⟩, + ⟨6, 3, 5, 7, 1, 6, -1055911470466873960598031227760167314317429964800000⟩, + ⟨6, 3, 6, 7, 2, 6, -653713192505459451182046865659912083130128793600000⟩, + ⟨6, 3, 7, 7, 3, 6, 367220127295430782253369343324664738895993241600000⟩, + ⟨6, 3, 8, 7, 4, 6, 24435835119393047207963220047098687254429696000000⟩ +] + +def collectedFourData_9_3_49 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 3, 7, -5841091707999553272203905834242560784758892134400000⟩, + ⟨6, 4, 1, 0, 4, 7, 80830850223540166447007706083716556447023104000000⟩, + ⟨6, 4, 2, 0, 5, 7, -663571196286833466063321726004516690499469312000000⟩, + ⟨6, 4, 3, 0, 6, 7, -26627526908163484527807074623764148633416499200000⟩, + ⟨6, 4, 4, 0, 7, 7, 76399345946909705597522487003045794294047703040000⟩, + ⟨6, 4, 5, 0, 8, 7, 1200329768840911357058355703499781446408601600000⟩, + ⟨6, 4, 0, 1, 2, 7, 2284756639362331346857832112656831919330793881600000⟩, + ⟨6, 4, 1, 1, 3, 7, -326450783757235632545714377755848456888804966400000⟩, + ⟨6, 4, 2, 1, 4, 7, 2287027679880739863491253099890657153026464153600000⟩, + ⟨6, 4, 3, 1, 5, 7, 356980018488763424013300654256252682071808409600000⟩, + ⟨6, 4, 4, 1, 6, 7, 171175357719569120367146637536492970643197788160000⟩, + ⟨6, 4, 5, 1, 7, 7, -9520459378000157280867609011575855342052966400000⟩, + ⟨6, 4, 6, 1, 8, 7, -743940163836844314331376491304497342473830400000⟩, + ⟨6, 4, 0, 2, 1, 7, 2360408829858797065251417910997931057035083776000000⟩, + ⟨6, 4, 1, 2, 2, 7, -56991219217743164446843675951380775302699417600000⟩, + ⟨6, 4, 2, 2, 3, 7, -852361172099036989563419372877601955755799347200000⟩, + ⟨6, 4, 3, 2, 4, 7, -464864700758243245597866524657313289323361075200000⟩, + ⟨6, 4, 4, 2, 5, 7, -21721255811685416459389887057194599838939873280000⟩, + ⟨6, 4, 5, 2, 6, 7, -6654306079874264302192400990678664044819251200000⟩, + ⟨6, 4, 6, 2, 7, 7, -995477029793308880812402655813244326353305600000⟩, + ⟨6, 4, 7, 2, 8, 7, -583574363895064316623126838292709611719884800000⟩, + ⟨6, 4, 0, 3, 0, 7, -13189383896015573905027841731744905485613426278400000⟩, + ⟨6, 4, 1, 3, 1, 7, 319835871610525184039594548849218988057559040000000⟩, + ⟨6, 4, 2, 3, 2, 7, -455782397909531211422325118536149210807402496000000⟩, + ⟨6, 4, 3, 3, 3, 7, 621357582373661059768184790021752485983132057600000⟩, + ⟨6, 4, 4, 3, 4, 7, 14902951151403049687955165145525737288399585280000⟩, + ⟨6, 4, 5, 3, 5, 7, 2514394499583092091700645436019432688189440000000⟩, + ⟨6, 4, 6, 3, 6, 7, 2637723062915881297148374384016402665596518400000⟩, + ⟨6, 4, 7, 3, 7, 7, 325855737322819471461461266962458025866035200000⟩, + ⟨6, 4, 8, 3, 8, 7, 163838349290697173848602775509529735987200000000⟩, + ⟨6, 4, 1, 4, 0, 7, -2559167815610625593150795291158482530468049715200000⟩, + ⟨6, 4, 2, 4, 1, 7, -1052145098976238995660730510206728819905973452800000⟩, + ⟨6, 4, 3, 4, 2, 7, -850610344114652331283382181731217806343536640000000⟩, + ⟨6, 4, 4, 4, 3, 7, 33310265938109001109885731821553113846356377600000⟩, + ⟨6, 4, 5, 4, 4, 7, -9058377293342406387188039132880540546996633600000⟩, + ⟨6, 4, 6, 4, 5, 7, -2098575782824516683794458954058615259503001600000⟩, + ⟨6, 4, 7, 4, 6, 7, -107019281602386231231932545245205386756096000000⟩, + ⟨6, 4, 8, 4, 7, 7, 58199717135686369482327912192959597405798400000⟩, + ⟨6, 4, 2, 5, 0, 7, 7850133655991025045821640724328406562266257817600000⟩, + ⟨6, 4, 3, 5, 1, 7, 706365809816578957764918110702014390048967884800000⟩, + ⟨6, 4, 4, 5, 2, 7, -228230666498286226941062567384228421060588994560000⟩, + ⟨6, 4, 5, 5, 3, 7, 23624768732115869463478356049544613603783475200000⟩, + ⟨6, 4, 6, 5, 4, 7, -2366943971550537836959313316098159107532390400000⟩, + ⟨6, 4, 7, 5, 5, 7, -283434349868743432415400950342033387343052800000⟩, + ⟨6, 4, 8, 5, 6, 7, 121187085987698206556852666815328454023577600000⟩, + ⟨6, 4, 3, 6, 0, 7, 384687180927114845762059193068444735354227916800000⟩, + ⟨6, 4, 4, 6, 1, 7, 122469970017405394781555910761514033994153328640000⟩, + ⟨6, 4, 5, 6, 2, 7, 349644795990441888711921422570934439300300800000⟩, + ⟨6, 4, 6, 6, 3, 7, 8764294783201382266680108581316568059111014400000⟩, + ⟨6, 4, 7, 6, 4, 7, 101465410158710138001091641806701886806425600000⟩, + ⟨6, 4, 8, 6, 5, 7, -127180440331643976377066157614699411354419200000⟩, + ⟨6, 4, 4, 7, 0, 7, 2336877973698251500323192875787502548144755834880000⟩, + ⟨6, 4, 5, 7, 1, 7, -16299237317235777418595572414891587517651353600000⟩, + ⟨6, 4, 6, 7, 2, 7, -8649285550975085591370100380607679448062361600000⟩, + ⟨6, 4, 7, 7, 3, 7, 4251356413294261138137814339905409136354918400000⟩, + ⟨6, 4, 8, 7, 4, 7, 251463932217555309881617840390580887093248000000⟩ +] + +def collectedFourData_9_3_50 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 3, 8, 32946466823078927469958641842954525297222457753600000⟩, + ⟨6, 5, 1, 0, 4, 8, -303948994274927949325449777837782944903593984000000⟩, + ⟨6, 5, 2, 0, 5, 8, 1871424683614694036908845736653003536637886464000000⟩, + ⟨6, 5, 3, 0, 6, 8, 60076641540072648963775964425149579914033233920000⟩, + ⟨6, 5, 4, 0, 7, 8, -143642583862508706299548431375643123763820625920000⟩, + ⟨6, 5, 5, 0, 8, 8, -1934404774353630554253686402143969360635494400000⟩, + ⟨6, 5, 0, 1, 2, 8, -12887087308434040542256782990649879906086184550400000⟩, + ⟨6, 5, 1, 1, 3, 8, 1227555903827136597014148517354325837500278374400000⟩, + ⟨6, 5, 2, 1, 4, 8, -6449948515228801862211469549332669823943127859200000⟩, + ⟨6, 5, 3, 1, 5, 8, -805413160662057920789674291786499372562209832960000⟩, + ⟨6, 5, 4, 1, 6, 8, -321836141025533254041803783665160045666689351680000⟩, + ⟨6, 5, 5, 1, 7, 8, 15342802080654025423397250843040673796037017600000⟩, + ⟨6, 5, 6, 1, 8, 8, 1049041906525753843153954693331303807739494400000⟩, + ⟨6, 5, 0, 2, 1, 8, -13313800756687478810403582751406205619346079744000000⟩, + ⟨6, 5, 1, 2, 2, 8, 214304609141550445346335937804906528945838489600000⟩, + ⟨6, 5, 2, 2, 3, 8, 2403856203745443564646203813252357684533290598400000⟩, + ⟨6, 5, 3, 2, 4, 8, 1048821022260391873533467799816958672033567211520000⟩, + ⟨6, 5, 4, 2, 5, 8, 40839319641521519777945143803688836429974077440000⟩, + ⟨6, 5, 5, 2, 6, 8, 10723820890778229333210458810892102885231820800000⟩, + ⟨6, 5, 6, 2, 7, 8, 1403738058516753578579377509145114240981401600000⟩, + ⟨6, 5, 7, 2, 8, 8, 731473360727967079076965862612934426466713600000⟩, + ⟨6, 5, 0, 3, 0, 8, 74394243519889933943659943872822549403580078489600000⟩, + ⟨6, 5, 1, 3, 1, 8, -1202681788453497923496032910793812685451427840000000⟩, + ⟨6, 5, 2, 3, 2, 8, 1285412077223876110963465934195025843125747712000000⟩, + ⟨6, 5, 3, 3, 3, 8, -1401898001012787491308927407155444834490919157760000⟩, + ⟨6, 5, 4, 3, 4, 8, -28019852578998064609483176424865084216904253440000⟩, + ⟨6, 5, 5, 3, 5, 8, -4052100390127610193841716312179416718376960000000⟩, + ⟨6, 5, 6, 3, 6, 8, -3719495418202859519804497801747888270108262400000⟩, + ⟨6, 5, 7, 3, 7, 8, -408439448403995151163030662963479284442726400000⟩, + ⟨6, 5, 8, 3, 8, 8, -184824858403143709009639771323560739471360000000⟩, + ⟨6, 5, 1, 4, 0, 8, 9623262424982889825239341076984325512960881459200000⟩, + ⟨6, 5, 2, 4, 1, 8, 2967293215839404830593016969313511352336751001600000⟩, + ⟨6, 5, 3, 4, 2, 8, 1919134770191030610697948869789304516943806464000000⟩, + ⟨6, 5, 4, 4, 3, 8, -62628450665300882543392772206587850957573324800000⟩, + ⟨6, 5, 5, 4, 4, 8, 14598128563501839449558366377130774025889382400000⟩, + ⟨6, 5, 6, 4, 5, 8, 2959235227802303978190882239841923799554457600000⟩, + ⟨6, 5, 7, 4, 6, 8, 134141865063946542192344404547454288003072000000⟩, + ⟨6, 5, 8, 4, 7, 8, -65654680514515070742056979945606883489873920000⟩, + ⟨6, 5, 2, 5, 0, 8, -22139197686250689272366466278823499983672783667200000⟩, + ⟨6, 5, 3, 5, 1, 8, -1593692335712321117369990441658393022660324884480000⟩, + ⟨6, 5, 4, 5, 2, 8, 429108943880983690250916343763119511870248058880000⟩, + ⟨6, 5, 5, 5, 3, 8, -38072758515799376594058378264576870818041036800000⟩, + ⟨6, 5, 6, 5, 4, 8, 3337665496844414196800715692231770688087654400000⟩, + ⟨6, 5, 7, 5, 5, 8, 355266936437112532289185293496340992072089600000⟩, + ⟨6, 5, 8, 5, 6, 8, -136710276348210949882004460037754594399354880000⟩, + ⟨6, 5, 3, 6, 0, 8, -867925660288565998266982220416729120161587527680000⟩, + ⟨6, 5, 4, 6, 1, 8, -230262480926064264568754796002783455221613854720000⟩, + ⟨6, 5, 5, 6, 2, 8, -563473955448866517112311404890915609981747200000⟩, + ⟨6, 5, 6, 6, 3, 8, -12358672048710202601369361506343100181014118400000⟩, + ⟨6, 5, 7, 6, 4, 8, -127180440331643976377066157614699411354419200000⟩, + ⟨6, 5, 8, 6, 5, 8, 143471336092619276448014477126643305372712960000⟩, + ⟨6, 5, 4, 7, 0, 8, -4393691937450130848469005058925768978806855434240000⟩, + ⟨6, 5, 5, 7, 1, 8, 26267216979238781631533411766460154152117862400000⟩, + ⟨6, 5, 6, 7, 2, 8, 12196495693530651591325503806799594649131417600000⟩, + ⟨6, 5, 7, 7, 3, 8, -5328804957312914388935941416014526943120588800000⟩, + ⟨6, 5, 8, 7, 4, 8, -283674645568748802595725411444675641239142400000⟩ +] + +def collectedFourData_9_3_51 : List CollectedFourTerm := [ + ⟨7, 0, 2, 0, 5, 4, -272908787015226981962711952607761427223742618009600000⟩, + ⟨7, 0, 3, 0, 6, 4, -43804710695013649040193559651143610563646917181440000⟩, + ⟨7, 0, 4, 0, 7, 4, 314209732848549365627762717430079657906046049976320000⟩, + ⟨7, 0, 5, 0, 8, 4, 9873259811929565656095586227572841856122853785600000⟩, + ⟨7, 0, 2, 1, 4, 4, 940592288331798241319488324204442487493330080890880000⟩, + ⟨7, 0, 3, 1, 5, 4, 587264693703371269190082751381164865700210902302720000⟩, + ⟨7, 0, 4, 1, 6, 4, 703997694649063233311798960220867116569604684513280000⟩, + ⟨7, 0, 5, 1, 7, 4, -78310120608510171272037885659864416733125568102400000⟩, + ⟨7, 0, 6, 1, 8, 4, -10708682519863589539289519157496096643121099571200000⟩, + ⟨7, 0, 2, 2, 3, 4, -350552969866815909076111420919771968052209133813760000⟩, + ⟨7, 0, 3, 2, 4, 4, -764744837148055038527032846473574272778430463344640000⟩, + ⟨7, 0, 4, 2, 5, 4, -89333617992848042088423956339168273417625655050240000⟩, + ⟨7, 0, 5, 2, 6, 4, -54734702496084485268601275775294315143101625139200000⟩, + ⟨7, 0, 6, 2, 7, 4, -14329442052024042202273842356746884039024889036800000⟩, + ⟨7, 0, 7, 2, 8, 4, -13440462861858107550846313757545145002533888983040000⟩, + ⟨7, 0, 2, 3, 2, 4, -187450905121286331673673042921719781071432502476800000⟩, + ⟨7, 0, 3, 3, 3, 4, 1022189902498481884632772659283997535869329546936320000⟩, + ⟨7, 0, 4, 3, 4, 4, 61291785183492700733128089202140472287783278346240000⟩, + ⟨7, 0, 5, 3, 5, 4, 20682041559331494095207044503075142665020375040000000⟩, + ⟨7, 0, 6, 3, 6, 4, 37968831673783882469210878551878087761875645235200000⟩, + ⟨7, 0, 7, 3, 7, 4, 7504873768920861986781181244036391639398177832960000⟩, + ⟨7, 0, 8, 3, 8, 4, 5660109624141363833502484580590934227251363840000000⟩, + ⟨7, 0, 2, 4, 1, 4, -432718665807644739643328758370368841022091548426240000⟩, + ⟨7, 0, 3, 4, 2, 4, -1399331607724520949342133893339837699895798530048000000⟩, + ⟨7, 0, 4, 4, 3, 4, 136996064976793443726576746212241372147656477900800000⟩, + ⟨7, 0, 5, 4, 4, 4, -74509284709330970752138896971940224097140185497600000⟩, + ⟨7, 0, 6, 4, 5, 4, -30208050182743682985376325030314224729105157324800000⟩, + ⟨7, 0, 7, 4, 6, 4, -2464790725691047084208572965190819258166987980800000⟩, + ⟨7, 0, 8, 4, 7, 4, 2010620715529315479062703765250390853067189780480000⟩, + ⟨7, 0, 2, 5, 0, 4, 3228546485971739787223412159625446138824156596142080000⟩, + ⟨7, 0, 3, 5, 1, 4, 1162036190990685244935085531298604335080318288527360000⟩, + ⟨7, 0, 4, 5, 2, 4, -938650663293716168142445724713265271647836286484480000⟩, + ⟨7, 0, 5, 5, 3, 4, 194324497937070352941303785242648163861065315123200000⟩, + ⟨7, 0, 6, 5, 4, 4, -34071089001182947021360719189892150830784787251200000⟩, + ⟨7, 0, 7, 5, 5, 4, -6527855041059940072397073047997609867216357949440000⟩, + ⟨7, 0, 8, 5, 6, 4, 4186640030799951546821463274138925818008274206720000⟩, + ⟨7, 0, 3, 6, 0, 4, 632845503328602921645180672415553966186774145269760000⟩, + ⟨7, 0, 4, 6, 1, 4, 503685680606213839397047982028364858048807824261120000⟩, + ⟨7, 0, 5, 6, 2, 4, 2875987917917145858200918011154034366488562892800000⟩, + ⟨7, 0, 6, 6, 3, 4, 126158063384763960349939007100104910146353967923200000⟩, + ⟨7, 0, 7, 6, 4, 4, 2336877973698251500323192875787502548144755834880000⟩, + ⟨7, 0, 8, 6, 5, 4, -4393691937450130848469005058925768978806855434240000⟩, + ⟨7, 0, 4, 7, 0, 4, 9610943584852608546174188875061382309431481508823040000⟩, + ⟨7, 0, 5, 7, 1, 4, -134068660918710807509412100557231719151931333017600000⟩, + ⟨7, 0, 6, 7, 2, 4, -124502557452119113076386511157443841481763507404800000⟩, + ⟨7, 0, 7, 7, 3, 4, 97914167449066516233583173756732469539506560696320000⟩, + ⟨7, 0, 8, 7, 4, 4, 8687303241462973213920982908789620627897686425600000⟩ +] + +def collectedFourData_9_3_52 : List CollectedFourTerm := [ + ⟨7, 1, 1, 0, 4, 5, -463733407236530992743422745263392610800631808000000⟩, + ⟨7, 1, 2, 0, 5, 5, 11420891811001795755134042955241607401436086272000000⟩, + ⟨7, 1, 3, 0, 6, 5, 916586210234539795176101797702132773253703270400000⟩, + ⟨7, 1, 4, 0, 7, 5, -4383094933261634010584156565773794072079420620800000⟩, + ⟨7, 1, 5, 0, 8, 5, -103295897291562810148691586546897518642331648000000⟩, + ⟨7, 1, 1, 1, 3, 5, 1872875688281342156530906643580499023503346892800000⟩, + ⟨7, 1, 2, 1, 4, 5, -39362612251472506350124822834670810359473478041600000⟩, + ⟨7, 1, 3, 1, 5, 5, -12288146901684569050758049232446231655706997555200000⟩, + ⟨7, 1, 4, 1, 6, 5, -9820474688896722154970564856392547490661086003200000⟩, + ⟨7, 1, 5, 1, 7, 5, 819295180047093175931066190832486587555643392000000⟩, + ⟨7, 1, 6, 1, 8, 5, 89628997171794434864859401416254934825618636800000⟩, + ⟨7, 1, 1, 2, 2, 5, 326963432864044383482462457923926606096839475200000⟩, + ⟨7, 1, 2, 2, 3, 5, 14670203867971807570345325706424737646649750323200000⟩, + ⟨7, 1, 3, 2, 4, 5, 16001808046588850203577075714815939714746836582400000⟩, + ⟨7, 1, 4, 2, 5, 5, 1246166771616572884351537531750640013662591385600000⟩, + ⟨7, 1, 5, 2, 6, 5, 572644730820147835275064241101698573570932736000000⟩, + ⟨7, 1, 6, 2, 7, 5, 119933849824377401884262987125899971406279475200000⟩, + ⟨7, 1, 7, 2, 8, 5, 93744430092012361670440536446464728759061708800000⟩, + ⟨7, 1, 1, 3, 1, 5, -1834925379211464338111119112618519233120174080000000⟩, + ⟨7, 1, 2, 3, 2, 5, 7844586210209216423638057050467079205920178176000000⟩, + ⟨7, 1, 3, 3, 3, 5, -21388685235118987851309269036098198248610804531200000⟩, + ⟨7, 1, 4, 3, 4, 5, -854994880816810548908108646652934539554953625600000⟩, + ⟨7, 1, 5, 3, 5, 5, -216379400662709928156951960849008278319923200000000⟩, + ⟨7, 1, 6, 3, 6, 5, -317789634756046945618480991828994503446678732800000⟩, + ⟨7, 1, 7, 3, 7, 5, -52344931987164954541046956056946779379413811200000⟩, + ⟨7, 1, 8, 3, 8, 5, -33838359570990373030746752211583949497958400000000⟩, + ⟨7, 1, 1, 4, 0, 5, 14682161668980752181262207239963749186043012710400000⟩, + ⟨7, 1, 2, 4, 1, 5, 18108735599320996485968992044996079950670646476800000⟩, + ⟨7, 1, 3, 4, 2, 5, 29280139848786294646628615030072818175500615680000000⟩, + ⟨7, 1, 4, 4, 3, 5, -1911038059938114209170033451147196928414973952000000⟩, + ⟨7, 1, 5, 4, 4, 5, 779530121480588160015558601196731871797444608000000⟩, + ⟨7, 1, 6, 4, 5, 5, 252833832674782397338022227241653202968589107200000⟩, + ⟨7, 1, 7, 4, 6, 5, 17191402130331195052200984335340740674584576000000⟩, + ⟨7, 1, 8, 4, 7, 5, -12020280745584317612545174546306602562800844800000⟩, + ⟨7, 1, 2, 5, 0, 5, -135110637243849314957996640724531557201929148825600000⟩, + ⟨7, 1, 3, 5, 1, 5, -24314881471795100720631169539265088082429974937600000⟩, + ⟨7, 1, 4, 5, 2, 5, 13093785889721059481734282925044278561017639731200000⟩, + ⟨7, 1, 5, 5, 3, 5, -2033059370714484097011769292188312276310163456000000⟩, + ⟨7, 1, 6, 5, 4, 5, 285166502421054362268244989064666706185342156800000⟩, + ⟨7, 1, 7, 5, 5, 5, 45530429780364989716065771893252285432384716800000⟩, + ⟨7, 1, 8, 5, 6, 5, -25029379316659807779277838338585124024824627200000⟩, + ⟨7, 1, 3, 6, 0, 5, -13241896872656728593692560887339250563312884121600000⟩, + ⟨7, 1, 4, 6, 1, 5, -7026205504861483184569169264748721642167651532800000⟩, + ⟨7, 1, 5, 6, 2, 5, -30089125399292630324480216431318275220045824000000⟩, + ⟨7, 1, 6, 6, 3, 5, -1055911470466873960598031227760167314317429964800000⟩, + ⟨7, 1, 7, 6, 4, 5, -16299237317235777418595572414891587517651353600000⟩, + ⟨7, 1, 8, 6, 5, 5, 26267216979238781631533411766460154152117862400000⟩, + ⟨7, 1, 4, 7, 0, 5, -134068660918710807509412100557231719151931333017600000⟩, + ⟨7, 1, 5, 7, 1, 5, 1402651494245445600690951305200587791514206208000000⟩, + ⟨7, 1, 6, 7, 2, 5, 1042055299431858156325648326399220187646866227200000⟩, + ⟨7, 1, 7, 7, 3, 5, -682930931753465614158838782509293855865988710400000⟩, + ⟨7, 1, 8, 7, 4, 5, -51936112603375330548080331197387624002093056000000⟩ +] + +def collectedFourData_9_3_53 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 3, 6, 62239523342113057513982808029465441849641323724800000⟩, + ⟨7, 2, 1, 0, 4, 6, -1722579901411559006665734181722674435337486336000000⟩, + ⟨7, 2, 2, 0, 5, 6, 21211970480048872196405576613403530937617088512000000⟩, + ⟨7, 2, 3, 0, 6, 6, 1134914269723711365535621501403797766910089625600000⟩, + ⟨7, 2, 4, 0, 7, 6, -4070351154453420971888403265586851700799858278400000⟩, + ⟨7, 2, 5, 0, 8, 6, -76740400323137114494483565986600276861334323200000⟩, + ⟨7, 2, 0, 1, 2, 6, -24345134658969556177416925012475234020656100147200000⟩, + ⟨7, 2, 1, 1, 3, 6, 6956967016245697768299374499971871770114890137600000⟩, + ⟨7, 2, 2, 1, 4, 6, -73108000926120811712104581839008436717400725913600000⟩, + ⟨7, 2, 3, 1, 5, 6, -15215146280254938414135786403524941954608319692800000⟩, + ⟨7, 2, 4, 1, 6, 6, -9119761514607681304243604015323197989667314073600000⟩, + ⟨7, 2, 5, 1, 7, 6, 608669286468999847532916934464766011404766412800000⟩, + ⟨7, 2, 6, 1, 8, 6, 55489176432878491728340499728116684609395097600000⟩, + ⟨7, 2, 0, 2, 1, 6, -25151243604295350368545865844542174286726561792000000⟩, + ⟨7, 2, 1, 2, 2, 6, 1214535397189651257937246961531671670096815718400000⟩, + ⟨7, 2, 2, 2, 3, 6, 27246903003139553685173796269531976140720386867200000⟩, + ⟨7, 2, 3, 2, 4, 6, 19813390263427991929586547049783875407523191193600000⟩, + ⟨7, 2, 4, 2, 5, 6, 1157249942044144652908323709782986163391089868800000⟩, + ⟨7, 2, 5, 2, 6, 6, 425428182902891122211919886591435567542986342400000⟩, + ⟨7, 2, 6, 2, 7, 6, 74250864822500974794125627069624807227549286400000⟩, + ⟨7, 2, 7, 2, 8, 6, 49746029761884934139633544282554807786196172800000⟩, + ⟨7, 2, 0, 3, 0, 6, 140538962218296017630787041055502971989459258572800000⟩, + ⟨7, 2, 1, 3, 1, 6, -6815997142960755452370627567740941923369615360000000⟩, + ⟨7, 2, 2, 3, 2, 6, 14569714333416882055850138417400099617265156096000000⟩, + ⟨7, 2, 3, 3, 3, 6, -26483405284652909378573241684815612458981706956800000⟩, + ⟨7, 2, 4, 3, 4, 6, -793989054121346212141778511428223859350621388800000⟩, + ⟨7, 2, 5, 3, 5, 6, -160752191170453551913223257933826900235386880000000⟩, + ⟨7, 2, 6, 3, 6, 6, -196743081680574170420528355147282552979036569600000⟩, + ⟨7, 2, 7, 3, 7, 6, -27777144113645044144070383215708862107824947200000⟩, + ⟨7, 2, 8, 3, 8, 6, -15711957879280670666254896923756254042521600000000⟩, + ⟨7, 2, 1, 4, 0, 6, 54538224345267957778693925892147925884911537356800000⟩, + ⟨7, 2, 2, 4, 1, 6, 33633272367905692445044678359838217755345865932800000⟩, + ⟨7, 2, 3, 4, 2, 6, 36254580488823082159497207600893680957280747520000000⟩, + ⟨7, 2, 4, 4, 3, 6, -1774681153822321768669129329540039209329360896000000⟩, + ⟨7, 2, 5, 4, 4, 6, 579127101413448364074501122266532804084052787200000⟩, + ⟨7, 2, 6, 4, 5, 6, 156529042968103959448571656320282786403870310400000⟩, + ⟨7, 2, 7, 4, 6, 6, 9122718023722421249887498149953819803385856000000⟩, + ⟨7, 2, 8, 4, 7, 6, -5581303206366445074237266934187293540561715200000⟩, + ⟨7, 2, 2, 5, 0, 6, -250940372799637998128858870607714181472906221977600000⟩, + ⟨7, 2, 3, 5, 1, 6, -30106612603215728252688473037554871866445162086400000⟩, + ⟨7, 2, 4, 5, 2, 6, 12159514526584105307364843461135761999289489817600000⟩, + ⟨7, 2, 5, 5, 3, 6, -1510396773542314137738277061632737111085311590400000⟩, + ⟨7, 2, 6, 5, 4, 6, 176546149849909745524771967391232809571555737600000⟩, + ⟨7, 2, 7, 5, 5, 6, 24160988687032811167298306329276126918921420800000⟩, + ⟨7, 2, 8, 5, 6, 6, -11621738126603513107536080432304531914411212800000⟩, + ⟨7, 2, 3, 6, 0, 6, -16396076605977277400864107130417944007260137062400000⟩, + ⟨7, 2, 4, 6, 1, 6, -6524869783474706174969993814614265050194929254400000⟩, + ⟨7, 2, 5, 6, 2, 6, -22353758368517432207719382744113776890059161600000⟩, + ⟨7, 2, 6, 6, 3, 6, -653713192505459451182046865659912083130128793600000⟩, + ⟨7, 2, 7, 6, 4, 6, -8649285550975085591370100380607679448062361600000⟩, + ⟨7, 2, 8, 6, 5, 6, 12196495693530651591325503806799594649131417600000⟩, + ⟨7, 2, 4, 7, 0, 6, -124502557452119113076386511157443841481763507404800000⟩, + ⟨7, 2, 5, 7, 1, 6, 1042055299431858156325648326399220187646866227200000⟩, + ⟨7, 2, 6, 7, 2, 6, 645134857998687915892559820697140971669186150400000⟩, + ⟨7, 2, 7, 7, 3, 6, -362401290647074291544607886344766885506475622400000⟩, + ⟨7, 2, 8, 7, 4, 6, -24115176503336865206247238113306267189510144000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0915.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0915.lean new file mode 100644 index 0000000000000000000000000000000000000000..528a99ba69afcd0641547c6986a2cd641cd1ac3d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0915.lean @@ -0,0 +1,654 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse0910 +import OAI.Analysis.LaughlinFock.Sparse0911 +import OAI.Analysis.LaughlinFock.Sparse0912 +import OAI.Analysis.LaughlinFock.Sparse0913 +import OAI.Analysis.LaughlinFock.Sparse0914 + +namespace OAI + +/-! Sparse0915. -/ +namespace LaughlinFock +def collectedFourData_9_3_54 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 3, 7, -244739193924325927987447259472941140439939520921600000⟩, + ⟨7, 3, 1, 0, 4, 7, 3386777355478674424160974151560547202137849856000000⟩, + ⟨7, 3, 2, 0, 5, 7, -27803343588703795323068318665374412732071149568000000⟩, + ⟨7, 3, 3, 0, 6, 7, -1115681759075495111342257825886010128202517708800000⟩, + ⟨7, 3, 4, 0, 7, 7, 3201099259884078600026324760554768826949498306560000⟩, + ⟨7, 3, 5, 0, 8, 7, 50293293575098853044412326474332003790906982400000⟩, + ⟨7, 3, 0, 1, 2, 7, 95730306282469272732295576742557410237687948902400000⟩, + ⟨7, 3, 1, 1, 3, 7, -13678145399308014197415142112440499408679311769600000⟩, + ⟨7, 3, 2, 1, 4, 7, 95825461889268525908568440376252584486481847910400000⟩, + ⟨7, 3, 3, 1, 5, 7, 14957307013752095786874112300575137383175317094400000⟩, + ⟨7, 3, 4, 1, 6, 7, 7172172799584932010460957476931824635275892490240000⟩, + ⟨7, 3, 5, 1, 7, 7, -398903093880549991414274106795616862941583769600000⟩, + ⟨7, 3, 6, 1, 8, 7, -31170768261694645577431190620137587469818265600000⟩, + ⟨7, 3, 0, 2, 1, 7, 98900100054985741924449258215397738650705854464000000⟩, + ⟨7, 3, 1, 2, 2, 7, -2387907218270999569639387822290827538990524006400000⟩, + ⟨7, 3, 2, 2, 3, 7, -35713561200591907317524537456835636409423154380800000⟩, + ⟨7, 3, 3, 2, 4, 7, -19477628127569562402114469988659282639965703372800000⟩, + ⟨7, 3, 4, 2, 5, 7, -910111140884072437041253974432764644881774673920000⟩, + ⟨7, 3, 5, 2, 6, 7, -278812521276423893888077492340100797695839436800000⟩, + ⟨7, 3, 6, 2, 7, 7, -41710053192305611148912660433663520888219238400000⟩, + ⟨7, 3, 7, 2, 8, 7, -24451511216469710007872215784437642509366067200000⟩, + ⟨7, 3, 0, 3, 0, 7, -552629430325250400458723039083877533461425789337600000⟩, + ⟨7, 3, 1, 3, 1, 7, 13400983466642417467400791929183524973245890560000000⟩, + ⟨7, 3, 2, 3, 2, 7, -19097083601085548098700139350861923697289068544000000⟩, + ⟨7, 3, 3, 3, 3, 7, 26034611584788592493610051388428224255058404966400000⟩, + ⟨7, 3, 4, 3, 4, 7, 624427150645974124141606081338438453693429841920000⟩, + ⟨7, 3, 5, 3, 5, 7, 105352032427937337189713098775174876139356160000000⟩, + ⟨7, 3, 6, 3, 6, 7, 110519445419685953946295743810644459942156697600000⟩, + ⟨7, 3, 7, 3, 7, 7, 13653213213342313780867951790624414423108812800000⟩, + ⟨7, 3, 8, 3, 8, 7, 6864755347768706811779810615176966491340800000000⟩, + ⟨7, 3, 1, 4, 0, 7, -107228014833570624991035997423647067833182768332800000⟩, + ⟨7, 3, 2, 4, 1, 7, -44084420565117849832231308199568158742470144819200000⟩, + ⟨7, 3, 3, 4, 2, 7, -35640202271984158373425556700968181358877736960000000⟩, + ⟨7, 3, 4, 4, 3, 7, 1395685608553768463444358882609539102347257446400000⟩, + ⟨7, 3, 5, 4, 4, 7, -379542056153453456717043084445009948128470630400000⟩, + ⟨7, 3, 6, 4, 5, 7, -87929409629742242394788091859387720141268582400000⟩, + ⟨7, 3, 7, 4, 6, 7, -4484061203466119768799414585487245069778944000000⟩, + ⟨7, 3, 8, 4, 7, 7, 2438542753729479791123501292019723741534617600000⟩, + ⟨7, 3, 2, 5, 0, 7, 328917174940820514472434559314710202833149781606400000⟩, + ⟨7, 3, 3, 5, 1, 7, 29596419223046115259625874155256971978947638067200000⟩, + ⟨7, 3, 4, 5, 2, 7, -9562765342496571126234153839374750805646995619840000⟩, + ⟨7, 3, 5, 5, 3, 7, 989867501691192340737397035614688452503456972800000⟩, + ⟨7, 3, 6, 5, 4, 7, -99173919640394315082320864597833509592734105600000⟩, + ⟨7, 3, 7, 5, 5, 7, -11875775588720982169930347734112712344679219200000⟩, + ⟨7, 3, 8, 5, 6, 7, 5077686025379127818931432769798846930118246400000⟩, + ⟨7, 3, 3, 6, 0, 7, 16118225030465591711370729679808409655705809715200000⟩, + ⟨7, 3, 4, 6, 1, 7, 5131438306463661041998987991486279287038762024960000⟩, + ⟨7, 3, 5, 6, 2, 7, 14649964391646678563483337501975805114397491200000⟩, + ⟨7, 3, 6, 6, 3, 7, 367220127295430782253369343324664738895993241600000⟩, + ⟨7, 3, 7, 6, 4, 7, 4251356413294261138137814339905409136354918400000⟩, + ⟨7, 3, 8, 6, 5, 7, -5328804957312914388935941416014526943120588800000⟩, + ⟨7, 3, 4, 7, 0, 7, 97914167449066516233583173756732469539506560696320000⟩, + ⟨7, 3, 5, 7, 1, 7, -682930931753465614158838782509293855865988710400000⟩, + ⟨7, 3, 6, 7, 2, 7, -362401290647074291544607886344766885506475622400000⟩, + ⟨7, 3, 7, 7, 3, 7, 178129978724643314573948725701961446722214297600000⟩, + ⟨7, 3, 8, 7, 4, 7, 10536229038773812435069896144826337719222272000000⟩ +] + +def collectedFourData_9_3_55 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 3, 8, -65142470637800484522553622228994705943884201984000000⟩, + ⟨7, 4, 1, 0, 4, 8, 600974560983080383161687207246527617522728960000000⟩, + ⟨7, 4, 2, 0, 5, 8, -3700221579384291439774233226362908592738140160000000⟩, + ⟨7, 4, 3, 0, 6, 8, -118784842045655125046284054478266910265625804800000⟩, + ⟨7, 4, 4, 0, 7, 8, 284013240383231203872951191414580921368366284800000⟩, + ⟨7, 4, 5, 0, 8, 8, 3824747184322702161772579978911686785499136000000⟩, + ⟨7, 4, 0, 1, 2, 8, 25480629261537997992260809791891125765224267776000000⟩, + ⟨7, 4, 1, 1, 3, 8, -2427150226782492414444829206145651394620686336000000⟩, + ⟨7, 4, 2, 1, 4, 8, 12752978461237973829432113258408811582191566848000000⟩, + ⟨7, 4, 3, 1, 5, 8, 1592480415319479791742576528308457004977251942400000⟩, + ⟨7, 4, 4, 1, 6, 8, 636341416502140330288495423493901383231550259200000⟩, + ⟨7, 4, 5, 1, 7, 8, -30336121909754033935518614592718099546374144000000⟩, + ⟨7, 4, 6, 1, 8, 8, -2074188469453911670312370290665736567259136000000⟩, + ⟨7, 4, 0, 2, 1, 8, 26324336370493679505717079166898012989801103360000000⟩, + ⟨7, 4, 1, 2, 2, 8, -423727733341335938352060515392842460324429824000000⟩, + ⟨7, 4, 2, 2, 3, 8, -4752956758941112077322872488649504291758800896000000⟩, + ⟨7, 4, 3, 2, 4, 8, -2073751732281213843694961244662530405972102348800000⟩, + ⟨7, 4, 4, 2, 5, 8, -80748390863932576690089677201471523901774233600000⟩, + ⟨7, 4, 5, 2, 6, 8, -21203371859382541128870540966665643834212352000000⟩, + ⟨7, 4, 6, 2, 7, 8, -2775501414192161039976079620551173528879104000000⟩, + ⟨7, 4, 7, 2, 8, 8, -1446285035036780638125860358843155437584384000000⟩, + ⟨7, 4, 0, 3, 0, 8, -147093916022613968692491158847182137394750029824000000⟩, + ⟨7, 4, 1, 3, 1, 8, 2377968584967308172182949882371665234074009600000000⟩, + ⟨7, 4, 2, 3, 2, 8, -2541544710930106546704777946860494819457761280000000⟩, + ⟨7, 4, 3, 3, 3, 8, 2771863212482470898172085316667435432620222054400000⟩, + ⟨7, 4, 4, 3, 4, 8, 55401461823040560023667638951051918891915673600000⟩, + ⟨7, 4, 5, 3, 5, 8, 8011901006040552219898370116130410227302400000000⟩, + ⟨7, 4, 6, 3, 6, 8, 7354267222911581227884817471055503143469056000000⟩, + ⟨7, 4, 7, 3, 7, 8, 807575359077311044664272478146974990729216000000⟩, + ⟨7, 4, 8, 3, 8, 8, 365439729131393968105916562272323790438400000000⟩, + ⟨7, 4, 1, 4, 0, 8, -19027323728690882386631229950584516592793550848000000⟩, + ⟨7, 4, 2, 4, 1, 8, -5866996671435463730243497171089100045081903104000000⟩, + ⟨7, 4, 3, 4, 2, 8, -3794555000039546956571079708065374738222940160000000⟩, + ⟨7, 4, 4, 4, 3, 8, 123830334538252449330718314808789822039130112000000⟩, + ⟨7, 4, 5, 4, 4, 8, -28863737238392161795475994375689366830841856000000⟩, + ⟨7, 4, 6, 4, 5, 8, -5851064242264063582970243677796122434207744000000⟩, + ⟨7, 4, 7, 4, 6, 8, -265228212577463679894518642898793849159680000000⟩, + ⟨7, 4, 8, 4, 7, 8, 129813862002799186282872502826818595507404800000⟩, + ⟨7, 4, 2, 5, 0, 8, 43774103091709566845561862515516858149128634368000000⟩, + ⟨7, 4, 3, 5, 1, 8, 3151083141701371499923758597333176986476163891200000⟩, + ⟨7, 4, 4, 5, 2, 8, -848443535001555587935033498036415636687762227200000⟩, + ⟨7, 4, 5, 5, 3, 8, 75278286046083312962827792731581138853691392000000⟩, + ⟨7, 4, 6, 5, 4, 8, -6599304799344436555121641778629331738689536000000⟩, + ⟨7, 4, 7, 5, 5, 8, -702441512157058902132263951638434177613824000000⟩, + ⟨7, 4, 8, 5, 6, 8, 270306531219928475662230495076171358876467200000⟩, + ⟨7, 4, 3, 6, 0, 8, 1716081488942425484328132613691086692479611699200000⟩, + ⟨7, 4, 4, 6, 1, 8, 455279984444519001813944708740922574736510156800000⟩, + ⟨7, 4, 5, 6, 2, 8, 1114112957699019589015333113491005340909568000000⟩, + ⟨7, 4, 6, 6, 3, 8, 24435835119393047207963220047098687254429696000000⟩, + ⟨7, 4, 7, 6, 4, 8, 251463932217555309881617840390580887093248000000⟩, + ⟨7, 4, 8, 6, 5, 8, -283674645568748802595725411444675641239142400000⟩, + ⟨7, 4, 4, 7, 0, 8, 8687303241462973213920982908789620627897686425600000⟩, + ⟨7, 4, 5, 7, 1, 8, -51936112603375330548080331197387624002093056000000⟩, + ⟨7, 4, 6, 7, 2, 8, -24115176503336865206247238113306267189510144000000⟩, + ⟨7, 4, 7, 7, 3, 8, 10536229038773812435069896144826337719222272000000⟩, + ⟨7, 4, 8, 7, 4, 8, 560887677846718063416793609178532865376256000000⟩ +] + +def collectedFourData_9_3 : List (List CollectedFourTerm) := [ + collectedFourData_9_3_0, + collectedFourData_9_3_1, + collectedFourData_9_3_2, + collectedFourData_9_3_3, + collectedFourData_9_3_4, + collectedFourData_9_3_5, + collectedFourData_9_3_6, + collectedFourData_9_3_7, + collectedFourData_9_3_8, + collectedFourData_9_3_9, + collectedFourData_9_3_10, + collectedFourData_9_3_11, + collectedFourData_9_3_12, + collectedFourData_9_3_13, + collectedFourData_9_3_14, + collectedFourData_9_3_15, + collectedFourData_9_3_16, + collectedFourData_9_3_17, + collectedFourData_9_3_18, + collectedFourData_9_3_19, + collectedFourData_9_3_20, + collectedFourData_9_3_21, + collectedFourData_9_3_22, + collectedFourData_9_3_23, + collectedFourData_9_3_24, + collectedFourData_9_3_25, + collectedFourData_9_3_26, + collectedFourData_9_3_27, + collectedFourData_9_3_28, + collectedFourData_9_3_29, + collectedFourData_9_3_30, + collectedFourData_9_3_31, + collectedFourData_9_3_32, + collectedFourData_9_3_33, + collectedFourData_9_3_34, + collectedFourData_9_3_35, + collectedFourData_9_3_36, + collectedFourData_9_3_37, + collectedFourData_9_3_38, + collectedFourData_9_3_39, + collectedFourData_9_3_40, + collectedFourData_9_3_41, + collectedFourData_9_3_42, + collectedFourData_9_3_43, + collectedFourData_9_3_44, + collectedFourData_9_3_45, + collectedFourData_9_3_46, + collectedFourData_9_3_47, + collectedFourData_9_3_48, + collectedFourData_9_3_49, + collectedFourData_9_3_50, + collectedFourData_9_3_51, + collectedFourData_9_3_52, + collectedFourData_9_3_53, + collectedFourData_9_3_54, + collectedFourData_9_3_55 +] + +theorem collectedFourChecked_9_3 : collectNumericRowParts 9 3 = collectedFourData_9_3 := by + decide +kernel + +def collectedFourData_9_4_0 : List CollectedFourTerm := [ + ⟨0, 4, 5, 1, 8, 0, -18251999086355370931237084206484977768443412480000000⟩, + ⟨0, 4, 5, 2, 7, 0, -9355763313468361111966814054150593710070431744000000⟩, + ⟨0, 4, 6, 2, 8, 0, 16583930293351227691354359490824658918569934848000000⟩, + ⟨0, 4, 5, 3, 6, 0, 6401353373465336945410484524876050553368477696000000⟩, + ⟨0, 4, 6, 3, 7, 0, 35162368662501569420137650780891221814411264000000⟩, + ⟨0, 4, 7, 3, 8, 0, -2813860614535427937723737541906344647864614912000000⟩, + ⟨0, 4, 5, 4, 5, 0, 3881472376803017318040818402069113566589353984000000⟩, + ⟨0, 4, 6, 4, 6, 0, 7105921119476529029727528628806701637345214464000000⟩, + ⟨0, 4, 7, 4, 7, 0, -7442894437936607809879337177339858616733138944000000⟩, + ⟨0, 4, 8, 4, 8, 0, 2657470219211649760568177501807114936930795520000000⟩, + ⟨0, 4, 5, 5, 4, 0, 2574722825081172232617745110726481352545271808000000⟩, + ⟨0, 4, 6, 5, 5, 0, 5936153571300723196221046736154972523459510272000000⟩, + ⟨0, 4, 7, 5, 6, 0, 2357894529862354367923554762117069742087864320000000⟩, + ⟨0, 4, 8, 5, 7, 0, -4356928371037522737610276082393140580164042752000000⟩, + ⟨0, 4, 5, 6, 3, 0, -23462299154294470723066048005051210234077380608000000⟩, + ⟨0, 4, 6, 6, 4, 0, -3957979446604358300870739188555310962785124352000000⟩, + ⟨0, 4, 7, 6, 5, 0, 14731400604096535237802023037003848706842165248000000⟩, + ⟨0, 4, 8, 6, 6, 0, 6508102984116758063096086991571452851610714112000000⟩, + ⟨0, 4, 5, 7, 2, 0, 1299804786025869516450414596723238967783194624000000⟩, + ⟨0, 4, 6, 7, 3, 0, -19980634441716701040968949177977154953212329984000000⟩, + ⟨0, 4, 7, 7, 4, 0, 11454982919195463297717750841646347017215016960000000⟩, + ⟨0, 4, 8, 7, 5, 0, 16811118859061199940152552673082448149395537920000000⟩ +] + +def collectedFourData_9_4_1 : List CollectedFourTerm := [ + ⟨0, 5, 4, 0, 8, 1, -10568502734428748029760526900472787977712141598720000⟩, + ⟨0, 5, 4, 1, 7, 1, 12325492291100151680637946161029617335830650552320000⟩, + ⟨0, 5, 5, 1, 8, 1, 60501914193336028043162039805250183442152292352000000⟩, + ⟨0, 5, 4, 2, 6, 1, -8126113373826084512055957517874752192101797068800000⟩, + ⟨0, 5, 5, 2, 7, 1, 31012580404290021038670170913750282248006506905600000⟩, + ⟨0, 5, 6, 2, 8, 1, -27486291305665319162805302160004321830258710937600000⟩, + ⟨0, 5, 4, 3, 5, 1, -22295575971646042086389478294445772514686580817920000⟩, + ⟨0, 5, 5, 3, 6, 1, -21219271965236456112557198817665658685510542950400000⟩, + ⟨0, 5, 6, 3, 7, 1, -58278290547458140798476161618938491428457676800000⟩, + ⟨0, 5, 7, 3, 8, 1, 3109138030071079559251164500892163563983575449600000⟩, + ⟨0, 5, 4, 4, 4, 1, 16709771373256256092434641522922383846719409356800000⟩, + ⟨0, 5, 5, 4, 5, 1, -12866344534319898122757597459775990012850051481600000⟩, + ⟨0, 5, 6, 4, 6, 1, -11777390186168141170338864624262681778409229516800000⟩, + ⟨0, 5, 7, 4, 7, 1, 8223927664097827660881869369654048057778713395200000⟩, + ⟨0, 5, 8, 4, 8, 1, -2202252400043740782550044752778725667700211712000000⟩, + ⟨0, 5, 4, 5, 3, 1, 15922472107236855273105772643336328753071354019840000⟩, + ⟨0, 5, 5, 5, 4, 1, -8534717687507329912312851295644753108652995379200000⟩, + ⟨0, 5, 6, 5, 5, 1, -9838611439494043794146680022575806940317116006400000⟩, + ⟨0, 5, 7, 5, 6, 1, -2605324341874686510367306694099066309528518656000000⟩, + ⟨0, 5, 8, 5, 7, 1, 3610597737867582194979546698596880289419703091200000⟩, + ⟨0, 5, 4, 6, 2, 1, -20167364011530427302783121259299662200372975370240000⟩, + ⟨0, 5, 5, 6, 3, 1, 77773070417951599778783698591811179789533000499200000⟩, + ⟨0, 5, 6, 6, 4, 1, 6559975477876869044417387399365504081615808102400000⟩, + ⟨0, 5, 7, 6, 5, 1, -16277266051421163240136188835673654265117042278400000⟩, + ⟨0, 5, 8, 6, 6, 1, -5393281667989775906650519805498419881828365107200000⟩, + ⟨0, 5, 4, 7, 1, 1, -19373118861401048616842932179829146691709215703040000⟩, + ⟨0, 5, 5, 7, 2, 1, -4308606266094654153552280053367357242131192217600000⟩, + ⟨0, 5, 6, 7, 3, 1, 33116006219419263550532567329450719811554036940800000⟩, + ⟨0, 5, 7, 7, 4, 1, -12657031710778378552948282487477210940249735168000000⟩, + ⟨0, 5, 8, 7, 5, 1, -13931417401084162310307027847099744315508785152000000⟩ +] + +def collectedFourData_9_4_2 : List CollectedFourTerm := [ + ⟨0, 6, 3, 0, 7, 2, -2336691224207528312703200991137761341355075829760000⟩, + ⟨0, 6, 4, 0, 8, 2, 9018511837268702694605446166422354306521429442560000⟩, + ⟨0, 6, 3, 1, 6, 2, 11079901744688731062269071949637899971455583518720000⟩, + ⟨0, 6, 4, 1, 7, 2, -10517818930522251074761054121710008008728494735360000⟩, + ⟨0, 6, 5, 1, 8, 2, -25814310836695319956788110164186675846104219648000000⟩, + ⟨0, 6, 3, 2, 5, 2, 4715044430245361599235154997631998184144366469120000⟩, + ⟨0, 6, 4, 2, 6, 2, 6934326601827700188898471083683873608310351462400000⟩, + ⟨0, 6, 5, 2, 7, 2, -13232116720242998060466591339800609614425646694400000⟩, + ⟨0, 6, 6, 2, 8, 2, 7818371555926216923254215500861026630077356441600000⟩, + ⟨0, 6, 3, 3, 4, 2, -513745068703405244241017299660481595526128599040000⟩, + ⟨0, 6, 4, 3, 5, 2, 19025676661272297390341393242333418709825261404160000⟩, + ⟨0, 6, 5, 3, 6, 2, 9053612427676241472053808529999074237223639449600000⟩, + ⟨0, 6, 6, 3, 7, 2, 16577039225744370487232235928449573494508748800000⟩, + ⟨0, 6, 7, 3, 8, 2, -663286910939469576195568855382307238036321075200000⟩, + ⟨0, 6, 3, 4, 3, 2, -7586972070758980515940043818016708004191058001920000⟩, + ⟨0, 6, 4, 4, 4, 2, -14259093715975727263436291039336587247753782886400000⟩, + ⟨0, 6, 5, 4, 5, 2, 5489674526323214798746439847503011232180758118400000⟩, + ⟨0, 6, 6, 4, 6, 2, 3350034073734878711760502878779249593133354188800000⟩, + ⟨0, 6, 7, 4, 7, 2, -1754448829016571655603416269966234983671948902400000⟩, + ⟨0, 6, 8, 4, 8, 2, 375853417225262642557969415004779725481784115200000⟩, + ⟨0, 6, 3, 5, 2, 2, -9473756864792812193285190537478332810622434017280000⟩, + ⟨0, 6, 4, 5, 3, 2, -13587260824554072778913748358172042049404346040320000⟩, + ⟨0, 6, 5, 5, 4, 2, 3641502227263787244631835696425470983102319820800000⟩, + ⟨0, 6, 6, 5, 5, 2, 2798555795430131828393757113909561480375068262400000⟩, + ⟨0, 6, 7, 5, 6, 2, 555805988027479414715812296169976649505308672000000⟩, + ⟨0, 6, 8, 5, 7, 2, -616212518590684805872846562462935047166513643520000⟩, + ⟨0, 6, 3, 6, 1, 2, -2306499215164945771665805881037539091079327907840000⟩, + ⟨0, 6, 4, 6, 2, 2, 17209591144068999573085684798526495993370268139520000⟩, + ⟨0, 6, 5, 6, 3, 2, -33183383389782555597187923528027608769197034700800000⟩, + ⟨0, 6, 6, 6, 4, 2, -1865960202249429880059497021961759844381124198400000⟩, + ⟨0, 6, 7, 6, 5, 2, 3472505052321596858950073811884094901663354060800000⟩, + ⟨0, 6, 8, 6, 6, 2, 920459137622944614879172761166168059735567237120000⟩, + ⟨0, 6, 3, 7, 0, 2, 242436226665345766027833514493948215810688412549120000⟩, + ⟨0, 6, 4, 7, 1, 2, 16531831061290137392542258438446222235884501073920000⟩, + ⟨0, 6, 5, 7, 2, 2, 1838350123443719136244345359564681740867233382400000⟩, + ⟨0, 6, 6, 7, 3, 2, -9419722660743886129713193372131576404312378572800000⟩, + ⟨0, 6, 7, 7, 4, 2, 2700183582686797846494955685943743106741436416000000⟩, + ⟨0, 6, 8, 7, 5, 2, 2377643378608632609619375913775961622025810739200000⟩ +] + +def collectedFourData_9_4_3 : List CollectedFourTerm := [ + ⟨0, 7, 2, 0, 6, 3, -2336691224207528312703200991137761341355075829760000⟩, + ⟨0, 7, 3, 0, 7, 3, 667884136030241275975895958679761448488570716160000⟩, + ⟨0, 7, 4, 0, 8, 3, -1288856851156163461740582777695837314345315860480000⟩, + ⟨0, 7, 2, 1, 5, 3, 1140977325389848929020535427699716047102552309760000⟩, + ⟨0, 7, 3, 1, 6, 3, -3166909914064954193519042876637529341790015979520000⟩, + ⟨0, 7, 4, 1, 7, 3, 1503126373001366523908118308557682196460999802880000⟩, + ⟨0, 7, 5, 1, 8, 3, 2459456133494844705544754773614197253347475456000000⟩, + ⟨0, 7, 2, 2, 4, 3, 4203505762068304325713717840459601679078213550080000⟩, + ⟨0, 7, 3, 2, 5, 3, -1347676296728772911947304076770100676942280785920000⟩, + ⟨0, 7, 4, 2, 6, 3, -991001011052261073280060491069668284284744499200000⟩, + ⟨0, 7, 5, 2, 7, 3, 1260688725435968392636532376735188506039340236800000⟩, + ⟨0, 7, 6, 2, 8, 3, -558670982894211701769970503278721474480203366400000⟩, + ⟨0, 7, 2, 3, 3, 3, -4788202712566668037262125136400531509950493491200000⟩, + ⟨0, 7, 3, 3, 4, 3, 146841045062399345877083536889373357303807344640000⟩, + ⟨0, 7, 4, 3, 5, 3, -2719004438340808553313193155419606860826966753280000⟩, + ⟨0, 7, 5, 3, 6, 3, -862582106351673615905584305318368252517364531200000⟩, + ⟨0, 7, 6, 3, 7, 3, -1184531936283165819933167295779263432831795200000⟩, + ⟨0, 7, 7, 3, 8, 3, 37916760320201486943100549602521592325881200640000⟩, + ⟨0, 7, 2, 4, 2, 3, 1141677901173846819057002337627268416426265804800000⟩, + ⟨0, 7, 3, 4, 3, 3, 2168544236426848477749395754876076788114228510720000⟩, + ⟨0, 7, 4, 4, 4, 3, 2037800798926372923650336603450844776341123891200000⟩, + ⟨0, 7, 5, 4, 5, 3, -523028244684469676658358418596483977712553164800000⟩, + ⟨0, 7, 6, 4, 6, 3, -239380645357528849597162558119735551816053555200000⟩, + ⟨0, 7, 7, 4, 7, 3, 100292972236791633928540241843000404870881607680000⟩, + ⟨0, 7, 8, 4, 8, 3, -17904700190090523701650332492943122620429107200000⟩, + ⟨0, 7, 2, 5, 1, 3, -1182438216106181205260832153565131753170046812160000⟩, + ⟨0, 7, 3, 5, 2, 3, 2707833988955300012626320016170750765202648596480000⟩, + ⟨0, 7, 4, 5, 3, 3, 1941787571847980028779025643748692900352423362560000⟩, + ⟨0, 7, 5, 5, 4, 3, -346943795812973858307625951027109332629690777600000⟩, + ⟨0, 7, 6, 5, 5, 3, -199974112989316071666861605122824962446039449600000⟩, + ⟨0, 7, 7, 5, 6, 3, -31772619186350752963561170844902628178421350400000⟩, + ⟨0, 7, 8, 5, 7, 3, 29354796027128458138526471234418774154904862720000⟩, + ⟨0, 7, 2, 6, 0, 3, 21286348240515043809717778858803534419183523594240000⟩, + ⟨0, 7, 3, 6, 1, 3, 659254513226200830173553576990451989046823485440000⟩, + ⟨0, 7, 4, 6, 2, 3, -2459463362898605797083151711140661647884062556160000⟩, + ⟨0, 7, 5, 6, 3, 3, 3161543855437651047019659765349071706094410137600000⟩, + ⟨0, 7, 6, 6, 4, 3, 133334392306029829931230604234252651408759193600000⟩, + ⟨0, 7, 7, 6, 5, 3, -198505563140205457714485474311572811344836034560000⟩, + ⟨0, 7, 8, 6, 6, 3, -43848330601955669168733648521912816886947512320000⟩, + ⟨0, 7, 3, 7, 0, 3, -69294268798279047346732539104403828364858538065920000⟩, + ⟨0, 7, 4, 7, 1, 3, -2362603066888365235528706390707118643525042831360000⟩, + ⟨0, 7, 5, 7, 2, 3, -175148641976818706240764614217517440500026572800000⟩, + ⟨0, 7, 6, 7, 3, 3, 673097419305909633823756262306635199861175091200000⟩, + ⟨0, 7, 7, 7, 4, 3, -154355848180790487838833473041717969332417331200000⟩, + ⟨0, 7, 8, 7, 5, 3, -113264879077651469990194769325348146098942771200000⟩ +] + +def collectedFourData_9_4_4 : List CollectedFourTerm := [ + ⟨0, 8, 1, 0, 5, 4, -10568502734428748029760526900472787977712141598720000⟩, + ⟨0, 8, 2, 0, 6, 4, 9018511837268702694605446166422354306521429442560000⟩, + ⟨0, 8, 3, 0, 7, 4, -1288856851156163461740582777695837314345315860480000⟩, + ⟨0, 8, 4, 0, 8, 4, 1658123910179699414160937642844021622270024744960000⟩, + ⟨0, 8, 1, 1, 4, 4, -4616484615000488825239969837350491039303152435200000⟩, + ⟨0, 8, 2, 1, 5, 4, -4403627406343894208256468083783164703927760322560000⟩, + ⟨0, 8, 3, 1, 6, 4, 6111379683305095252214285185141281548350846402560000⟩, + ⟨0, 8, 4, 1, 7, 4, -1933783241218360051530078482553724638653589749760000⟩, + ⟨0, 8, 5, 1, 8, 4, -2373081434913246939702072321220092173991542784000000⟩, + ⟨0, 8, 1, 2, 3, 4, -6972912945617263006752531925819504491841286307840000⟩, + ⟨0, 8, 2, 2, 4, 4, -16223524135542078322572600067186622484758113812480000⟩, + ⟨0, 8, 3, 2, 5, 4, 2600693345561059062192799979478696816499501301760000⟩, + ⟨0, 8, 4, 2, 6, 4, 1274930159981679097290770119695377220950713958400000⟩, + ⟨0, 8, 5, 2, 7, 4, -1216414055446218529367076340256541347566269235200000⟩, + ⟨0, 8, 6, 2, 8, 4, 431240620940725196777937119524076929811145031680000⟩, + ⟨0, 8, 1, 3, 2, 4, 17967879369470317468869331656245622613339684208640000⟩, + ⟨0, 8, 2, 3, 3, 4, 18480175042027481749959289099406983851028984627200000⟩, + ⟨0, 8, 3, 3, 4, 4, -283368142391444541149140657643964389044172881920000⟩, + ⟨0, 8, 4, 3, 5, 4, 3498019401497797583323960858296040910611871170560000⟩, + ⟨0, 8, 5, 3, 6, 4, 832288714075497982445906151035014532465216716800000⟩, + ⟨0, 8, 6, 3, 7, 4, 914345479481612910025075788963998022752010240000⟩, + ⟨0, 8, 7, 3, 8, 4, -24390096862611656016181426829175913215311216640000⟩, + ⟨0, 8, 1, 4, 1, 4, -8089289012174839236689048793014818607480721899520000⟩, + ⟨0, 8, 2, 4, 2, 4, -4406331294189851060189860985842737363905465548800000⟩, + ⟨0, 8, 3, 4, 3, 4, -4184772395952524823649836722905118770215423836160000⟩, + ⟨0, 8, 4, 4, 4, 4, -2621645860711421699195686855981946997322442342400000⟩, + ⟨0, 8, 5, 4, 5, 4, 504659790631138651072915367725751237541573427200000⟩, + ⟨0, 8, 6, 4, 6, 4, 184778986748842336122882616532500885499270922240000⟩, + ⟨0, 8, 7, 4, 7, 4, -64513826783647819248375514668941031551721799680000⟩, + ⟨0, 8, 8, 4, 8, 4, 9871941324201838757746567805942187842705817600000⟩, + ⟨0, 8, 1, 5, 0, 4, -42635498688827818376576451922515108363003368570880000⟩, + ⟨0, 8, 2, 5, 1, 4, 4563646637740527456562228787813603787160902696960000⟩, + ⟨0, 8, 3, 5, 2, 4, -5225472803115863375476737218314303521556990525440000⟩, + ⟨0, 8, 4, 5, 3, 4, -2498124131072179828790889670708951579465214853120000⟩, + ⟨0, 8, 5, 5, 4, 4, 334759327311997509207019160798929125581940326400000⟩, + ⟨0, 8, 6, 5, 5, 4, 154360908831939425736240944108951502159630827520000⟩, + ⟨0, 8, 7, 5, 6, 4, 20437855264788889162728699998232299102955110400000⟩, + ⟨0, 8, 8, 5, 7, 4, -16185069891542275195175514836764396099479797760000⟩, + ⟨0, 8, 2, 6, 0, 4, -82155135257297148176904146682609908328540080701440000⟩, + ⟨0, 8, 3, 6, 1, 4, -1272203740423529771057271097812725034983431864320000⟩, + ⟨0, 8, 4, 6, 2, 4, 3164117880565954101978774297224082980262452920320000⟩, + ⟨0, 8, 5, 6, 3, 4, -3050512235947901765567709124235593377105995366400000⟩, + ⟨0, 8, 6, 6, 4, 4, -102921411512962786207179689057287681444486840320000⟩, + ⟨0, 8, 7, 6, 5, 4, 127689440550050594806061889788488175055336898560000⟩, + ⟨0, 8, 8, 6, 6, 4, 24176229831889842800239712664381011444430274560000⟩, + ⟨0, 8, 3, 7, 0, 4, 133721387091719775038931311343595951808367569141760000⟩, + ⟨0, 8, 4, 7, 1, 4, 3039506390455479873103031031440316192057427230720000⟩, + ⟨0, 8, 5, 7, 2, 4, 168997521429599721473275159674916016173036339200000⟩, + ⟨0, 8, 6, 7, 3, 4, -519566897051541050302128490692460682619062845440000⟩, + ⟨0, 8, 7, 7, 4, 4, 99289972472523030581952485702296906834850611200000⟩, + ⟨0, 8, 8, 7, 5, 4, 62449760592262595739052659274775154141010329600000⟩ +] + +def collectedFourData_9_4_5 : List CollectedFourTerm := [ + ⟨1, 3, 5, 1, 8, 0, -14345390582823954456697221185531393324378750976000000⟩, + ⟨1, 3, 5, 2, 7, 0, -7353281045937135534852048959105250035376114892800000⟩, + ⟨1, 3, 6, 2, 8, 0, 13034350721302549426533276291080851199358507417600000⟩, + ⟨1, 3, 5, 3, 6, 0, 5031225016315456429658372086839407209448944435200000⟩, + ⟨1, 3, 6, 3, 7, 0, 27636310406015818026565606375018251164634316800000⟩, + ⟨1, 3, 7, 3, 8, 0, -2211589501519977153496758692861393701242824294400000⟩, + ⟨1, 3, 5, 4, 5, 0, 3050692530622954301483365778001136214837349580800000⟩, + ⟨1, 3, 6, 4, 6, 0, 5584988988183412456190766241455534111296638156800000⟩, + ⟨1, 3, 7, 4, 7, 0, -5849837449243982558558633155784526203215203532800000⟩, + ⟨1, 3, 8, 4, 8, 0, 2088672483295984364326562047527338217647898624000000⟩, + ⟨1, 3, 5, 5, 4, 0, 2023636117531536590513503705180289115828623769600000⟩, + ⟨1, 3, 6, 5, 5, 0, 4665595321204815189935340997354290992220890726400000⟩, + ⟨1, 3, 7, 5, 6, 0, 1853217163990874544738470302198695186539741184000000⟩, + ⟨1, 3, 8, 5, 7, 0, -3424383210201047483617568517132703841776985702400000⟩, + ⟨1, 3, 5, 6, 3, 0, -18440492120724902180749466294993617523058514329600000⟩, + ⟨1, 3, 6, 6, 4, 0, -3110824234194432489738166632954430731365803622400000⟩, + ⟨1, 3, 7, 6, 5, 0, 11578331474703808669804828925484064468608063897600000⟩, + ⟨1, 3, 8, 6, 6, 0, 5115126229114870885638552391870074040724383334400000⟩, + ⟨1, 3, 5, 7, 2, 0, 1021598086255896246469288468497206508664966348800000⟩, + ⟨1, 3, 6, 7, 3, 0, -15704033503558875140455282720796993656372120780800000⟩, + ⟨1, 3, 7, 7, 4, 0, 9003189366707838035145831526253643970853732352000000⟩, + ⟨1, 3, 8, 7, 5, 0, 13212912461068223959006485991180530375934869504000000⟩ +] + +def collectedFourData_9_4_6 : List CollectedFourTerm := [ + ⟨1, 4, 4, 0, 8, 1, -4616484615000488825239969837350491039303152435200000⟩, + ⟨1, 4, 4, 1, 7, 1, 5383964688659994665332807767314845712694588211200000⟩, + ⟨1, 4, 5, 1, 8, 1, 26428167080065824136203517721680154152214200320000000⟩, + ⟨1, 4, 4, 2, 6, 1, -3549611360539195391352522047190732607856836608000000⟩, + ⟨1, 4, 5, 2, 7, 1, 13546772320119870057767403226248168193545732096000000⟩, + ⟨1, 4, 6, 2, 8, 1, -12006434981812430205707016216292714751213961216000000⟩, + ⟨1, 4, 4, 3, 5, 1, -9739050652877744657313803638922394776284377907200000⟩, + ⟨1, 4, 5, 3, 6, 1, -9268904501477632153433324268414191437678116864000000⟩, + ⟨1, 4, 6, 3, 7, 1, -25456854056007508833522946539545312926629888000000⟩, + ⟨1, 4, 7, 3, 8, 1, 1358119332739321499689736952255686939441627136000000⟩, + ⟨1, 4, 4, 4, 4, 1, 7299085253913473457928746997996823625427058688000000⟩, + ⟨1, 4, 5, 4, 5, 1, -5620217270747955079667303235966731897857376256000000⟩, + ⟨1, 4, 6, 4, 6, 1, -5144545255420402577465621791506865307976204288000000⟩, + ⟨1, 4, 7, 4, 7, 1, 3592338147626609812236056966153864175924805632000000⟩, + ⟨1, 4, 8, 4, 8, 1, -961977735032431994039887068351732597569617920000000⟩, + ⟨1, 4, 4, 5, 3, 1, 6955180820115151021190110912119457635394545254400000⟩, + ⟨1, 4, 5, 5, 4, 1, -3728096012067675395031142006801179228160131072000000⟩, + ⟨1, 4, 6, 5, 5, 1, -4297656866324982871257553057377544188224077824000000⟩, + ⟨1, 4, 7, 5, 6, 1, -1138045761408498605529538300633512175164456960000000⟩, + ⟨1, 4, 8, 5, 7, 1, 1577164649210096407750985955565057555921108992000000⟩, + ⟨1, 4, 4, 6, 2, 1, -8809414921287537916757632391871372597226006118400000⟩, + ⟨1, 4, 5, 6, 3, 1, 33972473875243789703040147524429697523774390272000000⟩, + ⟨1, 4, 6, 6, 4, 1, 2865498228972731301330186347477255860921565184000000⟩, + ⟨1, 4, 7, 6, 5, 1, -7110160274251681762692055612490170310898745344000000⟩, + ⟨1, 4, 8, 6, 6, 1, -2355868420559647922485496275142199806684823552000000⟩, + ⟨1, 4, 4, 7, 1, 1, -8462476418431653524205004302632586351567332966400000⟩, + ⟨1, 4, 5, 7, 2, 1, -1882065514798374778729737210616349027274326016000000⟩, + ⟨1, 4, 6, 7, 3, 1, 14465581082188462342221263657837947081224880128000000⟩, + ⟨1, 4, 7, 7, 4, 1, -5528786208668188545974726043273970578232442880000000⟩, + ⟨1, 4, 8, 7, 5, 1, -6085457487534203607670440985678335762046648320000000⟩ +] + +def collectedFourData_9_4_7 : List CollectedFourTerm := [ + ⟨1, 5, 3, 0, 7, 2, 1140977325389848929020535427699716047102552309760000⟩, + ⟨1, 5, 4, 0, 8, 2, -4403627406343894208256468083783164703927760322560000⟩, + ⟨1, 5, 3, 1, 6, 2, -5410178515359761515146648932391794701819938078720000⟩, + ⟨1, 5, 4, 1, 7, 2, 5135720452903191084971925666107770194418320015360000⟩, + ⟨1, 5, 5, 1, 8, 2, 12604807614332429649786375234673224965997723648000000⟩, + ⟨1, 5, 3, 2, 5, 2, -2302297679463474049410344441218959784044260229120000⟩, + ⟨1, 5, 4, 2, 6, 2, -3385945621555674439373967413832061735752066662400000⟩, + ⟨1, 5, 5, 2, 7, 2, 6461078377965568597115800638756025892512097894400000⟩, + ⟨1, 5, 6, 2, 8, 2, -3817613801245869578145755620885785840474233241600000⟩, + ⟨1, 5, 3, 3, 4, 2, 250855341240146632693707655989573113873474519040000⟩, + ⟨1, 5, 4, 3, 5, 2, -9290001796481518452217497388254642200549429084160000⟩, + ⟨1, 5, 5, 3, 6, 2, -4420766589025756891557276937612627143483300249600000⟩, + ⟨1, 5, 6, 3, 7, 2, -8094362525406829089675791820146050532691148800000⟩, + ⟨1, 5, 7, 3, 8, 2, 323874766922391514884659362587495755504890675200000⟩, + ⟨1, 5, 3, 4, 3, 2, 3704624304410556049576236697052332655585966161920000⟩, + ⟨1, 5, 4, 4, 4, 2, 6962538499734727297867691795611963830259050086400000⟩, + ⟨1, 5, 5, 4, 5, 2, -2680539941869854649637165453275197389970761318400000⟩, + ⟨1, 5, 6, 4, 6, 2, -1635780062772817257429392188780617964064656588800000⟩, + ⟨1, 5, 7, 4, 7, 2, 856675589708508215644509002974727866702784102400000⟩, + ⟨1, 5, 8, 4, 8, 2, -183524559120879636773200461738621466968273715200000⟩, + ⟨1, 5, 3, 5, 2, 2, 4625917903488053912358913432503993750552607457280000⟩, + ⟨1, 5, 4, 5, 3, 2, 6634490836602352330720472149451962205241417400320000⟩, + ⟨1, 5, 5, 5, 4, 2, -1778100344889902157942051320301065490777558220800000⟩, + ⟨1, 5, 6, 5, 5, 2, -1366500063570464098729855228744794618863183462400000⟩, + ⟨1, 5, 7, 5, 6, 2, -271393166151136318223362204289494996507164672000000⟩, + ⟨1, 5, 8, 5, 7, 2, 300888925352894268051140875620469309879898603520000⟩, + ⟨1, 5, 3, 6, 1, 2, 1126234942070788498801129384577846127099736227840000⟩, + ⟨1, 5, 4, 6, 2, 2, -8403229776870497343841954992228725879960261099520000⟩, + ⟨1, 5, 5, 6, 3, 2, 16203034288495042820499043092301303517010513100800000⟩, + ⟨1, 5, 6, 6, 4, 2, 911125209351739233651146911526419815326967398400000⟩, + ⟨1, 5, 7, 6, 5, 2, -1695581121696698729195087529173845898534112460800000⟩, + ⟨1, 5, 8, 6, 6, 2, -449448773588752464406939338545196681598724997120000⟩, + ⟨1, 5, 3, 7, 0, 2, -118378600737906684744100575588463275784384146309120000⟩, + ⟨1, 5, 4, 7, 1, 2, -8072287939757512586620408117901407421852465233920000⟩, + ⟨1, 5, 5, 7, 2, 2, -897643550524425996416307866271290233457108582400000⟩, + ⟨1, 5, 6, 7, 3, 2, 4599533672239776013779712027142800645777312972800000⟩, + ⟨1, 5, 7, 7, 4, 2, -1318466132931367377641717328152494014166204416000000⟩, + ⟨1, 5, 8, 7, 5, 2, -1160973754149224577771315405789698000105452339200000⟩ +] + +def collectedFourData_9_4_8 : List CollectedFourTerm := [ + ⟨1, 6, 2, 0, 6, 3, 11079901744688731062269071949637899971455583518720000⟩, + ⟨1, 6, 3, 0, 7, 3, -3166909914064954193519042876637529341790015979520000⟩, + ⟨1, 6, 4, 0, 8, 3, 6111379683305095252214285185141281548350846402560000⟩, + ⟨1, 6, 2, 1, 5, 3, -5410178515359761515146648932391794701819938078720000⟩, + ⟨1, 6, 3, 1, 6, 3, 15016554313469688089172122820724646802913430077440000⟩, + ⟨1, 6, 4, 1, 7, 3, -7127382664071815587034445373856874039642276495360000⟩, + ⟨1, 6, 5, 1, 8, 3, -11662016796308527512553488065382648805098258432000000⟩, + ⟨1, 6, 2, 2, 4, 3, -19931786598267863008186155864019155235658017013760000⟩, + ⟨1, 6, 3, 2, 5, 3, 6390284174780045357426172157729588892789888778240000⟩, + ⟨1, 6, 4, 2, 6, 3, 4699034993410434923820742422740875985323189862400000⟩, + ⟨1, 6, 5, 2, 7, 3, -5977814725265914310369218277505194176974264729600000⟩, + ⟨1, 6, 6, 2, 8, 3, 2649053299789681967790769370352833546326691020800000⟩, + ⟨1, 6, 2, 3, 3, 3, 22704247373070531844641343746385596011623376486400000⟩, + ⟨1, 6, 3, 3, 4, 3, -696276998228798885385813284638576536916674478080000⟩, + ⟨1, 6, 4, 3, 5, 3, 12892718433692856574299359548905361660751023964160000⟩, + ⟨1, 6, 5, 3, 6, 3, 4090110360364145127091340094430755179448395366400000⟩, + ⟨1, 6, 6, 3, 7, 3, 5616701655527656129613514400886826513884774400000⟩, + ⟨1, 6, 7, 3, 8, 3, -179790112819558980579808928033315332317857710080000⟩, + ⟨1, 6, 2, 4, 2, 3, -5413500439442408518793495740655038798658902425600000⟩, + ⟨1, 6, 3, 4, 3, 3, -10282598239640840235249432232426029432979681443840000⟩, + ⟨1, 6, 4, 4, 4, 3, -9662651356517927188923103542258360767643805286400000⟩, + ⟨1, 6, 5, 4, 5, 3, 2480045930230386465196555122070268280649128345600000⟩, + ⟨1, 6, 6, 4, 6, 3, 1135072534472804012410145893771777674328827494400000⟩, + ⟨1, 6, 7, 4, 7, 3, -475559743005117727091181418398037604763130920960000⟩, + ⟨1, 6, 8, 4, 8, 3, 84898816248857422924396908197980419557582438400000⟩, + ⟨1, 6, 2, 5, 1, 3, 5606773850945889304628399569739876266627584491520000⟩, + ⟨1, 6, 3, 5, 2, 3, -12839751451854069518802334117007463950206956994560000⟩, + ⟨1, 6, 4, 5, 3, 3, -9207384904879728168605911122966365198526783160320000⟩, + ⟨1, 6, 5, 5, 4, 3, 1645105321881285067837413035218176950410621747200000⟩, + ⟨1, 6, 6, 5, 5, 3, 948218361266085031740843762340410853468353331200000⟩, + ⟨1, 6, 7, 5, 6, 3, 150656404709856046026128109329419263602904268800000⟩, + ⟨1, 6, 8, 5, 7, 3, -139191799218687096527379988583154515716173987840000⟩, + ⟨1, 6, 2, 6, 0, 3, -100933595575137040792118058301679997215921437409280000⟩, + ⟨1, 6, 3, 6, 1, 3, -3125990783727174691978689903183419059459514695680000⟩, + ⟨1, 6, 4, 6, 2, 3, 11662051076012459187610544261975490506601812459520000⟩, + ⟨1, 6, 5, 6, 3, 3, -14991110043499049579272531693383415313651151667200000⟩, + ⟨1, 6, 6, 6, 4, 3, -632232427902243665473790332404780864539669299200000⟩, + ⟨1, 6, 7, 6, 5, 3, 941254930297219478626658668434422572987522744320000⟩, + ⟨1, 6, 8, 6, 6, 3, 207915872540268703356525980584058909833077719040000⟩, + ⟨1, 6, 3, 7, 0, 3, 328573018891431293381697593372362433751448540938240000⟩, + ⟨1, 6, 4, 7, 1, 3, 11202768072919528023461004603442808220475635793920000⟩, + ⟨1, 6, 5, 7, 2, 3, 830503287603592486947139934791796084495194521600000⟩, + ⟨1, 6, 6, 7, 3, 3, -3191629768302958705908225355663120836388611686400000⟩, + ⟨1, 6, 7, 7, 4, 3, 731909981876731427823256432363103720661476966400000⟩, + ⟨1, 6, 8, 7, 5, 3, 537068705656666476170593721246081613579052646400000⟩ +] + +def collectedFourData_9_4_9 : List CollectedFourTerm := [ + ⟨1, 7, 1, 0, 5, 4, 12325492291100151680637946161029617335830650552320000⟩, + ⟨1, 7, 2, 0, 6, 4, -10517818930522251074761054121710008008728494735360000⟩, + ⟨1, 7, 3, 0, 7, 4, 1503126373001366523908118308557682196460999802880000⟩, + ⟨1, 7, 4, 0, 8, 4, -1933783241218360051530078482553724638653589749760000⟩, + ⟨1, 7, 1, 1, 4, 4, 5383964688659994665332807767314845712694588211200000⟩, + ⟨1, 7, 2, 1, 5, 4, 5135720452903191084971925666107770194418320015360000⟩, + ⟨1, 7, 3, 1, 6, 4, -7127382664071815587034445373856874039642276495360000⟩, + ⟨1, 7, 4, 1, 7, 4, 2255270309449741511761042253087432823041226178560000⟩, + ⟨1, 7, 5, 1, 8, 4, 2767600829291653575906820401370807331092168704000000⟩, + ⟨1, 7, 1, 2, 3, 4, 8132143872919528518849327220740997773890986967040000⟩, + ⟨1, 7, 2, 2, 4, 4, 18920648145899315624351251392271809271739323514880000⟩, + ⟨1, 7, 3, 2, 5, 4, -3033052702707270831065039789059538688083031490560000⟩, + ⟨1, 7, 4, 2, 6, 4, -1486884401075442826835213235844466506748814950400000⟩, + ⟨1, 7, 5, 2, 7, 4, 1418640127172057729379736003685444524935689011200000⟩, + ⟨1, 7, 6, 2, 8, 4, -502933393932783303193781559001029087324096430080000⟩, + ⟨1, 7, 1, 3, 2, 4, -20954998472429731191810544159384002588042948771840000⟩, + ⟨1, 7, 2, 3, 3, 4, -21552462136066527153805816144595287139075437363200000⟩, + ⟨1, 7, 3, 3, 4, 4, 330477451948911823556722402872152556639375851520000⟩, + ⟨1, 7, 4, 3, 5, 4, -4079557175760178819981129456292877119039849103360000⟩, + ⟨1, 7, 5, 3, 6, 4, -970654820941549121622007004003780194038762700800000⟩, + ⟨1, 7, 6, 3, 7, 4, -1066353337075807482391679818833201760504381440000⟩, + ⟨1, 7, 7, 3, 8, 4, 28444895025667527905746278438877170176454819840000⟩, + ⟨1, 7, 1, 4, 1, 4, 9434114922943377445500334257383918876966906757120000⟩, + ⟨1, 7, 2, 4, 2, 4, 5138873855957416813063519652321529320893631692800000⟩, + ⟨1, 7, 3, 4, 3, 4, 4880481294506618761794541673663178468716665896960000⟩, + ⟨1, 7, 4, 4, 4, 4, 3057488525874885579283046251621056386982897254400000⟩, + ⟨1, 7, 5, 4, 5, 4, -588558333697448875406757299623266133709370163200000⟩, + ⟨1, 7, 6, 4, 6, 4, -215498073280600517540656837612221533630433853440000⟩, + ⟨1, 7, 7, 4, 7, 4, 75239103842101827822485251366888393934981038080000⟩, + ⟨1, 7, 8, 4, 8, 4, -11513129129754602324981290816393242146871705600000⟩, + ⟨1, 7, 1, 5, 0, 4, 49723553432449632416257194354589011711349783265280000⟩, + ⟨1, 7, 2, 5, 1, 4, -5322342517784890023431777130469383822240393461760000⟩, + ⟨1, 7, 3, 5, 2, 4, 6094195778777872080785304908284042742527049072640000⟩, + ⟨1, 7, 4, 5, 3, 4, 2913431589456434096303595827885207040824149278720000⟩, + ⟨1, 7, 5, 5, 4, 4, -390412304546839061679057801546515982716397158400000⟩, + ⟨1, 7, 6, 5, 5, 4, -180023059052377795321404352646060429458664325120000⟩, + ⟨1, 7, 7, 5, 6, 4, -23835602245921379081319482439226063881397862400000⟩, + ⟨1, 7, 8, 5, 7, 4, 18875800971243664012193493684065020899030466560000⟩, + ⟨1, 7, 2, 6, 0, 4, 95813239749598246018882054745784234718307958128640000⟩, + ⟨1, 7, 3, 6, 1, 4, 1483704720463088743829599233323176740710692945920000⟩, + ⟨1, 7, 4, 6, 2, 4, -3690145285954341997863502344147251680319027281920000⟩, + ⟨1, 7, 5, 6, 3, 4, 3557652961151915383390702854123265296819447398400000⟩, + ⟨1, 7, 6, 6, 4, 4, 120031862229606326358518265440261904885790801920000⟩, + ⟨1, 7, 7, 6, 5, 4, -148917519794691063643726269793283726701347471360000⟩, + ⟨1, 7, 8, 6, 6, 4, -28195473087222557547800017189297664415875727360000⟩, + ⟨1, 7, 3, 7, 0, 4, -155952263737886940779852014532261240546240558530560000⟩, + ⟨1, 7, 4, 7, 1, 4, -3544817418863415638091888206641693741338140344320000⟩, + ⟨1, 7, 5, 7, 2, 4, -197092975224380618230185750414476246300963635200000⟩, + ⟨1, 7, 6, 7, 3, 4, 605943712675373772596417933383412896345242992640000⟩, + ⟨1, 7, 7, 7, 4, 4, -115796704703202026098579026093058240311145267200000⟩, + ⟨1, 7, 8, 7, 5, 4, -72831891338162011454623306440537650608314777600000⟩ +] + +def collectedFourData_9_4_10 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 4, 5, -18251999086355370931237084206484977768443412480000000⟩, + ⟨1, 8, 1, 0, 5, 5, 60501914193336028043162039805250183442152292352000000⟩, + ⟨1, 8, 2, 0, 6, 5, -25814310836695319956788110164186675846104219648000000⟩, + ⟨1, 8, 3, 0, 7, 5, 2459456133494844705544754773614197253347475456000000⟩, + ⟨1, 8, 4, 0, 8, 5, -2373081434913246939702072321220092173991542784000000⟩, + ⟨1, 8, 0, 1, 3, 5, -14345390582823954456697221185531393324378750976000000⟩, + ⟨1, 8, 1, 1, 4, 5, 26428167080065824136203517721680154152214200320000000⟩, + ⟨1, 8, 2, 1, 5, 5, 12604807614332429649786375234673224965997723648000000⟩, + ⟨1, 8, 3, 1, 6, 5, -11662016796308527512553488065382648805098258432000000⟩, + ⟨1, 8, 4, 1, 7, 5, 2767600829291653575906820401370807331092168704000000⟩, + ⟨1, 8, 5, 1, 8, 5, 2717054117442694028784669599575149621679226880000000⟩, + ⟨1, 8, 0, 2, 2, 5, -11966901740829127897567136507081724521625944064000000⟩, + ⟨1, 8, 1, 2, 3, 5, 39918103000438019107304733177328474253734969344000000⟩, + ⟨1, 8, 2, 2, 4, 5, 46437716383631997860138436587730153213247094784000000⟩, + ⟨1, 8, 3, 2, 5, 5, -4962763082914606865410039193904662991624732672000000⟩, + ⟨1, 8, 4, 2, 6, 5, -1824660433933196284373771886823026944492175360000000⟩, + ⟨1, 8, 5, 2, 7, 5, 1392730468175499926094476953191323865987416064000000⟩, + ⟨1, 8, 6, 2, 8, 5, -411456628885267480230747668785019425860354048000000⟩, + ⟨1, 8, 0, 3, 1, 5, -38360375014728808955137428362471321715848773632000000⟩, + ⟨1, 8, 1, 3, 2, 5, -102861410283456352437830086768323681452896026624000000⟩, + ⟨1, 8, 2, 3, 3, 5, -52897084514546035841012229372058642711062773760000000⟩, + ⟨1, 8, 3, 3, 4, 5, 540736168812307889443816302882855614177869824000000⟩, + ⟨1, 8, 4, 3, 5, 5, -5006311560733202077606861102221852997293441024000000⟩, + ⟨1, 8, 5, 3, 6, 5, -952927044226186120453644486008330840835096576000000⟩, + ⟨1, 8, 6, 3, 7, 5, -872398123820759412555478386639475115556864000000⟩, + ⟨1, 8, 7, 3, 8, 5, 19946703691549749058307187040467698300485632000000⟩, + ⟨1, 8, 0, 4, 0, 5, -122501078611279772395860536230777319036792340480000000⟩, + ⟨1, 8, 1, 4, 1, 5, 46309064017681046456114668965234218416453189632000000⟩, + ⟨1, 8, 2, 4, 2, 5, 12612547139720049662454571924296557143303127040000000⟩, + ⟨1, 8, 3, 4, 3, 5, 7985575843642157006831277206492806184385380352000000⟩, + ⟨1, 8, 4, 4, 4, 5, 3752059229576631628170218409605269675793448960000000⟩, + ⟨1, 8, 5, 4, 5, 5, -577809063721502621220134591756813392888725504000000⟩, + ⟨1, 8, 6, 4, 6, 5, -176301895704218547396643440848716422199640064000000⟩, + ⟨1, 8, 7, 4, 7, 5, 52760683736111914443234148468039671909187584000000⟩, + ⟨1, 8, 8, 4, 8, 5, -7064285286277966636732230652608720163307520000000⟩, + ⟨1, 8, 1, 5, 0, 5, 244077079609231979915055779610277066652944171008000000⟩, + ⟨1, 8, 2, 5, 1, 5, -13062841739436244229065349884257822364472967168000000⟩, + ⟨1, 8, 3, 5, 2, 5, 9971488396484946094525741017462990446335623168000000⟩, + ⟨1, 8, 4, 5, 3, 5, 3575276830133703054479399651081480333162446848000000⟩, + ⟨1, 8, 5, 5, 4, 5, -383281919972822260387443726388566256200450048000000⟩, + ⟨1, 8, 6, 5, 5, 5, -147279305555925028400742478813811700318339072000000⟩, + ⟨1, 8, 7, 5, 6, 5, -16714482330836939986918046391976485999083520000000⟩, + ⟨1, 8, 8, 5, 7, 5, 11581911534654188480950904091388438697213952000000⟩, + ⟨1, 8, 2, 6, 0, 5, 235158331732578048392765494566125698209181335552000000⟩, + ⟨1, 8, 3, 6, 1, 5, 2427677898932640280909895064137752616688943104000000⟩, + ⟨1, 8, 4, 6, 2, 5, -4528436840063634699026319374500455296142409728000000⟩, + ⟨1, 8, 5, 6, 3, 5, 3492676951178696425722452218427910233782222848000000⟩, + ⟨1, 8, 6, 6, 4, 5, 98199694010406761920271747267022455310385152000000⟩, + ⟨1, 8, 7, 6, 5, 5, -104426950394607376975518341725039557636784128000000⟩, + ⟨1, 8, 8, 6, 6, 5, -17300324127777603414699821350883427260301312000000⟩, + ⟨1, 8, 3, 7, 0, 5, -255173323063105481513195238184716060451953180672000000⟩, + ⟨1, 8, 4, 7, 1, 5, -4350094792197022545804485323780550081944485888000000⟩, + ⟨1, 8, 5, 7, 2, 5, -193493322514104949113396577811655589147705344000000⟩, + ⟨1, 8, 6, 7, 3, 5, 495730767372654915577061433283207580388163584000000⟩, + ⟨1, 8, 7, 7, 4, 5, -81201303611365741249428380709300220786114560000000⟩, + ⟨1, 8, 8, 7, 5, 5, -44688568377321765908560119410787274897489920000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0916.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0916.lean new file mode 100644 index 0000000000000000000000000000000000000000..d9679c486f034a2625dbbddb67a2ca710edf7846 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0916.lean @@ -0,0 +1,647 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0916. -/ +namespace LaughlinFock +def collectedFourData_9_4_11 : List CollectedFourTerm := [ + ⟨2, 2, 5, 1, 8, 0, -11966901740829127897567136507081724521625944064000000⟩, + ⟨2, 2, 5, 2, 7, 0, -6134095216256463342158955884402938020342477619200000⟩, + ⟨2, 2, 6, 2, 8, 0, 10873234397960000254778052118801630273477174886400000⟩, + ⟨2, 2, 5, 3, 6, 0, 4197039812797919906663943908442740833557204172800000⟩, + ⟨2, 2, 6, 3, 7, 0, 23054165670736371212959468688531252382479155200000⟩, + ⟨2, 2, 7, 3, 8, 0, -1844904403469292767367786871841646454150633881600000⟩, + ⟨2, 2, 5, 4, 5, 0, 2544882800134927819663995429199742038873158451200000⟩, + ⟨2, 2, 6, 4, 6, 0, 4658988827061048614331522003208199461745668915200000⟩, + ⟨2, 2, 7, 4, 7, 0, -4879924987106524225028003675579781667030774579200000⟩, + ⟨2, 2, 8, 4, 8, 0, 1742367224654279657820807651704126789790990336000000⟩, + ⟨2, 2, 5, 5, 4, 0, 1688113992984475843777138100720234183927424614400000⟩, + ⟨2, 2, 6, 5, 5, 0, 3892032109476325991482409827541368879615416729600000⟩, + ⟨2, 2, 7, 5, 6, 0, 1545950776164305831001213037693833367756210176000000⟩, + ⟨2, 2, 8, 5, 7, 0, -2856614963728230672906194967394860014421776793600000⟩, + ⟨2, 2, 5, 6, 3, 0, -15383028854262654418420414741080052187764516454400000⟩, + ⟨2, 2, 6, 6, 4, 0, -2595044570495514883121431907350049618189195673600000⟩, + ⟨2, 2, 7, 6, 5, 0, 9658625485347654654332471608292173333372757606400000⟩, + ⟨2, 2, 8, 6, 6, 0, 4267030069508611618137619522930793093237676441600000⟩, + ⟨2, 2, 5, 7, 2, 0, 852215479687327735946480526252267099089220403200000⟩, + ⟨2, 2, 6, 7, 3, 0, -13100279479095441873560753598913381165916435251200000⟩, + ⟨2, 2, 7, 7, 4, 0, 7510446082553519629496968610320658313907273728000000⟩, + ⟨2, 2, 8, 7, 5, 0, 11022190313946407893739943028500236137352134656000000⟩ +] + +def collectedFourData_9_4_12 : List CollectedFourTerm := [ + ⟨2, 3, 4, 0, 8, 1, -6972912945617263006752531925819504491841286307840000⟩, + ⟨2, 3, 4, 1, 7, 1, 8132143872919528518849327220740997773890986967040000⟩, + ⟨2, 3, 5, 1, 8, 1, 39918103000438019107304733177328474253734969344000000⟩, + ⟨2, 3, 4, 2, 6, 1, -5361467235781363193159388487858261820528236953600000⟩, + ⟨2, 3, 5, 2, 7, 1, 20461557215063619391270857221223547483731473203200000⟩, + ⟨2, 3, 6, 2, 8, 1, -18134973447839162238340590956529740969952883507200000⟩, + ⟨2, 3, 4, 3, 5, 1, -14710230410995595223138823253983271785366542090240000⟩, + ⟨2, 3, 5, 3, 6, 1, -14000103884248872586867008024892347388493876428800000⟩, + ⟨2, 3, 6, 3, 7, 1, -38450995076435512354166108040973185879480729600000⟩, + ⟨2, 3, 7, 3, 8, 1, 2051354800615985864074220867114162439146648371200000⟩, + ⟨2, 3, 4, 4, 4, 1, 11024814399424124819169260891664125550520801689600000⟩, + ⟨2, 3, 5, 4, 5, 1, -8488988707346962183365375832896549654715642675200000⟩, + ⟨2, 3, 6, 4, 6, 1, -7770515706750816410562569948386078900501453209600000⟩, + ⟨2, 3, 7, 4, 7, 1, 5426003390811186243944853408440977771697956454400000⟩, + ⟨2, 3, 8, 4, 8, 1, -1453007550422110103460939996959963531930763264000000⟩, + ⟨2, 3, 4, 5, 3, 1, 10505368137067796441192675574164537783995575828480000⟩, + ⟨2, 3, 5, 5, 4, 1, -5631057203262884290810744265447080325254899302400000⟩, + ⟨2, 3, 6, 5, 5, 1, -6491343456803704544929038940718006875036896460800000⟩, + ⟨2, 3, 7, 5, 6, 1, -1718947355883115976368658498494243367899103232000000⟩, + ⟨2, 3, 8, 5, 7, 1, 2382209130322386263572609461208367610133374566400000⟩, + ⟨2, 3, 4, 6, 2, 1, -13306073445660827964101654635097082727111097057280000⟩, + ⟨2, 3, 5, 6, 3, 1, 51313309289411896888020741097679162024250467942400000⟩, + ⟨2, 3, 6, 6, 4, 1, 4328156890531559257320534625642804617530887372800000⟩, + ⟨2, 3, 7, 6, 5, 1, -10739454965504719036916403676321345651484708044800000⟩, + ⟨2, 3, 8, 6, 6, 1, -3558392755065972235659028222621736663188399718400000⟩, + ⟨2, 3, 4, 7, 1, 1, -12782044410659568267481623458238724665636689018880000⟩, + ⟨2, 3, 5, 7, 2, 1, -2842742928243467431904724492939892054480335667200000⟩, + ⟨2, 3, 6, 7, 3, 1, 21849360716185864631098437492615237114598627737600000⟩, + ⟨2, 3, 7, 7, 4, 1, -8350887773503067592495920947358032030750212096000000⟩, + ⟨2, 3, 8, 7, 5, 1, -9191705124923558120630185960246867925290450944000000⟩ +] + +def collectedFourData_9_4_13 : List CollectedFourTerm := [ + ⟨2, 4, 3, 0, 7, 2, 4203505762068304325713717840459601679078213550080000⟩, + ⟨2, 4, 4, 0, 8, 2, -16223524135542078322572600067186622484758113812480000⟩, + ⟨2, 4, 3, 1, 6, 2, -19931786598267863008186155864019155235658017013760000⟩, + ⟨2, 4, 4, 1, 7, 2, 18920648145899315624351251392271809271739323514880000⟩, + ⟨2, 4, 5, 1, 8, 2, 46437716383631997860138436587730153213247094784000000⟩, + ⟨2, 4, 3, 2, 5, 2, -8481957832347384246995351559321796066583469096960000⟩, + ⟨2, 4, 4, 2, 6, 2, -12474254845858701662016839992426767117649654579200000⟩, + ⟨2, 4, 5, 2, 7, 2, 23803435516716738603347396618540960650882134835200000⟩, + ⟨2, 4, 6, 2, 8, 2, -14064575389704116542509682087427534902465973452800000⟩, + ⟨2, 4, 3, 3, 4, 2, 924183021768881638320402062599018668303392440320000⟩, + ⟨2, 4, 4, 3, 5, 2, -34225549633768723299676051099078024779948915425280000⟩, + ⟨2, 4, 5, 3, 6, 2, -16286667067094845927505534761778036563568807116800000⟩, + ⟨2, 4, 6, 3, 7, 2, -29820662302988189695600397732381086051624550400000⟩, + ⟨2, 4, 7, 3, 8, 2, 1193195884485816271177334657596461129265682841600000⟩, + ⟨2, 4, 3, 4, 3, 2, 13648307694955531298864275160816979535941976719360000⟩, + ⟨2, 4, 4, 4, 4, 2, 25650878462687561006921018404557165849981694771200000⟩, + ⟨2, 4, 5, 4, 5, 2, -9875450493509358521774728134632985305323615027200000⟩, + ⟨2, 4, 6, 4, 6, 2, -6026422056189938488347914542475325684989716070400000⟩, + ⟨2, 4, 7, 4, 7, 2, 3156101964018061325490779356074392767912162099200000⟩, + ⟨2, 4, 8, 4, 8, 2, -676127846346179589649824992211303383109835161600000⟩, + ⟨2, 4, 3, 5, 2, 2, 17042470634131993637464985942753623087635486474240000⟩, + ⟨2, 4, 4, 5, 3, 2, 24442309097175568255629280146027529583832135106560000⟩, + ⟨2, 4, 5, 5, 4, 2, -6550748098983072070220871078050273155504039526400000⟩, + ⟨2, 4, 6, 5, 5, 2, -5034360248239385516601160439237782245043548979200000⟩, + ⟨2, 4, 7, 5, 6, 2, -999846984086623218201159779498056835741515776000000⟩, + ⟨2, 4, 8, 5, 7, 2, 1108513117060655261312389299682719148015783772160000⟩, + ⟨2, 4, 3, 6, 1, 2, 4149192944583420147426542936913183374360413470720000⟩, + ⟨2, 4, 4, 6, 2, 2, -30958568589423915192859968937611675659474734940160000⟩, + ⟨2, 4, 5, 6, 3, 2, 59694041659774055480047530807381673847225214566400000⟩, + ⟨2, 4, 6, 6, 4, 2, 3356701296554793094539255737391210575615439667200000⟩, + ⟨2, 4, 7, 6, 5, 2, -6246736772504246049873124364726207710302201446400000⟩, + ⟨2, 4, 8, 6, 6, 2, -1655826515999633475663370448254167198318156840960000⟩, + ⟨2, 4, 3, 7, 0, 2, -436121839789719168589080287541079190625640733736960000⟩, + ⟨2, 4, 4, 7, 1, 2, -29739336718414922624236534188385443088677847695360000⟩, + ⟨2, 4, 5, 7, 2, 2, -3307033148641786026637269561392503775873413939200000⟩, + ⟨2, 4, 6, 7, 3, 2, 16945267766369495094836298417392981204913251942400000⟩, + ⟨2, 4, 7, 7, 4, 2, -4857397130986162755951054408392039866489110528000000⟩, + ⟨2, 4, 8, 7, 5, 2, -4277175152020557724662729476434005705184876953600000⟩ +] + +def collectedFourData_9_4_14 : List CollectedFourTerm := [ + ⟨2, 5, 2, 0, 6, 3, 4715044430245361599235154997631998184144366469120000⟩, + ⟨2, 5, 3, 0, 7, 3, -1347676296728772911947304076770100676942280785920000⟩, + ⟨2, 5, 4, 0, 8, 3, 2600693345561059062192799979478696816499501301760000⟩, + ⟨2, 5, 2, 1, 5, 3, -2302297679463474049410344441218959784044260229120000⟩, + ⟨2, 5, 3, 1, 6, 3, 6390284174780045357426172157729588892789888778240000⟩, + ⟨2, 5, 4, 1, 7, 3, -3033052702707270831065039789059538688083031490560000⟩, + ⟨2, 5, 5, 1, 8, 3, -4962763082914606865410039193904662991624732672000000⟩, + ⟨2, 5, 2, 2, 4, 3, -8481957832347384246995351559321796066583469096960000⟩, + ⟨2, 5, 3, 2, 5, 3, 2719380956642967821194405215708169101290546135040000⟩, + ⟨2, 5, 4, 2, 6, 3, 1999671051580282413083825461101034705623869030400000⟩, + ⟨2, 5, 5, 2, 7, 3, -2543854871178334508089963601650761368633711001600000⟩, + ⟨2, 5, 6, 2, 8, 3, 1127302777083185264809645262592261345526992076800000⟩, + ⟨2, 5, 2, 3, 3, 3, 9661776574022904798501949220499132833967007334400000⟩, + ⟨2, 5, 3, 3, 4, 3, -296300189122199362341204469333274669191192903680000⟩, + ⟨2, 5, 4, 3, 5, 3, 5486487303070662636956402702557291164114207375360000⟩, + ⟨2, 5, 5, 3, 6, 3, 1740543600304786676590887398831699095017907814400000⟩, + ⟨2, 5, 6, 3, 7, 3, 2390183457171945030746526351991303257351782400000⟩, + ⟨2, 5, 7, 3, 8, 3, -76509556636583856680031951270572125501186375680000⟩, + ⟨2, 5, 2, 4, 2, 3, -2303711321931115147593742162932589074576939417600000⟩, + ⟨2, 5, 3, 4, 3, 3, -4375752481876484323183928783991252613547572592640000⟩, + ⟨2, 5, 4, 4, 4, 3, -4111934519797725685243519035391483513043052134400000⟩, + ⟨2, 5, 5, 4, 5, 3, 1055381809291844756315498242549190523426019737600000⟩, + ⟨2, 5, 6, 4, 6, 3, 483029322363438772675435368751887943542924902400000⟩, + ⟨2, 5, 7, 4, 7, 3, -202374115689253224122878703479044064082562908160000⟩, + ⟨2, 5, 8, 4, 8, 3, 36128631815754907310216857299409410506253926400000⟩, + ⟨2, 5, 2, 5, 1, 3, 2385958686882780423224639669601027042546989137920000⟩, + ⟨2, 5, 3, 5, 2, 3, -5463947241032152551909155643443416500893657333760000⟩, + ⟨2, 5, 4, 5, 3, 3, -3918196200042024251302849205953869761634600222720000⟩, + ⟨2, 5, 5, 5, 4, 3, 700073417963443055981645253407744963548230451200000⟩, + ⟨2, 5, 6, 5, 5, 3, 403513659774754583674192151494500551832580915200000⟩, + ⟨2, 5, 7, 5, 6, 3, 64111727547449817357720384288215968277908684800000⟩, + ⟨2, 5, 8, 5, 7, 3, -59232972707226714973385762150417697371471216640000⟩, + ⟨2, 5, 2, 6, 0, 3, -42952220931861473946949127988883803683184055418880000⟩, + ⟨2, 5, 3, 6, 1, 3, -1330263189461633387329918197801040927184419553280000⟩, + ⟨2, 5, 4, 6, 2, 3, 4962777670618615250116202611103190910345590865920000⟩, + ⟨2, 5, 5, 6, 3, 3, -6379456383507958695839610540741126103216894771200000⟩, + ⟨2, 5, 6, 6, 4, 3, -269046067058306916645615162225795777380430643200000⟩, + ⟨2, 5, 7, 6, 5, 3, 400550376601157274288103041759079932428518686720000⟩, + ⟨2, 5, 8, 6, 6, 3, 88478453994461759177296206782086621695930531840000⟩, + ⟨2, 5, 3, 7, 0, 3, 139824018150304451961248754608484955878616769495040000⟩, + ⟨2, 5, 4, 7, 1, 3, 4767330110203401024355967406190007713597300408320000⟩, + ⟨2, 5, 5, 7, 2, 3, 353420092591785805152935729853865957380430233600000⟩, + ⟨2, 5, 6, 7, 3, 3, -1358195813393011595789684839851233393041106534400000⟩, + ⟨2, 5, 7, 7, 4, 3, 311463780366385827464731222735502141485901414400000⟩, + ⟨2, 5, 8, 7, 5, 3, 228549211682263980915341537422970580069934694400000⟩ +] + +def collectedFourData_9_4_15 : List CollectedFourTerm := [ + ⟨2, 6, 1, 0, 5, 4, -8126113373826084512055957517874752192101797068800000⟩, + ⟨2, 6, 2, 0, 6, 4, 6934326601827700188898471083683873608310351462400000⟩, + ⟨2, 6, 3, 0, 7, 4, -991001011052261073280060491069668284284744499200000⟩, + ⟨2, 6, 4, 0, 8, 4, 1274930159981679097290770119695377220950713958400000⟩, + ⟨2, 6, 1, 1, 4, 4, -3549611360539195391352522047190732607856836608000000⟩, + ⟨2, 6, 2, 1, 5, 4, -3385945621555674439373967413832061735752066662400000⟩, + ⟨2, 6, 3, 1, 6, 4, 4699034993410434923820742422740875985323189862400000⟩, + ⟨2, 6, 4, 1, 7, 4, -1486884401075442826835213235844466506748814950400000⟩, + ⟨2, 6, 5, 1, 8, 4, -1824660433933196284373771886823026944492175360000000⟩, + ⟨2, 6, 1, 2, 3, 4, -5361467235781363193159388487858261820528236953600000⟩, + ⟨2, 6, 2, 2, 4, 4, -12474254845858701662016839992426767117649654579200000⟩, + ⟨2, 6, 3, 2, 5, 4, 1999671051580282413083825461101034705623869030400000⟩, + ⟨2, 6, 4, 2, 6, 4, 980292789249237602044596521194867259904884736000000⟩, + ⟨2, 6, 5, 2, 7, 4, -935299802863308105144919158726861830234308608000000⟩, + ⟨2, 6, 6, 2, 8, 4, 331580571555097214494665910943118193388106547200000⟩, + ⟨2, 6, 1, 3, 2, 4, 13815488202306707017882196035274088768618469785600000⟩, + ⟨2, 6, 2, 3, 3, 4, 14209391938789490790163282385966811878982156288000000⟩, + ⟨2, 6, 3, 3, 4, 4, -217881540031397548697447228266205185873595596800000⟩, + ⟨2, 6, 4, 3, 5, 4, 2689624344592727403821516619617736803748308582400000⟩, + ⟨2, 6, 5, 3, 6, 4, 639946132416739994535766071533866004326121472000000⟩, + ⟨2, 6, 6, 3, 7, 4, 703039514283152723499087596535199961815449600000⟩, + ⟨2, 6, 7, 3, 8, 4, -18753526141268978124710042403497073794718105600000⟩, + ⟨2, 6, 1, 4, 1, 4, -6219847908298001464640881435558025580029725900800000⟩, + ⟨2, 6, 2, 4, 2, 4, -3388024638776796767165325476134177313497546752000000⟩, + ⟨2, 6, 3, 4, 3, 4, -3217668177573323776158033286617529600365192806400000⟩, + ⟨2, 6, 4, 4, 4, 4, -2015781423868307237114290326381171112302084096000000⟩, + ⟨2, 6, 5, 4, 5, 4, 388032512923566166548675752626152526250508288000000⟩, + ⟨2, 6, 6, 4, 6, 4, 142076416418977441060125131449814732095723929600000⟩, + ⟨2, 6, 7, 4, 7, 4, -49604630267585083575161882278882557587305267200000⟩, + ⟨2, 6, 8, 4, 8, 4, 7590527857734338969847535284933986095202304000000⟩, + ⟨2, 6, 1, 5, 0, 4, -32782401140548622564713274073066692373092971315200000⟩, + ⟨2, 6, 2, 5, 1, 4, 3508984281713795540712044554830043713118824038400000⟩, + ⟨2, 6, 3, 5, 2, 4, -4017861895577160686491948596226167617709775257600000⟩, + ⟨2, 6, 4, 5, 3, 4, -1920805663876338203815298613471003327054269644800000⟩, + ⟨2, 6, 5, 5, 4, 4, 257396181374038758216832450113714344171667456000000⟩, + ⟨2, 6, 6, 5, 5, 4, 118687980424028595921551330309344222417571020800000⟩, + ⟨2, 6, 7, 5, 6, 4, 15714650710027929904365631409496444754722816000000⟩, + ⟨2, 6, 8, 5, 7, 4, -12444687408133658378924469295268444179424870400000⟩, + ⟨2, 6, 2, 6, 0, 4, -63169018366999425548926704052483916233575078297600000⟩, + ⟨2, 6, 3, 6, 1, 4, -978196447412473552287090674546155642717785292800000⟩, + ⟨2, 6, 4, 6, 2, 4, 2432887729864322840723115322236781503208803532800000⟩, + ⟨2, 6, 5, 6, 3, 4, -2345536439783704999241668187715409180209709056000000⟩, + ⟨2, 6, 6, 6, 4, 4, -79136191716541344992576377994716545362480332800000⟩, + ⟨2, 6, 7, 6, 5, 4, 98180309607141581420372476529715778811225702400000⟩, + ⟨2, 6, 8, 6, 6, 4, 18589083950900094392398692895261490583856742400000⟩, + ⟨2, 6, 3, 7, 0, 4, 102818268520922509539257705504317099954091222630400000⟩, + ⟨2, 6, 4, 7, 1, 4, 2337074053909981967686635889630919349647494348800000⟩, + ⟨2, 6, 5, 7, 2, 4, 129942060246508538909195632964720070406176768000000⟩, + ⟨2, 6, 6, 7, 3, 4, -399494575231905849428826385917743259071388057600000⟩, + ⟨2, 6, 7, 7, 4, 4, 76343981117340821878844107003073950434459648000000⟩, + ⟨2, 6, 8, 7, 5, 4, 48017571409414258134591071004551557398134784000000⟩ +] + +def collectedFourData_9_4_16 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 4, 5, -9355763313468361111966814054150593710070431744000000⟩, + ⟨2, 7, 1, 0, 5, 5, 31012580404290021038670170913750282248006506905600000⟩, + ⟨2, 7, 2, 0, 6, 5, -13232116720242998060466591339800609614425646694400000⟩, + ⟨2, 7, 3, 0, 7, 5, 1260688725435968392636532376735188506039340236800000⟩, + ⟨2, 7, 4, 0, 8, 5, -1216414055446218529367076340256541347566269235200000⟩, + ⟨2, 7, 0, 1, 3, 5, -7353281045937135534852048959105250035376114892800000⟩, + ⟨2, 7, 1, 1, 4, 5, 13546772320119870057767403226248168193545732096000000⟩, + ⟨2, 7, 2, 1, 5, 5, 6461078377965568597115800638756025892512097894400000⟩, + ⟨2, 7, 3, 1, 6, 5, -5977814725265914310369218277505194176974264729600000⟩, + ⟨2, 7, 4, 1, 7, 5, 1418640127172057729379736003685444524935689011200000⟩, + ⟨2, 7, 5, 1, 8, 5, 1392730468175499926094476953191323865987416064000000⟩, + ⟨2, 7, 0, 2, 2, 5, -6134095216256463342158955884402938020342477619200000⟩, + ⟨2, 7, 1, 2, 3, 5, 20461557215063619391270857221223547483731473203200000⟩, + ⟨2, 7, 2, 2, 4, 5, 23803435516716738603347396618540960650882134835200000⟩, + ⟨2, 7, 3, 2, 5, 5, -2543854871178334508089963601650761368633711001600000⟩, + ⟨2, 7, 4, 2, 6, 5, -935299802863308105144919158726861830234308608000000⟩, + ⟨2, 7, 5, 2, 7, 5, 713897505585940101299309832285229662422119219200000⟩, + ⟨2, 7, 6, 2, 8, 5, -210907901945157993771668765164055841770727014400000⟩, + ⟨2, 7, 0, 3, 1, 5, -19663083893203984402714438093823327224169339289600000⟩, + ⟨2, 7, 1, 3, 2, 5, -52725567437760774796541232302256274882583278387200000⟩, + ⟨2, 7, 2, 3, 3, 5, -27114432799889384843238897306036896772158128128000000⟩, + ⟨2, 7, 3, 3, 4, 5, 277175096629364621699478526754425373046551347200000⟩, + ⟨2, 7, 4, 3, 5, 5, -2566177316473501395037945098488077089208742707200000⟩, + ⟨2, 7, 5, 3, 6, 5, -488459364840098057977315176545370554302778572800000⟩, + ⟨2, 7, 6, 3, 7, 5, -447181173030109939445842224241861008241459200000⟩, + ⟨2, 7, 7, 3, 8, 5, 10224449263836194705518279963859992780052889600000⟩, + ⟨2, 7, 0, 4, 0, 5, -62792633930630493083344751389332585919643910144000000⟩, + ⟨2, 7, 1, 4, 1, 5, 23737489804147937191612618124754462342664264089600000⟩, + ⟨2, 7, 2, 4, 2, 5, 6465045569030096052749016111842390873695322112000000⟩, + ⟨2, 7, 3, 4, 3, 5, 4093313678210634845352321086749292046881233305600000⟩, + ⟨2, 7, 4, 4, 4, 5, 1923262099891053100967099837606985624283250688000000⟩, + ⟨2, 7, 5, 4, 5, 5, -296178233133727192534491798783701462035936051200000⟩, + ⟨2, 7, 6, 4, 6, 5, -90370309582007512265180695089615797516186419200000⟩, + ⟨2, 7, 7, 4, 7, 5, 27044515340833818860046151600699576507642675200000⟩, + ⟨2, 7, 8, 4, 8, 5, -3621070810081395803235320468743587423584256000000⟩, + ⟨2, 7, 1, 5, 0, 5, 125111083792111488595312363028308517611133888102400000⟩, + ⟨2, 7, 2, 5, 1, 5, -6695861364951710454771668427393149806334862950400000⟩, + ⟨2, 7, 3, 5, 2, 5, 5111269449396953450913216691440506047111259750400000⟩, + ⟨2, 7, 4, 5, 3, 5, 1832645489658396951959921230042950845988234854400000⟩, + ⟨2, 7, 5, 5, 4, 5, -196465872512460882278983813635708223314355814400000⟩, + ⟨2, 7, 6, 5, 5, 5, -75493666049068752150586413668078023031232921600000⟩, + ⟨2, 7, 7, 5, 6, 5, -8567650034091980201301348581250969743917056000000⟩, + ⟨2, 7, 8, 5, 7, 5, 5936753696024371585236347789488026409343385600000⟩, + ⟨2, 7, 2, 6, 0, 5, 120539436938981240416050811324709698957313939865600000⟩, + ⟨2, 7, 3, 6, 1, 5, 1244399570495887120186655575050363250976961331200000⟩, + ⟨2, 7, 4, 6, 2, 5, -2321224270019725673024882724843166185751471718400000⟩, + ⟨2, 7, 5, 6, 3, 5, 1790305748484407499520255850193668875143767654400000⟩, + ⟨2, 7, 6, 6, 4, 5, 50336025674206763487216964459425621580814745600000⟩, + ⟨2, 7, 7, 6, 5, 5, -53528045164631769798861425880646533522024038400000⟩, + ⟨2, 7, 8, 6, 6, 5, -8867945753228371335000603881116292060125593600000⟩, + ⟨2, 7, 3, 7, 0, 5, -130798889655561874374662197626660549701593045401600000⟩, + ⟨2, 7, 4, 7, 1, 5, -2229808202070949217154473650840168000322430566400000⟩, + ⟨2, 7, 5, 7, 2, 5, -99182435831474060432895304670714670940894003200000⟩, + ⟨2, 7, 6, 7, 3, 5, 254105849162012249278846359659348760340935475200000⟩, + ⟨2, 7, 7, 7, 4, 5, -41622847652942841842955227967615878842810368000000⟩, + ⟨2, 7, 8, 7, 5, 5, -22906842509570618784478771341073590282878976000000⟩ +] + +def collectedFourData_9_4_17 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 4, 6, 16583930293351227691354359490824658918569934848000000⟩, + ⟨2, 8, 1, 0, 5, 6, -27486291305665319162805302160004321830258710937600000⟩, + ⟨2, 8, 2, 0, 6, 6, 7818371555926216923254215500861026630077356441600000⟩, + ⟨2, 8, 3, 0, 7, 6, -558670982894211701769970503278721474480203366400000⟩, + ⟨2, 8, 4, 0, 8, 6, 431240620940725196777937119524076929811145031680000⟩, + ⟨2, 8, 0, 1, 3, 6, 13034350721302549426533276291080851199358507417600000⟩, + ⟨2, 8, 1, 1, 4, 6, -12006434981812430205707016216292714751213961216000000⟩, + ⟨2, 8, 2, 1, 5, 6, -3817613801245869578145755620885785840474233241600000⟩, + ⟨2, 8, 3, 1, 6, 6, 2649053299789681967790769370352833546326691020800000⟩, + ⟨2, 8, 4, 1, 7, 6, -502933393932783303193781559001029087324096430080000⟩, + ⟨2, 8, 5, 1, 8, 6, -411456628885267480230747668785019425860354048000000⟩, + ⟨2, 8, 0, 2, 2, 6, 10873234397960000254778052118801630273477174886400000⟩, + ⟨2, 8, 1, 2, 3, 6, -18134973447839162238340590956529740969952883507200000⟩, + ⟨2, 8, 2, 2, 4, 6, -14064575389704116542509682087427534902465973452800000⟩, + ⟨2, 8, 3, 2, 5, 6, 1127302777083185264809645262592261345526992076800000⟩, + ⟨2, 8, 4, 2, 6, 6, 331580571555097214494665910943118193388106547200000⟩, + ⟨2, 8, 5, 2, 7, 6, -210907901945157993771668765164055841770727014400000⟩, + ⟨2, 8, 6, 2, 8, 6, 53407598335521107226111634727741178339812966400000⟩, + ⟨2, 8, 0, 3, 1, 6, 34854581257712886616095235954459580723010679603200000⟩, + ⟨2, 8, 1, 3, 2, 6, 46730400597375639262772642466036982457964901171200000⟩, + ⟨2, 8, 2, 3, 3, 6, 16020922021751555948363167800361969688292360192000000⟩, + ⟨2, 8, 3, 3, 4, 6, -122829434850522270519925895474123799417952665600000⟩, + ⟨2, 8, 4, 3, 5, 6, 909755929278609546588938851192549641070030356480000⟩, + ⟨2, 8, 5, 3, 6, 6, 144306345123498758934066456165626262071122329600000⟩, + ⟨2, 8, 6, 3, 7, 6, 113238395774329482703800241804249142604595200000⟩, + ⟨2, 8, 7, 3, 8, 6, -2265469264748132086019633495437393705461350400000⟩, + ⟨2, 8, 0, 4, 0, 6, 111305580223731553624674774421375934798021787648000000⟩, + ⟨2, 8, 1, 4, 1, 6, -21038415736983155380232590399614222463802120601600000⟩, + ⟨2, 8, 2, 4, 2, 6, -3819957868671482228296485081347695564101255168000000⟩, + ⟨2, 8, 3, 4, 3, 6, -1813941482747404764326193439389437885372222668800000⟩, + ⟨2, 8, 4, 4, 4, 6, -681830942741396710137898681354795842566042419200000⟩, + ⟨2, 8, 5, 4, 5, 6, 87500417445482283412442986913776141712385638400000⟩, + ⟨2, 8, 6, 4, 6, 6, 22884212260892755410856159813548628262466355200000⟩, + ⟨2, 8, 7, 4, 7, 6, -5992353886617119774632592399108252153728204800000⟩, + ⟨2, 8, 8, 4, 8, 6, 713185895149187208789234941095110537904128000000⟩, + ⟨2, 8, 1, 5, 0, 6, -110885313309877913645497964335530557145507849830400000⟩, + ⟨2, 8, 2, 5, 1, 6, 3956338441156250963936092388787632783811516825600000⟩, + ⟨2, 8, 3, 5, 2, 6, -2265045978057957003207366313495781063397684019200000⟩, + ⟨2, 8, 4, 5, 3, 6, -649705727573655620390803602316163073574919208960000⟩, + ⟨2, 8, 5, 5, 4, 6, 58042232465035354570045232587487973160570060800000⟩, + ⟨2, 8, 6, 5, 5, 6, 19117042823142053691928747030586068597053849600000⟩, + ⟨2, 8, 7, 5, 6, 6, 1898366095082090047375992328321136899129344000000⟩, + ⟨2, 8, 8, 5, 7, 6, -1169269870998245804439168609391662473202892800000⟩, + ⟨2, 8, 2, 6, 0, 6, -71222324066212286294726256658659446181979383398400000⟩, + ⟨2, 8, 3, 6, 1, 6, -551452485562331247362229214237179489788991897600000⟩, + ⟨2, 8, 4, 6, 2, 6, 822915676667997597749962858925695879384462786560000⟩, + ⟨2, 8, 5, 6, 3, 6, -528912941001650936150646505239653448764148940800000⟩, + ⟨2, 8, 6, 6, 4, 6, -12746446274514425480152028853517769216989593600000⟩, + ⟨2, 8, 7, 6, 5, 6, 11860408125006853189897473688439517034944921600000⟩, + ⟨2, 8, 8, 6, 6, 6, 1746581097652836248514057793379780459809996800000⟩, + ⟨2, 8, 3, 7, 0, 6, 57963193269674218451755567180705157480151043276800000⟩, + ⟨2, 8, 4, 7, 1, 6, 790507039387225179254256988293356564363618549760000⟩, + ⟨2, 8, 5, 7, 2, 6, 29301628437344737260147567009515828173760102400000⟩, + ⟨2, 8, 6, 7, 3, 6, -64346489636410842157262424970902314524291891200000⟩, + ⟨2, 8, 7, 7, 4, 6, 9222529217545015958039766609202275346808832000000⟩, + ⟨2, 8, 8, 7, 5, 6, 4511603842362406080940762616693555868991488000000⟩ +] + +def collectedFourData_9_4_18 : List CollectedFourTerm := [ + ⟨3, 1, 5, 1, 8, 0, -38360375014728808955137428362471321715848773632000000⟩, + ⟨3, 1, 5, 2, 7, 0, -19663083893203984402714438093823327224169339289600000⟩, + ⟨3, 1, 6, 2, 8, 0, 34854581257712886616095235954459580723010679603200000⟩, + ⟨3, 1, 5, 3, 6, 0, 13453776479284478775438902717256970903514146406400000⟩, + ⟨3, 1, 6, 3, 7, 0, 73901036369657758779214894172932317682178457600000⟩, + ⟨3, 1, 7, 3, 8, 0, -5913913752792560755492657009912333508144843980800000⟩, + ⟨3, 1, 5, 4, 5, 0, 8157722081784652422326872464136324802135300505600000⟩, + ⟨3, 1, 6, 4, 6, 0, 14934572244854971008598625161894854506491517337600000⟩, + ⟨3, 1, 7, 4, 7, 0, -15642791810554470382338631235439133403328911769600000⟩, + ⟨3, 1, 8, 4, 8, 0, 5585226786234106712720265599902690058403053568000000⟩, + ⟨3, 1, 5, 5, 4, 0, 5411315914591030815596764137400511675946447667200000⟩, + ⟨3, 1, 6, 5, 5, 0, 12476062269274859506284274943546262343327206604800000⟩, + ⟨3, 1, 7, 5, 6, 0, 4955606121978988994604745001414939744548159488000000⟩, + ⟨3, 1, 8, 5, 7, 0, -9156991814132548011331187218867617412076588236800000⟩, + ⟨3, 1, 5, 6, 3, 0, -49310905068986086459237039549610221947424289587200000⟩, + ⟨3, 1, 6, 6, 4, 0, -8318517613001365499987082083985017768369769676800000⟩, + ⟨3, 1, 7, 6, 5, 0, 30961104533902721920824011888858140769804038963200000⟩, + ⟨3, 1, 8, 6, 6, 0, 13678133004719879687078299284015083524352429260800000⟩, + ⟨3, 1, 5, 7, 2, 0, 2731810296613822915867758289733692922854480281600000⟩, + ⟨3, 1, 6, 7, 3, 0, -41993462008742070100771412308650157726378858905600000⟩, + ⟨3, 1, 7, 7, 4, 0, 24075030822029012196587397541675878036289880064000000⟩, + ⟨3, 1, 8, 7, 5, 0, 35332065315128163747809822142694295408348233728000000⟩ +] + +def collectedFourData_9_4_19 : List CollectedFourTerm := [ + ⟨3, 2, 4, 0, 8, 1, 17967879369470317468869331656245622613339684208640000⟩, + ⟨3, 2, 4, 1, 7, 1, -20954998472429731191810544159384002588042948771840000⟩, + ⟨3, 2, 5, 1, 8, 1, -102861410283456352437830086768323681452896026624000000⟩, + ⟨3, 2, 4, 2, 6, 1, 13815488202306707017882196035274088768618469785600000⟩, + ⟨3, 2, 5, 2, 7, 1, -52725567437760774796541232302256274882583278387200000⟩, + ⟨3, 2, 6, 2, 8, 1, 46730400597375639262772642466036982457964901171200000⟩, + ⟨3, 2, 4, 3, 5, 1, 37905484778497398978542316266285700523712619479040000⟩, + ⟨3, 2, 5, 3, 6, 1, 36075622872984029172154890021919603832048635084800000⟩, + ⟨3, 2, 6, 3, 7, 1, 99080950322739385621156604882395412259510681600000⟩, + ⟨3, 2, 7, 3, 8, 1, -5285953788454911674973862522684082044666065715200000⟩, + ⟨3, 2, 4, 4, 4, 1, -28408863948912570260518884629645470812205586841600000⟩, + ⟨3, 2, 5, 4, 5, 1, 21874520197226361344341258344071710734401352499200000⟩, + ⟨3, 2, 6, 4, 6, 1, 20023151005381368215550062072577459151219300761600000⟩, + ⟨3, 2, 7, 4, 7, 1, -13981785681938104649323633042819275324656084582400000⟩, + ⟨3, 2, 8, 4, 8, 1, 3744125961779510464540382674326830318767570944000000⟩, + ⟨3, 2, 4, 5, 3, 1, -27070349062274397421972069606786811307470440366080000⟩, + ⟨3, 2, 5, 5, 4, 1, 14510170618781160067752499378767169861462681190400000⟩, + ⟨3, 2, 6, 5, 5, 1, 16726965772741980018085257364509440126376266956800000⟩, + ⟨3, 2, 7, 5, 6, 1, 4429402600299305031634674386799660532154499072000000⟩, + ⟨3, 2, 8, 5, 7, 1, -6138502892594819320542044942207499519031404134400000⟩, + ⟨3, 2, 4, 6, 2, 1, 34287237545854915128357494694752476078229296250880000⟩, + ⟨3, 2, 5, 6, 3, 1, -132224704158966980983239648364836734978962646630400000⟩, + ⟨3, 2, 6, 6, 4, 1, -11152842650945868882932688085327881649362095308800000⟩, + ⟨3, 2, 7, 6, 5, 1, 27673546596524437829803880192205423610440764620800000⟩, + ⟨3, 2, 8, 6, 6, 1, 9169305894233081338823774709715811368064935526400000⟩, + ⟨3, 2, 4, 7, 1, 1, 32936913719867572609434428126821729680583274004480000⟩, + ⟨3, 2, 5, 7, 2, 1, 7325211487861455793538007676342367491185652531200000⟩, + ⟨3, 2, 6, 7, 3, 1, -56301674882550574619253801938718878586979850649600000⟩, + ⟨3, 2, 7, 7, 4, 1, 21518660180118598708505715050851750988130287616000000⟩, + ⟨3, 2, 8, 7, 5, 1, 23685287651292846489890489525121594351339700224000000⟩ +] + +def collectedFourData_9_4_20 : List CollectedFourTerm := [ + ⟨3, 3, 3, 0, 7, 2, -4788202712566668037262125136400531509950493491200000⟩, + ⟨3, 3, 4, 0, 8, 2, 18480175042027481749959289099406983851028984627200000⟩, + ⟨3, 3, 3, 1, 6, 2, 22704247373070531844641343746385596011623376486400000⟩, + ⟨3, 3, 4, 1, 7, 2, -21552462136066527153805816144595287139075437363200000⟩, + ⟨3, 3, 5, 1, 8, 2, -52897084514546035841012229372058642711062773760000000⟩, + ⟨3, 3, 3, 2, 5, 2, 9661776574022904798501949220499132833967007334400000⟩, + ⟨3, 3, 4, 2, 6, 2, 14209391938789490790163282385966811878982156288000000⟩, + ⟨3, 3, 5, 2, 7, 2, -27114432799889384843238897306036896772158128128000000⟩, + ⟨3, 3, 6, 2, 8, 2, 16020922021751555948363167800361969688292360192000000⟩, + ⟨3, 3, 3, 3, 4, 2, -1052734527373276086586157330404197405194767564800000⟩, + ⟨3, 3, 4, 3, 5, 2, 38986236458698496278175117473448800301958247219200000⟩, + ⟨3, 3, 5, 3, 6, 2, 18552100994614164666570658263684746291447857152000000⟩, + ⟨3, 3, 6, 3, 7, 2, 33968640513875528903301000129926905731219456000000⟩, + ⟨3, 3, 7, 3, 8, 2, -1359166394459086082492109883844846741486567424000000⟩, + ⟨3, 3, 3, 4, 3, 2, -15546752550370048230251900338310872736926688870400000⟩, + ⟨3, 3, 4, 4, 4, 2, -29218850356547395046195051492381343948019335168000000⟩, + ⟨3, 3, 5, 4, 5, 2, 11249100516891592830861970036497307521156907008000000⟩, + ⟨3, 3, 6, 4, 6, 2, 6864682022541586595433389053185519420237152256000000⟩, + ⟨3, 3, 7, 4, 7, 2, -3595107712618548410798614982574996664602329088000000⟩, + ⟨3, 3, 8, 4, 8, 2, 770175508531640291072859730874076644165812224000000⟩, + ⟨3, 3, 3, 5, 2, 2, -19413034913751737311256455339459820835793639833600000⟩, + ⟨3, 3, 4, 5, 3, 2, -27842172068988176634838724366384850355091826278400000⟩, + ⟨3, 3, 5, 5, 4, 2, 7461940483092885286583511225628737403770372096000000⟩, + ⟨3, 3, 6, 5, 5, 2, 5734626942630067024042159286310000606773772288000000⟩, + ⟨3, 3, 7, 5, 6, 2, 1138923154229133678598826056872821026078064640000000⟩, + ⟨3, 3, 8, 5, 7, 2, -1262704469664841098333905019191373681637353062400000⟩, + ⟨3, 3, 3, 6, 1, 2, -4726335120435594147467649003757749415036374220800000⟩, + ⟨3, 3, 4, 6, 2, 2, 35264826667948337247017787734058590085319124582400000⟩, + ⟨3, 3, 5, 6, 3, 2, -67997330889528422000923130173409762711433117696000000⟩, + ⟨3, 3, 6, 6, 4, 2, -3823609901638703354093783524839378736128196608000000⟩, + ⟨3, 3, 7, 6, 5, 2, 7115641955032665638089152109482175079588560896000000⟩, + ⟨3, 3, 8, 6, 6, 2, 1886147769082189332201000894151195760802555494400000⟩, + ⟨3, 3, 3, 7, 0, 2, 496785277454501692274919409395248781196739896934400000⟩, + ⟨3, 3, 4, 7, 1, 2, 33876002747521383531481801863060768182585681510400000⟩, + ⟨3, 3, 5, 7, 2, 2, 3767033040792863864040839217797452610496626688000000⟩, + ⟨3, 3, 6, 7, 3, 2, -19302311374536069702207227731070878299073806336000000⟩, + ⟨3, 3, 7, 7, 4, 2, 5533048706267852685749227942991479206492241920000000⟩, + ⟨3, 3, 8, 7, 5, 2, 4872119327118647684624927083511890521152815104000000⟩ +] + +def collectedFourData_9_4_21 : List CollectedFourTerm := [ + ⟨3, 4, 2, 0, 6, 3, -513745068703405244241017299660481595526128599040000⟩, + ⟨3, 4, 3, 0, 7, 3, 146841045062399345877083536889373357303807344640000⟩, + ⟨3, 4, 4, 0, 8, 3, -283368142391444541149140657643964389044172881920000⟩, + ⟨3, 4, 2, 1, 5, 3, 250855341240146632693707655989573113873474519040000⟩, + ⟨3, 4, 3, 1, 6, 3, -696276998228798885385813284638576536916674478080000⟩, + ⟨3, 4, 4, 1, 7, 3, 330477451948911823556722402872152556639375851520000⟩, + ⟨3, 4, 5, 1, 8, 3, 540736168812307889443816302882855614177869824000000⟩, + ⟨3, 4, 2, 2, 4, 3, 924183021768881638320402062599018668303392440320000⟩, + ⟨3, 4, 3, 2, 5, 3, -296300189122199362341204469333274669191192903680000⟩, + ⟨3, 4, 4, 2, 6, 3, -217881540031397548697447228266205185873595596800000⟩, + ⟨3, 4, 5, 2, 7, 3, 277175096629364621699478526754425373046551347200000⟩, + ⟨3, 4, 6, 2, 8, 3, -122829434850522270519925895474123799417952665600000⟩, + ⟨3, 4, 2, 3, 3, 3, -1052734527373276086586157330404197405194767564800000⟩, + ⟨3, 4, 3, 3, 4, 3, 32284480723227226682352052255798316914767298560000⟩, + ⟨3, 4, 4, 3, 5, 3, -597800474238526071807808466774589839873534853120000⟩, + ⟨3, 4, 5, 3, 6, 3, -189647352161498671298448311147870616619371724800000⟩, + ⟨3, 4, 6, 3, 7, 3, -260431260528894684331068006587608513432780800000⟩, + ⟨3, 4, 7, 3, 8, 3, 8336381133249134686059724231132043826230722560000⟩, + ⟨3, 4, 2, 4, 2, 3, 251009369872836003682180023732750351575757619200000⟩, + ⟨3, 4, 3, 4, 3, 3, 476776262172729486518023565730407762107438202880000⟩, + ⟨3, 4, 4, 4, 4, 3, 448031002386006494186907928260904360088489164800000⟩, + ⟨3, 4, 5, 4, 5, 3, -114993020350976426352998242113117093278987059200000⟩, + ⟨3, 4, 6, 4, 6, 3, -52630242636006441821228190384780441247599820800000⟩, + ⟨3, 4, 7, 4, 7, 3, 22050418719629319117536622335364964597597470720000⟩, + ⟨3, 4, 8, 4, 8, 3, -3936528427024634527905500961809619818958028800000⟩, + ⟨3, 4, 2, 5, 1, 3, -259970935088790606595901374000338137923599728640000⟩, + ⟨3, 4, 3, 5, 2, 3, 595344538585773211575415806972648642641311825920000⟩, + ⟨3, 4, 4, 5, 3, 3, 426921528686265414023179865970385228212197130240000⟩, + ⟨3, 4, 5, 5, 4, 3, -76279083162391500524147093826072282902455910400000⟩, + ⟨3, 4, 6, 5, 5, 3, -43966320133478813488300976057210451073066598400000⟩, + ⟨3, 4, 7, 5, 6, 3, -6985529905567533375315846959600739687176601600000⟩, + ⟨3, 4, 8, 5, 7, 3, 6453947164904566044970826875252689406399610880000⟩, + ⟨3, 4, 2, 6, 0, 3, 4680017764425332702877081774617511519232941096960000⟩, + ⟨3, 4, 3, 6, 1, 3, 144943735689891304982885330654060573538134261760000⟩, + ⟨3, 4, 4, 6, 2, 3, -540737758269440029882457972394754012785294704640000⟩, + ⟨3, 4, 5, 6, 3, 3, 695097216266342421230298030720941003815413350400000⟩, + ⟨3, 4, 6, 6, 4, 3, 29314907261236159516138054112268063441577574400000⟩, + ⟨3, 4, 7, 6, 5, 3, -43643444678087150678123761486433559679063818240000⟩, + ⟨3, 4, 8, 6, 6, 3, -9640496521003181509822456030632715153079009280000⟩, + ⟨3, 4, 3, 7, 0, 3, -15235041975474290126210481312724651529436062023680000⟩, + ⟨3, 4, 4, 7, 1, 3, -519442047944987789232866059474447686704761405440000⟩, + ⟨3, 4, 5, 7, 2, 3, -38508190630195696803277150166312076077904691200000⟩, + ⟨3, 4, 6, 7, 3, 3, 147987237827143810288747883352853342642293964800000⟩, + ⟨3, 4, 7, 7, 4, 3, -33936685774692572483677167957650055117982924800000⟩, + ⟨3, 4, 8, 7, 5, 3, -24902422913479039904376111066417686144404684800000⟩ +] + +def collectedFourData_9_4_22 : List CollectedFourTerm := [ + ⟨3, 5, 1, 0, 5, 4, -22295575971646042086389478294445772514686580817920000⟩, + ⟨3, 5, 2, 0, 6, 4, 19025676661272297390341393242333418709825261404160000⟩, + ⟨3, 5, 3, 0, 7, 4, -2719004438340808553313193155419606860826966753280000⟩, + ⟨3, 5, 4, 0, 8, 4, 3498019401497797583323960858296040910611871170560000⟩, + ⟨3, 5, 1, 1, 4, 4, -9739050652877744657313803638922394776284377907200000⟩, + ⟨3, 5, 2, 1, 5, 4, -9290001796481518452217497388254642200549429084160000⟩, + ⟨3, 5, 3, 1, 6, 4, 12892718433692856574299359548905361660751023964160000⟩, + ⟨3, 5, 4, 1, 7, 4, -4079557175760178819981129456292877119039849103360000⟩, + ⟨3, 5, 5, 1, 8, 4, -5006311560733202077606861102221852997293441024000000⟩, + ⟨3, 5, 1, 2, 3, 4, -14710230410995595223138823253983271785366542090240000⟩, + ⟨3, 5, 2, 2, 4, 4, -34225549633768723299676051099078024779948915425280000⟩, + ⟨3, 5, 3, 2, 5, 4, 5486487303070662636956402702557291164114207375360000⟩, + ⟨3, 5, 4, 2, 6, 4, 2689624344592727403821516619617736803748308582400000⟩, + ⟨3, 5, 5, 2, 7, 4, -2566177316473501395037945098488077089208742707200000⟩, + ⟨3, 5, 6, 2, 8, 4, 909755929278609546588938851192549641070030356480000⟩, + ⟨3, 5, 1, 3, 2, 4, 37905484778497398978542316266285700523712619479040000⟩, + ⟨3, 5, 2, 3, 3, 4, 38986236458698496278175117473448800301958247219200000⟩, + ⟨3, 5, 3, 3, 4, 4, -597800474238526071807808466774589839873534853120000⟩, + ⟨3, 5, 4, 3, 5, 4, 7379508647172765652376088867458120762198757212160000⟩, + ⟨3, 5, 5, 3, 6, 4, 1755816951682595153118274125970902672531573964800000⟩, + ⟨3, 5, 6, 3, 7, 4, 1928925942906077200315422342440057116966256640000⟩, + ⟨3, 5, 7, 3, 8, 4, -51453954379428670134995797340290393570321367040000⟩, + ⟨3, 5, 1, 4, 1, 4, -17065365100394641353480393021735630456994104606720000⟩, + ⟨3, 5, 2, 4, 2, 4, -9295705985466771138724066068676929098882010316800000⟩, + ⟨3, 5, 3, 4, 3, 4, -8828299828513970940993278331472993785376155893760000⟩, + ⟨3, 5, 4, 4, 4, 4, -5530689249653895963543103871335836886055151206400000⟩, + ⟨3, 5, 5, 4, 5, 4, 1064642833955770993494986661329309751710004019200000⟩, + ⟨3, 5, 6, 4, 6, 4, 389814341780105885000605213565227180124421488640000⟩, + ⟨3, 5, 7, 4, 7, 4, -136099972003667230822128531499207386924035604480000⟩, + ⟨3, 5, 8, 4, 8, 4, 20826092712675167134310095300012736442374553600000⟩, + ⟨3, 5, 1, 5, 0, 4, -89944907428474734236974162311720285183621652807680000⟩, + ⟨3, 5, 2, 5, 1, 4, 9627582343147373833834797480331170551840699842560000⟩, + ⟨3, 5, 3, 5, 2, 4, -11023787266488065392999745838303795816290939043840000⟩, + ⟨3, 5, 4, 5, 3, 4, -5270104739574786900874025238286236677111619256320000⟩, + ⟨3, 5, 5, 5, 4, 4, 706216594900203895513814436951426223309219430400000⟩, + ⟨3, 5, 6, 5, 5, 4, 325643608787016937313278784998315115561059614720000⟩, + ⟨3, 5, 7, 5, 6, 4, 43116207300507164284759489271828259510052454400000⟩, + ⟨3, 5, 8, 5, 7, 4, -34144425605126820615137954276236387176268431360000⟩, + ⟨3, 5, 2, 6, 0, 4, -173316514705801632627365013808698173526850236579840000⟩, + ⟨3, 5, 3, 6, 1, 4, -2683872622147572014479581968198359765971653099520000⟩, + ⟨3, 5, 4, 6, 2, 4, 6675101701926659195086482703391571170800718315520000⟩, + ⟨3, 5, 5, 6, 3, 4, -6435436411200260339524555969023422837754848870400000⟩, + ⟨3, 5, 6, 6, 4, 4, -217125567089172052203196282402443819327443435520000⟩, + ⟨3, 5, 7, 6, 5, 4, 269376816574624830636450831369650239069917020160000⟩, + ⟨3, 5, 8, 6, 6, 4, 51002775177311892555926737093194496537169756160000⟩, + ⟨3, 5, 3, 7, 0, 4, 282101960878990862492850035870879816448111657615360000⟩, + ⟨3, 5, 4, 7, 1, 4, 6412218206079385770054621385334627764174501969920000⟩, + ⟨3, 5, 5, 7, 2, 4, 356521370409351951106411368823790223188243251200000⟩, + ⟨3, 5, 6, 7, 3, 4, -1096091236067714917423657618180638009601126563840000⟩, + ⟨3, 5, 7, 7, 4, 4, 209464593056514783675241595973460251643163443200000⟩, + ⟨3, 5, 8, 7, 5, 4, 131745566679002022914739207654753970280831385600000⟩ +] + +def collectedFourData_9_4_23 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 4, 5, 6401353373465336945410484524876050553368477696000000⟩, + ⟨3, 6, 1, 0, 5, 5, -21219271965236456112557198817665658685510542950400000⟩, + ⟨3, 6, 2, 0, 6, 5, 9053612427676241472053808529999074237223639449600000⟩, + ⟨3, 6, 3, 0, 7, 5, -862582106351673615905584305318368252517364531200000⟩, + ⟨3, 6, 4, 0, 8, 5, 832288714075497982445906151035014532465216716800000⟩, + ⟨3, 6, 0, 1, 3, 5, 5031225016315456429658372086839407209448944435200000⟩, + ⟨3, 6, 1, 1, 4, 5, -9268904501477632153433324268414191437678116864000000⟩, + ⟨3, 6, 2, 1, 5, 5, -4420766589025756891557276937612627143483300249600000⟩, + ⟨3, 6, 3, 1, 6, 5, 4090110360364145127091340094430755179448395366400000⟩, + ⟨3, 6, 4, 1, 7, 5, -970654820941549121622007004003780194038762700800000⟩, + ⟨3, 6, 5, 1, 8, 5, -952927044226186120453644486008330840835096576000000⟩, + ⟨3, 6, 0, 2, 2, 5, 4197039812797919906663943908442740833557204172800000⟩, + ⟨3, 6, 1, 2, 3, 5, -14000103884248872586867008024892347388493876428800000⟩, + ⟨3, 6, 2, 2, 4, 5, -16286667067094845927505534761778036563568807116800000⟩, + ⟨3, 6, 3, 2, 5, 5, 1740543600304786676590887398831699095017907814400000⟩, + ⟨3, 6, 4, 2, 6, 5, 639946132416739994535766071533866004326121472000000⟩, + ⟨3, 6, 5, 2, 7, 5, -488459364840098057977315176545370554302778572800000⟩, + ⟨3, 6, 6, 2, 8, 5, 144306345123498758934066456165626262071122329600000⟩, + ⟨3, 6, 0, 3, 1, 5, 13453776479284478775438902717256970903514146406400000⟩, + ⟨3, 6, 1, 3, 2, 5, 36075622872984029172154890021919603832048635084800000⟩, + ⟨3, 6, 2, 3, 3, 5, 18552100994614164666570658263684746291447857152000000⟩, + ⟨3, 6, 3, 3, 4, 5, -189647352161498671298448311147870616619371724800000⟩, + ⟨3, 6, 4, 3, 5, 5, 1755816951682595153118274125970902672531573964800000⟩, + ⟨3, 6, 5, 3, 6, 5, 334211212720465063207412745073435755639157555200000⟩, + ⟨3, 6, 6, 3, 7, 5, 305968055690933582058826805538030850198732800000⟩, + ⟨3, 6, 7, 3, 8, 5, -6995721310377968309623656725942363935368806400000⟩, + ⟨3, 6, 0, 4, 0, 5, 42963660534460656204631340587620372389660983296000000⟩, + ⟨3, 6, 1, 4, 1, 5, -16241546022934807604226356411338899204054869606400000⟩, + ⟨3, 6, 2, 4, 2, 5, -4423481000565811105467613742456980500809515008000000⟩, + ⟨3, 6, 3, 4, 3, 5, -2800706521181925077077827084124365102378280550400000⟩, + ⟨3, 6, 4, 4, 4, 5, -1315924732028253763544897213498248495148040192000000⟩, + ⟨3, 6, 5, 4, 5, 5, 202649582753790900051795277224620656899706060800000⟩, + ⟨3, 6, 6, 4, 6, 5, 61832719225710344927177085204928755518983372800000⟩, + ⟨3, 6, 7, 4, 7, 5, -18504262422025954284306747269812164091497676800000⟩, + ⟨3, 6, 8, 4, 8, 5, 2477590878373581215101537103000381165666304000000⟩, + ⟨3, 6, 1, 5, 0, 5, -85602877227302966841817526020885851378445556121600000⟩, + ⟨3, 6, 2, 5, 1, 5, 4581408624893896323208645106699470809735993753600000⟩, + ⟨3, 6, 3, 5, 2, 5, -3497207105002950975487358640502513438905964953600000⟩, + ⟨3, 6, 4, 5, 3, 5, -1253923490208705817458086750912718825921812889600000⟩, + ⟨3, 6, 5, 5, 4, 5, 134424892297988053031753549393114457922181529600000⟩, + ⟨3, 6, 6, 5, 5, 5, 51653896923918382526151085446039255766165094400000⟩, + ⟨3, 6, 7, 5, 6, 5, 5862114464722726798730604132965615879061504000000⟩, + ⟨3, 6, 8, 5, 7, 5, -4062015789216228148508780982627317936711270400000⟩, + ⟨3, 6, 2, 6, 0, 5, -82474887984196675632817951930754075482558719590400000⟩, + ⟨3, 6, 3, 6, 1, 5, -851436822590969654368871862114796016207973580800000⟩, + ⟨3, 6, 4, 6, 2, 5, 1588216408817195386620681951339005449753696665600000⟩, + ⟨3, 6, 5, 6, 3, 5, -1224954005206280080390960096579025475752008089600000⟩, + ⟨3, 6, 6, 6, 4, 5, -34440662611949790989955324385610035972433510400000⟩, + ⟨3, 6, 7, 6, 5, 5, 36624690151828225961732924009838578526427545600000⟩, + ⟨3, 6, 8, 6, 6, 5, 6067581293064101711751721307589615615895142400000⟩, + ⟨3, 6, 3, 7, 0, 5, 89494559181163372090191181673446033303991117414400000⟩, + ⟨3, 6, 4, 7, 1, 5, 1525668166055387345753000472415138950285990297600000⟩, + ⟨3, 6, 5, 7, 2, 5, 67862107978332928962710892557192477193063628800000⟩, + ⟨3, 6, 6, 7, 3, 5, -173863027553173682359243627315384333701532876800000⟩, + ⟨3, 6, 7, 7, 4, 5, 28478975718938326893340414015556882962317312000000⟩, + ⟨3, 6, 8, 7, 5, 5, 15673204703991034566361333800986849820278784000000⟩ +] + +def collectedFourData_9_4_24 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 4, 6, 35162368662501569420137650780891221814411264000000⟩, + ⟨3, 7, 1, 0, 5, 6, -58278290547458140798476161618938491428457676800000⟩, + ⟨3, 7, 2, 0, 6, 6, 16577039225744370487232235928449573494508748800000⟩, + ⟨3, 7, 3, 0, 7, 6, -1184531936283165819933167295779263432831795200000⟩, + ⟨3, 7, 4, 0, 8, 6, 914345479481612910025075788963998022752010240000⟩, + ⟨3, 7, 0, 1, 3, 6, 27636310406015818026565606375018251164634316800000⟩, + ⟨3, 7, 1, 1, 4, 6, -25456854056007508833522946539545312926629888000000⟩, + ⟨3, 7, 2, 1, 5, 6, -8094362525406829089675791820146050532691148800000⟩, + ⟨3, 7, 3, 1, 6, 6, 5616701655527656129613514400886826513884774400000⟩, + ⟨3, 7, 4, 1, 7, 6, -1066353337075807482391679818833201760504381440000⟩, + ⟨3, 7, 5, 1, 8, 6, -872398123820759412555478386639475115556864000000⟩, + ⟨3, 7, 0, 2, 2, 6, 23054165670736371212959468688531252382479155200000⟩, + ⟨3, 7, 1, 2, 3, 6, -38450995076435512354166108040973185879480729600000⟩, + ⟨3, 7, 2, 2, 4, 6, -29820662302988189695600397732381086051624550400000⟩, + ⟨3, 7, 3, 2, 5, 6, 2390183457171945030746526351991303257351782400000⟩, + ⟨3, 7, 4, 2, 6, 6, 703039514283152723499087596535199961815449600000⟩, + ⟨3, 7, 5, 2, 7, 6, -447181173030109939445842224241861008241459200000⟩, + ⟨3, 7, 6, 2, 8, 6, 113238395774329482703800241804249142604595200000⟩, + ⟨3, 7, 0, 3, 1, 6, 73901036369657758779214894172932317682178457600000⟩, + ⟨3, 7, 1, 3, 2, 6, 99080950322739385621156604882395412259510681600000⟩, + ⟨3, 7, 2, 3, 3, 6, 33968640513875528903301000129926905731219456000000⟩, + ⟨3, 7, 3, 3, 4, 6, -260431260528894684331068006587608513432780800000⟩, + ⟨3, 7, 4, 3, 5, 6, 1928925942906077200315422342440057116966256640000⟩, + ⟨3, 7, 5, 3, 6, 6, 305968055690933582058826805538030850198732800000⟩, + ⟨3, 7, 6, 3, 7, 6, 240095691946050613299348004756723964313600000⟩, + ⟨3, 7, 7, 3, 8, 6, -4803400886976527505943888580410885747507200000⟩, + ⟨3, 7, 0, 4, 0, 6, 235997605922739988383183125195427983250161664000000⟩, + ⟨3, 7, 1, 4, 1, 6, -44607069442118833026099575200449095709543628800000⟩, + ⟨3, 7, 2, 4, 2, 6, -8099332575420980301421832485800673252737024000000⟩, + ⟨3, 7, 3, 4, 3, 6, -3846041198939459408247575829157688543438438400000⟩, + ⟨3, 7, 4, 4, 4, 6, -1445663998225190343464663642186578526837145600000⟩, + ⟨3, 7, 5, 4, 5, 6, 185524292608389740317079928143171185488691200000⟩, + ⟨3, 7, 6, 4, 6, 6, 48520651850005205249401762307396991555993600000⟩, + ⟨3, 7, 7, 4, 7, 6, -12705393280740004197668886880321752426086400000⟩, + ⟨3, 7, 8, 4, 8, 6, 1512144885231808855381619986967040098304000000⟩, + ⟨3, 7, 1, 5, 0, 6, -235106527637907951087672524068690107204580147200000⟩, + ⟨3, 7, 2, 5, 1, 6, 8388495872859286401376629648291273166867660800000⟩, + ⟨3, 7, 3, 5, 2, 6, -4802503405958060279886252444028777189185945600000⟩, + ⟨3, 7, 4, 5, 3, 6, -1377549948111076308432516316962669162953441280000⟩, + ⟨3, 7, 5, 5, 4, 6, 123065059960389602817086926494580620027494400000⟩, + ⟨3, 7, 6, 5, 5, 6, 40533244869803088672221838841123001126092800000⟩, + ⟨3, 7, 7, 5, 6, 6, 4025043961890720115709564153793129480192000000⟩, + ⟨3, 7, 8, 5, 7, 6, -2479164923074922356087806395920721274470400000⟩, + ⟨3, 7, 2, 6, 0, 6, -151010380019526968310020357138546546789528371200000⟩, + ⟨3, 7, 3, 6, 1, 6, -1169226790887407318222314532516261157194956800000⟩, + ⟨3, 7, 4, 6, 2, 6, 1744801376351229582974910452776676991518638080000⟩, + ⟨3, 7, 5, 6, 3, 6, -1121436926765434554995605808507555523487334400000⟩, + ⟨3, 7, 6, 6, 4, 6, -27025875960232105361552264453495796321484800000⟩, + ⟨3, 7, 7, 6, 5, 6, 25147238055288873903821565533264206941388800000⟩, + ⟨3, 7, 8, 6, 6, 6, 3703219162664205345225620540556063434342400000⟩, + ⟨3, 7, 3, 7, 0, 6, 122897475722098997995577134377024208819873382400000⟩, + ⟨3, 7, 4, 7, 1, 6, 1676086395537985184191110594796794171547975680000⟩, + ⟨3, 7, 5, 7, 2, 6, 62127290895489691730575395035247388341043200000⟩, + ⟨3, 7, 6, 7, 3, 6, -136431771643445606331617745922935406303641600000⟩, + ⟨3, 7, 7, 7, 4, 6, 19554229100807400601018865846683724414976000000⟩, + ⟨3, 7, 8, 7, 5, 6, 9565807064921541021768005671953874550784000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0917.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0917.lean new file mode 100644 index 0000000000000000000000000000000000000000..3a9241943cf14375c91571df9c7423be325cfee6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0917.lean @@ -0,0 +1,627 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0917. -/ +namespace LaughlinFock +def collectedFourData_9_4_25 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 4, 7, -2813860614535427937723737541906344647864614912000000⟩, + ⟨3, 8, 1, 0, 5, 7, 3109138030071079559251164500892163563983575449600000⟩, + ⟨3, 8, 2, 0, 6, 7, -663286910939469576195568855382307238036321075200000⟩, + ⟨3, 8, 3, 0, 7, 7, 37916760320201486943100549602521592325881200640000⟩, + ⟨3, 8, 4, 0, 8, 7, -24390096862611656016181426829175913215311216640000⟩, + ⟨3, 8, 0, 1, 3, 7, -2211589501519977153496758692861393701242824294400000⟩, + ⟨3, 8, 1, 1, 4, 7, 1358119332739321499689736952255686939441627136000000⟩, + ⟨3, 8, 2, 1, 5, 7, 323874766922391514884659362587495755504890675200000⟩, + ⟨3, 8, 3, 1, 6, 7, -179790112819558980579808928033315332317857710080000⟩, + ⟨3, 8, 4, 1, 7, 7, 28444895025667527905746278438877170176454819840000⟩, + ⟨3, 8, 5, 1, 8, 7, 19946703691549749058307187040467698300485632000000⟩, + ⟨3, 8, 0, 2, 2, 7, -1844904403469292767367786871841646454150633881600000⟩, + ⟨3, 8, 1, 2, 3, 7, 2051354800615985864074220867114162439146648371200000⟩, + ⟨3, 8, 2, 2, 4, 7, 1193195884485816271177334657596461129265682841600000⟩, + ⟨3, 8, 3, 2, 5, 7, -76509556636583856680031951270572125501186375680000⟩, + ⟨3, 8, 4, 2, 6, 7, -18753526141268978124710042403497073794718105600000⟩, + ⟨3, 8, 5, 2, 7, 7, 10224449263836194705518279963859992780052889600000⟩, + ⟨3, 8, 6, 2, 8, 7, -2265469264748132086019633495437393705461350400000⟩, + ⟨3, 8, 0, 3, 1, 7, -5913913752792560755492657009912333508144843980800000⟩, + ⟨3, 8, 1, 3, 2, 7, -5285953788454911674973862522684082044666065715200000⟩, + ⟨3, 8, 2, 3, 3, 7, -1359166394459086082492109883844846741486567424000000⟩, + ⟨3, 8, 3, 3, 4, 7, 8336381133249134686059724231132043826230722560000⟩, + ⟨3, 8, 4, 3, 5, 7, -51453954379428670134995797340290393570321367040000⟩, + ⟨3, 8, 5, 3, 6, 7, -6995721310377968309623656725942363935368806400000⟩, + ⟨3, 8, 6, 3, 7, 7, -4803400886976527505943888580410885747507200000⟩, + ⟨3, 8, 7, 3, 8, 7, 85420238142905146571678466600120743677132800000⟩, + ⟨3, 8, 0, 4, 0, 7, -18885655139007552693869109452793482877559898112000000⟩, + ⟨3, 8, 1, 4, 1, 7, 2379780441562081219780889851913164742641424793600000⟩, + ⟨3, 8, 2, 4, 2, 7, 324073630487604137835626794956501101624426496000000⟩, + ⟨3, 8, 3, 4, 3, 7, 123111431490308842307149237442848857793631354880000⟩, + ⟨3, 8, 4, 4, 4, 7, 38562978369503601401424817790256957506558361600000⟩, + ⟨3, 8, 5, 4, 5, 7, -4241868467158967035811467061969472282270105600000⟩, + ⟨3, 8, 6, 4, 6, 7, -970713552766967988626945018970933692674867200000⟩, + ⟨3, 8, 7, 4, 7, 7, 225943606473207016268930278036565627869593600000⟩, + ⟨3, 8, 8, 4, 8, 7, -24201810616715542216377159890758497887846400000⟩, + ⟨3, 8, 1, 5, 0, 7, 12542897866946085793940765555679626893929637478400000⟩, + ⟨3, 8, 2, 5, 1, 7, -335643744287966013852237319446532628921135923200000⟩, + ⟨3, 8, 3, 5, 2, 7, 153727700370868382406448184151836856764250193920000⟩, + ⟨3, 8, 4, 5, 3, 7, 36746041208147586819246143577669932318541742080000⟩, + ⟨3, 8, 5, 5, 4, 7, -2813786754907142941112656435280154855682867200000⟩, + ⟨3, 8, 6, 5, 5, 7, -810915942645890360522318512999000603990425600000⟩, + ⟨3, 8, 7, 5, 6, 7, -71578496538269025273068192845294844510208000000⟩, + ⟨3, 8, 8, 5, 7, 7, 39678922662668994684033881619821201341808640000⟩, + ⟨3, 8, 2, 6, 0, 7, 6042285785714531961348446702798960594250419404800000⟩, + ⟨3, 8, 3, 6, 1, 7, 37426843998098979371801588228144661868062965760000⟩, + ⟨3, 8, 4, 6, 2, 7, -46542445421561691061069055964539246022104186880000⟩, + ⟨3, 8, 5, 6, 3, 7, 25640781973469910679509488928265511420244787200000⟩, + ⟨3, 8, 6, 6, 4, 7, 540684905699458055946732566957651383654809600000⟩, + ⟨3, 8, 7, 6, 5, 7, -447200455232292881451454968078968953189171200000⟩, + ⟨3, 8, 8, 6, 6, 7, -59269855502802383947441552471620327403683840000⟩, + ⟨3, 8, 3, 7, 0, 7, -3933937100534748559425965110973305345581703495680000⟩, + ⟨3, 8, 4, 7, 1, 7, -44709478479025136115126954705992605231459860480000⟩, + ⟨3, 8, 5, 7, 2, 7, -1420492122591564847832387174502646322665881600000⟩, + ⟨3, 8, 6, 7, 3, 7, 2729480431790335807220978281601217722528563200000⟩, + ⟨3, 8, 7, 7, 4, 7, -347738393233147690555373661119436998836224000000⟩, + ⟨3, 8, 8, 7, 5, 7, -153100310190038888920786697771717004519014400000⟩ +] + +def collectedFourData_9_4_26 : List CollectedFourTerm := [ + ⟨4, 0, 5, 1, 8, 0, -122501078611279772395860536230777319036792340480000000⟩, + ⟨4, 0, 5, 2, 7, 0, -62792633930630493083344751389332585919643910144000000⟩, + ⟨4, 0, 6, 2, 8, 0, 111305580223731553624674774421375934798021787648000000⟩, + ⟨4, 0, 5, 3, 6, 0, 42963660534460656204631340587620372389660983296000000⟩, + ⟨4, 0, 6, 3, 7, 0, 235997605922739988383183125195427983250161664000000⟩, + ⟨4, 0, 7, 3, 8, 0, -18885655139007552693869109452793482877559898112000000⟩, + ⟨4, 0, 5, 4, 5, 0, 26051094486067276173781984390525271989114896384000000⟩, + ⟨4, 0, 6, 4, 6, 0, 47692474536298523641483275745784749019432484864000000⟩, + ⟨4, 0, 7, 4, 7, 0, -49954122412746275071821733622060909029012537344000000⟩, + ⟨4, 0, 8, 4, 8, 0, 17836017122866669124596777348481478750130667520000000⟩, + ⟨4, 0, 5, 5, 4, 0, 17280645353160959470467504601090710848938180608000000⟩, + ⟨4, 0, 6, 5, 5, 0, 39841401034813780830622851287865198973626089472000000⟩, + ⟨4, 0, 7, 5, 6, 0, 15825369144123293600433995179215985020575416320000000⟩, + ⟨4, 0, 8, 5, 7, 0, -29242189984722360209818593972249958454711549952000000⟩, + ⟨4, 0, 5, 6, 3, 0, -157470803033856196962717326156474682017901969408000000⟩, + ⟨4, 0, 6, 6, 4, 0, -26564583366255699246747629754252047452106391552000000⟩, + ⟨4, 0, 7, 6, 5, 0, 98872044367225306388556953609253007389043458048000000⟩, + ⟨4, 0, 8, 6, 6, 0, 43680126845041898995671404932431728729823117312000000⟩, + ⟨4, 0, 5, 7, 2, 0, 8723838277600302027583922776318036054087041024000000⟩, + ⟨4, 0, 6, 7, 3, 0, -134103078729483856276478377362108862095251472384000000⟩, + ⟨4, 0, 7, 7, 4, 0, 76881866826536006857804679059238105321004072960000000⟩, + ⟨4, 0, 8, 7, 5, 0, 112830390969992585798339086360273330619988049920000000⟩ +] + +def collectedFourData_9_4_27 : List CollectedFourTerm := [ + ⟨4, 1, 4, 0, 8, 1, -8089289012174839236689048793014818607480721899520000⟩, + ⟨4, 1, 4, 1, 7, 1, 9434114922943377445500334257383918876966906757120000⟩, + ⟨4, 1, 5, 1, 8, 1, 46309064017681046456114668965234218416453189632000000⟩, + ⟨4, 1, 4, 2, 6, 1, -6219847908298001464640881435558025580029725900800000⟩, + ⟨4, 1, 5, 2, 7, 1, 23737489804147937191612618124754462342664264089600000⟩, + ⟨4, 1, 6, 2, 8, 1, -21038415736983155380232590399614222463802120601600000⟩, + ⟨4, 1, 4, 3, 5, 1, -17065365100394641353480393021735630456994104606720000⟩, + ⟨4, 1, 5, 3, 6, 1, -16241546022934807604226356411338899204054869606400000⟩, + ⟨4, 1, 6, 3, 7, 1, -44607069442118833026099575200449095709543628800000⟩, + ⟨4, 1, 7, 3, 8, 1, 2379780441562081219780889851913164742641424793600000⟩, + ⟨4, 1, 4, 4, 4, 1, 12789907270903664715626543794342167437690850508800000⟩, + ⟨4, 1, 5, 4, 5, 1, -9848091265498971569623736270154751381639633305600000⟩, + ⟨4, 1, 6, 4, 6, 1, -9014589428519964387932543360065541503040933068800000⟩, + ⟨4, 1, 7, 4, 7, 1, 6294716419326651059645800916107170135758025523200000⟩, + ⟨4, 1, 8, 4, 8, 1, -1685636706482096023222962764526531875168059392000000⟩, + ⟨4, 1, 4, 5, 3, 1, 12187296715563888168143590709687451957654391357440000⟩, + ⟨4, 1, 5, 5, 4, 1, -6532599720739823181417763286669544490299241267200000⟩, + ⟨4, 1, 6, 5, 5, 1, -7530619370829800686076926652038924160385574502400000⟩, + ⟨4, 1, 7, 5, 6, 1, -1994153959313680431832563909461744530275434496000000⟩, + ⟨4, 1, 8, 5, 7, 1, 2763605152238651334513294385199167888707236659200000⟩, + ⟨4, 1, 4, 6, 2, 1, -15436400046673351913925707050004016638916915363840000⟩, + ⟨4, 1, 5, 6, 3, 1, 59528663594469115143701401440379235396954043187200000⟩, + ⟨4, 1, 6, 6, 4, 1, 5021102694183488022917791845776934184952424038400000⟩, + ⟨4, 1, 7, 6, 5, 1, -12458861271716830056998186482558022808108426854400000⟩, + ⟨4, 1, 8, 6, 6, 1, -4128097918195019295625997858644674737157124915200000⟩, + ⟨4, 1, 4, 7, 1, 1, -14828473008438827757679757101747440783354117488640000⟩, + ⟨4, 1, 5, 7, 2, 1, -3297871250254359032091614331656883547785501081600000⟩, + ⟨4, 1, 6, 7, 3, 1, 25347483174241870186159896198898356624391195852800000⟩, + ⟨4, 1, 7, 7, 4, 1, -9687880120540297704233413157501868201568370688000000⟩, + ⟨4, 1, 8, 7, 5, 1, -10663313861810048393882933153035592736473874432000000⟩ +] + +def collectedFourData_9_4_28 : List CollectedFourTerm := [ + ⟨4, 2, 3, 0, 7, 2, 1141677901173846819057002337627268416426265804800000⟩, + ⟨4, 2, 4, 0, 8, 2, -4406331294189851060189860985842737363905465548800000⟩, + ⟨4, 2, 3, 1, 6, 2, -5413500439442408518793495740655038798658902425600000⟩, + ⟨4, 2, 4, 1, 7, 2, 5138873855957416813063519652321529320893631692800000⟩, + ⟨4, 2, 5, 1, 8, 2, 12612547139720049662454571924296557143303127040000000⟩, + ⟨4, 2, 3, 2, 5, 2, -2303711321931115147593742162932589074576939417600000⟩, + ⟨4, 2, 4, 2, 6, 2, -3388024638776796767165325476134177313497546752000000⟩, + ⟨4, 2, 5, 2, 7, 2, 6465045569030096052749016111842390873695322112000000⟩, + ⟨4, 2, 6, 2, 8, 2, -3819957868671482228296485081347695564101255168000000⟩, + ⟨4, 2, 3, 3, 4, 2, 251009369872836003682180023732750351575757619200000⟩, + ⟨4, 2, 4, 3, 5, 2, -9295705985466771138724066068676929098882010316800000⟩, + ⟨4, 2, 5, 3, 6, 2, -4423481000565811105467613742456980500809515008000000⟩, + ⟨4, 2, 6, 3, 7, 2, -8099332575420980301421832485800673252737024000000⟩, + ⟨4, 2, 7, 3, 8, 2, 324073630487604137835626794956501101624426496000000⟩, + ⟨4, 2, 3, 4, 3, 2, 3706898994729746466226569292948678440430180761600000⟩, + ⟨4, 2, 4, 4, 4, 2, 6966813594216907746686916170048819896906678272000000⟩, + ⟨4, 2, 5, 4, 5, 2, -2682185830293335356553429555772448214070853632000000⟩, + ⟨4, 2, 6, 4, 6, 2, -1636784454248812298160370517711463967541428224000000⟩, + ⟨4, 2, 7, 4, 7, 2, 857201600313221002771537049135007881811197952000000⟩, + ⟨4, 2, 8, 4, 8, 2, -183637245726500871726014664913902394404765696000000⟩, + ⟨4, 2, 3, 5, 2, 2, 4628758280759213706133978829390122372693386854400000⟩, + ⟨4, 2, 4, 5, 3, 2, 6638564505303604912550917444529945523911235993600000⟩, + ⟨4, 2, 5, 5, 4, 2, -1779192122978237553522881123703170597161795584000000⟩, + ⟨4, 2, 6, 5, 5, 2, -1367339113420154969470527130878521599435210752000000⟩, + ⟨4, 2, 7, 5, 6, 2, -271559805291035998410892401891082611783106560000000⟩, + ⟨4, 2, 8, 5, 7, 2, 301073675294969902154381478576313719177451929600000⟩, + ⟨4, 2, 3, 6, 1, 2, 1126926465828491107943739387536345009229083443200000⟩, + ⟨4, 2, 4, 6, 2, 2, -8408389475628782448412071306591874454325402009600000⟩, + ⟨4, 2, 5, 6, 3, 2, 16212983174592256493349784899042045471158697984000000⟩, + ⟨4, 2, 6, 6, 4, 2, 911684652772443267349628910569792479042732032000000⟩, + ⟨4, 2, 7, 6, 5, 2, -1696622231846068972667155720411474441518710784000000⟩, + ⟨4, 2, 8, 6, 6, 2, -449724741322656593225016253942353583289244057600000⟩, + ⟨4, 2, 3, 7, 0, 2, -118451286828309222397646551854381223055875217817600000⟩, + ⟨4, 2, 4, 7, 1, 2, -8077244435672205761870882246023049722306599321600000⟩, + ⟨4, 2, 5, 7, 2, 2, -898194716021027279075337864466138964900708352000000⟩, + ⟨4, 2, 6, 7, 3, 2, 4602357849229755260644773628571797511989100544000000⟩, + ⟨4, 2, 7, 7, 4, 2, -1319275689286431186052914173535448418935111680000000⟩, + ⟨4, 2, 8, 7, 5, 2, -1161686608015743056859293514320366551449993216000000⟩ +] + +def collectedFourData_9_4_29 : List CollectedFourTerm := [ + ⟨4, 3, 2, 0, 6, 3, -7586972070758980515940043818016708004191058001920000⟩, + ⟨4, 3, 3, 0, 7, 3, 2168544236426848477749395754876076788114228510720000⟩, + ⟨4, 3, 4, 0, 8, 3, -4184772395952524823649836722905118770215423836160000⟩, + ⟨4, 3, 2, 1, 5, 3, 3704624304410556049576236697052332655585966161920000⟩, + ⟨4, 3, 3, 1, 6, 3, -10282598239640840235249432232426029432979681443840000⟩, + ⟨4, 3, 4, 1, 7, 3, 4880481294506618761794541673663178468716665896960000⟩, + ⟨4, 3, 5, 1, 8, 3, 7985575843642157006831277206492806184385380352000000⟩, + ⟨4, 3, 2, 2, 4, 3, 13648307694955531298864275160816979535941976719360000⟩, + ⟨4, 3, 3, 2, 5, 3, -4375752481876484323183928783991252613547572592640000⟩, + ⟨4, 3, 4, 2, 6, 3, -3217668177573323776158033286617529600365192806400000⟩, + ⟨4, 3, 5, 2, 7, 3, 4093313678210634845352321086749292046881233305600000⟩, + ⟨4, 3, 6, 2, 8, 3, -1813941482747404764326193439389437885372222668800000⟩, + ⟨4, 3, 2, 3, 3, 3, -15546752550370048230251900338310872736926688870400000⟩, + ⟨4, 3, 3, 3, 4, 3, 476776262172729486518023565730407762107438202880000⟩, + ⟨4, 3, 4, 3, 5, 3, -8828299828513970940993278331472993785376155893760000⟩, + ⟨4, 3, 5, 3, 6, 3, -2800706521181925077077827084124365102378280550400000⟩, + ⟨4, 3, 6, 3, 7, 3, -3846041198939459408247575829157688543438438400000⟩, + ⟨4, 3, 7, 3, 8, 3, 123111431490308842307149237442848857793631354880000⟩, + ⟨4, 3, 2, 4, 2, 3, 3706898994729746466226569292948678440430180761600000⟩, + ⟨4, 3, 3, 4, 3, 3, 7041017822778731107920788743765165711175177994240000⟩, + ⟨4, 3, 4, 4, 4, 3, 6616508671344937434207269987806767388547245670400000⟩, + ⟨4, 3, 5, 4, 5, 3, -1698213543804852435742783445798901196690921881600000⟩, + ⟨4, 3, 6, 4, 6, 3, -777241875945237040337014282371658438230304358400000⟩, + ⟨4, 3, 7, 4, 7, 3, 325639935379996299631221518894367220701918658560000⟩, + ⟨4, 3, 8, 4, 8, 3, -58134536078295833280370421045458645142627942400000⟩, + ⟨4, 3, 2, 5, 1, 3, -3839243126373344430349408729596240741708563742720000⟩, + ⟨4, 3, 3, 5, 2, 3, 8792030642997419682913023187373920749067865948160000⟩, + ⟨4, 3, 4, 5, 3, 3, 6304764584355328815669506210194554903651176939520000⟩, + ⟨4, 3, 5, 5, 4, 3, -1126487257574585382155872639625136935837840179200000⟩, + ⟨4, 3, 6, 5, 5, 3, -649293323142978925224295879623703675654058803200000⟩, + ⟨4, 3, 7, 5, 6, 3, -103162100274270140476204249310038329641454796800000⟩, + ⟨4, 3, 8, 5, 7, 3, 95311701988431149146396499094699524248295178240000⟩, + ⟨4, 3, 2, 6, 0, 3, 69114364754807679231520883787416724458407282606080000⟩, + ⟨4, 3, 3, 6, 1, 3, 2140524827393614208906482926894347974041120276480000⟩, + ⟨4, 3, 4, 6, 2, 3, -7985599316698355197143554697156486255468053790720000⟩, + ⟨4, 3, 5, 6, 3, 3, 10265175254304293910671672388963075206319125299200000⟩, + ⟨4, 3, 6, 6, 4, 3, 432921688590047920929053858879170976479916851200000⟩, + ⟨4, 3, 7, 6, 5, 3, -644525107910134791660881675522139046154883563520000⟩, + ⟨4, 3, 8, 6, 6, 3, -142370569196308178517308488091168881019128381440000⟩, + ⟨4, 3, 3, 7, 0, 3, -224990651991046578171416244623988980894363434352640000⟩, + ⟨4, 3, 4, 7, 1, 3, -7671104892710277534568381982109381898729024389120000⟩, + ⟨4, 3, 5, 7, 2, 3, -568687827104822769318564505944012893137246617600000⟩, + ⟨4, 3, 6, 7, 3, 3, 2185471177479089919509092967164893590863636070400000⟩, + ⟨4, 3, 7, 7, 4, 3, -501175977798751992062761193830189848037058150400000⟩, + ⟨4, 3, 8, 7, 5, 3, -367758249467245250104843636037809444173014630400000⟩ +] + +def collectedFourData_9_4_30 : List CollectedFourTerm := [ + ⟨4, 4, 1, 0, 5, 4, 16709771373256256092434641522922383846719409356800000⟩, + ⟨4, 4, 2, 0, 6, 4, -14259093715975727263436291039336587247753782886400000⟩, + ⟨4, 4, 3, 0, 7, 4, 2037800798926372923650336603450844776341123891200000⟩, + ⟨4, 4, 4, 0, 8, 4, -2621645860711421699195686855981946997322442342400000⟩, + ⟨4, 4, 1, 1, 4, 4, 7299085253913473457928746997996823625427058688000000⟩, + ⟨4, 4, 2, 1, 5, 4, 6962538499734727297867691795611963830259050086400000⟩, + ⟨4, 4, 3, 1, 6, 4, -9662651356517927188923103542258360767643805286400000⟩, + ⟨4, 4, 4, 1, 7, 4, 3057488525874885579283046251621056386982897254400000⟩, + ⟨4, 4, 5, 1, 8, 4, 3752059229576631628170218409605269675793448960000000⟩, + ⟨4, 4, 1, 2, 3, 4, 11024814399424124819169260891664125550520801689600000⟩, + ⟨4, 4, 2, 2, 4, 4, 25650878462687561006921018404557165849981694771200000⟩, + ⟨4, 4, 3, 2, 5, 4, -4111934519797725685243519035391483513043052134400000⟩, + ⟨4, 4, 4, 2, 6, 4, -2015781423868307237114290326381171112302084096000000⟩, + ⟨4, 4, 5, 2, 7, 4, 1923262099891053100967099837606985624283250688000000⟩, + ⟨4, 4, 6, 2, 8, 4, -681830942741396710137898681354795842566042419200000⟩, + ⟨4, 4, 1, 3, 2, 4, -28408863948912570260518884629645470812205586841600000⟩, + ⟨4, 4, 2, 3, 3, 4, -29218850356547395046195051492381343948019335168000000⟩, + ⟨4, 4, 3, 3, 4, 4, 448031002386006494186907928260904360088489164800000⟩, + ⟨4, 4, 4, 3, 5, 4, -5530689249653895963543103871335836886055151206400000⟩, + ⟨4, 4, 5, 3, 6, 4, -1315924732028253763544897213498248495148040192000000⟩, + ⟨4, 4, 6, 3, 7, 4, -1445663998225190343464663642186578526837145600000⟩, + ⟨4, 4, 7, 3, 8, 4, 38562978369503601401424817790256957506558361600000⟩, + ⟨4, 4, 1, 4, 1, 4, 12789907270903664715626543794342167437690850508800000⟩, + ⟨4, 4, 2, 4, 2, 4, 6966813594216907746686916170048819896906678272000000⟩, + ⟨4, 4, 3, 4, 3, 4, 6616508671344937434207269987806767388547245670400000⟩, + ⟨4, 4, 4, 4, 4, 4, 4145062366443087975504088621171930187018797056000000⟩, + ⟨4, 4, 5, 4, 5, 4, -797913378519602187490734852385496672835207168000000⟩, + ⟨4, 4, 6, 4, 6, 4, -292152512114763193870796543532394716495190425600000⟩, + ⟨4, 4, 7, 4, 7, 4, 102002272512718430487472501296148439052268339200000⟩, + ⟨4, 4, 8, 4, 8, 4, -15608443947337417878231583124237192836153344000000⟩, + ⟨4, 4, 1, 5, 0, 4, 67410630756068794863443042877633922664630530867200000⟩, + ⟨4, 4, 2, 5, 1, 4, -7215543569530591868713465432628894180198213222400000⟩, + ⟨4, 4, 3, 5, 2, 4, 8261951390028592757415498261068294544858651033600000⟩, + ⟨4, 4, 4, 5, 3, 4, 3949763191738141687990304869781253918747839692800000⟩, + ⟨4, 4, 5, 5, 4, 4, -529285175489041715731214664729962371419734016000000⟩, + ⟨4, 4, 6, 5, 5, 4, -244058743264277467729994333658099283256986828800000⟩, + ⟨4, 4, 7, 5, 6, 4, -32314122200280014018580143920162216372862976000000⟩, + ⟨4, 4, 8, 5, 7, 4, 25590078778785804095530161825745024733046374400000⟩, + ⟨4, 4, 2, 6, 0, 4, 129894797946757809032860143190418409666226264473600000⟩, + ⟨4, 4, 3, 6, 1, 4, 2011470704684232380667264913998838669729647820800000⟩, + ⟨4, 4, 4, 6, 2, 4, -5002760344665518419746081418826719750626528460800000⟩, + ⟨4, 4, 5, 6, 3, 4, 4823139409138394917339962231295152367249391616000000⟩, + ⟨4, 4, 6, 6, 4, 4, 162728183831746079190336331411526455814573260800000⟩, + ⟨4, 4, 7, 6, 5, 4, -201888707604679568818860790223297346951079526400000⟩, + ⟨4, 4, 8, 6, 6, 4, -38224834994094630964950299147579324195300966400000⟩, + ⟨4, 4, 3, 7, 0, 4, -211425767884623169270352004252434704849179141734400000⟩, + ⟨4, 4, 4, 7, 1, 4, -4805738158784487217787865748084081870899039436800000⟩, + ⟨4, 4, 5, 7, 2, 4, -267200569153112392772013556186506727362920448000000⟩, + ⟨4, 4, 6, 7, 3, 4, 821482879931590862605628784106695692085991833600000⟩, + ⟨4, 4, 7, 7, 4, 4, -156986545905686033728880677228585150870192128000000⟩, + ⟨4, 4, 8, 7, 5, 4, -98738794702852571122982385493570821631770624000000⟩ +] + +def collectedFourData_9_4_31 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 4, 5, 3881472376803017318040818402069113566589353984000000⟩, + ⟨4, 5, 1, 0, 5, 5, -12866344534319898122757597459775990012850051481600000⟩, + ⟨4, 5, 2, 0, 6, 5, 5489674526323214798746439847503011232180758118400000⟩, + ⟨4, 5, 3, 0, 7, 5, -523028244684469676658358418596483977712553164800000⟩, + ⟨4, 5, 4, 0, 8, 5, 504659790631138651072915367725751237541573427200000⟩, + ⟨4, 5, 0, 1, 3, 5, 3050692530622954301483365778001136214837349580800000⟩, + ⟨4, 5, 1, 1, 4, 5, -5620217270747955079667303235966731897857376256000000⟩, + ⟨4, 5, 2, 1, 5, 5, -2680539941869854649637165453275197389970761318400000⟩, + ⟨4, 5, 3, 1, 6, 5, 2480045930230386465196555122070268280649128345600000⟩, + ⟨4, 5, 4, 1, 7, 5, -588558333697448875406757299623266133709370163200000⟩, + ⟨4, 5, 5, 1, 8, 5, -577809063721502621220134591756813392888725504000000⟩, + ⟨4, 5, 0, 2, 2, 5, 2544882800134927819663995429199742038873158451200000⟩, + ⟨4, 5, 1, 2, 3, 5, -8488988707346962183365375832896549654715642675200000⟩, + ⟨4, 5, 2, 2, 4, 5, -9875450493509358521774728134632985305323615027200000⟩, + ⟨4, 5, 3, 2, 5, 5, 1055381809291844756315498242549190523426019737600000⟩, + ⟨4, 5, 4, 2, 6, 5, 388032512923566166548675752626152526250508288000000⟩, + ⟨4, 5, 5, 2, 7, 5, -296178233133727192534491798783701462035936051200000⟩, + ⟨4, 5, 6, 2, 8, 5, 87500417445482283412442986913776141712385638400000⟩, + ⟨4, 5, 0, 3, 1, 5, 8157722081784652422326872464136324802135300505600000⟩, + ⟨4, 5, 1, 3, 2, 5, 21874520197226361344341258344071710734401352499200000⟩, + ⟨4, 5, 2, 3, 3, 5, 11249100516891592830861970036497307521156907008000000⟩, + ⟨4, 5, 3, 3, 4, 5, -114993020350976426352998242113117093278987059200000⟩, + ⟨4, 5, 4, 3, 5, 5, 1064642833955770993494986661329309751710004019200000⟩, + ⟨4, 5, 5, 3, 6, 5, 202649582753790900051795277224620656899706060800000⟩, + ⟨4, 5, 6, 3, 7, 5, 185524292608389740317079928143171185488691200000⟩, + ⟨4, 5, 7, 3, 8, 5, -4241868467158967035811467061969472282270105600000⟩, + ⟨4, 5, 0, 4, 0, 5, 26051094486067276173781984390525271989114896384000000⟩, + ⟨4, 5, 1, 4, 1, 5, -9848091265498971569623736270154751381639633305600000⟩, + ⟨4, 5, 2, 4, 2, 5, -2682185830293335356553429555772448214070853632000000⟩, + ⟨4, 5, 3, 4, 3, 5, -1698213543804852435742783445798901196690921881600000⟩, + ⟨4, 5, 4, 4, 4, 5, -797913378519602187490734852385496672835207168000000⟩, + ⟨4, 5, 5, 4, 5, 5, 122876946754727662995405873632732227214455603200000⟩, + ⟨4, 5, 6, 4, 6, 5, 37492382884541150958331534155288680816915251200000⟩, + ⟨4, 5, 7, 4, 7, 5, -11220093510526889428546735436836564397929267200000⟩, + ⟨4, 5, 8, 4, 8, 5, 1502291780248999512438997279272950632022016000000⟩, + ⟨4, 5, 1, 5, 0, 5, -51905461852790454066111908095567010602498287206400000⟩, + ⟨4, 5, 2, 5, 1, 5, 2777945535405778993915147499194655723649132134400000⟩, + ⟨4, 5, 3, 5, 2, 5, -2120537952223660005500283488722406903072056934400000⟩, + ⟨4, 5, 4, 5, 3, 5, -760318811650724339719741018430361391698699878400000⟩, + ⟨4, 5, 5, 5, 4, 5, 81508780373251901372389302834388735789262438400000⟩, + ⟨4, 5, 6, 5, 5, 5, 31320435284122377342160530466045512581224857600000⟩, + ⟨4, 5, 7, 5, 6, 5, 3554503873945817868071943233516491889442816000000⟩, + ⟨4, 5, 8, 5, 7, 5, -2463010735407243292975242394070520212068761600000⟩, + ⟨4, 5, 2, 6, 0, 5, -50008799829353139230041719471968052103685446041600000⟩, + ⟨4, 5, 3, 6, 1, 5, -516270281403122960899990278861920451945509683200000⟩, + ⟨4, 5, 4, 6, 2, 5, 963017936919806439640190104702874487464814182400000⟩, + ⟨4, 5, 5, 6, 3, 5, -742753111204749160123975040767732579983320678400000⟩, + ⟨4, 5, 6, 6, 4, 5, -20883159039649827547592551186163840321165721600000⟩, + ⟨4, 5, 7, 6, 5, 5, 22207448150348630869078020416668461299033702400000⟩, + ⟨4, 5, 8, 6, 6, 5, 3679089062737644304396400785031006864906649600000⟩, + ⟨4, 5, 3, 7, 0, 5, 54265190354239313025100411637245059434511178137600000⟩, + ⟨4, 5, 4, 7, 1, 5, 925091695024789796721450291834335685698283110400000⟩, + ⟨4, 5, 5, 7, 2, 5, 41148313830225270955173837232615458482631475200000⟩, + ⟨4, 5, 6, 7, 3, 5, -105422166130107298567075734662133111929910067200000⟩, + ⟨4, 5, 7, 7, 4, 5, 17268279240904109086757107567117140542619648000000⟩, + ⟨4, 5, 8, 7, 5, 5, 9503476462757369123533359604645795448487936000000⟩ +] + +def collectedFourData_9_4_32 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 4, 6, 7105921119476529029727528628806701637345214464000000⟩, + ⟨4, 6, 1, 0, 5, 6, -11777390186168141170338864624262681778409229516800000⟩, + ⟨4, 6, 2, 0, 6, 6, 3350034073734878711760502878779249593133354188800000⟩, + ⟨4, 6, 3, 0, 7, 6, -239380645357528849597162558119735551816053555200000⟩, + ⟨4, 6, 4, 0, 8, 6, 184778986748842336122882616532500885499270922240000⟩, + ⟨4, 6, 0, 1, 3, 6, 5584988988183412456190766241455534111296638156800000⟩, + ⟨4, 6, 1, 1, 4, 6, -5144545255420402577465621791506865307976204288000000⟩, + ⟨4, 6, 2, 1, 5, 6, -1635780062772817257429392188780617964064656588800000⟩, + ⟨4, 6, 3, 1, 6, 6, 1135072534472804012410145893771777674328827494400000⟩, + ⟨4, 6, 4, 1, 7, 6, -215498073280600517540656837612221533630433853440000⟩, + ⟨4, 6, 5, 1, 8, 6, -176301895704218547396643440848716422199640064000000⟩, + ⟨4, 6, 0, 2, 2, 6, 4658988827061048614331522003208199461745668915200000⟩, + ⟨4, 6, 1, 2, 3, 6, -7770515706750816410562569948386078900501453209600000⟩, + ⟨4, 6, 2, 2, 4, 6, -6026422056189938488347914542475325684989716070400000⟩, + ⟨4, 6, 3, 2, 5, 6, 483029322363438772675435368751887943542924902400000⟩, + ⟨4, 6, 4, 2, 6, 6, 142076416418977441060125131449814732095723929600000⟩, + ⟨4, 6, 5, 2, 7, 6, -90370309582007512265180695089615797516186419200000⟩, + ⟨4, 6, 6, 2, 8, 6, 22884212260892755410856159813548628262466355200000⟩, + ⟨4, 6, 0, 3, 1, 6, 14934572244854971008598625161894854506491517337600000⟩, + ⟨4, 6, 1, 3, 2, 6, 20023151005381368215550062072577459151219300761600000⟩, + ⟨4, 6, 2, 3, 3, 6, 6864682022541586595433389053185519420237152256000000⟩, + ⟨4, 6, 3, 3, 4, 6, -52630242636006441821228190384780441247599820800000⟩, + ⟨4, 6, 4, 3, 5, 6, 389814341780105885000605213565227180124421488640000⟩, + ⟨4, 6, 5, 3, 6, 6, 61832719225710344927177085204928755518983372800000⟩, + ⟨4, 6, 6, 3, 7, 6, 48520651850005205249401762307396991555993600000⟩, + ⟨4, 6, 7, 3, 8, 6, -970713552766967988626945018970933692674867200000⟩, + ⟨4, 6, 0, 4, 0, 6, 47692474536298523641483275745784749019432484864000000⟩, + ⟨4, 6, 1, 4, 1, 6, -9014589428519964387932543360065541503040933068800000⟩, + ⟨4, 6, 2, 4, 2, 6, -1636784454248812298160370517711463967541428224000000⟩, + ⟨4, 6, 3, 4, 3, 6, -777241875945237040337014282371658438230304358400000⟩, + ⟨4, 6, 4, 4, 4, 6, -292152512114763193870796543532394716495190425600000⟩, + ⟨4, 6, 5, 4, 5, 6, 37492382884541150958331534155288680816915251200000⟩, + ⟨4, 6, 6, 4, 6, 6, 9805480626776148956507427245300426267531673600000⟩, + ⟨4, 6, 7, 4, 7, 6, -2567617765214640304743297441236736568354406400000⟩, + ⟨4, 6, 8, 4, 8, 6, 305587555230207696925270684481100661653504000000⟩, + ⟨4, 6, 1, 5, 0, 6, -47512397589148842603124430452413986489255539507200000⟩, + ⟨4, 6, 2, 5, 1, 6, 1695221119934409749743500273249138559513578700800000⟩, + ⟨4, 6, 3, 5, 2, 6, -970532181899019132572994866458615537682979225600000⟩, + ⟨4, 6, 4, 5, 3, 6, -278387425015976963160448328465110427793390305280000⟩, + ⟨4, 6, 5, 5, 4, 6, 24870071098900868142043559450940232417306214400000⟩, + ⟨4, 6, 6, 5, 5, 6, 8191315082490699808726007868663293513878732800000⟩, + ⟨4, 6, 7, 5, 6, 6, 813416330684302998699881122211764258209792000000⟩, + ⟨4, 6, 8, 5, 7, 6, -501011480615372748489114263150431369061990400000⟩, + ⟨4, 6, 2, 6, 0, 6, -30517507479104835791376895601458353299931738931200000⟩, + ⟨4, 6, 3, 6, 1, 6, -236287646789990312624689388261265876699630796800000⟩, + ⟨4, 6, 4, 6, 2, 6, 352604827863261829171756682199488741251303342080000⟩, + ⟨4, 6, 5, 6, 3, 6, -226629850183034418798438827784768094548158054400000⟩, + ⟨4, 6, 6, 6, 4, 6, -5461627019540602727503312668155029555563724800000⟩, + ⟨4, 6, 7, 6, 5, 6, 5081975327337580266327425214581038769818828800000⟩, + ⟨4, 6, 8, 6, 6, 6, 748379141081266455513193823947074182735462400000⟩, + ⟨4, 6, 3, 7, 0, 6, 24836204200183360764179292139097272885887526502400000⟩, + ⟨4, 6, 4, 7, 1, 6, 338718299396651987979192373761217301634015559680000⟩, + ⟨4, 6, 5, 7, 2, 6, 12555230073021886698791549148698936882705203200000⟩, + ⟨4, 6, 6, 7, 3, 6, -27571333910807917851492665525784531699341721600000⟩, + ⟨4, 6, 7, 7, 4, 6, 3951690822543819401023155884166526613323776000000⟩, + ⟨4, 6, 8, 7, 5, 6, 1933142533709726395227386861096080175529984000000⟩ +] + +def collectedFourData_9_4_33 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 4, 7, -7442894437936607809879337177339858616733138944000000⟩, + ⟨4, 7, 1, 0, 5, 7, 8223927664097827660881869369654048057778713395200000⟩, + ⟨4, 7, 2, 0, 6, 7, -1754448829016571655603416269966234983671948902400000⟩, + ⟨4, 7, 3, 0, 7, 7, 100292972236791633928540241843000404870881607680000⟩, + ⟨4, 7, 4, 0, 8, 7, -64513826783647819248375514668941031551721799680000⟩, + ⟨4, 7, 0, 1, 3, 7, -5849837449243982558558633155784526203215203532800000⟩, + ⟨4, 7, 1, 1, 4, 7, 3592338147626609812236056966153864175924805632000000⟩, + ⟨4, 7, 2, 1, 5, 7, 856675589708508215644509002974727866702784102400000⟩, + ⟨4, 7, 3, 1, 6, 7, -475559743005117727091181418398037604763130920960000⟩, + ⟨4, 7, 4, 1, 7, 7, 75239103842101827822485251366888393934981038080000⟩, + ⟨4, 7, 5, 1, 8, 7, 52760683736111914443234148468039671909187584000000⟩, + ⟨4, 7, 0, 2, 2, 7, -4879924987106524225028003675579781667030774579200000⟩, + ⟨4, 7, 1, 2, 3, 7, 5426003390811186243944853408440977771697956454400000⟩, + ⟨4, 7, 2, 2, 4, 7, 3156101964018061325490779356074392767912162099200000⟩, + ⟨4, 7, 3, 2, 5, 7, -202374115689253224122878703479044064082562908160000⟩, + ⟨4, 7, 4, 2, 6, 7, -49604630267585083575161882278882557587305267200000⟩, + ⟨4, 7, 5, 2, 7, 7, 27044515340833818860046151600699576507642675200000⟩, + ⟨4, 7, 6, 2, 8, 7, -5992353886617119774632592399108252153728204800000⟩, + ⟨4, 7, 0, 3, 1, 7, -15642791810554470382338631235439133403328911769600000⟩, + ⟨4, 7, 1, 3, 2, 7, -13981785681938104649323633042819275324656084582400000⟩, + ⟨4, 7, 2, 3, 3, 7, -3595107712618548410798614982574996664602329088000000⟩, + ⟨4, 7, 3, 3, 4, 7, 22050418719629319117536622335364964597597470720000⟩, + ⟨4, 7, 4, 3, 5, 7, -136099972003667230822128531499207386924035604480000⟩, + ⟨4, 7, 5, 3, 6, 7, -18504262422025954284306747269812164091497676800000⟩, + ⟨4, 7, 6, 3, 7, 7, -12705393280740004197668886880321752426086400000⟩, + ⟨4, 7, 7, 3, 8, 7, 225943606473207016268930278036565627869593600000⟩, + ⟨4, 7, 0, 4, 0, 7, -49954122412746275071821733622060909029012537344000000⟩, + ⟨4, 7, 1, 4, 1, 7, 6294716419326651059645800916107170135758025523200000⟩, + ⟨4, 7, 2, 4, 2, 7, 857201600313221002771537049135007881811197952000000⟩, + ⟨4, 7, 3, 4, 3, 7, 325639935379996299631221518894367220701918658560000⟩, + ⟨4, 7, 4, 4, 4, 7, 102002272512718430487472501296148439052268339200000⟩, + ⟨4, 7, 5, 4, 5, 7, -11220093510526889428546735436836564397929267200000⟩, + ⟨4, 7, 6, 4, 6, 7, -2567617765214640304743297441236736568354406400000⟩, + ⟨4, 7, 7, 4, 7, 7, 597639557275802333575784059284385099363123200000⟩, + ⟨4, 7, 8, 4, 8, 7, -64015794064798480672961336663931980926156800000⟩, + ⟨4, 7, 1, 5, 0, 7, 33177003966457334059594795810987866256185281740800000⟩, + ⟨4, 7, 2, 5, 1, 7, -887805509833886693562073106476616814216767078400000⟩, + ⟨4, 7, 3, 5, 2, 7, 406622502954371512037292531418509778416083927040000⟩, + ⟨4, 7, 4, 5, 3, 7, 97196323197929886979626760173271232306699304960000⟩, + ⟨4, 7, 5, 5, 4, 7, -7442699073100940131408892282830434364450406400000⟩, + ⟨4, 7, 6, 5, 5, 7, -2144939848113158141977745932694322012173107200000⟩, + ⟨4, 7, 7, 5, 6, 7, -189331053218677351770046102424947833962496000000⟩, + ⟨4, 7, 8, 5, 7, 7, 104954037617835093320701115461657268248903680000⟩, + ⟨4, 7, 2, 6, 0, 7, 15982346472532388645825056714014236127199336857600000⟩, + ⟨4, 7, 3, 6, 1, 7, 98997102978024835398391408156054174496320389120000⟩, + ⟨4, 7, 4, 6, 2, 7, -123108623919277705737259000541964925602952642560000⟩, + ⟨4, 7, 5, 6, 3, 7, 67821992514079322781638340827403654860793446400000⟩, + ⟨4, 7, 6, 6, 4, 7, 1430156368271705013813653964623160672465715200000⟩, + ⟨4, 7, 7, 6, 5, 7, -1182882252126296496161803835999748960446054400000⟩, + ⟨4, 7, 8, 6, 6, 7, -156773677978341148868927885190929601087406080000⟩, + ⟨4, 7, 3, 7, 0, 7, -10405589535427891896398795820893900425266368348160000⟩, + ⟨4, 7, 4, 7, 1, 7, -118260274505289620788772651304720794998548725760000⟩, + ⟨4, 7, 5, 7, 2, 7, -3757319344019842163087937537197748455158579200000⟩, + ⟨4, 7, 6, 7, 3, 7, 7219701864153343218567374843133732300678758400000⟩, + ⟨4, 7, 7, 7, 4, 7, -919796858267380741690202875988179773554688000000⟩, + ⟨4, 7, 8, 7, 5, 7, -404963003950337569678063916377637821140172800000⟩ +] + +def collectedFourData_9_4_34 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 4, 8, 2657470219211649760568177501807114936930795520000000⟩, + ⟨4, 8, 1, 0, 5, 8, -2202252400043740782550044752778725667700211712000000⟩, + ⟨4, 8, 2, 0, 6, 8, 375853417225262642557969415004779725481784115200000⟩, + ⟨4, 8, 3, 0, 7, 8, -17904700190090523701650332492943122620429107200000⟩, + ⟨4, 8, 4, 0, 8, 8, 9871941324201838757746567805942187842705817600000⟩, + ⟨4, 8, 0, 1, 3, 8, 2088672483295984364326562047527338217647898624000000⟩, + ⟨4, 8, 1, 1, 4, 8, -961977735032431994039887068351732597569617920000000⟩, + ⟨4, 8, 2, 1, 5, 8, -183524559120879636773200461738621466968273715200000⟩, + ⟨4, 8, 3, 1, 6, 8, 84898816248857422924396908197980419557582438400000⟩, + ⟨4, 8, 4, 1, 7, 8, -11513129129754602324981290816393242146871705600000⟩, + ⟨4, 8, 5, 1, 8, 8, -7064285286277966636732230652608720163307520000000⟩, + ⟨4, 8, 0, 2, 2, 8, 1742367224654279657820807651704126789790990336000000⟩, + ⟨4, 8, 1, 2, 3, 8, -1453007550422110103460939996959963531930763264000000⟩, + ⟨4, 8, 2, 2, 4, 8, -676127846346179589649824992211303383109835161600000⟩, + ⟨4, 8, 3, 2, 5, 8, 36128631815754907310216857299409410506253926400000⟩, + ⟨4, 8, 4, 2, 6, 8, 7590527857734338969847535284933986095202304000000⟩, + ⟨4, 8, 5, 2, 7, 8, -3621070810081395803235320468743587423584256000000⟩, + ⟨4, 8, 6, 2, 8, 8, 713185895149187208789234941095110537904128000000⟩, + ⟨4, 8, 0, 3, 1, 8, 5585226786234106712720265599902690058403053568000000⟩, + ⟨4, 8, 1, 3, 2, 8, 3744125961779510464540382674326830318767570944000000⟩, + ⟨4, 8, 2, 3, 3, 8, 770175508531640291072859730874076644165812224000000⟩, + ⟨4, 8, 3, 3, 4, 8, -3936528427024634527905500961809619818958028800000⟩, + ⟨4, 8, 4, 3, 5, 8, 20826092712675167134310095300012736442374553600000⟩, + ⟨4, 8, 5, 3, 6, 8, 2477590878373581215101537103000381165666304000000⟩, + ⟨4, 8, 6, 3, 7, 8, 1512144885231808855381619986967040098304000000⟩, + ⟨4, 8, 7, 3, 8, 8, -24201810616715542216377159890758497887846400000⟩, + ⟨4, 8, 0, 4, 0, 8, 17836017122866669124596777348481478750130667520000000⟩, + ⟨4, 8, 1, 4, 1, 8, -1685636706482096023222962764526531875168059392000000⟩, + ⟨4, 8, 2, 4, 2, 8, -183637245726500871726014664913902394404765696000000⟩, + ⟨4, 8, 3, 4, 3, 8, -58134536078295833280370421045458645142627942400000⟩, + ⟨4, 8, 4, 4, 4, 8, -15608443947337417878231583124237192836153344000000⟩, + ⟨4, 8, 5, 4, 5, 8, 1502291780248999512438997279272950632022016000000⟩, + ⟨4, 8, 6, 4, 6, 8, 305587555230207696925270684481100661653504000000⟩, + ⟨4, 8, 7, 4, 7, 8, -64015794064798480672961336663931980926156800000⟩, + ⟨4, 8, 8, 4, 8, 8, 6233647689262656334782105875822791360512000000⟩, + ⟨4, 8, 1, 5, 0, 8, -8884336000468283999377449982873103441432936448000000⟩, + ⟨4, 8, 2, 5, 1, 8, 190193483664909448595570774484060187261088563200000⟩, + ⟨4, 8, 3, 5, 2, 8, -72591866045739212675382100834770743996291481600000⟩, + ⟨4, 8, 4, 5, 3, 8, -14873034934913028957717237773501113918763827200000⟩, + ⟨4, 8, 5, 5, 4, 8, 996525174223911733739261584339678047240192000000⟩, + ⟨4, 8, 6, 5, 5, 8, 255282126950838879590181946976735374344192000000⟩, + ⟨4, 8, 7, 5, 6, 8, 20280079464895523397622359664633162235904000000⟩, + ⟨4, 8, 8, 5, 7, 8, -10220079335623924686420561316012811825971200000⟩, + ⟨4, 8, 2, 6, 0, 8, -3423878449818658793089646486180789437548252364800000⟩, + ⟨4, 8, 3, 6, 1, 8, -17673356457361234323143231895467270450498764800000⟩, + ⟨4, 8, 4, 6, 2, 8, 18838149470035551206512148328954738632766259200000⟩, + ⟨4, 8, 5, 6, 3, 8, -9080888833806690762876560996350919958331392000000⟩, + ⟨4, 8, 6, 6, 4, 8, -170211467648312003850213512488025768067072000000⟩, + ⟨4, 8, 7, 6, 5, 8, 126703705825946279346624603829609625655705600000⟩, + ⟨4, 8, 8, 6, 6, 8, 15266105650078692180721659253092408046387200000⟩, + ⟨4, 8, 3, 7, 0, 8, 1857647218721411706370616163204002399016871526400000⟩, + ⟨4, 8, 4, 7, 1, 8, 18096252371067452483668169600622364189733683200000⟩, + ⟨4, 8, 5, 7, 2, 8, 503078691901784772090799732244812583141376000000⟩, + ⟨4, 8, 6, 7, 3, 8, -859259922581646971209140402246276008116224000000⟩, + ⟨4, 8, 7, 7, 4, 8, 98523475468542784186683367982083721920512000000⟩, + ⟨4, 8, 8, 7, 5, 8, 39433966737280875229784570380787700989952000000⟩ +] + +def collectedFourData_9_4_35 : List CollectedFourTerm := [ + ⟨5, 0, 4, 0, 8, 1, -42635498688827818376576451922515108363003368570880000⟩, + ⟨5, 0, 4, 1, 7, 1, 49723553432449632416257194354589011711349783265280000⟩, + ⟨5, 0, 5, 1, 8, 1, 244077079609231979915055779610277066652944171008000000⟩, + ⟨5, 0, 4, 2, 6, 1, -32782401140548622564713274073066692373092971315200000⟩, + ⟨5, 0, 5, 2, 7, 1, 125111083792111488595312363028308517611133888102400000⟩, + ⟨5, 0, 6, 2, 8, 1, -110885313309877913645497964335530557145507849830400000⟩, + ⟨5, 0, 4, 3, 5, 1, -89944907428474734236974162311720285183621652807680000⟩, + ⟨5, 0, 5, 3, 6, 1, -85602877227302966841817526020885851378445556121600000⟩, + ⟨5, 0, 6, 3, 7, 1, -235106527637907951087672524068690107204580147200000⟩, + ⟨5, 0, 7, 3, 8, 1, 12542897866946085793940765555679626893929637478400000⟩, + ⟨5, 0, 4, 4, 4, 1, 67410630756068794863443042877633922664630530867200000⟩, + ⟨5, 0, 5, 4, 5, 1, -51905461852790454066111908095567010602498287206400000⟩, + ⟨5, 0, 6, 4, 6, 1, -47512397589148842603124430452413986489255539507200000⟩, + ⟨5, 0, 7, 4, 7, 1, 33177003966457334059594795810987866256185281740800000⟩, + ⟨5, 0, 8, 4, 8, 1, -8884336000468283999377449982873103441432936448000000⟩, + ⟨5, 0, 4, 5, 3, 1, 64234504707982983805741115931277218488453022351360000⟩, + ⟨5, 0, 5, 5, 4, 1, -34430794400972732846236450997642355800347036876800000⟩, + ⟨5, 0, 6, 5, 5, 1, -39690968121900970739457525919429148792193653145600000⟩, + ⟨5, 0, 7, 5, 6, 1, -10510410542839632266125849555227659414928359424000000⟩, + ⟨5, 0, 8, 5, 7, 1, 14565888753309650385233296283731185817002757324800000⟩, + ⟨5, 0, 4, 6, 2, 1, -81359265685726816012973177758141326643629612072960000⟩, + ⟨5, 0, 5, 6, 3, 1, 313752451520742377610718108330725516245778353356800000⟩, + ⟨5, 0, 6, 6, 4, 1, 26464280978480502240151115997244007531947858329600000⟩, + ⟨5, 0, 7, 6, 5, 1, -65665815946877388261856478487216756393470695833600000⟩, + ⟨5, 0, 8, 6, 6, 1, -21757599847608524247673907787726711568967978188800000⟩, + ⟨5, 0, 4, 7, 1, 1, -78155118522417277057224427503173088706530807644160000⟩, + ⟨5, 0, 5, 7, 2, 1, -17381797727157737797570853803498785094259598950400000⟩, + ⟨5, 0, 6, 7, 3, 1, 133596733163317035066747782578547099341646148403200000⟩, + ⟨5, 0, 7, 7, 4, 1, -51061051169658651157954506855654023089537155072000000⟩, + ⟨5, 0, 8, 7, 5, 1, -56202183342628662645776897595662701165132382208000000⟩ +] + +def collectedFourData_9_4_36 : List CollectedFourTerm := [ + ⟨5, 1, 3, 0, 7, 2, -1182438216106181205260832153565131753170046812160000⟩, + ⟨5, 1, 4, 0, 8, 2, 4563646637740527456562228787813603787160902696960000⟩, + ⟨5, 1, 3, 1, 6, 2, 5606773850945889304628399569739876266627584491520000⟩, + ⟨5, 1, 4, 1, 7, 2, -5322342517784890023431777130469383822240393461760000⟩, + ⟨5, 1, 5, 1, 8, 2, -13062841739436244229065349884257822364472967168000000⟩, + ⟨5, 1, 3, 2, 5, 2, 2385958686882780423224639669601027042546989137920000⟩, + ⟨5, 1, 4, 2, 6, 2, 3508984281713795540712044554830043713118824038400000⟩, + ⟨5, 1, 5, 2, 7, 2, -6695861364951710454771668427393149806334862950400000⟩, + ⟨5, 1, 6, 2, 8, 2, 3956338441156250963936092388787632783811516825600000⟩, + ⟨5, 1, 3, 3, 4, 2, -259970935088790606595901374000338137923599728640000⟩, + ⟨5, 1, 4, 3, 5, 2, 9627582343147373833834797480331170551840699842560000⟩, + ⟨5, 1, 5, 3, 6, 2, 4581408624893896323208645106699470809735993753600000⟩, + ⟨5, 1, 6, 3, 7, 2, 8388495872859286401376629648291273166867660800000⟩, + ⟨5, 1, 7, 3, 8, 2, -335643744287966013852237319446532628921135923200000⟩, + ⟨5, 1, 3, 4, 3, 2, -3839243126373344430349408729596240741708563742720000⟩, + ⟨5, 1, 4, 4, 4, 2, -7215543569530591868713465432628894180198213222400000⟩, + ⟨5, 1, 5, 4, 5, 2, 2777945535405778993915147499194655723649132134400000⟩, + ⟨5, 1, 6, 4, 6, 2, 1695221119934409749743500273249138559513578700800000⟩, + ⟨5, 1, 7, 4, 7, 2, -887805509833886693562073106476616814216767078400000⟩, + ⟨5, 1, 8, 4, 8, 2, 190193483664909448595570774484060187261088563200000⟩, + ⟨5, 1, 3, 5, 2, 2, -4794014738009906263956378498488057115986865684480000⟩, + ⟨5, 1, 4, 5, 3, 2, -6875575294122918314655437095067532371734686597120000⟩, + ⟨5, 1, 5, 5, 4, 2, 1842713043531361813201491851704676808657784012800000⟩, + ⟨5, 1, 6, 5, 5, 2, 1416156010747326533257139364694926581886772838400000⟩, + ⟨5, 1, 7, 5, 6, 2, 281255064501401096903348885632530251306237952000000⟩, + ⟨5, 1, 8, 5, 7, 2, -311822642065931059971649043329796964534787768320000⟩, + ⟨5, 1, 3, 6, 1, 2, -1167160123329896461979232751219443006073932349440000⟩, + ⟨5, 1, 4, 6, 2, 2, 8708586757846446060834897842058540438268485304320000⟩, + ⟨5, 1, 5, 6, 3, 2, -16791820953189487838633412072104358287069990092800000⟩, + ⟨5, 1, 6, 6, 4, 2, -944233722459938389539936336341672592864077414400000⟩, + ⟨5, 1, 7, 6, 5, 2, 1757195232707469892977214022489135422471195852800000⟩, + ⟨5, 1, 8, 6, 6, 2, 465780865445166688662761199966439437460486225920000⟩, + ⟨5, 1, 3, 7, 0, 2, 122680248210760439967369248367325346133708814417920000⟩, + ⟨5, 1, 4, 7, 1, 2, 8365619139820316986513531098662389103324792094720000⟩, + ⟨5, 1, 5, 7, 2, 2, 930262166444595473813705357015059564832646758400000⟩, + ⟨5, 1, 6, 7, 3, 2, -4766671755256163065423253622208827822791511244800000⟩, + ⟨5, 1, 7, 7, 4, 2, 1366376620751074744899953960770936216020320256000000⟩, + ⟨5, 1, 8, 7, 5, 2, 1203161276086932021277069597872286407020720947200000⟩ +] + +def collectedFourData_9_4_37 : List CollectedFourTerm := [ + ⟨5, 2, 2, 0, 6, 3, -9473756864792812193285190537478332810622434017280000⟩, + ⟨5, 2, 3, 0, 7, 3, 2707833988955300012626320016170750765202648596480000⟩, + ⟨5, 2, 4, 0, 8, 3, -5225472803115863375476737218314303521556990525440000⟩, + ⟨5, 2, 2, 1, 5, 3, 4625917903488053912358913432503993750552607457280000⟩, + ⟨5, 2, 3, 1, 6, 3, -12839751451854069518802334117007463950206956994560000⟩, + ⟨5, 2, 4, 1, 7, 3, 6094195778777872080785304908284042742527049072640000⟩, + ⟨5, 2, 5, 1, 8, 3, 9971488396484946094525741017462990446335623168000000⟩, + ⟨5, 2, 2, 2, 4, 3, 17042470634131993637464985942753623087635486474240000⟩, + ⟨5, 2, 3, 2, 5, 3, -5463947241032152551909155643443416500893657333760000⟩, + ⟨5, 2, 4, 2, 6, 3, -4017861895577160686491948596226167617709775257600000⟩, + ⟨5, 2, 5, 2, 7, 3, 5111269449396953450913216691440506047111259750400000⟩, + ⟨5, 2, 6, 2, 8, 3, -2265045978057957003207366313495781063397684019200000⟩, + ⟨5, 2, 2, 3, 3, 3, -19413034913751737311256455339459820835793639833600000⟩, + ⟨5, 2, 3, 3, 4, 3, 595344538585773211575415806972648642641311825920000⟩, + ⟨5, 2, 4, 3, 5, 3, -11023787266488065392999745838303795816290939043840000⟩, + ⟨5, 2, 5, 3, 6, 3, -3497207105002950975487358640502513438905964953600000⟩, + ⟨5, 2, 6, 3, 7, 3, -4802503405958060279886252444028777189185945600000⟩, + ⟨5, 2, 7, 3, 8, 3, 153727700370868382406448184151836856764250193920000⟩, + ⟨5, 2, 2, 4, 2, 3, 4628758280759213706133978829390122372693386854400000⟩, + ⟨5, 2, 3, 4, 3, 3, 8792030642997419682913023187373920749067865948160000⟩, + ⟨5, 2, 4, 4, 4, 3, 8261951390028592757415498261068294544858651033600000⟩, + ⟨5, 2, 5, 4, 5, 3, -2120537952223660005500283488722406903072056934400000⟩, + ⟨5, 2, 6, 4, 6, 3, -970532181899019132572994866458615537682979225600000⟩, + ⟨5, 2, 7, 4, 7, 3, 406622502954371512037292531418509778416083927040000⟩, + ⟨5, 2, 8, 4, 8, 3, -72591866045739212675382100834770743996291481600000⟩, + ⟨5, 2, 2, 5, 1, 3, -4794014738009906263956378498488057115986865684480000⟩, + ⟨5, 2, 3, 5, 2, 3, 10978498389441560311546797314540082628432169533440000⟩, + ⟨5, 2, 4, 5, 3, 3, 7872680458669948226703185692348915200818864455680000⟩, + ⟨5, 2, 5, 5, 4, 3, -1406630509512505947539619644889013296145681612800000⟩, + ⟨5, 2, 6, 5, 5, 3, -810764428815747558876807609454884072738049228800000⟩, + ⟨5, 2, 7, 5, 6, 3, -128817220696851917669254836549753503881573171200000⟩, + ⟨5, 2, 8, 5, 7, 3, 119014526821324731770768849235016947788320604160000⟩, + ⟨5, 2, 2, 6, 0, 3, 86302240399067650750352229197357184009351431454720000⟩, + ⟨5, 2, 3, 6, 1, 3, 2672846504330292546562374486761425029189410488320000⟩, + ⟨5, 2, 4, 6, 2, 3, -9971517706995808832792527296418777006395076116480000⟩, + ⟨5, 2, 5, 6, 3, 3, 12817995588592959876755354868857758612909247692800000⟩, + ⟨5, 2, 6, 6, 4, 3, 540583882601187687292598123974957371543571660800000⟩, + ⟨5, 2, 7, 6, 5, 3, -804810418260065127089251181909591958398624071680000⟩, + ⟨5, 2, 8, 6, 6, 3, -177776344065684152646494057845131258417339432960000⟩, + ⟨5, 2, 3, 7, 0, 3, -280943005185091956156855389166630093218572413173760000⟩, + ⟨5, 2, 4, 7, 1, 3, -9578812464323410752335548349160379099818051502080000⟩, + ⟨5, 2, 5, 7, 2, 3, -710113356911232230202792790811426376938579558400000⟩, + ⟨5, 2, 6, 7, 3, 3, 2728970447940257560541990110015268891146164633600000⟩, + ⟨5, 2, 7, 7, 4, 3, -625812157453374872839517584448166629194963353600000⟩, + ⟨5, 2, 8, 7, 5, 3, -459215113484128976363999992214846261746571673600000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0918.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0918.lean new file mode 100644 index 0000000000000000000000000000000000000000..a73439a00bad4200606577880b92f1e33bb1a108 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0918.lean @@ -0,0 +1,619 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0918. -/ +namespace LaughlinFock +def collectedFourData_9_4_38 : List CollectedFourTerm := [ + ⟨5, 3, 1, 0, 5, 4, 15922472107236855273105772643336328753071354019840000⟩, + ⟨5, 3, 2, 0, 6, 4, -13587260824554072778913748358172042049404346040320000⟩, + ⟨5, 3, 3, 0, 7, 4, 1941787571847980028779025643748692900352423362560000⟩, + ⟨5, 3, 4, 0, 8, 4, -2498124131072179828790889670708951579465214853120000⟩, + ⟨5, 3, 1, 1, 4, 4, 6955180820115151021190110912119457635394545254400000⟩, + ⟨5, 3, 2, 1, 5, 4, 6634490836602352330720472149451962205241417400320000⟩, + ⟨5, 3, 3, 1, 6, 4, -9207384904879728168605911122966365198526783160320000⟩, + ⟨5, 3, 4, 1, 7, 4, 2913431589456434096303595827885207040824149278720000⟩, + ⟨5, 3, 5, 1, 8, 4, 3575276830133703054479399651081480333162446848000000⟩, + ⟨5, 3, 1, 2, 3, 4, 10505368137067796441192675574164537783995575828480000⟩, + ⟨5, 3, 2, 2, 4, 4, 24442309097175568255629280146027529583832135106560000⟩, + ⟨5, 3, 3, 2, 5, 4, -3918196200042024251302849205953869761634600222720000⟩, + ⟨5, 3, 4, 2, 6, 4, -1920805663876338203815298613471003327054269644800000⟩, + ⟨5, 3, 5, 2, 7, 4, 1832645489658396951959921230042950845988234854400000⟩, + ⟨5, 3, 6, 2, 8, 4, -649705727573655620390803602316163073574919208960000⟩, + ⟨5, 3, 1, 3, 2, 4, -27070349062274397421972069606786811307470440366080000⟩, + ⟨5, 3, 2, 3, 3, 4, -27842172068988176634838724366384850355091826278400000⟩, + ⟨5, 3, 3, 3, 4, 4, 426921528686265414023179865970385228212197130240000⟩, + ⟨5, 3, 4, 3, 5, 4, -5270104739574786900874025238286236677111619256320000⟩, + ⟨5, 3, 5, 3, 6, 4, -1253923490208705817458086750912718825921812889600000⟩, + ⟨5, 3, 6, 3, 7, 4, -1377549948111076308432516316962669162953441280000⟩, + ⟨5, 3, 7, 3, 8, 4, 36746041208147586819246143577669932318541742080000⟩, + ⟨5, 3, 1, 4, 1, 4, 12187296715563888168143590709687451957654391357440000⟩, + ⟨5, 3, 2, 4, 2, 4, 6638564505303604912550917444529945523911235993600000⟩, + ⟨5, 3, 3, 4, 3, 4, 6304764584355328815669506210194554903651176939520000⟩, + ⟨5, 3, 4, 4, 4, 4, 3949763191738141687990304869781253918747839692800000⟩, + ⟨5, 3, 5, 4, 5, 4, -760318811650724339719741018430361391698699878400000⟩, + ⟨5, 3, 6, 4, 6, 4, -278387425015976963160448328465110427793390305280000⟩, + ⟨5, 3, 7, 4, 7, 4, 97196323197929886979626760173271232306699304960000⟩, + ⟨5, 3, 8, 4, 8, 4, -14873034934913028957717237773501113918763827200000⟩, + ⟨5, 3, 1, 5, 0, 4, 64234504707982983805741115931277218488453022351360000⟩, + ⟨5, 3, 2, 5, 1, 4, -6875575294122918314655437095067532371734686597120000⟩, + ⟨5, 3, 3, 5, 2, 4, 7872680458669948226703185692348915200818864455680000⟩, + ⟨5, 3, 4, 5, 3, 4, 3763665752560558019044809043367822742140894576640000⟩, + ⟨5, 3, 5, 5, 4, 4, -504347322009825125912742715542138774964980940800000⟩, + ⟨5, 3, 6, 5, 5, 4, -232559647008232222288277403701402475928422973440000⟩, + ⟨5, 3, 7, 5, 6, 4, -30791606773703954268202933376232354300611788800000⟩, + ⟨5, 3, 8, 5, 7, 4, 24384374057286037394319539144792563054773534720000⟩, + ⟨5, 3, 2, 6, 0, 4, 123774661602648627820225290595706264548668006727680000⟩, + ⟨5, 3, 3, 6, 1, 4, 1916698048970223107706475853105434973264978903040000⟩, + ⟨5, 3, 4, 6, 2, 4, -4767049785888519822553468843458535577162392535040000⟩, + ⟨5, 3, 5, 6, 3, 4, 4595891888397246156594800035773804177743727820800000⟩, + ⟨5, 3, 6, 6, 4, 4, 155061066381147608325127772412690431797666775040000⟩, + ⟨5, 3, 7, 6, 5, 4, -192376498983491506341988620877858710307020472320000⟩, + ⟨5, 3, 8, 6, 6, 4, -36423829829970779976996419341914978491113144320000⟩, + ⟨5, 3, 3, 7, 0, 4, -201464210173572653323610399851051572993593148702720000⟩, + ⟨5, 3, 4, 7, 1, 4, -4579310517102448625730908626463112281504706723840000⟩, + ⟨5, 3, 5, 7, 2, 4, -254611120304584127786051273601808155187504742400000⟩, + ⟨5, 3, 6, 7, 3, 4, 782777810067333860642624980062483760849543495680000⟩, + ⟨5, 3, 7, 7, 4, 4, -149589952044187713098620024067028329060263526400000⟩, + ⟨5, 3, 8, 7, 5, 4, -94086607736272464125680863546558410235523891200000⟩ +] + +def collectedFourData_9_4_39 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 4, 5, 2574722825081172232617745110726481352545271808000000⟩, + ⟨5, 4, 1, 0, 5, 5, -8534717687507329912312851295644753108652995379200000⟩, + ⟨5, 4, 2, 0, 6, 5, 3641502227263787244631835696425470983102319820800000⟩, + ⟨5, 4, 3, 0, 7, 5, -346943795812973858307625951027109332629690777600000⟩, + ⟨5, 4, 4, 0, 8, 5, 334759327311997509207019160798929125581940326400000⟩, + ⟨5, 4, 0, 1, 3, 5, 2023636117531536590513503705180289115828623769600000⟩, + ⟨5, 4, 1, 1, 4, 5, -3728096012067675395031142006801179228160131072000000⟩, + ⟨5, 4, 2, 1, 5, 5, -1778100344889902157942051320301065490777558220800000⟩, + ⟨5, 4, 3, 1, 6, 5, 1645105321881285067837413035218176950410621747200000⟩, + ⟨5, 4, 4, 1, 7, 5, -390412304546839061679057801546515982716397158400000⟩, + ⟨5, 4, 5, 1, 8, 5, -383281919972822260387443726388566256200450048000000⟩, + ⟨5, 4, 0, 2, 2, 5, 1688113992984475843777138100720234183927424614400000⟩, + ⟨5, 4, 1, 2, 3, 5, -5631057203262884290810744265447080325254899302400000⟩, + ⟨5, 4, 2, 2, 4, 5, -6550748098983072070220871078050273155504039526400000⟩, + ⟨5, 4, 3, 2, 5, 5, 700073417963443055981645253407744963548230451200000⟩, + ⟨5, 4, 4, 2, 6, 5, 257396181374038758216832450113714344171667456000000⟩, + ⟨5, 4, 5, 2, 7, 5, -196465872512460882278983813635708223314355814400000⟩, + ⟨5, 4, 6, 2, 8, 5, 58042232465035354570045232587487973160570060800000⟩, + ⟨5, 4, 0, 3, 1, 5, 5411315914591030815596764137400511675946447667200000⟩, + ⟨5, 4, 1, 3, 2, 5, 14510170618781160067752499378767169861462681190400000⟩, + ⟨5, 4, 2, 3, 3, 5, 7461940483092885286583511225628737403770372096000000⟩, + ⟨5, 4, 3, 3, 4, 5, -76279083162391500524147093826072282902455910400000⟩, + ⟨5, 4, 4, 3, 5, 5, 706216594900203895513814436951426223309219430400000⟩, + ⟨5, 4, 5, 3, 6, 5, 134424892297988053031753549393114457922181529600000⟩, + ⟨5, 4, 6, 3, 7, 5, 123065059960389602817086926494580620027494400000⟩, + ⟨5, 4, 7, 3, 8, 5, -2813786754907142941112656435280154855682867200000⟩, + ⟨5, 4, 0, 4, 0, 5, 17280645353160959470467504601090710848938180608000000⟩, + ⟨5, 4, 1, 4, 1, 5, -6532599720739823181417763286669544490299241267200000⟩, + ⟨5, 4, 2, 4, 2, 5, -1779192122978237553522881123703170597161795584000000⟩, + ⟨5, 4, 3, 4, 3, 5, -1126487257574585382155872639625136935837840179200000⟩, + ⟨5, 4, 4, 4, 4, 5, -529285175489041715731214664729962371419734016000000⟩, + ⟨5, 4, 5, 4, 5, 5, 81508780373251901372389302834388735789262438400000⟩, + ⟨5, 4, 6, 4, 6, 5, 24870071098900868142043559450940232417306214400000⟩, + ⟨5, 4, 7, 4, 7, 5, -7442699073100940131408892282830434364450406400000⟩, + ⟨5, 4, 8, 4, 8, 5, 996525174223911733739261584339678047240192000000⟩, + ⟨5, 4, 1, 5, 0, 5, -34430794400972732846236450997642355800347036876800000⟩, + ⟨5, 4, 2, 5, 1, 5, 1842713043531361813201491851704676808657784012800000⟩, + ⟨5, 4, 3, 5, 2, 5, -1406630509512505947539619644889013296145681612800000⟩, + ⟨5, 4, 4, 5, 3, 5, -504347322009825125912742715542138774964980940800000⟩, + ⟨5, 4, 5, 5, 4, 5, 54067760091698406542434147475703967567891660800000⟩, + ⟨5, 4, 6, 5, 5, 5, 20775992146549315852077116141903979323011891200000⟩, + ⟨5, 4, 7, 5, 6, 5, 2357832638661130240033301780527131805089792000000⟩, + ⟨5, 4, 8, 5, 7, 5, -1633805253071577996613174869559569651282739200000⟩, + ⟨5, 4, 2, 6, 0, 5, -33172668996707740785344130880403576936945890099200000⟩, + ⟨5, 4, 3, 6, 1, 5, -342460991190807438689041442200084692460791398400000⟩, + ⟨5, 4, 4, 6, 2, 5, 638805077673193418726088417639271002410896588800000⟩, + ⟨5, 4, 5, 6, 3, 5, -492695349385446442042734502113430652249230540800000⟩, + ⟨5, 4, 6, 6, 4, 5, -13852564444493878446001096582429413075006259200000⟩, + ⟨5, 4, 7, 6, 5, 5, 14731013926886187494956755944252662212250828800000⟩, + ⟨5, 4, 8, 6, 6, 5, 2440474558558951938222358495542652756505395200000⟩, + ⟨5, 4, 3, 7, 0, 5, 35996088764520203493232875527135251579232531251200000⟩, + ⟨5, 4, 4, 7, 1, 5, 613647211998240857841177044920734655777131724800000⟩, + ⟨5, 4, 5, 7, 2, 5, 27295184030021749418456253380065772775564902400000⟩, + ⟨5, 4, 6, 7, 3, 5, -69930384929920012331921564144415911577020006400000⟩, + ⟨5, 4, 7, 7, 4, 5, 11454682243043967979947649700754289669963776000000⟩, + ⟨5, 4, 8, 7, 5, 5, 6304004097135136910845299229665354665951232000000⟩ +] + +def collectedFourData_9_4_40 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 4, 6, 5936153571300723196221046736154972523459510272000000⟩, + ⟨5, 5, 1, 0, 5, 6, -9838611439494043794146680022575806940317116006400000⟩, + ⟨5, 5, 2, 0, 6, 6, 2798555795430131828393757113909561480375068262400000⟩, + ⟨5, 5, 3, 0, 7, 6, -199974112989316071666861605122824962446039449600000⟩, + ⟨5, 5, 4, 0, 8, 6, 154360908831939425736240944108951502159630827520000⟩, + ⟨5, 5, 0, 1, 3, 6, 4665595321204815189935340997354290992220890726400000⟩, + ⟨5, 5, 1, 1, 4, 6, -4297656866324982871257553057377544188224077824000000⟩, + ⟨5, 5, 2, 1, 5, 6, -1366500063570464098729855228744794618863183462400000⟩, + ⟨5, 5, 3, 1, 6, 6, 948218361266085031740843762340410853468353331200000⟩, + ⟨5, 5, 4, 1, 7, 6, -180023059052377795321404352646060429458664325120000⟩, + ⟨5, 5, 5, 1, 8, 6, -147279305555925028400742478813811700318339072000000⟩, + ⟨5, 5, 0, 2, 2, 6, 3892032109476325991482409827541368879615416729600000⟩, + ⟨5, 5, 1, 2, 3, 6, -6491343456803704544929038940718006875036896460800000⟩, + ⟨5, 5, 2, 2, 4, 6, -5034360248239385516601160439237782245043548979200000⟩, + ⟨5, 5, 3, 2, 5, 6, 403513659774754583674192151494500551832580915200000⟩, + ⟨5, 5, 4, 2, 6, 6, 118687980424028595921551330309344222417571020800000⟩, + ⟨5, 5, 5, 2, 7, 6, -75493666049068752150586413668078023031232921600000⟩, + ⟨5, 5, 6, 2, 8, 6, 19117042823142053691928747030586068597053849600000⟩, + ⟨5, 5, 0, 3, 1, 6, 12476062269274859506284274943546262343327206604800000⟩, + ⟨5, 5, 1, 3, 2, 6, 16726965772741980018085257364509440126376266956800000⟩, + ⟨5, 5, 2, 3, 3, 6, 5734626942630067024042159286310000606773772288000000⟩, + ⟨5, 5, 3, 3, 4, 6, -43966320133478813488300976057210451073066598400000⟩, + ⟨5, 5, 4, 3, 5, 6, 325643608787016937313278784998315115561059614720000⟩, + ⟨5, 5, 5, 3, 6, 6, 51653896923918382526151085446039255766165094400000⟩, + ⟨5, 5, 6, 3, 7, 6, 40533244869803088672221838841123001126092800000⟩, + ⟨5, 5, 7, 3, 8, 6, -810915942645890360522318512999000603990425600000⟩, + ⟨5, 5, 0, 4, 0, 6, 39841401034813780830622851287865198973626089472000000⟩, + ⟨5, 5, 1, 4, 1, 6, -7530619370829800686076926652038924160385574502400000⟩, + ⟨5, 5, 2, 4, 2, 6, -1367339113420154969470527130878521599435210752000000⟩, + ⟨5, 5, 3, 4, 3, 6, -649293323142978925224295879623703675654058803200000⟩, + ⟨5, 5, 4, 4, 4, 6, -244058743264277467729994333658099283256986828800000⟩, + ⟨5, 5, 5, 4, 5, 6, 31320435284122377342160530466045512581224857600000⟩, + ⟨5, 5, 6, 4, 6, 6, 8191315082490699808726007868663293513878732800000⟩, + ⟨5, 5, 7, 4, 7, 6, -2144939848113158141977745932694322012173107200000⟩, + ⟨5, 5, 8, 4, 8, 6, 255282126950838879590181946976735374344192000000⟩, + ⟨5, 5, 1, 5, 0, 6, -39690968121900970739457525919429148792193653145600000⟩, + ⟨5, 5, 2, 5, 1, 6, 1416156010747326533257139364694926581886772838400000⟩, + ⟨5, 5, 3, 5, 2, 6, -810764428815747558876807609454884072738049228800000⟩, + ⟨5, 5, 4, 5, 3, 6, -232559647008232222288277403701402475928422973440000⟩, + ⟨5, 5, 5, 5, 4, 6, 20775992146549315852077116141903979323011891200000⟩, + ⟨5, 5, 6, 5, 5, 6, 6842871383317394637669868175832448388982374400000⟩, + ⟨5, 5, 7, 5, 6, 6, 679512785909120884746393693803439263318016000000⟩, + ⟨5, 5, 8, 5, 7, 6, -418535618382532684021987506814068456633139200000⟩, + ⟨5, 5, 2, 6, 0, 6, -25493754850832053965133270946140618594270681497600000⟩, + ⟨5, 5, 3, 6, 1, 6, -197390279847346931853746398775864967368697446400000⟩, + ⟨5, 5, 4, 6, 2, 6, 294559476946821468936349773796703918161227939840000⟩, + ⟨5, 5, 5, 6, 3, 6, -189322337232259111994987072182342563052860211200000⟩, + ⟨5, 5, 6, 6, 4, 6, -4562541040358020661443648670344709207909990400000⟩, + ⟨5, 5, 7, 6, 5, 6, 4245387118912949008126865728995953897530982400000⟩, + ⟨5, 5, 8, 6, 6, 6, 625181934378662541665576112292158720127795200000⟩, + ⟨5, 5, 3, 7, 0, 6, 20747700372915664649155942065891221931163857715200000⟩, + ⟨5, 5, 4, 7, 1, 6, 282958930843924718316628444936028495016508784640000⟩, + ⟨5, 5, 5, 7, 2, 6, 10488404329762879157339923831133614567430553600000⟩, + ⟨5, 5, 6, 7, 3, 6, -23032576566544273982893950542613957812473036800000⟩, + ⟨5, 5, 7, 7, 4, 6, 3301168588070092714429891986665959480885248000000⟩, + ⟨5, 5, 8, 7, 5, 6, 1614911108971004184896847783290597101535232000000⟩ +] + +def collectedFourData_9_4_41 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 4, 7, 2357894529862354367923554762117069742087864320000000⟩, + ⟨5, 6, 1, 0, 5, 7, -2605324341874686510367306694099066309528518656000000⟩, + ⟨5, 6, 2, 0, 6, 7, 555805988027479414715812296169976649505308672000000⟩, + ⟨5, 6, 3, 0, 7, 7, -31772619186350752963561170844902628178421350400000⟩, + ⟨5, 6, 4, 0, 8, 7, 20437855264788889162728699998232299102955110400000⟩, + ⟨5, 6, 0, 1, 3, 7, 1853217163990874544738470302198695186539741184000000⟩, + ⟨5, 6, 1, 1, 4, 7, -1138045761408498605529538300633512175164456960000000⟩, + ⟨5, 6, 2, 1, 5, 7, -271393166151136318223362204289494996507164672000000⟩, + ⟨5, 6, 3, 1, 6, 7, 150656404709856046026128109329419263602904268800000⟩, + ⟨5, 6, 4, 1, 7, 7, -23835602245921379081319482439226063881397862400000⟩, + ⟨5, 6, 5, 1, 8, 7, -16714482330836939986918046391976485999083520000000⟩, + ⟨5, 6, 0, 2, 2, 7, 1545950776164305831001213037693833367756210176000000⟩, + ⟨5, 6, 1, 2, 3, 7, -1718947355883115976368658498494243367899103232000000⟩, + ⟨5, 6, 2, 2, 4, 7, -999846984086623218201159779498056835741515776000000⟩, + ⟨5, 6, 3, 2, 5, 7, 64111727547449817357720384288215968277908684800000⟩, + ⟨5, 6, 4, 2, 6, 7, 15714650710027929904365631409496444754722816000000⟩, + ⟨5, 6, 5, 2, 7, 7, -8567650034091980201301348581250969743917056000000⟩, + ⟨5, 6, 6, 2, 8, 7, 1898366095082090047375992328321136899129344000000⟩, + ⟨5, 6, 0, 3, 1, 7, 4955606121978988994604745001414939744548159488000000⟩, + ⟨5, 6, 1, 3, 2, 7, 4429402600299305031634674386799660532154499072000000⟩, + ⟨5, 6, 2, 3, 3, 7, 1138923154229133678598826056872821026078064640000000⟩, + ⟨5, 6, 3, 3, 4, 7, -6985529905567533375315846959600739687176601600000⟩, + ⟨5, 6, 4, 3, 5, 7, 43116207300507164284759489271828259510052454400000⟩, + ⟨5, 6, 5, 3, 6, 7, 5862114464722726798730604132965615879061504000000⟩, + ⟨5, 6, 6, 3, 7, 7, 4025043961890720115709564153793129480192000000⟩, + ⟨5, 6, 7, 3, 8, 7, -71578496538269025273068192845294844510208000000⟩, + ⟨5, 6, 0, 4, 0, 7, 15825369144123293600433995179215985020575416320000000⟩, + ⟨5, 6, 1, 4, 1, 7, -1994153959313680431832563909461744530275434496000000⟩, + ⟨5, 6, 2, 4, 2, 7, -271559805291035998410892401891082611783106560000000⟩, + ⟨5, 6, 3, 4, 3, 7, -103162100274270140476204249310038329641454796800000⟩, + ⟨5, 6, 4, 4, 4, 7, -32314122200280014018580143920162216372862976000000⟩, + ⟨5, 6, 5, 4, 5, 7, 3554503873945817868071943233516491889442816000000⟩, + ⟨5, 6, 6, 4, 6, 7, 813416330684302998699881122211764258209792000000⟩, + ⟨5, 6, 7, 4, 7, 7, -189331053218677351770046102424947833962496000000⟩, + ⟨5, 6, 8, 4, 8, 7, 20280079464895523397622359664633162235904000000⟩, + ⟨5, 6, 1, 5, 0, 7, -10510410542839632266125849555227659414928359424000000⟩, + ⟨5, 6, 2, 5, 1, 7, 281255064501401096903348885632530251306237952000000⟩, + ⟨5, 6, 3, 5, 2, 7, -128817220696851917669254836549753503881573171200000⟩, + ⟨5, 6, 4, 5, 3, 7, -30791606773703954268202933376232354300611788800000⟩, + ⟨5, 6, 5, 5, 4, 7, 2357832638661130240033301780527131805089792000000⟩, + ⟨5, 6, 6, 5, 5, 7, 679512785909120884746393693803439263318016000000⟩, + ⟨5, 6, 7, 5, 6, 7, 59979710640791957219186481999110870138880000000⟩, + ⟨5, 6, 8, 5, 7, 7, -33249235663574364132959479499240033904230400000⟩, + ⟨5, 6, 2, 6, 0, 7, -5063176380665736387175958339251221830333104128000000⟩, + ⟨5, 6, 3, 6, 1, 7, -31362090317220358562989595904203683406649753600000⟩, + ⟨5, 6, 4, 6, 2, 7, 39000573411144626974205165708717581933530316800000⟩, + ⟨5, 6, 5, 6, 3, 7, -21485875755299166969783363110048822294740992000000⟩, + ⟨5, 6, 6, 6, 4, 7, -453070765105534226393869095404330607968256000000⟩, + ⟨5, 6, 7, 6, 5, 7, 374734804452376684663228672228539060191232000000⟩, + ⟨5, 6, 8, 6, 6, 7, 49665597277235124529484514428508252300902400000⟩, + ⟨5, 6, 3, 7, 0, 7, 3296470593553157424723336779376129841273031884800000⟩, + ⟨5, 6, 4, 7, 1, 7, 37464625715334887753241139078295529039121612800000⟩, + ⟨5, 6, 5, 7, 2, 7, 1190311484609269142468376530617705143730176000000⟩, + ⟨5, 6, 6, 7, 3, 7, -2287187555147372957826067575795917732708352000000⟩, + ⟨5, 6, 7, 7, 4, 7, 291389861669795208484822457641173925232640000000⟩, + ⟨5, 6, 8, 7, 5, 7, 128291494629318379346533237637468739600384000000⟩ +] + +def collectedFourData_9_4_42 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 4, 8, -4356928371037522737610276082393140580164042752000000⟩, + ⟨5, 7, 1, 0, 5, 8, 3610597737867582194979546698596880289419703091200000⟩, + ⟨5, 7, 2, 0, 6, 8, -616212518590684805872846562462935047166513643520000⟩, + ⟨5, 7, 3, 0, 7, 8, 29354796027128458138526471234418774154904862720000⟩, + ⟨5, 7, 4, 0, 8, 8, -16185069891542275195175514836764396099479797760000⟩, + ⟨5, 7, 0, 1, 3, 8, -3424383210201047483617568517132703841776985702400000⟩, + ⟨5, 7, 1, 1, 4, 8, 1577164649210096407750985955565057555921108992000000⟩, + ⟨5, 7, 2, 1, 5, 8, 300888925352894268051140875620469309879898603520000⟩, + ⟨5, 7, 3, 1, 6, 8, -139191799218687096527379988583154515716173987840000⟩, + ⟨5, 7, 4, 1, 7, 8, 18875800971243664012193493684065020899030466560000⟩, + ⟨5, 7, 5, 1, 8, 8, 11581911534654188480950904091388438697213952000000⟩, + ⟨5, 7, 0, 2, 2, 8, -2856614963728230672906194967394860014421776793600000⟩, + ⟨5, 7, 1, 2, 3, 8, 2382209130322386263572609461208367610133374566400000⟩, + ⟨5, 7, 2, 2, 4, 8, 1108513117060655261312389299682719148015783772160000⟩, + ⟨5, 7, 3, 2, 5, 8, -59232972707226714973385762150417697371471216640000⟩, + ⟨5, 7, 4, 2, 6, 8, -12444687408133658378924469295268444179424870400000⟩, + ⟨5, 7, 5, 2, 7, 8, 5936753696024371585236347789488026409343385600000⟩, + ⟨5, 7, 6, 2, 8, 8, -1169269870998245804439168609391662473202892800000⟩, + ⟨5, 7, 0, 3, 1, 8, -9156991814132548011331187218867617412076588236800000⟩, + ⟨5, 7, 1, 3, 2, 8, -6138502892594819320542044942207499519031404134400000⟩, + ⟨5, 7, 2, 3, 3, 8, -1262704469664841098333905019191373681637353062400000⟩, + ⟨5, 7, 3, 3, 4, 8, 6453947164904566044970826875252689406399610880000⟩, + ⟨5, 7, 4, 3, 5, 8, -34144425605126820615137954276236387176268431360000⟩, + ⟨5, 7, 5, 3, 6, 8, -4062015789216228148508780982627317936711270400000⟩, + ⟨5, 7, 6, 3, 7, 8, -2479164923074922356087806395920721274470400000⟩, + ⟨5, 7, 7, 3, 8, 8, 39678922662668994684033881619821201341808640000⟩, + ⟨5, 7, 0, 4, 0, 8, -29242189984722360209818593972249958454711549952000000⟩, + ⟨5, 7, 1, 4, 1, 8, 2763605152238651334513294385199167888707236659200000⟩, + ⟨5, 7, 2, 4, 2, 8, 301073675294969902154381478576313719177451929600000⟩, + ⟨5, 7, 3, 4, 3, 8, 95311701988431149146396499094699524248295178240000⟩, + ⟨5, 7, 4, 4, 4, 8, 25590078778785804095530161825745024733046374400000⟩, + ⟨5, 7, 5, 4, 5, 8, -2463010735407243292975242394070520212068761600000⟩, + ⟨5, 7, 6, 4, 6, 8, -501011480615372748489114263150431369061990400000⟩, + ⟨5, 7, 7, 4, 7, 8, 104954037617835093320701115461657268248903680000⟩, + ⟨5, 7, 8, 4, 8, 8, -10220079335623924686420561316012811825971200000⟩, + ⟨5, 7, 1, 5, 0, 8, 14565888753309650385233296283731185817002757324800000⟩, + ⟨5, 7, 2, 5, 1, 8, -311822642065931059971649043329796964534787768320000⟩, + ⟨5, 7, 3, 5, 2, 8, 119014526821324731770768849235016947788320604160000⟩, + ⟨5, 7, 4, 5, 3, 8, 24384374057286037394319539144792563054773534720000⟩, + ⟨5, 7, 5, 5, 4, 8, -1633805253071577996613174869559569651282739200000⟩, + ⟨5, 7, 6, 5, 5, 8, -418535618382532684021987506814068456633139200000⟩, + ⟨5, 7, 7, 5, 6, 8, -33249235663574364132959479499240033904230400000⟩, + ⟨5, 7, 8, 5, 7, 8, 16755842940299690960136937048704638118789120000⟩, + ⟨5, 7, 2, 6, 0, 8, 5613456380114866263587544662849798638286646804480000⟩, + ⟨5, 7, 3, 6, 1, 8, 28975507459639270982532158401204985033895444480000⟩, + ⟨5, 7, 4, 6, 2, 8, -30885188210384427897918957519920266722850897920000⟩, + ⟨5, 7, 5, 6, 3, 8, 14888137563395642317367681220116334477783859200000⟩, + ⟨5, 7, 6, 6, 4, 8, 279062082092820095386770400858244893586227200000⟩, + ⟨5, 7, 7, 6, 5, 8, -207731009227423211981284173570296108348866560000⟩, + ⟨5, 7, 8, 6, 6, 8, -25028814374377279089936774906247083951390720000⟩, + ⟨5, 7, 3, 7, 0, 8, -3045616771964156847339466731669578043399748976640000⟩, + ⟨5, 7, 4, 7, 1, 8, -29668846256477811540705572252732033320951480320000⟩, + ⟨5, 7, 5, 7, 2, 8, -824798641115745453214661310100145572518297600000⟩, + ⟨5, 7, 6, 7, 3, 8, 1408758565844654390921695988719837126223462400000⟩, + ⟨5, 7, 7, 7, 4, 8, -161529458497358149981614643402714834481971200000⟩, + ⟨5, 7, 8, 7, 5, 8, -64652076707440017605634646116507556459315200000⟩ +] + +def collectedFourData_9_4_43 : List CollectedFourTerm := [ + ⟨6, 0, 3, 0, 7, 2, 21286348240515043809717778858803534419183523594240000⟩, + ⟨6, 0, 4, 0, 8, 2, -82155135257297148176904146682609908328540080701440000⟩, + ⟨6, 0, 3, 1, 6, 2, -100933595575137040792118058301679997215921437409280000⟩, + ⟨6, 0, 4, 1, 7, 2, 95813239749598246018882054745784234718307958128640000⟩, + ⟨6, 0, 5, 1, 8, 2, 235158331732578048392765494566125698209181335552000000⟩, + ⟨6, 0, 3, 2, 5, 2, -42952220931861473946949127988883803683184055418880000⟩, + ⟨6, 0, 4, 2, 6, 2, -63169018366999425548926704052483916233575078297600000⟩, + ⟨6, 0, 5, 2, 7, 2, 120539436938981240416050811324709698957313939865600000⟩, + ⟨6, 0, 6, 2, 8, 2, -71222324066212286294726256658659446181979383398400000⟩, + ⟨6, 0, 3, 3, 4, 2, 4680017764425332702877081774617511519232941096960000⟩, + ⟨6, 0, 4, 3, 5, 2, -173316514705801632627365013808698173526850236579840000⟩, + ⟨6, 0, 5, 3, 6, 2, -82474887984196675632817951930754075482558719590400000⟩, + ⟨6, 0, 6, 3, 7, 2, -151010380019526968310020357138546546789528371200000⟩, + ⟨6, 0, 7, 3, 8, 2, 6042285785714531961348446702798960594250419404800000⟩, + ⟨6, 0, 3, 4, 3, 2, 69114364754807679231520883787416724458407282606080000⟩, + ⟨6, 0, 4, 4, 4, 2, 129894797946757809032860143190418409666226264473600000⟩, + ⟨6, 0, 5, 4, 5, 2, -50008799829353139230041719471968052103685446041600000⟩, + ⟨6, 0, 6, 4, 6, 2, -30517507479104835791376895601458353299931738931200000⟩, + ⟨6, 0, 7, 4, 7, 2, 15982346472532388645825056714014236127199336857600000⟩, + ⟨6, 0, 8, 4, 8, 2, -3423878449818658793089646486180789437548252364800000⟩, + ⟨6, 0, 3, 5, 2, 2, 86302240399067650750352229197357184009351431454720000⟩, + ⟨6, 0, 4, 5, 3, 2, 123774661602648627820225290595706264548668006727680000⟩, + ⟨6, 0, 5, 5, 4, 2, -33172668996707740785344130880403576936945890099200000⟩, + ⟨6, 0, 6, 5, 5, 2, -25493754850832053965133270946140618594270681497600000⟩, + ⟨6, 0, 7, 5, 6, 2, -5063176380665736387175958339251221830333104128000000⟩, + ⟨6, 0, 8, 5, 7, 2, 5613456380114866263587544662849798638286646804480000⟩, + ⟨6, 0, 3, 6, 1, 2, 21011310780750050441954266039454267554069122908160000⟩, + ⟨6, 0, 4, 6, 2, 2, -156772681976316464617808389878261307099570482708480000⟩, + ⟨6, 0, 5, 6, 3, 2, 302287716629307104692716182345017929396470887219200000⟩, + ⟨6, 0, 6, 6, 4, 2, 16998171712436595826935387040278966447627671961600000⟩, + ⟨6, 0, 7, 6, 5, 2, -31633170461250743736536272928091784619459031859200000⟩, + ⟨6, 0, 8, 6, 6, 2, -8385024748509960436881738940620671250129097850880000⟩, + ⟨6, 0, 3, 7, 0, 2, -2208499733919770552485932580368255068781614601338880000⟩, + ⟨6, 0, 4, 7, 1, 2, -150598551224212498790730371570317232497594812334080000⟩, + ⟨6, 0, 5, 7, 2, 2, -16746654632936396668996181015769595800670804377600000⟩, + ⟨6, 0, 6, 7, 3, 2, 85810009815767297503893037654196970789438436147200000⟩, + ⟨6, 0, 7, 7, 4, 2, -24597622252758554293141988185081289794318761984000000⟩, + ⟨6, 0, 8, 7, 5, 2, -21659406439540413504756751213962785986687323340800000⟩ +] + +def collectedFourData_9_4_44 : List CollectedFourTerm := [ + ⟨6, 1, 2, 0, 6, 3, -2306499215164945771665805881037539091079327907840000⟩, + ⟨6, 1, 3, 0, 7, 3, 659254513226200830173553576990451989046823485440000⟩, + ⟨6, 1, 4, 0, 8, 3, -1272203740423529771057271097812725034983431864320000⟩, + ⟨6, 1, 2, 1, 5, 3, 1126234942070788498801129384577846127099736227840000⟩, + ⟨6, 1, 3, 1, 6, 3, -3125990783727174691978689903183419059459514695680000⟩, + ⟨6, 1, 4, 1, 7, 3, 1483704720463088743829599233323176740710692945920000⟩, + ⟨6, 1, 5, 1, 8, 3, 2427677898932640280909895064137752616688943104000000⟩, + ⟨6, 1, 2, 2, 4, 3, 4149192944583420147426542936913183374360413470720000⟩, + ⟨6, 1, 3, 2, 5, 3, -1330263189461633387329918197801040927184419553280000⟩, + ⟨6, 1, 4, 2, 6, 3, -978196447412473552287090674546155642717785292800000⟩, + ⟨6, 1, 5, 2, 7, 3, 1244399570495887120186655575050363250976961331200000⟩, + ⟨6, 1, 6, 2, 8, 3, -551452485562331247362229214237179489788991897600000⟩, + ⟨6, 1, 2, 3, 3, 3, -4726335120435594147467649003757749415036374220800000⟩, + ⟨6, 1, 3, 3, 4, 3, 144943735689891304982885330654060573538134261760000⟩, + ⟨6, 1, 4, 3, 5, 3, -2683872622147572014479581968198359765971653099520000⟩, + ⟨6, 1, 5, 3, 6, 3, -851436822590969654368871862114796016207973580800000⟩, + ⟨6, 1, 6, 3, 7, 3, -1169226790887407318222314532516261157194956800000⟩, + ⟨6, 1, 7, 3, 8, 3, 37426843998098979371801588228144661868062965760000⟩, + ⟨6, 1, 2, 4, 2, 3, 1126926465828491107943739387536345009229083443200000⟩, + ⟨6, 1, 3, 4, 3, 3, 2140524827393614208906482926894347974041120276480000⟩, + ⟨6, 1, 4, 4, 4, 3, 2011470704684232380667264913998838669729647820800000⟩, + ⟨6, 1, 5, 4, 5, 3, -516270281403122960899990278861920451945509683200000⟩, + ⟨6, 1, 6, 4, 6, 3, -236287646789990312624689388261265876699630796800000⟩, + ⟨6, 1, 7, 4, 7, 3, 98997102978024835398391408156054174496320389120000⟩, + ⟨6, 1, 8, 4, 8, 3, -17673356457361234323143231895467270450498764800000⟩, + ⟨6, 1, 2, 5, 1, 3, -1167160123329896461979232751219443006073932349440000⟩, + ⟨6, 1, 3, 5, 2, 3, 2672846504330292546562374486761425029189410488320000⟩, + ⟨6, 1, 4, 5, 3, 3, 1916698048970223107706475853105434973264978903040000⟩, + ⟨6, 1, 5, 5, 4, 3, -342460991190807438689041442200084692460791398400000⟩, + ⟨6, 1, 6, 5, 5, 3, -197390279847346931853746398775864967368697446400000⟩, + ⟨6, 1, 7, 5, 6, 3, -31362090317220358562989595904203683406649753600000⟩, + ⟨6, 1, 8, 5, 7, 3, 28975507459639270982532158401204985033895444480000⟩, + ⟨6, 1, 2, 6, 0, 3, 21011310780750050441954266039454267554069122908160000⟩, + ⟨6, 1, 3, 6, 1, 3, 650736392381441302109508806364812174842354728960000⟩, + ⟨6, 1, 4, 6, 2, 3, -2427685034926445676919583608830997995871210045440000⟩, + ⟨6, 1, 5, 6, 3, 3, 3120694059074733161980900611495351650991105638400000⟩, + ⟨6, 1, 6, 6, 4, 3, 131611600207319327617024950842566382780311142400000⟩, + ⟨6, 1, 7, 6, 5, 3, -195940704893106677997670570744283355973460951040000⟩, + ⟨6, 1, 8, 6, 6, 3, -43281773420449852180012553141753070637421690880000⟩, + ⟨6, 1, 3, 7, 0, 3, -68398928768546912819275163620038532639959055073280000⟩, + ⟨6, 1, 4, 7, 1, 3, -2332076255121132959785389247751583219962861322240000⟩, + ⟨6, 1, 5, 7, 2, 3, -172885574727035381049087504216014818131522355200000⟩, + ⟨6, 1, 6, 7, 3, 3, 664400436512594651213693288933846747982908620800000⟩, + ⟨6, 1, 7, 7, 4, 3, -152361441253691921232910126811654319946648780800000⟩, + ⟨6, 1, 8, 7, 5, 3, -111801401910496346419170686220351769548737740800000⟩ +] + +def collectedFourData_9_4_45 : List CollectedFourTerm := [ + ⟨6, 2, 1, 0, 5, 4, -20167364011530427302783121259299662200372975370240000⟩, + ⟨6, 2, 2, 0, 6, 4, 17209591144068999573085684798526495993370268139520000⟩, + ⟨6, 2, 3, 0, 7, 4, -2459463362898605797083151711140661647884062556160000⟩, + ⟨6, 2, 4, 0, 8, 4, 3164117880565954101978774297224082980262452920320000⟩, + ⟨6, 2, 1, 1, 4, 4, -8809414921287537916757632391871372597226006118400000⟩, + ⟨6, 2, 2, 1, 5, 4, -8403229776870497343841954992228725879960261099520000⟩, + ⟨6, 2, 3, 1, 6, 4, 11662051076012459187610544261975490506601812459520000⟩, + ⟨6, 2, 4, 1, 7, 4, -3690145285954341997863502344147251680319027281920000⟩, + ⟨6, 2, 5, 1, 8, 4, -4528436840063634699026319374500455296142409728000000⟩, + ⟨6, 2, 1, 2, 3, 4, -13306073445660827964101654635097082727111097057280000⟩, + ⟨6, 2, 2, 2, 4, 4, -30958568589423915192859968937611675659474734940160000⟩, + ⟨6, 2, 3, 2, 5, 4, 4962777670618615250116202611103190910345590865920000⟩, + ⟨6, 2, 4, 2, 6, 4, 2432887729864322840723115322236781503208803532800000⟩, + ⟨6, 2, 5, 2, 7, 4, -2321224270019725673024882724843166185751471718400000⟩, + ⟨6, 2, 6, 2, 8, 4, 822915676667997597749962858925695879384462786560000⟩, + ⟨6, 2, 1, 3, 2, 4, 34287237545854915128357494694752476078229296250880000⟩, + ⟨6, 2, 2, 3, 3, 4, 35264826667948337247017787734058590085319124582400000⟩, + ⟨6, 2, 3, 3, 4, 4, -540737758269440029882457972394754012785294704640000⟩, + ⟨6, 2, 4, 3, 5, 4, 6675101701926659195086482703391571170800718315520000⟩, + ⟨6, 2, 5, 3, 6, 4, 1588216408817195386620681951339005449753696665600000⟩, + ⟨6, 2, 6, 3, 7, 4, 1744801376351229582974910452776676991518638080000⟩, + ⟨6, 2, 7, 3, 8, 4, -46542445421561691061069055964539246022104186880000⟩, + ⟨6, 2, 1, 4, 1, 4, -15436400046673351913925707050004016638916915363840000⟩, + ⟨6, 2, 2, 4, 2, 4, -8408389475628782448412071306591874454325402009600000⟩, + ⟨6, 2, 3, 4, 3, 4, -7985599316698355197143554697156486255468053790720000⟩, + ⟨6, 2, 4, 4, 4, 4, -5002760344665518419746081418826719750626528460800000⟩, + ⟨6, 2, 5, 4, 5, 4, 963017936919806439640190104702874487464814182400000⟩, + ⟨6, 2, 6, 4, 6, 4, 352604827863261829171756682199488741251303342080000⟩, + ⟨6, 2, 7, 4, 7, 4, -123108623919277705737259000541964925602952642560000⟩, + ⟨6, 2, 8, 4, 8, 4, 18838149470035551206512148328954738632766259200000⟩, + ⟨6, 2, 1, 5, 0, 4, -81359265685726816012973177758141326643629612072960000⟩, + ⟨6, 2, 2, 5, 1, 4, 8708586757846446060834897842058540438268485304320000⟩, + ⟨6, 2, 3, 5, 2, 4, -9971517706995808832792527296418777006395076116480000⟩, + ⟨6, 2, 4, 5, 3, 4, -4767049785888519822553468843458535577162392535040000⟩, + ⟨6, 2, 5, 5, 4, 4, 638805077673193418726088417639271002410896588800000⟩, + ⟨6, 2, 6, 5, 5, 4, 294559476946821468936349773796703918161227939840000⟩, + ⟨6, 2, 7, 5, 6, 4, 39000573411144626974205165708717581933530316800000⟩, + ⟨6, 2, 8, 5, 7, 4, -30885188210384427897918957519920266722850897920000⟩, + ⟨6, 2, 2, 6, 0, 4, -156772681976316464617808389878261307099570482708480000⟩, + ⟨6, 2, 3, 6, 1, 4, -2427685034926445676919583608830997995871210045440000⟩, + ⟨6, 2, 4, 6, 2, 4, 6037933534793652585370397042860146877319809597440000⟩, + ⟨6, 2, 5, 6, 3, 4, -5821145362774443211877505653016335693967576268800000⟩, + ⟨6, 2, 6, 6, 4, 4, -196399965323435472280302352040065453197298237440000⟩, + ⟨6, 2, 7, 6, 5, 4, 243663600484533317132949449797453074878976491520000⟩, + ⟨6, 2, 8, 6, 6, 4, 46134333282404913620004310934049037535957483520000⟩, + ⟨6, 2, 3, 7, 0, 4, 255174073127705682892541856290092590258068568145920000⟩, + ⟨6, 2, 4, 7, 1, 4, 5800143438672435488947002388749824154094786314240000⟩, + ⟨6, 2, 5, 7, 2, 4, 322489818790908846447033256279399869717046886400000⟩, + ⟨6, 2, 6, 7, 3, 4, -991464449078950773222227465911754983987457556480000⟩, + ⟨6, 2, 7, 7, 4, 4, 189470265359820908255432757778391128636548710400000⟩, + ⟨6, 2, 8, 7, 5, 4, 119169865963531285130945204391198627435066163200000⟩ +] + +def collectedFourData_9_4_46 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 4, 5, -23462299154294470723066048005051210234077380608000000⟩, + ⟨6, 3, 1, 0, 5, 5, 77773070417951599778783698591811179789533000499200000⟩, + ⟨6, 3, 2, 0, 6, 5, -33183383389782555597187923528027608769197034700800000⟩, + ⟨6, 3, 3, 0, 7, 5, 3161543855437651047019659765349071706094410137600000⟩, + ⟨6, 3, 4, 0, 8, 5, -3050512235947901765567709124235593377105995366400000⟩, + ⟨6, 3, 0, 1, 3, 5, -18440492120724902180749466294993617523058514329600000⟩, + ⟨6, 3, 1, 1, 4, 5, 33972473875243789703040147524429697523774390272000000⟩, + ⟨6, 3, 2, 1, 5, 5, 16203034288495042820499043092301303517010513100800000⟩, + ⟨6, 3, 3, 1, 6, 5, -14991110043499049579272531693383415313651151667200000⟩, + ⟨6, 3, 4, 1, 7, 5, 3557652961151915383390702854123265296819447398400000⟩, + ⟨6, 3, 5, 1, 8, 5, 3492676951178696425722452218427910233782222848000000⟩, + ⟨6, 3, 0, 2, 2, 5, -15383028854262654418420414741080052187764516454400000⟩, + ⟨6, 3, 1, 2, 3, 5, 51313309289411896888020741097679162024250467942400000⟩, + ⟨6, 3, 2, 2, 4, 5, 59694041659774055480047530807381673847225214566400000⟩, + ⟨6, 3, 3, 2, 5, 5, -6379456383507958695839610540741126103216894771200000⟩, + ⟨6, 3, 4, 2, 6, 5, -2345536439783704999241668187715409180209709056000000⟩, + ⟨6, 3, 5, 2, 7, 5, 1790305748484407499520255850193668875143767654400000⟩, + ⟨6, 3, 6, 2, 8, 5, -528912941001650936150646505239653448764148940800000⟩, + ⟨6, 3, 0, 3, 1, 5, -49310905068986086459237039549610221947424289587200000⟩, + ⟨6, 3, 1, 3, 2, 5, -132224704158966980983239648364836734978962646630400000⟩, + ⟨6, 3, 2, 3, 3, 5, -67997330889528422000923130173409762711433117696000000⟩, + ⟨6, 3, 3, 3, 4, 5, 695097216266342421230298030720941003815413350400000⟩, + ⟨6, 3, 4, 3, 5, 5, -6435436411200260339524555969023422837754848870400000⟩, + ⟨6, 3, 5, 3, 6, 5, -1224954005206280080390960096579025475752008089600000⟩, + ⟨6, 3, 6, 3, 7, 5, -1121436926765434554995605808507555523487334400000⟩, + ⟨6, 3, 7, 3, 8, 5, 25640781973469910679509488928265511420244787200000⟩, + ⟨6, 3, 0, 4, 0, 5, -157470803033856196962717326156474682017901969408000000⟩, + ⟨6, 3, 1, 4, 1, 5, 59528663594469115143701401440379235396954043187200000⟩, + ⟨6, 3, 2, 4, 2, 5, 16212983174592256493349784899042045471158697984000000⟩, + ⟨6, 3, 3, 4, 3, 5, 10265175254304293910671672388963075206319125299200000⟩, + ⟨6, 3, 4, 4, 4, 5, 4823139409138394917339962231295152367249391616000000⟩, + ⟨6, 3, 5, 4, 5, 5, -742753111204749160123975040767732579983320678400000⟩, + ⟨6, 3, 6, 4, 6, 5, -226629850183034418798438827784768094548158054400000⟩, + ⟨6, 3, 7, 4, 7, 5, 67821992514079322781638340827403654860793446400000⟩, + ⟨6, 3, 8, 4, 8, 5, -9080888833806690762876560996350919958331392000000⟩, + ⟨6, 3, 1, 5, 0, 5, 313752451520742377610718108330725516245778353356800000⟩, + ⟨6, 3, 2, 5, 1, 5, -16791820953189487838633412072104358287069990092800000⟩, + ⟨6, 3, 3, 5, 2, 5, 12817995588592959876755354868857758612909247692800000⟩, + ⟨6, 3, 4, 5, 3, 5, 4595891888397246156594800035773804177743727820800000⟩, + ⟨6, 3, 5, 5, 4, 5, -492695349385446442042734502113430652249230540800000⟩, + ⟨6, 3, 6, 5, 5, 5, -189322337232259111994987072182342563052860211200000⟩, + ⟨6, 3, 7, 5, 6, 5, -21485875755299166969783363110048822294740992000000⟩, + ⟨6, 3, 8, 5, 7, 5, 14888137563395642317367681220116334477783859200000⟩, + ⟨6, 3, 2, 6, 0, 5, 302287716629307104692716182345017929396470887219200000⟩, + ⟨6, 3, 3, 6, 1, 5, 3120694059074733161980900611495351650991105638400000⟩, + ⟨6, 3, 4, 6, 2, 5, -5821145362774443211877505653016335693967576268800000⟩, + ⟨6, 3, 5, 6, 3, 5, 4489712666001839958025320023208510078646537420800000⟩, + ⟨6, 3, 6, 6, 4, 5, 126232232799898306228511724757271364490179379200000⟩, + ⟨6, 3, 7, 6, 5, 5, -134237150590291418194149522758729635252194508800000⟩, + ⟨6, 3, 8, 6, 6, 5, -22238954660896240054987081745425970259768115200000⟩, + ⟨6, 3, 3, 7, 0, 5, -328016279946982353777424410191388535341744075571200000⟩, + ⟨6, 3, 4, 7, 1, 5, -5591892969157788792187314168022294189671501004800000⟩, + ⟨6, 3, 5, 7, 2, 5, -248728821194064398301625096605697213687293542400000⟩, + ⟨6, 3, 6, 7, 3, 5, 637244364798382737692843479918860241643923046400000⟩, + ⟨6, 3, 7, 7, 4, 5, -104381403266275665745276103957499722518757376000000⟩, + ⟨6, 3, 8, 7, 5, 5, -57445573774419627376557522241081135104786432000000⟩ +] + +def collectedFourData_9_4_47 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 4, 6, -3957979446604358300870739188555310962785124352000000⟩, + ⟨6, 4, 1, 0, 5, 6, 6559975477876869044417387399365504081615808102400000⟩, + ⟨6, 4, 2, 0, 6, 6, -1865960202249429880059497021961759844381124198400000⟩, + ⟨6, 4, 3, 0, 7, 6, 133334392306029829931230604234252651408759193600000⟩, + ⟨6, 4, 4, 0, 8, 6, -102921411512962786207179689057287681444486840320000⟩, + ⟨6, 4, 0, 1, 3, 6, -3110824234194432489738166632954430731365803622400000⟩, + ⟨6, 4, 1, 1, 4, 6, 2865498228972731301330186347477255860921565184000000⟩, + ⟨6, 4, 2, 1, 5, 6, 911125209351739233651146911526419815326967398400000⟩, + ⟨6, 4, 3, 1, 6, 6, -632232427902243665473790332404780864539669299200000⟩, + ⟨6, 4, 4, 1, 7, 6, 120031862229606326358518265440261904885790801920000⟩, + ⟨6, 4, 5, 1, 8, 6, 98199694010406761920271747267022455310385152000000⟩, + ⟨6, 4, 0, 2, 2, 6, -2595044570495514883121431907350049618189195673600000⟩, + ⟨6, 4, 1, 2, 3, 6, 4328156890531559257320534625642804617530887372800000⟩, + ⟨6, 4, 2, 2, 4, 6, 3356701296554793094539255737391210575615439667200000⟩, + ⟨6, 4, 3, 2, 5, 6, -269046067058306916645615162225795777380430643200000⟩, + ⟨6, 4, 4, 2, 6, 6, -79136191716541344992576377994716545362480332800000⟩, + ⟨6, 4, 5, 2, 7, 6, 50336025674206763487216964459425621580814745600000⟩, + ⟨6, 4, 6, 2, 8, 6, -12746446274514425480152028853517769216989593600000⟩, + ⟨6, 4, 0, 3, 1, 6, -8318517613001365499987082083985017768369769676800000⟩, + ⟨6, 4, 1, 3, 2, 6, -11152842650945868882932688085327881649362095308800000⟩, + ⟨6, 4, 2, 3, 3, 6, -3823609901638703354093783524839378736128196608000000⟩, + ⟨6, 4, 3, 3, 4, 6, 29314907261236159516138054112268063441577574400000⟩, + ⟨6, 4, 4, 3, 5, 6, -217125567089172052203196282402443819327443435520000⟩, + ⟨6, 4, 5, 3, 6, 6, -34440662611949790989955324385610035972433510400000⟩, + ⟨6, 4, 6, 3, 7, 6, -27025875960232105361552264453495796321484800000⟩, + ⟨6, 4, 7, 3, 8, 6, 540684905699458055946732566957651383654809600000⟩, + ⟨6, 4, 0, 4, 0, 6, -26564583366255699246747629754252047452106391552000000⟩, + ⟨6, 4, 1, 4, 1, 6, 5021102694183488022917791845776934184952424038400000⟩, + ⟨6, 4, 2, 4, 2, 6, 911684652772443267349628910569792479042732032000000⟩, + ⟨6, 4, 3, 4, 3, 6, 432921688590047920929053858879170976479916851200000⟩, + ⟨6, 4, 4, 4, 4, 6, 162728183831746079190336331411526455814573260800000⟩, + ⟨6, 4, 5, 4, 5, 6, -20883159039649827547592551186163840321165721600000⟩, + ⟨6, 4, 6, 4, 6, 6, -5461627019540602727503312668155029555563724800000⟩, + ⟨6, 4, 7, 4, 7, 6, 1430156368271705013813653964623160672465715200000⟩, + ⟨6, 4, 8, 4, 8, 6, -170211467648312003850213512488025768067072000000⟩, + ⟨6, 4, 1, 5, 0, 6, 26464280978480502240151115997244007531947858329600000⟩, + ⟨6, 4, 2, 5, 1, 6, -944233722459938389539936336341672592864077414400000⟩, + ⟨6, 4, 3, 5, 2, 6, 540583882601187687292598123974957371543571660800000⟩, + ⟨6, 4, 4, 5, 3, 6, 155061066381147608325127772412690431797666775040000⟩, + ⟨6, 4, 5, 5, 4, 6, -13852564444493878446001096582429413075006259200000⟩, + ⟨6, 4, 6, 5, 5, 6, -4562541040358020661443648670344709207909990400000⟩, + ⟨6, 4, 7, 5, 6, 6, -453070765105534226393869095404330607968256000000⟩, + ⟨6, 4, 8, 5, 7, 6, 279062082092820095386770400858244893586227200000⟩, + ⟨6, 4, 2, 6, 0, 6, 16998171712436595826935387040278966447627671961600000⟩, + ⟨6, 4, 3, 6, 1, 6, 131611600207319327617024950842566382780311142400000⟩, + ⟨6, 4, 4, 6, 2, 6, -196399965323435472280302352040065453197298237440000⟩, + ⟨6, 4, 5, 6, 3, 6, 126232232799898306228511724757271364490179379200000⟩, + ⟨6, 4, 6, 6, 4, 6, 3042111940858862625931849413178885633631846400000⟩, + ⟨6, 4, 7, 6, 5, 6, -2830646942958798292025701599674139870127718400000⟩, + ⟨6, 4, 8, 6, 6, 6, -416845220888869417243631190898061379580723200000⟩, + ⟨6, 4, 3, 7, 0, 6, -13833700670636788354729611851546307806104859443200000⟩, + ⟨6, 4, 4, 7, 1, 6, -188665205349125905247120362463132476659455754240000⟩, + ⟨6, 4, 5, 7, 2, 6, -6993230256976215520372762393624647237736857600000⟩, + ⟨6, 4, 6, 7, 3, 6, 15357160753633939644080258578151347195792588800000⟩, + ⟨6, 4, 7, 7, 4, 6, -2201081435043527475733605917820272894803968000000⟩, + ⟨6, 4, 8, 7, 5, 6, -1076755326597745866220311972733982670323712000000⟩ +] + +def collectedFourData_9_4_48 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 4, 7, 14731400604096535237802023037003848706842165248000000⟩, + ⟨6, 5, 1, 0, 5, 7, -16277266051421163240136188835673654265117042278400000⟩, + ⟨6, 5, 2, 0, 6, 7, 3472505052321596858950073811884094901663354060800000⟩, + ⟨6, 5, 3, 0, 7, 7, -198505563140205457714485474311572811344836034560000⟩, + ⟨6, 5, 4, 0, 8, 7, 127689440550050594806061889788488175055336898560000⟩, + ⟨6, 5, 0, 1, 3, 7, 11578331474703808669804828925484064468608063897600000⟩, + ⟨6, 5, 1, 1, 4, 7, -7110160274251681762692055612490170310898745344000000⟩, + ⟨6, 5, 2, 1, 5, 7, -1695581121696698729195087529173845898534112460800000⟩, + ⟨6, 5, 3, 1, 6, 7, 941254930297219478626658668434422572987522744320000⟩, + ⟨6, 5, 4, 1, 7, 7, -148917519794691063643726269793283726701347471360000⟩, + ⟨6, 5, 5, 1, 8, 7, -104426950394607376975518341725039557636784128000000⟩, + ⟨6, 5, 0, 2, 2, 7, 9658625485347654654332471608292173333372757606400000⟩, + ⟨6, 5, 1, 2, 3, 7, -10739454965504719036916403676321345651484708044800000⟩, + ⟨6, 5, 2, 2, 4, 7, -6246736772504246049873124364726207710302201446400000⟩, + ⟨6, 5, 3, 2, 5, 7, 400550376601157274288103041759079932428518686720000⟩, + ⟨6, 5, 4, 2, 6, 7, 98180309607141581420372476529715778811225702400000⟩, + ⟨6, 5, 5, 2, 7, 7, -53528045164631769798861425880646533522024038400000⟩, + ⟨6, 5, 6, 2, 8, 7, 11860408125006853189897473688439517034944921600000⟩, + ⟨6, 5, 0, 3, 1, 7, 30961104533902721920824011888858140769804038963200000⟩, + ⟨6, 5, 1, 3, 2, 7, 27673546596524437829803880192205423610440764620800000⟩, + ⟨6, 5, 2, 3, 3, 7, 7115641955032665638089152109482175079588560896000000⟩, + ⟨6, 5, 3, 3, 4, 7, -43643444678087150678123761486433559679063818240000⟩, + ⟨6, 5, 4, 3, 5, 7, 269376816574624830636450831369650239069917020160000⟩, + ⟨6, 5, 5, 3, 6, 7, 36624690151828225961732924009838578526427545600000⟩, + ⟨6, 5, 6, 3, 7, 7, 25147238055288873903821565533264206941388800000⟩, + ⟨6, 5, 7, 3, 8, 7, -447200455232292881451454968078968953189171200000⟩, + ⟨6, 5, 0, 4, 0, 7, 98872044367225306388556953609253007389043458048000000⟩, + ⟨6, 5, 1, 4, 1, 7, -12458861271716830056998186482558022808108426854400000⟩, + ⟨6, 5, 2, 4, 2, 7, -1696622231846068972667155720411474441518710784000000⟩, + ⟨6, 5, 3, 4, 3, 7, -644525107910134791660881675522139046154883563520000⟩, + ⟨6, 5, 4, 4, 4, 7, -201888707604679568818860790223297346951079526400000⟩, + ⟨6, 5, 5, 4, 5, 7, 22207448150348630869078020416668461299033702400000⟩, + ⟨6, 5, 6, 4, 6, 7, 5081975327337580266327425214581038769818828800000⟩, + ⟨6, 5, 7, 4, 7, 7, -1182882252126296496161803835999748960446054400000⟩, + ⟨6, 5, 8, 4, 8, 7, 126703705825946279346624603829609625655705600000⟩, + ⟨6, 5, 1, 5, 0, 7, -65665815946877388261856478487216756393470695833600000⟩, + ⟨6, 5, 2, 5, 1, 7, 1757195232707469892977214022489135422471195852800000⟩, + ⟨6, 5, 3, 5, 2, 7, -804810418260065127089251181909591958398624071680000⟩, + ⟨6, 5, 4, 5, 3, 7, -192376498983491506341988620877858710307020472320000⟩, + ⟨6, 5, 5, 5, 4, 7, 14731013926886187494956755944252662212250828800000⟩, + ⟨6, 5, 6, 5, 5, 7, 4245387118912949008126865728995953897530982400000⟩, + ⟨6, 5, 7, 5, 6, 7, 374734804452376684663228672228539060191232000000⟩, + ⟨6, 5, 8, 5, 7, 7, -207731009227423211981284173570296108348866560000⟩, + ⟨6, 5, 2, 6, 0, 7, -31633170461250743736536272928091784619459031859200000⟩, + ⟨6, 5, 3, 6, 1, 7, -195940704893106677997670570744283355973460951040000⟩, + ⟨6, 5, 4, 6, 2, 7, 243663600484533317132949449797453074878976491520000⟩, + ⟨6, 5, 5, 6, 3, 7, -134237150590291418194149522758729635252194508800000⟩, + ⟨6, 5, 6, 6, 4, 7, -2830646942958798292025701599674139870127718400000⟩, + ⟨6, 5, 7, 6, 5, 7, 2341227928039681526015481868770048301911244800000⟩, + ⟨6, 5, 8, 6, 6, 7, 310295392973063792926983516161939881706127360000⟩, + ⟨6, 5, 3, 7, 0, 7, 20595335490298756211424391206292155227746043166720000⟩, + ⟨6, 5, 4, 7, 1, 7, 234067471171983811795417836597827482526070865920000⟩, + ⟨6, 5, 5, 7, 2, 7, 7436700455155498616087593008504033222485606400000⟩, + ⟨6, 5, 6, 7, 3, 7, -14289645149457552171857056002073940357598412800000⟩, + ⟨6, 5, 7, 7, 4, 7, 1820514331690914444043786366387122755076096000000⟩, + ⟨6, 5, 8, 7, 5, 7, 801525843309503207882577109035432917178777600000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0919.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0919.lean new file mode 100644 index 0000000000000000000000000000000000000000..2df6f2e2422974ed45ece4c0580630f33b3f9883 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0919.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse0915 +import OAI.Analysis.LaughlinFock.Sparse0916 +import OAI.Analysis.LaughlinFock.Sparse0917 +import OAI.Analysis.LaughlinFock.Sparse0918 + +namespace OAI + +/-! Sparse0919. -/ +namespace LaughlinFock +def collectedFourData_9_4_49 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 4, 8, 6508102984116758063096086991571452851610714112000000⟩, + ⟨6, 6, 1, 0, 5, 8, -5393281667989775906650519805498419881828365107200000⟩, + ⟨6, 6, 2, 0, 6, 8, 920459137622944614879172761166168059735567237120000⟩, + ⟨6, 6, 3, 0, 7, 8, -43848330601955669168733648521912816886947512320000⟩, + ⟨6, 6, 4, 0, 8, 8, 24176229831889842800239712664381011444430274560000⟩, + ⟨6, 6, 0, 1, 3, 8, 5115126229114870885638552391870074040724383334400000⟩, + ⟨6, 6, 1, 1, 4, 8, -2355868420559647922485496275142199806684823552000000⟩, + ⟨6, 6, 2, 1, 5, 8, -449448773588752464406939338545196681598724997120000⟩, + ⟨6, 6, 3, 1, 6, 8, 207915872540268703356525980584058909833077719040000⟩, + ⟨6, 6, 4, 1, 7, 8, -28195473087222557547800017189297664415875727360000⟩, + ⟨6, 6, 5, 1, 8, 8, -17300324127777603414699821350883427260301312000000⟩, + ⟨6, 6, 0, 2, 2, 8, 4267030069508611618137619522930793093237676441600000⟩, + ⟨6, 6, 1, 2, 3, 8, -3558392755065972235659028222621736663188399718400000⟩, + ⟨6, 6, 2, 2, 4, 8, -1655826515999633475663370448254167198318156840960000⟩, + ⟨6, 6, 3, 2, 5, 8, 88478453994461759177296206782086621695930531840000⟩, + ⟨6, 6, 4, 2, 6, 8, 18589083950900094392398692895261490583856742400000⟩, + ⟨6, 6, 5, 2, 7, 8, -8867945753228371335000603881116292060125593600000⟩, + ⟨6, 6, 6, 2, 8, 8, 1746581097652836248514057793379780459809996800000⟩, + ⟨6, 6, 0, 3, 1, 8, 13678133004719879687078299284015083524352429260800000⟩, + ⟨6, 6, 1, 3, 2, 8, 9169305894233081338823774709715811368064935526400000⟩, + ⟨6, 6, 2, 3, 3, 8, 1886147769082189332201000894151195760802555494400000⟩, + ⟨6, 6, 3, 3, 4, 8, -9640496521003181509822456030632715153079009280000⟩, + ⟨6, 6, 4, 3, 5, 8, 51002775177311892555926737093194496537169756160000⟩, + ⟨6, 6, 5, 3, 6, 8, 6067581293064101711751721307589615615895142400000⟩, + ⟨6, 6, 6, 3, 7, 8, 3703219162664205345225620540556063434342400000⟩, + ⟨6, 6, 7, 3, 8, 8, -59269855502802383947441552471620327403683840000⟩, + ⟨6, 6, 0, 4, 0, 8, 43680126845041898995671404932431728729823117312000000⟩, + ⟨6, 6, 1, 4, 1, 8, -4128097918195019295625997858644674737157124915200000⟩, + ⟨6, 6, 2, 4, 2, 8, -449724741322656593225016253942353583289244057600000⟩, + ⟨6, 6, 3, 4, 3, 8, -142370569196308178517308488091168881019128381440000⟩, + ⟨6, 6, 4, 4, 4, 8, -38224834994094630964950299147579324195300966400000⟩, + ⟨6, 6, 5, 4, 5, 8, 3679089062737644304396400785031006864906649600000⟩, + ⟨6, 6, 6, 4, 6, 8, 748379141081266455513193823947074182735462400000⟩, + ⟨6, 6, 7, 4, 7, 8, -156773677978341148868927885190929601087406080000⟩, + ⟨6, 6, 8, 4, 8, 8, 15266105650078692180721659253092408046387200000⟩, + ⟨6, 6, 1, 5, 0, 8, -21757599847608524247673907787726711568967978188800000⟩, + ⟨6, 6, 2, 5, 1, 8, 465780865445166688662761199966439437460486225920000⟩, + ⟨6, 6, 3, 5, 2, 8, -177776344065684152646494057845131258417339432960000⟩, + ⟨6, 6, 4, 5, 3, 8, -36423829829970779976996419341914978491113144320000⟩, + ⟨6, 6, 5, 5, 4, 8, 2440474558558951938222358495542652756505395200000⟩, + ⟨6, 6, 6, 5, 5, 8, 625181934378662541665576112292158720127795200000⟩, + ⟨6, 6, 7, 5, 6, 8, 49665597277235124529484514428508252300902400000⟩, + ⟨6, 6, 8, 5, 7, 8, -25028814374377279089936774906247083951390720000⟩, + ⟨6, 6, 2, 6, 0, 8, -8385024748509960436881738940620671250129097850880000⟩, + ⟨6, 6, 3, 6, 1, 8, -43281773420449852180012553141753070637421690880000⟩, + ⟨6, 6, 4, 6, 2, 8, 46134333282404913620004310934049037535957483520000⟩, + ⟨6, 6, 5, 6, 3, 8, -22238954660896240054987081745425970259768115200000⟩, + ⟨6, 6, 6, 6, 4, 8, -416845220888869417243631190898061379580723200000⟩, + ⟨6, 6, 7, 6, 5, 8, 310295392973063792926983516161939881706127360000⟩, + ⟨6, 6, 8, 6, 6, 8, 37386453860842307838014957680382534033080320000⟩, + ⟨6, 6, 3, 7, 0, 8, 4549348971136728611299899835581179789641085091840000⟩, + ⟨6, 6, 4, 7, 1, 8, 44317438895857771725072227117565871583574097920000⟩, + ⟨6, 6, 5, 7, 2, 8, 1232031844549826490044259002244339487840665600000⟩, + ⟨6, 6, 6, 7, 3, 8, -2104314105143382449586600582055244243297894400000⟩, + ⟨6, 6, 7, 7, 4, 8, 241282449777590576015969110343582636782387200000⟩, + ⟨6, 6, 8, 7, 5, 8, 96573167497091320716494999977579890553651200000⟩ +] + +def collectedFourData_9_4_50 : List CollectedFourTerm := [ + ⟨7, 0, 2, 0, 6, 3, 242436226665345766027833514493948215810688412549120000⟩, + ⟨7, 0, 3, 0, 7, 3, -69294268798279047346732539104403828364858538065920000⟩, + ⟨7, 0, 4, 0, 8, 3, 133721387091719775038931311343595951808367569141760000⟩, + ⟨7, 0, 2, 1, 5, 3, -118378600737906684744100575588463275784384146309120000⟩, + ⟨7, 0, 3, 1, 6, 3, 328573018891431293381697593372362433751448540938240000⟩, + ⟨7, 0, 4, 1, 7, 3, -155952263737886940779852014532261240546240558530560000⟩, + ⟨7, 0, 5, 1, 8, 3, -255173323063105481513195238184716060451953180672000000⟩, + ⟨7, 0, 2, 2, 4, 3, -436121839789719168589080287541079190625640733736960000⟩, + ⟨7, 0, 3, 2, 5, 3, 139824018150304451961248754608484955878616769495040000⟩, + ⟨7, 0, 4, 2, 6, 3, 102818268520922509539257705504317099954091222630400000⟩, + ⟨7, 0, 5, 2, 7, 3, -130798889655561874374662197626660549701593045401600000⟩, + ⟨7, 0, 6, 2, 8, 3, 57963193269674218451755567180705157480151043276800000⟩, + ⟨7, 0, 2, 3, 3, 3, 496785277454501692274919409395248781196739896934400000⟩, + ⟨7, 0, 3, 3, 4, 3, -15235041975474290126210481312724651529436062023680000⟩, + ⟨7, 0, 4, 3, 5, 3, 282101960878990862492850035870879816448111657615360000⟩, + ⟨7, 0, 5, 3, 6, 3, 89494559181163372090191181673446033303991117414400000⟩, + ⟨7, 0, 6, 3, 7, 3, 122897475722098997995577134377024208819873382400000⟩, + ⟨7, 0, 7, 3, 8, 3, -3933937100534748559425965110973305345581703495680000⟩, + ⟨7, 0, 2, 4, 2, 3, -118451286828309222397646551854381223055875217817600000⟩, + ⟨7, 0, 3, 4, 3, 3, -224990651991046578171416244623988980894363434352640000⟩, + ⟨7, 0, 4, 4, 4, 3, -211425767884623169270352004252434704849179141734400000⟩, + ⟨7, 0, 5, 4, 5, 3, 54265190354239313025100411637245059434511178137600000⟩, + ⟨7, 0, 6, 4, 6, 3, 24836204200183360764179292139097272885887526502400000⟩, + ⟨7, 0, 7, 4, 7, 3, -10405589535427891896398795820893900425266368348160000⟩, + ⟨7, 0, 8, 4, 8, 3, 1857647218721411706370616163204002399016871526400000⟩, + ⟨7, 0, 2, 5, 1, 3, 122680248210760439967369248367325346133708814417920000⟩, + ⟨7, 0, 3, 5, 2, 3, -280943005185091956156855389166630093218572413173760000⟩, + ⟨7, 0, 4, 5, 3, 3, -201464210173572653323610399851051572993593148702720000⟩, + ⟨7, 0, 5, 5, 4, 3, 35996088764520203493232875527135251579232531251200000⟩, + ⟨7, 0, 6, 5, 5, 3, 20747700372915664649155942065891221931163857715200000⟩, + ⟨7, 0, 7, 5, 6, 3, 3296470593553157424723336779376129841273031884800000⟩, + ⟨7, 0, 8, 5, 7, 3, -3045616771964156847339466731669578043399748976640000⟩, + ⟨7, 0, 2, 6, 0, 3, -2208499733919770552485932580368255068781614601338880000⟩, + ⟨7, 0, 3, 6, 1, 3, -68398928768546912819275163620038532639959055073280000⟩, + ⟨7, 0, 4, 6, 2, 3, 255174073127705682892541856290092590258068568145920000⟩, + ⟨7, 0, 5, 6, 3, 3, -328016279946982353777424410191388535341744075571200000⟩, + ⟨7, 0, 6, 6, 4, 3, -13833700670636788354729611851546307806104859443200000⟩, + ⟨7, 0, 7, 6, 5, 3, 20595335490298756211424391206292155227746043166720000⟩, + ⟨7, 0, 8, 6, 6, 3, 4549348971136728611299899835581179789641085091840000⟩, + ⟨7, 0, 3, 7, 0, 3, 7189414195145267037346388576456508719292625232855040000⟩, + ⟨7, 0, 4, 7, 1, 3, 245124630379284754580445188906573392483654639288320000⟩, + ⟨7, 0, 5, 7, 2, 3, 18172009817352019744733611733394436421859252633600000⟩, + ⟨7, 0, 6, 7, 3, 3, -69835157004986473505972198466701944562546796134400000⟩, + ⟨7, 0, 7, 7, 4, 3, 16014717310102036123915994820846198721121511014400000⟩, + ⟨7, 0, 8, 7, 5, 3, 11751449918936201083730363442488108310661064294400000⟩ +] + +def collectedFourData_9_4_51 : List CollectedFourTerm := [ + ⟨7, 1, 1, 0, 5, 4, -19373118861401048616842932179829146691709215703040000⟩, + ⟨7, 1, 2, 0, 6, 4, 16531831061290137392542258438446222235884501073920000⟩, + ⟨7, 1, 3, 0, 7, 4, -2362603066888365235528706390707118643525042831360000⟩, + ⟨7, 1, 4, 0, 8, 4, 3039506390455479873103031031440316192057427230720000⟩, + ⟨7, 1, 1, 1, 4, 4, -8462476418431653524205004302632586351567332966400000⟩, + ⟨7, 1, 2, 1, 5, 4, -8072287939757512586620408117901407421852465233920000⟩, + ⟨7, 1, 3, 1, 6, 4, 11202768072919528023461004603442808220475635793920000⟩, + ⟨7, 1, 4, 1, 7, 4, -3544817418863415638091888206641693741338140344320000⟩, + ⟨7, 1, 5, 1, 8, 4, -4350094792197022545804485323780550081944485888000000⟩, + ⟨7, 1, 1, 2, 3, 4, -12782044410659568267481623458238724665636689018880000⟩, + ⟨7, 1, 2, 2, 4, 4, -29739336718414922624236534188385443088677847695360000⟩, + ⟨7, 1, 3, 2, 5, 4, 4767330110203401024355967406190007713597300408320000⟩, + ⟨7, 1, 4, 2, 6, 4, 2337074053909981967686635889630919349647494348800000⟩, + ⟨7, 1, 5, 2, 7, 4, -2229808202070949217154473650840168000322430566400000⟩, + ⟨7, 1, 6, 2, 8, 4, 790507039387225179254256988293356564363618549760000⟩, + ⟨7, 1, 1, 3, 2, 4, 32936913719867572609434428126821729680583274004480000⟩, + ⟨7, 1, 2, 3, 3, 4, 33876002747521383531481801863060768182585681510400000⟩, + ⟨7, 1, 3, 3, 4, 4, -519442047944987789232866059474447686704761405440000⟩, + ⟨7, 1, 4, 3, 5, 4, 6412218206079385770054621385334627764174501969920000⟩, + ⟨7, 1, 5, 3, 6, 4, 1525668166055387345753000472415138950285990297600000⟩, + ⟨7, 1, 6, 3, 7, 4, 1676086395537985184191110594796794171547975680000⟩, + ⟨7, 1, 7, 3, 8, 4, -44709478479025136115126954705992605231459860480000⟩, + ⟨7, 1, 1, 4, 1, 4, -14828473008438827757679757101747440783354117488640000⟩, + ⟨7, 1, 2, 4, 2, 4, -8077244435672205761870882246023049722306599321600000⟩, + ⟨7, 1, 3, 4, 3, 4, -7671104892710277534568381982109381898729024389120000⟩, + ⟨7, 1, 4, 4, 4, 4, -4805738158784487217787865748084081870899039436800000⟩, + ⟨7, 1, 5, 4, 5, 4, 925091695024789796721450291834335685698283110400000⟩, + ⟨7, 1, 6, 4, 6, 4, 338718299396651987979192373761217301634015559680000⟩, + ⟨7, 1, 7, 4, 7, 4, -118260274505289620788772651304720794998548725760000⟩, + ⟨7, 1, 8, 4, 8, 4, 18096252371067452483668169600622364189733683200000⟩, + ⟨7, 1, 1, 5, 0, 4, -78155118522417277057224427503173088706530807644160000⟩, + ⟨7, 1, 2, 5, 1, 4, 8365619139820316986513531098662389103324792094720000⟩, + ⟨7, 1, 3, 5, 2, 4, -9578812464323410752335548349160379099818051502080000⟩, + ⟨7, 1, 4, 5, 3, 4, -4579310517102448625730908626463112281504706723840000⟩, + ⟨7, 1, 5, 5, 4, 4, 613647211998240857841177044920734655777131724800000⟩, + ⟨7, 1, 6, 5, 5, 4, 282958930843924718316628444936028495016508784640000⟩, + ⟨7, 1, 7, 5, 6, 4, 37464625715334887753241139078295529039121612800000⟩, + ⟨7, 1, 8, 5, 7, 4, -29668846256477811540705572252732033320951480320000⟩, + ⟨7, 1, 2, 6, 0, 4, -150598551224212498790730371570317232497594812334080000⟩, + ⟨7, 1, 3, 6, 1, 4, -2332076255121132959785389247751583219962861322240000⟩, + ⟨7, 1, 4, 6, 2, 4, 5800143438672435488947002388749824154094786314240000⟩, + ⟨7, 1, 5, 6, 3, 4, -5591892969157788792187314168022294189671501004800000⟩, + ⟨7, 1, 6, 6, 4, 4, -188665205349125905247120362463132476659455754240000⟩, + ⟨7, 1, 7, 6, 5, 4, 234067471171983811795417836597827482526070865920000⟩, + ⟨7, 1, 8, 6, 6, 4, 44317438895857771725072227117565871583574097920000⟩, + ⟨7, 1, 3, 7, 0, 4, 245124630379284754580445188906573392483654639288320000⟩, + ⟨7, 1, 4, 7, 1, 4, 5571718157431591213875716886921271482210362327040000⟩, + ⟨7, 1, 5, 7, 2, 4, 309789300547952596832119253513697382067758694400000⟩, + ⟨7, 1, 6, 7, 3, 4, -952417906865678395638148421652106863607629742080000⟩, + ⟨7, 1, 7, 7, 4, 4, 182008415647100601350145067837176643341149798400000⟩, + ⟨7, 1, 8, 7, 5, 4, 114476635453634806466654453337195989410460467200000⟩ +] + +def collectedFourData_9_4_52 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 4, 5, 1299804786025869516450414596723238967783194624000000⟩, + ⟨7, 2, 1, 0, 5, 5, -4308606266094654153552280053367357242131192217600000⟩, + ⟨7, 2, 2, 0, 6, 5, 1838350123443719136244345359564681740867233382400000⟩, + ⟨7, 2, 3, 0, 7, 5, -175148641976818706240764614217517440500026572800000⟩, + ⟨7, 2, 4, 0, 8, 5, 168997521429599721473275159674916016173036339200000⟩, + ⟨7, 2, 0, 1, 3, 5, 1021598086255896246469288468497206508664966348800000⟩, + ⟨7, 2, 1, 1, 4, 5, -1882065514798374778729737210616349027274326016000000⟩, + ⟨7, 2, 2, 1, 5, 5, -897643550524425996416307866271290233457108582400000⟩, + ⟨7, 2, 3, 1, 6, 5, 830503287603592486947139934791796084495194521600000⟩, + ⟨7, 2, 4, 1, 7, 5, -197092975224380618230185750414476246300963635200000⟩, + ⟨7, 2, 5, 1, 8, 5, -193493322514104949113396577811655589147705344000000⟩, + ⟨7, 2, 0, 2, 2, 5, 852215479687327735946480526252267099089220403200000⟩, + ⟨7, 2, 1, 2, 3, 5, -2842742928243467431904724492939892054480335667200000⟩, + ⟨7, 2, 2, 2, 4, 5, -3307033148641786026637269561392503775873413939200000⟩, + ⟨7, 2, 3, 2, 5, 5, 353420092591785805152935729853865957380430233600000⟩, + ⟨7, 2, 4, 2, 6, 5, 129942060246508538909195632964720070406176768000000⟩, + ⟨7, 2, 5, 2, 7, 5, -99182435831474060432895304670714670940894003200000⟩, + ⟨7, 2, 6, 2, 8, 5, 29301628437344737260147567009515828173760102400000⟩, + ⟨7, 2, 0, 3, 1, 5, 2731810296613822915867758289733692922854480281600000⟩, + ⟨7, 2, 1, 3, 2, 5, 7325211487861455793538007676342367491185652531200000⟩, + ⟨7, 2, 2, 3, 3, 5, 3767033040792863864040839217797452610496626688000000⟩, + ⟨7, 2, 3, 3, 4, 5, -38508190630195696803277150166312076077904691200000⟩, + ⟨7, 2, 4, 3, 5, 5, 356521370409351951106411368823790223188243251200000⟩, + ⟨7, 2, 5, 3, 6, 5, 67862107978332928962710892557192477193063628800000⟩, + ⟨7, 2, 6, 3, 7, 5, 62127290895489691730575395035247388341043200000⟩, + ⟨7, 2, 7, 3, 8, 5, -1420492122591564847832387174502646322665881600000⟩, + ⟨7, 2, 0, 4, 0, 5, 8723838277600302027583922776318036054087041024000000⟩, + ⟨7, 2, 1, 4, 1, 5, -3297871250254359032091614331656883547785501081600000⟩, + ⟨7, 2, 2, 4, 2, 5, -898194716021027279075337864466138964900708352000000⟩, + ⟨7, 2, 3, 4, 3, 5, -568687827104822769318564505944012893137246617600000⟩, + ⟨7, 2, 4, 4, 4, 5, -267200569153112392772013556186506727362920448000000⟩, + ⟨7, 2, 5, 4, 5, 5, 41148313830225270955173837232615458482631475200000⟩, + ⟨7, 2, 6, 4, 6, 5, 12555230073021886698791549148698936882705203200000⟩, + ⟨7, 2, 7, 4, 7, 5, -3757319344019842163087937537197748455158579200000⟩, + ⟨7, 2, 8, 4, 8, 5, 503078691901784772090799732244812583141376000000⟩, + ⟨7, 2, 1, 5, 0, 5, -17381797727157737797570853803498785094259598950400000⟩, + ⟨7, 2, 2, 5, 1, 5, 930262166444595473813705357015059564832646758400000⟩, + ⟨7, 2, 3, 5, 2, 5, -710113356911232230202792790811426376938579558400000⟩, + ⟨7, 2, 4, 5, 3, 5, -254611120304584127786051273601808155187504742400000⟩, + ⟨7, 2, 5, 5, 4, 5, 27295184030021749418456253380065772775564902400000⟩, + ⟨7, 2, 6, 5, 5, 5, 10488404329762879157339923831133614567430553600000⟩, + ⟨7, 2, 7, 5, 6, 5, 1190311484609269142468376530617705143730176000000⟩, + ⟨7, 2, 8, 5, 7, 5, -824798641115745453214661310100145572518297600000⟩, + ⟨7, 2, 2, 6, 0, 5, -16746654632936396668996181015769595800670804377600000⟩, + ⟨7, 2, 3, 6, 1, 5, -172885574727035381049087504216014818131522355200000⟩, + ⟨7, 2, 4, 6, 2, 5, 322489818790908846447033256279399869717046886400000⟩, + ⟨7, 2, 5, 6, 3, 5, -248728821194064398301625096605697213687293542400000⟩, + ⟨7, 2, 6, 6, 4, 5, -6993230256976215520372762393624647237736857600000⟩, + ⟨7, 2, 7, 6, 5, 5, 7436700455155498616087593008504033222485606400000⟩, + ⟨7, 2, 8, 6, 6, 5, 1232031844549826490044259002244339487840665600000⟩, + ⟨7, 2, 3, 7, 0, 5, 18172009817352019744733611733394436421859252633600000⟩, + ⟨7, 2, 4, 7, 1, 5, 309789300547952596832119253513697382067758694400000⟩, + ⟨7, 2, 5, 7, 2, 5, 13779506862670018647179791255249445167772467200000⟩, + ⟨7, 2, 6, 7, 3, 5, -35303158901259880524446267142364516307907379200000⟩, + ⟨7, 2, 7, 7, 4, 5, 5782700435509867814442302954529007733833728000000⟩, + ⟨7, 2, 8, 7, 5, 5, 3182468659058325354646486246362780580970496000000⟩ +] + +def collectedFourData_9_4_53 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 4, 6, -19980634441716701040968949177977154953212329984000000⟩, + ⟨7, 3, 1, 0, 5, 6, 33116006219419263550532567329450719811554036940800000⟩, + ⟨7, 3, 2, 0, 6, 6, -9419722660743886129713193372131576404312378572800000⟩, + ⟨7, 3, 3, 0, 7, 6, 673097419305909633823756262306635199861175091200000⟩, + ⟨7, 3, 4, 0, 8, 6, -519566897051541050302128490692460682619062845440000⟩, + ⟨7, 3, 0, 1, 3, 6, -15704033503558875140455282720796993656372120780800000⟩, + ⟨7, 3, 1, 1, 4, 6, 14465581082188462342221263657837947081224880128000000⟩, + ⟨7, 3, 2, 1, 5, 6, 4599533672239776013779712027142800645777312972800000⟩, + ⟨7, 3, 3, 1, 6, 6, -3191629768302958705908225355663120836388611686400000⟩, + ⟨7, 3, 4, 1, 7, 6, 605943712675373772596417933383412896345242992640000⟩, + ⟨7, 3, 5, 1, 8, 6, 495730767372654915577061433283207580388163584000000⟩, + ⟨7, 3, 0, 2, 2, 6, -13100279479095441873560753598913381165916435251200000⟩, + ⟨7, 3, 1, 2, 3, 6, 21849360716185864631098437492615237114598627737600000⟩, + ⟨7, 3, 2, 2, 4, 6, 16945267766369495094836298417392981204913251942400000⟩, + ⟨7, 3, 3, 2, 5, 6, -1358195813393011595789684839851233393041106534400000⟩, + ⟨7, 3, 4, 2, 6, 6, -399494575231905849428826385917743259071388057600000⟩, + ⟨7, 3, 5, 2, 7, 6, 254105849162012249278846359659348760340935475200000⟩, + ⟨7, 3, 6, 2, 8, 6, -64346489636410842157262424970902314524291891200000⟩, + ⟨7, 3, 0, 3, 1, 6, -41993462008742070100771412308650157726378858905600000⟩, + ⟨7, 3, 1, 3, 2, 6, -56301674882550574619253801938718878586979850649600000⟩, + ⟨7, 3, 2, 3, 3, 6, -19302311374536069702207227731070878299073806336000000⟩, + ⟨7, 3, 3, 3, 4, 6, 147987237827143810288747883352853342642293964800000⟩, + ⟨7, 3, 4, 3, 5, 6, -1096091236067714917423657618180638009601126563840000⟩, + ⟨7, 3, 5, 3, 6, 6, -173863027553173682359243627315384333701532876800000⟩, + ⟨7, 3, 6, 3, 7, 6, -136431771643445606331617745922935406303641600000⟩, + ⟨7, 3, 7, 3, 8, 6, 2729480431790335807220978281601217722528563200000⟩, + ⟨7, 3, 0, 4, 0, 6, -134103078729483856276478377362108862095251472384000000⟩, + ⟨7, 3, 1, 4, 1, 6, 25347483174241870186159896198898356624391195852800000⟩, + ⟨7, 3, 2, 4, 2, 6, 4602357849229755260644773628571797511989100544000000⟩, + ⟨7, 3, 3, 4, 3, 6, 2185471177479089919509092967164893590863636070400000⟩, + ⟨7, 3, 4, 4, 4, 6, 821482879931590862605628784106695692085991833600000⟩, + ⟨7, 3, 5, 4, 5, 6, -105422166130107298567075734662133111929910067200000⟩, + ⟨7, 3, 6, 4, 6, 6, -27571333910807917851492665525784531699341721600000⟩, + ⟨7, 3, 7, 4, 7, 6, 7219701864153343218567374843133732300678758400000⟩, + ⟨7, 3, 8, 4, 8, 6, -859259922581646971209140402246276008116224000000⟩, + ⟨7, 3, 1, 5, 0, 6, 133596733163317035066747782578547099341646148403200000⟩, + ⟨7, 3, 2, 5, 1, 6, -4766671755256163065423253622208827822791511244800000⟩, + ⟨7, 3, 3, 5, 2, 6, 2728970447940257560541990110015268891146164633600000⟩, + ⟨7, 3, 4, 5, 3, 6, 782777810067333860642624980062483760849543495680000⟩, + ⟨7, 3, 5, 5, 4, 6, -69930384929920012331921564144415911577020006400000⟩, + ⟨7, 3, 6, 5, 5, 6, -23032576566544273982893950542613957812473036800000⟩, + ⟨7, 3, 7, 5, 6, 6, -2287187555147372957826067575795917732708352000000⟩, + ⟨7, 3, 8, 5, 7, 6, 1408758565844654390921695988719837126223462400000⟩, + ⟨7, 3, 2, 6, 0, 6, 85810009815767297503893037654196970789438436147200000⟩, + ⟨7, 3, 3, 6, 1, 6, 664400436512594651213693288933846747982908620800000⟩, + ⟨7, 3, 4, 6, 2, 6, -991464449078950773222227465911754983987457556480000⟩, + ⟨7, 3, 5, 6, 3, 6, 637244364798382737692843479918860241643923046400000⟩, + ⟨7, 3, 6, 6, 4, 6, 15357160753633939644080258578151347195792588800000⟩, + ⟨7, 3, 7, 6, 5, 6, -14289645149457552171857056002073940357598412800000⟩, + ⟨7, 3, 8, 6, 6, 6, -2104314105143382449586600582055244243297894400000⟩, + ⟨7, 3, 3, 7, 0, 6, -69835157004986473505972198466701944562546796134400000⟩, + ⟨7, 3, 4, 7, 1, 6, -952417906865678395638148421652106863607629742080000⟩, + ⟨7, 3, 5, 7, 2, 6, -35303158901259880524446267142364516307907379200000⟩, + ⟨7, 3, 6, 7, 3, 6, 77525873800150325008560953076232059186944409600000⟩, + ⟨7, 3, 7, 7, 4, 6, -11111478501431968402455072025062278437011456000000⟩, + ⟨7, 3, 8, 7, 5, 6, -5435666065011633757700226645392812727599104000000⟩ +] + +def collectedFourData_9_4_54 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 4, 7, 11454982919195463297717750841646347017215016960000000⟩, + ⟨7, 4, 1, 0, 5, 7, -12657031710778378552948282487477210940249735168000000⟩, + ⟨7, 4, 2, 0, 6, 7, 2700183582686797846494955685943743106741436416000000⟩, + ⟨7, 4, 3, 0, 7, 7, -154355848180790487838833473041717969332417331200000⟩, + ⟨7, 4, 4, 0, 8, 7, 99289972472523030581952485702296906834850611200000⟩, + ⟨7, 4, 0, 1, 3, 7, 9003189366707838035145831526253643970853732352000000⟩, + ⟨7, 4, 1, 1, 4, 7, -5528786208668188545974726043273970578232442880000000⟩, + ⟨7, 4, 2, 1, 5, 7, -1318466132931367377641717328152494014166204416000000⟩, + ⟨7, 4, 3, 1, 6, 7, 731909981876731427823256432363103720661476966400000⟩, + ⟨7, 4, 4, 1, 7, 7, -115796704703202026098579026093058240311145267200000⟩, + ⟨7, 4, 5, 1, 8, 7, -81201303611365741249428380709300220786114560000000⟩, + ⟨7, 4, 0, 2, 2, 7, 7510446082553519629496968610320658313907273728000000⟩, + ⟨7, 4, 1, 2, 3, 7, -8350887773503067592495920947358032030750212096000000⟩, + ⟨7, 4, 2, 2, 4, 7, -4857397130986162755951054408392039866489110528000000⟩, + ⟨7, 4, 3, 2, 5, 7, 311463780366385827464731222735502141485901414400000⟩, + ⟨7, 4, 4, 2, 6, 7, 76343981117340821878844107003073950434459648000000⟩, + ⟨7, 4, 5, 2, 7, 7, -41622847652942841842955227967615878842810368000000⟩, + ⟨7, 4, 6, 2, 8, 7, 9222529217545015958039766609202275346808832000000⟩, + ⟨7, 4, 0, 3, 1, 7, 24075030822029012196587397541675878036289880064000000⟩, + ⟨7, 4, 1, 3, 2, 7, 21518660180118598708505715050851750988130287616000000⟩, + ⟨7, 4, 2, 3, 3, 7, 5533048706267852685749227942991479206492241920000000⟩, + ⟨7, 4, 3, 3, 4, 7, -33936685774692572483677167957650055117982924800000⟩, + ⟨7, 4, 4, 3, 5, 7, 209464593056514783675241595973460251643163443200000⟩, + ⟨7, 4, 5, 3, 6, 7, 28478975718938326893340414015556882962317312000000⟩, + ⟨7, 4, 6, 3, 7, 7, 19554229100807400601018865846683724414976000000⟩, + ⟨7, 4, 7, 3, 8, 7, -347738393233147690555373661119436998836224000000⟩, + ⟨7, 4, 0, 4, 0, 7, 76881866826536006857804679059238105321004072960000000⟩, + ⟨7, 4, 1, 4, 1, 7, -9687880120540297704233413157501868201568370688000000⟩, + ⟨7, 4, 2, 4, 2, 7, -1319275689286431186052914173535448418935111680000000⟩, + ⟨7, 4, 3, 4, 3, 7, -501175977798751992062761193830189848037058150400000⟩, + ⟨7, 4, 4, 4, 4, 7, -156986545905686033728880677228585150870192128000000⟩, + ⟨7, 4, 5, 4, 5, 7, 17268279240904109086757107567117140542619648000000⟩, + ⟨7, 4, 6, 4, 6, 7, 3951690822543819401023155884166526613323776000000⟩, + ⟨7, 4, 7, 4, 7, 7, -919796858267380741690202875988179773554688000000⟩, + ⟨7, 4, 8, 4, 8, 7, 98523475468542784186683367982083721920512000000⟩, + ⟨7, 4, 1, 5, 0, 7, -51061051169658651157954506855654023089537155072000000⟩, + ⟨7, 4, 2, 5, 1, 7, 1366376620751074744899953960770936216020320256000000⟩, + ⟨7, 4, 3, 5, 2, 7, -625812157453374872839517584448166629194963353600000⟩, + ⟨7, 4, 4, 5, 3, 7, -149589952044187713098620024067028329060263526400000⟩, + ⟨7, 4, 5, 5, 4, 7, 11454682243043967979947649700754289669963776000000⟩, + ⟨7, 4, 6, 5, 5, 7, 3301168588070092714429891986665959480885248000000⟩, + ⟨7, 4, 7, 5, 6, 7, 291389861669795208484822457641173925232640000000⟩, + ⟨7, 4, 8, 5, 7, 7, -161529458497358149981614643402714834481971200000⟩, + ⟨7, 4, 2, 6, 0, 7, -24597622252758554293141988185081289794318761984000000⟩, + ⟨7, 4, 3, 6, 1, 7, -152361441253691921232910126811654319946648780800000⟩, + ⟨7, 4, 4, 6, 2, 7, 189470265359820908255432757778391128636548710400000⟩, + ⟨7, 4, 5, 6, 3, 7, -104381403266275665745276103957499722518757376000000⟩, + ⟨7, 4, 6, 6, 4, 7, -2201081435043527475733605917820272894803968000000⟩, + ⟨7, 4, 7, 6, 5, 7, 1820514331690914444043786366387122755076096000000⟩, + ⟨7, 4, 8, 6, 6, 7, 241282449777590576015969110343582636782387200000⟩, + ⟨7, 4, 3, 7, 0, 7, 16014717310102036123915994820846198721121511014400000⟩, + ⟨7, 4, 4, 7, 1, 7, 182008415647100601350145067837176643341149798400000⟩, + ⟨7, 4, 5, 7, 2, 7, 5782700435509867814442302954529007733833728000000⟩, + ⟨7, 4, 6, 7, 3, 7, -11111478501431968402455072025062278437011456000000⟩, + ⟨7, 4, 7, 7, 4, 7, 1415612889372573371904990740859670411345920000000⟩, + ⟨7, 4, 8, 7, 5, 7, 623258106350790553228056898770684138749952000000⟩ +] + +def collectedFourData_9_4_55 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 4, 8, 16811118859061199940152552673082448149395537920000000⟩, + ⟨7, 5, 1, 0, 5, 8, -13931417401084162310307027847099744315508785152000000⟩, + ⟨7, 5, 2, 0, 6, 8, 2377643378608632609619375913775961622025810739200000⟩, + ⟨7, 5, 3, 0, 7, 8, -113264879077651469990194769325348146098942771200000⟩, + ⟨7, 5, 4, 0, 8, 8, 62449760592262595739052659274775154141010329600000⟩, + ⟨7, 5, 0, 1, 3, 8, 13212912461068223959006485991180530375934869504000000⟩, + ⟨7, 5, 1, 1, 4, 8, -6085457487534203607670440985678335762046648320000000⟩, + ⟨7, 5, 2, 1, 5, 8, -1160973754149224577771315405789698000105452339200000⟩, + ⟨7, 5, 3, 1, 6, 8, 537068705656666476170593721246081613579052646400000⟩, + ⟨7, 5, 4, 1, 7, 8, -72831891338162011454623306440537650608314777600000⟩, + ⟨7, 5, 5, 1, 8, 8, -44688568377321765908560119410787274897489920000000⟩, + ⟨7, 5, 0, 2, 2, 8, 11022190313946407893739943028500236137352134656000000⟩, + ⟨7, 5, 1, 2, 3, 8, -9191705124923558120630185960246867925290450944000000⟩, + ⟨7, 5, 2, 2, 4, 8, -4277175152020557724662729476434005705184876953600000⟩, + ⟨7, 5, 3, 2, 5, 8, 228549211682263980915341537422970580069934694400000⟩, + ⟨7, 5, 4, 2, 6, 8, 48017571409414258134591071004551557398134784000000⟩, + ⟨7, 5, 5, 2, 7, 8, -22906842509570618784478771341073590282878976000000⟩, + ⟨7, 5, 6, 2, 8, 8, 4511603842362406080940762616693555868991488000000⟩, + ⟨7, 5, 0, 3, 1, 8, 35332065315128163747809822142694295408348233728000000⟩, + ⟨7, 5, 1, 3, 2, 8, 23685287651292846489890489525121594351339700224000000⟩, + ⟨7, 5, 2, 3, 3, 8, 4872119327118647684624927083511890521152815104000000⟩, + ⟨7, 5, 3, 3, 4, 8, -24902422913479039904376111066417686144404684800000⟩, + ⟨7, 5, 4, 3, 5, 8, 131745566679002022914739207654753970280831385600000⟩, + ⟨7, 5, 5, 3, 6, 8, 15673204703991034566361333800986849820278784000000⟩, + ⟨7, 5, 6, 3, 7, 8, 9565807064921541021768005671953874550784000000⟩, + ⟨7, 5, 7, 3, 8, 8, -153100310190038888920786697771717004519014400000⟩, + ⟨7, 5, 0, 4, 0, 8, 112830390969992585798339086360273330619988049920000000⟩, + ⟨7, 5, 1, 4, 1, 8, -10663313861810048393882933153035592736473874432000000⟩, + ⟨7, 5, 2, 4, 2, 8, -1161686608015743056859293514320366551449993216000000⟩, + ⟨7, 5, 3, 4, 3, 8, -367758249467245250104843636037809444173014630400000⟩, + ⟨7, 5, 4, 4, 4, 8, -98738794702852571122982385493570821631770624000000⟩, + ⟨7, 5, 5, 4, 5, 8, 9503476462757369123533359604645795448487936000000⟩, + ⟨7, 5, 6, 4, 6, 8, 1933142533709726395227386861096080175529984000000⟩, + ⟨7, 5, 7, 4, 7, 8, -404963003950337569678063916377637821140172800000⟩, + ⟨7, 5, 8, 4, 8, 8, 39433966737280875229784570380787700989952000000⟩, + ⟨7, 5, 1, 5, 0, 8, -56202183342628662645776897595662701165132382208000000⟩, + ⟨7, 5, 2, 5, 1, 8, 1203161276086932021277069597872286407020720947200000⟩, + ⟨7, 5, 3, 5, 2, 8, -459215113484128976363999992214846261746571673600000⟩, + ⟨7, 5, 4, 5, 3, 8, -94086607736272464125680863546558410235523891200000⟩, + ⟨7, 5, 5, 5, 4, 8, 6304004097135136910845299229665354665951232000000⟩, + ⟨7, 5, 6, 5, 5, 8, 1614911108971004184896847783290597101535232000000⟩, + ⟨7, 5, 7, 5, 6, 8, 128291494629318379346533237637468739600384000000⟩, + ⟨7, 5, 8, 5, 7, 8, -64652076707440017605634646116507556459315200000⟩, + ⟨7, 5, 2, 6, 0, 8, -21659406439540413504756751213962785986687323340800000⟩, + ⟨7, 5, 3, 6, 1, 8, -111801401910496346419170686220351769548737740800000⟩, + ⟨7, 5, 4, 6, 2, 8, 119169865963531285130945204391198627435066163200000⟩, + ⟨7, 5, 5, 6, 3, 8, -57445573774419627376557522241081135104786432000000⟩, + ⟨7, 5, 6, 6, 4, 8, -1076755326597745866220311972733982670323712000000⟩, + ⟨7, 5, 7, 6, 5, 8, 801525843309503207882577109035432917178777600000⟩, + ⟨7, 5, 8, 6, 6, 8, 96573167497091320716494999977579890553651200000⟩, + ⟨7, 5, 3, 7, 0, 8, 11751449918936201083730363442488108310661064294400000⟩, + ⟨7, 5, 4, 7, 1, 8, 114476635453634806466654453337195989410460467200000⟩, + ⟨7, 5, 5, 7, 2, 8, 3182468659058325354646486246362780580970496000000⟩, + ⟨7, 5, 6, 7, 3, 8, -5435666065011633757700226645392812727599104000000⟩, + ⟨7, 5, 7, 7, 4, 8, 623258106350790553228056898770684138749952000000⟩, + ⟨7, 5, 8, 7, 5, 8, 249458713445660140956536198727693282312192000000⟩ +] + +def collectedFourData_9_4 : List (List CollectedFourTerm) := [ + collectedFourData_9_4_0, + collectedFourData_9_4_1, + collectedFourData_9_4_2, + collectedFourData_9_4_3, + collectedFourData_9_4_4, + collectedFourData_9_4_5, + collectedFourData_9_4_6, + collectedFourData_9_4_7, + collectedFourData_9_4_8, + collectedFourData_9_4_9, + collectedFourData_9_4_10, + collectedFourData_9_4_11, + collectedFourData_9_4_12, + collectedFourData_9_4_13, + collectedFourData_9_4_14, + collectedFourData_9_4_15, + collectedFourData_9_4_16, + collectedFourData_9_4_17, + collectedFourData_9_4_18, + collectedFourData_9_4_19, + collectedFourData_9_4_20, + collectedFourData_9_4_21, + collectedFourData_9_4_22, + collectedFourData_9_4_23, + collectedFourData_9_4_24, + collectedFourData_9_4_25, + collectedFourData_9_4_26, + collectedFourData_9_4_27, + collectedFourData_9_4_28, + collectedFourData_9_4_29, + collectedFourData_9_4_30, + collectedFourData_9_4_31, + collectedFourData_9_4_32, + collectedFourData_9_4_33, + collectedFourData_9_4_34, + collectedFourData_9_4_35, + collectedFourData_9_4_36, + collectedFourData_9_4_37, + collectedFourData_9_4_38, + collectedFourData_9_4_39, + collectedFourData_9_4_40, + collectedFourData_9_4_41, + collectedFourData_9_4_42, + collectedFourData_9_4_43, + collectedFourData_9_4_44, + collectedFourData_9_4_45, + collectedFourData_9_4_46, + collectedFourData_9_4_47, + collectedFourData_9_4_48, + collectedFourData_9_4_49, + collectedFourData_9_4_50, + collectedFourData_9_4_51, + collectedFourData_9_4_52, + collectedFourData_9_4_53, + collectedFourData_9_4_54, + collectedFourData_9_4_55 +] + +theorem collectedFourChecked_9_4 : collectNumericRowParts 9 4 = collectedFourData_9_4 := by + decide +kernel + +def collectedFourData_9_5_0 : List CollectedFourTerm := [ + ⟨0, 5, 4, 1, 8, 0, -65341630359759375672236861404773549337354646323200000⟩, + ⟨0, 5, 4, 2, 7, 0, 8859769464057849753802834686667269164821905408000000⟩, + ⟨0, 5, 5, 2, 8, 0, -110521483419612851171507922251763830313380216832000000⟩, + ⟨0, 5, 4, 3, 6, 0, 7215638668895064210200137878434780838470929612800000⟩, + ⟨0, 5, 5, 3, 7, 0, 8706749010138060840438276295289864045904003072000000⟩, + ⟨0, 5, 6, 3, 8, 0, -56414833310285525219406033457143744005960368128000000⟩, + ⟨0, 5, 4, 4, 5, 0, -18658857862137120813647738156188093428078634598400000⟩, + ⟨0, 5, 5, 4, 6, 0, 21322751479977628766885349273742460272886415360000000⟩, + ⟨0, 5, 6, 4, 7, 0, 24616975797588146787590362937252754482062688256000000⟩, + ⟨0, 5, 7, 4, 8, 0, -48157788824636969721200344780242283466242129920000000⟩, + ⟨0, 5, 4, 5, 4, 0, -2605685024978229081626533685174394880322961408000000⟩, + ⟨0, 5, 5, 5, 5, 0, 5868049365269121652806559789958141275778580480000000⟩, + ⟨0, 5, 6, 5, 6, 0, 41693359690713449568393494784761482963870285824000000⟩, + ⟨0, 5, 7, 5, 7, 0, -21966498444484284668719748586822523486539350016000000⟩, + ⟨0, 5, 8, 5, 8, 0, -33150924256380616672337452219205865680035381248000000⟩, + ⟨0, 5, 4, 6, 3, 0, 65132396007636868510564604408594382165091811328000000⟩, + ⟨0, 5, 5, 6, 4, 0, -48933931118765311885137336046764253991625818112000000⟩, + ⟨0, 5, 6, 6, 5, 0, -3965773230936130986080574431803248922501054464000000⟩, + ⟨0, 5, 7, 6, 6, 0, -6641055536732721201413207870973242548401733632000000⟩, + ⟨0, 5, 8, 6, 7, 0, -8936081589714980542518574708759497294502428672000000⟩, + ⟨0, 5, 4, 7, 2, 0, -66933816695952804786540942159238575060613595136000000⟩, + ⟨0, 5, 5, 7, 3, 0, -68223518681210202203229721311834559012965187584000000⟩, + ⟨0, 5, 6, 7, 4, 0, -137626769829932951132016403909322693931329126400000000⟩, + ⟨0, 5, 7, 7, 5, 0, 23858235615179351246424420241899410445047955456000000⟩, + ⟨0, 5, 8, 7, 6, 0, -13360049786009891199947684896902282183916388352000000⟩ +] + +def collectedFourData_9_5_1 : List CollectedFourTerm := [ + ⟨0, 6, 3, 0, 8, 1, 3777860355414456583290423351117857551229229465600000⟩, + ⟨0, 6, 3, 1, 7, 1, -50467386080368770506524952248011788079529249996800000⟩, + ⟨0, 6, 4, 1, 8, 1, 78561131415846401069948956914512253076922538393600000⟩, + ⟨0, 6, 3, 2, 6, 1, 16428187391662735754895159824176720251085180108800000⟩, + ⟨0, 6, 4, 2, 7, 1, -10652221399247543287624934189150541828832886784000000⟩, + ⟨0, 6, 5, 2, 8, 1, 66440741801185053938332475011463544771987898368000000⟩, + ⟨0, 6, 3, 3, 5, 1, 32814774362039865244242657972425703327391757107200000⟩, + ⟨0, 6, 4, 3, 6, 1, -8675460569245821668224815571480889572934968934400000⟩, + ⟨0, 6, 5, 3, 7, 1, -5234121412522141424491479629718726617100976128000000⟩, + ⟨0, 6, 6, 3, 8, 1, 22609440612824909508703993412084105747468648448000000⟩, + ⟨0, 6, 3, 4, 4, 1, -13420089697113229781017717956713440223534304460800000⟩, + ⟨0, 6, 4, 4, 5, 1, 22433798736061279019320881576791537094589887283200000⟩, + ⟨0, 6, 5, 4, 6, 1, -12818317142860809330235575479027966665178480640000000⟩, + ⟨0, 6, 6, 4, 7, 1, -9865775004628838235369452590695950262674128896000000⟩, + ⟨0, 6, 7, 4, 8, 1, 14475191220813366404304199459585276481938391040000000⟩, + ⟨0, 6, 3, 5, 3, 1, -33787601838395867444114296710152495069226703257600000⟩, + ⟨0, 6, 4, 5, 4, 1, 3132850566301227918277902967175830413753974784000000⟩, + ⟨0, 6, 5, 5, 5, 1, -3527617805076138810281582619320968506003947520000000⟩, + ⟨0, 6, 6, 5, 6, 1, -16709497920371728059707640560644542942500880384000000⟩, + ⟨0, 6, 7, 5, 7, 1, 6602655005475250875101454701862096383395233792000000⟩, + ⟨0, 6, 8, 5, 8, 1, 7971561476881026249687306112621364026551356620800000⟩, + ⟨0, 6, 3, 6, 2, 1, -37784036185187925977385739895376495680165196595200000⟩, + ⟨0, 6, 4, 6, 3, 1, -78309566106819020103627249118232879095238098944000000⟩, + ⟨0, 6, 5, 6, 4, 1, 29416965663002583261395452386281925247487705088000000⟩, + ⟨0, 6, 6, 6, 5, 1, 1589367708588686676005939780251229534105370624000000⟩, + ⟨0, 6, 7, 6, 6, 1, 1996157862486165562221441622292537653837430784000000⟩, + ⟨0, 6, 8, 6, 7, 1, 2148794501291379987462949839106860167380284211200000⟩, + ⟨0, 6, 3, 7, 1, 1, 347344368287509705792719096745786644740249223168000000⟩, + ⟨0, 6, 4, 7, 2, 1, 80475438715917075532900232244876324321443708928000000⟩, + ⟨0, 6, 5, 7, 3, 1, 41013032482173774401634116973309654893976354816000000⟩, + ⟨0, 6, 6, 7, 4, 1, 55156846109788556229962712074585536056419942400000000⟩, + ⟨0, 6, 7, 7, 5, 1, -7171270341720144778146424921874441731489923072000000⟩, + ⟨0, 6, 8, 7, 6, 1, 3212593934929905207104276613783794148598559539200000⟩ +] + +def collectedFourData_9_5_2 : List CollectedFourTerm := [ + ⟨0, 7, 2, 0, 7, 2, 605032072930613544970569357483345429512847360000000⟩, + ⟨0, 7, 3, 0, 8, 2, -368638484568712665467482958290880753553113088000000⟩, + ⟨0, 7, 2, 1, 6, 2, -1392675104319005964356966256102222539991810048000000⟩, + ⟨0, 7, 3, 1, 7, 2, 4924539018004618585678180866195478144314507264000000⟩, + ⟨0, 7, 4, 1, 8, 2, -3832944273553478572371694308374002096630923264000000⟩, + ⟨0, 7, 2, 2, 5, 2, -2920407840147413226816727229321863899088158720000000⟩, + ⟨0, 7, 3, 2, 6, 2, -1603040222382437112301154088569566262433153024000000⟩, + ⟨0, 7, 4, 2, 7, 2, 519714651215347530511472412459957619953500160000000⟩, + ⟨0, 7, 5, 2, 8, 2, -2161065794478699942694373902573742733530234880000000⟩, + ⟨0, 7, 2, 3, 4, 2, 215178808055211530584576970174073763918774272000000⟩, + ⟨0, 7, 3, 3, 5, 2, -3202021132133541269368548916376608064359366656000000⟩, + ⟨0, 7, 4, 3, 6, 2, 423269832168207166395102645732506624858259456000000⟩, + ⟨0, 7, 5, 3, 7, 2, 170246153822267918225676402924846664101396480000000⟩, + ⟨0, 7, 6, 3, 8, 2, -551549629971943955943361219440356741622005760000000⟩, + ⟨0, 7, 2, 4, 3, 2, 4576831192535574076649855625335993600481165312000000⟩, + ⟨0, 7, 3, 4, 4, 2, 1309514133212919785610775293904850634600873984000000⟩, + ⟨0, 7, 4, 4, 5, 2, -1094529812004374805979856225940074280221933568000000⟩, + ⟨0, 7, 5, 4, 6, 2, 416931328116543513908437923352699367482982400000000⟩, + ⟨0, 7, 6, 4, 7, 2, 240672232735510041401663820441601512591851520000000⟩, + ⟨0, 7, 7, 4, 8, 2, -282493901492955841905053684337226798690467840000000⟩, + ⟨0, 7, 2, 5, 2, 2, -622551544928256795061245420485486195930824704000000⟩, + ⟨0, 7, 3, 5, 3, 2, 3296948316542753929604146862762268980567605248000000⟩, + ⟨0, 7, 4, 5, 4, 2, -152849652513799554368246513628942694518620160000000⟩, + ⟨0, 7, 5, 5, 5, 2, 114740052080636168319095335838377682613043200000000⟩, + ⟨0, 7, 6, 5, 6, 2, 407622530465007241136759888274964659390382080000000⟩, + ⟨0, 7, 7, 5, 7, 2, -128855622302714595953158252469752434819858432000000⟩, + ⟨0, 7, 8, 5, 8, 2, -129642357755587455562672789835780613382078464000000⟩, + ⟨0, 7, 2, 6, 1, 2, 10446210435970146246873369372163993453763493888000000⟩, + ⟨0, 7, 3, 6, 2, 2, 3686914954448869257768662060974164982571728896000000⟩, + ⟨0, 7, 4, 6, 3, 2, 3820670572891541350069303186333660397237698560000000⟩, + ⟨0, 7, 5, 6, 4, 2, -956822524075663277686633084892520606943150080000000⟩, + ⟨0, 7, 6, 6, 5, 2, -38772085810216732912131713200884154242170880000000⟩, + ⟨0, 7, 7, 6, 6, 2, -38956474838048478645082996093976287918424064000000⟩, + ⟨0, 7, 8, 6, 7, 2, -34946075030290314691404331081773001627140096000000⟩, + ⟨0, 7, 2, 7, 0, 2, -85219913617001182446371939036378297785399640064000000⟩, + ⟨0, 7, 3, 7, 1, 2, -33893391894560130241203679845150955479383408640000000⟩, + ⟨0, 7, 4, 7, 2, 2, -3926342027269478314008870163912146543150366720000000⟩, + ⟨0, 7, 5, 7, 3, 2, -1333998676448984718242974384336689242371522560000000⟩, + ⟨0, 7, 6, 7, 4, 2, -1345532540288369699521610633115528685682688000000000⟩, + ⟨0, 7, 7, 7, 5, 2, 139952564811742337942025599598206726870925312000000⟩, + ⟨0, 7, 8, 7, 6, 2, -52246759112816813914495408139593730632974336000000⟩ +] + +def collectedFourData_9_5_3 : List CollectedFourTerm := [ + ⟨0, 8, 1, 0, 6, 3, 3777860355414456583290423351117857551229229465600000⟩, + ⟨0, 8, 2, 0, 7, 3, -368638484568712665467482958290880753553113088000000⟩, + ⟨0, 8, 3, 0, 8, 3, 112303411988459723583675207368939199240811315200000⟩, + ⟨0, 8, 1, 1, 5, 3, 822568073558143287895612965378401206582797926400000⟩, + ⟨0, 8, 2, 1, 6, 3, 848539545128559379336792884262910543652087398400000⟩, + ⟨0, 8, 3, 1, 7, 3, -1500230055576665521763833389693719405003381145600000⟩, + ⟨0, 8, 4, 1, 8, 3, 778455022830457613084086026133055638707005030400000⟩, + ⟨0, 8, 1, 2, 4, 3, -715185021285907614100920103968313759634974310400000⟩, + ⟨0, 8, 2, 2, 5, 3, 1779368018128178990683514982985080009576677376000000⟩, + ⟨0, 8, 3, 2, 6, 3, 488356191944823041577983061186961799359601049600000⟩, + ⟨0, 8, 4, 2, 7, 3, -105551881739749460875769243428187919693643776000000⟩, + ⟨0, 8, 5, 2, 8, 3, 329177598664786350913055933728696878420197376000000⟩, + ⟨0, 8, 1, 3, 3, 3, 1980664193826641752987624722874763382435191193600000⟩, + ⟨0, 8, 2, 3, 4, 3, -131105759945179045626807333871822263851522457600000⟩, + ⟨0, 8, 3, 3, 5, 3, 975475739648988756264861281313760743042475622400000⟩, + ⟨0, 8, 4, 3, 6, 3, -85964340556006369948013005997970435805387161600000⟩, + ⟨0, 8, 5, 3, 7, 3, -25932213743935758374840380457117196742557696000000⟩, + ⟨0, 8, 6, 3, 8, 3, 67210460024855284146558452039019433654065561600000⟩, + ⟨0, 8, 1, 4, 2, 3, -3414830530375355414630578520395474790383406284800000⟩, + ⟨0, 8, 2, 4, 3, 3, -2788606076320551523385010012300938764374088089600000⟩, + ⟨0, 8, 3, 4, 4, 3, -398935302099500008609940214938258248736283033600000⟩, + ⟨0, 8, 4, 4, 5, 3, 222294447553385249891374842958359295997824204800000⟩, + ⟨0, 8, 5, 4, 6, 3, -63507762580930820037148142958422023187988480000000⟩, + ⟨0, 8, 6, 4, 7, 3, -29327717032799903553929478016800395449545523200000⟩, + ⟨0, 8, 7, 4, 8, 3, 28686667590432911082890899494571669048000512000000⟩, + ⟨0, 8, 1, 5, 1, 3, -1548323957096496104494027746343393087563025612800000⟩, + ⟨0, 8, 2, 5, 2, 3, 379312880020796183961592045801262852712117043200000⟩, + ⟨0, 8, 3, 5, 3, 3, -1004394713510561259159456668077080085412393779200000⟩, + ⟨0, 8, 4, 5, 4, 3, 31043128009514799124763449384373632710475776000000⟩, + ⟨0, 8, 5, 5, 5, 3, -17477420128102724813058300726755906436464640000000⟩, + ⟨0, 8, 6, 5, 6, 3, -49671863238204548125190279190898681569922252800000⟩, + ⟨0, 8, 7, 5, 7, 3, 13085020188474829594224850377069299318233497600000⟩, + ⟨0, 8, 8, 5, 8, 3, 11284209887879413115298299728324639432743321600000⟩, + ⟨0, 8, 1, 6, 0, 3, 16879965108381274600373646298488333932983379558400000⟩, + ⟨0, 8, 2, 6, 1, 3, -6364745534809909313031352260244983701402183270400000⟩, + ⟨0, 8, 3, 6, 2, 3, -1123195614208062465593941883118132190131938918400000⟩, + ⟨0, 8, 4, 6, 3, 3, -775962285329699572109502105255166700490326016000000⟩, + ⟨0, 8, 5, 6, 4, 3, 145745003057430484527760449463231687390396416000000⟩, + ⟨0, 8, 6, 6, 5, 3, 4724669516250760724089662573843746967571660800000⟩, + ⟨0, 8, 7, 6, 6, 3, 3955948918784099169319265037430938523611955200000⟩, + ⟨0, 8, 8, 6, 7, 3, 3041743857688998421451893498485518329341542400000⟩, + ⟨0, 8, 2, 7, 0, 3, 51923428883167156347506671818687224248523764531200000⟩, + ⟨0, 8, 3, 7, 1, 3, 10325410159154507103614615861685948032646905856000000⟩, + ⟨0, 8, 4, 7, 2, 3, 797423717732431020948570269379453159412334592000000⟩, + ⟨0, 8, 5, 7, 3, 3, 203197182638951894698478350790105003628429312000000⟩, + ⟨0, 8, 6, 7, 4, 3, 163963233944683479322501364987174034950062080000000⟩, + ⟨0, 8, 7, 7, 5, 3, -14211891598244223353276937257218838848182681600000⟩, + ⟨0, 8, 8, 7, 6, 3, 4547613958872880297319628308180929052304998400000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0920.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0920.lean new file mode 100644 index 0000000000000000000000000000000000000000..18a2f53932149d4e5eccfbb210f803100586942e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0920.lean @@ -0,0 +1,657 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0920. -/ +namespace LaughlinFock +def collectedFourData_9_5_4 : List CollectedFourTerm := [ + ⟨1, 4, 4, 1, 8, 0, -46979529489734471588559533357847855185961733324800000⟩, + ⟨1, 4, 4, 2, 7, 0, 6370024722635150207169825091094251419532787712000000⟩, + ⟨1, 4, 5, 2, 8, 0, -79463081361351298590507752249747951113520283648000000⟩, + ⟨1, 4, 4, 3, 6, 0, 5187922428109312913263095685896526623816233779200000⟩, + ⟨1, 4, 5, 3, 7, 0, 6260005598718638379415798332007174433572651008000000⟩, + ⟨1, 4, 6, 3, 8, 0, -40561313064377193326952235611636539724285345792000000⟩, + ⟨1, 4, 4, 4, 5, 0, -13415403906402662912491170693274354040499181977600000⟩, + ⟨1, 4, 5, 4, 6, 0, 15330698460392338730087903077181072224592855040000000⟩, + ⟨1, 4, 6, 4, 7, 0, 17699190149731840301999152858950382635486019584000000⟩, + ⟨1, 4, 7, 4, 8, 0, -34624637429321854259617992526292162762904698880000000⟩, + ⟨1, 4, 4, 5, 4, 0, -1873443558079823407081846413585406064131571712000000⟩, + ⟨1, 4, 5, 5, 5, 0, 4219028461411864127467877083849332854850846720000000⟩, + ⟨1, 4, 6, 5, 6, 0, 29976821979058928461803767653503405618716737536000000⟩, + ⟨1, 4, 7, 5, 7, 0, -15793541663668034626992434873646306142111924224000000⟩, + ⟨1, 4, 8, 5, 8, 0, -23834955068303904185096893958495289933375209472000000⟩, + ⟨1, 4, 4, 6, 3, 0, 46829093521704839305245036367266115196490350592000000⟩, + ⟨1, 4, 5, 6, 4, 0, -35182670640223922927733170141050571300240621568000000⟩, + ⟨1, 4, 6, 6, 5, 0, -2851324024616052118164344693560577575140458496000000⟩, + ⟨1, 4, 7, 6, 6, 0, -4774806853044800575006592263708556548896718848000000⟩, + ⟨1, 4, 8, 6, 7, 0, -6424891853099978431975433937457233669189009408000000⟩, + ⟨1, 4, 4, 7, 2, 0, -48124284594902725040121267800198691222039035904000000⟩, + ⟨1, 4, 5, 7, 3, 0, -49051558556629322511147334042198345717358002176000000⟩, + ⟨1, 4, 6, 7, 4, 0, -98951324847628788809538992999608576166697369600000000⟩, + ⟨1, 4, 7, 7, 5, 0, 17153668763469145463371243041331760246380560384000000⟩, + ⟨1, 4, 8, 7, 6, 0, -9605650325075294821820053724453097971203964928000000⟩ +] + +def collectedFourData_9_5_5 : List CollectedFourTerm := [ + ⟨1, 5, 3, 0, 8, 1, 822568073558143287895612965378401206582797926400000⟩, + ⟨1, 5, 3, 1, 7, 1, -10988458185371374492794632594075664543948944179200000⟩, + ⟨1, 5, 4, 1, 8, 1, 17105417470676057082761117507246415764183737958400000⟩, + ⟨1, 5, 3, 2, 6, 1, 3576972461527021042002432844429053115673817907200000⟩, + ⟨1, 5, 4, 2, 7, 1, -2319349158296935430173805480026021651437060096000000⟩, + ⟨1, 5, 5, 2, 8, 1, 14466398396872215506098664375616008770019131392000000⟩, + ⟨1, 5, 3, 3, 5, 1, 7144887103236254178673802540631854505458977996800000⟩, + ⟨1, 5, 4, 3, 6, 1, -1888941415594299931162477205711578569694091673600000⟩, + ⟨1, 5, 5, 3, 7, 1, -1139645397664634466916030082250807120947576832000000⟩, + ⟨1, 5, 6, 3, 8, 1, 4922840512742649738068924382545614163423526912000000⟩, + ⟨1, 5, 3, 4, 4, 1, -2922007774403527605416594294584152749879014195200000⟩, + ⟨1, 5, 4, 4, 5, 1, 4884597330990701099861026741129020745481768140800000⟩, + ⟨1, 5, 5, 4, 6, 1, -2790981520359451890974524949011623431016284160000000⟩, + ⟨1, 5, 6, 4, 7, 1, -2148113158307918982385193713871247608144461824000000⟩, + ⟨1, 5, 7, 4, 8, 1, 3151739089515377309988080619069066926893301760000000⟩, + ⟨1, 5, 3, 5, 3, 1, -7356704573403914140465533709683745635795625574400000⟩, + ⟨1, 5, 4, 5, 4, 1, 682127609977586644605682741472754934896132096000000⟩, + ⟨1, 5, 5, 5, 5, 1, -768081800062339456450539013667844409660538880000000⟩, + ⟨1, 5, 6, 5, 6, 1, -3638223285512650535743186526517039899917418496000000⟩, + ⟨1, 5, 7, 5, 7, 1, 1437621483398365963965323273298790827738267648000000⟩, + ⟨1, 5, 8, 5, 8, 1, 1735678757392547892987803548122910473736893235200000⟩, + ⟨1, 5, 3, 6, 2, 1, -8226863603244946257484202487995703599257406668800000⟩, + ⟨1, 5, 4, 6, 3, 1, -17050643187840499442809935426861369118357979136000000⟩, + ⟨1, 5, 5, 6, 4, 1, 6405069139377297383233604847313260393447555072000000⟩, + ⟨1, 5, 6, 6, 5, 1, 346059147568965654716995843299192770245165056000000⟩, + ⟨1, 5, 7, 6, 6, 1, 434631133231246863737368815966481990702596096000000⟩, + ⟨1, 5, 8, 6, 7, 1, 467865295991246829382673894085664784685780172800000⟩, + ⟨1, 5, 3, 7, 1, 1, 75628625995674822787782094696202670352568942592000000⟩, + ⟨1, 5, 4, 7, 2, 1, 17522226965966328548606008097659463627578540032000000⟩, + ⟨1, 5, 5, 7, 3, 1, 8929925393162969595621866717036874776973410304000000⟩, + ⟨1, 5, 6, 7, 4, 1, 12009512364067866958466929395478011005475225600000000⟩, + ⟨1, 5, 7, 7, 5, 1, -1561428288766444668847941474012230626698067968000000⟩, + ⟨1, 5, 8, 7, 6, 1, 699490440506226398031906388665472495800601804800000⟩ +] + +def collectedFourData_9_5_6 : List CollectedFourTerm := [ + ⟨1, 6, 2, 0, 7, 2, -1392675104319005964356966256102222539991810048000000⟩, + ⟨1, 6, 3, 0, 8, 2, 848539545128559379336792884262910543652087398400000⟩, + ⟨1, 6, 2, 1, 6, 2, 3205687818821441981565378836178408377780954726400000⟩, + ⟨1, 6, 3, 1, 7, 2, -11335403852894788388220013397261358644073804595200000⟩, + ⟨1, 6, 4, 1, 8, 2, 8822748916704464650084479168439875156894233395200000⟩, + ⟨1, 6, 2, 2, 5, 2, 6722254034783665076265729075662935830923575296000000⟩, + ⟨1, 6, 3, 2, 6, 2, 3689910516843051616754766691965218287070163763200000⟩, + ⟨1, 6, 4, 2, 7, 2, -1196289731537019237676127891275953376579289088000000⟩, + ⟨1, 6, 5, 2, 8, 2, 4974385103566259857716472350338283448181981184000000⟩, + ⟨1, 6, 2, 3, 4, 2, -495302947336311532947453580370075749533194649600000⟩, + ⟨1, 6, 3, 3, 5, 2, 7370477225489420384670492471905754286863994060800000⟩, + ⟨1, 6, 4, 3, 6, 2, -974291089751119139152588475969851197479505100800000⟩, + ⟨1, 6, 5, 3, 7, 2, -391876051935394504389638285606600165308760064000000⟩, + ⟨1, 6, 6, 3, 8, 2, 1269568131715187633703468197588545088067207168000000⟩, + ⟨1, 6, 2, 4, 3, 2, -10535042923659933613515308409091885601130125721600000⟩, + ⟨1, 6, 3, 4, 4, 2, -3014266207815837528581983929049485585679594291200000⟩, + ⟨1, 6, 4, 4, 5, 2, 2519410934250204059940617863828326413062530662400000⟩, + ⟨1, 6, 5, 4, 6, 2, -959700992487978719941967448326605222780600320000000⟩, + ⟨1, 6, 6, 4, 7, 2, -553984229642737519696681692067331566611726336000000⟩, + ⟨1, 6, 7, 4, 8, 2, 650250195540135981872112311896084990302093312000000⟩, + ⟨1, 6, 2, 5, 2, 2, 1433001780512798160624171945245189021312955187200000⟩, + ⟨1, 6, 3, 5, 3, 2, -7588982545066042346145211089005420448271722086400000⟩, + ⟨1, 6, 4, 5, 4, 2, 351832432169578573480637375415536347238105088000000⟩, + ⟨1, 6, 5, 5, 5, 2, -264110980475730710120333734455945945950453760000000⟩, + ⟨1, 6, 6, 5, 6, 2, -938273813135910631428548946600992919879942144000000⟩, + ⟨1, 6, 7, 5, 7, 2, 296602486481908664942414371147126590687254937600000⟩, + ⟨1, 6, 8, 5, 8, 2, 298413410113765159479752927651678800225448755200000⟩, + ⟨1, 6, 2, 6, 1, 2, -24045299182546691652263899378230445020344116838400000⟩, + ⟨1, 6, 3, 6, 2, 2, -8486615666391686136413473062578628836492889292800000⟩, + ⟨1, 6, 4, 6, 3, 2, -8794497063431714315121738345185522351716958208000000⟩, + ⟨1, 6, 5, 6, 4, 2, 2202433504189897722043935050692170455181164544000000⟩, + ⟨1, 6, 6, 6, 5, 2, 89246373979584928400377068059801192427945984000000⟩, + ⟨1, 6, 7, 6, 6, 2, 89670804385938454561432939200326598126678835200000⟩, + ⟨1, 6, 8, 6, 7, 2, 80439584719223291748170478447147475473845452800000⟩, + ⟨1, 6, 2, 7, 0, 2, 196160926662518781832964314398384580770707747635200000⟩, + ⟨1, 6, 3, 7, 1, 2, 78016497313680044804804876491865952126083530752000000⟩, + ⟨1, 6, 4, 7, 2, 2, 9037733761672357457014811527806539736280989696000000⟩, + ⟨1, 6, 5, 7, 3, 2, 3070625226339142316153851589971051164790161408000000⟩, + ⟨1, 6, 6, 7, 4, 2, 3097174108199094263283710540096852090840678400000000⟩, + ⟨1, 6, 7, 7, 5, 2, -322145653956527109179872234336796269348493721600000⟩, + ⟨1, 6, 8, 7, 6, 2, 120262650449799759315873408156967882587950284800000⟩ +] + +def collectedFourData_9_5_7 : List CollectedFourTerm := [ + ⟨1, 7, 1, 0, 6, 3, -50467386080368770506524952248011788079529249996800000⟩, + ⟨1, 7, 2, 0, 7, 3, 4924539018004618585678180866195478144314507264000000⟩, + ⟨1, 7, 3, 0, 8, 3, -1500230055576665521763833389693719405003381145600000⟩, + ⟨1, 7, 1, 1, 5, 3, -10988458185371374492794632594075664543948944179200000⟩, + ⟨1, 7, 2, 1, 6, 3, -11335403852894788388220013397261358644073804595200000⟩, + ⟨1, 7, 3, 1, 7, 3, 20041156183988830208143899709460421200552185036800000⟩, + ⟨1, 7, 4, 1, 8, 3, -10399164206025023370605955282583288327649309491200000⟩, + ⟨1, 7, 1, 2, 4, 3, 9553957847172187506745927980521283704367297331200000⟩, + ⟨1, 7, 2, 2, 5, 3, -23770082613358999944042461675414995253883568128000000⟩, + ⟨1, 7, 3, 2, 6, 3, -6523814584172003878710834474213307053809388748800000⟩, + ⟨1, 7, 4, 2, 7, 3, 1410038240199845320656660807683649390224867328000000⟩, + ⟨1, 7, 5, 2, 8, 3, -4397392015037021714398175806609747587134128128000000⟩, + ⟨1, 7, 1, 3, 3, 3, -26459142255522921990023752834134478314873343180800000⟩, + ⟨1, 7, 2, 3, 4, 3, 1751405394069314923710291042895959717799840972800000⟩, + ⟨1, 7, 3, 3, 5, 3, -13031109181773336600380691330475327212253033267200000⟩, + ⟨1, 7, 4, 3, 6, 3, 1148373723704862933889038820634899625462779084800000⟩, + ⟨1, 7, 5, 3, 7, 3, 346421233134826830187060165989157672832729088000000⟩, + ⟨1, 7, 6, 3, 8, 3, -897845848074351370254716956389370182631214284800000⟩, + ⟨1, 7, 1, 4, 2, 3, 45617771585571730870153949917501972152502871654400000⟩, + ⟨1, 7, 2, 4, 3, 3, 37252213221177189391589172293396074117106289868800000⟩, + ⟨1, 7, 3, 4, 4, 3, 5329265779580481025073673971553109886202858700800000⟩, + ⟨1, 7, 4, 4, 5, 3, -2969569717451407156188974725864841550951245414400000⟩, + ⟨1, 7, 5, 4, 6, 3, 848382542430056285259963716826671189789245440000000⟩, + ⟨1, 7, 6, 4, 7, 3, 391780817474854444189473488070900299805071769600000⟩, + ⟨1, 7, 7, 4, 8, 3, -383217216213581546427079184420212008378433536000000⟩, + ⟨1, 7, 1, 5, 1, 3, 20683629242219762944324876568227267874241537638400000⟩, + ⟨1, 7, 2, 5, 2, 3, -5067135298908106746264665769554608851527506329600000⟩, + ⟨1, 7, 3, 5, 3, 3, 13417429712871940258736006018595338932838832537600000⟩, + ⟨1, 7, 4, 5, 4, 3, -414696515754780822204610343938482111227363328000000⟩, + ⟨1, 7, 5, 5, 5, 3, 233475996017063675855334315024897875556433920000000⟩, + ⟨1, 7, 6, 5, 6, 3, 663552610085486261125402474824939124061267558400000⟩, + ⟨1, 7, 7, 5, 7, 3, -174799146499614939842432523864141304517414092800000⟩, + ⟨1, 7, 8, 5, 8, 3, -150742622396652579747063450192900752046607564800000⟩, + ⟨1, 7, 1, 6, 0, 3, -225494760526788681257349106621432515517465441075200000⟩, + ⟨1, 7, 2, 6, 1, 3, 85024865926606169570459832333406484030471484211200000⟩, + ⟨1, 7, 3, 6, 2, 3, 15004457913531461634583655639314227625528079155200000⟩, + ⟨1, 7, 4, 6, 3, 3, 10365864418840600488839903251148763973495554048000000⟩, + ⟨1, 7, 5, 6, 4, 3, -1946966972466862887746152991089437403930165248000000⟩, + ⟨1, 7, 6, 6, 5, 3, -63115546406324921083783830573797300976903782400000⟩, + ⟨1, 7, 7, 6, 6, 3, -52846421682146053506020152652433295194823065600000⟩, + ⟨1, 7, 8, 6, 7, 3, -40633810459291054202561692945385691846751027200000⟩, + ⟨1, 7, 2, 7, 0, 3, -693630649504483373810664417726490060649056016793600000⟩, + ⟨1, 7, 3, 7, 1, 3, -137934283408166020282856447119652160523959533568000000⟩, + ⟨1, 7, 4, 7, 2, 3, -10652561727107719015404386584692657368938315776000000⟩, + ⟨1, 7, 5, 7, 3, 3, -2714454665320250578234102293985138225956519936000000⟩, + ⟨1, 7, 6, 7, 4, 3, -2190339253438171828871832935983487184525066240000000⟩, + ⟨1, 7, 7, 7, 5, 3, 189852708344021014438540691697986134589885644800000⟩, + ⟨1, 7, 8, 7, 6, 3, -60750310444371507588173314325835324908057395200000⟩ +] + +def collectedFourData_9_5_8 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 5, 4, -65341630359759375672236861404773549337354646323200000⟩, + ⟨1, 8, 1, 0, 6, 4, 78561131415846401069948956914512253076922538393600000⟩, + ⟨1, 8, 2, 0, 7, 4, -3832944273553478572371694308374002096630923264000000⟩, + ⟨1, 8, 3, 0, 8, 4, 778455022830457613084086026133055638707005030400000⟩, + ⟨1, 8, 0, 1, 4, 4, -46979529489734471588559533357847855185961733324800000⟩, + ⟨1, 8, 1, 1, 5, 4, 17105417470676057082761117507246415764183737958400000⟩, + ⟨1, 8, 2, 1, 6, 4, 8822748916704464650084479168439875156894233395200000⟩, + ⟨1, 8, 3, 1, 7, 4, -10399164206025023370605955282583288327649309491200000⟩, + ⟨1, 8, 4, 1, 8, 4, 4047020111679064064977887135183251353240181145600000⟩, + ⟨1, 8, 0, 2, 3, 4, -18388704118830444856144489592501221383563378688000000⟩, + ⟨1, 8, 1, 2, 4, 4, -14872371966677191077759158863039937233742620262400000⟩, + ⟨1, 8, 2, 2, 5, 4, 18501102682233237732597315312010454895194800128000000⟩, + ⟨1, 8, 3, 2, 6, 4, 3385144973056277843218414501274860573592597299200000⟩, + ⟨1, 8, 4, 2, 7, 4, -548741514536249799906853170904155795870449664000000⟩, + ⟨1, 8, 5, 2, 8, 4, 1369058787511480062725256939374072850034144051200000⟩, + ⟨1, 8, 0, 3, 2, 4, 80801163101317439943187235672692844650326235545600000⟩, + ⟨1, 8, 1, 3, 3, 4, 41188187329069646192657933478414180098812516761600000⟩, + ⟨1, 8, 2, 3, 4, 4, -1363181254392562554695562969797501651426004172800000⟩, + ⟨1, 8, 3, 3, 5, 4, 6761717883131130177298509394016905425987620044800000⟩, + ⟨1, 8, 4, 3, 6, 4, -446910103877839839326347073687842748170135142400000⟩, + ⟨1, 8, 5, 3, 7, 4, -107852798154454484348217779269380675831280435200000⟩, + ⟨1, 8, 6, 3, 8, 4, 232941810345311257035797396990950096965835161600000⟩, + ⟨1, 8, 0, 4, 1, 4, 66694072878460514916217871143740467089067999232000000⟩, + ⟨1, 8, 1, 4, 2, 4, -71011875723561895086325162781954165867857890508800000⟩, + ⟨1, 8, 2, 4, 3, 4, -28994725561370377503190421260577062091079077068800000⟩, + ⟨1, 8, 3, 4, 4, 4, -2765305026846861683358703159823031098961769267200000⟩, + ⟨1, 8, 4, 4, 5, 4, 1155660986927783682382517534746489992267379507200000⟩, + ⟨1, 8, 5, 4, 6, 4, -264130550770425474664535789567892607966642176000000⟩, + ⟨1, 8, 6, 4, 7, 4, -101645658970181099791550851977937476159484723200000⟩, + ⟨1, 8, 7, 4, 8, 4, 85220463075263688012614071633808254404919296000000⟩, + ⟨1, 8, 0, 5, 0, 4, -412719008714786071807833032305030747963655612006400000⟩, + ⟨1, 8, 1, 5, 1, 4, -32197611987809073768828291771259460471663414476800000⟩, + ⟨1, 8, 2, 5, 2, 4, 3943932042422961736309028657940334779993528729600000⟩, + ⟨1, 8, 3, 5, 3, 4, -6962175910710534182846154474994828663511737958400000⟩, + ⟨1, 8, 4, 5, 4, 4, 161386540903977086248149192755980668883697664000000⟩, + ⟨1, 8, 5, 5, 5, 4, -72689076372342771498526653386822223101165568000000⟩, + ⟨1, 8, 6, 5, 6, 4, -172155550514802413183244771662749542690639052800000⟩, + ⟨1, 8, 7, 5, 7, 4, 38872116334031496650170631765176046144244940800000⟩, + ⟨1, 8, 8, 5, 8, 4, 29332089216027710245019639832273168788304691200000⟩, + ⟨1, 8, 1, 6, 0, 4, 351021221648347612400508135698311886311333979750400000⟩, + ⟨1, 8, 2, 6, 1, 4, -66177884218508541252144804811659121489054217011200000⟩, + ⟨1, 8, 3, 6, 2, 4, -7785669660608850495144951942278920764734098636800000⟩, + ⟨1, 8, 4, 6, 3, 4, -4034060905940980552473324839653788721845633024000000⟩, + ⟨1, 8, 5, 6, 4, 4, 606157520988708008415317460208660701783470899200000⟩, + ⟨1, 8, 6, 6, 5, 4, 16375026595439939672255006586535846976736460800000⟩, + ⟨1, 8, 7, 6, 6, 4, 11752072550710029369792243247908897257265561600000⟩, + ⟨1, 8, 8, 6, 7, 4, 7906685810751505879604861559513989667146956800000⟩, + ⟨1, 8, 2, 7, 0, 4, 539877461882036420652211367289084116813819255193600000⟩, + ⟨1, 8, 3, 7, 1, 4, 71572780014951197287633973107154061050052083712000000⟩, + ⟨1, 8, 4, 7, 2, 4, 4145634273716926327828035847186178994641829888000000⟩, + ⟨1, 8, 5, 7, 3, 4, 845102733654492141886882136741815990190761574400000⟩, + ⟨1, 8, 6, 7, 4, 4, 568273041592361844420749927792249097242542080000000⟩, + ⟨1, 8, 7, 7, 5, 4, -42219751714268205738532378412448759208004812800000⟩, + ⟨1, 8, 8, 7, 6, 4, 11821033079594713466742911191326676052921548800000⟩ +] + +def collectedFourData_9_5_9 : List CollectedFourTerm := [ + ⟨2, 3, 4, 1, 8, 0, -18388704118830444856144489592501221383563378688000000⟩, + ⟨2, 3, 4, 2, 7, 0, 2493351915748077545591198652119390236673310720000000⟩, + ⟨2, 3, 5, 2, 8, 0, -31103399872144999082754564763592390989452410880000000⟩, + ⟨2, 3, 4, 3, 6, 0, 2030654022254358706934892885675518675021463552000000⟩, + ⟨2, 3, 5, 3, 7, 0, 2450288284862720358752969708737228834319892480000000⟩, + ⟨2, 3, 6, 3, 8, 0, -15876489030718465944793047527864520966427115520000000⟩, + ⟨2, 3, 4, 4, 5, 0, -5251050739521465360540448221817517358559789056000000⟩, + ⟨2, 3, 5, 4, 6, 0, 6000734383360839492465580448817794653775462400000000⟩, + ⟨2, 3, 6, 4, 7, 0, 6927808225015423833432920903179674837885911040000000⟩, + ⟨2, 3, 7, 4, 8, 0, -13552758399777243274149504676336917747125452800000000⟩, + ⟨2, 3, 4, 5, 4, 0, -733302347789297219547722121449204274136350720000000⟩, + ⟨2, 3, 5, 5, 5, 0, 1651410026632553163519141740159105754149683200000000⟩, + ⟨2, 3, 6, 5, 6, 0, 11733512782758257168661335667440310208859996160000000⟩, + ⟨2, 3, 7, 5, 7, 0, -6181900240296640206213538024222013838002749440000000⟩, + ⟨2, 3, 8, 5, 8, 0, -9329466284510799351536678025923113215401656320000000⟩, + ⟨2, 3, 4, 6, 3, 0, 18329820546879576015049154622184177972826603520000000⟩, + ⟨2, 3, 5, 6, 4, 0, -13771183482259205919425242757792399601256366080000000⟩, + ⟨2, 3, 6, 6, 5, 0, -1116063834718361394571170584823626571983093760000000⟩, + ⟨2, 3, 7, 6, 6, 0, -1868952528875167731237251896498342987699322880000000⟩, + ⟨2, 3, 8, 6, 7, 0, -2514827980726281665602897584525964141374996480000000⟩, + ⟨2, 3, 4, 7, 2, 0, -18836783593999718611837734940955449347004170240000000⟩, + ⟨2, 3, 5, 7, 3, 0, -19199736707930159586143612474563145847338434560000000⟩, + ⟨2, 3, 6, 7, 4, 0, -38731478466316269571383894817098580755480576000000000⟩, + ⟨2, 3, 7, 7, 5, 0, 6714280514724692092183524344566893029401559040000000⟩, + ⟨2, 3, 8, 7, 6, 0, -3759838883345006857334845962929788474286407680000000⟩ +] + +def collectedFourData_9_5_10 : List CollectedFourTerm := [ + ⟨2, 4, 3, 0, 8, 1, -715185021285907614100920103968313759634974310400000⟩, + ⟨2, 4, 3, 1, 7, 1, 9553957847172187506745927980521283704367297331200000⟩, + ⟨2, 4, 4, 1, 8, 1, -14872371966677191077759158863039937233742620262400000⟩, + ⟨2, 4, 3, 2, 6, 1, -3110012664326293641970425458917203867965010739200000⟩, + ⟨2, 4, 4, 2, 7, 1, 2016567175979503692840969080883450544291577856000000⟩, + ⟨2, 4, 5, 2, 8, 1, -12577866535280932850666218189767880494035238912000000⟩, + ⟨2, 4, 3, 3, 5, 1, -6212149971867626118335906594005988788136627404800000⟩, + ⟨2, 4, 4, 3, 6, 1, 1642347484598975715577710953243559479706491289600000⟩, + ⟨2, 4, 5, 3, 7, 1, 990869137993058588103403295742926879302090752000000⟩, + ⟨2, 4, 6, 3, 8, 1, -4280182893147647068157098942936651620660805632000000⟩, + ⟨2, 4, 3, 4, 4, 1, 2540551061378701117729135859787895727526720307200000⟩, + ⟨2, 4, 4, 4, 5, 1, -4246932209545258363985559595844263377873194188800000⟩, + ⟨2, 4, 5, 4, 6, 1, 2426629773524460966260363825080065444292853760000000⟩, + ⟨2, 4, 6, 4, 7, 1, 1867685367611576650581733229617678605839499264000000⟩, + ⟨2, 4, 7, 4, 8, 1, -2740291849733884215336759862467967860458127360000000⟩, + ⟨2, 4, 3, 5, 3, 1, 6396315497834732598330664714238081176760116838400000⟩, + ⟨2, 4, 4, 5, 4, 1, -593078512215125568877630006650279616478969856000000⟩, + ⟨2, 4, 5, 5, 5, 1, 667811718184894652819737074587500361212231680000000⟩, + ⟨2, 4, 6, 5, 6, 1, 3163267432246538485783520739920061288998240256000000⟩, + ⟨2, 4, 7, 5, 7, 1, -1249945608462352379685684003452742118856982528000000⟩, + ⟨2, 4, 8, 5, 8, 1, -1509092668381498316179027949565934787108221747200000⟩, + ⟨2, 4, 3, 6, 2, 1, 7152878661764768357894206811051265556833160396800000⟩, + ⟨2, 4, 4, 6, 3, 1, 14824748252731892159609231387543517429598519296000000⟩, + ⟨2, 4, 5, 6, 4, 1, -5568912356357662010985924301554766217994043392000000⟩, + ⟨2, 4, 6, 6, 5, 1, -300882476206146419928484773586910454183100416000000⟩, + ⟨2, 4, 7, 6, 6, 1, -377891734755659184342325767832667222081273856000000⟩, + ⟨2, 4, 8, 6, 7, 1, -406787307249878788868406447464106378952232140800000⟩, + ⟨2, 4, 3, 7, 1, 1, -65755603981288482439224475084288147284780122112000000⟩, + ⟨2, 4, 4, 7, 2, 1, -15234768608783517947537235036420117529941245952000000⟩, + ⟨2, 4, 5, 7, 3, 1, -7764158478416062215728486325804718832215916544000000⟩, + ⟨2, 4, 6, 7, 4, 1, -10441717387080343961928497382098176564631961600000000⟩, + ⟨2, 4, 7, 7, 5, 1, 1357589918494342449994263580005186488707842048000000⟩, + ⟨2, 4, 8, 7, 6, 1, -608174692969497002699544516325659975281855692800000⟩ +] + +def collectedFourData_9_5_11 : List CollectedFourTerm := [ + ⟨2, 5, 2, 0, 7, 2, -2920407840147413226816727229321863899088158720000000⟩, + ⟨2, 5, 3, 0, 8, 2, 1779368018128178990683514982985080009576677376000000⟩, + ⟨2, 5, 2, 1, 6, 2, 6722254034783665076265729075662935830923575296000000⟩, + ⟨2, 5, 3, 1, 7, 2, -23770082613358999944042461675414995253883568128000000⟩, + ⟨2, 5, 4, 1, 8, 2, 18501102682233237732597315312010454895194800128000000⟩, + ⟨2, 5, 2, 2, 5, 2, 14096412957883935535481545662675685681334845440000000⟩, + ⟨2, 5, 3, 2, 6, 2, 7737657957273631688704101004249529321571483648000000⟩, + ⟨2, 5, 4, 2, 7, 2, -2508592205198420266925432868637467360960184320000000⟩, + ⟨2, 5, 5, 2, 8, 2, 10431171786811665007169682672170850833934581760000000⟩, + ⟨2, 5, 2, 3, 4, 2, -1038638951872692845064304311428974050325561344000000⟩, + ⟨2, 5, 3, 3, 5, 2, 15455722162472712232933814904532953210355187712000000⟩, + ⟨2, 5, 4, 3, 6, 2, -2043066130981246502411476969322783171319693312000000⟩, + ⟨2, 5, 5, 3, 7, 2, -821755117822509889294443621850913925192744960000000⟩, + ⟨2, 5, 6, 3, 8, 2, 2662255334330340996176771104928653431558635520000000⟩, + ⟨2, 5, 2, 4, 3, 2, -22091744050806697105690641429194254716632039424000000⟩, + ⟨2, 5, 3, 4, 4, 2, -6320847294747358330031438464454143281954029568000000⟩, + ⟨2, 5, 4, 4, 5, 2, 5283147104532472145653063271091805711641870336000000⟩, + ⟨2, 5, 5, 4, 6, 2, -2012471030728755324727532616808876542315724800000000⟩, + ⟨2, 5, 6, 4, 7, 2, -1161692258696461120346179108761740543828951040000000⟩, + ⟨2, 5, 7, 4, 8, 2, 1363559787364316904426877875453583211290951680000000⟩, + ⟨2, 5, 2, 5, 2, 2, 3004971957764080492869747426533570579433259008000000⟩, + ⟨2, 5, 3, 5, 3, 2, -15913922819917159583839639940442176778399645696000000⟩, + ⟨2, 5, 4, 5, 4, 2, 737784563061172201141575186202306155978424320000000⟩, + ⟨2, 5, 5, 5, 5, 2, -553834685245919194354059312438421892785766400000000⟩, + ⟨2, 5, 6, 5, 6, 2, -1967538725715215898186132368837061990584156160000000⟩, + ⟨2, 5, 7, 5, 7, 2, 621968630187110395996066061921596730102513664000000⟩, + ⟨2, 5, 8, 5, 8, 2, 625766095623220123691961525352330284685590528000000⟩, + ⟨2, 5, 2, 6, 1, 2, -50422442415768555837938652011807050028575358976000000⟩, + ⟨2, 5, 3, 6, 2, 2, -17796238944450203755014542184633924522388488192000000⟩, + ⟨2, 5, 4, 6, 3, 2, -18441859192103658014956549428738558407076741120000000⟩, + ⟨2, 5, 5, 6, 4, 2, 4618452683682212239619450073345832905772892160000000⟩, + ⟨2, 5, 6, 6, 5, 2, 187147604970043837744770555785867282884853760000000⟩, + ⟨2, 5, 7, 6, 6, 2, 188037625824489921321189534282185131035721728000000⟩, + ⟨2, 5, 8, 6, 7, 2, 168679969322128301934457181982789011182190592000000⟩, + ⟨2, 5, 2, 7, 0, 2, 411344976570055853351992909592558180642196553728000000⟩, + ⟨2, 5, 3, 7, 1, 2, 163598810454158739249545812741154739194198753280000000⟩, + ⟨2, 5, 4, 7, 2, 2, 18951920984944346284119344931978908127398461440000000⟩, + ⟨2, 5, 5, 7, 3, 2, 6439030867533313240378874158267443220441989120000000⟩, + ⟨2, 5, 6, 7, 4, 2, 6494703265561038217750019794019881976856576000000000⟩, + ⟨2, 5, 7, 7, 5, 2, -675532068151739259009077440812926525635559424000000⟩, + ⟨2, 5, 8, 7, 6, 2, 252188027316135295868161195864229614895235072000000⟩ +] + +def collectedFourData_9_5_12 : List CollectedFourTerm := [ + ⟨2, 6, 1, 0, 6, 3, 16428187391662735754895159824176720251085180108800000⟩, + ⟨2, 6, 2, 0, 7, 3, -1603040222382437112301154088569566262433153024000000⟩, + ⟨2, 6, 3, 0, 8, 3, 488356191944823041577983061186961799359601049600000⟩, + ⟨2, 6, 1, 1, 5, 3, 3576972461527021042002432844429053115673817907200000⟩, + ⟨2, 6, 2, 1, 6, 3, 3689910516843051616754766691965218287070163763200000⟩, + ⟨2, 6, 3, 1, 7, 3, -6523814584172003878710834474213307053809388748800000⟩, + ⟨2, 6, 4, 1, 8, 3, 3385144973056277843218414501274860573592597299200000⟩, + ⟨2, 6, 1, 2, 4, 3, -3110012664326293641970425458917203867965010739200000⟩, + ⟨2, 6, 2, 2, 5, 3, 7737657957273631688704101004249529321571483648000000⟩, + ⟨2, 6, 3, 2, 6, 3, 2123637795041847994464717388948878870635662540800000⟩, + ⟨2, 6, 4, 2, 7, 3, -458996873793391965286224219048710335887310848000000⟩, + ⟨2, 6, 5, 2, 8, 3, 1431442871691160857730512796706011047052443648000000⟩, + ⟨2, 6, 1, 3, 3, 3, 8613002989775930263304349280604870729104411852800000⟩, + ⟨2, 6, 2, 3, 4, 3, -570119006495003743432769591058996434582686924800000⟩, + ⟨2, 6, 3, 3, 5, 3, 4241897989693246868251321259834835375043588915200000⟩, + ⟨2, 6, 4, 3, 6, 3, -373819612900925613672719192756267615053991116800000⟩, + ⟨2, 6, 5, 3, 7, 3, -112767340977930712012992333894188969396011008000000⟩, + ⟨2, 6, 6, 3, 8, 3, 292267561024512163533581053144694634847194316800000⟩, + ⟨2, 6, 1, 4, 2, 3, -14849536665211887743123160246308499550707803750400000⟩, + ⟨2, 6, 2, 4, 3, 3, -12126372833677046305588867043871057880653024460800000⟩, + ⟨2, 6, 3, 4, 4, 3, -1734787229667512834655212060147884367452884172800000⟩, + ⟨2, 6, 4, 4, 5, 3, 966656916076645061034284784494471496839095910400000⟩, + ⟨2, 6, 5, 4, 6, 3, -276166222769316540987960946922851335709655040000000⟩, + ⟨2, 6, 6, 4, 7, 3, -127532832306513090726101410736559679564519833600000⟩, + ⟨2, 6, 7, 4, 8, 3, 124745201379014051047136317670594320086859776000000⟩, + ⟨2, 6, 1, 5, 1, 3, -6732952972633498846244472487039718628591560294400000⟩, + ⟨2, 6, 2, 5, 2, 3, 1649458287710927062261950520225156300457744793600000⟩, + ⟨2, 6, 3, 5, 3, 3, -4367653384831559083092010781968718313293453721600000⟩, + ⟨2, 6, 4, 5, 4, 3, 134992370332792479648609172873035671402446848000000⟩, + ⟨2, 6, 5, 5, 5, 3, -76001309200268324055642072883349026473246720000000⟩, + ⟨2, 6, 6, 5, 6, 3, -216000222507098199123101558351216859712743014400000⟩, + ⟨2, 6, 7, 5, 7, 3, 56900770133514278882607219055106915497200844800000⟩, + ⟨2, 6, 8, 5, 8, 3, 49069869493521609317100023852099982051822796800000⟩, + ⟨2, 6, 1, 6, 0, 3, 73403250484835271215502083992515040843402523443200000⟩, + ⟨2, 6, 2, 6, 1, 3, -27677368274411715439238234155972846527110656819200000⟩, + ⟨2, 6, 3, 6, 2, 3, -4884264184423370168568336124266037481080828723200000⟩, + ⟨2, 6, 4, 6, 3, 3, -3374305197382201740010960437673486405355962368000000⟩, + ⟨2, 6, 5, 6, 4, 3, 633778381510147888152262859156287951699181568000000⟩, + ⟨2, 6, 6, 6, 5, 3, 20545427536886507452960489824909902603511398400000⟩, + ⟨2, 6, 7, 6, 6, 3, 17202613129013084856759787072954629042575769600000⟩, + ⟨2, 6, 8, 6, 7, 3, 13227153306483689207822579478259496633185075200000⟩, + ⟨2, 6, 2, 7, 0, 3, 225791252047685264965415909596277309673934789017600000⟩, + ⟨2, 6, 3, 7, 1, 3, 44900487850816574858317751638728442599532658688000000⟩, + ⟨2, 6, 4, 7, 2, 3, 3467631154415067059644392641722214993274863616000000⟩, + ⟨2, 6, 5, 7, 3, 3, 883611642517792587348383858026848571071922176000000⟩, + ⟨2, 6, 6, 7, 4, 3, 713001137992245509715474359345865576771747840000000⟩, + ⟨2, 6, 7, 7, 5, 3, -61801018672205388463860407217837351388368076800000⟩, + ⟨2, 6, 8, 7, 6, 3, 19775493870288603460019503151118243985568563200000⟩ +] + +def collectedFourData_9_5_13 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 5, 4, 8859769464057849753802834686667269164821905408000000⟩, + ⟨2, 7, 1, 0, 6, 4, -10652221399247543287624934189150541828832886784000000⟩, + ⟨2, 7, 2, 0, 7, 4, 519714651215347530511472412459957619953500160000000⟩, + ⟨2, 7, 3, 0, 8, 4, -105551881739749460875769243428187919693643776000000⟩, + ⟨2, 7, 0, 1, 4, 4, 6370024722635150207169825091094251419532787712000000⟩, + ⟨2, 7, 1, 1, 5, 4, -2319349158296935430173805480026021651437060096000000⟩, + ⟨2, 7, 2, 1, 6, 4, -1196289731537019237676127891275953376579289088000000⟩, + ⟨2, 7, 3, 1, 7, 4, 1410038240199845320656660807683649390224867328000000⟩, + ⟨2, 7, 4, 1, 8, 4, -548741514536249799906853170904155795870449664000000⟩, + ⟨2, 7, 0, 2, 3, 4, 2493351915748077545591198652119390236673310720000000⟩, + ⟨2, 7, 1, 2, 4, 4, 2016567175979503692840969080883450544291577856000000⟩, + ⟨2, 7, 2, 2, 5, 4, -2508592205198420266925432868637467360960184320000000⟩, + ⟨2, 7, 3, 2, 6, 4, -458996873793391965286224219048710335887310848000000⟩, + ⟨2, 7, 4, 2, 7, 4, 74404683314164954924045831653646867271516160000000⟩, + ⟨2, 7, 5, 2, 8, 4, -185632730210604788984866483343558145346633728000000⟩, + ⟨2, 7, 0, 3, 2, 4, -10955950648367727508773285476543808790188785664000000⟩, + ⟨2, 7, 1, 3, 3, 4, -5584767970569651522270307863773103154689736704000000⟩, + ⟨2, 7, 2, 3, 4, 4, 184835786697498884961668168950678316050808832000000⟩, + ⟨2, 7, 3, 3, 5, 4, -916831448736438958951098783632402860329664512000000⟩, + ⟨2, 7, 4, 3, 6, 4, 60597209921383850164604665761628421993005056000000⟩, + ⟨2, 7, 5, 3, 7, 4, 14623922336203389543153069354586710567026688000000⟩, + ⟨2, 7, 6, 3, 8, 4, -31584928732827285690088174371181109868232704000000⟩, + ⟨2, 7, 0, 4, 1, 4, -9043149169509171867108670619876927375230894080000000⟩, + ⟨2, 7, 1, 4, 2, 4, 9628606520178684441057993815486667340143132672000000⟩, + ⟨2, 7, 2, 4, 3, 4, 3931438238271605716564974519500672531611779072000000⟩, + ⟨2, 7, 3, 4, 4, 4, 374951847708284212113501661534269849382944768000000⟩, + ⟨2, 7, 4, 4, 5, 4, -156697803014896199621790964036564245301690368000000⟩, + ⟨2, 7, 5, 4, 6, 4, 35813856730482947001489754216658879580733440000000⟩, + ⟨2, 7, 6, 4, 7, 4, 13782287043340384817182778210949978189201408000000⟩, + ⟨2, 7, 7, 4, 8, 4, -11555170146658568845951534854702920619786240000000⟩, + ⟨2, 7, 0, 5, 0, 4, 55961188150876020483476069065345844130103689216000000⟩, + ⟨2, 7, 1, 5, 1, 4, 4365722402923897520333104297665747033985646592000000⟩, + ⟨2, 7, 2, 5, 2, 4, -534763648923236656211814001475588477234970624000000⟩, + ⟨2, 7, 3, 5, 3, 4, 944011852742198605834445991368244683757060096000000⟩, + ⟨2, 7, 4, 5, 4, 4, -21882642645102264214938873312690374348636160000000⟩, + ⟨2, 7, 5, 5, 5, 4, 9856020666586609250675398144242225166417920000000⟩, + ⟨2, 7, 6, 5, 6, 4, 23342828777324862406603251700008759205036032000000⟩, + ⟨2, 7, 7, 5, 7, 4, -5270728437649361491724039069139433005514752000000⟩, + ⟨2, 7, 8, 5, 8, 4, -3977181881173677336184607859439113577955328000000⟩, + ⟨2, 7, 1, 6, 0, 4, -47595492853076784586180989228074346114057240576000000⟩, + ⟨2, 7, 2, 6, 1, 4, 8973158376473314124395550995554962189611696128000000⟩, + ⟨2, 7, 3, 6, 2, 4, 1055670602899201310459081029123302050330836992000000⟩, + ⟨2, 7, 4, 6, 3, 4, 546984356432839133986967508237231013295554560000000⟩, + ⟨2, 7, 5, 6, 4, 4, -82189805569530592163194524008538988345294848000000⟩, + ⟨2, 7, 6, 6, 5, 4, -2220314366272084736869354198249552113303552000000⟩, + ⟨2, 7, 7, 6, 6, 4, -1593481107693569869368379410537535928008704000000⟩, + ⟨2, 7, 8, 6, 7, 4, -1072079363834435595003101911582823040417792000000⟩, + ⟨2, 7, 2, 7, 0, 4, -73202793147035524948528171725997749468905078784000000⟩, + ⟨2, 7, 3, 7, 1, 4, -9704660372611641186793272409371752287992545280000000⟩, + ⟨2, 7, 4, 7, 2, 4, -562112756372981991590589639935716768843038720000000⟩, + ⟨2, 7, 5, 7, 3, 4, -114588744608904130041332323001502244207067136000000⟩, + ⟨2, 7, 6, 7, 4, 4, -77052992302560365511845900435541726540595200000000⟩, + ⟨2, 7, 7, 7, 5, 4, 5724639329607860002607061877932924371730432000000⟩, + ⟨2, 7, 8, 7, 6, 4, -1602831569025402077381566226760149627830272000000⟩ +] + +def collectedFourData_9_5_14 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 5, 5, -110521483419612851171507922251763830313380216832000000⟩, + ⟨2, 8, 1, 0, 6, 5, 66440741801185053938332475011463544771987898368000000⟩, + ⟨2, 8, 2, 0, 7, 5, -2161065794478699942694373902573742733530234880000000⟩, + ⟨2, 8, 3, 0, 8, 5, 329177598664786350913055933728696878420197376000000⟩, + ⟨2, 8, 0, 1, 4, 5, -79463081361351298590507752249747951113520283648000000⟩, + ⟨2, 8, 1, 1, 5, 5, 14466398396872215506098664375616008770019131392000000⟩, + ⟨2, 8, 2, 1, 6, 5, 4974385103566259857716472350338283448181981184000000⟩, + ⟨2, 8, 3, 1, 7, 5, -4397392015037021714398175806609747587134128128000000⟩, + ⟨2, 8, 4, 1, 8, 5, 1369058787511480062725256939374072850034144051200000⟩, + ⟨2, 8, 0, 2, 3, 5, -31103399872144999082754564763592390989452410880000000⟩, + ⟨2, 8, 1, 2, 4, 5, -12577866535280932850666218189767880494035238912000000⟩, + ⟨2, 8, 2, 2, 5, 5, 10431171786811665007169682672170850833934581760000000⟩, + ⟨2, 8, 3, 2, 6, 5, 1431442871691160857730512796706011047052443648000000⟩, + ⟨2, 8, 4, 2, 7, 5, -185632730210604788984866483343558145346633728000000⟩, + ⟨2, 8, 5, 2, 8, 5, 385946925544345841611515055510342009305956352000000⟩, + ⟨2, 8, 0, 3, 2, 5, 136670364036208528998107747450655119317722464256000000⟩, + ⟨2, 8, 1, 3, 3, 5, 34833685185923502042516984807302221307427422208000000⟩, + ⟨2, 8, 2, 3, 4, 5, -768580018464813563947237743542691709505765376000000⟩, + ⟨2, 8, 3, 3, 5, 5, 2859260959643925165002439118934696260861427712000000⟩, + ⟨2, 8, 4, 3, 6, 5, -151184374689894180892626826915639347815173324800000⟩, + ⟨2, 8, 5, 3, 7, 5, -30404432767075431867024031500839401650388992000000⟩, + ⟨2, 8, 6, 3, 8, 5, 56286746373453157510531029732849526650175488000000⟩, + ⟨2, 8, 0, 4, 1, 5, 112809059541965942864683860655511722717945528320000000⟩, + ⟨2, 8, 1, 4, 2, 5, -60056183188005138444535524656056127496067743744000000⟩, + ⟨2, 8, 2, 4, 3, 5, -16347618216970275179180209393235679179698077696000000⟩, + ⟨2, 8, 3, 4, 4, 5, -1169337266273076269891288054561111690673389568000000⟩, + ⟨2, 8, 4, 4, 5, 5, 390946371867978668024694570260489488201836134400000⟩, + ⟨2, 8, 5, 4, 6, 5, -74460187496751780076417027463562199522344960000000⟩, + ⟨2, 8, 6, 4, 7, 5, -24561084237887043786916373128152218364542976000000⟩, + ⟨2, 8, 7, 4, 8, 5, 18018168403755088407715334553363463400325120000000⟩, + ⟨2, 8, 0, 5, 0, 5, -698089668523512152240133807642005294566304907264000000⟩, + ⟨2, 8, 1, 5, 1, 5, -27230173320356013574727392484562473491139395584000000⟩, + ⟨2, 8, 2, 5, 2, 5, 2223642198879952570994536646856458267925676032000000⟩, + ⟨2, 8, 3, 5, 3, 5, -2944026668922467653337308181227050969329565696000000⟩, + ⟨2, 8, 4, 5, 4, 5, 54595148013485408672128325472285425273929728000000⟩, + ⟨2, 8, 5, 5, 5, 5, -20491541928274281627973409638261852502753280000000⟩, + ⟨2, 8, 6, 5, 6, 5, -41598697091966393709530941413031887664840704000000⟩, + ⟨2, 8, 7, 5, 7, 5, 8218734245768720369941781704488519494270976000000⟩, + ⟨2, 8, 8, 5, 8, 5, 5512609468629034855894584373930194704007168000000⟩, + ⟨2, 8, 1, 6, 0, 5, 296865764710335615428321245064382322971720548352000000⟩, + ⟨2, 8, 2, 6, 1, 5, -37311985703095870447209198309123791298603515904000000⟩, + ⟨2, 8, 3, 6, 2, 5, -3292249349946938886584773825162724540984328192000000⟩, + ⟨2, 8, 4, 6, 3, 5, -1364674842286277931518769911656106861367656448000000⟩, + ⟨2, 8, 5, 6, 4, 5, 170879902130727479434528841017464312595218432000000⟩, + ⟨2, 8, 6, 6, 5, 5, 3956769149641968954006907697747430048006144000000⟩, + ⟨2, 8, 7, 6, 6, 5, 2484741512432643204155579860750940925591552000000⟩, + ⟨2, 8, 8, 6, 7, 5, 1485965447084722654421501543309410201239552000000⟩, + ⟨2, 8, 2, 7, 0, 5, 304390210975231056374952493455266248691036454912000000⟩, + ⟨2, 8, 3, 7, 1, 5, 30265275660268805969692943191842743100144353280000000⟩, + ⟨2, 8, 4, 7, 2, 5, 1402418786074719908014825868956079505146904576000000⟩, + ⟨2, 8, 5, 7, 3, 5, 238240172590352261459947824940773735948877824000000⟩, + ⟨2, 8, 6, 7, 4, 5, 137314295426672852009752474632251154785894400000000⟩, + ⟨2, 8, 7, 7, 5, 5, -8926525025809457517524589628389542452002816000000⟩, + ⟨2, 8, 8, 7, 6, 5, 2221619414956074272460484703621000233746432000000⟩ +] + +def collectedFourData_9_5_15 : List CollectedFourTerm := [ + ⟨3, 2, 4, 1, 8, 0, 80801163101317439943187235672692844650326235545600000⟩, + ⟨3, 2, 4, 2, 7, 0, -10955950648367727508773285476543808790188785664000000⟩, + ⟨3, 2, 5, 2, 8, 0, 136670364036208528998107747450655119317722464256000000⟩, + ⟨3, 2, 4, 3, 6, 0, -8922825980244031970839339904049593205823792742400000⟩, + ⟨3, 2, 5, 3, 7, 0, -10766726250584335169831759292442308108066226176000000⟩, + ⟨3, 2, 6, 3, 8, 0, 69762326445489128112378929855331076556848103424000000⟩, + ⟨3, 2, 4, 4, 5, 0, 23073458820998919035661502525799802033214272307200000⟩, + ⟨3, 2, 5, 4, 6, 0, -26367617560451622944367123968417997033182330880000000⟩, + ⟨3, 2, 6, 4, 7, 0, -30441240378156807371852607505691512721897422848000000⟩, + ⟨3, 2, 7, 4, 8, 0, 59551702765817300181470376124066678548316815360000000⟩, + ⟨3, 2, 4, 5, 4, 0, 3222178258098511730833216781458721225954033664000000⟩, + ⟨3, 2, 5, 5, 5, 0, -7256403172665473782340520590388595271757987840000000⟩, + ⟨3, 2, 6, 5, 6, 0, -51557819081997536446520111938786678776677793792000000⟩, + ⟨3, 2, 7, 5, 7, 0, 27163672130695619265426677464139677499211644928000000⟩, + ⟨3, 2, 8, 5, 8, 0, 40994282252388766333778415039122119067260944384000000⟩, + ⟨3, 2, 4, 6, 3, 0, -80542424852529252761483854780162439253300609024000000⟩, + ⟨3, 2, 5, 6, 4, 0, 60511476798886373626032544919308964048714858496000000⟩, + ⟨3, 2, 6, 6, 5, 0, 4904057151488697396572081202230693686948134912000000⟩, + ⟨3, 2, 7, 6, 6, 0, 8212299090702148768351041672720276010781638656000000⟩, + ⟨3, 2, 8, 6, 7, 0, 11050317876088868858486550379731145239325310976000000⟩, + ⟨3, 2, 4, 7, 2, 0, 82770053487586156116297213645393876801067941888000000⟩, + ⟨3, 2, 5, 7, 3, 0, 84364893100389163412843271619154161994009935872000000⟩, + ⟨3, 2, 6, 7, 4, 0, 170188638007789651009891410298750990434906931200000000⟩, + ⟨3, 2, 7, 7, 5, 0, -29502985717341175392324234908448943955087720448000000⟩, + ⟨3, 2, 8, 7, 6, 0, 16520976839076865195580656506846531787388092416000000⟩ +] + +def collectedFourData_9_5_16 : List CollectedFourTerm := [ + ⟨3, 3, 3, 0, 8, 1, 1980664193826641752987624722874763382435191193600000⟩, + ⟨3, 3, 3, 1, 7, 1, -26459142255522921990023752834134478314873343180800000⟩, + ⟨3, 3, 4, 1, 8, 1, 41188187329069646192657933478414180098812516761600000⟩, + ⟨3, 3, 3, 2, 6, 1, 8613002989775930263304349280604870729104411852800000⟩, + ⟨3, 3, 4, 2, 7, 1, -5584767970569651522270307863773103154689736704000000⟩, + ⟨3, 3, 5, 2, 8, 1, 34833685185923502042516984807302221307427422208000000⟩, + ⟨3, 3, 3, 3, 5, 1, 17204195627358611033776959072356121381440795443200000⟩, + ⟨3, 3, 4, 3, 6, 1, -4548387843355047632780002643093767632271599206400000⟩, + ⟨3, 3, 5, 3, 7, 1, -2744155657597512563723309577733824832516128768000000⟩, + ⟨3, 3, 6, 3, 8, 1, 11853722809020909141018748823757383105865842688000000⟩, + ⟨3, 3, 3, 4, 4, 1, -7035911505547937682676121637585413721612405964800000⟩, + ⟨3, 3, 4, 4, 5, 1, 11761636934077532906348005095997243748368200499200000⟩, + ⟨3, 3, 5, 4, 6, 1, -6720412985512088196930657538674225647022243840000000⟩, + ⟨3, 3, 6, 4, 7, 1, -5172448279622674261387465514022621442920677376000000⟩, + ⟨3, 3, 7, 4, 8, 1, 7589082245660042010883817183194030327191306240000000⟩, + ⟨3, 3, 3, 5, 3, 1, -17714231565142150345196357501154657795755841945600000⟩, + ⟨3, 3, 4, 5, 4, 1, 1642497169697956161914112604489183477528264704000000⟩, + ⟨3, 3, 5, 5, 5, 1, -1849466528323573878696704225607678176652165120000000⟩, + ⟨3, 3, 6, 5, 6, 1, -8760489037205339824034366441813968464384098304000000⟩, + ⟨3, 3, 7, 5, 7, 1, 3461653190751772430224878215106165695947210752000000⟩, + ⟨3, 3, 8, 5, 8, 1, 4179346217368035567187650556886081872870558924800000⟩, + ⟨3, 3, 3, 6, 2, 1, -19809490168950866436741399163812744508296344371200000⟩, + ⟨3, 3, 4, 6, 3, 1, -41056296164991718181637399442750415706116849664000000⟩, + ⟨3, 3, 5, 6, 4, 1, 15422785677144209460600531903939232310155542528000000⟩, + ⟨3, 3, 6, 6, 5, 1, 833276885609116402050386030973555200432799744000000⟩, + ⟨3, 3, 7, 6, 6, 1, 1046549642255933552809711438896187167373000704000000⟩, + ⟨3, 3, 8, 6, 7, 1, 1126574284965198435745992774511081184640054067200000⟩, + ⟨3, 3, 3, 7, 1, 1, 182106401103046955820759902055950424449910571008000000⟩, + ⟨3, 3, 4, 7, 2, 1, 42191824194523603321333794244048925260479725568000000⟩, + ⟨3, 3, 5, 7, 3, 1, 21502394814902781587815703357887449011004112896000000⟩, + ⟨3, 3, 6, 7, 4, 1, 28917741752283308957880291663543460979697254400000000⟩, + ⟨3, 3, 7, 7, 5, 1, -3759767978119925950810304136110516325090066432000000⟩, + ⟨3, 3, 8, 7, 6, 1, 1684305182720875906847729820809546061520778035200000⟩ +] + +def collectedFourData_9_5_17 : List CollectedFourTerm := [ + ⟨3, 4, 2, 0, 7, 2, 215178808055211530584576970174073763918774272000000⟩, + ⟨3, 4, 3, 0, 8, 2, -131105759945179045626807333871822263851522457600000⟩, + ⟨3, 4, 2, 1, 6, 2, -495302947336311532947453580370075749533194649600000⟩, + ⟨3, 4, 3, 1, 7, 2, 1751405394069314923710291042895959717799840972800000⟩, + ⟨3, 4, 4, 1, 8, 2, -1363181254392562554695562969797501651426004172800000⟩, + ⟨3, 4, 2, 2, 5, 2, -1038638951872692845064304311428974050325561344000000⟩, + ⟨3, 4, 3, 2, 6, 2, -570119006495003743432769591058996434582686924800000⟩, + ⟨3, 4, 4, 2, 7, 2, 184835786697498884961668168950678316050808832000000⟩, + ⟨3, 4, 5, 2, 8, 2, -768580018464813563947237743542691709505765376000000⟩, + ⟨3, 4, 2, 3, 4, 2, 76528041252073551105720239887491049806259814400000⟩, + ⟨3, 4, 3, 3, 5, 2, -1138794324146699072581165222663699162329199411200000⟩, + ⟨3, 4, 4, 3, 6, 2, 150535322087180262925635953940312148076081971200000⟩, + ⟨3, 4, 5, 3, 7, 2, 60547805801463690063718694939189200809885696000000⟩, + ⟨3, 4, 6, 3, 8, 2, -196157852237143420229438531048651703768317952000000⟩, + ⟨3, 4, 2, 4, 3, 2, 1627743593673356454341554343838914553464645222400000⟩, + ⟨3, 4, 3, 4, 4, 2, 465726864612885911308742871868972285146483916800000⟩, + ⟨3, 4, 4, 4, 5, 2, -389267992335021310137616892737806135023212953600000⟩, + ⟨3, 4, 5, 4, 6, 2, 148281042012268382721299648670999157124628480000000⟩, + ⟨3, 4, 6, 4, 7, 2, 85594741979823320927507985929621289937403904000000⟩, + ⟨3, 4, 7, 4, 8, 2, -100468559809872651738117192056030509576224768000000⟩, + ⟨3, 4, 2, 5, 2, 2, -221409583696492057644525526662856208338963660800000⟩, + ⟨3, 4, 3, 5, 3, 2, 1172555044126835028567063663243266318789089689600000⟩, + ⟨3, 4, 4, 5, 4, 2, -54360764513296397870076870720363795245432832000000⟩, + ⟨3, 4, 5, 5, 5, 2, 40807138575834883320290043135774106991984640000000⟩, + ⟨3, 4, 6, 5, 6, 2, 144970381185012630729745230977371465177890816000000⟩, + ⟨3, 4, 7, 5, 7, 2, -45827321325311713555094873389150652403705446400000⟩, + ⟨3, 4, 8, 5, 8, 2, -46107122685566830806284728454003715161771212800000⟩, + ⟨3, 4, 2, 6, 1, 2, 3715180088583090430825945583435753305352542617600000⟩, + ⟨3, 4, 3, 6, 2, 2, 1311246131889317084794687198229965341897995059200000⟩, + ⟨3, 4, 4, 6, 3, 2, 1358816129968547114484533292001496787962560512000000⟩, + ⟨3, 4, 5, 6, 4, 2, -340292588546114741831218355375296654570684416000000⟩, + ⟨3, 4, 6, 6, 5, 2, -13789237932537839773200999674772605764632576000000⟩, + ⟨3, 4, 7, 6, 6, 2, -13854815631642469679151445306432683584048332800000⟩, + ⟨3, 4, 8, 6, 7, 2, -12428522565428083052475478820244760988693299200000⟩, + ⟨3, 4, 2, 7, 0, 2, -30308342739340023881644193859271855238307171532800000⟩, + ⟨3, 4, 3, 7, 1, 2, -12054137284811363062168882667533570355314556928000000⟩, + ⟨3, 4, 4, 7, 2, 2, -1396398034492000064164931684803795325439442944000000⟩, + ⟨3, 4, 5, 7, 3, 2, -474434758070158801666570956195603199989645312000000⟩, + ⟨3, 4, 6, 7, 4, 2, -478536760566007628200556437968609825364377600000000⟩, + ⟨3, 4, 7, 7, 5, 2, 49773933362891478949602546921167603779397222400000⟩, + ⟨3, 4, 8, 7, 6, 2, -18581486591592618864270946857628898277143347200000⟩ +] + +def collectedFourData_9_5_18 : List CollectedFourTerm := [ + ⟨3, 5, 1, 0, 6, 3, 32814774362039865244242657972425703327391757107200000⟩, + ⟨3, 5, 2, 0, 7, 3, -3202021132133541269368548916376608064359366656000000⟩, + ⟨3, 5, 3, 0, 8, 3, 975475739648988756264861281313760743042475622400000⟩, + ⟨3, 5, 1, 1, 5, 3, 7144887103236254178673802540631854505458977996800000⟩, + ⟨3, 5, 2, 1, 6, 3, 7370477225489420384670492471905754286863994060800000⟩, + ⟨3, 5, 3, 1, 7, 3, -13031109181773336600380691330475327212253033267200000⟩, + ⟨3, 5, 4, 1, 8, 3, 6761717883131130177298509394016905425987620044800000⟩, + ⟨3, 5, 1, 2, 4, 3, -6212149971867626118335906594005988788136627404800000⟩, + ⟨3, 5, 2, 2, 5, 3, 15455722162472712232933814904532953210355187712000000⟩, + ⟨3, 5, 3, 2, 6, 3, 4241897989693246868251321259834835375043588915200000⟩, + ⟨3, 5, 4, 2, 7, 3, -916831448736438958951098783632402860329664512000000⟩, + ⟨3, 5, 5, 2, 8, 3, 2859260959643925165002439118934696260861427712000000⟩, + ⟨3, 5, 1, 3, 3, 3, 17204195627358611033776959072356121381440795443200000⟩, + ⟨3, 5, 2, 3, 4, 3, -1138794324146699072581165222663699162329199411200000⟩, + ⟨3, 5, 3, 3, 5, 3, 8473054396081243591092608707800690131037113548800000⟩, + ⟨3, 5, 4, 3, 6, 3, -746692617815787415986437523057506537983652659200000⟩, + ⟨3, 5, 5, 3, 7, 3, -225249125869843055072697109281819367468695552000000⟩, + ⟨3, 5, 6, 3, 8, 3, 583795024959986571814510635778146650889073459200000⟩, + ⟨3, 5, 1, 4, 2, 3, -29661470461254996929884276511457823411570055577600000⟩, + ⟨3, 5, 2, 4, 3, 3, -24222038553628124919492406276979449143026201395200000⟩, + ⟨3, 5, 3, 4, 4, 3, -3465181529191577016810520816738426456986825523200000⟩, + ⟨3, 5, 4, 4, 5, 3, 1930866006718340339224594221647104676931934617600000⟩, + ⟨3, 5, 5, 4, 6, 3, -551633121204294857339446121425493122885877760000000⟩, + ⟨3, 5, 6, 4, 7, 3, -254742718482378194759882595449385626567599718400000⟩, + ⟨3, 5, 7, 4, 8, 3, 249174515630190833166129406083417140619116544000000⟩, + ⟨3, 5, 1, 5, 1, 3, -13448856366181974871807686278952763959272905113600000⟩, + ⟨3, 5, 2, 5, 2, 3, 3294739720238388609685773702289712206240441958400000⟩, + ⟨3, 5, 3, 5, 3, 3, -8724246741158043563455996555625290013144933990400000⟩, + ⟨3, 5, 4, 5, 4, 3, 269642905054491509155222468958681833786048512000000⟩, + ⟨3, 5, 5, 5, 5, 3, -151810163420226809807562915633710715560263680000000⟩, + ⟨3, 5, 6, 5, 6, 3, -431453476560534845906503613635298756052752793600000⟩, + ⟨3, 5, 7, 5, 7, 3, 113657452793919325275367876297066652999299891200000⟩, + ⟨3, 5, 8, 5, 8, 3, 98015481380607819291454488141039876900598579200000⟩, + ⟨3, 5, 1, 6, 0, 3, 146620624946278471363437916485199445325639371980800000⟩, + ⟨3, 5, 2, 6, 1, 3, -55284650290805901303930142450446772120337566924800000⟩, + ⟨3, 5, 3, 6, 2, 3, -9756160148123538249770432715444299232120196300800000⟩, + ⟨3, 5, 4, 6, 3, 3, -6740065780899787527309117378426699118534459392000000⟩, + ⟨3, 5, 5, 6, 4, 3, 1265951872167522070802999992683575627262984192000000⟩, + ⟨3, 5, 6, 6, 5, 3, 41038828735099697123742660329911616504699289600000⟩, + ⟨3, 5, 7, 6, 6, 3, 34361664790390158378235284471398314249971302400000⟩, + ⟨3, 5, 8, 6, 7, 3, 26420812038256216155558318615522652589968588800000⟩, + ⟨3, 5, 2, 7, 0, 3, 451010742221473526222639174053127754626298701414400000⟩, + ⟨3, 5, 3, 7, 1, 3, 89687276048348749063996688111468796416435945472000000⟩, + ⟨3, 5, 4, 7, 2, 3, 6926481369494126240884732854798467637920661504000000⟩, + ⟨3, 5, 5, 7, 3, 3, 1764985751721333987159398159977077787689222144000000⟩, + ⟨3, 5, 6, 7, 4, 3, 1424196772613337178137815019996152750627880960000000⟩, + ⟨3, 5, 7, 7, 5, 3, -123445541174057368782756609083079961879982899200000⟩, + ⟨3, 5, 8, 7, 6, 3, 39500911073168821217195696175339529988525260800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0921.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0921.lean new file mode 100644 index 0000000000000000000000000000000000000000..950ebb7dfd2a278c5ea0559b206a50816c48d168 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0921.lean @@ -0,0 +1,631 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0921. -/ +namespace LaughlinFock +def collectedFourData_9_5_19 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 5, 4, 7215638668895064210200137878434780838470929612800000⟩, + ⟨3, 6, 1, 0, 6, 4, -8675460569245821668224815571480889572934968934400000⟩, + ⟨3, 6, 2, 0, 7, 4, 423269832168207166395102645732506624858259456000000⟩, + ⟨3, 6, 3, 0, 8, 4, -85964340556006369948013005997970435805387161600000⟩, + ⟨3, 6, 0, 1, 4, 4, 5187922428109312913263095685896526623816233779200000⟩, + ⟨3, 6, 1, 1, 5, 4, -1888941415594299931162477205711578569694091673600000⟩, + ⟨3, 6, 2, 1, 6, 4, -974291089751119139152588475969851197479505100800000⟩, + ⟨3, 6, 3, 1, 7, 4, 1148373723704862933889038820634899625462779084800000⟩, + ⟨3, 6, 4, 1, 8, 4, -446910103877839839326347073687842748170135142400000⟩, + ⟨3, 6, 0, 2, 3, 4, 2030654022254358706934892885675518675021463552000000⟩, + ⟨3, 6, 1, 2, 4, 4, 1642347484598975715577710953243559479706491289600000⟩, + ⟨3, 6, 2, 2, 5, 4, -2043066130981246502411476969322783171319693312000000⟩, + ⟨3, 6, 3, 2, 6, 4, -373819612900925613672719192756267615053991116800000⟩, + ⟨3, 6, 4, 2, 7, 4, 60597209921383850164604665761628421993005056000000⟩, + ⟨3, 6, 5, 2, 8, 4, -151184374689894180892626826915639347815173324800000⟩, + ⟨3, 6, 0, 3, 2, 4, -8922825980244031970839339904049593205823792742400000⟩, + ⟨3, 6, 1, 3, 3, 4, -4548387843355047632780002643093767632271599206400000⟩, + ⟨3, 6, 2, 3, 4, 4, 150535322087180262925635953940312148076081971200000⟩, + ⟨3, 6, 3, 3, 5, 4, -746692617815787415986437523057506537983652659200000⟩, + ⟨3, 6, 4, 3, 6, 4, 49352025795897609894637227197038860948838809600000⟩, + ⟨3, 6, 5, 3, 7, 4, 11910122484349376716766788173361961658797260800000⟩, + ⟨3, 6, 6, 3, 8, 4, -25723630173837583863444792407613283160712806400000⟩, + ⟨3, 6, 0, 4, 1, 4, -7364988118574662218172079282799994724709040128000000⟩, + ⟨3, 6, 1, 4, 2, 4, 7841800604003031266487947460434913859286020915200000⟩, + ⟨3, 6, 2, 4, 3, 4, 3201870871643715933481789956079867644939023155200000⟩, + ⟨3, 6, 3, 4, 4, 4, 305371044051793973922218470138337555202755788800000⟩, + ⟨3, 6, 4, 4, 5, 4, -127618978276137667549926537706311599824620748800000⟩, + ⟨3, 6, 5, 4, 6, 4, 29167784845316056286378237622542442958946304000000⟩, + ⟨3, 6, 6, 4, 7, 4, 11224671673363188533100809739890960318123212800000⟩, + ⟨3, 6, 7, 4, 8, 4, -9410846735249431365195712192364878478966784000000⟩, + ⟨3, 6, 0, 5, 0, 4, 45576322817076034597647943147626962223256672665600000⟩, + ⟨3, 6, 1, 5, 1, 4, 3555563778041151138729114081330901133135393587200000⟩, + ⟨3, 6, 2, 5, 2, 4, -435526147665994811592202994743650871251723878400000⟩, + ⟨3, 6, 3, 5, 3, 4, 768829082537107959432086730369452579806091673600000⟩, + ⟨3, 6, 4, 5, 4, 4, -17821822914034807065494687487561975050797056000000⟩, + ⟨3, 6, 5, 5, 5, 4, 8027012907249940145099231726298471252099072000000⟩, + ⟨3, 6, 6, 5, 6, 4, 19011038453128986008143106983574259578909491200000⟩, + ⟨3, 6, 7, 5, 7, 4, -4292625455124288419709545776360735536001843200000⟩, + ⟨3, 6, 8, 5, 8, 4, -3239125746041897004271640854716479150279884800000⟩, + ⟨3, 6, 1, 6, 0, 4, -38763071667836015117803008054934007354565958041600000⟩, + ⟨3, 6, 2, 6, 1, 4, 7307985701666981276173515940798515750376361164800000⟩, + ⟨3, 6, 3, 6, 2, 4, 859767023825746076526148716515499670752146227200000⟩, + ⟨3, 6, 4, 6, 3, 4, 445479026239785223965742628065887357549674496000000⟩, + ⟨3, 6, 5, 6, 4, 4, -66937626499465260986517560512204734680845516800000⟩, + ⟨3, 6, 6, 6, 5, 4, -1808284771220034166359654882660894358319923200000⟩, + ⟨3, 6, 7, 6, 6, 4, -1297774614280007298796359065816614333474406400000⟩, + ⟨3, 6, 8, 6, 7, 4, -873130767701165514025513996160249120371507200000⟩, + ⟨3, 6, 2, 7, 0, 4, -59618357683649457575405998681355758708881516134400000⟩, + ⟨3, 6, 3, 7, 1, 4, -7903740942378645959585339886522720126970626048000000⟩, + ⟨3, 6, 4, 7, 2, 4, -457800009088091513968814651858555995372388352000000⟩, + ⟨3, 6, 5, 7, 3, 4, -93324208939569161628394900014130809083107737600000⟩, + ⟨3, 6, 6, 7, 4, 4, -62754065223473855083034742445679294357176320000000⟩, + ⟨3, 6, 7, 7, 5, 4, 4662302905258334678555104098710992706548531200000⟩, + ⟨3, 6, 8, 7, 6, 4, -1305389885832126770641153979933103735649075200000⟩ +] + +def collectedFourData_9_5_20 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 5, 5, 8706749010138060840438276295289864045904003072000000⟩, + ⟨3, 7, 1, 0, 6, 5, -5234121412522141424491479629718726617100976128000000⟩, + ⟨3, 7, 2, 0, 7, 5, 170246153822267918225676402924846664101396480000000⟩, + ⟨3, 7, 3, 0, 8, 5, -25932213743935758374840380457117196742557696000000⟩, + ⟨3, 7, 0, 1, 4, 5, 6260005598718638379415798332007174433572651008000000⟩, + ⟨3, 7, 1, 1, 5, 5, -1139645397664634466916030082250807120947576832000000⟩, + ⟨3, 7, 2, 1, 6, 5, -391876051935394504389638285606600165308760064000000⟩, + ⟨3, 7, 3, 1, 7, 5, 346421233134826830187060165989157672832729088000000⟩, + ⟨3, 7, 4, 1, 8, 5, -107852798154454484348217779269380675831280435200000⟩, + ⟨3, 7, 0, 2, 3, 5, 2450288284862720358752969708737228834319892480000000⟩, + ⟨3, 7, 1, 2, 4, 5, 990869137993058588103403295742926879302090752000000⟩, + ⟨3, 7, 2, 2, 5, 5, -821755117822509889294443621850913925192744960000000⟩, + ⟨3, 7, 3, 2, 6, 5, -112767340977930712012992333894188969396011008000000⟩, + ⟨3, 7, 4, 2, 7, 5, 14623922336203389543153069354586710567026688000000⟩, + ⟨3, 7, 5, 2, 8, 5, -30404432767075431867024031500839401650388992000000⟩, + ⟨3, 7, 0, 3, 2, 5, -10766726250584335169831759292442308108066226176000000⟩, + ⟨3, 7, 1, 3, 3, 5, -2744155657597512563723309577733824832516128768000000⟩, + ⟨3, 7, 2, 3, 4, 5, 60547805801463690063718694939189200809885696000000⟩, + ⟨3, 7, 3, 3, 5, 5, -225249125869843055072697109281819367468695552000000⟩, + ⟨3, 7, 4, 3, 6, 5, 11910122484349376716766788173361961658797260800000⟩, + ⟨3, 7, 5, 3, 7, 5, 2395224500321591384804455467948244501266432000000⟩, + ⟨3, 7, 6, 3, 8, 5, -4434201913580070738994293936390773195931648000000⟩, + ⟨3, 7, 0, 4, 1, 5, -8886961494830233946128804745571325881058590720000000⟩, + ⟨3, 7, 1, 4, 2, 5, 4731153594270726001107465795151653032190541824000000⟩, + ⟨3, 7, 2, 4, 3, 5, 1287845623536596053140314385521042965886140416000000⟩, + ⟨3, 7, 3, 4, 4, 5, 92118977873164676372504354838823634183651328000000⟩, + ⟨3, 7, 4, 4, 5, 5, -30798283111666481307691492057111040425879142400000⟩, + ⟨3, 7, 5, 4, 6, 5, 5865883661013106454814781978855300304732160000000⟩, + ⟨3, 7, 6, 4, 7, 5, 1934892558980906576606518237174098397495296000000⟩, + ⟨3, 7, 7, 4, 8, 5, -1419449550077754810321156996483702608363520000000⟩, + ⟨3, 7, 0, 5, 0, 5, 54994661149527190794330240874695660642704031744000000⟩, + ⟨3, 7, 1, 5, 1, 5, 2145160173997672269946479748697487367118782464000000⟩, + ⟨3, 7, 2, 5, 2, 5, -175175847400574703499272477653409279636406272000000⟩, + ⟨3, 7, 3, 5, 3, 5, 231926866093004328028042239775101127193788416000000⟩, + ⟨3, 7, 4, 5, 4, 5, -4300939837371032858360323492142690429042688000000⟩, + ⟨3, 7, 5, 5, 5, 5, 1614298929763945490235137519138223559802880000000⟩, + ⟨3, 7, 6, 5, 6, 5, 3277095126866875272751442407255706890665984000000⟩, + ⟨3, 7, 7, 5, 7, 5, -647461959836814975917838812544258640183296000000⟩, + ⟨3, 7, 8, 5, 8, 5, -434276717514145726324974945025909931900928000000⟩, + ⟨3, 7, 1, 6, 0, 5, -23386726481241860598354740068422478583134420992000000⟩, + ⟨3, 7, 2, 6, 1, 5, 2939393179815622770456300952605944030045405184000000⟩, + ⟨3, 7, 3, 6, 2, 5, 259359428428476979216815733882943811335749632000000⟩, + ⟨3, 7, 4, 6, 3, 5, 107507436243185977049769946000667722339319808000000⟩, + ⟨3, 7, 5, 6, 4, 5, -13461712353972780952887936498208608639516672000000⟩, + ⟨3, 7, 6, 6, 5, 5, -311709495846999443803857108929453934772224000000⟩, + ⟨3, 7, 7, 6, 6, 5, -195744936047273032825323488968695393288192000000⟩, + ⟨3, 7, 8, 6, 7, 5, -117062563631934923502188723957294476296192000000⟩, + ⟨3, 7, 2, 7, 0, 5, -23979493272291731385182106776211657303892426752000000⟩, + ⟨3, 7, 3, 7, 1, 5, -2384261871478272240282423128808721436513402880000000⟩, + ⟨3, 7, 4, 7, 2, 5, -110480858559379812171085516162163682255568896000000⟩, + ⟨3, 7, 5, 7, 3, 5, -18768273123884536813470659762627107570581504000000⟩, + ⟨3, 7, 6, 7, 4, 5, -10817454387983974397999077847166114752102400000000⟩, + ⟨3, 7, 7, 7, 5, 5, 703220862837667596063647090734481000103936000000⟩, + ⟨3, 7, 8, 7, 6, 5, -175016494925544267905301672203798207004672000000⟩ +] + +def collectedFourData_9_5_21 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 5, 6, -56414833310285525219406033457143744005960368128000000⟩, + ⟨3, 8, 1, 0, 6, 6, 22609440612824909508703993412084105747468648448000000⟩, + ⟨3, 8, 2, 0, 7, 6, -551549629971943955943361219440356741622005760000000⟩, + ⟨3, 8, 3, 0, 8, 6, 67210460024855284146558452039019433654065561600000⟩, + ⟨3, 8, 0, 1, 4, 6, -40561313064377193326952235611636539724285345792000000⟩, + ⟨3, 8, 1, 1, 5, 6, 4922840512742649738068924382545614163423526912000000⟩, + ⟨3, 8, 2, 1, 6, 6, 1269568131715187633703468197588545088067207168000000⟩, + ⟨3, 8, 3, 1, 7, 6, -897845848074351370254716956389370182631214284800000⟩, + ⟨3, 8, 4, 1, 8, 6, 232941810345311257035797396990950096965835161600000⟩, + ⟨3, 8, 0, 2, 3, 6, -15876489030718465944793047527864520966427115520000000⟩, + ⟨3, 8, 1, 2, 4, 6, -4280182893147647068157098942936651620660805632000000⟩, + ⟨3, 8, 2, 2, 5, 6, 2662255334330340996176771104928653431558635520000000⟩, + ⟨3, 8, 3, 2, 6, 6, 292267561024512163533581053144694634847194316800000⟩, + ⟨3, 8, 4, 2, 7, 6, -31584928732827285690088174371181109868232704000000⟩, + ⟨3, 8, 5, 2, 8, 6, 56286746373453157510531029732849526650175488000000⟩, + ⟨3, 8, 0, 3, 2, 6, 69762326445489128112378929855331076556848103424000000⟩, + ⟨3, 8, 1, 3, 3, 6, 11853722809020909141018748823757383105865842688000000⟩, + ⟨3, 8, 2, 3, 4, 6, -196157852237143420229438531048651703768317952000000⟩, + ⟨3, 8, 3, 3, 5, 6, 583795024959986571814510635778146650889073459200000⟩, + ⟨3, 8, 4, 3, 6, 6, -25723630173837583863444792407613283160712806400000⟩, + ⟨3, 8, 5, 3, 7, 6, -4434201913580070738994293936390773195931648000000⟩, + ⟨3, 8, 6, 3, 8, 6, 7182783192885508141443898617250062205452288000000⟩, + ⟨3, 8, 0, 4, 1, 6, 57582508785081383308695107228513100518161121280000000⟩, + ⟨3, 8, 1, 4, 2, 6, -20436808356012623639183684648394732244391952384000000⟩, + ⟨3, 8, 2, 4, 3, 6, -4172257411842272727770326606096699930907246592000000⟩, + ⟨3, 8, 3, 4, 4, 6, -238751652327511400109268343742794865604086988800000⟩, + ⟨3, 8, 4, 4, 5, 6, 66518513625255539558463774376696155376661299200000⟩, + ⟨3, 8, 5, 4, 6, 6, -10859321350048867418946314709459901077258240000000⟩, + ⟨3, 8, 6, 4, 7, 6, -3134253699662142259648101076519624246296576000000⟩, + ⟨3, 8, 7, 4, 8, 6, 2043829822047093810207088507234203142717440000000⟩, + ⟨3, 8, 0, 5, 0, 6, -356334452514212992419125786413674522681494470656000000⟩, + ⟨3, 8, 1, 5, 1, 6, -9266287068344223672205051544712997454556954624000000⟩, + ⟨3, 8, 2, 5, 2, 6, 567520449916744017743023737517142823313342464000000⟩, + ⟨3, 8, 3, 5, 3, 6, -601102224289627450577035283219176947139058073600000⟩, + ⟨3, 8, 4, 5, 4, 6, 9289223173131908938257238773419080578760704000000⟩, + ⟨3, 8, 5, 5, 5, 6, -2988499575922203362259316398304044326584320000000⟩, + ⟨3, 8, 6, 5, 6, 6, -5308433007224478884122436767452672351535104000000⟩, + ⟨3, 8, 7, 5, 7, 6, 932264244321365364794790195668449348288512000000⟩, + ⟨3, 8, 8, 5, 8, 6, 562773742543199843390523035106216608425574400000⟩, + ⟨3, 8, 1, 6, 0, 6, 101021883489558954485458079549028688827852521472000000⟩, + ⟨3, 8, 2, 6, 1, 6, -9522806737601078074988123217015104022257860608000000⟩, + ⟨3, 8, 3, 6, 2, 6, -672201250097202286232705313255102622767199027200000⟩, + ⟨3, 8, 4, 6, 3, 6, -232195893408413684606049718125901609030385664000000⟩, + ⟨3, 8, 5, 6, 4, 6, 24921234177437701423964619209788100085547008000000⟩, + ⟨3, 8, 6, 6, 5, 6, 504925524698304414510038447651364267884544000000⟩, + ⟨3, 8, 7, 6, 6, 6, 281848226156542686401100680730280118452224000000⟩, + ⟨3, 8, 8, 6, 7, 6, 151699905590033360431231343927709329365401600000⟩, + ⟨3, 8, 2, 7, 0, 6, 77686810211610786127771521522679399071533236224000000⟩, + ⟨3, 8, 3, 7, 1, 6, 6179470013016180033776262114952523616299778048000000⟩, + ⟨3, 8, 4, 7, 2, 6, 238617927784039511705595045495731086392557568000000⟩, + ⟨3, 8, 5, 7, 3, 6, 34745099087517057653387538374327041844576256000000⟩, + ⟨3, 8, 6, 7, 4, 6, 17522754056340249724412443416906174981734400000000⟩, + ⟨3, 8, 7, 7, 5, 6, -1012550090895856980156706686911964713582592000000⟩, + ⟨3, 8, 8, 7, 6, 6, 226801677096201265304495257051631227345305600000⟩ +] + +def collectedFourData_9_5_22 : List CollectedFourTerm := [ + ⟨4, 1, 4, 1, 8, 0, 66694072878460514916217871143740467089067999232000000⟩, + ⟨4, 1, 4, 2, 7, 0, -9043149169509171867108670619876927375230894080000000⟩, + ⟨4, 1, 5, 2, 8, 0, 112809059541965942864683860655511722717945528320000000⟩, + ⟨4, 1, 4, 3, 6, 0, -7364988118574662218172079282799994724709040128000000⟩, + ⟨4, 1, 5, 3, 7, 0, -8886961494830233946128804745571325881058590720000000⟩, + ⟨4, 1, 6, 3, 8, 0, 57582508785081383308695107228513100518161121280000000⟩, + ⟨4, 1, 4, 4, 5, 0, 19045059317231150265639530224501504150270377984000000⟩, + ⟨4, 1, 5, 4, 6, 0, -21764090264431637996993380735424858510956953600000000⟩, + ⟨4, 1, 6, 4, 7, 0, -25126498510247588040754646821951288178701762560000000⟩, + ⟨4, 1, 7, 4, 8, 0, 49154559808992148684353129260243937928622899200000000⟩, + ⟨4, 1, 4, 5, 4, 0, 2659617551588303929179844836025078349121454080000000⟩, + ⟨4, 1, 5, 5, 5, 0, -5989506381565346463507418114497078933376204800000000⟩, + ⟨4, 1, 6, 5, 6, 0, -42556329777054415812386442163111358072346378240000000⟩, + ⟨4, 1, 7, 5, 7, 0, 22421161517929708050981898770335483096633180160000000⟩, + ⟨4, 1, 8, 5, 8, 0, 33837082824076557450409124773744750715448852480000000⟩, + ⟨4, 1, 4, 6, 3, 0, -66480507789063389087892367277490144728611553280000000⟩, + ⟨4, 1, 5, 6, 4, 0, 49946766713589529059916131056251980047575941120000000⟩, + ⟨4, 1, 6, 6, 5, 0, 4047856893488082147083916433813721292881264640000000⟩, + ⟨4, 1, 7, 6, 6, 0, 6778512251961306799297734708661673789824696320000000⟩, + ⟨4, 1, 8, 6, 7, 0, 9121040805240705823244638359196891582530846720000000⟩, + ⟨4, 1, 4, 7, 2, 0, 68319214322858423639885613020747556789273231360000000⟩, + ⟨4, 1, 5, 7, 3, 0, 69635610588495907327328549488052524671660195840000000⟩, + ⟨4, 1, 6, 7, 4, 0, 140475371773359909180725317809511516826763264000000000⟩, + ⟨4, 1, 7, 7, 5, 0, -24352053906665232848441034882605792711210434560000000⟩, + ⟨4, 1, 8, 7, 6, 0, 13636576393673042454426920107556466232676843520000000⟩ +] + +def collectedFourData_9_5_23 : List CollectedFourTerm := [ + ⟨4, 2, 3, 0, 8, 1, -3414830530375355414630578520395474790383406284800000⟩, + ⟨4, 2, 3, 1, 7, 1, 45617771585571730870153949917501972152502871654400000⟩, + ⟨4, 2, 4, 1, 8, 1, -71011875723561895086325162781954165867857890508800000⟩, + ⟨4, 2, 3, 2, 6, 1, -14849536665211887743123160246308499550707803750400000⟩, + ⟨4, 2, 4, 2, 7, 1, 9628606520178684441057993815486667340143132672000000⟩, + ⟨4, 2, 5, 2, 8, 1, -60056183188005138444535524656056127496067743744000000⟩, + ⟨4, 2, 3, 3, 5, 1, -29661470461254996929884276511457823411570055577600000⟩, + ⟨4, 2, 4, 3, 6, 1, 7841800604003031266487947460434913859286020915200000⟩, + ⟨4, 2, 5, 3, 7, 1, 4731153594270726001107465795151653032190541824000000⟩, + ⟨4, 2, 6, 3, 8, 1, -20436808356012623639183684648394732244391952384000000⟩, + ⟨4, 2, 3, 4, 4, 1, 12130499199738273016137799954947109192347313766400000⟩, + ⟨4, 2, 4, 4, 5, 1, -20278044614964002894016416608864556960255154585600000⟩, + ⟨4, 2, 5, 4, 6, 1, 11586553395161893075095205398530566709701509120000000⟩, + ⟨4, 2, 6, 4, 7, 1, 8917732928729338136625678938244571437641760768000000⟩, + ⟨4, 2, 7, 4, 8, 1, -13084211766327175089117156865448510948187832320000000⟩, + ⟨4, 2, 3, 5, 3, 1, 30540815025245381740731526221898288120422255820800000⟩, + ⟨4, 2, 4, 5, 4, 1, -2831802331067235960982307225341094395140636672000000⟩, + ⟨4, 2, 5, 5, 5, 1, 3188634795091082064417805241242809647927132160000000⟩, + ⟨4, 2, 6, 5, 6, 1, 15103814931631852473832960566989561024030441472000000⟩, + ⟨4, 2, 7, 5, 7, 1, -5968179279553861371426974852130327503396929536000000⟩, + ⟨4, 2, 8, 5, 8, 1, -7205542011896573147835471973364549093075347046400000⟩, + ⟨4, 2, 3, 6, 2, 1, 34153215891388309618167429879900406583721040281600000⟩, + ⟨4, 2, 4, 6, 3, 1, 70784484338801256501467957419206669613192445952000000⟩, + ⟨4, 2, 5, 6, 4, 1, -26590170892117122406562498864939196819915669504000000⟩, + ⟨4, 2, 6, 6, 5, 1, -1436638960861205197709490577269836796124987392000000⟩, + ⟨4, 2, 7, 6, 6, 1, -1804339009645248876758649120136668142393884672000000⟩, + ⟨4, 2, 8, 6, 7, 1, -1942308178754131860054988491891250047735142809600000⟩, + ⟨4, 2, 3, 7, 1, 1, -313966648259555376309204031777835610105282822144000000⟩, + ⟨4, 2, 4, 7, 2, 1, -72742229521163977019628378429119663034517684224000000⟩, + ⟨4, 2, 5, 7, 3, 1, -37071924922444214078230815108227513620918960128000000⟩, + ⟨4, 2, 6, 7, 4, 1, -49856602503841812165590758561124831083049779200000000⟩, + ⟨4, 2, 7, 7, 5, 1, 6482154076813325416296570549123142587594571776000000⟩, + ⟨4, 2, 8, 7, 6, 1, -2903882838065835517197270551797445432561998233600000⟩ +] + +def collectedFourData_9_5_24 : List CollectedFourTerm := [ + ⟨4, 3, 2, 0, 7, 2, 4576831192535574076649855625335993600481165312000000⟩, + ⟨4, 3, 3, 0, 8, 2, -2788606076320551523385010012300938764374088089600000⟩, + ⟨4, 3, 2, 1, 6, 2, -10535042923659933613515308409091885601130125721600000⟩, + ⟨4, 3, 3, 1, 7, 2, 37252213221177189391589172293396074117106289868800000⟩, + ⟨4, 3, 4, 1, 8, 2, -28994725561370377503190421260577062091079077068800000⟩, + ⟨4, 3, 2, 2, 5, 2, -22091744050806697105690641429194254716632039424000000⟩, + ⟨4, 3, 3, 2, 6, 2, -12126372833677046305588867043871057880653024460800000⟩, + ⟨4, 3, 4, 2, 7, 2, 3931438238271605716564974519500672531611779072000000⟩, + ⟨4, 3, 5, 2, 8, 2, -16347618216970275179180209393235679179698077696000000⟩, + ⟨4, 3, 2, 3, 4, 2, 1627743593673356454341554343838914553464645222400000⟩, + ⟨4, 3, 3, 3, 5, 2, -24222038553628124919492406276979449143026201395200000⟩, + ⟨4, 3, 4, 3, 6, 2, 3201870871643715933481789956079867644939023155200000⟩, + ⟨4, 3, 5, 3, 7, 2, 1287845623536596053140314385521042965886140416000000⟩, + ⟨4, 3, 6, 3, 8, 2, -4172257411842272727770326606096699930907246592000000⟩, + ⟨4, 3, 2, 4, 3, 2, 34621939401498305007833676881802805829446297190400000⟩, + ⟨4, 3, 3, 4, 4, 2, 9905962675539707972873611746649947973492722892800000⟩, + ⟨4, 3, 4, 4, 5, 2, -8279690298858286814287415261386020679881169305600000⟩, + ⟨4, 3, 5, 4, 6, 2, 3153922565503267267322932937266946444969902080000000⟩, + ⟨4, 3, 6, 4, 7, 2, 1820591388859129183501928110144050973517021184000000⟩, + ⟨4, 3, 7, 4, 8, 2, -2136955969609081988693398446779089843837206528000000⟩, + ⟨4, 3, 2, 5, 2, 2, -4709359151800905119401865116314012800418368716800000⟩, + ⟨4, 3, 3, 5, 3, 2, 24940125607293272766494015595787302975928113561600000⟩, + ⟨4, 3, 4, 5, 4, 2, -1156247889479421472861089048030587325694083072000000⟩, + ⟨4, 3, 5, 5, 5, 2, 867963654971456088290542567854895007205949440000000⟩, + ⟨4, 3, 6, 5, 6, 2, 3083505149034439629570774951230933484422823936000000⟩, + ⟨4, 3, 7, 5, 7, 2, -974742427508104486189081291630556524172437094400000⟩, + ⟨4, 3, 8, 5, 8, 2, -980693773762429499144292767495120343739976908800000⟩, + ⟨4, 3, 2, 6, 1, 2, 79021499695970374395737499761761357617304279449600000⟩, + ⟨4, 3, 3, 6, 2, 2, 27890070828828033395566965674395307063863620403200000⟩, + ⟨4, 3, 4, 6, 3, 2, 28901879812275947199372907800858648599542628352000000⟩, + ⟨4, 3, 5, 6, 4, 2, -7237988480012917198567588743779268006600769536000000⟩, + ⟨4, 3, 6, 6, 5, 2, -293295677494136094942104802270083458736848896000000⟩, + ⟨4, 3, 7, 6, 6, 2, -294690508432691027311618022875015178321972428800000⟩, + ⟨4, 3, 8, 6, 7, 2, -264353401102529343662542003222911102487835443200000⟩, + ⟨4, 3, 2, 7, 0, 2, -644655343605575235145615543287322259732738919628800000⟩, + ⟨4, 3, 3, 7, 1, 2, -256390264556512548447358940632440511723248549888000000⟩, + ⟨4, 3, 4, 7, 2, 2, -29701243069524305878494275168180407581775233024000000⟩, + ⟨4, 3, 5, 7, 3, 2, -10091178676858466774261172946434819013478449152000000⟩, + ⟨4, 3, 6, 7, 4, 2, -10178427849509532513189182469483142409984409600000000⟩, + ⟨4, 3, 7, 7, 5, 2, 1058686461038566142844819692272975003265689190400000⟩, + ⟨4, 3, 8, 7, 6, 2, -395226315289661683155117938418040163859116851200000⟩ +] + +def collectedFourData_9_5_25 : List CollectedFourTerm := [ + ⟨4, 4, 1, 0, 6, 3, -13420089697113229781017717956713440223534304460800000⟩, + ⟨4, 4, 2, 0, 7, 3, 1309514133212919785610775293904850634600873984000000⟩, + ⟨4, 4, 3, 0, 8, 3, -398935302099500008609940214938258248736283033600000⟩, + ⟨4, 4, 1, 1, 5, 3, -2922007774403527605416594294584152749879014195200000⟩, + ⟨4, 4, 2, 1, 6, 3, -3014266207815837528581983929049485585679594291200000⟩, + ⟨4, 4, 3, 1, 7, 3, 5329265779580481025073673971553109886202858700800000⟩, + ⟨4, 4, 4, 1, 8, 3, -2765305026846861683358703159823031098961769267200000⟩, + ⟨4, 4, 1, 2, 4, 3, 2540551061378701117729135859787895727526720307200000⟩, + ⟨4, 4, 2, 2, 5, 3, -6320847294747358330031438464454143281954029568000000⟩, + ⟨4, 4, 3, 2, 6, 3, -1734787229667512834655212060147884367452884172800000⟩, + ⟨4, 4, 4, 2, 7, 3, 374951847708284212113501661534269849382944768000000⟩, + ⟨4, 4, 5, 2, 8, 3, -1169337266273076269891288054561111690673389568000000⟩, + ⟨4, 4, 1, 3, 3, 3, -7035911505547937682676121637585413721612405964800000⟩, + ⟨4, 4, 2, 3, 4, 3, 465726864612885911308742871868972285146483916800000⟩, + ⟨4, 4, 3, 3, 5, 3, -3465181529191577016810520816738426456986825523200000⟩, + ⟨4, 4, 4, 3, 6, 3, 305371044051793973922218470138337555202755788800000⟩, + ⟨4, 4, 5, 3, 7, 3, 92118977873164676372504354838823634183651328000000⟩, + ⟨4, 4, 6, 3, 8, 3, -238751652327511400109268343742794865604086988800000⟩, + ⟨4, 4, 1, 4, 2, 3, 12130499199738273016137799954947109192347313766400000⟩, + ⟨4, 4, 2, 4, 3, 3, 9905962675539707972873611746649947973492722892800000⟩, + ⟨4, 4, 3, 4, 4, 3, 1417137488908827581475999426770501840587771084800000⟩, + ⟨4, 4, 4, 4, 5, 3, -789656351659770210769065050897738087474292326400000⟩, + ⟨4, 4, 5, 4, 6, 3, 225598563768395824351633807874588848831856640000000⟩, + ⟨4, 4, 6, 4, 7, 3, 104180820931522160679860838073163909963553177600000⟩, + ⟨4, 4, 7, 4, 8, 3, -101903621615639650619874730228879724239650816000000⟩, + ⟨4, 4, 1, 5, 1, 3, 5500109699566890718363370936677510381190932070400000⟩, + ⟨4, 4, 2, 5, 2, 3, -1347432777882807990431133926124538273849776537600000⟩, + ⟨4, 4, 3, 5, 3, 3, 3567910372150146165440123394013380666789042585600000⟩, + ⟨4, 4, 4, 5, 4, 3, -110274473689738248331914940065355907903520768000000⟩, + ⟨4, 4, 5, 5, 5, 3, 62085022665571558826908624562618401051115520000000⟩, + ⟨4, 4, 6, 5, 6, 3, 176449311876779433883075422994276995207423590400000⟩, + ⟨4, 4, 7, 5, 7, 3, -46481904596128180970865535693575394769554636800000⟩, + ⟨4, 4, 8, 5, 8, 3, -40084887902051715741652912059590849025854668800000⟩, + ⟨4, 4, 1, 6, 0, 3, -59962683775209689380541802209127394357418341171200000⟩, + ⟨4, 4, 2, 6, 1, 3, 22609479425048586788215378550920006304370209587200000⟩, + ⟨4, 4, 3, 6, 2, 3, 3989926697124498058853489122887698343380857651200000⟩, + ⟨4, 4, 4, 6, 3, 3, 2756450077826952561922090242839124301565657088000000⟩, + ⟨4, 4, 5, 6, 4, 3, -517729833802229696629468072282430294917644288000000⟩, + ⟨4, 4, 6, 6, 5, 3, -16783438966034988497278080174159639194527334400000⟩, + ⟨4, 4, 7, 6, 6, 3, -14052713529019912813638721259793976586246553600000⟩, + ⟨4, 4, 8, 6, 7, 3, -10805183772164945040393723697910539504268083200000⟩, + ⟨4, 4, 2, 7, 0, 3, -184447546345936217183245718952135253019330189721600000⟩, + ⟨4, 4, 3, 7, 1, 3, -36678944550383161239563685407557115731098206208000000⟩, + ⟨4, 4, 4, 7, 2, 3, -2832687503453446170516665945468220067603808256000000⟩, + ⟨4, 4, 5, 7, 3, 3, -721817155921919113183180280161223082787209216000000⟩, + ⟨4, 4, 6, 7, 4, 3, -582446437813081682658129539380957479897661440000000⟩, + ⟨4, 4, 7, 7, 5, 3, 50484888818280203466963257907768448976211148800000⟩, + ⟨4, 4, 8, 7, 6, 3, -16154484680316595613833436967239107531191091200000⟩ +] + +def collectedFourData_9_5_26 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 5, 4, -18658857862137120813647738156188093428078634598400000⟩, + ⟨4, 5, 1, 0, 6, 4, 22433798736061279019320881576791537094589887283200000⟩, + ⟨4, 5, 2, 0, 7, 4, -1094529812004374805979856225940074280221933568000000⟩, + ⟨4, 5, 3, 0, 8, 4, 222294447553385249891374842958359295997824204800000⟩, + ⟨4, 5, 0, 1, 4, 4, -13415403906402662912491170693274354040499181977600000⟩, + ⟨4, 5, 1, 1, 5, 4, 4884597330990701099861026741129020745481768140800000⟩, + ⟨4, 5, 2, 1, 6, 4, 2519410934250204059940617863828326413062530662400000⟩, + ⟨4, 5, 3, 1, 7, 4, -2969569717451407156188974725864841550951245414400000⟩, + ⟨4, 5, 4, 1, 8, 4, 1155660986927783682382517534746489992267379507200000⟩, + ⟨4, 5, 0, 2, 3, 4, -5251050739521465360540448221817517358559789056000000⟩, + ⟨4, 5, 1, 2, 4, 4, -4246932209545258363985559595844263377873194188800000⟩, + ⟨4, 5, 2, 2, 5, 4, 5283147104532472145653063271091805711641870336000000⟩, + ⟨4, 5, 3, 2, 6, 4, 966656916076645061034284784494471496839095910400000⟩, + ⟨4, 5, 4, 2, 7, 4, -156697803014896199621790964036564245301690368000000⟩, + ⟨4, 5, 5, 2, 8, 4, 390946371867978668024694570260489488201836134400000⟩, + ⟨4, 5, 0, 3, 2, 4, 23073458820998919035661502525799802033214272307200000⟩, + ⟨4, 5, 1, 3, 3, 4, 11761636934077532906348005095997243748368200499200000⟩, + ⟨4, 5, 2, 3, 4, 4, -389267992335021310137616892737806135023212953600000⟩, + ⟨4, 5, 3, 3, 5, 4, 1930866006718340339224594221647104676931934617600000⟩, + ⟨4, 5, 4, 3, 6, 4, -127618978276137667549926537706311599824620748800000⟩, + ⟨4, 5, 5, 3, 7, 4, -30798283111666481307691492057111040425879142400000⟩, + ⟨4, 5, 6, 3, 8, 4, 66518513625255539558463774376696155376661299200000⟩, + ⟨4, 5, 0, 4, 1, 4, 19045059317231150265639530224501504150270377984000000⟩, + ⟨4, 5, 1, 4, 2, 4, -20278044614964002894016416608864556960255154585600000⟩, + ⟨4, 5, 2, 4, 3, 4, -8279690298858286814287415261386020679881169305600000⟩, + ⟨4, 5, 3, 4, 4, 4, -789656351659770210769065050897738087474292326400000⟩, + ⟨4, 5, 4, 4, 5, 4, 330008816327031560659568382216298366843119206400000⟩, + ⟨4, 5, 5, 4, 6, 4, -75424723514528331772906888258024369356275712000000⟩, + ⟨4, 5, 6, 4, 7, 4, -29025781765553982147320771497599051097335398400000⟩, + ⟨4, 5, 7, 4, 8, 4, 24335427486457743138464197764023031957553152000000⟩, + ⟨4, 5, 0, 5, 0, 4, -117855420475609997607775133338967160369663757516800000⟩, + ⟨4, 5, 1, 5, 1, 4, -9194301738004324256880709976680580824465775001600000⟩, + ⟨4, 5, 2, 5, 2, 4, 1126223312646605180621025400220518133609476915200000⟩, + ⟨4, 5, 3, 5, 3, 4, -1988108500107852332456135848510888126217768140800000⟩, + ⟨4, 5, 4, 5, 4, 4, 46085298316091422064981225901029233281466368000000⟩, + ⟨4, 5, 5, 5, 5, 4, -20756983514094370109226354722875189405679616000000⟩, + ⟨4, 5, 6, 5, 6, 4, -49160480532054702029964188872819196972079513600000⟩, + ⟨4, 5, 7, 5, 7, 4, 11100263178064713642872296240541661291714969600000⟩, + ⟨4, 5, 8, 5, 8, 4, 8376027357567170039720335454963278109107814400000⟩, + ⟨4, 5, 1, 6, 0, 4, 100237093033476724617134360463791795489928432844800000⟩, + ⟨4, 5, 2, 6, 1, 4, -18897657258496747161060354870232911426275927654400000⟩, + ⟨4, 5, 3, 6, 2, 4, -2223264138941954471392010967598668687030720921600000⟩, + ⟨4, 5, 4, 6, 3, 4, -1151960375594063320433810091123859675768946688000000⟩, + ⟨4, 5, 5, 6, 4, 4, 173093431613532082965635338554468264764139110400000⟩, + ⟨4, 5, 6, 6, 5, 4, 4676028009261232868464061392352279673805209600000⟩, + ⟨4, 5, 7, 6, 6, 4, 3355904193114002231172749495280374077666099200000⟩, + ⟨4, 5, 8, 6, 7, 4, 2257821329084021305726596014942980188772761600000⟩, + ⟨4, 5, 2, 7, 0, 4, 154166597447376047608838682702693814674855768883200000⟩, + ⟨4, 5, 3, 7, 1, 4, 20438215602275961863179605234317937496496799744000000⟩, + ⟨4, 5, 4, 7, 2, 4, 1183821098980809692721310119305843245848723456000000⟩, + ⟨4, 5, 5, 7, 3, 4, 241326267791962129404646983073661883643645132800000⟩, + ⟨4, 5, 6, 7, 4, 4, 162275196556562676221539635086805424888872960000000⟩, + ⟨4, 5, 7, 7, 5, 4, -12056208911132402177372415427097071728564633600000⟩, + ⟨4, 5, 8, 7, 6, 4, 3375596458205531856049014517993972480711065600000⟩ +] + +def collectedFourData_9_5_27 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 5, 5, 21322751479977628766885349273742460272886415360000000⟩, + ⟨4, 6, 1, 0, 6, 5, -12818317142860809330235575479027966665178480640000000⟩, + ⟨4, 6, 2, 0, 7, 5, 416931328116543513908437923352699367482982400000000⟩, + ⟨4, 6, 3, 0, 8, 5, -63507762580930820037148142958422023187988480000000⟩, + ⟨4, 6, 0, 1, 4, 5, 15330698460392338730087903077181072224592855040000000⟩, + ⟨4, 6, 1, 1, 5, 5, -2790981520359451890974524949011623431016284160000000⟩, + ⟨4, 6, 2, 1, 6, 5, -959700992487978719941967448326605222780600320000000⟩, + ⟨4, 6, 3, 1, 7, 5, 848382542430056285259963716826671189789245440000000⟩, + ⟨4, 6, 4, 1, 8, 5, -264130550770425474664535789567892607966642176000000⟩, + ⟨4, 6, 0, 2, 3, 5, 6000734383360839492465580448817794653775462400000000⟩, + ⟨4, 6, 1, 2, 4, 5, 2426629773524460966260363825080065444292853760000000⟩, + ⟨4, 6, 2, 2, 5, 5, -2012471030728755324727532616808876542315724800000000⟩, + ⟨4, 6, 3, 2, 6, 5, -276166222769316540987960946922851335709655040000000⟩, + ⟨4, 6, 4, 2, 7, 5, 35813856730482947001489754216658879580733440000000⟩, + ⟨4, 6, 5, 2, 8, 5, -74460187496751780076417027463562199522344960000000⟩, + ⟨4, 6, 0, 3, 2, 5, -26367617560451622944367123968417997033182330880000000⟩, + ⟨4, 6, 1, 3, 3, 5, -6720412985512088196930657538674225647022243840000000⟩, + ⟨4, 6, 2, 3, 4, 5, 148281042012268382721299648670999157124628480000000⟩, + ⟨4, 6, 3, 3, 5, 5, -551633121204294857339446121425493122885877760000000⟩, + ⟨4, 6, 4, 3, 6, 5, 29167784845316056286378237622542442958946304000000⟩, + ⟨4, 6, 5, 3, 7, 5, 5865883661013106454814781978855300304732160000000⟩, + ⟨4, 6, 6, 3, 8, 5, -10859321350048867418946314709459901077258240000000⟩, + ⟨4, 6, 0, 4, 1, 5, -21764090264431637996993380735424858510956953600000000⟩, + ⟨4, 6, 1, 4, 2, 5, 11586553395161893075095205398530566709701509120000000⟩, + ⟨4, 6, 2, 4, 3, 5, 3153922565503267267322932937266946444969902080000000⟩, + ⟨4, 6, 3, 4, 4, 5, 225598563768395824351633807874588848831856640000000⟩, + ⟨4, 6, 4, 4, 5, 5, -75424723514528331772906888258024369356275712000000⟩, + ⟨4, 6, 5, 4, 6, 5, 14365497313475502870339806928100970515660800000000⟩, + ⟨4, 6, 6, 4, 7, 5, 4738534799563909901741361057895400582676480000000⟩, + ⟨4, 6, 7, 4, 8, 5, -3476219420065043988834502613338578065817600000000⟩, + ⟨4, 6, 0, 5, 0, 5, 134681439771783989631634119240439692194972958720000000⟩, + ⟨4, 6, 1, 5, 1, 5, 5253478332915977142468338991178432714710712320000000⟩, + ⟨4, 6, 2, 5, 2, 5, -429004104180293908001009144149495533388431360000000⟩, + ⟨4, 6, 3, 5, 3, 5, 567986848073017396135618917071163549108142080000000⟩, + ⟨4, 6, 4, 5, 4, 5, -10532963701585299636548335352424238090813440000000⟩, + ⟨4, 6, 5, 5, 5, 5, 3953403831174026301620969344751668455014400000000⟩, + ⟨4, 6, 6, 5, 6, 5, 8025577042023877281216154584819502594129920000000⟩, + ⟨4, 6, 7, 5, 7, 5, -1585628625134876759608437850972147396116480000000⟩, + ⟨4, 6, 8, 5, 8, 5, -1063539848261658365635735581606351093104640000000⟩, + ⟨4, 6, 1, 6, 0, 5, -57273886741088520761548913858248241025342504960000000⟩, + ⟨4, 6, 2, 6, 1, 5, 7198547954255991712034857995290848853407825920000000⟩, + ⟨4, 6, 3, 6, 2, 5, 635168951112530971338581913040099922317148160000000⟩, + ⟨4, 6, 4, 6, 3, 5, 263284762497896449934580327763708142986199040000000⟩, + ⟨4, 6, 5, 6, 4, 5, -32967614741676664828912160427226086883983360000000⟩, + ⟨4, 6, 6, 6, 5, 5, -763373804178294085125902588544870902661120000000⟩, + ⟨4, 6, 7, 6, 6, 5, -479377620733083941033372940932595276840960000000⟩, + ⟨4, 6, 8, 6, 7, 5, -286685185139296410459917305730720291880960000000⟩, + ⟨4, 6, 2, 7, 0, 5, -58725567380604256830806213021895117810444533760000000⟩, + ⟨4, 6, 3, 7, 1, 5, -5839036279732085450923356945242196053223014400000000⟩, + ⟨4, 6, 4, 7, 2, 5, -270566647506801198816484688703399792193044480000000⟩, + ⟨4, 6, 5, 7, 3, 5, -45963335231434175060012910893573313417707520000000⟩, + ⟨4, 6, 6, 7, 4, 5, -26491850321216310954309237815587752640512000000000⟩, + ⟨4, 6, 7, 7, 5, 5, 1722181686455350797443179326194805563719680000000⟩, + ⟨4, 6, 8, 7, 6, 5, -428613851375390848085561890729740321423360000000⟩ +] + +def collectedFourData_9_5_28 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 5, 6, 24616975797588146787590362937252754482062688256000000⟩, + ⟨4, 7, 1, 0, 6, 6, -9865775004628838235369452590695950262674128896000000⟩, + ⟨4, 7, 2, 0, 7, 6, 240672232735510041401663820441601512591851520000000⟩, + ⟨4, 7, 3, 0, 8, 6, -29327717032799903553929478016800395449545523200000⟩, + ⟨4, 7, 0, 1, 4, 6, 17699190149731840301999152858950382635486019584000000⟩, + ⟨4, 7, 1, 1, 5, 6, -2148113158307918982385193713871247608144461824000000⟩, + ⟨4, 7, 2, 1, 6, 6, -553984229642737519696681692067331566611726336000000⟩, + ⟨4, 7, 3, 1, 7, 6, 391780817474854444189473488070900299805071769600000⟩, + ⟨4, 7, 4, 1, 8, 6, -101645658970181099791550851977937476159484723200000⟩, + ⟨4, 7, 0, 2, 3, 6, 6927808225015423833432920903179674837885911040000000⟩, + ⟨4, 7, 1, 2, 4, 6, 1867685367611576650581733229617678605839499264000000⟩, + ⟨4, 7, 2, 2, 5, 6, -1161692258696461120346179108761740543828951040000000⟩, + ⟨4, 7, 3, 2, 6, 6, -127532832306513090726101410736559679564519833600000⟩, + ⟨4, 7, 4, 2, 7, 6, 13782287043340384817182778210949978189201408000000⟩, + ⟨4, 7, 5, 2, 8, 6, -24561084237887043786916373128152218364542976000000⟩, + ⟨4, 7, 0, 3, 2, 6, -30441240378156807371852607505691512721897422848000000⟩, + ⟨4, 7, 1, 3, 3, 6, -5172448279622674261387465514022621442920677376000000⟩, + ⟨4, 7, 2, 3, 4, 6, 85594741979823320927507985929621289937403904000000⟩, + ⟨4, 7, 3, 3, 5, 6, -254742718482378194759882595449385626567599718400000⟩, + ⟨4, 7, 4, 3, 6, 6, 11224671673363188533100809739890960318123212800000⟩, + ⟨4, 7, 5, 3, 7, 6, 1934892558980906576606518237174098397495296000000⟩, + ⟨4, 7, 6, 3, 8, 6, -3134253699662142259648101076519624246296576000000⟩, + ⟨4, 7, 0, 4, 1, 6, -25126498510247588040754646821951288178701762560000000⟩, + ⟨4, 7, 1, 4, 2, 6, 8917732928729338136625678938244571437641760768000000⟩, + ⟨4, 7, 2, 4, 3, 6, 1820591388859129183501928110144050973517021184000000⟩, + ⟨4, 7, 3, 4, 4, 6, 104180820931522160679860838073163909963553177600000⟩, + ⟨4, 7, 4, 4, 5, 6, -29025781765553982147320771497599051097335398400000⟩, + ⟨4, 7, 5, 4, 6, 6, 4738534799563909901741361057895400582676480000000⟩, + ⟨4, 7, 6, 4, 7, 6, 1367651784836826725207620841255729891377152000000⟩, + ⟨4, 7, 7, 4, 8, 6, -891838304067968803094050640408922166394880000000⟩, + ⟨4, 7, 0, 5, 0, 6, 155488832966026324917466219967483189757122445312000000⟩, + ⟨4, 7, 1, 5, 1, 6, 4043404032416865119548111391570915988495925248000000⟩, + ⟨4, 7, 2, 5, 2, 6, -247641202862327763750219333724960040763260928000000⟩, + ⟨4, 7, 3, 5, 3, 6, 262294826359370289228383272139717886667338547200000⟩, + ⟨4, 7, 4, 5, 4, 6, -4053412349437744325395004287516183162257408000000⟩, + ⟨4, 7, 5, 5, 5, 6, 1304051034360966032450036165331869384048640000000⟩, + ⟨4, 7, 6, 5, 6, 6, 2316368926293326291684333268909395917406208000000⟩, + ⟨4, 7, 7, 5, 7, 6, -406799506314090402784100642339374208385024000000⟩, + ⟨4, 7, 8, 5, 8, 6, -245569946533516344934356321526056001260748800000⟩, + ⟨4, 7, 1, 6, 0, 6, -44081549389880772599282799295975044201729490944000000⟩, + ⟨4, 7, 2, 6, 1, 6, 4155338041952438823904046222133583167897993216000000⟩, + ⟨4, 7, 3, 6, 2, 6, 293319344111832766370339981680913915706762854400000⟩, + ⟨4, 7, 4, 6, 3, 6, 101320173311442641116181705019449000306147328000000⟩, + ⟨4, 7, 5, 6, 4, 6, -10874541013314668030958860452190202170966016000000⟩, + ⟨4, 7, 6, 6, 5, 6, -220327504163988582124341150356325519065088000000⟩, + ⟨4, 7, 7, 6, 6, 6, -122986288441692217173086978167830057320448000000⟩, + ⟨4, 7, 8, 6, 7, 6, -66195230673940595261982686765286962705203200000⟩, + ⟨4, 7, 2, 7, 0, 6, -33899139899122523153976916376867128472342888448000000⟩, + ⟨4, 7, 3, 7, 1, 6, -2696451532802926744702102544417433284662788096000000⟩, + ⟨4, 7, 4, 7, 2, 6, -104122469365860602226871990169010895256027136000000⟩, + ⟨4, 7, 5, 7, 3, 6, -15161247727488508162128721404509202533056512000000⟩, + ⟨4, 7, 6, 7, 4, 6, -7646166570049452123130648153689275813068800000000⟩, + ⟨4, 7, 7, 7, 5, 6, 441832752466619581291413423713723753693184000000⟩, + ⟨4, 7, 8, 7, 6, 6, -98966372287617259491367839321450056201011200000⟩ +] + +def collectedFourData_9_5_29 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 5, 7, -48157788824636969721200344780242283466242129920000000⟩, + ⟨4, 8, 1, 0, 6, 7, 14475191220813366404304199459585276481938391040000000⟩, + ⟨4, 8, 2, 0, 7, 7, -282493901492955841905053684337226798690467840000000⟩, + ⟨4, 8, 3, 0, 8, 7, 28686667590432911082890899494571669048000512000000⟩, + ⟨4, 8, 0, 1, 4, 7, -34624637429321854259617992526292162762904698880000000⟩, + ⟨4, 8, 1, 1, 5, 7, 3151739089515377309988080619069066926893301760000000⟩, + ⟨4, 8, 2, 1, 6, 7, 650250195540135981872112311896084990302093312000000⟩, + ⟨4, 8, 3, 1, 7, 7, -383217216213581546427079184420212008378433536000000⟩, + ⟨4, 8, 4, 1, 8, 7, 85220463075263688012614071633808254404919296000000⟩, + ⟨4, 8, 0, 2, 3, 7, -13552758399777243274149504676336917747125452800000000⟩, + ⟨4, 8, 1, 2, 4, 7, -2740291849733884215336759862467967860458127360000000⟩, + ⟨4, 8, 2, 2, 5, 7, 1363559787364316904426877875453583211290951680000000⟩, + ⟨4, 8, 3, 2, 6, 7, 124745201379014051047136317670594320086859776000000⟩, + ⟨4, 8, 4, 2, 7, 7, -11555170146658568845951534854702920619786240000000⟩, + ⟨4, 8, 5, 2, 8, 7, 18018168403755088407715334553363463400325120000000⟩, + ⟨4, 8, 0, 3, 2, 7, 59551702765817300181470376124066678548316815360000000⟩, + ⟨4, 8, 1, 3, 3, 7, 7589082245660042010883817183194030327191306240000000⟩, + ⟨4, 8, 2, 3, 4, 7, -100468559809872651738117192056030509576224768000000⟩, + ⟨4, 8, 3, 3, 5, 7, 249174515630190833166129406083417140619116544000000⟩, + ⟨4, 8, 4, 3, 6, 7, -9410846735249431365195712192364878478966784000000⟩, + ⟨4, 8, 5, 3, 7, 7, -1419449550077754810321156996483702608363520000000⟩, + ⟨4, 8, 6, 3, 8, 7, 2043829822047093810207088507234203142717440000000⟩, + ⟨4, 8, 0, 4, 1, 7, 49154559808992148684353129260243937928622899200000000⟩, + ⟨4, 8, 1, 4, 2, 7, -13084211766327175089117156865448510948187832320000000⟩, + ⟨4, 8, 2, 4, 3, 7, -2136955969609081988693398446779089843837206528000000⟩, + ⟨4, 8, 3, 4, 4, 7, -101903621615639650619874730228879724239650816000000⟩, + ⟨4, 8, 4, 4, 5, 7, 24335427486457743138464197764023031957553152000000⟩, + ⟨4, 8, 5, 4, 6, 7, -3476219420065043988834502613338578065817600000000⟩, + ⟨4, 8, 6, 4, 7, 7, -891838304067968803094050640408922166394880000000⟩, + ⟨4, 8, 7, 4, 8, 7, 523406624755696622843895376203705986580480000000⟩, + ⟨4, 8, 0, 5, 0, 7, -304180271538504139303986362131206076993728675840000000⟩, + ⟨4, 8, 1, 5, 1, 7, -5932534091318850239628778586656691824644587520000000⟩, + ⟨4, 8, 2, 5, 2, 7, 290673871147685880802270888480591960212504576000000⟩, + ⟨4, 8, 3, 5, 3, 7, -256561548450784002767763470464142637218660352000000⟩, + ⟨4, 8, 4, 5, 4, 7, 3398410526861889772471071344291173619466240000000⟩, + ⟨4, 8, 5, 5, 5, 7, -956660174959290817613049082235633585356800000000⟩, + ⟨4, 8, 6, 5, 6, 7, -1510491601535586641381615164630750482923520000000⟩, + ⟨4, 8, 7, 5, 7, 7, 238744574639748341045336395182402284027904000000⟩, + ⟨4, 8, 8, 5, 8, 7, 131019405515616179379199602043027999162368000000⟩, + ⟨4, 8, 1, 6, 0, 7, 64677012847837451967008058817584250810332610560000000⟩, + ⟨4, 8, 2, 6, 1, 7, -4877412080949407994467735150727062141924278272000000⟩, + ⟨4, 8, 3, 6, 2, 7, -286907927847551147168084739461618781917282304000000⟩, + ⟨4, 8, 4, 6, 3, 7, -84947573521070468982201639554460203970723840000000⟩, + ⟨4, 8, 5, 6, 4, 7, 7977632802919843023463579388709957449809920000000⟩, + ⟨4, 8, 6, 6, 5, 7, 143674369332676101506060931817827697950720000000⟩, + ⟨4, 8, 7, 6, 6, 7, 72178821912980717785999419868048898654208000000⟩, + ⟨4, 8, 8, 6, 7, 7, 35317268636881313047888789949198056292352000000⟩, + ⟨4, 8, 2, 7, 0, 7, 39789801168640214325383276004634390951064764416000000⟩, + ⟨4, 8, 3, 7, 1, 7, 2637512108723659651685855876702773378925199360000000⟩, + ⟨4, 8, 4, 7, 2, 7, 87297039005883169681623920631420263942062080000000⟩, + ⟨4, 8, 5, 7, 3, 7, 11122388251229669414535847329366434843197440000000⟩, + ⟨4, 8, 6, 7, 4, 7, 4986023710170997352682934717067110121472000000000⟩, + ⟨4, 8, 7, 7, 5, 7, -259305065301891195415716610503004875915264000000⟩, + ⟨4, 8, 8, 7, 6, 7, 52801718802308915076239807472485617631232000000⟩ +] + +def collectedFourData_9_5_30 : List CollectedFourTerm := [ + ⟨5, 0, 4, 1, 8, 0, -412719008714786071807833032305030747963655612006400000⟩, + ⟨5, 0, 4, 2, 7, 0, 55961188150876020483476069065345844130103689216000000⟩, + ⟨5, 0, 5, 2, 8, 0, -698089668523512152240133807642005294566304907264000000⟩, + ⟨5, 0, 4, 3, 6, 0, 45576322817076034597647943147626962223256672665600000⟩, + ⟨5, 0, 5, 3, 7, 0, 54994661149527190794330240874695660642704031744000000⟩, + ⟨5, 0, 6, 3, 8, 0, -356334452514212992419125786413674522681494470656000000⟩, + ⟨5, 0, 4, 4, 5, 0, -117855420475609997607775133338967160369663757516800000⟩, + ⟨5, 0, 5, 4, 6, 0, 134681439771783989631634119240439692194972958720000000⟩, + ⟨5, 0, 6, 4, 7, 0, 155488832966026324917466219967483189757122445312000000⟩, + ⟨5, 0, 7, 4, 8, 0, -304180271538504139303986362131206076993728675840000000⟩, + ⟨5, 0, 4, 5, 4, 0, -16458354874387581352600862114396242731614601216000000⟩, + ⟨5, 0, 5, 5, 5, 0, 37064510080158644504546388498443835941018664960000000⟩, + ⟨5, 0, 6, 5, 6, 0, 263348832693614513106795619273740379346958286848000000⟩, + ⟨5, 0, 7, 5, 7, 0, -138747555165469706712103684797781170960394616832000000⟩, + ⟨5, 0, 8, 5, 8, 0, -209392029579635813755187157202983102227096272896000000⟩, + ⟨5, 0, 4, 6, 3, 0, 411397416432474987182278222207648404143452717056000000⟩, + ⟨5, 0, 5, 6, 4, 0, -309082638934153691826532142700934144000549453824000000⟩, + ⟨5, 0, 6, 6, 5, 0, -25049114747335511506387076785001674989662896128000000⟩, + ⟨5, 0, 7, 6, 6, 0, -41947068704121997061770787624420372457260580864000000⟩, + ⟨5, 0, 8, 6, 7, 0, -56443200379232135772228498108146667925687762944000000⟩, + ⟨5, 0, 4, 7, 2, 0, -422775775935698113339875823461615317381988483072000000⟩, + ⟨5, 0, 5, 7, 3, 0, -430921953525119450680818598789856749664618938368000000⟩, + ⟨5, 0, 6, 7, 4, 0, -869295481366025837266667252050129625245600972800000000⟩, + ⟨5, 0, 7, 7, 5, 0, 150696382973093714522933349862063799490903539712000000⟩, + ⟨5, 0, 8, 7, 6, 0, -84386423688900705084915265913388449073205346304000000⟩ +] + +def collectedFourData_9_5_31 : List CollectedFourTerm := [ + ⟨5, 1, 3, 0, 8, 1, -1548323957096496104494027746343393087563025612800000⟩, + ⟨5, 1, 3, 1, 7, 1, 20683629242219762944324876568227267874241537638400000⟩, + ⟨5, 1, 4, 1, 8, 1, -32197611987809073768828291771259460471663414476800000⟩, + ⟨5, 1, 3, 2, 6, 1, -6732952972633498846244472487039718628591560294400000⟩, + ⟨5, 1, 4, 2, 7, 1, 4365722402923897520333104297665747033985646592000000⟩, + ⟨5, 1, 5, 2, 8, 1, -27230173320356013574727392484562473491139395584000000⟩, + ⟨5, 1, 3, 3, 5, 1, -13448856366181974871807686278952763959272905113600000⟩, + ⟨5, 1, 4, 3, 6, 1, 3555563778041151138729114081330901133135393587200000⟩, + ⟨5, 1, 5, 3, 7, 1, 2145160173997672269946479748697487367118782464000000⟩, + ⟨5, 1, 6, 3, 8, 1, -9266287068344223672205051544712997454556954624000000⟩, + ⟨5, 1, 3, 4, 4, 1, 5500109699566890718363370936677510381190932070400000⟩, + ⟨5, 1, 4, 4, 5, 1, -9194301738004324256880709976680580824465775001600000⟩, + ⟨5, 1, 5, 4, 6, 1, 5253478332915977142468338991178432714710712320000000⟩, + ⟨5, 1, 6, 4, 7, 1, 4043404032416865119548111391570915988495925248000000⟩, + ⟨5, 1, 7, 4, 8, 1, -5932534091318850239628778586656691824644587520000000⟩, + ⟨5, 1, 3, 5, 3, 1, 13847561438910497518970341244580551124476284108800000⟩, + ⟨5, 1, 4, 5, 4, 1, -1283972177228706808137887590492335992148590592000000⟩, + ⟨5, 1, 5, 5, 5, 1, 1445764174753446339399715653139307773569269760000000⟩, + ⟨5, 1, 6, 5, 6, 1, 6848245701852398364411837457436042631044923392000000⟩, + ⟨5, 1, 7, 5, 7, 1, -2706042035346457545713384755014079228460138496000000⟩, + ⟨5, 1, 8, 5, 8, 1, -3267076717759822479356829127854393630623426150400000⟩, + ⟨5, 1, 3, 6, 2, 1, 15485466088623943665093519609638022202877647257600000⟩, + ⟨5, 1, 4, 6, 3, 1, 32094510084059974993918677803431409911880220672000000⟩, + ⟨5, 1, 5, 6, 4, 1, -12056293350238219871928884914272876374412754944000000⟩, + ⟨5, 1, 6, 6, 5, 1, -651388846683152118872936038782408883030720512000000⟩, + ⟨5, 1, 7, 6, 6, 1, -818108333783235562173036241308715730539118592000000⟩, + ⟨5, 1, 8, 6, 7, 1, -880665162876742673164067013767364052617107865600000⟩, + ⟨5, 1, 3, 7, 1, 1, -142356137121722510467086900687407572881437097984000000⟩, + ⟨5, 1, 4, 7, 2, 1, -32982174564267506451309054061257411767895588864000000⟩, + ⟨5, 1, 5, 7, 3, 1, -16808842776392112742613761694729854643714654208000000⟩, + ⟨5, 1, 6, 7, 4, 1, -22605564577651327597274209311224255428637491200000000⟩, + ⟨5, 1, 7, 7, 5, 1, 2939084198013654108993792006857860826724827136000000⟩, + ⟨5, 1, 8, 7, 6, 1, -1316654319089880202169596448028738992062699929600000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0922.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0922.lean new file mode 100644 index 0000000000000000000000000000000000000000..963f0bb9217f00ab6b60df6b84f0f756df53494b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0922.lean @@ -0,0 +1,634 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0922. -/ +namespace LaughlinFock +def collectedFourData_9_5_32 : List CollectedFourTerm := [ + ⟨5, 2, 2, 0, 7, 2, -622551544928256795061245420485486195930824704000000⟩, + ⟨5, 2, 3, 0, 8, 2, 379312880020796183961592045801262852712117043200000⟩, + ⟨5, 2, 2, 1, 6, 2, 1433001780512798160624171945245189021312955187200000⟩, + ⟨5, 2, 3, 1, 7, 2, -5067135298908106746264665769554608851527506329600000⟩, + ⟨5, 2, 4, 1, 8, 2, 3943932042422961736309028657940334779993528729600000⟩, + ⟨5, 2, 2, 2, 5, 2, 3004971957764080492869747426533570579433259008000000⟩, + ⟨5, 2, 3, 2, 6, 2, 1649458287710927062261950520225156300457744793600000⟩, + ⟨5, 2, 4, 2, 7, 2, -534763648923236656211814001475588477234970624000000⟩, + ⟨5, 2, 5, 2, 8, 2, 2223642198879952570994536646856458267925676032000000⟩, + ⟨5, 2, 2, 3, 4, 2, -221409583696492057644525526662856208338963660800000⟩, + ⟨5, 2, 3, 3, 5, 2, 3294739720238388609685773702289712206240441958400000⟩, + ⟨5, 2, 4, 3, 6, 2, -435526147665994811592202994743650871251723878400000⟩, + ⟨5, 2, 5, 3, 7, 2, -175175847400574703499272477653409279636406272000000⟩, + ⟨5, 2, 6, 3, 8, 2, 567520449916744017743023737517142823313342464000000⟩, + ⟨5, 2, 2, 4, 3, 2, -4709359151800905119401865116314012800418368716800000⟩, + ⟨5, 2, 3, 4, 4, 2, -1347432777882807990431133926124538273849776537600000⟩, + ⟨5, 2, 4, 4, 5, 2, 1126223312646605180621025400220518133609476915200000⟩, + ⟨5, 2, 5, 4, 6, 2, -429004104180293908001009144149495533388431360000000⟩, + ⟨5, 2, 6, 4, 7, 2, -247641202862327763750219333724960040763260928000000⟩, + ⟨5, 2, 7, 4, 8, 2, 290673871147685880802270888480591960212504576000000⟩, + ⟨5, 2, 2, 5, 2, 2, 640578315485445012647552264029693878810024345600000⟩, + ⟨5, 2, 3, 5, 3, 2, -3392415641819528093109738239488465798668956467200000⟩, + ⟨5, 2, 4, 5, 4, 2, 157275608305026036809839431542712710278938624000000⟩, + ⟨5, 2, 5, 5, 5, 2, -118062495996209163225519950740815140597268480000000⟩, + ⟨5, 2, 6, 5, 6, 2, -419425758471581301101447381414283721794650112000000⟩, + ⟨5, 2, 7, 5, 7, 2, 132586800479330361310069191047567197837511884800000⟩, + ⟨5, 2, 8, 5, 8, 2, 133396316856310925094710538460766941153434009600000⟩, + ⟨5, 2, 2, 6, 1, 2, -10748693724712189361043460210319059554374202163200000⟩, + ⟨5, 2, 3, 6, 2, 2, -3793674258942082055743337397008051281817134694400000⟩, + ⟨5, 2, 4, 6, 3, 2, -3931302941172072720411481855793415272880144384000000⟩, + ⟨5, 2, 5, 6, 4, 2, 984528535322409760796499638379493819586445312000000⟩, + ⟨5, 2, 6, 6, 5, 2, 39894780791248280774026887151501466174226432000000⟩, + ⟨5, 2, 7, 6, 6, 2, 40084509037535213097881706811137963096381849600000⟩, + ⟨5, 2, 8, 6, 7, 2, 35957983010565145292848569136617376075638374400000⟩, + ⟨5, 2, 2, 7, 0, 2, 87687564435945206358842510854816553127305124249600000⟩, + ⟨5, 2, 3, 7, 1, 2, 34874818097845046991264745780060038606876573696000000⟩, + ⟨5, 2, 4, 7, 2, 2, 4040034246702953133501721187907100356491870208000000⟩, + ⟨5, 2, 5, 7, 3, 2, 1372626302161020946038600952286838778950057984000000⟩, + ⟨5, 2, 6, 7, 4, 2, 1384494143674647188195069278990541828338483200000000⟩, + ⟨5, 2, 7, 7, 5, 2, -144005069050635572399513064747382148858432716800000⟩, + ⟨5, 2, 8, 7, 6, 2, 53759630370717185158457931707788327890871910400000⟩ +] + +def collectedFourData_9_5_33 : List CollectedFourTerm := [ + ⟨5, 3, 1, 0, 6, 3, -33787601838395867444114296710152495069226703257600000⟩, + ⟨5, 3, 2, 0, 7, 3, 3296948316542753929604146862762268980567605248000000⟩, + ⟨5, 3, 3, 0, 8, 3, -1004394713510561259159456668077080085412393779200000⟩, + ⟨5, 3, 1, 1, 5, 3, -7356704573403914140465533709683745635795625574400000⟩, + ⟨5, 3, 2, 1, 6, 3, -7588982545066042346145211089005420448271722086400000⟩, + ⟨5, 3, 3, 1, 7, 3, 13417429712871940258736006018595338932838832537600000⟩, + ⟨5, 3, 4, 1, 8, 3, -6962175910710534182846154474994828663511737958400000⟩, + ⟨5, 3, 1, 2, 4, 3, 6396315497834732598330664714238081176760116838400000⟩, + ⟨5, 3, 2, 2, 5, 3, -15913922819917159583839639940442176778399645696000000⟩, + ⟨5, 3, 3, 2, 6, 3, -4367653384831559083092010781968718313293453721600000⟩, + ⟨5, 3, 4, 2, 7, 3, 944011852742198605834445991368244683757060096000000⟩, + ⟨5, 3, 5, 2, 8, 3, -2944026668922467653337308181227050969329565696000000⟩, + ⟨5, 3, 1, 3, 3, 3, -17714231565142150345196357501154657795755841945600000⟩, + ⟨5, 3, 2, 3, 4, 3, 1172555044126835028567063663243266318789089689600000⟩, + ⟨5, 3, 3, 3, 5, 3, -8724246741158043563455996555625290013144933990400000⟩, + ⟨5, 3, 4, 3, 6, 3, 768829082537107959432086730369452579806091673600000⟩, + ⟨5, 3, 5, 3, 7, 3, 231926866093004328028042239775101127193788416000000⟩, + ⟨5, 3, 6, 3, 8, 3, -601102224289627450577035283219176947139058073600000⟩, + ⟨5, 3, 1, 4, 2, 3, 30540815025245381740731526221898288120422255820800000⟩, + ⟨5, 3, 2, 4, 3, 3, 24940125607293272766494015595787302975928113561600000⟩, + ⟨5, 3, 3, 4, 4, 3, 3567910372150146165440123394013380666789042585600000⟩, + ⟨5, 3, 4, 4, 5, 3, -1988108500107852332456135848510888126217768140800000⟩, + ⟨5, 3, 5, 4, 6, 3, 567986848073017396135618917071163549108142080000000⟩, + ⟨5, 3, 6, 4, 7, 3, 262294826359370289228383272139717886667338547200000⟩, + ⟨5, 3, 7, 4, 8, 3, -256561548450784002767763470464142637218660352000000⟩, + ⟨5, 3, 1, 5, 1, 3, 13847561438910497518970341244580551124476284108800000⟩, + ⟨5, 3, 2, 5, 2, 3, -3392415641819528093109738239488465798668956467200000⟩, + ⟨5, 3, 3, 5, 3, 3, 8982885939668755698584918483974728497530876723200000⟩, + ⟨5, 3, 4, 5, 4, 3, -277636744169378408841207665589132207216132096000000⟩, + ⟨5, 3, 5, 5, 5, 3, 156310730650581855777792725952038249630269440000000⟩, + ⟨5, 3, 6, 5, 6, 3, 444244355209785963089902614116631078071225548800000⟩, + ⟨5, 3, 7, 5, 7, 3, -117026943979525840615167416237645467179653529600000⟩, + ⟨5, 3, 8, 5, 8, 3, -100921250359644859667800616303129888988699033600000⟩, + ⟨5, 3, 1, 6, 0, 3, -150967343012188136414929996997156539699105785446400000⟩, + ⟨5, 3, 2, 6, 1, 3, 56923620171575349642075792029484093015817872998400000⟩, + ⟨5, 3, 3, 6, 2, 3, 10045391472743075551385690878183119053260220006400000⟩, + ⟨5, 3, 4, 6, 3, 3, 6939881909810648932903250252018840227477979136000000⟩, + ⟨5, 3, 5, 6, 4, 3, -1303482307434312970237202518130373433843777536000000⟩, + ⟨5, 3, 6, 6, 5, 3, -42255466696723378597027779847441741729549516800000⟩, + ⟨5, 3, 7, 6, 6, 3, -35380351412233751992154496666580428604519219200000⟩, + ⟨5, 3, 8, 6, 7, 3, -27204083975916899439607932940660068980254310400000⟩, + ⟨5, 3, 2, 7, 0, 3, -464381415971170739354366465777415061804181304115200000⟩, + ⟨5, 3, 3, 7, 1, 3, -92346146880637339479697364740062079875626827776000000⟩, + ⟨5, 3, 4, 7, 2, 3, -7131823978782540850626561231999709705018540032000000⟩, + ⟨5, 3, 5, 7, 3, 3, -1817310555655918508236026284141115056326705152000000⟩, + ⟨5, 3, 6, 7, 4, 3, -1466418539456827647907745073237425087242567680000000⟩, + ⟨5, 3, 7, 7, 5, 3, 127105210229307089514440025605235181851613593600000⟩, + ⟨5, 3, 8, 7, 6, 3, -40671955896122920398507496234205106202371686400000⟩ +] + +def collectedFourData_9_5_34 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 5, 4, -2605685024978229081626533685174394880322961408000000⟩, + ⟨5, 4, 1, 0, 6, 4, 3132850566301227918277902967175830413753974784000000⟩, + ⟨5, 4, 2, 0, 7, 4, -152849652513799554368246513628942694518620160000000⟩, + ⟨5, 4, 3, 0, 8, 4, 31043128009514799124763449384373632710475776000000⟩, + ⟨5, 4, 0, 1, 4, 4, -1873443558079823407081846413585406064131571712000000⟩, + ⟨5, 4, 1, 1, 5, 4, 682127609977586644605682741472754934896132096000000⟩, + ⟨5, 4, 2, 1, 6, 4, 351832432169578573480637375415536347238105088000000⟩, + ⟨5, 4, 3, 1, 7, 4, -414696515754780822204610343938482111227363328000000⟩, + ⟨5, 4, 4, 1, 8, 4, 161386540903977086248149192755980668883697664000000⟩, + ⟨5, 4, 0, 2, 3, 4, -733302347789297219547722121449204274136350720000000⟩, + ⟨5, 4, 1, 2, 4, 4, -593078512215125568877630006650279616478969856000000⟩, + ⟨5, 4, 2, 2, 5, 4, 737784563061172201141575186202306155978424320000000⟩, + ⟨5, 4, 3, 2, 6, 4, 134992370332792479648609172873035671402446848000000⟩, + ⟨5, 4, 4, 2, 7, 4, -21882642645102264214938873312690374348636160000000⟩, + ⟨5, 4, 5, 2, 8, 4, 54595148013485408672128325472285425273929728000000⟩, + ⟨5, 4, 0, 3, 2, 4, 3222178258098511730833216781458721225954033664000000⟩, + ⟨5, 4, 1, 3, 3, 4, 1642497169697956161914112604489183477528264704000000⟩, + ⟨5, 4, 2, 3, 4, 4, -54360764513296397870076870720363795245432832000000⟩, + ⟨5, 4, 3, 3, 5, 4, 269642905054491509155222468958681833786048512000000⟩, + ⟨5, 4, 4, 3, 6, 4, -17821822914034807065494687487561975050797056000000⟩, + ⟨5, 4, 5, 3, 7, 4, -4300939837371032858360323492142690429042688000000⟩, + ⟨5, 4, 6, 3, 8, 4, 9289223173131908938257238773419080578760704000000⟩, + ⟨5, 4, 0, 4, 1, 4, 2659617551588303929179844836025078349121454080000000⟩, + ⟨5, 4, 1, 4, 2, 4, -2831802331067235960982307225341094395140636672000000⟩, + ⟨5, 4, 2, 4, 3, 4, -1156247889479421472861089048030587325694083072000000⟩, + ⟨5, 4, 3, 4, 4, 4, -110274473689738248331914940065355907903520768000000⟩, + ⟨5, 4, 4, 4, 5, 4, 46085298316091422064981225901029233281466368000000⟩, + ⟨5, 4, 5, 4, 6, 4, -10532963701585299636548335352424238090813440000000⟩, + ⟨5, 4, 6, 4, 7, 4, -4053412349437744325395004287516183162257408000000⟩, + ⟨5, 4, 7, 4, 8, 4, 3398410526861889772471071344291173619466240000000⟩, + ⟨5, 4, 0, 5, 0, 4, -16458354874387581352600862114396242731614601216000000⟩, + ⟨5, 4, 1, 5, 1, 4, -1283972177228706808137887590492335992148590592000000⟩, + ⟨5, 4, 2, 5, 2, 4, 157275608305026036809839431542712710278938624000000⟩, + ⟨5, 4, 3, 5, 3, 4, -277636744169378408841207665589132207216132096000000⟩, + ⟨5, 4, 4, 5, 4, 4, 6435751458162393512392459727114269265756160000000⟩, + ⟨5, 4, 5, 5, 5, 4, -2898685520090072484182061268252957259857920000000⟩, + ⟨5, 4, 6, 5, 6, 4, -6865196620798790208660597642938008870060032000000⟩, + ⟨5, 4, 7, 5, 7, 4, 1550137192217596937043938046993477509578752000000⟩, + ⟨5, 4, 8, 5, 8, 4, 1169701233359465054881471446876541396451328000000⟩, + ⟨5, 4, 1, 6, 0, 4, 13997978557663148419841911521502357810971672576000000⟩, + ⟨5, 4, 2, 6, 1, 4, -2639033047438423236993182222018665349935792128000000⟩, + ⟨5, 4, 3, 6, 2, 4, -310475920670775882958810135861703500986580992000000⟩, + ⟨5, 4, 4, 6, 3, 4, -160869755385442918805158802483066304001474560000000⟩, + ⟨5, 4, 5, 6, 4, 4, 24172270672188649718526289528014723348430848000000⟩, + ⟨5, 4, 6, 6, 5, 4, 653001177785659596954060878100466658967552000000⟩, + ⟨5, 4, 7, 6, 6, 4, 468647618512768178380661148581835470536704000000⟩, + ⟨5, 4, 8, 6, 7, 4, 315301786944253962380336644797073081761792000000⟩, + ⟨5, 4, 2, 7, 0, 4, 21529163107867965816148539687529347435970166784000000⟩, + ⟨5, 4, 3, 7, 1, 4, 2854169999343527069962670145551877253921505280000000⟩, + ⟨5, 4, 4, 7, 2, 4, 165319063613589202530251492135323885602078720000000⟩, + ⟨5, 4, 5, 7, 3, 4, 33700896741135191519983821826708920531419136000000⟩, + ⟨5, 4, 6, 7, 4, 4, 22661518337135971319252287628323748786995200000000⟩, + ⟨5, 4, 7, 7, 5, 4, -1683633759893417862980106017845018657554432000000⟩, + ⟨5, 4, 8, 7, 6, 4, 471397617501775064952824469687476548534272000000⟩ +] + +def collectedFourData_9_5_35 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 5, 5, 5868049365269121652806559789958141275778580480000000⟩, + ⟨5, 5, 1, 0, 6, 5, -3527617805076138810281582619320968506003947520000000⟩, + ⟨5, 5, 2, 0, 7, 5, 114740052080636168319095335838377682613043200000000⟩, + ⟨5, 5, 3, 0, 8, 5, -17477420128102724813058300726755906436464640000000⟩, + ⟨5, 5, 0, 1, 4, 5, 4219028461411864127467877083849332854850846720000000⟩, + ⟨5, 5, 1, 1, 5, 5, -768081800062339456450539013667844409660538880000000⟩, + ⟨5, 5, 2, 1, 6, 5, -264110980475730710120333734455945945950453760000000⟩, + ⟨5, 5, 3, 1, 7, 5, 233475996017063675855334315024897875556433920000000⟩, + ⟨5, 5, 4, 1, 8, 5, -72689076372342771498526653386822223101165568000000⟩, + ⟨5, 5, 0, 2, 3, 5, 1651410026632553163519141740159105754149683200000000⟩, + ⟨5, 5, 1, 2, 4, 5, 667811718184894652819737074587500361212231680000000⟩, + ⟨5, 5, 2, 2, 5, 5, -553834685245919194354059312438421892785766400000000⟩, + ⟨5, 5, 3, 2, 6, 5, -76001309200268324055642072883349026473246720000000⟩, + ⟨5, 5, 4, 2, 7, 5, 9856020666586609250675398144242225166417920000000⟩, + ⟨5, 5, 5, 2, 8, 5, -20491541928274281627973409638261852502753280000000⟩, + ⟨5, 5, 0, 3, 2, 5, -7256403172665473782340520590388595271757987840000000⟩, + ⟨5, 5, 1, 3, 3, 5, -1849466528323573878696704225607678176652165120000000⟩, + ⟨5, 5, 2, 3, 4, 5, 40807138575834883320290043135774106991984640000000⟩, + ⟨5, 5, 3, 3, 5, 5, -151810163420226809807562915633710715560263680000000⟩, + ⟨5, 5, 4, 3, 6, 5, 8027012907249940145099231726298471252099072000000⟩, + ⟨5, 5, 5, 3, 7, 5, 1614298929763945490235137519138223559802880000000⟩, + ⟨5, 5, 6, 3, 8, 5, -2988499575922203362259316398304044326584320000000⟩, + ⟨5, 5, 0, 4, 1, 5, -5989506381565346463507418114497078933376204800000000⟩, + ⟨5, 5, 1, 4, 2, 5, 3188634795091082064417805241242809647927132160000000⟩, + ⟨5, 5, 2, 4, 3, 5, 867963654971456088290542567854895007205949440000000⟩, + ⟨5, 5, 3, 4, 4, 5, 62085022665571558826908624562618401051115520000000⟩, + ⟨5, 5, 4, 4, 5, 5, -20756983514094370109226354722875189405679616000000⟩, + ⟨5, 5, 5, 4, 6, 5, 3953403831174026301620969344751668455014400000000⟩, + ⟨5, 5, 6, 4, 7, 5, 1304051034360966032450036165331869384048640000000⟩, + ⟨5, 5, 7, 4, 8, 5, -956660174959290817613049082235633585356800000000⟩, + ⟨5, 5, 0, 5, 0, 5, 37064510080158644504546388498443835941018664960000000⟩, + ⟨5, 5, 1, 5, 1, 5, 1445764174753446339399715653139307773569269760000000⟩, + ⟨5, 5, 2, 5, 2, 5, -118062495996209163225519950740815140597268480000000⟩, + ⟨5, 5, 3, 5, 3, 5, 156310730650581855777792725952038249630269440000000⟩, + ⟨5, 5, 4, 5, 4, 5, -2898685520090072484182061268252957259857920000000⟩, + ⟨5, 5, 5, 5, 5, 5, 1087981955047276024197157847983486874419200000000⟩, + ⟨5, 5, 6, 5, 6, 5, 2208649400223467696850686272481184511426560000000⟩, + ⟨5, 5, 7, 5, 7, 5, -436367091555344886233040182863337241968640000000⟩, + ⟨5, 5, 8, 5, 8, 5, -292687570710118791384968493319738380779520000000⟩, + ⟨5, 5, 1, 6, 0, 5, -15761849264769120159075924734810429595089633280000000⟩, + ⟨5, 5, 2, 6, 1, 5, 1981049903127958084033472745461050772092354560000000⟩, + ⟨5, 5, 3, 6, 2, 5, 174799334125074725323066508485606134125690880000000⟩, + ⟨5, 5, 4, 6, 3, 5, 72456314322828361568228962226822305252638720000000⟩, + ⟨5, 5, 5, 6, 4, 5, -9072731112632920825830167292851874410004480000000⟩, + ⟨5, 5, 6, 6, 5, 5, -210081478991013084519408411939644280668160000000⟩, + ⟨5, 5, 7, 6, 6, 5, -131925354272803553077706039827214138081280000000⟩, + ⟨5, 5, 8, 6, 7, 5, -78896141535410979370476361400267864801280000000⟩, + ⟨5, 5, 2, 7, 0, 5, -16161353693795684279049372818329061625094471680000000⟩, + ⟨5, 5, 3, 7, 1, 5, -1606910494981822395844625083552103167898419200000000⟩, + ⟨5, 5, 4, 7, 2, 5, -74460298693447264244320196849483890965872640000000⟩, + ⟨5, 5, 5, 7, 3, 5, -12649170553046850278693129088153054200463360000000⟩, + ⟨5, 5, 6, 7, 4, 5, -7290592192484768837389672646682938966016000000000⟩, + ⟨5, 5, 7, 7, 5, 5, 473946674357292162241001039769945495306240000000⟩, + ⟨5, 5, 8, 7, 6, 5, -117955097908947476595811535862375099924480000000⟩ +] + +def collectedFourData_9_5_36 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 5, 6, 41693359690713449568393494784761482963870285824000000⟩, + ⟨5, 6, 1, 0, 6, 6, -16709497920371728059707640560644542942500880384000000⟩, + ⟨5, 6, 2, 0, 7, 6, 407622530465007241136759888274964659390382080000000⟩, + ⟨5, 6, 3, 0, 8, 6, -49671863238204548125190279190898681569922252800000⟩, + ⟨5, 6, 0, 1, 4, 6, 29976821979058928461803767653503405618716737536000000⟩, + ⟨5, 6, 1, 1, 5, 6, -3638223285512650535743186526517039899917418496000000⟩, + ⟨5, 6, 2, 1, 6, 6, -938273813135910631428548946600992919879942144000000⟩, + ⟨5, 6, 3, 1, 7, 6, 663552610085486261125402474824939124061267558400000⟩, + ⟨5, 6, 4, 1, 8, 6, -172155550514802413183244771662749542690639052800000⟩, + ⟨5, 6, 0, 2, 3, 6, 11733512782758257168661335667440310208859996160000000⟩, + ⟨5, 6, 1, 2, 4, 6, 3163267432246538485783520739920061288998240256000000⟩, + ⟨5, 6, 2, 2, 5, 6, -1967538725715215898186132368837061990584156160000000⟩, + ⟨5, 6, 3, 2, 6, 6, -216000222507098199123101558351216859712743014400000⟩, + ⟨5, 6, 4, 2, 7, 6, 23342828777324862406603251700008759205036032000000⟩, + ⟨5, 6, 5, 2, 8, 6, -41598697091966393709530941413031887664840704000000⟩, + ⟨5, 6, 0, 3, 2, 6, -51557819081997536446520111938786678776677793792000000⟩, + ⟨5, 6, 1, 3, 3, 6, -8760489037205339824034366441813968464384098304000000⟩, + ⟨5, 6, 2, 3, 4, 6, 144970381185012630729745230977371465177890816000000⟩, + ⟨5, 6, 3, 3, 5, 6, -431453476560534845906503613635298756052752793600000⟩, + ⟨5, 6, 4, 3, 6, 6, 19011038453128986008143106983574259578909491200000⟩, + ⟨5, 6, 5, 3, 7, 6, 3277095126866875272751442407255706890665984000000⟩, + ⟨5, 6, 6, 3, 8, 6, -5308433007224478884122436767452672351535104000000⟩, + ⟨5, 6, 0, 4, 1, 6, -42556329777054415812386442163111358072346378240000000⟩, + ⟨5, 6, 1, 4, 2, 6, 15103814931631852473832960566989561024030441472000000⟩, + ⟨5, 6, 2, 4, 3, 6, 3083505149034439629570774951230933484422823936000000⟩, + ⟨5, 6, 3, 4, 4, 6, 176449311876779433883075422994276995207423590400000⟩, + ⟨5, 6, 4, 4, 5, 6, -49160480532054702029964188872819196972079513600000⟩, + ⟨5, 6, 5, 4, 6, 6, 8025577042023877281216154584819502594129920000000⟩, + ⟨5, 6, 6, 4, 7, 6, 2316368926293326291684333268909395917406208000000⟩, + ⟨5, 6, 7, 4, 8, 6, -1510491601535586641381615164630750482923520000000⟩, + ⟨5, 6, 0, 5, 0, 6, 263348832693614513106795619273740379346958286848000000⟩, + ⟨5, 6, 1, 5, 1, 6, 6848245701852398364411837457436042631044923392000000⟩, + ⟨5, 6, 2, 5, 2, 6, -419425758471581301101447381414283721794650112000000⟩, + ⟨5, 6, 3, 5, 3, 6, 444244355209785963089902614116631078071225548800000⟩, + ⟨5, 6, 4, 5, 4, 6, -6865196620798790208660597642938008870060032000000⟩, + ⟨5, 6, 5, 5, 5, 6, 2208649400223467696850686272481184511426560000000⟩, + ⟨5, 6, 6, 5, 6, 6, 3923195262262943567285466012026856624095232000000⟩, + ⟨5, 6, 7, 5, 7, 6, -688989511880649847257145745060929833271296000000⟩, + ⟨5, 6, 8, 5, 8, 6, -415917706311199275675109220006121539056435200000⟩, + ⟨5, 6, 1, 6, 0, 6, -74660182044632731063852152996891544908491390976000000⟩, + ⟨5, 6, 2, 6, 1, 6, 7037826459438700437154866858792551380275953664000000⟩, + ⟨5, 6, 3, 6, 2, 6, 496790061413513693196129093547864057150282137600000⟩, + ⟨5, 6, 4, 6, 3, 6, 171604280904939086747730110087091962838515712000000⟩, + ⟨5, 6, 5, 6, 4, 6, -18418028017233763945925253888507826472484864000000⟩, + ⟨5, 6, 6, 6, 5, 6, -373165004361192103736872132962393891274752000000⟩, + ⟨5, 6, 7, 6, 6, 6, -208299817296310471279278766170327264264192000000⟩, + ⟨5, 6, 8, 6, 7, 6, -112113753736100891150419157900888074144972800000⟩, + ⟨5, 6, 2, 7, 0, 6, -57414405597230433095982592539826822882044936192000000⟩, + ⟨5, 6, 3, 7, 1, 6, -4566934808326163980799974524721906607072477184000000⟩, + ⟨5, 6, 4, 7, 2, 6, -176350482807130594178936284807444048688185344000000⟩, + ⟨5, 6, 5, 7, 3, 6, -25678351397011271835384518475308555355291648000000⟩, + ⟨5, 6, 6, 7, 4, 6, -12950184282645087795868945797447811281715200000000⟩, + ⟨5, 6, 7, 7, 5, 6, 748324734248370984788149145983370643111936000000⟩, + ⟨5, 6, 8, 7, 6, 6, -167617687525896308787683984908245999078604800000⟩ +] + +def collectedFourData_9_5_37 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 5, 7, -21966498444484284668719748586822523486539350016000000⟩, + ⟨5, 7, 1, 0, 6, 7, 6602655005475250875101454701862096383395233792000000⟩, + ⟨5, 7, 2, 0, 7, 7, -128855622302714595953158252469752434819858432000000⟩, + ⟨5, 7, 3, 0, 8, 7, 13085020188474829594224850377069299318233497600000⟩, + ⟨5, 7, 0, 1, 4, 7, -15793541663668034626992434873646306142111924224000000⟩, + ⟨5, 7, 1, 1, 5, 7, 1437621483398365963965323273298790827738267648000000⟩, + ⟨5, 7, 2, 1, 6, 7, 296602486481908664942414371147126590687254937600000⟩, + ⟨5, 7, 3, 1, 7, 7, -174799146499614939842432523864141304517414092800000⟩, + ⟨5, 7, 4, 1, 8, 7, 38872116334031496650170631765176046144244940800000⟩, + ⟨5, 7, 0, 2, 3, 7, -6181900240296640206213538024222013838002749440000000⟩, + ⟨5, 7, 1, 2, 4, 7, -1249945608462352379685684003452742118856982528000000⟩, + ⟨5, 7, 2, 2, 5, 7, 621968630187110395996066061921596730102513664000000⟩, + ⟨5, 7, 3, 2, 6, 7, 56900770133514278882607219055106915497200844800000⟩, + ⟨5, 7, 4, 2, 7, 7, -5270728437649361491724039069139433005514752000000⟩, + ⟨5, 7, 5, 2, 8, 7, 8218734245768720369941781704488519494270976000000⟩, + ⟨5, 7, 0, 3, 2, 7, 27163672130695619265426677464139677499211644928000000⟩, + ⟨5, 7, 1, 3, 3, 7, 3461653190751772430224878215106165695947210752000000⟩, + ⟨5, 7, 2, 3, 4, 7, -45827321325311713555094873389150652403705446400000⟩, + ⟨5, 7, 3, 3, 5, 7, 113657452793919325275367876297066652999299891200000⟩, + ⟨5, 7, 4, 3, 6, 7, -4292625455124288419709545776360735536001843200000⟩, + ⟨5, 7, 5, 3, 7, 7, -647461959836814975917838812544258640183296000000⟩, + ⟨5, 7, 6, 3, 8, 7, 932264244321365364794790195668449348288512000000⟩, + ⟨5, 7, 0, 4, 1, 7, 22421161517929708050981898770335483096633180160000000⟩, + ⟨5, 7, 1, 4, 2, 7, -5968179279553861371426974852130327503396929536000000⟩, + ⟨5, 7, 2, 4, 3, 7, -974742427508104486189081291630556524172437094400000⟩, + ⟨5, 7, 3, 4, 4, 7, -46481904596128180970865535693575394769554636800000⟩, + ⟨5, 7, 4, 4, 5, 7, 11100263178064713642872296240541661291714969600000⟩, + ⟨5, 7, 5, 4, 6, 7, -1585628625134876759608437850972147396116480000000⟩, + ⟨5, 7, 6, 4, 7, 7, -406799506314090402784100642339374208385024000000⟩, + ⟨5, 7, 7, 4, 8, 7, 238744574639748341045336395182402284027904000000⟩, + ⟨5, 7, 0, 5, 0, 7, -138747555165469706712103684797781170960394616832000000⟩, + ⟨5, 7, 1, 5, 1, 7, -2706042035346457545713384755014079228460138496000000⟩, + ⟨5, 7, 2, 5, 2, 7, 132586800479330361310069191047567197837511884800000⟩, + ⟨5, 7, 3, 5, 3, 7, -117026943979525840615167416237645467179653529600000⟩, + ⟨5, 7, 4, 5, 4, 7, 1550137192217596937043938046993477509578752000000⟩, + ⟨5, 7, 5, 5, 5, 7, -436367091555344886233040182863337241968640000000⟩, + ⟨5, 7, 6, 5, 6, 7, -688989511880649847257145745060929833271296000000⟩, + ⟨5, 7, 7, 5, 7, 7, 108899981819143003854955168670795410125619200000⟩, + ⟨5, 7, 8, 5, 8, 7, 59762660157346503057787185982675664397926400000⟩, + ⟨5, 7, 1, 6, 0, 7, 29501510280909817595664801222409852400475045888000000⟩, + ⟨5, 7, 2, 6, 1, 7, -2224762961593299128497503445024071517392705945600000⟩, + ⟨5, 7, 3, 6, 2, 7, -130869018378792873709088109347548772275794739200000⟩, + ⟨5, 7, 4, 6, 3, 7, -38747641599746464952979820617805901680607232000000⟩, + ⟨5, 7, 5, 6, 4, 7, 3638885065801742843011952098534465801814016000000⟩, + ⟨5, 7, 6, 6, 5, 7, 65535044018547323777502533187336306425856000000⟩, + ⟨5, 7, 7, 6, 6, 7, 32923355037120546455343091292704109651558400000⟩, + ⟨5, 7, 8, 6, 7, 7, 16109475653055696608982949970890781727129600000⟩, + ⟨5, 7, 2, 7, 0, 7, 18149558499457602111653567573463340789642611916800000⟩, + ⟨5, 7, 3, 7, 1, 7, 1203064074319518633523443590137245881365168128000000⟩, + ⟨5, 7, 4, 7, 2, 7, 39819317255483899163786600019547105561411584000000⟩, + ⟨5, 7, 5, 7, 3, 7, 5073321059429447040217177163135820352192512000000⟩, + ⟨5, 7, 6, 7, 4, 7, 2274304629568062744336231851267756497305600000000⟩, + ⟨5, 7, 7, 7, 5, 7, -118278360627032535442372769562612368356147200000⟩, + ⟨5, 7, 8, 7, 6, 7, 24084761826598646523889539590574554323353600000⟩ +] + +def collectedFourData_9_5_38 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 5, 8, -33150924256380616672337452219205865680035381248000000⟩, + ⟨5, 8, 1, 0, 6, 8, 7971561476881026249687306112621364026551356620800000⟩, + ⟨5, 8, 2, 0, 7, 8, -129642357755587455562672789835780613382078464000000⟩, + ⟨5, 8, 3, 0, 8, 8, 11284209887879413115298299728324639432743321600000⟩, + ⟨5, 8, 0, 1, 4, 8, -23834955068303904185096893958495289933375209472000000⟩, + ⟨5, 8, 1, 1, 5, 8, 1735678757392547892987803548122910473736893235200000⟩, + ⟨5, 8, 2, 1, 6, 8, 298413410113765159479752927651678800225448755200000⟩, + ⟨5, 8, 3, 1, 7, 8, -150742622396652579747063450192900752046607564800000⟩, + ⟨5, 8, 4, 1, 8, 8, 29332089216027710245019639832273168788304691200000⟩, + ⟨5, 8, 0, 2, 3, 8, -9329466284510799351536678025923113215401656320000000⟩, + ⟨5, 8, 1, 2, 4, 8, -1509092668381498316179027949565934787108221747200000⟩, + ⟨5, 8, 2, 2, 5, 8, 625766095623220123691961525352330284685590528000000⟩, + ⟨5, 8, 3, 2, 6, 8, 49069869493521609317100023852099982051822796800000⟩, + ⟨5, 8, 4, 2, 7, 8, -3977181881173677336184607859439113577955328000000⟩, + ⟨5, 8, 5, 2, 8, 8, 5512609468629034855894584373930194704007168000000⟩, + ⟨5, 8, 0, 3, 2, 8, 40994282252388766333778415039122119067260944384000000⟩, + ⟨5, 8, 1, 3, 3, 8, 4179346217368035567187650556886081872870558924800000⟩, + ⟨5, 8, 2, 3, 4, 8, -46107122685566830806284728454003715161771212800000⟩, + ⟨5, 8, 3, 3, 5, 8, 98015481380607819291454488141039876900598579200000⟩, + ⟨5, 8, 4, 3, 6, 8, -3239125746041897004271640854716479150279884800000⟩, + ⟨5, 8, 5, 3, 7, 8, -434276717514145726324974945025909931900928000000⟩, + ⟨5, 8, 6, 3, 8, 8, 562773742543199843390523035106216608425574400000⟩, + ⟨5, 8, 0, 4, 1, 8, 33837082824076557450409124773744750715448852480000000⟩, + ⟨5, 8, 1, 4, 2, 8, -7205542011896573147835471973364549093075347046400000⟩, + ⟨5, 8, 2, 4, 3, 8, -980693773762429499144292767495120343739976908800000⟩, + ⟨5, 8, 3, 4, 4, 8, -40084887902051715741652912059590849025854668800000⟩, + ⟨5, 8, 4, 4, 5, 8, 8376027357567170039720335454963278109107814400000⟩, + ⟨5, 8, 5, 4, 6, 8, -1063539848261658365635735581606351093104640000000⟩, + ⟨5, 8, 6, 4, 7, 8, -245569946533516344934356321526056001260748800000⟩, + ⟨5, 8, 7, 4, 8, 8, 131019405515616179379199602043027999162368000000⟩, + ⟨5, 8, 0, 5, 0, 8, -209392029579635813755187157202983102227096272896000000⟩, + ⟨5, 8, 1, 5, 1, 8, -3267076717759822479356829127854393630623426150400000⟩, + ⟨5, 8, 2, 5, 2, 8, 133396316856310925094710538460766941153434009600000⟩, + ⟨5, 8, 3, 5, 3, 8, -100921250359644859667800616303129888988699033600000⟩, + ⟨5, 8, 4, 5, 4, 8, 1169701233359465054881471446876541396451328000000⟩, + ⟨5, 8, 5, 5, 5, 8, -292687570710118791384968493319738380779520000000⟩, + ⟨5, 8, 6, 5, 6, 8, -415917706311199275675109220006121539056435200000⟩, + ⟨5, 8, 7, 5, 7, 8, 59762660157346503057787185982675664397926400000⟩, + ⟨5, 8, 8, 5, 8, 8, 30063772267316448554369161776426339690086400000⟩, + ⟨5, 8, 1, 6, 0, 8, 35617960149378239157047886207366169660616815411200000⟩, + ⟨5, 8, 2, 6, 1, 8, -2238346380499243095724428966857818335484261171200000⟩, + ⟨5, 8, 3, 6, 2, 8, -112858325775282992994720895342786271465648947200000⟩, + ⟨5, 8, 4, 6, 3, 8, -29238163174548115032582031189405073877762048000000⟩, + ⟨5, 8, 5, 6, 4, 8, 2440734992656431056530381306708283923365888000000⟩, + ⟨5, 8, 6, 6, 5, 8, 39561103211567183186473235456096434598707200000⟩, + ⟨5, 8, 7, 6, 6, 8, 18067838446390123086465219513114199641292800000⟩, + ⟨5, 8, 8, 6, 7, 8, 8103916494082131959745701574383553321369600000⟩, + ⟨5, 8, 2, 7, 0, 8, 18260371678349932228395924250992438709640075673600000⟩, + ⟨5, 8, 3, 7, 1, 8, 1037493815649294779635323442054375889172430848000000⟩, + ⟨5, 8, 4, 7, 2, 8, 30046827299614425571326991682411044616011776000000⟩, + ⟨5, 8, 5, 7, 3, 8, 3402864343010522184953578990568979264700416000000⟩, + ⟨5, 8, 6, 7, 4, 8, 1372914316795504304116190365885567567134720000000⟩, + ⟨5, 8, 7, 7, 5, 8, -64909372362070112772985560883144763532902400000⟩, + ⟨5, 8, 8, 7, 6, 8, 12115906366300006429668823510902975863193600000⟩ +] + +def collectedFourData_9_5_39 : List CollectedFourTerm := [ + ⟨6, 0, 3, 0, 8, 1, 16879965108381274600373646298488333932983379558400000⟩, + ⟨6, 0, 3, 1, 7, 1, -225494760526788681257349106621432515517465441075200000⟩, + ⟨6, 0, 4, 1, 8, 1, 351021221648347612400508135698311886311333979750400000⟩, + ⟨6, 0, 3, 2, 6, 1, 73403250484835271215502083992515040843402523443200000⟩, + ⟨6, 0, 4, 2, 7, 1, -47595492853076784586180989228074346114057240576000000⟩, + ⟨6, 0, 5, 2, 8, 1, 296865764710335615428321245064382322971720548352000000⟩, + ⟨6, 0, 3, 3, 5, 1, 146620624946278471363437916485199445325639371980800000⟩, + ⟨6, 0, 4, 3, 6, 1, -38763071667836015117803008054934007354565958041600000⟩, + ⟨6, 0, 5, 3, 7, 1, -23386726481241860598354740068422478583134420992000000⟩, + ⟨6, 0, 6, 3, 8, 1, 101021883489558954485458079549028688827852521472000000⟩, + ⟨6, 0, 3, 4, 4, 1, -59962683775209689380541802209127394357418341171200000⟩, + ⟨6, 0, 4, 4, 5, 1, 100237093033476724617134360463791795489928432844800000⟩, + ⟨6, 0, 5, 4, 6, 1, -57273886741088520761548913858248241025342504960000000⟩, + ⟨6, 0, 6, 4, 7, 1, -44081549389880772599282799295975044201729490944000000⟩, + ⟨6, 0, 7, 4, 8, 1, 64677012847837451967008058817584250810332610560000000⟩, + ⟨6, 0, 3, 5, 3, 1, -150967343012188136414929996997156539699105785446400000⟩, + ⟨6, 0, 4, 5, 4, 1, 13997978557663148419841911521502357810971672576000000⟩, + ⟨6, 0, 5, 5, 5, 1, -15761849264769120159075924734810429595089633280000000⟩, + ⟨6, 0, 6, 5, 6, 1, -74660182044632731063852152996891544908491390976000000⟩, + ⟨6, 0, 7, 5, 7, 1, 29501510280909817595664801222409852400475045888000000⟩, + ⟨6, 0, 8, 5, 8, 1, 35617960149378239157047886207366169660616815411200000⟩, + ⟨6, 0, 3, 6, 2, 1, -168823924776811270774854344040817884632714104012800000⟩, + ⟨6, 0, 4, 6, 3, 1, -349897195549083420944132628884234303446833954816000000⟩, + ⟨6, 0, 5, 6, 4, 1, 131438779433512959045758407142807976527561490432000000⟩, + ⟨6, 0, 6, 6, 5, 1, 7101498981272341271715729429489233574374670336000000⟩, + ⟨6, 0, 7, 6, 6, 1, 8919089616770878685822497152911952227730456576000000⟩, + ⟨6, 0, 8, 6, 7, 1, 9601089716006932991769616567757129074057465036800000⟩, + ⟨6, 0, 3, 7, 1, 1, 1551979233134643252556280653726551074151755415552000000⟩, + ⟨6, 0, 4, 7, 2, 1, 359574592443432902625356540743517165326216200192000000⟩, + ⟨6, 0, 5, 7, 3, 1, 183251494803346531595909632230381915567317581824000000⟩, + ⟨6, 0, 6, 7, 4, 1, 246447870019124708676670542395050528324819353600000000⟩, + ⟨6, 0, 7, 7, 5, 1, -32042156607910252161917096415874786833683447808000000⟩, + ⟨6, 0, 8, 7, 6, 1, 14354282166966141353804344436771992977139354828800000⟩ +] + +def collectedFourData_9_5_40 : List CollectedFourTerm := [ + ⟨6, 1, 2, 0, 7, 2, 10446210435970146246873369372163993453763493888000000⟩, + ⟨6, 1, 3, 0, 8, 2, -6364745534809909313031352260244983701402183270400000⟩, + ⟨6, 1, 2, 1, 6, 2, -24045299182546691652263899378230445020344116838400000⟩, + ⟨6, 1, 3, 1, 7, 2, 85024865926606169570459832333406484030471484211200000⟩, + ⟨6, 1, 4, 1, 8, 2, -66177884218508541252144804811659121489054217011200000⟩, + ⟨6, 1, 2, 2, 5, 2, -50422442415768555837938652011807050028575358976000000⟩, + ⟨6, 1, 3, 2, 6, 2, -27677368274411715439238234155972846527110656819200000⟩, + ⟨6, 1, 4, 2, 7, 2, 8973158376473314124395550995554962189611696128000000⟩, + ⟨6, 1, 5, 2, 8, 2, -37311985703095870447209198309123791298603515904000000⟩, + ⟨6, 1, 2, 3, 4, 2, 3715180088583090430825945583435753305352542617600000⟩, + ⟨6, 1, 3, 3, 5, 2, -55284650290805901303930142450446772120337566924800000⟩, + ⟨6, 1, 4, 3, 6, 2, 7307985701666981276173515940798515750376361164800000⟩, + ⟨6, 1, 5, 3, 7, 2, 2939393179815622770456300952605944030045405184000000⟩, + ⟨6, 1, 6, 3, 8, 2, -9522806737601078074988123217015104022257860608000000⟩, + ⟨6, 1, 2, 4, 3, 2, 79021499695970374395737499761761357617304279449600000⟩, + ⟨6, 1, 3, 4, 4, 2, 22609479425048586788215378550920006304370209587200000⟩, + ⟨6, 1, 4, 4, 5, 2, -18897657258496747161060354870232911426275927654400000⟩, + ⟨6, 1, 5, 4, 6, 2, 7198547954255991712034857995290848853407825920000000⟩, + ⟨6, 1, 6, 4, 7, 2, 4155338041952438823904046222133583167897993216000000⟩, + ⟨6, 1, 7, 4, 8, 2, -4877412080949407994467735150727062141924278272000000⟩, + ⟨6, 1, 2, 5, 2, 2, -10748693724712189361043460210319059554374202163200000⟩, + ⟨6, 1, 3, 5, 3, 2, 56923620171575349642075792029484093015817872998400000⟩, + ⟨6, 1, 4, 5, 4, 2, -2639033047438423236993182222018665349935792128000000⟩, + ⟨6, 1, 5, 5, 5, 2, 1981049903127958084033472745461050772092354560000000⟩, + ⟨6, 1, 6, 5, 6, 2, 7037826459438700437154866858792551380275953664000000⟩, + ⟨6, 1, 7, 5, 7, 2, -2224762961593299128497503445024071517392705945600000⟩, + ⟨6, 1, 8, 5, 8, 2, -2238346380499243095724428966857818335484261171200000⟩, + ⟨6, 1, 2, 6, 1, 2, 180359550104521653571126092540501821673942967910400000⟩, + ⟨6, 1, 3, 6, 2, 2, 63656607966492184268133300877344143608808000716800000⟩, + ⟨6, 1, 4, 6, 3, 2, 65965972047767460327881317891355759422470094848000000⟩, + ⟨6, 1, 5, 6, 4, 2, -16520065437120651650327207683236827464218968064000000⟩, + ⟨6, 1, 6, 6, 5, 2, -669421317539747732738403342321152402814664704000000⟩, + ⟨6, 1, 7, 6, 6, 2, -672604895192886906388128608527649822328697651200000⟩, + ⟨6, 1, 8, 6, 7, 2, -603363143889860628251855913234294637715049676800000⟩, + ⟨6, 1, 2, 7, 0, 2, -1471368528723410620056537529121447847679923270451200000⟩, + ⟨6, 1, 3, 7, 1, 2, -585187992438847319623099739934704892369187110912000000⟩, + ⟨6, 1, 4, 7, 2, 2, -67790447639879652709075158789867896754589925376000000⟩, + ⟨6, 1, 5, 7, 3, 2, -23032218487184018607300068822970720995191554048000000⟩, + ⟨6, 1, 6, 7, 4, 2, -23231356969582884102624802427214274777998950400000000⟩, + ⟨6, 1, 7, 7, 5, 2, 2416357757690101125469885825611096829072087449600000⟩, + ⟨6, 1, 8, 7, 6, 2, -902068939331281875554401494357652459863461068800000⟩ +] + +def collectedFourData_9_5_41 : List CollectedFourTerm := [ + ⟨6, 2, 1, 0, 6, 3, -37784036185187925977385739895376495680165196595200000⟩, + ⟨6, 2, 2, 0, 7, 3, 3686914954448869257768662060974164982571728896000000⟩, + ⟨6, 2, 3, 0, 8, 3, -1123195614208062465593941883118132190131938918400000⟩, + ⟨6, 2, 1, 1, 5, 3, -8226863603244946257484202487995703599257406668800000⟩, + ⟨6, 2, 2, 1, 6, 3, -8486615666391686136413473062578628836492889292800000⟩, + ⟨6, 2, 3, 1, 7, 3, 15004457913531461634583655639314227625528079155200000⟩, + ⟨6, 2, 4, 1, 8, 3, -7785669660608850495144951942278920764734098636800000⟩, + ⟨6, 2, 1, 2, 4, 3, 7152878661764768357894206811051265556833160396800000⟩, + ⟨6, 2, 2, 2, 5, 3, -17796238944450203755014542184633924522388488192000000⟩, + ⟨6, 2, 3, 2, 6, 3, -4884264184423370168568336124266037481080828723200000⟩, + ⟨6, 2, 4, 2, 7, 3, 1055670602899201310459081029123302050330836992000000⟩, + ⟨6, 2, 5, 2, 8, 3, -3292249349946938886584773825162724540984328192000000⟩, + ⟨6, 2, 1, 3, 3, 3, -19809490168950866436741399163812744508296344371200000⟩, + ⟨6, 2, 2, 3, 4, 3, 1311246131889317084794687198229965341897995059200000⟩, + ⟨6, 2, 3, 3, 5, 3, -9756160148123538249770432715444299232120196300800000⟩, + ⟨6, 2, 4, 3, 6, 3, 859767023825746076526148716515499670752146227200000⟩, + ⟨6, 2, 5, 3, 7, 3, 259359428428476979216815733882943811335749632000000⟩, + ⟨6, 2, 6, 3, 8, 3, -672201250097202286232705313255102622767199027200000⟩, + ⟨6, 2, 1, 4, 2, 3, 34153215891388309618167429879900406583721040281600000⟩, + ⟨6, 2, 2, 4, 3, 3, 27890070828828033395566965674395307063863620403200000⟩, + ⟨6, 2, 3, 4, 4, 3, 3989926697124498058853489122887698343380857651200000⟩, + ⟨6, 2, 4, 4, 5, 3, -2223264138941954471392010967598668687030720921600000⟩, + ⟨6, 2, 5, 4, 6, 3, 635168951112530971338581913040099922317148160000000⟩, + ⟨6, 2, 6, 4, 7, 3, 293319344111832766370339981680913915706762854400000⟩, + ⟨6, 2, 7, 4, 8, 3, -286907927847551147168084739461618781917282304000000⟩, + ⟨6, 2, 1, 5, 1, 3, 15485466088623943665093519609638022202877647257600000⟩, + ⟨6, 2, 2, 5, 2, 3, -3793674258942082055743337397008051281817134694400000⟩, + ⟨6, 2, 3, 5, 3, 3, 10045391472743075551385690878183119053260220006400000⟩, + ⟨6, 2, 4, 5, 4, 3, -310475920670775882958810135861703500986580992000000⟩, + ⟨6, 2, 5, 5, 5, 3, 174799334125074725323066508485606134125690880000000⟩, + ⟨6, 2, 6, 5, 6, 3, 496790061413513693196129093547864057150282137600000⟩, + ⟨6, 2, 7, 5, 7, 3, -130869018378792873709088109347548772275794739200000⟩, + ⟨6, 2, 8, 5, 8, 3, -112858325775282992994720895342786271465648947200000⟩, + ⟨6, 2, 1, 6, 0, 3, -168823924776811270774854344040817884632714104012800000⟩, + ⟨6, 2, 2, 6, 1, 3, 63656607966492184268133300877344143608808000716800000⟩, + ⟨6, 2, 3, 6, 2, 3, 11233571317547014615874389343527883597281021132800000⟩, + ⟨6, 2, 4, 6, 3, 3, 7760738700999973174716060459434398779621507072000000⟩, + ⟨6, 2, 5, 6, 4, 3, -1457659614506355068605731772508285510847823872000000⟩, + ⟨6, 2, 6, 6, 5, 3, -47253489322129419242773039153647686363224473600000⟩, + ⟨6, 2, 7, 6, 6, 3, -39565177913437037650365263126565287906141798400000⟩, + ⟨6, 2, 8, 6, 7, 3, -30421812659188592212464361423161530075892940800000⟩, + ⟨6, 2, 2, 7, 0, 3, -519308955654976484308656543622651858240888268390400000⟩, + ⟨6, 2, 3, 7, 1, 3, -103268949716803500574405174887690255149775716352000000⟩, + ⟨6, 2, 4, 7, 2, 3, -7975383886952540922827959700736768807391985664000000⟩, + ⟨6, 2, 5, 7, 3, 3, -2032264027587677470861160493319538118601211904000000⟩, + ⟨6, 2, 6, 7, 4, 3, -1639868121522109486070332521623800740430479360000000⟩, + ⟨6, 2, 7, 7, 5, 3, 142139352937813237593007958929260643433526067200000⟩, + ⟨6, 2, 8, 7, 6, 3, -45482679139279098624102633379610831337868492800000⟩ +] + +def collectedFourData_9_5_42 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 5, 4, 65132396007636868510564604408594382165091811328000000⟩, + ⟨6, 3, 1, 0, 6, 4, -78309566106819020103627249118232879095238098944000000⟩, + ⟨6, 3, 2, 0, 7, 4, 3820670572891541350069303186333660397237698560000000⟩, + ⟨6, 3, 3, 0, 8, 4, -775962285329699572109502105255166700490326016000000⟩, + ⟨6, 3, 0, 1, 4, 4, 46829093521704839305245036367266115196490350592000000⟩, + ⟨6, 3, 1, 1, 5, 4, -17050643187840499442809935426861369118357979136000000⟩, + ⟨6, 3, 2, 1, 6, 4, -8794497063431714315121738345185522351716958208000000⟩, + ⟨6, 3, 3, 1, 7, 4, 10365864418840600488839903251148763973495554048000000⟩, + ⟨6, 3, 4, 1, 8, 4, -4034060905940980552473324839653788721845633024000000⟩, + ⟨6, 3, 0, 2, 3, 4, 18329820546879576015049154622184177972826603520000000⟩, + ⟨6, 3, 1, 2, 4, 4, 14824748252731892159609231387543517429598519296000000⟩, + ⟨6, 3, 2, 2, 5, 4, -18441859192103658014956549428738558407076741120000000⟩, + ⟨6, 3, 3, 2, 6, 4, -3374305197382201740010960437673486405355962368000000⟩, + ⟨6, 3, 4, 2, 7, 4, 546984356432839133986967508237231013295554560000000⟩, + ⟨6, 3, 5, 2, 8, 4, -1364674842286277931518769911656106861367656448000000⟩, + ⟨6, 3, 0, 3, 2, 4, -80542424852529252761483854780162439253300609024000000⟩, + ⟨6, 3, 1, 3, 3, 4, -41056296164991718181637399442750415706116849664000000⟩, + ⟨6, 3, 2, 3, 4, 4, 1358816129968547114484533292001496787962560512000000⟩, + ⟨6, 3, 3, 3, 5, 4, -6740065780899787527309117378426699118534459392000000⟩, + ⟨6, 3, 4, 3, 6, 4, 445479026239785223965742628065887357549674496000000⟩, + ⟨6, 3, 5, 3, 7, 4, 107507436243185977049769946000667722339319808000000⟩, + ⟨6, 3, 6, 3, 8, 4, -232195893408413684606049718125901609030385664000000⟩, + ⟨6, 3, 0, 4, 1, 4, -66480507789063389087892367277490144728611553280000000⟩, + ⟨6, 3, 1, 4, 2, 4, 70784484338801256501467957419206669613192445952000000⟩, + ⟨6, 3, 2, 4, 3, 4, 28901879812275947199372907800858648599542628352000000⟩, + ⟨6, 3, 3, 4, 4, 4, 2756450077826952561922090242839124301565657088000000⟩, + ⟨6, 3, 4, 4, 5, 4, -1151960375594063320433810091123859675768946688000000⟩, + ⟨6, 3, 5, 4, 6, 4, 263284762497896449934580327763708142986199040000000⟩, + ⟨6, 3, 6, 4, 7, 4, 101320173311442641116181705019449000306147328000000⟩, + ⟨6, 3, 7, 4, 8, 4, -84947573521070468982201639554460203970723840000000⟩, + ⟨6, 3, 0, 5, 0, 4, 411397416432474987182278222207648404143452717056000000⟩, + ⟨6, 3, 1, 5, 1, 4, 32094510084059974993918677803431409911880220672000000⟩, + ⟨6, 3, 2, 5, 2, 4, -3931302941172072720411481855793415272880144384000000⟩, + ⟨6, 3, 3, 5, 3, 4, 6939881909810648932903250252018840227477979136000000⟩, + ⟨6, 3, 4, 5, 4, 4, -160869755385442918805158802483066304001474560000000⟩, + ⟨6, 3, 5, 5, 5, 4, 72456314322828361568228962226822305252638720000000⟩, + ⟨6, 3, 6, 5, 6, 4, 171604280904939086747730110087091962838515712000000⟩, + ⟨6, 3, 7, 5, 7, 4, -38747641599746464952979820617805901680607232000000⟩, + ⟨6, 3, 8, 5, 8, 4, -29238163174548115032582031189405073877762048000000⟩, + ⟨6, 3, 1, 6, 0, 4, -349897195549083420944132628884234303446833954816000000⟩, + ⟨6, 3, 2, 6, 1, 4, 65965972047767460327881317891355759422470094848000000⟩, + ⟨6, 3, 3, 6, 2, 4, 7760738700999973174716060459434398779621507072000000⟩, + ⟨6, 3, 4, 6, 3, 4, 4021143197652558168477359555815110215687208960000000⟩, + ⟨6, 3, 5, 6, 4, 4, -604216507648667981720294326156707811314106368000000⟩, + ⟨6, 3, 6, 6, 5, 4, -16322591141016449569295016035932788366508032000000⟩, + ⟨6, 3, 7, 6, 6, 4, -11714440534601676355540613245241427612401664000000⟩, + ⟨6, 3, 8, 6, 7, 4, -7881367338072751865069722817458158931279872000000⟩, + ⟨6, 3, 2, 7, 0, 4, -538148687893072741670319124720620847157628370944000000⟩, + ⟨6, 3, 3, 7, 1, 4, -71343592524930169439279489629102078087900692480000000⟩, + ⟨6, 3, 4, 7, 2, 4, -4132359289658184272834807345774952990659051520000000⟩, + ⟨6, 3, 5, 7, 3, 4, -842396579523051082463996740303776683472715776000000⟩, + ⟨6, 3, 6, 7, 4, 4, -566453340415155064659894626467460628558643200000000⟩, + ⟨6, 3, 7, 7, 5, 4, 42084557316025147418367722421050991666266112000000⟩, + ⟨6, 3, 8, 7, 6, 4, -11783180240842300772592722559160139542167552000000⟩ +] + +def collectedFourData_9_5_43 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 5, 5, -48933931118765311885137336046764253991625818112000000⟩, + ⟨6, 4, 1, 0, 6, 5, 29416965663002583261395452386281925247487705088000000⟩, + ⟨6, 4, 2, 0, 7, 5, -956822524075663277686633084892520606943150080000000⟩, + ⟨6, 4, 3, 0, 8, 5, 145745003057430484527760449463231687390396416000000⟩, + ⟨6, 4, 0, 1, 4, 5, -35182670640223922927733170141050571300240621568000000⟩, + ⟨6, 4, 1, 1, 5, 5, 6405069139377297383233604847313260393447555072000000⟩, + ⟨6, 4, 2, 1, 6, 5, 2202433504189897722043935050692170455181164544000000⟩, + ⟨6, 4, 3, 1, 7, 5, -1946966972466862887746152991089437403930165248000000⟩, + ⟨6, 4, 4, 1, 8, 5, 606157520988708008415317460208660701783470899200000⟩, + ⟨6, 4, 0, 2, 3, 5, -13771183482259205919425242757792399601256366080000000⟩, + ⟨6, 4, 1, 2, 4, 5, -5568912356357662010985924301554766217994043392000000⟩, + ⟨6, 4, 2, 2, 5, 5, 4618452683682212239619450073345832905772892160000000⟩, + ⟨6, 4, 3, 2, 6, 5, 633778381510147888152262859156287951699181568000000⟩, + ⟨6, 4, 4, 2, 7, 5, -82189805569530592163194524008538988345294848000000⟩, + ⟨6, 4, 5, 2, 8, 5, 170879902130727479434528841017464312595218432000000⟩, + ⟨6, 4, 0, 3, 2, 5, 60511476798886373626032544919308964048714858496000000⟩, + ⟨6, 4, 1, 3, 3, 5, 15422785677144209460600531903939232310155542528000000⟩, + ⟨6, 4, 2, 3, 4, 5, -340292588546114741831218355375296654570684416000000⟩, + ⟨6, 4, 3, 3, 5, 5, 1265951872167522070802999992683575627262984192000000⟩, + ⟨6, 4, 4, 3, 6, 5, -66937626499465260986517560512204734680845516800000⟩, + ⟨6, 4, 5, 3, 7, 5, -13461712353972780952887936498208608639516672000000⟩, + ⟨6, 4, 6, 3, 8, 5, 24921234177437701423964619209788100085547008000000⟩, + ⟨6, 4, 0, 4, 1, 5, 49946766713589529059916131056251980047575941120000000⟩, + ⟨6, 4, 1, 4, 2, 5, -26590170892117122406562498864939196819915669504000000⟩, + ⟨6, 4, 2, 4, 3, 5, -7237988480012917198567588743779268006600769536000000⟩, + ⟨6, 4, 3, 4, 4, 5, -517729833802229696629468072282430294917644288000000⟩, + ⟨6, 4, 4, 4, 5, 5, 173093431613532082965635338554468264764139110400000⟩, + ⟨6, 4, 5, 4, 6, 5, -32967614741676664828912160427226086883983360000000⟩, + ⟨6, 4, 6, 4, 7, 5, -10874541013314668030958860452190202170966016000000⟩, + ⟨6, 4, 7, 4, 8, 5, 7977632802919843023463579388709957449809920000000⟩, + ⟨6, 4, 0, 5, 0, 5, -309082638934153691826532142700934144000549453824000000⟩, + ⟨6, 4, 1, 5, 1, 5, -12056293350238219871928884914272876374412754944000000⟩, + ⟨6, 4, 2, 5, 2, 5, 984528535322409760796499638379493819586445312000000⟩, + ⟨6, 4, 3, 5, 3, 5, -1303482307434312970237202518130373433843777536000000⟩, + ⟨6, 4, 4, 5, 4, 5, 24172270672188649718526289528014723348430848000000⟩, + ⟨6, 4, 5, 5, 5, 5, -9072731112632920825830167292851874410004480000000⟩, + ⟨6, 4, 6, 5, 6, 5, -18418028017233763945925253888507826472484864000000⟩, + ⟨6, 4, 7, 5, 7, 5, 3638885065801742843011952098534465801814016000000⟩, + ⟨6, 4, 8, 5, 8, 5, 2440734992656431056530381306708283923365888000000⟩, + ⟨6, 4, 1, 6, 0, 5, 131438779433512959045758407142807976527561490432000000⟩, + ⟨6, 4, 2, 6, 1, 5, -16520065437120651650327207683236827464218968064000000⟩, + ⟨6, 4, 3, 6, 2, 5, -1457659614506355068605731772508285510847823872000000⟩, + ⟨6, 4, 4, 6, 3, 5, -604216507648667981720294326156707811314106368000000⟩, + ⟨6, 4, 5, 6, 4, 5, 75657918277294030952104191113172775927283712000000⟩, + ⟨6, 4, 6, 6, 5, 5, 1751879028680105129264357303550896876027904000000⟩, + ⟨6, 4, 7, 6, 6, 5, 1100131542350787785106504572574910101061632000000⟩, + ⟨6, 4, 8, 6, 7, 5, 657918520297434419682978420331627394629632000000⟩, + ⟨6, 4, 2, 7, 0, 5, 134770265076311565428000173807859977224707899392000000⟩, + ⟨6, 4, 3, 7, 1, 5, 13400099859564714561421061908641722074115604480000000⟩, + ⟨6, 4, 4, 7, 2, 5, 620927824655533390457972261548051854174191616000000⟩, + ⟨6, 4, 5, 7, 3, 5, 105482009782636108466300182247754132602486784000000⟩, + ⟨6, 4, 6, 7, 4, 5, 60796580593472252794055146166724162119270400000000⟩, + ⟨6, 4, 7, 7, 5, 5, -3952262919639563918639579602380331948179456000000⟩, + ⟨6, 4, 8, 7, 6, 5, 983632937777601189623246198659561618931712000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0923.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0923.lean new file mode 100644 index 0000000000000000000000000000000000000000..7bebfda7fc502592151281b6bcfca4d1f290172e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0923.lean @@ -0,0 +1,623 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse0919 +import OAI.Analysis.LaughlinFock.Sparse0920 +import OAI.Analysis.LaughlinFock.Sparse0921 +import OAI.Analysis.LaughlinFock.Sparse0922 + +namespace OAI + +/-! Sparse0923. -/ +namespace LaughlinFock +def collectedFourData_9_5_44 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 5, 6, -3965773230936130986080574431803248922501054464000000⟩, + ⟨6, 5, 1, 0, 6, 6, 1589367708588686676005939780251229534105370624000000⟩, + ⟨6, 5, 2, 0, 7, 6, -38772085810216732912131713200884154242170880000000⟩, + ⟨6, 5, 3, 0, 8, 6, 4724669516250760724089662573843746967571660800000⟩, + ⟨6, 5, 0, 1, 4, 6, -2851324024616052118164344693560577575140458496000000⟩, + ⟨6, 5, 1, 1, 5, 6, 346059147568965654716995843299192770245165056000000⟩, + ⟨6, 5, 2, 1, 6, 6, 89246373979584928400377068059801192427945984000000⟩, + ⟨6, 5, 3, 1, 7, 6, -63115546406324921083783830573797300976903782400000⟩, + ⟨6, 5, 4, 1, 8, 6, 16375026595439939672255006586535846976736460800000⟩, + ⟨6, 5, 0, 2, 3, 6, -1116063834718361394571170584823626571983093760000000⟩, + ⟨6, 5, 1, 2, 4, 6, -300882476206146419928484773586910454183100416000000⟩, + ⟨6, 5, 2, 2, 5, 6, 187147604970043837744770555785867282884853760000000⟩, + ⟨6, 5, 3, 2, 6, 6, 20545427536886507452960489824909902603511398400000⟩, + ⟨6, 5, 4, 2, 7, 6, -2220314366272084736869354198249552113303552000000⟩, + ⟨6, 5, 5, 2, 8, 6, 3956769149641968954006907697747430048006144000000⟩, + ⟨6, 5, 0, 3, 2, 6, 4904057151488697396572081202230693686948134912000000⟩, + ⟨6, 5, 1, 3, 3, 6, 833276885609116402050386030973555200432799744000000⟩, + ⟨6, 5, 2, 3, 4, 6, -13789237932537839773200999674772605764632576000000⟩, + ⟨6, 5, 3, 3, 5, 6, 41038828735099697123742660329911616504699289600000⟩, + ⟨6, 5, 4, 3, 6, 6, -1808284771220034166359654882660894358319923200000⟩, + ⟨6, 5, 5, 3, 7, 6, -311709495846999443803857108929453934772224000000⟩, + ⟨6, 5, 6, 3, 8, 6, 504925524698304414510038447651364267884544000000⟩, + ⟨6, 5, 0, 4, 1, 6, 4047856893488082147083916433813721292881264640000000⟩, + ⟨6, 5, 1, 4, 2, 6, -1436638960861205197709490577269836796124987392000000⟩, + ⟨6, 5, 2, 4, 3, 6, -293295677494136094942104802270083458736848896000000⟩, + ⟨6, 5, 3, 4, 4, 6, -16783438966034988497278080174159639194527334400000⟩, + ⟨6, 5, 4, 4, 5, 6, 4676028009261232868464061392352279673805209600000⟩, + ⟨6, 5, 5, 4, 6, 6, -763373804178294085125902588544870902661120000000⟩, + ⟨6, 5, 6, 4, 7, 6, -220327504163988582124341150356325519065088000000⟩, + ⟨6, 5, 7, 4, 8, 6, 143674369332676101506060931817827697950720000000⟩, + ⟨6, 5, 0, 5, 0, 6, -25049114747335511506387076785001674989662896128000000⟩, + ⟨6, 5, 1, 5, 1, 6, -651388846683152118872936038782408883030720512000000⟩, + ⟨6, 5, 2, 5, 2, 6, 39894780791248280774026887151501466174226432000000⟩, + ⟨6, 5, 3, 5, 3, 6, -42255466696723378597027779847441741729549516800000⟩, + ⟨6, 5, 4, 5, 4, 6, 653001177785659596954060878100466658967552000000⟩, + ⟨6, 5, 5, 5, 5, 6, -210081478991013084519408411939644280668160000000⟩, + ⟨6, 5, 6, 5, 6, 6, -373165004361192103736872132962393891274752000000⟩, + ⟨6, 5, 7, 5, 7, 6, 65535044018547323777502533187336306425856000000⟩, + ⟨6, 5, 8, 5, 8, 6, 39561103211567183186473235456096434598707200000⟩, + ⟨6, 5, 1, 6, 0, 6, 7101498981272341271715729429489233574374670336000000⟩, + ⟨6, 5, 2, 6, 1, 6, -669421317539747732738403342321152402814664704000000⟩, + ⟨6, 5, 3, 6, 2, 6, -47253489322129419242773039153647686363224473600000⟩, + ⟨6, 5, 4, 6, 3, 6, -16322591141016449569295016035932788366508032000000⟩, + ⟨6, 5, 5, 6, 4, 6, 1751879028680105129264357303550896876027904000000⟩, + ⟨6, 5, 6, 6, 5, 6, 35494567863942188230684940682101073641472000000⟩, + ⟨6, 5, 7, 6, 6, 6, 19812983304067703298754516333099915149312000000⟩, + ⟨6, 5, 8, 6, 7, 6, 10663993659532941703981502059782572133580800000⟩, + ⟨6, 5, 2, 7, 0, 6, 5461121734411846887936861715985903848953741312000000⟩, + ⟨6, 5, 3, 7, 1, 6, 434395979231301227508163965949729680522215424000000⟩, + ⟨6, 5, 4, 7, 2, 6, 16774038579936120381518063358077659653341184000000⟩, + ⟨6, 5, 5, 7, 3, 6, 2442463724205961910511055691087370076028928000000⟩, + ⟨6, 5, 6, 7, 4, 6, 1231790734658468848047425890743271764787200000000⟩, + ⟨6, 5, 7, 7, 5, 6, -71178869276648625492378220368529924816896000000⟩, + ⟨6, 5, 8, 7, 6, 6, 15943395858541852503807435340793221270732800000⟩ +] + +def collectedFourData_9_5_45 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 5, 7, -6641055536732721201413207870973242548401733632000000⟩, + ⟨6, 6, 1, 0, 6, 7, 1996157862486165562221441622292537653837430784000000⟩, + ⟨6, 6, 2, 0, 7, 7, -38956474838048478645082996093976287918424064000000⟩, + ⟨6, 6, 3, 0, 8, 7, 3955948918784099169319265037430938523611955200000⟩, + ⟨6, 6, 0, 1, 4, 7, -4774806853044800575006592263708556548896718848000000⟩, + ⟨6, 6, 1, 1, 5, 7, 434631133231246863737368815966481990702596096000000⟩, + ⟨6, 6, 2, 1, 6, 7, 89670804385938454561432939200326598126678835200000⟩, + ⟨6, 6, 3, 1, 7, 7, -52846421682146053506020152652433295194823065600000⟩, + ⟨6, 6, 4, 1, 8, 7, 11752072550710029369792243247908897257265561600000⟩, + ⟨6, 6, 0, 2, 3, 7, -1868952528875167731237251896498342987699322880000000⟩, + ⟨6, 6, 1, 2, 4, 7, -377891734755659184342325767832667222081273856000000⟩, + ⟨6, 6, 2, 2, 5, 7, 188037625824489921321189534282185131035721728000000⟩, + ⟨6, 6, 3, 2, 6, 7, 17202613129013084856759787072954629042575769600000⟩, + ⟨6, 6, 4, 2, 7, 7, -1593481107693569869368379410537535928008704000000⟩, + ⟨6, 6, 5, 2, 8, 7, 2484741512432643204155579860750940925591552000000⟩, + ⟨6, 6, 0, 3, 2, 7, 8212299090702148768351041672720276010781638656000000⟩, + ⟨6, 6, 1, 3, 3, 7, 1046549642255933552809711438896187167373000704000000⟩, + ⟨6, 6, 2, 3, 4, 7, -13854815631642469679151445306432683584048332800000⟩, + ⟨6, 6, 3, 3, 5, 7, 34361664790390158378235284471398314249971302400000⟩, + ⟨6, 6, 4, 3, 6, 7, -1297774614280007298796359065816614333474406400000⟩, + ⟨6, 6, 5, 3, 7, 7, -195744936047273032825323488968695393288192000000⟩, + ⟨6, 6, 6, 3, 8, 7, 281848226156542686401100680730280118452224000000⟩, + ⟨6, 6, 0, 4, 1, 7, 6778512251961306799297734708661673789824696320000000⟩, + ⟨6, 6, 1, 4, 2, 7, -1804339009645248876758649120136668142393884672000000⟩, + ⟨6, 6, 2, 4, 3, 7, -294690508432691027311618022875015178321972428800000⟩, + ⟨6, 6, 3, 4, 4, 7, -14052713529019912813638721259793976586246553600000⟩, + ⟨6, 6, 4, 4, 5, 7, 3355904193114002231172749495280374077666099200000⟩, + ⟨6, 6, 5, 4, 6, 7, -479377620733083941033372940932595276840960000000⟩, + ⟨6, 6, 6, 4, 7, 7, -122986288441692217173086978167830057320448000000⟩, + ⟨6, 6, 7, 4, 8, 7, 72178821912980717785999419868048898654208000000⟩, + ⟨6, 6, 0, 5, 0, 7, -41947068704121997061770787624420372457260580864000000⟩, + ⟨6, 6, 1, 5, 1, 7, -818108333783235562173036241308715730539118592000000⟩, + ⟨6, 6, 2, 5, 2, 7, 40084509037535213097881706811137963096381849600000⟩, + ⟨6, 6, 3, 5, 3, 7, -35380351412233751992154496666580428604519219200000⟩, + ⟨6, 6, 4, 5, 4, 7, 468647618512768178380661148581835470536704000000⟩, + ⟨6, 6, 5, 5, 5, 7, -131925354272803553077706039827214138081280000000⟩, + ⟨6, 6, 6, 5, 6, 7, -208299817296310471279278766170327264264192000000⟩, + ⟨6, 6, 7, 5, 7, 7, 32923355037120546455343091292704109651558400000⟩, + ⟨6, 6, 8, 5, 8, 7, 18067838446390123086465219513114199641292800000⟩, + ⟨6, 6, 1, 6, 0, 7, 8919089616770878685822497152911952227730456576000000⟩, + ⟨6, 6, 2, 6, 1, 7, -672604895192886906388128608527649822328697651200000⟩, + ⟨6, 6, 3, 6, 2, 7, -39565177913437037650365263126565287906141798400000⟩, + ⟨6, 6, 4, 6, 3, 7, -11714440534601676355540613245241427612401664000000⟩, + ⟨6, 6, 5, 6, 4, 7, 1100131542350787785106504572574910101061632000000⟩, + ⟨6, 6, 6, 6, 5, 7, 19812983304067703298754516333099915149312000000⟩, + ⟨6, 6, 7, 6, 6, 7, 9953604112629419897347281705596298775756800000⟩, + ⟨6, 6, 8, 6, 7, 7, 4870322083875403174344829753204963226419200000⟩, + ⟨6, 6, 2, 7, 0, 7, 5487093278279978770530802618787010822792649113600000⟩, + ⟨6, 6, 3, 7, 1, 7, 363718202607299538644278806932215195087405056000000⟩, + ⟨6, 6, 4, 7, 2, 7, 12038436530827639569343964652773996199149568000000⟩, + ⟨6, 6, 5, 7, 3, 7, 1533799617471880059012072807560002324660224000000⟩, + ⟨6, 6, 6, 7, 4, 7, 687582656406595098323031760435498136371200000000⟩, + ⟨6, 6, 7, 7, 5, 7, -35758687881138318438912132754999014221414400000⟩, + ⟨6, 6, 8, 7, 6, 7, 7281462782229832587223830047220592489267200000⟩ +] + +def collectedFourData_9_5_46 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 5, 8, -8936081589714980542518574708759497294502428672000000⟩, + ⟨6, 7, 1, 0, 6, 8, 2148794501291379987462949839106860167380284211200000⟩, + ⟨6, 7, 2, 0, 7, 8, -34946075030290314691404331081773001627140096000000⟩, + ⟨6, 7, 3, 0, 8, 8, 3041743857688998421451893498485518329341542400000⟩, + ⟨6, 7, 0, 1, 4, 8, -6424891853099978431975433937457233669189009408000000⟩, + ⟨6, 7, 1, 1, 5, 8, 467865295991246829382673894085664784685780172800000⟩, + ⟨6, 7, 2, 1, 6, 8, 80439584719223291748170478447147475473845452800000⟩, + ⟨6, 7, 3, 1, 7, 8, -40633810459291054202561692945385691846751027200000⟩, + ⟨6, 7, 4, 1, 8, 8, 7906685810751505879604861559513989667146956800000⟩, + ⟨6, 7, 0, 2, 3, 8, -2514827980726281665602897584525964141374996480000000⟩, + ⟨6, 7, 1, 2, 4, 8, -406787307249878788868406447464106378952232140800000⟩, + ⟨6, 7, 2, 2, 5, 8, 168679969322128301934457181982789011182190592000000⟩, + ⟨6, 7, 3, 2, 6, 8, 13227153306483689207822579478259496633185075200000⟩, + ⟨6, 7, 4, 2, 7, 8, -1072079363834435595003101911582823040417792000000⟩, + ⟨6, 7, 5, 2, 8, 8, 1485965447084722654421501543309410201239552000000⟩, + ⟨6, 7, 0, 3, 2, 8, 11050317876088868858486550379731145239325310976000000⟩, + ⟨6, 7, 1, 3, 3, 8, 1126574284965198435745992774511081184640054067200000⟩, + ⟨6, 7, 2, 3, 4, 8, -12428522565428083052475478820244760988693299200000⟩, + ⟨6, 7, 3, 3, 5, 8, 26420812038256216155558318615522652589968588800000⟩, + ⟨6, 7, 4, 3, 6, 8, -873130767701165514025513996160249120371507200000⟩, + ⟨6, 7, 5, 3, 7, 8, -117062563631934923502188723957294476296192000000⟩, + ⟨6, 7, 6, 3, 8, 8, 151699905590033360431231343927709329365401600000⟩, + ⟨6, 7, 0, 4, 1, 8, 9121040805240705823244638359196891582530846720000000⟩, + ⟨6, 7, 1, 4, 2, 8, -1942308178754131860054988491891250047735142809600000⟩, + ⟨6, 7, 2, 4, 3, 8, -264353401102529343662542003222911102487835443200000⟩, + ⟨6, 7, 3, 4, 4, 8, -10805183772164945040393723697910539504268083200000⟩, + ⟨6, 7, 4, 4, 5, 8, 2257821329084021305726596014942980188772761600000⟩, + ⟨6, 7, 5, 4, 6, 8, -286685185139296410459917305730720291880960000000⟩, + ⟨6, 7, 6, 4, 7, 8, -66195230673940595261982686765286962705203200000⟩, + ⟨6, 7, 7, 4, 8, 8, 35317268636881313047888789949198056292352000000⟩, + ⟨6, 7, 0, 5, 0, 8, -56443200379232135772228498108146667925687762944000000⟩, + ⟨6, 7, 1, 5, 1, 8, -880665162876742673164067013767364052617107865600000⟩, + ⟨6, 7, 2, 5, 2, 8, 35957983010565145292848569136617376075638374400000⟩, + ⟨6, 7, 3, 5, 3, 8, -27204083975916899439607932940660068980254310400000⟩, + ⟨6, 7, 4, 5, 4, 8, 315301786944253962380336644797073081761792000000⟩, + ⟨6, 7, 5, 5, 5, 8, -78896141535410979370476361400267864801280000000⟩, + ⟨6, 7, 6, 5, 6, 8, -112113753736100891150419157900888074144972800000⟩, + ⟨6, 7, 7, 5, 7, 8, 16109475653055696608982949970890781727129600000⟩, + ⟨6, 7, 8, 5, 8, 8, 8103916494082131959745701574383553321369600000⟩, + ⟨6, 7, 1, 6, 0, 8, 9601089716006932991769616567757129074057465036800000⟩, + ⟨6, 7, 2, 6, 1, 8, -603363143889860628251855913234294637715049676800000⟩, + ⟨6, 7, 3, 6, 2, 8, -30421812659188592212464361423161530075892940800000⟩, + ⟨6, 7, 4, 6, 3, 8, -7881367338072751865069722817458158931279872000000⟩, + ⟨6, 7, 5, 6, 4, 8, 657918520297434419682978420331627394629632000000⟩, + ⟨6, 7, 6, 6, 5, 8, 10663993659532941703981502059782572133580800000⟩, + ⟨6, 7, 7, 6, 6, 8, 4870322083875403174344829753204963226419200000⟩, + ⟨6, 7, 8, 6, 7, 8, 2184471794128534208844831518052250445414400000⟩, + ⟨6, 7, 2, 7, 0, 8, 4922220868241670975369981647832960193884743270400000⟩, + ⟨6, 7, 3, 7, 1, 8, 279664280662774597617786319241864251359363072000000⟩, + ⟨6, 7, 4, 7, 2, 8, 8099348850273793247898723051986370391179264000000⟩, + ⟨6, 7, 5, 7, 3, 8, 917267741095367984574128063630661830836224000000⟩, + ⟨6, 7, 6, 7, 4, 8, 370079405801516731054369271894159476654080000000⟩, + ⟨6, 7, 7, 7, 5, 8, -17496810733806574719042530261426318711193600000⟩, + ⟨6, 7, 8, 7, 6, 8, 3265933914399546263892071319314754856550400000⟩ +] + +def collectedFourData_9_5_47 : List CollectedFourTerm := [ + ⟨7, 0, 2, 0, 7, 2, -85219913617001182446371939036378297785399640064000000⟩, + ⟨7, 0, 3, 0, 8, 2, 51923428883167156347506671818687224248523764531200000⟩, + ⟨7, 0, 2, 1, 6, 2, 196160926662518781832964314398384580770707747635200000⟩, + ⟨7, 0, 3, 1, 7, 2, -693630649504483373810664417726490060649056016793600000⟩, + ⟨7, 0, 4, 1, 8, 2, 539877461882036420652211367289084116813819255193600000⟩, + ⟨7, 0, 2, 2, 5, 2, 411344976570055853351992909592558180642196553728000000⟩, + ⟨7, 0, 3, 2, 6, 2, 225791252047685264965415909596277309673934789017600000⟩, + ⟨7, 0, 4, 2, 7, 2, -73202793147035524948528171725997749468905078784000000⟩, + ⟨7, 0, 5, 2, 8, 2, 304390210975231056374952493455266248691036454912000000⟩, + ⟨7, 0, 2, 3, 4, 2, -30308342739340023881644193859271855238307171532800000⟩, + ⟨7, 0, 3, 3, 5, 2, 451010742221473526222639174053127754626298701414400000⟩, + ⟨7, 0, 4, 3, 6, 2, -59618357683649457575405998681355758708881516134400000⟩, + ⟨7, 0, 5, 3, 7, 2, -23979493272291731385182106776211657303892426752000000⟩, + ⟨7, 0, 6, 3, 8, 2, 77686810211610786127771521522679399071533236224000000⟩, + ⟨7, 0, 2, 4, 3, 2, -644655343605575235145615543287322259732738919628800000⟩, + ⟨7, 0, 3, 4, 4, 2, -184447546345936217183245718952135253019330189721600000⟩, + ⟨7, 0, 4, 4, 5, 2, 154166597447376047608838682702693814674855768883200000⟩, + ⟨7, 0, 5, 4, 6, 2, -58725567380604256830806213021895117810444533760000000⟩, + ⟨7, 0, 6, 4, 7, 2, -33899139899122523153976916376867128472342888448000000⟩, + ⟨7, 0, 7, 4, 8, 2, 39789801168640214325383276004634390951064764416000000⟩, + ⟨7, 0, 2, 5, 2, 2, 87687564435945206358842510854816553127305124249600000⟩, + ⟨7, 0, 3, 5, 3, 2, -464381415971170739354366465777415061804181304115200000⟩, + ⟨7, 0, 4, 5, 4, 2, 21529163107867965816148539687529347435970166784000000⟩, + ⟨7, 0, 5, 5, 5, 2, -16161353693795684279049372818329061625094471680000000⟩, + ⟨7, 0, 6, 5, 6, 2, -57414405597230433095982592539826822882044936192000000⟩, + ⟨7, 0, 7, 5, 7, 2, 18149558499457602111653567573463340789642611916800000⟩, + ⟨7, 0, 8, 5, 8, 2, 18260371678349932228395924250992438709640075673600000⟩, + ⟨7, 0, 2, 6, 1, 2, -1471368528723410620056537529121447847679923270451200000⟩, + ⟨7, 0, 3, 6, 2, 2, -519308955654976484308656543622651858240888268390400000⟩, + ⟨7, 0, 4, 6, 3, 2, -538148687893072741670319124720620847157628370944000000⟩, + ⟨7, 0, 5, 6, 4, 2, 134770265076311565428000173807859977224707899392000000⟩, + ⟨7, 0, 6, 6, 5, 2, 5461121734411846887936861715985903848953741312000000⟩, + ⟨7, 0, 7, 6, 6, 2, 5487093278279978770530802618787010822792649113600000⟩, + ⟨7, 0, 8, 6, 7, 2, 4922220868241670975369981647832960193884743270400000⟩, + ⟨7, 0, 2, 7, 0, 2, 12003386269610232679750090551856256093874703407513600000⟩, + ⟨7, 0, 3, 7, 1, 2, 4773948454419919170518672725071726428797676814336000000⟩, + ⟨7, 0, 4, 7, 2, 2, 553032712421311956497885136191483184640507772928000000⟩, + ⟨7, 0, 5, 7, 3, 2, 187896240643120156424331300715474166159763308544000000⟩, + ⟨7, 0, 6, 7, 4, 2, 189520807214114756607235369367951777497035571200000000⟩, + ⟨7, 0, 7, 7, 5, 2, -19712583873387862047320349174095663864656743628800000⟩, + ⟨7, 0, 8, 7, 6, 2, 7359054994879811862123474306828025137899923046400000⟩ +] + +def collectedFourData_9_5_48 : List CollectedFourTerm := [ + ⟨7, 1, 1, 0, 6, 3, 347344368287509705792719096745786644740249223168000000⟩, + ⟨7, 1, 2, 0, 7, 3, -33893391894560130241203679845150955479383408640000000⟩, + ⟨7, 1, 3, 0, 8, 3, 10325410159154507103614615861685948032646905856000000⟩, + ⟨7, 1, 1, 1, 5, 3, 75628625995674822787782094696202670352568942592000000⟩, + ⟨7, 1, 2, 1, 6, 3, 78016497313680044804804876491865952126083530752000000⟩, + ⟨7, 1, 3, 1, 7, 3, -137934283408166020282856447119652160523959533568000000⟩, + ⟨7, 1, 4, 1, 8, 3, 71572780014951197287633973107154061050052083712000000⟩, + ⟨7, 1, 1, 2, 4, 3, -65755603981288482439224475084288147284780122112000000⟩, + ⟨7, 1, 2, 2, 5, 3, 163598810454158739249545812741154739194198753280000000⟩, + ⟨7, 1, 3, 2, 6, 3, 44900487850816574858317751638728442599532658688000000⟩, + ⟨7, 1, 4, 2, 7, 3, -9704660372611641186793272409371752287992545280000000⟩, + ⟨7, 1, 5, 2, 8, 3, 30265275660268805969692943191842743100144353280000000⟩, + ⟨7, 1, 1, 3, 3, 3, 182106401103046955820759902055950424449910571008000000⟩, + ⟨7, 1, 2, 3, 4, 3, -12054137284811363062168882667533570355314556928000000⟩, + ⟨7, 1, 3, 3, 5, 3, 89687276048348749063996688111468796416435945472000000⟩, + ⟨7, 1, 4, 3, 6, 3, -7903740942378645959585339886522720126970626048000000⟩, + ⟨7, 1, 5, 3, 7, 3, -2384261871478272240282423128808721436513402880000000⟩, + ⟨7, 1, 6, 3, 8, 3, 6179470013016180033776262114952523616299778048000000⟩, + ⟨7, 1, 1, 4, 2, 3, -313966648259555376309204031777835610105282822144000000⟩, + ⟨7, 1, 2, 4, 3, 3, -256390264556512548447358940632440511723248549888000000⟩, + ⟨7, 1, 3, 4, 4, 3, -36678944550383161239563685407557115731098206208000000⟩, + ⟨7, 1, 4, 4, 5, 3, 20438215602275961863179605234317937496496799744000000⟩, + ⟨7, 1, 5, 4, 6, 3, -5839036279732085450923356945242196053223014400000000⟩, + ⟨7, 1, 6, 4, 7, 3, -2696451532802926744702102544417433284662788096000000⟩, + ⟨7, 1, 7, 4, 8, 3, 2637512108723659651685855876702773378925199360000000⟩, + ⟨7, 1, 1, 5, 1, 3, -142356137121722510467086900687407572881437097984000000⟩, + ⟨7, 1, 2, 5, 2, 3, 34874818097845046991264745780060038606876573696000000⟩, + ⟨7, 1, 3, 5, 3, 3, -92346146880637339479697364740062079875626827776000000⟩, + ⟨7, 1, 4, 5, 4, 3, 2854169999343527069962670145551877253921505280000000⟩, + ⟨7, 1, 5, 5, 5, 3, -1606910494981822395844625083552103167898419200000000⟩, + ⟨7, 1, 6, 5, 6, 3, -4566934808326163980799974524721906607072477184000000⟩, + ⟨7, 1, 7, 5, 7, 3, 1203064074319518633523443590137245881365168128000000⟩, + ⟨7, 1, 8, 5, 8, 3, 1037493815649294779635323442054375889172430848000000⟩, + ⟨7, 1, 1, 6, 0, 3, 1551979233134643252556280653726551074151755415552000000⟩, + ⟨7, 1, 2, 6, 1, 3, -585187992438847319623099739934704892369187110912000000⟩, + ⟨7, 1, 3, 6, 2, 3, -103268949716803500574405174887690255149775716352000000⟩, + ⟨7, 1, 4, 6, 3, 3, -71343592524930169439279489629102078087900692480000000⟩, + ⟨7, 1, 5, 6, 4, 3, 13400099859564714561421061908641722074115604480000000⟩, + ⟨7, 1, 6, 6, 5, 3, 434395979231301227508163965949729680522215424000000⟩, + ⟨7, 1, 7, 6, 6, 3, 363718202607299538644278806932215195087405056000000⟩, + ⟨7, 1, 8, 6, 7, 3, 279664280662774597617786319241864251359363072000000⟩, + ⟨7, 1, 2, 7, 0, 3, 4773948454419919170518672725071726428797676814336000000⟩, + ⟨7, 1, 3, 7, 1, 3, 949339766860571850107316838833470873651568967680000000⟩, + ⟨7, 1, 4, 7, 2, 3, 73316801426044789190081765220624981231937781760000000⟩, + ⟨7, 1, 5, 7, 3, 3, 18682373195815346033981651899118625595179663360000000⟩, + ⟨7, 1, 6, 7, 4, 3, 15075122042367092116407360239463771241080422400000000⟩, + ⟨7, 1, 7, 7, 5, 3, -1306670984354356330040629782317765807359131648000000⟩, + ⟨7, 1, 8, 7, 6, 3, 418117121639047549426108097363249369293258752000000⟩ +] + +def collectedFourData_9_5_49 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 5, 4, -66933816695952804786540942159238575060613595136000000⟩, + ⟨7, 2, 1, 0, 6, 4, 80475438715917075532900232244876324321443708928000000⟩, + ⟨7, 2, 2, 0, 7, 4, -3926342027269478314008870163912146543150366720000000⟩, + ⟨7, 2, 3, 0, 8, 4, 797423717732431020948570269379453159412334592000000⟩, + ⟨7, 2, 0, 1, 4, 4, -48124284594902725040121267800198691222039035904000000⟩, + ⟨7, 2, 1, 1, 5, 4, 17522226965966328548606008097659463627578540032000000⟩, + ⟨7, 2, 2, 1, 6, 4, 9037733761672357457014811527806539736280989696000000⟩, + ⟨7, 2, 3, 1, 7, 4, -10652561727107719015404386584692657368938315776000000⟩, + ⟨7, 2, 4, 1, 8, 4, 4145634273716926327828035847186178994641829888000000⟩, + ⟨7, 2, 0, 2, 3, 4, -18836783593999718611837734940955449347004170240000000⟩, + ⟨7, 2, 1, 2, 4, 4, -15234768608783517947537235036420117529941245952000000⟩, + ⟨7, 2, 2, 2, 5, 4, 18951920984944346284119344931978908127398461440000000⟩, + ⟨7, 2, 3, 2, 6, 4, 3467631154415067059644392641722214993274863616000000⟩, + ⟨7, 2, 4, 2, 7, 4, -562112756372981991590589639935716768843038720000000⟩, + ⟨7, 2, 5, 2, 8, 4, 1402418786074719908014825868956079505146904576000000⟩, + ⟨7, 2, 0, 3, 2, 4, 82770053487586156116297213645393876801067941888000000⟩, + ⟨7, 2, 1, 3, 3, 4, 42191824194523603321333794244048925260479725568000000⟩, + ⟨7, 2, 2, 3, 4, 4, -1396398034492000064164931684803795325439442944000000⟩, + ⟨7, 2, 3, 3, 5, 4, 6926481369494126240884732854798467637920661504000000⟩, + ⟨7, 2, 4, 3, 6, 4, -457800009088091513968814651858555995372388352000000⟩, + ⟨7, 2, 5, 3, 7, 4, -110480858559379812171085516162163682255568896000000⟩, + ⟨7, 2, 6, 3, 8, 4, 238617927784039511705595045495731086392557568000000⟩, + ⟨7, 2, 0, 4, 1, 4, 68319214322858423639885613020747556789273231360000000⟩, + ⟨7, 2, 1, 4, 2, 4, -72742229521163977019628378429119663034517684224000000⟩, + ⟨7, 2, 2, 4, 3, 4, -29701243069524305878494275168180407581775233024000000⟩, + ⟨7, 2, 3, 4, 4, 4, -2832687503453446170516665945468220067603808256000000⟩, + ⟨7, 2, 4, 4, 5, 4, 1183821098980809692721310119305843245848723456000000⟩, + ⟨7, 2, 5, 4, 6, 4, -270566647506801198816484688703399792193044480000000⟩, + ⟨7, 2, 6, 4, 7, 4, -104122469365860602226871990169010895256027136000000⟩, + ⟨7, 2, 7, 4, 8, 4, 87297039005883169681623920631420263942062080000000⟩, + ⟨7, 2, 0, 5, 0, 4, -422775775935698113339875823461615317381988483072000000⟩, + ⟨7, 2, 1, 5, 1, 4, -32982174564267506451309054061257411767895588864000000⟩, + ⟨7, 2, 2, 5, 2, 4, 4040034246702953133501721187907100356491870208000000⟩, + ⟨7, 2, 3, 5, 3, 4, -7131823978782540850626561231999709705018540032000000⟩, + ⟨7, 2, 4, 5, 4, 4, 165319063613589202530251492135323885602078720000000⟩, + ⟨7, 2, 5, 5, 5, 4, -74460298693447264244320196849483890965872640000000⟩, + ⟨7, 2, 6, 5, 6, 4, -176350482807130594178936284807444048688185344000000⟩, + ⟨7, 2, 7, 5, 7, 4, 39819317255483899163786600019547105561411584000000⟩, + ⟨7, 2, 8, 5, 8, 4, 30046827299614425571326991682411044616011776000000⟩, + ⟨7, 2, 1, 6, 0, 4, 359574592443432902625356540743517165326216200192000000⟩, + ⟨7, 2, 2, 6, 1, 4, -67790447639879652709075158789867896754589925376000000⟩, + ⟨7, 2, 3, 6, 2, 4, -7975383886952540922827959700736768807391985664000000⟩, + ⟨7, 2, 4, 6, 3, 4, -4132359289658184272834807345774952990659051520000000⟩, + ⟨7, 2, 5, 6, 4, 4, 620927824655533390457972261548051854174191616000000⟩, + ⟨7, 2, 6, 6, 5, 4, 16774038579936120381518063358077659653341184000000⟩, + ⟨7, 2, 7, 6, 6, 4, 12038436530827639569343964652773996199149568000000⟩, + ⟨7, 2, 8, 6, 7, 4, 8099348850273793247898723051986370391179264000000⟩, + ⟨7, 2, 2, 7, 0, 4, 553032712421311956497885136191483184640507772928000000⟩, + ⟨7, 2, 3, 7, 1, 4, 73316801426044789190081765220624981231937781760000000⟩, + ⟨7, 2, 4, 7, 2, 4, 4246651377347879676594981717346820542420746240000000⟩, + ⟨7, 2, 5, 7, 3, 4, 865695440291837704330693917810185884466675712000000⟩, + ⟨7, 2, 6, 7, 4, 4, 582120210190218831339798922360041419204198400000000⟩, + ⟨7, 2, 7, 7, 5, 4, -43248524816910826889569744643957630271750144000000⟩, + ⟨7, 2, 8, 7, 6, 4, 12109077428127105146662727583419987524583424000000⟩ +] + +def collectedFourData_9_5_50 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 5, 5, -68223518681210202203229721311834559012965187584000000⟩, + ⟨7, 3, 1, 0, 6, 5, 41013032482173774401634116973309654893976354816000000⟩, + ⟨7, 3, 2, 0, 7, 5, -1333998676448984718242974384336689242371522560000000⟩, + ⟨7, 3, 3, 0, 8, 5, 203197182638951894698478350790105003628429312000000⟩, + ⟨7, 3, 0, 1, 4, 5, -49051558556629322511147334042198345717358002176000000⟩, + ⟨7, 3, 1, 1, 5, 5, 8929925393162969595621866717036874776973410304000000⟩, + ⟨7, 3, 2, 1, 6, 5, 3070625226339142316153851589971051164790161408000000⟩, + ⟨7, 3, 3, 1, 7, 5, -2714454665320250578234102293985138225956519936000000⟩, + ⟨7, 3, 4, 1, 8, 5, 845102733654492141886882136741815990190761574400000⟩, + ⟨7, 3, 0, 2, 3, 5, -19199736707930159586143612474563145847338434560000000⟩, + ⟨7, 3, 1, 2, 4, 5, -7764158478416062215728486325804718832215916544000000⟩, + ⟨7, 3, 2, 2, 5, 5, 6439030867533313240378874158267443220441989120000000⟩, + ⟨7, 3, 3, 2, 6, 5, 883611642517792587348383858026848571071922176000000⟩, + ⟨7, 3, 4, 2, 7, 5, -114588744608904130041332323001502244207067136000000⟩, + ⟨7, 3, 5, 2, 8, 5, 238240172590352261459947824940773735948877824000000⟩, + ⟨7, 3, 0, 3, 2, 5, 84364893100389163412843271619154161994009935872000000⟩, + ⟨7, 3, 1, 3, 3, 5, 21502394814902781587815703357887449011004112896000000⟩, + ⟨7, 3, 2, 3, 4, 5, -474434758070158801666570956195603199989645312000000⟩, + ⟨7, 3, 3, 3, 5, 5, 1764985751721333987159398159977077787689222144000000⟩, + ⟨7, 3, 4, 3, 6, 5, -93324208939569161628394900014130809083107737600000⟩, + ⟨7, 3, 5, 3, 7, 5, -18768273123884536813470659762627107570581504000000⟩, + ⟨7, 3, 6, 3, 8, 5, 34745099087517057653387538374327041844576256000000⟩, + ⟨7, 3, 0, 4, 1, 5, 69635610588495907327328549488052524671660195840000000⟩, + ⟨7, 3, 1, 4, 2, 5, -37071924922444214078230815108227513620918960128000000⟩, + ⟨7, 3, 2, 4, 3, 5, -10091178676858466774261172946434819013478449152000000⟩, + ⟨7, 3, 3, 4, 4, 5, -721817155921919113183180280161223082787209216000000⟩, + ⟨7, 3, 4, 4, 5, 5, 241326267791962129404646983073661883643645132800000⟩, + ⟨7, 3, 5, 4, 6, 5, -45963335231434175060012910893573313417707520000000⟩, + ⟨7, 3, 6, 4, 7, 5, -15161247727488508162128721404509202533056512000000⟩, + ⟨7, 3, 7, 4, 8, 5, 11122388251229669414535847329366434843197440000000⟩, + ⟨7, 3, 0, 5, 0, 5, -430921953525119450680818598789856749664618938368000000⟩, + ⟨7, 3, 1, 5, 1, 5, -16808842776392112742613761694729854643714654208000000⟩, + ⟨7, 3, 2, 5, 2, 5, 1372626302161020946038600952286838778950057984000000⟩, + ⟨7, 3, 3, 5, 3, 5, -1817310555655918508236026284141115056326705152000000⟩, + ⟨7, 3, 4, 5, 4, 5, 33700896741135191519983821826708920531419136000000⟩, + ⟨7, 3, 5, 5, 5, 5, -12649170553046850278693129088153054200463360000000⟩, + ⟨7, 3, 6, 5, 6, 5, -25678351397011271835384518475308555355291648000000⟩, + ⟨7, 3, 7, 5, 7, 5, 5073321059429447040217177163135820352192512000000⟩, + ⟨7, 3, 8, 5, 8, 5, 3402864343010522184953578990568979264700416000000⟩, + ⟨7, 3, 1, 6, 0, 5, 183251494803346531595909632230381915567317581824000000⟩, + ⟨7, 3, 2, 6, 1, 5, -23032218487184018607300068822970720995191554048000000⟩, + ⟨7, 3, 3, 6, 2, 5, -2032264027587677470861160493319538118601211904000000⟩, + ⟨7, 3, 4, 6, 3, 5, -842396579523051082463996740303776683472715776000000⟩, + ⟨7, 3, 5, 6, 4, 5, 105482009782636108466300182247754132602486784000000⟩, + ⟨7, 3, 6, 6, 5, 5, 2442463724205961910511055691087370076028928000000⟩, + ⟨7, 3, 7, 6, 6, 5, 1533799617471880059012072807560002324660224000000⟩, + ⟨7, 3, 8, 6, 7, 5, 917267741095367984574128063630661830836224000000⟩, + ⟨7, 3, 2, 7, 0, 5, 187896240643120156424331300715474166159763308544000000⟩, + ⟨7, 3, 3, 7, 1, 5, 18682373195815346033981651899118625595179663360000000⟩, + ⟨7, 3, 4, 7, 2, 5, 865695440291837704330693917810185884466675712000000⟩, + ⟨7, 3, 5, 7, 3, 5, 147062655715751298899232190128332685692633088000000⟩, + ⟨7, 3, 6, 7, 4, 5, 84762383831489543083415454530469880450252800000000⟩, + ⟨7, 3, 7, 7, 5, 5, -5510231386819501910618243901617099444846592000000⟩, + ⟨7, 3, 8, 7, 6, 5, 1371377663140362692691571257838403567222784000000⟩ +] + +def collectedFourData_9_5_51 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 5, 6, -137626769829932951132016403909322693931329126400000000⟩, + ⟨7, 4, 1, 0, 6, 6, 55156846109788556229962712074585536056419942400000000⟩, + ⟨7, 4, 2, 0, 7, 6, -1345532540288369699521610633115528685682688000000000⟩, + ⟨7, 4, 3, 0, 8, 6, 163963233944683479322501364987174034950062080000000⟩, + ⟨7, 4, 0, 1, 4, 6, -98951324847628788809538992999608576166697369600000000⟩, + ⟨7, 4, 1, 1, 5, 6, 12009512364067866958466929395478011005475225600000000⟩, + ⟨7, 4, 2, 1, 6, 6, 3097174108199094263283710540096852090840678400000000⟩, + ⟨7, 4, 3, 1, 7, 6, -2190339253438171828871832935983487184525066240000000⟩, + ⟨7, 4, 4, 1, 8, 6, 568273041592361844420749927792249097242542080000000⟩, + ⟨7, 4, 0, 2, 3, 6, -38731478466316269571383894817098580755480576000000000⟩, + ⟨7, 4, 1, 2, 4, 6, -10441717387080343961928497382098176564631961600000000⟩, + ⟨7, 4, 2, 2, 5, 6, 6494703265561038217750019794019881976856576000000000⟩, + ⟨7, 4, 3, 2, 6, 6, 713001137992245509715474359345865576771747840000000⟩, + ⟨7, 4, 4, 2, 7, 6, -77052992302560365511845900435541726540595200000000⟩, + ⟨7, 4, 5, 2, 8, 6, 137314295426672852009752474632251154785894400000000⟩, + ⟨7, 4, 0, 3, 2, 6, 170188638007789651009891410298750990434906931200000000⟩, + ⟨7, 4, 1, 3, 3, 6, 28917741752283308957880291663543460979697254400000000⟩, + ⟨7, 4, 2, 3, 4, 6, -478536760566007628200556437968609825364377600000000⟩, + ⟨7, 4, 3, 3, 5, 6, 1424196772613337178137815019996152750627880960000000⟩, + ⟨7, 4, 4, 3, 6, 6, -62754065223473855083034742445679294357176320000000⟩, + ⟨7, 4, 5, 3, 7, 6, -10817454387983974397999077847166114752102400000000⟩, + ⟨7, 4, 6, 3, 8, 6, 17522754056340249724412443416906174981734400000000⟩, + ⟨7, 4, 0, 4, 1, 6, 140475371773359909180725317809511516826763264000000000⟩, + ⟨7, 4, 1, 4, 2, 6, -49856602503841812165590758561124831083049779200000000⟩, + ⟨7, 4, 2, 4, 3, 6, -10178427849509532513189182469483142409984409600000000⟩, + ⟨7, 4, 3, 4, 4, 6, -582446437813081682658129539380957479897661440000000⟩, + ⟨7, 4, 4, 4, 5, 6, 162275196556562676221539635086805424888872960000000⟩, + ⟨7, 4, 5, 4, 6, 6, -26491850321216310954309237815587752640512000000000⟩, + ⟨7, 4, 6, 4, 7, 6, -7646166570049452123130648153689275813068800000000⟩, + ⟨7, 4, 7, 4, 8, 6, 4986023710170997352682934717067110121472000000000⟩, + ⟨7, 4, 0, 5, 0, 6, -869295481366025837266667252050129625245600972800000000⟩, + ⟨7, 4, 1, 5, 1, 6, -22605564577651327597274209311224255428637491200000000⟩, + ⟨7, 4, 2, 5, 2, 6, 1384494143674647188195069278990541828338483200000000⟩, + ⟨7, 4, 3, 5, 3, 6, -1466418539456827647907745073237425087242567680000000⟩, + ⟨7, 4, 4, 5, 4, 6, 22661518337135971319252287628323748786995200000000⟩, + ⟨7, 4, 5, 5, 5, 6, -7290592192484768837389672646682938966016000000000⟩, + ⟨7, 4, 6, 5, 6, 6, -12950184282645087795868945797447811281715200000000⟩, + ⟨7, 4, 7, 5, 7, 6, 2274304629568062744336231851267756497305600000000⟩, + ⟨7, 4, 8, 5, 8, 6, 1372914316795504304116190365885567567134720000000⟩, + ⟨7, 4, 1, 6, 0, 6, 246447870019124708676670542395050528324819353600000000⟩, + ⟨7, 4, 2, 6, 1, 6, -23231356969582884102624802427214274777998950400000000⟩, + ⟨7, 4, 3, 6, 2, 6, -1639868121522109486070332521623800740430479360000000⟩, + ⟨7, 4, 4, 6, 3, 6, -566453340415155064659894626467460628558643200000000⟩, + ⟨7, 4, 5, 6, 4, 6, 60796580593472252794055146166724162119270400000000⟩, + ⟨7, 4, 6, 6, 5, 6, 1231790734658468848047425890743271764787200000000⟩, + ⟨7, 4, 7, 6, 6, 6, 687582656406595098323031760435498136371200000000⟩, + ⟨7, 4, 8, 6, 7, 6, 370079405801516731054369271894159476654080000000⟩, + ⟨7, 4, 2, 7, 0, 6, 189520807214114756607235369367951777497035571200000000⟩, + ⟨7, 4, 3, 7, 1, 6, 15075122042367092116407360239463771241080422400000000⟩, + ⟨7, 4, 4, 7, 2, 6, 582120210190218831339798922360041419204198400000000⟩, + ⟨7, 4, 5, 7, 3, 6, 84762383831489543083415454530469880450252800000000⟩, + ⟨7, 4, 6, 7, 4, 6, 42747623236507582896539970653670573342720000000000⟩, + ⟨7, 4, 7, 7, 5, 6, -2470165914247146112973598226413140941209600000000⟩, + ⟨7, 4, 8, 7, 6, 6, 553293883526741703922628553328330832609280000000⟩ +] + +def collectedFourData_9_5_52 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 5, 7, 23858235615179351246424420241899410445047955456000000⟩, + ⟨7, 5, 1, 0, 6, 7, -7171270341720144778146424921874441731489923072000000⟩, + ⟨7, 5, 2, 0, 7, 7, 139952564811742337942025599598206726870925312000000⟩, + ⟨7, 5, 3, 0, 8, 7, -14211891598244223353276937257218838848182681600000⟩, + ⟨7, 5, 0, 1, 4, 7, 17153668763469145463371243041331760246380560384000000⟩, + ⟨7, 5, 1, 1, 5, 7, -1561428288766444668847941474012230626698067968000000⟩, + ⟨7, 5, 2, 1, 6, 7, -322145653956527109179872234336796269348493721600000⟩, + ⟨7, 5, 3, 1, 7, 7, 189852708344021014438540691697986134589885644800000⟩, + ⟨7, 5, 4, 1, 8, 7, -42219751714268205738532378412448759208004812800000⟩, + ⟨7, 5, 0, 2, 3, 7, 6714280514724692092183524344566893029401559040000000⟩, + ⟨7, 5, 1, 2, 4, 7, 1357589918494342449994263580005186488707842048000000⟩, + ⟨7, 5, 2, 2, 5, 7, -675532068151739259009077440812926525635559424000000⟩, + ⟨7, 5, 3, 2, 6, 7, -61801018672205388463860407217837351388368076800000⟩, + ⟨7, 5, 4, 2, 7, 7, 5724639329607860002607061877932924371730432000000⟩, + ⟨7, 5, 5, 2, 8, 7, -8926525025809457517524589628389542452002816000000⟩, + ⟨7, 5, 0, 3, 2, 7, -29502985717341175392324234908448943955087720448000000⟩, + ⟨7, 5, 1, 3, 3, 7, -3759767978119925950810304136110516325090066432000000⟩, + ⟨7, 5, 2, 3, 4, 7, 49773933362891478949602546921167603779397222400000⟩, + ⟨7, 5, 3, 3, 5, 7, -123445541174057368782756609083079961879982899200000⟩, + ⟨7, 5, 4, 3, 6, 7, 4662302905258334678555104098710992706548531200000⟩, + ⟨7, 5, 5, 3, 7, 7, 703220862837667596063647090734481000103936000000⟩, + ⟨7, 5, 6, 3, 8, 7, -1012550090895856980156706686911964713582592000000⟩, + ⟨7, 5, 0, 4, 1, 7, -24352053906665232848441034882605792711210434560000000⟩, + ⟨7, 5, 1, 4, 2, 7, 6482154076813325416296570549123142587594571776000000⟩, + ⟨7, 5, 2, 4, 3, 7, 1058686461038566142844819692272975003265689190400000⟩, + ⟨7, 5, 3, 4, 4, 7, 50484888818280203466963257907768448976211148800000⟩, + ⟨7, 5, 4, 4, 5, 7, -12056208911132402177372415427097071728564633600000⟩, + ⟨7, 5, 5, 4, 6, 7, 1722181686455350797443179326194805563719680000000⟩, + ⟨7, 5, 6, 4, 7, 7, 441832752466619581291413423713723753693184000000⟩, + ⟨7, 5, 7, 4, 8, 7, -259305065301891195415716610503004875915264000000⟩, + ⟨7, 5, 0, 5, 0, 7, 150696382973093714522933349862063799490903539712000000⟩, + ⟨7, 5, 1, 5, 1, 7, 2939084198013654108993792006857860826724827136000000⟩, + ⟨7, 5, 2, 5, 2, 7, -144005069050635572399513064747382148858432716800000⟩, + ⟨7, 5, 3, 5, 3, 7, 127105210229307089514440025605235181851613593600000⟩, + ⟨7, 5, 4, 5, 4, 7, -1683633759893417862980106017845018657554432000000⟩, + ⟨7, 5, 5, 5, 5, 7, 473946674357292162241001039769945495306240000000⟩, + ⟨7, 5, 6, 5, 6, 7, 748324734248370984788149145983370643111936000000⟩, + ⟨7, 5, 7, 5, 7, 7, -118278360627032535442372769562612368356147200000⟩, + ⟨7, 5, 8, 5, 8, 7, -64909372362070112772985560883144763532902400000⟩, + ⟨7, 5, 1, 6, 0, 7, -32042156607910252161917096415874786833683447808000000⟩, + ⟨7, 5, 2, 6, 1, 7, 2416357757690101125469885825611096829072087449600000⟩, + ⟨7, 5, 3, 6, 2, 7, 142139352937813237593007958929260643433526067200000⟩, + ⟨7, 5, 4, 6, 3, 7, 42084557316025147418367722421050991666266112000000⟩, + ⟨7, 5, 5, 6, 4, 7, -3952262919639563918639579602380331948179456000000⟩, + ⟨7, 5, 6, 6, 5, 7, -71178869276648625492378220368529924816896000000⟩, + ⟨7, 5, 7, 6, 6, 7, -35758687881138318438912132754999014221414400000⟩, + ⟨7, 5, 8, 6, 7, 7, -17496810733806574719042530261426318711193600000⟩, + ⟨7, 5, 2, 7, 0, 7, -19712583873387862047320349174095663864656743628800000⟩, + ⟨7, 5, 3, 7, 1, 7, -1306670984354356330040629782317765807359131648000000⟩, + ⟨7, 5, 4, 7, 2, 7, -43248524816910826889569744643957630271750144000000⟩, + ⟨7, 5, 5, 7, 3, 7, -5510231386819501910618243901617099444846592000000⟩, + ⟨7, 5, 6, 7, 4, 7, -2470165914247146112973598226413140941209600000000⟩, + ⟨7, 5, 7, 7, 5, 7, 128464397871544601553108606816262401766195200000⟩, + ⟨7, 5, 8, 7, 6, 7, -26158922135300680237998396990822188423577600000⟩ +] + +def collectedFourData_9_5_53 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 5, 8, -13360049786009891199947684896902282183916388352000000⟩, + ⟨7, 6, 1, 0, 6, 8, 3212593934929905207104276613783794148598559539200000⟩, + ⟨7, 6, 2, 0, 7, 8, -52246759112816813914495408139593730632974336000000⟩, + ⟨7, 6, 3, 0, 8, 8, 4547613958872880297319628308180929052304998400000⟩, + ⟨7, 6, 0, 1, 4, 8, -9605650325075294821820053724453097971203964928000000⟩, + ⟨7, 6, 1, 1, 5, 8, 699490440506226398031906388665472495800601804800000⟩, + ⟨7, 6, 2, 1, 6, 8, 120262650449799759315873408156967882587950284800000⟩, + ⟨7, 6, 3, 1, 7, 8, -60750310444371507588173314325835324908057395200000⟩, + ⟨7, 6, 4, 1, 8, 8, 11821033079594713466742911191326676052921548800000⟩, + ⟨7, 6, 0, 2, 3, 8, -3759838883345006857334845962929788474286407680000000⟩, + ⟨7, 6, 1, 2, 4, 8, -608174692969497002699544516325659975281855692800000⟩, + ⟨7, 6, 2, 2, 5, 8, 252188027316135295868161195864229614895235072000000⟩, + ⟨7, 6, 3, 2, 6, 8, 19775493870288603460019503151118243985568563200000⟩, + ⟨7, 6, 4, 2, 7, 8, -1602831569025402077381566226760149627830272000000⟩, + ⟨7, 6, 5, 2, 8, 8, 2221619414956074272460484703621000233746432000000⟩, + ⟨7, 6, 0, 3, 2, 8, 16520976839076865195580656506846531787388092416000000⟩, + ⟨7, 6, 1, 3, 3, 8, 1684305182720875906847729820809546061520778035200000⟩, + ⟨7, 6, 2, 3, 4, 8, -18581486591592618864270946857628898277143347200000⟩, + ⟨7, 6, 3, 3, 5, 8, 39500911073168821217195696175339529988525260800000⟩, + ⟨7, 6, 4, 3, 6, 8, -1305389885832126770641153979933103735649075200000⟩, + ⟨7, 6, 5, 3, 7, 8, -175016494925544267905301672203798207004672000000⟩, + ⟨7, 6, 6, 3, 8, 8, 226801677096201265304495257051631227345305600000⟩, + ⟨7, 6, 0, 4, 1, 8, 13636576393673042454426920107556466232676843520000000⟩, + ⟨7, 6, 1, 4, 2, 8, -2903882838065835517197270551797445432561998233600000⟩, + ⟨7, 6, 2, 4, 3, 8, -395226315289661683155117938418040163859116851200000⟩, + ⟨7, 6, 3, 4, 4, 8, -16154484680316595613833436967239107531191091200000⟩, + ⟨7, 6, 4, 4, 5, 8, 3375596458205531856049014517993972480711065600000⟩, + ⟨7, 6, 5, 4, 6, 8, -428613851375390848085561890729740321423360000000⟩, + ⟨7, 6, 6, 4, 7, 8, -98966372287617259491367839321450056201011200000⟩, + ⟨7, 6, 7, 4, 8, 8, 52801718802308915076239807472485617631232000000⟩, + ⟨7, 6, 0, 5, 0, 8, -84386423688900705084915265913388449073205346304000000⟩, + ⟨7, 6, 1, 5, 1, 8, -1316654319089880202169596448028738992062699929600000⟩, + ⟨7, 6, 2, 5, 2, 8, 53759630370717185158457931707788327890871910400000⟩, + ⟨7, 6, 3, 5, 3, 8, -40671955896122920398507496234205106202371686400000⟩, + ⟨7, 6, 4, 5, 4, 8, 471397617501775064952824469687476548534272000000⟩, + ⟨7, 6, 5, 5, 5, 8, -117955097908947476595811535862375099924480000000⟩, + ⟨7, 6, 6, 5, 6, 8, -167617687525896308787683984908245999078604800000⟩, + ⟨7, 6, 7, 5, 7, 8, 24084761826598646523889539590574554323353600000⟩, + ⟨7, 6, 8, 5, 8, 8, 12115906366300006429668823510902975863193600000⟩, + ⟨7, 6, 1, 6, 0, 8, 14354282166966141353804344436771992977139354828800000⟩, + ⟨7, 6, 2, 6, 1, 8, -902068939331281875554401494357652459863461068800000⟩, + ⟨7, 6, 3, 6, 2, 8, -45482679139279098624102633379610831337868492800000⟩, + ⟨7, 6, 4, 6, 3, 8, -11783180240842300772592722559160139542167552000000⟩, + ⟨7, 6, 5, 6, 4, 8, 983632937777601189623246198659561618931712000000⟩, + ⟨7, 6, 6, 6, 5, 8, 15943395858541852503807435340793221270732800000⟩, + ⟨7, 6, 7, 6, 6, 8, 7281462782229832587223830047220592489267200000⟩, + ⟨7, 6, 8, 6, 7, 8, 3265933914399546263892071319314754856550400000⟩, + ⟨7, 6, 2, 7, 0, 8, 7359054994879811862123474306828025137899923046400000⟩, + ⟨7, 6, 3, 7, 1, 8, 418117121639047549426108097363249369293258752000000⟩, + ⟨7, 6, 4, 7, 2, 8, 12109077428127105146662727583419987524583424000000⟩, + ⟨7, 6, 5, 7, 3, 8, 1371377663140362692691571257838403567222784000000⟩, + ⟨7, 6, 6, 7, 4, 8, 553293883526741703922628553328330832609280000000⟩, + ⟨7, 6, 7, 7, 5, 8, -26158922135300680237998396990822188423577600000⟩, + ⟨7, 6, 8, 7, 6, 8, 4882793342488695371932214113746966439526400000⟩ +] + +def collectedFourData_9_5 : List (List CollectedFourTerm) := [ + collectedFourData_9_5_0, + collectedFourData_9_5_1, + collectedFourData_9_5_2, + collectedFourData_9_5_3, + collectedFourData_9_5_4, + collectedFourData_9_5_5, + collectedFourData_9_5_6, + collectedFourData_9_5_7, + collectedFourData_9_5_8, + collectedFourData_9_5_9, + collectedFourData_9_5_10, + collectedFourData_9_5_11, + collectedFourData_9_5_12, + collectedFourData_9_5_13, + collectedFourData_9_5_14, + collectedFourData_9_5_15, + collectedFourData_9_5_16, + collectedFourData_9_5_17, + collectedFourData_9_5_18, + collectedFourData_9_5_19, + collectedFourData_9_5_20, + collectedFourData_9_5_21, + collectedFourData_9_5_22, + collectedFourData_9_5_23, + collectedFourData_9_5_24, + collectedFourData_9_5_25, + collectedFourData_9_5_26, + collectedFourData_9_5_27, + collectedFourData_9_5_28, + collectedFourData_9_5_29, + collectedFourData_9_5_30, + collectedFourData_9_5_31, + collectedFourData_9_5_32, + collectedFourData_9_5_33, + collectedFourData_9_5_34, + collectedFourData_9_5_35, + collectedFourData_9_5_36, + collectedFourData_9_5_37, + collectedFourData_9_5_38, + collectedFourData_9_5_39, + collectedFourData_9_5_40, + collectedFourData_9_5_41, + collectedFourData_9_5_42, + collectedFourData_9_5_43, + collectedFourData_9_5_44, + collectedFourData_9_5_45, + collectedFourData_9_5_46, + collectedFourData_9_5_47, + collectedFourData_9_5_48, + collectedFourData_9_5_49, + collectedFourData_9_5_50, + collectedFourData_9_5_51, + collectedFourData_9_5_52, + collectedFourData_9_5_53 +] + +theorem collectedFourChecked_9_5 : collectNumericRowParts 9 5 = collectedFourData_9_5 := by + decide +kernel +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0924.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0924.lean new file mode 100644 index 0000000000000000000000000000000000000000..08c1cf8f8f7f0d3c761147daeaa089d9967b82ca --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0924.lean @@ -0,0 +1,624 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0924. -/ +namespace LaughlinFock +def collectedFourData_9_6_0 : List CollectedFourTerm := [ + ⟨0, 6, 3, 1, 8, 0, 165156036399368390338922433258186650714898432000000⟩, + ⟨0, 6, 3, 2, 7, 0, -5934055514420184108435881560919498683167277056000000⟩, + ⟨0, 6, 4, 2, 8, 0, 1984754345275280556824553256622804345403998208000000⟩, + ⟨0, 6, 3, 3, 6, 0, 6515914066942515402470386808155049321608249344000000⟩, + ⟨0, 6, 4, 3, 7, 0, 11965368689069917513920094458719269780835008512000000⟩, + ⟨0, 6, 5, 3, 8, 0, -4947734122060237923380672356302838050104279040000000⟩, + ⟨0, 6, 3, 4, 5, 0, 12189439432418804799693828275020905174383198208000000⟩, + ⟨0, 6, 4, 4, 6, 0, -14187742892555970890743783898504100971091591168000000⟩, + ⟨0, 6, 5, 4, 7, 0, -2956431315027031759130472784126202088731443200000000⟩, + ⟨0, 6, 6, 4, 8, 0, 3740390833266217564342818246249197109195571200000000⟩, + ⟨0, 6, 3, 5, 4, 0, -12478318987141663282587692522020924777511780352000000⟩, + ⟨0, 6, 4, 5, 5, 0, -7360672897212274745686547966267262923867947008000000⟩, + ⟨0, 6, 5, 5, 6, 0, 6566891357375989856085892473436817959000473600000000⟩, + ⟨0, 6, 6, 5, 7, 0, -4533799730473311960224628837943269612249415680000000⟩, + ⟨0, 6, 7, 5, 8, 0, -462881070881911715672398509368277458579619840000000⟩, + ⟨0, 6, 3, 6, 3, 0, -16599127059660804895701488488490053494613475328000000⟩, + ⟨0, 6, 4, 6, 4, 0, 14285774111187024808969856220185385447588888576000000⟩, + ⟨0, 6, 5, 6, 5, 0, -13310928434613363294989822975794160998589399040000000⟩, + ⟨0, 6, 6, 6, 6, 0, 2952205472455555155762753747665929054055301120000000⟩, + ⟨0, 6, 7, 6, 7, 0, 1529535519859803360289411693289353878165258240000000⟩, + ⟨0, 6, 8, 6, 8, 0, -3631329977632468699836954595472076717919567872000000⟩, + ⟨0, 6, 3, 7, 2, 0, -61100968963731478117236442407946085459753435136000000⟩, + ⟨0, 6, 4, 7, 3, 0, -51995190218142894496588310892962018121203318784000000⟩, + ⟨0, 6, 5, 7, 4, 0, -40252638493545670540241015417507211761292410880000000⟩, + ⟨0, 6, 6, 7, 5, 0, -3050927544850806126734794780285331385719193600000000⟩, + ⟨0, 6, 7, 7, 6, 0, -3830541104396225840300880976377804532073103360000000⟩, + ⟨0, 6, 8, 7, 7, 0, -2749634201385262317058014964030805095602978816000000⟩ +] + +def collectedFourData_9_6_1 : List CollectedFourTerm := [ + ⟨0, 7, 2, 0, 8, 1, -25199698675591391439348750463393705710489855590400000⟩, + ⟨0, 7, 2, 1, 7, 1, -11551852995078270225958572386060874376575713280000000⟩, + ⟨0, 7, 3, 1, 8, 1, -438314271403082846563970671734430208018192793600000⟩, + ⟨0, 7, 2, 2, 6, 1, -24334929038772394273581490730208762026739420364800000⟩, + ⟨0, 7, 3, 2, 7, 1, 15748629453537042864680653102882717089366068428800000⟩, + ⟨0, 7, 4, 2, 8, 1, -2633709835042893642491696142851045777839698739200000⟩, + ⟨0, 7, 2, 3, 5, 1, 6030753037131586808991469213129845239437905100800000⟩, + ⟨0, 7, 3, 3, 6, 1, -17292847352371610663482747418437532144370922291200000⟩, + ⟨0, 7, 4, 3, 7, 1, -15877687468645858214974880853907100330391030988800000⟩, + ⟨0, 7, 5, 3, 8, 1, 4376997099403423356391385175582370058169483264000000⟩, + ⟨0, 7, 2, 4, 4, 1, 761856033489558871391544155651846382607663104000000⟩, + ⟨0, 7, 3, 4, 5, 1, -32350045327517249245833446886309460202171557478400000⟩, + ⟨0, 7, 4, 4, 6, 1, 18826711770217560649825483574748156454453326643200000⟩, + ⟨0, 7, 5, 4, 7, 1, 2615397467047082456003031200092093833931653120000000⟩, + ⟨0, 7, 6, 4, 8, 1, -2481693552637416544757558072485914361662013440000000⟩, + ⟨0, 7, 2, 5, 3, 1, 12704254392358068401862002503320307319820622233600000⟩, + ⟨0, 7, 3, 5, 4, 1, 33116714438208506739675643244023618043001805209600000⟩, + ⟨0, 7, 4, 5, 5, 1, 9767393455048899083356216439128612664476119859200000⟩, + ⟨0, 7, 5, 5, 6, 1, -5809379347038036385576711132943207186049269760000000⟩, + ⟨0, 7, 6, 5, 7, 1, 3008108527054574735998893665999464390528598016000000⟩, + ⟨0, 7, 7, 5, 8, 1, 245691751573979752922518859373355456105178726400000⟩, + ⟨0, 7, 2, 6, 2, 1, -8501899882974526612610205369811385687578194739200000⟩, + ⟨0, 7, 3, 6, 3, 1, 44053093315275559314379492141620361200795018854400000⟩, + ⟨0, 7, 4, 6, 4, 1, -18956796274259312538362308441822570049052239462400000⟩, + ⟨0, 7, 5, 6, 5, 1, 11775470086175320131674277909422803083816075264000000⟩, + ⟨0, 7, 6, 6, 6, 1, -1958744316741939065470482383536470432776454144000000⟩, + ⟨0, 7, 7, 6, 7, 1, -811859210948040351420959666539588800437708390400000⟩, + ⟨0, 7, 8, 6, 8, 1, 1606222200603577899312918019200746843010603417600000⟩, + ⟨0, 7, 2, 7, 1, 1, 125397612217363722751635111477670896875406046003200000⟩, + ⟨0, 7, 3, 7, 2, 1, 162158327828838362307098397011682820901571448012800000⟩, + ⟨0, 7, 4, 7, 3, 1, 68996067033905762287039600954911633342497135001600000⟩, + ⟨0, 7, 5, 7, 4, 1, 35609367355459313899027571558415529739192107008000000⟩, + ⟨0, 7, 6, 7, 5, 1, 2024244939935467568054913221393292483436216320000000⟩, + ⟨0, 7, 7, 7, 6, 1, 2033205530790290869276622065957002205908801945600000⟩, + ⟨0, 7, 8, 7, 7, 1, 1216227532338813855898960812313452177158622412800000⟩ +] + +def collectedFourData_9_6_2 : List CollectedFourTerm := [ + ⟨0, 8, 1, 0, 7, 2, -25199698675591391439348750463393705710489855590400000⟩, + ⟨0, 8, 2, 0, 8, 2, 15320362795887692000775237144933669686802697420800000⟩, + ⟨0, 8, 1, 1, 6, 2, -12310227770952085769027856285045556239254578790400000⟩, + ⟨0, 8, 2, 1, 7, 2, 7023043454911770646526800490114149979321794560000000⟩, + ⟨0, 8, 3, 1, 8, 2, 133238372072574373710810344812160896208574873600000⟩, + ⟨0, 8, 1, 2, 5, 2, -7324609155632932664922911214974487238783323340800000⟩, + ⟨0, 8, 2, 2, 6, 2, 14794619026428744093248333369999866515989043609600000⟩, + ⟨0, 8, 3, 2, 7, 2, -4787254003951452863465677683303964752330149068800000⟩, + ⟨0, 8, 4, 2, 8, 2, 533728474182608201243999776027213581330992332800000⟩, + ⟨0, 8, 1, 3, 4, 2, -3993798218234894065495140125585281161727102156800000⟩, + ⟨0, 8, 2, 3, 5, 2, -3666445605190918528066510499547171520471734681600000⟩, + ⟨0, 8, 3, 3, 6, 2, 5256663951082373590484356794953087182292857651200000⟩, + ⟨0, 8, 4, 3, 7, 2, 3217656627709200807617718553643625020684186419200000⟩, + ⟨0, 8, 5, 3, 8, 2, -665257791200898537596743285011851925868511232000000⟩, + ⟨0, 8, 1, 4, 3, 2, 12586571897113959620112997529196455002239506841600000⟩, + ⟨0, 8, 2, 4, 4, 2, -463176603083809952855709545073915980685508608000000⟩, + ⟨0, 8, 3, 4, 5, 2, 9833737245458244660558902721649323504533136998400000⟩, + ⟨0, 8, 4, 4, 6, 2, -3815284437676224806541247304165947007417765068800000⟩, + ⟨0, 8, 5, 4, 7, 2, -397513067184192081244634088788453063456194560000000⟩, + ⟨0, 8, 6, 4, 8, 2, 301753176211170380958810839297014574849458176000000⟩, + ⟨0, 8, 1, 5, 2, 2, 2549254052238531899100343780477847050515382272000000⟩, + ⟨0, 8, 2, 5, 3, 2, -7723655304287389255237812079426460780474872627200000⟩, + ⟨0, 8, 3, 5, 4, 2, -10066788621813938225204604162014631526420552089600000⟩, + ⟨0, 8, 4, 5, 5, 2, -1979388897038287231481221546122760705176030412800000⟩, + ⟨0, 8, 5, 5, 6, 2, 882964915189319759782080195246817702450298880000000⟩, + ⟨0, 8, 6, 5, 7, 2, -365760833549315386548556679389859218190657126400000⟩, + ⟨0, 8, 7, 5, 8, 2, -24895051448349275267897796406620367449017548800000⟩, + ⟨0, 8, 1, 6, 1, 2, 56248596942742023678648142020373229550684654796800000⟩, + ⟨0, 8, 2, 6, 2, 2, 5168799529640727982734095361110097262247568998400000⟩, + ⟨0, 8, 3, 6, 3, 2, -13391219088759154735709136168693378235178051174400000⟩, + ⟨0, 8, 4, 6, 4, 2, 3841646416863607384598682639486078086966516121600000⟩, + ⟨0, 8, 5, 6, 5, 2, -1789748323330844765005473502621835505520607232000000⟩, + ⟨0, 8, 6, 6, 6, 2, 238166923685768327047727061802555804764182937600000⟩, + ⟨0, 8, 7, 6, 7, 2, 82262740592176268168553058338063036739013836800000⟩, + ⟨0, 8, 8, 6, 8, 2, -139502273764948437640346652514382552806037913600000⟩, + ⟨0, 8, 1, 7, 0, 2, -352320781057699192905682339971848111515388136652800000⟩, + ⟨0, 8, 2, 7, 1, 2, -76236503366164376283038340801703674297499149926400000⟩, + ⟨0, 8, 3, 7, 2, 2, -49292740454841815980108786445587155261684763852800000⟩, + ⟨0, 8, 4, 7, 3, 2, -13982240979104566852729964318202838545254999654400000⟩, + ⟨0, 8, 5, 7, 4, 2, -5412251489995976376033511523570412240664264704000000⟩, + ⟨0, 8, 6, 7, 5, 2, -246131251542224669047609236594883671965564928000000⟩, + ⟨0, 8, 7, 7, 6, 2, -206017320361084556955147758366057572634669875200000⟩, + ⟨0, 8, 8, 7, 7, 2, -105630781415572817104604750495788795314359500800000⟩ +] + +def collectedFourData_9_6_3 : List CollectedFourTerm := [ + ⟨1, 5, 3, 1, 8, 0, 252206666392253510197242914552330088354309734400000⟩, + ⟨1, 5, 3, 2, 7, 0, -9061784189707080986670120533336091311582950195200000⟩, + ⟨1, 5, 4, 2, 8, 0, 3030880904764390155380528831106544330797062553600000⟩, + ⟨1, 5, 3, 3, 6, 0, 9950329404540296369060300239088858151019924684800000⟩, + ⟨1, 5, 4, 3, 7, 0, 18272088716922690897989656284575374958070752870400000⟩, + ⟨1, 5, 5, 3, 8, 0, -7555591405103422058450556446339510248950202368000000⟩, + ⟨1, 5, 3, 4, 5, 0, 18614262920470440808138392911438486873501702553600000⟩, + ⟨1, 5, 4, 4, 6, 0, -21665834422844104646152548702369898908683442585600000⟩, + ⟨1, 5, 5, 4, 7, 0, -4514710467969825143922825732919640137861693440000000⟩, + ⟨1, 5, 6, 4, 8, 0, 5711880253538366793494081929467235813860311040000000⟩, + ⟨1, 5, 3, 5, 4, 0, -19055405436807853596763344886307343073771152998400000⟩, + ⟨1, 5, 4, 5, 5, 0, -11240344672117705287335038030226378736421935513600000⟩, + ⟨1, 5, 5, 5, 6, 0, 10028175862727552044993225186299808759016325120000000⟩, + ⟨1, 5, 6, 5, 7, 0, -6923480007401923864144036452984929394314182656000000⟩, + ⟨1, 5, 7, 5, 8, 0, -706856947940473921731166344083316486048841728000000⟩, + ⟨1, 5, 3, 6, 3, 0, -25348213677247771039587316466869066325019957657600000⟩, + ⟨1, 5, 4, 6, 4, 0, 21815536046789124650222719447058916119296553779200000⟩, + ⟨1, 5, 5, 6, 5, 0, -20326867611195181262537352095201580653758906368000000⟩, + ⟨1, 5, 6, 6, 6, 0, 4508257263528218319790724807760788187097595904000000⟩, + ⟨1, 5, 7, 6, 7, 0, 2335724827275273215003649309734433470187307008000000⟩, + ⟨1, 5, 8, 6, 8, 0, -5545335479075737385573058840808130988424455782400000⟩, + ⟨1, 5, 3, 7, 2, 0, -93306136618680645601899480342613259567645274931200000⟩, + ⟨1, 5, 4, 7, 3, 0, -79400873738812239792681407813516337345433750732800000⟩, + ⟨1, 5, 5, 7, 4, 0, -61469044603376539205389014611885057335671914496000000⟩, + ⟨1, 5, 6, 7, 5, 0, -4659013877218883158165249642951580524342149120000000⟩, + ⟨1, 5, 7, 7, 6, 0, -5849547031282278258510339394048752193175027712000000⟩, + ⟨1, 5, 8, 7, 7, 0, -4198914498363169320619537435044240178489275187200000⟩ +] + +def collectedFourData_9_6_4 : List CollectedFourTerm := [ + ⟨1, 6, 2, 0, 8, 1, -12310227770952085769027856285045556239254578790400000⟩, + ⟨1, 6, 2, 1, 7, 1, -5643160395553072364381088656813153926281953280000000⟩, + ⟨1, 6, 3, 1, 8, 1, -214119564908020933859973894813848946840541593600000⟩, + ⟨1, 6, 2, 2, 6, 1, -11887781799050180187733756970299954205142338764800000⟩, + ⟨1, 6, 3, 2, 7, 1, 7693314834797956775463841275491469148153498828800000⟩, + ⟨1, 6, 4, 2, 8, 1, -1286585540936583855312745906398467691589612339200000⟩, + ⟨1, 6, 2, 3, 5, 1, 2946064731693011712621061974428749578518711500800000⟩, + ⟨1, 6, 3, 3, 6, 1, -8447676000276791704551677875156122237509251891200000⟩, + ⟨1, 6, 4, 3, 7, 1, -7756360571261280096837902051245127276878941388800000⟩, + ⟨1, 6, 5, 3, 8, 1, 2138193473664154437288631292072991241235595264000000⟩, + ⟨1, 6, 2, 4, 4, 1, 372171962120117319173619026695455903112495104000000⟩, + ⟨1, 6, 3, 4, 5, 1, -15803221757095701246218548592066243966951384678400000⟩, + ⟨1, 6, 4, 4, 6, 1, 9196979418405831533667830046106682976426472243200000⟩, + ⟨1, 6, 5, 4, 7, 1, 1277639822023195354846034401162073063156613120000000⟩, + ⟨1, 6, 6, 4, 8, 1, -1212324531493744484436710101304385769769533440000000⟩, + ⟨1, 6, 2, 5, 3, 1, 6206116479540645343832999353377235390078491033600000⟩, + ⟨1, 6, 3, 5, 4, 1, 16177744940847269134442548630852519287523482009600000⟩, + ⟨1, 6, 4, 5, 5, 1, 4771439520291677139557555258611241845594993459200000⟩, + ⟨1, 6, 5, 5, 6, 1, -2837922147028403199742041666275884828207349760000000⟩, + ⟨1, 6, 6, 5, 7, 1, 1469481901529759483288400195970986136112726016000000⟩, + ⟨1, 6, 7, 5, 8, 1, 120022126544292352571748238574901800254989926400000⟩, + ⟨1, 6, 2, 6, 2, 1, -4153237123689183030157903883761106309296108339200000⟩, + ⟨1, 6, 3, 6, 3, 1, 21520241956358313154932298727996753998065854054400000⟩, + ⟨1, 6, 4, 6, 4, 1, -9260526601840068438586195397849475342487938662400000⟩, + ⟨1, 6, 5, 6, 5, 1, 5752398897184394884544128588981751039618187264000000⟩, + ⟨1, 6, 6, 6, 6, 1, -956860198789075713672967930490735895609606144000000⟩, + ⟨1, 6, 7, 6, 7, 1, -396598861493381281107641012861084352024831590400000⟩, + ⟨1, 6, 8, 6, 8, 1, 784650697404654621777824923741491076317944217600000⟩, + ⟨1, 6, 2, 7, 1, 1, 61257604235739705142722496925282362347134071603200000⟩, + ⟨1, 6, 3, 7, 2, 1, 79215469050955669830390290836538909566595550412800000⟩, + ⟨1, 6, 4, 7, 3, 1, 33705057803328100206466625892617622031257147801600000⟩, + ⟨1, 6, 5, 7, 4, 1, 17395423198048314544181734056870640434448171008000000⟩, + ⟨1, 6, 6, 7, 5, 1, 988857708006622729241583718882179109166776320000000⟩, + ⟨1, 6, 7, 7, 6, 1, 993235018854868274305209077147354879204366745600000⟩, + ⟨1, 6, 8, 7, 7, 1, 594135594125012909465271645794918659577924812800000⟩ +] + +def collectedFourData_9_6_5 : List CollectedFourTerm := [ + ⟨1, 7, 1, 0, 7, 2, -11551852995078270225958572386060874376575713280000000⟩, + ⟨1, 7, 2, 0, 8, 2, 7023043454911770646526800490114149979321794560000000⟩, + ⟨1, 7, 1, 1, 6, 2, -5643160395553072364381088656813153926281953280000000⟩, + ⟨1, 7, 2, 1, 7, 2, 3219449828095352228818590274349568928776192000000000⟩, + ⟨1, 7, 3, 1, 8, 2, 61078114754473355209775750714959412613611520000000⟩, + ⟨1, 7, 1, 2, 5, 2, -3357691268516340831500679462390839678399938560000000⟩, + ⟨1, 7, 2, 2, 6, 2, 6782036020019275557399283892123776165053726720000000⟩, + ⟨1, 7, 3, 2, 7, 2, -2194536340123487688614153916509338443353948160000000⟩, + ⟨1, 7, 4, 2, 8, 2, 244667722119110750770937832760337341832232960000000⟩, + ⟨1, 7, 1, 3, 4, 2, -1830806411734694953608100920961769844517109760000000⟩, + ⟨1, 7, 2, 3, 5, 2, -1680743932332845471927462180688816686361477120000000⟩, + ⟨1, 7, 3, 3, 6, 2, 2409719655348450453357717572657236858990755840000000⟩, + ⟨1, 7, 4, 3, 7, 2, 1475013524187057275545585518969418830776893440000000⟩, + ⟨1, 7, 5, 3, 8, 2, -304962384936251709053079640511214290101862400000000⟩, + ⟨1, 7, 1, 4, 3, 2, 5769839954803810612019509181430919106521989120000000⟩, + ⟨1, 7, 2, 4, 4, 2, -212325873355242469915549240684112778992025600000000⟩, + ⟨1, 7, 3, 4, 5, 2, 4507906563255507864315604201109983123608698880000000⟩, + ⟨1, 7, 4, 4, 6, 2, -1748973490747951715208106808635352076685148160000000⟩, + ⟨1, 7, 5, 4, 7, 2, -182224897799365956242980969791052622856192000000000⟩, + ⟨1, 7, 6, 4, 8, 2, 138327381500230735507924878352639625212723200000000⟩, + ⟨1, 7, 1, 5, 2, 2, 1168609531315199196164939696852166414591590400000000⟩, + ⟨1, 7, 2, 5, 3, 2, -3540618949789507926242731578366385162593239040000000⟩, + ⟨1, 7, 3, 5, 4, 2, -4614740191491280861342077003791685479269662720000000⟩, + ⟨1, 7, 4, 5, 5, 2, -907376308464521654435770520868059408718888960000000⟩, + ⟨1, 7, 5, 5, 6, 2, 404762018442643204732532904631721804169216000000000⟩, + ⟨1, 7, 6, 5, 7, 2, -167669281879610627266513280846198810848788480000000⟩, + ⟨1, 7, 7, 5, 8, 2, -11412198944854729611227196129732158721884160000000⟩, + ⟨1, 7, 1, 6, 1, 2, 25785051298702317579830847244377755133683957760000000⟩, + ⟨1, 7, 2, 6, 2, 2, 2369441519762066381042626932511370067711098880000000⟩, + ⟨1, 7, 3, 6, 3, 2, -6138700161842366612618457444196144157640622080000000⟩, + ⟨1, 7, 4, 6, 4, 2, 1761058147479459624640394305951593221188485120000000⟩, + ⟨1, 7, 5, 6, 5, 2, -820442728124030978092484882871719278569062400000000⟩, + ⟨1, 7, 6, 6, 6, 2, 109178658289788194967097371139596681027256320000000⟩, + ⟨1, 7, 7, 6, 7, 2, 37710255925144577062097067957148339415285760000000⟩, + ⟨1, 7, 8, 6, 8, 2, -63949564626055163923328049431711166517739520000000⟩, + ⟨1, 7, 1, 7, 0, 2, -161508195882988404506785860238985648747273256960000000⟩, + ⟨1, 7, 2, 7, 1, 2, -34947754379211948152707656283391995184393748480000000⟩, + ⟨1, 7, 3, 7, 2, 2, -22596400805793243482818627202687709337312296960000000⟩, + ⟨1, 7, 4, 7, 3, 2, -6409631893290272239561193738835839703664558080000000⟩, + ⟨1, 7, 5, 7, 4, 2, -2481042904111613661997488165441657931353292800000000⟩, + ⟨1, 7, 6, 7, 5, 2, -112829604508899338994279321676022944471449600000000⟩, + ⟨1, 7, 7, 7, 6, 2, -94440883198193345582877951233701104467312640000000⟩, + ⟨1, 7, 8, 7, 7, 2, -48422454346641361459340294092832320845250560000000⟩ +] + +def collectedFourData_9_6_6 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 6, 3, 165156036399368390338922433258186650714898432000000⟩, + ⟨1, 8, 1, 0, 7, 3, -438314271403082846563970671734430208018192793600000⟩, + ⟨1, 8, 2, 0, 8, 3, 133238372072574373710810344812160896208574873600000⟩, + ⟨1, 8, 0, 1, 5, 3, 252206666392253510197242914552330088354309734400000⟩, + ⟨1, 8, 1, 1, 6, 3, -214119564908020933859973894813848946840541593600000⟩, + ⟨1, 8, 2, 1, 7, 3, 61078114754473355209775750714959412613611520000000⟩, + ⟨1, 8, 3, 1, 8, 3, 772499712923025640656554377338510063226060800000⟩, + ⟨1, 8, 0, 2, 4, 3, 71866265993478316714529685744874843061354496000000⟩, + ⟨1, 8, 1, 2, 5, 3, -127401552165117488085544480374608414677087027200000⟩, + ⟨1, 8, 2, 2, 6, 3, 128666075391139926411009668829822858101470003200000⟩, + ⟨1, 8, 3, 2, 7, 3, -27755910600046468328359202844383643536090726400000⟩, + ⟨1, 8, 4, 2, 8, 3, 2320869093516441212145135172738965180304588800000⟩, + ⟨1, 8, 0, 3, 3, 3, 12782183495785631010484357747030722227050905600000⟩, + ⟨1, 8, 1, 3, 4, 3, -69466654291868276429680515799098466009035571200000⟩, + ⟨1, 8, 2, 3, 5, 3, -31886401793266242530930513030105053042783027200000⟩, + ⟨1, 8, 3, 3, 6, 3, 30477491806429955613399314207805941286017433600000⟩, + ⟨1, 8, 4, 3, 7, 3, 13991683378398181358985744836296500327953203200000⟩, + ⟨1, 8, 5, 3, 8, 3, -2314249767818725108003985381443971818559897600000⟩, + ⟨1, 8, 0, 4, 2, 3, -94738508998316018561961632555581449598245273600000⟩, + ⟨1, 8, 1, 4, 3, 3, 218926192791729973625083184043315830995707494400000⟩, + ⟨1, 8, 2, 4, 4, 3, -4028161565048368866846791162423748681793536000000⟩, + ⟨1, 8, 3, 4, 5, 3, 57014800473088529577375752725790009605698355200000⟩, + ⟨1, 8, 4, 4, 6, 3, -16590412846040999428452024408929520724004044800000⟩, + ⟨1, 8, 5, 4, 7, 3, -1382839157396828494285874683458513543364608000000⟩, + ⟨1, 8, 6, 4, 8, 3, 874763922624967984476122688562925313982464000000⟩, + ⟨1, 8, 0, 5, 1, 3, -73023439470432239667723651856356092075940249600000⟩, + ⟨1, 8, 1, 5, 2, 3, 44340785455922355251052433736459474958286848000000⟩, + ⟨1, 8, 2, 5, 3, 3, -67171206903088776881326055710594855665559142400000⟩, + ⟨1, 8, 3, 5, 4, 3, -58366003722802707671743683113835625079164108800000⟩, + ⟨1, 8, 4, 5, 5, 3, -8607190242606420407180888837077377282264268800000⟩, + ⟨1, 8, 5, 5, 6, 3, 3071593263538171724740392973359252907229184000000⟩, + ⟨1, 8, 6, 5, 7, 3, -1060318189573154063061341773226553533634969600000⟩, + ⟨1, 8, 7, 5, 8, 3, -61859335687186366012595417352488894437785600000⟩, + ⟨1, 8, 0, 6, 0, 3, 1684388616435610782438564603461337943802432716800000⟩, + ⟨1, 8, 1, 6, 1, 3, 978367364776636375260713811447603351824577331200000⟩, + ⟨1, 8, 2, 6, 2, 3, 44952097027602740465342004461245120142691532800000⟩, + ⟨1, 8, 3, 6, 3, 3, -77640643163375390065457007283663271722431283200000⟩, + ⟨1, 8, 4, 6, 4, 3, 16705045483607544236245727072963531514681753600000⟩, + ⟨1, 8, 5, 6, 5, 3, -6226044544695241016132089359701902127372697600000⟩, + ⟨1, 8, 6, 6, 6, 3, 690431282344101865220922426040568036877926400000⟩, + ⟨1, 8, 7, 6, 7, 3, 204406827412954927750667604835516831865241600000⟩, + ⟨1, 8, 8, 6, 8, 3, -303306392030309619259105069726565330111692800000⟩, + ⟨1, 8, 1, 7, 0, 3, -6128137817737075213799648955991075407155901235200000⟩, + ⟨1, 8, 2, 7, 1, 3, -663014821276921654831213620482585835128802508800000⟩, + ⟨1, 8, 3, 7, 2, 3, -285793253536700739649068725548869643296728678400000⟩, + ⟨1, 8, 4, 7, 3, 3, -60800486607353434940176513349956366984701542400000⟩, + ⟨1, 8, 5, 7, 4, 3, -18827741545859282694296425536672450674373427200000⟩, + ⟨1, 8, 6, 7, 5, 3, -713519379590539895707807584629666969812992000000⟩, + ⟨1, 8, 7, 7, 6, 3, -511912763226523532472484431885489114867302400000⟩, + ⟨1, 8, 8, 7, 7, 3, -229662860208875782513080988249727726675558400000⟩ +] + +def collectedFourData_9_6_7 : List CollectedFourTerm := [ + ⟨2, 4, 3, 1, 8, 0, 71866265993478316714529685744874843061354496000000⟩, + ⟨2, 4, 3, 2, 7, 0, -2582154557089011552514054709932185646968864768000000⟩, + ⟨2, 4, 4, 2, 8, 0, 863649230260957665363602237359121926585319424000000⟩, + ⟨2, 4, 3, 3, 6, 0, 2835345432928594563504696888011362140193554432000000⟩, + ⟨2, 4, 4, 3, 7, 0, 5206629970456376231250118191475502215631732736000000⟩, + ⟨2, 4, 5, 3, 8, 0, -2152965064026868382962558658377967371152261120000000⟩, + ⟨2, 4, 3, 4, 5, 0, 5304132477745471778879492651780964361042919424000000⟩, + ⟨2, 4, 4, 4, 6, 0, -6173677491859499557412197428492050227531874304000000⟩, + ⟨2, 4, 5, 4, 7, 0, -1286466325477850335842089992093580582820249600000000⟩, + ⟨2, 4, 6, 4, 8, 0, 1627599743875338023291853810713552553089433600000000⟩, + ⟨2, 4, 3, 5, 4, 0, -5429835996505079881253017148771744777037152256000000⟩, + ⟨2, 4, 4, 5, 5, 0, -3202935162738423666406290681103464168186445824000000⟩, + ⟨2, 4, 5, 5, 6, 0, 2857527773906189513982963521551325169765580800000000⟩, + ⟨2, 4, 6, 5, 7, 0, -1972844980388506134323823870789008686621655040000000⟩, + ⟨2, 4, 7, 5, 8, 0, -201418821186197807525501103258759415222763520000000⟩, + ⟨2, 4, 3, 6, 3, 0, -7222971115899758437462017305020338326716022784000000⟩, + ⟨2, 4, 4, 6, 4, 0, 6216334955597416502564743275857982021936611328000000⟩, + ⟨2, 4, 5, 6, 5, 0, -5792139024146115226050681941926546523679621120000000⟩, + ⟨2, 4, 6, 6, 6, 0, 1284627485475938886405986018152955105362575360000000⟩, + ⟨2, 4, 7, 6, 7, 0, 665564571015208389785346181441196334482718720000000⟩, + ⟨2, 4, 8, 6, 8, 0, -1580142825973175844965790426674983788469026816000000⟩, + ⟨2, 4, 3, 7, 2, 0, -26587574900311561122578172696355377924966187008000000⟩, + ⟨2, 4, 4, 7, 3, 0, -22625271543588881254010729176080809437012426752000000⟩, + ⟨2, 4, 5, 7, 4, 0, -17515598509044508068442341739018819230907760640000000⟩, + ⟨2, 4, 6, 7, 5, 0, -1327585568443178599525011688305623177153740800000000⟩, + ⟨2, 4, 7, 7, 6, 0, -1666827879314159566087873393409252330129326080000000⟩, + ⟨2, 4, 8, 7, 7, 0, -1196480293482474826804382628608770272865026048000000⟩ +] + +def collectedFourData_9_6_8 : List CollectedFourTerm := [ + ⟨2, 5, 2, 0, 8, 1, -7324609155632932664922911214974487238783323340800000⟩, + ⟨2, 5, 2, 1, 7, 1, -3357691268516340831500679462390839678399938560000000⟩, + ⟨2, 5, 3, 1, 8, 1, -127401552165117488085544480374608414677087027200000⟩, + ⟨2, 5, 2, 2, 6, 1, -7073252991382720939511909825213945860146698649600000⟩, + ⟨2, 5, 3, 2, 7, 1, 4577537095543892532499577124375920799863380377600000⟩, + ⟨2, 5, 4, 2, 8, 1, -765520866712623780561799619078577819880941158400000⟩, + ⟨2, 5, 2, 3, 5, 1, 1752914170911151890490207212710042470765402521600000⟩, + ⟨2, 5, 3, 3, 6, 1, -5026383437149224493695999698585029673203689062400000⟩, + ⟨2, 5, 4, 3, 7, 1, -4615049429768327769563847148633536381664729497600000⟩, + ⟨2, 5, 5, 3, 8, 1, 1272229221515352850645025582765248856224432128000000⟩, + ⟨2, 5, 2, 4, 4, 1, 221443031919144706300330506738773182862327808000000⟩, + ⟨2, 5, 3, 4, 5, 1, -9402947282881047986111585126760592720010202316800000⟩, + ⟨2, 5, 4, 4, 6, 1, 5472220409372082209058662956881628156853118566400000⟩, + ⟨2, 5, 5, 4, 7, 1, 760198146786081234192073351844634292377354240000000⟩, + ⟨2, 5, 6, 4, 8, 1, -721335423535442291898540666064408471803002880000000⟩, + ⟨2, 5, 2, 5, 3, 1, 3692651219194469400665406941060867489967321907200000⟩, + ⟨2, 5, 3, 5, 4, 1, 9625789296184540635204059946111338718816318259200000⟩, + ⟨2, 5, 4, 5, 5, 1, 2839015674295215754262253732139545269495031398400000⟩, + ⟨2, 5, 5, 5, 6, 1, -1688569125434634351601291334679852125540843520000000⟩, + ⟨2, 5, 6, 5, 7, 1, 874344552371293525358853980991679929287442432000000⟩, + ⟨2, 5, 7, 5, 8, 1, 71413395700059132641290468779748684467064012800000⟩, + ⟨2, 5, 2, 6, 2, 1, -2471184061554987593886219655141270056996333158400000⟩, + ⟨2, 5, 3, 6, 3, 1, 12804585276393063169637868116471530232751115468800000⟩, + ⟨2, 5, 4, 6, 4, 1, -5510031105506837645566428141911581432453319884800000⟩, + ⟨2, 5, 5, 6, 5, 1, 3422688386691882529918077473979775234634416128000000⟩, + ⟨2, 5, 6, 6, 6, 1, -569333655161862004363806676128700286933925888000000⟩, + ⟨2, 5, 7, 6, 7, 1, -235977083938500307243504091098571144252148940800000⟩, + ⟨2, 5, 8, 6, 8, 1, 466868671247940688698464159254721287196717875200000⟩, + ⟨2, 5, 2, 7, 1, 1, 36448392116349587717107039088266452989804701286400000⟩, + ⟨2, 5, 3, 7, 2, 1, 47133356155075603530169677004952770990178933145600000⟩, + ⟨2, 5, 4, 7, 3, 1, 20054574096503540949241782929613375279415374643200000⟩, + ⟨2, 5, 5, 7, 4, 1, 10350310196793362123261904603916352891142537216000000⟩, + ⟨2, 5, 6, 7, 5, 1, 588372234571848637384327396247979973819760640000000⟩, + ⟨2, 5, 7, 7, 6, 1, 590976742929668483209858940533314306536846131200000⟩, + ⟨2, 5, 8, 7, 7, 1, 353511819065140500155225458027812270559041945600000⟩ +] + +def collectedFourData_9_6_9 : List CollectedFourTerm := [ + ⟨2, 6, 1, 0, 7, 2, -24334929038772394273581490730208762026739420364800000⟩, + ⟨2, 6, 2, 0, 8, 2, 14794619026428744093248333369999866515989043609600000⟩, + ⟨2, 6, 1, 1, 6, 2, -11887781799050180187733756970299954205142338764800000⟩, + ⟨2, 6, 2, 1, 7, 2, 6782036020019275557399283892123776165053726720000000⟩, + ⟨2, 6, 3, 1, 8, 2, 128666075391139926411009668829822858101470003200000⟩, + ⟨2, 6, 1, 2, 5, 2, -7073252991382720939511909825213945860146698649600000⟩, + ⟨2, 6, 2, 2, 6, 2, 14286917030184141781693602092000422949756810035200000⟩, + ⟨2, 6, 3, 2, 7, 2, -4622971408367589891152089560149900211483416985600000⟩, + ⟨2, 6, 4, 2, 8, 2, 515412692525031702350091593172946679322220953600000⟩, + ⟨2, 6, 1, 3, 4, 2, -3856744379648457283110574631534952551726815641600000⟩, + ⟨2, 6, 2, 3, 5, 2, -3540625416813481514811856719283647081516053299200000⟩, + ⟨2, 6, 3, 3, 6, 2, 5076272771236238501978520350234158218529367654400000⟩, + ⟨2, 6, 4, 3, 7, 2, 3107237380670842173064611755129981901776250470400000⟩, + ⟨2, 6, 5, 3, 8, 2, -642428361932958763404411043768321173759197184000000⟩, + ⟨2, 6, 1, 4, 3, 2, 12154642716198545527302711337198707326665831219200000⟩, + ⟨2, 6, 2, 4, 4, 2, -447281926405798319453471486205179981406928896000000⟩, + ⟨2, 6, 3, 4, 5, 2, 9496276171188919087728242834757212838560582860800000⟩, + ⟨2, 6, 4, 4, 6, 2, -3684356596831595693188895802589382723466008985600000⟩, + ⟨2, 6, 5, 4, 7, 2, -383871744120569692722161356701540708746526720000000⟩, + ⟨2, 6, 6, 4, 8, 2, 291398013319724072390326100293523363239821312000000⟩, + ⟨2, 6, 1, 5, 2, 2, 2461772152978800531981396370654272745755377664000000⟩, + ⟨2, 6, 2, 5, 3, 2, -7458605206729150166868139184775854464629630566400000⟩, + ⟨2, 6, 3, 5, 4, 2, -9721330001356233442844048021007758811678847795200000⟩, + ⟨2, 6, 4, 5, 5, 2, -1911462869840456694213369240712173201437333913600000⟩, + ⟨2, 6, 5, 5, 6, 2, 852664503312896190658832313031972461540802560000000⟩, + ⟨2, 6, 6, 5, 7, 2, -353209141274620670281686075439746773351713996800000⟩, + ⟨2, 6, 7, 5, 8, 2, -24040736288603659084249817403426226805774745600000⟩, + ⟨2, 6, 1, 6, 1, 2, 54318332641730034202957333476735199553888295321600000⟩, + ⟨2, 6, 2, 6, 2, 2, 4991423563777806128338495879518069630436166860800000⟩, + ⟨2, 6, 3, 6, 3, 2, -12931677099109625435786703010960905521765076172800000⟩, + ⟨2, 6, 4, 6, 4, 2, 3709813920790311423359898777535985003464438579200000⟩, + ⟨2, 6, 5, 6, 5, 2, -1728330128316340229684908769222135063651549184000000⟩, + ⟨2, 6, 6, 6, 6, 2, 229993828969459930880314075975059723812811571200000⟩, + ⟨2, 6, 7, 6, 7, 2, 79439757618394254907988714411474700815931801600000⟩, + ⟨2, 6, 8, 6, 8, 2, -134715020862754453909140889801391374119154483200000⟩, + ⟨2, 6, 1, 7, 0, 2, -340230306572217999187983034108546663141000976793600000⟩, + ⟨2, 6, 2, 7, 1, 2, -73620320761085625888697437299581287792678587596800000⟩, + ⟨2, 6, 3, 7, 2, 2, -47601177956031648330864284629883911424519543193600000⟩, + ⟨2, 6, 4, 7, 3, 2, -13502417088784489766530276874482070795240393932800000⟩, + ⟨2, 6, 5, 7, 4, 2, -5226521064579805903539728530745212133858869248000000⟩, + ⟨2, 6, 6, 7, 5, 2, -237684847648826537684972442067739572999028736000000⟩, + ⟨2, 6, 7, 7, 6, 2, -198947492836533926713045198487763041714071142400000⟩, + ⟨2, 6, 8, 7, 7, 2, -102005885195280689036808706248846575140444569600000⟩ +] + +def collectedFourData_9_6_10 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 6, 3, -5934055514420184108435881560919498683167277056000000⟩, + ⟨2, 7, 1, 0, 7, 3, 15748629453537042864680653102882717089366068428800000⟩, + ⟨2, 7, 2, 0, 8, 3, -4787254003951452863465677683303964752330149068800000⟩, + ⟨2, 7, 0, 1, 5, 3, -9061784189707080986670120533336091311582950195200000⟩, + ⟨2, 7, 1, 1, 6, 3, 7693314834797956775463841275491469148153498828800000⟩, + ⟨2, 7, 2, 1, 7, 3, -2194536340123487688614153916509338443353948160000000⟩, + ⟨2, 7, 3, 1, 8, 3, -27755910600046468328359202844383643536090726400000⟩, + ⟨2, 7, 0, 2, 4, 3, -2582154557089011552514054709932185646968864768000000⟩, + ⟨2, 7, 1, 2, 5, 3, 4577537095543892532499577124375920799863380377600000⟩, + ⟨2, 7, 2, 2, 6, 3, -4622971408367589891152089560149900211483416985600000⟩, + ⟨2, 7, 3, 2, 7, 3, 997269721075658314720638124783896185474855731200000⟩, + ⟨2, 7, 4, 2, 8, 3, -83388814256390577293803477567181975894517350400000⟩, + ⟨2, 7, 0, 3, 3, 3, -459263785406438013062054695659254502407326924800000⟩, + ⟨2, 7, 1, 3, 4, 3, 2495936521340239386667607171118252389155051929600000⟩, + ⟨2, 7, 2, 3, 5, 3, 1145678247804406713887819357688236784177748377600000⟩, + ⟨2, 7, 3, 3, 6, 3, -1095056119428240919621434410497867415907257548800000⟩, + ⟨2, 7, 4, 3, 7, 3, -502721109792402859436164535347185326296242585600000⟩, + ⟨2, 7, 5, 3, 8, 3, 83150981919077197099035776640434448735456460800000⟩, + ⟨2, 7, 0, 4, 2, 3, 3403954127295545662010096891252107438780632268800000⟩, + ⟨2, 7, 1, 4, 3, 3, -7866016949240311648819603696419921115674260275200000⟩, + ⟨2, 7, 2, 4, 4, 3, 144731823729708534256134076303862304067289088000000⟩, + ⟨2, 7, 3, 4, 5, 3, -2048541479481711449226640789350999078397909401600000⟩, + ⟨2, 7, 4, 4, 6, 3, 596093445821720821692349197314650012142429798400000⟩, + ⟨2, 7, 5, 4, 7, 3, 49685403612278702227480180024727988300939264000000⟩, + ⟨2, 7, 6, 4, 8, 3, -31430263113824486157909214196560820711718912000000⟩, + ⟨2, 7, 0, 5, 1, 3, 2623731793996384227356007741473334887780764876800000⟩, + ⟨2, 7, 1, 5, 2, 3, -1593164186940033682169864058985022579156189184000000⟩, + ⟨2, 7, 2, 5, 3, 3, 2413461108800607297222825185214232196776407859200000⟩, + ⟨2, 7, 3, 5, 4, 3, 2097090205098255462036282548042889258944849510400000⟩, + ⟨2, 7, 4, 5, 5, 3, 309256299898691202630645059240646317032498790400000⟩, + ⟨2, 7, 5, 5, 6, 3, -110362329715151021045326944088143583009308672000000⟩, + ⟨2, 7, 6, 5, 7, 3, 38097226943989941890025227614876292168338636800000⟩, + ⟨2, 7, 7, 5, 8, 3, 2222605604104467133900882758114442272885964800000⟩, + ⟨2, 7, 0, 6, 0, 3, -60520074080831753249937809854251724722976220774400000⟩, + ⟨2, 7, 1, 6, 1, 3, -35152734242438780678082816852014098590402714009600000⟩, + ⟨2, 7, 2, 6, 2, 3, -1615128608477657434897955699372456283233216102400000⟩, + ⟨2, 7, 3, 6, 3, 3, 2789627898266269222643888597320449855801891225600000⟩, + ⟨2, 7, 4, 6, 4, 3, -600212195883264966460649526579051170521468108800000⟩, + ⟨2, 7, 5, 6, 5, 3, 223701747565163725147345170009969810473798860800000⟩, + ⟨2, 7, 6, 6, 6, 3, -24807192323355401339938786078012073093313331200000⟩, + ⟨2, 7, 7, 6, 7, 3, -7344336227964954953973604435339890029022412800000⟩, + ⟨2, 7, 8, 6, 8, 3, 10897797061647285518886985098188566091425382400000⟩, + ⟨2, 7, 1, 7, 0, 3, 220183959383325541081823979578816082707450796441600000⟩, + ⟨2, 7, 2, 7, 1, 3, 23822119022200486998832748149505032690105476710400000⟩, + ⟨2, 7, 3, 7, 2, 3, 10268550088188181563539276765105797519331504947200000⟩, + ⟨2, 7, 4, 7, 3, 3, 2184561162265674182445293275636610267264267059200000⟩, + ⟨2, 7, 5, 7, 4, 3, 676480654174330559631855811673605090739591577600000⟩, + ⟨2, 7, 6, 7, 5, 3, 25636747535321114379497122614512651165761536000000⟩, + ⟨2, 7, 7, 7, 6, 3, 18393022875535920877046422010567351336121139200000⟩, + ⟨2, 7, 8, 7, 7, 3, 8251785352758702560328910505664654865543987200000⟩ +] + +def collectedFourData_9_6_11 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 6, 4, 1984754345275280556824553256622804345403998208000000⟩, + ⟨2, 8, 1, 0, 7, 4, -2633709835042893642491696142851045777839698739200000⟩, + ⟨2, 8, 2, 0, 8, 4, 533728474182608201243999776027213581330992332800000⟩, + ⟨2, 8, 0, 1, 5, 4, 3030880904764390155380528831106544330797062553600000⟩, + ⟨2, 8, 1, 1, 6, 4, -1286585540936583855312745906398467691589612339200000⟩, + ⟨2, 8, 2, 1, 7, 4, 244667722119110750770937832760337341832232960000000⟩, + ⟨2, 8, 3, 1, 8, 4, 2320869093516441212145135172738965180304588800000⟩, + ⟨2, 8, 0, 2, 4, 4, 863649230260957665363602237359121926585319424000000⟩, + ⟨2, 8, 1, 2, 5, 4, -765520866712623780561799619078577819880941158400000⟩, + ⟨2, 8, 2, 2, 6, 4, 515412692525031702350091593172946679322220953600000⟩, + ⟨2, 8, 3, 2, 7, 4, -83388814256390577293803477567181975894517350400000⟩, + ⟨2, 8, 4, 2, 8, 4, 5578185476712583955319597518600142249724477440000⟩, + ⟨2, 8, 0, 3, 3, 4, 153609246070908541194733345374272083435349606400000⟩, + ⟨2, 8, 1, 3, 4, 4, -417406008776221013805897771407423655322740326400000⟩, + ⟨2, 8, 2, 3, 5, 4, -127731075602031303430618685533854584364702105600000⟩, + ⟨2, 8, 3, 3, 6, 4, 91565430508440908398823529438612715302656409600000⟩, + ⟨2, 8, 4, 3, 7, 4, 33628869992786905583011543094731542584528732160000⟩, + ⟨2, 8, 5, 3, 8, 4, -4635229995089348660207398197904999618864742400000⟩, + ⟨2, 8, 0, 4, 2, 4, -1138515258047377566334023061474124468918314598400000⟩, + ⟨2, 8, 1, 4, 3, 4, 1315467245130682953093736988053483067735329996800000⟩, + ⟨2, 8, 2, 4, 4, 4, -16136076210111808962257314170674197171273728000000⟩, + ⟨2, 8, 3, 4, 5, 4, 171293122932439092845520805784379354929902387200000⟩, + ⟨2, 8, 4, 4, 6, 4, -39874890078455085252953976749188042878867210240000⟩, + ⟨2, 8, 5, 4, 7, 4, -2769699982206906478435143169752642556526592000000⟩, + ⟨2, 8, 6, 4, 8, 4, 1501775908728797294243576326355812444274688000000⟩, + ⟨2, 8, 0, 5, 1, 4, -877555504210690129651548048345853137584023142400000⟩, + ⟨2, 8, 1, 5, 2, 4, 266431577450042928597950442071725562507821056000000⟩, + ⟨2, 8, 2, 5, 3, 4, -269075531408188204720074783381101721781744435200000⟩, + ⟨2, 8, 3, 5, 4, 4, -175352627174135933198275237466799469239258316800000⟩, + ⟨2, 8, 4, 5, 5, 4, -20687295005451487848449624856018909830515261440000⟩, + ⟨2, 8, 5, 5, 6, 4, 6152119544679043024877608052604986946748416000000⟩, + ⟨2, 8, 6, 5, 7, 4, -1820331487733953095185477242978999167300403200000⟩, + ⟨2, 8, 7, 5, 8, 4, -92923931193845623769858330056138613902540800000⟩, + ⟨2, 8, 0, 6, 0, 4, 20242055322269658362403862343602209988730368819200000⟩, + ⟨2, 8, 1, 6, 1, 4, 5878740253309265817172235514912431537301907046400000⟩, + ⟨2, 8, 2, 6, 2, 4, 180069853636327163133512278836158205834716774400000⟩, + ⟨2, 8, 3, 6, 3, 4, -233260629232844268670954308970007115024511795200000⟩, + ⟨2, 8, 4, 6, 4, 4, 40150408467586681378600919321701868096905543680000⟩, + ⟨2, 8, 5, 6, 5, 4, -12470196097949580298289900442505503951971942400000⟩, + ⟨2, 8, 6, 6, 6, 4, 1185317592140381906372315163640359623118028800000⟩, + ⟨2, 8, 7, 6, 7, 4, 307056093555951419173149431650508906220748800000⟩, + ⟨2, 8, 8, 6, 8, 4, -404996586969185394895679492591073964641484800000⟩, + ⟨2, 8, 1, 7, 0, 4, -36822293714981494681388945290310197318416492134400000⟩, + ⟨2, 8, 2, 7, 1, 4, -2655915735204529886112342055275248710364587622400000⟩, + ⟨2, 8, 3, 7, 2, 4, -858626505839141104410258984262855586000299622400000⟩, + ⟨2, 8, 4, 7, 3, 4, -146133356817780505849588460813432124003707781120000⟩, + ⟨2, 8, 5, 7, 4, 4, -37710239217356926280098542000868953049320652800000⟩, + ⟨2, 8, 6, 7, 5, 4, -1224954741462958068218300287774748011659264000000⟩, + ⟨2, 8, 7, 7, 6, 4, -768985729621509024476218728938435356341043200000⟩, + ⟨2, 8, 8, 7, 7, 4, -306662427770005609553738428533492578412134400000⟩ +] + +def collectedFourData_9_6_12 : List CollectedFourTerm := [ + ⟨3, 3, 3, 1, 8, 0, 12782183495785631010484357747030722227050905600000⟩, + ⟨3, 3, 3, 2, 7, 0, -459263785406438013062054695659254502407326924800000⟩, + ⟨3, 3, 4, 2, 8, 0, 153609246070908541194733345374272083435349606400000⟩, + ⟨3, 3, 3, 3, 6, 0, 504296488715858817850644304268146898218726195200000⟩, + ⟨3, 3, 4, 3, 7, 0, 926054787416807711618540310609126128405289369600000⟩, + ⟨3, 3, 5, 3, 8, 0, -382927846994369034552520309259822184825618432000000⟩, + ⟨3, 3, 3, 4, 5, 0, 943396650420814256689416995560623675514709606400000⟩, + ⟨3, 3, 4, 4, 6, 0, -1098054524662668412855562641390876007642588774400000⟩, + ⟨3, 3, 5, 4, 7, 0, -228811785419590359496481902228757354706370560000000⟩, + ⟨3, 3, 6, 4, 8, 0, 289486009831040921508354387949304603958312960000000⟩, + ⟨3, 3, 3, 5, 4, 0, -965754364720275036701833384210800018007366041600000⟩, + ⟨3, 3, 4, 5, 5, 0, -569676250870495918946247327141947978302252646400000⟩, + ⟨3, 3, 5, 5, 6, 0, 508241855138088600959268459131812709274746880000000⟩, + ⟨3, 3, 6, 5, 7, 0, -350891565040458532353256360186484638240210944000000⟩, + ⟨3, 3, 7, 5, 8, 0, -35824490062423039861669304701700593598595072000000⟩, + ⟨3, 3, 3, 6, 3, 0, -1284682610288511546946805374727029804312716902400000⟩, + ⟨3, 3, 4, 6, 4, 0, 1105641610500860654250811675135396624603073740800000⟩, + ⟨3, 3, 5, 6, 5, 0, -1030193830391229209399249078029858908439314432000000⟩, + ⟨3, 3, 6, 6, 6, 0, 228484728072184054685842568621537669463146496000000⟩, + ⟨3, 3, 7, 6, 7, 0, 118377772344291027721379285470547994363297792000000⟩, + ⟨3, 3, 8, 6, 8, 0, -281045289774360660008618354635172300442933657600000⟩, + ⟨3, 3, 3, 7, 2, 0, -4728884357433667366922331619831109947048643788800000⟩, + ⟨3, 3, 4, 7, 3, 0, -4024146357323953550232447598958479332298928947200000⟩, + ⟨3, 3, 5, 7, 4, 0, -3115336397210804773397354344322232605793583104000000⟩, + ⟨3, 3, 6, 7, 5, 0, -236125282253255192615326622651816478643322880000000⟩, + ⟨3, 3, 7, 7, 6, 0, -296463152979427827600193149752547097851199488000000⟩, + ⟨3, 3, 8, 7, 7, 0, -212806807880797597400089088845019572729597132800000⟩ +] + +def collectedFourData_9_6_13 : List CollectedFourTerm := [ + ⟨3, 4, 2, 0, 8, 1, -3993798218234894065495140125585281161727102156800000⟩, + ⟨3, 4, 2, 1, 7, 1, -1830806411734694953608100920961769844517109760000000⟩, + ⟨3, 4, 3, 1, 8, 1, -69466654291868276429680515799098466009035571200000⟩, + ⟨3, 4, 2, 2, 6, 1, -3856744379648457283110574631534952551726815641600000⟩, + ⟨3, 4, 3, 2, 7, 1, 2495936521340239386667607171118252389155051929600000⟩, + ⟨3, 4, 4, 2, 8, 1, -417406008776221013805897771407423655322740326400000⟩, + ⟨3, 4, 2, 3, 5, 1, 955789632422879021656327751462240292525676953600000⟩, + ⟨3, 4, 3, 3, 6, 1, -2740673364122634025686395050831039624255006310400000⟩, + ⟨3, 4, 4, 3, 7, 1, -2516390403643592862502536982118063473300183449600000⟩, + ⟨3, 4, 5, 3, 8, 1, 693692549337852265885333351457249133946994688000000⟩, + ⟨3, 4, 2, 4, 4, 1, 120743478256320751176602085131520078898003968000000⟩, + ⟨3, 4, 3, 4, 5, 1, -5127027709819405996183524857430808600660200652800000⟩, + ⟨3, 4, 4, 4, 6, 1, 2983769325620804329995743868611104584671585894400000⟩, + ⟨3, 4, 5, 4, 7, 1, 414503755713005921730441999594466596398039040000000⟩, + ⟨3, 4, 6, 4, 8, 1, -393313563639099196885639734112855674826260480000000⟩, + ⟨3, 4, 2, 5, 3, 1, 2013445843515100909401524687137868610547168051200000⟩, + ⟨3, 4, 3, 5, 4, 1, 5248533993194939936990479712489431436889371443200000⟩, + ⟨3, 4, 4, 5, 5, 1, 1547994643894605546880014928875186928732235366400000⟩, + ⟨3, 4, 5, 5, 6, 1, -920705012545417071943613356159874524690513920000000⟩, + ⟨3, 4, 6, 5, 7, 1, 476742941662409005622030887550657262960771072000000⟩, + ⟨3, 4, 7, 5, 8, 1, 38938690986079521376152186316472305643736268800000⟩, + ⟨3, 4, 2, 6, 2, 1, -1347431691202087724388102566547642293625972326400000⟩, + ⟨3, 4, 3, 6, 3, 1, 6981796403807756107254174366639275578684656844800000⟩, + ⟨3, 4, 4, 6, 4, 1, -3004385891999240444656302185008945812441189580800000⟩, + ⟨3, 4, 5, 6, 5, 1, 1866246579154447201678396861372481886316658688000000⟩, + ⟨3, 4, 6, 6, 6, 1, -310433456482514608191616021406332257092763648000000⟩, + ⟨3, 4, 7, 6, 7, 1, -128668279406153543532791942244904159356439756800000⟩, + ⟨3, 4, 8, 6, 8, 1, 254563653535803766352695275566178182616003379200000⟩, + ⟨3, 4, 2, 7, 1, 1, 19873759868791933007761240116143962418875623014400000⟩, + ⟨3, 4, 3, 7, 2, 1, 25699816854638077833645914378403592479585180057600000⟩, + ⟨3, 4, 4, 7, 3, 1, 10934907323004382516085103459681871395571315507200000⟩, + ⟨3, 4, 5, 7, 4, 1, 5643584462160940579227347036362634114195521536000000⟩, + ⟨3, 4, 6, 7, 5, 1, 320814385063100110693988796774284080384573440000000⟩, + ⟨3, 4, 7, 7, 6, 1, 322234512829349495631744393762091440186536755200000⟩, + ⟨3, 4, 8, 7, 7, 1, 192754977515975521321044354927759008399464857600000⟩ +] + +def collectedFourData_9_6_14 : List CollectedFourTerm := [ + ⟨3, 5, 1, 0, 7, 2, 6030753037131586808991469213129845239437905100800000⟩, + ⟨3, 5, 2, 0, 8, 2, -3666445605190918528066510499547171520471734681600000⟩, + ⟨3, 5, 1, 1, 6, 2, 2946064731693011712621061974428749578518711500800000⟩, + ⟨3, 5, 2, 1, 7, 2, -1680743932332845471927462180688816686361477120000000⟩, + ⟨3, 5, 3, 1, 8, 2, -31886401793266242530930513030105053042783027200000⟩, + ⟨3, 5, 1, 2, 5, 2, 1752914170911151890490207212710042470765402521600000⟩, + ⟨3, 5, 2, 2, 6, 2, -3540625416813481514811856719283647081516053299200000⟩, + ⟨3, 5, 3, 2, 7, 2, 1145678247804406713887819357688236784177748377600000⟩, + ⟨3, 5, 4, 2, 8, 2, -127731075602031303430618685533854584364702105600000⟩, + ⟨3, 5, 1, 3, 4, 2, 955789632422879021656327751462240292525676953600000⟩, + ⟨3, 5, 2, 3, 5, 2, 877448109742684272589222960834825950963381043200000⟩, + ⟨3, 5, 3, 3, 6, 2, -1258016712671115750506655318581071997548521062400000⟩, + ⟨3, 5, 4, 3, 7, 2, -770044623541453695305940696030449179000464998400000⟩, + ⟨3, 5, 5, 3, 8, 2, 159208468974524964514001371924056650299736064000000⟩, + ⟨3, 5, 1, 4, 3, 2, -3012198981931425878632871719661196042749293363200000⟩, + ⟨3, 5, 2, 4, 4, 2, 110846710579186105057591716473967191959535616000000⟩, + ⟨3, 5, 3, 4, 5, 2, -2353394837091619945248472940828714010942426316800000⟩, + ⟨3, 5, 4, 4, 6, 2, 913067989670983257765370809719689369309780377600000⟩, + ⟨3, 5, 5, 4, 7, 2, 95132214399952484003191569828267659750277120000000⟩, + ⟨3, 5, 6, 4, 8, 2, -72215104923547712659663616055915192256561152000000⟩, + ⟨3, 5, 1, 5, 2, 2, -610083549643743226878747915559080700510470144000000⟩, + ⟨3, 5, 2, 5, 3, 2, 1848413280005044633213031377970423573862835814400000⟩, + ⟨3, 5, 3, 5, 4, 2, 2409168333190053410982720295215172075251774259200000⟩, + ⟨3, 5, 4, 5, 5, 2, 473704299251826185889418464057299246509562265600000⟩, + ⟨3, 5, 5, 5, 6, 2, -211309802252373849022166739262926099327221760000000⟩, + ⟨3, 5, 6, 5, 7, 2, 87533318798287103020062577166813200869280972800000⟩, + ⟨3, 5, 7, 5, 8, 2, 5957845332377018278448072748872110616189337600000⟩, + ⟨3, 5, 1, 6, 1, 2, -13461327502911938447691931228387603656069454233600000⟩, + ⟨3, 5, 2, 6, 2, 2, -1236989134790660065394767883794171144444890316800000⟩, + ⟨3, 5, 3, 6, 3, 2, 3204765907326210584127820754119110043378699468800000⟩, + ⟨3, 5, 4, 6, 4, 2, -919376897888330270511322181604549994199855923200000⟩, + ⟨3, 5, 5, 6, 5, 2, 428319809517537916530070946323321826064728064000000⟩, + ⟨3, 5, 6, 6, 6, 2, -56997740998921933396000597824265603530306355200000⟩, + ⟨3, 5, 7, 6, 7, 2, -19686992255568793246444512574352324237564313600000⟩, + ⟨3, 5, 8, 6, 8, 2, 33385469089343426162282457490468662796301107200000⟩, + ⟨3, 5, 1, 7, 0, 2, 84316866156274702928828655644129864652659726745600000⟩, + ⟨3, 5, 2, 7, 1, 2, 18244802453178477680084656151580189523771706572800000⟩, + ⟨3, 5, 3, 7, 2, 2, 11796662651943391628443314418345149493543541145600000⟩, + ⟨3, 5, 4, 7, 3, 2, 3346208354956120505487059184552776830517300428800000⟩, + ⟨3, 5, 5, 7, 4, 2, 1295251682617478353386311171447956119232708608000000⟩, + ⟨3, 5, 6, 7, 5, 2, 58903751663071614410867236490925665477984256000000⟩, + ⟨3, 5, 7, 7, 6, 2, 49303747495709449234419078188932917132420710400000⟩, + ⟨3, 5, 8, 7, 7, 2, 25279395759346258336241982050673713345042841600000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0925.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0925.lean new file mode 100644 index 0000000000000000000000000000000000000000..5441ce503cbec6cad3532979a486af6ee6aae6de --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0925.lean @@ -0,0 +1,661 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0925. -/ +namespace LaughlinFock +def collectedFourData_9_6_15 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 6, 3, 6515914066942515402470386808155049321608249344000000⟩, + ⟨3, 6, 1, 0, 7, 3, -17292847352371610663482747418437532144370922291200000⟩, + ⟨3, 6, 2, 0, 8, 3, 5256663951082373590484356794953087182292857651200000⟩, + ⟨3, 6, 0, 1, 5, 3, 9950329404540296369060300239088858151019924684800000⟩, + ⟨3, 6, 1, 1, 6, 3, -8447676000276791704551677875156122237509251891200000⟩, + ⟨3, 6, 2, 1, 7, 3, 2409719655348450453357717572657236858990755840000000⟩, + ⟨3, 6, 3, 1, 8, 3, 30477491806429955613399314207805941286017433600000⟩, + ⟨3, 6, 0, 2, 4, 3, 2835345432928594563504696888011362140193554432000000⟩, + ⟨3, 6, 1, 2, 5, 3, -5026383437149224493695999698585029673203689062400000⟩, + ⟨3, 6, 2, 2, 6, 3, 5076272771236238501978520350234158218529367654400000⟩, + ⟨3, 6, 3, 2, 7, 3, -1095056119428240919621434410497867415907257548800000⟩, + ⟨3, 6, 4, 2, 8, 3, 91565430508440908398823529438612715302656409600000⟩, + ⟨3, 6, 0, 3, 3, 3, 504296488715858817850644304268146898218726195200000⟩, + ⟨3, 6, 1, 3, 4, 3, -2740673364122634025686395050831039624255006310400000⟩, + ⟨3, 6, 2, 3, 5, 3, -1258016712671115750506655318581071997548521062400000⟩, + ⟨3, 6, 3, 3, 6, 3, 1202430876376987631798283856879102762031461171200000⟩, + ⟨3, 6, 4, 3, 7, 3, 552014982516613274405757358183771805397182054400000⟩, + ⟨3, 6, 5, 3, 8, 3, -91304277732146820790841743211537075975435059200000⟩, + ⟨3, 6, 0, 4, 2, 3, -3737725831410472159675618815125830139024454451200000⟩, + ⟨3, 6, 1, 4, 3, 3, 8637312267438611539612810735187255320059366604800000⟩, + ⟨3, 6, 2, 4, 4, 3, -158923374390911590847412351167464344347738112000000⟩, + ⟨3, 6, 3, 4, 5, 3, 2249409398080826554994075060466081360886785638400000⟩, + ⟨3, 6, 4, 4, 6, 3, -654542860174354340604411475115396567601355161600000⟩, + ⟨3, 6, 5, 4, 7, 3, -54557261813988343137158667643014622620942336000000⟩, + ⟨3, 6, 6, 4, 8, 3, 34512129698382863334379124747146535148453888000000⟩, + ⟨3, 6, 0, 5, 1, 3, -2880999488939869018943252110480321399072437043200000⟩, + ⟨3, 6, 1, 5, 2, 3, 1749380488841941574057273837032724468298940416000000⟩, + ⟨3, 6, 2, 5, 3, 3, -2650110898126495562245389682898819314101308620800000⟩, + ⟨3, 6, 3, 5, 4, 3, -2302718525945950859706609067255006597406628249600000⟩, + ⟨3, 6, 4, 5, 5, 3, -339580152208496683888411932734991217878210969600000⟩, + ⟨3, 6, 5, 5, 6, 3, 121183810111652588045526168165841329746608128000000⟩, + ⟨3, 6, 6, 5, 7, 3, -41832816756197942589350995210980634230207283200000⟩, + ⟨3, 6, 7, 5, 8, 3, -2440541226123771667078660269736572816143155200000⟩, + ⟨3, 6, 0, 6, 0, 3, 66454316289662486012033597790043656816757938585600000⟩, + ⟨3, 6, 1, 6, 1, 3, 38599604433289391409605908729250817256246896230400000⟩, + ⟨3, 6, 2, 6, 2, 3, 1773498612260482230472925093584980947802626457600000⟩, + ⟨3, 6, 3, 6, 3, 3, -3063162388635748739505643593194358661116749414400000⟩, + ⟨3, 6, 4, 6, 4, 3, 659065470621630906967361063261213392708514611200000⟩, + ⟨3, 6, 5, 6, 5, 3, -245636624095839441960661003496423707135652659200000⟩, + ⟨3, 6, 6, 6, 6, 3, 27239639573357415189247932472432849310239948800000⟩, + ⟨3, 6, 7, 6, 7, 3, 8064478605544069536414594373840675712217907200000⟩, + ⟨3, 6, 8, 6, 8, 3, -11966370890888210781041229796826898767649177600000⟩, + ⟨3, 6, 1, 7, 0, 3, -241773902312589790932235056165366559652780074598400000⟩, + ⟨3, 6, 2, 7, 1, 3, -26157975782992290333465050611592466153581681049600000⟩, + ⟨3, 6, 3, 7, 2, 3, -11275423663316848687771784883567165266956438732800000⟩, + ⟨3, 6, 4, 7, 3, 3, -2398766370269463217024547449183732473329929420800000⟩, + ⟨3, 6, 5, 7, 4, 3, -742812364973247130016650242590138252952757862400000⟩, + ⟨3, 6, 6, 7, 5, 3, -28150536086175263665739170317527593059876864000000⟩, + ⟨3, 6, 7, 7, 6, 3, -20196534426929818351126149173669328302427340800000⟩, + ⟨3, 6, 8, 7, 7, 3, -9060906849754049611900461789317525597375692800000⟩ +] + +def collectedFourData_9_6_16 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 6, 4, 11965368689069917513920094458719269780835008512000000⟩, + ⟨3, 7, 1, 0, 7, 4, -15877687468645858214974880853907100330391030988800000⟩, + ⟨3, 7, 2, 0, 8, 4, 3217656627709200807617718553643625020684186419200000⟩, + ⟨3, 7, 0, 1, 5, 4, 18272088716922690897989656284575374958070752870400000⟩, + ⟨3, 7, 1, 1, 6, 4, -7756360571261280096837902051245127276878941388800000⟩, + ⟨3, 7, 2, 1, 7, 4, 1475013524187057275545585518969418830776893440000000⟩, + ⟨3, 7, 3, 1, 8, 4, 13991683378398181358985744836296500327953203200000⟩, + ⟨3, 7, 0, 2, 4, 4, 5206629970456376231250118191475502215631732736000000⟩, + ⟨3, 7, 1, 2, 5, 4, -4615049429768327769563847148633536381664729497600000⟩, + ⟨3, 7, 2, 2, 6, 4, 3107237380670842173064611755129981901776250470400000⟩, + ⟨3, 7, 3, 2, 7, 4, -502721109792402859436164535347185326296242585600000⟩, + ⟨3, 7, 4, 2, 8, 4, 33628869992786905583011543094731542584528732160000⟩, + ⟨3, 7, 0, 3, 3, 4, 926054787416807711618540310609126128405289369600000⟩, + ⟨3, 7, 1, 3, 4, 4, -2516390403643592862502536982118063473300183449600000⟩, + ⟨3, 7, 2, 3, 5, 4, -770044623541453695305940696030449179000464998400000⟩, + ⟨3, 7, 3, 3, 6, 4, 552014982516613274405757358183771805397182054400000⟩, + ⟨3, 7, 4, 3, 7, 4, 202736338135934888630951588023385995937568522240000⟩, + ⟨3, 7, 5, 3, 8, 4, -27944131212967478841151062031000394901592473600000⟩, + ⟨3, 7, 0, 4, 2, 4, -6863698196755430861998385198925953317457205657600000⟩, + ⟨3, 7, 1, 4, 3, 4, 7930477957563372575216011450311100108295582515200000⟩, + ⟨3, 7, 2, 4, 4, 4, -97278588409962097598823268045776678700449792000000⟩, + ⟨3, 7, 3, 4, 5, 4, 1032664508163370974970828261884433795436563660800000⟩, + ⟨3, 7, 4, 4, 6, 4, -240391342314293369738189593564670741802500751360000⟩, + ⟨3, 7, 5, 4, 7, 4, -16697523058260151076082355553598228752498688000000⟩, + ⟨3, 7, 6, 4, 8, 4, 9053665749153845649569775632420994633695232000000⟩, + ⟨3, 7, 0, 5, 1, 4, -5290465884606587643479619526724984838767090073600000⟩, + ⟨3, 7, 1, 5, 2, 4, 1606219964797753964249240602535558525415849984000000⟩, + ⟨3, 7, 2, 5, 3, 4, -1622159410392844042086408695789850848314313932800000⟩, + ⟨3, 7, 3, 5, 4, 4, -1057137796287100398951194532877336061311922995200000⟩, + ⟨3, 7, 4, 5, 5, 4, -124716246375291227035735514500706107167772508160000⟩, + ⟨3, 7, 5, 5, 6, 4, 37088911656272425298810581321242131010945024000000⟩, + ⟨3, 7, 6, 5, 7, 4, -10974122535068157473838572505793509116923084800000⟩, + ⟨3, 7, 7, 5, 8, 4, -560204893577353176858005177766351094362931200000⟩, + ⟨3, 7, 0, 6, 0, 4, 122032056779255165821723614404775166287700348108800000⟩, + ⟨3, 7, 1, 6, 1, 4, 35440806428044615172786387099319382033259141529600000⟩, + ⟨3, 7, 2, 6, 2, 4, 1085576254650634777353461574434621040992295321600000⟩, + ⟨3, 7, 3, 6, 3, 4, -1406244272022646812659430132443765022091168972800000⟩, + ⟨3, 7, 4, 6, 4, 4, 242052343392046868971187529413481324015538667520000⟩, + ⟨3, 7, 5, 6, 5, 4, -75178318310356257708812610767710712919333273600000⟩, + ⟨3, 7, 6, 6, 6, 4, 7145852602546215023321957917913115444589363200000⟩, + ⟨3, 7, 7, 6, 7, 4, 1851130532284046535538825360123673709851443200000⟩, + ⟨3, 7, 8, 6, 8, 4, -2441578471631537657737840193167740850352947200000⟩, + ⟨3, 7, 1, 7, 0, 4, -221988338922551403388584466510780481951908862361600000⟩, + ⟨3, 7, 2, 7, 1, 4, -16011558838238351912020005494868893094299408793600000⟩, + ⟨3, 7, 3, 7, 2, 4, -5176349774988510844479382989647731891029776793600000⟩, + ⟨3, 7, 4, 7, 3, 4, -880985345243637538319032917434007893608948039680000⟩, + ⟨3, 7, 5, 7, 4, 4, -227341442361783245463525216025678065182126899200000⟩, + ⟨3, 7, 6, 7, 5, 4, -7384810691519468377211944037717235776618496000000⟩, + ⟨3, 7, 7, 7, 6, 4, -4635937839591229575047061011489699538980044800000⟩, + ⟨3, 7, 8, 7, 7, 4, -1848757263128431825976734944442084639742361600000⟩ +] + +def collectedFourData_9_6_17 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 6, 5, -4947734122060237923380672356302838050104279040000000⟩, + ⟨3, 8, 1, 0, 7, 5, 4376997099403423356391385175582370058169483264000000⟩, + ⟨3, 8, 2, 0, 8, 5, -665257791200898537596743285011851925868511232000000⟩, + ⟨3, 8, 0, 1, 5, 5, -7555591405103422058450556446339510248950202368000000⟩, + ⟨3, 8, 1, 1, 6, 5, 2138193473664154437288631292072991241235595264000000⟩, + ⟨3, 8, 2, 1, 7, 5, -304962384936251709053079640511214290101862400000000⟩, + ⟨3, 8, 3, 1, 8, 5, -2314249767818725108003985381443971818559897600000⟩, + ⟨3, 8, 0, 2, 4, 5, -2152965064026868382962558658377967371152261120000000⟩, + ⟨3, 8, 1, 2, 5, 5, 1272229221515352850645025582765248856224432128000000⟩, + ⟨3, 8, 2, 2, 6, 5, -642428361932958763404411043768321173759197184000000⟩, + ⟨3, 8, 3, 2, 7, 5, 83150981919077197099035776640434448735456460800000⟩, + ⟨3, 8, 4, 2, 8, 5, -4635229995089348660207398197904999618864742400000⟩, + ⟨3, 8, 0, 3, 3, 5, -382927846994369034552520309259822184825618432000000⟩, + ⟨3, 8, 1, 3, 4, 5, 693692549337852265885333351457249133946994688000000⟩, + ⟨3, 8, 2, 3, 5, 5, 159208468974524964514001371924056650299736064000000⟩, + ⟨3, 8, 3, 3, 6, 5, -91304277732146820790841743211537075975435059200000⟩, + ⟨3, 8, 4, 3, 7, 5, -27944131212967478841151062031000394901592473600000⟩, + ⟨3, 8, 5, 3, 8, 5, 3301435646884235983799163579407286279340032000000⟩, + ⟨3, 8, 0, 4, 2, 5, 2838170277413315741158341866650503027351355392000000⟩, + ⟨3, 8, 1, 4, 3, 5, -2186192358659524700215568516997228626870009856000000⟩, + ⟨3, 8, 2, 4, 4, 5, 20112568351591502456219421089013793365688320000000⟩, + ⟨3, 8, 3, 4, 5, 5, -170804579664903566265275750909275738707748454400000⟩, + ⟨3, 8, 4, 4, 6, 5, 33134302778951681795641165831198600646256230400000⟩, + ⟨3, 8, 5, 4, 7, 5, 1972714679124839364165809841635062248898560000000⟩, + ⟨3, 8, 6, 4, 8, 5, -935932943665493690019411484346441646735360000000⟩, + ⟨3, 8, 0, 5, 1, 5, 2187631594066517037668398822431190387745882112000000⟩, + ⟨3, 8, 1, 5, 2, 5, -442786151371653941613895008580912979399147520000000⟩, + ⟨3, 8, 2, 5, 3, 5, 335385129985729803571666159079579876157554688000000⟩, + ⟨3, 8, 3, 5, 4, 5, 174852505838357730411892415126475462078470553600000⟩, + ⟨3, 8, 4, 5, 5, 5, 17190244162164771106757478653934953617057382400000⟩, + ⟨3, 8, 5, 5, 6, 5, -4381837964936861002109759411058423764090880000000⟩, + ⟨3, 8, 6, 5, 7, 5, 1134462337462822821011287724399659585634304000000⟩, + ⟨3, 8, 7, 5, 8, 5, 51477168806892180699670244738463392858112000000⟩, + ⟨3, 8, 0, 6, 0, 5, -50460807936779579256124476946531970074118455296000000⟩, + ⟨3, 8, 1, 6, 1, 5, -9769955936114630395053591643470015776673497088000000⟩, + ⟨3, 8, 2, 6, 2, 5, -224445347937323154499485244217069676722651136000000⟩, + ⟨3, 8, 3, 6, 3, 5, 232595349109264797016050325087633349059962470400000⟩, + ⟨3, 8, 4, 6, 4, 5, -33363246600707516841077211104194728005782732800000⟩, + ⟨3, 8, 5, 6, 5, 5, 8881878561586643355493290568924068977836032000000⟩, + ⟨3, 8, 6, 6, 6, 5, -738710600391434963823572241578894857076736000000⟩, + ⟨3, 8, 7, 6, 7, 5, -170100190102713283591783265784264740831232000000⟩, + ⟨3, 8, 8, 6, 8, 5, 201920750286852352136072559452365924388044800000⟩, + ⟨3, 8, 1, 7, 0, 5, 61195455414028179149433418468502129202375426048000000⟩, + ⟨3, 8, 2, 7, 1, 5, 3310426033244321773114343119798335960048992256000000⟩, + ⟨3, 8, 3, 7, 2, 5, 856177626447055326388431472777790458843417804800000⟩, + ⟨3, 8, 4, 7, 3, 5, 121430476206406687193500588939740705964897075200000⟩, + ⟨3, 8, 5, 7, 4, 5, 26859061607861861368258272441006850314338304000000⟩, + ⟨3, 8, 6, 7, 5, 5, 763413163289377174827390499030684485550080000000⟩, + ⟨3, 8, 7, 7, 6, 5, 425995840955546093441867566826404234395648000000⟩, + ⟨3, 8, 8, 7, 7, 5, 152893899584439125264620364214283098547814400000⟩ +] + +def collectedFourData_9_6_18 : List CollectedFourTerm := [ + ⟨4, 2, 3, 1, 8, 0, -94738508998316018561961632555581449598245273600000⟩, + ⟨4, 2, 3, 2, 7, 0, 3403954127295545662010096891252107438780632268800000⟩, + ⟨4, 2, 4, 2, 8, 0, -1138515258047377566334023061474124468918314598400000⟩, + ⟨4, 2, 3, 3, 6, 0, -3737725831410472159675618815125830139024454451200000⟩, + ⟨4, 2, 4, 3, 7, 0, -6863698196755430861998385198925953317457205657600000⟩, + ⟨4, 2, 5, 3, 8, 0, 2838170277413315741158341866650503027351355392000000⟩, + ⟨4, 2, 3, 4, 5, 0, -6992231967593122753120139463534226055698474598400000⟩, + ⟨4, 2, 4, 4, 6, 0, 8138519408651468176328276848167730460676744806400000⟩, + ⟨4, 2, 5, 4, 7, 0, 1695898623192333126571349873851453507224207360000000⟩, + ⟨4, 2, 6, 4, 8, 0, -2145601567706098607124282729463328412543221760000000⟩, + ⟨4, 2, 3, 5, 4, 0, 7157942037241208090437620574256900297897646489600000⟩, + ⟨4, 2, 4, 5, 5, 0, 4222305104367791536987115499323440590548788838400000⟩, + ⟨4, 2, 5, 5, 6, 0, -3766967950522383458966237225246897038719713280000000⟩, + ⟨4, 2, 6, 5, 7, 0, 2600724962443160496104839451541749868489867264000000⟩, + ⟨4, 2, 7, 5, 8, 0, 265522613977334797126877283580822365753311232000000⟩, + ⟨4, 2, 3, 6, 3, 0, 9521762465303872579895130152734650691532252774400000⟩, + ⟨4, 2, 4, 6, 4, 0, -8194753087364464368658647530342937355778575564800000⟩, + ⟨4, 2, 5, 6, 5, 0, 7635552055930674793560881820357619031727931392000000⟩, + ⟨4, 2, 6, 6, 6, 0, -1693474551791665665664014580598204419723493376000000⟩, + ⟨4, 2, 7, 6, 7, 0, -877387940341949963763948273608650472451735552000000⟩, + ⟨4, 2, 8, 6, 8, 0, 2083040954857306148850544697910780098579634585600000⟩, + ⟨4, 2, 3, 7, 2, 0, 35049368004804212745435702780398544539135823052800000⟩, + ⟨4, 2, 4, 7, 3, 0, 29826017284885156271678698351541759051639763763200000⟩, + ⟨4, 2, 5, 7, 4, 0, 23090133653397134964323451157757571894790324224000000⟩, + ⟨4, 2, 6, 7, 5, 0, 1750104525166260755980344824054078760057569280000000⟩, + ⟨4, 2, 7, 7, 6, 0, 2197314496030428266466014230846016053605040128000000⟩, + ⟨4, 2, 8, 7, 7, 0, 1577273529985316205706266362046339862397504716800000⟩ +] + +def collectedFourData_9_6_19 : List CollectedFourTerm := [ + ⟨4, 3, 2, 0, 8, 1, 12586571897113959620112997529196455002239506841600000⟩, + ⟨4, 3, 2, 1, 7, 1, 5769839954803810612019509181430919106521989120000000⟩, + ⟨4, 3, 3, 1, 8, 1, 218926192791729973625083184043315830995707494400000⟩, + ⟨4, 3, 2, 2, 6, 1, 12154642716198545527302711337198707326665831219200000⟩, + ⟨4, 3, 3, 2, 7, 1, -7866016949240311648819603696419921115674260275200000⟩, + ⟨4, 3, 4, 2, 8, 1, 1315467245130682953093736988053483067735329996800000⟩, + ⟨4, 3, 2, 3, 5, 1, -3012198981931425878632871719661196042749293363200000⟩, + ⟨4, 3, 3, 3, 6, 1, 8637312267438611539612810735187255320059366604800000⟩, + ⟨4, 3, 4, 3, 7, 1, 7930477957563372575216011450311100108295582515200000⟩, + ⟨4, 3, 5, 3, 8, 1, -2186192358659524700215568516997228626870009856000000⟩, + ⟨4, 3, 2, 4, 4, 1, -380526603282543146604325738471272596128137216000000⟩, + ⟨4, 3, 3, 4, 5, 1, 16157977785031418804346435611251174502431299993600000⟩, + ⟨4, 3, 4, 4, 6, 1, -9403436300276469224243713777608906114757086412800000⟩, + ⟨4, 3, 5, 4, 7, 1, -1306320709715601170123471023239430763163156480000000⟩, + ⟨4, 3, 6, 4, 8, 1, 1239539199614733381173431949786438895937781760000000⟩, + ⟨4, 3, 2, 5, 3, 1, -6345433465977267773092368618362218623034353254400000⟩, + ⟨4, 3, 3, 5, 4, 1, -16540908390958018093493767603190192839672096358400000⟩, + ⟨4, 3, 4, 5, 5, 1, -4878550396654223543805100933911547897359158476800000⟩, + ⟨4, 3, 5, 5, 6, 1, 2901628776217388448825215249766936501855191040000000⟩, + ⟨4, 3, 6, 5, 7, 1, -1502469324633915685737424029259918068903051264000000⟩, + ⟨4, 3, 7, 5, 8, 1, -122716423538393145921525428135081584692402585600000⟩, + ⟨4, 3, 2, 6, 2, 1, 4246470385091313496702743306749788995124513996800000⟩, + ⟨4, 3, 3, 6, 3, 1, -22003335573216873203791134118997760739668236697600000⟩, + ⟨4, 3, 4, 6, 4, 1, 9468410012220407645901888831789957877501368729600000⟩, + ⟨4, 3, 5, 6, 5, 1, -5881530678996585017227658878495261733846777856000000⟩, + ⟨4, 3, 6, 6, 6, 1, 978340117797348726850791234325810354770149376000000⟩, + ⟨4, 3, 7, 6, 7, 1, 405501845894270728274092888303576789886278041600000⟩, + ⟨4, 3, 8, 6, 8, 1, -802264799706502123970450646992836698948658790400000⟩, + ⟨4, 3, 2, 7, 1, 1, -62632735502867035328350315376889578324589595852800000⟩, + ⟨4, 3, 3, 7, 2, 1, -80993724496808907311237051253398297807024239411200000⟩, + ⟨4, 3, 4, 7, 3, 1, -34461680257371920207974721125559621351685645926400000⟩, + ⟨4, 3, 5, 7, 4, 1, -17785921498512243544100441758038794031052357632000000⟩, + ⟨4, 3, 6, 7, 5, 1, -1011055917844976432262406664645541283265249280000000⟩, + ⟨4, 3, 7, 7, 6, 1, -1015531492036825712354026653276424360084006502400000⟩, + ⟨4, 3, 8, 7, 7, 1, -607472949422984308228188688601645020318217011200000⟩ +] + +def collectedFourData_9_6_20 : List CollectedFourTerm := [ + ⟨4, 4, 1, 0, 7, 2, 761856033489558871391544155651846382607663104000000⟩, + ⟨4, 4, 2, 0, 8, 2, -463176603083809952855709545073915980685508608000000⟩, + ⟨4, 4, 1, 1, 6, 2, 372171962120117319173619026695455903112495104000000⟩, + ⟨4, 4, 2, 1, 7, 2, -212325873355242469915549240684112778992025600000000⟩, + ⟨4, 4, 3, 1, 8, 2, -4028161565048368866846791162423748681793536000000⟩, + ⟨4, 4, 1, 2, 5, 2, 221443031919144706300330506738773182862327808000000⟩, + ⟨4, 4, 2, 2, 6, 2, -447281926405798319453471486205179981406928896000000⟩, + ⟨4, 4, 3, 2, 7, 2, 144731823729708534256134076303862304067289088000000⟩, + ⟨4, 4, 4, 2, 8, 2, -16136076210111808962257314170674197171273728000000⟩, + ⟨4, 4, 1, 3, 4, 2, 120743478256320751176602085131520078898003968000000⟩, + ⟨4, 4, 2, 3, 5, 2, 110846710579186105057591716473967191959535616000000⟩, + ⟨4, 4, 3, 3, 6, 2, -158923374390911590847412351167464344347738112000000⟩, + ⟨4, 4, 4, 3, 7, 2, -97278588409962097598823268045776678700449792000000⟩, + ⟨4, 4, 5, 3, 8, 2, 20112568351591502456219421089013793365688320000000⟩, + ⟨4, 4, 1, 4, 3, 2, -380526603282543146604325738471272596128137216000000⟩, + ⟨4, 4, 2, 4, 4, 2, 14003099567710125369606434384898628339630080000000⟩, + ⟨4, 4, 3, 4, 5, 2, -297300858579712269873373488780628111795421184000000⟩, + ⟨4, 4, 4, 4, 6, 2, 115346516866802803952197594791725571231449088000000⟩, + ⟨4, 4, 5, 4, 7, 2, 12017910710914872411578233313219319536025600000000⟩, + ⟨4, 4, 6, 4, 8, 2, -9122826462357412281106582119576772552949760000000⟩, + ⟨4, 4, 1, 5, 2, 2, -77070944601287123217438130953456288761118720000000⟩, + ⟨4, 4, 2, 5, 3, 2, 233507291889349864627207904459501604408655872000000⟩, + ⟨4, 4, 3, 5, 4, 2, 304346641129549217454495948713895983050653696000000⟩, + ⟨4, 4, 4, 5, 5, 2, 59842357372770136740896907406795412003094528000000⟩, + ⟨4, 4, 5, 5, 6, 2, -26694452051053861781678764449555408538828800000000⟩, + ⟨4, 4, 6, 5, 7, 2, 11057953566866474130854559535803659886526464000000⟩, + ⟨4, 4, 7, 5, 8, 2, 752645711923885467389208522233557064613888000000⟩, + ⟨4, 4, 1, 6, 1, 2, -1700549419571370155279429811592840027589050368000000⟩, + ⟨4, 4, 2, 6, 2, 2, -156266991849749474796258716000749867115741184000000⟩, + ⟨4, 4, 3, 6, 3, 2, 404853295663952531360281035404269307710930944000000⟩, + ⟨4, 4, 4, 6, 4, 2, -116143511829210316126658190403208460701270016000000⟩, + ⟨4, 4, 5, 6, 5, 2, 54109002496849352012432633334529842814648320000000⟩, + ⟨4, 4, 6, 6, 6, 2, -7200439581581292389637418310317340859826176000000⟩, + ⟨4, 4, 7, 6, 7, 2, -2487028359281170240597043027652457443360768000000⟩, + ⟨4, 4, 8, 6, 8, 2, 4217536500001183124063810533975384639143936000000⟩, + ⟨4, 4, 1, 7, 0, 2, 10651623903445850864530587034485090019524476928000000⟩, + ⟨4, 4, 2, 7, 1, 2, 2304838673246410666743978649691227397201854464000000⟩, + ⟨4, 4, 3, 7, 2, 2, 1490254792575402730414307873449921574420348928000000⟩, + ⟨4, 4, 4, 7, 3, 2, 422721509045416291120835488895866451729055744000000⟩, + ⟨4, 4, 5, 7, 4, 2, 163627212590847447748917003145797017052119040000000⟩, + ⟨4, 4, 6, 7, 5, 2, 7441223065076173195772497200117529737953280000000⟩, + ⟨4, 4, 7, 7, 6, 2, 6228468861513486006695071813093791054692352000000⟩, + ⟨4, 4, 8, 7, 7, 2, 3193508350225632350588067351896990215569408000000⟩ +] + +def collectedFourData_9_6_21 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 6, 3, 12189439432418804799693828275020905174383198208000000⟩, + ⟨4, 5, 1, 0, 7, 3, -32350045327517249245833446886309460202171557478400000⟩, + ⟨4, 5, 2, 0, 8, 3, 9833737245458244660558902721649323504533136998400000⟩, + ⟨4, 5, 0, 1, 5, 3, 18614262920470440808138392911438486873501702553600000⟩, + ⟨4, 5, 1, 1, 6, 3, -15803221757095701246218548592066243966951384678400000⟩, + ⟨4, 5, 2, 1, 7, 3, 4507906563255507864315604201109983123608698880000000⟩, + ⟨4, 5, 3, 1, 8, 3, 57014800473088529577375752725790009605698355200000⟩, + ⟨4, 5, 0, 2, 4, 3, 5304132477745471778879492651780964361042919424000000⟩, + ⟨4, 5, 1, 2, 5, 3, -9402947282881047986111585126760592720010202316800000⟩, + ⟨4, 5, 2, 2, 6, 3, 9496276171188919087728242834757212838560582860800000⟩, + ⟨4, 5, 3, 2, 7, 3, -2048541479481711449226640789350999078397909401600000⟩, + ⟨4, 5, 4, 2, 8, 3, 171293122932439092845520805784379354929902387200000⟩, + ⟨4, 5, 0, 3, 3, 3, 943396650420814256689416995560623675514709606400000⟩, + ⟨4, 5, 1, 3, 4, 3, -5127027709819405996183524857430808600660200652800000⟩, + ⟨4, 5, 2, 3, 5, 3, -2353394837091619945248472940828714010942426316800000⟩, + ⟨4, 5, 3, 3, 6, 3, 2249409398080826554994075060466081360886785638400000⟩, + ⟨4, 5, 4, 3, 7, 3, 1032664508163370974970828261884433795436563660800000⟩, + ⟨4, 5, 5, 3, 8, 3, -170804579664903566265275750909275738707748454400000⟩, + ⟨4, 5, 0, 4, 2, 3, -6992231967593122753120139463534226055698474598400000⟩, + ⟨4, 5, 1, 4, 3, 3, 16157977785031418804346435611251174502431299993600000⟩, + ⟨4, 5, 2, 4, 4, 3, -297300858579712269873373488780628111795421184000000⟩, + ⟨4, 5, 3, 4, 5, 3, 4208011237552401505202499441091191482444729548800000⟩, + ⟨4, 5, 4, 4, 6, 3, -1224465281163728824821347889404434917109216051200000⟩, + ⟨4, 5, 5, 4, 7, 3, -102061265947952709997987832492118246583959552000000⟩, + ⟨4, 5, 6, 4, 8, 3, 64562471254262404348257813951741192428322816000000⟩, + ⟨4, 5, 0, 5, 1, 3, -5389538354016460228657672669852065151909783142400000⟩, + ⟨4, 5, 1, 5, 2, 3, 3272598025989616164757171338514440684004442112000000⟩, + ⟨4, 5, 2, 5, 3, 3, -4957610850915309555560560087129321518174673305600000⟩, + ⟨4, 5, 3, 5, 4, 3, -4307737596529986073410843752731209647550313267200000⟩, + ⟨4, 5, 4, 5, 5, 3, -635258791824325444657755083794000109441856307200000⟩, + ⟨4, 5, 5, 5, 6, 3, 226700766518681981729381716275719818230890496000000⟩, + ⟨4, 5, 6, 5, 7, 3, -78257414216701012272277192700665948528862822400000⟩, + ⟨4, 5, 7, 5, 8, 3, -4565565038538942247738513342398905918580326400000⟩, + ⟨4, 5, 0, 6, 0, 3, 124317303008224211701855752915182174332968448819200000⟩, + ⟨4, 5, 1, 6, 1, 3, 72208984882405497990196883345284771315274534092800000⟩, + ⟨4, 5, 2, 6, 2, 3, 3317716239890778177338200586521802837991830323200000⟩, + ⟨4, 5, 3, 6, 3, 3, -5730313816962156119279450683452838874259967180800000⟩, + ⟨4, 5, 4, 6, 4, 3, 1232925811115034669161560773523936737952687718400000⟩, + ⟨4, 5, 5, 6, 5, 3, -459516918277135342588196250914066420386391654400000⟩, + ⟨4, 5, 6, 6, 6, 3, 50957691174119639828707567647227796501666201600000⟩, + ⟨4, 5, 7, 6, 7, 3, 15086367393184949307547886161265844090725990400000⟩, + ⟨4, 5, 8, 6, 8, 3, -22385708544002523753424323271231467865453363200000⟩, + ⟨4, 5, 1, 7, 0, 3, -452290854099880168980365102443353357554086104268800000⟩, + ⟨4, 5, 2, 7, 1, 3, -48934202969174201590040520700458586788727042867200000⟩, + ⟨4, 5, 3, 7, 2, 3, -21093140947967480242632031842841288402712238489600000⟩, + ⟨4, 5, 4, 7, 3, 3, -4487416052839832452939408854442585802287978905600000⟩, + ⟨4, 5, 5, 7, 4, 3, -1389592655684273889913874420596883154384243916800000⟩, + ⟨4, 5, 6, 7, 5, 3, -52661721914568724852779403632290607396814848000000⟩, + ⟨4, 5, 7, 7, 6, 3, -37782025762248920801458216964633830176168345600000⟩, + ⟨4, 5, 8, 7, 7, 3, -16950403905447952290453146313396832844749209600000⟩ +] + +def collectedFourData_9_6_22 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 6, 4, -14187742892555970890743783898504100971091591168000000⟩, + ⟨4, 6, 1, 0, 7, 4, 18826711770217560649825483574748156454453326643200000⟩, + ⟨4, 6, 2, 0, 8, 4, -3815284437676224806541247304165947007417765068800000⟩, + ⟨4, 6, 0, 1, 5, 4, -21665834422844104646152548702369898908683442585600000⟩, + ⟨4, 6, 1, 1, 6, 4, 9196979418405831533667830046106682976426472243200000⟩, + ⟨4, 6, 2, 1, 7, 4, -1748973490747951715208106808635352076685148160000000⟩, + ⟨4, 6, 3, 1, 8, 4, -16590412846040999428452024408929520724004044800000⟩, + ⟨4, 6, 0, 2, 4, 4, -6173677491859499557412197428492050227531874304000000⟩, + ⟨4, 6, 1, 2, 5, 4, 5472220409372082209058662956881628156853118566400000⟩, + ⟨4, 6, 2, 2, 6, 4, -3684356596831595693188895802589382723466008985600000⟩, + ⟨4, 6, 3, 2, 7, 4, 596093445821720821692349197314650012142429798400000⟩, + ⟨4, 6, 4, 2, 8, 4, -39874890078455085252953976749188042878867210240000⟩, + ⟨4, 6, 0, 3, 3, 4, -1098054524662668412855562641390876007642588774400000⟩, + ⟨4, 6, 1, 3, 4, 4, 2983769325620804329995743868611104584671585894400000⟩, + ⟨4, 6, 2, 3, 5, 4, 913067989670983257765370809719689369309780377600000⟩, + ⟨4, 6, 3, 3, 6, 4, -654542860174354340604411475115396567601355161600000⟩, + ⟨4, 6, 4, 3, 7, 4, -240391342314293369738189593564670741802500751360000⟩, + ⟨4, 6, 5, 3, 8, 4, 33134302778951681795641165831198600646256230400000⟩, + ⟨4, 6, 0, 4, 2, 4, 8138519408651468176328276848167730460676744806400000⟩, + ⟨4, 6, 1, 4, 3, 4, -9403436300276469224243713777608906114757086412800000⟩, + ⟨4, 6, 2, 4, 4, 4, 115346516866802803952197594791725571231449088000000⟩, + ⟨4, 6, 3, 4, 5, 4, -1224465281163728824821347889404434917109216051200000⟩, + ⟨4, 6, 4, 4, 6, 4, 285040156051949957272290346003254332003230679040000⟩, + ⟨4, 6, 5, 4, 7, 4, 19798818594659988826839549906292378416709632000000⟩, + ⟨4, 6, 6, 4, 8, 4, -10735238104403079633395333935947656617525248000000⟩, + ⟨4, 6, 0, 5, 1, 4, 6273084574585844807928575115015640377668822630400000⟩, + ⟨4, 6, 1, 5, 2, 4, -1904549411022973134935410725888327496054603776000000⟩, + ⟨4, 6, 2, 5, 3, 4, 1923449351495313092002019831198483196641751859200000⟩, + ⟨4, 6, 3, 5, 4, 4, 1253484087742760069964899945204675929044733132800000⟩, + ⟨4, 6, 4, 5, 5, 4, 147880277163013046213093104793679323166136074240000⟩, + ⟨4, 6, 5, 5, 6, 4, -43977578662042730602463650438324256124174336000000⟩, + ⟨4, 6, 6, 5, 7, 4, 13012388756660548794219914057265207571591987200000⟩, + ⟨4, 6, 7, 5, 8, 4, 664253915091435225432954220473229169708236800000⟩, + ⟨4, 6, 0, 6, 0, 4, -144697542652022101079757446290562452380590486323200000⟩, + ⟨4, 6, 1, 6, 1, 4, -42023364475618774301218703015698128825781479014400000⟩, + ⟨4, 6, 2, 6, 2, 4, -1287204530965796816847352680988529756494784102400000⟩, + ⟨4, 6, 3, 6, 3, 4, 1667431459409354937059641771779208393815962419200000⟩, + ⟨4, 6, 4, 6, 4, 4, -287009661283907570994789475498537274509130465280000⟩, + ⟨4, 6, 5, 6, 5, 4, 89141478127321819239407976144143910699427430400000⟩, + ⟨4, 6, 6, 6, 6, 4, -8473079443480843725572348731512752045870284800000⟩, + ⟨4, 6, 7, 6, 7, 4, -2194948165416523851135279920272484068019404800000⟩, + ⟨4, 6, 8, 6, 8, 4, 2895062284135990575220593181149304560864460800000⟩, + ⟨4, 6, 1, 7, 0, 4, 263219091665411116856807693688548272502296962662400000⟩, + ⟨4, 6, 2, 7, 1, 4, 18985447587040959626472080243039546903657604710400000⟩, + ⟨4, 6, 3, 7, 2, 4, 6137773238576702754602638497897608385690756710400000⟩, + ⟨4, 6, 4, 7, 3, 4, 1044614160685588037254394681946556039484166635520000⟩, + ⟨4, 6, 5, 7, 4, 4, 269566447709897703898702755506407712047811788800000⟩, + ⟨4, 6, 6, 7, 5, 4, 8756420142505518978859607979386827066834944000000⟩, + ⟨4, 6, 7, 7, 6, 4, 5496988504338716102954658240019333054149427200000⟩, + ⟨4, 6, 8, 7, 7, 4, 2192134099801859350630908606844441809282662400000⟩ +] + +def collectedFourData_9_6_23 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 6, 5, -2956431315027031759130472784126202088731443200000000⟩, + ⟨4, 7, 1, 0, 7, 5, 2615397467047082456003031200092093833931653120000000⟩, + ⟨4, 7, 2, 0, 8, 5, -397513067184192081244634088788453063456194560000000⟩, + ⟨4, 7, 0, 1, 5, 5, -4514710467969825143922825732919640137861693440000000⟩, + ⟨4, 7, 1, 1, 6, 5, 1277639822023195354846034401162073063156613120000000⟩, + ⟨4, 7, 2, 1, 7, 5, -182224897799365956242980969791052622856192000000000⟩, + ⟨4, 7, 3, 1, 8, 5, -1382839157396828494285874683458513543364608000000⟩, + ⟨4, 7, 0, 2, 4, 5, -1286466325477850335842089992093580582820249600000000⟩, + ⟨4, 7, 1, 2, 5, 5, 760198146786081234192073351844634292377354240000000⟩, + ⟨4, 7, 2, 2, 6, 5, -383871744120569692722161356701540708746526720000000⟩, + ⟨4, 7, 3, 2, 7, 5, 49685403612278702227480180024727988300939264000000⟩, + ⟨4, 7, 4, 2, 8, 5, -2769699982206906478435143169752642556526592000000⟩, + ⟨4, 7, 0, 3, 3, 5, -228811785419590359496481902228757354706370560000000⟩, + ⟨4, 7, 1, 3, 4, 5, 414503755713005921730441999594466596398039040000000⟩, + ⟨4, 7, 2, 3, 5, 5, 95132214399952484003191569828267659750277120000000⟩, + ⟨4, 7, 3, 3, 6, 5, -54557261813988343137158667643014622620942336000000⟩, + ⟨4, 7, 4, 3, 7, 5, -16697523058260151076082355553598228752498688000000⟩, + ⟨4, 7, 5, 3, 8, 5, 1972714679124839364165809841635062248898560000000⟩, + ⟨4, 7, 0, 4, 2, 5, 1695898623192333126571349873851453507224207360000000⟩, + ⟨4, 7, 1, 4, 3, 5, -1306320709715601170123471023239430763163156480000000⟩, + ⟨4, 7, 2, 4, 4, 5, 12017910710914872411578233313219319536025600000000⟩, + ⟨4, 7, 3, 4, 5, 5, -102061265947952709997987832492118246583959552000000⟩, + ⟨4, 7, 4, 4, 6, 5, 19798818594659988826839549906292378416709632000000⟩, + ⟨4, 7, 5, 4, 7, 5, 1178760885103836169861740444461201935564800000000⟩, + ⟨4, 7, 6, 4, 8, 5, -559250233572758716496599994649751112908800000000⟩, + ⟨4, 7, 0, 5, 1, 5, 1307180699464839360388300686505508573502504960000000⟩, + ⟨4, 7, 1, 5, 2, 5, -264579060127499614209988833960116503550361600000000⟩, + ⟨4, 7, 2, 5, 3, 5, 200403472867160515423911973497373532922839040000000⟩, + ⟨4, 7, 3, 5, 4, 5, 104480032883459381847435637597837884640985088000000⟩, + ⟨4, 7, 4, 5, 5, 5, 10271727400910206488506111810035244221857792000000⟩, + ⟨4, 7, 5, 5, 6, 5, -2618290040920662126472921200357257143910400000000⟩, + ⟨4, 7, 6, 5, 7, 5, 677877973523214226496538960900036828856320000000⟩, + ⟨4, 7, 7, 5, 8, 5, 30759274875153825905982213527754988584960000000⟩, + ⟨4, 7, 0, 6, 0, 5, -30151966351769021134990650740318438640247111680000000⟩, + ⟨4, 7, 1, 6, 1, 5, -5837864962706634089995147271159654135145431040000000⟩, + ⟨4, 7, 2, 6, 2, 5, -134113361547757248994516603916084736562298880000000⟩, + ⟨4, 7, 3, 6, 3, 5, 138983251094732774233481406925428379543928832000000⟩, + ⟨4, 7, 4, 6, 4, 5, -19935619939947126941491440283956413699457024000000⟩, + ⟨4, 7, 5, 6, 5, 5, 5307209980961524673378894593981338416578560000000⟩, + ⟨4, 7, 6, 6, 6, 5, -441403498624186783196092854883215873146880000000⟩, + ⟨4, 7, 7, 6, 7, 5, -101640370380757117126421995029206201794560000000⟩, + ⟨4, 7, 8, 6, 8, 5, 120654185244139083137943258444443349417984000000⟩, + ⟨4, 7, 1, 7, 0, 5, 36566265741061731212083760030638234559934627840000000⟩, + ⟨4, 7, 2, 7, 1, 5, 1978086726028216990451829154422470719548948480000000⟩, + ⟨4, 7, 3, 7, 2, 5, 511593849549778453663666486924968623849078784000000⟩, + ⟨4, 7, 4, 7, 3, 5, 72558640702742036143090731817727420704751616000000⟩, + ⟨4, 7, 5, 7, 4, 5, 16049158841352214606036209216711276437176320000000⟩, + ⟨4, 7, 6, 7, 5, 5, 456164079672242564042265295978880198246400000000⟩, + ⟨4, 7, 7, 7, 6, 5, 254546306087244934148430033202098040995840000000⟩, + ⟨4, 7, 8, 7, 7, 5, 91359054762589570686857744051412613988352000000⟩ +] + +def collectedFourData_9_6_24 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 6, 6, 3740390833266217564342818246249197109195571200000000⟩, + ⟨4, 8, 1, 0, 7, 6, -2481693552637416544757558072485914361662013440000000⟩, + ⟨4, 8, 2, 0, 8, 6, 301753176211170380958810839297014574849458176000000⟩, + ⟨4, 8, 0, 1, 5, 6, 5711880253538366793494081929467235813860311040000000⟩, + ⟨4, 8, 1, 1, 6, 6, -1212324531493744484436710101304385769769533440000000⟩, + ⟨4, 8, 2, 1, 7, 6, 138327381500230735507924878352639625212723200000000⟩, + ⟨4, 8, 3, 1, 8, 6, 874763922624967984476122688562925313982464000000⟩, + ⟨4, 8, 0, 2, 4, 6, 1627599743875338023291853810713552553089433600000000⟩, + ⟨4, 8, 1, 2, 5, 6, -721335423535442291898540666064408471803002880000000⟩, + ⟨4, 8, 2, 2, 6, 6, 291398013319724072390326100293523363239821312000000⟩, + ⟨4, 8, 3, 2, 7, 6, -31430263113824486157909214196560820711718912000000⟩, + ⟨4, 8, 4, 2, 8, 6, 1501775908728797294243576326355812444274688000000⟩, + ⟨4, 8, 0, 3, 3, 6, 289486009831040921508354387949304603958312960000000⟩, + ⟨4, 8, 1, 3, 4, 6, -393313563639099196885639734112855674826260480000000⟩, + ⟨4, 8, 2, 3, 5, 6, -72215104923547712659663616055915192256561152000000⟩, + ⟨4, 8, 3, 3, 6, 6, 34512129698382863334379124747146535148453888000000⟩, + ⟨4, 8, 4, 3, 7, 6, 9053665749153845649569775632420994633695232000000⟩, + ⟨4, 8, 5, 3, 8, 6, -935932943665493690019411484346441646735360000000⟩, + ⟨4, 8, 0, 4, 2, 6, -2145601567706098607124282729463328412543221760000000⟩, + ⟨4, 8, 1, 4, 3, 6, 1239539199614733381173431949786438895937781760000000⟩, + ⟨4, 8, 2, 4, 4, 6, -9122826462357412281106582119576772552949760000000⟩, + ⟨4, 8, 3, 4, 5, 6, 64562471254262404348257813951741192428322816000000⟩, + ⟨4, 8, 4, 4, 6, 6, -10735238104403079633395333935947656617525248000000⟩, + ⟨4, 8, 5, 4, 7, 6, -559250233572758716496599994649751112908800000000⟩, + ⟨4, 8, 6, 4, 8, 6, 235849038278594512583032747266496108953600000000⟩, + ⟨4, 8, 0, 5, 1, 6, -1653806966814685596646855251995288468308623360000000⟩, + ⟨4, 8, 1, 5, 2, 6, 251053293411124556674369722051871510836019200000000⟩, + ⟨4, 8, 2, 5, 3, 6, -152126783881029602495280805113408096131088384000000⟩, + ⟨4, 8, 3, 5, 4, 6, -66092548010551574980595498941304616259682304000000⟩, + ⟨4, 8, 4, 5, 5, 6, -5569495920430001188908427764230879327551488000000⟩, + ⟨4, 8, 5, 5, 6, 6, 1242219126415210999966165904421911160422400000000⟩, + ⟨4, 8, 6, 5, 7, 6, -285877159325124491742222203692793242583040000000⟩, + ⟨4, 8, 7, 5, 8, 6, -11674721735913823004093037332426819371008000000⟩, + ⟨4, 8, 0, 6, 0, 6, 38147390055661445992218497628560068489122938880000000⟩, + ⟨4, 8, 1, 6, 1, 6, 5539422600831063809074260599451737546796564480000000⟩, + ⟨4, 8, 2, 6, 2, 6, 101805792463775723916423326035414998684008448000000⟩, + ⟨4, 8, 3, 6, 3, 6, -87918781628708710126484836639385969340973056000000⟩, + ⟨4, 8, 4, 6, 4, 6, 10809413995638134831769763785028151474651136000000⟩, + ⟨4, 8, 5, 6, 5, 6, -2517947837411448340642391016791451484815360000000⟩, + ⟨4, 8, 6, 6, 6, 6, 186150285496085202890832471560883126927360000000⟩, + ⟨4, 8, 7, 6, 7, 6, 38577731306958268963459132635458555609088000000⟩, + ⟨4, 8, 8, 6, 8, 6, -41631317108741558001996467604004811046912000000⟩, + ⟨4, 8, 1, 7, 0, 6, -34696931184259545667907671737501795934619566080000000⟩, + ⟨4, 8, 2, 7, 1, 6, -1501570644276688011078079398269446358311108608000000⟩, + ⟨4, 8, 3, 7, 2, 6, -323626822562233509759903979579125799764099072000000⟩, + ⟨4, 8, 4, 7, 3, 6, -39342462821789667037405164531347711091277824000000⟩, + ⟨4, 8, 5, 7, 4, 6, -7614348205897489479913220250429619615825920000000⟩, + ⟨4, 8, 6, 7, 5, 6, -192375171308608140109019584314412420300800000000⟩, + ⟨4, 8, 7, 7, 6, 6, -96613372861848709932251954827355416952832000000⟩, + ⟨4, 8, 8, 7, 7, 6, -31523131766048758471431968663408461479936000000⟩ +] + +def collectedFourData_9_6_25 : List CollectedFourTerm := [ + ⟨5, 1, 3, 1, 8, 0, -73023439470432239667723651856356092075940249600000⟩, + ⟨5, 1, 3, 2, 7, 0, 2623731793996384227356007741473334887780764876800000⟩, + ⟨5, 1, 4, 2, 8, 0, -877555504210690129651548048345853137584023142400000⟩, + ⟨5, 1, 3, 3, 6, 0, -2880999488939869018943252110480321399072437043200000⟩, + ⟨5, 1, 4, 3, 7, 0, -5290465884606587643479619526724984838767090073600000⟩, + ⟨5, 1, 5, 3, 8, 0, 2187631594066517037668398822431190387745882112000000⟩, + ⟨5, 1, 3, 4, 5, 0, -5389538354016460228657672669852065151909783142400000⟩, + ⟨5, 1, 4, 4, 6, 0, 6273084574585844807928575115015640377668822630400000⟩, + ⟨5, 1, 5, 4, 7, 0, 1307180699464839360388300686505508573502504960000000⟩, + ⟨5, 1, 6, 4, 8, 0, -1653806966814685596646855251995288468308623360000000⟩, + ⟨5, 1, 3, 5, 4, 0, 5517265920858399456856085589725700631828208025600000⟩, + ⟨5, 1, 4, 5, 5, 0, 3254508060919335735362175796664389192072455782400000⟩, + ⟨5, 1, 5, 5, 6, 0, -2903539004682023887031139769504596295239598080000000⟩, + ⟨5, 1, 6, 5, 7, 0, 2004611259794958546881832083719556348724117504000000⟩, + ⟨5, 1, 7, 5, 8, 0, 204662019012242423589820308372907710430052352000000⟩, + ⟨5, 1, 3, 6, 3, 0, 7339273674333529975387015773616140424785061478400000⟩, + ⟨5, 1, 4, 6, 4, 0, -6316428898632270347692110833013630019853667532800000⟩, + ⟨5, 1, 5, 6, 5, 0, 5885402665451479531215672228027058102166618112000000⟩, + ⟨5, 1, 6, 6, 6, 0, -1305312250899728496529510919260285125877825536000000⟩, + ⟨5, 1, 7, 6, 7, 0, -676281333019357961018575417350107436649807872000000⟩, + ⟨5, 1, 8, 6, 8, 0, 1605585908937596303588182013971341224193923481600000⟩, + ⟨5, 1, 3, 7, 2, 0, 27015681690971289534451040967217029945481809100800000⟩, + ⟨5, 1, 4, 7, 3, 0, 22989578270496013039248954631488112112891540275200000⟩, + ⟨5, 1, 5, 7, 4, 0, 17797630499261994887829150403100109186546008064000000⟩, + ⟨5, 1, 6, 7, 5, 0, 1348962034674618170590136693213043022186414080000000⟩, + ⟨5, 1, 7, 7, 6, 0, 1693666744335541565698384615205927149117636608000000⟩, + ⟨5, 1, 8, 7, 7, 0, 1215745733841399397280730108133987748512845004800000⟩ +] + +def collectedFourData_9_6_26 : List CollectedFourTerm := [ + ⟨5, 2, 2, 0, 8, 1, 2549254052238531899100343780477847050515382272000000⟩, + ⟨5, 2, 2, 1, 7, 1, 1168609531315199196164939696852166414591590400000000⟩, + ⟨5, 2, 3, 1, 8, 1, 44340785455922355251052433736459474958286848000000⟩, + ⟨5, 2, 2, 2, 6, 1, 2461772152978800531981396370654272745755377664000000⟩, + ⟨5, 2, 3, 2, 7, 1, -1593164186940033682169864058985022579156189184000000⟩, + ⟨5, 2, 4, 2, 8, 1, 266431577450042928597950442071725562507821056000000⟩, + ⟨5, 2, 2, 3, 5, 1, -610083549643743226878747915559080700510470144000000⟩, + ⟨5, 2, 3, 3, 6, 1, 1749380488841941574057273837032724468298940416000000⟩, + ⟨5, 2, 4, 3, 7, 1, 1606219964797753964249240602535558525415849984000000⟩, + ⟨5, 2, 5, 3, 8, 1, -442786151371653941613895008580912979399147520000000⟩, + ⟨5, 2, 2, 4, 4, 1, -77070944601287123217438130953456288761118720000000⟩, + ⟨5, 2, 3, 4, 5, 1, 3272598025989616164757171338514440684004442112000000⟩, + ⟨5, 2, 4, 4, 6, 1, -1904549411022973134935410725888327496054603776000000⟩, + ⟨5, 2, 5, 4, 7, 1, -264579060127499614209988833960116503550361600000000⟩, + ⟨5, 2, 6, 4, 8, 1, 251053293411124556674369722051871510836019200000000⟩, + ⟨5, 2, 2, 5, 3, 1, -1285188859093686125038101662964230258109186048000000⟩, + ⟨5, 2, 3, 5, 4, 1, -3350155871514526302604665929312162591935561728000000⟩, + ⟨5, 2, 4, 5, 5, 1, -988089884154425225788219751412319122836422656000000⟩, + ⟨5, 2, 5, 5, 6, 1, 587688925652599952870950400652401334602956800000000⟩, + ⟨5, 2, 6, 5, 7, 1, -304306529648898344772290826432488131138682880000000⟩, + ⟨5, 2, 7, 5, 8, 1, -24854689786756020892474619322927612797386752000000⟩, + ⟨5, 2, 2, 6, 2, 1, 860069916208649828997929955768833037677101056000000⟩, + ⟨5, 2, 3, 6, 3, 1, -4456502757962952646615018079296404233536929792000000⟩, + ⟨5, 2, 4, 6, 4, 1, 1917709030641087207342529301586676489736159232000000⟩, + ⟨5, 2, 5, 6, 5, 1, -1191231102428710504978298140250578064265707520000000⟩, + ⟨5, 2, 6, 6, 6, 1, 198150658507284631234569900926036703361105920000000⟩, + ⟨5, 2, 7, 6, 7, 1, 82129370275412562654737590736732347560886272000000⟩, + ⟨5, 2, 8, 6, 8, 1, -162488786330222599782032796660038047962759168000000⟩, + ⟨5, 2, 2, 7, 1, 1, -12685483870320462036332760307555830909502488576000000⟩, + ⟨5, 2, 3, 7, 2, 1, -16404274497230238962370235851774304680677474304000000⟩, + ⟨5, 2, 4, 7, 3, 1, -6979785978356658390493634909834909774971404288000000⟩, + ⟨5, 2, 5, 7, 4, 1, -3602317837097104510065056090339711840094781440000000⟩, + ⟨5, 2, 6, 7, 5, 1, -204776838099740930220331289856693834979737600000000⟩, + ⟨5, 2, 7, 7, 6, 1, -205683310150902222581540617151212977502814208000000⟩, + ⟨5, 2, 8, 7, 7, 1, -123036112660423659541752398937364060704866304000000⟩ +] + +def collectedFourData_9_6_27 : List CollectedFourTerm := [ + ⟨5, 3, 1, 0, 7, 2, 12704254392358068401862002503320307319820622233600000⟩, + ⟨5, 3, 2, 0, 8, 2, -7723655304287389255237812079426460780474872627200000⟩, + ⟨5, 3, 1, 1, 6, 2, 6206116479540645343832999353377235390078491033600000⟩, + ⟨5, 3, 2, 1, 7, 2, -3540618949789507926242731578366385162593239040000000⟩, + ⟨5, 3, 3, 1, 8, 2, -67171206903088776881326055710594855665559142400000⟩, + ⟨5, 3, 1, 2, 5, 2, 3692651219194469400665406941060867489967321907200000⟩, + ⟨5, 3, 2, 2, 6, 2, -7458605206729150166868139184775854464629630566400000⟩, + ⟨5, 3, 3, 2, 7, 2, 2413461108800607297222825185214232196776407859200000⟩, + ⟨5, 3, 4, 2, 8, 2, -269075531408188204720074783381101721781744435200000⟩, + ⟨5, 3, 1, 3, 4, 2, 2013445843515100909401524687137868610547168051200000⟩, + ⟨5, 3, 2, 3, 5, 2, 1848413280005044633213031377970423573862835814400000⟩, + ⟨5, 3, 3, 3, 6, 2, -2650110898126495562245389682898819314101308620800000⟩, + ⟨5, 3, 4, 3, 7, 2, -1622159410392844042086408695789850848314313932800000⟩, + ⟨5, 3, 5, 3, 8, 2, 335385129985729803571666159079579876157554688000000⟩, + ⟨5, 3, 1, 4, 3, 2, -6345433465977267773092368618362218623034353254400000⟩, + ⟨5, 3, 2, 4, 4, 2, 233507291889349864627207904459501604408655872000000⟩, + ⟨5, 3, 3, 4, 5, 2, -4957610850915309555560560087129321518174673305600000⟩, + ⟨5, 3, 4, 4, 6, 2, 1923449351495313092002019831198483196641751859200000⟩, + ⟨5, 3, 5, 4, 7, 2, 200403472867160515423911973497373532922839040000000⟩, + ⟨5, 3, 6, 4, 8, 2, -152126783881029602495280805113408096131088384000000⟩, + ⟨5, 3, 1, 5, 2, 2, -1285188859093686125038101662964230258109186048000000⟩, + ⟨5, 3, 2, 5, 3, 2, 3893827584517733602924676100944001417394048204800000⟩, + ⟨5, 3, 3, 5, 4, 2, 5075102095942763438011876701820714011859510886400000⟩, + ⟨5, 3, 4, 5, 5, 2, 997895269031160597885882228017748335987471155200000⟩, + ⟨5, 3, 5, 5, 6, 2, -445140675946147301331787366430027074680913920000000⟩, + ⟨5, 3, 6, 5, 7, 2, 184395803139990849349176519707149137281128857600000⟩, + ⟨5, 3, 7, 5, 8, 2, 12550668592597725369223082081856584720528179200000⟩, + ⟨5, 3, 1, 6, 1, 2, -28357342441795633196949021917403247073318613811200000⟩, + ⟨5, 3, 2, 6, 2, 2, -2605814655683198559672852972059563157918161305600000⟩, + ⟨5, 3, 3, 6, 3, 2, 6751090801422258057742791875196502762973665689600000⟩, + ⟨5, 3, 4, 6, 4, 2, -1936739561596394682952713022123670377903580774400000⟩, + ⟨5, 3, 5, 6, 5, 2, 902289280939497854539227344580783132207218688000000⟩, + ⟨5, 3, 6, 6, 6, 2, -120070212953779402700317602524313350190818918400000⟩, + ⟨5, 3, 7, 6, 7, 2, -41472193653960087420655376330488455240037171200000⟩, + ⟨5, 3, 8, 6, 8, 2, 70329109765860797036554011226560214254118502400000⟩, + ⟨5, 3, 1, 7, 0, 2, 177620093315114106746758083663497424610499179315200000⟩, + ⟨5, 3, 2, 7, 1, 2, 38434107693745462702145231716498986206639004057600000⟩, + ⟨5, 3, 3, 7, 2, 2, 24850595338322788964174487678107139562563384115200000⟩, + ⟨5, 3, 4, 7, 3, 2, 7049050413680370099810381991111891021924506009600000⟩, + ⟨5, 3, 5, 7, 4, 2, 2728549283445518917141545394505534165835841536000000⟩, + ⟨5, 3, 6, 7, 5, 2, 124085373946580070413737163413869874749898752000000⟩, + ⟨5, 3, 7, 7, 6, 2, 103862212036458986673506690130060617477573836800000⟩, + ⟨5, 3, 8, 7, 7, 2, 53253030365273310067009942155666425755415347200000⟩ +] + +def collectedFourData_9_6_28 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 6, 3, -12478318987141663282587692522020924777511780352000000⟩, + ⟨5, 4, 1, 0, 7, 3, 33116714438208506739675643244023618043001805209600000⟩, + ⟨5, 4, 2, 0, 8, 3, -10066788621813938225204604162014631526420552089600000⟩, + ⟨5, 4, 0, 1, 5, 3, -19055405436807853596763344886307343073771152998400000⟩, + ⟨5, 4, 1, 1, 6, 3, 16177744940847269134442548630852519287523482009600000⟩, + ⟨5, 4, 2, 1, 7, 3, -4614740191491280861342077003791685479269662720000000⟩, + ⟨5, 4, 3, 1, 8, 3, -58366003722802707671743683113835625079164108800000⟩, + ⟨5, 4, 0, 2, 4, 3, -5429835996505079881253017148771744777037152256000000⟩, + ⟨5, 4, 1, 2, 5, 3, 9625789296184540635204059946111338718816318259200000⟩, + ⟨5, 4, 2, 2, 6, 3, -9721330001356233442844048021007758811678847795200000⟩, + ⟨5, 4, 3, 2, 7, 3, 2097090205098255462036282548042889258944849510400000⟩, + ⟨5, 4, 4, 2, 8, 3, -175352627174135933198275237466799469239258316800000⟩, + ⟨5, 4, 0, 3, 3, 3, -965754364720275036701833384210800018007366041600000⟩, + ⟨5, 4, 1, 3, 4, 3, 5248533993194939936990479712489431436889371443200000⟩, + ⟨5, 4, 2, 3, 5, 3, 2409168333190053410982720295215172075251774259200000⟩, + ⟨5, 4, 3, 3, 6, 3, -2302718525945950859706609067255006597406628249600000⟩, + ⟨5, 4, 4, 3, 7, 3, -1057137796287100398951194532877336061311922995200000⟩, + ⟨5, 4, 5, 3, 8, 3, 174852505838357730411892415126475462078470553600000⟩, + ⟨5, 4, 0, 4, 2, 3, 7157942037241208090437620574256900297897646489600000⟩, + ⟨5, 4, 1, 4, 3, 3, -16540908390958018093493767603190192839672096358400000⟩, + ⟨5, 4, 2, 4, 4, 3, 304346641129549217454495948713895983050653696000000⟩, + ⟨5, 4, 3, 4, 5, 3, -4307737596529986073410843752731209647550313267200000⟩, + ⟨5, 4, 4, 4, 6, 3, 1253484087742760069964899945204675929044733132800000⟩, + ⟨5, 4, 5, 4, 7, 3, 104480032883459381847435637597837884640985088000000⟩, + ⟨5, 4, 6, 4, 8, 3, -66092548010551574980595498941304616259682304000000⟩, + ⟨5, 4, 0, 5, 1, 3, 5517265920858399456856085589725700631828208025600000⟩, + ⟨5, 4, 1, 5, 2, 3, -3350155871514526302604665929312162591935561728000000⟩, + ⟨5, 4, 2, 5, 3, 3, 5075102095942763438011876701820714011859510886400000⟩, + ⟨5, 4, 3, 5, 4, 3, 4409827387094010699179024969306563924173049036800000⟩, + ⟨5, 4, 4, 5, 5, 3, 650313895706126909073212163332661875821038796800000⟩, + ⟨5, 4, 5, 5, 6, 3, -232073385731430491081272983623730223040692224000000⟩, + ⟨5, 4, 6, 5, 7, 3, 80112049706546248105892964534184441204545945600000⟩, + ⟨5, 4, 7, 5, 8, 3, 4673765124580935483027457836318618289805721600000⟩, + ⟨5, 4, 0, 6, 0, 3, -127263519471784436565733599157568784289460178124800000⟩, + ⟨5, 4, 1, 6, 1, 3, -73920277638357904969602877866795290781405098803200000⟩, + ⟨5, 4, 2, 6, 2, 3, -3396343349479382179808165523333944846100253900800000⟩, + ⟨5, 4, 3, 6, 3, 3, 5866117478241581230556463922160725567508525875200000⟩, + ⟨5, 4, 4, 6, 4, 3, -1262145125202110330696526874914130962624911769600000⟩, + ⟨5, 4, 5, 6, 5, 3, 470407086235677618067290632565820966026451353600000⟩, + ⟨5, 4, 6, 6, 6, 3, -52165345982012929141729753196503831182468710400000⟩, + ⟨5, 4, 7, 6, 7, 3, -15443901726005692786266827648881906016688537600000⟩, + ⟨5, 4, 8, 6, 8, 3, 22916231178140089426498704086695099551763660800000⟩, + ⟨5, 4, 1, 7, 0, 3, 463009770360303128331472416619468219247972528947200000⟩, + ⟨5, 4, 2, 7, 1, 3, 50093902793175700838891193467750727340132191436800000⟩, + ⟨5, 4, 3, 7, 2, 3, 21593030807426440019647139934458183781190100582400000⟩, + ⟨5, 4, 4, 7, 3, 3, 4593764073057472837963158171751222142730397286400000⟩, + ⟨5, 4, 5, 7, 4, 3, 1422524843406754817105536112893596172045988659200000⟩, + ⟨5, 4, 6, 7, 5, 3, 53909760830711142505122041282612280019648512000000⟩, + ⟨5, 4, 7, 7, 6, 3, 38677428281719845494301824039156644070188646400000⟩, + ⟨5, 4, 8, 7, 7, 3, 17352114349945952206120377148818787068700262400000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0926.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0926.lean new file mode 100644 index 0000000000000000000000000000000000000000..8f3c1e07b023a8ae9ed158ebda804f5628a4b82f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0926.lean @@ -0,0 +1,653 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0926. -/ +namespace LaughlinFock +def collectedFourData_9_6_29 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 6, 4, -7360672897212274745686547966267262923867947008000000⟩, + ⟨5, 5, 1, 0, 7, 4, 9767393455048899083356216439128612664476119859200000⟩, + ⟨5, 5, 2, 0, 8, 4, -1979388897038287231481221546122760705176030412800000⟩, + ⟨5, 5, 0, 1, 5, 4, -11240344672117705287335038030226378736421935513600000⟩, + ⟨5, 5, 1, 1, 6, 4, 4771439520291677139557555258611241845594993459200000⟩, + ⟨5, 5, 2, 1, 7, 4, -907376308464521654435770520868059408718888960000000⟩, + ⟨5, 5, 3, 1, 8, 4, -8607190242606420407180888837077377282264268800000⟩, + ⟨5, 5, 0, 2, 4, 4, -3202935162738423666406290681103464168186445824000000⟩, + ⟨5, 5, 1, 2, 5, 4, 2839015674295215754262253732139545269495031398400000⟩, + ⟨5, 5, 2, 2, 6, 4, -1911462869840456694213369240712173201437333913600000⟩, + ⟨5, 5, 3, 2, 7, 4, 309256299898691202630645059240646317032498790400000⟩, + ⟨5, 5, 4, 2, 8, 4, -20687295005451487848449624856018909830515261440000⟩, + ⟨5, 5, 0, 3, 3, 4, -569676250870495918946247327141947978302252646400000⟩, + ⟨5, 5, 1, 3, 4, 4, 1547994643894605546880014928875186928732235366400000⟩, + ⟨5, 5, 2, 3, 5, 4, 473704299251826185889418464057299246509562265600000⟩, + ⟨5, 5, 3, 3, 6, 4, -339580152208496683888411932734991217878210969600000⟩, + ⟨5, 5, 4, 3, 7, 4, -124716246375291227035735514500706107167772508160000⟩, + ⟨5, 5, 5, 3, 8, 4, 17190244162164771106757478653934953617057382400000⟩, + ⟨5, 5, 0, 4, 2, 4, 4222305104367791536987115499323440590548788838400000⟩, + ⟨5, 5, 1, 4, 3, 4, -4878550396654223543805100933911547897359158476800000⟩, + ⟨5, 5, 2, 4, 4, 4, 59842357372770136740896907406795412003094528000000⟩, + ⟨5, 5, 3, 4, 5, 4, -635258791824325444657755083794000109441856307200000⟩, + ⟨5, 5, 4, 4, 6, 4, 147880277163013046213093104793679323166136074240000⟩, + ⟨5, 5, 5, 4, 7, 4, 10271727400910206488506111810035244221857792000000⟩, + ⟨5, 5, 6, 4, 8, 4, -5569495920430001188908427764230879327551488000000⟩, + ⟨5, 5, 0, 5, 1, 4, 3254508060919335735362175796664389192072455782400000⟩, + ⟨5, 5, 1, 5, 2, 4, -988089884154425225788219751412319122836422656000000⟩, + ⟨5, 5, 2, 5, 3, 4, 997895269031160597885882228017748335987471155200000⟩, + ⟨5, 5, 3, 5, 4, 4, 650313895706126909073212163332661875821038796800000⟩, + ⟨5, 5, 4, 5, 5, 4, 76721037052140482574815772310529903477328445440000⟩, + ⟨5, 5, 5, 5, 6, 4, -22815790629569428462439362836010220981846016000000⟩, + ⟨5, 5, 6, 5, 7, 4, 6750893216382915768024659789400758532911923200000⟩, + ⟨5, 5, 7, 5, 8, 4, 344618296702149818616029345236790606089420800000⟩, + ⟨5, 5, 0, 6, 0, 4, -75069818261985712195241923577296503616883077939200000⟩, + ⟨5, 5, 1, 6, 1, 4, -21801934408302145275256684989753458628447594086400000⟩, + ⟨5, 5, 2, 6, 2, 4, -667808232500460859096121085897322210141824614400000⟩, + ⟨5, 5, 3, 6, 3, 4, 865071889459821578046928371478270088760734515200000⟩, + ⟨5, 5, 4, 6, 4, 4, -148902066456177811064032262483808014707646791680000⟩, + ⟨5, 5, 5, 6, 5, 4, 46247050502549133789988662057093856496084582400000⟩, + ⟨5, 5, 6, 6, 6, 4, -4395876545541218081930790591589975325461708800000⟩, + ⟨5, 5, 7, 6, 7, 4, -1138750229287288659960227532790153314356428800000⟩, + ⟨5, 5, 8, 6, 8, 4, 1501972981323334953699548114234584444226764800000⟩, + ⟨5, 5, 1, 7, 0, 4, 136559398399232135985486758665158074413082895974400000⟩, + ⟨5, 5, 2, 7, 1, 4, 9849746401078241271072565802060634692709148262400000⟩, + ⟨5, 5, 3, 7, 2, 4, 3184307854220450064286101660094929882508060262400000⟩, + ⟨5, 5, 4, 7, 3, 4, 541951119274712534951623408939121812763175813120000⟩, + ⟨5, 5, 5, 7, 4, 4, 139852438875044706571985155405305145692310732800000⟩, + ⟨5, 5, 6, 7, 5, 4, 4542875135787899908307992379053038228209664000000⟩, + ⟨5, 5, 7, 7, 6, 4, 2851865487455569558417824244197540100256563200000⟩, + ⟨5, 5, 8, 7, 7, 4, 1137290277788470203704682208984066156815974400000⟩ +] + +def collectedFourData_9_6_30 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 6, 5, 6566891357375989856085892473436817959000473600000000⟩, + ⟨5, 6, 1, 0, 7, 5, -5809379347038036385576711132943207186049269760000000⟩, + ⟨5, 6, 2, 0, 8, 5, 882964915189319759782080195246817702450298880000000⟩, + ⟨5, 6, 0, 1, 5, 5, 10028175862727552044993225186299808759016325120000000⟩, + ⟨5, 6, 1, 1, 6, 5, -2837922147028403199742041666275884828207349760000000⟩, + ⟨5, 6, 2, 1, 7, 5, 404762018442643204732532904631721804169216000000000⟩, + ⟨5, 6, 3, 1, 8, 5, 3071593263538171724740392973359252907229184000000⟩, + ⟨5, 6, 0, 2, 4, 5, 2857527773906189513982963521551325169765580800000000⟩, + ⟨5, 6, 1, 2, 5, 5, -1688569125434634351601291334679852125540843520000000⟩, + ⟨5, 6, 2, 2, 6, 5, 852664503312896190658832313031972461540802560000000⟩, + ⟨5, 6, 3, 2, 7, 5, -110362329715151021045326944088143583009308672000000⟩, + ⟨5, 6, 4, 2, 8, 5, 6152119544679043024877608052604986946748416000000⟩, + ⟨5, 6, 0, 3, 3, 5, 508241855138088600959268459131812709274746880000000⟩, + ⟨5, 6, 1, 3, 4, 5, -920705012545417071943613356159874524690513920000000⟩, + ⟨5, 6, 2, 3, 5, 5, -211309802252373849022166739262926099327221760000000⟩, + ⟨5, 6, 3, 3, 6, 5, 121183810111652588045526168165841329746608128000000⟩, + ⟨5, 6, 4, 3, 7, 5, 37088911656272425298810581321242131010945024000000⟩, + ⟨5, 6, 5, 3, 8, 5, -4381837964936861002109759411058423764090880000000⟩, + ⟨5, 6, 0, 4, 2, 5, -3766967950522383458966237225246897038719713280000000⟩, + ⟨5, 6, 1, 4, 3, 5, 2901628776217388448825215249766936501855191040000000⟩, + ⟨5, 6, 2, 4, 4, 5, -26694452051053861781678764449555408538828800000000⟩, + ⟨5, 6, 3, 4, 5, 5, 226700766518681981729381716275719818230890496000000⟩, + ⟨5, 6, 4, 4, 6, 5, -43977578662042730602463650438324256124174336000000⟩, + ⟨5, 6, 5, 4, 7, 5, -2618290040920662126472921200357257143910400000000⟩, + ⟨5, 6, 6, 4, 8, 5, 1242219126415210999966165904421911160422400000000⟩, + ⟨5, 6, 0, 5, 1, 5, -2903539004682023887031139769504596295239598080000000⟩, + ⟨5, 6, 1, 5, 2, 5, 587688925652599952870950400652401334602956800000000⟩, + ⟨5, 6, 2, 5, 3, 5, -445140675946147301331787366430027074680913920000000⟩, + ⟨5, 6, 3, 5, 4, 5, -232073385731430491081272983623730223040692224000000⟩, + ⟨5, 6, 4, 5, 5, 5, -22815790629569428462439362836010220981846016000000⟩, + ⟨5, 6, 5, 5, 6, 5, 5815804396818301024228061771038415074099200000000⟩, + ⟨5, 6, 6, 5, 7, 5, -1505717715496611625474059655275517166223360000000⟩, + ⟨5, 6, 7, 5, 8, 5, -68323189282330136841141915670703851438080000000⟩, + ⟨5, 6, 0, 6, 0, 5, 66974222007763170037915823470286123829968240640000000⟩, + ⟨5, 6, 1, 6, 1, 5, 12967196218720804144420177713823875350837329920000000⟩, + ⟨5, 6, 2, 6, 2, 5, 297895598108476889343741804119076548892426240000000⟩, + ⟨5, 6, 3, 6, 3, 5, -308712705685054174314665065694671766537895936000000⟩, + ⟨5, 6, 4, 6, 4, 5, 44281444869749741664334037707352852662321152000000⟩, + ⟨5, 6, 5, 6, 5, 5, -11788493505196539405201717335386682692730880000000⟩, + ⟨5, 6, 6, 6, 6, 5, 980455323111131835482889426843281381130240000000⟩, + ⟨5, 6, 7, 6, 7, 5, 225765863871518899587104713530883839098880000000⟩, + ⟨5, 6, 8, 6, 8, 5, -267999774689077843282874426869146275807232000000⟩, + ⟨5, 6, 1, 7, 0, 5, -81221807266743979595377128192363601731067576320000000⟩, + ⟨5, 6, 2, 7, 1, 5, -4393770475664202701421695081606177189045207040000000⟩, + ⟨5, 6, 3, 7, 2, 5, -1136363700390730929820986010147585504032325632000000⟩, + ⟨5, 6, 4, 7, 3, 5, -161168875499287463744927287391367345437933568000000⟩, + ⟨5, 6, 5, 7, 4, 5, -35648750557043353727934547626184431485583360000000⟩, + ⟨5, 6, 6, 7, 5, 5, -1013241855854727490429052232642055058227200000000⟩, + ⟨5, 6, 7, 7, 6, 5, -565403947996345794240324679612494061240320000000⟩, + ⟨5, 6, 8, 7, 7, 5, -202928775679337469996116010171199333072896000000⟩ +] + +def collectedFourData_9_6_31 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 6, 6, -4533799730473311960224628837943269612249415680000000⟩, + ⟨5, 7, 1, 0, 7, 6, 3008108527054574735998893665999464390528598016000000⟩, + ⟨5, 7, 2, 0, 8, 6, -365760833549315386548556679389859218190657126400000⟩, + ⟨5, 7, 0, 1, 5, 6, -6923480007401923864144036452984929394314182656000000⟩, + ⟨5, 7, 1, 1, 6, 6, 1469481901529759483288400195970986136112726016000000⟩, + ⟨5, 7, 2, 1, 7, 6, -167669281879610627266513280846198810848788480000000⟩, + ⟨5, 7, 3, 1, 8, 6, -1060318189573154063061341773226553533634969600000⟩, + ⟨5, 7, 0, 2, 4, 6, -1972844980388506134323823870789008686621655040000000⟩, + ⟨5, 7, 1, 2, 5, 6, 874344552371293525358853980991679929287442432000000⟩, + ⟨5, 7, 2, 2, 6, 6, -353209141274620670281686075439746773351713996800000⟩, + ⟨5, 7, 3, 2, 7, 6, 38097226943989941890025227614876292168338636800000⟩, + ⟨5, 7, 4, 2, 8, 6, -1820331487733953095185477242978999167300403200000⟩, + ⟨5, 7, 0, 3, 3, 6, -350891565040458532353256360186484638240210944000000⟩, + ⟨5, 7, 1, 3, 4, 6, 476742941662409005622030887550657262960771072000000⟩, + ⟨5, 7, 2, 3, 5, 6, 87533318798287103020062577166813200869280972800000⟩, + ⟨5, 7, 3, 3, 6, 6, -41832816756197942589350995210980634230207283200000⟩, + ⟨5, 7, 4, 3, 7, 6, -10974122535068157473838572505793509116923084800000⟩, + ⟨5, 7, 5, 3, 8, 6, 1134462337462822821011287724399659585634304000000⟩, + ⟨5, 7, 0, 4, 2, 6, 2600724962443160496104839451541749868489867264000000⟩, + ⟨5, 7, 1, 4, 3, 6, -1502469324633915685737424029259918068903051264000000⟩, + ⟨5, 7, 2, 4, 4, 6, 11057953566866474130854559535803659886526464000000⟩, + ⟨5, 7, 3, 4, 5, 6, -78257414216701012272277192700665948528862822400000⟩, + ⟨5, 7, 4, 4, 6, 6, 13012388756660548794219914057265207571591987200000⟩, + ⟨5, 7, 5, 4, 7, 6, 677877973523214226496538960900036828856320000000⟩, + ⟨5, 7, 6, 4, 8, 6, -285877159325124491742222203692793242583040000000⟩, + ⟨5, 7, 0, 5, 1, 6, 2004611259794958546881832083719556348724117504000000⟩, + ⟨5, 7, 1, 5, 2, 6, -304306529648898344772290826432488131138682880000000⟩, + ⟨5, 7, 2, 5, 3, 6, 184395803139990849349176519707149137281128857600000⟩, + ⟨5, 7, 3, 5, 4, 6, 80112049706546248105892964534184441204545945600000⟩, + ⟨5, 7, 4, 5, 5, 6, 6750893216382915768024659789400758532911923200000⟩, + ⟨5, 7, 5, 5, 6, 6, -1505717715496611625474059655275517166223360000000⟩, + ⟨5, 7, 6, 5, 7, 6, 346517207872880196008678768003816626323456000000⟩, + ⟨5, 7, 7, 5, 8, 6, 14151154951210340928931002101555591852851200000⟩, + ⟨5, 7, 0, 6, 0, 6, -46239185812994553810387341519314552879507832832000000⟩, + ⟨5, 7, 1, 6, 1, 6, -6714440766794101427006028109929430808549916672000000⟩, + ⟨5, 7, 2, 6, 2, 6, -123400760778208457633031692230739213132444467200000⟩, + ⟨5, 7, 3, 6, 3, 6, 106568047623971715315699260394783368102176358400000⟩, + ⟨5, 7, 4, 6, 4, 6, -13102298782291599027673809589349736922900070400000⟩, + ⟨5, 7, 5, 6, 5, 6, 3052053043513961869688024030877255733346304000000⟩, + ⟨5, 7, 6, 6, 6, 6, -225636344390434668626817004821278940463104000000⟩, + ⟨5, 7, 7, 6, 7, 6, -46760810727639460941622445259306956960563200000⟩, + ⟨5, 7, 8, 6, 8, 6, 50462120858648664565941670147435818437836800000⟩, + ⟨5, 7, 1, 7, 0, 6, 42056818194605685797836720759435527178432806912000000⟩, + ⟨5, 7, 2, 7, 1, 6, 1820082682740268472975571204869043662567453491200000⟩, + ⟨5, 7, 3, 7, 2, 6, 392274301352977979414840849905220193669139660800000⟩, + ⟨5, 7, 4, 7, 3, 6, 47687756517633132147109407705231935042853273600000⟩, + ⟨5, 7, 5, 7, 4, 6, 9229498034429315424440305828443363515301888000000⟩, + ⟨5, 7, 6, 7, 5, 6, 233181648311094486972794386738169637765120000000⟩, + ⟨5, 7, 7, 7, 6, 6, 117106929026096068360205026495500454251724800000⟩, + ⟨5, 7, 8, 7, 7, 6, 38209794825046412763694899949455760844390400000⟩ +] + +def collectedFourData_9_6_32 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 6, 7, -462881070881911715672398509368277458579619840000000⟩, + ⟨5, 8, 1, 0, 7, 7, 245691751573979752922518859373355456105178726400000⟩, + ⟨5, 8, 2, 0, 8, 7, -24895051448349275267897796406620367449017548800000⟩, + ⟨5, 8, 0, 1, 5, 7, -706856947940473921731166344083316486048841728000000⟩, + ⟨5, 8, 1, 1, 6, 7, 120022126544292352571748238574901800254989926400000⟩, + ⟨5, 8, 2, 1, 7, 7, -11412198944854729611227196129732158721884160000000⟩, + ⟨5, 8, 3, 1, 8, 7, -61859335687186366012595417352488894437785600000⟩, + ⟨5, 8, 0, 2, 4, 7, -201418821186197807525501103258759415222763520000000⟩, + ⟨5, 8, 1, 2, 5, 7, 71413395700059132641290468779748684467064012800000⟩, + ⟨5, 8, 2, 2, 6, 7, -24040736288603659084249817403426226805774745600000⟩, + ⟨5, 8, 3, 2, 7, 7, 2222605604104467133900882758114442272885964800000⟩, + ⟨5, 8, 4, 2, 8, 7, -92923931193845623769858330056138613902540800000⟩, + ⟨5, 8, 0, 3, 3, 7, -35824490062423039861669304701700593598595072000000⟩, + ⟨5, 8, 1, 3, 4, 7, 38938690986079521376152186316472305643736268800000⟩, + ⟨5, 8, 2, 3, 5, 7, 5957845332377018278448072748872110616189337600000⟩, + ⟨5, 8, 3, 3, 6, 7, -2440541226123771667078660269736572816143155200000⟩, + ⟨5, 8, 4, 3, 7, 7, -560204893577353176858005177766351094362931200000⟩, + ⟨5, 8, 5, 3, 8, 7, 51477168806892180699670244738463392858112000000⟩, + ⟨5, 8, 0, 4, 2, 7, 265522613977334797126877283580822365753311232000000⟩, + ⟨5, 8, 1, 4, 3, 7, -122716423538393145921525428135081584692402585600000⟩, + ⟨5, 8, 2, 4, 4, 7, 752645711923885467389208522233557064613888000000⟩, + ⟨5, 8, 3, 4, 5, 7, -4565565038538942247738513342398905918580326400000⟩, + ⟨5, 8, 4, 4, 6, 7, 664253915091435225432954220473229169708236800000⟩, + ⟨5, 8, 5, 4, 7, 7, 30759274875153825905982213527754988584960000000⟩, + ⟨5, 8, 6, 4, 8, 7, -11674721735913823004093037332426819371008000000⟩, + ⟨5, 8, 0, 5, 1, 7, 204662019012242423589820308372907710430052352000000⟩, + ⟨5, 8, 1, 5, 2, 7, -24854689786756020892474619322927612797386752000000⟩, + ⟨5, 8, 2, 5, 3, 7, 12550668592597725369223082081856584720528179200000⟩, + ⟨5, 8, 3, 5, 4, 7, 4673765124580935483027457836318618289805721600000⟩, + ⟨5, 8, 4, 5, 5, 7, 344618296702149818616029345236790606089420800000⟩, + ⟨5, 8, 5, 5, 6, 7, -68323189282330136841141915670703851438080000000⟩, + ⟨5, 8, 6, 5, 7, 7, 14151154951210340928931002101555591852851200000⟩, + ⟨5, 8, 7, 5, 8, 7, 525371223612255097907711553078410241638400000⟩, + ⟨5, 8, 0, 6, 0, 7, -4720818103624572537761182537232608403669385216000000⟩, + ⟨5, 8, 1, 6, 1, 7, -548411966521927634600434690855102152493026508800000⟩, + ⟨5, 8, 2, 6, 2, 7, -8399117692640360762255513799488833650583142400000⟩, + ⟨5, 8, 3, 6, 3, 7, 6217217337517451914690537148305664998008422400000⟩, + ⟨5, 8, 4, 6, 4, 7, -668843624763368168673253539605272883468697600000⟩, + ⟨5, 8, 5, 6, 5, 7, 138489436396742353704217482597009941594112000000⟩, + ⟨5, 8, 6, 6, 6, 7, -9214592521087894692377566114443114106060800000⟩, + ⟨5, 8, 7, 6, 7, 7, -1736026807266344288718279750252329592422400000⟩, + ⟨5, 8, 8, 6, 8, 7, 1717320417796315212143264759158147960012800000⟩, + ⟨5, 8, 1, 7, 0, 7, 3435053368230296128395012616246001201834675404800000⟩, + ⟨5, 8, 2, 7, 1, 7, 123881640325929769469772920348550135409960550400000⟩, + ⟨5, 8, 3, 7, 2, 7, 22885420553446242850459267732760305932750028800000⟩, + ⟨5, 8, 4, 7, 3, 7, 2434355410151020298884576036923978713294438400000⟩, + ⟨5, 8, 5, 7, 4, 7, 418796122737540512143875128710797736280064000000⟩, + ⟨5, 8, 6, 7, 5, 7, 9522729498153698298691570519145629876224000000⟩, + ⟨5, 8, 7, 7, 6, 7, 4347674151547004060976923179380033296793600000⟩, + ⟨5, 8, 8, 7, 7, 7, 1300350831402162327565339141684318332518400000⟩ +] + +def collectedFourData_9_6_33 : List CollectedFourTerm := [ + ⟨6, 0, 3, 1, 8, 0, 1684388616435610782438564603461337943802432716800000⟩, + ⟨6, 0, 3, 2, 7, 0, -60520074080831753249937809854251724722976220774400000⟩, + ⟨6, 0, 4, 2, 8, 0, 20242055322269658362403862343602209988730368819200000⟩, + ⟨6, 0, 3, 3, 6, 0, 66454316289662486012033597790043656816757938585600000⟩, + ⟨6, 0, 4, 3, 7, 0, 122032056779255165821723614404775166287700348108800000⟩, + ⟨6, 0, 5, 3, 8, 0, -50460807936779579256124476946531970074118455296000000⟩, + ⟨6, 0, 3, 4, 5, 0, 124317303008224211701855752915182174332968448819200000⟩, + ⟨6, 0, 4, 4, 6, 0, -144697542652022101079757446290562452380590486323200000⟩, + ⟨6, 0, 5, 4, 7, 0, -30151966351769021134990650740318438640247111680000000⟩, + ⟨6, 0, 6, 4, 8, 0, 38147390055661445992218497628560068489122938880000000⟩, + ⟨6, 0, 3, 5, 4, 0, -127263519471784436565733599157568784289460178124800000⟩, + ⟨6, 0, 4, 5, 5, 0, -75069818261985712195241923577296503616883077939200000⟩, + ⟨6, 0, 5, 5, 6, 0, 66974222007763170037915823470286123829968240640000000⟩, + ⟨6, 0, 6, 5, 7, 0, -46239185812994553810387341519314552879507832832000000⟩, + ⟨6, 0, 7, 5, 8, 0, -4720818103624572537761182537232608403669385216000000⟩, + ⟨6, 0, 3, 6, 3, 0, -169290697885553621546513011763672709255887270707200000⟩, + ⟨6, 0, 4, 6, 4, 0, 145697340614708551587513933918924811292264261222400000⟩, + ⟨6, 0, 5, 6, 5, 0, -135755112669545620596169328726485841089759543296000000⟩, + ⟨6, 0, 6, 6, 6, 0, 30108867950539337707091735679559982833874239488000000⟩, + ⟨6, 0, 7, 6, 7, 0, 15599382706520496161943626050621041692299493376000000⟩, + ⟨6, 0, 8, 6, 8, 0, -37035103349506776683006767770576634898507680972800000⟩, + ⟨6, 0, 3, 7, 2, 0, -623154798452697973021961345617935884400183371366400000⟩, + ⟨6, 0, 4, 7, 3, 0, -530287045040631939421510399330983506755056146841600000⟩, + ⟨6, 0, 5, 7, 4, 0, -410527447486536395138559162180262514444375949312000000⟩, + ⟨6, 0, 6, 7, 5, 0, -31115711772653059246206775584167828526873968640000000⟩, + ⟨6, 0, 7, 7, 6, 0, -39066812038475212174127736460117433458007998464000000⟩, + ⟨6, 0, 8, 7, 7, 0, -28042889918815403002180750816250457783133431398400000⟩ +] + +def collectedFourData_9_6_34 : List CollectedFourTerm := [ + ⟨6, 1, 2, 0, 8, 1, 56248596942742023678648142020373229550684654796800000⟩, + ⟨6, 1, 2, 1, 7, 1, 25785051298702317579830847244377755133683957760000000⟩, + ⟨6, 1, 3, 1, 8, 1, 978367364776636375260713811447603351824577331200000⟩, + ⟨6, 1, 2, 2, 6, 1, 54318332641730034202957333476735199553888295321600000⟩, + ⟨6, 1, 3, 2, 7, 1, -35152734242438780678082816852014098590402714009600000⟩, + ⟨6, 1, 4, 2, 8, 1, 5878740253309265817172235514912431537301907046400000⟩, + ⟨6, 1, 2, 3, 5, 1, -13461327502911938447691931228387603656069454233600000⟩, + ⟨6, 1, 3, 3, 6, 1, 38599604433289391409605908729250817256246896230400000⟩, + ⟨6, 1, 4, 3, 7, 1, 35440806428044615172786387099319382033259141529600000⟩, + ⟨6, 1, 5, 3, 8, 1, -9769955936114630395053591643470015776673497088000000⟩, + ⟨6, 1, 2, 4, 4, 1, -1700549419571370155279429811592840027589050368000000⟩, + ⟨6, 1, 3, 4, 5, 1, 72208984882405497990196883345284771315274534092800000⟩, + ⟨6, 1, 4, 4, 6, 1, -42023364475618774301218703015698128825781479014400000⟩, + ⟨6, 1, 5, 4, 7, 1, -5837864962706634089995147271159654135145431040000000⟩, + ⟨6, 1, 6, 4, 8, 1, 5539422600831063809074260599451737546796564480000000⟩, + ⟨6, 1, 2, 5, 3, 1, -28357342441795633196949021917403247073318613811200000⟩, + ⟨6, 1, 3, 5, 4, 1, -73920277638357904969602877866795290781405098803200000⟩, + ⟨6, 1, 4, 5, 5, 1, -21801934408302145275256684989753458628447594086400000⟩, + ⟨6, 1, 5, 5, 6, 1, 12967196218720804144420177713823875350837329920000000⟩, + ⟨6, 1, 6, 5, 7, 1, -6714440766794101427006028109929430808549916672000000⟩, + ⟨6, 1, 7, 5, 8, 1, -548411966521927634600434690855102152493026508800000⟩, + ⟨6, 1, 2, 6, 2, 1, 18977208653220404738525207993691064559118739046400000⟩, + ⟨6, 1, 3, 6, 3, 1, -98331520621398282905544960656681999301056711884800000⟩, + ⟨6, 1, 4, 6, 4, 1, 42313727901409590002541238266917348781914377420800000⟩, + ⟨6, 1, 5, 6, 5, 1, -26284190109390148136150733561349173759430361088000000⟩, + ⟨6, 1, 6, 6, 6, 1, 4372140357893319190862269993802074803350274048000000⟩, + ⟨6, 1, 7, 6, 7, 1, 1812162205538642099458149031279622199534472396800000⟩, + ⟨6, 1, 8, 6, 8, 1, -3585270852851357707651108595322585187509023539200000⟩, + ⟨6, 1, 2, 7, 1, 1, -279901749540710467794649761470878261003843692134400000⟩, + ⟨6, 1, 3, 7, 2, 1, -361955852741532780716268209254896695568359856537600000⟩, + ⟨6, 1, 4, 7, 3, 1, -154007078226839032578441783111228995344874550067200000⟩, + ⟨6, 1, 5, 7, 4, 1, -79484162788952877473583604467352603263642894336000000⟩, + ⟨6, 1, 6, 7, 5, 1, -4518345207440979122221449440010366812097085440000000⟩, + ⟨6, 1, 7, 7, 6, 1, -4538346266574673212811171106337107553943761715200000⟩, + ⟨6, 1, 8, 7, 7, 1, -2714758344450172118799602923992658184941181337600000⟩ +] + +def collectedFourData_9_6_35 : List CollectedFourTerm := [ + ⟨6, 2, 1, 0, 7, 2, -8501899882974526612610205369811385687578194739200000⟩, + ⟨6, 2, 2, 0, 8, 2, 5168799529640727982734095361110097262247568998400000⟩, + ⟨6, 2, 1, 1, 6, 2, -4153237123689183030157903883761106309296108339200000⟩, + ⟨6, 2, 2, 1, 7, 2, 2369441519762066381042626932511370067711098880000000⟩, + ⟨6, 2, 3, 1, 8, 2, 44952097027602740465342004461245120142691532800000⟩, + ⟨6, 2, 1, 2, 5, 2, -2471184061554987593886219655141270056996333158400000⟩, + ⟨6, 2, 2, 2, 6, 2, 4991423563777806128338495879518069630436166860800000⟩, + ⟨6, 2, 3, 2, 7, 2, -1615128608477657434897955699372456283233216102400000⟩, + ⟨6, 2, 4, 2, 8, 2, 180069853636327163133512278836158205834716774400000⟩, + ⟨6, 2, 1, 3, 4, 2, -1347431691202087724388102566547642293625972326400000⟩, + ⟨6, 2, 2, 3, 5, 2, -1236989134790660065394767883794171144444890316800000⟩, + ⟨6, 2, 3, 3, 6, 2, 1773498612260482230472925093584980947802626457600000⟩, + ⟨6, 2, 4, 3, 7, 2, 1085576254650634777353461574434621040992295321600000⟩, + ⟨6, 2, 5, 3, 8, 2, -224445347937323154499485244217069676722651136000000⟩, + ⟨6, 2, 1, 4, 3, 2, 4246470385091313496702743306749788995124513996800000⟩, + ⟨6, 2, 2, 4, 4, 2, -156266991849749474796258716000749867115741184000000⟩, + ⟨6, 2, 3, 4, 5, 2, 3317716239890778177338200586521802837991830323200000⟩, + ⟨6, 2, 4, 4, 6, 2, -1287204530965796816847352680988529756494784102400000⟩, + ⟨6, 2, 5, 4, 7, 2, -134113361547757248994516603916084736562298880000000⟩, + ⟨6, 2, 6, 4, 8, 2, 101805792463775723916423326035414998684008448000000⟩, + ⟨6, 2, 1, 5, 2, 2, 860069916208649828997929955768833037677101056000000⟩, + ⟨6, 2, 2, 5, 3, 2, -2605814655683198559672852972059563157918161305600000⟩, + ⟨6, 2, 3, 5, 4, 2, -3396343349479382179808165523333944846100253900800000⟩, + ⟨6, 2, 4, 5, 5, 2, -667808232500460859096121085897322210141824614400000⟩, + ⟨6, 2, 5, 5, 6, 2, 297895598108476889343741804119076548892426240000000⟩, + ⟨6, 2, 6, 5, 7, 2, -123400760778208457633031692230739213132444467200000⟩, + ⟨6, 2, 7, 5, 8, 2, -8399117692640360762255513799488833650583142400000⟩, + ⟨6, 2, 1, 6, 1, 2, 18977208653220404738525207993691064559118739046400000⟩, + ⟨6, 2, 2, 6, 2, 2, 1743854824690279461085431314455426933596566323200000⟩, + ⟨6, 2, 3, 6, 3, 2, -4517943070243312411196040651762856397353726771200000⟩, + ⟨6, 2, 4, 6, 4, 2, 1296098562225991041872385322617984200345439436800000⟩, + ⟨6, 2, 5, 6, 5, 2, -603827103512906038574148593598485776759259136000000⟩, + ⟨6, 2, 6, 6, 6, 2, 80352998132225351895414638435679701769702604800000⟩, + ⟨6, 2, 7, 6, 7, 2, 27753886807036348157143655171824357040612966400000⟩, + ⟨6, 2, 8, 6, 8, 2, -47065418530011903422337616285703790597557452800000⟩, + ⟨6, 2, 1, 7, 0, 2, -118866342245009008761183540882640983557830764134400000⟩, + ⟨6, 2, 2, 7, 1, 2, -25720748783198257201066263052923424297584898867200000⟩, + ⟨6, 2, 3, 7, 2, 2, -16630434740493112354785248223326862088344069734400000⟩, + ⟨6, 2, 4, 7, 3, 2, -4717342634700410808714389008822636771038933811200000⟩, + ⟨6, 2, 5, 7, 4, 2, -1825990893851258459941168632273468132836769792000000⟩, + ⟨6, 2, 6, 7, 5, 2, -83040011137518275698435882654810242803564544000000⟩, + ⟨6, 2, 7, 7, 6, 2, -69506332373933630123973653824046770305997209600000⟩, + ⟨6, 2, 8, 7, 7, 2, -35637820107168024800832424348332777336628838400000⟩ +] + +def collectedFourData_9_6_36 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 6, 3, -16599127059660804895701488488490053494613475328000000⟩, + ⟨6, 3, 1, 0, 7, 3, 44053093315275559314379492141620361200795018854400000⟩, + ⟨6, 3, 2, 0, 8, 3, -13391219088759154735709136168693378235178051174400000⟩, + ⟨6, 3, 0, 1, 5, 3, -25348213677247771039587316466869066325019957657600000⟩, + ⟨6, 3, 1, 1, 6, 3, 21520241956358313154932298727996753998065854054400000⟩, + ⟨6, 3, 2, 1, 7, 3, -6138700161842366612618457444196144157640622080000000⟩, + ⟨6, 3, 3, 1, 8, 3, -77640643163375390065457007283663271722431283200000⟩, + ⟨6, 3, 0, 2, 4, 3, -7222971115899758437462017305020338326716022784000000⟩, + ⟨6, 3, 1, 2, 5, 3, 12804585276393063169637868116471530232751115468800000⟩, + ⟨6, 3, 2, 2, 6, 3, -12931677099109625435786703010960905521765076172800000⟩, + ⟨6, 3, 3, 2, 7, 3, 2789627898266269222643888597320449855801891225600000⟩, + ⟨6, 3, 4, 2, 8, 3, -233260629232844268670954308970007115024511795200000⟩, + ⟨6, 3, 0, 3, 3, 3, -1284682610288511546946805374727029804312716902400000⟩, + ⟨6, 3, 1, 3, 4, 3, 6981796403807756107254174366639275578684656844800000⟩, + ⟨6, 3, 2, 3, 5, 3, 3204765907326210584127820754119110043378699468800000⟩, + ⟨6, 3, 3, 3, 6, 3, -3063162388635748739505643593194358661116749414400000⟩, + ⟨6, 3, 4, 3, 7, 3, -1406244272022646812659430132443765022091168972800000⟩, + ⟨6, 3, 5, 3, 8, 3, 232595349109264797016050325087633349059962470400000⟩, + ⟨6, 3, 0, 4, 2, 3, 9521762465303872579895130152734650691532252774400000⟩, + ⟨6, 3, 1, 4, 3, 3, -22003335573216873203791134118997760739668236697600000⟩, + ⟨6, 3, 2, 4, 4, 3, 404853295663952531360281035404269307710930944000000⟩, + ⟨6, 3, 3, 4, 5, 3, -5730313816962156119279450683452838874259967180800000⟩, + ⟨6, 3, 4, 4, 6, 3, 1667431459409354937059641771779208393815962419200000⟩, + ⟨6, 3, 5, 4, 7, 3, 138983251094732774233481406925428379543928832000000⟩, + ⟨6, 3, 6, 4, 8, 3, -87918781628708710126484836639385969340973056000000⟩, + ⟨6, 3, 0, 5, 1, 3, 7339273674333529975387015773616140424785061478400000⟩, + ⟨6, 3, 1, 5, 2, 3, -4456502757962952646615018079296404233536929792000000⟩, + ⟨6, 3, 2, 5, 3, 3, 6751090801422258057742791875196502762973665689600000⟩, + ⟨6, 3, 3, 5, 4, 3, 5866117478241581230556463922160725567508525875200000⟩, + ⟨6, 3, 4, 5, 5, 3, 865071889459821578046928371478270088760734515200000⟩, + ⟨6, 3, 5, 5, 6, 3, -308712705685054174314665065694671766537895936000000⟩, + ⟨6, 3, 6, 5, 7, 3, 106568047623971715315699260394783368102176358400000⟩, + ⟨6, 3, 7, 5, 8, 3, 6217217337517451914690537148305664998008422400000⟩, + ⟨6, 3, 0, 6, 0, 3, -169290697885553621546513011763672709255887270707200000⟩, + ⟨6, 3, 1, 6, 1, 3, -98331520621398282905544960656681999301056711884800000⟩, + ⟨6, 3, 2, 6, 2, 3, -4517943070243312411196040651762856397353726771200000⟩, + ⟨6, 3, 3, 6, 3, 3, 7803329075700570458536130806271864240375385292800000⟩, + ⟨6, 3, 4, 6, 4, 3, -1678952695675584444153993782655725923954222694400000⟩, + ⟨6, 3, 5, 6, 5, 3, 625753116444368378467519572900901992519853670400000⟩, + ⟨6, 3, 6, 6, 6, 3, -69392296106460202239296529407184460060400025600000⟩, + ⟨6, 3, 7, 6, 7, 3, -20544056239550030549421729455508488890771046400000⟩, + ⟨6, 3, 8, 6, 8, 3, 30484028613668369101911554155224429359215411200000⟩, + ⟨6, 3, 1, 7, 0, 3, 615912929938292072970368730741236680615097322700800000⟩, + ⟨6, 3, 2, 7, 1, 3, 66636784829355538165698322141516977426540999475200000⟩, + ⟨6, 3, 3, 7, 2, 3, 28723857944726581876065102540525360463230900633600000⟩, + ⟨6, 3, 4, 7, 3, 3, 6110796943831987045009149270332034207679355289600000⟩, + ⟨6, 3, 5, 7, 4, 3, 1892295800865852971482280808469670706396581068800000⟩, + ⟨6, 3, 6, 7, 5, 3, 71712782042758049069012291646353064295661568000000⟩, + ⟨6, 3, 7, 7, 6, 3, 51450163042854531682853634174604321761106329600000⟩, + ⟨6, 3, 8, 7, 7, 3, 23082432108468944965491974959546839894432153600000⟩ +] + +def collectedFourData_9_6_37 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 6, 4, 14285774111187024808969856220185385447588888576000000⟩, + ⟨6, 4, 1, 0, 7, 4, -18956796274259312538362308441822570049052239462400000⟩, + ⟨6, 4, 2, 0, 8, 4, 3841646416863607384598682639486078086966516121600000⟩, + ⟨6, 4, 0, 1, 5, 4, 21815536046789124650222719447058916119296553779200000⟩, + ⟨6, 4, 1, 1, 6, 4, -9260526601840068438586195397849475342487938662400000⟩, + ⟨6, 4, 2, 1, 7, 4, 1761058147479459624640394305951593221188485120000000⟩, + ⟨6, 4, 3, 1, 8, 4, 16705045483607544236245727072963531514681753600000⟩, + ⟨6, 4, 0, 2, 4, 4, 6216334955597416502564743275857982021936611328000000⟩, + ⟨6, 4, 1, 2, 5, 4, -5510031105506837645566428141911581432453319884800000⟩, + ⟨6, 4, 2, 2, 6, 4, 3709813920790311423359898777535985003464438579200000⟩, + ⟨6, 4, 3, 2, 7, 4, -600212195883264966460649526579051170521468108800000⟩, + ⟨6, 4, 4, 2, 8, 4, 40150408467586681378600919321701868096905543680000⟩, + ⟨6, 4, 0, 3, 3, 4, 1105641610500860654250811675135396624603073740800000⟩, + ⟨6, 4, 1, 3, 4, 4, -3004385891999240444656302185008945812441189580800000⟩, + ⟨6, 4, 2, 3, 5, 4, -919376897888330270511322181604549994199855923200000⟩, + ⟨6, 4, 3, 3, 6, 4, 659065470621630906967361063261213392708514611200000⟩, + ⟨6, 4, 4, 3, 7, 4, 242052343392046868971187529413481324015538667520000⟩, + ⟨6, 4, 5, 3, 8, 4, -33363246600707516841077211104194728005782732800000⟩, + ⟨6, 4, 0, 4, 2, 4, -8194753087364464368658647530342937355778575564800000⟩, + ⟨6, 4, 1, 4, 3, 4, 9468410012220407645901888831789957877501368729600000⟩, + ⟨6, 4, 2, 4, 4, 4, -116143511829210316126658190403208460701270016000000⟩, + ⟨6, 4, 3, 4, 5, 4, 1232925811115034669161560773523936737952687718400000⟩, + ⟨6, 4, 4, 4, 6, 4, -287009661283907570994789475498537274509130465280000⟩, + ⟨6, 4, 5, 4, 7, 4, -19935619939947126941491440283956413699457024000000⟩, + ⟨6, 4, 6, 4, 8, 4, 10809413995638134831769763785028151474651136000000⟩, + ⟨6, 4, 0, 5, 1, 4, -6316428898632270347692110833013630019853667532800000⟩, + ⟨6, 4, 1, 5, 2, 4, 1917709030641087207342529301586676489736159232000000⟩, + ⟨6, 4, 2, 5, 3, 4, -1936739561596394682952713022123670377903580774400000⟩, + ⟨6, 4, 3, 5, 4, 4, -1262145125202110330696526874914130962624911769600000⟩, + ⟨6, 4, 4, 5, 5, 4, -148902066456177811064032262483808014707646791680000⟩, + ⟨6, 4, 5, 5, 6, 4, 44281444869749741664334037707352852662321152000000⟩, + ⟨6, 4, 6, 5, 7, 4, -13102298782291599027673809589349736922900070400000⟩, + ⟨6, 4, 7, 5, 8, 4, -668843624763368168673253539605272883468697600000⟩, + ⟨6, 4, 0, 6, 0, 4, 145697340614708551587513933918924811292264261222400000⟩, + ⟨6, 4, 1, 6, 1, 4, 42313727901409590002541238266917348781914377420800000⟩, + ⟨6, 4, 2, 6, 2, 4, 1296098562225991041872385322617984200345439436800000⟩, + ⟨6, 4, 3, 6, 3, 4, -1678952695675584444153993782655725923954222694400000⟩, + ⟨6, 4, 4, 6, 4, 4, 288992774952348083134378885459522849717836840960000⟩, + ⟨6, 4, 5, 6, 5, 4, -89757407510703850522612806988782273689341132800000⟩, + ⟨6, 4, 6, 6, 6, 4, 8531624788550352456608330692255268799617433600000⟩, + ⟨6, 4, 7, 6, 7, 4, 2210114315882971563272047297710665135397273600000⟩, + ⟨6, 4, 8, 6, 8, 4, -2915065922901925733300078983377344995629465600000⟩, + ⟨6, 4, 1, 7, 0, 4, -265037822700948702343645635990430172685582257356800000⟩, + ⟨6, 4, 2, 7, 1, 4, -19116628887499268946156154251752478920233766092800000⟩, + ⟨6, 4, 3, 7, 2, 4, -6180182619322842528084465829301907530011430092800000⟩, + ⟨6, 4, 4, 7, 3, 4, -1051831996527890589099289685464961258426613104640000⟩, + ⟨6, 4, 5, 7, 4, 4, -271429036253485613780777324780273227206859161600000⟩, + ⟨6, 4, 6, 7, 5, 4, -8816923250287780083500371656312224961527808000000⟩, + ⟨6, 4, 7, 7, 6, 4, -5534970337387294719999657785992396900034150400000⟩, + ⟨6, 4, 8, 7, 7, 4, -2207280806281789795924637903320611864497356800000⟩ +] + +def collectedFourData_9_6_38 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 6, 5, -13310928434613363294989822975794160998589399040000000⟩, + ⟨6, 5, 1, 0, 7, 5, 11775470086175320131674277909422803083816075264000000⟩, + ⟨6, 5, 2, 0, 8, 5, -1789748323330844765005473502621835505520607232000000⟩, + ⟨6, 5, 0, 1, 5, 5, -20326867611195181262537352095201580653758906368000000⟩, + ⟨6, 5, 1, 1, 6, 5, 5752398897184394884544128588981751039618187264000000⟩, + ⟨6, 5, 2, 1, 7, 5, -820442728124030978092484882871719278569062400000000⟩, + ⟨6, 5, 3, 1, 8, 5, -6226044544695241016132089359701902127372697600000⟩, + ⟨6, 5, 0, 2, 4, 5, -5792139024146115226050681941926546523679621120000000⟩, + ⟨6, 5, 1, 2, 5, 5, 3422688386691882529918077473979775234634416128000000⟩, + ⟨6, 5, 2, 2, 6, 5, -1728330128316340229684908769222135063651549184000000⟩, + ⟨6, 5, 3, 2, 7, 5, 223701747565163725147345170009969810473798860800000⟩, + ⟨6, 5, 4, 2, 8, 5, -12470196097949580298289900442505503951971942400000⟩, + ⟨6, 5, 0, 3, 3, 5, -1030193830391229209399249078029858908439314432000000⟩, + ⟨6, 5, 1, 3, 4, 5, 1866246579154447201678396861372481886316658688000000⟩, + ⟨6, 5, 2, 3, 5, 5, 428319809517537916530070946323321826064728064000000⟩, + ⟨6, 5, 3, 3, 6, 5, -245636624095839441960661003496423707135652659200000⟩, + ⟨6, 5, 4, 3, 7, 5, -75178318310356257708812610767710712919333273600000⟩, + ⟨6, 5, 5, 3, 8, 5, 8881878561586643355493290568924068977836032000000⟩, + ⟨6, 5, 0, 4, 2, 5, 7635552055930674793560881820357619031727931392000000⟩, + ⟨6, 5, 1, 4, 3, 5, -5881530678996585017227658878495261733846777856000000⟩, + ⟨6, 5, 2, 4, 4, 5, 54109002496849352012432633334529842814648320000000⟩, + ⟨6, 5, 3, 4, 5, 5, -459516918277135342588196250914066420386391654400000⟩, + ⟨6, 5, 4, 4, 6, 5, 89141478127321819239407976144143910699427430400000⟩, + ⟨6, 5, 5, 4, 7, 5, 5307209980961524673378894593981338416578560000000⟩, + ⟨6, 5, 6, 4, 8, 5, -2517947837411448340642391016791451484815360000000⟩, + ⟨6, 5, 0, 5, 1, 5, 5885402665451479531215672228027058102166618112000000⟩, + ⟨6, 5, 1, 5, 2, 5, -1191231102428710504978298140250578064265707520000000⟩, + ⟨6, 5, 2, 5, 3, 5, 902289280939497854539227344580783132207218688000000⟩, + ⟨6, 5, 3, 5, 4, 5, 470407086235677618067290632565820966026451353600000⟩, + ⟨6, 5, 4, 5, 5, 5, 46247050502549133789988662057093856496084582400000⟩, + ⟨6, 5, 5, 5, 6, 5, -11788493505196539405201717335386682692730880000000⟩, + ⟨6, 5, 6, 5, 7, 5, 3052053043513961869688024030877255733346304000000⟩, + ⟨6, 5, 7, 5, 8, 5, 138489436396742353704217482597009941594112000000⟩, + ⟨6, 5, 0, 6, 0, 5, -135755112669545620596169328726485841089759543296000000⟩, + ⟨6, 5, 1, 6, 1, 5, -26284190109390148136150733561349173759430361088000000⟩, + ⟨6, 5, 2, 6, 2, 5, -603827103512906038574148593598485776759259136000000⟩, + ⟨6, 5, 3, 6, 3, 5, 625753116444368378467519572900901992519853670400000⟩, + ⟨6, 5, 4, 6, 4, 5, -89757407510703850522612806988782273689341132800000⟩, + ⟨6, 5, 5, 6, 5, 5, 23894988489999363189234127353005062364332032000000⟩, + ⟨6, 5, 6, 6, 6, 5, -1987358999720508178666011279048020890484736000000⟩, + ⟨6, 5, 7, 6, 7, 5, -457621893439281021987958672237645352927232000000⟩, + ⟨6, 5, 8, 6, 8, 5, 543228999421768933178188681473476038282444800000⟩, + ⟨6, 5, 1, 7, 0, 5, 164634620099698382874668668011323067264871170048000000⟩, + ⟨6, 5, 2, 7, 1, 5, 8906065469469396619487687930254998230852960256000000⟩, + ⟨6, 5, 3, 7, 2, 5, 2303381473580147270679690249256794236958592204800000⟩, + ⟨6, 5, 4, 7, 3, 5, 326685375302957997936407662336977868250362675200000⟩, + ⟨6, 5, 5, 7, 4, 5, 72259146927290736501481132307097157374050304000000⟩, + ⟨6, 5, 6, 7, 5, 5, 2053816501028020999792799874117642831790080000000⟩, + ⟨6, 5, 7, 7, 6, 5, 1146059996861968437756083085640999158939648000000⟩, + ⟨6, 5, 8, 7, 7, 5, 411331673297349682574505199804363607271014400000⟩ +] + +def collectedFourData_9_6_39 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 6, 6, 2952205472455555155762753747665929054055301120000000⟩, + ⟨6, 6, 1, 0, 7, 6, -1958744316741939065470482383536470432776454144000000⟩, + ⟨6, 6, 2, 0, 8, 6, 238166923685768327047727061802555804764182937600000⟩, + ⟨6, 6, 0, 1, 5, 6, 4508257263528218319790724807760788187097595904000000⟩, + ⟨6, 6, 1, 1, 6, 6, -956860198789075713672967930490735895609606144000000⟩, + ⟨6, 6, 2, 1, 7, 6, 109178658289788194967097371139596681027256320000000⟩, + ⟨6, 6, 3, 1, 8, 6, 690431282344101865220922426040568036877926400000⟩, + ⟨6, 6, 0, 2, 4, 6, 1284627485475938886405986018152955105362575360000000⟩, + ⟨6, 6, 1, 2, 5, 6, -569333655161862004363806676128700286933925888000000⟩, + ⟨6, 6, 2, 2, 6, 6, 229993828969459930880314075975059723812811571200000⟩, + ⟨6, 6, 3, 2, 7, 6, -24807192323355401339938786078012073093313331200000⟩, + ⟨6, 6, 4, 2, 8, 6, 1185317592140381906372315163640359623118028800000⟩, + ⟨6, 6, 0, 3, 3, 6, 228484728072184054685842568621537669463146496000000⟩, + ⟨6, 6, 1, 3, 4, 6, -310433456482514608191616021406332257092763648000000⟩, + ⟨6, 6, 2, 3, 5, 6, -56997740998921933396000597824265603530306355200000⟩, + ⟨6, 6, 3, 3, 6, 6, 27239639573357415189247932472432849310239948800000⟩, + ⟨6, 6, 4, 3, 7, 6, 7145852602546215023321957917913115444589363200000⟩, + ⟨6, 6, 5, 3, 8, 6, -738710600391434963823572241578894857076736000000⟩, + ⟨6, 6, 0, 4, 2, 6, -1693474551791665665664014580598204419723493376000000⟩, + ⟨6, 6, 1, 4, 3, 6, 978340117797348726850791234325810354770149376000000⟩, + ⟨6, 6, 2, 4, 4, 6, -7200439581581292389637418310317340859826176000000⟩, + ⟨6, 6, 3, 4, 5, 6, 50957691174119639828707567647227796501666201600000⟩, + ⟨6, 6, 4, 4, 6, 6, -8473079443480843725572348731512752045870284800000⟩, + ⟨6, 6, 5, 4, 7, 6, -441403498624186783196092854883215873146880000000⟩, + ⟨6, 6, 6, 4, 8, 6, 186150285496085202890832471560883126927360000000⟩, + ⟨6, 6, 0, 5, 1, 6, -1305312250899728496529510919260285125877825536000000⟩, + ⟨6, 6, 1, 5, 2, 6, 198150658507284631234569900926036703361105920000000⟩, + ⟨6, 6, 2, 5, 3, 6, -120070212953779402700317602524313350190818918400000⟩, + ⟨6, 6, 3, 5, 4, 6, -52165345982012929141729753196503831182468710400000⟩, + ⟨6, 6, 4, 5, 5, 6, -4395876545541218081930790591589975325461708800000⟩, + ⟨6, 6, 5, 5, 6, 6, 980455323111131835482889426843281381130240000000⟩, + ⟨6, 6, 6, 5, 7, 6, -225636344390434668626817004821278940463104000000⟩, + ⟨6, 6, 7, 5, 8, 6, -9214592521087894692377566114443114106060800000⟩, + ⟨6, 6, 0, 6, 0, 6, 30108867950539337707091735679559982833874239488000000⟩, + ⟨6, 6, 1, 6, 1, 6, 4372140357893319190862269993802074803350274048000000⟩, + ⟨6, 6, 2, 6, 2, 6, 80352998132225351895414638435679701769702604800000⟩, + ⟨6, 6, 3, 6, 3, 6, -69392296106460202239296529407184460060400025600000⟩, + ⟨6, 6, 4, 6, 4, 6, 8531624788550352456608330692255268799617433600000⟩, + ⟨6, 6, 5, 6, 5, 6, -1987358999720508178666011279048020890484736000000⟩, + ⟨6, 6, 6, 6, 6, 6, 146924189486589112541767786538556180135936000000⟩, + ⟨6, 6, 7, 6, 7, 6, 30448526519318486720365186609016480779468800000⟩, + ⟨6, 6, 8, 6, 8, 6, -32858652390246582905808855561824990606131200000⟩, + ⟨6, 6, 1, 7, 0, 6, -27385499185960157652746360342592265055222366208000000⟩, + ⟨6, 6, 2, 7, 1, 6, -1185155581573617562330798016043365809217391820800000⟩, + ⟨6, 6, 3, 7, 2, 6, -255431295602693612484323446634296281197130547200000⟩, + ⟨6, 6, 4, 7, 3, 6, -31052111723026474460710751691973088334210662400000⟩, + ⟨6, 6, 5, 7, 4, 6, -6009831978708836672296023630348819200212992000000⟩, + ⟨6, 6, 6, 7, 5, 6, -151837350378145920204706215110681642926080000000⟩, + ⟨6, 6, 7, 7, 6, 6, -76254739354623594929657214138492579427123200000⟩, + ⟨6, 6, 8, 7, 7, 6, -24880491439821435887156759230967650556313600000⟩ +] + +def collectedFourData_9_6_40 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 6, 7, 1529535519859803360289411693289353878165258240000000⟩, + ⟨6, 7, 1, 0, 7, 7, -811859210948040351420959666539588800437708390400000⟩, + ⟨6, 7, 2, 0, 8, 7, 82262740592176268168553058338063036739013836800000⟩, + ⟨6, 7, 0, 1, 5, 7, 2335724827275273215003649309734433470187307008000000⟩, + ⟨6, 7, 1, 1, 6, 7, -396598861493381281107641012861084352024831590400000⟩, + ⟨6, 7, 2, 1, 7, 7, 37710255925144577062097067957148339415285760000000⟩, + ⟨6, 7, 3, 1, 8, 7, 204406827412954927750667604835516831865241600000⟩, + ⟨6, 7, 0, 2, 4, 7, 665564571015208389785346181441196334482718720000000⟩, + ⟨6, 7, 1, 2, 5, 7, -235977083938500307243504091098571144252148940800000⟩, + ⟨6, 7, 2, 2, 6, 7, 79439757618394254907988714411474700815931801600000⟩, + ⟨6, 7, 3, 2, 7, 7, -7344336227964954953973604435339890029022412800000⟩, + ⟨6, 7, 4, 2, 8, 7, 307056093555951419173149431650508906220748800000⟩, + ⟨6, 7, 0, 3, 3, 7, 118377772344291027721379285470547994363297792000000⟩, + ⟨6, 7, 1, 3, 4, 7, -128668279406153543532791942244904159356439756800000⟩, + ⟨6, 7, 2, 3, 5, 7, -19686992255568793246444512574352324237564313600000⟩, + ⟨6, 7, 3, 3, 6, 7, 8064478605544069536414594373840675712217907200000⟩, + ⟨6, 7, 4, 3, 7, 7, 1851130532284046535538825360123673709851443200000⟩, + ⟨6, 7, 5, 3, 8, 7, -170100190102713283591783265784264740831232000000⟩, + ⟨6, 7, 0, 4, 2, 7, -877387940341949963763948273608650472451735552000000⟩, + ⟨6, 7, 1, 4, 3, 7, 405501845894270728274092888303576789886278041600000⟩, + ⟨6, 7, 2, 4, 4, 7, -2487028359281170240597043027652457443360768000000⟩, + ⟨6, 7, 3, 4, 5, 7, 15086367393184949307547886161265844090725990400000⟩, + ⟨6, 7, 4, 4, 6, 7, -2194948165416523851135279920272484068019404800000⟩, + ⟨6, 7, 5, 4, 7, 7, -101640370380757117126421995029206201794560000000⟩, + ⟨6, 7, 6, 4, 8, 7, 38577731306958268963459132635458555609088000000⟩, + ⟨6, 7, 0, 5, 1, 7, -676281333019357961018575417350107436649807872000000⟩, + ⟨6, 7, 1, 5, 2, 7, 82129370275412562654737590736732347560886272000000⟩, + ⟨6, 7, 2, 5, 3, 7, -41472193653960087420655376330488455240037171200000⟩, + ⟨6, 7, 3, 5, 4, 7, -15443901726005692786266827648881906016688537600000⟩, + ⟨6, 7, 4, 5, 5, 7, -1138750229287288659960227532790153314356428800000⟩, + ⟨6, 7, 5, 5, 6, 7, 225765863871518899587104713530883839098880000000⟩, + ⟨6, 7, 6, 5, 7, 7, -46760810727639460941622445259306956960563200000⟩, + ⟨6, 7, 7, 5, 8, 7, -1736026807266344288718279750252329592422400000⟩, + ⟨6, 7, 0, 6, 0, 7, 15599382706520496161943626050621041692299493376000000⟩, + ⟨6, 7, 1, 6, 1, 7, 1812162205538642099458149031279622199534472396800000⟩, + ⟨6, 7, 2, 6, 2, 7, 27753886807036348157143655171824357040612966400000⟩, + ⟨6, 7, 3, 6, 3, 7, -20544056239550030549421729455508488890771046400000⟩, + ⟨6, 7, 4, 6, 4, 7, 2210114315882971563272047297710665135397273600000⟩, + ⟨6, 7, 5, 6, 5, 7, -457621893439281021987958672237645352927232000000⟩, + ⟨6, 7, 6, 6, 6, 7, 30448526519318486720365186609016480779468800000⟩, + ⟨6, 7, 7, 6, 7, 7, 5736494387388970039734418907922082195046400000⟩, + ⟨6, 7, 8, 6, 8, 7, -5674681345243549772148034571565878004940800000⟩, + ⟨6, 7, 1, 7, 0, 7, -11350725855589550066534786473395401689391746252800000⟩, + ⟨6, 7, 2, 7, 1, 7, -409352166369632913216006245097473925158692454400000⟩, + ⟨6, 7, 3, 7, 2, 7, -75622153994618021899514704439505693763751116800000⟩, + ⟨6, 7, 4, 7, 3, 7, -8044038311384680377818744121152326747973222400000⟩, + ⟨6, 7, 5, 7, 4, 7, -1383862044922662081082216947640034031304704000000⟩, + ⟨6, 7, 6, 7, 5, 7, -31466728560949629499675867145771327422464000000⟩, + ⟨6, 7, 7, 7, 6, 7, -14366372837190347484741802159585109842329600000⟩, + ⟨6, 7, 8, 7, 7, 7, -4296854872720085993176890691167476672102400000⟩ +] + +def collectedFourData_9_6_41 : List CollectedFourTerm := [ + ⟨6, 8, 0, 0, 6, 8, -3631329977632468699836954595472076717919567872000000⟩, + ⟨6, 8, 1, 0, 7, 8, 1606222200603577899312918019200746843010603417600000⟩, + ⟨6, 8, 2, 0, 8, 8, -139502273764948437640346652514382552806037913600000⟩, + ⟨6, 8, 0, 1, 5, 8, -5545335479075737385573058840808130988424455782400000⟩, + ⟨6, 8, 1, 1, 6, 8, 784650697404654621777824923741491076317944217600000⟩, + ⟨6, 8, 2, 1, 7, 8, -63949564626055163923328049431711166517739520000000⟩, + ⟨6, 8, 3, 1, 8, 8, -303306392030309619259105069726565330111692800000⟩, + ⟨6, 8, 0, 2, 4, 8, -1580142825973175844965790426674983788469026816000000⟩, + ⟨6, 8, 1, 2, 5, 8, 466868671247940688698464159254721287196717875200000⟩, + ⟨6, 8, 2, 2, 6, 8, -134715020862754453909140889801391374119154483200000⟩, + ⟨6, 8, 3, 2, 7, 8, 10897797061647285518886985098188566091425382400000⟩, + ⟨6, 8, 4, 2, 8, 8, -404996586969185394895679492591073964641484800000⟩, + ⟨6, 8, 0, 3, 3, 8, -281045289774360660008618354635172300442933657600000⟩, + ⟨6, 8, 1, 3, 4, 8, 254563653535803766352695275566178182616003379200000⟩, + ⟨6, 8, 2, 3, 5, 8, 33385469089343426162282457490468662796301107200000⟩, + ⟨6, 8, 3, 3, 6, 8, -11966370890888210781041229796826898767649177600000⟩, + ⟨6, 8, 4, 3, 7, 8, -2441578471631537657737840193167740850352947200000⟩, + ⟨6, 8, 5, 3, 8, 8, 201920750286852352136072559452365924388044800000⟩, + ⟨6, 8, 0, 4, 2, 8, 2083040954857306148850544697910780098579634585600000⟩, + ⟨6, 8, 1, 4, 3, 8, -802264799706502123970450646992836698948658790400000⟩, + ⟨6, 8, 2, 4, 4, 8, 4217536500001183124063810533975384639143936000000⟩, + ⟨6, 8, 3, 4, 5, 8, -22385708544002523753424323271231467865453363200000⟩, + ⟨6, 8, 4, 4, 6, 8, 2895062284135990575220593181149304560864460800000⟩, + ⟨6, 8, 5, 4, 7, 8, 120654185244139083137943258444443349417984000000⟩, + ⟨6, 8, 6, 4, 8, 8, -41631317108741558001996467604004811046912000000⟩, + ⟨6, 8, 0, 5, 1, 8, 1605585908937596303588182013971341224193923481600000⟩, + ⟨6, 8, 1, 5, 2, 8, -162488786330222599782032796660038047962759168000000⟩, + ⟨6, 8, 2, 5, 3, 8, 70329109765860797036554011226560214254118502400000⟩, + ⟨6, 8, 3, 5, 4, 8, 22916231178140089426498704086695099551763660800000⟩, + ⟨6, 8, 4, 5, 5, 8, 1501972981323334953699548114234584444226764800000⟩, + ⟨6, 8, 5, 5, 6, 8, -267999774689077843282874426869146275807232000000⟩, + ⟨6, 8, 6, 5, 7, 8, 50462120858648664565941670147435818437836800000⟩, + ⟨6, 8, 7, 5, 8, 8, 1717320417796315212143264759158147960012800000⟩, + ⟨6, 8, 0, 6, 0, 8, -37035103349506776683006767770576634898507680972800000⟩, + ⟨6, 8, 1, 6, 1, 8, -3585270852851357707651108595322585187509023539200000⟩, + ⟨6, 8, 2, 6, 2, 8, -47065418530011903422337616285703790597557452800000⟩, + ⟨6, 8, 3, 6, 3, 8, 30484028613668369101911554155224429359215411200000⟩, + ⟨6, 8, 4, 6, 4, 8, -2915065922901925733300078983377344995629465600000⟩, + ⟨6, 8, 5, 6, 5, 8, 543228999421768933178188681473476038282444800000⟩, + ⟨6, 8, 6, 6, 6, 8, -32858652390246582905808855561824990606131200000⟩, + ⟨6, 8, 7, 6, 7, 8, -5674681345243549772148034571565878004940800000⟩, + ⟨6, 8, 8, 6, 8, 8, 5181724027914104114914304035250883683942400000⟩, + ⟨6, 8, 1, 7, 0, 8, 22456834407191108282527778490966419040489386803200000⟩, + ⟨6, 8, 2, 7, 1, 8, 694184968408436014501510934039957767841434828800000⟩, + ⟨6, 8, 3, 7, 2, 8, 112210942148864709042865320234884636013389414400000⟩, + ⟨6, 8, 4, 7, 3, 8, 10609814069579865799787087713814729688770150400000⟩, + ⟨6, 8, 5, 7, 4, 8, 1642740447471284050757215757678892134537625600000⟩, + ⟨6, 8, 6, 7, 5, 8, 33957449303383578445712526903160954945536000000⟩, + ⟨6, 8, 7, 7, 6, 8, 14211569371921681131340497184122566030131200000⟩, + ⟨6, 8, 8, 7, 7, 8, 3923588794478446613075161837773182415667200000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0927.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0927.lean new file mode 100644 index 0000000000000000000000000000000000000000..b6a8ff53033404d963705fd10a00b320df625aac --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0927.lean @@ -0,0 +1,657 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PartsTrace +import OAI.Analysis.LaughlinFock.Sparse0924 +import OAI.Analysis.LaughlinFock.Sparse0925 +import OAI.Analysis.LaughlinFock.Sparse0926 + +namespace OAI + +/-! Sparse0927. -/ +namespace LaughlinFock +def collectedFourData_9_6_42 : List CollectedFourTerm := [ + ⟨7, 0, 2, 0, 8, 1, -352320781057699192905682339971848111515388136652800000⟩, + ⟨7, 0, 2, 1, 7, 1, -161508195882988404506785860238985648747273256960000000⟩, + ⟨7, 0, 3, 1, 8, 1, -6128137817737075213799648955991075407155901235200000⟩, + ⟨7, 0, 2, 2, 6, 1, -340230306572217999187983034108546663141000976793600000⟩, + ⟨7, 0, 3, 2, 7, 1, 220183959383325541081823979578816082707450796441600000⟩, + ⟨7, 0, 4, 2, 8, 1, -36822293714981494681388945290310197318416492134400000⟩, + ⟨7, 0, 2, 3, 5, 1, 84316866156274702928828655644129864652659726745600000⟩, + ⟨7, 0, 3, 3, 6, 1, -241773902312589790932235056165366559652780074598400000⟩, + ⟨7, 0, 4, 3, 7, 1, -221988338922551403388584466510780481951908862361600000⟩, + ⟨7, 0, 5, 3, 8, 1, 61195455414028179149433418468502129202375426048000000⟩, + ⟨7, 0, 2, 4, 4, 1, 10651623903445850864530587034485090019524476928000000⟩, + ⟨7, 0, 3, 4, 5, 1, -452290854099880168980365102443353357554086104268800000⟩, + ⟨7, 0, 4, 4, 6, 1, 263219091665411116856807693688548272502296962662400000⟩, + ⟨7, 0, 5, 4, 7, 1, 36566265741061731212083760030638234559934627840000000⟩, + ⟨7, 0, 6, 4, 8, 1, -34696931184259545667907671737501795934619566080000000⟩, + ⟨7, 0, 2, 5, 3, 1, 177620093315114106746758083663497424610499179315200000⟩, + ⟨7, 0, 3, 5, 4, 1, 463009770360303128331472416619468219247972528947200000⟩, + ⟨7, 0, 4, 5, 5, 1, 136559398399232135985486758665158074413082895974400000⟩, + ⟨7, 0, 5, 5, 6, 1, -81221807266743979595377128192363601731067576320000000⟩, + ⟨7, 0, 6, 5, 7, 1, 42056818194605685797836720759435527178432806912000000⟩, + ⟨7, 0, 7, 5, 8, 1, 3435053368230296128395012616246001201834675404800000⟩, + ⟨7, 0, 2, 6, 2, 1, -118866342245009008761183540882640983557830764134400000⟩, + ⟨7, 0, 3, 6, 3, 1, 615912929938292072970368730741236680615097322700800000⟩, + ⟨7, 0, 4, 6, 4, 1, -265037822700948702343645635990430172685582257356800000⟩, + ⟨7, 0, 5, 6, 5, 1, 164634620099698382874668668011323067264871170048000000⟩, + ⟨7, 0, 6, 6, 6, 1, -27385499185960157652746360342592265055222366208000000⟩, + ⟨7, 0, 7, 6, 7, 1, -11350725855589550066534786473395401689391746252800000⟩, + ⟨7, 0, 8, 6, 8, 1, 22456834407191108282527778490966419040489386803200000⟩, + ⟨7, 0, 2, 7, 1, 1, 1753202895318161592836290740537334661793293166182400000⟩, + ⟨7, 0, 3, 7, 2, 1, 2267159994694896555423211636401282576565046712729600000⟩, + ⟨7, 0, 4, 7, 3, 1, 964644400722167230052803860181465401948950967091200000⟩, + ⟨7, 0, 5, 7, 4, 1, 497859926071180759650420915933864171640461459456000000⟩, + ⟨7, 0, 6, 7, 5, 1, 28301273260102670323944703282833943085438730240000000⟩, + ⟨7, 0, 7, 7, 6, 1, 28426552629882108086086813138774802848556462899200000⟩, + ⟨7, 0, 8, 7, 7, 1, 17004260235561440791465858849355878469163653529600000⟩ +] + +def collectedFourData_9_6_43 : List CollectedFourTerm := [ + ⟨7, 1, 1, 0, 7, 2, 125397612217363722751635111477670896875406046003200000⟩, + ⟨7, 1, 2, 0, 8, 2, -76236503366164376283038340801703674297499149926400000⟩, + ⟨7, 1, 1, 1, 6, 2, 61257604235739705142722496925282362347134071603200000⟩, + ⟨7, 1, 2, 1, 7, 2, -34947754379211948152707656283391995184393748480000000⟩, + ⟨7, 1, 3, 1, 8, 2, -663014821276921654831213620482585835128802508800000⟩, + ⟨7, 1, 1, 2, 5, 2, 36448392116349587717107039088266452989804701286400000⟩, + ⟨7, 1, 2, 2, 6, 2, -73620320761085625888697437299581287792678587596800000⟩, + ⟨7, 1, 3, 2, 7, 2, 23822119022200486998832748149505032690105476710400000⟩, + ⟨7, 1, 4, 2, 8, 2, -2655915735204529886112342055275248710364587622400000⟩, + ⟨7, 1, 1, 3, 4, 2, 19873759868791933007761240116143962418875623014400000⟩, + ⟨7, 1, 2, 3, 5, 2, 18244802453178477680084656151580189523771706572800000⟩, + ⟨7, 1, 3, 3, 6, 2, -26157975782992290333465050611592466153581681049600000⟩, + ⟨7, 1, 4, 3, 7, 2, -16011558838238351912020005494868893094299408793600000⟩, + ⟨7, 1, 5, 3, 8, 2, 3310426033244321773114343119798335960048992256000000⟩, + ⟨7, 1, 1, 4, 3, 2, -62632735502867035328350315376889578324589595852800000⟩, + ⟨7, 1, 2, 4, 4, 2, 2304838673246410666743978649691227397201854464000000⟩, + ⟨7, 1, 3, 4, 5, 2, -48934202969174201590040520700458586788727042867200000⟩, + ⟨7, 1, 4, 4, 6, 2, 18985447587040959626472080243039546903657604710400000⟩, + ⟨7, 1, 5, 4, 7, 2, 1978086726028216990451829154422470719548948480000000⟩, + ⟨7, 1, 6, 4, 8, 2, -1501570644276688011078079398269446358311108608000000⟩, + ⟨7, 1, 1, 5, 2, 2, -12685483870320462036332760307555830909502488576000000⟩, + ⟨7, 1, 2, 5, 3, 2, 38434107693745462702145231716498986206639004057600000⟩, + ⟨7, 1, 3, 5, 4, 2, 50093902793175700838891193467750727340132191436800000⟩, + ⟨7, 1, 4, 5, 5, 2, 9849746401078241271072565802060634692709148262400000⟩, + ⟨7, 1, 5, 5, 6, 2, -4393770475664202701421695081606177189045207040000000⟩, + ⟨7, 1, 6, 5, 7, 2, 1820082682740268472975571204869043662567453491200000⟩, + ⟨7, 1, 7, 5, 8, 2, 123881640325929769469772920348550135409960550400000⟩, + ⟨7, 1, 1, 6, 1, 2, -279901749540710467794649761470878261003843692134400000⟩, + ⟨7, 1, 2, 6, 2, 2, -25720748783198257201066263052923424297584898867200000⟩, + ⟨7, 1, 3, 6, 3, 2, 66636784829355538165698322141516977426540999475200000⟩, + ⟨7, 1, 4, 6, 4, 2, -19116628887499268946156154251752478920233766092800000⟩, + ⟨7, 1, 5, 6, 5, 2, 8906065469469396619487687930254998230852960256000000⟩, + ⟨7, 1, 6, 6, 6, 2, -1185155581573617562330798016043365809217391820800000⟩, + ⟨7, 1, 7, 6, 7, 2, -409352166369632913216006245097473925158692454400000⟩, + ⟨7, 1, 8, 6, 8, 2, 694184968408436014501510934039957767841434828800000⟩, + ⟨7, 1, 1, 7, 0, 2, 1753202895318161592836290740537334661793293166182400000⟩, + ⟨7, 1, 2, 7, 1, 2, 379364674514056329116028862028659700750196355891200000⟩, + ⟨7, 1, 3, 7, 2, 2, 245288327938403402921986928089128481880489223782400000⟩, + ⟨7, 1, 4, 7, 3, 2, 69577801496721222881108983474643821359766123315200000⟩, + ⟨7, 1, 5, 7, 4, 2, 26932203527605751614710589750521166336918290432000000⟩, + ⟨7, 1, 6, 7, 5, 2, 1224787313245203597845061440402167586592129024000000⟩, + ⟨7, 1, 7, 7, 6, 2, 1025174165027725025057911533781678868578015641600000⟩, + ⟨7, 1, 8, 7, 7, 2, 525635164796519322904244971366308785093502566400000⟩ +] + +def collectedFourData_9_6_44 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 6, 3, -61100968963731478117236442407946085459753435136000000⟩, + ⟨7, 2, 1, 0, 7, 3, 162158327828838362307098397011682820901571448012800000⟩, + ⟨7, 2, 2, 0, 8, 3, -49292740454841815980108786445587155261684763852800000⟩, + ⟨7, 2, 0, 1, 5, 3, -93306136618680645601899480342613259567645274931200000⟩, + ⟨7, 2, 1, 1, 6, 3, 79215469050955669830390290836538909566595550412800000⟩, + ⟨7, 2, 2, 1, 7, 3, -22596400805793243482818627202687709337312296960000000⟩, + ⟨7, 2, 3, 1, 8, 3, -285793253536700739649068725548869643296728678400000⟩, + ⟨7, 2, 0, 2, 4, 3, -26587574900311561122578172696355377924966187008000000⟩, + ⟨7, 2, 1, 2, 5, 3, 47133356155075603530169677004952770990178933145600000⟩, + ⟨7, 2, 2, 2, 6, 3, -47601177956031648330864284629883911424519543193600000⟩, + ⟨7, 2, 3, 2, 7, 3, 10268550088188181563539276765105797519331504947200000⟩, + ⟨7, 2, 4, 2, 8, 3, -858626505839141104410258984262855586000299622400000⟩, + ⟨7, 2, 0, 3, 3, 3, -4728884357433667366922331619831109947048643788800000⟩, + ⟨7, 2, 1, 3, 4, 3, 25699816854638077833645914378403592479585180057600000⟩, + ⟨7, 2, 2, 3, 5, 3, 11796662651943391628443314418345149493543541145600000⟩, + ⟨7, 2, 3, 3, 6, 3, -11275423663316848687771784883567165266956438732800000⟩, + ⟨7, 2, 4, 3, 7, 3, -5176349774988510844479382989647731891029776793600000⟩, + ⟨7, 2, 5, 3, 8, 3, 856177626447055326388431472777790458843417804800000⟩, + ⟨7, 2, 0, 4, 2, 3, 35049368004804212745435702780398544539135823052800000⟩, + ⟨7, 2, 1, 4, 3, 3, -80993724496808907311237051253398297807024239411200000⟩, + ⟨7, 2, 2, 4, 4, 3, 1490254792575402730414307873449921574420348928000000⟩, + ⟨7, 2, 3, 4, 5, 3, -21093140947967480242632031842841288402712238489600000⟩, + ⟨7, 2, 4, 4, 6, 3, 6137773238576702754602638497897608385690756710400000⟩, + ⟨7, 2, 5, 4, 7, 3, 511593849549778453663666486924968623849078784000000⟩, + ⟨7, 2, 6, 4, 8, 3, -323626822562233509759903979579125799764099072000000⟩, + ⟨7, 2, 0, 5, 1, 3, 27015681690971289534451040967217029945481809100800000⟩, + ⟨7, 2, 1, 5, 2, 3, -16404274497230238962370235851774304680677474304000000⟩, + ⟨7, 2, 2, 5, 3, 3, 24850595338322788964174487678107139562563384115200000⟩, + ⟨7, 2, 3, 5, 4, 3, 21593030807426440019647139934458183781190100582400000⟩, + ⟨7, 2, 4, 5, 5, 3, 3184307854220450064286101660094929882508060262400000⟩, + ⟨7, 2, 5, 5, 6, 3, -1136363700390730929820986010147585504032325632000000⟩, + ⟨7, 2, 6, 5, 7, 3, 392274301352977979414840849905220193669139660800000⟩, + ⟨7, 2, 7, 5, 8, 3, 22885420553446242850459267732760305932750028800000⟩, + ⟨7, 2, 0, 6, 0, 3, -623154798452697973021961345617935884400183371366400000⟩, + ⟨7, 2, 1, 6, 1, 3, -361955852741532780716268209254896695568359856537600000⟩, + ⟨7, 2, 2, 6, 2, 3, -16630434740493112354785248223326862088344069734400000⟩, + ⟨7, 2, 3, 6, 3, 3, 28723857944726581876065102540525360463230900633600000⟩, + ⟨7, 2, 4, 6, 4, 3, -6180182619322842528084465829301907530011430092800000⟩, + ⟨7, 2, 5, 6, 5, 3, 2303381473580147270679690249256794236958592204800000⟩, + ⟨7, 2, 6, 6, 6, 3, -255431295602693612484323446634296281197130547200000⟩, + ⟨7, 2, 7, 6, 7, 3, -75622153994618021899514704439505693763751116800000⟩, + ⟨7, 2, 8, 6, 8, 3, 112210942148864709042865320234884636013389414400000⟩, + ⟨7, 2, 1, 7, 0, 3, 2267159994694896555423211636401282576565046712729600000⟩, + ⟨7, 2, 2, 7, 1, 3, 245288327938403402921986928089128481880489223782400000⟩, + ⟨7, 2, 3, 7, 2, 3, 105731798213925740657746943348883583774860981043200000⟩, + ⟨7, 2, 4, 7, 3, 3, 22493689762524967286566969547694000194427499315200000⟩, + ⟨7, 2, 5, 7, 4, 3, 6965493220416769621746710387821376812430760345600000⟩, + ⟨7, 2, 6, 7, 5, 3, 263972945935564033016274415674133240942166016000000⟩, + ⟨7, 2, 7, 7, 6, 3, 189386755337278447695756124255634958796927795200000⟩, + ⟨7, 2, 8, 7, 7, 3, 84965851685927148429830806821701244779967283200000⟩ +] + +def collectedFourData_9_6_45 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 6, 4, -51995190218142894496588310892962018121203318784000000⟩, + ⟨7, 3, 1, 0, 7, 4, 68996067033905762287039600954911633342497135001600000⟩, + ⟨7, 3, 2, 0, 8, 4, -13982240979104566852729964318202838545254999654400000⟩, + ⟨7, 3, 0, 1, 5, 4, -79400873738812239792681407813516337345433750732800000⟩, + ⟨7, 3, 1, 1, 6, 4, 33705057803328100206466625892617622031257147801600000⟩, + ⟨7, 3, 2, 1, 7, 4, -6409631893290272239561193738835839703664558080000000⟩, + ⟨7, 3, 3, 1, 8, 4, -60800486607353434940176513349956366984701542400000⟩, + ⟨7, 3, 0, 2, 4, 4, -22625271543588881254010729176080809437012426752000000⟩, + ⟨7, 3, 1, 2, 5, 4, 20054574096503540949241782929613375279415374643200000⟩, + ⟨7, 3, 2, 2, 6, 4, -13502417088784489766530276874482070795240393932800000⟩, + ⟨7, 3, 3, 2, 7, 4, 2184561162265674182445293275636610267264267059200000⟩, + ⟨7, 3, 4, 2, 8, 4, -146133356817780505849588460813432124003707781120000⟩, + ⟨7, 3, 0, 3, 3, 4, -4024146357323953550232447598958479332298928947200000⟩, + ⟨7, 3, 1, 3, 4, 4, 10934907323004382516085103459681871395571315507200000⟩, + ⟨7, 3, 2, 3, 5, 4, 3346208354956120505487059184552776830517300428800000⟩, + ⟨7, 3, 3, 3, 6, 4, -2398766370269463217024547449183732473329929420800000⟩, + ⟨7, 3, 4, 3, 7, 4, -880985345243637538319032917434007893608948039680000⟩, + ⟨7, 3, 5, 3, 8, 4, 121430476206406687193500588939740705964897075200000⟩, + ⟨7, 3, 0, 4, 2, 4, 29826017284885156271678698351541759051639763763200000⟩, + ⟨7, 3, 1, 4, 3, 4, -34461680257371920207974721125559621351685645926400000⟩, + ⟨7, 3, 2, 4, 4, 4, 422721509045416291120835488895866451729055744000000⟩, + ⟨7, 3, 3, 4, 5, 4, -4487416052839832452939408854442585802287978905600000⟩, + ⟨7, 3, 4, 4, 6, 4, 1044614160685588037254394681946556039484166635520000⟩, + ⟨7, 3, 5, 4, 7, 4, 72558640702742036143090731817727420704751616000000⟩, + ⟨7, 3, 6, 4, 8, 4, -39342462821789667037405164531347711091277824000000⟩, + ⟨7, 3, 0, 5, 1, 4, 22989578270496013039248954631488112112891540275200000⟩, + ⟨7, 3, 1, 5, 2, 4, -6979785978356658390493634909834909774971404288000000⟩, + ⟨7, 3, 2, 5, 3, 4, 7049050413680370099810381991111891021924506009600000⟩, + ⟨7, 3, 3, 5, 4, 4, 4593764073057472837963158171751222142730397286400000⟩, + ⟨7, 3, 4, 5, 5, 4, 541951119274712534951623408939121812763175813120000⟩, + ⟨7, 3, 5, 5, 6, 4, -161168875499287463744927287391367345437933568000000⟩, + ⟨7, 3, 6, 5, 7, 4, 47687756517633132147109407705231935042853273600000⟩, + ⟨7, 3, 7, 5, 8, 4, 2434355410151020298884576036923978713294438400000⟩, + ⟨7, 3, 0, 6, 0, 4, -530287045040631939421510399330983506755056146841600000⟩, + ⟨7, 3, 1, 6, 1, 4, -154007078226839032578441783111228995344874550067200000⟩, + ⟨7, 3, 2, 6, 2, 4, -4717342634700410808714389008822636771038933811200000⟩, + ⟨7, 3, 3, 6, 3, 4, 6110796943831987045009149270332034207679355289600000⟩, + ⟨7, 3, 4, 6, 4, 4, -1051831996527890589099289685464961258426613104640000⟩, + ⟨7, 3, 5, 6, 5, 4, 326685375302957997936407662336977868250362675200000⟩, + ⟨7, 3, 6, 6, 6, 4, -31052111723026474460710751691973088334210662400000⟩, + ⟨7, 3, 7, 6, 7, 4, -8044038311384680377818744121152326747973222400000⟩, + ⟨7, 3, 8, 6, 8, 4, 10609814069579865799787087713814729688770150400000⟩, + ⟨7, 3, 1, 7, 0, 4, 964644400722167230052803860181465401948950967091200000⟩, + ⟨7, 3, 2, 7, 1, 4, 69577801496721222881108983474643821359766123315200000⟩, + ⟨7, 3, 3, 7, 2, 4, 22493689762524967286566969547694000194427499315200000⟩, + ⟨7, 3, 4, 7, 3, 4, 3828298299506879341836183948824019231282309365760000⟩, + ⟨7, 3, 5, 7, 4, 4, 987906168814153196647187405293040899230951014400000⟩, + ⟨7, 3, 6, 7, 5, 4, 32090497719579833225189470360959871271043072000000⟩, + ⟨7, 3, 7, 7, 6, 4, 20145344123764667285688845077707649579587993600000⟩, + ⟨7, 3, 8, 7, 7, 4, 8033725333624307653901013424457321075127091200000⟩ +] + +def collectedFourData_9_6_46 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 6, 5, -40252638493545670540241015417507211761292410880000000⟩, + ⟨7, 4, 1, 0, 7, 5, 35609367355459313899027571558415529739192107008000000⟩, + ⟨7, 4, 2, 0, 8, 5, -5412251489995976376033511523570412240664264704000000⟩, + ⟨7, 4, 0, 1, 5, 5, -61469044603376539205389014611885057335671914496000000⟩, + ⟨7, 4, 1, 1, 6, 5, 17395423198048314544181734056870640434448171008000000⟩, + ⟨7, 4, 2, 1, 7, 5, -2481042904111613661997488165441657931353292800000000⟩, + ⟨7, 4, 3, 1, 8, 5, -18827741545859282694296425536672450674373427200000⟩, + ⟨7, 4, 0, 2, 4, 5, -17515598509044508068442341739018819230907760640000000⟩, + ⟨7, 4, 1, 2, 5, 5, 10350310196793362123261904603916352891142537216000000⟩, + ⟨7, 4, 2, 2, 6, 5, -5226521064579805903539728530745212133858869248000000⟩, + ⟨7, 4, 3, 2, 7, 5, 676480654174330559631855811673605090739591577600000⟩, + ⟨7, 4, 4, 2, 8, 5, -37710239217356926280098542000868953049320652800000⟩, + ⟨7, 4, 0, 3, 3, 5, -3115336397210804773397354344322232605793583104000000⟩, + ⟨7, 4, 1, 3, 4, 5, 5643584462160940579227347036362634114195521536000000⟩, + ⟨7, 4, 2, 3, 5, 5, 1295251682617478353386311171447956119232708608000000⟩, + ⟨7, 4, 3, 3, 6, 5, -742812364973247130016650242590138252952757862400000⟩, + ⟨7, 4, 4, 3, 7, 5, -227341442361783245463525216025678065182126899200000⟩, + ⟨7, 4, 5, 3, 8, 5, 26859061607861861368258272441006850314338304000000⟩, + ⟨7, 4, 0, 4, 2, 5, 23090133653397134964323451157757571894790324224000000⟩, + ⟨7, 4, 1, 4, 3, 5, -17785921498512243544100441758038794031052357632000000⟩, + ⟨7, 4, 2, 4, 4, 5, 163627212590847447748917003145797017052119040000000⟩, + ⟨7, 4, 3, 4, 5, 5, -1389592655684273889913874420596883154384243916800000⟩, + ⟨7, 4, 4, 4, 6, 5, 269566447709897703898702755506407712047811788800000⟩, + ⟨7, 4, 5, 4, 7, 5, 16049158841352214606036209216711276437176320000000⟩, + ⟨7, 4, 6, 4, 8, 5, -7614348205897489479913220250429619615825920000000⟩, + ⟨7, 4, 0, 5, 1, 5, 17797630499261994887829150403100109186546008064000000⟩, + ⟨7, 4, 1, 5, 2, 5, -3602317837097104510065056090339711840094781440000000⟩, + ⟨7, 4, 2, 5, 3, 5, 2728549283445518917141545394505534165835841536000000⟩, + ⟨7, 4, 3, 5, 4, 5, 1422524843406754817105536112893596172045988659200000⟩, + ⟨7, 4, 4, 5, 5, 5, 139852438875044706571985155405305145692310732800000⟩, + ⟨7, 4, 5, 5, 6, 5, -35648750557043353727934547626184431485583360000000⟩, + ⟨7, 4, 6, 5, 7, 5, 9229498034429315424440305828443363515301888000000⟩, + ⟨7, 4, 7, 5, 8, 5, 418796122737540512143875128710797736280064000000⟩, + ⟨7, 4, 0, 6, 0, 5, -410527447486536395138559162180262514444375949312000000⟩, + ⟨7, 4, 1, 6, 1, 5, -79484162788952877473583604467352603263642894336000000⟩, + ⟨7, 4, 2, 6, 2, 5, -1825990893851258459941168632273468132836769792000000⟩, + ⟨7, 4, 3, 6, 3, 5, 1892295800865852971482280808469670706396581068800000⟩, + ⟨7, 4, 4, 6, 4, 5, -271429036253485613780777324780273227206859161600000⟩, + ⟨7, 4, 5, 6, 5, 5, 72259146927290736501481132307097157374050304000000⟩, + ⟨7, 4, 6, 6, 6, 5, -6009831978708836672296023630348819200212992000000⟩, + ⟨7, 4, 7, 6, 7, 5, -1383862044922662081082216947640034031304704000000⟩, + ⟨7, 4, 8, 6, 8, 5, 1642740447471284050757215757678892134537625600000⟩, + ⟨7, 4, 1, 7, 0, 5, 497859926071180759650420915933864171640461459456000000⟩, + ⟨7, 4, 2, 7, 1, 5, 26932203527605751614710589750521166336918290432000000⟩, + ⟨7, 4, 3, 7, 2, 5, 6965493220416769621746710387821376812430760345600000⟩, + ⟨7, 4, 4, 7, 3, 5, 987906168814153196647187405293040899230951014400000⟩, + ⟨7, 4, 5, 7, 4, 5, 218513782370938042599296689540745920813989888000000⟩, + ⟨7, 4, 6, 7, 5, 5, 6210801414346355707220004720012536064245760000000⟩, + ⟨7, 4, 7, 7, 6, 5, 3465719087305638821986093980423338544070656000000⟩, + ⟨7, 4, 8, 7, 7, 5, 1243879059790345792297452260936287284677836800000⟩ +] + +def collectedFourData_9_6_47 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 6, 6, -3050927544850806126734794780285331385719193600000000⟩, + ⟨7, 5, 1, 0, 7, 6, 2024244939935467568054913221393292483436216320000000⟩, + ⟨7, 5, 2, 0, 8, 6, -246131251542224669047609236594883671965564928000000⟩, + ⟨7, 5, 0, 1, 5, 6, -4659013877218883158165249642951580524342149120000000⟩, + ⟨7, 5, 1, 1, 6, 6, 988857708006622729241583718882179109166776320000000⟩, + ⟨7, 5, 2, 1, 7, 6, -112829604508899338994279321676022944471449600000000⟩, + ⟨7, 5, 3, 1, 8, 6, -713519379590539895707807584629666969812992000000⟩, + ⟨7, 5, 0, 2, 4, 6, -1327585568443178599525011688305623177153740800000000⟩, + ⟨7, 5, 1, 2, 5, 6, 588372234571848637384327396247979973819760640000000⟩, + ⟨7, 5, 2, 2, 6, 6, -237684847648826537684972442067739572999028736000000⟩, + ⟨7, 5, 3, 2, 7, 6, 25636747535321114379497122614512651165761536000000⟩, + ⟨7, 5, 4, 2, 8, 6, -1224954741462958068218300287774748011659264000000⟩, + ⟨7, 5, 0, 3, 3, 6, -236125282253255192615326622651816478643322880000000⟩, + ⟨7, 5, 1, 3, 4, 6, 320814385063100110693988796774284080384573440000000⟩, + ⟨7, 5, 2, 3, 5, 6, 58903751663071614410867236490925665477984256000000⟩, + ⟨7, 5, 3, 3, 6, 6, -28150536086175263665739170317527593059876864000000⟩, + ⟨7, 5, 4, 3, 7, 6, -7384810691519468377211944037717235776618496000000⟩, + ⟨7, 5, 5, 3, 8, 6, 763413163289377174827390499030684485550080000000⟩, + ⟨7, 5, 0, 4, 2, 6, 1750104525166260755980344824054078760057569280000000⟩, + ⟨7, 5, 1, 4, 3, 6, -1011055917844976432262406664645541283265249280000000⟩, + ⟨7, 5, 2, 4, 4, 6, 7441223065076173195772497200117529737953280000000⟩, + ⟨7, 5, 3, 4, 5, 6, -52661721914568724852779403632290607396814848000000⟩, + ⟨7, 5, 4, 4, 6, 6, 8756420142505518978859607979386827066834944000000⟩, + ⟨7, 5, 5, 4, 7, 6, 456164079672242564042265295978880198246400000000⟩, + ⟨7, 5, 6, 4, 8, 6, -192375171308608140109019584314412420300800000000⟩, + ⟨7, 5, 0, 5, 1, 6, 1348962034674618170590136693213043022186414080000000⟩, + ⟨7, 5, 1, 5, 2, 6, -204776838099740930220331289856693834979737600000000⟩, + ⟨7, 5, 2, 5, 3, 6, 124085373946580070413737163413869874749898752000000⟩, + ⟨7, 5, 3, 5, 4, 6, 53909760830711142505122041282612280019648512000000⟩, + ⟨7, 5, 4, 5, 5, 6, 4542875135787899908307992379053038228209664000000⟩, + ⟨7, 5, 5, 5, 6, 6, -1013241855854727490429052232642055058227200000000⟩, + ⟨7, 5, 6, 5, 7, 6, 233181648311094486972794386738169637765120000000⟩, + ⟨7, 5, 7, 5, 8, 6, 9522729498153698298691570519145629876224000000⟩, + ⟨7, 5, 0, 6, 0, 6, -31115711772653059246206775584167828526873968640000000⟩, + ⟨7, 5, 1, 6, 1, 6, -4518345207440979122221449440010366812097085440000000⟩, + ⟨7, 5, 2, 6, 2, 6, -83040011137518275698435882654810242803564544000000⟩, + ⟨7, 5, 3, 6, 3, 6, 71712782042758049069012291646353064295661568000000⟩, + ⟨7, 5, 4, 6, 4, 6, -8816923250287780083500371656312224961527808000000⟩, + ⟨7, 5, 5, 6, 5, 6, 2053816501028020999792799874117642831790080000000⟩, + ⟨7, 5, 6, 6, 6, 6, -151837350378145920204706215110681642926080000000⟩, + ⟨7, 5, 7, 6, 7, 6, -31466728560949629499675867145771327422464000000⟩, + ⟨7, 5, 8, 6, 8, 6, 33957449303383578445712526903160954945536000000⟩, + ⟨7, 5, 1, 7, 0, 6, 28301273260102670323944703282833943085438730240000000⟩, + ⟨7, 5, 2, 7, 1, 6, 1224787313245203597845061440402167586592129024000000⟩, + ⟨7, 5, 3, 7, 2, 6, 263972945935564033016274415674133240942166016000000⟩, + ⟨7, 5, 4, 7, 3, 6, 32090497719579833225189470360959871271043072000000⟩, + ⟨7, 5, 5, 7, 4, 6, 6210801414346355707220004720012536064245760000000⟩, + ⟨7, 5, 6, 7, 5, 6, 156914807904795117802734377264891717222400000000⟩, + ⟨7, 5, 7, 7, 6, 6, 78804706140230343282189367821119621431296000000⟩, + ⟨7, 5, 8, 7, 7, 6, 25712497782221592877902472701018749534208000000⟩ +] + +def collectedFourData_9_6_48 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 6, 7, -3830541104396225840300880976377804532073103360000000⟩, + ⟨7, 6, 1, 0, 7, 7, 2033205530790290869276622065957002205908801945600000⟩, + ⟨7, 6, 2, 0, 8, 7, -206017320361084556955147758366057572634669875200000⟩, + ⟨7, 6, 0, 1, 5, 7, -5849547031282278258510339394048752193175027712000000⟩, + ⟨7, 6, 1, 1, 6, 7, 993235018854868274305209077147354879204366745600000⟩, + ⟨7, 6, 2, 1, 7, 7, -94440883198193345582877951233701104467312640000000⟩, + ⟨7, 6, 3, 1, 8, 7, -511912763226523532472484431885489114867302400000⟩, + ⟨7, 6, 0, 2, 4, 7, -1666827879314159566087873393409252330129326080000000⟩, + ⟨7, 6, 1, 2, 5, 7, 590976742929668483209858940533314306536846131200000⟩, + ⟨7, 6, 2, 2, 6, 7, -198947492836533926713045198487763041714071142400000⟩, + ⟨7, 6, 3, 2, 7, 7, 18393022875535920877046422010567351336121139200000⟩, + ⟨7, 6, 4, 2, 8, 7, -768985729621509024476218728938435356341043200000⟩, + ⟨7, 6, 0, 3, 3, 7, -296463152979427827600193149752547097851199488000000⟩, + ⟨7, 6, 1, 3, 4, 7, 322234512829349495631744393762091440186536755200000⟩, + ⟨7, 6, 2, 3, 5, 7, 49303747495709449234419078188932917132420710400000⟩, + ⟨7, 6, 3, 3, 6, 7, -20196534426929818351126149173669328302427340800000⟩, + ⟨7, 6, 4, 3, 7, 7, -4635937839591229575047061011489699538980044800000⟩, + ⟨7, 6, 5, 3, 8, 7, 425995840955546093441867566826404234395648000000⟩, + ⟨7, 6, 0, 4, 2, 7, 2197314496030428266466014230846016053605040128000000⟩, + ⟨7, 6, 1, 4, 3, 7, -1015531492036825712354026653276424360084006502400000⟩, + ⟨7, 6, 2, 4, 4, 7, 6228468861513486006695071813093791054692352000000⟩, + ⟨7, 6, 3, 4, 5, 7, -37782025762248920801458216964633830176168345600000⟩, + ⟨7, 6, 4, 4, 6, 7, 5496988504338716102954658240019333054149427200000⟩, + ⟨7, 6, 5, 4, 7, 7, 254546306087244934148430033202098040995840000000⟩, + ⟨7, 6, 6, 4, 8, 7, -96613372861848709932251954827355416952832000000⟩, + ⟨7, 6, 0, 5, 1, 7, 1693666744335541565698384615205927149117636608000000⟩, + ⟨7, 6, 1, 5, 2, 7, -205683310150902222581540617151212977502814208000000⟩, + ⟨7, 6, 2, 5, 3, 7, 103862212036458986673506690130060617477573836800000⟩, + ⟨7, 6, 3, 5, 4, 7, 38677428281719845494301824039156644070188646400000⟩, + ⟨7, 6, 4, 5, 5, 7, 2851865487455569558417824244197540100256563200000⟩, + ⟨7, 6, 5, 5, 6, 7, -565403947996345794240324679612494061240320000000⟩, + ⟨7, 6, 6, 5, 7, 7, 117106929026096068360205026495500454251724800000⟩, + ⟨7, 6, 7, 5, 8, 7, 4347674151547004060976923179380033296793600000⟩, + ⟨7, 6, 0, 6, 0, 7, -39066812038475212174127736460117433458007998464000000⟩, + ⟨7, 6, 1, 6, 1, 7, -4538346266574673212811171106337107553943761715200000⟩, + ⟨7, 6, 2, 6, 2, 7, -69506332373933630123973653824046770305997209600000⟩, + ⟨7, 6, 3, 6, 3, 7, 51450163042854531682853634174604321761106329600000⟩, + ⟨7, 6, 4, 6, 4, 7, -5534970337387294719999657785992396900034150400000⟩, + ⟨7, 6, 5, 6, 5, 7, 1146059996861968437756083085640999158939648000000⟩, + ⟨7, 6, 6, 6, 6, 7, -76254739354623594929657214138492579427123200000⟩, + ⟨7, 6, 7, 6, 7, 7, -14366372837190347484741802159585109842329600000⟩, + ⟨7, 6, 8, 6, 8, 7, 14211569371921681131340497184122566030131200000⟩, + ⟨7, 6, 1, 7, 0, 7, 28426552629882108086086813138774802848556462899200000⟩, + ⟨7, 6, 2, 7, 1, 7, 1025174165027725025057911533781678868578015641600000⟩, + ⟨7, 6, 3, 7, 2, 7, 189386755337278447695756124255634958796927795200000⟩, + ⟨7, 6, 4, 7, 3, 7, 20145344123764667285688845077707649579587993600000⟩, + ⟨7, 6, 5, 7, 4, 7, 3465719087305638821986093980423338544070656000000⟩, + ⟨7, 6, 6, 7, 5, 7, 78804706140230343282189367821119621431296000000⟩, + ⟨7, 6, 7, 7, 6, 7, 35978884412558900728905206975126206572134400000⟩, + ⟨7, 6, 8, 7, 7, 7, 10760965663019158810950335700191615228313600000⟩ +] + +def collectedFourData_9_6_49 : List CollectedFourTerm := [ + ⟨7, 7, 0, 0, 6, 8, -2749634201385262317058014964030805095602978816000000⟩, + ⟨7, 7, 1, 0, 7, 8, 1216227532338813855898960812313452177158622412800000⟩, + ⟨7, 7, 2, 0, 8, 8, -105630781415572817104604750495788795314359500800000⟩, + ⟨7, 7, 0, 1, 5, 8, -4198914498363169320619537435044240178489275187200000⟩, + ⟨7, 7, 1, 1, 6, 8, 594135594125012909465271645794918659577924812800000⟩, + ⟨7, 7, 2, 1, 7, 8, -48422454346641361459340294092832320845250560000000⟩, + ⟨7, 7, 3, 1, 8, 8, -229662860208875782513080988249727726675558400000⟩, + ⟨7, 7, 0, 2, 4, 8, -1196480293482474826804382628608770272865026048000000⟩, + ⟨7, 7, 1, 2, 5, 8, 353511819065140500155225458027812270559041945600000⟩, + ⟨7, 7, 2, 2, 6, 8, -102005885195280689036808706248846575140444569600000⟩, + ⟨7, 7, 3, 2, 7, 8, 8251785352758702560328910505664654865543987200000⟩, + ⟨7, 7, 4, 2, 8, 8, -306662427770005609553738428533492578412134400000⟩, + ⟨7, 7, 0, 3, 3, 8, -212806807880797597400089088845019572729597132800000⟩, + ⟨7, 7, 1, 3, 4, 8, 192754977515975521321044354927759008399464857600000⟩, + ⟨7, 7, 2, 3, 5, 8, 25279395759346258336241982050673713345042841600000⟩, + ⟨7, 7, 3, 3, 6, 8, -9060906849754049611900461789317525597375692800000⟩, + ⟨7, 7, 4, 3, 7, 8, -1848757263128431825976734944442084639742361600000⟩, + ⟨7, 7, 5, 3, 8, 8, 152893899584439125264620364214283098547814400000⟩, + ⟨7, 7, 0, 4, 2, 8, 1577273529985316205706266362046339862397504716800000⟩, + ⟨7, 7, 1, 4, 3, 8, -607472949422984308228188688601645020318217011200000⟩, + ⟨7, 7, 2, 4, 4, 8, 3193508350225632350588067351896990215569408000000⟩, + ⟨7, 7, 3, 4, 5, 8, -16950403905447952290453146313396832844749209600000⟩, + ⟨7, 7, 4, 4, 6, 8, 2192134099801859350630908606844441809282662400000⟩, + ⟨7, 7, 5, 4, 7, 8, 91359054762589570686857744051412613988352000000⟩, + ⟨7, 7, 6, 4, 8, 8, -31523131766048758471431968663408461479936000000⟩, + ⟨7, 7, 0, 5, 1, 8, 1215745733841399397280730108133987748512845004800000⟩, + ⟨7, 7, 1, 5, 2, 8, -123036112660423659541752398937364060704866304000000⟩, + ⟨7, 7, 2, 5, 3, 8, 53253030365273310067009942155666425755415347200000⟩, + ⟨7, 7, 3, 5, 4, 8, 17352114349945952206120377148818787068700262400000⟩, + ⟨7, 7, 4, 5, 5, 8, 1137290277788470203704682208984066156815974400000⟩, + ⟨7, 7, 5, 5, 6, 8, -202928775679337469996116010171199333072896000000⟩, + ⟨7, 7, 6, 5, 7, 8, 38209794825046412763694899949455760844390400000⟩, + ⟨7, 7, 7, 5, 8, 8, 1300350831402162327565339141684318332518400000⟩, + ⟨7, 7, 0, 6, 0, 8, -28042889918815403002180750816250457783133431398400000⟩, + ⟨7, 7, 1, 6, 1, 8, -2714758344450172118799602923992658184941181337600000⟩, + ⟨7, 7, 2, 6, 2, 8, -35637820107168024800832424348332777336628838400000⟩, + ⟨7, 7, 3, 6, 3, 8, 23082432108468944965491974959546839894432153600000⟩, + ⟨7, 7, 4, 6, 4, 8, -2207280806281789795924637903320611864497356800000⟩, + ⟨7, 7, 5, 6, 5, 8, 411331673297349682574505199804363607271014400000⟩, + ⟨7, 7, 6, 6, 6, 8, -24880491439821435887156759230967650556313600000⟩, + ⟨7, 7, 7, 6, 7, 8, -4296854872720085993176890691167476672102400000⟩, + ⟨7, 7, 8, 6, 8, 8, 3923588794478446613075161837773182415667200000⟩, + ⟨7, 7, 1, 7, 0, 8, 17004260235561440791465858849355878469163653529600000⟩, + ⟨7, 7, 2, 7, 1, 8, 525635164796519322904244971366308785093502566400000⟩, + ⟨7, 7, 3, 7, 2, 8, 84965851685927148429830806821701244779967283200000⟩, + ⟨7, 7, 4, 7, 3, 8, 8033725333624307653901013424457321075127091200000⟩, + ⟨7, 7, 5, 7, 4, 8, 1243879059790345792297452260936287284677836800000⟩, + ⟨7, 7, 6, 7, 5, 8, 25712497782221592877902472701018749534208000000⟩, + ⟨7, 7, 7, 7, 6, 8, 10760965663019158810950335700191615228313600000⟩, + ⟨7, 7, 8, 7, 7, 8, 2970931864612227241031099004611253082521600000⟩ +] + +def collectedFourData_9_6 : List (List CollectedFourTerm) := [ + collectedFourData_9_6_0, + collectedFourData_9_6_1, + collectedFourData_9_6_2, + collectedFourData_9_6_3, + collectedFourData_9_6_4, + collectedFourData_9_6_5, + collectedFourData_9_6_6, + collectedFourData_9_6_7, + collectedFourData_9_6_8, + collectedFourData_9_6_9, + collectedFourData_9_6_10, + collectedFourData_9_6_11, + collectedFourData_9_6_12, + collectedFourData_9_6_13, + collectedFourData_9_6_14, + collectedFourData_9_6_15, + collectedFourData_9_6_16, + collectedFourData_9_6_17, + collectedFourData_9_6_18, + collectedFourData_9_6_19, + collectedFourData_9_6_20, + collectedFourData_9_6_21, + collectedFourData_9_6_22, + collectedFourData_9_6_23, + collectedFourData_9_6_24, + collectedFourData_9_6_25, + collectedFourData_9_6_26, + collectedFourData_9_6_27, + collectedFourData_9_6_28, + collectedFourData_9_6_29, + collectedFourData_9_6_30, + collectedFourData_9_6_31, + collectedFourData_9_6_32, + collectedFourData_9_6_33, + collectedFourData_9_6_34, + collectedFourData_9_6_35, + collectedFourData_9_6_36, + collectedFourData_9_6_37, + collectedFourData_9_6_38, + collectedFourData_9_6_39, + collectedFourData_9_6_40, + collectedFourData_9_6_41, + collectedFourData_9_6_42, + collectedFourData_9_6_43, + collectedFourData_9_6_44, + collectedFourData_9_6_45, + collectedFourData_9_6_46, + collectedFourData_9_6_47, + collectedFourData_9_6_48, + collectedFourData_9_6_49 +] + +theorem collectedFourChecked_9_6 : collectNumericRowParts 9 6 = collectedFourData_9_6 := by + decide +kernel + +def collectedFourData_9_7_0 : List CollectedFourTerm := [ + ⟨0, 7, 2, 1, 8, 0, -6035629236369518737109976906039557613786287308800000⟩, + ⟨0, 7, 2, 2, 7, 0, -7336567906022294078368560924608599661039163801600000⟩, + ⟨0, 7, 3, 2, 8, 0, -3086177606496240931993294916182592967552270336000000⟩, + ⟨0, 7, 2, 3, 6, 0, -2914472781888764028984184857054862028480446464000000⟩, + ⟨0, 7, 3, 3, 7, 0, -7705844233072155772655338150199114312226491596800000⟩, + ⟨0, 7, 4, 3, 8, 0, -2238241603220267602157890857596731150302393139200000⟩, + ⟨0, 7, 2, 4, 5, 0, -1353537208459987034764482873162230043137959526400000⟩, + ⟨0, 7, 3, 4, 6, 0, -17700420917719596259902065832823926110635111219200000⟩, + ⟨0, 7, 4, 4, 7, 0, -5100472763669748551506838344725353348249891635200000⟩, + ⟨0, 7, 5, 4, 8, 0, 7387170878318117769738070787065721380147298304000000⟩, + ⟨0, 7, 2, 5, 4, 0, 7176770076371970088279236010326260972876778700800000⟩, + ⟨0, 7, 3, 5, 5, 0, -5817278317300779223675652810616818384205407846400000⟩, + ⟨0, 7, 4, 5, 6, 0, 4678555495035510740948935086498247056811465113600000⟩, + ⟨0, 7, 5, 5, 7, 0, -251300021027851133446563808814051038662230016000000⟩, + ⟨0, 7, 6, 5, 8, 0, 2601312972152033855917386303257822851227451392000000⟩, + ⟨0, 7, 2, 6, 3, 0, 3621270826063786312491702919691299435698978816000000⟩, + ⟨0, 7, 3, 6, 4, 0, 27445974996411339039852459194825464997440231833600000⟩, + ⟨0, 7, 4, 6, 5, 0, -7591347653824121985188309732773923356838513868800000⟩, + ⟨0, 7, 5, 6, 6, 0, 2390311646549860094746867647291305425102700544000000⟩, + ⟨0, 7, 6, 6, 7, 0, 2456671504082968420310104273573397944407687168000000⟩, + ⟨0, 7, 7, 6, 8, 0, 539018778530535973621369039909471179570256281600000⟩, + ⟨0, 7, 2, 7, 2, 0, -17514614975153126476461120880040940221136214425600000⟩, + ⟨0, 7, 3, 7, 3, 0, -48914425501456750088885123375909740575718165708800000⟩, + ⟨0, 7, 4, 7, 4, 0, -31394878788190018244384088139163307601882093977600000⟩, + ⟨0, 7, 5, 7, 5, 0, -2703204286944228247293543367688381834937237504000000⟩, + ⟨0, 7, 6, 7, 6, 0, -2658904326035601025373210895601250052310302720000000⟩, + ⟨0, 7, 7, 7, 7, 0, -190506830224444868291288918852714631296502988800000⟩, + ⟨0, 7, 8, 7, 8, 0, -851960134979922316443807045223642856832368640000000⟩ +] + +def collectedFourData_9_7_1 : List CollectedFourTerm := [ + ⟨0, 8, 1, 0, 8, 1, 120436213284088221186034662613473816296502067200000⟩, + ⟨0, 8, 1, 1, 7, 1, 1262977800432316104180204649005178390448386867200000⟩, + ⟨0, 8, 2, 1, 8, 1, -694499489856916957923482600531022841388413747200000⟩, + ⟨0, 8, 1, 2, 6, 1, 1497656865645179593575374673866991924084001996800000⟩, + ⟨0, 8, 2, 2, 7, 1, -844194112741415445229062317587529416269260390400000⟩, + ⟨0, 8, 3, 2, 8, 1, -177558021656141562073273273167624922560724992000000⟩, + ⟨0, 8, 1, 3, 5, 1, 1237295615076146085370819124849318393679760588800000⟩, + ⟨0, 8, 2, 3, 6, 1, -335358548538201652359272867352879218835849216000000⟩, + ⟨0, 8, 3, 3, 7, 1, -443342746812308566633766557111392885475482009600000⟩, + ⟨0, 8, 4, 3, 8, 1, -85848969551572555731151438529553869099866521600000⟩, + ⟨0, 8, 1, 4, 4, 1, -1393583883632997045132350944997971397938092441600000⟩, + ⟨0, 8, 2, 4, 5, 1, -155746959258758723397223243497550526725855641600000⟩, + ⟨0, 8, 3, 4, 6, 1, -1018363853724989846632118031760492005385725542400000⟩, + ⟨0, 8, 4, 4, 7, 1, -195631396698606584104744054936015499123333529600000⟩, + ⟨0, 8, 5, 4, 8, 1, 212504206502741383067802203701713609418604544000000⟩, + ⟨0, 8, 1, 5, 3, 1, -2661390074999738598026396199588160120028764569600000⟩, + ⟨0, 8, 2, 5, 4, 1, 825806715698593174339292850182716135105049395200000⟩, + ⟨0, 8, 3, 5, 5, 1, -334687293196893532426254532976839702872902860800000⟩, + ⟨0, 8, 4, 5, 6, 1, 179448531231290552211480564899074214894292172800000⟩, + ⟨0, 8, 5, 5, 7, 1, -7229061360877055950830256298918772763262976000000⟩, + ⟨0, 8, 6, 5, 8, 1, 59864861189003691227716582784993799762975129600000⟩, + ⟨0, 8, 1, 6, 2, 1, 6631967338099306923778284383041111674929440358400000⟩, + ⟨0, 8, 2, 6, 3, 1, 416687414491982894945606569453500489850159104000000⟩, + ⟨0, 8, 3, 6, 4, 1, 1579057865149686794134671853720129060165858099200000⟩, + ⟨0, 8, 4, 6, 5, 1, -291170252867654088191495381020038755917391462400000⟩, + ⟨0, 8, 5, 6, 6, 1, 68761273850482203359308293290152289510621184000000⟩, + ⟨0, 8, 6, 6, 7, 1, 56536180057273172242472687925345272535082598400000⟩, + ⟨0, 8, 7, 6, 8, 1, 10337178667221816111011598725973620176610918400000⟩, + ⟨0, 8, 1, 7, 1, 1, -18977868937450069109197746568669718156021229158400000⟩, + ⟨0, 8, 2, 7, 2, 1, -2015347644614573190772509750888503025877804646400000⟩, + ⟨0, 8, 3, 7, 3, 1, -2814208943841599196090071235112105914456971673600000⟩, + ⟨0, 8, 4, 7, 4, 1, -1204167588201780406810618231645758267100810444800000⟩, + ⟨0, 8, 5, 7, 5, 1, -77762148930102836389180846180838084123295744000000⟩, + ⟨0, 8, 6, 7, 6, 1, -61190229740514161440769628915593708606324736000000⟩, + ⟨0, 8, 7, 7, 7, 1, -3653496352622187411176493349768711971746611200000⟩, + ⟨0, 8, 8, 7, 8, 1, -14004596844839853640409536562178944799866880000000⟩ +] + +def collectedFourData_9_7_2 : List CollectedFourTerm := [ + ⟨1, 6, 2, 1, 8, 0, -759351827759896028992159870823426212304938598400000⟩, + ⟨1, 6, 2, 2, 7, 0, -923024929257193213578961284398079076465429708800000⟩, + ⟨1, 6, 3, 2, 8, 0, -388276766929807844763588765766514652739534848000000⟩, + ⟨1, 6, 2, 3, 6, 0, -366674317989569884645223565153705131142807552000000⟩, + ⟨1, 6, 3, 3, 7, 0, -969484153790747059960924844654153141691246182400000⟩, + ⟨1, 6, 4, 3, 8, 0, -281596629914245938992812699220784426878867865600000⟩, + ⟨1, 6, 2, 4, 5, 0, -170290604829026146596868952292646368056652595200000⟩, + ⟨1, 6, 3, 4, 6, 0, -2226917269039317776215383899845889015714257305600000⟩, + ⟨1, 6, 4, 4, 7, 0, -641698348896902358172401434239469389059037593600000⟩, + ⟨1, 6, 5, 4, 8, 0, 929391367286781382283619570134561220483612672000000⟩, + ⟨1, 6, 2, 5, 4, 0, 902920517726105409621316267892601447539697254400000⟩, + ⟨1, 6, 3, 5, 5, 0, -731880761696263254382531686913663306317378355200000⟩, + ⟨1, 6, 4, 5, 6, 0, 588616286272793100104325854320634995948702924800000⟩, + ⟨1, 6, 5, 5, 7, 0, -31616443424610019548458635209709582798553088000000⟩, + ⟨1, 6, 6, 5, 8, 0, 327275199092139878703593340416527867268038656000000⟩, + ⟨1, 6, 2, 6, 3, 0, 455597670581760830958964107452455176779071488000000⟩, + ⟨1, 6, 3, 6, 4, 0, 3453020465967767472922381322860796153927879884800000⟩, + ⟨1, 6, 4, 6, 5, 0, -955079162476776407642982145574260165730264678400000⟩, + ⟨1, 6, 5, 6, 6, 0, 300728796723635910333683729386938867218644992000000⟩, + ⟨1, 6, 6, 6, 7, 0, 309077632799253173591676323581578279779303424000000⟩, + ⟨1, 6, 7, 6, 8, 0, 67814784282586151680355205539498680531078348800000⟩, + ⟨1, 6, 2, 7, 2, 0, -2203540736689334138121083115947489034534440140800000⟩, + ⟨1, 6, 3, 7, 3, 0, -6153999351805518024005469580427207155141469798400000⟩, + ⟨1, 6, 4, 7, 4, 0, -3949838145533984701432983395786528774020713676800000⟩, + ⟨1, 6, 5, 7, 5, 0, -340094302633836428829192673513433879933878272000000⟩, + ⟨1, 6, 6, 7, 6, 0, -334520856192998999544140362026149575875624960000000⟩, + ⟨1, 6, 7, 7, 7, 0, -23967958280136444899814454324920808173364838400000⟩, + ⟨1, 6, 8, 7, 8, 0, -107186419234841871998239688163679863853547520000000⟩ +] + +def collectedFourData_9_7_3 : List CollectedFourTerm := [ + ⟨1, 7, 1, 0, 8, 1, 1262977800432316104180204649005178390448386867200000⟩, + ⟨1, 7, 1, 1, 7, 1, 13244462615428263752606675032861053703083471667200000⟩, + ⟨1, 7, 2, 1, 8, 1, -7283004124613573838119194244371124947577418547200000⟩, + ⟨1, 7, 1, 2, 6, 1, 15705470326546771752898422037695822624862293196800000⟩, + ⟨1, 7, 2, 2, 7, 1, -8852805934151098453714227467293191628453733990400000⟩, + ⟨1, 7, 3, 2, 8, 1, -1861996765967856110240166057166861758986452992000000⟩, + ⟨1, 7, 1, 3, 5, 1, 12975141378177806052780584288415183662826179788800000⟩, + ⟨1, 7, 2, 3, 6, 1, -3516802716055758181255225729947131671757193216000000⟩, + ⟨1, 7, 3, 3, 7, 1, -4649200036585737939094999687069841181732608409600000⟩, + ⟨1, 7, 4, 3, 8, 1, -900271934637045857190639738963825952766400921600000⟩, + ⟨1, 7, 1, 4, 4, 1, -14614088736890430931851266241841805027045906841600000⟩, + ⟨1, 7, 2, 4, 5, 1, -1633270813361224184198111326302191509382470041600000⟩, + ⟨1, 7, 3, 4, 6, 1, -10679270835122568328250473466442065233641367142400000⟩, + ⟨1, 7, 4, 4, 7, 1, -2051526732371545340928046728662867984892139929600000⟩, + ⟨1, 7, 5, 4, 8, 1, 2228466737644481109377247834458294673205100544000000⟩, + ⟨1, 7, 1, 5, 3, 1, -27909185213976263616393475839574324099572930969600000⟩, + ⟨1, 7, 2, 5, 4, 1, 8659982914898238047088298463818903173050086195200000⟩, + ⟨1, 7, 3, 5, 5, 1, -3509763466220710603288942706973135474472570060800000⟩, + ⟨1, 7, 4, 5, 6, 1, 1881821962723966326777047953476592206466567372800000⟩, + ⟨1, 7, 5, 5, 7, 1, -75808959512985661394569965766880503032446976000000⟩, + ⟨1, 7, 6, 5, 8, 1, 627784522993326112635925428344323598146181529600000⟩, + ⟨1, 7, 1, 6, 2, 1, 69547416784468498693099004509807211260336825958400000⟩, + ⟨1, 7, 2, 6, 3, 1, 4369673704216692069152145100076300714171695104000000⟩, + ⟨1, 7, 3, 6, 4, 1, 16559097757232333568841911442706685273318830899200000⟩, + ⟨1, 7, 4, 6, 5, 1, -3053413549715916565343013062879167426574313062400000⟩, + ⟨1, 7, 5, 6, 6, 1, 721078486565799304760641442451931187782877184000000⟩, + ⟨1, 7, 6, 6, 7, 1, 592877660186398307975010140289509272498628198400000⟩, + ⟨1, 7, 7, 6, 8, 1, 108402836819584331748477880915989345063036518400000⟩, + ⟨1, 7, 1, 7, 1, 1, -199015117745155383362253585606832805748647814758400000⟩, + ⟨1, 7, 2, 7, 2, 1, -21134335478463997922980429409975612063734982246400000⟩, + ⟨1, 7, 3, 7, 3, 1, -29511750037059648961190161777620779115954674073600000⟩, + ⟨1, 7, 4, 7, 4, 1, -12627737874085928162949261878834159743910333644800000⟩, + ⟨1, 7, 5, 7, 5, 1, -815467915625731554431332198522909661010591744000000⟩, + ⟨1, 7, 6, 7, 6, 1, -641683258367879873356937486066655992255348736000000⟩, + ⟨1, 7, 7, 7, 7, 1, -38313100864753686042657229615212995670127411200000⟩, + ⟨1, 7, 8, 7, 8, 1, -146861931612840130898379838896712492913786880000000⟩ +] + +def collectedFourData_9_7_4 : List CollectedFourTerm := [ + ⟨1, 8, 0, 0, 7, 2, -6035629236369518737109976906039557613786287308800000⟩, + ⟨1, 8, 1, 0, 8, 2, -694499489856916957923482600531022841388413747200000⟩, + ⟨1, 8, 0, 1, 6, 2, -759351827759896028992159870823426212304938598400000⟩, + ⟨1, 8, 1, 1, 7, 2, -7283004124613573838119194244371124947577418547200000⟩, + ⟨1, 8, 2, 1, 8, 2, 2002427377361100839094922305653740351881058713600000⟩, + ⟨1, 8, 0, 2, 5, 2, 3672566024041524166162858408401067156340893286400000⟩, + ⟨1, 8, 1, 2, 6, 2, -8636288876982693765557541923967837022827891916800000⟩, + ⟨1, 8, 2, 2, 7, 2, 2434036925655256304906091537741930713826145075200000⟩, + ⟨1, 8, 3, 2, 8, 2, 341298108759910970489581992457920204729483264000000⟩, + ⟨1, 8, 0, 3, 4, 2, -2332291169474980664478070748590701384087424204800000⟩, + ⟨1, 8, 1, 3, 5, 2, -7134906935720743122383733418432305899607215308800000⟩, + ⟨1, 8, 2, 3, 6, 2, 966928195963581773189887740045537717736439808000000⟩, + ⟨1, 8, 3, 3, 7, 2, 852183638948712195101907273699682482277004083200000⟩, + ⟨1, 8, 4, 3, 8, 2, 123762745300018243443892817483661778312652390400000⟩, + ⟨1, 8, 0, 4, 3, 2, -8950744880540562526445642743450990431390243225600000⟩, + ⟨1, 8, 1, 4, 4, 2, 8036148512681666911947614964378044767940483481600000⟩, + ⟨1, 8, 2, 4, 5, 2, 449060049309374338594844625170842880291163340800000⟩, + ⟨1, 8, 3, 4, 6, 2, 1957476514234251087981051299878632177365994700800000⟩, + ⟨1, 8, 4, 4, 7, 2, 282028763405849995733867128641823358962787942400000⟩, + ⟨1, 8, 5, 4, 8, 2, -245082536197775526304658178531561776526183628800000⟩, + ⟨1, 8, 0, 5, 2, 2, 15106245540082893417738201834192172345040515891200000⟩, + ⟨1, 8, 1, 5, 3, 2, 15346995716626192029912179202901756374144358809600000⟩, + ⟨1, 8, 2, 5, 4, 2, -2381021152750165303124049375675114536008522137600000⟩, + ⟨1, 8, 3, 5, 5, 2, 643328525113258592154456668418086283167504793600000⟩, + ⟨1, 8, 4, 5, 6, 2, -258699003392216757975394843214998822121059123200000⟩, + ⟨1, 8, 5, 5, 7, 2, 8337325278453891074529792697731013814727475200000⟩, + ⟨1, 8, 6, 5, 8, 2, -57535457182975545453169818426375693760305561600000⟩, + ⟨1, 8, 0, 6, 1, 2, -10980191056794126587483095115978659425511538688000000⟩, + ⟨1, 8, 1, 6, 2, 2, -38243463551890216224091109513902133927255369318400000⟩, + ⟨1, 8, 2, 6, 3, 2, -1201421021565418637598140706643728138189668352000000⟩, + ⟨1, 8, 3, 6, 4, 2, -3035230162913957990383182223926250254784423526400000⟩, + ⟨1, 8, 4, 6, 5, 2, 419760773283985005779011574962663455704324505600000⟩, + ⟨1, 8, 5, 6, 6, 2, -79302841411040778059384027696653827411070156800000⟩, + ⟨1, 8, 6, 6, 7, 2, -54336298495781616185074106532288894385677926400000⟩, + ⟨1, 8, 7, 6, 8, 2, -8515669967151521235499947974662723858543411200000⟩, + ⟨1, 8, 0, 7, 0, 2, 107092981543187298551581665309130111515122624102400000⟩, + ⟨1, 8, 1, 7, 1, 2, 109436521925019984069387663440111328929081878118400000⟩, + ⟨1, 8, 2, 7, 2, 2, 5810785115634651520203951231348216150583620403200000⟩, + ⟨1, 8, 3, 7, 3, 2, 5409410294334297556601188725606903770650981171200000⟩, + ⟨1, 8, 4, 7, 4, 2, 1735968262584979330343526802024144076381827891200000⟩, + ⟨1, 8, 5, 7, 5, 2, 89683611414689255483016725752321391102577868800000⟩, + ⟨1, 8, 6, 7, 6, 2, 58809254265814184752781655105191709146873856000000⟩, + ⟨1, 8, 7, 7, 7, 2, 3009715722895977481274365568775599813138841600000⟩, + ⟨1, 8, 8, 7, 8, 2, 10094747563021883768170106500796598567567360000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0928.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0928.lean new file mode 100644 index 0000000000000000000000000000000000000000..f74b78e37235aee7911bbb696b40bfa2d3f3e9a9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0928.lean @@ -0,0 +1,642 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0928. -/ +namespace LaughlinFock +def collectedFourData_9_7_5 : List CollectedFourTerm := [ + ⟨2, 5, 2, 1, 8, 0, 3672566024041524166162858408401067156340893286400000⟩, + ⟨2, 5, 2, 2, 7, 0, 4464162553652484722384663463043768588713118924800000⟩, + ⟨2, 5, 3, 2, 8, 0, 1877880595030303318713989741838731057936990208000000⟩, + ⟨2, 5, 2, 3, 6, 0, 1773401462810323179259364544440737384410120192000000⟩, + ⟨2, 5, 3, 3, 7, 0, 4688860201419518322337002347089844387258459750400000⟩, + ⟨2, 5, 4, 3, 8, 0, 1361927604175938008493577208170632917536053657600000⟩, + ⟨2, 5, 2, 4, 5, 0, 823601743810265746259617747930048427478692659200000⟩, + ⟨2, 5, 3, 4, 6, 0, 10770370731511750900323070049656322939397183897600000⟩, + ⟨2, 5, 4, 4, 7, 0, 3103541030242281834452108841427905729607080345600000⟩, + ⟨2, 5, 5, 4, 8, 0, -4494953503442658145715696691904012556238323712000000⟩, + ⟨2, 5, 2, 5, 4, 0, -4366928602243905291993634641141679028733109862400000⟩, + ⟨2, 5, 3, 5, 5, 0, 3539703627216690747533978208915896849640141619200000⟩, + ⟨2, 5, 4, 5, 6, 0, -2846812366989508701795794995907152899369389260800000⟩, + ⟨2, 5, 5, 5, 7, 0, 152911301029973184292062993173816974925365248000000⟩, + ⟨2, 5, 6, 5, 8, 0, -1582849652502932910309286407660780448515096576000000⟩, + ⟨2, 5, 2, 6, 3, 0, -2203474679908323702503505591267101654434971648000000⟩, + ⟨2, 5, 3, 6, 4, 0, -16700355724491752487719906634892584964651273420800000⟩, + ⟨2, 5, 4, 6, 5, 0, 4619191202488722711230217672263981290578404966400000⟩, + ⟨2, 5, 5, 6, 6, 0, -1454459344038527472585494146551032005559058432000000⟩, + ⟨2, 5, 6, 6, 7, 0, -1494838059925808150013943030486293266357551104000000⟩, + ⟨2, 5, 7, 6, 8, 0, -327982713123436399665707872354196525369052364800000⟩, + ⟨2, 5, 2, 7, 2, 0, 10657311336209151474689564375787690724988603596800000⟩, + ⟨2, 5, 3, 7, 3, 0, 29763501061277280599687103588900792044205008486400000⟩, + ⟨2, 5, 4, 7, 4, 0, 19103188855875177784517635954432988224047336652800000⟩, + ⟨2, 5, 5, 7, 5, 0, 1644848586863556205250578649394125294442381312000000⟩, + ⟨2, 5, 6, 7, 6, 0, 1617892900069704345245123732019873233145692160000000⟩, + ⟨2, 5, 7, 7, 7, 0, 115919796367576051363230147371233315333236326400000⟩, + ⟨2, 5, 8, 7, 8, 0, 518401598744846170609932290728320145733713920000000⟩ +] + +def collectedFourData_9_7_6 : List CollectedFourTerm := [ + ⟨2, 6, 1, 0, 8, 1, 1497656865645179593575374673866991924084001996800000⟩, + ⟨2, 6, 1, 1, 7, 1, 15705470326546771752898422037695822624862293196800000⟩, + ⟨2, 6, 2, 1, 8, 1, -8636288876982693765557541923967837022827891916800000⟩, + ⟨2, 6, 1, 2, 6, 1, 18623767935341427713571005817849817320106701619200000⟩, + ⟨2, 6, 2, 2, 7, 1, -10497781974447547752119576314021468296485378457600000⟩, + ⟨2, 6, 3, 2, 8, 1, -2207981992562604201288790894130280815602434048000000⟩, + ⟨2, 6, 1, 3, 5, 1, 15386105409844248819932813946762650953006134067200000⟩, + ⟨2, 6, 2, 3, 6, 1, -4170274197232639097580009768819556771329736704000000⟩, + ⟨2, 6, 3, 3, 7, 1, -5513086890495663763152082135916551823490967142400000⟩, + ⟨2, 6, 4, 3, 8, 1, -1067555141028859583019330357566229835038484070400000⟩, + ⟨2, 6, 1, 4, 4, 1, -17329592273482544705800430988440105584028968550400000⟩, + ⟨2, 6, 2, 4, 5, 1, -1936755536202642291630678361055893284108789350400000⟩, + ⟨2, 6, 3, 4, 6, 1, -12663629781007199096148938857461474129897691545600000⟩, + ⟨2, 6, 4, 4, 7, 1, -2432729296381264771212562812402060069114898022400000⟩, + ⟨2, 6, 5, 4, 8, 1, 2642547246952999962466887702475914975155060736000000⟩, + ⟨2, 6, 1, 5, 3, 1, -33095104946394889195719844427321454989360391782400000⟩, + ⟨2, 6, 2, 5, 4, 1, 10269129722175473781263351591655036846938574028800000⟩, + ⟨2, 6, 3, 5, 5, 1, -4161926955625667022442742154969254317360624435200000⟩, + ⟨2, 6, 4, 5, 6, 1, 2231490990127242067954721650986263042455712563200000⟩, + ⟨2, 6, 5, 5, 7, 1, -89895332010726733599941250837646293696774144000000⟩, + ⟨2, 6, 6, 5, 8, 1, 744435730133108761299691729404737897200248422400000⟩, + ⟨2, 6, 1, 6, 2, 1, 82470306445206562574769331617471236694951434649600000⟩, + ⟨2, 6, 2, 6, 3, 1, 5181620628255884296741339280248079651098853376000000⟩, + ⟨2, 6, 3, 6, 4, 1, 19636011366565378896367246534295107543912729804800000⟩, + ⟨2, 6, 4, 6, 5, 1, -3620780796638499511854593007138101711607536025600000⟩, + ⟨2, 6, 5, 6, 6, 1, 855065026245628661816712753983925683692240896000000⟩, + ⟨2, 6, 6, 6, 7, 1, 703042680529992293358603181308327911898061209600000⟩, + ⟨2, 6, 7, 6, 8, 1, 128545610827595070482451709667063819633531289600000⟩, + ⟨2, 6, 1, 7, 1, 1, -235994929884113057626650475333870920035498301849600000⟩, + ⟨2, 6, 2, 7, 2, 1, -25061392701705179981031343665348723848985024921600000⟩, + ⟨2, 6, 3, 7, 3, 1, -34995448886811526258847082304289346068286957158400000⟩, + ⟨2, 6, 4, 7, 4, 1, -14974149441279877407703144838321703885881946931200000⟩, + ⟨2, 6, 5, 7, 5, 1, -966993340763546356611553906295464884789313536000000⟩, + ⟨2, 6, 6, 7, 6, 1, -760917046313298807468971509057752495065923584000000⟩, + ⟨2, 6, 7, 7, 7, 1, -45432214671242477286159833512692750979222732800000⟩, + ⟨2, 6, 8, 7, 8, 1, -174150947155678117638717317700929490486558720000000⟩ +] + +def collectedFourData_9_7_7 : List CollectedFourTerm := [ + ⟨2, 7, 0, 0, 7, 2, -7336567906022294078368560924608599661039163801600000⟩, + ⟨2, 7, 1, 0, 8, 2, -844194112741415445229062317587529416269260390400000⟩, + ⟨2, 7, 0, 1, 6, 2, -923024929257193213578961284398079076465429708800000⟩, + ⟨2, 7, 1, 1, 7, 2, -8852805934151098453714227467293191628453733990400000⟩, + ⟨2, 7, 2, 1, 8, 2, 2434036925655256304906091537741930713826145075200000⟩, + ⟨2, 7, 0, 2, 5, 2, 4464162553652484722384663463043768588713118924800000⟩, + ⟨2, 7, 1, 2, 6, 2, -10497781974447547752119576314021468296485378457600000⟩, + ⟨2, 7, 2, 2, 7, 2, 2958676964984838485717271786498351355350378086400000⟩, + ⟨2, 7, 3, 2, 8, 2, 414862585664758303845868364859383900220162048000000⟩, + ⟨2, 7, 0, 3, 4, 2, -2835000605796283615776938974077008226291390873600000⟩, + ⟨2, 7, 1, 3, 5, 2, -8672787407423830978095141424656184425664059801600000⟩, + ⟨2, 7, 2, 3, 6, 2, 1175342966262372698601050850123999520600621056000000⟩, + ⟨2, 7, 3, 3, 7, 2, 1035866003477228869004458968249488173917693542400000⟩, + ⟨2, 7, 4, 3, 8, 2, 150438959977516973493690488944340454439963852800000⟩, + ⟨2, 7, 0, 4, 3, 2, -10880016822416172929840420287238566982576190259200000⟩, + ⟨2, 7, 1, 4, 4, 2, 9768285452476316668397043238995862874815148851200000⟩, + ⟨2, 7, 2, 4, 5, 2, 545851876683805320689366587144435742650505625600000⟩, + ⟨2, 7, 3, 4, 6, 2, 2379397210913133528399638877224766610735733145600000⟩, + ⟨2, 7, 4, 4, 7, 2, 342818137620247317894239318693069289429978316800000⟩, + ⟨2, 7, 5, 4, 8, 2, -297908403412251008445547320331330479531334041600000⟩, + ⟨2, 7, 0, 5, 2, 2, 18362293618374831648094564740373416800229418598400000⟩, + ⟨2, 7, 1, 5, 3, 2, 18654935851591131406290963338224742644902474547200000⟩, + ⟨2, 7, 2, 5, 4, 2, -2894234004230274985222328337340995732298216243200000⟩, + ⟨2, 7, 3, 5, 5, 2, 781993595950834699819008879510303895501091635200000⟩, + ⟨2, 7, 4, 5, 6, 2, -314459807135027149273481963093711418810590822400000⟩, + ⟨2, 7, 5, 5, 7, 2, 10134378813627371838907215766279593925174886400000⟩, + ⟨2, 7, 6, 5, 8, 2, -69936832117415253116862991774996597436527411200000⟩, + ⟨2, 7, 0, 6, 1, 2, -13346896264576460700099828837058912138051977216000000⟩, + ⟨2, 7, 1, 6, 2, 2, -46486580987983249615788385873920630844071660748800000⟩, + ⟨2, 7, 2, 6, 3, 2, -1460379119267976748631995805965446949386584064000000⟩, + ⟨2, 7, 3, 6, 4, 2, -3689453299490585403304938286918581927484902604800000⟩, + ⟨2, 7, 4, 6, 5, 2, 510237341771309979551811491554297599575143219200000⟩, + ⟨2, 7, 5, 6, 6, 2, -96396027384641254300435914834017861729098137600000⟩, + ⟨2, 7, 6, 6, 7, 2, -66048116619566464493710104311184529550003404800000⟩, + ⟨2, 7, 7, 6, 8, 2, -10351164482207572221716216884219753747867238400000⟩, + ⟨2, 7, 0, 7, 0, 2, 130176142466727772848482390943490868708771679436800000⟩, + ⟨2, 7, 1, 7, 1, 2, 133024816975794034270116109421168957693769862348800000⟩, + ⟨2, 7, 2, 7, 2, 2, 7063260170334827088665112924559066225392903782400000⟩, + ⟨2, 7, 3, 7, 3, 2, 6575371746954984072166201618918304788018259558400000⟩, + ⟨2, 7, 4, 7, 4, 2, 2110144368114811730151407749415528312412202598400000⟩, + ⟨2, 7, 5, 7, 5, 2, 109014301481009831066899658002294859892365721600000⟩, + ⟨2, 7, 6, 7, 6, 2, 71485187463768512162884855630771684525473792000000⟩, + ⟨2, 7, 7, 7, 7, 2, 3658439396143427173622573658716746632344371200000⟩, + ⟨2, 7, 8, 7, 8, 2, 12270601471672124553793232613663357555179520000000⟩ +] + +def collectedFourData_9_7_8 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 7, 3, -3086177606496240931993294916182592967552270336000000⟩, + ⟨2, 8, 1, 0, 8, 3, -177558021656141562073273273167624922560724992000000⟩, + ⟨2, 8, 0, 1, 6, 3, -388276766929807844763588765766514652739534848000000⟩, + ⟨2, 8, 1, 1, 7, 3, -1861996765967856110240166057166861758986452992000000⟩, + ⟨2, 8, 2, 1, 8, 3, 341298108759910970489581992457920204729483264000000⟩, + ⟨2, 8, 0, 2, 5, 3, 1877880595030303318713989741838731057936990208000000⟩, + ⟨2, 8, 1, 2, 6, 3, -2207981992562604201288790894130280815602434048000000⟩, + ⟨2, 8, 2, 2, 7, 3, 414862585664758303845868364859383900220162048000000⟩, + ⟨2, 8, 3, 2, 8, 3, 43628697984268846568595100667729216557547520000000⟩, + ⟨2, 8, 0, 3, 4, 3, -1192562448284545402417480504130020321794195456000000⟩, + ⟨2, 8, 1, 3, 5, 3, -1824133752017961807148682091057152733550215168000000⟩, + ⟨2, 8, 2, 3, 6, 3, 164805359894703280485613307766851973855313920000000⟩, + ⟨2, 8, 3, 3, 7, 3, 108936034676309668967815686009753586920062976000000⟩, + ⟨2, 8, 4, 3, 8, 3, 12656636055834423475665776874917064708037017600000⟩, + ⟨2, 8, 0, 4, 3, 3, -4576753695427616054399262433077570687763218432000000⟩, + ⟨2, 8, 1, 4, 4, 3, 2054548135003918023437794552427599240548581376000000⟩, + ⟨2, 8, 2, 4, 5, 3, 76538778525341550579567806482422443689377792000000⟩, + ⟨2, 8, 3, 4, 6, 3, 250227438883648609809199693235319360291078144000000⟩, + ⟨2, 8, 4, 4, 7, 3, 28841760152070179570366922937650323113220505600000⟩, + ⟨2, 8, 5, 4, 8, 3, -20886202176434576035500922074238307014803456000000⟩, + ⟨2, 8, 0, 5, 2, 3, 7724224745799692564484952837026863660258033664000000⟩, + ⟨2, 8, 1, 5, 3, 3, 3923663354124039579969082923026360255649939456000000⟩, + ⟨2, 8, 2, 5, 4, 3, -405826461193269149916478339200362274329985024000000⟩, + ⟨2, 8, 3, 5, 5, 3, 82237742332688561492846960834239985350606848000000⟩, + ⟨2, 8, 4, 5, 6, 3, -26455934910017544670320385566158281801256140800000⟩, + ⟨2, 8, 5, 5, 7, 3, 710515992196049387779524106179825603969024000000⟩, + ⟨2, 8, 6, 5, 8, 3, -4202772583171674444670460887927476071694336000000⟩, + ⟨2, 8, 0, 6, 1, 3, -5614463451521010298511205880356141241057935360000000⟩, + ⟨2, 8, 1, 6, 2, 3, -9777449557164355502161739671344373066182426624000000⟩, + ⟨2, 8, 2, 6, 3, 3, -204772830775542254628121048860776127245844480000000⟩, + ⟨2, 8, 3, 6, 4, 3, -387998458507926790503821782728810212729290752000000⟩, + ⟨2, 8, 4, 6, 5, 3, 42926967441552385198195740445742248101308006400000⟩, + ⟨2, 8, 5, 6, 6, 3, -6758275006343595723449615571457324735266816000000⟩, + ⟨2, 8, 6, 6, 7, 3, -3969084748259804815056482729961041789190144000000⟩, + ⟨2, 8, 7, 6, 8, 3, -544286041432354587594373643860744505131008000000⟩, + ⟨2, 8, 0, 7, 0, 3, 54759487123550215883037923823222380843633737728000000⟩, + ⟨2, 8, 1, 7, 1, 3, 27978900796512918159929528022892489572429594624000000⟩, + ⟨2, 8, 2, 7, 2, 3, 990402944345437704914108899690984101818400768000000⟩, + ⟨2, 8, 3, 7, 3, 3, 691493805406715548131154088167684661959458816000000⟩, + ⟨2, 8, 4, 7, 4, 3, 177529340115680601492051307847219655184534732800000⟩, + ⟨2, 8, 5, 7, 5, 3, 7642935596228732937847765113851364828512256000000⟩, + ⟨2, 8, 6, 7, 6, 3, 4295819196832065402913370624221765183733760000000⟩, + ⟨2, 8, 7, 7, 7, 3, 192368452860524195630599458156522183327744000000⟩, + ⟨2, 8, 8, 7, 8, 3, 573523629474227122595575033320260291788800000000⟩ +] + +def collectedFourData_9_7_9 : List CollectedFourTerm := [ + ⟨3, 4, 2, 1, 8, 0, -2332291169474980664478070748590701384087424204800000⟩, + ⟨3, 4, 2, 2, 7, 0, -2835000605796283615776938974077008226291390873600000⟩, + ⟨3, 4, 3, 2, 8, 0, -1192562448284545402417480504130020321794195456000000⟩, + ⟨3, 4, 2, 3, 6, 0, -1126212175511800970879989707509226487198777344000000⟩, + ⟨3, 4, 3, 3, 7, 0, -2977696567218957481292523226110626075710901452800000⟩, + ⟨3, 4, 4, 3, 8, 0, -864902551483126899569951887311398207711556403200000⟩, + ⟨3, 4, 2, 4, 5, 0, -523034592619527958621648141703656467316762214400000⟩, + ⟨3, 4, 3, 4, 6, 0, -6839806387315374029700833506611470159989388083200000⟩, + ⟨3, 4, 4, 4, 7, 0, -1970927490902343737702136452892954840351847219200000⟩, + ⟨3, 4, 5, 4, 8, 0, 2854554634185497135136319699070780964008361984000000⟩, + ⟨3, 4, 2, 5, 4, 0, 2773251440564441597138142834086514049864748236800000⟩, + ⟨3, 4, 3, 5, 5, 0, -2247915887222373276512993139761082492470584934400000⟩, + ⟨3, 4, 4, 5, 6, 0, 1807889987876968925066568666451878054939171225600000⟩, + ⟨3, 4, 5, 5, 7, 0, -97107492355624064813920297420317450081140736000000⟩, + ⟨3, 4, 6, 5, 8, 0, 1005200789576708241206319153648076177677484032000000⟩, + ⟨3, 4, 2, 6, 3, 0, 1399333464523110997790917626361394982379585536000000⟩, + ⟨3, 4, 3, 6, 4, 0, 10605688755041062542200951430378504309257640345600000⟩, + ⟨3, 4, 4, 6, 5, 0, -2933452736085965633645256609812250915299445964800000⟩, + ⟨3, 4, 5, 6, 6, 0, 923665541274167177327244481985763170555265024000000⟩, + ⟨3, 4, 6, 6, 7, 0, 949308353924001525487152743616035550268489728000000⟩, + ⟨3, 4, 7, 6, 8, 0, 208287932892336637854556270101256289998444953600000⟩, + ⟨3, 4, 2, 7, 2, 0, -6768007152784457303420411098553548476679559577600000⟩, + ⟨3, 4, 3, 7, 3, 0, -18901539208132516955249222974395674131897830604800000⟩, + ⟨3, 4, 4, 7, 4, 0, -12131626330393449335570112411484807636870338969600000⟩, + ⟨3, 4, 5, 7, 5, 0, -1044573687485025257323152128478275973817565184000000⟩, + ⟨3, 4, 6, 7, 6, 0, -1027455272223085444014578180724194773429125120000000⟩, + ⟨3, 4, 7, 7, 7, 0, -73615754125480830737183613776731143746145484800000⟩, + ⟨3, 4, 8, 7, 8, 0, -329214903987971590906066623460346753911357440000000⟩ +] + +def collectedFourData_9_7_10 : List CollectedFourTerm := [ + ⟨3, 5, 1, 0, 8, 1, 1237295615076146085370819124849318393679760588800000⟩, + ⟨3, 5, 1, 1, 7, 1, 12975141378177806052780584288415183662826179788800000⟩, + ⟨3, 5, 2, 1, 8, 1, -7134906935720743122383733418432305899607215308800000⟩, + ⟨3, 5, 1, 2, 6, 1, 15386105409844248819932813946762650953006134067200000⟩, + ⟨3, 5, 2, 2, 7, 1, -8672787407423830978095141424656184425664059801600000⟩, + ⟨3, 5, 3, 2, 8, 1, -1824133752017961807148682091057152733550215168000000⟩, + ⟨3, 5, 1, 3, 5, 1, 12711296688443109672300327587182806031972643635200000⟩, + ⟨3, 5, 2, 3, 6, 1, -3445289836586372439081591050977841258340286464000000⟩, + ⟨3, 5, 3, 3, 7, 1, -4554660277409736354415054478325551116864349798400000⟩, + ⟨3, 5, 4, 3, 8, 1, -881965238598214365505533877852160898804115046400000⟩, + ⟨3, 5, 1, 4, 4, 1, -14316916660212705988656409267551917762775770726400000⟩, + ⟨3, 5, 2, 4, 5, 1, -1600058856863487277028853458275109851256743526400000⟩, + ⟨3, 5, 3, 4, 6, 1, -10462111821747608726389286902392830651834931609600000⟩, + ⟨3, 5, 4, 4, 7, 1, -2009809696818055101630174108466465630425867878400000⟩, + ⟨3, 5, 5, 4, 8, 1, 2183151692679593647188295977750510169359384576000000⟩, + ⟨3, 5, 1, 5, 3, 1, -27341662279242439548983507843932963656704616038400000⟩, + ⟨3, 5, 2, 5, 4, 1, 8483885372783442141709086703879595593397226700800000⟩, + ⟨3, 5, 3, 5, 5, 1, -3438393727287104824285291065933703911291695923200000⟩, + ⟨3, 5, 4, 5, 6, 1, 1843555810747703959178010911911739441630360371200000⟩, + ⟨3, 5, 5, 5, 7, 1, -74267412425456133510032608017435434107797504000000⟩, + ⟨3, 5, 6, 5, 8, 1, 615018757452767494481711990046620696705394278400000⟩, + ⟨3, 5, 1, 6, 2, 1, 68133195847021981922772723621332846472702040473600000⟩, + ⟨3, 5, 2, 6, 3, 1, 4280818009382419144161098773410582040795938816000000⟩, + ⟨3, 5, 3, 6, 4, 1, 16222374643186616206664262063495967269041523916800000⟩, + ⟨3, 5, 4, 6, 5, 1, -2991323517154772017017936874788384721044347289600000⟩, + ⟨3, 5, 5, 6, 6, 1, 706415622862264358676489682630642650511835136000000⟩, + ⟨3, 5, 6, 6, 7, 1, 580821712760222263561664666328351396660353433600000⟩, + ⟨3, 5, 7, 6, 8, 1, 106198505320343213769987480188842724130658713600000⟩, + ⟨3, 5, 1, 7, 1, 1, -194968219105399765974562314763906256401390475673600000⟩, + ⟨3, 5, 2, 7, 2, 1, -20704576601505431515904709041116178243550550425600000⟩, + ⟨3, 5, 3, 7, 3, 1, -28911639540756953937877374770195559308721546854400000⟩, + ⟨3, 5, 4, 7, 4, 1, -12370957505816277769513641237693635581988516659200000⟩, + ⟨3, 5, 5, 7, 5, 1, -798885677874647661297999410048949362544869376000000⟩, + ⟨3, 5, 6, 7, 6, 1, -628634867196068304277363757878958029006700544000000⟩, + ⟨3, 5, 7, 7, 7, 1, -37534018162237907854601319636701436449705164800000⟩, + ⟨3, 5, 8, 7, 8, 1, -143875548678670532567836009971879574524395520000000⟩ +] + +def collectedFourData_9_7_11 : List CollectedFourTerm := [ + ⟨3, 6, 0, 0, 7, 2, -2914472781888764028984184857054862028480446464000000⟩, + ⟨3, 6, 1, 0, 8, 2, -335358548538201652359272867352879218835849216000000⟩, + ⟨3, 6, 0, 1, 6, 2, -366674317989569884645223565153705131142807552000000⟩, + ⟨3, 6, 1, 1, 7, 2, -3516802716055758181255225729947131671757193216000000⟩, + ⟨3, 6, 2, 1, 8, 2, 966928195963581773189887740045537717736439808000000⟩, + ⟨3, 6, 0, 2, 5, 2, 1773401462810323179259364544440737384410120192000000⟩, + ⟨3, 6, 1, 2, 6, 2, -4170274197232639097580009768819556771329736704000000⟩, + ⟨3, 6, 2, 2, 7, 2, 1175342966262372698601050850123999520600621056000000⟩, + ⟨3, 6, 3, 2, 8, 2, 164805359894703280485613307766851973855313920000000⟩, + ⟨3, 6, 0, 3, 4, 2, -1126212175511800970879989707509226487198777344000000⟩, + ⟨3, 6, 1, 3, 5, 2, -3445289836586372439081591050977841258340286464000000⟩, + ⟨3, 6, 2, 3, 6, 2, 466908386650961067587904068513534457403146240000000⟩, + ⟨3, 6, 3, 3, 7, 2, 411500760504117564499194670709879058041143296000000⟩, + ⟨3, 6, 4, 3, 8, 2, 59762311179621211530260063052297162102669312000000⟩, + ⟨3, 6, 0, 4, 3, 2, -4322118094128829372714396115101810937108103168000000⟩, + ⟨3, 6, 1, 4, 4, 2, 3880479597768434121535136592346617849575374848000000⟩, + ⟨3, 6, 2, 4, 5, 2, 216841233927920299731972223575090134645735424000000⟩, + ⟨3, 6, 3, 4, 6, 2, 945222411533321888010571191307756419598516224000000⟩, + ⟨3, 6, 4, 4, 7, 2, 136185494911300180582698025146350956940623872000000⟩, + ⟨3, 6, 5, 4, 8, 2, -118344973339405081603985759637072843651416064000000⟩, + ⟨3, 6, 0, 5, 2, 2, 7294474153217300129363392330163754923024449536000000⟩, + ⟨3, 6, 1, 5, 3, 2, 7410727125242535530786476312127065205860466688000000⟩, + ⟨3, 6, 2, 5, 4, 2, -1149742814050964761641809672196311347026198528000000⟩, + ⟨3, 6, 3, 5, 5, 2, 310649213665589656155403561233560589941342208000000⟩, + ⟨3, 6, 4, 5, 6, 2, -124920066253420950159695007448240070376554496000000⟩, + ⟨3, 6, 5, 5, 7, 2, 4025911242424662492583345780226877403693056000000⟩, + ⟨3, 6, 6, 5, 8, 2, -27782608471519176356389337139885591125557248000000⟩, + ⟨3, 6, 0, 6, 1, 2, -5302093074592841535102083779866504666430832640000000⟩, + ⟨3, 6, 1, 6, 2, 2, -18466928507719746709360839410785226725263409152000000⟩, + ⟨3, 6, 2, 6, 3, 2, -580139821353173968164705297625251825907138560000000⟩, + ⟨3, 6, 3, 6, 4, 2, -1465645974950828796522322752745600084598587392000000⟩, + ⟨3, 6, 4, 6, 5, 2, 202693257112099985566389320739853137050861568000000⟩, + ⟨3, 6, 5, 6, 6, 2, -38293600181104512530264224659924390619643904000000⟩, + ⟨3, 6, 6, 6, 7, 2, -26237805012985650315026977514143332949819392000000⟩, + ⟨3, 6, 7, 6, 8, 2, -4112029975144619994968075060353920072155136000000⟩, + ⟨3, 6, 0, 7, 0, 2, 51712848423187384952229314689958760505694748672000000⟩, + ⟨3, 6, 1, 7, 1, 2, 52844492596250768182208582328468875556685873152000000⟩, + ⟨3, 6, 2, 7, 2, 2, 2805900494827000897588391917592159431893712896000000⟩, + ⟨3, 6, 3, 7, 3, 2, 2612085410068913571870368925277567085954727936000000⟩, + ⟨3, 6, 4, 7, 4, 2, 838260942378551362060699054882316498591809536000000⟩, + ⟨3, 6, 5, 7, 5, 2, 43306245995789963590772196119449661041803264000000⟩, + ⟨3, 6, 6, 7, 6, 2, 28397697103075939977796119857950279524679680000000⟩, + ⟨3, 6, 7, 7, 7, 2, 1453325612306706788354485141147477918875648000000⟩, + ⟨3, 6, 8, 7, 8, 2, 4874531860767860461098378666461102918860800000000⟩ +] + +def collectedFourData_9_7_12 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 7, 3, -7705844233072155772655338150199114312226491596800000⟩, + ⟨3, 7, 1, 0, 8, 3, -443342746812308566633766557111392885475482009600000⟩, + ⟨3, 7, 0, 1, 6, 3, -969484153790747059960924844654153141691246182400000⟩, + ⟨3, 7, 1, 1, 7, 3, -4649200036585737939094999687069841181732608409600000⟩, + ⟨3, 7, 2, 1, 8, 3, 852183638948712195101907273699682482277004083200000⟩, + ⟨3, 7, 0, 2, 5, 3, 4688860201419518322337002347089844387258459750400000⟩, + ⟨3, 7, 1, 2, 6, 3, -5513086890495663763152082135916551823490967142400000⟩, + ⟨3, 7, 2, 2, 7, 3, 1035866003477228869004458968249488173917693542400000⟩, + ⟨3, 7, 3, 2, 8, 3, 108936034676309668967815686009753586920062976000000⟩, + ⟨3, 7, 0, 3, 4, 3, -2977696567218957481292523226110626075710901452800000⟩, + ⟨3, 7, 1, 3, 5, 3, -4554660277409736354415054478325551116864349798400000⟩, + ⟨3, 7, 2, 3, 6, 3, 411500760504117564499194670709879058041143296000000⟩, + ⟨3, 7, 3, 3, 7, 3, 272001233116721378563684681781451878268980428800000⟩, + ⟨3, 7, 4, 3, 8, 3, 31602220739224200055314197138966954935981178880000⟩, + ⟨3, 7, 0, 4, 3, 3, -11427647908489070344280659284970021904881129881600000⟩, + ⟨3, 7, 1, 4, 4, 3, 5129979513934490271312764555067133208705158348800000⟩, + ⟨3, 7, 2, 4, 5, 3, 191108866795093355499143179612679242597898649600000⟩, + ⟨3, 7, 3, 4, 6, 3, 624790246296645721291756728134790432148370227200000⟩, + ⟨3, 7, 4, 4, 7, 3, 72014685957041339786577498693663037448288993280000⟩, + ⟨3, 7, 5, 4, 8, 3, -52150537368061718426377216512996738694171852800000⟩, + ⟨3, 7, 0, 5, 2, 3, 19286535093470907382444606399450105057025143603200000⟩, + ⟨3, 7, 1, 5, 3, 3, 9796953540927103975972560692088054838348008652800000⟩, + ⟨3, 7, 2, 5, 4, 3, -1013303799830433763166865314622127398118961971200000⟩, + ⟨3, 7, 3, 5, 5, 3, 205338549266021941882448014119451823389959782400000⟩, + ⟨3, 7, 4, 5, 6, 3, -66057544137370868371028788066577736283497431040000⟩, + ⟨3, 7, 5, 5, 7, 3, 1774079868068713140498352371675177294181171200000⟩, + ⟨3, 7, 6, 5, 8, 3, -10493858423694275418532421393858303347182796800000⟩, + ⟨3, 7, 0, 6, 1, 3, -14018694425955509395346338026750176701414637568000000⟩, + ⟨3, 7, 1, 6, 2, 3, -24413210414603085490018813796264003410865632051200000⟩, + ⟨3, 7, 2, 6, 3, 3, -511295115938913068906575496176786699267866624000000⟩, + ⟨3, 7, 3, 6, 4, 3, -968789248434926558275454670365317357819763097600000⟩, + ⟨3, 7, 4, 6, 5, 3, 107183891104151057252605575559386745167748792320000⟩, + ⟨3, 7, 5, 6, 6, 3, -16874665402770920239248737102381388881775820800000⟩, + ⟨3, 7, 6, 6, 7, 3, -9910365739668495593868397654444225422635827200000⟩, + ⟨3, 7, 7, 6, 8, 3, -1359022061687132747537405510937480381490790400000⟩, + ⟨3, 7, 0, 7, 0, 3, 136728384383574644393093960604350055966411482726400000⟩, + ⟨3, 7, 1, 7, 1, 3, 69860221555842471712752111533896803319977030451200000⟩, + ⟨3, 7, 2, 7, 2, 3, 2472926639425173434967603067221046481176127078400000⟩, + ⟨3, 7, 3, 7, 3, 3, 1726583571010999376492326099241979967764745420800000⟩, + ⟨3, 7, 4, 7, 4, 3, 443271132177204127773453626360318886813515120640000⟩, + ⟨3, 7, 5, 7, 5, 3, 19083565075441427482939383574079173330521292800000⟩, + ⟨3, 7, 6, 7, 6, 3, 10726185529487721551423858595186626934079488000000⟩, + ⟨3, 7, 7, 7, 7, 3, 480322755884169100723535545099801295270707200000⟩, + ⟨3, 7, 8, 7, 8, 3, 1432025086116821324648583028312276142653440000000⟩ +] + +def collectedFourData_9_7_13 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 7, 4, -2238241603220267602157890857596731150302393139200000⟩, + ⟨3, 8, 1, 0, 8, 4, -85848969551572555731151438529553869099866521600000⟩, + ⟨3, 8, 0, 1, 6, 4, -281596629914245938992812699220784426878867865600000⟩, + ⟨3, 8, 1, 1, 7, 4, -900271934637045857190639738963825952766400921600000⟩, + ⟨3, 8, 2, 1, 8, 4, 123762745300018243443892817483661778312652390400000⟩, + ⟨3, 8, 0, 2, 5, 4, 1361927604175938008493577208170632917536053657600000⟩, + ⟨3, 8, 1, 2, 6, 4, -1067555141028859583019330357566229835038484070400000⟩, + ⟨3, 8, 2, 2, 7, 4, 150438959977516973493690488944340454439963852800000⟩, + ⟨3, 8, 3, 2, 8, 4, 12656636055834423475665776874917064708037017600000⟩, + ⟨3, 8, 0, 3, 4, 4, -864902551483126899569951887311398207711556403200000⟩, + ⟨3, 8, 1, 3, 5, 4, -881965238598214365505533877852160898804115046400000⟩, + ⟨3, 8, 2, 3, 6, 4, 59762311179621211530260063052297162102669312000000⟩, + ⟨3, 8, 3, 3, 7, 4, 31602220739224200055314197138966954935981178880000⟩, + ⟨3, 8, 4, 3, 8, 4, 3059729865336336789997441478329916580943626240000⟩, + ⟨3, 8, 0, 4, 3, 4, -3319277706906875348315975255077539735583221350400000⟩, + ⟨3, 8, 1, 4, 4, 4, 993370159450020513750383136563678140301102284800000⟩, + ⟨3, 8, 2, 4, 5, 4, 27754766607482045058375318084838327510577971200000⟩, + ⟨3, 8, 3, 4, 6, 4, 72590697670506394595352023704980164268754206720000⟩, + ⟨3, 8, 4, 4, 7, 4, 6972468396567054777443758831865708800313917440000⟩, + ⟨3, 8, 5, 4, 8, 4, -4327902631412557923561219107726957609169715200000⟩, + ⟨3, 8, 0, 5, 2, 4, 5601972207393575376921583620474395599097875660800000⟩, + ⟨3, 8, 1, 5, 3, 4, 1897083852799081138434317821273814524765195468800000⟩, + ⟨3, 8, 2, 5, 4, 4, -147162248086180720301963712182209025090676326400000⟩, + ⟨3, 8, 3, 5, 5, 4, 23857076255945714499011839106286452472010506240000⟩, + ⟨3, 8, 4, 5, 6, 4, -6395697387716198597938015402847617622653009920000⟩, + ⟨3, 8, 5, 5, 7, 4, 147228491149793064302171555323771712490700800000⟩, + ⟨3, 8, 6, 5, 8, 4, -762012240054452282206390436016610947681484800000⟩, + ⟨3, 8, 0, 6, 1, 4, -4071873780206981659026368143213050541262241792000000⟩, + ⟨3, 8, 1, 6, 2, 4, -4727378473221493205629414128290272649701176115200000⟩, + ⟨3, 8, 2, 6, 3, 4, -74255458935065750282687772048050751881084928000000⟩, + ⟨3, 8, 3, 6, 4, 4, -112557915006546117263899540252595692806875381760000⟩, + ⟨3, 8, 4, 6, 5, 4, 10377554014337905262376345799207597825704591360000⟩, + ⟨3, 8, 5, 6, 6, 4, -1400405681065623463206500708466692810027827200000⟩, + ⟨3, 8, 6, 6, 7, 4, -719641879291252522170640261889923575132979200000⟩, + ⟨3, 8, 7, 6, 8, 4, -87720425812437418891402376938476884774092800000⟩, + ⟨3, 8, 0, 7, 0, 4, 39714163563672375903104856799721158467892386201600000⟩, + ⟨3, 8, 1, 7, 1, 4, 13527745917432760193343388829864414176529822515200000⟩, + ⟨3, 8, 2, 7, 2, 4, 359143470764553686998930141912721864822410444800000⟩, + ⟨3, 8, 3, 7, 3, 4, 200601572686227829412256375603954721365247918080000⟩, + ⟨3, 8, 4, 7, 4, 4, 42917551040349380376104467834563777251738910720000⟩, + ⟨3, 8, 5, 7, 5, 4, 1583719280279497479897884842235775507706675200000⟩, + ⟨3, 8, 6, 7, 6, 4, 778882688574254927200192135174547274989568000000⟩, + ⟨3, 8, 7, 7, 7, 4, 31003261728699331171794259198256454461030400000⟩, + ⟨3, 8, 8, 7, 8, 4, 83189278881229184208539653770301849731072000000⟩ +] + +def collectedFourData_9_7_14 : List CollectedFourTerm := [ + ⟨4, 3, 2, 1, 8, 0, -8950744880540562526445642743450990431390243225600000⟩, + ⟨4, 3, 2, 2, 7, 0, -10880016822416172929840420287238566982576190259200000⟩, + ⟨4, 3, 3, 2, 8, 0, -4576753695427616054399262433077570687763218432000000⟩, + ⟨4, 3, 2, 3, 6, 0, -4322118094128829372714396115101810937108103168000000⟩, + ⟨4, 3, 3, 3, 7, 0, -11427647908489070344280659284970021904881129881600000⟩, + ⟨4, 3, 4, 3, 8, 0, -3319277706906875348315975255077539735583221350400000⟩, + ⟨4, 3, 2, 4, 5, 0, -2007274762048135107519572296197921678102940876800000⟩, + ⟨4, 3, 3, 4, 6, 0, -26249450671690015964954452112993261347018270310400000⟩, + ⟨4, 3, 4, 4, 7, 0, -7563922283803876333992649821571442523370841702400000⟩, + ⟨4, 3, 5, 4, 8, 0, 10955060248292581397403216964620360361860661248000000⟩, + ⟨4, 3, 2, 5, 4, 0, 10643039110623446326651064790612610573045176729600000⟩, + ⟨4, 3, 3, 5, 5, 0, -8626933842042870312274395035875286588752448716800000⟩, + ⟨4, 3, 4, 5, 6, 0, 6938225494895228623779616491544000115101610803200000⟩, + ⟨4, 3, 5, 5, 7, 0, -372674047494633780877557783354129493725806592000000⟩, + ⟨4, 3, 6, 5, 8, 0, 3857706935984508001116743308547691964482453504000000⟩, + ⟨4, 3, 2, 6, 3, 0, 5370288670504562270164811569530321466338312192000000⟩, + ⟨4, 3, 3, 6, 4, 0, 40701956758752260310366179168355542257110299443200000⟩, + ⟨4, 3, 4, 6, 5, 0, -11257851250939543856613215456460916457393985945600000⟩, + ⟨4, 3, 5, 6, 6, 0, 3544795231014215756798589945745328975671984128000000⟩, + ⟨4, 3, 6, 6, 7, 0, 3643205874184396373105213851748681966961033216000000⟩, + ⟨4, 3, 7, 6, 8, 0, 799356518351924314774023628048615968477492019200000⟩, + ⟨4, 3, 2, 7, 2, 0, -25973903330382283042776485766533356008355607347200000⟩, + ⟨4, 3, 3, 7, 3, 0, -72539337075830630031293863882206624805820144025600000⟩, + ⟨4, 3, 4, 7, 4, 0, -46558120054042896736117798185511633519620862771200000⟩, + ⟨4, 3, 5, 7, 5, 0, -4008810181152754674178952121524597324563611648000000⟩, + ⟨4, 3, 6, 7, 6, 0, -3943114023754333888858962716147545310641520640000000⟩, + ⟨4, 3, 7, 7, 7, 0, -282518685055137482510574143832470146898303385600000⟩, + ⟨4, 3, 8, 7, 8, 0, -1263443713647178074313777944601839244337479680000000⟩ +] + +def collectedFourData_9_7_15 : List CollectedFourTerm := [ + ⟨4, 4, 1, 0, 8, 1, -1393583883632997045132350944997971397938092441600000⟩, + ⟨4, 4, 1, 1, 7, 1, -14614088736890430931851266241841805027045906841600000⟩, + ⟨4, 4, 2, 1, 8, 1, 8036148512681666911947614964378044767940483481600000⟩, + ⟨4, 4, 1, 2, 6, 1, -17329592273482544705800430988440105584028968550400000⟩, + ⟨4, 4, 2, 2, 7, 1, 9768285452476316668397043238995862874815148851200000⟩, + ⟨4, 4, 3, 2, 8, 1, 2054548135003918023437794552427599240548581376000000⟩, + ⟨4, 4, 1, 3, 5, 1, -14316916660212705988656409267551917762775770726400000⟩, + ⟨4, 4, 2, 3, 6, 1, 3880479597768434121535136592346617849575374848000000⟩, + ⟨4, 4, 3, 3, 7, 1, 5129979513934490271312764555067133208705158348800000⟩, + ⟨4, 4, 4, 3, 8, 1, 993370159450020513750383136563678140301102284800000⟩, + ⟨4, 4, 1, 4, 4, 1, 16125349575219579286669459501982172409899044044800000⟩, + ⟨4, 4, 2, 4, 5, 1, 1802169351139229720466502685524139179491773644800000⟩, + ⟨4, 4, 3, 4, 6, 1, 11783627328749924642175209986335232049510822707200000⟩, + ⟨4, 4, 4, 4, 7, 1, 2263677627664259832128942460683474576551496908800000⟩, + ⟨4, 4, 5, 4, 8, 1, -2458915215873566796973701297642940791816978432000000⟩, + ⟨4, 4, 1, 5, 3, 1, 30795308283496631048237006518055101782890958028800000⟩, + ⟨4, 4, 2, 5, 4, 1, -9555522368333222104032434133687552350623472025600000⟩, + ⟨4, 4, 3, 5, 5, 1, 3872712410475331537003136627493099813063779942400000⟩, + ⟨4, 4, 4, 5, 6, 1, -2076423479669288473116238422723904144406898278400000⟩, + ⟨4, 4, 5, 5, 7, 1, 83648456984850105244502423459464961618608128000000⟩, + ⟨4, 4, 6, 5, 8, 1, -692704490402175421078869115435801765477141708800000⟩, + ⟨4, 4, 1, 6, 2, 1, -76739400443908527278967818866363608584437314355200000⟩, + ⟨4, 4, 2, 6, 3, 1, -4821547020736903947147290109051060023419994112000000⟩, + ⟨4, 4, 3, 6, 4, 1, -18271494363624780607838817773876396063475734937600000⟩, + ⟨4, 4, 4, 6, 5, 1, 3369170789458195954478127430053562677437084467200000⟩, + ⟨4, 4, 5, 6, 6, 1, -795646097159110683023630613122148149967716352000000⟩, + ⟨4, 4, 6, 6, 7, 1, -654187866104209682196538539634683175748449075200000⟩, + ⟨4, 4, 7, 6, 8, 1, -119612907115358474916174160989037785194378035200000⟩, + ⟨4, 4, 1, 7, 1, 1, 219595515134182997876461520942321087739241640755200000⟩, + ⟨4, 4, 2, 7, 2, 1, 23319863028470445541822026498877340015320576819200000⟩, + ⟨4, 4, 3, 7, 3, 1, 32563596300246974239353938490443942979206696140800000⟩, + ⟨4, 4, 4, 7, 4, 1, 13933587733722983285761594470500361632234235494400000⟩, + ⟨4, 4, 5, 7, 5, 1, 899796452832991710770720505319886283218092032000000⟩, + ⟨4, 4, 6, 7, 6, 1, 708040511046582582457630149055963528490385408000000⟩, + ⟨4, 4, 7, 7, 7, 1, 42275105610605325216129976996426531212990873600000⟩, + ⟨4, 4, 8, 7, 8, 1, 162049104065652566239401972919789062602096640000000⟩ +] + +def collectedFourData_9_7_16 : List CollectedFourTerm := [ + ⟨4, 5, 0, 0, 7, 2, -1353537208459987034764482873162230043137959526400000⟩, + ⟨4, 5, 1, 0, 8, 2, -155746959258758723397223243497550526725855641600000⟩, + ⟨4, 5, 0, 1, 6, 2, -170290604829026146596868952292646368056652595200000⟩, + ⟨4, 5, 1, 1, 7, 2, -1633270813361224184198111326302191509382470041600000⟩, + ⟨4, 5, 2, 1, 8, 2, 449060049309374338594844625170842880291163340800000⟩, + ⟨4, 5, 0, 2, 5, 2, 823601743810265746259617747930048427478692659200000⟩, + ⟨4, 5, 1, 2, 6, 2, -1936755536202642291630678361055893284108789350400000⟩, + ⟨4, 5, 2, 2, 7, 2, 545851876683805320689366587144435742650505625600000⟩, + ⟨4, 5, 3, 2, 8, 2, 76538778525341550579567806482422443689377792000000⟩, + ⟨4, 5, 0, 3, 4, 2, -523034592619527958621648141703656467316762214400000⟩, + ⟨4, 5, 1, 3, 5, 2, -1600058856863487277028853458275109851256743526400000⟩, + ⟨4, 5, 2, 3, 6, 2, 216841233927920299731972223575090134645735424000000⟩, + ⟨4, 5, 3, 3, 7, 2, 191108866795093355499143179612679242597898649600000⟩, + ⟨4, 5, 4, 3, 8, 2, 27754766607482045058375318084838327510577971200000⟩, + ⟨4, 5, 0, 4, 3, 2, -2007274762048135107519572296197921678102940876800000⟩, + ⟨4, 5, 1, 4, 4, 2, 1802169351139229720466502685524139179491773644800000⟩, + ⟨4, 5, 2, 4, 5, 2, 100705239134059724774046447154709847911851622400000⟩, + ⟨4, 5, 3, 4, 6, 2, 438979465593602468801018180910548157855065702400000⟩, + ⟨4, 5, 4, 4, 7, 2, 63247162835236378484716394288427072631288627200000⟩, + ⟨4, 5, 5, 4, 8, 2, -54961681524189873156259593507501671822288486400000⟩, + ⟨4, 5, 0, 5, 2, 2, 3387694077599420041702571843849393357668850073600000⟩, + ⟨4, 5, 1, 5, 3, 2, 3441684193481799118809643468939093311402855628800000⟩, + ⟨4, 5, 2, 5, 4, 2, -533962673677447524520689714028907595670801612800000⟩, + ⟨4, 5, 3, 5, 5, 2, 144271468955945273415632951416488393410661580800000⟩, + ⟨4, 5, 4, 5, 6, 2, -58015281119803372490534858022034110624143769600000⟩, + ⟨4, 5, 5, 5, 7, 2, 1869710603729746847128367716344930821052825600000⟩, + ⟨4, 5, 6, 5, 8, 2, -12902777664612997636513162850429952563399884800000⟩, + ⟨4, 5, 0, 6, 1, 2, -2462393988983675925103861671536373261416792064000000⟩, + ⟨4, 5, 1, 6, 2, 2, -8576396738545058717229801417572893724681384755200000⟩, + ⟨4, 5, 2, 6, 3, 2, -269428089769966761063915083532353251684909056000000⟩, + ⟨4, 5, 3, 6, 4, 2, -680674176768234559399347755145551892173763379200000⟩, + ⟨4, 5, 4, 6, 5, 2, 94134646619474035152979004892603983495744716800000⟩, + ⟨4, 5, 5, 6, 6, 2, -17784284352597295239712521943409167318804070400000⟩, + ⟨4, 5, 6, 6, 7, 2, -12185341230182570722671547185834575726326579200000⟩, + ⟨4, 5, 7, 6, 8, 2, -1909705799363840755980090195186810369972633600000⟩, + ⟨4, 5, 0, 7, 0, 2, 24016441303278908940993969222688204015919117107200000⟩, + ⟨4, 5, 1, 7, 1, 2, 24541998620024741934046357182636647907658511155200000⟩, + ⟨4, 5, 2, 7, 2, 2, 1303114150382752915431833930298967033422387609600000⟩, + ⟨4, 5, 3, 7, 3, 2, 1213102697741604245497148921299925946118805913600000⟩, + ⟨4, 5, 4, 7, 4, 2, 389304502330194387545100239980457429516786073600000⟩, + ⟨4, 5, 5, 7, 5, 2, 20112253467687468971276379894653645043951206400000⟩, + ⟨4, 5, 6, 7, 6, 2, 13188436653945975005330428084137375005933568000000⟩, + ⟨4, 5, 7, 7, 7, 2, 674952363422037360605169275709999876459724800000⟩, + ⟨4, 5, 8, 7, 8, 2, 2263826338806006033291739655262265493422080000000⟩ +] + +def collectedFourData_9_7_17 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 7, 3, -17700420917719596259902065832823926110635111219200000⟩, + ⟨4, 6, 1, 0, 8, 3, -1018363853724989846632118031760492005385725542400000⟩, + ⟨4, 6, 0, 1, 6, 3, -2226917269039317776215383899845889015714257305600000⟩, + ⟨4, 6, 1, 1, 7, 3, -10679270835122568328250473466442065233641367142400000⟩, + ⟨4, 6, 2, 1, 8, 3, 1957476514234251087981051299878632177365994700800000⟩, + ⟨4, 6, 0, 2, 5, 3, 10770370731511750900323070049656322939397183897600000⟩, + ⟨4, 6, 1, 2, 6, 3, -12663629781007199096148938857461474129897691545600000⟩, + ⟨4, 6, 2, 2, 7, 3, 2379397210913133528399638877224766610735733145600000⟩, + ⟨4, 6, 3, 2, 8, 3, 250227438883648609809199693235319360291078144000000⟩, + ⟨4, 6, 0, 3, 4, 3, -6839806387315374029700833506611470159989388083200000⟩, + ⟨4, 6, 1, 3, 5, 3, -10462111821747608726389286902392830651834931609600000⟩, + ⟨4, 6, 2, 3, 6, 3, 945222411533321888010571191307756419598516224000000⟩, + ⟨4, 6, 3, 3, 7, 3, 624790246296645721291756728134790432148370227200000⟩, + ⟨4, 6, 4, 3, 8, 3, 72590697670506394595352023704980164268754206720000⟩, + ⟨4, 6, 0, 4, 3, 3, -26249450671690015964954452112993261347018270310400000⟩, + ⟨4, 6, 1, 4, 4, 3, 11783627328749924642175209986335232049510822707200000⟩, + ⟨4, 6, 2, 4, 5, 3, 438979465593602468801018180910548157855065702400000⟩, + ⟨4, 6, 3, 4, 6, 3, 1435151037348093252662113358613281496133061836800000⟩, + ⟨4, 6, 4, 4, 7, 3, 165418637483777734086662296593622802341633720320000⟩, + ⟨4, 6, 5, 4, 8, 3, -119790438864340009109832890523995343152165683200000⟩, + ⟨4, 6, 0, 5, 2, 3, 44301413170754513872855839804291494814386277580800000⟩, + ⟨4, 6, 1, 5, 3, 3, 22503725242914523397231262009227146576729944883200000⟩, + ⟨4, 6, 2, 5, 4, 3, -2327571545963199167606997764207608157818375372800000⟩, + ⟨4, 6, 3, 5, 5, 3, 471665224822934369949239285409827478763575705600000⟩, + ⟨4, 6, 4, 5, 6, 3, -151735007957220440853746785868316400064145653760000⟩, + ⟨4, 6, 5, 5, 7, 3, 4075083723039309311264207993951547202260172800000⟩, + ⟨4, 6, 6, 5, 8, 3, -24104524505330324877176990759531440378164019200000⟩, + ⟨4, 6, 0, 6, 1, 3, -32201117041964285681386671300682460279542382592000000⟩, + ⟨4, 6, 1, 6, 2, 3, -56077450727167331748614433184199006391246834892800000⟩, + ⟨4, 6, 2, 6, 3, 3, -1174451298464010827269950908955065108718944256000000⟩, + ⟨4, 6, 3, 6, 4, 3, -2225321062715394097245094970414345128283367014400000⟩, + ⟨4, 6, 4, 6, 5, 3, 246202743107632419400760386741916215049013166080000⟩, + ⟨4, 6, 5, 6, 6, 3, -38761318220371652250051312299127854895149875200000⟩, + ⟨4, 6, 6, 6, 7, 3, -22764234486835014025108008804612170241068236800000⟩, + ⟨4, 6, 7, 6, 8, 3, -3121690732481756354260320853724059389237657600000⟩, + ⟨4, 6, 0, 7, 0, 3, 314066814976892913684097643996028937600050502041600000⟩, + ⟨4, 6, 1, 7, 1, 3, 160469805714016007827827239432694522287208844492800000⟩, + ⟨4, 6, 2, 7, 2, 3, 5680343527916923039779701830010596136435947929600000⟩, + ⟨4, 6, 3, 7, 3, 3, 3965984132582183047018946476378729681974932275200000⟩, + ⟨4, 6, 4, 7, 4, 3, 1018199354009335446886334665445293720384737116160000⟩, + ⟨4, 6, 5, 7, 5, 3, 43835188491908830177636708133039488214709043200000⟩, + ⟨4, 6, 6, 7, 6, 3, 24638182783224178198617707713038656389251072000000⟩, + ⟨4, 6, 7, 7, 7, 3, 1103307398690998175600307293821509982538956800000⟩, + ⟨4, 6, 8, 7, 8, 3, 3289379595841623165356600950643708248719360000000⟩ +] + +def collectedFourData_9_7_18 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 7, 4, -5100472763669748551506838344725353348249891635200000⟩, + ⟨4, 7, 1, 0, 8, 4, -195631396698606584104744054936015499123333529600000⟩, + ⟨4, 7, 0, 1, 6, 4, -641698348896902358172401434239469389059037593600000⟩, + ⟨4, 7, 1, 1, 7, 4, -2051526732371545340928046728662867984892139929600000⟩, + ⟨4, 7, 2, 1, 8, 4, 282028763405849995733867128641823358962787942400000⟩, + ⟨4, 7, 0, 2, 5, 4, 3103541030242281834452108841427905729607080345600000⟩, + ⟨4, 7, 1, 2, 6, 4, -2432729296381264771212562812402060069114898022400000⟩, + ⟨4, 7, 2, 2, 7, 4, 342818137620247317894239318693069289429978316800000⟩, + ⟨4, 7, 3, 2, 8, 4, 28841760152070179570366922937650323113220505600000⟩, + ⟨4, 7, 0, 3, 4, 4, -1970927490902343737702136452892954840351847219200000⟩, + ⟨4, 7, 1, 3, 5, 4, -2009809696818055101630174108466465630425867878400000⟩, + ⟨4, 7, 2, 3, 6, 4, 136185494911300180582698025146350956940623872000000⟩, + ⟨4, 7, 3, 3, 7, 4, 72014685957041339786577498693663037448288993280000⟩, + ⟨4, 7, 4, 3, 8, 4, 6972468396567054777443758831865708800313917440000⟩, + ⟨4, 7, 0, 4, 3, 4, -7563922283803876333992649821571442523370841702400000⟩, + ⟨4, 7, 1, 4, 4, 4, 2263677627664259832128942460683474576551496908800000⟩, + ⟨4, 7, 2, 4, 5, 4, 63247162835236378484716394288427072631288627200000⟩, + ⟨4, 7, 3, 4, 6, 4, 165418637483777734086662296593622802341633720320000⟩, + ⟨4, 7, 4, 4, 7, 4, 15888760668675037129474379779309113103236464640000⟩, + ⟨4, 7, 5, 4, 8, 4, -9862362250605538198988452543607968158135091200000⟩, + ⟨4, 7, 0, 5, 2, 4, 12765693670217228317705653395102498200490921164800000⟩, + ⟨4, 7, 1, 5, 3, 4, 4323047390271905574011594676631064629480312012800000⟩, + ⟨4, 7, 2, 5, 4, 4, -335351213704568217412699442058104597148755558400000⟩, + ⟨4, 7, 3, 5, 5, 4, 54365162138516684505223129940044924740635197440000⟩, + ⟨4, 7, 4, 5, 6, 4, -14574423191753154779823296697090389789135339520000⟩, + ⟨4, 7, 5, 5, 7, 4, 335502167444884138500121102386887649971404800000⟩, + ⟨4, 7, 6, 5, 8, 4, -1736462529509251400806799301604612923772108800000⟩, + ⟨4, 7, 0, 6, 1, 4, -9278927387984416324946818185848841600082378752000000⟩, + ⟨4, 7, 1, 6, 2, 4, -10772682051631060224754908756650044378527773491200000⟩, + ⟨4, 7, 2, 6, 3, 4, -169212271502411328244227164356691797966061568000000⟩, + ⟨4, 7, 3, 6, 4, 4, -256495357337813419697550066174231428284872130560000⟩, + ⟨4, 7, 4, 6, 5, 4, 23648220785230937444445533572537942085373788160000⟩, + ⟨4, 7, 5, 6, 6, 4, -3191224318271539892193003899994025307091763200000⟩, + ⟨4, 7, 6, 6, 7, 4, -1639909560987606838344895173351042800890675200000⟩, + ⟨4, 7, 7, 6, 8, 4, -199896044301084867049544796356755006999756800000⟩, + ⟨4, 7, 0, 7, 0, 4, 90500064558268440359686661014412312161067571609600000⟩, + ⟨4, 7, 1, 7, 1, 4, 30826832771958030639201831708614653803077251891200000⟩, + ⟨4, 7, 2, 7, 2, 4, 818410974154410471325812985711706338396785868800000⟩, + ⟨4, 7, 3, 7, 3, 4, 457127977767613641450243778302905586561822228480000⟩, + ⟨4, 7, 4, 7, 4, 4, 97799897852745858045974023381755821975477944320000⟩, + ⟨4, 7, 5, 7, 5, 4, 3608956710813715214694980290149999245996851200000⟩, + ⟨4, 7, 6, 7, 6, 4, 1774906664879778698556502048961332047249408000000⟩, + ⟨4, 7, 7, 7, 7, 4, 70649786781125149412921789907474267399782400000⟩, + ⟨4, 7, 8, 7, 8, 4, 189570531864195814679638686030396162834432000000⟩ +] + +def collectedFourData_9_7_19 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 7, 5, 7387170878318117769738070787065721380147298304000000⟩, + ⟨4, 8, 1, 0, 8, 5, 212504206502741383067802203701713609418604544000000⟩, + ⟨4, 8, 0, 1, 6, 5, 929391367286781382283619570134561220483612672000000⟩, + ⟨4, 8, 1, 1, 7, 5, 2228466737644481109377247834458294673205100544000000⟩, + ⟨4, 8, 2, 1, 8, 5, -245082536197775526304658178531561776526183628800000⟩, + ⟨4, 8, 0, 2, 5, 5, -4494953503442658145715696691904012556238323712000000⟩, + ⟨4, 8, 1, 2, 6, 5, 2642547246952999962466887702475914975155060736000000⟩, + ⟨4, 8, 2, 2, 7, 5, -297908403412251008445547320331330479531334041600000⟩, + ⟨4, 8, 3, 2, 8, 5, -20886202176434576035500922074238307014803456000000⟩, + ⟨4, 8, 0, 3, 4, 5, 2854554634185497135136319699070780964008361984000000⟩, + ⟨4, 8, 1, 3, 5, 5, 2183151692679593647188295977750510169359384576000000⟩, + ⟨4, 8, 2, 3, 6, 5, -118344973339405081603985759637072843651416064000000⟩, + ⟨4, 8, 3, 3, 7, 5, -52150537368061718426377216512996738694171852800000⟩, + ⟨4, 8, 4, 3, 8, 5, -4327902631412557923561219107726957609169715200000⟩, + ⟨4, 8, 0, 4, 3, 5, 10955060248292581397403216964620360361860661248000000⟩, + ⟨4, 8, 1, 4, 4, 5, -2458915215873566796973701297642940791816978432000000⟩, + ⟨4, 8, 2, 4, 5, 5, -54961681524189873156259593507501671822288486400000⟩, + ⟨4, 8, 3, 4, 6, 5, -119790438864340009109832890523995343152165683200000⟩, + ⟨4, 8, 4, 4, 7, 5, -9862362250605538198988452543607968158135091200000⟩, + ⟨4, 8, 5, 4, 8, 5, 5356485461115271422923579848230361349750784000000⟩, + ⟨4, 8, 0, 5, 2, 5, -18488945023658720557993900500892196236947357696000000⟩, + ⟨4, 8, 1, 5, 3, 5, -4695901429149391672564748024009620384741588992000000⟩, + ⟨4, 8, 2, 5, 4, 5, 291419658687242226640721546568405300502383820800000⟩, + ⟨4, 8, 3, 5, 5, 5, -39369364483748545835689326740399877421164134400000⟩, + ⟨4, 8, 4, 5, 6, 5, 9046535731013847472110156717556210075277721600000⟩, + ⟨4, 8, 5, 5, 7, 5, -182219273276120281262242160910642431655936000000⟩, + ⟨4, 8, 6, 5, 8, 5, 838323950454875275660793080427566640136192000000⟩, + ⟨4, 8, 0, 6, 1, 5, 13438954653534762668966150013453632550249431040000000⟩, + ⟨4, 8, 1, 6, 2, 5, 11701803953355346113613806411994672274570477568000000⟩, + ⟨4, 8, 2, 6, 3, 5, 147045188422569705774421776794562565521801216000000⟩, + ⟨4, 8, 3, 6, 4, 5, 185745039915321442757214790008253540074101145600000⟩, + ⟨4, 8, 4, 6, 5, 5, -14678760970077326319149234521772035693923532800000⟩, + ⟨4, 8, 5, 6, 6, 5, 1733230460372661711877682876086528008781824000000⟩, + ⟨4, 8, 6, 6, 7, 5, 791710410212180941306930418206020225466368000000⟩, + ⟨4, 8, 7, 6, 8, 5, 86854668512503525119279419818277916691660800000⟩, + ⟨4, 8, 0, 7, 0, 5, -131074014580119345698535943010998955629181140992000000⟩, + ⟨4, 8, 1, 7, 1, 5, -33485584357862452735775352349018881007779053568000000⟩, + ⟨4, 8, 2, 7, 2, 5, -711197803995670503035903177255042323049978265600000⟩, + ⟨4, 8, 3, 7, 3, 5, -331036223649955153566749836752569815106637004800000⟩, + ⟨4, 8, 4, 7, 4, 5, -60705679996653329618631284074512022226180505600000⟩, + ⟨4, 8, 5, 7, 5, 5, -1960110940974727890695543773925140001193984000000⟩, + ⟨4, 8, 6, 7, 6, 5, -856883889922587664940771855798052291870720000000⟩, + ⟨4, 8, 7, 7, 7, 5, -30697274840072339695503469753173147018854400000⟩, + ⟨4, 8, 8, 7, 8, 5, -74880219786112622388364705774449689886720000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0929.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0929.lean new file mode 100644 index 0000000000000000000000000000000000000000..2336e935b15977b7cad2bc43d70683fb8f6246cf --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0929.lean @@ -0,0 +1,619 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse0929. -/ +namespace LaughlinFock +def collectedFourData_9_7_20 : List CollectedFourTerm := [ + ⟨5, 2, 2, 1, 8, 0, 15106245540082893417738201834192172345040515891200000⟩, + ⟨5, 2, 2, 2, 7, 0, 18362293618374831648094564740373416800229418598400000⟩, + ⟨5, 2, 3, 2, 8, 0, 7724224745799692564484952837026863660258033664000000⟩, + ⟨5, 2, 2, 3, 6, 0, 7294474153217300129363392330163754923024449536000000⟩, + ⟨5, 2, 3, 3, 7, 0, 19286535093470907382444606399450105057025143603200000⟩, + ⟨5, 2, 4, 3, 8, 0, 5601972207393575376921583620474395599097875660800000⟩, + ⟨5, 2, 2, 4, 5, 0, 3387694077599420041702571843849393357668850073600000⟩, + ⟨5, 2, 3, 4, 6, 0, 44301413170754513872855839804291494814386277580800000⟩, + ⟨5, 2, 4, 4, 7, 0, 12765693670217228317705653395102498200490921164800000⟩, + ⟨5, 2, 5, 4, 8, 0, -18488945023658720557993900500892196236947357696000000⟩, + ⟨5, 2, 2, 5, 4, 0, -17962344390724436591657859791620928387792712499200000⟩, + ⟨5, 2, 3, 5, 5, 0, 14559746994831097962701236612657421960749881753600000⟩, + ⟨5, 2, 4, 5, 6, 0, -11709700068227243265675529798720590702870685286400000⟩, + ⟨5, 2, 5, 5, 7, 0, 628965046262211979988932700376684645511593984000000⟩, + ⟨5, 2, 6, 5, 8, 0, -6510683632974173923722807058976129284055236608000000⟩, + ⟨5, 2, 2, 6, 3, 0, -9063480231029426587052151848721972191438045184000000⟩, + ⟨5, 2, 3, 6, 4, 0, -68693026219111189412042997006217767741487998566400000⟩, + ⟨5, 2, 4, 6, 5, 0, 18999967882019606430731591686398058676136129331200000⟩, + ⟨5, 2, 5, 6, 6, 0, -5982579982302171045089699939652954101127315456000000⟩, + ⟨5, 2, 6, 6, 7, 0, -6148668431847662816354532242359307710425464832000000⟩, + ⟨5, 2, 7, 6, 8, 0, -1349080551557479295839516655018070948801046118400000⟩, + ⟨5, 2, 2, 7, 2, 0, 43836369663061525734576327292303316472031503974400000⟩, + ⟨5, 2, 3, 7, 3, 0, 122425234079083442320368481543500765982046237491200000⟩, + ⟨5, 2, 4, 7, 4, 0, 78576521039057243999029407133384899842898552422400000⟩, + ⟨5, 2, 5, 7, 5, 0, 6765701819044630335171473942120468017626218496000000⟩, + ⟨5, 2, 6, 7, 6, 0, 6654825875428131862242254409777312014039777280000000⟩, + ⟨5, 2, 7, 7, 7, 0, 476809101707578672043436176839063245077820211200000⟩, + ⟨5, 2, 8, 7, 8, 0, 2132324317043409851517284211370374127272591360000000⟩ +] + +def collectedFourData_9_7_21 : List CollectedFourTerm := [ + ⟨5, 3, 1, 0, 8, 1, -2661390074999738598026396199588160120028764569600000⟩, + ⟨5, 3, 1, 1, 7, 1, -27909185213976263616393475839574324099572930969600000⟩, + ⟨5, 3, 2, 1, 8, 1, 15346995716626192029912179202901756374144358809600000⟩, + ⟨5, 3, 1, 2, 6, 1, -33095104946394889195719844427321454989360391782400000⟩, + ⟨5, 3, 2, 2, 7, 1, 18654935851591131406290963338224742644902474547200000⟩, + ⟨5, 3, 3, 2, 8, 1, 3923663354124039579969082923026360255649939456000000⟩, + ⟨5, 3, 1, 3, 5, 1, -27341662279242439548983507843932963656704616038400000⟩, + ⟨5, 3, 2, 3, 6, 1, 7410727125242535530786476312127065205860466688000000⟩, + ⟨5, 3, 3, 3, 7, 1, 9796953540927103975972560692088054838348008652800000⟩, + ⟨5, 3, 4, 3, 8, 1, 1897083852799081138434317821273814524765195468800000⟩, + ⟨5, 3, 1, 4, 4, 1, 30795308283496631048237006518055101782890958028800000⟩, + ⟨5, 3, 2, 4, 5, 1, 3441684193481799118809643468939093311402855628800000⟩, + ⟨5, 3, 3, 4, 6, 1, 22503725242914523397231262009227146576729944883200000⟩, + ⟨5, 3, 4, 4, 7, 1, 4323047390271905574011594676631064629480312012800000⟩, + ⟨5, 3, 5, 4, 8, 1, -4695901429149391672564748024009620384741588992000000⟩, + ⟨5, 3, 1, 5, 3, 1, 58811190904844771478941134316893257878966422732800000⟩, + ⟨5, 3, 2, 5, 4, 1, -18248612581700412737950153702856623874903742873600000⟩, + ⟨5, 3, 3, 5, 5, 1, 7395893776912876469703511434157231846776530534400000⟩, + ⟨5, 3, 4, 5, 6, 1, -3965439687693456367640359687105411991806043750400000⟩, + ⟨5, 3, 5, 5, 7, 1, 159747235758899129996063011538851905423802368000000⟩, + ⟨5, 3, 6, 5, 8, 1, -1322889046949975735325037620140140397647940812800000⟩, + ⟨5, 3, 1, 6, 2, 1, -146552698478704538651865380965018561737477272371200000⟩, + ⟨5, 3, 2, 6, 3, 1, -9207926080259615766995513521703265403322499072000000⟩, + ⟨5, 3, 3, 6, 4, 1, -34893897903006188586435094582801100996582414745600000⟩, + ⟨5, 3, 4, 6, 5, 1, 6434257603975325668876672868810691834809627443200000⟩, + ⟨5, 3, 5, 6, 6, 1, -1519481282082040067963118340238653868067520512000000⟩, + ⟨5, 3, 6, 6, 7, 1, -1249332110167765210723454134237050057681744691200000⟩, + ⟨5, 3, 7, 6, 8, 1, -228430170280668376065246927575302874240070451200000⟩, + ⟨5, 3, 1, 7, 1, 1, 419371471898049081094919873645300454436614910771200000⟩, + ⟨5, 3, 2, 7, 2, 1, 44534995519989139949373046462941991910103003955200000⟩, + ⟨5, 3, 3, 7, 3, 1, 62188170384007359394664359407795840629756185804800000⟩, + ⟨5, 3, 4, 7, 4, 1, 26609601717691972611121300282050748196707526246400000⟩, + ⟨5, 3, 5, 7, 5, 1, 1718381919606316145602409177751957761364590592000000⟩, + ⟨5, 3, 6, 7, 6, 1, 1352176938129237576796595212060950203411202048000000⟩, + ⟨5, 3, 7, 7, 7, 1, 80734678273059479469996830311405839021873561600000⟩, + ⟨5, 3, 8, 7, 8, 1, 309472491959805734400775019607859469840547840000000⟩ +] + +def collectedFourData_9_7_22 : List CollectedFourTerm := [ + ⟨5, 4, 0, 0, 7, 2, 7176770076371970088279236010326260972876778700800000⟩, + ⟨5, 4, 1, 0, 8, 2, 825806715698593174339292850182716135105049395200000⟩, + ⟨5, 4, 0, 1, 6, 2, 902920517726105409621316267892601447539697254400000⟩, + ⟨5, 4, 1, 1, 7, 2, 8659982914898238047088298463818903173050086195200000⟩, + ⟨5, 4, 2, 1, 8, 2, -2381021152750165303124049375675114536008522137600000⟩, + ⟨5, 4, 0, 2, 5, 2, -4366928602243905291993634641141679028733109862400000⟩, + ⟨5, 4, 1, 2, 6, 2, 10269129722175473781263351591655036846938574028800000⟩, + ⟨5, 4, 2, 2, 7, 2, -2894234004230274985222328337340995732298216243200000⟩, + ⟨5, 4, 3, 2, 8, 2, -405826461193269149916478339200362274329985024000000⟩, + ⟨5, 4, 0, 3, 4, 2, 2773251440564441597138142834086514049864748236800000⟩, + ⟨5, 4, 1, 3, 5, 2, 8483885372783442141709086703879595593397226700800000⟩, + ⟨5, 4, 2, 3, 6, 2, -1149742814050964761641809672196311347026198528000000⟩, + ⟨5, 4, 3, 3, 7, 2, -1013303799830433763166865314622127398118961971200000⟩, + ⟨5, 4, 4, 3, 8, 2, -147162248086180720301963712182209025090676326400000⟩, + ⟨5, 4, 0, 4, 3, 2, 10643039110623446326651064790612610573045176729600000⟩, + ⟨5, 4, 1, 4, 4, 2, -9555522368333222104032434133687552350623472025600000⟩, + ⟨5, 4, 2, 4, 5, 2, -533962673677447524520689714028907595670801612800000⟩, + ⟨5, 4, 3, 4, 6, 2, -2327571545963199167606997764207608157818375372800000⟩, + ⟨5, 4, 4, 4, 7, 2, -335351213704568217412699442058104597148755558400000⟩, + ⟨5, 4, 5, 4, 8, 2, 291419658687242226640721546568405300502383820800000⟩, + ⟨5, 4, 0, 5, 2, 2, -17962344390724436591657859791620928387792712499200000⟩, + ⟨5, 4, 1, 5, 3, 2, -18248612581700412737950153702856623874903742873600000⟩, + ⟨5, 4, 2, 5, 4, 2, 2831194675991177901225310427640285489006221721600000⟩, + ⟨5, 4, 3, 5, 5, 2, -764960988738023324931427057164940664632875417600000⟩, + ⟨5, 4, 4, 5, 6, 2, 307610556186066586749751170312576150610850611200000⟩, + ⟨5, 4, 5, 5, 7, 2, -9913641847785000724244946056668532392014643200000⟩, + ⟨5, 4, 6, 5, 8, 2, 68413537556779032133447248507421752857041305600000⟩, + ⟨5, 4, 0, 6, 1, 2, 13056187436829279241233193692375120549519556608000000⟩, + ⟨5, 4, 1, 6, 2, 2, 45474056488121942953450257565777492844000732774400000⟩, + ⟨5, 4, 2, 6, 3, 2, 1428570592895023255007015059333399224917164032000000⟩, + ⟨5, 4, 3, 6, 4, 2, 3609093295002537147771977549073132849591641702400000⟩, + ⟨5, 4, 4, 6, 5, 2, -499123859163907508334296984149173910518733209600000⟩, + ⟨5, 4, 5, 6, 6, 2, 94296424932882517612885929372350445161073868800000⟩, + ⟨5, 4, 6, 6, 7, 2, 64609522194558201979255533215849962822592102400000⟩, + ⟨5, 4, 7, 6, 8, 2, 10125705706415077926644031438652285574656819200000⟩, + ⟨5, 4, 0, 7, 0, 2, -127340775125363828643904694466001033222777366118400000⟩, + ⟨5, 4, 1, 7, 1, 2, -130127402637828951063565344839682300757246633574400000⟩, + ⟨5, 4, 2, 7, 2, 2, -6909415258117960152145728128255810496156087091200000⟩, + ⟨5, 4, 3, 7, 3, 2, -6432153535419728790330833524353448894885212979200000⟩, + ⟨5, 4, 4, 7, 4, 2, -2064183300951947991134086530798855330316104499200000⟩, + ⟨5, 4, 5, 7, 5, 2, -106639860325328318416170580868657607659539660800000⟩, + ⟨5, 4, 6, 7, 6, 2, -69928168166028498245856273267702806291152896000000⟩, + ⟨5, 4, 7, 7, 7, 2, -3578754905670562047484789854517254701029785600000⟩, + ⟨5, 4, 8, 7, 8, 2, -12003335427277207647638923904119322978549760000000⟩ +] + +def collectedFourData_9_7_23 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 7, 3, -5817278317300779223675652810616818384205407846400000⟩, + ⟨5, 5, 1, 0, 8, 3, -334687293196893532426254532976839702872902860800000⟩, + ⟨5, 5, 0, 1, 6, 3, -731880761696263254382531686913663306317378355200000⟩, + ⟨5, 5, 1, 1, 7, 3, -3509763466220710603288942706973135474472570060800000⟩, + ⟨5, 5, 2, 1, 8, 3, 643328525113258592154456668418086283167504793600000⟩, + ⟨5, 5, 0, 2, 5, 3, 3539703627216690747533978208915896849640141619200000⟩, + ⟨5, 5, 1, 2, 6, 3, -4161926955625667022442742154969254317360624435200000⟩, + ⟨5, 5, 2, 2, 7, 3, 781993595950834699819008879510303895501091635200000⟩, + ⟨5, 5, 3, 2, 8, 3, 82237742332688561492846960834239985350606848000000⟩, + ⟨5, 5, 0, 3, 4, 3, -2247915887222373276512993139761082492470584934400000⟩, + ⟨5, 5, 1, 3, 5, 3, -3438393727287104824285291065933703911291695923200000⟩, + ⟨5, 5, 2, 3, 6, 3, 310649213665589656155403561233560589941342208000000⟩, + ⟨5, 5, 3, 3, 7, 3, 205338549266021941882448014119451823389959782400000⟩, + ⟨5, 5, 4, 3, 8, 3, 23857076255945714499011839106286452472010506240000⟩, + ⟨5, 5, 0, 4, 3, 3, -8626933842042870312274395035875286588752448716800000⟩, + ⟨5, 5, 1, 4, 4, 3, 3872712410475331537003136627493099813063779942400000⟩, + ⟨5, 5, 2, 4, 5, 3, 144271468955945273415632951416488393410661580800000⟩, + ⟨5, 5, 3, 4, 6, 3, 471665224822934369949239285409827478763575705600000⟩, + ⟨5, 5, 4, 4, 7, 3, 54365162138516684505223129940044924740635197440000⟩, + ⟨5, 5, 5, 4, 8, 3, -39369364483748545835689326740399877421164134400000⟩, + ⟨5, 5, 0, 5, 2, 3, 14559746994831097962701236612657421960749881753600000⟩, + ⟨5, 5, 1, 5, 3, 3, 7395893776912876469703511434157231846776530534400000⟩, + ⟨5, 5, 2, 5, 4, 3, -764960988738023324931427057164940664632875417600000⟩, + ⟨5, 5, 3, 5, 5, 3, 155013708326024781054185671948910351158031155200000⟩, + ⟨5, 5, 4, 5, 6, 3, -49868010250612665608418376170039465199188049920000⟩, + ⟨5, 5, 5, 5, 7, 3, 1339284319475721082732844091945025376197017600000⟩, + ⟨5, 5, 6, 5, 8, 3, -7921999618287537738223951151714085179385446400000⟩, + ⟨5, 5, 0, 6, 1, 3, -10582960757365812318801160426507529750015115264000000⟩, + ⟨5, 5, 1, 6, 2, 3, -18429965011627593263458795172298227591767759257600000⟩, + ⟨5, 5, 2, 6, 3, 3, -385985740397897806949746919254735690716413952000000⟩, + ⟨5, 5, 3, 6, 4, 3, -731356165333201403916433583200858343918587084800000⟩, + ⟨5, 5, 4, 6, 5, 3, 80915018111587532261734467372390704741728911360000⟩, + ⟨5, 5, 5, 6, 6, 3, -12738983840075463353026935440495634356266598400000⟩, + ⟨5, 5, 6, 6, 7, 3, -7481510654791638858944257759052980798724505600000⟩, + ⟨5, 5, 7, 6, 8, 3, -1025949828865679222485123146420021256991539200000⟩, + ⟨5, 5, 0, 7, 0, 3, 103218679456362613905384327938185027326812828467200000⟩, + ⟨5, 5, 1, 7, 1, 3, 52738718796630717666886768585237721166420482457600000⟩, + ⟨5, 5, 2, 7, 2, 3, 1866856126946167311105889939353451213276525363200000⟩, + ⟨5, 5, 3, 7, 3, 3, 1303428523450142651651832489024589247145207398400000⟩, + ⟨5, 5, 4, 7, 4, 3, 334633230040230376134024311414899813254923550720000⟩, + ⟨5, 5, 5, 7, 5, 3, 14406521332693062692790893453343332262897254400000⟩, + ⟨5, 5, 6, 7, 6, 3, 8097387466026920298674447372308024261607424000000⟩, + ⟨5, 5, 7, 7, 7, 3, 362604157130380472836534505765795503118745600000⟩, + ⟨5, 5, 8, 7, 8, 3, 1081061105225193177765151879939407080325120000000⟩ +] + +def collectedFourData_9_7_24 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 7, 4, 4678555495035510740948935086498247056811465113600000⟩, + ⟨5, 6, 1, 0, 8, 4, 179448531231290552211480564899074214894292172800000⟩, + ⟨5, 6, 0, 1, 6, 4, 588616286272793100104325854320634995948702924800000⟩, + ⟨5, 6, 1, 1, 7, 4, 1881821962723966326777047953476592206466567372800000⟩, + ⟨5, 6, 2, 1, 8, 4, -258699003392216757975394843214998822121059123200000⟩, + ⟨5, 6, 0, 2, 5, 4, -2846812366989508701795794995907152899369389260800000⟩, + ⟨5, 6, 1, 2, 6, 4, 2231490990127242067954721650986263042455712563200000⟩, + ⟨5, 6, 2, 2, 7, 4, -314459807135027149273481963093711418810590822400000⟩, + ⟨5, 6, 3, 2, 8, 4, -26455934910017544670320385566158281801256140800000⟩, + ⟨5, 6, 0, 3, 4, 4, 1807889987876968925066568666451878054939171225600000⟩, + ⟨5, 6, 1, 3, 5, 4, 1843555810747703959178010911911739441630360371200000⟩, + ⟨5, 6, 2, 3, 6, 4, -124920066253420950159695007448240070376554496000000⟩, + ⟨5, 6, 3, 3, 7, 4, -66057544137370868371028788066577736283497431040000⟩, + ⟨5, 6, 4, 3, 8, 4, -6395697387716198597938015402847617622653009920000⟩, + ⟨5, 6, 0, 4, 3, 4, 6938225494895228623779616491544000115101610803200000⟩, + ⟨5, 6, 1, 4, 4, 4, -2076423479669288473116238422723904144406898278400000⟩, + ⟨5, 6, 2, 4, 5, 4, -58015281119803372490534858022034110624143769600000⟩, + ⟨5, 6, 3, 4, 6, 4, -151735007957220440853746785868316400064145653760000⟩, + ⟨5, 6, 4, 4, 7, 4, -14574423191753154779823296697090389789135339520000⟩, + ⟨5, 6, 5, 4, 8, 4, 9046535731013847472110156717556210075277721600000⟩, + ⟨5, 6, 0, 5, 2, 4, -11709700068227243265675529798720590702870685286400000⟩, + ⟨5, 6, 1, 5, 3, 4, -3965439687693456367640359687105411991806043750400000⟩, + ⟨5, 6, 2, 5, 4, 4, 307610556186066586749751170312576150610850611200000⟩, + ⟨5, 6, 3, 5, 5, 4, -49868010250612665608418376170039465199188049920000⟩, + ⟨5, 6, 4, 5, 6, 4, 13368809298706957702852095707950939182056079360000⟩, + ⟨5, 6, 5, 5, 7, 4, -307749022850623987165515592973335371605606400000⟩, + ⟨5, 6, 6, 5, 8, 4, 1592820251335588165259508417958525899531878400000⟩, + ⟨5, 6, 0, 6, 1, 4, 8511363305046927924022853771067588925861134336000000⟩, + ⟨5, 6, 1, 6, 2, 4, 9881552778387174928023538225716364560251328921600000⟩, + ⟨5, 6, 2, 6, 3, 4, 155214827986935055892454703863204485397479424000000⟩, + ⟨5, 6, 3, 6, 4, 4, 235277751519746122192478401319708989396699054080000⟩, + ⟨5, 6, 4, 6, 5, 4, -21692011393655782542750277268878145287492730880000⟩, + ⟨5, 6, 5, 6, 6, 4, 2927242387507235916174811691806261717342617600000⟩, + ⟨5, 6, 6, 6, 7, 4, 1504254261010817575387964910323756657383833600000⟩, + ⟨5, 6, 7, 6, 8, 4, 183360402032186507762185744109059873072742400000⟩, + ⟨5, 6, 0, 7, 0, 4, -83013789889452433518411984705537802816562449612800000⟩, + ⟨5, 6, 1, 7, 1, 4, -28276799924722324027127793571509846532320500121600000⟩, + ⟨5, 6, 2, 7, 2, 4, -750711029691404871925959470614686927713363558400000⟩, + ⟨5, 6, 3, 7, 3, 4, -419313799213460240331249041916014556669951344640000⟩, + ⟨5, 6, 4, 7, 4, 4, -89709772155250854709833324776301027806423285760000⟩, + ⟨5, 6, 5, 7, 5, 4, -3310419451896922389886685485675120879573401600000⟩, + ⟨5, 6, 6, 7, 6, 4, -1628084241385847654001338340483008292716544000000⟩, + ⟨5, 6, 7, 7, 7, 4, -64805551070152206670291049605405399528243200000⟩, + ⟨5, 6, 8, 7, 8, 4, -173889028457806860685604058022658049048576000000⟩ +] + +def collectedFourData_9_7_25 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 7, 5, -251300021027851133446563808814051038662230016000000⟩, + ⟨5, 7, 1, 0, 8, 5, -7229061360877055950830256298918772763262976000000⟩, + ⟨5, 7, 0, 1, 6, 5, -31616443424610019548458635209709582798553088000000⟩, + ⟨5, 7, 1, 1, 7, 5, -75808959512985661394569965766880503032446976000000⟩, + ⟨5, 7, 2, 1, 8, 5, 8337325278453891074529792697731013814727475200000⟩, + ⟨5, 7, 0, 2, 5, 5, 152911301029973184292062993173816974925365248000000⟩, + ⟨5, 7, 1, 2, 6, 5, -89895332010726733599941250837646293696774144000000⟩, + ⟨5, 7, 2, 2, 7, 5, 10134378813627371838907215766279593925174886400000⟩, + ⟨5, 7, 3, 2, 8, 5, 710515992196049387779524106179825603969024000000⟩, + ⟨5, 7, 0, 3, 4, 5, -97107492355624064813920297420317450081140736000000⟩, + ⟨5, 7, 1, 3, 5, 5, -74267412425456133510032608017435434107797504000000⟩, + ⟨5, 7, 2, 3, 6, 5, 4025911242424662492583345780226877403693056000000⟩, + ⟨5, 7, 3, 3, 7, 5, 1774079868068713140498352371675177294181171200000⟩, + ⟨5, 7, 4, 3, 8, 5, 147228491149793064302171555323771712490700800000⟩, + ⟨5, 7, 0, 4, 3, 5, -372674047494633780877557783354129493725806592000000⟩, + ⟨5, 7, 1, 4, 4, 5, 83648456984850105244502423459464961618608128000000⟩, + ⟨5, 7, 2, 4, 5, 5, 1869710603729746847128367716344930821052825600000⟩, + ⟨5, 7, 3, 4, 6, 5, 4075083723039309311264207993951547202260172800000⟩, + ⟨5, 7, 4, 4, 7, 5, 335502167444884138500121102386887649971404800000⟩, + ⟨5, 7, 5, 4, 8, 5, -182219273276120281262242160910642431655936000000⟩, + ⟨5, 7, 0, 5, 2, 5, 628965046262211979988932700376684645511593984000000⟩, + ⟨5, 7, 1, 5, 3, 5, 159747235758899129996063011538851905423802368000000⟩, + ⟨5, 7, 2, 5, 4, 5, -9913641847785000724244946056668532392014643200000⟩, + ⟨5, 7, 3, 5, 5, 5, 1339284319475721082732844091945025376197017600000⟩, + ⟨5, 7, 4, 5, 6, 5, -307749022850623987165515592973335371605606400000⟩, + ⟨5, 7, 5, 5, 7, 5, 6198815210890919031800067945922710994944000000⟩, + ⟨5, 7, 6, 5, 8, 5, -28518472071059780324459467609227204231168000000⟩, + ⟨5, 7, 0, 6, 1, 5, -457172257506317980077338215229460756729692160000000⟩, + ⟨5, 7, 1, 6, 2, 5, -398077102585111555913527186760712861486415872000000⟩, + ⟨5, 7, 2, 6, 3, 5, -5002247755103952693617003064905331652952064000000⟩, + ⟨5, 7, 3, 6, 4, 5, -6318756287815387668166388248529707490240102400000⟩, + ⟨5, 7, 4, 6, 5, 5, 499348532909946443589307421361907277443891200000⟩, + ⟨5, 7, 5, 6, 6, 5, -58961794482941321004267975642369119748096000000⟩, + ⟨5, 7, 6, 6, 7, 5, -26932752201284862471121485058108211331072000000⟩, + ⟨5, 7, 7, 6, 8, 5, -2954660232325445560758098427134935774003200000⟩, + ⟨5, 7, 0, 7, 0, 5, 4458933353886117008548119971549369655380410368000000⟩, + ⟨5, 7, 1, 7, 1, 5, 1139127304873797008763963052485555485379919872000000⟩, + ⟨5, 7, 2, 7, 2, 5, 24193839027555395362703800888708613802452582400000⟩, + ⟨5, 7, 3, 7, 3, 5, 11261335541645735006662653728979569647760179200000⟩, + ⟨5, 7, 4, 7, 4, 5, 2065112464698022474241339654958935926269542400000⟩, + ⟨5, 7, 5, 7, 5, 5, 66679914245603311896489152553741226868736000000⟩, + ⟨5, 7, 6, 7, 6, 5, 29149852237477925329023480495929693306880000000⟩, + ⟨5, 7, 7, 7, 7, 5, 1044273367961436588038690830158898239897600000⟩, + ⟨5, 7, 8, 7, 8, 5, 2547308180192589354532291462063592570880000000⟩ +] + +def collectedFourData_9_7_26 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 7, 6, 2601312972152033855917386303257822851227451392000000⟩, + ⟨5, 8, 1, 0, 8, 6, 59864861189003691227716582784993799762975129600000⟩, + ⟨5, 8, 0, 1, 6, 6, 327275199092139878703593340416527867268038656000000⟩, + ⟨5, 8, 1, 1, 7, 6, 627784522993326112635925428344323598146181529600000⟩, + ⟨5, 8, 2, 1, 8, 6, -57535457182975545453169818426375693760305561600000⟩, + ⟨5, 8, 0, 2, 5, 6, -1582849652502932910309286407660780448515096576000000⟩, + ⟨5, 8, 1, 2, 6, 6, 744435730133108761299691729404737897200248422400000⟩, + ⟨5, 8, 2, 2, 7, 6, -69936832117415253116862991774996597436527411200000⟩, + ⟨5, 8, 3, 2, 8, 6, -4202772583171674444670460887927476071694336000000⟩, + ⟨5, 8, 0, 3, 4, 6, 1005200789576708241206319153648076177677484032000000⟩, + ⟨5, 8, 1, 3, 5, 6, 615018757452767494481711990046620696705394278400000⟩, + ⟨5, 8, 2, 3, 6, 6, -27782608471519176356389337139885591125557248000000⟩, + ⟨5, 8, 3, 3, 7, 6, -10493858423694275418532421393858303347182796800000⟩, + ⟨5, 8, 4, 3, 8, 6, -762012240054452282206390436016610947681484800000⟩, + ⟨5, 8, 0, 4, 3, 6, 3857706935984508001116743308547691964482453504000000⟩, + ⟨5, 8, 1, 4, 4, 6, -692704490402175421078869115435801765477141708800000⟩, + ⟨5, 8, 2, 4, 5, 6, -12902777664612997636513162850429952563399884800000⟩, + ⟨5, 8, 3, 4, 6, 6, -24104524505330324877176990759531440378164019200000⟩, + ⟨5, 8, 4, 4, 7, 6, -1736462529509251400806799301604612923772108800000⟩, + ⟨5, 8, 5, 4, 8, 6, 838323950454875275660793080427566640136192000000⟩, + ⟨5, 8, 0, 5, 2, 6, -6510683632974173923722807058976129284055236608000000⟩, + ⟨5, 8, 1, 5, 3, 6, -1322889046949975735325037620140140397647940812800000⟩, + ⟨5, 8, 2, 5, 4, 6, 68413537556779032133447248507421752857041305600000⟩, + ⟨5, 8, 3, 5, 5, 6, -7921999618287537738223951151714085179385446400000⟩, + ⟨5, 8, 4, 5, 6, 6, 1592820251335588165259508417958525899531878400000⟩, + ⟨5, 8, 5, 5, 7, 6, -28518472071059780324459467609227204231168000000⟩, + ⟨5, 8, 6, 5, 8, 6, 118082714105593237572557131321588859692646400000⟩, + ⟨5, 8, 0, 6, 1, 6, 4732383702536231561395209456154853720897617920000000⟩, + ⟨5, 8, 1, 6, 2, 6, 3296531776275757456649092277900358578760528691200000⟩, + ⟨5, 8, 2, 6, 3, 6, 34520257027298218801786591519337327427059712000000⟩, + ⟨5, 8, 3, 6, 4, 6, 37376070317705926498856338301341328855374233600000⟩, + ⟨5, 8, 4, 6, 5, 6, -2584484097873929050404462382491964043113267200000⟩, + ⟨5, 8, 5, 6, 6, 6, 271261560800689946213744071873416986099712000000⟩, + ⟨5, 8, 6, 6, 7, 6, 111516930862801441108459474958918914513305600000⟩, + ⟨5, 8, 7, 6, 8, 6, 11121796255854089119433303884811801827737600000⟩, + ⟨5, 8, 0, 7, 0, 6, -46156308017737197571158609637330730494004822016000000⟩, + ⟨5, 8, 1, 7, 1, 6, -9433271427454067014594120855735824516436407091200000⟩, + ⟨5, 8, 2, 7, 2, 6, -166960451100434359126851018151054443428393779200000⟩, + ⟨5, 8, 3, 7, 3, 6, -66611916950725308619421866395875359534664908800000⟩, + ⟨5, 8, 4, 7, 4, 6, -10688426967494076182929512492765480080533094400000⟩, + ⟨5, 8, 5, 7, 5, 6, -306769795100988690859326569756052833697792000000⟩, + ⟨5, 8, 6, 7, 6, 6, -120696987531509114185511661888181238759424000000⟩, + ⟨5, 8, 7, 7, 7, 6, -3930805818827016197718658312499454856396800000⟩, + ⟨5, 8, 8, 7, 8, 6, -8789422017158774444225469129028030955520000000⟩ +] + +def collectedFourData_9_7_27 : List CollectedFourTerm := [ + ⟨6, 1, 2, 1, 8, 0, -10980191056794126587483095115978659425511538688000000⟩, + ⟨6, 1, 2, 2, 7, 0, -13346896264576460700099828837058912138051977216000000⟩, + ⟨6, 1, 3, 2, 8, 0, -5614463451521010298511205880356141241057935360000000⟩, + ⟨6, 1, 2, 3, 6, 0, -5302093074592841535102083779866504666430832640000000⟩, + ⟨6, 1, 3, 3, 7, 0, -14018694425955509395346338026750176701414637568000000⟩, + ⟨6, 1, 4, 3, 8, 0, -4071873780206981659026368143213050541262241792000000⟩, + ⟨6, 1, 2, 4, 5, 0, -2462393988983675925103861671536373261416792064000000⟩, + ⟨6, 1, 3, 4, 6, 0, -32201117041964285681386671300682460279542382592000000⟩, + ⟨6, 1, 4, 4, 7, 0, -9278927387984416324946818185848841600082378752000000⟩, + ⟨6, 1, 5, 4, 8, 0, 13438954653534762668966150013453632550249431040000000⟩, + ⟨6, 1, 2, 5, 4, 0, 13056187436829279241233193692375120549519556608000000⟩, + ⟨6, 1, 3, 5, 5, 0, -10582960757365812318801160426507529750015115264000000⟩, + ⟨6, 1, 4, 5, 6, 0, 8511363305046927924022853771067588925861134336000000⟩, + ⟨6, 1, 5, 5, 7, 0, -457172257506317980077338215229460756729692160000000⟩, + ⟨6, 1, 6, 5, 8, 0, 4732383702536231561395209456154853720897617920000000⟩, + ⟨6, 1, 2, 6, 3, 0, 6587920493686982587272130378292704217042780160000000⟩, + ⟨6, 1, 3, 6, 4, 0, 49930510539753230178122241011567753555173441536000000⟩, + ⟨6, 1, 4, 6, 5, 0, -13810398941548154806121519942512879919104524288000000⟩, + ⟨6, 1, 5, 6, 6, 0, 4348523995848501123213831343432189173238333440000000⟩, + ⟨6, 1, 6, 6, 7, 0, 4469247765596401305944806989607421483868487680000000⟩, + ⟨6, 1, 7, 6, 8, 0, 980598532428265865784963778603839363288662016000000⟩, + ⟨6, 1, 2, 7, 2, 0, -31863093503908998713152946046006430150170771456000000⟩, + ⟨6, 1, 3, 7, 3, 0, -88986535853282783679370929771788110788651122688000000⟩, + ⟨6, 1, 4, 7, 4, 0, -57114470388935401091484333447247049598462590976000000⟩, + ⟨6, 1, 5, 7, 5, 0, -4917747325719819809387287627441714658059223040000000⟩, + ⟨6, 1, 6, 7, 6, 0, -4837155557150910010368161575188387255759667200000000⟩, + ⟨6, 1, 7, 7, 7, 0, -346575528676258205249006921889722763457855488000000⟩, + ⟨6, 1, 8, 7, 8, 0, -1549910487954124388682383029218950236235366400000000⟩ +] + +def collectedFourData_9_7_28 : List CollectedFourTerm := [ + ⟨6, 2, 1, 0, 8, 1, 6631967338099306923778284383041111674929440358400000⟩, + ⟨6, 2, 1, 1, 7, 1, 69547416784468498693099004509807211260336825958400000⟩, + ⟨6, 2, 2, 1, 8, 1, -38243463551890216224091109513902133927255369318400000⟩, + ⟨6, 2, 1, 2, 6, 1, 82470306445206562574769331617471236694951434649600000⟩, + ⟨6, 2, 2, 2, 7, 1, -46486580987983249615788385873920630844071660748800000⟩, + ⟨6, 2, 3, 2, 8, 1, -9777449557164355502161739671344373066182426624000000⟩, + ⟨6, 2, 1, 3, 5, 1, 68133195847021981922772723621332846472702040473600000⟩, + ⟨6, 2, 2, 3, 6, 1, -18466928507719746709360839410785226725263409152000000⟩, + ⟨6, 2, 3, 3, 7, 1, -24413210414603085490018813796264003410865632051200000⟩, + ⟨6, 2, 4, 3, 8, 1, -4727378473221493205629414128290272649701176115200000⟩, + ⟨6, 2, 1, 4, 4, 1, -76739400443908527278967818866363608584437314355200000⟩, + ⟨6, 2, 2, 4, 5, 1, -8576396738545058717229801417572893724681384755200000⟩, + ⟨6, 2, 3, 4, 6, 1, -56077450727167331748614433184199006391246834892800000⟩, + ⟨6, 2, 4, 4, 7, 1, -10772682051631060224754908756650044378527773491200000⟩, + ⟨6, 2, 5, 4, 8, 1, 11701803953355346113613806411994672274570477568000000⟩, + ⟨6, 2, 1, 5, 3, 1, -146552698478704538651865380965018561737477272371200000⟩, + ⟨6, 2, 2, 5, 4, 1, 45474056488121942953450257565777492844000732774400000⟩, + ⟨6, 2, 3, 5, 5, 1, -18429965011627593263458795172298227591767759257600000⟩, + ⟨6, 2, 4, 5, 6, 1, 9881552778387174928023538225716364560251328921600000⟩, + ⟨6, 2, 5, 5, 7, 1, -398077102585111555913527186760712861486415872000000⟩, + ⟨6, 2, 6, 5, 8, 1, 3296531776275757456649092277900358578760528691200000⟩, + ⟨6, 2, 1, 6, 2, 1, 365197390172569855197721225257183700984093527244800000⟩, + ⟨6, 2, 2, 6, 3, 1, 22945401949738821023410961971711844561492901888000000⟩, + ⟨6, 2, 3, 6, 4, 1, 86952752009391810029002436559789321078211765862400000⟩, + ⟨6, 2, 4, 6, 5, 1, -16033645978966708346973108976484198194214653132800000⟩, + ⟨6, 2, 5, 6, 6, 1, 3786423616847049058604194225370660515923099648000000⟩, + ⟨6, 2, 6, 6, 7, 1, 3113233879882158090669711402328413419460152524800000⟩, + ⟨6, 2, 7, 6, 8, 1, 569229382257316961726062186627224374245903564800000⟩, + ⟨6, 2, 1, 7, 1, 1, -1045039556690601259546517747795752977575900400844800000⟩, + ⟨6, 2, 2, 7, 2, 1, -110977582153565348898929645100816602928429976780800000⟩, + ⟨6, 2, 3, 7, 3, 1, -154967856338358047666788965973177219812026430259200000⟩, + ⟨6, 2, 4, 7, 4, 1, -66308960542577250756618165852978940796401719705600000⟩, + ⟨6, 2, 5, 7, 5, 1, -4282067808196285191085986991104095880078163968000000⟩, + ⟨6, 2, 6, 7, 6, 1, -3369514816051574762902744874136421691232878592000000⟩, + ⟨6, 2, 7, 7, 7, 1, -201184243673464069590092610142994871401997926400000⟩, + ⟨6, 2, 8, 7, 8, 1, -771180248245959806767697083710708605371023360000000⟩ +] + +def collectedFourData_9_7_29 : List CollectedFourTerm := [ + ⟨6, 3, 0, 0, 7, 2, 3621270826063786312491702919691299435698978816000000⟩, + ⟨6, 3, 1, 0, 8, 2, 416687414491982894945606569453500489850159104000000⟩, + ⟨6, 3, 0, 1, 6, 2, 455597670581760830958964107452455176779071488000000⟩, + ⟨6, 3, 1, 1, 7, 2, 4369673704216692069152145100076300714171695104000000⟩, + ⟨6, 3, 2, 1, 8, 2, -1201421021565418637598140706643728138189668352000000⟩, + ⟨6, 3, 0, 2, 5, 2, -2203474679908323702503505591267101654434971648000000⟩, + ⟨6, 3, 1, 2, 6, 2, 5181620628255884296741339280248079651098853376000000⟩, + ⟨6, 3, 2, 2, 7, 2, -1460379119267976748631995805965446949386584064000000⟩, + ⟨6, 3, 3, 2, 8, 2, -204772830775542254628121048860776127245844480000000⟩, + ⟨6, 3, 0, 3, 4, 2, 1399333464523110997790917626361394982379585536000000⟩, + ⟨6, 3, 1, 3, 5, 2, 4280818009382419144161098773410582040795938816000000⟩, + ⟨6, 3, 2, 3, 6, 2, -580139821353173968164705297625251825907138560000000⟩, + ⟨6, 3, 3, 3, 7, 2, -511295115938913068906575496176786699267866624000000⟩, + ⟨6, 3, 4, 3, 8, 2, -74255458935065750282687772048050751881084928000000⟩, + ⟨6, 3, 0, 4, 3, 2, 5370288670504562270164811569530321466338312192000000⟩, + ⟨6, 3, 1, 4, 4, 2, -4821547020736903947147290109051060023419994112000000⟩, + ⟨6, 3, 2, 4, 5, 2, -269428089769966761063915083532353251684909056000000⟩, + ⟨6, 3, 3, 4, 6, 2, -1174451298464010827269950908955065108718944256000000⟩, + ⟨6, 3, 4, 4, 7, 2, -169212271502411328244227164356691797966061568000000⟩, + ⟨6, 3, 5, 4, 8, 2, 147045188422569705774421776794562565521801216000000⟩, + ⟨6, 3, 0, 5, 2, 2, -9063480231029426587052151848721972191438045184000000⟩, + ⟨6, 3, 1, 5, 3, 2, -9207926080259615766995513521703265403322499072000000⟩, + ⟨6, 3, 2, 5, 4, 2, 1428570592895023255007015059333399224917164032000000⟩, + ⟨6, 3, 3, 5, 5, 2, -385985740397897806949746919254735690716413952000000⟩, + ⟨6, 3, 4, 5, 6, 2, 155214827986935055892454703863204485397479424000000⟩, + ⟨6, 3, 5, 5, 7, 2, -5002247755103952693617003064905331652952064000000⟩, + ⟨6, 3, 6, 5, 8, 2, 34520257027298218801786591519337327427059712000000⟩, + ⟨6, 3, 0, 6, 1, 2, 6587920493686982587272130378292704217042780160000000⟩, + ⟨6, 3, 1, 6, 2, 2, 22945401949738821023410961971711844561492901888000000⟩, + ⟨6, 3, 2, 6, 3, 2, 720831370654498049384984225698400524975472640000000⟩, + ⟨6, 3, 3, 6, 4, 2, 1821084431945750575418023407312490732556648448000000⟩, + ⟨6, 3, 4, 6, 5, 2, -251849042194249051498803985328717855868321792000000⟩, + ⟨6, 3, 5, 6, 6, 2, 47580302695747507036409655374996812307890176000000⟩, + ⟨6, 3, 6, 6, 7, 2, 32600818379199220519747517494013528478056448000000⟩, + ⟨6, 3, 7, 6, 8, 2, 5109251415016076581742880019404731222851584000000⟩, + ⟨6, 3, 0, 7, 0, 2, -64253895418500599130495660303672281606041632768000000⟩, + ⟨6, 3, 1, 7, 1, 2, -65659978211541386955992164687685860593015717888000000⟩, + ⟨6, 3, 2, 7, 2, 2, -3486368329084217153516304201227000986441089024000000⟩, + ⟨6, 3, 3, 7, 3, 2, -3245550532998746882299862536518897303010934784000000⟩, + ⟨6, 3, 4, 7, 4, 2, -1041550263954409619518576688083176870257885184000000⟩, + ⟨6, 3, 5, 7, 5, 2, -53808581155890619495466044586450297359958016000000⟩, + ⟨6, 3, 6, 7, 6, 2, -35284512755037939388005670936280374884433920000000⟩, + ⟨6, 3, 7, 7, 7, 2, -1805776219054919762028810734216474957709312000000⟩, + ⟨6, 3, 8, 7, 8, 2, -6056670052920327815638241424015323509555200000000⟩ +] + +def collectedFourData_9_7_30 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 7, 3, 27445974996411339039852459194825464997440231833600000⟩, + ⟨6, 4, 1, 0, 8, 3, 1579057865149686794134671853720129060165858099200000⟩, + ⟨6, 4, 0, 1, 6, 3, 3453020465967767472922381322860796153927879884800000⟩, + ⟨6, 4, 1, 1, 7, 3, 16559097757232333568841911442706685273318830899200000⟩, + ⟨6, 4, 2, 1, 8, 3, -3035230162913957990383182223926250254784423526400000⟩, + ⟨6, 4, 0, 2, 5, 3, -16700355724491752487719906634892584964651273420800000⟩, + ⟨6, 4, 1, 2, 6, 3, 19636011366565378896367246534295107543912729804800000⟩, + ⟨6, 4, 2, 2, 7, 3, -3689453299490585403304938286918581927484902604800000⟩, + ⟨6, 4, 3, 2, 8, 3, -387998458507926790503821782728810212729290752000000⟩, + ⟨6, 4, 0, 3, 4, 3, 10605688755041062542200951430378504309257640345600000⟩, + ⟨6, 4, 1, 3, 5, 3, 16222374643186616206664262063495967269041523916800000⟩, + ⟨6, 4, 2, 3, 6, 3, -1465645974950828796522322752745600084598587392000000⟩, + ⟨6, 4, 3, 3, 7, 3, -968789248434926558275454670365317357819763097600000⟩, + ⟨6, 4, 4, 3, 8, 3, -112557915006546117263899540252595692806875381760000⟩, + ⟨6, 4, 0, 4, 3, 3, 40701956758752260310366179168355542257110299443200000⟩, + ⟨6, 4, 1, 4, 4, 3, -18271494363624780607838817773876396063475734937600000⟩, + ⟨6, 4, 2, 4, 5, 3, -680674176768234559399347755145551892173763379200000⟩, + ⟨6, 4, 3, 4, 6, 3, -2225321062715394097245094970414345128283367014400000⟩, + ⟨6, 4, 4, 4, 7, 3, -256495357337813419697550066174231428284872130560000⟩, + ⟨6, 4, 5, 4, 8, 3, 185745039915321442757214790008253540074101145600000⟩, + ⟨6, 4, 0, 5, 2, 3, -68693026219111189412042997006217767741487998566400000⟩, + ⟨6, 4, 1, 5, 3, 3, -34893897903006188586435094582801100996582414745600000⟩, + ⟨6, 4, 2, 5, 4, 3, 3609093295002537147771977549073132849591641702400000⟩, + ⟨6, 4, 3, 5, 5, 3, -731356165333201403916433583200858343918587084800000⟩, + ⟨6, 4, 4, 5, 6, 3, 235277751519746122192478401319708989396699054080000⟩, + ⟨6, 4, 5, 5, 7, 3, -6318756287815387668166388248529707490240102400000⟩, + ⟨6, 4, 6, 5, 8, 3, 37376070317705926498856338301341328855374233600000⟩, + ⟨6, 4, 0, 6, 1, 3, 49930510539753230178122241011567753555173441536000000⟩, + ⟨6, 4, 1, 6, 2, 3, 86952752009391810029002436559789321078211765862400000⟩, + ⟨6, 4, 2, 6, 3, 3, 1821084431945750575418023407312490732556648448000000⟩, + ⟨6, 4, 3, 6, 4, 3, 3450545415286251416272660061309593361145082675200000⟩, + ⟨6, 4, 4, 6, 5, 3, -381757832923361096522517328719636507480702320640000⟩, + ⟨6, 4, 5, 6, 6, 3, 60102648160150189951330009375737748664195481600000⟩, + ⟨6, 4, 6, 6, 7, 3, 35297839155488954829598877034826725834778214400000⟩, + ⟨6, 4, 7, 6, 8, 3, 4840441150439118670235191410865511481527500800000⟩, + ⟨6, 4, 0, 7, 0, 3, -486986721452998955566356947061559888164854484172800000⟩, + ⟨6, 4, 1, 7, 1, 3, -248821782023095691203331058182337430072938882662400000⟩, + ⟨6, 4, 2, 7, 2, 3, -8807845144640791275482152658321720857242422476800000⟩, + ⟨6, 4, 3, 7, 3, 3, -6149588297645876157094103992923986570732214681600000⟩, + ⟨6, 4, 4, 7, 4, 3, -1578802794657083554162649009726262523081292513280000⟩, + ⟨6, 4, 5, 7, 5, 3, -67970106072873385081990154863357725251312025600000⟩, + ⟨6, 4, 6, 7, 6, 3, -38203551868556505045968840578148274983141376000000⟩, + ⟨6, 4, 7, 7, 7, 3, -1710769897427389457605491733304580761871974400000⟩, + ⟨6, 4, 8, 7, 8, 3, -5100456681840644369861251364416517969018880000000⟩ +] + +def collectedFourData_9_7_31 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 7, 4, -7591347653824121985188309732773923356838513868800000⟩, + ⟨6, 5, 1, 0, 8, 4, -291170252867654088191495381020038755917391462400000⟩, + ⟨6, 5, 0, 1, 6, 4, -955079162476776407642982145574260165730264678400000⟩, + ⟨6, 5, 1, 1, 7, 4, -3053413549715916565343013062879167426574313062400000⟩, + ⟨6, 5, 2, 1, 8, 4, 419760773283985005779011574962663455704324505600000⟩, + ⟨6, 5, 0, 2, 5, 4, 4619191202488722711230217672263981290578404966400000⟩, + ⟨6, 5, 1, 2, 6, 4, -3620780796638499511854593007138101711607536025600000⟩, + ⟨6, 5, 2, 2, 7, 4, 510237341771309979551811491554297599575143219200000⟩, + ⟨6, 5, 3, 2, 8, 4, 42926967441552385198195740445742248101308006400000⟩, + ⟨6, 5, 0, 3, 4, 4, -2933452736085965633645256609812250915299445964800000⟩, + ⟨6, 5, 1, 3, 5, 4, -2991323517154772017017936874788384721044347289600000⟩, + ⟨6, 5, 2, 3, 6, 4, 202693257112099985566389320739853137050861568000000⟩, + ⟨6, 5, 3, 3, 7, 4, 107183891104151057252605575559386745167748792320000⟩, + ⟨6, 5, 4, 3, 8, 4, 10377554014337905262376345799207597825704591360000⟩, + ⟨6, 5, 0, 4, 3, 4, -11257851250939543856613215456460916457393985945600000⟩, + ⟨6, 5, 1, 4, 4, 4, 3369170789458195954478127430053562677437084467200000⟩, + ⟨6, 5, 2, 4, 5, 4, 94134646619474035152979004892603983495744716800000⟩, + ⟨6, 5, 3, 4, 6, 4, 246202743107632419400760386741916215049013166080000⟩, + ⟨6, 5, 4, 4, 7, 4, 23648220785230937444445533572537942085373788160000⟩, + ⟨6, 5, 5, 4, 8, 4, -14678760970077326319149234521772035693923532800000⟩, + ⟨6, 5, 0, 5, 2, 4, 18999967882019606430731591686398058676136129331200000⟩, + ⟨6, 5, 1, 5, 3, 4, 6434257603975325668876672868810691834809627443200000⟩, + ⟨6, 5, 2, 5, 4, 4, -499123859163907508334296984149173910518733209600000⟩, + ⟨6, 5, 3, 5, 5, 4, 80915018111587532261734467372390704741728911360000⟩, + ⟨6, 5, 4, 5, 6, 4, -21692011393655782542750277268878145287492730880000⟩, + ⟨6, 5, 5, 5, 7, 4, 499348532909946443589307421361907277443891200000⟩, + ⟨6, 5, 6, 5, 8, 4, -2584484097873929050404462382491964043113267200000⟩, + ⟨6, 5, 0, 6, 1, 4, -13810398941548154806121519942512879919104524288000000⟩, + ⟨6, 5, 1, 6, 2, 4, -16033645978966708346973108976484198194214653132800000⟩, + ⟨6, 5, 2, 6, 3, 4, -251849042194249051498803985328717855868321792000000⟩, + ⟨6, 5, 3, 6, 4, 4, -381757832923361096522517328719636507480702320640000⟩, + ⟨6, 5, 4, 6, 5, 4, 35197103032055639254596128460288808973280215040000⟩, + ⟨6, 5, 5, 6, 6, 4, -4749695638783677928538850905769596882308300800000⟩, + ⟨6, 5, 6, 6, 7, 4, -2440778369989759962852447983775953630055628800000⟩, + ⟨6, 5, 7, 6, 8, 4, -297517590471740625276784029795262334710579200000⟩, + ⟨6, 5, 0, 7, 0, 4, 134696818233970775235590914972674209140863034982400000⟩, + ⟨6, 5, 1, 7, 1, 4, 45881473244032908186771982281075403195912342732800000⟩, + ⟨6, 5, 2, 7, 2, 4, 1218091442966731726920903517701459799407014707200000⟩, + ⟨6, 5, 3, 7, 3, 4, 680371714998973173097261997856448174837853061120000⟩, + ⟨6, 5, 4, 7, 4, 4, 145561609581953055883788064290294258032789422080000⟩, + ⟨6, 5, 5, 7, 5, 4, 5371432478678057036837113743462288811936972800000⟩, + ⟨6, 5, 6, 7, 6, 4, 2641702871578029929160145303431180296650752000000⟩, + ⟨6, 5, 7, 7, 7, 4, 105152427622843710917866259484352913709465600000⟩, + ⟨6, 5, 8, 7, 8, 4, 282149494562938545440460813142923524702208000000⟩ +] + +def collectedFourData_9_7_32 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 7, 5, 2390311646549860094746867647291305425102700544000000⟩, + ⟨6, 6, 1, 0, 8, 5, 68761273850482203359308293290152289510621184000000⟩, + ⟨6, 6, 0, 1, 6, 5, 300728796723635910333683729386938867218644992000000⟩, + ⟨6, 6, 1, 1, 7, 5, 721078486565799304760641442451931187782877184000000⟩, + ⟨6, 6, 2, 1, 8, 5, -79302841411040778059384027696653827411070156800000⟩, + ⟨6, 6, 0, 2, 5, 5, -1454459344038527472585494146551032005559058432000000⟩, + ⟨6, 6, 1, 2, 6, 5, 855065026245628661816712753983925683692240896000000⟩, + ⟨6, 6, 2, 2, 7, 5, -96396027384641254300435914834017861729098137600000⟩, + ⟨6, 6, 3, 2, 8, 5, -6758275006343595723449615571457324735266816000000⟩, + ⟨6, 6, 0, 3, 4, 5, 923665541274167177327244481985763170555265024000000⟩, + ⟨6, 6, 1, 3, 5, 5, 706415622862264358676489682630642650511835136000000⟩, + ⟨6, 6, 2, 3, 6, 5, -38293600181104512530264224659924390619643904000000⟩, + ⟨6, 6, 3, 3, 7, 5, -16874665402770920239248737102381388881775820800000⟩, + ⟨6, 6, 4, 3, 8, 5, -1400405681065623463206500708466692810027827200000⟩, + ⟨6, 6, 0, 4, 3, 5, 3544795231014215756798589945745328975671984128000000⟩, + ⟨6, 6, 1, 4, 4, 5, -795646097159110683023630613122148149967716352000000⟩, + ⟨6, 6, 2, 4, 5, 5, -17784284352597295239712521943409167318804070400000⟩, + ⟨6, 6, 3, 4, 6, 5, -38761318220371652250051312299127854895149875200000⟩, + ⟨6, 6, 4, 4, 7, 5, -3191224318271539892193003899994025307091763200000⟩, + ⟨6, 6, 5, 4, 8, 5, 1733230460372661711877682876086528008781824000000⟩, + ⟨6, 6, 0, 5, 2, 5, -5982579982302171045089699939652954101127315456000000⟩, + ⟨6, 6, 1, 5, 3, 5, -1519481282082040067963118340238653868067520512000000⟩, + ⟨6, 6, 2, 5, 4, 5, 94296424932882517612885929372350445161073868800000⟩, + ⟨6, 6, 3, 5, 5, 5, -12738983840075463353026935440495634356266598400000⟩, + ⟨6, 6, 4, 5, 6, 5, 2927242387507235916174811691806261717342617600000⟩, + ⟨6, 6, 5, 5, 7, 5, -58961794482941321004267975642369119748096000000⟩, + ⟨6, 6, 6, 5, 8, 5, 271261560800689946213744071873416986099712000000⟩, + ⟨6, 6, 0, 6, 1, 5, 4348523995848501123213831343432189173238333440000000⟩, + ⟨6, 6, 1, 6, 2, 5, 3786423616847049058604194225370660515923099648000000⟩, + ⟨6, 6, 2, 6, 3, 5, 47580302695747507036409655374996812307890176000000⟩, + ⟨6, 6, 3, 6, 4, 5, 60102648160150189951330009375737748664195481600000⟩, + ⟨6, 6, 4, 6, 5, 5, -4749695638783677928538850905769596882308300800000⟩, + ⟨6, 6, 5, 6, 6, 5, 560831883250953338402035450202791832715264000000⟩, + ⟨6, 6, 6, 6, 7, 5, 256178535111374805805886881246714106216448000000⟩, + ⟨6, 6, 7, 6, 8, 5, 28104091420440021136191033883480973692108800000⟩, + ⟨6, 6, 0, 7, 0, 5, -42412413191968577591518470999799782548032192512000000⟩, + ⟨6, 6, 1, 7, 1, 5, -10835133449674560315523815704905201855022235648000000⟩, + ⟨6, 6, 2, 7, 2, 5, -230126583220257338883064415975053125045819801600000⟩, + ⟨6, 6, 3, 7, 3, 5, -107115396929944515231392219965074163716902092800000⟩, + ⟨6, 6, 4, 7, 4, 5, -19642904746338611597180021344950099348396441600000⟩, + ⟨6, 6, 5, 7, 5, 5, -634244975230412269819086266891172550017024000000⟩, + ⟨6, 6, 6, 7, 6, 5, -277267112885473176039739471242953930833920000000⟩, + ⟨6, 6, 7, 7, 7, 5, -9932903242150651450281211835154944124518400000⟩, + ⟨6, 6, 8, 7, 8, 5, -24229446482184171512793625890910025809920000000⟩ +] + +def collectedFourData_9_7_33 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 7, 6, 2456671504082968420310104273573397944407687168000000⟩, + ⟨6, 7, 1, 0, 8, 6, 56536180057273172242472687925345272535082598400000⟩, + ⟨6, 7, 0, 1, 6, 6, 309077632799253173591676323581578279779303424000000⟩, + ⟨6, 7, 1, 1, 7, 6, 592877660186398307975010140289509272498628198400000⟩, + ⟨6, 7, 2, 1, 8, 6, -54336298495781616185074106532288894385677926400000⟩, + ⟨6, 7, 0, 2, 5, 6, -1494838059925808150013943030486293266357551104000000⟩, + ⟨6, 7, 1, 2, 6, 6, 703042680529992293358603181308327911898061209600000⟩, + ⟨6, 7, 2, 2, 7, 6, -66048116619566464493710104311184529550003404800000⟩, + ⟨6, 7, 3, 2, 8, 6, -3969084748259804815056482729961041789190144000000⟩, + ⟨6, 7, 0, 3, 4, 6, 949308353924001525487152743616035550268489728000000⟩, + ⟨6, 7, 1, 3, 5, 6, 580821712760222263561664666328351396660353433600000⟩, + ⟨6, 7, 2, 3, 6, 6, -26237805012985650315026977514143332949819392000000⟩, + ⟨6, 7, 3, 3, 7, 6, -9910365739668495593868397654444225422635827200000⟩, + ⟨6, 7, 4, 3, 8, 6, -719641879291252522170640261889923575132979200000⟩, + ⟨6, 7, 0, 4, 3, 6, 3643205874184396373105213851748681966961033216000000⟩, + ⟨6, 7, 1, 4, 4, 6, -654187866104209682196538539634683175748449075200000⟩, + ⟨6, 7, 2, 4, 5, 6, -12185341230182570722671547185834575726326579200000⟩, + ⟨6, 7, 3, 4, 6, 6, -22764234486835014025108008804612170241068236800000⟩, + ⟨6, 7, 4, 4, 7, 6, -1639909560987606838344895173351042800890675200000⟩, + ⟨6, 7, 5, 4, 8, 6, 791710410212180941306930418206020225466368000000⟩, + ⟨6, 7, 0, 5, 2, 6, -6148668431847662816354532242359307710425464832000000⟩, + ⟨6, 7, 1, 5, 3, 6, -1249332110167765210723454134237050057681744691200000⟩, + ⟨6, 7, 2, 5, 4, 6, 64609522194558201979255533215849962822592102400000⟩, + ⟨6, 7, 3, 5, 5, 6, -7481510654791638858944257759052980798724505600000⟩, + ⟨6, 7, 4, 5, 6, 6, 1504254261010817575387964910323756657383833600000⟩, + ⟨6, 7, 5, 5, 7, 6, -26932752201284862471121485058108211331072000000⟩, + ⟨6, 7, 6, 5, 8, 6, 111516930862801441108459474958918914513305600000⟩, + ⟨6, 7, 0, 6, 1, 6, 4469247765596401305944806989607421483868487680000000⟩, + ⟨6, 7, 1, 6, 2, 6, 3113233879882158090669711402328413419460152524800000⟩, + ⟨6, 7, 2, 6, 3, 6, 32600818379199220519747517494013528478056448000000⟩, + ⟨6, 7, 3, 6, 4, 6, 35297839155488954829598877034826725834778214400000⟩, + ⟨6, 7, 4, 6, 5, 6, -2440778369989759962852447983775953630055628800000⟩, + ⟨6, 7, 5, 6, 6, 6, 256178535111374805805886881246714106216448000000⟩, + ⟨6, 7, 6, 6, 7, 6, 105316226538781580166373144998122118080102400000⟩, + ⟨6, 7, 7, 6, 8, 6, 10503388184532730336169510913793851811430400000⟩, + ⟨6, 7, 0, 7, 0, 6, -43589867061264968092893992191347502880982564864000000⟩, + ⟨6, 7, 1, 7, 1, 6, -8908750832443871575745314938912471720619986124800000⟩, + ⟨6, 7, 2, 7, 2, 6, -157676906592269416812470498822824412280835276800000⟩, + ⟨6, 7, 3, 7, 3, 6, -62908077558160105058151280676199823609901875200000⟩, + ⟨6, 7, 4, 7, 4, 6, -10094115639146547809474993198924241124825497600000⟩, + ⟨6, 7, 5, 7, 5, 6, -289712396011503006369532163600371855392768000000⟩, + ⟨6, 7, 6, 7, 6, 6, -113985842177234979098589854334912766672896000000⟩, + ⟨6, 7, 7, 7, 7, 6, -3712240221216820177642391297727646610227200000⟩, + ⟨6, 7, 8, 7, 8, 6, -8300701544977886274190411890983782318080000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse0930.lean b/lean/OAI/Analysis/LaughlinFock/Sparse0930.lean new file mode 100644 index 0000000000000000000000000000000000000000..37d11d2a5426e4ba9b7b0ec3502f988a68f53001 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse0930.lean @@ -0,0 +1,525 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse0906 +import OAI.Analysis.LaughlinFock.Sparse0923 +import OAI.Analysis.LaughlinFock.Sparse0927 +import OAI.Analysis.LaughlinFock.Sparse0928 +import OAI.Analysis.LaughlinFock.Sparse0929 + +namespace OAI + +/-! Sparse0930. -/ +namespace LaughlinFock +def collectedFourData_9_7_34 : List CollectedFourTerm := [ + ⟨6, 8, 0, 0, 7, 7, 539018778530535973621369039909471179570256281600000⟩, + ⟨6, 8, 1, 0, 8, 7, 10337178667221816111011598725973620176610918400000⟩, + ⟨6, 8, 0, 1, 6, 7, 67814784282586151680355205539498680531078348800000⟩, + ⟨6, 8, 1, 1, 7, 7, 108402836819584331748477880915989345063036518400000⟩, + ⟨6, 8, 2, 1, 8, 7, -8515669967151521235499947974662723858543411200000⟩, + ⟨6, 8, 0, 2, 5, 7, -327982713123436399665707872354196525369052364800000⟩, + ⟨6, 8, 1, 2, 6, 7, 128545610827595070482451709667063819633531289600000⟩, + ⟨6, 8, 2, 2, 7, 7, -10351164482207572221716216884219753747867238400000⟩, + ⟨6, 8, 3, 2, 8, 7, -544286041432354587594373643860744505131008000000⟩, + ⟨6, 8, 0, 3, 4, 7, 208287932892336637854556270101256289998444953600000⟩, + ⟨6, 8, 1, 3, 5, 7, 106198505320343213769987480188842724130658713600000⟩, + ⟨6, 8, 2, 3, 6, 7, -4112029975144619994968075060353920072155136000000⟩, + ⟨6, 8, 3, 3, 7, 7, -1359022061687132747537405510937480381490790400000⟩, + ⟨6, 8, 4, 3, 8, 7, -87720425812437418891402376938476884774092800000⟩, + ⟨6, 8, 0, 4, 3, 7, 799356518351924314774023628048615968477492019200000⟩, + ⟨6, 8, 1, 4, 4, 7, -119612907115358474916174160989037785194378035200000⟩, + ⟨6, 8, 2, 4, 5, 7, -1909705799363840755980090195186810369972633600000⟩, + ⟨6, 8, 3, 4, 6, 7, -3121690732481756354260320853724059389237657600000⟩, + ⟨6, 8, 4, 4, 7, 7, -199896044301084867049544796356755006999756800000⟩, + ⟨6, 8, 5, 4, 8, 7, 86854668512503525119279419818277916691660800000⟩, + ⟨6, 8, 0, 5, 2, 7, -1349080551557479295839516655018070948801046118400000⟩, + ⟨6, 8, 1, 5, 3, 7, -228430170280668376065246927575302874240070451200000⟩, + ⟨6, 8, 2, 5, 4, 7, 10125705706415077926644031438652285574656819200000⟩, + ⟨6, 8, 3, 5, 5, 7, -1025949828865679222485123146420021256991539200000⟩, + ⟨6, 8, 4, 5, 6, 7, 183360402032186507762185744109059873072742400000⟩, + ⟨6, 8, 5, 5, 7, 7, -2954660232325445560758098427134935774003200000⟩, + ⟨6, 8, 6, 5, 8, 7, 11121796255854089119433303884811801827737600000⟩, + ⟨6, 8, 0, 6, 1, 7, 980598532428265865784963778603839363288662016000000⟩, + ⟨6, 8, 1, 6, 2, 7, 569229382257316961726062186627224374245903564800000⟩, + ⟨6, 8, 2, 6, 3, 7, 5109251415016076581742880019404731222851584000000⟩, + ⟨6, 8, 3, 6, 4, 7, 4840441150439118670235191410865511481527500800000⟩, + ⟨6, 8, 4, 6, 5, 7, -297517590471740625276784029795262334710579200000⟩, + ⟨6, 8, 5, 6, 6, 7, 28104091420440021136191033883480973692108800000⟩, + ⟨6, 8, 6, 6, 7, 7, 10503388184532730336169510913793851811430400000⟩, + ⟨6, 8, 7, 6, 8, 7, 960229362548996560846139296932781306675200000⟩, + ⟨6, 8, 0, 7, 0, 7, -9564061316550351348004973508810525688900406476800000⟩, + ⟨6, 8, 1, 7, 1, 7, -1628892312205061523964762058140513792431017164800000⟩, + ⟨6, 8, 2, 7, 2, 7, -24711372234628504175682788586289704452122214400000⟩, + ⟨6, 8, 3, 7, 3, 7, -8626671053890345421656722249706146885953126400000⟩, + ⟨6, 8, 4, 7, 4, 7, -1230417722406559390931666437543664065865318400000⟩, + ⟨6, 8, 5, 7, 5, 7, -31782926932587018366766018689908228279500800000⟩, + ⟨6, 8, 6, 7, 6, 7, -11368025491185942152584224895899864662016000000⟩, + ⟨6, 8, 7, 7, 7, 7, -339376399179171488774741406577352874393600000⟩, + ⟨6, 8, 8, 7, 8, 7, -700484061820477247638816521840450600960000000⟩ +] + +def collectedFourData_9_7_35 : List CollectedFourTerm := [ + ⟨7, 0, 2, 1, 8, 0, 107092981543187298551581665309130111515122624102400000⟩, + ⟨7, 0, 2, 2, 7, 0, 130176142466727772848482390943490868708771679436800000⟩, + ⟨7, 0, 3, 2, 8, 0, 54759487123550215883037923823222380843633737728000000⟩, + ⟨7, 0, 2, 3, 6, 0, 51712848423187384952229314689958760505694748672000000⟩, + ⟨7, 0, 3, 3, 7, 0, 136728384383574644393093960604350055966411482726400000⟩, + ⟨7, 0, 4, 3, 8, 0, 39714163563672375903104856799721158467892386201600000⟩, + ⟨7, 0, 2, 4, 5, 0, 24016441303278908940993969222688204015919117107200000⟩, + ⟨7, 0, 3, 4, 6, 0, 314066814976892913684097643996028937600050502041600000⟩, + ⟨7, 0, 4, 4, 7, 0, 90500064558268440359686661014412312161067571609600000⟩, + ⟨7, 0, 5, 4, 8, 0, -131074014580119345698535943010998955629181140992000000⟩, + ⟨7, 0, 2, 5, 4, 0, -127340775125363828643904694466001033222777366118400000⟩, + ⟨7, 0, 3, 5, 5, 0, 103218679456362613905384327938185027326812828467200000⟩, + ⟨7, 0, 4, 5, 6, 0, -83013789889452433518411984705537802816562449612800000⟩, + ⟨7, 0, 5, 5, 7, 0, 4458933353886117008548119971549369655380410368000000⟩, + ⟨7, 0, 6, 5, 8, 0, -46156308017737197571158609637330730494004822016000000⟩, + ⟨7, 0, 2, 6, 3, 0, -64253895418500599130495660303672281606041632768000000⟩, + ⟨7, 0, 3, 6, 4, 0, -486986721452998955566356947061559888164854484172800000⟩, + ⟨7, 0, 4, 6, 5, 0, 134696818233970775235590914972674209140863034982400000⟩, + ⟨7, 0, 5, 6, 6, 0, -42412413191968577591518470999799782548032192512000000⟩, + ⟨7, 0, 6, 6, 7, 0, -43589867061264968092893992191347502880982564864000000⟩, + ⟨7, 0, 7, 6, 8, 0, -9564061316550351348004973508810525688900406476800000⟩, + ⟨7, 0, 2, 7, 2, 0, 310769973570866689862581977935230405616419523788800000⟩, + ⟨7, 0, 3, 7, 3, 0, 867911440924435259388738338462416778506243827302400000⟩, + ⟨7, 0, 4, 7, 4, 0, 557053961226519940147667921190068069063799393484800000⟩, + ⟨7, 0, 5, 7, 5, 0, 47964213087302922985388408525286015202693742592000000⟩, + ⟨7, 0, 6, 7, 6, 0, 47178178241530120233731706334168806232487362560000000⟩, + ⟨7, 0, 7, 7, 7, 0, 3380251445887277532451312859845144879995184742400000⟩, + ⟨7, 0, 8, 7, 8, 0, 15116725603545715685760063230752929878869278720000000⟩ +] + +def collectedFourData_9_7_36 : List CollectedFourTerm := [ + ⟨7, 1, 1, 0, 8, 1, -18977868937450069109197746568669718156021229158400000⟩, + ⟨7, 1, 1, 1, 7, 1, -199015117745155383362253585606832805748647814758400000⟩, + ⟨7, 1, 2, 1, 8, 1, 109436521925019984069387663440111328929081878118400000⟩, + ⟨7, 1, 1, 2, 6, 1, -235994929884113057626650475333870920035498301849600000⟩, + ⟨7, 1, 2, 2, 7, 1, 133024816975794034270116109421168957693769862348800000⟩, + ⟨7, 1, 3, 2, 8, 1, 27978900796512918159929528022892489572429594624000000⟩, + ⟨7, 1, 1, 3, 5, 1, -194968219105399765974562314763906256401390475673600000⟩, + ⟨7, 1, 2, 3, 6, 1, 52844492596250768182208582328468875556685873152000000⟩, + ⟨7, 1, 3, 3, 7, 1, 69860221555842471712752111533896803319977030451200000⟩, + ⟨7, 1, 4, 3, 8, 1, 13527745917432760193343388829864414176529822515200000⟩, + ⟨7, 1, 1, 4, 4, 1, 219595515134182997876461520942321087739241640755200000⟩, + ⟨7, 1, 2, 4, 5, 1, 24541998620024741934046357182636647907658511155200000⟩, + ⟨7, 1, 3, 4, 6, 1, 160469805714016007827827239432694522287208844492800000⟩, + ⟨7, 1, 4, 4, 7, 1, 30826832771958030639201831708614653803077251891200000⟩, + ⟨7, 1, 5, 4, 8, 1, -33485584357862452735775352349018881007779053568000000⟩, + ⟨7, 1, 1, 5, 3, 1, 419371471898049081094919873645300454436614910771200000⟩, + ⟨7, 1, 2, 5, 4, 1, -130127402637828951063565344839682300757246633574400000⟩, + ⟨7, 1, 3, 5, 5, 1, 52738718796630717666886768585237721166420482457600000⟩, + ⟨7, 1, 4, 5, 6, 1, -28276799924722324027127793571509846532320500121600000⟩, + ⟨7, 1, 5, 5, 7, 1, 1139127304873797008763963052485555485379919872000000⟩, + ⟨7, 1, 6, 5, 8, 1, -9433271427454067014594120855735824516436407091200000⟩, + ⟨7, 1, 1, 6, 2, 1, -1045039556690601259546517747795752977575900400844800000⟩, + ⟨7, 1, 2, 6, 3, 1, -65659978211541386955992164687685860593015717888000000⟩, + ⟨7, 1, 3, 6, 4, 1, -248821782023095691203331058182337430072938882662400000⟩, + ⟨7, 1, 4, 6, 5, 1, 45881473244032908186771982281075403195912342732800000⟩, + ⟨7, 1, 5, 6, 6, 1, -10835133449674560315523815704905201855022235648000000⟩, + ⟨7, 1, 6, 6, 7, 1, -8908750832443871575745314938912471720619986124800000⟩, + ⟨7, 1, 7, 6, 8, 1, -1628892312205061523964762058140513792431017164800000⟩, + ⟨7, 1, 1, 7, 1, 1, 2990458597012496164648850317601466414100942474444800000⟩, + ⟨7, 1, 2, 7, 2, 1, 317570624482156341164065498589243678095594802380800000⟩, + ⟨7, 1, 3, 7, 3, 1, 443452073446099975077858985151177291571678884659200000⟩, + ⟨7, 1, 4, 7, 4, 1, 189748033788753830308983165236333481949539178905600000⟩, + ⟨7, 1, 5, 7, 5, 1, 12253456252472021466487253946786720633971539968000000⟩, + ⟨7, 1, 6, 7, 6, 1, 9642117836507571043990987364128878646989422592000000⟩, + ⟨7, 1, 7, 7, 7, 1, 575703711141806589252072759063176936262362726400000⟩, + ⟨7, 1, 8, 7, 8, 1, 2206789770251863724793431350673327502246543360000000⟩ +] + +def collectedFourData_9_7_37 : List CollectedFourTerm := [ + ⟨7, 2, 0, 0, 7, 2, -17514614975153126476461120880040940221136214425600000⟩, + ⟨7, 2, 1, 0, 8, 2, -2015347644614573190772509750888503025877804646400000⟩, + ⟨7, 2, 0, 1, 6, 2, -2203540736689334138121083115947489034534440140800000⟩, + ⟨7, 2, 1, 1, 7, 2, -21134335478463997922980429409975612063734982246400000⟩, + ⟨7, 2, 2, 1, 8, 2, 5810785115634651520203951231348216150583620403200000⟩, + ⟨7, 2, 0, 2, 5, 2, 10657311336209151474689564375787690724988603596800000⟩, + ⟨7, 2, 1, 2, 6, 2, -25061392701705179981031343665348723848985024921600000⟩, + ⟨7, 2, 2, 2, 7, 2, 7063260170334827088665112924559066225392903782400000⟩, + ⟨7, 2, 3, 2, 8, 2, 990402944345437704914108899690984101818400768000000⟩, + ⟨7, 2, 0, 3, 4, 2, -6768007152784457303420411098553548476679559577600000⟩, + ⟨7, 2, 1, 3, 5, 2, -20704576601505431515904709041116178243550550425600000⟩, + ⟨7, 2, 2, 3, 6, 2, 2805900494827000897588391917592159431893712896000000⟩, + ⟨7, 2, 3, 3, 7, 2, 2472926639425173434967603067221046481176127078400000⟩, + ⟨7, 2, 4, 3, 8, 2, 359143470764553686998930141912721864822410444800000⟩, + ⟨7, 2, 0, 4, 3, 2, -25973903330382283042776485766533356008355607347200000⟩, + ⟨7, 2, 1, 4, 4, 2, 23319863028470445541822026498877340015320576819200000⟩, + ⟨7, 2, 2, 4, 5, 2, 1303114150382752915431833930298967033422387609600000⟩, + ⟨7, 2, 3, 4, 6, 2, 5680343527916923039779701830010596136435947929600000⟩, + ⟨7, 2, 4, 4, 7, 2, 818410974154410471325812985711706338396785868800000⟩, + ⟨7, 2, 5, 4, 8, 2, -711197803995670503035903177255042323049978265600000⟩, + ⟨7, 2, 0, 5, 2, 2, 43836369663061525734576327292303316472031503974400000⟩, + ⟨7, 2, 1, 5, 3, 2, 44534995519989139949373046462941991910103003955200000⟩, + ⟨7, 2, 2, 5, 4, 2, -6909415258117960152145728128255810496156087091200000⟩, + ⟨7, 2, 3, 5, 5, 2, 1866856126946167311105889939353451213276525363200000⟩, + ⟨7, 2, 4, 5, 6, 2, -750711029691404871925959470614686927713363558400000⟩, + ⟨7, 2, 5, 5, 7, 2, 24193839027555395362703800888708613802452582400000⟩, + ⟨7, 2, 6, 5, 8, 2, -166960451100434359126851018151054443428393779200000⟩, + ⟨7, 2, 0, 6, 1, 2, -31863093503908998713152946046006430150170771456000000⟩, + ⟨7, 2, 1, 6, 2, 2, -110977582153565348898929645100816602928429976780800000⟩, + ⟨7, 2, 2, 6, 3, 2, -3486368329084217153516304201227000986441089024000000⟩, + ⟨7, 2, 3, 6, 4, 2, -8807845144640791275482152658321720857242422476800000⟩, + ⟨7, 2, 4, 6, 5, 2, 1218091442966731726920903517701459799407014707200000⟩, + ⟨7, 2, 5, 6, 6, 2, -230126583220257338883064415975053125045819801600000⟩, + ⟨7, 2, 6, 6, 7, 2, -157676906592269416812470498822824412280835276800000⟩, + ⟨7, 2, 7, 6, 8, 2, -24711372234628504175682788586289704452122214400000⟩, + ⟨7, 2, 0, 7, 0, 2, 310769973570866689862581977935230405616419523788800000⟩, + ⟨7, 2, 1, 7, 1, 2, 317570624482156341164065498589243678095594802380800000⟩, + ⟨7, 2, 2, 7, 2, 2, 16862146433784137786909793030259265498658530918400000⟩, + ⟨7, 2, 3, 7, 3, 2, 15697408644153913857304078249520741500169119334400000⟩, + ⟨7, 2, 4, 7, 4, 2, 5037555246940612910707781758211382687820047974400000⟩, + ⟨7, 2, 5, 7, 5, 2, 260250234398818689551304038576103307739765145600000⟩, + ⟨7, 2, 6, 7, 6, 2, 170656845393171215452482659765669803088412672000000⟩, + ⟨7, 2, 7, 7, 7, 2, 8733805541523889578216539731122954173625139200000⟩, + ⟨7, 2, 8, 7, 8, 2, 29293651069932795632559579756508110724792320000000⟩ +] + +def collectedFourData_9_7_38 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 7, 3, -48914425501456750088885123375909740575718165708800000⟩, + ⟨7, 3, 1, 0, 8, 3, -2814208943841599196090071235112105914456971673600000⟩, + ⟨7, 3, 0, 1, 6, 3, -6153999351805518024005469580427207155141469798400000⟩, + ⟨7, 3, 1, 1, 7, 3, -29511750037059648961190161777620779115954674073600000⟩, + ⟨7, 3, 2, 1, 8, 3, 5409410294334297556601188725606903770650981171200000⟩, + ⟨7, 3, 0, 2, 5, 3, 29763501061277280599687103588900792044205008486400000⟩, + ⟨7, 3, 1, 2, 6, 3, -34995448886811526258847082304289346068286957158400000⟩, + ⟨7, 3, 2, 2, 7, 3, 6575371746954984072166201618918304788018259558400000⟩, + ⟨7, 3, 3, 2, 8, 3, 691493805406715548131154088167684661959458816000000⟩, + ⟨7, 3, 0, 3, 4, 3, -18901539208132516955249222974395674131897830604800000⟩, + ⟨7, 3, 1, 3, 5, 3, -28911639540756953937877374770195559308721546854400000⟩, + ⟨7, 3, 2, 3, 6, 3, 2612085410068913571870368925277567085954727936000000⟩, + ⟨7, 3, 3, 3, 7, 3, 1726583571010999376492326099241979967764745420800000⟩, + ⟨7, 3, 4, 3, 8, 3, 200601572686227829412256375603954721365247918080000⟩, + ⟨7, 3, 0, 4, 3, 3, -72539337075830630031293863882206624805820144025600000⟩, + ⟨7, 3, 1, 4, 4, 3, 32563596300246974239353938490443942979206696140800000⟩, + ⟨7, 3, 2, 4, 5, 3, 1213102697741604245497148921299925946118805913600000⟩, + ⟨7, 3, 3, 4, 6, 3, 3965984132582183047018946476378729681974932275200000⟩, + ⟨7, 3, 4, 4, 7, 3, 457127977767613641450243778302905586561822228480000⟩, + ⟨7, 3, 5, 4, 8, 3, -331036223649955153566749836752569815106637004800000⟩, + ⟨7, 3, 0, 5, 2, 3, 122425234079083442320368481543500765982046237491200000⟩, + ⟨7, 3, 1, 5, 3, 3, 62188170384007359394664359407795840629756185804800000⟩, + ⟨7, 3, 2, 5, 4, 3, -6432153535419728790330833524353448894885212979200000⟩, + ⟨7, 3, 3, 5, 5, 3, 1303428523450142651651832489024589247145207398400000⟩, + ⟨7, 3, 4, 5, 6, 3, -419313799213460240331249041916014556669951344640000⟩, + ⟨7, 3, 5, 5, 7, 3, 11261335541645735006662653728979569647760179200000⟩, + ⟨7, 3, 6, 5, 8, 3, -66611916950725308619421866395875359534664908800000⟩, + ⟨7, 3, 0, 6, 1, 3, -88986535853282783679370929771788110788651122688000000⟩, + ⟨7, 3, 1, 6, 2, 3, -154967856338358047666788965973177219812026430259200000⟩, + ⟨7, 3, 2, 6, 3, 3, -3245550532998746882299862536518897303010934784000000⟩, + ⟨7, 3, 3, 6, 4, 3, -6149588297645876157094103992923986570732214681600000⟩, + ⟨7, 3, 4, 6, 5, 3, 680371714998973173097261997856448174837853061120000⟩, + ⟨7, 3, 5, 6, 6, 3, -107115396929944515231392219965074163716902092800000⟩, + ⟨7, 3, 6, 6, 7, 3, -62908077558160105058151280676199823609901875200000⟩, + ⟨7, 3, 7, 6, 8, 3, -8626671053890345421656722249706146885953126400000⟩, + ⟨7, 3, 0, 7, 0, 3, 867911440924435259388738338462416778506243827302400000⟩, + ⟨7, 3, 1, 7, 1, 3, 443452073446099975077858985151177291571678884659200000⟩, + ⟨7, 3, 2, 7, 2, 3, 15697408644153913857304078249520741500169119334400000⟩, + ⟨7, 3, 3, 7, 3, 3, 10959843062203496465120366622069125441055935692800000⟩, + ⟨7, 3, 4, 7, 4, 3, 2813754355268604707065806666908915682760709898240000⟩, + ⟨7, 3, 5, 7, 5, 3, 121136840293062908976064826878839647774756044800000⟩, + ⟨7, 3, 6, 7, 6, 3, 68086660867755141799647569405833509662097408000000⟩, + ⟨7, 3, 7, 7, 7, 3, 3048947130090604725063642859352642148315955200000⟩, + ⟨7, 3, 8, 7, 8, 3, 9090072712662701241075742274243227853783040000000⟩ +] + +def collectedFourData_9_7_39 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 7, 4, -31394878788190018244384088139163307601882093977600000⟩, + ⟨7, 4, 1, 0, 8, 4, -1204167588201780406810618231645758267100810444800000⟩, + ⟨7, 4, 0, 1, 6, 4, -3949838145533984701432983395786528774020713676800000⟩, + ⟨7, 4, 1, 1, 7, 4, -12627737874085928162949261878834159743910333644800000⟩, + ⟨7, 4, 2, 1, 8, 4, 1735968262584979330343526802024144076381827891200000⟩, + ⟨7, 4, 0, 2, 5, 4, 19103188855875177784517635954432988224047336652800000⟩, + ⟨7, 4, 1, 2, 6, 4, -14974149441279877407703144838321703885881946931200000⟩, + ⟨7, 4, 2, 2, 7, 4, 2110144368114811730151407749415528312412202598400000⟩, + ⟨7, 4, 3, 2, 8, 4, 177529340115680601492051307847219655184534732800000⟩, + ⟨7, 4, 0, 3, 4, 4, -12131626330393449335570112411484807636870338969600000⟩, + ⟨7, 4, 1, 3, 5, 4, -12370957505816277769513641237693635581988516659200000⟩, + ⟨7, 4, 2, 3, 6, 4, 838260942378551362060699054882316498591809536000000⟩, + ⟨7, 4, 3, 3, 7, 4, 443271132177204127773453626360318886813515120640000⟩, + ⟨7, 4, 4, 3, 8, 4, 42917551040349380376104467834563777251738910720000⟩, + ⟨7, 4, 0, 4, 3, 4, -46558120054042896736117798185511633519620862771200000⟩, + ⟨7, 4, 1, 4, 4, 4, 13933587733722983285761594470500361632234235494400000⟩, + ⟨7, 4, 2, 4, 5, 4, 389304502330194387545100239980457429516786073600000⟩, + ⟨7, 4, 3, 4, 6, 4, 1018199354009335446886334665445293720384737116160000⟩, + ⟨7, 4, 4, 4, 7, 4, 97799897852745858045974023381755821975477944320000⟩, + ⟨7, 4, 5, 4, 8, 4, -60705679996653329618631284074512022226180505600000⟩, + ⟨7, 4, 0, 5, 2, 4, 78576521039057243999029407133384899842898552422400000⟩, + ⟨7, 4, 1, 5, 3, 4, 26609601717691972611121300282050748196707526246400000⟩, + ⟨7, 4, 2, 5, 4, 4, -2064183300951947991134086530798855330316104499200000⟩, + ⟨7, 4, 3, 5, 5, 4, 334633230040230376134024311414899813254923550720000⟩, + ⟨7, 4, 4, 5, 6, 4, -89709772155250854709833324776301027806423285760000⟩, + ⟨7, 4, 5, 5, 7, 4, 2065112464698022474241339654958935926269542400000⟩, + ⟨7, 4, 6, 5, 8, 4, -10688426967494076182929512492765480080533094400000⟩, + ⟨7, 4, 0, 6, 1, 4, -57114470388935401091484333447247049598462590976000000⟩, + ⟨7, 4, 1, 6, 2, 4, -66308960542577250756618165852978940796401719705600000⟩, + ⟨7, 4, 2, 6, 3, 4, -1041550263954409619518576688083176870257885184000000⟩, + ⟨7, 4, 3, 6, 4, 4, -1578802794657083554162649009726262523081292513280000⟩, + ⟨7, 4, 4, 6, 5, 4, 145561609581953055883788064290294258032789422080000⟩, + ⟨7, 4, 5, 6, 6, 4, -19642904746338611597180021344950099348396441600000⟩, + ⟨7, 4, 6, 6, 7, 4, -10094115639146547809474993198924241124825497600000⟩, + ⟨7, 4, 7, 6, 8, 4, -1230417722406559390931666437543664065865318400000⟩, + ⟨7, 4, 0, 7, 0, 4, 557053961226519940147667921190068069063799393484800000⟩, + ⟨7, 4, 1, 7, 1, 4, 189748033788753830308983165236333481949539178905600000⟩, + ⟨7, 4, 2, 7, 2, 4, 5037555246940612910707781758211382687820047974400000⟩, + ⟨7, 4, 3, 7, 3, 4, 2813754355268604707065806666908915682760709898240000⟩, + ⟨7, 4, 4, 7, 4, 4, 601986537494062065575638839076358280137838428160000⟩, + ⟨7, 4, 5, 7, 5, 4, 22214167928680618039874001120802476251519385600000⟩, + ⟨7, 4, 6, 7, 6, 4, 10925061692547697119845432882129990376751104000000⟩, + ⟨7, 4, 7, 7, 7, 4, 434869784660712654835272081700966651605811200000⟩, + ⟨7, 4, 8, 7, 8, 4, 1166861219626835899047302453829373123362816000000⟩ +] + +def collectedFourData_9_7_40 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 7, 5, -2703204286944228247293543367688381834937237504000000⟩, + ⟨7, 5, 1, 0, 8, 5, -77762148930102836389180846180838084123295744000000⟩, + ⟨7, 5, 0, 1, 6, 5, -340094302633836428829192673513433879933878272000000⟩, + ⟨7, 5, 1, 1, 7, 5, -815467915625731554431332198522909661010591744000000⟩, + ⟨7, 5, 2, 1, 8, 5, 89683611414689255483016725752321391102577868800000⟩, + ⟨7, 5, 0, 2, 5, 5, 1644848586863556205250578649394125294442381312000000⟩, + ⟨7, 5, 1, 2, 6, 5, -966993340763546356611553906295464884789313536000000⟩, + ⟨7, 5, 2, 2, 7, 5, 109014301481009831066899658002294859892365721600000⟩, + ⟨7, 5, 3, 2, 8, 5, 7642935596228732937847765113851364828512256000000⟩, + ⟨7, 5, 0, 3, 4, 5, -1044573687485025257323152128478275973817565184000000⟩, + ⟨7, 5, 1, 3, 5, 5, -798885677874647661297999410048949362544869376000000⟩, + ⟨7, 5, 2, 3, 6, 5, 43306245995789963590772196119449661041803264000000⟩, + ⟨7, 5, 3, 3, 7, 5, 19083565075441427482939383574079173330521292800000⟩, + ⟨7, 5, 4, 3, 8, 5, 1583719280279497479897884842235775507706675200000⟩, + ⟨7, 5, 0, 4, 3, 5, -4008810181152754674178952121524597324563611648000000⟩, + ⟨7, 5, 1, 4, 4, 5, 899796452832991710770720505319886283218092032000000⟩, + ⟨7, 5, 2, 4, 5, 5, 20112253467687468971276379894653645043951206400000⟩, + ⟨7, 5, 3, 4, 6, 5, 43835188491908830177636708133039488214709043200000⟩, + ⟨7, 5, 4, 4, 7, 5, 3608956710813715214694980290149999245996851200000⟩, + ⟨7, 5, 5, 4, 8, 5, -1960110940974727890695543773925140001193984000000⟩, + ⟨7, 5, 0, 5, 2, 5, 6765701819044630335171473942120468017626218496000000⟩, + ⟨7, 5, 1, 5, 3, 5, 1718381919606316145602409177751957761364590592000000⟩, + ⟨7, 5, 2, 5, 4, 5, -106639860325328318416170580868657607659539660800000⟩, + ⟨7, 5, 3, 5, 5, 5, 14406521332693062692790893453343332262897254400000⟩, + ⟨7, 5, 4, 5, 6, 5, -3310419451896922389886685485675120879573401600000⟩, + ⟨7, 5, 5, 5, 7, 5, 66679914245603311896489152553741226868736000000⟩, + ⟨7, 5, 6, 5, 8, 5, -306769795100988690859326569756052833697792000000⟩, + ⟨7, 5, 0, 6, 1, 5, -4917747325719819809387287627441714658059223040000000⟩, + ⟨7, 5, 1, 6, 2, 5, -4282067808196285191085986991104095880078163968000000⟩, + ⟨7, 5, 2, 6, 3, 5, -53808581155890619495466044586450297359958016000000⟩, + ⟨7, 5, 3, 6, 4, 5, -67970106072873385081990154863357725251312025600000⟩, + ⟨7, 5, 4, 6, 5, 5, 5371432478678057036837113743462288811936972800000⟩, + ⟨7, 5, 5, 6, 6, 5, -634244975230412269819086266891172550017024000000⟩, + ⟨7, 5, 6, 6, 7, 5, -289712396011503006369532163600371855392768000000⟩, + ⟨7, 5, 7, 6, 8, 5, -31782926932587018366766018689908228279500800000⟩, + ⟨7, 5, 0, 7, 0, 5, 47964213087302922985388408525286015202693742592000000⟩, + ⟨7, 5, 1, 7, 1, 5, 12253456252472021466487253946786720633971539968000000⟩, + ⟨7, 5, 2, 7, 2, 5, 260250234398818689551304038576103307739765145600000⟩, + ⟨7, 5, 3, 7, 3, 5, 121136840293062908976064826878839647774756044800000⟩, + ⟨7, 5, 4, 7, 4, 5, 22214167928680618039874001120802476251519385600000⟩, + ⟨7, 5, 5, 7, 5, 5, 717267866928716511541517933626308043997184000000⟩, + ⟨7, 5, 6, 7, 6, 5, 313561476078858302016974282252461245726720000000⟩, + ⟨7, 5, 7, 7, 7, 5, 11233123791510497524748827846631745807974400000⟩, + ⟨7, 5, 8, 7, 8, 5, 27401089600790589603080643761897440542720000000⟩ +] + +def collectedFourData_9_7_41 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 7, 6, -2658904326035601025373210895601250052310302720000000⟩, + ⟨7, 6, 1, 0, 8, 6, -61190229740514161440769628915593708606324736000000⟩, + ⟨7, 6, 0, 1, 6, 6, -334520856192998999544140362026149575875624960000000⟩, + ⟨7, 6, 1, 1, 7, 6, -641683258367879873356937486066655992255348736000000⟩, + ⟨7, 6, 2, 1, 8, 6, 58809254265814184752781655105191709146873856000000⟩, + ⟨7, 6, 0, 2, 5, 6, 1617892900069704345245123732019873233145692160000000⟩, + ⟨7, 6, 1, 2, 6, 6, -760917046313298807468971509057752495065923584000000⟩, + ⟨7, 6, 2, 2, 7, 6, 71485187463768512162884855630771684525473792000000⟩, + ⟨7, 6, 3, 2, 8, 6, 4295819196832065402913370624221765183733760000000⟩, + ⟨7, 6, 0, 3, 4, 6, -1027455272223085444014578180724194773429125120000000⟩, + ⟨7, 6, 1, 3, 5, 6, -628634867196068304277363757878958029006700544000000⟩, + ⟨7, 6, 2, 3, 6, 6, 28397697103075939977796119857950279524679680000000⟩, + ⟨7, 6, 3, 3, 7, 6, 10726185529487721551423858595186626934079488000000⟩, + ⟨7, 6, 4, 3, 8, 6, 778882688574254927200192135174547274989568000000⟩, + ⟨7, 6, 0, 4, 3, 6, -3943114023754333888858962716147545310641520640000000⟩, + ⟨7, 6, 1, 4, 4, 6, 708040511046582582457630149055963528490385408000000⟩, + ⟨7, 6, 2, 4, 5, 6, 13188436653945975005330428084137375005933568000000⟩, + ⟨7, 6, 3, 4, 6, 6, 24638182783224178198617707713038656389251072000000⟩, + ⟨7, 6, 4, 4, 7, 6, 1774906664879778698556502048961332047249408000000⟩, + ⟨7, 6, 5, 4, 8, 6, -856883889922587664940771855798052291870720000000⟩, + ⟨7, 6, 0, 5, 2, 6, 6654825875428131862242254409777312014039777280000000⟩, + ⟨7, 6, 1, 5, 3, 6, 1352176938129237576796595212060950203411202048000000⟩, + ⟨7, 6, 2, 5, 4, 6, -69928168166028498245856273267702806291152896000000⟩, + ⟨7, 6, 3, 5, 5, 6, 8097387466026920298674447372308024261607424000000⟩, + ⟨7, 6, 4, 5, 6, 6, -1628084241385847654001338340483008292716544000000⟩, + ⟨7, 6, 5, 5, 7, 6, 29149852237477925329023480495929693306880000000⟩, + ⟨7, 6, 6, 5, 8, 6, -120696987531509114185511661888181238759424000000⟩, + ⟨7, 6, 0, 6, 1, 6, -4837155557150910010368161575188387255759667200000000⟩, + ⟨7, 6, 1, 6, 2, 6, -3369514816051574762902744874136421691232878592000000⟩, + ⟨7, 6, 2, 6, 3, 6, -35284512755037939388005670936280374884433920000000⟩, + ⟨7, 6, 3, 6, 4, 6, -38203551868556505045968840578148274983141376000000⟩, + ⟨7, 6, 4, 6, 5, 6, 2641702871578029929160145303431180296650752000000⟩, + ⟨7, 6, 5, 6, 6, 6, -277267112885473176039739471242953930833920000000⟩, + ⟨7, 6, 6, 6, 7, 6, -113985842177234979098589854334912766672896000000⟩, + ⟨7, 6, 7, 6, 8, 6, -11368025491185942152584224895899864662016000000⟩, + ⟨7, 6, 0, 7, 0, 6, 47178178241530120233731706334168806232487362560000000⟩, + ⟨7, 6, 1, 7, 1, 6, 9642117836507571043990987364128878646989422592000000⟩, + ⟨7, 6, 2, 7, 2, 6, 170656845393171215452482659765669803088412672000000⟩, + ⟨7, 6, 3, 7, 3, 6, 68086660867755141799647569405833509662097408000000⟩, + ⟨7, 6, 4, 7, 4, 6, 10925061692547697119845432882129990376751104000000⟩, + ⟨7, 6, 5, 7, 5, 6, 313561476078858302016974282252461245726720000000⟩, + ⟨7, 6, 6, 7, 6, 6, 123369139247208695959596439042564911267840000000⟩, + ⟨7, 6, 7, 7, 7, 6, 4017831267661175508654430695033025855488000000⟩, + ⟨7, 6, 8, 7, 8, 6, 8984014024826132970611226972513317683200000000⟩ +] + +def collectedFourData_9_7_42 : List CollectedFourTerm := [ + ⟨7, 7, 0, 0, 7, 7, -190506830224444868291288918852714631296502988800000⟩, + ⟨7, 7, 1, 0, 8, 7, -3653496352622187411176493349768711971746611200000⟩, + ⟨7, 7, 0, 1, 6, 7, -23967958280136444899814454324920808173364838400000⟩, + ⟨7, 7, 1, 1, 7, 7, -38313100864753686042657229615212995670127411200000⟩, + ⟨7, 7, 2, 1, 8, 7, 3009715722895977481274365568775599813138841600000⟩, + ⟨7, 7, 0, 2, 5, 7, 115919796367576051363230147371233315333236326400000⟩, + ⟨7, 7, 1, 2, 6, 7, -45432214671242477286159833512692750979222732800000⟩, + ⟨7, 7, 2, 2, 7, 7, 3658439396143427173622573658716746632344371200000⟩, + ⟨7, 7, 3, 2, 8, 7, 192368452860524195630599458156522183327744000000⟩, + ⟨7, 7, 0, 3, 4, 7, -73615754125480830737183613776731143746145484800000⟩, + ⟨7, 7, 1, 3, 5, 7, -37534018162237907854601319636701436449705164800000⟩, + ⟨7, 7, 2, 3, 6, 7, 1453325612306706788354485141147477918875648000000⟩, + ⟨7, 7, 3, 3, 7, 7, 480322755884169100723535545099801295270707200000⟩, + ⟨7, 7, 4, 3, 8, 7, 31003261728699331171794259198256454461030400000⟩, + ⟨7, 7, 0, 4, 3, 7, -282518685055137482510574143832470146898303385600000⟩, + ⟨7, 7, 1, 4, 4, 7, 42275105610605325216129976996426531212990873600000⟩, + ⟨7, 7, 2, 4, 5, 7, 674952363422037360605169275709999876459724800000⟩, + ⟨7, 7, 3, 4, 6, 7, 1103307398690998175600307293821509982538956800000⟩, + ⟨7, 7, 4, 4, 7, 7, 70649786781125149412921789907474267399782400000⟩, + ⟨7, 7, 5, 4, 8, 7, -30697274840072339695503469753173147018854400000⟩, + ⟨7, 7, 0, 5, 2, 7, 476809101707578672043436176839063245077820211200000⟩, + ⟨7, 7, 1, 5, 3, 7, 80734678273059479469996830311405839021873561600000⟩, + ⟨7, 7, 2, 5, 4, 7, -3578754905670562047484789854517254701029785600000⟩, + ⟨7, 7, 3, 5, 5, 7, 362604157130380472836534505765795503118745600000⟩, + ⟨7, 7, 4, 5, 6, 7, -64805551070152206670291049605405399528243200000⟩, + ⟨7, 7, 5, 5, 7, 7, 1044273367961436588038690830158898239897600000⟩, + ⟨7, 7, 6, 5, 8, 7, -3930805818827016197718658312499454856396800000⟩, + ⟨7, 7, 0, 6, 1, 7, -346575528676258205249006921889722763457855488000000⟩, + ⟨7, 7, 1, 6, 2, 7, -201184243673464069590092610142994871401997926400000⟩, + ⟨7, 7, 2, 6, 3, 7, -1805776219054919762028810734216474957709312000000⟩, + ⟨7, 7, 3, 6, 4, 7, -1710769897427389457605491733304580761871974400000⟩, + ⟨7, 7, 4, 6, 5, 7, 105152427622843710917866259484352913709465600000⟩, + ⟨7, 7, 5, 6, 6, 7, -9932903242150651450281211835154944124518400000⟩, + ⟨7, 7, 6, 6, 7, 7, -3712240221216820177642391297727646610227200000⟩, + ⟨7, 7, 7, 6, 8, 7, -339376399179171488774741406577352874393600000⟩, + ⟨7, 7, 0, 7, 0, 7, 3380251445887277532451312859845144879995184742400000⟩, + ⟨7, 7, 1, 7, 1, 7, 575703711141806589252072759063176936262362726400000⟩, + ⟨7, 7, 2, 7, 2, 7, 8733805541523889578216539731122954173625139200000⟩, + ⟨7, 7, 3, 7, 3, 7, 3048947130090604725063642859352642148315955200000⟩, + ⟨7, 7, 4, 7, 4, 7, 434869784660712654835272081700966651605811200000⟩, + ⟨7, 7, 5, 7, 5, 7, 11233123791510497524748827846631745807974400000⟩, + ⟨7, 7, 6, 7, 6, 7, 4017831267661175508654430695033025855488000000⟩, + ⟨7, 7, 7, 7, 7, 7, 119946696916324900162620888488078003404800000⟩, + ⟨7, 7, 8, 7, 8, 7, 247573931661461199878562339454483169280000000⟩ +] + +def collectedFourData_9_7_43 : List CollectedFourTerm := [ + ⟨7, 8, 0, 0, 7, 8, -851960134979922316443807045223642856832368640000000⟩, + ⟨7, 8, 1, 0, 8, 8, -14004596844839853640409536562178944799866880000000⟩, + ⟨7, 8, 0, 1, 6, 8, -107186419234841871998239688163679863853547520000000⟩, + ⟨7, 8, 1, 1, 7, 8, -146861931612840130898379838896712492913786880000000⟩, + ⟨7, 8, 2, 1, 8, 8, 10094747563021883768170106500796598567567360000000⟩, + ⟨7, 8, 0, 2, 5, 8, 518401598744846170609932290728320145733713920000000⟩, + ⟨7, 8, 1, 2, 6, 8, -174150947155678117638717317700929490486558720000000⟩, + ⟨7, 8, 2, 2, 7, 8, 12270601471672124553793232613663357555179520000000⟩, + ⟨7, 8, 3, 2, 8, 8, 573523629474227122595575033320260291788800000000⟩, + ⟨7, 8, 0, 3, 4, 8, -329214903987971590906066623460346753911357440000000⟩, + ⟨7, 8, 1, 3, 5, 8, -143875548678670532567836009971879574524395520000000⟩, + ⟨7, 8, 2, 3, 6, 8, 4874531860767860461098378666461102918860800000000⟩, + ⟨7, 8, 3, 3, 7, 8, 1432025086116821324648583028312276142653440000000⟩, + ⟨7, 8, 4, 3, 8, 8, 83189278881229184208539653770301849731072000000⟩, + ⟨7, 8, 0, 4, 3, 8, -1263443713647178074313777944601839244337479680000000⟩, + ⟨7, 8, 1, 4, 4, 8, 162049104065652566239401972919789062602096640000000⟩, + ⟨7, 8, 2, 4, 5, 8, 2263826338806006033291739655262265493422080000000⟩, + ⟨7, 8, 3, 4, 6, 8, 3289379595841623165356600950643708248719360000000⟩, + ⟨7, 8, 4, 4, 7, 8, 189570531864195814679638686030396162834432000000⟩, + ⟨7, 8, 5, 4, 8, 8, -74880219786112622388364705774449689886720000000⟩, + ⟨7, 8, 0, 5, 2, 8, 2132324317043409851517284211370374127272591360000000⟩, + ⟨7, 8, 1, 5, 3, 8, 309472491959805734400775019607859469840547840000000⟩, + ⟨7, 8, 2, 5, 4, 8, -12003335427277207647638923904119322978549760000000⟩, + ⟨7, 8, 3, 5, 5, 8, 1081061105225193177765151879939407080325120000000⟩, + ⟨7, 8, 4, 5, 6, 8, -173889028457806860685604058022658049048576000000⟩, + ⟨7, 8, 5, 5, 7, 8, 2547308180192589354532291462063592570880000000⟩, + ⟨7, 8, 6, 5, 8, 8, -8789422017158774444225469129028030955520000000⟩, + ⟨7, 8, 0, 6, 1, 8, -1549910487954124388682383029218950236235366400000000⟩, + ⟨7, 8, 1, 6, 2, 8, -771180248245959806767697083710708605371023360000000⟩, + ⟨7, 8, 2, 6, 3, 8, -6056670052920327815638241424015323509555200000000⟩, + ⟨7, 8, 3, 6, 4, 8, -5100456681840644369861251364416517969018880000000⟩, + ⟨7, 8, 4, 6, 5, 8, 282149494562938545440460813142923524702208000000⟩, + ⟨7, 8, 5, 6, 6, 8, -24229446482184171512793625890910025809920000000⟩, + ⟨7, 8, 6, 6, 7, 8, -8300701544977886274190411890983782318080000000⟩, + ⟨7, 8, 7, 6, 8, 8, -700484061820477247638816521840450600960000000⟩, + ⟨7, 8, 0, 7, 0, 8, 15116725603545715685760063230752929878869278720000000⟩, + ⟨7, 8, 1, 7, 1, 8, 2206789770251863724793431350673327502246543360000000⟩, + ⟨7, 8, 2, 7, 2, 8, 29293651069932795632559579756508110724792320000000⟩, + ⟨7, 8, 3, 7, 3, 8, 9090072712662701241075742274243227853783040000000⟩, + ⟨7, 8, 4, 7, 4, 8, 1166861219626835899047302453829373123362816000000⟩, + ⟨7, 8, 5, 7, 5, 8, 27401089600790589603080643761897440542720000000⟩, + ⟨7, 8, 6, 7, 6, 8, 8984014024826132970611226972513317683200000000⟩, + ⟨7, 8, 7, 7, 7, 8, 247573931661461199878562339454483169280000000⟩, + ⟨7, 8, 8, 7, 8, 8, 474500692976227768311657646717403136000000000⟩ +] + +def collectedFourData_9_7 : List (List CollectedFourTerm) := [ + collectedFourData_9_7_0, + collectedFourData_9_7_1, + collectedFourData_9_7_2, + collectedFourData_9_7_3, + collectedFourData_9_7_4, + collectedFourData_9_7_5, + collectedFourData_9_7_6, + collectedFourData_9_7_7, + collectedFourData_9_7_8, + collectedFourData_9_7_9, + collectedFourData_9_7_10, + collectedFourData_9_7_11, + collectedFourData_9_7_12, + collectedFourData_9_7_13, + collectedFourData_9_7_14, + collectedFourData_9_7_15, + collectedFourData_9_7_16, + collectedFourData_9_7_17, + collectedFourData_9_7_18, + collectedFourData_9_7_19, + collectedFourData_9_7_20, + collectedFourData_9_7_21, + collectedFourData_9_7_22, + collectedFourData_9_7_23, + collectedFourData_9_7_24, + collectedFourData_9_7_25, + collectedFourData_9_7_26, + collectedFourData_9_7_27, + collectedFourData_9_7_28, + collectedFourData_9_7_29, + collectedFourData_9_7_30, + collectedFourData_9_7_31, + collectedFourData_9_7_32, + collectedFourData_9_7_33, + collectedFourData_9_7_34, + collectedFourData_9_7_35, + collectedFourData_9_7_36, + collectedFourData_9_7_37, + collectedFourData_9_7_38, + collectedFourData_9_7_39, + collectedFourData_9_7_40, + collectedFourData_9_7_41, + collectedFourData_9_7_42, + collectedFourData_9_7_43 +] + +theorem collectedFourChecked_9_7 : collectNumericRowParts 9 7 = collectedFourData_9_7 := by + decide +kernel + +def collectedFourData_9 : Fin 8 → List (List CollectedFourTerm) := + ![collectedFourData_9_0, collectedFourData_9_1, collectedFourData_9_2, collectedFourData_9_3, collectedFourData_9_4, collectedFourData_9_5, collectedFourData_9_6, collectedFourData_9_7] + +theorem collectedFourChecked_9 (t : Fin 8) : + collectNumericRowParts 9 t = collectedFourData_9 t := by + fin_cases t + · exact collectedFourChecked_9_0 + · exact collectedFourChecked_9_1 + · exact collectedFourChecked_9_2 + · exact collectedFourChecked_9_3 + · exact collectedFourChecked_9_4 + · exact collectedFourChecked_9_5 + · exact collectedFourChecked_9_6 + · exact collectedFourChecked_9_7 + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1001.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1001.lean new file mode 100644 index 0000000000000000000000000000000000000000..d811508a805ee34cad6cd440e07cf6125e2fb87c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1001.lean @@ -0,0 +1,608 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1001. -/ +namespace LaughlinFock + +def collectedFourData_10_0_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_10_0_1 : List CollectedFourTerm := [ + +] + +def collectedFourData_10_0_2 : List CollectedFourTerm := [ + ⟨0, 2, 8, 0, 8, 2, -5307104128847786389487343432349438002920108851200000⟩, + ⟨0, 2, 8, 1, 7, 2, -4434694610774247672868520275806132377562906624000000⟩, + ⟨0, 2, 8, 2, 6, 2, -241320651209157159901267471087321464774328320000000⟩, + ⟨0, 2, 8, 3, 5, 2, -3839596996829086568264890875997395063505158144000000⟩, + ⟨0, 2, 8, 4, 4, 2, 5493289417998603593850991673925282282589913088000000⟩, + ⟨0, 2, 8, 5, 3, 2, -7684200979569531098105583043255061547570954240000000⟩, + ⟨0, 2, 8, 6, 2, 2, 27402986926665144561661120111883052421816831180800000⟩, + ⟨0, 2, 8, 7, 1, 2, -51237569422474422526596408340143451228480733184000000⟩ +] + +def collectedFourData_10_0_3 : List CollectedFourTerm := [ + ⟨0, 3, 7, 0, 7, 3, 72164520751697383330746241114596830437441536000000⟩, + ⟨0, 3, 8, 0, 8, 3, -9730653361403528761732841313494222608156065792000000⟩, + ⟨0, 3, 7, 1, 6, 3, 4994815477363109997725360107485417067348230144000000⟩, + ⟨0, 3, 8, 1, 7, 3, -8131077697640216670583869829869495201394851840000000⟩, + ⟨0, 3, 7, 2, 5, 3, -506574497889806841894974268430666446101544960000000⟩, + ⟨0, 3, 8, 2, 6, 3, -442464958073903065173349047047192367543091200000000⟩, + ⟨0, 3, 7, 3, 4, 3, 2035363618983743401292342175024822576067117056000000⟩, + ⟨0, 3, 8, 3, 5, 3, -7039957482752723038955785868192486037431255040000000⟩, + ⟨0, 3, 7, 4, 3, 3, -7219005175127151536120010153823066278070321152000000⟩, + ⟨0, 3, 8, 4, 4, 3, 10072026823414838973940589130256982330132398080000000⟩, + ⟨0, 3, 7, 5, 2, 3, 14022224327214846439497205903568886381504626688000000⟩, + ⟨0, 3, 8, 5, 3, 3, -14089095347707487631038098421247915661354598400000000⟩, + ⟨0, 3, 7, 6, 1, 3, -38525607274527745191004517029859350772906459136000000⟩, + ⟨0, 3, 8, 6, 2, 3, 50243778975624265509197954060299036113216995328000000⟩, + ⟨0, 3, 7, 7, 0, 3, 130588796802514265970903813995455142486888939520000000⟩, + ⟨0, 3, 8, 7, 1, 3, -93944836020994357263342490891120735403051581440000000⟩ +] + +def collectedFourData_10_0_4 : List CollectedFourTerm := [ + ⟨0, 4, 6, 0, 6, 4, -47838980931703452830730512304231251696252721561600000⟩, + ⟨0, 4, 7, 0, 7, 4, 876895747295130781018046667953877328942281523200000⟩, + ⟨0, 4, 8, 0, 8, 4, -59120246778726956386937405673370599756519387955200000⟩, + ⟨0, 4, 6, 1, 5, 4, 30083047848464350232685753945910838380995595468800000⟩, + ⟨0, 4, 7, 1, 6, 4, 60693709387941708654352856660543805668335602892800000⟩, + ⟨0, 4, 8, 1, 7, 4, -49401751579007623540108694273610904328107720704000000⟩, + ⟨0, 4, 6, 2, 4, 4, -10797228174276311611318570218432419743067327692800000⟩, + ⟨0, 4, 7, 2, 5, 4, -6155559799477910021597453823963560747049418752000000⟩, + ⟨0, 4, 8, 2, 6, 4, -2688271438794235212410669165122511079965982720000000⟩, + ⟨0, 4, 6, 3, 3, 4, -16391190905712743879552330490031987323530379264000000⟩, + ⟨0, 4, 7, 3, 4, 4, 24732398734098031738377918490031452835028349747200000⟩, + ⟨0, 4, 8, 3, 5, 4, -42772464318064457594634929416185992991026970624000000⟩, + ⟨0, 4, 6, 4, 2, 4, 49840608332983644557041530116427295432938356736000000⟩, + ⟨0, 4, 7, 4, 3, 4, -87720598319384592052547382053053402388168599142400000⟩, + ⟨0, 4, 8, 4, 4, 4, 61194319563794906930353274385656381369166594048000000⟩, + ⟨0, 4, 6, 5, 1, 4, -77018318878811381784103020861878239306859937792000000⟩, + ⟨0, 4, 7, 5, 2, 4, 170388838615876348641067700040765087133147437465600000⟩, + ⟨0, 4, 8, 5, 3, 4, -85600705616476455266225860449676902360196055040000000⟩, + ⟨0, 4, 6, 6, 0, 4, 112970825208989558059914145191193782674469263769600000⟩, + ⟨0, 4, 7, 6, 1, 4, -468137816604305855231795295708774047830720590643200000⟩, + ⟨0, 4, 8, 6, 2, 4, 305264662280218347649374021700305135615299341516800000⟩, + ⟨0, 4, 7, 7, 0, 4, 1586829086754785593011016525084370693074949505024000000⟩, + ⟨0, 4, 8, 7, 1, 4, -570777899784020318858755036717383333501902782464000000⟩ +] + +def collectedFourData_10_0_5 : List CollectedFourTerm := [ + ⟨0, 5, 5, 0, 5, 5, 217683470486240658578067546849306730344757592064000000⟩, + ⟨0, 5, 6, 0, 6, 5, 251622243928787722125828461136330215247669362688000000⟩, + ⟨0, 5, 7, 0, 7, 5, -2306136871320632487887394794312106056444018688000000⟩, + ⟨0, 5, 8, 0, 8, 5, 103653052150953337155279482489394070967090675712000000⟩, + ⟨0, 5, 5, 1, 4, 5, 116492900353042042377065971862895856119479009280000000⟩, + ⟨0, 5, 6, 1, 5, 5, -158230042873493793347491498548986141800277213184000000⟩, + ⟨0, 5, 7, 1, 6, 5, -159617607347847614827023474903451960542077386752000000⟩, + ⟨0, 5, 8, 1, 7, 5, 86614021621605653256944328342251864957638410240000000⟩, + ⟨0, 5, 5, 2, 3, 5, 171872558031754686900901530461199048171520524288000000⟩, + ⟨0, 5, 6, 2, 4, 5, 56790983597689120525678017731000227689350037504000000⟩, + ⟨0, 5, 7, 2, 5, 5, 16188427713308711017376548800599692628648263680000000⟩, + ⟨0, 5, 8, 2, 6, 5, 4713233702899935301991929873921887450641203200000000⟩, + ⟨0, 5, 5, 3, 2, 5, -466932053086114057614764352063960892874812293120000000⟩, + ⟨0, 5, 6, 3, 3, 5, 86213965181421718254549346733959920796324331520000000⟩, + ⟨0, 5, 7, 3, 4, 5, -65043418003612340136539698982750446891038670848000000⟩, + ⟨0, 5, 8, 3, 5, 5, 74991169965488310831034237188602994252778045440000000⟩, + ⟨0, 5, 5, 4, 1, 5, 129423388084579729722618086854805497664042434560000000⟩, + ⟨0, 5, 6, 4, 2, 5, -262150352354393679784430597346366438959984148480000000⟩, + ⟨0, 5, 7, 4, 3, 5, 230695275672895056877580102897918866197646934016000000⟩, + ⟨0, 5, 8, 4, 4, 5, -107289437082838944318694627854289601521652858880000000⟩, + ⟨0, 5, 5, 5, 0, 5, 1481642270946190090178591663754775448798701289472000000⟩, + ⟨0, 5, 6, 5, 1, 5, 405098976660399505155994686407473453746156994560000000⟩, + ⟨0, 5, 7, 5, 2, 5, -448103419825714057821343909680259247665739464704000000⟩, + ⟨0, 5, 8, 5, 3, 5, 150080131374142021178366703501375330742330982400000000⟩, + ⟨0, 5, 6, 6, 0, 5, -594201046593251883476200718611438784867758768128000000⟩, + ⟨0, 5, 7, 6, 1, 5, 1231149635587610837645205042364061740265518399488000000⟩, + ⟨0, 5, 8, 6, 2, 5, -535207744947372718805147340682820628096491716608000000⟩, + ⟨0, 5, 7, 7, 0, 5, -4173181449148508014446273369099980448142102364160000000⟩, + ⟨0, 5, 8, 7, 1, 5, 1000720982007352796121140406894969777509200035840000000⟩ +] + +def collectedFourData_10_0_6 : List CollectedFourTerm := [ + ⟨0, 6, 4, 0, 4, 6, -47838980931703452830730512304231251696252721561600000⟩, + ⟨0, 6, 5, 0, 5, 6, 251622243928787722125828461136330215247669362688000000⟩, + ⟨0, 6, 6, 0, 6, 6, 145426185778676950050294223018333873730589032448000000⟩, + ⟨0, 6, 7, 0, 7, 6, -888561318064937144678462551359922227099205632000000⟩, + ⟨0, 6, 8, 0, 8, 6, 29953369350957552407003504966096353564060286976000000⟩, + ⟨0, 6, 4, 1, 3, 6, 28523576974091326379835479701671278065150328832000000⟩, + ⟨0, 6, 5, 1, 4, 6, 134655171213185305284364323493606798254680309760000000⟩, + ⟨0, 6, 6, 1, 5, 6, -91449751227880601345909629244442863212758564864000000⟩, + ⟨0, 6, 7, 1, 6, 6, -61501133490899296807761636775927244613671190528000000⟩, + ⟨0, 6, 8, 1, 7, 6, 25029477924349919932915122328325340700103147520000000⟩, + ⟨0, 6, 4, 2, 2, 6, -18791117166610258140690067417285170214319475916800000⟩, + ⟨0, 6, 5, 2, 3, 6, 198669006080847355374383440139235803402229252096000000⟩, + ⟨0, 6, 6, 2, 4, 6, 32822599474030227576210136790771128737762115584000000⟩, + ⟨0, 6, 7, 2, 5, 6, 6237448802463822168954411956308722578903531520000000⟩, + ⟨0, 6, 8, 2, 6, 6, 1362017104279207034976001952630388255463833600000000⟩, + ⟨0, 6, 4, 3, 1, 6, 41720585766264582135687284029334926941475779379200000⟩, + ⟨0, 6, 5, 3, 2, 6, -539730879415716549548888334356388751682347991040000000⟩, + ⟨0, 6, 6, 3, 3, 6, 49827741464455613837244402275381654205675601920000000⟩, + ⟨0, 6, 7, 3, 4, 6, -25061420226823535332457896067275752486702415872000000⟩, + ⟨0, 6, 8, 3, 5, 6, 21670738732955357381799544745235358902512517120000000⟩, + ⟨0, 6, 4, 4, 0, 6, -69687110207117038620850698651215130723338315366400000⟩, + ⟨0, 6, 5, 4, 1, 6, 149601636054248313271782891010373344095130091520000000⟩, + ⟨0, 6, 6, 4, 2, 6, -151510952482504359647373237511006790292162478080000000⟩, + ⟨0, 6, 7, 4, 3, 6, 88887568111199683863899298019928251525679284224000000⟩, + ⟨0, 6, 8, 4, 4, 6, -31004201706655091940868950012425546697529098240000000⟩, + ⟨0, 6, 5, 5, 0, 6, 1712643371967877907943757460661996417476223565824000000⟩, + ⟨0, 6, 6, 5, 1, 6, 234128740443313180006129943565075226205890805760000000⟩, + ⟨0, 6, 7, 5, 2, 6, -172655565374889401627039102556408332306513657856000000⟩, + ⟨0, 6, 8, 5, 3, 6, 43369736963877359486799152336557012025553715200000000⟩, + ⟨0, 6, 6, 6, 0, 6, -343421115885964067502171608100494668020672626688000000⟩, + ⟨0, 6, 7, 6, 1, 6, 474365574974061250289089532650996556945090936832000000⟩, + ⟨0, 6, 8, 6, 2, 6, -154662838490803620705840169746663742279079952384000000⟩, + ⟨0, 6, 7, 7, 0, 6, -1607939084229656392165997505332033657524967178240000000⟩, + ⟨0, 6, 8, 7, 1, 6, 289185552854397970284232306778580930393349816320000000⟩ +] + +def collectedFourData_10_0_7 : List CollectedFourTerm := [ + ⟨0, 7, 3, 0, 3, 7, 72164520751697383330746241114596830437441536000000⟩, + ⟨0, 7, 4, 0, 4, 7, 876895747295130781018046667953877328942281523200000⟩, + ⟨0, 7, 5, 0, 5, 7, -2306136871320632487887394794312106056444018688000000⟩, + ⟨0, 7, 6, 0, 6, 7, -888561318064937144678462551359922227099205632000000⟩, + ⟨0, 7, 7, 0, 7, 7, 4071865797760601056012070273649210940194816000000⟩, + ⟨0, 7, 8, 0, 8, 7, -109809957024432413900179558330278160011519590400000⟩, + ⟨0, 7, 3, 1, 2, 7, -7773053006520858325229943878607814197352857600000⟩, + ⟨0, 7, 4, 1, 3, 7, -522841474861980573788147107882840785539825664000000⟩, + ⟨0, 7, 5, 1, 4, 7, -1234124815040613403339384941002894855645429760000000⟩, + ⟨0, 7, 6, 1, 5, 7, 558762584968179188222589883883049870296088576000000⟩, + ⟨0, 7, 7, 1, 6, 7, 281831266896091201179936275607456185805963264000000⟩, + ⟨0, 7, 8, 1, 7, 7, -91758822288517623610640648695782426707755008000000⟩, + ⟨0, 7, 3, 2, 1, 7, -60850181819601436601240711923365347731911475200000⟩, + ⟨0, 7, 4, 2, 2, 7, 344444016352467872710656404772729579806235033600000⟩, + ⟨0, 7, 5, 2, 3, 7, -1820816446742003928717752629012211623155204096000000⟩, + ⟨0, 7, 6, 2, 4, 7, -200547735573204458344897189130727843541549056000000⟩, + ⟨0, 7, 7, 2, 5, 7, -28583344703037293567235314435772376688885760000000⟩, + ⟨0, 7, 8, 2, 6, 7, -4993195855031926798113619690670066698813440000000⟩, + ⟨0, 7, 3, 3, 0, 7, 627704250327126019870408039637328061695787008000000⟩, + ⟨0, 7, 4, 3, 1, 7, -764744639634539781825427381608479044432979558400000⟩, + ⟨0, 7, 5, 3, 2, 7, 4946674277188141083569865273588892096832471040000000⟩, + ⟨0, 7, 6, 3, 3, 7, -304450009431158472963871766885312532609761280000000⟩, + ⟨0, 7, 7, 3, 4, 7, 114844904668076917089615440179112589379239936000000⟩, + ⟨0, 7, 8, 3, 5, 7, -79445582934978145491871808830360215877582848000000⟩, + ⟨0, 7, 4, 4, 0, 7, 1277375257410862306636392985195260139874864332800000⟩, + ⟨0, 7, 5, 4, 1, 7, -1371110294256147017973582779904670876324331520000000⟩, + ⟨0, 7, 6, 4, 2, 7, 925739549024655262842043497305383826588958720000000⟩, + ⟨0, 7, 7, 4, 3, 7, -407330637829610060713486783969113277162586112000000⟩, + ⟨0, 7, 8, 4, 4, 7, 113662340189311360431830360531002435143991296000000⟩, + ⟨0, 7, 5, 5, 0, 7, -15696505864703297509914007827016512451928653824000000⟩, + ⟨0, 7, 6, 5, 1, 7, -1430538393696201561440715987094895702405283840000000⟩, + ⟨0, 7, 7, 5, 2, 7, 791200648902941925597007357036935939178364928000000⟩, + ⟨0, 7, 8, 5, 3, 7, -158994766043308745225905477394598524438446080000000⟩, + ⟨0, 7, 6, 6, 0, 7, 2098320311084624107717167942470376730543521792000000⟩, + ⟨0, 7, 7, 6, 1, 7, -2173798162380462615101108622800722899203260416000000⟩, + ⟨0, 7, 8, 6, 2, 7, 566998638749431574676400339892792403724704153600000⟩, + ⟨0, 7, 7, 7, 0, 7, 7368441579491258660540834917997626078129029120000000⟩, + ⟨0, 7, 8, 7, 1, 7, -1060162973953145871770345653473739312912662528000000⟩ +] + +def collectedFourData_10_0_8 : List CollectedFourTerm := [ + ⟨0, 8, 2, 0, 2, 8, -5307104128847786389487343432349438002920108851200000⟩, + ⟨0, 8, 3, 0, 3, 8, -9730653361403528761732841313494222608156065792000000⟩, + ⟨0, 8, 4, 0, 4, 8, -59120246778726956386937405673370599756519387955200000⟩, + ⟨0, 8, 5, 0, 5, 8, 103653052150953337155279482489394070967090675712000000⟩, + ⟨0, 8, 6, 0, 6, 8, 29953369350957552407003504966096353564060286976000000⟩, + ⟨0, 8, 7, 0, 7, 8, -109809957024432413900179558330278160011519590400000⟩, + ⟨0, 8, 8, 0, 8, 8, 2467793075011489304559212149659167218262133964800000⟩, + ⟨0, 8, 2, 1, 1, 8, 27981811730568543391180624264410516232456057651200000⟩, + ⟨0, 8, 3, 1, 2, 8, 1048117323837294915583027709555447451958326067200000⟩, + ⟨0, 8, 4, 1, 3, 8, 35249933775298054303102747282954666324267106304000000⟩, + ⟨0, 8, 5, 1, 4, 8, 55469736165718215515008457019080054774421258240000000⟩, + ⟨0, 8, 6, 1, 5, 8, -18835866188161621404488568018012340884149895168000000⟩, + ⟨0, 8, 7, 1, 6, 8, -7600417313120064747058480311711685806382487961600000⟩, + ⟨0, 8, 8, 1, 7, 8, 2062124349656479812596750064392856859570077696000000⟩, + ⟨0, 8, 2, 2, 0, 8, -29578318260090271286637620250683132587342508851200000⟩, + ⟨0, 8, 3, 2, 1, 8, 8205029564351309474391033980098615456431498854400000⟩, + ⟨0, 8, 4, 2, 2, 8, -23222390245393813811451354289608646751577282969600000⟩, + ⟨0, 8, 5, 2, 3, 8, 81839540600806805833386751563946956983006920704000000⟩, + ⟨0, 8, 6, 2, 4, 8, 6760456790088804327309382534995964974027767808000000⟩, + ⟨0, 8, 7, 2, 5, 8, 770834798922221287142166893096513816802361344000000⟩, + ⟨0, 8, 8, 2, 6, 8, 112213632416614199127212544287818124655329280000000⟩, + ⟨0, 8, 3, 3, 0, 8, -84639548767034043032738331331965993102581170176000000⟩, + ⟨0, 8, 4, 3, 1, 8, 51559027350016274652766547552729497771402749542400000⟩, + ⟨0, 8, 5, 3, 2, 8, -222336277262475440363419946718221228991011880960000000⟩, + ⟨0, 8, 6, 3, 3, 8, 10262998620346817924576323891949005763027927040000000⟩, + ⟨0, 8, 7, 3, 4, 8, -3097134009920533828665350678329942092900886118400000⟩, + ⟨0, 8, 8, 3, 5, 8, 1785405119169368770159543943941748718909259776000000⟩, + ⟨0, 8, 4, 4, 0, 8, -86120545891703617804515911689718290701196512460800000⟩, + ⟨0, 8, 5, 4, 1, 8, 61626770120480779596966521755244213544922644480000000⟩, + ⟨0, 8, 6, 4, 2, 8, -31206646149205771505164031890625830218325032960000000⟩, + ⟨0, 8, 7, 4, 3, 8, 10984880655792647923663897784541392236637375692800000⟩, + ⟨0, 8, 8, 4, 4, 8, -2554368871543891671067249385432376985100746752000000⟩, + ⟨0, 8, 5, 5, 0, 8, 705504847181998864521161885580236561179660517376000000⟩, + ⟨0, 8, 6, 5, 1, 8, 48223396636737638020596900553599736272251781120000000⟩, + ⟨0, 8, 7, 5, 2, 8, -21337075819521683846608881602476407533279064883200000⟩, + ⟨0, 8, 8, 5, 3, 8, 3573138477027623393499962673696811670002728960000000⟩, + ⟨0, 8, 6, 6, 0, 8, -70734300511088209629773191628555749100781305856000000⟩, + ⟨0, 8, 7, 6, 1, 8, 58622924881775050129800510944364672122932848230400000⟩, + ⟨0, 8, 8, 6, 2, 8, -12742335505472079413466754202644217109752787763200000⟩, + ⟨0, 8, 7, 7, 0, 8, -198711915708511627287605934837563257151582896128000000⟩, + ⟨0, 8, 8, 7, 1, 8, 23825369906328694703282142640793362639865511936000000⟩ +] + +def collectedFourData_10_0_9 : List CollectedFourTerm := [ + +] + +def collectedFourData_10_0_10 : List CollectedFourTerm := [ + ⟨1, 1, 8, 0, 8, 2, 27981811730568543391180624264410516232456057651200000⟩, + ⟨1, 1, 8, 1, 7, 2, 23382015251355737095982736573466118645952282624000000⟩, + ⟨1, 1, 8, 2, 6, 2, 1272367917585757525726388663135698067726008320000000⟩, + ⟨1, 1, 8, 3, 5, 2, 20244351284257484867575977112358377099723014144000000⟩, + ⟨1, 1, 8, 4, 4, 2, -28963477358665183262743817889400144522628825088000000⟩, + ⟨1, 1, 8, 5, 3, 2, 40515102000994099445315102287051857441576714240000000⟩, + ⟨1, 1, 8, 6, 2, 2, -144482791824107325027745892586675137061868850380800000⟩, + ⟨1, 1, 8, 7, 1, 2, 270151100544335217009799667402102850397283549184000000⟩ +] + +def collectedFourData_10_0_11 : List CollectedFourTerm := [ + ⟨1, 2, 7, 0, 7, 3, -7773053006520858325229943878607814197352857600000⟩, + ⟨1, 2, 8, 0, 8, 3, 1048117323837294915583027709555447451958326067200000⟩, + ⟨1, 2, 7, 1, 6, 3, -538006281465134450459217191993399048300553830400000⟩, + ⟨1, 2, 8, 1, 7, 3, 875822319410475383833514080936982514650578944000000⟩, + ⟨1, 2, 7, 2, 5, 3, 54564630691551293634026068081800825783975936000000⟩, + ⟨1, 2, 8, 2, 6, 3, 47659203398168230896606208555183832479825920000000⟩, + ⟨1, 2, 7, 3, 4, 3, -219235008188322729877632564258206911949281689600000⟩, + ⟨1, 2, 8, 3, 5, 3, 758294548444055881996176532818050474588504064000000⟩, + ⟨1, 2, 7, 4, 3, 3, 777580302565674404225938048761894328811598643200000⟩, + ⟨1, 2, 8, 4, 4, 3, -1084887664547567497796685858027680323420028928000000⟩, + ⟨1, 2, 7, 5, 2, 3, -1510375068377400629230886162383073878517533900800000⟩, + ⟨1, 2, 8, 5, 3, 3, 1517577942885192832692634880249775489747517440000000⟩, + ⟨1, 2, 7, 6, 1, 3, 4149706591743229964906321552646151397806021017600000⟩, + ⟨1, 2, 8, 6, 2, 3, -5411905367864022160145668291136167136004459724800000⟩, + ⟨1, 2, 7, 7, 0, 3, -14066103800458612417791517456519178996240351232000000⟩, + ⟨1, 2, 8, 7, 1, 3, 10119074892670485430243329334080476261388386304000000⟩ +] + +def collectedFourData_10_0_12 : List CollectedFourTerm := [ + ⟨1, 3, 6, 0, 6, 4, 28523576974091326379835479701671278065150328832000000⟩, + ⟨1, 3, 7, 0, 7, 4, -522841474861980573788147107882840785539825664000000⟩, + ⟨1, 3, 8, 0, 8, 4, 35249933775298054303102747282954666324267106304000000⟩, + ⟨1, 3, 6, 1, 5, 4, -17936756055610044524714608931571990965231026176000000⟩, + ⟨1, 3, 7, 1, 6, 4, -36188097192990101061974130094807688427293638656000000⟩, + ⟨1, 3, 8, 1, 7, 4, 29455365402337090505693062314457438798038958080000000⟩, + ⟨1, 3, 6, 2, 4, 4, 6437753541938409415384449815486694015060934656000000⟩, + ⟨1, 3, 7, 2, 5, 4, 3670199079066760661773304891204675755353047040000000⟩, + ⟨1, 3, 8, 2, 6, 4, 1602858501964502739141965565899406672553574400000000⟩, + ⟨1, 3, 6, 3, 3, 4, 9773105245774204887767620293756070881688289280000000⟩, + ⟨1, 3, 7, 3, 4, 4, -14746477983155569646220698269441487084552454144000000⟩, + ⟨1, 3, 8, 3, 5, 4, 25502710437950868886330839422189336537837076480000000⟩, + ⟨1, 3, 6, 4, 2, 4, -29717029931113438794914168936067090094982430720000000⟩, + ⟨1, 3, 7, 4, 3, 4, 52302645032267780033311546702126592428760629248000000⟩, + ⟨1, 3, 8, 4, 4, 4, -36486581663329207046954467751530108998868008960000000⟩, + ⟨1, 3, 6, 5, 1, 4, 45921503848319172681602500462469587287240867840000000⟩, + ⟨1, 3, 7, 5, 2, 4, -101592865465182370273079008942712732275716390912000000⟩, + ⟨1, 3, 8, 5, 3, 4, 51038677416098460303865465530263627031694540800000000⟩, + ⟨1, 3, 6, 6, 0, 4, -67357873556619876605627245761314433536719060992000000⟩, + ⟨1, 3, 7, 6, 1, 4, 279123108108408730791247710596940886000810328064000000⟩, + ⟨1, 3, 8, 6, 2, 4, -182011404140287845207528669396954621813914075136000000⟩, + ⟨1, 3, 7, 7, 0, 4, -946133063858421054270345664228790982408646164480000000⟩, + ⟨1, 3, 8, 7, 1, 4, 340321366436347439652933759187411659839011553280000000⟩ +] + +def collectedFourData_10_0_13 : List CollectedFourTerm := [ + ⟨1, 4, 5, 0, 5, 5, 116492900353042042377065971862895856119479009280000000⟩, + ⟨1, 4, 6, 0, 6, 5, 134655171213185305284364323493606798254680309760000000⟩, + ⟨1, 4, 7, 0, 7, 5, -1234124815040613403339384941002894855645429760000000⟩, + ⟨1, 4, 8, 0, 8, 5, 55469736165718215515008457019080054774421258240000000⟩, + ⟨1, 4, 5, 1, 4, 5, 62340956813813538087929867023166625310939545600000000⟩, + ⟨1, 4, 6, 1, 5, 5, -84676510238220295349914433346630645412716871680000000⟩, + ⟨1, 4, 7, 1, 6, 5, -85419062760390498070313273034767814823551959040000000⟩, + ⟨1, 4, 8, 1, 7, 5, 46351330982568564315631204768004600417275084800000000⟩, + ⟨1, 4, 5, 2, 3, 5, 91977276600251470327334197620131305252202741760000000⟩, + ⟨1, 4, 6, 2, 4, 5, 30391588201066520688485743125248618436577198080000000⟩, + ⟨1, 4, 7, 2, 5, 5, 8663206683844632764746063922583604364417433600000000⟩, + ⟨1, 4, 8, 2, 6, 5, 2522278163179258997627467064331629928382464000000000⟩, + ⟨1, 4, 5, 3, 2, 5, -249877811164537530160000440465115449626355302400000000⟩, + ⟨1, 4, 6, 3, 3, 5, 46137241530035301830635252571762981014496870400000000⟩, + ⟨1, 4, 7, 3, 4, 5, -34807862972742371746973007175042200251620392960000000⟩, + ⟨1, 4, 8, 3, 5, 5, 40131383750149511055425628075453863668010188800000000⟩, + ⟨1, 4, 5, 4, 1, 5, 69260683035844086482212036132062183682159411200000000⟩, + ⟨1, 4, 6, 4, 2, 5, -140289268662066517586951587850460317781432729600000000⟩, + ⟨1, 4, 7, 4, 3, 5, 123456143458438674102786848654794407887052472320000000⟩, + ⟨1, 4, 8, 4, 4, 5, -57415740731748089387226657437983526687971737600000000⟩, + ⟨1, 4, 5, 5, 0, 5, 792898078309070308282554684256365634288814653440000000⟩, + ⟨1, 4, 6, 5, 1, 5, 216787956457181176318534376548490070795170611200000000⟩, + ⟨1, 4, 7, 5, 2, 5, -239801703441299118800128600349045635737012142080000000⟩, + ⟨1, 4, 8, 5, 3, 5, 80315100407426056942239864247011620262248448000000000⟩, + ⟨1, 4, 6, 6, 0, 5, -317985573988890697551786766421273375981237698560000000⟩, + ⟨1, 4, 7, 6, 1, 5, 658847415000473721757844169969013171162982645760000000⟩, + ⟨1, 4, 8, 6, 2, 5, -286415419420977663579925509712406266203246428160000000⟩, + ⟨1, 4, 7, 7, 0, 5, -2233270213971294888258521305706963377337873203200000000⟩, + ⟨1, 4, 8, 7, 1, 5, 535533953854110031725332292424888507156974796800000000⟩ +] + +def collectedFourData_10_0_14 : List CollectedFourTerm := [ + ⟨1, 5, 4, 0, 4, 6, 30083047848464350232685753945910838380995595468800000⟩, + ⟨1, 5, 5, 0, 5, 6, -158230042873493793347491498548986141800277213184000000⟩, + ⟨1, 5, 6, 0, 6, 6, -91449751227880601345909629244442863212758564864000000⟩, + ⟨1, 5, 7, 0, 7, 6, 558762584968179188222589883883049870296088576000000⟩, + ⟨1, 5, 8, 0, 8, 6, -18835866188161621404488568018012340884149895168000000⟩, + ⟨1, 5, 4, 1, 3, 6, -17936756055610044524714608931571990965231026176000000⟩, + ⟨1, 5, 5, 1, 4, 6, -84676510238220295349914433346630645412716871680000000⟩, + ⟨1, 5, 6, 1, 5, 6, 57507229216400716978767528759491340757685501952000000⟩, + ⟨1, 5, 7, 1, 6, 6, 38674351031491275358217049687972587473735778304000000⟩, + ⟨1, 5, 8, 1, 7, 6, -15739528045032067658059062257578177132348047360000000⟩, + ⟨1, 5, 4, 2, 2, 6, 11816599472640715037519781207973101506870535782400000⟩, + ⟨1, 5, 5, 2, 3, 6, -124930947514733608083216915895077636335707619328000000⟩, + ⟨1, 5, 6, 2, 4, 6, -20640151843909117864885113531218926194143526912000000⟩, + ⟨1, 5, 7, 2, 5, 6, -3922355098758251841053552013677964398281359360000000⟩, + ⟨1, 5, 8, 2, 6, 6, -856490354110042135167471944456050473487564800000000⟩, + ⟨1, 5, 4, 3, 1, 6, -26235558396703646005264038552890449694687861145600000⟩, + ⟨1, 5, 5, 3, 2, 6, 339404175309187222678927060006829975560488222720000000⟩, + ⟨1, 5, 6, 3, 3, 6, -31333659318456429649077177624954681388758466560000000⟩, + ⟨1, 5, 7, 3, 4, 6, 15759614631221596605566196713080946471674576896000000⟩, + ⟨1, 5, 8, 3, 5, 6, -13627419679900193402979686620958242623360860160000000⟩, + ⟨1, 5, 4, 4, 0, 6, 43822017734341013452041821389735190044286858035200000⟩, + ⟨1, 5, 5, 4, 1, 6, -94075439902315837477779644591295356130935439360000000⟩, + ⟨1, 5, 6, 4, 2, 6, 95276093769735927536348091424588632398694973440000000⟩, + ⟨1, 5, 7, 4, 3, 6, -55896026891550212461025817045065576954757906432000000⟩, + ⟨1, 5, 8, 4, 4, 6, 19496671235039486435012799193211806551449272320000000⟩, + ⟨1, 5, 5, 5, 0, 6, -1076978052267018014428391960824762086636474335232000000⟩, + ⟨1, 5, 6, 5, 1, 6, -147229434329133032061055345372195290500227399680000000⟩, + ⟨1, 5, 7, 5, 2, 6, 108572664662142379082069329767418447921579819008000000⟩, + ⟨1, 5, 8, 5, 3, 6, -27272610052506358765795319737706128000784793600000000⟩, + ⟨1, 5, 6, 6, 0, 6, 215956813045820986405550826350598398738310365184000000⟩, + ⟨1, 5, 7, 6, 1, 6, -298299880383778232393053210351049965160078770176000000⟩, + ⟨1, 5, 8, 6, 2, 6, 97258124652374038916548668690368411959465869312000000⟩, + ⟨1, 5, 7, 7, 0, 6, 1011135844999578675946049119779193174431702712320000000⟩, + ⟨1, 5, 8, 7, 1, 6, -181851340772147491370934750117206657517496565760000000⟩ +] + +def collectedFourData_10_0_15 : List CollectedFourTerm := [ + ⟨1, 6, 3, 0, 3, 7, 4994815477363109997725360107485417067348230144000000⟩, + ⟨1, 6, 4, 0, 4, 7, 60693709387941708654352856660543805668335602892800000⟩, + ⟨1, 6, 5, 0, 5, 7, -159617607347847614827023474903451960542077386752000000⟩, + ⟨1, 6, 6, 0, 6, 7, -61501133490899296807761636775927244613671190528000000⟩, + ⟨1, 6, 7, 0, 7, 7, 281831266896091201179936275607456185805963264000000⟩, + ⟨1, 6, 8, 0, 8, 7, -7600417313120064747058480311711685806382487961600000⟩, + ⟨1, 6, 3, 1, 2, 7, -538006281465134450459217191993399048300553830400000⟩, + ⟨1, 6, 4, 1, 3, 7, -36188097192990101061974130094807688427293638656000000⟩, + ⟨1, 6, 5, 1, 4, 7, -85419062760390498070313273034767814823551959040000000⟩, + ⟨1, 6, 6, 1, 5, 7, 38674351031491275358217049687972587473735778304000000⟩, + ⟨1, 6, 7, 1, 6, 7, 19506748735171769335120340570185237826220589056000000⟩, + ⟨1, 6, 8, 1, 7, 7, -6351020986175104812776030446829999004196012032000000⟩, + ⟨1, 6, 3, 2, 1, 7, -4211701633808130219476472894797105323144170700800000⟩, + ⟨1, 6, 4, 2, 2, 7, 23840445222134345144072634299752326694493906534400000⟩, + ⟨1, 6, 5, 2, 3, 7, -126026502703689732742630787528682947558856720384000000⟩, + ⟨1, 6, 6, 2, 4, 7, -13880767490132677136618982262998388828457140224000000⟩, + ⟨1, 6, 7, 2, 5, 7, -1978375675891639301903217412859215704269783040000000⟩, + ⟨1, 6, 8, 2, 6, 7, -345600465137602665604748276458958169581813760000000⟩, + ⟨1, 6, 3, 3, 0, 7, 43446098887406417950183210289574087036116140032000000⟩, + ⟨1, 6, 4, 3, 1, 7, -52931251014886407698395389496876008102128359833600000⟩, + ⟨1, 6, 5, 3, 2, 7, 342380507537592855757244793574871517020458844160000000⟩, + ⟨1, 6, 6, 3, 3, 7, -21072288755611633398912580469648212739877765120000000⟩, + ⟨1, 6, 7, 3, 4, 7, 7948907598321563344178634278163912137317023744000000⟩, + ⟨1, 6, 8, 3, 5, 7, -5498768967331219925181810008137354808647483392000000⟩, + ⟨1, 6, 4, 4, 0, 7, 88412611067834073181480565813921858337627124531200000⟩, + ⟨1, 6, 5, 4, 1, 7, -94900414325295838706636832652306611353765806080000000⟩, + ⟨1, 6, 6, 4, 2, 7, 64074398046449090175686064253057394298197114880000000⟩, + ⟨1, 6, 7, 4, 3, 7, -28193097564327264700287240413521490257744232448000000⟩, + ⟨1, 6, 8, 4, 4, 7, 7867057247207312927537117184387642626024669184000000⟩, + ⟨1, 6, 5, 5, 0, 7, -1086422380650214203566469912169971014726420791296000000⟩, + ⟨1, 6, 6, 5, 1, 7, -99013687548501947271868757264271006061937295360000000⟩, + ⟨1, 6, 7, 5, 2, 7, 54762384696460379495998809003114962932268531712000000⟩, + ⟨1, 6, 8, 5, 3, 7, -11004708546258390460300990067257403150507704320000000⟩, + ⟨1, 6, 6, 6, 0, 7, 145233733378938000017669167894231177525532295168000000⟩, + ⟨1, 6, 7, 6, 1, 7, -150457878650375946450440248312259384659792625664000000⟩, + ⟨1, 6, 8, 6, 2, 7, 39244403579065725758492891721712966308498663014400000⟩, + ⟨1, 6, 7, 7, 0, 7, 510001392123471581253457063077898396820286996480000000⟩, + ⟨1, 6, 8, 7, 1, 7, -73378418863869824053418514419628913156908122112000000⟩ +] + +def collectedFourData_10_0_16 : List CollectedFourTerm := [ + ⟨1, 7, 2, 0, 2, 8, -4434694610774247672868520275806132377562906624000000⟩, + ⟨1, 7, 3, 0, 3, 8, -8131077697640216670583869829869495201394851840000000⟩, + ⟨1, 7, 4, 0, 4, 8, -49401751579007623540108694273610904328107720704000000⟩, + ⟨1, 7, 5, 0, 5, 8, 86614021621605653256944328342251864957638410240000000⟩, + ⟨1, 7, 6, 0, 6, 8, 25029477924349919932915122328325340700103147520000000⟩, + ⟨1, 7, 7, 0, 7, 8, -91758822288517623610640648695782426707755008000000⟩, + ⟨1, 7, 8, 0, 8, 8, 2062124349656479812596750064392856859570077696000000⟩, + ⟨1, 7, 2, 1, 1, 8, 23382015251355737095982736573466118645952282624000000⟩, + ⟨1, 7, 3, 1, 2, 8, 875822319410475383833514080936982514650578944000000⟩, + ⟨1, 7, 4, 1, 3, 8, 29455365402337090505693062314457438798038958080000000⟩, + ⟨1, 7, 5, 1, 4, 8, 46351330982568564315631204768004600417275084800000000⟩, + ⟨1, 7, 6, 1, 5, 8, -15739528045032067658059062257578177132348047360000000⟩, + ⟨1, 7, 7, 1, 6, 8, -6351020986175104812776030446829999004196012032000000⟩, + ⟨1, 7, 8, 1, 7, 8, 1723141569892914184266141340264068030576721920000000⟩, + ⟨1, 7, 2, 2, 0, 8, -24716079692272036065830930680056831285210906624000000⟩, + ⟨1, 7, 3, 2, 1, 8, 6856243915110816352971300611619374269923852288000000⟩, + ⟨1, 7, 4, 2, 2, 8, -19404972348432718295733456750921948205984776192000000⟩, + ⟨1, 7, 5, 2, 3, 8, 68386329123983824400500782519183499130390446080000000⟩, + ⟨1, 7, 6, 2, 4, 8, 5649137564573846622164985700424203630710620160000000⟩, + ⟨1, 7, 7, 2, 5, 8, 644120945356274839213304152555873876448378880000000⟩, + ⟨1, 7, 8, 2, 6, 8, 93767368955204850260541662592939385788825600000000⟩, + ⟨1, 7, 3, 3, 0, 8, -70726057311602347595474236058119207258706411520000000⟩, + ⟨1, 7, 4, 3, 1, 8, 43083484924106923689452983572904549347175170048000000⟩, + ⟨1, 7, 5, 3, 2, 8, -185787477806578405404929249675468866227221299200000000⟩, + ⟨1, 7, 6, 3, 3, 8, 8575913260235362399087790786623504384838860800000000⟩, + ⟨1, 7, 7, 3, 4, 8, -2588010931984891752639561162425755882192109568000000⟩, + ⟨1, 7, 8, 3, 5, 8, 1491910892984146734151551414491091377345003520000000⟩, + ⟨1, 7, 4, 4, 0, 8, -71963600387428567312828278391106045905119215616000000⟩, + ⟨1, 7, 5, 4, 1, 8, 51496239511707906755366490008428457921976729600000000⟩, + ⟨1, 7, 6, 4, 2, 8, -26076734531354999487950327615014213201900339200000000⟩, + ⟨1, 7, 7, 4, 3, 8, 9179128553262107589530151597619980000093536256000000⟩, + ⟨1, 7, 8, 4, 4, 8, -2134468364204596156471437440490281089672151040000000⟩, + ⟨1, 7, 5, 5, 0, 8, 589530272576804394361576404587312682758590955520000000⟩, + ⟨1, 7, 6, 5, 1, 8, 40296182623535444745159548236187746961876582400000000⟩, + ⟨1, 7, 7, 5, 2, 8, -17829575762829022406116326513573477896121483264000000⟩, + ⟨1, 7, 8, 5, 3, 8, 2985767296611296404300798112054294210622259200000000⟩, + ⟨1, 7, 6, 6, 0, 8, -59106626449689136871941704888519490180082565120000000⟩, + ⟨1, 7, 7, 6, 1, 8, 48986182055085079120255818075070228903187447808000000⟩, + ⟨1, 7, 8, 6, 2, 8, -10647683788157136813813424959298252279186980864000000⟩, + ⟨1, 7, 7, 7, 0, 8, -166046612294468819783349687747983526848951746560000000⟩, + ⟨1, 7, 8, 7, 1, 8, 19908831060798882537063982008391579680343326720000000⟩ +] + +def collectedFourData_10_0_17 : List CollectedFourTerm := [ + ⟨2, 0, 8, 0, 8, 2, -29578318260090271286637620250683132587342508851200000⟩, + ⟨2, 0, 8, 1, 7, 2, -24716079692272036065830930680056831285210906624000000⟩, + ⟨2, 0, 8, 2, 6, 2, -1344963062887249844538052762290388713414328320000000⟩, + ⟨2, 0, 8, 3, 5, 2, -21399395829709151351066957494366666986193158144000000⟩, + ⟨2, 0, 8, 4, 4, 2, 30615992970091754999659202418367927401565913088000000⟩, + ⟨2, 0, 8, 5, 3, 2, -42826697315537789319428807733332507200050954240000000⟩, + ⟨2, 0, 8, 6, 2, 2, 152726279514317335831257094454548223896658431180800000⟩, + ⟨2, 0, 8, 7, 1, 2, -285564612726083741074268783644334054525248733184000000⟩ +] + +def collectedFourData_10_0_18 : List CollectedFourTerm := [ + ⟨2, 1, 7, 0, 7, 3, -60850181819601436601240711923365347731911475200000⟩, + ⟨2, 1, 8, 0, 8, 3, 8205029564351309474391033980098615456431498854400000⟩, + ⟨2, 1, 7, 1, 6, 3, -4211701633808130219476472894797105323144170700800000⟩, + ⟨2, 1, 8, 1, 7, 3, 6856243915110816352971300611619374269923852288000000⟩, + ⟨2, 1, 7, 2, 5, 3, 427151042931896856536693103967434464896745472000000⟩, + ⟨2, 1, 8, 2, 6, 3, 373092939122249300597573088402944101806243840000000⟩, + ⟨2, 1, 7, 3, 4, 3, -1716248441672768077724073431465299451523052339200000⟩, + ⟨2, 1, 8, 3, 5, 3, 5936195354248103180214935432739442589096214528000000⟩, + ⟨2, 1, 7, 4, 3, 3, 6087170993272322379802582817302518816284501606400000⟩, + ⟨2, 1, 8, 4, 4, 3, -8492880672006402391641900491423302838340550656000000⟩, + ⟨2, 1, 7, 5, 2, 3, -11823745116552892881131418525043359631971817881600000⟩, + ⟨2, 1, 8, 5, 3, 3, 11880131741352085501267644045828820967494778880000000⟩, + ⟨2, 1, 7, 6, 1, 3, 32485356833890328986207051421868731442088063795200000⟩, + ⟨2, 1, 8, 6, 2, 3, -42366290999011349171834536702384017208099051929600000⟩, + ⟨2, 1, 7, 7, 0, 3, -110114387877356941725709279837822597523690225664000000⟩, + ⟨2, 1, 8, 7, 1, 3, 79215662951044951790951932505833458588092203008000000⟩ +] + +def collectedFourData_10_0_19 : List CollectedFourTerm := [ + ⟨2, 2, 6, 0, 6, 4, -18791117166610258140690067417285170214319475916800000⟩, + ⟨2, 2, 7, 0, 7, 4, 344444016352467872710656404772729579806235033600000⟩, + ⟨2, 2, 8, 0, 8, 4, -23222390245393813811451354289608646751577282969600000⟩, + ⟨2, 2, 6, 1, 5, 4, 11816599472640715037519781207973101506870535782400000⟩, + ⟨2, 2, 7, 1, 6, 4, 23840445222134345144072634299752326694493906534400000⟩, + ⟨2, 2, 8, 1, 7, 4, -19404972348432718295733456750921948205984776192000000⟩, + ⟨2, 2, 6, 2, 4, 4, -4241143430440271867110948952613095005963576934400000⟩, + ⟨2, 2, 7, 2, 5, 4, -2417899444455130362863698107789189021010231296000000⟩, + ⟨2, 2, 8, 2, 6, 4, -1055951080023051158153137434009406171313602560000000⟩, + ⟨2, 2, 6, 3, 3, 4, -6438447952084273093572865333325590199713923072000000⟩, + ⟨2, 2, 7, 3, 4, 4, 9714868364091018302908841262764354356029004185600000⟩, + ⟨2, 2, 8, 3, 5, 4, -16800993099181096170031101847611886698183524352000000⟩, + ⟨2, 2, 6, 4, 2, 4, 19577354964506727076569208384123361083867004928000000⟩, + ⟨2, 2, 7, 4, 3, 4, -34456587678946939384273416673841202866878100275200000⟩, + ⟨2, 2, 8, 4, 4, 4, 24037084537731067418492822469613293242998063104000000⟩, + ⟨2, 2, 6, 5, 1, 4, -30252740042545077900234201345294561173324169216000000⟩, + ⟨2, 2, 7, 5, 2, 4, 66928612774686234856690687815786946225765141708800000⟩, + ⟨2, 2, 8, 5, 3, 4, -33623895355967507201557924622620025685981265920000000⟩, + ⟨2, 2, 6, 6, 0, 4, 44374858568609983751104585006888452061754346700800000⟩, + ⟨2, 2, 7, 6, 1, 4, -183884196331256976141048119312338736224323344793600000⟩, + ⟨2, 2, 8, 6, 2, 4, 119907738919492839678993346702053695641623094886400000⟩, + ⟨2, 2, 7, 7, 0, 4, 623305319466648574921887379396415873254321815552000000⟩, + ⟨2, 2, 8, 7, 1, 4, -224201146890344883601711324840962382820039196672000000⟩ +] + +def collectedFourData_10_0_20 : List CollectedFourTerm := [ + ⟨2, 3, 5, 0, 5, 5, 171872558031754686900901530461199048171520524288000000⟩, + ⟨2, 3, 6, 0, 6, 5, 198669006080847355374383440139235803402229252096000000⟩, + ⟨2, 3, 7, 0, 7, 5, -1820816446742003928717752629012211623155204096000000⟩, + ⟨2, 3, 8, 0, 8, 5, 81839540600806805833386751563946956983006920704000000⟩, + ⟨2, 3, 5, 1, 4, 5, 91977276600251470327334197620131305252202741760000000⟩, + ⟨2, 3, 6, 1, 5, 5, -124930947514733608083216915895077636335707619328000000⟩, + ⟨2, 3, 7, 1, 6, 5, -126026502703689732742630787528682947558856720384000000⟩, + ⟨2, 3, 8, 1, 7, 5, 68386329123983824400500782519183499130390446080000000⟩, + ⟨2, 3, 5, 2, 3, 5, 135702431325607052087575967062419998628743479296000000⟩, + ⟨2, 3, 6, 2, 4, 5, 44839470825559139203107686647386220520452128768000000⟩, + ⟨2, 3, 7, 2, 5, 5, 12781615780856378229903533329643902478120386560000000⟩, + ⟨2, 3, 8, 2, 6, 5, 3721346096281088234497468131750827717453414400000000⟩, + ⟨2, 3, 5, 3, 2, 5, -368667433552342779288553708295859907960284119040000000⟩, + ⟨2, 3, 6, 3, 3, 5, 68070463506911917834968359828915314505904291840000000⟩, + ⟨2, 3, 7, 3, 4, 5, -51355202167801497237345199983237472758389538816000000⟩, + ⟨2, 3, 8, 3, 5, 5, 59209475955948856572952023048924919379766804480000000⟩, + ⟨2, 3, 5, 4, 1, 5, 102186577279138232382127739749180536281125355520000000⟩, + ⟨2, 3, 6, 4, 2, 5, -206981501845007546383580657847361895552683868160000000⟩, + ⟨2, 3, 7, 4, 3, 5, 182146063121717414969124644509163802487079043072000000⟩, + ⟨2, 3, 8, 4, 4, 5, -84710657910886681718378570284268784748289064960000000⟩, + ⟨2, 3, 5, 5, 0, 5, 1169834561286067013077108055358966182425997082624000000⟩, + ⟨2, 3, 6, 5, 1, 5, 319846965041242463173578204583082574785040875520000000⟩, + ⟨2, 3, 7, 5, 2, 5, -353801236521037756511227167021098161233532551168000000⟩, + ⟨2, 3, 8, 5, 3, 5, 118496163403670197303787950457229370521865420800000000⟩, + ⟨2, 3, 6, 6, 0, 5, -469153002912930365506705502546261794501297176576000000⟩, + ⟨2, 3, 7, 6, 1, 5, 972057440629972633536294683645898892010581917696000000⟩, + ⟨2, 3, 8, 6, 2, 5, -422574686066144045190821041979964696175350644736000000⟩, + ⟨2, 3, 7, 7, 0, 5, -3294946415516447572085206481783708622797899038720000000⟩, + ⟨2, 3, 8, 7, 1, 5, 790121889684429843660130369932776530808961761280000000⟩ +] + +def collectedFourData_10_0_21 : List CollectedFourTerm := [ + ⟨2, 4, 4, 0, 4, 6, -10797228174276311611318570218432419743067327692800000⟩, + ⟨2, 4, 5, 0, 5, 6, 56790983597689120525678017731000227689350037504000000⟩, + ⟨2, 4, 6, 0, 6, 6, 32822599474030227576210136790771128737762115584000000⟩, + ⟨2, 4, 7, 0, 7, 6, -200547735573204458344897189130727843541549056000000⟩, + ⟨2, 4, 8, 0, 8, 6, 6760456790088804327309382534995964974027767808000000⟩, + ⟨2, 4, 4, 1, 3, 6, 6437753541938409415384449815486694015060934656000000⟩, + ⟨2, 4, 5, 1, 4, 6, 30391588201066520688485743125248618436577198080000000⟩, + ⟨2, 4, 6, 1, 5, 6, -20640151843909117864885113531218926194143526912000000⟩, + ⟨2, 4, 7, 1, 6, 6, -13880767490132677136618982262998388828457140224000000⟩, + ⟨2, 4, 8, 1, 7, 6, 5649137564573846622164985700424203630710620160000000⟩, + ⟨2, 4, 4, 2, 2, 6, -4241143430440271867110948952613095005963576934400000⟩, + ⟨2, 4, 5, 2, 3, 6, 44839470825559139203107686647386220520452128768000000⟩, + ⟨2, 4, 6, 2, 4, 6, 7408040240236922888491471842047095535327772672000000⟩, + ⟨2, 4, 7, 2, 5, 6, 1407788306396315200351532924830972557561692160000000⟩, + ⟨2, 4, 8, 2, 6, 6, 307406411377459895642954492373636123249868800000000⟩, + ⟨2, 4, 4, 3, 1, 6, 9416310199540510299652972327792972497486977433600000⟩, + ⟨2, 4, 5, 3, 2, 6, -121816923025053157498335572375115102907866808320000000⟩, + ⟨2, 4, 6, 3, 3, 6, 11246090186758896175865577696720661610087055360000000⟩, + ⟨2, 4, 7, 3, 4, 6, -5656346922329852134796878559394564398672510976000000⟩, + ⟨2, 4, 8, 3, 5, 6, 4891072222857127088920165520751041283316776960000000⟩, + ⟨2, 4, 4, 4, 0, 6, -15728337331984005991055420448013529654169383731200000⟩, + ⟨2, 4, 5, 4, 1, 6, 33764995998321816082029368865433671591694172160000000⟩, + ⟨2, 4, 6, 4, 2, 6, -34195927525943734603122843577692825370377584640000000⟩, + ⟨2, 4, 7, 4, 3, 6, 20061868711695724068583319813132458692855201792000000⟩, + ⟨2, 4, 8, 4, 4, 6, -6997628997698675100334974393680606844074065920000000⟩, + ⟨2, 4, 5, 5, 0, 6, 386542541420325765998393937601673078482604654592000000⟩, + ⟨2, 4, 6, 5, 1, 6, 52842710766170824060601315015974696549173166080000000⟩, + ⟨2, 4, 7, 5, 2, 6, -38968253474562065157341042830334498515974094848000000⟩, + ⟨2, 4, 8, 5, 3, 6, 9788522596788834262243051765570607672564121600000000⟩, + ⟨2, 4, 6, 6, 0, 6, -77509931772564347766294561898555488393184149504000000⟩, + ⟨2, 4, 7, 6, 1, 6, 107064014560193468329515097175255599203961798656000000⟩, + ⟨2, 4, 8, 6, 2, 6, -34907306233184609810305794034566957235880067072000000⟩, + ⟨2, 4, 7, 7, 0, 6, -362910848948685910273947203148257875661338705920000000⟩, + ⟨2, 4, 8, 7, 1, 6, 65268999005869804792371487387610603604997570560000000⟩ +] + +def collectedFourData_10_0_22 : List CollectedFourTerm := [ + ⟨2, 5, 3, 0, 3, 7, -506574497889806841894974268430666446101544960000000⟩, + ⟨2, 5, 4, 0, 4, 7, -6155559799477910021597453823963560747049418752000000⟩, + ⟨2, 5, 5, 0, 5, 7, 16188427713308711017376548800599692628648263680000000⟩, + ⟨2, 5, 6, 0, 6, 7, 6237448802463822168954411956308722578903531520000000⟩, + ⟨2, 5, 7, 0, 7, 7, -28583344703037293567235314435772376688885760000000⟩, + ⟨2, 5, 8, 0, 8, 7, 770834798922221287142166893096513816802361344000000⟩, + ⟨2, 5, 3, 1, 2, 7, 54564630691551293634026068081800825783975936000000⟩, + ⟨2, 5, 4, 1, 3, 7, 3670199079066760661773304891204675755353047040000000⟩, + ⟨2, 5, 5, 1, 4, 7, 8663206683844632764746063922583604364417433600000000⟩, + ⟨2, 5, 6, 1, 5, 7, -3922355098758251841053552013677964398281359360000000⟩, + ⟨2, 5, 7, 1, 6, 7, -1978375675891639301903217412859215704269783040000000⟩, + ⟨2, 5, 8, 1, 7, 7, 644120945356274839213304152555873876448378880000000⟩, + ⟨2, 5, 3, 2, 1, 7, 427151042931896856536693103967434464896745472000000⟩, + ⟨2, 5, 4, 2, 2, 7, -2417899444455130362863698107789189021010231296000000⟩, + ⟨2, 5, 5, 2, 3, 7, 12781615780856378229903533329643902478120386560000000⟩, + ⟨2, 5, 6, 2, 4, 7, 1407788306396315200351532924830972557561692160000000⟩, + ⟨2, 5, 7, 2, 5, 7, 200646984697280237877544011798610940893593600000000⟩, + ⟨2, 5, 8, 2, 6, 7, 35050820774262100154154428360100663420518400000000⟩, + ⟨2, 5, 3, 3, 0, 7, -4406306064539094096803540418982050794443898880000000⟩, + ⟨2, 5, 4, 3, 1, 7, 5368290786129501444226673943845023100461645824000000⟩, + ⟨2, 5, 5, 3, 2, 7, -34724252473221966113059136977801396066084454400000000⟩, + ⟨2, 5, 6, 3, 3, 7, 2137152842610799065903741575300039689686220800000000⟩, + ⟨2, 5, 7, 3, 4, 7, -806178705427977277410485988282556415433768960000000⟩, + ⟨2, 5, 8, 3, 5, 7, 557685492339432669951182071684862475270881280000000⟩, + ⟨2, 5, 4, 4, 0, 7, -8966812540282133320982783665976546634296721408000000⟩, + ⟨2, 5, 5, 4, 1, 7, 9624805952141184287223816441894261014868787200000000⟩, + ⟨2, 5, 6, 4, 2, 7, -6498429454516548411712280422319984569692979200000000⟩, + ⟨2, 5, 7, 4, 3, 7, 2859345717040822597153590078414552322875064320000000⟩, + ⟨2, 5, 8, 4, 4, 7, -797877437702328415873932985578854313162178560000000⟩, + ⟨2, 5, 5, 5, 0, 7, 110185025746872365622729336722080137652878704640000000⟩, + ⟨2, 5, 6, 5, 1, 7, 10041974379518054891013698029273878188418662400000000⟩, + ⟨2, 5, 7, 5, 2, 7, -5554004478560468841806837749287905136822190080000000⟩, + ⟨2, 5, 8, 5, 3, 7, 1116098228555089405907490207387570550918348800000000⟩, + ⟨2, 5, 6, 6, 0, 7, -14729614316390716823020330564873774867540869120000000⟩, + ⟨2, 5, 7, 6, 1, 7, 15259447456328690687081659235446606119315701760000000⟩, + ⟨2, 5, 8, 6, 2, 7, -3980169863761499491447938773268090638875754496000000⟩, + ⟨2, 5, 7, 7, 0, 7, -51724373064216095618740734039247527013987123200000000⟩, + ⟨2, 5, 8, 7, 1, 7, 7442043827320051012293959270617887161796526080000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1002.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1002.lean new file mode 100644 index 0000000000000000000000000000000000000000..de96ce316c1753c58e282ba19060c2aefda750a1 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1002.lean @@ -0,0 +1,623 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1002. -/ +namespace LaughlinFock +def collectedFourData_10_0_23 : List CollectedFourTerm := [ + ⟨2, 6, 2, 0, 2, 8, -241320651209157159901267471087321464774328320000000⟩, + ⟨2, 6, 3, 0, 3, 8, -442464958073903065173349047047192367543091200000000⟩, + ⟨2, 6, 4, 0, 4, 8, -2688271438794235212410669165122511079965982720000000⟩, + ⟨2, 6, 5, 0, 5, 8, 4713233702899935301991929873921887450641203200000000⟩, + ⟨2, 6, 6, 0, 6, 8, 1362017104279207034976001952630388255463833600000000⟩, + ⟨2, 6, 7, 0, 7, 8, -4993195855031926798113619690670066698813440000000⟩, + ⟨2, 6, 8, 0, 8, 8, 112213632416614199127212544287818124655329280000000⟩, + ⟨2, 6, 2, 1, 1, 8, 1272367917585757525726388663135698067726008320000000⟩, + ⟨2, 6, 3, 1, 2, 8, 47659203398168230896606208555183832479825920000000⟩, + ⟨2, 6, 4, 1, 3, 8, 1602858501964502739141965565899406672553574400000000⟩, + ⟨2, 6, 5, 1, 4, 8, 2522278163179258997627467064331629928382464000000000⟩, + ⟨2, 6, 6, 1, 5, 8, -856490354110042135167471944456050473487564800000000⟩, + ⟨2, 6, 7, 1, 6, 8, -345600465137602665604748276458958169581813760000000⟩, + ⟨2, 6, 8, 1, 7, 8, 93767368955204850260541662592939385788825600000000⟩, + ⟨2, 6, 2, 2, 0, 8, -1344963062887249844538052762290388713414328320000000⟩, + ⟨2, 6, 3, 2, 1, 8, 373092939122249300597573088402944101806243840000000⟩, + ⟨2, 6, 4, 2, 2, 8, -1055951080023051158153137434009406171313602560000000⟩, + ⟨2, 6, 5, 2, 3, 8, 3721346096281088234497468131750827717453414400000000⟩, + ⟨2, 6, 6, 2, 4, 8, 307406411377459895642954492373636123249868800000000⟩, + ⟨2, 6, 7, 2, 5, 8, 35050820774262100154154428360100663420518400000000⟩, + ⟨2, 6, 8, 2, 6, 8, 5102493976352691126638739218721310507008000000000⟩, + ⟨2, 6, 3, 3, 0, 8, -3848665963700311933572783138894984232147353600000000⟩, + ⟨2, 6, 4, 3, 1, 8, 2344453350403355105668209897758922472308080640000000⟩, + ⟨2, 6, 5, 3, 2, 8, -10109908137048192644336126202396873804742656000000000⟩, + ⟨2, 6, 6, 3, 3, 8, 466671361686374276099065227102955864326144000000000⟩, + ⟨2, 6, 7, 3, 4, 8, -140830550524419107683849748547161152542474240000000⟩, + ⟨2, 6, 8, 3, 5, 8, 81184600032269748585812494456489554581913600000000⟩, + ⟨2, 6, 4, 4, 0, 8, -3916008752137693578399073594983807124903034880000000⟩, + ⟨2, 6, 5, 4, 1, 8, 2802246184798382045642543346390472461385728000000000⟩, + ⟨2, 6, 6, 4, 2, 8, -1419005165141741896792067141538534817529856000000000⟩, + ⟨2, 6, 7, 4, 3, 8, 499496239182757758129496444229320991393710080000000⟩, + ⟨2, 6, 8, 4, 4, 8, -116150341983812150402860171561589546365747200000000⟩, + ⟨2, 6, 5, 5, 0, 8, 32080186297407377020945432838794452825381273600000000⟩, + ⟨2, 6, 6, 5, 1, 8, 2192778056989349995429955949078431957778432000000000⟩, + ⟨2, 6, 7, 5, 2, 8, -970223479067865610413402658410883605615083520000000⟩, + ⟨2, 6, 8, 5, 3, 8, 162475067984770840136558665724246366355456000000000⟩, + ⟨2, 6, 6, 6, 0, 8, -3216376963356469544625650659061511415765401600000000⟩, + ⟨2, 6, 7, 6, 1, 8, 2665657591181815489228883866241953609222717440000000⟩, + ⟨2, 6, 8, 6, 2, 8, -579409905562507014624959026979737454531051520000000⟩, + ⟨2, 6, 7, 7, 0, 8, -9035678919721555246320793739633831560662220800000000⟩, + ⟨2, 6, 8, 7, 1, 8, 1083369318088463661347922091170549275924889600000000⟩ +] + +def collectedFourData_10_0_24 : List CollectedFourTerm := [ + ⟨3, 0, 7, 0, 7, 3, 627704250327126019870408039637328061695787008000000⟩, + ⟨3, 0, 8, 0, 8, 3, -84639548767034043032738331331965993102581170176000000⟩, + ⟨3, 0, 7, 1, 6, 3, 43446098887406417950183210289574087036116140032000000⟩, + ⟨3, 0, 8, 1, 7, 3, -70726057311602347595474236058119207258706411520000000⟩, + ⟨3, 0, 7, 2, 5, 3, -4406306064539094096803540418982050794443898880000000⟩, + ⟨3, 0, 8, 2, 6, 3, -3848665963700311933572783138894984232147353600000000⟩, + ⟨3, 0, 7, 3, 4, 3, 17704079252369263528416883099672985716358381568000000⟩, + ⟨3, 0, 8, 3, 5, 3, -61235232881972677113178678794242059819674501120000000⟩, + ⟨3, 0, 7, 4, 3, 3, -62792632506386437441556306954498768597214560256000000⟩, + ⟨3, 0, 8, 4, 4, 3, 87608896735001321308390624836450169764697866240000000⟩, + ⟨3, 0, 7, 5, 2, 3, 121968658802825301638772061248054184640998539264000000⟩, + ⟨3, 0, 8, 5, 3, 3, -122550318922641948799727202068225671577154355200000000⟩, + ⟨3, 0, 7, 6, 1, 3, -335104940499253706054206042786986520085746679808000000⟩, + ⟨3, 0, 8, 6, 2, 3, 437032398843364227482985865566715692573926621184000000⟩, + ⟨3, 0, 7, 7, 0, 3, 1135892568040307586505083267333366291349697986560000000⟩, + ⟨3, 0, 8, 7, 1, 3, -817154638490078560012185014055785639440621240320000000⟩ +] + +def collectedFourData_10_0_25 : List CollectedFourTerm := [ + ⟨3, 1, 6, 0, 6, 4, 41720585766264582135687284029334926941475779379200000⟩, + ⟨3, 1, 7, 0, 7, 4, -764744639634539781825427381608479044432979558400000⟩, + ⟨3, 1, 8, 0, 8, 4, 51559027350016274652766547552729497771402749542400000⟩, + ⟨3, 1, 6, 1, 5, 4, -26235558396703646005264038552890449694687861145600000⟩, + ⟨3, 1, 7, 1, 6, 4, -52931251014886407698395389496876008102128359833600000⟩, + ⟨3, 1, 8, 1, 7, 4, 43083484924106923689452983572904549347175170048000000⟩, + ⟨3, 1, 6, 2, 4, 4, 9416310199540510299652972327792972497486977433600000⟩, + ⟨3, 1, 7, 2, 5, 4, 5368290786129501444226673943845023100461645824000000⟩, + ⟨3, 1, 8, 2, 6, 4, 2344453350403355105668209897758922472308080640000000⟩, + ⟨3, 1, 6, 3, 3, 4, 14294829711554518235959167751416406198104096768000000⟩, + ⟨3, 1, 7, 3, 4, 4, -21569233760737811359647334380916226009298527846400000⟩, + ⟨3, 1, 8, 3, 5, 4, 37302054334391053386160340668543207585861337088000000⟩, + ⟨3, 1, 6, 4, 2, 4, -43466213830257749159451298280538220759175135232000000⟩, + ⟨3, 1, 7, 4, 3, 4, 76501519772687451055667031504020937622902590668800000⟩, + ⟨3, 1, 8, 4, 4, 4, -53367835351976810108518040556369915987703627776000000⟩, + ⟨3, 1, 6, 5, 1, 4, 67168014781592199360472209671686831665057890304000000⟩, + ⟨3, 1, 7, 5, 2, 4, -148596855882790144559161164692107273986204971827200000⟩, + ⟨3, 1, 8, 5, 3, 4, 74652752018766818459784295820902179023597076480000000⟩, + ⟨3, 1, 6, 6, 0, 4, -98522353746332313669161834086819879556727649075200000⟩, + ⟨3, 1, 7, 6, 1, 4, 408265049708205018964927805518952007326203536998400000⟩, + ⟨3, 1, 8, 6, 2, 4, -266222655165956197952426364614676540524018112921600000⟩, + ⟨3, 1, 7, 7, 0, 4, -1383880628746473554917974028076162074301209509888000000⟩, + ⟨3, 1, 8, 7, 1, 4, 497777917874632473315159145748077066793326215168000000⟩ +] + +def collectedFourData_10_0_26 : List CollectedFourTerm := [ + ⟨3, 2, 5, 0, 5, 5, -466932053086114057614764352063960892874812293120000000⟩, + ⟨3, 2, 6, 0, 6, 5, -539730879415716549548888334356388751682347991040000000⟩, + ⟨3, 2, 7, 0, 7, 5, 4946674277188141083569865273588892096832471040000000⟩, + ⟨3, 2, 8, 0, 8, 5, -222336277262475440363419946718221228991011880960000000⟩, + ⟨3, 2, 5, 1, 4, 5, -249877811164537530160000440465115449626355302400000000⟩, + ⟨3, 2, 6, 1, 5, 5, 339404175309187222678927060006829975560488222720000000⟩, + ⟨3, 2, 7, 1, 6, 5, 342380507537592855757244793574871517020458844160000000⟩, + ⟨3, 2, 8, 1, 7, 5, -185787477806578405404929249675468866227221299200000000⟩, + ⟨3, 2, 5, 2, 3, 5, -368667433552342779288553708295859907960284119040000000⟩, + ⟨3, 2, 6, 2, 4, 5, -121816923025053157498335572375115102907866808320000000⟩, + ⟨3, 2, 7, 2, 5, 5, -34724252473221966113059136977801396066084454400000000⟩, + ⟨3, 2, 8, 2, 6, 5, -10109908137048192644336126202396873804742656000000000⟩, + ⟨3, 2, 5, 3, 2, 5, 1001571417950149777375426179311426501732833689600000000⟩, + ⟨3, 2, 6, 3, 3, 5, -184929354888250464846662264590902726850353561600000000⟩, + ⟨3, 2, 7, 3, 4, 5, 139518433073147397274794567647778392019660963840000000⟩, + ⟨3, 2, 8, 3, 5, 5, -160856407136013886183119199390411579379102515200000000⟩, + ⟨3, 2, 5, 4, 1, 5, -277613767277352859675115691632168286263495884800000000⟩, + ⟨3, 2, 6, 4, 2, 5, 562313720783050091480588509745797278527284838400000000⟩, + ⟨3, 2, 7, 4, 3, 5, -494842435517035077968813239596966537149577953280000000⟩, + ⟨3, 2, 8, 4, 4, 5, 230136339794848927577710515945128002889082470400000000⟩, + ⟨3, 2, 5, 5, 0, 5, -3178129538116703209296507701322011255934560501760000000⟩, + ⟨3, 2, 6, 5, 1, 5, -868939182440497576707745781611766888293780684800000000⟩, + ⟨3, 2, 7, 5, 2, 5, 961183912341910354378085115904566364041715384320000000⟩, + ⟨3, 2, 8, 5, 3, 5, -321922577370849555597481612194012292177723392000000000⟩, + ⟨3, 2, 6, 6, 0, 5, 1274563998873961274351118506409556655261079306240000000⟩, + ⟨3, 2, 7, 6, 1, 5, -2640821674319457560694823905388615927665304535040000000⟩, + ⟨3, 2, 8, 6, 2, 5, 1148023093428502063664457851884692876145868144640000000⟩, + ⟨3, 2, 7, 7, 0, 5, 8951493549782247673274175160628261412345269452800000000⟩, + ⟨3, 2, 8, 7, 1, 5, -2146551144426836839523963551956443175643722547200000000⟩ +] + +def collectedFourData_10_0_27 : List CollectedFourTerm := [ + ⟨3, 3, 4, 0, 4, 6, -16391190905712743879552330490031987323530379264000000⟩, + ⟨3, 3, 5, 0, 5, 6, 86213965181421718254549346733959920796324331520000000⟩, + ⟨3, 3, 6, 0, 6, 6, 49827741464455613837244402275381654205675601920000000⟩, + ⟨3, 3, 7, 0, 7, 6, -304450009431158472963871766885312532609761280000000⟩, + ⟨3, 3, 8, 0, 8, 6, 10262998620346817924576323891949005763027927040000000⟩, + ⟨3, 3, 4, 1, 3, 6, 9773105245774204887767620293756070881688289280000000⟩, + ⟨3, 3, 5, 1, 4, 6, 46137241530035301830635252571762981014496870400000000⟩, + ⟨3, 3, 6, 1, 5, 6, -31333659318456429649077177624954681388758466560000000⟩, + ⟨3, 3, 7, 1, 6, 6, -21072288755611633398912580469648212739877765120000000⟩, + ⟨3, 3, 8, 1, 7, 6, 8575913260235362399087790786623504384838860800000000⟩, + ⟨3, 3, 4, 2, 2, 6, -6438447952084273093572865333325590199713923072000000⟩, + ⟨3, 3, 5, 2, 3, 6, 68070463506911917834968359828915314505904291840000000⟩, + ⟨3, 3, 6, 2, 4, 6, 11246090186758896175865577696720661610087055360000000⟩, + ⟨3, 3, 7, 2, 5, 6, 2137152842610799065903741575300039689686220800000000⟩, + ⟨3, 3, 8, 2, 6, 6, 466671361686374276099065227102955864326144000000000⟩, + ⟨3, 3, 4, 3, 1, 6, 14294829711554518235959167751416406198104096768000000⟩, + ⟨3, 3, 5, 3, 2, 6, -184929354888250464846662264590902726850353561600000000⟩, + ⟨3, 3, 6, 3, 3, 6, 17072604951815144755275746267355034604588236800000000⟩, + ⟨3, 3, 7, 3, 4, 6, -8586857732036727065585703324841884930413690880000000⟩, + ⟨3, 3, 8, 3, 5, 6, 7425099964959610115405135806846132850314444800000000⟩, + ⟨3, 3, 4, 4, 0, 6, -23877070640426475895343580757903094712008441856000000⟩, + ⟨3, 3, 5, 4, 1, 6, 51258386541989962199788181429411942509628620800000000⟩, + ⟨3, 3, 6, 4, 2, 6, -51912580453846856294588950870501396864774963200000000⟩, + ⟨3, 3, 7, 4, 3, 6, 30455772043623638824627780890942841855892520960000000⟩, + ⟨3, 3, 8, 4, 4, 6, -10623047965393033192948065079222487618263449600000000⟩, + ⟨3, 3, 5, 5, 0, 6, 586807325670377523195653671430597294741740584960000000⟩, + ⟨3, 3, 6, 5, 1, 6, 80220121883431669021079505672753615240324710400000000⟩, + ⟨3, 3, 7, 5, 2, 6, -59157412592752054906320908768570038334773002240000000⟩, + ⟨3, 3, 8, 5, 3, 6, 14859882553107455876878812632335740680798208000000000⟩, + ⟨3, 3, 6, 6, 0, 6, -117667244617438717207375893293726416615526891520000000⟩, + ⟨3, 3, 7, 6, 1, 6, 162533075476638546977855143359913813641296609280000000⟩, + ⟨3, 3, 8, 6, 2, 6, -52992519120367244174906749431440611281846927360000000⟩, + ⟨3, 3, 7, 7, 0, 6, -550932231018716528062433564458504753071626649600000000⟩, + ⟨3, 3, 8, 7, 1, 6, 99084376625364173926638306701629412608888012800000000⟩ +] + +def collectedFourData_10_0_28 : List CollectedFourTerm := [ + ⟨3, 4, 3, 0, 3, 7, 2035363618983743401292342175024822576067117056000000⟩, + ⟨3, 4, 4, 0, 4, 7, 24732398734098031738377918490031452835028349747200000⟩, + ⟨3, 4, 5, 0, 5, 7, -65043418003612340136539698982750446891038670848000000⟩, + ⟨3, 4, 6, 0, 6, 7, -25061420226823535332457896067275752486702415872000000⟩, + ⟨3, 4, 7, 0, 7, 7, 114844904668076917089615440179112589379239936000000⟩, + ⟨3, 4, 8, 0, 8, 7, -3097134009920533828665350678329942092900886118400000⟩, + ⟨3, 4, 3, 1, 2, 7, -219235008188322729877632564258206911949281689600000⟩, + ⟨3, 4, 4, 1, 3, 7, -14746477983155569646220698269441487084552454144000000⟩, + ⟨3, 4, 5, 1, 4, 7, -34807862972742371746973007175042200251620392960000000⟩, + ⟨3, 4, 6, 1, 5, 7, 15759614631221596605566196713080946471674576896000000⟩, + ⟨3, 4, 7, 1, 6, 7, 7948907598321563344178634278163912137317023744000000⟩, + ⟨3, 4, 8, 1, 7, 7, -2588010931984891752639561162425755882192109568000000⟩, + ⟨3, 4, 3, 2, 1, 7, -1716248441672768077724073431465299451523052339200000⟩, + ⟨3, 4, 4, 2, 2, 7, 9714868364091018302908841262764354356029004185600000⟩, + ⟨3, 4, 5, 2, 3, 7, -51355202167801497237345199983237472758389538816000000⟩, + ⟨3, 4, 6, 2, 4, 7, -5656346922329852134796878559394564398672510976000000⟩, + ⟨3, 4, 7, 2, 5, 7, -806178705427977277410485988282556415433768960000000⟩, + ⟨3, 4, 8, 2, 6, 7, -140830550524419107683849748547161152542474240000000⟩, + ⟨3, 4, 3, 3, 0, 7, 17704079252369263528416883099672985716358381568000000⟩, + ⟨3, 4, 4, 3, 1, 7, -21569233760737811359647334380916226009298527846400000⟩, + ⟨3, 4, 5, 3, 2, 7, 139518433073147397274794567647778392019660963840000000⟩, + ⟨3, 4, 6, 3, 3, 7, -8586857732036727065585703324841884930413690880000000⟩, + ⟨3, 4, 7, 3, 4, 7, 3239142148415944054065317047496416919034003456000000⟩, + ⟨3, 4, 8, 3, 5, 7, -2240722276133273985513642539102740280883806208000000⟩, + ⟨3, 4, 4, 4, 0, 7, 36027719711045273539144109231408335570409934028800000⟩, + ⟨3, 4, 5, 4, 1, 7, -38671468769886016477087604066741141513353297920000000⟩, + ⟨3, 4, 6, 4, 2, 7, 26110013329436296135290673246408605932055429120000000⟩, + ⟨3, 4, 7, 4, 3, 7, -11488553550968204116013379611177960636732669952000000⟩, + ⟨3, 4, 8, 4, 4, 7, 3205788518514296384910016436761029501587030016000000⟩, + ⟨3, 4, 5, 5, 0, 7, -442711967728693109483621599937043155057853333504000000⟩, + ⟨3, 4, 6, 5, 1, 7, -40347608101037746455470315081831340504137072640000000⟩, + ⟨3, 4, 7, 5, 2, 7, 22315412051780309474972496917436734462270373888000000⟩, + ⟨3, 4, 8, 5, 3, 7, -4484366542485086693948474565672050942992711680000000⟩, + ⟨3, 4, 6, 6, 0, 7, 59182057577176387606920632572336576322686943232000000⟩, + ⟨3, 4, 7, 6, 1, 7, -61310871999643140797043574733463467512389697536000000⟩, + ⟨3, 4, 8, 6, 2, 7, 15991908340869218840390844071711953446434871705600000⟩, + ⟨3, 4, 7, 7, 0, 7, 207823148595507897974305639393683341724635627520000000⟩, + ⟨3, 4, 8, 7, 1, 7, -29901357687975624889920390540002077645354303488000000⟩ +] + +def collectedFourData_10_0_29 : List CollectedFourTerm := [ + ⟨3, 5, 2, 0, 2, 8, -3839596996829086568264890875997395063505158144000000⟩, + ⟨3, 5, 3, 0, 3, 8, -7039957482752723038955785868192486037431255040000000⟩, + ⟨3, 5, 4, 0, 4, 8, -42772464318064457594634929416185992991026970624000000⟩, + ⟨3, 5, 5, 0, 5, 8, 74991169965488310831034237188602994252778045440000000⟩, + ⟨3, 5, 6, 0, 6, 8, 21670738732955357381799544745235358902512517120000000⟩, + ⟨3, 5, 7, 0, 7, 8, -79445582934978145491871808830360215877582848000000⟩, + ⟨3, 5, 8, 0, 8, 8, 1785405119169368770159543943941748718909259776000000⟩, + ⟨3, 5, 2, 1, 1, 8, 20244351284257484867575977112358377099723014144000000⟩, + ⟨3, 5, 3, 1, 2, 8, 758294548444055881996176532818050474588504064000000⟩, + ⟨3, 5, 4, 1, 3, 8, 25502710437950868886330839422189336537837076480000000⟩, + ⟨3, 5, 5, 1, 4, 8, 40131383750149511055425628075453863668010188800000000⟩, + ⟨3, 5, 6, 1, 5, 8, -13627419679900193402979686620958242623360860160000000⟩, + ⟨3, 5, 7, 1, 6, 8, -5498768967331219925181810008137354808647483392000000⟩, + ⟨3, 5, 8, 1, 7, 8, 1491910892984146734151551414491091377345003520000000⟩, + ⟨3, 5, 2, 2, 0, 8, -21399395829709151351066957494366666986193158144000000⟩, + ⟨3, 5, 3, 2, 1, 8, 5936195354248103180214935432739442589096214528000000⟩, + ⟨3, 5, 4, 2, 2, 8, -16800993099181096170031101847611886698183524352000000⟩, + ⟨3, 5, 5, 2, 3, 8, 59209475955948856572952023048924919379766804480000000⟩, + ⟨3, 5, 6, 2, 4, 8, 4891072222857127088920165520751041283316776960000000⟩, + ⟨3, 5, 7, 2, 5, 8, 557685492339432669951182071684862475270881280000000⟩, + ⟨3, 5, 8, 2, 6, 8, 81184600032269748585812494456489554581913600000000⟩, + ⟨3, 5, 3, 3, 0, 8, -61235232881972677113178678794242059819674501120000000⟩, + ⟨3, 5, 4, 3, 1, 8, 37302054334391053386160340668543207585861337088000000⟩, + ⟨3, 5, 5, 3, 2, 8, -160856407136013886183119199390411579379102515200000000⟩, + ⟨3, 5, 6, 3, 3, 8, 7425099964959610115405135806846132850314444800000000⟩, + ⟨3, 5, 7, 3, 4, 8, -2240722276133273985513642539102740280883806208000000⟩, + ⟨3, 5, 8, 3, 5, 8, 1291709370544103280276724484654004698213253120000000⟩, + ⟨3, 5, 4, 4, 0, 8, -62306708393689908159472217163206128300034359296000000⟩, + ⟨3, 5, 5, 4, 1, 8, 44585890107689851600404029549961214235875737600000000⟩, + ⟨3, 5, 6, 4, 2, 8, -22577462572156563072085582704383240348840755200000000⟩, + ⟨3, 5, 7, 4, 3, 8, 7947368989284264277195479497855489976236507136000000⟩, + ⟨3, 5, 8, 4, 4, 8, -1848041193437628569770894366932482352469770240000000⟩, + ⟨3, 5, 5, 5, 0, 8, 510420415111862492796168647246433818520972165120000000⟩, + ⟨3, 5, 6, 5, 1, 8, 34888783865545717158514634961077089971103334400000000⟩, + ⟨3, 5, 7, 5, 2, 8, -15437001093011661180121407463398667273302441984000000⟩, + ⟨3, 5, 8, 5, 3, 8, 2585103181050323574175206649031771485844275200000000⟩, + ⟨3, 5, 6, 6, 0, 8, -51175029021739767109502677027838099832145182720000000⟩, + ⟨3, 5, 7, 6, 1, 8, 42412660625573416451667162859662653037528219648000000⟩, + ⟨3, 5, 8, 6, 2, 8, -9218856828803419239721410648001378469579587584000000⟩, + ⟨3, 5, 7, 7, 0, 8, -143764594827010367874992938479156367262597775360000000⟩, + ⟨3, 5, 8, 7, 1, 8, 17237238335578452718715905841305842004336312320000000⟩ +] + +def collectedFourData_10_0_30 : List CollectedFourTerm := [ + ⟨4, 0, 6, 0, 6, 4, -69687110207117038620850698651215130723338315366400000⟩, + ⟨4, 0, 7, 0, 7, 4, 1277375257410862306636392985195260139874864332800000⟩, + ⟨4, 0, 8, 0, 8, 4, -86120545891703617804515911689718290701196512460800000⟩, + ⟨4, 0, 6, 1, 5, 4, 43822017734341013452041821389735190044286858035200000⟩, + ⟨4, 0, 7, 1, 6, 4, 88412611067834073181480565813921858337627124531200000⟩, + ⟨4, 0, 8, 1, 7, 4, -71963600387428567312828278391106045905119215616000000⟩, + ⟨4, 0, 6, 2, 4, 4, -15728337331984005991055420448013529654169383731200000⟩, + ⟨4, 0, 7, 2, 5, 4, -8966812540282133320982783665976546634296721408000000⟩, + ⟨4, 0, 8, 2, 6, 4, -3916008752137693578399073594983807124903034880000000⟩, + ⟨4, 0, 6, 3, 3, 4, -23877070640426475895343580757903094712008441856000000⟩, + ⟨4, 0, 7, 3, 4, 4, 36027719711045273539144109231408335570409934028800000⟩, + ⟨4, 0, 8, 3, 5, 4, -62306708393689908159472217163206128300034359296000000⟩, + ⟨4, 0, 6, 4, 2, 4, 72602883632678407888347905855190089300541702144000000⟩, + ⟨4, 0, 7, 4, 3, 4, -127782717847696592148017721544427031882555300249600000⟩, + ⟨4, 0, 8, 4, 4, 4, 89141850608811975949637834111795067379664289792000000⟩, + ⟨4, 0, 6, 5, 1, 4, -112192692468449214472092168465008684517260525568000000⟩, + ⟨4, 0, 7, 5, 2, 4, 248205658720841984506785023312384049920294151782400000⟩, + ⟨4, 0, 8, 5, 3, 4, -124694667192400950625381383474514610540941148160000000⟩, + ⟨4, 0, 6, 6, 0, 4, 164564758554681921093627932634032233280719709798400000⟩, + ⟨4, 0, 7, 6, 1, 4, -681937009996039631746379597869927167106799684812800000⟩, + ⟨4, 0, 8, 6, 2, 4, 444679459059339313991334919126472664450426155827200000⟩, + ⟨4, 0, 7, 7, 0, 4, 2311536142594876029839688739922651628483322576896000000⟩, + ⟨4, 0, 8, 7, 1, 4, -831452962236407062484205918833680277799652294656000000⟩ +] + +def collectedFourData_10_0_31 : List CollectedFourTerm := [ + ⟨4, 1, 5, 0, 5, 5, 129423388084579729722618086854805497664042434560000000⟩, + ⟨4, 1, 6, 0, 6, 5, 149601636054248313271782891010373344095130091520000000⟩, + ⟨4, 1, 7, 0, 7, 5, -1371110294256147017973582779904670876324331520000000⟩, + ⟨4, 1, 8, 0, 8, 5, 61626770120480779596966521755244213544922644480000000⟩, + ⟨4, 1, 5, 1, 4, 5, 69260683035844086482212036132062183682159411200000000⟩, + ⟨4, 1, 6, 1, 5, 5, -94075439902315837477779644591295356130935439360000000⟩, + ⟨4, 1, 7, 1, 6, 5, -94900414325295838706636832652306611353765806080000000⟩, + ⟨4, 1, 8, 1, 7, 5, 51496239511707906755366490008428457921976729600000000⟩, + ⟨4, 1, 5, 2, 3, 5, 102186577279138232382127739749180536281125355520000000⟩, + ⟨4, 1, 6, 2, 4, 5, 33764995998321816082029368865433671591694172160000000⟩, + ⟨4, 1, 7, 2, 5, 5, 9624805952141184287223816441894261014868787200000000⟩, + ⟨4, 1, 8, 2, 6, 5, 2802246184798382045642543346390472461385728000000000⟩, + ⟨4, 1, 5, 3, 2, 5, -277613767277352859675115691632168286263495884800000000⟩, + ⟨4, 1, 6, 3, 3, 5, 51258386541989962199788181429411942509628620800000000⟩, + ⟨4, 1, 7, 3, 4, 5, -38671468769886016477087604066741141513353297920000000⟩, + ⟨4, 1, 8, 3, 5, 5, 44585890107689851600404029549961214235875737600000000⟩, + ⟨4, 1, 5, 4, 1, 5, 76948485550493347382545845165693215317583462400000000⟩, + ⟨4, 1, 6, 4, 2, 5, -155861107476309547648813716232416058607350579200000000⟩, + ⟨4, 1, 7, 4, 3, 5, 137159537772894093048462051676284106268360048640000000⟩, + ⟨4, 1, 8, 4, 4, 5, -63788777447969141921694230032206048636646195200000000⟩, + ⟨4, 1, 5, 5, 0, 5, 880908238952885985003255946802193681380938874880000000⟩, + ⟨4, 1, 6, 5, 1, 5, 240851002383752157797717473371791520728245862400000000⟩, + ⟨4, 1, 7, 5, 2, 5, -266419230989780191783845427829103112736640860160000000⟩, + ⟨4, 1, 8, 5, 3, 5, 89229921974475493691337118441412419173482496000000000⟩, + ⟨4, 1, 6, 6, 0, 5, -353281360691843616478859375807098034611940229120000000⟩, + ⟨4, 1, 7, 6, 1, 5, 731978210017171730844402798828458280253673963520000000⟩, + ⟨4, 1, 8, 6, 2, 5, -318206979728278927161617031831523996167642808320000000⟩, + ⟨4, 1, 7, 7, 0, 5, -2481158909466464492004838765370189588008953446400000000⟩, + ⟨4, 1, 8, 7, 1, 5, 594977192018379936176411065108478092046342553600000000⟩ +] + +def collectedFourData_10_0_32 : List CollectedFourTerm := [ + ⟨4, 2, 4, 0, 4, 6, 49840608332983644557041530116427295432938356736000000⟩, + ⟨4, 2, 5, 0, 5, 6, -262150352354393679784430597346366438959984148480000000⟩, + ⟨4, 2, 6, 0, 6, 6, -151510952482504359647373237511006790292162478080000000⟩, + ⟨4, 2, 7, 0, 7, 6, 925739549024655262842043497305383826588958720000000⟩, + ⟨4, 2, 8, 0, 8, 6, -31206646149205771505164031890625830218325032960000000⟩, + ⟨4, 2, 4, 1, 3, 6, -29717029931113438794914168936067090094982430720000000⟩, + ⟨4, 2, 5, 1, 4, 6, -140289268662066517586951587850460317781432729600000000⟩, + ⟨4, 2, 6, 1, 5, 6, 95276093769735927536348091424588632398694973440000000⟩, + ⟨4, 2, 7, 1, 6, 6, 64074398046449090175686064253057394298197114880000000⟩, + ⟨4, 2, 8, 1, 7, 6, -26076734531354999487950327615014213201900339200000000⟩, + ⟨4, 2, 4, 2, 2, 6, 19577354964506727076569208384123361083867004928000000⟩, + ⟨4, 2, 5, 2, 3, 6, -206981501845007546383580657847361895552683868160000000⟩, + ⟨4, 2, 6, 2, 4, 6, -34195927525943734603122843577692825370377584640000000⟩, + ⟨4, 2, 7, 2, 5, 6, -6498429454516548411712280422319984569692979200000000⟩, + ⟨4, 2, 8, 2, 6, 6, -1419005165141741896792067141538534817529856000000000⟩, + ⟨4, 2, 4, 3, 1, 6, -43466213830257749159451298280538220759175135232000000⟩, + ⟨4, 2, 5, 3, 2, 6, 562313720783050091480588509745797278527284838400000000⟩, + ⟨4, 2, 6, 3, 3, 6, -51912580453846856294588950870501396864774963200000000⟩, + ⟨4, 2, 7, 3, 4, 6, 26110013329436296135290673246408605932055429120000000⟩, + ⟨4, 2, 8, 3, 5, 6, -22577462572156563072085582704383240348840755200000000⟩, + ⟨4, 2, 4, 4, 0, 6, 72602883632678407888347905855190089300541702144000000⟩, + ⟨4, 2, 5, 4, 1, 6, -155861107476309547648813716232416058607350579200000000⟩, + ⟨4, 2, 6, 4, 2, 6, 157850311477546460258401430125377844702661836800000000⟩, + ⟨4, 2, 7, 4, 3, 6, -92606706531362541762207763935955370378306519040000000⟩, + ⟨4, 2, 8, 4, 4, 6, 32301446306816124716819557497415063065486950400000000⟩, + ⟨4, 2, 5, 5, 0, 6, -1784301961578008660116367537088477000092394455040000000⟩, + ⟨4, 2, 6, 5, 1, 6, -243924904432834563420981474505570172607764889600000000⟩, + ⟨4, 2, 7, 5, 2, 6, 179879634615228804136212099023314179027904757760000000⟩, + ⟨4, 2, 8, 5, 3, 6, -45184367045925810318460165802976269976993792000000000⟩, + ⟨4, 2, 6, 6, 0, 6, 357790174389048046359484067820599821858221588480000000⟩, + ⟨4, 2, 7, 6, 1, 6, -494213471283718367749612545606808005967054110720000000⟩, + ⟨4, 2, 8, 6, 2, 6, 161134075324316617002129497355597459042745712640000000⟩, + ⟨4, 2, 7, 7, 0, 6, 1675216749177793365584312416655922486648923750400000000⟩, + ⟨4, 2, 8, 7, 1, 6, -301285345019162060185673790790765000992699187200000000⟩ +] + +def collectedFourData_10_0_33 : List CollectedFourTerm := [ + ⟨4, 3, 3, 0, 3, 7, -7219005175127151536120010153823066278070321152000000⟩, + ⟨4, 3, 4, 0, 4, 7, -87720598319384592052547382053053402388168599142400000⟩, + ⟨4, 3, 5, 0, 5, 7, 230695275672895056877580102897918866197646934016000000⟩, + ⟨4, 3, 6, 0, 6, 7, 88887568111199683863899298019928251525679284224000000⟩, + ⟨4, 3, 7, 0, 7, 7, -407330637829610060713486783969113277162586112000000⟩, + ⟨4, 3, 8, 0, 8, 7, 10984880655792647923663897784541392236637375692800000⟩, + ⟨4, 3, 3, 1, 2, 7, 777580302565674404225938048761894328811598643200000⟩, + ⟨4, 3, 4, 1, 3, 7, 52302645032267780033311546702126592428760629248000000⟩, + ⟨4, 3, 5, 1, 4, 7, 123456143458438674102786848654794407887052472320000000⟩, + ⟨4, 3, 6, 1, 5, 7, -55896026891550212461025817045065576954757906432000000⟩, + ⟨4, 3, 7, 1, 6, 7, -28193097564327264700287240413521490257744232448000000⟩, + ⟨4, 3, 8, 1, 7, 7, 9179128553262107589530151597619980000093536256000000⟩, + ⟨4, 3, 3, 2, 1, 7, 6087170993272322379802582817302518816284501606400000⟩, + ⟨4, 3, 4, 2, 2, 7, -34456587678946939384273416673841202866878100275200000⟩, + ⟨4, 3, 5, 2, 3, 7, 182146063121717414969124644509163802487079043072000000⟩, + ⟨4, 3, 6, 2, 4, 7, 20061868711695724068583319813132458692855201792000000⟩, + ⟨4, 3, 7, 2, 5, 7, 2859345717040822597153590078414552322875064320000000⟩, + ⟨4, 3, 8, 2, 6, 7, 499496239182757758129496444229320991393710080000000⟩, + ⟨4, 3, 3, 3, 0, 7, -62792632506386437441556306954498768597214560256000000⟩, + ⟨4, 3, 4, 3, 1, 7, 76501519772687451055667031504020937622902590668800000⟩, + ⟨4, 3, 5, 3, 2, 7, -494842435517035077968813239596966537149577953280000000⟩, + ⟨4, 3, 6, 3, 3, 7, 30455772043623638824627780890942841855892520960000000⟩, + ⟨4, 3, 7, 3, 4, 7, -11488553550968204116013379611177960636732669952000000⟩, + ⟨4, 3, 8, 3, 5, 7, 7947368989284264277195479497855489976236507136000000⟩, + ⟨4, 3, 4, 4, 0, 7, -127782717847696592148017721544427031882555300249600000⟩, + ⟨4, 3, 5, 4, 1, 7, 137159537772894093048462051676284106268360048640000000⟩, + ⟨4, 3, 6, 4, 2, 7, -92606706531362541762207763935955370378306519040000000⟩, + ⟨4, 3, 7, 4, 3, 7, 40747474684928665982047713702411512564190019584000000⟩, + ⟨4, 3, 8, 4, 4, 7, -11370255265284247731169427198249558407718633472000000⟩, + ⟨4, 3, 5, 5, 0, 7, 1570205911275888963156575853624177875007326650368000000⟩, + ⟨4, 3, 6, 5, 1, 7, 143104450216529131398237563749015219986109562880000000⟩, + ⟨4, 3, 7, 5, 2, 7, -79148056683518592055790183978498486908219293696000000⟩, + ⟨4, 3, 8, 5, 3, 7, 15905101661161928802978102144575739718596034560000000⟩, + ⟨4, 3, 6, 6, 0, 7, -209906267332039678905200128067821865057956921344000000⟩, + ⟨4, 3, 7, 6, 1, 7, 217456722783506385254544038547053523537663885312000000⟩, + ⟨4, 3, 8, 6, 2, 7, -56719923652038129288956844649082140894717752115200000⟩, + ⟨4, 3, 7, 7, 0, 7, -737104845163380778443791042781854777258897571840000000⟩, + ⟨4, 3, 8, 7, 1, 7, 106053804774501154656795224635543932091704016896000000⟩ +] + +def collectedFourData_10_0_34 : List CollectedFourTerm := [ + ⟨4, 4, 2, 0, 2, 8, 5493289417998603593850991673925282282589913088000000⟩, + ⟨4, 4, 3, 0, 3, 8, 10072026823414838973940589130256982330132398080000000⟩, + ⟨4, 4, 4, 0, 4, 8, 61194319563794906930353274385656381369166594048000000⟩, + ⟨4, 4, 5, 0, 5, 8, -107289437082838944318694627854289601521652858880000000⟩, + ⟨4, 4, 6, 0, 6, 8, -31004201706655091940868950012425546697529098240000000⟩, + ⟨4, 4, 7, 0, 7, 8, 113662340189311360431830360531002435143991296000000⟩, + ⟨4, 4, 8, 0, 8, 8, -2554368871543891671067249385432376985100746752000000⟩, + ⟨4, 4, 2, 1, 1, 8, -28963477358665183262743817889400144522628825088000000⟩, + ⟨4, 4, 3, 1, 2, 8, -1084887664547567497796685858027680323420028928000000⟩, + ⟨4, 4, 4, 1, 3, 8, -36486581663329207046954467751530108998868008960000000⟩, + ⟨4, 4, 5, 1, 4, 8, -57415740731748089387226657437983526687971737600000000⟩, + ⟨4, 4, 6, 1, 5, 8, 19496671235039486435012799193211806551449272320000000⟩, + ⟨4, 4, 7, 1, 6, 8, 7867057247207312927537117184387642626024669184000000⟩, + ⟨4, 4, 8, 1, 7, 8, -2134468364204596156471437440490281089672151040000000⟩, + ⟨4, 4, 2, 2, 0, 8, 30615992970091754999659202418367927401565913088000000⟩, + ⟨4, 4, 3, 2, 1, 8, -8492880672006402391641900491423302838340550656000000⟩, + ⟨4, 4, 4, 2, 2, 8, 24037084537731067418492822469613293242998063104000000⟩, + ⟨4, 4, 5, 2, 3, 8, -84710657910886681718378570284268784748289064960000000⟩, + ⟨4, 4, 6, 2, 4, 8, -6997628997698675100334974393680606844074065920000000⟩, + ⟨4, 4, 7, 2, 5, 8, -797877437702328415873932985578854313162178560000000⟩, + ⟨4, 4, 8, 2, 6, 8, -116150341983812150402860171561589546365747200000000⟩, + ⟨4, 4, 3, 3, 0, 8, 87608896735001321308390624836450169764697866240000000⟩, + ⟨4, 4, 4, 3, 1, 8, -53367835351976810108518040556369915987703627776000000⟩, + ⟨4, 4, 5, 3, 2, 8, 230136339794848927577710515945128002889082470400000000⟩, + ⟨4, 4, 6, 3, 3, 8, -10623047965393033192948065079222487618263449600000000⟩, + ⟨4, 4, 7, 3, 4, 8, 3205788518514296384910016436761029501587030016000000⟩, + ⟨4, 4, 8, 3, 5, 8, -1848041193437628569770894366932482352469770240000000⟩, + ⟨4, 4, 4, 4, 0, 8, 89141850608811975949637834111795067379664289792000000⟩, + ⟨4, 4, 5, 4, 1, 8, -63788777447969141921694230032206048636646195200000000⟩, + ⟨4, 4, 6, 4, 2, 8, 32301446306816124716819557497415063065486950400000000⟩, + ⟨4, 4, 7, 4, 3, 8, -11370255265284247731169427198249558407718633472000000⟩, + ⟨4, 4, 8, 4, 4, 8, 2643981944021800545425633074876344070286868480000000⟩, + ⟨4, 4, 5, 5, 0, 8, -730255562596810533964777595301194060148233994240000000⟩, + ⟨4, 4, 6, 5, 1, 8, -49915183123051567277026742452100005247110348800000000⟩, + ⟨4, 4, 7, 5, 2, 8, 22085628991768004143775841578289742577053728768000000⟩, + ⟨4, 4, 8, 5, 3, 8, -3698492305475254223324790336303042721637990400000000⟩, + ⟨4, 4, 6, 6, 0, 8, 73215820728856576055209703031950706791090749440000000⟩, + ⟨4, 4, 7, 6, 1, 8, -60679550483042383128824379684795106817942224896000000⟩, + ⟨4, 4, 8, 6, 2, 8, 13189365630177418066586581551048296407360339968000000⟩, + ⟨4, 4, 7, 7, 0, 8, 205683181880357861714706488821683845824480542720000000⟩, + ⟨4, 4, 8, 7, 1, 8, -24661218097251238802003073771001118500470128640000000⟩ +] + +def collectedFourData_10_0_35 : List CollectedFourTerm := [ + ⟨5, 0, 5, 0, 5, 5, 1481642270946190090178591663754775448798701289472000000⟩, + ⟨5, 0, 6, 0, 6, 5, 1712643371967877907943757460661996417476223565824000000⟩, + ⟨5, 0, 7, 0, 7, 5, -15696505864703297509914007827016512451928653824000000⟩, + ⟨5, 0, 8, 0, 8, 5, 705504847181998864521161885580236561179660517376000000⟩, + ⟨5, 0, 5, 1, 4, 5, 792898078309070308282554684256365634288814653440000000⟩, + ⟨5, 0, 6, 1, 5, 5, -1076978052267018014428391960824762086636474335232000000⟩, + ⟨5, 0, 7, 1, 6, 5, -1086422380650214203566469912169971014726420791296000000⟩, + ⟨5, 0, 8, 1, 7, 5, 589530272576804394361576404587312682758590955520000000⟩, + ⟨5, 0, 5, 2, 3, 5, 1169834561286067013077108055358966182425997082624000000⟩, + ⟨5, 0, 6, 2, 4, 5, 386542541420325765998393937601673078482604654592000000⟩, + ⟨5, 0, 7, 2, 5, 5, 110185025746872365622729336722080137652878704640000000⟩, + ⟨5, 0, 8, 2, 6, 5, 32080186297407377020945432838794452825381273600000000⟩, + ⟨5, 0, 5, 3, 2, 5, -3178129538116703209296507701322011255934560501760000000⟩, + ⟨5, 0, 6, 3, 3, 5, 586807325670377523195653671430597294741740584960000000⟩, + ⟨5, 0, 7, 3, 4, 5, -442711967728693109483621599937043155057853333504000000⟩, + ⟨5, 0, 8, 3, 5, 5, 510420415111862492796168647246433818520972165120000000⟩, + ⟨5, 0, 5, 4, 1, 5, 880908238952885985003255946802193681380938874880000000⟩, + ⟨5, 0, 6, 4, 2, 5, -1784301961578008660116367537088477000092394455040000000⟩, + ⟨5, 0, 7, 4, 3, 5, 1570205911275888963156575853624177875007326650368000000⟩, + ⟨5, 0, 8, 4, 4, 5, -730255562596810533964777595301194060148233994240000000⟩, + ⟨5, 0, 5, 5, 0, 5, 10084660145076755605488052657091431422648549113856000000⟩, + ⟨5, 0, 6, 5, 1, 5, 2757268461387518063002953266514285395872453754880000000⟩, + ⟨5, 0, 7, 5, 2, 5, -3049974199172328211066682834228076340716547080192000000⟩, + ⟨5, 0, 8, 5, 3, 5, 1021506438575186132256541261766698052044927795200000000⟩, + ⟨5, 0, 6, 6, 0, 5, -4044374090997766195260067057901235960614637010944000000⟩, + ⟨5, 0, 7, 6, 1, 5, 8379705348651639201941684612732038100173637812224000000⟩, + ⟨5, 0, 8, 6, 2, 5, -3642841676864655244737983910206976432750653865984000000⟩, + ⟨5, 0, 7, 7, 0, 5, -28404370922493783701122241852518085603989578055680000000⟩, + ⟨5, 0, 8, 7, 1, 5, 6811314175821148657321187160084762220665577144320000000⟩ +] + +def collectedFourData_10_0_36 : List CollectedFourTerm := [ + ⟨5, 1, 4, 0, 4, 6, -77018318878811381784103020861878239306859937792000000⟩, + ⟨5, 1, 5, 0, 5, 6, 405098976660399505155994686407473453746156994560000000⟩, + ⟨5, 1, 6, 0, 6, 6, 234128740443313180006129943565075226205890805760000000⟩, + ⟨5, 1, 7, 0, 7, 6, -1430538393696201561440715987094895702405283840000000⟩, + ⟨5, 1, 8, 0, 8, 6, 48223396636737638020596900553599736272251781120000000⟩, + ⟨5, 1, 4, 1, 3, 6, 45921503848319172681602500462469587287240867840000000⟩, + ⟨5, 1, 5, 1, 4, 6, 216787956457181176318534376548490070795170611200000000⟩, + ⟨5, 1, 6, 1, 5, 6, -147229434329133032061055345372195290500227399680000000⟩, + ⟨5, 1, 7, 1, 6, 6, -99013687548501947271868757264271006061937295360000000⟩, + ⟨5, 1, 8, 1, 7, 6, 40296182623535444745159548236187746961876582400000000⟩, + ⟨5, 1, 4, 2, 2, 6, -30252740042545077900234201345294561173324169216000000⟩, + ⟨5, 1, 5, 2, 3, 6, 319846965041242463173578204583082574785040875520000000⟩, + ⟨5, 1, 6, 2, 4, 6, 52842710766170824060601315015974696549173166080000000⟩, + ⟨5, 1, 7, 2, 5, 6, 10041974379518054891013698029273878188418662400000000⟩, + ⟨5, 1, 8, 2, 6, 6, 2192778056989349995429955949078431957778432000000000⟩, + ⟨5, 1, 4, 3, 1, 6, 67168014781592199360472209671686831665057890304000000⟩, + ⟨5, 1, 5, 3, 2, 6, -868939182440497576707745781611766888293780684800000000⟩, + ⟨5, 1, 6, 3, 3, 6, 80220121883431669021079505672753615240324710400000000⟩, + ⟨5, 1, 7, 3, 4, 6, -40347608101037746455470315081831340504137072640000000⟩, + ⟨5, 1, 8, 3, 5, 6, 34888783865545717158514634961077089971103334400000000⟩, + ⟨5, 1, 4, 4, 0, 6, -112192692468449214472092168465008684517260525568000000⟩, + ⟨5, 1, 5, 4, 1, 6, 240851002383752157797717473371791520728245862400000000⟩, + ⟨5, 1, 6, 4, 2, 6, -243924904432834563420981474505570172607764889600000000⟩, + ⟨5, 1, 7, 4, 3, 6, 143104450216529131398237563749015219986109562880000000⟩, + ⟨5, 1, 8, 4, 4, 6, -49915183123051567277026742452100005247110348800000000⟩, + ⟨5, 1, 5, 5, 0, 6, 2757268461387518063002953266514285395872453754880000000⟩, + ⟨5, 1, 6, 5, 1, 6, 376935328449009790046424749349492332000654131200000000⟩, + ⟨5, 1, 7, 5, 2, 6, -277966652534443819475705125303720677351327006720000000⟩, + ⟨5, 1, 8, 5, 3, 6, 69823064081209289226248389660061984435994624000000000⟩, + ⟨5, 1, 6, 6, 0, 6, -552890477553920478631006721603531006355764674560000000⟩, + ⟨5, 1, 7, 6, 1, 6, 763704376785143678802274220721392767310065827840000000⟩, + ⟨5, 1, 8, 6, 2, 6, -248999280118291132069503814933692866306852782080000000⟩, + ⟨5, 1, 7, 7, 0, 6, -2588699899433537145530938502333594095047199948800000000⟩, + ⟨5, 1, 8, 7, 1, 6, 465573987804683416830434790386327234552424038400000000⟩ +] + +def collectedFourData_10_0_37 : List CollectedFourTerm := [ + ⟨5, 2, 3, 0, 3, 7, 14022224327214846439497205903568886381504626688000000⟩, + ⟨5, 2, 4, 0, 4, 7, 170388838615876348641067700040765087133147437465600000⟩, + ⟨5, 2, 5, 0, 5, 7, -448103419825714057821343909680259247665739464704000000⟩, + ⟨5, 2, 6, 0, 6, 7, -172655565374889401627039102556408332306513657856000000⟩, + ⟨5, 2, 7, 0, 7, 7, 791200648902941925597007357036935939178364928000000⟩, + ⟨5, 2, 8, 0, 8, 7, -21337075819521683846608881602476407533279064883200000⟩, + ⟨5, 2, 3, 1, 2, 7, -1510375068377400629230886162383073878517533900800000⟩, + ⟨5, 2, 4, 1, 3, 7, -101592865465182370273079008942712732275716390912000000⟩, + ⟨5, 2, 5, 1, 4, 7, -239801703441299118800128600349045635737012142080000000⟩, + ⟨5, 2, 6, 1, 5, 7, 108572664662142379082069329767418447921579819008000000⟩, + ⟨5, 2, 7, 1, 6, 7, 54762384696460379495998809003114962932268531712000000⟩, + ⟨5, 2, 8, 1, 7, 7, -17829575762829022406116326513573477896121483264000000⟩, + ⟨5, 2, 3, 2, 1, 7, -11823745116552892881131418525043359631971817881600000⟩, + ⟨5, 2, 4, 2, 2, 7, 66928612774686234856690687815786946225765141708800000⟩, + ⟨5, 2, 5, 2, 3, 7, -353801236521037756511227167021098161233532551168000000⟩, + ⟨5, 2, 6, 2, 4, 7, -38968253474562065157341042830334498515974094848000000⟩, + ⟨5, 2, 7, 2, 5, 7, -5554004478560468841806837749287905136822190080000000⟩, + ⟨5, 2, 8, 2, 6, 7, -970223479067865610413402658410883605615083520000000⟩, + ⟨5, 2, 3, 3, 0, 7, 121968658802825301638772061248054184640998539264000000⟩, + ⟨5, 2, 4, 3, 1, 7, -148596855882790144559161164692107273986204971827200000⟩, + ⟨5, 2, 5, 3, 2, 7, 961183912341910354378085115904566364041715384320000000⟩, + ⟨5, 2, 6, 3, 3, 7, -59157412592752054906320908768570038334773002240000000⟩, + ⟨5, 2, 7, 3, 4, 7, 22315412051780309474972496917436734462270373888000000⟩, + ⟨5, 2, 8, 3, 5, 7, -15437001093011661180121407463398667273302441984000000⟩, + ⟨5, 2, 4, 4, 0, 7, 248205658720841984506785023312384049920294151782400000⟩, + ⟨5, 2, 5, 4, 1, 7, -266419230989780191783845427829103112736640860160000000⟩, + ⟨5, 2, 6, 4, 2, 7, 179879634615228804136212099023314179027904757760000000⟩, + ⟨5, 2, 7, 4, 3, 7, -79148056683518592055790183978498486908219293696000000⟩, + ⟨5, 2, 8, 4, 4, 7, 22085628991768004143775841578289742577053728768000000⟩, + ⟨5, 2, 5, 5, 0, 7, -3049974199172328211066682834228076340716547080192000000⟩, + ⟨5, 2, 6, 5, 1, 7, -277966652534443819475705125303720677351327006720000000⟩, + ⟨5, 2, 7, 5, 2, 7, 153737499690858174292432870643831556779355930624000000⟩, + ⟨5, 2, 8, 5, 3, 7, -30894132644258954584596262201791787997740400640000000⟩, + ⟨5, 2, 6, 6, 0, 7, 407722767447156901372659797635922619069823451136000000⟩, + ⟨5, 2, 7, 6, 1, 7, -422388802107707424836827714856296500441517129728000000⟩, + ⟨5, 2, 8, 6, 2, 7, 110173005002364352296972475469593335968782142668800000⟩, + ⟨5, 2, 7, 7, 0, 7, 1431755379144168669580147098474173717281725480960000000⟩, + ⟨5, 2, 8, 7, 1, 7, -205999331656734958776253737402024749999717351424000000⟩ +] + +def collectedFourData_10_0_38 : List CollectedFourTerm := [ + ⟨5, 3, 2, 0, 2, 8, -7684200979569531098105583043255061547570954240000000⟩, + ⟨5, 3, 3, 0, 3, 8, -14089095347707487631038098421247915661354598400000000⟩, + ⟨5, 3, 4, 0, 4, 8, -85600705616476455266225860449676902360196055040000000⟩, + ⟨5, 3, 5, 0, 5, 8, 150080131374142021178366703501375330742330982400000000⟩, + ⟨5, 3, 6, 0, 6, 8, 43369736963877359486799152336557012025553715200000000⟩, + ⟨5, 3, 7, 0, 7, 8, -158994766043308745225905477394598524438446080000000⟩, + ⟨5, 3, 8, 0, 8, 8, 3573138477027623393499962673696811670002728960000000⟩, + ⟨5, 3, 2, 1, 1, 8, 40515102000994099445315102287051857441576714240000000⟩, + ⟨5, 3, 3, 1, 2, 8, 1517577942885192832692634880249775489747517440000000⟩, + ⟨5, 3, 4, 1, 3, 8, 51038677416098460303865465530263627031694540800000000⟩, + ⟨5, 3, 5, 1, 4, 8, 80315100407426056942239864247011620262248448000000000⟩, + ⟨5, 3, 6, 1, 5, 8, -27272610052506358765795319737706128000784793600000000⟩, + ⟨5, 3, 7, 1, 6, 8, -11004708546258390460300990067257403150507704320000000⟩, + ⟨5, 3, 8, 1, 7, 8, 2985767296611296404300798112054294210622259200000000⟩, + ⟨5, 3, 2, 2, 0, 8, -42826697315537789319428807733332507200050954240000000⟩, + ⟨5, 3, 3, 2, 1, 8, 11880131741352085501267644045828820967494778880000000⟩, + ⟨5, 3, 4, 2, 2, 8, -33623895355967507201557924622620025685981265920000000⟩, + ⟨5, 3, 5, 2, 3, 8, 118496163403670197303787950457229370521865420800000000⟩, + ⟨5, 3, 6, 2, 4, 8, 9788522596788834262243051765570607672564121600000000⟩, + ⟨5, 3, 7, 2, 5, 8, 1116098228555089405907490207387570550918348800000000⟩, + ⟨5, 3, 8, 2, 6, 8, 162475067984770840136558665724246366355456000000000⟩, + ⟨5, 3, 3, 3, 0, 8, -122550318922641948799727202068225671577154355200000000⟩, + ⟨5, 3, 4, 3, 1, 8, 74652752018766818459784295820902179023597076480000000⟩, + ⟨5, 3, 5, 3, 2, 8, -321922577370849555597481612194012292177723392000000000⟩, + ⟨5, 3, 6, 3, 3, 8, 14859882553107455876878812632335740680798208000000000⟩, + ⟨5, 3, 7, 3, 4, 8, -4484366542485086693948474565672050942992711680000000⟩, + ⟨5, 3, 8, 3, 5, 8, 2585103181050323574175206649031771485844275200000000⟩, + ⟨5, 3, 4, 4, 0, 8, -124694667192400950625381383474514610540941148160000000⟩, + ⟨5, 3, 5, 4, 1, 8, 89229921974475493691337118441412419173482496000000000⟩, + ⟨5, 3, 6, 4, 2, 8, -45184367045925810318460165802976269976993792000000000⟩, + ⟨5, 3, 7, 4, 3, 8, 15905101661161928802978102144575739718596034560000000⟩, + ⟨5, 3, 8, 4, 4, 8, -3698492305475254223324790336303042721637990400000000⟩, + ⟨5, 3, 5, 5, 0, 8, 1021506438575186132256541261766698052044927795200000000⟩, + ⟨5, 3, 6, 5, 1, 8, 69823064081209289226248389660061984435994624000000000⟩, + ⟨5, 3, 7, 5, 2, 8, -30894132644258954584596262201791787997740400640000000⟩, + ⟨5, 3, 8, 5, 3, 8, 5173577438601023362750162451839368919252992000000000⟩, + ⟨5, 3, 6, 6, 0, 8, -102416792299584222906306445274117079880119091200000000⟩, + ⟨5, 3, 7, 6, 1, 8, 84880629033289289216998515651816859094828974080000000⟩, + ⟨5, 3, 8, 6, 2, 8, -18449735410488394745197941798726738524126576640000000⟩, + ⟨5, 3, 7, 7, 0, 8, -287716664355518156610612247234098705901132185600000000⟩, + ⟨5, 3, 8, 7, 1, 8, 34496954709755288701692495810464937848025907200000000⟩ +] + +def collectedFourData_10_0_39 : List CollectedFourTerm := [ + ⟨6, 0, 4, 0, 4, 6, 112970825208989558059914145191193782674469263769600000⟩, + ⟨6, 0, 5, 0, 5, 6, -594201046593251883476200718611438784867758768128000000⟩, + ⟨6, 0, 6, 0, 6, 6, -343421115885964067502171608100494668020672626688000000⟩, + ⟨6, 0, 7, 0, 7, 6, 2098320311084624107717167942470376730543521792000000⟩, + ⟨6, 0, 8, 0, 8, 6, -70734300511088209629773191628555749100781305856000000⟩, + ⟨6, 0, 4, 1, 3, 6, -67357873556619876605627245761314433536719060992000000⟩, + ⟨6, 0, 5, 1, 4, 6, -317985573988890697551786766421273375981237698560000000⟩, + ⟨6, 0, 6, 1, 5, 6, 215956813045820986405550826350598398738310365184000000⟩, + ⟨6, 0, 7, 1, 6, 6, 145233733378938000017669167894231177525532295168000000⟩, + ⟨6, 0, 8, 1, 7, 6, -59106626449689136871941704888519490180082565120000000⟩, + ⟨6, 0, 4, 2, 2, 6, 44374858568609983751104585006888452061754346700800000⟩, + ⟨6, 0, 5, 2, 3, 6, -469153002912930365506705502546261794501297176576000000⟩, + ⟨6, 0, 6, 2, 4, 6, -77509931772564347766294561898555488393184149504000000⟩, + ⟨6, 0, 7, 2, 5, 6, -14729614316390716823020330564873774867540869120000000⟩, + ⟨6, 0, 8, 2, 6, 6, -3216376963356469544625650659061511415765401600000000⟩, + ⟨6, 0, 4, 3, 1, 6, -98522353746332313669161834086819879556727649075200000⟩, + ⟨6, 0, 5, 3, 2, 6, 1274563998873961274351118506409556655261079306240000000⟩, + ⟨6, 0, 6, 3, 3, 6, -117667244617438717207375893293726416615526891520000000⟩, + ⟨6, 0, 7, 3, 4, 6, 59182057577176387606920632572336576322686943232000000⟩, + ⟨6, 0, 8, 3, 5, 6, -51175029021739767109502677027838099832145182720000000⟩, + ⟨6, 0, 4, 4, 0, 6, 164564758554681921093627932634032233280719709798400000⟩, + ⟨6, 0, 5, 4, 1, 6, -353281360691843616478859375807098034611940229120000000⟩, + ⟨6, 0, 6, 4, 2, 6, 357790174389048046359484067820599821858221588480000000⟩, + ⟨6, 0, 7, 4, 3, 6, -209906267332039678905200128067821865057956921344000000⟩, + ⟨6, 0, 8, 4, 4, 6, 73215820728856576055209703031950706791090749440000000⟩, + ⟨6, 0, 5, 5, 0, 6, -4044374090997766195260067057901235960614637010944000000⟩, + ⟨6, 0, 6, 5, 1, 6, -552890477553920478631006721603531006355764674560000000⟩, + ⟨6, 0, 7, 5, 2, 6, 407722767447156901372659797635922619069823451136000000⟩, + ⟨6, 0, 8, 5, 3, 6, -102416792299584222906306445274117079880119091200000000⟩, + ⟨6, 0, 6, 6, 0, 6, 810982301467012536682392057839587434330354352128000000⟩, + ⟨6, 0, 7, 6, 1, 6, -1120205100774672550459838742643740921616234708992000000⟩, + ⟨6, 0, 8, 6, 2, 6, 365233292038869535413620225243865675111862370304000000⟩, + ⟨6, 0, 7, 7, 0, 6, 3797116947172040043656093365852673189642439229440000000⟩, + ⟨6, 0, 8, 7, 1, 6, -682906071747626296868239647217622574027421777920000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1003.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1003.lean new file mode 100644 index 0000000000000000000000000000000000000000..747114c9505102d838c74d6939f3ec9fa065d920 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1003.lean @@ -0,0 +1,627 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PartsTrace +import OAI.Analysis.LaughlinFock.Sparse1001 +import OAI.Analysis.LaughlinFock.Sparse1002 + +namespace OAI + +/-! Sparse1003. -/ +namespace LaughlinFock +def collectedFourData_10_0_40 : List CollectedFourTerm := [ + ⟨6, 1, 3, 0, 3, 7, -38525607274527745191004517029859350772906459136000000⟩, + ⟨6, 1, 4, 0, 4, 7, -468137816604305855231795295708774047830720590643200000⟩, + ⟨6, 1, 5, 0, 5, 7, 1231149635587610837645205042364061740265518399488000000⟩, + ⟨6, 1, 6, 0, 6, 7, 474365574974061250289089532650996556945090936832000000⟩, + ⟨6, 1, 7, 0, 7, 7, -2173798162380462615101108622800722899203260416000000⟩, + ⟨6, 1, 8, 0, 8, 7, 58622924881775050129800510944364672122932848230400000⟩, + ⟨6, 1, 3, 1, 2, 7, 4149706591743229964906321552646151397806021017600000⟩, + ⟨6, 1, 4, 1, 3, 7, 279123108108408730791247710596940886000810328064000000⟩, + ⟨6, 1, 5, 1, 4, 7, 658847415000473721757844169969013171162982645760000000⟩, + ⟨6, 1, 6, 1, 5, 7, -298299880383778232393053210351049965160078770176000000⟩, + ⟨6, 1, 7, 1, 6, 7, -150457878650375946450440248312259384659792625664000000⟩, + ⟨6, 1, 8, 1, 7, 7, 48986182055085079120255818075070228903187447808000000⟩, + ⟨6, 1, 3, 2, 1, 7, 32485356833890328986207051421868731442088063795200000⟩, + ⟨6, 1, 4, 2, 2, 7, -183884196331256976141048119312338736224323344793600000⟩, + ⟨6, 1, 5, 2, 3, 7, 972057440629972633536294683645898892010581917696000000⟩, + ⟨6, 1, 6, 2, 4, 7, 107064014560193468329515097175255599203961798656000000⟩, + ⟨6, 1, 7, 2, 5, 7, 15259447456328690687081659235446606119315701760000000⟩, + ⟨6, 1, 8, 2, 6, 7, 2665657591181815489228883866241953609222717440000000⟩, + ⟨6, 1, 3, 3, 0, 7, -335104940499253706054206042786986520085746679808000000⟩, + ⟨6, 1, 4, 3, 1, 7, 408265049708205018964927805518952007326203536998400000⟩, + ⟨6, 1, 5, 3, 2, 7, -2640821674319457560694823905388615927665304535040000000⟩, + ⟨6, 1, 6, 3, 3, 7, 162533075476638546977855143359913813641296609280000000⟩, + ⟨6, 1, 7, 3, 4, 7, -61310871999643140797043574733463467512389697536000000⟩, + ⟨6, 1, 8, 3, 5, 7, 42412660625573416451667162859662653037528219648000000⟩, + ⟨6, 1, 4, 4, 0, 7, -681937009996039631746379597869927167106799684812800000⟩, + ⟨6, 1, 5, 4, 1, 7, 731978210017171730844402798828458280253673963520000000⟩, + ⟨6, 1, 6, 4, 2, 7, -494213471283718367749612545606808005967054110720000000⟩, + ⟨6, 1, 7, 4, 3, 7, 217456722783506385254544038547053523537663885312000000⟩, + ⟨6, 1, 8, 4, 4, 7, -60679550483042383128824379684795106817942224896000000⟩, + ⟨6, 1, 5, 5, 0, 7, 8379705348651639201941684612732038100173637812224000000⟩, + ⟨6, 1, 6, 5, 1, 7, 763704376785143678802274220721392767310065827840000000⟩, + ⟨6, 1, 7, 5, 2, 7, -422388802107707424836827714856296500441517129728000000⟩, + ⟨6, 1, 8, 5, 3, 7, 84880629033289289216998515651816859094828974080000000⟩, + ⟨6, 1, 6, 6, 0, 7, -1120205100774672550459838742643740921616234708992000000⟩, + ⟨6, 1, 7, 6, 1, 7, 1160499556092319543387053704732215860316147286016000000⟩, + ⟨6, 1, 8, 6, 2, 7, -302696763646679351095667253320140026289107605913600000⟩, + ⟨6, 1, 7, 7, 0, 7, -3933701541419910892378298997357959930673490821120000000⟩, + ⟨6, 1, 8, 7, 1, 7, 565976493103137610442123512144438603336623587328000000⟩ +] + +def collectedFourData_10_0_41 : List CollectedFourTerm := [ + ⟨6, 2, 2, 0, 2, 8, 27402986926665144561661120111883052421816831180800000⟩, + ⟨6, 2, 3, 0, 3, 8, 50243778975624265509197954060299036113216995328000000⟩, + ⟨6, 2, 4, 0, 4, 8, 305264662280218347649374021700305135615299341516800000⟩, + ⟨6, 2, 5, 0, 5, 8, -535207744947372718805147340682820628096491716608000000⟩, + ⟨6, 2, 6, 0, 6, 8, -154662838490803620705840169746663742279079952384000000⟩, + ⟨6, 2, 7, 0, 7, 8, 566998638749431574676400339892792403724704153600000⟩, + ⟨6, 2, 8, 0, 8, 8, -12742335505472079413466754202644217109752787763200000⟩, + ⟨6, 2, 2, 1, 1, 8, -144482791824107325027745892586675137061868850380800000⟩, + ⟨6, 2, 3, 1, 2, 8, -5411905367864022160145668291136167136004459724800000⟩, + ⟨6, 2, 4, 1, 3, 8, -182011404140287845207528669396954621813914075136000000⟩, + ⟨6, 2, 5, 1, 4, 8, -286415419420977663579925509712406266203246428160000000⟩, + ⟨6, 2, 6, 1, 5, 8, 97258124652374038916548668690368411959465869312000000⟩, + ⟨6, 2, 7, 1, 6, 8, 39244403579065725758492891721712966308498663014400000⟩, + ⟨6, 2, 8, 1, 7, 8, -10647683788157136813813424959298252279186980864000000⟩, + ⟨6, 2, 2, 2, 0, 8, 152726279514317335831257094454548223896658431180800000⟩, + ⟨6, 2, 3, 2, 1, 8, -42366290999011349171834536702384017208099051929600000⟩, + ⟨6, 2, 4, 2, 2, 8, 119907738919492839678993346702053695641623094886400000⟩, + ⟨6, 2, 5, 2, 3, 8, -422574686066144045190821041979964696175350644736000000⟩, + ⟨6, 2, 6, 2, 4, 8, -34907306233184609810305794034566957235880067072000000⟩, + ⟨6, 2, 7, 2, 5, 8, -3980169863761499491447938773268090638875754496000000⟩, + ⟨6, 2, 8, 2, 6, 8, -579409905562507014624959026979737454531051520000000⟩, + ⟨6, 2, 3, 3, 0, 8, 437032398843364227482985865566715692573926621184000000⟩, + ⟨6, 2, 4, 3, 1, 8, -266222655165956197952426364614676540524018112921600000⟩, + ⟨6, 2, 5, 3, 2, 8, 1148023093428502063664457851884692876145868144640000000⟩, + ⟨6, 2, 6, 3, 3, 8, -52992519120367244174906749431440611281846927360000000⟩, + ⟨6, 2, 7, 3, 4, 8, 15991908340869218840390844071711953446434871705600000⟩, + ⟨6, 2, 8, 3, 5, 8, -9218856828803419239721410648001378469579587584000000⟩, + ⟨6, 2, 4, 4, 0, 8, 444679459059339313991334919126472664450426155827200000⟩, + ⟨6, 2, 5, 4, 1, 8, -318206979728278927161617031831523996167642808320000000⟩, + ⟨6, 2, 6, 4, 2, 8, 161134075324316617002129497355597459042745712640000000⟩, + ⟨6, 2, 7, 4, 3, 8, -56719923652038129288956844649082140894717752115200000⟩, + ⟨6, 2, 8, 4, 4, 8, 13189365630177418066586581551048296407360339968000000⟩, + ⟨6, 2, 5, 5, 0, 8, -3642841676864655244737983910206976432750653865984000000⟩, + ⟨6, 2, 6, 5, 1, 8, -248999280118291132069503814933692866306852782080000000⟩, + ⟨6, 2, 7, 5, 2, 8, 110173005002364352296972475469593335968782142668800000⟩, + ⟨6, 2, 8, 5, 3, 8, -18449735410488394745197941798726738524126576640000000⟩, + ⟨6, 2, 6, 6, 0, 8, 365233292038869535413620225243865675111862370304000000⟩, + ⟨6, 2, 7, 6, 1, 8, -302696763646679351095667253320140026289107605913600000⟩, + ⟨6, 2, 8, 6, 2, 8, 65794460555919365716017671005176315434897296588800000⟩, + ⟨6, 2, 7, 7, 0, 8, 1026039794232405105530539570031937302723876093952000000⟩, + ⟨6, 2, 8, 7, 1, 8, -123021196534885603962041103402119554989790593024000000⟩ +] + +def collectedFourData_10_0_42 : List CollectedFourTerm := [ + ⟨7, 0, 3, 0, 3, 7, 130588796802514265970903813995455142486888939520000000⟩, + ⟨7, 0, 4, 0, 4, 7, 1586829086754785593011016525084370693074949505024000000⟩, + ⟨7, 0, 5, 0, 5, 7, -4173181449148508014446273369099980448142102364160000000⟩, + ⟨7, 0, 6, 0, 6, 7, -1607939084229656392165997505332033657524967178240000000⟩, + ⟨7, 0, 7, 0, 7, 7, 7368441579491258660540834917997626078129029120000000⟩, + ⟨7, 0, 8, 0, 8, 7, -198711915708511627287605934837563257151582896128000000⟩, + ⟨7, 0, 3, 1, 2, 7, -14066103800458612417791517456519178996240351232000000⟩, + ⟨7, 0, 4, 1, 3, 7, -946133063858421054270345664228790982408646164480000000⟩, + ⟨7, 0, 5, 1, 4, 7, -2233270213971294888258521305706963377337873203200000000⟩, + ⟨7, 0, 6, 1, 5, 7, 1011135844999578675946049119779193174431702712320000000⟩, + ⟨7, 0, 7, 1, 6, 7, 510001392123471581253457063077898396820286996480000000⟩, + ⟨7, 0, 8, 1, 7, 7, -166046612294468819783349687747983526848951746560000000⟩, + ⟨7, 0, 3, 2, 1, 7, -110114387877356941725709279837822597523690225664000000⟩, + ⟨7, 0, 4, 2, 2, 7, 623305319466648574921887379396415873254321815552000000⟩, + ⟨7, 0, 5, 2, 3, 7, -3294946415516447572085206481783708622797899038720000000⟩, + ⟨7, 0, 6, 2, 4, 7, -362910848948685910273947203148257875661338705920000000⟩, + ⟨7, 0, 7, 2, 5, 7, -51724373064216095618740734039247527013987123200000000⟩, + ⟨7, 0, 8, 2, 6, 7, -9035678919721555246320793739633831560662220800000000⟩, + ⟨7, 0, 3, 3, 0, 7, 1135892568040307586505083267333366291349697986560000000⟩, + ⟨7, 0, 4, 3, 1, 7, -1383880628746473554917974028076162074301209509888000000⟩, + ⟨7, 0, 5, 3, 2, 7, 8951493549782247673274175160628261412345269452800000000⟩, + ⟨7, 0, 6, 3, 3, 7, -550932231018716528062433564458504753071626649600000000⟩, + ⟨7, 0, 7, 3, 4, 7, 207823148595507897974305639393683341724635627520000000⟩, + ⟨7, 0, 8, 3, 5, 7, -143764594827010367874992938479156367262597775360000000⟩, + ⟨7, 0, 4, 4, 0, 7, 2311536142594876029839688739922651628483322576896000000⟩, + ⟨7, 0, 5, 4, 1, 7, -2481158909466464492004838765370189588008953446400000000⟩, + ⟨7, 0, 6, 4, 2, 7, 1675216749177793365584312416655922486648923750400000000⟩, + ⟨7, 0, 7, 4, 3, 7, -737104845163380778443791042781854777258897571840000000⟩, + ⟨7, 0, 8, 4, 4, 7, 205683181880357861714706488821683845824480542720000000⟩, + ⟨7, 0, 5, 5, 0, 7, -28404370922493783701122241852518085603989578055680000000⟩, + ⟨7, 0, 6, 5, 1, 7, -2588699899433537145530938502333594095047199948800000000⟩, + ⟨7, 0, 7, 5, 2, 7, 1431755379144168669580147098474173717281725480960000000⟩, + ⟨7, 0, 8, 5, 3, 7, -287716664355518156610612247234098705901132185600000000⟩, + ⟨7, 0, 6, 6, 0, 7, 3797116947172040043656093365852673189642439229440000000⟩, + ⟨7, 0, 7, 6, 1, 7, -3933701541419910892378298997357959930673490821120000000⟩, + ⟨7, 0, 8, 6, 2, 7, 1026039794232405105530539570031937302723876093952000000⟩, + ⟨7, 0, 7, 7, 0, 7, 13333919634639137731655599048570639248207013478400000000⟩, + ⟨7, 0, 8, 7, 1, 7, -1918469155493701703732485166231528543230057512960000000⟩ +] + +def collectedFourData_10_0_43 : List CollectedFourTerm := [ + ⟨7, 1, 2, 0, 2, 8, -51237569422474422526596408340143451228480733184000000⟩, + ⟨7, 1, 3, 0, 3, 8, -93944836020994357263342490891120735403051581440000000⟩, + ⟨7, 1, 4, 0, 4, 8, -570777899784020318858755036717383333501902782464000000⟩, + ⟨7, 1, 5, 0, 5, 8, 1000720982007352796121140406894969777509200035840000000⟩, + ⟨7, 1, 6, 0, 6, 8, 289185552854397970284232306778580930393349816320000000⟩, + ⟨7, 1, 7, 0, 7, 8, -1060162973953145871770345653473739312912662528000000⟩, + ⟨7, 1, 8, 0, 8, 8, 23825369906328694703282142640793362639865511936000000⟩, + ⟨7, 1, 2, 1, 1, 8, 270151100544335217009799667402102850397283549184000000⟩, + ⟨7, 1, 3, 1, 2, 8, 10119074892670485430243329334080476261388386304000000⟩, + ⟨7, 1, 4, 1, 3, 8, 340321366436347439652933759187411659839011553280000000⟩, + ⟨7, 1, 5, 1, 4, 8, 535533953854110031725332292424888507156974796800000000⟩, + ⟨7, 1, 6, 1, 5, 8, -181851340772147491370934750117206657517496565760000000⟩, + ⟨7, 1, 7, 1, 6, 8, -73378418863869824053418514419628913156908122112000000⟩, + ⟨7, 1, 8, 1, 7, 8, 19908831060798882537063982008391579680343326720000000⟩, + ⟨7, 1, 2, 2, 0, 8, -285564612726083741074268783644334054525248733184000000⟩, + ⟨7, 1, 3, 2, 1, 8, 79215662951044951790951932505833458588092203008000000⟩, + ⟨7, 1, 4, 2, 2, 8, -224201146890344883601711324840962382820039196672000000⟩, + ⟨7, 1, 5, 2, 3, 8, 790121889684429843660130369932776530808961761280000000⟩, + ⟨7, 1, 6, 2, 4, 8, 65268999005869804792371487387610603604997570560000000⟩, + ⟨7, 1, 7, 2, 5, 8, 7442043827320051012293959270617887161796526080000000⟩, + ⟨7, 1, 8, 2, 6, 8, 1083369318088463661347922091170549275924889600000000⟩, + ⟨7, 1, 3, 3, 0, 8, -817154638490078560012185014055785639440621240320000000⟩, + ⟨7, 1, 4, 3, 1, 8, 497777917874632473315159145748077066793326215168000000⟩, + ⟨7, 1, 5, 3, 2, 8, -2146551144426836839523963551956443175643722547200000000⟩, + ⟨7, 1, 6, 3, 3, 8, 99084376625364173926638306701629412608888012800000000⟩, + ⟨7, 1, 7, 3, 4, 8, -29901357687975624889920390540002077645354303488000000⟩, + ⟨7, 1, 8, 3, 5, 8, 17237238335578452718715905841305842004336312320000000⟩, + ⟨7, 1, 4, 4, 0, 8, -831452962236407062484205918833680277799652294656000000⟩, + ⟨7, 1, 5, 4, 1, 8, 594977192018379936176411065108478092046342553600000000⟩, + ⟨7, 1, 6, 4, 2, 8, -301285345019162060185673790790765000992699187200000000⟩, + ⟨7, 1, 7, 4, 3, 8, 106053804774501154656795224635543932091704016896000000⟩, + ⟨7, 1, 8, 4, 4, 8, -24661218097251238802003073771001118500470128640000000⟩, + ⟨7, 1, 5, 5, 0, 8, 6811314175821148657321187160084762220665577144320000000⟩, + ⟨7, 1, 6, 5, 1, 8, 465573987804683416830434790386327234552424038400000000⟩, + ⟨7, 1, 7, 5, 2, 8, -205999331656734958776253737402024749999717351424000000⟩, + ⟨7, 1, 8, 5, 3, 8, 34496954709755288701692495810464937848025907200000000⟩, + ⟨7, 1, 6, 6, 0, 8, -682906071747626296868239647217622574027421777920000000⟩, + ⟨7, 1, 7, 6, 1, 8, 565976493103137610442123512144438603336623587328000000⟩, + ⟨7, 1, 8, 6, 2, 8, -123021196534885603962041103402119554989790593024000000⟩, + ⟨7, 1, 7, 7, 0, 8, -1918469155493701703732485166231528543230057512960000000⟩, + ⟨7, 1, 8, 7, 1, 8, 230022629093709647669150557971612106499838443520000000⟩ +] + +def collectedFourData_10_0 : List (List CollectedFourTerm) := [ + collectedFourData_10_0_0, + collectedFourData_10_0_1, + collectedFourData_10_0_2, + collectedFourData_10_0_3, + collectedFourData_10_0_4, + collectedFourData_10_0_5, + collectedFourData_10_0_6, + collectedFourData_10_0_7, + collectedFourData_10_0_8, + collectedFourData_10_0_9, + collectedFourData_10_0_10, + collectedFourData_10_0_11, + collectedFourData_10_0_12, + collectedFourData_10_0_13, + collectedFourData_10_0_14, + collectedFourData_10_0_15, + collectedFourData_10_0_16, + collectedFourData_10_0_17, + collectedFourData_10_0_18, + collectedFourData_10_0_19, + collectedFourData_10_0_20, + collectedFourData_10_0_21, + collectedFourData_10_0_22, + collectedFourData_10_0_23, + collectedFourData_10_0_24, + collectedFourData_10_0_25, + collectedFourData_10_0_26, + collectedFourData_10_0_27, + collectedFourData_10_0_28, + collectedFourData_10_0_29, + collectedFourData_10_0_30, + collectedFourData_10_0_31, + collectedFourData_10_0_32, + collectedFourData_10_0_33, + collectedFourData_10_0_34, + collectedFourData_10_0_35, + collectedFourData_10_0_36, + collectedFourData_10_0_37, + collectedFourData_10_0_38, + collectedFourData_10_0_39, + collectedFourData_10_0_40, + collectedFourData_10_0_41, + collectedFourData_10_0_42, + collectedFourData_10_0_43 +] + +theorem collectedFourChecked_10_0 : collectNumericRowParts 10 0 = collectedFourData_10_0 := by + decide +kernel + +def collectedFourData_10_1_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_10_1_1 : List CollectedFourTerm := [ + ⟨0, 2, 8, 1, 8, 1, -71821454090837103110257157637922310291793641472000000⟩, + ⟨0, 2, 8, 2, 7, 1, -30838505014981829971544030689925013690944323584000000⟩, + ⟨0, 2, 8, 3, 6, 1, 1655994705926514365409294010316987760409313280000000⟩, + ⟨0, 2, 8, 4, 5, 1, 22539964173521803300085276851997384862288838656000000⟩, + ⟨0, 2, 8, 5, 4, 1, 11283557899503119482351002190422054580852359168000000⟩, + ⟨0, 2, 8, 6, 3, 1, -59908931096597619089274501323259834772777598976000000⟩, + ⟨0, 2, 8, 7, 2, 1, 23563777749833530675844192329001860227183673344000000⟩ +] + +def collectedFourData_10_1_2 : List CollectedFourTerm := [ + ⟨0, 3, 7, 0, 8, 2, -59758950892437995811592191312328261029832163328000000⟩, + ⟨0, 3, 7, 1, 7, 2, 4727508290973887038058176422234107098158858240000000⟩, + ⟨0, 3, 8, 1, 8, 2, 68319216536856617967971449697165181962838815539200000⟩, + ⟨0, 3, 7, 2, 6, 2, 2965079809650524249543286340392774066089282764800000⟩, + ⟨0, 3, 8, 2, 7, 2, 29334723565006092389153157449310880485450606182400000⟩, + ⟨0, 3, 7, 3, 5, 2, 7111703583231803019824149737547895111802893107200000⟩, + ⟨0, 3, 8, 3, 6, 2, -1575243251897840978792958784844377255374225408000000⟩, + ⟨0, 3, 7, 4, 4, 2, -3676785488009098727411419561167070960119132979200000⟩, + ⟨0, 3, 8, 4, 5, 2, -21440845393581174392492549547360659013853878681600000⟩, + ⟨0, 3, 7, 5, 3, 2, -4194050760439917620923952247766944791285622374400000⟩, + ⟨0, 3, 8, 5, 4, 2, -10733336510666122824875037160044071881177615564800000⟩, + ⟨0, 3, 7, 6, 2, 2, -29683379782966650120397092102948926654612137574400000⟩, + ⟨0, 3, 8, 6, 3, 2, 56987585226323719135975243036695141167518030233600000⟩, + ⟨0, 3, 7, 7, 1, 2, 153568030105498116088661307828197845221917274931200000⟩, + ⟨0, 3, 8, 7, 2, 2, -22414734634600288298506910994836410911150204518400000⟩ +] + +def collectedFourData_10_1_3 : List CollectedFourTerm := [ + ⟨0, 4, 6, 0, 7, 3, -7457731428010067554426376679105246454379603558400000⟩, + ⟨0, 4, 7, 0, 8, 3, -21875770995296472956431072458786893832382316544000000⟩, + ⟨0, 4, 6, 1, 6, 3, 2748213688397789966811642217453542273563649638400000⟩, + ⟨0, 4, 7, 1, 7, 3, 1730584074975734568199980062829994736898539520000000⟩, + ⟨0, 4, 8, 1, 8, 3, 12504700243386203280518294734779027073364970700800000⟩, + ⟨0, 4, 6, 2, 5, 3, 49374508204002039818412679586577934515280281600000⟩, + ⟨0, 4, 7, 2, 6, 3, 1085417430025533741321892308754157746950399590400000⟩, + ⟨0, 4, 8, 2, 7, 3, 5369234945853145653235577657752586019854195097600000⟩, + ⟨0, 4, 6, 3, 4, 3, -799507214512309626441208002278672670749255270400000⟩, + ⟨0, 4, 7, 3, 5, 3, 2603358938700760957428199949953612411511085465600000⟩, + ⟨0, 4, 8, 3, 6, 3, -288322168694262270805220373604278810225672192000000⟩, + ⟨0, 4, 6, 4, 3, 3, 1009465616340567478172026025209479033206813491200000⟩, + ⟨0, 4, 7, 4, 4, 3, -1345949286815450166232319209536136759006042521600000⟩, + ⟨0, 4, 8, 4, 5, 3, -3924391382135956915810490276248628149940020838400000⟩, + ⟨0, 4, 6, 5, 2, 3, -2191283884392581917634213888076841152196431052800000⟩, + ⟨0, 4, 7, 5, 3, 3, -1535302956425271403941765039302245699101602611200000⟩, + ⟨0, 4, 8, 5, 4, 3, -1964559350660376418232390203747541779119026995200000⟩, + ⟨0, 4, 6, 6, 1, 3, 4103842100877123980339123731964914523522570649600000⟩, + ⟨0, 4, 7, 6, 2, 3, -10866101375631095010260707340823075604315452211200000⟩, + ⟨0, 4, 8, 6, 3, 3, 10430632945932047674861163206909398155585283686400000⟩, + ⟨0, 4, 6, 7, 0, 3, 1217744959141844593939359486117734847282885427200000⟩, + ⟨0, 4, 7, 7, 1, 3, 56216165254195888552096514251328943293986347417600000⟩, + ⟨0, 4, 8, 7, 2, 3, -4102645666165005586184404726923794815638935961600000⟩ +] + +def collectedFourData_10_1_4 : List CollectedFourTerm := [ + ⟨0, 5, 5, 0, 6, 4, 319049947695547491666948391203688417990899086131200000⟩, + ⟨0, 5, 6, 0, 7, 4, 439331265146748978460788413776534373382879392563200000⟩, + ⟨0, 5, 7, 0, 8, 4, 644345417919438489831634242030076740619632377856000000⟩, + ⟨0, 5, 5, 1, 5, 4, -104579090057856694817286802409440120427205623808000000⟩, + ⟨0, 5, 6, 1, 6, 4, -161895907391180532175759870353928557459106116403200000⟩, + ⟨0, 5, 7, 1, 7, 4, -50973925411576204575404918300461660474158612480000000⟩, + ⟨0, 5, 8, 1, 8, 4, -245548566220116427286835539525708288497279618252800000⟩, + ⟨0, 5, 5, 2, 4, 4, 78559755044625612243191090080679173082212781260800000⟩, + ⟨0, 5, 6, 2, 5, 4, -2908627826659443774219239867363299503056407756800000⟩, + ⟨0, 5, 7, 2, 6, 4, -31970701636857529805466873684572480474321623449600000⟩, + ⟨0, 5, 8, 2, 7, 4, -105432990554931274129765703201553693900770220441600000⟩, + ⟨0, 5, 5, 3, 3, 4, -23458380130554369869731194180832709004455470694400000⟩, + ⟨0, 5, 6, 3, 4, 4, 47098574068571572835133363753081387082474271539200000⟩, + ⟨0, 5, 7, 3, 5, 4, -76681292911327340342169649958238849558238357094400000⟩, + ⟨0, 5, 8, 3, 6, 4, 5661638724190575165977373385211134326626844672000000⟩, + ⟨0, 5, 5, 4, 2, 4, -48448237362729580644532747956432040299790860288000000⟩, + ⟨0, 5, 6, 4, 3, 4, -59467119542997511726680745659541089976411855257600000⟩, + ⟨0, 5, 7, 4, 4, 4, 39644602967270999557060538547766780028632065638400000⟩, + ⟨0, 5, 8, 4, 5, 4, 77061317617728032919871821943916188002003871334400000⟩, + ⟨0, 5, 5, 5, 1, 4, -16356867533270341127274107657095141721663707545600000⟩, + ⟨0, 5, 6, 5, 2, 4, 129087448444459569928292150459004222321956644454400000⟩, + ⟨0, 5, 7, 5, 3, 4, 45221968419009950105208187102570692495329250508800000⟩, + ⟨0, 5, 8, 5, 4, 4, 38577072814209943625263297217646736710034469683200000⟩, + ⟨0, 5, 5, 6, 0, 4, 868530401107110443506212556194925609449052490956800000⟩, + ⟨0, 5, 6, 6, 1, 4, -241755305825208008444395200505493963320601660620800000⟩, + ⟨0, 5, 7, 6, 2, 4, 320058325420457472372299847721612768389836360908800000⟩, + ⟨0, 5, 8, 6, 3, 4, -204821140434499330369067339263266641738436339302400000⟩, + ⟨0, 5, 6, 7, 0, 4, -71736752481661037768421193516365164374461618585600000⟩, + ⟨0, 5, 7, 7, 1, 4, -1655833227653156693774873508286222275092689610342400000⟩, + ⟨0, 5, 8, 7, 2, 4, 80561608149608356044014789928465773174399277465600000⟩ +] + +def collectedFourData_10_1_5 : List CollectedFourTerm := [ + ⟨0, 6, 4, 0, 5, 5, 319049947695547491666948391203688417990899086131200000⟩, + ⟨0, 6, 5, 0, 6, 5, 556545034187044471198146433947542465747833847808000000⟩, + ⟨0, 6, 6, 0, 7, 5, 383180808752013377724146650532194672934695993344000000⟩, + ⟨0, 6, 7, 0, 8, 5, 374661548799708414800720917899349659263623495680000000⟩, + ⟨0, 6, 4, 1, 4, 5, 98182255570566771770447077405437769477153986969600000⟩, + ⟨0, 6, 5, 1, 5, 5, -182425898113733210977064412650571694036714782720000000⟩, + ⟨0, 6, 6, 1, 6, 5, -141204165624479399366522774314055978850812166144000000⟩, + ⟨0, 6, 7, 1, 7, 5, -29639335226078607141499087487839807151171174400000000⟩, + ⟨0, 6, 8, 1, 8, 5, -107082634058257828318312844947588597695998066688000000⟩, + ⟨0, 6, 4, 2, 3, 5, 154157029435069959229951926148407651263125546598400000⟩, + ⟨0, 6, 5, 2, 4, 5, 137038234523575709722952627699937844348921577472000000⟩, + ⟨0, 6, 6, 2, 5, 5, -2536879233044550577971803936855234042507821056000000⟩, + ⟨0, 6, 7, 2, 6, 5, -18589707101752107091347780705731467175408959488000000⟩, + ⟨0, 6, 8, 2, 7, 5, -45978856724990028704092526820823344601613991936000000⟩, + ⟨0, 6, 4, 3, 2, 5, -411262730782341956940361388539909446245198227046400000⟩, + ⟨0, 6, 5, 3, 3, 5, -40920379602100354319703144579942504633515114496000000⟩, + ⟨0, 6, 6, 3, 4, 5, 41078955982414694819044158893637489601768587264000000⟩, + ⟨0, 6, 7, 3, 5, 5, -44587159568680307082246158099986293889362296832000000⟩, + ⟨0, 6, 8, 3, 6, 5, 2469015384635112217107949484706367055981445120000000⟩, + ⟨0, 6, 4, 4, 1, 5, 5279867205243499130732348572950362653993205760000000⟩, + ⟨0, 6, 5, 4, 2, 5, -84512240525650683834280962844770687990544465920000000⟩, + ⟨0, 6, 6, 4, 3, 5, -51866690965021719547357579618003255887598190592000000⟩, + ⟨0, 6, 7, 4, 4, 5, 23051779272719767791060788040870536743225393152000000⟩, + ⟨0, 6, 8, 4, 5, 5, 33606096755250828545395103682743613849310593024000000⟩, + ⟨0, 6, 4, 5, 0, 5, 1694671685459190136644044124846551090557848492441600000⟩, + ⟨0, 6, 5, 5, 1, 5, -28532627778969987071522002590556110832590127104000000⟩, + ⟨0, 6, 6, 5, 2, 5, 112588920522557255701519436579138277248700776448000000⟩, + ⟨0, 6, 7, 5, 3, 5, 26294798188129767788560443754516487386655883264000000⟩, + ⟨0, 6, 8, 5, 4, 5, 16823289318251313011014437291404929038519631872000000⟩, + ⟨0, 6, 5, 6, 0, 5, 1515048929698946937022109148483524419512919130112000000⟩, + ⟨0, 6, 6, 6, 1, 5, -210856820252140517672128829942750796220974759936000000⟩, + ⟨0, 6, 7, 6, 2, 5, 186101343430771923024810084232285619703213195264000000⟩, + ⟨0, 6, 8, 6, 3, 5, -89321585404336587914553346671493849940496482304000000⟩, + ⟨0, 6, 6, 7, 0, 5, -62568155316658527132189283533488353802402660352000000⟩, + ⟨0, 6, 7, 7, 1, 5, -962801976042167868446248511000296563924661174272000000⟩, + ⟨0, 6, 8, 7, 2, 5, 35132557837442308897882491248078872836336254976000000⟩ +] + +def collectedFourData_10_1_6 : List CollectedFourTerm := [ + ⟨0, 7, 3, 0, 4, 6, -7457731428010067554426376679105246454379603558400000⟩, + ⟨0, 7, 4, 0, 5, 6, 439331265146748978460788413776534373382879392563200000⟩, + ⟨0, 7, 5, 0, 6, 6, 383180808752013377724146650532194672934695993344000000⟩, + ⟨0, 7, 6, 0, 7, 6, 175879785913246857032046102282667363523497033728000000⟩, + ⟨0, 7, 7, 0, 8, 6, 128977087619746235183318031551692119789923205120000000⟩, + ⟨0, 7, 3, 1, 3, 6, 35798397629754409893451483455205999395689044377600000⟩, + ⟨0, 7, 4, 1, 4, 6, 135196808105856671894156955844452918157750409625600000⟩, + ⟨0, 7, 5, 1, 5, 6, -125600084238717476660877005192886311776640040960000000⟩, + ⟨0, 7, 6, 1, 6, 6, -64812636366047117790574479616380853173331427328000000⟩, + ⟨0, 7, 7, 1, 7, 6, -10203329241263059502989456686536183271496089600000000⟩, + ⟨0, 7, 8, 1, 8, 6, -29490522995448399860115940807419808464611416473600000⟩, + ⟨0, 7, 3, 2, 2, 6, -27937555473975275414139855678259908537976514150400000⟩, + ⟨0, 7, 4, 2, 3, 6, 212273981745332405885081892997584833441266296422400000⟩, + ⟨0, 7, 5, 2, 4, 6, 94350714334186371794015708391828220245700509696000000⟩, + ⟨0, 7, 6, 2, 5, 6, -1164426208736355477857756215553629625172099072000000⟩, + ⟨0, 7, 7, 2, 6, 6, -6399499199662643249808074256751586264368545792000000⟩, + ⟨0, 7, 8, 2, 7, 6, -12662562361092577919451118282809301780491612979200000⟩, + ⟨0, 7, 3, 3, 1, 6, -625946527720038255238678570641545376795564441600000⟩, + ⟨0, 7, 4, 3, 2, 6, -566308119237577950076145780494483468484839106150400000⟩, + ⟨0, 7, 5, 3, 3, 6, -28173648469033828389217107891596087899642134528000000⟩, + ⟨0, 7, 6, 3, 4, 6, 18855218786290076875421962075625048006373408768000000⟩, + ⟨0, 7, 7, 3, 5, 6, -15349111764547753601112738490842422850342617088000000⟩, + ⟨0, 7, 8, 3, 6, 6, 679966043206261695698753718653830407508721664000000⟩, + ⟨0, 7, 3, 4, 0, 6, 120021089212769463978440105534641714720178543001600000⟩, + ⟨0, 7, 4, 4, 1, 6, 7270368654941571087208264757467983828599439360000000⟩, + ⟨0, 7, 5, 4, 2, 6, -58186609680861918490377965784233528321963458560000000⟩, + ⟨0, 7, 6, 4, 3, 6, -23806783363360764908012059670072607024196091904000000⟩, + ⟨0, 7, 7, 4, 4, 6, 7935565751472550174525413061295282757952339968000000⟩, + ⟨0, 7, 8, 4, 5, 6, 9255108242937000487029933592935061739927293132800000⟩, + ⟨0, 7, 4, 5, 0, 6, 2333560186919753704297025102952715332114026437017600000⟩, + ⟨0, 7, 5, 5, 1, 6, -19644691294633763545842344487703716395086774272000000⟩, + ⟨0, 7, 6, 5, 2, 6, 51678254195988325944594998051757923813950488576000000⟩, + ⟨0, 7, 7, 5, 3, 6, 9051973709922903705541908983738433464042520576000000⟩, + ⟨0, 7, 8, 5, 4, 6, 4633128470009953034352241790253545331913811558400000⟩, + ⟨0, 7, 5, 6, 0, 6, 1043109970478699472660846173627852112583999881216000000⟩, + ⟨0, 7, 6, 6, 1, 6, -96783167521041950782306537291727655343994437632000000⟩, + ⟨0, 7, 7, 6, 2, 6, 64065312692802908318824670970960022590587928576000000⟩, + ⟨0, 7, 8, 6, 3, 6, -24599135905859432526026668391348083280250195148800000⟩, + ⟨0, 7, 6, 7, 0, 6, -28718749767038947961433167392695704766092673024000000⟩, + ⟨0, 7, 7, 7, 1, 6, -331444193358739846584329959762499138490936066048000000⟩, + ⟨0, 7, 8, 7, 2, 6, 9675495134256222929037688037805054803288732467200000⟩ +] + +def collectedFourData_10_1_7 : List CollectedFourTerm := [ + ⟨0, 8, 2, 0, 3, 7, -59758950892437995811592191312328261029832163328000000⟩, + ⟨0, 8, 3, 0, 4, 7, -21875770995296472956431072458786893832382316544000000⟩, + ⟨0, 8, 4, 0, 5, 7, 644345417919438489831634242030076740619632377856000000⟩, + ⟨0, 8, 5, 0, 6, 7, 374661548799708414800720917899349659263623495680000000⟩, + ⟨0, 8, 6, 0, 7, 7, 128977087619746235183318031551692119789923205120000000⟩, + ⟨0, 8, 7, 0, 8, 7, 75665723810134709919425759138046735000891555840000000⟩, + ⟨0, 8, 2, 1, 2, 7, 57321579620308519101743254388388733976051712000000000⟩, + ⟨0, 8, 3, 1, 3, 7, 105007475276704796512386656555326278691996041216000000⟩, + ⟨0, 8, 4, 1, 4, 7, 198286465661040559429388542538304727905309032448000000⟩, + ⟨0, 8, 5, 1, 5, 7, -122807617227788622868806075476752543903855411200000000⟩, + ⟨0, 8, 6, 1, 6, 7, -47528742635459416254227061091648614637366149120000000⟩, + ⟨0, 8, 7, 1, 7, 7, -5985887156868033279954772664833386990482227200000000⟩, + ⟨0, 8, 8, 1, 8, 7, -14417430059158799634178135557913115519505924096000000⟩, + ⟨0, 8, 2, 2, 1, 7, 79432523991935027999686078820741145760559529984000000⟩, + ⟨0, 8, 3, 2, 2, 7, -81949259183787478742599978229047951631019147264000000⟩, + ⟨0, 8, 4, 2, 3, 7, 311331740606787571068149300901760466479472443392000000⟩, + ⟨0, 8, 5, 2, 4, 7, 92253014648451846318304778107381982973520773120000000⟩, + ⟨0, 8, 6, 2, 5, 7, -853903138277622310613399354709638340547706880000000⟩, + ⟨0, 8, 7, 2, 6, 7, -3754331470039472136232038906915330035804012544000000⟩, + ⟨0, 8, 8, 2, 7, 7, -6190517789018720247275571452075714660335091712000000⟩, + ⟨0, 8, 2, 3, 0, 7, -137558249562460946508878114441955578221833486336000000⟩, + ⟨0, 8, 3, 3, 1, 7, -1836089570653558219044698773800901702588563456000000⟩, + ⟨0, 8, 4, 3, 2, 7, -830576083947547362443568507087137362138084933632000000⟩, + ⟨0, 8, 5, 3, 3, 7, -27547263666793137426317708675299902797025116160000000⟩, + ⟨0, 8, 6, 3, 4, 7, 13827007992199609055274645232148213832320286720000000⟩, + ⟨0, 8, 7, 3, 5, 7, -9004712952824890515065701667426170883713007616000000⟩, + ⟨0, 8, 8, 3, 6, 7, 332424178168772741105882081875402104546263040000000⟩, + ⟨0, 8, 3, 4, 0, 7, 352057980039804708826657636447064046182445613056000000⟩, + ⟨0, 8, 4, 4, 1, 7, 10663089793602362843432676781443776122768588800000000⟩, + ⟨0, 8, 5, 4, 2, 7, -56892946631219528044687954759790108704191283200000000⟩, + ⟨0, 8, 6, 4, 3, 7, -17458115313575857562986651250721718022606684160000000⟩, + ⟨0, 8, 7, 4, 4, 7, 4655480578057011944339350602407713564079947776000000⟩, + ⟨0, 8, 8, 4, 5, 7, 4524669698230946270422453538278122147815620608000000⟩, + ⟨0, 8, 4, 5, 0, 7, 3422517205504872949693151125036174163352703991808000000⟩, + ⟨0, 8, 5, 5, 1, 7, -19207930820206981614895388760691945705926819840000000⟩, + ⟨0, 8, 6, 5, 2, 7, 37896968573518653120610339957249152675521495040000000⟩, + ⟨0, 8, 7, 5, 3, 7, 5310432692440217776756203668422640109493420032000000⟩, + ⟨0, 8, 8, 5, 4, 7, 2265060056133136861666628853288789804186599424000000⟩, + ⟨0, 8, 5, 6, 0, 7, 1019918503697542460005714574512378063695139307520000000⟩, + ⟨0, 8, 6, 6, 1, 7, -70973540322792884268954547559254948884806369280000000⟩, + ⟨0, 8, 7, 6, 2, 7, 37584569053964192078132633283501564102319276032000000⟩, + ⟨0, 8, 8, 6, 3, 7, -12026111625528254004494380016564178053253562368000000⟩, + ⟨0, 8, 6, 7, 0, 7, -21060184294629437119896557750792230364208168960000000⟩, + ⟨0, 8, 7, 7, 1, 7, -194445116229432795058392870286045023388708110336000000⟩, + ⟨0, 8, 8, 7, 2, 7, 4730189912447477015578845730757387651899195392000000⟩ +] + +def collectedFourData_10_1_8 : List CollectedFourTerm := [ + +] + +def collectedFourData_10_1_9 : List CollectedFourTerm := [ + ⟨1, 1, 8, 1, 8, 1, 70993500039696456769917706874495824031300085350400000⟩, + ⟨1, 1, 8, 2, 7, 1, 30483000305678919914152270691593694684474297548800000⟩, + ⟨1, 1, 8, 3, 6, 1, -1636904483613482100989894414561073601336836096000000⟩, + ⟨1, 1, 8, 4, 5, 1, -22280124618805613134572321967673622015014810419200000⟩, + ⟨1, 1, 8, 5, 4, 1, -11153481620869747656535490120069611448253913497600000⟩, + ⟨1, 1, 8, 6, 3, 1, 59218304001548843297146685157705890352493441843200000⟩, + ⟨1, 1, 8, 7, 2, 1, -23292135724548476982223805214617009717374667980800000⟩ +] + +def collectedFourData_10_1_10 : List CollectedFourTerm := [ + ⟨1, 2, 7, 0, 8, 2, 57321579620308519101743254388388733976051712000000000⟩, + ⟨1, 2, 7, 1, 7, 2, -4534688759755647838836990051510777764904960000000000⟩, + ⟨1, 2, 8, 1, 8, 2, -65532700153377083929535023243088130061683916800000000⟩, + ⟨1, 2, 7, 2, 6, 2, -2844143945822837099624412615096181571400499200000000⟩, + ⟨1, 2, 8, 2, 7, 2, -28138256568423441102594602132985011638999449600000000⟩, + ⟨1, 2, 7, 3, 5, 2, -6821640559185928824576235606997934411664588800000000⟩, + ⟨1, 2, 8, 3, 6, 2, 1510994255028696383795939464557677386924032000000000⟩, + ⟨1, 2, 7, 4, 4, 2, 3526821487831345201988223912055078510185676800000000⟩, + ⟨1, 2, 8, 4, 5, 2, 20566343752704855680992206898047530383599206400000000⟩, + ⟨1, 2, 7, 5, 3, 2, 4022989209246544690555329550499914341521817600000000⟩, + ⟨1, 2, 8, 5, 4, 2, 10295558978187611359101133146760068264571699200000000⟩, + ⟨1, 2, 7, 6, 2, 2, 28472692244744371212821487410838720162142617600000000⟩, + ⟨1, 2, 8, 6, 3, 2, -54663248854544336750428255482650833751271014400000000⟩, + ⟨1, 2, 7, 7, 1, 2, -147304494696880013964735347636728251730939084800000000⟩, + ⟨1, 2, 8, 7, 2, 2, 21500511251242771775431311590861295817693593600000000⟩ +] + +def collectedFourData_10_1_11 : List CollectedFourTerm := [ + ⟨1, 3, 6, 0, 7, 3, 35798397629754409893451483455205999395689044377600000⟩, + ⟨1, 3, 7, 0, 8, 3, 105007475276704796512386656555326278691996041216000000⟩, + ⟨1, 3, 6, 1, 6, 3, -13191899887852231004541841458216734010457561497600000⟩, + ⟨1, 3, 7, 1, 7, 3, -8307102159112296762007027960600000720042721280000000⟩, + ⟨1, 3, 8, 1, 8, 3, -60024718759960921175697507179048210728999924531200000⟩, + ⟨1, 3, 6, 2, 5, 3, -237006158578180728717327622369795712013985382400000⟩, + ⟨1, 3, 7, 2, 6, 3, -5210190944713078538824710410984595073904777625600000⟩, + ⟨1, 3, 8, 2, 7, 3, -25773254161086199289635459104110073140820207206400000⟩, + ⟨1, 3, 6, 3, 4, 3, 3837772578598465786787735749359242739057269145600000⟩, + ⟨1, 3, 7, 3, 5, 3, -12496572095712034968006618078630554810741843558400000⟩, + ⟨1, 3, 8, 3, 6, 3, 1383996157547924524296785397504206945793343488000000⟩, + ⟨1, 3, 6, 4, 3, 3, -4845609134112674817751262411842417655699786956800000⟩, + ⟨1, 3, 7, 4, 4, 3, 6460788810111439334403064188791910927341872742400000⟩, + ⟨1, 3, 8, 4, 5, 3, 18837755758384870408300145143012865025116838297600000⟩, + ⟨1, 3, 6, 5, 2, 3, 10518540734590334577792726585361278114064446259200000⟩, + ⟨1, 3, 7, 5, 3, 3, 7369719095786024708829054128379628577962642636800000⟩, + ⟨1, 3, 8, 5, 4, 3, 9430223853067579584231582559565332663346449612800000⟩, + ⟨1, 3, 6, 6, 1, 3, -19699150171210438866138466172175066112201221734400000⟩, + ⟨1, 3, 7, 6, 2, 3, 52159161466861314971198197589383300531069177036800000⟩, + ⟨1, 3, 8, 6, 3, 3, -50068837867512973493196212804344067168193321369600000⟩, + ⟨1, 3, 6, 7, 0, 3, -5845385916588405936141481138830530728533216460800000⟩, + ⟨1, 3, 7, 7, 1, 3, -269847292895430292233976899380287785671649027686400000⟩, + ⟨1, 3, 8, 7, 2, 3, 19693407078156485408301854097151678196033676902400000⟩ +] + +def collectedFourData_10_1_12 : List CollectedFourTerm := [ + ⟨1, 4, 5, 0, 6, 4, 98182255570566771770447077405437769477153986969600000⟩, + ⟨1, 4, 6, 0, 7, 4, 135196808105856671894156955844452918157750409625600000⟩, + ⟨1, 4, 7, 0, 8, 4, 198286465661040559429388542538304727905309032448000000⟩, + ⟨1, 4, 5, 1, 5, 4, -32182456137544438867622066636575411184037003264000000⟩, + ⟨1, 4, 6, 1, 6, 4, -49820742708529597029668616474096941390443944345600000⟩, + ⟨1, 4, 7, 1, 7, 4, -15686368257831958959723967958049406414844067840000000⟩, + ⟨1, 4, 8, 1, 8, 4, -75563441579420628088525319690586318547894822502400000⟩, + ⟨1, 4, 5, 2, 4, 4, 24175443384534977094453537663814864399222859366400000⟩, + ⟨1, 4, 6, 2, 5, 4, -895081295889286406756655532357708606293304934400000⟩, + ⟨1, 4, 7, 2, 6, 4, -9838445740400568559164843359793989168814410956800000⟩, + ⟨1, 4, 8, 2, 7, 4, -32445229654484840959336414674891306841756454092800000⟩, + ⟨1, 4, 5, 3, 3, 4, -7218921958412021285356096365766680561587532595200000⟩, + ⟨1, 4, 6, 3, 4, 4, 14493794058297213599475580649494467198230043033600000⟩, + ⟨1, 4, 7, 3, 5, 4, -23597378255287200577925789259993355481204863795200000⟩, + ⟨1, 4, 8, 3, 6, 4, 1742274099029586329811569138256644431807512576000000⟩, + ⟨1, 4, 5, 4, 2, 4, -14909130238222510761846432731276007698652463104000000⟩, + ⟨1, 4, 6, 4, 3, 4, -18300005911887847376278971256406260753221078220800000⟩, + ⟨1, 4, 7, 4, 4, 4, 12199959813942860861053767786567375142578762547200000⟩, + ⟨1, 4, 8, 4, 5, 4, 23714324467366091022916817117717251409969361715200000⟩, + ⟨1, 4, 5, 5, 1, 4, -5033550890965611176988674429249303711228677324800000⟩, + ⟨1, 4, 6, 5, 2, 4, 39724491245554168116938682966530693234777338675200000⟩, + ⟨1, 4, 7, 5, 3, 4, 13916300230696752267321772768651600913204930150400000⟩, + ⟨1, 4, 8, 5, 4, 4, 11871445363230134508226462251782959956823218585600000⟩, + ⟨1, 4, 5, 6, 0, 4, 267275623858361892356820214108672033499963090534400000⟩, + ⟨1, 4, 6, 6, 1, 4, -74396129488543877616471346114474758685187270246400000⟩, + ⟨1, 4, 7, 6, 2, 4, 98492566856350944505075004707238628571134453350400000⟩, + ⟨1, 4, 8, 6, 3, 4, -63030261254218045130077632599851601306970174259200000⟩, + ⟨1, 4, 6, 7, 0, 4, -22075779096124348635600190295875943667319229644800000⟩, + ⟨1, 4, 7, 7, 1, 4, -509554827743817550458538946087463184089679606579200000⟩, + ⟨1, 4, 8, 7, 2, 4, 24791480010109673260841995756289155050005908684800000⟩ +] + +def collectedFourData_10_1_13 : List CollectedFourTerm := [ + ⟨1, 5, 4, 0, 5, 5, -104579090057856694817286802409440120427205623808000000⟩, + ⟨1, 5, 5, 0, 6, 5, -182425898113733210977064412650571694036714782720000000⟩, + ⟨1, 5, 6, 0, 7, 5, -125600084238717476660877005192886311776640040960000000⟩, + ⟨1, 5, 7, 0, 8, 5, -122807617227788622868806075476752543903855411200000000⟩, + ⟨1, 5, 4, 1, 4, 5, -32182456137544438867622066636575411184037003264000000⟩, + ⟨1, 5, 5, 1, 5, 5, 59796074456425111460678458952018317263293644800000000⟩, + ⟨1, 5, 6, 1, 6, 5, 46284298932022751914862438045208700477463592960000000⟩, + ⟨1, 5, 7, 1, 7, 5, 9715264742249435176167033145417087315869696000000000⟩, + ⟨1, 5, 8, 1, 8, 5, 35099847254942334260212392345414692312627281920000000⟩, + ⟨1, 5, 4, 2, 3, 5, -50530025097279876427275652912549489889935097856000000⟩, + ⟨1, 5, 5, 2, 4, 5, -44918778307672205949044392780983309724790292480000000⟩, + ⟨1, 5, 6, 2, 5, 5, 831545416931516204025489389706185840567255040000000⟩, + ⟨1, 5, 7, 2, 6, 5, 6093386528301388685726103080273871393175633920000000⟩, + ⟨1, 5, 8, 2, 7, 5, 15071079098838937837597517547918590818375434240000000⟩, + ⟨1, 5, 4, 3, 2, 5, 134804855699171869739117033209050426202103218176000000⟩, + ⟨1, 5, 5, 3, 3, 5, 13412997226670463860418681537623794412830064640000000⟩, + ⟨1, 5, 6, 3, 4, 5, -13464975839040484894015684254121156360808693760000000⟩, + ⟨1, 5, 7, 3, 5, 5, 14614904686982080594217275533153073143616634880000000⟩, + ⟨1, 5, 8, 3, 6, 5, -809300813646842374761371821780087237037260800000000⟩, + ⟨1, 5, 4, 4, 1, 5, -1730649736628650653909155291959141427734118400000000⟩, + ⟨1, 5, 5, 4, 2, 5, 27701660121747172297737274370651139208957132800000000⟩, + ⟨1, 5, 6, 4, 3, 5, 17001009981703644421119223329064198914472673280000000⟩, + ⟨1, 5, 7, 4, 4, 5, -7555977106305722017856409388461508209074503680000000⟩, + ⟨1, 5, 8, 4, 5, 5, -11015501003667673270092724569661334135934812160000000⟩, + ⟨1, 5, 4, 5, 0, 5, -555484255967517080482798484767403545944070815744000000⟩, + ⟨1, 5, 5, 5, 1, 5, 9352505059588975540544711681737672011137679360000000⟩, + ⟨1, 5, 6, 5, 2, 5, -36904713333728917054735117253102187594456760320000000⟩, + ⟨1, 5, 7, 5, 3, 5, -8618982976275742936960936722713819838425333760000000⟩, + ⟨1, 5, 8, 5, 4, 5, -5514385134335301656181154859081569111879188480000000⟩, + ⟨1, 5, 5, 6, 0, 5, -496607003403237715095269296323509143201728430080000000⟩, + ⟨1, 5, 6, 6, 1, 5, 69115242154824652809015273696814795006924554240000000⟩, + ⟨1, 5, 7, 6, 2, 5, -61000822269705142499619978975957332967303413760000000⟩, + ⟨1, 5, 8, 6, 3, 5, 29278080725543447639782038446207749624021647360000000⟩, + ⟨1, 5, 6, 7, 0, 5, 20508766094074845471587747331233648891060551680000000⟩, + ⟨1, 5, 7, 7, 1, 5, 315589942225843606537875678992620607597162004480000000⟩, + ⟨1, 5, 8, 7, 2, 5, -11515848714542863036973614525659811183161507840000000⟩ +] + +def collectedFourData_10_1_14 : List CollectedFourTerm := [ + ⟨1, 6, 3, 0, 4, 6, 2748213688397789966811642217453542273563649638400000⟩, + ⟨1, 6, 4, 0, 5, 6, -161895907391180532175759870353928557459106116403200000⟩, + ⟨1, 6, 5, 0, 6, 6, -141204165624479399366522774314055978850812166144000000⟩, + ⟨1, 6, 6, 0, 7, 6, -64812636366047117790574479616380853173331427328000000⟩, + ⟨1, 6, 7, 0, 8, 6, -47528742635459416254227061091648614637366149120000000⟩, + ⟨1, 6, 3, 1, 3, 6, -13191899887852231004541841458216734010457561497600000⟩, + ⟨1, 6, 4, 1, 4, 6, -49820742708529597029668616474096941390443944345600000⟩, + ⟨1, 6, 5, 1, 5, 6, 46284298932022751914862438045208700477463592960000000⟩, + ⟨1, 6, 6, 1, 6, 6, 23883801148071945903019323448809683925942140928000000⟩, + ⟨1, 6, 7, 1, 7, 6, 3759981082551625875060093085776038109747609600000000⟩, + ⟨1, 6, 8, 1, 8, 6, 10867414542404151600604630032787983663023888793600000⟩, + ⟨1, 6, 3, 2, 2, 6, 10295137752692991195210385673343502683944150630400000⟩, + ⟨1, 6, 4, 2, 3, 6, -78224091059670375518195405317877706219818739302400000⟩, + ⟨1, 6, 5, 2, 4, 6, -34768739950790639366160705992932817844773584896000000⟩, + ⟨1, 6, 6, 2, 5, 6, 429097249863323237187122288449961164089065472000000⟩, + ⟨1, 6, 7, 2, 6, 6, 2358249485004092578404263951454674070842376192000000⟩, + ⟨1, 6, 8, 2, 7, 6, 4666221564408189907699942344184891054625076019200000⟩, + ⟨1, 6, 3, 3, 1, 6, 230664623993342548237699579652290723333118361600000⟩, + ⟨1, 6, 4, 3, 2, 6, 208687553334807293763223270382217650636797142630400000⟩, + ⟨1, 6, 5, 3, 3, 6, 10382139276818387894823194555677536776909488128000000⟩, + ⟨1, 6, 6, 3, 4, 6, -6948248387116308071214469601579849057323450368000000⟩, + ⟨1, 6, 7, 3, 5, 6, 5656229305556154420321826131918554601187442688000000⟩, + ⟨1, 6, 8, 3, 6, 6, -250571102703781736530418894682432208543678464000000⟩, + ⟨1, 6, 3, 4, 0, 6, -44228409598139271913157905949206144012728768921600000⟩, + ⟨1, 6, 4, 4, 1, 6, -2679169510203187961086622654451444518077071360000000⟩, + ⟨1, 6, 5, 4, 2, 6, 21442075080071952452877468344427991351752130560000000⟩, + ⟨1, 6, 6, 4, 3, 6, 8772926264169097596753644611214127503668936704000000⟩, + ⟨1, 6, 7, 4, 4, 6, -2924298177521889227752737959606940782787821568000000⟩, + ⟨1, 6, 8, 4, 5, 6, -3410556602415684001311201076898597278824844492800000⟩, + ⟨1, 6, 4, 5, 0, 6, -859929337801880833785693247565278042287995722137600000⟩, + ⟨1, 6, 5, 5, 1, 6, 7239173204533979398154059495476313370941980672000000⟩, + ⟨1, 6, 6, 5, 2, 6, -19043711475114268417563532377150334635161419776000000⟩, + ⟨1, 6, 7, 5, 3, 6, -3335700446813337210475891005681450848171851776000000⟩, + ⟨1, 6, 8, 5, 4, 6, -1707332478287480880695804430662301173267457638400000⟩, + ⟨1, 6, 5, 6, 0, 6, -384391570955068536517550710449468888698811580416000000⟩, + ⟨1, 6, 6, 6, 1, 6, 35665111884941538243773500218584331506556076032000000⟩, + ⟨1, 6, 7, 6, 2, 6, -23608408400518757780259156262074609178326859776000000⟩, + ⟨1, 6, 8, 6, 3, 6, 9064912389487727182426808953030033363696405708800000⟩, + ⟨1, 6, 6, 7, 0, 6, 10583012003759802529066049114819906157699661824000000⟩, + ⟨1, 6, 7, 7, 1, 6, 122138947737824472778296108750019142155814043648000000⟩, + ⟨1, 6, 8, 7, 2, 6, -3565471407312962418959075782794609821605901107200000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1004.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1004.lean new file mode 100644 index 0000000000000000000000000000000000000000..b442a847c93df06b560ff79776f2a30bc77334e4 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1004.lean @@ -0,0 +1,636 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1004. -/ +namespace LaughlinFock +def collectedFourData_10_1_15 : List CollectedFourTerm := [ + ⟨1, 7, 2, 0, 3, 7, 4727508290973887038058176422234107098158858240000000⟩, + ⟨1, 7, 3, 0, 4, 7, 1730584074975734568199980062829994736898539520000000⟩, + ⟨1, 7, 4, 0, 5, 7, -50973925411576204575404918300461660474158612480000000⟩, + ⟨1, 7, 5, 0, 6, 7, -29639335226078607141499087487839807151171174400000000⟩, + ⟨1, 7, 6, 0, 7, 7, -10203329241263059502989456686536183271496089600000000⟩, + ⟨1, 7, 7, 0, 8, 7, -5985887156868033279954772664833386990482227200000000⟩, + ⟨1, 7, 2, 1, 2, 7, -4534688759755647838836990051510777764904960000000000⟩, + ⟨1, 7, 3, 1, 3, 7, -8307102159112296762007027960600000720042721280000000⟩, + ⟨1, 7, 4, 1, 4, 7, -15686368257831958959723967958049406414844067840000000⟩, + ⟨1, 7, 5, 1, 5, 7, 9715264742249435176167033145417087315869696000000000⟩, + ⟨1, 7, 6, 1, 6, 7, 3759981082551625875060093085776038109747609600000000⟩, + ⟨1, 7, 7, 1, 7, 7, 473541297836081271600022057168110643838976000000000⟩, + ⟨1, 7, 8, 1, 8, 7, 1140557508479190263194376080900498669625671680000000⟩, + ⟨1, 7, 2, 2, 1, 7, -6283877312718583051365237836610413318079774720000000⟩, + ⟨1, 7, 3, 2, 2, 7, 6482975293991440317904047907186471100083077120000000⟩, + ⟨1, 7, 4, 2, 3, 7, -24629337747429682109939025256647241233711759360000000⟩, + ⟨1, 7, 5, 2, 4, 7, -7298101541355536560242161134659328760453529600000000⟩, + ⟨1, 7, 6, 2, 5, 7, 67551958419787272161519103365371595744870400000000⟩, + ⟨1, 7, 7, 2, 6, 7, 297003760718994308667427086606949768778219520000000⟩, + ⟨1, 7, 8, 2, 7, 7, 489729550735983099088049505268131769048104960000000⟩, + ⟨1, 7, 2, 3, 0, 7, 10882181758326020038686736622115653120038010880000000⟩, + ⟨1, 7, 3, 3, 1, 7, 145252360334421131702460406594311285091860480000000⟩, + ⟨1, 7, 4, 3, 2, 7, 65706563862109678945658992849755059715110338560000000⟩, + ⟨1, 7, 5, 3, 3, 7, 2179253742469695930442551551612258377059532800000000⟩, + ⟨1, 7, 6, 3, 4, 7, -1093849439226978548634827328541036744645017600000000⟩, + ⟨1, 7, 7, 3, 5, 7, 712359479317875498727337650696709479889633280000000⟩, + ⟨1, 7, 8, 3, 6, 7, -26297952606994628125582344144354974839603200000000⟩, + ⟨1, 7, 3, 4, 0, 7, -27851175341706119190771003120516363989790228480000000⟩, + ⟨1, 7, 4, 4, 1, 7, -843553051950133146556741596667281150050304000000000⟩, + ⟨1, 7, 5, 4, 2, 7, 4500779764041341467877271959352809625747456000000000⟩, + ⟨1, 7, 6, 4, 3, 7, 1381104983557399935144896106336852600736972800000000⟩, + ⟨1, 7, 7, 4, 4, 7, -368293330163154921711502910076040983431086080000000⟩, + ⟨1, 7, 8, 4, 5, 7, -357944930305192072251650818776682591829360640000000⟩, + ⟨1, 7, 4, 5, 0, 7, -270754058151856025484814181690247499395775856640000000⟩, + ⟨1, 7, 5, 5, 1, 7, 1519532234901936156291565584432147576599347200000000⟩, + ⟨1, 7, 6, 5, 2, 7, -2998015033037624424051054069133739790906163200000000⟩, + ⟨1, 7, 7, 5, 3, 7, -420106347371415407379040550207012259558850560000000⟩, + ⟨1, 7, 8, 5, 4, 7, -179188055262164974029524002563528511633489920000000⟩, + ⟨1, 7, 5, 6, 0, 7, -80685371987645722941306772822844404569577881600000000⟩, + ⟨1, 7, 6, 6, 1, 7, 5614690273256305753904011286742062997071462400000000⟩, + ⟨1, 7, 7, 6, 2, 7, -2973301223696355358075277700955748726011330560000000⟩, + ⟨1, 7, 8, 6, 3, 7, 951381200118367862543636735818312705313341440000000⟩, + ⟨1, 7, 6, 7, 0, 7, 1666063315627876672395386597190337452362956800000000⟩, + ⟨1, 7, 7, 7, 1, 7, 15382480538665999928179418212117328308343930880000000⟩, + ⟨1, 7, 8, 7, 2, 7, -374203557710150853647948737581424215179919360000000⟩ +] + +def collectedFourData_10_1_16 : List CollectedFourTerm := [ + ⟨1, 8, 1, 0, 2, 8, -71821454090837103110257157637922310291793641472000000⟩, + ⟨1, 8, 2, 0, 3, 8, 68319216536856617967971449697165181962838815539200000⟩, + ⟨1, 8, 3, 0, 4, 8, 12504700243386203280518294734779027073364970700800000⟩, + ⟨1, 8, 4, 0, 5, 8, -245548566220116427286835539525708288497279618252800000⟩, + ⟨1, 8, 5, 0, 6, 8, -107082634058257828318312844947588597695998066688000000⟩, + ⟨1, 8, 6, 0, 7, 8, -29490522995448399860115940807419808464611416473600000⟩, + ⟨1, 8, 7, 0, 8, 8, -14417430059158799634178135557913115519505924096000000⟩, + ⟨1, 8, 1, 1, 1, 8, 70993500039696456769917706874495824031300085350400000⟩, + ⟨1, 8, 2, 1, 2, 8, -65532700153377083929535023243088130061683916800000000⟩, + ⟨1, 8, 3, 1, 3, 8, -60024718759960921175697507179048210728999924531200000⟩, + ⟨1, 8, 4, 1, 4, 8, -75563441579420628088525319690586318547894822502400000⟩, + ⟨1, 8, 5, 1, 5, 8, 35099847254942334260212392345414692312627281920000000⟩, + ⟨1, 8, 6, 1, 6, 8, 10867414542404151600604630032787983663023888793600000⟩, + ⟨1, 8, 7, 1, 7, 8, 1140557508479190263194376080900498669625671680000000⟩, + ⟨1, 8, 8, 1, 8, 8, 2354668240147381908219921481635234153820795699200000⟩, + ⟨1, 8, 1, 2, 0, 8, 134771161807576179966215825446176160802909297049600000⟩, + ⟨1, 8, 2, 2, 1, 8, -90810961799544919660363233829137711803083102617600000⟩, + ⟨1, 8, 3, 2, 2, 8, 46844105356613892886444802547149373273952537804800000⟩, + ⟨1, 8, 4, 2, 3, 8, -118642983093841052617968289278011878086666721689600000⟩, + ⟨1, 8, 5, 2, 4, 8, -26366985990474174429153501939112861135527739392000000⟩, + ⟨1, 8, 6, 2, 5, 8, 195244369368179424273672690929222845209142886400000⟩, + ⟨1, 8, 7, 2, 6, 8, 715354438741825928733248184402761418815412633600000⟩, + ⟨1, 8, 8, 2, 7, 8, 1011041188898284128335275050214839232886105702400000⟩, + ⟨1, 8, 2, 3, 0, 8, 157262999064428940425194896602146023765967267430400000⟩, + ⟨1, 8, 3, 3, 1, 8, 1049551565792447412223304604431026775297045299200000⟩, + ⟨1, 8, 4, 3, 2, 8, 316517757212542889176984914983123108633647880601600000⟩, + ⟨1, 8, 5, 3, 3, 8, 7873328778968222191405242296040792180765229056000000⟩, + ⟨1, 8, 6, 3, 4, 8, -3161535933842740513501420543991086562726746521600000⟩, + ⟨1, 8, 7, 3, 5, 8, 1715767888851746644568567001916766341290157670400000⟩, + ⟨1, 8, 8, 3, 6, 8, -54291829499381261421061730769849716790263808000000⟩, + ⟨1, 8, 3, 4, 0, 8, -201244541718614634579298077786565757258567988019200000⟩, + ⟨1, 8, 4, 4, 1, 8, -4063513664378661255592545710771653427268157440000000⟩, + ⟨1, 8, 5, 4, 2, 8, 16260666738085118870831437692894931911306117120000000⟩, + ⟨1, 8, 6, 4, 3, 8, 3991786142900748300222664839422436616306478284800000⟩, + ⟨1, 8, 7, 4, 4, 8, -887060378809447783469288308128194007394575974400000⟩, + ⟨1, 8, 8, 4, 5, 8, -738973311600255645169473813327433931834366361600000⟩, + ⟨1, 8, 4, 5, 0, 8, -1304260369211586918445714888322540280058625812070400000⟩, + ⟨1, 8, 5, 5, 1, 8, 5489850329253101917696678852279817966708588544000000⟩, + ⟨1, 8, 6, 5, 2, 8, -8665115981453079153428423053658599300793578291200000⟩, + ⟨1, 8, 7, 5, 3, 8, -1011855673504735956450369414604174050565344460800000⟩, + ⟨1, 8, 8, 5, 4, 8, -369931739173932234589077586382957018815974604800000⟩, + ⟨1, 8, 5, 6, 0, 8, -291504586607780609949558616226531491685892882432000000⟩, + ⟨1, 8, 6, 6, 1, 8, 16228051521278612588260070292126149405183469158400000⟩, + ⟨1, 8, 7, 6, 2, 8, -7161405037224717450276270931643486824825670860800000⟩, + ⟨1, 8, 8, 6, 3, 8, 1964115863985734444421032753168142217661487513600000⟩, + ⟨1, 8, 6, 7, 0, 8, 4815396755276591446690921112689123292525415628800000⟩, + ⟨1, 8, 7, 7, 1, 8, 37049785853067622424865172716190256854527796838400000⟩, + ⟨1, 8, 8, 7, 2, 8, -772539066324796817322429683032946405601076838400000⟩ +] + +def collectedFourData_10_1_17 : List CollectedFourTerm := [ + ⟨2, 0, 8, 1, 8, 1, 134771161807576179966215825446176160802909297049600000⟩, + ⟨2, 0, 8, 2, 7, 1, 57867683158034269165026248429261880815739155251200000⟩, + ⟨2, 0, 8, 3, 6, 1, -3107432636808517153215063811966461713426939904000000⟩, + ⟨2, 0, 8, 4, 5, 1, -42295678877855356563070309818695611558837144780800000⟩, + ⟨2, 0, 8, 5, 4, 1, -21173314111905431537176821456952826898963392102400000⟩, + ⟨2, 0, 8, 6, 3, 1, 112417610430537927083171212384029616324263857356800000⟩, + ⟨2, 0, 8, 7, 2, 1, -44216839440538874404104891381816422272523776819200000⟩ +] + +def collectedFourData_10_1_18 : List CollectedFourTerm := [ + ⟨2, 1, 7, 0, 8, 2, 79432523991935027999686078820741145760559529984000000⟩, + ⟨2, 1, 7, 1, 7, 2, -6283877312718583051365237836610413318079774720000000⟩, + ⟨2, 1, 8, 1, 8, 2, -90810961799544919660363233829137711803083102617600000⟩, + ⟨2, 1, 7, 2, 6, 2, -3941230051745620781633912200764249790547912294400000⟩, + ⟨2, 1, 8, 2, 7, 2, -38992169349964060657538036240180121308555850547200000⟩, + ⟨2, 1, 7, 3, 5, 2, -9452986658272711165767452442558167622721575321600000⟩, + ⟨2, 1, 8, 3, 6, 2, 2093837752016871772534976482508911039400116224000000⟩, + ⟨2, 1, 7, 4, 4, 2, 4887240273263207609082956704930393410783254937600000⟩, + ⟨2, 1, 8, 4, 5, 2, 28499504102715424887250447792015982639065124044800000⟩, + ⟨2, 1, 7, 5, 3, 2, 5574797292738178666861973212355117237071459123200000⟩, + ⟨2, 1, 8, 5, 4, 2, 14266917292968834350310907211040083302116910694400000⟩, + ⟨2, 1, 7, 6, 2, 2, 39455608600226967464297135810949244857387004723200000⟩, + ⟨2, 1, 8, 6, 3, 2, -75748781783001708919419077846373571923112938700800000⟩, + ⟨2, 1, 7, 7, 1, 2, -204125006439709334470244536375948630132705040793600000⟩, + ⟨2, 1, 8, 7, 2, 2, 29794012780452724997399689018526149912523125555200000⟩ +] + +def collectedFourData_10_1_19 : List CollectedFourTerm := [ + ⟨2, 2, 6, 0, 7, 3, -27937555473975275414139855678259908537976514150400000⟩, + ⟨2, 2, 7, 0, 8, 3, -81949259183787478742599978229047951631019147264000000⟩, + ⟨2, 2, 6, 1, 6, 3, 10295137752692991195210385673343502683944150630400000⟩, + ⟨2, 2, 7, 1, 7, 3, 6482975293991440317904047907186471100083077120000000⟩, + ⟨2, 2, 8, 1, 8, 3, 46844105356613892886444802547149373273952537804800000⟩, + ⟨2, 2, 6, 2, 5, 3, 184962823516107478773646199152168980258068889600000⟩, + ⟨2, 2, 7, 2, 6, 3, 4066103741664145366093206450415524735365834342400000⟩, + ⟨2, 2, 8, 2, 7, 3, 20113797419573205108453822012397798899859429785600000⟩, + ⟨2, 2, 6, 3, 4, 3, -2995049818151073773521856816990209490385528422400000⟩, + ⟨2, 2, 7, 3, 5, 3, 9752494504622931024828637270116192844905027993600000⟩, + ⟨2, 2, 8, 3, 6, 3, -1080089389116297877923596133230083224373297152000000⟩, + ⟨2, 2, 6, 4, 3, 3, 3781579147468754210664824241752256124401431347200000⟩, + ⟨2, 2, 7, 4, 4, 3, -5042087292703367152208854990739233000400722329600000⟩, + ⟨2, 2, 8, 4, 5, 3, -14701240316623774569216122203159704551712777830400000⟩, + ⟨2, 2, 6, 5, 2, 3, -8208811978602018767962672967922805508519283916800000⟩, + ⟨2, 2, 7, 5, 3, 3, -5751428826384301651285262307940938704305206067200000⟩, + ⟨2, 2, 8, 5, 4, 3, -7359474710345793360145407138607970613808280371200000⟩, + ⟨2, 2, 6, 6, 1, 3, 15373484209833242076482404060134409466206067097600000⟩, + ⟨2, 2, 7, 6, 2, 3, -40705717670036073833790582586501631340631503667200000⟩, + ⟨2, 2, 8, 6, 3, 3, 39074400756934491716949588067285267891500770918400000⟩, + ⟨2, 2, 6, 7, 0, 3, 4561818520495682320759413641331303289216774963200000⟩, + ⟨2, 2, 7, 7, 1, 3, 210592490556115917415671054642237028767561783705600000⟩, + ⟨2, 2, 8, 7, 2, 3, -15369002222051373652680999046829024800826562969600000⟩ +] + +def collectedFourData_10_1_20 : List CollectedFourTerm := [ + ⟨2, 3, 5, 0, 6, 4, 154157029435069959229951926148407651263125546598400000⟩, + ⟨2, 3, 6, 0, 7, 4, 212273981745332405885081892997584833441266296422400000⟩, + ⟨2, 3, 7, 0, 8, 4, 311331740606787571068149300901760466479472443392000000⟩, + ⟨2, 3, 5, 1, 5, 4, -50530025097279876427275652912549489889935097856000000⟩, + ⟨2, 3, 6, 1, 6, 4, -78224091059670375518195405317877706219818739302400000⟩, + ⟨2, 3, 7, 1, 7, 4, -24629337747429682109939025256647241233711759360000000⟩, + ⟨2, 3, 8, 1, 8, 4, -118642983093841052617968289278011878086666721689600000⟩, + ⟨2, 3, 5, 2, 4, 4, 37958127115515728706654494819941578913009473945600000⟩, + ⟨2, 3, 6, 2, 5, 4, -1405376897030160175547703731959009669700753817600000⟩, + ⟨2, 3, 7, 2, 6, 4, -15447450873729340694482017157602619459735073587200000⟩, + ⟨2, 3, 8, 2, 7, 4, -50942608659862870150912498305022260775528641331200000⟩, + ⟨2, 3, 5, 3, 3, 4, -11334508036765922530726754499736317684519587020800000⟩, + ⟨2, 3, 6, 3, 4, 4, 22756864000388412439534222054324235685513815654400000⟩, + ⟨2, 3, 7, 3, 5, 4, -37050500756486028653293188527335021706960751820800000⟩, + ⟨2, 3, 8, 3, 6, 4, 2735563549719267187321596962055508361692053504000000⟩, + ⟨2, 3, 5, 4, 2, 4, -23408987862710716408212999157908318137106825216000000⟩, + ⟨2, 3, 6, 4, 3, 4, -28733038710780598982577465877031075574713627443200000⟩, + ⟨2, 3, 7, 4, 4, 4, 19155289855741124805518029038359588704111873228800000⟩, + ⟨2, 3, 8, 4, 5, 4, 37234119278519351487279342605257363473711287500800000⟩, + ⟨2, 3, 5, 5, 1, 4, -7903233108184224736354591095638699293036196659200000⟩, + ⟨2, 3, 6, 5, 2, 4, 62371856611429060434549305544657041306399067340800000⟩, + ⟨2, 3, 7, 5, 3, 4, 21850134648301053122579227514841531239536105881600000⟩, + ⟨2, 3, 8, 5, 4, 4, 18639485736615251147346802218009371338795804262400000⟩, + ⟨2, 3, 5, 6, 0, 4, 419652369717628537378340401767131265903149816217600000⟩, + ⟨2, 3, 6, 6, 1, 4, -116810173658903342955771799707699726071570733465600000⟩, + ⟨2, 3, 7, 6, 2, 4, 154644252566568332262602744312529618368160438681600000⟩, + ⟨2, 3, 8, 6, 3, 4, -98964500082023838400228873920899608068664118476800000⟩, + ⟨2, 3, 6, 7, 0, 4, -34661421334707458446796101295195538295409029939200000⟩, + ⟨2, 3, 7, 7, 1, 4, -800057588031558346210904483283752782226728471756800000⟩, + ⟨2, 3, 8, 7, 2, 4, 38925372934731444251003138018887307198159074099200000⟩ +] + +def collectedFourData_10_1_21 : List CollectedFourTerm := [ + ⟨2, 4, 4, 0, 5, 5, 78559755044625612243191090080679173082212781260800000⟩, + ⟨2, 4, 5, 0, 6, 5, 137038234523575709722952627699937844348921577472000000⟩, + ⟨2, 4, 6, 0, 7, 5, 94350714334186371794015708391828220245700509696000000⟩, + ⟨2, 4, 7, 0, 8, 5, 92253014648451846318304778107381982973520773120000000⟩, + ⟨2, 4, 4, 1, 4, 5, 24175443384534977094453537663814864399222859366400000⟩, + ⟨2, 4, 5, 1, 5, 5, -44918778307672205949044392780983309724790292480000000⟩, + ⟨2, 4, 6, 1, 6, 5, -34768739950790639366160705992932817844773584896000000⟩, + ⟨2, 4, 7, 1, 7, 5, -7298101541355536560242161134659328760453529600000000⟩, + ⟨2, 4, 8, 1, 8, 5, -26366985990474174429153501939112861135527739392000000⟩, + ⟨2, 4, 4, 2, 3, 5, 37958127115515728706654494819941578913009473945600000⟩, + ⟨2, 4, 5, 2, 4, 5, 33742961607356832717842959939052224580627202048000000⟩, + ⟨2, 4, 6, 2, 5, 5, -624656460736849306021524791194136612022779904000000⟩, + ⟨2, 4, 7, 2, 6, 5, -4577348615203560328055197333407451702301294592000000⟩, + ⟨2, 4, 8, 2, 7, 5, -11321386346046287821029435066272997933343309824000000⟩, + ⟨2, 4, 4, 3, 2, 5, -101265333602483704024560573557656706543263521177600000⟩, + ⟨2, 4, 5, 3, 3, 5, -10075836153847960835049082025667662874478116864000000⟩, + ⟨2, 4, 6, 3, 4, 5, 10114882458927583434443058359078121912429182976000000⟩, + ⟨2, 4, 7, 3, 5, 5, -10978708378268267875298638332221887695487500288000000⟩, + ⟨2, 4, 8, 3, 6, 5, 607946326960182696928696201315320781162414080000000⟩, + ⟨2, 4, 4, 4, 1, 5, 1300063132145969806655313232481225914806435840000000⟩, + ⟨2, 4, 5, 4, 2, 5, -20809471877121557541141848129403264271940321280000000⟩, + ⟨2, 4, 6, 4, 3, 5, -12771149365852932705670245270843033052017328128000000⟩, + ⟨2, 4, 7, 4, 4, 5, 5676045854537262931915405461642545819358855168000000⟩, + ⟨2, 4, 8, 4, 5, 5, 8274838307191286473912985178095616075094818816000000⟩, + ⟨2, 4, 4, 5, 0, 5, 417279468159570368916193915982570655344161613414400000⟩, + ⟨2, 4, 5, 5, 1, 5, -7025596666871492008520577424158650769170497536000000⟩, + ⟨2, 4, 6, 5, 2, 5, 27722800398109438371460759374878896498233311232000000⟩, + ⟨2, 4, 7, 5, 3, 5, 6474575280540527209815993262530831086021246976000000⟩, + ⟨2, 4, 8, 5, 4, 5, 4142403085888779942287659142861031022314651648000000⟩, + ⟨2, 4, 5, 6, 0, 5, 373050908352907068897657739953608563305436151808000000⟩, + ⟨2, 4, 6, 6, 1, 5, -51919331967118148038893856299746508596601421824000000⟩, + ⟨2, 4, 7, 6, 2, 5, 45823784203683224438921801606917583311497854976000000⟩, + ⟨2, 4, 8, 6, 3, 5, -21993678169345193579004426170157513093295374336000000⟩, + ⟨2, 4, 6, 7, 0, 5, -15406173831945685868124594568372089587622739968000000⟩, + ⟨2, 4, 7, 7, 1, 5, -237070991362553248362159280259827281839152693248000000⟩, + ⟨2, 4, 8, 7, 2, 5, 8650699232943728914576337451619603301410013184000000⟩ +] + +def collectedFourData_10_1_22 : List CollectedFourTerm := [ + ⟨2, 5, 3, 0, 4, 6, 49374508204002039818412679586577934515280281600000⟩, + ⟨2, 5, 4, 0, 5, 6, -2908627826659443774219239867363299503056407756800000⟩, + ⟨2, 5, 5, 0, 6, 6, -2536879233044550577971803936855234042507821056000000⟩, + ⟨2, 5, 6, 0, 7, 6, -1164426208736355477857756215553629625172099072000000⟩, + ⟨2, 5, 7, 0, 8, 6, -853903138277622310613399354709638340547706880000000⟩, + ⟨2, 5, 3, 1, 3, 6, -237006158578180728717327622369795712013985382400000⟩, + ⟨2, 5, 4, 1, 4, 6, -895081295889286406756655532357708606293304934400000⟩, + ⟨2, 5, 5, 1, 5, 6, 831545416931516204025489389706185840567255040000000⟩, + ⟨2, 5, 6, 1, 6, 6, 429097249863323237187122288449961164089065472000000⟩, + ⟨2, 5, 7, 1, 7, 6, 67551958419787272161519103365371595744870400000000⟩, + ⟨2, 5, 8, 1, 8, 6, 195244369368179424273672690929222845209142886400000⟩, + ⟨2, 5, 3, 2, 2, 6, 184962823516107478773646199152168980258068889600000⟩, + ⟨2, 5, 4, 2, 3, 6, -1405376897030160175547703731959009669700753817600000⟩, + ⟨2, 5, 5, 2, 4, 6, -624656460736849306021524791194136612022779904000000⟩, + ⟨2, 5, 6, 2, 5, 6, 7709176973077041555512809863153608848048128000000⟩, + ⟨2, 5, 7, 2, 6, 6, 42368396983096763892164088238697348918673408000000⟩, + ⟨2, 5, 8, 2, 7, 6, 83833508248000283151020373522182424840948940800000⟩, + ⟨2, 5, 3, 3, 1, 6, 4144129118420956070433452711655722386351718400000⟩, + ⟨2, 5, 4, 3, 2, 6, 3749288258661466472327995406039553208294676889600000⟩, + ⟨2, 5, 5, 3, 3, 6, 186525896098427105931566418917373085873078272000000⟩, + ⟨2, 5, 6, 3, 4, 6, -124832486076847232206872811040095971450028032000000⟩, + ⟨2, 5, 7, 3, 5, 6, 101620023737570322813845284561841103896051712000000⟩, + ⟨2, 5, 8, 3, 6, 6, -4501769647085372588824601674405708862324736000000⟩, + ⟨2, 5, 3, 4, 0, 6, -794609233544142969677005163853208864296429158400000⟩, + ⟨2, 5, 4, 4, 1, 6, -48134057959139378754468735044803371875696640000000⟩, + ⟨2, 5, 5, 4, 2, 6, 385229109519885353450600087876663822977597440000000⟩, + ⟨2, 5, 6, 4, 3, 6, 157614715926931415201187870079458240412778496000000⟩, + ⟨2, 5, 7, 4, 4, 6, -52538048611925705716387905360921448868216832000000⟩, + ⟨2, 5, 8, 4, 5, 6, -61274185357966333183189755144736136397796147200000⟩, + ⟨2, 5, 4, 5, 0, 6, -15449522110820423861581441277531495156324656742400000⟩, + ⟨2, 5, 5, 5, 1, 6, 130059252046676523515854533390060313984892928000000⟩, + ⟨2, 5, 6, 5, 2, 6, -342140020782320390663095924406777867900289024000000⟩, + ⟨2, 5, 7, 5, 3, 6, -59929316913233825284874018353043080451457024000000⟩, + ⟨2, 5, 8, 5, 4, 6, -30673998099947805287430510702343977761872281600000⟩, + ⟨2, 5, 5, 6, 0, 6, -6905993101553582282428310402070145471698960384000000⟩, + ⟨2, 5, 6, 6, 1, 6, 640760711874020930252682953886748450454765568000000⟩, + ⟨2, 5, 7, 6, 2, 6, -424149533631942834511062195479048479806849024000000⟩, + ⟨2, 5, 8, 6, 3, 6, 162860549393543820877390256664445232811815731200000⟩, + ⟨2, 5, 6, 7, 0, 6, 190134782898678556927606106660504244244709376000000⟩, + ⟨2, 5, 7, 7, 1, 6, 2194352827281493139568817399649202707210698752000000⟩, + ⟨2, 5, 8, 7, 2, 6, -64057390440458054456540817225009332740738252800000⟩ +] + +def collectedFourData_10_1_23 : List CollectedFourTerm := [ + ⟨2, 6, 2, 0, 3, 7, 2965079809650524249543286340392774066089282764800000⟩, + ⟨2, 6, 3, 0, 4, 7, 1085417430025533741321892308754157746950399590400000⟩, + ⟨2, 6, 4, 0, 5, 7, -31970701636857529805466873684572480474321623449600000⟩, + ⟨2, 6, 5, 0, 6, 7, -18589707101752107091347780705731467175408959488000000⟩, + ⟨2, 6, 6, 0, 7, 7, -6399499199662643249808074256751586264368545792000000⟩, + ⟨2, 6, 7, 0, 8, 7, -3754331470039472136232038906915330035804012544000000⟩, + ⟨2, 6, 2, 1, 2, 7, -2844143945822837099624412615096181571400499200000000⟩, + ⟨2, 6, 3, 1, 3, 7, -5210190944713078538824710410984595073904777625600000⟩, + ⟨2, 6, 4, 1, 4, 7, -9838445740400568559164843359793989168814410956800000⟩, + ⟨2, 6, 5, 1, 5, 7, 6093386528301388685726103080273871393175633920000000⟩, + ⟨2, 6, 6, 1, 6, 7, 2358249485004092578404263951454674070842376192000000⟩, + ⟨2, 6, 7, 1, 7, 7, 297003760718994308667427086606949768778219520000000⟩, + ⟨2, 6, 8, 1, 8, 7, 715354438741825928733248184402761418815412633600000⟩, + ⟨2, 6, 2, 2, 1, 7, -3941230051745620781633912200764249790547912294400000⟩, + ⟨2, 6, 3, 2, 2, 7, 4066103741664145366093206450415524735365834342400000⟩, + ⟨2, 6, 4, 2, 3, 7, -15447450873729340694482017157602619459735073587200000⟩, + ⟨2, 6, 5, 2, 4, 7, -4577348615203560328055197333407451702301294592000000⟩, + ⟨2, 6, 6, 2, 5, 7, 42368396983096763892164088238697348918673408000000⟩, + ⟨2, 6, 7, 2, 6, 7, 186279917473555588178760595080963818007193190400000⟩, + ⟨2, 6, 8, 2, 7, 7, 307156987085336092974150356081459492405064499200000⟩, + ⟨2, 6, 2, 3, 0, 7, 6825273575546215977411363251652357218891307417600000⟩, + ⟨2, 6, 3, 3, 1, 7, 91101868981165094619263911107977550065408409600000⟩, + ⟨2, 6, 4, 3, 2, 7, 41210970743515999651225961896658247058856293171200000⟩, + ⟨2, 6, 5, 3, 3, 7, 1366821774641691552369537544088183161441222656000000⟩, + ⟨2, 6, 6, 3, 4, 7, -686059270005281792494102055336569183615844352000000⟩, + ⟨2, 6, 7, 3, 5, 7, 446789847702936552296699327925679301166995865600000⟩, + ⟨2, 6, 8, 3, 6, 7, -16494001387374160639269982567849736288600064000000⟩, + ⟨2, 6, 3, 4, 0, 7, -17468178287153743341191701330421848506577295769600000⟩, + ⟨2, 6, 4, 4, 1, 7, -529074084858169797174692698638968820942766080000000⟩, + ⟨2, 6, 5, 4, 2, 7, 2822876319756484138960170103237082229107589120000000⟩, + ⟨2, 6, 6, 4, 3, 7, 866225133771295913134218178668526290868371456000000⟩, + ⟨2, 6, 7, 4, 4, 7, -230992533504529178108253965673985437022656921600000⟩, + ⟨2, 6, 8, 4, 5, 7, -224502046424978230008355363675187193108548812800000⟩, + ⟨2, 6, 4, 5, 0, 7, -169816178374513323710857772682077639923437718732800000⟩, + ⟨2, 6, 5, 5, 1, 7, 953046313725810326857599472764998029299154944000000⟩, + ⟨2, 6, 6, 5, 2, 7, -1880346536982458570610043281198790363016331264000000⟩, + ⟨2, 6, 7, 5, 3, 7, -263489511139578434236895435303524669714543411200000⟩, + ⟨2, 6, 8, 5, 4, 7, -112386240718561751735521220016935779244074598400000⟩, + ⟨2, 6, 5, 6, 0, 7, -50605636773071877129143232526427128979502661632000000⟩, + ⟨2, 6, 6, 6, 1, 7, 3521517836036178896780536617808495623429685248000000⟩, + ⟨2, 6, 7, 6, 2, 7, -1864846105764335045925858010258787367094793011200000⟩, + ⟨2, 6, 8, 6, 3, 7, 596703593971050573190656818820502607331380428800000⟩, + ⟨2, 6, 6, 7, 0, 7, 1044950192514620089443715760728165014501851136000000⟩, + ⟨2, 6, 7, 7, 1, 7, 9647848223687570193593086904576654285102225817600000⟩, + ⟨2, 6, 8, 7, 2, 7, -234699411481559209358826456793273709674836787200000⟩ +] + +def collectedFourData_10_1_24 : List CollectedFourTerm := [ + ⟨2, 7, 1, 0, 2, 8, -30838505014981829971544030689925013690944323584000000⟩, + ⟨2, 7, 2, 0, 3, 8, 29334723565006092389153157449310880485450606182400000⟩, + ⟨2, 7, 3, 0, 4, 8, 5369234945853145653235577657752586019854195097600000⟩, + ⟨2, 7, 4, 0, 5, 8, -105432990554931274129765703201553693900770220441600000⟩, + ⟨2, 7, 5, 0, 6, 8, -45978856724990028704092526820823344601613991936000000⟩, + ⟨2, 7, 6, 0, 7, 8, -12662562361092577919451118282809301780491612979200000⟩, + ⟨2, 7, 7, 0, 8, 8, -6190517789018720247275571452075714660335091712000000⟩, + ⟨2, 7, 1, 1, 1, 8, 30483000305678919914152270691593694684474297548800000⟩, + ⟨2, 7, 2, 1, 2, 8, -28138256568423441102594602132985011638999449600000000⟩, + ⟨2, 7, 3, 1, 3, 8, -25773254161086199289635459104110073140820207206400000⟩, + ⟨2, 7, 4, 1, 4, 8, -32445229654484840959336414674891306841756454092800000⟩, + ⟨2, 7, 5, 1, 5, 8, 15071079098838937837597517547918590818375434240000000⟩, + ⟨2, 7, 6, 1, 6, 8, 4666221564408189907699942344184891054625076019200000⟩, + ⟨2, 7, 7, 1, 7, 8, 489729550735983099088049505268131769048104960000000⟩, + ⟨2, 7, 8, 1, 8, 8, 1011041188898284128335275050214839232886105702400000⟩, + ⟨2, 7, 1, 2, 0, 8, 57867683158034269165026248429261880815739155251200000⟩, + ⟨2, 7, 2, 2, 1, 8, -38992169349964060657538036240180121308555850547200000⟩, + ⟨2, 7, 3, 2, 2, 8, 20113797419573205108453822012397798899859429785600000⟩, + ⟨2, 7, 4, 2, 3, 8, -50942608659862870150912498305022260775528641331200000⟩, + ⟨2, 7, 5, 2, 4, 8, -11321386346046287821029435066272997933343309824000000⟩, + ⟨2, 7, 6, 2, 5, 8, 83833508248000283151020373522182424840948940800000⟩, + ⟨2, 7, 7, 2, 6, 8, 307156987085336092974150356081459492405064499200000⟩, + ⟨2, 7, 8, 2, 7, 8, 434118177762857447774702757415866239531404492800000⟩, + ⟨2, 7, 2, 3, 0, 8, 67525168443201999584035356271011484798391471308800000⟩, + ⟨2, 7, 3, 3, 1, 8, 450653661011044812833788381468962648303756902400000⟩, + ⟨2, 7, 4, 3, 2, 8, 135905553106520767893923591077702853867607372595200000⟩, + ⟨2, 7, 5, 3, 3, 8, 3380628979298104223806197189709613689661816832000000⟩, + ⟨2, 7, 6, 3, 4, 8, -1357491894100946288184151666114881244884054835200000⟩, + ⟨2, 7, 7, 3, 5, 8, 736711854621859997958802443628228422274960588800000⟩, + ⟨2, 7, 8, 3, 6, 8, -23311681411680162832365545439324422931480576000000⟩, + ⟨2, 7, 3, 4, 0, 8, -86409846299937027036344708264337497320495408742400000⟩, + ⟨2, 7, 4, 4, 1, 8, -1744780694065281858803218886898418850652487680000000⟩, + ⟨2, 7, 5, 4, 2, 8, 6981961853837782011329338579619777495055728640000000⟩, + ⟨2, 7, 6, 4, 3, 8, 1713982521585910739058343019232407505941928345600000⟩, + ⟨2, 7, 7, 4, 4, 8, -380883627138883487044827166406792176590441676800000⟩, + ⟨2, 7, 8, 4, 5, 8, -317298395920803094793426353837198223579755315200000⟩, + ⟨2, 7, 4, 5, 0, 8, -560019849861338027031991194024083345761557597388800000⟩, + ⟨2, 7, 5, 5, 1, 8, 2357217339209655090823142411614792213875130368000000⟩, + ⟨2, 7, 6, 5, 2, 8, -3720604463277380207215336041932444828483085926400000⟩, + ⟨2, 7, 7, 5, 3, 8, -434467898997809368124235159204438671776913817600000⟩, + ⟨2, 7, 8, 5, 4, 8, -158840306676159273910142792506070425000319385600000⟩, + ⟨2, 7, 5, 6, 0, 8, -125165464411575117021691620194868513057175240704000000⟩, + ⟨2, 7, 6, 6, 1, 8, 6967957618755322395374989004999595894206418124800000⟩, + ⟨2, 7, 7, 6, 2, 8, -3074945055769150632201262832230625914333534617600000⟩, + ⟨2, 7, 8, 6, 3, 8, 843346847933797844417408445359330308620759859200000⟩, + ⟨2, 7, 6, 7, 0, 8, 2067622256699336399120431400998008765225212313600000⟩, + ⟨2, 7, 7, 7, 1, 8, 15908338550048866212544591135339097288002555084800000⟩, + ⟨2, 7, 8, 7, 2, 8, -331710770447434575121785474272560774302715084800000⟩ +] + +def collectedFourData_10_1_25 : List CollectedFourTerm := [ + ⟨3, 0, 7, 0, 8, 2, -137558249562460946508878114441955578221833486336000000⟩, + ⟨3, 0, 7, 1, 7, 2, 10882181758326020038686736622115653120038010880000000⟩, + ⟨3, 0, 8, 1, 8, 2, 157262999064428940425194896602146023765967267430400000⟩, + ⟨3, 0, 7, 2, 6, 2, 6825273575546215977411363251652357218891307417600000⟩, + ⟨3, 0, 8, 2, 7, 2, 67525168443201999584035356271011484798391471308800000⟩, + ⟨3, 0, 7, 3, 5, 2, 16370325812400441347005556290938220454888236646400000⟩, + ⟨3, 0, 8, 3, 6, 2, -3626029258046526228492163545442938123290935296000000⟩, + ⟨3, 0, 7, 4, 4, 2, -8463538402097210772017713097792430902639748710400000⟩, + ⟨3, 0, 8, 4, 5, 2, -49354366457822108598786749514358312368990270259200000⟩, + ⟨3, 0, 7, 5, 3, 2, -9654223719901826092257994134232885987065515212800000⟩, + ⟨3, 0, 8, 5, 4, 2, -24706909347013286412312784500615443618303941017600000⟩, + ⟨3, 0, 7, 6, 2, 2, -68327735060009711833404939140836959671133457612800000⟩, + ⟨3, 0, 8, 6, 3, 2, 131178883722950797406143223870292500816113906483200000⟩, + ⟨3, 0, 7, 7, 1, 2, 353495988376542330385624443625347028884918789734400000⟩, + ⟨3, 0, 8, 7, 2, 2, -51596147768599023666800422442542386287246888140800000⟩ +] + +def collectedFourData_10_1_26 : List CollectedFourTerm := [ + ⟨3, 1, 6, 0, 7, 3, -625946527720038255238678570641545376795564441600000⟩, + ⟨3, 1, 7, 0, 8, 3, -1836089570653558219044698773800901702588563456000000⟩, + ⟨3, 1, 6, 1, 6, 3, 230664623993342548237699579652290723333118361600000⟩, + ⟨3, 1, 7, 1, 7, 3, 145252360334421131702460406594311285091860480000000⟩, + ⟨3, 1, 8, 1, 8, 3, 1049551565792447412223304604431026775297045299200000⟩, + ⟨3, 1, 6, 2, 5, 3, 4144129118420956070433452711655722386351718400000⟩, + ⟨3, 1, 7, 2, 6, 3, 91101868981165094619263911107977550065408409600000⟩, + ⟨3, 1, 8, 2, 7, 3, 450653661011044812833788381468962648303756902400000⟩, + ⟨3, 1, 6, 3, 4, 3, -67104691237806319280665176558771064180152729600000⟩, + ⟨3, 1, 7, 3, 5, 3, 218506593301051416532844067825116128534226534400000⟩, + ⟨3, 1, 8, 3, 6, 3, -24199619160466360729330646044995762738167808000000⟩, + ⟨3, 1, 6, 4, 3, 3, 84727038443344373169523237951443333335010508800000⟩, + ⟨3, 1, 7, 4, 4, 3, -112968975981774330034085645290492607540389478400000⟩, + ⟨3, 1, 8, 4, 5, 3, -329384234706598488039570816272655446380747161600000⟩, + ⟨3, 1, 6, 5, 2, 3, -183920077026748455786739412566700114792624947200000⟩, + ⟨3, 1, 7, 5, 3, 3, -128861915161395713912885738451583990422621388800000⟩, + ⟨3, 1, 8, 5, 4, 3, -164890505365639940893086226942713177932877004800000⟩, + ⟨3, 1, 6, 6, 1, 3, 344445993818896073357305289089070013266421350400000⟩, + ⟨3, 1, 7, 6, 2, 3, -912019759840704365743969851790335738200771788800000⟩, + ⟨3, 1, 8, 6, 3, 3, 875469777566195419161112793827199748872444313600000⟩, + ⟨3, 1, 6, 7, 0, 3, 102208457917987186926535115452520780857658572800000⟩, + ⟨3, 1, 7, 7, 1, 3, 4718366943389514046026345339136188036418004582400000⟩, + ⟨3, 1, 8, 7, 2, 3, -344345573984671222344818863751581775176296038400000⟩ +] + +def collectedFourData_10_1_27 : List CollectedFourTerm := [ + ⟨3, 2, 5, 0, 6, 4, -411262730782341956940361388539909446245198227046400000⟩, + ⟨3, 2, 6, 0, 7, 4, -566308119237577950076145780494483468484839106150400000⟩, + ⟨3, 2, 7, 0, 8, 4, -830576083947547362443568507087137362138084933632000000⟩, + ⟨3, 2, 5, 1, 5, 4, 134804855699171869739117033209050426202103218176000000⟩, + ⟨3, 2, 6, 1, 6, 4, 208687553334807293763223270382217650636797142630400000⟩, + ⟨3, 2, 7, 1, 7, 4, 65706563862109678945658992849755059715110338560000000⟩, + ⟨3, 2, 8, 1, 8, 4, 316517757212542889176984914983123108633647880601600000⟩, + ⟨3, 2, 5, 2, 4, 4, -101265333602483704024560573557656706543263521177600000⟩, + ⟨3, 2, 6, 2, 5, 4, 3749288258661466472327995406039553208294676889600000⟩, + ⟨3, 2, 7, 2, 6, 4, 41210970743515999651225961896658247058856293171200000⟩, + ⟨3, 2, 8, 2, 7, 4, 135905553106520767893923591077702853867607372595200000⟩, + ⟨3, 2, 5, 3, 3, 4, 30238392270254110678249708638072743630876757196800000⟩, + ⟨3, 2, 6, 3, 4, 4, -60711146725774748456989830062813936403970680422400000⟩, + ⟨3, 2, 7, 3, 5, 4, 98843952648838582437935406281740011055807777996800000⟩, + ⟨3, 2, 8, 3, 6, 4, -7297982711583327524364407166983386651252752384000000⟩, + ⟨3, 2, 5, 4, 2, 4, 62450893796731123994260906225490963436442484736000000⟩, + ⟨3, 2, 6, 4, 3, 4, 76654486708616490626156365124174217221355287347200000⟩, + ⟨3, 2, 7, 4, 4, 4, -51102806299971519682204621065844553633764265164800000⟩, + ⟨3, 2, 8, 4, 5, 4, -99333813247932758952314558971510957544273923276800000⟩, + ⟨3, 2, 5, 5, 1, 4, 21084378973780563476660251714663618815085196083200000⟩, + ⟨3, 2, 6, 5, 2, 4, -166396694124059578408736590869571237777356147916800000⟩, + ⟨3, 2, 7, 5, 3, 4, -58292158822423795589180662370635663621922331033600000⟩, + ⟨3, 2, 8, 5, 4, 4, -49726735345842012656360375154997445400839218790400000⟩, + ⟨3, 2, 5, 6, 0, 4, -1119555690595644840200994049503136876560614267289600000⟩, + ⟨3, 2, 6, 6, 1, 4, 311628157198982654456193765509590915809990515097600000⟩, + ⟨3, 2, 7, 6, 2, 4, -412562552894214853951827998280365653640309479833600000⟩, + ⟨3, 2, 8, 6, 3, 4, 264019167360676236098301945565122527168260000972800000⟩, + ⟨3, 2, 6, 7, 0, 4, 92470326154755202757511933280326407811522310963200000⟩, + ⟨3, 2, 7, 7, 1, 4, 2134407166788198750690231017140093286485163035852800000⟩, + ⟨3, 2, 8, 7, 2, 4, -103845768360510786758163795968032806261367190323200000⟩ +] + +def collectedFourData_10_1_28 : List CollectedFourTerm := [ + ⟨3, 3, 4, 0, 5, 5, -23458380130554369869731194180832709004455470694400000⟩, + ⟨3, 3, 5, 0, 6, 5, -40920379602100354319703144579942504633515114496000000⟩, + ⟨3, 3, 6, 0, 7, 5, -28173648469033828389217107891596087899642134528000000⟩, + ⟨3, 3, 7, 0, 8, 5, -27547263666793137426317708675299902797025116160000000⟩, + ⟨3, 3, 4, 1, 4, 5, -7218921958412021285356096365766680561587532595200000⟩, + ⟨3, 3, 5, 1, 5, 5, 13412997226670463860418681537623794412830064640000000⟩, + ⟨3, 3, 6, 1, 6, 5, 10382139276818387894823194555677536776909488128000000⟩, + ⟨3, 3, 7, 1, 7, 5, 2179253742469695930442551551612258377059532800000000⟩, + ⟨3, 3, 8, 1, 8, 5, 7873328778968222191405242296040792180765229056000000⟩, + ⟨3, 3, 4, 2, 3, 5, -11334508036765922530726754499736317684519587020800000⟩, + ⟨3, 3, 5, 2, 4, 5, -10075836153847960835049082025667662874478116864000000⟩, + ⟨3, 3, 6, 2, 5, 5, 186525896098427105931566418917373085873078272000000⟩, + ⟨3, 3, 7, 2, 6, 5, 1366821774641691552369537544088183161441222656000000⟩, + ⟨3, 3, 8, 2, 7, 5, 3380628979298104223806197189709613689661816832000000⟩, + ⟨3, 3, 4, 3, 2, 5, 30238392270254110678249708638072743630876757196800000⟩, + ⟨3, 3, 5, 3, 3, 5, 3008700759006736388660400013293930922798743552000000⟩, + ⟨3, 3, 6, 3, 4, 5, -3020360203040530449247271723464763383971053568000000⟩, + ⟨3, 3, 7, 3, 5, 5, 3278303430727639442787538538952517308785885184000000⟩, + ⟨3, 3, 8, 3, 6, 5, -181536157141848240847381575449984374344253440000000⟩, + ⟨3, 3, 4, 4, 1, 5, -388206087586135723897915163422568576314245120000000⟩, + ⟨3, 3, 5, 4, 2, 5, 6213824130845400230957666399581239262618583040000000⟩, + ⟨3, 3, 6, 4, 3, 5, 3813536286589553212004076158075460942041186304000000⟩, + ⟨3, 3, 7, 4, 4, 5, -1694898885804271251078621275229184634099073024000000⟩, + ⟨3, 3, 8, 4, 5, 5, -2470912777397284860069954238787746213750898688000000⟩, + ⟨3, 3, 4, 5, 0, 5, -124601971826443719134073647565919127541193585459200000⟩, + ⟨3, 3, 5, 5, 1, 5, 2097882270149746976496582742618604499420315648000000⟩, + ⟨3, 3, 6, 5, 2, 5, -8278182507734606112700920528819064786623922176000000⟩, + ⟨3, 3, 7, 5, 3, 5, -1933344217131707185784559714539428653268205568000000⟩, + ⟨3, 3, 8, 5, 4, 5, -1236944618622614738681999960045410572948209664000000⟩, + ⟨3, 3, 5, 6, 0, 5, -111395077686024108064178662982848624614696812544000000⟩, + ⟨3, 3, 6, 6, 1, 5, 15503401515410172882284733561798377601427832832000000⟩, + ⟨3, 3, 7, 6, 2, 5, -13683237024604658206740035707471015605927149568000000⟩, + ⟨3, 3, 8, 6, 3, 5, 6567434721155875567173024112310915051236098048000000⟩, + ⟨3, 3, 6, 7, 0, 5, 4600369259067662067653569796228513098496999424000000⟩, + ⟨3, 3, 7, 7, 1, 5, 70790717590082436591767252423156911602048958464000000⟩, + ⟨3, 3, 8, 7, 2, 5, -2583146941919747394672491980767430523656077312000000⟩ +] + +def collectedFourData_10_1_29 : List CollectedFourTerm := [ + ⟨3, 4, 3, 0, 4, 6, -799507214512309626441208002278672670749255270400000⟩, + ⟨3, 4, 4, 0, 5, 6, 47098574068571572835133363753081387082474271539200000⟩, + ⟨3, 4, 5, 0, 6, 6, 41078955982414694819044158893637489601768587264000000⟩, + ⟨3, 4, 6, 0, 7, 6, 18855218786290076875421962075625048006373408768000000⟩, + ⟨3, 4, 7, 0, 8, 6, 13827007992199609055274645232148213832320286720000000⟩, + ⟨3, 4, 3, 1, 3, 6, 3837772578598465786787735749359242739057269145600000⟩, + ⟨3, 4, 4, 1, 4, 6, 14493794058297213599475580649494467198230043033600000⟩, + ⟨3, 4, 5, 1, 5, 6, -13464975839040484894015684254121156360808693760000000⟩, + ⟨3, 4, 6, 1, 6, 6, -6948248387116308071214469601579849057323450368000000⟩, + ⟨3, 4, 7, 1, 7, 6, -1093849439226978548634827328541036744645017600000000⟩, + ⟨3, 4, 8, 1, 8, 6, -3161535933842740513501420543991086562726746521600000⟩, + ⟨3, 4, 3, 2, 2, 6, -2995049818151073773521856816990209490385528422400000⟩, + ⟨3, 4, 4, 2, 3, 6, 22756864000388412439534222054324235685513815654400000⟩, + ⟨3, 4, 5, 2, 4, 6, 10114882458927583434443058359078121912429182976000000⟩, + ⟨3, 4, 6, 2, 5, 6, -124832486076847232206872811040095971450028032000000⟩, + ⟨3, 4, 7, 2, 6, 6, -686059270005281792494102055336569183615844352000000⟩, + ⟨3, 4, 8, 2, 7, 6, -1357491894100946288184151666114881244884054835200000⟩, + ⟨3, 4, 3, 3, 1, 6, -67104691237806319280665176558771064180152729600000⟩, + ⟨3, 4, 4, 3, 2, 6, -60711146725774748456989830062813936403970680422400000⟩, + ⟨3, 4, 5, 3, 3, 6, -3020360203040530449247271723464763383971053568000000⟩, + ⟨3, 4, 6, 3, 4, 6, 2021376553495618927096262247413962943924011008000000⟩, + ⟨3, 4, 7, 3, 5, 6, -1645503825200921403650861292736973760708476928000000⟩, + ⟨3, 4, 8, 3, 6, 6, 72895861484764262312313604392042910590173184000000⟩, + ⟨3, 4, 3, 4, 0, 6, 12866878841846272604374476876050306583777352089600000⟩, + ⟨3, 4, 4, 4, 1, 6, 779420960368498780897670899278645907591004160000000⟩, + ⟨3, 4, 5, 4, 2, 6, -6237904204103781973889899798829423203304079360000000⟩, + ⟨3, 4, 6, 4, 3, 6, -2552209775462145351118671480137525604724506624000000⟩, + ⟨3, 4, 7, 4, 4, 6, 850733514713334740818297779459904057752158208000000⟩, + ⟨3, 4, 8, 4, 5, 6, 992195265108236679139483032953615471740767436800000⟩, + ⟨3, 4, 4, 5, 0, 6, 250169669282238769911130851227514868350808856985600000⟩, + ⟨3, 4, 5, 5, 1, 6, -2106012071973699333708514288052502921039839232000000⟩, + ⟨3, 4, 6, 5, 2, 6, 5540174979741564319259826796279020236367200256000000⟩, + ⟨3, 4, 7, 5, 3, 6, 970418197077684898936387470583543100400992256000000⟩, + ⟨3, 4, 8, 5, 4, 6, 496695231424246444748083301310618035384903270400000⟩, + ⟨3, 4, 5, 6, 0, 6, 111826760587699286486673715072803654823990788096000000⟩, + ⟨3, 4, 6, 6, 1, 6, -10375653967076866874880182343086934538051387392000000⟩, + ⟨3, 4, 7, 6, 2, 6, 6868131440816726365958112463600515017663840256000000⟩, + ⟨3, 4, 8, 6, 3, 6, -2637154048433086803471112761264596736092720332800000⟩, + ⟨3, 4, 6, 7, 0, 6, -3078797869320422826311179406590659919393849344000000⟩, + ⟨3, 4, 7, 7, 1, 6, -35532524381778759136622058739582838053628018688000000⟩, + ⟨3, 4, 8, 7, 2, 6, 1037262904743766183433336085188662931460666163200000⟩ +] + +def collectedFourData_10_1_30 : List CollectedFourTerm := [ + ⟨3, 5, 2, 0, 3, 7, 7111703583231803019824149737547895111802893107200000⟩, + ⟨3, 5, 3, 0, 4, 7, 2603358938700760957428199949953612411511085465600000⟩, + ⟨3, 5, 4, 0, 5, 7, -76681292911327340342169649958238849558238357094400000⟩, + ⟨3, 5, 5, 0, 6, 7, -44587159568680307082246158099986293889362296832000000⟩, + ⟨3, 5, 6, 0, 7, 7, -15349111764547753601112738490842422850342617088000000⟩, + ⟨3, 5, 7, 0, 8, 7, -9004712952824890515065701667426170883713007616000000⟩, + ⟨3, 5, 2, 1, 2, 7, -6821640559185928824576235606997934411664588800000000⟩, + ⟨3, 5, 3, 1, 3, 7, -12496572095712034968006618078630554810741843558400000⟩, + ⟨3, 5, 4, 1, 4, 7, -23597378255287200577925789259993355481204863795200000⟩, + ⟨3, 5, 5, 1, 5, 7, 14614904686982080594217275533153073143616634880000000⟩, + ⟨3, 5, 6, 1, 6, 7, 5656229305556154420321826131918554601187442688000000⟩, + ⟨3, 5, 7, 1, 7, 7, 712359479317875498727337650696709479889633280000000⟩, + ⟨3, 5, 8, 1, 8, 7, 1715767888851746644568567001916766341290157670400000⟩, + ⟨3, 5, 2, 2, 1, 7, -9452986658272711165767452442558167622721575321600000⟩, + ⟨3, 5, 3, 2, 2, 7, 9752494504622931024828637270116192844905027993600000⟩, + ⟨3, 5, 4, 2, 3, 7, -37050500756486028653293188527335021706960751820800000⟩, + ⟨3, 5, 5, 2, 4, 7, -10978708378268267875298638332221887695487500288000000⟩, + ⟨3, 5, 6, 2, 5, 7, 101620023737570322813845284561841103896051712000000⟩, + ⟨3, 5, 7, 2, 6, 7, 446789847702936552296699327925679301166995865600000⟩, + ⟨3, 5, 8, 2, 7, 7, 736711854621859997958802443628228422274960588800000⟩, + ⟨3, 5, 2, 3, 0, 7, 16370325812400441347005556290938220454888236646400000⟩, + ⟨3, 5, 3, 3, 1, 7, 218506593301051416532844067825116128534226534400000⟩, + ⟨3, 5, 4, 3, 2, 7, 98843952648838582437935406281740011055807777996800000⟩, + ⟨3, 5, 5, 3, 3, 7, 3278303430727639442787538538952517308785885184000000⟩, + ⟨3, 5, 6, 3, 4, 7, -1645503825200921403650861292736973760708476928000000⟩, + ⟨3, 5, 7, 3, 5, 7, 1071619371093781930420067545615997058299618918400000⟩, + ⟨3, 5, 8, 3, 6, 7, -39560637925036032044577324940322468995792896000000⟩, + ⟨3, 5, 3, 4, 0, 7, -41897187965380704904341751576919025982210729574400000⟩, + ⟨3, 5, 4, 4, 1, 7, -1268976994425121343161920414930569329240965120000000⟩, + ⟨3, 5, 5, 4, 2, 7, 6770630447414015594646147090965459633889607680000000⟩, + ⟨3, 5, 6, 4, 3, 7, 2077629198268647639903276875333618238052368384000000⟩, + ⟨3, 5, 7, 4, 4, 7, -554032448933498817143846534646578265322841702400000⟩, + ⟨3, 5, 8, 4, 5, 7, -538465103976938404120907380514479748037161779200000⟩, + ⟨3, 5, 4, 5, 0, 7, -407301793464743036043745210910092860397211300659200000⟩, + ⟨3, 5, 5, 5, 1, 7, 2285868617178490735154751702156032998392201216000000⟩, + ⟨3, 5, 6, 5, 2, 7, -4509985586644898178233727626681938174537629696000000⟩, + ⟨3, 5, 7, 5, 3, 7, -631976007666450070292061657638251839406001356800000⟩, + ⟨3, 5, 8, 5, 4, 7, -269556869337136380019351724119753586541959577600000⟩, + ⟨3, 5, 5, 6, 0, 7, -121376931305333282100103103806890932895479758848000000⟩, + ⟨3, 5, 6, 6, 1, 7, 8446312619121365197849554842632256083797737472000000⟩, + ⟨3, 5, 7, 6, 2, 7, -4472808013253185719688041751039184848758295756800000⟩, + ⟨3, 5, 8, 6, 3, 7, 1431185451925956712953087520573043942320452403200000⟩, + ⟨3, 5, 6, 7, 0, 7, 2506298820091752181602056265176755257584123904000000⟩, + ⟨3, 5, 7, 7, 1, 7, 23140232704549841092325046703950403491716294246400000⟩, + ⟨3, 5, 8, 7, 2, 7, -562923345328950204046827340468506951167036620800000⟩ +] + +def collectedFourData_10_1_31 : List CollectedFourTerm := [ + ⟨3, 6, 1, 0, 2, 8, 1655994705926514365409294010316987760409313280000000⟩, + ⟨3, 6, 2, 0, 3, 8, -1575243251897840978792958784844377255374225408000000⟩, + ⟨3, 6, 3, 0, 4, 8, -288322168694262270805220373604278810225672192000000⟩, + ⟨3, 6, 4, 0, 5, 8, 5661638724190575165977373385211134326626844672000000⟩, + ⟨3, 6, 5, 0, 6, 8, 2469015384635112217107949484706367055981445120000000⟩, + ⟨3, 6, 6, 0, 7, 8, 679966043206261695698753718653830407508721664000000⟩, + ⟨3, 6, 7, 0, 8, 8, 332424178168772741105882081875402104546263040000000⟩, + ⟨3, 6, 1, 1, 1, 8, -1636904483613482100989894414561073601336836096000000⟩, + ⟨3, 6, 2, 1, 2, 8, 1510994255028696383795939464557677386924032000000000⟩, + ⟨3, 6, 3, 1, 3, 8, 1383996157547924524296785397504206945793343488000000⟩, + ⟨3, 6, 4, 1, 4, 8, 1742274099029586329811569138256644431807512576000000⟩, + ⟨3, 6, 5, 1, 5, 8, -809300813646842374761371821780087237037260800000000⟩, + ⟨3, 6, 6, 1, 6, 8, -250571102703781736530418894682432208543678464000000⟩, + ⟨3, 6, 7, 1, 7, 8, -26297952606994628125582344144354974839603200000000⟩, + ⟨3, 6, 8, 1, 8, 8, -54291829499381261421061730769849716790263808000000⟩, + ⟨3, 6, 1, 2, 0, 8, -3107432636808517153215063811966461713426939904000000⟩, + ⟨3, 6, 2, 2, 1, 8, 2093837752016871772534976482508911039400116224000000⟩, + ⟨3, 6, 3, 2, 2, 8, -1080089389116297877923596133230083224373297152000000⟩, + ⟨3, 6, 4, 2, 3, 8, 2735563549719267187321596962055508361692053504000000⟩, + ⟨3, 6, 5, 2, 4, 8, 607946326960182696928696201315320781162414080000000⟩, + ⟨3, 6, 6, 2, 5, 8, -4501769647085372588824601674405708862324736000000⟩, + ⟨3, 6, 7, 2, 6, 8, -16494001387374160639269982567849736288600064000000⟩, + ⟨3, 6, 8, 2, 7, 8, -23311681411680162832365545439324422931480576000000⟩, + ⟨3, 6, 2, 3, 0, 8, -3626029258046526228492163545442938123290935296000000⟩, + ⟨3, 6, 3, 3, 1, 8, -24199619160466360729330646044995762738167808000000⟩, + ⟨3, 6, 4, 3, 2, 8, -7297982711583327524364407166983386651252752384000000⟩, + ⟨3, 6, 5, 3, 3, 8, -181536157141848240847381575449984374344253440000000⟩, + ⟨3, 6, 6, 3, 4, 8, 72895861484764262312313604392042910590173184000000⟩, + ⟨3, 6, 7, 3, 5, 8, -39560637925036032044577324940322468995792896000000⟩, + ⟨3, 6, 8, 3, 6, 8, 1251812336078984468873732647741281974353920000000⟩, + ⟨3, 6, 3, 4, 0, 8, 4640116242441132925311283183271177991758020608000000⟩, + ⟨3, 6, 4, 4, 1, 8, 93692855440664378195067578951415591704985600000000⟩, + ⟨3, 6, 5, 4, 2, 8, -374923877189221498114291639789038598933708800000000⟩, + ⟨3, 6, 6, 4, 3, 8, -92039026548723187725658120793364306541412352000000⟩, + ⟨3, 6, 7, 4, 4, 8, 20453043032068366905088979400992060243705856000000⟩, + ⟨3, 6, 8, 4, 5, 8, 17038584185211179175151452429935718678134784000000⟩, + ⟨3, 6, 4, 5, 0, 8, 30072466422532370295630836631507362293424848896000000⟩, + ⟨3, 6, 5, 5, 1, 8, -126580047656427336236646401760421130859970560000000⟩, + ⟨3, 6, 6, 5, 2, 8, 199792476679418964617386520567883346779045888000000⟩, + ⟨3, 6, 7, 5, 3, 8, 23330461067611898471443564235824822424174592000000⟩, + ⟨3, 6, 8, 5, 4, 8, 8529554426055199469920174032792951982129152000000⟩, + ⟨3, 6, 5, 6, 0, 8, 6721251446193818051985872273553251775471943680000000⟩, + ⟨3, 6, 6, 6, 1, 8, -374171864757171469587171300319236931259990016000000⟩, + ⟨3, 6, 7, 6, 2, 8, 165121257690501057326887295867321460134510592000000⟩, + ⟨3, 6, 8, 6, 3, 8, -45286822910504348694346640901295342840971264000000⟩, + ⟨3, 6, 6, 7, 0, 8, -111029101744280873952970168571130202829094912000000⟩, + ⟨3, 6, 7, 7, 1, 8, -854260749869982829249543517346032575857033216000000⟩, + ⟨3, 6, 8, 7, 2, 8, 17812513268489924724358273536974919844233216000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1005.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1005.lean new file mode 100644 index 0000000000000000000000000000000000000000..a4a1e66fb68f2972262a54fac406964ad4e598b6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1005.lean @@ -0,0 +1,647 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1005. -/ +namespace LaughlinFock +def collectedFourData_10_1_32 : List CollectedFourTerm := [ + ⟨4, 0, 6, 0, 7, 3, 120021089212769463978440105534641714720178543001600000⟩, + ⟨4, 0, 7, 0, 8, 3, 352057980039804708826657636447064046182445613056000000⟩, + ⟨4, 0, 6, 1, 6, 3, -44228409598139271913157905949206144012728768921600000⟩, + ⟨4, 0, 7, 1, 7, 3, -27851175341706119190771003120516363989790228480000000⟩, + ⟨4, 0, 8, 1, 8, 3, -201244541718614634579298077786565757258567988019200000⟩, + ⟨4, 0, 6, 2, 5, 3, -794609233544142969677005163853208864296429158400000⟩, + ⟨4, 0, 7, 2, 6, 3, -17468178287153743341191701330421848506577295769600000⟩, + ⟨4, 0, 8, 2, 7, 3, -86409846299937027036344708264337497320495408742400000⟩, + ⟨4, 0, 6, 3, 4, 3, 12866878841846272604374476876050306583777352089600000⟩, + ⟨4, 0, 7, 3, 5, 3, -41897187965380704904341751576919025982210729574400000⟩, + ⟨4, 0, 8, 3, 6, 3, 4640116242441132925311283183271177991758020608000000⟩, + ⟨4, 0, 6, 4, 3, 3, -16245846872547232436223708148114748134264720588800000⟩, + ⟨4, 0, 7, 4, 4, 3, 21661050815267104234784712365722848615610082918400000⟩, + ⟨4, 0, 8, 4, 5, 3, 63157239266102397776988228174749448195278477721600000⟩, + ⟨4, 0, 6, 5, 2, 3, 35265453190148193938636398073444995514475164467200000⟩, + ⟨4, 0, 7, 5, 3, 3, 24708416343562842335496413318062776018019339468800000⟩, + ⟨4, 0, 8, 5, 4, 3, 31616659216743140729600273045180616444241300684800000⟩, + ⟨4, 0, 6, 6, 1, 3, -66045231537108075836838104372430254608021349990400000⟩, + ⟨4, 0, 7, 6, 2, 3, 174873731400596114335394908142171193747606129868800000⟩, + ⟨4, 0, 8, 6, 3, 3, -167865515060979300740432347375541812028457458073600000⟩, + ⟨4, 0, 6, 7, 0, 3, -19597792946877669996631701572281222460387151052800000⟩, + ⟨4, 0, 7, 7, 1, 3, -904715522448621950916584539673393111616551544422400000⟩, + ⟨4, 0, 8, 7, 2, 3, 66025976700874487875744329398236861744491685478400000⟩ +] + +def collectedFourData_10_1_33 : List CollectedFourTerm := [ + ⟨4, 1, 5, 0, 6, 4, 5279867205243499130732348572950362653993205760000000⟩, + ⟨4, 1, 6, 0, 7, 4, 7270368654941571087208264757467983828599439360000000⟩, + ⟨4, 1, 7, 0, 8, 4, 10663089793602362843432676781443776122768588800000000⟩, + ⟨4, 1, 5, 1, 5, 4, -1730649736628650653909155291959141427734118400000000⟩, + ⟨4, 1, 6, 1, 6, 4, -2679169510203187961086622654451444518077071360000000⟩, + ⟨4, 1, 7, 1, 7, 4, -843553051950133146556741596667281150050304000000000⟩, + ⟨4, 1, 8, 1, 8, 4, -4063513664378661255592545710771653427268157440000000⟩, + ⟨4, 1, 5, 2, 4, 4, 1300063132145969806655313232481225914806435840000000⟩, + ⟨4, 1, 6, 2, 5, 4, -48134057959139378754468735044803371875696640000000⟩, + ⟨4, 1, 7, 2, 6, 4, -529074084858169797174692698638968820942766080000000⟩, + ⟨4, 1, 8, 2, 7, 4, -1744780694065281858803218886898418850652487680000000⟩, + ⟨4, 1, 5, 3, 3, 4, -388206087586135723897915163422568576314245120000000⟩, + ⟨4, 1, 6, 3, 4, 4, 779420960368498780897670899278645907591004160000000⟩, + ⟨4, 1, 7, 3, 5, 4, -1268976994425121343161920414930569329240965120000000⟩, + ⟨4, 1, 8, 3, 6, 4, 93692855440664378195067578951415591704985600000000⟩, + ⟨4, 1, 5, 4, 2, 4, -801756155896397069921897047216176541099622400000000⟩, + ⟨4, 1, 6, 4, 3, 4, -984104515713572314229185322524206818635284480000000⟩, + ⟨4, 1, 7, 4, 4, 4, 656067304143659041284322972189369462759096320000000⟩, + ⟨4, 1, 8, 4, 5, 4, 1275265915639494911573807354432226289904517120000000⟩, + ⟨4, 1, 5, 5, 1, 4, -270685167301255857582311414816988736656506880000000⟩, + ⟨4, 1, 6, 5, 2, 4, 2136231616940567885174528379764795337993093120000000⟩, + ⟨4, 1, 7, 5, 3, 4, 748365545071110970612478429969662196569866240000000⟩, + ⟨4, 1, 8, 5, 4, 4, 638401050046246752679047502051180809667215360000000⟩, + ⟨4, 1, 5, 6, 0, 4, 14373063574165916423377337547030490637811056640000000⟩, + ⟨4, 1, 6, 6, 1, 4, -4000740072642681587937184165973552514560163840000000⟩, + ⟨4, 1, 7, 6, 2, 4, 5296554562563898272739037746374009189291786240000000⟩, + ⟨4, 1, 8, 6, 3, 4, -3389527032151831730318342844727892869927403520000000⟩, + ⟨4, 1, 6, 7, 0, 4, -1187151195523854068637610048474194958488698880000000⟩, + ⟨4, 1, 7, 7, 1, 4, -27401915026737371092687959183360899690287595520000000⟩, + ⟨4, 1, 8, 7, 2, 4, 1333191232103532544462721657253446839833722880000000⟩ +] + +def collectedFourData_10_1_34 : List CollectedFourTerm := [ + ⟨4, 2, 4, 0, 5, 5, -48448237362729580644532747956432040299790860288000000⟩, + ⟨4, 2, 5, 0, 6, 5, -84512240525650683834280962844770687990544465920000000⟩, + ⟨4, 2, 6, 0, 7, 5, -58186609680861918490377965784233528321963458560000000⟩, + ⟨4, 2, 7, 0, 8, 5, -56892946631219528044687954759790108704191283200000000⟩, + ⟨4, 2, 4, 1, 4, 5, -14909130238222510761846432731276007698652463104000000⟩, + ⟨4, 2, 5, 1, 5, 5, 27701660121747172297737274370651139208957132800000000⟩, + ⟨4, 2, 6, 1, 6, 5, 21442075080071952452877468344427991351752130560000000⟩, + ⟨4, 2, 7, 1, 7, 5, 4500779764041341467877271959352809625747456000000000⟩, + ⟨4, 2, 8, 1, 8, 5, 16260666738085118870831437692894931911306117120000000⟩, + ⟨4, 2, 4, 2, 3, 5, -23408987862710716408212999157908318137106825216000000⟩, + ⟨4, 2, 5, 2, 4, 5, -20809471877121557541141848129403264271940321280000000⟩, + ⟨4, 2, 6, 2, 5, 5, 385229109519885353450600087876663822977597440000000⟩, + ⟨4, 2, 7, 2, 6, 5, 2822876319756484138960170103237082229107589120000000⟩, + ⟨4, 2, 8, 2, 7, 5, 6981961853837782011329338579619777495055728640000000⟩, + ⟨4, 2, 4, 3, 2, 5, 62450893796731123994260906225490963436442484736000000⟩, + ⟨4, 2, 5, 3, 3, 5, 6213824130845400230957666399581239262618583040000000⟩, + ⟨4, 2, 6, 3, 4, 5, -6237904204103781973889899798829423203304079360000000⟩, + ⟨4, 2, 7, 3, 5, 5, 6770630447414015594646147090965459633889607680000000⟩, + ⟨4, 2, 8, 3, 6, 5, -374923877189221498114291639789038598933708800000000⟩, + ⟨4, 2, 4, 4, 1, 5, -801756155896397069921897047216176541099622400000000⟩, + ⟨4, 2, 5, 4, 2, 5, 12833316910460533904983269371912649221917900800000000⟩, + ⟨4, 2, 6, 4, 3, 5, 7876038762089357240033977786308757987346350080000000⟩, + ⟨4, 2, 7, 4, 4, 5, -3500449010898123245862858244929689211088404480000000⟩, + ⟨4, 2, 8, 4, 5, 5, -5103138753644027902690396208884140327315701760000000⟩, + ⟨4, 2, 4, 5, 0, 5, -257338566146298883957317528588963372923967504384000000⟩, + ⟨4, 2, 5, 5, 1, 5, 4332724494087861436108005928541157399157800960000000⟩, + ⟨4, 2, 6, 5, 2, 5, -17096805015293451381637031919043777727582699520000000⟩, + ⟨4, 2, 7, 5, 3, 5, -3992906544022483618631318350136078874559119360000000⟩, + ⟨4, 2, 8, 5, 4, 5, -2554642995554665270410373856116979061258977280000000⟩, + ⟨4, 2, 5, 6, 0, 5, -230062567608527265965505857711780860756104314880000000⟩, + ⟨4, 2, 6, 6, 1, 5, 32018940454033097911608281191847316905672048640000000⟩, + ⟨4, 2, 7, 6, 2, 5, -28259782285439065739724509327647774854201999360000000⟩, + ⟨4, 2, 8, 6, 3, 5, 13563623509551865699861070008419183773047848960000000⟩, + ⟨4, 2, 6, 7, 0, 5, 9501072988804337976515390721271170142285332480000000⟩, + ⟨4, 2, 7, 7, 1, 5, 146202997384935781833839916116623066794326753280000000⟩, + ⟨4, 2, 8, 7, 2, 5, -5334934274593470701173761165992460193879818240000000⟩ +] + +def collectedFourData_10_1_35 : List CollectedFourTerm := [ + ⟨4, 3, 3, 0, 4, 6, 1009465616340567478172026025209479033206813491200000⟩, + ⟨4, 3, 4, 0, 5, 6, -59467119542997511726680745659541089976411855257600000⟩, + ⟨4, 3, 5, 0, 6, 6, -51866690965021719547357579618003255887598190592000000⟩, + ⟨4, 3, 6, 0, 7, 6, -23806783363360764908012059670072607024196091904000000⟩, + ⟨4, 3, 7, 0, 8, 6, -17458115313575857562986651250721718022606684160000000⟩, + ⟨4, 3, 3, 1, 3, 6, -4845609134112674817751262411842417655699786956800000⟩, + ⟨4, 3, 4, 1, 4, 6, -18300005911887847376278971256406260753221078220800000⟩, + ⟨4, 3, 5, 1, 5, 6, 17001009981703644421119223329064198914472673280000000⟩, + ⟨4, 3, 6, 1, 6, 6, 8772926264169097596753644611214127503668936704000000⟩, + ⟨4, 3, 7, 1, 7, 6, 1381104983557399935144896106336852600736972800000000⟩, + ⟨4, 3, 8, 1, 8, 6, 3991786142900748300222664839422436616306478284800000⟩, + ⟨4, 3, 3, 2, 2, 6, 3781579147468754210664824241752256124401431347200000⟩, + ⟨4, 3, 4, 2, 3, 6, -28733038710780598982577465877031075574713627443200000⟩, + ⟨4, 3, 5, 2, 4, 6, -12771149365852932705670245270843033052017328128000000⟩, + ⟨4, 3, 6, 2, 5, 6, 157614715926931415201187870079458240412778496000000⟩, + ⟨4, 3, 7, 2, 6, 6, 866225133771295913134218178668526290868371456000000⟩, + ⟨4, 3, 8, 2, 7, 6, 1713982521585910739058343019232407505941928345600000⟩, + ⟨4, 3, 3, 3, 1, 6, 84727038443344373169523237951443333335010508800000⟩, + ⟨4, 3, 4, 3, 2, 6, 76654486708616490626156365124174217221355287347200000⟩, + ⟨4, 3, 5, 3, 3, 6, 3813536286589553212004076158075460942041186304000000⟩, + ⟨4, 3, 6, 3, 4, 6, -2552209775462145351118671480137525604724506624000000⟩, + ⟨4, 3, 7, 3, 5, 6, 2077629198268647639903276875333618238052368384000000⟩, + ⟨4, 3, 8, 3, 6, 6, -92039026548723187725658120793364306541412352000000⟩, + ⟨4, 3, 3, 4, 0, 6, -16245846872547232436223708148114748134264720588800000⟩, + ⟨4, 3, 4, 4, 1, 6, -984104515713572314229185322524206818635284480000000⟩, + ⟨4, 3, 5, 4, 2, 6, 7876038762089357240033977786308757987346350080000000⟩, + ⟨4, 3, 6, 4, 3, 6, 3222444985176114123168828017273748846828060672000000⟩, + ⟨4, 3, 7, 4, 4, 6, -1074144443206211203509934178304845747243188224000000⟩, + ⟨4, 3, 8, 4, 5, 6, -1252755430648159503131032794876690109238240870400000⟩, + ⟨4, 3, 4, 5, 0, 6, -315866667376799375247371315874434514335738678476800000⟩, + ⟨4, 3, 5, 5, 1, 6, 2659071407569986072145816026787472347125252096000000⟩, + ⟨4, 3, 6, 5, 2, 6, -6995079029988293317698008257250603020182355968000000⟩, + ⟨4, 3, 7, 5, 3, 6, -1225259491896736321284210596354295391970131968000000⟩, + ⟨4, 3, 8, 5, 4, 6, -627132249493138217765470023444267522275357491200000⟩, + ⟨4, 3, 5, 6, 0, 6, -141193559921644584638067017573652285450237247488000000⟩, + ⟨4, 3, 6, 6, 1, 6, 13100402018511669590539183754734363244626968576000000⟩, + ⟨4, 3, 7, 6, 2, 6, -8671769825418304816977063904370701789160275968000000⟩, + ⟨4, 3, 8, 6, 3, 6, 3329696453721671062125874457102830617995142758400000⟩, + ⟨4, 3, 6, 7, 0, 6, 3887320254686351045686540869393111086197112832000000⟩, + ⟨4, 3, 7, 7, 1, 6, 44863712264395433983433660436973395395859185664000000⟩, + ⟨4, 3, 8, 7, 2, 6, -1309658272543645520898331369526790448595179929600000⟩ +] + +def collectedFourData_10_1_36 : List CollectedFourTerm := [ + ⟨4, 4, 2, 0, 3, 7, -3676785488009098727411419561167070960119132979200000⟩, + ⟨4, 4, 3, 0, 4, 7, -1345949286815450166232319209536136759006042521600000⟩, + ⟨4, 4, 4, 0, 5, 7, 39644602967270999557060538547766780028632065638400000⟩, + ⟨4, 4, 5, 0, 6, 7, 23051779272719767791060788040870536743225393152000000⟩, + ⟨4, 4, 6, 0, 7, 7, 7935565751472550174525413061295282757952339968000000⟩, + ⟨4, 4, 7, 0, 8, 7, 4655480578057011944339350602407713564079947776000000⟩, + ⟨4, 4, 2, 1, 2, 7, 3526821487831345201988223912055078510185676800000000⟩, + ⟨4, 4, 3, 1, 3, 7, 6460788810111439334403064188791910927341872742400000⟩, + ⟨4, 4, 4, 1, 4, 7, 12199959813942860861053767786567375142578762547200000⟩, + ⟨4, 4, 5, 1, 5, 7, -7555977106305722017856409388461508209074503680000000⟩, + ⟨4, 4, 6, 1, 6, 7, -2924298177521889227752737959606940782787821568000000⟩, + ⟨4, 4, 7, 1, 7, 7, -368293330163154921711502910076040983431086080000000⟩, + ⟨4, 4, 8, 1, 8, 7, -887060378809447783469288308128194007394575974400000⟩, + ⟨4, 4, 2, 2, 1, 7, 4887240273263207609082956704930393410783254937600000⟩, + ⟨4, 4, 3, 2, 2, 7, -5042087292703367152208854990739233000400722329600000⟩, + ⟨4, 4, 4, 2, 3, 7, 19155289855741124805518029038359588704111873228800000⟩, + ⟨4, 4, 5, 2, 4, 7, 5676045854537262931915405461642545819358855168000000⟩, + ⟨4, 4, 6, 2, 5, 7, -52538048611925705716387905360921448868216832000000⟩, + ⟨4, 4, 7, 2, 6, 7, -230992533504529178108253965673985437022656921600000⟩, + ⟨4, 4, 8, 2, 7, 7, -380883627138883487044827166406792176590441676800000⟩, + ⟨4, 4, 2, 3, 0, 7, -8463538402097210772017713097792430902639748710400000⟩, + ⟨4, 4, 3, 3, 1, 7, -112968975981774330034085645290492607540389478400000⟩, + ⟨4, 4, 4, 3, 2, 7, -51102806299971519682204621065844553633764265164800000⟩, + ⟨4, 4, 5, 3, 3, 7, -1694898885804271251078621275229184634099073024000000⟩, + ⟨4, 4, 6, 3, 4, 7, 850733514713334740818297779459904057752158208000000⟩, + ⟨4, 4, 7, 3, 5, 7, -554032448933498817143846534646578265322841702400000⟩, + ⟨4, 4, 8, 3, 6, 7, 20453043032068366905088979400992060243705856000000⟩, + ⟨4, 4, 3, 4, 0, 7, 21661050815267104234784712365722848615610082918400000⟩, + ⟨4, 4, 4, 4, 1, 7, 656067304143659041284322972189369462759096320000000⟩, + ⟨4, 4, 5, 4, 2, 7, -3500449010898123245862858244929689211088404480000000⟩, + ⟨4, 4, 6, 4, 3, 7, -1074144443206211203509934178304845747243188224000000⟩, + ⟨4, 4, 7, 4, 4, 7, 286437482142516547123941959910530240423028326400000⟩, + ⟨4, 4, 8, 4, 5, 7, 278389088764863686906773435679960793959576371200000⟩, + ⟨4, 4, 4, 5, 0, 7, 210577016593076693508161652773307799835782624051200000⟩, + ⟨4, 4, 5, 5, 1, 7, -1181805239880082149475219689435514355765477376000000⟩, + ⟨4, 4, 6, 5, 2, 7, 2331684576281316002985935782209999691271110656000000⟩, + ⟨4, 4, 7, 5, 3, 7, 326734682704813803010620391323305689182162124800000⟩, + ⟨4, 4, 8, 5, 4, 7, 139362218035746170527352570414762482606905753600000⟩, + ⟨4, 4, 5, 6, 0, 7, 62752466322523959031276848187325436397331939328000000⟩, + ⟨4, 4, 6, 6, 1, 7, -4366784878154464504581120409998727686433800192000000⟩, + ⟨4, 4, 7, 6, 2, 7, 2312463589252505793248260101132290862995000524800000⟩, + ⟨4, 4, 8, 6, 3, 7, -739929868941443376932944858238950254727869235200000⟩, + ⟨4, 4, 6, 7, 0, 7, -1295768731426797189480657122823537986522578944000000⟩, + ⟨4, 4, 7, 7, 1, 7, -11963613331389488575702041495323446619018782310400000⟩, + ⟨4, 4, 8, 7, 2, 7, 291034119004500696289717946741762177440206028800000⟩ +] + +def collectedFourData_10_1_37 : List CollectedFourTerm := [ + ⟨4, 5, 1, 0, 2, 8, 22539964173521803300085276851997384862288838656000000⟩, + ⟨4, 5, 2, 0, 3, 8, -21440845393581174392492549547360659013853878681600000⟩, + ⟨4, 5, 3, 0, 4, 8, -3924391382135956915810490276248628149940020838400000⟩, + ⟨4, 5, 4, 0, 5, 8, 77061317617728032919871821943916188002003871334400000⟩, + ⟨4, 5, 5, 0, 6, 8, 33606096755250828545395103682743613849310593024000000⟩, + ⟨4, 5, 6, 0, 7, 8, 9255108242937000487029933592935061739927293132800000⟩, + ⟨4, 5, 7, 0, 8, 8, 4524669698230946270422453538278122147815620608000000⟩, + ⟨4, 5, 1, 1, 1, 8, -22280124618805613134572321967673622015014810419200000⟩, + ⟨4, 5, 2, 1, 2, 8, 20566343752704855680992206898047530383599206400000000⟩, + ⟨4, 5, 3, 1, 3, 8, 18837755758384870408300145143012865025116838297600000⟩, + ⟨4, 5, 4, 1, 4, 8, 23714324467366091022916817117717251409969361715200000⟩, + ⟨4, 5, 5, 1, 5, 8, -11015501003667673270092724569661334135934812160000000⟩, + ⟨4, 5, 6, 1, 6, 8, -3410556602415684001311201076898597278824844492800000⟩, + ⟨4, 5, 7, 1, 7, 8, -357944930305192072251650818776682591829360640000000⟩, + ⟨4, 5, 8, 1, 8, 8, -738973311600255645169473813327433931834366361600000⟩, + ⟨4, 5, 1, 2, 0, 8, -42295678877855356563070309818695611558837144780800000⟩, + ⟨4, 5, 2, 2, 1, 8, 28499504102715424887250447792015982639065124044800000⟩, + ⟨4, 5, 3, 2, 2, 8, -14701240316623774569216122203159704551712777830400000⟩, + ⟨4, 5, 4, 2, 3, 8, 37234119278519351487279342605257363473711287500800000⟩, + ⟨4, 5, 5, 2, 4, 8, 8274838307191286473912985178095616075094818816000000⟩, + ⟨4, 5, 6, 2, 5, 8, -61274185357966333183189755144736136397796147200000⟩, + ⟨4, 5, 7, 2, 6, 8, -224502046424978230008355363675187193108548812800000⟩, + ⟨4, 5, 8, 2, 7, 8, -317298395920803094793426353837198223579755315200000⟩, + ⟨4, 5, 2, 3, 0, 8, -49354366457822108598786749514358312368990270259200000⟩, + ⟨4, 5, 3, 3, 1, 8, -329384234706598488039570816272655446380747161600000⟩, + ⟨4, 5, 4, 3, 2, 8, -99333813247932758952314558971510957544273923276800000⟩, + ⟨4, 5, 5, 3, 3, 8, -2470912777397284860069954238787746213750898688000000⟩, + ⟨4, 5, 6, 3, 4, 8, 992195265108236679139483032953615471740767436800000⟩, + ⟨4, 5, 7, 3, 5, 8, -538465103976938404120907380514479748037161779200000⟩, + ⟨4, 5, 8, 3, 6, 8, 17038584185211179175151452429935718678134784000000⟩, + ⟨4, 5, 3, 4, 0, 8, 63157239266102397776988228174749448195278477721600000⟩, + ⟨4, 5, 4, 4, 1, 8, 1275265915639494911573807354432226289904517120000000⟩, + ⟨4, 5, 5, 4, 2, 8, -5103138753644027902690396208884140327315701760000000⟩, + ⟨4, 5, 6, 4, 3, 8, -1252755430648159503131032794876690109238240870400000⟩, + ⟨4, 5, 7, 4, 4, 8, 278389088764863686906773435679960793959576371200000⟩, + ⟨4, 5, 8, 4, 5, 8, 231914435310542317611226630369033684461079756800000⟩, + ⟨4, 5, 4, 5, 0, 8, 409320339822026087769373918040661663989198172979200000⟩, + ⟨4, 5, 5, 5, 1, 8, -1722897862564279780559526134169986961990746112000000⟩, + ⟨4, 5, 6, 5, 2, 8, 2719401970535726351596327241354078638160058777600000⟩, + ⟨4, 5, 7, 5, 3, 8, 317554008315201154761606614060576890985801318400000⟩, + ⟨4, 5, 8, 5, 4, 8, 116096899640644127617306607725789271608944230400000⟩, + ⟨4, 5, 5, 6, 0, 8, 91483847295078862326053352882193511254365044736000000⟩, + ⟨4, 5, 6, 6, 1, 8, -5092903012421070863567503917804379080242705203200000⟩, + ⟨4, 5, 7, 6, 2, 8, 2247487397943356353589862113552154087379068518400000⟩, + ⟨4, 5, 8, 6, 3, 8, -616404969340941437111837636628910351626063052800000⟩, + ⟨4, 5, 6, 7, 0, 8, -1511231869629812627672852028066430153184929382400000⟩, + ⟨4, 5, 7, 7, 1, 8, -11627456674834161269505589907795083964871553843200000⟩, + ⟨4, 5, 8, 7, 2, 8, 242448486988074430611548333754931067908993843200000⟩ +] + +def collectedFourData_10_1_38 : List CollectedFourTerm := [ + ⟨5, 0, 5, 0, 6, 4, 1694671685459190136644044124846551090557848492441600000⟩, + ⟨5, 0, 6, 0, 7, 4, 2333560186919753704297025102952715332114026437017600000⟩, + ⟨5, 0, 7, 0, 8, 4, 3422517205504872949693151125036174163352703991808000000⟩, + ⟨5, 0, 5, 1, 5, 4, -555484255967517080482798484767403545944070815744000000⟩, + ⟨5, 0, 6, 1, 6, 4, -859929337801880833785693247565278042287995722137600000⟩, + ⟨5, 0, 7, 1, 7, 4, -270754058151856025484814181690247499395775856640000000⟩, + ⟨5, 0, 8, 1, 8, 4, -1304260369211586918445714888322540280058625812070400000⟩, + ⟨5, 0, 5, 2, 4, 4, 417279468159570368916193915982570655344161613414400000⟩, + ⟨5, 0, 6, 2, 5, 4, -15449522110820423861581441277531495156324656742400000⟩, + ⟨5, 0, 7, 2, 6, 4, -169816178374513323710857772682077639923437718732800000⟩, + ⟨5, 0, 8, 2, 7, 4, -560019849861338027031991194024083345761557597388800000⟩, + ⟨5, 0, 5, 3, 3, 4, -124601971826443719134073647565919127541193585459200000⟩, + ⟨5, 0, 6, 3, 4, 4, 250169669282238769911130851227514868350808856985600000⟩, + ⟨5, 0, 7, 3, 5, 4, -407301793464743036043745210910092860397211300659200000⟩, + ⟨5, 0, 8, 3, 6, 4, 30072466422532370295630836631507362293424848896000000⟩, + ⟨5, 0, 5, 4, 2, 4, -257338566146298883957317528588963372923967504384000000⟩, + ⟨5, 0, 6, 4, 3, 4, -315866667376799375247371315874434514335738678476800000⟩, + ⟨5, 0, 7, 4, 4, 4, 210577016593076693508161652773307799835782624051200000⟩, + ⟨5, 0, 8, 4, 5, 4, 409320339822026087769373918040661663989198172979200000⟩, + ⟨5, 0, 5, 5, 1, 4, -86881444337020322762621442915444945780736838860800000⟩, + ⟨5, 0, 6, 5, 2, 4, 685663311989477354756192275981896270477786297139200000⟩, + ⟨5, 0, 7, 5, 3, 4, 240201855521242452776994150152842433041057343078400000⟩, + ⟨5, 0, 8, 5, 4, 4, 204906703412230075875688204180704581276409633177600000⟩, + ⟨5, 0, 5, 6, 0, 4, 4613302366440958615995147246819883106475193034342400000⟩, + ⟨5, 0, 6, 6, 1, 4, -1284112016161364011139712719806739201352180065894400000⟩, + ⟨5, 0, 7, 6, 2, 4, 1700027803493358830979566217222366564862392690278400000⟩, + ⟨5, 0, 8, 6, 3, 4, -1087931810629945717569059725600660096549035127603200000⟩, + ⟨5, 0, 6, 7, 0, 4, -381038279791455448542284757221599682859599973580800000⟩, + ⟨5, 0, 7, 7, 1, 4, -8795154824548076351310039453913324380111118742323200000⟩, + ⟨5, 0, 8, 7, 2, 4, 427912548653600374404231835069429106367068425420800000⟩ +] + +def collectedFourData_10_1_39 : List CollectedFourTerm := [ + ⟨5, 1, 4, 0, 5, 5, -16356867533270341127274107657095141721663707545600000⟩, + ⟨5, 1, 5, 0, 6, 5, -28532627778969987071522002590556110832590127104000000⟩, + ⟨5, 1, 6, 0, 7, 5, -19644691294633763545842344487703716395086774272000000⟩, + ⟨5, 1, 7, 0, 8, 5, -19207930820206981614895388760691945705926819840000000⟩, + ⟨5, 1, 4, 1, 4, 5, -5033550890965611176988674429249303711228677324800000⟩, + ⟨5, 1, 5, 1, 5, 5, 9352505059588975540544711681737672011137679360000000⟩, + ⟨5, 1, 6, 1, 6, 5, 7239173204533979398154059495476313370941980672000000⟩, + ⟨5, 1, 7, 1, 7, 5, 1519532234901936156291565584432147576599347200000000⟩, + ⟨5, 1, 8, 1, 8, 5, 5489850329253101917696678852279817966708588544000000⟩, + ⟨5, 1, 4, 2, 3, 5, -7903233108184224736354591095638699293036196659200000⟩, + ⟨5, 1, 5, 2, 4, 5, -7025596666871492008520577424158650769170497536000000⟩, + ⟨5, 1, 6, 2, 5, 5, 130059252046676523515854533390060313984892928000000⟩, + ⟨5, 1, 7, 2, 6, 5, 953046313725810326857599472764998029299154944000000⟩, + ⟨5, 1, 8, 2, 7, 5, 2357217339209655090823142411614792213875130368000000⟩, + ⟨5, 1, 4, 3, 2, 5, 21084378973780563476660251714663618815085196083200000⟩, + ⟨5, 1, 5, 3, 3, 5, 2097882270149746976496582742618604499420315648000000⟩, + ⟨5, 1, 6, 3, 4, 5, -2106012071973699333708514288052502921039839232000000⟩, + ⟨5, 1, 7, 3, 5, 5, 2285868617178490735154751702156032998392201216000000⟩, + ⟨5, 1, 8, 3, 6, 5, -126580047656427336236646401760421130859970560000000⟩, + ⟨5, 1, 4, 4, 1, 5, -270685167301255857582311414816988736656506880000000⟩, + ⟨5, 1, 5, 4, 2, 5, 4332724494087861436108005928541157399157800960000000⟩, + ⟨5, 1, 6, 4, 3, 5, 2659071407569986072145816026787472347125252096000000⟩, + ⟨5, 1, 7, 4, 4, 5, -1181805239880082149475219689435514355765477376000000⟩, + ⟨5, 1, 8, 4, 5, 5, -1722897862564279780559526134169986961990746112000000⟩, + ⟨5, 1, 4, 5, 0, 5, -86881444337020322762621442915444945780736838860800000⟩, + ⟨5, 1, 5, 5, 1, 5, 1462794199866388907212197970116917819344945152000000⟩, + ⟨5, 1, 6, 5, 2, 5, -5772143427707799314965515371281354259561447424000000⟩, + ⟨5, 1, 7, 5, 3, 5, -1348066451299775176935649615124199713361887232000000⟩, + ⟨5, 1, 8, 5, 4, 5, -862486632077761227728008443242544914535284736000000⟩, + ⟨5, 1, 5, 6, 0, 5, -77672649152590733277211819623090742954196729856000000⟩, + ⟨5, 1, 6, 6, 1, 5, 10810085073707690727250774803444676751542714368000000⟩, + ⟨5, 1, 7, 6, 2, 5, -9540935656775436115640190105162487251685343232000000⟩, + ⟨5, 1, 8, 6, 3, 5, 4579287195854996922009078759331482885792202752000000⟩, + ⟨5, 1, 6, 7, 0, 5, 3207707870531490101728075288319835999332990976000000⟩, + ⟨5, 1, 7, 7, 1, 5, 49360372871524660931333647734210034626447015936000000⟩, + ⟨5, 1, 8, 7, 2, 5, -1801155583326936961933291962123627044051877888000000⟩ +] + +def collectedFourData_10_1_40 : List CollectedFourTerm := [ + ⟨5, 2, 3, 0, 4, 6, -2191283884392581917634213888076841152196431052800000⟩, + ⟨5, 2, 4, 0, 5, 6, 129087448444459569928292150459004222321956644454400000⟩, + ⟨5, 2, 5, 0, 6, 6, 112588920522557255701519436579138277248700776448000000⟩, + ⟨5, 2, 6, 0, 7, 6, 51678254195988325944594998051757923813950488576000000⟩, + ⟨5, 2, 7, 0, 8, 6, 37896968573518653120610339957249152675521495040000000⟩, + ⟨5, 2, 3, 1, 3, 6, 10518540734590334577792726585361278114064446259200000⟩, + ⟨5, 2, 4, 1, 4, 6, 39724491245554168116938682966530693234777338675200000⟩, + ⟨5, 2, 5, 1, 5, 6, -36904713333728917054735117253102187594456760320000000⟩, + ⟨5, 2, 6, 1, 6, 6, -19043711475114268417563532377150334635161419776000000⟩, + ⟨5, 2, 7, 1, 7, 6, -2998015033037624424051054069133739790906163200000000⟩, + ⟨5, 2, 8, 1, 8, 6, -8665115981453079153428423053658599300793578291200000⟩, + ⟨5, 2, 3, 2, 2, 6, -8208811978602018767962672967922805508519283916800000⟩, + ⟨5, 2, 4, 2, 3, 6, 62371856611429060434549305544657041306399067340800000⟩, + ⟨5, 2, 5, 2, 4, 6, 27722800398109438371460759374878896498233311232000000⟩, + ⟨5, 2, 6, 2, 5, 6, -342140020782320390663095924406777867900289024000000⟩, + ⟨5, 2, 7, 2, 6, 6, -1880346536982458570610043281198790363016331264000000⟩, + ⟨5, 2, 8, 2, 7, 6, -3720604463277380207215336041932444828483085926400000⟩, + ⟨5, 2, 3, 3, 1, 6, -183920077026748455786739412566700114792624947200000⟩, + ⟨5, 2, 4, 3, 2, 6, -166396694124059578408736590869571237777356147916800000⟩, + ⟨5, 2, 5, 3, 3, 6, -8278182507734606112700920528819064786623922176000000⟩, + ⟨5, 2, 6, 3, 4, 6, 5540174979741564319259826796279020236367200256000000⟩, + ⟨5, 2, 7, 3, 5, 6, -4509985586644898178233727626681938174537629696000000⟩, + ⟨5, 2, 8, 3, 6, 6, 199792476679418964617386520567883346779045888000000⟩, + ⟨5, 2, 3, 4, 0, 6, 35265453190148193938636398073444995514475164467200000⟩, + ⟨5, 2, 4, 4, 1, 6, 2136231616940567885174528379764795337993093120000000⟩, + ⟨5, 2, 5, 4, 2, 6, -17096805015293451381637031919043777727582699520000000⟩, + ⟨5, 2, 6, 4, 3, 6, -6995079029988293317698008257250603020182355968000000⟩, + ⟨5, 2, 7, 4, 4, 6, 2331684576281316002985935782209999691271110656000000⟩, + ⟨5, 2, 8, 4, 5, 6, 2719401970535726351596327241354078638160058777600000⟩, + ⟨5, 2, 4, 5, 0, 6, 685663311989477354756192275981896270477786297139200000⟩, + ⟨5, 2, 5, 5, 1, 6, -5772143427707799314965515371281354259561447424000000⟩, + ⟨5, 2, 6, 5, 2, 6, 15184473547531413424466363592536510219201544192000000⟩, + ⟨5, 2, 7, 5, 3, 6, 2659715531991481919450114836619883018234888192000000⟩, + ⟨5, 2, 8, 5, 4, 6, 1361338880148201082403809770612456391225167052800000⟩, + ⟨5, 2, 5, 6, 0, 6, 306494017654521305594917858013469120242827395072000000⟩, + ⟨5, 2, 6, 6, 1, 6, -28437521157277116529237314024123401852675948544000000⟩, + ⟨5, 2, 7, 6, 2, 6, 18824127498751893398168026068482875224534024192000000⟩, + ⟨5, 2, 8, 6, 3, 6, -7227893710148759247651952569233904875213527449600000⟩, + ⟨5, 2, 6, 7, 0, 6, -8438348062261529511789078692350427554809643008000000⟩, + ⟨5, 2, 7, 7, 1, 6, -97387298871434365825294503804381236338429526016000000⟩, + ⟨5, 2, 8, 7, 2, 6, 2842923047829804576124827963196390070647416422400000⟩ +] + +def collectedFourData_10_1_41 : List CollectedFourTerm := [ + ⟨5, 3, 2, 0, 3, 7, -4194050760439917620923952247766944791285622374400000⟩, + ⟨5, 3, 3, 0, 4, 7, -1535302956425271403941765039302245699101602611200000⟩, + ⟨5, 3, 4, 0, 5, 7, 45221968419009950105208187102570692495329250508800000⟩, + ⟨5, 3, 5, 0, 6, 7, 26294798188129767788560443754516487386655883264000000⟩, + ⟨5, 3, 6, 0, 7, 7, 9051973709922903705541908983738433464042520576000000⟩, + ⟨5, 3, 7, 0, 8, 7, 5310432692440217776756203668422640109493420032000000⟩, + ⟨5, 3, 2, 1, 2, 7, 4022989209246544690555329550499914341521817600000000⟩, + ⟨5, 3, 3, 1, 3, 7, 7369719095786024708829054128379628577962642636800000⟩, + ⟨5, 3, 4, 1, 4, 7, 13916300230696752267321772768651600913204930150400000⟩, + ⟨5, 3, 5, 1, 5, 7, -8618982976275742936960936722713819838425333760000000⟩, + ⟨5, 3, 6, 1, 6, 7, -3335700446813337210475891005681450848171851776000000⟩, + ⟨5, 3, 7, 1, 7, 7, -420106347371415407379040550207012259558850560000000⟩, + ⟨5, 3, 8, 1, 8, 7, -1011855673504735956450369414604174050565344460800000⟩, + ⟨5, 3, 2, 2, 1, 7, 5574797292738178666861973212355117237071459123200000⟩, + ⟨5, 3, 3, 2, 2, 7, -5751428826384301651285262307940938704305206067200000⟩, + ⟨5, 3, 4, 2, 3, 7, 21850134648301053122579227514841531239536105881600000⟩, + ⟨5, 3, 5, 2, 4, 7, 6474575280540527209815993262530831086021246976000000⟩, + ⟨5, 3, 6, 2, 5, 7, -59929316913233825284874018353043080451457024000000⟩, + ⟨5, 3, 7, 2, 6, 7, -263489511139578434236895435303524669714543411200000⟩, + ⟨5, 3, 8, 2, 7, 7, -434467898997809368124235159204438671776913817600000⟩, + ⟨5, 3, 2, 3, 0, 7, -9654223719901826092257994134232885987065515212800000⟩, + ⟨5, 3, 3, 3, 1, 7, -128861915161395713912885738451583990422621388800000⟩, + ⟨5, 3, 4, 3, 2, 7, -58292158822423795589180662370635663621922331033600000⟩, + ⟨5, 3, 5, 3, 3, 7, -1933344217131707185784559714539428653268205568000000⟩, + ⟨5, 3, 6, 3, 4, 7, 970418197077684898936387470583543100400992256000000⟩, + ⟨5, 3, 7, 3, 5, 7, -631976007666450070292061657638251839406001356800000⟩, + ⟨5, 3, 8, 3, 6, 7, 23330461067611898471443564235824822424174592000000⟩, + ⟨5, 3, 3, 4, 0, 7, 24708416343562842335496413318062776018019339468800000⟩, + ⟨5, 3, 4, 4, 1, 7, 748365545071110970612478429969662196569866240000000⟩, + ⟨5, 3, 5, 4, 2, 7, -3992906544022483618631318350136078874559119360000000⟩, + ⟨5, 3, 6, 4, 3, 7, -1225259491896736321284210596354295391970131968000000⟩, + ⟨5, 3, 7, 4, 4, 7, 326734682704813803010620391323305689182162124800000⟩, + ⟨5, 3, 8, 4, 5, 7, 317554008315201154761606614060576890985801318400000⟩, + ⟨5, 3, 4, 5, 0, 7, 240201855521242452776994150152842433041057343078400000⟩, + ⟨5, 3, 5, 5, 1, 7, -1348066451299775176935649615124199713361887232000000⟩, + ⟨5, 3, 6, 5, 2, 7, 2659715531991481919450114836619883018234888192000000⟩, + ⟨5, 3, 7, 5, 3, 7, 372701058826858714234517725499595694940985753600000⟩, + ⟨5, 3, 8, 5, 4, 7, 158968266828616361245103952327606704637424435200000⟩, + ⟨5, 3, 5, 6, 0, 7, 71580740828579618658553622681303089842902532096000000⟩, + ⟨5, 3, 6, 6, 1, 7, -4981122096632889831335086282088073964283756544000000⟩, + ⟨5, 3, 7, 6, 2, 7, 2637790457622175182604002426084511928741894553600000⟩, + ⟨5, 3, 8, 6, 3, 7, -844026239666878714963819777122609809731249766400000⟩, + ⟨5, 3, 6, 7, 0, 7, -1478062794557401071867889031057824552486699008000000⟩, + ⟨5, 3, 7, 7, 1, 7, -13646703554982877232141144625195181828370910412800000⟩, + ⟨5, 3, 8, 7, 2, 7, 331977993305702214158352995119372719370115481600000⟩ +] + +def collectedFourData_10_1_42 : List CollectedFourTerm := [ + ⟨5, 4, 1, 0, 2, 8, 11283557899503119482351002190422054580852359168000000⟩, + ⟨5, 4, 2, 0, 3, 8, -10733336510666122824875037160044071881177615564800000⟩, + ⟨5, 4, 3, 0, 4, 8, -1964559350660376418232390203747541779119026995200000⟩, + ⟨5, 4, 4, 0, 5, 8, 38577072814209943625263297217646736710034469683200000⟩, + ⟨5, 4, 5, 0, 6, 8, 16823289318251313011014437291404929038519631872000000⟩, + ⟨5, 4, 6, 0, 7, 8, 4633128470009953034352241790253545331913811558400000⟩, + ⟨5, 4, 7, 0, 8, 8, 2265060056133136861666628853288789804186599424000000⟩, + ⟨5, 4, 1, 1, 1, 8, -11153481620869747656535490120069611448253913497600000⟩, + ⟨5, 4, 2, 1, 2, 8, 10295558978187611359101133146760068264571699200000000⟩, + ⟨5, 4, 3, 1, 3, 8, 9430223853067579584231582559565332663346449612800000⟩, + ⟨5, 4, 4, 1, 4, 8, 11871445363230134508226462251782959956823218585600000⟩, + ⟨5, 4, 5, 1, 5, 8, -5514385134335301656181154859081569111879188480000000⟩, + ⟨5, 4, 6, 1, 6, 8, -1707332478287480880695804430662301173267457638400000⟩, + ⟨5, 4, 7, 1, 7, 8, -179188055262164974029524002563528511633489920000000⟩, + ⟨5, 4, 8, 1, 8, 8, -369931739173932234589077586382957018815974604800000⟩, + ⟨5, 4, 1, 2, 0, 8, -21173314111905431537176821456952826898963392102400000⟩, + ⟨5, 4, 2, 2, 1, 8, 14266917292968834350310907211040083302116910694400000⟩, + ⟨5, 4, 3, 2, 2, 8, -7359474710345793360145407138607970613808280371200000⟩, + ⟨5, 4, 4, 2, 3, 8, 18639485736615251147346802218009371338795804262400000⟩, + ⟨5, 4, 5, 2, 4, 8, 4142403085888779942287659142861031022314651648000000⟩, + ⟨5, 4, 6, 2, 5, 8, -30673998099947805287430510702343977761872281600000⟩, + ⟨5, 4, 7, 2, 6, 8, -112386240718561751735521220016935779244074598400000⟩, + ⟨5, 4, 8, 2, 7, 8, -158840306676159273910142792506070425000319385600000⟩, + ⟨5, 4, 2, 3, 0, 8, -24706909347013286412312784500615443618303941017600000⟩, + ⟨5, 4, 3, 3, 1, 8, -164890505365639940893086226942713177932877004800000⟩, + ⟨5, 4, 4, 3, 2, 8, -49726735345842012656360375154997445400839218790400000⟩, + ⟨5, 4, 5, 3, 3, 8, -1236944618622614738681999960045410572948209664000000⟩, + ⟨5, 4, 6, 3, 4, 8, 496695231424246444748083301310618035384903270400000⟩, + ⟨5, 4, 7, 3, 5, 8, -269556869337136380019351724119753586541959577600000⟩, + ⟨5, 4, 8, 3, 6, 8, 8529554426055199469920174032792951982129152000000⟩, + ⟨5, 4, 3, 4, 0, 8, 31616659216743140729600273045180616444241300684800000⟩, + ⟨5, 4, 4, 4, 1, 8, 638401050046246752679047502051180809667215360000000⟩, + ⟨5, 4, 5, 4, 2, 8, -2554642995554665270410373856116979061258977280000000⟩, + ⟨5, 4, 6, 4, 3, 8, -627132249493138217765470023444267522275357491200000⟩, + ⟨5, 4, 7, 4, 4, 8, 139362218035746170527352570414762482606905753600000⟩, + ⟨5, 4, 8, 4, 5, 8, 116096899640644127617306607725789271608944230400000⟩, + ⟨5, 4, 4, 5, 0, 8, 204906703412230075875688204180704581276409633177600000⟩, + ⟨5, 4, 5, 5, 1, 8, -862486632077761227728008443242544914535284736000000⟩, + ⟨5, 4, 6, 5, 2, 8, 1361338880148201082403809770612456391225167052800000⟩, + ⟨5, 4, 7, 5, 3, 8, 158968266828616361245103952327606704637424435200000⟩, + ⟨5, 4, 8, 5, 4, 8, 58118374943420747904527325302329868582859571200000⟩, + ⟨5, 4, 5, 6, 0, 8, 45797024337596188613436426565897733988478353408000000⟩, + ⟨5, 4, 6, 6, 1, 8, -2549518959959735539238118920353022017357322649600000⟩, + ⟨5, 4, 7, 6, 2, 8, 1125097359865727685381322231753957791965066035200000⟩, + ⟨5, 4, 8, 6, 3, 8, -308573745173492078884764681030534357359945318400000⟩, + ⟨5, 4, 6, 7, 0, 8, -756526149255099032740877225751989066071749427200000⟩, + ⟨5, 4, 7, 7, 1, 8, -5820731550610792444175360716024090724662876569600000⟩, + ⟨5, 4, 8, 7, 2, 8, 121370270135146550221995612806076508143196569600000⟩ +] + +def collectedFourData_10_1_43 : List CollectedFourTerm := [ + ⟨6, 0, 4, 0, 5, 5, 868530401107110443506212556194925609449052490956800000⟩, + ⟨6, 0, 5, 0, 6, 5, 1515048929698946937022109148483524419512919130112000000⟩, + ⟨6, 0, 6, 0, 7, 5, 1043109970478699472660846173627852112583999881216000000⟩, + ⟨6, 0, 7, 0, 8, 5, 1019918503697542460005714574512378063695139307520000000⟩, + ⟨6, 0, 4, 1, 4, 5, 267275623858361892356820214108672033499963090534400000⟩, + ⟨6, 0, 5, 1, 5, 5, -496607003403237715095269296323509143201728430080000000⟩, + ⟨6, 0, 6, 1, 6, 5, -384391570955068536517550710449468888698811580416000000⟩, + ⟨6, 0, 7, 1, 7, 5, -80685371987645722941306772822844404569577881600000000⟩, + ⟨6, 0, 8, 1, 8, 5, -291504586607780609949558616226531491685892882432000000⟩, + ⟨6, 0, 4, 2, 3, 5, 419652369717628537378340401767131265903149816217600000⟩, + ⟨6, 0, 5, 2, 4, 5, 373050908352907068897657739953608563305436151808000000⟩, + ⟨6, 0, 6, 2, 5, 5, -6905993101553582282428310402070145471698960384000000⟩, + ⟨6, 0, 7, 2, 6, 5, -50605636773071877129143232526427128979502661632000000⟩, + ⟨6, 0, 8, 2, 7, 5, -125165464411575117021691620194868513057175240704000000⟩, + ⟨6, 0, 4, 3, 2, 5, -1119555690595644840200994049503136876560614267289600000⟩, + ⟨6, 0, 5, 3, 3, 5, -111395077686024108064178662982848624614696812544000000⟩, + ⟨6, 0, 6, 3, 4, 5, 111826760587699286486673715072803654823990788096000000⟩, + ⟨6, 0, 7, 3, 5, 5, -121376931305333282100103103806890932895479758848000000⟩, + ⟨6, 0, 8, 3, 6, 5, 6721251446193818051985872273553251775471943680000000⟩, + ⟨6, 0, 4, 4, 1, 5, 14373063574165916423377337547030490637811056640000000⟩, + ⟨6, 0, 5, 4, 2, 5, -230062567608527265965505857711780860756104314880000000⟩, + ⟨6, 0, 6, 4, 3, 5, -141193559921644584638067017573652285450237247488000000⟩, + ⟨6, 0, 7, 4, 4, 5, 62752466322523959031276848187325436397331939328000000⟩, + ⟨6, 0, 8, 4, 5, 5, 91483847295078862326053352882193511254365044736000000⟩, + ⟨6, 0, 4, 5, 0, 5, 4613302366440958615995147246819883106475193034342400000⟩, + ⟨6, 0, 5, 5, 1, 5, -77672649152590733277211819623090742954196729856000000⟩, + ⟨6, 0, 6, 5, 2, 5, 306494017654521305594917858013469120242827395072000000⟩, + ⟨6, 0, 7, 5, 3, 5, 71580740828579618658553622681303089842902532096000000⟩, + ⟨6, 0, 8, 5, 4, 5, 45797024337596188613436426565897733988478353408000000⟩, + ⟨6, 0, 5, 6, 0, 5, 4124326188149029908159917846435366329245675552768000000⟩, + ⟨6, 0, 6, 6, 1, 5, -574002785433828311644562939639822691342382792704000000⟩, + ⟨6, 0, 7, 6, 2, 5, 506612446182689493713110793132764485257156100096000000⟩, + ⟨6, 0, 8, 6, 3, 5, -243154756673963018637558807137708707201633222656000000⟩, + ⟨6, 0, 6, 7, 0, 5, -170325509927885787168890359878710527632372400128000000⟩, + ⟨6, 0, 7, 7, 1, 5, -2620977663461602639970515260982722680998758187008000000⟩, + ⟨6, 0, 8, 7, 2, 5, 95639240096632555337092875442789923672255627264000000⟩ +] + +def collectedFourData_10_1_44 : List CollectedFourTerm := [ + ⟨6, 1, 3, 0, 4, 6, 4103842100877123980339123731964914523522570649600000⟩, + ⟨6, 1, 4, 0, 5, 6, -241755305825208008444395200505493963320601660620800000⟩, + ⟨6, 1, 5, 0, 6, 6, -210856820252140517672128829942750796220974759936000000⟩, + ⟨6, 1, 6, 0, 7, 6, -96783167521041950782306537291727655343994437632000000⟩, + ⟨6, 1, 7, 0, 8, 6, -70973540322792884268954547559254948884806369280000000⟩, + ⟨6, 1, 3, 1, 3, 6, -19699150171210438866138466172175066112201221734400000⟩, + ⟨6, 1, 4, 1, 4, 6, -74396129488543877616471346114474758685187270246400000⟩, + ⟨6, 1, 5, 1, 5, 6, 69115242154824652809015273696814795006924554240000000⟩, + ⟨6, 1, 6, 1, 6, 6, 35665111884941538243773500218584331506556076032000000⟩, + ⟨6, 1, 7, 1, 7, 6, 5614690273256305753904011286742062997071462400000000⟩, + ⟨6, 1, 8, 1, 8, 6, 16228051521278612588260070292126149405183469158400000⟩, + ⟨6, 1, 3, 2, 2, 6, 15373484209833242076482404060134409466206067097600000⟩, + ⟨6, 1, 4, 2, 3, 6, -116810173658903342955771799707699726071570733465600000⟩, + ⟨6, 1, 5, 2, 4, 6, -51919331967118148038893856299746508596601421824000000⟩, + ⟨6, 1, 6, 2, 5, 6, 640760711874020930252682953886748450454765568000000⟩, + ⟨6, 1, 7, 2, 6, 6, 3521517836036178896780536617808495623429685248000000⟩, + ⟨6, 1, 8, 2, 7, 6, 6967957618755322395374989004999595894206418124800000⟩, + ⟨6, 1, 3, 3, 1, 6, 344445993818896073357305289089070013266421350400000⟩, + ⟨6, 1, 4, 3, 2, 6, 311628157198982654456193765509590915809990515097600000⟩, + ⟨6, 1, 5, 3, 3, 6, 15503401515410172882284733561798377601427832832000000⟩, + ⟨6, 1, 6, 3, 4, 6, -10375653967076866874880182343086934538051387392000000⟩, + ⟨6, 1, 7, 3, 5, 6, 8446312619121365197849554842632256083797737472000000⟩, + ⟨6, 1, 8, 3, 6, 6, -374171864757171469587171300319236931259990016000000⟩, + ⟨6, 1, 3, 4, 0, 6, -66045231537108075836838104372430254608021349990400000⟩, + ⟨6, 1, 4, 4, 1, 6, -4000740072642681587937184165973552514560163840000000⟩, + ⟨6, 1, 5, 4, 2, 6, 32018940454033097911608281191847316905672048640000000⟩, + ⟨6, 1, 6, 4, 3, 6, 13100402018511669590539183754734363244626968576000000⟩, + ⟨6, 1, 7, 4, 4, 6, -4366784878154464504581120409998727686433800192000000⟩, + ⟨6, 1, 8, 4, 5, 6, -5092903012421070863567503917804379080242705203200000⟩, + ⟨6, 1, 4, 5, 0, 6, -1284112016161364011139712719806739201352180065894400000⟩, + ⟨6, 1, 5, 5, 1, 6, 10810085073707690727250774803444676751542714368000000⟩, + ⟨6, 1, 6, 5, 2, 6, -28437521157277116529237314024123401852675948544000000⟩, + ⟨6, 1, 7, 5, 3, 6, -4981122096632889831335086282088073964283756544000000⟩, + ⟨6, 1, 8, 5, 4, 6, -2549518959959735539238118920353022017357322649600000⟩, + ⟨6, 1, 5, 6, 0, 6, -574002785433828311644562939639822691342382792704000000⟩, + ⟨6, 1, 6, 6, 1, 6, 53257862845172875831217951330915160949373534208000000⟩, + ⟨6, 1, 7, 6, 2, 6, -35253874448618350530960239360470328220051308544000000⟩, + ⟨6, 1, 8, 6, 3, 6, 13536417950974754417853574706495175208591373107200000⟩, + ⟨6, 1, 6, 7, 0, 6, 15803359978327504596102177843582601020473081856000000⟩, + ⟨6, 1, 7, 7, 1, 6, 182387184082303807333754841552078391962041843712000000⟩, + ⟨6, 1, 8, 7, 2, 6, -5324233604023377098676282642470827782189141196800000⟩ +] + +def collectedFourData_10_1_45 : List CollectedFourTerm := [ + ⟨6, 2, 2, 0, 3, 7, -29683379782966650120397092102948926654612137574400000⟩, + ⟨6, 2, 3, 0, 4, 7, -10866101375631095010260707340823075604315452211200000⟩, + ⟨6, 2, 4, 0, 5, 7, 320058325420457472372299847721612768389836360908800000⟩, + ⟨6, 2, 5, 0, 6, 7, 186101343430771923024810084232285619703213195264000000⟩, + ⟨6, 2, 6, 0, 7, 7, 64065312692802908318824670970960022590587928576000000⟩, + ⟨6, 2, 7, 0, 8, 7, 37584569053964192078132633283501564102319276032000000⟩, + ⟨6, 2, 2, 1, 2, 7, 28472692244744371212821487410838720162142617600000000⟩, + ⟨6, 2, 3, 1, 3, 7, 52159161466861314971198197589383300531069177036800000⟩, + ⟨6, 2, 4, 1, 4, 7, 98492566856350944505075004707238628571134453350400000⟩, + ⟨6, 2, 5, 1, 5, 7, -61000822269705142499619978975957332967303413760000000⟩, + ⟨6, 2, 6, 1, 6, 7, -23608408400518757780259156262074609178326859776000000⟩, + ⟨6, 2, 7, 1, 7, 7, -2973301223696355358075277700955748726011330560000000⟩, + ⟨6, 2, 8, 1, 8, 7, -7161405037224717450276270931643486824825670860800000⟩, + ⟨6, 2, 2, 2, 1, 7, 39455608600226967464297135810949244857387004723200000⟩, + ⟨6, 2, 3, 2, 2, 7, -40705717670036073833790582586501631340631503667200000⟩, + ⟨6, 2, 4, 2, 3, 7, 154644252566568332262602744312529618368160438681600000⟩, + ⟨6, 2, 5, 2, 4, 7, 45823784203683224438921801606917583311497854976000000⟩, + ⟨6, 2, 6, 2, 5, 7, -424149533631942834511062195479048479806849024000000⟩, + ⟨6, 2, 7, 2, 6, 7, -1864846105764335045925858010258787367094793011200000⟩, + ⟨6, 2, 8, 2, 7, 7, -3074945055769150632201262832230625914333534617600000⟩, + ⟨6, 2, 2, 3, 0, 7, -68327735060009711833404939140836959671133457612800000⟩, + ⟨6, 2, 3, 3, 1, 7, -912019759840704365743969851790335738200771788800000⟩, + ⟨6, 2, 4, 3, 2, 7, -412562552894214853951827998280365653640309479833600000⟩, + ⟨6, 2, 5, 3, 3, 7, -13683237024604658206740035707471015605927149568000000⟩, + ⟨6, 2, 6, 3, 4, 7, 6868131440816726365958112463600515017663840256000000⟩, + ⟨6, 2, 7, 3, 5, 7, -4472808013253185719688041751039184848758295756800000⟩, + ⟨6, 2, 8, 3, 6, 7, 165121257690501057326887295867321460134510592000000⟩, + ⟨6, 2, 3, 4, 0, 7, 174873731400596114335394908142171193747606129868800000⟩, + ⟨6, 2, 4, 4, 1, 7, 5296554562563898272739037746374009189291786240000000⟩, + ⟨6, 2, 5, 4, 2, 7, -28259782285439065739724509327647774854201999360000000⟩, + ⟨6, 2, 6, 4, 3, 7, -8671769825418304816977063904370701789160275968000000⟩, + ⟨6, 2, 7, 4, 4, 7, 2312463589252505793248260101132290862995000524800000⟩, + ⟨6, 2, 8, 4, 5, 7, 2247487397943356353589862113552154087379068518400000⟩, + ⟨6, 2, 4, 5, 0, 7, 1700027803493358830979566217222366564862392690278400000⟩, + ⟨6, 2, 5, 5, 1, 7, -9540935656775436115640190105162487251685343232000000⟩, + ⟨6, 2, 6, 5, 2, 7, 18824127498751893398168026068482875224534024192000000⟩, + ⟨6, 2, 7, 5, 3, 7, 2637790457622175182604002426084511928741894553600000⟩, + ⟨6, 2, 8, 5, 4, 7, 1125097359865727685381322231753957791965066035200000⟩, + ⟨6, 2, 5, 6, 0, 7, 506612446182689493713110793132764485257156100096000000⟩, + ⟨6, 2, 6, 6, 1, 7, -35253874448618350530960239360470328220051308544000000⟩, + ⟨6, 2, 7, 6, 2, 7, 18668952860568531065191461595358567392853203353600000⟩, + ⟨6, 2, 8, 6, 3, 7, -5973592798431772770613992844246562220630500966400000⟩, + ⟨6, 2, 6, 7, 0, 7, -10460984327552196067260351396637083612645163008000000⟩, + ⟨6, 2, 7, 7, 1, 7, -96584497314388400188674062653819961855760452812800000⟩, + ⟨6, 2, 8, 7, 2, 7, 2349573101935156456491863429842518559751248281600000⟩ +] + +def collectedFourData_10_1_46 : List CollectedFourTerm := [ + ⟨6, 3, 1, 0, 2, 8, -59908931096597619089274501323259834772777598976000000⟩, + ⟨6, 3, 2, 0, 3, 8, 56987585226323719135975243036695141167518030233600000⟩, + ⟨6, 3, 3, 0, 4, 8, 10430632945932047674861163206909398155585283686400000⟩, + ⟨6, 3, 4, 0, 5, 8, -204821140434499330369067339263266641738436339302400000⟩, + ⟨6, 3, 5, 0, 6, 8, -89321585404336587914553346671493849940496482304000000⟩, + ⟨6, 3, 6, 0, 7, 8, -24599135905859432526026668391348083280250195148800000⟩, + ⟨6, 3, 7, 0, 8, 8, -12026111625528254004494380016564178053253562368000000⟩, + ⟨6, 3, 1, 1, 1, 8, 59218304001548843297146685157705890352493441843200000⟩, + ⟨6, 3, 2, 1, 2, 8, -54663248854544336750428255482650833751271014400000000⟩, + ⟨6, 3, 3, 1, 3, 8, -50068837867512973493196212804344067168193321369600000⟩, + ⟨6, 3, 4, 1, 4, 8, -63030261254218045130077632599851601306970174259200000⟩, + ⟨6, 3, 5, 1, 5, 8, 29278080725543447639782038446207749624021647360000000⟩, + ⟨6, 3, 6, 1, 6, 8, 9064912389487727182426808953030033363696405708800000⟩, + ⟨6, 3, 7, 1, 7, 8, 951381200118367862543636735818312705313341440000000⟩, + ⟨6, 3, 8, 1, 8, 8, 1964115863985734444421032753168142217661487513600000⟩, + ⟨6, 3, 1, 2, 0, 8, 112417610430537927083171212384029616324263857356800000⟩, + ⟨6, 3, 2, 2, 1, 8, -75748781783001708919419077846373571923112938700800000⟩, + ⟨6, 3, 3, 2, 2, 8, 39074400756934491716949588067285267891500770918400000⟩, + ⟨6, 3, 4, 2, 3, 8, -98964500082023838400228873920899608068664118476800000⟩, + ⟨6, 3, 5, 2, 4, 8, -21993678169345193579004426170157513093295374336000000⟩, + ⟨6, 3, 6, 2, 5, 8, 162860549393543820877390256664445232811815731200000⟩, + ⟨6, 3, 7, 2, 6, 8, 596703593971050573190656818820502607331380428800000⟩, + ⟨6, 3, 8, 2, 7, 8, 843346847933797844417408445359330308620759859200000⟩, + ⟨6, 3, 2, 3, 0, 8, 131178883722950797406143223870292500816113906483200000⟩, + ⟨6, 3, 3, 3, 1, 8, 875469777566195419161112793827199748872444313600000⟩, + ⟨6, 3, 4, 3, 2, 8, 264019167360676236098301945565122527168260000972800000⟩, + ⟨6, 3, 5, 3, 3, 8, 6567434721155875567173024112310915051236098048000000⟩, + ⟨6, 3, 6, 3, 4, 8, -2637154048433086803471112761264596736092720332800000⟩, + ⟨6, 3, 7, 3, 5, 8, 1431185451925956712953087520573043942320452403200000⟩, + ⟨6, 3, 8, 3, 6, 8, -45286822910504348694346640901295342840971264000000⟩, + ⟨6, 3, 3, 4, 0, 8, -167865515060979300740432347375541812028457458073600000⟩, + ⟨6, 3, 4, 4, 1, 8, -3389527032151831730318342844727892869927403520000000⟩, + ⟨6, 3, 5, 4, 2, 8, 13563623509551865699861070008419183773047848960000000⟩, + ⟨6, 3, 6, 4, 3, 8, 3329696453721671062125874457102830617995142758400000⟩, + ⟨6, 3, 7, 4, 4, 8, -739929868941443376932944858238950254727869235200000⟩, + ⟨6, 3, 8, 4, 5, 8, -616404969340941437111837636628910351626063052800000⟩, + ⟨6, 3, 4, 5, 0, 8, -1087931810629945717569059725600660096549035127603200000⟩, + ⟨6, 3, 5, 5, 1, 8, 4579287195854996922009078759331482885792202752000000⟩, + ⟨6, 3, 6, 5, 2, 8, -7227893710148759247651952569233904875213527449600000⟩, + ⟨6, 3, 7, 5, 3, 8, -844026239666878714963819777122609809731249766400000⟩, + ⟨6, 3, 8, 5, 4, 8, -308573745173492078884764681030534357359945318400000⟩, + ⟨6, 3, 5, 6, 0, 8, -243154756673963018637558807137708707201633222656000000⟩, + ⟨6, 3, 6, 6, 1, 8, 13536417950974754417853574706495175208591373107200000⟩, + ⟨6, 3, 7, 6, 2, 8, -5973592798431772770613992844246562220630500966400000⟩, + ⟨6, 3, 8, 6, 3, 8, 1638341682868651663819926339888914998240267468800000⟩, + ⟨6, 3, 6, 7, 0, 8, 4016700525859301380816206106776495062233015910400000⟩, + ⟨6, 3, 7, 7, 1, 8, 30904596626626932406649710285191390890879562547200000⟩, + ⟨6, 3, 8, 7, 2, 8, -644403406750110793842390607993625043593802547200000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1006.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1006.lean new file mode 100644 index 0000000000000000000000000000000000000000..838b6c7b004fc3e55ec458cdf63adbf8773ac84f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1006.lean @@ -0,0 +1,640 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1003 +import OAI.Analysis.LaughlinFock.Sparse1004 +import OAI.Analysis.LaughlinFock.Sparse1005 + +namespace OAI + +/-! Sparse1006. -/ +namespace LaughlinFock +def collectedFourData_10_1_47 : List CollectedFourTerm := [ + ⟨7, 0, 3, 0, 4, 6, 1217744959141844593939359486117734847282885427200000⟩, + ⟨7, 0, 4, 0, 5, 6, -71736752481661037768421193516365164374461618585600000⟩, + ⟨7, 0, 5, 0, 6, 6, -62568155316658527132189283533488353802402660352000000⟩, + ⟨7, 0, 6, 0, 7, 6, -28718749767038947961433167392695704766092673024000000⟩, + ⟨7, 0, 7, 0, 8, 6, -21060184294629437119896557750792230364208168960000000⟩, + ⟨7, 0, 3, 1, 3, 6, -5845385916588405936141481138830530728533216460800000⟩, + ⟨7, 0, 4, 1, 4, 6, -22075779096124348635600190295875943667319229644800000⟩, + ⟨7, 0, 5, 1, 5, 6, 20508766094074845471587747331233648891060551680000000⟩, + ⟨7, 0, 6, 1, 6, 6, 10583012003759802529066049114819906157699661824000000⟩, + ⟨7, 0, 7, 1, 7, 6, 1666063315627876672395386597190337452362956800000000⟩, + ⟨7, 0, 8, 1, 8, 6, 4815396755276591446690921112689123292525415628800000⟩, + ⟨7, 0, 3, 2, 2, 6, 4561818520495682320759413641331303289216774963200000⟩, + ⟨7, 0, 4, 2, 3, 6, -34661421334707458446796101295195538295409029939200000⟩, + ⟨7, 0, 5, 2, 4, 6, -15406173831945685868124594568372089587622739968000000⟩, + ⟨7, 0, 6, 2, 5, 6, 190134782898678556927606106660504244244709376000000⟩, + ⟨7, 0, 7, 2, 6, 6, 1044950192514620089443715760728165014501851136000000⟩, + ⟨7, 0, 8, 2, 7, 6, 2067622256699336399120431400998008765225212313600000⟩, + ⟨7, 0, 3, 3, 1, 6, 102208457917987186926535115452520780857658572800000⟩, + ⟨7, 0, 4, 3, 2, 6, 92470326154755202757511933280326407811522310963200000⟩, + ⟨7, 0, 5, 3, 3, 6, 4600369259067662067653569796228513098496999424000000⟩, + ⟨7, 0, 6, 3, 4, 6, -3078797869320422826311179406590659919393849344000000⟩, + ⟨7, 0, 7, 3, 5, 6, 2506298820091752181602056265176755257584123904000000⟩, + ⟨7, 0, 8, 3, 6, 6, -111029101744280873952970168571130202829094912000000⟩, + ⟨7, 0, 3, 4, 0, 6, -19597792946877669996631701572281222460387151052800000⟩, + ⟨7, 0, 4, 4, 1, 6, -1187151195523854068637610048474194958488698880000000⟩, + ⟨7, 0, 5, 4, 2, 6, 9501072988804337976515390721271170142285332480000000⟩, + ⟨7, 0, 6, 4, 3, 6, 3887320254686351045686540869393111086197112832000000⟩, + ⟨7, 0, 7, 4, 4, 6, -1295768731426797189480657122823537986522578944000000⟩, + ⟨7, 0, 8, 4, 5, 6, -1511231869629812627672852028066430153184929382400000⟩, + ⟨7, 0, 4, 5, 0, 6, -381038279791455448542284757221599682859599973580800000⟩, + ⟨7, 0, 5, 5, 1, 6, 3207707870531490101728075288319835999332990976000000⟩, + ⟨7, 0, 6, 5, 2, 6, -8438348062261529511789078692350427554809643008000000⟩, + ⟨7, 0, 7, 5, 3, 6, -1478062794557401071867889031057824552486699008000000⟩, + ⟨7, 0, 8, 5, 4, 6, -756526149255099032740877225751989066071749427200000⟩, + ⟨7, 0, 5, 6, 0, 6, -170325509927885787168890359878710527632372400128000000⟩, + ⟨7, 0, 6, 6, 1, 6, 15803359978327504596102177843582601020473081856000000⟩, + ⟨7, 0, 7, 6, 2, 6, -10460984327552196067260351396637083612645163008000000⟩, + ⟨7, 0, 8, 6, 3, 6, 4016700525859301380816206106776495062233015910400000⟩, + ⟨7, 0, 6, 7, 0, 6, 4689376803020546113404512211974803605046689792000000⟩, + ⟨7, 0, 7, 7, 1, 6, 54120277673653902323120779895906273703267139584000000⟩, + ⟨7, 0, 8, 7, 2, 6, -1579875266450270309260164378129874256655915417600000⟩ +] + +def collectedFourData_10_1_48 : List CollectedFourTerm := [ + ⟨7, 1, 2, 0, 3, 7, 153568030105498116088661307828197845221917274931200000⟩, + ⟨7, 1, 3, 0, 4, 7, 56216165254195888552096514251328943293986347417600000⟩, + ⟨7, 1, 4, 0, 5, 7, -1655833227653156693774873508286222275092689610342400000⟩, + ⟨7, 1, 5, 0, 6, 7, -962801976042167868446248511000296563924661174272000000⟩, + ⟨7, 1, 6, 0, 7, 7, -331444193358739846584329959762499138490936066048000000⟩, + ⟨7, 1, 7, 0, 8, 7, -194445116229432795058392870286045023388708110336000000⟩, + ⟨7, 1, 2, 1, 2, 7, -147304494696880013964735347636728251730939084800000000⟩, + ⟨7, 1, 3, 1, 3, 7, -269847292895430292233976899380287785671649027686400000⟩, + ⟨7, 1, 4, 1, 4, 7, -509554827743817550458538946087463184089679606579200000⟩, + ⟨7, 1, 5, 1, 5, 7, 315589942225843606537875678992620607597162004480000000⟩, + ⟨7, 1, 6, 1, 6, 7, 122138947737824472778296108750019142155814043648000000⟩, + ⟨7, 1, 7, 1, 7, 7, 15382480538665999928179418212117328308343930880000000⟩, + ⟨7, 1, 8, 1, 8, 7, 37049785853067622424865172716190256854527796838400000⟩, + ⟨7, 1, 2, 2, 1, 7, -204125006439709334470244536375948630132705040793600000⟩, + ⟨7, 1, 3, 2, 2, 7, 210592490556115917415671054642237028767561783705600000⟩, + ⟨7, 1, 4, 2, 3, 7, -800057588031558346210904483283752782226728471756800000⟩, + ⟨7, 1, 5, 2, 4, 7, -237070991362553248362159280259827281839152693248000000⟩, + ⟨7, 1, 6, 2, 5, 7, 2194352827281493139568817399649202707210698752000000⟩, + ⟨7, 1, 7, 2, 6, 7, 9647848223687570193593086904576654285102225817600000⟩, + ⟨7, 1, 8, 2, 7, 7, 15908338550048866212544591135339097288002555084800000⟩, + ⟨7, 1, 2, 3, 0, 7, 353495988376542330385624443625347028884918789734400000⟩, + ⟨7, 1, 3, 3, 1, 7, 4718366943389514046026345339136188036418004582400000⟩, + ⟨7, 1, 4, 3, 2, 7, 2134407166788198750690231017140093286485163035852800000⟩, + ⟨7, 1, 5, 3, 3, 7, 70790717590082436591767252423156911602048958464000000⟩, + ⟨7, 1, 6, 3, 4, 7, -35532524381778759136622058739582838053628018688000000⟩, + ⟨7, 1, 7, 3, 5, 7, 23140232704549841092325046703950403491716294246400000⟩, + ⟨7, 1, 8, 3, 6, 7, -854260749869982829249543517346032575857033216000000⟩, + ⟨7, 1, 3, 4, 0, 7, -904715522448621950916584539673393111616551544422400000⟩, + ⟨7, 1, 4, 4, 1, 7, -27401915026737371092687959183360899690287595520000000⟩, + ⟨7, 1, 5, 4, 2, 7, 146202997384935781833839916116623066794326753280000000⟩, + ⟨7, 1, 6, 4, 3, 7, 44863712264395433983433660436973395395859185664000000⟩, + ⟨7, 1, 7, 4, 4, 7, -11963613331389488575702041495323446619018782310400000⟩, + ⟨7, 1, 8, 4, 5, 7, -11627456674834161269505589907795083964871553843200000⟩, + ⟨7, 1, 4, 5, 0, 7, -8795154824548076351310039453913324380111118742323200000⟩, + ⟨7, 1, 5, 5, 1, 7, 49360372871524660931333647734210034626447015936000000⟩, + ⟨7, 1, 6, 5, 2, 7, -97387298871434365825294503804381236338429526016000000⟩, + ⟨7, 1, 7, 5, 3, 7, -13646703554982877232141144625195181828370910412800000⟩, + ⟨7, 1, 8, 5, 4, 7, -5820731550610792444175360716024090724662876569600000⟩, + ⟨7, 1, 5, 6, 0, 7, -2620977663461602639970515260982722680998758187008000000⟩, + ⟨7, 1, 6, 6, 1, 7, 182387184082303807333754841552078391962041843712000000⟩, + ⟨7, 1, 7, 6, 2, 7, -96584497314388400188674062653819961855760452812800000⟩, + ⟨7, 1, 8, 6, 3, 7, 30904596626626932406649710285191390890879562547200000⟩, + ⟨7, 1, 6, 7, 0, 7, 54120277673653902323120779895906273703267139584000000⟩, + ⟨7, 1, 7, 7, 1, 7, 499683361522453090321362276957459720004545439334400000⟩, + ⟨7, 1, 8, 7, 2, 7, -12155600726440770764325438601205826273145572556800000⟩ +] + +def collectedFourData_10_1_49 : List CollectedFourTerm := [ + ⟨7, 2, 1, 0, 2, 8, 23563777749833530675844192329001860227183673344000000⟩, + ⟨7, 2, 2, 0, 3, 8, -22414734634600288298506910994836410911150204518400000⟩, + ⟨7, 2, 3, 0, 4, 8, -4102645666165005586184404726923794815638935961600000⟩, + ⟨7, 2, 4, 0, 5, 8, 80561608149608356044014789928465773174399277465600000⟩, + ⟨7, 2, 5, 0, 6, 8, 35132557837442308897882491248078872836336254976000000⟩, + ⟨7, 2, 6, 0, 7, 8, 9675495134256222929037688037805054803288732467200000⟩, + ⟨7, 2, 7, 0, 8, 8, 4730189912447477015578845730757387651899195392000000⟩, + ⟨7, 2, 1, 1, 1, 8, -23292135724548476982223805214617009717374667980800000⟩, + ⟨7, 2, 2, 1, 2, 8, 21500511251242771775431311590861295817693593600000000⟩, + ⟨7, 2, 3, 1, 3, 8, 19693407078156485408301854097151678196033676902400000⟩, + ⟨7, 2, 4, 1, 4, 8, 24791480010109673260841995756289155050005908684800000⟩, + ⟨7, 2, 5, 1, 5, 8, -11515848714542863036973614525659811183161507840000000⟩, + ⟨7, 2, 6, 1, 6, 8, -3565471407312962418959075782794609821605901107200000⟩, + ⟨7, 2, 7, 1, 7, 8, -374203557710150853647948737581424215179919360000000⟩, + ⟨7, 2, 8, 1, 8, 8, -772539066324796817322429683032946405601076838400000⟩, + ⟨7, 2, 1, 2, 0, 8, -44216839440538874404104891381816422272523776819200000⟩, + ⟨7, 2, 2, 2, 1, 8, 29794012780452724997399689018526149912523125555200000⟩, + ⟨7, 2, 3, 2, 2, 8, -15369002222051373652680999046829024800826562969600000⟩, + ⟨7, 2, 4, 2, 3, 8, 38925372934731444251003138018887307198159074099200000⟩, + ⟨7, 2, 5, 2, 4, 8, 8650699232943728914576337451619603301410013184000000⟩, + ⟨7, 2, 6, 2, 5, 8, -64057390440458054456540817225009332740738252800000⟩, + ⟨7, 2, 7, 2, 6, 8, -234699411481559209358826456793273709674836787200000⟩, + ⟨7, 2, 8, 2, 7, 8, -331710770447434575121785474272560774302715084800000⟩, + ⟨7, 2, 2, 3, 0, 8, -51596147768599023666800422442542386287246888140800000⟩, + ⟨7, 2, 3, 3, 1, 8, -344345573984671222344818863751581775176296038400000⟩, + ⟨7, 2, 4, 3, 2, 8, -103845768360510786758163795968032806261367190323200000⟩, + ⟨7, 2, 5, 3, 3, 8, -2583146941919747394672491980767430523656077312000000⟩, + ⟨7, 2, 6, 3, 4, 8, 1037262904743766183433336085188662931460666163200000⟩, + ⟨7, 2, 7, 3, 5, 8, -562923345328950204046827340468506951167036620800000⟩, + ⟨7, 2, 8, 3, 6, 8, 17812513268489924724358273536974919844233216000000⟩, + ⟨7, 2, 3, 4, 0, 8, 66025976700874487875744329398236861744491685478400000⟩, + ⟨7, 2, 4, 4, 1, 8, 1333191232103532544462721657253446839833722880000000⟩, + ⟨7, 2, 5, 4, 2, 8, -5334934274593470701173761165992460193879818240000000⟩, + ⟨7, 2, 6, 4, 3, 8, -1309658272543645520898331369526790448595179929600000⟩, + ⟨7, 2, 7, 4, 4, 8, 291034119004500696289717946741762177440206028800000⟩, + ⟨7, 2, 8, 4, 5, 8, 242448486988074430611548333754931067908993843200000⟩, + ⟨7, 2, 4, 5, 0, 8, 427912548653600374404231835069429106367068425420800000⟩, + ⟨7, 2, 5, 5, 1, 8, -1801155583326936961933291962123627044051877888000000⟩, + ⟨7, 2, 6, 5, 2, 8, 2842923047829804576124827963196390070647416422400000⟩, + ⟨7, 2, 7, 5, 3, 8, 331977993305702214158352995119372719370115481600000⟩, + ⟨7, 2, 8, 5, 4, 8, 121370270135146550221995612806076508143196569600000⟩, + ⟨7, 2, 5, 6, 0, 8, 95639240096632555337092875442789923672255627264000000⟩, + ⟨7, 2, 6, 6, 1, 8, -5324233604023377098676282642470827782189141196800000⟩, + ⟨7, 2, 7, 6, 2, 8, 2349573101935156456491863429842518559751248281600000⟩, + ⟨7, 2, 8, 6, 3, 8, -644403406750110793842390607993625043593802547200000⟩, + ⟨7, 2, 6, 7, 0, 8, -1579875266450270309260164378129874256655915417600000⟩, + ⟨7, 2, 7, 7, 1, 8, -12155600726440770764325438601205826273145572556800000⟩, + ⟨7, 2, 8, 7, 2, 8, 253461017914198072937026429688808092988132556800000⟩ +] + +def collectedFourData_10_1 : List (List CollectedFourTerm) := [ + collectedFourData_10_1_0, + collectedFourData_10_1_1, + collectedFourData_10_1_2, + collectedFourData_10_1_3, + collectedFourData_10_1_4, + collectedFourData_10_1_5, + collectedFourData_10_1_6, + collectedFourData_10_1_7, + collectedFourData_10_1_8, + collectedFourData_10_1_9, + collectedFourData_10_1_10, + collectedFourData_10_1_11, + collectedFourData_10_1_12, + collectedFourData_10_1_13, + collectedFourData_10_1_14, + collectedFourData_10_1_15, + collectedFourData_10_1_16, + collectedFourData_10_1_17, + collectedFourData_10_1_18, + collectedFourData_10_1_19, + collectedFourData_10_1_20, + collectedFourData_10_1_21, + collectedFourData_10_1_22, + collectedFourData_10_1_23, + collectedFourData_10_1_24, + collectedFourData_10_1_25, + collectedFourData_10_1_26, + collectedFourData_10_1_27, + collectedFourData_10_1_28, + collectedFourData_10_1_29, + collectedFourData_10_1_30, + collectedFourData_10_1_31, + collectedFourData_10_1_32, + collectedFourData_10_1_33, + collectedFourData_10_1_34, + collectedFourData_10_1_35, + collectedFourData_10_1_36, + collectedFourData_10_1_37, + collectedFourData_10_1_38, + collectedFourData_10_1_39, + collectedFourData_10_1_40, + collectedFourData_10_1_41, + collectedFourData_10_1_42, + collectedFourData_10_1_43, + collectedFourData_10_1_44, + collectedFourData_10_1_45, + collectedFourData_10_1_46, + collectedFourData_10_1_47, + collectedFourData_10_1_48, + collectedFourData_10_1_49 +] + +theorem collectedFourChecked_10_1 : collectNumericRowParts 10 1 = collectedFourData_10_1 := by + decide +kernel + +def collectedFourData_10_2_0 : List CollectedFourTerm := [ + ⟨0, 2, 8, 2, 8, 0, -10360280526650034221496974501387895406964873625600000⟩, + ⟨0, 2, 8, 3, 7, 0, -6346259885375588231536913599774296931427155968000000⟩, + ⟨0, 2, 8, 4, 6, 0, 8094897445109575113615655379798753956628476723200000⟩, + ⟨0, 2, 8, 5, 5, 0, 2705879587310989387891446164834364596249060966400000⟩, + ⟨0, 2, 8, 6, 4, 0, -4030822154818050410845093447836384849092306534400000⟩, + ⟨0, 2, 8, 7, 3, 0, -19305415248362306533418426668214241592757295513600000⟩ +] + +def collectedFourData_10_2_1 : List CollectedFourTerm := [ + ⟨0, 3, 7, 1, 8, 1, 22907903798457579660196277770108374178315055923200000⟩, + ⟨0, 3, 7, 2, 7, 1, -1352508879285030363940207362529923410033639424000000⟩, + ⟨0, 3, 8, 2, 8, 1, -21864487203824184209264182982834026260214893772800000⟩, + ⟨0, 3, 7, 3, 6, 1, -1056067462920454296776439542620830497162605363200000⟩, + ⟨0, 3, 8, 3, 7, 1, -13393239468661779258381002264152076487474806784000000⟩, + ⟨0, 3, 7, 4, 5, 1, -3635945253508706422283668519252910982366756864000000⟩, + ⟨0, 3, 8, 4, 6, 1, 17083589691378446438109520648786630182449027481600000⟩, + ⟨0, 3, 7, 5, 4, 1, 2303959319293077366780963179399335596729040896000000⟩, + ⟨0, 3, 8, 5, 5, 1, 5710527766083595081418582309107653368121340723200000⟩, + ⟨0, 3, 7, 6, 3, 1, 6908464510682967075694846332303980127009216921600000⟩, + ⟨0, 3, 8, 6, 4, 1, -8506705894517651792398791776545472237343552307200000⟩, + ⟨0, 3, 7, 7, 2, 1, -12268132495297847970776523365050572415611332198400000⟩, + ⟨0, 3, 8, 7, 3, 1, -40742430050667332915479222317224372342837005516800000⟩ +] + +def collectedFourData_10_2_2 : List CollectedFourTerm := [ + ⟨0, 4, 6, 0, 8, 2, -6816458612947291212272759929710082820606106009600000⟩, + ⟨0, 4, 6, 1, 7, 2, 22797146151350977527157680182592132607213830144000000⟩, + ⟨0, 4, 7, 1, 8, 2, 42856935179538209640966968958651560054286503116800000⟩, + ⟨0, 4, 6, 2, 6, 2, -1573678291185118444917270723254497260929758003200000⟩, + ⟨0, 4, 7, 2, 7, 2, -2530322541915477942843079749338673398862053376000000⟩, + ⟨0, 4, 8, 2, 8, 2, -20452436832985744651948111380315536762154359193600000⟩, + ⟨0, 4, 6, 3, 5, 2, 3833698172355380038356423746766390284508148531200000⟩, + ⟨0, 4, 7, 3, 6, 2, -1975729215636425295638673423240250652745321676800000⟩, + ⟨0, 4, 8, 3, 7, 2, -12528278466734227974553615178902043933181739008000000⟩, + ⟨0, 4, 6, 4, 4, 2, -1771702606655818610071521634126747725050413056000000⟩, + ⟨0, 4, 7, 4, 5, 2, -6802257920101104807938540653022299818804903936000000⟩, + ⟨0, 4, 8, 4, 6, 2, 15980298819102992799792067528800151696445748019200000⟩, + ⟨0, 4, 6, 5, 3, 2, -656284757606650889695694936200884003391773081600000⟩, + ⟨0, 4, 7, 5, 4, 2, 4310330446292721697270272530563150447644770304000000⟩, + ⟨0, 4, 8, 5, 5, 2, 5341730969039518997612674867237833876049389158400000⟩, + ⟨0, 4, 6, 6, 2, 2, -47024753736468710097188565875612986307314817433600000⟩, + ⟨0, 4, 7, 6, 3, 2, 12924605338373005099847469898281017759045674598400000⟩, + ⟨0, 4, 8, 6, 4, 2, -7957326569908279651654604038420259299798705766400000⟩, + ⟨0, 4, 6, 7, 1, 2, 93224415289957355207680338836067562387766299852800000⟩, + ⟨0, 4, 7, 7, 2, 2, -22951666104009365387618019715310762208066640281600000⟩, + ⟨0, 4, 8, 7, 3, 2, -38111206051421573978268677444328367324137101721600000⟩ +] + +def collectedFourData_10_2_3 : List CollectedFourTerm := [ + ⟨0, 5, 5, 0, 7, 3, 760543587660090356488100226921669037475758080000000⟩, + ⟨0, 5, 6, 0, 8, 3, 46853259058863797197497723969135541008759521280000000⟩, + ⟨0, 5, 5, 1, 6, 3, -125483792307616783448153558261864877178339983360000000⟩, + ⟨0, 5, 6, 1, 7, 3, -156697290350039195922340435120574557249024819200000000⟩, + ⟨0, 5, 7, 1, 8, 3, -147289611839044557798217270453788174783212421120000000⟩, + ⟨0, 5, 5, 2, 5, 3, 21949854844140572880607229972824007493329879040000000⟩, + ⟨0, 5, 6, 2, 6, 3, 10816754100458966467077784688238888203593973760000000⟩, + ⟨0, 5, 7, 2, 7, 3, 8696147390498750460915093813808334769645158400000000⟩, + ⟨0, 5, 8, 2, 8, 3, 46860272356126789648685983391987381968211804160000000⟩, + ⟨0, 5, 5, 3, 4, 3, -29708212259109458993806929994533315305558507520000000⟩, + ⟨0, 5, 6, 3, 5, 3, -26351110425827832690796129669356551376375644160000000⟩, + ⟨0, 5, 7, 3, 6, 3, 6790135320014375893016800314703814769896325120000000⟩, + ⟨0, 5, 8, 3, 7, 3, 28704576667251827346664996987791300503588044800000000⟩, + ⟨0, 5, 5, 4, 3, 3, 2771075305512380725105156172883584572792504320000000⟩, + ⟨0, 5, 6, 4, 4, 3, 12177883842386826448348679125621584513780940800000000⟩, + ⟨0, 5, 7, 4, 5, 3, 23377824953733752983942284215108100719797862400000000⟩, + ⟨0, 5, 8, 4, 6, 3, -36613786470066224257618891272624285903507947520000000⟩, + ⟨0, 5, 5, 5, 2, 3, 215231387446322466677461574296143940659204587520000000⟩, + ⟨0, 5, 6, 5, 3, 3, 4511005128986296501238641888598442623505530880000000⟩, + ⟨0, 5, 7, 5, 4, 3, -14813632745152157354524917179688703107897753600000000⟩, + ⟨0, 5, 8, 5, 5, 3, -12238882344750249627914161704642378988561367040000000⟩, + ⟨0, 5, 5, 6, 1, 3, -274973065618596652508273941146704637347443507200000000⟩, + ⟨0, 5, 6, 6, 2, 3, 323226926781177639383210877090443432483597844480000000⟩, + ⟨0, 5, 7, 6, 3, 3, -44418950993273413729821001652391233186231746560000000⟩, + ⟨0, 5, 8, 6, 4, 3, 18231690108005139543084667861435814451703971840000000⟩, + ⟨0, 5, 5, 7, 0, 3, -1199688339056445036341049542717885286042052853760000000⟩, + ⟨0, 5, 6, 7, 1, 3, -640782542403334916131861509151348409750299607040000000⟩, + ⟨0, 5, 7, 7, 2, 3, 78879695371518663694514383061273607245597245440000000⟩, + ⟨0, 5, 8, 7, 3, 3, 87319741406548471080550324897133367739243560960000000⟩ +] + +def collectedFourData_10_2_4 : List CollectedFourTerm := [ + ⟨0, 6, 4, 0, 6, 4, 61748649476041066677476536676065941184680296448000000⟩, + ⟨0, 6, 5, 0, 7, 4, 798240391803679460621891199066224327789641728000000⟩, + ⟨0, 6, 6, 0, 8, 4, 24587784628816028934384449878336710478789607424000000⟩, + ⟨0, 6, 4, 1, 5, 4, -95686996353423751595247903121820139925319083622400000⟩, + ⟨0, 6, 5, 1, 6, 4, -131703472571266803484470202381246337021405822976000000⟩, + ⟨0, 6, 6, 1, 7, 4, -82232043286579609849658468658446619953709711360000000⟩, + ⟨0, 6, 7, 1, 8, 4, -51530036923869887881703299755681789160313585664000000⟩, + ⟨0, 6, 4, 2, 4, 4, 25512003468642075488908551472252196170742995353600000⟩, + ⟨0, 6, 5, 2, 5, 4, 23037812710678506388023426987339021824362020864000000⟩, + ⟨0, 6, 6, 2, 6, 4, 5676446538560114461148545931813450072413175808000000⟩, + ⟨0, 6, 7, 2, 7, 4, 3042392403189336926731145620068527008886292480000000⟩, + ⟨0, 6, 8, 2, 8, 4, 12295732543306752093925023120928316857792856064000000⟩, + ⟨0, 6, 4, 3, 3, 4, -32540132914388526472770876592021331443011551232000000⟩, + ⟨0, 6, 5, 3, 4, 4, -31180717815869659978901898833226856645087199232000000⟩, + ⟨0, 6, 6, 3, 5, 4, -13828609597176557483832162747831599116087984128000000⟩, + ⟨0, 6, 7, 3, 6, 4, 2375564164978408984747488104870870972538814464000000⟩, + ⟨0, 6, 8, 3, 7, 4, 7531834104315144930107921373998262240852049920000000⟩, + ⟨0, 6, 4, 4, 2, 4, 108485777193429676188589311842835132715071071846400000⟩, + ⟨0, 6, 5, 4, 3, 4, 2908425333510674960184172401592977044759642112000000⟩, + ⟨0, 6, 6, 4, 4, 4, 6390744020072593708213499957719027688291696640000000⟩, + ⟨0, 6, 7, 4, 5, 4, 8178853674908846623551228207399039826950881280000000⟩, + ⟨0, 6, 8, 4, 6, 4, -9607142750095791576871226295145568059741175808000000⟩, + ⟨0, 6, 4, 5, 1, 4, -104593829688984557734121377876683942513433431244800000⟩, + ⟨0, 6, 5, 5, 2, 4, 225899461689219301099118220870543508151029727232000000⟩, + ⟨0, 6, 6, 5, 3, 4, 2367297916920814079475870009338314229079343104000000⟩, + ⟨0, 6, 7, 5, 4, 4, -5182626478563272024673440796541203953662033920000000⟩, + ⟨0, 6, 8, 5, 5, 4, -3211377492567489483752142382191709051385020416000000⟩, + ⟨0, 6, 4, 6, 0, 4, -326335217833134928190318362464016013112194472345600000⟩, + ⟨0, 6, 5, 6, 1, 4, -288602272369622751127947246288081713437889003520000000⟩, + ⟨0, 6, 6, 6, 2, 4, 169623932711809328589063576900049124436668841984000000⟩, + ⟨0, 6, 7, 6, 3, 4, -15540201078839327636141492937573897346882732032000000⟩, + ⟨0, 6, 8, 6, 4, 4, 4783838721141641308661988775168032336129294336000000⟩, + ⟨0, 6, 5, 7, 0, 4, -1259151619116299632924388922916719925922277359616000000⟩, + ⟨0, 6, 6, 7, 1, 4, -336271658855665660139162627262224982866323832832000000⟩, + ⟨0, 6, 7, 7, 2, 4, 27596471769372084100040775167160618754787770368000000⟩, + ⟨0, 6, 8, 7, 3, 4, 22911949335805587751084334528308298276388470784000000⟩ +] + +def collectedFourData_10_2_5 : List CollectedFourTerm := [ + ⟨0, 7, 3, 0, 5, 5, 760543587660090356488100226921669037475758080000000⟩, + ⟨0, 7, 4, 0, 6, 5, 798240391803679460621891199066224327789641728000000⟩, + ⟨0, 7, 5, 0, 7, 5, 5159527605167504522934793555138195859963904000000⟩, + ⟨0, 7, 6, 0, 8, 5, 105950834564708448856732443157429360879730688000000⟩, + ⟨0, 7, 3, 1, 4, 5, -727542889806413753658319529141512104668508979200000⟩, + ⟨0, 7, 4, 1, 5, 5, -1236969975988069252536245855298949908273718886400000⟩, + ⟨0, 7, 5, 1, 6, 5, -851282031585037201855611771910289595373191168000000⟩, + ⟨0, 7, 6, 1, 7, 5, -354344799488910858883515186241030498623160320000000⟩, + ⟨0, 7, 7, 1, 8, 5, -166535451434156531324657132904668363464114176000000⟩, + ⟨0, 7, 3, 2, 3, 5, 504680884280110899652792354646429576263945420800000⟩, + ⟨0, 7, 4, 2, 4, 5, 329800114128930685497107714871006078309079449600000⟩, + ⟨0, 7, 5, 2, 5, 5, 148907812563634629875815800707932009059581952000000⟩, + ⟨0, 7, 6, 2, 6, 5, 24460286162485183488271762233920296002256896000000⟩, + ⟨0, 7, 7, 2, 7, 5, 9832443804640187730224311923249787510456320000000⟩, + ⟨0, 7, 8, 2, 8, 5, 31790008190189511288037840137485068125654220800000⟩, + ⟨0, 7, 3, 3, 2, 5, -332793010982906456958308131886327928388897996800000⟩, + ⟨0, 7, 4, 3, 3, 5, -420654519043428422516650714054659368395210752000000⟩, + ⟨0, 7, 5, 3, 4, 5, -201540508312794412317994739666179084964069376000000⟩, + ⟨0, 7, 6, 3, 5, 5, -59588643296203469943515912962099625104244736000000⟩, + ⟨0, 7, 7, 3, 6, 5, 7677379529340609782348365322049305104613376000000⟩, + ⟨0, 7, 8, 3, 7, 5, 19473184458104205458696452346581326678196224000000⟩, + ⟨0, 7, 3, 4, 1, 5, 307279193278667007286334833065465989658417561600000⟩, + ⟨0, 7, 4, 4, 2, 5, 1402423049359331147498463049040967195762779750400000⟩, + ⟨0, 7, 5, 4, 3, 5, 18798974531856887338624128846105203982729216000000⟩, + ⟨0, 7, 6, 4, 4, 5, 27538254163108621741278588834126736580935680000000⟩, + ⟨0, 7, 7, 4, 5, 5, 26432526935254599898775755610782288073195520000000⟩, + ⟨0, 7, 8, 4, 6, 5, -24838792291079655437195039757573275482954137600000⟩, + ⟨0, 7, 3, 5, 0, 5, -369085275671963326255728201275713876474095206400000⟩, + ⟨0, 7, 4, 5, 1, 5, -1352110860717326106768608889393263222469741772800000⟩, + ⟨0, 7, 5, 5, 2, 5, 1460129705970403396874579179994955932422373376000000⟩, + ⟨0, 7, 6, 5, 3, 5, 10200886080119112068537707589223474001870848000000⟩, + ⟨0, 7, 7, 5, 4, 5, -16749280453597812720030148336973329496801280000000⟩, + ⟨0, 7, 8, 5, 5, 5, -8302857632185878308021464172569479133475635200000⟩, + ⟨0, 7, 4, 6, 0, 5, -4218617805455555629578227747977761955608369561600000⟩, + ⟨0, 7, 5, 6, 1, 5, -1865417243345109067357990031284186176144015360000000⟩, + ⟨0, 7, 6, 6, 2, 5, 730923810512876636762400409455850344476049408000000⟩, + ⟨0, 7, 7, 6, 3, 5, -50223026346081575830142019268876676930469888000000⟩, + ⟨0, 7, 8, 6, 4, 5, 12368378345088769619507077074591009492644659200000⟩, + ⟨0, 7, 5, 7, 0, 5, -8138685544641918331715189348369213491865714688000000⟩, + ⟨0, 7, 6, 7, 1, 5, -1449022896290608608864759275565619609583222784000000⟩, + ⟨0, 7, 7, 7, 2, 5, 89186640616852757590972851594397159325171712000000⟩, + ⟨0, 7, 8, 7, 3, 5, 59237711496494729492095846053938958533709004800000⟩ +] + +def collectedFourData_10_2_6 : List CollectedFourTerm := [ + ⟨0, 8, 2, 0, 4, 6, -6816458612947291212272759929710082820606106009600000⟩, + ⟨0, 8, 3, 0, 5, 6, 46853259058863797197497723969135541008759521280000000⟩, + ⟨0, 8, 4, 0, 6, 6, 24587784628816028934384449878336710478789607424000000⟩, + ⟨0, 8, 5, 0, 7, 6, 105950834564708448856732443157429360879730688000000⟩, + ⟨0, 8, 6, 0, 8, 6, 1631774292725260910694796536564411664592535552000000⟩, + ⟨0, 8, 2, 1, 3, 6, 4069735820059318987939931031955863263963932262400000⟩, + ⟨0, 8, 3, 1, 4, 6, -44820252311126100197362902962397712221740413747200000⟩, + ⟨0, 8, 4, 1, 5, 6, -38101744379513354140207610143981288021537534771200000⟩, + ⟨0, 8, 5, 1, 6, 6, -17481065825879427863254359188040532805912887296000000⟩, + ⟨0, 8, 6, 1, 7, 6, -5457349505007959982088963864464981446916833280000000⟩, + ⟨0, 8, 7, 1, 8, 6, -2051882042036659420313315301945272124732289843200000⟩, + ⟨0, 8, 2, 2, 2, 6, 993607991822548920139024622803169771467151769600000⟩, + ⟨0, 8, 3, 2, 3, 6, 31090846858603160591059278805045506630109416652800000⟩, + ⟨0, 8, 4, 2, 4, 6, 10158661801663687195245557643468306339391655116800000⟩, + ⟨0, 8, 5, 2, 5, 6, 3057820060604185539891344769536690896811065344000000⟩, + ⟨0, 8, 6, 2, 6, 6, 376718751830782990000043621395273888441565184000000⟩, + ⟨0, 8, 7, 2, 7, 6, 121145466015399410989930446951644138594893824000000⟩, + ⟨0, 8, 8, 2, 8, 6, 326403709439998951025766875840538214346312908800000⟩, + ⟨0, 8, 2, 3, 1, 6, 5694431390258088605398675829075379933161717760000000⟩, + ⟨0, 8, 3, 3, 2, 6, -20501700901237690735234624362437352111796440268800000⟩, + ⟨0, 8, 4, 3, 3, 6, -12957202897246740618597110355507745517696188416000000⟩, + ⟨0, 8, 5, 3, 4, 6, -4138631806708375803013363247262042543957737472000000⟩, + ⟨0, 8, 6, 3, 5, 6, -917739031208242234225443007991404513978220544000000⟩, + ⟨0, 8, 7, 3, 6, 6, 94592935320934861551168209058788456365503283200000⟩, + ⟨0, 8, 8, 3, 7, 6, 199940799124929620426757268322946388133412864000000⟩, + ⟨0, 8, 2, 4, 0, 6, -21807212599951052825734733367044666910485721907200000⟩, + ⟨0, 8, 3, 4, 1, 6, 18929923122984146444146871436095414619923388825600000⟩, + ⟨0, 8, 4, 4, 2, 6, 43198109554715870092484183856652589554774258483200000⟩, + ⟨0, 8, 5, 4, 3, 6, 386036705882935892519398054672560735966461952000000⟩, + ⟨0, 8, 6, 4, 4, 6, 424123277504253009379722347968894574757150720000000⟩, + ⟨0, 8, 7, 4, 5, 6, 325674965162254240575675766407729498254475264000000⟩, + ⟨0, 8, 8, 4, 6, 6, -255032143852043412508852775484354729034226073600000⟩, + ⟨0, 8, 3, 5, 0, 6, -22737484499835593683283523698955546754896258662400000⟩, + ⟨0, 8, 4, 5, 1, 6, -41648369312006841935982796921250035600418301542400000⟩, + ⟨0, 8, 5, 5, 2, 6, 29983745171814850222644504665010286365845225472000000⟩, + ⟨0, 8, 6, 5, 3, 6, 157106300643542531790108085296735553629192192000000⟩, + ⟨0, 8, 7, 5, 4, 6, -206367758238917400407131699492576795343978496000000⟩, + ⟨0, 8, 8, 5, 5, 6, -85249538593513692201896567340735172304909107200000⟩, + ⟨0, 8, 4, 6, 0, 6, -129943895469198926588407086724608849819103710412800000⟩, + ⟨0, 8, 5, 6, 1, 6, -38306319661099216401486708513809988117772369920000000⟩, + ⟨0, 8, 6, 6, 2, 6, 11257133450961825648597525858412083426657042432000000⟩, + ⟨0, 8, 7, 6, 3, 6, -618797529107504087616605017977777695135209881600000⟩, + ⟨0, 8, 8, 6, 4, 6, 126992246980300742460627894041115686056702771200000⟩, + ⟨0, 8, 5, 7, 0, 6, -167127805431432574908111227536980467271635828736000000⟩, + ⟨0, 8, 6, 7, 1, 6, -22316750230912382888265690207052941062660161536000000⟩, + ⟨0, 8, 7, 7, 2, 6, 1098867926890934584738459643681700086502811238400000⟩, + ⟨0, 8, 8, 7, 3, 6, 608222830755964207026707224643987583452105932800000⟩ +] + +def collectedFourData_10_2_7 : List CollectedFourTerm := [ + ⟨1, 1, 8, 2, 8, 0, 76331577568473640276555581865597789251432559411200000⟩, + ⟨1, 1, 8, 3, 7, 0, 46757423938874280297367366027109775636468596736000000⟩, + ⟨1, 1, 8, 4, 6, 0, -59640884303353467777668271020347856812859876966400000⟩, + ⟨1, 1, 8, 5, 5, 0, -19936145269279077423212471366267363633883040972800000⟩, + ⟨1, 1, 8, 6, 4, 0, 29697942365920005662230663698561285503266376908800000⟩, + ⟨1, 1, 8, 7, 3, 0, 142236766439996148285686545693173527430820999987200000⟩ +] + +def collectedFourData_10_2_8 : List CollectedFourTerm := [ + ⟨1, 2, 7, 1, 8, 1, 6722736166706000464345515570901377811224723456000000⟩, + ⟨1, 2, 7, 2, 7, 1, -396918043595620835920946408205632418003025920000000⟩, + ⟨1, 2, 8, 2, 8, 1, -6416526810345972217275350222259198067394740224000000⟩, + ⟨1, 2, 7, 3, 6, 1, -309921981073397740069563742567598782892998656000000⟩, + ⟨1, 2, 8, 3, 7, 1, -3930486881623331386512110997856145659102494720000000⟩, + ⟨1, 2, 7, 4, 5, 1, -1067033495119348819004506475999608320420741120000000⟩, + ⟨1, 2, 8, 4, 6, 1, 5013486492951336126059407185322366358758883328000000⟩, + ⟨1, 2, 7, 5, 4, 1, 676138278678898527149512879584558819500359680000000⟩, + ⟨1, 2, 8, 5, 5, 1, 1675857026543558474870545192914215053301907456000000⟩, + ⟨1, 2, 7, 6, 3, 1, 2027413098596143854632254671623864221358358528000000⟩, + ⟨1, 2, 8, 6, 4, 1, -2496445762988384204048577509245842701131186176000000⟩, + ⟨1, 2, 7, 7, 2, 1, -3600304015142282764251616042859169514700931072000000⟩, + ⟨1, 2, 8, 7, 3, 1, -11956598492418706886204199461846942175140511744000000⟩ +] + +def collectedFourData_10_2_9 : List CollectedFourTerm := [ + ⟨1, 3, 6, 0, 8, 2, 4069735820059318987939931031955863263963932262400000⟩, + ⟨1, 3, 6, 1, 7, 2, -13610933118710029796586577798757045127333543936000000⟩, + ⟨1, 3, 7, 1, 8, 2, -25587539533627870505682831298963572599783895859200000⟩, + ⟨1, 3, 6, 2, 6, 2, 939557514325854049952373660420197306136841420800000⟩, + ⟨1, 3, 7, 2, 7, 2, 1510717642380644241474022446158738614275538944000000⟩, + ⟨1, 3, 8, 2, 8, 2, 12211035012902863386852010440204547682654905958400000⟩, + ⟨1, 3, 6, 3, 5, 2, -2288892174258299092999556917005705122249755852800000⟩, + ⟨1, 3, 7, 3, 6, 2, 1179600202418985577812385559759283212369736499200000⟩, + ⟨1, 3, 8, 3, 7, 2, 7479952059402372551700281757022980806962839552000000⟩, + ⟨1, 3, 6, 4, 4, 2, 1057787037260693434330640643814954083878436864000000⟩, + ⟨1, 3, 7, 4, 5, 2, 4061257360550152182973637941454518568651587584000000⟩, + ⟨1, 3, 8, 4, 6, 2, -9540965215548353822258005074632795989857848524800000⟩, + ⟨1, 3, 6, 5, 3, 2, 391831849623142093217844659579507710676592230400000⟩, + ⟨1, 3, 7, 5, 4, 2, -2573463320124966519516823648802242618485374976000000⟩, + ⟨1, 3, 8, 5, 5, 2, -3189256342659820000385678157413066238601042329600000⟩, + ⟨1, 3, 6, 6, 2, 2, 28075916774036878925151360066678973067939964518400000⟩, + ⟨1, 3, 7, 6, 3, 2, -7716577227623408635688711726181047231441377689600000⟩, + ⟨1, 3, 8, 6, 4, 2, 4750885879649350085050846642434546211552336281600000⟩, + ⟨1, 3, 6, 7, 1, 2, -55659215987754848930968708224401822440439886643200000⟩, + ⟨1, 3, 7, 7, 2, 2, 13703188558367985501504820438381224508365629030400000⟩, + ⟨1, 3, 8, 7, 3, 2, 22754123397526040546116063946773320381980108390400000⟩ +] + +def collectedFourData_10_2_10 : List CollectedFourTerm := [ + ⟨1, 4, 5, 0, 7, 3, -727542889806413753658319529141512104668508979200000⟩, + ⟨1, 4, 6, 0, 8, 3, -44820252311126100197362902962397712221740413747200000⟩, + ⟨1, 4, 5, 1, 6, 3, 120038933153366797286749209096070977377068803686400000⟩, + ⟨1, 4, 6, 1, 7, 3, 149898048311537379141698132535878101712353886208000000⟩, + ⟨1, 4, 7, 1, 8, 3, 140898577773212696759294309381425259375932263628800000⟩, + ⟨1, 4, 5, 2, 5, 3, -20997430105576764042935187551482748648732334489600000⟩, + ⟨1, 4, 6, 2, 6, 3, -10347405019593005519422156104161851649558996582400000⟩, + ⟨1, 4, 7, 2, 7, 3, -8318813418874829596767434695387299373400457216000000⟩, + ⟨1, 4, 8, 2, 8, 3, -44826961294859021220113085459431761404282431078400000⟩, + ⟨1, 4, 5, 3, 4, 3, 28419145133381579199019641778460678757448207564800000⟩, + ⟨1, 4, 6, 3, 5, 3, 25207711089641115446834896366067442301427672678400000⟩, + ⟨1, 4, 7, 3, 6, 3, -6495504995445102427751497020744193470500752588800000⟩, + ⟨1, 4, 8, 3, 7, 3, -27459058228883194883349148483001095505578033152000000⟩, + ⟨1, 4, 5, 4, 3, 3, -2650835755313360124464287093961175662735445196800000⟩, + ⟨1, 4, 6, 4, 4, 3, -11649474068508896518966309307256628030778376192000000⟩, + ⟨1, 4, 7, 4, 5, 3, -22363439256067325126521447233241449338215858176000000⟩, + ⟨1, 4, 8, 4, 6, 3, 35025080018283339026284288262689024518394793164800000⟩, + ⟨1, 4, 5, 5, 2, 3, -205892296168732025231884312642733794948394306764800000⟩, + ⟨1, 4, 6, 5, 3, 3, -4315268395821444646564240933186537302850220851200000⟩, + ⟨1, 4, 7, 5, 4, 3, 14170855360305435758151073455829415287968497664000000⟩, + ⟨1, 4, 8, 5, 5, 3, 11707825788782925798778885031416733675856435609600000⟩, + ⟨1, 4, 5, 6, 1, 3, 263041727029184897099245994961599285562156515328000000⟩, + ⟨1, 4, 6, 6, 2, 3, -309201808008306772052428530988323766235378692915200000⟩, + ⟨1, 4, 7, 6, 3, 3, 42491571150106003914965420826434401806030628454400000⟩, + ⟨1, 4, 8, 6, 4, 3, -17440600016157515799977228149422082115440843161600000⟩, + ⟨1, 4, 5, 7, 0, 3, 1147632739564000068745151178184047317822946567782400000⟩, + ⟨1, 4, 6, 7, 1, 3, 612978388355014846146587708607452993207286733209600000⟩, + ⟨1, 4, 7, 7, 2, 3, -75457031587376765631253923054112633358758025625600000⟩, + ⟨1, 4, 8, 7, 3, 3, -83530856128211789135995365520355905796236011110400000⟩ +] + +def collectedFourData_10_2_11 : List CollectedFourTerm := [ + ⟨1, 5, 4, 0, 6, 4, -95686996353423751595247903121820139925319083622400000⟩, + ⟨1, 5, 5, 0, 7, 4, -1236969975988069252536245855298949908273718886400000⟩, + ⟨1, 5, 6, 0, 8, 4, -38101744379513354140207610143981288021537534771200000⟩, + ⟨1, 5, 4, 1, 5, 4, 148278567204821647801818626170190705614931487621120000⟩, + ⟨1, 5, 5, 1, 6, 4, 204090450667262629177192617223989832697290476748800000⟩, + ⟨1, 5, 6, 1, 7, 4, 127428491033647269340142401444702529421016301568000000⟩, + ⟨1, 5, 7, 1, 8, 4, 79852021008804386608510730793680044413936677683200000⟩, + ⟨1, 5, 4, 2, 4, 4, -39533933188606485208721375634941397948245401927680000⟩, + ⟨1, 5, 5, 2, 5, 4, -35699875536433951197479467000016652797480219443200000⟩, + ⟨1, 5, 6, 2, 6, 4, -8796340063216402403231205445819792722137343590400000⟩, + ⟨1, 5, 7, 2, 7, 4, -4714554783949046698176810564066084600491802624000000⟩, + ⟨1, 5, 8, 2, 8, 4, -19053723846876583716130308678580165288932881203200000⟩, + ⟨1, 5, 4, 3, 3, 4, 50424869303856519299344032331987128728726116761600000⟩, + ⟨1, 5, 5, 3, 4, 4, 48318291286709191559509613102674227021418699161600000⟩, + ⟨1, 5, 6, 3, 5, 4, 21429102131397584323801400661439142650054076006400000⟩, + ⟨1, 5, 7, 3, 6, 4, -3681223824657272158025853981358248488005219123200000⟩, + ⟨1, 5, 8, 3, 7, 4, -11671487370000412865373903394800271728360554496000000⟩, + ⟨1, 5, 4, 4, 2, 4, -168111825194392745913044085224644762110565621432320000⟩, + ⟨1, 5, 5, 4, 3, 4, -4506956615947091871627544672152804197700049305600000⟩, + ⟨1, 5, 6, 4, 4, 4, -9903230352942727219162064125784200613128568832000000⟩, + ⟨1, 5, 7, 4, 5, 4, -12674122404407366194720119017534420432468312064000000⟩, + ⟨1, 5, 8, 4, 6, 4, 14887428973680215616813785868895130218303743590400000⟩, + ⟨1, 5, 4, 5, 1, 4, 162080782089392464418257344545542629249761138442240000⟩, + ⟨1, 5, 5, 5, 2, 4, -350058521932269053542642013544371450381432625561600000⟩, + ⟨1, 5, 6, 5, 3, 4, -3668414274092923652908498491053993113645429555200000⟩, + ⟨1, 5, 7, 5, 4, 4, 8031106188773536283177664556598627517591453696000000⟩, + ⟨1, 5, 8, 5, 5, 4, 4976417606347846276202294119350585689123900620800000⟩, + ⟨1, 5, 4, 6, 0, 4, 505695866448202418599527182874998328177512970977280000⟩, + ⟨1, 5, 5, 6, 1, 4, 447224106407977604014293236118454210661424562176000000⟩, + ⟨1, 5, 6, 6, 2, 4, -262852787365753925402813763855125028768956232499200000⟩, + ⟨1, 5, 7, 6, 3, 4, 24081420024244185788429628842771967447748155801600000⟩, + ⟨1, 5, 8, 6, 4, 4, -7413136354388745211560310158780297358613466316800000⟩, + ⟨1, 5, 5, 7, 0, 4, 1951207636266406591150729601785807371094952037580800000⟩, + ⟨1, 5, 6, 7, 1, 4, 521093582899601427469058123768157734577500690841600000⟩, + ⟨1, 5, 7, 7, 2, 4, -42764068784821756950837403284280041006996809318400000⟩, + ⟨1, 5, 8, 7, 3, 4, -35504835023083654606593007876176910101039493939200000⟩ +] + +def collectedFourData_10_2_12 : List CollectedFourTerm := [ + ⟨1, 6, 3, 0, 5, 5, -125483792307616783448153558261864877178339983360000000⟩, + ⟨1, 6, 4, 0, 6, 5, -131703472571266803484470202381246337021405822976000000⟩, + ⟨1, 6, 5, 0, 7, 5, -851282031585037201855611771910289595373191168000000⟩, + ⟨1, 6, 6, 0, 8, 5, -17481065825879427863254359188040532805912887296000000⟩, + ⟨1, 6, 3, 1, 4, 5, 120038933153366797286749209096070977377068803686400000⟩, + ⟨1, 6, 4, 1, 5, 5, 204090450667262629177192617223989832697290476748800000⟩, + ⟨1, 6, 5, 1, 6, 5, 140454931682843751318450224736003167413868691456000000⟩, + ⟨1, 6, 6, 1, 7, 5, 58464143207296529135764506688442472869595709440000000⟩, + ⟨1, 6, 7, 1, 8, 5, 27477057644930952519305946948574317521972232192000000⟩, + ⟨1, 6, 3, 2, 3, 5, -83268431017176044960390771467349769859360201113600000⟩, + ⟨1, 6, 4, 2, 4, 5, -54414460519886796399786550848020653275845178163200000⟩, + ⟨1, 6, 5, 2, 5, 5, -24568633971663663023797967275685053530409795584000000⟩, + ⟨1, 6, 6, 2, 6, 5, -4035757474520916484163547526817174643573522432000000⟩, + ⟨1, 6, 7, 2, 7, 5, -1622276955951682114994920670932643184314941440000000⟩, + ⟨1, 6, 8, 2, 8, 5, -5245104751284864985934451808098142442323810713600000⟩, + ⟨1, 6, 3, 3, 2, 5, 54908265284420902739482888994890677454724766105600000⟩, + ⟨1, 6, 4, 3, 3, 5, 69404732558862016375527649826926855446734045184000000⟩, + ⟨1, 6, 5, 3, 4, 5, 33252620490171161961609666631927809530073710592000000⟩, + ⟨1, 6, 6, 3, 5, 5, 9831663905389910099535004262457769505127923712000000⟩, + ⟨1, 6, 7, 3, 6, 5, -1266708067699983105943131892364927337435758592000000⟩, + ⟨1, 6, 8, 3, 7, 5, -3212924379030808657486144242230785538531524608000000⟩, + ⟨1, 6, 3, 4, 1, 5, -50698683277920498615825062644925273980773020467200000⟩, + ⟨1, 6, 4, 4, 2, 5, -231388924327992937112523559880877537249383468236800000⟩, + ⟨1, 6, 5, 4, 3, 5, -3101684971152501170007341620083981060377935872000000⟩, + ⟨1, 6, 6, 4, 4, 5, -4543598318341615439496998495040463616669122560000000⟩, + ⟨1, 6, 7, 4, 5, 5, -4361161903045819357736641831321920675344547840000000⟩, + ⟨1, 6, 8, 4, 6, 5, 4098208049607398392544224081045669356051313459200000⟩, + ⟨1, 6, 3, 5, 0, 5, 60896207433306688720210886016270916878838058188800000⟩, + ⟨1, 6, 4, 5, 1, 5, 223087803481627156352270466424108990951144921497600000⟩, + ⟨1, 6, 5, 5, 2, 5, -240910075029203085331669775871746459515949678592000000⟩, + ⟨1, 6, 6, 5, 3, 5, -1683067073340991058656210891341024014962262016000000⟩, + ⟨1, 6, 7, 5, 4, 5, 2763501348039284395727092170177971503245557760000000⟩, + ⟨1, 6, 8, 5, 5, 5, 1369907102737375588942484741241419978252904038400000⟩, + ⟨1, 6, 4, 6, 0, 5, 696039213417955327868690350268388120480424604467200000⟩, + ⟨1, 6, 5, 6, 1, 5, 307779374816820992232872525313284123906927493120000000⟩, + ⟨1, 6, 6, 6, 2, 5, -120596758843599189021115974011112599530594369536000000⟩, + ⟨1, 6, 7, 6, 3, 5, 8286409759184370223568490569857965385838493696000000⟩, + ⟨1, 6, 8, 6, 4, 5, -2040686483482381507601636331295581041712326246400000⟩, + ⟨1, 6, 5, 7, 0, 5, 1342819981801341443261784786564243562275375415296000000⟩, + ⟨1, 6, 6, 7, 1, 5, 239077537589307537888970503651028721467945648128000000⟩, + ⟨1, 6, 7, 7, 2, 5, -14715103866973915439726816842948092558525333504000000⟩, + ⟨1, 6, 8, 7, 3, 5, -9773762880671165280539595891239479459050002841600000⟩ +] + +def collectedFourData_10_2_13 : List CollectedFourTerm := [ + ⟨1, 7, 2, 0, 4, 6, 22797146151350977527157680182592132607213830144000000⟩, + ⟨1, 7, 3, 0, 5, 6, -156697290350039195922340435120574557249024819200000000⟩, + ⟨1, 7, 4, 0, 6, 6, -82232043286579609849658468658446619953709711360000000⟩, + ⟨1, 7, 5, 0, 7, 6, -354344799488910858883515186241030498623160320000000⟩, + ⟨1, 7, 6, 0, 8, 6, -5457349505007959982088963864464981446916833280000000⟩, + ⟨1, 7, 2, 1, 3, 6, -13610933118710029796586577798757045127333543936000000⟩, + ⟨1, 7, 3, 1, 4, 6, 149898048311537379141698132535878101712353886208000000⟩, + ⟨1, 7, 4, 1, 5, 6, 127428491033647269340142401444702529421016301568000000⟩, + ⟨1, 7, 5, 1, 6, 6, 58464143207296529135764506688442472869595709440000000⟩, + ⟨1, 7, 6, 1, 7, 6, 18251705369172084846062301553755185594184499200000000⟩, + ⟨1, 7, 7, 1, 8, 6, 6862369076633594480945925994094591628854427648000000⟩, + ⟨1, 7, 2, 2, 2, 6, -3323049092340194122866585264497836479473516544000000⟩, + ⟨1, 7, 3, 2, 3, 6, -103981058207934341605795413081189160639153569792000000⟩, + ⟨1, 7, 4, 2, 4, 6, -33974899716223699122037940679271609058828746752000000⟩, + ⟨1, 7, 5, 2, 5, 6, -10226655039571287107032612601067151774879580160000000⟩, + ⟨1, 7, 6, 2, 6, 6, -1259908250176782331512063777255160320633077760000000⟩, + ⟨1, 7, 7, 2, 7, 6, -405162130535177200788896602993613230949007360000000⟩, + ⟨1, 7, 8, 2, 8, 6, -1091633279238732683758000683178330391033413632000000⟩, + ⟨1, 7, 2, 3, 1, 6, -19044608355133014465533932237506439163569766400000000⟩, + ⟨1, 7, 3, 3, 2, 6, 68566435789553548702074424103574499701169324032000000⟩, + ⟨1, 7, 4, 3, 3, 6, 43334415263694108622576711068709323767273226240000000⟩, + ⟨1, 7, 5, 3, 4, 6, 13841350695646063770817668012718537861842862080000000⟩, + ⟨1, 7, 6, 3, 5, 6, 3069310915130371636966654343978203675266908160000000⟩, + ⟨1, 7, 7, 3, 6, 6, -316359138057502210189375625949167094488629248000000⟩, + ⟨1, 7, 8, 3, 7, 6, -668687346037902789081416233850869289802792960000000⟩, + ⟨1, 7, 2, 4, 0, 6, 72932623965527607973773887452834978327437508608000000⟩, + ⟨1, 7, 3, 4, 1, 6, -63309740229159210037588856827844394934163472384000000⟩, + ⟨1, 7, 4, 4, 2, 6, -144472910773696467455277399364561274253499957248000000⟩, + ⟨1, 7, 5, 4, 3, 6, -1291071464452744277068754683637619913685729280000000⟩, + ⟨1, 7, 6, 4, 4, 6, -1418449211308841384208710419316467460525260800000000⟩, + ⟨1, 7, 7, 4, 5, 6, -1089196047422324186303973771685054536178728960000000⟩, + ⟨1, 7, 8, 4, 6, 6, 852936310013558294755742008229915173117231104000000⟩, + ⟨1, 7, 3, 5, 0, 6, 76043850141225480056803974801691476847478439936000000⟩, + ⟨1, 7, 4, 5, 1, 6, 139289918135471959495836349328113928022981083136000000⟩, + ⟨1, 7, 5, 5, 2, 6, -100278437772422358880285206821395210537355182080000000⟩, + ⟨1, 7, 6, 5, 3, 6, -525430505844489902942273301016807983682682880000000⟩, + ⟨1, 7, 7, 5, 4, 6, 690181839667196032112159138598430472342077440000000⟩, + ⟨1, 7, 8, 5, 5, 6, 285110832619177693868646190066524438405316608000000⟩, + ⟨1, 7, 4, 6, 0, 6, 434587832875632341679286990215004212774611976192000000⟩, + ⟨1, 7, 5, 6, 1, 6, 128112678066545600680933938961819560930233548800000000⟩, + ⟨1, 7, 6, 6, 2, 6, -37648657623973627256479069565832094412156436480000000⟩, + ⟨1, 7, 7, 6, 3, 6, 2069522975224101657727005074677878559787188224000000⟩, + ⟨1, 7, 8, 6, 4, 6, -424716260874737911045076930525083128003821568000000⟩, + ⟨1, 7, 5, 7, 0, 6, 558946693982425493528928941171227417549775831040000000⟩, + ⟨1, 7, 6, 7, 1, 6, 74636735220685081627899993449260129719460823040000000⟩, + ⟨1, 7, 7, 7, 2, 6, -3675083229109955118966013434820885153711128576000000⟩, + ⟨1, 7, 8, 7, 3, 6, -2034156671764324599124242235876437396125908992000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1007.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1007.lean new file mode 100644 index 0000000000000000000000000000000000000000..e02bd52a0b18e4256a7d504d047188c2e1279aae --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1007.lean @@ -0,0 +1,649 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1007. -/ +namespace LaughlinFock +def collectedFourData_10_2_14 : List CollectedFourTerm := [ + ⟨1, 8, 1, 0, 3, 7, 22907903798457579660196277770108374178315055923200000⟩, + ⟨1, 8, 2, 0, 4, 7, 42856935179538209640966968958651560054286503116800000⟩, + ⟨1, 8, 3, 0, 5, 7, -147289611839044557798217270453788174783212421120000000⟩, + ⟨1, 8, 4, 0, 6, 7, -51530036923869887881703299755681789160313585664000000⟩, + ⟨1, 8, 5, 0, 7, 7, -166535451434156531324657132904668363464114176000000⟩, + ⟨1, 8, 6, 0, 8, 7, -2051882042036659420313315301945272124732289843200000⟩, + ⟨1, 8, 1, 1, 2, 7, 6722736166706000464345515570901377811224723456000000⟩, + ⟨1, 8, 2, 1, 3, 7, -25587539533627870505682831298963572599783895859200000⟩, + ⟨1, 8, 3, 1, 4, 7, 140898577773212696759294309381425259375932263628800000⟩, + ⟨1, 8, 4, 1, 5, 7, 79852021008804386608510730793680044413936677683200000⟩, + ⟨1, 8, 5, 1, 6, 7, 27477057644930952519305946948574317521972232192000000⟩, + ⟨1, 8, 6, 1, 7, 7, 6862369076633594480945925994094591628854427648000000⟩, + ⟨1, 8, 7, 1, 8, 7, 2150123709511806755452394965009594746475747737600000⟩, + ⟨1, 8, 1, 2, 1, 7, 24626943702468280027813728072457544427100333670400000⟩, + ⟨1, 8, 2, 2, 2, 7, -6247084551870862623699176998033912402423893196800000⟩, + ⟨1, 8, 3, 2, 3, 7, -97738318689796771897891543629316395426047537971200000⟩, + ⟨1, 8, 4, 2, 4, 7, -21290092850550694559025664356067210834136059084800000⟩, + ⟨1, 8, 5, 2, 5, 7, -4806337262837956159182421160661241013194457088000000⟩, + ⟨1, 8, 6, 2, 6, 7, -473706716196070312065453105742567880926848614400000⟩, + ⟨1, 8, 7, 2, 7, 7, -126945766590472135122257884885158874193068032000000⟩, + ⟨1, 8, 8, 2, 8, 7, -293169882991746059810353849618780609982968627200000⟩, + ⟨1, 8, 1, 3, 0, 7, 21613572924435090276243175024472511573847651123200000⟩, + ⟨1, 8, 2, 3, 1, 7, -35802443883848115242838279678321098154395566080000000⟩, + ⟨1, 8, 3, 3, 2, 7, 64449893741430536969167023835613472310999331635200000⟩, + ⟨1, 8, 4, 3, 3, 7, 27155156668433424157436225099859971926262808576000000⟩, + ⟨1, 8, 5, 3, 4, 7, 6505176850013374042463390335918858392928518144000000⟩, + ⟨1, 8, 6, 3, 5, 7, 1154015139108069434477302869900114717374309990400000⟩, + ⟨1, 8, 7, 3, 6, 7, -99121932362145562654324015579054827359541657600000⟩, + ⟨1, 8, 8, 3, 7, 7, -179583194030786588919848197193693646569865216000000⟩, + ⟨1, 8, 2, 4, 0, 7, 137107895743302149285959516201221122400313776537600000⟩, + ⟨1, 8, 3, 4, 1, 7, -59508795864645730909777474315481302192559122022400000⟩, + ⟨1, 8, 4, 4, 2, 7, -90532767144344128877418667361985412666674590515200000⟩, + ⟨1, 8, 5, 4, 3, 7, -606779525130646114785523263196767388491055104000000⟩, + ⟨1, 8, 6, 4, 4, 7, -533315753655662061920271929457424537592266752000000⟩, + ⟨1, 8, 7, 4, 5, 7, -341267894471530171234104218493176038085885952000000⟩, + ⟨1, 8, 8, 4, 6, 7, 229065239180383368555759970313315045907785318400000⟩, + ⟨1, 8, 3, 5, 0, 7, 71478384501910265321096495665327727577356933529600000⟩, + ⟨1, 8, 4, 5, 1, 7, 87284887226134161273898219308725530662520907366400000⟩, + ⟨1, 8, 5, 5, 2, 7, -47128996750141246828664664201939237899436294144000000⟩, + ⟨1, 8, 6, 5, 3, 7, -197554035762452844344718751023291549799887667200000⟩, + ⟨1, 8, 7, 5, 4, 7, 216248400628270258467202242676862193110089728000000⟩, + ⟨1, 8, 8, 5, 5, 7, 76569587084165796386441116210062139134364876800000⟩, + ⟨1, 8, 4, 6, 0, 7, 272330908727409885097427855092506939428417883340800000⟩, + ⟨1, 8, 5, 6, 1, 7, 60210570910096337020110081408335766894768291840000000⟩, + ⟨1, 8, 6, 6, 2, 7, -14155333906052508947543575353885254970728723251200000⟩, + ⟨1, 8, 7, 6, 3, 7, 648424817540069891759187268385657418089811148800000⟩, + ⟨1, 8, 8, 6, 4, 7, -114062129538750027537389554683843570075225292800000⟩, + ⟨1, 8, 5, 7, 0, 7, 262694528448711239488724074081088769450754179072000000⟩, + ⟨1, 8, 6, 7, 1, 7, 28062299571437360227288037939266719558997219737600000⟩, + ⟨1, 8, 7, 7, 2, 7, -1151480413993541121730739770870667635821065011200000⟩, + ⟨1, 8, 8, 7, 3, 7, -546294698769080160329421881155662491621208883200000⟩ +] + +def collectedFourData_10_2_15 : List CollectedFourTerm := [ + ⟨2, 0, 8, 2, 8, 0, 12273470924112170725411678455544734093755075788800000⟩, + ⟨2, 0, 8, 3, 7, 0, 7518197598960423538521648151082881327262859264000000⟩, + ⟨2, 0, 8, 4, 6, 0, -9589748865453510764463276763569677700236417433600000⟩, + ⟨2, 0, 8, 5, 5, 0, -3205563242576462863173251561582486869337387827200000⟩, + ⟨2, 0, 8, 6, 4, 0, 4775177505104023443017797241703688213208707891200000⟩, + ⟨2, 0, 8, 7, 3, 0, 22870466887377015041055879703927084402818731212800000⟩ +] + +def collectedFourData_10_2_16 : List CollectedFourTerm := [ + ⟨2, 1, 7, 1, 8, 1, 24626943702468280027813728072457544427100333670400000⟩, + ⟨2, 1, 7, 2, 7, 1, -1454002964229472337223993751664265752664342528000000⟩, + ⟨2, 1, 8, 2, 8, 1, -23505227723549774451038493845426132886457260441600000⟩, + ⟨2, 1, 7, 3, 6, 1, -1135316185372738929884725024547862681926133350400000⟩, + ⟨2, 1, 8, 3, 7, 1, -14398286167528694924470215214113118235758952448000000⟩, + ⟨2, 1, 7, 4, 5, 1, -3908791474383818175760323114124293916179038208000000⟩, + ⟨2, 1, 8, 4, 6, 1, 18365565233165152388627048051250512068540052275200000⟩, + ⟨2, 1, 7, 5, 4, 1, 2476851524617809118545792656379218147527360512000000⟩, + ⟨2, 1, 8, 5, 5, 1, 6139053448277168341468114068556639828013639270400000⟩, + ⟨2, 1, 7, 6, 3, 1, 7426884976989683453558108340953996524115931955200000⟩, + ⟨2, 1, 8, 6, 4, 1, -9145060543332943846232913682272059519966537318400000⟩, + ⟨2, 1, 7, 7, 2, 1, -13188749654015239877475012351310228286367124684800000⟩, + ⟨2, 1, 8, 7, 3, 1, -43799796785731830206083987994836001575602330009600000⟩ +] + +def collectedFourData_10_2_17 : List CollectedFourTerm := [ + ⟨2, 2, 6, 0, 8, 2, 993607991822548920139024622803169771467151769600000⟩, + ⟨2, 2, 6, 1, 7, 2, -3323049092340194122866585264497836479473516544000000⟩, + ⟨2, 2, 7, 1, 8, 2, -6247084551870862623699176998033912402423893196800000⟩, + ⟨2, 2, 6, 2, 6, 2, 229388809565897195931856444776603732917039923200000⟩, + ⟨2, 2, 7, 2, 7, 2, 368835027437935425225581202168160829860478976000000⟩, + ⟨2, 2, 8, 2, 8, 2, 2981270164378483147506638241992889459784915353600000⟩, + ⟨2, 2, 6, 3, 5, 2, -558822895961337228640347497173295183388947251200000⟩, + ⟨2, 2, 7, 3, 6, 2, 287994169671169700210701998798767404557847756800000⟩, + ⟨2, 2, 8, 3, 7, 2, 1826197196397726467516140370431048669156343808000000⟩, + ⟨2, 2, 6, 4, 4, 2, 258254024422942018980440041131875679816646656000000⟩, + ⟨2, 2, 7, 4, 5, 2, 991538013450702357907356372594211468697665536000000⟩, + ⟨2, 2, 8, 4, 6, 2, -2329384438455176118142247530240371128689439539200000⟩, + ⟨2, 2, 6, 5, 3, 2, 95664012223400410974573839691958730433862041600000⟩, + ⟨2, 2, 7, 5, 4, 2, -628299681992893392801785039132456141092552704000000⟩, + ⟨2, 2, 8, 5, 5, 2, -778642823550979877471867082045143890440644198400000⟩, + ⟨2, 2, 6, 6, 2, 2, 6854610844008344176782067722963286032356317593600000⟩, + ⟨2, 2, 7, 6, 3, 2, -1883968184148805987813478799731909548424193638400000⟩, + ⟨2, 2, 8, 6, 4, 2, 1159907764771741379950907129543836503351125606400000⟩, + ⟨2, 2, 6, 7, 1, 2, -13588951290505269508034801450282126952652131532800000⟩, + ⟨2, 2, 7, 7, 2, 2, 3345572849700914313521900037926088042109049241600000⟩, + ⟨2, 2, 8, 7, 3, 2, 5555318540152512226965705542411589664072374681600000⟩ +] + +def collectedFourData_10_2_18 : List CollectedFourTerm := [ + ⟨2, 3, 5, 0, 7, 3, 504680884280110899652792354646429576263945420800000⟩, + ⟨2, 3, 6, 0, 8, 3, 31090846858603160591059278805045506630109416652800000⟩, + ⟨2, 3, 5, 1, 6, 3, -83268431017176044960390771467349769859360201113600000⟩, + ⟨2, 3, 6, 1, 7, 3, -103981058207934341605795413081189160639153569792000000⟩, + ⟨2, 3, 7, 1, 8, 3, -97738318689796771897891543629316395426047537971200000⟩, + ⟨2, 3, 5, 2, 5, 3, 14565466506190415291484124392277308018293892710400000⟩, + ⟨2, 3, 6, 2, 6, 3, 7177772731284851611994964497537569049068280217600000⟩, + ⟨2, 3, 7, 2, 7, 3, 5770582286243092776358924238226715240808054784000000⟩, + ⟨2, 3, 8, 2, 8, 3, 31095500736594947972699820915074011250034317721600000⟩, + ⟨2, 3, 5, 3, 4, 3, -19713750896824978452587611791153868218507146035200000⟩, + ⟨2, 3, 6, 3, 5, 3, -17486048041487553292787457298428169230380276121600000⟩, + ⟨2, 3, 7, 3, 6, 3, 4505792374411591661955233930378600899381769011200000⟩, + ⟨2, 3, 8, 3, 7, 3, 19047759221644253632280082136761641530030030848000000⟩, + ⟨2, 3, 5, 4, 3, 3, 1838827857184961364158961747107101587499332403200000⟩, + ⟨2, 3, 6, 4, 4, 3, 8080990078616065720760445451730517034750967808000000⟩, + ⟨2, 3, 7, 4, 5, 3, 15513037729362888614168266099960956828279373824000000⟩, + ⟨2, 3, 8, 4, 6, 3, -24296146114921524562690595455059510216459760435200000⟩, + ⟨2, 3, 5, 5, 2, 3, 142823065901374899263187089054269876579855446835200000⟩, + ⟨2, 3, 6, 5, 3, 3, 2993409049037184769340874906590283286801337548800000⟩, + ⟨2, 3, 7, 5, 4, 3, -9830018153496700638583173840500987389947150336000000⟩, + ⟨2, 3, 8, 5, 5, 3, -8121467414316506182105756461726930078437631590400000⟩, + ⟨2, 3, 5, 6, 1, 3, -182466399245520175154606214112712461090314780672000000⟩, + ⟨2, 3, 6, 6, 2, 3, 214486656488613344016173413308414045099209313484800000⟩, + ⟨2, 3, 7, 6, 3, 3, -29475490727691389549668780073991238790755752345600000⟩, + ⟨2, 3, 8, 6, 4, 3, 12098169828684781460686282885051616066282088038400000⟩, + ⟨2, 3, 5, 7, 0, 3, -796088194863779774992011632769192546054279109017600000⟩, + ⟨2, 3, 6, 7, 1, 3, -425209949013343975023735608469502850347890533990400000⟩, + ⟨2, 3, 7, 7, 2, 3, 52342922953727767582300569119452732004074153574400000⟩, + ⟨2, 3, 8, 7, 3, 3, 57943561714523418614123492848644088327956961689600000⟩ +] + +def collectedFourData_10_2_19 : List CollectedFourTerm := [ + ⟨2, 4, 4, 0, 6, 4, 25512003468642075488908551472252196170742995353600000⟩, + ⟨2, 4, 5, 0, 7, 4, 329800114128930685497107714871006078309079449600000⟩, + ⟨2, 4, 6, 0, 8, 4, 10158661801663687195245557643468306339391655116800000⟩, + ⟨2, 4, 4, 1, 5, 4, -39533933188606485208721375634941397948245401927680000⟩, + ⟨2, 4, 5, 1, 6, 4, -54414460519886796399786550848020653275845178163200000⟩, + ⟨2, 4, 6, 1, 7, 4, -33974899716223699122037940679271609058828746752000000⟩, + ⟨2, 4, 7, 1, 8, 4, -21290092850550694559025664356067210834136059084800000⟩, + ⟨2, 4, 4, 2, 4, 4, 10540511031525388943341304766633357321543635435520000⟩, + ⟨2, 4, 5, 2, 5, 4, 9518277124632568967168722273641693099657579724800000⟩, + ⟨2, 4, 6, 2, 6, 4, 2345274350291615929632100822965512814393399705600000⟩, + ⟨2, 4, 7, 2, 7, 4, 1256991467857978631427479405059840914946523136000000⟩, + ⟨2, 4, 8, 2, 8, 4, 5080091207760757174314259180344940567938780364800000⟩, + ⟨2, 4, 4, 3, 3, 4, -13444245191209631723698571714935213890304632422400000⟩, + ⟨2, 4, 5, 3, 4, 4, -12882590758229775672286635594911646769681426022400000⟩, + ⟨2, 4, 6, 3, 5, 4, -5713412989648505748565207126210983687418911129600000⟩, + ⟨2, 4, 7, 3, 6, 4, 981485453223172601005033096053938065595223244800000⟩, + ⟨2, 4, 8, 3, 7, 4, 3111844217242048757644887788118327892371308544000000⟩, + ⟨2, 4, 4, 4, 2, 4, 44821863272183682295723978077855548154512387604480000⟩, + ⟨2, 4, 5, 4, 3, 4, 1201641782070082037201196081007570732615886438400000⟩, + ⟨2, 4, 6, 4, 4, 4, 2640392704791974521584696349993998019196878848000000⟩, + ⟨2, 4, 7, 4, 5, 4, 3379166104754269913311812830351531364682039296000000⟩, + ⟨2, 4, 8, 4, 6, 4, -3969276433475407949252832701430117783762999705600000⟩, + ⟨2, 4, 4, 5, 1, 4, -43213870561805416911088539360564349108164608655360000⟩, + ⟨2, 4, 5, 5, 2, 4, 93332370814294238197618150478009488075435435622400000⟩, + ⟨2, 4, 6, 5, 3, 4, 978070179352286673997959289835832841320844492800000⟩, + ⟨2, 4, 7, 5, 4, 4, -2141248202506590591779318876692968838313017344000000⟩, + ⟨2, 4, 8, 5, 5, 4, -1326809159790447156229401873487520825114571571200000⟩, + ⟨2, 4, 4, 6, 0, 4, -134828296326211113969557327566346022229246916689920000⟩, + ⟨2, 4, 5, 6, 1, 4, -119238594466890003546771792725151544419563864064000000⟩, + ⟨2, 4, 6, 6, 2, 4, 70081635735004550063136512400578333503545724108800000⟩, + ⟨2, 4, 7, 6, 3, 4, -6420572226127379711060642729552324108120122982400000⟩, + ⟨2, 4, 8, 6, 4, 4, 1976485495355559278550569727833029297124356915200000⟩, + ⟨2, 4, 5, 7, 0, 4, -520229685135145669226313366806078299091995145011200000⟩, + ⟨2, 4, 6, 7, 1, 4, -138933625268362646323881611808159584193308157542400000⟩, + ⟨2, 4, 7, 7, 2, 4, 11401727640629240905900416196963910076363020697600000⟩, + ⟨2, 4, 8, 7, 3, 4, 9466275552394478151680555616351156115402968268800000⟩ +] + +def collectedFourData_10_2_20 : List CollectedFourTerm := [ + ⟨2, 5, 3, 0, 5, 5, 21949854844140572880607229972824007493329879040000000⟩, + ⟨2, 5, 4, 0, 6, 5, 23037812710678506388023426987339021824362020864000000⟩, + ⟨2, 5, 5, 0, 7, 5, 148907812563634629875815800707932009059581952000000⟩, + ⟨2, 5, 6, 0, 8, 5, 3057820060604185539891344769536690896811065344000000⟩, + ⟨2, 5, 3, 1, 4, 5, -20997430105576764042935187551482748648732334489600000⟩, + ⟨2, 5, 4, 1, 5, 5, -35699875536433951197479467000016652797480219443200000⟩, + ⟨2, 5, 5, 1, 6, 5, -24568633971663663023797967275685053530409795584000000⟩, + ⟨2, 5, 6, 1, 7, 5, -10226655039571287107032612601067151774879580160000000⟩, + ⟨2, 5, 7, 1, 8, 5, -4806337262837956159182421160661241013194457088000000⟩, + ⟨2, 5, 3, 2, 3, 5, 14565466506190415291484124392277308018293892710400000⟩, + ⟨2, 5, 4, 2, 4, 5, 9518277124632568967168722273641693099657579724800000⟩, + ⟨2, 5, 5, 2, 5, 5, 4297590465506711341932107397114882500094590976000000⟩, + ⟨2, 5, 6, 2, 6, 5, 705942091188396888187954185806219718791528448000000⟩, + ⟨2, 5, 7, 2, 7, 5, 283771657241922749769134119461121169723228160000000⟩, + ⟨2, 5, 8, 2, 8, 5, 917483332435328036853759683561591737344747110400000⟩, + ⟨2, 5, 3, 3, 2, 5, -9604654358724263949476616741131766933978768998400000⟩, + ⟨2, 5, 4, 3, 3, 5, -12140402972750669315202031811639864360882405376000000⟩, + ⟨2, 5, 5, 3, 4, 5, -5816609296898398702644221994356520554424434688000000⟩, + ⟨2, 5, 6, 3, 5, 5, -1719772662517672453806563358024113603758522368000000⟩, + ⟨2, 5, 7, 3, 6, 5, 221574895885807006481104418310312330094706688000000⟩, + ⟨2, 5, 8, 3, 7, 5, 562010618646612454133639354057229952836698112000000⟩, + ⟨2, 5, 3, 4, 1, 5, 8868306561945242900557905889613422876081048780800000⟩, + ⟨2, 5, 4, 4, 2, 5, 40474974561579161859658225139561508047458349875200000⟩, + ⟨2, 5, 5, 4, 3, 5, 542552417623397221682650614335263527149764608000000⟩, + ⟨2, 5, 6, 4, 4, 5, 794774541983825928959939454369838913122467840000000⟩, + ⟨2, 5, 7, 4, 5, 5, 762862429986036049573028518665267242084597760000000⟩, + ⟨2, 5, 8, 4, 6, 5, -716866060195653086536853072747162220215717068800000⟩, + ⟨2, 5, 3, 5, 0, 5, -10652076169669773569492804716704151665548407603200000⟩, + ⟨2, 5, 4, 5, 1, 5, -39022927294990946901001448890573894587521590886400000⟩, + ⟨2, 5, 5, 5, 2, 5, 42140431685543246565403368064119342667753586688000000⟩, + ⟨2, 5, 6, 5, 3, 5, 294405175946733233756106589238897960156135424000000⟩, + ⟨2, 5, 7, 5, 4, 5, -483396718696133649724286503716073151020400640000000⟩, + ⟨2, 5, 8, 5, 5, 5, -239626660161253164800471990420226904579217817600000⟩, + ⟨2, 5, 4, 6, 0, 5, -121752454395869726259662954988323269623856024780800000⟩, + ⟨2, 5, 5, 6, 1, 5, -53837332112885848782424160676634624683336007680000000⟩, + ⟨2, 5, 6, 6, 2, 5, 21095005997281706625576368607417111190337224704000000⟩, + ⟨2, 5, 7, 6, 3, 5, -1449473976266865161833858788684685576916434944000000⟩, + ⟨2, 5, 8, 6, 4, 5, 356960618348470579106062502936855325976402329600000⟩, + ⟨2, 5, 5, 7, 0, 5, -234888531341922436618694281641583262283904057344000000⟩, + ⟨2, 5, 6, 7, 1, 5, -41819880879240282450410084950829616044433211392000000⟩, + ⟨2, 5, 7, 7, 2, 5, 2573992927347347369343615009209999185051385856000000⟩, + ⟨2, 5, 8, 7, 3, 5, 1709644509195784842460611256114570598990374502400000⟩ +] + +def collectedFourData_10_2_21 : List CollectedFourTerm := [ + ⟨2, 6, 2, 0, 4, 6, -1573678291185118444917270723254497260929758003200000⟩, + ⟨2, 6, 3, 0, 5, 6, 10816754100458966467077784688238888203593973760000000⟩, + ⟨2, 6, 4, 0, 6, 6, 5676446538560114461148545931813450072413175808000000⟩, + ⟨2, 6, 5, 0, 7, 6, 24460286162485183488271762233920296002256896000000⟩, + ⟨2, 6, 6, 0, 8, 6, 376718751830782990000043621395273888441565184000000⟩, + ⟨2, 6, 2, 1, 3, 6, 939557514325854049952373660420197306136841420800000⟩, + ⟨2, 6, 3, 1, 4, 6, -10347405019593005519422156104161851649558996582400000⟩, + ⟨2, 6, 4, 1, 5, 6, -8796340063216402403231205445819792722137343590400000⟩, + ⟨2, 6, 5, 1, 6, 6, -4035757474520916484163547526817174643573522432000000⟩, + ⟨2, 6, 6, 1, 7, 6, -1259908250176782331512063777255160320633077760000000⟩, + ⟨2, 6, 7, 1, 8, 6, -473706716196070312065453105742567880926848614400000⟩, + ⟨2, 6, 2, 2, 2, 6, 229388809565897195931856444776603732917039923200000⟩, + ⟨2, 6, 3, 2, 3, 6, 7177772731284851611994964497537569049068280217600000⟩, + ⟨2, 6, 4, 2, 4, 6, 2345274350291615929632100822965512814393399705600000⟩, + ⟨2, 6, 5, 2, 5, 6, 705942091188396888187954185806219718791528448000000⟩, + ⟨2, 6, 6, 2, 6, 6, 86970985272677899497780610697843697650761728000000⟩, + ⟨2, 6, 7, 2, 7, 6, 27968187114321551340183230987314807185604608000000⟩, + ⟨2, 6, 8, 2, 8, 6, 75355028303462147873208271137575833068738969600000⟩, + ⟨2, 6, 2, 3, 1, 6, 1314642040438886238033384196006358540007505920000000⟩, + ⟨2, 6, 3, 3, 2, 6, -4733114872782637501964809344255733152895048089600000⟩, + ⟨2, 6, 4, 3, 3, 6, -2991358133554589733366541712842622990624489472000000⟩, + ⟨2, 6, 5, 3, 4, 6, -955463151650999037270382015934477500441165824000000⟩, + ⟨2, 6, 6, 3, 5, 6, -211873360111434790065560977350561444919246848000000⟩, + ⟨2, 6, 7, 3, 6, 6, 21838150462952758629482011805595004949653094400000⟩, + ⟨2, 6, 8, 3, 7, 6, 46159232083866723763755416131513220792844288000000⟩, + ⟨2, 6, 2, 4, 0, 6, -5034511174852330869680865558614600236371699302400000⟩, + ⟨2, 6, 3, 4, 1, 6, 4370247186106358709361848213204620932478612275200000⟩, + ⟨2, 6, 4, 4, 2, 6, 9972909847552017740099633134409635800824571494400000⟩, + ⟨2, 6, 5, 4, 3, 6, 89122170050985129867395160486309644136873984000000⟩, + ⟨2, 6, 6, 4, 4, 6, 97915007263007590118882286742878491498250240000000⟩, + ⟨2, 6, 7, 4, 5, 6, 75186787122105312270347874829273174363865088000000⟩, + ⟨2, 6, 8, 4, 6, 6, -58877867691010708870932805851388206279504691200000⟩, + ⟨2, 6, 3, 5, 0, 6, -5249277929390705111073732271404162625684950220800000⟩, + ⟨2, 6, 4, 5, 1, 6, -9615129845441409708812479529704121052242431180800000⟩, + ⟨2, 6, 5, 5, 2, 6, 6922182256881620265620103731797238398083661824000000⟩, + ⟨2, 6, 6, 5, 3, 6, 36270267123978978596602881877572043684184064000000⟩, + ⟨2, 6, 7, 5, 4, 6, -47642988769017908072322779457692860082552832000000⟩, + ⟨2, 6, 8, 5, 5, 6, -19681091874209227203821758134913234236761702400000⟩, + ⟨2, 6, 4, 6, 0, 6, -29999432107384212396055704701145000924379978137600000⟩, + ⟨2, 6, 5, 6, 1, 6, -8843569232763953728378375425579739479948656640000000⟩, + ⟨2, 6, 6, 6, 2, 6, 2598872455427820338792172112432595624886534144000000⟩, + ⟨2, 6, 7, 6, 3, 6, -142858380500666661384438585675716655198712627200000⟩, + ⟨2, 6, 8, 6, 4, 6, 29318001262727465289483646384357718790399590400000⟩, + ⟨2, 6, 5, 7, 0, 6, -38583876789231740176400972665172589682372902912000000⟩, + ⟨2, 6, 6, 7, 1, 6, -5152145323890175214493605221987816822655680512000000⟩, + ⟨2, 6, 7, 7, 2, 6, 253689591563464726831146050971184067670494412800000⟩, + ⟨2, 6, 8, 7, 3, 6, 140417058081420858891875208708866716003309977600000⟩ +] + +def collectedFourData_10_2_22 : List CollectedFourTerm := [ + ⟨2, 7, 1, 0, 3, 7, -1352508879285030363940207362529923410033639424000000⟩, + ⟨2, 7, 2, 0, 4, 7, -2530322541915477942843079749338673398862053376000000⟩, + ⟨2, 7, 3, 0, 5, 7, 8696147390498750460915093813808334769645158400000000⟩, + ⟨2, 7, 4, 0, 6, 7, 3042392403189336926731145620068527008886292480000000⟩, + ⟨2, 7, 5, 0, 7, 7, 9832443804640187730224311923249787510456320000000⟩, + ⟨2, 7, 6, 0, 8, 7, 121145466015399410989930446951644138594893824000000⟩, + ⟨2, 7, 1, 1, 2, 7, -396918043595620835920946408205632418003025920000000⟩, + ⟨2, 7, 2, 1, 3, 7, 1510717642380644241474022446158738614275538944000000⟩, + ⟨2, 7, 3, 1, 4, 7, -8318813418874829596767434695387299373400457216000000⟩, + ⟨2, 7, 4, 1, 5, 7, -4714554783949046698176810564066084600491802624000000⟩, + ⟨2, 7, 5, 1, 6, 7, -1622276955951682114994920670932643184314941440000000⟩, + ⟨2, 7, 6, 1, 7, 7, -405162130535177200788896602993613230949007360000000⟩, + ⟨2, 7, 7, 1, 8, 7, -126945766590472135122257884885158874193068032000000⟩, + ⟨2, 7, 1, 2, 1, 7, -1454002964229472337223993751664265752664342528000000⟩, + ⟨2, 7, 2, 2, 2, 7, 368835027437935425225581202168160829860478976000000⟩, + ⟨2, 7, 3, 2, 3, 7, 5770582286243092776358924238226715240808054784000000⟩, + ⟨2, 7, 4, 2, 4, 7, 1256991467857978631427479405059840914946523136000000⟩, + ⟨2, 7, 5, 2, 5, 7, 283771657241922749769134119461121169723228160000000⟩, + ⟨2, 7, 6, 2, 6, 7, 27968187114321551340183230987314807185604608000000⟩, + ⟨2, 7, 7, 2, 7, 7, 7495023464906422133939215531540639635210240000000⟩, + ⟨2, 7, 8, 2, 8, 7, 17309085692597846245883158562118511261384704000000⟩, + ⟨2, 7, 1, 3, 0, 7, -1276090101938582767365108199063954278448103424000000⟩, + ⟨2, 7, 2, 3, 1, 7, 2113817295507806303723705597767084907534745600000000⟩, + ⟨2, 7, 3, 3, 2, 7, -3805195548277565190934566474492262501280907264000000⟩, + ⟨2, 7, 4, 3, 3, 7, -1603271553589518218417160562221122710740664320000000⟩, + ⟨2, 7, 5, 3, 4, 7, -384073092342692426350911436407241336506286080000000⟩, + ⟨2, 7, 6, 3, 5, 7, -68134375637552016112217580861867643191164928000000⟩, + ⟨2, 7, 7, 3, 6, 7, 5852272422268454848943545384940987253522432000000⟩, + ⟨2, 7, 8, 3, 7, 7, 10602797472606781878529011528890198387589120000000⟩, + ⟨2, 7, 2, 4, 0, 7, -8095007209930237217221392079788720426458284032000000⟩, + ⟨2, 7, 3, 4, 1, 7, 3513467470031583189941530148861942892664455168000000⟩, + ⟨2, 7, 4, 4, 2, 7, 5345158269662978824823498368975732201293348864000000⟩, + ⟨2, 7, 5, 4, 3, 7, 35824958177221358782678822022134300441313280000000⟩, + ⟨2, 7, 6, 4, 4, 7, 31487572962936831597800861723745019641200640000000⟩, + ⟨2, 7, 7, 4, 5, 7, 20148847382479809152122540099630065663344640000000⟩, + ⟨2, 7, 8, 4, 6, 7, -13524274095645444980934231539872998661029888000000⟩, + ⟨2, 7, 3, 5, 0, 7, -4220165693305050707396542507548423213885161472000000⟩, + ⟨2, 7, 4, 5, 1, 7, -5153399719126098551480260400990778340040245248000000⟩, + ⟨2, 7, 5, 5, 2, 7, 2782549950321217848645952621318111724914606080000000⟩, + ⟨2, 7, 6, 5, 3, 7, 11663816552490516980281994443146480272277504000000⟩, + ⟨2, 7, 7, 5, 4, 7, -12767553266947759627380104897678374034472960000000⟩, + ⟨2, 7, 8, 5, 5, 7, -4520756125293992346565756978910962517016576000000⟩, + ⟨2, 7, 4, 6, 0, 7, -16078728782787327603765330377467919125557805056000000⟩, + ⟨2, 7, 5, 6, 1, 7, -3554901072537653978837638252050343242026188800000000⟩, + ⟨2, 7, 6, 6, 2, 7, 835747127525022325925083738886242567804944384000000⟩, + ⟨2, 7, 7, 6, 3, 7, -38283743942157197899373018308736614574063616000000⟩, + ⟨2, 7, 8, 6, 4, 7, 6734358776279913007671558168404585607069696000000⟩, + ⟨2, 7, 5, 7, 0, 7, -15509785853492128499808801564768180607427543040000000⟩, + ⟨2, 7, 6, 7, 1, 7, -1656830309636670498361414671001264779304108032000000⟩, + ⟨2, 7, 7, 7, 2, 7, 67984722563481697358135067663667691293507584000000⟩, + ⟨2, 7, 8, 7, 3, 7, 32253864748693020150656731604339010645786624000000⟩ +] + +def collectedFourData_10_2_23 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 2, 8, -10360280526650034221496974501387895406964873625600000⟩, + ⟨2, 8, 1, 0, 3, 8, -21864487203824184209264182982834026260214893772800000⟩, + ⟨2, 8, 2, 0, 4, 8, -20452436832985744651948111380315536762154359193600000⟩, + ⟨2, 8, 3, 0, 5, 8, 46860272356126789648685983391987381968211804160000000⟩, + ⟨2, 8, 4, 0, 6, 8, 12295732543306752093925023120928316857792856064000000⟩, + ⟨2, 8, 5, 0, 7, 8, 31790008190189511288037840137485068125654220800000⟩, + ⟨2, 8, 6, 0, 8, 8, 326403709439998951025766875840538214346312908800000⟩, + ⟨2, 8, 0, 1, 1, 8, 76331577568473640276555581865597789251432559411200000⟩, + ⟨2, 8, 1, 1, 2, 8, -6416526810345972217275350222259198067394740224000000⟩, + ⟨2, 8, 2, 1, 3, 8, 12211035012902863386852010440204547682654905958400000⟩, + ⟨2, 8, 3, 1, 4, 8, -44826961294859021220113085459431761404282431078400000⟩, + ⟨2, 8, 4, 1, 5, 8, -19053723846876583716130308678580165288932881203200000⟩, + ⟨2, 8, 5, 1, 6, 8, -5245104751284864985934451808098142442323810713600000⟩, + ⟨2, 8, 6, 1, 7, 8, -1091633279238732683758000683178330391033413632000000⟩, + ⟨2, 8, 7, 1, 8, 8, -293169882991746059810353849618780609982968627200000⟩, + ⟨2, 8, 0, 2, 0, 8, 12273470924112170725411678455544734093755075788800000⟩, + ⟨2, 8, 1, 2, 1, 8, -23505227723549774451038493845426132886457260441600000⟩, + ⟨2, 8, 2, 2, 2, 8, 2981270164378483147506638241992889459784915353600000⟩, + ⟨2, 8, 3, 2, 3, 8, 31095500736594947972699820915074011250034317721600000⟩, + ⟨2, 8, 4, 2, 4, 8, 5080091207760757174314259180344940567938780364800000⟩, + ⟨2, 8, 5, 2, 5, 8, 917483332435328036853759683561591737344747110400000⟩, + ⟨2, 8, 6, 2, 6, 8, 75355028303462147873208271137575833068738969600000⟩, + ⟨2, 8, 7, 2, 7, 8, 17309085692597846245883158562118511261384704000000⟩, + ⟨2, 8, 8, 2, 8, 8, 34977060819349497332757437369221292127525273600000⟩, + ⟨2, 8, 1, 3, 0, 8, -20629110930134543482318741357983757734052154572800000⟩, + ⟨2, 8, 2, 3, 1, 8, 17085851308157180059966219734899116092854108160000000⟩, + ⟨2, 8, 3, 3, 2, 8, -20504769727733553005685835709518596785154136473600000⟩, + ⟨2, 8, 4, 3, 3, 8, -6479571207370580733447258841324299268103602176000000⟩, + ⟨2, 8, 5, 3, 4, 8, -1241775391123367903022424460637894692197053235200000⟩, + ⟨2, 8, 6, 3, 5, 8, -183575280858206615435748924669716816811628953600000⟩, + ⟨2, 8, 7, 3, 6, 8, 13515299228584414574253687589435813267714867200000⟩, + ⟨2, 8, 8, 3, 7, 8, 21425435094657074260896533726462641761681408000000⟩, + ⟨2, 8, 2, 4, 0, 8, -65431430531512353332190193899467626233415807795200000⟩, + ⟨2, 8, 3, 4, 1, 8, 18932756675669569854236658760250672207566680883200000⟩, + ⟨2, 8, 4, 4, 2, 8, 21602287862842190404973177669793894112842429235200000⟩, + ⟨2, 8, 5, 4, 3, 8, 115828347102232959223871795049822117076087603200000⟩, + ⟨2, 8, 6, 4, 4, 8, 84837352601035478952791444393806161896275968000000⟩, + ⟨2, 8, 7, 4, 5, 8, 46531959183769305288549596805343073160658944000000⟩, + ⟨2, 8, 8, 4, 6, 8, -27328962718304458673041294550930285541929779200000⟩, + ⟨2, 8, 3, 5, 0, 8, -22740887992805200935837992498588450083771829452800000⟩, + ⟨2, 8, 4, 5, 1, 8, -20827301753942510199116442400175012571540514406400000⟩, + ⟨2, 8, 5, 5, 2, 8, 8996469999510968316674446657041518634934154035200000⟩, + ⟨2, 8, 6, 5, 3, 8, 31425963465084394083646131221240496064875724800000⟩, + ⟨2, 8, 7, 5, 4, 8, -29485521241815825138980703169383695715926016000000⟩, + ⟨2, 8, 8, 5, 5, 8, -9135246352814305197775680220082954723288678400000⟩, + ⟨2, 8, 4, 6, 0, 8, -64981673153756450429386670955626653478143446220800000⟩, + ⟨2, 8, 5, 6, 1, 8, -11493616079245015531633827699164610203769372672000000⟩, + ⟨2, 8, 6, 6, 2, 8, 2251763698224705349537339487520806266754354380800000⟩, + ⟨2, 8, 7, 6, 3, 8, -88412879243273471318064261372537076033624473600000⟩, + ⟨2, 8, 8, 6, 4, 8, 13608348856808402239596902293530798253827686400000⟩, + ⟨2, 8, 5, 7, 0, 8, -50145846658987671225234583352443023525620062617600000⟩, + ⟨2, 8, 6, 7, 1, 8, -4464018149133934910934707471524698794353911398400000⟩, + ⟨2, 8, 7, 7, 2, 8, 157004630358884030375507586342648291699091046400000⟩, + ⟨2, 8, 8, 7, 3, 8, 65176486442409545067474454807714303816866201600000⟩ +] + +def collectedFourData_10_2_24 : List CollectedFourTerm := [ + ⟨3, 0, 7, 1, 8, 1, 21613572924435090276243175024472511573847651123200000⟩, + ⟨3, 0, 7, 2, 7, 1, -1276090101938582767365108199063954278448103424000000⟩, + ⟨3, 0, 8, 2, 8, 1, -20629110930134543482318741357983757734052154572800000⟩, + ⟨3, 0, 7, 3, 6, 1, -996398069582047672464239983158272491387040563200000⟩, + ⟨3, 0, 8, 3, 7, 1, -12636501379486081293238912809518887503642230784000000⟩, + ⟨3, 0, 7, 4, 5, 1, -3430508901091829460913447943136283776321060864000000⟩, + ⟨3, 0, 8, 4, 6, 1, 16118341287542724331492918928962158728694045081600000⟩, + ⟨3, 0, 7, 5, 4, 1, 2173782167088795087431739448183405479142096896000000⟩, + ⟨3, 0, 8, 5, 5, 1, 5387874394582081243508580937756387588946735923200000⟩, + ⟨3, 0, 7, 6, 3, 1, 6518125918949065154638010946771297198986074521600000⟩, + ⟨3, 0, 8, 6, 4, 1, -8026064270894077554918607724359742355949171507200000⟩, + ⟨3, 0, 7, 7, 2, 1, -11574964635201817560402662273086340939978794598400000⟩, + ⟨3, 0, 8, 7, 3, 1, -38440421732436528667874095252827610246028250316800000⟩ +] + +def collectedFourData_10_2_25 : List CollectedFourTerm := [ + ⟨3, 1, 6, 0, 8, 2, 5694431390258088605398675829075379933161717760000000⟩, + ⟨3, 1, 6, 1, 7, 2, -19044608355133014465533932237506439163569766400000000⟩, + ⟨3, 1, 7, 1, 8, 2, -35802443883848115242838279678321098154395566080000000⟩, + ⟨3, 1, 6, 2, 6, 2, 1314642040438886238033384196006358540007505920000000⟩, + ⟨3, 1, 7, 2, 7, 2, 2113817295507806303723705597767084907534745600000000⟩, + ⟨3, 1, 8, 2, 8, 2, 17085851308157180059966219734899116092854108160000000⟩, + ⟨3, 1, 6, 3, 5, 2, -3202650005381078360831404833109555972637982720000000⟩, + ⟨3, 1, 7, 3, 6, 2, 1650513133432715052439363143210387443369902080000000⟩, + ⟨3, 1, 8, 3, 7, 2, 10466053741067072402427233258596778120105164800000000⟩, + ⟨3, 1, 6, 4, 4, 2, 1480070445726769263847302663955308120480153600000000⟩, + ⟨3, 1, 7, 4, 5, 2, 5682568210900828032906898048251187493968281600000000⟩, + ⟨3, 1, 8, 4, 6, 2, -13349852230945834894866290996639052544365035520000000⟩, + ⟨3, 1, 6, 5, 3, 2, 548256614888674841342269835231143467637800960000000⟩, + ⟨3, 1, 7, 5, 4, 2, -3600825940486675688014026164805932398569062400000000⟩, + ⟨3, 1, 8, 5, 5, 2, -4462452166970650610291191095720059627152343040000000⟩, + ⟨3, 1, 6, 6, 2, 2, 39284216189251054292794859168648790624341852160000000⟩, + ⟨3, 1, 7, 6, 3, 2, -10797142992364796370011452472137229574120407040000000⟩, + ⟨3, 1, 8, 6, 4, 2, 6647506098863893208279683279993625210876067840000000⟩, + ⟨3, 1, 6, 7, 1, 2, -77879154984857558679020276090075017297715527680000000⟩, + ⟨3, 1, 7, 7, 2, 2, 19173693459114694217255867777099445975342120960000000⟩, + ⟨3, 1, 8, 7, 3, 2, 31837888320424130696925881130106618645535784960000000⟩ +] + +def collectedFourData_10_2_26 : List CollectedFourTerm := [ + ⟨3, 2, 5, 0, 7, 3, -332793010982906456958308131886327928388897996800000⟩, + ⟨3, 2, 6, 0, 8, 3, -20501700901237690735234624362437352111796440268800000⟩, + ⟨3, 2, 5, 1, 6, 3, 54908265284420902739482888994890677454724766105600000⟩, + ⟨3, 2, 6, 1, 7, 3, 68566435789553548702074424103574499701169324032000000⟩, + ⟨3, 2, 7, 1, 8, 3, 64449893741430536969167023835613472310999331635200000⟩, + ⟨3, 2, 5, 2, 5, 3, -9604654358724263949476616741131766933978768998400000⟩, + ⟨3, 2, 6, 2, 6, 3, -4733114872782637501964809344255733152895048089600000⟩, + ⟨3, 2, 7, 2, 7, 3, -3805195548277565190934566474492262501280907264000000⟩, + ⟨3, 2, 8, 2, 8, 3, -20504769727733553005685835709518596785154136473600000⟩, + ⟨3, 2, 5, 3, 4, 3, 12999498738850698737786695707361826074409513779200000⟩, + ⟨3, 2, 6, 3, 5, 3, 11530523067500555607726540311380838487690942873600000⟩, + ⟨3, 2, 7, 3, 6, 3, -2971176951318794031703599603284167372712391475200000⟩, + ⟨3, 2, 8, 3, 7, 3, -12560335335249446488513593790740819810774417408000000⟩, + ⟨3, 2, 5, 4, 3, 3, -1212546538481892829943273603613376671244301107200000⟩, + ⟨3, 2, 6, 4, 4, 3, -5328707909794747260246710344798785020853485568000000⟩, + ⟨3, 2, 7, 4, 5, 3, -10229494907084122912837389951328606012890415104000000⟩, + ⟨3, 2, 8, 4, 6, 3, 16021188582164862462490993362599500295217296179200000⟩, + ⟨3, 2, 5, 5, 2, 3, -94179350991126437843137405173425238645343990579200000⟩, + ⟨3, 2, 6, 5, 3, 3, -1973892100061500867081418064603238468026158284800000⟩, + ⟨3, 2, 7, 5, 4, 3, 6482039326663118625860064039568299554563424256000000⟩, + ⟨3, 2, 8, 5, 5, 3, 5355399181138480101232137623015967659601061478400000⟩, + ⟨3, 2, 5, 6, 1, 3, 120320670545593042173615712816448229488052928512000000⟩, + ⟨3, 2, 6, 6, 2, 3, -141435236506569235808233868424446222441152040140800000⟩, + ⟨3, 2, 7, 6, 3, 3, 19436514468859451557100562812214841872699988377600000⟩, + ⟨3, 2, 8, 6, 4, 3, -7977687465642001198398192169853958022083536486400000⟩, + ⟨3, 2, 5, 7, 0, 3, 524950707722109053219454279592353667371048212889600000⟩, + ⟨3, 2, 6, 7, 1, 3, 280388862823460734533269144119717050947572491878400000⟩, + ⟨3, 2, 7, 7, 2, 3, -34515590893173513234255827791844636836613219942400000⟩, + ⟨3, 2, 8, 7, 3, 3, -38208723513584537167602534334009121748740053401600000⟩ +] + +def collectedFourData_10_2_27 : List CollectedFourTerm := [ + ⟨3, 3, 4, 0, 6, 4, -32540132914388526472770876592021331443011551232000000⟩, + ⟨3, 3, 5, 0, 7, 4, -420654519043428422516650714054659368395210752000000⟩, + ⟨3, 3, 6, 0, 8, 4, -12957202897246740618597110355507745517696188416000000⟩, + ⟨3, 3, 4, 1, 5, 4, 50424869303856519299344032331987128728726116761600000⟩, + ⟨3, 3, 5, 1, 6, 4, 69404732558862016375527649826926855446734045184000000⟩, + ⟨3, 3, 6, 1, 7, 4, 43334415263694108622576711068709323767273226240000000⟩, + ⟨3, 3, 7, 1, 8, 4, 27155156668433424157436225099859971926262808576000000⟩, + ⟨3, 3, 4, 2, 4, 4, -13444245191209631723698571714935213890304632422400000⟩, + ⟨3, 3, 5, 2, 5, 4, -12140402972750669315202031811639864360882405376000000⟩, + ⟨3, 3, 6, 2, 6, 4, -2991358133554589733366541712842622990624489472000000⟩, + ⟨3, 3, 7, 2, 7, 4, -1603271553589518218417160562221122710740664320000000⟩, + ⟨3, 3, 8, 2, 8, 4, -6479571207370580733447258841324299268103602176000000⟩, + ⟨3, 3, 4, 3, 3, 4, 17147909453419174078300037371743380491770789888000000⟩, + ⟨3, 3, 5, 3, 4, 4, 16431528635911672003447796225883678632614821888000000⟩, + ⟨3, 3, 6, 3, 5, 4, 7287362527465663738145113287368574221892452352000000⟩, + ⟨3, 3, 7, 3, 6, 4, -1251868248633506547659628147361512117843787776000000⟩, + ⟨3, 3, 8, 3, 7, 4, -3969105153281689174829487098594479991716577280000000⟩, + ⟨3, 3, 4, 4, 2, 4, -57169535514532382388699303361279473823994452377600000⟩, + ⟨3, 3, 5, 4, 3, 4, -1532673956873070961920893511862140425950199808000000⟩, + ⟨3, 3, 6, 4, 4, 4, -3367776649361119915888724863925852835686645760000000⟩, + ⟨3, 3, 7, 4, 5, 4, -4310069741235937324914552571314727235899883520000000⟩, + ⟨3, 3, 8, 4, 6, 4, 5062745576920174701729523952667660351776489472000000⟩, + ⟨3, 3, 4, 5, 1, 4, 55118567757907909416370028630090146767787209523200000⟩, + ⟨3, 3, 5, 5, 2, 4, -119043874983989394017543106741113261113252773888000000⟩, + ⟨3, 3, 6, 5, 3, 4, -1247512124041634910053208660259818858438721536000000⟩, + ⟨3, 3, 7, 5, 4, 4, 2731126200962712578374353521431412376632033280000000⟩, + ⟨3, 3, 8, 5, 5, 4, 1692322849700026401430217747426755984326918144000000⟩, + ⟨3, 3, 4, 6, 0, 4, 171971232618721334195957518219582616044537538150400000⟩, + ⟨3, 3, 5, 6, 1, 4, 152086829136982532374026404130015757356163399680000000⟩, + ⟨3, 3, 6, 6, 2, 4, -89387952007682554741156992344180521926138003456000000⟩, + ⟨3, 3, 7, 6, 3, 4, 8189332283582386037124397721806737671442137088000000⟩, + ⟨3, 3, 8, 6, 4, 4, -2520974128953982856775176267013299425115111424000000⟩, + ⟨3, 3, 5, 7, 0, 4, 663544245794553277768509612446019425723895250944000000⟩, + ⟨3, 3, 6, 7, 1, 4, 177207510890598167690454491370852141807370764288000000⟩, + ⟨3, 3, 7, 7, 2, 4, -14542712544538584782444733290328537750948544512000000⟩, + ⟨3, 3, 8, 7, 3, 4, -12074075838761975215278350176154359334128582656000000⟩ +] + +def collectedFourData_10_2_28 : List CollectedFourTerm := [ + ⟨3, 4, 3, 0, 5, 5, -29708212259109458993806929994533315305558507520000000⟩, + ⟨3, 4, 4, 0, 6, 5, -31180717815869659978901898833226856645087199232000000⟩, + ⟨3, 4, 5, 0, 7, 5, -201540508312794412317994739666179084964069376000000⟩, + ⟨3, 4, 6, 0, 8, 5, -4138631806708375803013363247262042543957737472000000⟩, + ⟨3, 4, 3, 1, 4, 5, 28419145133381579199019641778460678757448207564800000⟩, + ⟨3, 4, 4, 1, 5, 5, 48318291286709191559509613102674227021418699161600000⟩, + ⟨3, 4, 5, 1, 6, 5, 33252620490171161961609666631927809530073710592000000⟩, + ⟨3, 4, 6, 1, 7, 5, 13841350695646063770817668012718537861842862080000000⟩, + ⟨3, 4, 7, 1, 8, 5, 6505176850013374042463390335918858392928518144000000⟩, + ⟨3, 4, 3, 2, 3, 5, -19713750896824978452587611791153868218507146035200000⟩, + ⟨3, 4, 4, 2, 4, 5, -12882590758229775672286635594911646769681426022400000⟩, + ⟨3, 4, 5, 2, 5, 5, -5816609296898398702644221994356520554424434688000000⟩, + ⟨3, 4, 6, 2, 6, 5, -955463151650999037270382015934477500441165824000000⟩, + ⟨3, 4, 7, 2, 7, 5, -384073092342692426350911436407241336506286080000000⟩, + ⟨3, 4, 8, 2, 8, 5, -1241775391123367903022424460637894692197053235200000⟩, + ⟨3, 4, 3, 3, 2, 5, 12999498738850698737786695707361826074409513779200000⟩, + ⟨3, 4, 4, 3, 3, 5, 16431528635911672003447796225883678632614821888000000⟩, + ⟨3, 4, 5, 3, 4, 5, 7872537875424521139468058238169846154153426944000000⟩, + ⟨3, 4, 6, 3, 5, 5, 2327640508708305699910413561966322939575926784000000⟩, + ⟨3, 4, 7, 3, 6, 5, -299892372182262118132883737054835500010962944000000⟩, + ⟨3, 4, 8, 3, 7, 5, -760657911825963751768256215786874118346899456000000⟩, + ⟨3, 4, 3, 4, 1, 5, -12002882733935369989029388034808944175161435750400000⟩, + ⟨3, 4, 4, 4, 2, 5, -54781188486011147276238865040469152865564858777600000⟩, + ⟨3, 4, 5, 4, 3, 5, -734322049002141385751844720595458671618555904000000⟩, + ⟨3, 4, 6, 4, 4, 5, -1075694165590117987962456346139624260679761920000000⟩, + ⟨3, 4, 7, 4, 5, 5, -1032502454136960290712375873641425922823290880000000⟩, + ⟨3, 4, 8, 4, 6, 5, 970248287693305613411071550627317678095099494400000⟩, + ⟨3, 4, 3, 5, 0, 5, 14417140436499400374675637749994289814329465241600000⟩, + ⟨3, 4, 4, 5, 1, 5, 52815903124792558866515277260976661854036374323200000⟩, + ⟨3, 4, 5, 5, 2, 5, -57035315180629307554275637025554516471336402944000000⟩, + ⟨3, 4, 6, 5, 3, 5, -398465116025165641921153852283961756207808512000000⟩, + ⟨3, 4, 7, 5, 4, 5, 654257279893371921589125231454981345058488320000000⟩, + ⟨3, 4, 8, 5, 5, 5, 324324681578126896596120163980733390382746828800000⟩, + ⟨3, 4, 4, 6, 0, 5, 164786864603143330816210467745522746658988123750400000⟩, + ⟨3, 4, 5, 6, 1, 5, 72866581634854826814341107886804019007287459840000000⟩, + ⟨3, 4, 6, 6, 2, 5, -28551210029606445890468285611886292239124529152000000⟩, + ⟨3, 4, 7, 6, 3, 5, 1961802520187802312914413402117477718946742272000000⟩, + ⟨3, 4, 8, 6, 4, 5, -483131296008100899139655167142500674908769484800000⟩, + ⟨3, 4, 5, 7, 0, 5, 317911822009114455075127336186368654899750633472000000⟩, + ⟨3, 4, 6, 7, 1, 5, 56601463045337430436229995482960320537712132096000000⟩, + ⟨3, 4, 7, 7, 2, 5, -3483791978674270519976855269522916644516528128000000⟩, + ⟨3, 4, 8, 7, 3, 5, -2313932475975699135788795393760613523302593331200000⟩ +] + +def collectedFourData_10_2_29 : List CollectedFourTerm := [ + ⟨3, 5, 2, 0, 4, 6, 3833698172355380038356423746766390284508148531200000⟩, + ⟨3, 5, 3, 0, 5, 6, -26351110425827832690796129669356551376375644160000000⟩, + ⟨3, 5, 4, 0, 6, 6, -13828609597176557483832162747831599116087984128000000⟩, + ⟨3, 5, 5, 0, 7, 6, -59588643296203469943515912962099625104244736000000⟩, + ⟨3, 5, 6, 0, 8, 6, -917739031208242234225443007991404513978220544000000⟩, + ⟨3, 5, 2, 1, 3, 6, -2288892174258299092999556917005705122249755852800000⟩, + ⟨3, 5, 3, 1, 4, 6, 25207711089641115446834896366067442301427672678400000⟩, + ⟨3, 5, 4, 1, 5, 6, 21429102131397584323801400661439142650054076006400000⟩, + ⟨3, 5, 5, 1, 6, 6, 9831663905389910099535004262457769505127923712000000⟩, + ⟨3, 5, 6, 1, 7, 6, 3069310915130371636966654343978203675266908160000000⟩, + ⟨3, 5, 7, 1, 8, 6, 1154015139108069434477302869900114717374309990400000⟩, + ⟨3, 5, 2, 2, 2, 6, -558822895961337228640347497173295183388947251200000⟩, + ⟨3, 5, 3, 2, 3, 6, -17486048041487553292787457298428169230380276121600000⟩, + ⟨3, 5, 4, 2, 4, 6, -5713412989648505748565207126210983687418911129600000⟩, + ⟨3, 5, 5, 2, 5, 6, -1719772662517672453806563358024113603758522368000000⟩, + ⟨3, 5, 6, 2, 6, 6, -211873360111434790065560977350561444919246848000000⟩, + ⟨3, 5, 7, 2, 7, 6, -68134375637552016112217580861867643191164928000000⟩, + ⟨3, 5, 8, 2, 8, 6, -183575280858206615435748924669716816811628953600000⟩, + ⟨3, 5, 2, 3, 1, 6, -3202650005381078360831404833109555972637982720000000⟩, + ⟨3, 5, 3, 3, 2, 6, 11530523067500555607726540311380838487690942873600000⟩, + ⟨3, 5, 4, 3, 3, 6, 7287362527465663738145113287368574221892452352000000⟩, + ⟨3, 5, 5, 3, 4, 6, 2327640508708305699910413561966322939575926784000000⟩, + ⟨3, 5, 6, 3, 5, 6, 516152836307031081372307480277628528799776768000000⟩, + ⟨3, 5, 7, 3, 6, 6, -53200757731997807479185730011395700807853670400000⟩, + ⟨3, 5, 8, 3, 7, 6, -112450279493898831691249855454815189160951808000000⟩, + ⟨3, 5, 2, 4, 0, 6, 12264766183689880714164957617859200195408324198400000⟩, + ⟨3, 5, 3, 4, 1, 6, -10646527148506188069910508392794407928325157683200000⟩, + ⟨3, 5, 4, 4, 2, 6, -24295389006626143727945053255006858923884308070400000⟩, + ⟨3, 5, 5, 4, 3, 6, -217113944034584946621345069021886002279481344000000⟩, + ⟨3, 5, 6, 4, 4, 6, -238534512735550485166461140549514991333539840000000⟩, + ⟨3, 5, 7, 4, 5, 6, -183165422049646144379090126412847976030404608000000⟩, + ⟨3, 5, 8, 4, 6, 6, 143434636560451374646274793580775216354898739200000⟩, + ⟨3, 5, 3, 5, 0, 6, 12787967729373278334365101173157951490115816652800000⟩, + ⟨3, 5, 4, 5, 1, 6, 23423787391556655242093999770242363557153656012800000⟩, + ⟨3, 5, 5, 5, 2, 6, -16863394262707143176017493149766003237830262784000000⟩, + ⟨3, 5, 6, 5, 3, 6, -88359391854686698045048916145285317340954624000000⟩, + ⟨3, 5, 7, 5, 4, 6, 116064916185493782600934512947310844666970112000000⟩, + ⟨3, 5, 8, 5, 5, 6, 47945864393473145779859290346994523248682598400000⟩, + ⟨3, 5, 4, 6, 0, 6, 73082769639763171538503191303678851362714130841600000⟩, + ⟨3, 5, 5, 6, 1, 6, 21544158926671765780600764209506728850741002240000000⟩, + ⟨3, 5, 6, 6, 2, 6, -6331213081077159870191331749434335891139067904000000⟩, + ⟨3, 5, 7, 6, 3, 6, 348022791760447436499756304663062090377016115200000⟩, + ⟨3, 5, 8, 6, 4, 6, -71422709767055779295816531953618840061372006400000⟩, + ⟨3, 5, 5, 7, 0, 6, 93995665288022048354520476052984548239073083392000000⟩, + ⟨3, 5, 6, 7, 1, 6, 12551339255644340490398127627966033227774164992000000⟩, + ⟨3, 5, 7, 7, 2, 6, -618022965030550905534400085862316436215352524800000⟩, + ⟨3, 5, 8, 7, 3, 6, -342075392378236682875991381637167066971216281600000⟩ +] + +def collectedFourData_10_2_30 : List CollectedFourTerm := [ + ⟨3, 6, 1, 0, 3, 7, -1056067462920454296776439542620830497162605363200000⟩, + ⟨3, 6, 2, 0, 4, 7, -1975729215636425295638673423240250652745321676800000⟩, + ⟨3, 6, 3, 0, 5, 7, 6790135320014375893016800314703814769896325120000000⟩, + ⟨3, 6, 4, 0, 6, 7, 2375564164978408984747488104870870972538814464000000⟩, + ⟨3, 6, 5, 0, 7, 7, 7677379529340609782348365322049305104613376000000⟩, + ⟨3, 6, 6, 0, 8, 7, 94592935320934861551168209058788456365503283200000⟩, + ⟨3, 6, 1, 1, 2, 7, -309921981073397740069563742567598782892998656000000⟩, + ⟨3, 6, 2, 1, 3, 7, 1179600202418985577812385559759283212369736499200000⟩, + ⟨3, 6, 3, 1, 4, 7, -6495504995445102427751497020744193470500752588800000⟩, + ⟨3, 6, 4, 1, 5, 7, -3681223824657272158025853981358248488005219123200000⟩, + ⟨3, 6, 5, 1, 6, 7, -1266708067699983105943131892364927337435758592000000⟩, + ⟨3, 6, 6, 1, 7, 7, -316359138057502210189375625949167094488629248000000⟩, + ⟨3, 6, 7, 1, 8, 7, -99121932362145562654324015579054827359541657600000⟩, + ⟨3, 6, 1, 2, 1, 7, -1135316185372738929884725024547862681926133350400000⟩, + ⟨3, 6, 2, 2, 2, 7, 287994169671169700210701998798767404557847756800000⟩, + ⟨3, 6, 3, 2, 3, 7, 4505792374411591661955233930378600899381769011200000⟩, + ⟨3, 6, 4, 2, 4, 7, 981485453223172601005033096053938065595223244800000⟩, + ⟨3, 6, 5, 2, 5, 7, 221574895885807006481104418310312330094706688000000⟩, + ⟨3, 6, 6, 2, 6, 7, 21838150462952758629482011805595004949653094400000⟩, + ⟨3, 6, 7, 2, 7, 7, 5852272422268454848943545384940987253522432000000⟩, + ⟨3, 6, 8, 2, 8, 7, 13515299228584414574253687589435813267714867200000⟩, + ⟨3, 6, 1, 3, 0, 7, -996398069582047672464239983158272491387040563200000⟩, + ⟨3, 6, 2, 3, 1, 7, 1650513133432715052439363143210387443369902080000000⟩, + ⟨3, 6, 3, 3, 2, 7, -2971176951318794031703599603284167372712391475200000⟩, + ⟨3, 6, 4, 3, 3, 7, -1251868248633506547659628147361512117843787776000000⟩, + ⟨3, 6, 5, 3, 4, 7, -299892372182262118132883737054835500010962944000000⟩, + ⟨3, 6, 6, 3, 5, 7, -53200757731997807479185730011395700807853670400000⟩, + ⟨3, 6, 7, 3, 6, 7, 4569577755801128667621554815824698180999577600000⟩, + ⟨3, 6, 8, 3, 7, 7, 8278887923216003313337632060650831443132416000000⟩, + ⟨3, 6, 2, 4, 0, 7, -6320752386507774364683662434041127886166530457600000⟩, + ⟨3, 6, 3, 4, 1, 7, 2743389514079376359488165309877658616617920102400000⟩, + ⟨3, 6, 4, 4, 2, 7, 4173612328323695461865476563464150602759746355200000⟩, + ⟨3, 6, 5, 4, 3, 7, 27972883040479043120862262649583991630331904000000⟩, + ⟨3, 6, 6, 4, 4, 7, 24586161171873230396660627757941723498545152000000⟩, + ⟨3, 6, 7, 4, 5, 7, 15732645058297326652237148275188890024804352000000⟩, + ⟨3, 6, 8, 4, 6, 7, -10560038496441674686508011843293120108586598400000⟩, + ⟨3, 6, 3, 5, 0, 7, -3295194393983253458909048224320325233965373849600000⟩, + ⟨3, 6, 4, 5, 1, 7, -4023883207088026647055054207621909884296390246400000⟩, + ⟨3, 6, 5, 5, 2, 7, 2172673696633001328682770613004859756137938944000000⟩, + ⟨3, 6, 6, 5, 3, 7, 9107354002045252143036838364605440503001907200000⟩, + ⟨3, 6, 7, 5, 4, 7, -9969174911040092851826789701496644281827328000000⟩, + ⟨3, 6, 8, 5, 5, 7, -3529901743968662495363792865032913422175436800000⟩, + ⟨3, 6, 4, 6, 0, 7, -12554610600117067412325393375583261009736682700800000⟩, + ⟨3, 6, 5, 6, 1, 7, -2775741744921196501763452347712404761440419840000000⟩, + ⟨3, 6, 6, 6, 2, 7, 652568986515618821352946288198366845469930291200000⟩, + ⟨3, 6, 7, 6, 3, 7, -29892754831644931929523420727688803017084108800000⟩, + ⟨3, 6, 8, 6, 4, 7, 5258329387842221673222231026630913208143052800000⟩, + ⟨3, 6, 5, 7, 0, 7, -12110367959577115963415515632814972185159401472000000⟩, + ⟨3, 6, 6, 7, 1, 7, -1293688055129558196187375608765212587183413657600000⟩, + ⟨3, 6, 7, 7, 2, 7, 53083905454964894999386167422932374007264051200000⟩, + ⟨3, 6, 8, 7, 3, 7, 25184497962436938192784113834364333072790323200000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1008.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1008.lean new file mode 100644 index 0000000000000000000000000000000000000000..9676b4c2fbb5756b63dd46e74a8fe8369f740a05 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1008.lean @@ -0,0 +1,644 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1008. -/ +namespace LaughlinFock +def collectedFourData_10_2_31 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 2, 8, -6346259885375588231536913599774296931427155968000000⟩, + ⟨3, 7, 1, 0, 3, 8, -13393239468661779258381002264152076487474806784000000⟩, + ⟨3, 7, 2, 0, 4, 8, -12528278466734227974553615178902043933181739008000000⟩, + ⟨3, 7, 3, 0, 5, 8, 28704576667251827346664996987791300503588044800000000⟩, + ⟨3, 7, 4, 0, 6, 8, 7531834104315144930107921373998262240852049920000000⟩, + ⟨3, 7, 5, 0, 7, 8, 19473184458104205458696452346581326678196224000000⟩, + ⟨3, 7, 6, 0, 8, 8, 199940799124929620426757268322946388133412864000000⟩, + ⟨3, 7, 0, 1, 1, 8, 46757423938874280297367366027109775636468596736000000⟩, + ⟨3, 7, 1, 1, 2, 8, -3930486881623331386512110997856145659102494720000000⟩, + ⟨3, 7, 2, 1, 3, 8, 7479952059402372551700281757022980806962839552000000⟩, + ⟨3, 7, 3, 1, 4, 8, -27459058228883194883349148483001095505578033152000000⟩, + ⟨3, 7, 4, 1, 5, 8, -11671487370000412865373903394800271728360554496000000⟩, + ⟨3, 7, 5, 1, 6, 8, -3212924379030808657486144242230785538531524608000000⟩, + ⟨3, 7, 6, 1, 7, 8, -668687346037902789081416233850869289802792960000000⟩, + ⟨3, 7, 7, 1, 8, 8, -179583194030786588919848197193693646569865216000000⟩, + ⟨3, 7, 0, 2, 0, 8, 7518197598960423538521648151082881327262859264000000⟩, + ⟨3, 7, 1, 2, 1, 8, -14398286167528694924470215214113118235758952448000000⟩, + ⟨3, 7, 2, 2, 2, 8, 1826197196397726467516140370431048669156343808000000⟩, + ⟨3, 7, 3, 2, 3, 8, 19047759221644253632280082136761641530030030848000000⟩, + ⟨3, 7, 4, 2, 4, 8, 3111844217242048757644887788118327892371308544000000⟩, + ⟨3, 7, 5, 2, 5, 8, 562010618646612454133639354057229952836698112000000⟩, + ⟨3, 7, 6, 2, 6, 8, 46159232083866723763755416131513220792844288000000⟩, + ⟨3, 7, 7, 2, 7, 8, 10602797472606781878529011528890198387589120000000⟩, + ⟨3, 7, 8, 2, 8, 8, 21425435094657074260896533726462641761681408000000⟩, + ⟨3, 7, 1, 3, 0, 8, -12636501379486081293238912809518887503642230784000000⟩, + ⟨3, 7, 2, 3, 1, 8, 10466053741067072402427233258596778120105164800000000⟩, + ⟨3, 7, 3, 3, 2, 8, -12560335335249446488513593790740819810774417408000000⟩, + ⟨3, 7, 4, 3, 3, 8, -3969105153281689174829487098594479991716577280000000⟩, + ⟨3, 7, 5, 3, 4, 8, -760657911825963751768256215786874118346899456000000⟩, + ⟨3, 7, 6, 3, 5, 8, -112450279493898831691249855454815189160951808000000⟩, + ⟨3, 7, 7, 3, 6, 8, 8278887923216003313337632060650831443132416000000⟩, + ⟨3, 7, 8, 3, 7, 8, 13124295130636433552741917746523149686538240000000⟩, + ⟨3, 7, 2, 4, 0, 8, -40080465172417926633919850614084711440508256256000000⟩, + ⟨3, 7, 3, 4, 1, 8, 11597388111384424121596298971645076121002704896000000⟩, + ⟨3, 7, 4, 4, 2, 8, 13232627489539628266977590202670825544620179456000000⟩, + ⟨3, 7, 5, 4, 3, 8, 70951437165567337541730451403887810493546496000000⟩, + ⟨3, 7, 6, 4, 4, 8, 51967693945011909544795639906479245403095040000000⟩, + ⟨3, 7, 7, 4, 5, 8, 28503466213706375177801674519366863232696320000000⟩, + ⟨3, 7, 8, 4, 6, 8, -16740540891915483409406858839146935957323776000000⟩, + ⟨3, 7, 3, 5, 0, 8, -13930084697544800193908803153443996391843037184000000⟩, + ⟨3, 7, 4, 5, 1, 8, -12757904508633660136579060891601931088787668992000000⟩, + ⟨3, 7, 5, 5, 2, 8, 5510848525869265248069892136651500015589523456000000⟩, + ⟨3, 7, 6, 5, 3, 8, 19250186400332093712686980542581455762489344000000⟩, + ⟨3, 7, 7, 5, 4, 8, -18061555396592254524788064406095639588372480000000⟩, + ⟨3, 7, 8, 5, 5, 8, -5595856919391255338378218998593783334961152000000⟩, + ⟨3, 7, 4, 6, 0, 8, -39804963249737178190417870975494147261515956224000000⟩, + ⟨3, 7, 5, 6, 1, 8, -7040492240918682745617820139997388731486044160000000⟩, + ⟨3, 7, 6, 6, 2, 8, 1379333078156441370989620877334879655925121024000000⟩, + ⟨3, 7, 7, 6, 3, 8, -54157906964857983342485995192003942215057408000000⟩, + ⟨3, 7, 8, 6, 4, 8, 8335886102119364244759777178007886618427392000000⟩, + ⟨3, 7, 5, 7, 0, 8, -30717177421162978455077341139072206149651529728000000⟩, + ⟨3, 7, 6, 7, 1, 8, -2734464499736633463176792975596422309454282752000000⟩, + ⟨3, 7, 7, 7, 2, 8, 96174247878883295640483161640221122800648192000000⟩, + ⟨3, 7, 8, 7, 3, 8, 39924297446889173189344267644774167240245248000000⟩ +] + +def collectedFourData_10_2_32 : List CollectedFourTerm := [ + ⟨4, 0, 6, 0, 8, 2, -21807212599951052825734733367044666910485721907200000⟩, + ⟨4, 0, 6, 1, 7, 2, 72932623965527607973773887452834978327437508608000000⟩, + ⟨4, 0, 7, 1, 8, 2, 137107895743302149285959516201221122400313776537600000⟩, + ⟨4, 0, 6, 2, 6, 2, -5034511174852330869680865558614600236371699302400000⟩, + ⟨4, 0, 7, 2, 7, 2, -8095007209930237217221392079788720426458284032000000⟩, + ⟨4, 0, 8, 2, 8, 2, -65431430531512353332190193899467626233415807795200000⟩, + ⟨4, 0, 6, 3, 5, 2, 12264766183689880714164957617859200195408324198400000⟩, + ⟨4, 0, 7, 3, 6, 2, -6320752386507774364683662434041127886166530457600000⟩, + ⟨4, 0, 8, 3, 7, 2, -40080465172417926633919850614084711440508256256000000⟩, + ⟨4, 0, 6, 4, 4, 2, -5668030512771727238500167013830841238701473792000000⟩, + ⟨4, 0, 7, 4, 5, 2, -21761781747136193148696195858015019098232061952000000⟩, + ⟨4, 0, 8, 4, 6, 2, 51124167774892115774546958210176962713180595814400000⟩, + ⟨4, 0, 6, 5, 3, 2, -2099586023753100791432332574423535425076540211200000⟩, + ⟨4, 0, 7, 5, 4, 2, 13789608028985786627551222770303483863239753728000000⟩, + ⟨4, 0, 8, 5, 5, 2, 17089264309817368262656773178812068713210891468800000⟩, + ⟨4, 0, 6, 6, 2, 2, -150441579773359858997923650164743415877216711475200000⟩, + ⟨4, 0, 7, 6, 3, 2, 41348393995822513934104474768657570085825465548800000⟩, + ⟨4, 0, 8, 6, 4, 2, -25457077067500848315484351409513753509379230924800000⟩, + ⟨4, 0, 6, 7, 1, 2, 298243524852154438348833444127604187384795208089600000⟩, + ⟨4, 0, 7, 7, 2, 2, -73426964157391381562786290654592067299779490611200000⟩, + ⟨4, 0, 8, 7, 3, 2, -121925360366054040628380472646757481384143696691200000⟩ +] + +def collectedFourData_10_2_33 : List CollectedFourTerm := [ + ⟨4, 1, 5, 0, 7, 3, 307279193278667007286334833065465989658417561600000⟩, + ⟨4, 1, 6, 0, 8, 3, 18929923122984146444146871436095414619923388825600000⟩, + ⟨4, 1, 5, 1, 6, 3, -50698683277920498615825062644925273980773020467200000⟩, + ⟨4, 1, 6, 1, 7, 3, -63309740229159210037588856827844394934163472384000000⟩, + ⟨4, 1, 7, 1, 8, 3, -59508795864645730909777474315481302192559122022400000⟩, + ⟨4, 1, 5, 2, 5, 3, 8868306561945242900557905889613422876081048780800000⟩, + ⟨4, 1, 6, 2, 6, 3, 4370247186106358709361848213204620932478612275200000⟩, + ⟨4, 1, 7, 2, 7, 3, 3513467470031583189941530148861942892664455168000000⟩, + ⟨4, 1, 8, 2, 8, 3, 18932756675669569854236658760250672207566680883200000⟩, + ⟨4, 1, 5, 3, 4, 3, -12002882733935369989029388034808944175161435750400000⟩, + ⟨4, 1, 6, 3, 5, 3, -10646527148506188069910508392794407928325157683200000⟩, + ⟨4, 1, 7, 3, 6, 3, 2743389514079376359488165309877658616617920102400000⟩, + ⟨4, 1, 8, 3, 7, 3, 11597388111384424121596298971645076121002704896000000⟩, + ⟨4, 1, 5, 4, 3, 3, 1119585778130099843529893125866481200719619686400000⟩, + ⟨4, 1, 6, 4, 4, 3, 4920178650697340231197347571168827036785442816000000⟩, + ⟨4, 1, 7, 4, 5, 3, 9445243256200758001244612616101450877656629248000000⟩, + ⟨4, 1, 8, 4, 6, 3, -14792912532486666593121900814374929584483624550400000⟩, + ⟨4, 1, 5, 5, 2, 3, 86959022698791585102235495264099589703776757350400000⟩, + ⟨4, 1, 6, 5, 3, 3, 1822562229701349969021486940625465121017797017600000⟩, + ⟨4, 1, 7, 5, 4, 3, -5985089077486496109876132344395178044997763072000000⟩, + ⟨4, 1, 8, 5, 5, 3, -4944823616352900526220548332708078457906318540800000⟩, + ⟨4, 1, 5, 6, 1, 3, -111096199018125198971903169833411169958068486144000000⟩, + ⟨4, 1, 6, 6, 2, 3, 130592001456269609152623872697350039696016251289600000⟩, + ⟨4, 1, 7, 6, 3, 3, -17946399981479895875968105293568578606010151731200000⟩, + ⟨4, 1, 8, 6, 4, 3, 7366072266456701278500952032234369013856914636800000⟩, + ⟨4, 1, 5, 7, 0, 3, -484704980743121153694800770053088705280774189875200000⟩, + ⟨4, 1, 6, 7, 1, 3, -258892647169027338322210017620962740761768283340800000⟩, + ⟨4, 1, 7, 7, 2, 3, 31869428068414646529096234640589008703480188108800000⟩, + ⟨4, 1, 8, 7, 3, 3, 35279423996271791009659744836052034912653620019200000⟩ +] + +def collectedFourData_10_2_34 : List CollectedFourTerm := [ + ⟨4, 2, 4, 0, 6, 4, 108485777193429676188589311842835132715071071846400000⟩, + ⟨4, 2, 5, 0, 7, 4, 1402423049359331147498463049040967195762779750400000⟩, + ⟨4, 2, 6, 0, 8, 4, 43198109554715870092484183856652589554774258483200000⟩, + ⟨4, 2, 4, 1, 5, 4, -168111825194392745913044085224644762110565621432320000⟩, + ⟨4, 2, 5, 1, 6, 4, -231388924327992937112523559880877537249383468236800000⟩, + ⟨4, 2, 6, 1, 7, 4, -144472910773696467455277399364561274253499957248000000⟩, + ⟨4, 2, 7, 1, 8, 4, -90532767144344128877418667361985412666674590515200000⟩, + ⟨4, 2, 4, 2, 4, 4, 44821863272183682295723978077855548154512387604480000⟩, + ⟨4, 2, 5, 2, 5, 4, 40474974561579161859658225139561508047458349875200000⟩, + ⟨4, 2, 6, 2, 6, 4, 9972909847552017740099633134409635800824571494400000⟩, + ⟨4, 2, 7, 2, 7, 4, 5345158269662978824823498368975732201293348864000000⟩, + ⟨4, 2, 8, 2, 8, 4, 21602287862842190404973177669793894112842429235200000⟩, + ⟨4, 2, 4, 3, 3, 4, -57169535514532382388699303361279473823994452377600000⟩, + ⟨4, 2, 5, 3, 4, 4, -54781188486011147276238865040469152865564858777600000⟩, + ⟨4, 2, 6, 3, 5, 4, -24295389006626143727945053255006858923884308070400000⟩, + ⟨4, 2, 7, 3, 6, 4, 4173612328323695461865476563464150602759746355200000⟩, + ⟨4, 2, 8, 3, 7, 4, 13232627489539628266977590202670825544620179456000000⟩, + ⟨4, 2, 4, 4, 2, 4, 190597915146775626407564456666284006726981669355520000⟩, + ⟨4, 2, 5, 4, 3, 4, 5109792447159361078222591211356197370872830361600000⟩, + ⟨4, 2, 6, 4, 4, 4, 11227854175674657966368380471544039330285617152000000⟩, + ⟨4, 2, 7, 4, 5, 4, 14369371719102933044159855432434919267006152704000000⟩, + ⟨4, 2, 8, 4, 6, 4, -16878722963111306311857752180993474530654971494400000⟩, + ⟨4, 2, 4, 5, 1, 4, -183760179367961830155722005432200762121547038064640000⟩, + ⟨4, 2, 5, 5, 2, 4, 396881209174318841684579885359835411236790049177600000⟩, + ⟨4, 2, 6, 5, 3, 4, 4159089414015264873917598716324206500241421107200000⟩, + ⟨4, 2, 7, 5, 4, 4, -9105320783547467614610176747633383356976070656000000⟩, + ⟨4, 2, 8, 5, 5, 4, -5642047009916370044724016182614306810881690828800000⟩, + ⟨4, 2, 4, 6, 0, 4, -573336097754677790685317843829627782169849055150080000⟩, + ⟨4, 2, 5, 6, 1, 4, -507043345619350220024867097272538377499690663936000000⟩, + ⟨4, 2, 6, 6, 2, 4, 298011119708564363218684935438960419465017373491200000⟩, + ⟨4, 2, 7, 6, 3, 4, -27302472298348758100143103538981071231016081817600000⟩, + ⟨4, 2, 8, 6, 4, 4, 8404693317745210702793938429100889044496993484800000⟩, + ⟨4, 2, 5, 7, 0, 4, -2212194811761817349415141820919763225037691997388800000⟩, + ⟨4, 2, 6, 7, 1, 4, -590793362585776339251730669249075674290153167257600000⟩, + ⟨4, 2, 7, 7, 2, 4, 48484051280481820024814146996563356959556134502400000⟩, + ⟨4, 2, 8, 7, 3, 4, 40253846064694795678591343762695309024864449331200000⟩ +] + +def collectedFourData_10_2_35 : List CollectedFourTerm := [ + ⟨4, 3, 3, 0, 5, 5, 2771075305512380725105156172883584572792504320000000⟩, + ⟨4, 3, 4, 0, 6, 5, 2908425333510674960184172401592977044759642112000000⟩, + ⟨4, 3, 5, 0, 7, 5, 18798974531856887338624128846105203982729216000000⟩, + ⟨4, 3, 6, 0, 8, 5, 386036705882935892519398054672560735966461952000000⟩, + ⟨4, 3, 3, 1, 4, 5, -2650835755313360124464287093961175662735445196800000⟩, + ⟨4, 3, 4, 1, 5, 5, -4506956615947091871627544672152804197700049305600000⟩, + ⟨4, 3, 5, 1, 6, 5, -3101684971152501170007341620083981060377935872000000⟩, + ⟨4, 3, 6, 1, 7, 5, -1291071464452744277068754683637619913685729280000000⟩, + ⟨4, 3, 7, 1, 8, 5, -606779525130646114785523263196767388491055104000000⟩, + ⟨4, 3, 3, 2, 3, 5, 1838827857184961364158961747107101587499332403200000⟩, + ⟨4, 3, 4, 2, 4, 5, 1201641782070082037201196081007570732615886438400000⟩, + ⟨4, 3, 5, 2, 5, 5, 542552417623397221682650614335263527149764608000000⟩, + ⟨4, 3, 6, 2, 6, 5, 89122170050985129867395160486309644136873984000000⟩, + ⟨4, 3, 7, 2, 7, 5, 35824958177221358782678822022134300441313280000000⟩, + ⟨4, 3, 8, 2, 8, 5, 115828347102232959223871795049822117076087603200000⟩, + ⟨4, 3, 3, 3, 2, 5, -1212546538481892829943273603613376671244301107200000⟩, + ⟨4, 3, 4, 3, 3, 5, -1532673956873070961920893511862140425950199808000000⟩, + ⟨4, 3, 5, 3, 4, 5, -734322049002141385751844720595458671618555904000000⟩, + ⟨4, 3, 6, 3, 5, 5, -217113944034584946621345069021886002279481344000000⟩, + ⟨4, 3, 7, 3, 6, 5, 27972883040479043120862262649583991630331904000000⟩, + ⟨4, 3, 8, 3, 7, 5, 70951437165567337541730451403887810493546496000000⟩, + ⟨4, 3, 3, 4, 1, 5, 1119585778130099843529893125866481200719619686400000⟩, + ⟨4, 3, 4, 4, 2, 5, 5109792447159361078222591211356197370872830361600000⟩, + ⟨4, 3, 5, 4, 3, 5, 68494922499388520502834147720360846912651264000000⟩, + ⟨4, 3, 6, 4, 4, 5, 100336887071907428784703233986747255457054720000000⟩, + ⟨4, 3, 7, 4, 5, 5, 96308119404342320901444237604580610885550080000000⟩, + ⟨4, 3, 8, 4, 6, 5, -90501274421794716782024550844317215448524390400000⟩, + ⟨4, 3, 3, 5, 0, 5, -1344779062814096602798194662321631454629042585600000⟩, + ⟨4, 3, 4, 5, 1, 5, -4926477689433139732840311615290600580522914611200000⟩, + ⟨4, 3, 5, 5, 2, 5, 5320049286731971354124091784582756245285371904000000⟩, + ⟨4, 3, 6, 5, 3, 5, 37167394439457973725341774325765887955566592000000⟩, + ⟨4, 3, 7, 5, 4, 5, -61026768489184465803604170753717832903557120000000⟩, + ⟨4, 3, 8, 5, 5, 5, -30251841081879158885023605542694555600342220800000⟩, + ⟨4, 3, 4, 6, 0, 5, -15370726693073351058269916762997952827156227686400000⟩, + ⟨4, 3, 5, 6, 1, 5, -6796732943886033052530347408079169663732285440000000⟩, + ⟨4, 3, 6, 6, 2, 5, 2663154294357781018440842827712631040043384832000000⟩, + ⟨4, 3, 7, 6, 3, 5, -182989890827827710924229683321122167562698752000000⟩, + ⟨4, 3, 8, 6, 4, 5, 45064751524310424948139200270404098045299916800000⟩, + ⟨4, 3, 5, 7, 0, 5, -29653672581047872608521443100361814189855997952000000⟩, + ⟨4, 3, 6, 7, 1, 5, -5279581118271834746629710021642370464387956736000000⟩, + ⟨4, 3, 7, 7, 2, 5, 324955599396130469932232957223337224881307648000000⟩, + ⟨4, 3, 8, 7, 3, 5, 215835307990747143245604433558096873992172339200000⟩ +] + +def collectedFourData_10_2_36 : List CollectedFourTerm := [ + ⟨4, 4, 2, 0, 4, 6, -1771702606655818610071521634126747725050413056000000⟩, + ⟨4, 4, 3, 0, 5, 6, 12177883842386826448348679125621584513780940800000000⟩, + ⟨4, 4, 4, 0, 6, 6, 6390744020072593708213499957719027688291696640000000⟩, + ⟨4, 4, 5, 0, 7, 6, 27538254163108621741278588834126736580935680000000⟩, + ⟨4, 4, 6, 0, 8, 6, 424123277504253009379722347968894574757150720000000⟩, + ⟨4, 4, 2, 1, 3, 6, 1057787037260693434330640643814954083878436864000000⟩, + ⟨4, 4, 3, 1, 4, 6, -11649474068508896518966309307256628030778376192000000⟩, + ⟨4, 4, 4, 1, 5, 6, -9903230352942727219162064125784200613128568832000000⟩, + ⟨4, 4, 5, 1, 6, 6, -4543598318341615439496998495040463616669122560000000⟩, + ⟨4, 4, 6, 1, 7, 6, -1418449211308841384208710419316467460525260800000000⟩, + ⟨4, 4, 7, 1, 8, 6, -533315753655662061920271929457424537592266752000000⟩, + ⟨4, 4, 2, 2, 2, 6, 258254024422942018980440041131875679816646656000000⟩, + ⟨4, 4, 3, 2, 3, 6, 8080990078616065720760445451730517034750967808000000⟩, + ⟨4, 4, 4, 2, 4, 6, 2640392704791974521584696349993998019196878848000000⟩, + ⟨4, 4, 5, 2, 5, 6, 794774541983825928959939454369838913122467840000000⟩, + ⟨4, 4, 6, 2, 6, 6, 97915007263007590118882286742878491498250240000000⟩, + ⟨4, 4, 7, 2, 7, 6, 31487572962936831597800861723745019641200640000000⟩, + ⟨4, 4, 8, 2, 8, 6, 84837352601035478952791444393806161896275968000000⟩, + ⟨4, 4, 2, 3, 1, 6, 1480070445726769263847302663955308120480153600000000⟩, + ⟨4, 4, 3, 3, 2, 6, -5328707909794747260246710344798785020853485568000000⟩, + ⟨4, 4, 4, 3, 3, 6, -3367776649361119915888724863925852835686645760000000⟩, + ⟨4, 4, 5, 3, 4, 6, -1075694165590117987962456346139624260679761920000000⟩, + ⟨4, 4, 6, 3, 5, 6, -238534512735550485166461140549514991333539840000000⟩, + ⟨4, 4, 7, 3, 6, 6, 24586161171873230396660627757941723498545152000000⟩, + ⟨4, 4, 8, 3, 7, 6, 51967693945011909544795639906479245403095040000000⟩, + ⟨4, 4, 2, 4, 0, 6, -5668030512771727238500167013830841238701473792000000⟩, + ⟨4, 4, 3, 4, 1, 6, 4920178650697340231197347571168827036785442816000000⟩, + ⟨4, 4, 4, 4, 2, 6, 11227854175674657966368380471544039330285617152000000⟩, + ⟨4, 4, 5, 4, 3, 6, 100336887071907428784703233986747255457054720000000⟩, + ⟨4, 4, 6, 4, 4, 6, 110236173791246135779543965499723705692979200000000⟩, + ⟨4, 4, 7, 4, 5, 6, 84647940736344707590186976831144660607959040000000⟩, + ⟨4, 4, 8, 4, 6, 6, -66286783167061666491005683184505010935300096000000⟩, + ⟨4, 4, 3, 5, 0, 6, -5909822511155396779885305902427690324002340864000000⟩, + ⟨4, 4, 4, 5, 1, 6, -10825052811571629508922222164456725113852657664000000⟩, + ⟨4, 4, 5, 5, 2, 6, 7793237294407813646111580081746284094863441920000000⟩, + ⟨4, 4, 6, 5, 3, 6, 40834347889023021834748987112355347426181120000000⟩, + ⟨4, 4, 7, 5, 4, 6, -53638159631328043634667748121471932233154560000000⟩, + ⟨4, 4, 8, 5, 5, 6, -22157668419705832507441289310430664476065792000000⟩, + ⟨4, 4, 4, 6, 0, 6, -33774420325020928082688378411244854661934481408000000⟩, + ⟨4, 4, 5, 6, 1, 6, -9956402620277349251237736389722645778871091200000000⟩, + ⟨4, 4, 6, 6, 2, 6, 2925902409303705999093389108506954063958507520000000⟩, + ⟨4, 4, 7, 6, 3, 6, -160835010899877989193858358265311510948478976000000⟩, + ⟨4, 4, 8, 6, 4, 6, 33007241410183870013421684277669018397048832000000⟩, + ⟨4, 4, 5, 7, 0, 6, -43439091372918630553794289021691732687805480960000000⟩, + ⟨4, 4, 6, 7, 1, 6, -5800467192904827841951138277054691417218088960000000⟩, + ⟨4, 4, 7, 7, 2, 6, 285612703163081409494016689707466278488244224000000⟩, + ⟨4, 4, 8, 7, 3, 6, 158086483886387990900546654605912440840388608000000⟩ +] + +def collectedFourData_10_2_37 : List CollectedFourTerm := [ + ⟨4, 5, 1, 0, 3, 7, -3635945253508706422283668519252910982366756864000000⟩, + ⟨4, 5, 2, 0, 4, 7, -6802257920101104807938540653022299818804903936000000⟩, + ⟨4, 5, 3, 0, 5, 7, 23377824953733752983942284215108100719797862400000000⟩, + ⟨4, 5, 4, 0, 6, 7, 8178853674908846623551228207399039826950881280000000⟩, + ⟨4, 5, 5, 0, 7, 7, 26432526935254599898775755610782288073195520000000⟩, + ⟨4, 5, 6, 0, 8, 7, 325674965162254240575675766407729498254475264000000⟩, + ⟨4, 5, 1, 1, 2, 7, -1067033495119348819004506475999608320420741120000000⟩, + ⟨4, 5, 2, 1, 3, 7, 4061257360550152182973637941454518568651587584000000⟩, + ⟨4, 5, 3, 1, 4, 7, -22363439256067325126521447233241449338215858176000000⟩, + ⟨4, 5, 4, 1, 5, 7, -12674122404407366194720119017534420432468312064000000⟩, + ⟨4, 5, 5, 1, 6, 7, -4361161903045819357736641831321920675344547840000000⟩, + ⟨4, 5, 6, 1, 7, 7, -1089196047422324186303973771685054536178728960000000⟩, + ⟨4, 5, 7, 1, 8, 7, -341267894471530171234104218493176038085885952000000⟩, + ⟨4, 5, 1, 2, 1, 7, -3908791474383818175760323114124293916179038208000000⟩, + ⟨4, 5, 2, 2, 2, 7, 991538013450702357907356372594211468697665536000000⟩, + ⟨4, 5, 3, 2, 3, 7, 15513037729362888614168266099960956828279373824000000⟩, + ⟨4, 5, 4, 2, 4, 7, 3379166104754269913311812830351531364682039296000000⟩, + ⟨4, 5, 5, 2, 5, 7, 762862429986036049573028518665267242084597760000000⟩, + ⟨4, 5, 6, 2, 6, 7, 75186787122105312270347874829273174363865088000000⟩, + ⟨4, 5, 7, 2, 7, 7, 20148847382479809152122540099630065663344640000000⟩, + ⟨4, 5, 8, 2, 8, 7, 46531959183769305288549596805343073160658944000000⟩, + ⟨4, 5, 1, 3, 0, 7, -3430508901091829460913447943136283776321060864000000⟩, + ⟨4, 5, 2, 3, 1, 7, 5682568210900828032906898048251187493968281600000000⟩, + ⟨4, 5, 3, 3, 2, 7, -10229494907084122912837389951328606012890415104000000⟩, + ⟨4, 5, 4, 3, 3, 7, -4310069741235937324914552571314727235899883520000000⟩, + ⟨4, 5, 5, 3, 4, 7, -1032502454136960290712375873641425922823290880000000⟩, + ⟨4, 5, 6, 3, 5, 7, -183165422049646144379090126412847976030404608000000⟩, + ⟨4, 5, 7, 3, 6, 7, 15732645058297326652237148275188890024804352000000⟩, + ⟨4, 5, 8, 3, 7, 7, 28503466213706375177801674519366863232696320000000⟩, + ⟨4, 5, 2, 4, 0, 7, -21761781747136193148696195858015019098232061952000000⟩, + ⟨4, 5, 3, 4, 1, 7, 9445243256200758001244612616101450877656629248000000⟩, + ⟨4, 5, 4, 4, 2, 7, 14369371719102933044159855432434919267006152704000000⟩, + ⟨4, 5, 5, 4, 3, 7, 96308119404342320901444237604580610885550080000000⟩, + ⟨4, 5, 6, 4, 4, 7, 84647940736344707590186976831144660607959040000000⟩, + ⟨4, 5, 7, 4, 5, 7, 54166081366301926979833856408685825270743040000000⟩, + ⟨4, 5, 8, 4, 6, 7, -36357262387221551843565098188788026906247168000000⟩, + ⟨4, 5, 3, 5, 0, 7, -11345057808200231738200838283311919649932705792000000⟩, + ⟨4, 5, 4, 5, 1, 7, -13853867826801058569410318358046063530111664128000000⟩, + ⟨4, 5, 5, 5, 2, 7, 7480320047783731071836907343408346447090810880000000⟩, + ⟨4, 5, 6, 5, 3, 7, 31355800380580587476091030212215690959519744000000⟩, + ⟨4, 5, 7, 5, 4, 7, -34322972226561771425277547976408305300930560000000⟩, + ⟨4, 5, 8, 5, 5, 7, -12153134096038041715526154141877160311259136000000⟩, + ⟨4, 5, 4, 6, 0, 7, -43224394675422415144083347217627224976094396416000000⟩, + ⟨4, 5, 5, 6, 1, 7, -9556629076046430295343885538556309255539916800000000⟩, + ⟨4, 5, 6, 6, 2, 7, 2246736304655159627421490127851754386750439424000000⟩, + ⟨4, 5, 7, 6, 3, 7, -102918065237850747672377499440842391553048576000000⟩, + ⟨4, 5, 8, 6, 4, 7, 18103954955906410274378101328033375066259456000000⟩, + ⟨4, 5, 5, 7, 0, 7, -41694907235471739317048848181171275062250045440000000⟩, + ⟨4, 5, 6, 7, 1, 7, -4454051572199159316392453902462085483779325952000000⟩, + ⟨4, 5, 7, 7, 2, 7, 182763110173788735503917671331780250906394624000000⟩, + ⟨4, 5, 8, 7, 3, 7, 86707960469964331511701375520733121493336064000000⟩ +] + +def collectedFourData_10_2_38 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 2, 8, 8094897445109575113615655379798753956628476723200000⟩, + ⟨4, 6, 1, 0, 3, 8, 17083589691378446438109520648786630182449027481600000⟩, + ⟨4, 6, 2, 0, 4, 8, 15980298819102992799792067528800151696445748019200000⟩, + ⟨4, 6, 3, 0, 5, 8, -36613786470066224257618891272624285903507947520000000⟩, + ⟨4, 6, 4, 0, 6, 8, -9607142750095791576871226295145568059741175808000000⟩, + ⟨4, 6, 5, 0, 7, 8, -24838792291079655437195039757573275482954137600000⟩, + ⟨4, 6, 6, 0, 8, 8, -255032143852043412508852775484354729034226073600000⟩, + ⟨4, 6, 0, 1, 1, 8, -59640884303353467777668271020347856812859876966400000⟩, + ⟨4, 6, 1, 1, 2, 8, 5013486492951336126059407185322366358758883328000000⟩, + ⟨4, 6, 2, 1, 3, 8, -9540965215548353822258005074632795989857848524800000⟩, + ⟨4, 6, 3, 1, 4, 8, 35025080018283339026284288262689024518394793164800000⟩, + ⟨4, 6, 4, 1, 5, 8, 14887428973680215616813785868895130218303743590400000⟩, + ⟨4, 6, 5, 1, 6, 8, 4098208049607398392544224081045669356051313459200000⟩, + ⟨4, 6, 6, 1, 7, 8, 852936310013558294755742008229915173117231104000000⟩, + ⟨4, 6, 7, 1, 8, 8, 229065239180383368555759970313315045907785318400000⟩, + ⟨4, 6, 0, 2, 0, 8, -9589748865453510764463276763569677700236417433600000⟩, + ⟨4, 6, 1, 2, 1, 8, 18365565233165152388627048051250512068540052275200000⟩, + ⟨4, 6, 2, 2, 2, 8, -2329384438455176118142247530240371128689439539200000⟩, + ⟨4, 6, 3, 2, 3, 8, -24296146114921524562690595455059510216459760435200000⟩, + ⟨4, 6, 4, 2, 4, 8, -3969276433475407949252832701430117783762999705600000⟩, + ⟨4, 6, 5, 2, 5, 8, -716866060195653086536853072747162220215717068800000⟩, + ⟨4, 6, 6, 2, 6, 8, -58877867691010708870932805851388206279504691200000⟩, + ⟨4, 6, 7, 2, 7, 8, -13524274095645444980934231539872998661029888000000⟩, + ⟨4, 6, 8, 2, 8, 8, -27328962718304458673041294550930285541929779200000⟩, + ⟨4, 6, 1, 3, 0, 8, 16118341287542724331492918928962158728694045081600000⟩, + ⟨4, 6, 2, 3, 1, 8, -13349852230945834894866290996639052544365035520000000⟩, + ⟨4, 6, 3, 3, 2, 8, 16021188582164862462490993362599500295217296179200000⟩, + ⟨4, 6, 4, 3, 3, 8, 5062745576920174701729523952667660351776489472000000⟩, + ⟨4, 6, 5, 3, 4, 8, 970248287693305613411071550627317678095099494400000⟩, + ⟨4, 6, 6, 3, 5, 8, 143434636560451374646274793580775216354898739200000⟩, + ⟨4, 6, 7, 3, 6, 8, -10560038496441674686508011843293120108586598400000⟩, + ⟨4, 6, 8, 3, 7, 8, -16740540891915483409406858839146935957323776000000⟩, + ⟨4, 6, 2, 4, 0, 8, 51124167774892115774546958210176962713180595814400000⟩, + ⟨4, 6, 3, 4, 1, 8, -14792912532486666593121900814374929584483624550400000⟩, + ⟨4, 6, 4, 4, 2, 8, -16878722963111306311857752180993474530654971494400000⟩, + ⟨4, 6, 5, 4, 3, 8, -90501274421794716782024550844317215448524390400000⟩, + ⟨4, 6, 6, 4, 4, 8, -66286783167061666491005683184505010935300096000000⟩, + ⟨4, 6, 7, 4, 5, 8, -36357262387221551843565098188788026906247168000000⟩, + ⟨4, 6, 8, 4, 6, 8, 21353200805406191389971973067508457178293862400000⟩, + ⟨4, 6, 3, 5, 0, 8, 17768356333494496647690017014406777797315500441600000⟩, + ⟨4, 6, 4, 5, 1, 8, 16273195626588891883960193015645179148575231180800000⟩, + ⟨4, 6, 5, 5, 2, 8, -7029298273026028433226970796760621858280597094400000⟩, + ⟨4, 6, 6, 5, 3, 8, -24554349731095046246475684266384025563273625600000⟩, + ⟨4, 6, 7, 5, 4, 8, 23038205380069590551863933889953052284157952000000⟩, + ⟨4, 6, 8, 5, 5, 8, 7137729733439393045582588236880593241820364800000⟩, + ⟨4, 6, 4, 6, 0, 8, 50772754525149479431273175024892363206261578137600000⟩, + ⟨4, 6, 5, 6, 1, 8, 8980417392716575309377252673497022522913193984000000⟩, + ⟨4, 6, 6, 6, 2, 8, -1759392147815090014658484339907055436156213657600000⟩, + ⟨4, 6, 7, 6, 3, 8, 69080483724370064343819754320767552626832179200000⟩, + ⟨4, 6, 8, 6, 4, 8, -10632741855761068263699595785575338062171340800000⟩, + ⟨4, 6, 5, 7, 0, 8, 39180935782435865853291529448767317270338941747200000⟩, + ⟨4, 6, 6, 7, 1, 8, 3487914156126760501008969406544212284979072204800000⟩, + ⟨4, 6, 7, 7, 2, 8, -122673935121084704384707583597476535232941260800000⟩, + ⟨4, 6, 8, 7, 3, 8, -50924969862227928805617878372722546998194995200000⟩ +] + +def collectedFourData_10_2_39 : List CollectedFourTerm := [ + ⟨5, 0, 5, 0, 7, 3, -369085275671963326255728201275713876474095206400000⟩, + ⟨5, 0, 6, 0, 8, 3, -22737484499835593683283523698955546754896258662400000⟩, + ⟨5, 0, 5, 1, 6, 3, 60896207433306688720210886016270916878838058188800000⟩, + ⟨5, 0, 6, 1, 7, 3, 76043850141225480056803974801691476847478439936000000⟩, + ⟨5, 0, 7, 1, 8, 3, 71478384501910265321096495665327727577356933529600000⟩, + ⟨5, 0, 5, 2, 5, 3, -10652076169669773569492804716704151665548407603200000⟩, + ⟨5, 0, 6, 2, 6, 3, -5249277929390705111073732271404162625684950220800000⟩, + ⟨5, 0, 7, 2, 7, 3, -4220165693305050707396542507548423213885161472000000⟩, + ⟨5, 0, 8, 2, 8, 3, -22740887992805200935837992498588450083771829452800000⟩, + ⟨5, 0, 5, 3, 4, 3, 14417140436499400374675637749994289814329465241600000⟩, + ⟨5, 0, 6, 3, 5, 3, 12787967729373278334365101173157951490115816652800000⟩, + ⟨5, 0, 7, 3, 6, 3, -3295194393983253458909048224320325233965373849600000⟩, + ⟨5, 0, 8, 3, 7, 3, -13930084697544800193908803153443996391843037184000000⟩, + ⟨5, 0, 5, 4, 3, 3, -1344779062814096602798194662321631454629042585600000⟩, + ⟨5, 0, 6, 4, 4, 3, -5909822511155396779885305902427690324002340864000000⟩, + ⟨5, 0, 7, 4, 5, 3, -11345057808200231738200838283311919649932705792000000⟩, + ⟨5, 0, 8, 4, 6, 3, 17768356333494496647690017014406777797315500441600000⟩, + ⟨5, 0, 5, 5, 2, 3, -104449945088996816281664427676957179164671711641600000⟩, + ⟨5, 0, 6, 5, 3, 3, -2189152073074425324552927910550266499249366630400000⟩, + ⟨5, 0, 7, 5, 4, 3, 7188928832164834560376158362075760789697855488000000⟩, + ⟨5, 0, 8, 5, 5, 3, 5939424560828377485979443240715821564248142643200000⟩, + ⟨5, 0, 5, 6, 1, 3, 133442068768796000201890350531238776308263550976000000⟩, + ⟨5, 0, 6, 6, 2, 3, -156859253448798292455295568034532256615380706918400000⟩, + ⟨5, 0, 7, 6, 3, 3, 21556135688226833768493053930650716589244861644800000⟩, + ⟨5, 0, 8, 6, 4, 3, -8847682734636764095825027320511841966633464627200000⟩, + ⟨5, 0, 5, 7, 0, 3, 582198454533525950489730126791099409316981820620800000⟩, + ⟨5, 0, 6, 7, 1, 3, 310966268266555723599484108844519554176938881843200000⟩, + ⟨5, 0, 7, 7, 2, 3, -38279639173197623669049149411113914769211601715200000⟩, + ⟨5, 0, 8, 7, 3, 3, -42375521076701709561637230405631628368975547596800000⟩ +] + +def collectedFourData_10_2_40 : List CollectedFourTerm := [ + ⟨5, 1, 4, 0, 6, 4, -104593829688984557734121377876683942513433431244800000⟩, + ⟨5, 1, 5, 0, 7, 4, -1352110860717326106768608889393263222469741772800000⟩, + ⟨5, 1, 6, 0, 8, 4, -41648369312006841935982796921250035600418301542400000⟩, + ⟨5, 1, 4, 1, 5, 4, 162080782089392464418257344545542629249761138442240000⟩, + ⟨5, 1, 5, 1, 6, 4, 223087803481627156352270466424108990951144921497600000⟩, + ⟨5, 1, 6, 1, 7, 4, 139289918135471959495836349328113928022981083136000000⟩, + ⟨5, 1, 7, 1, 8, 4, 87284887226134161273898219308725530662520907366400000⟩, + ⟨5, 1, 4, 2, 4, 4, -43213870561805416911088539360564349108164608655360000⟩, + ⟨5, 1, 5, 2, 5, 4, -39022927294990946901001448890573894587521590886400000⟩, + ⟨5, 1, 6, 2, 6, 4, -9615129845441409708812479529704121052242431180800000⟩, + ⟨5, 1, 7, 2, 7, 4, -5153399719126098551480260400990778340040245248000000⟩, + ⟨5, 1, 8, 2, 8, 4, -20827301753942510199116442400175012571540514406400000⟩, + ⟨5, 1, 4, 3, 3, 4, 55118567757907909416370028630090146767787209523200000⟩, + ⟨5, 1, 5, 3, 4, 4, 52815903124792558866515277260976661854036374323200000⟩, + ⟨5, 1, 6, 3, 5, 4, 23423787391556655242093999770242363557153656012800000⟩, + ⟨5, 1, 7, 3, 6, 4, -4023883207088026647055054207621909884296390246400000⟩, + ⟨5, 1, 8, 3, 7, 4, -12757904508633660136579060891601931088787668992000000⟩, + ⟨5, 1, 4, 4, 2, 4, -183760179367961830155722005432200762121547038064640000⟩, + ⟨5, 1, 5, 4, 3, 4, -4926477689433139732840311615290600580522914611200000⟩, + ⟨5, 1, 6, 4, 4, 4, -10825052811571629508922222164456725113852657664000000⟩, + ⟨5, 1, 7, 4, 5, 4, -13853867826801058569410318358046063530111664128000000⟩, + ⟨5, 1, 8, 4, 6, 4, 16273195626588891883960193015645179148575231180800000⟩, + ⟨5, 1, 4, 5, 1, 4, 177167748636398238665080783067966474799670603284480000⟩, + ⟨5, 1, 5, 5, 2, 4, -382643021721846954251949551717341176230768227123200000⟩, + ⟨5, 1, 6, 5, 3, 4, -4009881305040947033226935220175988954948331110400000⟩, + ⟨5, 1, 7, 5, 4, 4, 8778665701033609135937919559920892280561467392000000⟩, + ⟨5, 1, 8, 5, 5, 4, 5439637520412008040872884650771011445741689241600000⟩, + ⟨5, 1, 4, 6, 0, 4, 552767558241096625370707186652223351751602402754560000⟩, + ⟨5, 1, 5, 6, 1, 4, 488853070961408701696516664144925706017520484352000000⟩, + ⟨5, 1, 6, 6, 2, 4, -287319915168648994426613334145665641328901776998400000⟩, + ⟨5, 1, 7, 6, 3, 4, 26322991008950981301798815417105948407405687603200000⟩, + ⟨5, 1, 8, 6, 4, 4, -8103173376331119792328922816741958806419380633600000⟩, + ⟨5, 1, 5, 7, 0, 4, 2132831910008975562387939671228271000407183563161600000⟩, + ⟨5, 1, 6, 7, 1, 4, 569598540438180487557430519671925590295045157683200000⟩, + ⟨5, 1, 7, 7, 2, 4, -46744676891800308857116333774229142516087442636800000⟩, + ⟨5, 1, 8, 7, 3, 4, -38809731824203414837098986178620131725906699878400000⟩ +] + +def collectedFourData_10_2_41 : List CollectedFourTerm := [ + ⟨5, 2, 3, 0, 5, 5, 215231387446322466677461574296143940659204587520000000⟩, + ⟨5, 2, 4, 0, 6, 5, 225899461689219301099118220870543508151029727232000000⟩, + ⟨5, 2, 5, 0, 7, 5, 1460129705970403396874579179994955932422373376000000⟩, + ⟨5, 2, 6, 0, 8, 5, 29983745171814850222644504665010286365845225472000000⟩, + ⟨5, 2, 3, 1, 4, 5, -205892296168732025231884312642733794948394306764800000⟩, + ⟨5, 2, 4, 1, 5, 5, -350058521932269053542642013544371450381432625561600000⟩, + ⟨5, 2, 5, 1, 6, 5, -240910075029203085331669775871746459515949678592000000⟩, + ⟨5, 2, 6, 1, 7, 5, -100278437772422358880285206821395210537355182080000000⟩, + ⟨5, 2, 7, 1, 8, 5, -47128996750141246828664664201939237899436294144000000⟩, + ⟨5, 2, 3, 2, 3, 5, 142823065901374899263187089054269876579855446835200000⟩, + ⟨5, 2, 4, 2, 4, 5, 93332370814294238197618150478009488075435435622400000⟩, + ⟨5, 2, 5, 2, 5, 5, 42140431685543246565403368064119342667753586688000000⟩, + ⟨5, 2, 6, 2, 6, 5, 6922182256881620265620103731797238398083661824000000⟩, + ⟨5, 2, 7, 2, 7, 5, 2782549950321217848645952621318111724914606080000000⟩, + ⟨5, 2, 8, 2, 8, 5, 8996469999510968316674446657041518634934154035200000⟩, + ⟨5, 2, 3, 3, 2, 5, -94179350991126437843137405173425238645343990579200000⟩, + ⟨5, 2, 4, 3, 3, 5, -119043874983989394017543106741113261113252773888000000⟩, + ⟨5, 2, 5, 3, 4, 5, -57035315180629307554275637025554516471336402944000000⟩, + ⟨5, 2, 6, 3, 5, 5, -16863394262707143176017493149766003237830262784000000⟩, + ⟨5, 2, 7, 3, 6, 5, 2172673696633001328682770613004859756137938944000000⟩, + ⟨5, 2, 8, 3, 7, 5, 5510848525869265248069892136651500015589523456000000⟩, + ⟨5, 2, 3, 4, 1, 5, 86959022698791585102235495264099589703776757350400000⟩, + ⟨5, 2, 4, 4, 2, 5, 396881209174318841684579885359835411236790049177600000⟩, + ⟨5, 2, 5, 4, 3, 5, 5320049286731971354124091784582756245285371904000000⟩, + ⟨5, 2, 6, 4, 4, 5, 7793237294407813646111580081746284094863441920000000⟩, + ⟨5, 2, 7, 4, 5, 5, 7480320047783731071836907343408346447090810880000000⟩, + ⟨5, 2, 8, 4, 6, 5, -7029298273026028433226970796760621858280597094400000⟩, + ⟨5, 2, 3, 5, 0, 5, -104449945088996816281664427676957179164671711641600000⟩, + ⟨5, 2, 4, 5, 1, 5, -382643021721846954251949551717341176230768227123200000⟩, + ⟨5, 2, 5, 5, 2, 5, 413212007262436537930532946668873185581223378944000000⟩, + ⟨5, 2, 6, 5, 3, 5, 2886817928425124670473323355258605342411456512000000⟩, + ⟨5, 2, 7, 5, 4, 5, -4739992459665041165575557866488999627267768320000000⟩, + ⟨5, 2, 8, 5, 5, 5, -2349681986594217260493470874840875490417102028800000⟩, + ⟨5, 2, 4, 6, 0, 5, -1193855261034377724703353708864981816684755445350400000⟩, + ⟨5, 2, 5, 6, 1, 5, -527907075893857480842619114824491181216198819840000000⟩, + ⟨5, 2, 6, 6, 2, 5, 206849085846936805655717253343306849303922737152000000⟩, + ⟨5, 2, 7, 6, 3, 5, -14212954809700486208652968902812023964693430272000000⟩, + ⟨5, 2, 8, 6, 4, 5, 3500211263189640115402849376197272463238548684800000⟩, + ⟨5, 2, 5, 7, 0, 5, -2303221814218353536986704159585419885490022121472000000⟩, + ⟨5, 2, 6, 7, 1, 5, -410068815871080178408830901906011472677197316096000000⟩, + ⟨5, 2, 7, 7, 2, 5, 25239532241274929310703403533462242740171440128000000⟩, + ⟨5, 2, 8, 7, 3, 5, 16764081692887536137180231484843275345556878131200000⟩ +] + +def collectedFourData_10_2_42 : List CollectedFourTerm := [ + ⟨5, 3, 2, 0, 4, 6, -656284757606650889695694936200884003391773081600000⟩, + ⟨5, 3, 3, 0, 5, 6, 4511005128986296501238641888598442623505530880000000⟩, + ⟨5, 3, 4, 0, 6, 6, 2367297916920814079475870009338314229079343104000000⟩, + ⟨5, 3, 5, 0, 7, 6, 10200886080119112068537707589223474001870848000000⟩, + ⟨5, 3, 6, 0, 8, 6, 157106300643542531790108085296735553629192192000000⟩, + ⟨5, 3, 2, 1, 3, 6, 391831849623142093217844659579507710676592230400000⟩, + ⟨5, 3, 3, 1, 4, 6, -4315268395821444646564240933186537302850220851200000⟩, + ⟨5, 3, 4, 1, 5, 6, -3668414274092923652908498491053993113645429555200000⟩, + ⟨5, 3, 5, 1, 6, 6, -1683067073340991058656210891341024014962262016000000⟩, + ⟨5, 3, 6, 1, 7, 6, -525430505844489902942273301016807983682682880000000⟩, + ⟨5, 3, 7, 1, 8, 6, -197554035762452844344718751023291549799887667200000⟩, + ⟨5, 3, 2, 2, 2, 6, 95664012223400410974573839691958730433862041600000⟩, + ⟨5, 3, 3, 2, 3, 6, 2993409049037184769340874906590283286801337548800000⟩, + ⟨5, 3, 4, 2, 4, 6, 978070179352286673997959289835832841320844492800000⟩, + ⟨5, 3, 5, 2, 5, 6, 294405175946733233756106589238897960156135424000000⟩, + ⟨5, 3, 6, 2, 6, 6, 36270267123978978596602881877572043684184064000000⟩, + ⟨5, 3, 7, 2, 7, 6, 11663816552490516980281994443146480272277504000000⟩, + ⟨5, 3, 8, 2, 8, 6, 31425963465084394083646131221240496064875724800000⟩, + ⟨5, 3, 2, 3, 1, 6, 548256614888674841342269835231143467637800960000000⟩, + ⟨5, 3, 3, 3, 2, 6, -1973892100061500867081418064603238468026158284800000⟩, + ⟨5, 3, 4, 3, 3, 6, -1247512124041634910053208660259818858438721536000000⟩, + ⟨5, 3, 5, 3, 4, 6, -398465116025165641921153852283961756207808512000000⟩, + ⟨5, 3, 6, 3, 5, 6, -88359391854686698045048916145285317340954624000000⟩, + ⟨5, 3, 7, 3, 6, 6, 9107354002045252143036838364605440503001907200000⟩, + ⟨5, 3, 8, 3, 7, 6, 19250186400332093712686980542581455762489344000000⟩, + ⟨5, 3, 2, 4, 0, 6, -2099586023753100791432332574423535425076540211200000⟩, + ⟨5, 3, 3, 4, 1, 6, 1822562229701349969021486940625465121017797017600000⟩, + ⟨5, 3, 4, 4, 2, 6, 4159089414015264873917598716324206500241421107200000⟩, + ⟨5, 3, 5, 4, 3, 6, 37167394439457973725341774325765887955566592000000⟩, + ⟨5, 3, 6, 4, 4, 6, 40834347889023021834748987112355347426181120000000⟩, + ⟨5, 3, 7, 4, 5, 6, 31355800380580587476091030212215690959519744000000⟩, + ⟨5, 3, 8, 4, 6, 6, -24554349731095046246475684266384025563273625600000⟩, + ⟨5, 3, 3, 5, 0, 6, -2189152073074425324552927910550266499249366630400000⟩, + ⟨5, 3, 4, 5, 1, 6, -4009881305040947033226935220175988954948331110400000⟩, + ⟨5, 3, 5, 5, 2, 6, 2886817928425124670473323355258605342411456512000000⟩, + ⟨5, 3, 6, 5, 3, 6, 15126105253611140766152077425188409685573632000000⟩, + ⟨5, 3, 7, 5, 4, 6, -19868970367751737356713574404713883910537216000000⟩, + ⟨5, 3, 8, 5, 5, 6, -8207777080264887640216826943162968043631411200000⟩, + ⟨5, 3, 4, 6, 0, 6, -12510924335179651441786292450048015861336034508800000⟩, + ⟨5, 3, 5, 6, 1, 6, -3688110665828197310366822054976069566799544320000000⟩, + ⟨5, 3, 6, 6, 2, 6, 1083830404864123330701966452611547700419100672000000⟩, + ⟨5, 3, 7, 6, 3, 6, -59577474089924922577633256185512497904195993600000⟩, + ⟨5, 3, 8, 6, 4, 6, 12226741297759431269564889414386939818357555200000⟩, + ⟨5, 3, 5, 7, 0, 6, -16090970033701189724681656972138441782388064256000000⟩, + ⟨5, 3, 6, 7, 1, 6, -2148644017003695096917573158363367774990893056000000⟩, + ⟨5, 3, 7, 7, 2, 6, 105798378893042430220266153578294709737383526400000⟩, + ⟨5, 3, 8, 7, 3, 6, 58559348148219382370296811987306597023796428800000⟩ +] + +def collectedFourData_10_2_43 : List CollectedFourTerm := [ + ⟨5, 4, 1, 0, 3, 7, 2303959319293077366780963179399335596729040896000000⟩, + ⟨5, 4, 2, 0, 4, 7, 4310330446292721697270272530563150447644770304000000⟩, + ⟨5, 4, 3, 0, 5, 7, -14813632745152157354524917179688703107897753600000000⟩, + ⟨5, 4, 4, 0, 6, 7, -5182626478563272024673440796541203953662033920000000⟩, + ⟨5, 4, 5, 0, 7, 7, -16749280453597812720030148336973329496801280000000⟩, + ⟨5, 4, 6, 0, 8, 7, -206367758238917400407131699492576795343978496000000⟩, + ⟨5, 4, 1, 1, 2, 7, 676138278678898527149512879584558819500359680000000⟩, + ⟨5, 4, 2, 1, 3, 7, -2573463320124966519516823648802242618485374976000000⟩, + ⟨5, 4, 3, 1, 4, 7, 14170855360305435758151073455829415287968497664000000⟩, + ⟨5, 4, 4, 1, 5, 7, 8031106188773536283177664556598627517591453696000000⟩, + ⟨5, 4, 5, 1, 6, 7, 2763501348039284395727092170177971503245557760000000⟩, + ⟨5, 4, 6, 1, 7, 7, 690181839667196032112159138598430472342077440000000⟩, + ⟨5, 4, 7, 1, 8, 7, 216248400628270258467202242676862193110089728000000⟩, + ⟨5, 4, 1, 2, 1, 7, 2476851524617809118545792656379218147527360512000000⟩, + ⟨5, 4, 2, 2, 2, 7, -628299681992893392801785039132456141092552704000000⟩, + ⟨5, 4, 3, 2, 3, 7, -9830018153496700638583173840500987389947150336000000⟩, + ⟨5, 4, 4, 2, 4, 7, -2141248202506590591779318876692968838313017344000000⟩, + ⟨5, 4, 5, 2, 5, 7, -483396718696133649724286503716073151020400640000000⟩, + ⟨5, 4, 6, 2, 6, 7, -47642988769017908072322779457692860082552832000000⟩, + ⟨5, 4, 7, 2, 7, 7, -12767553266947759627380104897678374034472960000000⟩, + ⟨5, 4, 8, 2, 8, 7, -29485521241815825138980703169383695715926016000000⟩, + ⟨5, 4, 1, 3, 0, 7, 2173782167088795087431739448183405479142096896000000⟩, + ⟨5, 4, 2, 3, 1, 7, -3600825940486675688014026164805932398569062400000000⟩, + ⟨5, 4, 3, 3, 2, 7, 6482039326663118625860064039568299554563424256000000⟩, + ⟨5, 4, 4, 3, 3, 7, 2731126200962712578374353521431412376632033280000000⟩, + ⟨5, 4, 5, 3, 4, 7, 654257279893371921589125231454981345058488320000000⟩, + ⟨5, 4, 6, 3, 5, 7, 116064916185493782600934512947310844666970112000000⟩, + ⟨5, 4, 7, 3, 6, 7, -9969174911040092851826789701496644281827328000000⟩, + ⟨5, 4, 8, 3, 7, 7, -18061555396592254524788064406095639588372480000000⟩, + ⟨5, 4, 2, 4, 0, 7, 13789608028985786627551222770303483863239753728000000⟩, + ⟨5, 4, 3, 4, 1, 7, -5985089077486496109876132344395178044997763072000000⟩, + ⟨5, 4, 4, 4, 2, 7, -9105320783547467614610176747633383356976070656000000⟩, + ⟨5, 4, 5, 4, 3, 7, -61026768489184465803604170753717832903557120000000⟩, + ⟨5, 4, 6, 4, 4, 7, -53638159631328043634667748121471932233154560000000⟩, + ⟨5, 4, 7, 4, 5, 7, -34322972226561771425277547976408305300930560000000⟩, + ⟨5, 4, 8, 4, 6, 7, 23038205380069590551863933889953052284157952000000⟩, + ⟨5, 4, 3, 5, 0, 7, 7188928832164834560376158362075760789697855488000000⟩, + ⟨5, 4, 4, 5, 1, 7, 8778665701033609135937919559920892280561467392000000⟩, + ⟨5, 4, 5, 5, 2, 7, -4739992459665041165575557866488999627267768320000000⟩, + ⟨5, 4, 6, 5, 3, 7, -19868970367751737356713574404713883910537216000000⟩, + ⟨5, 4, 7, 5, 4, 7, 21749153580052687558787709858085750010019840000000⟩, + ⟨5, 4, 8, 5, 5, 7, 7700975841747020897581130527738079534383104000000⟩, + ⟨5, 4, 4, 6, 0, 7, 27389644229967248486791855064106318765987201024000000⟩, + ⟨5, 4, 5, 6, 1, 7, 6055670007554925694718033793699214529868595200000000⟩, + ⟨5, 4, 6, 6, 2, 7, -1423670788802197399744099524557809047343988736000000⟩, + ⟨5, 4, 7, 6, 3, 7, 65215238128114831303941416998856928226443264000000⟩, + ⟨5, 4, 8, 6, 4, 7, -11471783216887423715236109887253385087811584000000⟩, + ⟨5, 4, 5, 7, 0, 7, 26420466589678107495834076839351496655146844160000000⟩, + ⟨5, 4, 6, 7, 1, 7, 2822361975466323797897366675133843512626249728000000⟩, + ⟨5, 4, 7, 7, 2, 7, -115809986550689880217783665929442747048001536000000⟩, + ⟨5, 4, 8, 7, 3, 7, -54943515276774153021973147363659267698589696000000⟩ +] + +def collectedFourData_10_2_44 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 2, 8, 2705879587310989387891446164834364596249060966400000⟩, + ⟨5, 5, 1, 0, 3, 8, 5710527766083595081418582309107653368121340723200000⟩, + ⟨5, 5, 2, 0, 4, 8, 5341730969039518997612674867237833876049389158400000⟩, + ⟨5, 5, 3, 0, 5, 8, -12238882344750249627914161704642378988561367040000000⟩, + ⟨5, 5, 4, 0, 6, 8, -3211377492567489483752142382191709051385020416000000⟩, + ⟨5, 5, 5, 0, 7, 8, -8302857632185878308021464172569479133475635200000⟩, + ⟨5, 5, 6, 0, 8, 8, -85249538593513692201896567340735172304909107200000⟩, + ⟨5, 5, 0, 1, 1, 8, -19936145269279077423212471366267363633883040972800000⟩, + ⟨5, 5, 1, 1, 2, 8, 1675857026543558474870545192914215053301907456000000⟩, + ⟨5, 5, 2, 1, 3, 8, -3189256342659820000385678157413066238601042329600000⟩, + ⟨5, 5, 3, 1, 4, 8, 11707825788782925798778885031416733675856435609600000⟩, + ⟨5, 5, 4, 1, 5, 8, 4976417606347846276202294119350585689123900620800000⟩, + ⟨5, 5, 5, 1, 6, 8, 1369907102737375588942484741241419978252904038400000⟩, + ⟨5, 5, 6, 1, 7, 8, 285110832619177693868646190066524438405316608000000⟩, + ⟨5, 5, 7, 1, 8, 8, 76569587084165796386441116210062139134364876800000⟩, + ⟨5, 5, 0, 2, 0, 8, -3205563242576462863173251561582486869337387827200000⟩, + ⟨5, 5, 1, 2, 1, 8, 6139053448277168341468114068556639828013639270400000⟩, + ⟨5, 5, 2, 2, 2, 8, -778642823550979877471867082045143890440644198400000⟩, + ⟨5, 5, 3, 2, 3, 8, -8121467414316506182105756461726930078437631590400000⟩, + ⟨5, 5, 4, 2, 4, 8, -1326809159790447156229401873487520825114571571200000⟩, + ⟨5, 5, 5, 2, 5, 8, -239626660161253164800471990420226904579217817600000⟩, + ⟨5, 5, 6, 2, 6, 8, -19681091874209227203821758134913234236761702400000⟩, + ⟨5, 5, 7, 2, 7, 8, -4520756125293992346565756978910962517016576000000⟩, + ⟨5, 5, 8, 2, 8, 8, -9135246352814305197775680220082954723288678400000⟩, + ⟨5, 5, 1, 3, 0, 8, 5387874394582081243508580937756387588946735923200000⟩, + ⟨5, 5, 2, 3, 1, 8, -4462452166970650610291191095720059627152343040000000⟩, + ⟨5, 5, 3, 3, 2, 8, 5355399181138480101232137623015967659601061478400000⟩, + ⟨5, 5, 4, 3, 3, 8, 1692322849700026401430217747426755984326918144000000⟩, + ⟨5, 5, 5, 3, 4, 8, 324324681578126896596120163980733390382746828800000⟩, + ⟨5, 5, 6, 3, 5, 8, 47945864393473145779859290346994523248682598400000⟩, + ⟨5, 5, 7, 3, 6, 8, -3529901743968662495363792865032913422175436800000⟩, + ⟨5, 5, 8, 3, 7, 8, -5595856919391255338378218998593783334961152000000⟩, + ⟨5, 5, 2, 4, 0, 8, 17089264309817368262656773178812068713210891468800000⟩, + ⟨5, 5, 3, 4, 1, 8, -4944823616352900526220548332708078457906318540800000⟩, + ⟨5, 5, 4, 4, 2, 8, -5642047009916370044724016182614306810881690828800000⟩, + ⟨5, 5, 5, 4, 3, 8, -30251841081879158885023605542694555600342220800000⟩, + ⟨5, 5, 6, 4, 4, 8, -22157668419705832507441289310430664476065792000000⟩, + ⟨5, 5, 7, 4, 5, 8, -12153134096038041715526154141877160311259136000000⟩, + ⟨5, 5, 8, 4, 6, 8, 7137729733439393045582588236880593241820364800000⟩, + ⟨5, 5, 3, 5, 0, 8, 5939424560828377485979443240715821564248142643200000⟩, + ⟨5, 5, 4, 5, 1, 8, 5439637520412008040872884650771011445741689241600000⟩, + ⟨5, 5, 5, 5, 2, 8, -2349681986594217260493470874840875490417102028800000⟩, + ⟨5, 5, 6, 5, 3, 8, -8207777080264887640216826943162968043631411200000⟩, + ⟨5, 5, 7, 5, 4, 8, 7700975841747020897581130527738079534383104000000⟩, + ⟨5, 5, 8, 5, 5, 8, 2385927347001111375330368015197313632410009600000⟩, + ⟨5, 5, 4, 6, 0, 8, 16971797480171035784005007710492955217017123635200000⟩, + ⟨5, 5, 5, 6, 1, 8, 3001882145296953362085617056193377840417210368000000⟩, + ⟨5, 5, 6, 6, 2, 8, -588111626012532961756743298945409033788666675200000⟩, + ⟨5, 5, 7, 6, 3, 8, 23091518090111113590794032793603010669733478400000⟩, + ⟨5, 5, 8, 6, 4, 8, -3554204279886536661071602674948180375345561600000⟩, + ⟨5, 5, 5, 7, 0, 8, 13097002780373190041989683270142368121025357414400000⟩, + ⟨5, 5, 6, 7, 1, 8, 1165904297287694966802578737163753078778337689600000⟩, + ⟨5, 5, 7, 7, 2, 8, -41006189292712220276356662940360180950997401600000⟩, + ⟨5, 5, 8, 7, 3, 8, -17022678467394050867453311090856154922116710400000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1009.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1009.lean new file mode 100644 index 0000000000000000000000000000000000000000..ffde494b237be601617a47dc30961b30577351b6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1009.lean @@ -0,0 +1,623 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1006 +import OAI.Analysis.LaughlinFock.Sparse1007 +import OAI.Analysis.LaughlinFock.Sparse1008 + +namespace OAI + +/-! Sparse1009. -/ +namespace LaughlinFock +def collectedFourData_10_2_45 : List CollectedFourTerm := [ + ⟨6, 0, 4, 0, 6, 4, -326335217833134928190318362464016013112194472345600000⟩, + ⟨6, 0, 5, 0, 7, 4, -4218617805455555629578227747977761955608369561600000⟩, + ⟨6, 0, 6, 0, 8, 4, -129943895469198926588407086724608849819103710412800000⟩, + ⟨6, 0, 4, 1, 5, 4, 505695866448202418599527182874998328177512970977280000⟩, + ⟨6, 0, 5, 1, 6, 4, 696039213417955327868690350268388120480424604467200000⟩, + ⟨6, 0, 6, 1, 7, 4, 434587832875632341679286990215004212774611976192000000⟩, + ⟨6, 0, 7, 1, 8, 4, 272330908727409885097427855092506939428417883340800000⟩, + ⟨6, 0, 4, 2, 4, 4, -134828296326211113969557327566346022229246916689920000⟩, + ⟨6, 0, 5, 2, 5, 4, -121752454395869726259662954988323269623856024780800000⟩, + ⟨6, 0, 6, 2, 6, 4, -29999432107384212396055704701145000924379978137600000⟩, + ⟨6, 0, 7, 2, 7, 4, -16078728782787327603765330377467919125557805056000000⟩, + ⟨6, 0, 8, 2, 8, 4, -64981673153756450429386670955626653478143446220800000⟩, + ⟨6, 0, 4, 3, 3, 4, 171971232618721334195957518219582616044537538150400000⟩, + ⟨6, 0, 5, 3, 4, 4, 164786864603143330816210467745522746658988123750400000⟩, + ⟨6, 0, 6, 3, 5, 4, 73082769639763171538503191303678851362714130841600000⟩, + ⟨6, 0, 7, 3, 6, 4, -12554610600117067412325393375583261009736682700800000⟩, + ⟨6, 0, 8, 3, 7, 4, -39804963249737178190417870975494147261515956224000000⟩, + ⟨6, 0, 4, 4, 2, 4, -573336097754677790685317843829627782169849055150080000⟩, + ⟨6, 0, 5, 4, 3, 4, -15370726693073351058269916762997952827156227686400000⟩, + ⟨6, 0, 6, 4, 4, 4, -33774420325020928082688378411244854661934481408000000⟩, + ⟨6, 0, 7, 4, 5, 4, -43224394675422415144083347217627224976094396416000000⟩, + ⟨6, 0, 8, 4, 6, 4, 50772754525149479431273175024892363206261578137600000⟩, + ⟨6, 0, 4, 5, 1, 4, 552767558241096625370707186652223351751602402754560000⟩, + ⟨6, 0, 5, 5, 2, 4, -1193855261034377724703353708864981816684755445350400000⟩, + ⟨6, 0, 6, 5, 3, 4, -12510924335179651441786292450048015861336034508800000⟩, + ⟨6, 0, 7, 5, 4, 4, 27389644229967248486791855064106318765987201024000000⟩, + ⟨6, 0, 8, 5, 5, 4, 16971797480171035784005007710492955217017123635200000⟩, + ⟨6, 0, 4, 6, 0, 4, 1724647831197026377866482490707069904957806550712320000⟩, + ⟨6, 0, 5, 6, 1, 4, 1525233122020288667778756863876494698355196166144000000⟩, + ⟨6, 0, 6, 6, 2, 4, -896444918243907224731608026397337659173749181644800000⟩, + ⟨6, 0, 7, 6, 3, 4, 82128353369112277417750627982654326891065271910400000⟩, + ⟨6, 0, 8, 6, 4, 4, -25282092230180274559811345672306178832486052659200000⟩, + ⟨6, 0, 5, 7, 0, 4, 6654485910152521909610319994051665535774527533875200000⟩, + ⟨6, 0, 6, 7, 1, 4, 1777160892990091525364647665461730092091693229670400000⟩, + ⟨6, 0, 7, 7, 2, 4, -145844495429463215804624236647021900628806441369600000⟩, + ⟨6, 0, 8, 7, 3, 4, -121087279493991033257359627927270695396803661004800000⟩ +] + +def collectedFourData_10_2_46 : List CollectedFourTerm := [ + ⟨6, 1, 3, 0, 5, 5, -274973065618596652508273941146704637347443507200000000⟩, + ⟨6, 1, 4, 0, 6, 5, -288602272369622751127947246288081713437889003520000000⟩, + ⟨6, 1, 5, 0, 7, 5, -1865417243345109067357990031284186176144015360000000⟩, + ⟨6, 1, 6, 0, 8, 5, -38306319661099216401486708513809988117772369920000000⟩, + ⟨6, 1, 3, 1, 4, 5, 263041727029184897099245994961599285562156515328000000⟩, + ⟨6, 1, 4, 1, 5, 5, 447224106407977604014293236118454210661424562176000000⟩, + ⟨6, 1, 5, 1, 6, 5, 307779374816820992232872525313284123906927493120000000⟩, + ⟨6, 1, 6, 1, 7, 5, 128112678066545600680933938961819560930233548800000000⟩, + ⟨6, 1, 7, 1, 8, 5, 60210570910096337020110081408335766894768291840000000⟩, + ⟨6, 1, 3, 2, 3, 5, -182466399245520175154606214112712461090314780672000000⟩, + ⟨6, 1, 4, 2, 4, 5, -119238594466890003546771792725151544419563864064000000⟩, + ⟨6, 1, 5, 2, 5, 5, -53837332112885848782424160676634624683336007680000000⟩, + ⟨6, 1, 6, 2, 6, 5, -8843569232763953728378375425579739479948656640000000⟩, + ⟨6, 1, 7, 2, 7, 5, -3554901072537653978837638252050343242026188800000000⟩, + ⟨6, 1, 8, 2, 8, 5, -11493616079245015531633827699164610203769372672000000⟩, + ⟨6, 1, 3, 3, 2, 5, 120320670545593042173615712816448229488052928512000000⟩, + ⟨6, 1, 4, 3, 3, 5, 152086829136982532374026404130015757356163399680000000⟩, + ⟨6, 1, 5, 3, 4, 5, 72866581634854826814341107886804019007287459840000000⟩, + ⟨6, 1, 6, 3, 5, 5, 21544158926671765780600764209506728850741002240000000⟩, + ⟨6, 1, 7, 3, 6, 5, -2775741744921196501763452347712404761440419840000000⟩, + ⟨6, 1, 8, 3, 7, 5, -7040492240918682745617820139997388731486044160000000⟩, + ⟨6, 1, 3, 4, 1, 5, -111096199018125198971903169833411169958068486144000000⟩, + ⟨6, 1, 4, 4, 2, 5, -507043345619350220024867097272538377499690663936000000⟩, + ⟨6, 1, 5, 4, 3, 5, -6796732943886033052530347408079169663732285440000000⟩, + ⟨6, 1, 6, 4, 4, 5, -9956402620277349251237736389722645778871091200000000⟩, + ⟨6, 1, 7, 4, 5, 5, -9556629076046430295343885538556309255539916800000000⟩, + ⟨6, 1, 8, 4, 6, 5, 8980417392716575309377252673497022522913193984000000⟩, + ⟨6, 1, 3, 5, 0, 5, 133442068768796000201890350531238776308263550976000000⟩, + ⟨6, 1, 4, 5, 1, 5, 488853070961408701696516664144925706017520484352000000⟩, + ⟨6, 1, 5, 5, 2, 5, -527907075893857480842619114824491181216198819840000000⟩, + ⟨6, 1, 6, 5, 3, 5, -3688110665828197310366822054976069566799544320000000⟩, + ⟨6, 1, 7, 5, 4, 5, 6055670007554925694718033793699214529868595200000000⟩, + ⟨6, 1, 8, 5, 5, 5, 3001882145296953362085617056193377840417210368000000⟩, + ⟨6, 1, 4, 6, 0, 5, 1525233122020288667778756863876494698355196166144000000⟩, + ⟨6, 1, 5, 6, 1, 5, 674438002479937200218757118435996292153239142400000000⟩, + ⟨6, 1, 6, 6, 2, 5, -264264092382536589913437143090086122200204574720000000⟩, + ⟨6, 1, 7, 6, 3, 5, 18158038202009915458896262457938000933206097920000000⟩, + ⟨6, 1, 8, 6, 4, 5, -4471763309113217575180910952109522214115606528000000⟩, + ⟨6, 1, 5, 7, 0, 5, 2942526044038042989243942194243380364303054929920000000⟩, + ⟨6, 1, 6, 7, 1, 5, 523891430299774274423675598949482216074835394560000000⟩, + ⟨6, 1, 7, 7, 2, 5, -32245257708491159871796809633894037045987246080000000⟩, + ⟨6, 1, 8, 7, 3, 5, -21417280212085730766366737760495431668551647232000000⟩ +] + +def collectedFourData_10_2_47 : List CollectedFourTerm := [ + ⟨6, 2, 2, 0, 4, 6, -47024753736468710097188565875612986307314817433600000⟩, + ⟨6, 2, 3, 0, 5, 6, 323226926781177639383210877090443432483597844480000000⟩, + ⟨6, 2, 4, 0, 6, 6, 169623932711809328589063576900049124436668841984000000⟩, + ⟨6, 2, 5, 0, 7, 6, 730923810512876636762400409455850344476049408000000⟩, + ⟨6, 2, 6, 0, 8, 6, 11257133450961825648597525858412083426657042432000000⟩, + ⟨6, 2, 2, 1, 3, 6, 28075916774036878925151360066678973067939964518400000⟩, + ⟨6, 2, 3, 1, 4, 6, -309201808008306772052428530988323766235378692915200000⟩, + ⟨6, 2, 4, 1, 5, 6, -262852787365753925402813763855125028768956232499200000⟩, + ⟨6, 2, 5, 1, 6, 6, -120596758843599189021115974011112599530594369536000000⟩, + ⟨6, 2, 6, 1, 7, 6, -37648657623973627256479069565832094412156436480000000⟩, + ⟨6, 2, 7, 1, 8, 6, -14155333906052508947543575353885254970728723251200000⟩, + ⟨6, 2, 2, 2, 2, 6, 6854610844008344176782067722963286032356317593600000⟩, + ⟨6, 2, 3, 2, 3, 6, 214486656488613344016173413308414045099209313484800000⟩, + ⟨6, 2, 4, 2, 4, 6, 70081635735004550063136512400578333503545724108800000⟩, + ⟨6, 2, 5, 2, 5, 6, 21095005997281706625576368607417111190337224704000000⟩, + ⟨6, 2, 6, 2, 6, 6, 2598872455427820338792172112432595624886534144000000⟩, + ⟨6, 2, 7, 2, 7, 6, 835747127525022325925083738886242567804944384000000⟩, + ⟨6, 2, 8, 2, 8, 6, 2251763698224705349537339487520806266754354380800000⟩, + ⟨6, 2, 2, 3, 1, 6, 39284216189251054292794859168648790624341852160000000⟩, + ⟨6, 2, 3, 3, 2, 6, -141435236506569235808233868424446222441152040140800000⟩, + ⟨6, 2, 4, 3, 3, 6, -89387952007682554741156992344180521926138003456000000⟩, + ⟨6, 2, 5, 3, 4, 6, -28551210029606445890468285611886292239124529152000000⟩, + ⟨6, 2, 6, 3, 5, 6, -6331213081077159870191331749434335891139067904000000⟩, + ⟨6, 2, 7, 3, 6, 6, 652568986515618821352946288198366845469930291200000⟩, + ⟨6, 2, 8, 3, 7, 6, 1379333078156441370989620877334879655925121024000000⟩, + ⟨6, 2, 2, 4, 0, 6, -150441579773359858997923650164743415877216711475200000⟩, + ⟨6, 2, 3, 4, 1, 6, 130592001456269609152623872697350039696016251289600000⟩, + ⟨6, 2, 4, 4, 2, 6, 298011119708564363218684935438960419465017373491200000⟩, + ⟨6, 2, 5, 4, 3, 6, 2663154294357781018440842827712631040043384832000000⟩, + ⟨6, 2, 6, 4, 4, 6, 2925902409303705999093389108506954063958507520000000⟩, + ⟨6, 2, 7, 4, 5, 6, 2246736304655159627421490127851754386750439424000000⟩, + ⟨6, 2, 8, 4, 6, 6, -1759392147815090014658484339907055436156213657600000⟩, + ⟨6, 2, 3, 5, 0, 6, -156859253448798292455295568034532256615380706918400000⟩, + ⟨6, 2, 4, 5, 1, 6, -287319915168648994426613334145665641328901776998400000⟩, + ⟨6, 2, 5, 5, 2, 6, 206849085846936805655717253343306849303922737152000000⟩, + ⟨6, 2, 6, 5, 3, 6, 1083830404864123330701966452611547700419100672000000⟩, + ⟨6, 2, 7, 5, 4, 6, -1423670788802197399744099524557809047343988736000000⟩, + ⟨6, 2, 8, 5, 5, 6, -588111626012532961756743298945409033788666675200000⟩, + ⟨6, 2, 4, 6, 0, 6, -896444918243907224731608026397337659173749181644800000⟩, + ⟨6, 2, 5, 6, 1, 6, -264264092382536589913437143090086122200204574720000000⟩, + ⟨6, 2, 6, 6, 2, 6, 77659670272854242686137091164578385332652736512000000⟩, + ⟨6, 2, 7, 6, 3, 6, -4268903116897823809615340756380969847976728985600000⟩, + ⟨6, 2, 8, 6, 4, 6, 876082358858096956648821614065982856085320499200000⟩, + ⟨6, 2, 5, 7, 0, 6, -1152965834487983267697391521220889357567001624576000000⟩, + ⟨6, 2, 6, 7, 1, 6, -153956730818201316162993740118159115619061989376000000⟩, + ⟨6, 2, 7, 7, 2, 6, 7580768341026773953702357593021833336538424934400000⟩, + ⟨6, 2, 8, 7, 3, 6, 4195951366721555306343310143872107626160245964800000⟩ +] + +def collectedFourData_10_2_48 : List CollectedFourTerm := [ + ⟨6, 3, 1, 0, 3, 7, 6908464510682967075694846332303980127009216921600000⟩, + ⟨6, 3, 2, 0, 4, 7, 12924605338373005099847469898281017759045674598400000⟩, + ⟨6, 3, 3, 0, 5, 7, -44418950993273413729821001652391233186231746560000000⟩, + ⟨6, 3, 4, 0, 6, 7, -15540201078839327636141492937573897346882732032000000⟩, + ⟨6, 3, 5, 0, 7, 7, -50223026346081575830142019268876676930469888000000⟩, + ⟨6, 3, 6, 0, 8, 7, -618797529107504087616605017977777695135209881600000⟩, + ⟨6, 3, 1, 1, 2, 7, 2027413098596143854632254671623864221358358528000000⟩, + ⟨6, 3, 2, 1, 3, 7, -7716577227623408635688711726181047231441377689600000⟩, + ⟨6, 3, 3, 1, 4, 7, 42491571150106003914965420826434401806030628454400000⟩, + ⟨6, 3, 4, 1, 5, 7, 24081420024244185788429628842771967447748155801600000⟩, + ⟨6, 3, 5, 1, 6, 7, 8286409759184370223568490569857965385838493696000000⟩, + ⟨6, 3, 6, 1, 7, 7, 2069522975224101657727005074677878559787188224000000⟩, + ⟨6, 3, 7, 1, 8, 7, 648424817540069891759187268385657418089811148800000⟩, + ⟨6, 3, 1, 2, 1, 7, 7426884976989683453558108340953996524115931955200000⟩, + ⟨6, 3, 2, 2, 2, 7, -1883968184148805987813478799731909548424193638400000⟩, + ⟨6, 3, 3, 2, 3, 7, -29475490727691389549668780073991238790755752345600000⟩, + ⟨6, 3, 4, 2, 4, 7, -6420572226127379711060642729552324108120122982400000⟩, + ⟨6, 3, 5, 2, 5, 7, -1449473976266865161833858788684685576916434944000000⟩, + ⟨6, 3, 6, 2, 6, 7, -142858380500666661384438585675716655198712627200000⟩, + ⟨6, 3, 7, 2, 7, 7, -38283743942157197899373018308736614574063616000000⟩, + ⟨6, 3, 8, 2, 8, 7, -88412879243273471318064261372537076033624473600000⟩, + ⟨6, 3, 1, 3, 0, 7, 6518125918949065154638010946771297198986074521600000⟩, + ⟨6, 3, 2, 3, 1, 7, -10797142992364796370011452472137229574120407040000000⟩, + ⟨6, 3, 3, 3, 2, 7, 19436514468859451557100562812214841872699988377600000⟩, + ⟨6, 3, 4, 3, 3, 7, 8189332283582386037124397721806737671442137088000000⟩, + ⟨6, 3, 5, 3, 4, 7, 1961802520187802312914413402117477718946742272000000⟩, + ⟨6, 3, 6, 3, 5, 7, 348022791760447436499756304663062090377016115200000⟩, + ⟨6, 3, 7, 3, 6, 7, -29892754831644931929523420727688803017084108800000⟩, + ⟨6, 3, 8, 3, 7, 7, -54157906964857983342485995192003942215057408000000⟩, + ⟨6, 3, 2, 4, 0, 7, 41348393995822513934104474768657570085825465548800000⟩, + ⟨6, 3, 3, 4, 1, 7, -17946399981479895875968105293568578606010151731200000⟩, + ⟨6, 3, 4, 4, 2, 7, -27302472298348758100143103538981071231016081817600000⟩, + ⟨6, 3, 5, 4, 3, 7, -182989890827827710924229683321122167562698752000000⟩, + ⟨6, 3, 6, 4, 4, 7, -160835010899877989193858358265311510948478976000000⟩, + ⟨6, 3, 7, 4, 5, 7, -102918065237850747672377499440842391553048576000000⟩, + ⟨6, 3, 8, 4, 6, 7, 69080483724370064343819754320767552626832179200000⟩, + ⟨6, 3, 3, 5, 0, 7, 21556135688226833768493053930650716589244861644800000⟩, + ⟨6, 3, 4, 5, 1, 7, 26322991008950981301798815417105948407405687603200000⟩, + ⟨6, 3, 5, 5, 2, 7, -14212954809700486208652968902812023964693430272000000⟩, + ⟨6, 3, 6, 5, 3, 7, -59577474089924922577633256185512497904195993600000⟩, + ⟨6, 3, 7, 5, 4, 7, 65215238128114831303941416998856928226443264000000⟩, + ⟨6, 3, 8, 5, 5, 7, 23091518090111113590794032793603010669733478400000⟩, + ⟨6, 3, 4, 6, 0, 7, 82128353369112277417750627982654326891065271910400000⟩, + ⟨6, 3, 5, 6, 1, 7, 18158038202009915458896262457938000933206097920000000⟩, + ⟨6, 3, 6, 6, 2, 7, -4268903116897823809615340756380969847976728985600000⟩, + ⟨6, 3, 7, 6, 3, 7, 195549094287853175463438656407923179896858214400000⟩, + ⟨6, 3, 8, 6, 4, 7, -34398353549242451167980564443836414800848486400000⟩, + ⟨6, 3, 5, 7, 0, 7, 79222256340220561197132071472782259980794331136000000⟩, + ⟨6, 3, 6, 7, 1, 7, 8462904436087347085415931037486217928312147148800000⟩, + ⟨6, 3, 7, 7, 2, 7, -347258380548836066314076772302157659867027865600000⟩, + ⟨6, 3, 8, 7, 3, 7, -164749143877343534869764083734364472141781401600000⟩ +] + +def collectedFourData_10_2_49 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 2, 8, -4030822154818050410845093447836384849092306534400000⟩, + ⟨6, 4, 1, 0, 3, 8, -8506705894517651792398791776545472237343552307200000⟩, + ⟨6, 4, 2, 0, 4, 8, -7957326569908279651654604038420259299798705766400000⟩, + ⟨6, 4, 3, 0, 5, 8, 18231690108005139543084667861435814451703971840000000⟩, + ⟨6, 4, 4, 0, 6, 8, 4783838721141641308661988775168032336129294336000000⟩, + ⟨6, 4, 5, 0, 7, 8, 12368378345088769619507077074591009492644659200000⟩, + ⟨6, 4, 6, 0, 8, 8, 126992246980300742460627894041115686056702771200000⟩, + ⟨6, 4, 0, 1, 1, 8, 29697942365920005662230663698561285503266376908800000⟩, + ⟨6, 4, 1, 1, 2, 8, -2496445762988384204048577509245842701131186176000000⟩, + ⟨6, 4, 2, 1, 3, 8, 4750885879649350085050846642434546211552336281600000⟩, + ⟨6, 4, 3, 1, 4, 8, -17440600016157515799977228149422082115440843161600000⟩, + ⟨6, 4, 4, 1, 5, 8, -7413136354388745211560310158780297358613466316800000⟩, + ⟨6, 4, 5, 1, 6, 8, -2040686483482381507601636331295581041712326246400000⟩, + ⟨6, 4, 6, 1, 7, 8, -424716260874737911045076930525083128003821568000000⟩, + ⟨6, 4, 7, 1, 8, 8, -114062129538750027537389554683843570075225292800000⟩, + ⟨6, 4, 0, 2, 0, 8, 4775177505104023443017797241703688213208707891200000⟩, + ⟨6, 4, 1, 2, 1, 8, -9145060543332943846232913682272059519966537318400000⟩, + ⟨6, 4, 2, 2, 2, 8, 1159907764771741379950907129543836503351125606400000⟩, + ⟨6, 4, 3, 2, 3, 8, 12098169828684781460686282885051616066282088038400000⟩, + ⟨6, 4, 4, 2, 4, 8, 1976485495355559278550569727833029297124356915200000⟩, + ⟨6, 4, 5, 2, 5, 8, 356960618348470579106062502936855325976402329600000⟩, + ⟨6, 4, 6, 2, 6, 8, 29318001262727465289483646384357718790399590400000⟩, + ⟨6, 4, 7, 2, 7, 8, 6734358776279913007671558168404585607069696000000⟩, + ⟨6, 4, 8, 2, 8, 8, 13608348856808402239596902293530798253827686400000⟩, + ⟨6, 4, 1, 3, 0, 8, -8026064270894077554918607724359742355949171507200000⟩, + ⟨6, 4, 2, 3, 1, 8, 6647506098863893208279683279993625210876067840000000⟩, + ⟨6, 4, 3, 3, 2, 8, -7977687465642001198398192169853958022083536486400000⟩, + ⟨6, 4, 4, 3, 3, 8, -2520974128953982856775176267013299425115111424000000⟩, + ⟨6, 4, 5, 3, 4, 8, -483131296008100899139655167142500674908769484800000⟩, + ⟨6, 4, 6, 3, 5, 8, -71422709767055779295816531953618840061372006400000⟩, + ⟨6, 4, 7, 3, 6, 8, 5258329387842221673222231026630913208143052800000⟩, + ⟨6, 4, 8, 3, 7, 8, 8335886102119364244759777178007886618427392000000⟩, + ⟨6, 4, 2, 4, 0, 8, -25457077067500848315484351409513753509379230924800000⟩, + ⟨6, 4, 3, 4, 1, 8, 7366072266456701278500952032234369013856914636800000⟩, + ⟨6, 4, 4, 4, 2, 8, 8404693317745210702793938429100889044496993484800000⟩, + ⟨6, 4, 5, 4, 3, 8, 45064751524310424948139200270404098045299916800000⟩, + ⟨6, 4, 6, 4, 4, 8, 33007241410183870013421684277669018397048832000000⟩, + ⟨6, 4, 7, 4, 5, 8, 18103954955906410274378101328033375066259456000000⟩, + ⟨6, 4, 8, 4, 6, 8, -10632741855761068263699595785575338062171340800000⟩, + ⟨6, 4, 3, 5, 0, 8, -8847682734636764095825027320511841966633464627200000⟩, + ⟨6, 4, 4, 5, 1, 8, -8103173376331119792328922816741958806419380633600000⟩, + ⟨6, 4, 5, 5, 2, 8, 3500211263189640115402849376197272463238548684800000⟩, + ⟨6, 4, 6, 5, 3, 8, 12226741297759431269564889414386939818357555200000⟩, + ⟨6, 4, 7, 5, 4, 8, -11471783216887423715236109887253385087811584000000⟩, + ⟨6, 4, 8, 5, 5, 8, -3554204279886536661071602674948180375345561600000⟩, + ⟨6, 4, 4, 6, 0, 8, -25282092230180274559811345672306178832486052659200000⟩, + ⟨6, 4, 5, 6, 1, 8, -4471763309113217575180910952109522214115606528000000⟩, + ⟨6, 4, 6, 6, 2, 8, 876082358858096956648821614065982856085320499200000⟩, + ⟨6, 4, 7, 6, 3, 8, -34398353549242451167980564443836414800848486400000⟩, + ⟨6, 4, 8, 6, 4, 8, 5294531737959869411886435813279901400275353600000⟩, + ⟨6, 4, 5, 7, 0, 8, -19509991951010811502018227490148766683142448742400000⟩, + ⟨6, 4, 6, 7, 1, 8, -1736793053890127618772335819969288216900114841600000⟩, + ⟨6, 4, 7, 7, 2, 8, 61085000626352835293562259042122043619907993600000⟩, + ⟨6, 4, 8, 7, 3, 8, 25357887255028869901670026023577577616467558400000⟩ +] + +def collectedFourData_10_2_50 : List CollectedFourTerm := [ + ⟨7, 0, 3, 0, 5, 5, -1199688339056445036341049542717885286042052853760000000⟩, + ⟨7, 0, 4, 0, 6, 5, -1259151619116299632924388922916719925922277359616000000⟩, + ⟨7, 0, 5, 0, 7, 5, -8138685544641918331715189348369213491865714688000000⟩, + ⟨7, 0, 6, 0, 8, 5, -167127805431432574908111227536980467271635828736000000⟩, + ⟨7, 0, 3, 1, 4, 5, 1147632739564000068745151178184047317822946567782400000⟩, + ⟨7, 0, 4, 1, 5, 5, 1951207636266406591150729601785807371094952037580800000⟩, + ⟨7, 0, 5, 1, 6, 5, 1342819981801341443261784786564243562275375415296000000⟩, + ⟨7, 0, 6, 1, 7, 5, 558946693982425493528928941171227417549775831040000000⟩, + ⟨7, 0, 7, 1, 8, 5, 262694528448711239488724074081088769450754179072000000⟩, + ⟨7, 0, 3, 2, 3, 5, -796088194863779774992011632769192546054279109017600000⟩, + ⟨7, 0, 4, 2, 4, 5, -520229685135145669226313366806078299091995145011200000⟩, + ⟨7, 0, 5, 2, 5, 5, -234888531341922436618694281641583262283904057344000000⟩, + ⟨7, 0, 6, 2, 6, 5, -38583876789231740176400972665172589682372902912000000⟩, + ⟨7, 0, 7, 2, 7, 5, -15509785853492128499808801564768180607427543040000000⟩, + ⟨7, 0, 8, 2, 8, 5, -50145846658987671225234583352443023525620062617600000⟩, + ⟨7, 0, 3, 3, 2, 5, 524950707722109053219454279592353667371048212889600000⟩, + ⟨7, 0, 4, 3, 3, 5, 663544245794553277768509612446019425723895250944000000⟩, + ⟨7, 0, 5, 3, 4, 5, 317911822009114455075127336186368654899750633472000000⟩, + ⟨7, 0, 6, 3, 5, 5, 93995665288022048354520476052984548239073083392000000⟩, + ⟨7, 0, 7, 3, 6, 5, -12110367959577115963415515632814972185159401472000000⟩, + ⟨7, 0, 8, 3, 7, 5, -30717177421162978455077341139072206149651529728000000⟩, + ⟨7, 0, 3, 4, 1, 5, -484704980743121153694800770053088705280774189875200000⟩, + ⟨7, 0, 4, 4, 2, 5, -2212194811761817349415141820919763225037691997388800000⟩, + ⟨7, 0, 5, 4, 3, 5, -29653672581047872608521443100361814189855997952000000⟩, + ⟨7, 0, 6, 4, 4, 5, -43439091372918630553794289021691732687805480960000000⟩, + ⟨7, 0, 7, 4, 5, 5, -41694907235471739317048848181171275062250045440000000⟩, + ⟨7, 0, 8, 4, 6, 5, 39180935782435865853291529448767317270338941747200000⟩, + ⟨7, 0, 3, 5, 0, 5, 582198454533525950489730126791099409316981820620800000⟩, + ⟨7, 0, 4, 5, 1, 5, 2132831910008975562387939671228271000407183563161600000⟩, + ⟨7, 0, 5, 5, 2, 5, -2303221814218353536986704159585419885490022121472000000⟩, + ⟨7, 0, 6, 5, 3, 5, -16090970033701189724681656972138441782388064256000000⟩, + ⟨7, 0, 7, 5, 4, 5, 26420466589678107495834076839351496655146844160000000⟩, + ⟨7, 0, 8, 5, 5, 5, 13097002780373190041989683270142368121025357414400000⟩, + ⟨7, 0, 4, 6, 0, 5, 6654485910152521909610319994051665535774527533875200000⟩, + ⟨7, 0, 5, 6, 1, 5, 2942526044038042989243942194243380364303054929920000000⟩, + ⟨7, 0, 6, 6, 2, 5, -1152965834487983267697391521220889357567001624576000000⟩, + ⟨7, 0, 7, 6, 3, 5, 79222256340220561197132071472782259980794331136000000⟩, + ⟨7, 0, 8, 6, 4, 5, -19509991951010811502018227490148766683142448742400000⟩, + ⟨7, 0, 5, 7, 0, 5, 12838036243516307282852552448451073626986812276736000000⟩, + ⟨7, 0, 6, 7, 1, 5, 2285701832098769529342727082631522179386649346048000000⟩, + ⟨7, 0, 7, 7, 2, 5, -140683814160926103885544808376069273268009304064000000⟩, + ⟨7, 0, 8, 7, 3, 5, -93442102290784828500151889628044154440406112665600000⟩ +] + +def collectedFourData_10_2_51 : List CollectedFourTerm := [ + ⟨7, 1, 2, 0, 4, 6, 93224415289957355207680338836067562387766299852800000⟩, + ⟨7, 1, 3, 0, 5, 6, -640782542403334916131861509151348409750299607040000000⟩, + ⟨7, 1, 4, 0, 6, 6, -336271658855665660139162627262224982866323832832000000⟩, + ⟨7, 1, 5, 0, 7, 6, -1449022896290608608864759275565619609583222784000000⟩, + ⟨7, 1, 6, 0, 8, 6, -22316750230912382888265690207052941062660161536000000⟩, + ⟨7, 1, 2, 1, 3, 6, -55659215987754848930968708224401822440439886643200000⟩, + ⟨7, 1, 3, 1, 4, 6, 612978388355014846146587708607452993207286733209600000⟩, + ⟨7, 1, 4, 1, 5, 6, 521093582899601427469058123768157734577500690841600000⟩, + ⟨7, 1, 5, 1, 6, 6, 239077537589307537888970503651028721467945648128000000⟩, + ⟨7, 1, 6, 1, 7, 6, 74636735220685081627899993449260129719460823040000000⟩, + ⟨7, 1, 7, 1, 8, 6, 28062299571437360227288037939266719558997219737600000⟩, + ⟨7, 1, 2, 2, 2, 6, -13588951290505269508034801450282126952652131532800000⟩, + ⟨7, 1, 3, 2, 3, 6, -425209949013343975023735608469502850347890533990400000⟩, + ⟨7, 1, 4, 2, 4, 6, -138933625268362646323881611808159584193308157542400000⟩, + ⟨7, 1, 5, 2, 5, 6, -41819880879240282450410084950829616044433211392000000⟩, + ⟨7, 1, 6, 2, 6, 6, -5152145323890175214493605221987816822655680512000000⟩, + ⟨7, 1, 7, 2, 7, 6, -1656830309636670498361414671001264779304108032000000⟩, + ⟨7, 1, 8, 2, 8, 6, -4464018149133934910934707471524698794353911398400000⟩, + ⟨7, 1, 2, 3, 1, 6, -77879154984857558679020276090075017297715527680000000⟩, + ⟨7, 1, 3, 3, 2, 6, 280388862823460734533269144119717050947572491878400000⟩, + ⟨7, 1, 4, 3, 3, 6, 177207510890598167690454491370852141807370764288000000⟩, + ⟨7, 1, 5, 3, 4, 6, 56601463045337430436229995482960320537712132096000000⟩, + ⟨7, 1, 6, 3, 5, 6, 12551339255644340490398127627966033227774164992000000⟩, + ⟨7, 1, 7, 3, 6, 6, -1293688055129558196187375608765212587183413657600000⟩, + ⟨7, 1, 8, 3, 7, 6, -2734464499736633463176792975596422309454282752000000⟩, + ⟨7, 1, 2, 4, 0, 6, 298243524852154438348833444127604187384795208089600000⟩, + ⟨7, 1, 3, 4, 1, 6, -258892647169027338322210017620962740761768283340800000⟩, + ⟨7, 1, 4, 4, 2, 6, -590793362585776339251730669249075674290153167257600000⟩, + ⟨7, 1, 5, 4, 3, 6, -5279581118271834746629710021642370464387956736000000⟩, + ⟨7, 1, 6, 4, 4, 6, -5800467192904827841951138277054691417218088960000000⟩, + ⟨7, 1, 7, 4, 5, 6, -4454051572199159316392453902462085483779325952000000⟩, + ⟨7, 1, 8, 4, 6, 6, 3487914156126760501008969406544212284979072204800000⟩, + ⟨7, 1, 3, 5, 0, 6, 310966268266555723599484108844519554176938881843200000⟩, + ⟨7, 1, 4, 5, 1, 6, 569598540438180487557430519671925590295045157683200000⟩, + ⟨7, 1, 5, 5, 2, 6, -410068815871080178408830901906011472677197316096000000⟩, + ⟨7, 1, 6, 5, 3, 6, -2148644017003695096917573158363367774990893056000000⟩, + ⟨7, 1, 7, 5, 4, 6, 2822361975466323797897366675133843512626249728000000⟩, + ⟨7, 1, 8, 5, 5, 6, 1165904297287694966802578737163753078778337689600000⟩, + ⟨7, 1, 4, 6, 0, 6, 1777160892990091525364647665461730092091693229670400000⟩, + ⟨7, 1, 5, 6, 1, 6, 523891430299774274423675598949482216074835394560000000⟩, + ⟨7, 1, 6, 6, 2, 6, -153956730818201316162993740118159115619061989376000000⟩, + ⟨7, 1, 7, 6, 3, 6, 8462904436087347085415931037486217928312147148800000⟩, + ⟨7, 1, 8, 6, 4, 6, -1736793053890127618772335819969288216900114841600000⟩, + ⟨7, 1, 5, 7, 0, 6, 2285701832098769529342727082631522179386649346048000000⟩, + ⟨7, 1, 6, 7, 1, 6, 305212150411528515980170169257379708099465576448000000⟩, + ⟨7, 1, 7, 7, 2, 6, -15028525189123321478809635798836091581073929011200000⟩, + ⟨7, 1, 8, 7, 3, 6, -8318280940711390606706399062098069389941565030400000⟩ +] + +def collectedFourData_10_2_52 : List CollectedFourTerm := [ + ⟨7, 2, 1, 0, 3, 7, -12268132495297847970776523365050572415611332198400000⟩, + ⟨7, 2, 2, 0, 4, 7, -22951666104009365387618019715310762208066640281600000⟩, + ⟨7, 2, 3, 0, 5, 7, 78879695371518663694514383061273607245597245440000000⟩, + ⟨7, 2, 4, 0, 6, 7, 27596471769372084100040775167160618754787770368000000⟩, + ⟨7, 2, 5, 0, 7, 7, 89186640616852757590972851594397159325171712000000⟩, + ⟨7, 2, 6, 0, 8, 7, 1098867926890934584738459643681700086502811238400000⟩, + ⟨7, 2, 1, 1, 2, 7, -3600304015142282764251616042859169514700931072000000⟩, + ⟨7, 2, 2, 1, 3, 7, 13703188558367985501504820438381224508365629030400000⟩, + ⟨7, 2, 3, 1, 4, 7, -75457031587376765631253923054112633358758025625600000⟩, + ⟨7, 2, 4, 1, 5, 7, -42764068784821756950837403284280041006996809318400000⟩, + ⟨7, 2, 5, 1, 6, 7, -14715103866973915439726816842948092558525333504000000⟩, + ⟨7, 2, 6, 1, 7, 7, -3675083229109955118966013434820885153711128576000000⟩, + ⟨7, 2, 7, 1, 8, 7, -1151480413993541121730739770870667635821065011200000⟩, + ⟨7, 2, 1, 2, 1, 7, -13188749654015239877475012351310228286367124684800000⟩, + ⟨7, 2, 2, 2, 2, 7, 3345572849700914313521900037926088042109049241600000⟩, + ⟨7, 2, 3, 2, 3, 7, 52342922953727767582300569119452732004074153574400000⟩, + ⟨7, 2, 4, 2, 4, 7, 11401727640629240905900416196963910076363020697600000⟩, + ⟨7, 2, 5, 2, 5, 7, 2573992927347347369343615009209999185051385856000000⟩, + ⟨7, 2, 6, 2, 6, 7, 253689591563464726831146050971184067670494412800000⟩, + ⟨7, 2, 7, 2, 7, 7, 67984722563481697358135067663667691293507584000000⟩, + ⟨7, 2, 8, 2, 8, 7, 157004630358884030375507586342648291699091046400000⟩, + ⟨7, 2, 1, 3, 0, 7, -11574964635201817560402662273086340939978794598400000⟩, + ⟨7, 2, 2, 3, 1, 7, 19173693459114694217255867777099445975342120960000000⟩, + ⟨7, 2, 3, 3, 2, 7, -34515590893173513234255827791844636836613219942400000⟩, + ⟨7, 2, 4, 3, 3, 7, -14542712544538584782444733290328537750948544512000000⟩, + ⟨7, 2, 5, 3, 4, 7, -3483791978674270519976855269522916644516528128000000⟩, + ⟨7, 2, 6, 3, 5, 7, -618022965030550905534400085862316436215352524800000⟩, + ⟨7, 2, 7, 3, 6, 7, 53083905454964894999386167422932374007264051200000⟩, + ⟨7, 2, 8, 3, 7, 7, 96174247878883295640483161640221122800648192000000⟩, + ⟨7, 2, 2, 4, 0, 7, -73426964157391381562786290654592067299779490611200000⟩, + ⟨7, 2, 3, 4, 1, 7, 31869428068414646529096234640589008703480188108800000⟩, + ⟨7, 2, 4, 4, 2, 7, 48484051280481820024814146996563356959556134502400000⟩, + ⟨7, 2, 5, 4, 3, 7, 324955599396130469932232957223337224881307648000000⟩, + ⟨7, 2, 6, 4, 4, 7, 285612703163081409494016689707466278488244224000000⟩, + ⟨7, 2, 7, 4, 5, 7, 182763110173788735503917671331780250906394624000000⟩, + ⟨7, 2, 8, 4, 6, 7, -122673935121084704384707583597476535232941260800000⟩, + ⟨7, 2, 3, 5, 0, 7, -38279639173197623669049149411113914769211601715200000⟩, + ⟨7, 2, 4, 5, 1, 7, -46744676891800308857116333774229142516087442636800000⟩, + ⟨7, 2, 5, 5, 2, 7, 25239532241274929310703403533462242740171440128000000⟩, + ⟨7, 2, 6, 5, 3, 7, 105798378893042430220266153578294709737383526400000⟩, + ⟨7, 2, 7, 5, 4, 7, -115809986550689880217783665929442747048001536000000⟩, + ⟨7, 2, 8, 5, 5, 7, -41006189292712220276356662940360180950997401600000⟩, + ⟨7, 2, 4, 6, 0, 7, -145844495429463215804624236647021900628806441369600000⟩, + ⟨7, 2, 5, 6, 1, 7, -32245257708491159871796809633894037045987246080000000⟩, + ⟨7, 2, 6, 6, 2, 7, 7580768341026773953702357593021833336538424934400000⟩, + ⟨7, 2, 7, 6, 3, 7, -347258380548836066314076772302157659867027865600000⟩, + ⟨7, 2, 8, 6, 4, 7, 61085000626352835293562259042122043619907993600000⟩, + ⟨7, 2, 5, 7, 0, 7, -140683814160926103885544808376069273268009304064000000⟩, + ⟨7, 2, 6, 7, 1, 7, -15028525189123321478809635798836091581073929011200000⟩, + ⟨7, 2, 7, 7, 2, 7, 616665514614407368557105514634102561124542054400000⟩, + ⟨7, 2, 8, 7, 3, 7, 292563466519758888856303583933015584605103718400000⟩ +] + +def collectedFourData_10_2_53 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 2, 8, -19305415248362306533418426668214241592757295513600000⟩, + ⟨7, 3, 1, 0, 3, 8, -40742430050667332915479222317224372342837005516800000⟩, + ⟨7, 3, 2, 0, 4, 8, -38111206051421573978268677444328367324137101721600000⟩, + ⟨7, 3, 3, 0, 5, 8, 87319741406548471080550324897133367739243560960000000⟩, + ⟨7, 3, 4, 0, 6, 8, 22911949335805587751084334528308298276388470784000000⟩, + ⟨7, 3, 5, 0, 7, 8, 59237711496494729492095846053938958533709004800000⟩, + ⟨7, 3, 6, 0, 8, 8, 608222830755964207026707224643987583452105932800000⟩, + ⟨7, 3, 0, 1, 1, 8, 142236766439996148285686545693173527430820999987200000⟩, + ⟨7, 3, 1, 1, 2, 8, -11956598492418706886204199461846942175140511744000000⟩, + ⟨7, 3, 2, 1, 3, 8, 22754123397526040546116063946773320381980108390400000⟩, + ⟨7, 3, 3, 1, 4, 8, -83530856128211789135995365520355905796236011110400000⟩, + ⟨7, 3, 4, 1, 5, 8, -35504835023083654606593007876176910101039493939200000⟩, + ⟨7, 3, 5, 1, 6, 8, -9773762880671165280539595891239479459050002841600000⟩, + ⟨7, 3, 6, 1, 7, 8, -2034156671764324599124242235876437396125908992000000⟩, + ⟨7, 3, 7, 1, 8, 8, -546294698769080160329421881155662491621208883200000⟩, + ⟨7, 3, 0, 2, 0, 8, 22870466887377015041055879703927084402818731212800000⟩, + ⟨7, 3, 1, 2, 1, 8, -43799796785731830206083987994836001575602330009600000⟩, + ⟨7, 3, 2, 2, 2, 8, 5555318540152512226965705542411589664072374681600000⟩, + ⟨7, 3, 3, 2, 3, 8, 57943561714523418614123492848644088327956961689600000⟩, + ⟨7, 3, 4, 2, 4, 8, 9466275552394478151680555616351156115402968268800000⟩, + ⟨7, 3, 5, 2, 5, 8, 1709644509195784842460611256114570598990374502400000⟩, + ⟨7, 3, 6, 2, 6, 8, 140417058081420858891875208708866716003309977600000⟩, + ⟨7, 3, 7, 2, 7, 8, 32253864748693020150656731604339010645786624000000⟩, + ⟨7, 3, 8, 2, 8, 8, 65176486442409545067474454807714303816866201600000⟩, + ⟨7, 3, 1, 3, 0, 8, -38440421732436528667874095252827610246028250316800000⟩, + ⟨7, 3, 2, 3, 1, 8, 31837888320424130696925881130106618645535784960000000⟩, + ⟨7, 3, 3, 3, 2, 8, -38208723513584537167602534334009121748740053401600000⟩, + ⟨7, 3, 4, 3, 3, 8, -12074075838761975215278350176154359334128582656000000⟩, + ⟨7, 3, 5, 3, 4, 8, -2313932475975699135788795393760613523302593331200000⟩, + ⟨7, 3, 6, 3, 5, 8, -342075392378236682875991381637167066971216281600000⟩, + ⟨7, 3, 7, 3, 6, 8, 25184497962436938192784113834364333072790323200000⟩, + ⟨7, 3, 8, 3, 7, 8, 39924297446889173189344267644774167240245248000000⟩, + ⟨7, 3, 2, 4, 0, 8, -121925360366054040628380472646757481384143696691200000⟩, + ⟨7, 3, 3, 4, 1, 8, 35279423996271791009659744836052034912653620019200000⟩, + ⟨7, 3, 4, 4, 2, 8, 40253846064694795678591343762695309024864449331200000⟩, + ⟨7, 3, 5, 4, 3, 8, 215835307990747143245604433558096873992172339200000⟩, + ⟨7, 3, 6, 4, 4, 8, 158086483886387990900546654605912440840388608000000⟩, + ⟨7, 3, 7, 4, 5, 8, 86707960469964331511701375520733121493336064000000⟩, + ⟨7, 3, 8, 4, 6, 8, -50924969862227928805617878372722546998194995200000⟩, + ⟨7, 3, 3, 5, 0, 8, -42375521076701709561637230405631628368975547596800000⟩, + ⟨7, 3, 4, 5, 1, 8, -38809731824203414837098986178620131725906699878400000⟩, + ⟨7, 3, 5, 5, 2, 8, 16764081692887536137180231484843275345556878131200000⟩, + ⟨7, 3, 6, 5, 3, 8, 58559348148219382370296811987306597023796428800000⟩, + ⟨7, 3, 7, 5, 4, 8, -54943515276774153021973147363659267698589696000000⟩, + ⟨7, 3, 8, 5, 5, 8, -17022678467394050867453311090856154922116710400000⟩, + ⟨7, 3, 4, 6, 0, 8, -121087279493991033257359627927270695396803661004800000⟩, + ⟨7, 3, 5, 6, 1, 8, -21417280212085730766366737760495431668551647232000000⟩, + ⟨7, 3, 6, 6, 2, 8, 4195951366721555306343310143872107626160245964800000⟩, + ⟨7, 3, 7, 6, 3, 8, -164749143877343534869764083734364472141781401600000⟩, + ⟨7, 3, 8, 6, 4, 8, 25357887255028869901670026023577577616467558400000⟩, + ⟨7, 3, 5, 7, 0, 8, -93442102290784828500151889628044154440406112665600000⟩, + ⟨7, 3, 6, 7, 1, 8, -8318280940711390606706399062098069389941565030400000⟩, + ⟨7, 3, 7, 7, 2, 8, 292563466519758888856303583933015584605103718400000⟩, + ⟨7, 3, 8, 7, 3, 8, 121450295864413886387742539078094695956060569600000⟩ +] + +def collectedFourData_10_2 : List (List CollectedFourTerm) := [ + collectedFourData_10_2_0, + collectedFourData_10_2_1, + collectedFourData_10_2_2, + collectedFourData_10_2_3, + collectedFourData_10_2_4, + collectedFourData_10_2_5, + collectedFourData_10_2_6, + collectedFourData_10_2_7, + collectedFourData_10_2_8, + collectedFourData_10_2_9, + collectedFourData_10_2_10, + collectedFourData_10_2_11, + collectedFourData_10_2_12, + collectedFourData_10_2_13, + collectedFourData_10_2_14, + collectedFourData_10_2_15, + collectedFourData_10_2_16, + collectedFourData_10_2_17, + collectedFourData_10_2_18, + collectedFourData_10_2_19, + collectedFourData_10_2_20, + collectedFourData_10_2_21, + collectedFourData_10_2_22, + collectedFourData_10_2_23, + collectedFourData_10_2_24, + collectedFourData_10_2_25, + collectedFourData_10_2_26, + collectedFourData_10_2_27, + collectedFourData_10_2_28, + collectedFourData_10_2_29, + collectedFourData_10_2_30, + collectedFourData_10_2_31, + collectedFourData_10_2_32, + collectedFourData_10_2_33, + collectedFourData_10_2_34, + collectedFourData_10_2_35, + collectedFourData_10_2_36, + collectedFourData_10_2_37, + collectedFourData_10_2_38, + collectedFourData_10_2_39, + collectedFourData_10_2_40, + collectedFourData_10_2_41, + collectedFourData_10_2_42, + collectedFourData_10_2_43, + collectedFourData_10_2_44, + collectedFourData_10_2_45, + collectedFourData_10_2_46, + collectedFourData_10_2_47, + collectedFourData_10_2_48, + collectedFourData_10_2_49, + collectedFourData_10_2_50, + collectedFourData_10_2_51, + collectedFourData_10_2_52, + collectedFourData_10_2_53 +] + +theorem collectedFourChecked_10_2 : collectNumericRowParts 10 2 = collectedFourData_10_2 := by + decide +kernel + +def collectedFourData_10_3_0 : List CollectedFourTerm := [ + ⟨0, 3, 7, 2, 8, 0, 33594811991758933568905936798481115232605516595200000⟩, + ⟨0, 3, 7, 3, 7, 0, -18758641415859994034370653273875794453934689484800000⟩, + ⟨0, 3, 8, 3, 8, 0, -84885611736805918588385660890005403080012595200000000⟩, + ⟨0, 3, 7, 4, 6, 0, 6160813201129171472566306472872648288977813504000000⟩, + ⟨0, 3, 8, 4, 7, 0, -30153615520174904903311449035998227125391222374400000⟩, + ⟨0, 3, 7, 5, 5, 0, 16316555840960566800422264219249342846847890227200000⟩, + ⟨0, 3, 8, 5, 6, 0, -62787741534275616650945660052133779629588191641600000⟩, + ⟨0, 3, 7, 6, 4, 0, -5841091707999553272203905834242560784758892134400000⟩, + ⟨0, 3, 8, 6, 5, 0, 65892933646157854939917283685909050594444915507200000⟩, + ⟨0, 3, 7, 7, 3, 0, -244739193924325927987447259472941140439939520921600000⟩, + ⟨0, 3, 8, 7, 4, 0, -130284941275600969045107244457989411887768403968000000⟩ +] + +def collectedFourData_10_3_1 : List CollectedFourTerm := [ + ⟨0, 4, 6, 1, 8, 1, -148162107323847065951276968648774306165161984000000⟩, + ⟨0, 4, 6, 2, 7, 1, -198257846122968067666810047619553801143320576000000⟩, + ⟨0, 4, 7, 2, 8, 1, -929790988446526592902270314628075515820376064000000⟩, + ⟨0, 4, 6, 3, 6, 1, 525325323911452675495800683308782892785598464000000⟩, + ⟨0, 4, 7, 3, 7, 1, 519175870019602365866598049636661474975809536000000⟩, + ⟨0, 4, 8, 3, 8, 1, 1174673590389700352993643468782172773548032000000000⟩, + ⟨0, 4, 6, 4, 5, 1, -417949487709421813544999555483580728120180736000000⟩, + ⟨0, 4, 7, 4, 6, 1, -170510512078992745801025028747636566686433280000000⟩, + ⟨0, 4, 8, 4, 7, 1, 417275143355729067893614642962564880483221504000000⟩, + ⟨0, 4, 6, 5, 4, 1, -471397329771423334425634804481032524172099584000000⟩, + ⟨0, 4, 7, 5, 5, 1, -451587185162138497882361548596735511105634304000000⟩, + ⟨0, 4, 8, 5, 6, 1, 868876365163170037459279865098099218035245056000000⟩, + ⟨0, 4, 6, 6, 3, 1, 1745484983078964334360290884814777997930266624000000⟩, + ⟨0, 4, 7, 6, 4, 1, 161661700447080332894015412167433112894046208000000⟩, + ⟨0, 4, 8, 6, 5, 1, -911846982824783847976349333513348834710781952000000⟩, + ⟨0, 4, 6, 7, 2, 1, -1722579901411559006665734181722674435337486336000000⟩, + ⟨0, 4, 7, 7, 3, 1, 6773554710957348848321948303121094404275699712000000⟩, + ⟨0, 4, 8, 7, 4, 1, 1802923682949241149485061621739582852568186880000000⟩ +] + +def collectedFourData_10_3_2 : List CollectedFourTerm := [ + ⟨0, 5, 5, 0, 8, 2, -841072263728580026708948695330462129541087232000000⟩, + ⟨0, 5, 5, 1, 7, 2, 6670995361985278601957511995033851257189040128000000⟩, + ⟨0, 5, 6, 1, 8, 2, 3648957292767572064238941888907412916305657856000000⟩, + ⟨0, 5, 5, 2, 6, 2, 4662678893273769994379737596261845026077671424000000⟩, + ⟨0, 5, 6, 2, 7, 2, 4882722219099787632512236702580313038398685184000000⟩, + ⟨0, 5, 7, 2, 8, 2, 11449511853343651865709169655076996485153292288000000⟩, + ⟨0, 5, 5, 3, 5, 2, -1761838728463069523488898964768191685643468800000000⟩, + ⟨0, 5, 6, 3, 6, 2, -12937786228784652311527062006586303816113586176000000⟩, + ⟨0, 5, 7, 3, 7, 2, -6393168305159697595978563019699462102069542912000000⟩, + ⟨0, 5, 8, 3, 8, 2, -9643342331124427331113167713756062307844096000000000⟩, + ⟨0, 5, 5, 4, 4, 2, 6347213985350083409995485689470426073763151872000000⟩, + ⟨0, 5, 6, 4, 5, 2, 10293318978328948201547875646781503596998426624000000⟩, + ⟨0, 5, 7, 4, 6, 2, 2099678479816112277877140326637007282120949760000000⟩, + ⟨0, 5, 8, 4, 7, 2, -3425570376800052139735035953524859023248064512000000⟩, + ⟨0, 5, 5, 5, 3, 2, -16553898964592293689392062044660575509785083904000000⟩, + ⟨0, 5, 6, 5, 4, 2, 11609639976980399229642424020811873833248096256000000⟩, + ⟨0, 5, 7, 5, 5, 2, 5560876469636119998085003159978540844992954368000000⟩, + ⟨0, 5, 8, 5, 6, 2, -7132936588718075635855389778743825341683335168000000⟩, + ⟨0, 5, 5, 6, 2, 2, -244996456555910556867378916501551114004463616000000⟩, + ⟨0, 5, 6, 6, 3, 2, -42988050544534406435103160768086869008623599616000000⟩, + ⟨0, 5, 7, 6, 4, 2, -1990713588860500398189965178013550071498407936000000⟩, + ⟨0, 5, 8, 6, 5, 2, 7485698734458776147635382946612014146551545856000000⟩, + ⟨0, 5, 5, 7, 1, 2, 11420891811001795755134042955241607401436086272000000⟩, + ⟨0, 5, 6, 7, 2, 2, 42423940960097744392811153226807061875234177024000000⟩, + ⟨0, 5, 7, 7, 3, 2, -83410030766111385969204955996123238196213448704000000⟩, + ⟨0, 5, 8, 7, 4, 2, -14800886317537165759096932905451634370952560640000000⟩ +] + +def collectedFourData_10_3_3 : List CollectedFourTerm := [ + ⟨0, 6, 4, 0, 7, 3, -1432103551901070876753730022195934380665885163520000⟩, + ⟨0, 6, 5, 0, 8, 3, -135000882856054810335128030481387264435604684800000⟩, + ⟨0, 6, 4, 1, 6, 3, -3208677178447063475818341603580998767456896942080000⟩, + ⟨0, 6, 5, 1, 7, 3, 1070764430400104603533830993639283472758682419200000⟩, + ⟨0, 6, 6, 1, 8, 3, 292847878399799080474239116990983199364690739200000⟩, + ⟨0, 6, 4, 2, 5, 3, 407164318151138842807129738632462796568804720640000⟩, + ⟨0, 6, 5, 2, 6, 3, 748408661433858162797115735568779819397781913600000⟩, + ⟨0, 6, 6, 2, 7, 3, 391863956728970097705322428928762746795510988800000⟩, + ⟨0, 6, 7, 2, 8, 3, 612588745395074166800397765302449152652109414400000⟩, + ⟨0, 6, 4, 3, 4, 3, -279355392552228410228541361311164837384568176640000⟩, + ⟨0, 6, 5, 3, 5, 3, -282793517334747371428879717739385812491960320000000⟩, + ⟨0, 6, 6, 3, 6, 3, -1038324908816919579454359588786445876118893363200000⟩, + ⟨0, 6, 7, 3, 7, 3, -342056762010654025027306544929480794518952345600000⟩, + ⟨0, 6, 8, 3, 8, 3, -386964290860589679863852985379830611155353600000000⟩, + ⟨0, 6, 4, 4, 3, 3, -624399981092570295947141149314506558022667468800000⟩, + ⟨0, 6, 5, 4, 4, 3, 1018794137735447285135455006908872246973746380800000⟩, + ⟨0, 6, 6, 4, 5, 3, 826092601979934142129965758808693004080827596800000⟩, + ⟨0, 6, 7, 4, 6, 3, 112340108657816932443128095668669496833343488000000⟩, + ⟨0, 6, 8, 4, 7, 3, -137459955908970767688109894405636462140928819200000⟩, + ⟨0, 6, 4, 5, 2, 3, 4278177307592058975824838930031306611558218465280000⟩, + ⟨0, 6, 5, 5, 3, 3, -2657073679998409891887023981594344178335717785600000⟩, + ⟨0, 6, 6, 5, 4, 3, 931734236238638053754333562297394888944333619200000⟩, + ⟨0, 6, 7, 5, 5, 3, 297526251203151144761237188660709561716860518400000⟩, + ⟨0, 6, 8, 5, 6, 3, -286227705501874629496950888382010375231294668800000⟩, + ⟨0, 6, 4, 6, 1, 3, -2295696080762564403615548413374587481056681656320000⟩, + ⟨0, 6, 5, 6, 2, 3, -39324490127671663061870520023181106098890342400000⟩, + ⟨0, 6, 6, 6, 3, 3, -3450015549226135734344605575088786602544280371200000⟩, + ⟨0, 6, 7, 6, 4, 3, -106510107632653938111228298495056594533665996800000⟩, + ⟨0, 6, 8, 6, 5, 3, 300383207700363244818879822125747899570166169600000⟩, + ⟨0, 6, 4, 7, 0, 3, -43804710695013649040193559651143610563646917181440000⟩, + ⟨0, 6, 5, 7, 1, 3, 1833172420469079590352203595404265546507406540800000⟩, + ⟨0, 6, 6, 7, 2, 3, 3404742809171134096606864504211393300730268876800000⟩, + ⟨0, 6, 7, 7, 3, 3, -4462727036301980445369031303544040512810070835200000⟩, + ⟨0, 6, 8, 7, 4, 3, -593924210228275625231420272391334551328129024000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1010.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1010.lean new file mode 100644 index 0000000000000000000000000000000000000000..afa7ab900d383a4dccae545b2f89bd0c3d8c48d1 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1010.lean @@ -0,0 +1,662 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1010. -/ +namespace LaughlinFock +def collectedFourData_10_3_4 : List CollectedFourTerm := [ + ⟨0, 7, 3, 0, 6, 4, -1432103551901070876753730022195934380665885163520000⟩, + ⟨0, 7, 4, 0, 7, 4, 20544862290599082900808836194710801404751113093120000⟩, + ⟨0, 7, 5, 0, 8, 4, 968356842528989858403155440338202499496699494400000⟩, + ⟨0, 7, 3, 1, 5, 4, 19199392951462349440685317852690423453146949877760000⟩, + ⟨0, 7, 4, 1, 6, 4, 46031469357557177333696345540067082359835962900480000⟩, + ⟨0, 7, 5, 1, 7, 4, -7680557645094639430790238818322909838282693017600000⟩, + ⟨0, 7, 6, 1, 8, 4, -1400392060995692697154290285220228491156809318400000⟩, + ⟨0, 7, 3, 2, 4, 4, -25001735662699013394886274677938411189436541829120000⟩, + ⟨0, 7, 4, 2, 5, 4, -5841152223214847651712911324067732340583788707840000⟩, + ⟨0, 7, 5, 2, 6, 4, -5368310436015304715702216455595588736999279820800000⟩, + ⟨0, 7, 6, 2, 7, 4, -1873884752015966378374430740985635562919139737600000⟩, + ⟨0, 7, 7, 2, 8, 4, -2197039347854027693509940321225759618825296281600000⟩, + ⟨0, 7, 3, 3, 3, 4, 33418364528820434026706817323823756008200140226560000⟩, + ⟨0, 7, 4, 3, 4, 4, 4007613878551605664205826706428621725227643043840000⟩, + ⟨0, 7, 5, 3, 5, 4, 2028468493987046042158789697292195117095976960000000⟩, + ⟨0, 7, 6, 3, 6, 4, 4965246690488874365426047425483780299147339366400000⟩, + ⟨0, 7, 7, 3, 7, 4, 1226780888460949827511099969427930954678560358400000⟩, + ⟨0, 7, 8, 3, 8, 4, 1110272795086166481596233328713753598172856320000000⟩, + ⟨0, 7, 3, 4, 2, 4, -45748225108991283582428990812933780362215030784000000⟩, + ⟨0, 7, 4, 4, 3, 4, 8957600593037070686195675972035029531710246092800000⟩, + ⟨0, 7, 5, 4, 4, 4, -7307776464369213054302731652623072723523233382400000⟩, + ⟨0, 7, 6, 4, 5, 4, -3950356505163494900299491581811597621260294553600000⟩, + ⟨0, 7, 7, 4, 6, 4, -402905931456907518627050237832186648625938432000000⟩, + ⟨0, 7, 8, 4, 7, 4, 394398276699018128758494783563476226297340887040000⟩, + ⟨0, 7, 3, 5, 1, 4, 37990346931906223490198113172669181284582298746880000⟩, + ⟨0, 7, 4, 5, 2, 4, -61374447066043256532230714351577877876261445959680000⟩, + ⟨0, 7, 5, 5, 3, 4, 19059101131017118790435059560012521394381049036800000⟩, + ⟨0, 7, 6, 5, 4, 4, -4455532457725905703099956697990030178436671078400000⟩, + ⟨0, 7, 7, 5, 5, 4, -1067072952003471523255303939899378199290288537600000⟩, + ⟨0, 7, 8, 5, 6, 4, 821240724594807352067097882161317921115665858560000⟩, + ⟨0, 7, 3, 6, 0, 4, 20689562349390852969835001772698012048498444206080000⟩, + ⟨0, 7, 4, 6, 1, 4, 32933903262599434081860699114889533147752347729920000⟩, + ⟨0, 7, 5, 6, 2, 4, 282073259733402290351001559559096344518013747200000⟩, + ⟨0, 7, 6, 6, 3, 4, 16497897856893914462127531670521321075142714982400000⟩, + ⟨0, 7, 7, 6, 4, 4, 381996729734548527987612435015228971470238515200000⟩, + ⟨0, 7, 8, 6, 5, 4, -861855503175052237797290588253858742582923755520000⟩, + ⟨0, 7, 4, 7, 0, 4, 628419465697098731255525434860159315812092099952640000⟩, + ⟨0, 7, 5, 7, 1, 4, -13149284799784902031752469697321382216238261862400000⟩, + ⟨0, 7, 6, 7, 2, 4, -16281404617813683887553613062347406803199433113600000⟩, + ⟨0, 7, 7, 7, 3, 4, 16005496299420393000131623802773844134747491532800000⟩, + ⟨0, 7, 8, 7, 4, 4, 1704079442299387223237707148487485528210197708800000⟩ +] + +def collectedFourData_10_3_5 : List CollectedFourTerm := [ + ⟨0, 8, 2, 0, 5, 5, -841072263728580026708948695330462129541087232000000⟩, + ⟨0, 8, 3, 0, 6, 5, -135000882856054810335128030481387264435604684800000⟩, + ⟨0, 8, 4, 0, 7, 5, 968356842528989858403155440338202499496699494400000⟩, + ⟨0, 8, 5, 0, 8, 5, 30428206695802302349263581794647069689905152000000⟩, + ⟨0, 8, 2, 1, 4, 5, 2898793013757856493301143080724443012330527129600000⟩, + ⟨0, 8, 3, 1, 5, 5, 1809879596560614394431356399484804321826465382400000⟩, + ⟨0, 8, 4, 1, 6, 5, 2169636753635024012359364257116405271801469337600000⟩, + ⟨0, 8, 5, 1, 7, 5, -241342432148888118115638668351352162440183808000000⟩, + ⟨0, 8, 6, 1, 8, 5, -33002879632563130510600367410677015908450304000000⟩, + ⟨0, 8, 2, 2, 3, 5, -1080362355303015213292202569289664457405051699200000⟩, + ⟨0, 8, 3, 2, 4, 5, -2356852186364271171110358116432408321110887628800000⟩, + ⟨0, 8, 4, 2, 5, 5, -275315533567325868822179555458572315599359180800000⟩, + ⟨0, 8, 5, 2, 6, 5, -168685811242580334598753792033931223172644864000000⟩, + ⟨0, 8, 6, 2, 7, 5, -44161627760233758501564461231489622585901056000000⟩, + ⟨0, 8, 7, 2, 8, 5, -41421900146264536242918715587732181086948556800000⟩, + ⟨0, 8, 2, 3, 2, 5, -577701285593031941679721595974608392716025856000000⟩, + ⟨0, 8, 3, 3, 3, 5, 3150267108134285169803884380219374125149742694400000⟩, + ⟨0, 8, 4, 3, 4, 5, 188893956387596129943748694208735541870775500800000⟩, + ⟨0, 8, 5, 3, 5, 5, 63739580183854429940908680437002022997196800000000⟩, + ⟨0, 8, 6, 3, 6, 5, 117015401212482868104486063147880141956317184000000⟩, + ⟨0, 8, 7, 3, 7, 5, 23129123978962695827376862010442049622586163200000⟩, + ⟨0, 8, 8, 3, 8, 5, 17443781369571229629212453428250628902092800000000⟩, + ⟨0, 8, 2, 4, 1, 5, -1333587209810654255606524636950853960063569100800000⟩, + ⟨0, 8, 3, 4, 2, 5, -4312572767948833790515747869141092180070236160000000⟩, + ⟨0, 8, 4, 4, 3, 5, 422205498592137252681672776956809115846311936000000⟩, + ⟨0, 8, 5, 4, 4, 5, -229628710180657250885936541811765392747528192000000⟩, + ⟨0, 8, 6, 4, 5, 5, -93097600219846272399848925211507179720278016000000⟩, + ⟨0, 8, 7, 4, 6, 5, -7596190426651639648740435833172561059905536000000⟩, + ⟨0, 8, 8, 4, 7, 5, 6196492737390184597807748968978247310743961600000⟩, + ⟨0, 8, 2, 5, 0, 5, 9949994396324421157848572371667337577668123033600000⟩, + ⟨0, 8, 3, 5, 1, 5, 3581256654944351350102700642664784227541922611200000⟩, + ⟨0, 8, 4, 5, 2, 5, -2892809157452047389335518830595484796501727641600000⟩, + ⟨0, 8, 5, 5, 3, 5, 598884877124650193157858386035570147426566144000000⟩, + ⟨0, 8, 6, 5, 4, 5, -105003024150790669513970292302139473635835904000000⟩, + ⟨0, 8, 7, 5, 5, 5, -20118069032236653637775778725874094922583244800000⟩, + ⟨0, 8, 8, 5, 6, 5, 12902724190867250106946092097567103891433062400000⟩, + ⟨0, 8, 3, 6, 0, 5, 1950354204041596789510755352650894153434215219200000⟩, + ⟨0, 8, 4, 6, 1, 5, 1552299067495770967942821475904967796620420710400000⟩, + ⟨0, 8, 5, 6, 2, 5, 8863451027114256524805709475515553154072576000000⟩, + ⟨0, 8, 6, 6, 3, 5, 388804073035276788048781078552535480238342144000000⟩, + ⟨0, 8, 7, 6, 4, 5, 7201978613045468142350134220998688678451609600000⟩, + ⟨0, 8, 8, 6, 5, 5, -13540833420475413879775804815007785524448460800000⟩, + ⟨0, 8, 4, 7, 0, 5, 29619779435788696968286758682718525568368561356800000⟩, + ⟨0, 8, 5, 7, 1, 5, -413183589166251240594766346187590074569326592000000⟩, + ⟨0, 8, 6, 7, 2, 5, -383702001615685572472417829933001384306671616000000⟩, + ⟨0, 8, 7, 7, 3, 5, 301759761450593118266473958845992022745441894400000⟩, + ⟨0, 8, 8, 7, 4, 5, 26773230290258915132408059852381807498493952000000⟩ +] + +def collectedFourData_10_3_6 : List CollectedFourTerm := [ + ⟨1, 2, 7, 2, 8, 0, -13140689032699289464156826665601664014690864332800000⟩, + ⟨1, 2, 7, 3, 7, 0, 7337486323251304605788679354088548509204820787200000⟩, + ⟨1, 2, 8, 3, 8, 0, 33203204931090117028054315511679952693808332800000000⟩, + ⟨1, 2, 7, 4, 6, 0, -2409816446790848621856663760226268714218029056000000⟩, + ⟨1, 2, 8, 4, 7, 0, 11794657010117931458477368938219558803101817241600000⟩, + ⟨1, 2, 7, 5, 5, 0, -6382258857210829794565761012587973176009215180800000⟩, + ⟨1, 2, 8, 5, 6, 0, 24559571482936422267620414842482468066324538982400000⟩, + ⟨1, 2, 7, 6, 4, 0, 2284756639362331346857832112656831919330793881600000⟩, + ⟨1, 2, 8, 6, 5, 0, -25774174616868081084513565981299759812172369100800000⟩, + ⟨1, 2, 7, 7, 3, 0, 95730306282469272732295576742557410237687948902400000⟩, + ⟨1, 2, 8, 7, 4, 0, 50961258523075995984521619583782251530448535552000000⟩ +] + +def collectedFourData_10_3_7 : List CollectedFourTerm := [ + ⟨1, 3, 6, 1, 8, 1, 598380889539468812518549160720901295774787174400000⟩, + ⟨1, 3, 6, 2, 7, 1, 800702071967265852677253833223395095034304921600000⟩, + ⟨1, 3, 7, 2, 8, 1, 3755137995819161304600665644640666943878489702400000⟩, + ⟨1, 3, 6, 3, 6, 1, -2121626374634792156747049428727088136283645542400000⟩, + ⟨1, 3, 7, 3, 7, 1, -2096790633861043880210885476445880197670607257600000⟩, + ⟨1, 3, 8, 3, 8, 1, -4744143024366774978962636550340284840620851200000000⟩, + ⟨1, 3, 6, 4, 5, 1, 1687968609217236838968057190832093699252001177600000⟩, + ⟨1, 3, 7, 4, 6, 1, 688639178643998653631431478522883081920053248000000⟩, + ⟨1, 3, 8, 4, 7, 1, -1685245141108507822531904344383578206399522406400000⟩, + ⟨1, 3, 6, 5, 4, 1, 1903827899117319789194362557810556414045087334400000⟩, + ⟨1, 3, 7, 5, 5, 1, 1823820857051568608261566743734723670972982886400000⟩, + ⟨1, 3, 8, 5, 6, 1, -3509122687825564815284975885745834096873544089600000⟩, + ⟨1, 3, 6, 6, 3, 1, -7049473551085663358338656713391747359905834598400000⟩, + ⟨1, 3, 7, 6, 4, 1, -652901567514471265091428755511696913777609932800000⟩, + ⟨1, 3, 8, 6, 5, 1, 3682667711481409791042445552062977512500835123200000⟩, + ⟨1, 3, 6, 7, 2, 1, 6956967016245697768299374499971871770114890137600000⟩, + ⟨1, 3, 7, 7, 3, 1, -27356290798616028394830284224880998817358623539200000⟩, + ⟨1, 3, 8, 7, 4, 1, -7281450680347477243334487618436954183862059008000000⟩ +] + +def collectedFourData_10_3_8 : List CollectedFourTerm := [ + ⟨1, 4, 5, 0, 8, 2, 2898793013757856493301143080724443012330527129600000⟩, + ⟨1, 4, 5, 1, 7, 2, -22991882605196031924658129995749099448144651878400000⟩, + ⟨1, 4, 6, 1, 8, 2, -12576293814378923143388113953205544649466105036800000⟩, + ⟨1, 4, 5, 2, 6, 2, -16070130456210089708214417331465546828252132147200000⟩, + ⟨1, 4, 6, 2, 7, 2, -16828519578211080578549204818231542068527969075200000⟩, + ⟨1, 4, 7, 2, 8, 2, -39461252501985867078274599242519954171831412326400000⟩, + ⟨1, 4, 5, 3, 5, 2, 6072255640431988549655124949604619430542704640000000⟩, + ⟨1, 4, 6, 3, 6, 2, 44590656416648105849740133776677487341074173132800000⟩, + ⟨1, 4, 7, 3, 7, 2, 22034339280929667099762772414620856694722894233600000⟩, + ⟨1, 4, 8, 3, 8, 2, 33236208806619097940452209303286264783228108800000000⟩, + ⟨1, 4, 5, 4, 4, 2, -21875955671148555179333411720785338158810765721600000⟩, + ⟨1, 4, 6, 4, 5, 2, -35476382267659834298356719470542750503893414707200000⟩, + ⟨1, 4, 7, 4, 6, 2, -7236635389028629470670917180043617296845897728000000⟩, + ⟨1, 4, 8, 4, 7, 2, 11806380860049793262135533939487647402131298713600000⟩, + ⟨1, 4, 5, 5, 3, 2, 57053750002745403172777216090447331839968490291200000⟩, + ⟨1, 4, 6, 5, 4, 2, -40013141211341941107161113068353243152642788556800000⟩, + ⟨1, 4, 7, 5, 5, 2, -19165808404013214313956171739210396145990133350400000⟩, + ⟨1, 4, 8, 5, 6, 2, 24583983615498630646075752715359141414998271590400000⟩, + ⟨1, 4, 5, 6, 2, 2, 844391198339276538118264038088561132993039564800000⟩, + ⟨1, 4, 6, 6, 3, 2, 148160230657397592889282668424860018631984860364800000⟩, + ⟨1, 4, 7, 6, 4, 2, 6861083039642219590473759299671971459079392460800000⟩, + ⟨1, 4, 8, 6, 5, 2, -25799794060915207448845878197330679295772511436800000⟩, + ⟨1, 4, 5, 7, 1, 2, -39362612251472506350124822834670810359473478041600000⟩, + ⟨1, 4, 6, 7, 2, 2, -146216001852241623424209163678016873434801451827200000⟩, + ⟨1, 4, 7, 7, 3, 2, 287476385667805577725705321128757753459445543731200000⟩, + ⟨1, 4, 8, 7, 4, 2, 51011913844951895317728453033635246328766267392000000⟩ +] + +def collectedFourData_10_3_9 : List CollectedFourTerm := [ + ⟨1, 5, 4, 0, 7, 3, 19199392951462349440685317852690423453146949877760000⟩, + ⟨1, 5, 5, 0, 8, 3, 1809879596560614394431356399484804321826465382400000⟩, + ⟨1, 5, 4, 1, 6, 3, 43016899107342116163212742009355668870489220055040000⟩, + ⟨1, 5, 5, 1, 7, 3, -14355126087363063678906224543827239394921257369600000⟩, + ⟨1, 5, 6, 1, 8, 3, -3926043954668025126523143739460260977662597529600000⟩, + ⟨1, 5, 4, 2, 5, 3, -5458619056995373644196949059497214636812738232320000⟩, + ⟨1, 5, 5, 2, 6, 3, -10033486726621282994015279745080199749489708236800000⟩, + ⟨1, 5, 6, 2, 7, 3, -5253495865412153752227305664414668056433157734400000⟩, + ⟨1, 5, 7, 2, 8, 3, -8212626820784408404932362965705803718812971827200000⟩, + ⟨1, 5, 4, 3, 4, 3, 3745157916549010163537227400389990800179928760320000⟩, + ⟨1, 5, 5, 3, 5, 3, 3791250888407167040769499753858705752493916160000000⟩, + ⟨1, 5, 6, 3, 6, 3, 13920227981561816846715814366708504647247174041600000⟩, + ⟨1, 5, 7, 3, 7, 3, 4585759302691157891102672344387562776080207052800000⟩, + ⟨1, 5, 8, 3, 8, 3, 5187808848427224156253008669092067301706956800000000⟩, + ⟨1, 5, 4, 4, 3, 3, 8370973300057879787867644276998430365575439974400000⟩, + ⟨1, 5, 5, 4, 4, 3, -13658390108078107166907508974141587536059197030400000⟩, + ⟨1, 5, 6, 4, 5, 3, -11074950871153467290620004403282350466828494438400000⟩, + ⟨1, 5, 7, 4, 6, 3, -1506079562101665676770383614911331790323974144000000⟩, + ⟨1, 5, 8, 4, 7, 3, 1842846982038160551086578564404938985963100569600000⟩, + ⟨1, 5, 4, 5, 2, 3, -57355075431139797979826419509962665073561976176640000⟩, + ⟨1, 5, 5, 5, 3, 3, 35621866600049908353589412681239013443515501772800000⟩, + ⟨1, 5, 6, 5, 4, 3, -12491227819475451746197282078507411008283842969600000⟩, + ⟨1, 5, 7, 5, 5, 3, -3988764222141529470127315022839613625403126579200000⟩, + ⟨1, 5, 8, 5, 6, 3, 3837291084315076638402855068461507126854313574400000⟩, + ⟨1, 5, 4, 6, 1, 3, 30777083886973886535964095241515226631128649564160000⟩, + ⟨1, 5, 5, 6, 2, 3, 527200939886521279018426224445954897636176691200000⟩, + ⟨1, 5, 6, 6, 3, 3, 46252384564173949158299708030469851884998465945600000⟩, + ⟨1, 5, 7, 6, 4, 3, 1427920073955053696053202617025010728287233638400000⟩, + ⟨1, 5, 8, 6, 5, 3, -4027065803310289603948371458932496862811049164800000⟩, + ⟨1, 5, 4, 7, 0, 3, 587264693703371269190082751381164865700210902302720000⟩, + ⟨1, 5, 5, 7, 1, 3, -24576293803369138101516098464892463311413995110400000⟩, + ⟨1, 5, 6, 7, 2, 3, -45645438840764815242407359210574825863824959078400000⟩, + ⟨1, 5, 7, 7, 3, 3, 59829228055008383147496449202300549532701268377600000⟩, + ⟨1, 5, 8, 7, 4, 3, 7962402076597398958712882641542285024886259712000000⟩ +] + +def collectedFourData_10_3_10 : List CollectedFourTerm := [ + ⟨1, 6, 3, 0, 6, 4, -3208677178447063475818341603580998767456896942080000⟩, + ⟨1, 6, 4, 0, 7, 4, 46031469357557177333696345540067082359835962900480000⟩, + ⟨1, 6, 5, 0, 8, 4, 2169636753635024012359364257116405271801469337600000⟩, + ⟨1, 6, 3, 1, 5, 4, 43016899107342116163212742009355668870489220055040000⟩, + ⟨1, 6, 4, 1, 6, 4, 103135087558376567183336495763877292138351736913920000⟩, + ⟨1, 6, 5, 1, 7, 4, -17208553111154295258935341157075871776721233510400000⟩, + ⟨1, 6, 6, 1, 8, 4, -3137626494278627341963770600800964419113294233600000⟩, + ⟨1, 6, 3, 2, 4, 4, -56017247171809354020457171982866320046506356244480000⟩, + ⟨1, 6, 4, 2, 5, 4, -13087302108555572236825956613011763100453814927360000⟩, + ⟨1, 6, 5, 2, 6, 4, -12027883849597086277274291386323539628249002803200000⟩, + ⟨1, 6, 6, 2, 7, 4, -4198503125595851097774890071583630536957388390400000⟩, + ⟨1, 6, 7, 2, 8, 4, -4922542092889397956258274366102098549183768166400000⟩, + ⟨1, 6, 3, 3, 3, 4, 74874993126236096052233431173833399701195708170240000⟩, + ⟨1, 6, 4, 3, 4, 4, 8979196493903090756996940782218186199934550671360000⟩, + ⟨1, 6, 5, 3, 5, 4, 4544853307021709971686843742344616244768931840000000⟩, + ⟨1, 6, 6, 3, 6, 4, 11124805688794233614242718037319143408119945625600000⟩, + ⟨1, 6, 7, 3, 7, 4, 2748644701379515323081713504088041098338474393600000⟩, + ⟨1, 6, 8, 3, 8, 4, 2487604317938115037956005972522660693048033280000000⟩, + ⟨1, 6, 3, 4, 2, 4, -102500469094444042201116123635664536754230132736000000⟩, + ⟨1, 6, 4, 4, 3, 4, 20069811682519602708417740727679706294020944691200000⟩, + ⟨1, 6, 5, 4, 4, 4, -16373324076521711354112022543178793404354632089600000⟩, + ⟨1, 6, 6, 4, 5, 4, -8850909382929606797327294794993347866472638054400000⟩, + ⟨1, 6, 7, 4, 6, 4, -902724572961635753387291133496108470163734528000000⟩, + ⟨1, 6, 8, 4, 7, 4, 883662880371383719041211707812987526396940124160000⟩, + ⟨1, 6, 3, 5, 1, 4, 85118676676611323670251427454557148720215380459520000⟩, + ⟨1, 6, 4, 5, 2, 4, -137511555906136197677391643633510912041897657630720000⟩, + ⟨1, 6, 5, 5, 3, 4, 42702570466799437729788040611694437690326070067200000⟩, + ⟨1, 6, 6, 5, 4, 4, -9982773449557686915799326630938925884142885273600000⟩, + ⟨1, 6, 7, 5, 5, 4, -2390813586270749566754538784465860643688703590400000⟩, + ⟨1, 6, 8, 5, 6, 4, 1840018040260205815190589058377687496749471498240000⟩, + ⟨1, 6, 3, 6, 0, 4, 46355674807469485313820534496676792642654510776320000⟩, + ⟨1, 6, 4, 6, 1, 4, 73789541025582223370834884515283399087763415367680000⟩, + ⟨1, 6, 5, 6, 2, 4, 631994823248131737776830843371052215260990668800000⟩, + ⟨1, 6, 6, 6, 3, 4, 36964106593754923888502135422399932803495598489600000⟩, + ⟨1, 6, 7, 6, 4, 4, 855876788597845601835733187682464853215988940800000⟩, + ⟨1, 6, 8, 6, 5, 4, -1931016846153199524250822701990960274000136110080000⟩, + ⟨1, 6, 4, 7, 0, 4, 1407995389298126466623597920441734233139209369026560000⟩, + ⟨1, 6, 5, 7, 1, 4, -29461424066690166464911694569177642471983258009600000⟩, + ⟨1, 6, 6, 7, 2, 4, -36479046058430725216974416061292791958669256294400000⟩, + ⟨1, 6, 7, 7, 3, 4, 35860863997924660052304787384659123176379462451200000⟩, + ⟨1, 6, 8, 7, 4, 4, 3818048499012841981730972540963408299389301555200000⟩ +] + +def collectedFourData_10_3_11 : List CollectedFourTerm := [ + ⟨1, 7, 2, 0, 5, 5, 6670995361985278601957511995033851257189040128000000⟩, + ⟨1, 7, 3, 0, 6, 5, 1070764430400104603533830993639283472758682419200000⟩, + ⟨1, 7, 4, 0, 7, 5, -7680557645094639430790238818322909838282693017600000⟩, + ⟨1, 7, 5, 0, 8, 5, -241342432148888118115638668351352162440183808000000⟩, + ⟨1, 7, 2, 1, 4, 5, -22991882605196031924658129995749099448144651878400000⟩, + ⟨1, 7, 3, 1, 5, 5, -14355126087363063678906224543827239394921257369600000⟩, + ⟨1, 7, 4, 1, 6, 5, -17208553111154295258935341157075871776721233510400000⟩, + ⟨1, 7, 5, 1, 7, 5, 1914216310472741937023302184300092256296108032000000⟩, + ⟨1, 7, 6, 1, 8, 5, 261763544531810780941637925263005419218927616000000⟩, + ⟨1, 7, 2, 2, 3, 5, 8568933458273789704474972964602323215011597516800000⟩, + ⟨1, 7, 3, 2, 4, 5, 18693459149896179014894860881990764913759564595200000⟩, + ⟨1, 7, 4, 2, 5, 5, 2183675204515870495741949957824200569324254003200000⟩, + ⟨1, 7, 5, 2, 6, 5, 1337937669521248871637766253039532152356601856000000⟩, + ⟨1, 7, 6, 2, 7, 5, 350269562641658916285663280835659419378253824000000⟩, + ⟨1, 7, 7, 2, 8, 5, 328539313061356861243537721750561330421773107200000⟩, + ⟨1, 7, 2, 3, 2, 5, 4582058834896630497464691453965878587266433024000000⟩, + ⟨1, 7, 3, 3, 3, 5, -24986458564469338417173533965019273085475985817600000⟩, + ⟨1, 7, 4, 3, 4, 5, -1498219310410347712143565071404426904567231283200000⟩, + ⟨1, 7, 5, 3, 5, 5, -505552806956666928026772611827882186191667200000000⟩, + ⟨1, 7, 6, 3, 6, 5, -928111926208076543531860158528943462218203136000000⟩, + ⟨1, 7, 7, 3, 7, 5, -183449491136988072620163932785607176107117772800000⟩, + ⟨1, 7, 8, 3, 8, 5, -138355988694744858085571476583901625004851200000000⟩, + ⟨1, 7, 2, 4, 1, 5, 10577395635436956473047928391708469627184165683200000⟩, + ⟨1, 7, 3, 4, 2, 5, 34205328333707476379558496832048031767084400640000000⟩, + ⟨1, 7, 4, 4, 3, 5, -3348738324132567226828847728302331454338105344000000⟩, + ⟨1, 7, 5, 4, 4, 5, 1821308497087909857364605444625253546713939968000000⟩, + ⟨1, 7, 6, 4, 5, 5, 738407014547530661252621829491708583072497664000000⟩, + ⟨1, 7, 7, 4, 6, 5, 60249461657795161840605486309564046318239744000000⟩, + ⟨1, 7, 8, 4, 7, 5, -49147708341319235424890991333915728833570406400000⟩, + ⟨1, 7, 2, 5, 0, 5, -78918743765731702797385195514916111717409121894400000⟩, + ⟨1, 7, 3, 5, 1, 5, -28404867887692382165317862097006626143946460364800000⟩, + ⟨1, 7, 4, 5, 2, 5, 22944421430473807573366222021063212819280193126400000⟩, + ⟨1, 7, 5, 5, 3, 5, -4750077264408437032952577494461035384171134976000000⟩, + ⟨1, 7, 6, 5, 4, 5, 832835319047449760747412840195293858041430016000000⟩, + ⟨1, 7, 7, 5, 5, 5, 159567198912482630230791615947349436681892659200000⟩, + ⟨1, 7, 8, 5, 6, 5, -102338427916614041922871862858734588678216089600000⟩, + ⟨1, 7, 3, 6, 0, 5, -15469305564436803732799529802202147110033083596800000⟩, + ⟨1, 7, 4, 6, 1, 5, -12312116718451335663335573161210276100190083481600000⟩, + ⟨1, 7, 5, 6, 2, 5, -70300785370023682552357517734303388248571904000000⟩, + ⟨1, 7, 6, 6, 3, 5, -3083813698053804336960426082503353402419838976000000⟩, + ⟨1, 7, 7, 6, 4, 5, -57122756268000943685205654069455132052317798400000⟩, + ⟨1, 7, 8, 6, 5, 5, 107399614564578177963780755901284716572259123200000⟩, + ⟨1, 7, 4, 7, 0, 5, -234930361825530513816113656979593250199376704307200000⟩, + ⟨1, 7, 5, 7, 1, 5, 3277180720188372703724264763329946350222573568000000⟩, + ⟨1, 7, 6, 7, 2, 5, 3043346432344999237664584672323830057023832064000000⟩, + ⟨1, 7, 7, 7, 3, 5, -2393418563283299948485644640773701177649502617600000⟩, + ⟨1, 7, 8, 7, 4, 5, -212352853368278237548630302149026696824619008000000⟩ +] + +def collectedFourData_10_3_12 : List CollectedFourTerm := [ + ⟨1, 8, 1, 0, 4, 6, -148162107323847065951276968648774306165161984000000⟩, + ⟨1, 8, 2, 0, 5, 6, 3648957292767572064238941888907412916305657856000000⟩, + ⟨1, 8, 3, 0, 6, 6, 292847878399799080474239116990983199364690739200000⟩, + ⟨1, 8, 4, 0, 7, 6, -1400392060995692697154290285220228491156809318400000⟩, + ⟨1, 8, 5, 0, 8, 6, -33002879632563130510600367410677015908450304000000⟩, + ⟨1, 8, 1, 1, 3, 6, 598380889539468812518549160720901295774787174400000⟩, + ⟨1, 8, 2, 1, 4, 6, -12576293814378923143388113953205544649466105036800000⟩, + ⟨1, 8, 3, 1, 5, 6, -3926043954668025126523143739460260977662597529600000⟩, + ⟨1, 8, 4, 1, 6, 6, -3137626494278627341963770600800964419113294233600000⟩, + ⟨1, 8, 5, 1, 7, 6, 261763544531810780941637925263005419218927616000000⟩, + ⟨1, 8, 6, 1, 8, 6, 28636326154356210840937846308808439739344486400000⟩, + ⟨1, 8, 1, 2, 2, 6, 104464311768392742591045162983638359730657689600000⟩, + ⟨1, 8, 2, 2, 3, 6, 4687107476042822856985007318273163772007389593600000⟩, + ⟨1, 8, 3, 2, 4, 6, 5112552954299062540773596339995101557869982515200000⟩, + ⟨1, 8, 4, 2, 5, 6, 398148358687240880187732222864605868918099148800000⟩, + ⟨1, 8, 5, 2, 6, 6, 182959106983066152118411817897604312861769728000000⟩, + ⟨1, 8, 6, 2, 7, 6, 38318679767614856857126579178021374519777689600000⟩, + ⟨1, 8, 7, 2, 8, 6, 29951200615618418869360582771658271136048742400000⟩, + ⟨1, 8, 1, 3, 1, 6, -586255824410148831562882352638252684243107840000000⟩, + ⟨1, 8, 2, 3, 2, 6, 2506333177319190138368090586555507241383886848000000⟩, + ⟨1, 8, 3, 3, 3, 6, -6833651895398840926774996117478413202995386777600000⟩, + ⟨1, 8, 4, 3, 4, 6, -273169543785546276425745224870753717671742668800000⟩, + ⟨1, 8, 5, 3, 5, 6, -69132884289498823125019553086785740970393600000000⟩, + ⟨1, 8, 6, 3, 6, 6, -101533297442846975263424348387442517097211494400000⟩, + ⟨1, 8, 7, 3, 7, 6, -16724124917284717840853946292710521750264217600000⟩, + ⟨1, 8, 8, 3, 8, 6, -10811303615792327058997160318655291142963200000000⟩, + ⟨1, 8, 1, 4, 0, 6, 4690927974995016723323773548169308780331479859200000⟩, + ⟨1, 8, 2, 4, 1, 6, 5785713053011225150900075777029060010365576806400000⟩, + ⟨1, 8, 3, 4, 2, 6, 9354959455229388598307189775317395892223344640000000⟩, + ⟨1, 8, 4, 4, 3, 6, -610573708337747067019671004728745897802858496000000⟩, + ⟨1, 8, 5, 4, 4, 6, 249058669741402412364911031962523038996496384000000⟩, + ⟨1, 8, 6, 4, 5, 6, 80780019009399774709202815056875116356540825600000⟩, + ⟨1, 8, 7, 4, 6, 6, 5492626426593344880170516302031898487554048000000⟩, + ⟨1, 8, 8, 4, 7, 6, -3840461131543296407290207031871513024685670400000⟩, + ⟨1, 8, 2, 5, 0, 6, -43167639905886888204242116413862500805963992268800000⟩, + ⟨1, 8, 3, 5, 1, 6, -7768567073178791573726318176406281046494858444800000⟩, + ⟨1, 8, 4, 5, 2, 6, 4183444366945967531870883084392143706870356377600000⟩, + ⟨1, 8, 5, 5, 3, 6, -649559328655206111750590826625706379379212288000000⟩, + ⟨1, 8, 6, 5, 4, 6, 91110257051901268442055571492327914016761446400000⟩, + ⟨1, 8, 7, 5, 5, 6, 14546901987974584355706303397524573463668326400000⟩, + ⟨1, 8, 8, 5, 6, 6, -7996848030991060287114598481901841039333785600000⟩, + ⟨1, 8, 3, 6, 0, 6, -4230765597219899793056672839617180032373148876800000⟩, + ⟨1, 8, 4, 6, 1, 6, -2244861806041316186082307852965346144592225894400000⟩, + ⟨1, 8, 5, 6, 2, 6, -9613429089047305729145341793994262972465152000000⟩, + ⟨1, 8, 6, 6, 3, 6, -337362083840549280754836633303390602658211430400000⟩, + ⟨1, 8, 7, 6, 4, 6, -5207581146857910200319635439131481397316812800000⟩, + ⟨1, 8, 8, 6, 5, 6, 8392335252206030745231637546650430461915955200000⟩, + ⟨1, 8, 4, 7, 0, 6, -42834730079454358157158076629984386572484398284800000⟩, + ⟨1, 8, 5, 7, 1, 6, 448144985858972174324297007081274674128093184000000⟩, + ⟨1, 8, 6, 7, 2, 6, 332935058597270950370042998368700107656370585600000⟩, + ⟨1, 8, 7, 7, 3, 6, -218195377831862519042018334340963112288727859200000⟩, + ⟨1, 8, 8, 7, 4, 6, -16593507755631293362498962325325892538073088000000⟩ +] + +def collectedFourData_10_3_13 : List CollectedFourTerm := [ + ⟨2, 1, 7, 2, 8, 0, -13575799666729021791439933448034483938166571008000000⟩, + ⟨2, 1, 7, 3, 7, 0, 7580443014361630210730686989804950473452552192000000⟩, + ⟨2, 1, 8, 3, 8, 0, 34302619696437327819955230726096229402411008000000000⟩, + ⟨2, 1, 7, 4, 6, 0, -2489609580883685311895392364986669583208284160000000⟩, + ⟨2, 1, 8, 4, 7, 0, 12185198227329998486681287515867601262792933376000000⟩, + ⟨2, 1, 7, 5, 5, 0, -6593586337146822541564786458486382053229068288000000⟩, + ⟨2, 1, 8, 5, 6, 0, 25372780797367928357162235300478567070526603264000000⟩, + ⟨2, 1, 7, 6, 4, 0, 2360408829858797065251417910997931057035083776000000⟩, + ⟨2, 1, 8, 6, 5, 0, -26627601513374957620807165502812411238692159488000000⟩, + ⟨2, 1, 7, 7, 3, 0, 98900100054985741924449258215397738650705854464000000⟩, + ⟨2, 1, 8, 7, 4, 0, 52648672740987359011434158333796025979602206720000000⟩ +] + +def collectedFourData_10_3_14 : List CollectedFourTerm := [ + ⟨2, 2, 6, 1, 8, 1, 104464311768392742591045162983638359730657689600000⟩, + ⟨2, 2, 6, 2, 7, 1, 139785197592058706905591011158581294131471974400000⟩, + ⟨2, 2, 7, 2, 8, 1, 655565565655846292353573699104553123836434841600000⟩, + ⟨2, 2, 6, 3, 6, 1, -370389902034588453279375256794355477440469401600000⟩, + ⟨2, 2, 7, 3, 7, 1, -366054120908315209503239963700906808593245798400000⟩, + ⟨2, 2, 8, 3, 8, 1, -828224371190596648853903983075706075401420800000000⟩, + ⟨2, 2, 6, 4, 5, 1, 294682671407237429230104672455708167161407078400000⟩, + ⟨2, 2, 7, 4, 6, 1, 120221449433591215853893526368210434373189632000000⟩, + ⟨2, 2, 8, 4, 7, 1, -294207213005114148956792826295610130256468377600000⟩, + ⟨2, 2, 6, 5, 4, 1, 332367016867502633191741336745158221034527129600000⟩, + ⟨2, 2, 7, 5, 5, 1, 318399524368776595667954304575450848719116697600000⟩, + ⟨2, 2, 8, 5, 6, 1, -612616634158686432652156444182521933994550886400000⟩, + ⟨2, 2, 6, 6, 3, 1, -1230685029748226549504507892007994512308279705600000⟩, + ⟨2, 2, 7, 6, 4, 1, -113982438435486328893687351902761550605398835200000⟩, + ⟨2, 2, 8, 6, 5, 1, 642913827424651336039007813414719586837515468800000⟩, + ⟨2, 2, 6, 7, 2, 1, 1214535397189651257937246961531671670096815718400000⟩, + ⟨2, 2, 7, 7, 3, 1, -4775814436541999139278775644581655077981048012800000⟩, + ⟨2, 2, 8, 7, 4, 1, -1271183200024007815056181546178527380973289472000000⟩ +] + +def collectedFourData_10_3_15 : List CollectedFourTerm := [ + ⟨2, 3, 5, 0, 8, 2, -1080362355303015213292202569289664457405051699200000⟩, + ⟨2, 3, 5, 1, 7, 2, 8568933458273789704474972964602323215011597516800000⟩, + ⟨2, 3, 6, 1, 8, 2, 4687107476042822856985007318273163772007389593600000⟩, + ⟨2, 3, 5, 2, 6, 2, 5989238937481483187584677230341441047121782374400000⟩, + ⟨2, 3, 6, 2, 7, 2, 6271885906131041751311991745702308095984035430400000⟩, + ⟨2, 3, 7, 2, 8, 2, 14706966483607528734823875563189982174487825612800000⟩, + ⟨2, 3, 5, 3, 5, 2, -2263092388647213474987094402114861430766305280000000⟩, + ⟨2, 3, 6, 3, 6, 2, -16618663823929567963978891547956456444307020185600000⟩, + ⟨2, 3, 7, 3, 7, 2, -8212062941407178191886401766045260570707571507200000⟩, + ⟨2, 3, 8, 3, 8, 2, -12386930925127874628902857371613666075056537600000000⟩, + ⟨2, 3, 5, 4, 4, 2, 8153034342644724728876465856433924146979877683200000⟩, + ⟨2, 3, 6, 4, 5, 2, 13221829817587894427759696643123086525217531494400000⟩, + ⟨2, 3, 7, 4, 6, 2, 2697049570719434248669504174511488415255494656000000⟩, + ⟨2, 3, 8, 4, 7, 2, -4400165645850181637012475369923791831671452467200000⟩, + ⟨2, 3, 5, 5, 3, 2, -21263582270032431104518061161144573891898140262400000⟩, + ⟨2, 3, 6, 5, 4, 2, 14912652016543228973338226748378061483816884633600000⟩, + ⟨2, 3, 7, 5, 5, 2, 7142979098671053026083289989285394524301741260800000⟩, + ⟨2, 3, 8, 5, 6, 2, -9162299728030677366763943018378474245461953740800000⟩, + ⟨2, 3, 5, 6, 2, 2, -314699414378800724037583489025781402204477849600000⟩, + ⟨2, 3, 6, 6, 3, 2, -55218408142829491620026164476919418893505239449600000⟩, + ⟨2, 3, 7, 6, 4, 2, -2557083516297110968690258118632805867267398041600000⟩, + ⟨2, 3, 8, 6, 5, 2, 9615424814981774258584815253009430738133162393600000⟩, + ⟨2, 3, 5, 7, 1, 2, 14670203867971807570345325706424737646649750323200000⟩, + ⟨2, 3, 6, 7, 2, 2, 54493806006279107370347592539063952281440773734400000⟩, + ⟨2, 3, 7, 7, 3, 2, -107140683601775721952573612370506909228269463142400000⟩, + ⟨2, 3, 8, 7, 4, 2, -19011827035764448309291489954598017167035203584000000⟩ +] + +def collectedFourData_10_3_16 : List CollectedFourTerm := [ + ⟨2, 4, 4, 0, 7, 3, -25001735662699013394886274677938411189436541829120000⟩, + ⟨2, 4, 5, 0, 8, 3, -2356852186364271171110358116432408321110887628800000⟩, + ⟨2, 4, 4, 1, 6, 3, -56017247171809354020457171982866320046506356244480000⟩, + ⟨2, 4, 5, 1, 7, 3, 18693459149896179014894860881990764913759564595200000⟩, + ⟨2, 4, 6, 1, 8, 3, 5112552954299062540773596339995101557869982515200000⟩, + ⟨2, 4, 4, 2, 5, 3, 7108295095130853097673810608032462271971946659840000⟩, + ⟨2, 4, 5, 2, 6, 3, 13065755961574702626024863293831232317975796121600000⟩, + ⟨2, 4, 6, 2, 7, 3, 6841180617750347368414939357481243338125135052800000⟩, + ⟨2, 4, 7, 2, 8, 3, 10694605052812605352127536432231699255044499046400000⟩, + ⟨2, 4, 4, 3, 4, 3, -4877000459407287876365122039375420274998341795840000⟩, + ⟨2, 4, 5, 3, 5, 3, -4937023414363167784704599840670843001550929920000000⟩, + ⟨2, 4, 6, 3, 6, 3, -18127128354493446862996006654179554102575575859200000⟩, + ⟨2, 4, 7, 3, 7, 3, -5971644113358003413707880304838971098549295513600000⟩, + ⟨2, 4, 8, 3, 8, 3, -6755642005186904691508153492381181717092761600000000⟩, + ⟨2, 4, 4, 4, 3, 3, -10900806198230218230645375261806671568225225932800000⟩, + ⟨2, 4, 5, 4, 4, 3, 17786159173026471337253543076169669412960128204800000⟩, + ⟨2, 4, 6, 4, 5, 3, 14421966093301256964552447521748140828436253900800000⟩, + ⟨2, 4, 7, 4, 6, 3, 1961239253441672544280336951768072789193392128000000⟩, + ⟨2, 4, 8, 4, 7, 3, -2399782807102315480991339954655052682132402995200000⟩, + ⟨2, 4, 4, 5, 2, 3, 74688634086959452338734783953110055079911285063680000⟩, + ⟨2, 4, 5, 5, 3, 3, -46387325620029052371299989992103019006691744153600000⟩, + ⟨2, 4, 6, 5, 4, 3, 16266263044597484263456506179178449839540351795200000⟩, + ⟨2, 4, 7, 5, 5, 3, 5194228221430198408977601185192740317131335270400000⟩, + ⟨2, 4, 8, 5, 6, 3, -4996977643690025670330712697494398813206269132800000⟩, + ⟨2, 4, 4, 6, 1, 3, -40078377361000135030001289268087942029762279505920000⟩, + ⟨2, 4, 5, 6, 2, 3, -686528921695169150068306006749001079413171814400000⟩, + ⟨2, 4, 6, 6, 3, 3, -60230544557654833844742304331128884536664077107200000⟩, + ⟨2, 4, 7, 6, 4, 3, -1859458803032972982391466098629253157293444300800000⟩, + ⟨2, 4, 8, 6, 5, 3, 5244105111301959367667338999084793360167836057600000⟩, + ⟨2, 4, 4, 7, 0, 3, -764744837148055038527032846473574272778430463344640000⟩, + ⟨2, 4, 5, 7, 1, 3, 32003616093177700407154151429631879429493673164800000⟩, + ⟨2, 4, 6, 7, 2, 3, 59440170790283975788759641149351626222569573580800000⟩, + ⟨2, 4, 7, 7, 3, 3, -77910512510278249608457879954637130559862813491200000⟩, + ⟨2, 4, 8, 7, 4, 3, -10368758661406069218474806223312652029860511744000000⟩ +] + +def collectedFourData_10_3_17 : List CollectedFourTerm := [ + ⟨2, 5, 3, 0, 6, 4, 407164318151138842807129738632462796568804720640000⟩, + ⟨2, 5, 4, 0, 7, 4, -5841152223214847651712911324067732340583788707840000⟩, + ⟨2, 5, 5, 0, 8, 4, -275315533567325868822179555458572315599359180800000⟩, + ⟨2, 5, 3, 1, 5, 4, -5458619056995373644196949059497214636812738232320000⟩, + ⟨2, 5, 4, 1, 6, 4, -13087302108555572236825956613011763100453814927360000⟩, + ⟨2, 5, 5, 1, 7, 4, 2183675204515870495741949957824200569324254003200000⟩, + ⟨2, 5, 6, 1, 8, 4, 398148358687240880187732222864605868918099148800000⟩, + ⟨2, 5, 3, 2, 4, 4, 7108295095130853097673810608032462271971946659840000⟩, + ⟨2, 5, 4, 2, 5, 4, 1660710050628081109972331819389446286633473146880000⟩, + ⟨2, 5, 5, 2, 6, 4, 1526275425685703137586577400378223508078565785600000⟩, + ⟨2, 5, 6, 2, 7, 4, 532768043439014613914194013062022605416117043200000⟩, + ⟨2, 5, 7, 2, 8, 4, 624644793899654747744328237006212144573920051200000⟩, + ⟨2, 5, 3, 3, 3, 4, -9501244228492302538199593280267849332686764113920000⟩, + ⟨2, 5, 4, 3, 4, 4, -1139412977579310269723238657842409966563890298880000⟩, + ⟨2, 5, 5, 3, 5, 4, -576718066336000049321161697387498189849886720000000⟩, + ⟨2, 5, 6, 3, 6, 4, -1411679539863858584872937935840654749571271884800000⟩, + ⟨2, 5, 7, 3, 7, 4, -348788607714839534990680188926351440838708428800000⟩, + ⟨2, 5, 8, 3, 8, 4, -315663951096915113360197735345926074259210240000000⟩, + ⟨2, 5, 3, 4, 2, 4, 13006772351343203732392896646597637345208434688000000⟩, + ⟨2, 5, 4, 4, 3, 4, -2546753922153615296155199284169921092617083289600000⟩, + ⟨2, 5, 5, 4, 4, 4, 2077689017226440595143796987574227197741550796800000⟩, + ⟨2, 5, 6, 4, 5, 4, 1123134015514208328620800426684730778022261555200000⟩, + ⟨2, 5, 7, 4, 6, 4, 114551017377850665485633781406810693775130624000000⟩, + ⟨2, 5, 8, 4, 7, 4, -112132188485231161486242780152257457826331361280000⟩, + ⟨2, 5, 3, 5, 1, 4, -10801113986709357548789860969080095219017486172160000⟩, + ⟨2, 5, 4, 5, 2, 4, 17449495784278963740020234633540131248364333301760000⟩, + ⟨2, 5, 5, 5, 3, 4, -5418732399820383068178332289997047415887731097600000⟩, + ⟨2, 5, 6, 5, 4, 4, 1266761633781323003154804871347271216145419468800000⟩, + ⟨2, 5, 7, 5, 5, 4, 303381714501906126533986356911037536747598643200000⟩, + ⟨2, 5, 8, 5, 6, 4, -233488646280999351708661521702402391512365137920000⟩, + ⟨2, 5, 3, 6, 0, 4, -5882292195737205242387873824383927656743761346560000⟩, + ⟨2, 5, 4, 6, 1, 4, -9363506045474977606191978018783814453934099005440000⟩, + ⟨2, 5, 5, 6, 2, 4, -80196830959297581301772742266719808950527590400000⟩, + ⟨2, 5, 6, 6, 3, 4, -4690551408040483380843306054473034036084001996800000⟩, + ⟨2, 5, 7, 6, 4, 4, -108606279058427082296949435285972999194699366400000⟩, + ⟨2, 5, 8, 6, 5, 4, 245035917849129118667670862822133018579844464640000⟩, + ⟨2, 5, 4, 7, 0, 4, -178667235985696084176847912678336546835251310100480000⟩, + ⟨2, 5, 5, 7, 1, 4, 3738500314849718653054612595251920040987774156800000⟩, + ⟨2, 5, 6, 7, 2, 4, 4628999768176578611633294839131944653564359475200000⟩, + ⟨2, 5, 7, 7, 3, 4, -4550555704420362185206269872163823224408873369600000⟩, + ⟨2, 5, 8, 7, 4, 4, -484490345183595460140538063208829143410645401600000⟩ +] + +def collectedFourData_10_3_18 : List CollectedFourTerm := [ + ⟨2, 6, 2, 0, 5, 5, 4662678893273769994379737596261845026077671424000000⟩, + ⟨2, 6, 3, 0, 6, 5, 748408661433858162797115735568779819397781913600000⟩, + ⟨2, 6, 4, 0, 7, 5, -5368310436015304715702216455595588736999279820800000⟩, + ⟨2, 6, 5, 0, 8, 5, -168685811242580334598753792033931223172644864000000⟩, + ⟨2, 6, 2, 1, 4, 5, -16070130456210089708214417331465546828252132147200000⟩, + ⟨2, 6, 3, 1, 5, 5, -10033486726621282994015279745080199749489708236800000⟩, + ⟨2, 6, 4, 1, 6, 5, -12027883849597086277274291386323539628249002803200000⟩, + ⟨2, 6, 5, 1, 7, 5, 1337937669521248871637766253039532152356601856000000⟩, + ⟨2, 6, 6, 1, 8, 5, 182959106983066152118411817897604312861769728000000⟩, + ⟨2, 6, 2, 2, 3, 5, 5989238937481483187584677230341441047121782374400000⟩, + ⟨2, 6, 3, 2, 4, 5, 13065755961574702626024863293831232317975796121600000⟩, + ⟨2, 6, 4, 2, 5, 5, 1526275425685703137586577400378223508078565785600000⟩, + ⟨2, 6, 5, 2, 6, 5, 935148863652648783793527325916836411786395648000000⟩, + ⟨2, 6, 6, 2, 7, 5, 244820211687189858887404446266888088339873792000000⟩, + ⟨2, 6, 7, 2, 8, 5, 229631897115570586318149137725769006341265817600000⟩, + ⟨2, 6, 2, 3, 2, 5, 3202620877081981118537718191771984520535867392000000⟩, + ⟨2, 6, 3, 3, 3, 5, -17464235341866499796281628109942988942984662220800000⟩, + ⟨2, 6, 4, 3, 4, 5, -1047177396637639403244168363187904109352688025600000⟩, + ⟨2, 6, 5, 3, 5, 5, -353355125363278812231858383238442912422297600000000⟩, + ⟨2, 6, 6, 3, 6, 5, -648701978356376351279268996016718972492709888000000⟩, + ⟨2, 6, 7, 3, 7, 5, -128221655673838171375896983342841702008645222400000⟩, + ⟨2, 6, 8, 3, 8, 5, -96703642146293970226782442560489678018969600000000⟩, + ⟨2, 6, 2, 4, 1, 5, 7393049567415788191060041576429762100546083225600000⟩, + ⟨2, 6, 3, 4, 2, 5, 23907745966654902096694554526412063798061957120000000⟩, + ⟨2, 6, 4, 4, 3, 5, -2340593967731850842511532142559718731732221952000000⟩, + ⟨2, 6, 5, 4, 4, 5, 1272999938795446761583160348458995099730182144000000⟩, + ⟨2, 6, 6, 4, 5, 5, 516108108993115902667151708065661657926336512000000⟩, + ⟨2, 6, 7, 4, 6, 5, 42111240970688703823377004765862259591217152000000⟩, + ⟨2, 6, 8, 4, 7, 5, -34351692648703435205271221131698983645950771200000⟩, + ⟨2, 6, 2, 5, 0, 5, -55160098437041930165963716223779713435550561075200000⟩, + ⟨2, 6, 3, 5, 1, 5, -19853525715352676477500216674356886459675731558400000⟩, + ⟨2, 6, 4, 5, 2, 5, 16036957562868212667694378895853681213168628531200000⟩, + ⟨2, 6, 5, 5, 3, 5, -3320057023032555361504951636869666269307076608000000⟩, + ⟨2, 6, 6, 5, 4, 5, 582108583948980961335885131442826354442108928000000⟩, + ⟨2, 6, 7, 5, 5, 5, 111529175191426537036923815434156856011495833600000⟩, + ⟨2, 6, 8, 5, 6, 5, -71529239929738158098488073635890233539873996800000⟩, + ⟨2, 6, 3, 6, 0, 5, -10812240248273333934776033167663879953091815014400000⟩, + ⟨2, 6, 4, 6, 1, 5, -8605529405968853976495633676227522272923798732800000⟩, + ⟨2, 6, 5, 6, 2, 5, -49136593617392208361686145358855938278162432000000⟩, + ⟨2, 6, 6, 6, 3, 5, -2155425429110909220682265631639027995123908608000000⟩, + ⟨2, 6, 7, 6, 4, 5, -39925836479245585813154405944071984268915507200000⟩, + ⟨2, 6, 8, 6, 5, 5, 75066746235447605332473211676244720196622745600000⟩, + ⟨2, 6, 4, 7, 0, 5, -164204107488253455805803827325882945429304875417600000⟩, + ⟨2, 6, 5, 7, 1, 5, 2290578923280591341100256964406794294283730944000000⟩, + ⟨2, 6, 6, 7, 2, 5, 2127140914514455611059599432957177837714931712000000⟩, + ⟨2, 6, 7, 7, 3, 5, -1672875127658543363328464954040604786175036620800000⟩, + ⟨2, 6, 8, 7, 4, 5, -148423603015677787902093786766659506839486464000000⟩ +] + +def collectedFourData_10_3_19 : List CollectedFourTerm := [ + ⟨2, 7, 1, 0, 4, 6, -198257846122968067666810047619553801143320576000000⟩, + ⟨2, 7, 2, 0, 5, 6, 4882722219099787632512236702580313038398685184000000⟩, + ⟨2, 7, 3, 0, 6, 6, 391863956728970097705322428928762746795510988800000⟩, + ⟨2, 7, 4, 0, 7, 6, -1873884752015966378374430740985635562919139737600000⟩, + ⟨2, 7, 5, 0, 8, 6, -44161627760233758501564461231489622585901056000000⟩, + ⟨2, 7, 1, 1, 3, 6, 800702071967265852677253833223395095034304921600000⟩, + ⟨2, 7, 2, 1, 4, 6, -16828519578211080578549204818231542068527969075200000⟩, + ⟨2, 7, 3, 1, 5, 6, -5253495865412153752227305664414668056433157734400000⟩, + ⟨2, 7, 4, 1, 6, 6, -4198503125595851097774890071583630536957388390400000⟩, + ⟨2, 7, 5, 1, 7, 6, 350269562641658916285663280835659419378253824000000⟩, + ⟨2, 7, 6, 1, 8, 6, 38318679767614856857126579178021374519777689600000⟩, + ⟨2, 7, 1, 2, 2, 6, 139785197592058706905591011158581294131471974400000⟩, + ⟨2, 7, 2, 2, 3, 6, 6271885906131041751311991745702308095984035430400000⟩, + ⟨2, 7, 3, 2, 4, 6, 6841180617750347368414939357481243338125135052800000⟩, + ⟨2, 7, 4, 2, 5, 6, 532768043439014613914194013062022605416117043200000⟩, + ⟨2, 7, 5, 2, 6, 6, 244820211687189858887404446266888088339873792000000⟩, + ⟨2, 7, 6, 2, 7, 6, 51274776352889542840180705791679305083151974400000⟩, + ⟨2, 7, 7, 2, 8, 6, 40078132189833379114160318066588533499992473600000⟩, + ⟨2, 7, 1, 3, 1, 6, -784477347980414360079979548489061075003637760000000⟩, + ⟨2, 7, 2, 3, 2, 6, 3353760461274569710015571988057668604471017472000000⟩, + ⟨2, 7, 3, 3, 3, 6, -9144207857239689475448652307821775304970888806400000⟩, + ⟨2, 7, 4, 3, 4, 6, -365532094241476502565488507142156382511510323200000⟩, + ⟨2, 7, 5, 3, 5, 6, -92507706478189223947596051406086157526630400000000⟩, + ⟨2, 7, 6, 3, 6, 6, -135863165180167256930797359903003409835989401600000⟩, + ⟨2, 7, 7, 3, 7, 6, -22378792015592917550495521452614718939620966400000⟩, + ⟨2, 7, 8, 3, 8, 6, -14466760815998826316349224261782355102924800000000⟩, + ⟨2, 7, 1, 4, 0, 6, 6276998170711090011585414997420676174534462668800000⟩, + ⟨2, 7, 2, 4, 1, 6, 7741945824706318642978153194305564264208374169600000⟩, + ⟨2, 7, 3, 4, 2, 6, 12518005755058234096059703202130205481065512960000000⟩, + ⟨2, 7, 4, 4, 3, 6, -817017458112730108797729643292436355973382144000000⟩, + ⟨2, 7, 5, 4, 4, 6, 333268987010652454021077484060007646338482176000000⟩, + ⟨2, 7, 6, 4, 5, 6, 108092904912390627816718495164584196621887078400000⟩, + ⟨2, 7, 7, 4, 6, 6, 7349762395821573627092989463219526300598272000000⟩, + ⟨2, 7, 8, 4, 7, 6, -5138976259257087253696983086424884034247065600000⟩, + ⟨2, 7, 2, 5, 0, 6, -57763239633508740293677910190834451630819324723200000⟩, + ⟨2, 7, 3, 5, 1, 6, -10395231299078192210963753969613721431071470387200000⟩, + ⟨2, 7, 4, 5, 2, 6, 5597927058050672417142601264018597796460783206400000⟩, + ⟨2, 7, 5, 5, 3, 6, -869184677204809110866676046043572157527621632000000⟩, + ⟨2, 7, 6, 5, 4, 6, 121915944967884311133356668151726049391647129600000⟩, + ⟨2, 7, 7, 5, 5, 6, 19465418709211152677629085335490468647639449600000⟩, + ⟨2, 7, 8, 5, 6, 6, -10700697331009178840144358026737997828220518400000⟩, + ⟨2, 7, 3, 6, 0, 6, -5661248276677054461199200106100629196237910835200000⟩, + ⟨2, 7, 4, 6, 1, 6, -3003881859864945938869591308146832302178671001600000⟩, + ⟨2, 7, 5, 6, 2, 6, -12863867688412935549154274009999037356310528000000⟩, + ⟨2, 7, 6, 6, 3, 6, -451429055065945413728221391417070252652599705600000⟩, + ⟨2, 7, 7, 6, 4, 6, -6968339208553162165686818590692710284473139200000⟩, + ⟨2, 7, 8, 6, 5, 6, 11229904468134028628635020073160913927851212800000⟩, + ⟨2, 7, 4, 7, 0, 6, -57317768208096168809095369426987536156099556147200000⟩, + ⟨2, 7, 5, 7, 1, 6, 599669249121887009421314935629499857031397376000000⟩, + ⟨2, 7, 6, 7, 2, 6, 445505188935005848764753762417748843365295718400000⟩, + ⟨2, 7, 7, 7, 3, 6, -291970372346139278042388623035644646217534668800000⟩, + ⟨2, 7, 8, 7, 4, 6, -22204011313537288319808636964409388231032832000000⟩ +] + +def collectedFourData_10_3_20 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 3, 7, 33594811991758933568905936798481115232605516595200000⟩, + ⟨2, 8, 1, 0, 4, 7, -929790988446526592902270314628075515820376064000000⟩, + ⟨2, 8, 2, 0, 5, 7, 11449511853343651865709169655076996485153292288000000⟩, + ⟨2, 8, 3, 0, 6, 7, 612588745395074166800397765302449152652109414400000⟩, + ⟨2, 8, 4, 0, 7, 7, -2197039347854027693509940321225759618825296281600000⟩, + ⟨2, 8, 5, 0, 8, 7, -41421900146264536242918715587732181086948556800000⟩, + ⟨2, 8, 0, 1, 2, 7, -13140689032699289464156826665601664014690864332800000⟩, + ⟨2, 8, 1, 1, 3, 7, 3755137995819161304600665644640666943878489702400000⟩, + ⟨2, 8, 2, 1, 4, 7, -39461252501985867078274599242519954171831412326400000⟩, + ⟨2, 8, 3, 1, 5, 7, -8212626820784408404932362965705803718812971827200000⟩, + ⟨2, 8, 4, 1, 6, 7, -4922542092889397956258274366102098549183768166400000⟩, + ⟨2, 8, 5, 1, 7, 7, 328539313061356861243537721750561330421773107200000⟩, + ⟨2, 8, 6, 1, 8, 7, 29951200615618418869360582771658271136048742400000⟩, + ⟨2, 8, 0, 2, 1, 7, -13575799666729021791439933448034483938166571008000000⟩, + ⟨2, 8, 1, 2, 2, 7, 655565565655846292353573699104553123836434841600000⟩, + ⟨2, 8, 2, 2, 3, 7, 14706966483607528734823875563189982174487825612800000⟩, + ⟨2, 8, 3, 2, 4, 7, 10694605052812605352127536432231699255044499046400000⟩, + ⟨2, 8, 4, 2, 5, 7, 624644793899654747744328237006212144573920051200000⟩, + ⟨2, 8, 5, 2, 6, 7, 229631897115570586318149137725769006341265817600000⟩, + ⟨2, 8, 6, 2, 7, 7, 40078132189833379114160318066588533499992473600000⟩, + ⟨2, 8, 7, 2, 8, 7, 26851242224346870664202068440629321512727347200000⟩, + ⟨2, 8, 0, 3, 0, 7, 75858228979172544352508066054612146845339824947200000⟩, + ⟨2, 8, 1, 3, 1, 7, -3679047175465701104655411024886193948605808640000000⟩, + ⟨2, 8, 2, 3, 2, 7, 7864244253837145247268539201033068487381090304000000⟩, + ⟨2, 8, 3, 3, 3, 7, -14294855963934887370683036914059123079483962163200000⟩, + ⟨2, 8, 4, 3, 4, 7, -428568722322987255131459575244929180883956531200000⟩, + ⟨2, 8, 5, 3, 5, 7, -86768653576441904502854497877752494025605120000000⟩, + ⟨2, 8, 6, 3, 6, 7, -106195331918069982720508054981774502412052070400000⟩, + ⟨2, 8, 7, 3, 7, 7, -14993172891709635741047961848479215279459532800000⟩, + ⟨2, 8, 8, 3, 8, 7, -8480789097234579536139313888978679522918400000000⟩, + ⟨2, 8, 1, 4, 0, 7, 29437908500239536178676746245867992716225491763200000⟩, + ⟨2, 8, 2, 4, 1, 7, 18154114960949375588745686148890191516241441587200000⟩, + ⟨2, 8, 3, 4, 2, 7, 19569009368328377334293363297642165677043220480000000⟩, + ⟨2, 8, 4, 4, 3, 7, -957913501044408699325347505837894437389205504000000⟩, + ⟨2, 8, 5, 4, 4, 7, 312593430132406590047517883497318451178687692800000⟩, + ⟨2, 8, 6, 4, 5, 7, 84489139495149576149927167037420436434033049600000⟩, + ⟨2, 8, 7, 4, 6, 7, 4924137917576480754945917654818021435244544000000⟩, + ⟨2, 8, 8, 4, 7, 7, -3012600704800260064550725107746210635893964800000⟩, + ⟨2, 8, 2, 5, 0, 7, -135449216071382656397563006125559205418796213862400000⟩, + ⟨2, 8, 3, 5, 1, 7, -16250542031856988538227682110918247378901899673600000⟩, + ⟨2, 8, 4, 5, 2, 7, 6563299050127108904547467364847832059024402022400000⟩, + ⟨2, 8, 5, 5, 3, 7, -815261636262888555531472371125450366726543769600000⟩, + ⟨2, 8, 6, 5, 4, 7, 95293703961635392749686428611657519356864102400000⟩, + ⟨2, 8, 7, 5, 5, 7, 13041293199086457103958841041560361667605299200000⟩, + ⟨2, 8, 8, 5, 6, 7, -6273025344918177230060519243740279280448307200000⟩, + ⟨2, 8, 3, 6, 0, 7, -8850053493381764738967747965499417465902963097600000⟩, + ⟨2, 8, 4, 6, 1, 7, -3521906368749828292747846213759007665092663705600000⟩, + ⟨2, 8, 5, 6, 2, 7, -12065810748126711054883810345795909056882278400000⟩, + ⟨2, 8, 6, 6, 3, 7, -352852506244914113927972889598836225937401446400000⟩, + ⟨2, 8, 7, 6, 4, 7, -4668594911160514532985014706341676893759078400000⟩, + ⟨2, 8, 8, 6, 5, 7, 6583260246551703711692692763516409838200422400000⟩, + ⟨2, 8, 4, 7, 0, 7, -67202314309290537754231568787725725012669444915200000⟩, + ⟨2, 8, 5, 7, 1, 7, 562466580552074170022643218678788372554370252800000⟩, + ⟨2, 8, 6, 7, 2, 7, 348222208333194538977434809977883654503373209600000⟩, + ⟨2, 8, 7, 7, 3, 7, -195612089731757680062977726275501140074928537600000⟩, + ⟨2, 8, 8, 7, 4, 7, -13016565315331025743132743229588398938259456000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1011.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1011.lean new file mode 100644 index 0000000000000000000000000000000000000000..cbfacf6b9caf622ac4b56e33d98c9a29efde07a9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1011.lean @@ -0,0 +1,613 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1011. -/ +namespace LaughlinFock +def collectedFourData_10_3_21 : List CollectedFourTerm := [ + ⟨3, 0, 7, 2, 8, 0, 75858228979172544352508066054612146845339824947200000⟩, + ⟨3, 0, 7, 3, 7, 0, -42357650824525200546200168178203149581075401932800000⟩, + ⟨3, 0, 8, 3, 8, 0, -191674600642127805457573931710934814511280947200000000⟩, + ⟨3, 0, 7, 4, 6, 0, 13911325910197379447092549885199051162117996544000000⟩, + ⟨3, 0, 8, 4, 7, 0, -68087890214729458606980160945652105796531938918400000⟩, + ⟨3, 0, 7, 5, 5, 0, 36843338472579346868040453063706692947289518899200000⟩, + ⟨3, 0, 8, 5, 6, 0, -141776857556475525939154281259800021259609807257600000⟩, + ⟨3, 0, 7, 6, 4, 0, -13189383896015573905027841731744905485613426278400000⟩, + ⟨3, 0, 8, 6, 5, 0, 148788487039779867887319887745645098807160156979200000⟩, + ⟨3, 0, 7, 7, 3, 0, -552629430325250400458723039083877533461425789337600000⟩, + ⟨3, 0, 8, 7, 4, 0, -294187832045227937384982317694364274789500059648000000⟩ +] + +def collectedFourData_10_3_22 : List CollectedFourTerm := [ + ⟨3, 1, 6, 1, 8, 1, -586255824410148831562882352638252684243107840000000⟩, + ⟨3, 1, 6, 2, 7, 1, -784477347980414360079979548489061075003637760000000⟩, + ⟨3, 1, 7, 2, 8, 1, -3679047175465701104655411024886193948605808640000000⟩, + ⟨3, 1, 6, 3, 6, 1, 2078635599992359172261721020707162234174832640000000⟩, + ⟨3, 1, 7, 3, 7, 1, 2054303108870598224114920102311949904495247360000000⟩, + ⟨3, 1, 8, 3, 8, 1, 4648011874193300005913756959521070456504320000000000⟩, + ⟨3, 1, 6, 4, 5, 1, -1653765094899193611926588776810803990217359360000000⟩, + ⟨3, 1, 7, 4, 6, 1, -674685198766589560694327469600862144089292800000000⟩, + ⟨3, 1, 8, 4, 7, 1, 1651096812757752722112721841553545127568343040000000⟩, + ⟨3, 1, 6, 5, 4, 1, -1865250401614717268814035688118509377515683840000000⟩, + ⟨3, 1, 7, 5, 5, 1, -1786864552024879023862479621839385424602071040000000⟩, + ⟨3, 1, 8, 5, 6, 1, 3438016905738496841792208796492960671266242560000000⟩, + ⟨3, 1, 6, 6, 3, 1, 6906629206574399721953759691422625196922634240000000⟩, + ⟨3, 1, 7, 6, 4, 1, 639671743221050368079189097698437976115118080000000⟩, + ⟨3, 1, 8, 6, 5, 1, -3608045365360493770488098732381438056354283520000000⟩, + ⟨3, 1, 6, 7, 2, 1, -6815997142960755452370627567740941923369615360000000⟩, + ⟨3, 1, 7, 7, 3, 1, 26801966933284834934801583858367049946491781120000000⟩, + ⟨3, 1, 8, 7, 4, 1, 7133905754901924516548849647114995702222028800000000⟩ +] + +def collectedFourData_10_3_23 : List CollectedFourTerm := [ + ⟨3, 2, 5, 0, 8, 2, -577701285593031941679721595974608392716025856000000⟩, + ⟨3, 2, 5, 1, 7, 2, 4582058834896630497464691453965878587266433024000000⟩, + ⟨3, 2, 6, 1, 8, 2, 2506333177319190138368090586555507241383886848000000⟩, + ⟨3, 2, 5, 2, 6, 2, 3202620877081981118537718191771984520535867392000000⟩, + ⟨3, 2, 6, 2, 7, 2, 3353760461274569710015571988057668604471017472000000⟩, + ⟨3, 2, 7, 2, 8, 2, 7864244253837145247268539201033068487381090304000000⟩, + ⟨3, 2, 5, 3, 5, 2, -1210141556598951846783690009828207645582950400000000⟩, + ⟨3, 2, 6, 3, 6, 2, -8886484621384075905668116546675756939144593408000000⟩, + ⟨3, 2, 7, 3, 7, 2, -4391229752994505959805346355398234999982391296000000⟩, + ⟨3, 2, 8, 3, 8, 2, -6623653522240128290662266899669556834336768000000000⟩, + ⟨3, 2, 5, 4, 4, 2, 4359665438276912757184270930938354659519102976000000⟩, + ⟨3, 2, 6, 4, 5, 2, 7070098329528024203810142308457221773162708992000000⟩, + ⟨3, 2, 7, 4, 6, 2, 1442191128434631759516320380441974645278638080000000⟩, + ⟨3, 2, 8, 4, 7, 2, -2352897005298726868302692394475380477416964096000000⟩, + ⟨3, 2, 5, 5, 3, 2, -11370258092957686164650676267472452345221087232000000⟩, + ⟨3, 2, 6, 5, 4, 2, 7974230311960685188897994408664862904756994048000000⟩, + ⟨3, 2, 7, 5, 5, 2, 3819559417274437777153353955572035157642706944000000⟩, + ⟨3, 2, 8, 5, 6, 2, -4899349098837706095366767860241859533648953344000000⟩, + ⟨3, 2, 5, 6, 2, 2, -168278962488485054700869326970383829909372928000000⟩, + ⟨3, 2, 6, 6, 3, 2, -29526894579334210866110782198088001706606460928000000⟩, + ⟨3, 2, 7, 6, 4, 2, -1367347193728593634266975355608447632422207488000000⟩, + ⟨3, 2, 8, 6, 5, 2, 5141648308895504443853863736780103372502990848000000⟩, + ⟨3, 2, 5, 7, 1, 2, 7844586210209216423638057050467079205920178176000000⟩, + ⟨3, 2, 6, 7, 2, 2, 29139428666833764111700276834800199234530312192000000⟩, + ⟨3, 2, 7, 7, 3, 2, -57291250803256644296100418052585771091867205632000000⟩, + ⟨3, 2, 8, 7, 4, 2, -10166178843720426186819111787441979277831045120000000⟩ +] + +def collectedFourData_10_3_24 : List CollectedFourTerm := [ + ⟨3, 3, 4, 0, 7, 3, 33418364528820434026706817323823756008200140226560000⟩, + ⟨3, 3, 5, 0, 8, 3, 3150267108134285169803884380219374125149742694400000⟩, + ⟨3, 3, 4, 1, 6, 3, 74874993126236096052233431173833399701195708170240000⟩, + ⟨3, 3, 5, 1, 7, 3, -24986458564469338417173533965019273085475985817600000⟩, + ⟨3, 3, 6, 1, 8, 3, -6833651895398840926774996117478413202995386777600000⟩, + ⟨3, 3, 4, 2, 5, 3, -9501244228492302538199593280267849332686764113920000⟩, + ⟨3, 3, 5, 2, 6, 3, -17464235341866499796281628109942988942984662220800000⟩, + ⟨3, 3, 6, 2, 7, 3, -9144207857239689475448652307821775304970888806400000⟩, + ⟨3, 3, 7, 2, 8, 3, -14294855963934887370683036914059123079483962163200000⟩, + ⟨3, 3, 4, 3, 4, 3, 6518802588688082093412498186259192552953395281920000⟩, + ⟨3, 3, 5, 3, 5, 3, 6599031778208119765522408798733182880930856960000000⟩, + ⟨3, 3, 6, 3, 6, 3, 24229477160458196907283807112829625536379197849600000⟩, + ⟨3, 3, 7, 3, 7, 3, 7981949033815161331562291467765216124135591116800000⟩, + ⟨3, 3, 8, 3, 8, 3, 9029873373646238172270954961100254405774540800000000⟩, + ⟨3, 3, 4, 4, 3, 3, 14570473030557461375101954863568252304743622246400000⟩, + ⟨3, 3, 5, 4, 4, 3, -23773723505868648806568290183794240925469140582400000⟩, + ⟨3, 3, 6, 4, 5, 3, -19277002470163739344036447827896943454296893030400000⟩, + ⟨3, 3, 7, 4, 6, 3, -2621474332181226843348621441828296547436068864000000⟩, + ⟨3, 3, 8, 4, 7, 3, 3207649969573498777416222428370710800994245017600000⟩, + ⟨3, 3, 4, 5, 2, 3, -99831949019504462618697693334020067925816078499840000⟩, + ⟨3, 3, 5, 5, 3, 3, 62003237615219017222075292218029402739312479436800000⟩, + ⟨3, 3, 6, 5, 4, 3, -21742166835122711889164746089258691176429099417600000⟩, + ⟨3, 3, 7, 5, 5, 3, -6942822470066153105983815237069296225836282675200000⟩, + ⟨3, 3, 8, 5, 6, 3, 6679169106180858664996906006375025995642463846400000⟩, + ⟨3, 3, 4, 6, 1, 3, 53570433766794713375732053711604866121164872744960000⟩, + ⟨3, 3, 5, 6, 2, 3, 917643241825653741027727460991819739936535347200000⟩, + ⟨3, 3, 6, 6, 3, 3, 80506662455440998694337368221511903265060133273600000⟩, + ⟨3, 3, 7, 6, 4, 3, 2485430329494644239072739160087009943932528230400000⟩, + ⟨3, 3, 8, 6, 5, 3, -7009490005063937456544637035777224172454595788800000⟩, + ⟨3, 3, 4, 7, 0, 3, 1022189902498481884632772659283997535869329546936320000⟩, + ⟨3, 3, 5, 7, 1, 3, -42777370470237975702618538072196396497221609062400000⟩, + ⟨3, 3, 6, 7, 2, 3, -79450215853958728135719725054446837376945120870400000⟩, + ⟨3, 3, 7, 7, 3, 3, 104138446339154369974440205553712897020233619865600000⟩, + ⟨3, 3, 8, 7, 4, 3, 13859316062412354490860426583337177163101110272000000⟩ +] + +def collectedFourData_10_3_25 : List CollectedFourTerm := [ + ⟨3, 4, 3, 0, 6, 4, -279355392552228410228541361311164837384568176640000⟩, + ⟨3, 4, 4, 0, 7, 4, 4007613878551605664205826706428621725227643043840000⟩, + ⟨3, 4, 5, 0, 8, 4, 188893956387596129943748694208735541870775500800000⟩, + ⟨3, 4, 3, 1, 5, 4, 3745157916549010163537227400389990800179928760320000⟩, + ⟨3, 4, 4, 1, 6, 4, 8979196493903090756996940782218186199934550671360000⟩, + ⟨3, 4, 5, 1, 7, 4, -1498219310410347712143565071404426904567231283200000⟩, + ⟨3, 4, 6, 1, 8, 4, -273169543785546276425745224870753717671742668800000⟩, + ⟨3, 4, 3, 2, 4, 4, -4877000459407287876365122039375420274998341795840000⟩, + ⟨3, 4, 4, 2, 5, 4, -1139412977579310269723238657842409966563890298880000⟩, + ⟨3, 4, 5, 2, 6, 4, -1047177396637639403244168363187904109352688025600000⟩, + ⟨3, 4, 6, 2, 7, 4, -365532094241476502565488507142156382511510323200000⟩, + ⟨3, 4, 7, 2, 8, 4, -428568722322987255131459575244929180883956531200000⟩, + ⟨3, 4, 3, 3, 3, 4, 6518802588688082093412498186259192552953395281920000⟩, + ⟨3, 4, 4, 3, 4, 4, 781751114822931733013575882042896773236528250880000⟩, + ⟨3, 4, 5, 3, 5, 4, 395686199971609113435329790843727853094174720000000⟩, + ⟨3, 4, 6, 3, 6, 4, 968553172358859265249834066193381477470489804800000⟩, + ⟨3, 4, 7, 3, 7, 4, 239303824235787031279822888553665247826463948800000⟩, + ⟨3, 4, 8, 3, 8, 4, 216577001083216128093562864950291462346506240000000⟩, + ⟨3, 4, 3, 4, 2, 4, -8923945036603617355483947875138390364298149888000000⟩, + ⟨3, 4, 4, 4, 3, 4, 1747327577445186360580777395153293542224927129600000⟩, + ⟨3, 4, 5, 4, 4, 4, -1425502199319187923852516986221190464884493516800000⟩, + ⟨3, 4, 6, 4, 5, 4, -770582120794453729729332752159892850915619635200000⟩, + ⟨3, 4, 7, 4, 6, 4, -78593440044439477160384346853860892395700224000000⟩, + ⟨3, 4, 8, 4, 7, 4, 76933881815263879876702618128961357372226273280000⟩, + ⟨3, 4, 3, 5, 1, 4, 7410643082526994307340877828301344111081983836160000⟩, + ⟨3, 4, 4, 5, 2, 4, -11972097080585179790864888739655828664393410805760000⟩, + ⟨3, 4, 5, 5, 3, 4, 3717791685580363373224750995259033773112138137600000⟩, + ⟨3, 4, 6, 5, 4, 4, -869125013414670448121814709783575335564790988800000⟩, + ⟨3, 4, 7, 5, 5, 4, -208150159946944315273717238819052543523631923200000⟩, + ⟨3, 4, 8, 5, 6, 4, 160196533759387681059965476394832572859725905920000⟩, + ⟨3, 4, 3, 6, 0, 4, 4035840009038081717422744560879387247083320770560000⟩, + ⟨3, 4, 4, 6, 1, 4, 6424300436925479602426039904770192009890040381440000⟩, + ⟨3, 4, 5, 6, 2, 4, 55023036634961618248891251800981547065435750400000⟩, + ⟨3, 4, 6, 6, 3, 4, 3218186789622277034997223356149881014223424716800000⟩, + ⟨3, 4, 7, 6, 4, 4, 74514755757015248439775825727628686441997926400000⟩, + ⟨3, 4, 8, 6, 5, 4, -168119115473988387656899058549190505301425520640000⟩, + ⟨3, 4, 4, 7, 0, 4, 122583570366985401466256178404280944575566556692480000⟩, + ⟨3, 4, 5, 7, 1, 4, -2564984642450431646724325939958803618664860876800000⟩, + ⟨3, 4, 6, 7, 2, 4, -3175956216485384848567114045712895437402485555200000⟩, + ⟨3, 4, 7, 7, 3, 4, 3122135753229870620708030406692192268467149209600000⟩, + ⟨3, 4, 8, 7, 4, 4, 332408770938243360142005833706311513351494041600000⟩ +] + +def collectedFourData_10_3_26 : List CollectedFourTerm := [ + ⟨3, 5, 2, 0, 5, 5, -1761838728463069523488898964768191685643468800000000⟩, + ⟨3, 5, 3, 0, 6, 5, -282793517334747371428879717739385812491960320000000⟩, + ⟨3, 5, 4, 0, 7, 5, 2028468493987046042158789697292195117095976960000000⟩, + ⟨3, 5, 5, 0, 8, 5, 63739580183854429940908680437002022997196800000000⟩, + ⟨3, 5, 2, 1, 4, 5, 6072255640431988549655124949604619430542704640000000⟩, + ⟨3, 5, 3, 1, 5, 5, 3791250888407167040769499753858705752493916160000000⟩, + ⟨3, 5, 4, 1, 6, 5, 4544853307021709971686843742344616244768931840000000⟩, + ⟨3, 5, 5, 1, 7, 5, -505552806956666928026772611827882186191667200000000⟩, + ⟨3, 5, 6, 1, 8, 5, -69132884289498823125019553086785740970393600000000⟩, + ⟨3, 5, 2, 2, 3, 5, -2263092388647213474987094402114861430766305280000000⟩, + ⟨3, 5, 3, 2, 4, 5, -4937023414363167784704599840670843001550929920000000⟩, + ⟨3, 5, 4, 2, 5, 5, -576718066336000049321161697387498189849886720000000⟩, + ⟨3, 5, 5, 2, 6, 5, -353355125363278812231858383238442912422297600000000⟩, + ⟨3, 5, 6, 2, 7, 5, -92507706478189223947596051406086157526630400000000⟩, + ⟨3, 5, 7, 2, 8, 5, -86768653576441904502854497877752494025605120000000⟩, + ⟨3, 5, 2, 3, 2, 5, -1210141556598951846783690009828207645582950400000000⟩, + ⟨3, 5, 3, 3, 3, 5, 6599031778208119765522408798733182880930856960000000⟩, + ⟨3, 5, 4, 3, 4, 5, 395686199971609113435329790843727853094174720000000⟩, + ⟨3, 5, 5, 3, 5, 5, 133518682932257042496773091562594888581120000000000⟩, + ⟨3, 5, 6, 3, 6, 5, 245118373977585786447320688001061188376985600000000⟩, + ⟨3, 5, 7, 3, 7, 5, 48449804064292116189313925142237724677242880000000⟩, + ⟨3, 5, 8, 3, 8, 5, 36540415031057254212050622120600293867520000000000⟩, + ⟨3, 5, 2, 4, 1, 5, -2793535936628671490266670158015556160816414720000000⟩, + ⟨3, 5, 3, 4, 2, 5, -9033775157682979453530795868482135700537344000000000⟩, + ⟨3, 5, 4, 4, 3, 5, 884416275353167072155496305366485688542822400000000⟩, + ⟨3, 5, 5, 4, 4, 5, -481015451597225752212754861324317882109132800000000⟩, + ⟨3, 5, 6, 4, 5, 5, -195016486297101942948304913728956231214694400000000⟩, + ⟨3, 5, 7, 4, 6, 5, -15912143414556992120280123605060138985062400000000⟩, + ⟨3, 5, 8, 4, 7, 5, 12980122346416160349417186815754439690813440000000⟩, + ⟨3, 5, 2, 5, 0, 5, 20842781567568173224511360896549310410512138240000000⟩, + ⟨3, 5, 3, 5, 1, 5, 7501848465761811420709432496133830449645486080000000⟩, + ⟨3, 5, 4, 5, 2, 5, -6059720938908963887671546683023420164606525440000000⟩, + ⟨3, 5, 5, 5, 3, 5, 1254515950545666803992145219911427848509849600000000⟩, + ⟨3, 5, 6, 5, 4, 5, -219955409936459758491498575472468755585433600000000⟩, + ⟨3, 5, 7, 5, 5, 5, -42142387392204348259002028074357143969464320000000⟩, + ⟨3, 5, 8, 5, 6, 5, 27028021446541469054059308758020659515228160000000⟩, + ⟨3, 5, 3, 6, 0, 5, 4085510507347009711171572817956253149199073280000000⟩, + ⟨3, 5, 4, 6, 1, 5, 3251683277661536875279828204813799799505551360000000⟩, + ⟨3, 5, 5, 6, 2, 5, 18566741480902113955300621604162443306598400000000⟩, + ⟨3, 5, 6, 6, 3, 5, 814448535754820791517966467359422996388249600000000⟩, + ⟨3, 5, 7, 6, 4, 5, 15086366997498552550203872616116596129136640000000⟩, + ⟨3, 5, 8, 6, 5, 5, -28364702730893271356892014185255917028638720000000⟩, + ⟨3, 5, 4, 7, 0, 5, 62046124677994482285621133509225427995061125120000000⟩, + ⟨3, 5, 5, 7, 1, 5, -865517602650839712627807843396033113279692800000000⟩, + ⟨3, 5, 6, 7, 2, 5, -803760955852267759566116289669134501176934400000000⟩, + ⟨3, 5, 7, 7, 3, 5, 632112194567624023138278592651049256836136960000000⟩, + ⟨3, 5, 8, 7, 4, 5, 56083307042283865539288590812912871591116800000000⟩ +] + +def collectedFourData_10_3_27 : List CollectedFourTerm := [ + ⟨3, 6, 1, 0, 4, 6, 525325323911452675495800683308782892785598464000000⟩, + ⟨3, 6, 2, 0, 5, 6, -12937786228784652311527062006586303816113586176000000⟩, + ⟨3, 6, 3, 0, 6, 6, -1038324908816919579454359588786445876118893363200000⟩, + ⟨3, 6, 4, 0, 7, 6, 4965246690488874365426047425483780299147339366400000⟩, + ⟨3, 6, 5, 0, 8, 6, 117015401212482868104486063147880141956317184000000⟩, + ⟨3, 6, 1, 1, 3, 6, -2121626374634792156747049428727088136283645542400000⟩, + ⟨3, 6, 2, 1, 4, 6, 44590656416648105849740133776677487341074173132800000⟩, + ⟨3, 6, 3, 1, 5, 6, 13920227981561816846715814366708504647247174041600000⟩, + ⟨3, 6, 4, 1, 6, 6, 11124805688794233614242718037319143408119945625600000⟩, + ⟨3, 6, 5, 1, 7, 6, -928111926208076543531860158528943462218203136000000⟩, + ⟨3, 6, 6, 1, 8, 6, -101533297442846975263424348387442517097211494400000⟩, + ⟨3, 6, 1, 2, 2, 6, -370389902034588453279375256794355477440469401600000⟩, + ⟨3, 6, 2, 2, 3, 6, -16618663823929567963978891547956456444307020185600000⟩, + ⟨3, 6, 3, 2, 4, 6, -18127128354493446862996006654179554102575575859200000⟩, + ⟨3, 6, 4, 2, 5, 6, -1411679539863858584872937935840654749571271884800000⟩, + ⟨3, 6, 5, 2, 6, 6, -648701978356376351279268996016718972492709888000000⟩, + ⟨3, 6, 6, 2, 7, 6, -135863165180167256930797359903003409835989401600000⟩, + ⟨3, 6, 7, 2, 8, 6, -106195331918069982720508054981774502412052070400000⟩, + ⟨3, 6, 1, 3, 1, 6, 2078635599992359172261721020707162234174832640000000⟩, + ⟨3, 6, 2, 3, 2, 6, -8886484621384075905668116546675756939144593408000000⟩, + ⟨3, 6, 3, 3, 3, 6, 24229477160458196907283807112829625536379197849600000⟩, + ⟨3, 6, 4, 3, 4, 6, 968553172358859265249834066193381477470489804800000⟩, + ⟨3, 6, 5, 3, 5, 6, 245118373977585786447320688001061188376985600000000⟩, + ⟨3, 6, 6, 3, 6, 6, 359997662900253369415577307138122223643420262400000⟩, + ⟨3, 6, 7, 3, 7, 6, 59297255539872613031513885012058338775112089600000⟩, + ⟨3, 6, 8, 3, 8, 6, 38332686247889521090509183563195877634867200000000⟩, + ⟨3, 6, 1, 4, 0, 6, -16632209830299319265953396621137803671443288883200000⟩, + ⟨3, 6, 2, 4, 1, 6, -20513892779538277144963979590008219218198554214400000⟩, + ⟨3, 6, 3, 4, 2, 6, -33169055129967774047014535248358321702767165440000000⟩, + ⟨3, 6, 4, 4, 3, 6, 2164857377488976322559063849542070011602927616000000⟩, + ⟨3, 6, 5, 4, 4, 6, -883065371558732017879124373470300856190500864000000⟩, + ⟨3, 6, 6, 4, 5, 6, -286414592895413640298386808443532506339842457600000⟩, + ⟨3, 6, 7, 4, 6, 6, -19474721362918538727608628910183762895044608000000⟩, + ⟨3, 6, 8, 4, 7, 6, 13616784509466854005023000452591433682413158400000⟩, + ⟨3, 6, 2, 5, 0, 6, 153055695721756589542803891214884193787177651404800000⟩, + ⟨3, 6, 3, 5, 1, 6, 27544323496461522485590496525462864476966276300800000⟩, + ⟨3, 6, 4, 5, 2, 6, -14832869934333824439992631794140088273867479449600000⟩, + ⟨3, 6, 5, 5, 3, 6, 2303085254988001026601789896789231019279515648000000⟩, + ⟨3, 6, 6, 5, 4, 6, -323041607344512672493198201575175894518359654400000⟩, + ⟨3, 6, 7, 5, 5, 6, -51577668114814450444980421638427841820780134400000⟩, + ⟨3, 6, 8, 5, 6, 6, 28353719166323495440036674465782930549086617600000⟩, + ⟨3, 6, 3, 6, 0, 6, 15000652649297549716727066745756862319178861772800000⟩, + ⟨3, 6, 4, 6, 1, 6, 7959408628128323965498634691664730403721602662400000⟩, + ⟨3, 6, 5, 6, 2, 6, 34085488127305532897148721730033258009198592000000⟩, + ⟨3, 6, 6, 6, 3, 6, 1196155003260097516759374833638368588163606118400000⟩, + ⟨3, 6, 7, 6, 4, 6, 18464061440411169080038620688114818659175628800000⟩, + ⟨3, 6, 8, 6, 5, 6, -29755963345622876158435982413983106160866099200000⟩, + ⟨3, 6, 4, 7, 0, 6, 151875326695135529876843514207512351047502580940800000⟩, + ⟨3, 6, 5, 7, 1, 6, -1588948173780234728092404959144972517233393664000000⟩, + ⟨3, 6, 6, 7, 2, 6, -1180458490083445022523170130883695317874219417600000⟩, + ⟨3, 6, 7, 7, 3, 6, 773636117937801677624070206674511219595096883200000⟩, + ⟨3, 6, 8, 7, 4, 6, 58834137783292649823078539768444025147752448000000⟩ +] + +def collectedFourData_10_3_28 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 3, 7, -18758641415859994034370653273875794453934689484800000⟩, + ⟨3, 7, 1, 0, 4, 7, 519175870019602365866598049636661474975809536000000⟩, + ⟨3, 7, 2, 0, 5, 7, -6393168305159697595978563019699462102069542912000000⟩, + ⟨3, 7, 3, 0, 6, 7, -342056762010654025027306544929480794518952345600000⟩, + ⟨3, 7, 4, 0, 7, 7, 1226780888460949827511099969427930954678560358400000⟩, + ⟨3, 7, 5, 0, 8, 7, 23129123978962695827376862010442049622586163200000⟩, + ⟨3, 7, 0, 1, 2, 7, 7337486323251304605788679354088548509204820787200000⟩, + ⟨3, 7, 1, 1, 3, 7, -2096790633861043880210885476445880197670607257600000⟩, + ⟨3, 7, 2, 1, 4, 7, 22034339280929667099762772414620856694722894233600000⟩, + ⟨3, 7, 3, 1, 5, 7, 4585759302691157891102672344387562776080207052800000⟩, + ⟨3, 7, 4, 1, 6, 7, 2748644701379515323081713504088041098338474393600000⟩, + ⟨3, 7, 5, 1, 7, 7, -183449491136988072620163932785607176107117772800000⟩, + ⟨3, 7, 6, 1, 8, 7, -16724124917284717840853946292710521750264217600000⟩, + ⟨3, 7, 0, 2, 1, 7, 7580443014361630210730686989804950473452552192000000⟩, + ⟨3, 7, 1, 2, 2, 7, -366054120908315209503239963700906808593245798400000⟩, + ⟨3, 7, 2, 2, 3, 7, -8212062941407178191886401766045260570707571507200000⟩, + ⟨3, 7, 3, 2, 4, 7, -5971644113358003413707880304838971098549295513600000⟩, + ⟨3, 7, 4, 2, 5, 7, -348788607714839534990680188926351440838708428800000⟩, + ⟨3, 7, 5, 2, 6, 7, -128221655673838171375896983342841702008645222400000⟩, + ⟨3, 7, 6, 2, 7, 7, -22378792015592917550495521452614718939620966400000⟩, + ⟨3, 7, 7, 2, 8, 7, -14993172891709635741047961848479215279459532800000⟩, + ⟨3, 7, 0, 3, 0, 7, -42357650824525200546200168178203149581075401932800000⟩, + ⟨3, 7, 1, 3, 1, 7, 2054303108870598224114920102311949904495247360000000⟩, + ⟨3, 7, 2, 3, 2, 7, -4391229752994505959805346355398234999982391296000000⟩, + ⟨3, 7, 3, 3, 3, 7, 7981949033815161331562291467765216124135591116800000⟩, + ⟨3, 7, 4, 3, 4, 7, 239303824235787031279822888553665247826463948800000⟩, + ⟨3, 7, 5, 3, 5, 7, 48449804064292116189313925142237724677242880000000⟩, + ⟨3, 7, 6, 3, 6, 7, 59297255539872613031513885012058338775112089600000⟩, + ⟨3, 7, 7, 3, 7, 7, 8371874622503227502109082400414357622305587200000⟩, + ⟨3, 7, 8, 3, 8, 7, 4735495517509787131151624083523472300441600000000⟩, + ⟨3, 7, 1, 4, 0, 7, -16437513319745708525063021367153836241669901516800000⟩, + ⟨3, 7, 2, 4, 1, 7, -10136878660261208952331173464248857904318041292800000⟩, + ⟨3, 7, 3, 4, 2, 7, -10926926148422156491750404619056520246088171520000000⟩, + ⟨3, 7, 4, 4, 3, 7, 534878893738445780663415480530621623588356096000000⟩, + ⟨3, 7, 5, 4, 4, 7, -174545643126264314830611527889697083948741427200000⟩, + ⟨3, 7, 6, 4, 5, 7, -47176971007096980891214494586964712473650790400000⟩, + ⟨3, 7, 7, 4, 6, 7, -2749535776557281062995423754349369471533056000000⟩, + ⟨3, 7, 8, 4, 7, 7, 1682173317843781011326551317151878338523955200000⟩, + ⟨3, 7, 2, 5, 0, 7, 75632013507493248065393733196401394157016947097600000⟩, + ⟨3, 7, 3, 5, 1, 7, 9073963291229171278868689583011918445948593766400000⟩, + ⟨3, 7, 4, 5, 2, 7, -3664809120425822878802474056244272816998422937600000⟩, + ⟨3, 7, 5, 5, 3, 7, 455225071612674816731200994926311049150228070400000⟩, + ⟨3, 7, 6, 5, 4, 7, -53210014160637140281702263333141347237992857600000⟩, + ⟨3, 7, 7, 5, 5, 7, -7281985765563082097078647738070054491442380800000⟩, + ⟨3, 7, 8, 5, 6, 7, 3502726345567516319245186527488891486522572800000⟩, + ⟨3, 7, 3, 6, 0, 7, 4941685044531648171744073917649853395881059942400000⟩, + ⟨3, 7, 4, 6, 1, 7, 1966558964158458523819354612584742419226322534400000⟩, + ⟨3, 7, 5, 6, 2, 7, 6737296737105148583703723867118418381085081600000⟩, + ⟨3, 7, 6, 6, 3, 7, 197025470449411744635505709935968926033353113600000⟩, + ⟨3, 7, 7, 6, 4, 7, 2606845898582555771691690135699664206928281600000⟩, + ⟨3, 7, 8, 6, 5, 7, -3675955035635956360467275966671313559984537600000⟩, + ⟨3, 7, 4, 7, 0, 7, 37524368844604309933905906220181958196990889164800000⟩, + ⟨3, 7, 5, 7, 1, 7, -314069591922989727246281736341680676276482867200000⟩, + ⟨3, 7, 6, 7, 2, 7, -194440008795515309008492682509962034754774630400000⟩, + ⟨3, 7, 7, 7, 3, 7, 109225705706738510246943614324995315384870502400000⟩, + ⟨3, 7, 8, 7, 4, 7, 7268178231695799401978452303322774916562944000000⟩ +] + +def collectedFourData_10_3_29 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 3, 8, -84885611736805918588385660890005403080012595200000000⟩, + ⟨3, 8, 1, 0, 4, 8, 1174673590389700352993643468782172773548032000000000⟩, + ⟨3, 8, 2, 0, 5, 8, -9643342331124427331113167713756062307844096000000000⟩, + ⟨3, 8, 3, 0, 6, 8, -386964290860589679863852985379830611155353600000000⟩, + ⟨3, 8, 4, 0, 7, 8, 1110272795086166481596233328713753598172856320000000⟩, + ⟨3, 8, 5, 0, 8, 8, 17443781369571229629212453428250628902092800000000⟩, + ⟨3, 8, 0, 1, 2, 8, 33203204931090117028054315511679952693808332800000000⟩, + ⟨3, 8, 1, 1, 3, 8, -4744143024366774978962636550340284840620851200000000⟩, + ⟨3, 8, 2, 1, 4, 8, 33236208806619097940452209303286264783228108800000000⟩, + ⟨3, 8, 3, 1, 5, 8, 5187808848427224156253008669092067301706956800000000⟩, + ⟨3, 8, 4, 1, 6, 8, 2487604317938115037956005972522660693048033280000000⟩, + ⟨3, 8, 5, 1, 7, 8, -138355988694744858085571476583901625004851200000000⟩, + ⟨3, 8, 6, 1, 8, 8, -10811303615792327058997160318655291142963200000000⟩, + ⟨3, 8, 0, 2, 1, 8, 34302619696437327819955230726096229402411008000000000⟩, + ⟨3, 8, 1, 2, 2, 8, -828224371190596648853903983075706075401420800000000⟩, + ⟨3, 8, 2, 2, 3, 8, -12386930925127874628902857371613666075056537600000000⟩, + ⟨3, 8, 3, 2, 4, 8, -6755642005186904691508153492381181717092761600000000⟩, + ⟨3, 8, 4, 2, 5, 8, -315663951096915113360197735345926074259210240000000⟩, + ⟨3, 8, 5, 2, 6, 8, -96703642146293970226782442560489678018969600000000⟩, + ⟨3, 8, 6, 2, 7, 8, -14466760815998826316349224261782355102924800000000⟩, + ⟨3, 8, 7, 2, 8, 8, -8480789097234579536139313888978679522918400000000⟩, + ⟨3, 8, 0, 3, 0, 8, -191674600642127805457573931710934814511280947200000000⟩, + ⟨3, 8, 1, 3, 1, 8, 4648011874193300005913756959521070456504320000000000⟩, + ⟨3, 8, 2, 3, 2, 8, -6623653522240128290662266899669556834336768000000000⟩, + ⟨3, 8, 3, 3, 3, 8, 9029873373646238172270954961100254405774540800000000⟩, + ⟨3, 8, 4, 3, 4, 8, 216577001083216128093562864950291462346506240000000⟩, + ⟨3, 8, 5, 3, 5, 8, 36540415031057254212050622120600293867520000000000⟩, + ⟨3, 8, 6, 3, 6, 8, 38332686247889521090509183563195877634867200000000⟩, + ⟨3, 8, 7, 3, 7, 8, 4735495517509787131151624083523472300441600000000⟩, + ⟨3, 8, 8, 3, 8, 8, 2380979310159184940653316100836661657600000000000⟩, + ⟨3, 8, 1, 4, 0, 8, -37191082836063203111778937802750625486313881600000000⟩, + ⟨3, 8, 2, 4, 1, 8, -15290289012268849719839953344146005853365862400000000⟩, + ⟨3, 8, 3, 4, 2, 8, -12361487033483976822642700276294222998405120000000000⟩, + ⟨3, 8, 4, 4, 3, 8, 484081134593322514097142593483980921425100800000000⟩, + ⟨3, 8, 5, 4, 4, 8, -131640785032547071340359668610358039071948800000000⟩, + ⟨3, 8, 6, 4, 5, 8, -30497533339039826965647746229517977177292800000000⟩, + ⟨3, 8, 7, 4, 6, 8, -1555256729492997914121486802721144045568000000000⟩, + ⟨3, 8, 8, 4, 7, 8, 845786856112169307532632218097541133107200000000⟩, + ⟨3, 8, 2, 5, 0, 8, 114081995441345649656993879681903357078588620800000000⟩, + ⟨3, 8, 3, 5, 1, 8, 10265254660207981431600962753164918535906918400000000⟩, + ⟨3, 8, 4, 5, 2, 8, -3316760070086446996596671185475915364150804480000000⟩, + ⟨3, 8, 5, 5, 3, 8, 343326735175165940555739668921430826391961600000000⟩, + ⟨3, 8, 6, 5, 4, 8, -34397591583204725679805130804039781659443200000000⟩, + ⟨3, 8, 7, 5, 5, 8, -4119007092951810003035247254870512002662400000000⟩, + ⟨3, 8, 8, 5, 6, 8, 1761150216932606618501204226283500522700800000000⟩, + ⟨3, 8, 3, 6, 0, 8, 5590462932739829408110298141041835161052774400000000⟩, + ⟨3, 8, 4, 6, 1, 8, 1779793717341945115068867457241199135550341120000000⟩, + ⟨3, 8, 5, 6, 2, 8, 5081209794667657166382698457293040019046400000000⟩, + ⟨3, 8, 6, 6, 3, 8, 127367033647985147618578255071690930467635200000000⟩, + ⟨3, 8, 7, 6, 4, 8, 1474545143616274564637424979585767623884800000000⟩, + ⟨3, 8, 8, 6, 5, 8, -1848248584031437090096397713235607394713600000000⟩, + ⟨3, 8, 4, 7, 0, 8, 33960657744848183001014907483545605363508183040000000⟩, + ⟨3, 8, 5, 7, 1, 8, -236868516996932611215227265481087646485708800000000⟩, + ⟨3, 8, 6, 7, 2, 8, -125695663034245365330039175390050032340172800000000⟩, + ⟨3, 8, 7, 7, 3, 8, 61782798129918361306018295536592698422067200000000⟩, + ⟨3, 8, 8, 7, 4, 8, 3654397291313939681059165622723237904384000000000⟩ +] + +def collectedFourData_10_3_30 : List CollectedFourTerm := [ + ⟨4, 0, 6, 1, 8, 1, 4690927974995016723323773548169308780331479859200000⟩, + ⟨4, 0, 6, 2, 7, 1, 6276998170711090011585414997420676174534462668800000⟩, + ⟨4, 0, 7, 2, 8, 1, 29437908500239536178676746245867992716225491763200000⟩, + ⟨4, 0, 6, 3, 6, 1, -16632209830299319265953396621137803671443288883200000⟩, + ⟨4, 0, 7, 3, 7, 1, -16437513319745708525063021367153836241669901516800000⟩, + ⟨4, 0, 8, 3, 8, 1, -37191082836063203111778937802750625486313881600000000⟩, + ⟨4, 0, 6, 4, 5, 1, 13232607037274528867168128877485895670318288076800000⟩, + ⟨4, 0, 7, 4, 6, 1, 5398495914976328714245127399174677937063460864000000⟩, + ⟨4, 0, 8, 4, 7, 1, -13211256768635307822410252401584094821792035635200000⟩, + ⟨4, 0, 6, 5, 4, 1, 14924807438985501689059123737977830267524690739200000⟩, + ⟨4, 0, 7, 5, 5, 1, 14297602796618526023202848904040620552025748275200000⟩, + ⟨4, 0, 8, 5, 6, 1, -27509303976401284155301188903067437970576166092800000⟩, + ⟨4, 0, 6, 6, 3, 1, -55263417110840099686797106905088705710156624691200000⟩, + ⟨4, 0, 7, 6, 4, 1, -5118335631221251186301590582316965060936099430400000⟩, + ⟨4, 0, 8, 6, 5, 1, 28869787274948669475718023230952976538882644377600000⟩, + ⟨4, 0, 6, 7, 2, 1, 54538224345267957778693925892147925884911537356800000⟩, + ⟨4, 0, 7, 7, 3, 1, -214456029667141249982071994847294135666365536665600000⟩, + ⟨4, 0, 8, 7, 4, 1, -57081971186072647159893689851753549778380652544000000⟩ +] + +def collectedFourData_10_3_31 : List CollectedFourTerm := [ + ⟨4, 1, 5, 0, 8, 2, -1333587209810654255606524636950853960063569100800000⟩, + ⟨4, 1, 5, 1, 7, 2, 10577395635436956473047928391708469627184165683200000⟩, + ⟨4, 1, 6, 1, 8, 2, 5785713053011225150900075777029060010365576806400000⟩, + ⟨4, 1, 5, 2, 6, 2, 7393049567415788191060041576429762100546083225600000⟩, + ⟨4, 1, 6, 2, 7, 2, 7741945824706318642978153194305564264208374169600000⟩, + ⟨4, 1, 7, 2, 8, 2, 18154114960949375588745686148890191516241441587200000⟩, + ⟨4, 1, 5, 3, 5, 2, -2793535936628671490266670158015556160816414720000000⟩, + ⟨4, 1, 6, 3, 6, 2, -20513892779538277144963979590008219218198554214400000⟩, + ⟨4, 1, 7, 3, 7, 2, -10136878660261208952331173464248857904318041292800000⟩, + ⟨4, 1, 8, 3, 8, 2, -15290289012268849719839953344146005853365862400000000⟩, + ⟨4, 1, 5, 4, 4, 2, 10064014418059272937423579101541063629269159116800000⟩, + ⟨4, 1, 6, 4, 5, 2, 16320878868537470707380847724883507747053214105600000⟩, + ⟨4, 1, 7, 4, 6, 2, 3329207829282382329346864397183010707387449344000000⟩, + ⟨4, 1, 8, 4, 7, 2, -5431515266660885653130238005369588287089200332800000⟩, + ⟨4, 1, 5, 5, 3, 2, -26247528165786975470143282992494691984256637337600000⟩, + ⟨4, 1, 6, 5, 4, 2, 18408010882646132213762527110232514531045041766400000⟩, + ⟨4, 1, 7, 5, 5, 2, 8817213520236737407158303329996082794252677939200000⟩, + ⟨4, 1, 8, 5, 6, 2, -11309840323274031224213781677261583907887985459200000⟩, + ⟨4, 1, 5, 6, 2, 2, -388461437859672572903256828146495523777832550400000⟩, + ⟨4, 1, 6, 6, 3, 2, -68160985510021845474906688165998520027075470950400000⟩, + ⟨4, 1, 7, 6, 4, 2, -3156435296928716986982191530620186459717920358400000⟩, + ⟨4, 1, 8, 6, 5, 2, 11869172863357619322372067877254045409347004006400000⟩, + ⟨4, 1, 5, 7, 1, 2, 18108735599320996485968992044996079950670646476800000⟩, + ⟨4, 1, 6, 7, 2, 2, 67266544735811384890089356719676435510691731865600000⟩, + ⟨4, 1, 7, 7, 3, 2, -132253261695353549496693924598704476227410434457600000⟩, + ⟨4, 1, 8, 7, 4, 2, -23467986685741854920973988684356400180327612416000000⟩ +] + +def collectedFourData_10_3_32 : List CollectedFourTerm := [ + ⟨4, 2, 4, 0, 7, 3, -45748225108991283582428990812933780362215030784000000⟩, + ⟨4, 2, 5, 0, 8, 3, -4312572767948833790515747869141092180070236160000000⟩, + ⟨4, 2, 4, 1, 6, 3, -102500469094444042201116123635664536754230132736000000⟩, + ⟨4, 2, 5, 1, 7, 3, 34205328333707476379558496832048031767084400640000000⟩, + ⟨4, 2, 6, 1, 8, 3, 9354959455229388598307189775317395892223344640000000⟩, + ⟨4, 2, 4, 2, 5, 3, 13006772351343203732392896646597637345208434688000000⟩, + ⟨4, 2, 5, 2, 6, 3, 23907745966654902096694554526412063798061957120000000⟩, + ⟨4, 2, 6, 2, 7, 3, 12518005755058234096059703202130205481065512960000000⟩, + ⟨4, 2, 7, 2, 8, 3, 19569009368328377334293363297642165677043220480000000⟩, + ⟨4, 2, 4, 3, 4, 3, -8923945036603617355483947875138390364298149888000000⟩, + ⟨4, 2, 5, 3, 5, 3, -9033775157682979453530795868482135700537344000000000⟩, + ⟨4, 2, 6, 3, 6, 3, -33169055129967774047014535248358321702767165440000000⟩, + ⟨4, 2, 7, 3, 7, 3, -10926926148422156491750404619056520246088171520000000⟩, + ⟨4, 2, 8, 3, 8, 3, -12361487033483976822642700276294222998405120000000000⟩, + ⟨4, 2, 4, 4, 3, 3, -19946316629934647876372252580920975841778728960000000⟩, + ⟨4, 2, 5, 4, 4, 3, 32545149050828956197976102080544365396476559360000000⟩, + ⟨4, 2, 6, 4, 5, 3, 26389341934165554061609031135371196486972866560000000⟩, + ⟨4, 2, 7, 4, 6, 3, 3588679444879538002651975076201916981156249600000000⟩, + ⟨4, 2, 8, 4, 7, 3, -4391127302245544328064839759130401746599280640000000⟩, + ⟨4, 2, 4, 5, 2, 3, 136665409609583837927490470324984056025947570176000000⟩, + ⟨4, 2, 5, 5, 3, 3, -84879619691174533648466819273173532027671019520000000⟩, + ⟨4, 2, 6, 5, 4, 3, 29764040124483825130433457825349495635459440640000000⟩, + ⟨4, 2, 7, 5, 5, 3, 9504409019730097107489151822276002820946657280000000⟩, + ⟨4, 2, 8, 5, 6, 3, -9143479524471132590485387730794305433852968960000000⟩, + ⟨4, 2, 4, 6, 1, 3, -73335493753324512786982522174967480263108460544000000⟩, + ⟨4, 2, 5, 6, 2, 3, -1256211971731290400495408851141688224204718080000000⟩, + ⟨4, 2, 6, 6, 3, 3, -110209968941142904270359928253673738003850199040000000⟩, + ⟨4, 2, 7, 6, 4, 3, -3402441376458609325133528726924871225374146560000000⟩, + ⟨4, 2, 8, 6, 5, 3, 9595673850955153053489744348946522584719032320000000⟩, + ⟨4, 2, 4, 7, 0, 3, -1399331607724520949342133893339837699895798530048000000⟩, + ⟨4, 2, 5, 7, 1, 3, 58560279697572589293257230060145636351001231360000000⟩, + ⟨4, 2, 6, 7, 2, 3, 108763741466469246478491622802681042871842242560000000⟩, + ⟨4, 2, 7, 7, 3, 3, -142560809087936633493702226803872725435510947840000000⟩, + ⟨4, 2, 8, 7, 4, 3, -18972775000197734782855398540326873691114700800000000⟩ +] + +def collectedFourData_10_3_33 : List CollectedFourTerm := [ + ⟨4, 3, 3, 0, 6, 4, -624399981092570295947141149314506558022667468800000⟩, + ⟨4, 3, 4, 0, 7, 4, 8957600593037070686195675972035029531710246092800000⟩, + ⟨4, 3, 5, 0, 8, 4, 422205498592137252681672776956809115846311936000000⟩, + ⟨4, 3, 3, 1, 5, 4, 8370973300057879787867644276998430365575439974400000⟩, + ⟨4, 3, 4, 1, 6, 4, 20069811682519602708417740727679706294020944691200000⟩, + ⟨4, 3, 5, 1, 7, 4, -3348738324132567226828847728302331454338105344000000⟩, + ⟨4, 3, 6, 1, 8, 4, -610573708337747067019671004728745897802858496000000⟩, + ⟨4, 3, 3, 2, 4, 4, -10900806198230218230645375261806671568225225932800000⟩, + ⟨4, 3, 4, 2, 5, 4, -2546753922153615296155199284169921092617083289600000⟩, + ⟨4, 3, 5, 2, 6, 4, -2340593967731850842511532142559718731732221952000000⟩, + ⟨4, 3, 6, 2, 7, 4, -817017458112730108797729643292436355973382144000000⟩, + ⟨4, 3, 7, 2, 8, 4, -957913501044408699325347505837894437389205504000000⟩, + ⟨4, 3, 3, 3, 3, 4, 14570473030557461375101954863568252304743622246400000⟩, + ⟨4, 3, 4, 3, 4, 4, 1747327577445186360580777395153293542224927129600000⟩, + ⟨4, 3, 5, 3, 5, 4, 884416275353167072155496305366485688542822400000000⟩, + ⟨4, 3, 6, 3, 6, 4, 2164857377488976322559063849542070011602927616000000⟩, + ⟨4, 3, 7, 3, 7, 4, 534878893738445780663415480530621623588356096000000⟩, + ⟨4, 3, 8, 3, 8, 4, 484081134593322514097142593483980921425100800000000⟩, + ⟨4, 3, 3, 4, 2, 4, -19946316629934647876372252580920975841778728960000000⟩, + ⟨4, 3, 4, 4, 3, 4, 3905531575214970363523409840856872684598853632000000⟩, + ⟨4, 3, 5, 4, 4, 4, -3186204992036829543775114256563922676435910656000000⟩, + ⟨4, 3, 6, 4, 5, 4, -1722363249402365964242277839707172204061917184000000⟩, + ⟨4, 3, 7, 4, 6, 4, -175667782996432466091505712137075117082542080000000⟩, + ⟨4, 3, 8, 4, 7, 4, 171958428695260246164209357916121838562941337600000⟩, + ⟨4, 3, 3, 5, 1, 4, 16563866400927047404107438891115983876146803507200000⟩, + ⟨4, 3, 4, 5, 2, 4, -26759380309289008651945735398651564876155269939200000⟩, + ⟨4, 3, 5, 5, 3, 4, 8309805788869767370458142954158221989345492992000000⟩, + ⟨4, 3, 6, 5, 4, 4, -1942620963873966127271402947669084402819792896000000⟩, + ⟨4, 3, 7, 5, 5, 4, -465245917567130760623674775917840584507654144000000⟩, + ⟨4, 3, 8, 5, 6, 4, 358062580201511334129820611876400842351732326400000⟩, + ⟨4, 3, 3, 6, 0, 4, 9020690104863039840284616925912383072674984755200000⟩, + ⟨4, 3, 4, 6, 1, 4, 14359246960300936070366759966700162023083003084800000⟩, + ⟨4, 3, 5, 6, 2, 4, 122984499137966532301023435226256968639315968000000⟩, + ⟨4, 3, 6, 6, 3, 4, 7193116095716048377655481607120019091049414656000000⟩, + ⟨4, 3, 7, 6, 4, 4, 166551329690545005549428659107765569231781888000000⟩, + ⟨4, 3, 8, 6, 5, 4, -375770703991805295260356633239527105745439948800000⟩, + ⟨4, 3, 4, 7, 0, 4, 273992129953586887453153492424482744295312955801600000⟩, + ⟨4, 3, 5, 7, 1, 4, -5733114179814342627510100353441590785244921856000000⟩, + ⟨4, 3, 6, 7, 2, 4, -7098724615289287074676517318160156837317443584000000⟩, + ⟨4, 3, 7, 7, 3, 4, 6978428042768842317221794413047695511736287232000000⟩, + ⟨4, 3, 8, 7, 4, 4, 742982007229514695984309888852738932234780672000000⟩ +] + +def collectedFourData_10_3_34 : List CollectedFourTerm := [ + ⟨4, 4, 2, 0, 5, 5, 6347213985350083409995485689470426073763151872000000⟩, + ⟨4, 4, 3, 0, 6, 5, 1018794137735447285135455006908872246973746380800000⟩, + ⟨4, 4, 4, 0, 7, 5, -7307776464369213054302731652623072723523233382400000⟩, + ⟨4, 4, 5, 0, 8, 5, -229628710180657250885936541811765392747528192000000⟩, + ⟨4, 4, 2, 1, 4, 5, -21875955671148555179333411720785338158810765721600000⟩, + ⟨4, 4, 3, 1, 5, 5, -13658390108078107166907508974141587536059197030400000⟩, + ⟨4, 4, 4, 1, 6, 5, -16373324076521711354112022543178793404354632089600000⟩, + ⟨4, 4, 5, 1, 7, 5, 1821308497087909857364605444625253546713939968000000⟩, + ⟨4, 4, 6, 1, 8, 5, 249058669741402412364911031962523038996496384000000⟩, + ⟨4, 4, 2, 2, 3, 5, 8153034342644724728876465856433924146979877683200000⟩, + ⟨4, 4, 3, 2, 4, 5, 17786159173026471337253543076169669412960128204800000⟩, + ⟨4, 4, 4, 2, 5, 5, 2077689017226440595143796987574227197741550796800000⟩, + ⟨4, 4, 5, 2, 6, 5, 1272999938795446761583160348458995099730182144000000⟩, + ⟨4, 4, 6, 2, 7, 5, 333268987010652454021077484060007646338482176000000⟩, + ⟨4, 4, 7, 2, 8, 5, 312593430132406590047517883497318451178687692800000⟩, + ⟨4, 4, 2, 3, 2, 5, 4359665438276912757184270930938354659519102976000000⟩, + ⟨4, 4, 3, 3, 3, 5, -23773723505868648806568290183794240925469140582400000⟩, + ⟨4, 4, 4, 3, 4, 5, -1425502199319187923852516986221190464884493516800000⟩, + ⟨4, 4, 5, 3, 5, 5, -481015451597225752212754861324317882109132800000000⟩, + ⟨4, 4, 6, 3, 6, 5, -883065371558732017879124373470300856190500864000000⟩, + ⟨4, 4, 7, 3, 7, 5, -174545643126264314830611527889697083948741427200000⟩, + ⟨4, 4, 8, 3, 8, 5, -131640785032547071340359668610358039071948800000000⟩, + ⟨4, 4, 2, 4, 1, 5, 10064014418059272937423579101541063629269159116800000⟩, + ⟨4, 4, 3, 4, 2, 5, 32545149050828956197976102080544365396476559360000000⟩, + ⟨4, 4, 4, 4, 3, 5, -3186204992036829543775114256563922676435910656000000⟩, + ⟨4, 4, 5, 4, 4, 5, 1732910028723661698253018193063615437348012032000000⟩, + ⟨4, 4, 6, 4, 5, 5, 702567919073158529341049645829181005769998336000000⟩, + ⟨4, 4, 7, 4, 6, 5, 57325212339881548812311739633134816257376256000000⟩, + ⟨4, 4, 8, 4, 7, 5, -46762290303720467203183100851196436491639193600000⟩, + ⟨4, 4, 2, 5, 0, 5, -75088367920411900960336994642294243489675319705600000⟩, + ⟨4, 4, 3, 5, 1, 5, -27026217966838459657819441893835322629811286835200000⟩, + ⟨4, 4, 4, 5, 2, 5, 21830798057387541287936926624149422678059096473600000⟩, + ⟨4, 4, 5, 5, 3, 5, -4519528977033222425293915885091088077395329024000000⟩, + ⟨4, 4, 6, 5, 4, 5, 792413080463949100378534514248476347527593984000000⟩, + ⟨4, 4, 7, 5, 5, 5, 151822494482898039550797154094275959225896140800000⟩, + ⟨4, 4, 8, 5, 6, 5, -97371361493161759018673689602702543820318310400000⟩, + ⟨4, 4, 3, 6, 0, 5, -14718492113150988475348976354854646405307511603200000⟩, + ⟨4, 4, 4, 6, 1, 5, -11714539612775306778849898576749077361997538918400000⟩, + ⟨4, 4, 5, 6, 2, 5, -66888688099599603851032749465910652065284096000000⟩, + ⟨4, 4, 6, 6, 3, 5, -2934138666029020214514249230544300088202625024000000⟩, + ⟨4, 4, 7, 6, 4, 5, -54350263760054438323128234797283243281979801600000⟩, + ⟨4, 4, 8, 6, 5, 5, 102186899944512876146908564639915418181225676800000⟩, + ⟨4, 4, 4, 7, 0, 5, -223527854127992912256416690915820672291420556492800000⟩, + ⟨4, 4, 5, 7, 1, 5, 3118120485922352640062234404786927487189778432000000⟩, + ⟨4, 4, 6, 7, 2, 5, 2895635507067241820372505611332664020420263936000000⟩, + ⟨4, 4, 7, 7, 3, 5, -2277252336920720740302258506670059688770823782400000⟩, + ⟨4, 4, 8, 7, 4, 5, -202046160668745132568331960629825567815892992000000⟩ +] + +def collectedFourData_10_3_35 : List CollectedFourTerm := [ + ⟨4, 5, 1, 0, 4, 6, -417949487709421813544999555483580728120180736000000⟩, + ⟨4, 5, 2, 0, 5, 6, 10293318978328948201547875646781503596998426624000000⟩, + ⟨4, 5, 3, 0, 6, 6, 826092601979934142129965758808693004080827596800000⟩, + ⟨4, 5, 4, 0, 7, 6, -3950356505163494900299491581811597621260294553600000⟩, + ⟨4, 5, 5, 0, 8, 6, -93097600219846272399848925211507179720278016000000⟩, + ⟨4, 5, 1, 1, 3, 6, 1687968609217236838968057190832093699252001177600000⟩, + ⟨4, 5, 2, 1, 4, 6, -35476382267659834298356719470542750503893414707200000⟩, + ⟨4, 5, 3, 1, 5, 6, -11074950871153467290620004403282350466828494438400000⟩, + ⟨4, 5, 4, 1, 6, 6, -8850909382929606797327294794993347866472638054400000⟩, + ⟨4, 5, 5, 1, 7, 6, 738407014547530661252621829491708583072497664000000⟩, + ⟨4, 5, 6, 1, 8, 6, 80780019009399774709202815056875116356540825600000⟩, + ⟨4, 5, 1, 2, 2, 6, 294682671407237429230104672455708167161407078400000⟩, + ⟨4, 5, 2, 2, 3, 6, 13221829817587894427759696643123086525217531494400000⟩, + ⟨4, 5, 3, 2, 4, 6, 14421966093301256964552447521748140828436253900800000⟩, + ⟨4, 5, 4, 2, 5, 6, 1123134015514208328620800426684730778022261555200000⟩, + ⟨4, 5, 5, 2, 6, 6, 516108108993115902667151708065661657926336512000000⟩, + ⟨4, 5, 6, 2, 7, 6, 108092904912390627816718495164584196621887078400000⟩, + ⟨4, 5, 7, 2, 8, 6, 84489139495149576149927167037420436434033049600000⟩, + ⟨4, 5, 1, 3, 1, 6, -1653765094899193611926588776810803990217359360000000⟩, + ⟨4, 5, 2, 3, 2, 6, 7070098329528024203810142308457221773162708992000000⟩, + ⟨4, 5, 3, 3, 3, 6, -19277002470163739344036447827896943454296893030400000⟩, + ⟨4, 5, 4, 3, 4, 6, -770582120794453729729332752159892850915619635200000⟩, + ⟨4, 5, 5, 3, 5, 6, -195016486297101942948304913728956231214694400000000⟩, + ⟨4, 5, 6, 3, 6, 6, -286414592895413640298386808443532506339842457600000⟩, + ⟨4, 5, 7, 3, 7, 6, -47176971007096980891214494586964712473650790400000⟩, + ⟨4, 5, 8, 3, 8, 6, -30497533339039826965647746229517977177292800000000⟩, + ⟨4, 5, 1, 4, 0, 6, 13232607037274528867168128877485895670318288076800000⟩, + ⟨4, 5, 2, 4, 1, 6, 16320878868537470707380847724883507747053214105600000⟩, + ⟨4, 5, 3, 4, 2, 6, 26389341934165554061609031135371196486972866560000000⟩, + ⟨4, 5, 4, 4, 3, 6, -1722363249402365964242277839707172204061917184000000⟩, + ⟨4, 5, 5, 4, 4, 6, 702567919073158529341049645829181005769998336000000⟩, + ⟨4, 5, 6, 4, 5, 6, 227871809951652311043506015723880027250910822400000⟩, + ⟨4, 5, 7, 4, 6, 6, 15494112783886082872597816032138364339617792000000⟩, + ⟨4, 5, 8, 4, 7, 6, -10833530863515999866701078885938010670078361600000⟩, + ⟨4, 5, 2, 5, 0, 6, -121771303811540282273741177559387164436012938035200000⟩, + ⟨4, 5, 3, 5, 1, 6, -21914298379777206506300790791892756262603141939200000⟩, + ⟨4, 5, 4, 5, 2, 6, 11801049955399177558449820311145887685149091430400000⟩, + ⟨4, 5, 5, 5, 3, 6, -1832337522406604414455726961991126100582858752000000⟩, + ⟨4, 5, 6, 5, 4, 6, 257012308664611453155960582534888468665440665600000⟩, + ⟨4, 5, 7, 5, 5, 6, 41035257553026021229392409489607106405964185600000⟩, + ⟨4, 5, 8, 5, 6, 6, -22558254591623670814129340911369872560514662400000⟩, + ⟨4, 5, 3, 6, 0, 6, -11934538094222283178419877158795079594097718067200000⟩, + ⟨4, 5, 4, 6, 1, 6, -6332515504538882996188378214688556734100380057600000⟩, + ⟨4, 5, 5, 6, 2, 6, -27118457178230748680371261274983398541099008000000⟩, + ⟨4, 5, 6, 6, 3, 6, -951662423412671226597163586453462701500373401600000⟩, + ⟨4, 5, 7, 6, 4, 6, -14690030479771616786561212678410306816521011200000⟩, + ⟨4, 5, 8, 6, 5, 6, 23673881822418431825527057918735390396435660800000⟩, + ⟨4, 5, 4, 7, 0, 6, -120832200730974731941505300121256898916420629299200000⟩, + ⟨4, 5, 5, 7, 1, 6, 1264169163373911986690111136208266014842945536000000⟩, + ⟨4, 5, 6, 7, 2, 6, 939174257808623756691429937921696718423221862400000⟩, + ⟨4, 5, 7, 7, 3, 6, -615505867408195696763516643015714040988880076800000⟩, + ⟨4, 5, 8, 7, 4, 6, -46808513938112508663761949422368979473661952000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1012.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1012.lean new file mode 100644 index 0000000000000000000000000000000000000000..10d03ebe8140a26f43ef6eed38068581cb1bb4e5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1012.lean @@ -0,0 +1,646 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1012. -/ +namespace LaughlinFock +def collectedFourData_10_3_36 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 3, 7, 6160813201129171472566306472872648288977813504000000⟩, + ⟨4, 6, 1, 0, 4, 7, -170510512078992745801025028747636566686433280000000⟩, + ⟨4, 6, 2, 0, 5, 7, 2099678479816112277877140326637007282120949760000000⟩, + ⟨4, 6, 3, 0, 6, 7, 112340108657816932443128095668669496833343488000000⟩, + ⟨4, 6, 4, 0, 7, 7, -402905931456907518627050237832186648625938432000000⟩, + ⟨4, 6, 5, 0, 8, 7, -7596190426651639648740435833172561059905536000000⟩, + ⟨4, 6, 0, 1, 2, 7, -2409816446790848621856663760226268714218029056000000⟩, + ⟨4, 6, 1, 1, 3, 7, 688639178643998653631431478522883081920053248000000⟩, + ⟨4, 6, 2, 1, 4, 7, -7236635389028629470670917180043617296845897728000000⟩, + ⟨4, 6, 3, 1, 5, 7, -1506079562101665676770383614911331790323974144000000⟩, + ⟨4, 6, 4, 1, 6, 7, -902724572961635753387291133496108470163734528000000⟩, + ⟨4, 6, 5, 1, 7, 7, 60249461657795161840605486309564046318239744000000⟩, + ⟨4, 6, 6, 1, 8, 7, 5492626426593344880170516302031898487554048000000⟩, + ⟨4, 6, 0, 2, 1, 7, -2489609580883685311895392364986669583208284160000000⟩, + ⟨4, 6, 1, 2, 2, 7, 120221449433591215853893526368210434373189632000000⟩, + ⟨4, 6, 2, 2, 3, 7, 2697049570719434248669504174511488415255494656000000⟩, + ⟨4, 6, 3, 2, 4, 7, 1961239253441672544280336951768072789193392128000000⟩, + ⟨4, 6, 4, 2, 5, 7, 114551017377850665485633781406810693775130624000000⟩, + ⟨4, 6, 5, 2, 6, 7, 42111240970688703823377004765862259591217152000000⟩, + ⟨4, 6, 6, 2, 7, 7, 7349762395821573627092989463219526300598272000000⟩, + ⟨4, 6, 7, 2, 8, 7, 4924137917576480754945917654818021435244544000000⟩, + ⟨4, 6, 0, 3, 0, 7, 13911325910197379447092549885199051162117996544000000⟩, + ⟨4, 6, 1, 3, 1, 7, -674685198766589560694327469600862144089292800000000⟩, + ⟨4, 6, 2, 3, 2, 7, 1442191128434631759516320380441974645278638080000000⟩, + ⟨4, 6, 3, 3, 3, 7, -2621474332181226843348621441828296547436068864000000⟩, + ⟨4, 6, 4, 3, 4, 7, -78593440044439477160384346853860892395700224000000⟩, + ⟨4, 6, 5, 3, 5, 7, -15912143414556992120280123605060138985062400000000⟩, + ⟨4, 6, 6, 3, 6, 7, -19474721362918538727608628910183762895044608000000⟩, + ⟨4, 6, 7, 3, 7, 7, -2749535776557281062995423754349369471533056000000⟩, + ⟨4, 6, 8, 3, 8, 7, -1555256729492997914121486802721144045568000000000⟩, + ⟨4, 6, 1, 4, 0, 7, 5398495914976328714245127399174677937063460864000000⟩, + ⟨4, 6, 2, 4, 1, 7, 3329207829282382329346864397183010707387449344000000⟩, + ⟨4, 6, 3, 4, 2, 7, 3588679444879538002651975076201916981156249600000000⟩, + ⟨4, 6, 4, 4, 3, 7, -175667782996432466091505712137075117082542080000000⟩, + ⟨4, 6, 5, 4, 4, 7, 57325212339881548812311739633134816257376256000000⟩, + ⟨4, 6, 6, 4, 5, 7, 15494112783886082872597816032138364339617792000000⟩, + ⟨4, 6, 7, 4, 6, 7, 903017224630627956624058218142705259642880000000⟩, + ⟨4, 6, 8, 4, 7, 7, -552468345303358645910331455506202750877696000000⟩, + ⟨4, 6, 2, 5, 0, 7, -24839469816347700455181081063250956202643816448000000⟩, + ⟨4, 6, 3, 5, 1, 7, -2980119486899595289856420120060335027516342272000000⟩, + ⟨4, 6, 4, 5, 2, 7, 1203616184573401547980325670419790223688859648000000⟩, + ⟨4, 6, 5, 5, 3, 7, -149507449313741463626317727350992400067592192000000⟩, + ⟨4, 6, 6, 5, 4, 7, 17475517038028236326972652994535190322741248000000⟩, + ⟨4, 6, 7, 5, 5, 7, 2391588657214011797804867365166474103619584000000⟩, + ⟨4, 6, 8, 5, 6, 7, -1150384093992553737313067764594915613343744000000⟩, + ⟨4, 6, 3, 6, 0, 7, -1622974595187517591509601414854473683411402752000000⟩, + ⟨4, 6, 4, 6, 1, 7, -645867798130779397558066258735801154679078912000000⟩, + ⟨4, 6, 5, 6, 2, 7, -2212698977378420373189532110114706862112768000000⟩, + ⟨4, 6, 6, 6, 3, 7, -64708157291025903431103257105079302910640128000000⟩, + ⟨4, 6, 7, 6, 4, 7, -856154252819089849855460361961643094048768000000⟩, + ⟨4, 6, 8, 6, 5, 7, 1207276785575518879731099640927088592027648000000⟩, + ⟨4, 6, 4, 7, 0, 7, -12323953628455235421042864825954096290834939904000000⟩, + ⟨4, 6, 5, 7, 1, 7, 103148412781987170313205906012044444047507456000000⟩, + ⟨4, 6, 6, 7, 2, 7, 63859026166056948749212487049676738623700992000000⟩, + ⟨4, 6, 7, 7, 3, 7, -35872489627728958150395316683897960558231552000000⟩, + ⟨4, 6, 8, 7, 4, 7, -2387053913197173119050667786089144642437120000000⟩ +] + +def collectedFourData_10_3_37 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 3, 8, -30153615520174904903311449035998227125391222374400000⟩, + ⟨4, 7, 1, 0, 4, 8, 417275143355729067893614642962564880483221504000000⟩, + ⟨4, 7, 2, 0, 5, 8, -3425570376800052139735035953524859023248064512000000⟩, + ⟨4, 7, 3, 0, 6, 8, -137459955908970767688109894405636462140928819200000⟩, + ⟨4, 7, 4, 0, 7, 8, 394398276699018128758494783563476226297340887040000⟩, + ⟨4, 7, 5, 0, 8, 8, 6196492737390184597807748968978247310743961600000⟩, + ⟨4, 7, 0, 1, 2, 8, 11794657010117931458477368938219558803101817241600000⟩, + ⟨4, 7, 1, 1, 3, 8, -1685245141108507822531904344383578206399522406400000⟩, + ⟨4, 7, 2, 1, 4, 8, 11806380860049793262135533939487647402131298713600000⟩, + ⟨4, 7, 3, 1, 5, 8, 1842846982038160551086578564404938985963100569600000⟩, + ⟨4, 7, 4, 1, 6, 8, 883662880371383719041211707812987526396940124160000⟩, + ⟨4, 7, 5, 1, 7, 8, -49147708341319235424890991333915728833570406400000⟩, + ⟨4, 7, 6, 1, 8, 8, -3840461131543296407290207031871513024685670400000⟩, + ⟨4, 7, 0, 2, 1, 8, 12185198227329998486681287515867601262792933376000000⟩, + ⟨4, 7, 1, 2, 2, 8, -294207213005114148956792826295610130256468377600000⟩, + ⟨4, 7, 2, 2, 3, 8, -4400165645850181637012475369923791831671452467200000⟩, + ⟨4, 7, 3, 2, 4, 8, -2399782807102315480991339954655052682132402995200000⟩, + ⟨4, 7, 4, 2, 5, 8, -112132188485231161486242780152257457826331361280000⟩, + ⟨4, 7, 5, 2, 6, 8, -34351692648703435205271221131698983645950771200000⟩, + ⟨4, 7, 6, 2, 7, 8, -5138976259257087253696983086424884034247065600000⟩, + ⟨4, 7, 7, 2, 8, 8, -3012600704800260064550725107746210635893964800000⟩, + ⟨4, 7, 0, 3, 0, 8, -68087890214729458606980160945652105796531938918400000⟩, + ⟨4, 7, 1, 3, 1, 8, 1651096812757752722112721841553545127568343040000000⟩, + ⟨4, 7, 2, 3, 2, 8, -2352897005298726868302692394475380477416964096000000⟩, + ⟨4, 7, 3, 3, 3, 8, 3207649969573498777416222428370710800994245017600000⟩, + ⟨4, 7, 4, 3, 4, 8, 76933881815263879876702618128961357372226273280000⟩, + ⟨4, 7, 5, 3, 5, 8, 12980122346416160349417186815754439690813440000000⟩, + ⟨4, 7, 6, 3, 6, 8, 13616784509466854005023000452591433682413158400000⟩, + ⟨4, 7, 7, 3, 7, 8, 1682173317843781011326551317151878338523955200000⟩, + ⟨4, 7, 8, 3, 8, 8, 845786856112169307532632218097541133107200000000⟩, + ⟨4, 7, 1, 4, 0, 8, -13211256768635307822410252401584094821792035635200000⟩, + ⟨4, 7, 2, 4, 1, 8, -5431515266660885653130238005369588287089200332800000⟩, + ⟨4, 7, 3, 4, 2, 8, -4391127302245544328064839759130401746599280640000000⟩, + ⟨4, 7, 4, 4, 3, 8, 171958428695260246164209357916121838562941337600000⟩, + ⟨4, 7, 5, 4, 4, 8, -46762290303720467203183100851196436491639193600000⟩, + ⟨4, 7, 6, 4, 5, 8, -10833530863515999866701078885938010670078361600000⟩, + ⟨4, 7, 7, 4, 6, 8, -552468345303358645910331455506202750877696000000⟩, + ⟨4, 7, 8, 4, 7, 8, 300445872385292138285250233474630191310438400000⟩, + ⟨4, 7, 2, 5, 0, 8, 40524943602675660008524841794935007801620666777600000⟩, + ⟨4, 7, 3, 5, 1, 8, 3646490093048157196698629202212567461453941964800000⟩, + ⟨4, 7, 4, 5, 2, 8, -1178200944538758921992287018654314477616952770560000⟩, + ⟨4, 7, 5, 5, 3, 8, 121958741398573907503326688730137883107865395200000⟩, + ⟨4, 7, 6, 5, 4, 8, -12218934754642647844755394059821891767920230400000⟩, + ⟨4, 7, 7, 5, 5, 8, -1463180316009768704603242394433708278729932800000⟩, + ⟨4, 7, 8, 5, 6, 8, 625607160366759792358686302529680695728537600000⟩, + ⟨4, 7, 3, 6, 0, 8, 1985880367762421206645167505201257540890709196800000⟩, + ⟨4, 7, 4, 6, 1, 8, 632229825053873818602553772899146597279612272640000⟩, + ⟨4, 7, 5, 6, 2, 8, 1804980177333415568960722777270347493067980800000⟩, + ⟨4, 7, 6, 6, 3, 8, 45244140720508845937971912966693215560689254400000⟩, + ⟨4, 7, 7, 6, 4, 8, 523797454221177325340951209736636376652185600000⟩, + ⟨4, 7, 8, 6, 5, 8, -656546805145150707420569799456068834898739200000⟩, + ⟨4, 7, 4, 7, 0, 8, 12063724293175892874376222591502345118403138682880000⟩, + ⟨4, 7, 5, 7, 1, 8, -84141965219090223287816221824146217939605913600000⟩, + ⟨4, 7, 6, 7, 2, 8, -44650425650931560593898135473498348324493721600000⟩, + ⟨4, 7, 7, 7, 3, 8, 21946884783565318120111511628177513673811558400000⟩, + ⟨4, 7, 8, 7, 4, 8, 1298138620027991862828725028268185955074048000000⟩ +] + +def collectedFourData_10_3_38 : List CollectedFourTerm := [ + ⟨5, 0, 5, 0, 8, 2, 9949994396324421157848572371667337577668123033600000⟩, + ⟨5, 0, 5, 1, 7, 2, -78918743765731702797385195514916111717409121894400000⟩, + ⟨5, 0, 6, 1, 8, 2, -43167639905886888204242116413862500805963992268800000⟩, + ⟨5, 0, 5, 2, 6, 2, -55160098437041930165963716223779713435550561075200000⟩, + ⟨5, 0, 6, 2, 7, 2, -57763239633508740293677910190834451630819324723200000⟩, + ⟨5, 0, 7, 2, 8, 2, -135449216071382656397563006125559205418796213862400000⟩, + ⟨5, 0, 5, 3, 5, 2, 20842781567568173224511360896549310410512138240000000⟩, + ⟨5, 0, 6, 3, 6, 2, 153055695721756589542803891214884193787177651404800000⟩, + ⟨5, 0, 7, 3, 7, 2, 75632013507493248065393733196401394157016947097600000⟩, + ⟨5, 0, 8, 3, 8, 2, 114081995441345649656993879681903357078588620800000000⟩, + ⟨5, 0, 5, 4, 4, 2, -75088367920411900960336994642294243489675319705600000⟩, + ⟨5, 0, 6, 4, 5, 2, -121771303811540282273741177559387164436012938035200000⟩, + ⟨5, 0, 7, 4, 6, 2, -24839469816347700455181081063250956202643816448000000⟩, + ⟨5, 0, 8, 4, 7, 2, 40524943602675660008524841794935007801620666777600000⟩, + ⟨5, 0, 5, 5, 3, 2, 195834780242102277344873661316335111094024745779200000⟩, + ⟨5, 0, 6, 5, 4, 2, -137343552624363722408191064974040964070510480588800000⟩, + ⟨5, 0, 7, 5, 5, 2, -65785892720137694812974219435266734020117292646400000⟩, + ⟨5, 0, 8, 5, 6, 2, 84383568627565241992969800163009967525835728486400000⟩, + ⟨5, 0, 5, 6, 2, 2, 2898339982160340144278816847836017119416077516800000⟩, + ⟨5, 0, 6, 6, 3, 2, 508554235436136201715124797294486999273315290316800000⟩, + ⟨5, 0, 7, 6, 4, 2, 23550400967973075137464922172985219686798773452800000⟩, + ⟨5, 0, 8, 6, 5, 2, -88556790745002757089465865115293999934691134668800000⟩, + ⟨5, 0, 5, 7, 1, 2, -135110637243849314957996640724531557201929148825600000⟩, + ⟨5, 0, 6, 7, 2, 2, -501880745599275996257717741215428362945812443955200000⟩, + ⟨5, 0, 7, 7, 3, 2, 986751524822461543417303677944130608499449344819200000⟩, + ⟨5, 0, 8, 7, 4, 2, 175096412366838267382247450062067432596514537472000000⟩ +] + +def collectedFourData_10_3_39 : List CollectedFourTerm := [ + ⟨5, 1, 4, 0, 7, 3, 37990346931906223490198113172669181284582298746880000⟩, + ⟨5, 1, 5, 0, 8, 3, 3581256654944351350102700642664784227541922611200000⟩, + ⟨5, 1, 4, 1, 6, 3, 85118676676611323670251427454557148720215380459520000⟩, + ⟨5, 1, 5, 1, 7, 3, -28404867887692382165317862097006626143946460364800000⟩, + ⟨5, 1, 6, 1, 8, 3, -7768567073178791573726318176406281046494858444800000⟩, + ⟨5, 1, 4, 2, 5, 3, -10801113986709357548789860969080095219017486172160000⟩, + ⟨5, 1, 5, 2, 6, 3, -19853525715352676477500216674356886459675731558400000⟩, + ⟨5, 1, 6, 2, 7, 3, -10395231299078192210963753969613721431071470387200000⟩, + ⟨5, 1, 7, 2, 8, 3, -16250542031856988538227682110918247378901899673600000⟩, + ⟨5, 1, 4, 3, 4, 3, 7410643082526994307340877828301344111081983836160000⟩, + ⟨5, 1, 5, 3, 5, 3, 7501848465761811420709432496133830449645486080000000⟩, + ⟨5, 1, 6, 3, 6, 3, 27544323496461522485590496525462864476966276300800000⟩, + ⟨5, 1, 7, 3, 7, 3, 9073963291229171278868689583011918445948593766400000⟩, + ⟨5, 1, 8, 3, 8, 3, 10265254660207981431600962753164918535906918400000000⟩, + ⟨5, 1, 4, 4, 3, 3, 16563866400927047404107438891115983876146803507200000⟩, + ⟨5, 1, 5, 4, 4, 3, -27026217966838459657819441893835322629811286835200000⟩, + ⟨5, 1, 6, 4, 5, 3, -21914298379777206506300790791892756262603141939200000⟩, + ⟨5, 1, 7, 4, 6, 3, -2980119486899595289856420120060335027516342272000000⟩, + ⟨5, 1, 8, 4, 7, 3, 3646490093048157196698629202212567461453941964800000⟩, + ⟨5, 1, 4, 5, 2, 3, -113490005618572945370803947605752554356532911800320000⟩, + ⟨5, 1, 5, 5, 3, 3, 70485930149937566229891661637834119313617217126400000⟩, + ⟨5, 1, 6, 5, 4, 3, -24716723058225984598520269840796116923192233164800000⟩, + ⟨5, 1, 7, 5, 5, 3, -7892673326277741597234696665631139444377098649600000⟩, + ⟨5, 1, 8, 5, 6, 3, 7592949419827194692052782109818050792461120307200000⟩, + ⟨5, 1, 4, 6, 1, 3, 60899430381701865717589951044582287202869921710080000⟩, + ⟨5, 1, 5, 6, 2, 3, 1043186451766980367581445189728893243527633305600000⟩, + ⟨5, 1, 6, 6, 3, 3, 91520817374961698631547308266390983129372085452800000⟩, + ⟨5, 1, 7, 6, 4, 3, 2825463239266315831059672442808057560195871539200000⟩, + ⟨5, 1, 8, 6, 5, 3, -7968461678561605586849952208291965113301624422400000⟩, + ⟨5, 1, 4, 7, 0, 3, 1162036190990685244935085531298604335080318288527360000⟩, + ⟨5, 1, 5, 7, 1, 3, -48629762943590201441262339078530176164859949875200000⟩, + ⟨5, 1, 6, 7, 2, 3, -90319837809647184758065419112664615599335486259200000⟩, + ⟨5, 1, 7, 7, 3, 3, 118385676892184461038503496621027887915790552268800000⟩, + ⟨5, 1, 8, 7, 4, 3, 15755415708506857499618792986665884932380819456000000⟩ +] + +def collectedFourData_10_3_40 : List CollectedFourTerm := [ + ⟨5, 2, 3, 0, 6, 4, 4278177307592058975824838930031306611558218465280000⟩, + ⟨5, 2, 4, 0, 7, 4, -61374447066043256532230714351577877876261445959680000⟩, + ⟨5, 2, 5, 0, 8, 4, -2892809157452047389335518830595484796501727641600000⟩, + ⟨5, 2, 3, 1, 5, 4, -57355075431139797979826419509962665073561976176640000⟩, + ⟨5, 2, 4, 1, 6, 4, -137511555906136197677391643633510912041897657630720000⟩, + ⟨5, 2, 5, 1, 7, 4, 22944421430473807573366222021063212819280193126400000⟩, + ⟨5, 2, 6, 1, 8, 4, 4183444366945967531870883084392143706870356377600000⟩, + ⟨5, 2, 3, 2, 4, 4, 74688634086959452338734783953110055079911285063680000⟩, + ⟨5, 2, 4, 2, 5, 4, 17449495784278963740020234633540131248364333301760000⟩, + ⟨5, 2, 5, 2, 6, 4, 16036957562868212667694378895853681213168628531200000⟩, + ⟨5, 2, 6, 2, 7, 4, 5597927058050672417142601264018597796460783206400000⟩, + ⟨5, 2, 7, 2, 8, 4, 6563299050127108904547467364847832059024402022400000⟩, + ⟨5, 2, 3, 3, 3, 4, -99831949019504462618697693334020067925816078499840000⟩, + ⟨5, 2, 4, 3, 4, 4, -11972097080585179790864888739655828664393410805760000⟩, + ⟨5, 2, 5, 3, 5, 4, -6059720938908963887671546683023420164606525440000000⟩, + ⟨5, 2, 6, 3, 6, 4, -14832869934333824439992631794140088273867479449600000⟩, + ⟨5, 2, 7, 3, 7, 4, -3664809120425822878802474056244272816998422937600000⟩, + ⟨5, 2, 8, 3, 8, 4, -3316760070086446996596671185475915364150804480000000⟩, + ⟨5, 2, 3, 4, 2, 4, 136665409609583837927490470324984056025947570176000000⟩, + ⟨5, 2, 4, 4, 3, 4, -26759380309289008651945735398651564876155269939200000⟩, + ⟨5, 2, 5, 4, 4, 4, 21830798057387541287936926624149422678059096473600000⟩, + ⟨5, 2, 6, 4, 5, 4, 11801049955399177558449820311145887685149091430400000⟩, + ⟨5, 2, 7, 4, 6, 4, 1203616184573401547980325670419790223688859648000000⟩, + ⟨5, 2, 8, 4, 7, 4, -1178200944538758921992287018654314477616952770560000⟩, + ⟨5, 2, 3, 5, 1, 4, -113490005618572945370803947605752554356532911800320000⟩, + ⟨5, 2, 4, 5, 2, 4, 183346215680704186268312459908465959248105853419520000⟩, + ⟨5, 2, 5, 5, 3, 4, -56935976350020399610748584964892991561416258355200000⟩, + ⟨5, 2, 6, 5, 4, 4, 13310181256501491556006049299382161315565509017600000⟩, + ⟨5, 2, 7, 5, 5, 4, 3187707538848335519727080370634894094134306406400000⟩, + ⟨5, 2, 8, 5, 6, 4, -2453323593372855259904580616754840076518518947840000⟩, + ⟨5, 2, 3, 6, 0, 4, -61806715044925380978241347701035143126303501189120000⟩, + ⟨5, 2, 4, 6, 1, 4, -98384699487302218364132876232929500348409582714880000⟩, + ⟨5, 2, 5, 6, 2, 4, -842648157158767383002492439726671241109359820800000⟩, + ⟨5, 2, 6, 6, 3, 4, -49284796578181316166122306588389766267145918873600000⟩, + ⟨5, 2, 7, 6, 4, 4, -1141153332491431134705312836921142105302944972800000⟩, + ⟨5, 2, 8, 6, 5, 4, 2574653663285902141505498062578717071221488353280000⟩, + ⟨5, 2, 4, 7, 0, 4, -1877301326587432336284891449426530543295672572968960000⟩, + ⟨5, 2, 5, 7, 1, 4, 39281357669163178445202848775132835683052919193600000⟩, + ⟨5, 2, 6, 7, 2, 4, 48638058106336421229459373844543047997157959270400000⟩, + ⟨5, 2, 7, 7, 3, 4, -47813826712482855631170769196873754028234978099200000⟩, + ⟨5, 2, 8, 7, 4, 4, -5090661210009333527610200988218493820126573363200000⟩ +] + +def collectedFourData_10_3_41 : List CollectedFourTerm := [ + ⟨5, 3, 2, 0, 5, 5, -16553898964592293689392062044660575509785083904000000⟩, + ⟨5, 3, 3, 0, 6, 5, -2657073679998409891887023981594344178335717785600000⟩, + ⟨5, 3, 4, 0, 7, 5, 19059101131017118790435059560012521394381049036800000⟩, + ⟨5, 3, 5, 0, 8, 5, 598884877124650193157858386035570147426566144000000⟩, + ⟨5, 3, 2, 1, 4, 5, 57053750002745403172777216090447331839968490291200000⟩, + ⟨5, 3, 3, 1, 5, 5, 35621866600049908353589412681239013443515501772800000⟩, + ⟨5, 3, 4, 1, 6, 5, 42702570466799437729788040611694437690326070067200000⟩, + ⟨5, 3, 5, 1, 7, 5, -4750077264408437032952577494461035384171134976000000⟩, + ⟨5, 3, 6, 1, 8, 5, -649559328655206111750590826625706379379212288000000⟩, + ⟨5, 3, 2, 2, 3, 5, -21263582270032431104518061161144573891898140262400000⟩, + ⟨5, 3, 3, 2, 4, 5, -46387325620029052371299989992103019006691744153600000⟩, + ⟨5, 3, 4, 2, 5, 5, -5418732399820383068178332289997047415887731097600000⟩, + ⟨5, 3, 5, 2, 6, 5, -3320057023032555361504951636869666269307076608000000⟩, + ⟨5, 3, 6, 2, 7, 5, -869184677204809110866676046043572157527621632000000⟩, + ⟨5, 3, 7, 2, 8, 5, -815261636262888555531472371125450366726543769600000⟩, + ⟨5, 3, 2, 3, 2, 5, -11370258092957686164650676267472452345221087232000000⟩, + ⟨5, 3, 3, 3, 3, 5, 62003237615219017222075292218029402739312479436800000⟩, + ⟨5, 3, 4, 3, 4, 5, 3717791685580363373224750995259033773112138137600000⟩, + ⟨5, 3, 5, 3, 5, 5, 1254515950545666803992145219911427848509849600000000⟩, + ⟨5, 3, 6, 3, 6, 5, 2303085254988001026601789896789231019279515648000000⟩, + ⟨5, 3, 7, 3, 7, 5, 455225071612674816731200994926311049150228070400000⟩, + ⟨5, 3, 8, 3, 8, 5, 343326735175165940555739668921430826391961600000000⟩, + ⟨5, 3, 2, 4, 1, 5, -26247528165786975470143282992494691984256637337600000⟩, + ⟨5, 3, 3, 4, 2, 5, -84879619691174533648466819273173532027671019520000000⟩, + ⟨5, 3, 4, 4, 3, 5, 8309805788869767370458142954158221989345492992000000⟩, + ⟨5, 3, 5, 4, 4, 5, -4519528977033222425293915885091088077395329024000000⟩, + ⟨5, 3, 6, 4, 5, 5, -1832337522406604414455726961991126100582858752000000⟩, + ⟨5, 3, 7, 4, 6, 5, -149507449313741463626317727350992400067592192000000⟩, + ⟨5, 3, 8, 4, 7, 5, 121958741398573907503326688730137883107865395200000⟩, + ⟨5, 3, 2, 5, 0, 5, 195834780242102277344873661316335111094024745779200000⟩, + ⟨5, 3, 3, 5, 1, 5, 70485930149937566229891661637834119313617217126400000⟩, + ⟨5, 3, 4, 5, 2, 5, -56935976350020399610748584964892991561416258355200000⟩, + ⟨5, 3, 5, 5, 3, 5, 11787191392323702922217099668582462915784736768000000⟩, + ⟨5, 3, 6, 5, 4, 5, -2066658868363023046106036892022494226953535488000000⟩, + ⟨5, 3, 7, 5, 5, 5, -395961793634667482080171353724385319542430105600000⟩, + ⟨5, 3, 8, 5, 6, 5, 253950108492157391585702932672633361109142732800000⟩, + ⟨5, 3, 3, 6, 0, 5, 38386673572785091995113715529041537041823065702400000⟩, + ⟨5, 3, 4, 6, 1, 5, 30552192759560909007837583791726834796964138188800000⟩, + ⟨5, 3, 5, 6, 2, 5, 174449543883437682409041581943017995681923072000000⟩, + ⟨5, 3, 6, 6, 3, 5, 7652402319766604251315699413799400188850208768000000⟩, + ⟨5, 3, 7, 6, 4, 5, 141748612392695216780870136297267681622700851200000⟩, + ⟨5, 3, 8, 6, 5, 5, -266509309610595636158408647852038095726287257600000⟩, + ⟨5, 3, 4, 7, 0, 5, 582973493811211058823911355727944491583195945369600000⟩, + ⟨5, 3, 5, 7, 1, 5, -8132237482857936388047077168753249105240653824000000⟩, + ⟨5, 3, 6, 7, 2, 5, -7551983867711570688691385308163685555426557952000000⟩, + ⟨5, 3, 7, 7, 3, 5, 5939205010147154044424382213688130715020741836800000⟩, + ⟨5, 3, 8, 7, 4, 5, 526948002322583190739794549121067971975839744000000⟩ +] + +def collectedFourData_10_3_42 : List CollectedFourTerm := [ + ⟨5, 4, 1, 0, 4, 6, -471397329771423334425634804481032524172099584000000⟩, + ⟨5, 4, 2, 0, 5, 6, 11609639976980399229642424020811873833248096256000000⟩, + ⟨5, 4, 3, 0, 6, 6, 931734236238638053754333562297394888944333619200000⟩, + ⟨5, 4, 4, 0, 7, 6, -4455532457725905703099956697990030178436671078400000⟩, + ⟨5, 4, 5, 0, 8, 6, -105003024150790669513970292302139473635835904000000⟩, + ⟨5, 4, 1, 1, 3, 6, 1903827899117319789194362557810556414045087334400000⟩, + ⟨5, 4, 2, 1, 4, 6, -40013141211341941107161113068353243152642788556800000⟩, + ⟨5, 4, 3, 1, 5, 6, -12491227819475451746197282078507411008283842969600000⟩, + ⟨5, 4, 4, 1, 6, 6, -9982773449557686915799326630938925884142885273600000⟩, + ⟨5, 4, 5, 1, 7, 6, 832835319047449760747412840195293858041430016000000⟩, + ⟨5, 4, 6, 1, 8, 6, 91110257051901268442055571492327914016761446400000⟩, + ⟨5, 4, 1, 2, 2, 6, 332367016867502633191741336745158221034527129600000⟩, + ⟨5, 4, 2, 2, 3, 6, 14912652016543228973338226748378061483816884633600000⟩, + ⟨5, 4, 3, 2, 4, 6, 16266263044597484263456506179178449839540351795200000⟩, + ⟨5, 4, 4, 2, 5, 6, 1266761633781323003154804871347271216145419468800000⟩, + ⟨5, 4, 5, 2, 6, 6, 582108583948980961335885131442826354442108928000000⟩, + ⟨5, 4, 6, 2, 7, 6, 121915944967884311133356668151726049391647129600000⟩, + ⟨5, 4, 7, 2, 8, 6, 95293703961635392749686428611657519356864102400000⟩, + ⟨5, 4, 1, 3, 1, 6, -1865250401614717268814035688118509377515683840000000⟩, + ⟨5, 4, 2, 3, 2, 6, 7974230311960685188897994408664862904756994048000000⟩, + ⟨5, 4, 3, 3, 3, 6, -21742166835122711889164746089258691176429099417600000⟩, + ⟨5, 4, 4, 3, 4, 6, -869125013414670448121814709783575335564790988800000⟩, + ⟨5, 4, 5, 3, 5, 6, -219955409936459758491498575472468755585433600000000⟩, + ⟨5, 4, 6, 3, 6, 6, -323041607344512672493198201575175894518359654400000⟩, + ⟨5, 4, 7, 3, 7, 6, -53210014160637140281702263333141347237992857600000⟩, + ⟨5, 4, 8, 3, 8, 6, -34397591583204725679805130804039781659443200000000⟩, + ⟨5, 4, 1, 4, 0, 6, 14924807438985501689059123737977830267524690739200000⟩, + ⟨5, 4, 2, 4, 1, 6, 18408010882646132213762527110232514531045041766400000⟩, + ⟨5, 4, 3, 4, 2, 6, 29764040124483825130433457825349495635459440640000000⟩, + ⟨5, 4, 4, 4, 3, 6, -1942620963873966127271402947669084402819792896000000⟩, + ⟨5, 4, 5, 4, 4, 6, 792413080463949100378534514248476347527593984000000⟩, + ⟨5, 4, 6, 4, 5, 6, 257012308664611453155960582534888468665440665600000⟩, + ⟨5, 4, 7, 4, 6, 6, 17475517038028236326972652994535190322741248000000⟩, + ⟨5, 4, 8, 4, 7, 6, -12218934754642647844755394059821891767920230400000⟩, + ⟨5, 4, 2, 5, 0, 6, -137343552624363722408191064974040964070510480588800000⟩, + ⟨5, 4, 3, 5, 1, 6, -24716723058225984598520269840796116923192233164800000⟩, + ⟨5, 4, 4, 5, 2, 6, 13310181256501491556006049299382161315565509017600000⟩, + ⟨5, 4, 5, 5, 3, 6, -2066658868363023046106036892022494226953535488000000⟩, + ⟨5, 4, 6, 5, 4, 6, 289879326535074728873390509601767898508322406400000⟩, + ⟨5, 4, 7, 5, 5, 6, 46282891607293693329619987640716802556061286400000⟩, + ⟨5, 4, 8, 5, 6, 6, -25443029101613679749542480470579817328777625600000⟩, + ⟨5, 4, 3, 6, 0, 6, -13460740005938500427906629033080480318972808396800000⟩, + ⟨5, 4, 4, 6, 1, 6, -7142324580742567557841538967281848504889534054400000⟩, + ⟨5, 4, 5, 6, 2, 6, -30586395431178041900350574556456334972157952000000⟩, + ⟨5, 4, 6, 6, 3, 6, -1073362065112591986665266355381908309079909990400000⟩, + ⟨5, 4, 7, 6, 4, 6, -16568607800853764858715193212687113752726732800000⟩, + ⟨5, 4, 8, 6, 5, 6, 26701323974755313574405725537854165504701235200000⟩, + ⟨5, 4, 4, 7, 0, 6, -136284356004731788085442876759568603323139149004800000⟩, + ⟨5, 4, 5, 7, 1, 6, 1425832512105271811341224945323333530926710784000000⟩, + ⟨5, 4, 6, 7, 2, 6, 1059276899099458473148631804347396857429334425600000⟩, + ⟨5, 4, 7, 7, 3, 6, -694217437482760205576246052184834567149138739200000⟩, + ⟨5, 4, 8, 7, 4, 6, -52794438394755492440973134229034653909516288000000⟩ +] + +def collectedFourData_10_3_43 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 3, 7, 16316555840960566800422264219249342846847890227200000⟩, + ⟨5, 5, 1, 0, 4, 7, -451587185162138497882361548596735511105634304000000⟩, + ⟨5, 5, 2, 0, 5, 7, 5560876469636119998085003159978540844992954368000000⟩, + ⟨5, 5, 3, 0, 6, 7, 297526251203151144761237188660709561716860518400000⟩, + ⟨5, 5, 4, 0, 7, 7, -1067072952003471523255303939899378199290288537600000⟩, + ⟨5, 5, 5, 0, 8, 7, -20118069032236653637775778725874094922583244800000⟩, + ⟨5, 5, 0, 1, 2, 7, -6382258857210829794565761012587973176009215180800000⟩, + ⟨5, 5, 1, 1, 3, 7, 1823820857051568608261566743734723670972982886400000⟩, + ⟨5, 5, 2, 1, 4, 7, -19165808404013214313956171739210396145990133350400000⟩, + ⟨5, 5, 3, 1, 5, 7, -3988764222141529470127315022839613625403126579200000⟩, + ⟨5, 5, 4, 1, 6, 7, -2390813586270749566754538784465860643688703590400000⟩, + ⟨5, 5, 5, 1, 7, 7, 159567198912482630230791615947349436681892659200000⟩, + ⟨5, 5, 6, 1, 8, 7, 14546901987974584355706303397524573463668326400000⟩, + ⟨5, 5, 0, 2, 1, 7, -6593586337146822541564786458486382053229068288000000⟩, + ⟨5, 5, 1, 2, 2, 7, 318399524368776595667954304575450848719116697600000⟩, + ⟨5, 5, 2, 2, 3, 7, 7142979098671053026083289989285394524301741260800000⟩, + ⟨5, 5, 3, 2, 4, 7, 5194228221430198408977601185192740317131335270400000⟩, + ⟨5, 5, 4, 2, 5, 7, 303381714501906126533986356911037536747598643200000⟩, + ⟨5, 5, 5, 2, 6, 7, 111529175191426537036923815434156856011495833600000⟩, + ⟨5, 5, 6, 2, 7, 7, 19465418709211152677629085335490468647639449600000⟩, + ⟨5, 5, 7, 2, 8, 7, 13041293199086457103958841041560361667605299200000⟩, + ⟨5, 5, 0, 3, 0, 7, 36843338472579346868040453063706692947289518899200000⟩, + ⟨5, 5, 1, 3, 1, 7, -1786864552024879023862479621839385424602071040000000⟩, + ⟨5, 5, 2, 3, 2, 7, 3819559417274437777153353955572035157642706944000000⟩, + ⟨5, 5, 3, 3, 3, 7, -6942822470066153105983815237069296225836282675200000⟩, + ⟨5, 5, 4, 3, 4, 7, -208150159946944315273717238819052543523631923200000⟩, + ⟨5, 5, 5, 3, 5, 7, -42142387392204348259002028074357143969464320000000⟩, + ⟨5, 5, 6, 3, 6, 7, -51577668114814450444980421638427841820780134400000⟩, + ⟨5, 5, 7, 3, 7, 7, -7281985765563082097078647738070054491442380800000⟩, + ⟨5, 5, 8, 3, 8, 7, -4119007092951810003035247254870512002662400000000⟩, + ⟨5, 5, 1, 4, 0, 7, 14297602796618526023202848904040620552025748275200000⟩, + ⟨5, 5, 2, 4, 1, 7, 8817213520236737407158303329996082794252677939200000⟩, + ⟨5, 5, 3, 4, 2, 7, 9504409019730097107489151822276002820946657280000000⟩, + ⟨5, 5, 4, 4, 3, 7, -465245917567130760623674775917840584507654144000000⟩, + ⟨5, 5, 5, 4, 4, 7, 151822494482898039550797154094275959225896140800000⟩, + ⟨5, 5, 6, 4, 5, 7, 41035257553026021229392409489607106405964185600000⟩, + ⟨5, 5, 7, 4, 6, 7, 2391588657214011797804867365166474103619584000000⟩, + ⟨5, 5, 8, 4, 7, 7, -1463180316009768704603242394433708278729932800000⟩, + ⟨5, 5, 2, 5, 0, 7, -65785892720137694812974219435266734020117292646400000⟩, + ⟨5, 5, 3, 5, 1, 7, -7892673326277741597234696665631139444377098649600000⟩, + ⟨5, 5, 4, 5, 2, 7, 3187707538848335519727080370634894094134306406400000⟩, + ⟨5, 5, 5, 5, 3, 7, -395961793634667482080171353724385319542430105600000⟩, + ⟨5, 5, 6, 5, 4, 7, 46282891607293693329619987640716802556061286400000⟩, + ⟨5, 5, 7, 5, 5, 7, 6333983615488969765773065870868151304139571200000⟩, + ⟨5, 5, 8, 5, 6, 7, -3046725439547827373894895362777418006999859200000⟩, + ⟨5, 5, 3, 6, 0, 7, -4298353926066760624166732687081525234938517913600000⟩, + ⟨5, 5, 4, 6, 1, 7, -1710543340633605330622955107978321710894651801600000⟩, + ⟨5, 5, 5, 6, 2, 7, -5860204691324541709249638439060460055979622400000⟩, + ⟨5, 5, 6, 6, 3, 7, -171375795262088312096849672432751621429421670400000⟩, + ⟨5, 5, 7, 6, 4, 7, -2267474798949947459323207602736267098744422400000⟩, + ⟨5, 5, 8, 6, 5, 7, 3197402427934012790602667641467068928648806400000⟩, + ⟨5, 5, 4, 7, 0, 7, -32639275205299700361985365239988049336081789747200000⟩, + ⟨5, 5, 5, 7, 1, 7, 273182578682189938296394631359513712594308300800000⟩, + ⟨5, 5, 6, 7, 2, 7, 169126920809229678171088144304932888432449945600000⟩, + ⟨5, 5, 7, 7, 3, 7, -95006204709767857359442781872901698757433753600000⟩, + ⟨5, 5, 8, 7, 4, 7, -6321973609413530119190375564745907598524416000000⟩ +] + +def collectedFourData_10_3_44 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 3, 8, -62787741534275616650945660052133779629588191641600000⟩, + ⟨5, 6, 1, 0, 4, 8, 868876365163170037459279865098099218035245056000000⟩, + ⟨5, 6, 2, 0, 5, 8, -7132936588718075635855389778743825341683335168000000⟩, + ⟨5, 6, 3, 0, 6, 8, -286227705501874629496950888382010375231294668800000⟩, + ⟨5, 6, 4, 0, 7, 8, 821240724594807352067097882161317921115665858560000⟩, + ⟨5, 6, 5, 0, 8, 8, 12902724190867250106946092097567103891433062400000⟩, + ⟨5, 6, 0, 1, 2, 8, 24559571482936422267620414842482468066324538982400000⟩, + ⟨5, 6, 1, 1, 3, 8, -3509122687825564815284975885745834096873544089600000⟩, + ⟨5, 6, 2, 1, 4, 8, 24583983615498630646075752715359141414998271590400000⟩, + ⟨5, 6, 3, 1, 5, 8, 3837291084315076638402855068461507126854313574400000⟩, + ⟨5, 6, 4, 1, 6, 8, 1840018040260205815190589058377687496749471498240000⟩, + ⟨5, 6, 5, 1, 7, 8, -102338427916614041922871862858734588678216089600000⟩, + ⟨5, 6, 6, 1, 8, 8, -7996848030991060287114598481901841039333785600000⟩, + ⟨5, 6, 0, 2, 1, 8, 25372780797367928357162235300478567070526603264000000⟩, + ⟨5, 6, 1, 2, 2, 8, -612616634158686432652156444182521933994550886400000⟩, + ⟨5, 6, 2, 2, 3, 8, -9162299728030677366763943018378474245461953740800000⟩, + ⟨5, 6, 3, 2, 4, 8, -4996977643690025670330712697494398813206269132800000⟩, + ⟨5, 6, 4, 2, 5, 8, -233488646280999351708661521702402391512365137920000⟩, + ⟨5, 6, 5, 2, 6, 8, -71529239929738158098488073635890233539873996800000⟩, + ⟨5, 6, 6, 2, 7, 8, -10700697331009178840144358026737997828220518400000⟩, + ⟨5, 6, 7, 2, 8, 8, -6273025344918177230060519243740279280448307200000⟩, + ⟨5, 6, 0, 3, 0, 8, -141776857556475525939154281259800021259609807257600000⟩, + ⟨5, 6, 1, 3, 1, 8, 3438016905738496841792208796492960671266242560000000⟩, + ⟨5, 6, 2, 3, 2, 8, -4899349098837706095366767860241859533648953344000000⟩, + ⟨5, 6, 3, 3, 3, 8, 6679169106180858664996906006375025995642463846400000⟩, + ⟨5, 6, 4, 3, 4, 8, 160196533759387681059965476394832572859725905920000⟩, + ⟨5, 6, 5, 3, 5, 8, 27028021446541469054059308758020659515228160000000⟩, + ⟨5, 6, 6, 3, 6, 8, 28353719166323495440036674465782930549086617600000⟩, + ⟨5, 6, 7, 3, 7, 8, 3502726345567516319245186527488891486522572800000⟩, + ⟨5, 6, 8, 3, 8, 8, 1761150216932606618501204226283500522700800000000⟩, + ⟨5, 6, 1, 4, 0, 8, -27509303976401284155301188903067437970576166092800000⟩, + ⟨5, 6, 2, 4, 1, 8, -11309840323274031224213781677261583907887985459200000⟩, + ⟨5, 6, 3, 4, 2, 8, -9143479524471132590485387730794305433852968960000000⟩, + ⟨5, 6, 4, 4, 3, 8, 358062580201511334129820611876400842351732326400000⟩, + ⟨5, 6, 5, 4, 4, 8, -97371361493161759018673689602702543820318310400000⟩, + ⟨5, 6, 6, 4, 5, 8, -22558254591623670814129340911369872560514662400000⟩, + ⟨5, 6, 7, 4, 6, 8, -1150384093992553737313067764594915613343744000000⟩, + ⟨5, 6, 8, 4, 7, 8, 625607160366759792358686302529680695728537600000⟩, + ⟨5, 6, 2, 5, 0, 8, 84383568627565241992969800163009967525835728486400000⟩, + ⟨5, 6, 3, 5, 1, 8, 7592949419827194692052782109818050792461120307200000⟩, + ⟨5, 6, 4, 5, 2, 8, -2453323593372855259904580616754840076518518947840000⟩, + ⟨5, 6, 5, 5, 3, 8, 253950108492157391585702932672633361109142732800000⟩, + ⟨5, 6, 6, 5, 4, 8, -25443029101613679749542480470579817328777625600000⟩, + ⟨5, 6, 7, 5, 5, 8, -3046725439547827373894895362777418006999859200000⟩, + ⟨5, 6, 8, 5, 6, 8, 1302678302733508668662731815520865349953126400000⟩, + ⟨5, 6, 3, 6, 0, 8, 4135124133476908405253552715101448435364213555200000⟩, + ⟨5, 6, 4, 6, 1, 8, 1316468428775424779695821886731888984771746856960000⟩, + ⟨5, 6, 5, 6, 2, 8, 3758442458519617506285970439864346729460531200000⟩, + ⟨5, 6, 6, 6, 3, 8, 94210175612242009796571593868950421888407961600000⟩, + ⟨5, 6, 7, 6, 4, 8, 1090683773889283859011674001337956086212198400000⟩, + ⟨5, 6, 8, 6, 5, 8, -1367102763482109498820044600377545943993548800000⟩, + ⟨5, 6, 4, 7, 0, 8, 25119840184799709280928779644833554908049645240320000⟩, + ⟨5, 6, 5, 7, 1, 8, -175205655216618654454944868370095868173772390400000⟩, + ⟨5, 6, 6, 7, 2, 8, -92973905012828104860288643458436255315289702400000⟩, + ⟨5, 6, 7, 7, 3, 8, 45699174228412150370382894928189622371064217600000⟩, + ⟨5, 6, 8, 7, 4, 8, 2703065312199284756622304950761713588764672000000⟩ +] + +def collectedFourData_10_3_45 : List CollectedFourTerm := [ + ⟨6, 0, 4, 0, 7, 3, 20689562349390852969835001772698012048498444206080000⟩, + ⟨6, 0, 5, 0, 8, 3, 1950354204041596789510755352650894153434215219200000⟩, + ⟨6, 0, 4, 1, 6, 3, 46355674807469485313820534496676792642654510776320000⟩, + ⟨6, 0, 5, 1, 7, 3, -15469305564436803732799529802202147110033083596800000⟩, + ⟨6, 0, 6, 1, 8, 3, -4230765597219899793056672839617180032373148876800000⟩, + ⟨6, 0, 4, 2, 5, 3, -5882292195737205242387873824383927656743761346560000⟩, + ⟨6, 0, 5, 2, 6, 3, -10812240248273333934776033167663879953091815014400000⟩, + ⟨6, 0, 6, 2, 7, 3, -5661248276677054461199200106100629196237910835200000⟩, + ⟨6, 0, 7, 2, 8, 3, -8850053493381764738967747965499417465902963097600000⟩, + ⟨6, 0, 4, 3, 4, 3, 4035840009038081717422744560879387247083320770560000⟩, + ⟨6, 0, 5, 3, 5, 3, 4085510507347009711171572817956253149199073280000000⟩, + ⟨6, 0, 6, 3, 6, 3, 15000652649297549716727066745756862319178861772800000⟩, + ⟨6, 0, 7, 3, 7, 3, 4941685044531648171744073917649853395881059942400000⟩, + ⟨6, 0, 8, 3, 8, 3, 5590462932739829408110298141041835161052774400000000⟩, + ⟨6, 0, 4, 4, 3, 3, 9020690104863039840284616925912383072674984755200000⟩, + ⟨6, 0, 5, 4, 4, 3, -14718492113150988475348976354854646405307511603200000⟩, + ⟨6, 0, 6, 4, 5, 3, -11934538094222283178419877158795079594097718067200000⟩, + ⟨6, 0, 7, 4, 6, 3, -1622974595187517591509601414854473683411402752000000⟩, + ⟨6, 0, 8, 4, 7, 3, 1985880367762421206645167505201257540890709196800000⟩, + ⟨6, 0, 4, 5, 2, 3, -61806715044925380978241347701035143126303501189120000⟩, + ⟨6, 0, 5, 5, 3, 3, 38386673572785091995113715529041537041823065702400000⟩, + ⟨6, 0, 6, 5, 4, 3, -13460740005938500427906629033080480318972808396800000⟩, + ⟨6, 0, 7, 5, 5, 3, -4298353926066760624166732687081525234938517913600000⟩, + ⟨6, 0, 8, 5, 6, 3, 4135124133476908405253552715101448435364213555200000⟩, + ⟨6, 0, 4, 6, 1, 3, 33165860901007223299855974764194090051731487457280000⟩, + ⟨6, 0, 5, 6, 2, 3, 568119874623892796523180876962408240030259609600000⟩, + ⟨6, 0, 6, 6, 3, 3, 49842283902814393862035956299489300483349990604800000⟩, + ⟨6, 0, 7, 6, 4, 3, 1538748723708459383048236772273778941416911667200000⟩, + ⟨6, 0, 8, 6, 5, 3, -4339628301442829991334911102083645600807937638400000⟩, + ⟨6, 0, 4, 7, 0, 3, 632845503328602921645180672415553966186774145269760000⟩, + ⟨6, 0, 5, 7, 1, 3, -26483793745313457187385121774678501126625768243200000⟩, + ⟨6, 0, 6, 7, 2, 3, -49188229817931832202592321391253832021780411187200000⟩, + ⟨6, 0, 7, 7, 3, 3, 64472900121862366845482918719233638622823238860800000⟩, + ⟨6, 0, 8, 7, 4, 3, 8580407444712127421640663068455433462398058496000000⟩ +] + +def collectedFourData_10_3_46 : List CollectedFourTerm := [ + ⟨6, 1, 3, 0, 6, 4, -2295696080762564403615548413374587481056681656320000⟩, + ⟨6, 1, 4, 0, 7, 4, 32933903262599434081860699114889533147752347729920000⟩, + ⟨6, 1, 5, 0, 8, 4, 1552299067495770967942821475904967796620420710400000⟩, + ⟨6, 1, 3, 1, 5, 4, 30777083886973886535964095241515226631128649564160000⟩, + ⟨6, 1, 4, 1, 6, 4, 73789541025582223370834884515283399087763415367680000⟩, + ⟨6, 1, 5, 1, 7, 4, -12312116718451335663335573161210276100190083481600000⟩, + ⟨6, 1, 6, 1, 8, 4, -2244861806041316186082307852965346144592225894400000⟩, + ⟨6, 1, 3, 2, 4, 4, -40078377361000135030001289268087942029762279505920000⟩, + ⟨6, 1, 4, 2, 5, 4, -9363506045474977606191978018783814453934099005440000⟩, + ⟨6, 1, 5, 2, 6, 4, -8605529405968853976495633676227522272923798732800000⟩, + ⟨6, 1, 6, 2, 7, 4, -3003881859864945938869591308146832302178671001600000⟩, + ⟨6, 1, 7, 2, 8, 4, -3521906368749828292747846213759007665092663705600000⟩, + ⟨6, 1, 3, 3, 3, 4, 53570433766794713375732053711604866121164872744960000⟩, + ⟨6, 1, 4, 3, 4, 4, 6424300436925479602426039904770192009890040381440000⟩, + ⟨6, 1, 5, 3, 5, 4, 3251683277661536875279828204813799799505551360000000⟩, + ⟨6, 1, 6, 3, 6, 4, 7959408628128323965498634691664730403721602662400000⟩, + ⟨6, 1, 7, 3, 7, 4, 1966558964158458523819354612584742419226322534400000⟩, + ⟨6, 1, 8, 3, 8, 4, 1779793717341945115068867457241199135550341120000000⟩, + ⟨6, 1, 3, 4, 2, 4, -73335493753324512786982522174967480263108460544000000⟩, + ⟨6, 1, 4, 4, 3, 4, 14359246960300936070366759966700162023083003084800000⟩, + ⟨6, 1, 5, 4, 4, 4, -11714539612775306778849898576749077361997538918400000⟩, + ⟨6, 1, 6, 4, 5, 4, -6332515504538882996188378214688556734100380057600000⟩, + ⟨6, 1, 7, 4, 6, 4, -645867798130779397558066258735801154679078912000000⟩, + ⟨6, 1, 8, 4, 7, 4, 632229825053873818602553772899146597279612272640000⟩, + ⟨6, 1, 3, 5, 1, 4, 60899430381701865717589951044582287202869921710080000⟩, + ⟨6, 1, 4, 5, 2, 4, -98384699487302218364132876232929500348409582714880000⟩, + ⟨6, 1, 5, 5, 3, 4, 30552192759560909007837583791726834796964138188800000⟩, + ⟨6, 1, 6, 5, 4, 4, -7142324580742567557841538967281848504889534054400000⟩, + ⟨6, 1, 7, 5, 5, 4, -1710543340633605330622955107978321710894651801600000⟩, + ⟨6, 1, 8, 5, 6, 4, 1316468428775424779695821886731888984771746856960000⟩, + ⟨6, 1, 3, 6, 0, 4, 33165860901007223299855974764194090051731487457280000⟩, + ⟨6, 1, 4, 6, 1, 4, 52793830825849247756446787305250010016770655518720000⟩, + ⟨6, 1, 5, 6, 2, 4, 452170149287239046337784151458151408352834355200000⟩, + ⟨6, 1, 6, 6, 3, 4, 26446522949137131513088042203995754242232444518400000⟩, + ⟨6, 1, 7, 6, 4, 4, 612349850087026973907779553807570169970766643200000⟩, + ⟨6, 1, 8, 6, 5, 4, -1381574885556385587412528776016700731329683128320000⟩, + ⟨6, 1, 4, 7, 0, 4, 1007371361212427678794095964056729716097615648522240000⟩, + ⟨6, 1, 5, 7, 1, 4, -21078616514584449553707507794246164926502954598400000⟩, + ⟨6, 1, 6, 7, 2, 4, -26099479133898824699879975258457060200779717017600000⟩, + ⟨6, 1, 7, 7, 3, 4, 25657191532318305209994939957431396435193810124800000⟩, + ⟨6, 1, 8, 7, 4, 4, 2731679906667114010883668252445535448419060940800000⟩ +] + +def collectedFourData_10_3_47 : List CollectedFourTerm := [ + ⟨6, 2, 2, 0, 5, 5, -244996456555910556867378916501551114004463616000000⟩, + ⟨6, 2, 3, 0, 6, 5, -39324490127671663061870520023181106098890342400000⟩, + ⟨6, 2, 4, 0, 7, 5, 282073259733402290351001559559096344518013747200000⟩, + ⟨6, 2, 5, 0, 8, 5, 8863451027114256524805709475515553154072576000000⟩, + ⟨6, 2, 2, 1, 4, 5, 844391198339276538118264038088561132993039564800000⟩, + ⟨6, 2, 3, 1, 5, 5, 527200939886521279018426224445954897636176691200000⟩, + ⟨6, 2, 4, 1, 6, 5, 631994823248131737776830843371052215260990668800000⟩, + ⟨6, 2, 5, 1, 7, 5, -70300785370023682552357517734303388248571904000000⟩, + ⟨6, 2, 6, 1, 8, 5, -9613429089047305729145341793994262972465152000000⟩, + ⟨6, 2, 2, 2, 3, 5, -314699414378800724037583489025781402204477849600000⟩, + ⟨6, 2, 3, 2, 4, 5, -686528921695169150068306006749001079413171814400000⟩, + ⟨6, 2, 4, 2, 5, 5, -80196830959297581301772742266719808950527590400000⟩, + ⟨6, 2, 5, 2, 6, 5, -49136593617392208361686145358855938278162432000000⟩, + ⟨6, 2, 6, 2, 7, 5, -12863867688412935549154274009999037356310528000000⟩, + ⟨6, 2, 7, 2, 8, 5, -12065810748126711054883810345795909056882278400000⟩, + ⟨6, 2, 2, 3, 2, 5, -168278962488485054700869326970383829909372928000000⟩, + ⟨6, 2, 3, 3, 3, 5, 917643241825653741027727460991819739936535347200000⟩, + ⟨6, 2, 4, 3, 4, 5, 55023036634961618248891251800981547065435750400000⟩, + ⟨6, 2, 5, 3, 5, 5, 18566741480902113955300621604162443306598400000000⟩, + ⟨6, 2, 6, 3, 6, 5, 34085488127305532897148721730033258009198592000000⟩, + ⟨6, 2, 7, 3, 7, 5, 6737296737105148583703723867118418381085081600000⟩, + ⟨6, 2, 8, 3, 8, 5, 5081209794667657166382698457293040019046400000000⟩, + ⟨6, 2, 2, 4, 1, 5, -388461437859672572903256828146495523777832550400000⟩, + ⟨6, 2, 3, 4, 2, 5, -1256211971731290400495408851141688224204718080000000⟩, + ⟨6, 2, 4, 4, 3, 5, 122984499137966532301023435226256968639315968000000⟩, + ⟨6, 2, 5, 4, 4, 5, -66888688099599603851032749465910652065284096000000⟩, + ⟨6, 2, 6, 4, 5, 5, -27118457178230748680371261274983398541099008000000⟩, + ⟨6, 2, 7, 4, 6, 5, -2212698977378420373189532110114706862112768000000⟩, + ⟨6, 2, 8, 4, 7, 5, 1804980177333415568960722777270347493067980800000⟩, + ⟨6, 2, 2, 5, 0, 5, 2898339982160340144278816847836017119416077516800000⟩, + ⟨6, 2, 3, 5, 1, 5, 1043186451766980367581445189728893243527633305600000⟩, + ⟨6, 2, 4, 5, 2, 5, -842648157158767383002492439726671241109359820800000⟩, + ⟨6, 2, 5, 5, 3, 5, 174449543883437682409041581943017995681923072000000⟩, + ⟨6, 2, 6, 5, 4, 5, -30586395431178041900350574556456334972157952000000⟩, + ⟨6, 2, 7, 5, 5, 5, -5860204691324541709249638439060460055979622400000⟩, + ⟨6, 2, 8, 5, 6, 5, 3758442458519617506285970439864346729460531200000⟩, + ⟨6, 2, 3, 6, 0, 5, 568119874623892796523180876962408240030259609600000⟩, + ⟨6, 2, 4, 6, 1, 5, 452170149287239046337784151458151408352834355200000⟩, + ⟨6, 2, 5, 6, 2, 5, 2581840096442178863622834185392332931596288000000⟩, + ⟨6, 2, 6, 6, 3, 5, 113254977361716837847070065917181368647811072000000⟩, + ⟨6, 2, 7, 6, 4, 5, 2097868775942651332271528535425606635801804800000⟩, + ⟨6, 2, 8, 6, 5, 5, -3944317688142065619786179834236409269872230400000⟩, + ⟨6, 2, 4, 7, 0, 5, 8627963753751437574602754033462103099465688678400000⟩, + ⟨6, 2, 5, 7, 1, 5, -120356501597170521297920865725273100880183296000000⟩, + ⟨6, 2, 6, 7, 2, 5, -111768791842587161038596913720568884450295808000000⟩, + ⟨6, 2, 7, 7, 3, 5, 87899786349880071380900025011854830686384947200000⟩, + ⟨6, 2, 8, 7, 4, 5, 7798790703893137123107331794437037386366976000000⟩ +] + +def collectedFourData_10_3_48 : List CollectedFourTerm := [ + ⟨6, 3, 1, 0, 4, 6, 1745484983078964334360290884814777997930266624000000⟩, + ⟨6, 3, 2, 0, 5, 6, -42988050544534406435103160768086869008623599616000000⟩, + ⟨6, 3, 3, 0, 6, 6, -3450015549226135734344605575088786602544280371200000⟩, + ⟨6, 3, 4, 0, 7, 6, 16497897856893914462127531670521321075142714982400000⟩, + ⟨6, 3, 5, 0, 8, 6, 388804073035276788048781078552535480238342144000000⟩, + ⟨6, 3, 1, 1, 3, 6, -7049473551085663358338656713391747359905834598400000⟩, + ⟨6, 3, 2, 1, 4, 6, 148160230657397592889282668424860018631984860364800000⟩, + ⟨6, 3, 3, 1, 5, 6, 46252384564173949158299708030469851884998465945600000⟩, + ⟨6, 3, 4, 1, 6, 6, 36964106593754923888502135422399932803495598489600000⟩, + ⟨6, 3, 5, 1, 7, 6, -3083813698053804336960426082503353402419838976000000⟩, + ⟨6, 3, 6, 1, 8, 6, -337362083840549280754836633303390602658211430400000⟩, + ⟨6, 3, 1, 2, 2, 6, -1230685029748226549504507892007994512308279705600000⟩, + ⟨6, 3, 2, 2, 3, 6, -55218408142829491620026164476919418893505239449600000⟩, + ⟨6, 3, 3, 2, 4, 6, -60230544557654833844742304331128884536664077107200000⟩, + ⟨6, 3, 4, 2, 5, 6, -4690551408040483380843306054473034036084001996800000⟩, + ⟨6, 3, 5, 2, 6, 6, -2155425429110909220682265631639027995123908608000000⟩, + ⟨6, 3, 6, 2, 7, 6, -451429055065945413728221391417070252652599705600000⟩, + ⟨6, 3, 7, 2, 8, 6, -352852506244914113927972889598836225937401446400000⟩, + ⟨6, 3, 1, 3, 1, 6, 6906629206574399721953759691422625196922634240000000⟩, + ⟨6, 3, 2, 3, 2, 6, -29526894579334210866110782198088001706606460928000000⟩, + ⟨6, 3, 3, 3, 3, 6, 80506662455440998694337368221511903265060133273600000⟩, + ⟨6, 3, 4, 3, 4, 6, 3218186789622277034997223356149881014223424716800000⟩, + ⟨6, 3, 5, 3, 5, 6, 814448535754820791517966467359422996388249600000000⟩, + ⟨6, 3, 6, 3, 6, 6, 1196155003260097516759374833638368588163606118400000⟩, + ⟨6, 3, 7, 3, 7, 6, 197025470449411744635505709935968926033353113600000⟩, + ⟨6, 3, 8, 3, 8, 6, 127367033647985147618578255071690930467635200000000⟩, + ⟨6, 3, 1, 4, 0, 6, -55263417110840099686797106905088705710156624691200000⟩, + ⟨6, 3, 2, 4, 1, 6, -68160985510021845474906688165998520027075470950400000⟩, + ⟨6, 3, 3, 4, 2, 6, -110209968941142904270359928253673738003850199040000000⟩, + ⟨6, 3, 4, 4, 3, 6, 7193116095716048377655481607120019091049414656000000⟩, + ⟨6, 3, 5, 4, 4, 6, -2934138666029020214514249230544300088202625024000000⟩, + ⟨6, 3, 6, 4, 5, 6, -951662423412671226597163586453462701500373401600000⟩, + ⟨6, 3, 7, 4, 6, 6, -64708157291025903431103257105079302910640128000000⟩, + ⟨6, 3, 8, 4, 7, 6, 45244140720508845937971912966693215560689254400000⟩, + ⟨6, 3, 2, 5, 0, 6, 508554235436136201715124797294486999273315290316800000⟩, + ⟨6, 3, 3, 5, 1, 6, 91520817374961698631547308266390983129372085452800000⟩, + ⟨6, 3, 4, 5, 2, 6, -49284796578181316166122306588389766267145918873600000⟩, + ⟨6, 3, 5, 5, 3, 6, 7652402319766604251315699413799400188850208768000000⟩, + ⟨6, 3, 6, 5, 4, 6, -1073362065112591986665266355381908309079909990400000⟩, + ⟨6, 3, 7, 5, 5, 6, -171375795262088312096849672432751621429421670400000⟩, + ⟨6, 3, 8, 5, 6, 6, 94210175612242009796571593868950421888407961600000⟩, + ⟨6, 3, 3, 6, 0, 6, 49842283902814393862035956299489300483349990604800000⟩, + ⟨6, 3, 4, 6, 1, 6, 26446522949137131513088042203995754242232444518400000⟩, + ⟨6, 3, 5, 6, 2, 6, 113254977361716837847070065917181368647811072000000⟩, + ⟨6, 3, 6, 6, 3, 6, 3974433556866174036040670658561868893922944614400000⟩, + ⟨6, 3, 7, 6, 4, 6, 61350063482409675866760760069215976413777100800000⟩, + ⟨6, 3, 8, 6, 5, 6, -98869376389681620810954892050744801448112947200000⟩, + ⟨6, 3, 4, 7, 0, 6, 504632253539055841399756028400419640585415871692800000⟩, + ⟨6, 3, 5, 7, 1, 6, -5279557352334369802990156138800836571587149824000000⟩, + ⟨6, 3, 6, 7, 2, 6, -3922279155032756707092281193959472498780772761600000⟩, + ⟨6, 3, 7, 7, 3, 6, 2570540891068015475773585403272653172271952691200000⟩, + ⟨6, 3, 8, 7, 4, 6, 195486680955144377663705760376789498035437568000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1013.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1013.lean new file mode 100644 index 0000000000000000000000000000000000000000..f3a0d28f2befab9fd4f32c543c9789de9f5ca685 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1013.lean @@ -0,0 +1,624 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1009 +import OAI.Analysis.LaughlinFock.Sparse1010 +import OAI.Analysis.LaughlinFock.Sparse1011 +import OAI.Analysis.LaughlinFock.Sparse1012 + +namespace OAI + +/-! Sparse1013. -/ +namespace LaughlinFock +def collectedFourData_10_3_49 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 3, 7, -5841091707999553272203905834242560784758892134400000⟩, + ⟨6, 4, 1, 0, 4, 7, 161661700447080332894015412167433112894046208000000⟩, + ⟨6, 4, 2, 0, 5, 7, -1990713588860500398189965178013550071498407936000000⟩, + ⟨6, 4, 3, 0, 6, 7, -106510107632653938111228298495056594533665996800000⟩, + ⟨6, 4, 4, 0, 7, 7, 381996729734548527987612435015228971470238515200000⟩, + ⟨6, 4, 5, 0, 8, 7, 7201978613045468142350134220998688678451609600000⟩, + ⟨6, 4, 0, 1, 2, 7, 2284756639362331346857832112656831919330793881600000⟩, + ⟨6, 4, 1, 1, 3, 7, -652901567514471265091428755511696913777609932800000⟩, + ⟨6, 4, 2, 1, 4, 7, 6861083039642219590473759299671971459079392460800000⟩, + ⟨6, 4, 3, 1, 5, 7, 1427920073955053696053202617025010728287233638400000⟩, + ⟨6, 4, 4, 1, 6, 7, 855876788597845601835733187682464853215988940800000⟩, + ⟨6, 4, 5, 1, 7, 7, -57122756268000943685205654069455132052317798400000⟩, + ⟨6, 4, 6, 1, 8, 7, -5207581146857910200319635439131481397316812800000⟩, + ⟨6, 4, 0, 2, 1, 7, 2360408829858797065251417910997931057035083776000000⟩, + ⟨6, 4, 1, 2, 2, 7, -113982438435486328893687351902761550605398835200000⟩, + ⟨6, 4, 2, 2, 3, 7, -2557083516297110968690258118632805867267398041600000⟩, + ⟨6, 4, 3, 2, 4, 7, -1859458803032972982391466098629253157293444300800000⟩, + ⟨6, 4, 4, 2, 5, 7, -108606279058427082296949435285972999194699366400000⟩, + ⟨6, 4, 5, 2, 6, 7, -39925836479245585813154405944071984268915507200000⟩, + ⟨6, 4, 6, 2, 7, 7, -6968339208553162165686818590692710284473139200000⟩, + ⟨6, 4, 7, 2, 8, 7, -4668594911160514532985014706341676893759078400000⟩, + ⟨6, 4, 0, 3, 0, 7, -13189383896015573905027841731744905485613426278400000⟩, + ⟨6, 4, 1, 3, 1, 7, 639671743221050368079189097698437976115118080000000⟩, + ⟨6, 4, 2, 3, 2, 7, -1367347193728593634266975355608447632422207488000000⟩, + ⟨6, 4, 3, 3, 3, 7, 2485430329494644239072739160087009943932528230400000⟩, + ⟨6, 4, 4, 3, 4, 7, 74514755757015248439775825727628686441997926400000⟩, + ⟨6, 4, 5, 3, 5, 7, 15086366997498552550203872616116596129136640000000⟩, + ⟨6, 4, 6, 3, 6, 7, 18464061440411169080038620688114818659175628800000⟩, + ⟨6, 4, 7, 3, 7, 7, 2606845898582555771691690135699664206928281600000⟩, + ⟨6, 4, 8, 3, 8, 7, 1474545143616274564637424979585767623884800000000⟩, + ⟨6, 4, 1, 4, 0, 7, -5118335631221251186301590582316965060936099430400000⟩, + ⟨6, 4, 2, 4, 1, 7, -3156435296928716986982191530620186459717920358400000⟩, + ⟨6, 4, 3, 4, 2, 7, -3402441376458609325133528726924871225374146560000000⟩, + ⟨6, 4, 4, 4, 3, 7, 166551329690545005549428659107765569231781888000000⟩, + ⟨6, 4, 5, 4, 4, 7, -54350263760054438323128234797283243281979801600000⟩, + ⟨6, 4, 6, 4, 5, 7, -14690030479771616786561212678410306816521011200000⟩, + ⟨6, 4, 7, 4, 6, 7, -856154252819089849855460361961643094048768000000⟩, + ⟨6, 4, 8, 4, 7, 7, 523797454221177325340951209736636376652185600000⟩, + ⟨6, 4, 2, 5, 0, 7, 23550400967973075137464922172985219686798773452800000⟩, + ⟨6, 4, 3, 5, 1, 7, 2825463239266315831059672442808057560195871539200000⟩, + ⟨6, 4, 4, 5, 2, 7, -1141153332491431134705312836921142105302944972800000⟩, + ⟨6, 4, 5, 5, 3, 7, 141748612392695216780870136297267681622700851200000⟩, + ⟨6, 4, 6, 5, 4, 7, -16568607800853764858715193212687113752726732800000⟩, + ⟨6, 4, 7, 5, 5, 7, -2267474798949947459323207602736267098744422400000⟩, + ⟨6, 4, 8, 5, 6, 7, 1090683773889283859011674001337956086212198400000⟩, + ⟨6, 4, 3, 6, 0, 7, 1538748723708459383048236772273778941416911667200000⟩, + ⟨6, 4, 4, 6, 1, 7, 612349850087026973907779553807570169970766643200000⟩, + ⟨6, 4, 5, 6, 2, 7, 2097868775942651332271528535425606635801804800000⟩, + ⟨6, 4, 6, 6, 3, 7, 61350063482409675866760760069215976413777100800000⟩, + ⟨6, 4, 7, 6, 4, 7, 811723281269681104008733134453615094451404800000⟩, + ⟨6, 4, 8, 6, 5, 7, -1144623962984795787393595418532294702189772800000⟩, + ⟨6, 4, 4, 7, 0, 7, 11684389868491257501615964378937512740723779174400000⟩, + ⟨6, 4, 5, 7, 1, 7, -97795423903414664511573434489349525105908121600000⟩, + ⟨6, 4, 6, 7, 2, 7, -60544998856825599139590702664253756136436531200000⟩, + ⟨6, 4, 7, 7, 3, 7, 34010851306354089105102514719243273090839347200000⟩, + ⟨6, 4, 8, 7, 4, 7, 2263175389957997788934560563515227983839232000000⟩ +] + +def collectedFourData_10_3_50 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 3, 8, 65892933646157854939917283685909050594444915507200000⟩, + ⟨6, 5, 1, 0, 4, 8, -911846982824783847976349333513348834710781952000000⟩, + ⟨6, 5, 2, 0, 5, 8, 7485698734458776147635382946612014146551545856000000⟩, + ⟨6, 5, 3, 0, 6, 8, 300383207700363244818879822125747899570166169600000⟩, + ⟨6, 5, 4, 0, 7, 8, -861855503175052237797290588253858742582923755520000⟩, + ⟨6, 5, 5, 0, 8, 8, -13540833420475413879775804815007785524448460800000⟩, + ⟨6, 5, 0, 1, 2, 8, -25774174616868081084513565981299759812172369100800000⟩, + ⟨6, 5, 1, 1, 3, 8, 3682667711481409791042445552062977512500835123200000⟩, + ⟨6, 5, 2, 1, 4, 8, -25799794060915207448845878197330679295772511436800000⟩, + ⟨6, 5, 3, 1, 5, 8, -4027065803310289603948371458932496862811049164800000⟩, + ⟨6, 5, 4, 1, 6, 8, -1931016846153199524250822701990960274000136110080000⟩, + ⟨6, 5, 5, 1, 7, 8, 107399614564578177963780755901284716572259123200000⟩, + ⟨6, 5, 6, 1, 8, 8, 8392335252206030745231637546650430461915955200000⟩, + ⟨6, 5, 0, 2, 1, 8, -26627601513374957620807165502812411238692159488000000⟩, + ⟨6, 5, 1, 2, 2, 8, 642913827424651336039007813414719586837515468800000⟩, + ⟨6, 5, 2, 2, 3, 8, 9615424814981774258584815253009430738133162393600000⟩, + ⟨6, 5, 3, 2, 4, 8, 5244105111301959367667338999084793360167836057600000⟩, + ⟨6, 5, 4, 2, 5, 8, 245035917849129118667670862822133018579844464640000⟩, + ⟨6, 5, 5, 2, 6, 8, 75066746235447605332473211676244720196622745600000⟩, + ⟨6, 5, 6, 2, 7, 8, 11229904468134028628635020073160913927851212800000⟩, + ⟨6, 5, 7, 2, 8, 8, 6583260246551703711692692763516409838200422400000⟩, + ⟨6, 5, 0, 3, 0, 8, 148788487039779867887319887745645098807160156979200000⟩, + ⟨6, 5, 1, 3, 1, 8, -3608045365360493770488098732381438056354283520000000⟩, + ⟨6, 5, 2, 3, 2, 8, 5141648308895504443853863736780103372502990848000000⟩, + ⟨6, 5, 3, 3, 3, 8, -7009490005063937456544637035777224172454595788800000⟩, + ⟨6, 5, 4, 3, 4, 8, -168119115473988387656899058549190505301425520640000⟩, + ⟨6, 5, 5, 3, 5, 8, -28364702730893271356892014185255917028638720000000⟩, + ⟨6, 5, 6, 3, 6, 8, -29755963345622876158435982413983106160866099200000⟩, + ⟨6, 5, 7, 3, 7, 8, -3675955035635956360467275966671313559984537600000⟩, + ⟨6, 5, 8, 3, 8, 8, -1848248584031437090096397713235607394713600000000⟩, + ⟨6, 5, 1, 4, 0, 8, 28869787274948669475718023230952976538882644377600000⟩, + ⟨6, 5, 2, 4, 1, 8, 11869172863357619322372067877254045409347004006400000⟩, + ⟨6, 5, 3, 4, 2, 8, 9595673850955153053489744348946522584719032320000000⟩, + ⟨6, 5, 4, 4, 3, 8, -375770703991805295260356633239527105745439948800000⟩, + ⟨6, 5, 5, 4, 4, 8, 102186899944512876146908564639915418181225676800000⟩, + ⟨6, 5, 6, 4, 5, 8, 23673881822418431825527057918735390396435660800000⟩, + ⟨6, 5, 7, 4, 6, 8, 1207276785575518879731099640927088592027648000000⟩, + ⟨6, 5, 8, 4, 7, 8, -656546805145150707420569799456068834898739200000⟩, + ⟨6, 5, 2, 5, 0, 8, -88556790745002757089465865115293999934691134668800000⟩, + ⟨6, 5, 3, 5, 1, 8, -7968461678561605586849952208291965113301624422400000⟩, + ⟨6, 5, 4, 5, 2, 8, 2574653663285902141505498062578717071221488353280000⟩, + ⟨6, 5, 5, 5, 3, 8, -266509309610595636158408647852038095726287257600000⟩, + ⟨6, 5, 6, 5, 4, 8, 26701323974755313574405725537854165504701235200000⟩, + ⟨6, 5, 7, 5, 5, 8, 3197402427934012790602667641467068928648806400000⟩, + ⟨6, 5, 8, 5, 6, 8, -1367102763482109498820044600377545943993548800000⟩, + ⟨6, 5, 3, 6, 0, 8, -4339628301442829991334911102083645600807937638400000⟩, + ⟨6, 5, 4, 6, 1, 8, -1381574885556385587412528776016700731329683128320000⟩, + ⟨6, 5, 5, 6, 2, 8, -3944317688142065619786179834236409269872230400000⟩, + ⟨6, 5, 6, 6, 3, 8, -98869376389681620810954892050744801448112947200000⟩, + ⟨6, 5, 7, 6, 4, 8, -1144623962984795787393595418532294702189772800000⟩, + ⟨6, 5, 8, 6, 5, 8, 1434713360926192764480144771266433053727129600000⟩, + ⟨6, 5, 4, 7, 0, 8, -26362151624700785090814030353554613872841132605440000⟩, + ⟨6, 5, 5, 7, 1, 8, 183870518854671471420733882365221079064825036800000⟩, + ⟨6, 5, 6, 7, 2, 8, 97571965548245212730604030454396757193051340800000⟩, + ⟨6, 5, 7, 7, 3, 8, -47959244615816229500423472744130742488085299200000⟩, + ⟨6, 5, 8, 7, 4, 8, -2836746455687488025957254114446756412391424000000⟩ +] + +def collectedFourData_10_3_51 : List CollectedFourTerm := [ + ⟨7, 0, 3, 0, 6, 4, -43804710695013649040193559651143610563646917181440000⟩, + ⟨7, 0, 4, 0, 7, 4, 628419465697098731255525434860159315812092099952640000⟩, + ⟨7, 0, 5, 0, 8, 4, 29619779435788696968286758682718525568368561356800000⟩, + ⟨7, 0, 3, 1, 5, 4, 587264693703371269190082751381164865700210902302720000⟩, + ⟨7, 0, 4, 1, 6, 4, 1407995389298126466623597920441734233139209369026560000⟩, + ⟨7, 0, 5, 1, 7, 4, -234930361825530513816113656979593250199376704307200000⟩, + ⟨7, 0, 6, 1, 8, 4, -42834730079454358157158076629984386572484398284800000⟩, + ⟨7, 0, 3, 2, 4, 4, -764744837148055038527032846473574272778430463344640000⟩, + ⟨7, 0, 4, 2, 5, 4, -178667235985696084176847912678336546835251310100480000⟩, + ⟨7, 0, 5, 2, 6, 4, -164204107488253455805803827325882945429304875417600000⟩, + ⟨7, 0, 6, 2, 7, 4, -57317768208096168809095369426987536156099556147200000⟩, + ⟨7, 0, 7, 2, 8, 4, -67202314309290537754231568787725725012669444915200000⟩, + ⟨7, 0, 3, 3, 3, 4, 1022189902498481884632772659283997535869329546936320000⟩, + ⟨7, 0, 4, 3, 4, 4, 122583570366985401466256178404280944575566556692480000⟩, + ⟨7, 0, 5, 3, 5, 4, 62046124677994482285621133509225427995061125120000000⟩, + ⟨7, 0, 6, 3, 6, 4, 151875326695135529876843514207512351047502580940800000⟩, + ⟨7, 0, 7, 3, 7, 4, 37524368844604309933905906220181958196990889164800000⟩, + ⟨7, 0, 8, 3, 8, 4, 33960657744848183001014907483545605363508183040000000⟩, + ⟨7, 0, 3, 4, 2, 4, -1399331607724520949342133893339837699895798530048000000⟩, + ⟨7, 0, 4, 4, 3, 4, 273992129953586887453153492424482744295312955801600000⟩, + ⟨7, 0, 5, 4, 4, 4, -223527854127992912256416690915820672291420556492800000⟩, + ⟨7, 0, 6, 4, 5, 4, -120832200730974731941505300121256898916420629299200000⟩, + ⟨7, 0, 7, 4, 6, 4, -12323953628455235421042864825954096290834939904000000⟩, + ⟨7, 0, 8, 4, 7, 4, 12063724293175892874376222591502345118403138682880000⟩, + ⟨7, 0, 3, 5, 1, 4, 1162036190990685244935085531298604335080318288527360000⟩, + ⟨7, 0, 4, 5, 2, 4, -1877301326587432336284891449426530543295672572968960000⟩, + ⟨7, 0, 5, 5, 3, 4, 582973493811211058823911355727944491583195945369600000⟩, + ⟨7, 0, 6, 5, 4, 4, -136284356004731788085442876759568603323139149004800000⟩, + ⟨7, 0, 7, 5, 5, 4, -32639275205299700361985365239988049336081789747200000⟩, + ⟨7, 0, 8, 5, 6, 4, 25119840184799709280928779644833554908049645240320000⟩, + ⟨7, 0, 3, 6, 0, 4, 632845503328602921645180672415553966186774145269760000⟩, + ⟨7, 0, 4, 6, 1, 4, 1007371361212427678794095964056729716097615648522240000⟩, + ⟨7, 0, 5, 6, 2, 4, 8627963753751437574602754033462103099465688678400000⟩, + ⟨7, 0, 6, 6, 3, 4, 504632253539055841399756028400419640585415871692800000⟩, + ⟨7, 0, 7, 6, 4, 4, 11684389868491257501615964378937512740723779174400000⟩, + ⟨7, 0, 8, 6, 5, 4, -26362151624700785090814030353554613872841132605440000⟩, + ⟨7, 0, 4, 7, 0, 4, 19221887169705217092348377750122764618862963017646080000⟩, + ⟨7, 0, 5, 7, 1, 4, -402205982756132422528236301671695157455793999052800000⟩, + ⟨7, 0, 6, 7, 2, 4, -498010229808476452305546044629775365927054029619200000⟩, + ⟨7, 0, 7, 7, 3, 4, 489570837245332581167915868783662347697532803481600000⟩, + ⟨7, 0, 8, 7, 4, 4, 52123819448777839283525897452737723767386118553600000⟩ +] + +def collectedFourData_10_3_52 : List CollectedFourTerm := [ + ⟨7, 1, 2, 0, 5, 5, 11420891811001795755134042955241607401436086272000000⟩, + ⟨7, 1, 3, 0, 6, 5, 1833172420469079590352203595404265546507406540800000⟩, + ⟨7, 1, 4, 0, 7, 5, -13149284799784902031752469697321382216238261862400000⟩, + ⟨7, 1, 5, 0, 8, 5, -413183589166251240594766346187590074569326592000000⟩, + ⟨7, 1, 2, 1, 4, 5, -39362612251472506350124822834670810359473478041600000⟩, + ⟨7, 1, 3, 1, 5, 5, -24576293803369138101516098464892463311413995110400000⟩, + ⟨7, 1, 4, 1, 6, 5, -29461424066690166464911694569177642471983258009600000⟩, + ⟨7, 1, 5, 1, 7, 5, 3277180720188372703724264763329946350222573568000000⟩, + ⟨7, 1, 6, 1, 8, 5, 448144985858972174324297007081274674128093184000000⟩, + ⟨7, 1, 2, 2, 3, 5, 14670203867971807570345325706424737646649750323200000⟩, + ⟨7, 1, 3, 2, 4, 5, 32003616093177700407154151429631879429493673164800000⟩, + ⟨7, 1, 4, 2, 5, 5, 3738500314849718653054612595251920040987774156800000⟩, + ⟨7, 1, 5, 2, 6, 5, 2290578923280591341100256964406794294283730944000000⟩, + ⟨7, 1, 6, 2, 7, 5, 599669249121887009421314935629499857031397376000000⟩, + ⟨7, 1, 7, 2, 8, 5, 562466580552074170022643218678788372554370252800000⟩, + ⟨7, 1, 2, 3, 2, 5, 7844586210209216423638057050467079205920178176000000⟩, + ⟨7, 1, 3, 3, 3, 5, -42777370470237975702618538072196396497221609062400000⟩, + ⟨7, 1, 4, 3, 4, 5, -2564984642450431646724325939958803618664860876800000⟩, + ⟨7, 1, 5, 3, 5, 5, -865517602650839712627807843396033113279692800000000⟩, + ⟨7, 1, 6, 3, 6, 5, -1588948173780234728092404959144972517233393664000000⟩, + ⟨7, 1, 7, 3, 7, 5, -314069591922989727246281736341680676276482867200000⟩, + ⟨7, 1, 8, 3, 8, 5, -236868516996932611215227265481087646485708800000000⟩, + ⟨7, 1, 2, 4, 1, 5, 18108735599320996485968992044996079950670646476800000⟩, + ⟨7, 1, 3, 4, 2, 5, 58560279697572589293257230060145636351001231360000000⟩, + ⟨7, 1, 4, 4, 3, 5, -5733114179814342627510100353441590785244921856000000⟩, + ⟨7, 1, 5, 4, 4, 5, 3118120485922352640062234404786927487189778432000000⟩, + ⟨7, 1, 6, 4, 5, 5, 1264169163373911986690111136208266014842945536000000⟩, + ⟨7, 1, 7, 4, 6, 5, 103148412781987170313205906012044444047507456000000⟩, + ⟨7, 1, 8, 4, 7, 5, -84141965219090223287816221824146217939605913600000⟩, + ⟨7, 1, 2, 5, 0, 5, -135110637243849314957996640724531557201929148825600000⟩, + ⟨7, 1, 3, 5, 1, 5, -48629762943590201441262339078530176164859949875200000⟩, + ⟨7, 1, 4, 5, 2, 5, 39281357669163178445202848775132835683052919193600000⟩, + ⟨7, 1, 5, 5, 3, 5, -8132237482857936388047077168753249105240653824000000⟩, + ⟨7, 1, 6, 5, 4, 5, 1425832512105271811341224945323333530926710784000000⟩, + ⟨7, 1, 7, 5, 5, 5, 273182578682189938296394631359513712594308300800000⟩, + ⟨7, 1, 8, 5, 6, 5, -175205655216618654454944868370095868173772390400000⟩, + ⟨7, 1, 3, 6, 0, 5, -26483793745313457187385121774678501126625768243200000⟩, + ⟨7, 1, 4, 6, 1, 5, -21078616514584449553707507794246164926502954598400000⟩, + ⟨7, 1, 5, 6, 2, 5, -120356501597170521297920865725273100880183296000000⟩, + ⟨7, 1, 6, 6, 3, 5, -5279557352334369802990156138800836571587149824000000⟩, + ⟨7, 1, 7, 6, 4, 5, -97795423903414664511573434489349525105908121600000⟩, + ⟨7, 1, 8, 6, 5, 5, 183870518854671471420733882365221079064825036800000⟩, + ⟨7, 1, 4, 7, 0, 5, -402205982756132422528236301671695157455793999052800000⟩, + ⟨7, 1, 5, 7, 1, 5, 5610605976981782402763805220802351166056824832000000⟩, + ⟨7, 1, 6, 7, 2, 5, 5210276497159290781628241631996100938234331136000000⟩, + ⟨7, 1, 7, 7, 3, 5, -4097585590520793684953032695055763135195932262400000⟩, + ⟨7, 1, 8, 7, 4, 5, -363552788223627313836562318381713368014651392000000⟩ +] + +def collectedFourData_10_3_53 : List CollectedFourTerm := [ + ⟨7, 2, 1, 0, 4, 6, -1722579901411559006665734181722674435337486336000000⟩, + ⟨7, 2, 2, 0, 5, 6, 42423940960097744392811153226807061875234177024000000⟩, + ⟨7, 2, 3, 0, 6, 6, 3404742809171134096606864504211393300730268876800000⟩, + ⟨7, 2, 4, 0, 7, 6, -16281404617813683887553613062347406803199433113600000⟩, + ⟨7, 2, 5, 0, 8, 6, -383702001615685572472417829933001384306671616000000⟩, + ⟨7, 2, 1, 1, 3, 6, 6956967016245697768299374499971871770114890137600000⟩, + ⟨7, 2, 2, 1, 4, 6, -146216001852241623424209163678016873434801451827200000⟩, + ⟨7, 2, 3, 1, 5, 6, -45645438840764815242407359210574825863824959078400000⟩, + ⟨7, 2, 4, 1, 6, 6, -36479046058430725216974416061292791958669256294400000⟩, + ⟨7, 2, 5, 1, 7, 6, 3043346432344999237664584672323830057023832064000000⟩, + ⟨7, 2, 6, 1, 8, 6, 332935058597270950370042998368700107656370585600000⟩, + ⟨7, 2, 1, 2, 2, 6, 1214535397189651257937246961531671670096815718400000⟩, + ⟨7, 2, 2, 2, 3, 6, 54493806006279107370347592539063952281440773734400000⟩, + ⟨7, 2, 3, 2, 4, 6, 59440170790283975788759641149351626222569573580800000⟩, + ⟨7, 2, 4, 2, 5, 6, 4628999768176578611633294839131944653564359475200000⟩, + ⟨7, 2, 5, 2, 6, 6, 2127140914514455611059599432957177837714931712000000⟩, + ⟨7, 2, 6, 2, 7, 6, 445505188935005848764753762417748843365295718400000⟩, + ⟨7, 2, 7, 2, 8, 6, 348222208333194538977434809977883654503373209600000⟩, + ⟨7, 2, 1, 3, 1, 6, -6815997142960755452370627567740941923369615360000000⟩, + ⟨7, 2, 2, 3, 2, 6, 29139428666833764111700276834800199234530312192000000⟩, + ⟨7, 2, 3, 3, 3, 6, -79450215853958728135719725054446837376945120870400000⟩, + ⟨7, 2, 4, 3, 4, 6, -3175956216485384848567114045712895437402485555200000⟩, + ⟨7, 2, 5, 3, 5, 6, -803760955852267759566116289669134501176934400000000⟩, + ⟨7, 2, 6, 3, 6, 6, -1180458490083445022523170130883695317874219417600000⟩, + ⟨7, 2, 7, 3, 7, 6, -194440008795515309008492682509962034754774630400000⟩, + ⟨7, 2, 8, 3, 8, 6, -125695663034245365330039175390050032340172800000000⟩, + ⟨7, 2, 1, 4, 0, 6, 54538224345267957778693925892147925884911537356800000⟩, + ⟨7, 2, 2, 4, 1, 6, 67266544735811384890089356719676435510691731865600000⟩, + ⟨7, 2, 3, 4, 2, 6, 108763741466469246478491622802681042871842242560000000⟩, + ⟨7, 2, 4, 4, 3, 6, -7098724615289287074676517318160156837317443584000000⟩, + ⟨7, 2, 5, 4, 4, 6, 2895635507067241820372505611332664020420263936000000⟩, + ⟨7, 2, 6, 4, 5, 6, 939174257808623756691429937921696718423221862400000⟩, + ⟨7, 2, 7, 4, 6, 6, 63859026166056948749212487049676738623700992000000⟩, + ⟨7, 2, 8, 4, 7, 6, -44650425650931560593898135473498348324493721600000⟩, + ⟨7, 2, 2, 5, 0, 6, -501880745599275996257717741215428362945812443955200000⟩, + ⟨7, 2, 3, 5, 1, 6, -90319837809647184758065419112664615599335486259200000⟩, + ⟨7, 2, 4, 5, 2, 6, 48638058106336421229459373844543047997157959270400000⟩, + ⟨7, 2, 5, 5, 3, 6, -7551983867711570688691385308163685555426557952000000⟩, + ⟨7, 2, 6, 5, 4, 6, 1059276899099458473148631804347396857429334425600000⟩, + ⟨7, 2, 7, 5, 5, 6, 169126920809229678171088144304932888432449945600000⟩, + ⟨7, 2, 8, 5, 6, 6, -92973905012828104860288643458436255315289702400000⟩, + ⟨7, 2, 3, 6, 0, 6, -49188229817931832202592321391253832021780411187200000⟩, + ⟨7, 2, 4, 6, 1, 6, -26099479133898824699879975258457060200779717017600000⟩, + ⟨7, 2, 5, 6, 2, 6, -111768791842587161038596913720568884450295808000000⟩, + ⟨7, 2, 6, 6, 3, 6, -3922279155032756707092281193959472498780772761600000⟩, + ⟨7, 2, 7, 6, 4, 6, -60544998856825599139590702664253756136436531200000⟩, + ⟨7, 2, 8, 6, 5, 6, 97571965548245212730604030454396757193051340800000⟩, + ⟨7, 2, 4, 7, 0, 6, -498010229808476452305546044629775365927054029619200000⟩, + ⟨7, 2, 5, 7, 1, 6, 5210276497159290781628241631996100938234331136000000⟩, + ⟨7, 2, 6, 7, 2, 6, 3870809147992127495355358924182845830015116902400000⟩, + ⟨7, 2, 7, 7, 3, 6, -2536809034529520040812255204413368198545329356800000⟩, + ⟨7, 2, 8, 7, 4, 6, -192921412026694921649977904906450137516081152000000⟩ +] + +def collectedFourData_10_3_54 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 3, 7, -244739193924325927987447259472941140439939520921600000⟩, + ⟨7, 3, 1, 0, 4, 7, 6773554710957348848321948303121094404275699712000000⟩, + ⟨7, 3, 2, 0, 5, 7, -83410030766111385969204955996123238196213448704000000⟩, + ⟨7, 3, 3, 0, 6, 7, -4462727036301980445369031303544040512810070835200000⟩, + ⟨7, 3, 4, 0, 7, 7, 16005496299420393000131623802773844134747491532800000⟩, + ⟨7, 3, 5, 0, 8, 7, 301759761450593118266473958845992022745441894400000⟩, + ⟨7, 3, 0, 1, 2, 7, 95730306282469272732295576742557410237687948902400000⟩, + ⟨7, 3, 1, 1, 3, 7, -27356290798616028394830284224880998817358623539200000⟩, + ⟨7, 3, 2, 1, 4, 7, 287476385667805577725705321128757753459445543731200000⟩, + ⟨7, 3, 3, 1, 5, 7, 59829228055008383147496449202300549532701268377600000⟩, + ⟨7, 3, 4, 1, 6, 7, 35860863997924660052304787384659123176379462451200000⟩, + ⟨7, 3, 5, 1, 7, 7, -2393418563283299948485644640773701177649502617600000⟩, + ⟨7, 3, 6, 1, 8, 7, -218195377831862519042018334340963112288727859200000⟩, + ⟨7, 3, 0, 2, 1, 7, 98900100054985741924449258215397738650705854464000000⟩, + ⟨7, 3, 1, 2, 2, 7, -4775814436541999139278775644581655077981048012800000⟩, + ⟨7, 3, 2, 2, 3, 7, -107140683601775721952573612370506909228269463142400000⟩, + ⟨7, 3, 3, 2, 4, 7, -77910512510278249608457879954637130559862813491200000⟩, + ⟨7, 3, 4, 2, 5, 7, -4550555704420362185206269872163823224408873369600000⟩, + ⟨7, 3, 5, 2, 6, 7, -1672875127658543363328464954040604786175036620800000⟩, + ⟨7, 3, 6, 2, 7, 7, -291970372346139278042388623035644646217534668800000⟩, + ⟨7, 3, 7, 2, 8, 7, -195612089731757680062977726275501140074928537600000⟩, + ⟨7, 3, 0, 3, 0, 7, -552629430325250400458723039083877533461425789337600000⟩, + ⟨7, 3, 1, 3, 1, 7, 26801966933284834934801583858367049946491781120000000⟩, + ⟨7, 3, 2, 3, 2, 7, -57291250803256644296100418052585771091867205632000000⟩, + ⟨7, 3, 3, 3, 3, 7, 104138446339154369974440205553712897020233619865600000⟩, + ⟨7, 3, 4, 3, 4, 7, 3122135753229870620708030406692192268467149209600000⟩, + ⟨7, 3, 5, 3, 5, 7, 632112194567624023138278592651049256836136960000000⟩, + ⟨7, 3, 6, 3, 6, 7, 773636117937801677624070206674511219595096883200000⟩, + ⟨7, 3, 7, 3, 7, 7, 109225705706738510246943614324995315384870502400000⟩, + ⟨7, 3, 8, 3, 8, 7, 61782798129918361306018295536592698422067200000000⟩, + ⟨7, 3, 1, 4, 0, 7, -214456029667141249982071994847294135666365536665600000⟩, + ⟨7, 3, 2, 4, 1, 7, -132253261695353549496693924598704476227410434457600000⟩, + ⟨7, 3, 3, 4, 2, 7, -142560809087936633493702226803872725435510947840000000⟩, + ⟨7, 3, 4, 4, 3, 7, 6978428042768842317221794413047695511736287232000000⟩, + ⟨7, 3, 5, 4, 4, 7, -2277252336920720740302258506670059688770823782400000⟩, + ⟨7, 3, 6, 4, 5, 7, -615505867408195696763516643015714040988880076800000⟩, + ⟨7, 3, 7, 4, 6, 7, -35872489627728958150395316683897960558231552000000⟩, + ⟨7, 3, 8, 4, 7, 7, 21946884783565318120111511628177513673811558400000⟩, + ⟨7, 3, 2, 5, 0, 7, 986751524822461543417303677944130608499449344819200000⟩, + ⟨7, 3, 3, 5, 1, 7, 118385676892184461038503496621027887915790552268800000⟩, + ⟨7, 3, 4, 5, 2, 7, -47813826712482855631170769196873754028234978099200000⟩, + ⟨7, 3, 5, 5, 3, 7, 5939205010147154044424382213688130715020741836800000⟩, + ⟨7, 3, 6, 5, 4, 7, -694217437482760205576246052184834567149138739200000⟩, + ⟨7, 3, 7, 5, 5, 7, -95006204709767857359442781872901698757433753600000⟩, + ⟨7, 3, 8, 5, 6, 7, 45699174228412150370382894928189622371064217600000⟩, + ⟨7, 3, 3, 6, 0, 7, 64472900121862366845482918719233638622823238860800000⟩, + ⟨7, 3, 4, 6, 1, 7, 25657191532318305209994939957431396435193810124800000⟩, + ⟨7, 3, 5, 6, 2, 7, 87899786349880071380900025011854830686384947200000⟩, + ⟨7, 3, 6, 6, 3, 7, 2570540891068015475773585403272653172271952691200000⟩, + ⟨7, 3, 7, 6, 4, 7, 34010851306354089105102514719243273090839347200000⟩, + ⟨7, 3, 8, 6, 5, 7, -47959244615816229500423472744130742488085299200000⟩, + ⟨7, 3, 4, 7, 0, 7, 489570837245332581167915868783662347697532803481600000⟩, + ⟨7, 3, 5, 7, 1, 7, -4097585590520793684953032695055763135195932262400000⟩, + ⟨7, 3, 6, 7, 2, 7, -2536809034529520040812255204413368198545329356800000⟩, + ⟨7, 3, 7, 7, 3, 7, 1425039829797146516591589805615691573777714380800000⟩, + ⟨7, 3, 8, 7, 4, 7, 94826061348964311915629065303437039473000448000000⟩ +] + +def collectedFourData_10_3_55 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 3, 8, -130284941275600969045107244457989411887768403968000000⟩, + ⟨7, 4, 1, 0, 4, 8, 1802923682949241149485061621739582852568186880000000⟩, + ⟨7, 4, 2, 0, 5, 8, -14800886317537165759096932905451634370952560640000000⟩, + ⟨7, 4, 3, 0, 6, 8, -593924210228275625231420272391334551328129024000000⟩, + ⟨7, 4, 4, 0, 7, 8, 1704079442299387223237707148487485528210197708800000⟩, + ⟨7, 4, 5, 0, 8, 8, 26773230290258915132408059852381807498493952000000⟩, + ⟨7, 4, 0, 1, 2, 8, 50961258523075995984521619583782251530448535552000000⟩, + ⟨7, 4, 1, 1, 3, 8, -7281450680347477243334487618436954183862059008000000⟩, + ⟨7, 4, 2, 1, 4, 8, 51011913844951895317728453033635246328766267392000000⟩, + ⟨7, 4, 3, 1, 5, 8, 7962402076597398958712882641542285024886259712000000⟩, + ⟨7, 4, 4, 1, 6, 8, 3818048499012841981730972540963408299389301555200000⟩, + ⟨7, 4, 5, 1, 7, 8, -212352853368278237548630302149026696824619008000000⟩, + ⟨7, 4, 6, 1, 8, 8, -16593507755631293362498962325325892538073088000000⟩, + ⟨7, 4, 0, 2, 1, 8, 52648672740987359011434158333796025979602206720000000⟩, + ⟨7, 4, 1, 2, 2, 8, -1271183200024007815056181546178527380973289472000000⟩, + ⟨7, 4, 2, 2, 3, 8, -19011827035764448309291489954598017167035203584000000⟩, + ⟨7, 4, 3, 2, 4, 8, -10368758661406069218474806223312652029860511744000000⟩, + ⟨7, 4, 4, 2, 5, 8, -484490345183595460140538063208829143410645401600000⟩, + ⟨7, 4, 5, 2, 6, 8, -148423603015677787902093786766659506839486464000000⟩, + ⟨7, 4, 6, 2, 7, 8, -22204011313537288319808636964409388231032832000000⟩, + ⟨7, 4, 7, 2, 8, 8, -13016565315331025743132743229588398938259456000000⟩, + ⟨7, 4, 0, 3, 0, 8, -294187832045227937384982317694364274789500059648000000⟩, + ⟨7, 4, 1, 3, 1, 8, 7133905754901924516548849647114995702222028800000000⟩, + ⟨7, 4, 2, 3, 2, 8, -10166178843720426186819111787441979277831045120000000⟩, + ⟨7, 4, 3, 3, 3, 8, 13859316062412354490860426583337177163101110272000000⟩, + ⟨7, 4, 4, 3, 4, 8, 332408770938243360142005833706311513351494041600000⟩, + ⟨7, 4, 5, 3, 5, 8, 56083307042283865539288590812912871591116800000000⟩, + ⟨7, 4, 6, 3, 6, 8, 58834137783292649823078539768444025147752448000000⟩, + ⟨7, 4, 7, 3, 7, 8, 7268178231695799401978452303322774916562944000000⟩, + ⟨7, 4, 8, 3, 8, 8, 3654397291313939681059165622723237904384000000000⟩, + ⟨7, 4, 1, 4, 0, 8, -57081971186072647159893689851753549778380652544000000⟩, + ⟨7, 4, 2, 4, 1, 8, -23467986685741854920973988684356400180327612416000000⟩, + ⟨7, 4, 3, 4, 2, 8, -18972775000197734782855398540326873691114700800000000⟩, + ⟨7, 4, 4, 4, 3, 8, 742982007229514695984309888852738932234780672000000⟩, + ⟨7, 4, 5, 4, 4, 8, -202046160668745132568331960629825567815892992000000⟩, + ⟨7, 4, 6, 4, 5, 8, -46808513938112508663761949422368979473661952000000⟩, + ⟨7, 4, 7, 4, 6, 8, -2387053913197173119050667786089144642437120000000⟩, + ⟨7, 4, 8, 4, 7, 8, 1298138620027991862828725028268185955074048000000⟩, + ⟨7, 4, 2, 5, 0, 8, 175096412366838267382247450062067432596514537472000000⟩, + ⟨7, 4, 3, 5, 1, 8, 15755415708506857499618792986665884932380819456000000⟩, + ⟨7, 4, 4, 5, 2, 8, -5090661210009333527610200988218493820126573363200000⟩, + ⟨7, 4, 5, 5, 3, 8, 526948002322583190739794549121067971975839744000000⟩, + ⟨7, 4, 6, 5, 4, 8, -52794438394755492440973134229034653909516288000000⟩, + ⟨7, 4, 7, 5, 5, 8, -6321973609413530119190375564745907598524416000000⟩, + ⟨7, 4, 8, 5, 6, 8, 2703065312199284756622304950761713588764672000000⟩, + ⟨7, 4, 3, 6, 0, 8, 8580407444712127421640663068455433462398058496000000⟩, + ⟨7, 4, 4, 6, 1, 8, 2731679906667114010883668252445535448419060940800000⟩, + ⟨7, 4, 5, 6, 2, 8, 7798790703893137123107331794437037386366976000000⟩, + ⟨7, 4, 6, 6, 3, 8, 195486680955144377663705760376789498035437568000000⟩, + ⟨7, 4, 7, 6, 4, 8, 2263175389957997788934560563515227983839232000000⟩, + ⟨7, 4, 8, 6, 5, 8, -2836746455687488025957254114446756412391424000000⟩, + ⟨7, 4, 4, 7, 0, 8, 52123819448777839283525897452737723767386118553600000⟩, + ⟨7, 4, 5, 7, 1, 8, -363552788223627313836562318381713368014651392000000⟩, + ⟨7, 4, 6, 7, 2, 8, -192921412026694921649977904906450137516081152000000⟩, + ⟨7, 4, 7, 7, 3, 8, 94826061348964311915629065303437039473000448000000⟩, + ⟨7, 4, 8, 7, 4, 8, 5608876778467180634167936091785328653762560000000⟩ +] + +def collectedFourData_10_3 : List (List CollectedFourTerm) := [ + collectedFourData_10_3_0, + collectedFourData_10_3_1, + collectedFourData_10_3_2, + collectedFourData_10_3_3, + collectedFourData_10_3_4, + collectedFourData_10_3_5, + collectedFourData_10_3_6, + collectedFourData_10_3_7, + collectedFourData_10_3_8, + collectedFourData_10_3_9, + collectedFourData_10_3_10, + collectedFourData_10_3_11, + collectedFourData_10_3_12, + collectedFourData_10_3_13, + collectedFourData_10_3_14, + collectedFourData_10_3_15, + collectedFourData_10_3_16, + collectedFourData_10_3_17, + collectedFourData_10_3_18, + collectedFourData_10_3_19, + collectedFourData_10_3_20, + collectedFourData_10_3_21, + collectedFourData_10_3_22, + collectedFourData_10_3_23, + collectedFourData_10_3_24, + collectedFourData_10_3_25, + collectedFourData_10_3_26, + collectedFourData_10_3_27, + collectedFourData_10_3_28, + collectedFourData_10_3_29, + collectedFourData_10_3_30, + collectedFourData_10_3_31, + collectedFourData_10_3_32, + collectedFourData_10_3_33, + collectedFourData_10_3_34, + collectedFourData_10_3_35, + collectedFourData_10_3_36, + collectedFourData_10_3_37, + collectedFourData_10_3_38, + collectedFourData_10_3_39, + collectedFourData_10_3_40, + collectedFourData_10_3_41, + collectedFourData_10_3_42, + collectedFourData_10_3_43, + collectedFourData_10_3_44, + collectedFourData_10_3_45, + collectedFourData_10_3_46, + collectedFourData_10_3_47, + collectedFourData_10_3_48, + collectedFourData_10_3_49, + collectedFourData_10_3_50, + collectedFourData_10_3_51, + collectedFourData_10_3_52, + collectedFourData_10_3_53, + collectedFourData_10_3_54, + collectedFourData_10_3_55 +] + +theorem collectedFourChecked_10_3 : collectNumericRowParts 10 3 = collectedFourData_10_3 := by + decide +kernel + +def collectedFourData_10_4_0 : List CollectedFourTerm := [ + ⟨0, 4, 6, 2, 8, 0, 16583930293351227691354359490824658918569934848000000⟩, + ⟨0, 4, 6, 3, 7, 0, 35162368662501569420137650780891221814411264000000⟩, + ⟨0, 4, 7, 3, 8, 0, -5627721229070855875447475083812689295729229824000000⟩, + ⟨0, 4, 6, 4, 6, 0, 7105921119476529029727528628806701637345214464000000⟩, + ⟨0, 4, 7, 4, 7, 0, -14885788875873215619758674354679717233466277888000000⟩, + ⟨0, 4, 8, 4, 8, 0, 7972410657634949281704532505421344810792386560000000⟩, + ⟨0, 4, 6, 5, 5, 0, 5936153571300723196221046736154972523459510272000000⟩, + ⟨0, 4, 7, 5, 6, 0, 4715789059724708735847109524234139484175728640000000⟩, + ⟨0, 4, 8, 5, 7, 0, -13070785113112568212830828247179421740492128256000000⟩, + ⟨0, 4, 6, 6, 4, 0, -3957979446604358300870739188555310962785124352000000⟩, + ⟨0, 4, 7, 6, 5, 0, 29462801208193070475604046074007697413684330496000000⟩, + ⟨0, 4, 8, 6, 6, 0, 19524308952350274189288260974714358554832142336000000⟩, + ⟨0, 4, 6, 7, 3, 0, -19980634441716701040968949177977154953212329984000000⟩, + ⟨0, 4, 7, 7, 4, 0, 22909965838390926595435501683292694034430033920000000⟩, + ⟨0, 4, 8, 7, 5, 0, 50433356577183599820457658019247344448186613760000000⟩ +] + +def collectedFourData_10_4_1 : List CollectedFourTerm := [ + ⟨0, 5, 5, 1, 8, 1, 60501914193336028043162039805250183442152292352000000⟩, + ⟨0, 5, 5, 2, 7, 1, 31012580404290021038670170913750282248006506905600000⟩, + ⟨0, 5, 6, 2, 8, 1, -54972582611330638325610604320008643660517421875200000⟩, + ⟨0, 5, 5, 3, 6, 1, -21219271965236456112557198817665658685510542950400000⟩, + ⟨0, 5, 6, 3, 7, 1, -116556581094916281596952323237876982856915353600000⟩, + ⟨0, 5, 7, 3, 8, 1, 9327414090213238677753493502676490691950726348800000⟩, + ⟨0, 5, 5, 4, 5, 1, -12866344534319898122757597459775990012850051481600000⟩, + ⟨0, 5, 6, 4, 6, 1, -23554780372336282340677729248525363556818459033600000⟩, + ⟨0, 5, 7, 4, 7, 1, 24671782992293482982645608108962144173336140185600000⟩, + ⟨0, 5, 8, 4, 8, 1, -8809009600174963130200179011114902670800846848000000⟩, + ⟨0, 5, 5, 5, 4, 1, -8534717687507329912312851295644753108652995379200000⟩, + ⟨0, 5, 6, 5, 5, 1, -19677222878988087588293360045151613880634232012800000⟩, + ⟨0, 5, 7, 5, 6, 1, -7815973025624059531101920082297198928585555968000000⟩, + ⟨0, 5, 8, 5, 7, 1, 14442390951470328779918186794387521157678812364800000⟩, + ⟨0, 5, 5, 6, 3, 1, 77773070417951599778783698591811179789533000499200000⟩, + ⟨0, 5, 6, 6, 4, 1, 13119950955753738088834774798731008163231616204800000⟩, + ⟨0, 5, 7, 6, 5, 1, -48831798154263489720408566507020962795351126835200000⟩, + ⟨0, 5, 8, 6, 6, 1, -21573126671959103626602079221993679527313460428800000⟩, + ⟨0, 5, 5, 7, 2, 1, -4308606266094654153552280053367357242131192217600000⟩, + ⟨0, 5, 6, 7, 3, 1, 66232012438838527101065134658901439623108073881600000⟩, + ⟨0, 5, 7, 7, 4, 1, -37971095132335135658844847462431632820749205504000000⟩, + ⟨0, 5, 8, 7, 5, 1, -55725669604336649241228111388398977262035140608000000⟩ +] + +def collectedFourData_10_4_2 : List CollectedFourTerm := [ + ⟨0, 6, 4, 0, 8, 2, 9018511837268702694605446166422354306521429442560000⟩, + ⟨0, 6, 4, 1, 7, 2, -10517818930522251074761054121710008008728494735360000⟩, + ⟨0, 6, 5, 1, 8, 2, -51628621673390639913576220328373351692208439296000000⟩, + ⟨0, 6, 4, 2, 6, 2, 6934326601827700188898471083683873608310351462400000⟩, + ⟨0, 6, 5, 2, 7, 2, -26464233440485996120933182679601219228851293388800000⟩, + ⟨0, 6, 6, 2, 8, 2, 23455114667778650769762646502583079890232069324800000⟩, + ⟨0, 6, 4, 3, 5, 2, 19025676661272297390341393242333418709825261404160000⟩, + ⟨0, 6, 5, 3, 6, 2, 18107224855352482944107617059998148474447278899200000⟩, + ⟨0, 6, 6, 3, 7, 2, 49731117677233111461696707785348720483526246400000⟩, + ⟨0, 6, 7, 3, 8, 2, -2653147643757878304782275421529228952145284300800000⟩, + ⟨0, 6, 4, 4, 4, 2, -14259093715975727263436291039336587247753782886400000⟩, + ⟨0, 6, 5, 4, 5, 2, 10979349052646429597492879695006022464361516236800000⟩, + ⟨0, 6, 6, 4, 6, 2, 10050102221204636135281508636337748779400062566400000⟩, + ⟨0, 6, 7, 4, 7, 2, -7017795316066286622413665079864939934687795609600000⟩, + ⟨0, 6, 8, 4, 8, 2, 1879267086126313212789847075023898627408920576000000⟩, + ⟨0, 6, 4, 5, 3, 2, -13587260824554072778913748358172042049404346040320000⟩, + ⟨0, 6, 5, 5, 4, 2, 7283004454527574489263671392850941966204639641600000⟩, + ⟨0, 6, 6, 5, 5, 2, 8395667386290395485181271341728684441125204787200000⟩, + ⟨0, 6, 7, 5, 6, 2, 2223223952109917658863249184679906598021234688000000⟩, + ⟨0, 6, 8, 5, 7, 2, -3081062592953424029364232812314675235832568217600000⟩, + ⟨0, 6, 4, 6, 2, 2, 17209591144068999573085684798526495993370268139520000⟩, + ⟨0, 6, 5, 6, 3, 2, -66366766779565111194375847056055217538394069401600000⟩, + ⟨0, 6, 6, 6, 4, 2, -5597880606748289640178491065885279533143372595200000⟩, + ⟨0, 6, 7, 6, 5, 2, 13890020209286387435800295247536379606653416243200000⟩, + ⟨0, 6, 8, 6, 6, 2, 4602295688114723074395863805830840298677836185600000⟩, + ⟨0, 6, 4, 7, 1, 2, 16531831061290137392542258438446222235884501073920000⟩, + ⟨0, 6, 5, 7, 2, 2, 3676700246887438272488690719129363481734466764800000⟩, + ⟨0, 6, 6, 7, 3, 2, -28259167982231658389139580116394729212937135718400000⟩, + ⟨0, 6, 7, 7, 4, 2, 10800734330747191385979822743774972426965745664000000⟩, + ⟨0, 6, 8, 7, 5, 2, 11888216893043163048096879568879808110129053696000000⟩ +] + +def collectedFourData_10_4_3 : List CollectedFourTerm := [ + ⟨0, 7, 3, 0, 7, 3, 667884136030241275975895958679761448488570716160000⟩, + ⟨0, 7, 4, 0, 8, 3, -2577713702312326923481165555391674628690631720960000⟩, + ⟨0, 7, 3, 1, 6, 3, -3166909914064954193519042876637529341790015979520000⟩, + ⟨0, 7, 4, 1, 7, 3, 3006252746002733047816236617115364392921999605760000⟩, + ⟨0, 7, 5, 1, 8, 3, 7378368400484534116634264320842591760042426368000000⟩, + ⟨0, 7, 3, 2, 5, 3, -1347676296728772911947304076770100676942280785920000⟩, + ⟨0, 7, 4, 2, 6, 3, -1982002022104522146560120982139336568569488998400000⟩, + ⟨0, 7, 5, 2, 7, 3, 3782066176307905177909597130205565518118020710400000⟩, + ⟨0, 7, 6, 2, 8, 3, -2234683931576846807079882013114885897920813465600000⟩, + ⟨0, 7, 3, 3, 4, 3, 146841045062399345877083536889373357303807344640000⟩, + ⟨0, 7, 4, 3, 5, 3, -5438008876681617106626386310839213721653933506560000⟩, + ⟨0, 7, 5, 3, 6, 3, -2587746319055020847716752915955104757552093593600000⟩, + ⟨0, 7, 6, 3, 7, 3, -4738127745132663279732669183117053731327180800000⟩, + ⟨0, 7, 7, 3, 8, 3, 189583801601007434715502748012607961629406003200000⟩, + ⟨0, 7, 3, 4, 3, 3, 2168544236426848477749395754876076788114228510720000⟩, + ⟨0, 7, 4, 4, 4, 3, 4075601597852745847300673206901689552682247782400000⟩, + ⟨0, 7, 5, 4, 5, 3, -1569084734053409029975075255789451933137659494400000⟩, + ⟨0, 7, 6, 4, 6, 3, -957522581430115398388650232478942207264214220800000⟩, + ⟨0, 7, 7, 4, 7, 3, 501464861183958169642701209215002024354408038400000⟩, + ⟨0, 7, 8, 4, 8, 3, -107428201140543142209901994957658735722574643200000⟩, + ⟨0, 7, 3, 5, 2, 3, 2707833988955300012626320016170750765202648596480000⟩, + ⟨0, 7, 4, 5, 3, 3, 3883575143695960057558051287497385800704846725120000⟩, + ⟨0, 7, 5, 5, 4, 3, -1040831387438921574922877853081327997889072332800000⟩, + ⟨0, 7, 6, 5, 5, 3, -799896451957264286667446420491299849784157798400000⟩, + ⟨0, 7, 7, 5, 6, 3, -158863095931753764817805854224513140892106752000000⟩, + ⟨0, 7, 8, 5, 7, 3, 176128776162770748831158827406512644929429176320000⟩, + ⟨0, 7, 3, 6, 1, 3, 659254513226200830173553576990451989046823485440000⟩, + ⟨0, 7, 4, 6, 2, 3, -4918926725797211594166303422281323295768125112320000⟩, + ⟨0, 7, 5, 6, 3, 3, 9484631566312953141058979296047215118283230412800000⟩, + ⟨0, 7, 6, 6, 4, 3, 533337569224119319724922416937010605635036774400000⟩, + ⟨0, 7, 7, 6, 5, 3, -992527815701027288572427371557864056724180172800000⟩, + ⟨0, 7, 8, 6, 6, 3, -263089983611734015012401891131476901321685073920000⟩, + ⟨0, 7, 3, 7, 0, 3, -69294268798279047346732539104403828364858538065920000⟩, + ⟨0, 7, 4, 7, 1, 3, -4725206133776730471057412781414237287050085662720000⟩, + ⟨0, 7, 5, 7, 2, 3, -525445925930456118722293842652552321500079718400000⟩, + ⟨0, 7, 6, 7, 3, 3, 2692389677223638535295025049226540799444700364800000⟩, + ⟨0, 7, 7, 7, 4, 3, -771779240903952439194167365208589846662086656000000⟩, + ⟨0, 7, 8, 7, 5, 3, -679589274465908819941168615952088876593656627200000⟩ +] + +def collectedFourData_10_4_4 : List CollectedFourTerm := [ + ⟨0, 8, 2, 0, 6, 4, 9018511837268702694605446166422354306521429442560000⟩, + ⟨0, 8, 3, 0, 7, 4, -2577713702312326923481165555391674628690631720960000⟩, + ⟨0, 8, 4, 0, 8, 4, 4974371730539098242482812928532064866810074234880000⟩, + ⟨0, 8, 2, 1, 5, 4, -4403627406343894208256468083783164703927760322560000⟩, + ⟨0, 8, 3, 1, 6, 4, 12222759366610190504428570370282563096701692805120000⟩, + ⟨0, 8, 4, 1, 7, 4, -5801349723655080154590235447661173915960769249280000⟩, + ⟨0, 8, 5, 1, 8, 4, -9492325739652987758808289284880368695966171136000000⟩, + ⟨0, 8, 2, 2, 4, 4, -16223524135542078322572600067186622484758113812480000⟩, + ⟨0, 8, 3, 2, 5, 4, 5201386691122118124385599958957393632999002603520000⟩, + ⟨0, 8, 4, 2, 6, 4, 3824790479945037291872310359086131662852141875200000⟩, + ⟨0, 8, 5, 2, 7, 4, -4865656221784874117468305361026165390265076940800000⟩, + ⟨0, 8, 6, 2, 8, 4, 2156203104703625983889685597620384649055725158400000⟩, + ⟨0, 8, 2, 3, 3, 4, 18480175042027481749959289099406983851028984627200000⟩, + ⟨0, 8, 3, 3, 4, 4, -566736284782889082298281315287928778088345763840000⟩, + ⟨0, 8, 4, 3, 5, 4, 10494058204493392749971882574888122731835613511680000⟩, + ⟨0, 8, 5, 3, 6, 4, 3329154856301991929783624604140058129860866867200000⟩, + ⟨0, 8, 6, 3, 7, 4, 4571727397408064550125378944819990113760051200000⟩, + ⟨0, 8, 7, 3, 8, 4, -146340581175669936097088560975055479291867299840000⟩, + ⟨0, 8, 2, 4, 2, 4, -4406331294189851060189860985842737363905465548800000⟩, + ⟨0, 8, 3, 4, 3, 4, -8369544791905049647299673445810237540430847672320000⟩, + ⟨0, 8, 4, 4, 4, 4, -7864937582134265097587060567945840991967327027200000⟩, + ⟨0, 8, 5, 4, 5, 4, 2018639162524554604291661470903004950166293708800000⟩, + ⟨0, 8, 6, 4, 6, 4, 923894933744211680614413082662504427496354611200000⟩, + ⟨0, 8, 7, 4, 7, 4, -387082960701886915490253088013646189310330798080000⟩, + ⟨0, 8, 8, 4, 8, 4, 69103589269412871304225974641595314898940723200000⟩, + ⟨0, 8, 2, 5, 1, 4, 4563646637740527456562228787813603787160902696960000⟩, + ⟨0, 8, 3, 5, 2, 4, -10450945606231726750953474436628607043113981050880000⟩, + ⟨0, 8, 4, 5, 3, 4, -7494372393216539486372669012126854738395644559360000⟩, + ⟨0, 8, 5, 5, 4, 4, 1339037309247990036828076643195716502327761305600000⟩, + ⟨0, 8, 6, 5, 5, 4, 771804544159697128681204720544757510798154137600000⟩, + ⟨0, 8, 7, 5, 6, 4, 122627131588733334976372199989393794617730662400000⟩, + ⟨0, 8, 8, 5, 7, 4, -113295489240795926366228603857350772696358584320000⟩, + ⟨0, 8, 2, 6, 0, 4, -82155135257297148176904146682609908328540080701440000⟩, + ⟨0, 8, 3, 6, 1, 4, -2544407480847059542114542195625450069966863728640000⟩, + ⟨0, 8, 4, 6, 2, 4, 9492353641697862305936322891672248940787358760960000⟩, + ⟨0, 8, 5, 6, 3, 4, -12202048943791607062270836496942373508423981465600000⟩, + ⟨0, 8, 6, 6, 4, 4, -514607057564813931035898445286438407222434201600000⟩, + ⟨0, 8, 7, 6, 5, 4, 766136643300303568836371338730929050332021391360000⟩, + ⟨0, 8, 8, 6, 6, 4, 169233608823228899601677988650667080111011921920000⟩, + ⟨0, 8, 3, 7, 0, 4, 267442774183439550077862622687191903616735138283520000⟩, + ⟨0, 8, 4, 7, 1, 4, 9118519171366439619309093094320948576172281692160000⟩, + ⟨0, 8, 5, 7, 2, 4, 675990085718398885893100638699664064692145356800000⟩, + ⟨0, 8, 6, 7, 3, 4, -2597834485257705251510642453462303413095314227200000⟩, + ⟨0, 8, 7, 7, 4, 4, 595739834835138183491714914213781441009103667200000⟩, + ⟨0, 8, 8, 7, 5, 4, 437148324145838170173368614923426078987072307200000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1014.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1014.lean new file mode 100644 index 0000000000000000000000000000000000000000..93983d816a33722d774707f83bdede55a8a4b8bb --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1014.lean @@ -0,0 +1,623 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1014. -/ +namespace LaughlinFock +def collectedFourData_10_4_5 : List CollectedFourTerm := [ + ⟨1, 3, 6, 2, 8, 0, 13034350721302549426533276291080851199358507417600000⟩, + ⟨1, 3, 6, 3, 7, 0, 27636310406015818026565606375018251164634316800000⟩, + ⟨1, 3, 7, 3, 8, 0, -4423179003039954306993517385722787402485648588800000⟩, + ⟨1, 3, 6, 4, 6, 0, 5584988988183412456190766241455534111296638156800000⟩, + ⟨1, 3, 7, 4, 7, 0, -11699674898487965117117266311569052406430407065600000⟩, + ⟨1, 3, 8, 4, 8, 0, 6266017449887953092979686142582014652943695872000000⟩, + ⟨1, 3, 6, 5, 5, 0, 4665595321204815189935340997354290992220890726400000⟩, + ⟨1, 3, 7, 5, 6, 0, 3706434327981749089476940604397390373079482368000000⟩, + ⟨1, 3, 8, 5, 7, 0, -10273149630603142450852705551398111525330957107200000⟩, + ⟨1, 3, 6, 6, 4, 0, -3110824234194432489738166632954430731365803622400000⟩, + ⟨1, 3, 7, 6, 5, 0, 23156662949407617339609657850968128937216127795200000⟩, + ⟨1, 3, 8, 6, 6, 0, 15345378687344612656915657175610222122173150003200000⟩, + ⟨1, 3, 6, 7, 3, 0, -15704033503558875140455282720796993656372120780800000⟩, + ⟨1, 3, 7, 7, 4, 0, 18006378733415676070291663052507287941707464704000000⟩, + ⟨1, 3, 8, 7, 5, 0, 39638737383204671877019457973541591127804608512000000⟩ +] + +def collectedFourData_10_4_6 : List CollectedFourTerm := [ + ⟨1, 4, 5, 1, 8, 1, 26428167080065824136203517721680154152214200320000000⟩, + ⟨1, 4, 5, 2, 7, 1, 13546772320119870057767403226248168193545732096000000⟩, + ⟨1, 4, 6, 2, 8, 1, -24012869963624860411414032432585429502427922432000000⟩, + ⟨1, 4, 5, 3, 6, 1, -9268904501477632153433324268414191437678116864000000⟩, + ⟨1, 4, 6, 3, 7, 1, -50913708112015017667045893079090625853259776000000⟩, + ⟨1, 4, 7, 3, 8, 1, 4074357998217964499069210856767060818324881408000000⟩, + ⟨1, 4, 5, 4, 5, 1, -5620217270747955079667303235966731897857376256000000⟩, + ⟨1, 4, 6, 4, 6, 1, -10289090510840805154931243583013730615952408576000000⟩, + ⟨1, 4, 7, 4, 7, 1, 10777014442879829436708170898461592527774416896000000⟩, + ⟨1, 4, 8, 4, 8, 1, -3847910940129727976159548273406930390278471680000000⟩, + ⟨1, 4, 5, 5, 4, 1, -3728096012067675395031142006801179228160131072000000⟩, + ⟨1, 4, 6, 5, 5, 1, -8595313732649965742515106114755088376448155648000000⟩, + ⟨1, 4, 7, 5, 6, 1, -3414137284225495816588614901900536525493370880000000⟩, + ⟨1, 4, 8, 5, 7, 1, 6308658596840385631003943822260230223684435968000000⟩, + ⟨1, 4, 5, 6, 3, 1, 33972473875243789703040147524429697523774390272000000⟩, + ⟨1, 4, 6, 6, 4, 1, 5730996457945462602660372694954511721843130368000000⟩, + ⟨1, 4, 7, 6, 5, 1, -21330480822755045288076166837470510932696236032000000⟩, + ⟨1, 4, 8, 6, 6, 1, -9423473682238591689941985100568799226739294208000000⟩, + ⟨1, 4, 5, 7, 2, 1, -1882065514798374778729737210616349027274326016000000⟩, + ⟨1, 4, 6, 7, 3, 1, 28931162164376924684442527315675894162449760256000000⟩, + ⟨1, 4, 7, 7, 4, 1, -16586358626004565637924178129821911734697328640000000⟩, + ⟨1, 4, 8, 7, 5, 1, -24341829950136814430681763942713343048186593280000000⟩ +] + +def collectedFourData_10_4_7 : List CollectedFourTerm := [ + ⟨1, 5, 4, 0, 8, 2, -4403627406343894208256468083783164703927760322560000⟩, + ⟨1, 5, 4, 1, 7, 2, 5135720452903191084971925666107770194418320015360000⟩, + ⟨1, 5, 5, 1, 8, 2, 25209615228664859299572750469346449931995447296000000⟩, + ⟨1, 5, 4, 2, 6, 2, -3385945621555674439373967413832061735752066662400000⟩, + ⟨1, 5, 5, 2, 7, 2, 12922156755931137194231601277512051785024195788800000⟩, + ⟨1, 5, 6, 2, 8, 2, -11452841403737608734437266862657357521422699724800000⟩, + ⟨1, 5, 4, 3, 5, 2, -9290001796481518452217497388254642200549429084160000⟩, + ⟨1, 5, 5, 3, 6, 2, -8841533178051513783114553875225254286966600499200000⟩, + ⟨1, 5, 6, 3, 7, 2, -24283087576220487269027375460438151598073446400000⟩, + ⟨1, 5, 7, 3, 8, 2, 1295499067689566059538637450349983022019562700800000⟩, + ⟨1, 5, 4, 4, 4, 2, 6962538499734727297867691795611963830259050086400000⟩, + ⟨1, 5, 5, 4, 5, 2, -5361079883739709299274330906550394779941522636800000⟩, + ⟨1, 5, 6, 4, 6, 2, -4907340188318451772288176566341853892193969766400000⟩, + ⟨1, 5, 7, 4, 7, 2, 3426702358834032862578036011898911466811136409600000⟩, + ⟨1, 5, 8, 4, 8, 2, -917622795604398183866002308693107334841368576000000⟩, + ⟨1, 5, 4, 5, 3, 2, 6634490836602352330720472149451962205241417400320000⟩, + ⟨1, 5, 5, 5, 4, 2, -3556200689779804315884102640602130981555116441600000⟩, + ⟨1, 5, 6, 5, 5, 2, -4099500190711392296189565686234383856589550387200000⟩, + ⟨1, 5, 7, 5, 6, 2, -1085572664604545272893448817157979986028658688000000⟩, + ⟨1, 5, 8, 5, 7, 2, 1504444626764471340255704378102346549399493017600000⟩, + ⟨1, 5, 4, 6, 2, 2, -8403229776870497343841954992228725879960261099520000⟩, + ⟨1, 5, 5, 6, 3, 2, 32406068576990085640998086184602607034021026201600000⟩, + ⟨1, 5, 6, 6, 4, 2, 2733375628055217700953440734579259445980902195200000⟩, + ⟨1, 5, 7, 6, 5, 2, -6782324486786794916780350116695383594136449843200000⟩, + ⟨1, 5, 8, 6, 6, 2, -2247243867943762322034696692725983407993624985600000⟩, + ⟨1, 5, 4, 7, 1, 2, -8072287939757512586620408117901407421852465233920000⟩, + ⟨1, 5, 5, 7, 2, 2, -1795287101048851992832615732542580466914217164800000⟩, + ⟨1, 5, 6, 7, 3, 2, 13798601016719328041339136081428401937331938918400000⟩, + ⟨1, 5, 7, 7, 4, 2, -5273864531725469510566869312609976056664817664000000⟩, + ⟨1, 5, 8, 7, 5, 2, -5804868770746122888856577028948490000527261696000000⟩ +] + +def collectedFourData_10_4_8 : List CollectedFourTerm := [ + ⟨1, 6, 3, 0, 7, 3, -3166909914064954193519042876637529341790015979520000⟩, + ⟨1, 6, 4, 0, 8, 3, 12222759366610190504428570370282563096701692805120000⟩, + ⟨1, 6, 3, 1, 6, 3, 15016554313469688089172122820724646802913430077440000⟩, + ⟨1, 6, 4, 1, 7, 3, -14254765328143631174068890747713748079284552990720000⟩, + ⟨1, 6, 5, 1, 8, 3, -34986050388925582537660464196147946415294775296000000⟩, + ⟨1, 6, 3, 2, 5, 3, 6390284174780045357426172157729588892789888778240000⟩, + ⟨1, 6, 4, 2, 6, 3, 9398069986820869847641484845481751970646379724800000⟩, + ⟨1, 6, 5, 2, 7, 3, -17933444175797742931107654832515582530922794188800000⟩, + ⟨1, 6, 6, 2, 8, 3, 10596213199158727871163077481411334185306764083200000⟩, + ⟨1, 6, 3, 3, 4, 3, -696276998228798885385813284638576536916674478080000⟩, + ⟨1, 6, 4, 3, 5, 3, 25785436867385713148598719097810723321502047928320000⟩, + ⟨1, 6, 5, 3, 6, 3, 12270331081092435381274020283292265538345186099200000⟩, + ⟨1, 6, 6, 3, 7, 3, 22466806622110624518454057603547306055539097600000⟩, + ⟨1, 6, 7, 3, 8, 3, -898950564097794902899044640166576661589288550400000⟩, + ⟨1, 6, 3, 4, 3, 3, -10282598239640840235249432232426029432979681443840000⟩, + ⟨1, 6, 4, 4, 4, 3, -19325302713035854377846207084516721535287610572800000⟩, + ⟨1, 6, 5, 4, 5, 3, 7440137790691159395589665366210804841947385036800000⟩, + ⟨1, 6, 6, 4, 6, 3, 4540290137891216049640583575087110697315309977600000⟩, + ⟨1, 6, 7, 4, 7, 3, -2377798715025588635455907091990188023815654604800000⟩, + ⟨1, 6, 8, 4, 8, 3, 509392897493144537546381449187882517345494630400000⟩, + ⟨1, 6, 3, 5, 2, 3, -12839751451854069518802334117007463950206956994560000⟩, + ⟨1, 6, 4, 5, 3, 3, -18414769809759456337211822245932730397053566320640000⟩, + ⟨1, 6, 5, 5, 4, 3, 4935315965643855203512239105654530851231865241600000⟩, + ⟨1, 6, 6, 5, 5, 3, 3792873445064340126963375049361643413873413324800000⟩, + ⟨1, 6, 7, 5, 6, 3, 753282023549280230130640546647096318014521344000000⟩, + ⟨1, 6, 8, 5, 7, 3, -835150795312122579164279931498927094297043927040000⟩, + ⟨1, 6, 3, 6, 1, 3, -3125990783727174691978689903183419059459514695680000⟩, + ⟨1, 6, 4, 6, 2, 3, 23324102152024918375221088523950981013203624919040000⟩, + ⟨1, 6, 5, 6, 3, 3, -44973330130497148737817595080150245940953455001600000⟩, + ⟨1, 6, 6, 6, 4, 3, -2528929711608974661895161329619123458158677196800000⟩, + ⟨1, 6, 7, 6, 5, 3, 4706274651486097393133293342172112864937613721600000⟩, + ⟨1, 6, 8, 6, 6, 3, 1247495235241612220139155883504353458998466314240000⟩, + ⟨1, 6, 3, 7, 0, 3, 328573018891431293381697593372362433751448540938240000⟩, + ⟨1, 6, 4, 7, 1, 3, 22405536145839056046922009206885616440951271587840000⟩, + ⟨1, 6, 5, 7, 2, 3, 2491509862810777460841419804375388253485583564800000⟩, + ⟨1, 6, 6, 7, 3, 3, -12766519073211834823632901422652483345554446745600000⟩, + ⟨1, 6, 7, 7, 4, 3, 3659549909383657139116282161815518603307384832000000⟩, + ⟨1, 6, 8, 7, 5, 3, 3222412233939998857023562327476489681474315878400000⟩ +] + +def collectedFourData_10_4_9 : List CollectedFourTerm := [ + ⟨1, 7, 2, 0, 6, 4, -10517818930522251074761054121710008008728494735360000⟩, + ⟨1, 7, 3, 0, 7, 4, 3006252746002733047816236617115364392921999605760000⟩, + ⟨1, 7, 4, 0, 8, 4, -5801349723655080154590235447661173915960769249280000⟩, + ⟨1, 7, 2, 1, 5, 4, 5135720452903191084971925666107770194418320015360000⟩, + ⟨1, 7, 3, 1, 6, 4, -14254765328143631174068890747713748079284552990720000⟩, + ⟨1, 7, 4, 1, 7, 4, 6765810928349224535283126759262298469123678535680000⟩, + ⟨1, 7, 5, 1, 8, 4, 11070403317166614303627281605483229324368674816000000⟩, + ⟨1, 7, 2, 2, 4, 4, 18920648145899315624351251392271809271739323514880000⟩, + ⟨1, 7, 3, 2, 5, 4, -6066105405414541662130079578119077376166062981120000⟩, + ⟨1, 7, 4, 2, 6, 4, -4460653203226328480505639707533399520246444851200000⟩, + ⟨1, 7, 5, 2, 7, 4, 5674560508688230917518944014741778099742756044800000⟩, + ⟨1, 7, 6, 2, 8, 4, -2514666969663916515968907795005145436620482150400000⟩, + ⟨1, 7, 2, 3, 3, 4, -21552462136066527153805816144595287139075437363200000⟩, + ⟨1, 7, 3, 3, 4, 4, 660954903897823647113444805744305113278751703040000⟩, + ⟨1, 7, 4, 3, 5, 4, -12238671527280536459943388368878631357119547310080000⟩, + ⟨1, 7, 5, 3, 6, 4, -3882619283766196486488028016015120776155050803200000⟩, + ⟨1, 7, 6, 3, 7, 4, -5331766685379037411958399094166008802521907200000⟩, + ⟨1, 7, 7, 3, 8, 4, 170669370154005167434477670633263021058728919040000⟩, + ⟨1, 7, 2, 4, 2, 4, 5138873855957416813063519652321529320893631692800000⟩, + ⟨1, 7, 3, 4, 3, 4, 9760962589013237523589083347326356937433331793920000⟩, + ⟨1, 7, 4, 4, 4, 4, 9172465577624656737849138754863169160948691763200000⟩, + ⟨1, 7, 5, 4, 5, 4, -2354233334789795501627029198493064534837480652800000⟩, + ⟨1, 7, 6, 4, 6, 4, -1077490366403002587703284188061107668152169267200000⟩, + ⟨1, 7, 7, 4, 7, 4, 451434623052610966934911508201330363609886228480000⟩, + ⟨1, 7, 8, 4, 8, 4, -80591903908282216274869035714752695028101939200000⟩, + ⟨1, 7, 2, 5, 1, 4, -5322342517784890023431777130469383822240393461760000⟩, + ⟨1, 7, 3, 5, 2, 4, 12188391557555744161570609816568085485054098145280000⟩, + ⟨1, 7, 4, 5, 3, 4, 8740294768369302288910787483655621122472447836160000⟩, + ⟨1, 7, 5, 5, 4, 4, -1561649218187356246716231206186063930865588633600000⟩, + ⟨1, 7, 6, 5, 5, 4, -900115295261888976607021763230302147293321625600000⟩, + ⟨1, 7, 7, 5, 6, 4, -143013613475528274487916894635356383288387174400000⟩, + ⟨1, 7, 8, 5, 7, 4, 132130606798705648085354455788455146293213265920000⟩, + ⟨1, 7, 2, 6, 0, 4, 95813239749598246018882054745784234718307958128640000⟩, + ⟨1, 7, 3, 6, 1, 4, 2967409440926177487659198466646353481421385891840000⟩, + ⟨1, 7, 4, 6, 2, 4, -11070435857863025993590507032441755040957081845760000⟩, + ⟨1, 7, 5, 6, 3, 4, 14230611844607661533562811416493061187277789593600000⟩, + ⟨1, 7, 6, 6, 4, 4, 600159311148031631792591327201309524428954009600000⟩, + ⟨1, 7, 7, 6, 5, 4, -893505118768146381862357618759702360208084828160000⟩, + ⟨1, 7, 8, 6, 6, 4, -197368311610557902834600120325083650911130091520000⟩, + ⟨1, 7, 3, 7, 0, 4, -311904527475773881559704029064522481092481117061120000⟩, + ⟨1, 7, 4, 7, 1, 4, -10634452256590246914275664619925081224014421032960000⟩, + ⟨1, 7, 5, 7, 2, 4, -788371900897522472920743001657904985203854540800000⟩, + ⟨1, 7, 6, 7, 3, 4, 3029718563376868862982089666917064481726214963200000⟩, + ⟨1, 7, 7, 7, 4, 4, -694780228219212156591474156558349441866871603200000⟩, + ⟨1, 7, 8, 7, 5, 4, -509823239367134080182363145083763554258203443200000⟩ +] + +def collectedFourData_10_4_10 : List CollectedFourTerm := [ + ⟨1, 8, 1, 0, 5, 5, 60501914193336028043162039805250183442152292352000000⟩, + ⟨1, 8, 2, 0, 6, 5, -51628621673390639913576220328373351692208439296000000⟩, + ⟨1, 8, 3, 0, 7, 5, 7378368400484534116634264320842591760042426368000000⟩, + ⟨1, 8, 4, 0, 8, 5, -9492325739652987758808289284880368695966171136000000⟩, + ⟨1, 8, 1, 1, 4, 5, 26428167080065824136203517721680154152214200320000000⟩, + ⟨1, 8, 2, 1, 5, 5, 25209615228664859299572750469346449931995447296000000⟩, + ⟨1, 8, 3, 1, 6, 5, -34986050388925582537660464196147946415294775296000000⟩, + ⟨1, 8, 4, 1, 7, 5, 11070403317166614303627281605483229324368674816000000⟩, + ⟨1, 8, 5, 1, 8, 5, 13585270587213470143923347997875748108396134400000000⟩, + ⟨1, 8, 1, 2, 3, 5, 39918103000438019107304733177328474253734969344000000⟩, + ⟨1, 8, 2, 2, 4, 5, 92875432767263995720276873175460306426494189568000000⟩, + ⟨1, 8, 3, 2, 5, 5, -14888289248743820596230117581713988974874198016000000⟩, + ⟨1, 8, 4, 2, 6, 5, -7298641735732785137495087547292107777968701440000000⟩, + ⟨1, 8, 5, 2, 7, 5, 6963652340877499630472384765956619329937080320000000⟩, + ⟨1, 8, 6, 2, 8, 5, -2468739773311604881384486012710116555162124288000000⟩, + ⟨1, 8, 1, 3, 2, 5, -102861410283456352437830086768323681452896026624000000⟩, + ⟨1, 8, 2, 3, 3, 5, -105794169029092071682024458744117285422125547520000000⟩, + ⟨1, 8, 3, 3, 4, 5, 1622208506436923668331448908648566842533609472000000⟩, + ⟨1, 8, 4, 3, 5, 5, -20025246242932808310427444408887411989173764096000000⟩, + ⟨1, 8, 5, 3, 6, 5, -4764635221130930602268222430041654204175482880000000⟩, + ⟨1, 8, 6, 3, 7, 5, -5234388742924556475332870319836850693341184000000⟩, + ⟨1, 8, 7, 3, 8, 5, 139626925840848243408150309283273888103399424000000⟩, + ⟨1, 8, 1, 4, 1, 5, 46309064017681046456114668965234218416453189632000000⟩, + ⟨1, 8, 2, 4, 2, 5, 25225094279440099324909143848593114286606254080000000⟩, + ⟨1, 8, 3, 4, 3, 5, 23956727530926471020493831619478418553156141056000000⟩, + ⟨1, 8, 4, 4, 4, 5, 15008236918306526512680873638421078703173795840000000⟩, + ⟨1, 8, 5, 4, 5, 5, -2889045318607513106100672958784066964443627520000000⟩, + ⟨1, 8, 6, 4, 6, 5, -1057811374225311284379860645092298533197840384000000⟩, + ⟨1, 8, 7, 4, 7, 5, 369324786152783401102639039276277703364313088000000⟩, + ⟨1, 8, 8, 4, 8, 5, -56514282290223733093857845220869761306460160000000⟩, + ⟨1, 8, 1, 5, 0, 5, 244077079609231979915055779610277066652944171008000000⟩, + ⟨1, 8, 2, 5, 1, 5, -26125683478872488458130699768515644728945934336000000⟩, + ⟨1, 8, 3, 5, 2, 5, 29914465189454838283577223052388971339006869504000000⟩, + ⟨1, 8, 4, 5, 3, 5, 14301107320534812217917598604325921332649787392000000⟩, + ⟨1, 8, 5, 5, 4, 5, -1916409599864111301937218631942831281002250240000000⟩, + ⟨1, 8, 6, 5, 5, 5, -883675833335550170404454872882870201910034432000000⟩, + ⟨1, 8, 7, 5, 6, 5, -117001376315858579908426324743835401993584640000000⟩, + ⟨1, 8, 8, 5, 7, 5, 92655292277233507847607232731107509577711616000000⟩, + ⟨1, 8, 2, 6, 0, 5, 470316663465156096785530989132251396418362671104000000⟩, + ⟨1, 8, 3, 6, 1, 5, 7283033696797920842729685192413257850066829312000000⟩, + ⟨1, 8, 4, 6, 2, 5, -18113747360254538796105277498001821184569638912000000⟩, + ⟨1, 8, 5, 6, 3, 5, 17463384755893482128612261092139551168911114240000000⟩, + ⟨1, 8, 6, 6, 4, 5, 589198164062440571521630483602134731862310912000000⟩, + ⟨1, 8, 7, 6, 5, 5, -730988652762251638828628392075276903457488896000000⟩, + ⟨1, 8, 8, 6, 6, 5, -138402593022220827317598570807067418082410496000000⟩, + ⟨1, 8, 3, 7, 0, 5, -765519969189316444539585714554148181355859542016000000⟩, + ⟨1, 8, 4, 7, 1, 5, -17400379168788090183217941295122200327777943552000000⟩, + ⟨1, 8, 5, 7, 2, 5, -967466612570524745566982889058277945738526720000000⟩, + ⟨1, 8, 6, 7, 3, 5, 2974384604235929493462368599699245482328981504000000⟩, + ⟨1, 8, 7, 7, 4, 5, -568409125279560188745998664965101545502801920000000⟩, + ⟨1, 8, 8, 7, 5, 5, -357508547018574127268480955286298199179919360000000⟩ +] + +def collectedFourData_10_4_11 : List CollectedFourTerm := [ + ⟨2, 2, 6, 2, 8, 0, 10873234397960000254778052118801630273477174886400000⟩, + ⟨2, 2, 6, 3, 7, 0, 23054165670736371212959468688531252382479155200000⟩, + ⟨2, 2, 7, 3, 8, 0, -3689808806938585534735573743683292908301267763200000⟩, + ⟨2, 2, 6, 4, 6, 0, 4658988827061048614331522003208199461745668915200000⟩, + ⟨2, 2, 7, 4, 7, 0, -9759849974213048450056007351159563334061549158400000⟩, + ⟨2, 2, 8, 4, 8, 0, 5227101673962838973462422955112380369372971008000000⟩, + ⟨2, 2, 6, 5, 5, 0, 3892032109476325991482409827541368879615416729600000⟩, + ⟨2, 2, 7, 5, 6, 0, 3091901552328611662002426075387666735512420352000000⟩, + ⟨2, 2, 8, 5, 7, 0, -8569844891184692018718584902184580043265330380800000⟩, + ⟨2, 2, 6, 6, 4, 0, -2595044570495514883121431907350049618189195673600000⟩, + ⟨2, 2, 7, 6, 5, 0, 19317250970695309308664943216584346666745515212800000⟩, + ⟨2, 2, 8, 6, 6, 0, 12801090208525834854412858568792379279713029324800000⟩, + ⟨2, 2, 6, 7, 3, 0, -13100279479095441873560753598913381165916435251200000⟩, + ⟨2, 2, 7, 7, 4, 0, 15020892165107039258993937220641316627814547456000000⟩, + ⟨2, 2, 8, 7, 5, 0, 33066570941839223681219829085500708412056403968000000⟩ +] + +def collectedFourData_10_4_12 : List CollectedFourTerm := [ + ⟨2, 3, 5, 1, 8, 1, 39918103000438019107304733177328474253734969344000000⟩, + ⟨2, 3, 5, 2, 7, 1, 20461557215063619391270857221223547483731473203200000⟩, + ⟨2, 3, 6, 2, 8, 1, -36269946895678324476681181913059481939905767014400000⟩, + ⟨2, 3, 5, 3, 6, 1, -14000103884248872586867008024892347388493876428800000⟩, + ⟨2, 3, 6, 3, 7, 1, -76901990152871024708332216081946371758961459200000⟩, + ⟨2, 3, 7, 3, 8, 1, 6154064401847957592222662601342487317439945113600000⟩, + ⟨2, 3, 5, 4, 5, 1, -8488988707346962183365375832896549654715642675200000⟩, + ⟨2, 3, 6, 4, 6, 1, -15541031413501632821125139896772157801002906419200000⟩, + ⟨2, 3, 7, 4, 7, 1, 16278010172433558731834560225322933315093869363200000⟩, + ⟨2, 3, 8, 4, 8, 1, -5812030201688440413843759987839854127723053056000000⟩, + ⟨2, 3, 5, 5, 4, 1, -5631057203262884290810744265447080325254899302400000⟩, + ⟨2, 3, 6, 5, 5, 1, -12982686913607409089858077881436013750073792921600000⟩, + ⟨2, 3, 7, 5, 6, 1, -5156842067649347929105975495482730103697309696000000⟩, + ⟨2, 3, 8, 5, 7, 1, 9528836521289545054290437844833470440533498265600000⟩, + ⟨2, 3, 5, 6, 3, 1, 51313309289411896888020741097679162024250467942400000⟩, + ⟨2, 3, 6, 6, 4, 1, 8656313781063118514641069251285609235061774745600000⟩, + ⟨2, 3, 7, 6, 5, 1, -32218364896514157110749211028964036954454124134400000⟩, + ⟨2, 3, 8, 6, 6, 1, -14233571020263888942636112890486946652753598873600000⟩, + ⟨2, 3, 5, 7, 2, 1, -2842742928243467431904724492939892054480335667200000⟩, + ⟨2, 3, 6, 7, 3, 1, 43698721432371729262196874985230474229197255475200000⟩, + ⟨2, 3, 7, 7, 4, 1, -25052663320509202777487762842074096092250636288000000⟩, + ⟨2, 3, 8, 7, 5, 1, -36766820499694232482520743840987471701161803776000000⟩ +] + +def collectedFourData_10_4_13 : List CollectedFourTerm := [ + ⟨2, 4, 4, 0, 8, 2, -16223524135542078322572600067186622484758113812480000⟩, + ⟨2, 4, 4, 1, 7, 2, 18920648145899315624351251392271809271739323514880000⟩, + ⟨2, 4, 5, 1, 8, 2, 92875432767263995720276873175460306426494189568000000⟩, + ⟨2, 4, 4, 2, 6, 2, -12474254845858701662016839992426767117649654579200000⟩, + ⟨2, 4, 5, 2, 7, 2, 47606871033433477206694793237081921301764269670400000⟩, + ⟨2, 4, 6, 2, 8, 2, -42193726169112349627529046262282604707397920358400000⟩, + ⟨2, 4, 4, 3, 5, 2, -34225549633768723299676051099078024779948915425280000⟩, + ⟨2, 4, 5, 3, 6, 2, -32573334134189691855011069523556073127137614233600000⟩, + ⟨2, 4, 6, 3, 7, 2, -89461986908964569086801193197143258154873651200000⟩, + ⟨2, 4, 7, 3, 8, 2, 4772783537943265084709338630385844517062731366400000⟩, + ⟨2, 4, 4, 4, 4, 2, 25650878462687561006921018404557165849981694771200000⟩, + ⟨2, 4, 5, 4, 5, 2, -19750900987018717043549456269265970610647230054400000⟩, + ⟨2, 4, 6, 4, 6, 2, -18079266168569815465043743627425977054969148211200000⟩, + ⟨2, 4, 7, 4, 7, 2, 12624407856072245301963117424297571071648648396800000⟩, + ⟨2, 4, 8, 4, 8, 2, -3380639231730897948249124961056516915549175808000000⟩, + ⟨2, 4, 4, 5, 3, 2, 24442309097175568255629280146027529583832135106560000⟩, + ⟨2, 4, 5, 5, 4, 2, -13101496197966144140441742156100546311008079052800000⟩, + ⟨2, 4, 6, 5, 5, 2, -15103080744718156549803481317713346735130646937600000⟩, + ⟨2, 4, 7, 5, 6, 2, -3999387936346492872804639117992227342966063104000000⟩, + ⟨2, 4, 8, 5, 7, 2, 5542565585303276306561946498413595740078918860800000⟩, + ⟨2, 4, 4, 6, 2, 2, -30958568589423915192859968937611675659474734940160000⟩, + ⟨2, 4, 5, 6, 3, 2, 119388083319548110960095061614763347694450429132800000⟩, + ⟨2, 4, 6, 6, 4, 2, 10070103889664379283617767212173631726846319001600000⟩, + ⟨2, 4, 7, 6, 5, 2, -24986947090016984199492497458904830841208805785600000⟩, + ⟨2, 4, 8, 6, 6, 2, -8279132579998167378316852241270835991590784204800000⟩, + ⟨2, 4, 4, 7, 1, 2, -29739336718414922624236534188385443088677847695360000⟩, + ⟨2, 4, 5, 7, 2, 2, -6614066297283572053274539122785007551746827878400000⟩, + ⟨2, 4, 6, 7, 3, 2, 50835803299108485284508895252178943614739755827200000⟩, + ⟨2, 4, 7, 7, 4, 2, -19429588523944651023804217633568159465956442112000000⟩, + ⟨2, 4, 8, 7, 5, 2, -21385875760102788623313647382170028525924384768000000⟩ +] + +def collectedFourData_10_4_14 : List CollectedFourTerm := [ + ⟨2, 5, 3, 0, 7, 3, -1347676296728772911947304076770100676942280785920000⟩, + ⟨2, 5, 4, 0, 8, 3, 5201386691122118124385599958957393632999002603520000⟩, + ⟨2, 5, 3, 1, 6, 3, 6390284174780045357426172157729588892789888778240000⟩, + ⟨2, 5, 4, 1, 7, 3, -6066105405414541662130079578119077376166062981120000⟩, + ⟨2, 5, 5, 1, 8, 3, -14888289248743820596230117581713988974874198016000000⟩, + ⟨2, 5, 3, 2, 5, 3, 2719380956642967821194405215708169101290546135040000⟩, + ⟨2, 5, 4, 2, 6, 3, 3999342103160564826167650922202069411247738060800000⟩, + ⟨2, 5, 5, 2, 7, 3, -7631564613535003524269890804952284105901133004800000⟩, + ⟨2, 5, 6, 2, 8, 3, 4509211108332741059238581050369045382107968307200000⟩, + ⟨2, 5, 3, 3, 4, 3, -296300189122199362341204469333274669191192903680000⟩, + ⟨2, 5, 4, 3, 5, 3, 10972974606141325273912805405114582328228414750720000⟩, + ⟨2, 5, 5, 3, 6, 3, 5221630800914360029772662196495097285053723443200000⟩, + ⟨2, 5, 6, 3, 7, 3, 9560733828687780122986105407965213029407129600000⟩, + ⟨2, 5, 7, 3, 8, 3, -382547783182919283400159756352860627505931878400000⟩, + ⟨2, 5, 3, 4, 3, 3, -4375752481876484323183928783991252613547572592640000⟩, + ⟨2, 5, 4, 4, 4, 3, -8223869039595451370487038070782967026086104268800000⟩, + ⟨2, 5, 5, 4, 5, 3, 3166145427875534268946494727647571570278059212800000⟩, + ⟨2, 5, 6, 4, 6, 3, 1932117289453755090701741475007551774171699609600000⟩, + ⟨2, 5, 7, 4, 7, 3, -1011870578446266120614393517395220320412814540800000⟩, + ⟨2, 5, 8, 4, 8, 3, 216771790894529443861301143796456463037523558400000⟩, + ⟨2, 5, 3, 5, 2, 3, -5463947241032152551909155643443416500893657333760000⟩, + ⟨2, 5, 4, 5, 3, 3, -7836392400084048502605698411907739523269200445440000⟩, + ⟨2, 5, 5, 5, 4, 3, 2100220253890329167944935760223234890644691353600000⟩, + ⟨2, 5, 6, 5, 5, 3, 1614054639099018334696768605978002207330323660800000⟩, + ⟨2, 5, 7, 5, 6, 3, 320558637737249086788601921441079841389543424000000⟩, + ⟨2, 5, 8, 5, 7, 3, -355397836243360289840314572902506184228827299840000⟩, + ⟨2, 5, 3, 6, 1, 3, -1330263189461633387329918197801040927184419553280000⟩, + ⟨2, 5, 4, 6, 2, 3, 9925555341237230500232405222206381820691181731840000⟩, + ⟨2, 5, 5, 6, 3, 3, -19138369150523876087518831622223378309650684313600000⟩, + ⟨2, 5, 6, 6, 4, 3, -1076184268233227666582460648903183109521722572800000⟩, + ⟨2, 5, 7, 6, 5, 3, 2002751883005786371440515208795399662142593433600000⟩, + ⟨2, 5, 8, 6, 6, 3, 530870723966770555063777240692519730175583191040000⟩, + ⟨2, 5, 3, 7, 0, 3, 139824018150304451961248754608484955878616769495040000⟩, + ⟨2, 5, 4, 7, 1, 3, 9534660220406802048711934812380015427194600816640000⟩, + ⟨2, 5, 5, 7, 2, 3, 1060260277775357415458807189561597872141290700800000⟩, + ⟨2, 5, 6, 7, 3, 3, -5432783253572046383158739359404933572164426137600000⟩, + ⟨2, 5, 7, 7, 4, 3, 1557318901831929137323656113677510707429507072000000⟩, + ⟨2, 5, 8, 7, 5, 3, 1371295270093583885492049224537823480419608166400000⟩ +] + +def collectedFourData_10_4_15 : List CollectedFourTerm := [ + ⟨2, 6, 2, 0, 6, 4, 6934326601827700188898471083683873608310351462400000⟩, + ⟨2, 6, 3, 0, 7, 4, -1982002022104522146560120982139336568569488998400000⟩, + ⟨2, 6, 4, 0, 8, 4, 3824790479945037291872310359086131662852141875200000⟩, + ⟨2, 6, 2, 1, 5, 4, -3385945621555674439373967413832061735752066662400000⟩, + ⟨2, 6, 3, 1, 6, 4, 9398069986820869847641484845481751970646379724800000⟩, + ⟨2, 6, 4, 1, 7, 4, -4460653203226328480505639707533399520246444851200000⟩, + ⟨2, 6, 5, 1, 8, 4, -7298641735732785137495087547292107777968701440000000⟩, + ⟨2, 6, 2, 2, 4, 4, -12474254845858701662016839992426767117649654579200000⟩, + ⟨2, 6, 3, 2, 5, 4, 3999342103160564826167650922202069411247738060800000⟩, + ⟨2, 6, 4, 2, 6, 4, 2940878367747712806133789563584601779714654208000000⟩, + ⟨2, 6, 5, 2, 7, 4, -3741199211453232420579676634907447320937234432000000⟩, + ⟨2, 6, 6, 2, 8, 4, 1657902857775486072473329554715590966940532736000000⟩, + ⟨2, 6, 2, 3, 3, 4, 14209391938789490790163282385966811878982156288000000⟩, + ⟨2, 6, 3, 3, 4, 4, -435763080062795097394894456532410371747191193600000⟩, + ⟨2, 6, 4, 3, 5, 4, 8068873033778182211464549858853210411244925747200000⟩, + ⟨2, 6, 5, 3, 6, 4, 2559784529666959978143064286135464017304485888000000⟩, + ⟨2, 6, 6, 3, 7, 4, 3515197571415763617495437982675999809077248000000⟩, + ⟨2, 6, 7, 3, 8, 4, -112521156847613868748260254420982442768308633600000⟩, + ⟨2, 6, 2, 4, 2, 4, -3388024638776796767165325476134177313497546752000000⟩, + ⟨2, 6, 3, 4, 3, 4, -6435336355146647552316066573235059200730385612800000⟩, + ⟨2, 6, 4, 4, 4, 4, -6047344271604921711342870979143513336906252288000000⟩, + ⟨2, 6, 5, 4, 5, 4, 1552130051694264666194703010504610105002033152000000⟩, + ⟨2, 6, 6, 4, 6, 4, 710382082094887205300625657249073660478619648000000⟩, + ⟨2, 6, 7, 4, 7, 4, -297627781605510501450971293673295345523831603200000⟩, + ⟨2, 6, 8, 4, 8, 4, 53133695004140372788932746994537902666416128000000⟩, + ⟨2, 6, 2, 5, 1, 4, 3508984281713795540712044554830043713118824038400000⟩, + ⟨2, 6, 3, 5, 2, 4, -8035723791154321372983897192452335235419550515200000⟩, + ⟨2, 6, 4, 5, 3, 4, -5762416991629014611445895840413009981162808934400000⟩, + ⟨2, 6, 5, 5, 4, 4, 1029584725496155032867329800454857376686669824000000⟩, + ⟨2, 6, 6, 5, 5, 4, 593439902120142979607756651546721112087855104000000⟩, + ⟨2, 6, 7, 5, 6, 4, 94287904260167579426193788456978668528336896000000⟩, + ⟨2, 6, 8, 5, 7, 4, -87112811856935608652471285066879109255974092800000⟩, + ⟨2, 6, 2, 6, 0, 4, -63169018366999425548926704052483916233575078297600000⟩, + ⟨2, 6, 3, 6, 1, 4, -1956392894824947104574181349092311285435570585600000⟩, + ⟨2, 6, 4, 6, 2, 4, 7298663189592968522169345966710344509626410598400000⟩, + ⟨2, 6, 5, 6, 3, 4, -9382145759134819996966672750861636720838836224000000⟩, + ⟨2, 6, 6, 6, 4, 4, -395680958582706724962881889973582726812401664000000⟩, + ⟨2, 6, 7, 6, 5, 4, 589081857642849488522234859178294672867354214400000⟩, + ⟨2, 6, 8, 6, 6, 4, 130123587656300660746790850266830434086997196800000⟩, + ⟨2, 6, 3, 7, 0, 4, 205636537041845019078515411008634199908182445260800000⟩, + ⟨2, 6, 4, 7, 1, 4, 7011222161729945903059907668892758048942483046400000⟩, + ⟨2, 6, 5, 7, 2, 4, 519768240986034155636782531858880281624707072000000⟩, + ⟨2, 6, 6, 7, 3, 4, -1997472876159529247144131929588716295356940288000000⟩, + ⟨2, 6, 7, 7, 4, 4, 458063886704044931273064642018443702606757888000000⟩, + ⟨2, 6, 8, 7, 5, 4, 336122999865899806942137497031860901786943488000000⟩ +] + +def collectedFourData_10_4_16 : List CollectedFourTerm := [ + ⟨2, 7, 1, 0, 5, 5, 31012580404290021038670170913750282248006506905600000⟩, + ⟨2, 7, 2, 0, 6, 5, -26464233440485996120933182679601219228851293388800000⟩, + ⟨2, 7, 3, 0, 7, 5, 3782066176307905177909597130205565518118020710400000⟩, + ⟨2, 7, 4, 0, 8, 5, -4865656221784874117468305361026165390265076940800000⟩, + ⟨2, 7, 1, 1, 4, 5, 13546772320119870057767403226248168193545732096000000⟩, + ⟨2, 7, 2, 1, 5, 5, 12922156755931137194231601277512051785024195788800000⟩, + ⟨2, 7, 3, 1, 6, 5, -17933444175797742931107654832515582530922794188800000⟩, + ⟨2, 7, 4, 1, 7, 5, 5674560508688230917518944014741778099742756044800000⟩, + ⟨2, 7, 5, 1, 8, 5, 6963652340877499630472384765956619329937080320000000⟩, + ⟨2, 7, 1, 2, 3, 5, 20461557215063619391270857221223547483731473203200000⟩, + ⟨2, 7, 2, 2, 4, 5, 47606871033433477206694793237081921301764269670400000⟩, + ⟨2, 7, 3, 2, 5, 5, -7631564613535003524269890804952284105901133004800000⟩, + ⟨2, 7, 4, 2, 6, 5, -3741199211453232420579676634907447320937234432000000⟩, + ⟨2, 7, 5, 2, 7, 5, 3569487527929700506496549161426148312110596096000000⟩, + ⟨2, 7, 6, 2, 8, 5, -1265447411670947962630012590984335050624362086400000⟩, + ⟨2, 7, 1, 3, 2, 5, -52725567437760774796541232302256274882583278387200000⟩, + ⟨2, 7, 2, 3, 3, 5, -54228865599778769686477794612073793544316256256000000⟩, + ⟨2, 7, 3, 3, 4, 5, 831525289888093865098435580263276119139654041600000⟩, + ⟨2, 7, 4, 3, 5, 5, -10264709265894005580151780393952308356834970828800000⟩, + ⟨2, 7, 5, 3, 6, 5, -2442296824200490289886575882726852771513892864000000⟩, + ⟨2, 7, 6, 3, 7, 5, -2683087038180659636675053345451166049448755200000⟩, + ⟨2, 7, 7, 3, 8, 5, 71571144846853362938627959747019949460370227200000⟩, + ⟨2, 7, 1, 4, 1, 5, 23737489804147937191612618124754462342664264089600000⟩, + ⟨2, 7, 2, 4, 2, 5, 12930091138060192105498032223684781747390644224000000⟩, + ⟨2, 7, 3, 4, 3, 5, 12279941034631904536056963260247876140643699916800000⟩, + ⟨2, 7, 4, 4, 4, 5, 7693048399564212403868399350427942497133002752000000⟩, + ⟨2, 7, 5, 4, 5, 5, -1480891165668635962672458993918507310179680256000000⟩, + ⟨2, 7, 6, 4, 6, 5, -542221857492045073591084170537694785097118515200000⟩, + ⟨2, 7, 7, 4, 7, 5, 189311607385836732020323061204897035553498726400000⟩, + ⟨2, 7, 8, 4, 8, 5, -28968566480651166425882563749948699388674048000000⟩, + ⟨2, 7, 1, 5, 0, 5, 125111083792111488595312363028308517611133888102400000⟩, + ⟨2, 7, 2, 5, 1, 5, -13391722729903420909543336854786299612669725900800000⟩, + ⟨2, 7, 3, 5, 2, 5, 15333808348190860352739650074321518141333779251200000⟩, + ⟨2, 7, 4, 5, 3, 5, 7330581958633587807839684920171803383952939417600000⟩, + ⟨2, 7, 5, 5, 4, 5, -982329362562304411394919068178541116571779072000000⟩, + ⟨2, 7, 6, 5, 5, 5, -452961996294412512903518482008468138187397529600000⟩, + ⟨2, 7, 7, 5, 6, 5, -59973550238643861409109440068756788207419392000000⟩, + ⟨2, 7, 8, 5, 7, 5, 47494029568194972681890782315904211274747084800000⟩, + ⟨2, 7, 2, 6, 0, 5, 241078873877962480832101622649419397914627879731200000⟩, + ⟨2, 7, 3, 6, 1, 5, 3733198711487661360559966725151089752930883993600000⟩, + ⟨2, 7, 4, 6, 2, 5, -9284897080078902692099530899372664743005886873600000⟩, + ⟨2, 7, 5, 6, 3, 5, 8951528742422037497601279250968344375718838272000000⟩, + ⟨2, 7, 6, 6, 4, 5, 302016154045240580923301786756553729484888473600000⟩, + ⟨2, 7, 7, 6, 5, 5, -374696316152422388592029981164525734654168268800000⟩, + ⟨2, 7, 8, 6, 6, 5, -70943566025826970680004831048930336481004748800000⟩, + ⟨2, 7, 3, 7, 0, 5, -392396668966685623123986592879981649104779136204800000⟩, + ⟨2, 7, 4, 7, 1, 5, -8919232808283796868617894603360672001289722265600000⟩, + ⟨2, 7, 5, 7, 2, 5, -495912179157370302164476523353573354704470016000000⟩, + ⟨2, 7, 6, 7, 3, 5, 1524635094972073495673078157956092562045612851200000⟩, + ⟨2, 7, 7, 7, 4, 5, -291359933570599892900686595773311151899672576000000⟩, + ⟨2, 7, 8, 7, 5, 5, -183254740076564950275830170728588722263031808000000⟩ +] + +def collectedFourData_10_4_17 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 4, 6, 16583930293351227691354359490824658918569934848000000⟩, + ⟨2, 8, 1, 0, 5, 6, -54972582611330638325610604320008643660517421875200000⟩, + ⟨2, 8, 2, 0, 6, 6, 23455114667778650769762646502583079890232069324800000⟩, + ⟨2, 8, 3, 0, 7, 6, -2234683931576846807079882013114885897920813465600000⟩, + ⟨2, 8, 4, 0, 8, 6, 2156203104703625983889685597620384649055725158400000⟩, + ⟨2, 8, 0, 1, 3, 6, 13034350721302549426533276291080851199358507417600000⟩, + ⟨2, 8, 1, 1, 4, 6, -24012869963624860411414032432585429502427922432000000⟩, + ⟨2, 8, 2, 1, 5, 6, -11452841403737608734437266862657357521422699724800000⟩, + ⟨2, 8, 3, 1, 6, 6, 10596213199158727871163077481411334185306764083200000⟩, + ⟨2, 8, 4, 1, 7, 6, -2514666969663916515968907795005145436620482150400000⟩, + ⟨2, 8, 5, 1, 8, 6, -2468739773311604881384486012710116555162124288000000⟩, + ⟨2, 8, 0, 2, 2, 6, 10873234397960000254778052118801630273477174886400000⟩, + ⟨2, 8, 1, 2, 3, 6, -36269946895678324476681181913059481939905767014400000⟩, + ⟨2, 8, 2, 2, 4, 6, -42193726169112349627529046262282604707397920358400000⟩, + ⟨2, 8, 3, 2, 5, 6, 4509211108332741059238581050369045382107968307200000⟩, + ⟨2, 8, 4, 2, 6, 6, 1657902857775486072473329554715590966940532736000000⟩, + ⟨2, 8, 5, 2, 7, 6, -1265447411670947962630012590984335050624362086400000⟩, + ⟨2, 8, 6, 2, 8, 6, 373853188348647750582781443094188248378690764800000⟩, + ⟨2, 8, 0, 3, 1, 6, 34854581257712886616095235954459580723010679603200000⟩, + ⟨2, 8, 1, 3, 2, 6, 93460801194751278525545284932073964915929802342400000⟩, + ⟨2, 8, 2, 3, 3, 6, 48062766065254667845089503401085909064877080576000000⟩, + ⟨2, 8, 3, 3, 4, 6, -491317739402089082079703581896495197671810662400000⟩, + ⟨2, 8, 4, 3, 5, 6, 4548779646393047732944694255962748205350151782400000⟩, + ⟨2, 8, 5, 3, 6, 6, 865838070740992553604398736993757572426733977600000⟩, + ⟨2, 8, 6, 3, 7, 6, 792668770420306378926601692629743998232166400000⟩, + ⟨2, 8, 7, 3, 8, 6, -18123754117985056688157067963499149643690803200000⟩, + ⟨2, 8, 0, 4, 0, 6, 111305580223731553624674774421375934798021787648000000⟩, + ⟨2, 8, 1, 4, 1, 6, -42076831473966310760465180799228444927604241203200000⟩, + ⟨2, 8, 2, 4, 2, 6, -11459873606014446684889455244043086692303765504000000⟩, + ⟨2, 8, 3, 4, 3, 6, -7255765930989619057304773757557751541488890675200000⟩, + ⟨2, 8, 4, 4, 4, 6, -3409154713706983550689493406773979212830212096000000⟩, + ⟨2, 8, 5, 4, 5, 6, 525002504672893700474657921482656850274313830400000⟩, + ⟨2, 8, 6, 4, 6, 6, 160189485826249287875993118694840397837264486400000⟩, + ⟨2, 8, 7, 4, 7, 6, -47938831092936958197060739192866017229825638400000⟩, + ⟨2, 8, 8, 4, 8, 6, 6418673056342684879103114469855994841137152000000⟩, + ⟨2, 8, 1, 5, 0, 6, -221770626619755827290995928671061114291015699660800000⟩, + ⟨2, 8, 2, 5, 1, 6, 11869015323468752891808277166362898351434550476800000⟩, + ⟨2, 8, 3, 5, 2, 6, -9060183912231828012829465253983124253590736076800000⟩, + ⟨2, 8, 4, 5, 3, 6, -3248528637868278101954018011580815367874596044800000⟩, + ⟨2, 8, 5, 5, 4, 6, 348253394790212127420271395524927838963420364800000⟩, + ⟨2, 8, 6, 5, 5, 6, 133819299761994375843501229214102480179376947200000⟩, + ⟨2, 8, 7, 5, 6, 6, 15186928760656720379007938626569095193034752000000⟩, + ⟨2, 8, 8, 5, 7, 6, -10523428838984212239952517484524962258826035200000⟩, + ⟨2, 8, 2, 6, 0, 6, -213666972198636858884178769975978338545938150195200000⟩, + ⟨2, 8, 3, 6, 1, 6, -2205809942249324989448916856948717959155967590400000⟩, + ⟨2, 8, 4, 6, 2, 6, 4114578383339987988749814294628479396922313932800000⟩, + ⟨2, 8, 5, 6, 3, 6, -3173477646009905616903879031437920692584893644800000⟩, + ⟨2, 8, 6, 6, 4, 6, -89225123921600978361064201974624384518927155200000⟩, + ⟨2, 8, 7, 6, 5, 6, 94883265000054825519179789507516136279559372800000⟩, + ⟨2, 8, 8, 6, 6, 6, 15719229878875526236626520140418024138289971200000⟩, + ⟨2, 8, 3, 7, 0, 6, 231852773078696873807022268722820629920604173107200000⟩, + ⟨2, 8, 4, 7, 1, 6, 3952535196936125896271284941466782821818092748800000⟩, + ⟨2, 8, 5, 7, 2, 6, 175809770624068423560885402057094969042560614400000⟩, + ⟨2, 8, 6, 7, 3, 6, -450425427454875895100836974796316201670043238400000⟩, + ⟨2, 8, 7, 7, 4, 6, 73780233740360127664318132873618202774470656000000⟩, + ⟨2, 8, 8, 7, 5, 6, 40604434581261654728466863550242002820923392000000⟩ +] + +def collectedFourData_10_4_18 : List CollectedFourTerm := [ + ⟨3, 1, 6, 2, 8, 0, 34854581257712886616095235954459580723010679603200000⟩, + ⟨3, 1, 6, 3, 7, 0, 73901036369657758779214894172932317682178457600000⟩, + ⟨3, 1, 7, 3, 8, 0, -11827827505585121510985314019824667016289687961600000⟩, + ⟨3, 1, 6, 4, 6, 0, 14934572244854971008598625161894854506491517337600000⟩, + ⟨3, 1, 7, 4, 7, 0, -31285583621108940764677262470878266806657823539200000⟩, + ⟨3, 1, 8, 4, 8, 0, 16755680358702320138160796799708070175209160704000000⟩, + ⟨3, 1, 6, 5, 5, 0, 12476062269274859506284274943546262343327206604800000⟩, + ⟨3, 1, 7, 5, 6, 0, 9911212243957977989209490002829879489096318976000000⟩, + ⟨3, 1, 8, 5, 7, 0, -27470975442397644033993561656602852236229764710400000⟩, + ⟨3, 1, 6, 6, 4, 0, -8318517613001365499987082083985017768369769676800000⟩, + ⟨3, 1, 7, 6, 5, 0, 61922209067805443841648023777716281539608077926400000⟩, + ⟨3, 1, 8, 6, 6, 0, 41034399014159639061234897852045250573057287782400000⟩, + ⟨3, 1, 6, 7, 3, 0, -41993462008742070100771412308650157726378858905600000⟩, + ⟨3, 1, 7, 7, 4, 0, 48150061644058024393174795083351756072579760128000000⟩, + ⟨3, 1, 8, 7, 5, 0, 105996195945384491243429466428082886225044701184000000⟩ +] + +def collectedFourData_10_4_19 : List CollectedFourTerm := [ + ⟨3, 2, 5, 1, 8, 1, -102861410283456352437830086768323681452896026624000000⟩, + ⟨3, 2, 5, 2, 7, 1, -52725567437760774796541232302256274882583278387200000⟩, + ⟨3, 2, 6, 2, 8, 1, 93460801194751278525545284932073964915929802342400000⟩, + ⟨3, 2, 5, 3, 6, 1, 36075622872984029172154890021919603832048635084800000⟩, + ⟨3, 2, 6, 3, 7, 1, 198161900645478771242313209764790824519021363200000⟩, + ⟨3, 2, 7, 3, 8, 1, -15857861365364735024921587568052246133998197145600000⟩, + ⟨3, 2, 5, 4, 5, 1, 21874520197226361344341258344071710734401352499200000⟩, + ⟨3, 2, 6, 4, 6, 1, 40046302010762736431100124145154918302438601523200000⟩, + ⟨3, 2, 7, 4, 7, 1, -41945357045814313947970899128457825973968253747200000⟩, + ⟨3, 2, 8, 4, 8, 1, 14976503847118041858161530697307321275070283776000000⟩, + ⟨3, 2, 5, 5, 4, 1, 14510170618781160067752499378767169861462681190400000⟩, + ⟨3, 2, 6, 5, 5, 1, 33453931545483960036170514729018880252752533913600000⟩, + ⟨3, 2, 7, 5, 6, 1, 13288207800897915094904023160398981596463497216000000⟩, + ⟨3, 2, 8, 5, 7, 1, -24554011570379277282168179768829998076125616537600000⟩, + ⟨3, 2, 5, 6, 3, 1, -132224704158966980983239648364836734978962646630400000⟩, + ⟨3, 2, 6, 6, 4, 1, -22305685301891737765865376170655763298724190617600000⟩, + ⟨3, 2, 7, 6, 5, 1, 83020639789573313489411640576616270831322293862400000⟩, + ⟨3, 2, 8, 6, 6, 1, 36677223576932325355295098838863245472259742105600000⟩, + ⟨3, 2, 5, 7, 2, 1, 7325211487861455793538007676342367491185652531200000⟩, + ⟨3, 2, 6, 7, 3, 1, -112603349765101149238507603877437757173959701299200000⟩, + ⟨3, 2, 7, 7, 4, 1, 64555980540355796125517145152555252964390862848000000⟩, + ⟨3, 2, 8, 7, 5, 1, 94741150605171385959561958100486377405358800896000000⟩ +] + +def collectedFourData_10_4_20 : List CollectedFourTerm := [ + ⟨3, 3, 4, 0, 8, 2, 18480175042027481749959289099406983851028984627200000⟩, + ⟨3, 3, 4, 1, 7, 2, -21552462136066527153805816144595287139075437363200000⟩, + ⟨3, 3, 5, 1, 8, 2, -105794169029092071682024458744117285422125547520000000⟩, + ⟨3, 3, 4, 2, 6, 2, 14209391938789490790163282385966811878982156288000000⟩, + ⟨3, 3, 5, 2, 7, 2, -54228865599778769686477794612073793544316256256000000⟩, + ⟨3, 3, 6, 2, 8, 2, 48062766065254667845089503401085909064877080576000000⟩, + ⟨3, 3, 4, 3, 5, 2, 38986236458698496278175117473448800301958247219200000⟩, + ⟨3, 3, 5, 3, 6, 2, 37104201989228329333141316527369492582895714304000000⟩, + ⟨3, 3, 6, 3, 7, 2, 101905921541626586709903000389780717193658368000000⟩, + ⟨3, 3, 7, 3, 8, 2, -5436665577836344329968439535379386965946269696000000⟩, + ⟨3, 3, 4, 4, 4, 2, -29218850356547395046195051492381343948019335168000000⟩, + ⟨3, 3, 5, 4, 5, 2, 22498201033783185661723940072994615042313814016000000⟩, + ⟨3, 3, 6, 4, 6, 2, 20594046067624759786300167159556558260711456768000000⟩, + ⟨3, 3, 7, 4, 7, 2, -14380430850474193643194459930299986658409316352000000⟩, + ⟨3, 3, 8, 4, 8, 2, 3850877542658201455364298654370383220829061120000000⟩, + ⟨3, 3, 4, 5, 3, 2, -27842172068988176634838724366384850355091826278400000⟩, + ⟨3, 3, 5, 5, 4, 2, 14923880966185770573167022451257474807540744192000000⟩, + ⟨3, 3, 6, 5, 5, 2, 17203880827890201072126477858930001820321316864000000⟩, + ⟨3, 3, 7, 5, 6, 2, 4555692616916534714395304227491284104312258560000000⟩, + ⟨3, 3, 8, 5, 7, 2, -6313522348324205491669525095956868408186765312000000⟩, + ⟨3, 3, 4, 6, 2, 2, 35264826667948337247017787734058590085319124582400000⟩, + ⟨3, 3, 5, 6, 3, 2, -135994661779056844001846260346819525422866235392000000⟩, + ⟨3, 3, 6, 6, 4, 2, -11470829704916110062281350574518136208384589824000000⟩, + ⟨3, 3, 7, 6, 5, 2, 28462567820130662552356608437928700318354243584000000⟩, + ⟨3, 3, 8, 6, 6, 2, 9430738845410946661005004470755978804012777472000000⟩, + ⟨3, 3, 4, 7, 1, 2, 33876002747521383531481801863060768182585681510400000⟩, + ⟨3, 3, 5, 7, 2, 2, 7534066081585727728081678435594905220993253376000000⟩, + ⟨3, 3, 6, 7, 3, 2, -57906934123608209106621683193212634897221419008000000⟩, + ⟨3, 3, 7, 7, 4, 2, 22132194825071410742996911771965916825968967680000000⟩, + ⟨3, 3, 8, 7, 5, 2, 24360596635593238423124635417559452605764075520000000⟩ +] + +def collectedFourData_10_4_21 : List CollectedFourTerm := [ + ⟨3, 4, 3, 0, 7, 3, 146841045062399345877083536889373357303807344640000⟩, + ⟨3, 4, 4, 0, 8, 3, -566736284782889082298281315287928778088345763840000⟩, + ⟨3, 4, 3, 1, 6, 3, -696276998228798885385813284638576536916674478080000⟩, + ⟨3, 4, 4, 1, 7, 3, 660954903897823647113444805744305113278751703040000⟩, + ⟨3, 4, 5, 1, 8, 3, 1622208506436923668331448908648566842533609472000000⟩, + ⟨3, 4, 3, 2, 5, 3, -296300189122199362341204469333274669191192903680000⟩, + ⟨3, 4, 4, 2, 6, 3, -435763080062795097394894456532410371747191193600000⟩, + ⟨3, 4, 5, 2, 7, 3, 831525289888093865098435580263276119139654041600000⟩, + ⟨3, 4, 6, 2, 8, 3, -491317739402089082079703581896495197671810662400000⟩, + ⟨3, 4, 3, 3, 4, 3, 32284480723227226682352052255798316914767298560000⟩, + ⟨3, 4, 4, 3, 5, 3, -1195600948477052143615616933549179679747069706240000⟩, + ⟨3, 4, 5, 3, 6, 3, -568942056484496013895344933443611849858115174400000⟩, + ⟨3, 4, 6, 3, 7, 3, -1041725042115578737324272026350434053731123200000⟩, + ⟨3, 4, 7, 3, 8, 3, 41681905666245673430298621155660219131153612800000⟩, + ⟨3, 4, 3, 4, 3, 3, 476776262172729486518023565730407762107438202880000⟩, + ⟨3, 4, 4, 4, 4, 3, 896062004772012988373815856521808720176978329600000⟩, + ⟨3, 4, 5, 4, 5, 3, -344979061052929279058994726339351279836961177600000⟩, + ⟨3, 4, 6, 4, 6, 3, -210520970544025767284912761539121764990399283200000⟩, + ⟨3, 4, 7, 4, 7, 3, 110252093598146595587683111676824822987987353600000⟩, + ⟨3, 4, 8, 4, 8, 3, -23619170562147807167433005770857718913748172800000⟩, + ⟨3, 4, 3, 5, 2, 3, 595344538585773211575415806972648642641311825920000⟩, + ⟨3, 4, 4, 5, 3, 3, 853843057372530828046359731940770456424394260480000⟩, + ⟨3, 4, 5, 5, 4, 3, -228837249487174501572441281478216848707367731200000⟩, + ⟨3, 4, 6, 5, 5, 3, -175865280533915253953203904228841804292266393600000⟩, + ⟨3, 4, 7, 5, 6, 3, -34927649527837666876579234798003698435883008000000⟩, + ⟨3, 4, 8, 5, 7, 3, 38723682989427396269824961251516136438397665280000⟩, + ⟨3, 4, 3, 6, 1, 3, 144943735689891304982885330654060573538134261760000⟩, + ⟨3, 4, 4, 6, 2, 3, -1081475516538880059764915944789508025570589409280000⟩, + ⟨3, 4, 5, 6, 3, 3, 2085291648799027263690894092162823011446240051200000⟩, + ⟨3, 4, 6, 6, 4, 3, 117259629044944638064552216449072253766310297600000⟩, + ⟨3, 4, 7, 6, 5, 3, -218217223390435753390618807432167798395319091200000⟩, + ⟨3, 4, 8, 6, 6, 3, -57842979126019089058934736183796290918474055680000⟩, + ⟨3, 4, 3, 7, 0, 3, -15235041975474290126210481312724651529436062023680000⟩, + ⟨3, 4, 4, 7, 1, 3, -1038884095889975578465732118948895373409522810880000⟩, + ⟨3, 4, 5, 7, 2, 3, -115524571890587090409831450498936228233714073600000⟩, + ⟨3, 4, 6, 7, 3, 3, 591948951308575241154991533411413370569175859200000⟩, + ⟨3, 4, 7, 7, 4, 3, -169683428873462862418385839788250275589914624000000⟩, + ⟨3, 4, 8, 7, 5, 3, -149414537480874239426256666398506116866428108800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1015.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1015.lean new file mode 100644 index 0000000000000000000000000000000000000000..3764dbff2982cfc2091c2a7c2c417f2cbda7b04e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1015.lean @@ -0,0 +1,625 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1015. -/ +namespace LaughlinFock +def collectedFourData_10_4_22 : List CollectedFourTerm := [ + ⟨3, 5, 2, 0, 6, 4, 19025676661272297390341393242333418709825261404160000⟩, + ⟨3, 5, 3, 0, 7, 4, -5438008876681617106626386310839213721653933506560000⟩, + ⟨3, 5, 4, 0, 8, 4, 10494058204493392749971882574888122731835613511680000⟩, + ⟨3, 5, 2, 1, 5, 4, -9290001796481518452217497388254642200549429084160000⟩, + ⟨3, 5, 3, 1, 6, 4, 25785436867385713148598719097810723321502047928320000⟩, + ⟨3, 5, 4, 1, 7, 4, -12238671527280536459943388368878631357119547310080000⟩, + ⟨3, 5, 5, 1, 8, 4, -20025246242932808310427444408887411989173764096000000⟩, + ⟨3, 5, 2, 2, 4, 4, -34225549633768723299676051099078024779948915425280000⟩, + ⟨3, 5, 3, 2, 5, 4, 10972974606141325273912805405114582328228414750720000⟩, + ⟨3, 5, 4, 2, 6, 4, 8068873033778182211464549858853210411244925747200000⟩, + ⟨3, 5, 5, 2, 7, 4, -10264709265894005580151780393952308356834970828800000⟩, + ⟨3, 5, 6, 2, 8, 4, 4548779646393047732944694255962748205350151782400000⟩, + ⟨3, 5, 2, 3, 3, 4, 38986236458698496278175117473448800301958247219200000⟩, + ⟨3, 5, 3, 3, 4, 4, -1195600948477052143615616933549179679747069706240000⟩, + ⟨3, 5, 4, 3, 5, 4, 22138525941518296957128266602374362286596271636480000⟩, + ⟨3, 5, 5, 3, 6, 4, 7023267806730380612473096503883610690126295859200000⟩, + ⟨3, 5, 6, 3, 7, 4, 9644629714530386001577111712200285584831283200000⟩, + ⟨3, 5, 7, 3, 8, 4, -308723726276572020809974784041742361421928202240000⟩, + ⟨3, 5, 2, 4, 2, 4, -9295705985466771138724066068676929098882010316800000⟩, + ⟨3, 5, 3, 4, 3, 4, -17656599657027941881986556662945987570752311787520000⟩, + ⟨3, 5, 4, 4, 4, 4, -16592067748961687890629311614007510658165453619200000⟩, + ⟨3, 5, 5, 4, 5, 4, 4258571335823083973979946645317239006840016076800000⟩, + ⟨3, 5, 6, 4, 6, 4, 1949071708900529425003026067826135900622107443200000⟩, + ⟨3, 5, 7, 4, 7, 4, -816599832022003384932771188995244321544213626880000⟩, + ⟨3, 5, 8, 4, 8, 4, 145782648988726169940170667100089155096621875200000⟩, + ⟨3, 5, 2, 5, 1, 4, 9627582343147373833834797480331170551840699842560000⟩, + ⟨3, 5, 3, 5, 2, 4, -22047574532976130785999491676607591632581878087680000⟩, + ⟨3, 5, 4, 5, 3, 4, -15810314218724360702622075714858710031334857768960000⟩, + ⟨3, 5, 5, 5, 4, 4, 2824866379600815582055257747805704893236877721600000⟩, + ⟨3, 5, 6, 5, 5, 4, 1628218043935084686566393924991575577805298073600000⟩, + ⟨3, 5, 7, 5, 6, 4, 258697243803042985708556935630969557060314726400000⟩, + ⟨3, 5, 8, 5, 7, 4, -239010979235887744305965679933654710233879019520000⟩, + ⟨3, 5, 2, 6, 0, 4, -173316514705801632627365013808698173526850236579840000⟩, + ⟨3, 5, 3, 6, 1, 4, -5367745244295144028959163936396719531943306199040000⟩, + ⟨3, 5, 4, 6, 2, 4, 20025305105779977585259448110174713512402154946560000⟩, + ⟨3, 5, 5, 6, 3, 4, -25741745644801041358098223876093691351019395481600000⟩, + ⟨3, 5, 6, 6, 4, 4, -1085627835445860261015981412012219096637217177600000⟩, + ⟨3, 5, 7, 6, 5, 4, 1616260899447748983818704988217901434419502120960000⟩, + ⟨3, 5, 8, 6, 6, 4, 357019426241183247891487159652361475760188293120000⟩, + ⟨3, 5, 3, 7, 0, 4, 564203921757981724985700071741759632896223315230720000⟩, + ⟨3, 5, 4, 7, 1, 4, 19236654618238157310163864156003883292523505909760000⟩, + ⟨3, 5, 5, 7, 2, 4, 1426085481637407804425645475295160892752973004800000⟩, + ⟨3, 5, 6, 7, 3, 4, -5480456180338574587118288090903190048005632819200000⟩, + ⟨3, 5, 7, 7, 4, 4, 1256787558339088702051449575840761509858980659200000⟩, + ⟨3, 5, 8, 7, 5, 4, 922218966753014160403174453583277791965819699200000⟩ +] + +def collectedFourData_10_4_23 : List CollectedFourTerm := [ + ⟨3, 6, 1, 0, 5, 5, -21219271965236456112557198817665658685510542950400000⟩, + ⟨3, 6, 2, 0, 6, 5, 18107224855352482944107617059998148474447278899200000⟩, + ⟨3, 6, 3, 0, 7, 5, -2587746319055020847716752915955104757552093593600000⟩, + ⟨3, 6, 4, 0, 8, 5, 3329154856301991929783624604140058129860866867200000⟩, + ⟨3, 6, 1, 1, 4, 5, -9268904501477632153433324268414191437678116864000000⟩, + ⟨3, 6, 2, 1, 5, 5, -8841533178051513783114553875225254286966600499200000⟩, + ⟨3, 6, 3, 1, 6, 5, 12270331081092435381274020283292265538345186099200000⟩, + ⟨3, 6, 4, 1, 7, 5, -3882619283766196486488028016015120776155050803200000⟩, + ⟨3, 6, 5, 1, 8, 5, -4764635221130930602268222430041654204175482880000000⟩, + ⟨3, 6, 1, 2, 3, 5, -14000103884248872586867008024892347388493876428800000⟩, + ⟨3, 6, 2, 2, 4, 5, -32573334134189691855011069523556073127137614233600000⟩, + ⟨3, 6, 3, 2, 5, 5, 5221630800914360029772662196495097285053723443200000⟩, + ⟨3, 6, 4, 2, 6, 5, 2559784529666959978143064286135464017304485888000000⟩, + ⟨3, 6, 5, 2, 7, 5, -2442296824200490289886575882726852771513892864000000⟩, + ⟨3, 6, 6, 2, 8, 5, 865838070740992553604398736993757572426733977600000⟩, + ⟨3, 6, 1, 3, 2, 5, 36075622872984029172154890021919603832048635084800000⟩, + ⟨3, 6, 2, 3, 3, 5, 37104201989228329333141316527369492582895714304000000⟩, + ⟨3, 6, 3, 3, 4, 5, -568942056484496013895344933443611849858115174400000⟩, + ⟨3, 6, 4, 3, 5, 5, 7023267806730380612473096503883610690126295859200000⟩, + ⟨3, 6, 5, 3, 6, 5, 1671056063602325316037063725367178778195787776000000⟩, + ⟨3, 6, 6, 3, 7, 5, 1835808334145601492352960833228185101192396800000⟩, + ⟨3, 6, 7, 3, 8, 5, -48970049172645778167365597081596547547581644800000⟩, + ⟨3, 6, 1, 4, 1, 5, -16241546022934807604226356411338899204054869606400000⟩, + ⟨3, 6, 2, 4, 2, 5, -8846962001131622210935227484913961001619030016000000⟩, + ⟨3, 6, 3, 4, 3, 5, -8402119563545775231233481252373095307134841651200000⟩, + ⟨3, 6, 4, 4, 4, 5, -5263698928113015054179588853992993980592160768000000⟩, + ⟨3, 6, 5, 4, 5, 5, 1013247913768954500258976386123103284498530304000000⟩, + ⟨3, 6, 6, 4, 6, 5, 370996315354262069563062511229572533113900236800000⟩, + ⟨3, 6, 7, 4, 7, 5, -129529836954181679990147230888685148640483737600000⟩, + ⟨3, 6, 8, 4, 8, 5, 19820727026988649720812296824003049325330432000000⟩, + ⟨3, 6, 1, 5, 0, 5, -85602877227302966841817526020885851378445556121600000⟩, + ⟨3, 6, 2, 5, 1, 5, 9162817249787792646417290213398941619471987507200000⟩, + ⟨3, 6, 3, 5, 2, 5, -10491621315008852926462075921507540316717894860800000⟩, + ⟨3, 6, 4, 5, 3, 5, -5015693960834823269832347003650875303687251558400000⟩, + ⟨3, 6, 5, 5, 4, 5, 672124461489940265158767746965572289610907648000000⟩, + ⟨3, 6, 6, 5, 5, 5, 309923381543510295156906512676235534596990566400000⟩, + ⟨3, 6, 7, 5, 6, 5, 41034801253059087591114228930759311153430528000000⟩, + ⟨3, 6, 8, 5, 7, 5, -32496126313729825188070247861018543493690163200000⟩, + ⟨3, 6, 2, 6, 0, 5, -164949775968393351265635903861508150965117439180800000⟩, + ⟨3, 6, 3, 6, 1, 5, -2554310467772908963106615586344388048623920742400000⟩, + ⟨3, 6, 4, 6, 2, 5, 6352865635268781546482727805356021799014786662400000⟩, + ⟨3, 6, 5, 6, 3, 5, -6124770026031400401954800482895127378760040448000000⟩, + ⟨3, 6, 6, 6, 4, 5, -206643975671698745939731946313660215834601062400000⟩, + ⟨3, 6, 7, 6, 5, 5, 256372831062797581732130468068870049684992819200000⟩, + ⟨3, 6, 8, 6, 6, 5, 48540650344512813694013770460716924927161139200000⟩, + ⟨3, 6, 3, 7, 0, 5, 268483677543490116270573545020338099911973352243200000⟩, + ⟨3, 6, 4, 7, 1, 5, 6102672664221549383012001889660555801143961190400000⟩, + ⟨3, 6, 5, 7, 2, 5, 339310539891664644813554462785962385965318144000000⟩, + ⟨3, 6, 6, 7, 3, 5, -1043178165319042094155461763892306002209197260800000⟩, + ⟨3, 6, 7, 7, 4, 5, 199352830032568288253382898108898180736221184000000⟩, + ⟨3, 6, 8, 7, 5, 5, 125385637631928276530890670407894798562230272000000⟩ +] + +def collectedFourData_10_4_24 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 4, 6, 35162368662501569420137650780891221814411264000000⟩, + ⟨3, 7, 1, 0, 5, 6, -116556581094916281596952323237876982856915353600000⟩, + ⟨3, 7, 2, 0, 6, 6, 49731117677233111461696707785348720483526246400000⟩, + ⟨3, 7, 3, 0, 7, 6, -4738127745132663279732669183117053731327180800000⟩, + ⟨3, 7, 4, 0, 8, 6, 4571727397408064550125378944819990113760051200000⟩, + ⟨3, 7, 0, 1, 3, 6, 27636310406015818026565606375018251164634316800000⟩, + ⟨3, 7, 1, 1, 4, 6, -50913708112015017667045893079090625853259776000000⟩, + ⟨3, 7, 2, 1, 5, 6, -24283087576220487269027375460438151598073446400000⟩, + ⟨3, 7, 3, 1, 6, 6, 22466806622110624518454057603547306055539097600000⟩, + ⟨3, 7, 4, 1, 7, 6, -5331766685379037411958399094166008802521907200000⟩, + ⟨3, 7, 5, 1, 8, 6, -5234388742924556475332870319836850693341184000000⟩, + ⟨3, 7, 0, 2, 2, 6, 23054165670736371212959468688531252382479155200000⟩, + ⟨3, 7, 1, 2, 3, 6, -76901990152871024708332216081946371758961459200000⟩, + ⟨3, 7, 2, 2, 4, 6, -89461986908964569086801193197143258154873651200000⟩, + ⟨3, 7, 3, 2, 5, 6, 9560733828687780122986105407965213029407129600000⟩, + ⟨3, 7, 4, 2, 6, 6, 3515197571415763617495437982675999809077248000000⟩, + ⟨3, 7, 5, 2, 7, 6, -2683087038180659636675053345451166049448755200000⟩, + ⟨3, 7, 6, 2, 8, 6, 792668770420306378926601692629743998232166400000⟩, + ⟨3, 7, 0, 3, 1, 6, 73901036369657758779214894172932317682178457600000⟩, + ⟨3, 7, 1, 3, 2, 6, 198161900645478771242313209764790824519021363200000⟩, + ⟨3, 7, 2, 3, 3, 6, 101905921541626586709903000389780717193658368000000⟩, + ⟨3, 7, 3, 3, 4, 6, -1041725042115578737324272026350434053731123200000⟩, + ⟨3, 7, 4, 3, 5, 6, 9644629714530386001577111712200285584831283200000⟩, + ⟨3, 7, 5, 3, 6, 6, 1835808334145601492352960833228185101192396800000⟩, + ⟨3, 7, 6, 3, 7, 6, 1680669843622354293095436033297067750195200000⟩, + ⟨3, 7, 7, 3, 8, 6, -38427207095812220047551108643287085980057600000⟩, + ⟨3, 7, 0, 4, 0, 6, 235997605922739988383183125195427983250161664000000⟩, + ⟨3, 7, 1, 4, 1, 6, -89214138884237666052199150400898191419087257600000⟩, + ⟨3, 7, 2, 4, 2, 6, -24297997726262940904265497457402019758211072000000⟩, + ⟨3, 7, 3, 4, 3, 6, -15384164795757837632990303316630754173753753600000⟩, + ⟨3, 7, 4, 4, 4, 6, -7228319991125951717323318210932892634185728000000⟩, + ⟨3, 7, 5, 4, 5, 6, 1113145755650338441902479568859027112932147200000⟩, + ⟨3, 7, 6, 4, 6, 6, 339644562950036436745812336151778940891955200000⟩, + ⟨3, 7, 7, 4, 7, 6, -101643146245920033581351095042574019408691200000⟩, + ⟨3, 7, 8, 4, 8, 6, 13609303967086279698434579882703360884736000000⟩, + ⟨3, 7, 1, 5, 0, 6, -470213055275815902175345048137380214409160294400000⟩, + ⟨3, 7, 2, 5, 1, 6, 25165487618577859204129888944873819500602982400000⟩, + ⟨3, 7, 3, 5, 2, 6, -19210013623832241119545009776115108756743782400000⟩, + ⟨3, 7, 4, 5, 3, 6, -6887749740555381542162581584813345814767206400000⟩, + ⟨3, 7, 5, 5, 4, 6, 738390359762337616902521558967483720164966400000⟩, + ⟨3, 7, 6, 5, 5, 6, 283732714088621620705552871887861007882649600000⟩, + ⟨3, 7, 7, 5, 6, 6, 32200351695125760925676513230345035841536000000⟩, + ⟨3, 7, 8, 5, 7, 6, -22312484307674301204790257563286491470233600000⟩, + ⟨3, 7, 2, 6, 0, 6, -453031140058580904930061071415639640368585113600000⟩, + ⟨3, 7, 3, 6, 1, 6, -4676907163549629272889258130065044628779827200000⟩, + ⟨3, 7, 4, 6, 2, 6, 8724006881756147914874552263883384957593190400000⟩, + ⟨3, 7, 5, 6, 3, 6, -6728621560592607329973634851045333140924006400000⟩, + ⟨3, 7, 6, 6, 4, 6, -189181131721624737530865851174470574250393600000⟩, + ⟨3, 7, 7, 6, 5, 6, 201177904442310991230572524266113655531110400000⟩, + ⟨3, 7, 8, 6, 6, 6, 33328972463977848107030584865004570909081600000⟩, + ⟨3, 7, 3, 7, 0, 6, 491589902888395991982308537508096835279493529600000⟩, + ⟨3, 7, 4, 7, 1, 6, 8380431977689925920955552973983970857739878400000⟩, + ⟨3, 7, 5, 7, 2, 6, 372763745372938150383452370211484330046259200000⟩, + ⟨3, 7, 6, 7, 3, 6, -955022401504119244321324221460547844125491200000⟩, + ⟨3, 7, 7, 7, 4, 6, 156433832806459204808150926773469795319808000000⟩, + ⟨3, 7, 8, 7, 5, 6, 86092263584293869195912051047584870957056000000⟩ +] + +def collectedFourData_10_4_25 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 4, 7, -5627721229070855875447475083812689295729229824000000⟩, + ⟨3, 8, 1, 0, 5, 7, 9327414090213238677753493502676490691950726348800000⟩, + ⟨3, 8, 2, 0, 6, 7, -2653147643757878304782275421529228952145284300800000⟩, + ⟨3, 8, 3, 0, 7, 7, 189583801601007434715502748012607961629406003200000⟩, + ⟨3, 8, 4, 0, 8, 7, -146340581175669936097088560975055479291867299840000⟩, + ⟨3, 8, 0, 1, 3, 7, -4423179003039954306993517385722787402485648588800000⟩, + ⟨3, 8, 1, 1, 4, 7, 4074357998217964499069210856767060818324881408000000⟩, + ⟨3, 8, 2, 1, 5, 7, 1295499067689566059538637450349983022019562700800000⟩, + ⟨3, 8, 3, 1, 6, 7, -898950564097794902899044640166576661589288550400000⟩, + ⟨3, 8, 4, 1, 7, 7, 170669370154005167434477670633263021058728919040000⟩, + ⟨3, 8, 5, 1, 8, 7, 139626925840848243408150309283273888103399424000000⟩, + ⟨3, 8, 0, 2, 2, 7, -3689808806938585534735573743683292908301267763200000⟩, + ⟨3, 8, 1, 2, 3, 7, 6154064401847957592222662601342487317439945113600000⟩, + ⟨3, 8, 2, 2, 4, 7, 4772783537943265084709338630385844517062731366400000⟩, + ⟨3, 8, 3, 2, 5, 7, -382547783182919283400159756352860627505931878400000⟩, + ⟨3, 8, 4, 2, 6, 7, -112521156847613868748260254420982442768308633600000⟩, + ⟨3, 8, 5, 2, 7, 7, 71571144846853362938627959747019949460370227200000⟩, + ⟨3, 8, 6, 2, 8, 7, -18123754117985056688157067963499149643690803200000⟩, + ⟨3, 8, 0, 3, 1, 7, -11827827505585121510985314019824667016289687961600000⟩, + ⟨3, 8, 1, 3, 2, 7, -15857861365364735024921587568052246133998197145600000⟩, + ⟨3, 8, 2, 3, 3, 7, -5436665577836344329968439535379386965946269696000000⟩, + ⟨3, 8, 3, 3, 4, 7, 41681905666245673430298621155660219131153612800000⟩, + ⟨3, 8, 4, 3, 5, 7, -308723726276572020809974784041742361421928202240000⟩, + ⟨3, 8, 5, 3, 6, 7, -48970049172645778167365597081596547547581644800000⟩, + ⟨3, 8, 6, 3, 7, 7, -38427207095812220047551108643287085980057600000⟩, + ⟨3, 8, 7, 3, 8, 7, 768782143286146319145106199401086693094195200000⟩, + ⟨3, 8, 0, 4, 0, 7, -37771310278015105387738218905586965755119796224000000⟩, + ⟨3, 8, 1, 4, 1, 7, 7139341324686243659342669555739494227924274380800000⟩, + ⟨3, 8, 2, 4, 2, 7, 1296294521950416551342507179826004406497705984000000⟩, + ⟨3, 8, 3, 4, 3, 7, 615557157451544211535746187214244288968156774400000⟩, + ⟨3, 8, 4, 4, 4, 7, 231377870217021608408548906741541745039350169600000⟩, + ⟨3, 8, 5, 4, 5, 7, -29693079270112769250680269433786305975890739200000⟩, + ⟨3, 8, 6, 4, 6, 7, -7765708422135743909015560151767469541398937600000⟩, + ⟨3, 8, 7, 4, 7, 7, 2033492458258863146420372502329090650826342400000⟩, + ⟨3, 8, 8, 4, 8, 7, -242018106167155422163771598907584978878464000000⟩, + ⟨3, 8, 1, 5, 0, 7, 37628693600838257381822296667038880681788912435200000⟩, + ⟨3, 8, 2, 5, 1, 7, -1342574977151864055408949277786130515684543692800000⟩, + ⟨3, 8, 3, 5, 2, 7, 768638501854341912032240920759184283821250969600000⟩, + ⟨3, 8, 4, 5, 3, 7, 220476247248885520915476861466019593911250452480000⟩, + ⟨3, 8, 5, 5, 4, 7, -19696507284350000587788595046961083989780070400000⟩, + ⟨3, 8, 6, 5, 5, 7, -6487327541167122884178548103992004831923404800000⟩, + ⟨3, 8, 7, 5, 6, 7, -644206468844421227457613735607653600591872000000⟩, + ⟨3, 8, 8, 5, 7, 7, 396789226626689946840338816198212013418086400000⟩, + ⟨3, 8, 2, 6, 0, 7, 24169143142858127845393786811195842377001677619200000⟩, + ⟨3, 8, 3, 6, 1, 7, 187134219990494896859007941140723309340314828800000⟩, + ⟨3, 8, 4, 6, 2, 7, -279254672529370146366414335787235476132625121280000⟩, + ⟨3, 8, 5, 6, 3, 7, 179485473814289374756566422497858579941713510400000⟩, + ⟨3, 8, 6, 6, 4, 7, 4325479245595664447573860535661211069238476800000⟩, + ⟨3, 8, 7, 6, 5, 7, -4024804097090635933063094712710720578702540800000⟩, + ⟨3, 8, 8, 6, 6, 7, -592698555028023839474415524716203274036838400000⟩, + ⟨3, 8, 3, 7, 0, 7, -19669685502673742797129825554866526727908517478400000⟩, + ⟨3, 8, 4, 7, 1, 7, -268256870874150816690761728235955631388759162880000⟩, + ⟨3, 8, 5, 7, 2, 7, -9943444858140953934826710221518524258661171200000⟩, + ⟨3, 8, 6, 7, 3, 7, 21835843454322686457767826252809741780228505600000⟩, + ⟨3, 8, 7, 7, 4, 7, -3129645539098329214998362950074932989526016000000⟩, + ⟨3, 8, 8, 7, 5, 7, -1531003101900388889207866977717170045190144000000⟩ +] + +def collectedFourData_10_4_26 : List CollectedFourTerm := [ + ⟨4, 0, 6, 2, 8, 0, 111305580223731553624674774421375934798021787648000000⟩, + ⟨4, 0, 6, 3, 7, 0, 235997605922739988383183125195427983250161664000000⟩, + ⟨4, 0, 7, 3, 8, 0, -37771310278015105387738218905586965755119796224000000⟩, + ⟨4, 0, 6, 4, 6, 0, 47692474536298523641483275745784749019432484864000000⟩, + ⟨4, 0, 7, 4, 7, 0, -99908244825492550143643467244121818058025074688000000⟩, + ⟨4, 0, 8, 4, 8, 0, 53508051368600007373790332045444436250392002560000000⟩, + ⟨4, 0, 6, 5, 5, 0, 39841401034813780830622851287865198973626089472000000⟩, + ⟨4, 0, 7, 5, 6, 0, 31650738288246587200867990358431970041150832640000000⟩, + ⟨4, 0, 8, 5, 7, 0, -87726569954167080629455781916749875364134649856000000⟩, + ⟨4, 0, 6, 6, 4, 0, -26564583366255699246747629754252047452106391552000000⟩, + ⟨4, 0, 7, 6, 5, 0, 197744088734450612777113907218506014778086916096000000⟩, + ⟨4, 0, 8, 6, 6, 0, 131040380535125696987014214797295186189469351936000000⟩, + ⟨4, 0, 6, 7, 3, 0, -134103078729483856276478377362108862095251472384000000⟩, + ⟨4, 0, 7, 7, 4, 0, 153763733653072013715609358118476210642008145920000000⟩, + ⟨4, 0, 8, 7, 5, 0, 338491172909977757395017259080819991859964149760000000⟩ +] + +def collectedFourData_10_4_27 : List CollectedFourTerm := [ + ⟨4, 1, 5, 1, 8, 1, 46309064017681046456114668965234218416453189632000000⟩, + ⟨4, 1, 5, 2, 7, 1, 23737489804147937191612618124754462342664264089600000⟩, + ⟨4, 1, 6, 2, 8, 1, -42076831473966310760465180799228444927604241203200000⟩, + ⟨4, 1, 5, 3, 6, 1, -16241546022934807604226356411338899204054869606400000⟩, + ⟨4, 1, 6, 3, 7, 1, -89214138884237666052199150400898191419087257600000⟩, + ⟨4, 1, 7, 3, 8, 1, 7139341324686243659342669555739494227924274380800000⟩, + ⟨4, 1, 5, 4, 5, 1, -9848091265498971569623736270154751381639633305600000⟩, + ⟨4, 1, 6, 4, 6, 1, -18029178857039928775865086720131083006081866137600000⟩, + ⟨4, 1, 7, 4, 7, 1, 18884149257979953178937402748321510407274076569600000⟩, + ⟨4, 1, 8, 4, 8, 1, -6742546825928384092891851058106127500672237568000000⟩, + ⟨4, 1, 5, 5, 4, 1, -6532599720739823181417763286669544490299241267200000⟩, + ⟨4, 1, 6, 5, 5, 1, -15061238741659601372153853304077848320771149004800000⟩, + ⟨4, 1, 7, 5, 6, 1, -5982461877941041295497691728385233590826303488000000⟩, + ⟨4, 1, 8, 5, 7, 1, 11054420608954605338053177540796671554828946636800000⟩, + ⟨4, 1, 5, 6, 3, 1, 59528663594469115143701401440379235396954043187200000⟩, + ⟨4, 1, 6, 6, 4, 1, 10042205388366976045835583691553868369904848076800000⟩, + ⟨4, 1, 7, 6, 5, 1, -37376583815150490170994559447674068424325280563200000⟩, + ⟨4, 1, 8, 6, 6, 1, -16512391672780077182503991434578698948628499660800000⟩, + ⟨4, 1, 5, 7, 2, 1, -3297871250254359032091614331656883547785501081600000⟩, + ⟨4, 1, 6, 7, 3, 1, 50694966348483740372319792397796713248782391705600000⟩, + ⟨4, 1, 7, 7, 4, 1, -29063640361620893112700239472505604604705112064000000⟩, + ⟨4, 1, 8, 7, 5, 1, -42653255447240193575531732612142370945895497728000000⟩ +] + +def collectedFourData_10_4_28 : List CollectedFourTerm := [ + ⟨4, 2, 4, 0, 8, 2, -4406331294189851060189860985842737363905465548800000⟩, + ⟨4, 2, 4, 1, 7, 2, 5138873855957416813063519652321529320893631692800000⟩, + ⟨4, 2, 5, 1, 8, 2, 25225094279440099324909143848593114286606254080000000⟩, + ⟨4, 2, 4, 2, 6, 2, -3388024638776796767165325476134177313497546752000000⟩, + ⟨4, 2, 5, 2, 7, 2, 12930091138060192105498032223684781747390644224000000⟩, + ⟨4, 2, 6, 2, 8, 2, -11459873606014446684889455244043086692303765504000000⟩, + ⟨4, 2, 4, 3, 5, 2, -9295705985466771138724066068676929098882010316800000⟩, + ⟨4, 2, 5, 3, 6, 2, -8846962001131622210935227484913961001619030016000000⟩, + ⟨4, 2, 6, 3, 7, 2, -24297997726262940904265497457402019758211072000000⟩, + ⟨4, 2, 7, 3, 8, 2, 1296294521950416551342507179826004406497705984000000⟩, + ⟨4, 2, 4, 4, 4, 2, 6966813594216907746686916170048819896906678272000000⟩, + ⟨4, 2, 5, 4, 5, 2, -5364371660586670713106859111544896428141707264000000⟩, + ⟨4, 2, 6, 4, 6, 2, -4910353362746436894481111553134391902624284672000000⟩, + ⟨4, 2, 7, 4, 7, 2, 3428806401252884011086148196540031527244791808000000⟩, + ⟨4, 2, 8, 4, 8, 2, -918186228632504358630073324569511972023828480000000⟩, + ⟨4, 2, 4, 5, 3, 2, 6638564505303604912550917444529945523911235993600000⟩, + ⟨4, 2, 5, 5, 4, 2, -3558384245956475107045762247406341194323591168000000⟩, + ⟨4, 2, 6, 5, 5, 2, -4102017340260464908411581392635564798305632256000000⟩, + ⟨4, 2, 7, 5, 6, 2, -1086239221164143993643569607564330447132426240000000⟩, + ⟨4, 2, 8, 5, 7, 2, 1505368376474849510771907392881568595887259648000000⟩, + ⟨4, 2, 4, 6, 2, 2, -8408389475628782448412071306591874454325402009600000⟩, + ⟨4, 2, 5, 6, 3, 2, 32425966349184512986699569798084090942317395968000000⟩, + ⟨4, 2, 6, 6, 4, 2, 2735053958317329802048886731709377437128196096000000⟩, + ⟨4, 2, 7, 6, 5, 2, -6786488927384275890668622881645897766074843136000000⟩, + ⟨4, 2, 8, 6, 6, 2, -2248623706613282966125081269711767916446220288000000⟩, + ⟨4, 2, 4, 7, 1, 2, -8077244435672205761870882246023049722306599321600000⟩, + ⟨4, 2, 5, 7, 2, 2, -1796389432042054558150675728932277929801416704000000⟩, + ⟨4, 2, 6, 7, 3, 2, 13807073547689265781934320885715392535967301632000000⟩, + ⟨4, 2, 7, 7, 4, 2, -5277102757145724744211656694141793675740446720000000⟩, + ⟨4, 2, 8, 7, 5, 2, -5808433040078715284296467571601832757249966080000000⟩ +] + +def collectedFourData_10_4_29 : List CollectedFourTerm := [ + ⟨4, 3, 3, 0, 7, 3, 2168544236426848477749395754876076788114228510720000⟩, + ⟨4, 3, 4, 0, 8, 3, -8369544791905049647299673445810237540430847672320000⟩, + ⟨4, 3, 3, 1, 6, 3, -10282598239640840235249432232426029432979681443840000⟩, + ⟨4, 3, 4, 1, 7, 3, 9760962589013237523589083347326356937433331793920000⟩, + ⟨4, 3, 5, 1, 8, 3, 23956727530926471020493831619478418553156141056000000⟩, + ⟨4, 3, 3, 2, 5, 3, -4375752481876484323183928783991252613547572592640000⟩, + ⟨4, 3, 4, 2, 6, 3, -6435336355146647552316066573235059200730385612800000⟩, + ⟨4, 3, 5, 2, 7, 3, 12279941034631904536056963260247876140643699916800000⟩, + ⟨4, 3, 6, 2, 8, 3, -7255765930989619057304773757557751541488890675200000⟩, + ⟨4, 3, 3, 3, 4, 3, 476776262172729486518023565730407762107438202880000⟩, + ⟨4, 3, 4, 3, 5, 3, -17656599657027941881986556662945987570752311787520000⟩, + ⟨4, 3, 5, 3, 6, 3, -8402119563545775231233481252373095307134841651200000⟩, + ⟨4, 3, 6, 3, 7, 3, -15384164795757837632990303316630754173753753600000⟩, + ⟨4, 3, 7, 3, 8, 3, 615557157451544211535746187214244288968156774400000⟩, + ⟨4, 3, 3, 4, 3, 3, 7041017822778731107920788743765165711175177994240000⟩, + ⟨4, 3, 4, 4, 4, 3, 13233017342689874868414539975613534777094491340800000⟩, + ⟨4, 3, 5, 4, 5, 3, -5094640631414557307228350337396703590072765644800000⟩, + ⟨4, 3, 6, 4, 6, 3, -3108967503780948161348057129486633752921217433600000⟩, + ⟨4, 3, 7, 4, 7, 3, 1628199676899981498156107594471836103509593292800000⟩, + ⟨4, 3, 8, 4, 8, 3, -348807216469774999682222526272751870855767654400000⟩, + ⟨4, 3, 3, 5, 2, 3, 8792030642997419682913023187373920749067865948160000⟩, + ⟨4, 3, 4, 5, 3, 3, 12609529168710657631339012420389109807302353879040000⟩, + ⟨4, 3, 5, 5, 4, 3, -3379461772723756146467617918875410807513520537600000⟩, + ⟨4, 3, 6, 5, 5, 3, -2597173292571915700897183518494814702616235212800000⟩, + ⟨4, 3, 7, 5, 6, 3, -515810501371350702381021246550191648207273984000000⟩, + ⟨4, 3, 8, 5, 7, 3, 571870211930586894878378994568197145489771069440000⟩, + ⟨4, 3, 3, 6, 1, 3, 2140524827393614208906482926894347974041120276480000⟩, + ⟨4, 3, 4, 6, 2, 3, -15971198633396710394287109394312972510936107581440000⟩, + ⟨4, 3, 5, 6, 3, 3, 30795525762912881732015017166889225618957375897600000⟩, + ⟨4, 3, 6, 6, 4, 3, 1731686754360191683716215435516683905919667404800000⟩, + ⟨4, 3, 7, 6, 5, 3, -3222625539550673958304408377610695230774417817600000⟩, + ⟨4, 3, 8, 6, 6, 3, -854223415177849071103850928547013286114770288640000⟩, + ⟨4, 3, 3, 7, 0, 3, -224990651991046578171416244623988980894363434352640000⟩, + ⟨4, 3, 4, 7, 1, 3, -15342209785420555069136763964218763797458048778240000⟩, + ⟨4, 3, 5, 7, 2, 3, -1706063481314468307955693517832038679411739852800000⟩, + ⟨4, 3, 6, 7, 3, 3, 8741884709916359678036371868659574363454544281600000⟩, + ⟨4, 3, 7, 7, 4, 3, -2505879888993759960313805969150949240185290752000000⟩, + ⟨4, 3, 8, 7, 5, 3, -2206549496803471500629061816226856665038087782400000⟩ +] + +def collectedFourData_10_4_30 : List CollectedFourTerm := [ + ⟨4, 4, 2, 0, 6, 4, -14259093715975727263436291039336587247753782886400000⟩, + ⟨4, 4, 3, 0, 7, 4, 4075601597852745847300673206901689552682247782400000⟩, + ⟨4, 4, 4, 0, 8, 4, -7864937582134265097587060567945840991967327027200000⟩, + ⟨4, 4, 2, 1, 5, 4, 6962538499734727297867691795611963830259050086400000⟩, + ⟨4, 4, 3, 1, 6, 4, -19325302713035854377846207084516721535287610572800000⟩, + ⟨4, 4, 4, 1, 7, 4, 9172465577624656737849138754863169160948691763200000⟩, + ⟨4, 4, 5, 1, 8, 4, 15008236918306526512680873638421078703173795840000000⟩, + ⟨4, 4, 2, 2, 4, 4, 25650878462687561006921018404557165849981694771200000⟩, + ⟨4, 4, 3, 2, 5, 4, -8223869039595451370487038070782967026086104268800000⟩, + ⟨4, 4, 4, 2, 6, 4, -6047344271604921711342870979143513336906252288000000⟩, + ⟨4, 4, 5, 2, 7, 4, 7693048399564212403868399350427942497133002752000000⟩, + ⟨4, 4, 6, 2, 8, 4, -3409154713706983550689493406773979212830212096000000⟩, + ⟨4, 4, 2, 3, 3, 4, -29218850356547395046195051492381343948019335168000000⟩, + ⟨4, 4, 3, 3, 4, 4, 896062004772012988373815856521808720176978329600000⟩, + ⟨4, 4, 4, 3, 5, 4, -16592067748961687890629311614007510658165453619200000⟩, + ⟨4, 4, 5, 3, 6, 4, -5263698928113015054179588853992993980592160768000000⟩, + ⟨4, 4, 6, 3, 7, 4, -7228319991125951717323318210932892634185728000000⟩, + ⟨4, 4, 7, 3, 8, 4, 231377870217021608408548906741541745039350169600000⟩, + ⟨4, 4, 2, 4, 2, 4, 6966813594216907746686916170048819896906678272000000⟩, + ⟨4, 4, 3, 4, 3, 4, 13233017342689874868414539975613534777094491340800000⟩, + ⟨4, 4, 4, 4, 4, 4, 12435187099329263926512265863515790561056391168000000⟩, + ⟨4, 4, 5, 4, 5, 4, -3191653514078408749962939409541986691340828672000000⟩, + ⟨4, 4, 6, 4, 6, 4, -1460762560573815969353982717661973582475952128000000⟩, + ⟨4, 4, 7, 4, 7, 4, 612013635076310582924835007776890634313610035200000⟩, + ⟨4, 4, 8, 4, 8, 4, -109259107631361925147621081869660349853073408000000⟩, + ⟨4, 4, 2, 5, 1, 4, -7215543569530591868713465432628894180198213222400000⟩, + ⟨4, 4, 3, 5, 2, 4, 16523902780057185514830996522136589089717302067200000⟩, + ⟨4, 4, 4, 5, 3, 4, 11849289575214425063970914609343761756243519078400000⟩, + ⟨4, 4, 5, 5, 4, 4, -2117140701956166862924858658919849485678936064000000⟩, + ⟨4, 4, 6, 5, 5, 4, -1220293716321387338649971668290496416284934144000000⟩, + ⟨4, 4, 7, 5, 6, 4, -193884733201680084111480863520973298237177856000000⟩, + ⟨4, 4, 8, 5, 7, 4, 179130551451500628668711132780215173131324620800000⟩, + ⟨4, 4, 2, 6, 0, 4, 129894797946757809032860143190418409666226264473600000⟩, + ⟨4, 4, 3, 6, 1, 4, 4022941409368464761334529827997677339459295641600000⟩, + ⟨4, 4, 4, 6, 2, 4, -15008281033996555259238244256480159251879585382400000⟩, + ⟨4, 4, 5, 6, 3, 4, 19292557636553579669359848925180609468997566464000000⟩, + ⟨4, 4, 6, 6, 4, 4, 813640919158730395951681657057632279072866304000000⟩, + ⟨4, 4, 7, 6, 5, 4, -1211332245628077412913164741339784081706477158400000⟩, + ⟨4, 4, 8, 6, 6, 4, -267573844958662416754652094033055269367106764800000⟩, + ⟨4, 4, 3, 7, 0, 4, -422851535769246338540704008504869409698358283468800000⟩, + ⟨4, 4, 4, 7, 1, 4, -14417214476353461653363597244252245612697118310400000⟩, + ⟨4, 4, 5, 7, 2, 4, -1068802276612449571088054224746026909451681792000000⟩, + ⟨4, 4, 6, 7, 3, 4, 4107414399657954313028143920533478460429959168000000⟩, + ⟨4, 4, 7, 7, 4, 4, -941919275434116202373284063371510905221152768000000⟩, + ⟨4, 4, 8, 7, 5, 4, -691171562919967997860876698454995751422394368000000⟩ +] + +def collectedFourData_10_4_31 : List CollectedFourTerm := [ + ⟨4, 5, 1, 0, 5, 5, -12866344534319898122757597459775990012850051481600000⟩, + ⟨4, 5, 2, 0, 6, 5, 10979349052646429597492879695006022464361516236800000⟩, + ⟨4, 5, 3, 0, 7, 5, -1569084734053409029975075255789451933137659494400000⟩, + ⟨4, 5, 4, 0, 8, 5, 2018639162524554604291661470903004950166293708800000⟩, + ⟨4, 5, 1, 1, 4, 5, -5620217270747955079667303235966731897857376256000000⟩, + ⟨4, 5, 2, 1, 5, 5, -5361079883739709299274330906550394779941522636800000⟩, + ⟨4, 5, 3, 1, 6, 5, 7440137790691159395589665366210804841947385036800000⟩, + ⟨4, 5, 4, 1, 7, 5, -2354233334789795501627029198493064534837480652800000⟩, + ⟨4, 5, 5, 1, 8, 5, -2889045318607513106100672958784066964443627520000000⟩, + ⟨4, 5, 1, 2, 3, 5, -8488988707346962183365375832896549654715642675200000⟩, + ⟨4, 5, 2, 2, 4, 5, -19750900987018717043549456269265970610647230054400000⟩, + ⟨4, 5, 3, 2, 5, 5, 3166145427875534268946494727647571570278059212800000⟩, + ⟨4, 5, 4, 2, 6, 5, 1552130051694264666194703010504610105002033152000000⟩, + ⟨4, 5, 5, 2, 7, 5, -1480891165668635962672458993918507310179680256000000⟩, + ⟨4, 5, 6, 2, 8, 5, 525002504672893700474657921482656850274313830400000⟩, + ⟨4, 5, 1, 3, 2, 5, 21874520197226361344341258344071710734401352499200000⟩, + ⟨4, 5, 2, 3, 3, 5, 22498201033783185661723940072994615042313814016000000⟩, + ⟨4, 5, 3, 3, 4, 5, -344979061052929279058994726339351279836961177600000⟩, + ⟨4, 5, 4, 3, 5, 5, 4258571335823083973979946645317239006840016076800000⟩, + ⟨4, 5, 5, 3, 6, 5, 1013247913768954500258976386123103284498530304000000⟩, + ⟨4, 5, 6, 3, 7, 5, 1113145755650338441902479568859027112932147200000⟩, + ⟨4, 5, 7, 3, 8, 5, -29693079270112769250680269433786305975890739200000⟩, + ⟨4, 5, 1, 4, 1, 5, -9848091265498971569623736270154751381639633305600000⟩, + ⟨4, 5, 2, 4, 2, 5, -5364371660586670713106859111544896428141707264000000⟩, + ⟨4, 5, 3, 4, 3, 5, -5094640631414557307228350337396703590072765644800000⟩, + ⟨4, 5, 4, 4, 4, 5, -3191653514078408749962939409541986691340828672000000⟩, + ⟨4, 5, 5, 4, 5, 5, 614384733773638314977029368163661136072278016000000⟩, + ⟨4, 5, 6, 4, 6, 5, 224954297307246905749989204931732084901491507200000⟩, + ⟨4, 5, 7, 4, 7, 5, -78540654573688225999827148057855950785504870400000⟩, + ⟨4, 5, 8, 4, 8, 5, 12018334241991996099511978234183605056176128000000⟩, + ⟨4, 5, 1, 5, 0, 5, -51905461852790454066111908095567010602498287206400000⟩, + ⟨4, 5, 2, 5, 1, 5, 5555891070811557987830294998389311447298264268800000⟩, + ⟨4, 5, 3, 5, 2, 5, -6361613856670980016500850466167220709216170803200000⟩, + ⟨4, 5, 4, 5, 3, 5, -3041275246602897358878964073721445566794799513600000⟩, + ⟨4, 5, 5, 5, 4, 5, 407543901866259506861946514171943678946312192000000⟩, + ⟨4, 5, 6, 5, 5, 5, 187922611704734264052963182796273075487349145600000⟩, + ⟨4, 5, 7, 5, 6, 5, 24881527117620725076503602634615443226099712000000⟩, + ⟨4, 5, 8, 5, 7, 5, -19704085883257946343801939152564161696550092800000⟩, + ⟨4, 5, 2, 6, 0, 5, -100017599658706278460083438943936104207370892083200000⟩, + ⟨4, 5, 3, 6, 1, 5, -1548810844209368882699970836585761355836529049600000⟩, + ⟨4, 5, 4, 6, 2, 5, 3852071747679225758560760418811497949859256729600000⟩, + ⟨4, 5, 5, 6, 3, 5, -3713765556023745800619875203838662899916603392000000⟩, + ⟨4, 5, 6, 6, 4, 5, -125298954237898965285555307116983041926994329600000⟩, + ⟨4, 5, 7, 6, 5, 5, 155452137052440416083546142916679229093235916800000⟩, + ⟨4, 5, 8, 6, 6, 5, 29432712501901154435171206280248054919253196800000⟩, + ⟨4, 5, 3, 7, 0, 5, 162795571062717939075301234911735178303533534412800000⟩, + ⟨4, 5, 4, 7, 1, 5, 3700366780099159186885801167337342742793132441600000⟩, + ⟨4, 5, 5, 7, 2, 5, 205741569151126354775869186163077292413157376000000⟩, + ⟨4, 5, 6, 7, 3, 5, -632532996780643791402454407972798671579460403200000⟩, + ⟨4, 5, 7, 7, 4, 5, 120877954686328763607299752969819983798337536000000⟩, + ⟨4, 5, 8, 7, 5, 5, 76027811702058952988266876837166363587903488000000⟩ +] + +def collectedFourData_10_4_32 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 4, 6, 7105921119476529029727528628806701637345214464000000⟩, + ⟨4, 6, 1, 0, 5, 6, -23554780372336282340677729248525363556818459033600000⟩, + ⟨4, 6, 2, 0, 6, 6, 10050102221204636135281508636337748779400062566400000⟩, + ⟨4, 6, 3, 0, 7, 6, -957522581430115398388650232478942207264214220800000⟩, + ⟨4, 6, 4, 0, 8, 6, 923894933744211680614413082662504427496354611200000⟩, + ⟨4, 6, 0, 1, 3, 6, 5584988988183412456190766241455534111296638156800000⟩, + ⟨4, 6, 1, 1, 4, 6, -10289090510840805154931243583013730615952408576000000⟩, + ⟨4, 6, 2, 1, 5, 6, -4907340188318451772288176566341853892193969766400000⟩, + ⟨4, 6, 3, 1, 6, 6, 4540290137891216049640583575087110697315309977600000⟩, + ⟨4, 6, 4, 1, 7, 6, -1077490366403002587703284188061107668152169267200000⟩, + ⟨4, 6, 5, 1, 8, 6, -1057811374225311284379860645092298533197840384000000⟩, + ⟨4, 6, 0, 2, 2, 6, 4658988827061048614331522003208199461745668915200000⟩, + ⟨4, 6, 1, 2, 3, 6, -15541031413501632821125139896772157801002906419200000⟩, + ⟨4, 6, 2, 2, 4, 6, -18079266168569815465043743627425977054969148211200000⟩, + ⟨4, 6, 3, 2, 5, 6, 1932117289453755090701741475007551774171699609600000⟩, + ⟨4, 6, 4, 2, 6, 6, 710382082094887205300625657249073660478619648000000⟩, + ⟨4, 6, 5, 2, 7, 6, -542221857492045073591084170537694785097118515200000⟩, + ⟨4, 6, 6, 2, 8, 6, 160189485826249287875993118694840397837264486400000⟩, + ⟨4, 6, 0, 3, 1, 6, 14934572244854971008598625161894854506491517337600000⟩, + ⟨4, 6, 1, 3, 2, 6, 40046302010762736431100124145154918302438601523200000⟩, + ⟨4, 6, 2, 3, 3, 6, 20594046067624759786300167159556558260711456768000000⟩, + ⟨4, 6, 3, 3, 4, 6, -210520970544025767284912761539121764990399283200000⟩, + ⟨4, 6, 4, 3, 5, 6, 1949071708900529425003026067826135900622107443200000⟩, + ⟨4, 6, 5, 3, 6, 6, 370996315354262069563062511229572533113900236800000⟩, + ⟨4, 6, 6, 3, 7, 6, 339644562950036436745812336151778940891955200000⟩, + ⟨4, 6, 7, 3, 8, 6, -7765708422135743909015560151767469541398937600000⟩, + ⟨4, 6, 0, 4, 0, 6, 47692474536298523641483275745784749019432484864000000⟩, + ⟨4, 6, 1, 4, 1, 6, -18029178857039928775865086720131083006081866137600000⟩, + ⟨4, 6, 2, 4, 2, 6, -4910353362746436894481111553134391902624284672000000⟩, + ⟨4, 6, 3, 4, 3, 6, -3108967503780948161348057129486633752921217433600000⟩, + ⟨4, 6, 4, 4, 4, 6, -1460762560573815969353982717661973582475952128000000⟩, + ⟨4, 6, 5, 4, 5, 6, 224954297307246905749989204931732084901491507200000⟩, + ⟨4, 6, 6, 4, 6, 6, 68638364387433042695551990717102983872721715200000⟩, + ⟨4, 6, 7, 4, 7, 6, -20540942121717122437946379529893892546835251200000⟩, + ⟨4, 6, 8, 4, 8, 6, 2750287997071869272327436160329905954881536000000⟩, + ⟨4, 6, 1, 5, 0, 6, -95024795178297685206248860904827972978511079014400000⟩, + ⟨4, 6, 2, 5, 1, 6, 5085663359803229249230500819747415678540736102400000⟩, + ⟨4, 6, 3, 5, 2, 6, -3882128727596076530291979465834462150731916902400000⟩, + ⟨4, 6, 4, 5, 3, 6, -1391937125079884815802241642325552138966951526400000⟩, + ⟨4, 6, 5, 5, 4, 6, 149220426593405208852261356705641394503837286400000⟩, + ⟨4, 6, 6, 5, 5, 6, 57339205577434898661082055080643054597151129600000⟩, + ⟨4, 6, 7, 5, 6, 6, 6507330645474423989599048977694114065678336000000⟩, + ⟨4, 6, 8, 5, 7, 6, -4509103325538354736402028368353882321557913600000⟩, + ⟨4, 6, 2, 6, 0, 6, -91552522437314507374130686804375059899795216793600000⟩, + ⟨4, 6, 3, 6, 1, 6, -945150587159961250498757553045063506798523187200000⟩, + ⟨4, 6, 4, 6, 2, 6, 1763024139316309145858783410997443706256516710400000⟩, + ⟨4, 6, 5, 6, 3, 6, -1359779101098206512790632966708608567288948326400000⟩, + ⟨4, 6, 6, 6, 4, 6, -38231389136784219092523188677085206888946073600000⟩, + ⟨4, 6, 7, 6, 5, 6, 40655802618700642130619401716648310158550630400000⟩, + ⟨4, 6, 8, 6, 6, 6, 6735412269731398099618744415523667644619161600000⟩, + ⟨4, 6, 3, 7, 0, 6, 99344816800733443056717168556389091543550106009600000⟩, + ⟨4, 6, 4, 7, 1, 6, 1693591496983259939895961868806086508170077798400000⟩, + ⟨4, 6, 5, 7, 2, 6, 75331380438131320192749294892193621296231219200000⟩, + ⟨4, 6, 6, 7, 3, 6, -192999337375655424960448658680491721895392051200000⟩, + ⟨4, 6, 7, 7, 4, 6, 31613526580350555208185247073332212906590208000000⟩, + ⟨4, 6, 8, 7, 5, 6, 17398282803387537557046481749864721579769856000000⟩ +] + +def collectedFourData_10_4_33 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 4, 7, -14885788875873215619758674354679717233466277888000000⟩, + ⟨4, 7, 1, 0, 5, 7, 24671782992293482982645608108962144173336140185600000⟩, + ⟨4, 7, 2, 0, 6, 7, -7017795316066286622413665079864939934687795609600000⟩, + ⟨4, 7, 3, 0, 7, 7, 501464861183958169642701209215002024354408038400000⟩, + ⟨4, 7, 4, 0, 8, 7, -387082960701886915490253088013646189310330798080000⟩, + ⟨4, 7, 0, 1, 3, 7, -11699674898487965117117266311569052406430407065600000⟩, + ⟨4, 7, 1, 1, 4, 7, 10777014442879829436708170898461592527774416896000000⟩, + ⟨4, 7, 2, 1, 5, 7, 3426702358834032862578036011898911466811136409600000⟩, + ⟨4, 7, 3, 1, 6, 7, -2377798715025588635455907091990188023815654604800000⟩, + ⟨4, 7, 4, 1, 7, 7, 451434623052610966934911508201330363609886228480000⟩, + ⟨4, 7, 5, 1, 8, 7, 369324786152783401102639039276277703364313088000000⟩, + ⟨4, 7, 0, 2, 2, 7, -9759849974213048450056007351159563334061549158400000⟩, + ⟨4, 7, 1, 2, 3, 7, 16278010172433558731834560225322933315093869363200000⟩, + ⟨4, 7, 2, 2, 4, 7, 12624407856072245301963117424297571071648648396800000⟩, + ⟨4, 7, 3, 2, 5, 7, -1011870578446266120614393517395220320412814540800000⟩, + ⟨4, 7, 4, 2, 6, 7, -297627781605510501450971293673295345523831603200000⟩, + ⟨4, 7, 5, 2, 7, 7, 189311607385836732020323061204897035553498726400000⟩, + ⟨4, 7, 6, 2, 8, 7, -47938831092936958197060739192866017229825638400000⟩, + ⟨4, 7, 0, 3, 1, 7, -31285583621108940764677262470878266806657823539200000⟩, + ⟨4, 7, 1, 3, 2, 7, -41945357045814313947970899128457825973968253747200000⟩, + ⟨4, 7, 2, 3, 3, 7, -14380430850474193643194459930299986658409316352000000⟩, + ⟨4, 7, 3, 3, 4, 7, 110252093598146595587683111676824822987987353600000⟩, + ⟨4, 7, 4, 3, 5, 7, -816599832022003384932771188995244321544213626880000⟩, + ⟨4, 7, 5, 3, 6, 7, -129529836954181679990147230888685148640483737600000⟩, + ⟨4, 7, 6, 3, 7, 7, -101643146245920033581351095042574019408691200000⟩, + ⟨4, 7, 7, 3, 8, 7, 2033492458258863146420372502329090650826342400000⟩, + ⟨4, 7, 0, 4, 0, 7, -99908244825492550143643467244121818058025074688000000⟩, + ⟨4, 7, 1, 4, 1, 7, 18884149257979953178937402748321510407274076569600000⟩, + ⟨4, 7, 2, 4, 2, 7, 3428806401252884011086148196540031527244791808000000⟩, + ⟨4, 7, 3, 4, 3, 7, 1628199676899981498156107594471836103509593292800000⟩, + ⟨4, 7, 4, 4, 4, 7, 612013635076310582924835007776890634313610035200000⟩, + ⟨4, 7, 5, 4, 5, 7, -78540654573688225999827148057855950785504870400000⟩, + ⟨4, 7, 6, 4, 6, 7, -20540942121717122437946379529893892546835251200000⟩, + ⟨4, 7, 7, 4, 7, 7, 5378756015482221002182056533559465894268108800000⟩, + ⟨4, 7, 8, 4, 8, 7, -640157940647984806729613366639319809261568000000⟩, + ⟨4, 7, 1, 5, 0, 7, 99531011899372002178784387432963598768555845222400000⟩, + ⟨4, 7, 2, 5, 1, 7, -3551222039335546774248292425906467256867068313600000⟩, + ⟨4, 7, 3, 5, 2, 7, 2033112514771857560186462657092548892080419635200000⟩, + ⟨4, 7, 4, 5, 3, 7, 583177939187579321877760561039627393840195829760000⟩, + ⟨4, 7, 5, 5, 4, 7, -52098893511706580919862245979813040551152844800000⟩, + ⟨4, 7, 6, 5, 5, 7, -17159518784905265135821967461554576097384857600000⟩, + ⟨4, 7, 7, 5, 6, 7, -1703979478968096165930414921824530505662464000000⟩, + ⟨4, 7, 8, 5, 7, 7, 1049540376178350933207011154616572682489036800000⟩, + ⟨4, 7, 2, 6, 0, 7, 63929385890129554583300226856056944508797347430400000⟩, + ⟨4, 7, 3, 6, 1, 7, 494985514890124176991957040780270872481601945600000⟩, + ⟨4, 7, 4, 6, 2, 7, -738651743515666234423554003251789553617715855360000⟩, + ⟨4, 7, 5, 6, 3, 7, 474753947598555259471468385791825584025554124800000⟩, + ⟨4, 7, 6, 6, 4, 7, 11441250946173640110509231716985285379725721600000⟩, + ⟨4, 7, 7, 6, 5, 7, -10645940269136668465456234523997740644014489600000⟩, + ⟨4, 7, 8, 6, 6, 7, -1567736779783411488689278851909296010874060800000⟩, + ⟨4, 7, 3, 7, 0, 7, -52027947677139459481993979104469502126331841740800000⟩, + ⟨4, 7, 4, 7, 1, 7, -709561647031737724732635907828324769991292354560000⟩, + ⟨4, 7, 5, 7, 2, 7, -26301235408138895141615562760384239186110054400000⟩, + ⟨4, 7, 6, 7, 3, 7, 57757614913226745748538998745069858405430067200000⟩, + ⟨4, 7, 7, 7, 4, 7, -8278171724406426675211825883893617961992192000000⟩, + ⟨4, 7, 8, 7, 5, 7, -4049630039503375696780639163776378211401728000000⟩ +] + +def collectedFourData_10_4_34 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 4, 8, 7972410657634949281704532505421344810792386560000000⟩, + ⟨4, 8, 1, 0, 5, 8, -8809009600174963130200179011114902670800846848000000⟩, + ⟨4, 8, 2, 0, 6, 8, 1879267086126313212789847075023898627408920576000000⟩, + ⟨4, 8, 3, 0, 7, 8, -107428201140543142209901994957658735722574643200000⟩, + ⟨4, 8, 4, 0, 8, 8, 69103589269412871304225974641595314898940723200000⟩, + ⟨4, 8, 0, 1, 3, 8, 6266017449887953092979686142582014652943695872000000⟩, + ⟨4, 8, 1, 1, 4, 8, -3847910940129727976159548273406930390278471680000000⟩, + ⟨4, 8, 2, 1, 5, 8, -917622795604398183866002308693107334841368576000000⟩, + ⟨4, 8, 3, 1, 6, 8, 509392897493144537546381449187882517345494630400000⟩, + ⟨4, 8, 4, 1, 7, 8, -80591903908282216274869035714752695028101939200000⟩, + ⟨4, 8, 5, 1, 8, 8, -56514282290223733093857845220869761306460160000000⟩, + ⟨4, 8, 0, 2, 2, 8, 5227101673962838973462422955112380369372971008000000⟩, + ⟨4, 8, 1, 2, 3, 8, -5812030201688440413843759987839854127723053056000000⟩, + ⟨4, 8, 2, 2, 4, 8, -3380639231730897948249124961056516915549175808000000⟩, + ⟨4, 8, 3, 2, 5, 8, 216771790894529443861301143796456463037523558400000⟩, + ⟨4, 8, 4, 2, 6, 8, 53133695004140372788932746994537902666416128000000⟩, + ⟨4, 8, 5, 2, 7, 8, -28968566480651166425882563749948699388674048000000⟩, + ⟨4, 8, 6, 2, 8, 8, 6418673056342684879103114469855994841137152000000⟩, + ⟨4, 8, 0, 3, 1, 8, 16755680358702320138160796799708070175209160704000000⟩, + ⟨4, 8, 1, 3, 2, 8, 14976503847118041858161530697307321275070283776000000⟩, + ⟨4, 8, 2, 3, 3, 8, 3850877542658201455364298654370383220829061120000000⟩, + ⟨4, 8, 3, 3, 4, 8, -23619170562147807167433005770857718913748172800000⟩, + ⟨4, 8, 4, 3, 5, 8, 145782648988726169940170667100089155096621875200000⟩, + ⟨4, 8, 5, 3, 6, 8, 19820727026988649720812296824003049325330432000000⟩, + ⟨4, 8, 6, 3, 7, 8, 13609303967086279698434579882703360884736000000⟩, + ⟨4, 8, 7, 3, 8, 8, -242018106167155422163771598907584978878464000000⟩, + ⟨4, 8, 0, 4, 0, 8, 53508051368600007373790332045444436250392002560000000⟩, + ⟨4, 8, 1, 4, 1, 8, -6742546825928384092891851058106127500672237568000000⟩, + ⟨4, 8, 2, 4, 2, 8, -918186228632504358630073324569511972023828480000000⟩, + ⟨4, 8, 3, 4, 3, 8, -348807216469774999682222526272751870855767654400000⟩, + ⟨4, 8, 4, 4, 4, 8, -109259107631361925147621081869660349853073408000000⟩, + ⟨4, 8, 5, 4, 5, 8, 12018334241991996099511978234183605056176128000000⟩, + ⟨4, 8, 6, 4, 6, 8, 2750287997071869272327436160329905954881536000000⟩, + ⟨4, 8, 7, 4, 7, 8, -640157940647984806729613366639319809261568000000⟩, + ⟨4, 8, 8, 4, 8, 8, 68570124581889219682603164634050704965632000000⟩, + ⟨4, 8, 1, 5, 0, 8, -35537344001873135997509799931492413765731745792000000⟩, + ⟨4, 8, 2, 5, 1, 8, 950967418324547242977853872420300936305442816000000⟩, + ⟨4, 8, 3, 5, 2, 8, -435551196274435276052292605008624463977748889600000⟩, + ⟨4, 8, 4, 5, 3, 8, -104111244544391202704020664414507797431346790400000⟩, + ⟨4, 8, 5, 5, 4, 8, 7972201393791293869914092674717424377921536000000⟩, + ⟨4, 8, 6, 5, 5, 8, 2297539142557549916311637522790618369097728000000⟩, + ⟨4, 8, 7, 5, 6, 8, 202800794648955233976223596646331622359040000000⟩, + ⟨4, 8, 8, 5, 7, 8, -112420872691863171550626174476140930085683200000⟩, + ⟨4, 8, 2, 6, 0, 8, -17119392249093293965448232430903947187741261824000000⟩, + ⟨4, 8, 3, 6, 1, 8, -106040138744167405938859391372803622702992588800000⟩, + ⟨4, 8, 4, 6, 2, 8, 131867046290248858445585038302683170429363814400000⟩, + ⟨4, 8, 5, 6, 3, 8, -72647110670453526103012487970807359666651136000000⟩, + ⟨4, 8, 6, 6, 4, 8, -1531903208834808034651921612392231912603648000000⟩, + ⟨4, 8, 7, 6, 5, 8, 1267037058259462793466246038296096256557056000000⟩, + ⟨4, 8, 8, 6, 6, 8, 167927162150865613987938251784016488510259200000⟩, + ⟨4, 8, 3, 7, 0, 8, 11145883312328470238223696979224014394101229158400000⟩, + ⟨4, 8, 4, 7, 1, 8, 126673766597472167385677187204356549328135782400000⟩, + ⟨4, 8, 5, 7, 2, 8, 4024629535214278176726397857958500665131008000000⟩, + ⟨4, 8, 6, 7, 3, 8, -7733339303234822740882263620216484073046016000000⟩, + ⟨4, 8, 7, 7, 4, 8, 985234754685427841866833679820837219205120000000⟩, + ⟨4, 8, 8, 7, 5, 8, 433773634110089627527630274188664710889472000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1016.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1016.lean new file mode 100644 index 0000000000000000000000000000000000000000..61bda77a21b9a919fe85c546842bf254ccc0b011 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1016.lean @@ -0,0 +1,622 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1016. -/ +namespace LaughlinFock +def collectedFourData_10_4_35 : List CollectedFourTerm := [ + ⟨5, 0, 5, 1, 8, 1, 244077079609231979915055779610277066652944171008000000⟩, + ⟨5, 0, 5, 2, 7, 1, 125111083792111488595312363028308517611133888102400000⟩, + ⟨5, 0, 6, 2, 8, 1, -221770626619755827290995928671061114291015699660800000⟩, + ⟨5, 0, 5, 3, 6, 1, -85602877227302966841817526020885851378445556121600000⟩, + ⟨5, 0, 6, 3, 7, 1, -470213055275815902175345048137380214409160294400000⟩, + ⟨5, 0, 7, 3, 8, 1, 37628693600838257381822296667038880681788912435200000⟩, + ⟨5, 0, 5, 4, 5, 1, -51905461852790454066111908095567010602498287206400000⟩, + ⟨5, 0, 6, 4, 6, 1, -95024795178297685206248860904827972978511079014400000⟩, + ⟨5, 0, 7, 4, 7, 1, 99531011899372002178784387432963598768555845222400000⟩, + ⟨5, 0, 8, 4, 8, 1, -35537344001873135997509799931492413765731745792000000⟩, + ⟨5, 0, 5, 5, 4, 1, -34430794400972732846236450997642355800347036876800000⟩, + ⟨5, 0, 6, 5, 5, 1, -79381936243801941478915051838858297584387306291200000⟩, + ⟨5, 0, 7, 5, 6, 1, -31531231628518896798377548665682978244785078272000000⟩, + ⟨5, 0, 8, 5, 7, 1, 58263555013238601540933185134924743268011029299200000⟩, + ⟨5, 0, 5, 6, 3, 1, 313752451520742377610718108330725516245778353356800000⟩, + ⟨5, 0, 6, 6, 4, 1, 52928561956961004480302231994488015063895716659200000⟩, + ⟨5, 0, 7, 6, 5, 1, -196997447840632164785569435461650269180412087500800000⟩, + ⟨5, 0, 8, 6, 6, 1, -87030399390434096990695631150906846275871912755200000⟩, + ⟨5, 0, 5, 7, 2, 1, -17381797727157737797570853803498785094259598950400000⟩, + ⟨5, 0, 6, 7, 3, 1, 267193466326634070133495565157094198683292296806400000⟩, + ⟨5, 0, 7, 7, 4, 1, -153183153508975953473863520566962069268611465216000000⟩, + ⟨5, 0, 8, 7, 5, 1, -224808733370514650583107590382650804660529528832000000⟩ +] + +def collectedFourData_10_4_36 : List CollectedFourTerm := [ + ⟨5, 1, 4, 0, 8, 2, 4563646637740527456562228787813603787160902696960000⟩, + ⟨5, 1, 4, 1, 7, 2, -5322342517784890023431777130469383822240393461760000⟩, + ⟨5, 1, 5, 1, 8, 2, -26125683478872488458130699768515644728945934336000000⟩, + ⟨5, 1, 4, 2, 6, 2, 3508984281713795540712044554830043713118824038400000⟩, + ⟨5, 1, 5, 2, 7, 2, -13391722729903420909543336854786299612669725900800000⟩, + ⟨5, 1, 6, 2, 8, 2, 11869015323468752891808277166362898351434550476800000⟩, + ⟨5, 1, 4, 3, 5, 2, 9627582343147373833834797480331170551840699842560000⟩, + ⟨5, 1, 5, 3, 6, 2, 9162817249787792646417290213398941619471987507200000⟩, + ⟨5, 1, 6, 3, 7, 2, 25165487618577859204129888944873819500602982400000⟩, + ⟨5, 1, 7, 3, 8, 2, -1342574977151864055408949277786130515684543692800000⟩, + ⟨5, 1, 4, 4, 4, 2, -7215543569530591868713465432628894180198213222400000⟩, + ⟨5, 1, 5, 4, 5, 2, 5555891070811557987830294998389311447298264268800000⟩, + ⟨5, 1, 6, 4, 6, 2, 5085663359803229249230500819747415678540736102400000⟩, + ⟨5, 1, 7, 4, 7, 2, -3551222039335546774248292425906467256867068313600000⟩, + ⟨5, 1, 8, 4, 8, 2, 950967418324547242977853872420300936305442816000000⟩, + ⟨5, 1, 4, 5, 3, 2, -6875575294122918314655437095067532371734686597120000⟩, + ⟨5, 1, 5, 5, 4, 2, 3685426087062723626402983703409353617315568025600000⟩, + ⟨5, 1, 6, 5, 5, 2, 4248468032241979599771418094084779745660318515200000⟩, + ⟨5, 1, 7, 5, 6, 2, 1125020258005604387613395542530121005224951808000000⟩, + ⟨5, 1, 8, 5, 7, 2, -1559113210329655299858245216648984822673938841600000⟩, + ⟨5, 1, 4, 6, 2, 2, 8708586757846446060834897842058540438268485304320000⟩, + ⟨5, 1, 5, 6, 3, 2, -33583641906378975677266824144208716574139980185600000⟩, + ⟨5, 1, 6, 6, 4, 2, -2832701167379815168619809009025017778592232243200000⟩, + ⟨5, 1, 7, 6, 5, 2, 7028780930829879571908856089956541689884783411200000⟩, + ⟨5, 1, 8, 6, 6, 2, 2328904327225833443313805999832197187302431129600000⟩, + ⟨5, 1, 4, 7, 1, 2, 8365619139820316986513531098662389103324792094720000⟩, + ⟨5, 1, 5, 7, 2, 2, 1860524332889190947627410714030119129665293516800000⟩, + ⟨5, 1, 6, 7, 3, 2, -14300015265768489196269760866626483468374533734400000⟩, + ⟨5, 1, 7, 7, 4, 2, 5465506483004298979599815843083744864081281024000000⟩, + ⟨5, 1, 8, 7, 5, 2, 6015806380434660106385347989361432035103604736000000⟩ +] + +def collectedFourData_10_4_37 : List CollectedFourTerm := [ + ⟨5, 2, 3, 0, 7, 3, 2707833988955300012626320016170750765202648596480000⟩, + ⟨5, 2, 4, 0, 8, 3, -10450945606231726750953474436628607043113981050880000⟩, + ⟨5, 2, 3, 1, 6, 3, -12839751451854069518802334117007463950206956994560000⟩, + ⟨5, 2, 4, 1, 7, 3, 12188391557555744161570609816568085485054098145280000⟩, + ⟨5, 2, 5, 1, 8, 3, 29914465189454838283577223052388971339006869504000000⟩, + ⟨5, 2, 3, 2, 5, 3, -5463947241032152551909155643443416500893657333760000⟩, + ⟨5, 2, 4, 2, 6, 3, -8035723791154321372983897192452335235419550515200000⟩, + ⟨5, 2, 5, 2, 7, 3, 15333808348190860352739650074321518141333779251200000⟩, + ⟨5, 2, 6, 2, 8, 3, -9060183912231828012829465253983124253590736076800000⟩, + ⟨5, 2, 3, 3, 4, 3, 595344538585773211575415806972648642641311825920000⟩, + ⟨5, 2, 4, 3, 5, 3, -22047574532976130785999491676607591632581878087680000⟩, + ⟨5, 2, 5, 3, 6, 3, -10491621315008852926462075921507540316717894860800000⟩, + ⟨5, 2, 6, 3, 7, 3, -19210013623832241119545009776115108756743782400000⟩, + ⟨5, 2, 7, 3, 8, 3, 768638501854341912032240920759184283821250969600000⟩, + ⟨5, 2, 3, 4, 3, 3, 8792030642997419682913023187373920749067865948160000⟩, + ⟨5, 2, 4, 4, 4, 3, 16523902780057185514830996522136589089717302067200000⟩, + ⟨5, 2, 5, 4, 5, 3, -6361613856670980016500850466167220709216170803200000⟩, + ⟨5, 2, 6, 4, 6, 3, -3882128727596076530291979465834462150731916902400000⟩, + ⟨5, 2, 7, 4, 7, 3, 2033112514771857560186462657092548892080419635200000⟩, + ⟨5, 2, 8, 4, 8, 3, -435551196274435276052292605008624463977748889600000⟩, + ⟨5, 2, 3, 5, 2, 3, 10978498389441560311546797314540082628432169533440000⟩, + ⟨5, 2, 4, 5, 3, 3, 15745360917339896453406371384697830401637728911360000⟩, + ⟨5, 2, 5, 5, 4, 3, -4219891528537517842618858934667039888437044838400000⟩, + ⟨5, 2, 6, 5, 5, 3, -3243057715262990235507230437819536290952196915200000⟩, + ⟨5, 2, 7, 5, 6, 3, -644086103484259588346274182748767519407865856000000⟩, + ⟨5, 2, 8, 5, 7, 3, 714087160927948390624613095410101686729923624960000⟩, + ⟨5, 2, 3, 6, 1, 3, 2672846504330292546562374486761425029189410488320000⟩, + ⟨5, 2, 4, 6, 2, 3, -19943035413991617665585054592837554012790152232960000⟩, + ⟨5, 2, 5, 6, 3, 3, 38453986765778879630266064606573275838727743078400000⟩, + ⟨5, 2, 6, 6, 4, 3, 2162335530404750749170392495899829486174286643200000⟩, + ⟨5, 2, 7, 6, 5, 3, -4024052091300325635446255909547959791993120358400000⟩, + ⟨5, 2, 8, 6, 6, 3, -1066658064394104915878964347070787550504036597760000⟩, + ⟨5, 2, 3, 7, 0, 3, -280943005185091956156855389166630093218572413173760000⟩, + ⟨5, 2, 4, 7, 1, 3, -19157624928646821504671096698320758199636103004160000⟩, + ⟨5, 2, 5, 7, 2, 3, -2130340070733696690608378372434279130815738675200000⟩, + ⟨5, 2, 6, 7, 3, 3, 10915881791761030242167960440061075564584658534400000⟩, + ⟨5, 2, 7, 7, 4, 3, -3129060787266874364197587922240833145974816768000000⟩, + ⟨5, 2, 8, 7, 5, 3, -2755290680904773858183999953289077570479430041600000⟩ +] + +def collectedFourData_10_4_38 : List CollectedFourTerm := [ + ⟨5, 3, 2, 0, 6, 4, -13587260824554072778913748358172042049404346040320000⟩, + ⟨5, 3, 3, 0, 7, 4, 3883575143695960057558051287497385800704846725120000⟩, + ⟨5, 3, 4, 0, 8, 4, -7494372393216539486372669012126854738395644559360000⟩, + ⟨5, 3, 2, 1, 5, 4, 6634490836602352330720472149451962205241417400320000⟩, + ⟨5, 3, 3, 1, 6, 4, -18414769809759456337211822245932730397053566320640000⟩, + ⟨5, 3, 4, 1, 7, 4, 8740294768369302288910787483655621122472447836160000⟩, + ⟨5, 3, 5, 1, 8, 4, 14301107320534812217917598604325921332649787392000000⟩, + ⟨5, 3, 2, 2, 4, 4, 24442309097175568255629280146027529583832135106560000⟩, + ⟨5, 3, 3, 2, 5, 4, -7836392400084048502605698411907739523269200445440000⟩, + ⟨5, 3, 4, 2, 6, 4, -5762416991629014611445895840413009981162808934400000⟩, + ⟨5, 3, 5, 2, 7, 4, 7330581958633587807839684920171803383952939417600000⟩, + ⟨5, 3, 6, 2, 8, 4, -3248528637868278101954018011580815367874596044800000⟩, + ⟨5, 3, 2, 3, 3, 4, -27842172068988176634838724366384850355091826278400000⟩, + ⟨5, 3, 3, 3, 4, 4, 853843057372530828046359731940770456424394260480000⟩, + ⟨5, 3, 4, 3, 5, 4, -15810314218724360702622075714858710031334857768960000⟩, + ⟨5, 3, 5, 3, 6, 4, -5015693960834823269832347003650875303687251558400000⟩, + ⟨5, 3, 6, 3, 7, 4, -6887749740555381542162581584813345814767206400000⟩, + ⟨5, 3, 7, 3, 8, 4, 220476247248885520915476861466019593911250452480000⟩, + ⟨5, 3, 2, 4, 2, 4, 6638564505303604912550917444529945523911235993600000⟩, + ⟨5, 3, 3, 4, 3, 4, 12609529168710657631339012420389109807302353879040000⟩, + ⟨5, 3, 4, 4, 4, 4, 11849289575214425063970914609343761756243519078400000⟩, + ⟨5, 3, 5, 4, 5, 4, -3041275246602897358878964073721445566794799513600000⟩, + ⟨5, 3, 6, 4, 6, 4, -1391937125079884815802241642325552138966951526400000⟩, + ⟨5, 3, 7, 4, 7, 4, 583177939187579321877760561039627393840195829760000⟩, + ⟨5, 3, 8, 4, 8, 4, -104111244544391202704020664414507797431346790400000⟩, + ⟨5, 3, 2, 5, 1, 4, -6875575294122918314655437095067532371734686597120000⟩, + ⟨5, 3, 3, 5, 2, 4, 15745360917339896453406371384697830401637728911360000⟩, + ⟨5, 3, 4, 5, 3, 4, 11290997257681674057134427130103468226422683729920000⟩, + ⟨5, 3, 5, 5, 4, 4, -2017389288039300503650970862168555099859923763200000⟩, + ⟨5, 3, 6, 5, 5, 4, -1162798235041161111441387018507012379642114867200000⟩, + ⟨5, 3, 7, 5, 6, 4, -184749640642223725609217600257394125803670732800000⟩, + ⟨5, 3, 8, 5, 7, 4, 170690618401002261760236774013547941383414743040000⟩, + ⟨5, 3, 2, 6, 0, 4, 123774661602648627820225290595706264548668006727680000⟩, + ⟨5, 3, 3, 6, 1, 4, 3833396097940446215412951706210869946529957806080000⟩, + ⟨5, 3, 4, 6, 2, 4, -14301149357665559467660406530375606731487177605120000⟩, + ⟨5, 3, 5, 6, 3, 4, 18383567553588984626379200143095216710974911283200000⟩, + ⟨5, 3, 6, 6, 4, 4, 775305331905738041625638862063452158988333875200000⟩, + ⟨5, 3, 7, 6, 5, 4, -1154258993900949038051931725267152261842122833920000⟩, + ⟨5, 3, 8, 6, 6, 4, -254966808809795459838974935393404849437792010240000⟩, + ⟨5, 3, 3, 7, 0, 4, -402928420347145306647220799702103145987186297405440000⟩, + ⟨5, 3, 4, 7, 1, 4, -13737931551307345877192725879389336844514120171520000⟩, + ⟨5, 3, 5, 7, 2, 4, -1018444481218336511144205094407232620750018969600000⟩, + ⟨5, 3, 6, 7, 3, 4, 3913889050336669303213124900312418804247717478400000⟩, + ⟨5, 3, 7, 7, 4, 4, -897539712265126278591720144402169974361581158400000⟩, + ⟨5, 3, 8, 7, 5, 4, -658606254153907248879766044825908871648667238400000⟩ +] + +def collectedFourData_10_4_39 : List CollectedFourTerm := [ + ⟨5, 4, 1, 0, 5, 5, -8534717687507329912312851295644753108652995379200000⟩, + ⟨5, 4, 2, 0, 6, 5, 7283004454527574489263671392850941966204639641600000⟩, + ⟨5, 4, 3, 0, 7, 5, -1040831387438921574922877853081327997889072332800000⟩, + ⟨5, 4, 4, 0, 8, 5, 1339037309247990036828076643195716502327761305600000⟩, + ⟨5, 4, 1, 1, 4, 5, -3728096012067675395031142006801179228160131072000000⟩, + ⟨5, 4, 2, 1, 5, 5, -3556200689779804315884102640602130981555116441600000⟩, + ⟨5, 4, 3, 1, 6, 5, 4935315965643855203512239105654530851231865241600000⟩, + ⟨5, 4, 4, 1, 7, 5, -1561649218187356246716231206186063930865588633600000⟩, + ⟨5, 4, 5, 1, 8, 5, -1916409599864111301937218631942831281002250240000000⟩, + ⟨5, 4, 1, 2, 3, 5, -5631057203262884290810744265447080325254899302400000⟩, + ⟨5, 4, 2, 2, 4, 5, -13101496197966144140441742156100546311008079052800000⟩, + ⟨5, 4, 3, 2, 5, 5, 2100220253890329167944935760223234890644691353600000⟩, + ⟨5, 4, 4, 2, 6, 5, 1029584725496155032867329800454857376686669824000000⟩, + ⟨5, 4, 5, 2, 7, 5, -982329362562304411394919068178541116571779072000000⟩, + ⟨5, 4, 6, 2, 8, 5, 348253394790212127420271395524927838963420364800000⟩, + ⟨5, 4, 1, 3, 2, 5, 14510170618781160067752499378767169861462681190400000⟩, + ⟨5, 4, 2, 3, 3, 5, 14923880966185770573167022451257474807540744192000000⟩, + ⟨5, 4, 3, 3, 4, 5, -228837249487174501572441281478216848707367731200000⟩, + ⟨5, 4, 4, 3, 5, 5, 2824866379600815582055257747805704893236877721600000⟩, + ⟨5, 4, 5, 3, 6, 5, 672124461489940265158767746965572289610907648000000⟩, + ⟨5, 4, 6, 3, 7, 5, 738390359762337616902521558967483720164966400000⟩, + ⟨5, 4, 7, 3, 8, 5, -19696507284350000587788595046961083989780070400000⟩, + ⟨5, 4, 1, 4, 1, 5, -6532599720739823181417763286669544490299241267200000⟩, + ⟨5, 4, 2, 4, 2, 5, -3558384245956475107045762247406341194323591168000000⟩, + ⟨5, 4, 3, 4, 3, 5, -3379461772723756146467617918875410807513520537600000⟩, + ⟨5, 4, 4, 4, 4, 5, -2117140701956166862924858658919849485678936064000000⟩, + ⟨5, 4, 5, 4, 5, 5, 407543901866259506861946514171943678946312192000000⟩, + ⟨5, 4, 6, 4, 6, 5, 149220426593405208852261356705641394503837286400000⟩, + ⟨5, 4, 7, 4, 7, 5, -52098893511706580919862245979813040551152844800000⟩, + ⟨5, 4, 8, 4, 8, 5, 7972201393791293869914092674717424377921536000000⟩, + ⟨5, 4, 1, 5, 0, 5, -34430794400972732846236450997642355800347036876800000⟩, + ⟨5, 4, 2, 5, 1, 5, 3685426087062723626402983703409353617315568025600000⟩, + ⟨5, 4, 3, 5, 2, 5, -4219891528537517842618858934667039888437044838400000⟩, + ⟨5, 4, 4, 5, 3, 5, -2017389288039300503650970862168555099859923763200000⟩, + ⟨5, 4, 5, 5, 4, 5, 270338800458492032712170737378519837839458304000000⟩, + ⟨5, 4, 6, 5, 5, 5, 124655952879295895112462696851423875938071347200000⟩, + ⟨5, 4, 7, 5, 6, 5, 16504828470627911680233112463689922635628544000000⟩, + ⟨5, 4, 8, 5, 7, 5, -13070442024572623972905398956476557210261913600000⟩, + ⟨5, 4, 2, 6, 0, 5, -66345337993415481570688261760807153873891780198400000⟩, + ⟨5, 4, 3, 6, 1, 5, -1027382973572422316067124326600254077382374195200000⟩, + ⟨5, 4, 4, 6, 2, 5, 2555220310692773674904353670557084009643586355200000⟩, + ⟨5, 4, 5, 6, 3, 5, -2463476746927232210213672510567153261246152704000000⟩, + ⟨5, 4, 6, 6, 4, 5, -83115386666963270676006579494576478450037555200000⟩, + ⟨5, 4, 7, 6, 5, 5, 103117097488203312464697291609768635485755801600000⟩, + ⟨5, 4, 8, 6, 6, 5, 19523796468471615505778867964341222052043161600000⟩, + ⟨5, 4, 3, 7, 0, 5, 107988266293560610479698626581405754737697593753600000⟩, + ⟨5, 4, 4, 7, 1, 5, 2454588847992963431364708179682938623108526899200000⟩, + ⟨5, 4, 5, 7, 2, 5, 136475920150108747092281266900328863877824512000000⟩, + ⟨5, 4, 6, 7, 3, 5, -419582309579520073991529384866495469462120038400000⟩, + ⟨5, 4, 7, 7, 4, 5, 80182775701307775859633547905280027689746432000000⟩, + ⟨5, 4, 8, 7, 5, 5, 50432032777081095286762393837322837327609856000000⟩ +] + +def collectedFourData_10_4_40 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 4, 6, 5936153571300723196221046736154972523459510272000000⟩, + ⟨5, 5, 1, 0, 5, 6, -19677222878988087588293360045151613880634232012800000⟩, + ⟨5, 5, 2, 0, 6, 6, 8395667386290395485181271341728684441125204787200000⟩, + ⟨5, 5, 3, 0, 7, 6, -799896451957264286667446420491299849784157798400000⟩, + ⟨5, 5, 4, 0, 8, 6, 771804544159697128681204720544757510798154137600000⟩, + ⟨5, 5, 0, 1, 3, 6, 4665595321204815189935340997354290992220890726400000⟩, + ⟨5, 5, 1, 1, 4, 6, -8595313732649965742515106114755088376448155648000000⟩, + ⟨5, 5, 2, 1, 5, 6, -4099500190711392296189565686234383856589550387200000⟩, + ⟨5, 5, 3, 1, 6, 6, 3792873445064340126963375049361643413873413324800000⟩, + ⟨5, 5, 4, 1, 7, 6, -900115295261888976607021763230302147293321625600000⟩, + ⟨5, 5, 5, 1, 8, 6, -883675833335550170404454872882870201910034432000000⟩, + ⟨5, 5, 0, 2, 2, 6, 3892032109476325991482409827541368879615416729600000⟩, + ⟨5, 5, 1, 2, 3, 6, -12982686913607409089858077881436013750073792921600000⟩, + ⟨5, 5, 2, 2, 4, 6, -15103080744718156549803481317713346735130646937600000⟩, + ⟨5, 5, 3, 2, 5, 6, 1614054639099018334696768605978002207330323660800000⟩, + ⟨5, 5, 4, 2, 6, 6, 593439902120142979607756651546721112087855104000000⟩, + ⟨5, 5, 5, 2, 7, 6, -452961996294412512903518482008468138187397529600000⟩, + ⟨5, 5, 6, 2, 8, 6, 133819299761994375843501229214102480179376947200000⟩, + ⟨5, 5, 0, 3, 1, 6, 12476062269274859506284274943546262343327206604800000⟩, + ⟨5, 5, 1, 3, 2, 6, 33453931545483960036170514729018880252752533913600000⟩, + ⟨5, 5, 2, 3, 3, 6, 17203880827890201072126477858930001820321316864000000⟩, + ⟨5, 5, 3, 3, 4, 6, -175865280533915253953203904228841804292266393600000⟩, + ⟨5, 5, 4, 3, 5, 6, 1628218043935084686566393924991575577805298073600000⟩, + ⟨5, 5, 5, 3, 6, 6, 309923381543510295156906512676235534596990566400000⟩, + ⟨5, 5, 6, 3, 7, 6, 283732714088621620705552871887861007882649600000⟩, + ⟨5, 5, 7, 3, 8, 6, -6487327541167122884178548103992004831923404800000⟩, + ⟨5, 5, 0, 4, 0, 6, 39841401034813780830622851287865198973626089472000000⟩, + ⟨5, 5, 1, 4, 1, 6, -15061238741659601372153853304077848320771149004800000⟩, + ⟨5, 5, 2, 4, 2, 6, -4102017340260464908411581392635564798305632256000000⟩, + ⟨5, 5, 3, 4, 3, 6, -2597173292571915700897183518494814702616235212800000⟩, + ⟨5, 5, 4, 4, 4, 6, -1220293716321387338649971668290496416284934144000000⟩, + ⟨5, 5, 5, 4, 5, 6, 187922611704734264052963182796273075487349145600000⟩, + ⟨5, 5, 6, 4, 6, 6, 57339205577434898661082055080643054597151129600000⟩, + ⟨5, 5, 7, 4, 7, 6, -17159518784905265135821967461554576097384857600000⟩, + ⟨5, 5, 8, 4, 8, 6, 2297539142557549916311637522790618369097728000000⟩, + ⟨5, 5, 1, 5, 0, 6, -79381936243801941478915051838858297584387306291200000⟩, + ⟨5, 5, 2, 5, 1, 6, 4248468032241979599771418094084779745660318515200000⟩, + ⟨5, 5, 3, 5, 2, 6, -3243057715262990235507230437819536290952196915200000⟩, + ⟨5, 5, 4, 5, 3, 6, -1162798235041161111441387018507012379642114867200000⟩, + ⟨5, 5, 5, 5, 4, 6, 124655952879295895112462696851423875938071347200000⟩, + ⟨5, 5, 6, 5, 5, 6, 47900099683221762463689077230827138722876620800000⟩, + ⟨5, 5, 7, 5, 6, 6, 5436102287272967077971149550427514106544128000000⟩, + ⟨5, 5, 8, 5, 7, 6, -3766820565442794156197887561326616109698252800000⟩, + ⟨5, 5, 2, 6, 0, 6, -76481264552496161895399812838421855782812044492800000⟩, + ⟨5, 5, 3, 6, 1, 6, -789561119389387727414985595103459869474789785600000⟩, + ⟨5, 5, 4, 6, 2, 6, 1472797384734107344681748868983519590806139699200000⟩, + ⟨5, 5, 5, 6, 3, 6, -1135934023393554671969922433094055378317161267200000⟩, + ⟨5, 5, 6, 6, 4, 6, -31937787282506144630105540692412964455369932800000⟩, + ⟨5, 5, 7, 6, 5, 6, 33963096951303592065014925831967631180247859200000⟩, + ⟨5, 5, 8, 6, 6, 6, 5626637409407962874990185010629428481150156800000⟩, + ⟨5, 5, 3, 7, 0, 6, 82990801491662658596623768263564887724655430860800000⟩, + ⟨5, 5, 4, 7, 1, 6, 1414794654219623591583142224680142475082543923200000⟩, + ⟨5, 5, 5, 7, 2, 6, 62930425978577274944039542986801687404583321600000⟩, + ⟨5, 5, 6, 7, 3, 6, -161228035965809917880257653798297704687311257600000⟩, + ⟨5, 5, 7, 7, 4, 6, 26409348704560741715439135893327675847081984000000⟩, + ⟨5, 5, 8, 7, 5, 6, 14534199980739037664071630049615373913817088000000⟩ +] + +def collectedFourData_10_4_41 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 4, 7, 4715789059724708735847109524234139484175728640000000⟩, + ⟨5, 6, 1, 0, 5, 7, -7815973025624059531101920082297198928585555968000000⟩, + ⟨5, 6, 2, 0, 6, 7, 2223223952109917658863249184679906598021234688000000⟩, + ⟨5, 6, 3, 0, 7, 7, -158863095931753764817805854224513140892106752000000⟩, + ⟨5, 6, 4, 0, 8, 7, 122627131588733334976372199989393794617730662400000⟩, + ⟨5, 6, 0, 1, 3, 7, 3706434327981749089476940604397390373079482368000000⟩, + ⟨5, 6, 1, 1, 4, 7, -3414137284225495816588614901900536525493370880000000⟩, + ⟨5, 6, 2, 1, 5, 7, -1085572664604545272893448817157979986028658688000000⟩, + ⟨5, 6, 3, 1, 6, 7, 753282023549280230130640546647096318014521344000000⟩, + ⟨5, 6, 4, 1, 7, 7, -143013613475528274487916894635356383288387174400000⟩, + ⟨5, 6, 5, 1, 8, 7, -117001376315858579908426324743835401993584640000000⟩, + ⟨5, 6, 0, 2, 2, 7, 3091901552328611662002426075387666735512420352000000⟩, + ⟨5, 6, 1, 2, 3, 7, -5156842067649347929105975495482730103697309696000000⟩, + ⟨5, 6, 2, 2, 4, 7, -3999387936346492872804639117992227342966063104000000⟩, + ⟨5, 6, 3, 2, 5, 7, 320558637737249086788601921441079841389543424000000⟩, + ⟨5, 6, 4, 2, 6, 7, 94287904260167579426193788456978668528336896000000⟩, + ⟨5, 6, 5, 2, 7, 7, -59973550238643861409109440068756788207419392000000⟩, + ⟨5, 6, 6, 2, 8, 7, 15186928760656720379007938626569095193034752000000⟩, + ⟨5, 6, 0, 3, 1, 7, 9911212243957977989209490002829879489096318976000000⟩, + ⟨5, 6, 1, 3, 2, 7, 13288207800897915094904023160398981596463497216000000⟩, + ⟨5, 6, 2, 3, 3, 7, 4555692616916534714395304227491284104312258560000000⟩, + ⟨5, 6, 3, 3, 4, 7, -34927649527837666876579234798003698435883008000000⟩, + ⟨5, 6, 4, 3, 5, 7, 258697243803042985708556935630969557060314726400000⟩, + ⟨5, 6, 5, 3, 6, 7, 41034801253059087591114228930759311153430528000000⟩, + ⟨5, 6, 6, 3, 7, 7, 32200351695125760925676513230345035841536000000⟩, + ⟨5, 6, 7, 3, 8, 7, -644206468844421227457613735607653600591872000000⟩, + ⟨5, 6, 0, 4, 0, 7, 31650738288246587200867990358431970041150832640000000⟩, + ⟨5, 6, 1, 4, 1, 7, -5982461877941041295497691728385233590826303488000000⟩, + ⟨5, 6, 2, 4, 2, 7, -1086239221164143993643569607564330447132426240000000⟩, + ⟨5, 6, 3, 4, 3, 7, -515810501371350702381021246550191648207273984000000⟩, + ⟨5, 6, 4, 4, 4, 7, -193884733201680084111480863520973298237177856000000⟩, + ⟨5, 6, 5, 4, 5, 7, 24881527117620725076503602634615443226099712000000⟩, + ⟨5, 6, 6, 4, 6, 7, 6507330645474423989599048977694114065678336000000⟩, + ⟨5, 6, 7, 4, 7, 7, -1703979478968096165930414921824530505662464000000⟩, + ⟨5, 6, 8, 4, 8, 7, 202800794648955233976223596646331622359040000000⟩, + ⟨5, 6, 1, 5, 0, 7, -31531231628518896798377548665682978244785078272000000⟩, + ⟨5, 6, 2, 5, 1, 7, 1125020258005604387613395542530121005224951808000000⟩, + ⟨5, 6, 3, 5, 2, 7, -644086103484259588346274182748767519407865856000000⟩, + ⟨5, 6, 4, 5, 3, 7, -184749640642223725609217600257394125803670732800000⟩, + ⟨5, 6, 5, 5, 4, 7, 16504828470627911680233112463689922635628544000000⟩, + ⟨5, 6, 6, 5, 5, 7, 5436102287272967077971149550427514106544128000000⟩, + ⟨5, 6, 7, 5, 6, 7, 539817395767127614972678337991997831249920000000⟩, + ⟨5, 6, 8, 5, 7, 7, -332492356635743641329594794992400339042304000000⟩, + ⟨5, 6, 2, 6, 0, 7, -20252705522662945548703833357004887321332416512000000⟩, + ⟨5, 6, 3, 6, 1, 7, -156810451586101792814947979521018417033248768000000⟩, + ⟨5, 6, 4, 6, 2, 7, 234003440466867761845230994252305491601181900800000⟩, + ⟨5, 6, 5, 6, 3, 7, -150401130287094168788483541770341756063186944000000⟩, + ⟨5, 6, 6, 6, 4, 7, -3624566120844273811150952763234644863746048000000⟩, + ⟨5, 6, 7, 6, 5, 7, 3372613240071390161969058050056851541721088000000⟩, + ⟨5, 6, 8, 6, 6, 7, 496655972772351245294845144285082523009024000000⟩, + ⟨5, 6, 3, 7, 0, 7, 16482352967765787123616683896880649206365159424000000⟩, + ⟨5, 6, 4, 7, 1, 7, 224787754292009326519446834469773174234729676800000⟩, + ⟨5, 6, 5, 7, 2, 7, 8332180392264883997278635714323936006111232000000⟩, + ⟨5, 6, 6, 7, 3, 7, -18297500441178983662608540606367341861666816000000⟩, + ⟨5, 6, 7, 7, 4, 7, 2622508755028156876363402118770565327093760000000⟩, + ⟨5, 6, 8, 7, 5, 7, 1282914946293183793465332376374687396003840000000⟩ +] + +def collectedFourData_10_4_42 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 4, 8, -13070785113112568212830828247179421740492128256000000⟩, + ⟨5, 7, 1, 0, 5, 8, 14442390951470328779918186794387521157678812364800000⟩, + ⟨5, 7, 2, 0, 6, 8, -3081062592953424029364232812314675235832568217600000⟩, + ⟨5, 7, 3, 0, 7, 8, 176128776162770748831158827406512644929429176320000⟩, + ⟨5, 7, 4, 0, 8, 8, -113295489240795926366228603857350772696358584320000⟩, + ⟨5, 7, 0, 1, 3, 8, -10273149630603142450852705551398111525330957107200000⟩, + ⟨5, 7, 1, 1, 4, 8, 6308658596840385631003943822260230223684435968000000⟩, + ⟨5, 7, 2, 1, 5, 8, 1504444626764471340255704378102346549399493017600000⟩, + ⟨5, 7, 3, 1, 6, 8, -835150795312122579164279931498927094297043927040000⟩, + ⟨5, 7, 4, 1, 7, 8, 132130606798705648085354455788455146293213265920000⟩, + ⟨5, 7, 5, 1, 8, 8, 92655292277233507847607232731107509577711616000000⟩, + ⟨5, 7, 0, 2, 2, 8, -8569844891184692018718584902184580043265330380800000⟩, + ⟨5, 7, 1, 2, 3, 8, 9528836521289545054290437844833470440533498265600000⟩, + ⟨5, 7, 2, 2, 4, 8, 5542565585303276306561946498413595740078918860800000⟩, + ⟨5, 7, 3, 2, 5, 8, -355397836243360289840314572902506184228827299840000⟩, + ⟨5, 7, 4, 2, 6, 8, -87112811856935608652471285066879109255974092800000⟩, + ⟨5, 7, 5, 2, 7, 8, 47494029568194972681890782315904211274747084800000⟩, + ⟨5, 7, 6, 2, 8, 8, -10523428838984212239952517484524962258826035200000⟩, + ⟨5, 7, 0, 3, 1, 8, -27470975442397644033993561656602852236229764710400000⟩, + ⟨5, 7, 1, 3, 2, 8, -24554011570379277282168179768829998076125616537600000⟩, + ⟨5, 7, 2, 3, 3, 8, -6313522348324205491669525095956868408186765312000000⟩, + ⟨5, 7, 3, 3, 4, 8, 38723682989427396269824961251516136438397665280000⟩, + ⟨5, 7, 4, 3, 5, 8, -239010979235887744305965679933654710233879019520000⟩, + ⟨5, 7, 5, 3, 6, 8, -32496126313729825188070247861018543493690163200000⟩, + ⟨5, 7, 6, 3, 7, 8, -22312484307674301204790257563286491470233600000⟩, + ⟨5, 7, 7, 3, 8, 8, 396789226626689946840338816198212013418086400000⟩, + ⟨5, 7, 0, 4, 0, 8, -87726569954167080629455781916749875364134649856000000⟩, + ⟨5, 7, 1, 4, 1, 8, 11054420608954605338053177540796671554828946636800000⟩, + ⟨5, 7, 2, 4, 2, 8, 1505368376474849510771907392881568595887259648000000⟩, + ⟨5, 7, 3, 4, 3, 8, 571870211930586894878378994568197145489771069440000⟩, + ⟨5, 7, 4, 4, 4, 8, 179130551451500628668711132780215173131324620800000⟩, + ⟨5, 7, 5, 4, 5, 8, -19704085883257946343801939152564161696550092800000⟩, + ⟨5, 7, 6, 4, 6, 8, -4509103325538354736402028368353882321557913600000⟩, + ⟨5, 7, 7, 4, 7, 8, 1049540376178350933207011154616572682489036800000⟩, + ⟨5, 7, 8, 4, 8, 8, -112420872691863171550626174476140930085683200000⟩, + ⟨5, 7, 1, 5, 0, 8, 58263555013238601540933185134924743268011029299200000⟩, + ⟨5, 7, 2, 5, 1, 8, -1559113210329655299858245216648984822673938841600000⟩, + ⟨5, 7, 3, 5, 2, 8, 714087160927948390624613095410101686729923624960000⟩, + ⟨5, 7, 4, 5, 3, 8, 170690618401002261760236774013547941383414743040000⟩, + ⟨5, 7, 5, 5, 4, 8, -13070442024572623972905398956476557210261913600000⟩, + ⟨5, 7, 6, 5, 5, 8, -3766820565442794156197887561326616109698252800000⟩, + ⟨5, 7, 7, 5, 6, 8, -332492356635743641329594794992400339042304000000⟩, + ⟨5, 7, 8, 5, 7, 8, 184314272343296600561506307535751019306680320000⟩, + ⟨5, 7, 2, 6, 0, 8, 28067281900574331317937723314248993191433234022400000⟩, + ⟨5, 7, 3, 6, 1, 8, 173853044757835625895192950407229910203372666880000⟩, + ⟨5, 7, 4, 6, 2, 8, -216196317472690995285432702639441867059956285440000⟩, + ⟨5, 7, 5, 6, 3, 8, 119105100507165138538941449760930675822270873600000⟩, + ⟨5, 7, 6, 6, 4, 8, 2511558738835380858480933607724204042276044800000⟩, + ⟨5, 7, 7, 6, 5, 8, -2077310092274232119812841735702961083488665600000⟩, + ⟨5, 7, 8, 6, 6, 8, -275316958118150069989304523968717923465297920000⟩, + ⟨5, 7, 3, 7, 0, 8, -18273700631784941084036800390017468260398493859840000⟩, + ⟨5, 7, 4, 7, 1, 8, -207681923795344680784939005769124233246660362240000⟩, + ⟨5, 7, 5, 7, 2, 8, -6598389128925963625717290480801164580146380800000⟩, + ⟨5, 7, 6, 7, 3, 8, 12678827092601889518295263898478534136011161600000⟩, + ⟨5, 7, 7, 7, 4, 8, -1615294584973581499816146434027148344819712000000⟩, + ⟨5, 7, 8, 7, 5, 8, -711172843781840193661981107281583121052467200000⟩ +] + +def collectedFourData_10_4_43 : List CollectedFourTerm := [ + ⟨6, 0, 4, 0, 8, 2, -82155135257297148176904146682609908328540080701440000⟩, + ⟨6, 0, 4, 1, 7, 2, 95813239749598246018882054745784234718307958128640000⟩, + ⟨6, 0, 5, 1, 8, 2, 470316663465156096785530989132251396418362671104000000⟩, + ⟨6, 0, 4, 2, 6, 2, -63169018366999425548926704052483916233575078297600000⟩, + ⟨6, 0, 5, 2, 7, 2, 241078873877962480832101622649419397914627879731200000⟩, + ⟨6, 0, 6, 2, 8, 2, -213666972198636858884178769975978338545938150195200000⟩, + ⟨6, 0, 4, 3, 5, 2, -173316514705801632627365013808698173526850236579840000⟩, + ⟨6, 0, 5, 3, 6, 2, -164949775968393351265635903861508150965117439180800000⟩, + ⟨6, 0, 6, 3, 7, 2, -453031140058580904930061071415639640368585113600000⟩, + ⟨6, 0, 7, 3, 8, 2, 24169143142858127845393786811195842377001677619200000⟩, + ⟨6, 0, 4, 4, 4, 2, 129894797946757809032860143190418409666226264473600000⟩, + ⟨6, 0, 5, 4, 5, 2, -100017599658706278460083438943936104207370892083200000⟩, + ⟨6, 0, 6, 4, 6, 2, -91552522437314507374130686804375059899795216793600000⟩, + ⟨6, 0, 7, 4, 7, 2, 63929385890129554583300226856056944508797347430400000⟩, + ⟨6, 0, 8, 4, 8, 2, -17119392249093293965448232430903947187741261824000000⟩, + ⟨6, 0, 4, 5, 3, 2, 123774661602648627820225290595706264548668006727680000⟩, + ⟨6, 0, 5, 5, 4, 2, -66345337993415481570688261760807153873891780198400000⟩, + ⟨6, 0, 6, 5, 5, 2, -76481264552496161895399812838421855782812044492800000⟩, + ⟨6, 0, 7, 5, 6, 2, -20252705522662945548703833357004887321332416512000000⟩, + ⟨6, 0, 8, 5, 7, 2, 28067281900574331317937723314248993191433234022400000⟩, + ⟨6, 0, 4, 6, 2, 2, -156772681976316464617808389878261307099570482708480000⟩, + ⟨6, 0, 5, 6, 3, 2, 604575433258614209385432364690035858792941774438400000⟩, + ⟨6, 0, 6, 6, 4, 2, 50994515137309787480806161120836899342883015884800000⟩, + ⟨6, 0, 7, 6, 5, 2, -126532681845002974946145091712367138477836127436800000⟩, + ⟨6, 0, 8, 6, 6, 2, -41925123742549802184408694703103356250645489254400000⟩, + ⟨6, 0, 4, 7, 1, 2, -150598551224212498790730371570317232497594812334080000⟩, + ⟨6, 0, 5, 7, 2, 2, -33493309265872793337992362031539191601341608755200000⟩, + ⟨6, 0, 6, 7, 3, 2, 257430029447301892511679112962590912368315308441600000⟩, + ⟨6, 0, 7, 7, 4, 2, -98390489011034217172567952740325159177275047936000000⟩, + ⟨6, 0, 8, 7, 5, 2, -108297032197702067523783756069813929933436616704000000⟩ +] + +def collectedFourData_10_4_44 : List CollectedFourTerm := [ + ⟨6, 1, 3, 0, 7, 3, 659254513226200830173553576990451989046823485440000⟩, + ⟨6, 1, 4, 0, 8, 3, -2544407480847059542114542195625450069966863728640000⟩, + ⟨6, 1, 3, 1, 6, 3, -3125990783727174691978689903183419059459514695680000⟩, + ⟨6, 1, 4, 1, 7, 3, 2967409440926177487659198466646353481421385891840000⟩, + ⟨6, 1, 5, 1, 8, 3, 7283033696797920842729685192413257850066829312000000⟩, + ⟨6, 1, 3, 2, 5, 3, -1330263189461633387329918197801040927184419553280000⟩, + ⟨6, 1, 4, 2, 6, 3, -1956392894824947104574181349092311285435570585600000⟩, + ⟨6, 1, 5, 2, 7, 3, 3733198711487661360559966725151089752930883993600000⟩, + ⟨6, 1, 6, 2, 8, 3, -2205809942249324989448916856948717959155967590400000⟩, + ⟨6, 1, 3, 3, 4, 3, 144943735689891304982885330654060573538134261760000⟩, + ⟨6, 1, 4, 3, 5, 3, -5367745244295144028959163936396719531943306199040000⟩, + ⟨6, 1, 5, 3, 6, 3, -2554310467772908963106615586344388048623920742400000⟩, + ⟨6, 1, 6, 3, 7, 3, -4676907163549629272889258130065044628779827200000⟩, + ⟨6, 1, 7, 3, 8, 3, 187134219990494896859007941140723309340314828800000⟩, + ⟨6, 1, 3, 4, 3, 3, 2140524827393614208906482926894347974041120276480000⟩, + ⟨6, 1, 4, 4, 4, 3, 4022941409368464761334529827997677339459295641600000⟩, + ⟨6, 1, 5, 4, 5, 3, -1548810844209368882699970836585761355836529049600000⟩, + ⟨6, 1, 6, 4, 6, 3, -945150587159961250498757553045063506798523187200000⟩, + ⟨6, 1, 7, 4, 7, 3, 494985514890124176991957040780270872481601945600000⟩, + ⟨6, 1, 8, 4, 8, 3, -106040138744167405938859391372803622702992588800000⟩, + ⟨6, 1, 3, 5, 2, 3, 2672846504330292546562374486761425029189410488320000⟩, + ⟨6, 1, 4, 5, 3, 3, 3833396097940446215412951706210869946529957806080000⟩, + ⟨6, 1, 5, 5, 4, 3, -1027382973572422316067124326600254077382374195200000⟩, + ⟨6, 1, 6, 5, 5, 3, -789561119389387727414985595103459869474789785600000⟩, + ⟨6, 1, 7, 5, 6, 3, -156810451586101792814947979521018417033248768000000⟩, + ⟨6, 1, 8, 5, 7, 3, 173853044757835625895192950407229910203372666880000⟩, + ⟨6, 1, 3, 6, 1, 3, 650736392381441302109508806364812174842354728960000⟩, + ⟨6, 1, 4, 6, 2, 3, -4855370069852891353839167217661995991742420090880000⟩, + ⟨6, 1, 5, 6, 3, 3, 9362082177224199485942701834486054952973316915200000⟩, + ⟨6, 1, 6, 6, 4, 3, 526446400829277310468099803370265531121244569600000⟩, + ⟨6, 1, 7, 6, 5, 3, -979703524465533389988352853721416779867304755200000⟩, + ⟨6, 1, 8, 6, 6, 3, -259690640522699113080075318850518423824530145280000⟩, + ⟨6, 1, 3, 7, 0, 3, -68398928768546912819275163620038532639959055073280000⟩, + ⟨6, 1, 4, 7, 1, 3, -4664152510242265919570778495503166439925722644480000⟩, + ⟨6, 1, 5, 7, 2, 3, -518656724181106143147262512648044454394567065600000⟩, + ⟨6, 1, 6, 7, 3, 3, 2657601746050378604854773155735386991931634483200000⟩, + ⟨6, 1, 7, 7, 4, 3, -761807206268459606164550634058271599733243904000000⟩, + ⟨6, 1, 8, 7, 5, 3, -670808411462978078515024117322110617292426444800000⟩ +] + +def collectedFourData_10_4_45 : List CollectedFourTerm := [ + ⟨6, 2, 2, 0, 6, 4, 17209591144068999573085684798526495993370268139520000⟩, + ⟨6, 2, 3, 0, 7, 4, -4918926725797211594166303422281323295768125112320000⟩, + ⟨6, 2, 4, 0, 8, 4, 9492353641697862305936322891672248940787358760960000⟩, + ⟨6, 2, 2, 1, 5, 4, -8403229776870497343841954992228725879960261099520000⟩, + ⟨6, 2, 3, 1, 6, 4, 23324102152024918375221088523950981013203624919040000⟩, + ⟨6, 2, 4, 1, 7, 4, -11070435857863025993590507032441755040957081845760000⟩, + ⟨6, 2, 5, 1, 8, 4, -18113747360254538796105277498001821184569638912000000⟩, + ⟨6, 2, 2, 2, 4, 4, -30958568589423915192859968937611675659474734940160000⟩, + ⟨6, 2, 3, 2, 5, 4, 9925555341237230500232405222206381820691181731840000⟩, + ⟨6, 2, 4, 2, 6, 4, 7298663189592968522169345966710344509626410598400000⟩, + ⟨6, 2, 5, 2, 7, 4, -9284897080078902692099530899372664743005886873600000⟩, + ⟨6, 2, 6, 2, 8, 4, 4114578383339987988749814294628479396922313932800000⟩, + ⟨6, 2, 2, 3, 3, 4, 35264826667948337247017787734058590085319124582400000⟩, + ⟨6, 2, 3, 3, 4, 4, -1081475516538880059764915944789508025570589409280000⟩, + ⟨6, 2, 4, 3, 5, 4, 20025305105779977585259448110174713512402154946560000⟩, + ⟨6, 2, 5, 3, 6, 4, 6352865635268781546482727805356021799014786662400000⟩, + ⟨6, 2, 6, 3, 7, 4, 8724006881756147914874552263883384957593190400000⟩, + ⟨6, 2, 7, 3, 8, 4, -279254672529370146366414335787235476132625121280000⟩, + ⟨6, 2, 2, 4, 2, 4, -8408389475628782448412071306591874454325402009600000⟩, + ⟨6, 2, 3, 4, 3, 4, -15971198633396710394287109394312972510936107581440000⟩, + ⟨6, 2, 4, 4, 4, 4, -15008281033996555259238244256480159251879585382400000⟩, + ⟨6, 2, 5, 4, 5, 4, 3852071747679225758560760418811497949859256729600000⟩, + ⟨6, 2, 6, 4, 6, 4, 1763024139316309145858783410997443706256516710400000⟩, + ⟨6, 2, 7, 4, 7, 4, -738651743515666234423554003251789553617715855360000⟩, + ⟨6, 2, 8, 4, 8, 4, 131867046290248858445585038302683170429363814400000⟩, + ⟨6, 2, 2, 5, 1, 4, 8708586757846446060834897842058540438268485304320000⟩, + ⟨6, 2, 3, 5, 2, 4, -19943035413991617665585054592837554012790152232960000⟩, + ⟨6, 2, 4, 5, 3, 4, -14301149357665559467660406530375606731487177605120000⟩, + ⟨6, 2, 5, 5, 4, 4, 2555220310692773674904353670557084009643586355200000⟩, + ⟨6, 2, 6, 5, 5, 4, 1472797384734107344681748868983519590806139699200000⟩, + ⟨6, 2, 7, 5, 6, 4, 234003440466867761845230994252305491601181900800000⟩, + ⟨6, 2, 8, 5, 7, 4, -216196317472690995285432702639441867059956285440000⟩, + ⟨6, 2, 2, 6, 0, 4, -156772681976316464617808389878261307099570482708480000⟩, + ⟨6, 2, 3, 6, 1, 4, -4855370069852891353839167217661995991742420090880000⟩, + ⟨6, 2, 4, 6, 2, 4, 18113800604380957756111191128580440631959428792320000⟩, + ⟨6, 2, 5, 6, 3, 4, -23284581451097772847510022612065342775870305075200000⟩, + ⟨6, 2, 6, 6, 4, 4, -981999826617177361401511760200327265986491187200000⟩, + ⟨6, 2, 7, 6, 5, 4, 1461981602907199902797696698784718449273858949120000⟩, + ⟨6, 2, 8, 6, 6, 4, 322940332976834395340030176538343262751702384640000⟩, + ⟨6, 2, 3, 7, 0, 4, 510348146255411365785083712580185180516137136291840000⟩, + ⟨6, 2, 4, 7, 1, 4, 17400430316017306466841007166249472462284358942720000⟩, + ⟨6, 2, 5, 7, 2, 4, 1289959275163635385788133025117599478868187545600000⟩, + ⟨6, 2, 6, 7, 3, 4, -4957322245394753866111137329558774919937287782400000⟩, + ⟨6, 2, 7, 7, 4, 4, 1136821592158925449532596546670346771819292262400000⟩, + ⟨6, 2, 8, 7, 5, 4, 834189061744718995916616430738390392045463142400000⟩ +] + +def collectedFourData_10_4_46 : List CollectedFourTerm := [ + ⟨6, 3, 1, 0, 5, 5, 77773070417951599778783698591811179789533000499200000⟩, + ⟨6, 3, 2, 0, 6, 5, -66366766779565111194375847056055217538394069401600000⟩, + ⟨6, 3, 3, 0, 7, 5, 9484631566312953141058979296047215118283230412800000⟩, + ⟨6, 3, 4, 0, 8, 5, -12202048943791607062270836496942373508423981465600000⟩, + ⟨6, 3, 1, 1, 4, 5, 33972473875243789703040147524429697523774390272000000⟩, + ⟨6, 3, 2, 1, 5, 5, 32406068576990085640998086184602607034021026201600000⟩, + ⟨6, 3, 3, 1, 6, 5, -44973330130497148737817595080150245940953455001600000⟩, + ⟨6, 3, 4, 1, 7, 5, 14230611844607661533562811416493061187277789593600000⟩, + ⟨6, 3, 5, 1, 8, 5, 17463384755893482128612261092139551168911114240000000⟩, + ⟨6, 3, 1, 2, 3, 5, 51313309289411896888020741097679162024250467942400000⟩, + ⟨6, 3, 2, 2, 4, 5, 119388083319548110960095061614763347694450429132800000⟩, + ⟨6, 3, 3, 2, 5, 5, -19138369150523876087518831622223378309650684313600000⟩, + ⟨6, 3, 4, 2, 6, 5, -9382145759134819996966672750861636720838836224000000⟩, + ⟨6, 3, 5, 2, 7, 5, 8951528742422037497601279250968344375718838272000000⟩, + ⟨6, 3, 6, 2, 8, 5, -3173477646009905616903879031437920692584893644800000⟩, + ⟨6, 3, 1, 3, 2, 5, -132224704158966980983239648364836734978962646630400000⟩, + ⟨6, 3, 2, 3, 3, 5, -135994661779056844001846260346819525422866235392000000⟩, + ⟨6, 3, 3, 3, 4, 5, 2085291648799027263690894092162823011446240051200000⟩, + ⟨6, 3, 4, 3, 5, 5, -25741745644801041358098223876093691351019395481600000⟩, + ⟨6, 3, 5, 3, 6, 5, -6124770026031400401954800482895127378760040448000000⟩, + ⟨6, 3, 6, 3, 7, 5, -6728621560592607329973634851045333140924006400000⟩, + ⟨6, 3, 7, 3, 8, 5, 179485473814289374756566422497858579941713510400000⟩, + ⟨6, 3, 1, 4, 1, 5, 59528663594469115143701401440379235396954043187200000⟩, + ⟨6, 3, 2, 4, 2, 5, 32425966349184512986699569798084090942317395968000000⟩, + ⟨6, 3, 3, 4, 3, 5, 30795525762912881732015017166889225618957375897600000⟩, + ⟨6, 3, 4, 4, 4, 5, 19292557636553579669359848925180609468997566464000000⟩, + ⟨6, 3, 5, 4, 5, 5, -3713765556023745800619875203838662899916603392000000⟩, + ⟨6, 3, 6, 4, 6, 5, -1359779101098206512790632966708608567288948326400000⟩, + ⟨6, 3, 7, 4, 7, 5, 474753947598555259471468385791825584025554124800000⟩, + ⟨6, 3, 8, 4, 8, 5, -72647110670453526103012487970807359666651136000000⟩, + ⟨6, 3, 1, 5, 0, 5, 313752451520742377610718108330725516245778353356800000⟩, + ⟨6, 3, 2, 5, 1, 5, -33583641906378975677266824144208716574139980185600000⟩, + ⟨6, 3, 3, 5, 2, 5, 38453986765778879630266064606573275838727743078400000⟩, + ⟨6, 3, 4, 5, 3, 5, 18383567553588984626379200143095216710974911283200000⟩, + ⟨6, 3, 5, 5, 4, 5, -2463476746927232210213672510567153261246152704000000⟩, + ⟨6, 3, 6, 5, 5, 5, -1135934023393554671969922433094055378317161267200000⟩, + ⟨6, 3, 7, 5, 6, 5, -150401130287094168788483541770341756063186944000000⟩, + ⟨6, 3, 8, 5, 7, 5, 119105100507165138538941449760930675822270873600000⟩, + ⟨6, 3, 2, 6, 0, 5, 604575433258614209385432364690035858792941774438400000⟩, + ⟨6, 3, 3, 6, 1, 5, 9362082177224199485942701834486054952973316915200000⟩, + ⟨6, 3, 4, 6, 2, 5, -23284581451097772847510022612065342775870305075200000⟩, + ⟨6, 3, 5, 6, 3, 5, 22448563330009199790126600116042550393232687104000000⟩, + ⟨6, 3, 6, 6, 4, 5, 757393396799389837371070348543628186941076275200000⟩, + ⟨6, 3, 7, 6, 5, 5, -939660054132039927359046659311107446765361561600000⟩, + ⟨6, 3, 8, 6, 6, 5, -177911637287169920439896653963407762078144921600000⟩, + ⟨6, 3, 3, 7, 0, 5, -984048839840947061332273230574165606025232226713600000⟩, + ⟨6, 3, 4, 7, 1, 5, -22367571876631155168749256672089176758686004019200000⟩, + ⟨6, 3, 5, 7, 2, 5, -1243644105970321991508125483028486068436467712000000⟩, + ⟨6, 3, 6, 7, 3, 5, 3823466188790296426157060879513161449863538278400000⟩, + ⟨6, 3, 7, 7, 4, 5, -730669822863929660216932727702498057631301632000000⟩, + ⟨6, 3, 8, 7, 5, 5, -459564590195357019012460177928649080838291456000000⟩ +] + +def collectedFourData_10_4_47 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 4, 6, -3957979446604358300870739188555310962785124352000000⟩, + ⟨6, 4, 1, 0, 5, 6, 13119950955753738088834774798731008163231616204800000⟩, + ⟨6, 4, 2, 0, 6, 6, -5597880606748289640178491065885279533143372595200000⟩, + ⟨6, 4, 3, 0, 7, 6, 533337569224119319724922416937010605635036774400000⟩, + ⟨6, 4, 4, 0, 8, 6, -514607057564813931035898445286438407222434201600000⟩, + ⟨6, 4, 0, 1, 3, 6, -3110824234194432489738166632954430731365803622400000⟩, + ⟨6, 4, 1, 1, 4, 6, 5730996457945462602660372694954511721843130368000000⟩, + ⟨6, 4, 2, 1, 5, 6, 2733375628055217700953440734579259445980902195200000⟩, + ⟨6, 4, 3, 1, 6, 6, -2528929711608974661895161329619123458158677196800000⟩, + ⟨6, 4, 4, 1, 7, 6, 600159311148031631792591327201309524428954009600000⟩, + ⟨6, 4, 5, 1, 8, 6, 589198164062440571521630483602134731862310912000000⟩, + ⟨6, 4, 0, 2, 2, 6, -2595044570495514883121431907350049618189195673600000⟩, + ⟨6, 4, 1, 2, 3, 6, 8656313781063118514641069251285609235061774745600000⟩, + ⟨6, 4, 2, 2, 4, 6, 10070103889664379283617767212173631726846319001600000⟩, + ⟨6, 4, 3, 2, 5, 6, -1076184268233227666582460648903183109521722572800000⟩, + ⟨6, 4, 4, 2, 6, 6, -395680958582706724962881889973582726812401664000000⟩, + ⟨6, 4, 5, 2, 7, 6, 302016154045240580923301786756553729484888473600000⟩, + ⟨6, 4, 6, 2, 8, 6, -89225123921600978361064201974624384518927155200000⟩, + ⟨6, 4, 0, 3, 1, 6, -8318517613001365499987082083985017768369769676800000⟩, + ⟨6, 4, 1, 3, 2, 6, -22305685301891737765865376170655763298724190617600000⟩, + ⟨6, 4, 2, 3, 3, 6, -11470829704916110062281350574518136208384589824000000⟩, + ⟨6, 4, 3, 3, 4, 6, 117259629044944638064552216449072253766310297600000⟩, + ⟨6, 4, 4, 3, 5, 6, -1085627835445860261015981412012219096637217177600000⟩, + ⟨6, 4, 5, 3, 6, 6, -206643975671698745939731946313660215834601062400000⟩, + ⟨6, 4, 6, 3, 7, 6, -189181131721624737530865851174470574250393600000⟩, + ⟨6, 4, 7, 3, 8, 6, 4325479245595664447573860535661211069238476800000⟩, + ⟨6, 4, 0, 4, 0, 6, -26564583366255699246747629754252047452106391552000000⟩, + ⟨6, 4, 1, 4, 1, 6, 10042205388366976045835583691553868369904848076800000⟩, + ⟨6, 4, 2, 4, 2, 6, 2735053958317329802048886731709377437128196096000000⟩, + ⟨6, 4, 3, 4, 3, 6, 1731686754360191683716215435516683905919667404800000⟩, + ⟨6, 4, 4, 4, 4, 6, 813640919158730395951681657057632279072866304000000⟩, + ⟨6, 4, 5, 4, 5, 6, -125298954237898965285555307116983041926994329600000⟩, + ⟨6, 4, 6, 4, 6, 6, -38231389136784219092523188677085206888946073600000⟩, + ⟨6, 4, 7, 4, 7, 6, 11441250946173640110509231716985285379725721600000⟩, + ⟨6, 4, 8, 4, 8, 6, -1531903208834808034651921612392231912603648000000⟩, + ⟨6, 4, 1, 5, 0, 6, 52928561956961004480302231994488015063895716659200000⟩, + ⟨6, 4, 2, 5, 1, 6, -2832701167379815168619809009025017778592232243200000⟩, + ⟨6, 4, 3, 5, 2, 6, 2162335530404750749170392495899829486174286643200000⟩, + ⟨6, 4, 4, 5, 3, 6, 775305331905738041625638862063452158988333875200000⟩, + ⟨6, 4, 5, 5, 4, 6, -83115386666963270676006579494576478450037555200000⟩, + ⟨6, 4, 6, 5, 5, 6, -31937787282506144630105540692412964455369932800000⟩, + ⟨6, 4, 7, 5, 6, 6, -3624566120844273811150952763234644863746048000000⟩, + ⟨6, 4, 8, 5, 7, 6, 2511558738835380858480933607724204042276044800000⟩, + ⟨6, 4, 2, 6, 0, 6, 50994515137309787480806161120836899342883015884800000⟩, + ⟨6, 4, 3, 6, 1, 6, 526446400829277310468099803370265531121244569600000⟩, + ⟨6, 4, 4, 6, 2, 6, -981999826617177361401511760200327265986491187200000⟩, + ⟨6, 4, 5, 6, 3, 6, 757393396799389837371070348543628186941076275200000⟩, + ⟨6, 4, 6, 6, 4, 6, 21294783586012038381522945892252199435422924800000⟩, + ⟨6, 4, 7, 6, 5, 6, -22645175543670386336205612797393118961021747200000⟩, + ⟨6, 4, 8, 6, 6, 6, -3751606987999824755192680718082552416226508800000⟩, + ⟨6, 4, 3, 7, 0, 6, -55334802682547153418918447406185231224419437772800000⟩, + ⟨6, 4, 4, 7, 1, 6, -943326026745629526235601812315662383297278771200000⟩, + ⟨6, 4, 5, 7, 2, 6, -41959381541857293122236574361747883426421145600000⟩, + ⟨6, 4, 6, 7, 3, 6, 107500125275437577508561810047059430370548121600000⟩, + ⟨6, 4, 7, 7, 4, 6, -17608651480348219805868847342562183158431744000000⟩, + ⟨6, 4, 8, 7, 5, 6, -9690797939379712795982807754605844032913408000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1017.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1017.lean new file mode 100644 index 0000000000000000000000000000000000000000..a80af89540f7100d1300f1eda3834f8087489e6d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1017.lean @@ -0,0 +1,641 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1013 +import OAI.Analysis.LaughlinFock.Sparse1014 +import OAI.Analysis.LaughlinFock.Sparse1015 +import OAI.Analysis.LaughlinFock.Sparse1016 + +namespace OAI + +/-! Sparse1017. -/ +namespace LaughlinFock +def collectedFourData_10_4_48 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 4, 7, 29462801208193070475604046074007697413684330496000000⟩, + ⟨6, 5, 1, 0, 5, 7, -48831798154263489720408566507020962795351126835200000⟩, + ⟨6, 5, 2, 0, 6, 7, 13890020209286387435800295247536379606653416243200000⟩, + ⟨6, 5, 3, 0, 7, 7, -992527815701027288572427371557864056724180172800000⟩, + ⟨6, 5, 4, 0, 8, 7, 766136643300303568836371338730929050332021391360000⟩, + ⟨6, 5, 0, 1, 3, 7, 23156662949407617339609657850968128937216127795200000⟩, + ⟨6, 5, 1, 1, 4, 7, -21330480822755045288076166837470510932696236032000000⟩, + ⟨6, 5, 2, 1, 5, 7, -6782324486786794916780350116695383594136449843200000⟩, + ⟨6, 5, 3, 1, 6, 7, 4706274651486097393133293342172112864937613721600000⟩, + ⟨6, 5, 4, 1, 7, 7, -893505118768146381862357618759702360208084828160000⟩, + ⟨6, 5, 5, 1, 8, 7, -730988652762251638828628392075276903457488896000000⟩, + ⟨6, 5, 0, 2, 2, 7, 19317250970695309308664943216584346666745515212800000⟩, + ⟨6, 5, 1, 2, 3, 7, -32218364896514157110749211028964036954454124134400000⟩, + ⟨6, 5, 2, 2, 4, 7, -24986947090016984199492497458904830841208805785600000⟩, + ⟨6, 5, 3, 2, 5, 7, 2002751883005786371440515208795399662142593433600000⟩, + ⟨6, 5, 4, 2, 6, 7, 589081857642849488522234859178294672867354214400000⟩, + ⟨6, 5, 5, 2, 7, 7, -374696316152422388592029981164525734654168268800000⟩, + ⟨6, 5, 6, 2, 8, 7, 94883265000054825519179789507516136279559372800000⟩, + ⟨6, 5, 0, 3, 1, 7, 61922209067805443841648023777716281539608077926400000⟩, + ⟨6, 5, 1, 3, 2, 7, 83020639789573313489411640576616270831322293862400000⟩, + ⟨6, 5, 2, 3, 3, 7, 28462567820130662552356608437928700318354243584000000⟩, + ⟨6, 5, 3, 3, 4, 7, -218217223390435753390618807432167798395319091200000⟩, + ⟨6, 5, 4, 3, 5, 7, 1616260899447748983818704988217901434419502120960000⟩, + ⟨6, 5, 5, 3, 6, 7, 256372831062797581732130468068870049684992819200000⟩, + ⟨6, 5, 6, 3, 7, 7, 201177904442310991230572524266113655531110400000⟩, + ⟨6, 5, 7, 3, 8, 7, -4024804097090635933063094712710720578702540800000⟩, + ⟨6, 5, 0, 4, 0, 7, 197744088734450612777113907218506014778086916096000000⟩, + ⟨6, 5, 1, 4, 1, 7, -37376583815150490170994559447674068424325280563200000⟩, + ⟨6, 5, 2, 4, 2, 7, -6786488927384275890668622881645897766074843136000000⟩, + ⟨6, 5, 3, 4, 3, 7, -3222625539550673958304408377610695230774417817600000⟩, + ⟨6, 5, 4, 4, 4, 7, -1211332245628077412913164741339784081706477158400000⟩, + ⟨6, 5, 5, 4, 5, 7, 155452137052440416083546142916679229093235916800000⟩, + ⟨6, 5, 6, 4, 6, 7, 40655802618700642130619401716648310158550630400000⟩, + ⟨6, 5, 7, 4, 7, 7, -10645940269136668465456234523997740644014489600000⟩, + ⟨6, 5, 8, 4, 8, 7, 1267037058259462793466246038296096256557056000000⟩, + ⟨6, 5, 1, 5, 0, 7, -196997447840632164785569435461650269180412087500800000⟩, + ⟨6, 5, 2, 5, 1, 7, 7028780930829879571908856089956541689884783411200000⟩, + ⟨6, 5, 3, 5, 2, 7, -4024052091300325635446255909547959791993120358400000⟩, + ⟨6, 5, 4, 5, 3, 7, -1154258993900949038051931725267152261842122833920000⟩, + ⟨6, 5, 5, 5, 4, 7, 103117097488203312464697291609768635485755801600000⟩, + ⟨6, 5, 6, 5, 5, 7, 33963096951303592065014925831967631180247859200000⟩, + ⟨6, 5, 7, 5, 6, 7, 3372613240071390161969058050056851541721088000000⟩, + ⟨6, 5, 8, 5, 7, 7, -2077310092274232119812841735702961083488665600000⟩, + ⟨6, 5, 2, 6, 0, 7, -126532681845002974946145091712367138477836127436800000⟩, + ⟨6, 5, 3, 6, 1, 7, -979703524465533389988352853721416779867304755200000⟩, + ⟨6, 5, 4, 6, 2, 7, 1461981602907199902797696698784718449273858949120000⟩, + ⟨6, 5, 5, 6, 3, 7, -939660054132039927359046659311107446765361561600000⟩, + ⟨6, 5, 6, 6, 4, 7, -22645175543670386336205612797393118961021747200000⟩, + ⟨6, 5, 7, 6, 5, 7, 21071051352357133734139336818930434717201203200000⟩, + ⟨6, 5, 8, 6, 6, 7, 3102953929730637929269835161619398817061273600000⟩, + ⟨6, 5, 3, 7, 0, 7, 102976677451493781057121956031460776138730215833600000⟩, + ⟨6, 5, 4, 7, 1, 7, 1404404827031902870772507019586964895156425195520000⟩, + ⟨6, 5, 5, 7, 2, 7, 52056903186088490312613151059528232557399244800000⟩, + ⟨6, 5, 6, 7, 3, 7, -114317161195660417374856448016591522860787302400000⟩, + ⟨6, 5, 7, 7, 4, 7, 16384628985218229996394077297484104795684864000000⟩, + ⟨6, 5, 8, 7, 5, 7, 8015258433095032078825771090354329171787776000000⟩ +] + +def collectedFourData_10_4_49 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 4, 8, 19524308952350274189288260974714358554832142336000000⟩, + ⟨6, 6, 1, 0, 5, 8, -21573126671959103626602079221993679527313460428800000⟩, + ⟨6, 6, 2, 0, 6, 8, 4602295688114723074395863805830840298677836185600000⟩, + ⟨6, 6, 3, 0, 7, 8, -263089983611734015012401891131476901321685073920000⟩, + ⟨6, 6, 4, 0, 8, 8, 169233608823228899601677988650667080111011921920000⟩, + ⟨6, 6, 0, 1, 3, 8, 15345378687344612656915657175610222122173150003200000⟩, + ⟨6, 6, 1, 1, 4, 8, -9423473682238591689941985100568799226739294208000000⟩, + ⟨6, 6, 2, 1, 5, 8, -2247243867943762322034696692725983407993624985600000⟩, + ⟨6, 6, 3, 1, 6, 8, 1247495235241612220139155883504353458998466314240000⟩, + ⟨6, 6, 4, 1, 7, 8, -197368311610557902834600120325083650911130091520000⟩, + ⟨6, 6, 5, 1, 8, 8, -138402593022220827317598570807067418082410496000000⟩, + ⟨6, 6, 0, 2, 2, 8, 12801090208525834854412858568792379279713029324800000⟩, + ⟨6, 6, 1, 2, 3, 8, -14233571020263888942636112890486946652753598873600000⟩, + ⟨6, 6, 2, 2, 4, 8, -8279132579998167378316852241270835991590784204800000⟩, + ⟨6, 6, 3, 2, 5, 8, 530870723966770555063777240692519730175583191040000⟩, + ⟨6, 6, 4, 2, 6, 8, 130123587656300660746790850266830434086997196800000⟩, + ⟨6, 6, 5, 2, 7, 8, -70943566025826970680004831048930336481004748800000⟩, + ⟨6, 6, 6, 2, 8, 8, 15719229878875526236626520140418024138289971200000⟩, + ⟨6, 6, 0, 3, 1, 8, 41034399014159639061234897852045250573057287782400000⟩, + ⟨6, 6, 1, 3, 2, 8, 36677223576932325355295098838863245472259742105600000⟩, + ⟨6, 6, 2, 3, 3, 8, 9430738845410946661005004470755978804012777472000000⟩, + ⟨6, 6, 3, 3, 4, 8, -57842979126019089058934736183796290918474055680000⟩, + ⟨6, 6, 4, 3, 5, 8, 357019426241183247891487159652361475760188293120000⟩, + ⟨6, 6, 5, 3, 6, 8, 48540650344512813694013770460716924927161139200000⟩, + ⟨6, 6, 6, 3, 7, 8, 33328972463977848107030584865004570909081600000⟩, + ⟨6, 6, 7, 3, 8, 8, -592698555028023839474415524716203274036838400000⟩, + ⟨6, 6, 0, 4, 0, 8, 131040380535125696987014214797295186189469351936000000⟩, + ⟨6, 6, 1, 4, 1, 8, -16512391672780077182503991434578698948628499660800000⟩, + ⟨6, 6, 2, 4, 2, 8, -2248623706613282966125081269711767916446220288000000⟩, + ⟨6, 6, 3, 4, 3, 8, -854223415177849071103850928547013286114770288640000⟩, + ⟨6, 6, 4, 4, 4, 8, -267573844958662416754652094033055269367106764800000⟩, + ⟨6, 6, 5, 4, 5, 8, 29432712501901154435171206280248054919253196800000⟩, + ⟨6, 6, 6, 4, 6, 8, 6735412269731398099618744415523667644619161600000⟩, + ⟨6, 6, 7, 4, 7, 8, -1567736779783411488689278851909296010874060800000⟩, + ⟨6, 6, 8, 4, 8, 8, 167927162150865613987938251784016488510259200000⟩, + ⟨6, 6, 1, 5, 0, 8, -87030399390434096990695631150906846275871912755200000⟩, + ⟨6, 6, 2, 5, 1, 8, 2328904327225833443313805999832197187302431129600000⟩, + ⟨6, 6, 3, 5, 2, 8, -1066658064394104915878964347070787550504036597760000⟩, + ⟨6, 6, 4, 5, 3, 8, -254966808809795459838974935393404849437792010240000⟩, + ⟨6, 6, 5, 5, 4, 8, 19523796468471615505778867964341222052043161600000⟩, + ⟨6, 6, 6, 5, 5, 8, 5626637409407962874990185010629428481150156800000⟩, + ⟨6, 6, 7, 5, 6, 8, 496655972772351245294845144285082523009024000000⟩, + ⟨6, 6, 8, 5, 7, 8, -275316958118150069989304523968717923465297920000⟩, + ⟨6, 6, 2, 6, 0, 8, -41925123742549802184408694703103356250645489254400000⟩, + ⟨6, 6, 3, 6, 1, 8, -259690640522699113080075318850518423824530145280000⟩, + ⟨6, 6, 4, 6, 2, 8, 322940332976834395340030176538343262751702384640000⟩, + ⟨6, 6, 5, 6, 3, 8, -177911637287169920439896653963407762078144921600000⟩, + ⟨6, 6, 6, 6, 4, 8, -3751606987999824755192680718082552416226508800000⟩, + ⟨6, 6, 7, 6, 5, 8, 3102953929730637929269835161619398817061273600000⟩, + ⟨6, 6, 8, 6, 6, 8, 411250992469265386218164534484207874363883520000⟩, + ⟨6, 6, 3, 7, 0, 8, 27296093826820371667799399013487078737846510551040000⟩, + ⟨6, 6, 4, 7, 1, 8, 310222072271004402075505589822961101085018685440000⟩, + ⟨6, 6, 5, 7, 2, 8, 9856254756398611920354072017954715902725324800000⟩, + ⟨6, 6, 6, 7, 3, 8, -18938826946290442046279405238497198189681049600000⟩, + ⟨6, 6, 7, 7, 4, 8, 2412824497775905760159691103435826367823872000000⟩, + ⟨6, 6, 8, 7, 5, 8, 1062304842468004527881444999753378796090163200000⟩ +] + +def collectedFourData_10_4_50 : List CollectedFourTerm := [ + ⟨7, 0, 3, 0, 7, 3, -69294268798279047346732539104403828364858538065920000⟩, + ⟨7, 0, 4, 0, 8, 3, 267442774183439550077862622687191903616735138283520000⟩, + ⟨7, 0, 3, 1, 6, 3, 328573018891431293381697593372362433751448540938240000⟩, + ⟨7, 0, 4, 1, 7, 3, -311904527475773881559704029064522481092481117061120000⟩, + ⟨7, 0, 5, 1, 8, 3, -765519969189316444539585714554148181355859542016000000⟩, + ⟨7, 0, 3, 2, 5, 3, 139824018150304451961248754608484955878616769495040000⟩, + ⟨7, 0, 4, 2, 6, 3, 205636537041845019078515411008634199908182445260800000⟩, + ⟨7, 0, 5, 2, 7, 3, -392396668966685623123986592879981649104779136204800000⟩, + ⟨7, 0, 6, 2, 8, 3, 231852773078696873807022268722820629920604173107200000⟩, + ⟨7, 0, 3, 3, 4, 3, -15235041975474290126210481312724651529436062023680000⟩, + ⟨7, 0, 4, 3, 5, 3, 564203921757981724985700071741759632896223315230720000⟩, + ⟨7, 0, 5, 3, 6, 3, 268483677543490116270573545020338099911973352243200000⟩, + ⟨7, 0, 6, 3, 7, 3, 491589902888395991982308537508096835279493529600000⟩, + ⟨7, 0, 7, 3, 8, 3, -19669685502673742797129825554866526727908517478400000⟩, + ⟨7, 0, 3, 4, 3, 3, -224990651991046578171416244623988980894363434352640000⟩, + ⟨7, 0, 4, 4, 4, 3, -422851535769246338540704008504869409698358283468800000⟩, + ⟨7, 0, 5, 4, 5, 3, 162795571062717939075301234911735178303533534412800000⟩, + ⟨7, 0, 6, 4, 6, 3, 99344816800733443056717168556389091543550106009600000⟩, + ⟨7, 0, 7, 4, 7, 3, -52027947677139459481993979104469502126331841740800000⟩, + ⟨7, 0, 8, 4, 8, 3, 11145883312328470238223696979224014394101229158400000⟩, + ⟨7, 0, 3, 5, 2, 3, -280943005185091956156855389166630093218572413173760000⟩, + ⟨7, 0, 4, 5, 3, 3, -402928420347145306647220799702103145987186297405440000⟩, + ⟨7, 0, 5, 5, 4, 3, 107988266293560610479698626581405754737697593753600000⟩, + ⟨7, 0, 6, 5, 5, 3, 82990801491662658596623768263564887724655430860800000⟩, + ⟨7, 0, 7, 5, 6, 3, 16482352967765787123616683896880649206365159424000000⟩, + ⟨7, 0, 8, 5, 7, 3, -18273700631784941084036800390017468260398493859840000⟩, + ⟨7, 0, 3, 6, 1, 3, -68398928768546912819275163620038532639959055073280000⟩, + ⟨7, 0, 4, 6, 2, 3, 510348146255411365785083712580185180516137136291840000⟩, + ⟨7, 0, 5, 6, 3, 3, -984048839840947061332273230574165606025232226713600000⟩, + ⟨7, 0, 6, 6, 4, 3, -55334802682547153418918447406185231224419437772800000⟩, + ⟨7, 0, 7, 6, 5, 3, 102976677451493781057121956031460776138730215833600000⟩, + ⟨7, 0, 8, 6, 6, 3, 27296093826820371667799399013487078737846510551040000⟩, + ⟨7, 0, 3, 7, 0, 3, 7189414195145267037346388576456508719292625232855040000⟩, + ⟨7, 0, 4, 7, 1, 3, 490249260758569509160890377813146784967309278576640000⟩, + ⟨7, 0, 5, 7, 2, 3, 54516029452056059234200835200183309265577757900800000⟩, + ⟨7, 0, 6, 7, 3, 3, -279340628019945894023888793866807778250187184537600000⟩, + ⟨7, 0, 7, 7, 4, 3, 80073586550510180619579974104230993605607555072000000⟩, + ⟨7, 0, 8, 7, 5, 3, 70508699513617206502382180654928649863966385766400000⟩ +] + +def collectedFourData_10_4_51 : List CollectedFourTerm := [ + ⟨7, 1, 2, 0, 6, 4, 16531831061290137392542258438446222235884501073920000⟩, + ⟨7, 1, 3, 0, 7, 4, -4725206133776730471057412781414237287050085662720000⟩, + ⟨7, 1, 4, 0, 8, 4, 9118519171366439619309093094320948576172281692160000⟩, + ⟨7, 1, 2, 1, 5, 4, -8072287939757512586620408117901407421852465233920000⟩, + ⟨7, 1, 3, 1, 6, 4, 22405536145839056046922009206885616440951271587840000⟩, + ⟨7, 1, 4, 1, 7, 4, -10634452256590246914275664619925081224014421032960000⟩, + ⟨7, 1, 5, 1, 8, 4, -17400379168788090183217941295122200327777943552000000⟩, + ⟨7, 1, 2, 2, 4, 4, -29739336718414922624236534188385443088677847695360000⟩, + ⟨7, 1, 3, 2, 5, 4, 9534660220406802048711934812380015427194600816640000⟩, + ⟨7, 1, 4, 2, 6, 4, 7011222161729945903059907668892758048942483046400000⟩, + ⟨7, 1, 5, 2, 7, 4, -8919232808283796868617894603360672001289722265600000⟩, + ⟨7, 1, 6, 2, 8, 4, 3952535196936125896271284941466782821818092748800000⟩, + ⟨7, 1, 2, 3, 3, 4, 33876002747521383531481801863060768182585681510400000⟩, + ⟨7, 1, 3, 3, 4, 4, -1038884095889975578465732118948895373409522810880000⟩, + ⟨7, 1, 4, 3, 5, 4, 19236654618238157310163864156003883292523505909760000⟩, + ⟨7, 1, 5, 3, 6, 4, 6102672664221549383012001889660555801143961190400000⟩, + ⟨7, 1, 6, 3, 7, 4, 8380431977689925920955552973983970857739878400000⟩, + ⟨7, 1, 7, 3, 8, 4, -268256870874150816690761728235955631388759162880000⟩, + ⟨7, 1, 2, 4, 2, 4, -8077244435672205761870882246023049722306599321600000⟩, + ⟨7, 1, 3, 4, 3, 4, -15342209785420555069136763964218763797458048778240000⟩, + ⟨7, 1, 4, 4, 4, 4, -14417214476353461653363597244252245612697118310400000⟩, + ⟨7, 1, 5, 4, 5, 4, 3700366780099159186885801167337342742793132441600000⟩, + ⟨7, 1, 6, 4, 6, 4, 1693591496983259939895961868806086508170077798400000⟩, + ⟨7, 1, 7, 4, 7, 4, -709561647031737724732635907828324769991292354560000⟩, + ⟨7, 1, 8, 4, 8, 4, 126673766597472167385677187204356549328135782400000⟩, + ⟨7, 1, 2, 5, 1, 4, 8365619139820316986513531098662389103324792094720000⟩, + ⟨7, 1, 3, 5, 2, 4, -19157624928646821504671096698320758199636103004160000⟩, + ⟨7, 1, 4, 5, 3, 4, -13737931551307345877192725879389336844514120171520000⟩, + ⟨7, 1, 5, 5, 4, 4, 2454588847992963431364708179682938623108526899200000⟩, + ⟨7, 1, 6, 5, 5, 4, 1414794654219623591583142224680142475082543923200000⟩, + ⟨7, 1, 7, 5, 6, 4, 224787754292009326519446834469773174234729676800000⟩, + ⟨7, 1, 8, 5, 7, 4, -207681923795344680784939005769124233246660362240000⟩, + ⟨7, 1, 2, 6, 0, 4, -150598551224212498790730371570317232497594812334080000⟩, + ⟨7, 1, 3, 6, 1, 4, -4664152510242265919570778495503166439925722644480000⟩, + ⟨7, 1, 4, 6, 2, 4, 17400430316017306466841007166249472462284358942720000⟩, + ⟨7, 1, 5, 6, 3, 4, -22367571876631155168749256672089176758686004019200000⟩, + ⟨7, 1, 6, 6, 4, 4, -943326026745629526235601812315662383297278771200000⟩, + ⟨7, 1, 7, 6, 5, 4, 1404404827031902870772507019586964895156425195520000⟩, + ⟨7, 1, 8, 6, 6, 4, 310222072271004402075505589822961101085018685440000⟩, + ⟨7, 1, 3, 7, 0, 4, 490249260758569509160890377813146784967309278576640000⟩, + ⟨7, 1, 4, 7, 1, 4, 16715154472294773641627150660763814446631086981120000⟩, + ⟨7, 1, 5, 7, 2, 4, 1239157202191810387328477014054789528271034777600000⟩, + ⟨7, 1, 6, 7, 3, 4, -4762089534328391978190742108260534318038148710400000⟩, + ⟨7, 1, 7, 7, 4, 4, 1092050493882603608100870407023059860046898790400000⟩, + ⟨7, 1, 8, 7, 5, 4, 801336448175443645266581173360371925873223270400000⟩ +] + +def collectedFourData_10_4_52 : List CollectedFourTerm := [ + ⟨7, 2, 1, 0, 5, 5, -4308606266094654153552280053367357242131192217600000⟩, + ⟨7, 2, 2, 0, 6, 5, 3676700246887438272488690719129363481734466764800000⟩, + ⟨7, 2, 3, 0, 7, 5, -525445925930456118722293842652552321500079718400000⟩, + ⟨7, 2, 4, 0, 8, 5, 675990085718398885893100638699664064692145356800000⟩, + ⟨7, 2, 1, 1, 4, 5, -1882065514798374778729737210616349027274326016000000⟩, + ⟨7, 2, 2, 1, 5, 5, -1795287101048851992832615732542580466914217164800000⟩, + ⟨7, 2, 3, 1, 6, 5, 2491509862810777460841419804375388253485583564800000⟩, + ⟨7, 2, 4, 1, 7, 5, -788371900897522472920743001657904985203854540800000⟩, + ⟨7, 2, 5, 1, 8, 5, -967466612570524745566982889058277945738526720000000⟩, + ⟨7, 2, 1, 2, 3, 5, -2842742928243467431904724492939892054480335667200000⟩, + ⟨7, 2, 2, 2, 4, 5, -6614066297283572053274539122785007551746827878400000⟩, + ⟨7, 2, 3, 2, 5, 5, 1060260277775357415458807189561597872141290700800000⟩, + ⟨7, 2, 4, 2, 6, 5, 519768240986034155636782531858880281624707072000000⟩, + ⟨7, 2, 5, 2, 7, 5, -495912179157370302164476523353573354704470016000000⟩, + ⟨7, 2, 6, 2, 8, 5, 175809770624068423560885402057094969042560614400000⟩, + ⟨7, 2, 1, 3, 2, 5, 7325211487861455793538007676342367491185652531200000⟩, + ⟨7, 2, 2, 3, 3, 5, 7534066081585727728081678435594905220993253376000000⟩, + ⟨7, 2, 3, 3, 4, 5, -115524571890587090409831450498936228233714073600000⟩, + ⟨7, 2, 4, 3, 5, 5, 1426085481637407804425645475295160892752973004800000⟩, + ⟨7, 2, 5, 3, 6, 5, 339310539891664644813554462785962385965318144000000⟩, + ⟨7, 2, 6, 3, 7, 5, 372763745372938150383452370211484330046259200000⟩, + ⟨7, 2, 7, 3, 8, 5, -9943444858140953934826710221518524258661171200000⟩, + ⟨7, 2, 1, 4, 1, 5, -3297871250254359032091614331656883547785501081600000⟩, + ⟨7, 2, 2, 4, 2, 5, -1796389432042054558150675728932277929801416704000000⟩, + ⟨7, 2, 3, 4, 3, 5, -1706063481314468307955693517832038679411739852800000⟩, + ⟨7, 2, 4, 4, 4, 5, -1068802276612449571088054224746026909451681792000000⟩, + ⟨7, 2, 5, 4, 5, 5, 205741569151126354775869186163077292413157376000000⟩, + ⟨7, 2, 6, 4, 6, 5, 75331380438131320192749294892193621296231219200000⟩, + ⟨7, 2, 7, 4, 7, 5, -26301235408138895141615562760384239186110054400000⟩, + ⟨7, 2, 8, 4, 8, 5, 4024629535214278176726397857958500665131008000000⟩, + ⟨7, 2, 1, 5, 0, 5, -17381797727157737797570853803498785094259598950400000⟩, + ⟨7, 2, 2, 5, 1, 5, 1860524332889190947627410714030119129665293516800000⟩, + ⟨7, 2, 3, 5, 2, 5, -2130340070733696690608378372434279130815738675200000⟩, + ⟨7, 2, 4, 5, 3, 5, -1018444481218336511144205094407232620750018969600000⟩, + ⟨7, 2, 5, 5, 4, 5, 136475920150108747092281266900328863877824512000000⟩, + ⟨7, 2, 6, 5, 5, 5, 62930425978577274944039542986801687404583321600000⟩, + ⟨7, 2, 7, 5, 6, 5, 8332180392264883997278635714323936006111232000000⟩, + ⟨7, 2, 8, 5, 7, 5, -6598389128925963625717290480801164580146380800000⟩, + ⟨7, 2, 2, 6, 0, 5, -33493309265872793337992362031539191601341608755200000⟩, + ⟨7, 2, 3, 6, 1, 5, -518656724181106143147262512648044454394567065600000⟩, + ⟨7, 2, 4, 6, 2, 5, 1289959275163635385788133025117599478868187545600000⟩, + ⟨7, 2, 5, 6, 3, 5, -1243644105970321991508125483028486068436467712000000⟩, + ⟨7, 2, 6, 6, 4, 5, -41959381541857293122236574361747883426421145600000⟩, + ⟨7, 2, 7, 6, 5, 5, 52056903186088490312613151059528232557399244800000⟩, + ⟨7, 2, 8, 6, 6, 5, 9856254756398611920354072017954715902725324800000⟩, + ⟨7, 2, 3, 7, 0, 5, 54516029452056059234200835200183309265577757900800000⟩, + ⟨7, 2, 4, 7, 1, 5, 1239157202191810387328477014054789528271034777600000⟩, + ⟨7, 2, 5, 7, 2, 5, 68897534313350093235898956276247225838862336000000⟩, + ⟨7, 2, 6, 7, 3, 5, -211818953407559283146677602854187097847444275200000⟩, + ⟨7, 2, 7, 7, 4, 5, 40478903048569074701096120681703054136836096000000⟩, + ⟨7, 2, 8, 7, 5, 5, 25459749272466602837171889970902244647763968000000⟩ +] + +def collectedFourData_10_4_53 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 4, 6, -19980634441716701040968949177977154953212329984000000⟩, + ⟨7, 3, 1, 0, 5, 6, 66232012438838527101065134658901439623108073881600000⟩, + ⟨7, 3, 2, 0, 6, 6, -28259167982231658389139580116394729212937135718400000⟩, + ⟨7, 3, 3, 0, 7, 6, 2692389677223638535295025049226540799444700364800000⟩, + ⟨7, 3, 4, 0, 8, 6, -2597834485257705251510642453462303413095314227200000⟩, + ⟨7, 3, 0, 1, 3, 6, -15704033503558875140455282720796993656372120780800000⟩, + ⟨7, 3, 1, 1, 4, 6, 28931162164376924684442527315675894162449760256000000⟩, + ⟨7, 3, 2, 1, 5, 6, 13798601016719328041339136081428401937331938918400000⟩, + ⟨7, 3, 3, 1, 6, 6, -12766519073211834823632901422652483345554446745600000⟩, + ⟨7, 3, 4, 1, 7, 6, 3029718563376868862982089666917064481726214963200000⟩, + ⟨7, 3, 5, 1, 8, 6, 2974384604235929493462368599699245482328981504000000⟩, + ⟨7, 3, 0, 2, 2, 6, -13100279479095441873560753598913381165916435251200000⟩, + ⟨7, 3, 1, 2, 3, 6, 43698721432371729262196874985230474229197255475200000⟩, + ⟨7, 3, 2, 2, 4, 6, 50835803299108485284508895252178943614739755827200000⟩, + ⟨7, 3, 3, 2, 5, 6, -5432783253572046383158739359404933572164426137600000⟩, + ⟨7, 3, 4, 2, 6, 6, -1997472876159529247144131929588716295356940288000000⟩, + ⟨7, 3, 5, 2, 7, 6, 1524635094972073495673078157956092562045612851200000⟩, + ⟨7, 3, 6, 2, 8, 6, -450425427454875895100836974796316201670043238400000⟩, + ⟨7, 3, 0, 3, 1, 6, -41993462008742070100771412308650157726378858905600000⟩, + ⟨7, 3, 1, 3, 2, 6, -112603349765101149238507603877437757173959701299200000⟩, + ⟨7, 3, 2, 3, 3, 6, -57906934123608209106621683193212634897221419008000000⟩, + ⟨7, 3, 3, 3, 4, 6, 591948951308575241154991533411413370569175859200000⟩, + ⟨7, 3, 4, 3, 5, 6, -5480456180338574587118288090903190048005632819200000⟩, + ⟨7, 3, 5, 3, 6, 6, -1043178165319042094155461763892306002209197260800000⟩, + ⟨7, 3, 6, 3, 7, 6, -955022401504119244321324221460547844125491200000⟩, + ⟨7, 3, 7, 3, 8, 6, 21835843454322686457767826252809741780228505600000⟩, + ⟨7, 3, 0, 4, 0, 6, -134103078729483856276478377362108862095251472384000000⟩, + ⟨7, 3, 1, 4, 1, 6, 50694966348483740372319792397796713248782391705600000⟩, + ⟨7, 3, 2, 4, 2, 6, 13807073547689265781934320885715392535967301632000000⟩, + ⟨7, 3, 3, 4, 3, 6, 8741884709916359678036371868659574363454544281600000⟩, + ⟨7, 3, 4, 4, 4, 6, 4107414399657954313028143920533478460429959168000000⟩, + ⟨7, 3, 5, 4, 5, 6, -632532996780643791402454407972798671579460403200000⟩, + ⟨7, 3, 6, 4, 6, 6, -192999337375655424960448658680491721895392051200000⟩, + ⟨7, 3, 7, 4, 7, 6, 57757614913226745748538998745069858405430067200000⟩, + ⟨7, 3, 8, 4, 8, 6, -7733339303234822740882263620216484073046016000000⟩, + ⟨7, 3, 1, 5, 0, 6, 267193466326634070133495565157094198683292296806400000⟩, + ⟨7, 3, 2, 5, 1, 6, -14300015265768489196269760866626483468374533734400000⟩, + ⟨7, 3, 3, 5, 2, 6, 10915881791761030242167960440061075564584658534400000⟩, + ⟨7, 3, 4, 5, 3, 6, 3913889050336669303213124900312418804247717478400000⟩, + ⟨7, 3, 5, 5, 4, 6, -419582309579520073991529384866495469462120038400000⟩, + ⟨7, 3, 6, 5, 5, 6, -161228035965809917880257653798297704687311257600000⟩, + ⟨7, 3, 7, 5, 6, 6, -18297500441178983662608540606367341861666816000000⟩, + ⟨7, 3, 8, 5, 7, 6, 12678827092601889518295263898478534136011161600000⟩, + ⟨7, 3, 2, 6, 0, 6, 257430029447301892511679112962590912368315308441600000⟩, + ⟨7, 3, 3, 6, 1, 6, 2657601746050378604854773155735386991931634483200000⟩, + ⟨7, 3, 4, 6, 2, 6, -4957322245394753866111137329558774919937287782400000⟩, + ⟨7, 3, 5, 6, 3, 6, 3823466188790296426157060879513161449863538278400000⟩, + ⟨7, 3, 6, 6, 4, 6, 107500125275437577508561810047059430370548121600000⟩, + ⟨7, 3, 7, 6, 5, 6, -114317161195660417374856448016591522860787302400000⟩, + ⟨7, 3, 8, 6, 6, 6, -18938826946290442046279405238497198189681049600000⟩, + ⟨7, 3, 3, 7, 0, 6, -279340628019945894023888793866807778250187184537600000⟩, + ⟨7, 3, 4, 7, 1, 6, -4762089534328391978190742108260534318038148710400000⟩, + ⟨7, 3, 5, 7, 2, 6, -211818953407559283146677602854187097847444275200000⟩, + ⟨7, 3, 6, 7, 3, 6, 542681116601052275059926671533624414308610867200000⟩, + ⟨7, 3, 7, 7, 4, 6, -88891828011455747219640576200498227496091648000000⟩, + ⟨7, 3, 8, 7, 5, 6, -48920994585104703819302039808535314548391936000000⟩ +] + +def collectedFourData_10_4_54 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 4, 7, 22909965838390926595435501683292694034430033920000000⟩, + ⟨7, 4, 1, 0, 5, 7, -37971095132335135658844847462431632820749205504000000⟩, + ⟨7, 4, 2, 0, 6, 7, 10800734330747191385979822743774972426965745664000000⟩, + ⟨7, 4, 3, 0, 7, 7, -771779240903952439194167365208589846662086656000000⟩, + ⟨7, 4, 4, 0, 8, 7, 595739834835138183491714914213781441009103667200000⟩, + ⟨7, 4, 0, 1, 3, 7, 18006378733415676070291663052507287941707464704000000⟩, + ⟨7, 4, 1, 1, 4, 7, -16586358626004565637924178129821911734697328640000000⟩, + ⟨7, 4, 2, 1, 5, 7, -5273864531725469510566869312609976056664817664000000⟩, + ⟨7, 4, 3, 1, 6, 7, 3659549909383657139116282161815518603307384832000000⟩, + ⟨7, 4, 4, 1, 7, 7, -694780228219212156591474156558349441866871603200000⟩, + ⟨7, 4, 5, 1, 8, 7, -568409125279560188745998664965101545502801920000000⟩, + ⟨7, 4, 0, 2, 2, 7, 15020892165107039258993937220641316627814547456000000⟩, + ⟨7, 4, 1, 2, 3, 7, -25052663320509202777487762842074096092250636288000000⟩, + ⟨7, 4, 2, 2, 4, 7, -19429588523944651023804217633568159465956442112000000⟩, + ⟨7, 4, 3, 2, 5, 7, 1557318901831929137323656113677510707429507072000000⟩, + ⟨7, 4, 4, 2, 6, 7, 458063886704044931273064642018443702606757888000000⟩, + ⟨7, 4, 5, 2, 7, 7, -291359933570599892900686595773311151899672576000000⟩, + ⟨7, 4, 6, 2, 8, 7, 73780233740360127664318132873618202774470656000000⟩, + ⟨7, 4, 0, 3, 1, 7, 48150061644058024393174795083351756072579760128000000⟩, + ⟨7, 4, 1, 3, 2, 7, 64555980540355796125517145152555252964390862848000000⟩, + ⟨7, 4, 2, 3, 3, 7, 22132194825071410742996911771965916825968967680000000⟩, + ⟨7, 4, 3, 3, 4, 7, -169683428873462862418385839788250275589914624000000⟩, + ⟨7, 4, 4, 3, 5, 7, 1256787558339088702051449575840761509858980659200000⟩, + ⟨7, 4, 5, 3, 6, 7, 199352830032568288253382898108898180736221184000000⟩, + ⟨7, 4, 6, 3, 7, 7, 156433832806459204808150926773469795319808000000⟩, + ⟨7, 4, 7, 3, 8, 7, -3129645539098329214998362950074932989526016000000⟩, + ⟨7, 4, 0, 4, 0, 7, 153763733653072013715609358118476210642008145920000000⟩, + ⟨7, 4, 1, 4, 1, 7, -29063640361620893112700239472505604604705112064000000⟩, + ⟨7, 4, 2, 4, 2, 7, -5277102757145724744211656694141793675740446720000000⟩, + ⟨7, 4, 3, 4, 3, 7, -2505879888993759960313805969150949240185290752000000⟩, + ⟨7, 4, 4, 4, 4, 7, -941919275434116202373284063371510905221152768000000⟩, + ⟨7, 4, 5, 4, 5, 7, 120877954686328763607299752969819983798337536000000⟩, + ⟨7, 4, 6, 4, 6, 7, 31613526580350555208185247073332212906590208000000⟩, + ⟨7, 4, 7, 4, 7, 7, -8278171724406426675211825883893617961992192000000⟩, + ⟨7, 4, 8, 4, 8, 7, 985234754685427841866833679820837219205120000000⟩, + ⟨7, 4, 1, 5, 0, 7, -153183153508975953473863520566962069268611465216000000⟩, + ⟨7, 4, 2, 5, 1, 7, 5465506483004298979599815843083744864081281024000000⟩, + ⟨7, 4, 3, 5, 2, 7, -3129060787266874364197587922240833145974816768000000⟩, + ⟨7, 4, 4, 5, 3, 7, -897539712265126278591720144402169974361581158400000⟩, + ⟨7, 4, 5, 5, 4, 7, 80182775701307775859633547905280027689746432000000⟩, + ⟨7, 4, 6, 5, 5, 7, 26409348704560741715439135893327675847081984000000⟩, + ⟨7, 4, 7, 5, 6, 7, 2622508755028156876363402118770565327093760000000⟩, + ⟨7, 4, 8, 5, 7, 7, -1615294584973581499816146434027148344819712000000⟩, + ⟨7, 4, 2, 6, 0, 7, -98390489011034217172567952740325159177275047936000000⟩, + ⟨7, 4, 3, 6, 1, 7, -761807206268459606164550634058271599733243904000000⟩, + ⟨7, 4, 4, 6, 2, 7, 1136821592158925449532596546670346771819292262400000⟩, + ⟨7, 4, 5, 6, 3, 7, -730669822863929660216932727702498057631301632000000⟩, + ⟨7, 4, 6, 6, 4, 7, -17608651480348219805868847342562183158431744000000⟩, + ⟨7, 4, 7, 6, 5, 7, 16384628985218229996394077297484104795684864000000⟩, + ⟨7, 4, 8, 6, 6, 7, 2412824497775905760159691103435826367823872000000⟩, + ⟨7, 4, 3, 7, 0, 7, 80073586550510180619579974104230993605607555072000000⟩, + ⟨7, 4, 4, 7, 1, 7, 1092050493882603608100870407023059860046898790400000⟩, + ⟨7, 4, 5, 7, 2, 7, 40478903048569074701096120681703054136836096000000⟩, + ⟨7, 4, 6, 7, 3, 7, -88891828011455747219640576200498227496091648000000⟩, + ⟨7, 4, 7, 7, 4, 7, 12740516004353160347144916667737033702113280000000⟩, + ⟨7, 4, 8, 7, 5, 7, 6232581063507905532280568987706841387499520000000⟩ +] + +def collectedFourData_10_4_55 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 4, 8, 50433356577183599820457658019247344448186613760000000⟩, + ⟨7, 5, 1, 0, 5, 8, -55725669604336649241228111388398977262035140608000000⟩, + ⟨7, 5, 2, 0, 6, 8, 11888216893043163048096879568879808110129053696000000⟩, + ⟨7, 5, 3, 0, 7, 8, -679589274465908819941168615952088876593656627200000⟩, + ⟨7, 5, 4, 0, 8, 8, 437148324145838170173368614923426078987072307200000⟩, + ⟨7, 5, 0, 1, 3, 8, 39638737383204671877019457973541591127804608512000000⟩, + ⟨7, 5, 1, 1, 4, 8, -24341829950136814430681763942713343048186593280000000⟩, + ⟨7, 5, 2, 1, 5, 8, -5804868770746122888856577028948490000527261696000000⟩, + ⟨7, 5, 3, 1, 6, 8, 3222412233939998857023562327476489681474315878400000⟩, + ⟨7, 5, 4, 1, 7, 8, -509823239367134080182363145083763554258203443200000⟩, + ⟨7, 5, 5, 1, 8, 8, -357508547018574127268480955286298199179919360000000⟩, + ⟨7, 5, 0, 2, 2, 8, 33066570941839223681219829085500708412056403968000000⟩, + ⟨7, 5, 1, 2, 3, 8, -36766820499694232482520743840987471701161803776000000⟩, + ⟨7, 5, 2, 2, 4, 8, -21385875760102788623313647382170028525924384768000000⟩, + ⟨7, 5, 3, 2, 5, 8, 1371295270093583885492049224537823480419608166400000⟩, + ⟨7, 5, 4, 2, 6, 8, 336122999865899806942137497031860901786943488000000⟩, + ⟨7, 5, 5, 2, 7, 8, -183254740076564950275830170728588722263031808000000⟩, + ⟨7, 5, 6, 2, 8, 8, 40604434581261654728466863550242002820923392000000⟩, + ⟨7, 5, 0, 3, 1, 8, 105996195945384491243429466428082886225044701184000000⟩, + ⟨7, 5, 1, 3, 2, 8, 94741150605171385959561958100486377405358800896000000⟩, + ⟨7, 5, 2, 3, 3, 8, 24360596635593238423124635417559452605764075520000000⟩, + ⟨7, 5, 3, 3, 4, 8, -149414537480874239426256666398506116866428108800000⟩, + ⟨7, 5, 4, 3, 5, 8, 922218966753014160403174453583277791965819699200000⟩, + ⟨7, 5, 5, 3, 6, 8, 125385637631928276530890670407894798562230272000000⟩, + ⟨7, 5, 6, 3, 7, 8, 86092263584293869195912051047584870957056000000⟩, + ⟨7, 5, 7, 3, 8, 8, -1531003101900388889207866977717170045190144000000⟩, + ⟨7, 5, 0, 4, 0, 8, 338491172909977757395017259080819991859964149760000000⟩, + ⟨7, 5, 1, 4, 1, 8, -42653255447240193575531732612142370945895497728000000⟩, + ⟨7, 5, 2, 4, 2, 8, -5808433040078715284296467571601832757249966080000000⟩, + ⟨7, 5, 3, 4, 3, 8, -2206549496803471500629061816226856665038087782400000⟩, + ⟨7, 5, 4, 4, 4, 8, -691171562919967997860876698454995751422394368000000⟩, + ⟨7, 5, 5, 4, 5, 8, 76027811702058952988266876837166363587903488000000⟩, + ⟨7, 5, 6, 4, 6, 8, 17398282803387537557046481749864721579769856000000⟩, + ⟨7, 5, 7, 4, 7, 8, -4049630039503375696780639163776378211401728000000⟩, + ⟨7, 5, 8, 4, 8, 8, 433773634110089627527630274188664710889472000000⟩, + ⟨7, 5, 1, 5, 0, 8, -224808733370514650583107590382650804660529528832000000⟩, + ⟨7, 5, 2, 5, 1, 8, 6015806380434660106385347989361432035103604736000000⟩, + ⟨7, 5, 3, 5, 2, 8, -2755290680904773858183999953289077570479430041600000⟩, + ⟨7, 5, 4, 5, 3, 8, -658606254153907248879766044825908871648667238400000⟩, + ⟨7, 5, 5, 5, 4, 8, 50432032777081095286762393837322837327609856000000⟩, + ⟨7, 5, 6, 5, 5, 8, 14534199980739037664071630049615373913817088000000⟩, + ⟨7, 5, 7, 5, 6, 8, 1282914946293183793465332376374687396003840000000⟩, + ⟨7, 5, 8, 5, 7, 8, -711172843781840193661981107281583121052467200000⟩, + ⟨7, 5, 2, 6, 0, 8, -108297032197702067523783756069813929933436616704000000⟩, + ⟨7, 5, 3, 6, 1, 8, -670808411462978078515024117322110617292426444800000⟩, + ⟨7, 5, 4, 6, 2, 8, 834189061744718995916616430738390392045463142400000⟩, + ⟨7, 5, 5, 6, 3, 8, -459564590195357019012460177928649080838291456000000⟩, + ⟨7, 5, 6, 6, 4, 8, -9690797939379712795982807754605844032913408000000⟩, + ⟨7, 5, 7, 6, 5, 8, 8015258433095032078825771090354329171787776000000⟩, + ⟨7, 5, 8, 6, 6, 8, 1062304842468004527881444999753378796090163200000⟩, + ⟨7, 5, 3, 7, 0, 8, 70508699513617206502382180654928649863966385766400000⟩, + ⟨7, 5, 4, 7, 1, 8, 801336448175443645266581173360371925873223270400000⟩, + ⟨7, 5, 5, 7, 2, 8, 25459749272466602837171889970902244647763968000000⟩, + ⟨7, 5, 6, 7, 3, 8, -48920994585104703819302039808535314548391936000000⟩, + ⟨7, 5, 7, 7, 4, 8, 6232581063507905532280568987706841387499520000000⟩, + ⟨7, 5, 8, 7, 5, 8, 2744045847902261550521898186004626105434112000000⟩ +] + +def collectedFourData_10_4 : List (List CollectedFourTerm) := [ + collectedFourData_10_4_0, + collectedFourData_10_4_1, + collectedFourData_10_4_2, + collectedFourData_10_4_3, + collectedFourData_10_4_4, + collectedFourData_10_4_5, + collectedFourData_10_4_6, + collectedFourData_10_4_7, + collectedFourData_10_4_8, + collectedFourData_10_4_9, + collectedFourData_10_4_10, + collectedFourData_10_4_11, + collectedFourData_10_4_12, + collectedFourData_10_4_13, + collectedFourData_10_4_14, + collectedFourData_10_4_15, + collectedFourData_10_4_16, + collectedFourData_10_4_17, + collectedFourData_10_4_18, + collectedFourData_10_4_19, + collectedFourData_10_4_20, + collectedFourData_10_4_21, + collectedFourData_10_4_22, + collectedFourData_10_4_23, + collectedFourData_10_4_24, + collectedFourData_10_4_25, + collectedFourData_10_4_26, + collectedFourData_10_4_27, + collectedFourData_10_4_28, + collectedFourData_10_4_29, + collectedFourData_10_4_30, + collectedFourData_10_4_31, + collectedFourData_10_4_32, + collectedFourData_10_4_33, + collectedFourData_10_4_34, + collectedFourData_10_4_35, + collectedFourData_10_4_36, + collectedFourData_10_4_37, + collectedFourData_10_4_38, + collectedFourData_10_4_39, + collectedFourData_10_4_40, + collectedFourData_10_4_41, + collectedFourData_10_4_42, + collectedFourData_10_4_43, + collectedFourData_10_4_44, + collectedFourData_10_4_45, + collectedFourData_10_4_46, + collectedFourData_10_4_47, + collectedFourData_10_4_48, + collectedFourData_10_4_49, + collectedFourData_10_4_50, + collectedFourData_10_4_51, + collectedFourData_10_4_52, + collectedFourData_10_4_53, + collectedFourData_10_4_54, + collectedFourData_10_4_55 +] + +theorem collectedFourChecked_10_4 : collectNumericRowParts 10 4 = collectedFourData_10_4 := by + decide +kernel + +def collectedFourData_10_5_0 : List CollectedFourTerm := [ + ⟨0, 5, 5, 2, 8, 0, -110521483419612851171507922251763830313380216832000000⟩, + ⟨0, 5, 5, 3, 7, 0, 8706749010138060840438276295289864045904003072000000⟩, + ⟨0, 5, 6, 3, 8, 0, -112829666620571050438812066914287488011920736256000000⟩, + ⟨0, 5, 5, 4, 6, 0, 21322751479977628766885349273742460272886415360000000⟩, + ⟨0, 5, 6, 4, 7, 0, 49233951595176293575180725874505508964125376512000000⟩, + ⟨0, 5, 7, 4, 8, 0, -144473366473910909163601034340726850398726389760000000⟩, + ⟨0, 5, 5, 5, 5, 0, 5868049365269121652806559789958141275778580480000000⟩, + ⟨0, 5, 6, 5, 6, 0, 83386719381426899136786989569522965927740571648000000⟩, + ⟨0, 5, 7, 5, 7, 0, -65899495333452854006159245760467570459618050048000000⟩, + ⟨0, 5, 8, 5, 8, 0, -132603697025522466689349808876823462720141524992000000⟩, + ⟨0, 5, 5, 6, 4, 0, -48933931118765311885137336046764253991625818112000000⟩, + ⟨0, 5, 6, 6, 5, 0, -7931546461872261972161148863606497845002108928000000⟩, + ⟨0, 5, 7, 6, 6, 0, -19923166610198163604239623612919727645205200896000000⟩, + ⟨0, 5, 8, 6, 7, 0, -35744326358859922170074298835037989178009714688000000⟩, + ⟨0, 5, 5, 7, 3, 0, -68223518681210202203229721311834559012965187584000000⟩, + ⟨0, 5, 6, 7, 4, 0, -275253539659865902264032807818645387862658252800000000⟩, + ⟨0, 5, 7, 7, 5, 0, 71574706845538053739273260725698231335143866368000000⟩, + ⟨0, 5, 8, 7, 6, 0, -53440199144039564799790739587609128735665553408000000⟩ +] + +def collectedFourData_10_5_1 : List CollectedFourTerm := [ + ⟨0, 6, 4, 1, 8, 1, 78561131415846401069948956914512253076922538393600000⟩, + ⟨0, 6, 4, 2, 7, 1, -10652221399247543287624934189150541828832886784000000⟩, + ⟨0, 6, 5, 2, 8, 1, 132881483602370107876664950022927089543975796736000000⟩, + ⟨0, 6, 4, 3, 6, 1, -8675460569245821668224815571480889572934968934400000⟩, + ⟨0, 6, 5, 3, 7, 1, -10468242825044282848982959259437453234201952256000000⟩, + ⟨0, 6, 6, 3, 8, 1, 67828321838474728526111980236252317242405945344000000⟩, + ⟨0, 6, 4, 4, 5, 1, 22433798736061279019320881576791537094589887283200000⟩, + ⟨0, 6, 5, 4, 6, 1, -25636634285721618660471150958055933330356961280000000⟩, + ⟨0, 6, 6, 4, 7, 1, -29597325013886514706108357772087850788022386688000000⟩, + ⟨0, 6, 7, 4, 8, 1, 57900764883253465617216797838341105927753564160000000⟩, + ⟨0, 6, 4, 5, 4, 1, 3132850566301227918277902967175830413753974784000000⟩, + ⟨0, 6, 5, 5, 5, 1, -7055235610152277620563165238641937012007895040000000⟩, + ⟨0, 6, 6, 5, 6, 1, -50128493761115184179122921681933628827502641152000000⟩, + ⟨0, 6, 7, 5, 7, 1, 26410620021901003500405818807448385533580935168000000⟩, + ⟨0, 6, 8, 5, 8, 1, 39857807384405131248436530563106820132756783104000000⟩, + ⟨0, 6, 4, 6, 3, 1, -78309566106819020103627249118232879095238098944000000⟩, + ⟨0, 6, 5, 6, 4, 1, 58833931326005166522790904772563850494975410176000000⟩, + ⟨0, 6, 6, 6, 5, 1, 4768103125766060028017819340753688602316111872000000⟩, + ⟨0, 6, 7, 6, 6, 1, 7984631449944662248885766489170150615349723136000000⟩, + ⟨0, 6, 8, 6, 7, 1, 10743972506456899937314749195534300836901421056000000⟩, + ⟨0, 6, 4, 7, 2, 1, 80475438715917075532900232244876324321443708928000000⟩, + ⟨0, 6, 5, 7, 3, 1, 82026064964347548803268233946619309787952709632000000⟩, + ⟨0, 6, 6, 7, 4, 1, 165470538329365668689888136223756608169259827200000000⟩, + ⟨0, 6, 7, 7, 5, 1, -28685081366880579112585699687497766925959692288000000⟩, + ⟨0, 6, 8, 7, 6, 1, 16062969674649526035521383068918970742992797696000000⟩ +] + +def collectedFourData_10_5_2 : List CollectedFourTerm := [ + ⟨0, 7, 3, 0, 8, 2, -368638484568712665467482958290880753553113088000000⟩, + ⟨0, 7, 3, 1, 7, 2, 4924539018004618585678180866195478144314507264000000⟩, + ⟨0, 7, 4, 1, 8, 2, -7665888547106957144743388616748004193261846528000000⟩, + ⟨0, 7, 3, 2, 6, 2, -1603040222382437112301154088569566262433153024000000⟩, + ⟨0, 7, 4, 2, 7, 2, 1039429302430695061022944824919915239907000320000000⟩, + ⟨0, 7, 5, 2, 8, 2, -6483197383436099828083121707721228200590704640000000⟩, + ⟨0, 7, 3, 3, 5, 2, -3202021132133541269368548916376608064359366656000000⟩, + ⟨0, 7, 4, 3, 6, 2, 846539664336414332790205291465013249716518912000000⟩, + ⟨0, 7, 5, 3, 7, 2, 510738461466803754677029208774539992304189440000000⟩, + ⟨0, 7, 6, 3, 8, 2, -2206198519887775823773444877761426966488023040000000⟩, + ⟨0, 7, 3, 4, 4, 2, 1309514133212919785610775293904850634600873984000000⟩, + ⟨0, 7, 4, 4, 5, 2, -2189059624008749611959712451880148560443867136000000⟩, + ⟨0, 7, 5, 4, 6, 2, 1250793984349630541725313770058098102448947200000000⟩, + ⟨0, 7, 6, 4, 7, 2, 962688930942040165606655281766406050367406080000000⟩, + ⟨0, 7, 7, 4, 8, 2, -1412469507464779209525268421686133993452339200000000⟩, + ⟨0, 7, 3, 5, 3, 2, 3296948316542753929604146862762268980567605248000000⟩, + ⟨0, 7, 4, 5, 4, 2, -305699305027599108736493027257885389037240320000000⟩, + ⟨0, 7, 5, 5, 5, 2, 344220156241908504957286007515133047839129600000000⟩, + ⟨0, 7, 6, 5, 6, 2, 1630490121860028964547039553099858637561528320000000⟩, + ⟨0, 7, 7, 5, 7, 2, -644278111513572979765791262348762174099292160000000⟩, + ⟨0, 7, 8, 5, 8, 2, -777854146533524733376036739014683680292470784000000⟩, + ⟨0, 7, 3, 6, 2, 2, 3686914954448869257768662060974164982571728896000000⟩, + ⟨0, 7, 4, 6, 3, 2, 7641341145783082700138606372667320794475397120000000⟩, + ⟨0, 7, 5, 6, 4, 2, -2870467572226989833059899254677561820829450240000000⟩, + ⟨0, 7, 6, 6, 5, 2, -155088343240866931648526852803536616968683520000000⟩, + ⟨0, 7, 7, 6, 6, 2, -194782374190242393225414980469881439592120320000000⟩, + ⟨0, 7, 8, 6, 7, 2, -209676450181741888148425986490638009762840576000000⟩, + ⟨0, 7, 3, 7, 1, 2, -33893391894560130241203679845150955479383408640000000⟩, + ⟨0, 7, 4, 7, 2, 2, -7852684054538956628017740327824293086300733440000000⟩, + ⟨0, 7, 5, 7, 3, 2, -4001996029346954154728923153010067727114567680000000⟩, + ⟨0, 7, 6, 7, 4, 2, -5382130161153478798086442532462114742730752000000000⟩, + ⟨0, 7, 7, 7, 5, 2, 699762824058711689710127997991033634354626560000000⟩, + ⟨0, 7, 8, 7, 6, 2, -313480554676900883486972448837562383797846016000000⟩ +] + +def collectedFourData_10_5_3 : List CollectedFourTerm := [ + ⟨0, 8, 2, 0, 7, 3, -368638484568712665467482958290880753553113088000000⟩, + ⟨0, 8, 3, 0, 8, 3, 224606823976919447167350414737878398481622630400000⟩, + ⟨0, 8, 2, 1, 6, 3, 848539545128559379336792884262910543652087398400000⟩, + ⟨0, 8, 3, 1, 7, 3, -3000460111153331043527666779387438810006762291200000⟩, + ⟨0, 8, 4, 1, 8, 3, 2335365068491372839252258078399166916121015091200000⟩, + ⟨0, 8, 2, 2, 5, 3, 1779368018128178990683514982985080009576677376000000⟩, + ⟨0, 8, 3, 2, 6, 3, 976712383889646083155966122373923598719202099200000⟩, + ⟨0, 8, 4, 2, 7, 3, -316655645219248382627307730284563759080931328000000⟩, + ⟨0, 8, 5, 2, 8, 3, 1316710394659145403652223734914787513680789504000000⟩, + ⟨0, 8, 2, 3, 4, 3, -131105759945179045626807333871822263851522457600000⟩, + ⟨0, 8, 3, 3, 5, 3, 1950951479297977512529722562627521486084951244800000⟩, + ⟨0, 8, 4, 3, 6, 3, -257893021668019109844039017993911307416161484800000⟩, + ⟨0, 8, 5, 3, 7, 3, -103728854975743033499361521828468786970230784000000⟩, + ⟨0, 8, 6, 3, 8, 3, 336052300124276420732792260195097168270327808000000⟩, + ⟨0, 8, 2, 4, 3, 3, -2788606076320551523385010012300938764374088089600000⟩, + ⟨0, 8, 3, 4, 4, 3, -797870604199000017219880429876516497472566067200000⟩, + ⟨0, 8, 4, 4, 5, 3, 666883342660155749674124528875077887993472614400000⟩, + ⟨0, 8, 5, 4, 6, 3, -254031050323723280148592571833688092751953920000000⟩, + ⟨0, 8, 6, 4, 7, 3, -146638585163999517769647390084001977247727616000000⟩, + ⟨0, 8, 7, 4, 8, 3, 172120005542597466497345396967430014288003072000000⟩, + ⟨0, 8, 2, 5, 2, 3, 379312880020796183961592045801262852712117043200000⟩, + ⟨0, 8, 3, 5, 3, 3, -2008789427021122518318913336154160170824787558400000⟩, + ⟨0, 8, 4, 5, 4, 3, 93129384028544397374290348153120898131427328000000⟩, + ⟨0, 8, 5, 5, 5, 3, -69909680512410899252233202907023625745858560000000⟩, + ⟨0, 8, 6, 5, 6, 3, -248359316191022740625951395954493407849611264000000⟩, + ⟨0, 8, 7, 5, 7, 3, 78510121130848977565349102262415795909400985600000⟩, + ⟨0, 8, 8, 5, 8, 3, 78989469215155891807088098098272476029203251200000⟩, + ⟨0, 8, 2, 6, 1, 3, -6364745534809909313031352260244983701402183270400000⟩, + ⟨0, 8, 3, 6, 2, 3, -2246391228416124931187883766236264380263877836800000⟩, + ⟨0, 8, 4, 6, 3, 3, -2327886855989098716328506315765500101470978048000000⟩, + ⟨0, 8, 5, 6, 4, 3, 582980012229721938111041797852926749561585664000000⟩, + ⟨0, 8, 6, 6, 5, 3, 23623347581253803620448312869218734837858304000000⟩, + ⟨0, 8, 7, 6, 6, 3, 23735693512704595015915590224585631141671731200000⟩, + ⟨0, 8, 8, 6, 7, 3, 21292207003822988950163254489398628305390796800000⟩, + ⟨0, 8, 2, 7, 0, 3, 51923428883167156347506671818687224248523764531200000⟩, + ⟨0, 8, 3, 7, 1, 3, 20650820318309014207229231723371896065293811712000000⟩, + ⟨0, 8, 4, 7, 2, 3, 2392271153197293062845710808138359478237003776000000⟩, + ⟨0, 8, 5, 7, 3, 3, 812788730555807578793913403160420014513717248000000⟩, + ⟨0, 8, 6, 7, 4, 3, 819816169723417396612506824935870174750310400000000⟩, + ⟨0, 8, 7, 7, 5, 3, -85271349589465340119661623543313033089096089600000⟩, + ⟨0, 8, 8, 7, 6, 3, 31833297712110162081237398157266503366134988800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1018.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1018.lean new file mode 100644 index 0000000000000000000000000000000000000000..63367c154d976fb548698750b0dbce6a9b03fdc1 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1018.lean @@ -0,0 +1,663 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1018. -/ +namespace LaughlinFock +def collectedFourData_10_5_4 : List CollectedFourTerm := [ + ⟨1, 4, 5, 2, 8, 0, -79463081361351298590507752249747951113520283648000000⟩, + ⟨1, 4, 5, 3, 7, 0, 6260005598718638379415798332007174433572651008000000⟩, + ⟨1, 4, 6, 3, 8, 0, -81122626128754386653904471223273079448570691584000000⟩, + ⟨1, 4, 5, 4, 6, 0, 15330698460392338730087903077181072224592855040000000⟩, + ⟨1, 4, 6, 4, 7, 0, 35398380299463680603998305717900765270972039168000000⟩, + ⟨1, 4, 7, 4, 8, 0, -103873912287965562778853977578876488288714096640000000⟩, + ⟨1, 4, 5, 5, 5, 0, 4219028461411864127467877083849332854850846720000000⟩, + ⟨1, 4, 6, 5, 6, 0, 59953643958117856923607535307006811237433475072000000⟩, + ⟨1, 4, 7, 5, 7, 0, -47380624991004103880977304620938918426335772672000000⟩, + ⟨1, 4, 8, 5, 8, 0, -95339820273215616740387575833981159733500837888000000⟩, + ⟨1, 4, 5, 6, 4, 0, -35182670640223922927733170141050571300240621568000000⟩, + ⟨1, 4, 6, 6, 5, 0, -5702648049232104236328689387121155150280916992000000⟩, + ⟨1, 4, 7, 6, 6, 0, -14324420559134401725019776791125669646690156544000000⟩, + ⟨1, 4, 8, 6, 7, 0, -25699567412399913727901735749828934676756037632000000⟩, + ⟨1, 4, 5, 7, 3, 0, -49051558556629322511147334042198345717358002176000000⟩, + ⟨1, 4, 6, 7, 4, 0, -197902649695257577619077985999217152333394739200000000⟩, + ⟨1, 4, 7, 7, 5, 0, 51461006290407436390113729123995280739141681152000000⟩, + ⟨1, 4, 8, 7, 6, 0, -38422601300301179287280214897812391884815859712000000⟩ +] + +def collectedFourData_10_5_5 : List CollectedFourTerm := [ + ⟨1, 5, 4, 1, 8, 1, 17105417470676057082761117507246415764183737958400000⟩, + ⟨1, 5, 4, 2, 7, 1, -2319349158296935430173805480026021651437060096000000⟩, + ⟨1, 5, 5, 2, 8, 1, 28932796793744431012197328751232017540038262784000000⟩, + ⟨1, 5, 4, 3, 6, 1, -1888941415594299931162477205711578569694091673600000⟩, + ⟨1, 5, 5, 3, 7, 1, -2279290795329268933832060164501614241895153664000000⟩, + ⟨1, 5, 6, 3, 8, 1, 14768521538227949214206773147636842490270580736000000⟩, + ⟨1, 5, 4, 4, 5, 1, 4884597330990701099861026741129020745481768140800000⟩, + ⟨1, 5, 5, 4, 6, 1, -5581963040718903781949049898023246862032568320000000⟩, + ⟨1, 5, 6, 4, 7, 1, -6444339474923756947155581141613742824433385472000000⟩, + ⟨1, 5, 7, 4, 8, 1, 12606956358061509239952322476276267707573207040000000⟩, + ⟨1, 5, 4, 5, 4, 1, 682127609977586644605682741472754934896132096000000⟩, + ⟨1, 5, 5, 5, 5, 1, -1536163600124678912901078027335688819321077760000000⟩, + ⟨1, 5, 6, 5, 6, 1, -10914669856537951607229559579551119699752255488000000⟩, + ⟨1, 5, 7, 5, 7, 1, 5750485933593463855861293093195163310953070592000000⟩, + ⟨1, 5, 8, 5, 8, 1, 8678393786962739464939017740614552368684466176000000⟩, + ⟨1, 5, 4, 6, 3, 1, -17050643187840499442809935426861369118357979136000000⟩, + ⟨1, 5, 5, 6, 4, 1, 12810138278754594766467209694626520786895110144000000⟩, + ⟨1, 5, 6, 6, 5, 1, 1038177442706896964150987529897578310735495168000000⟩, + ⟨1, 5, 7, 6, 6, 1, 1738524532924987454949475263865927962810384384000000⟩, + ⟨1, 5, 8, 6, 7, 1, 2339326479956234146913369470428323923428900864000000⟩, + ⟨1, 5, 4, 7, 2, 1, 17522226965966328548606008097659463627578540032000000⟩, + ⟨1, 5, 5, 7, 3, 1, 17859850786325939191243733434073749553946820608000000⟩, + ⟨1, 5, 6, 7, 4, 1, 36028537092203600875400788186434033016425676800000000⟩, + ⟨1, 5, 7, 7, 5, 1, -6245713155065778675391765896048922506792271872000000⟩, + ⟨1, 5, 8, 7, 6, 1, 3497452202531131990159531943327362479003009024000000⟩ +] + +def collectedFourData_10_5_6 : List CollectedFourTerm := [ + ⟨1, 6, 3, 0, 8, 2, 848539545128559379336792884262910543652087398400000⟩, + ⟨1, 6, 3, 1, 7, 2, -11335403852894788388220013397261358644073804595200000⟩, + ⟨1, 6, 4, 1, 8, 2, 17645497833408929300168958336879750313788466790400000⟩, + ⟨1, 6, 3, 2, 6, 2, 3689910516843051616754766691965218287070163763200000⟩, + ⟨1, 6, 4, 2, 7, 2, -2392579463074038475352255782551906753158578176000000⟩, + ⟨1, 6, 5, 2, 8, 2, 14923155310698779573149417051014850344545943552000000⟩, + ⟨1, 6, 3, 3, 5, 2, 7370477225489420384670492471905754286863994060800000⟩, + ⟨1, 6, 4, 3, 6, 2, -1948582179502238278305176951939702394959010201600000⟩, + ⟨1, 6, 5, 3, 7, 2, -1175628155806183513168914856819800495926280192000000⟩, + ⟨1, 6, 6, 3, 8, 2, 5078272526860750534813872790354180352268828672000000⟩, + ⟨1, 6, 3, 4, 4, 2, -3014266207815837528581983929049485585679594291200000⟩, + ⟨1, 6, 4, 4, 5, 2, 5038821868500408119881235727656652826125061324800000⟩, + ⟨1, 6, 5, 4, 6, 2, -2879102977463936159825902344979815668341800960000000⟩, + ⟨1, 6, 6, 4, 7, 2, -2215936918570950078786726768269326266446905344000000⟩, + ⟨1, 6, 7, 4, 8, 2, 3251250977700679909360561559480424951510466560000000⟩, + ⟨1, 6, 3, 5, 3, 2, -7588982545066042346145211089005420448271722086400000⟩, + ⟨1, 6, 4, 5, 4, 2, 703664864339157146961274750831072694476210176000000⟩, + ⟨1, 6, 5, 5, 5, 2, -792332941427192130361001203367837837851361280000000⟩, + ⟨1, 6, 6, 5, 6, 2, -3753095252543642525714195786403971679519768576000000⟩, + ⟨1, 6, 7, 5, 7, 2, 1483012432409543324712071855735632953436274688000000⟩, + ⟨1, 6, 8, 5, 8, 2, 1790480460682590956878517565910072801352692531200000⟩, + ⟨1, 6, 3, 6, 2, 2, -8486615666391686136413473062578628836492889292800000⟩, + ⟨1, 6, 4, 6, 3, 2, -17588994126863428630243476690371044703433916416000000⟩, + ⟨1, 6, 5, 6, 4, 2, 6607300512569693166131805152076511365543493632000000⟩, + ⟨1, 6, 6, 6, 5, 2, 356985495918339713601508272239204769711783936000000⟩, + ⟨1, 6, 7, 6, 6, 2, 448354021929692272807164696001632990633394176000000⟩, + ⟨1, 6, 8, 6, 7, 2, 482637508315339750489022870682884852843072716800000⟩, + ⟨1, 6, 3, 7, 1, 2, 78016497313680044804804876491865952126083530752000000⟩, + ⟨1, 6, 4, 7, 2, 2, 18075467523344714914029623055613079472561979392000000⟩, + ⟨1, 6, 5, 7, 3, 2, 9211875679017426948461554769913153494370484224000000⟩, + ⟨1, 6, 6, 7, 4, 2, 12388696432796377053134842160387408363362713600000000⟩, + ⟨1, 6, 7, 7, 5, 2, -1610728269782635545899361171683981346742468608000000⟩, + ⟨1, 6, 8, 7, 6, 2, 721575902698798555895240448941807295527701708800000⟩ +] + +def collectedFourData_10_5_7 : List CollectedFourTerm := [ + ⟨1, 7, 2, 0, 7, 3, 4924539018004618585678180866195478144314507264000000⟩, + ⟨1, 7, 3, 0, 8, 3, -3000460111153331043527666779387438810006762291200000⟩, + ⟨1, 7, 2, 1, 6, 3, -11335403852894788388220013397261358644073804595200000⟩, + ⟨1, 7, 3, 1, 7, 3, 40082312367977660416287799418920842401104370073600000⟩, + ⟨1, 7, 4, 1, 8, 3, -31197492618075070111817865847749864982947928473600000⟩, + ⟨1, 7, 2, 2, 5, 3, -23770082613358999944042461675414995253883568128000000⟩, + ⟨1, 7, 3, 2, 6, 3, -13047629168344007757421668948426614107618777497600000⟩, + ⟨1, 7, 4, 2, 7, 3, 4230114720599535961969982423050948170674601984000000⟩, + ⟨1, 7, 5, 2, 8, 3, -17589568060148086857592703226438990348536512512000000⟩, + ⟨1, 7, 2, 3, 4, 3, 1751405394069314923710291042895959717799840972800000⟩, + ⟨1, 7, 3, 3, 5, 3, -26062218363546673200761382660950654424506066534400000⟩, + ⟨1, 7, 4, 3, 6, 3, 3445121171114588801667116461904698876388337254400000⟩, + ⟨1, 7, 5, 3, 7, 3, 1385684932539307320748240663956630691330916352000000⟩, + ⟨1, 7, 6, 3, 8, 3, -4489229240371756851273584781946850913156071424000000⟩, + ⟨1, 7, 2, 4, 3, 3, 37252213221177189391589172293396074117106289868800000⟩, + ⟨1, 7, 3, 4, 4, 3, 10658531559160962050147347943106219772405717401600000⟩, + ⟨1, 7, 4, 4, 5, 3, -8908709152354221468566924177594524652853736243200000⟩, + ⟨1, 7, 5, 4, 6, 3, 3393530169720225141039854867306684759156981760000000⟩, + ⟨1, 7, 6, 4, 7, 3, 1958904087374272220947367440354501499025358848000000⟩, + ⟨1, 7, 7, 4, 8, 3, -2299303297281489278562475106521272050270601216000000⟩, + ⟨1, 7, 2, 5, 2, 3, -5067135298908106746264665769554608851527506329600000⟩, + ⟨1, 7, 3, 5, 3, 3, 26834859425743880517472012037190677865677665075200000⟩, + ⟨1, 7, 4, 5, 4, 3, -1244089547264342466613831031815446333682089984000000⟩, + ⟨1, 7, 5, 5, 5, 3, 933903984068254703421337260099591502225735680000000⟩, + ⟨1, 7, 6, 5, 6, 3, 3317763050427431305627012374124695620306337792000000⟩, + ⟨1, 7, 7, 5, 7, 3, -1048794878997689639054595143184847827104484556800000⟩, + ⟨1, 7, 8, 5, 8, 3, -1055198356776568058229444151350305264326252953600000⟩, + ⟨1, 7, 2, 6, 1, 3, 85024865926606169570459832333406484030471484211200000⟩, + ⟨1, 7, 3, 6, 2, 3, 30008915827062923269167311278628455251056158310400000⟩, + ⟨1, 7, 4, 6, 3, 3, 31097593256521801466519709753446291920486662144000000⟩, + ⟨1, 7, 5, 6, 4, 3, -7787867889867451550984611964357749615720660992000000⟩, + ⟨1, 7, 6, 6, 5, 3, -315577732031624605418919152868986504884518912000000⟩, + ⟨1, 7, 7, 6, 6, 3, -317078530092876321036120915914599771168938393600000⟩, + ⟨1, 7, 8, 6, 7, 3, -284436673215037379417931850617699842927257190400000⟩, + ⟨1, 7, 2, 7, 0, 3, -693630649504483373810664417726490060649056016793600000⟩, + ⟨1, 7, 3, 7, 1, 3, -275868566816332040565712894239304321047919067136000000⟩, + ⟨1, 7, 4, 7, 2, 3, -31957685181323157046213159754077972106814947328000000⟩, + ⟨1, 7, 5, 7, 3, 3, -10857818661281002312936409175940552903826079744000000⟩, + ⟨1, 7, 6, 7, 4, 3, -10951696267190859144359164679917435922625331200000000⟩, + ⟨1, 7, 7, 7, 5, 3, 1139116250064126086631244150187916807539313868800000⟩, + ⟨1, 7, 8, 7, 6, 3, -425252173110600553117213200280847274356401766400000⟩ +] + +def collectedFourData_10_5_8 : List CollectedFourTerm := [ + ⟨1, 8, 1, 0, 6, 4, 78561131415846401069948956914512253076922538393600000⟩, + ⟨1, 8, 2, 0, 7, 4, -7665888547106957144743388616748004193261846528000000⟩, + ⟨1, 8, 3, 0, 8, 4, 2335365068491372839252258078399166916121015091200000⟩, + ⟨1, 8, 1, 1, 5, 4, 17105417470676057082761117507246415764183737958400000⟩, + ⟨1, 8, 2, 1, 6, 4, 17645497833408929300168958336879750313788466790400000⟩, + ⟨1, 8, 3, 1, 7, 4, -31197492618075070111817865847749864982947928473600000⟩, + ⟨1, 8, 4, 1, 8, 4, 16188080446716256259911548540733005412960724582400000⟩, + ⟨1, 8, 1, 2, 4, 4, -14872371966677191077759158863039937233742620262400000⟩, + ⟨1, 8, 2, 2, 5, 4, 37002205364466475465194630624020909790389600256000000⟩, + ⟨1, 8, 3, 2, 6, 4, 10155434919168833529655243503824581720777791897600000⟩, + ⟨1, 8, 4, 2, 7, 4, -2194966058144999199627412683616623183481798656000000⟩, + ⟨1, 8, 5, 2, 8, 4, 6845293937557400313626284696870364250170720256000000⟩, + ⟨1, 8, 1, 3, 3, 4, 41188187329069646192657933478414180098812516761600000⟩, + ⟨1, 8, 2, 3, 4, 4, -2726362508785125109391125939595003302852008345600000⟩, + ⟨1, 8, 3, 3, 5, 4, 20285153649393390531895528182050716277962860134400000⟩, + ⟨1, 8, 4, 3, 6, 4, -1787640415511359357305388294751370992680540569600000⟩, + ⟨1, 8, 5, 3, 7, 4, -539263990772272421741088896346903379156402176000000⟩, + ⟨1, 8, 6, 3, 8, 4, 1397650862071867542214784381945700581795010969600000⟩, + ⟨1, 8, 1, 4, 2, 4, -71011875723561895086325162781954165867857890508800000⟩, + ⟨1, 8, 2, 4, 3, 4, -57989451122740755006380842521154124182158154137600000⟩, + ⟨1, 8, 3, 4, 4, 4, -8295915080540585050076109479469093296885307801600000⟩, + ⟨1, 8, 4, 4, 5, 4, 4622643947711134729530070138985959969069518028800000⟩, + ⟨1, 8, 5, 4, 6, 4, -1320652753852127373322678947839463039833210880000000⟩, + ⟨1, 8, 6, 4, 7, 4, -609873953821086598749305111867624856956908339200000⟩, + ⟨1, 8, 7, 4, 8, 4, 596543241526845816088298501436657780834435072000000⟩, + ⟨1, 8, 1, 5, 1, 4, -32197611987809073768828291771259460471663414476800000⟩, + ⟨1, 8, 2, 5, 2, 4, 7887864084845923472618057315880669559987057459200000⟩, + ⟨1, 8, 3, 5, 3, 4, -20886527732131602548538463424984485990535213875200000⟩, + ⟨1, 8, 4, 5, 4, 4, 645546163615908344992596771023922675534790656000000⟩, + ⟨1, 8, 5, 5, 5, 4, -363445381861713857492633266934111115505827840000000⟩, + ⟨1, 8, 6, 5, 6, 4, -1032933303088814479099468629976497256143834316800000⟩, + ⟨1, 8, 7, 5, 7, 4, 272104814338220476551194422356232323009714585600000⟩, + ⟨1, 8, 8, 5, 8, 4, 234656713728221681960157118658185350306437529600000⟩, + ⟨1, 8, 1, 6, 0, 4, 351021221648347612400508135698311886311333979750400000⟩, + ⟨1, 8, 2, 6, 1, 4, -132355768437017082504289609623318242978108434022400000⟩, + ⟨1, 8, 3, 6, 2, 4, -23357008981826551485434855826836762294202295910400000⟩, + ⟨1, 8, 4, 6, 3, 4, -16136243623763922209893299358615154887382532096000000⟩, + ⟨1, 8, 5, 6, 4, 4, 3030787604943540042076587301043303508917354496000000⟩, + ⟨1, 8, 6, 6, 5, 4, 98250159572639638033530039519215081860418764800000⟩, + ⟨1, 8, 7, 6, 6, 4, 82264507854970205588545702735362280800858931200000⟩, + ⟨1, 8, 8, 6, 7, 4, 63253486486012047036838892476111917337175654400000⟩, + ⟨1, 8, 2, 7, 0, 4, 1079754923764072841304422734578168233627638510387200000⟩, + ⟨1, 8, 3, 7, 1, 4, 214718340044853591862901919321462183150156251136000000⟩, + ⟨1, 8, 4, 7, 2, 4, 16582537094867705311312143388744715978567319552000000⟩, + ⟨1, 8, 5, 7, 3, 4, 4225513668272460709434410683709079950953807872000000⟩, + ⟨1, 8, 6, 7, 4, 4, 3409638249554171066524499566753494583455252480000000⟩, + ⟨1, 8, 7, 7, 5, 4, -295538261999877440169726648887141314456033689600000⟩, + ⟨1, 8, 8, 7, 6, 4, 94568264636757707733943289530613408423372390400000⟩ +] + +def collectedFourData_10_5_9 : List CollectedFourTerm := [ + ⟨2, 3, 5, 2, 8, 0, -31103399872144999082754564763592390989452410880000000⟩, + ⟨2, 3, 5, 3, 7, 0, 2450288284862720358752969708737228834319892480000000⟩, + ⟨2, 3, 6, 3, 8, 0, -31752978061436931889586095055729041932854231040000000⟩, + ⟨2, 3, 5, 4, 6, 0, 6000734383360839492465580448817794653775462400000000⟩, + ⟨2, 3, 6, 4, 7, 0, 13855616450030847666865841806359349675771822080000000⟩, + ⟨2, 3, 7, 4, 8, 0, -40658275199331729822448514029010753241376358400000000⟩, + ⟨2, 3, 5, 5, 5, 0, 1651410026632553163519141740159105754149683200000000⟩, + ⟨2, 3, 6, 5, 6, 0, 23467025565516514337322671334880620417719992320000000⟩, + ⟨2, 3, 7, 5, 7, 0, -18545700720889920618640614072666041514008248320000000⟩, + ⟨2, 3, 8, 5, 8, 0, -37317865138043197406146712103692452861606625280000000⟩, + ⟨2, 3, 5, 6, 4, 0, -13771183482259205919425242757792399601256366080000000⟩, + ⟨2, 3, 6, 6, 5, 0, -2232127669436722789142341169647253143966187520000000⟩, + ⟨2, 3, 7, 6, 6, 0, -5606857586625503193711755689495028963097968640000000⟩, + ⟨2, 3, 8, 6, 7, 0, -10059311922905126662411590338103856565499985920000000⟩, + ⟨2, 3, 5, 7, 3, 0, -19199736707930159586143612474563145847338434560000000⟩, + ⟨2, 3, 6, 7, 4, 0, -77462956932632539142767789634197161510961152000000000⟩, + ⟨2, 3, 7, 7, 5, 0, 20142841544174076276550573033700679088204677120000000⟩, + ⟨2, 3, 8, 7, 6, 0, -15039355533380027429339383851719153897145630720000000⟩ +] + +def collectedFourData_10_5_10 : List CollectedFourTerm := [ + ⟨2, 4, 4, 1, 8, 1, -14872371966677191077759158863039937233742620262400000⟩, + ⟨2, 4, 4, 2, 7, 1, 2016567175979503692840969080883450544291577856000000⟩, + ⟨2, 4, 5, 2, 8, 1, -25155733070561865701332436379535760988070477824000000⟩, + ⟨2, 4, 4, 3, 6, 1, 1642347484598975715577710953243559479706491289600000⟩, + ⟨2, 4, 5, 3, 7, 1, 1981738275986117176206806591485853758604181504000000⟩, + ⟨2, 4, 6, 3, 8, 1, -12840548679442941204471296828809954861982416896000000⟩, + ⟨2, 4, 4, 4, 5, 1, -4246932209545258363985559595844263377873194188800000⟩, + ⟨2, 4, 5, 4, 6, 1, 4853259547048921932520727650160130888585707520000000⟩, + ⟨2, 4, 6, 4, 7, 1, 5603056102834729951745199688853035817518497792000000⟩, + ⟨2, 4, 7, 4, 8, 1, -10961167398935536861347039449871871441832509440000000⟩, + ⟨2, 4, 4, 5, 4, 1, -593078512215125568877630006650279616478969856000000⟩, + ⟨2, 4, 5, 5, 5, 1, 1335623436369789305639474149175000722424463360000000⟩, + ⟨2, 4, 6, 5, 6, 1, 9489802296739615457350562219760183866994720768000000⟩, + ⟨2, 4, 7, 5, 7, 1, -4999782433849409518742736013810968475427930112000000⟩, + ⟨2, 4, 8, 5, 8, 1, -7545463341907491580895139747829673935541108736000000⟩, + ⟨2, 4, 4, 6, 3, 1, 14824748252731892159609231387543517429598519296000000⟩, + ⟨2, 4, 5, 6, 4, 1, -11137824712715324021971848603109532435988086784000000⟩, + ⟨2, 4, 6, 6, 5, 1, -902647428618439259785454320760731362549301248000000⟩, + ⟨2, 4, 7, 6, 6, 1, -1511566939022636737369303071330668888325095424000000⟩, + ⟨2, 4, 8, 6, 7, 1, -2033936536249393944342032237320531894761160704000000⟩, + ⟨2, 4, 4, 7, 2, 1, -15234768608783517947537235036420117529941245952000000⟩, + ⟨2, 4, 5, 7, 3, 1, -15528316956832124431456972651609437664431833088000000⟩, + ⟨2, 4, 6, 7, 4, 1, -31325152161241031885785492146294529693895884800000000⟩, + ⟨2, 4, 7, 7, 5, 1, 5430359673977369799977054320020745954831368192000000⟩, + ⟨2, 4, 8, 7, 6, 1, -3040873464847485013497722581628299876409278464000000⟩ +] + +def collectedFourData_10_5_11 : List CollectedFourTerm := [ + ⟨2, 5, 3, 0, 8, 2, 1779368018128178990683514982985080009576677376000000⟩, + ⟨2, 5, 3, 1, 7, 2, -23770082613358999944042461675414995253883568128000000⟩, + ⟨2, 5, 4, 1, 8, 2, 37002205364466475465194630624020909790389600256000000⟩, + ⟨2, 5, 3, 2, 6, 2, 7737657957273631688704101004249529321571483648000000⟩, + ⟨2, 5, 4, 2, 7, 2, -5017184410396840533850865737274934721920368640000000⟩, + ⟨2, 5, 5, 2, 8, 2, 31293515360434995021509048016512552501803745280000000⟩, + ⟨2, 5, 3, 3, 5, 2, 15455722162472712232933814904532953210355187712000000⟩, + ⟨2, 5, 4, 3, 6, 2, -4086132261962493004822953938645566342639386624000000⟩, + ⟨2, 5, 5, 3, 7, 2, -2465265353467529667883330865552741775578234880000000⟩, + ⟨2, 5, 6, 3, 8, 2, 10649021337321363984707084419714613726234542080000000⟩, + ⟨2, 5, 3, 4, 4, 2, -6320847294747358330031438464454143281954029568000000⟩, + ⟨2, 5, 4, 4, 5, 2, 10566294209064944291306126542183611423283740672000000⟩, + ⟨2, 5, 5, 4, 6, 2, -6037413092186265974182597850426629626947174400000000⟩, + ⟨2, 5, 6, 4, 7, 2, -4646769034785844481384716435046962175315804160000000⟩, + ⟨2, 5, 7, 4, 8, 2, 6817798936821584522134389377267916056454758400000000⟩, + ⟨2, 5, 3, 5, 3, 2, -15913922819917159583839639940442176778399645696000000⟩, + ⟨2, 5, 4, 5, 4, 2, 1475569126122344402283150372404612311956848640000000⟩, + ⟨2, 5, 5, 5, 5, 2, -1661504055737757583062177937315265678357299200000000⟩, + ⟨2, 5, 6, 5, 6, 2, -7870154902860863592744529475348247962336624640000000⟩, + ⟨2, 5, 7, 5, 7, 2, 3109843150935551979980330309607983650512568320000000⟩, + ⟨2, 5, 8, 5, 8, 2, 3754596573739320742151769152113981708113543168000000⟩, + ⟨2, 5, 3, 6, 2, 2, -17796238944450203755014542184633924522388488192000000⟩, + ⟨2, 5, 4, 6, 3, 2, -36883718384207316029913098857477116814153482240000000⟩, + ⟨2, 5, 5, 6, 4, 2, 13855358051046636718858350220037498717318676480000000⟩, + ⟨2, 5, 6, 6, 5, 2, 748590419880175350979082223143469131539415040000000⟩, + ⟨2, 5, 7, 6, 6, 2, 940188129122449606605947671410925655178608640000000⟩, + ⟨2, 5, 8, 6, 7, 2, 1012079815932769811606743091896734067093143552000000⟩, + ⟨2, 5, 3, 7, 1, 2, 163598810454158739249545812741154739194198753280000000⟩, + ⟨2, 5, 4, 7, 2, 2, 37903841969888692568238689863957816254796922880000000⟩, + ⟨2, 5, 5, 7, 3, 2, 19317092602599939721136622474802329661325967360000000⟩, + ⟨2, 5, 6, 7, 4, 2, 25978813062244152871000079176079527907426304000000000⟩, + ⟨2, 5, 7, 7, 5, 2, -3377660340758696295045387204064632628177797120000000⟩, + ⟨2, 5, 8, 7, 6, 2, 1513128163896811775208967175185377689371410432000000⟩ +] + +def collectedFourData_10_5_12 : List CollectedFourTerm := [ + ⟨2, 6, 2, 0, 7, 3, -1603040222382437112301154088569566262433153024000000⟩, + ⟨2, 6, 3, 0, 8, 3, 976712383889646083155966122373923598719202099200000⟩, + ⟨2, 6, 2, 1, 6, 3, 3689910516843051616754766691965218287070163763200000⟩, + ⟨2, 6, 3, 1, 7, 3, -13047629168344007757421668948426614107618777497600000⟩, + ⟨2, 6, 4, 1, 8, 3, 10155434919168833529655243503824581720777791897600000⟩, + ⟨2, 6, 2, 2, 5, 3, 7737657957273631688704101004249529321571483648000000⟩, + ⟨2, 6, 3, 2, 6, 3, 4247275590083695988929434777897757741271325081600000⟩, + ⟨2, 6, 4, 2, 7, 3, -1376990621380175895858672657146131007661932544000000⟩, + ⟨2, 6, 5, 2, 8, 3, 5725771486764643430922051186824044188209774592000000⟩, + ⟨2, 6, 2, 3, 4, 3, -570119006495003743432769591058996434582686924800000⟩, + ⟨2, 6, 3, 3, 5, 3, 8483795979386493736502642519669670750087177830400000⟩, + ⟨2, 6, 4, 3, 6, 3, -1121458838702776841018157578268802845161973350400000⟩, + ⟨2, 6, 5, 3, 7, 3, -451069363911722848051969335576755877584044032000000⟩, + ⟨2, 6, 6, 3, 8, 3, 1461337805122560817667905265723473174235971584000000⟩, + ⟨2, 6, 2, 4, 3, 3, -12126372833677046305588867043871057880653024460800000⟩, + ⟨2, 6, 3, 4, 4, 3, -3469574459335025669310424120295768734905768345600000⟩, + ⟨2, 6, 4, 4, 5, 3, 2899970748229935183102854353483414490517287731200000⟩, + ⟨2, 6, 5, 4, 6, 3, -1104664891077266163951843787691405342838620160000000⟩, + ⟨2, 6, 6, 4, 7, 3, -637664161532565453630507053682798397822599168000000⟩, + ⟨2, 6, 7, 4, 8, 3, 748471208274084306282817906023565920521158656000000⟩, + ⟨2, 6, 2, 5, 2, 3, 1649458287710927062261950520225156300457744793600000⟩, + ⟨2, 6, 3, 5, 3, 3, -8735306769663118166184021563937436626586907443200000⟩, + ⟨2, 6, 4, 5, 4, 3, 404977110998377438945827518619107014207340544000000⟩, + ⟨2, 6, 5, 5, 5, 3, -304005236801073296222568291533396105892986880000000⟩, + ⟨2, 6, 6, 5, 6, 3, -1080001112535490995615507791756084298563715072000000⟩, + ⟨2, 6, 7, 5, 7, 3, 341404620801085673295643314330641492983205068800000⟩, + ⟨2, 6, 8, 5, 8, 3, 343489086454651265219700166964699874362759577600000⟩, + ⟨2, 6, 2, 6, 1, 3, -27677368274411715439238234155972846527110656819200000⟩, + ⟨2, 6, 3, 6, 2, 3, -9768528368846740337136672248532074962161657446400000⟩, + ⟨2, 6, 4, 6, 3, 3, -10122915592146605220032881313020459216067887104000000⟩, + ⟨2, 6, 5, 6, 4, 3, 2535113526040591552609051436625151806796726272000000⟩, + ⟨2, 6, 6, 6, 5, 3, 102727137684432537264802449124549513017556992000000⟩, + ⟨2, 6, 7, 6, 6, 3, 103215678774078509140558722437727774255454617600000⟩, + ⟨2, 6, 8, 6, 7, 3, 92590073145385824454758056347816476432295526400000⟩, + ⟨2, 6, 2, 7, 0, 3, 225791252047685264965415909596277309673934789017600000⟩, + ⟨2, 6, 3, 7, 1, 3, 89800975701633149716635503277456885199065317376000000⟩, + ⟨2, 6, 4, 7, 2, 3, 10402893463245201178933177925166644979824590848000000⟩, + ⟨2, 6, 5, 7, 3, 3, 3534446570071170349393535432107394284287688704000000⟩, + ⟨2, 6, 6, 7, 4, 3, 3565005689961227548577371796729327883858739200000000⟩, + ⟨2, 6, 7, 7, 5, 3, -370806112033232330783162443307024108330208460800000⟩, + ⟨2, 6, 8, 7, 6, 3, 138428457092020224220136522057827707898979942400000⟩ +] + +def collectedFourData_10_5_13 : List CollectedFourTerm := [ + ⟨2, 7, 1, 0, 6, 4, -10652221399247543287624934189150541828832886784000000⟩, + ⟨2, 7, 2, 0, 7, 4, 1039429302430695061022944824919915239907000320000000⟩, + ⟨2, 7, 3, 0, 8, 4, -316655645219248382627307730284563759080931328000000⟩, + ⟨2, 7, 1, 1, 5, 4, -2319349158296935430173805480026021651437060096000000⟩, + ⟨2, 7, 2, 1, 6, 4, -2392579463074038475352255782551906753158578176000000⟩, + ⟨2, 7, 3, 1, 7, 4, 4230114720599535961969982423050948170674601984000000⟩, + ⟨2, 7, 4, 1, 8, 4, -2194966058144999199627412683616623183481798656000000⟩, + ⟨2, 7, 1, 2, 4, 4, 2016567175979503692840969080883450544291577856000000⟩, + ⟨2, 7, 2, 2, 5, 4, -5017184410396840533850865737274934721920368640000000⟩, + ⟨2, 7, 3, 2, 6, 4, -1376990621380175895858672657146131007661932544000000⟩, + ⟨2, 7, 4, 2, 7, 4, 297618733256659819696183326614587469086064640000000⟩, + ⟨2, 7, 5, 2, 8, 4, -928163651053023944924332416717790726733168640000000⟩, + ⟨2, 7, 1, 3, 3, 4, -5584767970569651522270307863773103154689736704000000⟩, + ⟨2, 7, 2, 3, 4, 4, 369671573394997769923336337901356632101617664000000⟩, + ⟨2, 7, 3, 3, 5, 4, -2750494346209316876853296350897208580988993536000000⟩, + ⟨2, 7, 4, 3, 6, 4, 242388839685535400658418663046513687972020224000000⟩, + ⟨2, 7, 5, 3, 7, 4, 73119611681016947715765346772933552835133440000000⟩, + ⟨2, 7, 6, 3, 8, 4, -189509572396963714140529046227086659209396224000000⟩, + ⟨2, 7, 1, 4, 2, 4, 9628606520178684441057993815486667340143132672000000⟩, + ⟨2, 7, 2, 4, 3, 4, 7862876476543211433129949039001345063223558144000000⟩, + ⟨2, 7, 3, 4, 4, 4, 1124855543124852636340504984602809548148834304000000⟩, + ⟨2, 7, 4, 4, 5, 4, -626791212059584798487163856146256981206761472000000⟩, + ⟨2, 7, 5, 4, 6, 4, 179069283652414735007448771083294397903667200000000⟩, + ⟨2, 7, 6, 4, 7, 4, 82693722260042308903096669265699869135208448000000⟩, + ⟨2, 7, 7, 4, 8, 4, -80886191026609981921660743982920444338503680000000⟩, + ⟨2, 7, 1, 5, 1, 4, 4365722402923897520333104297665747033985646592000000⟩, + ⟨2, 7, 2, 5, 2, 4, -1069527297846473312423628002951176954469941248000000⟩, + ⟨2, 7, 3, 5, 3, 4, 2832035558226595817503337974104734051271180288000000⟩, + ⟨2, 7, 4, 5, 4, 4, -87530570580409056859755493250761497394544640000000⟩, + ⟨2, 7, 5, 5, 5, 4, 49280103332933046253376990721211125832089600000000⟩, + ⟨2, 7, 6, 5, 6, 4, 140056972663949174439619510200052555230216192000000⟩, + ⟨2, 7, 7, 5, 7, 4, -36895099063545530442068273483976031038603264000000⟩, + ⟨2, 7, 8, 5, 8, 4, -31817455049389418689476862875512908623642624000000⟩, + ⟨2, 7, 1, 6, 0, 4, -47595492853076784586180989228074346114057240576000000⟩, + ⟨2, 7, 2, 6, 1, 4, 17946316752946628248791101991109924379223392256000000⟩, + ⟨2, 7, 3, 6, 2, 4, 3167011808697603931377243087369906150992510976000000⟩, + ⟨2, 7, 4, 6, 3, 4, 2187937425731356535947870032948924053182218240000000⟩, + ⟨2, 7, 5, 6, 4, 4, -410949027847652960815972620042694941726474240000000⟩, + ⟨2, 7, 6, 6, 5, 4, -13321886197632508421216125189497312679821312000000⟩, + ⟨2, 7, 7, 6, 6, 4, -11154367753854989085578655873762751496060928000000⟩, + ⟨2, 7, 8, 6, 7, 4, -8576634910675484760024815292662584323342336000000⟩, + ⟨2, 7, 2, 7, 0, 4, -146405586294071049897056343451995498937810157568000000⟩, + ⟨2, 7, 3, 7, 1, 4, -29113981117834923560379817228115256863977635840000000⟩, + ⟨2, 7, 4, 7, 2, 4, -2248451025491927966362358559742867075372154880000000⟩, + ⟨2, 7, 5, 7, 3, 4, -572943723044520650206661615007511221035335680000000⟩, + ⟨2, 7, 6, 7, 4, 4, -462317953815362193071075402613250359243571200000000⟩, + ⟨2, 7, 7, 7, 5, 4, 40072475307255020018249433145530470602113024000000⟩, + ⟨2, 7, 8, 7, 6, 4, -12822652552203216619052529814081197022642176000000⟩ +] + +def collectedFourData_10_5_14 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 5, 5, -110521483419612851171507922251763830313380216832000000⟩, + ⟨2, 8, 1, 0, 6, 5, 132881483602370107876664950022927089543975796736000000⟩, + ⟨2, 8, 2, 0, 7, 5, -6483197383436099828083121707721228200590704640000000⟩, + ⟨2, 8, 3, 0, 8, 5, 1316710394659145403652223734914787513680789504000000⟩, + ⟨2, 8, 0, 1, 4, 5, -79463081361351298590507752249747951113520283648000000⟩, + ⟨2, 8, 1, 1, 5, 5, 28932796793744431012197328751232017540038262784000000⟩, + ⟨2, 8, 2, 1, 6, 5, 14923155310698779573149417051014850344545943552000000⟩, + ⟨2, 8, 3, 1, 7, 5, -17589568060148086857592703226438990348536512512000000⟩, + ⟨2, 8, 4, 1, 8, 5, 6845293937557400313626284696870364250170720256000000⟩, + ⟨2, 8, 0, 2, 3, 5, -31103399872144999082754564763592390989452410880000000⟩, + ⟨2, 8, 1, 2, 4, 5, -25155733070561865701332436379535760988070477824000000⟩, + ⟨2, 8, 2, 2, 5, 5, 31293515360434995021509048016512552501803745280000000⟩, + ⟨2, 8, 3, 2, 6, 5, 5725771486764643430922051186824044188209774592000000⟩, + ⟨2, 8, 4, 2, 7, 5, -928163651053023944924332416717790726733168640000000⟩, + ⟨2, 8, 5, 2, 8, 5, 2315681553266075049669090333062052055835738112000000⟩, + ⟨2, 8, 0, 3, 2, 5, 136670364036208528998107747450655119317722464256000000⟩, + ⟨2, 8, 1, 3, 3, 5, 69667370371847004085033969614604442614854844416000000⟩, + ⟨2, 8, 2, 3, 4, 5, -2305740055394440691841713230628075128517296128000000⟩, + ⟨2, 8, 3, 3, 5, 5, 11437043838575700660009756475738785043445710848000000⟩, + ⟨2, 8, 4, 3, 6, 5, -755921873449470904463134134578196739075866624000000⟩, + ⟨2, 8, 5, 3, 7, 5, -182426596602452591202144189005036409902333952000000⟩, + ⟨2, 8, 6, 3, 8, 5, 394007224614172102573717208129946686551228416000000⟩, + ⟨2, 8, 0, 4, 1, 5, 112809059541965942864683860655511722717945528320000000⟩, + ⟨2, 8, 1, 4, 2, 5, -120112366376010276889071049312112254992135487488000000⟩, + ⟨2, 8, 2, 4, 3, 5, -49042854650910825537540628179707037539094233088000000⟩, + ⟨2, 8, 3, 4, 4, 5, -4677349065092305079565152218244446762693558272000000⟩, + ⟨2, 8, 4, 4, 5, 5, 1954731859339893340123472851302447441009180672000000⟩, + ⟨2, 8, 5, 4, 6, 5, -446761124980510680458502164781373197134069760000000⟩, + ⟨2, 8, 6, 4, 7, 5, -171927589665209306508414611897065528551800832000000⟩, + ⟨2, 8, 7, 4, 8, 5, 144145347230040707261722676426907707202600960000000⟩, + ⟨2, 8, 0, 5, 0, 5, -698089668523512152240133807642005294566304907264000000⟩, + ⟨2, 8, 1, 5, 1, 5, -54460346640712027149454784969124946982278791168000000⟩, + ⟨2, 8, 2, 5, 2, 5, 6670926596639857712983609940569374803777028096000000⟩, + ⟨2, 8, 3, 5, 3, 5, -11776106675689870613349232724908203877318262784000000⟩, + ⟨2, 8, 4, 5, 4, 5, 272975740067427043360641627361427126369648640000000⟩, + ⟨2, 8, 5, 5, 5, 5, -122949251569645689767840457829571115016519680000000⟩, + ⟨2, 8, 6, 5, 6, 5, -291190879643764755966716589891223213653884928000000⟩, + ⟨2, 8, 7, 5, 7, 5, 65749873966149762959534253635908155954167808000000⟩, + ⟨2, 8, 8, 5, 8, 5, 49613485217661313703051259365371752336064512000000⟩, + ⟨2, 8, 1, 6, 0, 5, 593731529420671230856642490128764645943441096704000000⟩, + ⟨2, 8, 2, 6, 1, 5, -111935957109287611341627594927371373895810547712000000⟩, + ⟨2, 8, 3, 6, 2, 5, -13168997399787755546339095300650898163937312768000000⟩, + ⟨2, 8, 4, 6, 3, 5, -6823374211431389657593849558280534306838282240000000⟩, + ⟨2, 8, 5, 6, 4, 5, 1025279412784364876607173046104785875571310592000000⟩, + ⟨2, 8, 6, 6, 5, 5, 27697384047493782678048353884232010336043008000000⟩, + ⟨2, 8, 7, 6, 6, 5, 19877932099461145633244638886007527404732416000000⟩, + ⟨2, 8, 8, 6, 7, 5, 13373689023762503889793513889784691811155968000000⟩, + ⟨2, 8, 2, 7, 0, 5, 913170632925693169124857480365798746073109364736000000⟩, + ⟨2, 8, 3, 7, 1, 5, 121061102641075223878771772767370972400577413120000000⟩, + ⟨2, 8, 4, 7, 2, 5, 7012093930373599540074129344780397525734522880000000⟩, + ⟨2, 8, 5, 7, 3, 5, 1429441035542113568759686949644642415693266944000000⟩, + ⟨2, 8, 6, 7, 4, 5, 961200067986709964068267322425758083501260800000000⟩, + ⟨2, 8, 7, 7, 5, 5, -71412200206475660140196717027116339616022528000000⟩, + ⟨2, 8, 8, 7, 6, 5, 19994574734604668452144362332589002103717888000000⟩ +] + +def collectedFourData_10_5_15 : List CollectedFourTerm := [ + ⟨3, 2, 5, 2, 8, 0, 136670364036208528998107747450655119317722464256000000⟩, + ⟨3, 2, 5, 3, 7, 0, -10766726250584335169831759292442308108066226176000000⟩, + ⟨3, 2, 6, 3, 8, 0, 139524652890978256224757859710662153113696206848000000⟩, + ⟨3, 2, 5, 4, 6, 0, -26367617560451622944367123968417997033182330880000000⟩, + ⟨3, 2, 6, 4, 7, 0, -60882480756313614743705215011383025443794845696000000⟩, + ⟨3, 2, 7, 4, 8, 0, 178655108297451900544411128372200035644950446080000000⟩, + ⟨3, 2, 5, 5, 5, 0, -7256403172665473782340520590388595271757987840000000⟩, + ⟨3, 2, 6, 5, 6, 0, -103115638163995072893040223877573357553355587584000000⟩, + ⟨3, 2, 7, 5, 7, 0, 81491016392086857796280032392419032497634934784000000⟩, + ⟨3, 2, 8, 5, 8, 0, 163977129009555065335113660156488476269043777536000000⟩, + ⟨3, 2, 5, 6, 4, 0, 60511476798886373626032544919308964048714858496000000⟩, + ⟨3, 2, 6, 6, 5, 0, 9808114302977394793144162404461387373896269824000000⟩, + ⟨3, 2, 7, 6, 6, 0, 24636897272106446305053125018160828032344915968000000⟩, + ⟨3, 2, 8, 6, 7, 0, 44201271504355475433946201518924580957301243904000000⟩, + ⟨3, 2, 5, 7, 3, 0, 84364893100389163412843271619154161994009935872000000⟩, + ⟨3, 2, 6, 7, 4, 0, 340377276015579302019782820597501980869813862400000000⟩, + ⟨3, 2, 7, 7, 5, 0, -88508957152023526176972704725346831865263161344000000⟩, + ⟨3, 2, 8, 7, 6, 0, 66083907356307460782322626027386127149552369664000000⟩ +] + +def collectedFourData_10_5_16 : List CollectedFourTerm := [ + ⟨3, 3, 4, 1, 8, 1, 41188187329069646192657933478414180098812516761600000⟩, + ⟨3, 3, 4, 2, 7, 1, -5584767970569651522270307863773103154689736704000000⟩, + ⟨3, 3, 5, 2, 8, 1, 69667370371847004085033969614604442614854844416000000⟩, + ⟨3, 3, 4, 3, 6, 1, -4548387843355047632780002643093767632271599206400000⟩, + ⟨3, 3, 5, 3, 7, 1, -5488311315195025127446619155467649665032257536000000⟩, + ⟨3, 3, 6, 3, 8, 1, 35561168427062727423056246471272149317597528064000000⟩, + ⟨3, 3, 4, 4, 5, 1, 11761636934077532906348005095997243748368200499200000⟩, + ⟨3, 3, 5, 4, 6, 1, -13440825971024176393861315077348451294044487680000000⟩, + ⟨3, 3, 6, 4, 7, 1, -15517344838868022784162396542067864328762032128000000⟩, + ⟨3, 3, 7, 4, 8, 1, 30356328982640168043535268732776121308765224960000000⟩, + ⟨3, 3, 4, 5, 4, 1, 1642497169697956161914112604489183477528264704000000⟩, + ⟨3, 3, 5, 5, 5, 1, -3698933056647147757393408451215356353304330240000000⟩, + ⟨3, 3, 6, 5, 6, 1, -26281467111616019472103099325441905393152294912000000⟩, + ⟨3, 3, 7, 5, 7, 1, 13846612763007089720899512860424662783788843008000000⟩, + ⟨3, 3, 8, 5, 8, 1, 20896731086840177835938252784430409364352794624000000⟩, + ⟨3, 3, 4, 6, 3, 1, -41056296164991718181637399442750415706116849664000000⟩, + ⟨3, 3, 5, 6, 4, 1, 30845571354288418921201063807878464620311085056000000⟩, + ⟨3, 3, 6, 6, 5, 1, 2499830656827349206151158092920665601298399232000000⟩, + ⟨3, 3, 7, 6, 6, 1, 4186198569023734211238845755584748669492002816000000⟩, + ⟨3, 3, 8, 6, 7, 1, 5632871424825992178729963872555405923200270336000000⟩, + ⟨3, 3, 4, 7, 2, 1, 42191824194523603321333794244048925260479725568000000⟩, + ⟨3, 3, 5, 7, 3, 1, 43004789629805563175631406715774898022008225792000000⟩, + ⟨3, 3, 6, 7, 4, 1, 86753225256849926873640874990630382939091763200000000⟩, + ⟨3, 3, 7, 7, 5, 1, -15039071912479703803241216544442065300360265728000000⟩, + ⟨3, 3, 8, 7, 6, 1, 8421525913604379534238649104047730307603890176000000⟩ +] + +def collectedFourData_10_5_17 : List CollectedFourTerm := [ + ⟨3, 4, 3, 0, 8, 2, -131105759945179045626807333871822263851522457600000⟩, + ⟨3, 4, 3, 1, 7, 2, 1751405394069314923710291042895959717799840972800000⟩, + ⟨3, 4, 4, 1, 8, 2, -2726362508785125109391125939595003302852008345600000⟩, + ⟨3, 4, 3, 2, 6, 2, -570119006495003743432769591058996434582686924800000⟩, + ⟨3, 4, 4, 2, 7, 2, 369671573394997769923336337901356632101617664000000⟩, + ⟨3, 4, 5, 2, 8, 2, -2305740055394440691841713230628075128517296128000000⟩, + ⟨3, 4, 3, 3, 5, 2, -1138794324146699072581165222663699162329199411200000⟩, + ⟨3, 4, 4, 3, 6, 2, 301070644174360525851271907880624296152163942400000⟩, + ⟨3, 4, 5, 3, 7, 2, 181643417404391070191156084817567602429657088000000⟩, + ⟨3, 4, 6, 3, 8, 2, -784631408948573680917754124194606815073271808000000⟩, + ⟨3, 4, 3, 4, 4, 2, 465726864612885911308742871868972285146483916800000⟩, + ⟨3, 4, 4, 4, 5, 2, -778535984670042620275233785475612270046425907200000⟩, + ⟨3, 4, 5, 4, 6, 2, 444843126036805148163898946012997471373885440000000⟩, + ⟨3, 4, 6, 4, 7, 2, 342378967919293283710031943718485159749615616000000⟩, + ⟨3, 4, 7, 4, 8, 2, -502342799049363258690585960280152547881123840000000⟩, + ⟨3, 4, 3, 5, 3, 2, 1172555044126835028567063663243266318789089689600000⟩, + ⟨3, 4, 4, 5, 4, 2, -108721529026592795740153741440727590490865664000000⟩, + ⟨3, 4, 5, 5, 5, 2, 122421415727504649960870129407322320975953920000000⟩, + ⟨3, 4, 6, 5, 6, 2, 579881524740050522918980923909485860711563264000000⟩, + ⟨3, 4, 7, 5, 7, 2, -229136606626558567775474366945753262018527232000000⟩, + ⟨3, 4, 8, 5, 8, 2, -276642736113400984837708370724022290970627276800000⟩, + ⟨3, 4, 3, 6, 2, 2, 1311246131889317084794687198229965341897995059200000⟩, + ⟨3, 4, 4, 6, 3, 2, 2717632259937094228969066584002993575925121024000000⟩, + ⟨3, 4, 5, 6, 4, 2, -1020877765638344225493655066125889963712053248000000⟩, + ⟨3, 4, 6, 6, 5, 2, -55156951730151359092803998699090423058530304000000⟩, + ⟨3, 4, 7, 6, 6, 2, -69274078158212348395757226532163417920241664000000⟩, + ⟨3, 4, 8, 6, 7, 2, -74571135392568498314852872921468565932159795200000⟩, + ⟨3, 4, 3, 7, 1, 2, -12054137284811363062168882667533570355314556928000000⟩, + ⟨3, 4, 4, 7, 2, 2, -2792796068984000128329863369607590650878885888000000⟩, + ⟨3, 4, 5, 7, 3, 2, -1423304274210476404999712868586809599968935936000000⟩, + ⟨3, 4, 6, 7, 4, 2, -1914147042264030512802225751874439301457510400000000⟩, + ⟨3, 4, 7, 7, 5, 2, 248869666814457394748012734605838018896986112000000⟩, + ⟨3, 4, 8, 7, 6, 2, -111488919549555713185625681145773389662860083200000⟩ +] + +def collectedFourData_10_5_18 : List CollectedFourTerm := [ + ⟨3, 5, 2, 0, 7, 3, -3202021132133541269368548916376608064359366656000000⟩, + ⟨3, 5, 3, 0, 8, 3, 1950951479297977512529722562627521486084951244800000⟩, + ⟨3, 5, 2, 1, 6, 3, 7370477225489420384670492471905754286863994060800000⟩, + ⟨3, 5, 3, 1, 7, 3, -26062218363546673200761382660950654424506066534400000⟩, + ⟨3, 5, 4, 1, 8, 3, 20285153649393390531895528182050716277962860134400000⟩, + ⟨3, 5, 2, 2, 5, 3, 15455722162472712232933814904532953210355187712000000⟩, + ⟨3, 5, 3, 2, 6, 3, 8483795979386493736502642519669670750087177830400000⟩, + ⟨3, 5, 4, 2, 7, 3, -2750494346209316876853296350897208580988993536000000⟩, + ⟨3, 5, 5, 2, 8, 3, 11437043838575700660009756475738785043445710848000000⟩, + ⟨3, 5, 2, 3, 4, 3, -1138794324146699072581165222663699162329199411200000⟩, + ⟨3, 5, 3, 3, 5, 3, 16946108792162487182185217415601380262074227097600000⟩, + ⟨3, 5, 4, 3, 6, 3, -2240077853447362247959312569172519613950957977600000⟩, + ⟨3, 5, 5, 3, 7, 3, -900996503479372220290788437127277469874782208000000⟩, + ⟨3, 5, 6, 3, 8, 3, 2918975124799932859072553178890733254445367296000000⟩, + ⟨3, 5, 2, 4, 3, 3, -24222038553628124919492406276979449143026201395200000⟩, + ⟨3, 5, 3, 4, 4, 3, -6930363058383154033621041633476852913973651046400000⟩, + ⟨3, 5, 4, 4, 5, 3, 5792598020155021017673782664941314030795803852800000⟩, + ⟨3, 5, 5, 4, 6, 3, -2206532484817179429357784485701972491543511040000000⟩, + ⟨3, 5, 6, 4, 7, 3, -1273713592411890973799412977246928132837998592000000⟩, + ⟨3, 5, 7, 4, 8, 3, 1495047093781144998996776436500502843714699264000000⟩, + ⟨3, 5, 2, 5, 2, 3, 3294739720238388609685773702289712206240441958400000⟩, + ⟨3, 5, 3, 5, 3, 3, -17448493482316087126911993111250580026289867980800000⟩, + ⟨3, 5, 4, 5, 4, 3, 808928715163474527465667406876045501358145536000000⟩, + ⟨3, 5, 5, 5, 5, 3, -607240653680907239230251662534842862241054720000000⟩, + ⟨3, 5, 6, 5, 6, 3, -2157267382802674229532518068176493780263763968000000⟩, + ⟨3, 5, 7, 5, 7, 3, 681944716763515951652207257782399917995799347200000⟩, + ⟨3, 5, 8, 5, 8, 3, 686108369664254735040181416987279138304190054400000⟩, + ⟨3, 5, 2, 6, 1, 3, -55284650290805901303930142450446772120337566924800000⟩, + ⟨3, 5, 3, 6, 2, 3, -19512320296247076499540865430888598464240392601600000⟩, + ⟨3, 5, 4, 6, 3, 3, -20220197342699362581927352135280097355603378176000000⟩, + ⟨3, 5, 5, 6, 4, 3, 5063807488670088283211999970734302509051936768000000⟩, + ⟨3, 5, 6, 6, 5, 3, 205194143675498485618713301649558082523496448000000⟩, + ⟨3, 5, 7, 6, 6, 3, 206169988742340950269411706828389885499827814400000⟩, + ⟨3, 5, 8, 6, 7, 3, 184945684267793513088908230308658568129780121600000⟩, + ⟨3, 5, 2, 7, 0, 3, 451010742221473526222639174053127754626298701414400000⟩, + ⟨3, 5, 3, 7, 1, 3, 179374552096697498127993376222937592832871890944000000⟩, + ⟨3, 5, 4, 7, 2, 3, 20779444108482378722654198564395402913761984512000000⟩, + ⟨3, 5, 5, 7, 3, 3, 7059943006885335948637592639908311150756888576000000⟩, + ⟨3, 5, 6, 7, 4, 3, 7120983863066685890689075099980763753139404800000000⟩, + ⟨3, 5, 7, 7, 5, 3, -740673247044344212696539654498479771279897395200000⟩, + ⟨3, 5, 8, 7, 6, 3, 276506377512181748520369873227376709919676825600000⟩ +] + +def collectedFourData_10_5_19 : List CollectedFourTerm := [ + ⟨3, 6, 1, 0, 6, 4, -8675460569245821668224815571480889572934968934400000⟩, + ⟨3, 6, 2, 0, 7, 4, 846539664336414332790205291465013249716518912000000⟩, + ⟨3, 6, 3, 0, 8, 4, -257893021668019109844039017993911307416161484800000⟩, + ⟨3, 6, 1, 1, 5, 4, -1888941415594299931162477205711578569694091673600000⟩, + ⟨3, 6, 2, 1, 6, 4, -1948582179502238278305176951939702394959010201600000⟩, + ⟨3, 6, 3, 1, 7, 4, 3445121171114588801667116461904698876388337254400000⟩, + ⟨3, 6, 4, 1, 8, 4, -1787640415511359357305388294751370992680540569600000⟩, + ⟨3, 6, 1, 2, 4, 4, 1642347484598975715577710953243559479706491289600000⟩, + ⟨3, 6, 2, 2, 5, 4, -4086132261962493004822953938645566342639386624000000⟩, + ⟨3, 6, 3, 2, 6, 4, -1121458838702776841018157578268802845161973350400000⟩, + ⟨3, 6, 4, 2, 7, 4, 242388839685535400658418663046513687972020224000000⟩, + ⟨3, 6, 5, 2, 8, 4, -755921873449470904463134134578196739075866624000000⟩, + ⟨3, 6, 1, 3, 3, 4, -4548387843355047632780002643093767632271599206400000⟩, + ⟨3, 6, 2, 3, 4, 4, 301070644174360525851271907880624296152163942400000⟩, + ⟨3, 6, 3, 3, 5, 4, -2240077853447362247959312569172519613950957977600000⟩, + ⟨3, 6, 4, 3, 6, 4, 197408103183590439578548908788155443795355238400000⟩, + ⟨3, 6, 5, 3, 7, 4, 59550612421746883583833940866809808293986304000000⟩, + ⟨3, 6, 6, 3, 8, 4, -154341781043025503180668754445679698964276838400000⟩, + ⟨3, 6, 1, 4, 2, 4, 7841800604003031266487947460434913859286020915200000⟩, + ⟨3, 6, 2, 4, 3, 4, 6403741743287431866963579912159735289878046310400000⟩, + ⟨3, 6, 3, 4, 4, 4, 916113132155381921766655410415012665608267366400000⟩, + ⟨3, 6, 4, 4, 5, 4, -510475913104550670199706150825246399298482995200000⟩, + ⟨3, 6, 5, 4, 6, 4, 145838924226580281431891188112712214794731520000000⟩, + ⟨3, 6, 6, 4, 7, 4, 67348030040179131198604858439345761908739276800000⟩, + ⟨3, 6, 7, 4, 8, 4, -65875927146746019556369985346554149352767488000000⟩, + ⟨3, 6, 1, 5, 1, 4, 3555563778041151138729114081330901133135393587200000⟩, + ⟨3, 6, 2, 5, 2, 4, -871052295331989623184405989487301742503447756800000⟩, + ⟨3, 6, 3, 5, 3, 4, 2306487247611323878296260191108357739418275020800000⟩, + ⟨3, 6, 4, 5, 4, 4, -71287291656139228261978749950247900203188224000000⟩, + ⟨3, 6, 5, 5, 5, 4, 40135064536249700725496158631492356260495360000000⟩, + ⟨3, 6, 6, 5, 6, 4, 114066230718773916048858641901445557473456947200000⟩, + ⟨3, 6, 7, 5, 7, 4, -30048378185870018937966820434525148752012902400000⟩, + ⟨3, 6, 8, 5, 8, 4, -25913005968335176034173126837731833202239078400000⟩, + ⟨3, 6, 1, 6, 0, 4, -38763071667836015117803008054934007354565958041600000⟩, + ⟨3, 6, 2, 6, 1, 4, 14615971403333962552347031881597031500752722329600000⟩, + ⟨3, 6, 3, 6, 2, 4, 2579301071477238229578446149546499012256438681600000⟩, + ⟨3, 6, 4, 6, 3, 4, 1781916104959140895862970512263549430198697984000000⟩, + ⟨3, 6, 5, 6, 4, 4, -334688132497326304932587802561023673404227584000000⟩, + ⟨3, 6, 6, 6, 5, 4, -10849708627320204998157929295965366149919539200000⟩, + ⟨3, 6, 7, 6, 6, 4, -9084422299960051091574513460716300334320844800000⟩, + ⟨3, 6, 8, 6, 7, 4, -6985046141609324112204111969281992962972057600000⟩, + ⟨3, 6, 2, 7, 0, 4, -119236715367298915150811997362711517417763032268800000⟩, + ⟨3, 6, 3, 7, 1, 4, -23711222827135937878756019659568160380911878144000000⟩, + ⟨3, 6, 4, 7, 2, 4, -1831200036352366055875258607434223981489553408000000⟩, + ⟨3, 6, 5, 7, 3, 4, -466621044697845808141974500070654045415538688000000⟩, + ⟨3, 6, 6, 7, 4, 4, -376524391340843130498208454674075766143057920000000⟩, + ⟨3, 6, 7, 7, 5, 4, 32636120336808342749885728690976948945839718400000⟩, + ⟨3, 6, 8, 7, 6, 4, -10443119086657014165129231839464829885192601600000⟩ +] + +def collectedFourData_10_5_20 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 5, 5, 8706749010138060840438276295289864045904003072000000⟩, + ⟨3, 7, 1, 0, 6, 5, -10468242825044282848982959259437453234201952256000000⟩, + ⟨3, 7, 2, 0, 7, 5, 510738461466803754677029208774539992304189440000000⟩, + ⟨3, 7, 3, 0, 8, 5, -103728854975743033499361521828468786970230784000000⟩, + ⟨3, 7, 0, 1, 4, 5, 6260005598718638379415798332007174433572651008000000⟩, + ⟨3, 7, 1, 1, 5, 5, -2279290795329268933832060164501614241895153664000000⟩, + ⟨3, 7, 2, 1, 6, 5, -1175628155806183513168914856819800495926280192000000⟩, + ⟨3, 7, 3, 1, 7, 5, 1385684932539307320748240663956630691330916352000000⟩, + ⟨3, 7, 4, 1, 8, 5, -539263990772272421741088896346903379156402176000000⟩, + ⟨3, 7, 0, 2, 3, 5, 2450288284862720358752969708737228834319892480000000⟩, + ⟨3, 7, 1, 2, 4, 5, 1981738275986117176206806591485853758604181504000000⟩, + ⟨3, 7, 2, 2, 5, 5, -2465265353467529667883330865552741775578234880000000⟩, + ⟨3, 7, 3, 2, 6, 5, -451069363911722848051969335576755877584044032000000⟩, + ⟨3, 7, 4, 2, 7, 5, 73119611681016947715765346772933552835133440000000⟩, + ⟨3, 7, 5, 2, 8, 5, -182426596602452591202144189005036409902333952000000⟩, + ⟨3, 7, 0, 3, 2, 5, -10766726250584335169831759292442308108066226176000000⟩, + ⟨3, 7, 1, 3, 3, 5, -5488311315195025127446619155467649665032257536000000⟩, + ⟨3, 7, 2, 3, 4, 5, 181643417404391070191156084817567602429657088000000⟩, + ⟨3, 7, 3, 3, 5, 5, -900996503479372220290788437127277469874782208000000⟩, + ⟨3, 7, 4, 3, 6, 5, 59550612421746883583833940866809808293986304000000⟩, + ⟨3, 7, 5, 3, 7, 5, 14371347001929548308826732807689467007598592000000⟩, + ⟨3, 7, 6, 3, 8, 5, -31039413395060495172960057554735412371521536000000⟩, + ⟨3, 7, 0, 4, 1, 5, -8886961494830233946128804745571325881058590720000000⟩, + ⟨3, 7, 1, 4, 2, 5, 9462307188541452002214931590303306064381083648000000⟩, + ⟨3, 7, 2, 4, 3, 5, 3863536870609788159420943156563128897658421248000000⟩, + ⟨3, 7, 3, 4, 4, 5, 368475911492658705490017419355294536734605312000000⟩, + ⟨3, 7, 4, 4, 5, 5, -153991415558332406538457460285555202129395712000000⟩, + ⟨3, 7, 5, 4, 6, 5, 35195301966078638728888691873131801828392960000000⟩, + ⟨3, 7, 6, 4, 7, 5, 13544247912866346036245627660218688782467072000000⟩, + ⟨3, 7, 7, 4, 8, 5, -11355596400622038482569255971869620866908160000000⟩, + ⟨3, 7, 0, 5, 0, 5, 54994661149527190794330240874695660642704031744000000⟩, + ⟨3, 7, 1, 5, 1, 5, 4290320347995344539892959497394974734237564928000000⟩, + ⟨3, 7, 2, 5, 2, 5, -525527542201724110497817432960227838909218816000000⟩, + ⟨3, 7, 3, 5, 3, 5, 927707464372017312112168959100404508775153664000000⟩, + ⟨3, 7, 4, 5, 4, 5, -21504699186855164291801617460713452145213440000000⟩, + ⟨3, 7, 5, 5, 5, 5, 9685793578583672941410825114829341358817280000000⟩, + ⟨3, 7, 6, 5, 6, 5, 22939665888068126909260096850789948234661888000000⟩, + ⟨3, 7, 7, 5, 7, 5, -5179695678694519807342710500354069121466368000000⟩, + ⟨3, 7, 8, 5, 8, 5, -3908490457627311536924774505233189387108352000000⟩, + ⟨3, 7, 1, 6, 0, 5, -46773452962483721196709480136844957166268841984000000⟩, + ⟨3, 7, 2, 6, 1, 5, 8818179539446868311368902857817832090136215552000000⟩, + ⟨3, 7, 3, 6, 2, 5, 1037437713713907916867262935531775245342998528000000⟩, + ⟨3, 7, 4, 6, 3, 5, 537537181215929885248849730003338611696599040000000⟩, + ⟨3, 7, 5, 6, 4, 5, -80770274123836685717327618989251651837100032000000⟩, + ⟨3, 7, 6, 6, 5, 5, -2181966470928996106626999762506177543405568000000⟩, + ⟨3, 7, 7, 6, 6, 5, -1565959488378184262602587911749563146305536000000⟩, + ⟨3, 7, 8, 6, 7, 5, -1053563072687414311519698515615650286665728000000⟩, + ⟨3, 7, 2, 7, 0, 5, -71938479816875194155546320328634971911677280256000000⟩, + ⟨3, 7, 3, 7, 1, 5, -9537047485913088961129692515234885746053611520000000⟩, + ⟨3, 7, 4, 7, 2, 5, -552404292796899060855427580810818411277844480000000⟩, + ⟨3, 7, 5, 7, 3, 5, -112609638743307220880823958575762645423489024000000⟩, + ⟨3, 7, 6, 7, 4, 5, -75722180715887820785993544930162803264716800000000⟩, + ⟨3, 7, 7, 7, 5, 5, 5625766902701340768509176725875848000831488000000⟩, + ⟨3, 7, 8, 7, 6, 5, -1575148454329898411147715049834183863042048000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1019.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1019.lean new file mode 100644 index 0000000000000000000000000000000000000000..38d39b36cd6380742a9032c81bf6a06067d6fd2d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1019.lean @@ -0,0 +1,654 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1019. -/ +namespace LaughlinFock +def collectedFourData_10_5_21 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 5, 6, -112829666620571050438812066914287488011920736256000000⟩, + ⟨3, 8, 1, 0, 6, 6, 67828321838474728526111980236252317242405945344000000⟩, + ⟨3, 8, 2, 0, 7, 6, -2206198519887775823773444877761426966488023040000000⟩, + ⟨3, 8, 3, 0, 8, 6, 336052300124276420732792260195097168270327808000000⟩, + ⟨3, 8, 0, 1, 4, 6, -81122626128754386653904471223273079448570691584000000⟩, + ⟨3, 8, 1, 1, 5, 6, 14768521538227949214206773147636842490270580736000000⟩, + ⟨3, 8, 2, 1, 6, 6, 5078272526860750534813872790354180352268828672000000⟩, + ⟨3, 8, 3, 1, 7, 6, -4489229240371756851273584781946850913156071424000000⟩, + ⟨3, 8, 4, 1, 8, 6, 1397650862071867542214784381945700581795010969600000⟩, + ⟨3, 8, 0, 2, 3, 6, -31752978061436931889586095055729041932854231040000000⟩, + ⟨3, 8, 1, 2, 4, 6, -12840548679442941204471296828809954861982416896000000⟩, + ⟨3, 8, 2, 2, 5, 6, 10649021337321363984707084419714613726234542080000000⟩, + ⟨3, 8, 3, 2, 6, 6, 1461337805122560817667905265723473174235971584000000⟩, + ⟨3, 8, 4, 2, 7, 6, -189509572396963714140529046227086659209396224000000⟩, + ⟨3, 8, 5, 2, 8, 6, 394007224614172102573717208129946686551228416000000⟩, + ⟨3, 8, 0, 3, 2, 6, 139524652890978256224757859710662153113696206848000000⟩, + ⟨3, 8, 1, 3, 3, 6, 35561168427062727423056246471272149317597528064000000⟩, + ⟨3, 8, 2, 3, 4, 6, -784631408948573680917754124194606815073271808000000⟩, + ⟨3, 8, 3, 3, 5, 6, 2918975124799932859072553178890733254445367296000000⟩, + ⟨3, 8, 4, 3, 6, 6, -154341781043025503180668754445679698964276838400000⟩, + ⟨3, 8, 5, 3, 7, 6, -31039413395060495172960057554735412371521536000000⟩, + ⟨3, 8, 6, 3, 8, 6, 57462265543084065131551188938000497643618304000000⟩, + ⟨3, 8, 0, 4, 1, 6, 115165017570162766617390214457026201036322242560000000⟩, + ⟨3, 8, 1, 4, 2, 6, -61310425068037870917551053945184196733175857152000000⟩, + ⟨3, 8, 2, 4, 3, 6, -16689029647369090911081306424386799723628986368000000⟩, + ⟨3, 8, 3, 4, 4, 6, -1193758261637557000546341718713974328020434944000000⟩, + ⟨3, 8, 4, 4, 5, 6, 399111081751533237350782646260176932259967795200000⟩, + ⟨3, 8, 5, 4, 6, 6, -76015249450342071932624202966219307540807680000000⟩, + ⟨3, 8, 6, 4, 7, 6, -25074029597297138077184808612156993970372608000000⟩, + ⟨3, 8, 7, 4, 8, 6, 18394468398423844291863796565107828284456960000000⟩, + ⟨3, 8, 0, 5, 0, 6, -712668905028425984838251572827349045362988941312000000⟩, + ⟨3, 8, 1, 5, 1, 6, -27798861205032671016615154634138992363670863872000000⟩, + ⟨3, 8, 2, 5, 2, 6, 2270081799666976070972094950068571293253369856000000⟩, + ⟨3, 8, 3, 5, 3, 6, -3005511121448137252885176416095884735695290368000000⟩, + ⟨3, 8, 4, 5, 4, 6, 55735339038791453629543432640514483472564224000000⟩, + ⟨3, 8, 5, 5, 5, 6, -20919497031455423535815214788128310286090240000000⟩, + ⟨3, 8, 6, 5, 6, 6, -42467464057795831072979494139621378812280832000000⟩, + ⟨3, 8, 7, 5, 7, 6, 8390378198892288283153111761016044134596608000000⟩, + ⟨3, 8, 8, 5, 8, 6, 5627737425431998433905230351062166084255744000000⟩, + ⟨3, 8, 1, 6, 0, 6, 303065650468676863456374238647086066483557564416000000⟩, + ⟨3, 8, 2, 6, 1, 6, -38091226950404312299952492868060416089031442432000000⟩, + ⟨3, 8, 3, 6, 2, 6, -3361006250486011431163526566275513113835995136000000⟩, + ⟨3, 8, 4, 6, 3, 6, -1393175360450482107636298308755409654182313984000000⟩, + ⟨3, 8, 5, 6, 4, 6, 174448639242063909967752334468516700598829056000000⟩, + ⟨3, 8, 6, 6, 5, 6, 4039404197586435316080307581210914143076352000000⟩, + ⟨3, 8, 7, 6, 6, 6, 2536634035408884177609906126572521066070016000000⟩, + ⟨3, 8, 8, 6, 7, 6, 1516999055900333604312313439277093293654016000000⟩, + ⟨3, 8, 2, 7, 0, 6, 310747240846443144511086086090717596286132944896000000⟩, + ⟨3, 8, 3, 7, 1, 6, 30897350065080900168881310574762618081498890240000000⟩, + ⟨3, 8, 4, 7, 2, 6, 1431707566704237070233570272974386518355345408000000⟩, + ⟨3, 8, 5, 7, 3, 6, 243215693612619403573712768620289292912033792000000⟩, + ⟨3, 8, 6, 7, 4, 6, 140182032450721997795299547335249399853875200000000⟩, + ⟨3, 8, 7, 7, 5, 6, -9112950818062712821410360182207682422243328000000⟩, + ⟨3, 8, 8, 7, 6, 6, 2268016770962012653044952570516312273453056000000⟩ +] + +def collectedFourData_10_5_22 : List CollectedFourTerm := [ + ⟨4, 1, 5, 2, 8, 0, 112809059541965942864683860655511722717945528320000000⟩, + ⟨4, 1, 5, 3, 7, 0, -8886961494830233946128804745571325881058590720000000⟩, + ⟨4, 1, 6, 3, 8, 0, 115165017570162766617390214457026201036322242560000000⟩, + ⟨4, 1, 5, 4, 6, 0, -21764090264431637996993380735424858510956953600000000⟩, + ⟨4, 1, 6, 4, 7, 0, -50252997020495176081509293643902576357403525120000000⟩, + ⟨4, 1, 7, 4, 8, 0, 147463679426976446053059387780731813785868697600000000⟩, + ⟨4, 1, 5, 5, 5, 0, -5989506381565346463507418114497078933376204800000000⟩, + ⟨4, 1, 6, 5, 6, 0, -85112659554108831624772884326222716144692756480000000⟩, + ⟨4, 1, 7, 5, 7, 0, 67263484553789124152945696311006449289899540480000000⟩, + ⟨4, 1, 8, 5, 8, 0, 135348331296306229801636499094979002861795409920000000⟩, + ⟨4, 1, 5, 6, 4, 0, 49946766713589529059916131056251980047575941120000000⟩, + ⟨4, 1, 6, 6, 5, 0, 8095713786976164294167832867627442585762529280000000⟩, + ⟨4, 1, 7, 6, 6, 0, 20335536755883920397893204125985021369474088960000000⟩, + ⟨4, 1, 8, 6, 7, 0, 36484163220962823292978553436787566330123386880000000⟩, + ⟨4, 1, 5, 7, 3, 0, 69635610588495907327328549488052524671660195840000000⟩, + ⟨4, 1, 6, 7, 4, 0, 280950743546719818361450635619023033653526528000000000⟩, + ⟨4, 1, 7, 7, 5, 0, -73056161719995698545323104647817378133631303680000000⟩, + ⟨4, 1, 8, 7, 6, 0, 54546305574692169817707680430225864930707374080000000⟩ +] + +def collectedFourData_10_5_23 : List CollectedFourTerm := [ + ⟨4, 2, 4, 1, 8, 1, -71011875723561895086325162781954165867857890508800000⟩, + ⟨4, 2, 4, 2, 7, 1, 9628606520178684441057993815486667340143132672000000⟩, + ⟨4, 2, 5, 2, 8, 1, -120112366376010276889071049312112254992135487488000000⟩, + ⟨4, 2, 4, 3, 6, 1, 7841800604003031266487947460434913859286020915200000⟩, + ⟨4, 2, 5, 3, 7, 1, 9462307188541452002214931590303306064381083648000000⟩, + ⟨4, 2, 6, 3, 8, 1, -61310425068037870917551053945184196733175857152000000⟩, + ⟨4, 2, 4, 4, 5, 1, -20278044614964002894016416608864556960255154585600000⟩, + ⟨4, 2, 5, 4, 6, 1, 23173106790323786150190410797061133419403018240000000⟩, + ⟨4, 2, 6, 4, 7, 1, 26753198786188014409877036814733714312925282304000000⟩, + ⟨4, 2, 7, 4, 8, 1, -52336847065308700356468627461794043792751329280000000⟩, + ⟨4, 2, 4, 5, 4, 1, -2831802331067235960982307225341094395140636672000000⟩, + ⟨4, 2, 5, 5, 5, 1, 6377269590182164128835610482485619295854264320000000⟩, + ⟨4, 2, 6, 5, 6, 1, 45311444794895557421498881700968683072091324416000000⟩, + ⟨4, 2, 7, 5, 7, 1, -23872717118215445485707899408521310013587718144000000⟩, + ⟨4, 2, 8, 5, 8, 1, -36027710059482865739177359866822745465376735232000000⟩, + ⟨4, 2, 4, 6, 3, 1, 70784484338801256501467957419206669613192445952000000⟩, + ⟨4, 2, 5, 6, 4, 1, -53180341784234244813124997729878393639831339008000000⟩, + ⟨4, 2, 6, 6, 5, 1, -4309916882583615593128471731809510388374962176000000⟩, + ⟨4, 2, 7, 6, 6, 1, -7217356038580995507034596480546672569575538688000000⟩, + ⟨4, 2, 8, 6, 7, 1, -9711540893770659300274942459456250238675714048000000⟩, + ⟨4, 2, 4, 7, 2, 1, -72742229521163977019628378429119663034517684224000000⟩, + ⟨4, 2, 5, 7, 3, 1, -74143849844888428156461630216455027241837920256000000⟩, + ⟨4, 2, 6, 7, 4, 1, -149569807511525436496772275683374493249149337600000000⟩, + ⟨4, 2, 7, 7, 5, 1, 25928616307253301665186282196492570350378287104000000⟩, + ⟨4, 2, 8, 7, 6, 1, -14519414190329177585986352758987227162809991168000000⟩ +] + +def collectedFourData_10_5_24 : List CollectedFourTerm := [ + ⟨4, 3, 3, 0, 8, 2, -2788606076320551523385010012300938764374088089600000⟩, + ⟨4, 3, 3, 1, 7, 2, 37252213221177189391589172293396074117106289868800000⟩, + ⟨4, 3, 4, 1, 8, 2, -57989451122740755006380842521154124182158154137600000⟩, + ⟨4, 3, 3, 2, 6, 2, -12126372833677046305588867043871057880653024460800000⟩, + ⟨4, 3, 4, 2, 7, 2, 7862876476543211433129949039001345063223558144000000⟩, + ⟨4, 3, 5, 2, 8, 2, -49042854650910825537540628179707037539094233088000000⟩, + ⟨4, 3, 3, 3, 5, 2, -24222038553628124919492406276979449143026201395200000⟩, + ⟨4, 3, 4, 3, 6, 2, 6403741743287431866963579912159735289878046310400000⟩, + ⟨4, 3, 5, 3, 7, 2, 3863536870609788159420943156563128897658421248000000⟩, + ⟨4, 3, 6, 3, 8, 2, -16689029647369090911081306424386799723628986368000000⟩, + ⟨4, 3, 3, 4, 4, 2, 9905962675539707972873611746649947973492722892800000⟩, + ⟨4, 3, 4, 4, 5, 2, -16559380597716573628574830522772041359762338611200000⟩, + ⟨4, 3, 5, 4, 6, 2, 9461767696509801801968798811800839334909706240000000⟩, + ⟨4, 3, 6, 4, 7, 2, 7282365555436516734007712440576203894068084736000000⟩, + ⟨4, 3, 7, 4, 8, 2, -10684779848045409943466992233895449219186032640000000⟩, + ⟨4, 3, 3, 5, 3, 2, 24940125607293272766494015595787302975928113561600000⟩, + ⟨4, 3, 4, 5, 4, 2, -2312495778958842945722178096061174651388166144000000⟩, + ⟨4, 3, 5, 5, 5, 2, 2603890964914368264871627703564685021617848320000000⟩, + ⟨4, 3, 6, 5, 6, 2, 12334020596137758518283099804923733937691295744000000⟩, + ⟨4, 3, 7, 5, 7, 2, -4873712137540522430945406458152782620862185472000000⟩, + ⟨4, 3, 8, 5, 8, 2, -5884162642574576994865756604970722062439861452800000⟩, + ⟨4, 3, 3, 6, 2, 2, 27890070828828033395566965674395307063863620403200000⟩, + ⟨4, 3, 4, 6, 3, 2, 57803759624551894398745815601717297199085256704000000⟩, + ⟨4, 3, 5, 6, 4, 2, -21713965440038751595702766231337804019802308608000000⟩, + ⟨4, 3, 6, 6, 5, 2, -1173182709976544379768419209080333834947395584000000⟩, + ⟨4, 3, 7, 6, 6, 2, -1473452542163455136558090114375075891609862144000000⟩, + ⟨4, 3, 8, 6, 7, 2, -1586120406615176061975252019337466614927012659200000⟩, + ⟨4, 3, 3, 7, 1, 2, -256390264556512548447358940632440511723248549888000000⟩, + ⟨4, 3, 4, 7, 2, 2, -59402486139048611756988550336360815163550466048000000⟩, + ⟨4, 3, 5, 7, 3, 2, -30273536030575400322783518839304457040435347456000000⟩, + ⟨4, 3, 6, 7, 4, 2, -40713711398038130052756729877932569639937638400000000⟩, + ⟨4, 3, 7, 7, 5, 2, 5293432305192830714224098461364875016328445952000000⟩, + ⟨4, 3, 8, 7, 6, 2, -2371357891737970098930707630508240983154701107200000⟩ +] + +def collectedFourData_10_5_25 : List CollectedFourTerm := [ + ⟨4, 4, 2, 0, 7, 3, 1309514133212919785610775293904850634600873984000000⟩, + ⟨4, 4, 3, 0, 8, 3, -797870604199000017219880429876516497472566067200000⟩, + ⟨4, 4, 2, 1, 6, 3, -3014266207815837528581983929049485585679594291200000⟩, + ⟨4, 4, 3, 1, 7, 3, 10658531559160962050147347943106219772405717401600000⟩, + ⟨4, 4, 4, 1, 8, 3, -8295915080540585050076109479469093296885307801600000⟩, + ⟨4, 4, 2, 2, 5, 3, -6320847294747358330031438464454143281954029568000000⟩, + ⟨4, 4, 3, 2, 6, 3, -3469574459335025669310424120295768734905768345600000⟩, + ⟨4, 4, 4, 2, 7, 3, 1124855543124852636340504984602809548148834304000000⟩, + ⟨4, 4, 5, 2, 8, 3, -4677349065092305079565152218244446762693558272000000⟩, + ⟨4, 4, 2, 3, 4, 3, 465726864612885911308742871868972285146483916800000⟩, + ⟨4, 4, 3, 3, 5, 3, -6930363058383154033621041633476852913973651046400000⟩, + ⟨4, 4, 4, 3, 6, 3, 916113132155381921766655410415012665608267366400000⟩, + ⟨4, 4, 5, 3, 7, 3, 368475911492658705490017419355294536734605312000000⟩, + ⟨4, 4, 6, 3, 8, 3, -1193758261637557000546341718713974328020434944000000⟩, + ⟨4, 4, 2, 4, 3, 3, 9905962675539707972873611746649947973492722892800000⟩, + ⟨4, 4, 3, 4, 4, 3, 2834274977817655162951998853541003681175542169600000⟩, + ⟨4, 4, 4, 4, 5, 3, -2368969054979310632307195152693214262422876979200000⟩, + ⟨4, 4, 5, 4, 6, 3, 902394255073583297406535231498355395327426560000000⟩, + ⟨4, 4, 6, 4, 7, 3, 520904104657610803399304190365819549817765888000000⟩, + ⟨4, 4, 7, 4, 8, 3, -611421729693837903719248381373278345437904896000000⟩, + ⟨4, 4, 2, 5, 2, 3, -1347432777882807990431133926124538273849776537600000⟩, + ⟨4, 4, 3, 5, 3, 3, 7135820744300292330880246788026761333578085171200000⟩, + ⟨4, 4, 4, 5, 4, 3, -330823421069214744995744820196067723710562304000000⟩, + ⟨4, 4, 5, 5, 5, 3, 248340090662286235307634498250473604204462080000000⟩, + ⟨4, 4, 6, 5, 6, 3, 882246559383897169415377114971384976037117952000000⟩, + ⟨4, 4, 7, 5, 7, 3, -278891427576769085825193214161452368617327820800000⟩, + ⟨4, 4, 8, 5, 8, 3, -280594215314362010191570384417135943180982681600000⟩, + ⟨4, 4, 2, 6, 1, 3, 22609479425048586788215378550920006304370209587200000⟩, + ⟨4, 4, 3, 6, 2, 3, 7979853394248996117706978245775396686761715302400000⟩, + ⟨4, 4, 4, 6, 3, 3, 8269350233480857685766270728517372904696971264000000⟩, + ⟨4, 4, 5, 6, 4, 3, -2070919335208918786517872289129721179670577152000000⟩, + ⟨4, 4, 6, 6, 5, 3, -83917194830174942486390400870798195972636672000000⟩, + ⟨4, 4, 7, 6, 6, 3, -84316281174119476881832327558763859517479321600000⟩, + ⟨4, 4, 8, 6, 7, 3, -75636286405154615282756065885373776529876582400000⟩, + ⟨4, 4, 2, 7, 0, 3, -184447546345936217183245718952135253019330189721600000⟩, + ⟨4, 4, 3, 7, 1, 3, -73357889100766322479127370815114231462196412416000000⟩, + ⟨4, 4, 4, 7, 2, 3, -8498062510360338511549997836404660202811424768000000⟩, + ⟨4, 4, 5, 7, 3, 3, -2887268623687676452732721120644892331148836864000000⟩, + ⟨4, 4, 6, 7, 4, 3, -2912232189065408413290647696904787399488307200000000⟩, + ⟨4, 4, 7, 7, 5, 3, 302909332909681220801779547446610693857266892800000⟩, + ⟨4, 4, 8, 7, 6, 3, -113081392762216169296834058770673752718337638400000⟩ +] + +def collectedFourData_10_5_26 : List CollectedFourTerm := [ + ⟨4, 5, 1, 0, 6, 4, 22433798736061279019320881576791537094589887283200000⟩, + ⟨4, 5, 2, 0, 7, 4, -2189059624008749611959712451880148560443867136000000⟩, + ⟨4, 5, 3, 0, 8, 4, 666883342660155749674124528875077887993472614400000⟩, + ⟨4, 5, 1, 1, 5, 4, 4884597330990701099861026741129020745481768140800000⟩, + ⟨4, 5, 2, 1, 6, 4, 5038821868500408119881235727656652826125061324800000⟩, + ⟨4, 5, 3, 1, 7, 4, -8908709152354221468566924177594524652853736243200000⟩, + ⟨4, 5, 4, 1, 8, 4, 4622643947711134729530070138985959969069518028800000⟩, + ⟨4, 5, 1, 2, 4, 4, -4246932209545258363985559595844263377873194188800000⟩, + ⟨4, 5, 2, 2, 5, 4, 10566294209064944291306126542183611423283740672000000⟩, + ⟨4, 5, 3, 2, 6, 4, 2899970748229935183102854353483414490517287731200000⟩, + ⟨4, 5, 4, 2, 7, 4, -626791212059584798487163856146256981206761472000000⟩, + ⟨4, 5, 5, 2, 8, 4, 1954731859339893340123472851302447441009180672000000⟩, + ⟨4, 5, 1, 3, 3, 4, 11761636934077532906348005095997243748368200499200000⟩, + ⟨4, 5, 2, 3, 4, 4, -778535984670042620275233785475612270046425907200000⟩, + ⟨4, 5, 3, 3, 5, 4, 5792598020155021017673782664941314030795803852800000⟩, + ⟨4, 5, 4, 3, 6, 4, -510475913104550670199706150825246399298482995200000⟩, + ⟨4, 5, 5, 3, 7, 4, -153991415558332406538457460285555202129395712000000⟩, + ⟨4, 5, 6, 3, 8, 4, 399111081751533237350782646260176932259967795200000⟩, + ⟨4, 5, 1, 4, 2, 4, -20278044614964002894016416608864556960255154585600000⟩, + ⟨4, 5, 2, 4, 3, 4, -16559380597716573628574830522772041359762338611200000⟩, + ⟨4, 5, 3, 4, 4, 4, -2368969054979310632307195152693214262422876979200000⟩, + ⟨4, 5, 4, 4, 5, 4, 1320035265308126242638273528865193467372476825600000⟩, + ⟨4, 5, 5, 4, 6, 4, -377123617572641658864534441290121846781378560000000⟩, + ⟨4, 5, 6, 4, 7, 4, -174154690593323892883924628985594306584012390400000⟩, + ⟨4, 5, 7, 4, 8, 4, 170347992405204201969249384348161223702872064000000⟩, + ⟨4, 5, 1, 5, 1, 4, -9194301738004324256880709976680580824465775001600000⟩, + ⟨4, 5, 2, 5, 2, 4, 2252446625293210361242050800441036267218953830400000⟩, + ⟨4, 5, 3, 5, 3, 4, -5964325500323556997368407545532664378653304422400000⟩, + ⟨4, 5, 4, 5, 4, 4, 184341193264365688259924903604116933125865472000000⟩, + ⟨4, 5, 5, 5, 5, 4, -103784917570471850546131773614375947028398080000000⟩, + ⟨4, 5, 6, 5, 6, 4, -294962883192328212179785133236915181832477081600000⟩, + ⟨4, 5, 7, 5, 7, 4, 77701842246452995500106073683791629042004787200000⟩, + ⟨4, 5, 8, 5, 8, 4, 67008218860537360317762683639706224872862515200000⟩, + ⟨4, 5, 1, 6, 0, 4, 100237093033476724617134360463791795489928432844800000⟩, + ⟨4, 5, 2, 6, 1, 4, -37795314516993494322120709740465822852551855308800000⟩, + ⟨4, 5, 3, 6, 2, 4, -6669792416825863414176032902796006061092162764800000⟩, + ⟨4, 5, 4, 6, 3, 4, -4607841502376253281735240364495438703075786752000000⟩, + ⟨4, 5, 5, 6, 4, 4, 865467158067660414828176692772341323820695552000000⟩, + ⟨4, 5, 6, 6, 5, 4, 28056168055567397210784368354113678042831257600000⟩, + ⟨4, 5, 7, 6, 6, 4, 23491329351798015618209246466962618543662694400000⟩, + ⟨4, 5, 8, 6, 7, 4, 18062570632672170445812768119543841510182092800000⟩, + ⟨4, 5, 2, 7, 0, 4, 308333194894752095217677365405387629349711537766400000⟩, + ⟨4, 5, 3, 7, 1, 4, 61314646806827885589538815702953812489490399232000000⟩, + ⟨4, 5, 4, 7, 2, 4, 4735284395923238770885240477223372983394893824000000⟩, + ⟨4, 5, 5, 7, 3, 4, 1206631338959810647023234915368309418218225664000000⟩, + ⟨4, 5, 6, 7, 4, 4, 973651179339376057329237810520832549333237760000000⟩, + ⟨4, 5, 7, 7, 5, 4, -84393462377926815241606907989679502099952435200000⟩, + ⟨4, 5, 8, 7, 6, 4, 27004771665644254848392116143951779845688524800000⟩ +] + +def collectedFourData_10_5_27 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 5, 5, 21322751479977628766885349273742460272886415360000000⟩, + ⟨4, 6, 1, 0, 6, 5, -25636634285721618660471150958055933330356961280000000⟩, + ⟨4, 6, 2, 0, 7, 5, 1250793984349630541725313770058098102448947200000000⟩, + ⟨4, 6, 3, 0, 8, 5, -254031050323723280148592571833688092751953920000000⟩, + ⟨4, 6, 0, 1, 4, 5, 15330698460392338730087903077181072224592855040000000⟩, + ⟨4, 6, 1, 1, 5, 5, -5581963040718903781949049898023246862032568320000000⟩, + ⟨4, 6, 2, 1, 6, 5, -2879102977463936159825902344979815668341800960000000⟩, + ⟨4, 6, 3, 1, 7, 5, 3393530169720225141039854867306684759156981760000000⟩, + ⟨4, 6, 4, 1, 8, 5, -1320652753852127373322678947839463039833210880000000⟩, + ⟨4, 6, 0, 2, 3, 5, 6000734383360839492465580448817794653775462400000000⟩, + ⟨4, 6, 1, 2, 4, 5, 4853259547048921932520727650160130888585707520000000⟩, + ⟨4, 6, 2, 2, 5, 5, -6037413092186265974182597850426629626947174400000000⟩, + ⟨4, 6, 3, 2, 6, 5, -1104664891077266163951843787691405342838620160000000⟩, + ⟨4, 6, 4, 2, 7, 5, 179069283652414735007448771083294397903667200000000⟩, + ⟨4, 6, 5, 2, 8, 5, -446761124980510680458502164781373197134069760000000⟩, + ⟨4, 6, 0, 3, 2, 5, -26367617560451622944367123968417997033182330880000000⟩, + ⟨4, 6, 1, 3, 3, 5, -13440825971024176393861315077348451294044487680000000⟩, + ⟨4, 6, 2, 3, 4, 5, 444843126036805148163898946012997471373885440000000⟩, + ⟨4, 6, 3, 3, 5, 5, -2206532484817179429357784485701972491543511040000000⟩, + ⟨4, 6, 4, 3, 6, 5, 145838924226580281431891188112712214794731520000000⟩, + ⟨4, 6, 5, 3, 7, 5, 35195301966078638728888691873131801828392960000000⟩, + ⟨4, 6, 6, 3, 8, 5, -76015249450342071932624202966219307540807680000000⟩, + ⟨4, 6, 0, 4, 1, 5, -21764090264431637996993380735424858510956953600000000⟩, + ⟨4, 6, 1, 4, 2, 5, 23173106790323786150190410797061133419403018240000000⟩, + ⟨4, 6, 2, 4, 3, 5, 9461767696509801801968798811800839334909706240000000⟩, + ⟨4, 6, 3, 4, 4, 5, 902394255073583297406535231498355395327426560000000⟩, + ⟨4, 6, 4, 4, 5, 5, -377123617572641658864534441290121846781378560000000⟩, + ⟨4, 6, 5, 4, 6, 5, 86192983880853017222038841568605823093964800000000⟩, + ⟨4, 6, 6, 4, 7, 5, 33169743596947369312189527405267804078735360000000⟩, + ⟨4, 6, 7, 4, 8, 5, -27809755360520351910676020906708624526540800000000⟩, + ⟨4, 6, 0, 5, 0, 5, 134681439771783989631634119240439692194972958720000000⟩, + ⟨4, 6, 1, 5, 1, 5, 10506956665831954284936677982356865429421424640000000⟩, + ⟨4, 6, 2, 5, 2, 5, -1287012312540881724003027432448486600165294080000000⟩, + ⟨4, 6, 3, 5, 3, 5, 2271947392292069584542475668284654196432568320000000⟩, + ⟨4, 6, 4, 5, 4, 5, -52664818507926498182741676762121190454067200000000⟩, + ⟨4, 6, 5, 5, 5, 5, 23720422987044157809725816068510010730086400000000⟩, + ⟨4, 6, 6, 5, 6, 5, 56179039294167140968513082093736518158909440000000⟩, + ⟨4, 6, 7, 5, 7, 5, -12685029001079014076867502807777179168931840000000⟩, + ⟨4, 6, 8, 5, 8, 5, -9571858634354925290721620234457159837941760000000⟩, + ⟨4, 6, 1, 6, 0, 5, -114547773482177041523097827716496482050685009920000000⟩, + ⟨4, 6, 2, 6, 1, 5, 21595643862767975136104573985872546560223477760000000⟩, + ⟨4, 6, 3, 6, 2, 5, 2540675804450123885354327652160399689268592640000000⟩, + ⟨4, 6, 4, 6, 3, 5, 1316423812489482249672901638818540714930995200000000⟩, + ⟨4, 6, 5, 6, 4, 5, -197805688450059988973472962563356521303900160000000⟩, + ⟨4, 6, 6, 6, 5, 5, -5343616629248058595881318119814096318627840000000⟩, + ⟨4, 6, 7, 6, 6, 5, -3835020965864671528266983527460762214727680000000⟩, + ⟨4, 6, 8, 6, 7, 5, -2580166666253667694139255751576482626928640000000⟩, + ⟨4, 6, 2, 7, 0, 5, -176176702141812770492418639065685353431333601280000000⟩, + ⟨4, 6, 3, 7, 1, 5, -23356145118928341803693427780968784212892057600000000⟩, + ⟨4, 6, 4, 7, 2, 5, -1352833237534005994082423443516998960965222400000000⟩, + ⟨4, 6, 5, 7, 3, 5, -275780011388605050360077465361439880506245120000000⟩, + ⟨4, 6, 6, 7, 4, 5, -185442952248514176680164664709114268483584000000000⟩, + ⟨4, 6, 7, 7, 5, 5, 13777453491642806379545434609558444509757440000000⟩, + ⟨4, 6, 8, 7, 6, 5, -3857524662378517632770057016567662892810240000000⟩ +] + +def collectedFourData_10_5_28 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 5, 6, 49233951595176293575180725874505508964125376512000000⟩, + ⟨4, 7, 1, 0, 6, 6, -29597325013886514706108357772087850788022386688000000⟩, + ⟨4, 7, 2, 0, 7, 6, 962688930942040165606655281766406050367406080000000⟩, + ⟨4, 7, 3, 0, 8, 6, -146638585163999517769647390084001977247727616000000⟩, + ⟨4, 7, 0, 1, 4, 6, 35398380299463680603998305717900765270972039168000000⟩, + ⟨4, 7, 1, 1, 5, 6, -6444339474923756947155581141613742824433385472000000⟩, + ⟨4, 7, 2, 1, 6, 6, -2215936918570950078786726768269326266446905344000000⟩, + ⟨4, 7, 3, 1, 7, 6, 1958904087374272220947367440354501499025358848000000⟩, + ⟨4, 7, 4, 1, 8, 6, -609873953821086598749305111867624856956908339200000⟩, + ⟨4, 7, 0, 2, 3, 6, 13855616450030847666865841806359349675771822080000000⟩, + ⟨4, 7, 1, 2, 4, 6, 5603056102834729951745199688853035817518497792000000⟩, + ⟨4, 7, 2, 2, 5, 6, -4646769034785844481384716435046962175315804160000000⟩, + ⟨4, 7, 3, 2, 6, 6, -637664161532565453630507053682798397822599168000000⟩, + ⟨4, 7, 4, 2, 7, 6, 82693722260042308903096669265699869135208448000000⟩, + ⟨4, 7, 5, 2, 8, 6, -171927589665209306508414611897065528551800832000000⟩, + ⟨4, 7, 0, 3, 2, 6, -60882480756313614743705215011383025443794845696000000⟩, + ⟨4, 7, 1, 3, 3, 6, -15517344838868022784162396542067864328762032128000000⟩, + ⟨4, 7, 2, 3, 4, 6, 342378967919293283710031943718485159749615616000000⟩, + ⟨4, 7, 3, 3, 5, 6, -1273713592411890973799412977246928132837998592000000⟩, + ⟨4, 7, 4, 3, 6, 6, 67348030040179131198604858439345761908739276800000⟩, + ⟨4, 7, 5, 3, 7, 6, 13544247912866346036245627660218688782467072000000⟩, + ⟨4, 7, 6, 3, 8, 6, -25074029597297138077184808612156993970372608000000⟩, + ⟨4, 7, 0, 4, 1, 6, -50252997020495176081509293643902576357403525120000000⟩, + ⟨4, 7, 1, 4, 2, 6, 26753198786188014409877036814733714312925282304000000⟩, + ⟨4, 7, 2, 4, 3, 6, 7282365555436516734007712440576203894068084736000000⟩, + ⟨4, 7, 3, 4, 4, 6, 520904104657610803399304190365819549817765888000000⟩, + ⟨4, 7, 4, 4, 5, 6, -174154690593323892883924628985594306584012390400000⟩, + ⟨4, 7, 5, 4, 6, 6, 33169743596947369312189527405267804078735360000000⟩, + ⟨4, 7, 6, 4, 7, 6, 10941214278694613801660966730045839131017216000000⟩, + ⟨4, 7, 7, 4, 8, 6, -8026544736611719227846455763680299497553920000000⟩, + ⟨4, 7, 0, 5, 0, 6, 310977665932052649834932439934966379514244890624000000⟩, + ⟨4, 7, 1, 5, 1, 6, 12130212097250595358644334174712747965487775744000000⟩, + ⟨4, 7, 2, 5, 2, 6, -990564811449311055000877334899840163053043712000000⟩, + ⟨4, 7, 3, 5, 3, 6, 1311474131796851446141916360698589433336692736000000⟩, + ⟨4, 7, 4, 5, 4, 6, -24320474096626465952370025725097098973544448000000⟩, + ⟨4, 7, 5, 5, 5, 6, 9128357240526762227150253157323085688340480000000⟩, + ⟨4, 7, 6, 5, 6, 6, 18530951410346610333474666151275167339249664000000⟩, + ⟨4, 7, 7, 5, 7, 6, -3661195556826813625056905781054367875465216000000⟩, + ⟨4, 7, 8, 5, 8, 6, -2455699465335163449343563215260560012607488000000⟩, + ⟨4, 7, 1, 6, 0, 6, -132244648169642317797848397887925132605188472832000000⟩, + ⟨4, 7, 2, 6, 1, 6, 16621352167809755295616184888534332671591972864000000⟩, + ⟨4, 7, 3, 6, 2, 6, 1466596720559163831851699908404569578533814272000000⟩, + ⟨4, 7, 4, 6, 3, 6, 607921039868655846697090230116694001836883968000000⟩, + ⟨4, 7, 5, 6, 4, 6, -76121787093202676216712023165331415196762112000000⟩, + ⟨4, 7, 6, 6, 5, 6, -1762620033311908656994729202850604152520704000000⟩, + ⟨4, 7, 7, 6, 6, 6, -1106876595975229954557782803510470515884032000000⟩, + ⟨4, 7, 8, 6, 7, 6, -661952306739405952619826867652869627052032000000⟩, + ⟨4, 7, 2, 7, 0, 6, -135596559596490092615907665507468513889371553792000000⟩, + ⟨4, 7, 3, 7, 1, 6, -13482257664014633723510512722087166423313940480000000⟩, + ⟨4, 7, 4, 7, 2, 6, -624734816195163613361231941014065371536162816000000⟩, + ⟨4, 7, 5, 7, 3, 6, -106128734092419557134901049831564417731395584000000⟩, + ⟨4, 7, 6, 7, 4, 6, -61169332560395616985045185229514206504550400000000⟩, + ⟨4, 7, 7, 7, 5, 6, 3976494772199576231622720813423513783238656000000⟩, + ⟨4, 7, 8, 7, 6, 6, -989663722876172594913678393214500562010112000000⟩ +] + +def collectedFourData_10_5_29 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 5, 7, -144473366473910909163601034340726850398726389760000000⟩, + ⟨4, 8, 1, 0, 6, 7, 57900764883253465617216797838341105927753564160000000⟩, + ⟨4, 8, 2, 0, 7, 7, -1412469507464779209525268421686133993452339200000000⟩, + ⟨4, 8, 3, 0, 8, 7, 172120005542597466497345396967430014288003072000000⟩, + ⟨4, 8, 0, 1, 4, 7, -103873912287965562778853977578876488288714096640000000⟩, + ⟨4, 8, 1, 1, 5, 7, 12606956358061509239952322476276267707573207040000000⟩, + ⟨4, 8, 2, 1, 6, 7, 3251250977700679909360561559480424951510466560000000⟩, + ⟨4, 8, 3, 1, 7, 7, -2299303297281489278562475106521272050270601216000000⟩, + ⟨4, 8, 4, 1, 8, 7, 596543241526845816088298501436657780834435072000000⟩, + ⟨4, 8, 0, 2, 3, 7, -40658275199331729822448514029010753241376358400000000⟩, + ⟨4, 8, 1, 2, 4, 7, -10961167398935536861347039449871871441832509440000000⟩, + ⟨4, 8, 2, 2, 5, 7, 6817798936821584522134389377267916056454758400000000⟩, + ⟨4, 8, 3, 2, 6, 7, 748471208274084306282817906023565920521158656000000⟩, + ⟨4, 8, 4, 2, 7, 7, -80886191026609981921660743982920444338503680000000⟩, + ⟨4, 8, 5, 2, 8, 7, 144145347230040707261722676426907707202600960000000⟩, + ⟨4, 8, 0, 3, 2, 7, 178655108297451900544411128372200035644950446080000000⟩, + ⟨4, 8, 1, 3, 3, 7, 30356328982640168043535268732776121308765224960000000⟩, + ⟨4, 8, 2, 3, 4, 7, -502342799049363258690585960280152547881123840000000⟩, + ⟨4, 8, 3, 3, 5, 7, 1495047093781144998996776436500502843714699264000000⟩, + ⟨4, 8, 4, 3, 6, 7, -65875927146746019556369985346554149352767488000000⟩, + ⟨4, 8, 5, 3, 7, 7, -11355596400622038482569255971869620866908160000000⟩, + ⟨4, 8, 6, 3, 8, 7, 18394468398423844291863796565107828284456960000000⟩, + ⟨4, 8, 0, 4, 1, 7, 147463679426976446053059387780731813785868697600000000⟩, + ⟨4, 8, 1, 4, 2, 7, -52336847065308700356468627461794043792751329280000000⟩, + ⟨4, 8, 2, 4, 3, 7, -10684779848045409943466992233895449219186032640000000⟩, + ⟨4, 8, 3, 4, 4, 7, -611421729693837903719248381373278345437904896000000⟩, + ⟨4, 8, 4, 4, 5, 7, 170347992405204201969249384348161223702872064000000⟩, + ⟨4, 8, 5, 4, 6, 7, -27809755360520351910676020906708624526540800000000⟩, + ⟨4, 8, 6, 4, 7, 7, -8026544736611719227846455763680299497553920000000⟩, + ⟨4, 8, 7, 4, 8, 7, 5234066247556966228438953762037059865804800000000⟩, + ⟨4, 8, 0, 5, 0, 7, -912540814615512417911959086393618230981186027520000000⟩, + ⟨4, 8, 1, 5, 1, 7, -23730136365275400958515114346626767298578350080000000⟩, + ⟨4, 8, 2, 5, 2, 7, 1453369355738429404011354442402959801062522880000000⟩, + ⟨4, 8, 3, 5, 3, 7, -1539369290704704016606580822784855823311962112000000⟩, + ⟨4, 8, 4, 5, 4, 7, 23788873688033228407297499410038215336263680000000⟩, + ⟨4, 8, 5, 5, 5, 7, -7653281399674326540904392657885068682854400000000⟩, + ⟨4, 8, 6, 5, 6, 7, -13594424413820279772434536481676754346311680000000⟩, + ⟨4, 8, 7, 5, 7, 7, 2387445746397483410453363951824022840279040000000⟩, + ⟨4, 8, 8, 5, 8, 7, 1441213460671777973171195622473307990786048000000⟩, + ⟨4, 8, 1, 6, 0, 7, 258708051391349807868032235270337003241330442240000000⟩, + ⟨4, 8, 2, 6, 1, 7, -24387060404747039972338675753635310709621391360000000⟩, + ⟨4, 8, 3, 6, 2, 7, -1721447567085306883008508436769712691503693824000000⟩, + ⟨4, 8, 4, 6, 3, 7, -594633014647493282875411476881221427795066880000000⟩, + ⟨4, 8, 5, 6, 4, 7, 63821062423358744187708635109679659598479360000000⟩, + ⟨4, 8, 6, 6, 5, 7, 1293069323994084913554548386360449281556480000000⟩, + ⟨4, 8, 7, 6, 6, 7, 721788219129807177859994198680488986542080000000⟩, + ⟨4, 8, 8, 6, 7, 7, 388489955005694443526776689441178619215872000000⟩, + ⟨4, 8, 2, 7, 0, 7, 198949005843201071626916380023171954755323822080000000⟩, + ⟨4, 8, 3, 7, 1, 7, 15825072652341957910115135260216640273551196160000000⟩, + ⟨4, 8, 4, 7, 2, 7, 611079273041182187771367444419941847594434560000000⟩, + ⟨4, 8, 5, 7, 3, 7, 88979106009837355316286778634931478745579520000000⟩, + ⟨4, 8, 6, 7, 4, 7, 44874213391538976174146412453603991093248000000000⟩, + ⟨4, 8, 7, 7, 5, 7, -2593050653018911954157166105030048759152640000000⟩, + ⟨4, 8, 8, 7, 6, 7, 580818906825398065838637882197341793943552000000⟩ +] + +def collectedFourData_10_5_30 : List CollectedFourTerm := [ + ⟨5, 0, 5, 2, 8, 0, -698089668523512152240133807642005294566304907264000000⟩, + ⟨5, 0, 5, 3, 7, 0, 54994661149527190794330240874695660642704031744000000⟩, + ⟨5, 0, 6, 3, 8, 0, -712668905028425984838251572827349045362988941312000000⟩, + ⟨5, 0, 5, 4, 6, 0, 134681439771783989631634119240439692194972958720000000⟩, + ⟨5, 0, 6, 4, 7, 0, 310977665932052649834932439934966379514244890624000000⟩, + ⟨5, 0, 7, 4, 8, 0, -912540814615512417911959086393618230981186027520000000⟩, + ⟨5, 0, 5, 5, 5, 0, 37064510080158644504546388498443835941018664960000000⟩, + ⟨5, 0, 6, 5, 6, 0, 526697665387229026213591238547480758693916573696000000⟩, + ⟨5, 0, 7, 5, 7, 0, -416242665496409120136311054393343512881183850496000000⟩, + ⟨5, 0, 8, 5, 8, 0, -837568118318543255020748628811932408908385091584000000⟩, + ⟨5, 0, 5, 6, 4, 0, -309082638934153691826532142700934144000549453824000000⟩, + ⟨5, 0, 6, 6, 5, 0, -50098229494671023012774153570003349979325792256000000⟩, + ⟨5, 0, 7, 6, 6, 0, -125841206112365991185312362873261117371781742592000000⟩, + ⟨5, 0, 8, 6, 7, 0, -225772801516928543088913992432586671702751051776000000⟩, + ⟨5, 0, 5, 7, 3, 0, -430921953525119450680818598789856749664618938368000000⟩, + ⟨5, 0, 6, 7, 4, 0, -1738590962732051674533334504100259250491201945600000000⟩, + ⟨5, 0, 7, 7, 5, 0, 452089148919281143568800049586191398472710619136000000⟩, + ⟨5, 0, 8, 7, 6, 0, -337545694755602820339661063653553796292821385216000000⟩ +] + +def collectedFourData_10_5_31 : List CollectedFourTerm := [ + ⟨5, 1, 4, 1, 8, 1, -32197611987809073768828291771259460471663414476800000⟩, + ⟨5, 1, 4, 2, 7, 1, 4365722402923897520333104297665747033985646592000000⟩, + ⟨5, 1, 5, 2, 8, 1, -54460346640712027149454784969124946982278791168000000⟩, + ⟨5, 1, 4, 3, 6, 1, 3555563778041151138729114081330901133135393587200000⟩, + ⟨5, 1, 5, 3, 7, 1, 4290320347995344539892959497394974734237564928000000⟩, + ⟨5, 1, 6, 3, 8, 1, -27798861205032671016615154634138992363670863872000000⟩, + ⟨5, 1, 4, 4, 5, 1, -9194301738004324256880709976680580824465775001600000⟩, + ⟨5, 1, 5, 4, 6, 1, 10506956665831954284936677982356865429421424640000000⟩, + ⟨5, 1, 6, 4, 7, 1, 12130212097250595358644334174712747965487775744000000⟩, + ⟨5, 1, 7, 4, 8, 1, -23730136365275400958515114346626767298578350080000000⟩, + ⟨5, 1, 4, 5, 4, 1, -1283972177228706808137887590492335992148590592000000⟩, + ⟨5, 1, 5, 5, 5, 1, 2891528349506892678799431306278615547138539520000000⟩, + ⟨5, 1, 6, 5, 6, 1, 20544737105557195093235512372308127893134770176000000⟩, + ⟨5, 1, 7, 5, 7, 1, -10824168141385830182853539020056316913840553984000000⟩, + ⟨5, 1, 8, 5, 8, 1, -16335383588799112396784145639271968153117130752000000⟩, + ⟨5, 1, 4, 6, 3, 1, 32094510084059974993918677803431409911880220672000000⟩, + ⟨5, 1, 5, 6, 4, 1, -24112586700476439743857769828545752748825509888000000⟩, + ⟨5, 1, 6, 6, 5, 1, -1954166540049456356618808116347226649092161536000000⟩, + ⟨5, 1, 7, 6, 6, 1, -3272433335132942248692144965234862922156474368000000⟩, + ⟨5, 1, 8, 6, 7, 1, -4403325814383713365820335068836820263085539328000000⟩, + ⟨5, 1, 4, 7, 2, 1, -32982174564267506451309054061257411767895588864000000⟩, + ⟨5, 1, 5, 7, 3, 1, -33617685552784225485227523389459709287429308416000000⟩, + ⟨5, 1, 6, 7, 4, 1, -67816693732953982791822627933672766285912473600000000⟩, + ⟨5, 1, 7, 7, 5, 1, 11756336792054616435975168027431443306899308544000000⟩, + ⟨5, 1, 8, 7, 6, 1, -6583271595449401010847982240143694960313499648000000⟩ +] + +def collectedFourData_10_5_32 : List CollectedFourTerm := [ + ⟨5, 2, 3, 0, 8, 2, 379312880020796183961592045801262852712117043200000⟩, + ⟨5, 2, 3, 1, 7, 2, -5067135298908106746264665769554608851527506329600000⟩, + ⟨5, 2, 4, 1, 8, 2, 7887864084845923472618057315880669559987057459200000⟩, + ⟨5, 2, 3, 2, 6, 2, 1649458287710927062261950520225156300457744793600000⟩, + ⟨5, 2, 4, 2, 7, 2, -1069527297846473312423628002951176954469941248000000⟩, + ⟨5, 2, 5, 2, 8, 2, 6670926596639857712983609940569374803777028096000000⟩, + ⟨5, 2, 3, 3, 5, 2, 3294739720238388609685773702289712206240441958400000⟩, + ⟨5, 2, 4, 3, 6, 2, -871052295331989623184405989487301742503447756800000⟩, + ⟨5, 2, 5, 3, 7, 2, -525527542201724110497817432960227838909218816000000⟩, + ⟨5, 2, 6, 3, 8, 2, 2270081799666976070972094950068571293253369856000000⟩, + ⟨5, 2, 3, 4, 4, 2, -1347432777882807990431133926124538273849776537600000⟩, + ⟨5, 2, 4, 4, 5, 2, 2252446625293210361242050800441036267218953830400000⟩, + ⟨5, 2, 5, 4, 6, 2, -1287012312540881724003027432448486600165294080000000⟩, + ⟨5, 2, 6, 4, 7, 2, -990564811449311055000877334899840163053043712000000⟩, + ⟨5, 2, 7, 4, 8, 2, 1453369355738429404011354442402959801062522880000000⟩, + ⟨5, 2, 3, 5, 3, 2, -3392415641819528093109738239488465798668956467200000⟩, + ⟨5, 2, 4, 5, 4, 2, 314551216610052073619678863085425420557877248000000⟩, + ⟨5, 2, 5, 5, 5, 2, -354187487988627489676559852222445421791805440000000⟩, + ⟨5, 2, 6, 5, 6, 2, -1677703033886325204405789525657134887178600448000000⟩, + ⟨5, 2, 7, 5, 7, 2, 662934002396651806550345955237835989187559424000000⟩, + ⟨5, 2, 8, 5, 8, 2, 800377901137865550568263230764601646920604057600000⟩, + ⟨5, 2, 3, 6, 2, 2, -3793674258942082055743337397008051281817134694400000⟩, + ⟨5, 2, 4, 6, 3, 2, -7862605882344145440822963711586830545760288768000000⟩, + ⟨5, 2, 5, 6, 4, 2, 2953585605967229282389498915138481458759335936000000⟩, + ⟨5, 2, 6, 6, 5, 2, 159579123164993123096107548606005864696905728000000⟩, + ⟨5, 2, 7, 6, 6, 2, 200422545187676065489408534055689815481909248000000⟩, + ⟨5, 2, 8, 6, 7, 2, 215747898063390871757091414819704256453830246400000⟩, + ⟨5, 2, 3, 7, 1, 2, 34874818097845046991264745780060038606876573696000000⟩, + ⟨5, 2, 4, 7, 2, 2, 8080068493405906267003442375814200712983740416000000⟩, + ⟨5, 2, 5, 7, 3, 2, 4117878906483062838115802856860516336850173952000000⟩, + ⟨5, 2, 6, 7, 4, 2, 5537976574698588752780277115962167313353932800000000⟩, + ⟨5, 2, 7, 7, 5, 2, -720025345253177861997565323736910744292163584000000⟩, + ⟨5, 2, 8, 7, 6, 2, 322557782224303110950747590246729967345231462400000⟩ +] + +def collectedFourData_10_5_33 : List CollectedFourTerm := [ + ⟨5, 3, 2, 0, 7, 3, 3296948316542753929604146862762268980567605248000000⟩, + ⟨5, 3, 3, 0, 8, 3, -2008789427021122518318913336154160170824787558400000⟩, + ⟨5, 3, 2, 1, 6, 3, -7588982545066042346145211089005420448271722086400000⟩, + ⟨5, 3, 3, 1, 7, 3, 26834859425743880517472012037190677865677665075200000⟩, + ⟨5, 3, 4, 1, 8, 3, -20886527732131602548538463424984485990535213875200000⟩, + ⟨5, 3, 2, 2, 5, 3, -15913922819917159583839639940442176778399645696000000⟩, + ⟨5, 3, 3, 2, 6, 3, -8735306769663118166184021563937436626586907443200000⟩, + ⟨5, 3, 4, 2, 7, 3, 2832035558226595817503337974104734051271180288000000⟩, + ⟨5, 3, 5, 2, 8, 3, -11776106675689870613349232724908203877318262784000000⟩, + ⟨5, 3, 2, 3, 4, 3, 1172555044126835028567063663243266318789089689600000⟩, + ⟨5, 3, 3, 3, 5, 3, -17448493482316087126911993111250580026289867980800000⟩, + ⟨5, 3, 4, 3, 6, 3, 2306487247611323878296260191108357739418275020800000⟩, + ⟨5, 3, 5, 3, 7, 3, 927707464372017312112168959100404508775153664000000⟩, + ⟨5, 3, 6, 3, 8, 3, -3005511121448137252885176416095884735695290368000000⟩, + ⟨5, 3, 2, 4, 3, 3, 24940125607293272766494015595787302975928113561600000⟩, + ⟨5, 3, 3, 4, 4, 3, 7135820744300292330880246788026761333578085171200000⟩, + ⟨5, 3, 4, 4, 5, 3, -5964325500323556997368407545532664378653304422400000⟩, + ⟨5, 3, 5, 4, 6, 3, 2271947392292069584542475668284654196432568320000000⟩, + ⟨5, 3, 6, 4, 7, 3, 1311474131796851446141916360698589433336692736000000⟩, + ⟨5, 3, 7, 4, 8, 3, -1539369290704704016606580822784855823311962112000000⟩, + ⟨5, 3, 2, 5, 2, 3, -3392415641819528093109738239488465798668956467200000⟩, + ⟨5, 3, 3, 5, 3, 3, 17965771879337511397169836967949456995061753446400000⟩, + ⟨5, 3, 4, 5, 4, 3, -832910232508135226523622996767396621648396288000000⟩, + ⟨5, 3, 5, 5, 5, 3, 625242922602327423111170903808152998521077760000000⟩, + ⟨5, 3, 6, 5, 6, 3, 2221221776048929815449513070583155390356127744000000⟩, + ⟨5, 3, 7, 5, 7, 3, -702161663877155043691004497425872803077921177600000⟩, + ⟨5, 3, 8, 5, 8, 3, -706448752517514017674604314121909222920893235200000⟩, + ⟨5, 3, 2, 6, 1, 3, 56923620171575349642075792029484093015817872998400000⟩, + ⟨5, 3, 3, 6, 2, 3, 20090782945486151102771381756366238106520440012800000⟩, + ⟨5, 3, 4, 6, 3, 3, 20819645729431946798709750756056520682433937408000000⟩, + ⟨5, 3, 5, 6, 4, 3, -5213929229737251880948810072521493735375110144000000⟩, + ⟨5, 3, 6, 6, 5, 3, -211277333483616892985138899237208708647747584000000⟩, + ⟨5, 3, 7, 6, 6, 3, -212282108473402511952926979999482571627115315200000⟩, + ⟨5, 3, 8, 6, 7, 3, -190428587831418296077255530584620482861780172800000⟩, + ⟨5, 3, 2, 7, 0, 3, -464381415971170739354366465777415061804181304115200000⟩, + ⟨5, 3, 3, 7, 1, 3, -184692293761274678959394729480124159751253655552000000⟩, + ⟨5, 3, 4, 7, 2, 3, -21395471936347622551879683695999129115055620096000000⟩, + ⟨5, 3, 5, 7, 3, 3, -7269242222623674032944105136564460225306820608000000⟩, + ⟨5, 3, 6, 7, 4, 3, -7332092697284138239538725366187125436212838400000000⟩, + ⟨5, 3, 7, 7, 5, 3, 762631261375842537086640153631411091109681561600000⟩, + ⟨5, 3, 8, 7, 6, 3, -284703691272860442789552473639435743416601804800000⟩ +] + +def collectedFourData_10_5_34 : List CollectedFourTerm := [ + ⟨5, 4, 1, 0, 6, 4, 3132850566301227918277902967175830413753974784000000⟩, + ⟨5, 4, 2, 0, 7, 4, -305699305027599108736493027257885389037240320000000⟩, + ⟨5, 4, 3, 0, 8, 4, 93129384028544397374290348153120898131427328000000⟩, + ⟨5, 4, 1, 1, 5, 4, 682127609977586644605682741472754934896132096000000⟩, + ⟨5, 4, 2, 1, 6, 4, 703664864339157146961274750831072694476210176000000⟩, + ⟨5, 4, 3, 1, 7, 4, -1244089547264342466613831031815446333682089984000000⟩, + ⟨5, 4, 4, 1, 8, 4, 645546163615908344992596771023922675534790656000000⟩, + ⟨5, 4, 1, 2, 4, 4, -593078512215125568877630006650279616478969856000000⟩, + ⟨5, 4, 2, 2, 5, 4, 1475569126122344402283150372404612311956848640000000⟩, + ⟨5, 4, 3, 2, 6, 4, 404977110998377438945827518619107014207340544000000⟩, + ⟨5, 4, 4, 2, 7, 4, -87530570580409056859755493250761497394544640000000⟩, + ⟨5, 4, 5, 2, 8, 4, 272975740067427043360641627361427126369648640000000⟩, + ⟨5, 4, 1, 3, 3, 4, 1642497169697956161914112604489183477528264704000000⟩, + ⟨5, 4, 2, 3, 4, 4, -108721529026592795740153741440727590490865664000000⟩, + ⟨5, 4, 3, 3, 5, 4, 808928715163474527465667406876045501358145536000000⟩, + ⟨5, 4, 4, 3, 6, 4, -71287291656139228261978749950247900203188224000000⟩, + ⟨5, 4, 5, 3, 7, 4, -21504699186855164291801617460713452145213440000000⟩, + ⟨5, 4, 6, 3, 8, 4, 55735339038791453629543432640514483472564224000000⟩, + ⟨5, 4, 1, 4, 2, 4, -2831802331067235960982307225341094395140636672000000⟩, + ⟨5, 4, 2, 4, 3, 4, -2312495778958842945722178096061174651388166144000000⟩, + ⟨5, 4, 3, 4, 4, 4, -330823421069214744995744820196067723710562304000000⟩, + ⟨5, 4, 4, 4, 5, 4, 184341193264365688259924903604116933125865472000000⟩, + ⟨5, 4, 5, 4, 6, 4, -52664818507926498182741676762121190454067200000000⟩, + ⟨5, 4, 6, 4, 7, 4, -24320474096626465952370025725097098973544448000000⟩, + ⟨5, 4, 7, 4, 8, 4, 23788873688033228407297499410038215336263680000000⟩, + ⟨5, 4, 1, 5, 1, 4, -1283972177228706808137887590492335992148590592000000⟩, + ⟨5, 4, 2, 5, 2, 4, 314551216610052073619678863085425420557877248000000⟩, + ⟨5, 4, 3, 5, 3, 4, -832910232508135226523622996767396621648396288000000⟩, + ⟨5, 4, 4, 5, 4, 4, 25743005832649574049569838908457077063024640000000⟩, + ⟨5, 4, 5, 5, 5, 4, -14493427600450362420910306341264786299289600000000⟩, + ⟨5, 4, 6, 5, 6, 4, -41191179724792741251963585857628053220360192000000⟩, + ⟨5, 4, 7, 5, 7, 4, 10850960345523178559307566328954342567051264000000⟩, + ⟨5, 4, 8, 5, 8, 4, 9357609866875720439051771575012331171610624000000⟩, + ⟨5, 4, 1, 6, 0, 4, 13997978557663148419841911521502357810971672576000000⟩, + ⟨5, 4, 2, 6, 1, 4, -5278066094876846473986364444037330699871584256000000⟩, + ⟨5, 4, 3, 6, 2, 4, -931427762012327648876430407585110502959742976000000⟩, + ⟨5, 4, 4, 6, 3, 4, -643479021541771675220635209932265216005898240000000⟩, + ⟨5, 4, 5, 6, 4, 4, 120861353360943248592631447640073616742154240000000⟩, + ⟨5, 4, 6, 6, 5, 4, 3918007066713957581724365268602799953805312000000⟩, + ⟨5, 4, 7, 6, 6, 4, 3280533329589377248664628040072848293756928000000⟩, + ⟨5, 4, 8, 6, 7, 4, 2522414295554031699042693158376584654094336000000⟩, + ⟨5, 4, 2, 7, 0, 4, 43058326215735931632297079375058694871940333568000000⟩, + ⟨5, 4, 3, 7, 1, 4, 8562509998030581209888010436655631761764515840000000⟩, + ⟨5, 4, 4, 7, 2, 4, 661276254454356810121005968541295542408314880000000⟩, + ⟨5, 4, 5, 7, 3, 4, 168504483705675957599919109133544602657095680000000⟩, + ⟨5, 4, 6, 7, 4, 4, 135969110022815827915513725769942492721971200000000⟩, + ⟨5, 4, 7, 7, 5, 4, -11785436319253925040860742124915130602881024000000⟩, + ⟨5, 4, 8, 7, 6, 4, 3771180940014200519622595757499812388274176000000⟩ +] + +def collectedFourData_10_5_35 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 5, 5, 5868049365269121652806559789958141275778580480000000⟩, + ⟨5, 5, 1, 0, 6, 5, -7055235610152277620563165238641937012007895040000000⟩, + ⟨5, 5, 2, 0, 7, 5, 344220156241908504957286007515133047839129600000000⟩, + ⟨5, 5, 3, 0, 8, 5, -69909680512410899252233202907023625745858560000000⟩, + ⟨5, 5, 0, 1, 4, 5, 4219028461411864127467877083849332854850846720000000⟩, + ⟨5, 5, 1, 1, 5, 5, -1536163600124678912901078027335688819321077760000000⟩, + ⟨5, 5, 2, 1, 6, 5, -792332941427192130361001203367837837851361280000000⟩, + ⟨5, 5, 3, 1, 7, 5, 933903984068254703421337260099591502225735680000000⟩, + ⟨5, 5, 4, 1, 8, 5, -363445381861713857492633266934111115505827840000000⟩, + ⟨5, 5, 0, 2, 3, 5, 1651410026632553163519141740159105754149683200000000⟩, + ⟨5, 5, 1, 2, 4, 5, 1335623436369789305639474149175000722424463360000000⟩, + ⟨5, 5, 2, 2, 5, 5, -1661504055737757583062177937315265678357299200000000⟩, + ⟨5, 5, 3, 2, 6, 5, -304005236801073296222568291533396105892986880000000⟩, + ⟨5, 5, 4, 2, 7, 5, 49280103332933046253376990721211125832089600000000⟩, + ⟨5, 5, 5, 2, 8, 5, -122949251569645689767840457829571115016519680000000⟩, + ⟨5, 5, 0, 3, 2, 5, -7256403172665473782340520590388595271757987840000000⟩, + ⟨5, 5, 1, 3, 3, 5, -3698933056647147757393408451215356353304330240000000⟩, + ⟨5, 5, 2, 3, 4, 5, 122421415727504649960870129407322320975953920000000⟩, + ⟨5, 5, 3, 3, 5, 5, -607240653680907239230251662534842862241054720000000⟩, + ⟨5, 5, 4, 3, 6, 5, 40135064536249700725496158631492356260495360000000⟩, + ⟨5, 5, 5, 3, 7, 5, 9685793578583672941410825114829341358817280000000⟩, + ⟨5, 5, 6, 3, 8, 5, -20919497031455423535815214788128310286090240000000⟩, + ⟨5, 5, 0, 4, 1, 5, -5989506381565346463507418114497078933376204800000000⟩, + ⟨5, 5, 1, 4, 2, 5, 6377269590182164128835610482485619295854264320000000⟩, + ⟨5, 5, 2, 4, 3, 5, 2603890964914368264871627703564685021617848320000000⟩, + ⟨5, 5, 3, 4, 4, 5, 248340090662286235307634498250473604204462080000000⟩, + ⟨5, 5, 4, 4, 5, 5, -103784917570471850546131773614375947028398080000000⟩, + ⟨5, 5, 5, 4, 6, 5, 23720422987044157809725816068510010730086400000000⟩, + ⟨5, 5, 6, 4, 7, 5, 9128357240526762227150253157323085688340480000000⟩, + ⟨5, 5, 7, 4, 8, 5, -7653281399674326540904392657885068682854400000000⟩, + ⟨5, 5, 0, 5, 0, 5, 37064510080158644504546388498443835941018664960000000⟩, + ⟨5, 5, 1, 5, 1, 5, 2891528349506892678799431306278615547138539520000000⟩, + ⟨5, 5, 2, 5, 2, 5, -354187487988627489676559852222445421791805440000000⟩, + ⟨5, 5, 3, 5, 3, 5, 625242922602327423111170903808152998521077760000000⟩, + ⟨5, 5, 4, 5, 4, 5, -14493427600450362420910306341264786299289600000000⟩, + ⟨5, 5, 5, 5, 5, 5, 6527891730283656145182947087900921246515200000000⟩, + ⟨5, 5, 6, 5, 6, 5, 15460545801564273877954803907368291579985920000000⟩, + ⟨5, 5, 7, 5, 7, 5, -3490936732442759089864321462906697935749120000000⟩, + ⟨5, 5, 8, 5, 8, 5, -2634188136391069122464716439877645427015680000000⟩, + ⟨5, 5, 1, 6, 0, 5, -31523698529538240318151849469620859190179266560000000⟩, + ⟨5, 5, 2, 6, 1, 5, 5943149709383874252100418236383152316277063680000000⟩, + ⟨5, 5, 3, 6, 2, 5, 699197336500298901292266033942424536502763520000000⟩, + ⟨5, 5, 4, 6, 3, 5, 362281571614141807841144811134111526263193600000000⟩, + ⟨5, 5, 5, 6, 4, 5, -54436386675797524954981003757111246460026880000000⟩, + ⟨5, 5, 6, 6, 5, 5, -1470570352937091591635858883577509964677120000000⟩, + ⟨5, 5, 7, 6, 6, 5, -1055402834182428424621648318617713104650240000000⟩, + ⟨5, 5, 8, 6, 7, 5, -710065273818698814334287252602410783211520000000⟩, + ⟨5, 5, 2, 7, 0, 5, -48484061081387052837148118454987184875283415040000000⟩, + ⟨5, 5, 3, 7, 1, 5, -6427641979927289583378500334208412671593676800000000⟩, + ⟨5, 5, 4, 7, 2, 5, -372301493467236321221600984247419454829363200000000⟩, + ⟨5, 5, 5, 7, 3, 5, -75895023318281101672158774528918325202780160000000⟩, + ⟨5, 5, 6, 7, 4, 5, -51034145347393381861727708526780572762112000000000⟩, + ⟨5, 5, 7, 7, 5, 5, 3791573394858337297928008318159563962449920000000⟩, + ⟨5, 5, 8, 7, 6, 5, -1061595881180527289362303822761375899320320000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1020.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1020.lean new file mode 100644 index 0000000000000000000000000000000000000000..7fcb9284cde3e1c5e9c87d07c1bb6649345ff840 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1020.lean @@ -0,0 +1,647 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1020. -/ +namespace LaughlinFock +def collectedFourData_10_5_36 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 5, 6, 83386719381426899136786989569522965927740571648000000⟩, + ⟨5, 6, 1, 0, 6, 6, -50128493761115184179122921681933628827502641152000000⟩, + ⟨5, 6, 2, 0, 7, 6, 1630490121860028964547039553099858637561528320000000⟩, + ⟨5, 6, 3, 0, 8, 6, -248359316191022740625951395954493407849611264000000⟩, + ⟨5, 6, 0, 1, 4, 6, 59953643958117856923607535307006811237433475072000000⟩, + ⟨5, 6, 1, 1, 5, 6, -10914669856537951607229559579551119699752255488000000⟩, + ⟨5, 6, 2, 1, 6, 6, -3753095252543642525714195786403971679519768576000000⟩, + ⟨5, 6, 3, 1, 7, 6, 3317763050427431305627012374124695620306337792000000⟩, + ⟨5, 6, 4, 1, 8, 6, -1032933303088814479099468629976497256143834316800000⟩, + ⟨5, 6, 0, 2, 3, 6, 23467025565516514337322671334880620417719992320000000⟩, + ⟨5, 6, 1, 2, 4, 6, 9489802296739615457350562219760183866994720768000000⟩, + ⟨5, 6, 2, 2, 5, 6, -7870154902860863592744529475348247962336624640000000⟩, + ⟨5, 6, 3, 2, 6, 6, -1080001112535490995615507791756084298563715072000000⟩, + ⟨5, 6, 4, 2, 7, 6, 140056972663949174439619510200052555230216192000000⟩, + ⟨5, 6, 5, 2, 8, 6, -291190879643764755966716589891223213653884928000000⟩, + ⟨5, 6, 0, 3, 2, 6, -103115638163995072893040223877573357553355587584000000⟩, + ⟨5, 6, 1, 3, 3, 6, -26281467111616019472103099325441905393152294912000000⟩, + ⟨5, 6, 2, 3, 4, 6, 579881524740050522918980923909485860711563264000000⟩, + ⟨5, 6, 3, 3, 5, 6, -2157267382802674229532518068176493780263763968000000⟩, + ⟨5, 6, 4, 3, 6, 6, 114066230718773916048858641901445557473456947200000⟩, + ⟨5, 6, 5, 3, 7, 6, 22939665888068126909260096850789948234661888000000⟩, + ⟨5, 6, 6, 3, 8, 6, -42467464057795831072979494139621378812280832000000⟩, + ⟨5, 6, 0, 4, 1, 6, -85112659554108831624772884326222716144692756480000000⟩, + ⟨5, 6, 1, 4, 2, 6, 45311444794895557421498881700968683072091324416000000⟩, + ⟨5, 6, 2, 4, 3, 6, 12334020596137758518283099804923733937691295744000000⟩, + ⟨5, 6, 3, 4, 4, 6, 882246559383897169415377114971384976037117952000000⟩, + ⟨5, 6, 4, 4, 5, 6, -294962883192328212179785133236915181832477081600000⟩, + ⟨5, 6, 5, 4, 6, 6, 56179039294167140968513082093736518158909440000000⟩, + ⟨5, 6, 6, 4, 7, 6, 18530951410346610333474666151275167339249664000000⟩, + ⟨5, 6, 7, 4, 8, 6, -13594424413820279772434536481676754346311680000000⟩, + ⟨5, 6, 0, 5, 0, 6, 526697665387229026213591238547480758693916573696000000⟩, + ⟨5, 6, 1, 5, 1, 6, 20544737105557195093235512372308127893134770176000000⟩, + ⟨5, 6, 2, 5, 2, 6, -1677703033886325204405789525657134887178600448000000⟩, + ⟨5, 6, 3, 5, 3, 6, 2221221776048929815449513070583155390356127744000000⟩, + ⟨5, 6, 4, 5, 4, 6, -41191179724792741251963585857628053220360192000000⟩, + ⟨5, 6, 5, 5, 5, 6, 15460545801564273877954803907368291579985920000000⟩, + ⟨5, 6, 6, 5, 6, 6, 31385562098103548538283728096214852992761856000000⟩, + ⟨5, 6, 7, 5, 7, 6, -6200905606925848625314311705548368499441664000000⟩, + ⟨5, 6, 8, 5, 8, 6, -4159177063111992756751092200061215390564352000000⟩, + ⟨5, 6, 1, 6, 0, 6, -223980546133898193191556458990674634725474172928000000⟩, + ⟨5, 6, 2, 6, 1, 6, 28151305837754801748619467435170205521103814656000000⟩, + ⟨5, 6, 3, 6, 2, 6, 2483950307067568465980645467739320285751410688000000⟩, + ⟨5, 6, 4, 6, 3, 6, 1029625685429634520486380660522551777031094272000000⟩, + ⟨5, 6, 5, 6, 4, 6, -128926196120636347621476777219554785307394048000000⟩, + ⟨5, 6, 6, 6, 5, 6, -2985320034889536829894977063699151130198016000000⟩, + ⟨5, 6, 7, 6, 6, 6, -1874698355666794241513508895532945378377728000000⟩, + ⟨5, 6, 8, 6, 7, 6, -1121137537361008911504191579008880741449728000000⟩, + ⟨5, 6, 2, 7, 0, 6, -229657622388921732383930370159307291528179744768000000⟩, + ⟨5, 6, 3, 7, 1, 6, -22834674041630819903999872623609533035362385920000000⟩, + ⟨5, 6, 4, 7, 2, 6, -1058102896842783565073617708844664292129112064000000⟩, + ⟨5, 6, 5, 7, 3, 6, -179748459779078902847691629327159887487041536000000⟩, + ⟨5, 6, 6, 7, 4, 6, -103601474261160702366951566379582490253721600000000⟩, + ⟨5, 6, 7, 7, 5, 6, 6734922608235338863093342313850335788007424000000⟩, + ⟨5, 6, 8, 7, 6, 6, -1676176875258963087876839849082459990786048000000⟩ +] + +def collectedFourData_10_5_37 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 5, 7, -65899495333452854006159245760467570459618050048000000⟩, + ⟨5, 7, 1, 0, 6, 7, 26410620021901003500405818807448385533580935168000000⟩, + ⟨5, 7, 2, 0, 7, 7, -644278111513572979765791262348762174099292160000000⟩, + ⟨5, 7, 3, 0, 8, 7, 78510121130848977565349102262415795909400985600000⟩, + ⟨5, 7, 0, 1, 4, 7, -47380624991004103880977304620938918426335772672000000⟩, + ⟨5, 7, 1, 1, 5, 7, 5750485933593463855861293093195163310953070592000000⟩, + ⟨5, 7, 2, 1, 6, 7, 1483012432409543324712071855735632953436274688000000⟩, + ⟨5, 7, 3, 1, 7, 7, -1048794878997689639054595143184847827104484556800000⟩, + ⟨5, 7, 4, 1, 8, 7, 272104814338220476551194422356232323009714585600000⟩, + ⟨5, 7, 0, 2, 3, 7, -18545700720889920618640614072666041514008248320000000⟩, + ⟨5, 7, 1, 2, 4, 7, -4999782433849409518742736013810968475427930112000000⟩, + ⟨5, 7, 2, 2, 5, 7, 3109843150935551979980330309607983650512568320000000⟩, + ⟨5, 7, 3, 2, 6, 7, 341404620801085673295643314330641492983205068800000⟩, + ⟨5, 7, 4, 2, 7, 7, -36895099063545530442068273483976031038603264000000⟩, + ⟨5, 7, 5, 2, 8, 7, 65749873966149762959534253635908155954167808000000⟩, + ⟨5, 7, 0, 3, 2, 7, 81491016392086857796280032392419032497634934784000000⟩, + ⟨5, 7, 1, 3, 3, 7, 13846612763007089720899512860424662783788843008000000⟩, + ⟨5, 7, 2, 3, 4, 7, -229136606626558567775474366945753262018527232000000⟩, + ⟨5, 7, 3, 3, 5, 7, 681944716763515951652207257782399917995799347200000⟩, + ⟨5, 7, 4, 3, 6, 7, -30048378185870018937966820434525148752012902400000⟩, + ⟨5, 7, 5, 3, 7, 7, -5179695678694519807342710500354069121466368000000⟩, + ⟨5, 7, 6, 3, 8, 7, 8390378198892288283153111761016044134596608000000⟩, + ⟨5, 7, 0, 4, 1, 7, 67263484553789124152945696311006449289899540480000000⟩, + ⟨5, 7, 1, 4, 2, 7, -23872717118215445485707899408521310013587718144000000⟩, + ⟨5, 7, 2, 4, 3, 7, -4873712137540522430945406458152782620862185472000000⟩, + ⟨5, 7, 3, 4, 4, 7, -278891427576769085825193214161452368617327820800000⟩, + ⟨5, 7, 4, 4, 5, 7, 77701842246452995500106073683791629042004787200000⟩, + ⟨5, 7, 5, 4, 6, 7, -12685029001079014076867502807777179168931840000000⟩, + ⟨5, 7, 6, 4, 7, 7, -3661195556826813625056905781054367875465216000000⟩, + ⟨5, 7, 7, 4, 8, 7, 2387445746397483410453363951824022840279040000000⟩, + ⟨5, 7, 0, 5, 0, 7, -416242665496409120136311054393343512881183850496000000⟩, + ⟨5, 7, 1, 5, 1, 7, -10824168141385830182853539020056316913840553984000000⟩, + ⟨5, 7, 2, 5, 2, 7, 662934002396651806550345955237835989187559424000000⟩, + ⟨5, 7, 3, 5, 3, 7, -702161663877155043691004497425872803077921177600000⟩, + ⟨5, 7, 4, 5, 4, 7, 10850960345523178559307566328954342567051264000000⟩, + ⟨5, 7, 5, 5, 5, 7, -3490936732442759089864321462906697935749120000000⟩, + ⟨5, 7, 6, 5, 6, 7, -6200905606925848625314311705548368499441664000000⟩, + ⟨5, 7, 7, 5, 7, 7, 1088999818191430038549551686707954101256192000000⟩, + ⟨5, 7, 8, 5, 8, 7, 657389261730811533635659045809432308377190400000⟩, + ⟨5, 7, 1, 6, 0, 7, 118006041123639270382659204889639409601900183552000000⟩, + ⟨5, 7, 2, 6, 1, 7, -11123814807966495642487517225120357586963529728000000⟩, + ⟨5, 7, 3, 6, 2, 7, -785214110272757242254528656085292633654768435200000⟩, + ⟨5, 7, 4, 6, 3, 7, -271233491198225254670858744324641311764250624000000⟩, + ⟨5, 7, 5, 6, 4, 7, 29111080526413942744095616788275726414512128000000⟩, + ⟨5, 7, 6, 6, 5, 7, 589815396166925913997522798686026757832704000000⟩, + ⟨5, 7, 7, 6, 6, 7, 329233550371205464553430912927041096515584000000⟩, + ⟨5, 7, 8, 6, 7, 7, 177204232183612662698812449679798598998425600000⟩, + ⟨5, 7, 2, 7, 0, 7, 90747792497288010558267837867316703948213059584000000⟩, + ⟨5, 7, 3, 7, 1, 7, 7218384445917111801140661540823475288191008768000000⟩, + ⟨5, 7, 4, 7, 2, 7, 278735220788387294146506200136829738929881088000000⟩, + ⟨5, 7, 5, 7, 3, 7, 40586568475435576321737417305086562817540096000000⟩, + ⟨5, 7, 6, 7, 4, 7, 20468741666112564699026086661409808475750400000000⟩, + ⟨5, 7, 7, 7, 5, 7, -1182783606270325354423727695626123683561472000000⟩, + ⟨5, 7, 8, 7, 6, 7, 264932380092585111762784935496320097556889600000⟩ +] + +def collectedFourData_10_5_38 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 5, 8, -132603697025522466689349808876823462720141524992000000⟩, + ⟨5, 8, 1, 0, 6, 8, 39857807384405131248436530563106820132756783104000000⟩, + ⟨5, 8, 2, 0, 7, 8, -777854146533524733376036739014683680292470784000000⟩, + ⟨5, 8, 3, 0, 8, 8, 78989469215155891807088098098272476029203251200000⟩, + ⟨5, 8, 0, 1, 4, 8, -95339820273215616740387575833981159733500837888000000⟩, + ⟨5, 8, 1, 1, 5, 8, 8678393786962739464939017740614552368684466176000000⟩, + ⟨5, 8, 2, 1, 6, 8, 1790480460682590956878517565910072801352692531200000⟩, + ⟨5, 8, 3, 1, 7, 8, -1055198356776568058229444151350305264326252953600000⟩, + ⟨5, 8, 4, 1, 8, 8, 234656713728221681960157118658185350306437529600000⟩, + ⟨5, 8, 0, 2, 3, 8, -37317865138043197406146712103692452861606625280000000⟩, + ⟨5, 8, 1, 2, 4, 8, -7545463341907491580895139747829673935541108736000000⟩, + ⟨5, 8, 2, 2, 5, 8, 3754596573739320742151769152113981708113543168000000⟩, + ⟨5, 8, 3, 2, 6, 8, 343489086454651265219700166964699874362759577600000⟩, + ⟨5, 8, 4, 2, 7, 8, -31817455049389418689476862875512908623642624000000⟩, + ⟨5, 8, 5, 2, 8, 8, 49613485217661313703051259365371752336064512000000⟩, + ⟨5, 8, 0, 3, 2, 8, 163977129009555065335113660156488476269043777536000000⟩, + ⟨5, 8, 1, 3, 3, 8, 20896731086840177835938252784430409364352794624000000⟩, + ⟨5, 8, 2, 3, 4, 8, -276642736113400984837708370724022290970627276800000⟩, + ⟨5, 8, 3, 3, 5, 8, 686108369664254735040181416987279138304190054400000⟩, + ⟨5, 8, 4, 3, 6, 8, -25913005968335176034173126837731833202239078400000⟩, + ⟨5, 8, 5, 3, 7, 8, -3908490457627311536924774505233189387108352000000⟩, + ⟨5, 8, 6, 3, 8, 8, 5627737425431998433905230351062166084255744000000⟩, + ⟨5, 8, 0, 4, 1, 8, 135348331296306229801636499094979002861795409920000000⟩, + ⟨5, 8, 1, 4, 2, 8, -36027710059482865739177359866822745465376735232000000⟩, + ⟨5, 8, 2, 4, 3, 8, -5884162642574576994865756604970722062439861452800000⟩, + ⟨5, 8, 3, 4, 4, 8, -280594215314362010191570384417135943180982681600000⟩, + ⟨5, 8, 4, 4, 5, 8, 67008218860537360317762683639706224872862515200000⟩, + ⟨5, 8, 5, 4, 6, 8, -9571858634354925290721620234457159837941760000000⟩, + ⟨5, 8, 6, 4, 7, 8, -2455699465335163449343563215260560012607488000000⟩, + ⟨5, 8, 7, 4, 8, 8, 1441213460671777973171195622473307990786048000000⟩, + ⟨5, 8, 0, 5, 0, 8, -837568118318543255020748628811932408908385091584000000⟩, + ⟨5, 8, 1, 5, 1, 8, -16335383588799112396784145639271968153117130752000000⟩, + ⟨5, 8, 2, 5, 2, 8, 800377901137865550568263230764601646920604057600000⟩, + ⟨5, 8, 3, 5, 3, 8, -706448752517514017674604314121909222920893235200000⟩, + ⟨5, 8, 4, 5, 4, 8, 9357609866875720439051771575012331171610624000000⟩, + ⟨5, 8, 5, 5, 5, 8, -2634188136391069122464716439877645427015680000000⟩, + ⟨5, 8, 6, 5, 6, 8, -4159177063111992756751092200061215390564352000000⟩, + ⟨5, 8, 7, 5, 7, 8, 657389261730811533635659045809432308377190400000⟩, + ⟨5, 8, 8, 5, 8, 8, 360765267207797382652429941317116076281036800000⟩, + ⟨5, 8, 1, 6, 0, 8, 178089800746891195785239431036830848303084077056000000⟩, + ⟨5, 8, 2, 6, 1, 8, -13430078282995458574346573801146910012905567027200000⟩, + ⟨5, 8, 3, 6, 2, 8, -790008280426980950963046267399503900259542630400000⟩, + ⟨5, 8, 4, 6, 3, 8, -233905305396384920260656249515240591022096384000000⟩, + ⟨5, 8, 5, 6, 4, 8, 21966614933907879508773431760374555310292992000000⟩, + ⟨5, 8, 6, 6, 5, 8, 395611032115671831864732354560964345987072000000⟩, + ⟨5, 8, 7, 6, 6, 8, 198746222910291353951117414644256196054220800000⟩, + ⟨5, 8, 8, 6, 7, 8, 97246997928985583516948418892602639856435200000⟩, + ⟨5, 8, 2, 7, 0, 8, 109562230070099593370375545505954632257840454041600000⟩, + ⟨5, 8, 3, 7, 1, 8, 7262456709545063457447264094380631224207015936000000⟩, + ⟨5, 8, 4, 7, 2, 8, 240374618396915404570615933459288356928094208000000⟩, + ⟨5, 8, 5, 7, 3, 8, 30625779087094699664582210915120813382303744000000⟩, + ⟨5, 8, 6, 7, 4, 8, 13729143167955043041161903658855675671347200000000⟩, + ⟨5, 8, 7, 7, 5, 8, -714003095982771240502841169714592398861926400000⟩, + ⟨5, 8, 8, 7, 6, 8, 145390876395600077156025882130835710358323200000⟩ +] + +def collectedFourData_10_5_39 : List CollectedFourTerm := [ + ⟨6, 0, 4, 1, 8, 1, 351021221648347612400508135698311886311333979750400000⟩, + ⟨6, 0, 4, 2, 7, 1, -47595492853076784586180989228074346114057240576000000⟩, + ⟨6, 0, 5, 2, 8, 1, 593731529420671230856642490128764645943441096704000000⟩, + ⟨6, 0, 4, 3, 6, 1, -38763071667836015117803008054934007354565958041600000⟩, + ⟨6, 0, 5, 3, 7, 1, -46773452962483721196709480136844957166268841984000000⟩, + ⟨6, 0, 6, 3, 8, 1, 303065650468676863456374238647086066483557564416000000⟩, + ⟨6, 0, 4, 4, 5, 1, 100237093033476724617134360463791795489928432844800000⟩, + ⟨6, 0, 5, 4, 6, 1, -114547773482177041523097827716496482050685009920000000⟩, + ⟨6, 0, 6, 4, 7, 1, -132244648169642317797848397887925132605188472832000000⟩, + ⟨6, 0, 7, 4, 8, 1, 258708051391349807868032235270337003241330442240000000⟩, + ⟨6, 0, 4, 5, 4, 1, 13997978557663148419841911521502357810971672576000000⟩, + ⟨6, 0, 5, 5, 5, 1, -31523698529538240318151849469620859190179266560000000⟩, + ⟨6, 0, 6, 5, 6, 1, -223980546133898193191556458990674634725474172928000000⟩, + ⟨6, 0, 7, 5, 7, 1, 118006041123639270382659204889639409601900183552000000⟩, + ⟨6, 0, 8, 5, 8, 1, 178089800746891195785239431036830848303084077056000000⟩, + ⟨6, 0, 4, 6, 3, 1, -349897195549083420944132628884234303446833954816000000⟩, + ⟨6, 0, 5, 6, 4, 1, 262877558867025918091516814285615953055122980864000000⟩, + ⟨6, 0, 6, 6, 5, 1, 21304496943817023815147188288467700723124011008000000⟩, + ⟨6, 0, 7, 6, 6, 1, 35676358467083514743289988611647808910921826304000000⟩, + ⟨6, 0, 8, 6, 7, 1, 48005448580034664958848082838785645370287325184000000⟩, + ⟨6, 0, 4, 7, 2, 1, 359574592443432902625356540743517165326216200192000000⟩, + ⟨6, 0, 5, 7, 3, 1, 366502989606693063191819264460763831134635163648000000⟩, + ⟨6, 0, 6, 7, 4, 1, 739343610057374126030011627185151584974458060800000000⟩, + ⟨6, 0, 7, 7, 5, 1, -128168626431641008647668385663499147334733791232000000⟩, + ⟨6, 0, 8, 7, 6, 1, 71771410834830706769021722183859964885696774144000000⟩ +] + +def collectedFourData_10_5_40 : List CollectedFourTerm := [ + ⟨6, 1, 3, 0, 8, 2, -6364745534809909313031352260244983701402183270400000⟩, + ⟨6, 1, 3, 1, 7, 2, 85024865926606169570459832333406484030471484211200000⟩, + ⟨6, 1, 4, 1, 8, 2, -132355768437017082504289609623318242978108434022400000⟩, + ⟨6, 1, 3, 2, 6, 2, -27677368274411715439238234155972846527110656819200000⟩, + ⟨6, 1, 4, 2, 7, 2, 17946316752946628248791101991109924379223392256000000⟩, + ⟨6, 1, 5, 2, 8, 2, -111935957109287611341627594927371373895810547712000000⟩, + ⟨6, 1, 3, 3, 5, 2, -55284650290805901303930142450446772120337566924800000⟩, + ⟨6, 1, 4, 3, 6, 2, 14615971403333962552347031881597031500752722329600000⟩, + ⟨6, 1, 5, 3, 7, 2, 8818179539446868311368902857817832090136215552000000⟩, + ⟨6, 1, 6, 3, 8, 2, -38091226950404312299952492868060416089031442432000000⟩, + ⟨6, 1, 3, 4, 4, 2, 22609479425048586788215378550920006304370209587200000⟩, + ⟨6, 1, 4, 4, 5, 2, -37795314516993494322120709740465822852551855308800000⟩, + ⟨6, 1, 5, 4, 6, 2, 21595643862767975136104573985872546560223477760000000⟩, + ⟨6, 1, 6, 4, 7, 2, 16621352167809755295616184888534332671591972864000000⟩, + ⟨6, 1, 7, 4, 8, 2, -24387060404747039972338675753635310709621391360000000⟩, + ⟨6, 1, 3, 5, 3, 2, 56923620171575349642075792029484093015817872998400000⟩, + ⟨6, 1, 4, 5, 4, 2, -5278066094876846473986364444037330699871584256000000⟩, + ⟨6, 1, 5, 5, 5, 2, 5943149709383874252100418236383152316277063680000000⟩, + ⟨6, 1, 6, 5, 6, 2, 28151305837754801748619467435170205521103814656000000⟩, + ⟨6, 1, 7, 5, 7, 2, -11123814807966495642487517225120357586963529728000000⟩, + ⟨6, 1, 8, 5, 8, 2, -13430078282995458574346573801146910012905567027200000⟩, + ⟨6, 1, 3, 6, 2, 2, 63656607966492184268133300877344143608808000716800000⟩, + ⟨6, 1, 4, 6, 3, 2, 131931944095534920655762635782711518844940189696000000⟩, + ⟨6, 1, 5, 6, 4, 2, -49560196311361954950981623049710482392656904192000000⟩, + ⟨6, 1, 6, 6, 5, 2, -2677685270158990930953613369284609611258658816000000⟩, + ⟨6, 1, 7, 6, 6, 2, -3363024475964434531940643042638249111643488256000000⟩, + ⟨6, 1, 8, 6, 7, 2, -3620178863339163769511135479405767826290298060800000⟩, + ⟨6, 1, 3, 7, 1, 2, -585187992438847319623099739934704892369187110912000000⟩, + ⟨6, 1, 4, 7, 2, 2, -135580895279759305418150317579735793509179850752000000⟩, + ⟨6, 1, 5, 7, 3, 2, -69096655461552055821900206468912162985574662144000000⟩, + ⟨6, 1, 6, 7, 4, 2, -92925427878331536410499209708857099111995801600000000⟩, + ⟨6, 1, 7, 7, 5, 2, 12081788788450505627349429128055484145360437248000000⟩, + ⟨6, 1, 8, 7, 6, 2, -5412413635987691253326408966145914759180766412800000⟩ +] + +def collectedFourData_10_5_41 : List CollectedFourTerm := [ + ⟨6, 2, 2, 0, 7, 3, 3686914954448869257768662060974164982571728896000000⟩, + ⟨6, 2, 3, 0, 8, 3, -2246391228416124931187883766236264380263877836800000⟩, + ⟨6, 2, 2, 1, 6, 3, -8486615666391686136413473062578628836492889292800000⟩, + ⟨6, 2, 3, 1, 7, 3, 30008915827062923269167311278628455251056158310400000⟩, + ⟨6, 2, 4, 1, 8, 3, -23357008981826551485434855826836762294202295910400000⟩, + ⟨6, 2, 2, 2, 5, 3, -17796238944450203755014542184633924522388488192000000⟩, + ⟨6, 2, 3, 2, 6, 3, -9768528368846740337136672248532074962161657446400000⟩, + ⟨6, 2, 4, 2, 7, 3, 3167011808697603931377243087369906150992510976000000⟩, + ⟨6, 2, 5, 2, 8, 3, -13168997399787755546339095300650898163937312768000000⟩, + ⟨6, 2, 2, 3, 4, 3, 1311246131889317084794687198229965341897995059200000⟩, + ⟨6, 2, 3, 3, 5, 3, -19512320296247076499540865430888598464240392601600000⟩, + ⟨6, 2, 4, 3, 6, 3, 2579301071477238229578446149546499012256438681600000⟩, + ⟨6, 2, 5, 3, 7, 3, 1037437713713907916867262935531775245342998528000000⟩, + ⟨6, 2, 6, 3, 8, 3, -3361006250486011431163526566275513113835995136000000⟩, + ⟨6, 2, 2, 4, 3, 3, 27890070828828033395566965674395307063863620403200000⟩, + ⟨6, 2, 3, 4, 4, 3, 7979853394248996117706978245775396686761715302400000⟩, + ⟨6, 2, 4, 4, 5, 3, -6669792416825863414176032902796006061092162764800000⟩, + ⟨6, 2, 5, 4, 6, 3, 2540675804450123885354327652160399689268592640000000⟩, + ⟨6, 2, 6, 4, 7, 3, 1466596720559163831851699908404569578533814272000000⟩, + ⟨6, 2, 7, 4, 8, 3, -1721447567085306883008508436769712691503693824000000⟩, + ⟨6, 2, 2, 5, 2, 3, -3793674258942082055743337397008051281817134694400000⟩, + ⟨6, 2, 3, 5, 3, 3, 20090782945486151102771381756366238106520440012800000⟩, + ⟨6, 2, 4, 5, 4, 3, -931427762012327648876430407585110502959742976000000⟩, + ⟨6, 2, 5, 5, 5, 3, 699197336500298901292266033942424536502763520000000⟩, + ⟨6, 2, 6, 5, 6, 3, 2483950307067568465980645467739320285751410688000000⟩, + ⟨6, 2, 7, 5, 7, 3, -785214110272757242254528656085292633654768435200000⟩, + ⟨6, 2, 8, 5, 8, 3, -790008280426980950963046267399503900259542630400000⟩, + ⟨6, 2, 2, 6, 1, 3, 63656607966492184268133300877344143608808000716800000⟩, + ⟨6, 2, 3, 6, 2, 3, 22467142635094029231748778687055767194562042265600000⟩, + ⟨6, 2, 4, 6, 3, 3, 23282216102999919524148181378303196338864521216000000⟩, + ⟨6, 2, 5, 6, 4, 3, -5830638458025420274422927090033142043391295488000000⟩, + ⟨6, 2, 6, 6, 5, 3, -236267446610647096213865195768238431816122368000000⟩, + ⟨6, 2, 7, 6, 6, 3, -237391067480622225902191578759391727436850790400000⟩, + ⟨6, 2, 8, 6, 7, 3, -212952688614320145487250529962130710531250585600000⟩, + ⟨6, 2, 2, 7, 0, 3, -519308955654976484308656543622651858240888268390400000⟩, + ⟨6, 2, 3, 7, 1, 3, -206537899433607001148810349775380510299551432704000000⟩, + ⟨6, 2, 4, 7, 2, 3, -23926151660857622768483879102210306422175956992000000⟩, + ⟨6, 2, 5, 7, 3, 3, -8129056110350709883444641973278152474404847616000000⟩, + ⟨6, 2, 6, 7, 4, 3, -8199340607610547430351662608119003702152396800000000⟩, + ⟨6, 2, 7, 7, 5, 3, 852836117626879425558047753575563860601156403200000⟩, + ⟨6, 2, 8, 7, 6, 3, -318378753974953690368718433657275819365079449600000⟩ +] + +def collectedFourData_10_5_42 : List CollectedFourTerm := [ + ⟨6, 3, 1, 0, 6, 4, -78309566106819020103627249118232879095238098944000000⟩, + ⟨6, 3, 2, 0, 7, 4, 7641341145783082700138606372667320794475397120000000⟩, + ⟨6, 3, 3, 0, 8, 4, -2327886855989098716328506315765500101470978048000000⟩, + ⟨6, 3, 1, 1, 5, 4, -17050643187840499442809935426861369118357979136000000⟩, + ⟨6, 3, 2, 1, 6, 4, -17588994126863428630243476690371044703433916416000000⟩, + ⟨6, 3, 3, 1, 7, 4, 31097593256521801466519709753446291920486662144000000⟩, + ⟨6, 3, 4, 1, 8, 4, -16136243623763922209893299358615154887382532096000000⟩, + ⟨6, 3, 1, 2, 4, 4, 14824748252731892159609231387543517429598519296000000⟩, + ⟨6, 3, 2, 2, 5, 4, -36883718384207316029913098857477116814153482240000000⟩, + ⟨6, 3, 3, 2, 6, 4, -10122915592146605220032881313020459216067887104000000⟩, + ⟨6, 3, 4, 2, 7, 4, 2187937425731356535947870032948924053182218240000000⟩, + ⟨6, 3, 5, 2, 8, 4, -6823374211431389657593849558280534306838282240000000⟩, + ⟨6, 3, 1, 3, 3, 4, -41056296164991718181637399442750415706116849664000000⟩, + ⟨6, 3, 2, 3, 4, 4, 2717632259937094228969066584002993575925121024000000⟩, + ⟨6, 3, 3, 3, 5, 4, -20220197342699362581927352135280097355603378176000000⟩, + ⟨6, 3, 4, 3, 6, 4, 1781916104959140895862970512263549430198697984000000⟩, + ⟨6, 3, 5, 3, 7, 4, 537537181215929885248849730003338611696599040000000⟩, + ⟨6, 3, 6, 3, 8, 4, -1393175360450482107636298308755409654182313984000000⟩, + ⟨6, 3, 1, 4, 2, 4, 70784484338801256501467957419206669613192445952000000⟩, + ⟨6, 3, 2, 4, 3, 4, 57803759624551894398745815601717297199085256704000000⟩, + ⟨6, 3, 3, 4, 4, 4, 8269350233480857685766270728517372904696971264000000⟩, + ⟨6, 3, 4, 4, 5, 4, -4607841502376253281735240364495438703075786752000000⟩, + ⟨6, 3, 5, 4, 6, 4, 1316423812489482249672901638818540714930995200000000⟩, + ⟨6, 3, 6, 4, 7, 4, 607921039868655846697090230116694001836883968000000⟩, + ⟨6, 3, 7, 4, 8, 4, -594633014647493282875411476881221427795066880000000⟩, + ⟨6, 3, 1, 5, 1, 4, 32094510084059974993918677803431409911880220672000000⟩, + ⟨6, 3, 2, 5, 2, 4, -7862605882344145440822963711586830545760288768000000⟩, + ⟨6, 3, 3, 5, 3, 4, 20819645729431946798709750756056520682433937408000000⟩, + ⟨6, 3, 4, 5, 4, 4, -643479021541771675220635209932265216005898240000000⟩, + ⟨6, 3, 5, 5, 5, 4, 362281571614141807841144811134111526263193600000000⟩, + ⟨6, 3, 6, 5, 6, 4, 1029625685429634520486380660522551777031094272000000⟩, + ⟨6, 3, 7, 5, 7, 4, -271233491198225254670858744324641311764250624000000⟩, + ⟨6, 3, 8, 5, 8, 4, -233905305396384920260656249515240591022096384000000⟩, + ⟨6, 3, 1, 6, 0, 4, -349897195549083420944132628884234303446833954816000000⟩, + ⟨6, 3, 2, 6, 1, 4, 131931944095534920655762635782711518844940189696000000⟩, + ⟨6, 3, 3, 6, 2, 4, 23282216102999919524148181378303196338864521216000000⟩, + ⟨6, 3, 4, 6, 3, 4, 16084572790610232673909438223260440862748835840000000⟩, + ⟨6, 3, 5, 6, 4, 4, -3021082538243339908601471630783539056570531840000000⟩, + ⟨6, 3, 6, 6, 5, 4, -97935546846098697415770096215596730199048192000000⟩, + ⟨6, 3, 7, 6, 6, 4, -82001083742211734488784292716689993286811648000000⟩, + ⟨6, 3, 8, 6, 7, 4, -63050938704582014920557782539665271450238976000000⟩, + ⟨6, 3, 2, 7, 0, 4, -1076297375786145483340638249441241694315256741888000000⟩, + ⟨6, 3, 3, 7, 1, 4, -214030777574790508317838468887306234263702077440000000⟩, + ⟨6, 3, 4, 7, 2, 4, -16529437158632737091339229383099811962636206080000000⟩, + ⟨6, 3, 5, 7, 3, 4, -4211982897615255412319983701518883417363578880000000⟩, + ⟨6, 3, 6, 7, 4, 4, -3398720042490930387959367758804763771351859200000000⟩, + ⟨6, 3, 7, 7, 5, 4, 294591901212176031928574056947356941663862784000000⟩, + ⟨6, 3, 8, 7, 6, 4, -94265441926738406180741780473281116337340416000000⟩ +] + +def collectedFourData_10_5_43 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 5, 5, -48933931118765311885137336046764253991625818112000000⟩, + ⟨6, 4, 1, 0, 6, 5, 58833931326005166522790904772563850494975410176000000⟩, + ⟨6, 4, 2, 0, 7, 5, -2870467572226989833059899254677561820829450240000000⟩, + ⟨6, 4, 3, 0, 8, 5, 582980012229721938111041797852926749561585664000000⟩, + ⟨6, 4, 0, 1, 4, 5, -35182670640223922927733170141050571300240621568000000⟩, + ⟨6, 4, 1, 1, 5, 5, 12810138278754594766467209694626520786895110144000000⟩, + ⟨6, 4, 2, 1, 6, 5, 6607300512569693166131805152076511365543493632000000⟩, + ⟨6, 4, 3, 1, 7, 5, -7787867889867451550984611964357749615720660992000000⟩, + ⟨6, 4, 4, 1, 8, 5, 3030787604943540042076587301043303508917354496000000⟩, + ⟨6, 4, 0, 2, 3, 5, -13771183482259205919425242757792399601256366080000000⟩, + ⟨6, 4, 1, 2, 4, 5, -11137824712715324021971848603109532435988086784000000⟩, + ⟨6, 4, 2, 2, 5, 5, 13855358051046636718858350220037498717318676480000000⟩, + ⟨6, 4, 3, 2, 6, 5, 2535113526040591552609051436625151806796726272000000⟩, + ⟨6, 4, 4, 2, 7, 5, -410949027847652960815972620042694941726474240000000⟩, + ⟨6, 4, 5, 2, 8, 5, 1025279412784364876607173046104785875571310592000000⟩, + ⟨6, 4, 0, 3, 2, 5, 60511476798886373626032544919308964048714858496000000⟩, + ⟨6, 4, 1, 3, 3, 5, 30845571354288418921201063807878464620311085056000000⟩, + ⟨6, 4, 2, 3, 4, 5, -1020877765638344225493655066125889963712053248000000⟩, + ⟨6, 4, 3, 3, 5, 5, 5063807488670088283211999970734302509051936768000000⟩, + ⟨6, 4, 4, 3, 6, 5, -334688132497326304932587802561023673404227584000000⟩, + ⟨6, 4, 5, 3, 7, 5, -80770274123836685717327618989251651837100032000000⟩, + ⟨6, 4, 6, 3, 8, 5, 174448639242063909967752334468516700598829056000000⟩, + ⟨6, 4, 0, 4, 1, 5, 49946766713589529059916131056251980047575941120000000⟩, + ⟨6, 4, 1, 4, 2, 5, -53180341784234244813124997729878393639831339008000000⟩, + ⟨6, 4, 2, 4, 3, 5, -21713965440038751595702766231337804019802308608000000⟩, + ⟨6, 4, 3, 4, 4, 5, -2070919335208918786517872289129721179670577152000000⟩, + ⟨6, 4, 4, 4, 5, 5, 865467158067660414828176692772341323820695552000000⟩, + ⟨6, 4, 5, 4, 6, 5, -197805688450059988973472962563356521303900160000000⟩, + ⟨6, 4, 6, 4, 7, 5, -76121787093202676216712023165331415196762112000000⟩, + ⟨6, 4, 7, 4, 8, 5, 63821062423358744187708635109679659598479360000000⟩, + ⟨6, 4, 0, 5, 0, 5, -309082638934153691826532142700934144000549453824000000⟩, + ⟨6, 4, 1, 5, 1, 5, -24112586700476439743857769828545752748825509888000000⟩, + ⟨6, 4, 2, 5, 2, 5, 2953585605967229282389498915138481458759335936000000⟩, + ⟨6, 4, 3, 5, 3, 5, -5213929229737251880948810072521493735375110144000000⟩, + ⟨6, 4, 4, 5, 4, 5, 120861353360943248592631447640073616742154240000000⟩, + ⟨6, 4, 5, 5, 5, 5, -54436386675797524954981003757111246460026880000000⟩, + ⟨6, 4, 6, 5, 6, 5, -128926196120636347621476777219554785307394048000000⟩, + ⟨6, 4, 7, 5, 7, 5, 29111080526413942744095616788275726414512128000000⟩, + ⟨6, 4, 8, 5, 8, 5, 21966614933907879508773431760374555310292992000000⟩, + ⟨6, 4, 1, 6, 0, 5, 262877558867025918091516814285615953055122980864000000⟩, + ⟨6, 4, 2, 6, 1, 5, -49560196311361954950981623049710482392656904192000000⟩, + ⟨6, 4, 3, 6, 2, 5, -5830638458025420274422927090033142043391295488000000⟩, + ⟨6, 4, 4, 6, 3, 5, -3021082538243339908601471630783539056570531840000000⟩, + ⟨6, 4, 5, 6, 4, 5, 453947509663764185712625146679036655563702272000000⟩, + ⟨6, 4, 6, 6, 5, 5, 12263153200760735904850501124856278132195328000000⟩, + ⟨6, 4, 7, 6, 6, 5, 8801052338806302280852036580599280808493056000000⟩, + ⟨6, 4, 8, 6, 7, 5, 5921266682676909777146805782984646551666688000000⟩, + ⟨6, 4, 2, 7, 0, 5, 404310795228934696284000521423579931674123698176000000⟩, + ⟨6, 4, 3, 7, 1, 5, 53600399438258858245684247634566888296462417920000000⟩, + ⟨6, 4, 4, 7, 2, 5, 3104639123277666952289861307740259270870958080000000⟩, + ⟨6, 4, 5, 7, 3, 5, 632892058695816650797801093486524795614920704000000⟩, + ⟨6, 4, 6, 7, 4, 5, 425576064154305769558386023167069134834892800000000⟩, + ⟨6, 4, 7, 7, 5, 5, -31618103357116511349116636819042655585435648000000⟩, + ⟨6, 4, 8, 7, 6, 5, 8852696439998410706609215787936054570385408000000⟩ +] + +def collectedFourData_10_5_44 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 5, 6, -7931546461872261972161148863606497845002108928000000⟩, + ⟨6, 5, 1, 0, 6, 6, 4768103125766060028017819340753688602316111872000000⟩, + ⟨6, 5, 2, 0, 7, 6, -155088343240866931648526852803536616968683520000000⟩, + ⟨6, 5, 3, 0, 8, 6, 23623347581253803620448312869218734837858304000000⟩, + ⟨6, 5, 0, 1, 4, 6, -5702648049232104236328689387121155150280916992000000⟩, + ⟨6, 5, 1, 1, 5, 6, 1038177442706896964150987529897578310735495168000000⟩, + ⟨6, 5, 2, 1, 6, 6, 356985495918339713601508272239204769711783936000000⟩, + ⟨6, 5, 3, 1, 7, 6, -315577732031624605418919152868986504884518912000000⟩, + ⟨6, 5, 4, 1, 8, 6, 98250159572639638033530039519215081860418764800000⟩, + ⟨6, 5, 0, 2, 3, 6, -2232127669436722789142341169647253143966187520000000⟩, + ⟨6, 5, 1, 2, 4, 6, -902647428618439259785454320760731362549301248000000⟩, + ⟨6, 5, 2, 2, 5, 6, 748590419880175350979082223143469131539415040000000⟩, + ⟨6, 5, 3, 2, 6, 6, 102727137684432537264802449124549513017556992000000⟩, + ⟨6, 5, 4, 2, 7, 6, -13321886197632508421216125189497312679821312000000⟩, + ⟨6, 5, 5, 2, 8, 6, 27697384047493782678048353884232010336043008000000⟩, + ⟨6, 5, 0, 3, 2, 6, 9808114302977394793144162404461387373896269824000000⟩, + ⟨6, 5, 1, 3, 3, 6, 2499830656827349206151158092920665601298399232000000⟩, + ⟨6, 5, 2, 3, 4, 6, -55156951730151359092803998699090423058530304000000⟩, + ⟨6, 5, 3, 3, 5, 6, 205194143675498485618713301649558082523496448000000⟩, + ⟨6, 5, 4, 3, 6, 6, -10849708627320204998157929295965366149919539200000⟩, + ⟨6, 5, 5, 3, 7, 6, -2181966470928996106626999762506177543405568000000⟩, + ⟨6, 5, 6, 3, 8, 6, 4039404197586435316080307581210914143076352000000⟩, + ⟨6, 5, 0, 4, 1, 6, 8095713786976164294167832867627442585762529280000000⟩, + ⟨6, 5, 1, 4, 2, 6, -4309916882583615593128471731809510388374962176000000⟩, + ⟨6, 5, 2, 4, 3, 6, -1173182709976544379768419209080333834947395584000000⟩, + ⟨6, 5, 3, 4, 4, 6, -83917194830174942486390400870798195972636672000000⟩, + ⟨6, 5, 4, 4, 5, 6, 28056168055567397210784368354113678042831257600000⟩, + ⟨6, 5, 5, 4, 6, 6, -5343616629248058595881318119814096318627840000000⟩, + ⟨6, 5, 6, 4, 7, 6, -1762620033311908656994729202850604152520704000000⟩, + ⟨6, 5, 7, 4, 8, 6, 1293069323994084913554548386360449281556480000000⟩, + ⟨6, 5, 0, 5, 0, 6, -50098229494671023012774153570003349979325792256000000⟩, + ⟨6, 5, 1, 5, 1, 6, -1954166540049456356618808116347226649092161536000000⟩, + ⟨6, 5, 2, 5, 2, 6, 159579123164993123096107548606005864696905728000000⟩, + ⟨6, 5, 3, 5, 3, 6, -211277333483616892985138899237208708647747584000000⟩, + ⟨6, 5, 4, 5, 4, 6, 3918007066713957581724365268602799953805312000000⟩, + ⟨6, 5, 5, 5, 5, 6, -1470570352937091591635858883577509964677120000000⟩, + ⟨6, 5, 6, 5, 6, 6, -2985320034889536829894977063699151130198016000000⟩, + ⟨6, 5, 7, 5, 7, 6, 589815396166925913997522798686026757832704000000⟩, + ⟨6, 5, 8, 5, 8, 6, 395611032115671831864732354560964345987072000000⟩, + ⟨6, 5, 1, 6, 0, 6, 21304496943817023815147188288467700723124011008000000⟩, + ⟨6, 5, 2, 6, 1, 6, -2677685270158990930953613369284609611258658816000000⟩, + ⟨6, 5, 3, 6, 2, 6, -236267446610647096213865195768238431816122368000000⟩, + ⟨6, 5, 4, 6, 3, 6, -97935546846098697415770096215596730199048192000000⟩, + ⟨6, 5, 5, 6, 4, 6, 12263153200760735904850501124856278132195328000000⟩, + ⟨6, 5, 6, 6, 5, 6, 283956542911537505845479525456808589131776000000⟩, + ⟨6, 5, 7, 6, 6, 6, 178316849736609329688790646997899236343808000000⟩, + ⟨6, 5, 8, 6, 7, 6, 106639936595329417039815020597825721335808000000⟩, + ⟨6, 5, 2, 7, 0, 6, 21844486937647387551747446863943615395814965248000000⟩, + ⟨6, 5, 3, 7, 1, 6, 2171979896156506137540819829748648402611077120000000⟩, + ⟨6, 5, 4, 7, 2, 6, 100644231479616722289108380148465957920047104000000⟩, + ⟨6, 5, 5, 7, 3, 6, 17097246069441733373577389837611590532202496000000⟩, + ⟨6, 5, 6, 7, 4, 6, 9854325877267750784379407125946174118297600000000⟩, + ⟨6, 5, 7, 7, 5, 6, -640609823489837629431403983316769323352064000000⟩, + ⟨6, 5, 8, 7, 6, 6, 159433958585418525038074353407932212707328000000⟩ +] + +def collectedFourData_10_5_45 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 5, 7, -19923166610198163604239623612919727645205200896000000⟩, + ⟨6, 6, 1, 0, 6, 7, 7984631449944662248885766489170150615349723136000000⟩, + ⟨6, 6, 2, 0, 7, 7, -194782374190242393225414980469881439592120320000000⟩, + ⟨6, 6, 3, 0, 8, 7, 23735693512704595015915590224585631141671731200000⟩, + ⟨6, 6, 0, 1, 4, 7, -14324420559134401725019776791125669646690156544000000⟩, + ⟨6, 6, 1, 1, 5, 7, 1738524532924987454949475263865927962810384384000000⟩, + ⟨6, 6, 2, 1, 6, 7, 448354021929692272807164696001632990633394176000000⟩, + ⟨6, 6, 3, 1, 7, 7, -317078530092876321036120915914599771168938393600000⟩, + ⟨6, 6, 4, 1, 8, 7, 82264507854970205588545702735362280800858931200000⟩, + ⟨6, 6, 0, 2, 3, 7, -5606857586625503193711755689495028963097968640000000⟩, + ⟨6, 6, 1, 2, 4, 7, -1511566939022636737369303071330668888325095424000000⟩, + ⟨6, 6, 2, 2, 5, 7, 940188129122449606605947671410925655178608640000000⟩, + ⟨6, 6, 3, 2, 6, 7, 103215678774078509140558722437727774255454617600000⟩, + ⟨6, 6, 4, 2, 7, 7, -11154367753854989085578655873762751496060928000000⟩, + ⟨6, 6, 5, 2, 8, 7, 19877932099461145633244638886007527404732416000000⟩, + ⟨6, 6, 0, 3, 2, 7, 24636897272106446305053125018160828032344915968000000⟩, + ⟨6, 6, 1, 3, 3, 7, 4186198569023734211238845755584748669492002816000000⟩, + ⟨6, 6, 2, 3, 4, 7, -69274078158212348395757226532163417920241664000000⟩, + ⟨6, 6, 3, 3, 5, 7, 206169988742340950269411706828389885499827814400000⟩, + ⟨6, 6, 4, 3, 6, 7, -9084422299960051091574513460716300334320844800000⟩, + ⟨6, 6, 5, 3, 7, 7, -1565959488378184262602587911749563146305536000000⟩, + ⟨6, 6, 6, 3, 8, 7, 2536634035408884177609906126572521066070016000000⟩, + ⟨6, 6, 0, 4, 1, 7, 20335536755883920397893204125985021369474088960000000⟩, + ⟨6, 6, 1, 4, 2, 7, -7217356038580995507034596480546672569575538688000000⟩, + ⟨6, 6, 2, 4, 3, 7, -1473452542163455136558090114375075891609862144000000⟩, + ⟨6, 6, 3, 4, 4, 7, -84316281174119476881832327558763859517479321600000⟩, + ⟨6, 6, 4, 4, 5, 7, 23491329351798015618209246466962618543662694400000⟩, + ⟨6, 6, 5, 4, 6, 7, -3835020965864671528266983527460762214727680000000⟩, + ⟨6, 6, 6, 4, 7, 7, -1106876595975229954557782803510470515884032000000⟩, + ⟨6, 6, 7, 4, 8, 7, 721788219129807177859994198680488986542080000000⟩, + ⟨6, 6, 0, 5, 0, 7, -125841206112365991185312362873261117371781742592000000⟩, + ⟨6, 6, 1, 5, 1, 7, -3272433335132942248692144965234862922156474368000000⟩, + ⟨6, 6, 2, 5, 2, 7, 200422545187676065489408534055689815481909248000000⟩, + ⟨6, 6, 3, 5, 3, 7, -212282108473402511952926979999482571627115315200000⟩, + ⟨6, 6, 4, 5, 4, 7, 3280533329589377248664628040072848293756928000000⟩, + ⟨6, 6, 5, 5, 5, 7, -1055402834182428424621648318617713104650240000000⟩, + ⟨6, 6, 6, 5, 6, 7, -1874698355666794241513508895532945378377728000000⟩, + ⟨6, 6, 7, 5, 7, 7, 329233550371205464553430912927041096515584000000⟩, + ⟨6, 6, 8, 5, 8, 7, 198746222910291353951117414644256196054220800000⟩, + ⟨6, 6, 1, 6, 0, 7, 35676358467083514743289988611647808910921826304000000⟩, + ⟨6, 6, 2, 6, 1, 7, -3363024475964434531940643042638249111643488256000000⟩, + ⟨6, 6, 3, 6, 2, 7, -237391067480622225902191578759391727436850790400000⟩, + ⟨6, 6, 4, 6, 3, 7, -82001083742211734488784292716689993286811648000000⟩, + ⟨6, 6, 5, 6, 4, 7, 8801052338806302280852036580599280808493056000000⟩, + ⟨6, 6, 6, 6, 5, 7, 178316849736609329688790646997899236343808000000⟩, + ⟨6, 6, 7, 6, 6, 7, 99536041126294198973472817055962987757568000000⟩, + ⟨6, 6, 8, 6, 7, 7, 53573542922629434917793127285254595490611200000⟩, + ⟨6, 6, 2, 7, 0, 7, 27435466391399893852654013093935054113963245568000000⟩, + ⟨6, 6, 3, 7, 1, 7, 2182309215643797231865672841593291170524430336000000⟩, + ⟨6, 6, 4, 7, 2, 7, 84269055715793476985407752569417973394046976000000⟩, + ⟨6, 6, 5, 7, 3, 7, 12270396939775040472096582460480018597281792000000⟩, + ⟨6, 6, 6, 7, 4, 7, 6188243907659355884907285843919483227340800000000⟩, + ⟨6, 6, 7, 7, 5, 7, -357586878811383184389121327549990142214144000000⟩, + ⟨6, 6, 8, 7, 6, 7, 80096090604528158459462130519426517381939200000⟩ +] + +def collectedFourData_10_5_46 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 5, 8, -35744326358859922170074298835037989178009714688000000⟩, + ⟨6, 7, 1, 0, 6, 8, 10743972506456899937314749195534300836901421056000000⟩, + ⟨6, 7, 2, 0, 7, 8, -209676450181741888148425986490638009762840576000000⟩, + ⟨6, 7, 3, 0, 8, 8, 21292207003822988950163254489398628305390796800000⟩, + ⟨6, 7, 0, 1, 4, 8, -25699567412399913727901735749828934676756037632000000⟩, + ⟨6, 7, 1, 1, 5, 8, 2339326479956234146913369470428323923428900864000000⟩, + ⟨6, 7, 2, 1, 6, 8, 482637508315339750489022870682884852843072716800000⟩, + ⟨6, 7, 3, 1, 7, 8, -284436673215037379417931850617699842927257190400000⟩, + ⟨6, 7, 4, 1, 8, 8, 63253486486012047036838892476111917337175654400000⟩, + ⟨6, 7, 0, 2, 3, 8, -10059311922905126662411590338103856565499985920000000⟩, + ⟨6, 7, 1, 2, 4, 8, -2033936536249393944342032237320531894761160704000000⟩, + ⟨6, 7, 2, 2, 5, 8, 1012079815932769811606743091896734067093143552000000⟩, + ⟨6, 7, 3, 2, 6, 8, 92590073145385824454758056347816476432295526400000⟩, + ⟨6, 7, 4, 2, 7, 8, -8576634910675484760024815292662584323342336000000⟩, + ⟨6, 7, 5, 2, 8, 8, 13373689023762503889793513889784691811155968000000⟩, + ⟨6, 7, 0, 3, 2, 8, 44201271504355475433946201518924580957301243904000000⟩, + ⟨6, 7, 1, 3, 3, 8, 5632871424825992178729963872555405923200270336000000⟩, + ⟨6, 7, 2, 3, 4, 8, -74571135392568498314852872921468565932159795200000⟩, + ⟨6, 7, 3, 3, 5, 8, 184945684267793513088908230308658568129780121600000⟩, + ⟨6, 7, 4, 3, 6, 8, -6985046141609324112204111969281992962972057600000⟩, + ⟨6, 7, 5, 3, 7, 8, -1053563072687414311519698515615650286665728000000⟩, + ⟨6, 7, 6, 3, 8, 8, 1516999055900333604312313439277093293654016000000⟩, + ⟨6, 7, 0, 4, 1, 8, 36484163220962823292978553436787566330123386880000000⟩, + ⟨6, 7, 1, 4, 2, 8, -9711540893770659300274942459456250238675714048000000⟩, + ⟨6, 7, 2, 4, 3, 8, -1586120406615176061975252019337466614927012659200000⟩, + ⟨6, 7, 3, 4, 4, 8, -75636286405154615282756065885373776529876582400000⟩, + ⟨6, 7, 4, 4, 5, 8, 18062570632672170445812768119543841510182092800000⟩, + ⟨6, 7, 5, 4, 6, 8, -2580166666253667694139255751576482626928640000000⟩, + ⟨6, 7, 6, 4, 7, 8, -661952306739405952619826867652869627052032000000⟩, + ⟨6, 7, 7, 4, 8, 8, 388489955005694443526776689441178619215872000000⟩, + ⟨6, 7, 0, 5, 0, 8, -225772801516928543088913992432586671702751051776000000⟩, + ⟨6, 7, 1, 5, 1, 8, -4403325814383713365820335068836820263085539328000000⟩, + ⟨6, 7, 2, 5, 2, 8, 215747898063390871757091414819704256453830246400000⟩, + ⟨6, 7, 3, 5, 3, 8, -190428587831418296077255530584620482861780172800000⟩, + ⟨6, 7, 4, 5, 4, 8, 2522414295554031699042693158376584654094336000000⟩, + ⟨6, 7, 5, 5, 5, 8, -710065273818698814334287252602410783211520000000⟩, + ⟨6, 7, 6, 5, 6, 8, -1121137537361008911504191579008880741449728000000⟩, + ⟨6, 7, 7, 5, 7, 8, 177204232183612662698812449679798598998425600000⟩, + ⟨6, 7, 8, 5, 8, 8, 97246997928985583516948418892602639856435200000⟩, + ⟨6, 7, 1, 6, 0, 8, 48005448580034664958848082838785645370287325184000000⟩, + ⟨6, 7, 2, 6, 1, 8, -3620178863339163769511135479405767826290298060800000⟩, + ⟨6, 7, 3, 6, 2, 8, -212952688614320145487250529962130710531250585600000⟩, + ⟨6, 7, 4, 6, 3, 8, -63050938704582014920557782539665271450238976000000⟩, + ⟨6, 7, 5, 6, 4, 8, 5921266682676909777146805782984646551666688000000⟩, + ⟨6, 7, 6, 6, 5, 8, 106639936595329417039815020597825721335808000000⟩, + ⟨6, 7, 7, 6, 6, 8, 53573542922629434917793127285254595490611200000⟩, + ⟨6, 7, 8, 6, 7, 8, 26213661529542410506137978216627005344972800000⟩, + ⟨6, 7, 2, 7, 0, 8, 29533325209450025852219889886997761163308459622400000⟩, + ⟨6, 7, 3, 7, 1, 8, 1957649964639422183324504234693049759515541504000000⟩, + ⟨6, 7, 4, 7, 2, 8, 64794790802190345983189784415890963129434112000000⟩, + ⟨6, 7, 5, 7, 3, 8, 8255409669858311861167152572675956477526016000000⟩, + ⟨6, 7, 6, 7, 4, 8, 3700794058015167310543692718941594766540800000000⟩, + ⟨6, 7, 7, 7, 5, 8, -192464918071872321909467832875689505823129600000⟩, + ⟨6, 7, 8, 7, 6, 8, 39191206972794555166704855831777058278604800000⟩ +] + +def collectedFourData_10_5_47 : List CollectedFourTerm := [ + ⟨7, 0, 3, 0, 8, 2, 51923428883167156347506671818687224248523764531200000⟩, + ⟨7, 0, 3, 1, 7, 2, -693630649504483373810664417726490060649056016793600000⟩, + ⟨7, 0, 4, 1, 8, 2, 1079754923764072841304422734578168233627638510387200000⟩, + ⟨7, 0, 3, 2, 6, 2, 225791252047685264965415909596277309673934789017600000⟩, + ⟨7, 0, 4, 2, 7, 2, -146405586294071049897056343451995498937810157568000000⟩, + ⟨7, 0, 5, 2, 8, 2, 913170632925693169124857480365798746073109364736000000⟩, + ⟨7, 0, 3, 3, 5, 2, 451010742221473526222639174053127754626298701414400000⟩, + ⟨7, 0, 4, 3, 6, 2, -119236715367298915150811997362711517417763032268800000⟩, + ⟨7, 0, 5, 3, 7, 2, -71938479816875194155546320328634971911677280256000000⟩, + ⟨7, 0, 6, 3, 8, 2, 310747240846443144511086086090717596286132944896000000⟩, + ⟨7, 0, 3, 4, 4, 2, -184447546345936217183245718952135253019330189721600000⟩, + ⟨7, 0, 4, 4, 5, 2, 308333194894752095217677365405387629349711537766400000⟩, + ⟨7, 0, 5, 4, 6, 2, -176176702141812770492418639065685353431333601280000000⟩, + ⟨7, 0, 6, 4, 7, 2, -135596559596490092615907665507468513889371553792000000⟩, + ⟨7, 0, 7, 4, 8, 2, 198949005843201071626916380023171954755323822080000000⟩, + ⟨7, 0, 3, 5, 3, 2, -464381415971170739354366465777415061804181304115200000⟩, + ⟨7, 0, 4, 5, 4, 2, 43058326215735931632297079375058694871940333568000000⟩, + ⟨7, 0, 5, 5, 5, 2, -48484061081387052837148118454987184875283415040000000⟩, + ⟨7, 0, 6, 5, 6, 2, -229657622388921732383930370159307291528179744768000000⟩, + ⟨7, 0, 7, 5, 7, 2, 90747792497288010558267837867316703948213059584000000⟩, + ⟨7, 0, 8, 5, 8, 2, 109562230070099593370375545505954632257840454041600000⟩, + ⟨7, 0, 3, 6, 2, 2, -519308955654976484308656543622651858240888268390400000⟩, + ⟨7, 0, 4, 6, 3, 2, -1076297375786145483340638249441241694315256741888000000⟩, + ⟨7, 0, 5, 6, 4, 2, 404310795228934696284000521423579931674123698176000000⟩, + ⟨7, 0, 6, 6, 5, 2, 21844486937647387551747446863943615395814965248000000⟩, + ⟨7, 0, 7, 6, 6, 2, 27435466391399893852654013093935054113963245568000000⟩, + ⟨7, 0, 8, 6, 7, 2, 29533325209450025852219889886997761163308459622400000⟩, + ⟨7, 0, 3, 7, 1, 2, 4773948454419919170518672725071726428797676814336000000⟩, + ⟨7, 0, 4, 7, 2, 2, 1106065424842623912995770272382966369281015545856000000⟩, + ⟨7, 0, 5, 7, 3, 2, 563688721929360469272993902146422498479289925632000000⟩, + ⟨7, 0, 6, 7, 4, 2, 758083228856459026428941477471807109988142284800000000⟩, + ⟨7, 0, 7, 7, 5, 2, -98562919366939310236601745870478319323283718144000000⟩, + ⟨7, 0, 8, 7, 6, 2, 44154329969278871172740845840968150827399538278400000⟩ +] + +def collectedFourData_10_5_48 : List CollectedFourTerm := [ + ⟨7, 1, 2, 0, 7, 3, -33893391894560130241203679845150955479383408640000000⟩, + ⟨7, 1, 3, 0, 8, 3, 20650820318309014207229231723371896065293811712000000⟩, + ⟨7, 1, 2, 1, 6, 3, 78016497313680044804804876491865952126083530752000000⟩, + ⟨7, 1, 3, 1, 7, 3, -275868566816332040565712894239304321047919067136000000⟩, + ⟨7, 1, 4, 1, 8, 3, 214718340044853591862901919321462183150156251136000000⟩, + ⟨7, 1, 2, 2, 5, 3, 163598810454158739249545812741154739194198753280000000⟩, + ⟨7, 1, 3, 2, 6, 3, 89800975701633149716635503277456885199065317376000000⟩, + ⟨7, 1, 4, 2, 7, 3, -29113981117834923560379817228115256863977635840000000⟩, + ⟨7, 1, 5, 2, 8, 3, 121061102641075223878771772767370972400577413120000000⟩, + ⟨7, 1, 2, 3, 4, 3, -12054137284811363062168882667533570355314556928000000⟩, + ⟨7, 1, 3, 3, 5, 3, 179374552096697498127993376222937592832871890944000000⟩, + ⟨7, 1, 4, 3, 6, 3, -23711222827135937878756019659568160380911878144000000⟩, + ⟨7, 1, 5, 3, 7, 3, -9537047485913088961129692515234885746053611520000000⟩, + ⟨7, 1, 6, 3, 8, 3, 30897350065080900168881310574762618081498890240000000⟩, + ⟨7, 1, 2, 4, 3, 3, -256390264556512548447358940632440511723248549888000000⟩, + ⟨7, 1, 3, 4, 4, 3, -73357889100766322479127370815114231462196412416000000⟩, + ⟨7, 1, 4, 4, 5, 3, 61314646806827885589538815702953812489490399232000000⟩, + ⟨7, 1, 5, 4, 6, 3, -23356145118928341803693427780968784212892057600000000⟩, + ⟨7, 1, 6, 4, 7, 3, -13482257664014633723510512722087166423313940480000000⟩, + ⟨7, 1, 7, 4, 8, 3, 15825072652341957910115135260216640273551196160000000⟩, + ⟨7, 1, 2, 5, 2, 3, 34874818097845046991264745780060038606876573696000000⟩, + ⟨7, 1, 3, 5, 3, 3, -184692293761274678959394729480124159751253655552000000⟩, + ⟨7, 1, 4, 5, 4, 3, 8562509998030581209888010436655631761764515840000000⟩, + ⟨7, 1, 5, 5, 5, 3, -6427641979927289583378500334208412671593676800000000⟩, + ⟨7, 1, 6, 5, 6, 3, -22834674041630819903999872623609533035362385920000000⟩, + ⟨7, 1, 7, 5, 7, 3, 7218384445917111801140661540823475288191008768000000⟩, + ⟨7, 1, 8, 5, 8, 3, 7262456709545063457447264094380631224207015936000000⟩, + ⟨7, 1, 2, 6, 1, 3, -585187992438847319623099739934704892369187110912000000⟩, + ⟨7, 1, 3, 6, 2, 3, -206537899433607001148810349775380510299551432704000000⟩, + ⟨7, 1, 4, 6, 3, 3, -214030777574790508317838468887306234263702077440000000⟩, + ⟨7, 1, 5, 6, 4, 3, 53600399438258858245684247634566888296462417920000000⟩, + ⟨7, 1, 6, 6, 5, 3, 2171979896156506137540819829748648402611077120000000⟩, + ⟨7, 1, 7, 6, 6, 3, 2182309215643797231865672841593291170524430336000000⟩, + ⟨7, 1, 8, 6, 7, 3, 1957649964639422183324504234693049759515541504000000⟩, + ⟨7, 1, 2, 7, 0, 3, 4773948454419919170518672725071726428797676814336000000⟩, + ⟨7, 1, 3, 7, 1, 3, 1898679533721143700214633677666941747303137935360000000⟩, + ⟨7, 1, 4, 7, 2, 3, 219950404278134367570245295661874943695813345280000000⟩, + ⟨7, 1, 5, 7, 3, 3, 74729492783261384135926607596474502380718653440000000⟩, + ⟨7, 1, 6, 7, 4, 3, 75375610211835460582036801197318856205402112000000000⟩, + ⟨7, 1, 7, 7, 5, 3, -7840025906126137980243778693906594844154789888000000⟩, + ⟨7, 1, 8, 7, 6, 3, 2926819851473332845982756681542745585052811264000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1021.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1021.lean new file mode 100644 index 0000000000000000000000000000000000000000..6dbb648cb8119264325a805490db172cbef23803 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1021.lean @@ -0,0 +1,632 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1017 +import OAI.Analysis.LaughlinFock.Sparse1018 +import OAI.Analysis.LaughlinFock.Sparse1019 +import OAI.Analysis.LaughlinFock.Sparse1020 + +namespace OAI + +/-! Sparse1021. -/ +namespace LaughlinFock +def collectedFourData_10_5_49 : List CollectedFourTerm := [ + ⟨7, 2, 1, 0, 6, 4, 80475438715917075532900232244876324321443708928000000⟩, + ⟨7, 2, 2, 0, 7, 4, -7852684054538956628017740327824293086300733440000000⟩, + ⟨7, 2, 3, 0, 8, 4, 2392271153197293062845710808138359478237003776000000⟩, + ⟨7, 2, 1, 1, 5, 4, 17522226965966328548606008097659463627578540032000000⟩, + ⟨7, 2, 2, 1, 6, 4, 18075467523344714914029623055613079472561979392000000⟩, + ⟨7, 2, 3, 1, 7, 4, -31957685181323157046213159754077972106814947328000000⟩, + ⟨7, 2, 4, 1, 8, 4, 16582537094867705311312143388744715978567319552000000⟩, + ⟨7, 2, 1, 2, 4, 4, -15234768608783517947537235036420117529941245952000000⟩, + ⟨7, 2, 2, 2, 5, 4, 37903841969888692568238689863957816254796922880000000⟩, + ⟨7, 2, 3, 2, 6, 4, 10402893463245201178933177925166644979824590848000000⟩, + ⟨7, 2, 4, 2, 7, 4, -2248451025491927966362358559742867075372154880000000⟩, + ⟨7, 2, 5, 2, 8, 4, 7012093930373599540074129344780397525734522880000000⟩, + ⟨7, 2, 1, 3, 3, 4, 42191824194523603321333794244048925260479725568000000⟩, + ⟨7, 2, 2, 3, 4, 4, -2792796068984000128329863369607590650878885888000000⟩, + ⟨7, 2, 3, 3, 5, 4, 20779444108482378722654198564395402913761984512000000⟩, + ⟨7, 2, 4, 3, 6, 4, -1831200036352366055875258607434223981489553408000000⟩, + ⟨7, 2, 5, 3, 7, 4, -552404292796899060855427580810818411277844480000000⟩, + ⟨7, 2, 6, 3, 8, 4, 1431707566704237070233570272974386518355345408000000⟩, + ⟨7, 2, 1, 4, 2, 4, -72742229521163977019628378429119663034517684224000000⟩, + ⟨7, 2, 2, 4, 3, 4, -59402486139048611756988550336360815163550466048000000⟩, + ⟨7, 2, 3, 4, 4, 4, -8498062510360338511549997836404660202811424768000000⟩, + ⟨7, 2, 4, 4, 5, 4, 4735284395923238770885240477223372983394893824000000⟩, + ⟨7, 2, 5, 4, 6, 4, -1352833237534005994082423443516998960965222400000000⟩, + ⟨7, 2, 6, 4, 7, 4, -624734816195163613361231941014065371536162816000000⟩, + ⟨7, 2, 7, 4, 8, 4, 611079273041182187771367444419941847594434560000000⟩, + ⟨7, 2, 1, 5, 1, 4, -32982174564267506451309054061257411767895588864000000⟩, + ⟨7, 2, 2, 5, 2, 4, 8080068493405906267003442375814200712983740416000000⟩, + ⟨7, 2, 3, 5, 3, 4, -21395471936347622551879683695999129115055620096000000⟩, + ⟨7, 2, 4, 5, 4, 4, 661276254454356810121005968541295542408314880000000⟩, + ⟨7, 2, 5, 5, 5, 4, -372301493467236321221600984247419454829363200000000⟩, + ⟨7, 2, 6, 5, 6, 4, -1058102896842783565073617708844664292129112064000000⟩, + ⟨7, 2, 7, 5, 7, 4, 278735220788387294146506200136829738929881088000000⟩, + ⟨7, 2, 8, 5, 8, 4, 240374618396915404570615933459288356928094208000000⟩, + ⟨7, 2, 1, 6, 0, 4, 359574592443432902625356540743517165326216200192000000⟩, + ⟨7, 2, 2, 6, 1, 4, -135580895279759305418150317579735793509179850752000000⟩, + ⟨7, 2, 3, 6, 2, 4, -23926151660857622768483879102210306422175956992000000⟩, + ⟨7, 2, 4, 6, 3, 4, -16529437158632737091339229383099811962636206080000000⟩, + ⟨7, 2, 5, 6, 4, 4, 3104639123277666952289861307740259270870958080000000⟩, + ⟨7, 2, 6, 6, 5, 4, 100644231479616722289108380148465957920047104000000⟩, + ⟨7, 2, 7, 6, 6, 4, 84269055715793476985407752569417973394046976000000⟩, + ⟨7, 2, 8, 6, 7, 4, 64794790802190345983189784415890963129434112000000⟩, + ⟨7, 2, 2, 7, 0, 4, 1106065424842623912995770272382966369281015545856000000⟩, + ⟨7, 2, 3, 7, 1, 4, 219950404278134367570245295661874943695813345280000000⟩, + ⟨7, 2, 4, 7, 2, 4, 16986605509391518706379926869387282169682984960000000⟩, + ⟨7, 2, 5, 7, 3, 4, 4328477201459188521653469589050929422333378560000000⟩, + ⟨7, 2, 6, 7, 4, 4, 3492721261141312988038793534160248515225190400000000⟩, + ⟨7, 2, 7, 7, 5, 4, -302739673718375788226988212507703411902251008000000⟩, + ⟨7, 2, 8, 7, 6, 4, 96872619425016841173301820667359900196667392000000⟩ +] + +def collectedFourData_10_5_50 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 5, 5, -68223518681210202203229721311834559012965187584000000⟩, + ⟨7, 3, 1, 0, 6, 5, 82026064964347548803268233946619309787952709632000000⟩, + ⟨7, 3, 2, 0, 7, 5, -4001996029346954154728923153010067727114567680000000⟩, + ⟨7, 3, 3, 0, 8, 5, 812788730555807578793913403160420014513717248000000⟩, + ⟨7, 3, 0, 1, 4, 5, -49051558556629322511147334042198345717358002176000000⟩, + ⟨7, 3, 1, 1, 5, 5, 17859850786325939191243733434073749553946820608000000⟩, + ⟨7, 3, 2, 1, 6, 5, 9211875679017426948461554769913153494370484224000000⟩, + ⟨7, 3, 3, 1, 7, 5, -10857818661281002312936409175940552903826079744000000⟩, + ⟨7, 3, 4, 1, 8, 5, 4225513668272460709434410683709079950953807872000000⟩, + ⟨7, 3, 0, 2, 3, 5, -19199736707930159586143612474563145847338434560000000⟩, + ⟨7, 3, 1, 2, 4, 5, -15528316956832124431456972651609437664431833088000000⟩, + ⟨7, 3, 2, 2, 5, 5, 19317092602599939721136622474802329661325967360000000⟩, + ⟨7, 3, 3, 2, 6, 5, 3534446570071170349393535432107394284287688704000000⟩, + ⟨7, 3, 4, 2, 7, 5, -572943723044520650206661615007511221035335680000000⟩, + ⟨7, 3, 5, 2, 8, 5, 1429441035542113568759686949644642415693266944000000⟩, + ⟨7, 3, 0, 3, 2, 5, 84364893100389163412843271619154161994009935872000000⟩, + ⟨7, 3, 1, 3, 3, 5, 43004789629805563175631406715774898022008225792000000⟩, + ⟨7, 3, 2, 3, 4, 5, -1423304274210476404999712868586809599968935936000000⟩, + ⟨7, 3, 3, 3, 5, 5, 7059943006885335948637592639908311150756888576000000⟩, + ⟨7, 3, 4, 3, 6, 5, -466621044697845808141974500070654045415538688000000⟩, + ⟨7, 3, 5, 3, 7, 5, -112609638743307220880823958575762645423489024000000⟩, + ⟨7, 3, 6, 3, 8, 5, 243215693612619403573712768620289292912033792000000⟩, + ⟨7, 3, 0, 4, 1, 5, 69635610588495907327328549488052524671660195840000000⟩, + ⟨7, 3, 1, 4, 2, 5, -74143849844888428156461630216455027241837920256000000⟩, + ⟨7, 3, 2, 4, 3, 5, -30273536030575400322783518839304457040435347456000000⟩, + ⟨7, 3, 3, 4, 4, 5, -2887268623687676452732721120644892331148836864000000⟩, + ⟨7, 3, 4, 4, 5, 5, 1206631338959810647023234915368309418218225664000000⟩, + ⟨7, 3, 5, 4, 6, 5, -275780011388605050360077465361439880506245120000000⟩, + ⟨7, 3, 6, 4, 7, 5, -106128734092419557134901049831564417731395584000000⟩, + ⟨7, 3, 7, 4, 8, 5, 88979106009837355316286778634931478745579520000000⟩, + ⟨7, 3, 0, 5, 0, 5, -430921953525119450680818598789856749664618938368000000⟩, + ⟨7, 3, 1, 5, 1, 5, -33617685552784225485227523389459709287429308416000000⟩, + ⟨7, 3, 2, 5, 2, 5, 4117878906483062838115802856860516336850173952000000⟩, + ⟨7, 3, 3, 5, 3, 5, -7269242222623674032944105136564460225306820608000000⟩, + ⟨7, 3, 4, 5, 4, 5, 168504483705675957599919109133544602657095680000000⟩, + ⟨7, 3, 5, 5, 5, 5, -75895023318281101672158774528918325202780160000000⟩, + ⟨7, 3, 6, 5, 6, 5, -179748459779078902847691629327159887487041536000000⟩, + ⟨7, 3, 7, 5, 7, 5, 40586568475435576321737417305086562817540096000000⟩, + ⟨7, 3, 8, 5, 8, 5, 30625779087094699664582210915120813382303744000000⟩, + ⟨7, 3, 1, 6, 0, 5, 366502989606693063191819264460763831134635163648000000⟩, + ⟨7, 3, 2, 6, 1, 5, -69096655461552055821900206468912162985574662144000000⟩, + ⟨7, 3, 3, 6, 2, 5, -8129056110350709883444641973278152474404847616000000⟩, + ⟨7, 3, 4, 6, 3, 5, -4211982897615255412319983701518883417363578880000000⟩, + ⟨7, 3, 5, 6, 4, 5, 632892058695816650797801093486524795614920704000000⟩, + ⟨7, 3, 6, 6, 5, 5, 17097246069441733373577389837611590532202496000000⟩, + ⟨7, 3, 7, 6, 6, 5, 12270396939775040472096582460480018597281792000000⟩, + ⟨7, 3, 8, 6, 7, 5, 8255409669858311861167152572675956477526016000000⟩, + ⟨7, 3, 2, 7, 0, 5, 563688721929360469272993902146422498479289925632000000⟩, + ⟨7, 3, 3, 7, 1, 5, 74729492783261384135926607596474502380718653440000000⟩, + ⟨7, 3, 4, 7, 2, 5, 4328477201459188521653469589050929422333378560000000⟩, + ⟨7, 3, 5, 7, 3, 5, 882375934294507793395393140769996114155798528000000⟩, + ⟨7, 3, 6, 7, 4, 5, 593336686820426801583908181713289163151769600000000⟩, + ⟨7, 3, 7, 7, 5, 5, -44081851094556015284945951212936795558772736000000⟩, + ⟨7, 3, 8, 7, 6, 5, 12342398968263264234224141320545632105005056000000⟩ +] + +def collectedFourData_10_5_51 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 5, 6, -275253539659865902264032807818645387862658252800000000⟩, + ⟨7, 4, 1, 0, 6, 6, 165470538329365668689888136223756608169259827200000000⟩, + ⟨7, 4, 2, 0, 7, 6, -5382130161153478798086442532462114742730752000000000⟩, + ⟨7, 4, 3, 0, 8, 6, 819816169723417396612506824935870174750310400000000⟩, + ⟨7, 4, 0, 1, 4, 6, -197902649695257577619077985999217152333394739200000000⟩, + ⟨7, 4, 1, 1, 5, 6, 36028537092203600875400788186434033016425676800000000⟩, + ⟨7, 4, 2, 1, 6, 6, 12388696432796377053134842160387408363362713600000000⟩, + ⟨7, 4, 3, 1, 7, 6, -10951696267190859144359164679917435922625331200000000⟩, + ⟨7, 4, 4, 1, 8, 6, 3409638249554171066524499566753494583455252480000000⟩, + ⟨7, 4, 0, 2, 3, 6, -77462956932632539142767789634197161510961152000000000⟩, + ⟨7, 4, 1, 2, 4, 6, -31325152161241031885785492146294529693895884800000000⟩, + ⟨7, 4, 2, 2, 5, 6, 25978813062244152871000079176079527907426304000000000⟩, + ⟨7, 4, 3, 2, 6, 6, 3565005689961227548577371796729327883858739200000000⟩, + ⟨7, 4, 4, 2, 7, 6, -462317953815362193071075402613250359243571200000000⟩, + ⟨7, 4, 5, 2, 8, 6, 961200067986709964068267322425758083501260800000000⟩, + ⟨7, 4, 0, 3, 2, 6, 340377276015579302019782820597501980869813862400000000⟩, + ⟨7, 4, 1, 3, 3, 6, 86753225256849926873640874990630382939091763200000000⟩, + ⟨7, 4, 2, 3, 4, 6, -1914147042264030512802225751874439301457510400000000⟩, + ⟨7, 4, 3, 3, 5, 6, 7120983863066685890689075099980763753139404800000000⟩, + ⟨7, 4, 4, 3, 6, 6, -376524391340843130498208454674075766143057920000000⟩, + ⟨7, 4, 5, 3, 7, 6, -75722180715887820785993544930162803264716800000000⟩, + ⟨7, 4, 6, 3, 8, 6, 140182032450721997795299547335249399853875200000000⟩, + ⟨7, 4, 0, 4, 1, 6, 280950743546719818361450635619023033653526528000000000⟩, + ⟨7, 4, 1, 4, 2, 6, -149569807511525436496772275683374493249149337600000000⟩, + ⟨7, 4, 2, 4, 3, 6, -40713711398038130052756729877932569639937638400000000⟩, + ⟨7, 4, 3, 4, 4, 6, -2912232189065408413290647696904787399488307200000000⟩, + ⟨7, 4, 4, 4, 5, 6, 973651179339376057329237810520832549333237760000000⟩, + ⟨7, 4, 5, 4, 6, 6, -185442952248514176680164664709114268483584000000000⟩, + ⟨7, 4, 6, 4, 7, 6, -61169332560395616985045185229514206504550400000000⟩, + ⟨7, 4, 7, 4, 8, 6, 44874213391538976174146412453603991093248000000000⟩, + ⟨7, 4, 0, 5, 0, 6, -1738590962732051674533334504100259250491201945600000000⟩, + ⟨7, 4, 1, 5, 1, 6, -67816693732953982791822627933672766285912473600000000⟩, + ⟨7, 4, 2, 5, 2, 6, 5537976574698588752780277115962167313353932800000000⟩, + ⟨7, 4, 3, 5, 3, 6, -7332092697284138239538725366187125436212838400000000⟩, + ⟨7, 4, 4, 5, 4, 6, 135969110022815827915513725769942492721971200000000⟩, + ⟨7, 4, 5, 5, 5, 6, -51034145347393381861727708526780572762112000000000⟩, + ⟨7, 4, 6, 5, 6, 6, -103601474261160702366951566379582490253721600000000⟩, + ⟨7, 4, 7, 5, 7, 6, 20468741666112564699026086661409808475750400000000⟩, + ⟨7, 4, 8, 5, 8, 6, 13729143167955043041161903658855675671347200000000⟩, + ⟨7, 4, 1, 6, 0, 6, 739343610057374126030011627185151584974458060800000000⟩, + ⟨7, 4, 2, 6, 1, 6, -92925427878331536410499209708857099111995801600000000⟩, + ⟨7, 4, 3, 6, 2, 6, -8199340607610547430351662608119003702152396800000000⟩, + ⟨7, 4, 4, 6, 3, 6, -3398720042490930387959367758804763771351859200000000⟩, + ⟨7, 4, 5, 6, 4, 6, 425576064154305769558386023167069134834892800000000⟩, + ⟨7, 4, 6, 6, 5, 6, 9854325877267750784379407125946174118297600000000⟩, + ⟨7, 4, 7, 6, 6, 6, 6188243907659355884907285843919483227340800000000⟩, + ⟨7, 4, 8, 6, 7, 6, 3700794058015167310543692718941594766540800000000⟩, + ⟨7, 4, 2, 7, 0, 6, 758083228856459026428941477471807109988142284800000000⟩, + ⟨7, 4, 3, 7, 1, 6, 75375610211835460582036801197318856205402112000000000⟩, + ⟨7, 4, 4, 7, 2, 6, 3492721261141312988038793534160248515225190400000000⟩, + ⟨7, 4, 5, 7, 3, 6, 593336686820426801583908181713289163151769600000000⟩, + ⟨7, 4, 6, 7, 4, 6, 341980985892060663172319765229364586741760000000000⟩, + ⟨7, 4, 7, 7, 5, 6, -22231493228224315016762384037718268470886400000000⟩, + ⟨7, 4, 8, 7, 6, 6, 5532938835267417039226285533283308326092800000000⟩ +] + +def collectedFourData_10_5_52 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 5, 7, 71574706845538053739273260725698231335143866368000000⟩, + ⟨7, 5, 1, 0, 6, 7, -28685081366880579112585699687497766925959692288000000⟩, + ⟨7, 5, 2, 0, 7, 7, 699762824058711689710127997991033634354626560000000⟩, + ⟨7, 5, 3, 0, 8, 7, -85271349589465340119661623543313033089096089600000⟩, + ⟨7, 5, 0, 1, 4, 7, 51461006290407436390113729123995280739141681152000000⟩, + ⟨7, 5, 1, 1, 5, 7, -6245713155065778675391765896048922506792271872000000⟩, + ⟨7, 5, 2, 1, 6, 7, -1610728269782635545899361171683981346742468608000000⟩, + ⟨7, 5, 3, 1, 7, 7, 1139116250064126086631244150187916807539313868800000⟩, + ⟨7, 5, 4, 1, 8, 7, -295538261999877440169726648887141314456033689600000⟩, + ⟨7, 5, 0, 2, 3, 7, 20142841544174076276550573033700679088204677120000000⟩, + ⟨7, 5, 1, 2, 4, 7, 5430359673977369799977054320020745954831368192000000⟩, + ⟨7, 5, 2, 2, 5, 7, -3377660340758696295045387204064632628177797120000000⟩, + ⟨7, 5, 3, 2, 6, 7, -370806112033232330783162443307024108330208460800000⟩, + ⟨7, 5, 4, 2, 7, 7, 40072475307255020018249433145530470602113024000000⟩, + ⟨7, 5, 5, 2, 8, 7, -71412200206475660140196717027116339616022528000000⟩, + ⟨7, 5, 0, 3, 2, 7, -88508957152023526176972704725346831865263161344000000⟩, + ⟨7, 5, 1, 3, 3, 7, -15039071912479703803241216544442065300360265728000000⟩, + ⟨7, 5, 2, 3, 4, 7, 248869666814457394748012734605838018896986112000000⟩, + ⟨7, 5, 3, 3, 5, 7, -740673247044344212696539654498479771279897395200000⟩, + ⟨7, 5, 4, 3, 6, 7, 32636120336808342749885728690976948945839718400000⟩, + ⟨7, 5, 5, 3, 7, 7, 5625766902701340768509176725875848000831488000000⟩, + ⟨7, 5, 6, 3, 8, 7, -9112950818062712821410360182207682422243328000000⟩, + ⟨7, 5, 0, 4, 1, 7, -73056161719995698545323104647817378133631303680000000⟩, + ⟨7, 5, 1, 4, 2, 7, 25928616307253301665186282196492570350378287104000000⟩, + ⟨7, 5, 2, 4, 3, 7, 5293432305192830714224098461364875016328445952000000⟩, + ⟨7, 5, 3, 4, 4, 7, 302909332909681220801779547446610693857266892800000⟩, + ⟨7, 5, 4, 4, 5, 7, -84393462377926815241606907989679502099952435200000⟩, + ⟨7, 5, 5, 4, 6, 7, 13777453491642806379545434609558444509757440000000⟩, + ⟨7, 5, 6, 4, 7, 7, 3976494772199576231622720813423513783238656000000⟩, + ⟨7, 5, 7, 4, 8, 7, -2593050653018911954157166105030048759152640000000⟩, + ⟨7, 5, 0, 5, 0, 7, 452089148919281143568800049586191398472710619136000000⟩, + ⟨7, 5, 1, 5, 1, 7, 11756336792054616435975168027431443306899308544000000⟩, + ⟨7, 5, 2, 5, 2, 7, -720025345253177861997565323736910744292163584000000⟩, + ⟨7, 5, 3, 5, 3, 7, 762631261375842537086640153631411091109681561600000⟩, + ⟨7, 5, 4, 5, 4, 7, -11785436319253925040860742124915130602881024000000⟩, + ⟨7, 5, 5, 5, 5, 7, 3791573394858337297928008318159563962449920000000⟩, + ⟨7, 5, 6, 5, 6, 7, 6734922608235338863093342313850335788007424000000⟩, + ⟨7, 5, 7, 5, 7, 7, -1182783606270325354423727695626123683561472000000⟩, + ⟨7, 5, 8, 5, 8, 7, -714003095982771240502841169714592398861926400000⟩, + ⟨7, 5, 1, 6, 0, 7, -128168626431641008647668385663499147334733791232000000⟩, + ⟨7, 5, 2, 6, 1, 7, 12081788788450505627349429128055484145360437248000000⟩, + ⟨7, 5, 3, 6, 2, 7, 852836117626879425558047753575563860601156403200000⟩, + ⟨7, 5, 4, 6, 3, 7, 294591901212176031928574056947356941663862784000000⟩, + ⟨7, 5, 5, 6, 4, 7, -31618103357116511349116636819042655585435648000000⟩, + ⟨7, 5, 6, 6, 5, 7, -640609823489837629431403983316769323352064000000⟩, + ⟨7, 5, 7, 6, 6, 7, -357586878811383184389121327549990142214144000000⟩, + ⟨7, 5, 8, 6, 7, 7, -192464918071872321909467832875689505823129600000⟩, + ⟨7, 5, 2, 7, 0, 7, -98562919366939310236601745870478319323283718144000000⟩, + ⟨7, 5, 3, 7, 1, 7, -7840025906126137980243778693906594844154789888000000⟩, + ⟨7, 5, 4, 7, 2, 7, -302739673718375788226988212507703411902251008000000⟩, + ⟨7, 5, 5, 7, 3, 7, -44081851094556015284945951212936795558772736000000⟩, + ⟨7, 5, 6, 7, 4, 7, -22231493228224315016762384037718268470886400000000⟩, + ⟨7, 5, 7, 7, 5, 7, 1284643978715446015531086068162624017661952000000⟩, + ⟨7, 5, 8, 7, 6, 7, -287748143488307482617982366899044072659353600000⟩ +] + +def collectedFourData_10_5_53 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 5, 8, -53440199144039564799790739587609128735665553408000000⟩, + ⟨7, 6, 1, 0, 6, 8, 16062969674649526035521383068918970742992797696000000⟩, + ⟨7, 6, 2, 0, 7, 8, -313480554676900883486972448837562383797846016000000⟩, + ⟨7, 6, 3, 0, 8, 8, 31833297712110162081237398157266503366134988800000⟩, + ⟨7, 6, 0, 1, 4, 8, -38422601300301179287280214897812391884815859712000000⟩, + ⟨7, 6, 1, 1, 5, 8, 3497452202531131990159531943327362479003009024000000⟩, + ⟨7, 6, 2, 1, 6, 8, 721575902698798555895240448941807295527701708800000⟩, + ⟨7, 6, 3, 1, 7, 8, -425252173110600553117213200280847274356401766400000⟩, + ⟨7, 6, 4, 1, 8, 8, 94568264636757707733943289530613408423372390400000⟩, + ⟨7, 6, 0, 2, 3, 8, -15039355533380027429339383851719153897145630720000000⟩, + ⟨7, 6, 1, 2, 4, 8, -3040873464847485013497722581628299876409278464000000⟩, + ⟨7, 6, 2, 2, 5, 8, 1513128163896811775208967175185377689371410432000000⟩, + ⟨7, 6, 3, 2, 6, 8, 138428457092020224220136522057827707898979942400000⟩, + ⟨7, 6, 4, 2, 7, 8, -12822652552203216619052529814081197022642176000000⟩, + ⟨7, 6, 5, 2, 8, 8, 19994574734604668452144362332589002103717888000000⟩, + ⟨7, 6, 0, 3, 2, 8, 66083907356307460782322626027386127149552369664000000⟩, + ⟨7, 6, 1, 3, 3, 8, 8421525913604379534238649104047730307603890176000000⟩, + ⟨7, 6, 2, 3, 4, 8, -111488919549555713185625681145773389662860083200000⟩, + ⟨7, 6, 3, 3, 5, 8, 276506377512181748520369873227376709919676825600000⟩, + ⟨7, 6, 4, 3, 6, 8, -10443119086657014165129231839464829885192601600000⟩, + ⟨7, 6, 5, 3, 7, 8, -1575148454329898411147715049834183863042048000000⟩, + ⟨7, 6, 6, 3, 8, 8, 2268016770962012653044952570516312273453056000000⟩, + ⟨7, 6, 0, 4, 1, 8, 54546305574692169817707680430225864930707374080000000⟩, + ⟨7, 6, 1, 4, 2, 8, -14519414190329177585986352758987227162809991168000000⟩, + ⟨7, 6, 2, 4, 3, 8, -2371357891737970098930707630508240983154701107200000⟩, + ⟨7, 6, 3, 4, 4, 8, -113081392762216169296834058770673752718337638400000⟩, + ⟨7, 6, 4, 4, 5, 8, 27004771665644254848392116143951779845688524800000⟩, + ⟨7, 6, 5, 4, 6, 8, -3857524662378517632770057016567662892810240000000⟩, + ⟨7, 6, 6, 4, 7, 8, -989663722876172594913678393214500562010112000000⟩, + ⟨7, 6, 7, 4, 8, 8, 580818906825398065838637882197341793943552000000⟩, + ⟨7, 6, 0, 5, 0, 8, -337545694755602820339661063653553796292821385216000000⟩, + ⟨7, 6, 1, 5, 1, 8, -6583271595449401010847982240143694960313499648000000⟩, + ⟨7, 6, 2, 5, 2, 8, 322557782224303110950747590246729967345231462400000⟩, + ⟨7, 6, 3, 5, 3, 8, -284703691272860442789552473639435743416601804800000⟩, + ⟨7, 6, 4, 5, 4, 8, 3771180940014200519622595757499812388274176000000⟩, + ⟨7, 6, 5, 5, 5, 8, -1061595881180527289362303822761375899320320000000⟩, + ⟨7, 6, 6, 5, 6, 8, -1676176875258963087876839849082459990786048000000⟩, + ⟨7, 6, 7, 5, 7, 8, 264932380092585111762784935496320097556889600000⟩, + ⟨7, 6, 8, 5, 8, 8, 145390876395600077156025882130835710358323200000⟩, + ⟨7, 6, 1, 6, 0, 8, 71771410834830706769021722183859964885696774144000000⟩, + ⟨7, 6, 2, 6, 1, 8, -5412413635987691253326408966145914759180766412800000⟩, + ⟨7, 6, 3, 6, 2, 8, -318378753974953690368718433657275819365079449600000⟩, + ⟨7, 6, 4, 6, 3, 8, -94265441926738406180741780473281116337340416000000⟩, + ⟨7, 6, 5, 6, 4, 8, 8852696439998410706609215787936054570385408000000⟩, + ⟨7, 6, 6, 6, 5, 8, 159433958585418525038074353407932212707328000000⟩, + ⟨7, 6, 7, 6, 6, 8, 80096090604528158459462130519426517381939200000⟩, + ⟨7, 6, 8, 6, 7, 8, 39191206972794555166704855831777058278604800000⟩, + ⟨7, 6, 2, 7, 0, 8, 44154329969278871172740845840968150827399538278400000⟩, + ⟨7, 6, 3, 7, 1, 8, 2926819851473332845982756681542745585052811264000000⟩, + ⟨7, 6, 4, 7, 2, 8, 96872619425016841173301820667359900196667392000000⟩, + ⟨7, 6, 5, 7, 3, 8, 12342398968263264234224141320545632105005056000000⟩, + ⟨7, 6, 6, 7, 4, 8, 5532938835267417039226285533283308326092800000000⟩, + ⟨7, 6, 7, 7, 5, 8, -287748143488307482617982366899044072659353600000⟩, + ⟨7, 6, 8, 7, 6, 8, 58593520109864344463186569364963597274316800000⟩ +] + +def collectedFourData_10_5 : List (List CollectedFourTerm) := [ + collectedFourData_10_5_0, + collectedFourData_10_5_1, + collectedFourData_10_5_2, + collectedFourData_10_5_3, + collectedFourData_10_5_4, + collectedFourData_10_5_5, + collectedFourData_10_5_6, + collectedFourData_10_5_7, + collectedFourData_10_5_8, + collectedFourData_10_5_9, + collectedFourData_10_5_10, + collectedFourData_10_5_11, + collectedFourData_10_5_12, + collectedFourData_10_5_13, + collectedFourData_10_5_14, + collectedFourData_10_5_15, + collectedFourData_10_5_16, + collectedFourData_10_5_17, + collectedFourData_10_5_18, + collectedFourData_10_5_19, + collectedFourData_10_5_20, + collectedFourData_10_5_21, + collectedFourData_10_5_22, + collectedFourData_10_5_23, + collectedFourData_10_5_24, + collectedFourData_10_5_25, + collectedFourData_10_5_26, + collectedFourData_10_5_27, + collectedFourData_10_5_28, + collectedFourData_10_5_29, + collectedFourData_10_5_30, + collectedFourData_10_5_31, + collectedFourData_10_5_32, + collectedFourData_10_5_33, + collectedFourData_10_5_34, + collectedFourData_10_5_35, + collectedFourData_10_5_36, + collectedFourData_10_5_37, + collectedFourData_10_5_38, + collectedFourData_10_5_39, + collectedFourData_10_5_40, + collectedFourData_10_5_41, + collectedFourData_10_5_42, + collectedFourData_10_5_43, + collectedFourData_10_5_44, + collectedFourData_10_5_45, + collectedFourData_10_5_46, + collectedFourData_10_5_47, + collectedFourData_10_5_48, + collectedFourData_10_5_49, + collectedFourData_10_5_50, + collectedFourData_10_5_51, + collectedFourData_10_5_52, + collectedFourData_10_5_53 +] + +theorem collectedFourChecked_10_5 : collectNumericRowParts 10 5 = collectedFourData_10_5 := by + decide +kernel + +def collectedFourData_10_6_0 : List CollectedFourTerm := [ + ⟨0, 6, 4, 2, 8, 0, 1984754345275280556824553256622804345403998208000000⟩, + ⟨0, 6, 4, 3, 7, 0, 11965368689069917513920094458719269780835008512000000⟩, + ⟨0, 6, 5, 3, 8, 0, -9895468244120475846761344712605676100208558080000000⟩, + ⟨0, 6, 4, 4, 6, 0, -14187742892555970890743783898504100971091591168000000⟩, + ⟨0, 6, 5, 4, 7, 0, -5912862630054063518260945568252404177462886400000000⟩, + ⟨0, 6, 6, 4, 8, 0, 11221172499798652693028454738747591327586713600000000⟩, + ⟨0, 6, 4, 5, 5, 0, -7360672897212274745686547966267262923867947008000000⟩, + ⟨0, 6, 5, 5, 6, 0, 13133782714751979712171784946873635918000947200000000⟩, + ⟨0, 6, 6, 5, 7, 0, -13601399191419935880673886513829808836748247040000000⟩, + ⟨0, 6, 7, 5, 8, 0, -1851524283527646862689594037473109834318479360000000⟩, + ⟨0, 6, 4, 6, 4, 0, 14285774111187024808969856220185385447588888576000000⟩, + ⟨0, 6, 5, 6, 5, 0, -26621856869226726589979645951588321997178798080000000⟩, + ⟨0, 6, 6, 6, 6, 0, 8856616417366665467288261242997787162165903360000000⟩, + ⟨0, 6, 7, 6, 7, 0, 6118142079439213441157646773157415512661032960000000⟩, + ⟨0, 6, 8, 6, 8, 0, -18156649888162343499184772977360383589597839360000000⟩, + ⟨0, 6, 4, 7, 3, 0, -51995190218142894496588310892962018121203318784000000⟩, + ⟨0, 6, 5, 7, 4, 0, -80505276987091341080482030835014423522584821760000000⟩, + ⟨0, 6, 6, 7, 5, 0, -9152782634552418380204384340855994157157580800000000⟩, + ⟨0, 6, 7, 7, 6, 0, -15322164417584903361203523905511218128292413440000000⟩, + ⟨0, 6, 8, 7, 7, 0, -13748171006926311585290074820154025478014894080000000⟩ +] + +def collectedFourData_10_6_1 : List CollectedFourTerm := [ + ⟨0, 7, 3, 1, 8, 1, -438314271403082846563970671734430208018192793600000⟩, + ⟨0, 7, 3, 2, 7, 1, 15748629453537042864680653102882717089366068428800000⟩, + ⟨0, 7, 4, 2, 8, 1, -5267419670085787284983392285702091555679397478400000⟩, + ⟨0, 7, 3, 3, 6, 1, -17292847352371610663482747418437532144370922291200000⟩, + ⟨0, 7, 4, 3, 7, 1, -31755374937291716429949761707814200660782061977600000⟩, + ⟨0, 7, 5, 3, 8, 1, 13130991298210270069174155526747110174508449792000000⟩, + ⟨0, 7, 3, 4, 5, 1, -32350045327517249245833446886309460202171557478400000⟩, + ⟨0, 7, 4, 4, 6, 1, 37653423540435121299650967149496312908906653286400000⟩, + ⟨0, 7, 5, 4, 7, 1, 7846192401141247368009093600276281501794959360000000⟩, + ⟨0, 7, 6, 4, 8, 1, -9926774210549666179030232289943657446648053760000000⟩, + ⟨0, 7, 3, 5, 4, 1, 33116714438208506739675643244023618043001805209600000⟩, + ⟨0, 7, 4, 5, 5, 1, 19534786910097798166712432878257225328952239718400000⟩, + ⟨0, 7, 5, 5, 6, 1, -17428138041114109156730133398829621558147809280000000⟩, + ⟨0, 7, 6, 5, 7, 1, 12032434108218298943995574663997857562114392064000000⟩, + ⟨0, 7, 7, 5, 8, 1, 1228458757869898764612594296866777280525893632000000⟩, + ⟨0, 7, 3, 6, 3, 1, 44053093315275559314379492141620361200795018854400000⟩, + ⟨0, 7, 4, 6, 4, 1, -37913592548518625076724616883645140098104478924800000⟩, + ⟨0, 7, 5, 6, 5, 1, 35326410258525960395022833728268409251448225792000000⟩, + ⟨0, 7, 6, 6, 6, 1, -7834977266967756261881929534145881731105816576000000⟩, + ⟨0, 7, 7, 6, 7, 1, -4059296054740201757104798332697944002188541952000000⟩, + ⟨0, 7, 8, 6, 8, 1, 9637333203621467395877508115204481058063620505600000⟩, + ⟨0, 7, 3, 7, 2, 1, 162158327828838362307098397011682820901571448012800000⟩, + ⟨0, 7, 4, 7, 3, 1, 137992134067811524574079201909823266684994270003200000⟩, + ⟨0, 7, 5, 7, 4, 1, 106828102066377941697082714675246589217576321024000000⟩, + ⟨0, 7, 6, 7, 5, 1, 8096979759741870272219652885573169933744865280000000⟩, + ⟨0, 7, 7, 7, 6, 1, 10166027653951454346383110329785011029544009728000000⟩, + ⟨0, 7, 8, 7, 7, 1, 7297365194032883135393764873880713062951734476800000⟩ +] + +def collectedFourData_10_6_2 : List CollectedFourTerm := [ + ⟨0, 8, 2, 0, 8, 2, 15320362795887692000775237144933669686802697420800000⟩, + ⟨0, 8, 2, 1, 7, 2, 7023043454911770646526800490114149979321794560000000⟩, + ⟨0, 8, 3, 1, 8, 2, 266476744145148747421620689624321792417149747200000⟩, + ⟨0, 8, 2, 2, 6, 2, 14794619026428744093248333369999866515989043609600000⟩, + ⟨0, 8, 3, 2, 7, 2, -9574508007902905726931355366607929504660298137600000⟩, + ⟨0, 8, 4, 2, 8, 2, 1601185422547824603731999328081640743992976998400000⟩, + ⟨0, 8, 2, 3, 5, 2, -3666445605190918528066510499547171520471734681600000⟩, + ⟨0, 8, 3, 3, 6, 2, 10513327902164747180968713589906174364585715302400000⟩, + ⟨0, 8, 4, 3, 7, 2, 9652969883127602422853155660930875062052559257600000⟩, + ⟨0, 8, 5, 3, 8, 2, -2661031164803594150386973140047407703474044928000000⟩, + ⟨0, 8, 2, 4, 4, 2, -463176603083809952855709545073915980685508608000000⟩, + ⟨0, 8, 3, 4, 5, 2, 19667474490916489321117805443298647009066273996800000⟩, + ⟨0, 8, 4, 4, 6, 2, -11445853313028674419623741912497841022253295206400000⟩, + ⟨0, 8, 5, 4, 7, 2, -1590052268736768324978536355153812253824778240000000⟩, + ⟨0, 8, 6, 4, 8, 2, 1508765881055851904794054196485072874247290880000000⟩, + ⟨0, 8, 2, 5, 3, 2, -7723655304287389255237812079426460780474872627200000⟩, + ⟨0, 8, 3, 5, 4, 2, -20133577243627876450409208324029263052841104179200000⟩, + ⟨0, 8, 4, 5, 5, 2, -5938166691114861694443664638368282115528091238400000⟩, + ⟨0, 8, 5, 5, 6, 2, 3531859660757279039128320780987270809801195520000000⟩, + ⟨0, 8, 6, 5, 7, 2, -1828804167746576932742783396949296090953285632000000⟩, + ⟨0, 8, 7, 5, 8, 2, -149370308690095651607386778439722204694105292800000⟩, + ⟨0, 8, 2, 6, 2, 2, 5168799529640727982734095361110097262247568998400000⟩, + ⟨0, 8, 3, 6, 3, 2, -26782438177518309471418272337386756470356102348800000⟩, + ⟨0, 8, 4, 6, 4, 2, 11524939250590822153796047918458234260899548364800000⟩, + ⟨0, 8, 5, 6, 5, 2, -7158993293323379060021894010487342022082428928000000⟩, + ⟨0, 8, 6, 6, 6, 2, 1190834618428841635238635309012779023820914688000000⟩, + ⟨0, 8, 7, 6, 7, 2, 493576443553057609011318350028378220434083020800000⟩, + ⟨0, 8, 8, 6, 8, 2, -976515916354639063482426567600677869642265395200000⟩, + ⟨0, 8, 2, 7, 1, 2, -76236503366164376283038340801703674297499149926400000⟩, + ⟨0, 8, 3, 7, 2, 2, -98585480909683631960217572891174310523369527705600000⟩, + ⟨0, 8, 4, 7, 3, 2, -41946722937313700558189892954608515635764998963200000⟩, + ⟨0, 8, 5, 7, 4, 2, -21649005959983905504134046094281648962657058816000000⟩, + ⟨0, 8, 6, 7, 5, 2, -1230656257711123345238046182974418359827824640000000⟩, + ⟨0, 8, 7, 7, 6, 2, -1236103922166507341730886550196345435808019251200000⟩, + ⟨0, 8, 8, 7, 7, 2, -739415469909009719732233253470521567200516505600000⟩ +] + +def collectedFourData_10_6_3 : List CollectedFourTerm := [ + ⟨1, 5, 4, 2, 8, 0, 3030880904764390155380528831106544330797062553600000⟩, + ⟨1, 5, 4, 3, 7, 0, 18272088716922690897989656284575374958070752870400000⟩, + ⟨1, 5, 5, 3, 8, 0, -15111182810206844116901112892679020497900404736000000⟩, + ⟨1, 5, 4, 4, 6, 0, -21665834422844104646152548702369898908683442585600000⟩, + ⟨1, 5, 5, 4, 7, 0, -9029420935939650287845651465839280275723386880000000⟩, + ⟨1, 5, 6, 4, 8, 0, 17135640760615100380482245788401707441580933120000000⟩, + ⟨1, 5, 4, 5, 5, 0, -11240344672117705287335038030226378736421935513600000⟩, + ⟨1, 5, 5, 5, 6, 0, 20056351725455104089986450372599617518032650240000000⟩, + ⟨1, 5, 6, 5, 7, 0, -20770440022205771592432109358954788182942547968000000⟩, + ⟨1, 5, 7, 5, 8, 0, -2827427791761895686924665376333265944195366912000000⟩, + ⟨1, 5, 4, 6, 4, 0, 21815536046789124650222719447058916119296553779200000⟩, + ⟨1, 5, 5, 6, 5, 0, -40653735222390362525074704190403161307517812736000000⟩, + ⟨1, 5, 6, 6, 6, 0, 13524771790584654959372174423282364561292787712000000⟩, + ⟨1, 5, 7, 6, 7, 0, 9342899309101092860014597238937733880749228032000000⟩, + ⟨1, 5, 8, 6, 8, 0, -27726677395378686927865294204040654942122278912000000⟩, + ⟨1, 5, 4, 7, 3, 0, -79400873738812239792681407813516337345433750732800000⟩, + ⟨1, 5, 5, 7, 4, 0, -122938089206753078410778029223770114671343828992000000⟩, + ⟨1, 5, 6, 7, 5, 0, -13977041631656649474495748928854741573026447360000000⟩, + ⟨1, 5, 7, 7, 6, 0, -23398188125129113034041357576195008772700110848000000⟩, + ⟨1, 5, 8, 7, 7, 0, -20994572491815846603097687175221200892446375936000000⟩ +] + +def collectedFourData_10_6_4 : List CollectedFourTerm := [ + ⟨1, 6, 3, 1, 8, 1, -214119564908020933859973894813848946840541593600000⟩, + ⟨1, 6, 3, 2, 7, 1, 7693314834797956775463841275491469148153498828800000⟩, + ⟨1, 6, 4, 2, 8, 1, -2573171081873167710625491812796935383179224678400000⟩, + ⟨1, 6, 3, 3, 6, 1, -8447676000276791704551677875156122237509251891200000⟩, + ⟨1, 6, 4, 3, 7, 1, -15512721142522560193675804102490254553757882777600000⟩, + ⟨1, 6, 5, 3, 8, 1, 6414580420992463311865893876218973723706785792000000⟩, + ⟨1, 6, 3, 4, 5, 1, -15803221757095701246218548592066243966951384678400000⟩, + ⟨1, 6, 4, 4, 6, 1, 18393958836811663067335660092213365952852944486400000⟩, + ⟨1, 6, 5, 4, 7, 1, 3832919466069586064538103203486219189469839360000000⟩, + ⟨1, 6, 6, 4, 8, 1, -4849298125974977937746840405217543079078133760000000⟩, + ⟨1, 6, 3, 5, 4, 1, 16177744940847269134442548630852519287523482009600000⟩, + ⟨1, 6, 4, 5, 5, 1, 9542879040583354279115110517222483691189986918400000⟩, + ⟨1, 6, 5, 5, 6, 1, -8513766441085209599226124998827654484622049280000000⟩, + ⟨1, 6, 6, 5, 7, 1, 5877927606119037933153600783883944544450904064000000⟩, + ⟨1, 6, 7, 5, 8, 1, 600110632721461762858741192874509001274949632000000⟩, + ⟨1, 6, 3, 6, 3, 1, 21520241956358313154932298727996753998065854054400000⟩, + ⟨1, 6, 4, 6, 4, 1, -18521053203680136877172390795698950684975877324800000⟩, + ⟨1, 6, 5, 6, 5, 1, 17257196691553184653632385766945253118854561792000000⟩, + ⟨1, 6, 6, 6, 6, 1, -3827440795156302854691871721962943582438424576000000⟩, + ⟨1, 6, 7, 6, 7, 1, -1982994307466906405538205064305421760124157952000000⟩, + ⟨1, 6, 8, 6, 8, 1, 4707904184427927730666949542448946457907665305600000⟩, + ⟨1, 6, 3, 7, 2, 1, 79215469050955669830390290836538909566595550412800000⟩, + ⟨1, 6, 4, 7, 3, 1, 67410115606656200412933251785235244062514295603200000⟩, + ⟨1, 6, 5, 7, 4, 1, 52186269594144943632545202170611921303344513024000000⟩, + ⟨1, 6, 6, 7, 5, 1, 3955430832026490916966334875528716436667105280000000⟩, + ⟨1, 6, 7, 7, 6, 1, 4966175094274341371526045385736774396021833728000000⟩, + ⟨1, 6, 8, 7, 7, 1, 3564813564750077456791629874769511957467548876800000⟩ +] + +def collectedFourData_10_6_5 : List CollectedFourTerm := [ + ⟨1, 7, 2, 0, 8, 2, 7023043454911770646526800490114149979321794560000000⟩, + ⟨1, 7, 2, 1, 7, 2, 3219449828095352228818590274349568928776192000000000⟩, + ⟨1, 7, 3, 1, 8, 2, 122156229508946710419551501429918825227223040000000⟩, + ⟨1, 7, 2, 2, 6, 2, 6782036020019275557399283892123776165053726720000000⟩, + ⟨1, 7, 3, 2, 7, 2, -4389072680246975377228307833018676886707896320000000⟩, + ⟨1, 7, 4, 2, 8, 2, 734003166357332252312813498281012025496698880000000⟩, + ⟨1, 7, 2, 3, 5, 2, -1680743932332845471927462180688816686361477120000000⟩, + ⟨1, 7, 3, 3, 6, 2, 4819439310696900906715435145314473717981511680000000⟩, + ⟨1, 7, 4, 3, 7, 2, 4425040572561171826636756556908256492330680320000000⟩, + ⟨1, 7, 5, 3, 8, 2, -1219849539745006836212318562044857160407449600000000⟩, + ⟨1, 7, 2, 4, 4, 2, -212325873355242469915549240684112778992025600000000⟩, + ⟨1, 7, 3, 4, 5, 2, 9015813126511015728631208402219966247217397760000000⟩, + ⟨1, 7, 4, 4, 6, 2, -5246920472243855145624320425906056230055444480000000⟩, + ⟨1, 7, 5, 4, 7, 2, -728899591197463824971923879164210491424768000000000⟩, + ⟨1, 7, 6, 4, 8, 2, 691636907501153677539624391763198126063616000000000⟩, + ⟨1, 7, 2, 5, 3, 2, -3540618949789507926242731578366385162593239040000000⟩, + ⟨1, 7, 3, 5, 4, 2, -9229480382982561722684154007583370958539325440000000⟩, + ⟨1, 7, 4, 5, 5, 2, -2722128925393564963307311562604178226156666880000000⟩, + ⟨1, 7, 5, 5, 6, 2, 1619048073770572818930131618526887216676864000000000⟩, + ⟨1, 7, 6, 5, 7, 2, -838346409398053136332566404230994054243942400000000⟩, + ⟨1, 7, 7, 5, 8, 2, -68473193669128377667363176778392952331304960000000⟩, + ⟨1, 7, 2, 6, 2, 2, 2369441519762066381042626932511370067711098880000000⟩, + ⟨1, 7, 3, 6, 3, 2, -12277400323684733225236914888392288315281244160000000⟩, + ⟨1, 7, 4, 6, 4, 2, 5283174442438378873921182917854779663565455360000000⟩, + ⟨1, 7, 5, 6, 5, 2, -3281770912496123912369939531486877114276249600000000⟩, + ⟨1, 7, 6, 6, 6, 2, 545893291448940974835486855697983405136281600000000⟩, + ⟨1, 7, 7, 6, 7, 2, 226261535550867462372582407742890036491714560000000⟩, + ⟨1, 7, 8, 6, 8, 2, -447646952382386147463296346021978165624176640000000⟩, + ⟨1, 7, 2, 7, 1, 2, -34947754379211948152707656283391995184393748480000000⟩, + ⟨1, 7, 3, 7, 2, 2, -45192801611586486965637254405375418674624593920000000⟩, + ⟨1, 7, 4, 7, 3, 2, -19228895679870816718683581216507519110993674240000000⟩, + ⟨1, 7, 5, 7, 4, 2, -9924171616446454647989952661766631725413171200000000⟩, + ⟨1, 7, 6, 7, 5, 2, -564148022544496694971396608380114722357248000000000⟩, + ⟨1, 7, 7, 7, 6, 2, -566645299189160073497267707402206626803875840000000⟩, + ⟨1, 7, 8, 7, 7, 2, -338957180426489530215382058649826245916753920000000⟩ +] + +def collectedFourData_10_6_6 : List CollectedFourTerm := [ + ⟨1, 8, 1, 0, 7, 3, -438314271403082846563970671734430208018192793600000⟩, + ⟨1, 8, 2, 0, 8, 3, 266476744145148747421620689624321792417149747200000⟩, + ⟨1, 8, 1, 1, 6, 3, -214119564908020933859973894813848946840541593600000⟩, + ⟨1, 8, 2, 1, 7, 3, 122156229508946710419551501429918825227223040000000⟩, + ⟨1, 8, 3, 1, 8, 3, 2317499138769076921969663132015530189678182400000⟩, + ⟨1, 8, 1, 2, 5, 3, -127401552165117488085544480374608414677087027200000⟩, + ⟨1, 8, 2, 2, 6, 3, 257332150782279852822019337659645716202940006400000⟩, + ⟨1, 8, 3, 2, 7, 3, -83267731800139404985077608533150930608272179200000⟩, + ⟨1, 8, 4, 2, 8, 3, 9283476374065764848580540690955860721218355200000⟩, + ⟨1, 8, 1, 3, 4, 3, -69466654291868276429680515799098466009035571200000⟩, + ⟨1, 8, 2, 3, 5, 3, -63772803586532485061861026060210106085566054400000⟩, + ⟨1, 8, 3, 3, 6, 3, 91432475419289866840197942623417823858052300800000⟩, + ⟨1, 8, 4, 3, 7, 3, 55966733513592725435942979345186001311812812800000⟩, + ⟨1, 8, 5, 3, 8, 3, -11571248839093625540019926907219859092799488000000⟩, + ⟨1, 8, 1, 4, 3, 3, 218926192791729973625083184043315830995707494400000⟩, + ⟨1, 8, 2, 4, 4, 3, -8056323130096737733693582324847497363587072000000⟩, + ⟨1, 8, 3, 4, 5, 3, 171044401419265588732127258177370028817095065600000⟩, + ⟨1, 8, 4, 4, 6, 3, -66361651384163997713808097635718082896016179200000⟩, + ⟨1, 8, 5, 4, 7, 3, -6914195786984142471429373417292567716823040000000⟩, + ⟨1, 8, 6, 4, 8, 3, 5248583535749807906856736131377551883894784000000⟩, + ⟨1, 8, 1, 5, 2, 3, 44340785455922355251052433736459474958286848000000⟩, + ⟨1, 8, 2, 5, 3, 3, -134342413806177553762652111421189711331118284800000⟩, + ⟨1, 8, 3, 5, 4, 3, -175098011168408123015231049341506875237492326400000⟩, + ⟨1, 8, 4, 5, 5, 3, -34428760970425681628723555348309509129057075200000⟩, + ⟨1, 8, 5, 5, 6, 3, 15357966317690858623701964866796264536145920000000⟩, + ⟨1, 8, 6, 5, 7, 3, -6361909137438924378368050639359321201809817600000⟩, + ⟨1, 8, 7, 5, 8, 3, -433015349810304562088167921467422261064499200000⟩, + ⟨1, 8, 1, 6, 1, 3, 978367364776636375260713811447603351824577331200000⟩, + ⟨1, 8, 2, 6, 2, 3, 89904194055205480930684008922490240285383065600000⟩, + ⟨1, 8, 3, 6, 3, 3, -232921929490126170196371021850989815167293849600000⟩, + ⟨1, 8, 4, 6, 4, 3, 66820181934430176944982908291854126058727014400000⟩, + ⟨1, 8, 5, 6, 5, 3, -31130222723476205080660446798509510636863488000000⟩, + ⟨1, 8, 6, 6, 6, 3, 4142587694064611191325534556243408221267558400000⟩, + ⟨1, 8, 7, 6, 7, 3, 1430847791890684494254673233848617823056691200000⟩, + ⟨1, 8, 8, 6, 8, 3, -2426451136242476954072840557812522640893542400000⟩, + ⟨1, 8, 1, 7, 0, 3, -6128137817737075213799648955991075407155901235200000⟩, + ⟨1, 8, 2, 7, 1, 3, -1326029642553843309662427240965171670257605017600000⟩, + ⟨1, 8, 3, 7, 2, 3, -857379760610102218947206176646608929890186035200000⟩, + ⟨1, 8, 4, 7, 3, 3, -243201946429413739760706053399825467938806169600000⟩, + ⟨1, 8, 5, 7, 4, 3, -94138707729296413471482127683362253371867136000000⟩, + ⟨1, 8, 6, 7, 5, 3, -4281116277543239374246845507778001818877952000000⟩, + ⟨1, 8, 7, 7, 6, 3, -3583389342585664727307391023198423804071116800000⟩, + ⟨1, 8, 8, 7, 7, 3, -1837302881671006260104647905997821813404467200000⟩ +] + +def collectedFourData_10_6_7 : List CollectedFourTerm := [ + ⟨2, 4, 4, 2, 8, 0, 863649230260957665363602237359121926585319424000000⟩, + ⟨2, 4, 4, 3, 7, 0, 5206629970456376231250118191475502215631732736000000⟩, + ⟨2, 4, 5, 3, 8, 0, -4305930128053736765925117316755934742304522240000000⟩, + ⟨2, 4, 4, 4, 6, 0, -6173677491859499557412197428492050227531874304000000⟩, + ⟨2, 4, 5, 4, 7, 0, -2572932650955700671684179984187161165640499200000000⟩, + ⟨2, 4, 6, 4, 8, 0, 4882799231626014069875561432140657659268300800000000⟩, + ⟨2, 4, 4, 5, 5, 0, -3202935162738423666406290681103464168186445824000000⟩, + ⟨2, 4, 5, 5, 6, 0, 5715055547812379027965927043102650339531161600000000⟩, + ⟨2, 4, 6, 5, 7, 0, -5918534941165518402971471612367026059864965120000000⟩, + ⟨2, 4, 7, 5, 8, 0, -805675284744791230102004413035037660891054080000000⟩, + ⟨2, 4, 4, 6, 4, 0, 6216334955597416502564743275857982021936611328000000⟩, + ⟨2, 4, 5, 6, 5, 0, -11584278048292230452101363883853093047359242240000000⟩, + ⟨2, 4, 6, 6, 6, 0, 3853882456427816659217958054458865316087726080000000⟩, + ⟨2, 4, 7, 6, 7, 0, 2662258284060833559141384725764785337930874880000000⟩, + ⟨2, 4, 8, 6, 8, 0, -7900714129865879224828952133374918942345134080000000⟩, + ⟨2, 4, 4, 7, 3, 0, -22625271543588881254010729176080809437012426752000000⟩, + ⟨2, 4, 5, 7, 4, 0, -35031197018089016136884683478037638461815521280000000⟩, + ⟨2, 4, 6, 7, 5, 0, -3982756705329535798575035064916869531461222400000000⟩, + ⟨2, 4, 7, 7, 6, 0, -6667311517256638264351493573637009320517304320000000⟩, + ⟨2, 4, 8, 7, 7, 0, -5982401467412374134021913143043851364325130240000000⟩ +] + +def collectedFourData_10_6_8 : List CollectedFourTerm := [ + ⟨2, 5, 3, 1, 8, 1, -127401552165117488085544480374608414677087027200000⟩, + ⟨2, 5, 3, 2, 7, 1, 4577537095543892532499577124375920799863380377600000⟩, + ⟨2, 5, 4, 2, 8, 1, -1531041733425247561123599238157155639761882316800000⟩, + ⟨2, 5, 3, 3, 6, 1, -5026383437149224493695999698585029673203689062400000⟩, + ⟨2, 5, 4, 3, 7, 1, -9230098859536655539127694297267072763329458995200000⟩, + ⟨2, 5, 5, 3, 8, 1, 3816687664546058551935076748295746568673296384000000⟩, + ⟨2, 5, 3, 4, 5, 1, -9402947282881047986111585126760592720010202316800000⟩, + ⟨2, 5, 4, 4, 6, 1, 10944440818744164418117325913763256313706237132800000⟩, + ⟨2, 5, 5, 4, 7, 1, 2280594440358243702576220055533902877132062720000000⟩, + ⟨2, 5, 6, 4, 8, 1, -2885341694141769167594162664257633887212011520000000⟩, + ⟨2, 5, 3, 5, 4, 1, 9625789296184540635204059946111338718816318259200000⟩, + ⟨2, 5, 4, 5, 5, 1, 5678031348590431508524507464279090538990062796800000⟩, + ⟨2, 5, 5, 5, 6, 1, -5065707376303903054803874004039556376622530560000000⟩, + ⟨2, 5, 6, 5, 7, 1, 3497378209485174101435415923966719717149769728000000⟩, + ⟨2, 5, 7, 5, 8, 1, 357066978500295663206452343898743422335320064000000⟩, + ⟨2, 5, 3, 6, 3, 1, 12804585276393063169637868116471530232751115468800000⟩, + ⟨2, 5, 4, 6, 4, 1, -11020062211013675291132856283823162864906639769600000⟩, + ⟨2, 5, 5, 6, 5, 1, 10268065160075647589754232421939325703903248384000000⟩, + ⟨2, 5, 6, 6, 6, 1, -2277334620647448017455226704514801147735703552000000⟩, + ⟨2, 5, 7, 6, 7, 1, -1179885419692501536217520455492855721260744704000000⟩, + ⟨2, 5, 8, 6, 8, 1, 2801212027487644132190784955528327723180307251200000⟩, + ⟨2, 5, 3, 7, 2, 1, 47133356155075603530169677004952770990178933145600000⟩, + ⟨2, 5, 4, 7, 3, 1, 40109148193007081898483565859226750558830749286400000⟩, + ⟨2, 5, 5, 7, 4, 1, 31050930590380086369785713811749058673427611648000000⟩, + ⟨2, 5, 6, 7, 5, 1, 2353488938287394549537309584991919895279042560000000⟩, + ⟨2, 5, 7, 7, 6, 1, 2954883714648342416049294702666571532684230656000000⟩, + ⟨2, 5, 8, 7, 7, 1, 2121070914390843000931352748166873623354251673600000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1022.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1022.lean new file mode 100644 index 0000000000000000000000000000000000000000..260b5770f43d4b5ea1a799cf43bafa93a2da8adf --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1022.lean @@ -0,0 +1,632 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1022. -/ +namespace LaughlinFock +def collectedFourData_10_6_9 : List CollectedFourTerm := [ + ⟨2, 6, 2, 0, 8, 2, 14794619026428744093248333369999866515989043609600000⟩, + ⟨2, 6, 2, 1, 7, 2, 6782036020019275557399283892123776165053726720000000⟩, + ⟨2, 6, 3, 1, 8, 2, 257332150782279852822019337659645716202940006400000⟩, + ⟨2, 6, 2, 2, 6, 2, 14286917030184141781693602092000422949756810035200000⟩, + ⟨2, 6, 3, 2, 7, 2, -9245942816735179782304179120299800422966833971200000⟩, + ⟨2, 6, 4, 2, 8, 2, 1546238077575095107050274779518840037966662860800000⟩, + ⟨2, 6, 2, 3, 5, 2, -3540625416813481514811856719283647081516053299200000⟩, + ⟨2, 6, 3, 3, 6, 2, 10152545542472477003957040700468316437058735308800000⟩, + ⟨2, 6, 4, 3, 7, 2, 9321712142012526519193835265389945705328751411200000⟩, + ⟨2, 6, 5, 3, 8, 2, -2569713447731835053617644175073284695036788736000000⟩, + ⟨2, 6, 2, 4, 4, 2, -447281926405798319453471486205179981406928896000000⟩, + ⟨2, 6, 3, 4, 5, 2, 18992552342377838175456485669514425677121165721600000⟩, + ⟨2, 6, 4, 4, 6, 2, -11053069790494787079566687407768148170398026956800000⟩, + ⟨2, 6, 5, 4, 7, 2, -1535486976482278770888645426806162834986106880000000⟩, + ⟨2, 6, 6, 4, 8, 2, 1456990066598620361951630501467616816199106560000000⟩, + ⟨2, 6, 2, 5, 3, 2, -7458605206729150166868139184775854464629630566400000⟩, + ⟨2, 6, 3, 5, 4, 2, -19442660002712466885688096042015517623357695590400000⟩, + ⟨2, 6, 4, 5, 5, 2, -5734388609521370082640107722136519604312001740800000⟩, + ⟨2, 6, 5, 5, 6, 2, 3410658013251584762635329252127889846163210240000000⟩, + ⟨2, 6, 6, 5, 7, 2, -1766045706373103351408430377198733866758569984000000⟩, + ⟨2, 6, 7, 5, 8, 2, -144244417731621954505498904420557360834648473600000⟩, + ⟨2, 6, 2, 6, 2, 2, 4991423563777806128338495879518069630436166860800000⟩, + ⟨2, 6, 3, 6, 3, 2, -25863354198219250871573406021921811043530152345600000⟩, + ⟨2, 6, 4, 6, 4, 2, 11129441762370934270079696332607955010393315737600000⟩, + ⟨2, 6, 5, 6, 5, 2, -6913320513265360918739635076888540254606196736000000⟩, + ⟨2, 6, 6, 6, 6, 2, 1149969144847299654401570379875298619064057856000000⟩, + ⟨2, 6, 7, 6, 7, 2, 476638545710365529447932286468848204895590809600000⟩, + ⟨2, 6, 8, 6, 8, 2, -943005146039281177363986228609739618834081382400000⟩, + ⟨2, 6, 2, 7, 1, 2, -73620320761085625888697437299581287792678587596800000⟩, + ⟨2, 6, 3, 7, 2, 2, -95202355912063296661728569259767822849039086387200000⟩, + ⟨2, 6, 4, 7, 3, 2, -40507251266353469299590830623446212385721181798400000⟩, + ⟨2, 6, 5, 7, 4, 2, -20906084258319223614158914122980848535435476992000000⟩, + ⟨2, 6, 6, 7, 5, 2, -1188424238244132688424862210338697864995143680000000⟩, + ⟨2, 6, 7, 7, 6, 2, -1193684957019203560278271190926578250284426854400000⟩, + ⟨2, 6, 8, 7, 7, 2, -714041196366964823257660943741926025983111987200000⟩ +] + +def collectedFourData_10_6_10 : List CollectedFourTerm := [ + ⟨2, 7, 1, 0, 7, 3, 15748629453537042864680653102882717089366068428800000⟩, + ⟨2, 7, 2, 0, 8, 3, -9574508007902905726931355366607929504660298137600000⟩, + ⟨2, 7, 1, 1, 6, 3, 7693314834797956775463841275491469148153498828800000⟩, + ⟨2, 7, 2, 1, 7, 3, -4389072680246975377228307833018676886707896320000000⟩, + ⟨2, 7, 3, 1, 8, 3, -83267731800139404985077608533150930608272179200000⟩, + ⟨2, 7, 1, 2, 5, 3, 4577537095543892532499577124375920799863380377600000⟩, + ⟨2, 7, 2, 2, 6, 3, -9245942816735179782304179120299800422966833971200000⟩, + ⟨2, 7, 3, 2, 7, 3, 2991809163226974944161914374351688556424567193600000⟩, + ⟨2, 7, 4, 2, 8, 3, -333555257025562309175213910268727903578069401600000⟩, + ⟨2, 7, 1, 3, 4, 3, 2495936521340239386667607171118252389155051929600000⟩, + ⟨2, 7, 2, 3, 5, 3, 2291356495608813427775638715376473568355496755200000⟩, + ⟨2, 7, 3, 3, 6, 3, -3285168358284722758864303231493602247721772646400000⟩, + ⟨2, 7, 4, 3, 7, 3, -2010884439169611437744658141388741305184970342400000⟩, + ⟨2, 7, 5, 3, 8, 3, 415754909595385985495178883202172243677282304000000⟩, + ⟨2, 7, 1, 4, 3, 3, -7866016949240311648819603696419921115674260275200000⟩, + ⟨2, 7, 2, 4, 4, 3, 289463647459417068512268152607724608134578176000000⟩, + ⟨2, 7, 3, 4, 5, 3, -6145624438445134347679922368052997235193728204800000⟩, + ⟨2, 7, 4, 4, 6, 3, 2384373783286883286769396789258600048569719193600000⟩, + ⟨2, 7, 5, 4, 7, 3, 248427018061393511137400900123639941504696320000000⟩, + ⟨2, 7, 6, 4, 8, 3, -188581578682946916947455285179364924270313472000000⟩, + ⟨2, 7, 1, 5, 2, 3, -1593164186940033682169864058985022579156189184000000⟩, + ⟨2, 7, 2, 5, 3, 3, 4826922217601214594445650370428464393552815718400000⟩, + ⟨2, 7, 3, 5, 4, 3, 6291270615294766386108847644128667776834548531200000⟩, + ⟨2, 7, 4, 5, 5, 3, 1237025199594764810522580236962585268129995161600000⟩, + ⟨2, 7, 5, 5, 6, 3, -551811648575755105226634720440717915046543360000000⟩, + ⟨2, 7, 6, 5, 7, 3, 228583361663939651340151365689257753010031820800000⟩, + ⟨2, 7, 7, 5, 8, 3, 15558239228731269937306179306801095910201753600000⟩, + ⟨2, 7, 1, 6, 1, 3, -35152734242438780678082816852014098590402714009600000⟩, + ⟨2, 7, 2, 6, 2, 3, -3230257216955314869795911398744912566466432204800000⟩, + ⟨2, 7, 3, 6, 3, 3, 8368883694798807667931665791961349567405673676800000⟩, + ⟨2, 7, 4, 6, 4, 3, -2400848783533059865842598106316204682085872435200000⟩, + ⟨2, 7, 5, 6, 5, 3, 1118508737825818625736725850049849052368994304000000⟩, + ⟨2, 7, 6, 6, 6, 3, -148843153940132408039632716468072438559879987200000⟩, + ⟨2, 7, 7, 6, 7, 3, -51410353595754684677815231047379230203156889600000⟩, + ⟨2, 7, 8, 6, 8, 3, 87182376493178284151095880785508528731403059200000⟩, + ⟨2, 7, 1, 7, 0, 3, 220183959383325541081823979578816082707450796441600000⟩, + ⟨2, 7, 2, 7, 1, 3, 47644238044400973997665496299010065380210953420800000⟩, + ⟨2, 7, 3, 7, 2, 3, 30805650264564544690617830295317392557994514841600000⟩, + ⟨2, 7, 4, 7, 3, 3, 8738244649062696729781173102546441069057068236800000⟩, + ⟨2, 7, 5, 7, 4, 3, 3382403270871652798159279058368025453697957888000000⟩, + ⟨2, 7, 6, 7, 5, 3, 153820485211926686276982735687075906994569216000000⟩, + ⟨2, 7, 7, 7, 6, 3, 128751160128751446139324954073971459352847974400000⟩, + ⟨2, 7, 8, 7, 7, 3, 66014282822069620482631284045317238924351897600000⟩ +] + +def collectedFourData_10_6_11 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 6, 4, 1984754345275280556824553256622804345403998208000000⟩, + ⟨2, 8, 1, 0, 7, 4, -5267419670085787284983392285702091555679397478400000⟩, + ⟨2, 8, 2, 0, 8, 4, 1601185422547824603731999328081640743992976998400000⟩, + ⟨2, 8, 0, 1, 5, 4, 3030880904764390155380528831106544330797062553600000⟩, + ⟨2, 8, 1, 1, 6, 4, -2573171081873167710625491812796935383179224678400000⟩, + ⟨2, 8, 2, 1, 7, 4, 734003166357332252312813498281012025496698880000000⟩, + ⟨2, 8, 3, 1, 8, 4, 9283476374065764848580540690955860721218355200000⟩, + ⟨2, 8, 0, 2, 4, 4, 863649230260957665363602237359121926585319424000000⟩, + ⟨2, 8, 1, 2, 5, 4, -1531041733425247561123599238157155639761882316800000⟩, + ⟨2, 8, 2, 2, 6, 4, 1546238077575095107050274779518840037966662860800000⟩, + ⟨2, 8, 3, 2, 7, 4, -333555257025562309175213910268727903578069401600000⟩, + ⟨2, 8, 4, 2, 8, 4, 27890927383562919776597987593000711248622387200000⟩, + ⟨2, 8, 0, 3, 3, 4, 153609246070908541194733345374272083435349606400000⟩, + ⟨2, 8, 1, 3, 4, 4, -834812017552442027611795542814847310645480652800000⟩, + ⟨2, 8, 2, 3, 5, 4, -383193226806093910291856056601563753094106316800000⟩, + ⟨2, 8, 3, 3, 6, 4, 366261722033763633595294117754450861210625638400000⟩, + ⟨2, 8, 4, 3, 7, 4, 168144349963934527915057715473657712922643660800000⟩, + ⟨2, 8, 5, 3, 8, 4, -27811379970536091961244389187429997713188454400000⟩, + ⟨2, 8, 0, 4, 2, 4, -1138515258047377566334023061474124468918314598400000⟩, + ⟨2, 8, 1, 4, 3, 4, 2630934490261365906187473976106966135470659993600000⟩, + ⟨2, 8, 2, 4, 4, 4, -48408228630335426886771942512022591513821184000000⟩, + ⟨2, 8, 3, 4, 5, 4, 685172491729756371382083223137517419719609548800000⟩, + ⟨2, 8, 4, 4, 6, 4, -199374450392275426264769883745940214394336051200000⟩, + ⟨2, 8, 5, 4, 7, 4, -16618199893241438870610859018515855339159552000000⟩, + ⟨2, 8, 6, 4, 8, 4, 10512431361101581059705034284490687109922816000000⟩, + ⟨2, 8, 0, 5, 1, 4, -877555504210690129651548048345853137584023142400000⟩, + ⟨2, 8, 1, 5, 2, 4, 532863154900085857195900884143451125015642112000000⟩, + ⟨2, 8, 2, 5, 3, 4, -807226594224564614160224350143305165345233305600000⟩, + ⟨2, 8, 3, 5, 4, 4, -701410508696543732793100949867197876957033267200000⟩, + ⟨2, 8, 4, 5, 5, 4, -103436475027257439242248124280094549152576307200000⟩, + ⟨2, 8, 5, 5, 6, 4, 36912717268074258149265648315629921680490496000000⟩, + ⟨2, 8, 6, 5, 7, 4, -12742320414137671666298340700852994171102822400000⟩, + ⟨2, 8, 7, 5, 8, 4, -743391449550764990158866640449108911220326400000⟩, + ⟨2, 8, 0, 6, 0, 4, 20242055322269658362403862343602209988730368819200000⟩, + ⟨2, 8, 1, 6, 1, 4, 11757480506618531634344471029824863074603814092800000⟩, + ⟨2, 8, 2, 6, 2, 4, 540209560908981489400536836508474617504150323200000⟩, + ⟨2, 8, 3, 6, 3, 4, -933042516931377074683817235880028460098047180800000⟩, + ⟨2, 8, 4, 6, 4, 4, 200752042337933406893004596608509340484527718400000⟩, + ⟨2, 8, 5, 6, 5, 4, -74821176587697481789739402655033023711831654400000⟩, + ⟨2, 8, 6, 6, 6, 4, 8297223144982673344606206145482517361826201600000⟩, + ⟨2, 8, 7, 6, 7, 4, 2456448748447611353385195453204071249765990400000⟩, + ⟨2, 8, 8, 6, 8, 4, -3644969282722668554061115433319665681773363200000⟩, + ⟨2, 8, 1, 7, 0, 4, -73644587429962989362777890580620394636832984268800000⟩, + ⟨2, 8, 2, 7, 1, 4, -7967747205613589658337026165825746131093762867200000⟩, + ⟨2, 8, 3, 7, 2, 4, -3434506023356564417641035937051422344001198489600000⟩, + ⟨2, 8, 4, 7, 3, 4, -730666784088902529247942304067160620018538905600000⟩, + ⟨2, 8, 5, 7, 4, 4, -226261435304141557680591252005213718295923916800000⟩, + ⟨2, 8, 6, 7, 5, 4, -8574683190240706477528102014423236081614848000000⟩, + ⟨2, 8, 7, 7, 6, 4, -6151885836972072195809749831507482850728345600000⟩, + ⟨2, 8, 8, 7, 7, 4, -2759961849930050485983645856801433205709209600000⟩ +] + +def collectedFourData_10_6_12 : List CollectedFourTerm := [ + ⟨3, 3, 4, 2, 8, 0, 153609246070908541194733345374272083435349606400000⟩, + ⟨3, 3, 4, 3, 7, 0, 926054787416807711618540310609126128405289369600000⟩, + ⟨3, 3, 5, 3, 8, 0, -765855693988738069105040618519644369651236864000000⟩, + ⟨3, 3, 4, 4, 6, 0, -1098054524662668412855562641390876007642588774400000⟩, + ⟨3, 3, 5, 4, 7, 0, -457623570839180718992963804457514709412741120000000⟩, + ⟨3, 3, 6, 4, 8, 0, 868458029493122764525063163847913811874938880000000⟩, + ⟨3, 3, 4, 5, 5, 0, -569676250870495918946247327141947978302252646400000⟩, + ⟨3, 3, 5, 5, 6, 0, 1016483710276177201918536918263625418549493760000000⟩, + ⟨3, 3, 6, 5, 7, 0, -1052674695121375597059769080559453914720632832000000⟩, + ⟨3, 3, 7, 5, 8, 0, -143297960249692159446677218806802374394380288000000⟩, + ⟨3, 3, 4, 6, 4, 0, 1105641610500860654250811675135396624603073740800000⟩, + ⟨3, 3, 5, 6, 5, 0, -2060387660782458418798498156059717816878628864000000⟩, + ⟨3, 3, 6, 6, 6, 0, 685454184216552164057527705864613008389439488000000⟩, + ⟨3, 3, 7, 6, 7, 0, 473511089377164110885517141882191977453191168000000⟩, + ⟨3, 3, 8, 6, 8, 0, -1405226448871803300043091773175861502214668288000000⟩, + ⟨3, 3, 4, 7, 3, 0, -4024146357323953550232447598958479332298928947200000⟩, + ⟨3, 3, 5, 7, 4, 0, -6230672794421609546794708688644465211587166208000000⟩, + ⟨3, 3, 6, 7, 5, 0, -708375846759765577845979867955449435929968640000000⟩, + ⟨3, 3, 7, 7, 6, 0, -1185852611917711310400772599010188391404797952000000⟩, + ⟨3, 3, 8, 7, 7, 0, -1064034039403987987000445444225097863647985664000000⟩ +] + +def collectedFourData_10_6_13 : List CollectedFourTerm := [ + ⟨3, 4, 3, 1, 8, 1, -69466654291868276429680515799098466009035571200000⟩, + ⟨3, 4, 3, 2, 7, 1, 2495936521340239386667607171118252389155051929600000⟩, + ⟨3, 4, 4, 2, 8, 1, -834812017552442027611795542814847310645480652800000⟩, + ⟨3, 4, 3, 3, 6, 1, -2740673364122634025686395050831039624255006310400000⟩, + ⟨3, 4, 4, 3, 7, 1, -5032780807287185725005073964236126946600366899200000⟩, + ⟨3, 4, 5, 3, 8, 1, 2081077648013556797656000054371747401840984064000000⟩, + ⟨3, 4, 3, 4, 5, 1, -5127027709819405996183524857430808600660200652800000⟩, + ⟨3, 4, 4, 4, 6, 1, 5967538651241608659991487737222209169343171788800000⟩, + ⟨3, 4, 5, 4, 7, 1, 1243511267139017765191325998783399789194117120000000⟩, + ⟨3, 4, 6, 4, 8, 1, -1573254254556396787542558936451422699305041920000000⟩, + ⟨3, 4, 3, 5, 4, 1, 5248533993194939936990479712489431436889371443200000⟩, + ⟨3, 4, 4, 5, 5, 1, 3095989287789211093760029857750373857464470732800000⟩, + ⟨3, 4, 5, 5, 6, 1, -2762115037636251215830840068479623574071541760000000⟩, + ⟨3, 4, 6, 5, 7, 1, 1906971766649636022488123550202629051843084288000000⟩, + ⟨3, 4, 7, 5, 8, 1, 194693454930397606880760931582361528218681344000000⟩, + ⟨3, 4, 3, 6, 3, 1, 6981796403807756107254174366639275578684656844800000⟩, + ⟨3, 4, 4, 6, 4, 1, -6008771783998480889312604370017891624882379161600000⟩, + ⟨3, 4, 5, 6, 5, 1, 5598739737463341605035190584117445658949976064000000⟩, + ⟨3, 4, 6, 6, 6, 1, -1241733825930058432766464085625329028371054592000000⟩, + ⟨3, 4, 7, 6, 7, 1, -643341397030767717663959711224520796782198784000000⟩, + ⟨3, 4, 8, 6, 8, 1, 1527381921214822598116171653397069095696020275200000⟩, + ⟨3, 4, 3, 7, 2, 1, 25699816854638077833645914378403592479585180057600000⟩, + ⟨3, 4, 4, 7, 3, 1, 21869814646008765032170206919363742791142631014400000⟩, + ⟨3, 4, 5, 7, 4, 1, 16930753386482821737682041109087902342586564608000000⟩, + ⟨3, 4, 6, 7, 5, 1, 1283257540252400442775955187097136321538293760000000⟩, + ⟨3, 4, 7, 7, 6, 1, 1611172564146747478158721968810457200932683776000000⟩, + ⟨3, 4, 8, 7, 7, 1, 1156529865095853127926266129566554050396789145600000⟩ +] + +def collectedFourData_10_6_14 : List CollectedFourTerm := [ + ⟨3, 5, 2, 0, 8, 2, -3666445605190918528066510499547171520471734681600000⟩, + ⟨3, 5, 2, 1, 7, 2, -1680743932332845471927462180688816686361477120000000⟩, + ⟨3, 5, 3, 1, 8, 2, -63772803586532485061861026060210106085566054400000⟩, + ⟨3, 5, 2, 2, 6, 2, -3540625416813481514811856719283647081516053299200000⟩, + ⟨3, 5, 3, 2, 7, 2, 2291356495608813427775638715376473568355496755200000⟩, + ⟨3, 5, 4, 2, 8, 2, -383193226806093910291856056601563753094106316800000⟩, + ⟨3, 5, 2, 3, 5, 2, 877448109742684272589222960834825950963381043200000⟩, + ⟨3, 5, 3, 3, 6, 2, -2516033425342231501013310637162143995097042124800000⟩, + ⟨3, 5, 4, 3, 7, 2, -2310133870624361085917822088091347537001394995200000⟩, + ⟨3, 5, 5, 3, 8, 2, 636833875898099858056005487696226601198944256000000⟩, + ⟨3, 5, 2, 4, 4, 2, 110846710579186105057591716473967191959535616000000⟩, + ⟨3, 5, 3, 4, 5, 2, -4706789674183239890496945881657428021884852633600000⟩, + ⟨3, 5, 4, 4, 6, 2, 2739203969012949773296112429159068107929341132800000⟩, + ⟨3, 5, 5, 4, 7, 2, 380528857599809936012766279313070639001108480000000⟩, + ⟨3, 5, 6, 4, 8, 2, -361075524617738563298318080279575961282805760000000⟩, + ⟨3, 5, 2, 5, 3, 2, 1848413280005044633213031377970423573862835814400000⟩, + ⟨3, 5, 3, 5, 4, 2, 4818336666380106821965440590430344150503548518400000⟩, + ⟨3, 5, 4, 5, 5, 2, 1421112897755478557668255392171897739528686796800000⟩, + ⟨3, 5, 5, 5, 6, 2, -845239209009495396088666957051704397308887040000000⟩, + ⟨3, 5, 6, 5, 7, 2, 437666593991435515100312885834066004346404864000000⟩, + ⟨3, 5, 7, 5, 8, 2, 35747071994262109670688436493232663697136025600000⟩, + ⟨3, 5, 2, 6, 2, 2, -1236989134790660065394767883794171144444890316800000⟩, + ⟨3, 5, 3, 6, 3, 2, 6409531814652421168255641508238220086757398937600000⟩, + ⟨3, 5, 4, 6, 4, 2, -2758130693664990811533966544813649982599567769600000⟩, + ⟨3, 5, 5, 6, 5, 2, 1713279238070151666120283785293287304258912256000000⟩, + ⟨3, 5, 6, 6, 6, 2, -284988704994609666980002989121328017651531776000000⟩, + ⟨3, 5, 7, 6, 7, 2, -118121953533412759478667075446113945425385881600000⟩, + ⟨3, 5, 8, 6, 8, 2, 233698283625403983135977202433280639574107750400000⟩, + ⟨3, 5, 2, 7, 1, 2, 18244802453178477680084656151580189523771706572800000⟩, + ⟨3, 5, 3, 7, 2, 2, 23593325303886783256886628836690298987087082291200000⟩, + ⟨3, 5, 4, 7, 3, 2, 10038625064868361516461177553658330491551901286400000⟩, + ⟨3, 5, 5, 7, 4, 2, 5181006730469913413545244685791824476930834432000000⟩, + ⟨3, 5, 6, 7, 5, 2, 294518758315358072054336182454628327389921280000000⟩, + ⟨3, 5, 7, 7, 6, 2, 295822484974256695406514469133597502794524262400000⟩, + ⟨3, 5, 8, 7, 7, 2, 176955770315423808353693874354715993415299891200000⟩ +] + +def collectedFourData_10_6_15 : List CollectedFourTerm := [ + ⟨3, 6, 1, 0, 7, 3, -17292847352371610663482747418437532144370922291200000⟩, + ⟨3, 6, 2, 0, 8, 3, 10513327902164747180968713589906174364585715302400000⟩, + ⟨3, 6, 1, 1, 6, 3, -8447676000276791704551677875156122237509251891200000⟩, + ⟨3, 6, 2, 1, 7, 3, 4819439310696900906715435145314473717981511680000000⟩, + ⟨3, 6, 3, 1, 8, 3, 91432475419289866840197942623417823858052300800000⟩, + ⟨3, 6, 1, 2, 5, 3, -5026383437149224493695999698585029673203689062400000⟩, + ⟨3, 6, 2, 2, 6, 3, 10152545542472477003957040700468316437058735308800000⟩, + ⟨3, 6, 3, 2, 7, 3, -3285168358284722758864303231493602247721772646400000⟩, + ⟨3, 6, 4, 2, 8, 3, 366261722033763633595294117754450861210625638400000⟩, + ⟨3, 6, 1, 3, 4, 3, -2740673364122634025686395050831039624255006310400000⟩, + ⟨3, 6, 2, 3, 5, 3, -2516033425342231501013310637162143995097042124800000⟩, + ⟨3, 6, 3, 3, 6, 3, 3607292629130962895394851570637308286094383513600000⟩, + ⟨3, 6, 4, 3, 7, 3, 2208059930066453097623029432735087221588728217600000⟩, + ⟨3, 6, 5, 3, 8, 3, -456521388660734103954208716057685379877175296000000⟩, + ⟨3, 6, 1, 4, 3, 3, 8637312267438611539612810735187255320059366604800000⟩, + ⟨3, 6, 2, 4, 4, 3, -317846748781823181694824702334928688695476224000000⟩, + ⟨3, 6, 3, 4, 5, 3, 6748228194242479664982225181398244082660356915200000⟩, + ⟨3, 6, 4, 4, 6, 3, -2618171440697417362417645900461586270405420646400000⟩, + ⟨3, 6, 5, 4, 7, 3, -272786309069941715685793338215073113104711680000000⟩, + ⟨3, 6, 6, 4, 8, 3, 207072778190297180006274748482879210890723328000000⟩, + ⟨3, 6, 1, 5, 2, 3, 1749380488841941574057273837032724468298940416000000⟩, + ⟨3, 6, 2, 5, 3, 3, -5300221796252991124490779365797638628202617241600000⟩, + ⟨3, 6, 3, 5, 4, 3, -6908155577837852579119827201765019792219884748800000⟩, + ⟨3, 6, 4, 5, 5, 3, -1358320608833986735553647730939964871512843878400000⟩, + ⟨3, 6, 5, 5, 6, 3, 605919050558262940227630840829206648733040640000000⟩, + ⟨3, 6, 6, 5, 7, 3, -250996900537187655536105971265883805381243699200000⟩, + ⟨3, 6, 7, 5, 8, 3, -17083788582866401669550621888156009713002086400000⟩, + ⟨3, 6, 1, 6, 1, 3, 38599604433289391409605908729250817256246896230400000⟩, + ⟨3, 6, 2, 6, 2, 3, 3546997224520964460945850187169961895605252915200000⟩, + ⟨3, 6, 3, 6, 3, 3, -9189487165907246218516930779583075983350248243200000⟩, + ⟨3, 6, 4, 6, 4, 3, 2636261882486523627869444253044853570834058444800000⟩, + ⟨3, 6, 5, 6, 5, 3, -1228183120479197209803305017482118535678263296000000⟩, + ⟨3, 6, 6, 6, 6, 3, 163437837440144491135487594834597095861439692800000⟩, + ⟨3, 6, 7, 6, 7, 3, 56451350238808486754902160616884729985525350400000⟩, + ⟨3, 6, 8, 6, 8, 3, -95730967127105686248329838374615190141193420800000⟩, + ⟨3, 6, 1, 7, 0, 3, -241773902312589790932235056165366559652780074598400000⟩, + ⟨3, 6, 2, 7, 1, 3, -52315951565984580666930101223184932307163362099200000⟩, + ⟨3, 6, 3, 7, 2, 3, -33826270989950546063315354650701495800869316198400000⟩, + ⟨3, 6, 4, 7, 3, 3, -9595065481077852868098189796734929893319717683200000⟩, + ⟨3, 6, 5, 7, 4, 3, -3714061824866235650083251212950691264763789312000000⟩, + ⟨3, 6, 6, 7, 5, 3, -168903216517051581994435021905165558359261184000000⟩, + ⟨3, 6, 7, 7, 6, 3, -141375740988508728457883044215685298116991385600000⟩, + ⟨3, 6, 8, 7, 7, 3, -72487254798032396895203694314540204779005542400000⟩ +] + +def collectedFourData_10_6_16 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 6, 4, 11965368689069917513920094458719269780835008512000000⟩, + ⟨3, 7, 1, 0, 7, 4, -31755374937291716429949761707814200660782061977600000⟩, + ⟨3, 7, 2, 0, 8, 4, 9652969883127602422853155660930875062052559257600000⟩, + ⟨3, 7, 0, 1, 5, 4, 18272088716922690897989656284575374958070752870400000⟩, + ⟨3, 7, 1, 1, 6, 4, -15512721142522560193675804102490254553757882777600000⟩, + ⟨3, 7, 2, 1, 7, 4, 4425040572561171826636756556908256492330680320000000⟩, + ⟨3, 7, 3, 1, 8, 4, 55966733513592725435942979345186001311812812800000⟩, + ⟨3, 7, 0, 2, 4, 4, 5206629970456376231250118191475502215631732736000000⟩, + ⟨3, 7, 1, 2, 5, 4, -9230098859536655539127694297267072763329458995200000⟩, + ⟨3, 7, 2, 2, 6, 4, 9321712142012526519193835265389945705328751411200000⟩, + ⟨3, 7, 3, 2, 7, 4, -2010884439169611437744658141388741305184970342400000⟩, + ⟨3, 7, 4, 2, 8, 4, 168144349963934527915057715473657712922643660800000⟩, + ⟨3, 7, 0, 3, 3, 4, 926054787416807711618540310609126128405289369600000⟩, + ⟨3, 7, 1, 3, 4, 4, -5032780807287185725005073964236126946600366899200000⟩, + ⟨3, 7, 2, 3, 5, 4, -2310133870624361085917822088091347537001394995200000⟩, + ⟨3, 7, 3, 3, 6, 4, 2208059930066453097623029432735087221588728217600000⟩, + ⟨3, 7, 4, 3, 7, 4, 1013681690679674443154757940116929979687842611200000⟩, + ⟨3, 7, 5, 3, 8, 4, -167664787277804873046906372186002369409554841600000⟩, + ⟨3, 7, 0, 4, 2, 4, -6863698196755430861998385198925953317457205657600000⟩, + ⟨3, 7, 1, 4, 3, 4, 15860955915126745150432022900622200216591165030400000⟩, + ⟨3, 7, 2, 4, 4, 4, -291835765229886292796469804137330036101349376000000⟩, + ⟨3, 7, 3, 4, 5, 4, 4130658032653483899883313047537735181746254643200000⟩, + ⟨3, 7, 4, 4, 6, 4, -1201956711571466848690947967823353709012503756800000⟩, + ⟨3, 7, 5, 4, 7, 4, -100185138349560906456494133321589372514992128000000⟩, + ⟨3, 7, 6, 4, 8, 4, 63375660244076919546988429426946962435866624000000⟩, + ⟨3, 7, 0, 5, 1, 4, -5290465884606587643479619526724984838767090073600000⟩, + ⟨3, 7, 1, 5, 2, 4, 3212439929595507928498481205071117050831699968000000⟩, + ⟨3, 7, 2, 5, 3, 4, -4866478231178532126259226087369552544942941798400000⟩, + ⟨3, 7, 3, 5, 4, 4, -4228551185148401595804778131509344245247691980800000⟩, + ⟨3, 7, 4, 5, 5, 4, -623581231876456135178677572503530535838862540800000⟩, + ⟨3, 7, 5, 5, 6, 4, 222533469937634551792863487927452786065670144000000⟩, + ⟨3, 7, 6, 5, 7, 4, -76818857745477102316870007540554563818461593600000⟩, + ⟨3, 7, 7, 5, 8, 4, -4481639148618825414864041422130808754903449600000⟩, + ⟨3, 7, 0, 6, 0, 4, 122032056779255165821723614404775166287700348108800000⟩, + ⟨3, 7, 1, 6, 1, 4, 70881612856089230345572774198638764066518283059200000⟩, + ⟨3, 7, 2, 6, 2, 4, 3256728763951904332060384723303863122976885964800000⟩, + ⟨3, 7, 3, 6, 3, 4, -5624977088090587250637720529775060088364675891200000⟩, + ⟨3, 7, 4, 6, 4, 4, 1210261716960234344855937647067406620077693337600000⟩, + ⟨3, 7, 5, 6, 5, 4, -451069909862137546252875664606264277515999641600000⟩, + ⟨3, 7, 6, 6, 6, 4, 50020968217823505163253705425391808112125542400000⟩, + ⟨3, 7, 7, 6, 7, 4, 14809044258272372284310602880989389678811545600000⟩, + ⟨3, 7, 8, 6, 8, 4, -21974206244683838919640561738509667653176524800000⟩, + ⟨3, 7, 1, 7, 0, 4, -443976677845102806777168933021560963903817724723200000⟩, + ⟨3, 7, 2, 7, 1, 4, -48034676514715055736060016484606679282898226380800000⟩, + ⟨3, 7, 3, 7, 2, 4, -20705399099954043377917531958590927564119107174400000⟩, + ⟨3, 7, 4, 7, 3, 4, -4404926726218187691595164587170039468044740198400000⟩, + ⟨3, 7, 5, 7, 4, 4, -1364048654170699472781151296154068391092761395200000⟩, + ⟨3, 7, 6, 7, 5, 4, -51693674840636278640483608264020650436329472000000⟩, + ⟨3, 7, 7, 7, 6, 4, -37087502716729836600376488091917596311840358400000⟩, + ⟨3, 7, 8, 7, 7, 4, -16638815368155886433790614499978761757681254400000⟩ +] + +def collectedFourData_10_6_17 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 6, 5, -9895468244120475846761344712605676100208558080000000⟩, + ⟨3, 8, 1, 0, 7, 5, 13130991298210270069174155526747110174508449792000000⟩, + ⟨3, 8, 2, 0, 8, 5, -2661031164803594150386973140047407703474044928000000⟩, + ⟨3, 8, 0, 1, 5, 5, -15111182810206844116901112892679020497900404736000000⟩, + ⟨3, 8, 1, 1, 6, 5, 6414580420992463311865893876218973723706785792000000⟩, + ⟨3, 8, 2, 1, 7, 5, -1219849539745006836212318562044857160407449600000000⟩, + ⟨3, 8, 3, 1, 8, 5, -11571248839093625540019926907219859092799488000000⟩, + ⟨3, 8, 0, 2, 4, 5, -4305930128053736765925117316755934742304522240000000⟩, + ⟨3, 8, 1, 2, 5, 5, 3816687664546058551935076748295746568673296384000000⟩, + ⟨3, 8, 2, 2, 6, 5, -2569713447731835053617644175073284695036788736000000⟩, + ⟨3, 8, 3, 2, 7, 5, 415754909595385985495178883202172243677282304000000⟩, + ⟨3, 8, 4, 2, 8, 5, -27811379970536091961244389187429997713188454400000⟩, + ⟨3, 8, 0, 3, 3, 5, -765855693988738069105040618519644369651236864000000⟩, + ⟨3, 8, 1, 3, 4, 5, 2081077648013556797656000054371747401840984064000000⟩, + ⟨3, 8, 2, 3, 5, 5, 636833875898099858056005487696226601198944256000000⟩, + ⟨3, 8, 3, 3, 6, 5, -456521388660734103954208716057685379877175296000000⟩, + ⟨3, 8, 4, 3, 7, 5, -167664787277804873046906372186002369409554841600000⟩, + ⟨3, 8, 5, 3, 8, 5, 23110049528189651886594145055851003955380224000000⟩, + ⟨3, 8, 0, 4, 2, 5, 5676340554826631482316683733301006054702710784000000⟩, + ⟨3, 8, 1, 4, 3, 5, -6558577075978574100646705550991685880610029568000000⟩, + ⟨3, 8, 2, 4, 4, 5, 80450273406366009824877684356055173462753280000000⟩, + ⟨3, 8, 3, 4, 5, 5, -854022898324517831326378754546378693538742272000000⟩, + ⟨3, 8, 4, 4, 6, 5, 198805816673710090773846994987191603877537382400000⟩, + ⟨3, 8, 5, 4, 7, 5, 13809002753873875549160668891445435742289920000000⟩, + ⟨3, 8, 6, 4, 8, 5, -7487463549323949520155291874771533173882880000000⟩, + ⟨3, 8, 0, 5, 1, 5, 4375263188133034075336797644862380775491764224000000⟩, + ⟨3, 8, 1, 5, 2, 5, -1328358454114961824841685025742738938197442560000000⟩, + ⟨3, 8, 2, 5, 3, 5, 1341540519942919214286664636318319504630218752000000⟩, + ⟨3, 8, 3, 5, 4, 5, 874262529191788652059462075632377310392352768000000⟩, + ⟨3, 8, 4, 5, 5, 5, 103141464972988626640544871923609721702344294400000⟩, + ⟨3, 8, 5, 5, 6, 5, -30672865754558027014768315877408966348636160000000⟩, + ⟨3, 8, 6, 5, 7, 5, 9075698699702582568090301795197276685074432000000⟩, + ⟨3, 8, 7, 5, 8, 5, 463294519262029626297032202646170535723008000000⟩, + ⟨3, 8, 0, 6, 0, 5, -100921615873559158512248953893063940148236910592000000⟩, + ⟨3, 8, 1, 6, 1, 5, -29309867808343891185160774930410047330020491264000000⟩, + ⟨3, 8, 2, 6, 2, 5, -897781391749292617997940976868278706890604544000000⟩, + ⟨3, 8, 3, 6, 3, 5, 1162976745546323985080251625438166745299812352000000⟩, + ⟨3, 8, 4, 6, 4, 5, -200179479604245101046463266625168368034696396800000⟩, + ⟨3, 8, 5, 6, 5, 5, 62173149931106503488453033982468482844852224000000⟩, + ⟨3, 8, 6, 6, 6, 5, -5909684803131479710588577932631158856613888000000⟩, + ⟨3, 8, 7, 6, 7, 5, -1530901710924419552326049392058382667481088000000⟩, + ⟨3, 8, 8, 6, 8, 5, 2019207502868523521360725594523659243880448000000⟩, + ⟨3, 8, 1, 7, 0, 5, 183586366242084537448300255405506387607126278144000000⟩, + ⟨3, 8, 2, 7, 1, 5, 13241704132977287092457372479193343840195969024000000⟩, + ⟨3, 8, 3, 7, 2, 5, 4280888132235276631942157363888952294217089024000000⟩, + ⟨3, 8, 4, 7, 3, 5, 728582857238440123161003533638444235789382451200000⟩, + ⟨3, 8, 5, 7, 4, 5, 188013431255033029577807907087047952200368128000000⟩, + ⟨3, 8, 6, 7, 5, 5, 6107305306315017398619123992245475884400640000000⟩, + ⟨3, 8, 7, 7, 6, 5, 3833962568599914840976808101437638109560832000000⟩, + ⟨3, 8, 8, 7, 7, 5, 1528938995844391252646203642142830985478144000000⟩ +] + +def collectedFourData_10_6_18 : List CollectedFourTerm := [ + ⟨4, 2, 4, 2, 8, 0, -1138515258047377566334023061474124468918314598400000⟩, + ⟨4, 2, 4, 3, 7, 0, -6863698196755430861998385198925953317457205657600000⟩, + ⟨4, 2, 5, 3, 8, 0, 5676340554826631482316683733301006054702710784000000⟩, + ⟨4, 2, 4, 4, 6, 0, 8138519408651468176328276848167730460676744806400000⟩, + ⟨4, 2, 5, 4, 7, 0, 3391797246384666253142699747702907014448414720000000⟩, + ⟨4, 2, 6, 4, 8, 0, -6436804703118295821372848188389985237629665280000000⟩, + ⟨4, 2, 4, 5, 5, 0, 4222305104367791536987115499323440590548788838400000⟩, + ⟨4, 2, 5, 5, 6, 0, -7533935901044766917932474450493794077439426560000000⟩, + ⟨4, 2, 6, 5, 7, 0, 7802174887329481488314518354625249605469601792000000⟩, + ⟨4, 2, 7, 5, 8, 0, 1062090455909339188507509134323289463013244928000000⟩, + ⟨4, 2, 4, 6, 4, 0, -8194753087364464368658647530342937355778575564800000⟩, + ⟨4, 2, 5, 6, 5, 0, 15271104111861349587121763640715238063455862784000000⟩, + ⟨4, 2, 6, 6, 6, 0, -5080423655374996996992043741794613259170480128000000⟩, + ⟨4, 2, 7, 6, 7, 0, -3509551761367799855055793094434601889806942208000000⟩, + ⟨4, 2, 8, 6, 8, 0, 10415204774286530744252723489553900492898172928000000⟩, + ⟨4, 2, 4, 7, 3, 0, 29826017284885156271678698351541759051639763763200000⟩, + ⟨4, 2, 5, 7, 4, 0, 46180267306794269928646902315515143789580648448000000⟩, + ⟨4, 2, 6, 7, 5, 0, 5250313575498782267941034472162236280172707840000000⟩, + ⟨4, 2, 7, 7, 6, 0, 8789257984121713065864056923384064214420160512000000⟩, + ⟨4, 2, 8, 7, 7, 0, 7886367649926581028531331810231699311987523584000000⟩ +] + +def collectedFourData_10_6_19 : List CollectedFourTerm := [ + ⟨4, 3, 3, 1, 8, 1, 218926192791729973625083184043315830995707494400000⟩, + ⟨4, 3, 3, 2, 7, 1, -7866016949240311648819603696419921115674260275200000⟩, + ⟨4, 3, 4, 2, 8, 1, 2630934490261365906187473976106966135470659993600000⟩, + ⟨4, 3, 3, 3, 6, 1, 8637312267438611539612810735187255320059366604800000⟩, + ⟨4, 3, 4, 3, 7, 1, 15860955915126745150432022900622200216591165030400000⟩, + ⟨4, 3, 5, 3, 8, 1, -6558577075978574100646705550991685880610029568000000⟩, + ⟨4, 3, 3, 4, 5, 1, 16157977785031418804346435611251174502431299993600000⟩, + ⟨4, 3, 4, 4, 6, 1, -18806872600552938448487427555217812229514172825600000⟩, + ⟨4, 3, 5, 4, 7, 1, -3918962129146803510370413069718292289489469440000000⟩, + ⟨4, 3, 6, 4, 8, 1, 4958156798458933524693727799145755583751127040000000⟩, + ⟨4, 3, 3, 5, 4, 1, -16540908390958018093493767603190192839672096358400000⟩, + ⟨4, 3, 4, 5, 5, 1, -9757100793308447087610201867823095794718316953600000⟩, + ⟨4, 3, 5, 5, 6, 1, 8704886328652165346475645749300809505565573120000000⟩, + ⟨4, 3, 6, 5, 7, 1, -6009877298535662742949696117039672275612205056000000⟩, + ⟨4, 3, 7, 5, 8, 1, -613582117691965729607627140675407923462012928000000⟩, + ⟨4, 3, 3, 6, 3, 1, -22003335573216873203791134118997760739668236697600000⟩, + ⟨4, 3, 4, 6, 4, 1, 18936820024440815291803777663579915755002737459200000⟩, + ⟨4, 3, 5, 6, 5, 1, -17644592036989755051682976635485785201540333568000000⟩, + ⟨4, 3, 6, 6, 6, 1, 3913360471189394907403164937303241419080597504000000⟩, + ⟨4, 3, 7, 6, 7, 1, 2027509229471353641370464441517883949431390208000000⟩, + ⟨4, 3, 8, 6, 8, 1, -4813588798239012743822703881957020193691952742400000⟩, + ⟨4, 3, 3, 7, 2, 1, -80993724496808907311237051253398297807024239411200000⟩, + ⟨4, 3, 4, 7, 3, 1, -68923360514743840415949442251119242703371291852800000⟩, + ⟨4, 3, 5, 7, 4, 1, -53357764495536730632301325274116382093157072896000000⟩, + ⟨4, 3, 6, 7, 5, 1, -4044223671379905729049626658582165133060997120000000⟩, + ⟨4, 3, 7, 7, 6, 1, -5077657460184128561770133266382121800420032512000000⟩, + ⟨4, 3, 8, 7, 7, 1, -3644837696537905849369132131609870121909302067200000⟩ +] + +def collectedFourData_10_6_20 : List CollectedFourTerm := [ + ⟨4, 4, 2, 0, 8, 2, -463176603083809952855709545073915980685508608000000⟩, + ⟨4, 4, 2, 1, 7, 2, -212325873355242469915549240684112778992025600000000⟩, + ⟨4, 4, 3, 1, 8, 2, -8056323130096737733693582324847497363587072000000⟩, + ⟨4, 4, 2, 2, 6, 2, -447281926405798319453471486205179981406928896000000⟩, + ⟨4, 4, 3, 2, 7, 2, 289463647459417068512268152607724608134578176000000⟩, + ⟨4, 4, 4, 2, 8, 2, -48408228630335426886771942512022591513821184000000⟩, + ⟨4, 4, 2, 3, 5, 2, 110846710579186105057591716473967191959535616000000⟩, + ⟨4, 4, 3, 3, 6, 2, -317846748781823181694824702334928688695476224000000⟩, + ⟨4, 4, 4, 3, 7, 2, -291835765229886292796469804137330036101349376000000⟩, + ⟨4, 4, 5, 3, 8, 2, 80450273406366009824877684356055173462753280000000⟩, + ⟨4, 4, 2, 4, 4, 2, 14003099567710125369606434384898628339630080000000⟩, + ⟨4, 4, 3, 4, 5, 2, -594601717159424539746746977561256223590842368000000⟩, + ⟨4, 4, 4, 4, 6, 2, 346039550600408411856592784375176713694347264000000⟩, + ⟨4, 4, 5, 4, 7, 2, 48071642843659489646312933252877278144102400000000⟩, + ⟨4, 4, 6, 4, 8, 2, -45614132311787061405532910597883862764748800000000⟩, + ⟨4, 4, 2, 5, 3, 2, 233507291889349864627207904459501604408655872000000⟩, + ⟨4, 4, 3, 5, 4, 2, 608693282259098434908991897427791966101307392000000⟩, + ⟨4, 4, 4, 5, 5, 2, 179527072118310410222690722220386236009283584000000⟩, + ⟨4, 4, 5, 5, 6, 2, -106777808204215447126715057798221634155315200000000⟩, + ⟨4, 4, 6, 5, 7, 2, 55289767834332370654272797679018299432632320000000⟩, + ⟨4, 4, 7, 5, 8, 2, 4515874271543312804335251133401342387683328000000⟩, + ⟨4, 4, 2, 6, 2, 2, -156266991849749474796258716000749867115741184000000⟩, + ⟨4, 4, 3, 6, 3, 2, 809706591327905062720562070808538615421861888000000⟩, + ⟨4, 4, 4, 6, 4, 2, -348430535487630948379974571209625382103810048000000⟩, + ⟨4, 4, 5, 6, 5, 2, 216436009987397408049730533338119371258593280000000⟩, + ⟨4, 4, 6, 6, 6, 2, -36002197907906461948187091551586704299130880000000⟩, + ⟨4, 4, 7, 6, 7, 2, -14922170155687021443582258165914744660164608000000⟩, + ⟨4, 4, 8, 6, 8, 2, 29522755500008281868446673737827692474007552000000⟩, + ⟨4, 4, 2, 7, 1, 2, 2304838673246410666743978649691227397201854464000000⟩, + ⟨4, 4, 3, 7, 2, 2, 2980509585150805460828615746899843148840697856000000⟩, + ⟨4, 4, 4, 7, 3, 2, 1268164527136248873362506466687599355187167232000000⟩, + ⟨4, 4, 5, 7, 4, 2, 654508850363389790995668012583188068208476160000000⟩, + ⟨4, 4, 6, 7, 5, 2, 37206115325380865978862486000587648689766400000000⟩, + ⟨4, 4, 7, 7, 6, 2, 37370813169080916040170430878562746328154112000000⟩, + ⟨4, 4, 8, 7, 7, 2, 22354558451579426454116471463278931508985856000000⟩ +] + +def collectedFourData_10_6_21 : List CollectedFourTerm := [ + ⟨4, 5, 1, 0, 7, 3, -32350045327517249245833446886309460202171557478400000⟩, + ⟨4, 5, 2, 0, 8, 3, 19667474490916489321117805443298647009066273996800000⟩, + ⟨4, 5, 1, 1, 6, 3, -15803221757095701246218548592066243966951384678400000⟩, + ⟨4, 5, 2, 1, 7, 3, 9015813126511015728631208402219966247217397760000000⟩, + ⟨4, 5, 3, 1, 8, 3, 171044401419265588732127258177370028817095065600000⟩, + ⟨4, 5, 1, 2, 5, 3, -9402947282881047986111585126760592720010202316800000⟩, + ⟨4, 5, 2, 2, 6, 3, 18992552342377838175456485669514425677121165721600000⟩, + ⟨4, 5, 3, 2, 7, 3, -6145624438445134347679922368052997235193728204800000⟩, + ⟨4, 5, 4, 2, 8, 3, 685172491729756371382083223137517419719609548800000⟩, + ⟨4, 5, 1, 3, 4, 3, -5127027709819405996183524857430808600660200652800000⟩, + ⟨4, 5, 2, 3, 5, 3, -4706789674183239890496945881657428021884852633600000⟩, + ⟨4, 5, 3, 3, 6, 3, 6748228194242479664982225181398244082660356915200000⟩, + ⟨4, 5, 4, 3, 7, 3, 4130658032653483899883313047537735181746254643200000⟩, + ⟨4, 5, 5, 3, 8, 3, -854022898324517831326378754546378693538742272000000⟩, + ⟨4, 5, 1, 4, 3, 3, 16157977785031418804346435611251174502431299993600000⟩, + ⟨4, 5, 2, 4, 4, 3, -594601717159424539746746977561256223590842368000000⟩, + ⟨4, 5, 3, 4, 5, 3, 12624033712657204515607498323273574447334188646400000⟩, + ⟨4, 5, 4, 4, 6, 3, -4897861124654915299285391557617739668436864204800000⟩, + ⟨4, 5, 5, 4, 7, 3, -510306329739763549989939162460591232919797760000000⟩, + ⟨4, 5, 6, 4, 8, 3, 387374827525574426089546883710447154569936896000000⟩, + ⟨4, 5, 1, 5, 2, 3, 3272598025989616164757171338514440684004442112000000⟩, + ⟨4, 5, 2, 5, 3, 3, -9915221701830619111121120174258643036349346611200000⟩, + ⟨4, 5, 3, 5, 4, 3, -12923212789589958220232531258193628942650939801600000⟩, + ⟨4, 5, 4, 5, 5, 3, -2541035167297301778631020335176000437767425228800000⟩, + ⟨4, 5, 5, 5, 6, 3, 1133503832593409908646908581378599091154452480000000⟩, + ⟨4, 5, 6, 5, 7, 3, -469544485300206073633663156203995691173176934400000⟩, + ⟨4, 5, 7, 5, 8, 3, -31958955269772595734169593396792341430062284800000⟩, + ⟨4, 5, 1, 6, 1, 3, 72208984882405497990196883345284771315274534092800000⟩, + ⟨4, 5, 2, 6, 2, 3, 6635432479781556354676401173043605675983660646400000⟩, + ⟨4, 5, 3, 6, 3, 3, -17190941450886468357838352050358516622779901542400000⟩, + ⟨4, 5, 4, 6, 4, 3, 4931703244460138676646243094095746951810750873600000⟩, + ⟨4, 5, 5, 6, 5, 3, -2297584591385676712940981254570332101931958272000000⟩, + ⟨4, 5, 6, 6, 6, 3, 305746147044717838972245405883366779009997209600000⟩, + ⟨4, 5, 7, 6, 7, 3, 105604571752294645152835203128860908635081932800000⟩, + ⟨4, 5, 8, 6, 8, 3, -179085668352020190027394586169851742923626905600000⟩, + ⟨4, 5, 1, 7, 0, 3, -452290854099880168980365102443353357554086104268800000⟩, + ⟨4, 5, 2, 7, 1, 3, -97868405938348403180081041400917173577454085734400000⟩, + ⟨4, 5, 3, 7, 2, 3, -63279422843902440727896095528523865208136715468800000⟩, + ⟨4, 5, 4, 7, 3, 3, -17949664211359329811757635417770343209151915622400000⟩, + ⟨4, 5, 5, 7, 4, 3, -6947963278421369449569372102984415771921219584000000⟩, + ⟨4, 5, 6, 7, 5, 3, -315970331487412349116676421793743644380889088000000⟩, + ⟨4, 5, 7, 7, 6, 3, -264474180335742445610207518752436811233178419200000⟩, + ⟨4, 5, 8, 7, 7, 3, -135603231243583618323625170507174662757993676800000⟩ +] + +def collectedFourData_10_6_22 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 6, 4, -14187742892555970890743783898504100971091591168000000⟩, + ⟨4, 6, 1, 0, 7, 4, 37653423540435121299650967149496312908906653286400000⟩, + ⟨4, 6, 2, 0, 8, 4, -11445853313028674419623741912497841022253295206400000⟩, + ⟨4, 6, 0, 1, 5, 4, -21665834422844104646152548702369898908683442585600000⟩, + ⟨4, 6, 1, 1, 6, 4, 18393958836811663067335660092213365952852944486400000⟩, + ⟨4, 6, 2, 1, 7, 4, -5246920472243855145624320425906056230055444480000000⟩, + ⟨4, 6, 3, 1, 8, 4, -66361651384163997713808097635718082896016179200000⟩, + ⟨4, 6, 0, 2, 4, 4, -6173677491859499557412197428492050227531874304000000⟩, + ⟨4, 6, 1, 2, 5, 4, 10944440818744164418117325913763256313706237132800000⟩, + ⟨4, 6, 2, 2, 6, 4, -11053069790494787079566687407768148170398026956800000⟩, + ⟨4, 6, 3, 2, 7, 4, 2384373783286883286769396789258600048569719193600000⟩, + ⟨4, 6, 4, 2, 8, 4, -199374450392275426264769883745940214394336051200000⟩, + ⟨4, 6, 0, 3, 3, 4, -1098054524662668412855562641390876007642588774400000⟩, + ⟨4, 6, 1, 3, 4, 4, 5967538651241608659991487737222209169343171788800000⟩, + ⟨4, 6, 2, 3, 5, 4, 2739203969012949773296112429159068107929341132800000⟩, + ⟨4, 6, 3, 3, 6, 4, -2618171440697417362417645900461586270405420646400000⟩, + ⟨4, 6, 4, 3, 7, 4, -1201956711571466848690947967823353709012503756800000⟩, + ⟨4, 6, 5, 3, 8, 4, 198805816673710090773846994987191603877537382400000⟩, + ⟨4, 6, 0, 4, 2, 4, 8138519408651468176328276848167730460676744806400000⟩, + ⟨4, 6, 1, 4, 3, 4, -18806872600552938448487427555217812229514172825600000⟩, + ⟨4, 6, 2, 4, 4, 4, 346039550600408411856592784375176713694347264000000⟩, + ⟨4, 6, 3, 4, 5, 4, -4897861124654915299285391557617739668436864204800000⟩, + ⟨4, 6, 4, 4, 6, 4, 1425200780259749786361451730016271660016153395200000⟩, + ⟨4, 6, 5, 4, 7, 4, 118792911567959932961037299437754270500257792000000⟩, + ⟨4, 6, 6, 4, 8, 4, -75146666730821557433767337551633596322676736000000⟩, + ⟨4, 6, 0, 5, 1, 4, 6273084574585844807928575115015640377668822630400000⟩, + ⟨4, 6, 1, 5, 2, 4, -3809098822045946269870821451776654992109207552000000⟩, + ⟨4, 6, 2, 5, 3, 4, 5770348054485939276006059493595449589925255577600000⟩, + ⟨4, 6, 3, 5, 4, 4, 5013936350971040279859599780818703716178932531200000⟩, + ⟨4, 6, 4, 5, 5, 4, 739401385815065231065465523968396615830680371200000⟩, + ⟨4, 6, 5, 5, 6, 4, -263865471972256383614781902629945536745046016000000⟩, + ⟨4, 6, 6, 5, 7, 4, 91086721296623841559539398400856453001143910400000⟩, + ⟨4, 6, 7, 5, 8, 4, 5314031320731481803463633763785833357665894400000⟩, + ⟨4, 6, 0, 6, 0, 4, -144697542652022101079757446290562452380590486323200000⟩, + ⟨4, 6, 1, 6, 1, 4, -84046728951237548602437406031396257651562958028800000⟩, + ⟨4, 6, 2, 6, 2, 4, -3861613592897390450542058042965589269484352307200000⟩, + ⟨4, 6, 3, 6, 3, 4, 6669725837637419748238567087116833575263849676800000⟩, + ⟨4, 6, 4, 6, 4, 4, -1435048306419537854973947377492686372545652326400000⟩, + ⟨4, 6, 5, 6, 5, 4, 534848868763930915436447856864863464196564582400000⟩, + ⟨4, 6, 6, 6, 6, 4, -59311556104365906079006441120589264321091993600000⟩, + ⟨4, 6, 7, 6, 7, 4, -17559585323332190809082239362179872544155238400000⟩, + ⟨4, 6, 8, 6, 8, 4, 26055560557223915176985338630343741047780147200000⟩, + ⟨4, 6, 1, 7, 0, 4, 526438183330822233713615387377096545004593925324800000⟩, + ⟨4, 6, 2, 7, 1, 4, 56956342761122878879416240729118640710972814131200000⟩, + ⟨4, 6, 3, 7, 2, 4, 24551092954306811018410553991590433542763026841600000⟩, + ⟨4, 6, 4, 7, 3, 4, 5223070803427940186271973409732780197420833177600000⟩, + ⟨4, 6, 5, 7, 4, 4, 1617398686259386223392216533038446272286870732800000⟩, + ⟨4, 6, 6, 7, 5, 4, 61294940997538632852017255855707789467844608000000⟩, + ⟨4, 6, 7, 7, 6, 4, 43975908034709728823637265920154664433195417600000⟩, + ⟨4, 6, 8, 7, 7, 4, 19729206898216734155678177461599976283543961600000⟩ +] + +def collectedFourData_10_6_23 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 6, 5, -5912862630054063518260945568252404177462886400000000⟩, + ⟨4, 7, 1, 0, 7, 5, 7846192401141247368009093600276281501794959360000000⟩, + ⟨4, 7, 2, 0, 8, 5, -1590052268736768324978536355153812253824778240000000⟩, + ⟨4, 7, 0, 1, 5, 5, -9029420935939650287845651465839280275723386880000000⟩, + ⟨4, 7, 1, 1, 6, 5, 3832919466069586064538103203486219189469839360000000⟩, + ⟨4, 7, 2, 1, 7, 5, -728899591197463824971923879164210491424768000000000⟩, + ⟨4, 7, 3, 1, 8, 5, -6914195786984142471429373417292567716823040000000⟩, + ⟨4, 7, 0, 2, 4, 5, -2572932650955700671684179984187161165640499200000000⟩, + ⟨4, 7, 1, 2, 5, 5, 2280594440358243702576220055533902877132062720000000⟩, + ⟨4, 7, 2, 2, 6, 5, -1535486976482278770888645426806162834986106880000000⟩, + ⟨4, 7, 3, 2, 7, 5, 248427018061393511137400900123639941504696320000000⟩, + ⟨4, 7, 4, 2, 8, 5, -16618199893241438870610859018515855339159552000000⟩, + ⟨4, 7, 0, 3, 3, 5, -457623570839180718992963804457514709412741120000000⟩, + ⟨4, 7, 1, 3, 4, 5, 1243511267139017765191325998783399789194117120000000⟩, + ⟨4, 7, 2, 3, 5, 5, 380528857599809936012766279313070639001108480000000⟩, + ⟨4, 7, 3, 3, 6, 5, -272786309069941715685793338215073113104711680000000⟩, + ⟨4, 7, 4, 3, 7, 5, -100185138349560906456494133321589372514992128000000⟩, + ⟨4, 7, 5, 3, 8, 5, 13809002753873875549160668891445435742289920000000⟩, + ⟨4, 7, 0, 4, 2, 5, 3391797246384666253142699747702907014448414720000000⟩, + ⟨4, 7, 1, 4, 3, 5, -3918962129146803510370413069718292289489469440000000⟩, + ⟨4, 7, 2, 4, 4, 5, 48071642843659489646312933252877278144102400000000⟩, + ⟨4, 7, 3, 4, 5, 5, -510306329739763549989939162460591232919797760000000⟩, + ⟨4, 7, 4, 4, 6, 5, 118792911567959932961037299437754270500257792000000⟩, + ⟨4, 7, 5, 4, 7, 5, 8251326195726853189032183111228413548953600000000⟩, + ⟨4, 7, 6, 4, 8, 5, -4474001868582069731972799957198008903270400000000⟩, + ⟨4, 7, 0, 5, 1, 5, 2614361398929678720776601373011017147005009920000000⟩, + ⟨4, 7, 1, 5, 2, 5, -793737180382498842629966501880349510651084800000000⟩, + ⟨4, 7, 2, 5, 3, 5, 801613891468642061695647893989494131691356160000000⟩, + ⟨4, 7, 3, 5, 4, 5, 522400164417296909237178187989189423204925440000000⟩, + ⟨4, 7, 4, 5, 5, 5, 61630364405461238931036670860211465331146752000000⟩, + ⟨4, 7, 5, 5, 6, 5, -18328030286444634885310448402500800007372800000000⟩, + ⟨4, 7, 6, 5, 7, 5, 5423023788185713811972311687200294630850560000000⟩, + ⟨4, 7, 7, 5, 8, 5, 276833473876384433153839921749794897264640000000⟩, + ⟨4, 7, 0, 6, 0, 5, -60303932703538042269981301480636877280494223360000000⟩, + ⟨4, 7, 1, 6, 1, 5, -17513594888119902269985441813478962405436293120000000⟩, + ⟨4, 7, 2, 6, 2, 5, -536453446191028995978066415664338946249195520000000⟩, + ⟨4, 7, 3, 6, 3, 5, 694916255473663871167407034627141897719644160000000⟩, + ⟨4, 7, 4, 6, 4, 5, -119613719639682761648948641703738482196742144000000⟩, + ⟨4, 7, 5, 6, 5, 5, 37150469866730672713652262157869368916049920000000⟩, + ⟨4, 7, 6, 6, 6, 5, -3531227988993494265568742839065726985175040000000⟩, + ⟨4, 7, 7, 6, 7, 5, -914763333426814054137797955262855816151040000000⟩, + ⟨4, 7, 8, 6, 8, 5, 1206541852441390831379432584444433494179840000000⟩, + ⟨4, 7, 1, 7, 0, 5, 109698797223185193636251280091914703679803883520000000⟩, + ⟨4, 7, 2, 7, 1, 5, 7912346904112867961807316617689882878195793920000000⟩, + ⟨4, 7, 3, 7, 2, 5, 2557969247748892268318332434624843119245393920000000⟩, + ⟨4, 7, 4, 7, 3, 5, 435351844216452216858544390906364524228509696000000⟩, + ⟨4, 7, 5, 7, 4, 5, 112344111889465502242253464516978935060234240000000⟩, + ⟨4, 7, 6, 7, 5, 5, 3649312637377940512338122367831041585971200000000⟩, + ⟨4, 7, 7, 7, 6, 5, 2290916754785204407335870298818882368962560000000⟩, + ⟨4, 7, 8, 7, 7, 5, 913590547625895706868577440514126139883520000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1023.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1023.lean new file mode 100644 index 0000000000000000000000000000000000000000..7332b98bca67518aa4a00d10f6b5a344eacd8657 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1023.lean @@ -0,0 +1,654 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1023. -/ +namespace LaughlinFock +def collectedFourData_10_6_24 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 6, 6, 11221172499798652693028454738747591327586713600000000⟩, + ⟨4, 8, 1, 0, 7, 6, -9926774210549666179030232289943657446648053760000000⟩, + ⟨4, 8, 2, 0, 8, 6, 1508765881055851904794054196485072874247290880000000⟩, + ⟨4, 8, 0, 1, 5, 6, 17135640760615100380482245788401707441580933120000000⟩, + ⟨4, 8, 1, 1, 6, 6, -4849298125974977937746840405217543079078133760000000⟩, + ⟨4, 8, 2, 1, 7, 6, 691636907501153677539624391763198126063616000000000⟩, + ⟨4, 8, 3, 1, 8, 6, 5248583535749807906856736131377551883894784000000⟩, + ⟨4, 8, 0, 2, 4, 6, 4882799231626014069875561432140657659268300800000000⟩, + ⟨4, 8, 1, 2, 5, 6, -2885341694141769167594162664257633887212011520000000⟩, + ⟨4, 8, 2, 2, 6, 6, 1456990066598620361951630501467616816199106560000000⟩, + ⟨4, 8, 3, 2, 7, 6, -188581578682946916947455285179364924270313472000000⟩, + ⟨4, 8, 4, 2, 8, 6, 10512431361101581059705034284490687109922816000000⟩, + ⟨4, 8, 0, 3, 3, 6, 868458029493122764525063163847913811874938880000000⟩, + ⟨4, 8, 1, 3, 4, 6, -1573254254556396787542558936451422699305041920000000⟩, + ⟨4, 8, 2, 3, 5, 6, -361075524617738563298318080279575961282805760000000⟩, + ⟨4, 8, 3, 3, 6, 6, 207072778190297180006274748482879210890723328000000⟩, + ⟨4, 8, 4, 3, 7, 6, 63375660244076919546988429426946962435866624000000⟩, + ⟨4, 8, 5, 3, 8, 6, -7487463549323949520155291874771533173882880000000⟩, + ⟨4, 8, 0, 4, 2, 6, -6436804703118295821372848188389985237629665280000000⟩, + ⟨4, 8, 1, 4, 3, 6, 4958156798458933524693727799145755583751127040000000⟩, + ⟨4, 8, 2, 4, 4, 6, -45614132311787061405532910597883862764748800000000⟩, + ⟨4, 8, 3, 4, 5, 6, 387374827525574426089546883710447154569936896000000⟩, + ⟨4, 8, 4, 4, 6, 6, -75146666730821557433767337551633596322676736000000⟩, + ⟨4, 8, 5, 4, 7, 6, -4474001868582069731972799957198008903270400000000⟩, + ⟨4, 8, 6, 4, 8, 6, 2122641344507350613247294725398464980582400000000⟩, + ⟨4, 8, 0, 5, 1, 6, -4961420900444056789940565755985865404925870080000000⟩, + ⟨4, 8, 1, 5, 2, 6, 1004213173644498226697478888207486043344076800000000⟩, + ⟨4, 8, 2, 5, 3, 6, -760633919405148012476404025567040480655441920000000⟩, + ⟨4, 8, 3, 5, 4, 6, -396555288063309449883572993647827697558093824000000⟩, + ⟨4, 8, 4, 5, 5, 6, -38986471443010008322358994349616155292860416000000⟩, + ⟨4, 8, 5, 5, 6, 6, 9937753011321687999729327235375289283379200000000⟩, + ⟨4, 8, 6, 5, 7, 6, -2572894433926120425679999833235139183247360000000⟩, + ⟨4, 8, 7, 5, 8, 6, -116747217359138230040930373324268193710080000000⟩, + ⟨4, 8, 0, 6, 0, 6, 114442170166984337976655492885680205467368816640000000⟩, + ⟨4, 8, 1, 6, 1, 6, 22157690403324255236297042397806950187186257920000000⟩, + ⟨4, 8, 2, 6, 2, 6, 509028962318878619582116630177074993420042240000000⟩, + ⟨4, 8, 3, 6, 3, 6, -527512689772252260758909019836315816045838336000000⟩, + ⟨4, 8, 4, 6, 4, 6, 75665897969466943822388346495197060322557952000000⟩, + ⟨4, 8, 5, 6, 5, 6, -20143582699291586725139128134331611878522880000000⟩, + ⟨4, 8, 6, 6, 6, 6, 1675352569464766826017492244047948142346240000000⟩, + ⟨4, 8, 7, 6, 7, 6, 385777313069582689634591326354585556090880000000⟩, + ⟨4, 8, 8, 6, 8, 6, -457944488196157138021961143644052921516032000000⟩, + ⟨4, 8, 1, 7, 0, 6, -138787724737038182671630686950007183738478264320000000⟩, + ⟨4, 8, 2, 7, 1, 6, -7507853221383440055390396991347231791555543040000000⟩, + ⟨4, 8, 3, 7, 2, 6, -1941760935373401058559423877474754798584594432000000⟩, + ⟨4, 8, 4, 7, 3, 6, -275397239752527669261836151719433977638944768000000⟩, + ⟨4, 8, 5, 7, 4, 6, -60914785647179915839305762003436956926607360000000⟩, + ⟨4, 8, 6, 7, 5, 6, -1731376541777473260981176258829711782707200000000⟩, + ⟨4, 8, 7, 7, 6, 6, -966133728618487099322519548273554169528320000000⟩, + ⟨4, 8, 8, 7, 7, 6, -346754449426536343185751655297493076279296000000⟩ +] + +def collectedFourData_10_6_25 : List CollectedFourTerm := [ + ⟨5, 1, 4, 2, 8, 0, -877555504210690129651548048345853137584023142400000⟩, + ⟨5, 1, 4, 3, 7, 0, -5290465884606587643479619526724984838767090073600000⟩, + ⟨5, 1, 5, 3, 8, 0, 4375263188133034075336797644862380775491764224000000⟩, + ⟨5, 1, 4, 4, 6, 0, 6273084574585844807928575115015640377668822630400000⟩, + ⟨5, 1, 5, 4, 7, 0, 2614361398929678720776601373011017147005009920000000⟩, + ⟨5, 1, 6, 4, 8, 0, -4961420900444056789940565755985865404925870080000000⟩, + ⟨5, 1, 4, 5, 5, 0, 3254508060919335735362175796664389192072455782400000⟩, + ⟨5, 1, 5, 5, 6, 0, -5807078009364047774062279539009192590479196160000000⟩, + ⟨5, 1, 6, 5, 7, 0, 6013833779384875640645496251158669046172352512000000⟩, + ⟨5, 1, 7, 5, 8, 0, 818648076048969694359281233491630841720209408000000⟩, + ⟨5, 1, 4, 6, 4, 0, -6316428898632270347692110833013630019853667532800000⟩, + ⟨5, 1, 5, 6, 5, 0, 11770805330902959062431344456054116204333236224000000⟩, + ⟨5, 1, 6, 6, 6, 0, -3915936752699185489588532757780855377633476608000000⟩, + ⟨5, 1, 7, 6, 7, 0, -2705125332077431844074301669400429746599231488000000⟩, + ⟨5, 1, 8, 6, 8, 0, 8027929544687981517940910069856706120969617408000000⟩, + ⟨5, 1, 4, 7, 3, 0, 22989578270496013039248954631488112112891540275200000⟩, + ⟨5, 1, 5, 7, 4, 0, 35595260998523989775658300806200218373092016128000000⟩, + ⟨5, 1, 6, 7, 5, 0, 4046886104023854511770410079639129066559242240000000⟩, + ⟨5, 1, 7, 7, 6, 0, 6774666977342166262793538460823708596470546432000000⟩, + ⟨5, 1, 8, 7, 7, 0, 6078728669206996986403650540669938742564225024000000⟩ +] + +def collectedFourData_10_6_26 : List CollectedFourTerm := [ + ⟨5, 2, 3, 1, 8, 1, 44340785455922355251052433736459474958286848000000⟩, + ⟨5, 2, 3, 2, 7, 1, -1593164186940033682169864058985022579156189184000000⟩, + ⟨5, 2, 4, 2, 8, 1, 532863154900085857195900884143451125015642112000000⟩, + ⟨5, 2, 3, 3, 6, 1, 1749380488841941574057273837032724468298940416000000⟩, + ⟨5, 2, 4, 3, 7, 1, 3212439929595507928498481205071117050831699968000000⟩, + ⟨5, 2, 5, 3, 8, 1, -1328358454114961824841685025742738938197442560000000⟩, + ⟨5, 2, 3, 4, 5, 1, 3272598025989616164757171338514440684004442112000000⟩, + ⟨5, 2, 4, 4, 6, 1, -3809098822045946269870821451776654992109207552000000⟩, + ⟨5, 2, 5, 4, 7, 1, -793737180382498842629966501880349510651084800000000⟩, + ⟨5, 2, 6, 4, 8, 1, 1004213173644498226697478888207486043344076800000000⟩, + ⟨5, 2, 3, 5, 4, 1, -3350155871514526302604665929312162591935561728000000⟩, + ⟨5, 2, 4, 5, 5, 1, -1976179768308850451576439502824638245672845312000000⟩, + ⟨5, 2, 5, 5, 6, 1, 1763066776957799858612851201957204003808870400000000⟩, + ⟨5, 2, 6, 5, 7, 1, -1217226118595593379089163305729952524554731520000000⟩, + ⟨5, 2, 7, 5, 8, 1, -124273448933780104462373096614638063986933760000000⟩, + ⟨5, 2, 3, 6, 3, 1, -4456502757962952646615018079296404233536929792000000⟩, + ⟨5, 2, 4, 6, 4, 1, 3835418061282174414685058603173352979472318464000000⟩, + ⟨5, 2, 5, 6, 5, 1, -3573693307286131514934894420751734192797122560000000⟩, + ⟨5, 2, 6, 6, 6, 1, 792602634029138524938279603704146813444423680000000⟩, + ⟨5, 2, 7, 6, 7, 1, 410646851377062813273687953683661737804431360000000⟩, + ⟨5, 2, 8, 6, 8, 1, -974932717981335598692196779960228287776555008000000⟩, + ⟨5, 2, 3, 7, 2, 1, -16404274497230238962370235851774304680677474304000000⟩, + ⟨5, 2, 4, 7, 3, 1, -13959571956713316780987269819669819549942808576000000⟩, + ⟨5, 2, 5, 7, 4, 1, -10806953511291313530195168271019135520284344320000000⟩, + ⟨5, 2, 6, 7, 5, 1, -819107352398963720881325159426775339918950400000000⟩, + ⟨5, 2, 7, 7, 6, 1, -1028416550754511112907703085756064887514071040000000⟩, + ⟨5, 2, 8, 7, 7, 1, -738216675962541957250514393624184364229197824000000⟩ +] + +def collectedFourData_10_6_27 : List CollectedFourTerm := [ + ⟨5, 3, 2, 0, 8, 2, -7723655304287389255237812079426460780474872627200000⟩, + ⟨5, 3, 2, 1, 7, 2, -3540618949789507926242731578366385162593239040000000⟩, + ⟨5, 3, 3, 1, 8, 2, -134342413806177553762652111421189711331118284800000⟩, + ⟨5, 3, 2, 2, 6, 2, -7458605206729150166868139184775854464629630566400000⟩, + ⟨5, 3, 3, 2, 7, 2, 4826922217601214594445650370428464393552815718400000⟩, + ⟨5, 3, 4, 2, 8, 2, -807226594224564614160224350143305165345233305600000⟩, + ⟨5, 3, 2, 3, 5, 2, 1848413280005044633213031377970423573862835814400000⟩, + ⟨5, 3, 3, 3, 6, 2, -5300221796252991124490779365797638628202617241600000⟩, + ⟨5, 3, 4, 3, 7, 2, -4866478231178532126259226087369552544942941798400000⟩, + ⟨5, 3, 5, 3, 8, 2, 1341540519942919214286664636318319504630218752000000⟩, + ⟨5, 3, 2, 4, 4, 2, 233507291889349864627207904459501604408655872000000⟩, + ⟨5, 3, 3, 4, 5, 2, -9915221701830619111121120174258643036349346611200000⟩, + ⟨5, 3, 4, 4, 6, 2, 5770348054485939276006059493595449589925255577600000⟩, + ⟨5, 3, 5, 4, 7, 2, 801613891468642061695647893989494131691356160000000⟩, + ⟨5, 3, 6, 4, 8, 2, -760633919405148012476404025567040480655441920000000⟩, + ⟨5, 3, 2, 5, 3, 2, 3893827584517733602924676100944001417394048204800000⟩, + ⟨5, 3, 3, 5, 4, 2, 10150204191885526876023753403641428023719021772800000⟩, + ⟨5, 3, 4, 5, 5, 2, 2993685807093481793657646684053245007962413465600000⟩, + ⟨5, 3, 5, 5, 6, 2, -1780562703784589205327149465720108298723655680000000⟩, + ⟨5, 3, 6, 5, 7, 2, 921979015699954246745882598535745686405644288000000⟩, + ⟨5, 3, 7, 5, 8, 2, 75304011555586352215338492491139508323169075200000⟩, + ⟨5, 3, 2, 6, 2, 2, -2605814655683198559672852972059563157918161305600000⟩, + ⟨5, 3, 3, 6, 3, 2, 13502181602844516115485583750393005525947331379200000⟩, + ⟨5, 3, 4, 6, 4, 2, -5810218684789184048858139066371011133710742323200000⟩, + ⟨5, 3, 5, 6, 5, 2, 3609157123757991418156909378323132528828874752000000⟩, + ⟨5, 3, 6, 6, 6, 2, -600351064768897013501588012621566750954094592000000⟩, + ⟨5, 3, 7, 6, 7, 2, -248833161923760524523932257982930731440223027200000⟩, + ⟨5, 3, 8, 6, 8, 2, 492303768361025579255878078585921499778829516800000⟩, + ⟨5, 3, 2, 7, 1, 2, 38434107693745462702145231716498986206639004057600000⟩, + ⟨5, 3, 3, 7, 2, 2, 49701190676645577928348975356214279125126768230400000⟩, + ⟨5, 3, 4, 7, 3, 2, 21147151241041110299431145973335673065773518028800000⟩, + ⟨5, 3, 5, 7, 4, 2, 10914197133782075668566181578022136663343366144000000⟩, + ⟨5, 3, 6, 7, 5, 2, 620426869732900352068685817069349373749493760000000⟩, + ⟨5, 3, 7, 7, 6, 2, 623173272218753920041040140780363704865443020800000⟩, + ⟨5, 3, 8, 7, 7, 2, 372771212556913170469069595089664980287907430400000⟩ +] + +def collectedFourData_10_6_28 : List CollectedFourTerm := [ + ⟨5, 4, 1, 0, 7, 3, 33116714438208506739675643244023618043001805209600000⟩, + ⟨5, 4, 2, 0, 8, 3, -20133577243627876450409208324029263052841104179200000⟩, + ⟨5, 4, 1, 1, 6, 3, 16177744940847269134442548630852519287523482009600000⟩, + ⟨5, 4, 2, 1, 7, 3, -9229480382982561722684154007583370958539325440000000⟩, + ⟨5, 4, 3, 1, 8, 3, -175098011168408123015231049341506875237492326400000⟩, + ⟨5, 4, 1, 2, 5, 3, 9625789296184540635204059946111338718816318259200000⟩, + ⟨5, 4, 2, 2, 6, 3, -19442660002712466885688096042015517623357695590400000⟩, + ⟨5, 4, 3, 2, 7, 3, 6291270615294766386108847644128667776834548531200000⟩, + ⟨5, 4, 4, 2, 8, 3, -701410508696543732793100949867197876957033267200000⟩, + ⟨5, 4, 1, 3, 4, 3, 5248533993194939936990479712489431436889371443200000⟩, + ⟨5, 4, 2, 3, 5, 3, 4818336666380106821965440590430344150503548518400000⟩, + ⟨5, 4, 3, 3, 6, 3, -6908155577837852579119827201765019792219884748800000⟩, + ⟨5, 4, 4, 3, 7, 3, -4228551185148401595804778131509344245247691980800000⟩, + ⟨5, 4, 5, 3, 8, 3, 874262529191788652059462075632377310392352768000000⟩, + ⟨5, 4, 1, 4, 3, 3, -16540908390958018093493767603190192839672096358400000⟩, + ⟨5, 4, 2, 4, 4, 3, 608693282259098434908991897427791966101307392000000⟩, + ⟨5, 4, 3, 4, 5, 3, -12923212789589958220232531258193628942650939801600000⟩, + ⟨5, 4, 4, 4, 6, 3, 5013936350971040279859599780818703716178932531200000⟩, + ⟨5, 4, 5, 4, 7, 3, 522400164417296909237178187989189423204925440000000⟩, + ⟨5, 4, 6, 4, 8, 3, -396555288063309449883572993647827697558093824000000⟩, + ⟨5, 4, 1, 5, 2, 3, -3350155871514526302604665929312162591935561728000000⟩, + ⟨5, 4, 2, 5, 3, 3, 10150204191885526876023753403641428023719021772800000⟩, + ⟨5, 4, 3, 5, 4, 3, 13229482161282032097537074907919691772519147110400000⟩, + ⟨5, 4, 4, 5, 5, 3, 2601255582824507636292848653330647503284155187200000⟩, + ⟨5, 4, 5, 5, 6, 3, -1160366928657152455406364918118651115203461120000000⟩, + ⟨5, 4, 6, 5, 7, 3, 480672298239277488635357787205106647227275673600000⟩, + ⟨5, 4, 7, 5, 8, 3, 32716355872066548381192204854230328028640051200000⟩, + ⟨5, 4, 1, 6, 1, 3, -73920277638357904969602877866795290781405098803200000⟩, + ⟨5, 4, 2, 6, 2, 3, -6792686698958764359616331046667889692200507801600000⟩, + ⟨5, 4, 3, 6, 3, 3, 17598352434724743691669391766482176702525577625600000⟩, + ⟨5, 4, 4, 6, 4, 3, -5048580500808441322786107499656523850499647078400000⟩, + ⟨5, 4, 5, 6, 5, 3, 2352035431178388090336453162829104830132256768000000⟩, + ⟨5, 4, 6, 6, 6, 3, -312992075892077574850378519179022987094812262400000⟩, + ⟨5, 4, 7, 6, 7, 3, -108107312082039849503867793542173342116819763200000⟩, + ⟨5, 4, 8, 6, 8, 3, 183329849425120715411989632693560796414109286400000⟩, + ⟨5, 4, 1, 7, 0, 3, 463009770360303128331472416619468219247972528947200000⟩, + ⟨5, 4, 2, 7, 1, 3, 100187805586351401677782386935501454680264382873600000⟩, + ⟨5, 4, 3, 7, 2, 3, 64779092422279320058941419803374551343570301747200000⟩, + ⟨5, 4, 4, 7, 3, 3, 18375056292229891351852632687004888570921589145600000⟩, + ⟨5, 4, 5, 7, 4, 3, 7112624217033774085527680564467980860229943296000000⟩, + ⟨5, 4, 6, 7, 5, 3, 323458564984266855030732247695673680117891072000000⟩, + ⟨5, 4, 7, 7, 6, 3, 270741997972038918460112768274096508491320524800000⟩, + ⟨5, 4, 8, 7, 7, 3, 138816914799567617648963017190550296549602099200000⟩ +] + +def collectedFourData_10_6_29 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 6, 4, -7360672897212274745686547966267262923867947008000000⟩, + ⟨5, 5, 1, 0, 7, 4, 19534786910097798166712432878257225328952239718400000⟩, + ⟨5, 5, 2, 0, 8, 4, -5938166691114861694443664638368282115528091238400000⟩, + ⟨5, 5, 0, 1, 5, 4, -11240344672117705287335038030226378736421935513600000⟩, + ⟨5, 5, 1, 1, 6, 4, 9542879040583354279115110517222483691189986918400000⟩, + ⟨5, 5, 2, 1, 7, 4, -2722128925393564963307311562604178226156666880000000⟩, + ⟨5, 5, 3, 1, 8, 4, -34428760970425681628723555348309509129057075200000⟩, + ⟨5, 5, 0, 2, 4, 4, -3202935162738423666406290681103464168186445824000000⟩, + ⟨5, 5, 1, 2, 5, 4, 5678031348590431508524507464279090538990062796800000⟩, + ⟨5, 5, 2, 2, 6, 4, -5734388609521370082640107722136519604312001740800000⟩, + ⟨5, 5, 3, 2, 7, 4, 1237025199594764810522580236962585268129995161600000⟩, + ⟨5, 5, 4, 2, 8, 4, -103436475027257439242248124280094549152576307200000⟩, + ⟨5, 5, 0, 3, 3, 4, -569676250870495918946247327141947978302252646400000⟩, + ⟨5, 5, 1, 3, 4, 4, 3095989287789211093760029857750373857464470732800000⟩, + ⟨5, 5, 2, 3, 5, 4, 1421112897755478557668255392171897739528686796800000⟩, + ⟨5, 5, 3, 3, 6, 4, -1358320608833986735553647730939964871512843878400000⟩, + ⟨5, 5, 4, 3, 7, 4, -623581231876456135178677572503530535838862540800000⟩, + ⟨5, 5, 5, 3, 8, 4, 103141464972988626640544871923609721702344294400000⟩, + ⟨5, 5, 0, 4, 2, 4, 4222305104367791536987115499323440590548788838400000⟩, + ⟨5, 5, 1, 4, 3, 4, -9757100793308447087610201867823095794718316953600000⟩, + ⟨5, 5, 2, 4, 4, 4, 179527072118310410222690722220386236009283584000000⟩, + ⟨5, 5, 3, 4, 5, 4, -2541035167297301778631020335176000437767425228800000⟩, + ⟨5, 5, 4, 4, 6, 4, 739401385815065231065465523968396615830680371200000⟩, + ⟨5, 5, 5, 4, 7, 4, 61630364405461238931036670860211465331146752000000⟩, + ⟨5, 5, 6, 4, 8, 4, -38986471443010008322358994349616155292860416000000⟩, + ⟨5, 5, 0, 5, 1, 4, 3254508060919335735362175796664389192072455782400000⟩, + ⟨5, 5, 1, 5, 2, 4, -1976179768308850451576439502824638245672845312000000⟩, + ⟨5, 5, 2, 5, 3, 4, 2993685807093481793657646684053245007962413465600000⟩, + ⟨5, 5, 3, 5, 4, 4, 2601255582824507636292848653330647503284155187200000⟩, + ⟨5, 5, 4, 5, 5, 4, 383605185260702412874078861552649517386642227200000⟩, + ⟨5, 5, 5, 5, 6, 4, -136894743777416570774636177016061325891076096000000⟩, + ⟨5, 5, 6, 5, 7, 4, 47256252514680410376172618525805309730383462400000⟩, + ⟨5, 5, 7, 5, 8, 4, 2756946373617198548928234761894324848715366400000⟩, + ⟨5, 5, 0, 6, 0, 4, -75069818261985712195241923577296503616883077939200000⟩, + ⟨5, 5, 1, 6, 1, 4, -43603868816604290550513369979506917256895188172800000⟩, + ⟨5, 5, 2, 6, 2, 4, -2003424697501382577288363257691966630425473843200000⟩, + ⟨5, 5, 3, 6, 3, 4, 3460287557839286312187713485913080355042938060800000⟩, + ⟨5, 5, 4, 6, 4, 4, -744510332280889055320161312419040073538233958400000⟩, + ⟨5, 5, 5, 6, 5, 4, 277482303015294802739931972342563138976507494400000⟩, + ⟨5, 5, 6, 6, 6, 4, -30771135818788526573515534141129827278231961600000⟩, + ⟨5, 5, 7, 6, 7, 4, -9110001834298309279681820262321226514851430400000⟩, + ⟨5, 5, 8, 6, 8, 4, 13517756831910014583295933028111259998040883200000⟩, + ⟨5, 5, 1, 7, 0, 4, 273118796798464271970973517330316148826165791948800000⟩, + ⟨5, 5, 2, 7, 1, 4, 29549239203234723813217697406181904078127444787200000⟩, + ⟨5, 5, 3, 7, 2, 4, 12737231416881800257144406640379719530032241049600000⟩, + ⟨5, 5, 4, 7, 3, 4, 2709755596373562674758117044695609063815879065600000⟩, + ⟨5, 5, 5, 7, 4, 4, 839114633250268239431910932431830874153864396800000⟩, + ⟨5, 5, 6, 7, 5, 4, 31800125950515299358155946653371267597467648000000⟩, + ⟨5, 5, 7, 7, 6, 4, 22814923899644556467342593953580320802052505600000⟩, + ⟨5, 5, 8, 7, 7, 4, 10235612500096231833342139880856595411343769600000⟩ +] + +def collectedFourData_10_6_30 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 6, 5, 13133782714751979712171784946873635918000947200000000⟩, + ⟨5, 6, 1, 0, 7, 5, -17428138041114109156730133398829621558147809280000000⟩, + ⟨5, 6, 2, 0, 8, 5, 3531859660757279039128320780987270809801195520000000⟩, + ⟨5, 6, 0, 1, 5, 5, 20056351725455104089986450372599617518032650240000000⟩, + ⟨5, 6, 1, 1, 6, 5, -8513766441085209599226124998827654484622049280000000⟩, + ⟨5, 6, 2, 1, 7, 5, 1619048073770572818930131618526887216676864000000000⟩, + ⟨5, 6, 3, 1, 8, 5, 15357966317690858623701964866796264536145920000000⟩, + ⟨5, 6, 0, 2, 4, 5, 5715055547812379027965927043102650339531161600000000⟩, + ⟨5, 6, 1, 2, 5, 5, -5065707376303903054803874004039556376622530560000000⟩, + ⟨5, 6, 2, 2, 6, 5, 3410658013251584762635329252127889846163210240000000⟩, + ⟨5, 6, 3, 2, 7, 5, -551811648575755105226634720440717915046543360000000⟩, + ⟨5, 6, 4, 2, 8, 5, 36912717268074258149265648315629921680490496000000⟩, + ⟨5, 6, 0, 3, 3, 5, 1016483710276177201918536918263625418549493760000000⟩, + ⟨5, 6, 1, 3, 4, 5, -2762115037636251215830840068479623574071541760000000⟩, + ⟨5, 6, 2, 3, 5, 5, -845239209009495396088666957051704397308887040000000⟩, + ⟨5, 6, 3, 3, 6, 5, 605919050558262940227630840829206648733040640000000⟩, + ⟨5, 6, 4, 3, 7, 5, 222533469937634551792863487927452786065670144000000⟩, + ⟨5, 6, 5, 3, 8, 5, -30672865754558027014768315877408966348636160000000⟩, + ⟨5, 6, 0, 4, 2, 5, -7533935901044766917932474450493794077439426560000000⟩, + ⟨5, 6, 1, 4, 3, 5, 8704886328652165346475645749300809505565573120000000⟩, + ⟨5, 6, 2, 4, 4, 5, -106777808204215447126715057798221634155315200000000⟩, + ⟨5, 6, 3, 4, 5, 5, 1133503832593409908646908581378599091154452480000000⟩, + ⟨5, 6, 4, 4, 6, 5, -263865471972256383614781902629945536745046016000000⟩, + ⟨5, 6, 5, 4, 7, 5, -18328030286444634885310448402500800007372800000000⟩, + ⟨5, 6, 6, 4, 8, 5, 9937753011321687999729327235375289283379200000000⟩, + ⟨5, 6, 0, 5, 1, 5, -5807078009364047774062279539009192590479196160000000⟩, + ⟨5, 6, 1, 5, 2, 5, 1763066776957799858612851201957204003808870400000000⟩, + ⟨5, 6, 2, 5, 3, 5, -1780562703784589205327149465720108298723655680000000⟩, + ⟨5, 6, 3, 5, 4, 5, -1160366928657152455406364918118651115203461120000000⟩, + ⟨5, 6, 4, 5, 5, 5, -136894743777416570774636177016061325891076096000000⟩, + ⟨5, 6, 5, 5, 6, 5, 40710630777728107169596432397268905518694400000000⟩, + ⟨5, 6, 6, 5, 7, 5, -12045741723972893003792477242204137329786880000000⟩, + ⟨5, 6, 7, 5, 8, 5, -614908703540971231570277241036334662942720000000⟩, + ⟨5, 6, 0, 6, 0, 5, 133948444015526340075831646940572247659936481280000000⟩, + ⟨5, 6, 1, 6, 1, 5, 38901588656162412433260533141471626052511989760000000⟩, + ⟨5, 6, 2, 6, 2, 5, 1191582392433907557374967216476306195569704960000000⟩, + ⟨5, 6, 3, 6, 3, 5, -1543563528425270871573325328473358832689479680000000⟩, + ⟨5, 6, 4, 6, 4, 5, 265688669218498449986004226244117115973926912000000⟩, + ⟨5, 6, 5, 6, 5, 5, -82519454536375775836412021347706778849116160000000⟩, + ⟨5, 6, 6, 6, 6, 5, 7843642584889054683863115414746251049041920000000⟩, + ⟨5, 6, 7, 6, 7, 5, 2031892774843670096283942421777954551889920000000⟩, + ⟨5, 6, 8, 6, 8, 5, -2679997746890778432828744268691462758072320000000⟩, + ⟨5, 6, 1, 7, 0, 5, -243665421800231938786131384577090805193202728960000000⟩, + ⟨5, 6, 2, 7, 1, 5, -17575081902656810805686780326424708756180828160000000⟩, + ⟨5, 6, 3, 7, 2, 5, -5681818501953654649104930050737927520161628160000000⟩, + ⟨5, 6, 4, 7, 3, 5, -967013252995724782469563724348204072627601408000000⟩, + ⟨5, 6, 5, 7, 4, 5, -249541253899303476095541833383291020399083520000000⟩, + ⟨5, 6, 6, 7, 5, 5, -8105934846837819923432417861136440465817600000000⟩, + ⟨5, 6, 7, 7, 6, 5, -5088635531967112148162922116512446551162880000000⟩, + ⟨5, 6, 8, 7, 7, 5, -2029287756793374699961160101711993330728960000000⟩ +] + +def collectedFourData_10_6_31 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 6, 6, -13601399191419935880673886513829808836748247040000000⟩, + ⟨5, 7, 1, 0, 7, 6, 12032434108218298943995574663997857562114392064000000⟩, + ⟨5, 7, 2, 0, 8, 6, -1828804167746576932742783396949296090953285632000000⟩, + ⟨5, 7, 0, 1, 5, 6, -20770440022205771592432109358954788182942547968000000⟩, + ⟨5, 7, 1, 1, 6, 6, 5877927606119037933153600783883944544450904064000000⟩, + ⟨5, 7, 2, 1, 7, 6, -838346409398053136332566404230994054243942400000000⟩, + ⟨5, 7, 3, 1, 8, 6, -6361909137438924378368050639359321201809817600000⟩, + ⟨5, 7, 0, 2, 4, 6, -5918534941165518402971471612367026059864965120000000⟩, + ⟨5, 7, 1, 2, 5, 6, 3497378209485174101435415923966719717149769728000000⟩, + ⟨5, 7, 2, 2, 6, 6, -1766045706373103351408430377198733866758569984000000⟩, + ⟨5, 7, 3, 2, 7, 6, 228583361663939651340151365689257753010031820800000⟩, + ⟨5, 7, 4, 2, 8, 6, -12742320414137671666298340700852994171102822400000⟩, + ⟨5, 7, 0, 3, 3, 6, -1052674695121375597059769080559453914720632832000000⟩, + ⟨5, 7, 1, 3, 4, 6, 1906971766649636022488123550202629051843084288000000⟩, + ⟨5, 7, 2, 3, 5, 6, 437666593991435515100312885834066004346404864000000⟩, + ⟨5, 7, 3, 3, 6, 6, -250996900537187655536105971265883805381243699200000⟩, + ⟨5, 7, 4, 3, 7, 6, -76818857745477102316870007540554563818461593600000⟩, + ⟨5, 7, 5, 3, 8, 6, 9075698699702582568090301795197276685074432000000⟩, + ⟨5, 7, 0, 4, 2, 6, 7802174887329481488314518354625249605469601792000000⟩, + ⟨5, 7, 1, 4, 3, 6, -6009877298535662742949696117039672275612205056000000⟩, + ⟨5, 7, 2, 4, 4, 6, 55289767834332370654272797679018299432632320000000⟩, + ⟨5, 7, 3, 4, 5, 6, -469544485300206073633663156203995691173176934400000⟩, + ⟨5, 7, 4, 4, 6, 6, 91086721296623841559539398400856453001143910400000⟩, + ⟨5, 7, 5, 4, 7, 6, 5423023788185713811972311687200294630850560000000⟩, + ⟨5, 7, 6, 4, 8, 6, -2572894433926120425679999833235139183247360000000⟩, + ⟨5, 7, 0, 5, 1, 6, 6013833779384875640645496251158669046172352512000000⟩, + ⟨5, 7, 1, 5, 2, 6, -1217226118595593379089163305729952524554731520000000⟩, + ⟨5, 7, 2, 5, 3, 6, 921979015699954246745882598535745686405644288000000⟩, + ⟨5, 7, 3, 5, 4, 6, 480672298239277488635357787205106647227275673600000⟩, + ⟨5, 7, 4, 5, 5, 6, 47256252514680410376172618525805309730383462400000⟩, + ⟨5, 7, 5, 5, 6, 6, -12045741723972893003792477242204137329786880000000⟩, + ⟨5, 7, 6, 5, 7, 6, 3118654870855921764078108912034349636911104000000⟩, + ⟨5, 7, 7, 5, 8, 6, 141511549512103409289310021015555918528512000000⟩, + ⟨5, 7, 0, 6, 0, 6, -138717557438983661431162024557943658638523498496000000⟩, + ⟨5, 7, 1, 6, 1, 6, -26857763067176405708024112439717723234199666688000000⟩, + ⟨5, 7, 2, 6, 2, 6, -617003803891042288165158461153696065662222336000000⟩, + ⟨5, 7, 3, 6, 3, 6, 639408285743830291894195562368700208613058150400000⟩, + ⟨5, 7, 4, 6, 4, 6, -91716091476041193193716667125448158460300492800000⟩, + ⟨5, 7, 5, 6, 5, 6, 24416424348111694957504192247018045866770432000000⟩, + ⟨5, 7, 6, 6, 6, 6, -2030727099513912017641353043391510464167936000000⟩, + ⟨5, 7, 7, 6, 7, 6, -467608107276394609416224452593069569605632000000⟩, + ⟨5, 7, 8, 6, 8, 6, 555083329445135310225358371621794002816204800000⟩, + ⟨5, 7, 1, 7, 0, 6, 168227272778422743191346883037742108713731227648000000⟩, + ⟨5, 7, 2, 7, 1, 6, 9100413413701342364877856024345218312837267456000000⟩, + ⟨5, 7, 3, 7, 2, 6, 2353645808117867876489045099431321162014837964800000⟩, + ⟨5, 7, 4, 7, 3, 6, 333814295623431925029765853936623545299972915200000⟩, + ⟨5, 7, 5, 7, 4, 6, 73835984275434523395522446627546908122415104000000⟩, + ⟨5, 7, 6, 7, 5, 6, 2098634834799850382755149480643526739886080000000⟩, + ⟨5, 7, 7, 7, 6, 6, 1171069290260960683602050264955004542517248000000⟩, + ⟨5, 7, 8, 7, 7, 6, 420307743075510540400643899444013369288294400000⟩ +] + +def collectedFourData_10_6_32 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 6, 7, -1851524283527646862689594037473109834318479360000000⟩, + ⟨5, 8, 1, 0, 7, 7, 1228458757869898764612594296866777280525893632000000⟩, + ⟨5, 8, 2, 0, 8, 7, -149370308690095651607386778439722204694105292800000⟩, + ⟨5, 8, 0, 1, 5, 7, -2827427791761895686924665376333265944195366912000000⟩, + ⟨5, 8, 1, 1, 6, 7, 600110632721461762858741192874509001274949632000000⟩, + ⟨5, 8, 2, 1, 7, 7, -68473193669128377667363176778392952331304960000000⟩, + ⟨5, 8, 3, 1, 8, 7, -433015349810304562088167921467422261064499200000⟩, + ⟨5, 8, 0, 2, 4, 7, -805675284744791230102004413035037660891054080000000⟩, + ⟨5, 8, 1, 2, 5, 7, 357066978500295663206452343898743422335320064000000⟩, + ⟨5, 8, 2, 2, 6, 7, -144244417731621954505498904420557360834648473600000⟩, + ⟨5, 8, 3, 2, 7, 7, 15558239228731269937306179306801095910201753600000⟩, + ⟨5, 8, 4, 2, 8, 7, -743391449550764990158866640449108911220326400000⟩, + ⟨5, 8, 0, 3, 3, 7, -143297960249692159446677218806802374394380288000000⟩, + ⟨5, 8, 1, 3, 4, 7, 194693454930397606880760931582361528218681344000000⟩, + ⟨5, 8, 2, 3, 5, 7, 35747071994262109670688436493232663697136025600000⟩, + ⟨5, 8, 3, 3, 6, 7, -17083788582866401669550621888156009713002086400000⟩, + ⟨5, 8, 4, 3, 7, 7, -4481639148618825414864041422130808754903449600000⟩, + ⟨5, 8, 5, 3, 8, 7, 463294519262029626297032202646170535723008000000⟩, + ⟨5, 8, 0, 4, 2, 7, 1062090455909339188507509134323289463013244928000000⟩, + ⟨5, 8, 1, 4, 3, 7, -613582117691965729607627140675407923462012928000000⟩, + ⟨5, 8, 2, 4, 4, 7, 4515874271543312804335251133401342387683328000000⟩, + ⟨5, 8, 3, 4, 5, 7, -31958955269772595734169593396792341430062284800000⟩, + ⟨5, 8, 4, 4, 6, 7, 5314031320731481803463633763785833357665894400000⟩, + ⟨5, 8, 5, 4, 7, 7, 276833473876384433153839921749794897264640000000⟩, + ⟨5, 8, 6, 4, 8, 7, -116747217359138230040930373324268193710080000000⟩, + ⟨5, 8, 0, 5, 1, 7, 818648076048969694359281233491630841720209408000000⟩, + ⟨5, 8, 1, 5, 2, 7, -124273448933780104462373096614638063986933760000000⟩, + ⟨5, 8, 2, 5, 3, 7, 75304011555586352215338492491139508323169075200000⟩, + ⟨5, 8, 3, 5, 4, 7, 32716355872066548381192204854230328028640051200000⟩, + ⟨5, 8, 4, 5, 5, 7, 2756946373617198548928234761894324848715366400000⟩, + ⟨5, 8, 5, 5, 6, 7, -614908703540971231570277241036334662942720000000⟩, + ⟨5, 8, 6, 5, 7, 7, 141511549512103409289310021015555918528512000000⟩, + ⟨5, 8, 7, 5, 8, 7, 5779083459734806076984827083862512658022400000⟩, + ⟨5, 8, 0, 6, 0, 7, -18883272414498290151044730148930433614677540864000000⟩, + ⟨5, 8, 1, 6, 1, 7, -2742059832609638173002173454275510762465132544000000⟩, + ⟨5, 8, 2, 6, 2, 7, -50394706155842164573533082796933001903498854400000⟩, + ⟨5, 8, 3, 6, 3, 7, 43520521362622163402833760038139654986058956800000⟩, + ⟨5, 8, 4, 6, 4, 7, -5350748998106945349386028316842183067749580800000⟩, + ⟨5, 8, 5, 6, 5, 7, 1246404927570681183337957343373089474347008000000⟩, + ⟨5, 8, 6, 6, 6, 7, -92145925210878946923775661144431141060608000000⟩, + ⟨5, 8, 7, 6, 7, 7, -19096294879929787175901077252775625516646400000⟩, + ⟨5, 8, 8, 6, 8, 7, 20607845013555782545719177109897775520153600000⟩, + ⟨5, 8, 1, 7, 0, 7, 17175266841151480641975063081230006009173377024000000⟩, + ⟨5, 8, 2, 7, 1, 7, 743289841955578616818637522091300812459763302400000⟩, + ⟨5, 8, 3, 7, 2, 7, 160197943874123699953214874129322141529250201600000⟩, + ⟨5, 8, 4, 7, 3, 7, 19474843281208162391076608295391829706355507200000⟩, + ⟨5, 8, 5, 7, 4, 7, 3769165104637864609294876158397179626520576000000⟩, + ⟨5, 8, 6, 7, 5, 7, 95227294981536982986915705191456298762240000000⟩, + ⟨5, 8, 7, 7, 6, 7, 47824415667017044670746154973180366264729600000⟩, + ⟨5, 8, 8, 7, 7, 7, 15604209976825947930784069700211819990220800000⟩ +] + +def collectedFourData_10_6_33 : List CollectedFourTerm := [ + ⟨6, 0, 4, 2, 8, 0, 20242055322269658362403862343602209988730368819200000⟩, + ⟨6, 0, 4, 3, 7, 0, 122032056779255165821723614404775166287700348108800000⟩, + ⟨6, 0, 5, 3, 8, 0, -100921615873559158512248953893063940148236910592000000⟩, + ⟨6, 0, 4, 4, 6, 0, -144697542652022101079757446290562452380590486323200000⟩, + ⟨6, 0, 5, 4, 7, 0, -60303932703538042269981301480636877280494223360000000⟩, + ⟨6, 0, 6, 4, 8, 0, 114442170166984337976655492885680205467368816640000000⟩, + ⟨6, 0, 4, 5, 5, 0, -75069818261985712195241923577296503616883077939200000⟩, + ⟨6, 0, 5, 5, 6, 0, 133948444015526340075831646940572247659936481280000000⟩, + ⟨6, 0, 6, 5, 7, 0, -138717557438983661431162024557943658638523498496000000⟩, + ⟨6, 0, 7, 5, 8, 0, -18883272414498290151044730148930433614677540864000000⟩, + ⟨6, 0, 4, 6, 4, 0, 145697340614708551587513933918924811292264261222400000⟩, + ⟨6, 0, 5, 6, 5, 0, -271510225339091241192338657452971682179519086592000000⟩, + ⟨6, 0, 6, 6, 6, 0, 90326603851618013121275207038679948501622718464000000⟩, + ⟨6, 0, 7, 6, 7, 0, 62397530826081984647774504202484166769197973504000000⟩, + ⟨6, 0, 8, 6, 8, 0, -185175516747533883415033838852883174492538404864000000⟩, + ⟨6, 0, 4, 7, 3, 0, -530287045040631939421510399330983506755056146841600000⟩, + ⟨6, 0, 5, 7, 4, 0, -821054894973072790277118324360525028888751898624000000⟩, + ⟨6, 0, 6, 7, 5, 0, -93347135317959177738620326752503485580621905920000000⟩, + ⟨6, 0, 7, 7, 6, 0, -156267248153900848696510945840469733832031993856000000⟩, + ⟨6, 0, 8, 7, 7, 0, -140214449594077015010903754081252288915667156992000000⟩ +] + +def collectedFourData_10_6_34 : List CollectedFourTerm := [ + ⟨6, 1, 3, 1, 8, 1, 978367364776636375260713811447603351824577331200000⟩, + ⟨6, 1, 3, 2, 7, 1, -35152734242438780678082816852014098590402714009600000⟩, + ⟨6, 1, 4, 2, 8, 1, 11757480506618531634344471029824863074603814092800000⟩, + ⟨6, 1, 3, 3, 6, 1, 38599604433289391409605908729250817256246896230400000⟩, + ⟨6, 1, 4, 3, 7, 1, 70881612856089230345572774198638764066518283059200000⟩, + ⟨6, 1, 5, 3, 8, 1, -29309867808343891185160774930410047330020491264000000⟩, + ⟨6, 1, 3, 4, 5, 1, 72208984882405497990196883345284771315274534092800000⟩, + ⟨6, 1, 4, 4, 6, 1, -84046728951237548602437406031396257651562958028800000⟩, + ⟨6, 1, 5, 4, 7, 1, -17513594888119902269985441813478962405436293120000000⟩, + ⟨6, 1, 6, 4, 8, 1, 22157690403324255236297042397806950187186257920000000⟩, + ⟨6, 1, 3, 5, 4, 1, -73920277638357904969602877866795290781405098803200000⟩, + ⟨6, 1, 4, 5, 5, 1, -43603868816604290550513369979506917256895188172800000⟩, + ⟨6, 1, 5, 5, 6, 1, 38901588656162412433260533141471626052511989760000000⟩, + ⟨6, 1, 6, 5, 7, 1, -26857763067176405708024112439717723234199666688000000⟩, + ⟨6, 1, 7, 5, 8, 1, -2742059832609638173002173454275510762465132544000000⟩, + ⟨6, 1, 3, 6, 3, 1, -98331520621398282905544960656681999301056711884800000⟩, + ⟨6, 1, 4, 6, 4, 1, 84627455802819180005082476533834697563828754841600000⟩, + ⟨6, 1, 5, 6, 5, 1, -78852570328170444408452200684047521278291083264000000⟩, + ⟨6, 1, 6, 6, 6, 1, 17488561431573276763449079975208299213401096192000000⟩, + ⟨6, 1, 7, 6, 7, 1, 9060811027693210497290745156398110997672361984000000⟩, + ⟨6, 1, 8, 6, 8, 1, -21511625117108146245906651571935511125054141235200000⟩, + ⟨6, 1, 3, 7, 2, 1, -361955852741532780716268209254896695568359856537600000⟩, + ⟨6, 1, 4, 7, 3, 1, -308014156453678065156883566222457990689749100134400000⟩, + ⟨6, 1, 5, 7, 4, 1, -238452488366858632420750813402057809790928683008000000⟩, + ⟨6, 1, 6, 7, 5, 1, -18073380829763916488885797760041467248388341760000000⟩, + ⟨6, 1, 7, 7, 6, 1, -22691731332873366064055855531685537769718808576000000⟩, + ⟨6, 1, 8, 7, 7, 1, -16288550066701032712797617543955949109647088025600000⟩ +] + +def collectedFourData_10_6_35 : List CollectedFourTerm := [ + ⟨6, 2, 2, 0, 8, 2, 5168799529640727982734095361110097262247568998400000⟩, + ⟨6, 2, 2, 1, 7, 2, 2369441519762066381042626932511370067711098880000000⟩, + ⟨6, 2, 3, 1, 8, 2, 89904194055205480930684008922490240285383065600000⟩, + ⟨6, 2, 2, 2, 6, 2, 4991423563777806128338495879518069630436166860800000⟩, + ⟨6, 2, 3, 2, 7, 2, -3230257216955314869795911398744912566466432204800000⟩, + ⟨6, 2, 4, 2, 8, 2, 540209560908981489400536836508474617504150323200000⟩, + ⟨6, 2, 2, 3, 5, 2, -1236989134790660065394767883794171144444890316800000⟩, + ⟨6, 2, 3, 3, 6, 2, 3546997224520964460945850187169961895605252915200000⟩, + ⟨6, 2, 4, 3, 7, 2, 3256728763951904332060384723303863122976885964800000⟩, + ⟨6, 2, 5, 3, 8, 2, -897781391749292617997940976868278706890604544000000⟩, + ⟨6, 2, 2, 4, 4, 2, -156266991849749474796258716000749867115741184000000⟩, + ⟨6, 2, 3, 4, 5, 2, 6635432479781556354676401173043605675983660646400000⟩, + ⟨6, 2, 4, 4, 6, 2, -3861613592897390450542058042965589269484352307200000⟩, + ⟨6, 2, 5, 4, 7, 2, -536453446191028995978066415664338946249195520000000⟩, + ⟨6, 2, 6, 4, 8, 2, 509028962318878619582116630177074993420042240000000⟩, + ⟨6, 2, 2, 5, 3, 2, -2605814655683198559672852972059563157918161305600000⟩, + ⟨6, 2, 3, 5, 4, 2, -6792686698958764359616331046667889692200507801600000⟩, + ⟨6, 2, 4, 5, 5, 2, -2003424697501382577288363257691966630425473843200000⟩, + ⟨6, 2, 5, 5, 6, 2, 1191582392433907557374967216476306195569704960000000⟩, + ⟨6, 2, 6, 5, 7, 2, -617003803891042288165158461153696065662222336000000⟩, + ⟨6, 2, 7, 5, 8, 2, -50394706155842164573533082796933001903498854400000⟩, + ⟨6, 2, 2, 6, 2, 2, 1743854824690279461085431314455426933596566323200000⟩, + ⟨6, 2, 3, 6, 3, 2, -9035886140486624822392081303525712794707453542400000⟩, + ⟨6, 2, 4, 6, 4, 2, 3888295686677973125617155967853952601036318310400000⟩, + ⟨6, 2, 5, 6, 5, 2, -2415308414051624154296594374393943107037036544000000⟩, + ⟨6, 2, 6, 6, 6, 2, 401764990661126759477073192178398508848513024000000⟩, + ⟨6, 2, 7, 6, 7, 2, 166523320842218088942861931030946142243677798400000⟩, + ⟨6, 2, 8, 6, 8, 2, -329457929710083323956363313999926534182902169600000⟩, + ⟨6, 2, 2, 7, 1, 2, -25720748783198257201066263052923424297584898867200000⟩, + ⟨6, 2, 3, 7, 2, 2, -33260869480986224709570496446653724176688139468800000⟩, + ⟨6, 2, 4, 7, 3, 2, -14152027904101232426143167026467910313116801433600000⟩, + ⟨6, 2, 5, 7, 4, 2, -7303963575405033839764674529093872531347079168000000⟩, + ⟨6, 2, 6, 7, 5, 2, -415200055687591378492179413274051214017822720000000⟩, + ⟨6, 2, 7, 7, 6, 2, -417037994243601780743841922944280621835983257600000⟩, + ⟨6, 2, 8, 7, 7, 2, -249464740750176173605826970438329441356401868800000⟩ +] + +def collectedFourData_10_6_36 : List CollectedFourTerm := [ + ⟨6, 3, 1, 0, 7, 3, 44053093315275559314379492141620361200795018854400000⟩, + ⟨6, 3, 2, 0, 8, 3, -26782438177518309471418272337386756470356102348800000⟩, + ⟨6, 3, 1, 1, 6, 3, 21520241956358313154932298727996753998065854054400000⟩, + ⟨6, 3, 2, 1, 7, 3, -12277400323684733225236914888392288315281244160000000⟩, + ⟨6, 3, 3, 1, 8, 3, -232921929490126170196371021850989815167293849600000⟩, + ⟨6, 3, 1, 2, 5, 3, 12804585276393063169637868116471530232751115468800000⟩, + ⟨6, 3, 2, 2, 6, 3, -25863354198219250871573406021921811043530152345600000⟩, + ⟨6, 3, 3, 2, 7, 3, 8368883694798807667931665791961349567405673676800000⟩, + ⟨6, 3, 4, 2, 8, 3, -933042516931377074683817235880028460098047180800000⟩, + ⟨6, 3, 1, 3, 4, 3, 6981796403807756107254174366639275578684656844800000⟩, + ⟨6, 3, 2, 3, 5, 3, 6409531814652421168255641508238220086757398937600000⟩, + ⟨6, 3, 3, 3, 6, 3, -9189487165907246218516930779583075983350248243200000⟩, + ⟨6, 3, 4, 3, 7, 3, -5624977088090587250637720529775060088364675891200000⟩, + ⟨6, 3, 5, 3, 8, 3, 1162976745546323985080251625438166745299812352000000⟩, + ⟨6, 3, 1, 4, 3, 3, -22003335573216873203791134118997760739668236697600000⟩, + ⟨6, 3, 2, 4, 4, 3, 809706591327905062720562070808538615421861888000000⟩, + ⟨6, 3, 3, 4, 5, 3, -17190941450886468357838352050358516622779901542400000⟩, + ⟨6, 3, 4, 4, 6, 3, 6669725837637419748238567087116833575263849676800000⟩, + ⟨6, 3, 5, 4, 7, 3, 694916255473663871167407034627141897719644160000000⟩, + ⟨6, 3, 6, 4, 8, 3, -527512689772252260758909019836315816045838336000000⟩, + ⟨6, 3, 1, 5, 2, 3, -4456502757962952646615018079296404233536929792000000⟩, + ⟨6, 3, 2, 5, 3, 3, 13502181602844516115485583750393005525947331379200000⟩, + ⟨6, 3, 3, 5, 4, 3, 17598352434724743691669391766482176702525577625600000⟩, + ⟨6, 3, 4, 5, 5, 3, 3460287557839286312187713485913080355042938060800000⟩, + ⟨6, 3, 5, 5, 6, 3, -1543563528425270871573325328473358832689479680000000⟩, + ⟨6, 3, 6, 5, 7, 3, 639408285743830291894195562368700208613058150400000⟩, + ⟨6, 3, 7, 5, 8, 3, 43520521362622163402833760038139654986058956800000⟩, + ⟨6, 3, 1, 6, 1, 3, -98331520621398282905544960656681999301056711884800000⟩, + ⟨6, 3, 2, 6, 2, 3, -9035886140486624822392081303525712794707453542400000⟩, + ⟨6, 3, 3, 6, 3, 3, 23409987227101711375608392418815592721126155878400000⟩, + ⟨6, 3, 4, 6, 4, 3, -6715810782702337776615975130622903695816890777600000⟩, + ⟨6, 3, 5, 6, 5, 3, 3128765582221841892337597864504509962599268352000000⟩, + ⟨6, 3, 6, 6, 6, 3, -416353776638761213435779176443106760362400153600000⟩, + ⟨6, 3, 7, 6, 7, 3, -143808393676850213845952106188559422235397324800000⟩, + ⟨6, 3, 8, 6, 8, 3, 243872228909346952815292433241795434873723289600000⟩, + ⟨6, 3, 1, 7, 0, 3, 615912929938292072970368730741236680615097322700800000⟩, + ⟨6, 3, 2, 7, 1, 3, 133273569658711076331396644283033954853081998950400000⟩, + ⟨6, 3, 3, 7, 2, 3, 86171573834179745628195307621576081389692701900800000⟩, + ⟨6, 3, 4, 7, 3, 3, 24443187775327948180036597081328136830717421158400000⟩, + ⟨6, 3, 5, 7, 4, 3, 9461479004329264857411404042348353531982905344000000⟩, + ⟨6, 3, 6, 7, 5, 3, 430276692256548294414073749878118385773969408000000⟩, + ⟨6, 3, 7, 7, 6, 3, 360151141299981721779975439222230252327744307200000⟩, + ⟨6, 3, 8, 7, 7, 3, 184659456867751559723935799676374719155457228800000⟩ +] + +def collectedFourData_10_6_37 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 6, 4, 14285774111187024808969856220185385447588888576000000⟩, + ⟨6, 4, 1, 0, 7, 4, -37913592548518625076724616883645140098104478924800000⟩, + ⟨6, 4, 2, 0, 8, 4, 11524939250590822153796047918458234260899548364800000⟩, + ⟨6, 4, 0, 1, 5, 4, 21815536046789124650222719447058916119296553779200000⟩, + ⟨6, 4, 1, 1, 6, 4, -18521053203680136877172390795698950684975877324800000⟩, + ⟨6, 4, 2, 1, 7, 4, 5283174442438378873921182917854779663565455360000000⟩, + ⟨6, 4, 3, 1, 8, 4, 66820181934430176944982908291854126058727014400000⟩, + ⟨6, 4, 0, 2, 4, 4, 6216334955597416502564743275857982021936611328000000⟩, + ⟨6, 4, 1, 2, 5, 4, -11020062211013675291132856283823162864906639769600000⟩, + ⟨6, 4, 2, 2, 6, 4, 11129441762370934270079696332607955010393315737600000⟩, + ⟨6, 4, 3, 2, 7, 4, -2400848783533059865842598106316204682085872435200000⟩, + ⟨6, 4, 4, 2, 8, 4, 200752042337933406893004596608509340484527718400000⟩, + ⟨6, 4, 0, 3, 3, 4, 1105641610500860654250811675135396624603073740800000⟩, + ⟨6, 4, 1, 3, 4, 4, -6008771783998480889312604370017891624882379161600000⟩, + ⟨6, 4, 2, 3, 5, 4, -2758130693664990811533966544813649982599567769600000⟩, + ⟨6, 4, 3, 3, 6, 4, 2636261882486523627869444253044853570834058444800000⟩, + ⟨6, 4, 4, 3, 7, 4, 1210261716960234344855937647067406620077693337600000⟩, + ⟨6, 4, 5, 3, 8, 4, -200179479604245101046463266625168368034696396800000⟩, + ⟨6, 4, 0, 4, 2, 4, -8194753087364464368658647530342937355778575564800000⟩, + ⟨6, 4, 1, 4, 3, 4, 18936820024440815291803777663579915755002737459200000⟩, + ⟨6, 4, 2, 4, 4, 4, -348430535487630948379974571209625382103810048000000⟩, + ⟨6, 4, 3, 4, 5, 4, 4931703244460138676646243094095746951810750873600000⟩, + ⟨6, 4, 4, 4, 6, 4, -1435048306419537854973947377492686372545652326400000⟩, + ⟨6, 4, 5, 4, 7, 4, -119613719639682761648948641703738482196742144000000⟩, + ⟨6, 4, 6, 4, 8, 4, 75665897969466943822388346495197060322557952000000⟩, + ⟨6, 4, 0, 5, 1, 4, -6316428898632270347692110833013630019853667532800000⟩, + ⟨6, 4, 1, 5, 2, 4, 3835418061282174414685058603173352979472318464000000⟩, + ⟨6, 4, 2, 5, 3, 4, -5810218684789184048858139066371011133710742323200000⟩, + ⟨6, 4, 3, 5, 4, 4, -5048580500808441322786107499656523850499647078400000⟩, + ⟨6, 4, 4, 5, 5, 4, -744510332280889055320161312419040073538233958400000⟩, + ⟨6, 4, 5, 5, 6, 4, 265688669218498449986004226244117115973926912000000⟩, + ⟨6, 4, 6, 5, 7, 4, -91716091476041193193716667125448158460300492800000⟩, + ⟨6, 4, 7, 5, 8, 4, -5350748998106945349386028316842183067749580800000⟩, + ⟨6, 4, 0, 6, 0, 4, 145697340614708551587513933918924811292264261222400000⟩, + ⟨6, 4, 1, 6, 1, 4, 84627455802819180005082476533834697563828754841600000⟩, + ⟨6, 4, 2, 6, 2, 4, 3888295686677973125617155967853952601036318310400000⟩, + ⟨6, 4, 3, 6, 3, 4, -6715810782702337776615975130622903695816890777600000⟩, + ⟨6, 4, 4, 6, 4, 4, 1444963874761740415671894427297614248589184204800000⟩, + ⟨6, 4, 5, 6, 5, 4, -538544445064223103135676841932693642136046796800000⟩, + ⟨6, 4, 6, 6, 6, 4, 59721373519852467196258314845786881597322035200000⟩, + ⟨6, 4, 7, 6, 7, 4, 17680914527063772506176378381685321083178188800000⟩, + ⟨6, 4, 8, 6, 8, 4, -26235593306117331599700710850396104960665190400000⟩, + ⟨6, 4, 1, 7, 0, 4, -530075645401897404687291271980860345371164514713600000⟩, + ⟨6, 4, 2, 7, 1, 4, -57349886662497806838468462755257436760701298278400000⟩, + ⟨6, 4, 3, 7, 2, 4, -24720730477291370112337863317207630120045720371200000⟩, + ⟨6, 4, 4, 7, 3, 4, -5259159982639452945496448427324806292133065523200000⟩, + ⟨6, 4, 5, 7, 4, 4, -1628574217520913682684663948681639363241154969600000⟩, + ⟨6, 4, 6, 7, 5, 4, -61718462752014460584502601594185574730694656000000⟩, + ⟨6, 4, 7, 7, 6, 4, -44279762699098357759997262287939175200273203200000⟩, + ⟨6, 4, 8, 7, 7, 4, -19865527256536108163321741129885506780476211200000⟩ +] + +def collectedFourData_10_6_38 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 6, 5, -26621856869226726589979645951588321997178798080000000⟩, + ⟨6, 5, 1, 0, 7, 5, 35326410258525960395022833728268409251448225792000000⟩, + ⟨6, 5, 2, 0, 8, 5, -7158993293323379060021894010487342022082428928000000⟩, + ⟨6, 5, 0, 1, 5, 5, -40653735222390362525074704190403161307517812736000000⟩, + ⟨6, 5, 1, 1, 6, 5, 17257196691553184653632385766945253118854561792000000⟩, + ⟨6, 5, 2, 1, 7, 5, -3281770912496123912369939531486877114276249600000000⟩, + ⟨6, 5, 3, 1, 8, 5, -31130222723476205080660446798509510636863488000000⟩, + ⟨6, 5, 0, 2, 4, 5, -11584278048292230452101363883853093047359242240000000⟩, + ⟨6, 5, 1, 2, 5, 5, 10268065160075647589754232421939325703903248384000000⟩, + ⟨6, 5, 2, 2, 6, 5, -6913320513265360918739635076888540254606196736000000⟩, + ⟨6, 5, 3, 2, 7, 5, 1118508737825818625736725850049849052368994304000000⟩, + ⟨6, 5, 4, 2, 8, 5, -74821176587697481789739402655033023711831654400000⟩, + ⟨6, 5, 0, 3, 3, 5, -2060387660782458418798498156059717816878628864000000⟩, + ⟨6, 5, 1, 3, 4, 5, 5598739737463341605035190584117445658949976064000000⟩, + ⟨6, 5, 2, 3, 5, 5, 1713279238070151666120283785293287304258912256000000⟩, + ⟨6, 5, 3, 3, 6, 5, -1228183120479197209803305017482118535678263296000000⟩, + ⟨6, 5, 4, 3, 7, 5, -451069909862137546252875664606264277515999641600000⟩, + ⟨6, 5, 5, 3, 8, 5, 62173149931106503488453033982468482844852224000000⟩, + ⟨6, 5, 0, 4, 2, 5, 15271104111861349587121763640715238063455862784000000⟩, + ⟨6, 5, 1, 4, 3, 5, -17644592036989755051682976635485785201540333568000000⟩, + ⟨6, 5, 2, 4, 4, 5, 216436009987397408049730533338119371258593280000000⟩, + ⟨6, 5, 3, 4, 5, 5, -2297584591385676712940981254570332101931958272000000⟩, + ⟨6, 5, 4, 4, 6, 5, 534848868763930915436447856864863464196564582400000⟩, + ⟨6, 5, 5, 4, 7, 5, 37150469866730672713652262157869368916049920000000⟩, + ⟨6, 5, 6, 4, 8, 5, -20143582699291586725139128134331611878522880000000⟩, + ⟨6, 5, 0, 5, 1, 5, 11770805330902959062431344456054116204333236224000000⟩, + ⟨6, 5, 1, 5, 2, 5, -3573693307286131514934894420751734192797122560000000⟩, + ⟨6, 5, 2, 5, 3, 5, 3609157123757991418156909378323132528828874752000000⟩, + ⟨6, 5, 3, 5, 4, 5, 2352035431178388090336453162829104830132256768000000⟩, + ⟨6, 5, 4, 5, 5, 5, 277482303015294802739931972342563138976507494400000⟩, + ⟨6, 5, 5, 5, 6, 5, -82519454536375775836412021347706778849116160000000⟩, + ⟨6, 5, 6, 5, 7, 5, 24416424348111694957504192247018045866770432000000⟩, + ⟨6, 5, 7, 5, 8, 5, 1246404927570681183337957343373089474347008000000⟩, + ⟨6, 5, 0, 6, 0, 5, -271510225339091241192338657452971682179519086592000000⟩, + ⟨6, 5, 1, 6, 1, 5, -78852570328170444408452200684047521278291083264000000⟩, + ⟨6, 5, 2, 6, 2, 5, -2415308414051624154296594374393943107037036544000000⟩, + ⟨6, 5, 3, 6, 3, 5, 3128765582221841892337597864504509962599268352000000⟩, + ⟨6, 5, 4, 6, 4, 5, -538544445064223103135676841932693642136046796800000⟩, + ⟨6, 5, 5, 6, 5, 5, 167264919429995542324638891471035436550324224000000⟩, + ⟨6, 5, 6, 6, 6, 5, -15898871997764065429328090232384167123877888000000⟩, + ⟨6, 5, 7, 6, 7, 5, -4118597040953529197891628050138808176345088000000⟩, + ⟨6, 5, 8, 6, 8, 5, 5432289994217689331781886814734760382824448000000⟩, + ⟨6, 5, 1, 7, 0, 5, 493903860299095148624006004033969201794613510144000000⟩, + ⟨6, 5, 2, 7, 1, 5, 35624261877877586477950751721019992923411841024000000⟩, + ⟨6, 5, 3, 7, 2, 5, 11516907367900736353398451246283971184792961024000000⟩, + ⟨6, 5, 4, 7, 3, 5, 1960112251817747987618445974021867209502176051200000⟩, + ⟨6, 5, 5, 7, 4, 5, 505814028491035155510367926149680101618352128000000⟩, + ⟨6, 5, 6, 7, 5, 5, 16430532008224167998342398992941142654320640000000⟩, + ⟨6, 5, 7, 7, 6, 5, 10314539971757715939804747770768992430456832000000⟩, + ⟨6, 5, 8, 7, 7, 5, 4113316732973496825745051998043636072710144000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1024.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1024.lean new file mode 100644 index 0000000000000000000000000000000000000000..2a3878b4cb943ba1cb734c068331f5468966bc06 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1024.lean @@ -0,0 +1,629 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1021 +import OAI.Analysis.LaughlinFock.Sparse1022 +import OAI.Analysis.LaughlinFock.Sparse1023 + +namespace OAI + +/-! Sparse1024. -/ +namespace LaughlinFock +def collectedFourData_10_6_39 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 6, 6, 8856616417366665467288261242997787162165903360000000⟩, + ⟨6, 6, 1, 0, 7, 6, -7834977266967756261881929534145881731105816576000000⟩, + ⟨6, 6, 2, 0, 8, 6, 1190834618428841635238635309012779023820914688000000⟩, + ⟨6, 6, 0, 1, 5, 6, 13524771790584654959372174423282364561292787712000000⟩, + ⟨6, 6, 1, 1, 6, 6, -3827440795156302854691871721962943582438424576000000⟩, + ⟨6, 6, 2, 1, 7, 6, 545893291448940974835486855697983405136281600000000⟩, + ⟨6, 6, 3, 1, 8, 6, 4142587694064611191325534556243408221267558400000⟩, + ⟨6, 6, 0, 2, 4, 6, 3853882456427816659217958054458865316087726080000000⟩, + ⟨6, 6, 1, 2, 5, 6, -2277334620647448017455226704514801147735703552000000⟩, + ⟨6, 6, 2, 2, 6, 6, 1149969144847299654401570379875298619064057856000000⟩, + ⟨6, 6, 3, 2, 7, 6, -148843153940132408039632716468072438559879987200000⟩, + ⟨6, 6, 4, 2, 8, 6, 8297223144982673344606206145482517361826201600000⟩, + ⟨6, 6, 0, 3, 3, 6, 685454184216552164057527705864613008389439488000000⟩, + ⟨6, 6, 1, 3, 4, 6, -1241733825930058432766464085625329028371054592000000⟩, + ⟨6, 6, 2, 3, 5, 6, -284988704994609666980002989121328017651531776000000⟩, + ⟨6, 6, 3, 3, 6, 6, 163437837440144491135487594834597095861439692800000⟩, + ⟨6, 6, 4, 3, 7, 6, 50020968217823505163253705425391808112125542400000⟩, + ⟨6, 6, 5, 3, 8, 6, -5909684803131479710588577932631158856613888000000⟩, + ⟨6, 6, 0, 4, 2, 6, -5080423655374996996992043741794613259170480128000000⟩, + ⟨6, 6, 1, 4, 3, 6, 3913360471189394907403164937303241419080597504000000⟩, + ⟨6, 6, 2, 4, 4, 6, -36002197907906461948187091551586704299130880000000⟩, + ⟨6, 6, 3, 4, 5, 6, 305746147044717838972245405883366779009997209600000⟩, + ⟨6, 6, 4, 4, 6, 6, -59311556104365906079006441120589264321091993600000⟩, + ⟨6, 6, 5, 4, 7, 6, -3531227988993494265568742839065726985175040000000⟩, + ⟨6, 6, 6, 4, 8, 6, 1675352569464766826017492244047948142346240000000⟩, + ⟨6, 6, 0, 5, 1, 6, -3915936752699185489588532757780855377633476608000000⟩, + ⟨6, 6, 1, 5, 2, 6, 792602634029138524938279603704146813444423680000000⟩, + ⟨6, 6, 2, 5, 3, 6, -600351064768897013501588012621566750954094592000000⟩, + ⟨6, 6, 3, 5, 4, 6, -312992075892077574850378519179022987094812262400000⟩, + ⟨6, 6, 4, 5, 5, 6, -30771135818788526573515534141129827278231961600000⟩, + ⟨6, 6, 5, 5, 6, 6, 7843642584889054683863115414746251049041920000000⟩, + ⟨6, 6, 6, 5, 7, 6, -2030727099513912017641353043391510464167936000000⟩, + ⟨6, 6, 7, 5, 8, 6, -92145925210878946923775661144431141060608000000⟩, + ⟨6, 6, 0, 6, 0, 6, 90326603851618013121275207038679948501622718464000000⟩, + ⟨6, 6, 1, 6, 1, 6, 17488561431573276763449079975208299213401096192000000⟩, + ⟨6, 6, 2, 6, 2, 6, 401764990661126759477073192178398508848513024000000⟩, + ⟨6, 6, 3, 6, 3, 6, -416353776638761213435779176443106760362400153600000⟩, + ⟨6, 6, 4, 6, 4, 6, 59721373519852467196258314845786881597322035200000⟩, + ⟨6, 6, 5, 6, 5, 6, -15898871997764065429328090232384167123877888000000⟩, + ⟨6, 6, 6, 6, 6, 6, 1322317705379302012875910078847005621223424000000⟩, + ⟨6, 6, 7, 6, 7, 6, 304485265193184867203651866090164807794688000000⟩, + ⟨6, 6, 8, 6, 8, 6, -361445176292712411963897411180074896667443200000⟩, + ⟨6, 6, 1, 7, 0, 6, -109541996743840630610985441370369060220889464832000000⟩, + ⟨6, 6, 2, 7, 1, 6, -5925777907868087811653990080216829046086959104000000⟩, + ⟨6, 6, 3, 7, 2, 6, -1532587773616161674905940679805777687182783283200000⟩, + ⟨6, 6, 4, 7, 3, 6, -217364782061185321224975261843811618339474636800000⟩, + ⟨6, 6, 5, 7, 4, 6, -48078655829670693378368189042790553601703936000000⟩, + ⟨6, 6, 6, 7, 5, 6, -1366536153403313281842355935996134786334720000000⟩, + ⟨6, 6, 7, 7, 6, 6, -762547393546235949296572141384925794271232000000⟩, + ⟨6, 6, 8, 7, 7, 6, -273685405838035794758724351540644156119449600000⟩ +] + +def collectedFourData_10_6_40 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 6, 7, 6118142079439213441157646773157415512661032960000000⟩, + ⟨6, 7, 1, 0, 7, 7, -4059296054740201757104798332697944002188541952000000⟩, + ⟨6, 7, 2, 0, 8, 7, 493576443553057609011318350028378220434083020800000⟩, + ⟨6, 7, 0, 1, 5, 7, 9342899309101092860014597238937733880749228032000000⟩, + ⟨6, 7, 1, 1, 6, 7, -1982994307466906405538205064305421760124157952000000⟩, + ⟨6, 7, 2, 1, 7, 7, 226261535550867462372582407742890036491714560000000⟩, + ⟨6, 7, 3, 1, 8, 7, 1430847791890684494254673233848617823056691200000⟩, + ⟨6, 7, 0, 2, 4, 7, 2662258284060833559141384725764785337930874880000000⟩, + ⟨6, 7, 1, 2, 5, 7, -1179885419692501536217520455492855721260744704000000⟩, + ⟨6, 7, 2, 2, 6, 7, 476638545710365529447932286468848204895590809600000⟩, + ⟨6, 7, 3, 2, 7, 7, -51410353595754684677815231047379230203156889600000⟩, + ⟨6, 7, 4, 2, 8, 7, 2456448748447611353385195453204071249765990400000⟩, + ⟨6, 7, 0, 3, 3, 7, 473511089377164110885517141882191977453191168000000⟩, + ⟨6, 7, 1, 3, 4, 7, -643341397030767717663959711224520796782198784000000⟩, + ⟨6, 7, 2, 3, 5, 7, -118121953533412759478667075446113945425385881600000⟩, + ⟨6, 7, 3, 3, 6, 7, 56451350238808486754902160616884729985525350400000⟩, + ⟨6, 7, 4, 3, 7, 7, 14809044258272372284310602880989389678811545600000⟩, + ⟨6, 7, 5, 3, 8, 7, -1530901710924419552326049392058382667481088000000⟩, + ⟨6, 7, 0, 4, 2, 7, -3509551761367799855055793094434601889806942208000000⟩, + ⟨6, 7, 1, 4, 3, 7, 2027509229471353641370464441517883949431390208000000⟩, + ⟨6, 7, 2, 4, 4, 7, -14922170155687021443582258165914744660164608000000⟩, + ⟨6, 7, 3, 4, 5, 7, 105604571752294645152835203128860908635081932800000⟩, + ⟨6, 7, 4, 4, 6, 7, -17559585323332190809082239362179872544155238400000⟩, + ⟨6, 7, 5, 4, 7, 7, -914763333426814054137797955262855816151040000000⟩, + ⟨6, 7, 6, 4, 8, 7, 385777313069582689634591326354585556090880000000⟩, + ⟨6, 7, 0, 5, 1, 7, -2705125332077431844074301669400429746599231488000000⟩, + ⟨6, 7, 1, 5, 2, 7, 410646851377062813273687953683661737804431360000000⟩, + ⟨6, 7, 2, 5, 3, 7, -248833161923760524523932257982930731440223027200000⟩, + ⟨6, 7, 3, 5, 4, 7, -108107312082039849503867793542173342116819763200000⟩, + ⟨6, 7, 4, 5, 5, 7, -9110001834298309279681820262321226514851430400000⟩, + ⟨6, 7, 5, 5, 6, 7, 2031892774843670096283942421777954551889920000000⟩, + ⟨6, 7, 6, 5, 7, 7, -467608107276394609416224452593069569605632000000⟩, + ⟨6, 7, 7, 5, 8, 7, -19096294879929787175901077252775625516646400000⟩, + ⟨6, 7, 0, 6, 0, 7, 62397530826081984647774504202484166769197973504000000⟩, + ⟨6, 7, 1, 6, 1, 7, 9060811027693210497290745156398110997672361984000000⟩, + ⟨6, 7, 2, 6, 2, 7, 166523320842218088942861931030946142243677798400000⟩, + ⟨6, 7, 3, 6, 3, 7, -143808393676850213845952106188559422235397324800000⟩, + ⟨6, 7, 4, 6, 4, 7, 17680914527063772506176378381685321083178188800000⟩, + ⟨6, 7, 5, 6, 5, 7, -4118597040953529197891628050138808176345088000000⟩, + ⟨6, 7, 6, 6, 6, 7, 304485265193184867203651866090164807794688000000⟩, + ⟨6, 7, 7, 6, 7, 7, 63101438261278670437078607987142904145510400000⟩, + ⟨6, 7, 8, 6, 8, 7, -68096176142922597265776414858790536059289600000⟩, + ⟨6, 7, 1, 7, 0, 7, -56753629277947750332673932366977008446958731264000000⟩, + ⟨6, 7, 2, 7, 1, 7, -2456112998217797479296037470584843550952154726400000⟩, + ⟨6, 7, 3, 7, 2, 7, -529355077962326153296602931076539856346257817600000⟩, + ⟨6, 7, 4, 7, 3, 7, -64352306491077443022549952969218613983785779200000⟩, + ⟨6, 7, 5, 7, 4, 7, -12454758404303958729739952528760306281742336000000⟩, + ⟨6, 7, 6, 7, 5, 7, -314667285609496294996758671457713274224640000000⟩, + ⟨6, 7, 7, 7, 6, 7, -158030101209093822332159823755436208265625600000⟩, + ⟨6, 7, 8, 7, 7, 7, -51562258472641031918122688294009720065228800000⟩ +] + +def collectedFourData_10_6_41 : List CollectedFourTerm := [ + ⟨6, 8, 0, 0, 6, 8, -18156649888162343499184772977360383589597839360000000⟩, + ⟨6, 8, 1, 0, 7, 8, 9637333203621467395877508115204481058063620505600000⟩, + ⟨6, 8, 2, 0, 8, 8, -976515916354639063482426567600677869642265395200000⟩, + ⟨6, 8, 0, 1, 5, 8, -27726677395378686927865294204040654942122278912000000⟩, + ⟨6, 8, 1, 1, 6, 8, 4707904184427927730666949542448946457907665305600000⟩, + ⟨6, 8, 2, 1, 7, 8, -447646952382386147463296346021978165624176640000000⟩, + ⟨6, 8, 3, 1, 8, 8, -2426451136242476954072840557812522640893542400000⟩, + ⟨6, 8, 0, 2, 4, 8, -7900714129865879224828952133374918942345134080000000⟩, + ⟨6, 8, 1, 2, 5, 8, 2801212027487644132190784955528327723180307251200000⟩, + ⟨6, 8, 2, 2, 6, 8, -943005146039281177363986228609739618834081382400000⟩, + ⟨6, 8, 3, 2, 7, 8, 87182376493178284151095880785508528731403059200000⟩, + ⟨6, 8, 4, 2, 8, 8, -3644969282722668554061115433319665681773363200000⟩, + ⟨6, 8, 0, 3, 3, 8, -1405226448871803300043091773175861502214668288000000⟩, + ⟨6, 8, 1, 3, 4, 8, 1527381921214822598116171653397069095696020275200000⟩, + ⟨6, 8, 2, 3, 5, 8, 233698283625403983135977202433280639574107750400000⟩, + ⟨6, 8, 3, 3, 6, 8, -95730967127105686248329838374615190141193420800000⟩, + ⟨6, 8, 4, 3, 7, 8, -21974206244683838919640561738509667653176524800000⟩, + ⟨6, 8, 5, 3, 8, 8, 2019207502868523521360725594523659243880448000000⟩, + ⟨6, 8, 0, 4, 2, 8, 10415204774286530744252723489553900492898172928000000⟩, + ⟨6, 8, 1, 4, 3, 8, -4813588798239012743822703881957020193691952742400000⟩, + ⟨6, 8, 2, 4, 4, 8, 29522755500008281868446673737827692474007552000000⟩, + ⟨6, 8, 3, 4, 5, 8, -179085668352020190027394586169851742923626905600000⟩, + ⟨6, 8, 4, 4, 6, 8, 26055560557223915176985338630343741047780147200000⟩, + ⟨6, 8, 5, 4, 7, 8, 1206541852441390831379432584444433494179840000000⟩, + ⟨6, 8, 6, 4, 8, 8, -457944488196157138021961143644052921516032000000⟩, + ⟨6, 8, 0, 5, 1, 8, 8027929544687981517940910069856706120969617408000000⟩, + ⟨6, 8, 1, 5, 2, 8, -974932717981335598692196779960228287776555008000000⟩, + ⟨6, 8, 2, 5, 3, 8, 492303768361025579255878078585921499778829516800000⟩, + ⟨6, 8, 3, 5, 4, 8, 183329849425120715411989632693560796414109286400000⟩, + ⟨6, 8, 4, 5, 5, 8, 13517756831910014583295933028111259998040883200000⟩, + ⟨6, 8, 5, 5, 6, 8, -2679997746890778432828744268691462758072320000000⟩, + ⟨6, 8, 6, 5, 7, 8, 555083329445135310225358371621794002816204800000⟩, + ⟨6, 8, 7, 5, 8, 8, 20607845013555782545719177109897775520153600000⟩, + ⟨6, 8, 0, 6, 0, 8, -185175516747533883415033838852883174492538404864000000⟩, + ⟨6, 8, 1, 6, 1, 8, -21511625117108146245906651571935511125054141235200000⟩, + ⟨6, 8, 2, 6, 2, 8, -329457929710083323956363313999926534182902169600000⟩, + ⟨6, 8, 3, 6, 3, 8, 243872228909346952815292433241795434873723289600000⟩, + ⟨6, 8, 4, 6, 4, 8, -26235593306117331599700710850396104960665190400000⟩, + ⟨6, 8, 5, 6, 5, 8, 5432289994217689331781886814734760382824448000000⟩, + ⟨6, 8, 6, 6, 6, 8, -361445176292712411963897411180074896667443200000⟩, + ⟨6, 8, 7, 6, 7, 8, -68096176142922597265776414858790536059289600000⟩, + ⟨6, 8, 8, 6, 8, 8, 67362412362883353493885952458261487891251200000⟩, + ⟨6, 8, 1, 7, 0, 8, 134741006443146649695166670945798514242936320819200000⟩, + ⟨6, 8, 2, 7, 1, 8, 4859294778859052101510576538279704374890043801600000⟩, + ⟨6, 8, 3, 7, 2, 8, 897687537190917672342922561879077088107115315200000⟩, + ⟨6, 8, 4, 7, 3, 8, 95488326626218792198083789424332567198931353600000⟩, + ⟨6, 8, 5, 7, 4, 8, 16427404474712840507572157576788921345376256000000⟩, + ⟨6, 8, 6, 7, 5, 8, 373531942337219362902837795934770504400896000000⟩, + ⟨6, 8, 7, 7, 6, 8, 170538832463060173576085966209470792361574400000⟩, + ⟨6, 8, 8, 7, 7, 8, 51006654328219805969977103891051371403673600000⟩ +] + +def collectedFourData_10_6_42 : List CollectedFourTerm := [ + ⟨7, 0, 3, 1, 8, 1, -6128137817737075213799648955991075407155901235200000⟩, + ⟨7, 0, 3, 2, 7, 1, 220183959383325541081823979578816082707450796441600000⟩, + ⟨7, 0, 4, 2, 8, 1, -73644587429962989362777890580620394636832984268800000⟩, + ⟨7, 0, 3, 3, 6, 1, -241773902312589790932235056165366559652780074598400000⟩, + ⟨7, 0, 4, 3, 7, 1, -443976677845102806777168933021560963903817724723200000⟩, + ⟨7, 0, 5, 3, 8, 1, 183586366242084537448300255405506387607126278144000000⟩, + ⟨7, 0, 3, 4, 5, 1, -452290854099880168980365102443353357554086104268800000⟩, + ⟨7, 0, 4, 4, 6, 1, 526438183330822233713615387377096545004593925324800000⟩, + ⟨7, 0, 5, 4, 7, 1, 109698797223185193636251280091914703679803883520000000⟩, + ⟨7, 0, 6, 4, 8, 1, -138787724737038182671630686950007183738478264320000000⟩, + ⟨7, 0, 3, 5, 4, 1, 463009770360303128331472416619468219247972528947200000⟩, + ⟨7, 0, 4, 5, 5, 1, 273118796798464271970973517330316148826165791948800000⟩, + ⟨7, 0, 5, 5, 6, 1, -243665421800231938786131384577090805193202728960000000⟩, + ⟨7, 0, 6, 5, 7, 1, 168227272778422743191346883037742108713731227648000000⟩, + ⟨7, 0, 7, 5, 8, 1, 17175266841151480641975063081230006009173377024000000⟩, + ⟨7, 0, 3, 6, 3, 1, 615912929938292072970368730741236680615097322700800000⟩, + ⟨7, 0, 4, 6, 4, 1, -530075645401897404687291271980860345371164514713600000⟩, + ⟨7, 0, 5, 6, 5, 1, 493903860299095148624006004033969201794613510144000000⟩, + ⟨7, 0, 6, 6, 6, 1, -109541996743840630610985441370369060220889464832000000⟩, + ⟨7, 0, 7, 6, 7, 1, -56753629277947750332673932366977008446958731264000000⟩, + ⟨7, 0, 8, 6, 8, 1, 134741006443146649695166670945798514242936320819200000⟩, + ⟨7, 0, 3, 7, 2, 1, 2267159994694896555423211636401282576565046712729600000⟩, + ⟨7, 0, 4, 7, 3, 1, 1929288801444334460105607720362930803897901934182400000⟩, + ⟨7, 0, 5, 7, 4, 1, 1493579778213542278951262747801592514921384378368000000⟩, + ⟨7, 0, 6, 7, 5, 1, 113205093040410681295778813131335772341754920960000000⟩, + ⟨7, 0, 7, 7, 6, 1, 142132763149410540430434065693874014242782314496000000⟩, + ⟨7, 0, 8, 7, 7, 1, 102025561413368644748795153096135270814981921177600000⟩ +] + +def collectedFourData_10_6_43 : List CollectedFourTerm := [ + ⟨7, 1, 2, 0, 8, 2, -76236503366164376283038340801703674297499149926400000⟩, + ⟨7, 1, 2, 1, 7, 2, -34947754379211948152707656283391995184393748480000000⟩, + ⟨7, 1, 3, 1, 8, 2, -1326029642553843309662427240965171670257605017600000⟩, + ⟨7, 1, 2, 2, 6, 2, -73620320761085625888697437299581287792678587596800000⟩, + ⟨7, 1, 3, 2, 7, 2, 47644238044400973997665496299010065380210953420800000⟩, + ⟨7, 1, 4, 2, 8, 2, -7967747205613589658337026165825746131093762867200000⟩, + ⟨7, 1, 2, 3, 5, 2, 18244802453178477680084656151580189523771706572800000⟩, + ⟨7, 1, 3, 3, 6, 2, -52315951565984580666930101223184932307163362099200000⟩, + ⟨7, 1, 4, 3, 7, 2, -48034676514715055736060016484606679282898226380800000⟩, + ⟨7, 1, 5, 3, 8, 2, 13241704132977287092457372479193343840195969024000000⟩, + ⟨7, 1, 2, 4, 4, 2, 2304838673246410666743978649691227397201854464000000⟩, + ⟨7, 1, 3, 4, 5, 2, -97868405938348403180081041400917173577454085734400000⟩, + ⟨7, 1, 4, 4, 6, 2, 56956342761122878879416240729118640710972814131200000⟩, + ⟨7, 1, 5, 4, 7, 2, 7912346904112867961807316617689882878195793920000000⟩, + ⟨7, 1, 6, 4, 8, 2, -7507853221383440055390396991347231791555543040000000⟩, + ⟨7, 1, 2, 5, 3, 2, 38434107693745462702145231716498986206639004057600000⟩, + ⟨7, 1, 3, 5, 4, 2, 100187805586351401677782386935501454680264382873600000⟩, + ⟨7, 1, 4, 5, 5, 2, 29549239203234723813217697406181904078127444787200000⟩, + ⟨7, 1, 5, 5, 6, 2, -17575081902656810805686780326424708756180828160000000⟩, + ⟨7, 1, 6, 5, 7, 2, 9100413413701342364877856024345218312837267456000000⟩, + ⟨7, 1, 7, 5, 8, 2, 743289841955578616818637522091300812459763302400000⟩, + ⟨7, 1, 2, 6, 2, 2, -25720748783198257201066263052923424297584898867200000⟩, + ⟨7, 1, 3, 6, 3, 2, 133273569658711076331396644283033954853081998950400000⟩, + ⟨7, 1, 4, 6, 4, 2, -57349886662497806838468462755257436760701298278400000⟩, + ⟨7, 1, 5, 6, 5, 2, 35624261877877586477950751721019992923411841024000000⟩, + ⟨7, 1, 6, 6, 6, 2, -5925777907868087811653990080216829046086959104000000⟩, + ⟨7, 1, 7, 6, 7, 2, -2456112998217797479296037470584843550952154726400000⟩, + ⟨7, 1, 8, 6, 8, 2, 4859294778859052101510576538279704374890043801600000⟩, + ⟨7, 1, 2, 7, 1, 2, 379364674514056329116028862028659700750196355891200000⟩, + ⟨7, 1, 3, 7, 2, 2, 490576655876806805843973856178256963760978447564800000⟩, + ⟨7, 1, 4, 7, 3, 2, 208733404490163668643326950423931464079298369945600000⟩, + ⟨7, 1, 5, 7, 4, 2, 107728814110423006458842359002084665347673161728000000⟩, + ⟨7, 1, 6, 7, 5, 2, 6123936566226017989225307202010837932960645120000000⟩, + ⟨7, 1, 7, 7, 6, 2, 6151044990166350150347469202690073211468093849600000⟩, + ⟨7, 1, 8, 7, 7, 2, 3679446153575635260329714799564161495654517964800000⟩ +] + +def collectedFourData_10_6_44 : List CollectedFourTerm := [ + ⟨7, 2, 1, 0, 7, 3, 162158327828838362307098397011682820901571448012800000⟩, + ⟨7, 2, 2, 0, 8, 3, -98585480909683631960217572891174310523369527705600000⟩, + ⟨7, 2, 1, 1, 6, 3, 79215469050955669830390290836538909566595550412800000⟩, + ⟨7, 2, 2, 1, 7, 3, -45192801611586486965637254405375418674624593920000000⟩, + ⟨7, 2, 3, 1, 8, 3, -857379760610102218947206176646608929890186035200000⟩, + ⟨7, 2, 1, 2, 5, 3, 47133356155075603530169677004952770990178933145600000⟩, + ⟨7, 2, 2, 2, 6, 3, -95202355912063296661728569259767822849039086387200000⟩, + ⟨7, 2, 3, 2, 7, 3, 30805650264564544690617830295317392557994514841600000⟩, + ⟨7, 2, 4, 2, 8, 3, -3434506023356564417641035937051422344001198489600000⟩, + ⟨7, 2, 1, 3, 4, 3, 25699816854638077833645914378403592479585180057600000⟩, + ⟨7, 2, 2, 3, 5, 3, 23593325303886783256886628836690298987087082291200000⟩, + ⟨7, 2, 3, 3, 6, 3, -33826270989950546063315354650701495800869316198400000⟩, + ⟨7, 2, 4, 3, 7, 3, -20705399099954043377917531958590927564119107174400000⟩, + ⟨7, 2, 5, 3, 8, 3, 4280888132235276631942157363888952294217089024000000⟩, + ⟨7, 2, 1, 4, 3, 3, -80993724496808907311237051253398297807024239411200000⟩, + ⟨7, 2, 2, 4, 4, 3, 2980509585150805460828615746899843148840697856000000⟩, + ⟨7, 2, 3, 4, 5, 3, -63279422843902440727896095528523865208136715468800000⟩, + ⟨7, 2, 4, 4, 6, 3, 24551092954306811018410553991590433542763026841600000⟩, + ⟨7, 2, 5, 4, 7, 3, 2557969247748892268318332434624843119245393920000000⟩, + ⟨7, 2, 6, 4, 8, 3, -1941760935373401058559423877474754798584594432000000⟩, + ⟨7, 2, 1, 5, 2, 3, -16404274497230238962370235851774304680677474304000000⟩, + ⟨7, 2, 2, 5, 3, 3, 49701190676645577928348975356214279125126768230400000⟩, + ⟨7, 2, 3, 5, 4, 3, 64779092422279320058941419803374551343570301747200000⟩, + ⟨7, 2, 4, 5, 5, 3, 12737231416881800257144406640379719530032241049600000⟩, + ⟨7, 2, 5, 5, 6, 3, -5681818501953654649104930050737927520161628160000000⟩, + ⟨7, 2, 6, 5, 7, 3, 2353645808117867876489045099431321162014837964800000⟩, + ⟨7, 2, 7, 5, 8, 3, 160197943874123699953214874129322141529250201600000⟩, + ⟨7, 2, 1, 6, 1, 3, -361955852741532780716268209254896695568359856537600000⟩, + ⟨7, 2, 2, 6, 2, 3, -33260869480986224709570496446653724176688139468800000⟩, + ⟨7, 2, 3, 6, 3, 3, 86171573834179745628195307621576081389692701900800000⟩, + ⟨7, 2, 4, 6, 4, 3, -24720730477291370112337863317207630120045720371200000⟩, + ⟨7, 2, 5, 6, 5, 3, 11516907367900736353398451246283971184792961024000000⟩, + ⟨7, 2, 6, 6, 6, 3, -1532587773616161674905940679805777687182783283200000⟩, + ⟨7, 2, 7, 6, 7, 3, -529355077962326153296602931076539856346257817600000⟩, + ⟨7, 2, 8, 6, 8, 3, 897687537190917672342922561879077088107115315200000⟩, + ⟨7, 2, 1, 7, 0, 3, 2267159994694896555423211636401282576565046712729600000⟩, + ⟨7, 2, 2, 7, 1, 3, 490576655876806805843973856178256963760978447564800000⟩, + ⟨7, 2, 3, 7, 2, 3, 317195394641777221973240830046650751324582943129600000⟩, + ⟨7, 2, 4, 7, 3, 3, 89974759050099869146267878190776000777709997260800000⟩, + ⟨7, 2, 5, 7, 4, 3, 34827466102083848108733551939106884062153801728000000⟩, + ⟨7, 2, 6, 7, 5, 3, 1583837675613384198097646494044799445652996096000000⟩, + ⟨7, 2, 7, 7, 6, 3, 1325707287360949133870292869789444711578494566400000⟩, + ⟨7, 2, 8, 7, 7, 3, 679726813487417187438646454573609958239738265600000⟩ +] + +def collectedFourData_10_6_45 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 6, 4, -51995190218142894496588310892962018121203318784000000⟩, + ⟨7, 3, 1, 0, 7, 4, 137992134067811524574079201909823266684994270003200000⟩, + ⟨7, 3, 2, 0, 8, 4, -41946722937313700558189892954608515635764998963200000⟩, + ⟨7, 3, 0, 1, 5, 4, -79400873738812239792681407813516337345433750732800000⟩, + ⟨7, 3, 1, 1, 6, 4, 67410115606656200412933251785235244062514295603200000⟩, + ⟨7, 3, 2, 1, 7, 4, -19228895679870816718683581216507519110993674240000000⟩, + ⟨7, 3, 3, 1, 8, 4, -243201946429413739760706053399825467938806169600000⟩, + ⟨7, 3, 0, 2, 4, 4, -22625271543588881254010729176080809437012426752000000⟩, + ⟨7, 3, 1, 2, 5, 4, 40109148193007081898483565859226750558830749286400000⟩, + ⟨7, 3, 2, 2, 6, 4, -40507251266353469299590830623446212385721181798400000⟩, + ⟨7, 3, 3, 2, 7, 4, 8738244649062696729781173102546441069057068236800000⟩, + ⟨7, 3, 4, 2, 8, 4, -730666784088902529247942304067160620018538905600000⟩, + ⟨7, 3, 0, 3, 3, 4, -4024146357323953550232447598958479332298928947200000⟩, + ⟨7, 3, 1, 3, 4, 4, 21869814646008765032170206919363742791142631014400000⟩, + ⟨7, 3, 2, 3, 5, 4, 10038625064868361516461177553658330491551901286400000⟩, + ⟨7, 3, 3, 3, 6, 4, -9595065481077852868098189796734929893319717683200000⟩, + ⟨7, 3, 4, 3, 7, 4, -4404926726218187691595164587170039468044740198400000⟩, + ⟨7, 3, 5, 3, 8, 4, 728582857238440123161003533638444235789382451200000⟩, + ⟨7, 3, 0, 4, 2, 4, 29826017284885156271678698351541759051639763763200000⟩, + ⟨7, 3, 1, 4, 3, 4, -68923360514743840415949442251119242703371291852800000⟩, + ⟨7, 3, 2, 4, 4, 4, 1268164527136248873362506466687599355187167232000000⟩, + ⟨7, 3, 3, 4, 5, 4, -17949664211359329811757635417770343209151915622400000⟩, + ⟨7, 3, 4, 4, 6, 4, 5223070803427940186271973409732780197420833177600000⟩, + ⟨7, 3, 5, 4, 7, 4, 435351844216452216858544390906364524228509696000000⟩, + ⟨7, 3, 6, 4, 8, 4, -275397239752527669261836151719433977638944768000000⟩, + ⟨7, 3, 0, 5, 1, 4, 22989578270496013039248954631488112112891540275200000⟩, + ⟨7, 3, 1, 5, 2, 4, -13959571956713316780987269819669819549942808576000000⟩, + ⟨7, 3, 2, 5, 3, 4, 21147151241041110299431145973335673065773518028800000⟩, + ⟨7, 3, 3, 5, 4, 4, 18375056292229891351852632687004888570921589145600000⟩, + ⟨7, 3, 4, 5, 5, 4, 2709755596373562674758117044695609063815879065600000⟩, + ⟨7, 3, 5, 5, 6, 4, -967013252995724782469563724348204072627601408000000⟩, + ⟨7, 3, 6, 5, 7, 4, 333814295623431925029765853936623545299972915200000⟩, + ⟨7, 3, 7, 5, 8, 4, 19474843281208162391076608295391829706355507200000⟩, + ⟨7, 3, 0, 6, 0, 4, -530287045040631939421510399330983506755056146841600000⟩, + ⟨7, 3, 1, 6, 1, 4, -308014156453678065156883566222457990689749100134400000⟩, + ⟨7, 3, 2, 6, 2, 4, -14152027904101232426143167026467910313116801433600000⟩, + ⟨7, 3, 3, 6, 3, 4, 24443187775327948180036597081328136830717421158400000⟩, + ⟨7, 3, 4, 6, 4, 4, -5259159982639452945496448427324806292133065523200000⟩, + ⟨7, 3, 5, 6, 5, 4, 1960112251817747987618445974021867209502176051200000⟩, + ⟨7, 3, 6, 6, 6, 4, -217364782061185321224975261843811618339474636800000⟩, + ⟨7, 3, 7, 6, 7, 4, -64352306491077443022549952969218613983785779200000⟩, + ⟨7, 3, 8, 6, 8, 4, 95488326626218792198083789424332567198931353600000⟩, + ⟨7, 3, 1, 7, 0, 4, 1929288801444334460105607720362930803897901934182400000⟩, + ⟨7, 3, 2, 7, 1, 4, 208733404490163668643326950423931464079298369945600000⟩, + ⟨7, 3, 3, 7, 2, 4, 89974759050099869146267878190776000777709997260800000⟩, + ⟨7, 3, 4, 7, 3, 4, 19141491497534396709180919744120096156411546828800000⟩, + ⟨7, 3, 5, 7, 4, 4, 5927437012884919179883124431758245395385706086400000⟩, + ⟨7, 3, 6, 7, 5, 4, 224633484037058832576326292526719098897301504000000⟩, + ⟨7, 3, 7, 7, 6, 4, 161162752990117338285510760621661196636703948800000⟩, + ⟨7, 3, 8, 7, 7, 4, 72303528002618768885109120820115889676143820800000⟩ +] + +def collectedFourData_10_6_46 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 6, 5, -80505276987091341080482030835014423522584821760000000⟩, + ⟨7, 4, 1, 0, 7, 5, 106828102066377941697082714675246589217576321024000000⟩, + ⟨7, 4, 2, 0, 8, 5, -21649005959983905504134046094281648962657058816000000⟩, + ⟨7, 4, 0, 1, 5, 5, -122938089206753078410778029223770114671343828992000000⟩, + ⟨7, 4, 1, 1, 6, 5, 52186269594144943632545202170611921303344513024000000⟩, + ⟨7, 4, 2, 1, 7, 5, -9924171616446454647989952661766631725413171200000000⟩, + ⟨7, 4, 3, 1, 8, 5, -94138707729296413471482127683362253371867136000000⟩, + ⟨7, 4, 0, 2, 4, 5, -35031197018089016136884683478037638461815521280000000⟩, + ⟨7, 4, 1, 2, 5, 5, 31050930590380086369785713811749058673427611648000000⟩, + ⟨7, 4, 2, 2, 6, 5, -20906084258319223614158914122980848535435476992000000⟩, + ⟨7, 4, 3, 2, 7, 5, 3382403270871652798159279058368025453697957888000000⟩, + ⟨7, 4, 4, 2, 8, 5, -226261435304141557680591252005213718295923916800000⟩, + ⟨7, 4, 0, 3, 3, 5, -6230672794421609546794708688644465211587166208000000⟩, + ⟨7, 4, 1, 3, 4, 5, 16930753386482821737682041109087902342586564608000000⟩, + ⟨7, 4, 2, 3, 5, 5, 5181006730469913413545244685791824476930834432000000⟩, + ⟨7, 4, 3, 3, 6, 5, -3714061824866235650083251212950691264763789312000000⟩, + ⟨7, 4, 4, 3, 7, 5, -1364048654170699472781151296154068391092761395200000⟩, + ⟨7, 4, 5, 3, 8, 5, 188013431255033029577807907087047952200368128000000⟩, + ⟨7, 4, 0, 4, 2, 5, 46180267306794269928646902315515143789580648448000000⟩, + ⟨7, 4, 1, 4, 3, 5, -53357764495536730632301325274116382093157072896000000⟩, + ⟨7, 4, 2, 4, 4, 5, 654508850363389790995668012583188068208476160000000⟩, + ⟨7, 4, 3, 4, 5, 5, -6947963278421369449569372102984415771921219584000000⟩, + ⟨7, 4, 4, 4, 6, 5, 1617398686259386223392216533038446272286870732800000⟩, + ⟨7, 4, 5, 4, 7, 5, 112344111889465502242253464516978935060234240000000⟩, + ⟨7, 4, 6, 4, 8, 5, -60914785647179915839305762003436956926607360000000⟩, + ⟨7, 4, 0, 5, 1, 5, 35595260998523989775658300806200218373092016128000000⟩, + ⟨7, 4, 1, 5, 2, 5, -10806953511291313530195168271019135520284344320000000⟩, + ⟨7, 4, 2, 5, 3, 5, 10914197133782075668566181578022136663343366144000000⟩, + ⟨7, 4, 3, 5, 4, 5, 7112624217033774085527680564467980860229943296000000⟩, + ⟨7, 4, 4, 5, 5, 5, 839114633250268239431910932431830874153864396800000⟩, + ⟨7, 4, 5, 5, 6, 5, -249541253899303476095541833383291020399083520000000⟩, + ⟨7, 4, 6, 5, 7, 5, 73835984275434523395522446627546908122415104000000⟩, + ⟨7, 4, 7, 5, 8, 5, 3769165104637864609294876158397179626520576000000⟩, + ⟨7, 4, 0, 6, 0, 5, -821054894973072790277118324360525028888751898624000000⟩, + ⟨7, 4, 1, 6, 1, 5, -238452488366858632420750813402057809790928683008000000⟩, + ⟨7, 4, 2, 6, 2, 5, -7303963575405033839764674529093872531347079168000000⟩, + ⟨7, 4, 3, 6, 3, 5, 9461479004329264857411404042348353531982905344000000⟩, + ⟨7, 4, 4, 6, 4, 5, -1628574217520913682684663948681639363241154969600000⟩, + ⟨7, 4, 5, 6, 5, 5, 505814028491035155510367926149680101618352128000000⟩, + ⟨7, 4, 6, 6, 6, 5, -48078655829670693378368189042790553601703936000000⟩, + ⟨7, 4, 7, 6, 7, 5, -12454758404303958729739952528760306281742336000000⟩, + ⟨7, 4, 8, 6, 8, 5, 16427404474712840507572157576788921345376256000000⟩, + ⟨7, 4, 1, 7, 0, 5, 1493579778213542278951262747801592514921384378368000000⟩, + ⟨7, 4, 2, 7, 1, 5, 107728814110423006458842359002084665347673161728000000⟩, + ⟨7, 4, 3, 7, 2, 5, 34827466102083848108733551939106884062153801728000000⟩, + ⟨7, 4, 4, 7, 3, 5, 5927437012884919179883124431758245395385706086400000⟩, + ⟨7, 4, 5, 7, 4, 5, 1529596476596566298195076826785221445697929216000000⟩, + ⟨7, 4, 6, 7, 5, 5, 49686411314770845657760037760100288513966080000000⟩, + ⟨7, 4, 7, 7, 6, 5, 31191471785750749397874845823810046896635904000000⟩, + ⟨7, 4, 8, 7, 7, 5, 12438790597903457922974522609362872846778368000000⟩ +] + +def collectedFourData_10_6_47 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 6, 6, -9152782634552418380204384340855994157157580800000000⟩, + ⟨7, 5, 1, 0, 7, 6, 8096979759741870272219652885573169933744865280000000⟩, + ⟨7, 5, 2, 0, 8, 6, -1230656257711123345238046182974418359827824640000000⟩, + ⟨7, 5, 0, 1, 5, 6, -13977041631656649474495748928854741573026447360000000⟩, + ⟨7, 5, 1, 1, 6, 6, 3955430832026490916966334875528716436667105280000000⟩, + ⟨7, 5, 2, 1, 7, 6, -564148022544496694971396608380114722357248000000000⟩, + ⟨7, 5, 3, 1, 8, 6, -4281116277543239374246845507778001818877952000000⟩, + ⟨7, 5, 0, 2, 4, 6, -3982756705329535798575035064916869531461222400000000⟩, + ⟨7, 5, 1, 2, 5, 6, 2353488938287394549537309584991919895279042560000000⟩, + ⟨7, 5, 2, 2, 6, 6, -1188424238244132688424862210338697864995143680000000⟩, + ⟨7, 5, 3, 2, 7, 6, 153820485211926686276982735687075906994569216000000⟩, + ⟨7, 5, 4, 2, 8, 6, -8574683190240706477528102014423236081614848000000⟩, + ⟨7, 5, 0, 3, 3, 6, -708375846759765577845979867955449435929968640000000⟩, + ⟨7, 5, 1, 3, 4, 6, 1283257540252400442775955187097136321538293760000000⟩, + ⟨7, 5, 2, 3, 5, 6, 294518758315358072054336182454628327389921280000000⟩, + ⟨7, 5, 3, 3, 6, 6, -168903216517051581994435021905165558359261184000000⟩, + ⟨7, 5, 4, 3, 7, 6, -51693674840636278640483608264020650436329472000000⟩, + ⟨7, 5, 5, 3, 8, 6, 6107305306315017398619123992245475884400640000000⟩, + ⟨7, 5, 0, 4, 2, 6, 5250313575498782267941034472162236280172707840000000⟩, + ⟨7, 5, 1, 4, 3, 6, -4044223671379905729049626658582165133060997120000000⟩, + ⟨7, 5, 2, 4, 4, 6, 37206115325380865978862486000587648689766400000000⟩, + ⟨7, 5, 3, 4, 5, 6, -315970331487412349116676421793743644380889088000000⟩, + ⟨7, 5, 4, 4, 6, 6, 61294940997538632852017255855707789467844608000000⟩, + ⟨7, 5, 5, 4, 7, 6, 3649312637377940512338122367831041585971200000000⟩, + ⟨7, 5, 6, 4, 8, 6, -1731376541777473260981176258829711782707200000000⟩, + ⟨7, 5, 0, 5, 1, 6, 4046886104023854511770410079639129066559242240000000⟩, + ⟨7, 5, 1, 5, 2, 6, -819107352398963720881325159426775339918950400000000⟩, + ⟨7, 5, 2, 5, 3, 6, 620426869732900352068685817069349373749493760000000⟩, + ⟨7, 5, 3, 5, 4, 6, 323458564984266855030732247695673680117891072000000⟩, + ⟨7, 5, 4, 5, 5, 6, 31800125950515299358155946653371267597467648000000⟩, + ⟨7, 5, 5, 5, 6, 6, -8105934846837819923432417861136440465817600000000⟩, + ⟨7, 5, 6, 5, 7, 6, 2098634834799850382755149480643526739886080000000⟩, + ⟨7, 5, 7, 5, 8, 6, 95227294981536982986915705191456298762240000000⟩, + ⟨7, 5, 0, 6, 0, 6, -93347135317959177738620326752503485580621905920000000⟩, + ⟨7, 5, 1, 6, 1, 6, -18073380829763916488885797760041467248388341760000000⟩, + ⟨7, 5, 2, 6, 2, 6, -415200055687591378492179413274051214017822720000000⟩, + ⟨7, 5, 3, 6, 3, 6, 430276692256548294414073749878118385773969408000000⟩, + ⟨7, 5, 4, 6, 4, 6, -61718462752014460584502601594185574730694656000000⟩, + ⟨7, 5, 5, 6, 5, 6, 16430532008224167998342398992941142654320640000000⟩, + ⟨7, 5, 6, 6, 6, 6, -1366536153403313281842355935996134786334720000000⟩, + ⟨7, 5, 7, 6, 7, 6, -314667285609496294996758671457713274224640000000⟩, + ⟨7, 5, 8, 6, 8, 6, 373531942337219362902837795934770504400896000000⟩, + ⟨7, 5, 1, 7, 0, 6, 113205093040410681295778813131335772341754920960000000⟩, + ⟨7, 5, 2, 7, 1, 6, 6123936566226017989225307202010837932960645120000000⟩, + ⟨7, 5, 3, 7, 2, 6, 1583837675613384198097646494044799445652996096000000⟩, + ⟨7, 5, 4, 7, 3, 6, 224633484037058832576326292526719098897301504000000⟩, + ⟨7, 5, 5, 7, 4, 6, 49686411314770845657760037760100288513966080000000⟩, + ⟨7, 5, 6, 7, 5, 6, 1412233271143156060224609395384025455001600000000⟩, + ⟨7, 5, 7, 7, 6, 6, 788047061402303432821893678211196214312960000000⟩, + ⟨7, 5, 8, 7, 7, 6, 282837475604437521656927199711206244876288000000⟩ +] + +def collectedFourData_10_6_48 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 6, 7, -15322164417584903361203523905511218128292413440000000⟩, + ⟨7, 6, 1, 0, 7, 7, 10166027653951454346383110329785011029544009728000000⟩, + ⟨7, 6, 2, 0, 8, 7, -1236103922166507341730886550196345435808019251200000⟩, + ⟨7, 6, 0, 1, 5, 7, -23398188125129113034041357576195008772700110848000000⟩, + ⟨7, 6, 1, 1, 6, 7, 4966175094274341371526045385736774396021833728000000⟩, + ⟨7, 6, 2, 1, 7, 7, -566645299189160073497267707402206626803875840000000⟩, + ⟨7, 6, 3, 1, 8, 7, -3583389342585664727307391023198423804071116800000⟩, + ⟨7, 6, 0, 2, 4, 7, -6667311517256638264351493573637009320517304320000000⟩, + ⟨7, 6, 1, 2, 5, 7, 2954883714648342416049294702666571532684230656000000⟩, + ⟨7, 6, 2, 2, 6, 7, -1193684957019203560278271190926578250284426854400000⟩, + ⟨7, 6, 3, 2, 7, 7, 128751160128751446139324954073971459352847974400000⟩, + ⟨7, 6, 4, 2, 8, 7, -6151885836972072195809749831507482850728345600000⟩, + ⟨7, 6, 0, 3, 3, 7, -1185852611917711310400772599010188391404797952000000⟩, + ⟨7, 6, 1, 3, 4, 7, 1611172564146747478158721968810457200932683776000000⟩, + ⟨7, 6, 2, 3, 5, 7, 295822484974256695406514469133597502794524262400000⟩, + ⟨7, 6, 3, 3, 6, 7, -141375740988508728457883044215685298116991385600000⟩, + ⟨7, 6, 4, 3, 7, 7, -37087502716729836600376488091917596311840358400000⟩, + ⟨7, 6, 5, 3, 8, 7, 3833962568599914840976808101437638109560832000000⟩, + ⟨7, 6, 0, 4, 2, 7, 8789257984121713065864056923384064214420160512000000⟩, + ⟨7, 6, 1, 4, 3, 7, -5077657460184128561770133266382121800420032512000000⟩, + ⟨7, 6, 2, 4, 4, 7, 37370813169080916040170430878562746328154112000000⟩, + ⟨7, 6, 3, 4, 5, 7, -264474180335742445610207518752436811233178419200000⟩, + ⟨7, 6, 4, 4, 6, 7, 43975908034709728823637265920154664433195417600000⟩, + ⟨7, 6, 5, 4, 7, 7, 2290916754785204407335870298818882368962560000000⟩, + ⟨7, 6, 6, 4, 8, 7, -966133728618487099322519548273554169528320000000⟩, + ⟨7, 6, 0, 5, 1, 7, 6774666977342166262793538460823708596470546432000000⟩, + ⟨7, 6, 1, 5, 2, 7, -1028416550754511112907703085756064887514071040000000⟩, + ⟨7, 6, 2, 5, 3, 7, 623173272218753920041040140780363704865443020800000⟩, + ⟨7, 6, 3, 5, 4, 7, 270741997972038918460112768274096508491320524800000⟩, + ⟨7, 6, 4, 5, 5, 7, 22814923899644556467342593953580320802052505600000⟩, + ⟨7, 6, 5, 5, 6, 7, -5088635531967112148162922116512446551162880000000⟩, + ⟨7, 6, 6, 5, 7, 7, 1171069290260960683602050264955004542517248000000⟩, + ⟨7, 6, 7, 5, 8, 7, 47824415667017044670746154973180366264729600000⟩, + ⟨7, 6, 0, 6, 0, 7, -156267248153900848696510945840469733832031993856000000⟩, + ⟨7, 6, 1, 6, 1, 7, -22691731332873366064055855531685537769718808576000000⟩, + ⟨7, 6, 2, 6, 2, 7, -417037994243601780743841922944280621835983257600000⟩, + ⟨7, 6, 3, 6, 3, 7, 360151141299981721779975439222230252327744307200000⟩, + ⟨7, 6, 4, 6, 4, 7, -44279762699098357759997262287939175200273203200000⟩, + ⟨7, 6, 5, 6, 5, 7, 10314539971757715939804747770768992430456832000000⟩, + ⟨7, 6, 6, 6, 6, 7, -762547393546235949296572141384925794271232000000⟩, + ⟨7, 6, 7, 6, 7, 7, -158030101209093822332159823755436208265625600000⟩, + ⟨7, 6, 8, 6, 8, 7, 170538832463060173576085966209470792361574400000⟩, + ⟨7, 6, 1, 7, 0, 7, 142132763149410540430434065693874014242782314496000000⟩, + ⟨7, 6, 2, 7, 1, 7, 6151044990166350150347469202690073211468093849600000⟩, + ⟨7, 6, 3, 7, 2, 7, 1325707287360949133870292869789444711578494566400000⟩, + ⟨7, 6, 4, 7, 3, 7, 161162752990117338285510760621661196636703948800000⟩, + ⟨7, 6, 5, 7, 4, 7, 31191471785750749397874845823810046896635904000000⟩, + ⟨7, 6, 6, 7, 5, 7, 788047061402303432821893678211196214312960000000⟩, + ⟨7, 6, 7, 7, 6, 7, 395767728538147908017957276726388272293478400000⟩, + ⟨7, 6, 8, 7, 7, 7, 129131587956229905731404028402299382739763200000⟩ +] + +def collectedFourData_10_6_49 : List CollectedFourTerm := [ + ⟨7, 7, 0, 0, 6, 8, -13748171006926311585290074820154025478014894080000000⟩, + ⟨7, 7, 1, 0, 7, 8, 7297365194032883135393764873880713062951734476800000⟩, + ⟨7, 7, 2, 0, 8, 8, -739415469909009719732233253470521567200516505600000⟩, + ⟨7, 7, 0, 1, 5, 8, -20994572491815846603097687175221200892446375936000000⟩, + ⟨7, 7, 1, 1, 6, 8, 3564813564750077456791629874769511957467548876800000⟩, + ⟨7, 7, 2, 1, 7, 8, -338957180426489530215382058649826245916753920000000⟩, + ⟨7, 7, 3, 1, 8, 8, -1837302881671006260104647905997821813404467200000⟩, + ⟨7, 7, 0, 2, 4, 8, -5982401467412374134021913143043851364325130240000000⟩, + ⟨7, 7, 1, 2, 5, 8, 2121070914390843000931352748166873623354251673600000⟩, + ⟨7, 7, 2, 2, 6, 8, -714041196366964823257660943741926025983111987200000⟩, + ⟨7, 7, 3, 2, 7, 8, 66014282822069620482631284045317238924351897600000⟩, + ⟨7, 7, 4, 2, 8, 8, -2759961849930050485983645856801433205709209600000⟩, + ⟨7, 7, 0, 3, 3, 8, -1064034039403987987000445444225097863647985664000000⟩, + ⟨7, 7, 1, 3, 4, 8, 1156529865095853127926266129566554050396789145600000⟩, + ⟨7, 7, 2, 3, 5, 8, 176955770315423808353693874354715993415299891200000⟩, + ⟨7, 7, 3, 3, 6, 8, -72487254798032396895203694314540204779005542400000⟩, + ⟨7, 7, 4, 3, 7, 8, -16638815368155886433790614499978761757681254400000⟩, + ⟨7, 7, 5, 3, 8, 8, 1528938995844391252646203642142830985478144000000⟩, + ⟨7, 7, 0, 4, 2, 8, 7886367649926581028531331810231699311987523584000000⟩, + ⟨7, 7, 1, 4, 3, 8, -3644837696537905849369132131609870121909302067200000⟩, + ⟨7, 7, 2, 4, 4, 8, 22354558451579426454116471463278931508985856000000⟩, + ⟨7, 7, 3, 4, 5, 8, -135603231243583618323625170507174662757993676800000⟩, + ⟨7, 7, 4, 4, 6, 8, 19729206898216734155678177461599976283543961600000⟩, + ⟨7, 7, 5, 4, 7, 8, 913590547625895706868577440514126139883520000000⟩, + ⟨7, 7, 6, 4, 8, 8, -346754449426536343185751655297493076279296000000⟩, + ⟨7, 7, 0, 5, 1, 8, 6078728669206996986403650540669938742564225024000000⟩, + ⟨7, 7, 1, 5, 2, 8, -738216675962541957250514393624184364229197824000000⟩, + ⟨7, 7, 2, 5, 3, 8, 372771212556913170469069595089664980287907430400000⟩, + ⟨7, 7, 3, 5, 4, 8, 138816914799567617648963017190550296549602099200000⟩, + ⟨7, 7, 4, 5, 5, 8, 10235612500096231833342139880856595411343769600000⟩, + ⟨7, 7, 5, 5, 6, 8, -2029287756793374699961160101711993330728960000000⟩, + ⟨7, 7, 6, 5, 7, 8, 420307743075510540400643899444013369288294400000⟩, + ⟨7, 7, 7, 5, 8, 8, 15604209976825947930784069700211819990220800000⟩, + ⟨7, 7, 0, 6, 0, 8, -140214449594077015010903754081252288915667156992000000⟩, + ⟨7, 7, 1, 6, 1, 8, -16288550066701032712797617543955949109647088025600000⟩, + ⟨7, 7, 2, 6, 2, 8, -249464740750176173605826970438329441356401868800000⟩, + ⟨7, 7, 3, 6, 3, 8, 184659456867751559723935799676374719155457228800000⟩, + ⟨7, 7, 4, 6, 4, 8, -19865527256536108163321741129885506780476211200000⟩, + ⟨7, 7, 5, 6, 5, 8, 4113316732973496825745051998043636072710144000000⟩, + ⟨7, 7, 6, 6, 6, 8, -273685405838035794758724351540644156119449600000⟩, + ⟨7, 7, 7, 6, 7, 8, -51562258472641031918122688294009720065228800000⟩, + ⟨7, 7, 8, 6, 8, 8, 51006654328219805969977103891051371403673600000⟩, + ⟨7, 7, 1, 7, 0, 8, 102025561413368644748795153096135270814981921177600000⟩, + ⟨7, 7, 2, 7, 1, 8, 3679446153575635260329714799564161495654517964800000⟩, + ⟨7, 7, 3, 7, 2, 8, 679726813487417187438646454573609958239738265600000⟩, + ⟨7, 7, 4, 7, 3, 8, 72303528002618768885109120820115889676143820800000⟩, + ⟨7, 7, 5, 7, 4, 8, 12438790597903457922974522609362872846778368000000⟩, + ⟨7, 7, 6, 7, 5, 8, 282837475604437521656927199711206244876288000000⟩, + ⟨7, 7, 7, 7, 6, 8, 129131587956229905731404028402299382739763200000⟩, + ⟨7, 7, 8, 7, 7, 8, 38622114239958954133404287059946290072780800000⟩ +] + +def collectedFourData_10_6 : List (List CollectedFourTerm) := [ + collectedFourData_10_6_0, + collectedFourData_10_6_1, + collectedFourData_10_6_2, + collectedFourData_10_6_3, + collectedFourData_10_6_4, + collectedFourData_10_6_5, + collectedFourData_10_6_6, + collectedFourData_10_6_7, + collectedFourData_10_6_8, + collectedFourData_10_6_9, + collectedFourData_10_6_10, + collectedFourData_10_6_11, + collectedFourData_10_6_12, + collectedFourData_10_6_13, + collectedFourData_10_6_14, + collectedFourData_10_6_15, + collectedFourData_10_6_16, + collectedFourData_10_6_17, + collectedFourData_10_6_18, + collectedFourData_10_6_19, + collectedFourData_10_6_20, + collectedFourData_10_6_21, + collectedFourData_10_6_22, + collectedFourData_10_6_23, + collectedFourData_10_6_24, + collectedFourData_10_6_25, + collectedFourData_10_6_26, + collectedFourData_10_6_27, + collectedFourData_10_6_28, + collectedFourData_10_6_29, + collectedFourData_10_6_30, + collectedFourData_10_6_31, + collectedFourData_10_6_32, + collectedFourData_10_6_33, + collectedFourData_10_6_34, + collectedFourData_10_6_35, + collectedFourData_10_6_36, + collectedFourData_10_6_37, + collectedFourData_10_6_38, + collectedFourData_10_6_39, + collectedFourData_10_6_40, + collectedFourData_10_6_41, + collectedFourData_10_6_42, + collectedFourData_10_6_43, + collectedFourData_10_6_44, + collectedFourData_10_6_45, + collectedFourData_10_6_46, + collectedFourData_10_6_47, + collectedFourData_10_6_48, + collectedFourData_10_6_49 +] + +theorem collectedFourChecked_10_6 : collectNumericRowParts 10 6 = collectedFourData_10_6 := by + decide +kernel + +def collectedFourData_10_7_0 : List CollectedFourTerm := [ + ⟨0, 7, 3, 2, 8, 0, -3086177606496240931993294916182592967552270336000000⟩, + ⟨0, 7, 3, 3, 7, 0, -7705844233072155772655338150199114312226491596800000⟩, + ⟨0, 7, 4, 3, 8, 0, -4476483206440535204315781715193462300604786278400000⟩, + ⟨0, 7, 3, 4, 6, 0, -17700420917719596259902065832823926110635111219200000⟩, + ⟨0, 7, 4, 4, 7, 0, -10200945527339497103013676689450706696499783270400000⟩, + ⟨0, 7, 5, 4, 8, 0, 22161512634954353309214212361197164140441894912000000⟩, + ⟨0, 7, 3, 5, 5, 0, -5817278317300779223675652810616818384205407846400000⟩, + ⟨0, 7, 4, 5, 6, 0, 9357110990071021481897870172996494113622930227200000⟩, + ⟨0, 7, 5, 5, 7, 0, -753900063083553400339691426442153115986690048000000⟩, + ⟨0, 7, 6, 5, 8, 0, 10405251888608135423669545213031291404909805568000000⟩, + ⟨0, 7, 3, 6, 4, 0, 27445974996411339039852459194825464997440231833600000⟩, + ⟨0, 7, 4, 6, 5, 0, -15182695307648243970376619465547846713677027737600000⟩, + ⟨0, 7, 5, 6, 6, 0, 7170934939649580284240602941873916275308101632000000⟩, + ⟨0, 7, 6, 6, 7, 0, 9826686016331873681240417094293591777630748672000000⟩, + ⟨0, 7, 7, 6, 8, 0, 2695093892652679868106845199547355897851281408000000⟩, + ⟨0, 7, 3, 7, 3, 0, -48914425501456750088885123375909740575718165708800000⟩, + ⟨0, 7, 4, 7, 4, 0, -62789757576380036488768176278326615203764187955200000⟩, + ⟨0, 7, 5, 7, 5, 0, -8109612860832684741880630103065145504811712512000000⟩, + ⟨0, 7, 6, 7, 6, 0, -10635617304142404101492843582405000209241210880000000⟩, + ⟨0, 7, 7, 7, 7, 0, -952534151122224341456444594263573156482514944000000⟩, + ⟨0, 7, 8, 7, 8, 0, -5111760809879533898662842271341857140994211840000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1025.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1025.lean new file mode 100644 index 0000000000000000000000000000000000000000..fd2e9bc62d9b3e1e658aac24f12307d9b323869b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1025.lean @@ -0,0 +1,651 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1025. -/ +namespace LaughlinFock +def collectedFourData_10_7_1 : List CollectedFourTerm := [ + ⟨0, 8, 2, 1, 8, 1, -694499489856916957923482600531022841388413747200000⟩, + ⟨0, 8, 2, 2, 7, 1, -844194112741415445229062317587529416269260390400000⟩, + ⟨0, 8, 3, 2, 8, 1, -355116043312283124146546546335249845121449984000000⟩, + ⟨0, 8, 2, 3, 6, 1, -335358548538201652359272867352879218835849216000000⟩, + ⟨0, 8, 3, 3, 7, 1, -886685493624617133267533114222785770950964019200000⟩, + ⟨0, 8, 4, 3, 8, 1, -257546908654717667193454315588661607299599564800000⟩, + ⟨0, 8, 2, 4, 5, 1, -155746959258758723397223243497550526725855641600000⟩, + ⟨0, 8, 3, 4, 6, 1, -2036727707449979693264236063520984010771451084800000⟩, + ⟨0, 8, 4, 4, 7, 1, -586894190095819752314232164808046497370000588800000⟩, + ⟨0, 8, 5, 4, 8, 1, 850016826010965532271208814806854437674418176000000⟩, + ⟨0, 8, 2, 5, 4, 1, 825806715698593174339292850182716135105049395200000⟩, + ⟨0, 8, 3, 5, 5, 1, -669374586393787064852509065953679405745805721600000⟩, + ⟨0, 8, 4, 5, 6, 1, 538345593693871656634441694697222644682876518400000⟩, + ⟨0, 8, 5, 5, 7, 1, -28916245443508223803321025195675091053051904000000⟩, + ⟨0, 8, 6, 5, 8, 1, 299324305945018456138582913924968998814875648000000⟩, + ⟨0, 8, 2, 6, 3, 1, 416687414491982894945606569453500489850159104000000⟩, + ⟨0, 8, 3, 6, 4, 1, 3158115730299373588269343707440258120331716198400000⟩, + ⟨0, 8, 4, 6, 5, 1, -873510758602962264574486143060116267752174387200000⟩, + ⟨0, 8, 5, 6, 6, 1, 275045095401928813437233173160609158042484736000000⟩, + ⟨0, 8, 6, 6, 7, 1, 282680900286365861212363439626726362675412992000000⟩, + ⟨0, 8, 7, 6, 8, 1, 62023072003330896666069592355841721059665510400000⟩, + ⟨0, 8, 2, 7, 2, 1, -2015347644614573190772509750888503025877804646400000⟩, + ⟨0, 8, 3, 7, 3, 1, -5628417887683198392180142470224211828913943347200000⟩, + ⟨0, 8, 4, 7, 4, 1, -3612502764605341220431854694937274801302431334400000⟩, + ⟨0, 8, 5, 7, 5, 1, -311048595720411345556723384723352336493182976000000⟩, + ⟨0, 8, 6, 7, 6, 1, -305951148702570807203848144577968543031623680000000⟩, + ⟨0, 8, 7, 7, 7, 1, -21920978115733124467058960098612271830479667200000⟩, + ⟨0, 8, 8, 7, 8, 1, -98032177913878975482866755935252613599068160000000⟩ +] + +def collectedFourData_10_7_2 : List CollectedFourTerm := [ + ⟨1, 6, 3, 2, 8, 0, -388276766929807844763588765766514652739534848000000⟩, + ⟨1, 6, 3, 3, 7, 0, -969484153790747059960924844654153141691246182400000⟩, + ⟨1, 6, 4, 3, 8, 0, -563193259828491877985625398441568853757735731200000⟩, + ⟨1, 6, 3, 4, 6, 0, -2226917269039317776215383899845889015714257305600000⟩, + ⟨1, 6, 4, 4, 7, 0, -1283396697793804716344802868478938778118075187200000⟩, + ⟨1, 6, 5, 4, 8, 0, 2788174101860344146850858710403683661450838016000000⟩, + ⟨1, 6, 3, 5, 5, 0, -731880761696263254382531686913663306317378355200000⟩, + ⟨1, 6, 4, 5, 6, 0, 1177232572545586200208651708641269991897405849600000⟩, + ⟨1, 6, 5, 5, 7, 0, -94849330273830058645375905629128748395659264000000⟩, + ⟨1, 6, 6, 5, 8, 0, 1309100796368559514814373361666111469072154624000000⟩, + ⟨1, 6, 3, 6, 4, 0, 3453020465967767472922381322860796153927879884800000⟩, + ⟨1, 6, 4, 6, 5, 0, -1910158324953552815285964291148520331460529356800000⟩, + ⟨1, 6, 5, 6, 6, 0, 902186390170907731001051188160816601655934976000000⟩, + ⟨1, 6, 6, 6, 7, 0, 1236310531197012694366705294326313119117213696000000⟩, + ⟨1, 6, 7, 6, 8, 0, 339073921412930758401776027697493402655391744000000⟩, + ⟨1, 6, 3, 7, 3, 0, -6153999351805518024005469580427207155141469798400000⟩, + ⟨1, 6, 4, 7, 4, 0, -7899676291067969402865966791573057548041427353600000⟩, + ⟨1, 6, 5, 7, 5, 0, -1020282907901509286487578020540301639801634816000000⟩, + ⟨1, 6, 6, 7, 6, 0, -1338083424771995998176561448104598303502499840000000⟩, + ⟨1, 6, 7, 7, 7, 0, -119839791400682224499072271624604040866824192000000⟩, + ⟨1, 6, 8, 7, 8, 0, -643118515409051231989438128982079183121285120000000⟩ +] + +def collectedFourData_10_7_3 : List CollectedFourTerm := [ + ⟨1, 7, 2, 1, 8, 1, -7283004124613573838119194244371124947577418547200000⟩, + ⟨1, 7, 2, 2, 7, 1, -8852805934151098453714227467293191628453733990400000⟩, + ⟨1, 7, 3, 2, 8, 1, -3723993531935712220480332114333723517972905984000000⟩, + ⟨1, 7, 2, 3, 6, 1, -3516802716055758181255225729947131671757193216000000⟩, + ⟨1, 7, 3, 3, 7, 1, -9298400073171475878189999374139682363465216819200000⟩, + ⟨1, 7, 4, 3, 8, 1, -2700815803911137571571919216891477858299202764800000⟩, + ⟨1, 7, 2, 4, 5, 1, -1633270813361224184198111326302191509382470041600000⟩, + ⟨1, 7, 3, 4, 6, 1, -21358541670245136656500946932884130467282734284800000⟩, + ⟨1, 7, 4, 4, 7, 1, -6154580197114636022784140185988603954676419788800000⟩, + ⟨1, 7, 5, 4, 8, 1, 8913866950577924437508991337833178692820402176000000⟩, + ⟨1, 7, 2, 5, 4, 1, 8659982914898238047088298463818903173050086195200000⟩, + ⟨1, 7, 3, 5, 5, 1, -7019526932441421206577885413946270948945140121600000⟩, + ⟨1, 7, 4, 5, 6, 1, 5645465888171898980331143860429776619399702118400000⟩, + ⟨1, 7, 5, 5, 7, 1, -303235838051942645578279863067522012129787904000000⟩, + ⟨1, 7, 6, 5, 8, 1, 3138922614966630563179627141721617990730907648000000⟩, + ⟨1, 7, 2, 6, 3, 1, 4369673704216692069152145100076300714171695104000000⟩, + ⟨1, 7, 3, 6, 4, 1, 33118195514464667137683822885413370546637661798400000⟩, + ⟨1, 7, 4, 6, 5, 1, -9160240649147749696029039188637502279722939187200000⟩, + ⟨1, 7, 5, 6, 6, 1, 2884313946263197219042565769807724751131508736000000⟩, + ⟨1, 7, 6, 6, 7, 1, 2964388300931991539875050701447546362493140992000000⟩, + ⟨1, 7, 7, 6, 8, 1, 650417020917505990490867285495936070378219110400000⟩, + ⟨1, 7, 2, 7, 2, 1, -21134335478463997922980429409975612063734982246400000⟩, + ⟨1, 7, 3, 7, 3, 1, -59023500074119297922380323555241558231909348147200000⟩, + ⟨1, 7, 4, 7, 4, 1, -37883213622257784488847785636502479231731000934400000⟩, + ⟨1, 7, 5, 7, 5, 1, -3261871662502926217725328794091638644042366976000000⟩, + ⟨1, 7, 6, 7, 6, 1, -3208416291839399366784687430333279961276743680000000⟩, + ⟨1, 7, 7, 7, 7, 1, -229878605188522116255943377691277974020764467200000⟩, + ⟨1, 7, 8, 7, 8, 1, -1028033521289880916288658872276987450396508160000000⟩ +] + +def collectedFourData_10_7_4 : List CollectedFourTerm := [ + ⟨1, 8, 1, 0, 8, 2, -694499489856916957923482600531022841388413747200000⟩, + ⟨1, 8, 1, 1, 7, 2, -7283004124613573838119194244371124947577418547200000⟩, + ⟨1, 8, 2, 1, 8, 2, 4004854754722201678189844611307480703762117427200000⟩, + ⟨1, 8, 1, 2, 6, 2, -8636288876982693765557541923967837022827891916800000⟩, + ⟨1, 8, 2, 2, 7, 2, 4868073851310512609812183075483861427652290150400000⟩, + ⟨1, 8, 3, 2, 8, 2, 1023894326279732911468745977373760614188449792000000⟩, + ⟨1, 8, 1, 3, 5, 2, -7134906935720743122383733418432305899607215308800000⟩, + ⟨1, 8, 2, 3, 6, 2, 1933856391927163546379775480091075435472879616000000⟩, + ⟨1, 8, 3, 3, 7, 2, 2556550916846136585305721821099047446831012249600000⟩, + ⟨1, 8, 4, 3, 8, 2, 495050981200072973775571269934647113250609561600000⟩, + ⟨1, 8, 1, 4, 4, 2, 8036148512681666911947614964378044767940483481600000⟩, + ⟨1, 8, 2, 4, 5, 2, 898120098618748677189689250341685760582326681600000⟩, + ⟨1, 8, 3, 4, 6, 2, 5872429542702753263943153899635896532097984102400000⟩, + ⟨1, 8, 4, 4, 7, 2, 1128115053623399982935468514567293435851151769600000⟩, + ⟨1, 8, 5, 4, 8, 2, -1225412680988877631523290892657808882630918144000000⟩, + ⟨1, 8, 1, 5, 3, 2, 15346995716626192029912179202901756374144358809600000⟩, + ⟨1, 8, 2, 5, 4, 2, -4762042305500330606248098751350229072017044275200000⟩, + ⟨1, 8, 3, 5, 5, 2, 1929985575339775776463370005254258849502514380800000⟩, + ⟨1, 8, 4, 5, 6, 2, -1034796013568867031901579372859995288484236492800000⟩, + ⟨1, 8, 5, 5, 7, 2, 41686626392269455372648963488655069073637376000000⟩, + ⟨1, 8, 6, 5, 8, 2, -345212743097853272719018910558254162561833369600000⟩, + ⟨1, 8, 1, 6, 2, 2, -38243463551890216224091109513902133927255369318400000⟩, + ⟨1, 8, 2, 6, 3, 2, -2402842043130837275196281413287456276379336704000000⟩, + ⟨1, 8, 3, 6, 4, 2, -9105690488741873971149546671778750764353270579200000⟩, + ⟨1, 8, 4, 6, 5, 2, 1679043093135940023116046299850653822817298022400000⟩, + ⟨1, 8, 5, 6, 6, 2, -396514207055203890296920138483269137055350784000000⟩, + ⟨1, 8, 6, 6, 7, 2, -326017790974689697110444639193733366314067558400000⟩, + ⟨1, 8, 7, 6, 8, 2, -59609689770060648648499635822639067009803878400000⟩, + ⟨1, 8, 1, 7, 1, 2, 109436521925019984069387663440111328929081878118400000⟩, + ⟨1, 8, 2, 7, 2, 2, 11621570231269303040407902462696432301167240806400000⟩, + ⟨1, 8, 3, 7, 3, 2, 16228230883002892669803566176820711311952943513600000⟩, + ⟨1, 8, 4, 7, 4, 2, 6943873050339917321374107208096576305527311564800000⟩, + ⟨1, 8, 5, 7, 5, 2, 448418057073446277415083628761606955512889344000000⟩, + ⟨1, 8, 6, 7, 6, 2, 352855525594885108516689930631150254881243136000000⟩, + ⟨1, 8, 7, 7, 7, 2, 21068010060271842368920558981429198691971891200000⟩, + ⟨1, 8, 8, 7, 8, 2, 80757980504175070145360852006372788540538880000000⟩ +] + +def collectedFourData_10_7_5 : List CollectedFourTerm := [ + ⟨2, 5, 3, 2, 8, 0, 1877880595030303318713989741838731057936990208000000⟩, + ⟨2, 5, 3, 3, 7, 0, 4688860201419518322337002347089844387258459750400000⟩, + ⟨2, 5, 4, 3, 8, 0, 2723855208351876016987154416341265835072107315200000⟩, + ⟨2, 5, 3, 4, 6, 0, 10770370731511750900323070049656322939397183897600000⟩, + ⟨2, 5, 4, 4, 7, 0, 6207082060484563668904217682855811459214160691200000⟩, + ⟨2, 5, 5, 4, 8, 0, -13484860510327974437147090075712037668714971136000000⟩, + ⟨2, 5, 3, 5, 5, 0, 3539703627216690747533978208915896849640141619200000⟩, + ⟨2, 5, 4, 5, 6, 0, -5693624733979017403591589991814305798738778521600000⟩, + ⟨2, 5, 5, 5, 7, 0, 458733903089919552876188979521450924776095744000000⟩, + ⟨2, 5, 6, 5, 8, 0, -6331398610011731641237145630643121794060386304000000⟩, + ⟨2, 5, 3, 6, 4, 0, -16700355724491752487719906634892584964651273420800000⟩, + ⟨2, 5, 4, 6, 5, 0, 9238382404977445422460435344527962581156809932800000⟩, + ⟨2, 5, 5, 6, 6, 0, -4363378032115582417756482439653096016677175296000000⟩, + ⟨2, 5, 6, 6, 7, 0, -5979352239703232600055772121945173065430204416000000⟩, + ⟨2, 5, 7, 6, 8, 0, -1639913565617181998328539361770982626845261824000000⟩, + ⟨2, 5, 3, 7, 3, 0, 29763501061277280599687103588900792044205008486400000⟩, + ⟨2, 5, 4, 7, 4, 0, 38206377711750355569035271908865976448094673305600000⟩, + ⟨2, 5, 5, 7, 5, 0, 4934545760590668615751735948182375883327143936000000⟩, + ⟨2, 5, 6, 7, 6, 0, 6471571600278817380980494928079492932582768640000000⟩, + ⟨2, 5, 7, 7, 7, 0, 579598981837880256816150736856166576666181632000000⟩, + ⟨2, 5, 8, 7, 8, 0, 3110409592469077023659593744369920874402283520000000⟩ +] + +def collectedFourData_10_7_6 : List CollectedFourTerm := [ + ⟨2, 6, 2, 1, 8, 1, -8636288876982693765557541923967837022827891916800000⟩, + ⟨2, 6, 2, 2, 7, 1, -10497781974447547752119576314021468296485378457600000⟩, + ⟨2, 6, 3, 2, 8, 1, -4415963985125208402577581788260561631204868096000000⟩, + ⟨2, 6, 2, 3, 6, 1, -4170274197232639097580009768819556771329736704000000⟩, + ⟨2, 6, 3, 3, 7, 1, -11026173780991327526304164271833103646981934284800000⟩, + ⟨2, 6, 4, 3, 8, 1, -3202665423086578749057991072698689505115452211200000⟩, + ⟨2, 6, 2, 4, 5, 1, -1936755536202642291630678361055893284108789350400000⟩, + ⟨2, 6, 3, 4, 6, 1, -25327259562014398192297877714922948259795383091200000⟩, + ⟨2, 6, 4, 4, 7, 1, -7298187889143794313637688437206180207344694067200000⟩, + ⟨2, 6, 5, 4, 8, 1, 10570188987811999849867550809903659900620242944000000⟩, + ⟨2, 6, 2, 5, 4, 1, 10269129722175473781263351591655036846938574028800000⟩, + ⟨2, 6, 3, 5, 5, 1, -8323853911251334044885484309938508634721248870400000⟩, + ⟨2, 6, 4, 5, 6, 1, 6694472970381726203864164952958789127367137689600000⟩, + ⟨2, 6, 5, 5, 7, 1, -359581328042906934399765003350585174787096576000000⟩, + ⟨2, 6, 6, 5, 8, 1, 3722178650665543806498458647023689486001242112000000⟩, + ⟨2, 6, 2, 6, 3, 1, 5181620628255884296741339280248079651098853376000000⟩, + ⟨2, 6, 3, 6, 4, 1, 39272022733130757792734493068590215087825459609600000⟩, + ⟨2, 6, 4, 6, 5, 1, -10862342389915498535563779021414305134822608076800000⟩, + ⟨2, 6, 5, 6, 6, 1, 3420260104982514647266851015935702734768963584000000⟩, + ⟨2, 6, 6, 6, 7, 1, 3515213402649961466793015906541639559490306048000000⟩, + ⟨2, 6, 7, 6, 8, 1, 771273664965570422894710258002382917801187737600000⟩, + ⟨2, 6, 2, 7, 2, 1, -25061392701705179981031343665348723848985024921600000⟩, + ⟨2, 6, 3, 7, 3, 1, -69990897773623052517694164608578692136573914316800000⟩, + ⟨2, 6, 4, 7, 4, 1, -44922448323839632223109434514965111657645840793600000⟩, + ⟨2, 6, 5, 7, 5, 1, -3867973363054185426446215625181859539157254144000000⟩, + ⟨2, 6, 6, 7, 6, 1, -3804585231566494037344857545288762475329617920000000⟩, + ⟨2, 6, 7, 7, 7, 1, -272593288027454863716959001076156505875336396800000⟩, + ⟨2, 6, 8, 7, 8, 1, -1219056630089746823471021223906506433405911040000000⟩ +] + +def collectedFourData_10_7_7 : List CollectedFourTerm := [ + ⟨2, 7, 1, 0, 8, 2, -844194112741415445229062317587529416269260390400000⟩, + ⟨2, 7, 1, 1, 7, 2, -8852805934151098453714227467293191628453733990400000⟩, + ⟨2, 7, 2, 1, 8, 2, 4868073851310512609812183075483861427652290150400000⟩, + ⟨2, 7, 1, 2, 6, 2, -10497781974447547752119576314021468296485378457600000⟩, + ⟨2, 7, 2, 2, 7, 2, 5917353929969676971434543572996702710700756172800000⟩, + ⟨2, 7, 3, 2, 8, 2, 1244587756994274911537605094578151700660486144000000⟩, + ⟨2, 7, 1, 3, 5, 2, -8672787407423830978095141424656184425664059801600000⟩, + ⟨2, 7, 2, 3, 6, 2, 2350685932524745397202101700247999041201242112000000⟩, + ⟨2, 7, 3, 3, 7, 2, 3107598010431686607013376904748464521753080627200000⟩, + ⟨2, 7, 4, 3, 8, 2, 601755839910067893974761955777361817759855411200000⟩, + ⟨2, 7, 1, 4, 4, 2, 9768285452476316668397043238995862874815148851200000⟩, + ⟨2, 7, 2, 4, 5, 2, 1091703753367610641378733174288871485301011251200000⟩, + ⟨2, 7, 3, 4, 6, 2, 7138191632739400585198916631674299832207199436800000⟩, + ⟨2, 7, 4, 4, 7, 2, 1371272550480989271576957274772277157719913267200000⟩, + ⟨2, 7, 5, 4, 8, 2, -1489542017061255042227736601656652397656670208000000⟩, + ⟨2, 7, 1, 5, 3, 2, 18654935851591131406290963338224742644902474547200000⟩, + ⟨2, 7, 2, 5, 4, 2, -5788468008460549970444656674681991464596432486400000⟩, + ⟨2, 7, 3, 5, 5, 2, 2345980787852504099457026638530911686503274905600000⟩, + ⟨2, 7, 4, 5, 6, 2, -1257839228540108597093927852374845675242363289600000⟩, + ⟨2, 7, 5, 5, 7, 2, 50671894068136859194536078831397969625874432000000⟩, + ⟨2, 7, 6, 5, 8, 2, -419620992704491518701177950649979584619164467200000⟩, + ⟨2, 7, 1, 6, 2, 2, -46486580987983249615788385873920630844071660748800000⟩, + ⟨2, 7, 2, 6, 3, 2, -2920758238535953497263991611930893898773168128000000⟩, + ⟨2, 7, 3, 6, 4, 2, -11068359898471756209914814860755745782454707814400000⟩, + ⟨2, 7, 4, 6, 5, 2, 2040949367085239918207245966217190398300572876800000⟩, + ⟨2, 7, 5, 6, 6, 2, -481980136923206271502179574170089308645490688000000⟩, + ⟨2, 7, 6, 6, 7, 2, -396288699717398786962260625867107177300020428800000⟩, + ⟨2, 7, 7, 6, 8, 2, -72458151375453005552013518189538276235070668800000⟩, + ⟨2, 7, 1, 7, 1, 2, 133024816975794034270116109421168957693769862348800000⟩, + ⟨2, 7, 2, 7, 2, 2, 14126520340669654177330225849118132450785807564800000⟩, + ⟨2, 7, 3, 7, 3, 2, 19726115240864952216498604856754914364054778675200000⟩, + ⟨2, 7, 4, 7, 4, 2, 8440577472459246920605630997662113249648810393600000⟩, + ⟨2, 7, 5, 7, 5, 2, 545071507405049155334498290011474299461828608000000⟩, + ⟨2, 7, 6, 7, 6, 2, 428911124782611072977309133784630107152842752000000⟩, + ⟨2, 7, 7, 7, 7, 2, 25609075773003990215358015611017226426410598400000⟩, + ⟨2, 7, 8, 7, 8, 2, 98164811773376996430345860909306860441436160000000⟩ +] + +def collectedFourData_10_7_8 : List CollectedFourTerm := [ + ⟨2, 8, 0, 0, 7, 3, -3086177606496240931993294916182592967552270336000000⟩, + ⟨2, 8, 1, 0, 8, 3, -355116043312283124146546546335249845121449984000000⟩, + ⟨2, 8, 0, 1, 6, 3, -388276766929807844763588765766514652739534848000000⟩, + ⟨2, 8, 1, 1, 7, 3, -3723993531935712220480332114333723517972905984000000⟩, + ⟨2, 8, 2, 1, 8, 3, 1023894326279732911468745977373760614188449792000000⟩, + ⟨2, 8, 0, 2, 5, 3, 1877880595030303318713989741838731057936990208000000⟩, + ⟨2, 8, 1, 2, 6, 3, -4415963985125208402577581788260561631204868096000000⟩, + ⟨2, 8, 2, 2, 7, 3, 1244587756994274911537605094578151700660486144000000⟩, + ⟨2, 8, 3, 2, 8, 3, 174514791937075386274380402670916866230190080000000⟩, + ⟨2, 8, 0, 3, 4, 3, -1192562448284545402417480504130020321794195456000000⟩, + ⟨2, 8, 1, 3, 5, 3, -3648267504035923614297364182114305467100430336000000⟩, + ⟨2, 8, 2, 3, 6, 3, 494416079684109841456839923300555921565941760000000⟩, + ⟨2, 8, 3, 3, 7, 3, 435744138705238675871262744039014347680251904000000⟩, + ⟨2, 8, 4, 3, 8, 3, 63283180279172117378328884374585323540185088000000⟩, + ⟨2, 8, 0, 4, 3, 3, -4576753695427616054399262433077570687763218432000000⟩, + ⟨2, 8, 1, 4, 4, 3, 4109096270007836046875589104855198481097162752000000⟩, + ⟨2, 8, 2, 4, 5, 3, 229616335576024651738703419447267331068133376000000⟩, + ⟨2, 8, 3, 4, 6, 3, 1000909755534594439236798772941277441164312576000000⟩, + ⟨2, 8, 4, 4, 7, 3, 144208800760350897851834614688251615566102528000000⟩, + ⟨2, 8, 5, 4, 8, 3, -125317213058607456213005532445429842088820736000000⟩, + ⟨2, 8, 0, 5, 2, 3, 7724224745799692564484952837026863660258033664000000⟩, + ⟨2, 8, 1, 5, 3, 3, 7847326708248079159938165846052720511299878912000000⟩, + ⟨2, 8, 2, 5, 4, 3, -1217479383579807449749435017601086822989955072000000⟩, + ⟨2, 8, 3, 5, 5, 3, 328950969330754245971387843336959941402427392000000⟩, + ⟨2, 8, 4, 5, 6, 3, -132279674550087723351601927830791409006280704000000⟩, + ⟨2, 8, 5, 5, 7, 3, 4263095953176296326677144637078953623814144000000⟩, + ⟨2, 8, 6, 5, 8, 3, -29419408082201721112693226215492332501860352000000⟩, + ⟨2, 8, 0, 6, 1, 3, -5614463451521010298511205880356141241057935360000000⟩, + ⟨2, 8, 1, 6, 2, 3, -19554899114328711004323479342688746132364853248000000⟩, + ⟨2, 8, 2, 6, 3, 3, -614318492326626763884363146582328381737533440000000⟩, + ⟨2, 8, 3, 6, 4, 3, -1551993834031707162015287130915240850917163008000000⟩, + ⟨2, 8, 4, 6, 5, 3, 214634837207761925990978702228711240506540032000000⟩, + ⟨2, 8, 5, 6, 6, 3, -40549650038061574340697693428743948411600896000000⟩, + ⟨2, 8, 6, 6, 7, 3, -27783593237818633705395379109727292524331008000000⟩, + ⟨2, 8, 7, 6, 8, 3, -4354288331458836700754989150885956041048064000000⟩, + ⟨2, 8, 0, 7, 0, 3, 54759487123550215883037923823222380843633737728000000⟩, + ⟨2, 8, 1, 7, 1, 3, 55957801593025836319859056045784979144859189248000000⟩, + ⟨2, 8, 2, 7, 2, 3, 2971208833036313114742326699072952305455202304000000⟩, + ⟨2, 8, 3, 7, 3, 3, 2765975221626862192524616352670738647837835264000000⟩, + ⟨2, 8, 4, 7, 4, 3, 887646700578403007460256539236098275922673664000000⟩, + ⟨2, 8, 5, 7, 5, 3, 45857613577372397627086590683108188971073536000000⟩, + ⟨2, 8, 6, 7, 6, 3, 30070734377824457820393594369552356286136320000000⟩, + ⟨2, 8, 7, 7, 7, 3, 1538947622884193565044795665252177466621952000000⟩, + ⟨2, 8, 8, 7, 8, 3, 5161712665268044103360175299882342626099200000000⟩ +] + +def collectedFourData_10_7_9 : List CollectedFourTerm := [ + ⟨3, 4, 3, 2, 8, 0, -1192562448284545402417480504130020321794195456000000⟩, + ⟨3, 4, 3, 3, 7, 0, -2977696567218957481292523226110626075710901452800000⟩, + ⟨3, 4, 4, 3, 8, 0, -1729805102966253799139903774622796415423112806400000⟩, + ⟨3, 4, 3, 4, 6, 0, -6839806387315374029700833506611470159989388083200000⟩, + ⟨3, 4, 4, 4, 7, 0, -3941854981804687475404272905785909680703694438400000⟩, + ⟨3, 4, 5, 4, 8, 0, 8563663902556491405408959097212342892025085952000000⟩, + ⟨3, 4, 3, 5, 5, 0, -2247915887222373276512993139761082492470584934400000⟩, + ⟨3, 4, 4, 5, 6, 0, 3615779975753937850133137332903756109878342451200000⟩, + ⟨3, 4, 5, 5, 7, 0, -291322477066872194441760892260952350243422208000000⟩, + ⟨3, 4, 6, 5, 8, 0, 4020803158306832964825276614592304710709936128000000⟩, + ⟨3, 4, 3, 6, 4, 0, 10605688755041062542200951430378504309257640345600000⟩, + ⟨3, 4, 4, 6, 5, 0, -5866905472171931267290513219624501830598891929600000⟩, + ⟨3, 4, 5, 6, 6, 0, 2770996623822501531981733445957289511665795072000000⟩, + ⟨3, 4, 6, 6, 7, 0, 3797233415696006101948610974464142201073958912000000⟩, + ⟨3, 4, 7, 6, 8, 0, 1041439664461683189272781350506281449992224768000000⟩, + ⟨3, 4, 3, 7, 3, 0, -18901539208132516955249222974395674131897830604800000⟩, + ⟨3, 4, 4, 7, 4, 0, -24263252660786898671140224822969615273740677939200000⟩, + ⟨3, 4, 5, 7, 5, 0, -3133721062455075771969456385434827921452695552000000⟩, + ⟨3, 4, 6, 7, 6, 0, -4109821088892341776058312722896779093716500480000000⟩, + ⟨3, 4, 7, 7, 7, 0, -368078770627404153685918068883655718730727424000000⟩, + ⟨3, 4, 8, 7, 8, 0, -1975289423927829545436399740762080523468144640000000⟩ +] + +def collectedFourData_10_7_10 : List CollectedFourTerm := [ + ⟨3, 5, 2, 1, 8, 1, -7134906935720743122383733418432305899607215308800000⟩, + ⟨3, 5, 2, 2, 7, 1, -8672787407423830978095141424656184425664059801600000⟩, + ⟨3, 5, 3, 2, 8, 1, -3648267504035923614297364182114305467100430336000000⟩, + ⟨3, 5, 2, 3, 6, 1, -3445289836586372439081591050977841258340286464000000⟩, + ⟨3, 5, 3, 3, 7, 1, -9109320554819472708830108956651102233728699596800000⟩, + ⟨3, 5, 4, 3, 8, 1, -2645895715794643096516601633556482696412345139200000⟩, + ⟨3, 5, 2, 4, 5, 1, -1600058856863487277028853458275109851256743526400000⟩, + ⟨3, 5, 3, 4, 6, 1, -20924223643495217452778573804785661303669863219200000⟩, + ⟨3, 5, 4, 4, 7, 1, -6029429090454165304890522325399396891277603635200000⟩, + ⟨3, 5, 5, 4, 8, 1, 8732606770718374588753183911002040677437538304000000⟩, + ⟨3, 5, 2, 5, 4, 1, 8483885372783442141709086703879595593397226700800000⟩, + ⟨3, 5, 3, 5, 5, 1, -6876787454574209648570582131867407822583391846400000⟩, + ⟨3, 5, 4, 5, 6, 1, 5530667432243111877534032735735218324891081113600000⟩, + ⟨3, 5, 5, 5, 7, 1, -297069649701824534040130432069741736431190016000000⟩, + ⟨3, 5, 6, 5, 8, 1, 3075093787263837472408559950233103483526971392000000⟩, + ⟨3, 5, 2, 6, 3, 1, 4280818009382419144161098773410582040795938816000000⟩, + ⟨3, 5, 3, 6, 4, 1, 32444749286373232413328524126991934538083047833600000⟩, + ⟨3, 5, 4, 6, 5, 1, -8973970551464316051053810624365154163133041868800000⟩, + ⟨3, 5, 5, 6, 6, 1, 2825662491449057434705958730522570602047340544000000⟩, + ⟨3, 5, 6, 6, 7, 1, 2904108563801111317808323331641756983301767168000000⟩, + ⟨3, 5, 7, 6, 8, 1, 637191031922059282619924881133056344783952281600000⟩, + ⟨3, 5, 2, 7, 2, 1, -20704576601505431515904709041116178243550550425600000⟩, + ⟨3, 5, 3, 7, 3, 1, -57823279081513907875754749540391118617443093708800000⟩, + ⟨3, 5, 4, 7, 4, 1, -37112872517448833308540923713080906745965549977600000⟩, + ⟨3, 5, 5, 7, 5, 1, -3195542711498590645191997640195797450179477504000000⟩, + ⟨3, 5, 6, 7, 6, 1, -3143174335980341521386818789394790145033502720000000⟩, + ⟨3, 5, 7, 7, 7, 1, -225204108973427447127607917820208618698230988800000⟩, + ⟨3, 5, 8, 7, 8, 1, -1007128840750693727974852069803157021670768640000000⟩ +] + +def collectedFourData_10_7_11 : List CollectedFourTerm := [ + ⟨3, 6, 1, 0, 8, 2, -335358548538201652359272867352879218835849216000000⟩, + ⟨3, 6, 1, 1, 7, 2, -3516802716055758181255225729947131671757193216000000⟩, + ⟨3, 6, 2, 1, 8, 2, 1933856391927163546379775480091075435472879616000000⟩, + ⟨3, 6, 1, 2, 6, 2, -4170274197232639097580009768819556771329736704000000⟩, + ⟨3, 6, 2, 2, 7, 2, 2350685932524745397202101700247999041201242112000000⟩, + ⟨3, 6, 3, 2, 8, 2, 494416079684109841456839923300555921565941760000000⟩, + ⟨3, 6, 1, 3, 5, 2, -3445289836586372439081591050977841258340286464000000⟩, + ⟨3, 6, 2, 3, 6, 2, 933816773301922135175808137027068914806292480000000⟩, + ⟨3, 6, 3, 3, 7, 2, 1234502281512352693497584012129637174123429888000000⟩, + ⟨3, 6, 4, 3, 8, 2, 239049244718484846121040252209188648410677248000000⟩, + ⟨3, 6, 1, 4, 4, 2, 3880479597768434121535136592346617849575374848000000⟩, + ⟨3, 6, 2, 4, 5, 2, 433682467855840599463944447150180269291470848000000⟩, + ⟨3, 6, 3, 4, 6, 2, 2835667234599965664031713573923269258795548672000000⟩, + ⟨3, 6, 4, 4, 7, 2, 544741979645200722330792100585403827762495488000000⟩, + ⟨3, 6, 5, 4, 8, 2, -591724866697025408019928798185364218257080320000000⟩, + ⟨3, 6, 1, 5, 3, 2, 7410727125242535530786476312127065205860466688000000⟩, + ⟨3, 6, 2, 5, 4, 2, -2299485628101929523283619344392622694052397056000000⟩, + ⟨3, 6, 3, 5, 5, 2, 931947640996768968466210683700681769824026624000000⟩, + ⟨3, 6, 4, 5, 6, 2, -499680265013683800638780029792960281506217984000000⟩, + ⟨3, 6, 5, 5, 7, 2, 20129556212123312462916728901134387018465280000000⟩, + ⟨3, 6, 6, 5, 8, 2, -166695650829115058138336022839313546753343488000000⟩, + ⟨3, 6, 1, 6, 2, 2, -18466928507719746709360839410785226725263409152000000⟩, + ⟨3, 6, 2, 6, 3, 2, -1160279642706347936329410595250503651814277120000000⟩, + ⟨3, 6, 3, 6, 4, 2, -4396937924852486389566968258236800253795762176000000⟩, + ⟨3, 6, 4, 6, 5, 2, 810773028448399942265557282959412548203446272000000⟩, + ⟨3, 6, 5, 6, 6, 2, -191468000905522562651321123299621953098219520000000⟩, + ⟨3, 6, 6, 6, 7, 2, -157426830077913901890161865084859997698916352000000⟩, + ⟨3, 6, 7, 6, 8, 2, -28784209826012339964776525422477440505085952000000⟩, + ⟨3, 6, 1, 7, 1, 2, 52844492596250768182208582328468875556685873152000000⟩, + ⟨3, 6, 2, 7, 2, 2, 5611800989654001795176783835184318863787425792000000⟩, + ⟨3, 6, 3, 7, 3, 2, 7836256230206740715611106775832701257864183808000000⟩, + ⟨3, 6, 4, 7, 4, 2, 3353043769514205448242796219529265994367238144000000⟩, + ⟨3, 6, 5, 7, 5, 2, 216531229978949817953860980597248305209016320000000⟩, + ⟨3, 6, 6, 7, 6, 2, 170386182618455639866776719147701677148078080000000⟩, + ⟨3, 6, 7, 7, 7, 2, 10173279286146947518481395988032345432129536000000⟩, + ⟨3, 6, 8, 7, 8, 2, 38996254886142883688787029331688823350886400000000⟩ +] + +def collectedFourData_10_7_12 : List CollectedFourTerm := [ + ⟨3, 7, 0, 0, 7, 3, -7705844233072155772655338150199114312226491596800000⟩, + ⟨3, 7, 1, 0, 8, 3, -886685493624617133267533114222785770950964019200000⟩, + ⟨3, 7, 0, 1, 6, 3, -969484153790747059960924844654153141691246182400000⟩, + ⟨3, 7, 1, 1, 7, 3, -9298400073171475878189999374139682363465216819200000⟩, + ⟨3, 7, 2, 1, 8, 3, 2556550916846136585305721821099047446831012249600000⟩, + ⟨3, 7, 0, 2, 5, 3, 4688860201419518322337002347089844387258459750400000⟩, + ⟨3, 7, 1, 2, 6, 3, -11026173780991327526304164271833103646981934284800000⟩, + ⟨3, 7, 2, 2, 7, 3, 3107598010431686607013376904748464521753080627200000⟩, + ⟨3, 7, 3, 2, 8, 3, 435744138705238675871262744039014347680251904000000⟩, + ⟨3, 7, 0, 3, 4, 3, -2977696567218957481292523226110626075710901452800000⟩, + ⟨3, 7, 1, 3, 5, 3, -9109320554819472708830108956651102233728699596800000⟩, + ⟨3, 7, 2, 3, 6, 3, 1234502281512352693497584012129637174123429888000000⟩, + ⟨3, 7, 3, 3, 7, 3, 1088004932466885514254738727125807513075921715200000⟩, + ⟨3, 7, 4, 3, 8, 3, 158011103696121000276570985694834774679905894400000⟩, + ⟨3, 7, 0, 4, 3, 3, -11427647908489070344280659284970021904881129881600000⟩, + ⟨3, 7, 1, 4, 4, 3, 10259959027868980542625529110134266417410316697600000⟩, + ⟨3, 7, 2, 4, 5, 3, 573326600385280066497429538838037727793695948800000⟩, + ⟨3, 7, 3, 4, 6, 3, 2499160985186582885167026912539161728593480908800000⟩, + ⟨3, 7, 4, 4, 7, 3, 360073429785206698932887493468315187241444966400000⟩, + ⟨3, 7, 5, 4, 8, 3, -312903224208370310558263299077980432165031116800000⟩, + ⟨3, 7, 0, 5, 2, 3, 19286535093470907382444606399450105057025143603200000⟩, + ⟨3, 7, 1, 5, 3, 3, 19593907081854207951945121384176109676696017305600000⟩, + ⟨3, 7, 2, 5, 4, 3, -3039911399491301289500595943866382194356885913600000⟩, + ⟨3, 7, 3, 5, 5, 3, 821354197064087767529792056477807293559839129600000⟩, + ⟨3, 7, 4, 5, 6, 3, -330287720686854341855143940332888681417487155200000⟩, + ⟨3, 7, 5, 5, 7, 3, 10644479208412278842990114230051063765087027200000⟩, + ⟨3, 7, 6, 5, 8, 3, -73457008965859927929726949757008123430279577600000⟩, + ⟨3, 7, 0, 6, 1, 3, -14018694425955509395346338026750176701414637568000000⟩, + ⟨3, 7, 1, 6, 2, 3, -48826420829206170980037627592528006821731264102400000⟩, + ⟨3, 7, 2, 6, 3, 3, -1533885347816739206719726488530360097803599872000000⟩, + ⟨3, 7, 3, 6, 4, 3, -3875156993739706233101818681461269431279052390400000⟩, + ⟨3, 7, 4, 6, 5, 3, 535919455520755286263027877796933725838743961600000⟩, + ⟨3, 7, 5, 6, 6, 3, -101247992416625521435492422614288333290654924800000⟩, + ⟨3, 7, 6, 6, 7, 3, -69372560177679469157078783581109577958450790400000⟩, + ⟨3, 7, 7, 6, 8, 3, -10872176493497061980299244087499843051926323200000⟩, + ⟨3, 7, 0, 7, 0, 3, 136728384383574644393093960604350055966411482726400000⟩, + ⟨3, 7, 1, 7, 1, 3, 139720443111684943425504223067793606639954060902400000⟩, + ⟨3, 7, 2, 7, 2, 3, 7418779918275520304902809201663139443528381235200000⟩, + ⟨3, 7, 3, 7, 3, 3, 6906334284043997505969304396967919871058981683200000⟩, + ⟨3, 7, 4, 7, 4, 3, 2216355660886020638867268131801594434067575603200000⟩, + ⟨3, 7, 5, 7, 5, 3, 114501390452648564897636301444475039983127756800000⟩, + ⟨3, 7, 6, 7, 6, 3, 75083298706414050859967010166306388538556416000000⟩, + ⟨3, 7, 7, 7, 7, 3, 3842582047073352805788284360798410362165657600000⟩, + ⟨3, 7, 8, 7, 8, 3, 12888225775051391921837247254810485283880960000000⟩ +] + +def collectedFourData_10_7_13 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 7, 4, -4476483206440535204315781715193462300604786278400000⟩, + ⟨3, 8, 1, 0, 8, 4, -257546908654717667193454315588661607299599564800000⟩, + ⟨3, 8, 0, 1, 6, 4, -563193259828491877985625398441568853757735731200000⟩, + ⟨3, 8, 1, 1, 7, 4, -2700815803911137571571919216891477858299202764800000⟩, + ⟨3, 8, 2, 1, 8, 4, 495050981200072973775571269934647113250609561600000⟩, + ⟨3, 8, 0, 2, 5, 4, 2723855208351876016987154416341265835072107315200000⟩, + ⟨3, 8, 1, 2, 6, 4, -3202665423086578749057991072698689505115452211200000⟩, + ⟨3, 8, 2, 2, 7, 4, 601755839910067893974761955777361817759855411200000⟩, + ⟨3, 8, 3, 2, 8, 4, 63283180279172117378328884374585323540185088000000⟩, + ⟨3, 8, 0, 3, 4, 4, -1729805102966253799139903774622796415423112806400000⟩, + ⟨3, 8, 1, 3, 5, 4, -2645895715794643096516601633556482696412345139200000⟩, + ⟨3, 8, 2, 3, 6, 4, 239049244718484846121040252209188648410677248000000⟩, + ⟨3, 8, 3, 3, 7, 4, 158011103696121000276570985694834774679905894400000⟩, + ⟨3, 8, 4, 3, 8, 4, 18358379192018020739984648869979499485661757440000⟩, + ⟨3, 8, 0, 4, 3, 4, -6638555413813750696631950510155079471166442700800000⟩, + ⟨3, 8, 1, 4, 4, 4, 2980110478350061541251149409691034420903306854400000⟩, + ⟨3, 8, 2, 4, 5, 4, 111019066429928180233501272339353310042311884800000⟩, + ⟨3, 8, 3, 4, 6, 4, 362953488352531972976760118524900821343771033600000⟩, + ⟨3, 8, 4, 4, 7, 4, 41834810379402328664662552991194252801883504640000⟩, + ⟨3, 8, 5, 4, 8, 4, -30295318419887905464928533754088703264188006400000⟩, + ⟨3, 8, 0, 5, 2, 4, 11203944414787150753843167240948791198195751321600000⟩, + ⟨3, 8, 1, 5, 3, 4, 5691251558397243415302953463821443574295586406400000⟩, + ⟨3, 8, 2, 5, 4, 4, -588648992344722881207854848728836100362705305600000⟩, + ⟨3, 8, 3, 5, 5, 4, 119285381279728572495059195531432262360052531200000⟩, + ⟨3, 8, 4, 5, 6, 4, -38374184326297191587628092417085705735918059520000⟩, + ⟨3, 8, 5, 5, 7, 4, 1030599438048551450115200887266401987434905600000⟩, + ⟨3, 8, 6, 5, 8, 4, -6096097920435618257651123488132887581451878400000⟩, + ⟨3, 8, 0, 6, 1, 4, -8143747560413963318052736286426101082524483584000000⟩, + ⟨3, 8, 1, 6, 2, 4, -14182135419664479616888242384870817949103528345600000⟩, + ⟨3, 8, 2, 6, 3, 4, -297021835740263001130751088192203007524339712000000⟩, + ⟨3, 8, 3, 6, 4, 4, -562789575032730586319497701262978464034376908800000⟩, + ⟨3, 8, 4, 6, 5, 4, 62265324086027431574258074795245586954227548160000⟩, + ⟨3, 8, 5, 6, 6, 4, -9802839767459364242445504959266849670194790400000⟩, + ⟨3, 8, 6, 6, 7, 4, -5757135034330020177365122095119388601063833600000⟩, + ⟨3, 8, 7, 6, 8, 4, -789483832311936770022621392446291962966835200000⟩, + ⟨3, 8, 0, 7, 0, 4, 79428327127344751806209713599442316935784772403200000⟩, + ⟨3, 8, 1, 7, 1, 4, 40583237752298280580030166489593242529589467545600000⟩, + ⟨3, 8, 2, 7, 2, 4, 1436573883058214747995720567650887459289641779200000⟩, + ⟨3, 8, 3, 7, 3, 4, 1003007863431139147061281878019773606826239590400000⟩, + ⟨3, 8, 4, 7, 4, 4, 257505306242096282256626807007382663510433464320000⟩, + ⟨3, 8, 5, 7, 5, 4, 11086034961956482359285193895650428553946726400000⟩, + ⟨3, 8, 6, 7, 6, 4, 6231061508594039417601537081396378199916544000000⟩, + ⟨3, 8, 7, 7, 7, 4, 279029355558293980546148332784308090149273600000⟩, + ⟨3, 8, 8, 7, 8, 4, 831892788812291842085396537703018497310720000000⟩ +] + +def collectedFourData_10_7_14 : List CollectedFourTerm := [ + ⟨4, 3, 3, 2, 8, 0, -4576753695427616054399262433077570687763218432000000⟩, + ⟨4, 3, 3, 3, 7, 0, -11427647908489070344280659284970021904881129881600000⟩, + ⟨4, 3, 4, 3, 8, 0, -6638555413813750696631950510155079471166442700800000⟩, + ⟨4, 3, 3, 4, 6, 0, -26249450671690015964954452112993261347018270310400000⟩, + ⟨4, 3, 4, 4, 7, 0, -15127844567607752667985299643142885046741683404800000⟩, + ⟨4, 3, 5, 4, 8, 0, 32865180744877744192209650893861081085581983744000000⟩, + ⟨4, 3, 3, 5, 5, 0, -8626933842042870312274395035875286588752448716800000⟩, + ⟨4, 3, 4, 5, 6, 0, 13876450989790457247559232983088000230203221606400000⟩, + ⟨4, 3, 5, 5, 7, 0, -1118022142483901342632673350062388481177419776000000⟩, + ⟨4, 3, 6, 5, 8, 0, 15430827743938032004466973234190767857929814016000000⟩, + ⟨4, 3, 3, 6, 4, 0, 40701956758752260310366179168355542257110299443200000⟩, + ⟨4, 3, 4, 6, 5, 0, -22515702501879087713226430912921832914787971891200000⟩, + ⟨4, 3, 5, 6, 6, 0, 10634385693042647270395769837235986927015952384000000⟩, + ⟨4, 3, 6, 6, 7, 0, 14572823496737585492420855406994727867844132864000000⟩, + ⟨4, 3, 7, 6, 8, 0, 3996782591759621573870118140243079842387460096000000⟩, + ⟨4, 3, 3, 7, 3, 0, -72539337075830630031293863882206624805820144025600000⟩, + ⟨4, 3, 4, 7, 4, 0, -93116240108085793472235596371023267039241725542400000⟩, + ⟨4, 3, 5, 7, 5, 0, -12026430543458264022536856364573791973690834944000000⟩, + ⟨4, 3, 6, 7, 6, 0, -15772456095017335555435850864590181242566082560000000⟩, + ⟨4, 3, 7, 7, 7, 0, -1412593425275687412552870719162350734491516928000000⟩, + ⟨4, 3, 8, 7, 8, 0, -7580662281883068445882667667611035466024878080000000⟩ +] + +def collectedFourData_10_7_15 : List CollectedFourTerm := [ + ⟨4, 4, 2, 1, 8, 1, 8036148512681666911947614964378044767940483481600000⟩, + ⟨4, 4, 2, 2, 7, 1, 9768285452476316668397043238995862874815148851200000⟩, + ⟨4, 4, 3, 2, 8, 1, 4109096270007836046875589104855198481097162752000000⟩, + ⟨4, 4, 2, 3, 6, 1, 3880479597768434121535136592346617849575374848000000⟩, + ⟨4, 4, 3, 3, 7, 1, 10259959027868980542625529110134266417410316697600000⟩, + ⟨4, 4, 4, 3, 8, 1, 2980110478350061541251149409691034420903306854400000⟩, + ⟨4, 4, 2, 4, 5, 1, 1802169351139229720466502685524139179491773644800000⟩, + ⟨4, 4, 3, 4, 6, 1, 23567254657499849284350419972670464099021645414400000⟩, + ⟨4, 4, 4, 4, 7, 1, 6791032882992779496386827382050423729654490726400000⟩, + ⟨4, 4, 5, 4, 8, 1, -9835660863494267187894805190571763167267913728000000⟩, + ⟨4, 4, 2, 5, 4, 1, -9555522368333222104032434133687552350623472025600000⟩, + ⟨4, 4, 3, 5, 5, 1, 7745424820950663074006273254986199626127559884800000⟩, + ⟨4, 4, 4, 5, 6, 1, -6229270439007865419348715268171712433220694835200000⟩, + ⟨4, 4, 5, 5, 7, 1, 334593827939400420978009693837859846474432512000000⟩, + ⟨4, 4, 6, 5, 8, 1, -3463522452010877105394345577179008827385708544000000⟩, + ⟨4, 4, 2, 6, 3, 1, -4821547020736903947147290109051060023419994112000000⟩, + ⟨4, 4, 3, 6, 4, 1, -36542988727249561215677635547752792126951469875200000⟩, + ⟨4, 4, 4, 6, 5, 1, 10107512368374587863434382290160688032311253401600000⟩, + ⟨4, 4, 5, 6, 6, 1, -3182584388636442732094522452488592599870865408000000⟩, + ⟨4, 4, 6, 6, 7, 1, -3270939330521048410982692698173415878742245376000000⟩, + ⟨4, 4, 7, 6, 8, 1, -717677442692150849497044965934226711166268211200000⟩, + ⟨4, 4, 2, 7, 2, 1, 23319863028470445541822026498877340015320576819200000⟩, + ⟨4, 4, 3, 7, 3, 1, 65127192600493948478707876980887885958413392281600000⟩, + ⟨4, 4, 4, 7, 4, 1, 41800763201168949857284783411501084896702706483200000⟩, + ⟨4, 4, 5, 7, 5, 1, 3599185811331966843082882021279545132872368128000000⟩, + ⟨4, 4, 6, 7, 6, 1, 3540202555232912912288150745279817642451927040000000⟩, + ⟨4, 4, 7, 7, 7, 1, 253650633663631951296779861978559187277945241600000⟩, + ⟨4, 4, 8, 7, 8, 1, 1134343728459567963675813810438523438214676480000000⟩ +] + +def collectedFourData_10_7_16 : List CollectedFourTerm := [ + ⟨4, 5, 1, 0, 8, 2, -155746959258758723397223243497550526725855641600000⟩, + ⟨4, 5, 1, 1, 7, 2, -1633270813361224184198111326302191509382470041600000⟩, + ⟨4, 5, 2, 1, 8, 2, 898120098618748677189689250341685760582326681600000⟩, + ⟨4, 5, 1, 2, 6, 2, -1936755536202642291630678361055893284108789350400000⟩, + ⟨4, 5, 2, 2, 7, 2, 1091703753367610641378733174288871485301011251200000⟩, + ⟨4, 5, 3, 2, 8, 2, 229616335576024651738703419447267331068133376000000⟩, + ⟨4, 5, 1, 3, 5, 2, -1600058856863487277028853458275109851256743526400000⟩, + ⟨4, 5, 2, 3, 6, 2, 433682467855840599463944447150180269291470848000000⟩, + ⟨4, 5, 3, 3, 7, 2, 573326600385280066497429538838037727793695948800000⟩, + ⟨4, 5, 4, 3, 8, 2, 111019066429928180233501272339353310042311884800000⟩, + ⟨4, 5, 1, 4, 4, 2, 1802169351139229720466502685524139179491773644800000⟩, + ⟨4, 5, 2, 4, 5, 2, 201410478268119449548092894309419695823703244800000⟩, + ⟨4, 5, 3, 4, 6, 2, 1316938396780807406403054542731644473565197107200000⟩, + ⟨4, 5, 4, 4, 7, 2, 252988651340945513938865577153708290525154508800000⟩, + ⟨4, 5, 5, 4, 8, 2, -274808407620949365781297967537508359111442432000000⟩, + ⟨4, 5, 1, 5, 3, 2, 3441684193481799118809643468939093311402855628800000⟩, + ⟨4, 5, 2, 5, 4, 2, -1067925347354895049041379428057815191341603225600000⟩, + ⟨4, 5, 3, 5, 5, 2, 432814406867835820246898854249465180231984742400000⟩, + ⟨4, 5, 4, 5, 6, 2, -232061124479213489962139432088136442496575078400000⟩, + ⟨4, 5, 5, 5, 7, 2, 9348553018648734235641838581724654105264128000000⟩, + ⟨4, 5, 6, 5, 8, 2, -77416665987677985819078977102579715380399308800000⟩, + ⟨4, 5, 1, 6, 2, 2, -8576396738545058717229801417572893724681384755200000⟩, + ⟨4, 5, 2, 6, 3, 2, -538856179539933522127830167064706503369818112000000⟩, + ⟨4, 5, 3, 6, 4, 2, -2042022530304703678198043265436655676521290137600000⟩, + ⟨4, 5, 4, 6, 5, 2, 376538586477896140611916019570415933982978867200000⟩, + ⟨4, 5, 5, 6, 6, 2, -88921421762986476198562609717045836594020352000000⟩, + ⟨4, 5, 6, 6, 7, 2, -73112047381095424336029283115007454357959475200000⟩, + ⟨4, 5, 7, 6, 8, 2, -13367940595546885291860631366307672589808435200000⟩, + ⟨4, 5, 1, 7, 1, 2, 24541998620024741934046357182636647907658511155200000⟩, + ⟨4, 5, 2, 7, 2, 2, 2606228300765505830863667860597934066844775219200000⟩, + ⟨4, 5, 3, 7, 3, 2, 3639308093224812736491446763899777838356417740800000⟩, + ⟨4, 5, 4, 7, 4, 2, 1557218009320777550180400959921829718067144294400000⟩, + ⟨4, 5, 5, 7, 5, 2, 100561267338437344856381899473268225219756032000000⟩, + ⟨4, 5, 6, 7, 6, 2, 79130619923675850031982568504824250035601408000000⟩, + ⟨4, 5, 7, 7, 7, 2, 4724666543954261524236184929969999135218073600000⟩, + ⟨4, 5, 8, 7, 8, 2, 18110610710448048266333917242098123947376640000000⟩ +] + +def collectedFourData_10_7_17 : List CollectedFourTerm := [ + ⟨4, 6, 0, 0, 7, 3, -17700420917719596259902065832823926110635111219200000⟩, + ⟨4, 6, 1, 0, 8, 3, -2036727707449979693264236063520984010771451084800000⟩, + ⟨4, 6, 0, 1, 6, 3, -2226917269039317776215383899845889015714257305600000⟩, + ⟨4, 6, 1, 1, 7, 3, -21358541670245136656500946932884130467282734284800000⟩, + ⟨4, 6, 2, 1, 8, 3, 5872429542702753263943153899635896532097984102400000⟩, + ⟨4, 6, 0, 2, 5, 3, 10770370731511750900323070049656322939397183897600000⟩, + ⟨4, 6, 1, 2, 6, 3, -25327259562014398192297877714922948259795383091200000⟩, + ⟨4, 6, 2, 2, 7, 3, 7138191632739400585198916631674299832207199436800000⟩, + ⟨4, 6, 3, 2, 8, 3, 1000909755534594439236798772941277441164312576000000⟩, + ⟨4, 6, 0, 3, 4, 3, -6839806387315374029700833506611470159989388083200000⟩, + ⟨4, 6, 1, 3, 5, 3, -20924223643495217452778573804785661303669863219200000⟩, + ⟨4, 6, 2, 3, 6, 3, 2835667234599965664031713573923269258795548672000000⟩, + ⟨4, 6, 3, 3, 7, 3, 2499160985186582885167026912539161728593480908800000⟩, + ⟨4, 6, 4, 3, 8, 3, 362953488352531972976760118524900821343771033600000⟩, + ⟨4, 6, 0, 4, 3, 3, -26249450671690015964954452112993261347018270310400000⟩, + ⟨4, 6, 1, 4, 4, 3, 23567254657499849284350419972670464099021645414400000⟩, + ⟨4, 6, 2, 4, 5, 3, 1316938396780807406403054542731644473565197107200000⟩, + ⟨4, 6, 3, 4, 6, 3, 5740604149392373010648453434453125984532247347200000⟩, + ⟨4, 6, 4, 4, 7, 3, 827093187418888670433311482968114011708168601600000⟩, + ⟨4, 6, 5, 4, 8, 3, -718742633186040054658997343143972058912994099200000⟩, + ⟨4, 6, 0, 5, 2, 3, 44301413170754513872855839804291494814386277580800000⟩, + ⟨4, 6, 1, 5, 3, 3, 45007450485829046794462524018454293153459889766400000⟩, + ⟨4, 6, 2, 5, 4, 3, -6982714637889597502820993292622824473455126118400000⟩, + ⟨4, 6, 3, 5, 5, 3, 1886660899291737479796957141639309915054302822400000⟩, + ⟨4, 6, 4, 5, 6, 3, -758675039786102204268733929341582000320728268800000⟩, + ⟨4, 6, 5, 5, 7, 3, 24450502338235855867585247963709283213561036800000⟩, + ⟨4, 6, 6, 5, 8, 3, -168731671537312274140238935316720082647148134400000⟩, + ⟨4, 6, 0, 6, 1, 3, -32201117041964285681386671300682460279542382592000000⟩, + ⟨4, 6, 1, 6, 2, 3, -112154901454334663497228866368398012782493669785600000⟩, + ⟨4, 6, 2, 6, 3, 3, -3523353895392032481809852726865195326156832768000000⟩, + ⟨4, 6, 3, 6, 4, 3, -8901284250861576388980379881657380513133468057600000⟩, + ⟨4, 6, 4, 6, 5, 3, 1231013715538162097003801933709581075245065830400000⟩, + ⟨4, 6, 5, 6, 6, 3, -232567909322229913500307873794767129370899251200000⟩, + ⟨4, 6, 6, 6, 7, 3, -159349641407845098175756061632285191687477657600000⟩, + ⟨4, 6, 7, 6, 8, 3, -24973525859854050834082566829792475113901260800000⟩, + ⟨4, 6, 0, 7, 0, 3, 314066814976892913684097643996028937600050502041600000⟩, + ⟨4, 6, 1, 7, 1, 3, 320939611428032015655654478865389044574417688985600000⟩, + ⟨4, 6, 2, 7, 2, 3, 17041030583750769119339105490031788409307843788800000⟩, + ⟨4, 6, 3, 7, 3, 3, 15863936530328732188075785905514918727899729100800000⟩, + ⟨4, 6, 4, 7, 4, 3, 5090996770046677234431673327226468601923685580800000⟩, + ⟨4, 6, 5, 7, 5, 3, 263011130951452981065820248798236929288254259200000⟩, + ⟨4, 6, 6, 7, 6, 3, 172467279482569247390323953991270594724757504000000⟩, + ⟨4, 6, 7, 7, 7, 3, 8826459189527985404802458350572079860311654400000⟩, + ⟨4, 6, 8, 7, 8, 3, 29604416362574608488209408555793374238474240000000⟩ +] + +def collectedFourData_10_7_18 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 7, 4, -10200945527339497103013676689450706696499783270400000⟩, + ⟨4, 7, 1, 0, 8, 4, -586894190095819752314232164808046497370000588800000⟩, + ⟨4, 7, 0, 1, 6, 4, -1283396697793804716344802868478938778118075187200000⟩, + ⟨4, 7, 1, 1, 7, 4, -6154580197114636022784140185988603954676419788800000⟩, + ⟨4, 7, 2, 1, 8, 4, 1128115053623399982935468514567293435851151769600000⟩, + ⟨4, 7, 0, 2, 5, 4, 6207082060484563668904217682855811459214160691200000⟩, + ⟨4, 7, 1, 2, 6, 4, -7298187889143794313637688437206180207344694067200000⟩, + ⟨4, 7, 2, 2, 7, 4, 1371272550480989271576957274772277157719913267200000⟩, + ⟨4, 7, 3, 2, 8, 4, 144208800760350897851834614688251615566102528000000⟩, + ⟨4, 7, 0, 3, 4, 4, -3941854981804687475404272905785909680703694438400000⟩, + ⟨4, 7, 1, 3, 5, 4, -6029429090454165304890522325399396891277603635200000⟩, + ⟨4, 7, 2, 3, 6, 4, 544741979645200722330792100585403827762495488000000⟩, + ⟨4, 7, 3, 3, 7, 4, 360073429785206698932887493468315187241444966400000⟩, + ⟨4, 7, 4, 3, 8, 4, 41834810379402328664662552991194252801883504640000⟩, + ⟨4, 7, 0, 4, 3, 4, -15127844567607752667985299643142885046741683404800000⟩, + ⟨4, 7, 1, 4, 4, 4, 6791032882992779496386827382050423729654490726400000⟩, + ⟨4, 7, 2, 4, 5, 4, 252988651340945513938865577153708290525154508800000⟩, + ⟨4, 7, 3, 4, 6, 4, 827093187418888670433311482968114011708168601600000⟩, + ⟨4, 7, 4, 4, 7, 4, 95332564012050222776846278675854678619418787840000⟩, + ⟨4, 7, 5, 4, 8, 4, -69036535754238767392919167805255777106945638400000⟩, + ⟨4, 7, 0, 5, 2, 4, 25531387340434456635411306790204996400981842329600000⟩, + ⟨4, 7, 1, 5, 3, 4, 12969142170815716722034784029893193888440936038400000⟩, + ⟨4, 7, 2, 5, 4, 4, -1341404854818272869650797768232418388595022233600000⟩, + ⟨4, 7, 3, 5, 5, 4, 271825810692583422526115649700224623703175987200000⟩, + ⟨4, 7, 4, 5, 6, 4, -87446539150518928678939780182542338734812037120000⟩, + ⟨4, 7, 5, 5, 7, 4, 2348515172114188969500847716708213549799833600000⟩, + ⟨4, 7, 6, 5, 8, 4, -13891700236074011206454394412836903390176870400000⟩, + ⟨4, 7, 0, 6, 1, 4, -18557854775968832649893636371697683200164757504000000⟩, + ⟨4, 7, 1, 6, 2, 4, -32318046154893180674264726269950133135583320473600000⟩, + ⟨4, 7, 2, 6, 3, 4, -676849086009645312976908657426767191864246272000000⟩, + ⟨4, 7, 3, 6, 4, 4, -1282476786689067098487750330871157141424360652800000⟩, + ⟨4, 7, 4, 6, 5, 4, 141889324711385624666673201435227652512242728960000⟩, + ⟨4, 7, 5, 6, 6, 4, -22338570227900779245351027299958177149642342400000⟩, + ⟨4, 7, 6, 6, 7, 4, -13119276487900854706759161386808342407125401600000⟩, + ⟨4, 7, 7, 6, 8, 4, -1799064398709763803445903167210795062997811200000⟩, + ⟨4, 7, 0, 7, 0, 4, 181000129116536880719373322028824624322135143219200000⟩, + ⟨4, 7, 1, 7, 1, 4, 92480498315874091917605495125843961409231755673600000⟩, + ⟨4, 7, 2, 7, 2, 4, 3273643896617641885303251942846825353587143475200000⟩, + ⟨4, 7, 3, 7, 3, 4, 2285639888838068207251218891514527932809111142400000⟩, + ⟨4, 7, 4, 7, 4, 4, 586799387116475148275844140290534931852867665920000⟩, + ⟨4, 7, 5, 7, 5, 4, 25262696975696006502864862031049994721977958400000⟩, + ⟨4, 7, 6, 7, 6, 4, 14199253319038229588452016391690656377995264000000⟩, + ⟨4, 7, 7, 7, 7, 4, 635848081030126344716296109167268406598041600000⟩, + ⟨4, 7, 8, 7, 8, 4, 1895705318641958146796386860303961628344320000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1026.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1026.lean new file mode 100644 index 0000000000000000000000000000000000000000..e8d46b1d4a8e76cba5b722e7e84ce20908edb183 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1026.lean @@ -0,0 +1,620 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1026. -/ +namespace LaughlinFock +def collectedFourData_10_7_19 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 7, 5, 22161512634954353309214212361197164140441894912000000⟩, + ⟨4, 8, 1, 0, 8, 5, 850016826010965532271208814806854437674418176000000⟩, + ⟨4, 8, 0, 1, 6, 5, 2788174101860344146850858710403683661450838016000000⟩, + ⟨4, 8, 1, 1, 7, 5, 8913866950577924437508991337833178692820402176000000⟩, + ⟨4, 8, 2, 1, 8, 5, -1225412680988877631523290892657808882630918144000000⟩, + ⟨4, 8, 0, 2, 5, 5, -13484860510327974437147090075712037668714971136000000⟩, + ⟨4, 8, 1, 2, 6, 5, 10570188987811999849867550809903659900620242944000000⟩, + ⟨4, 8, 2, 2, 7, 5, -1489542017061255042227736601656652397656670208000000⟩, + ⟨4, 8, 3, 2, 8, 5, -125317213058607456213005532445429842088820736000000⟩, + ⟨4, 8, 0, 3, 4, 5, 8563663902556491405408959097212342892025085952000000⟩, + ⟨4, 8, 1, 3, 5, 5, 8732606770718374588753183911002040677437538304000000⟩, + ⟨4, 8, 2, 3, 6, 5, -591724866697025408019928798185364218257080320000000⟩, + ⟨4, 8, 3, 3, 7, 5, -312903224208370310558263299077980432165031116800000⟩, + ⟨4, 8, 4, 3, 8, 5, -30295318419887905464928533754088703264188006400000⟩, + ⟨4, 8, 0, 4, 3, 5, 32865180744877744192209650893861081085581983744000000⟩, + ⟨4, 8, 1, 4, 4, 5, -9835660863494267187894805190571763167267913728000000⟩, + ⟨4, 8, 2, 4, 5, 5, -274808407620949365781297967537508359111442432000000⟩, + ⟨4, 8, 3, 4, 6, 5, -718742633186040054658997343143972058912994099200000⟩, + ⟨4, 8, 4, 4, 7, 5, -69036535754238767392919167805255777106945638400000⟩, + ⟨4, 8, 5, 4, 8, 5, 42851883688922171383388638785842890798006272000000⟩, + ⟨4, 8, 0, 5, 2, 5, -55466835070976161673981701502676588710842073088000000⟩, + ⟨4, 8, 1, 5, 3, 5, -18783605716597566690258992096038481538966355968000000⟩, + ⟨4, 8, 2, 5, 4, 5, 1457098293436211133203607732842026502511919104000000⟩, + ⟨4, 8, 3, 5, 5, 5, -236216186902491275014135960442399264526984806400000⟩, + ⟨4, 8, 4, 5, 6, 5, 63325750117096932304771097022893470526944051200000⟩, + ⟨4, 8, 5, 5, 7, 5, -1457754186208962250097937287285139453247488000000⟩, + ⟨4, 8, 6, 5, 8, 5, 7544915554093877480947137723848099761225728000000⟩, + ⟨4, 8, 0, 6, 1, 5, 40316863960604288006898450040360897650748293120000000⟩, + ⟨4, 8, 1, 6, 2, 5, 46807215813421384454455225647978689098281910272000000⟩, + ⟨4, 8, 2, 6, 3, 5, 735225942112848528872108883972812827609006080000000⟩, + ⟨4, 8, 3, 6, 4, 5, 1114470239491928656543288740049521240444606873600000⟩, + ⟨4, 8, 4, 6, 5, 5, -102751326790541284234044641652404249857464729600000⟩, + ⟨4, 8, 5, 6, 6, 5, 13865843682981293695021463008692224070254592000000⟩, + ⟨4, 8, 6, 6, 7, 5, 7125393691909628471762373763854182029197312000000⟩, + ⟨4, 8, 7, 6, 8, 5, 868546685125035251192794198182779166916608000000⟩, + ⟨4, 8, 0, 7, 0, 5, -393222043740358037095607829032996866887543422976000000⟩, + ⟨4, 8, 1, 7, 1, 5, -133942337431449810943101409396075524031116214272000000⟩, + ⟨4, 8, 2, 7, 2, 5, -3555989019978352515179515886275211615249891328000000⟩, + ⟨4, 8, 3, 7, 3, 5, -1986217341899730921400499020515418890639822028800000⟩, + ⟨4, 8, 4, 7, 4, 5, -424939759976573307330418988521584155583263539200000⟩, + ⟨4, 8, 5, 7, 5, 5, -15680887527797823125564350191401120009551872000000⟩, + ⟨4, 8, 6, 7, 6, 5, -7711955009303288984466946702182470626836480000000⟩, + ⟨4, 8, 7, 7, 7, 5, -306972748400723396955034697531731470188544000000⟩, + ⟨4, 8, 8, 7, 8, 5, -823682417647238846272011763518946588753920000000⟩ +] + +def collectedFourData_10_7_20 : List CollectedFourTerm := [ + ⟨5, 2, 3, 2, 8, 0, 7724224745799692564484952837026863660258033664000000⟩, + ⟨5, 2, 3, 3, 7, 0, 19286535093470907382444606399450105057025143603200000⟩, + ⟨5, 2, 4, 3, 8, 0, 11203944414787150753843167240948791198195751321600000⟩, + ⟨5, 2, 3, 4, 6, 0, 44301413170754513872855839804291494814386277580800000⟩, + ⟨5, 2, 4, 4, 7, 0, 25531387340434456635411306790204996400981842329600000⟩, + ⟨5, 2, 5, 4, 8, 0, -55466835070976161673981701502676588710842073088000000⟩, + ⟨5, 2, 3, 5, 5, 0, 14559746994831097962701236612657421960749881753600000⟩, + ⟨5, 2, 4, 5, 6, 0, -23419400136454486531351059597441181405741370572800000⟩, + ⟨5, 2, 5, 5, 7, 0, 1886895138786635939966798101130053936534781952000000⟩, + ⟨5, 2, 6, 5, 8, 0, -26042734531896695694891228235904517136220946432000000⟩, + ⟨5, 2, 3, 6, 4, 0, -68693026219111189412042997006217767741487998566400000⟩, + ⟨5, 2, 4, 6, 5, 0, 37999935764039212861463183372796117352272258662400000⟩, + ⟨5, 2, 5, 6, 6, 0, -17947739946906513135269099818958862303381946368000000⟩, + ⟨5, 2, 6, 6, 7, 0, -24594673727390651265418128969437230841701859328000000⟩, + ⟨5, 2, 7, 6, 8, 0, -6745402757787396479197583275090354744005230592000000⟩, + ⟨5, 2, 3, 7, 3, 0, 122425234079083442320368481543500765982046237491200000⟩, + ⟨5, 2, 4, 7, 4, 0, 157153042078114487998058814266769799685797104844800000⟩, + ⟨5, 2, 5, 7, 5, 0, 20297105457133891005514421826361404052878655488000000⟩, + ⟨5, 2, 6, 7, 6, 0, 26619303501712527448969017639109248056159109120000000⟩, + ⟨5, 2, 7, 7, 7, 0, 2384045508537893360217180884195316225389101056000000⟩, + ⟨5, 2, 8, 7, 8, 0, 12793945902260459109103705268222244763635548160000000⟩ +] + +def collectedFourData_10_7_21 : List CollectedFourTerm := [ + ⟨5, 3, 2, 1, 8, 1, 15346995716626192029912179202901756374144358809600000⟩, + ⟨5, 3, 2, 2, 7, 1, 18654935851591131406290963338224742644902474547200000⟩, + ⟨5, 3, 3, 2, 8, 1, 7847326708248079159938165846052720511299878912000000⟩, + ⟨5, 3, 2, 3, 6, 1, 7410727125242535530786476312127065205860466688000000⟩, + ⟨5, 3, 3, 3, 7, 1, 19593907081854207951945121384176109676696017305600000⟩, + ⟨5, 3, 4, 3, 8, 1, 5691251558397243415302953463821443574295586406400000⟩, + ⟨5, 3, 2, 4, 5, 1, 3441684193481799118809643468939093311402855628800000⟩, + ⟨5, 3, 3, 4, 6, 1, 45007450485829046794462524018454293153459889766400000⟩, + ⟨5, 3, 4, 4, 7, 1, 12969142170815716722034784029893193888440936038400000⟩, + ⟨5, 3, 5, 4, 8, 1, -18783605716597566690258992096038481538966355968000000⟩, + ⟨5, 3, 2, 5, 4, 1, -18248612581700412737950153702856623874903742873600000⟩, + ⟨5, 3, 3, 5, 5, 1, 14791787553825752939407022868314463693553061068800000⟩, + ⟨5, 3, 4, 5, 6, 1, -11896319063080369102921079061316235975418131251200000⟩, + ⟨5, 3, 5, 5, 7, 1, 638988943035596519984252046155407621695209472000000⟩, + ⟨5, 3, 6, 5, 8, 1, -6614445234749878676625188100700701988239704064000000⟩, + ⟨5, 3, 2, 6, 3, 1, -9207926080259615766995513521703265403322499072000000⟩, + ⟨5, 3, 3, 6, 4, 1, -69787795806012377172870189165602201993164829491200000⟩, + ⟨5, 3, 4, 6, 5, 1, 19302772811925977006630018606432075504428882329600000⟩, + ⟨5, 3, 5, 6, 6, 1, -6077925128328160271852473360954615472270082048000000⟩, + ⟨5, 3, 6, 6, 7, 1, -6246660550838826053617270671185250288408723456000000⟩, + ⟨5, 3, 7, 6, 8, 1, -1370581021684010256391481565451817245440422707200000⟩, + ⟨5, 3, 2, 7, 2, 1, 44534995519989139949373046462941991910103003955200000⟩, + ⟨5, 3, 3, 7, 3, 1, 124376340768014718789328718815591681259512371609600000⟩, + ⟨5, 3, 4, 7, 4, 1, 79828805153075917833363900846152244590122578739200000⟩, + ⟨5, 3, 5, 7, 5, 1, 6873527678425264582409636711007831045458362368000000⟩, + ⟨5, 3, 6, 7, 6, 1, 6760884690646187883982976060304751017056010240000000⟩, + ⟨5, 3, 7, 7, 7, 1, 484408069638356876819980981868435034131241369600000⟩, + ⟨5, 3, 8, 7, 8, 1, 2166307443718640140805425137255016288883834880000000⟩ +] + +def collectedFourData_10_7_22 : List CollectedFourTerm := [ + ⟨5, 4, 1, 0, 8, 2, 825806715698593174339292850182716135105049395200000⟩, + ⟨5, 4, 1, 1, 7, 2, 8659982914898238047088298463818903173050086195200000⟩, + ⟨5, 4, 2, 1, 8, 2, -4762042305500330606248098751350229072017044275200000⟩, + ⟨5, 4, 1, 2, 6, 2, 10269129722175473781263351591655036846938574028800000⟩, + ⟨5, 4, 2, 2, 7, 2, -5788468008460549970444656674681991464596432486400000⟩, + ⟨5, 4, 3, 2, 8, 2, -1217479383579807449749435017601086822989955072000000⟩, + ⟨5, 4, 1, 3, 5, 2, 8483885372783442141709086703879595593397226700800000⟩, + ⟨5, 4, 2, 3, 6, 2, -2299485628101929523283619344392622694052397056000000⟩, + ⟨5, 4, 3, 3, 7, 2, -3039911399491301289500595943866382194356885913600000⟩, + ⟨5, 4, 4, 3, 8, 2, -588648992344722881207854848728836100362705305600000⟩, + ⟨5, 4, 1, 4, 4, 2, -9555522368333222104032434133687552350623472025600000⟩, + ⟨5, 4, 2, 4, 5, 2, -1067925347354895049041379428057815191341603225600000⟩, + ⟨5, 4, 3, 4, 6, 2, -6982714637889597502820993292622824473455126118400000⟩, + ⟨5, 4, 4, 4, 7, 2, -1341404854818272869650797768232418388595022233600000⟩, + ⟨5, 4, 5, 4, 8, 2, 1457098293436211133203607732842026502511919104000000⟩, + ⟨5, 4, 1, 5, 3, 2, -18248612581700412737950153702856623874903742873600000⟩, + ⟨5, 4, 2, 5, 4, 2, 5662389351982355802450620855280570978012443443200000⟩, + ⟨5, 4, 3, 5, 5, 2, -2294882966214069974794281171494821993898626252800000⟩, + ⟨5, 4, 4, 5, 6, 2, 1230442224744266346999004681250304602443402444800000⟩, + ⟨5, 4, 5, 5, 7, 2, -49568209238925003621224730283342661960073216000000⟩, + ⟨5, 4, 6, 5, 8, 2, 410481225340674192800683491044530517142247833600000⟩, + ⟨5, 4, 1, 6, 2, 2, 45474056488121942953450257565777492844000732774400000⟩, + ⟨5, 4, 2, 6, 3, 2, 2857141185790046510014030118666798449834328064000000⟩, + ⟨5, 4, 3, 6, 4, 2, 10827279885007611443315932647219398548774925107200000⟩, + ⟨5, 4, 4, 6, 5, 2, -1996495436655630033337187936596695642074932838400000⟩, + ⟨5, 4, 5, 6, 6, 2, 471482124664412588064429646861752225805369344000000⟩, + ⟨5, 4, 6, 6, 7, 2, 387657133167349211875533199295099776935552614400000⟩, + ⟨5, 4, 7, 6, 8, 2, 70879939944905545486508220070565999022597734400000⟩, + ⟨5, 4, 1, 7, 1, 2, -130127402637828951063565344839682300757246633574400000⟩, + ⟨5, 4, 2, 7, 2, 2, -13818830516235920304291456256511620992312174182400000⟩, + ⟨5, 4, 3, 7, 3, 2, -19296460606259186370992500573060346684655638937600000⟩, + ⟨5, 4, 4, 7, 4, 2, -8256733203807791964536346123195421321264417996800000⟩, + ⟨5, 4, 5, 7, 5, 2, -533199301626641592080852904343288038297698304000000⟩, + ⟨5, 4, 6, 7, 6, 2, -419569008996170989475137639606216837746917376000000⟩, + ⟨5, 4, 7, 7, 7, 2, -25051284339693934332393528981620782907208499200000⟩, + ⟨5, 4, 8, 7, 8, 2, -96026683418217661181111391232954583828398080000000⟩ +] + +def collectedFourData_10_7_23 : List CollectedFourTerm := [ + ⟨5, 5, 0, 0, 7, 3, -5817278317300779223675652810616818384205407846400000⟩, + ⟨5, 5, 1, 0, 8, 3, -669374586393787064852509065953679405745805721600000⟩, + ⟨5, 5, 0, 1, 6, 3, -731880761696263254382531686913663306317378355200000⟩, + ⟨5, 5, 1, 1, 7, 3, -7019526932441421206577885413946270948945140121600000⟩, + ⟨5, 5, 2, 1, 8, 3, 1929985575339775776463370005254258849502514380800000⟩, + ⟨5, 5, 0, 2, 5, 3, 3539703627216690747533978208915896849640141619200000⟩, + ⟨5, 5, 1, 2, 6, 3, -8323853911251334044885484309938508634721248870400000⟩, + ⟨5, 5, 2, 2, 7, 3, 2345980787852504099457026638530911686503274905600000⟩, + ⟨5, 5, 3, 2, 8, 3, 328950969330754245971387843336959941402427392000000⟩, + ⟨5, 5, 0, 3, 4, 3, -2247915887222373276512993139761082492470584934400000⟩, + ⟨5, 5, 1, 3, 5, 3, -6876787454574209648570582131867407822583391846400000⟩, + ⟨5, 5, 2, 3, 6, 3, 931947640996768968466210683700681769824026624000000⟩, + ⟨5, 5, 3, 3, 7, 3, 821354197064087767529792056477807293559839129600000⟩, + ⟨5, 5, 4, 3, 8, 3, 119285381279728572495059195531432262360052531200000⟩, + ⟨5, 5, 0, 4, 3, 3, -8626933842042870312274395035875286588752448716800000⟩, + ⟨5, 5, 1, 4, 4, 3, 7745424820950663074006273254986199626127559884800000⟩, + ⟨5, 5, 2, 4, 5, 3, 432814406867835820246898854249465180231984742400000⟩, + ⟨5, 5, 3, 4, 6, 3, 1886660899291737479796957141639309915054302822400000⟩, + ⟨5, 5, 4, 4, 7, 3, 271825810692583422526115649700224623703175987200000⟩, + ⟨5, 5, 5, 4, 8, 3, -236216186902491275014135960442399264526984806400000⟩, + ⟨5, 5, 0, 5, 2, 3, 14559746994831097962701236612657421960749881753600000⟩, + ⟨5, 5, 1, 5, 3, 3, 14791787553825752939407022868314463693553061068800000⟩, + ⟨5, 5, 2, 5, 4, 3, -2294882966214069974794281171494821993898626252800000⟩, + ⟨5, 5, 3, 5, 5, 3, 620054833304099124216742687795641404632124620800000⟩, + ⟨5, 5, 4, 5, 6, 3, -249340051253063328042091880850197325995940249600000⟩, + ⟨5, 5, 5, 5, 7, 3, 8035705916854326496397064551670152257182105600000⟩, + ⟨5, 5, 6, 5, 8, 3, -55453997328012764167567658061998596255698124800000⟩, + ⟨5, 5, 0, 6, 1, 3, -10582960757365812318801160426507529750015115264000000⟩, + ⟨5, 5, 1, 6, 2, 3, -36859930023255186526917590344596455183535518515200000⟩, + ⟨5, 5, 2, 6, 3, 3, -1157957221193693420849240757764207072149241856000000⟩, + ⟨5, 5, 3, 6, 4, 3, -2925424661332805615665734332803433375674348339200000⟩, + ⟨5, 5, 4, 6, 5, 3, 404575090557937661308672336861953523708644556800000⟩, + ⟨5, 5, 5, 6, 6, 3, -76433903040452780118161612642973806137599590400000⟩, + ⟨5, 5, 6, 6, 7, 3, -52370574583541472012609804313370865591071539200000⟩, + ⟨5, 5, 7, 6, 8, 3, -8207598630925433779880985171360170055932313600000⟩, + ⟨5, 5, 0, 7, 0, 3, 103218679456362613905384327938185027326812828467200000⟩, + ⟨5, 5, 1, 7, 1, 3, 105477437593261435333773537170475442332840964915200000⟩, + ⟨5, 5, 2, 7, 2, 3, 5600568380838501933317669818060353639829576089600000⟩, + ⟨5, 5, 3, 7, 3, 3, 5213714093800570606607329956098356988580829593600000⟩, + ⟨5, 5, 4, 7, 4, 3, 1673166150201151880670121557074499066274617753600000⟩, + ⟨5, 5, 5, 7, 5, 3, 86439127996158376156745360720059993577383526400000⟩, + ⟨5, 5, 6, 7, 6, 3, 56681712262188442090721131606156169831251968000000⟩, + ⟨5, 5, 7, 7, 7, 3, 2900833257043043782692276046126364024949964800000⟩, + ⟨5, 5, 8, 7, 8, 3, 9729549947026738599886366919454663722926080000000⟩ +] + +def collectedFourData_10_7_24 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 7, 4, 9357110990071021481897870172996494113622930227200000⟩, + ⟨5, 6, 1, 0, 8, 4, 538345593693871656634441694697222644682876518400000⟩, + ⟨5, 6, 0, 1, 6, 4, 1177232572545586200208651708641269991897405849600000⟩, + ⟨5, 6, 1, 1, 7, 4, 5645465888171898980331143860429776619399702118400000⟩, + ⟨5, 6, 2, 1, 8, 4, -1034796013568867031901579372859995288484236492800000⟩, + ⟨5, 6, 0, 2, 5, 4, -5693624733979017403591589991814305798738778521600000⟩, + ⟨5, 6, 1, 2, 6, 4, 6694472970381726203864164952958789127367137689600000⟩, + ⟨5, 6, 2, 2, 7, 4, -1257839228540108597093927852374845675242363289600000⟩, + ⟨5, 6, 3, 2, 8, 4, -132279674550087723351601927830791409006280704000000⟩, + ⟨5, 6, 0, 3, 4, 4, 3615779975753937850133137332903756109878342451200000⟩, + ⟨5, 6, 1, 3, 5, 4, 5530667432243111877534032735735218324891081113600000⟩, + ⟨5, 6, 2, 3, 6, 4, -499680265013683800638780029792960281506217984000000⟩, + ⟨5, 6, 3, 3, 7, 4, -330287720686854341855143940332888681417487155200000⟩, + ⟨5, 6, 4, 3, 8, 4, -38374184326297191587628092417085705735918059520000⟩, + ⟨5, 6, 0, 4, 3, 4, 13876450989790457247559232983088000230203221606400000⟩, + ⟨5, 6, 1, 4, 4, 4, -6229270439007865419348715268171712433220694835200000⟩, + ⟨5, 6, 2, 4, 5, 4, -232061124479213489962139432088136442496575078400000⟩, + ⟨5, 6, 3, 4, 6, 4, -758675039786102204268733929341582000320728268800000⟩, + ⟨5, 6, 4, 4, 7, 4, -87446539150518928678939780182542338734812037120000⟩, + ⟨5, 6, 5, 4, 8, 4, 63325750117096932304771097022893470526944051200000⟩, + ⟨5, 6, 0, 5, 2, 4, -23419400136454486531351059597441181405741370572800000⟩, + ⟨5, 6, 1, 5, 3, 4, -11896319063080369102921079061316235975418131251200000⟩, + ⟨5, 6, 2, 5, 4, 4, 1230442224744266346999004681250304602443402444800000⟩, + ⟨5, 6, 3, 5, 5, 4, -249340051253063328042091880850197325995940249600000⟩, + ⟨5, 6, 4, 5, 6, 4, 80212855792241746217112574247705635092336476160000⟩, + ⟨5, 6, 5, 5, 7, 4, -2154243159954367910158609150813347601239244800000⟩, + ⟨5, 6, 6, 5, 8, 4, 12742562010684705322076067343668207196255027200000⟩, + ⟨5, 6, 0, 6, 1, 4, 17022726610093855848045707542135177851722268672000000⟩, + ⟨5, 6, 1, 6, 2, 4, 29644658335161524784070614677149093680753986764800000⟩, + ⟨5, 6, 2, 6, 3, 4, 620859311947740223569818815452817941589917696000000⟩, + ⟨5, 6, 3, 6, 4, 4, 1176388757598730610962392006598544946983495270400000⟩, + ⟨5, 6, 4, 6, 5, 4, -130152068361934695256501663613268871724956385280000⟩, + ⟨5, 6, 5, 6, 6, 4, 20490696712550651413223681842643832021398323200000⟩, + ⟨5, 6, 6, 6, 7, 4, 12034034088086540603103719282590053259070668800000⟩, + ⟨5, 6, 7, 6, 8, 4, 1650243618289678569859671696981538857654681600000⟩, + ⟨5, 6, 0, 7, 0, 4, -166027579778904867036823969411075605633124899225600000⟩, + ⟨5, 6, 1, 7, 1, 4, -84830399774166972081383380714529539596961500364800000⟩, + ⟨5, 6, 2, 7, 2, 4, -3002844118765619487703837882458747710853454233600000⟩, + ⟨5, 6, 3, 7, 3, 4, -2096568996067301201656245209580072783349756723200000⟩, + ⟨5, 6, 4, 7, 4, 4, -538258632931505128258999948657806166838539714560000⟩, + ⟨5, 6, 5, 7, 5, 4, -23172936163278456729206798399725846157013811200000⟩, + ⟨5, 6, 6, 7, 6, 4, -13024673931086781232010706723864066341732352000000⟩, + ⟨5, 6, 7, 7, 7, 4, -583249959631369860032619446448648595754188800000⟩, + ⟨5, 6, 8, 7, 8, 4, -1738890284578068606856040580226580490485760000000⟩ +] + +def collectedFourData_10_7_25 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 7, 5, -753900063083553400339691426442153115986690048000000⟩, + ⟨5, 7, 1, 0, 8, 5, -28916245443508223803321025195675091053051904000000⟩, + ⟨5, 7, 0, 1, 6, 5, -94849330273830058645375905629128748395659264000000⟩, + ⟨5, 7, 1, 1, 7, 5, -303235838051942645578279863067522012129787904000000⟩, + ⟨5, 7, 2, 1, 8, 5, 41686626392269455372648963488655069073637376000000⟩, + ⟨5, 7, 0, 2, 5, 5, 458733903089919552876188979521450924776095744000000⟩, + ⟨5, 7, 1, 2, 6, 5, -359581328042906934399765003350585174787096576000000⟩, + ⟨5, 7, 2, 2, 7, 5, 50671894068136859194536078831397969625874432000000⟩, + ⟨5, 7, 3, 2, 8, 5, 4263095953176296326677144637078953623814144000000⟩, + ⟨5, 7, 0, 3, 4, 5, -291322477066872194441760892260952350243422208000000⟩, + ⟨5, 7, 1, 3, 5, 5, -297069649701824534040130432069741736431190016000000⟩, + ⟨5, 7, 2, 3, 6, 5, 20129556212123312462916728901134387018465280000000⟩, + ⟨5, 7, 3, 3, 7, 5, 10644479208412278842990114230051063765087027200000⟩, + ⟨5, 7, 4, 3, 8, 5, 1030599438048551450115200887266401987434905600000⟩, + ⟨5, 7, 0, 4, 3, 5, -1118022142483901342632673350062388481177419776000000⟩, + ⟨5, 7, 1, 4, 4, 5, 334593827939400420978009693837859846474432512000000⟩, + ⟨5, 7, 2, 4, 5, 5, 9348553018648734235641838581724654105264128000000⟩, + ⟨5, 7, 3, 4, 6, 5, 24450502338235855867585247963709283213561036800000⟩, + ⟨5, 7, 4, 4, 7, 5, 2348515172114188969500847716708213549799833600000⟩, + ⟨5, 7, 5, 4, 8, 5, -1457754186208962250097937287285139453247488000000⟩, + ⟨5, 7, 0, 5, 2, 5, 1886895138786635939966798101130053936534781952000000⟩, + ⟨5, 7, 1, 5, 3, 5, 638988943035596519984252046155407621695209472000000⟩, + ⟨5, 7, 2, 5, 4, 5, -49568209238925003621224730283342661960073216000000⟩, + ⟨5, 7, 3, 5, 5, 5, 8035705916854326496397064551670152257182105600000⟩, + ⟨5, 7, 4, 5, 6, 5, -2154243159954367910158609150813347601239244800000⟩, + ⟨5, 7, 5, 5, 7, 5, 49590521687127352254400543567381687959552000000⟩, + ⟨5, 7, 6, 5, 8, 5, -256666248639538022920135208483044838080512000000⟩, + ⟨5, 7, 0, 6, 1, 5, -1371516772518953940232014645688382270189076480000000⟩, + ⟨5, 7, 1, 6, 2, 5, -1592308410340446223654108747042851445945663488000000⟩, + ⟨5, 7, 2, 6, 3, 5, -25011238775519763468085015324526658264760320000000⟩, + ⟨5, 7, 3, 6, 4, 5, -37912537726892326008998329491178244941440614400000⟩, + ⟨5, 7, 4, 6, 5, 5, 3495439730369625105125151949533350942107238400000⟩, + ⟨5, 7, 5, 6, 6, 5, -471694355863530568034143805138952957984768000000⟩, + ⟨5, 7, 6, 6, 7, 5, -242394769811563762240093365522973901979648000000⟩, + ⟨5, 7, 7, 6, 8, 5, -29546602323254455607580984271349357740032000000⟩, + ⟨5, 7, 0, 7, 0, 5, 13376800061658351025644359914648108966141231104000000⟩, + ⟨5, 7, 1, 7, 1, 5, 4556509219495188035055852209942221941519679488000000⟩, + ⟨5, 7, 2, 7, 2, 5, 120969195137776976813519004443543069012262912000000⟩, + ⟨5, 7, 3, 7, 3, 5, 67568013249874410039975922373877417886561075200000⟩, + ⟨5, 7, 4, 7, 4, 5, 14455787252886157319689377584712551483886796800000⟩, + ⟨5, 7, 5, 7, 5, 5, 533439313964826495171913220429929814949888000000⟩, + ⟨5, 7, 6, 7, 6, 5, 262348670137301327961211324463367239761920000000⟩, + ⟨5, 7, 7, 7, 7, 5, 10442733679614365880386908301588982398976000000⟩, + ⟨5, 7, 8, 7, 8, 5, 28020389982118482899855206082699518279680000000⟩ +] + +def collectedFourData_10_7_26 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 7, 6, 10405251888608135423669545213031291404909805568000000⟩, + ⟨5, 8, 1, 0, 8, 6, 299324305945018456138582913924968998814875648000000⟩, + ⟨5, 8, 0, 1, 6, 6, 1309100796368559514814373361666111469072154624000000⟩, + ⟨5, 8, 1, 1, 7, 6, 3138922614966630563179627141721617990730907648000000⟩, + ⟨5, 8, 2, 1, 8, 6, -345212743097853272719018910558254162561833369600000⟩, + ⟨5, 8, 0, 2, 5, 6, -6331398610011731641237145630643121794060386304000000⟩, + ⟨5, 8, 1, 2, 6, 6, 3722178650665543806498458647023689486001242112000000⟩, + ⟨5, 8, 2, 2, 7, 6, -419620992704491518701177950649979584619164467200000⟩, + ⟨5, 8, 3, 2, 8, 6, -29419408082201721112693226215492332501860352000000⟩, + ⟨5, 8, 0, 3, 4, 6, 4020803158306832964825276614592304710709936128000000⟩, + ⟨5, 8, 1, 3, 5, 6, 3075093787263837472408559950233103483526971392000000⟩, + ⟨5, 8, 2, 3, 6, 6, -166695650829115058138336022839313546753343488000000⟩, + ⟨5, 8, 3, 3, 7, 6, -73457008965859927929726949757008123430279577600000⟩, + ⟨5, 8, 4, 3, 8, 6, -6096097920435618257651123488132887581451878400000⟩, + ⟨5, 8, 0, 4, 3, 6, 15430827743938032004466973234190767857929814016000000⟩, + ⟨5, 8, 1, 4, 4, 6, -3463522452010877105394345577179008827385708544000000⟩, + ⟨5, 8, 2, 4, 5, 6, -77416665987677985819078977102579715380399308800000⟩, + ⟨5, 8, 3, 4, 6, 6, -168731671537312274140238935316720082647148134400000⟩, + ⟨5, 8, 4, 4, 7, 6, -13891700236074011206454394412836903390176870400000⟩, + ⟨5, 8, 5, 4, 8, 6, 7544915554093877480947137723848099761225728000000⟩, + ⟨5, 8, 0, 5, 2, 6, -26042734531896695694891228235904517136220946432000000⟩, + ⟨5, 8, 1, 5, 3, 6, -6614445234749878676625188100700701988239704064000000⟩, + ⟨5, 8, 2, 5, 4, 6, 410481225340674192800683491044530517142247833600000⟩, + ⟨5, 8, 3, 5, 5, 6, -55453997328012764167567658061998596255698124800000⟩, + ⟨5, 8, 4, 5, 6, 6, 12742562010684705322076067343668207196255027200000⟩, + ⟨5, 8, 5, 5, 7, 6, -256666248639538022920135208483044838080512000000⟩, + ⟨5, 8, 6, 5, 8, 6, 1180827141055932375725571313215888596926464000000⟩, + ⟨5, 8, 0, 6, 1, 6, 18929534810144926245580837824619414883590471680000000⟩, + ⟨5, 8, 1, 6, 2, 6, 16482658881378787283245461389501792893802643456000000⟩, + ⟨5, 8, 2, 6, 3, 6, 207121542163789312810719549116023964562358272000000⟩, + ⟨5, 8, 3, 6, 4, 6, 261632492223941485491994368109389301987619635200000⟩, + ⟨5, 8, 4, 6, 5, 6, -20675872782991432403235699059935712344906137600000⟩, + ⟨5, 8, 5, 6, 6, 6, 2441354047206209515923696646860752874897408000000⟩, + ⟨5, 8, 6, 6, 7, 6, 1115169308628014411084594749589189145133056000000⟩, + ⟨5, 8, 7, 6, 8, 6, 122339758814394980313766342732929820105113600000⟩, + ⟨5, 8, 0, 7, 0, 6, -184625232070948790284634438549322921976019288064000000⟩, + ⟨5, 8, 1, 7, 1, 6, -47166357137270335072970604278679122582182035456000000⟩, + ⟨5, 8, 2, 7, 2, 6, -1001762706602606154761106108906326660570362675200000⟩, + ⟨5, 8, 3, 7, 3, 6, -466283418655077160335953064771127516742654361600000⟩, + ⟨5, 8, 4, 7, 4, 6, -85507415739952609463436099942123840644264755200000⟩, + ⟨5, 8, 5, 7, 5, 6, -2760928155908898217733939127804475503280128000000⟩, + ⟨5, 8, 6, 7, 6, 6, -1206969875315091141855116618881812387594240000000⟩, + ⟨5, 8, 7, 7, 7, 6, -43238864007097178174905241437494003420364800000⟩, + ⟨5, 8, 8, 7, 8, 6, -105473064205905293330705629548336371466240000000⟩ +] + +def collectedFourData_10_7_27 : List CollectedFourTerm := [ + ⟨6, 1, 3, 2, 8, 0, -5614463451521010298511205880356141241057935360000000⟩, + ⟨6, 1, 3, 3, 7, 0, -14018694425955509395346338026750176701414637568000000⟩, + ⟨6, 1, 4, 3, 8, 0, -8143747560413963318052736286426101082524483584000000⟩, + ⟨6, 1, 3, 4, 6, 0, -32201117041964285681386671300682460279542382592000000⟩, + ⟨6, 1, 4, 4, 7, 0, -18557854775968832649893636371697683200164757504000000⟩, + ⟨6, 1, 5, 4, 8, 0, 40316863960604288006898450040360897650748293120000000⟩, + ⟨6, 1, 3, 5, 5, 0, -10582960757365812318801160426507529750015115264000000⟩, + ⟨6, 1, 4, 5, 6, 0, 17022726610093855848045707542135177851722268672000000⟩, + ⟨6, 1, 5, 5, 7, 0, -1371516772518953940232014645688382270189076480000000⟩, + ⟨6, 1, 6, 5, 8, 0, 18929534810144926245580837824619414883590471680000000⟩, + ⟨6, 1, 3, 6, 4, 0, 49930510539753230178122241011567753555173441536000000⟩, + ⟨6, 1, 4, 6, 5, 0, -27620797883096309612243039885025759838209048576000000⟩, + ⟨6, 1, 5, 6, 6, 0, 13045571987545503369641494030296567519715000320000000⟩, + ⟨6, 1, 6, 6, 7, 0, 17876991062385605223779227958429685935473950720000000⟩, + ⟨6, 1, 7, 6, 8, 0, 4902992662141329328924818893019196816443310080000000⟩, + ⟨6, 1, 3, 7, 3, 0, -88986535853282783679370929771788110788651122688000000⟩, + ⟨6, 1, 4, 7, 4, 0, -114228940777870802182968666894494099196925181952000000⟩, + ⟨6, 1, 5, 7, 5, 0, -14753241977159459428161862882325143974177669120000000⟩, + ⟨6, 1, 6, 7, 6, 0, -19348622228603640041472646300753549023038668800000000⟩, + ⟨6, 1, 7, 7, 7, 0, -1732877643381291026245034609448613817289277440000000⟩, + ⟨6, 1, 8, 7, 8, 0, -9299462927724746332094298175313701417412198400000000⟩ +] + +def collectedFourData_10_7_28 : List CollectedFourTerm := [ + ⟨6, 2, 2, 1, 8, 1, -38243463551890216224091109513902133927255369318400000⟩, + ⟨6, 2, 2, 2, 7, 1, -46486580987983249615788385873920630844071660748800000⟩, + ⟨6, 2, 3, 2, 8, 1, -19554899114328711004323479342688746132364853248000000⟩, + ⟨6, 2, 2, 3, 6, 1, -18466928507719746709360839410785226725263409152000000⟩, + ⟨6, 2, 3, 3, 7, 1, -48826420829206170980037627592528006821731264102400000⟩, + ⟨6, 2, 4, 3, 8, 1, -14182135419664479616888242384870817949103528345600000⟩, + ⟨6, 2, 2, 4, 5, 1, -8576396738545058717229801417572893724681384755200000⟩, + ⟨6, 2, 3, 4, 6, 1, -112154901454334663497228866368398012782493669785600000⟩, + ⟨6, 2, 4, 4, 7, 1, -32318046154893180674264726269950133135583320473600000⟩, + ⟨6, 2, 5, 4, 8, 1, 46807215813421384454455225647978689098281910272000000⟩, + ⟨6, 2, 2, 5, 4, 1, 45474056488121942953450257565777492844000732774400000⟩, + ⟨6, 2, 3, 5, 5, 1, -36859930023255186526917590344596455183535518515200000⟩, + ⟨6, 2, 4, 5, 6, 1, 29644658335161524784070614677149093680753986764800000⟩, + ⟨6, 2, 5, 5, 7, 1, -1592308410340446223654108747042851445945663488000000⟩, + ⟨6, 2, 6, 5, 8, 1, 16482658881378787283245461389501792893802643456000000⟩, + ⟨6, 2, 2, 6, 3, 1, 22945401949738821023410961971711844561492901888000000⟩, + ⟨6, 2, 3, 6, 4, 1, 173905504018783620058004873119578642156423531724800000⟩, + ⟨6, 2, 4, 6, 5, 1, -48100937936900125040919326929452594582643959398400000⟩, + ⟨6, 2, 5, 6, 6, 1, 15145694467388196234416776901482642063692398592000000⟩, + ⟨6, 2, 6, 6, 7, 1, 15566169399410790453348557011642067097300762624000000⟩, + ⟨6, 2, 7, 6, 8, 1, 3415376293543901770356373119763346245475421388800000⟩, + ⟨6, 2, 2, 7, 2, 1, -110977582153565348898929645100816602928429976780800000⟩, + ⟨6, 2, 3, 7, 3, 1, -309935712676716095333577931946354439624052860518400000⟩, + ⟨6, 2, 4, 7, 4, 1, -198926881627731752269854497558936822389205159116800000⟩, + ⟨6, 2, 5, 7, 5, 1, -17128271232785140764343947964416383520312655872000000⟩, + ⟨6, 2, 6, 7, 6, 1, -16847574080257873814513724370682108456164392960000000⟩, + ⟨6, 2, 7, 7, 7, 1, -1207105462040784417540555660857969228411987558400000⟩, + ⟨6, 2, 8, 7, 8, 1, -5398261737721718647373879585974960237597163520000000⟩ +] + +def collectedFourData_10_7_29 : List CollectedFourTerm := [ + ⟨6, 3, 1, 0, 8, 2, 416687414491982894945606569453500489850159104000000⟩, + ⟨6, 3, 1, 1, 7, 2, 4369673704216692069152145100076300714171695104000000⟩, + ⟨6, 3, 2, 1, 8, 2, -2402842043130837275196281413287456276379336704000000⟩, + ⟨6, 3, 1, 2, 6, 2, 5181620628255884296741339280248079651098853376000000⟩, + ⟨6, 3, 2, 2, 7, 2, -2920758238535953497263991611930893898773168128000000⟩, + ⟨6, 3, 3, 2, 8, 2, -614318492326626763884363146582328381737533440000000⟩, + ⟨6, 3, 1, 3, 5, 2, 4280818009382419144161098773410582040795938816000000⟩, + ⟨6, 3, 2, 3, 6, 2, -1160279642706347936329410595250503651814277120000000⟩, + ⟨6, 3, 3, 3, 7, 2, -1533885347816739206719726488530360097803599872000000⟩, + ⟨6, 3, 4, 3, 8, 2, -297021835740263001130751088192203007524339712000000⟩, + ⟨6, 3, 1, 4, 4, 2, -4821547020736903947147290109051060023419994112000000⟩, + ⟨6, 3, 2, 4, 5, 2, -538856179539933522127830167064706503369818112000000⟩, + ⟨6, 3, 3, 4, 6, 2, -3523353895392032481809852726865195326156832768000000⟩, + ⟨6, 3, 4, 4, 7, 2, -676849086009645312976908657426767191864246272000000⟩, + ⟨6, 3, 5, 4, 8, 2, 735225942112848528872108883972812827609006080000000⟩, + ⟨6, 3, 1, 5, 3, 2, -9207926080259615766995513521703265403322499072000000⟩, + ⟨6, 3, 2, 5, 4, 2, 2857141185790046510014030118666798449834328064000000⟩, + ⟨6, 3, 3, 5, 5, 2, -1157957221193693420849240757764207072149241856000000⟩, + ⟨6, 3, 4, 5, 6, 2, 620859311947740223569818815452817941589917696000000⟩, + ⟨6, 3, 5, 5, 7, 2, -25011238775519763468085015324526658264760320000000⟩, + ⟨6, 3, 6, 5, 8, 2, 207121542163789312810719549116023964562358272000000⟩, + ⟨6, 3, 1, 6, 2, 2, 22945401949738821023410961971711844561492901888000000⟩, + ⟨6, 3, 2, 6, 3, 2, 1441662741308996098769968451396801049950945280000000⟩, + ⟨6, 3, 3, 6, 4, 2, 5463253295837251726254070221937472197669945344000000⟩, + ⟨6, 3, 4, 6, 5, 2, -1007396168776996205995215941314871423473287168000000⟩, + ⟨6, 3, 5, 6, 6, 2, 237901513478737535182048276874984061539450880000000⟩, + ⟨6, 3, 6, 6, 7, 2, 195604910275195323118485104964081170868338688000000⟩, + ⟨6, 3, 7, 6, 8, 2, 35764759905112536072200160135833118559961088000000⟩, + ⟨6, 3, 1, 7, 1, 2, -65659978211541386955992164687685860593015717888000000⟩, + ⟨6, 3, 2, 7, 2, 2, -6972736658168434307032608402454001972882178048000000⟩, + ⟨6, 3, 3, 7, 3, 2, -9736651598996240646899587609556691909032804352000000⟩, + ⟨6, 3, 4, 7, 4, 2, -4166201055817638478074306752332707481031540736000000⟩, + ⟨6, 3, 5, 7, 5, 2, -269042905779453097477330222932251486799790080000000⟩, + ⟨6, 3, 6, 7, 6, 2, -211707076530227636328034025617682249306603520000000⟩, + ⟨6, 3, 7, 7, 7, 2, -12640433533384438334201675139515324703965184000000⟩, + ⟨6, 3, 8, 7, 8, 2, -48453360423362622525105931392122588076441600000000⟩ +] + +def collectedFourData_10_7_30 : List CollectedFourTerm := [ + ⟨6, 4, 0, 0, 7, 3, 27445974996411339039852459194825464997440231833600000⟩, + ⟨6, 4, 1, 0, 8, 3, 3158115730299373588269343707440258120331716198400000⟩, + ⟨6, 4, 0, 1, 6, 3, 3453020465967767472922381322860796153927879884800000⟩, + ⟨6, 4, 1, 1, 7, 3, 33118195514464667137683822885413370546637661798400000⟩, + ⟨6, 4, 2, 1, 8, 3, -9105690488741873971149546671778750764353270579200000⟩, + ⟨6, 4, 0, 2, 5, 3, -16700355724491752487719906634892584964651273420800000⟩, + ⟨6, 4, 1, 2, 6, 3, 39272022733130757792734493068590215087825459609600000⟩, + ⟨6, 4, 2, 2, 7, 3, -11068359898471756209914814860755745782454707814400000⟩, + ⟨6, 4, 3, 2, 8, 3, -1551993834031707162015287130915240850917163008000000⟩, + ⟨6, 4, 0, 3, 4, 3, 10605688755041062542200951430378504309257640345600000⟩, + ⟨6, 4, 1, 3, 5, 3, 32444749286373232413328524126991934538083047833600000⟩, + ⟨6, 4, 2, 3, 6, 3, -4396937924852486389566968258236800253795762176000000⟩, + ⟨6, 4, 3, 3, 7, 3, -3875156993739706233101818681461269431279052390400000⟩, + ⟨6, 4, 4, 3, 8, 3, -562789575032730586319497701262978464034376908800000⟩, + ⟨6, 4, 0, 4, 3, 3, 40701956758752260310366179168355542257110299443200000⟩, + ⟨6, 4, 1, 4, 4, 3, -36542988727249561215677635547752792126951469875200000⟩, + ⟨6, 4, 2, 4, 5, 3, -2042022530304703678198043265436655676521290137600000⟩, + ⟨6, 4, 3, 4, 6, 3, -8901284250861576388980379881657380513133468057600000⟩, + ⟨6, 4, 4, 4, 7, 3, -1282476786689067098487750330871157141424360652800000⟩, + ⟨6, 4, 5, 4, 8, 3, 1114470239491928656543288740049521240444606873600000⟩, + ⟨6, 4, 0, 5, 2, 3, -68693026219111189412042997006217767741487998566400000⟩, + ⟨6, 4, 1, 5, 3, 3, -69787795806012377172870189165602201993164829491200000⟩, + ⟨6, 4, 2, 5, 4, 3, 10827279885007611443315932647219398548774925107200000⟩, + ⟨6, 4, 3, 5, 5, 3, -2925424661332805615665734332803433375674348339200000⟩, + ⟨6, 4, 4, 5, 6, 3, 1176388757598730610962392006598544946983495270400000⟩, + ⟨6, 4, 5, 5, 7, 3, -37912537726892326008998329491178244941440614400000⟩, + ⟨6, 4, 6, 5, 8, 3, 261632492223941485491994368109389301987619635200000⟩, + ⟨6, 4, 0, 6, 1, 3, 49930510539753230178122241011567753555173441536000000⟩, + ⟨6, 4, 1, 6, 2, 3, 173905504018783620058004873119578642156423531724800000⟩, + ⟨6, 4, 2, 6, 3, 3, 5463253295837251726254070221937472197669945344000000⟩, + ⟨6, 4, 3, 6, 4, 3, 13802181661145005665090640245238373444580330700800000⟩, + ⟨6, 4, 4, 6, 5, 3, -1908789164616805482612586643598182537403511603200000⟩, + ⟨6, 4, 5, 6, 6, 3, 360615888960901139707980056254426491985172889600000⟩, + ⟨6, 4, 6, 6, 7, 3, 247084874088422683807192139243787080843447500800000⟩, + ⟨6, 4, 7, 6, 8, 3, 38723529203512949361881531286924091852220006400000⟩, + ⟨6, 4, 0, 7, 0, 3, -486986721452998955566356947061559888164854484172800000⟩, + ⟨6, 4, 1, 7, 1, 3, -497643564046191382406662116364674860145877765324800000⟩, + ⟨6, 4, 2, 7, 2, 3, -26423535433922373826446457974965162571727267430400000⟩, + ⟨6, 4, 3, 7, 3, 3, -24598353190583504628376415971695946282928858726400000⟩, + ⟨6, 4, 4, 7, 4, 3, -7894013973285417770813245048631312615406462566400000⟩, + ⟨6, 4, 5, 7, 5, 3, -407820636437240310491940929180146351507872153600000⟩, + ⟨6, 4, 6, 7, 6, 3, -267424863079895535321781884047037924881989632000000⟩, + ⟨6, 4, 7, 7, 7, 3, -13686159179419115660843933866436646094975795200000⟩, + ⟨6, 4, 8, 7, 8, 3, -45904110136565799328751262279748661721169920000000⟩ +] + +def collectedFourData_10_7_31 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 7, 4, -15182695307648243970376619465547846713677027737600000⟩, + ⟨6, 5, 1, 0, 8, 4, -873510758602962264574486143060116267752174387200000⟩, + ⟨6, 5, 0, 1, 6, 4, -1910158324953552815285964291148520331460529356800000⟩, + ⟨6, 5, 1, 1, 7, 4, -9160240649147749696029039188637502279722939187200000⟩, + ⟨6, 5, 2, 1, 8, 4, 1679043093135940023116046299850653822817298022400000⟩, + ⟨6, 5, 0, 2, 5, 4, 9238382404977445422460435344527962581156809932800000⟩, + ⟨6, 5, 1, 2, 6, 4, -10862342389915498535563779021414305134822608076800000⟩, + ⟨6, 5, 2, 2, 7, 4, 2040949367085239918207245966217190398300572876800000⟩, + ⟨6, 5, 3, 2, 8, 4, 214634837207761925990978702228711240506540032000000⟩, + ⟨6, 5, 0, 3, 4, 4, -5866905472171931267290513219624501830598891929600000⟩, + ⟨6, 5, 1, 3, 5, 4, -8973970551464316051053810624365154163133041868800000⟩, + ⟨6, 5, 2, 3, 6, 4, 810773028448399942265557282959412548203446272000000⟩, + ⟨6, 5, 3, 3, 7, 4, 535919455520755286263027877796933725838743961600000⟩, + ⟨6, 5, 4, 3, 8, 4, 62265324086027431574258074795245586954227548160000⟩, + ⟨6, 5, 0, 4, 3, 4, -22515702501879087713226430912921832914787971891200000⟩, + ⟨6, 5, 1, 4, 4, 4, 10107512368374587863434382290160688032311253401600000⟩, + ⟨6, 5, 2, 4, 5, 4, 376538586477896140611916019570415933982978867200000⟩, + ⟨6, 5, 3, 4, 6, 4, 1231013715538162097003801933709581075245065830400000⟩, + ⟨6, 5, 4, 4, 7, 4, 141889324711385624666673201435227652512242728960000⟩, + ⟨6, 5, 5, 4, 8, 4, -102751326790541284234044641652404249857464729600000⟩, + ⟨6, 5, 0, 5, 2, 4, 37999935764039212861463183372796117352272258662400000⟩, + ⟨6, 5, 1, 5, 3, 4, 19302772811925977006630018606432075504428882329600000⟩, + ⟨6, 5, 2, 5, 4, 4, -1996495436655630033337187936596695642074932838400000⟩, + ⟨6, 5, 3, 5, 5, 4, 404575090557937661308672336861953523708644556800000⟩, + ⟨6, 5, 4, 5, 6, 4, -130152068361934695256501663613268871724956385280000⟩, + ⟨6, 5, 5, 5, 7, 4, 3495439730369625105125151949533350942107238400000⟩, + ⟨6, 5, 6, 5, 8, 4, -20675872782991432403235699059935712344906137600000⟩, + ⟨6, 5, 0, 6, 1, 4, -27620797883096309612243039885025759838209048576000000⟩, + ⟨6, 5, 1, 6, 2, 4, -48100937936900125040919326929452594582643959398400000⟩, + ⟨6, 5, 2, 6, 3, 4, -1007396168776996205995215941314871423473287168000000⟩, + ⟨6, 5, 3, 6, 4, 4, -1908789164616805482612586643598182537403511603200000⟩, + ⟨6, 5, 4, 6, 5, 4, 211182618192333835527576770761732853839681290240000⟩, + ⟨6, 5, 5, 6, 6, 4, -33247869471485745499771956340387178176158105600000⟩, + ⟨6, 5, 6, 6, 7, 4, -19526226959918079702819583870207629040445030400000⟩, + ⟨6, 5, 7, 6, 8, 4, -2677658314245665627491056268157361012395212800000⟩, + ⟨6, 5, 0, 7, 0, 4, 269393636467941550471181829945348418281726069964800000⟩, + ⟨6, 5, 1, 7, 1, 4, 137644419732098724560315946843226209587737028198400000⟩, + ⟨6, 5, 2, 7, 2, 4, 4872365771866926907683614070805839197628058828800000⟩, + ⟨6, 5, 3, 7, 3, 4, 3401858574994865865486309989282240874189265305600000⟩, + ⟨6, 5, 4, 7, 4, 4, 873369657491718335302728385741765548196736532480000⟩, + ⟨6, 5, 5, 7, 5, 4, 37600027350746399257859796204236021683558809600000⟩, + ⟨6, 5, 6, 7, 6, 4, 21133622972624239433281162427449442373206016000000⟩, + ⟨6, 5, 7, 7, 7, 4, 946371848605593398260796335359176223385190400000⟩, + ⟨6, 5, 8, 7, 8, 4, 2821494945629385454404608131429235247022080000000⟩ +] + +def collectedFourData_10_7_32 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 7, 5, 7170934939649580284240602941873916275308101632000000⟩, + ⟨6, 6, 1, 0, 8, 5, 275045095401928813437233173160609158042484736000000⟩, + ⟨6, 6, 0, 1, 6, 5, 902186390170907731001051188160816601655934976000000⟩, + ⟨6, 6, 1, 1, 7, 5, 2884313946263197219042565769807724751131508736000000⟩, + ⟨6, 6, 2, 1, 8, 5, -396514207055203890296920138483269137055350784000000⟩, + ⟨6, 6, 0, 2, 5, 5, -4363378032115582417756482439653096016677175296000000⟩, + ⟨6, 6, 1, 2, 6, 5, 3420260104982514647266851015935702734768963584000000⟩, + ⟨6, 6, 2, 2, 7, 5, -481980136923206271502179574170089308645490688000000⟩, + ⟨6, 6, 3, 2, 8, 5, -40549650038061574340697693428743948411600896000000⟩, + ⟨6, 6, 0, 3, 4, 5, 2770996623822501531981733445957289511665795072000000⟩, + ⟨6, 6, 1, 3, 5, 5, 2825662491449057434705958730522570602047340544000000⟩, + ⟨6, 6, 2, 3, 6, 5, -191468000905522562651321123299621953098219520000000⟩, + ⟨6, 6, 3, 3, 7, 5, -101247992416625521435492422614288333290654924800000⟩, + ⟨6, 6, 4, 3, 8, 5, -9802839767459364242445504959266849670194790400000⟩, + ⟨6, 6, 0, 4, 3, 5, 10634385693042647270395769837235986927015952384000000⟩, + ⟨6, 6, 1, 4, 4, 5, -3182584388636442732094522452488592599870865408000000⟩, + ⟨6, 6, 2, 4, 5, 5, -88921421762986476198562609717045836594020352000000⟩, + ⟨6, 6, 3, 4, 6, 5, -232567909322229913500307873794767129370899251200000⟩, + ⟨6, 6, 4, 4, 7, 5, -22338570227900779245351027299958177149642342400000⟩, + ⟨6, 6, 5, 4, 8, 5, 13865843682981293695021463008692224070254592000000⟩, + ⟨6, 6, 0, 5, 2, 5, -17947739946906513135269099818958862303381946368000000⟩, + ⟨6, 6, 1, 5, 3, 5, -6077925128328160271852473360954615472270082048000000⟩, + ⟨6, 6, 2, 5, 4, 5, 471482124664412588064429646861752225805369344000000⟩, + ⟨6, 6, 3, 5, 5, 5, -76433903040452780118161612642973806137599590400000⟩, + ⟨6, 6, 4, 5, 6, 5, 20490696712550651413223681842643832021398323200000⟩, + ⟨6, 6, 5, 5, 7, 5, -471694355863530568034143805138952957984768000000⟩, + ⟨6, 6, 6, 5, 8, 5, 2441354047206209515923696646860752874897408000000⟩, + ⟨6, 6, 0, 6, 1, 5, 13045571987545503369641494030296567519715000320000000⟩, + ⟨6, 6, 1, 6, 2, 5, 15145694467388196234416776901482642063692398592000000⟩, + ⟨6, 6, 2, 6, 3, 5, 237901513478737535182048276874984061539450880000000⟩, + ⟨6, 6, 3, 6, 4, 5, 360615888960901139707980056254426491985172889600000⟩, + ⟨6, 6, 4, 6, 5, 5, -33247869471485745499771956340387178176158105600000⟩, + ⟨6, 6, 5, 6, 6, 5, 4486655066007626707216283601622334661722112000000⟩, + ⟨6, 6, 6, 6, 7, 5, 2305606816002373252252981931220426955948032000000⟩, + ⟨6, 6, 7, 6, 8, 5, 281040914204400211361910338834809736921088000000⟩, + ⟨6, 6, 0, 7, 0, 5, -127237239575905732774555412999399347644096577536000000⟩, + ⟨6, 6, 1, 7, 1, 5, -43340533798698241262095262819620807420088942592000000⟩, + ⟨6, 6, 2, 7, 2, 5, -1150632916101286694415322079875265625229099008000000⟩, + ⟨6, 6, 3, 7, 3, 5, -642692381579667091388353319790444982301412556800000⟩, + ⟨6, 6, 4, 7, 4, 5, -137500333224370281180260149414650695438775091200000⟩, + ⟨6, 6, 5, 7, 5, 5, -5073959801843298158552690135129380400136192000000⟩, + ⟨6, 6, 6, 7, 6, 5, -2495404015969258584357655241186585377505280000000⟩, + ⟨6, 6, 7, 7, 7, 5, -99329032421506514502812118351549441245184000000⟩, + ⟨6, 6, 8, 7, 8, 5, -266523911304025886640729884800010283909120000000⟩ +] + +def collectedFourData_10_7_33 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 7, 6, 9826686016331873681240417094293591777630748672000000⟩, + ⟨6, 7, 1, 0, 8, 6, 282680900286365861212363439626726362675412992000000⟩, + ⟨6, 7, 0, 1, 6, 6, 1236310531197012694366705294326313119117213696000000⟩, + ⟨6, 7, 1, 1, 7, 6, 2964388300931991539875050701447546362493140992000000⟩, + ⟨6, 7, 2, 1, 8, 6, -326017790974689697110444639193733366314067558400000⟩, + ⟨6, 7, 0, 2, 5, 6, -5979352239703232600055772121945173065430204416000000⟩, + ⟨6, 7, 1, 2, 6, 6, 3515213402649961466793015906541639559490306048000000⟩, + ⟨6, 7, 2, 2, 7, 6, -396288699717398786962260625867107177300020428800000⟩, + ⟨6, 7, 3, 2, 8, 6, -27783593237818633705395379109727292524331008000000⟩, + ⟨6, 7, 0, 3, 4, 6, 3797233415696006101948610974464142201073958912000000⟩, + ⟨6, 7, 1, 3, 5, 6, 2904108563801111317808323331641756983301767168000000⟩, + ⟨6, 7, 2, 3, 6, 6, -157426830077913901890161865084859997698916352000000⟩, + ⟨6, 7, 3, 3, 7, 6, -69372560177679469157078783581109577958450790400000⟩, + ⟨6, 7, 4, 3, 8, 6, -5757135034330020177365122095119388601063833600000⟩, + ⟨6, 7, 0, 4, 3, 6, 14572823496737585492420855406994727867844132864000000⟩, + ⟨6, 7, 1, 4, 4, 6, -3270939330521048410982692698173415878742245376000000⟩, + ⟨6, 7, 2, 4, 5, 6, -73112047381095424336029283115007454357959475200000⟩, + ⟨6, 7, 3, 4, 6, 6, -159349641407845098175756061632285191687477657600000⟩, + ⟨6, 7, 4, 4, 7, 6, -13119276487900854706759161386808342407125401600000⟩, + ⟨6, 7, 5, 4, 8, 6, 7125393691909628471762373763854182029197312000000⟩, + ⟨6, 7, 0, 5, 2, 6, -24594673727390651265418128969437230841701859328000000⟩, + ⟨6, 7, 1, 5, 3, 6, -6246660550838826053617270671185250288408723456000000⟩, + ⟨6, 7, 2, 5, 4, 6, 387657133167349211875533199295099776935552614400000⟩, + ⟨6, 7, 3, 5, 5, 6, -52370574583541472012609804313370865591071539200000⟩, + ⟨6, 7, 4, 5, 6, 6, 12034034088086540603103719282590053259070668800000⟩, + ⟨6, 7, 5, 5, 7, 6, -242394769811563762240093365522973901979648000000⟩, + ⟨6, 7, 6, 5, 8, 6, 1115169308628014411084594749589189145133056000000⟩, + ⟨6, 7, 0, 6, 1, 6, 17876991062385605223779227958429685935473950720000000⟩, + ⟨6, 7, 1, 6, 2, 6, 15566169399410790453348557011642067097300762624000000⟩, + ⟨6, 7, 2, 6, 3, 6, 195604910275195323118485104964081170868338688000000⟩, + ⟨6, 7, 3, 6, 4, 6, 247084874088422683807192139243787080843447500800000⟩, + ⟨6, 7, 4, 6, 5, 6, -19526226959918079702819583870207629040445030400000⟩, + ⟨6, 7, 5, 6, 6, 6, 2305606816002373252252981931220426955948032000000⟩, + ⟨6, 7, 6, 6, 7, 6, 1053162265387815801663731449981221180801024000000⟩, + ⟨6, 7, 7, 6, 8, 6, 115537270029860033697864620051732369925734400000⟩, + ⟨6, 7, 0, 7, 0, 6, -174359468245059872371575968765390011523930259456000000⟩, + ⟨6, 7, 1, 7, 1, 6, -44543754162219357878726574694562358603099930624000000⟩, + ⟨6, 7, 2, 7, 2, 6, -946061439553616500874822992936946473685011660800000⟩, + ⟨6, 7, 3, 7, 3, 6, -440356542907120735407058964733398765269313126400000⟩, + ⟨6, 7, 4, 7, 4, 6, -80752925113172382475799945591393928998603980800000⟩, + ⟨6, 7, 5, 7, 5, 6, -2607411564103527057325789472403346698534912000000⟩, + ⟨6, 7, 6, 7, 6, 6, -1139858421772349790985898543349127666728960000000⟩, + ⟨6, 7, 7, 7, 7, 6, -40834642433385021954066304275004112712499200000⟩, + ⟨6, 7, 8, 7, 8, 6, -99608418539734635290284942691805387816960000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1027.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1027.lean new file mode 100644 index 0000000000000000000000000000000000000000..bca536b45cb5e1804ef49467d6b01e621b78d548 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1027.lean @@ -0,0 +1,500 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1024 +import OAI.Analysis.LaughlinFock.Sparse1025 +import OAI.Analysis.LaughlinFock.Sparse1026 + +namespace OAI + +/-! Sparse1027. -/ +namespace LaughlinFock +def collectedFourData_10_7_34 : List CollectedFourTerm := [ + ⟨6, 8, 0, 0, 7, 7, 2695093892652679868106845199547355897851281408000000⟩, + ⟨6, 8, 1, 0, 8, 7, 62023072003330896666069592355841721059665510400000⟩, + ⟨6, 8, 0, 1, 6, 7, 339073921412930758401776027697493402655391744000000⟩, + ⟨6, 8, 1, 1, 7, 7, 650417020917505990490867285495936070378219110400000⟩, + ⟨6, 8, 2, 1, 8, 7, -59609689770060648648499635822639067009803878400000⟩, + ⟨6, 8, 0, 2, 5, 7, -1639913565617181998328539361770982626845261824000000⟩, + ⟨6, 8, 1, 2, 6, 7, 771273664965570422894710258002382917801187737600000⟩, + ⟨6, 8, 2, 2, 7, 7, -72458151375453005552013518189538276235070668800000⟩, + ⟨6, 8, 3, 2, 8, 7, -4354288331458836700754989150885956041048064000000⟩, + ⟨6, 8, 0, 3, 4, 7, 1041439664461683189272781350506281449992224768000000⟩, + ⟨6, 8, 1, 3, 5, 7, 637191031922059282619924881133056344783952281600000⟩, + ⟨6, 8, 2, 3, 6, 7, -28784209826012339964776525422477440505085952000000⟩, + ⟨6, 8, 3, 3, 7, 7, -10872176493497061980299244087499843051926323200000⟩, + ⟨6, 8, 4, 3, 8, 7, -789483832311936770022621392446291962966835200000⟩, + ⟨6, 8, 0, 4, 3, 7, 3996782591759621573870118140243079842387460096000000⟩, + ⟨6, 8, 1, 4, 4, 7, -717677442692150849497044965934226711166268211200000⟩, + ⟨6, 8, 2, 4, 5, 7, -13367940595546885291860631366307672589808435200000⟩, + ⟨6, 8, 3, 4, 6, 7, -24973525859854050834082566829792475113901260800000⟩, + ⟨6, 8, 4, 4, 7, 7, -1799064398709763803445903167210795062997811200000⟩, + ⟨6, 8, 5, 4, 8, 7, 868546685125035251192794198182779166916608000000⟩, + ⟨6, 8, 0, 5, 2, 7, -6745402757787396479197583275090354744005230592000000⟩, + ⟨6, 8, 1, 5, 3, 7, -1370581021684010256391481565451817245440422707200000⟩, + ⟨6, 8, 2, 5, 4, 7, 70879939944905545486508220070565999022597734400000⟩, + ⟨6, 8, 3, 5, 5, 7, -8207598630925433779880985171360170055932313600000⟩, + ⟨6, 8, 4, 5, 6, 7, 1650243618289678569859671696981538857654681600000⟩, + ⟨6, 8, 5, 5, 7, 7, -29546602323254455607580984271349357740032000000⟩, + ⟨6, 8, 6, 5, 8, 7, 122339758814394980313766342732929820105113600000⟩, + ⟨6, 8, 0, 6, 1, 7, 4902992662141329328924818893019196816443310080000000⟩, + ⟨6, 8, 1, 6, 2, 7, 3415376293543901770356373119763346245475421388800000⟩, + ⟨6, 8, 2, 6, 3, 7, 35764759905112536072200160135833118559961088000000⟩, + ⟨6, 8, 3, 6, 4, 7, 38723529203512949361881531286924091852220006400000⟩, + ⟨6, 8, 4, 6, 5, 7, -2677658314245665627491056268157361012395212800000⟩, + ⟨6, 8, 5, 6, 6, 7, 281040914204400211361910338834809736921088000000⟩, + ⟨6, 8, 6, 6, 7, 7, 115537270029860033697864620051732369925734400000⟩, + ⟨6, 8, 7, 6, 8, 7, 11522752350587958730153671563193375680102400000⟩, + ⟨6, 8, 0, 7, 0, 7, -47820306582751756740024867544052628444502032384000000⟩, + ⟨6, 8, 1, 7, 1, 7, -9773353873230369143788572348843082754586102988800000⟩, + ⟨6, 8, 2, 7, 2, 7, -172979605642399529229779520104027931164855500800000⟩, + ⟨6, 8, 3, 7, 3, 7, -69013368431122763373253777997649175087625011200000⟩, + ⟨6, 8, 4, 7, 4, 7, -11073759501659034518384997937892976592787865600000⟩, + ⟨6, 8, 5, 7, 5, 7, -317829269325870183667660186899082282795008000000⟩, + ⟨6, 8, 6, 7, 6, 7, -125048280403045363678426473854898511282176000000⟩, + ⟨6, 8, 7, 7, 7, 7, -4072516790150057865296896878928234492723200000⟩, + ⟨6, 8, 8, 7, 8, 7, -9106292803666204219304614783925857812480000000⟩ +] + +def collectedFourData_10_7_35 : List CollectedFourTerm := [ + ⟨7, 0, 3, 2, 8, 0, 54759487123550215883037923823222380843633737728000000⟩, + ⟨7, 0, 3, 3, 7, 0, 136728384383574644393093960604350055966411482726400000⟩, + ⟨7, 0, 4, 3, 8, 0, 79428327127344751806209713599442316935784772403200000⟩, + ⟨7, 0, 3, 4, 6, 0, 314066814976892913684097643996028937600050502041600000⟩, + ⟨7, 0, 4, 4, 7, 0, 181000129116536880719373322028824624322135143219200000⟩, + ⟨7, 0, 5, 4, 8, 0, -393222043740358037095607829032996866887543422976000000⟩, + ⟨7, 0, 3, 5, 5, 0, 103218679456362613905384327938185027326812828467200000⟩, + ⟨7, 0, 4, 5, 6, 0, -166027579778904867036823969411075605633124899225600000⟩, + ⟨7, 0, 5, 5, 7, 0, 13376800061658351025644359914648108966141231104000000⟩, + ⟨7, 0, 6, 5, 8, 0, -184625232070948790284634438549322921976019288064000000⟩, + ⟨7, 0, 3, 6, 4, 0, -486986721452998955566356947061559888164854484172800000⟩, + ⟨7, 0, 4, 6, 5, 0, 269393636467941550471181829945348418281726069964800000⟩, + ⟨7, 0, 5, 6, 6, 0, -127237239575905732774555412999399347644096577536000000⟩, + ⟨7, 0, 6, 6, 7, 0, -174359468245059872371575968765390011523930259456000000⟩, + ⟨7, 0, 7, 6, 8, 0, -47820306582751756740024867544052628444502032384000000⟩, + ⟨7, 0, 3, 7, 3, 0, 867911440924435259388738338462416778506243827302400000⟩, + ⟨7, 0, 4, 7, 4, 0, 1114107922453039880295335842380136138127598786969600000⟩, + ⟨7, 0, 5, 7, 5, 0, 143892639261908768956165225575858045608081227776000000⟩, + ⟨7, 0, 6, 7, 6, 0, 188712712966120480934926825336675224929949450240000000⟩, + ⟨7, 0, 7, 7, 7, 0, 16901257229436387662256564299225724399975923712000000⟩, + ⟨7, 0, 8, 7, 8, 0, 90700353621274294114560379384517579273215672320000000⟩ +] + +def collectedFourData_10_7_36 : List CollectedFourTerm := [ + ⟨7, 1, 2, 1, 8, 1, 109436521925019984069387663440111328929081878118400000⟩, + ⟨7, 1, 2, 2, 7, 1, 133024816975794034270116109421168957693769862348800000⟩, + ⟨7, 1, 3, 2, 8, 1, 55957801593025836319859056045784979144859189248000000⟩, + ⟨7, 1, 2, 3, 6, 1, 52844492596250768182208582328468875556685873152000000⟩, + ⟨7, 1, 3, 3, 7, 1, 139720443111684943425504223067793606639954060902400000⟩, + ⟨7, 1, 4, 3, 8, 1, 40583237752298280580030166489593242529589467545600000⟩, + ⟨7, 1, 2, 4, 5, 1, 24541998620024741934046357182636647907658511155200000⟩, + ⟨7, 1, 3, 4, 6, 1, 320939611428032015655654478865389044574417688985600000⟩, + ⟨7, 1, 4, 4, 7, 1, 92480498315874091917605495125843961409231755673600000⟩, + ⟨7, 1, 5, 4, 8, 1, -133942337431449810943101409396075524031116214272000000⟩, + ⟨7, 1, 2, 5, 4, 1, -130127402637828951063565344839682300757246633574400000⟩, + ⟨7, 1, 3, 5, 5, 1, 105477437593261435333773537170475442332840964915200000⟩, + ⟨7, 1, 4, 5, 6, 1, -84830399774166972081383380714529539596961500364800000⟩, + ⟨7, 1, 5, 5, 7, 1, 4556509219495188035055852209942221941519679488000000⟩, + ⟨7, 1, 6, 5, 8, 1, -47166357137270335072970604278679122582182035456000000⟩, + ⟨7, 1, 2, 6, 3, 1, -65659978211541386955992164687685860593015717888000000⟩, + ⟨7, 1, 3, 6, 4, 1, -497643564046191382406662116364674860145877765324800000⟩, + ⟨7, 1, 4, 6, 5, 1, 137644419732098724560315946843226209587737028198400000⟩, + ⟨7, 1, 5, 6, 6, 1, -43340533798698241262095262819620807420088942592000000⟩, + ⟨7, 1, 6, 6, 7, 1, -44543754162219357878726574694562358603099930624000000⟩, + ⟨7, 1, 7, 6, 8, 1, -9773353873230369143788572348843082754586102988800000⟩, + ⟨7, 1, 2, 7, 2, 1, 317570624482156341164065498589243678095594802380800000⟩, + ⟨7, 1, 3, 7, 3, 1, 886904146892199950155717970302354583143357769318400000⟩, + ⟨7, 1, 4, 7, 4, 1, 569244101366261490926949495709000445848617536716800000⟩, + ⟨7, 1, 5, 7, 5, 1, 49013825009888085865949015787146882535886159872000000⟩, + ⟨7, 1, 6, 7, 6, 1, 48210589182537855219954936820644393234947112960000000⟩, + ⟨7, 1, 7, 7, 7, 1, 3454222266850839535512436554379061617574176358400000⟩, + ⟨7, 1, 8, 7, 8, 1, 15447528391763046073554019454713292515725803520000000⟩ +] + +def collectedFourData_10_7_37 : List CollectedFourTerm := [ + ⟨7, 2, 1, 0, 8, 2, -2015347644614573190772509750888503025877804646400000⟩, + ⟨7, 2, 1, 1, 7, 2, -21134335478463997922980429409975612063734982246400000⟩, + ⟨7, 2, 2, 1, 8, 2, 11621570231269303040407902462696432301167240806400000⟩, + ⟨7, 2, 1, 2, 6, 2, -25061392701705179981031343665348723848985024921600000⟩, + ⟨7, 2, 2, 2, 7, 2, 14126520340669654177330225849118132450785807564800000⟩, + ⟨7, 2, 3, 2, 8, 2, 2971208833036313114742326699072952305455202304000000⟩, + ⟨7, 2, 1, 3, 5, 2, -20704576601505431515904709041116178243550550425600000⟩, + ⟨7, 2, 2, 3, 6, 2, 5611800989654001795176783835184318863787425792000000⟩, + ⟨7, 2, 3, 3, 7, 2, 7418779918275520304902809201663139443528381235200000⟩, + ⟨7, 2, 4, 3, 8, 2, 1436573883058214747995720567650887459289641779200000⟩, + ⟨7, 2, 1, 4, 4, 2, 23319863028470445541822026498877340015320576819200000⟩, + ⟨7, 2, 2, 4, 5, 2, 2606228300765505830863667860597934066844775219200000⟩, + ⟨7, 2, 3, 4, 6, 2, 17041030583750769119339105490031788409307843788800000⟩, + ⟨7, 2, 4, 4, 7, 2, 3273643896617641885303251942846825353587143475200000⟩, + ⟨7, 2, 5, 4, 8, 2, -3555989019978352515179515886275211615249891328000000⟩, + ⟨7, 2, 1, 5, 3, 2, 44534995519989139949373046462941991910103003955200000⟩, + ⟨7, 2, 2, 5, 4, 2, -13818830516235920304291456256511620992312174182400000⟩, + ⟨7, 2, 3, 5, 5, 2, 5600568380838501933317669818060353639829576089600000⟩, + ⟨7, 2, 4, 5, 6, 2, -3002844118765619487703837882458747710853454233600000⟩, + ⟨7, 2, 5, 5, 7, 2, 120969195137776976813519004443543069012262912000000⟩, + ⟨7, 2, 6, 5, 8, 2, -1001762706602606154761106108906326660570362675200000⟩, + ⟨7, 2, 1, 6, 2, 2, -110977582153565348898929645100816602928429976780800000⟩, + ⟨7, 2, 2, 6, 3, 2, -6972736658168434307032608402454001972882178048000000⟩, + ⟨7, 2, 3, 6, 4, 2, -26423535433922373826446457974965162571727267430400000⟩, + ⟨7, 2, 4, 6, 5, 2, 4872365771866926907683614070805839197628058828800000⟩, + ⟨7, 2, 5, 6, 6, 2, -1150632916101286694415322079875265625229099008000000⟩, + ⟨7, 2, 6, 6, 7, 2, -946061439553616500874822992936946473685011660800000⟩, + ⟨7, 2, 7, 6, 8, 2, -172979605642399529229779520104027931164855500800000⟩, + ⟨7, 2, 1, 7, 1, 2, 317570624482156341164065498589243678095594802380800000⟩, + ⟨7, 2, 2, 7, 2, 2, 33724292867568275573819586060518530997317061836800000⟩, + ⟨7, 2, 3, 7, 3, 2, 47092225932461741571912234748562224500507358003200000⟩, + ⟨7, 2, 4, 7, 4, 2, 20150220987762451642831127032845530751280191897600000⟩, + ⟨7, 2, 5, 7, 5, 2, 1301251171994093447756520192880516538698825728000000⟩, + ⟨7, 2, 6, 7, 6, 2, 1023941072359027292714895958594018818530476032000000⟩, + ⟨7, 2, 7, 7, 7, 2, 61136638790667227047515778117860679215375974400000⟩, + ⟨7, 2, 8, 7, 8, 2, 234349208559462365060476638052064885798338560000000⟩ +] + +def collectedFourData_10_7_38 : List CollectedFourTerm := [ + ⟨7, 3, 0, 0, 7, 3, -48914425501456750088885123375909740575718165708800000⟩, + ⟨7, 3, 1, 0, 8, 3, -5628417887683198392180142470224211828913943347200000⟩, + ⟨7, 3, 0, 1, 6, 3, -6153999351805518024005469580427207155141469798400000⟩, + ⟨7, 3, 1, 1, 7, 3, -59023500074119297922380323555241558231909348147200000⟩, + ⟨7, 3, 2, 1, 8, 3, 16228230883002892669803566176820711311952943513600000⟩, + ⟨7, 3, 0, 2, 5, 3, 29763501061277280599687103588900792044205008486400000⟩, + ⟨7, 3, 1, 2, 6, 3, -69990897773623052517694164608578692136573914316800000⟩, + ⟨7, 3, 2, 2, 7, 3, 19726115240864952216498604856754914364054778675200000⟩, + ⟨7, 3, 3, 2, 8, 3, 2765975221626862192524616352670738647837835264000000⟩, + ⟨7, 3, 0, 3, 4, 3, -18901539208132516955249222974395674131897830604800000⟩, + ⟨7, 3, 1, 3, 5, 3, -57823279081513907875754749540391118617443093708800000⟩, + ⟨7, 3, 2, 3, 6, 3, 7836256230206740715611106775832701257864183808000000⟩, + ⟨7, 3, 3, 3, 7, 3, 6906334284043997505969304396967919871058981683200000⟩, + ⟨7, 3, 4, 3, 8, 3, 1003007863431139147061281878019773606826239590400000⟩, + ⟨7, 3, 0, 4, 3, 3, -72539337075830630031293863882206624805820144025600000⟩, + ⟨7, 3, 1, 4, 4, 3, 65127192600493948478707876980887885958413392281600000⟩, + ⟨7, 3, 2, 4, 5, 3, 3639308093224812736491446763899777838356417740800000⟩, + ⟨7, 3, 3, 4, 6, 3, 15863936530328732188075785905514918727899729100800000⟩, + ⟨7, 3, 4, 4, 7, 3, 2285639888838068207251218891514527932809111142400000⟩, + ⟨7, 3, 5, 4, 8, 3, -1986217341899730921400499020515418890639822028800000⟩, + ⟨7, 3, 0, 5, 2, 3, 122425234079083442320368481543500765982046237491200000⟩, + ⟨7, 3, 1, 5, 3, 3, 124376340768014718789328718815591681259512371609600000⟩, + ⟨7, 3, 2, 5, 4, 3, -19296460606259186370992500573060346684655638937600000⟩, + ⟨7, 3, 3, 5, 5, 3, 5213714093800570606607329956098356988580829593600000⟩, + ⟨7, 3, 4, 5, 6, 3, -2096568996067301201656245209580072783349756723200000⟩, + ⟨7, 3, 5, 5, 7, 3, 67568013249874410039975922373877417886561075200000⟩, + ⟨7, 3, 6, 5, 8, 3, -466283418655077160335953064771127516742654361600000⟩, + ⟨7, 3, 0, 6, 1, 3, -88986535853282783679370929771788110788651122688000000⟩, + ⟨7, 3, 1, 6, 2, 3, -309935712676716095333577931946354439624052860518400000⟩, + ⟨7, 3, 2, 6, 3, 3, -9736651598996240646899587609556691909032804352000000⟩, + ⟨7, 3, 3, 6, 4, 3, -24598353190583504628376415971695946282928858726400000⟩, + ⟨7, 3, 4, 6, 5, 3, 3401858574994865865486309989282240874189265305600000⟩, + ⟨7, 3, 5, 6, 6, 3, -642692381579667091388353319790444982301412556800000⟩, + ⟨7, 3, 6, 6, 7, 3, -440356542907120735407058964733398765269313126400000⟩, + ⟨7, 3, 7, 6, 8, 3, -69013368431122763373253777997649175087625011200000⟩, + ⟨7, 3, 0, 7, 0, 3, 867911440924435259388738338462416778506243827302400000⟩, + ⟨7, 3, 1, 7, 1, 3, 886904146892199950155717970302354583143357769318400000⟩, + ⟨7, 3, 2, 7, 2, 3, 47092225932461741571912234748562224500507358003200000⟩, + ⟨7, 3, 3, 7, 3, 3, 43839372248813985860481466488276501764223742771200000⟩, + ⟨7, 3, 4, 7, 4, 3, 14068771776343023535329033334544578413803549491200000⟩, + ⟨7, 3, 5, 7, 5, 3, 726821041758377453856388961273037886648536268800000⟩, + ⟨7, 3, 6, 7, 6, 3, 476606626074285992597532985840834567634681856000000⟩, + ⟨7, 3, 7, 7, 7, 3, 24391577040724837800509142874821137186527641600000⟩, + ⟨7, 3, 8, 7, 8, 3, 81810654413964311169681680468189050684047360000000⟩ +] + +def collectedFourData_10_7_39 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 7, 4, -62789757576380036488768176278326615203764187955200000⟩, + ⟨7, 4, 1, 0, 8, 4, -3612502764605341220431854694937274801302431334400000⟩, + ⟨7, 4, 0, 1, 6, 4, -7899676291067969402865966791573057548041427353600000⟩, + ⟨7, 4, 1, 1, 7, 4, -37883213622257784488847785636502479231731000934400000⟩, + ⟨7, 4, 2, 1, 8, 4, 6943873050339917321374107208096576305527311564800000⟩, + ⟨7, 4, 0, 2, 5, 4, 38206377711750355569035271908865976448094673305600000⟩, + ⟨7, 4, 1, 2, 6, 4, -44922448323839632223109434514965111657645840793600000⟩, + ⟨7, 4, 2, 2, 7, 4, 8440577472459246920605630997662113249648810393600000⟩, + ⟨7, 4, 3, 2, 8, 4, 887646700578403007460256539236098275922673664000000⟩, + ⟨7, 4, 0, 3, 4, 4, -24263252660786898671140224822969615273740677939200000⟩, + ⟨7, 4, 1, 3, 5, 4, -37112872517448833308540923713080906745965549977600000⟩, + ⟨7, 4, 2, 3, 6, 4, 3353043769514205448242796219529265994367238144000000⟩, + ⟨7, 4, 3, 3, 7, 4, 2216355660886020638867268131801594434067575603200000⟩, + ⟨7, 4, 4, 3, 8, 4, 257505306242096282256626807007382663510433464320000⟩, + ⟨7, 4, 0, 4, 3, 4, -93116240108085793472235596371023267039241725542400000⟩, + ⟨7, 4, 1, 4, 4, 4, 41800763201168949857284783411501084896702706483200000⟩, + ⟨7, 4, 2, 4, 5, 4, 1557218009320777550180400959921829718067144294400000⟩, + ⟨7, 4, 3, 4, 6, 4, 5090996770046677234431673327226468601923685580800000⟩, + ⟨7, 4, 4, 4, 7, 4, 586799387116475148275844140290534931852867665920000⟩, + ⟨7, 4, 5, 4, 8, 4, -424939759976573307330418988521584155583263539200000⟩, + ⟨7, 4, 0, 5, 2, 4, 157153042078114487998058814266769799685797104844800000⟩, + ⟨7, 4, 1, 5, 3, 4, 79828805153075917833363900846152244590122578739200000⟩, + ⟨7, 4, 2, 5, 4, 4, -8256733203807791964536346123195421321264417996800000⟩, + ⟨7, 4, 3, 5, 5, 4, 1673166150201151880670121557074499066274617753600000⟩, + ⟨7, 4, 4, 5, 6, 4, -538258632931505128258999948657806166838539714560000⟩, + ⟨7, 4, 5, 5, 7, 4, 14455787252886157319689377584712551483886796800000⟩, + ⟨7, 4, 6, 5, 8, 4, -85507415739952609463436099942123840644264755200000⟩, + ⟨7, 4, 0, 6, 1, 4, -114228940777870802182968666894494099196925181952000000⟩, + ⟨7, 4, 1, 6, 2, 4, -198926881627731752269854497558936822389205159116800000⟩, + ⟨7, 4, 2, 6, 3, 4, -4166201055817638478074306752332707481031540736000000⟩, + ⟨7, 4, 3, 6, 4, 4, -7894013973285417770813245048631312615406462566400000⟩, + ⟨7, 4, 4, 6, 5, 4, 873369657491718335302728385741765548196736532480000⟩, + ⟨7, 4, 5, 6, 6, 4, -137500333224370281180260149414650695438775091200000⟩, + ⟨7, 4, 6, 6, 7, 4, -80752925113172382475799945591393928998603980800000⟩, + ⟨7, 4, 7, 6, 8, 4, -11073759501659034518384997937892976592787865600000⟩, + ⟨7, 4, 0, 7, 0, 4, 1114107922453039880295335842380136138127598786969600000⟩, + ⟨7, 4, 1, 7, 1, 4, 569244101366261490926949495709000445848617536716800000⟩, + ⟨7, 4, 2, 7, 2, 4, 20150220987762451642831127032845530751280191897600000⟩, + ⟨7, 4, 3, 7, 3, 4, 14068771776343023535329033334544578413803549491200000⟩, + ⟨7, 4, 4, 7, 4, 4, 3611919224964372393453833034458149680827030568960000⟩, + ⟨7, 4, 5, 7, 5, 4, 155499175500764326279118007845617333760635699200000⟩, + ⟨7, 4, 6, 7, 6, 4, 87400493540381576958763463057039923014008832000000⟩, + ⟨7, 4, 7, 7, 7, 4, 3913828061946413893517448735308699864452300800000⟩, + ⟨7, 4, 8, 7, 8, 4, 11668612196268358990473024538293731233628160000000⟩ +] + +def collectedFourData_10_7_40 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 7, 5, -8109612860832684741880630103065145504811712512000000⟩, + ⟨7, 5, 1, 0, 8, 5, -311048595720411345556723384723352336493182976000000⟩, + ⟨7, 5, 0, 1, 6, 5, -1020282907901509286487578020540301639801634816000000⟩, + ⟨7, 5, 1, 1, 7, 5, -3261871662502926217725328794091638644042366976000000⟩, + ⟨7, 5, 2, 1, 8, 5, 448418057073446277415083628761606955512889344000000⟩, + ⟨7, 5, 0, 2, 5, 5, 4934545760590668615751735948182375883327143936000000⟩, + ⟨7, 5, 1, 2, 6, 5, -3867973363054185426446215625181859539157254144000000⟩, + ⟨7, 5, 2, 2, 7, 5, 545071507405049155334498290011474299461828608000000⟩, + ⟨7, 5, 3, 2, 8, 5, 45857613577372397627086590683108188971073536000000⟩, + ⟨7, 5, 0, 3, 4, 5, -3133721062455075771969456385434827921452695552000000⟩, + ⟨7, 5, 1, 3, 5, 5, -3195542711498590645191997640195797450179477504000000⟩, + ⟨7, 5, 2, 3, 6, 5, 216531229978949817953860980597248305209016320000000⟩, + ⟨7, 5, 3, 3, 7, 5, 114501390452648564897636301444475039983127756800000⟩, + ⟨7, 5, 4, 3, 8, 5, 11086034961956482359285193895650428553946726400000⟩, + ⟨7, 5, 0, 4, 3, 5, -12026430543458264022536856364573791973690834944000000⟩, + ⟨7, 5, 1, 4, 4, 5, 3599185811331966843082882021279545132872368128000000⟩, + ⟨7, 5, 2, 4, 5, 5, 100561267338437344856381899473268225219756032000000⟩, + ⟨7, 5, 3, 4, 6, 5, 263011130951452981065820248798236929288254259200000⟩, + ⟨7, 5, 4, 4, 7, 5, 25262696975696006502864862031049994721977958400000⟩, + ⟨7, 5, 5, 4, 8, 5, -15680887527797823125564350191401120009551872000000⟩, + ⟨7, 5, 0, 5, 2, 5, 20297105457133891005514421826361404052878655488000000⟩, + ⟨7, 5, 1, 5, 3, 5, 6873527678425264582409636711007831045458362368000000⟩, + ⟨7, 5, 2, 5, 4, 5, -533199301626641592080852904343288038297698304000000⟩, + ⟨7, 5, 3, 5, 5, 5, 86439127996158376156745360720059993577383526400000⟩, + ⟨7, 5, 4, 5, 6, 5, -23172936163278456729206798399725846157013811200000⟩, + ⟨7, 5, 5, 5, 7, 5, 533439313964826495171913220429929814949888000000⟩, + ⟨7, 5, 6, 5, 8, 5, -2760928155908898217733939127804475503280128000000⟩, + ⟨7, 5, 0, 6, 1, 5, -14753241977159459428161862882325143974177669120000000⟩, + ⟨7, 5, 1, 6, 2, 5, -17128271232785140764343947964416383520312655872000000⟩, + ⟨7, 5, 2, 6, 3, 5, -269042905779453097477330222932251486799790080000000⟩, + ⟨7, 5, 3, 6, 4, 5, -407820636437240310491940929180146351507872153600000⟩, + ⟨7, 5, 4, 6, 5, 5, 37600027350746399257859796204236021683558809600000⟩, + ⟨7, 5, 5, 6, 6, 5, -5073959801843298158552690135129380400136192000000⟩, + ⟨7, 5, 6, 6, 7, 5, -2607411564103527057325789472403346698534912000000⟩, + ⟨7, 5, 7, 6, 8, 5, -317829269325870183667660186899082282795008000000⟩, + ⟨7, 5, 0, 7, 0, 5, 143892639261908768956165225575858045608081227776000000⟩, + ⟨7, 5, 1, 7, 1, 5, 49013825009888085865949015787146882535886159872000000⟩, + ⟨7, 5, 2, 7, 2, 5, 1301251171994093447756520192880516538698825728000000⟩, + ⟨7, 5, 3, 7, 3, 5, 726821041758377453856388961273037886648536268800000⟩, + ⟨7, 5, 4, 7, 4, 5, 155499175500764326279118007845617333760635699200000⟩, + ⟨7, 5, 5, 7, 5, 5, 5738142935429732092332143469010464351977472000000⟩, + ⟨7, 5, 6, 7, 6, 5, 2822053284709724718152768540272151211540480000000⟩, + ⟨7, 5, 7, 7, 7, 5, 112331237915104975247488278466317458079744000000⟩, + ⟨7, 5, 8, 7, 8, 5, 301411985608696485633887081380871845969920000000⟩ +] + +def collectedFourData_10_7_41 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 7, 6, -10635617304142404101492843582405000209241210880000000⟩, + ⟨7, 6, 1, 0, 8, 6, -305951148702570807203848144577968543031623680000000⟩, + ⟨7, 6, 0, 1, 6, 6, -1338083424771995998176561448104598303502499840000000⟩, + ⟨7, 6, 1, 1, 7, 6, -3208416291839399366784687430333279961276743680000000⟩, + ⟨7, 6, 2, 1, 8, 6, 352855525594885108516689930631150254881243136000000⟩, + ⟨7, 6, 0, 2, 5, 6, 6471571600278817380980494928079492932582768640000000⟩, + ⟨7, 6, 1, 2, 6, 6, -3804585231566494037344857545288762475329617920000000⟩, + ⟨7, 6, 2, 2, 7, 6, 428911124782611072977309133784630107152842752000000⟩, + ⟨7, 6, 3, 2, 8, 6, 30070734377824457820393594369552356286136320000000⟩, + ⟨7, 6, 0, 3, 4, 6, -4109821088892341776058312722896779093716500480000000⟩, + ⟨7, 6, 1, 3, 5, 6, -3143174335980341521386818789394790145033502720000000⟩, + ⟨7, 6, 2, 3, 6, 6, 170386182618455639866776719147701677148078080000000⟩, + ⟨7, 6, 3, 3, 7, 6, 75083298706414050859967010166306388538556416000000⟩, + ⟨7, 6, 4, 3, 8, 6, 6231061508594039417601537081396378199916544000000⟩, + ⟨7, 6, 0, 4, 3, 6, -15772456095017335555435850864590181242566082560000000⟩, + ⟨7, 6, 1, 4, 4, 6, 3540202555232912912288150745279817642451927040000000⟩, + ⟨7, 6, 2, 4, 5, 6, 79130619923675850031982568504824250035601408000000⟩, + ⟨7, 6, 3, 4, 6, 6, 172467279482569247390323953991270594724757504000000⟩, + ⟨7, 6, 4, 4, 7, 6, 14199253319038229588452016391690656377995264000000⟩, + ⟨7, 6, 5, 4, 8, 6, -7711955009303288984466946702182470626836480000000⟩, + ⟨7, 6, 0, 5, 2, 6, 26619303501712527448969017639109248056159109120000000⟩, + ⟨7, 6, 1, 5, 3, 6, 6760884690646187883982976060304751017056010240000000⟩, + ⟨7, 6, 2, 5, 4, 6, -419569008996170989475137639606216837746917376000000⟩, + ⟨7, 6, 3, 5, 5, 6, 56681712262188442090721131606156169831251968000000⟩, + ⟨7, 6, 4, 5, 6, 6, -13024673931086781232010706723864066341732352000000⟩, + ⟨7, 6, 5, 5, 7, 6, 262348670137301327961211324463367239761920000000⟩, + ⟨7, 6, 6, 5, 8, 6, -1206969875315091141855116618881812387594240000000⟩, + ⟨7, 6, 0, 6, 1, 6, -19348622228603640041472646300753549023038668800000000⟩, + ⟨7, 6, 1, 6, 2, 6, -16847574080257873814513724370682108456164392960000000⟩, + ⟨7, 6, 2, 6, 3, 6, -211707076530227636328034025617682249306603520000000⟩, + ⟨7, 6, 3, 6, 4, 6, -267424863079895535321781884047037924881989632000000⟩, + ⟨7, 6, 4, 6, 5, 6, 21133622972624239433281162427449442373206016000000⟩, + ⟨7, 6, 5, 6, 6, 6, -2495404015969258584357655241186585377505280000000⟩, + ⟨7, 6, 6, 6, 7, 6, -1139858421772349790985898543349127666728960000000⟩, + ⟨7, 6, 7, 6, 8, 6, -125048280403045363678426473854898511282176000000⟩, + ⟨7, 6, 0, 7, 0, 6, 188712712966120480934926825336675224929949450240000000⟩, + ⟨7, 6, 1, 7, 1, 6, 48210589182537855219954936820644393234947112960000000⟩, + ⟨7, 6, 2, 7, 2, 6, 1023941072359027292714895958594018818530476032000000⟩, + ⟨7, 6, 3, 7, 3, 6, 476606626074285992597532985840834567634681856000000⟩, + ⟨7, 6, 4, 7, 4, 6, 87400493540381576958763463057039923014008832000000⟩, + ⟨7, 6, 5, 7, 5, 6, 2822053284709724718152768540272151211540480000000⟩, + ⟨7, 6, 6, 7, 6, 6, 1233691392472086959595964390425649112678400000000⟩, + ⟨7, 6, 7, 7, 7, 6, 44196143944272930595198737645363284410368000000⟩, + ⟨7, 6, 8, 7, 8, 6, 107808168297913595647334723670159812198400000000⟩ +] + +def collectedFourData_10_7_42 : List CollectedFourTerm := [ + ⟨7, 7, 0, 0, 7, 7, -952534151122224341456444594263573156482514944000000⟩, + ⟨7, 7, 1, 0, 8, 7, -21920978115733124467058960098612271830479667200000⟩, + ⟨7, 7, 0, 1, 6, 7, -119839791400682224499072271624604040866824192000000⟩, + ⟨7, 7, 1, 1, 7, 7, -229878605188522116255943377691277974020764467200000⟩, + ⟨7, 7, 2, 1, 8, 7, 21068010060271842368920558981429198691971891200000⟩, + ⟨7, 7, 0, 2, 5, 7, 579598981837880256816150736856166576666181632000000⟩, + ⟨7, 7, 1, 2, 6, 7, -272593288027454863716959001076156505875336396800000⟩, + ⟨7, 7, 2, 2, 7, 7, 25609075773003990215358015611017226426410598400000⟩, + ⟨7, 7, 3, 2, 8, 7, 1538947622884193565044795665252177466621952000000⟩, + ⟨7, 7, 0, 3, 4, 7, -368078770627404153685918068883655718730727424000000⟩, + ⟨7, 7, 1, 3, 5, 7, -225204108973427447127607917820208618698230988800000⟩, + ⟨7, 7, 2, 3, 6, 7, 10173279286146947518481395988032345432129536000000⟩, + ⟨7, 7, 3, 3, 7, 7, 3842582047073352805788284360798410362165657600000⟩, + ⟨7, 7, 4, 3, 8, 7, 279029355558293980546148332784308090149273600000⟩, + ⟨7, 7, 0, 4, 3, 7, -1412593425275687412552870719162350734491516928000000⟩, + ⟨7, 7, 1, 4, 4, 7, 253650633663631951296779861978559187277945241600000⟩, + ⟨7, 7, 2, 4, 5, 7, 4724666543954261524236184929969999135218073600000⟩, + ⟨7, 7, 3, 4, 6, 7, 8826459189527985404802458350572079860311654400000⟩, + ⟨7, 7, 4, 4, 7, 7, 635848081030126344716296109167268406598041600000⟩, + ⟨7, 7, 5, 4, 8, 7, -306972748400723396955034697531731470188544000000⟩, + ⟨7, 7, 0, 5, 2, 7, 2384045508537893360217180884195316225389101056000000⟩, + ⟨7, 7, 1, 5, 3, 7, 484408069638356876819980981868435034131241369600000⟩, + ⟨7, 7, 2, 5, 4, 7, -25051284339693934332393528981620782907208499200000⟩, + ⟨7, 7, 3, 5, 5, 7, 2900833257043043782692276046126364024949964800000⟩, + ⟨7, 7, 4, 5, 6, 7, -583249959631369860032619446448648595754188800000⟩, + ⟨7, 7, 5, 5, 7, 7, 10442733679614365880386908301588982398976000000⟩, + ⟨7, 7, 6, 5, 8, 7, -43238864007097178174905241437494003420364800000⟩, + ⟨7, 7, 0, 6, 1, 7, -1732877643381291026245034609448613817289277440000000⟩, + ⟨7, 7, 1, 6, 2, 7, -1207105462040784417540555660857969228411987558400000⟩, + ⟨7, 7, 2, 6, 3, 7, -12640433533384438334201675139515324703965184000000⟩, + ⟨7, 7, 3, 6, 4, 7, -13686159179419115660843933866436646094975795200000⟩, + ⟨7, 7, 4, 6, 5, 7, 946371848605593398260796335359176223385190400000⟩, + ⟨7, 7, 5, 6, 6, 7, -99329032421506514502812118351549441245184000000⟩, + ⟨7, 7, 6, 6, 7, 7, -40834642433385021954066304275004112712499200000⟩, + ⟨7, 7, 7, 6, 8, 7, -4072516790150057865296896878928234492723200000⟩, + ⟨7, 7, 0, 7, 0, 7, 16901257229436387662256564299225724399975923712000000⟩, + ⟨7, 7, 1, 7, 1, 7, 3454222266850839535512436554379061617574176358400000⟩, + ⟨7, 7, 2, 7, 2, 7, 61136638790667227047515778117860679215375974400000⟩, + ⟨7, 7, 3, 7, 3, 7, 24391577040724837800509142874821137186527641600000⟩, + ⟨7, 7, 4, 7, 4, 7, 3913828061946413893517448735308699864452300800000⟩, + ⟨7, 7, 5, 7, 5, 7, 112331237915104975247488278466317458079744000000⟩, + ⟨7, 7, 6, 7, 6, 7, 44196143944272930595198737645363284410368000000⟩, + ⟨7, 7, 7, 7, 7, 7, 1439360362995898801951450661856936040857600000⟩, + ⟨7, 7, 8, 7, 8, 7, 3218461111598995598421310412908281200640000000⟩ +] + +def collectedFourData_10_7_43 : List CollectedFourTerm := [ + ⟨7, 8, 0, 0, 7, 8, -5111760809879533898662842271341857140994211840000000⟩, + ⟨7, 8, 1, 0, 8, 8, -98032177913878975482866755935252613599068160000000⟩, + ⟨7, 8, 0, 1, 6, 8, -643118515409051231989438128982079183121285120000000⟩, + ⟨7, 8, 1, 1, 7, 8, -1028033521289880916288658872276987450396508160000000⟩, + ⟨7, 8, 2, 1, 8, 8, 80757980504175070145360852006372788540538880000000⟩, + ⟨7, 8, 0, 2, 5, 8, 3110409592469077023659593744369920874402283520000000⟩, + ⟨7, 8, 1, 2, 6, 8, -1219056630089746823471021223906506433405911040000000⟩, + ⟨7, 8, 2, 2, 7, 8, 98164811773376996430345860909306860441436160000000⟩, + ⟨7, 8, 3, 2, 8, 8, 5161712665268044103360175299882342626099200000000⟩, + ⟨7, 8, 0, 3, 4, 8, -1975289423927829545436399740762080523468144640000000⟩, + ⟨7, 8, 1, 3, 5, 8, -1007128840750693727974852069803157021670768640000000⟩, + ⟨7, 8, 2, 3, 6, 8, 38996254886142883688787029331688823350886400000000⟩, + ⟨7, 8, 3, 3, 7, 8, 12888225775051391921837247254810485283880960000000⟩, + ⟨7, 8, 4, 3, 8, 8, 831892788812291842085396537703018497310720000000⟩, + ⟨7, 8, 0, 4, 3, 8, -7580662281883068445882667667611035466024878080000000⟩, + ⟨7, 8, 1, 4, 4, 8, 1134343728459567963675813810438523438214676480000000⟩, + ⟨7, 8, 2, 4, 5, 8, 18110610710448048266333917242098123947376640000000⟩, + ⟨7, 8, 3, 4, 6, 8, 29604416362574608488209408555793374238474240000000⟩, + ⟨7, 8, 4, 4, 7, 8, 1895705318641958146796386860303961628344320000000⟩, + ⟨7, 8, 5, 4, 8, 8, -823682417647238846272011763518946588753920000000⟩, + ⟨7, 8, 0, 5, 2, 8, 12793945902260459109103705268222244763635548160000000⟩, + ⟨7, 8, 1, 5, 3, 8, 2166307443718640140805425137255016288883834880000000⟩, + ⟨7, 8, 2, 5, 4, 8, -96026683418217661181111391232954583828398080000000⟩, + ⟨7, 8, 3, 5, 5, 8, 9729549947026738599886366919454663722926080000000⟩, + ⟨7, 8, 4, 5, 6, 8, -1738890284578068606856040580226580490485760000000⟩, + ⟨7, 8, 5, 5, 7, 8, 28020389982118482899855206082699518279680000000⟩, + ⟨7, 8, 6, 5, 8, 8, -105473064205905293330705629548336371466240000000⟩, + ⟨7, 8, 0, 6, 1, 8, -9299462927724746332094298175313701417412198400000000⟩, + ⟨7, 8, 1, 6, 2, 8, -5398261737721718647373879585974960237597163520000000⟩, + ⟨7, 8, 2, 6, 3, 8, -48453360423362622525105931392122588076441600000000⟩, + ⟨7, 8, 3, 6, 4, 8, -45904110136565799328751262279748661721169920000000⟩, + ⟨7, 8, 4, 6, 5, 8, 2821494945629385454404608131429235247022080000000⟩, + ⟨7, 8, 5, 6, 6, 8, -266523911304025886640729884800010283909120000000⟩, + ⟨7, 8, 6, 6, 7, 8, -99608418539734635290284942691805387816960000000⟩, + ⟨7, 8, 7, 6, 8, 8, -9106292803666204219304614783925857812480000000⟩, + ⟨7, 8, 0, 7, 0, 8, 90700353621274294114560379384517579273215672320000000⟩, + ⟨7, 8, 1, 7, 1, 8, 15447528391763046073554019454713292515725803520000000⟩, + ⟨7, 8, 2, 7, 2, 8, 234349208559462365060476638052064885798338560000000⟩, + ⟨7, 8, 3, 7, 3, 8, 81810654413964311169681680468189050684047360000000⟩, + ⟨7, 8, 4, 7, 4, 8, 11668612196268358990473024538293731233628160000000⟩, + ⟨7, 8, 5, 7, 5, 8, 301411985608696485633887081380871845969920000000⟩, + ⟨7, 8, 6, 7, 6, 8, 107808168297913595647334723670159812198400000000⟩, + ⟨7, 8, 7, 7, 7, 8, 3218461111598995598421310412908281200640000000⟩, + ⟨7, 8, 8, 7, 8, 8, 6643009701667188756363207054043643904000000000⟩ +] + +def collectedFourData_10_7 : List (List CollectedFourTerm) := [ + collectedFourData_10_7_0, + collectedFourData_10_7_1, + collectedFourData_10_7_2, + collectedFourData_10_7_3, + collectedFourData_10_7_4, + collectedFourData_10_7_5, + collectedFourData_10_7_6, + collectedFourData_10_7_7, + collectedFourData_10_7_8, + collectedFourData_10_7_9, + collectedFourData_10_7_10, + collectedFourData_10_7_11, + collectedFourData_10_7_12, + collectedFourData_10_7_13, + collectedFourData_10_7_14, + collectedFourData_10_7_15, + collectedFourData_10_7_16, + collectedFourData_10_7_17, + collectedFourData_10_7_18, + collectedFourData_10_7_19, + collectedFourData_10_7_20, + collectedFourData_10_7_21, + collectedFourData_10_7_22, + collectedFourData_10_7_23, + collectedFourData_10_7_24, + collectedFourData_10_7_25, + collectedFourData_10_7_26, + collectedFourData_10_7_27, + collectedFourData_10_7_28, + collectedFourData_10_7_29, + collectedFourData_10_7_30, + collectedFourData_10_7_31, + collectedFourData_10_7_32, + collectedFourData_10_7_33, + collectedFourData_10_7_34, + collectedFourData_10_7_35, + collectedFourData_10_7_36, + collectedFourData_10_7_37, + collectedFourData_10_7_38, + collectedFourData_10_7_39, + collectedFourData_10_7_40, + collectedFourData_10_7_41, + collectedFourData_10_7_42, + collectedFourData_10_7_43 +] + +theorem collectedFourChecked_10_7 : collectNumericRowParts 10 7 = collectedFourData_10_7 := by + decide +kernel + +def collectedFourData_10 : Fin 8 → List (List CollectedFourTerm) := + ![collectedFourData_10_0, collectedFourData_10_1, collectedFourData_10_2, collectedFourData_10_3, collectedFourData_10_4, collectedFourData_10_5, collectedFourData_10_6, collectedFourData_10_7] + +theorem collectedFourChecked_10 (t : Fin 8) : + collectNumericRowParts 10 t = collectedFourData_10 t := by + fin_cases t + · exact collectedFourChecked_10_0 + · exact collectedFourChecked_10_1 + · exact collectedFourChecked_10_2 + · exact collectedFourChecked_10_3 + · exact collectedFourChecked_10_4 + · exact collectedFourChecked_10_5 + · exact collectedFourChecked_10_6 + · exact collectedFourChecked_10_7 + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1101.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1101.lean new file mode 100644 index 0000000000000000000000000000000000000000..ae9d4d9c6323ab5328449d8aead190e7c9a342c5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1101.lean @@ -0,0 +1,620 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1101. -/ +namespace LaughlinFock + +def collectedFourData_11_0_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_0_1 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_0_2 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_0_3 : List CollectedFourTerm := [ + ⟨0, 3, 8, 0, 8, 3, -9730653361403528761732841313494222608156065792000000⟩, + ⟨0, 3, 8, 1, 7, 3, -8131077697640216670583869829869495201394851840000000⟩, + ⟨0, 3, 8, 2, 6, 3, -442464958073903065173349047047192367543091200000000⟩, + ⟨0, 3, 8, 3, 5, 3, -7039957482752723038955785868192486037431255040000000⟩, + ⟨0, 3, 8, 4, 4, 3, 10072026823414838973940589130256982330132398080000000⟩, + ⟨0, 3, 8, 5, 3, 3, -14089095347707487631038098421247915661354598400000000⟩, + ⟨0, 3, 8, 6, 2, 3, 50243778975624265509197954060299036113216995328000000⟩, + ⟨0, 3, 8, 7, 1, 3, -93944836020994357263342490891120735403051581440000000⟩ +] + +def collectedFourData_11_0_4 : List CollectedFourTerm := [ + ⟨0, 4, 7, 0, 7, 4, 876895747295130781018046667953877328942281523200000⟩, + ⟨0, 4, 8, 0, 8, 4, -118240493557453912773874811346741199513038775910400000⟩, + ⟨0, 4, 7, 1, 6, 4, 60693709387941708654352856660543805668335602892800000⟩, + ⟨0, 4, 8, 1, 7, 4, -98803503158015247080217388547221808656215441408000000⟩, + ⟨0, 4, 7, 2, 5, 4, -6155559799477910021597453823963560747049418752000000⟩, + ⟨0, 4, 8, 2, 6, 4, -5376542877588470424821338330245022159931965440000000⟩, + ⟨0, 4, 7, 3, 4, 4, 24732398734098031738377918490031452835028349747200000⟩, + ⟨0, 4, 8, 3, 5, 4, -85544928636128915189269858832371985982053941248000000⟩, + ⟨0, 4, 7, 4, 3, 4, -87720598319384592052547382053053402388168599142400000⟩, + ⟨0, 4, 8, 4, 4, 4, 122388639127589813860706548771312762738333188096000000⟩, + ⟨0, 4, 7, 5, 2, 4, 170388838615876348641067700040765087133147437465600000⟩, + ⟨0, 4, 8, 5, 3, 4, -171201411232952910532451720899353804720392110080000000⟩, + ⟨0, 4, 7, 6, 1, 4, -468137816604305855231795295708774047830720590643200000⟩, + ⟨0, 4, 8, 6, 2, 4, 610529324560436695298748043400610271230598683033600000⟩, + ⟨0, 4, 7, 7, 0, 4, 1586829086754785593011016525084370693074949505024000000⟩, + ⟨0, 4, 8, 7, 1, 4, -1141555799568040637717510073434766667003805564928000000⟩ +] + +def collectedFourData_11_0_5 : List CollectedFourTerm := [ + ⟨0, 5, 6, 0, 6, 5, 251622243928787722125828461136330215247669362688000000⟩, + ⟨0, 5, 7, 0, 7, 5, -4612273742641264975774789588624212112888037376000000⟩, + ⟨0, 5, 8, 0, 8, 5, 310959156452860011465838447468182212901272027136000000⟩, + ⟨0, 5, 6, 1, 5, 5, -158230042873493793347491498548986141800277213184000000⟩, + ⟨0, 5, 7, 1, 6, 5, -319235214695695229654046949806903921084154773504000000⟩, + ⟨0, 5, 8, 1, 7, 5, 259842064864816959770832985026755594872915230720000000⟩, + ⟨0, 5, 6, 2, 4, 5, 56790983597689120525678017731000227689350037504000000⟩, + ⟨0, 5, 7, 2, 5, 5, 32376855426617422034753097601199385257296527360000000⟩, + ⟨0, 5, 8, 2, 6, 5, 14139701108699805905975789621765662351923609600000000⟩, + ⟨0, 5, 6, 3, 3, 5, 86213965181421718254549346733959920796324331520000000⟩, + ⟨0, 5, 7, 3, 4, 5, -130086836007224680273079397965500893782077341696000000⟩, + ⟨0, 5, 8, 3, 5, 5, 224973509896464932493102711565808982758334136320000000⟩, + ⟨0, 5, 6, 4, 2, 5, -262150352354393679784430597346366438959984148480000000⟩, + ⟨0, 5, 7, 4, 3, 5, 461390551345790113755160205795837732395293868032000000⟩, + ⟨0, 5, 8, 4, 4, 5, -321868311248516832956083883562868804564958576640000000⟩, + ⟨0, 5, 6, 5, 1, 5, 405098976660399505155994686407473453746156994560000000⟩, + ⟨0, 5, 7, 5, 2, 5, -896206839651428115642687819360518495331478929408000000⟩, + ⟨0, 5, 8, 5, 3, 5, 450240394122426063535100110504125992226992947200000000⟩, + ⟨0, 5, 6, 6, 0, 5, -594201046593251883476200718611438784867758768128000000⟩, + ⟨0, 5, 7, 6, 1, 5, 2462299271175221675290410084728123480531036798976000000⟩, + ⟨0, 5, 8, 6, 2, 5, -1605623234842118156415442022048461884289475149824000000⟩, + ⟨0, 5, 7, 7, 0, 5, -8346362898297016028892546738199960896284204728320000000⟩, + ⟨0, 5, 8, 7, 1, 5, 3002162946022058388363421220684909332527600107520000000⟩ +] + +def collectedFourData_11_0_6 : List CollectedFourTerm := [ + ⟨0, 6, 5, 0, 5, 6, 251622243928787722125828461136330215247669362688000000⟩, + ⟨0, 6, 6, 0, 6, 6, 290852371557353900100588446036667747461178064896000000⟩, + ⟨0, 6, 7, 0, 7, 6, -2665683954194811434035387654079766681297616896000000⟩, + ⟨0, 6, 8, 0, 8, 6, 119813477403830209628014019864385414256241147904000000⟩, + ⟨0, 6, 5, 1, 4, 6, 134655171213185305284364323493606798254680309760000000⟩, + ⟨0, 6, 6, 1, 5, 6, -182899502455761202691819258488885726425517129728000000⟩, + ⟨0, 6, 7, 1, 6, 6, -184503400472697890423284910327781733841013571584000000⟩, + ⟨0, 6, 8, 1, 7, 6, 100117911697399679731660489313301362800412590080000000⟩, + ⟨0, 6, 5, 2, 3, 6, 198669006080847355374383440139235803402229252096000000⟩, + ⟨0, 6, 6, 2, 4, 6, 65645198948060455152420273581542257475524231168000000⟩, + ⟨0, 6, 7, 2, 5, 6, 18712346407391466506863235868926167736710594560000000⟩, + ⟨0, 6, 8, 2, 6, 6, 5448068417116828139904007810521553021855334400000000⟩, + ⟨0, 6, 5, 3, 2, 6, -539730879415716549548888334356388751682347991040000000⟩, + ⟨0, 6, 6, 3, 3, 6, 99655482928911227674488804550763308411351203840000000⟩, + ⟨0, 6, 7, 3, 4, 6, -75184260680470605997373688201827257460107247616000000⟩, + ⟨0, 6, 8, 3, 5, 6, 86682954931821429527198178980941435610050068480000000⟩, + ⟨0, 6, 5, 4, 1, 6, 149601636054248313271782891010373344095130091520000000⟩, + ⟨0, 6, 6, 4, 2, 6, -303021904965008719294746475022013580584324956160000000⟩, + ⟨0, 6, 7, 4, 3, 6, 266662704333599051591697894059784754577037852672000000⟩, + ⟨0, 6, 8, 4, 4, 6, -124016806826620367763475800049702186790116392960000000⟩, + ⟨0, 6, 5, 5, 0, 6, 1712643371967877907943757460661996417476223565824000000⟩, + ⟨0, 6, 6, 5, 1, 6, 468257480886626360012259887130150452411781611520000000⟩, + ⟨0, 6, 7, 5, 2, 6, -517966696124668204881117307669224996919540973568000000⟩, + ⟨0, 6, 8, 5, 3, 6, 173478947855509437947196609346228048102214860800000000⟩, + ⟨0, 6, 6, 6, 0, 6, -686842231771928135004343216200989336041345253376000000⟩, + ⟨0, 6, 7, 6, 1, 6, 1423096724922183750867268597952989670835272810496000000⟩, + ⟨0, 6, 8, 6, 2, 6, -618651353963214482823360678986654969116319809536000000⟩, + ⟨0, 6, 7, 7, 0, 6, -4823817252688969176497992515996100972574901534720000000⟩, + ⟨0, 6, 8, 7, 1, 6, 1156742211417591881136929227114323721573399265280000000⟩ +] + +def collectedFourData_11_0_7 : List CollectedFourTerm := [ + ⟨0, 7, 4, 0, 4, 7, 876895747295130781018046667953877328942281523200000⟩, + ⟨0, 7, 5, 0, 5, 7, -4612273742641264975774789588624212112888037376000000⟩, + ⟨0, 7, 6, 0, 6, 7, -2665683954194811434035387654079766681297616896000000⟩, + ⟨0, 7, 7, 0, 7, 7, 16287463191042404224048281094596843760779264000000⟩, + ⟨0, 7, 8, 0, 8, 7, -549049785122162069500897791651390800057597952000000⟩, + ⟨0, 7, 4, 1, 3, 7, -522841474861980573788147107882840785539825664000000⟩, + ⟨0, 7, 5, 1, 4, 7, -2468249630081226806678769882005789711290859520000000⟩, + ⟨0, 7, 6, 1, 5, 7, 1676287754904537564667769651649149610888265728000000⟩, + ⟨0, 7, 7, 1, 6, 7, 1127325067584364804719745102429824743223853056000000⟩, + ⟨0, 7, 8, 1, 7, 7, -458794111442588118053203243478912133538775040000000⟩, + ⟨0, 7, 4, 2, 2, 7, 344444016352467872710656404772729579806235033600000⟩, + ⟨0, 7, 5, 2, 3, 7, -3641632893484007857435505258024423246310408192000000⟩, + ⟨0, 7, 6, 2, 4, 7, -601643206719613375034691567392183530624647168000000⟩, + ⟨0, 7, 7, 2, 5, 7, -114333378812149174268941257743089506755543040000000⟩, + ⟨0, 7, 8, 2, 6, 7, -24965979275159633990568098453350333494067200000000⟩, + ⟨0, 7, 4, 3, 1, 7, -764744639634539781825427381608479044432979558400000⟩, + ⟨0, 7, 5, 3, 2, 7, 9893348554376282167139730547177784193664942080000000⟩, + ⟨0, 7, 6, 3, 3, 7, -913350028293475418891615300655937597829283840000000⟩, + ⟨0, 7, 7, 3, 4, 7, 459379618672307668358461760716450357516959744000000⟩, + ⟨0, 7, 8, 3, 5, 7, -397227914674890727459359044151801079387914240000000⟩, + ⟨0, 7, 4, 4, 0, 7, 1277375257410862306636392985195260139874864332800000⟩, + ⟨0, 7, 5, 4, 1, 7, -2742220588512294035947165559809341752648663040000000⟩, + ⟨0, 7, 6, 4, 2, 7, 2777218647073965788526130491916151479766876160000000⟩, + ⟨0, 7, 7, 4, 3, 7, -1629322551318440242853947135876453108650344448000000⟩, + ⟨0, 7, 8, 4, 4, 7, 568311700946556802159151802655012175719956480000000⟩, + ⟨0, 7, 5, 5, 0, 7, -31393011729406595019828015654033024903857307648000000⟩, + ⟨0, 7, 6, 5, 1, 7, -4291615181088604684322147961284687107215851520000000⟩, + ⟨0, 7, 7, 5, 2, 7, 3164802595611767702388029428147743756713459712000000⟩, + ⟨0, 7, 8, 5, 3, 7, -794973830216543726129527386972992622192230400000000⟩, + ⟨0, 7, 6, 6, 0, 7, 6294960933253872323151503827411130191630565376000000⟩, + ⟨0, 7, 7, 6, 1, 7, -8695192649521850460404434491202891596813041664000000⟩, + ⟨0, 7, 8, 6, 2, 7, 2834993193747157873382001699463962018623520768000000⟩, + ⟨0, 7, 7, 7, 0, 7, 29473766317965034642163339671990504312516116480000000⟩, + ⟨0, 7, 8, 7, 1, 7, -5300814869765729358851728267368696564563312640000000⟩ +] + +def collectedFourData_11_0_8 : List CollectedFourTerm := [ + ⟨0, 8, 3, 0, 3, 8, -9730653361403528761732841313494222608156065792000000⟩, + ⟨0, 8, 4, 0, 4, 8, -118240493557453912773874811346741199513038775910400000⟩, + ⟨0, 8, 5, 0, 5, 8, 310959156452860011465838447468182212901272027136000000⟩, + ⟨0, 8, 6, 0, 6, 8, 119813477403830209628014019864385414256241147904000000⟩, + ⟨0, 8, 7, 0, 7, 8, -549049785122162069500897791651390800057597952000000⟩, + ⟨0, 8, 8, 0, 8, 8, 14806758450068935827355272897955003309572803788800000⟩, + ⟨0, 8, 3, 1, 2, 8, 1048117323837294915583027709555447451958326067200000⟩, + ⟨0, 8, 4, 1, 3, 8, 70499867550596108606205494565909332648534212608000000⟩, + ⟨0, 8, 5, 1, 4, 8, 166409208497154646545025371057240164323263774720000000⟩, + ⟨0, 8, 6, 1, 5, 8, -75343464752646485617954272072049363536599580672000000⟩, + ⟨0, 8, 7, 1, 6, 8, -38002086565600323735292401558558429031912439808000000⟩, + ⟨0, 8, 8, 1, 7, 8, 12372746097938878875580500386357141157420466176000000⟩, + ⟨0, 8, 3, 2, 1, 8, 8205029564351309474391033980098615456431498854400000⟩, + ⟨0, 8, 4, 2, 2, 8, -46444780490787627622902708579217293503154565939200000⟩, + ⟨0, 8, 5, 2, 3, 8, 245518621802420417500160254691840870949020762112000000⟩, + ⟨0, 8, 6, 2, 4, 8, 27041827160355217309237530139983859896111071232000000⟩, + ⟨0, 8, 7, 2, 5, 8, 3854173994611106435710834465482569084011806720000000⟩, + ⟨0, 8, 8, 2, 6, 8, 673281794499685194763275265726908747931975680000000⟩, + ⟨0, 8, 3, 3, 0, 8, -84639548767034043032738331331965993102581170176000000⟩, + ⟨0, 8, 4, 3, 1, 8, 103118054700032549305533095105458995542805499084800000⟩, + ⟨0, 8, 5, 3, 2, 8, -667008831787426321090259840154663686973035642880000000⟩, + ⟨0, 8, 6, 3, 3, 8, 41051994481387271698305295567796023052111708160000000⟩, + ⟨0, 8, 7, 3, 4, 8, -15485670049602669143326753391649710464504430592000000⟩, + ⟨0, 8, 8, 3, 5, 8, 10712430715016212620957263663650492313455558656000000⟩, + ⟨0, 8, 4, 4, 0, 8, -172241091783407235609031823379436581402393024921600000⟩, + ⟨0, 8, 5, 4, 1, 8, 184880310361442338790899565265732640634767933440000000⟩, + ⟨0, 8, 6, 4, 2, 8, -124826584596823086020656127562503320873300131840000000⟩, + ⟨0, 8, 7, 4, 3, 8, 54924403278963239618319488922706961183186878464000000⟩, + ⟨0, 8, 8, 4, 4, 8, -15326213229263350026403496312594261910604480512000000⟩, + ⟨0, 8, 5, 5, 0, 8, 2116514541545996593563485656740709683538981552128000000⟩, + ⟨0, 8, 6, 5, 1, 8, 192893586546950552082387602214398945089007124480000000⟩, + ⟨0, 8, 7, 5, 2, 8, -106685379097608419233044408012382037666395324416000000⟩, + ⟨0, 8, 8, 5, 3, 8, 21438830862165740360999776042180870020016373760000000⟩, + ⟨0, 8, 6, 6, 0, 8, -282937202044352838519092766514222996403125223424000000⟩, + ⟨0, 8, 7, 6, 1, 8, 293114624408875250649002554721823360614664241152000000⟩, + ⟨0, 8, 8, 6, 2, 8, -76454013032832476480800525215865302658516726579200000⟩, + ⟨0, 8, 7, 7, 0, 8, -993559578542558136438029674187816285757914480640000000⟩, + ⟨0, 8, 8, 7, 1, 8, 142952219437972168219692855844760175839193071616000000⟩ +] + +def collectedFourData_11_0_9 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_0_10 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_0_11 : List CollectedFourTerm := [ + ⟨1, 2, 8, 0, 8, 3, 1048117323837294915583027709555447451958326067200000⟩, + ⟨1, 2, 8, 1, 7, 3, 875822319410475383833514080936982514650578944000000⟩, + ⟨1, 2, 8, 2, 6, 3, 47659203398168230896606208555183832479825920000000⟩, + ⟨1, 2, 8, 3, 5, 3, 758294548444055881996176532818050474588504064000000⟩, + ⟨1, 2, 8, 4, 4, 3, -1084887664547567497796685858027680323420028928000000⟩, + ⟨1, 2, 8, 5, 3, 3, 1517577942885192832692634880249775489747517440000000⟩, + ⟨1, 2, 8, 6, 2, 3, -5411905367864022160145668291136167136004459724800000⟩, + ⟨1, 2, 8, 7, 1, 3, 10119074892670485430243329334080476261388386304000000⟩ +] + +def collectedFourData_11_0_12 : List CollectedFourTerm := [ + ⟨1, 3, 7, 0, 7, 4, -522841474861980573788147107882840785539825664000000⟩, + ⟨1, 3, 8, 0, 8, 4, 70499867550596108606205494565909332648534212608000000⟩, + ⟨1, 3, 7, 1, 6, 4, -36188097192990101061974130094807688427293638656000000⟩, + ⟨1, 3, 8, 1, 7, 4, 58910730804674181011386124628914877596077916160000000⟩, + ⟨1, 3, 7, 2, 5, 4, 3670199079066760661773304891204675755353047040000000⟩, + ⟨1, 3, 8, 2, 6, 4, 3205717003929005478283931131798813345107148800000000⟩, + ⟨1, 3, 7, 3, 4, 4, -14746477983155569646220698269441487084552454144000000⟩, + ⟨1, 3, 8, 3, 5, 4, 51005420875901737772661678844378673075674152960000000⟩, + ⟨1, 3, 7, 4, 3, 4, 52302645032267780033311546702126592428760629248000000⟩, + ⟨1, 3, 8, 4, 4, 4, -72973163326658414093908935503060217997736017920000000⟩, + ⟨1, 3, 7, 5, 2, 4, -101592865465182370273079008942712732275716390912000000⟩, + ⟨1, 3, 8, 5, 3, 4, 102077354832196920607730931060527254063389081600000000⟩, + ⟨1, 3, 7, 6, 1, 4, 279123108108408730791247710596940886000810328064000000⟩, + ⟨1, 3, 8, 6, 2, 4, -364022808280575690415057338793909243627828150272000000⟩, + ⟨1, 3, 7, 7, 0, 4, -946133063858421054270345664228790982408646164480000000⟩, + ⟨1, 3, 8, 7, 1, 4, 680642732872694879305867518374823319678023106560000000⟩ +] + +def collectedFourData_11_0_13 : List CollectedFourTerm := [ + ⟨1, 4, 6, 0, 6, 5, 134655171213185305284364323493606798254680309760000000⟩, + ⟨1, 4, 7, 0, 7, 5, -2468249630081226806678769882005789711290859520000000⟩, + ⟨1, 4, 8, 0, 8, 5, 166409208497154646545025371057240164323263774720000000⟩, + ⟨1, 4, 6, 1, 5, 5, -84676510238220295349914433346630645412716871680000000⟩, + ⟨1, 4, 7, 1, 6, 5, -170838125520780996140626546069535629647103918080000000⟩, + ⟨1, 4, 8, 1, 7, 5, 139053992947705692946893614304013801251825254400000000⟩, + ⟨1, 4, 6, 2, 4, 5, 30391588201066520688485743125248618436577198080000000⟩, + ⟨1, 4, 7, 2, 5, 5, 17326413367689265529492127845167208728834867200000000⟩, + ⟨1, 4, 8, 2, 6, 5, 7566834489537776992882401192994889785147392000000000⟩, + ⟨1, 4, 6, 3, 3, 5, 46137241530035301830635252571762981014496870400000000⟩, + ⟨1, 4, 7, 3, 4, 5, -69615725945484743493946014350084400503240785920000000⟩, + ⟨1, 4, 8, 3, 5, 5, 120394151250448533166276884226361591004030566400000000⟩, + ⟨1, 4, 6, 4, 2, 5, -140289268662066517586951587850460317781432729600000000⟩, + ⟨1, 4, 7, 4, 3, 5, 246912286916877348205573697309588815774104944640000000⟩, + ⟨1, 4, 8, 4, 4, 5, -172247222195244268161679972313950580063915212800000000⟩, + ⟨1, 4, 6, 5, 1, 5, 216787956457181176318534376548490070795170611200000000⟩, + ⟨1, 4, 7, 5, 2, 5, -479603406882598237600257200698091271474024284160000000⟩, + ⟨1, 4, 8, 5, 3, 5, 240945301222278170826719592741034860786745344000000000⟩, + ⟨1, 4, 6, 6, 0, 5, -317985573988890697551786766421273375981237698560000000⟩, + ⟨1, 4, 7, 6, 1, 5, 1317694830000947443515688339938026342325965291520000000⟩, + ⟨1, 4, 8, 6, 2, 5, -859246258262932990739776529137218798609739284480000000⟩, + ⟨1, 4, 7, 7, 0, 5, -4466540427942589776517042611413926754675746406400000000⟩, + ⟨1, 4, 8, 7, 1, 5, 1606601861562330095175996877274665521470924390400000000⟩ +] + +def collectedFourData_11_0_14 : List CollectedFourTerm := [ + ⟨1, 5, 5, 0, 5, 6, -158230042873493793347491498548986141800277213184000000⟩, + ⟨1, 5, 6, 0, 6, 6, -182899502455761202691819258488885726425517129728000000⟩, + ⟨1, 5, 7, 0, 7, 6, 1676287754904537564667769651649149610888265728000000⟩, + ⟨1, 5, 8, 0, 8, 6, -75343464752646485617954272072049363536599580672000000⟩, + ⟨1, 5, 5, 1, 4, 6, -84676510238220295349914433346630645412716871680000000⟩, + ⟨1, 5, 6, 1, 5, 6, 115014458432801433957535057518982681515371003904000000⟩, + ⟨1, 5, 7, 1, 6, 6, 116023053094473826074651149063917762421207334912000000⟩, + ⟨1, 5, 8, 1, 7, 6, -62958112180128270632236249030312708529392189440000000⟩, + ⟨1, 5, 5, 2, 3, 6, -124930947514733608083216915895077636335707619328000000⟩, + ⟨1, 5, 6, 2, 4, 6, -41280303687818235729770227062437852388287053824000000⟩, + ⟨1, 5, 7, 2, 5, 6, -11767065296274755523160656041033893194844078080000000⟩, + ⟨1, 5, 8, 2, 6, 6, -3425961416440168540669887777824201893950259200000000⟩, + ⟨1, 5, 5, 3, 2, 6, 339404175309187222678927060006829975560488222720000000⟩, + ⟨1, 5, 6, 3, 3, 6, -62667318636912859298154355249909362777516933120000000⟩, + ⟨1, 5, 7, 3, 4, 6, 47278843893664789816698590139242839415023730688000000⟩, + ⟨1, 5, 8, 3, 5, 6, -54509678719600773611918746483832970493443440640000000⟩, + ⟨1, 5, 5, 4, 1, 6, -94075439902315837477779644591295356130935439360000000⟩, + ⟨1, 5, 6, 4, 2, 6, 190552187539471855072696182849177264797389946880000000⟩, + ⟨1, 5, 7, 4, 3, 6, -167688080674650637383077451135196730864273719296000000⟩, + ⟨1, 5, 8, 4, 4, 6, 77986684940157945740051196772847226205797089280000000⟩, + ⟨1, 5, 5, 5, 0, 6, -1076978052267018014428391960824762086636474335232000000⟩, + ⟨1, 5, 6, 5, 1, 6, -294458868658266064122110690744390581000454799360000000⟩, + ⟨1, 5, 7, 5, 2, 6, 325717993986427137246207989302255343764739457024000000⟩, + ⟨1, 5, 8, 5, 3, 6, -109090440210025435063181278950824512003139174400000000⟩, + ⟨1, 5, 6, 6, 0, 6, 431913626091641972811101652701196797476620730368000000⟩, + ⟨1, 5, 7, 6, 1, 6, -894899641151334697179159631053149895480236310528000000⟩, + ⟨1, 5, 8, 6, 2, 6, 389032498609496155666194674761473647837863477248000000⟩, + ⟨1, 5, 7, 7, 0, 6, 3033407534998736027838147359337579523295108136960000000⟩, + ⟨1, 5, 8, 7, 1, 6, -727405363088589965483739000468826630069986263040000000⟩ +] + +def collectedFourData_11_0_15 : List CollectedFourTerm := [ + ⟨1, 6, 4, 0, 4, 7, 60693709387941708654352856660543805668335602892800000⟩, + ⟨1, 6, 5, 0, 5, 7, -319235214695695229654046949806903921084154773504000000⟩, + ⟨1, 6, 6, 0, 6, 7, -184503400472697890423284910327781733841013571584000000⟩, + ⟨1, 6, 7, 0, 7, 7, 1127325067584364804719745102429824743223853056000000⟩, + ⟨1, 6, 8, 0, 8, 7, -38002086565600323735292401558558429031912439808000000⟩, + ⟨1, 6, 4, 1, 3, 7, -36188097192990101061974130094807688427293638656000000⟩, + ⟨1, 6, 5, 1, 4, 7, -170838125520780996140626546069535629647103918080000000⟩, + ⟨1, 6, 6, 1, 5, 7, 116023053094473826074651149063917762421207334912000000⟩, + ⟨1, 6, 7, 1, 6, 7, 78026994940687077340481362280740951304882356224000000⟩, + ⟨1, 6, 8, 1, 7, 7, -31755104930875524063880152234149995020980060160000000⟩, + ⟨1, 6, 4, 2, 2, 7, 23840445222134345144072634299752326694493906534400000⟩, + ⟨1, 6, 5, 2, 3, 7, -252053005407379465485261575057365895117713440768000000⟩, + ⟨1, 6, 6, 2, 4, 7, -41642302470398031409856946788995166485371420672000000⟩, + ⟨1, 6, 7, 2, 5, 7, -7913502703566557207612869651436862817079132160000000⟩, + ⟨1, 6, 8, 2, 6, 7, -1728002325688013328023741382294790847909068800000000⟩, + ⟨1, 6, 4, 3, 1, 7, -52931251014886407698395389496876008102128359833600000⟩, + ⟨1, 6, 5, 3, 2, 7, 684761015075185711514489587149743034040917688320000000⟩, + ⟨1, 6, 6, 3, 3, 7, -63216866266834900196737741408944638219633295360000000⟩, + ⟨1, 6, 7, 3, 4, 7, 31795630393286253376714537112655648549268094976000000⟩, + ⟨1, 6, 8, 3, 5, 7, -27493844836656099625909050040686774043237416960000000⟩, + ⟨1, 6, 4, 4, 0, 7, 88412611067834073181480565813921858337627124531200000⟩, + ⟨1, 6, 5, 4, 1, 7, -189800828650591677413273665304613222707531612160000000⟩, + ⟨1, 6, 6, 4, 2, 7, 192223194139347270527058192759172182894591344640000000⟩, + ⟨1, 6, 7, 4, 3, 7, -112772390257309058801148961654085961030976929792000000⟩, + ⟨1, 6, 8, 4, 4, 7, 39335286236036564637685585921938213130123345920000000⟩, + ⟨1, 6, 5, 5, 0, 7, -2172844761300428407132939824339942029452841582592000000⟩, + ⟨1, 6, 6, 5, 1, 7, -297041062645505841815606271792813018185811886080000000⟩, + ⟨1, 6, 7, 5, 2, 7, 219049538785841517983995236012459851729074126848000000⟩, + ⟨1, 6, 8, 5, 3, 7, -55023542731291952301504950336287015752538521600000000⟩, + ⟨1, 6, 6, 6, 0, 7, 435701200136814000053007503682693532576596885504000000⟩, + ⟨1, 6, 7, 6, 1, 7, -601831514601503785801760993249037538639170502656000000⟩, + ⟨1, 6, 8, 6, 2, 7, 196222017895328628792464458608564831542493315072000000⟩, + ⟨1, 6, 7, 7, 0, 7, 2040005568493886325013828252311593587281147985920000000⟩, + ⟨1, 6, 8, 7, 1, 7, -366892094319349120267092572098144565784540610560000000⟩ +] + +def collectedFourData_11_0_16 : List CollectedFourTerm := [ + ⟨1, 7, 3, 0, 3, 8, -8131077697640216670583869829869495201394851840000000⟩, + ⟨1, 7, 4, 0, 4, 8, -98803503158015247080217388547221808656215441408000000⟩, + ⟨1, 7, 5, 0, 5, 8, 259842064864816959770832985026755594872915230720000000⟩, + ⟨1, 7, 6, 0, 6, 8, 100117911697399679731660489313301362800412590080000000⟩, + ⟨1, 7, 7, 0, 7, 8, -458794111442588118053203243478912133538775040000000⟩, + ⟨1, 7, 8, 0, 8, 8, 12372746097938878875580500386357141157420466176000000⟩, + ⟨1, 7, 3, 1, 2, 8, 875822319410475383833514080936982514650578944000000⟩, + ⟨1, 7, 4, 1, 3, 8, 58910730804674181011386124628914877596077916160000000⟩, + ⟨1, 7, 5, 1, 4, 8, 139053992947705692946893614304013801251825254400000000⟩, + ⟨1, 7, 6, 1, 5, 8, -62958112180128270632236249030312708529392189440000000⟩, + ⟨1, 7, 7, 1, 6, 8, -31755104930875524063880152234149995020980060160000000⟩, + ⟨1, 7, 8, 1, 7, 8, 10338849419357485105596848041584408183460331520000000⟩, + ⟨1, 7, 3, 2, 1, 8, 6856243915110816352971300611619374269923852288000000⟩, + ⟨1, 7, 4, 2, 2, 8, -38809944696865436591466913501843896411969552384000000⟩, + ⟨1, 7, 5, 2, 3, 8, 205158987371951473201502347557550497391171338240000000⟩, + ⟨1, 7, 6, 2, 4, 8, 22596550258295386488659942801696814522842480640000000⟩, + ⟨1, 7, 7, 2, 5, 8, 3220604726781374196066520762779369382241894400000000⟩, + ⟨1, 7, 8, 2, 6, 8, 562604213731229101563249975557636314732953600000000⟩, + ⟨1, 7, 3, 3, 0, 8, -70726057311602347595474236058119207258706411520000000⟩, + ⟨1, 7, 4, 3, 1, 8, 86166969848213847378905967145809098694350340096000000⟩, + ⟨1, 7, 5, 3, 2, 8, -557362433419735216214787749026406598681663897600000000⟩, + ⟨1, 7, 6, 3, 3, 8, 34303653040941449596351163146494017539355443200000000⟩, + ⟨1, 7, 7, 3, 4, 8, -12940054659924458763197805812128779410960547840000000⟩, + ⟨1, 7, 8, 3, 5, 8, 8951465357904880404909308486946548264070021120000000⟩, + ⟨1, 7, 4, 4, 0, 8, -143927200774857134625656556782212091810238431232000000⟩, + ⟨1, 7, 5, 4, 1, 8, 154488718535123720266099470025285373765930188800000000⟩, + ⟨1, 7, 6, 4, 2, 8, -104306938125419997951801310460056852807601356800000000⟩, + ⟨1, 7, 7, 4, 3, 8, 45895642766310537947650757988099900000467681280000000⟩, + ⟨1, 7, 8, 4, 4, 8, -12806810185227576938828624642941686538032906240000000⟩, + ⟨1, 7, 5, 5, 0, 8, 1768590817730413183084729213761938048275772866560000000⟩, + ⟨1, 7, 6, 5, 1, 8, 161184730494141778980638192944750987847506329600000000⟩, + ⟨1, 7, 7, 5, 2, 8, -89147878814145112030581632567867389480607416320000000⟩, + ⟨1, 7, 8, 5, 3, 8, 17914603779667778425804788672325765263733555200000000⟩, + ⟨1, 7, 6, 6, 0, 8, -236426505798756547487766819554077960720330260480000000⟩, + ⟨1, 7, 7, 6, 1, 8, 244930910275425395601279090375351144515937239040000000⟩, + ⟨1, 7, 8, 6, 2, 8, -63886102728942820882880549755789513675121885184000000⟩, + ⟨1, 7, 7, 7, 0, 8, -830233061472344098916748438739917634244758732800000000⟩, + ⟨1, 7, 8, 7, 1, 8, 119452986364793295222383892050349478082059960320000000⟩ +] + +def collectedFourData_11_0_17 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_0_18 : List CollectedFourTerm := [ + ⟨2, 1, 8, 0, 8, 3, 8205029564351309474391033980098615456431498854400000⟩, + ⟨2, 1, 8, 1, 7, 3, 6856243915110816352971300611619374269923852288000000⟩, + ⟨2, 1, 8, 2, 6, 3, 373092939122249300597573088402944101806243840000000⟩, + ⟨2, 1, 8, 3, 5, 3, 5936195354248103180214935432739442589096214528000000⟩, + ⟨2, 1, 8, 4, 4, 3, -8492880672006402391641900491423302838340550656000000⟩, + ⟨2, 1, 8, 5, 3, 3, 11880131741352085501267644045828820967494778880000000⟩, + ⟨2, 1, 8, 6, 2, 3, -42366290999011349171834536702384017208099051929600000⟩, + ⟨2, 1, 8, 7, 1, 3, 79215662951044951790951932505833458588092203008000000⟩ +] + +def collectedFourData_11_0_19 : List CollectedFourTerm := [ + ⟨2, 2, 7, 0, 7, 4, 344444016352467872710656404772729579806235033600000⟩, + ⟨2, 2, 8, 0, 8, 4, -46444780490787627622902708579217293503154565939200000⟩, + ⟨2, 2, 7, 1, 6, 4, 23840445222134345144072634299752326694493906534400000⟩, + ⟨2, 2, 8, 1, 7, 4, -38809944696865436591466913501843896411969552384000000⟩, + ⟨2, 2, 7, 2, 5, 4, -2417899444455130362863698107789189021010231296000000⟩, + ⟨2, 2, 8, 2, 6, 4, -2111902160046102316306274868018812342627205120000000⟩, + ⟨2, 2, 7, 3, 4, 4, 9714868364091018302908841262764354356029004185600000⟩, + ⟨2, 2, 8, 3, 5, 4, -33601986198362192340062203695223773396367048704000000⟩, + ⟨2, 2, 7, 4, 3, 4, -34456587678946939384273416673841202866878100275200000⟩, + ⟨2, 2, 8, 4, 4, 4, 48074169075462134836985644939226586485996126208000000⟩, + ⟨2, 2, 7, 5, 2, 4, 66928612774686234856690687815786946225765141708800000⟩, + ⟨2, 2, 8, 5, 3, 4, -67247790711935014403115849245240051371962531840000000⟩, + ⟨2, 2, 7, 6, 1, 4, -183884196331256976141048119312338736224323344793600000⟩, + ⟨2, 2, 8, 6, 2, 4, 239815477838985679357986693404107391283246189772800000⟩, + ⟨2, 2, 7, 7, 0, 4, 623305319466648574921887379396415873254321815552000000⟩, + ⟨2, 2, 8, 7, 1, 4, -448402293780689767203422649681924765640078393344000000⟩ +] + +def collectedFourData_11_0_20 : List CollectedFourTerm := [ + ⟨2, 3, 6, 0, 6, 5, 198669006080847355374383440139235803402229252096000000⟩, + ⟨2, 3, 7, 0, 7, 5, -3641632893484007857435505258024423246310408192000000⟩, + ⟨2, 3, 8, 0, 8, 5, 245518621802420417500160254691840870949020762112000000⟩, + ⟨2, 3, 6, 1, 5, 5, -124930947514733608083216915895077636335707619328000000⟩, + ⟨2, 3, 7, 1, 6, 5, -252053005407379465485261575057365895117713440768000000⟩, + ⟨2, 3, 8, 1, 7, 5, 205158987371951473201502347557550497391171338240000000⟩, + ⟨2, 3, 6, 2, 4, 5, 44839470825559139203107686647386220520452128768000000⟩, + ⟨2, 3, 7, 2, 5, 5, 25563231561712756459807066659287804956240773120000000⟩, + ⟨2, 3, 8, 2, 6, 5, 11164038288843264703492404395252483152360243200000000⟩, + ⟨2, 3, 6, 3, 3, 5, 68070463506911917834968359828915314505904291840000000⟩, + ⟨2, 3, 7, 3, 4, 5, -102710404335602994474690399966474945516779077632000000⟩, + ⟨2, 3, 8, 3, 5, 5, 177628427867846569718856069146774758139300413440000000⟩, + ⟨2, 3, 6, 4, 2, 5, -206981501845007546383580657847361895552683868160000000⟩, + ⟨2, 3, 7, 4, 3, 5, 364292126243434829938249289018327604974158086144000000⟩, + ⟨2, 3, 8, 4, 4, 5, -254131973732660045155135710852806354244867194880000000⟩, + ⟨2, 3, 6, 5, 1, 5, 319846965041242463173578204583082574785040875520000000⟩, + ⟨2, 3, 7, 5, 2, 5, -707602473042075513022454334042196322467065102336000000⟩, + ⟨2, 3, 8, 5, 3, 5, 355488490211010591911363851371688111565596262400000000⟩, + ⟨2, 3, 6, 6, 0, 5, -469153002912930365506705502546261794501297176576000000⟩, + ⟨2, 3, 7, 6, 1, 5, 1944114881259945267072589367291797784021163835392000000⟩, + ⟨2, 3, 8, 6, 2, 5, -1267724058198432135572463125939894088526051934208000000⟩, + ⟨2, 3, 7, 7, 0, 5, -6589892831032895144170412963567417245595798077440000000⟩, + ⟨2, 3, 8, 7, 1, 5, 2370365669053289530980391109798329592426885283840000000⟩ +] + +def collectedFourData_11_0_21 : List CollectedFourTerm := [ + ⟨2, 4, 5, 0, 5, 6, 56790983597689120525678017731000227689350037504000000⟩, + ⟨2, 4, 6, 0, 6, 6, 65645198948060455152420273581542257475524231168000000⟩, + ⟨2, 4, 7, 0, 7, 6, -601643206719613375034691567392183530624647168000000⟩, + ⟨2, 4, 8, 0, 8, 6, 27041827160355217309237530139983859896111071232000000⟩, + ⟨2, 4, 5, 1, 4, 6, 30391588201066520688485743125248618436577198080000000⟩, + ⟨2, 4, 6, 1, 5, 6, -41280303687818235729770227062437852388287053824000000⟩, + ⟨2, 4, 7, 1, 6, 6, -41642302470398031409856946788995166485371420672000000⟩, + ⟨2, 4, 8, 1, 7, 6, 22596550258295386488659942801696814522842480640000000⟩, + ⟨2, 4, 5, 2, 3, 6, 44839470825559139203107686647386220520452128768000000⟩, + ⟨2, 4, 6, 2, 4, 6, 14816080480473845776982943684094191070655545344000000⟩, + ⟨2, 4, 7, 2, 5, 6, 4223364919188945601054598774492917672685076480000000⟩, + ⟨2, 4, 8, 2, 6, 6, 1229625645509839582571817969494544492999475200000000⟩, + ⟨2, 4, 5, 3, 2, 6, -121816923025053157498335572375115102907866808320000000⟩, + ⟨2, 4, 6, 3, 3, 6, 22492180373517792351731155393441323220174110720000000⟩, + ⟨2, 4, 7, 3, 4, 6, -16969040766989556404390635678183693196017532928000000⟩, + ⟨2, 4, 8, 3, 5, 6, 19564288891428508355680662083004165133267107840000000⟩, + ⟨2, 4, 5, 4, 1, 6, 33764995998321816082029368865433671591694172160000000⟩, + ⟨2, 4, 6, 4, 2, 6, -68391855051887469206245687155385650740755169280000000⟩, + ⟨2, 4, 7, 4, 3, 6, 60185606135087172205749959439397376078565605376000000⟩, + ⟨2, 4, 8, 4, 4, 6, -27990515990794700401339897574722427376296263680000000⟩, + ⟨2, 4, 5, 5, 0, 6, 386542541420325765998393937601673078482604654592000000⟩, + ⟨2, 4, 6, 5, 1, 6, 105685421532341648121202630031949393098346332160000000⟩, + ⟨2, 4, 7, 5, 2, 6, -116904760423686195472023128491003495547922284544000000⟩, + ⟨2, 4, 8, 5, 3, 6, 39154090387155337048972207062282430690256486400000000⟩, + ⟨2, 4, 6, 6, 0, 6, -155019863545128695532589123797110976786368299008000000⟩, + ⟨2, 4, 7, 6, 1, 6, 321192043680580404988545291525766797611885395968000000⟩, + ⟨2, 4, 8, 6, 2, 6, -139629224932738439241223176138267828943520268288000000⟩, + ⟨2, 4, 7, 7, 0, 6, -1088732546846057730821841609444773626984016117760000000⟩, + ⟨2, 4, 8, 7, 1, 6, 261075996023479219169485949550442414419990282240000000⟩ +] + +def collectedFourData_11_0_22 : List CollectedFourTerm := [ + ⟨2, 5, 4, 0, 4, 7, -6155559799477910021597453823963560747049418752000000⟩, + ⟨2, 5, 5, 0, 5, 7, 32376855426617422034753097601199385257296527360000000⟩, + ⟨2, 5, 6, 0, 6, 7, 18712346407391466506863235868926167736710594560000000⟩, + ⟨2, 5, 7, 0, 7, 7, -114333378812149174268941257743089506755543040000000⟩, + ⟨2, 5, 8, 0, 8, 7, 3854173994611106435710834465482569084011806720000000⟩, + ⟨2, 5, 4, 1, 3, 7, 3670199079066760661773304891204675755353047040000000⟩, + ⟨2, 5, 5, 1, 4, 7, 17326413367689265529492127845167208728834867200000000⟩, + ⟨2, 5, 6, 1, 5, 7, -11767065296274755523160656041033893194844078080000000⟩, + ⟨2, 5, 7, 1, 6, 7, -7913502703566557207612869651436862817079132160000000⟩, + ⟨2, 5, 8, 1, 7, 7, 3220604726781374196066520762779369382241894400000000⟩, + ⟨2, 5, 4, 2, 2, 7, -2417899444455130362863698107789189021010231296000000⟩, + ⟨2, 5, 5, 2, 3, 7, 25563231561712756459807066659287804956240773120000000⟩, + ⟨2, 5, 6, 2, 4, 7, 4223364919188945601054598774492917672685076480000000⟩, + ⟨2, 5, 7, 2, 5, 7, 802587938789120951510176047194443763574374400000000⟩, + ⟨2, 5, 8, 2, 6, 7, 175254103871310500770772141800503317102592000000000⟩, + ⟨2, 5, 4, 3, 1, 7, 5368290786129501444226673943845023100461645824000000⟩, + ⟨2, 5, 5, 3, 2, 7, -69448504946443932226118273955602792132168908800000000⟩, + ⟨2, 5, 6, 3, 3, 7, 6411458527832397197711224725900119069058662400000000⟩, + ⟨2, 5, 7, 3, 4, 7, -3224714821711909109641943953130225661735075840000000⟩, + ⟨2, 5, 8, 3, 5, 7, 2788427461697163349755910358424312376354406400000000⟩, + ⟨2, 5, 4, 4, 0, 7, -8966812540282133320982783665976546634296721408000000⟩, + ⟨2, 5, 5, 4, 1, 7, 19249611904282368574447632883788522029737574400000000⟩, + ⟨2, 5, 6, 4, 2, 7, -19495288363549645235136841266959953709078937600000000⟩, + ⟨2, 5, 7, 4, 3, 7, 11437382868163290388614360313658209291500257280000000⟩, + ⟨2, 5, 8, 4, 4, 7, -3989387188511642079369664927894271565810892800000000⟩, + ⟨2, 5, 5, 5, 0, 7, 220370051493744731245458673444160275305757409280000000⟩, + ⟨2, 5, 6, 5, 1, 7, 30125923138554164673041094087821634565255987200000000⟩, + ⟨2, 5, 7, 5, 2, 7, -22216017914241875367227350997151620547288760320000000⟩, + ⟨2, 5, 8, 5, 3, 7, 5580491142775447029537451036937852754591744000000000⟩, + ⟨2, 5, 6, 6, 0, 7, -44188842949172150469060991694621324602622607360000000⟩, + ⟨2, 5, 7, 6, 1, 7, 61037789825314762748326636941786424477262807040000000⟩, + ⟨2, 5, 8, 6, 2, 7, -19900849318807497457239693866340453194378772480000000⟩, + ⟨2, 5, 7, 7, 0, 7, -206897492256864382474962936156990108055948492800000000⟩, + ⟨2, 5, 8, 7, 1, 7, 37210219136600255061469796353089435808982630400000000⟩ +] + +def collectedFourData_11_0_23 : List CollectedFourTerm := [ + ⟨2, 6, 3, 0, 3, 8, -442464958073903065173349047047192367543091200000000⟩, + ⟨2, 6, 4, 0, 4, 8, -5376542877588470424821338330245022159931965440000000⟩, + ⟨2, 6, 5, 0, 5, 8, 14139701108699805905975789621765662351923609600000000⟩, + ⟨2, 6, 6, 0, 6, 8, 5448068417116828139904007810521553021855334400000000⟩, + ⟨2, 6, 7, 0, 7, 8, -24965979275159633990568098453350333494067200000000⟩, + ⟨2, 6, 8, 0, 8, 8, 673281794499685194763275265726908747931975680000000⟩, + ⟨2, 6, 3, 1, 2, 8, 47659203398168230896606208555183832479825920000000⟩, + ⟨2, 6, 4, 1, 3, 8, 3205717003929005478283931131798813345107148800000000⟩, + ⟨2, 6, 5, 1, 4, 8, 7566834489537776992882401192994889785147392000000000⟩, + ⟨2, 6, 6, 1, 5, 8, -3425961416440168540669887777824201893950259200000000⟩, + ⟨2, 6, 7, 1, 6, 8, -1728002325688013328023741382294790847909068800000000⟩, + ⟨2, 6, 8, 1, 7, 8, 562604213731229101563249975557636314732953600000000⟩, + ⟨2, 6, 3, 2, 1, 8, 373092939122249300597573088402944101806243840000000⟩, + ⟨2, 6, 4, 2, 2, 8, -2111902160046102316306274868018812342627205120000000⟩, + ⟨2, 6, 5, 2, 3, 8, 11164038288843264703492404395252483152360243200000000⟩, + ⟨2, 6, 6, 2, 4, 8, 1229625645509839582571817969494544492999475200000000⟩, + ⟨2, 6, 7, 2, 5, 8, 175254103871310500770772141800503317102592000000000⟩, + ⟨2, 6, 8, 2, 6, 8, 30614963858116146759832435312327863042048000000000⟩, + ⟨2, 6, 3, 3, 0, 8, -3848665963700311933572783138894984232147353600000000⟩, + ⟨2, 6, 4, 3, 1, 8, 4688906700806710211336419795517844944616161280000000⟩, + ⟨2, 6, 5, 3, 2, 8, -30329724411144577933008378607190621414227968000000000⟩, + ⟨2, 6, 6, 3, 3, 8, 1866685446745497104396260908411823457304576000000000⟩, + ⟨2, 6, 7, 3, 4, 8, -704152752622095538419248742735805762712371200000000⟩, + ⟨2, 6, 8, 3, 5, 8, 487107600193618491514874966738937327491481600000000⟩, + ⟨2, 6, 4, 4, 0, 8, -7832017504275387156798147189967614249806069760000000⟩, + ⟨2, 6, 5, 4, 1, 8, 8406738554395146136927630039171417384157184000000000⟩, + ⟨2, 6, 6, 4, 2, 8, -5676020660566967587168268566154139270119424000000000⟩, + ⟨2, 6, 7, 4, 3, 8, 2497481195913788790647482221146604956968550400000000⟩, + ⟨2, 6, 8, 4, 4, 8, -696902051902872902417161029369537278194483200000000⟩, + ⟨2, 6, 5, 5, 0, 8, 96240558892222131062836298516383358476143820800000000⟩, + ⟨2, 6, 6, 5, 1, 8, 8771112227957399981719823796313727831113728000000000⟩, + ⟨2, 6, 7, 5, 2, 8, -4851117395339328052067013292054418028075417600000000⟩, + ⟨2, 6, 8, 5, 3, 8, 974850407908625040819351994345478198132736000000000⟩, + ⟨2, 6, 6, 6, 0, 8, -12865507853425878178502602636246045663061606400000000⟩, + ⟨2, 6, 7, 6, 1, 8, 13328287955909077446144419331209768046113587200000000⟩, + ⟨2, 6, 8, 6, 2, 8, -3476459433375042087749754161878424727186309120000000⟩, + ⟨2, 6, 7, 7, 0, 8, -45178394598607776231603968698169157803311104000000000⟩, + ⟨2, 6, 8, 7, 1, 8, 6500215908530781968087532547023295655549337600000000⟩ +] + +def collectedFourData_11_0_24 : List CollectedFourTerm := [ + ⟨3, 0, 8, 0, 8, 3, -84639548767034043032738331331965993102581170176000000⟩, + ⟨3, 0, 8, 1, 7, 3, -70726057311602347595474236058119207258706411520000000⟩, + ⟨3, 0, 8, 2, 6, 3, -3848665963700311933572783138894984232147353600000000⟩, + ⟨3, 0, 8, 3, 5, 3, -61235232881972677113178678794242059819674501120000000⟩, + ⟨3, 0, 8, 4, 4, 3, 87608896735001321308390624836450169764697866240000000⟩, + ⟨3, 0, 8, 5, 3, 3, -122550318922641948799727202068225671577154355200000000⟩, + ⟨3, 0, 8, 6, 2, 3, 437032398843364227482985865566715692573926621184000000⟩, + ⟨3, 0, 8, 7, 1, 3, -817154638490078560012185014055785639440621240320000000⟩ +] + +def collectedFourData_11_0_25 : List CollectedFourTerm := [ + ⟨3, 1, 7, 0, 7, 4, -764744639634539781825427381608479044432979558400000⟩, + ⟨3, 1, 8, 0, 8, 4, 103118054700032549305533095105458995542805499084800000⟩, + ⟨3, 1, 7, 1, 6, 4, -52931251014886407698395389496876008102128359833600000⟩, + ⟨3, 1, 8, 1, 7, 4, 86166969848213847378905967145809098694350340096000000⟩, + ⟨3, 1, 7, 2, 5, 4, 5368290786129501444226673943845023100461645824000000⟩, + ⟨3, 1, 8, 2, 6, 4, 4688906700806710211336419795517844944616161280000000⟩, + ⟨3, 1, 7, 3, 4, 4, -21569233760737811359647334380916226009298527846400000⟩, + ⟨3, 1, 8, 3, 5, 4, 74604108668782106772320681337086415171722674176000000⟩, + ⟨3, 1, 7, 4, 3, 4, 76501519772687451055667031504020937622902590668800000⟩, + ⟨3, 1, 8, 4, 4, 4, -106735670703953620217036081112739831975407255552000000⟩, + ⟨3, 1, 7, 5, 2, 4, -148596855882790144559161164692107273986204971827200000⟩, + ⟨3, 1, 8, 5, 3, 4, 149305504037533636919568591641804358047194152960000000⟩, + ⟨3, 1, 7, 6, 1, 4, 408265049708205018964927805518952007326203536998400000⟩, + ⟨3, 1, 8, 6, 2, 4, -532445310331912395904852729229353081048036225843200000⟩, + ⟨3, 1, 7, 7, 0, 4, -1383880628746473554917974028076162074301209509888000000⟩, + ⟨3, 1, 8, 7, 1, 4, 995555835749264946630318291496154133586652430336000000⟩ +] + +def collectedFourData_11_0_26 : List CollectedFourTerm := [ + ⟨3, 2, 6, 0, 6, 5, -539730879415716549548888334356388751682347991040000000⟩, + ⟨3, 2, 7, 0, 7, 5, 9893348554376282167139730547177784193664942080000000⟩, + ⟨3, 2, 8, 0, 8, 5, -667008831787426321090259840154663686973035642880000000⟩, + ⟨3, 2, 6, 1, 5, 5, 339404175309187222678927060006829975560488222720000000⟩, + ⟨3, 2, 7, 1, 6, 5, 684761015075185711514489587149743034040917688320000000⟩, + ⟨3, 2, 8, 1, 7, 5, -557362433419735216214787749026406598681663897600000000⟩, + ⟨3, 2, 6, 2, 4, 5, -121816923025053157498335572375115102907866808320000000⟩, + ⟨3, 2, 7, 2, 5, 5, -69448504946443932226118273955602792132168908800000000⟩, + ⟨3, 2, 8, 2, 6, 5, -30329724411144577933008378607190621414227968000000000⟩, + ⟨3, 2, 6, 3, 3, 5, -184929354888250464846662264590902726850353561600000000⟩, + ⟨3, 2, 7, 3, 4, 5, 279036866146294794549589135295556784039321927680000000⟩, + ⟨3, 2, 8, 3, 5, 5, -482569221408041658549357598171234738137307545600000000⟩, + ⟨3, 2, 6, 4, 2, 5, 562313720783050091480588509745797278527284838400000000⟩, + ⟨3, 2, 7, 4, 3, 5, -989684871034070155937626479193933074299155906560000000⟩, + ⟨3, 2, 8, 4, 4, 5, 690409019384546782733131547835384008667247411200000000⟩, + ⟨3, 2, 6, 5, 1, 5, -868939182440497576707745781611766888293780684800000000⟩, + ⟨3, 2, 7, 5, 2, 5, 1922367824683820708756170231809132728083430768640000000⟩, + ⟨3, 2, 8, 5, 3, 5, -965767732112548666792444836582036876533170176000000000⟩, + ⟨3, 2, 6, 6, 0, 5, 1274563998873961274351118506409556655261079306240000000⟩, + ⟨3, 2, 7, 6, 1, 5, -5281643348638915121389647810777231855330609070080000000⟩, + ⟨3, 2, 8, 6, 2, 5, 3444069280285506190993373555654078628437604433920000000⟩, + ⟨3, 2, 7, 7, 0, 5, 17902987099564495346548350321256522824690538905600000000⟩, + ⟨3, 2, 8, 7, 1, 5, -6439653433280510518571890655869329526931167641600000000⟩ +] + +def collectedFourData_11_0_27 : List CollectedFourTerm := [ + ⟨3, 3, 5, 0, 5, 6, 86213965181421718254549346733959920796324331520000000⟩, + ⟨3, 3, 6, 0, 6, 6, 99655482928911227674488804550763308411351203840000000⟩, + ⟨3, 3, 7, 0, 7, 6, -913350028293475418891615300655937597829283840000000⟩, + ⟨3, 3, 8, 0, 8, 6, 41051994481387271698305295567796023052111708160000000⟩, + ⟨3, 3, 5, 1, 4, 6, 46137241530035301830635252571762981014496870400000000⟩, + ⟨3, 3, 6, 1, 5, 6, -62667318636912859298154355249909362777516933120000000⟩, + ⟨3, 3, 7, 1, 6, 6, -63216866266834900196737741408944638219633295360000000⟩, + ⟨3, 3, 8, 1, 7, 6, 34303653040941449596351163146494017539355443200000000⟩, + ⟨3, 3, 5, 2, 3, 6, 68070463506911917834968359828915314505904291840000000⟩, + ⟨3, 3, 6, 2, 4, 6, 22492180373517792351731155393441323220174110720000000⟩, + ⟨3, 3, 7, 2, 5, 6, 6411458527832397197711224725900119069058662400000000⟩, + ⟨3, 3, 8, 2, 6, 6, 1866685446745497104396260908411823457304576000000000⟩, + ⟨3, 3, 5, 3, 2, 6, -184929354888250464846662264590902726850353561600000000⟩, + ⟨3, 3, 6, 3, 3, 6, 34145209903630289510551492534710069209176473600000000⟩, + ⟨3, 3, 7, 3, 4, 6, -25760573196110181196757109974525654791241072640000000⟩, + ⟨3, 3, 8, 3, 5, 6, 29700399859838440461620543227384531401257779200000000⟩, + ⟨3, 3, 5, 4, 1, 6, 51258386541989962199788181429411942509628620800000000⟩, + ⟨3, 3, 6, 4, 2, 6, -103825160907693712589177901741002793729549926400000000⟩, + ⟨3, 3, 7, 4, 3, 6, 91367316130870916473883342672828525567677562880000000⟩, + ⟨3, 3, 8, 4, 4, 6, -42492191861572132771792260316889950473053798400000000⟩, + ⟨3, 3, 5, 5, 0, 6, 586807325670377523195653671430597294741740584960000000⟩, + ⟨3, 3, 6, 5, 1, 6, 160440243766863338042159011345507230480649420800000000⟩, + ⟨3, 3, 7, 5, 2, 6, -177472237778256164718962726305710115004319006720000000⟩, + ⟨3, 3, 8, 5, 3, 6, 59439530212429823507515250529342962723192832000000000⟩, + ⟨3, 3, 6, 6, 0, 6, -235334489234877434414751786587452833231053783040000000⟩, + ⟨3, 3, 7, 6, 1, 6, 487599226429915640933565430079741440923889827840000000⟩, + ⟨3, 3, 8, 6, 2, 6, -211970076481468976699626997725762445127387709440000000⟩, + ⟨3, 3, 7, 7, 0, 6, -1652796693056149584187300693375514259214879948800000000⟩, + ⟨3, 3, 8, 7, 1, 6, 396337506501456695706553226806517650435552051200000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1102.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1102.lean new file mode 100644 index 0000000000000000000000000000000000000000..14bb4c5a6a34122e5dc58368a2234699a054bfc9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1102.lean @@ -0,0 +1,617 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PartsTrace +import OAI.Analysis.LaughlinFock.Sparse1101 + +namespace OAI + +/-! Sparse1102. -/ +namespace LaughlinFock +def collectedFourData_11_0_28 : List CollectedFourTerm := [ + ⟨3, 4, 4, 0, 4, 7, 24732398734098031738377918490031452835028349747200000⟩, + ⟨3, 4, 5, 0, 5, 7, -130086836007224680273079397965500893782077341696000000⟩, + ⟨3, 4, 6, 0, 6, 7, -75184260680470605997373688201827257460107247616000000⟩, + ⟨3, 4, 7, 0, 7, 7, 459379618672307668358461760716450357516959744000000⟩, + ⟨3, 4, 8, 0, 8, 7, -15485670049602669143326753391649710464504430592000000⟩, + ⟨3, 4, 4, 1, 3, 7, -14746477983155569646220698269441487084552454144000000⟩, + ⟨3, 4, 5, 1, 4, 7, -69615725945484743493946014350084400503240785920000000⟩, + ⟨3, 4, 6, 1, 5, 7, 47278843893664789816698590139242839415023730688000000⟩, + ⟨3, 4, 7, 1, 6, 7, 31795630393286253376714537112655648549268094976000000⟩, + ⟨3, 4, 8, 1, 7, 7, -12940054659924458763197805812128779410960547840000000⟩, + ⟨3, 4, 4, 2, 2, 7, 9714868364091018302908841262764354356029004185600000⟩, + ⟨3, 4, 5, 2, 3, 7, -102710404335602994474690399966474945516779077632000000⟩, + ⟨3, 4, 6, 2, 4, 7, -16969040766989556404390635678183693196017532928000000⟩, + ⟨3, 4, 7, 2, 5, 7, -3224714821711909109641943953130225661735075840000000⟩, + ⟨3, 4, 8, 2, 6, 7, -704152752622095538419248742735805762712371200000000⟩, + ⟨3, 4, 4, 3, 1, 7, -21569233760737811359647334380916226009298527846400000⟩, + ⟨3, 4, 5, 3, 2, 7, 279036866146294794549589135295556784039321927680000000⟩, + ⟨3, 4, 6, 3, 3, 7, -25760573196110181196757109974525654791241072640000000⟩, + ⟨3, 4, 7, 3, 4, 7, 12956568593663776216261268189985667676136013824000000⟩, + ⟨3, 4, 8, 3, 5, 7, -11203611380666369927568212695513701404419031040000000⟩, + ⟨3, 4, 4, 4, 0, 7, 36027719711045273539144109231408335570409934028800000⟩, + ⟨3, 4, 5, 4, 1, 7, -77342937539772032954175208133482283026706595840000000⟩, + ⟨3, 4, 6, 4, 2, 7, 78330039988308888405872019739225817796166287360000000⟩, + ⟨3, 4, 7, 4, 3, 7, -45954214203872816464053518444711842546930679808000000⟩, + ⟨3, 4, 8, 4, 4, 7, 16028942592571481924550082183805147507935150080000000⟩, + ⟨3, 4, 5, 5, 0, 7, -885423935457386218967243199874086310115706667008000000⟩, + ⟨3, 4, 6, 5, 1, 7, -121042824303113239366410945245494021512411217920000000⟩, + ⟨3, 4, 7, 5, 2, 7, 89261648207121237899889987669746937849081495552000000⟩, + ⟨3, 4, 8, 5, 3, 7, -22421832712425433469742372828360254714963558400000000⟩, + ⟨3, 4, 6, 6, 0, 7, 177546172731529162820761897717009728968060829696000000⟩, + ⟨3, 4, 7, 6, 1, 7, -245243487998572563188174298933853870049558790144000000⟩, + ⟨3, 4, 8, 6, 2, 7, 79959541704346094201954220358559767232174358528000000⟩, + ⟨3, 4, 7, 7, 0, 7, 831292594382031591897222557574733366898542510080000000⟩, + ⟨3, 4, 8, 7, 1, 7, -149506788439878124449601952700010388226771517440000000⟩ +] + +def collectedFourData_11_0_29 : List CollectedFourTerm := [ + ⟨3, 5, 3, 0, 3, 8, -7039957482752723038955785868192486037431255040000000⟩, + ⟨3, 5, 4, 0, 4, 8, -85544928636128915189269858832371985982053941248000000⟩, + ⟨3, 5, 5, 0, 5, 8, 224973509896464932493102711565808982758334136320000000⟩, + ⟨3, 5, 6, 0, 6, 8, 86682954931821429527198178980941435610050068480000000⟩, + ⟨3, 5, 7, 0, 7, 8, -397227914674890727459359044151801079387914240000000⟩, + ⟨3, 5, 8, 0, 8, 8, 10712430715016212620957263663650492313455558656000000⟩, + ⟨3, 5, 3, 1, 2, 8, 758294548444055881996176532818050474588504064000000⟩, + ⟨3, 5, 4, 1, 3, 8, 51005420875901737772661678844378673075674152960000000⟩, + ⟨3, 5, 5, 1, 4, 8, 120394151250448533166276884226361591004030566400000000⟩, + ⟨3, 5, 6, 1, 5, 8, -54509678719600773611918746483832970493443440640000000⟩, + ⟨3, 5, 7, 1, 6, 8, -27493844836656099625909050040686774043237416960000000⟩, + ⟨3, 5, 8, 1, 7, 8, 8951465357904880404909308486946548264070021120000000⟩, + ⟨3, 5, 3, 2, 1, 8, 5936195354248103180214935432739442589096214528000000⟩, + ⟨3, 5, 4, 2, 2, 8, -33601986198362192340062203695223773396367048704000000⟩, + ⟨3, 5, 5, 2, 3, 8, 177628427867846569718856069146774758139300413440000000⟩, + ⟨3, 5, 6, 2, 4, 8, 19564288891428508355680662083004165133267107840000000⟩, + ⟨3, 5, 7, 2, 5, 8, 2788427461697163349755910358424312376354406400000000⟩, + ⟨3, 5, 8, 2, 6, 8, 487107600193618491514874966738937327491481600000000⟩, + ⟨3, 5, 3, 3, 0, 8, -61235232881972677113178678794242059819674501120000000⟩, + ⟨3, 5, 4, 3, 1, 8, 74604108668782106772320681337086415171722674176000000⟩, + ⟨3, 5, 5, 3, 2, 8, -482569221408041658549357598171234738137307545600000000⟩, + ⟨3, 5, 6, 3, 3, 8, 29700399859838440461620543227384531401257779200000000⟩, + ⟨3, 5, 7, 3, 4, 8, -11203611380666369927568212695513701404419031040000000⟩, + ⟨3, 5, 8, 3, 5, 8, 7750256223264619681660346907924028189279518720000000⟩, + ⟨3, 5, 4, 4, 0, 8, -124613416787379816318944434326412256600068718592000000⟩, + ⟨3, 5, 5, 4, 1, 8, 133757670323069554801212088649883642707627212800000000⟩, + ⟨3, 5, 6, 4, 2, 8, -90309850288626252288342330817532961395363020800000000⟩, + ⟨3, 5, 7, 4, 3, 8, 39736844946421321385977397489277449881182535680000000⟩, + ⟨3, 5, 8, 4, 4, 8, -11088247160625771418625366201594894114818621440000000⟩, + ⟨3, 5, 5, 5, 0, 8, 1531261245335587478388505941739301455562916495360000000⟩, + ⟨3, 5, 6, 5, 1, 8, 139555135462182868634058539844308359884413337600000000⟩, + ⟨3, 5, 7, 5, 2, 8, -77185005465058305900607037316993336366512209920000000⟩, + ⟨3, 5, 8, 5, 3, 8, 15510619086301941445051239894190628915065651200000000⟩, + ⟨3, 5, 6, 6, 0, 8, -204700116086959068438010708111352399328580730880000000⟩, + ⟨3, 5, 7, 6, 1, 8, 212063303127867082258335814298313265187641098240000000⟩, + ⟨3, 5, 8, 6, 2, 8, -55313140972820515438328463888008270817477525504000000⟩, + ⟨3, 5, 7, 7, 0, 8, -718822974135051839374964692395781836312988876800000000⟩, + ⟨3, 5, 8, 7, 1, 8, 103423430013470716312295435047835052026017873920000000⟩ +] + +def collectedFourData_11_0_30 : List CollectedFourTerm := [ + ⟨4, 0, 7, 0, 7, 4, 1277375257410862306636392985195260139874864332800000⟩, + ⟨4, 0, 8, 0, 8, 4, -172241091783407235609031823379436581402393024921600000⟩, + ⟨4, 0, 7, 1, 6, 4, 88412611067834073181480565813921858337627124531200000⟩, + ⟨4, 0, 8, 1, 7, 4, -143927200774857134625656556782212091810238431232000000⟩, + ⟨4, 0, 7, 2, 5, 4, -8966812540282133320982783665976546634296721408000000⟩, + ⟨4, 0, 8, 2, 6, 4, -7832017504275387156798147189967614249806069760000000⟩, + ⟨4, 0, 7, 3, 4, 4, 36027719711045273539144109231408335570409934028800000⟩, + ⟨4, 0, 8, 3, 5, 4, -124613416787379816318944434326412256600068718592000000⟩, + ⟨4, 0, 7, 4, 3, 4, -127782717847696592148017721544427031882555300249600000⟩, + ⟨4, 0, 8, 4, 4, 4, 178283701217623951899275668223590134759328579584000000⟩, + ⟨4, 0, 7, 5, 2, 4, 248205658720841984506785023312384049920294151782400000⟩, + ⟨4, 0, 8, 5, 3, 4, -249389334384801901250762766949029221081882296320000000⟩, + ⟨4, 0, 7, 6, 1, 4, -681937009996039631746379597869927167106799684812800000⟩, + ⟨4, 0, 8, 6, 2, 4, 889358918118678627982669838252945328900852311654400000⟩, + ⟨4, 0, 7, 7, 0, 4, 2311536142594876029839688739922651628483322576896000000⟩, + ⟨4, 0, 8, 7, 1, 4, -1662905924472814124968411837667360555599304589312000000⟩ +] + +def collectedFourData_11_0_31 : List CollectedFourTerm := [ + ⟨4, 1, 6, 0, 6, 5, 149601636054248313271782891010373344095130091520000000⟩, + ⟨4, 1, 7, 0, 7, 5, -2742220588512294035947165559809341752648663040000000⟩, + ⟨4, 1, 8, 0, 8, 5, 184880310361442338790899565265732640634767933440000000⟩, + ⟨4, 1, 6, 1, 5, 5, -94075439902315837477779644591295356130935439360000000⟩, + ⟨4, 1, 7, 1, 6, 5, -189800828650591677413273665304613222707531612160000000⟩, + ⟨4, 1, 8, 1, 7, 5, 154488718535123720266099470025285373765930188800000000⟩, + ⟨4, 1, 6, 2, 4, 5, 33764995998321816082029368865433671591694172160000000⟩, + ⟨4, 1, 7, 2, 5, 5, 19249611904282368574447632883788522029737574400000000⟩, + ⟨4, 1, 8, 2, 6, 5, 8406738554395146136927630039171417384157184000000000⟩, + ⟨4, 1, 6, 3, 3, 5, 51258386541989962199788181429411942509628620800000000⟩, + ⟨4, 1, 7, 3, 4, 5, -77342937539772032954175208133482283026706595840000000⟩, + ⟨4, 1, 8, 3, 5, 5, 133757670323069554801212088649883642707627212800000000⟩, + ⟨4, 1, 6, 4, 2, 5, -155861107476309547648813716232416058607350579200000000⟩, + ⟨4, 1, 7, 4, 3, 5, 274319075545788186096924103352568212536720097280000000⟩, + ⟨4, 1, 8, 4, 4, 5, -191366332343907425765082690096618145909938585600000000⟩, + ⟨4, 1, 6, 5, 1, 5, 240851002383752157797717473371791520728245862400000000⟩, + ⟨4, 1, 7, 5, 2, 5, -532838461979560383567690855658206225473281720320000000⟩, + ⟨4, 1, 8, 5, 3, 5, 267689765923426481074011355324237257520447488000000000⟩, + ⟨4, 1, 6, 6, 0, 5, -353281360691843616478859375807098034611940229120000000⟩, + ⟨4, 1, 7, 6, 1, 5, 1463956420034343461688805597656916560507347927040000000⟩, + ⟨4, 1, 8, 6, 2, 5, -954620939184836781484851095494571988502928424960000000⟩, + ⟨4, 1, 7, 7, 0, 5, -4962317818932928984009677530740379176017906892800000000⟩, + ⟨4, 1, 8, 7, 1, 5, 1784931576055139808529233195325434276139027660800000000⟩ +] + +def collectedFourData_11_0_32 : List CollectedFourTerm := [ + ⟨4, 2, 5, 0, 5, 6, -262150352354393679784430597346366438959984148480000000⟩, + ⟨4, 2, 6, 0, 6, 6, -303021904965008719294746475022013580584324956160000000⟩, + ⟨4, 2, 7, 0, 7, 6, 2777218647073965788526130491916151479766876160000000⟩, + ⟨4, 2, 8, 0, 8, 6, -124826584596823086020656127562503320873300131840000000⟩, + ⟨4, 2, 5, 1, 4, 6, -140289268662066517586951587850460317781432729600000000⟩, + ⟨4, 2, 6, 1, 5, 6, 190552187539471855072696182849177264797389946880000000⟩, + ⟨4, 2, 7, 1, 6, 6, 192223194139347270527058192759172182894591344640000000⟩, + ⟨4, 2, 8, 1, 7, 6, -104306938125419997951801310460056852807601356800000000⟩, + ⟨4, 2, 5, 2, 3, 6, -206981501845007546383580657847361895552683868160000000⟩, + ⟨4, 2, 6, 2, 4, 6, -68391855051887469206245687155385650740755169280000000⟩, + ⟨4, 2, 7, 2, 5, 6, -19495288363549645235136841266959953709078937600000000⟩, + ⟨4, 2, 8, 2, 6, 6, -5676020660566967587168268566154139270119424000000000⟩, + ⟨4, 2, 5, 3, 2, 6, 562313720783050091480588509745797278527284838400000000⟩, + ⟨4, 2, 6, 3, 3, 6, -103825160907693712589177901741002793729549926400000000⟩, + ⟨4, 2, 7, 3, 4, 6, 78330039988308888405872019739225817796166287360000000⟩, + ⟨4, 2, 8, 3, 5, 6, -90309850288626252288342330817532961395363020800000000⟩, + ⟨4, 2, 5, 4, 1, 6, -155861107476309547648813716232416058607350579200000000⟩, + ⟨4, 2, 6, 4, 2, 6, 315700622955092920516802860250755689405323673600000000⟩, + ⟨4, 2, 7, 4, 3, 6, -277820119594087625286623291807866111134919557120000000⟩, + ⟨4, 2, 8, 4, 4, 6, 129205785227264498867278229989660252261947801600000000⟩, + ⟨4, 2, 5, 5, 0, 6, -1784301961578008660116367537088477000092394455040000000⟩, + ⟨4, 2, 6, 5, 1, 6, -487849808865669126841962949011140345215529779200000000⟩, + ⟨4, 2, 7, 5, 2, 6, 539638903845686412408636297069942537083714273280000000⟩, + ⟨4, 2, 8, 5, 3, 6, -180737468183703241273840663211905079907975168000000000⟩, + ⟨4, 2, 6, 6, 0, 6, 715580348778096092718968135641199643716443176960000000⟩, + ⟨4, 2, 7, 6, 1, 6, -1482640413851155103248837636820424017901162332160000000⟩, + ⟨4, 2, 8, 6, 2, 6, 644536301297266468008517989422389836170982850560000000⟩, + ⟨4, 2, 7, 7, 0, 6, 5025650247533380096752937249967767459946771251200000000⟩, + ⟨4, 2, 8, 7, 1, 6, -1205141380076648240742695163163060003970796748800000000⟩ +] + +def collectedFourData_11_0_33 : List CollectedFourTerm := [ + ⟨4, 3, 4, 0, 4, 7, -87720598319384592052547382053053402388168599142400000⟩, + ⟨4, 3, 5, 0, 5, 7, 461390551345790113755160205795837732395293868032000000⟩, + ⟨4, 3, 6, 0, 6, 7, 266662704333599051591697894059784754577037852672000000⟩, + ⟨4, 3, 7, 0, 7, 7, -1629322551318440242853947135876453108650344448000000⟩, + ⟨4, 3, 8, 0, 8, 7, 54924403278963239618319488922706961183186878464000000⟩, + ⟨4, 3, 4, 1, 3, 7, 52302645032267780033311546702126592428760629248000000⟩, + ⟨4, 3, 5, 1, 4, 7, 246912286916877348205573697309588815774104944640000000⟩, + ⟨4, 3, 6, 1, 5, 7, -167688080674650637383077451135196730864273719296000000⟩, + ⟨4, 3, 7, 1, 6, 7, -112772390257309058801148961654085961030976929792000000⟩, + ⟨4, 3, 8, 1, 7, 7, 45895642766310537947650757988099900000467681280000000⟩, + ⟨4, 3, 4, 2, 2, 7, -34456587678946939384273416673841202866878100275200000⟩, + ⟨4, 3, 5, 2, 3, 7, 364292126243434829938249289018327604974158086144000000⟩, + ⟨4, 3, 6, 2, 4, 7, 60185606135087172205749959439397376078565605376000000⟩, + ⟨4, 3, 7, 2, 5, 7, 11437382868163290388614360313658209291500257280000000⟩, + ⟨4, 3, 8, 2, 6, 7, 2497481195913788790647482221146604956968550400000000⟩, + ⟨4, 3, 4, 3, 1, 7, 76501519772687451055667031504020937622902590668800000⟩, + ⟨4, 3, 5, 3, 2, 7, -989684871034070155937626479193933074299155906560000000⟩, + ⟨4, 3, 6, 3, 3, 7, 91367316130870916473883342672828525567677562880000000⟩, + ⟨4, 3, 7, 3, 4, 7, -45954214203872816464053518444711842546930679808000000⟩, + ⟨4, 3, 8, 3, 5, 7, 39736844946421321385977397489277449881182535680000000⟩, + ⟨4, 3, 4, 4, 0, 7, -127782717847696592148017721544427031882555300249600000⟩, + ⟨4, 3, 5, 4, 1, 7, 274319075545788186096924103352568212536720097280000000⟩, + ⟨4, 3, 6, 4, 2, 7, -277820119594087625286623291807866111134919557120000000⟩, + ⟨4, 3, 7, 4, 3, 7, 162989898739714663928190854809646050256760078336000000⟩, + ⟨4, 3, 8, 4, 4, 7, -56851276326421238655847135991247792038593167360000000⟩, + ⟨4, 3, 5, 5, 0, 7, 3140411822551777926313151707248355750014653300736000000⟩, + ⟨4, 3, 6, 5, 1, 7, 429313350649587394194712691247045659958328688640000000⟩, + ⟨4, 3, 7, 5, 2, 7, -316592226734074368223160735913993947632877174784000000⟩, + ⟨4, 3, 8, 5, 3, 7, 79525508305809644014890510722878698592980172800000000⟩, + ⟨4, 3, 6, 6, 0, 7, -629718801996119036715600384203465595173870764032000000⟩, + ⟨4, 3, 7, 6, 1, 7, 869826891134025541018176154188214094150655541248000000⟩, + ⟨4, 3, 8, 6, 2, 7, -283599618260190646444784223245410704473588760576000000⟩, + ⟨4, 3, 7, 7, 0, 7, -2948419380653523113775164171127419109035590287360000000⟩, + ⟨4, 3, 8, 7, 1, 7, 530269023872505773283976123177719660458520084480000000⟩ +] + +def collectedFourData_11_0_34 : List CollectedFourTerm := [ + ⟨4, 4, 3, 0, 3, 8, 10072026823414838973940589130256982330132398080000000⟩, + ⟨4, 4, 4, 0, 4, 8, 122388639127589813860706548771312762738333188096000000⟩, + ⟨4, 4, 5, 0, 5, 8, -321868311248516832956083883562868804564958576640000000⟩, + ⟨4, 4, 6, 0, 6, 8, -124016806826620367763475800049702186790116392960000000⟩, + ⟨4, 4, 7, 0, 7, 8, 568311700946556802159151802655012175719956480000000⟩, + ⟨4, 4, 8, 0, 8, 8, -15326213229263350026403496312594261910604480512000000⟩, + ⟨4, 4, 3, 1, 2, 8, -1084887664547567497796685858027680323420028928000000⟩, + ⟨4, 4, 4, 1, 3, 8, -72973163326658414093908935503060217997736017920000000⟩, + ⟨4, 4, 5, 1, 4, 8, -172247222195244268161679972313950580063915212800000000⟩, + ⟨4, 4, 6, 1, 5, 8, 77986684940157945740051196772847226205797089280000000⟩, + ⟨4, 4, 7, 1, 6, 8, 39335286236036564637685585921938213130123345920000000⟩, + ⟨4, 4, 8, 1, 7, 8, -12806810185227576938828624642941686538032906240000000⟩, + ⟨4, 4, 3, 2, 1, 8, -8492880672006402391641900491423302838340550656000000⟩, + ⟨4, 4, 4, 2, 2, 8, 48074169075462134836985644939226586485996126208000000⟩, + ⟨4, 4, 5, 2, 3, 8, -254131973732660045155135710852806354244867194880000000⟩, + ⟨4, 4, 6, 2, 4, 8, -27990515990794700401339897574722427376296263680000000⟩, + ⟨4, 4, 7, 2, 5, 8, -3989387188511642079369664927894271565810892800000000⟩, + ⟨4, 4, 8, 2, 6, 8, -696902051902872902417161029369537278194483200000000⟩, + ⟨4, 4, 3, 3, 0, 8, 87608896735001321308390624836450169764697866240000000⟩, + ⟨4, 4, 4, 3, 1, 8, -106735670703953620217036081112739831975407255552000000⟩, + ⟨4, 4, 5, 3, 2, 8, 690409019384546782733131547835384008667247411200000000⟩, + ⟨4, 4, 6, 3, 3, 8, -42492191861572132771792260316889950473053798400000000⟩, + ⟨4, 4, 7, 3, 4, 8, 16028942592571481924550082183805147507935150080000000⟩, + ⟨4, 4, 8, 3, 5, 8, -11088247160625771418625366201594894114818621440000000⟩, + ⟨4, 4, 4, 4, 0, 8, 178283701217623951899275668223590134759328579584000000⟩, + ⟨4, 4, 5, 4, 1, 8, -191366332343907425765082690096618145909938585600000000⟩, + ⟨4, 4, 6, 4, 2, 8, 129205785227264498867278229989660252261947801600000000⟩, + ⟨4, 4, 7, 4, 3, 8, -56851276326421238655847135991247792038593167360000000⟩, + ⟨4, 4, 8, 4, 4, 8, 15863891664130803272553798449258064421721210880000000⟩, + ⟨4, 4, 5, 5, 0, 8, -2190766687790431601894332785903582180444701982720000000⟩, + ⟨4, 4, 6, 5, 1, 8, -199660732492206269108106969808400020988441395200000000⟩, + ⟨4, 4, 7, 5, 2, 8, 110428144958840020718879207891448712885268643840000000⟩, + ⟨4, 4, 8, 5, 3, 8, -22190953832851525339948742017818256329827942400000000⟩, + ⟨4, 4, 6, 6, 0, 8, 292863282915426304220838812127802827164362997760000000⟩, + ⟨4, 4, 7, 6, 1, 8, -303397752415211915644121898423975534089711124480000000⟩, + ⟨4, 4, 8, 6, 2, 8, 79136193781064508399519489306289778444162039808000000⟩, + ⟨4, 4, 7, 7, 0, 8, 1028415909401789308573532444108419229122402713600000000⟩, + ⟨4, 4, 8, 7, 1, 8, -147967308583507432812018442626006711002820771840000000⟩ +] + +def collectedFourData_11_0_35 : List CollectedFourTerm := [ + ⟨5, 0, 6, 0, 6, 5, 1712643371967877907943757460661996417476223565824000000⟩, + ⟨5, 0, 7, 0, 7, 5, -31393011729406595019828015654033024903857307648000000⟩, + ⟨5, 0, 8, 0, 8, 5, 2116514541545996593563485656740709683538981552128000000⟩, + ⟨5, 0, 6, 1, 5, 5, -1076978052267018014428391960824762086636474335232000000⟩, + ⟨5, 0, 7, 1, 6, 5, -2172844761300428407132939824339942029452841582592000000⟩, + ⟨5, 0, 8, 1, 7, 5, 1768590817730413183084729213761938048275772866560000000⟩, + ⟨5, 0, 6, 2, 4, 5, 386542541420325765998393937601673078482604654592000000⟩, + ⟨5, 0, 7, 2, 5, 5, 220370051493744731245458673444160275305757409280000000⟩, + ⟨5, 0, 8, 2, 6, 5, 96240558892222131062836298516383358476143820800000000⟩, + ⟨5, 0, 6, 3, 3, 5, 586807325670377523195653671430597294741740584960000000⟩, + ⟨5, 0, 7, 3, 4, 5, -885423935457386218967243199874086310115706667008000000⟩, + ⟨5, 0, 8, 3, 5, 5, 1531261245335587478388505941739301455562916495360000000⟩, + ⟨5, 0, 6, 4, 2, 5, -1784301961578008660116367537088477000092394455040000000⟩, + ⟨5, 0, 7, 4, 3, 5, 3140411822551777926313151707248355750014653300736000000⟩, + ⟨5, 0, 8, 4, 4, 5, -2190766687790431601894332785903582180444701982720000000⟩, + ⟨5, 0, 6, 5, 1, 5, 2757268461387518063002953266514285395872453754880000000⟩, + ⟨5, 0, 7, 5, 2, 5, -6099948398344656422133365668456152681433094160384000000⟩, + ⟨5, 0, 8, 5, 3, 5, 3064519315725558396769623785300094156134783385600000000⟩, + ⟨5, 0, 6, 6, 0, 5, -4044374090997766195260067057901235960614637010944000000⟩, + ⟨5, 0, 7, 6, 1, 5, 16759410697303278403883369225464076200347275624448000000⟩, + ⟨5, 0, 8, 6, 2, 5, -10928525030593965734213951730620929298251961597952000000⟩, + ⟨5, 0, 7, 7, 0, 5, -56808741844987567402244483705036171207979156111360000000⟩, + ⟨5, 0, 8, 7, 1, 5, 20433942527463445971963561480254286661996731432960000000⟩ +] + +def collectedFourData_11_0_36 : List CollectedFourTerm := [ + ⟨5, 1, 5, 0, 5, 6, 405098976660399505155994686407473453746156994560000000⟩, + ⟨5, 1, 6, 0, 6, 6, 468257480886626360012259887130150452411781611520000000⟩, + ⟨5, 1, 7, 0, 7, 6, -4291615181088604684322147961284687107215851520000000⟩, + ⟨5, 1, 8, 0, 8, 6, 192893586546950552082387602214398945089007124480000000⟩, + ⟨5, 1, 5, 1, 4, 6, 216787956457181176318534376548490070795170611200000000⟩, + ⟨5, 1, 6, 1, 5, 6, -294458868658266064122110690744390581000454799360000000⟩, + ⟨5, 1, 7, 1, 6, 6, -297041062645505841815606271792813018185811886080000000⟩, + ⟨5, 1, 8, 1, 7, 6, 161184730494141778980638192944750987847506329600000000⟩, + ⟨5, 1, 5, 2, 3, 6, 319846965041242463173578204583082574785040875520000000⟩, + ⟨5, 1, 6, 2, 4, 6, 105685421532341648121202630031949393098346332160000000⟩, + ⟨5, 1, 7, 2, 5, 6, 30125923138554164673041094087821634565255987200000000⟩, + ⟨5, 1, 8, 2, 6, 6, 8771112227957399981719823796313727831113728000000000⟩, + ⟨5, 1, 5, 3, 2, 6, -868939182440497576707745781611766888293780684800000000⟩, + ⟨5, 1, 6, 3, 3, 6, 160440243766863338042159011345507230480649420800000000⟩, + ⟨5, 1, 7, 3, 4, 6, -121042824303113239366410945245494021512411217920000000⟩, + ⟨5, 1, 8, 3, 5, 6, 139555135462182868634058539844308359884413337600000000⟩, + ⟨5, 1, 5, 4, 1, 6, 240851002383752157797717473371791520728245862400000000⟩, + ⟨5, 1, 6, 4, 2, 6, -487849808865669126841962949011140345215529779200000000⟩, + ⟨5, 1, 7, 4, 3, 6, 429313350649587394194712691247045659958328688640000000⟩, + ⟨5, 1, 8, 4, 4, 6, -199660732492206269108106969808400020988441395200000000⟩, + ⟨5, 1, 5, 5, 0, 6, 2757268461387518063002953266514285395872453754880000000⟩, + ⟨5, 1, 6, 5, 1, 6, 753870656898019580092849498698984664001308262400000000⟩, + ⟨5, 1, 7, 5, 2, 6, -833899957603331458427115375911162032053981020160000000⟩, + ⟨5, 1, 8, 5, 3, 6, 279292256324837156904993558640247937743978496000000000⟩, + ⟨5, 1, 6, 6, 0, 6, -1105780955107840957262013443207062012711529349120000000⟩, + ⟨5, 1, 7, 6, 1, 6, 2291113130355431036406822662164178301930197483520000000⟩, + ⟨5, 1, 8, 6, 2, 6, -995997120473164528278015259734771465227411128320000000⟩, + ⟨5, 1, 7, 7, 0, 6, -7766099698300611436592815507000782285141599846400000000⟩, + ⟨5, 1, 8, 7, 1, 6, 1862295951218733667321739161545308938209696153600000000⟩ +] + +def collectedFourData_11_0_37 : List CollectedFourTerm := [ + ⟨5, 2, 4, 0, 4, 7, 170388838615876348641067700040765087133147437465600000⟩, + ⟨5, 2, 5, 0, 5, 7, -896206839651428115642687819360518495331478929408000000⟩, + ⟨5, 2, 6, 0, 6, 7, -517966696124668204881117307669224996919540973568000000⟩, + ⟨5, 2, 7, 0, 7, 7, 3164802595611767702388029428147743756713459712000000⟩, + ⟨5, 2, 8, 0, 8, 7, -106685379097608419233044408012382037666395324416000000⟩, + ⟨5, 2, 4, 1, 3, 7, -101592865465182370273079008942712732275716390912000000⟩, + ⟨5, 2, 5, 1, 4, 7, -479603406882598237600257200698091271474024284160000000⟩, + ⟨5, 2, 6, 1, 5, 7, 325717993986427137246207989302255343764739457024000000⟩, + ⟨5, 2, 7, 1, 6, 7, 219049538785841517983995236012459851729074126848000000⟩, + ⟨5, 2, 8, 1, 7, 7, -89147878814145112030581632567867389480607416320000000⟩, + ⟨5, 2, 4, 2, 2, 7, 66928612774686234856690687815786946225765141708800000⟩, + ⟨5, 2, 5, 2, 3, 7, -707602473042075513022454334042196322467065102336000000⟩, + ⟨5, 2, 6, 2, 4, 7, -116904760423686195472023128491003495547922284544000000⟩, + ⟨5, 2, 7, 2, 5, 7, -22216017914241875367227350997151620547288760320000000⟩, + ⟨5, 2, 8, 2, 6, 7, -4851117395339328052067013292054418028075417600000000⟩, + ⟨5, 2, 4, 3, 1, 7, -148596855882790144559161164692107273986204971827200000⟩, + ⟨5, 2, 5, 3, 2, 7, 1922367824683820708756170231809132728083430768640000000⟩, + ⟨5, 2, 6, 3, 3, 7, -177472237778256164718962726305710115004319006720000000⟩, + ⟨5, 2, 7, 3, 4, 7, 89261648207121237899889987669746937849081495552000000⟩, + ⟨5, 2, 8, 3, 5, 7, -77185005465058305900607037316993336366512209920000000⟩, + ⟨5, 2, 4, 4, 0, 7, 248205658720841984506785023312384049920294151782400000⟩, + ⟨5, 2, 5, 4, 1, 7, -532838461979560383567690855658206225473281720320000000⟩, + ⟨5, 2, 6, 4, 2, 7, 539638903845686412408636297069942537083714273280000000⟩, + ⟨5, 2, 7, 4, 3, 7, -316592226734074368223160735913993947632877174784000000⟩, + ⟨5, 2, 8, 4, 4, 7, 110428144958840020718879207891448712885268643840000000⟩, + ⟨5, 2, 5, 5, 0, 7, -6099948398344656422133365668456152681433094160384000000⟩, + ⟨5, 2, 6, 5, 1, 7, -833899957603331458427115375911162032053981020160000000⟩, + ⟨5, 2, 7, 5, 2, 7, 614949998763432697169731482575326227117423722496000000⟩, + ⟨5, 2, 8, 5, 3, 7, -154470663221294772922981311008958939988702003200000000⟩, + ⟨5, 2, 6, 6, 0, 7, 1223168302341470704117979392907767857209470353408000000⟩, + ⟨5, 2, 7, 6, 1, 7, -1689555208430829699347310859425186001766068518912000000⟩, + ⟨5, 2, 8, 6, 2, 7, 550865025011821761484862377347966679843910713344000000⟩, + ⟨5, 2, 7, 7, 0, 7, 5727021516576674678320588393896694869126901923840000000⟩, + ⟨5, 2, 8, 7, 1, 7, -1029996658283674793881268687010123749998586757120000000⟩ +] + +def collectedFourData_11_0_38 : List CollectedFourTerm := [ + ⟨5, 3, 3, 0, 3, 8, -14089095347707487631038098421247915661354598400000000⟩, + ⟨5, 3, 4, 0, 4, 8, -171201411232952910532451720899353804720392110080000000⟩, + ⟨5, 3, 5, 0, 5, 8, 450240394122426063535100110504125992226992947200000000⟩, + ⟨5, 3, 6, 0, 6, 8, 173478947855509437947196609346228048102214860800000000⟩, + ⟨5, 3, 7, 0, 7, 8, -794973830216543726129527386972992622192230400000000⟩, + ⟨5, 3, 8, 0, 8, 8, 21438830862165740360999776042180870020016373760000000⟩, + ⟨5, 3, 3, 1, 2, 8, 1517577942885192832692634880249775489747517440000000⟩, + ⟨5, 3, 4, 1, 3, 8, 102077354832196920607730931060527254063389081600000000⟩, + ⟨5, 3, 5, 1, 4, 8, 240945301222278170826719592741034860786745344000000000⟩, + ⟨5, 3, 6, 1, 5, 8, -109090440210025435063181278950824512003139174400000000⟩, + ⟨5, 3, 7, 1, 6, 8, -55023542731291952301504950336287015752538521600000000⟩, + ⟨5, 3, 8, 1, 7, 8, 17914603779667778425804788672325765263733555200000000⟩, + ⟨5, 3, 3, 2, 1, 8, 11880131741352085501267644045828820967494778880000000⟩, + ⟨5, 3, 4, 2, 2, 8, -67247790711935014403115849245240051371962531840000000⟩, + ⟨5, 3, 5, 2, 3, 8, 355488490211010591911363851371688111565596262400000000⟩, + ⟨5, 3, 6, 2, 4, 8, 39154090387155337048972207062282430690256486400000000⟩, + ⟨5, 3, 7, 2, 5, 8, 5580491142775447029537451036937852754591744000000000⟩, + ⟨5, 3, 8, 2, 6, 8, 974850407908625040819351994345478198132736000000000⟩, + ⟨5, 3, 3, 3, 0, 8, -122550318922641948799727202068225671577154355200000000⟩, + ⟨5, 3, 4, 3, 1, 8, 149305504037533636919568591641804358047194152960000000⟩, + ⟨5, 3, 5, 3, 2, 8, -965767732112548666792444836582036876533170176000000000⟩, + ⟨5, 3, 6, 3, 3, 8, 59439530212429823507515250529342962723192832000000000⟩, + ⟨5, 3, 7, 3, 4, 8, -22421832712425433469742372828360254714963558400000000⟩, + ⟨5, 3, 8, 3, 5, 8, 15510619086301941445051239894190628915065651200000000⟩, + ⟨5, 3, 4, 4, 0, 8, -249389334384801901250762766949029221081882296320000000⟩, + ⟨5, 3, 5, 4, 1, 8, 267689765923426481074011355324237257520447488000000000⟩, + ⟨5, 3, 6, 4, 2, 8, -180737468183703241273840663211905079907975168000000000⟩, + ⟨5, 3, 7, 4, 3, 8, 79525508305809644014890510722878698592980172800000000⟩, + ⟨5, 3, 8, 4, 4, 8, -22190953832851525339948742017818256329827942400000000⟩, + ⟨5, 3, 5, 5, 0, 8, 3064519315725558396769623785300094156134783385600000000⟩, + ⟨5, 3, 6, 5, 1, 8, 279292256324837156904993558640247937743978496000000000⟩, + ⟨5, 3, 7, 5, 2, 8, -154470663221294772922981311008958939988702003200000000⟩, + ⟨5, 3, 8, 5, 3, 8, 31041464631606140176500974711036213515517952000000000⟩, + ⟨5, 3, 6, 6, 0, 8, -409667169198336891625225781096468319520476364800000000⟩, + ⟨5, 3, 7, 6, 1, 8, 424403145166446446084992578259084295474144870400000000⟩, + ⟨5, 3, 8, 6, 2, 8, -110698412462930368471187650792360431144759459840000000⟩, + ⟨5, 3, 7, 7, 0, 8, -1438583321777590783053061236170493529505660928000000000⟩, + ⟨5, 3, 8, 7, 1, 8, 206981728258531732210154974862789627088155443200000000⟩ +] + +def collectedFourData_11_0_39 : List CollectedFourTerm := [ + ⟨6, 0, 5, 0, 5, 6, -594201046593251883476200718611438784867758768128000000⟩, + ⟨6, 0, 6, 0, 6, 6, -686842231771928135004343216200989336041345253376000000⟩, + ⟨6, 0, 7, 0, 7, 6, 6294960933253872323151503827411130191630565376000000⟩, + ⟨6, 0, 8, 0, 8, 6, -282937202044352838519092766514222996403125223424000000⟩, + ⟨6, 0, 5, 1, 4, 6, -317985573988890697551786766421273375981237698560000000⟩, + ⟨6, 0, 6, 1, 5, 6, 431913626091641972811101652701196797476620730368000000⟩, + ⟨6, 0, 7, 1, 6, 6, 435701200136814000053007503682693532576596885504000000⟩, + ⟨6, 0, 8, 1, 7, 6, -236426505798756547487766819554077960720330260480000000⟩, + ⟨6, 0, 5, 2, 3, 6, -469153002912930365506705502546261794501297176576000000⟩, + ⟨6, 0, 6, 2, 4, 6, -155019863545128695532589123797110976786368299008000000⟩, + ⟨6, 0, 7, 2, 5, 6, -44188842949172150469060991694621324602622607360000000⟩, + ⟨6, 0, 8, 2, 6, 6, -12865507853425878178502602636246045663061606400000000⟩, + ⟨6, 0, 5, 3, 2, 6, 1274563998873961274351118506409556655261079306240000000⟩, + ⟨6, 0, 6, 3, 3, 6, -235334489234877434414751786587452833231053783040000000⟩, + ⟨6, 0, 7, 3, 4, 6, 177546172731529162820761897717009728968060829696000000⟩, + ⟨6, 0, 8, 3, 5, 6, -204700116086959068438010708111352399328580730880000000⟩, + ⟨6, 0, 5, 4, 1, 6, -353281360691843616478859375807098034611940229120000000⟩, + ⟨6, 0, 6, 4, 2, 6, 715580348778096092718968135641199643716443176960000000⟩, + ⟨6, 0, 7, 4, 3, 6, -629718801996119036715600384203465595173870764032000000⟩, + ⟨6, 0, 8, 4, 4, 6, 292863282915426304220838812127802827164362997760000000⟩, + ⟨6, 0, 5, 5, 0, 6, -4044374090997766195260067057901235960614637010944000000⟩, + ⟨6, 0, 6, 5, 1, 6, -1105780955107840957262013443207062012711529349120000000⟩, + ⟨6, 0, 7, 5, 2, 6, 1223168302341470704117979392907767857209470353408000000⟩, + ⟨6, 0, 8, 5, 3, 6, -409667169198336891625225781096468319520476364800000000⟩, + ⟨6, 0, 6, 6, 0, 6, 1621964602934025073364784115679174868660708704256000000⟩, + ⟨6, 0, 7, 6, 1, 6, -3360615302324017651379516227931222764848704126976000000⟩, + ⟨6, 0, 8, 6, 2, 6, 1460933168155478141654480900975462700447449481216000000⟩, + ⟨6, 0, 7, 7, 0, 6, 11391350841516120130968280097558019568927317688320000000⟩, + ⟨6, 0, 8, 7, 1, 6, -2731624286990505187472958588870490296109687111680000000⟩ +] + +def collectedFourData_11_0_40 : List CollectedFourTerm := [ + ⟨6, 1, 4, 0, 4, 7, -468137816604305855231795295708774047830720590643200000⟩, + ⟨6, 1, 5, 0, 5, 7, 2462299271175221675290410084728123480531036798976000000⟩, + ⟨6, 1, 6, 0, 6, 7, 1423096724922183750867268597952989670835272810496000000⟩, + ⟨6, 1, 7, 0, 7, 7, -8695192649521850460404434491202891596813041664000000⟩, + ⟨6, 1, 8, 0, 8, 7, 293114624408875250649002554721823360614664241152000000⟩, + ⟨6, 1, 4, 1, 3, 7, 279123108108408730791247710596940886000810328064000000⟩, + ⟨6, 1, 5, 1, 4, 7, 1317694830000947443515688339938026342325965291520000000⟩, + ⟨6, 1, 6, 1, 5, 7, -894899641151334697179159631053149895480236310528000000⟩, + ⟨6, 1, 7, 1, 6, 7, -601831514601503785801760993249037538639170502656000000⟩, + ⟨6, 1, 8, 1, 7, 7, 244930910275425395601279090375351144515937239040000000⟩, + ⟨6, 1, 4, 2, 2, 7, -183884196331256976141048119312338736224323344793600000⟩, + ⟨6, 1, 5, 2, 3, 7, 1944114881259945267072589367291797784021163835392000000⟩, + ⟨6, 1, 6, 2, 4, 7, 321192043680580404988545291525766797611885395968000000⟩, + ⟨6, 1, 7, 2, 5, 7, 61037789825314762748326636941786424477262807040000000⟩, + ⟨6, 1, 8, 2, 6, 7, 13328287955909077446144419331209768046113587200000000⟩, + ⟨6, 1, 4, 3, 1, 7, 408265049708205018964927805518952007326203536998400000⟩, + ⟨6, 1, 5, 3, 2, 7, -5281643348638915121389647810777231855330609070080000000⟩, + ⟨6, 1, 6, 3, 3, 7, 487599226429915640933565430079741440923889827840000000⟩, + ⟨6, 1, 7, 3, 4, 7, -245243487998572563188174298933853870049558790144000000⟩, + ⟨6, 1, 8, 3, 5, 7, 212063303127867082258335814298313265187641098240000000⟩, + ⟨6, 1, 4, 4, 0, 7, -681937009996039631746379597869927167106799684812800000⟩, + ⟨6, 1, 5, 4, 1, 7, 1463956420034343461688805597656916560507347927040000000⟩, + ⟨6, 1, 6, 4, 2, 7, -1482640413851155103248837636820424017901162332160000000⟩, + ⟨6, 1, 7, 4, 3, 7, 869826891134025541018176154188214094150655541248000000⟩, + ⟨6, 1, 8, 4, 4, 7, -303397752415211915644121898423975534089711124480000000⟩, + ⟨6, 1, 5, 5, 0, 7, 16759410697303278403883369225464076200347275624448000000⟩, + ⟨6, 1, 6, 5, 1, 7, 2291113130355431036406822662164178301930197483520000000⟩, + ⟨6, 1, 7, 5, 2, 7, -1689555208430829699347310859425186001766068518912000000⟩, + ⟨6, 1, 8, 5, 3, 7, 424403145166446446084992578259084295474144870400000000⟩, + ⟨6, 1, 6, 6, 0, 7, -3360615302324017651379516227931222764848704126976000000⟩, + ⟨6, 1, 7, 6, 1, 7, 4641998224369278173548214818928863441264589144064000000⟩, + ⟨6, 1, 8, 6, 2, 7, -1513483818233396755478336266600700131445538029568000000⟩, + ⟨6, 1, 7, 7, 0, 7, -15734806165679643569513195989431839722693963284480000000⟩, + ⟨6, 1, 8, 7, 1, 7, 2829882465515688052210617560722193016683117936640000000⟩ +] + +def collectedFourData_11_0_41 : List CollectedFourTerm := [ + ⟨6, 2, 3, 0, 3, 8, 50243778975624265509197954060299036113216995328000000⟩, + ⟨6, 2, 4, 0, 4, 8, 610529324560436695298748043400610271230598683033600000⟩, + ⟨6, 2, 5, 0, 5, 8, -1605623234842118156415442022048461884289475149824000000⟩, + ⟨6, 2, 6, 0, 6, 8, -618651353963214482823360678986654969116319809536000000⟩, + ⟨6, 2, 7, 0, 7, 8, 2834993193747157873382001699463962018623520768000000⟩, + ⟨6, 2, 8, 0, 8, 8, -76454013032832476480800525215865302658516726579200000⟩, + ⟨6, 2, 3, 1, 2, 8, -5411905367864022160145668291136167136004459724800000⟩, + ⟨6, 2, 4, 1, 3, 8, -364022808280575690415057338793909243627828150272000000⟩, + ⟨6, 2, 5, 1, 4, 8, -859246258262932990739776529137218798609739284480000000⟩, + ⟨6, 2, 6, 1, 5, 8, 389032498609496155666194674761473647837863477248000000⟩, + ⟨6, 2, 7, 1, 6, 8, 196222017895328628792464458608564831542493315072000000⟩, + ⟨6, 2, 8, 1, 7, 8, -63886102728942820882880549755789513675121885184000000⟩, + ⟨6, 2, 3, 2, 1, 8, -42366290999011349171834536702384017208099051929600000⟩, + ⟨6, 2, 4, 2, 2, 8, 239815477838985679357986693404107391283246189772800000⟩, + ⟨6, 2, 5, 2, 3, 8, -1267724058198432135572463125939894088526051934208000000⟩, + ⟨6, 2, 6, 2, 4, 8, -139629224932738439241223176138267828943520268288000000⟩, + ⟨6, 2, 7, 2, 5, 8, -19900849318807497457239693866340453194378772480000000⟩, + ⟨6, 2, 8, 2, 6, 8, -3476459433375042087749754161878424727186309120000000⟩, + ⟨6, 2, 3, 3, 0, 8, 437032398843364227482985865566715692573926621184000000⟩, + ⟨6, 2, 4, 3, 1, 8, -532445310331912395904852729229353081048036225843200000⟩, + ⟨6, 2, 5, 3, 2, 8, 3444069280285506190993373555654078628437604433920000000⟩, + ⟨6, 2, 6, 3, 3, 8, -211970076481468976699626997725762445127387709440000000⟩, + ⟨6, 2, 7, 3, 4, 8, 79959541704346094201954220358559767232174358528000000⟩, + ⟨6, 2, 8, 3, 5, 8, -55313140972820515438328463888008270817477525504000000⟩, + ⟨6, 2, 4, 4, 0, 8, 889358918118678627982669838252945328900852311654400000⟩, + ⟨6, 2, 5, 4, 1, 8, -954620939184836781484851095494571988502928424960000000⟩, + ⟨6, 2, 6, 4, 2, 8, 644536301297266468008517989422389836170982850560000000⟩, + ⟨6, 2, 7, 4, 3, 8, -283599618260190646444784223245410704473588760576000000⟩, + ⟨6, 2, 8, 4, 4, 8, 79136193781064508399519489306289778444162039808000000⟩, + ⟨6, 2, 5, 5, 0, 8, -10928525030593965734213951730620929298251961597952000000⟩, + ⟨6, 2, 6, 5, 1, 8, -995997120473164528278015259734771465227411128320000000⟩, + ⟨6, 2, 7, 5, 2, 8, 550865025011821761484862377347966679843910713344000000⟩, + ⟨6, 2, 8, 5, 3, 8, -110698412462930368471187650792360431144759459840000000⟩, + ⟨6, 2, 6, 6, 0, 8, 1460933168155478141654480900975462700447449481216000000⟩, + ⟨6, 2, 7, 6, 1, 8, -1513483818233396755478336266600700131445538029568000000⟩, + ⟨6, 2, 8, 6, 2, 8, 394766763335516194296106026031057892609383779532800000⟩, + ⟨6, 2, 7, 7, 0, 8, 5130198971162025527652697850159686513619380469760000000⟩, + ⟨6, 2, 8, 7, 1, 8, -738127179209313623772246620412717329938743558144000000⟩ +] + +def collectedFourData_11_0_42 : List CollectedFourTerm := [ + ⟨7, 0, 4, 0, 4, 7, 1586829086754785593011016525084370693074949505024000000⟩, + ⟨7, 0, 5, 0, 5, 7, -8346362898297016028892546738199960896284204728320000000⟩, + ⟨7, 0, 6, 0, 6, 7, -4823817252688969176497992515996100972574901534720000000⟩, + ⟨7, 0, 7, 0, 7, 7, 29473766317965034642163339671990504312516116480000000⟩, + ⟨7, 0, 8, 0, 8, 7, -993559578542558136438029674187816285757914480640000000⟩, + ⟨7, 0, 4, 1, 3, 7, -946133063858421054270345664228790982408646164480000000⟩, + ⟨7, 0, 5, 1, 4, 7, -4466540427942589776517042611413926754675746406400000000⟩, + ⟨7, 0, 6, 1, 5, 7, 3033407534998736027838147359337579523295108136960000000⟩, + ⟨7, 0, 7, 1, 6, 7, 2040005568493886325013828252311593587281147985920000000⟩, + ⟨7, 0, 8, 1, 7, 7, -830233061472344098916748438739917634244758732800000000⟩, + ⟨7, 0, 4, 2, 2, 7, 623305319466648574921887379396415873254321815552000000⟩, + ⟨7, 0, 5, 2, 3, 7, -6589892831032895144170412963567417245595798077440000000⟩, + ⟨7, 0, 6, 2, 4, 7, -1088732546846057730821841609444773626984016117760000000⟩, + ⟨7, 0, 7, 2, 5, 7, -206897492256864382474962936156990108055948492800000000⟩, + ⟨7, 0, 8, 2, 6, 7, -45178394598607776231603968698169157803311104000000000⟩, + ⟨7, 0, 4, 3, 1, 7, -1383880628746473554917974028076162074301209509888000000⟩, + ⟨7, 0, 5, 3, 2, 7, 17902987099564495346548350321256522824690538905600000000⟩, + ⟨7, 0, 6, 3, 3, 7, -1652796693056149584187300693375514259214879948800000000⟩, + ⟨7, 0, 7, 3, 4, 7, 831292594382031591897222557574733366898542510080000000⟩, + ⟨7, 0, 8, 3, 5, 7, -718822974135051839374964692395781836312988876800000000⟩, + ⟨7, 0, 4, 4, 0, 7, 2311536142594876029839688739922651628483322576896000000⟩, + ⟨7, 0, 5, 4, 1, 7, -4962317818932928984009677530740379176017906892800000000⟩, + ⟨7, 0, 6, 4, 2, 7, 5025650247533380096752937249967767459946771251200000000⟩, + ⟨7, 0, 7, 4, 3, 7, -2948419380653523113775164171127419109035590287360000000⟩, + ⟨7, 0, 8, 4, 4, 7, 1028415909401789308573532444108419229122402713600000000⟩, + ⟨7, 0, 5, 5, 0, 7, -56808741844987567402244483705036171207979156111360000000⟩, + ⟨7, 0, 6, 5, 1, 7, -7766099698300611436592815507000782285141599846400000000⟩, + ⟨7, 0, 7, 5, 2, 7, 5727021516576674678320588393896694869126901923840000000⟩, + ⟨7, 0, 8, 5, 3, 7, -1438583321777590783053061236170493529505660928000000000⟩, + ⟨7, 0, 6, 6, 0, 7, 11391350841516120130968280097558019568927317688320000000⟩, + ⟨7, 0, 7, 6, 1, 7, -15734806165679643569513195989431839722693963284480000000⟩, + ⟨7, 0, 8, 6, 2, 7, 5130198971162025527652697850159686513619380469760000000⟩, + ⟨7, 0, 7, 7, 0, 7, 53335678538556550926622396194282556992828053913600000000⟩, + ⟨7, 0, 8, 7, 1, 7, -9592345777468508518662425831157642716150287564800000000⟩ +] + +def collectedFourData_11_0_43 : List CollectedFourTerm := [ + ⟨7, 1, 3, 0, 3, 8, -93944836020994357263342490891120735403051581440000000⟩, + ⟨7, 1, 4, 0, 4, 8, -1141555799568040637717510073434766667003805564928000000⟩, + ⟨7, 1, 5, 0, 5, 8, 3002162946022058388363421220684909332527600107520000000⟩, + ⟨7, 1, 6, 0, 6, 8, 1156742211417591881136929227114323721573399265280000000⟩, + ⟨7, 1, 7, 0, 7, 8, -5300814869765729358851728267368696564563312640000000⟩, + ⟨7, 1, 8, 0, 8, 8, 142952219437972168219692855844760175839193071616000000⟩, + ⟨7, 1, 3, 1, 2, 8, 10119074892670485430243329334080476261388386304000000⟩, + ⟨7, 1, 4, 1, 3, 8, 680642732872694879305867518374823319678023106560000000⟩, + ⟨7, 1, 5, 1, 4, 8, 1606601861562330095175996877274665521470924390400000000⟩, + ⟨7, 1, 6, 1, 5, 8, -727405363088589965483739000468826630069986263040000000⟩, + ⟨7, 1, 7, 1, 6, 8, -366892094319349120267092572098144565784540610560000000⟩, + ⟨7, 1, 8, 1, 7, 8, 119452986364793295222383892050349478082059960320000000⟩, + ⟨7, 1, 3, 2, 1, 8, 79215662951044951790951932505833458588092203008000000⟩, + ⟨7, 1, 4, 2, 2, 8, -448402293780689767203422649681924765640078393344000000⟩, + ⟨7, 1, 5, 2, 3, 8, 2370365669053289530980391109798329592426885283840000000⟩, + ⟨7, 1, 6, 2, 4, 8, 261075996023479219169485949550442414419990282240000000⟩, + ⟨7, 1, 7, 2, 5, 8, 37210219136600255061469796353089435808982630400000000⟩, + ⟨7, 1, 8, 2, 6, 8, 6500215908530781968087532547023295655549337600000000⟩, + ⟨7, 1, 3, 3, 0, 8, -817154638490078560012185014055785639440621240320000000⟩, + ⟨7, 1, 4, 3, 1, 8, 995555835749264946630318291496154133586652430336000000⟩, + ⟨7, 1, 5, 3, 2, 8, -6439653433280510518571890655869329526931167641600000000⟩, + ⟨7, 1, 6, 3, 3, 8, 396337506501456695706553226806517650435552051200000000⟩, + ⟨7, 1, 7, 3, 4, 8, -149506788439878124449601952700010388226771517440000000⟩, + ⟨7, 1, 8, 3, 5, 8, 103423430013470716312295435047835052026017873920000000⟩, + ⟨7, 1, 4, 4, 0, 8, -1662905924472814124968411837667360555599304589312000000⟩, + ⟨7, 1, 5, 4, 1, 8, 1784931576055139808529233195325434276139027660800000000⟩, + ⟨7, 1, 6, 4, 2, 8, -1205141380076648240742695163163060003970796748800000000⟩, + ⟨7, 1, 7, 4, 3, 8, 530269023872505773283976123177719660458520084480000000⟩, + ⟨7, 1, 8, 4, 4, 8, -147967308583507432812018442626006711002820771840000000⟩, + ⟨7, 1, 5, 5, 0, 8, 20433942527463445971963561480254286661996731432960000000⟩, + ⟨7, 1, 6, 5, 1, 8, 1862295951218733667321739161545308938209696153600000000⟩, + ⟨7, 1, 7, 5, 2, 8, -1029996658283674793881268687010123749998586757120000000⟩, + ⟨7, 1, 8, 5, 3, 8, 206981728258531732210154974862789627088155443200000000⟩, + ⟨7, 1, 6, 6, 0, 8, -2731624286990505187472958588870490296109687111680000000⟩, + ⟨7, 1, 7, 6, 1, 8, 2829882465515688052210617560722193016683117936640000000⟩, + ⟨7, 1, 8, 6, 2, 8, -738127179209313623772246620412717329938743558144000000⟩, + ⟨7, 1, 7, 7, 0, 8, -9592345777468508518662425831157642716150287564800000000⟩, + ⟨7, 1, 8, 7, 1, 8, 1380135774562257886014903347829672638999030661120000000⟩ +] + +def collectedFourData_11_0 : List (List CollectedFourTerm) := [ + collectedFourData_11_0_0, + collectedFourData_11_0_1, + collectedFourData_11_0_2, + collectedFourData_11_0_3, + collectedFourData_11_0_4, + collectedFourData_11_0_5, + collectedFourData_11_0_6, + collectedFourData_11_0_7, + collectedFourData_11_0_8, + collectedFourData_11_0_9, + collectedFourData_11_0_10, + collectedFourData_11_0_11, + collectedFourData_11_0_12, + collectedFourData_11_0_13, + collectedFourData_11_0_14, + collectedFourData_11_0_15, + collectedFourData_11_0_16, + collectedFourData_11_0_17, + collectedFourData_11_0_18, + collectedFourData_11_0_19, + collectedFourData_11_0_20, + collectedFourData_11_0_21, + collectedFourData_11_0_22, + collectedFourData_11_0_23, + collectedFourData_11_0_24, + collectedFourData_11_0_25, + collectedFourData_11_0_26, + collectedFourData_11_0_27, + collectedFourData_11_0_28, + collectedFourData_11_0_29, + collectedFourData_11_0_30, + collectedFourData_11_0_31, + collectedFourData_11_0_32, + collectedFourData_11_0_33, + collectedFourData_11_0_34, + collectedFourData_11_0_35, + collectedFourData_11_0_36, + collectedFourData_11_0_37, + collectedFourData_11_0_38, + collectedFourData_11_0_39, + collectedFourData_11_0_40, + collectedFourData_11_0_41, + collectedFourData_11_0_42, + collectedFourData_11_0_43 +] + +theorem collectedFourChecked_11_0 : collectNumericRowParts 11 0 = collectedFourData_11_0 := by + decide +kernel +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1103.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1103.lean new file mode 100644 index 0000000000000000000000000000000000000000..f8e90ef24ee5cf53cae6594a9742060e28fb0760 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1103.lean @@ -0,0 +1,635 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1103. -/ +namespace LaughlinFock +def collectedFourData_11_1_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_1_1 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_1_2 : List CollectedFourTerm := [ + ⟨0, 3, 8, 1, 8, 2, 68319216536856617967971449697165181962838815539200000⟩, + ⟨0, 3, 8, 2, 7, 2, 29334723565006092389153157449310880485450606182400000⟩, + ⟨0, 3, 8, 3, 6, 2, -1575243251897840978792958784844377255374225408000000⟩, + ⟨0, 3, 8, 4, 5, 2, -21440845393581174392492549547360659013853878681600000⟩, + ⟨0, 3, 8, 5, 4, 2, -10733336510666122824875037160044071881177615564800000⟩, + ⟨0, 3, 8, 6, 3, 2, 56987585226323719135975243036695141167518030233600000⟩, + ⟨0, 3, 8, 7, 2, 2, -22414734634600288298506910994836410911150204518400000⟩ +] + +def collectedFourData_11_1_3 : List CollectedFourTerm := [ + ⟨0, 4, 7, 0, 8, 3, -21875770995296472956431072458786893832382316544000000⟩, + ⟨0, 4, 7, 1, 7, 3, 1730584074975734568199980062829994736898539520000000⟩, + ⟨0, 4, 8, 1, 8, 3, 25009400486772406561036589469558054146729941401600000⟩, + ⟨0, 4, 7, 2, 6, 3, 1085417430025533741321892308754157746950399590400000⟩, + ⟨0, 4, 8, 2, 7, 3, 10738469891706291306471155315505172039708390195200000⟩, + ⟨0, 4, 7, 3, 5, 3, 2603358938700760957428199949953612411511085465600000⟩, + ⟨0, 4, 8, 3, 6, 3, -576644337388524541610440747208557620451344384000000⟩, + ⟨0, 4, 7, 4, 4, 3, -1345949286815450166232319209536136759006042521600000⟩, + ⟨0, 4, 8, 4, 5, 3, -7848782764271913831620980552497256299880041676800000⟩, + ⟨0, 4, 7, 5, 3, 3, -1535302956425271403941765039302245699101602611200000⟩, + ⟨0, 4, 8, 5, 4, 3, -3929118701320752836464780407495083558238053990400000⟩, + ⟨0, 4, 7, 6, 2, 3, -10866101375631095010260707340823075604315452211200000⟩, + ⟨0, 4, 8, 6, 3, 3, 20861265891864095349722326413818796311170567372800000⟩, + ⟨0, 4, 7, 7, 1, 3, 56216165254195888552096514251328943293986347417600000⟩, + ⟨0, 4, 8, 7, 2, 3, -8205291332330011172368809453847589631277871923200000⟩ +] + +def collectedFourData_11_1_4 : List CollectedFourTerm := [ + ⟨0, 5, 6, 0, 7, 4, 439331265146748978460788413776534373382879392563200000⟩, + ⟨0, 5, 7, 0, 8, 4, 1288690835838876979663268484060153481239264755712000000⟩, + ⟨0, 5, 6, 1, 6, 4, -161895907391180532175759870353928557459106116403200000⟩, + ⟨0, 5, 7, 1, 7, 4, -101947850823152409150809836600923320948317224960000000⟩, + ⟨0, 5, 8, 1, 8, 4, -736645698660349281860506618577124865491838854758400000⟩, + ⟨0, 5, 6, 2, 5, 4, -2908627826659443774219239867363299503056407756800000⟩, + ⟨0, 5, 7, 2, 6, 4, -63941403273715059610933747369144960948643246899200000⟩, + ⟨0, 5, 8, 2, 7, 4, -316298971664793822389297109604661081702310661324800000⟩, + ⟨0, 5, 6, 3, 4, 4, 47098574068571572835133363753081387082474271539200000⟩, + ⟨0, 5, 7, 3, 5, 4, -153362585822654680684339299916477699116476714188800000⟩, + ⟨0, 5, 8, 3, 6, 4, 16984916172571725497932120155633402979880534016000000⟩, + ⟨0, 5, 6, 4, 3, 4, -59467119542997511726680745659541089976411855257600000⟩, + ⟨0, 5, 7, 4, 4, 4, 79289205934541999114121077095533560057264131276800000⟩, + ⟨0, 5, 8, 4, 5, 4, 231183952853184098759615465831748564006011614003200000⟩, + ⟨0, 5, 6, 5, 2, 4, 129087448444459569928292150459004222321956644454400000⟩, + ⟨0, 5, 7, 5, 3, 4, 90443936838019900210416374205141384990658501017600000⟩, + ⟨0, 5, 8, 5, 4, 4, 115731218442629830875789891652940210130103409049600000⟩, + ⟨0, 5, 6, 6, 1, 4, -241755305825208008444395200505493963320601660620800000⟩, + ⟨0, 5, 7, 6, 2, 4, 640116650840914944744599695443225536779672721817600000⟩, + ⟨0, 5, 8, 6, 3, 4, -614463421303497991107202017789799925215309017907200000⟩, + ⟨0, 5, 6, 7, 0, 4, -71736752481661037768421193516365164374461618585600000⟩, + ⟨0, 5, 7, 7, 1, 4, -3311666455306313387549747016572444550185379220684800000⟩, + ⟨0, 5, 8, 7, 2, 4, 241684824448825068132044369785397319523197832396800000⟩ +] + +def collectedFourData_11_1_5 : List CollectedFourTerm := [ + ⟨0, 6, 5, 0, 6, 5, 556545034187044471198146433947542465747833847808000000⟩, + ⟨0, 6, 6, 0, 7, 5, 766361617504026755448293301064389345869391986688000000⟩, + ⟨0, 6, 7, 0, 8, 5, 1123984646399125244402162753698048977790870487040000000⟩, + ⟨0, 6, 5, 1, 5, 5, -182425898113733210977064412650571694036714782720000000⟩, + ⟨0, 6, 6, 1, 6, 5, -282408331248958798733045548628111957701624332288000000⟩, + ⟨0, 6, 7, 1, 7, 5, -88918005678235821424497262463519421453513523200000000⟩, + ⟨0, 6, 8, 1, 8, 5, -428330536233031313273251379790354390783992266752000000⟩, + ⟨0, 6, 5, 2, 4, 5, 137038234523575709722952627699937844348921577472000000⟩, + ⟨0, 6, 6, 2, 5, 5, -5073758466089101155943607873710468085015642112000000⟩, + ⟨0, 6, 7, 2, 6, 5, -55769121305256321274043342117194401526226878464000000⟩, + ⟨0, 6, 8, 2, 7, 5, -183915426899960114816370107283293378406455967744000000⟩, + ⟨0, 6, 5, 3, 3, 5, -40920379602100354319703144579942504633515114496000000⟩, + ⟨0, 6, 6, 3, 4, 5, 82157911964829389638088317787274979203537174528000000⟩, + ⟨0, 6, 7, 3, 5, 5, -133761478706040921246738474299958881668086890496000000⟩, + ⟨0, 6, 8, 3, 6, 5, 9876061538540448868431797938825468223925780480000000⟩, + ⟨0, 6, 5, 4, 2, 5, -84512240525650683834280962844770687990544465920000000⟩, + ⟨0, 6, 6, 4, 3, 5, -103733381930043439094715159236006511775196381184000000⟩, + ⟨0, 6, 7, 4, 4, 5, 69155337818159303373182364122611610229676179456000000⟩, + ⟨0, 6, 8, 4, 5, 5, 134424387021003314181580414730974455397242372096000000⟩, + ⟨0, 6, 5, 5, 1, 5, -28532627778969987071522002590556110832590127104000000⟩, + ⟨0, 6, 6, 5, 2, 5, 225177841045114511403038873158276554497401552896000000⟩, + ⟨0, 6, 7, 5, 3, 5, 78884394564389303365681331263549462159967649792000000⟩, + ⟨0, 6, 8, 5, 4, 5, 67293157273005252044057749165619716154078527488000000⟩, + ⟨0, 6, 5, 6, 0, 5, 1515048929698946937022109148483524419512919130112000000⟩, + ⟨0, 6, 6, 6, 1, 5, -421713640504281035344257659885501592441949519872000000⟩, + ⟨0, 6, 7, 6, 2, 5, 558304030292315769074430252696856859109639585792000000⟩, + ⟨0, 6, 8, 6, 3, 5, -357286341617346351658213386685975399761985929216000000⟩, + ⟨0, 6, 6, 7, 0, 5, -125136310633317054264378567066976707604805320704000000⟩, + ⟨0, 6, 7, 7, 1, 5, -2888405928126503605338745533000889691773983522816000000⟩, + ⟨0, 6, 8, 7, 2, 5, 140530231349769235591529964992315491345345019904000000⟩ +] + +def collectedFourData_11_1_6 : List CollectedFourTerm := [ + ⟨0, 7, 4, 0, 5, 6, 439331265146748978460788413776534373382879392563200000⟩, + ⟨0, 7, 5, 0, 6, 6, 766361617504026755448293301064389345869391986688000000⟩, + ⟨0, 7, 6, 0, 7, 6, 527639357739740571096138306848002090570491101184000000⟩, + ⟨0, 7, 7, 0, 8, 6, 515908350478984940733272126206768479159692820480000000⟩, + ⟨0, 7, 4, 1, 4, 6, 135196808105856671894156955844452918157750409625600000⟩, + ⟨0, 7, 5, 1, 5, 6, -251200168477434953321754010385772623553280081920000000⟩, + ⟨0, 7, 6, 1, 6, 6, -194437909098141353371723438849142559519994281984000000⟩, + ⟨0, 7, 7, 1, 7, 6, -40813316965052238011957826746144733085984358400000000⟩, + ⟨0, 7, 8, 1, 8, 6, -147452614977241999300579704037099042323057082368000000⟩, + ⟨0, 7, 4, 2, 3, 6, 212273981745332405885081892997584833441266296422400000⟩, + ⟨0, 7, 5, 2, 4, 6, 188701428668372743588031416783656440491401019392000000⟩, + ⟨0, 7, 6, 2, 5, 6, -3493278626209066433573268646660888875516297216000000⟩, + ⟨0, 7, 7, 2, 6, 6, -25597996798650572999232297027006345057474183168000000⟩, + ⟨0, 7, 8, 2, 7, 6, -63312811805462889597255591414046508902458064896000000⟩, + ⟨0, 7, 4, 3, 2, 6, -566308119237577950076145780494483468484839106150400000⟩, + ⟨0, 7, 5, 3, 3, 6, -56347296938067656778434215783192175799284269056000000⟩, + ⟨0, 7, 6, 3, 4, 6, 56565656358870230626265886226875144019120226304000000⟩, + ⟨0, 7, 7, 3, 5, 6, -61396447058191014404450953963369691401370468352000000⟩, + ⟨0, 7, 8, 3, 6, 6, 3399830216031308478493768593269152037543608320000000⟩, + ⟨0, 7, 4, 4, 1, 6, 7270368654941571087208264757467983828599439360000000⟩, + ⟨0, 7, 5, 4, 2, 6, -116373219361723836980755931568467056643926917120000000⟩, + ⟨0, 7, 6, 4, 3, 6, -71420350090082294724036179010217821072588275712000000⟩, + ⟨0, 7, 7, 4, 4, 6, 31742263005890200698101652245181131031809359872000000⟩, + ⟨0, 7, 8, 4, 5, 6, 46275541214685002435149667964675308699636465664000000⟩, + ⟨0, 7, 4, 5, 0, 6, 2333560186919753704297025102952715332114026437017600000⟩, + ⟨0, 7, 5, 5, 1, 6, -39289382589267527091684688975407432790173548544000000⟩, + ⟨0, 7, 6, 5, 2, 6, 155034762587964977833784994155273771441851465728000000⟩, + ⟨0, 7, 7, 5, 3, 6, 36207894839691614822167635934953733856170082304000000⟩, + ⟨0, 7, 8, 5, 4, 6, 23165642350049765171761208951267726659569057792000000⟩, + ⟨0, 7, 5, 6, 0, 6, 2086219940957398945321692347255704225167999762432000000⟩, + ⟨0, 7, 6, 6, 1, 6, -290349502563125852346919611875182966031983312896000000⟩, + ⟨0, 7, 7, 6, 2, 6, 256261250771211633275298683883840090362351714304000000⟩, + ⟨0, 7, 8, 6, 3, 6, -122995679529297162630133341956740416401250975744000000⟩, + ⟨0, 7, 6, 7, 0, 6, -86156249301116843884299502178087114298278019072000000⟩, + ⟨0, 7, 7, 7, 1, 6, -1325776773434959386337319839049996553963744264192000000⟩, + ⟨0, 7, 8, 7, 2, 6, 48377475671281114645188440189025274016443662336000000⟩ +] + +def collectedFourData_11_1_7 : List CollectedFourTerm := [ + ⟨0, 8, 3, 0, 4, 7, -21875770995296472956431072458786893832382316544000000⟩, + ⟨0, 8, 4, 0, 5, 7, 1288690835838876979663268484060153481239264755712000000⟩, + ⟨0, 8, 5, 0, 6, 7, 1123984646399125244402162753698048977790870487040000000⟩, + ⟨0, 8, 6, 0, 7, 7, 515908350478984940733272126206768479159692820480000000⟩, + ⟨0, 8, 7, 0, 8, 7, 378328619050673549597128795690233675004457779200000000⟩, + ⟨0, 8, 3, 1, 3, 7, 105007475276704796512386656555326278691996041216000000⟩, + ⟨0, 8, 4, 1, 4, 7, 396572931322081118858777085076609455810618064896000000⟩, + ⟨0, 8, 5, 1, 5, 7, -368422851683365868606418226430257631711566233600000000⟩, + ⟨0, 8, 6, 1, 6, 7, -190114970541837665016908244366594458549464596480000000⟩, + ⟨0, 8, 7, 1, 7, 7, -29929435784340166399773863324166934952411136000000000⟩, + ⟨0, 8, 8, 1, 8, 7, -86504580354952797805068813347478693117035544576000000⟩, + ⟨0, 8, 3, 2, 2, 7, -81949259183787478742599978229047951631019147264000000⟩, + ⟨0, 8, 4, 2, 3, 7, 622663481213575142136298601803520932958944886784000000⟩, + ⟨0, 8, 5, 2, 4, 7, 276759043945355538954914334322145948920562319360000000⟩, + ⟨0, 8, 6, 2, 5, 7, -3415612553110489242453597418838553362190827520000000⟩, + ⟨0, 8, 7, 2, 6, 7, -18771657350197360681160194534576650179020062720000000⟩, + ⟨0, 8, 8, 2, 7, 7, -37143106734112321483653428712454287962010550272000000⟩, + ⟨0, 8, 3, 3, 1, 7, -1836089570653558219044698773800901702588563456000000⟩, + ⟨0, 8, 4, 3, 2, 7, -1661152167895094724887137014174274724276169867264000000⟩, + ⟨0, 8, 5, 3, 3, 7, -82641791000379412278953126025899708391075348480000000⟩, + ⟨0, 8, 6, 3, 4, 7, 55308031968798436221098580928592855329281146880000000⟩, + ⟨0, 8, 7, 3, 5, 7, -45023564764124452575328508337130854418565038080000000⟩, + ⟨0, 8, 8, 3, 6, 7, 1994545069012636446635292491252412627277578240000000⟩, + ⟨0, 8, 3, 4, 0, 7, 352057980039804708826657636447064046182445613056000000⟩, + ⟨0, 8, 4, 4, 1, 7, 21326179587204725686865353562887552245537177600000000⟩, + ⟨0, 8, 5, 4, 2, 7, -170678839893658584134063864279370326112573849600000000⟩, + ⟨0, 8, 6, 4, 3, 7, -69832461254303430251946605002886872090426736640000000⟩, + ⟨0, 8, 7, 4, 4, 7, 23277402890285059721696753012038567820399738880000000⟩, + ⟨0, 8, 8, 4, 5, 7, 27148018189385677622534721229668732886893723648000000⟩, + ⟨0, 8, 4, 5, 0, 7, 6845034411009745899386302250072348326705407983616000000⟩, + ⟨0, 8, 5, 5, 1, 7, -57623792460620944844686166282075837117780459520000000⟩, + ⟨0, 8, 6, 5, 2, 7, 151587874294074612482441359828996610702085980160000000⟩, + ⟨0, 8, 7, 5, 3, 7, 26552163462201088883781018342113200547467100160000000⟩, + ⟨0, 8, 8, 5, 4, 7, 13590360336798821169999773119732738825119596544000000⟩, + ⟨0, 8, 5, 6, 0, 7, 3059755511092627380017143723537134191085417922560000000⟩, + ⟨0, 8, 6, 6, 1, 7, -283894161291171537075818190237019795539225477120000000⟩, + ⟨0, 8, 7, 6, 2, 7, 187922845269820960390663166417507820511596380160000000⟩, + ⟨0, 8, 8, 6, 3, 7, -72156669753169524026966280099385068319521374208000000⟩, + ⟨0, 8, 6, 7, 0, 7, -84240737178517748479586231003168921456832675840000000⟩, + ⟨0, 8, 7, 7, 1, 7, -972225581147163975291964351430225116943540551680000000⟩, + ⟨0, 8, 8, 7, 2, 7, 28381139474684862093473074384544325911395172352000000⟩ +] + +def collectedFourData_11_1_8 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_1_9 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_1_10 : List CollectedFourTerm := [ + ⟨1, 2, 8, 1, 8, 2, -65532700153377083929535023243088130061683916800000000⟩, + ⟨1, 2, 8, 2, 7, 2, -28138256568423441102594602132985011638999449600000000⟩, + ⟨1, 2, 8, 3, 6, 2, 1510994255028696383795939464557677386924032000000000⟩, + ⟨1, 2, 8, 4, 5, 2, 20566343752704855680992206898047530383599206400000000⟩, + ⟨1, 2, 8, 5, 4, 2, 10295558978187611359101133146760068264571699200000000⟩, + ⟨1, 2, 8, 6, 3, 2, -54663248854544336750428255482650833751271014400000000⟩, + ⟨1, 2, 8, 7, 2, 2, 21500511251242771775431311590861295817693593600000000⟩ +] + +def collectedFourData_11_1_11 : List CollectedFourTerm := [ + ⟨1, 3, 7, 0, 8, 3, 105007475276704796512386656555326278691996041216000000⟩, + ⟨1, 3, 7, 1, 7, 3, -8307102159112296762007027960600000720042721280000000⟩, + ⟨1, 3, 8, 1, 8, 3, -120049437519921842351395014358096421457999849062400000⟩, + ⟨1, 3, 7, 2, 6, 3, -5210190944713078538824710410984595073904777625600000⟩, + ⟨1, 3, 8, 2, 7, 3, -51546508322172398579270918208220146281640414412800000⟩, + ⟨1, 3, 7, 3, 5, 3, -12496572095712034968006618078630554810741843558400000⟩, + ⟨1, 3, 8, 3, 6, 3, 2767992315095849048593570795008413891586686976000000⟩, + ⟨1, 3, 7, 4, 4, 3, 6460788810111439334403064188791910927341872742400000⟩, + ⟨1, 3, 8, 4, 5, 3, 37675511516769740816600290286025730050233676595200000⟩, + ⟨1, 3, 7, 5, 3, 3, 7369719095786024708829054128379628577962642636800000⟩, + ⟨1, 3, 8, 5, 4, 3, 18860447706135159168463165119130665326692899225600000⟩, + ⟨1, 3, 7, 6, 2, 3, 52159161466861314971198197589383300531069177036800000⟩, + ⟨1, 3, 8, 6, 3, 3, -100137675735025946986392425608688134336386642739200000⟩, + ⟨1, 3, 7, 7, 1, 3, -269847292895430292233976899380287785671649027686400000⟩, + ⟨1, 3, 8, 7, 2, 3, 39386814156312970816603708194303356392067353804800000⟩ +] + +def collectedFourData_11_1_12 : List CollectedFourTerm := [ + ⟨1, 4, 6, 0, 7, 4, 135196808105856671894156955844452918157750409625600000⟩, + ⟨1, 4, 7, 0, 8, 4, 396572931322081118858777085076609455810618064896000000⟩, + ⟨1, 4, 6, 1, 6, 4, -49820742708529597029668616474096941390443944345600000⟩, + ⟨1, 4, 7, 1, 7, 4, -31372736515663917919447935916098812829688135680000000⟩, + ⟨1, 4, 8, 1, 8, 4, -226690324738261884265575959071758955643684467507200000⟩, + ⟨1, 4, 6, 2, 5, 4, -895081295889286406756655532357708606293304934400000⟩, + ⟨1, 4, 7, 2, 6, 4, -19676891480801137118329686719587978337628821913600000⟩, + ⟨1, 4, 8, 2, 7, 4, -97335688963454522878009244024673920525269362278400000⟩, + ⟨1, 4, 6, 3, 4, 4, 14493794058297213599475580649494467198230043033600000⟩, + ⟨1, 4, 7, 3, 5, 4, -47194756510574401155851578519986710962409727590400000⟩, + ⟨1, 4, 8, 3, 6, 4, 5226822297088758989434707414769933295422537728000000⟩, + ⟨1, 4, 6, 4, 3, 4, -18300005911887847376278971256406260753221078220800000⟩, + ⟨1, 4, 7, 4, 4, 4, 24399919627885721722107535573134750285157525094400000⟩, + ⟨1, 4, 8, 4, 5, 4, 71142973402098273068750451353151754229908085145600000⟩, + ⟨1, 4, 6, 5, 2, 4, 39724491245554168116938682966530693234777338675200000⟩, + ⟨1, 4, 7, 5, 3, 4, 27832600461393504534643545537303201826409860300800000⟩, + ⟨1, 4, 8, 5, 4, 4, 35614336089690403524679386755348879870469655756800000⟩, + ⟨1, 4, 6, 6, 1, 4, -74396129488543877616471346114474758685187270246400000⟩, + ⟨1, 4, 7, 6, 2, 4, 196985133712701889010150009414477257142268906700800000⟩, + ⟨1, 4, 8, 6, 3, 4, -189090783762654135390232897799554803920910522777600000⟩, + ⟨1, 4, 6, 7, 0, 4, -22075779096124348635600190295875943667319229644800000⟩, + ⟨1, 4, 7, 7, 1, 4, -1019109655487635100917077892174926368179359213158400000⟩, + ⟨1, 4, 8, 7, 2, 4, 74374440030329019782525987268867465150017726054400000⟩ +] + +def collectedFourData_11_1_13 : List CollectedFourTerm := [ + ⟨1, 5, 5, 0, 6, 5, -182425898113733210977064412650571694036714782720000000⟩, + ⟨1, 5, 6, 0, 7, 5, -251200168477434953321754010385772623553280081920000000⟩, + ⟨1, 5, 7, 0, 8, 5, -368422851683365868606418226430257631711566233600000000⟩, + ⟨1, 5, 5, 1, 5, 5, 59796074456425111460678458952018317263293644800000000⟩, + ⟨1, 5, 6, 1, 6, 5, 92568597864045503829724876090417400954927185920000000⟩, + ⟨1, 5, 7, 1, 7, 5, 29145794226748305528501099436251261947609088000000000⟩, + ⟨1, 5, 8, 1, 8, 5, 140399389019769337040849569381658769250509127680000000⟩, + ⟨1, 5, 5, 2, 4, 5, -44918778307672205949044392780983309724790292480000000⟩, + ⟨1, 5, 6, 2, 5, 5, 1663090833863032408050978779412371681134510080000000⟩, + ⟨1, 5, 7, 2, 6, 5, 18280159584904166057178309240821614179526901760000000⟩, + ⟨1, 5, 8, 2, 7, 5, 60284316395355751350390070191674363273501736960000000⟩, + ⟨1, 5, 5, 3, 3, 5, 13412997226670463860418681537623794412830064640000000⟩, + ⟨1, 5, 6, 3, 4, 5, -26929951678080969788031368508242312721617387520000000⟩, + ⟨1, 5, 7, 3, 5, 5, 43844714060946241782651826599459219430849904640000000⟩, + ⟨1, 5, 8, 3, 6, 5, -3237203254587369499045487287120348948149043200000000⟩, + ⟨1, 5, 5, 4, 2, 5, 27701660121747172297737274370651139208957132800000000⟩, + ⟨1, 5, 6, 4, 3, 5, 34002019963407288842238446658128397828945346560000000⟩, + ⟨1, 5, 7, 4, 4, 5, -22667931318917166053569228165384524627223511040000000⟩, + ⟨1, 5, 8, 4, 5, 5, -44062004014670693080370898278645336543739248640000000⟩, + ⟨1, 5, 5, 5, 1, 5, 9352505059588975540544711681737672011137679360000000⟩, + ⟨1, 5, 6, 5, 2, 5, -73809426667457834109470234506204375188913520640000000⟩, + ⟨1, 5, 7, 5, 3, 5, -25856948928827228810882810168141459515276001280000000⟩, + ⟨1, 5, 8, 5, 4, 5, -22057540537341206624724619436326276447516753920000000⟩, + ⟨1, 5, 5, 6, 0, 5, -496607003403237715095269296323509143201728430080000000⟩, + ⟨1, 5, 6, 6, 1, 5, 138230484309649305618030547393629590013849108480000000⟩, + ⟨1, 5, 7, 6, 2, 5, -183002466809115427498859936927871998901910241280000000⟩, + ⟨1, 5, 8, 6, 3, 5, 117112322902173790559128153784830998496086589440000000⟩, + ⟨1, 5, 6, 7, 0, 5, 41017532188149690943175494662467297782121103360000000⟩, + ⟨1, 5, 7, 7, 1, 5, 946769826677530819613627036977861822791486013440000000⟩, + ⟨1, 5, 8, 7, 2, 5, -46063394858171452147894458102639244732646031360000000⟩ +] + +def collectedFourData_11_1_14 : List CollectedFourTerm := [ + ⟨1, 6, 4, 0, 5, 6, -161895907391180532175759870353928557459106116403200000⟩, + ⟨1, 6, 5, 0, 6, 6, -282408331248958798733045548628111957701624332288000000⟩, + ⟨1, 6, 6, 0, 7, 6, -194437909098141353371723438849142559519994281984000000⟩, + ⟨1, 6, 7, 0, 8, 6, -190114970541837665016908244366594458549464596480000000⟩, + ⟨1, 6, 4, 1, 4, 6, -49820742708529597029668616474096941390443944345600000⟩, + ⟨1, 6, 5, 1, 5, 6, 92568597864045503829724876090417400954927185920000000⟩, + ⟨1, 6, 6, 1, 6, 6, 71651403444215837709057970346429051777826422784000000⟩, + ⟨1, 6, 7, 1, 7, 6, 15039924330206503500240372343104152438990438400000000⟩, + ⟨1, 6, 8, 1, 8, 6, 54337072712020758003023150163939918315119443968000000⟩, + ⟨1, 6, 4, 2, 3, 6, -78224091059670375518195405317877706219818739302400000⟩, + ⟨1, 6, 5, 2, 4, 6, -69537479901581278732321411985865635689547169792000000⟩, + ⟨1, 6, 6, 2, 5, 6, 1287291749589969711561366865349883492267196416000000⟩, + ⟨1, 6, 7, 2, 6, 6, 9432997940016370313617055805818696283369504768000000⟩, + ⟨1, 6, 8, 2, 7, 6, 23331107822040949538499711720924455273125380096000000⟩, + ⟨1, 6, 4, 3, 2, 6, 208687553334807293763223270382217650636797142630400000⟩, + ⟨1, 6, 5, 3, 3, 6, 20764278553636775789646389111355073553818976256000000⟩, + ⟨1, 6, 6, 3, 4, 6, -20844745161348924213643408804739547171970351104000000⟩, + ⟨1, 6, 7, 3, 5, 6, 22624917222224617681287304527674218404749770752000000⟩, + ⟨1, 6, 8, 3, 6, 6, -1252855513518908682652094473412161042718392320000000⟩, + ⟨1, 6, 4, 4, 1, 6, -2679169510203187961086622654451444518077071360000000⟩, + ⟨1, 6, 5, 4, 2, 6, 42884150160143904905754936688855982703504261120000000⟩, + ⟨1, 6, 6, 4, 3, 6, 26318778792507292790260933833642382511006810112000000⟩, + ⟨1, 6, 7, 4, 4, 6, -11697192710087556911010951838427763131151286272000000⟩, + ⟨1, 6, 8, 4, 5, 6, -17052783012078420006556005384492986394124222464000000⟩, + ⟨1, 6, 4, 5, 0, 6, -859929337801880833785693247565278042287995722137600000⟩, + ⟨1, 6, 5, 5, 1, 6, 14478346409067958796308118990952626741883961344000000⟩, + ⟨1, 6, 6, 5, 2, 6, -57131134425342805252690597131451003905484259328000000⟩, + ⟨1, 6, 7, 5, 3, 6, -13342801787253348841903564022725803392687407104000000⟩, + ⟨1, 6, 8, 5, 4, 6, -8536662391437404403479022153311505866337288192000000⟩, + ⟨1, 6, 5, 6, 0, 6, -768783141910137073035101420898937777397623160832000000⟩, + ⟨1, 6, 6, 6, 1, 6, 106995335654824614731320500655752994519668228096000000⟩, + ⟨1, 6, 7, 6, 2, 6, -94433633602075031121036625048298436713307439104000000⟩, + ⟨1, 6, 8, 6, 3, 6, 45324561947438635912134044765150166818482028544000000⟩, + ⟨1, 6, 6, 7, 0, 6, 31749036011279407587198147344459718473098985472000000⟩, + ⟨1, 6, 7, 7, 1, 6, 488555790951297891113184435000076568623256174592000000⟩, + ⟨1, 6, 8, 7, 2, 6, -17827357036564812094795378913973049108029505536000000⟩ +] + +def collectedFourData_11_1_15 : List CollectedFourTerm := [ + ⟨1, 7, 3, 0, 4, 7, 1730584074975734568199980062829994736898539520000000⟩, + ⟨1, 7, 4, 0, 5, 7, -101947850823152409150809836600923320948317224960000000⟩, + ⟨1, 7, 5, 0, 6, 7, -88918005678235821424497262463519421453513523200000000⟩, + ⟨1, 7, 6, 0, 7, 7, -40813316965052238011957826746144733085984358400000000⟩, + ⟨1, 7, 7, 0, 8, 7, -29929435784340166399773863324166934952411136000000000⟩, + ⟨1, 7, 3, 1, 3, 7, -8307102159112296762007027960600000720042721280000000⟩, + ⟨1, 7, 4, 1, 4, 7, -31372736515663917919447935916098812829688135680000000⟩, + ⟨1, 7, 5, 1, 5, 7, 29145794226748305528501099436251261947609088000000000⟩, + ⟨1, 7, 6, 1, 6, 7, 15039924330206503500240372343104152438990438400000000⟩, + ⟨1, 7, 7, 1, 7, 7, 2367706489180406358000110285840553219194880000000000⟩, + ⟨1, 7, 8, 1, 8, 7, 6843345050875141579166256485402992017754030080000000⟩, + ⟨1, 7, 3, 2, 2, 7, 6482975293991440317904047907186471100083077120000000⟩, + ⟨1, 7, 4, 2, 3, 7, -49258675494859364219878050513294482467423518720000000⟩, + ⟨1, 7, 5, 2, 4, 7, -21894304624066609680726483403977986281360588800000000⟩, + ⟨1, 7, 6, 2, 5, 7, 270207833679149088646076413461486382979481600000000⟩, + ⟨1, 7, 7, 2, 6, 7, 1485018803594971543337135433034748843891097600000000⟩, + ⟨1, 7, 8, 2, 7, 7, 2938377304415898594528297031608790614288629760000000⟩, + ⟨1, 7, 3, 3, 1, 7, 145252360334421131702460406594311285091860480000000⟩, + ⟨1, 7, 4, 3, 2, 7, 131413127724219357891317985699510119430220677120000000⟩, + ⟨1, 7, 5, 3, 3, 7, 6537761227409087791327654654836775131178598400000000⟩, + ⟨1, 7, 6, 3, 4, 7, -4375397756907914194539309314164146978580070400000000⟩, + ⟨1, 7, 7, 3, 5, 7, 3561797396589377493636688253483547399448166400000000⟩, + ⟨1, 7, 8, 3, 6, 7, -157787715641967768753494064866129849037619200000000⟩, + ⟨1, 7, 3, 4, 0, 7, -27851175341706119190771003120516363989790228480000000⟩, + ⟨1, 7, 4, 4, 1, 7, -1687106103900266293113483193334562300100608000000000⟩, + ⟨1, 7, 5, 4, 2, 7, 13502339292124024403631815878058428877242368000000000⟩, + ⟨1, 7, 6, 4, 3, 7, 5524419934229599740579584425347410402947891200000000⟩, + ⟨1, 7, 7, 4, 4, 7, -1841466650815774608557514550380204917155430400000000⟩, + ⟨1, 7, 8, 4, 5, 7, -2147669581831152433509904912660095550976163840000000⟩, + ⟨1, 7, 4, 5, 0, 7, -541508116303712050969628363380494998791551713280000000⟩, + ⟨1, 7, 5, 5, 1, 7, 4558596704705808468874696753296442729798041600000000⟩, + ⟨1, 7, 6, 5, 2, 7, -11992060132150497696204216276534959163624652800000000⟩, + ⟨1, 7, 7, 5, 3, 7, -2100531736857077036895202751035061297794252800000000⟩, + ⟨1, 7, 8, 5, 4, 7, -1075128331572989844177144015381171069800939520000000⟩, + ⟨1, 7, 5, 6, 0, 7, -242056115962937168823920318468533213708733644800000000⟩, + ⟨1, 7, 6, 6, 1, 7, 22458761093025223015616045146968251988285849600000000⟩, + ⟨1, 7, 7, 6, 2, 7, -14866506118481776790376388504778743630056652800000000⟩, + ⟨1, 7, 8, 6, 3, 7, 5708287200710207175261820414909876231880048640000000⟩, + ⟨1, 7, 6, 7, 0, 7, 6664253262511506689581546388761349809451827200000000⟩, + ⟨1, 7, 7, 7, 1, 7, 76912402693329999640897091060586641541719654400000000⟩, + ⟨1, 7, 8, 7, 2, 7, -2245221346260905121887692425488545291079516160000000⟩ +] + +def collectedFourData_11_1_16 : List CollectedFourTerm := [ + ⟨1, 8, 2, 0, 3, 8, 68319216536856617967971449697165181962838815539200000⟩, + ⟨1, 8, 3, 0, 4, 8, 25009400486772406561036589469558054146729941401600000⟩, + ⟨1, 8, 4, 0, 5, 8, -736645698660349281860506618577124865491838854758400000⟩, + ⟨1, 8, 5, 0, 6, 8, -428330536233031313273251379790354390783992266752000000⟩, + ⟨1, 8, 6, 0, 7, 8, -147452614977241999300579704037099042323057082368000000⟩, + ⟨1, 8, 7, 0, 8, 8, -86504580354952797805068813347478693117035544576000000⟩, + ⟨1, 8, 2, 1, 2, 8, -65532700153377083929535023243088130061683916800000000⟩, + ⟨1, 8, 3, 1, 3, 8, -120049437519921842351395014358096421457999849062400000⟩, + ⟨1, 8, 4, 1, 4, 8, -226690324738261884265575959071758955643684467507200000⟩, + ⟨1, 8, 5, 1, 5, 8, 140399389019769337040849569381658769250509127680000000⟩, + ⟨1, 8, 6, 1, 6, 8, 54337072712020758003023150163939918315119443968000000⟩, + ⟨1, 8, 7, 1, 7, 8, 6843345050875141579166256485402992017754030080000000⟩, + ⟨1, 8, 8, 1, 8, 8, 16482677681031673357539450371446639076745569894400000⟩, + ⟨1, 8, 2, 2, 1, 8, -90810961799544919660363233829137711803083102617600000⟩, + ⟨1, 8, 3, 2, 2, 8, 93688210713227785772889605094298746547905075609600000⟩, + ⟨1, 8, 4, 2, 3, 8, -355928949281523157853904867834035634260000165068800000⟩, + ⟨1, 8, 5, 2, 4, 8, -105467943961896697716614007756451444542110957568000000⟩, + ⟨1, 8, 6, 2, 5, 8, 976221846840897121368363454646114226045714432000000⟩, + ⟨1, 8, 7, 2, 6, 8, 4292126632450955572399489106416568512892475801600000⟩, + ⟨1, 8, 8, 2, 7, 8, 7077288322287988898346925351503874630202739916800000⟩, + ⟨1, 8, 2, 3, 0, 8, 157262999064428940425194896602146023765967267430400000⟩, + ⟨1, 8, 3, 3, 1, 8, 2099103131584894824446609208862053550594090598400000⟩, + ⟨1, 8, 4, 3, 2, 8, 949553271637628667530954744949369325900943641804800000⟩, + ⟨1, 8, 5, 3, 3, 8, 31493315115872888765620969184163168723060916224000000⟩, + ⟨1, 8, 6, 3, 4, 8, -15807679669213702567507102719955432813633732608000000⟩, + ⟨1, 8, 7, 3, 5, 8, 10294607333110479867411402011500598047740946022400000⟩, + ⟨1, 8, 8, 3, 6, 8, -380042806495668829947432115388948017531846656000000⟩, + ⟨1, 8, 3, 4, 0, 8, -402489083437229269158596155573131514517135976038400000⟩, + ⟨1, 8, 4, 4, 1, 8, -12190540993135983766777637132314960281804472320000000⟩, + ⟨1, 8, 5, 4, 2, 8, 65042666952340475483325750771579727645224468480000000⟩, + ⟨1, 8, 6, 4, 3, 8, 19958930714503741501113324197112183081532391424000000⟩, + ⟨1, 8, 7, 4, 4, 8, -5322362272856686700815729848769164044367455846400000⟩, + ⟨1, 8, 8, 4, 5, 8, -5172813181201789516186316693292037522840564531200000⟩, + ⟨1, 8, 4, 5, 0, 8, -3912781107634760755337144664967620840175877436211200000⟩, + ⟨1, 8, 5, 5, 1, 8, 21959401317012407670786715409119271866834354176000000⟩, + ⟨1, 8, 6, 5, 2, 8, -43325579907265395767142115268292996503967891456000000⟩, + ⟨1, 8, 7, 5, 3, 8, -6071134041028415738702216487625044303392066764800000⟩, + ⟨1, 8, 8, 5, 4, 8, -2589522174217525642123543104680699131711822233600000⟩, + ⟨1, 8, 5, 6, 0, 8, -1166018346431122439798234464906125966743571529728000000⟩, + ⟨1, 8, 6, 6, 1, 8, 81140257606393062941300351460630747025917345792000000⟩, + ⟨1, 8, 7, 6, 2, 8, -42968430223348304701657625589860920948954025164800000⟩, + ⟨1, 8, 8, 6, 3, 8, 13748811047900141110947229272176995523630412595200000⟩, + ⟨1, 8, 6, 7, 0, 8, 24076983776382957233454605563445616462627078144000000⟩, + ⟨1, 8, 7, 7, 1, 8, 222298715118405734549191036297141541127166781030400000⟩, + ⟨1, 8, 8, 7, 2, 8, -5407773464273577721257007781230624839207537868800000⟩ +] + +def collectedFourData_11_1_17 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_1_18 : List CollectedFourTerm := [ + ⟨2, 1, 8, 1, 8, 2, -90810961799544919660363233829137711803083102617600000⟩, + ⟨2, 1, 8, 2, 7, 2, -38992169349964060657538036240180121308555850547200000⟩, + ⟨2, 1, 8, 3, 6, 2, 2093837752016871772534976482508911039400116224000000⟩, + ⟨2, 1, 8, 4, 5, 2, 28499504102715424887250447792015982639065124044800000⟩, + ⟨2, 1, 8, 5, 4, 2, 14266917292968834350310907211040083302116910694400000⟩, + ⟨2, 1, 8, 6, 3, 2, -75748781783001708919419077846373571923112938700800000⟩, + ⟨2, 1, 8, 7, 2, 2, 29794012780452724997399689018526149912523125555200000⟩ +] + +def collectedFourData_11_1_19 : List CollectedFourTerm := [ + ⟨2, 2, 7, 0, 8, 3, -81949259183787478742599978229047951631019147264000000⟩, + ⟨2, 2, 7, 1, 7, 3, 6482975293991440317904047907186471100083077120000000⟩, + ⟨2, 2, 8, 1, 8, 3, 93688210713227785772889605094298746547905075609600000⟩, + ⟨2, 2, 7, 2, 6, 3, 4066103741664145366093206450415524735365834342400000⟩, + ⟨2, 2, 8, 2, 7, 3, 40227594839146410216907644024795597799718859571200000⟩, + ⟨2, 2, 7, 3, 5, 3, 9752494504622931024828637270116192844905027993600000⟩, + ⟨2, 2, 8, 3, 6, 3, -2160178778232595755847192266460166448746594304000000⟩, + ⟨2, 2, 7, 4, 4, 3, -5042087292703367152208854990739233000400722329600000⟩, + ⟨2, 2, 8, 4, 5, 3, -29402480633247549138432244406319409103425555660800000⟩, + ⟨2, 2, 7, 5, 3, 3, -5751428826384301651285262307940938704305206067200000⟩, + ⟨2, 2, 8, 5, 4, 3, -14718949420691586720290814277215941227616560742400000⟩, + ⟨2, 2, 7, 6, 2, 3, -40705717670036073833790582586501631340631503667200000⟩, + ⟨2, 2, 8, 6, 3, 3, 78148801513868983433899176134570535783001541836800000⟩, + ⟨2, 2, 7, 7, 1, 3, 210592490556115917415671054642237028767561783705600000⟩, + ⟨2, 2, 8, 7, 2, 3, -30738004444102747305361998093658049601653125939200000⟩ +] + +def collectedFourData_11_1_20 : List CollectedFourTerm := [ + ⟨2, 3, 6, 0, 7, 4, 212273981745332405885081892997584833441266296422400000⟩, + ⟨2, 3, 7, 0, 8, 4, 622663481213575142136298601803520932958944886784000000⟩, + ⟨2, 3, 6, 1, 6, 4, -78224091059670375518195405317877706219818739302400000⟩, + ⟨2, 3, 7, 1, 7, 4, -49258675494859364219878050513294482467423518720000000⟩, + ⟨2, 3, 8, 1, 8, 4, -355928949281523157853904867834035634260000165068800000⟩, + ⟨2, 3, 6, 2, 5, 4, -1405376897030160175547703731959009669700753817600000⟩, + ⟨2, 3, 7, 2, 6, 4, -30894901747458681388964034315205238919470147174400000⟩, + ⟨2, 3, 8, 2, 7, 4, -152827825979588610452737494915066782326585923993600000⟩, + ⟨2, 3, 6, 3, 4, 4, 22756864000388412439534222054324235685513815654400000⟩, + ⟨2, 3, 7, 3, 5, 4, -74101001512972057306586377054670043413921503641600000⟩, + ⟨2, 3, 8, 3, 6, 4, 8206690649157801561964790886166525085076160512000000⟩, + ⟨2, 3, 6, 4, 3, 4, -28733038710780598982577465877031075574713627443200000⟩, + ⟨2, 3, 7, 4, 4, 4, 38310579711482249611036058076719177408223746457600000⟩, + ⟨2, 3, 8, 4, 5, 4, 111702357835558054461838027815772090421133862502400000⟩, + ⟨2, 3, 6, 5, 2, 4, 62371856611429060434549305544657041306399067340800000⟩, + ⟨2, 3, 7, 5, 3, 4, 43700269296602106245158455029683062479072211763200000⟩, + ⟨2, 3, 8, 5, 4, 4, 55918457209845753442040406654028114016387412787200000⟩, + ⟨2, 3, 6, 6, 1, 4, -116810173658903342955771799707699726071570733465600000⟩, + ⟨2, 3, 7, 6, 2, 4, 309288505133136664525205488625059236736320877363200000⟩, + ⟨2, 3, 8, 6, 3, 4, -296893500246071515200686621762698824205992355430400000⟩, + ⟨2, 3, 6, 7, 0, 4, -34661421334707458446796101295195538295409029939200000⟩, + ⟨2, 3, 7, 7, 1, 4, -1600115176063116692421808966567505564453456943513600000⟩, + ⟨2, 3, 8, 7, 2, 4, 116776118804194332753009414056661921594477222297600000⟩ +] + +def collectedFourData_11_1_21 : List CollectedFourTerm := [ + ⟨2, 4, 5, 0, 6, 5, 137038234523575709722952627699937844348921577472000000⟩, + ⟨2, 4, 6, 0, 7, 5, 188701428668372743588031416783656440491401019392000000⟩, + ⟨2, 4, 7, 0, 8, 5, 276759043945355538954914334322145948920562319360000000⟩, + ⟨2, 4, 5, 1, 5, 5, -44918778307672205949044392780983309724790292480000000⟩, + ⟨2, 4, 6, 1, 6, 5, -69537479901581278732321411985865635689547169792000000⟩, + ⟨2, 4, 7, 1, 7, 5, -21894304624066609680726483403977986281360588800000000⟩, + ⟨2, 4, 8, 1, 8, 5, -105467943961896697716614007756451444542110957568000000⟩, + ⟨2, 4, 5, 2, 4, 5, 33742961607356832717842959939052224580627202048000000⟩, + ⟨2, 4, 6, 2, 5, 5, -1249312921473698612043049582388273224045559808000000⟩, + ⟨2, 4, 7, 2, 6, 5, -13732045845610680984165592000222355106903883776000000⟩, + ⟨2, 4, 8, 2, 7, 5, -45285545384185151284117740265091991733373239296000000⟩, + ⟨2, 4, 5, 3, 3, 5, -10075836153847960835049082025667662874478116864000000⟩, + ⟨2, 4, 6, 3, 4, 5, 20229764917855166868886116718156243824858365952000000⟩, + ⟨2, 4, 7, 3, 5, 5, -32936125134804803625895914996665663086462500864000000⟩, + ⟨2, 4, 8, 3, 6, 5, 2431785307840730787714784805261283124649656320000000⟩, + ⟨2, 4, 5, 4, 2, 5, -20809471877121557541141848129403264271940321280000000⟩, + ⟨2, 4, 6, 4, 3, 5, -25542298731705865411340490541686066104034656256000000⟩, + ⟨2, 4, 7, 4, 4, 5, 17028137563611788795746216384927637458076565504000000⟩, + ⟨2, 4, 8, 4, 5, 5, 33099353228765145895651940712382464300379275264000000⟩, + ⟨2, 4, 5, 5, 1, 5, -7025596666871492008520577424158650769170497536000000⟩, + ⟨2, 4, 6, 5, 2, 5, 55445600796218876742921518749757792996466622464000000⟩, + ⟨2, 4, 7, 5, 3, 5, 19423725841621581629447979787592493258063740928000000⟩, + ⟨2, 4, 8, 5, 4, 5, 16569612343555119769150636571444124089258606592000000⟩, + ⟨2, 4, 5, 6, 0, 5, 373050908352907068897657739953608563305436151808000000⟩, + ⟨2, 4, 6, 6, 1, 5, -103838663934236296077787712599493017193202843648000000⟩, + ⟨2, 4, 7, 6, 2, 5, 137471352611049673316765404820752749934493564928000000⟩, + ⟨2, 4, 8, 6, 3, 5, -87974712677380774316017704680630052373181497344000000⟩, + ⟨2, 4, 6, 7, 0, 5, -30812347663891371736249189136744179175245479936000000⟩, + ⟨2, 4, 7, 7, 1, 5, -711212974087659745086477840779481845517458079744000000⟩, + ⟨2, 4, 8, 7, 2, 5, 34602796931774915658305349806478413205640052736000000⟩ +] + +def collectedFourData_11_1_22 : List CollectedFourTerm := [ + ⟨2, 5, 4, 0, 5, 6, -2908627826659443774219239867363299503056407756800000⟩, + ⟨2, 5, 5, 0, 6, 6, -5073758466089101155943607873710468085015642112000000⟩, + ⟨2, 5, 6, 0, 7, 6, -3493278626209066433573268646660888875516297216000000⟩, + ⟨2, 5, 7, 0, 8, 6, -3415612553110489242453597418838553362190827520000000⟩, + ⟨2, 5, 4, 1, 4, 6, -895081295889286406756655532357708606293304934400000⟩, + ⟨2, 5, 5, 1, 5, 6, 1663090833863032408050978779412371681134510080000000⟩, + ⟨2, 5, 6, 1, 6, 6, 1287291749589969711561366865349883492267196416000000⟩, + ⟨2, 5, 7, 1, 7, 6, 270207833679149088646076413461486382979481600000000⟩, + ⟨2, 5, 8, 1, 8, 6, 976221846840897121368363454646114226045714432000000⟩, + ⟨2, 5, 4, 2, 3, 6, -1405376897030160175547703731959009669700753817600000⟩, + ⟨2, 5, 5, 2, 4, 6, -1249312921473698612043049582388273224045559808000000⟩, + ⟨2, 5, 6, 2, 5, 6, 23127530919231124666538429589460826544144384000000⟩, + ⟨2, 5, 7, 2, 6, 6, 169473587932387055568656352954789395674693632000000⟩, + ⟨2, 5, 8, 2, 7, 6, 419167541240001415755101867610912124204744704000000⟩, + ⟨2, 5, 4, 3, 2, 6, 3749288258661466472327995406039553208294676889600000⟩, + ⟨2, 5, 5, 3, 3, 6, 373051792196854211863132837834746171746156544000000⟩, + ⟨2, 5, 6, 3, 4, 6, -374497458230541696620618433120287914350084096000000⟩, + ⟨2, 5, 7, 3, 5, 6, 406480094950281291255381138247364415584206848000000⟩, + ⟨2, 5, 8, 3, 6, 6, -22508848235426862944123008372028544311623680000000⟩, + ⟨2, 5, 4, 4, 1, 6, -48134057959139378754468735044803371875696640000000⟩, + ⟨2, 5, 5, 4, 2, 6, 770458219039770706901200175753327645955194880000000⟩, + ⟨2, 5, 6, 4, 3, 6, 472844147780794245603563610238374721238335488000000⟩, + ⟨2, 5, 7, 4, 4, 6, -210152194447702822865551621443685795472867328000000⟩, + ⟨2, 5, 8, 4, 5, 6, -306370926789831665915948775723680681988980736000000⟩, + ⟨2, 5, 4, 5, 0, 6, -15449522110820423861581441277531495156324656742400000⟩, + ⟨2, 5, 5, 5, 1, 6, 260118504093353047031709066780120627969785856000000⟩, + ⟨2, 5, 6, 5, 2, 6, -1026420062346961171989287773220333603700867072000000⟩, + ⟨2, 5, 7, 5, 3, 6, -239717267652935301139496073412172321805828096000000⟩, + ⟨2, 5, 8, 5, 4, 6, -153369990499739026437152553511719888809361408000000⟩, + ⟨2, 5, 5, 6, 0, 6, -13811986203107164564856620804140290943397920768000000⟩, + ⟨2, 5, 6, 6, 1, 6, 1922282135622062790758048861660245351364296704000000⟩, + ⟨2, 5, 7, 6, 2, 6, -1696598134527771338044248781916193919227396096000000⟩, + ⟨2, 5, 8, 6, 3, 6, 814302746967719104386951283322226164059078656000000⟩, + ⟨2, 5, 6, 7, 0, 6, 570404348696035670782818319981512732734128128000000⟩, + ⟨2, 5, 7, 7, 1, 6, 8777411309125972558275269598596810828842795008000000⟩, + ⟨2, 5, 8, 7, 2, 6, -320286952202290272282704086125046663703691264000000⟩ +] + +def collectedFourData_11_1_23 : List CollectedFourTerm := [ + ⟨2, 6, 3, 0, 4, 7, 1085417430025533741321892308754157746950399590400000⟩, + ⟨2, 6, 4, 0, 5, 7, -63941403273715059610933747369144960948643246899200000⟩, + ⟨2, 6, 5, 0, 6, 7, -55769121305256321274043342117194401526226878464000000⟩, + ⟨2, 6, 6, 0, 7, 7, -25597996798650572999232297027006345057474183168000000⟩, + ⟨2, 6, 7, 0, 8, 7, -18771657350197360681160194534576650179020062720000000⟩, + ⟨2, 6, 3, 1, 3, 7, -5210190944713078538824710410984595073904777625600000⟩, + ⟨2, 6, 4, 1, 4, 7, -19676891480801137118329686719587978337628821913600000⟩, + ⟨2, 6, 5, 1, 5, 7, 18280159584904166057178309240821614179526901760000000⟩, + ⟨2, 6, 6, 1, 6, 7, 9432997940016370313617055805818696283369504768000000⟩, + ⟨2, 6, 7, 1, 7, 7, 1485018803594971543337135433034748843891097600000000⟩, + ⟨2, 6, 8, 1, 8, 7, 4292126632450955572399489106416568512892475801600000⟩, + ⟨2, 6, 3, 2, 2, 7, 4066103741664145366093206450415524735365834342400000⟩, + ⟨2, 6, 4, 2, 3, 7, -30894901747458681388964034315205238919470147174400000⟩, + ⟨2, 6, 5, 2, 4, 7, -13732045845610680984165592000222355106903883776000000⟩, + ⟨2, 6, 6, 2, 5, 7, 169473587932387055568656352954789395674693632000000⟩, + ⟨2, 6, 7, 2, 6, 7, 931399587367777940893802975404819090035965952000000⟩, + ⟨2, 6, 8, 2, 7, 7, 1842941922512016557844902136488756954430386995200000⟩, + ⟨2, 6, 3, 3, 1, 7, 91101868981165094619263911107977550065408409600000⟩, + ⟨2, 6, 4, 3, 2, 7, 82421941487031999302451923793316494117712586342400000⟩, + ⟨2, 6, 5, 3, 3, 7, 4100465323925074657108612632264549484323667968000000⟩, + ⟨2, 6, 6, 3, 4, 7, -2744237080021127169976408221346276734463377408000000⟩, + ⟨2, 6, 7, 3, 5, 7, 2233949238514682761483496639628396505834979328000000⟩, + ⟨2, 6, 8, 3, 6, 7, -98964008324244963835619895407098417731600384000000⟩, + ⟨2, 6, 3, 4, 0, 7, -17468178287153743341191701330421848506577295769600000⟩, + ⟨2, 6, 4, 4, 1, 7, -1058148169716339594349385397277937641885532160000000⟩, + ⟨2, 6, 5, 4, 2, 7, 8468628959269452416880510309711246687322767360000000⟩, + ⟨2, 6, 6, 4, 3, 7, 3464900535085183652536872714674105163473485824000000⟩, + ⟨2, 6, 7, 4, 4, 7, -1154962667522645890541269828369927185113284608000000⟩, + ⟨2, 6, 8, 4, 5, 7, -1347012278549869380050132182051123158651292876800000⟩, + ⟨2, 6, 4, 5, 0, 7, -339632356749026647421715545364155279846875437465600000⟩, + ⟨2, 6, 5, 5, 1, 7, 2859138941177430980572798418294994087897464832000000⟩, + ⟨2, 6, 6, 5, 2, 7, -7521386147929834282440173124795161452065325056000000⟩, + ⟨2, 6, 7, 5, 3, 7, -1317447555697892171184477176517623348572717056000000⟩, + ⟨2, 6, 8, 5, 4, 7, -674317444311370510413127320101614675464447590400000⟩, + ⟨2, 6, 5, 6, 0, 7, -151816910319215631387429697579281386938507984896000000⟩, + ⟨2, 6, 6, 6, 1, 7, 14086071344144715587122146471233982493718740992000000⟩, + ⟨2, 6, 7, 6, 2, 7, -9324230528821675229629290051293936835473965056000000⟩, + ⟨2, 6, 8, 6, 3, 7, 3580221563826303439143940912923015643988282572800000⟩, + ⟨2, 6, 6, 7, 0, 7, 4179800770058480357774863042912660058007404544000000⟩, + ⟨2, 6, 7, 7, 1, 7, 48239241118437850967965434522883271425511129088000000⟩, + ⟨2, 6, 8, 7, 2, 7, -1408196468889355256152958740759642258049020723200000⟩ +] + +def collectedFourData_11_1_24 : List CollectedFourTerm := [ + ⟨2, 7, 2, 0, 3, 8, 29334723565006092389153157449310880485450606182400000⟩, + ⟨2, 7, 3, 0, 4, 8, 10738469891706291306471155315505172039708390195200000⟩, + ⟨2, 7, 4, 0, 5, 8, -316298971664793822389297109604661081702310661324800000⟩, + ⟨2, 7, 5, 0, 6, 8, -183915426899960114816370107283293378406455967744000000⟩, + ⟨2, 7, 6, 0, 7, 8, -63312811805462889597255591414046508902458064896000000⟩, + ⟨2, 7, 7, 0, 8, 8, -37143106734112321483653428712454287962010550272000000⟩, + ⟨2, 7, 2, 1, 2, 8, -28138256568423441102594602132985011638999449600000000⟩, + ⟨2, 7, 3, 1, 3, 8, -51546508322172398579270918208220146281640414412800000⟩, + ⟨2, 7, 4, 1, 4, 8, -97335688963454522878009244024673920525269362278400000⟩, + ⟨2, 7, 5, 1, 5, 8, 60284316395355751350390070191674363273501736960000000⟩, + ⟨2, 7, 6, 1, 6, 8, 23331107822040949538499711720924455273125380096000000⟩, + ⟨2, 7, 7, 1, 7, 8, 2938377304415898594528297031608790614288629760000000⟩, + ⟨2, 7, 8, 1, 8, 8, 7077288322287988898346925351503874630202739916800000⟩, + ⟨2, 7, 2, 2, 1, 8, -38992169349964060657538036240180121308555850547200000⟩, + ⟨2, 7, 3, 2, 2, 8, 40227594839146410216907644024795597799718859571200000⟩, + ⟨2, 7, 4, 2, 3, 8, -152827825979588610452737494915066782326585923993600000⟩, + ⟨2, 7, 5, 2, 4, 8, -45285545384185151284117740265091991733373239296000000⟩, + ⟨2, 7, 6, 2, 5, 8, 419167541240001415755101867610912124204744704000000⟩, + ⟨2, 7, 7, 2, 6, 8, 1842941922512016557844902136488756954430386995200000⟩, + ⟨2, 7, 8, 2, 7, 8, 3038827244340002134422919301911063676719831449600000⟩, + ⟨2, 7, 2, 3, 0, 8, 67525168443201999584035356271011484798391471308800000⟩, + ⟨2, 7, 3, 3, 1, 8, 901307322022089625667576762937925296607513804800000⟩, + ⟨2, 7, 4, 3, 2, 8, 407716659319562303681770773233108561602822117785600000⟩, + ⟨2, 7, 5, 3, 3, 8, 13522515917192416895224788758838454758647267328000000⟩, + ⟨2, 7, 6, 3, 4, 8, -6787459470504731440920758330574406224420274176000000⟩, + ⟨2, 7, 7, 3, 5, 8, 4420271127731159987752814661769370533649763532800000⟩, + ⟨2, 7, 8, 3, 6, 8, -163181769881761139826558818075270960520364032000000⟩, + ⟨2, 7, 3, 4, 0, 8, -172819692599874054072689416528674994640990817484800000⟩, + ⟨2, 7, 4, 4, 1, 8, -5234342082195845576409656660695256551957463040000000⟩, + ⟨2, 7, 5, 4, 2, 8, 27927847415351128045317354318479109980222914560000000⟩, + ⟨2, 7, 6, 4, 3, 8, 8569912607929553695291715096162037529709641728000000⟩, + ⟨2, 7, 7, 4, 4, 8, -2285301762833300922268962998440753059542650060800000⟩, + ⟨2, 7, 8, 4, 5, 8, -2221088771445621663553984476860387565058287206400000⟩, + ⟨2, 7, 4, 5, 0, 8, -1680059549584014081095973582072250037284672792166400000⟩, + ⟨2, 7, 5, 5, 1, 8, 9428869356838620363292569646459168855500521472000000⟩, + ⟨2, 7, 6, 5, 2, 8, -18603022316386901036076680209662224142415429632000000⟩, + ⟨2, 7, 7, 5, 3, 8, -2606807393986856208745410955226632030661482905600000⟩, + ⟨2, 7, 8, 5, 4, 8, -1111882146733114917370999547542492975002235699200000⟩, + ⟨2, 7, 5, 6, 0, 8, -500661857646300468086766480779474052228700962816000000⟩, + ⟨2, 7, 6, 6, 1, 8, 34839788093776611976874945024997979471032090624000000⟩, + ⟨2, 7, 7, 6, 2, 8, -18449670334614903793207576993383755486001207705600000⟩, + ⟨2, 7, 8, 6, 3, 8, 5903427935536584910921859117515312160345319014400000⟩, + ⟨2, 7, 6, 7, 0, 8, 10338111283496681995602157004990043826126061568000000⟩, + ⟨2, 7, 7, 7, 1, 8, 95450031300293197275267546812034583728015330508800000⟩, + ⟨2, 7, 8, 7, 2, 8, -2321975393132042025852498319907925420119005593600000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1104.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1104.lean new file mode 100644 index 0000000000000000000000000000000000000000..5baba29ec593692d8a59b300c7ab707718172b4e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1104.lean @@ -0,0 +1,625 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1104. -/ +namespace LaughlinFock +def collectedFourData_11_1_25 : List CollectedFourTerm := [ + ⟨3, 0, 8, 1, 8, 2, 157262999064428940425194896602146023765967267430400000⟩, + ⟨3, 0, 8, 2, 7, 2, 67525168443201999584035356271011484798391471308800000⟩, + ⟨3, 0, 8, 3, 6, 2, -3626029258046526228492163545442938123290935296000000⟩, + ⟨3, 0, 8, 4, 5, 2, -49354366457822108598786749514358312368990270259200000⟩, + ⟨3, 0, 8, 5, 4, 2, -24706909347013286412312784500615443618303941017600000⟩, + ⟨3, 0, 8, 6, 3, 2, 131178883722950797406143223870292500816113906483200000⟩, + ⟨3, 0, 8, 7, 2, 2, -51596147768599023666800422442542386287246888140800000⟩ +] + +def collectedFourData_11_1_26 : List CollectedFourTerm := [ + ⟨3, 1, 7, 0, 8, 3, -1836089570653558219044698773800901702588563456000000⟩, + ⟨3, 1, 7, 1, 7, 3, 145252360334421131702460406594311285091860480000000⟩, + ⟨3, 1, 8, 1, 8, 3, 2099103131584894824446609208862053550594090598400000⟩, + ⟨3, 1, 7, 2, 6, 3, 91101868981165094619263911107977550065408409600000⟩, + ⟨3, 1, 8, 2, 7, 3, 901307322022089625667576762937925296607513804800000⟩, + ⟨3, 1, 7, 3, 5, 3, 218506593301051416532844067825116128534226534400000⟩, + ⟨3, 1, 8, 3, 6, 3, -48399238320932721458661292089991525476335616000000⟩, + ⟨3, 1, 7, 4, 4, 3, -112968975981774330034085645290492607540389478400000⟩, + ⟨3, 1, 8, 4, 5, 3, -658768469413196976079141632545310892761494323200000⟩, + ⟨3, 1, 7, 5, 3, 3, -128861915161395713912885738451583990422621388800000⟩, + ⟨3, 1, 8, 5, 4, 3, -329781010731279881786172453885426355865754009600000⟩, + ⟨3, 1, 7, 6, 2, 3, -912019759840704365743969851790335738200771788800000⟩, + ⟨3, 1, 8, 6, 3, 3, 1750939555132390838322225587654399497744888627200000⟩, + ⟨3, 1, 7, 7, 1, 3, 4718366943389514046026345339136188036418004582400000⟩, + ⟨3, 1, 8, 7, 2, 3, -688691147969342444689637727503163550352592076800000⟩ +] + +def collectedFourData_11_1_27 : List CollectedFourTerm := [ + ⟨3, 2, 6, 0, 7, 4, -566308119237577950076145780494483468484839106150400000⟩, + ⟨3, 2, 7, 0, 8, 4, -1661152167895094724887137014174274724276169867264000000⟩, + ⟨3, 2, 6, 1, 6, 4, 208687553334807293763223270382217650636797142630400000⟩, + ⟨3, 2, 7, 1, 7, 4, 131413127724219357891317985699510119430220677120000000⟩, + ⟨3, 2, 8, 1, 8, 4, 949553271637628667530954744949369325900943641804800000⟩, + ⟨3, 2, 6, 2, 5, 4, 3749288258661466472327995406039553208294676889600000⟩, + ⟨3, 2, 7, 2, 6, 4, 82421941487031999302451923793316494117712586342400000⟩, + ⟨3, 2, 8, 2, 7, 4, 407716659319562303681770773233108561602822117785600000⟩, + ⟨3, 2, 6, 3, 4, 4, -60711146725774748456989830062813936403970680422400000⟩, + ⟨3, 2, 7, 3, 5, 4, 197687905297677164875870812563480022111615555993600000⟩, + ⟨3, 2, 8, 3, 6, 4, -21893948134749982573093221500950159953758257152000000⟩, + ⟨3, 2, 6, 4, 3, 4, 76654486708616490626156365124174217221355287347200000⟩, + ⟨3, 2, 7, 4, 4, 4, -102205612599943039364409242131689107267528530329600000⟩, + ⟨3, 2, 8, 4, 5, 4, -298001439743798276856943676914532872632821769830400000⟩, + ⟨3, 2, 6, 5, 2, 4, -166396694124059578408736590869571237777356147916800000⟩, + ⟨3, 2, 7, 5, 3, 4, -116584317644847591178361324741271327243844662067200000⟩, + ⟨3, 2, 8, 5, 4, 4, -149180206037526037969081125464992336202517656371200000⟩, + ⟨3, 2, 6, 6, 1, 4, 311628157198982654456193765509590915809990515097600000⟩, + ⟨3, 2, 7, 6, 2, 4, -825125105788429707903655996560731307280618959667200000⟩, + ⟨3, 2, 8, 6, 3, 4, 792057502082028708294905836695367581504780002918400000⟩, + ⟨3, 2, 6, 7, 0, 4, 92470326154755202757511933280326407811522310963200000⟩, + ⟨3, 2, 7, 7, 1, 4, 4268814333576397501380462034280186572970326071705600000⟩, + ⟨3, 2, 8, 7, 2, 4, -311537305081532360274491387904098418784101570969600000⟩ +] + +def collectedFourData_11_1_28 : List CollectedFourTerm := [ + ⟨3, 3, 5, 0, 6, 5, -40920379602100354319703144579942504633515114496000000⟩, + ⟨3, 3, 6, 0, 7, 5, -56347296938067656778434215783192175799284269056000000⟩, + ⟨3, 3, 7, 0, 8, 5, -82641791000379412278953126025899708391075348480000000⟩, + ⟨3, 3, 5, 1, 5, 5, 13412997226670463860418681537623794412830064640000000⟩, + ⟨3, 3, 6, 1, 6, 5, 20764278553636775789646389111355073553818976256000000⟩, + ⟨3, 3, 7, 1, 7, 5, 6537761227409087791327654654836775131178598400000000⟩, + ⟨3, 3, 8, 1, 8, 5, 31493315115872888765620969184163168723060916224000000⟩, + ⟨3, 3, 5, 2, 4, 5, -10075836153847960835049082025667662874478116864000000⟩, + ⟨3, 3, 6, 2, 5, 5, 373051792196854211863132837834746171746156544000000⟩, + ⟨3, 3, 7, 2, 6, 5, 4100465323925074657108612632264549484323667968000000⟩, + ⟨3, 3, 8, 2, 7, 5, 13522515917192416895224788758838454758647267328000000⟩, + ⟨3, 3, 5, 3, 3, 5, 3008700759006736388660400013293930922798743552000000⟩, + ⟨3, 3, 6, 3, 4, 5, -6040720406081060898494543446929526767942107136000000⟩, + ⟨3, 3, 7, 3, 5, 5, 9834910292182918328362615616857551926357655552000000⟩, + ⟨3, 3, 8, 3, 6, 5, -726144628567392963389526301799937497377013760000000⟩, + ⟨3, 3, 5, 4, 2, 5, 6213824130845400230957666399581239262618583040000000⟩, + ⟨3, 3, 6, 4, 3, 5, 7627072573179106424008152316150921884082372608000000⟩, + ⟨3, 3, 7, 4, 4, 5, -5084696657412813753235863825687553902297219072000000⟩, + ⟨3, 3, 8, 4, 5, 5, -9883651109589139440279816955150984855003594752000000⟩, + ⟨3, 3, 5, 5, 1, 5, 2097882270149746976496582742618604499420315648000000⟩, + ⟨3, 3, 6, 5, 2, 5, -16556365015469212225401841057638129573247844352000000⟩, + ⟨3, 3, 7, 5, 3, 5, -5800032651395121557353679143618285959804616704000000⟩, + ⟨3, 3, 8, 5, 4, 5, -4947778474490458954727999840181642291792838656000000⟩, + ⟨3, 3, 5, 6, 0, 5, -111395077686024108064178662982848624614696812544000000⟩, + ⟨3, 3, 6, 6, 1, 5, 31006803030820345764569467123596755202855665664000000⟩, + ⟨3, 3, 7, 6, 2, 5, -41049711073813974620220107122413046817781448704000000⟩, + ⟨3, 3, 8, 6, 3, 5, 26269738884623502268692096449243660204944392192000000⟩, + ⟨3, 3, 6, 7, 0, 5, 9200738518135324135307139592457026196993998848000000⟩, + ⟨3, 3, 7, 7, 1, 5, 212372152770247309775301757269470734806146875392000000⟩, + ⟨3, 3, 8, 7, 2, 5, -10332587767678989578689967923069722094624309248000000⟩ +] + +def collectedFourData_11_1_29 : List CollectedFourTerm := [ + ⟨3, 4, 4, 0, 5, 6, 47098574068571572835133363753081387082474271539200000⟩, + ⟨3, 4, 5, 0, 6, 6, 82157911964829389638088317787274979203537174528000000⟩, + ⟨3, 4, 6, 0, 7, 6, 56565656358870230626265886226875144019120226304000000⟩, + ⟨3, 4, 7, 0, 8, 6, 55308031968798436221098580928592855329281146880000000⟩, + ⟨3, 4, 4, 1, 4, 6, 14493794058297213599475580649494467198230043033600000⟩, + ⟨3, 4, 5, 1, 5, 6, -26929951678080969788031368508242312721617387520000000⟩, + ⟨3, 4, 6, 1, 6, 6, -20844745161348924213643408804739547171970351104000000⟩, + ⟨3, 4, 7, 1, 7, 6, -4375397756907914194539309314164146978580070400000000⟩, + ⟨3, 4, 8, 1, 8, 6, -15807679669213702567507102719955432813633732608000000⟩, + ⟨3, 4, 4, 2, 3, 6, 22756864000388412439534222054324235685513815654400000⟩, + ⟨3, 4, 5, 2, 4, 6, 20229764917855166868886116718156243824858365952000000⟩, + ⟨3, 4, 6, 2, 5, 6, -374497458230541696620618433120287914350084096000000⟩, + ⟨3, 4, 7, 2, 6, 6, -2744237080021127169976408221346276734463377408000000⟩, + ⟨3, 4, 8, 2, 7, 6, -6787459470504731440920758330574406224420274176000000⟩, + ⟨3, 4, 4, 3, 2, 6, -60711146725774748456989830062813936403970680422400000⟩, + ⟨3, 4, 5, 3, 3, 6, -6040720406081060898494543446929526767942107136000000⟩, + ⟨3, 4, 6, 3, 4, 6, 6064129660486856781288786742241888831772033024000000⟩, + ⟨3, 4, 7, 3, 5, 6, -6582015300803685614603445170947895042833907712000000⟩, + ⟨3, 4, 8, 3, 6, 6, 364479307423821311561568021960214552950865920000000⟩, + ⟨3, 4, 4, 4, 1, 6, 779420960368498780897670899278645907591004160000000⟩, + ⟨3, 4, 5, 4, 2, 6, -12475808408207563947779799597658846406608158720000000⟩, + ⟨3, 4, 6, 4, 3, 6, -7656629326386436053356014440412576814173519872000000⟩, + ⟨3, 4, 7, 4, 4, 6, 3402934058853338963273191117839616231008632832000000⟩, + ⟨3, 4, 8, 4, 5, 6, 4960976325541183395697415164768077358703837184000000⟩, + ⟨3, 4, 4, 5, 0, 6, 250169669282238769911130851227514868350808856985600000⟩, + ⟨3, 4, 5, 5, 1, 6, -4212024143947398667417028576105005842079678464000000⟩, + ⟨3, 4, 6, 5, 2, 6, 16620524939224692957779480388837060709101600768000000⟩, + ⟨3, 4, 7, 5, 3, 6, 3881672788310739595745549882334172401603969024000000⟩, + ⟨3, 4, 8, 5, 4, 6, 2483476157121232223740416506553090176924516352000000⟩, + ⟨3, 4, 5, 6, 0, 6, 223653521175398572973347430145607309647981576192000000⟩, + ⟨3, 4, 6, 6, 1, 6, -31126961901230600624640547029260803614154162176000000⟩, + ⟨3, 4, 7, 6, 2, 6, 27472525763266905463832449854402060070655361024000000⟩, + ⟨3, 4, 8, 6, 3, 6, -13185770242165434017355563806322983680463601664000000⟩, + ⟨3, 4, 6, 7, 0, 6, -9236393607961268478933538219771979758181548032000000⟩, + ⟨3, 4, 7, 7, 1, 6, -142130097527115036546488234958331352214512074752000000⟩, + ⟨3, 4, 8, 7, 2, 6, 5186314523718830917166680425943314657303330816000000⟩ +] + +def collectedFourData_11_1_30 : List CollectedFourTerm := [ + ⟨3, 5, 3, 0, 4, 7, 2603358938700760957428199949953612411511085465600000⟩, + ⟨3, 5, 4, 0, 5, 7, -153362585822654680684339299916477699116476714188800000⟩, + ⟨3, 5, 5, 0, 6, 7, -133761478706040921246738474299958881668086890496000000⟩, + ⟨3, 5, 6, 0, 7, 7, -61396447058191014404450953963369691401370468352000000⟩, + ⟨3, 5, 7, 0, 8, 7, -45023564764124452575328508337130854418565038080000000⟩, + ⟨3, 5, 3, 1, 3, 7, -12496572095712034968006618078630554810741843558400000⟩, + ⟨3, 5, 4, 1, 4, 7, -47194756510574401155851578519986710962409727590400000⟩, + ⟨3, 5, 5, 1, 5, 7, 43844714060946241782651826599459219430849904640000000⟩, + ⟨3, 5, 6, 1, 6, 7, 22624917222224617681287304527674218404749770752000000⟩, + ⟨3, 5, 7, 1, 7, 7, 3561797396589377493636688253483547399448166400000000⟩, + ⟨3, 5, 8, 1, 8, 7, 10294607333110479867411402011500598047740946022400000⟩, + ⟨3, 5, 3, 2, 2, 7, 9752494504622931024828637270116192844905027993600000⟩, + ⟨3, 5, 4, 2, 3, 7, -74101001512972057306586377054670043413921503641600000⟩, + ⟨3, 5, 5, 2, 4, 7, -32936125134804803625895914996665663086462500864000000⟩, + ⟨3, 5, 6, 2, 5, 7, 406480094950281291255381138247364415584206848000000⟩, + ⟨3, 5, 7, 2, 6, 7, 2233949238514682761483496639628396505834979328000000⟩, + ⟨3, 5, 8, 2, 7, 7, 4420271127731159987752814661769370533649763532800000⟩, + ⟨3, 5, 3, 3, 1, 7, 218506593301051416532844067825116128534226534400000⟩, + ⟨3, 5, 4, 3, 2, 7, 197687905297677164875870812563480022111615555993600000⟩, + ⟨3, 5, 5, 3, 3, 7, 9834910292182918328362615616857551926357655552000000⟩, + ⟨3, 5, 6, 3, 4, 7, -6582015300803685614603445170947895042833907712000000⟩, + ⟨3, 5, 7, 3, 5, 7, 5358096855468909652100337728079985291498094592000000⟩, + ⟨3, 5, 8, 3, 6, 7, -237363827550216192267463949641934813974757376000000⟩, + ⟨3, 5, 3, 4, 0, 7, -41897187965380704904341751576919025982210729574400000⟩, + ⟨3, 5, 4, 4, 1, 7, -2537953988850242686323840829861138658481930240000000⟩, + ⟨3, 5, 5, 4, 2, 7, 20311891342242046783938441272896378901668823040000000⟩, + ⟨3, 5, 6, 4, 3, 7, 8310516793074590559613107501334472952209473536000000⟩, + ⟨3, 5, 7, 4, 4, 7, -2770162244667494085719232673232891326614208512000000⟩, + ⟨3, 5, 8, 4, 5, 7, -3230790623861630424725444283086878488222970675200000⟩, + ⟨3, 5, 4, 5, 0, 7, -814603586929486072087490421820185720794422601318400000⟩, + ⟨3, 5, 5, 5, 1, 7, 6857605851535472205464255106468098995176603648000000⟩, + ⟨3, 5, 6, 5, 2, 7, -18039942346579592712934910506727752698150518784000000⟩, + ⟨3, 5, 7, 5, 3, 7, -3159880038332250351460308288191259197030006784000000⟩, + ⟨3, 5, 8, 5, 4, 7, -1617341216022818280116110344718521519251757465600000⟩, + ⟨3, 5, 5, 6, 0, 7, -364130793915999846300309311420672798686439276544000000⟩, + ⟨3, 5, 6, 6, 1, 7, 33785250476485460791398219370529024335190949888000000⟩, + ⟨3, 5, 7, 6, 2, 7, -22364040066265928598440208755195924243791478784000000⟩, + ⟨3, 5, 8, 6, 3, 7, 8587112711555740277718525123438263653922714419200000⟩, + ⟨3, 5, 6, 7, 0, 7, 10025195280367008726408225060707021030336495616000000⟩, + ⟨3, 5, 7, 7, 1, 7, 115701163522749205461625233519752017458581471232000000⟩, + ⟨3, 5, 8, 7, 2, 7, -3377540071973701224280964042811041707002219724800000⟩ +] + +def collectedFourData_11_1_31 : List CollectedFourTerm := [ + ⟨3, 6, 2, 0, 3, 8, -1575243251897840978792958784844377255374225408000000⟩, + ⟨3, 6, 3, 0, 4, 8, -576644337388524541610440747208557620451344384000000⟩, + ⟨3, 6, 4, 0, 5, 8, 16984916172571725497932120155633402979880534016000000⟩, + ⟨3, 6, 5, 0, 6, 8, 9876061538540448868431797938825468223925780480000000⟩, + ⟨3, 6, 6, 0, 7, 8, 3399830216031308478493768593269152037543608320000000⟩, + ⟨3, 6, 7, 0, 8, 8, 1994545069012636446635292491252412627277578240000000⟩, + ⟨3, 6, 2, 1, 2, 8, 1510994255028696383795939464557677386924032000000000⟩, + ⟨3, 6, 3, 1, 3, 8, 2767992315095849048593570795008413891586686976000000⟩, + ⟨3, 6, 4, 1, 4, 8, 5226822297088758989434707414769933295422537728000000⟩, + ⟨3, 6, 5, 1, 5, 8, -3237203254587369499045487287120348948149043200000000⟩, + ⟨3, 6, 6, 1, 6, 8, -1252855513518908682652094473412161042718392320000000⟩, + ⟨3, 6, 7, 1, 7, 8, -157787715641967768753494064866129849037619200000000⟩, + ⟨3, 6, 8, 1, 8, 8, -380042806495668829947432115388948017531846656000000⟩, + ⟨3, 6, 2, 2, 1, 8, 2093837752016871772534976482508911039400116224000000⟩, + ⟨3, 6, 3, 2, 2, 8, -2160178778232595755847192266460166448746594304000000⟩, + ⟨3, 6, 4, 2, 3, 8, 8206690649157801561964790886166525085076160512000000⟩, + ⟨3, 6, 5, 2, 4, 8, 2431785307840730787714784805261283124649656320000000⟩, + ⟨3, 6, 6, 2, 5, 8, -22508848235426862944123008372028544311623680000000⟩, + ⟨3, 6, 7, 2, 6, 8, -98964008324244963835619895407098417731600384000000⟩, + ⟨3, 6, 8, 2, 7, 8, -163181769881761139826558818075270960520364032000000⟩, + ⟨3, 6, 2, 3, 0, 8, -3626029258046526228492163545442938123290935296000000⟩, + ⟨3, 6, 3, 3, 1, 8, -48399238320932721458661292089991525476335616000000⟩, + ⟨3, 6, 4, 3, 2, 8, -21893948134749982573093221500950159953758257152000000⟩, + ⟨3, 6, 5, 3, 3, 8, -726144628567392963389526301799937497377013760000000⟩, + ⟨3, 6, 6, 3, 4, 8, 364479307423821311561568021960214552950865920000000⟩, + ⟨3, 6, 7, 3, 5, 8, -237363827550216192267463949641934813974757376000000⟩, + ⟨3, 6, 8, 3, 6, 8, 8762686352552891282116128534188973820477440000000⟩, + ⟨3, 6, 3, 4, 0, 8, 9280232484882265850622566366542355983516041216000000⟩, + ⟨3, 6, 4, 4, 1, 8, 281078566321993134585202736854246775114956800000000⟩, + ⟨3, 6, 5, 4, 2, 8, -1499695508756885992457166559156154395734835200000000⟩, + ⟨3, 6, 6, 4, 3, 8, -460195132743615938628290603966821532707061760000000⟩, + ⟨3, 6, 7, 4, 4, 8, 122718258192410201430533876405952361462235136000000⟩, + ⟨3, 6, 8, 4, 5, 8, 119270089296478254226060167009550030746943488000000⟩, + ⟨3, 6, 4, 5, 0, 8, 90217399267597110886892509894522086880274546688000000⟩, + ⟨3, 6, 5, 5, 1, 8, -506320190625709344946585607041684523439882240000000⟩, + ⟨3, 6, 6, 5, 2, 8, 998962383397094823086932602839416733895229440000000⟩, + ⟨3, 6, 7, 5, 3, 8, 139982766405671390828661385414948934545047552000000⟩, + ⟨3, 6, 8, 5, 4, 8, 59706880982386396289441218229550663874904064000000⟩, + ⟨3, 6, 5, 6, 0, 8, 26885005784775272207943489094213007101887774720000000⟩, + ⟨3, 6, 6, 6, 1, 8, -1870859323785857347935856501596184656299950080000000⟩, + ⟨3, 6, 7, 6, 2, 8, 990727546143006343961323775203928760807063552000000⟩, + ⟨3, 6, 8, 6, 3, 8, -317007760373530440860426486309067399886798848000000⟩, + ⟨3, 6, 6, 7, 0, 8, -555145508721404369764850842855651014145474560000000⟩, + ⟨3, 6, 7, 7, 1, 8, -5125564499219896975497261104076195455142199296000000⟩, + ⟨3, 6, 8, 7, 2, 8, 124687592879429473070507914758824438909632512000000⟩ +] + +def collectedFourData_11_1_32 : List CollectedFourTerm := [ + ⟨4, 0, 7, 0, 8, 3, 352057980039804708826657636447064046182445613056000000⟩, + ⟨4, 0, 7, 1, 7, 3, -27851175341706119190771003120516363989790228480000000⟩, + ⟨4, 0, 8, 1, 8, 3, -402489083437229269158596155573131514517135976038400000⟩, + ⟨4, 0, 7, 2, 6, 3, -17468178287153743341191701330421848506577295769600000⟩, + ⟨4, 0, 8, 2, 7, 3, -172819692599874054072689416528674994640990817484800000⟩, + ⟨4, 0, 7, 3, 5, 3, -41897187965380704904341751576919025982210729574400000⟩, + ⟨4, 0, 8, 3, 6, 3, 9280232484882265850622566366542355983516041216000000⟩, + ⟨4, 0, 7, 4, 4, 3, 21661050815267104234784712365722848615610082918400000⟩, + ⟨4, 0, 8, 4, 5, 3, 126314478532204795553976456349498896390556955443200000⟩, + ⟨4, 0, 7, 5, 3, 3, 24708416343562842335496413318062776018019339468800000⟩, + ⟨4, 0, 8, 5, 4, 3, 63233318433486281459200546090361232888482601369600000⟩, + ⟨4, 0, 7, 6, 2, 3, 174873731400596114335394908142171193747606129868800000⟩, + ⟨4, 0, 8, 6, 3, 3, -335731030121958601480864694751083624056914916147200000⟩, + ⟨4, 0, 7, 7, 1, 3, -904715522448621950916584539673393111616551544422400000⟩, + ⟨4, 0, 8, 7, 2, 3, 132051953401748975751488658796473723488983370956800000⟩ +] + +def collectedFourData_11_1_33 : List CollectedFourTerm := [ + ⟨4, 1, 6, 0, 7, 4, 7270368654941571087208264757467983828599439360000000⟩, + ⟨4, 1, 7, 0, 8, 4, 21326179587204725686865353562887552245537177600000000⟩, + ⟨4, 1, 6, 1, 6, 4, -2679169510203187961086622654451444518077071360000000⟩, + ⟨4, 1, 7, 1, 7, 4, -1687106103900266293113483193334562300100608000000000⟩, + ⟨4, 1, 8, 1, 8, 4, -12190540993135983766777637132314960281804472320000000⟩, + ⟨4, 1, 6, 2, 5, 4, -48134057959139378754468735044803371875696640000000⟩, + ⟨4, 1, 7, 2, 6, 4, -1058148169716339594349385397277937641885532160000000⟩, + ⟨4, 1, 8, 2, 7, 4, -5234342082195845576409656660695256551957463040000000⟩, + ⟨4, 1, 6, 3, 4, 4, 779420960368498780897670899278645907591004160000000⟩, + ⟨4, 1, 7, 3, 5, 4, -2537953988850242686323840829861138658481930240000000⟩, + ⟨4, 1, 8, 3, 6, 4, 281078566321993134585202736854246775114956800000000⟩, + ⟨4, 1, 6, 4, 3, 4, -984104515713572314229185322524206818635284480000000⟩, + ⟨4, 1, 7, 4, 4, 4, 1312134608287318082568645944378738925518192640000000⟩, + ⟨4, 1, 8, 4, 5, 4, 3825797746918484734721422063296678869713551360000000⟩, + ⟨4, 1, 6, 5, 2, 4, 2136231616940567885174528379764795337993093120000000⟩, + ⟨4, 1, 7, 5, 3, 4, 1496731090142221941224956859939324393139732480000000⟩, + ⟨4, 1, 8, 5, 4, 4, 1915203150138740258037142506153542429001646080000000⟩, + ⟨4, 1, 6, 6, 1, 4, -4000740072642681587937184165973552514560163840000000⟩, + ⟨4, 1, 7, 6, 2, 4, 10593109125127796545478075492748018378583572480000000⟩, + ⟨4, 1, 8, 6, 3, 4, -10168581096455495190955028534183678609782210560000000⟩, + ⟨4, 1, 6, 7, 0, 4, -1187151195523854068637610048474194958488698880000000⟩, + ⟨4, 1, 7, 7, 1, 4, -54803830053474742185375918366721799380575191040000000⟩, + ⟨4, 1, 8, 7, 2, 4, 3999573696310597633388164971760340519501168640000000⟩ +] + +def collectedFourData_11_1_34 : List CollectedFourTerm := [ + ⟨4, 2, 5, 0, 6, 5, -84512240525650683834280962844770687990544465920000000⟩, + ⟨4, 2, 6, 0, 7, 5, -116373219361723836980755931568467056643926917120000000⟩, + ⟨4, 2, 7, 0, 8, 5, -170678839893658584134063864279370326112573849600000000⟩, + ⟨4, 2, 5, 1, 5, 5, 27701660121747172297737274370651139208957132800000000⟩, + ⟨4, 2, 6, 1, 6, 5, 42884150160143904905754936688855982703504261120000000⟩, + ⟨4, 2, 7, 1, 7, 5, 13502339292124024403631815878058428877242368000000000⟩, + ⟨4, 2, 8, 1, 8, 5, 65042666952340475483325750771579727645224468480000000⟩, + ⟨4, 2, 5, 2, 4, 5, -20809471877121557541141848129403264271940321280000000⟩, + ⟨4, 2, 6, 2, 5, 5, 770458219039770706901200175753327645955194880000000⟩, + ⟨4, 2, 7, 2, 6, 5, 8468628959269452416880510309711246687322767360000000⟩, + ⟨4, 2, 8, 2, 7, 5, 27927847415351128045317354318479109980222914560000000⟩, + ⟨4, 2, 5, 3, 3, 5, 6213824130845400230957666399581239262618583040000000⟩, + ⟨4, 2, 6, 3, 4, 5, -12475808408207563947779799597658846406608158720000000⟩, + ⟨4, 2, 7, 3, 5, 5, 20311891342242046783938441272896378901668823040000000⟩, + ⟨4, 2, 8, 3, 6, 5, -1499695508756885992457166559156154395734835200000000⟩, + ⟨4, 2, 5, 4, 2, 5, 12833316910460533904983269371912649221917900800000000⟩, + ⟨4, 2, 6, 4, 3, 5, 15752077524178714480067955572617515974692700160000000⟩, + ⟨4, 2, 7, 4, 4, 5, -10501347032694369737588574734789067633265213440000000⟩, + ⟨4, 2, 8, 4, 5, 5, -20412555014576111610761584835536561309262807040000000⟩, + ⟨4, 2, 5, 5, 1, 5, 4332724494087861436108005928541157399157800960000000⟩, + ⟨4, 2, 6, 5, 2, 5, -34193610030586902763274063838087555455165399040000000⟩, + ⟨4, 2, 7, 5, 3, 5, -11978719632067450855893955050408236623677358080000000⟩, + ⟨4, 2, 8, 5, 4, 5, -10218571982218661081641495424467916245035909120000000⟩, + ⟨4, 2, 5, 6, 0, 5, -230062567608527265965505857711780860756104314880000000⟩, + ⟨4, 2, 6, 6, 1, 5, 64037880908066195823216562383694633811344097280000000⟩, + ⟨4, 2, 7, 6, 2, 5, -84779346856317197219173527982943324562605998080000000⟩, + ⟨4, 2, 8, 6, 3, 5, 54254494038207462799444280033676735092191395840000000⟩, + ⟨4, 2, 6, 7, 0, 5, 19002145977608675953030781442542340284570664960000000⟩, + ⟨4, 2, 7, 7, 1, 5, 438608992154807345501519748349869200382980259840000000⟩, + ⟨4, 2, 8, 7, 2, 5, -21339737098373882804695044663969840775519272960000000⟩ +] + +def collectedFourData_11_1_35 : List CollectedFourTerm := [ + ⟨4, 3, 4, 0, 5, 6, -59467119542997511726680745659541089976411855257600000⟩, + ⟨4, 3, 5, 0, 6, 6, -103733381930043439094715159236006511775196381184000000⟩, + ⟨4, 3, 6, 0, 7, 6, -71420350090082294724036179010217821072588275712000000⟩, + ⟨4, 3, 7, 0, 8, 6, -69832461254303430251946605002886872090426736640000000⟩, + ⟨4, 3, 4, 1, 4, 6, -18300005911887847376278971256406260753221078220800000⟩, + ⟨4, 3, 5, 1, 5, 6, 34002019963407288842238446658128397828945346560000000⟩, + ⟨4, 3, 6, 1, 6, 6, 26318778792507292790260933833642382511006810112000000⟩, + ⟨4, 3, 7, 1, 7, 6, 5524419934229599740579584425347410402947891200000000⟩, + ⟨4, 3, 8, 1, 8, 6, 19958930714503741501113324197112183081532391424000000⟩, + ⟨4, 3, 4, 2, 3, 6, -28733038710780598982577465877031075574713627443200000⟩, + ⟨4, 3, 5, 2, 4, 6, -25542298731705865411340490541686066104034656256000000⟩, + ⟨4, 3, 6, 2, 5, 6, 472844147780794245603563610238374721238335488000000⟩, + ⟨4, 3, 7, 2, 6, 6, 3464900535085183652536872714674105163473485824000000⟩, + ⟨4, 3, 8, 2, 7, 6, 8569912607929553695291715096162037529709641728000000⟩, + ⟨4, 3, 4, 3, 2, 6, 76654486708616490626156365124174217221355287347200000⟩, + ⟨4, 3, 5, 3, 3, 6, 7627072573179106424008152316150921884082372608000000⟩, + ⟨4, 3, 6, 3, 4, 6, -7656629326386436053356014440412576814173519872000000⟩, + ⟨4, 3, 7, 3, 5, 6, 8310516793074590559613107501334472952209473536000000⟩, + ⟨4, 3, 8, 3, 6, 6, -460195132743615938628290603966821532707061760000000⟩, + ⟨4, 3, 4, 4, 1, 6, -984104515713572314229185322524206818635284480000000⟩, + ⟨4, 3, 5, 4, 2, 6, 15752077524178714480067955572617515974692700160000000⟩, + ⟨4, 3, 6, 4, 3, 6, 9667334955528342369506484051821246540484182016000000⟩, + ⟨4, 3, 7, 4, 4, 6, -4296577772824844814039736713219382988972752896000000⟩, + ⟨4, 3, 8, 4, 5, 6, -6263777153240797515655163974383450546191204352000000⟩, + ⟨4, 3, 4, 5, 0, 6, -315866667376799375247371315874434514335738678476800000⟩, + ⟨4, 3, 5, 5, 1, 6, 5318142815139972144291632053574944694250504192000000⟩, + ⟨4, 3, 6, 5, 2, 6, -20985237089964879953094024771751809060547067904000000⟩, + ⟨4, 3, 7, 5, 3, 6, -4901037967586945285136842385417181567880527872000000⟩, + ⟨4, 3, 8, 5, 4, 6, -3135661247465691088827350117221337611376787456000000⟩, + ⟨4, 3, 5, 6, 0, 6, -282387119843289169276134035147304570900474494976000000⟩, + ⟨4, 3, 6, 6, 1, 6, 39301206055535008771617551264203089733880905728000000⟩, + ⟨4, 3, 7, 6, 2, 6, -34687079301673219267908255617482807156641103872000000⟩, + ⟨4, 3, 8, 6, 3, 6, 16648482268608355310629372285514153089975713792000000⟩, + ⟨4, 3, 6, 7, 0, 6, 11661960764059053137059622608179333258591338496000000⟩, + ⟨4, 3, 7, 7, 1, 6, 179454849057581735933734641747893581583436742656000000⟩, + ⟨4, 3, 8, 7, 2, 6, -6548291362718227604491656847633952242975899648000000⟩ +] + +def collectedFourData_11_1_36 : List CollectedFourTerm := [ + ⟨4, 4, 3, 0, 4, 7, -1345949286815450166232319209536136759006042521600000⟩, + ⟨4, 4, 4, 0, 5, 7, 79289205934541999114121077095533560057264131276800000⟩, + ⟨4, 4, 5, 0, 6, 7, 69155337818159303373182364122611610229676179456000000⟩, + ⟨4, 4, 6, 0, 7, 7, 31742263005890200698101652245181131031809359872000000⟩, + ⟨4, 4, 7, 0, 8, 7, 23277402890285059721696753012038567820399738880000000⟩, + ⟨4, 4, 3, 1, 3, 7, 6460788810111439334403064188791910927341872742400000⟩, + ⟨4, 4, 4, 1, 4, 7, 24399919627885721722107535573134750285157525094400000⟩, + ⟨4, 4, 5, 1, 5, 7, -22667931318917166053569228165384524627223511040000000⟩, + ⟨4, 4, 6, 1, 6, 7, -11697192710087556911010951838427763131151286272000000⟩, + ⟨4, 4, 7, 1, 7, 7, -1841466650815774608557514550380204917155430400000000⟩, + ⟨4, 4, 8, 1, 8, 7, -5322362272856686700815729848769164044367455846400000⟩, + ⟨4, 4, 3, 2, 2, 7, -5042087292703367152208854990739233000400722329600000⟩, + ⟨4, 4, 4, 2, 3, 7, 38310579711482249611036058076719177408223746457600000⟩, + ⟨4, 4, 5, 2, 4, 7, 17028137563611788795746216384927637458076565504000000⟩, + ⟨4, 4, 6, 2, 5, 7, -210152194447702822865551621443685795472867328000000⟩, + ⟨4, 4, 7, 2, 6, 7, -1154962667522645890541269828369927185113284608000000⟩, + ⟨4, 4, 8, 2, 7, 7, -2285301762833300922268962998440753059542650060800000⟩, + ⟨4, 4, 3, 3, 1, 7, -112968975981774330034085645290492607540389478400000⟩, + ⟨4, 4, 4, 3, 2, 7, -102205612599943039364409242131689107267528530329600000⟩, + ⟨4, 4, 5, 3, 3, 7, -5084696657412813753235863825687553902297219072000000⟩, + ⟨4, 4, 6, 3, 4, 7, 3402934058853338963273191117839616231008632832000000⟩, + ⟨4, 4, 7, 3, 5, 7, -2770162244667494085719232673232891326614208512000000⟩, + ⟨4, 4, 8, 3, 6, 7, 122718258192410201430533876405952361462235136000000⟩, + ⟨4, 4, 3, 4, 0, 7, 21661050815267104234784712365722848615610082918400000⟩, + ⟨4, 4, 4, 4, 1, 7, 1312134608287318082568645944378738925518192640000000⟩, + ⟨4, 4, 5, 4, 2, 7, -10501347032694369737588574734789067633265213440000000⟩, + ⟨4, 4, 6, 4, 3, 7, -4296577772824844814039736713219382988972752896000000⟩, + ⟨4, 4, 7, 4, 4, 7, 1432187410712582735619709799552651202115141632000000⟩, + ⟨4, 4, 8, 4, 5, 7, 1670334532589182121440640614079764763757458227200000⟩, + ⟨4, 4, 4, 5, 0, 7, 421154033186153387016323305546615599671565248102400000⟩, + ⟨4, 4, 5, 5, 1, 7, -3545415719640246448425659068306543067296432128000000⟩, + ⟨4, 4, 6, 5, 2, 7, 9326738305125264011943743128839998765084442624000000⟩, + ⟨4, 4, 7, 5, 3, 7, 1633673413524069015053101956616528445910810624000000⟩, + ⟨4, 4, 8, 5, 4, 7, 836173308214477023164115422488574895641434521600000⟩, + ⟨4, 4, 5, 6, 0, 7, 188257398967571877093830544561976309191995817984000000⟩, + ⟨4, 4, 6, 6, 1, 7, -17467139512617858018324481639994910745735200768000000⟩, + ⟨4, 4, 7, 6, 2, 7, 11562317946262528966241300505661454314975002624000000⟩, + ⟨4, 4, 8, 6, 3, 7, -4439579213648660261597669149433701528367215411200000⟩, + ⟨4, 4, 6, 7, 0, 7, -5183074925707188757922628491294151946090315776000000⟩, + ⟨4, 4, 7, 7, 1, 7, -59818066656947442878510207476617233095093911552000000⟩, + ⟨4, 4, 8, 7, 2, 7, 1746204714027004177738307680450573064641236172800000⟩ +] + +def collectedFourData_11_1_37 : List CollectedFourTerm := [ + ⟨4, 5, 2, 0, 3, 8, -21440845393581174392492549547360659013853878681600000⟩, + ⟨4, 5, 3, 0, 4, 8, -7848782764271913831620980552497256299880041676800000⟩, + ⟨4, 5, 4, 0, 5, 8, 231183952853184098759615465831748564006011614003200000⟩, + ⟨4, 5, 5, 0, 6, 8, 134424387021003314181580414730974455397242372096000000⟩, + ⟨4, 5, 6, 0, 7, 8, 46275541214685002435149667964675308699636465664000000⟩, + ⟨4, 5, 7, 0, 8, 8, 27148018189385677622534721229668732886893723648000000⟩, + ⟨4, 5, 2, 1, 2, 8, 20566343752704855680992206898047530383599206400000000⟩, + ⟨4, 5, 3, 1, 3, 8, 37675511516769740816600290286025730050233676595200000⟩, + ⟨4, 5, 4, 1, 4, 8, 71142973402098273068750451353151754229908085145600000⟩, + ⟨4, 5, 5, 1, 5, 8, -44062004014670693080370898278645336543739248640000000⟩, + ⟨4, 5, 6, 1, 6, 8, -17052783012078420006556005384492986394124222464000000⟩, + ⟨4, 5, 7, 1, 7, 8, -2147669581831152433509904912660095550976163840000000⟩, + ⟨4, 5, 8, 1, 8, 8, -5172813181201789516186316693292037522840564531200000⟩, + ⟨4, 5, 2, 2, 1, 8, 28499504102715424887250447792015982639065124044800000⟩, + ⟨4, 5, 3, 2, 2, 8, -29402480633247549138432244406319409103425555660800000⟩, + ⟨4, 5, 4, 2, 3, 8, 111702357835558054461838027815772090421133862502400000⟩, + ⟨4, 5, 5, 2, 4, 8, 33099353228765145895651940712382464300379275264000000⟩, + ⟨4, 5, 6, 2, 5, 8, -306370926789831665915948775723680681988980736000000⟩, + ⟨4, 5, 7, 2, 6, 8, -1347012278549869380050132182051123158651292876800000⟩, + ⟨4, 5, 8, 2, 7, 8, -2221088771445621663553984476860387565058287206400000⟩, + ⟨4, 5, 2, 3, 0, 8, -49354366457822108598786749514358312368990270259200000⟩, + ⟨4, 5, 3, 3, 1, 8, -658768469413196976079141632545310892761494323200000⟩, + ⟨4, 5, 4, 3, 2, 8, -298001439743798276856943676914532872632821769830400000⟩, + ⟨4, 5, 5, 3, 3, 8, -9883651109589139440279816955150984855003594752000000⟩, + ⟨4, 5, 6, 3, 4, 8, 4960976325541183395697415164768077358703837184000000⟩, + ⟨4, 5, 7, 3, 5, 8, -3230790623861630424725444283086878488222970675200000⟩, + ⟨4, 5, 8, 3, 6, 8, 119270089296478254226060167009550030746943488000000⟩, + ⟨4, 5, 3, 4, 0, 8, 126314478532204795553976456349498896390556955443200000⟩, + ⟨4, 5, 4, 4, 1, 8, 3825797746918484734721422063296678869713551360000000⟩, + ⟨4, 5, 5, 4, 2, 8, -20412555014576111610761584835536561309262807040000000⟩, + ⟨4, 5, 6, 4, 3, 8, -6263777153240797515655163974383450546191204352000000⟩, + ⟨4, 5, 7, 4, 4, 8, 1670334532589182121440640614079764763757458227200000⟩, + ⟨4, 5, 8, 4, 5, 8, 1623401047173796223278586412583235791227558297600000⟩, + ⟨4, 5, 4, 5, 0, 8, 1227961019466078263308121754121984991967594518937600000⟩, + ⟨4, 5, 5, 5, 1, 8, -6891591450257119122238104536679947847962984448000000⟩, + ⟨4, 5, 6, 5, 2, 8, 13597009852678631757981636206770393190800293888000000⟩, + ⟨4, 5, 7, 5, 3, 8, 1905324049891206928569639684363461345914807910400000⟩, + ⟨4, 5, 8, 5, 4, 8, 812678297484508893321146254080524901262609612800000⟩, + ⟨4, 5, 5, 6, 0, 8, 365935389180315449304213411528774045017460178944000000⟩, + ⟨4, 5, 6, 6, 1, 8, -25464515062105354317837519589021895401213526016000000⟩, + ⟨4, 5, 7, 6, 2, 8, 13484924387660138121539172681312924524274411110400000⟩, + ⟨4, 5, 8, 6, 3, 8, -4314834785386590059782863456402372461382441369600000⟩, + ⟨4, 5, 6, 7, 0, 8, -7556159348149063138364260140332150765924646912000000⟩, + ⟨4, 5, 7, 7, 1, 8, -69764740049004967617033539446770503789229323059200000⟩, + ⟨4, 5, 8, 7, 2, 8, 1697139408916521014280838336284517475362956902400000⟩ +] + +def collectedFourData_11_1_38 : List CollectedFourTerm := [ + ⟨5, 0, 6, 0, 7, 4, 2333560186919753704297025102952715332114026437017600000⟩, + ⟨5, 0, 7, 0, 8, 4, 6845034411009745899386302250072348326705407983616000000⟩, + ⟨5, 0, 6, 1, 6, 4, -859929337801880833785693247565278042287995722137600000⟩, + ⟨5, 0, 7, 1, 7, 4, -541508116303712050969628363380494998791551713280000000⟩, + ⟨5, 0, 8, 1, 8, 4, -3912781107634760755337144664967620840175877436211200000⟩, + ⟨5, 0, 6, 2, 5, 4, -15449522110820423861581441277531495156324656742400000⟩, + ⟨5, 0, 7, 2, 6, 4, -339632356749026647421715545364155279846875437465600000⟩, + ⟨5, 0, 8, 2, 7, 4, -1680059549584014081095973582072250037284672792166400000⟩, + ⟨5, 0, 6, 3, 4, 4, 250169669282238769911130851227514868350808856985600000⟩, + ⟨5, 0, 7, 3, 5, 4, -814603586929486072087490421820185720794422601318400000⟩, + ⟨5, 0, 8, 3, 6, 4, 90217399267597110886892509894522086880274546688000000⟩, + ⟨5, 0, 6, 4, 3, 4, -315866667376799375247371315874434514335738678476800000⟩, + ⟨5, 0, 7, 4, 4, 4, 421154033186153387016323305546615599671565248102400000⟩, + ⟨5, 0, 8, 4, 5, 4, 1227961019466078263308121754121984991967594518937600000⟩, + ⟨5, 0, 6, 5, 2, 4, 685663311989477354756192275981896270477786297139200000⟩, + ⟨5, 0, 7, 5, 3, 4, 480403711042484905553988300305684866082114686156800000⟩, + ⟨5, 0, 8, 5, 4, 4, 614720110236690227627064612542113743829228899532800000⟩, + ⟨5, 0, 6, 6, 1, 4, -1284112016161364011139712719806739201352180065894400000⟩, + ⟨5, 0, 7, 6, 2, 4, 3400055606986717661959132434444733129724785380556800000⟩, + ⟨5, 0, 8, 6, 3, 4, -3263795431889837152707179176801980289647105382809600000⟩, + ⟨5, 0, 6, 7, 0, 4, -381038279791455448542284757221599682859599973580800000⟩, + ⟨5, 0, 7, 7, 1, 4, -17590309649096152702620078907826648760222237484646400000⟩, + ⟨5, 0, 8, 7, 2, 4, 1283737645960801123212695505208287319101205276262400000⟩ +] + +def collectedFourData_11_1_39 : List CollectedFourTerm := [ + ⟨5, 1, 5, 0, 6, 5, -28532627778969987071522002590556110832590127104000000⟩, + ⟨5, 1, 6, 0, 7, 5, -39289382589267527091684688975407432790173548544000000⟩, + ⟨5, 1, 7, 0, 8, 5, -57623792460620944844686166282075837117780459520000000⟩, + ⟨5, 1, 5, 1, 5, 5, 9352505059588975540544711681737672011137679360000000⟩, + ⟨5, 1, 6, 1, 6, 5, 14478346409067958796308118990952626741883961344000000⟩, + ⟨5, 1, 7, 1, 7, 5, 4558596704705808468874696753296442729798041600000000⟩, + ⟨5, 1, 8, 1, 8, 5, 21959401317012407670786715409119271866834354176000000⟩, + ⟨5, 1, 5, 2, 4, 5, -7025596666871492008520577424158650769170497536000000⟩, + ⟨5, 1, 6, 2, 5, 5, 260118504093353047031709066780120627969785856000000⟩, + ⟨5, 1, 7, 2, 6, 5, 2859138941177430980572798418294994087897464832000000⟩, + ⟨5, 1, 8, 2, 7, 5, 9428869356838620363292569646459168855500521472000000⟩, + ⟨5, 1, 5, 3, 3, 5, 2097882270149746976496582742618604499420315648000000⟩, + ⟨5, 1, 6, 3, 4, 5, -4212024143947398667417028576105005842079678464000000⟩, + ⟨5, 1, 7, 3, 5, 5, 6857605851535472205464255106468098995176603648000000⟩, + ⟨5, 1, 8, 3, 6, 5, -506320190625709344946585607041684523439882240000000⟩, + ⟨5, 1, 5, 4, 2, 5, 4332724494087861436108005928541157399157800960000000⟩, + ⟨5, 1, 6, 4, 3, 5, 5318142815139972144291632053574944694250504192000000⟩, + ⟨5, 1, 7, 4, 4, 5, -3545415719640246448425659068306543067296432128000000⟩, + ⟨5, 1, 8, 4, 5, 5, -6891591450257119122238104536679947847962984448000000⟩, + ⟨5, 1, 5, 5, 1, 5, 1462794199866388907212197970116917819344945152000000⟩, + ⟨5, 1, 6, 5, 2, 5, -11544286855415598629931030742562708519122894848000000⟩, + ⟨5, 1, 7, 5, 3, 5, -4044199353899325530806948845372599140085661696000000⟩, + ⟨5, 1, 8, 5, 4, 5, -3449946528311044910912033772970179658141138944000000⟩, + ⟨5, 1, 5, 6, 0, 5, -77672649152590733277211819623090742954196729856000000⟩, + ⟨5, 1, 6, 6, 1, 5, 21620170147415381454501549606889353503085428736000000⟩, + ⟨5, 1, 7, 6, 2, 5, -28622806970326308346920570315487461755056029696000000⟩, + ⟨5, 1, 8, 6, 3, 5, 18317148783419987688036315037325931543168811008000000⟩, + ⟨5, 1, 6, 7, 0, 5, 6415415741062980203456150576639671998665981952000000⟩, + ⟨5, 1, 7, 7, 1, 5, 148081118614573982794000943202630103879341047808000000⟩, + ⟨5, 1, 8, 7, 2, 5, -7204622333307747847733167848494508176207511552000000⟩ +] + +def collectedFourData_11_1_40 : List CollectedFourTerm := [ + ⟨5, 2, 4, 0, 5, 6, 129087448444459569928292150459004222321956644454400000⟩, + ⟨5, 2, 5, 0, 6, 6, 225177841045114511403038873158276554497401552896000000⟩, + ⟨5, 2, 6, 0, 7, 6, 155034762587964977833784994155273771441851465728000000⟩, + ⟨5, 2, 7, 0, 8, 6, 151587874294074612482441359828996610702085980160000000⟩, + ⟨5, 2, 4, 1, 4, 6, 39724491245554168116938682966530693234777338675200000⟩, + ⟨5, 2, 5, 1, 5, 6, -73809426667457834109470234506204375188913520640000000⟩, + ⟨5, 2, 6, 1, 6, 6, -57131134425342805252690597131451003905484259328000000⟩, + ⟨5, 2, 7, 1, 7, 6, -11992060132150497696204216276534959163624652800000000⟩, + ⟨5, 2, 8, 1, 8, 6, -43325579907265395767142115268292996503967891456000000⟩, + ⟨5, 2, 4, 2, 3, 6, 62371856611429060434549305544657041306399067340800000⟩, + ⟨5, 2, 5, 2, 4, 6, 55445600796218876742921518749757792996466622464000000⟩, + ⟨5, 2, 6, 2, 5, 6, -1026420062346961171989287773220333603700867072000000⟩, + ⟨5, 2, 7, 2, 6, 6, -7521386147929834282440173124795161452065325056000000⟩, + ⟨5, 2, 8, 2, 7, 6, -18603022316386901036076680209662224142415429632000000⟩, + ⟨5, 2, 4, 3, 2, 6, -166396694124059578408736590869571237777356147916800000⟩, + ⟨5, 2, 5, 3, 3, 6, -16556365015469212225401841057638129573247844352000000⟩, + ⟨5, 2, 6, 3, 4, 6, 16620524939224692957779480388837060709101600768000000⟩, + ⟨5, 2, 7, 3, 5, 6, -18039942346579592712934910506727752698150518784000000⟩, + ⟨5, 2, 8, 3, 6, 6, 998962383397094823086932602839416733895229440000000⟩, + ⟨5, 2, 4, 4, 1, 6, 2136231616940567885174528379764795337993093120000000⟩, + ⟨5, 2, 5, 4, 2, 6, -34193610030586902763274063838087555455165399040000000⟩, + ⟨5, 2, 6, 4, 3, 6, -20985237089964879953094024771751809060547067904000000⟩, + ⟨5, 2, 7, 4, 4, 6, 9326738305125264011943743128839998765084442624000000⟩, + ⟨5, 2, 8, 4, 5, 6, 13597009852678631757981636206770393190800293888000000⟩, + ⟨5, 2, 4, 5, 0, 6, 685663311989477354756192275981896270477786297139200000⟩, + ⟨5, 2, 5, 5, 1, 6, -11544286855415598629931030742562708519122894848000000⟩, + ⟨5, 2, 6, 5, 2, 6, 45553420642594240273399090777609530657604632576000000⟩, + ⟨5, 2, 7, 5, 3, 6, 10638862127965927677800459346479532072939552768000000⟩, + ⟨5, 2, 8, 5, 4, 6, 6806694400741005412019048853062281956125835264000000⟩, + ⟨5, 2, 5, 6, 0, 6, 612988035309042611189835716026938240485654790144000000⟩, + ⟨5, 2, 6, 6, 1, 6, -85312563471831349587711942072370205558027845632000000⟩, + ⟨5, 2, 7, 6, 2, 6, 75296509995007573592672104273931500898136096768000000⟩, + ⟨5, 2, 8, 6, 3, 6, -36139468550743796238259762846169524376067637248000000⟩, + ⟨5, 2, 6, 7, 0, 6, -25315044186784588535367236077051282664428929024000000⟩, + ⟨5, 2, 7, 7, 1, 6, -389549195485737463301178015217524945353718104064000000⟩, + ⟨5, 2, 8, 7, 2, 6, 14214615239149022880624139815981950353237082112000000⟩ +] + +def collectedFourData_11_1_41 : List CollectedFourTerm := [ + ⟨5, 3, 3, 0, 4, 7, -1535302956425271403941765039302245699101602611200000⟩, + ⟨5, 3, 4, 0, 5, 7, 90443936838019900210416374205141384990658501017600000⟩, + ⟨5, 3, 5, 0, 6, 7, 78884394564389303365681331263549462159967649792000000⟩, + ⟨5, 3, 6, 0, 7, 7, 36207894839691614822167635934953733856170082304000000⟩, + ⟨5, 3, 7, 0, 8, 7, 26552163462201088883781018342113200547467100160000000⟩, + ⟨5, 3, 3, 1, 3, 7, 7369719095786024708829054128379628577962642636800000⟩, + ⟨5, 3, 4, 1, 4, 7, 27832600461393504534643545537303201826409860300800000⟩, + ⟨5, 3, 5, 1, 5, 7, -25856948928827228810882810168141459515276001280000000⟩, + ⟨5, 3, 6, 1, 6, 7, -13342801787253348841903564022725803392687407104000000⟩, + ⟨5, 3, 7, 1, 7, 7, -2100531736857077036895202751035061297794252800000000⟩, + ⟨5, 3, 8, 1, 8, 7, -6071134041028415738702216487625044303392066764800000⟩, + ⟨5, 3, 3, 2, 2, 7, -5751428826384301651285262307940938704305206067200000⟩, + ⟨5, 3, 4, 2, 3, 7, 43700269296602106245158455029683062479072211763200000⟩, + ⟨5, 3, 5, 2, 4, 7, 19423725841621581629447979787592493258063740928000000⟩, + ⟨5, 3, 6, 2, 5, 7, -239717267652935301139496073412172321805828096000000⟩, + ⟨5, 3, 7, 2, 6, 7, -1317447555697892171184477176517623348572717056000000⟩, + ⟨5, 3, 8, 2, 7, 7, -2606807393986856208745410955226632030661482905600000⟩, + ⟨5, 3, 3, 3, 1, 7, -128861915161395713912885738451583990422621388800000⟩, + ⟨5, 3, 4, 3, 2, 7, -116584317644847591178361324741271327243844662067200000⟩, + ⟨5, 3, 5, 3, 3, 7, -5800032651395121557353679143618285959804616704000000⟩, + ⟨5, 3, 6, 3, 4, 7, 3881672788310739595745549882334172401603969024000000⟩, + ⟨5, 3, 7, 3, 5, 7, -3159880038332250351460308288191259197030006784000000⟩, + ⟨5, 3, 8, 3, 6, 7, 139982766405671390828661385414948934545047552000000⟩, + ⟨5, 3, 3, 4, 0, 7, 24708416343562842335496413318062776018019339468800000⟩, + ⟨5, 3, 4, 4, 1, 7, 1496731090142221941224956859939324393139732480000000⟩, + ⟨5, 3, 5, 4, 2, 7, -11978719632067450855893955050408236623677358080000000⟩, + ⟨5, 3, 6, 4, 3, 7, -4901037967586945285136842385417181567880527872000000⟩, + ⟨5, 3, 7, 4, 4, 7, 1633673413524069015053101956616528445910810624000000⟩, + ⟨5, 3, 8, 4, 5, 7, 1905324049891206928569639684363461345914807910400000⟩, + ⟨5, 3, 4, 5, 0, 7, 480403711042484905553988300305684866082114686156800000⟩, + ⟨5, 3, 5, 5, 1, 7, -4044199353899325530806948845372599140085661696000000⟩, + ⟨5, 3, 6, 5, 2, 7, 10638862127965927677800459346479532072939552768000000⟩, + ⟨5, 3, 7, 5, 3, 7, 1863505294134293571172588627497978474704928768000000⟩, + ⟨5, 3, 8, 5, 4, 7, 953809600971698167470623713965640227824546611200000⟩, + ⟨5, 3, 5, 6, 0, 7, 214742222485738855975660868043909269528707596288000000⟩, + ⟨5, 3, 6, 6, 1, 7, -19924488386531559325340345128352295857135026176000000⟩, + ⟨5, 3, 7, 6, 2, 7, 13188952288110875913020012130422559643709472768000000⟩, + ⟨5, 3, 8, 6, 3, 7, -5064157438001272289782918662735658858387498598400000⟩, + ⟨5, 3, 6, 7, 0, 7, -5912251178229604287471556124231298209946796032000000⟩, + ⟨5, 3, 7, 7, 1, 7, -68233517774914386160705723125975909141854552064000000⟩, + ⟨5, 3, 8, 7, 2, 7, 1991867959834213284950117970716236316220692889600000⟩ +] + +def collectedFourData_11_1_42 : List CollectedFourTerm := [ + ⟨5, 4, 2, 0, 3, 8, -10733336510666122824875037160044071881177615564800000⟩, + ⟨5, 4, 3, 0, 4, 8, -3929118701320752836464780407495083558238053990400000⟩, + ⟨5, 4, 4, 0, 5, 8, 115731218442629830875789891652940210130103409049600000⟩, + ⟨5, 4, 5, 0, 6, 8, 67293157273005252044057749165619716154078527488000000⟩, + ⟨5, 4, 6, 0, 7, 8, 23165642350049765171761208951267726659569057792000000⟩, + ⟨5, 4, 7, 0, 8, 8, 13590360336798821169999773119732738825119596544000000⟩, + ⟨5, 4, 2, 1, 2, 8, 10295558978187611359101133146760068264571699200000000⟩, + ⟨5, 4, 3, 1, 3, 8, 18860447706135159168463165119130665326692899225600000⟩, + ⟨5, 4, 4, 1, 4, 8, 35614336089690403524679386755348879870469655756800000⟩, + ⟨5, 4, 5, 1, 5, 8, -22057540537341206624724619436326276447516753920000000⟩, + ⟨5, 4, 6, 1, 6, 8, -8536662391437404403479022153311505866337288192000000⟩, + ⟨5, 4, 7, 1, 7, 8, -1075128331572989844177144015381171069800939520000000⟩, + ⟨5, 4, 8, 1, 8, 8, -2589522174217525642123543104680699131711822233600000⟩, + ⟨5, 4, 2, 2, 1, 8, 14266917292968834350310907211040083302116910694400000⟩, + ⟨5, 4, 3, 2, 2, 8, -14718949420691586720290814277215941227616560742400000⟩, + ⟨5, 4, 4, 2, 3, 8, 55918457209845753442040406654028114016387412787200000⟩, + ⟨5, 4, 5, 2, 4, 8, 16569612343555119769150636571444124089258606592000000⟩, + ⟨5, 4, 6, 2, 5, 8, -153369990499739026437152553511719888809361408000000⟩, + ⟨5, 4, 7, 2, 6, 8, -674317444311370510413127320101614675464447590400000⟩, + ⟨5, 4, 8, 2, 7, 8, -1111882146733114917370999547542492975002235699200000⟩, + ⟨5, 4, 2, 3, 0, 8, -24706909347013286412312784500615443618303941017600000⟩, + ⟨5, 4, 3, 3, 1, 8, -329781010731279881786172453885426355865754009600000⟩, + ⟨5, 4, 4, 3, 2, 8, -149180206037526037969081125464992336202517656371200000⟩, + ⟨5, 4, 5, 3, 3, 8, -4947778474490458954727999840181642291792838656000000⟩, + ⟨5, 4, 6, 3, 4, 8, 2483476157121232223740416506553090176924516352000000⟩, + ⟨5, 4, 7, 3, 5, 8, -1617341216022818280116110344718521519251757465600000⟩, + ⟨5, 4, 8, 3, 6, 8, 59706880982386396289441218229550663874904064000000⟩, + ⟨5, 4, 3, 4, 0, 8, 63233318433486281459200546090361232888482601369600000⟩, + ⟨5, 4, 4, 4, 1, 8, 1915203150138740258037142506153542429001646080000000⟩, + ⟨5, 4, 5, 4, 2, 8, -10218571982218661081641495424467916245035909120000000⟩, + ⟨5, 4, 6, 4, 3, 8, -3135661247465691088827350117221337611376787456000000⟩, + ⟨5, 4, 7, 4, 4, 8, 836173308214477023164115422488574895641434521600000⟩, + ⟨5, 4, 8, 4, 5, 8, 812678297484508893321146254080524901262609612800000⟩, + ⟨5, 4, 4, 5, 0, 8, 614720110236690227627064612542113743829228899532800000⟩, + ⟨5, 4, 5, 5, 1, 8, -3449946528311044910912033772970179658141138944000000⟩, + ⟨5, 4, 6, 5, 2, 8, 6806694400741005412019048853062281956125835264000000⟩, + ⟨5, 4, 7, 5, 3, 8, 953809600971698167470623713965640227824546611200000⟩, + ⟨5, 4, 8, 5, 4, 8, 406828624603945235331691277116309080080016998400000⟩, + ⟨5, 4, 5, 6, 0, 8, 183188097350384754453745706263590935953913413632000000⟩, + ⟨5, 4, 6, 6, 1, 8, -12747594799798677696190594601765110086786613248000000⟩, + ⟨5, 4, 7, 6, 2, 8, 6750584159194366112287933390523746751790396211200000⟩, + ⟨5, 4, 8, 6, 3, 8, -2160016216214444552193352767213740501519617228800000⟩, + ⟨5, 4, 6, 7, 0, 8, -3782630746275495163704386128759945330358747136000000⟩, + ⟨5, 4, 7, 7, 1, 8, -34924389303664754665052164296144544347977259417600000⟩, + ⟨5, 4, 8, 7, 2, 8, 849591890946025851553969289642535557002375987200000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1105.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1105.lean new file mode 100644 index 0000000000000000000000000000000000000000..c00dc567bd8af11777769635d0ccc89d038af4fd --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1105.lean @@ -0,0 +1,616 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PartsTrace +import OAI.Analysis.LaughlinFock.Sparse1103 +import OAI.Analysis.LaughlinFock.Sparse1104 + +namespace OAI + +/-! Sparse1105. -/ +namespace LaughlinFock +def collectedFourData_11_1_43 : List CollectedFourTerm := [ + ⟨6, 0, 5, 0, 6, 5, 1515048929698946937022109148483524419512919130112000000⟩, + ⟨6, 0, 6, 0, 7, 5, 2086219940957398945321692347255704225167999762432000000⟩, + ⟨6, 0, 7, 0, 8, 5, 3059755511092627380017143723537134191085417922560000000⟩, + ⟨6, 0, 5, 1, 5, 5, -496607003403237715095269296323509143201728430080000000⟩, + ⟨6, 0, 6, 1, 6, 5, -768783141910137073035101420898937777397623160832000000⟩, + ⟨6, 0, 7, 1, 7, 5, -242056115962937168823920318468533213708733644800000000⟩, + ⟨6, 0, 8, 1, 8, 5, -1166018346431122439798234464906125966743571529728000000⟩, + ⟨6, 0, 5, 2, 4, 5, 373050908352907068897657739953608563305436151808000000⟩, + ⟨6, 0, 6, 2, 5, 5, -13811986203107164564856620804140290943397920768000000⟩, + ⟨6, 0, 7, 2, 6, 5, -151816910319215631387429697579281386938507984896000000⟩, + ⟨6, 0, 8, 2, 7, 5, -500661857646300468086766480779474052228700962816000000⟩, + ⟨6, 0, 5, 3, 3, 5, -111395077686024108064178662982848624614696812544000000⟩, + ⟨6, 0, 6, 3, 4, 5, 223653521175398572973347430145607309647981576192000000⟩, + ⟨6, 0, 7, 3, 5, 5, -364130793915999846300309311420672798686439276544000000⟩, + ⟨6, 0, 8, 3, 6, 5, 26885005784775272207943489094213007101887774720000000⟩, + ⟨6, 0, 5, 4, 2, 5, -230062567608527265965505857711780860756104314880000000⟩, + ⟨6, 0, 6, 4, 3, 5, -282387119843289169276134035147304570900474494976000000⟩, + ⟨6, 0, 7, 4, 4, 5, 188257398967571877093830544561976309191995817984000000⟩, + ⟨6, 0, 8, 4, 5, 5, 365935389180315449304213411528774045017460178944000000⟩, + ⟨6, 0, 5, 5, 1, 5, -77672649152590733277211819623090742954196729856000000⟩, + ⟨6, 0, 6, 5, 2, 5, 612988035309042611189835716026938240485654790144000000⟩, + ⟨6, 0, 7, 5, 3, 5, 214742222485738855975660868043909269528707596288000000⟩, + ⟨6, 0, 8, 5, 4, 5, 183188097350384754453745706263590935953913413632000000⟩, + ⟨6, 0, 5, 6, 0, 5, 4124326188149029908159917846435366329245675552768000000⟩, + ⟨6, 0, 6, 6, 1, 5, -1148005570867656623289125879279645382684765585408000000⟩, + ⟨6, 0, 7, 6, 2, 5, 1519837338548068481139332379398293455771468300288000000⟩, + ⟨6, 0, 8, 6, 3, 5, -972619026695852074550235228550834828806532890624000000⟩, + ⟨6, 0, 6, 7, 0, 5, -340651019855771574337780719757421055264744800256000000⟩, + ⟨6, 0, 7, 7, 1, 5, -7862932990384807919911545782948168042996274561024000000⟩, + ⟨6, 0, 8, 7, 2, 5, 382556960386530221348371501771159694689022509056000000⟩ +] + +def collectedFourData_11_1_44 : List CollectedFourTerm := [ + ⟨6, 1, 4, 0, 5, 6, -241755305825208008444395200505493963320601660620800000⟩, + ⟨6, 1, 5, 0, 6, 6, -421713640504281035344257659885501592441949519872000000⟩, + ⟨6, 1, 6, 0, 7, 6, -290349502563125852346919611875182966031983312896000000⟩, + ⟨6, 1, 7, 0, 8, 6, -283894161291171537075818190237019795539225477120000000⟩, + ⟨6, 1, 4, 1, 4, 6, -74396129488543877616471346114474758685187270246400000⟩, + ⟨6, 1, 5, 1, 5, 6, 138230484309649305618030547393629590013849108480000000⟩, + ⟨6, 1, 6, 1, 6, 6, 106995335654824614731320500655752994519668228096000000⟩, + ⟨6, 1, 7, 1, 7, 6, 22458761093025223015616045146968251988285849600000000⟩, + ⟨6, 1, 8, 1, 8, 6, 81140257606393062941300351460630747025917345792000000⟩, + ⟨6, 1, 4, 2, 3, 6, -116810173658903342955771799707699726071570733465600000⟩, + ⟨6, 1, 5, 2, 4, 6, -103838663934236296077787712599493017193202843648000000⟩, + ⟨6, 1, 6, 2, 5, 6, 1922282135622062790758048861660245351364296704000000⟩, + ⟨6, 1, 7, 2, 6, 6, 14086071344144715587122146471233982493718740992000000⟩, + ⟨6, 1, 8, 2, 7, 6, 34839788093776611976874945024997979471032090624000000⟩, + ⟨6, 1, 4, 3, 2, 6, 311628157198982654456193765509590915809990515097600000⟩, + ⟨6, 1, 5, 3, 3, 6, 31006803030820345764569467123596755202855665664000000⟩, + ⟨6, 1, 6, 3, 4, 6, -31126961901230600624640547029260803614154162176000000⟩, + ⟨6, 1, 7, 3, 5, 6, 33785250476485460791398219370529024335190949888000000⟩, + ⟨6, 1, 8, 3, 6, 6, -1870859323785857347935856501596184656299950080000000⟩, + ⟨6, 1, 4, 4, 1, 6, -4000740072642681587937184165973552514560163840000000⟩, + ⟨6, 1, 5, 4, 2, 6, 64037880908066195823216562383694633811344097280000000⟩, + ⟨6, 1, 6, 4, 3, 6, 39301206055535008771617551264203089733880905728000000⟩, + ⟨6, 1, 7, 4, 4, 6, -17467139512617858018324481639994910745735200768000000⟩, + ⟨6, 1, 8, 4, 5, 6, -25464515062105354317837519589021895401213526016000000⟩, + ⟨6, 1, 4, 5, 0, 6, -1284112016161364011139712719806739201352180065894400000⟩, + ⟨6, 1, 5, 5, 1, 6, 21620170147415381454501549606889353503085428736000000⟩, + ⟨6, 1, 6, 5, 2, 6, -85312563471831349587711942072370205558027845632000000⟩, + ⟨6, 1, 7, 5, 3, 6, -19924488386531559325340345128352295857135026176000000⟩, + ⟨6, 1, 8, 5, 4, 6, -12747594799798677696190594601765110086786613248000000⟩, + ⟨6, 1, 5, 6, 0, 6, -1148005570867656623289125879279645382684765585408000000⟩, + ⟨6, 1, 6, 6, 1, 6, 159773588535518627493653853992745482848120602624000000⟩, + ⟨6, 1, 7, 6, 2, 6, -141015497794473402123840957441881312880205234176000000⟩, + ⟨6, 1, 8, 6, 3, 6, 67682089754873772089267873532475876042956865536000000⟩, + ⟨6, 1, 6, 7, 0, 6, 47410079934982513788306533530747803061419245568000000⟩, + ⟨6, 1, 7, 7, 1, 6, 729548736329215229335019366208313567848167374848000000⟩, + ⟨6, 1, 8, 7, 2, 6, -26621168020116885493381413212354138910945705984000000⟩ +] + +def collectedFourData_11_1_45 : List CollectedFourTerm := [ + ⟨6, 2, 3, 0, 4, 7, -10866101375631095010260707340823075604315452211200000⟩, + ⟨6, 2, 4, 0, 5, 7, 640116650840914944744599695443225536779672721817600000⟩, + ⟨6, 2, 5, 0, 6, 7, 558304030292315769074430252696856859109639585792000000⟩, + ⟨6, 2, 6, 0, 7, 7, 256261250771211633275298683883840090362351714304000000⟩, + ⟨6, 2, 7, 0, 8, 7, 187922845269820960390663166417507820511596380160000000⟩, + ⟨6, 2, 3, 1, 3, 7, 52159161466861314971198197589383300531069177036800000⟩, + ⟨6, 2, 4, 1, 4, 7, 196985133712701889010150009414477257142268906700800000⟩, + ⟨6, 2, 5, 1, 5, 7, -183002466809115427498859936927871998901910241280000000⟩, + ⟨6, 2, 6, 1, 6, 7, -94433633602075031121036625048298436713307439104000000⟩, + ⟨6, 2, 7, 1, 7, 7, -14866506118481776790376388504778743630056652800000000⟩, + ⟨6, 2, 8, 1, 8, 7, -42968430223348304701657625589860920948954025164800000⟩, + ⟨6, 2, 3, 2, 2, 7, -40705717670036073833790582586501631340631503667200000⟩, + ⟨6, 2, 4, 2, 3, 7, 309288505133136664525205488625059236736320877363200000⟩, + ⟨6, 2, 5, 2, 4, 7, 137471352611049673316765404820752749934493564928000000⟩, + ⟨6, 2, 6, 2, 5, 7, -1696598134527771338044248781916193919227396096000000⟩, + ⟨6, 2, 7, 2, 6, 7, -9324230528821675229629290051293936835473965056000000⟩, + ⟨6, 2, 8, 2, 7, 7, -18449670334614903793207576993383755486001207705600000⟩, + ⟨6, 2, 3, 3, 1, 7, -912019759840704365743969851790335738200771788800000⟩, + ⟨6, 2, 4, 3, 2, 7, -825125105788429707903655996560731307280618959667200000⟩, + ⟨6, 2, 5, 3, 3, 7, -41049711073813974620220107122413046817781448704000000⟩, + ⟨6, 2, 6, 3, 4, 7, 27472525763266905463832449854402060070655361024000000⟩, + ⟨6, 2, 7, 3, 5, 7, -22364040066265928598440208755195924243791478784000000⟩, + ⟨6, 2, 8, 3, 6, 7, 990727546143006343961323775203928760807063552000000⟩, + ⟨6, 2, 3, 4, 0, 7, 174873731400596114335394908142171193747606129868800000⟩, + ⟨6, 2, 4, 4, 1, 7, 10593109125127796545478075492748018378583572480000000⟩, + ⟨6, 2, 5, 4, 2, 7, -84779346856317197219173527982943324562605998080000000⟩, + ⟨6, 2, 6, 4, 3, 7, -34687079301673219267908255617482807156641103872000000⟩, + ⟨6, 2, 7, 4, 4, 7, 11562317946262528966241300505661454314975002624000000⟩, + ⟨6, 2, 8, 4, 5, 7, 13484924387660138121539172681312924524274411110400000⟩, + ⟨6, 2, 4, 5, 0, 7, 3400055606986717661959132434444733129724785380556800000⟩, + ⟨6, 2, 5, 5, 1, 7, -28622806970326308346920570315487461755056029696000000⟩, + ⟨6, 2, 6, 5, 2, 7, 75296509995007573592672104273931500898136096768000000⟩, + ⟨6, 2, 7, 5, 3, 7, 13188952288110875913020012130422559643709472768000000⟩, + ⟨6, 2, 8, 5, 4, 7, 6750584159194366112287933390523746751790396211200000⟩, + ⟨6, 2, 5, 6, 0, 7, 1519837338548068481139332379398293455771468300288000000⟩, + ⟨6, 2, 6, 6, 1, 7, -141015497794473402123840957441881312880205234176000000⟩, + ⟨6, 2, 7, 6, 2, 7, 93344764302842655325957307976792836964266016768000000⟩, + ⟨6, 2, 8, 6, 3, 7, -35841556790590636623683957065479373323783005798400000⟩, + ⟨6, 2, 6, 7, 0, 7, -41843937310208784269041405586548334450580652032000000⟩, + ⟨6, 2, 7, 7, 1, 7, -482922486571942000943370313269099809278802264064000000⟩, + ⟨6, 2, 8, 7, 2, 7, 14097438611610938738951180579055111358507489689600000⟩ +] + +def collectedFourData_11_1_46 : List CollectedFourTerm := [ + ⟨6, 3, 2, 0, 3, 8, 56987585226323719135975243036695141167518030233600000⟩, + ⟨6, 3, 3, 0, 4, 8, 20861265891864095349722326413818796311170567372800000⟩, + ⟨6, 3, 4, 0, 5, 8, -614463421303497991107202017789799925215309017907200000⟩, + ⟨6, 3, 5, 0, 6, 8, -357286341617346351658213386685975399761985929216000000⟩, + ⟨6, 3, 6, 0, 7, 8, -122995679529297162630133341956740416401250975744000000⟩, + ⟨6, 3, 7, 0, 8, 8, -72156669753169524026966280099385068319521374208000000⟩, + ⟨6, 3, 2, 1, 2, 8, -54663248854544336750428255482650833751271014400000000⟩, + ⟨6, 3, 3, 1, 3, 8, -100137675735025946986392425608688134336386642739200000⟩, + ⟨6, 3, 4, 1, 4, 8, -189090783762654135390232897799554803920910522777600000⟩, + ⟨6, 3, 5, 1, 5, 8, 117112322902173790559128153784830998496086589440000000⟩, + ⟨6, 3, 6, 1, 6, 8, 45324561947438635912134044765150166818482028544000000⟩, + ⟨6, 3, 7, 1, 7, 8, 5708287200710207175261820414909876231880048640000000⟩, + ⟨6, 3, 8, 1, 8, 8, 13748811047900141110947229272176995523630412595200000⟩, + ⟨6, 3, 2, 2, 1, 8, -75748781783001708919419077846373571923112938700800000⟩, + ⟨6, 3, 3, 2, 2, 8, 78148801513868983433899176134570535783001541836800000⟩, + ⟨6, 3, 4, 2, 3, 8, -296893500246071515200686621762698824205992355430400000⟩, + ⟨6, 3, 5, 2, 4, 8, -87974712677380774316017704680630052373181497344000000⟩, + ⟨6, 3, 6, 2, 5, 8, 814302746967719104386951283322226164059078656000000⟩, + ⟨6, 3, 7, 2, 6, 8, 3580221563826303439143940912923015643988282572800000⟩, + ⟨6, 3, 8, 2, 7, 8, 5903427935536584910921859117515312160345319014400000⟩, + ⟨6, 3, 2, 3, 0, 8, 131178883722950797406143223870292500816113906483200000⟩, + ⟨6, 3, 3, 3, 1, 8, 1750939555132390838322225587654399497744888627200000⟩, + ⟨6, 3, 4, 3, 2, 8, 792057502082028708294905836695367581504780002918400000⟩, + ⟨6, 3, 5, 3, 3, 8, 26269738884623502268692096449243660204944392192000000⟩, + ⟨6, 3, 6, 3, 4, 8, -13185770242165434017355563806322983680463601664000000⟩, + ⟨6, 3, 7, 3, 5, 8, 8587112711555740277718525123438263653922714419200000⟩, + ⟨6, 3, 8, 3, 6, 8, -317007760373530440860426486309067399886798848000000⟩, + ⟨6, 3, 3, 4, 0, 8, -335731030121958601480864694751083624056914916147200000⟩, + ⟨6, 3, 4, 4, 1, 8, -10168581096455495190955028534183678609782210560000000⟩, + ⟨6, 3, 5, 4, 2, 8, 54254494038207462799444280033676735092191395840000000⟩, + ⟨6, 3, 6, 4, 3, 8, 16648482268608355310629372285514153089975713792000000⟩, + ⟨6, 3, 7, 4, 4, 8, -4439579213648660261597669149433701528367215411200000⟩, + ⟨6, 3, 8, 4, 5, 8, -4314834785386590059782863456402372461382441369600000⟩, + ⟨6, 3, 4, 5, 0, 8, -3263795431889837152707179176801980289647105382809600000⟩, + ⟨6, 3, 5, 5, 1, 8, 18317148783419987688036315037325931543168811008000000⟩, + ⟨6, 3, 6, 5, 2, 8, -36139468550743796238259762846169524376067637248000000⟩, + ⟨6, 3, 7, 5, 3, 8, -5064157438001272289782918662735658858387498598400000⟩, + ⟨6, 3, 8, 5, 4, 8, -2160016216214444552193352767213740501519617228800000⟩, + ⟨6, 3, 5, 6, 0, 8, -972619026695852074550235228550834828806532890624000000⟩, + ⟨6, 3, 6, 6, 1, 8, 67682089754873772089267873532475876042956865536000000⟩, + ⟨6, 3, 7, 6, 2, 8, -35841556790590636623683957065479373323783005798400000⟩, + ⟨6, 3, 8, 6, 3, 8, 11468391780080561646739484379222404987681872281600000⟩, + ⟨6, 3, 6, 7, 0, 8, 20083502629296506904081030533882475311165079552000000⟩, + ⟨6, 3, 7, 7, 1, 8, 185427579759761594439898261711148345345277375283200000⟩, + ⟨6, 3, 8, 7, 2, 8, -4510823847250775556896734255955375305156617830400000⟩ +] + +def collectedFourData_11_1_47 : List CollectedFourTerm := [ + ⟨7, 0, 4, 0, 5, 6, -71736752481661037768421193516365164374461618585600000⟩, + ⟨7, 0, 5, 0, 6, 6, -125136310633317054264378567066976707604805320704000000⟩, + ⟨7, 0, 6, 0, 7, 6, -86156249301116843884299502178087114298278019072000000⟩, + ⟨7, 0, 7, 0, 8, 6, -84240737178517748479586231003168921456832675840000000⟩, + ⟨7, 0, 4, 1, 4, 6, -22075779096124348635600190295875943667319229644800000⟩, + ⟨7, 0, 5, 1, 5, 6, 41017532188149690943175494662467297782121103360000000⟩, + ⟨7, 0, 6, 1, 6, 6, 31749036011279407587198147344459718473098985472000000⟩, + ⟨7, 0, 7, 1, 7, 6, 6664253262511506689581546388761349809451827200000000⟩, + ⟨7, 0, 8, 1, 8, 6, 24076983776382957233454605563445616462627078144000000⟩, + ⟨7, 0, 4, 2, 3, 6, -34661421334707458446796101295195538295409029939200000⟩, + ⟨7, 0, 5, 2, 4, 6, -30812347663891371736249189136744179175245479936000000⟩, + ⟨7, 0, 6, 2, 5, 6, 570404348696035670782818319981512732734128128000000⟩, + ⟨7, 0, 7, 2, 6, 6, 4179800770058480357774863042912660058007404544000000⟩, + ⟨7, 0, 8, 2, 7, 6, 10338111283496681995602157004990043826126061568000000⟩, + ⟨7, 0, 4, 3, 2, 6, 92470326154755202757511933280326407811522310963200000⟩, + ⟨7, 0, 5, 3, 3, 6, 9200738518135324135307139592457026196993998848000000⟩, + ⟨7, 0, 6, 3, 4, 6, -9236393607961268478933538219771979758181548032000000⟩, + ⟨7, 0, 7, 3, 5, 6, 10025195280367008726408225060707021030336495616000000⟩, + ⟨7, 0, 8, 3, 6, 6, -555145508721404369764850842855651014145474560000000⟩, + ⟨7, 0, 4, 4, 1, 6, -1187151195523854068637610048474194958488698880000000⟩, + ⟨7, 0, 5, 4, 2, 6, 19002145977608675953030781442542340284570664960000000⟩, + ⟨7, 0, 6, 4, 3, 6, 11661960764059053137059622608179333258591338496000000⟩, + ⟨7, 0, 7, 4, 4, 6, -5183074925707188757922628491294151946090315776000000⟩, + ⟨7, 0, 8, 4, 5, 6, -7556159348149063138364260140332150765924646912000000⟩, + ⟨7, 0, 4, 5, 0, 6, -381038279791455448542284757221599682859599973580800000⟩, + ⟨7, 0, 5, 5, 1, 6, 6415415741062980203456150576639671998665981952000000⟩, + ⟨7, 0, 6, 5, 2, 6, -25315044186784588535367236077051282664428929024000000⟩, + ⟨7, 0, 7, 5, 3, 6, -5912251178229604287471556124231298209946796032000000⟩, + ⟨7, 0, 8, 5, 4, 6, -3782630746275495163704386128759945330358747136000000⟩, + ⟨7, 0, 5, 6, 0, 6, -340651019855771574337780719757421055264744800256000000⟩, + ⟨7, 0, 6, 6, 1, 6, 47410079934982513788306533530747803061419245568000000⟩, + ⟨7, 0, 7, 6, 2, 6, -41843937310208784269041405586548334450580652032000000⟩, + ⟨7, 0, 8, 6, 3, 6, 20083502629296506904081030533882475311165079552000000⟩, + ⟨7, 0, 6, 7, 0, 6, 14068130409061638340213536635924410815140069376000000⟩, + ⟨7, 0, 7, 7, 1, 6, 216481110694615609292483119583625094813068558336000000⟩, + ⟨7, 0, 8, 7, 2, 6, -7899376332251351546300821890649371283279577088000000⟩ +] + +def collectedFourData_11_1_48 : List CollectedFourTerm := [ + ⟨7, 1, 3, 0, 4, 7, 56216165254195888552096514251328943293986347417600000⟩, + ⟨7, 1, 4, 0, 5, 7, -3311666455306313387549747016572444550185379220684800000⟩, + ⟨7, 1, 5, 0, 6, 7, -2888405928126503605338745533000889691773983522816000000⟩, + ⟨7, 1, 6, 0, 7, 7, -1325776773434959386337319839049996553963744264192000000⟩, + ⟨7, 1, 7, 0, 8, 7, -972225581147163975291964351430225116943540551680000000⟩, + ⟨7, 1, 3, 1, 3, 7, -269847292895430292233976899380287785671649027686400000⟩, + ⟨7, 1, 4, 1, 4, 7, -1019109655487635100917077892174926368179359213158400000⟩, + ⟨7, 1, 5, 1, 5, 7, 946769826677530819613627036977861822791486013440000000⟩, + ⟨7, 1, 6, 1, 6, 7, 488555790951297891113184435000076568623256174592000000⟩, + ⟨7, 1, 7, 1, 7, 7, 76912402693329999640897091060586641541719654400000000⟩, + ⟨7, 1, 8, 1, 8, 7, 222298715118405734549191036297141541127166781030400000⟩, + ⟨7, 1, 3, 2, 2, 7, 210592490556115917415671054642237028767561783705600000⟩, + ⟨7, 1, 4, 2, 3, 7, -1600115176063116692421808966567505564453456943513600000⟩, + ⟨7, 1, 5, 2, 4, 7, -711212974087659745086477840779481845517458079744000000⟩, + ⟨7, 1, 6, 2, 5, 7, 8777411309125972558275269598596810828842795008000000⟩, + ⟨7, 1, 7, 2, 6, 7, 48239241118437850967965434522883271425511129088000000⟩, + ⟨7, 1, 8, 2, 7, 7, 95450031300293197275267546812034583728015330508800000⟩, + ⟨7, 1, 3, 3, 1, 7, 4718366943389514046026345339136188036418004582400000⟩, + ⟨7, 1, 4, 3, 2, 7, 4268814333576397501380462034280186572970326071705600000⟩, + ⟨7, 1, 5, 3, 3, 7, 212372152770247309775301757269470734806146875392000000⟩, + ⟨7, 1, 6, 3, 4, 7, -142130097527115036546488234958331352214512074752000000⟩, + ⟨7, 1, 7, 3, 5, 7, 115701163522749205461625233519752017458581471232000000⟩, + ⟨7, 1, 8, 3, 6, 7, -5125564499219896975497261104076195455142199296000000⟩, + ⟨7, 1, 3, 4, 0, 7, -904715522448621950916584539673393111616551544422400000⟩, + ⟨7, 1, 4, 4, 1, 7, -54803830053474742185375918366721799380575191040000000⟩, + ⟨7, 1, 5, 4, 2, 7, 438608992154807345501519748349869200382980259840000000⟩, + ⟨7, 1, 6, 4, 3, 7, 179454849057581735933734641747893581583436742656000000⟩, + ⟨7, 1, 7, 4, 4, 7, -59818066656947442878510207476617233095093911552000000⟩, + ⟨7, 1, 8, 4, 5, 7, -69764740049004967617033539446770503789229323059200000⟩, + ⟨7, 1, 4, 5, 0, 7, -17590309649096152702620078907826648760222237484646400000⟩, + ⟨7, 1, 5, 5, 1, 7, 148081118614573982794000943202630103879341047808000000⟩, + ⟨7, 1, 6, 5, 2, 7, -389549195485737463301178015217524945353718104064000000⟩, + ⟨7, 1, 7, 5, 3, 7, -68233517774914386160705723125975909141854552064000000⟩, + ⟨7, 1, 8, 5, 4, 7, -34924389303664754665052164296144544347977259417600000⟩, + ⟨7, 1, 5, 6, 0, 7, -7862932990384807919911545782948168042996274561024000000⟩, + ⟨7, 1, 6, 6, 1, 7, 729548736329215229335019366208313567848167374848000000⟩, + ⟨7, 1, 7, 6, 2, 7, -482922486571942000943370313269099809278802264064000000⟩, + ⟨7, 1, 8, 6, 3, 7, 185427579759761594439898261711148345345277375283200000⟩, + ⟨7, 1, 6, 7, 0, 7, 216481110694615609292483119583625094813068558336000000⟩, + ⟨7, 1, 7, 7, 1, 7, 2498416807612265451606811384787298600022727196672000000⟩, + ⟨7, 1, 8, 7, 2, 7, -72933604358644624585952631607234957638873435340800000⟩ +] + +def collectedFourData_11_1_49 : List CollectedFourTerm := [ + ⟨7, 2, 2, 0, 3, 8, -22414734634600288298506910994836410911150204518400000⟩, + ⟨7, 2, 3, 0, 4, 8, -8205291332330011172368809453847589631277871923200000⟩, + ⟨7, 2, 4, 0, 5, 8, 241684824448825068132044369785397319523197832396800000⟩, + ⟨7, 2, 5, 0, 6, 8, 140530231349769235591529964992315491345345019904000000⟩, + ⟨7, 2, 6, 0, 7, 8, 48377475671281114645188440189025274016443662336000000⟩, + ⟨7, 2, 7, 0, 8, 8, 28381139474684862093473074384544325911395172352000000⟩, + ⟨7, 2, 2, 1, 2, 8, 21500511251242771775431311590861295817693593600000000⟩, + ⟨7, 2, 3, 1, 3, 8, 39386814156312970816603708194303356392067353804800000⟩, + ⟨7, 2, 4, 1, 4, 8, 74374440030329019782525987268867465150017726054400000⟩, + ⟨7, 2, 5, 1, 5, 8, -46063394858171452147894458102639244732646031360000000⟩, + ⟨7, 2, 6, 1, 6, 8, -17827357036564812094795378913973049108029505536000000⟩, + ⟨7, 2, 7, 1, 7, 8, -2245221346260905121887692425488545291079516160000000⟩, + ⟨7, 2, 8, 1, 8, 8, -5407773464273577721257007781230624839207537868800000⟩, + ⟨7, 2, 2, 2, 1, 8, 29794012780452724997399689018526149912523125555200000⟩, + ⟨7, 2, 3, 2, 2, 8, -30738004444102747305361998093658049601653125939200000⟩, + ⟨7, 2, 4, 2, 3, 8, 116776118804194332753009414056661921594477222297600000⟩, + ⟨7, 2, 5, 2, 4, 8, 34602796931774915658305349806478413205640052736000000⟩, + ⟨7, 2, 6, 2, 5, 8, -320286952202290272282704086125046663703691264000000⟩, + ⟨7, 2, 7, 2, 6, 8, -1408196468889355256152958740759642258049020723200000⟩, + ⟨7, 2, 8, 2, 7, 8, -2321975393132042025852498319907925420119005593600000⟩, + ⟨7, 2, 2, 3, 0, 8, -51596147768599023666800422442542386287246888140800000⟩, + ⟨7, 2, 3, 3, 1, 8, -688691147969342444689637727503163550352592076800000⟩, + ⟨7, 2, 4, 3, 2, 8, -311537305081532360274491387904098418784101570969600000⟩, + ⟨7, 2, 5, 3, 3, 8, -10332587767678989578689967923069722094624309248000000⟩, + ⟨7, 2, 6, 3, 4, 8, 5186314523718830917166680425943314657303330816000000⟩, + ⟨7, 2, 7, 3, 5, 8, -3377540071973701224280964042811041707002219724800000⟩, + ⟨7, 2, 8, 3, 6, 8, 124687592879429473070507914758824438909632512000000⟩, + ⟨7, 2, 3, 4, 0, 8, 132051953401748975751488658796473723488983370956800000⟩, + ⟨7, 2, 4, 4, 1, 8, 3999573696310597633388164971760340519501168640000000⟩, + ⟨7, 2, 5, 4, 2, 8, -21339737098373882804695044663969840775519272960000000⟩, + ⟨7, 2, 6, 4, 3, 8, -6548291362718227604491656847633952242975899648000000⟩, + ⟨7, 2, 7, 4, 4, 8, 1746204714027004177738307680450573064641236172800000⟩, + ⟨7, 2, 8, 4, 5, 8, 1697139408916521014280838336284517475362956902400000⟩, + ⟨7, 2, 4, 5, 0, 8, 1283737645960801123212695505208287319101205276262400000⟩, + ⟨7, 2, 5, 5, 1, 8, -7204622333307747847733167848494508176207511552000000⟩, + ⟨7, 2, 6, 5, 2, 8, 14214615239149022880624139815981950353237082112000000⟩, + ⟨7, 2, 7, 5, 3, 8, 1991867959834213284950117970716236316220692889600000⟩, + ⟨7, 2, 8, 5, 4, 8, 849591890946025851553969289642535557002375987200000⟩, + ⟨7, 2, 5, 6, 0, 8, 382556960386530221348371501771159694689022509056000000⟩, + ⟨7, 2, 6, 6, 1, 8, -26621168020116885493381413212354138910945705984000000⟩, + ⟨7, 2, 7, 6, 2, 8, 14097438611610938738951180579055111358507489689600000⟩, + ⟨7, 2, 8, 6, 3, 8, -4510823847250775556896734255955375305156617830400000⟩, + ⟨7, 2, 6, 7, 0, 8, -7899376332251351546300821890649371283279577088000000⟩, + ⟨7, 2, 7, 7, 1, 8, -72933604358644624585952631607234957638873435340800000⟩, + ⟨7, 2, 8, 7, 2, 8, 1774227125399386510559185007821656650916927897600000⟩ +] + +def collectedFourData_11_1 : List (List CollectedFourTerm) := [ + collectedFourData_11_1_0, + collectedFourData_11_1_1, + collectedFourData_11_1_2, + collectedFourData_11_1_3, + collectedFourData_11_1_4, + collectedFourData_11_1_5, + collectedFourData_11_1_6, + collectedFourData_11_1_7, + collectedFourData_11_1_8, + collectedFourData_11_1_9, + collectedFourData_11_1_10, + collectedFourData_11_1_11, + collectedFourData_11_1_12, + collectedFourData_11_1_13, + collectedFourData_11_1_14, + collectedFourData_11_1_15, + collectedFourData_11_1_16, + collectedFourData_11_1_17, + collectedFourData_11_1_18, + collectedFourData_11_1_19, + collectedFourData_11_1_20, + collectedFourData_11_1_21, + collectedFourData_11_1_22, + collectedFourData_11_1_23, + collectedFourData_11_1_24, + collectedFourData_11_1_25, + collectedFourData_11_1_26, + collectedFourData_11_1_27, + collectedFourData_11_1_28, + collectedFourData_11_1_29, + collectedFourData_11_1_30, + collectedFourData_11_1_31, + collectedFourData_11_1_32, + collectedFourData_11_1_33, + collectedFourData_11_1_34, + collectedFourData_11_1_35, + collectedFourData_11_1_36, + collectedFourData_11_1_37, + collectedFourData_11_1_38, + collectedFourData_11_1_39, + collectedFourData_11_1_40, + collectedFourData_11_1_41, + collectedFourData_11_1_42, + collectedFourData_11_1_43, + collectedFourData_11_1_44, + collectedFourData_11_1_45, + collectedFourData_11_1_46, + collectedFourData_11_1_47, + collectedFourData_11_1_48, + collectedFourData_11_1_49 +] + +theorem collectedFourChecked_11_1 : collectNumericRowParts 11 1 = collectedFourData_11_1 := by + decide +kernel + +def collectedFourData_11_2_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_2_1 : List CollectedFourTerm := [ + ⟨0, 3, 8, 2, 8, 1, -21864487203824184209264182982834026260214893772800000⟩, + ⟨0, 3, 8, 3, 7, 1, -13393239468661779258381002264152076487474806784000000⟩, + ⟨0, 3, 8, 4, 6, 1, 17083589691378446438109520648786630182449027481600000⟩, + ⟨0, 3, 8, 5, 5, 1, 5710527766083595081418582309107653368121340723200000⟩, + ⟨0, 3, 8, 6, 4, 1, -8506705894517651792398791776545472237343552307200000⟩, + ⟨0, 3, 8, 7, 3, 1, -40742430050667332915479222317224372342837005516800000⟩ +] + +def collectedFourData_11_2_2 : List CollectedFourTerm := [ + ⟨0, 4, 7, 1, 8, 2, 42856935179538209640966968958651560054286503116800000⟩, + ⟨0, 4, 7, 2, 7, 2, -2530322541915477942843079749338673398862053376000000⟩, + ⟨0, 4, 8, 2, 8, 2, -40904873665971489303896222760631073524308718387200000⟩, + ⟨0, 4, 7, 3, 6, 2, -1975729215636425295638673423240250652745321676800000⟩, + ⟨0, 4, 8, 3, 7, 2, -25056556933468455949107230357804087866363478016000000⟩, + ⟨0, 4, 7, 4, 5, 2, -6802257920101104807938540653022299818804903936000000⟩, + ⟨0, 4, 8, 4, 6, 2, 31960597638205985599584135057600303392891496038400000⟩, + ⟨0, 4, 7, 5, 4, 2, 4310330446292721697270272530563150447644770304000000⟩, + ⟨0, 4, 8, 5, 5, 2, 10683461938079037995225349734475667752098778316800000⟩, + ⟨0, 4, 7, 6, 3, 2, 12924605338373005099847469898281017759045674598400000⟩, + ⟨0, 4, 8, 6, 4, 2, -15914653139816559303309208076840518599597411532800000⟩, + ⟨0, 4, 7, 7, 2, 2, -22951666104009365387618019715310762208066640281600000⟩, + ⟨0, 4, 8, 7, 3, 2, -76222412102843147956537354888656734648274203443200000⟩ +] + +def collectedFourData_11_2_3 : List CollectedFourTerm := [ + ⟨0, 5, 6, 0, 8, 3, 46853259058863797197497723969135541008759521280000000⟩, + ⟨0, 5, 6, 1, 7, 3, -156697290350039195922340435120574557249024819200000000⟩, + ⟨0, 5, 7, 1, 8, 3, -294579223678089115596434540907576349566424842240000000⟩, + ⟨0, 5, 6, 2, 6, 3, 10816754100458966467077784688238888203593973760000000⟩, + ⟨0, 5, 7, 2, 7, 3, 17392294780997500921830187627616669539290316800000000⟩, + ⟨0, 5, 8, 2, 8, 3, 140580817068380368946057950175962145904635412480000000⟩, + ⟨0, 5, 6, 3, 5, 3, -26351110425827832690796129669356551376375644160000000⟩, + ⟨0, 5, 7, 3, 6, 3, 13580270640028751786033600629407629539792650240000000⟩, + ⟨0, 5, 8, 3, 7, 3, 86113730001755482039994990963373901510764134400000000⟩, + ⟨0, 5, 6, 4, 4, 3, 12177883842386826448348679125621584513780940800000000⟩, + ⟨0, 5, 7, 4, 5, 3, 46755649907467505967884568430216201439595724800000000⟩, + ⟨0, 5, 8, 4, 6, 3, -109841359410198672772856673817872857710523842560000000⟩, + ⟨0, 5, 6, 5, 3, 3, 4511005128986296501238641888598442623505530880000000⟩, + ⟨0, 5, 7, 5, 4, 3, -29627265490304314709049834359377406215795507200000000⟩, + ⟨0, 5, 8, 5, 5, 3, -36716647034250748883742485113927136965684101120000000⟩, + ⟨0, 5, 6, 6, 2, 3, 323226926781177639383210877090443432483597844480000000⟩, + ⟨0, 5, 7, 6, 3, 3, -88837901986546827459642003304782466372463493120000000⟩, + ⟨0, 5, 8, 6, 4, 3, 54695070324015418629254003584307443355111915520000000⟩, + ⟨0, 5, 6, 7, 1, 3, -640782542403334916131861509151348409750299607040000000⟩, + ⟨0, 5, 7, 7, 2, 3, 157759390743037327389028766122547214491194490880000000⟩, + ⟨0, 5, 8, 7, 3, 3, 261959224219645413241650974691400103217730682880000000⟩ +] + +def collectedFourData_11_2_4 : List CollectedFourTerm := [ + ⟨0, 6, 5, 0, 7, 4, 798240391803679460621891199066224327789641728000000⟩, + ⟨0, 6, 6, 0, 8, 4, 49175569257632057868768899756673420957579214848000000⟩, + ⟨0, 6, 5, 1, 6, 4, -131703472571266803484470202381246337021405822976000000⟩, + ⟨0, 6, 6, 1, 7, 4, -164464086573159219699316937316893239907419422720000000⟩, + ⟨0, 6, 7, 1, 8, 4, -154590110771609663645109899267045367480940756992000000⟩, + ⟨0, 6, 5, 2, 5, 4, 23037812710678506388023426987339021824362020864000000⟩, + ⟨0, 6, 6, 2, 6, 4, 11352893077120228922297091863626900144826351616000000⟩, + ⟨0, 6, 7, 2, 7, 4, 9127177209568010780193436860205581026658877440000000⟩, + ⟨0, 6, 8, 2, 8, 4, 49182930173227008375700092483713267431171424256000000⟩, + ⟨0, 6, 5, 3, 4, 4, -31180717815869659978901898833226856645087199232000000⟩, + ⟨0, 6, 6, 3, 5, 4, -27657219194353114967664325495663198232175968256000000⟩, + ⟨0, 6, 7, 3, 6, 4, 7126692494935226954242464314612612917616443392000000⟩, + ⟨0, 6, 8, 3, 7, 4, 30127336417260579720431685495993048963408199680000000⟩, + ⟨0, 6, 5, 4, 3, 4, 2908425333510674960184172401592977044759642112000000⟩, + ⟨0, 6, 6, 4, 4, 4, 12781488040145187416426999915438055376583393280000000⟩, + ⟨0, 6, 7, 4, 5, 4, 24536561024726539870653684622197119480852643840000000⟩, + ⟨0, 6, 8, 4, 6, 4, -38428571000383166307484905180582272238964703232000000⟩, + ⟨0, 6, 5, 5, 2, 4, 225899461689219301099118220870543508151029727232000000⟩, + ⟨0, 6, 6, 5, 3, 4, 4734595833841628158951740018676628458158686208000000⟩, + ⟨0, 6, 7, 5, 4, 4, -15547879435689816074020322389623611860986101760000000⟩, + ⟨0, 6, 8, 5, 5, 4, -12845509970269957935008569528766836205540081664000000⟩, + ⟨0, 6, 5, 6, 1, 4, -288602272369622751127947246288081713437889003520000000⟩, + ⟨0, 6, 6, 6, 2, 4, 339247865423618657178127153800098248873337683968000000⟩, + ⟨0, 6, 7, 6, 3, 4, -46620603236517982908424478812721692040648196096000000⟩, + ⟨0, 6, 8, 6, 4, 4, 19135354884566565234647955100672129344517177344000000⟩, + ⟨0, 6, 5, 7, 0, 4, -1259151619116299632924388922916719925922277359616000000⟩, + ⟨0, 6, 6, 7, 1, 4, -672543317711331320278325254524449965732647665664000000⟩, + ⟨0, 6, 7, 7, 2, 4, 82789415308116252300122325501481856264363311104000000⟩, + ⟨0, 6, 8, 7, 3, 4, 91647797343222351004337338113233193105553883136000000⟩ +] + +def collectedFourData_11_2_5 : List CollectedFourTerm := [ + ⟨0, 7, 4, 0, 6, 5, 798240391803679460621891199066224327789641728000000⟩, + ⟨0, 7, 5, 0, 7, 5, 10319055210335009045869587110276391719927808000000⟩, + ⟨0, 7, 6, 0, 8, 5, 317852503694125346570197329472288082639192064000000⟩, + ⟨0, 7, 4, 1, 5, 5, -1236969975988069252536245855298949908273718886400000⟩, + ⟨0, 7, 5, 1, 6, 5, -1702564063170074403711223543820579190746382336000000⟩, + ⟨0, 7, 6, 1, 7, 5, -1063034398466732576650545558723091495869480960000000⟩, + ⟨0, 7, 7, 1, 8, 5, -666141805736626125298628531618673453856456704000000⟩, + ⟨0, 7, 4, 2, 4, 5, 329800114128930685497107714871006078309079449600000⟩, + ⟨0, 7, 5, 2, 5, 5, 297815625127269259751631601415864018119163904000000⟩, + ⟨0, 7, 6, 2, 6, 5, 73380858487455550464815286701760888006770688000000⟩, + ⟨0, 7, 7, 2, 7, 5, 39329775218560750920897247692999150041825280000000⟩, + ⟨0, 7, 8, 2, 8, 5, 158950040950947556440189200687425340628271104000000⟩, + ⟨0, 7, 4, 3, 3, 5, -420654519043428422516650714054659368395210752000000⟩, + ⟨0, 7, 5, 3, 4, 5, -403081016625588824635989479332358169928138752000000⟩, + ⟨0, 7, 6, 3, 5, 5, -178765929888610409830547738886298875312734208000000⟩, + ⟨0, 7, 7, 3, 6, 5, 30709518117362439129393461288197220418453504000000⟩, + ⟨0, 7, 8, 3, 7, 5, 97365922290521027293482261732906633390981120000000⟩, + ⟨0, 7, 4, 4, 2, 5, 1402423049359331147498463049040967195762779750400000⟩, + ⟨0, 7, 5, 4, 3, 5, 37597949063713774677248257692210407965458432000000⟩, + ⟨0, 7, 6, 4, 4, 5, 82614762489325865223835766502380209742807040000000⟩, + ⟨0, 7, 7, 4, 5, 5, 105730107741018399595103022443129152292782080000000⟩, + ⟨0, 7, 8, 4, 6, 5, -124193961455398277185975198787866377414770688000000⟩, + ⟨0, 7, 4, 5, 1, 5, -1352110860717326106768608889393263222469741772800000⟩, + ⟨0, 7, 5, 5, 2, 5, 2920259411940806793749158359989911864844746752000000⟩, + ⟨0, 7, 6, 5, 3, 5, 30602658240357336205613122767670422005612544000000⟩, + ⟨0, 7, 7, 5, 4, 5, -66997121814391250880120593347893317987205120000000⟩, + ⟨0, 7, 8, 5, 5, 5, -41514288160929391540107320862847395667378176000000⟩, + ⟨0, 7, 4, 6, 0, 5, -4218617805455555629578227747977761955608369561600000⟩, + ⟨0, 7, 5, 6, 1, 5, -3730834486690218134715980062568372352288030720000000⟩, + ⟨0, 7, 6, 6, 2, 5, 2192771431538629910287201228367551033428148224000000⟩, + ⟨0, 7, 7, 6, 3, 5, -200892105384326303320568077075506707721879552000000⟩, + ⟨0, 7, 8, 6, 4, 5, 61841891725443848097535385372955047463223296000000⟩, + ⟨0, 7, 5, 7, 0, 5, -16277371089283836663430378696738426983731429376000000⟩, + ⟨0, 7, 6, 7, 1, 5, -4347068688871825826594277826696858828749668352000000⟩, + ⟨0, 7, 7, 7, 2, 5, 356746562467411030363891406377588637300686848000000⟩, + ⟨0, 7, 8, 7, 3, 5, 296188557482473647460479230269694792668545024000000⟩ +] + +def collectedFourData_11_2_6 : List CollectedFourTerm := [ + ⟨0, 8, 3, 0, 5, 6, 46853259058863797197497723969135541008759521280000000⟩, + ⟨0, 8, 4, 0, 6, 6, 49175569257632057868768899756673420957579214848000000⟩, + ⟨0, 8, 5, 0, 7, 6, 317852503694125346570197329472288082639192064000000⟩, + ⟨0, 8, 6, 0, 8, 6, 6527097170901043642779186146257646658370142208000000⟩, + ⟨0, 8, 3, 1, 4, 6, -44820252311126100197362902962397712221740413747200000⟩, + ⟨0, 8, 4, 1, 5, 6, -76203488759026708280415220287962576043075069542400000⟩, + ⟨0, 8, 5, 1, 6, 6, -52443197477638283589763077564121598417738661888000000⟩, + ⟨0, 8, 6, 1, 7, 6, -21829398020031839928355855457859925787667333120000000⟩, + ⟨0, 8, 7, 1, 8, 6, -10259410210183297101566576509726360623661449216000000⟩, + ⟨0, 8, 3, 2, 3, 6, 31090846858603160591059278805045506630109416652800000⟩, + ⟨0, 8, 4, 2, 4, 6, 20317323603327374390491115286936612678783310233600000⟩, + ⟨0, 8, 5, 2, 5, 6, 9173460181812556619674034308610072690433196032000000⟩, + ⟨0, 8, 6, 2, 6, 6, 1506875007323131960000174485581095553766260736000000⟩, + ⟨0, 8, 7, 2, 7, 6, 605727330076997054949652234758220692974469120000000⟩, + ⟨0, 8, 8, 2, 8, 6, 1958422256639993706154601255043229286077877452800000⟩, + ⟨0, 8, 3, 3, 2, 6, -20501700901237690735234624362437352111796440268800000⟩, + ⟨0, 8, 4, 3, 3, 6, -25914405794493481237194220711015491035392376832000000⟩, + ⟨0, 8, 5, 3, 4, 6, -12415895420125127409040089741786127631873212416000000⟩, + ⟨0, 8, 6, 3, 5, 6, -3670956124832968936901772031965618055912882176000000⟩, + ⟨0, 8, 7, 3, 6, 6, 472964676604674307755841045293942281827516416000000⟩, + ⟨0, 8, 8, 3, 7, 6, 1199644794749577722560543609937678328800477184000000⟩, + ⟨0, 8, 3, 4, 1, 6, 18929923122984146444146871436095414619923388825600000⟩, + ⟨0, 8, 4, 4, 2, 6, 86396219109431740184968367713305179109548516966400000⟩, + ⟨0, 8, 5, 4, 3, 6, 1158110117648807677558194164017682207899385856000000⟩, + ⟨0, 8, 6, 4, 4, 6, 1696493110017012037518889391875578299028602880000000⟩, + ⟨0, 8, 7, 4, 5, 6, 1628374825811271202878378832038647491272376320000000⟩, + ⟨0, 8, 8, 4, 6, 6, -1530192863112260475053116652906128374205356441600000⟩, + ⟨0, 8, 3, 5, 0, 6, -22737484499835593683283523698955546754896258662400000⟩, + ⟨0, 8, 4, 5, 1, 6, -83296738624013683871965593842500071200836603084800000⟩, + ⟨0, 8, 5, 5, 2, 6, 89951235515444550667933513995030859097535676416000000⟩, + ⟨0, 8, 6, 5, 3, 6, 628425202574170127160432341186942214516768768000000⟩, + ⟨0, 8, 7, 5, 4, 6, -1031838791194587002035658497462883976719892480000000⟩, + ⟨0, 8, 8, 5, 5, 6, -511497231561082153211379404044411033829454643200000⟩, + ⟨0, 8, 4, 6, 0, 6, -259887790938397853176814173449217699638207420825600000⟩, + ⟨0, 8, 5, 6, 1, 6, -114918958983297649204460125541429964353317109760000000⟩, + ⟨0, 8, 6, 6, 2, 6, 45028533803847302594390103433648333706628169728000000⟩, + ⟨0, 8, 7, 6, 3, 6, -3093987645537520438083025089888888475676049408000000⟩, + ⟨0, 8, 8, 6, 4, 6, 761953481881804454763767364246694116340216627200000⟩, + ⟨0, 8, 5, 7, 0, 6, -501383416294297724724333682610941401814907486208000000⟩, + ⟨0, 8, 6, 7, 1, 6, -89267000923649531553062760828211764250640646144000000⟩, + ⟨0, 8, 7, 7, 2, 6, 5494339634454672923692298218408500432514056192000000⟩, + ⟨0, 8, 8, 7, 3, 6, 3649336984535785242160243347863925500712635596800000⟩ +] + +def collectedFourData_11_2_7 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_2_8 : List CollectedFourTerm := [ + ⟨1, 2, 8, 2, 8, 1, -6416526810345972217275350222259198067394740224000000⟩, + ⟨1, 2, 8, 3, 7, 1, -3930486881623331386512110997856145659102494720000000⟩, + ⟨1, 2, 8, 4, 6, 1, 5013486492951336126059407185322366358758883328000000⟩, + ⟨1, 2, 8, 5, 5, 1, 1675857026543558474870545192914215053301907456000000⟩, + ⟨1, 2, 8, 6, 4, 1, -2496445762988384204048577509245842701131186176000000⟩, + ⟨1, 2, 8, 7, 3, 1, -11956598492418706886204199461846942175140511744000000⟩ +] + +def collectedFourData_11_2_9 : List CollectedFourTerm := [ + ⟨1, 3, 7, 1, 8, 2, -25587539533627870505682831298963572599783895859200000⟩, + ⟨1, 3, 7, 2, 7, 2, 1510717642380644241474022446158738614275538944000000⟩, + ⟨1, 3, 8, 2, 8, 2, 24422070025805726773704020880409095365309811916800000⟩, + ⟨1, 3, 7, 3, 6, 2, 1179600202418985577812385559759283212369736499200000⟩, + ⟨1, 3, 8, 3, 7, 2, 14959904118804745103400563514045961613925679104000000⟩, + ⟨1, 3, 7, 4, 5, 2, 4061257360550152182973637941454518568651587584000000⟩, + ⟨1, 3, 8, 4, 6, 2, -19081930431096707644516010149265591979715697049600000⟩, + ⟨1, 3, 7, 5, 4, 2, -2573463320124966519516823648802242618485374976000000⟩, + ⟨1, 3, 8, 5, 5, 2, -6378512685319640000771356314826132477202084659200000⟩, + ⟨1, 3, 7, 6, 3, 2, -7716577227623408635688711726181047231441377689600000⟩, + ⟨1, 3, 8, 6, 4, 2, 9501771759298700170101693284869092423104672563200000⟩, + ⟨1, 3, 7, 7, 2, 2, 13703188558367985501504820438381224508365629030400000⟩, + ⟨1, 3, 8, 7, 3, 2, 45508246795052081092232127893546640763960216780800000⟩ +] + +def collectedFourData_11_2_10 : List CollectedFourTerm := [ + ⟨1, 4, 6, 0, 8, 3, -44820252311126100197362902962397712221740413747200000⟩, + ⟨1, 4, 6, 1, 7, 3, 149898048311537379141698132535878101712353886208000000⟩, + ⟨1, 4, 7, 1, 8, 3, 281797155546425393518588618762850518751864527257600000⟩, + ⟨1, 4, 6, 2, 6, 3, -10347405019593005519422156104161851649558996582400000⟩, + ⟨1, 4, 7, 2, 7, 3, -16637626837749659193534869390774598746800914432000000⟩, + ⟨1, 4, 8, 2, 8, 3, -134480883884577063660339256378295284212847293235200000⟩, + ⟨1, 4, 6, 3, 5, 3, 25207711089641115446834896366067442301427672678400000⟩, + ⟨1, 4, 7, 3, 6, 3, -12991009990890204855502994041488386941001505177600000⟩, + ⟨1, 4, 8, 3, 7, 3, -82377174686649584650047445449003286516734099456000000⟩, + ⟨1, 4, 6, 4, 4, 3, -11649474068508896518966309307256628030778376192000000⟩, + ⟨1, 4, 7, 4, 5, 3, -44726878512134650253042894466482898676431716352000000⟩, + ⟨1, 4, 8, 4, 6, 3, 105075240054850017078852864788067073555184379494400000⟩, + ⟨1, 4, 6, 5, 3, 3, -4315268395821444646564240933186537302850220851200000⟩, + ⟨1, 4, 7, 5, 4, 3, 28341710720610871516302146911658830575936995328000000⟩, + ⟨1, 4, 8, 5, 5, 3, 35123477366348777396336655094250201027569306828800000⟩, + ⟨1, 4, 6, 6, 2, 3, -309201808008306772052428530988323766235378692915200000⟩, + ⟨1, 4, 7, 6, 3, 3, 84983142300212007829930841652868803612061256908800000⟩, + ⟨1, 4, 8, 6, 4, 3, -52321800048472547399931684448266246346322529484800000⟩, + ⟨1, 4, 6, 7, 1, 3, 612978388355014846146587708607452993207286733209600000⟩, + ⟨1, 4, 7, 7, 2, 3, -150914063174753531262507846108225266717516051251200000⟩, + ⟨1, 4, 8, 7, 3, 3, -250592568384635367407986096561067717388708033331200000⟩ +] + +def collectedFourData_11_2_11 : List CollectedFourTerm := [ + ⟨1, 5, 5, 0, 7, 4, -1236969975988069252536245855298949908273718886400000⟩, + ⟨1, 5, 6, 0, 8, 4, -76203488759026708280415220287962576043075069542400000⟩, + ⟨1, 5, 5, 1, 6, 4, 204090450667262629177192617223989832697290476748800000⟩, + ⟨1, 5, 6, 1, 7, 4, 254856982067294538680284802889405058842032603136000000⟩, + ⟨1, 5, 7, 1, 8, 4, 239556063026413159825532192381040133241810033049600000⟩, + ⟨1, 5, 5, 2, 5, 4, -35699875536433951197479467000016652797480219443200000⟩, + ⟨1, 5, 6, 2, 6, 4, -17592680126432804806462410891639585444274687180800000⟩, + ⟨1, 5, 7, 2, 7, 4, -14143664351847140094530431692198253801475407872000000⟩, + ⟨1, 5, 8, 2, 8, 4, -76214895387506334864521234714320661155731524812800000⟩, + ⟨1, 5, 5, 3, 4, 4, 48318291286709191559509613102674227021418699161600000⟩, + ⟨1, 5, 6, 3, 5, 4, 42858204262795168647602801322878285300108152012800000⟩, + ⟨1, 5, 7, 3, 6, 4, -11043671473971816474077561944074745464015657369600000⟩, + ⟨1, 5, 8, 3, 7, 4, -46685949480001651461495613579201086913442217984000000⟩, + ⟨1, 5, 5, 4, 3, 4, -4506956615947091871627544672152804197700049305600000⟩, + ⟨1, 5, 6, 4, 4, 4, -19806460705885454438324128251568401226257137664000000⟩, + ⟨1, 5, 7, 4, 5, 4, -38022367213222098584160357052603261297404936192000000⟩, + ⟨1, 5, 8, 4, 6, 4, 59549715894720862467255143475580520873214974361600000⟩, + ⟨1, 5, 5, 5, 2, 4, -350058521932269053542642013544371450381432625561600000⟩, + ⟨1, 5, 6, 5, 3, 4, -7336828548185847305816996982107986227290859110400000⟩, + ⟨1, 5, 7, 5, 4, 4, 24093318566320608849532993669795882552774361088000000⟩, + ⟨1, 5, 8, 5, 5, 4, 19905670425391385104809176477402342756495602483200000⟩, + ⟨1, 5, 5, 6, 1, 4, 447224106407977604014293236118454210661424562176000000⟩, + ⟨1, 5, 6, 6, 2, 4, -525705574731507850805627527710250057537912464998400000⟩, + ⟨1, 5, 7, 6, 3, 4, 72244260072732557365288886528315902343244467404800000⟩, + ⟨1, 5, 8, 6, 4, 4, -29652545417554980846241240635121189434453865267200000⟩, + ⟨1, 5, 5, 7, 0, 4, 1951207636266406591150729601785807371094952037580800000⟩, + ⟨1, 5, 6, 7, 1, 4, 1042187165799202854938116247536315469155001381683200000⟩, + ⟨1, 5, 7, 7, 2, 4, -128292206354465270852512209852840123020990427955200000⟩, + ⟨1, 5, 8, 7, 3, 4, -142019340092334618426372031504707640404157975756800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1106.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1106.lean new file mode 100644 index 0000000000000000000000000000000000000000..d8a706666b963a17f9616557add7db6cc67d3e83 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1106.lean @@ -0,0 +1,631 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1106. -/ +namespace LaughlinFock +def collectedFourData_11_2_12 : List CollectedFourTerm := [ + ⟨1, 6, 4, 0, 6, 5, -131703472571266803484470202381246337021405822976000000⟩, + ⟨1, 6, 5, 0, 7, 5, -1702564063170074403711223543820579190746382336000000⟩, + ⟨1, 6, 6, 0, 8, 5, -52443197477638283589763077564121598417738661888000000⟩, + ⟨1, 6, 4, 1, 5, 5, 204090450667262629177192617223989832697290476748800000⟩, + ⟨1, 6, 5, 1, 6, 5, 280909863365687502636900449472006334827737382912000000⟩, + ⟨1, 6, 6, 1, 7, 5, 175392429621889587407293520065327418608787128320000000⟩, + ⟨1, 6, 7, 1, 8, 5, 109908230579723810077223787794297270087888928768000000⟩, + ⟨1, 6, 4, 2, 4, 5, -54414460519886796399786550848020653275845178163200000⟩, + ⟨1, 6, 5, 2, 5, 5, -49137267943327326047595934551370107060819591168000000⟩, + ⟨1, 6, 6, 2, 6, 5, -12107272423562749452490642580451523930720567296000000⟩, + ⟨1, 6, 7, 2, 7, 5, -6489107823806728459979682683730572737259765760000000⟩, + ⟨1, 6, 8, 2, 8, 5, -26225523756424324929672259040490712211619053568000000⟩, + ⟨1, 6, 4, 3, 3, 5, 69404732558862016375527649826926855446734045184000000⟩, + ⟨1, 6, 5, 3, 4, 5, 66505240980342323923219333263855619060147421184000000⟩, + ⟨1, 6, 6, 3, 5, 5, 29494991716169730298605012787373308515383771136000000⟩, + ⟨1, 6, 7, 3, 6, 5, -5066832270799932423772527569459709349743034368000000⟩, + ⟨1, 6, 8, 3, 7, 5, -16064621895154043287430721211153927692657623040000000⟩, + ⟨1, 6, 4, 4, 2, 5, -231388924327992937112523559880877537249383468236800000⟩, + ⟨1, 6, 5, 4, 3, 5, -6203369942305002340014683240167962120755871744000000⟩, + ⟨1, 6, 6, 4, 4, 5, -13630794955024846318490995485121390850007367680000000⟩, + ⟨1, 6, 7, 4, 5, 5, -17444647612183277430946567325287682701378191360000000⟩, + ⟨1, 6, 8, 4, 6, 5, 20491040248036991962721120405228346780256567296000000⟩, + ⟨1, 6, 4, 5, 1, 5, 223087803481627156352270466424108990951144921497600000⟩, + ⟨1, 6, 5, 5, 2, 5, -481820150058406170663339551743492919031899357184000000⟩, + ⟨1, 6, 6, 5, 3, 5, -5049201220022973175968632674023072044886786048000000⟩, + ⟨1, 6, 7, 5, 4, 5, 11054005392157137582908368680711886012982231040000000⟩, + ⟨1, 6, 8, 5, 5, 5, 6849535513686877944712423706207099891264520192000000⟩, + ⟨1, 6, 4, 6, 0, 5, 696039213417955327868690350268388120480424604467200000⟩, + ⟨1, 6, 5, 6, 1, 5, 615558749633641984465745050626568247813854986240000000⟩, + ⟨1, 6, 6, 6, 2, 5, -361790276530797567063347922033337798591783108608000000⟩, + ⟨1, 6, 7, 6, 3, 5, 33145639036737480894273962279431861543353974784000000⟩, + ⟨1, 6, 8, 6, 4, 5, -10203432417411907538008181656477905208561631232000000⟩, + ⟨1, 6, 5, 7, 0, 5, 2685639963602682886523569573128487124550750830592000000⟩, + ⟨1, 6, 6, 7, 1, 5, 717232612767922613666911510953086164403836944384000000⟩, + ⟨1, 6, 7, 7, 2, 5, -58860415467895661758907267371792370234101334016000000⟩, + ⟨1, 6, 8, 7, 3, 5, -48868814403355826402697979456197397295250014208000000⟩ +] + +def collectedFourData_11_2_13 : List CollectedFourTerm := [ + ⟨1, 7, 3, 0, 5, 6, -156697290350039195922340435120574557249024819200000000⟩, + ⟨1, 7, 4, 0, 6, 6, -164464086573159219699316937316893239907419422720000000⟩, + ⟨1, 7, 5, 0, 7, 6, -1063034398466732576650545558723091495869480960000000⟩, + ⟨1, 7, 6, 0, 8, 6, -21829398020031839928355855457859925787667333120000000⟩, + ⟨1, 7, 3, 1, 4, 6, 149898048311537379141698132535878101712353886208000000⟩, + ⟨1, 7, 4, 1, 5, 6, 254856982067294538680284802889405058842032603136000000⟩, + ⟨1, 7, 5, 1, 6, 6, 175392429621889587407293520065327418608787128320000000⟩, + ⟨1, 7, 6, 1, 7, 6, 73006821476688339384249206215020742376737996800000000⟩, + ⟨1, 7, 7, 1, 8, 6, 34311845383167972404729629970472958144272138240000000⟩, + ⟨1, 7, 3, 2, 3, 6, -103981058207934341605795413081189160639153569792000000⟩, + ⟨1, 7, 4, 2, 4, 6, -67949799432447398244075881358543218117657493504000000⟩, + ⟨1, 7, 5, 2, 5, 6, -30679965118713861321097837803201455324638740480000000⟩, + ⟨1, 7, 6, 2, 6, 6, -5039633000707129326048255109020641282532311040000000⟩, + ⟨1, 7, 7, 2, 7, 6, -2025810652675886003944483014968066154745036800000000⟩, + ⟨1, 7, 8, 2, 8, 6, -6549799675432396102548004099069982346200481792000000⟩, + ⟨1, 7, 3, 3, 2, 6, 68566435789553548702074424103574499701169324032000000⟩, + ⟨1, 7, 4, 3, 3, 6, 86668830527388217245153422137418647534546452480000000⟩, + ⟨1, 7, 5, 3, 4, 6, 41524052086938191312453004038155613585528586240000000⟩, + ⟨1, 7, 6, 3, 5, 6, 12277243660521486547866617375912814701067632640000000⟩, + ⟨1, 7, 7, 3, 6, 6, -1581795690287511050946878129745835472443146240000000⟩, + ⟨1, 7, 8, 3, 7, 6, -4012124076227416734488497403105215738816757760000000⟩, + ⟨1, 7, 3, 4, 1, 6, -63309740229159210037588856827844394934163472384000000⟩, + ⟨1, 7, 4, 4, 2, 6, -288945821547392934910554798729122548506999914496000000⟩, + ⟨1, 7, 5, 4, 3, 6, -3873214393358232831206264050912859741057187840000000⟩, + ⟨1, 7, 6, 4, 4, 6, -5673796845235365536834841677265869842101043200000000⟩, + ⟨1, 7, 7, 4, 5, 6, -5445980237111620931519868858425272680893644800000000⟩, + ⟨1, 7, 8, 4, 6, 6, 5117617860081349768534452049379491038703386624000000⟩, + ⟨1, 7, 3, 5, 0, 6, 76043850141225480056803974801691476847478439936000000⟩, + ⟨1, 7, 4, 5, 1, 6, 278579836270943918991672698656227856045962166272000000⟩, + ⟨1, 7, 5, 5, 2, 6, -300835313317267076640855620464185631612065546240000000⟩, + ⟨1, 7, 6, 5, 3, 6, -2101722023377959611769093204067231934730731520000000⟩, + ⟨1, 7, 7, 5, 4, 6, 3450909198335980160560795692992152361710387200000000⟩, + ⟨1, 7, 8, 5, 5, 6, 1710664995715066163211877140399146630431899648000000⟩, + ⟨1, 7, 4, 6, 0, 6, 869175665751264683358573980430008425549223952384000000⟩, + ⟨1, 7, 5, 6, 1, 6, 384338034199636802042801816885458682790700646400000000⟩, + ⟨1, 7, 6, 6, 2, 6, -150594630495894509025916278263328377648625745920000000⟩, + ⟨1, 7, 7, 6, 3, 6, 10347614876120508288635025373389392798935941120000000⟩, + ⟨1, 7, 8, 6, 4, 6, -2548297565248427466270461583150498768022929408000000⟩, + ⟨1, 7, 5, 7, 0, 6, 1676840081947276480586786823513682252649327493120000000⟩, + ⟨1, 7, 6, 7, 1, 6, 298546940882740326511599973797040518877843292160000000⟩, + ⟨1, 7, 7, 7, 2, 6, -18375416145549775594830067174104425768555642880000000⟩, + ⟨1, 7, 8, 7, 3, 6, -12204940030585947594745453415258624376755453952000000⟩ +] + +def collectedFourData_11_2_14 : List CollectedFourTerm := [ + ⟨1, 8, 2, 0, 4, 7, 42856935179538209640966968958651560054286503116800000⟩, + ⟨1, 8, 3, 0, 5, 7, -294579223678089115596434540907576349566424842240000000⟩, + ⟨1, 8, 4, 0, 6, 7, -154590110771609663645109899267045367480940756992000000⟩, + ⟨1, 8, 5, 0, 7, 7, -666141805736626125298628531618673453856456704000000⟩, + ⟨1, 8, 6, 0, 8, 7, -10259410210183297101566576509726360623661449216000000⟩, + ⟨1, 8, 2, 1, 3, 7, -25587539533627870505682831298963572599783895859200000⟩, + ⟨1, 8, 3, 1, 4, 7, 281797155546425393518588618762850518751864527257600000⟩, + ⟨1, 8, 4, 1, 5, 7, 239556063026413159825532192381040133241810033049600000⟩, + ⟨1, 8, 5, 1, 6, 7, 109908230579723810077223787794297270087888928768000000⟩, + ⟨1, 8, 6, 1, 7, 7, 34311845383167972404729629970472958144272138240000000⟩, + ⟨1, 8, 7, 1, 8, 7, 12900742257070840532714369790057568478854486425600000⟩, + ⟨1, 8, 2, 2, 2, 7, -6247084551870862623699176998033912402423893196800000⟩, + ⟨1, 8, 3, 2, 3, 7, -195476637379593543795783087258632790852095075942400000⟩, + ⟨1, 8, 4, 2, 4, 7, -63870278551652083677076993068201632502408177254400000⟩, + ⟨1, 8, 5, 2, 5, 7, -19225349051351824636729684642644964052777828352000000⟩, + ⟨1, 8, 6, 2, 6, 7, -2368533580980351560327265528712839404634243072000000⟩, + ⟨1, 8, 7, 2, 7, 7, -761674599542832810733547309310953245158408192000000⟩, + ⟨1, 8, 8, 2, 8, 7, -2052189180942222418672476947331464269880780390400000⟩, + ⟨1, 8, 2, 3, 1, 7, -35802443883848115242838279678321098154395566080000000⟩, + ⟨1, 8, 3, 3, 2, 7, 128899787482861073938334047671226944621998663270400000⟩, + ⟨1, 8, 4, 3, 3, 7, 81465470005300272472308675299579915778788425728000000⟩, + ⟨1, 8, 5, 3, 4, 7, 26020707400053496169853561343675433571714072576000000⟩, + ⟨1, 8, 6, 3, 5, 7, 5770075695540347172386514349500573586871549952000000⟩, + ⟨1, 8, 7, 3, 6, 7, -594731594172873375925944093474328964157249945600000⟩, + ⟨1, 8, 8, 3, 7, 7, -1257082358215506122438937380355855525989056512000000⟩, + ⟨1, 8, 2, 4, 0, 7, 137107895743302149285959516201221122400313776537600000⟩, + ⟨1, 8, 3, 4, 1, 7, -119017591729291461819554948630962604385118244044800000⟩, + ⟨1, 8, 4, 4, 2, 7, -271598301433032386632256002085956238000023771545600000⟩, + ⟨1, 8, 5, 4, 3, 7, -2427118100522584459142093052787069553964220416000000⟩, + ⟨1, 8, 6, 4, 4, 7, -2666578768278310309601359647287122687961333760000000⟩, + ⟨1, 8, 7, 4, 5, 7, -2047607366829181027404625310959056228515315712000000⟩, + ⟨1, 8, 8, 4, 6, 7, 1603456674262683579890319792193205321354497228800000⟩, + ⟨1, 8, 3, 5, 0, 7, 142956769003820530642192991330655455154713867059200000⟩, + ⟨1, 8, 4, 5, 1, 7, 261854661678402483821694657926176591987562722099200000⟩, + ⟨1, 8, 5, 5, 2, 7, -188515987000564987314658656807756951597745176576000000⟩, + ⟨1, 8, 6, 5, 3, 7, -987770178812264221723593755116457748999438336000000⟩, + ⟨1, 8, 7, 5, 4, 7, 1297490403769621550803213456061173158660538368000000⟩, + ⟨1, 8, 8, 5, 5, 7, 535987109589160574705087813470434973940554137600000⟩, + ⟨1, 8, 4, 6, 0, 7, 816992726182229655292283565277520818285253650022400000⟩, + ⟨1, 8, 5, 6, 1, 7, 240842283640385348080440325633343067579073167360000000⟩, + ⟨1, 8, 6, 6, 2, 7, -70776669530262544737717876769426274853643616256000000⟩, + ⟨1, 8, 7, 6, 3, 7, 3890548905240419350555123610313944508538866892800000⟩, + ⟨1, 8, 8, 6, 4, 7, -798434906771250192761726882786904990526577049600000⟩, + ⟨1, 8, 5, 7, 0, 7, 1050778113794844957954896296324355077803016716288000000⟩, + ⟨1, 8, 6, 7, 1, 7, 140311497857186801136440189696333597794986098688000000⟩, + ⟨1, 8, 7, 7, 2, 7, -6908882483961246730384438625224005814926390067200000⟩, + ⟨1, 8, 8, 7, 3, 7, -3824062891383561122305953168089637441348462182400000⟩ +] + +def collectedFourData_11_2_15 : List CollectedFourTerm := [ + +] + +def collectedFourData_11_2_16 : List CollectedFourTerm := [ + ⟨2, 1, 8, 2, 8, 1, -23505227723549774451038493845426132886457260441600000⟩, + ⟨2, 1, 8, 3, 7, 1, -14398286167528694924470215214113118235758952448000000⟩, + ⟨2, 1, 8, 4, 6, 1, 18365565233165152388627048051250512068540052275200000⟩, + ⟨2, 1, 8, 5, 5, 1, 6139053448277168341468114068556639828013639270400000⟩, + ⟨2, 1, 8, 6, 4, 1, -9145060543332943846232913682272059519966537318400000⟩, + ⟨2, 1, 8, 7, 3, 1, -43799796785731830206083987994836001575602330009600000⟩ +] + +def collectedFourData_11_2_17 : List CollectedFourTerm := [ + ⟨2, 2, 7, 1, 8, 2, -6247084551870862623699176998033912402423893196800000⟩, + ⟨2, 2, 7, 2, 7, 2, 368835027437935425225581202168160829860478976000000⟩, + ⟨2, 2, 8, 2, 8, 2, 5962540328756966295013276483985778919569830707200000⟩, + ⟨2, 2, 7, 3, 6, 2, 287994169671169700210701998798767404557847756800000⟩, + ⟨2, 2, 8, 3, 7, 2, 3652394392795452935032280740862097338312687616000000⟩, + ⟨2, 2, 7, 4, 5, 2, 991538013450702357907356372594211468697665536000000⟩, + ⟨2, 2, 8, 4, 6, 2, -4658768876910352236284495060480742257378879078400000⟩, + ⟨2, 2, 7, 5, 4, 2, -628299681992893392801785039132456141092552704000000⟩, + ⟨2, 2, 8, 5, 5, 2, -1557285647101959754943734164090287780881288396800000⟩, + ⟨2, 2, 7, 6, 3, 2, -1883968184148805987813478799731909548424193638400000⟩, + ⟨2, 2, 8, 6, 4, 2, 2319815529543482759901814259087673006702251212800000⟩, + ⟨2, 2, 7, 7, 2, 2, 3345572849700914313521900037926088042109049241600000⟩, + ⟨2, 2, 8, 7, 3, 2, 11110637080305024453931411084823179328144749363200000⟩ +] + +def collectedFourData_11_2_18 : List CollectedFourTerm := [ + ⟨2, 3, 6, 0, 8, 3, 31090846858603160591059278805045506630109416652800000⟩, + ⟨2, 3, 6, 1, 7, 3, -103981058207934341605795413081189160639153569792000000⟩, + ⟨2, 3, 7, 1, 8, 3, -195476637379593543795783087258632790852095075942400000⟩, + ⟨2, 3, 6, 2, 6, 3, 7177772731284851611994964497537569049068280217600000⟩, + ⟨2, 3, 7, 2, 7, 3, 11541164572486185552717848476453430481616109568000000⟩, + ⟨2, 3, 8, 2, 8, 3, 93286502209784843918099462745222033750102953164800000⟩, + ⟨2, 3, 6, 3, 5, 3, -17486048041487553292787457298428169230380276121600000⟩, + ⟨2, 3, 7, 3, 6, 3, 9011584748823183323910467860757201798763538022400000⟩, + ⟨2, 3, 8, 3, 7, 3, 57143277664932760896840246410284924590090092544000000⟩, + ⟨2, 3, 6, 4, 4, 3, 8080990078616065720760445451730517034750967808000000⟩, + ⟨2, 3, 7, 4, 5, 3, 31026075458725777228336532199921913656558747648000000⟩, + ⟨2, 3, 8, 4, 6, 3, -72888438344764573688071786365178530649379281305600000⟩, + ⟨2, 3, 6, 5, 3, 3, 2993409049037184769340874906590283286801337548800000⟩, + ⟨2, 3, 7, 5, 4, 3, -19660036306993401277166347681001974779894300672000000⟩, + ⟨2, 3, 8, 5, 5, 3, -24364402242949518546317269385180790235312894771200000⟩, + ⟨2, 3, 6, 6, 2, 3, 214486656488613344016173413308414045099209313484800000⟩, + ⟨2, 3, 7, 6, 3, 3, -58950981455382779099337560147982477581511504691200000⟩, + ⟨2, 3, 8, 6, 4, 3, 36294509486054344382058848655154848198846264115200000⟩, + ⟨2, 3, 6, 7, 1, 3, -425209949013343975023735608469502850347890533990400000⟩, + ⟨2, 3, 7, 7, 2, 3, 104685845907455535164601138238905464008148307148800000⟩, + ⟨2, 3, 8, 7, 3, 3, 173830685143570255842370478545932264983870885068800000⟩ +] + +def collectedFourData_11_2_19 : List CollectedFourTerm := [ + ⟨2, 4, 5, 0, 7, 4, 329800114128930685497107714871006078309079449600000⟩, + ⟨2, 4, 6, 0, 8, 4, 20317323603327374390491115286936612678783310233600000⟩, + ⟨2, 4, 5, 1, 6, 4, -54414460519886796399786550848020653275845178163200000⟩, + ⟨2, 4, 6, 1, 7, 4, -67949799432447398244075881358543218117657493504000000⟩, + ⟨2, 4, 7, 1, 8, 4, -63870278551652083677076993068201632502408177254400000⟩, + ⟨2, 4, 5, 2, 5, 4, 9518277124632568967168722273641693099657579724800000⟩, + ⟨2, 4, 6, 2, 6, 4, 4690548700583231859264201645931025628786799411200000⟩, + ⟨2, 4, 7, 2, 7, 4, 3770974403573935894282438215179522744839569408000000⟩, + ⟨2, 4, 8, 2, 8, 4, 20320364831043028697257036721379762271755121459200000⟩, + ⟨2, 4, 5, 3, 4, 4, -12882590758229775672286635594911646769681426022400000⟩, + ⟨2, 4, 6, 3, 5, 4, -11426825979297011497130414252421967374837822259200000⟩, + ⟨2, 4, 7, 3, 6, 4, 2944456359669517803015099288161814196785669734400000⟩, + ⟨2, 4, 8, 3, 7, 4, 12447376868968195030579551152473311569485234176000000⟩, + ⟨2, 4, 5, 4, 3, 4, 1201641782070082037201196081007570732615886438400000⟩, + ⟨2, 4, 6, 4, 4, 4, 5280785409583949043169392699987996038393757696000000⟩, + ⟨2, 4, 7, 4, 5, 4, 10137498314262809739935438491054594094046117888000000⟩, + ⟨2, 4, 8, 4, 6, 4, -15877105733901631797011330805720471135051998822400000⟩, + ⟨2, 4, 5, 5, 2, 4, 93332370814294238197618150478009488075435435622400000⟩, + ⟨2, 4, 6, 5, 3, 4, 1956140358704573347995918579671665682641688985600000⟩, + ⟨2, 4, 7, 5, 4, 4, -6423744607519771775337956630078906514939052032000000⟩, + ⟨2, 4, 8, 5, 5, 4, -5307236639161788624917607493950083300458286284800000⟩, + ⟨2, 4, 5, 6, 1, 4, -119238594466890003546771792725151544419563864064000000⟩, + ⟨2, 4, 6, 6, 2, 4, 140163271470009100126273024801156667007091448217600000⟩, + ⟨2, 4, 7, 6, 3, 4, -19261716678382139133181928188656972324360368947200000⟩, + ⟨2, 4, 8, 6, 4, 4, 7905941981422237114202278911332117188497427660800000⟩, + ⟨2, 4, 5, 7, 0, 4, -520229685135145669226313366806078299091995145011200000⟩, + ⟨2, 4, 6, 7, 1, 4, -277867250536725292647763223616319168386616315084800000⟩, + ⟨2, 4, 7, 7, 2, 4, 34205182921887722717701248590891730229089062092800000⟩, + ⟨2, 4, 8, 7, 3, 4, 37865102209577912606722222465404624461611873075200000⟩ +] + +def collectedFourData_11_2_20 : List CollectedFourTerm := [ + ⟨2, 5, 4, 0, 6, 5, 23037812710678506388023426987339021824362020864000000⟩, + ⟨2, 5, 5, 0, 7, 5, 297815625127269259751631601415864018119163904000000⟩, + ⟨2, 5, 6, 0, 8, 5, 9173460181812556619674034308610072690433196032000000⟩, + ⟨2, 5, 4, 1, 5, 5, -35699875536433951197479467000016652797480219443200000⟩, + ⟨2, 5, 5, 1, 6, 5, -49137267943327326047595934551370107060819591168000000⟩, + ⟨2, 5, 6, 1, 7, 5, -30679965118713861321097837803201455324638740480000000⟩, + ⟨2, 5, 7, 1, 8, 5, -19225349051351824636729684642644964052777828352000000⟩, + ⟨2, 5, 4, 2, 4, 5, 9518277124632568967168722273641693099657579724800000⟩, + ⟨2, 5, 5, 2, 5, 5, 8595180931013422683864214794229765000189181952000000⟩, + ⟨2, 5, 6, 2, 6, 5, 2117826273565190664563862557418659156374585344000000⟩, + ⟨2, 5, 7, 2, 7, 5, 1135086628967690999076536477844484678892912640000000⟩, + ⟨2, 5, 8, 2, 8, 5, 4587416662176640184268798417807958686723735552000000⟩, + ⟨2, 5, 4, 3, 3, 5, -12140402972750669315202031811639864360882405376000000⟩, + ⟨2, 5, 5, 3, 4, 5, -11633218593796797405288443988713041108848869376000000⟩, + ⟨2, 5, 6, 3, 5, 5, -5159317987553017361419690074072340811275567104000000⟩, + ⟨2, 5, 7, 3, 6, 5, 886299583543228025924417673241249320378826752000000⟩, + ⟨2, 5, 8, 3, 7, 5, 2810053093233062270668196770286149764183490560000000⟩, + ⟨2, 5, 4, 4, 2, 5, 40474974561579161859658225139561508047458349875200000⟩, + ⟨2, 5, 5, 4, 3, 5, 1085104835246794443365301228670527054299529216000000⟩, + ⟨2, 5, 6, 4, 4, 5, 2384323625951477786879818363109516739367403520000000⟩, + ⟨2, 5, 7, 4, 5, 5, 3051449719944144198292114074661068968338391040000000⟩, + ⟨2, 5, 8, 4, 6, 5, -3584330300978265432684265363735811101078585344000000⟩, + ⟨2, 5, 4, 5, 1, 5, -39022927294990946901001448890573894587521590886400000⟩, + ⟨2, 5, 5, 5, 2, 5, 84280863371086493130806736128238685335507173376000000⟩, + ⟨2, 5, 6, 5, 3, 5, 883215527840199701268319767716693880468406272000000⟩, + ⟨2, 5, 7, 5, 4, 5, -1933586874784534598897146014864292604081602560000000⟩, + ⟨2, 5, 8, 5, 5, 5, -1198133300806265824002359952101134522896089088000000⟩, + ⟨2, 5, 4, 6, 0, 5, -121752454395869726259662954988323269623856024780800000⟩, + ⟨2, 5, 5, 6, 1, 5, -107674664225771697564848321353269249366672015360000000⟩, + ⟨2, 5, 6, 6, 2, 5, 63285017991845119876729105822251333571011674112000000⟩, + ⟨2, 5, 7, 6, 3, 5, -5797895905067460647335435154738742307665739776000000⟩, + ⟨2, 5, 8, 6, 4, 5, 1784803091742352895530312514684276629882011648000000⟩, + ⟨2, 5, 5, 7, 0, 5, -469777062683844873237388563283166524567808114688000000⟩, + ⟨2, 5, 6, 7, 1, 5, -125459642637720847351230254852488848133299634176000000⟩, + ⟨2, 5, 7, 7, 2, 5, 10295971709389389477374460036839996740205543424000000⟩, + ⟨2, 5, 8, 7, 3, 5, 8548222545978924212303056280572852994951872512000000⟩ +] + +def collectedFourData_11_2_21 : List CollectedFourTerm := [ + ⟨2, 6, 3, 0, 5, 6, 10816754100458966467077784688238888203593973760000000⟩, + ⟨2, 6, 4, 0, 6, 6, 11352893077120228922297091863626900144826351616000000⟩, + ⟨2, 6, 5, 0, 7, 6, 73380858487455550464815286701760888006770688000000⟩, + ⟨2, 6, 6, 0, 8, 6, 1506875007323131960000174485581095553766260736000000⟩, + ⟨2, 6, 3, 1, 4, 6, -10347405019593005519422156104161851649558996582400000⟩, + ⟨2, 6, 4, 1, 5, 6, -17592680126432804806462410891639585444274687180800000⟩, + ⟨2, 6, 5, 1, 6, 6, -12107272423562749452490642580451523930720567296000000⟩, + ⟨2, 6, 6, 1, 7, 6, -5039633000707129326048255109020641282532311040000000⟩, + ⟨2, 6, 7, 1, 8, 6, -2368533580980351560327265528712839404634243072000000⟩, + ⟨2, 6, 3, 2, 3, 6, 7177772731284851611994964497537569049068280217600000⟩, + ⟨2, 6, 4, 2, 4, 6, 4690548700583231859264201645931025628786799411200000⟩, + ⟨2, 6, 5, 2, 5, 6, 2117826273565190664563862557418659156374585344000000⟩, + ⟨2, 6, 6, 2, 6, 6, 347883941090711597991122442791374790603046912000000⟩, + ⟨2, 6, 7, 2, 7, 6, 139840935571607756700916154936574035928023040000000⟩, + ⟨2, 6, 8, 2, 8, 6, 452130169820772887239249626825454998412433817600000⟩, + ⟨2, 6, 3, 3, 2, 6, -4733114872782637501964809344255733152895048089600000⟩, + ⟨2, 6, 4, 3, 3, 6, -5982716267109179466733083425685245981248978944000000⟩, + ⟨2, 6, 5, 3, 4, 6, -2866389454952997111811146047803432501323497472000000⟩, + ⟨2, 6, 6, 3, 5, 6, -847493440445739160262243909402245779676987392000000⟩, + ⟨2, 6, 7, 3, 6, 6, 109190752314763793147410059027975024748265472000000⟩, + ⟨2, 6, 8, 3, 7, 6, 276955392503200342582532496789079324757065728000000⟩, + ⟨2, 6, 3, 4, 1, 6, 4370247186106358709361848213204620932478612275200000⟩, + ⟨2, 6, 4, 4, 2, 6, 19945819695104035480199266268819271601649142988800000⟩, + ⟨2, 6, 5, 4, 3, 6, 267366510152955389602185481458928932410621952000000⟩, + ⟨2, 6, 6, 4, 4, 6, 391660029052030360475529146971513965993000960000000⟩, + ⟨2, 6, 7, 4, 5, 6, 375933935610526561351739374146365871819325440000000⟩, + ⟨2, 6, 8, 4, 6, 6, -353267206146064253225596835108329237677028147200000⟩, + ⟨2, 6, 3, 5, 0, 6, -5249277929390705111073732271404162625684950220800000⟩, + ⟨2, 6, 4, 5, 1, 6, -19230259690882819417624959059408242104484862361600000⟩, + ⟨2, 6, 5, 5, 2, 6, 20766546770644860796860311195391715194250985472000000⟩, + ⟨2, 6, 6, 5, 3, 6, 145081068495915914386411527510288174736736256000000⟩, + ⟨2, 6, 7, 5, 4, 6, -238214943845089540361613897288464300412764160000000⟩, + ⟨2, 6, 8, 5, 5, 6, -118086551245255363222930548809479405420570214400000⟩, + ⟨2, 6, 4, 6, 0, 6, -59998864214768424792111409402290001848759956275200000⟩, + ⟨2, 6, 5, 6, 1, 6, -26530707698291861185135126276739218439845969920000000⟩, + ⟨2, 6, 6, 6, 2, 6, 10395489821711281355168688449730382499546136576000000⟩, + ⟨2, 6, 7, 6, 3, 6, -714291902503333306922192928378583275993563136000000⟩, + ⟨2, 6, 8, 6, 4, 6, 175908007576364791736901878306146312742397542400000⟩, + ⟨2, 6, 5, 7, 0, 6, -115751630367695220529202917995517769047118708736000000⟩, + ⟨2, 6, 6, 7, 1, 6, -20608581295560700857974420887951267290622722048000000⟩, + ⟨2, 6, 7, 7, 2, 6, 1268447957817323634155730254855920338352472064000000⟩, + ⟨2, 6, 8, 7, 3, 6, 842502348488525153351251252253200296019859865600000⟩ +] + +def collectedFourData_11_2_22 : List CollectedFourTerm := [ + ⟨2, 7, 2, 0, 4, 7, -2530322541915477942843079749338673398862053376000000⟩, + ⟨2, 7, 3, 0, 5, 7, 17392294780997500921830187627616669539290316800000000⟩, + ⟨2, 7, 4, 0, 6, 7, 9127177209568010780193436860205581026658877440000000⟩, + ⟨2, 7, 5, 0, 7, 7, 39329775218560750920897247692999150041825280000000⟩, + ⟨2, 7, 6, 0, 8, 7, 605727330076997054949652234758220692974469120000000⟩, + ⟨2, 7, 2, 1, 3, 7, 1510717642380644241474022446158738614275538944000000⟩, + ⟨2, 7, 3, 1, 4, 7, -16637626837749659193534869390774598746800914432000000⟩, + ⟨2, 7, 4, 1, 5, 7, -14143664351847140094530431692198253801475407872000000⟩, + ⟨2, 7, 5, 1, 6, 7, -6489107823806728459979682683730572737259765760000000⟩, + ⟨2, 7, 6, 1, 7, 7, -2025810652675886003944483014968066154745036800000000⟩, + ⟨2, 7, 7, 1, 8, 7, -761674599542832810733547309310953245158408192000000⟩, + ⟨2, 7, 2, 2, 2, 7, 368835027437935425225581202168160829860478976000000⟩, + ⟨2, 7, 3, 2, 3, 7, 11541164572486185552717848476453430481616109568000000⟩, + ⟨2, 7, 4, 2, 4, 7, 3770974403573935894282438215179522744839569408000000⟩, + ⟨2, 7, 5, 2, 5, 7, 1135086628967690999076536477844484678892912640000000⟩, + ⟨2, 7, 6, 2, 6, 7, 139840935571607756700916154936574035928023040000000⟩, + ⟨2, 7, 7, 2, 7, 7, 44970140789438532803635293189243837811261440000000⟩, + ⟨2, 7, 8, 2, 8, 7, 121163599848184923721182109934829578829692928000000⟩, + ⟨2, 7, 2, 3, 1, 7, 2113817295507806303723705597767084907534745600000000⟩, + ⟨2, 7, 3, 3, 2, 7, -7610391096555130381869132948984525002561814528000000⟩, + ⟨2, 7, 4, 3, 3, 7, -4809814660768554655251481686663368132221992960000000⟩, + ⟨2, 7, 5, 3, 4, 7, -1536292369370769705403645745628965346025144320000000⟩, + ⟨2, 7, 6, 3, 5, 7, -340671878187760080561087904309338215955824640000000⟩, + ⟨2, 7, 7, 3, 6, 7, 35113634533610729093661272309645923521134592000000⟩, + ⟨2, 7, 8, 3, 7, 7, 74219582308247473149703080702231388713123840000000⟩, + ⟨2, 7, 2, 4, 0, 7, -8095007209930237217221392079788720426458284032000000⟩, + ⟨2, 7, 3, 4, 1, 7, 7026934940063166379883060297723885785328910336000000⟩, + ⟨2, 7, 4, 4, 2, 7, 16035474808988936474470495106927196603880046592000000⟩, + ⟨2, 7, 5, 4, 3, 7, 143299832708885435130715288088537201765253120000000⟩, + ⟨2, 7, 6, 4, 4, 7, 157437864814684157989004308618725098206003200000000⟩, + ⟨2, 7, 7, 4, 5, 7, 120893084294878854912735240597780393980067840000000⟩, + ⟨2, 7, 8, 4, 6, 7, -94669918669518114866539620779110990627209216000000⟩, + ⟨2, 7, 3, 5, 0, 7, -8440331386610101414793085015096846427770322944000000⟩, + ⟨2, 7, 4, 5, 1, 7, -15460199157378295654440781202972335020120735744000000⟩, + ⟨2, 7, 5, 5, 2, 7, 11130199801284871394583810485272446899658424320000000⟩, + ⟨2, 7, 6, 5, 3, 7, 58319082762452584901409972215732401361387520000000⟩, + ⟨2, 7, 7, 5, 4, 7, -76605319601686557764280629386070244206837760000000⟩, + ⟨2, 7, 8, 5, 5, 7, -31645292877057946425960298852376737619116032000000⟩, + ⟨2, 7, 4, 6, 0, 7, -48236186348361982811295991132403757376673415168000000⟩, + ⟨2, 7, 5, 6, 1, 7, -14219604290150615915350553008201372968104755200000000⟩, + ⟨2, 7, 6, 6, 2, 7, 4178735637625111629625418694431212839024721920000000⟩, + ⟨2, 7, 7, 6, 3, 7, -229702463652943187396238109852419687444381696000000⟩, + ⟨2, 7, 8, 6, 4, 7, 47140511433959391053700907178832099249487872000000⟩, + ⟨2, 7, 5, 7, 0, 7, -62039143413968513999235206259072722429710172160000000⟩, + ⟨2, 7, 6, 7, 1, 7, -8284151548183352491807073355006323896520540160000000⟩, + ⟨2, 7, 7, 7, 2, 7, 407908335380890184148810405982006147761045504000000⟩, + ⟨2, 7, 8, 7, 3, 7, 225777053240851141054597121230373074520506368000000⟩ +] + +def collectedFourData_11_2_23 : List CollectedFourTerm := [ + ⟨2, 8, 1, 0, 3, 8, -21864487203824184209264182982834026260214893772800000⟩, + ⟨2, 8, 2, 0, 4, 8, -40904873665971489303896222760631073524308718387200000⟩, + ⟨2, 8, 3, 0, 5, 8, 140580817068380368946057950175962145904635412480000000⟩, + ⟨2, 8, 4, 0, 6, 8, 49182930173227008375700092483713267431171424256000000⟩, + ⟨2, 8, 5, 0, 7, 8, 158950040950947556440189200687425340628271104000000⟩, + ⟨2, 8, 6, 0, 8, 8, 1958422256639993706154601255043229286077877452800000⟩, + ⟨2, 8, 1, 1, 2, 8, -6416526810345972217275350222259198067394740224000000⟩, + ⟨2, 8, 2, 1, 3, 8, 24422070025805726773704020880409095365309811916800000⟩, + ⟨2, 8, 3, 1, 4, 8, -134480883884577063660339256378295284212847293235200000⟩, + ⟨2, 8, 4, 1, 5, 8, -76214895387506334864521234714320661155731524812800000⟩, + ⟨2, 8, 5, 1, 6, 8, -26225523756424324929672259040490712211619053568000000⟩, + ⟨2, 8, 6, 1, 7, 8, -6549799675432396102548004099069982346200481792000000⟩, + ⟨2, 8, 7, 1, 8, 8, -2052189180942222418672476947331464269880780390400000⟩, + ⟨2, 8, 1, 2, 1, 8, -23505227723549774451038493845426132886457260441600000⟩, + ⟨2, 8, 2, 2, 2, 8, 5962540328756966295013276483985778919569830707200000⟩, + ⟨2, 8, 3, 2, 3, 8, 93286502209784843918099462745222033750102953164800000⟩, + ⟨2, 8, 4, 2, 4, 8, 20320364831043028697257036721379762271755121459200000⟩, + ⟨2, 8, 5, 2, 5, 8, 4587416662176640184268798417807958686723735552000000⟩, + ⟨2, 8, 6, 2, 6, 8, 452130169820772887239249626825454998412433817600000⟩, + ⟨2, 8, 7, 2, 7, 8, 121163599848184923721182109934829578829692928000000⟩, + ⟨2, 8, 8, 2, 8, 8, 279816486554795978662059498953770337020202188800000⟩, + ⟨2, 8, 1, 3, 0, 8, -20629110930134543482318741357983757734052154572800000⟩, + ⟨2, 8, 2, 3, 1, 8, 34171702616314360119932439469798232185708216320000000⟩, + ⟨2, 8, 3, 3, 2, 8, -61514309183200659017057507128555790355462409420800000⟩, + ⟨2, 8, 4, 3, 3, 8, -25918284829482322933789035365297197072414408704000000⟩, + ⟨2, 8, 5, 3, 4, 8, -6208876955616839515112122303189473460985266176000000⟩, + ⟨2, 8, 6, 3, 5, 8, -1101451685149239692614493548018300900869773721600000⟩, + ⟨2, 8, 7, 3, 6, 8, 94607094600090902019775813126050692874004070400000⟩, + ⟨2, 8, 8, 3, 7, 8, 171403480757256594087172269811701134093451264000000⟩, + ⟨2, 8, 2, 4, 0, 8, -130862861063024706664380387798935252466831615590400000⟩, + ⟨2, 8, 3, 4, 1, 8, 56798270027008709562709976280752016622700042649600000⟩, + ⟨2, 8, 4, 4, 2, 8, 86409151451368761619892710679175576451369716940800000⟩, + ⟨2, 8, 5, 4, 3, 8, 579141735511164796119358975249110585380438016000000⟩, + ⟨2, 8, 6, 4, 4, 8, 509024115606212873716748666362836971377655808000000⟩, + ⟨2, 8, 7, 4, 5, 8, 325723714286385137019847177637401512124612608000000⟩, + ⟨2, 8, 8, 4, 6, 8, -218631701746435669384330356407442284335438233600000⟩, + ⟨2, 8, 3, 5, 0, 8, -68222663978415602807513977495765350251315488358400000⟩, + ⟨2, 8, 4, 5, 1, 8, -83309207015770040796465769600700050286162057625600000⟩, + ⟨2, 8, 5, 5, 2, 8, 44982349997554841583372233285207593174670770176000000⟩, + ⟨2, 8, 6, 5, 3, 8, 188555780790506364501876787327442976389254348800000⟩, + ⟨2, 8, 7, 5, 4, 8, -206398648692710775972864922185685870011482112000000⟩, + ⟨2, 8, 8, 5, 5, 8, -73081970822514441582205441760663637786309427200000⟩, + ⟨2, 8, 4, 6, 0, 8, -259926692615025801717546683822506613912573784883200000⟩, + ⟨2, 8, 5, 6, 1, 8, -57468080396225077658169138495823051018846863360000000⟩, + ⟨2, 8, 6, 6, 2, 8, 13510582189348232097224036925124837600526126284800000⟩, + ⟨2, 8, 7, 6, 3, 8, -618890154702914299226449829607759532235371315200000⟩, + ⟨2, 8, 8, 6, 4, 8, 108866790854467217916775218348246386030621491200000⟩, + ⟨2, 8, 5, 7, 0, 8, -250729233294938356126172916762215117628100313088000000⟩, + ⟨2, 8, 6, 7, 1, 8, -26784108894803609465608244829148192766123468390400000⟩, + ⟨2, 8, 7, 7, 2, 8, 1099032412512188212628553104398538041893637324800000⟩, + ⟨2, 8, 8, 7, 3, 8, 521411891539276360539795638461714430534929612800000⟩ +] + +def collectedFourData_11_2_24 : List CollectedFourTerm := [ + ⟨3, 0, 8, 2, 8, 1, -20629110930134543482318741357983757734052154572800000⟩, + ⟨3, 0, 8, 3, 7, 1, -12636501379486081293238912809518887503642230784000000⟩, + ⟨3, 0, 8, 4, 6, 1, 16118341287542724331492918928962158728694045081600000⟩, + ⟨3, 0, 8, 5, 5, 1, 5387874394582081243508580937756387588946735923200000⟩, + ⟨3, 0, 8, 6, 4, 1, -8026064270894077554918607724359742355949171507200000⟩, + ⟨3, 0, 8, 7, 3, 1, -38440421732436528667874095252827610246028250316800000⟩ +] + +def collectedFourData_11_2_25 : List CollectedFourTerm := [ + ⟨3, 1, 7, 1, 8, 2, -35802443883848115242838279678321098154395566080000000⟩, + ⟨3, 1, 7, 2, 7, 2, 2113817295507806303723705597767084907534745600000000⟩, + ⟨3, 1, 8, 2, 8, 2, 34171702616314360119932439469798232185708216320000000⟩, + ⟨3, 1, 7, 3, 6, 2, 1650513133432715052439363143210387443369902080000000⟩, + ⟨3, 1, 8, 3, 7, 2, 20932107482134144804854466517193556240210329600000000⟩, + ⟨3, 1, 7, 4, 5, 2, 5682568210900828032906898048251187493968281600000000⟩, + ⟨3, 1, 8, 4, 6, 2, -26699704461891669789732581993278105088730071040000000⟩, + ⟨3, 1, 7, 5, 4, 2, -3600825940486675688014026164805932398569062400000000⟩, + ⟨3, 1, 8, 5, 5, 2, -8924904333941301220582382191440119254304686080000000⟩, + ⟨3, 1, 7, 6, 3, 2, -10797142992364796370011452472137229574120407040000000⟩, + ⟨3, 1, 8, 6, 4, 2, 13295012197727786416559366559987250421752135680000000⟩, + ⟨3, 1, 7, 7, 2, 2, 19173693459114694217255867777099445975342120960000000⟩, + ⟨3, 1, 8, 7, 3, 2, 63675776640848261393851762260213237291071569920000000⟩ +] + +def collectedFourData_11_2_26 : List CollectedFourTerm := [ + ⟨3, 2, 6, 0, 8, 3, -20501700901237690735234624362437352111796440268800000⟩, + ⟨3, 2, 6, 1, 7, 3, 68566435789553548702074424103574499701169324032000000⟩, + ⟨3, 2, 7, 1, 8, 3, 128899787482861073938334047671226944621998663270400000⟩, + ⟨3, 2, 6, 2, 6, 3, -4733114872782637501964809344255733152895048089600000⟩, + ⟨3, 2, 7, 2, 7, 3, -7610391096555130381869132948984525002561814528000000⟩, + ⟨3, 2, 8, 2, 8, 3, -61514309183200659017057507128555790355462409420800000⟩, + ⟨3, 2, 6, 3, 5, 3, 11530523067500555607726540311380838487690942873600000⟩, + ⟨3, 2, 7, 3, 6, 3, -5942353902637588063407199206568334745424782950400000⟩, + ⟨3, 2, 8, 3, 7, 3, -37681006005748339465540781372222459432323252224000000⟩, + ⟨3, 2, 6, 4, 4, 3, -5328707909794747260246710344798785020853485568000000⟩, + ⟨3, 2, 7, 4, 5, 3, -20458989814168245825674779902657212025780830208000000⟩, + ⟨3, 2, 8, 4, 6, 3, 48063565746494587387472980087798500885651888537600000⟩, + ⟨3, 2, 6, 5, 3, 3, -1973892100061500867081418064603238468026158284800000⟩, + ⟨3, 2, 7, 5, 4, 3, 12964078653326237251720128079136599109126848512000000⟩, + ⟨3, 2, 8, 5, 5, 3, 16066197543415440303696412869047902978803184435200000⟩, + ⟨3, 2, 6, 6, 2, 3, -141435236506569235808233868424446222441152040140800000⟩, + ⟨3, 2, 7, 6, 3, 3, 38873028937718903114201125624429683745399976755200000⟩, + ⟨3, 2, 8, 6, 4, 3, -23933062396926003595194576509561874066250609459200000⟩, + ⟨3, 2, 6, 7, 1, 3, 280388862823460734533269144119717050947572491878400000⟩, + ⟨3, 2, 7, 7, 2, 3, -69031181786347026468511655583689273673226439884800000⟩, + ⟨3, 2, 8, 7, 3, 3, -114626170540753611502807603002027365246220160204800000⟩ +] + +def collectedFourData_11_2_27 : List CollectedFourTerm := [ + ⟨3, 3, 5, 0, 7, 4, -420654519043428422516650714054659368395210752000000⟩, + ⟨3, 3, 6, 0, 8, 4, -25914405794493481237194220711015491035392376832000000⟩, + ⟨3, 3, 5, 1, 6, 4, 69404732558862016375527649826926855446734045184000000⟩, + ⟨3, 3, 6, 1, 7, 4, 86668830527388217245153422137418647534546452480000000⟩, + ⟨3, 3, 7, 1, 8, 4, 81465470005300272472308675299579915778788425728000000⟩, + ⟨3, 3, 5, 2, 5, 4, -12140402972750669315202031811639864360882405376000000⟩, + ⟨3, 3, 6, 2, 6, 4, -5982716267109179466733083425685245981248978944000000⟩, + ⟨3, 3, 7, 2, 7, 4, -4809814660768554655251481686663368132221992960000000⟩, + ⟨3, 3, 8, 2, 8, 4, -25918284829482322933789035365297197072414408704000000⟩, + ⟨3, 3, 5, 3, 4, 4, 16431528635911672003447796225883678632614821888000000⟩, + ⟨3, 3, 6, 3, 5, 4, 14574725054931327476290226574737148443784904704000000⟩, + ⟨3, 3, 7, 3, 6, 4, -3755604745900519642978884442084536353531363328000000⟩, + ⟨3, 3, 8, 3, 7, 4, -15876420613126756699317948394377919966866309120000000⟩, + ⟨3, 3, 5, 4, 3, 4, -1532673956873070961920893511862140425950199808000000⟩, + ⟨3, 3, 6, 4, 4, 4, -6735553298722239831777449727851705671373291520000000⟩, + ⟨3, 3, 7, 4, 5, 4, -12930209223707811974743657713944181707699650560000000⟩, + ⟨3, 3, 8, 4, 6, 4, 20250982307680698806918095810670641407105957888000000⟩, + ⟨3, 3, 5, 5, 2, 4, -119043874983989394017543106741113261113252773888000000⟩, + ⟨3, 3, 6, 5, 3, 4, -2495024248083269820106417320519637716877443072000000⟩, + ⟨3, 3, 7, 5, 4, 4, 8193378602888137735123060564294237129896099840000000⟩, + ⟨3, 3, 8, 5, 5, 4, 6769291398800105605720870989707023937307672576000000⟩, + ⟨3, 3, 5, 6, 1, 4, 152086829136982532374026404130015757356163399680000000⟩, + ⟨3, 3, 6, 6, 2, 4, -178775904015365109482313984688361043852276006912000000⟩, + ⟨3, 3, 7, 6, 3, 4, 24567996850747158111373193165420213014326411264000000⟩, + ⟨3, 3, 8, 6, 4, 4, -10083896515815931427100705068053197700460445696000000⟩, + ⟨3, 3, 5, 7, 0, 4, 663544245794553277768509612446019425723895250944000000⟩, + ⟨3, 3, 6, 7, 1, 4, 354415021781196335380908982741704283614741528576000000⟩, + ⟨3, 3, 7, 7, 2, 4, -43628137633615754347334199870985613252845633536000000⟩, + ⟨3, 3, 8, 7, 3, 4, -48296303355047900861113400704617437336514330624000000⟩ +] + +def collectedFourData_11_2_28 : List CollectedFourTerm := [ + ⟨3, 4, 4, 0, 6, 5, -31180717815869659978901898833226856645087199232000000⟩, + ⟨3, 4, 5, 0, 7, 5, -403081016625588824635989479332358169928138752000000⟩, + ⟨3, 4, 6, 0, 8, 5, -12415895420125127409040089741786127631873212416000000⟩, + ⟨3, 4, 4, 1, 5, 5, 48318291286709191559509613102674227021418699161600000⟩, + ⟨3, 4, 5, 1, 6, 5, 66505240980342323923219333263855619060147421184000000⟩, + ⟨3, 4, 6, 1, 7, 5, 41524052086938191312453004038155613585528586240000000⟩, + ⟨3, 4, 7, 1, 8, 5, 26020707400053496169853561343675433571714072576000000⟩, + ⟨3, 4, 4, 2, 4, 5, -12882590758229775672286635594911646769681426022400000⟩, + ⟨3, 4, 5, 2, 5, 5, -11633218593796797405288443988713041108848869376000000⟩, + ⟨3, 4, 6, 2, 6, 5, -2866389454952997111811146047803432501323497472000000⟩, + ⟨3, 4, 7, 2, 7, 5, -1536292369370769705403645745628965346025144320000000⟩, + ⟨3, 4, 8, 2, 8, 5, -6208876955616839515112122303189473460985266176000000⟩, + ⟨3, 4, 4, 3, 3, 5, 16431528635911672003447796225883678632614821888000000⟩, + ⟨3, 4, 5, 3, 4, 5, 15745075750849042278936116476339692308306853888000000⟩, + ⟨3, 4, 6, 3, 5, 5, 6982921526124917099731240685898968818727780352000000⟩, + ⟨3, 4, 7, 3, 6, 5, -1199569488729048472531534948219342000043851776000000⟩, + ⟨3, 4, 8, 3, 7, 5, -3803289559129818758841281078934370591734497280000000⟩, + ⟨3, 4, 4, 4, 2, 5, -54781188486011147276238865040469152865564858777600000⟩, + ⟨3, 4, 5, 4, 3, 5, -1468644098004282771503689441190917343237111808000000⟩, + ⟨3, 4, 6, 4, 4, 5, -3227082496770353963887369038418872782039285760000000⟩, + ⟨3, 4, 7, 4, 5, 5, -4130009816547841162849503494565703691293163520000000⟩, + ⟨3, 4, 8, 4, 6, 5, 4851241438466528067055357753136588390475497472000000⟩, + ⟨3, 4, 4, 5, 1, 5, 52815903124792558866515277260976661854036374323200000⟩, + ⟨3, 4, 5, 5, 2, 5, -114070630361258615108551274051109032942672805888000000⟩, + ⟨3, 4, 6, 5, 3, 5, -1195395348075496925763461556851885268623425536000000⟩, + ⟨3, 4, 7, 5, 4, 5, 2617029119573487686356500925819925380233953280000000⟩, + ⟨3, 4, 8, 5, 5, 5, 1621623407890634482980600819903666951913734144000000⟩, + ⟨3, 4, 4, 6, 0, 5, 164786864603143330816210467745522746658988123750400000⟩, + ⟨3, 4, 5, 6, 1, 5, 145733163269709653628682215773608038014574919680000000⟩, + ⟨3, 4, 6, 6, 2, 5, -85653630088819337671404856835658876717373587456000000⟩, + ⟨3, 4, 7, 6, 3, 5, 7847210080751209251657653608469910875786969088000000⟩, + ⟨3, 4, 8, 6, 4, 5, -2415656480040504495698275835712503374543847424000000⟩, + ⟨3, 4, 5, 7, 0, 5, 635823644018228910150254672372737309799501266944000000⟩, + ⟨3, 4, 6, 7, 1, 5, 169804389136012291308689986448880961613136396288000000⟩, + ⟨3, 4, 7, 7, 2, 5, -13935167914697082079907421078091666578066112512000000⟩, + ⟨3, 4, 8, 7, 3, 5, -11569662379878495678943976968803067616512966656000000⟩ +] + +def collectedFourData_11_2_29 : List CollectedFourTerm := [ + ⟨3, 5, 3, 0, 5, 6, -26351110425827832690796129669356551376375644160000000⟩, + ⟨3, 5, 4, 0, 6, 6, -27657219194353114967664325495663198232175968256000000⟩, + ⟨3, 5, 5, 0, 7, 6, -178765929888610409830547738886298875312734208000000⟩, + ⟨3, 5, 6, 0, 8, 6, -3670956124832968936901772031965618055912882176000000⟩, + ⟨3, 5, 3, 1, 4, 6, 25207711089641115446834896366067442301427672678400000⟩, + ⟨3, 5, 4, 1, 5, 6, 42858204262795168647602801322878285300108152012800000⟩, + ⟨3, 5, 5, 1, 6, 6, 29494991716169730298605012787373308515383771136000000⟩, + ⟨3, 5, 6, 1, 7, 6, 12277243660521486547866617375912814701067632640000000⟩, + ⟨3, 5, 7, 1, 8, 6, 5770075695540347172386514349500573586871549952000000⟩, + ⟨3, 5, 3, 2, 3, 6, -17486048041487553292787457298428169230380276121600000⟩, + ⟨3, 5, 4, 2, 4, 6, -11426825979297011497130414252421967374837822259200000⟩, + ⟨3, 5, 5, 2, 5, 6, -5159317987553017361419690074072340811275567104000000⟩, + ⟨3, 5, 6, 2, 6, 6, -847493440445739160262243909402245779676987392000000⟩, + ⟨3, 5, 7, 2, 7, 6, -340671878187760080561087904309338215955824640000000⟩, + ⟨3, 5, 8, 2, 8, 6, -1101451685149239692614493548018300900869773721600000⟩, + ⟨3, 5, 3, 3, 2, 6, 11530523067500555607726540311380838487690942873600000⟩, + ⟨3, 5, 4, 3, 3, 6, 14574725054931327476290226574737148443784904704000000⟩, + ⟨3, 5, 5, 3, 4, 6, 6982921526124917099731240685898968818727780352000000⟩, + ⟨3, 5, 6, 3, 5, 6, 2064611345228124325489229921110514115199107072000000⟩, + ⟨3, 5, 7, 3, 6, 6, -266003788659989037395928650056978504039268352000000⟩, + ⟨3, 5, 8, 3, 7, 6, -674701676963392990147499132728891134965710848000000⟩, + ⟨3, 5, 3, 4, 1, 6, -10646527148506188069910508392794407928325157683200000⟩, + ⟨3, 5, 4, 4, 2, 6, -48590778013252287455890106510013717847768616140800000⟩, + ⟨3, 5, 5, 4, 3, 6, -651341832103754839864035207065658006838444032000000⟩, + ⟨3, 5, 6, 4, 4, 6, -954138050942201940665844562198059965334159360000000⟩, + ⟨3, 5, 7, 4, 5, 6, -915827110248230721895450632064239880152023040000000⟩, + ⟨3, 5, 8, 4, 6, 6, 860607819362708247877648761484651298129392435200000⟩, + ⟨3, 5, 3, 5, 0, 6, 12787967729373278334365101173157951490115816652800000⟩, + ⟨3, 5, 4, 5, 1, 6, 46847574783113310484187999540484727114307312025600000⟩, + ⟨3, 5, 5, 5, 2, 6, -50590182788121429528052479449298009713490788352000000⟩, + ⟨3, 5, 6, 5, 3, 6, -353437567418746792180195664581141269363818496000000⟩, + ⟨3, 5, 7, 5, 4, 6, 580324580927468913004672564736554223334850560000000⟩, + ⟨3, 5, 8, 5, 5, 6, 287675186360838874679155742081967139492095590400000⟩, + ⟨3, 5, 4, 6, 0, 6, 146165539279526343077006382607357702725428261683200000⟩, + ⟨3, 5, 5, 6, 1, 6, 64632476780015297341802292628520186552223006720000000⟩, + ⟨3, 5, 6, 6, 2, 6, -25324852324308639480765326997737343564556271616000000⟩, + ⟨3, 5, 7, 6, 3, 6, 1740113958802237182498781523315310451885080576000000⟩, + ⟨3, 5, 8, 6, 4, 6, -428536258602334675774899191721713040368232038400000⟩, + ⟨3, 5, 5, 7, 0, 6, 281986995864066145063561428158953644717219250176000000⟩, + ⟨3, 5, 6, 7, 1, 6, 50205357022577361961592510511864132911096659968000000⟩, + ⟨3, 5, 7, 7, 2, 6, -3090114825152754527672000429311582181076762624000000⟩, + ⟨3, 5, 8, 7, 3, 6, -2052452354269420097255948289823002401827297689600000⟩ +] + +def collectedFourData_11_2_30 : List CollectedFourTerm := [ + ⟨3, 6, 2, 0, 4, 7, -1975729215636425295638673423240250652745321676800000⟩, + ⟨3, 6, 3, 0, 5, 7, 13580270640028751786033600629407629539792650240000000⟩, + ⟨3, 6, 4, 0, 6, 7, 7126692494935226954242464314612612917616443392000000⟩, + ⟨3, 6, 5, 0, 7, 7, 30709518117362439129393461288197220418453504000000⟩, + ⟨3, 6, 6, 0, 8, 7, 472964676604674307755841045293942281827516416000000⟩, + ⟨3, 6, 2, 1, 3, 7, 1179600202418985577812385559759283212369736499200000⟩, + ⟨3, 6, 3, 1, 4, 7, -12991009990890204855502994041488386941001505177600000⟩, + ⟨3, 6, 4, 1, 5, 7, -11043671473971816474077561944074745464015657369600000⟩, + ⟨3, 6, 5, 1, 6, 7, -5066832270799932423772527569459709349743034368000000⟩, + ⟨3, 6, 6, 1, 7, 7, -1581795690287511050946878129745835472443146240000000⟩, + ⟨3, 6, 7, 1, 8, 7, -594731594172873375925944093474328964157249945600000⟩, + ⟨3, 6, 2, 2, 2, 7, 287994169671169700210701998798767404557847756800000⟩, + ⟨3, 6, 3, 2, 3, 7, 9011584748823183323910467860757201798763538022400000⟩, + ⟨3, 6, 4, 2, 4, 7, 2944456359669517803015099288161814196785669734400000⟩, + ⟨3, 6, 5, 2, 5, 7, 886299583543228025924417673241249320378826752000000⟩, + ⟨3, 6, 6, 2, 6, 7, 109190752314763793147410059027975024748265472000000⟩, + ⟨3, 6, 7, 2, 7, 7, 35113634533610729093661272309645923521134592000000⟩, + ⟨3, 6, 8, 2, 8, 7, 94607094600090902019775813126050692874004070400000⟩, + ⟨3, 6, 2, 3, 1, 7, 1650513133432715052439363143210387443369902080000000⟩, + ⟨3, 6, 3, 3, 2, 7, -5942353902637588063407199206568334745424782950400000⟩, + ⟨3, 6, 4, 3, 3, 7, -3755604745900519642978884442084536353531363328000000⟩, + ⟨3, 6, 5, 3, 4, 7, -1199569488729048472531534948219342000043851776000000⟩, + ⟨3, 6, 6, 3, 5, 7, -266003788659989037395928650056978504039268352000000⟩, + ⟨3, 6, 7, 3, 6, 7, 27417466534806772005729328894948189085997465600000⟩, + ⟨3, 6, 8, 3, 7, 7, 57952215462512023193363424424555820101926912000000⟩, + ⟨3, 6, 2, 4, 0, 7, -6320752386507774364683662434041127886166530457600000⟩, + ⟨3, 6, 3, 4, 1, 7, 5486779028158752718976330619755317233235840204800000⟩, + ⟨3, 6, 4, 4, 2, 7, 12520836984971086385596429690392451808279239065600000⟩, + ⟨3, 6, 5, 4, 3, 7, 111891532161916172483449050598335966521327616000000⟩, + ⟨3, 6, 6, 4, 4, 7, 122930805859366151983303138789708617492725760000000⟩, + ⟨3, 6, 7, 4, 5, 7, 94395870349783959913422889651133340148826112000000⟩, + ⟨3, 6, 8, 4, 6, 7, -73920269475091722805556082903051840760106188800000⟩, + ⟨3, 6, 3, 5, 0, 7, -6590388787966506917818096448640650467930747699200000⟩, + ⟨3, 6, 4, 5, 1, 7, -12071649621264079941165162622865729652889170739200000⟩, + ⟨3, 6, 5, 5, 2, 7, 8690694786532005314731082452019439024551755776000000⟩, + ⟨3, 6, 6, 5, 3, 7, 45536770010226260715184191823027202515009536000000⟩, + ⟨3, 6, 7, 5, 4, 7, -59815049466240557110960738208979865690963968000000⟩, + ⟨3, 6, 8, 5, 5, 7, -24709312207780637467546550055230393955228057600000⟩, + ⟨3, 6, 4, 6, 0, 7, -37663831800351202236976180126749783029210048102400000⟩, + ⟨3, 6, 5, 6, 1, 7, -11102966979684786007053809390849619045761679360000000⟩, + ⟨3, 6, 6, 6, 2, 7, 3262844932578094106764731440991834227349651456000000⟩, + ⟨3, 6, 7, 6, 3, 7, -179356528989869591577140524366132818102504652800000⟩, + ⟨3, 6, 8, 6, 4, 7, 36808305714895551712555617186416392457001369600000⟩, + ⟨3, 6, 5, 7, 0, 7, -48441471838308463853662062531259888740637605888000000⟩, + ⟨3, 6, 6, 7, 1, 7, -6468440275647790980936878043826062935917068288000000⟩, + ⟨3, 6, 7, 7, 2, 7, 318503432729789369996317004537594244043584307200000⟩, + ⟨3, 6, 8, 7, 3, 7, 176291485737058567349488796840550331509532262400000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1107.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1107.lean new file mode 100644 index 0000000000000000000000000000000000000000..2c963edaf28b501d32f3783b4a717a86523d8c24 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1107.lean @@ -0,0 +1,638 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1107. -/ +namespace LaughlinFock +def collectedFourData_11_2_31 : List CollectedFourTerm := [ + ⟨3, 7, 1, 0, 3, 8, -13393239468661779258381002264152076487474806784000000⟩, + ⟨3, 7, 2, 0, 4, 8, -25056556933468455949107230357804087866363478016000000⟩, + ⟨3, 7, 3, 0, 5, 8, 86113730001755482039994990963373901510764134400000000⟩, + ⟨3, 7, 4, 0, 6, 8, 30127336417260579720431685495993048963408199680000000⟩, + ⟨3, 7, 5, 0, 7, 8, 97365922290521027293482261732906633390981120000000⟩, + ⟨3, 7, 6, 0, 8, 8, 1199644794749577722560543609937678328800477184000000⟩, + ⟨3, 7, 1, 1, 2, 8, -3930486881623331386512110997856145659102494720000000⟩, + ⟨3, 7, 2, 1, 3, 8, 14959904118804745103400563514045961613925679104000000⟩, + ⟨3, 7, 3, 1, 4, 8, -82377174686649584650047445449003286516734099456000000⟩, + ⟨3, 7, 4, 1, 5, 8, -46685949480001651461495613579201086913442217984000000⟩, + ⟨3, 7, 5, 1, 6, 8, -16064621895154043287430721211153927692657623040000000⟩, + ⟨3, 7, 6, 1, 7, 8, -4012124076227416734488497403105215738816757760000000⟩, + ⟨3, 7, 7, 1, 8, 8, -1257082358215506122438937380355855525989056512000000⟩, + ⟨3, 7, 1, 2, 1, 8, -14398286167528694924470215214113118235758952448000000⟩, + ⟨3, 7, 2, 2, 2, 8, 3652394392795452935032280740862097338312687616000000⟩, + ⟨3, 7, 3, 2, 3, 8, 57143277664932760896840246410284924590090092544000000⟩, + ⟨3, 7, 4, 2, 4, 8, 12447376868968195030579551152473311569485234176000000⟩, + ⟨3, 7, 5, 2, 5, 8, 2810053093233062270668196770286149764183490560000000⟩, + ⟨3, 7, 6, 2, 6, 8, 276955392503200342582532496789079324757065728000000⟩, + ⟨3, 7, 7, 2, 7, 8, 74219582308247473149703080702231388713123840000000⟩, + ⟨3, 7, 8, 2, 8, 8, 171403480757256594087172269811701134093451264000000⟩, + ⟨3, 7, 1, 3, 0, 8, -12636501379486081293238912809518887503642230784000000⟩, + ⟨3, 7, 2, 3, 1, 8, 20932107482134144804854466517193556240210329600000000⟩, + ⟨3, 7, 3, 3, 2, 8, -37681006005748339465540781372222459432323252224000000⟩, + ⟨3, 7, 4, 3, 3, 8, -15876420613126756699317948394377919966866309120000000⟩, + ⟨3, 7, 5, 3, 4, 8, -3803289559129818758841281078934370591734497280000000⟩, + ⟨3, 7, 6, 3, 5, 8, -674701676963392990147499132728891134965710848000000⟩, + ⟨3, 7, 7, 3, 6, 8, 57952215462512023193363424424555820101926912000000⟩, + ⟨3, 7, 8, 3, 7, 8, 104994361045091468421935341972185197492305920000000⟩, + ⟨3, 7, 2, 4, 0, 8, -80160930344835853267839701228169422881016512512000000⟩, + ⟨3, 7, 3, 4, 1, 8, 34792164334153272364788896914935228363008114688000000⟩, + ⟨3, 7, 4, 4, 2, 8, 52930509958158513067910360810683302178480717824000000⟩, + ⟨3, 7, 5, 4, 3, 8, 354757185827836687708652257019439052467732480000000⟩, + ⟨3, 7, 6, 4, 4, 8, 311806163670071457268773839438875472418570240000000⟩, + ⟨3, 7, 7, 4, 5, 8, 199524263495944626244611721635568042628874240000000⟩, + ⟨3, 7, 8, 4, 6, 8, -133924327135323867275254870713175487658590208000000⟩, + ⟨3, 7, 3, 5, 0, 8, -41790254092634400581726409460331989175529111552000000⟩, + ⟨3, 7, 4, 5, 1, 8, -51031618034534640546316243566407724355150675968000000⟩, + ⟨3, 7, 5, 5, 2, 8, 27554242629346326240349460683257500077947617280000000⟩, + ⟨3, 7, 6, 5, 3, 8, 115501118401992562276121883255488734574936064000000⟩, + ⟨3, 7, 7, 5, 4, 8, -126430887776145781673516450842669477118607360000000⟩, + ⟨3, 7, 8, 5, 5, 8, -44766855355130042707025751988750266679689216000000⟩, + ⟨3, 7, 4, 6, 0, 8, -159219852998948712761671483901976589046063824896000000⟩, + ⟨3, 7, 5, 6, 1, 8, -35202461204593413728089100699986943657430220800000000⟩, + ⟨3, 7, 6, 6, 2, 8, 8275998468938648225937725264009277935550726144000000⟩, + ⟨3, 7, 7, 6, 3, 8, -379105348754005883397401966344027595505401856000000⟩, + ⟨3, 7, 8, 6, 4, 8, 66687088816954913958078217424063092947419136000000⟩, + ⟨3, 7, 5, 7, 0, 8, -153585887105814892275386705695361030748257648640000000⟩, + ⟨3, 7, 6, 7, 1, 8, -16406786998419800779060757853578533856725696512000000⟩, + ⟨3, 7, 7, 7, 2, 8, 673219735152183069483382131481547859604537344000000⟩, + ⟨3, 7, 8, 7, 3, 8, 319394379575113385514754141158193337921961984000000⟩ +] + +def collectedFourData_11_2_32 : List CollectedFourTerm := [ + ⟨4, 0, 7, 1, 8, 2, 137107895743302149285959516201221122400313776537600000⟩, + ⟨4, 0, 7, 2, 7, 2, -8095007209930237217221392079788720426458284032000000⟩, + ⟨4, 0, 8, 2, 8, 2, -130862861063024706664380387798935252466831615590400000⟩, + ⟨4, 0, 7, 3, 6, 2, -6320752386507774364683662434041127886166530457600000⟩, + ⟨4, 0, 8, 3, 7, 2, -80160930344835853267839701228169422881016512512000000⟩, + ⟨4, 0, 7, 4, 5, 2, -21761781747136193148696195858015019098232061952000000⟩, + ⟨4, 0, 8, 4, 6, 2, 102248335549784231549093916420353925426361191628800000⟩, + ⟨4, 0, 7, 5, 4, 2, 13789608028985786627551222770303483863239753728000000⟩, + ⟨4, 0, 8, 5, 5, 2, 34178528619634736525313546357624137426421782937600000⟩, + ⟨4, 0, 7, 6, 3, 2, 41348393995822513934104474768657570085825465548800000⟩, + ⟨4, 0, 8, 6, 4, 2, -50914154135001696630968702819027507018758461849600000⟩, + ⟨4, 0, 7, 7, 2, 2, -73426964157391381562786290654592067299779490611200000⟩, + ⟨4, 0, 8, 7, 3, 2, -243850720732108081256760945293514962768287393382400000⟩ +] + +def collectedFourData_11_2_33 : List CollectedFourTerm := [ + ⟨4, 1, 6, 0, 8, 3, 18929923122984146444146871436095414619923388825600000⟩, + ⟨4, 1, 6, 1, 7, 3, -63309740229159210037588856827844394934163472384000000⟩, + ⟨4, 1, 7, 1, 8, 3, -119017591729291461819554948630962604385118244044800000⟩, + ⟨4, 1, 6, 2, 6, 3, 4370247186106358709361848213204620932478612275200000⟩, + ⟨4, 1, 7, 2, 7, 3, 7026934940063166379883060297723885785328910336000000⟩, + ⟨4, 1, 8, 2, 8, 3, 56798270027008709562709976280752016622700042649600000⟩, + ⟨4, 1, 6, 3, 5, 3, -10646527148506188069910508392794407928325157683200000⟩, + ⟨4, 1, 7, 3, 6, 3, 5486779028158752718976330619755317233235840204800000⟩, + ⟨4, 1, 8, 3, 7, 3, 34792164334153272364788896914935228363008114688000000⟩, + ⟨4, 1, 6, 4, 4, 3, 4920178650697340231197347571168827036785442816000000⟩, + ⟨4, 1, 7, 4, 5, 3, 18890486512401516002489225232202901755313258496000000⟩, + ⟨4, 1, 8, 4, 6, 3, -44378737597459999779365702443124788753450873651200000⟩, + ⟨4, 1, 6, 5, 3, 3, 1822562229701349969021486940625465121017797017600000⟩, + ⟨4, 1, 7, 5, 4, 3, -11970178154972992219752264688790356089995526144000000⟩, + ⟨4, 1, 8, 5, 5, 3, -14834470849058701578661644998124235373718955622400000⟩, + ⟨4, 1, 6, 6, 2, 3, 130592001456269609152623872697350039696016251289600000⟩, + ⟨4, 1, 7, 6, 3, 3, -35892799962959791751936210587137157212020303462400000⟩, + ⟨4, 1, 8, 6, 4, 3, 22098216799370103835502856096703107041570743910400000⟩, + ⟨4, 1, 6, 7, 1, 3, -258892647169027338322210017620962740761768283340800000⟩, + ⟨4, 1, 7, 7, 2, 3, 63738856136829293058192469281178017406960376217600000⟩, + ⟨4, 1, 8, 7, 3, 3, 105838271988815373028979234508156104737960860057600000⟩ +] + +def collectedFourData_11_2_34 : List CollectedFourTerm := [ + ⟨4, 2, 5, 0, 7, 4, 1402423049359331147498463049040967195762779750400000⟩, + ⟨4, 2, 6, 0, 8, 4, 86396219109431740184968367713305179109548516966400000⟩, + ⟨4, 2, 5, 1, 6, 4, -231388924327992937112523559880877537249383468236800000⟩, + ⟨4, 2, 6, 1, 7, 4, -288945821547392934910554798729122548506999914496000000⟩, + ⟨4, 2, 7, 1, 8, 4, -271598301433032386632256002085956238000023771545600000⟩, + ⟨4, 2, 5, 2, 5, 4, 40474974561579161859658225139561508047458349875200000⟩, + ⟨4, 2, 6, 2, 6, 4, 19945819695104035480199266268819271601649142988800000⟩, + ⟨4, 2, 7, 2, 7, 4, 16035474808988936474470495106927196603880046592000000⟩, + ⟨4, 2, 8, 2, 8, 4, 86409151451368761619892710679175576451369716940800000⟩, + ⟨4, 2, 5, 3, 4, 4, -54781188486011147276238865040469152865564858777600000⟩, + ⟨4, 2, 6, 3, 5, 4, -48590778013252287455890106510013717847768616140800000⟩, + ⟨4, 2, 7, 3, 6, 4, 12520836984971086385596429690392451808279239065600000⟩, + ⟨4, 2, 8, 3, 7, 4, 52930509958158513067910360810683302178480717824000000⟩, + ⟨4, 2, 5, 4, 3, 4, 5109792447159361078222591211356197370872830361600000⟩, + ⟨4, 2, 6, 4, 4, 4, 22455708351349315932736760943088078660571234304000000⟩, + ⟨4, 2, 7, 4, 5, 4, 43108115157308799132479566297304757801018458112000000⟩, + ⟨4, 2, 8, 4, 6, 4, -67514891852445225247431008723973898122619885977600000⟩, + ⟨4, 2, 5, 5, 2, 4, 396881209174318841684579885359835411236790049177600000⟩, + ⟨4, 2, 6, 5, 3, 4, 8318178828030529747835197432648413000482842214400000⟩, + ⟨4, 2, 7, 5, 4, 4, -27315962350642402843830530242900150070928211968000000⟩, + ⟨4, 2, 8, 5, 5, 4, -22568188039665480178896064730457227243526763315200000⟩, + ⟨4, 2, 5, 6, 1, 4, -507043345619350220024867097272538377499690663936000000⟩, + ⟨4, 2, 6, 6, 2, 4, 596022239417128726437369870877920838930034746982400000⟩, + ⟨4, 2, 7, 6, 3, 4, -81907416895046274300429310616943213693048245452800000⟩, + ⟨4, 2, 8, 6, 4, 4, 33618773270980842811175753716403556177987973939200000⟩, + ⟨4, 2, 5, 7, 0, 4, -2212194811761817349415141820919763225037691997388800000⟩, + ⟨4, 2, 6, 7, 1, 4, -1181586725171552678503461338498151348580306334515200000⟩, + ⟨4, 2, 7, 7, 2, 4, 145452153841445460074442440989690070878668403507200000⟩, + ⟨4, 2, 8, 7, 3, 4, 161015384258779182714365375050781236099457797324800000⟩ +] + +def collectedFourData_11_2_35 : List CollectedFourTerm := [ + ⟨4, 3, 4, 0, 6, 5, 2908425333510674960184172401592977044759642112000000⟩, + ⟨4, 3, 5, 0, 7, 5, 37597949063713774677248257692210407965458432000000⟩, + ⟨4, 3, 6, 0, 8, 5, 1158110117648807677558194164017682207899385856000000⟩, + ⟨4, 3, 4, 1, 5, 5, -4506956615947091871627544672152804197700049305600000⟩, + ⟨4, 3, 5, 1, 6, 5, -6203369942305002340014683240167962120755871744000000⟩, + ⟨4, 3, 6, 1, 7, 5, -3873214393358232831206264050912859741057187840000000⟩, + ⟨4, 3, 7, 1, 8, 5, -2427118100522584459142093052787069553964220416000000⟩, + ⟨4, 3, 4, 2, 4, 5, 1201641782070082037201196081007570732615886438400000⟩, + ⟨4, 3, 5, 2, 5, 5, 1085104835246794443365301228670527054299529216000000⟩, + ⟨4, 3, 6, 2, 6, 5, 267366510152955389602185481458928932410621952000000⟩, + ⟨4, 3, 7, 2, 7, 5, 143299832708885435130715288088537201765253120000000⟩, + ⟨4, 3, 8, 2, 8, 5, 579141735511164796119358975249110585380438016000000⟩, + ⟨4, 3, 4, 3, 3, 5, -1532673956873070961920893511862140425950199808000000⟩, + ⟨4, 3, 5, 3, 4, 5, -1468644098004282771503689441190917343237111808000000⟩, + ⟨4, 3, 6, 3, 5, 5, -651341832103754839864035207065658006838444032000000⟩, + ⟨4, 3, 7, 3, 6, 5, 111891532161916172483449050598335966521327616000000⟩, + ⟨4, 3, 8, 3, 7, 5, 354757185827836687708652257019439052467732480000000⟩, + ⟨4, 3, 4, 4, 2, 5, 5109792447159361078222591211356197370872830361600000⟩, + ⟨4, 3, 5, 4, 3, 5, 136989844998777041005668295440721693825302528000000⟩, + ⟨4, 3, 6, 4, 4, 5, 301010661215722286354109701960241766371164160000000⟩, + ⟨4, 3, 7, 4, 5, 5, 385232477617369283605776950418322443542200320000000⟩, + ⟨4, 3, 8, 4, 6, 5, -452506372108973583910122754221586077242621952000000⟩, + ⟨4, 3, 4, 5, 1, 5, -4926477689433139732840311615290600580522914611200000⟩, + ⟨4, 3, 5, 5, 2, 5, 10640098573463942708248183569165512490570743808000000⟩, + ⟨4, 3, 6, 5, 3, 5, 111502183318373921176025322977297663866699776000000⟩, + ⟨4, 3, 7, 5, 4, 5, -244107073956737863214416683014871331614228480000000⟩, + ⟨4, 3, 8, 5, 5, 5, -151259205409395794425118027713472778001711104000000⟩, + ⟨4, 3, 4, 6, 0, 5, -15370726693073351058269916762997952827156227686400000⟩, + ⟨4, 3, 5, 6, 1, 5, -13593465887772066105060694816158339327464570880000000⟩, + ⟨4, 3, 6, 6, 2, 5, 7989462883073343055322528483137893120130154496000000⟩, + ⟨4, 3, 7, 6, 3, 5, -731959563311310843696918733284488670250795008000000⟩, + ⟨4, 3, 8, 6, 4, 5, 225323757621552124740696001352020490226499584000000⟩, + ⟨4, 3, 5, 7, 0, 5, -59307345162095745217042886200723628379711995904000000⟩, + ⟨4, 3, 6, 7, 1, 5, -15838743354815504239889130064927111393163870208000000⟩, + ⟨4, 3, 7, 7, 2, 5, 1299822397584521879728931828893348899525230592000000⟩, + ⟨4, 3, 8, 7, 3, 5, 1079176539953735716228022167790484369960861696000000⟩ +] + +def collectedFourData_11_2_36 : List CollectedFourTerm := [ + ⟨4, 4, 3, 0, 5, 6, 12177883842386826448348679125621584513780940800000000⟩, + ⟨4, 4, 4, 0, 6, 6, 12781488040145187416426999915438055376583393280000000⟩, + ⟨4, 4, 5, 0, 7, 6, 82614762489325865223835766502380209742807040000000⟩, + ⟨4, 4, 6, 0, 8, 6, 1696493110017012037518889391875578299028602880000000⟩, + ⟨4, 4, 3, 1, 4, 6, -11649474068508896518966309307256628030778376192000000⟩, + ⟨4, 4, 4, 1, 5, 6, -19806460705885454438324128251568401226257137664000000⟩, + ⟨4, 4, 5, 1, 6, 6, -13630794955024846318490995485121390850007367680000000⟩, + ⟨4, 4, 6, 1, 7, 6, -5673796845235365536834841677265869842101043200000000⟩, + ⟨4, 4, 7, 1, 8, 6, -2666578768278310309601359647287122687961333760000000⟩, + ⟨4, 4, 3, 2, 3, 6, 8080990078616065720760445451730517034750967808000000⟩, + ⟨4, 4, 4, 2, 4, 6, 5280785409583949043169392699987996038393757696000000⟩, + ⟨4, 4, 5, 2, 5, 6, 2384323625951477786879818363109516739367403520000000⟩, + ⟨4, 4, 6, 2, 6, 6, 391660029052030360475529146971513965993000960000000⟩, + ⟨4, 4, 7, 2, 7, 6, 157437864814684157989004308618725098206003200000000⟩, + ⟨4, 4, 8, 2, 8, 6, 509024115606212873716748666362836971377655808000000⟩, + ⟨4, 4, 3, 3, 2, 6, -5328707909794747260246710344798785020853485568000000⟩, + ⟨4, 4, 4, 3, 3, 6, -6735553298722239831777449727851705671373291520000000⟩, + ⟨4, 4, 5, 3, 4, 6, -3227082496770353963887369038418872782039285760000000⟩, + ⟨4, 4, 6, 3, 5, 6, -954138050942201940665844562198059965334159360000000⟩, + ⟨4, 4, 7, 3, 6, 6, 122930805859366151983303138789708617492725760000000⟩, + ⟨4, 4, 8, 3, 7, 6, 311806163670071457268773839438875472418570240000000⟩, + ⟨4, 4, 3, 4, 1, 6, 4920178650697340231197347571168827036785442816000000⟩, + ⟨4, 4, 4, 4, 2, 6, 22455708351349315932736760943088078660571234304000000⟩, + ⟨4, 4, 5, 4, 3, 6, 301010661215722286354109701960241766371164160000000⟩, + ⟨4, 4, 6, 4, 4, 6, 440944695164984543118175861998894822771916800000000⟩, + ⟨4, 4, 7, 4, 5, 6, 423239703681723537950934884155723303039795200000000⟩, + ⟨4, 4, 8, 4, 6, 6, -397720699002369998946034099107030065611800576000000⟩, + ⟨4, 4, 3, 5, 0, 6, -5909822511155396779885305902427690324002340864000000⟩, + ⟨4, 4, 4, 5, 1, 6, -21650105623143259017844444328913450227705315328000000⟩, + ⟨4, 4, 5, 5, 2, 6, 23379711883223440938334740245238852284590325760000000⟩, + ⟨4, 4, 6, 5, 3, 6, 163337391556092087338995948449421389704724480000000⟩, + ⟨4, 4, 7, 5, 4, 6, -268190798156640218173338740607359661165772800000000⟩, + ⟨4, 4, 8, 5, 5, 6, -132946010518234995044647735862583986856394752000000⟩, + ⟨4, 4, 4, 6, 0, 6, -67548840650041856165376756822489709323868962816000000⟩, + ⟨4, 4, 5, 6, 1, 6, -29869207860832047753713209169167937336613273600000000⟩, + ⟨4, 4, 6, 6, 2, 6, 11703609637214823996373556434027816255834030080000000⟩, + ⟨4, 4, 7, 6, 3, 6, -804175054499389945969291791326557554742394880000000⟩, + ⟨4, 4, 8, 6, 4, 6, 198043448461103220080530105666014110382292992000000⟩, + ⟨4, 4, 5, 7, 0, 6, -130317274118755891661382867065075198063416442880000000⟩, + ⟨4, 4, 6, 7, 1, 6, -23201868771619311367804553108218765668872355840000000⟩, + ⟨4, 4, 7, 7, 2, 6, 1428063515815407047470083448537331392441221120000000⟩, + ⟨4, 4, 8, 7, 3, 6, 948518903318327945403279927635474645042331648000000⟩ +] + +def collectedFourData_11_2_37 : List CollectedFourTerm := [ + ⟨4, 5, 2, 0, 4, 7, -6802257920101104807938540653022299818804903936000000⟩, + ⟨4, 5, 3, 0, 5, 7, 46755649907467505967884568430216201439595724800000000⟩, + ⟨4, 5, 4, 0, 6, 7, 24536561024726539870653684622197119480852643840000000⟩, + ⟨4, 5, 5, 0, 7, 7, 105730107741018399595103022443129152292782080000000⟩, + ⟨4, 5, 6, 0, 8, 7, 1628374825811271202878378832038647491272376320000000⟩, + ⟨4, 5, 2, 1, 3, 7, 4061257360550152182973637941454518568651587584000000⟩, + ⟨4, 5, 3, 1, 4, 7, -44726878512134650253042894466482898676431716352000000⟩, + ⟨4, 5, 4, 1, 5, 7, -38022367213222098584160357052603261297404936192000000⟩, + ⟨4, 5, 5, 1, 6, 7, -17444647612183277430946567325287682701378191360000000⟩, + ⟨4, 5, 6, 1, 7, 7, -5445980237111620931519868858425272680893644800000000⟩, + ⟨4, 5, 7, 1, 8, 7, -2047607366829181027404625310959056228515315712000000⟩, + ⟨4, 5, 2, 2, 2, 7, 991538013450702357907356372594211468697665536000000⟩, + ⟨4, 5, 3, 2, 3, 7, 31026075458725777228336532199921913656558747648000000⟩, + ⟨4, 5, 4, 2, 4, 7, 10137498314262809739935438491054594094046117888000000⟩, + ⟨4, 5, 5, 2, 5, 7, 3051449719944144198292114074661068968338391040000000⟩, + ⟨4, 5, 6, 2, 6, 7, 375933935610526561351739374146365871819325440000000⟩, + ⟨4, 5, 7, 2, 7, 7, 120893084294878854912735240597780393980067840000000⟩, + ⟨4, 5, 8, 2, 8, 7, 325723714286385137019847177637401512124612608000000⟩, + ⟨4, 5, 2, 3, 1, 7, 5682568210900828032906898048251187493968281600000000⟩, + ⟨4, 5, 3, 3, 2, 7, -20458989814168245825674779902657212025780830208000000⟩, + ⟨4, 5, 4, 3, 3, 7, -12930209223707811974743657713944181707699650560000000⟩, + ⟨4, 5, 5, 3, 4, 7, -4130009816547841162849503494565703691293163520000000⟩, + ⟨4, 5, 6, 3, 5, 7, -915827110248230721895450632064239880152023040000000⟩, + ⟨4, 5, 7, 3, 6, 7, 94395870349783959913422889651133340148826112000000⟩, + ⟨4, 5, 8, 3, 7, 7, 199524263495944626244611721635568042628874240000000⟩, + ⟨4, 5, 2, 4, 0, 7, -21761781747136193148696195858015019098232061952000000⟩, + ⟨4, 5, 3, 4, 1, 7, 18890486512401516002489225232202901755313258496000000⟩, + ⟨4, 5, 4, 4, 2, 7, 43108115157308799132479566297304757801018458112000000⟩, + ⟨4, 5, 5, 4, 3, 7, 385232477617369283605776950418322443542200320000000⟩, + ⟨4, 5, 6, 4, 4, 7, 423239703681723537950934884155723303039795200000000⟩, + ⟨4, 5, 7, 4, 5, 7, 324996488197811561879003138452114951624458240000000⟩, + ⟨4, 5, 8, 4, 6, 7, -254500836710550862904955687321516188343730176000000⟩, + ⟨4, 5, 3, 5, 0, 7, -22690115616400463476401676566623839299865411584000000⟩, + ⟨4, 5, 4, 5, 1, 7, -41561603480403175708230955074138190590334992384000000⟩, + ⟨4, 5, 5, 5, 2, 7, 29921280191134924287347629373633385788363243520000000⟩, + ⟨4, 5, 6, 5, 3, 7, 156779001902902937380455151061078454797598720000000⟩, + ⟨4, 5, 7, 5, 4, 7, -205937833359370628551665287858449831805583360000000⟩, + ⟨4, 5, 8, 5, 5, 7, -85071938672266292008683078993140122178813952000000⟩, + ⟨4, 5, 4, 6, 0, 7, -129673184026267245432250041652881674928283189248000000⟩, + ⟨4, 5, 5, 6, 1, 7, -38226516304185721181375542154225237022159667200000000⟩, + ⟨4, 5, 6, 6, 2, 7, 11233681523275798137107450639258771933752197120000000⟩, + ⟨4, 5, 7, 6, 3, 7, -617508391427104486034264996645054349318291456000000⟩, + ⟨4, 5, 8, 6, 4, 7, 126727684691344871920646709296233625463816192000000⟩, + ⟨4, 5, 5, 7, 0, 7, -166779628941886957268195392724685100249000181760000000⟩, + ⟨4, 5, 6, 7, 1, 7, -22270257860995796581962269512310427418896629760000000⟩, + ⟨4, 5, 7, 7, 2, 7, 1096578661042732413023506027990681505438367744000000⟩, + ⟨4, 5, 8, 7, 3, 7, 606955723289750320581909628645131850453352448000000⟩ +] + +def collectedFourData_11_2_38 : List CollectedFourTerm := [ + ⟨4, 6, 1, 0, 3, 8, 17083589691378446438109520648786630182449027481600000⟩, + ⟨4, 6, 2, 0, 4, 8, 31960597638205985599584135057600303392891496038400000⟩, + ⟨4, 6, 3, 0, 5, 8, -109841359410198672772856673817872857710523842560000000⟩, + ⟨4, 6, 4, 0, 6, 8, -38428571000383166307484905180582272238964703232000000⟩, + ⟨4, 6, 5, 0, 7, 8, -124193961455398277185975198787866377414770688000000⟩, + ⟨4, 6, 6, 0, 8, 8, -1530192863112260475053116652906128374205356441600000⟩, + ⟨4, 6, 1, 1, 2, 8, 5013486492951336126059407185322366358758883328000000⟩, + ⟨4, 6, 2, 1, 3, 8, -19081930431096707644516010149265591979715697049600000⟩, + ⟨4, 6, 3, 1, 4, 8, 105075240054850017078852864788067073555184379494400000⟩, + ⟨4, 6, 4, 1, 5, 8, 59549715894720862467255143475580520873214974361600000⟩, + ⟨4, 6, 5, 1, 6, 8, 20491040248036991962721120405228346780256567296000000⟩, + ⟨4, 6, 6, 1, 7, 8, 5117617860081349768534452049379491038703386624000000⟩, + ⟨4, 6, 7, 1, 8, 8, 1603456674262683579890319792193205321354497228800000⟩, + ⟨4, 6, 1, 2, 1, 8, 18365565233165152388627048051250512068540052275200000⟩, + ⟨4, 6, 2, 2, 2, 8, -4658768876910352236284495060480742257378879078400000⟩, + ⟨4, 6, 3, 2, 3, 8, -72888438344764573688071786365178530649379281305600000⟩, + ⟨4, 6, 4, 2, 4, 8, -15877105733901631797011330805720471135051998822400000⟩, + ⟨4, 6, 5, 2, 5, 8, -3584330300978265432684265363735811101078585344000000⟩, + ⟨4, 6, 6, 2, 6, 8, -353267206146064253225596835108329237677028147200000⟩, + ⟨4, 6, 7, 2, 7, 8, -94669918669518114866539620779110990627209216000000⟩, + ⟨4, 6, 8, 2, 8, 8, -218631701746435669384330356407442284335438233600000⟩, + ⟨4, 6, 1, 3, 0, 8, 16118341287542724331492918928962158728694045081600000⟩, + ⟨4, 6, 2, 3, 1, 8, -26699704461891669789732581993278105088730071040000000⟩, + ⟨4, 6, 3, 3, 2, 8, 48063565746494587387472980087798500885651888537600000⟩, + ⟨4, 6, 4, 3, 3, 8, 20250982307680698806918095810670641407105957888000000⟩, + ⟨4, 6, 5, 3, 4, 8, 4851241438466528067055357753136588390475497472000000⟩, + ⟨4, 6, 6, 3, 5, 8, 860607819362708247877648761484651298129392435200000⟩, + ⟨4, 6, 7, 3, 6, 8, -73920269475091722805556082903051840760106188800000⟩, + ⟨4, 6, 8, 3, 7, 8, -133924327135323867275254870713175487658590208000000⟩, + ⟨4, 6, 2, 4, 0, 8, 102248335549784231549093916420353925426361191628800000⟩, + ⟨4, 6, 3, 4, 1, 8, -44378737597459999779365702443124788753450873651200000⟩, + ⟨4, 6, 4, 4, 2, 8, -67514891852445225247431008723973898122619885977600000⟩, + ⟨4, 6, 5, 4, 3, 8, -452506372108973583910122754221586077242621952000000⟩, + ⟨4, 6, 6, 4, 4, 8, -397720699002369998946034099107030065611800576000000⟩, + ⟨4, 6, 7, 4, 5, 8, -254500836710550862904955687321516188343730176000000⟩, + ⟨4, 6, 8, 4, 6, 8, 170825606443249531119775784540067657426350899200000⟩, + ⟨4, 6, 3, 5, 0, 8, 53305069000483489943070051043220333391946501324800000⟩, + ⟨4, 6, 4, 5, 1, 8, 65092782506355567535840772062580716594300924723200000⟩, + ⟨4, 6, 5, 5, 2, 8, -35146491365130142166134853983803109291402985472000000⟩, + ⟨4, 6, 6, 5, 3, 8, -147326098386570277478854105598304153379641753600000⟩, + ⟨4, 6, 7, 5, 4, 8, 161267437660487133863047537229671365989105664000000⟩, + ⟨4, 6, 8, 5, 5, 8, 57101837867515144364660705895044745934562918400000⟩, + ⟨4, 6, 4, 6, 0, 8, 203091018100597917725092700099569452825046312550400000⟩, + ⟨4, 6, 5, 6, 1, 8, 44902086963582876546886263367485112614565969920000000⟩, + ⟨4, 6, 6, 6, 2, 8, -10556352886890540087950906039442332616937281945600000⟩, + ⟨4, 6, 7, 6, 3, 8, 483563386070590450406738280245372868387825254400000⟩, + ⟨4, 6, 8, 6, 4, 8, -85061934846088546109596766284602704497370726400000⟩, + ⟨4, 6, 5, 7, 0, 8, 195904678912179329266457647243836586351694708736000000⟩, + ⟨4, 6, 6, 7, 1, 8, 20927484936760563006053816439265273709874433228800000⟩, + ⟨4, 6, 7, 7, 2, 8, -858717545847592930692953085182335746630588825600000⟩, + ⟨4, 6, 8, 7, 3, 8, -407399758897823430444943026981780375985559961600000⟩ +] + +def collectedFourData_11_2_39 : List CollectedFourTerm := [ + ⟨5, 0, 6, 0, 8, 3, -22737484499835593683283523698955546754896258662400000⟩, + ⟨5, 0, 6, 1, 7, 3, 76043850141225480056803974801691476847478439936000000⟩, + ⟨5, 0, 7, 1, 8, 3, 142956769003820530642192991330655455154713867059200000⟩, + ⟨5, 0, 6, 2, 6, 3, -5249277929390705111073732271404162625684950220800000⟩, + ⟨5, 0, 7, 2, 7, 3, -8440331386610101414793085015096846427770322944000000⟩, + ⟨5, 0, 8, 2, 8, 3, -68222663978415602807513977495765350251315488358400000⟩, + ⟨5, 0, 6, 3, 5, 3, 12787967729373278334365101173157951490115816652800000⟩, + ⟨5, 0, 7, 3, 6, 3, -6590388787966506917818096448640650467930747699200000⟩, + ⟨5, 0, 8, 3, 7, 3, -41790254092634400581726409460331989175529111552000000⟩, + ⟨5, 0, 6, 4, 4, 3, -5909822511155396779885305902427690324002340864000000⟩, + ⟨5, 0, 7, 4, 5, 3, -22690115616400463476401676566623839299865411584000000⟩, + ⟨5, 0, 8, 4, 6, 3, 53305069000483489943070051043220333391946501324800000⟩, + ⟨5, 0, 6, 5, 3, 3, -2189152073074425324552927910550266499249366630400000⟩, + ⟨5, 0, 7, 5, 4, 3, 14377857664329669120752316724151521579395710976000000⟩, + ⟨5, 0, 8, 5, 5, 3, 17818273682485132457938329722147464692744427929600000⟩, + ⟨5, 0, 6, 6, 2, 3, -156859253448798292455295568034532256615380706918400000⟩, + ⟨5, 0, 7, 6, 3, 3, 43112271376453667536986107861301433178489723289600000⟩, + ⟨5, 0, 8, 6, 4, 3, -26543048203910292287475081961535525899900393881600000⟩, + ⟨5, 0, 6, 7, 1, 3, 310966268266555723599484108844519554176938881843200000⟩, + ⟨5, 0, 7, 7, 2, 3, -76559278346395247338098298822227829538423203430400000⟩, + ⟨5, 0, 8, 7, 3, 3, -127126563230105128684911691216894885106926642790400000⟩ +] + +def collectedFourData_11_2_40 : List CollectedFourTerm := [ + ⟨5, 1, 5, 0, 7, 4, -1352110860717326106768608889393263222469741772800000⟩, + ⟨5, 1, 6, 0, 8, 4, -83296738624013683871965593842500071200836603084800000⟩, + ⟨5, 1, 5, 1, 6, 4, 223087803481627156352270466424108990951144921497600000⟩, + ⟨5, 1, 6, 1, 7, 4, 278579836270943918991672698656227856045962166272000000⟩, + ⟨5, 1, 7, 1, 8, 4, 261854661678402483821694657926176591987562722099200000⟩, + ⟨5, 1, 5, 2, 5, 4, -39022927294990946901001448890573894587521590886400000⟩, + ⟨5, 1, 6, 2, 6, 4, -19230259690882819417624959059408242104484862361600000⟩, + ⟨5, 1, 7, 2, 7, 4, -15460199157378295654440781202972335020120735744000000⟩, + ⟨5, 1, 8, 2, 8, 4, -83309207015770040796465769600700050286162057625600000⟩, + ⟨5, 1, 5, 3, 4, 4, 52815903124792558866515277260976661854036374323200000⟩, + ⟨5, 1, 6, 3, 5, 4, 46847574783113310484187999540484727114307312025600000⟩, + ⟨5, 1, 7, 3, 6, 4, -12071649621264079941165162622865729652889170739200000⟩, + ⟨5, 1, 8, 3, 7, 4, -51031618034534640546316243566407724355150675968000000⟩, + ⟨5, 1, 5, 4, 3, 4, -4926477689433139732840311615290600580522914611200000⟩, + ⟨5, 1, 6, 4, 4, 4, -21650105623143259017844444328913450227705315328000000⟩, + ⟨5, 1, 7, 4, 5, 4, -41561603480403175708230955074138190590334992384000000⟩, + ⟨5, 1, 8, 4, 6, 4, 65092782506355567535840772062580716594300924723200000⟩, + ⟨5, 1, 5, 5, 2, 4, -382643021721846954251949551717341176230768227123200000⟩, + ⟨5, 1, 6, 5, 3, 4, -8019762610081894066453870440351977909896662220800000⟩, + ⟨5, 1, 7, 5, 4, 4, 26335997103100827407813758679762676841684402176000000⟩, + ⟨5, 1, 8, 5, 5, 4, 21758550081648032163491538603084045782966756966400000⟩, + ⟨5, 1, 5, 6, 1, 4, 488853070961408701696516664144925706017520484352000000⟩, + ⟨5, 1, 6, 6, 2, 4, -574639830337297988853226668291331282657803553996800000⟩, + ⟨5, 1, 7, 6, 3, 4, 78968973026852943905396446251317845222217062809600000⟩, + ⟨5, 1, 8, 6, 4, 4, -32412693505324479169315691266967835225677522534400000⟩, + ⟨5, 1, 5, 7, 0, 4, 2132831910008975562387939671228271000407183563161600000⟩, + ⟨5, 1, 6, 7, 1, 4, 1139197080876360975114861039343851180590090315366400000⟩, + ⟨5, 1, 7, 7, 2, 4, -140234030675400926571349001322687427548262327910400000⟩, + ⟨5, 1, 8, 7, 3, 4, -155238927296813659348395944714480526903626799513600000⟩ +] + +def collectedFourData_11_2_41 : List CollectedFourTerm := [ + ⟨5, 2, 4, 0, 6, 5, 225899461689219301099118220870543508151029727232000000⟩, + ⟨5, 2, 5, 0, 7, 5, 2920259411940806793749158359989911864844746752000000⟩, + ⟨5, 2, 6, 0, 8, 5, 89951235515444550667933513995030859097535676416000000⟩, + ⟨5, 2, 4, 1, 5, 5, -350058521932269053542642013544371450381432625561600000⟩, + ⟨5, 2, 5, 1, 6, 5, -481820150058406170663339551743492919031899357184000000⟩, + ⟨5, 2, 6, 1, 7, 5, -300835313317267076640855620464185631612065546240000000⟩, + ⟨5, 2, 7, 1, 8, 5, -188515987000564987314658656807756951597745176576000000⟩, + ⟨5, 2, 4, 2, 4, 5, 93332370814294238197618150478009488075435435622400000⟩, + ⟨5, 2, 5, 2, 5, 5, 84280863371086493130806736128238685335507173376000000⟩, + ⟨5, 2, 6, 2, 6, 5, 20766546770644860796860311195391715194250985472000000⟩, + ⟨5, 2, 7, 2, 7, 5, 11130199801284871394583810485272446899658424320000000⟩, + ⟨5, 2, 8, 2, 8, 5, 44982349997554841583372233285207593174670770176000000⟩, + ⟨5, 2, 4, 3, 3, 5, -119043874983989394017543106741113261113252773888000000⟩, + ⟨5, 2, 5, 3, 4, 5, -114070630361258615108551274051109032942672805888000000⟩, + ⟨5, 2, 6, 3, 5, 5, -50590182788121429528052479449298009713490788352000000⟩, + ⟨5, 2, 7, 3, 6, 5, 8690694786532005314731082452019439024551755776000000⟩, + ⟨5, 2, 8, 3, 7, 5, 27554242629346326240349460683257500077947617280000000⟩, + ⟨5, 2, 4, 4, 2, 5, 396881209174318841684579885359835411236790049177600000⟩, + ⟨5, 2, 5, 4, 3, 5, 10640098573463942708248183569165512490570743808000000⟩, + ⟨5, 2, 6, 4, 4, 5, 23379711883223440938334740245238852284590325760000000⟩, + ⟨5, 2, 7, 4, 5, 5, 29921280191134924287347629373633385788363243520000000⟩, + ⟨5, 2, 8, 4, 6, 5, -35146491365130142166134853983803109291402985472000000⟩, + ⟨5, 2, 4, 5, 1, 5, -382643021721846954251949551717341176230768227123200000⟩, + ⟨5, 2, 5, 5, 2, 5, 826424014524873075861065893337746371162446757888000000⟩, + ⟨5, 2, 6, 5, 3, 5, 8660453785275374011419970065775816027234369536000000⟩, + ⟨5, 2, 7, 5, 4, 5, -18959969838660164662302231465955998509071073280000000⟩, + ⟨5, 2, 8, 5, 5, 5, -11748409932971086302467354374204377452085510144000000⟩, + ⟨5, 2, 4, 6, 0, 5, -1193855261034377724703353708864981816684755445350400000⟩, + ⟨5, 2, 5, 6, 1, 5, -1055814151787714961685238229648982362432397639680000000⟩, + ⟨5, 2, 6, 6, 2, 5, 620547257540810416967151760029920547911768211456000000⟩, + ⟨5, 2, 7, 6, 3, 5, -56851819238801944834611875611248095858773721088000000⟩, + ⟨5, 2, 8, 6, 4, 5, 17501056315948200577014246880986362316192743424000000⟩, + ⟨5, 2, 5, 7, 0, 5, -4606443628436707073973408319170839770980044242944000000⟩, + ⟨5, 2, 6, 7, 1, 5, -1230206447613240535226492705718034418031591948288000000⟩, + ⟨5, 2, 7, 7, 2, 5, 100958128965099717242813614133848970960685760512000000⟩, + ⟨5, 2, 8, 7, 3, 5, 83820408464437680685901157424216376727784390656000000⟩ +] + +def collectedFourData_11_2_42 : List CollectedFourTerm := [ + ⟨5, 3, 3, 0, 5, 6, 4511005128986296501238641888598442623505530880000000⟩, + ⟨5, 3, 4, 0, 6, 6, 4734595833841628158951740018676628458158686208000000⟩, + ⟨5, 3, 5, 0, 7, 6, 30602658240357336205613122767670422005612544000000⟩, + ⟨5, 3, 6, 0, 8, 6, 628425202574170127160432341186942214516768768000000⟩, + ⟨5, 3, 3, 1, 4, 6, -4315268395821444646564240933186537302850220851200000⟩, + ⟨5, 3, 4, 1, 5, 6, -7336828548185847305816996982107986227290859110400000⟩, + ⟨5, 3, 5, 1, 6, 6, -5049201220022973175968632674023072044886786048000000⟩, + ⟨5, 3, 6, 1, 7, 6, -2101722023377959611769093204067231934730731520000000⟩, + ⟨5, 3, 7, 1, 8, 6, -987770178812264221723593755116457748999438336000000⟩, + ⟨5, 3, 3, 2, 3, 6, 2993409049037184769340874906590283286801337548800000⟩, + ⟨5, 3, 4, 2, 4, 6, 1956140358704573347995918579671665682641688985600000⟩, + ⟨5, 3, 5, 2, 5, 6, 883215527840199701268319767716693880468406272000000⟩, + ⟨5, 3, 6, 2, 6, 6, 145081068495915914386411527510288174736736256000000⟩, + ⟨5, 3, 7, 2, 7, 6, 58319082762452584901409972215732401361387520000000⟩, + ⟨5, 3, 8, 2, 8, 6, 188555780790506364501876787327442976389254348800000⟩, + ⟨5, 3, 3, 3, 2, 6, -1973892100061500867081418064603238468026158284800000⟩, + ⟨5, 3, 4, 3, 3, 6, -2495024248083269820106417320519637716877443072000000⟩, + ⟨5, 3, 5, 3, 4, 6, -1195395348075496925763461556851885268623425536000000⟩, + ⟨5, 3, 6, 3, 5, 6, -353437567418746792180195664581141269363818496000000⟩, + ⟨5, 3, 7, 3, 6, 6, 45536770010226260715184191823027202515009536000000⟩, + ⟨5, 3, 8, 3, 7, 6, 115501118401992562276121883255488734574936064000000⟩, + ⟨5, 3, 3, 4, 1, 6, 1822562229701349969021486940625465121017797017600000⟩, + ⟨5, 3, 4, 4, 2, 6, 8318178828030529747835197432648413000482842214400000⟩, + ⟨5, 3, 5, 4, 3, 6, 111502183318373921176025322977297663866699776000000⟩, + ⟨5, 3, 6, 4, 4, 6, 163337391556092087338995948449421389704724480000000⟩, + ⟨5, 3, 7, 4, 5, 6, 156779001902902937380455151061078454797598720000000⟩, + ⟨5, 3, 8, 4, 6, 6, -147326098386570277478854105598304153379641753600000⟩, + ⟨5, 3, 3, 5, 0, 6, -2189152073074425324552927910550266499249366630400000⟩, + ⟨5, 3, 4, 5, 1, 6, -8019762610081894066453870440351977909896662220800000⟩, + ⟨5, 3, 5, 5, 2, 6, 8660453785275374011419970065775816027234369536000000⟩, + ⟨5, 3, 6, 5, 3, 6, 60504421014444563064608309700753638742294528000000⟩, + ⟨5, 3, 7, 5, 4, 6, -99344851838758686783567872023569419552686080000000⟩, + ⟨5, 3, 8, 5, 5, 6, -49246662481589325841300961658977808261788467200000⟩, + ⟨5, 3, 4, 6, 0, 6, -25021848670359302883572584900096031722672069017600000⟩, + ⟨5, 3, 5, 6, 1, 6, -11064331997484591931100466164928208700398632960000000⟩, + ⟨5, 3, 6, 6, 2, 6, 4335321619456493322807865810446190801676402688000000⟩, + ⟨5, 3, 7, 6, 3, 6, -297887370449624612888166280927562489520979968000000⟩, + ⟨5, 3, 8, 6, 4, 6, 73360447786556587617389336486321638910145331200000⟩, + ⟨5, 3, 5, 7, 0, 6, -48272910101103569174044970916415325347164192768000000⟩, + ⟨5, 3, 6, 7, 1, 6, -8594576068014780387670292633453471099963572224000000⟩, + ⟨5, 3, 7, 7, 2, 6, 528991894465212151101330767891473548686917632000000⟩, + ⟨5, 3, 8, 7, 3, 6, 351356088889316294221780871923839582142778572800000⟩ +] + +def collectedFourData_11_2_43 : List CollectedFourTerm := [ + ⟨5, 4, 2, 0, 4, 7, 4310330446292721697270272530563150447644770304000000⟩, + ⟨5, 4, 3, 0, 5, 7, -29627265490304314709049834359377406215795507200000000⟩, + ⟨5, 4, 4, 0, 6, 7, -15547879435689816074020322389623611860986101760000000⟩, + ⟨5, 4, 5, 0, 7, 7, -66997121814391250880120593347893317987205120000000⟩, + ⟨5, 4, 6, 0, 8, 7, -1031838791194587002035658497462883976719892480000000⟩, + ⟨5, 4, 2, 1, 3, 7, -2573463320124966519516823648802242618485374976000000⟩, + ⟨5, 4, 3, 1, 4, 7, 28341710720610871516302146911658830575936995328000000⟩, + ⟨5, 4, 4, 1, 5, 7, 24093318566320608849532993669795882552774361088000000⟩, + ⟨5, 4, 5, 1, 6, 7, 11054005392157137582908368680711886012982231040000000⟩, + ⟨5, 4, 6, 1, 7, 7, 3450909198335980160560795692992152361710387200000000⟩, + ⟨5, 4, 7, 1, 8, 7, 1297490403769621550803213456061173158660538368000000⟩, + ⟨5, 4, 2, 2, 2, 7, -628299681992893392801785039132456141092552704000000⟩, + ⟨5, 4, 3, 2, 3, 7, -19660036306993401277166347681001974779894300672000000⟩, + ⟨5, 4, 4, 2, 4, 7, -6423744607519771775337956630078906514939052032000000⟩, + ⟨5, 4, 5, 2, 5, 7, -1933586874784534598897146014864292604081602560000000⟩, + ⟨5, 4, 6, 2, 6, 7, -238214943845089540361613897288464300412764160000000⟩, + ⟨5, 4, 7, 2, 7, 7, -76605319601686557764280629386070244206837760000000⟩, + ⟨5, 4, 8, 2, 8, 7, -206398648692710775972864922185685870011482112000000⟩, + ⟨5, 4, 2, 3, 1, 7, -3600825940486675688014026164805932398569062400000000⟩, + ⟨5, 4, 3, 3, 2, 7, 12964078653326237251720128079136599109126848512000000⟩, + ⟨5, 4, 4, 3, 3, 7, 8193378602888137735123060564294237129896099840000000⟩, + ⟨5, 4, 5, 3, 4, 7, 2617029119573487686356500925819925380233953280000000⟩, + ⟨5, 4, 6, 3, 5, 7, 580324580927468913004672564736554223334850560000000⟩, + ⟨5, 4, 7, 3, 6, 7, -59815049466240557110960738208979865690963968000000⟩, + ⟨5, 4, 8, 3, 7, 7, -126430887776145781673516450842669477118607360000000⟩, + ⟨5, 4, 2, 4, 0, 7, 13789608028985786627551222770303483863239753728000000⟩, + ⟨5, 4, 3, 4, 1, 7, -11970178154972992219752264688790356089995526144000000⟩, + ⟨5, 4, 4, 4, 2, 7, -27315962350642402843830530242900150070928211968000000⟩, + ⟨5, 4, 5, 4, 3, 7, -244107073956737863214416683014871331614228480000000⟩, + ⟨5, 4, 6, 4, 4, 7, -268190798156640218173338740607359661165772800000000⟩, + ⟨5, 4, 7, 4, 5, 7, -205937833359370628551665287858449831805583360000000⟩, + ⟨5, 4, 8, 4, 6, 7, 161267437660487133863047537229671365989105664000000⟩, + ⟨5, 4, 3, 5, 0, 7, 14377857664329669120752316724151521579395710976000000⟩, + ⟨5, 4, 4, 5, 1, 7, 26335997103100827407813758679762676841684402176000000⟩, + ⟨5, 4, 5, 5, 2, 7, -18959969838660164662302231465955998509071073280000000⟩, + ⟨5, 4, 6, 5, 3, 7, -99344851838758686783567872023569419552686080000000⟩, + ⟨5, 4, 7, 5, 4, 7, 130494921480316125352726259148514500060119040000000⟩, + ⟨5, 4, 8, 5, 5, 7, 53906830892229146283067913694166556740681728000000⟩, + ⟨5, 4, 4, 6, 0, 7, 82168932689901745460375565192318956297961603072000000⟩, + ⟨5, 4, 5, 6, 1, 7, 24222680030219702778872135174796858119474380800000000⟩, + ⟨5, 4, 6, 6, 2, 7, -7118353944010986998720497622789045236719943680000000⟩, + ⟨5, 4, 7, 6, 3, 7, 391291428768688987823648501993141569358659584000000⟩, + ⟨5, 4, 8, 6, 4, 7, -80302482518211966006652769210773695614681088000000⟩, + ⟨5, 4, 5, 7, 0, 7, 105681866358712429983336307357405986620587376640000000⟩, + ⟨5, 4, 6, 7, 1, 7, 14111809877331618989486833375669217563131248640000000⟩, + ⟨5, 4, 7, 7, 2, 7, -694859919304139281306701995576656482288009216000000⟩, + ⟨5, 4, 8, 7, 3, 7, -384604606937419071153812031545614873890127872000000⟩ +] + +def collectedFourData_11_2_44 : List CollectedFourTerm := [ + ⟨5, 5, 1, 0, 3, 8, 5710527766083595081418582309107653368121340723200000⟩, + ⟨5, 5, 2, 0, 4, 8, 10683461938079037995225349734475667752098778316800000⟩, + ⟨5, 5, 3, 0, 5, 8, -36716647034250748883742485113927136965684101120000000⟩, + ⟨5, 5, 4, 0, 6, 8, -12845509970269957935008569528766836205540081664000000⟩, + ⟨5, 5, 5, 0, 7, 8, -41514288160929391540107320862847395667378176000000⟩, + ⟨5, 5, 6, 0, 8, 8, -511497231561082153211379404044411033829454643200000⟩, + ⟨5, 5, 1, 1, 2, 8, 1675857026543558474870545192914215053301907456000000⟩, + ⟨5, 5, 2, 1, 3, 8, -6378512685319640000771356314826132477202084659200000⟩, + ⟨5, 5, 3, 1, 4, 8, 35123477366348777396336655094250201027569306828800000⟩, + ⟨5, 5, 4, 1, 5, 8, 19905670425391385104809176477402342756495602483200000⟩, + ⟨5, 5, 5, 1, 6, 8, 6849535513686877944712423706207099891264520192000000⟩, + ⟨5, 5, 6, 1, 7, 8, 1710664995715066163211877140399146630431899648000000⟩, + ⟨5, 5, 7, 1, 8, 8, 535987109589160574705087813470434973940554137600000⟩, + ⟨5, 5, 1, 2, 1, 8, 6139053448277168341468114068556639828013639270400000⟩, + ⟨5, 5, 2, 2, 2, 8, -1557285647101959754943734164090287780881288396800000⟩, + ⟨5, 5, 3, 2, 3, 8, -24364402242949518546317269385180790235312894771200000⟩, + ⟨5, 5, 4, 2, 4, 8, -5307236639161788624917607493950083300458286284800000⟩, + ⟨5, 5, 5, 2, 5, 8, -1198133300806265824002359952101134522896089088000000⟩, + ⟨5, 5, 6, 2, 6, 8, -118086551245255363222930548809479405420570214400000⟩, + ⟨5, 5, 7, 2, 7, 8, -31645292877057946425960298852376737619116032000000⟩, + ⟨5, 5, 8, 2, 8, 8, -73081970822514441582205441760663637786309427200000⟩, + ⟨5, 5, 1, 3, 0, 8, 5387874394582081243508580937756387588946735923200000⟩, + ⟨5, 5, 2, 3, 1, 8, -8924904333941301220582382191440119254304686080000000⟩, + ⟨5, 5, 3, 3, 2, 8, 16066197543415440303696412869047902978803184435200000⟩, + ⟨5, 5, 4, 3, 3, 8, 6769291398800105605720870989707023937307672576000000⟩, + ⟨5, 5, 5, 3, 4, 8, 1621623407890634482980600819903666951913734144000000⟩, + ⟨5, 5, 6, 3, 5, 8, 287675186360838874679155742081967139492095590400000⟩, + ⟨5, 5, 7, 3, 6, 8, -24709312207780637467546550055230393955228057600000⟩, + ⟨5, 5, 8, 3, 7, 8, -44766855355130042707025751988750266679689216000000⟩, + ⟨5, 5, 2, 4, 0, 8, 34178528619634736525313546357624137426421782937600000⟩, + ⟨5, 5, 3, 4, 1, 8, -14834470849058701578661644998124235373718955622400000⟩, + ⟨5, 5, 4, 4, 2, 8, -22568188039665480178896064730457227243526763315200000⟩, + ⟨5, 5, 5, 4, 3, 8, -151259205409395794425118027713472778001711104000000⟩, + ⟨5, 5, 6, 4, 4, 8, -132946010518234995044647735862583986856394752000000⟩, + ⟨5, 5, 7, 4, 5, 8, -85071938672266292008683078993140122178813952000000⟩, + ⟨5, 5, 8, 4, 6, 8, 57101837867515144364660705895044745934562918400000⟩, + ⟨5, 5, 3, 5, 0, 8, 17818273682485132457938329722147464692744427929600000⟩, + ⟨5, 5, 4, 5, 1, 8, 21758550081648032163491538603084045782966756966400000⟩, + ⟨5, 5, 5, 5, 2, 8, -11748409932971086302467354374204377452085510144000000⟩, + ⟨5, 5, 6, 5, 3, 8, -49246662481589325841300961658977808261788467200000⟩, + ⟨5, 5, 7, 5, 4, 8, 53906830892229146283067913694166556740681728000000⟩, + ⟨5, 5, 8, 5, 5, 8, 19087418776008891002642944121578509059280076800000⟩, + ⟨5, 5, 4, 6, 0, 8, 67887189920684143136020030841971820868068494540800000⟩, + ⟨5, 5, 5, 6, 1, 8, 15009410726484766810428085280966889202086051840000000⟩, + ⟨5, 5, 6, 6, 2, 8, -3528669756075197770540459793672454202732000051200000⟩, + ⟨5, 5, 7, 6, 3, 8, 161640626630777795135558229555221074688134348800000⟩, + ⟨5, 5, 8, 6, 4, 8, -28433634239092293288572821399585443002764492800000⟩, + ⟨5, 5, 5, 7, 0, 8, 65485013901865950209948416350711840605126787072000000⟩, + ⟨5, 5, 6, 7, 1, 8, 6995425783726169800815472422982518472670026137600000⟩, + ⟨5, 5, 7, 7, 2, 8, -287043325048985541934496640582521266656981811200000⟩, + ⟨5, 5, 8, 7, 3, 8, -136181427739152406939626488726849239376933683200000⟩ +] + +def collectedFourData_11_2_45 : List CollectedFourTerm := [ + ⟨6, 0, 5, 0, 7, 4, -4218617805455555629578227747977761955608369561600000⟩, + ⟨6, 0, 6, 0, 8, 4, -259887790938397853176814173449217699638207420825600000⟩, + ⟨6, 0, 5, 1, 6, 4, 696039213417955327868690350268388120480424604467200000⟩, + ⟨6, 0, 6, 1, 7, 4, 869175665751264683358573980430008425549223952384000000⟩, + ⟨6, 0, 7, 1, 8, 4, 816992726182229655292283565277520818285253650022400000⟩, + ⟨6, 0, 5, 2, 5, 4, -121752454395869726259662954988323269623856024780800000⟩, + ⟨6, 0, 6, 2, 6, 4, -59998864214768424792111409402290001848759956275200000⟩, + ⟨6, 0, 7, 2, 7, 4, -48236186348361982811295991132403757376673415168000000⟩, + ⟨6, 0, 8, 2, 8, 4, -259926692615025801717546683822506613912573784883200000⟩, + ⟨6, 0, 5, 3, 4, 4, 164786864603143330816210467745522746658988123750400000⟩, + ⟨6, 0, 6, 3, 5, 4, 146165539279526343077006382607357702725428261683200000⟩, + ⟨6, 0, 7, 3, 6, 4, -37663831800351202236976180126749783029210048102400000⟩, + ⟨6, 0, 8, 3, 7, 4, -159219852998948712761671483901976589046063824896000000⟩, + ⟨6, 0, 5, 4, 3, 4, -15370726693073351058269916762997952827156227686400000⟩, + ⟨6, 0, 6, 4, 4, 4, -67548840650041856165376756822489709323868962816000000⟩, + ⟨6, 0, 7, 4, 5, 4, -129673184026267245432250041652881674928283189248000000⟩, + ⟨6, 0, 8, 4, 6, 4, 203091018100597917725092700099569452825046312550400000⟩, + ⟨6, 0, 5, 5, 2, 4, -1193855261034377724703353708864981816684755445350400000⟩, + ⟨6, 0, 6, 5, 3, 4, -25021848670359302883572584900096031722672069017600000⟩, + ⟨6, 0, 7, 5, 4, 4, 82168932689901745460375565192318956297961603072000000⟩, + ⟨6, 0, 8, 5, 5, 4, 67887189920684143136020030841971820868068494540800000⟩, + ⟨6, 0, 5, 6, 1, 4, 1525233122020288667778756863876494698355196166144000000⟩, + ⟨6, 0, 6, 6, 2, 4, -1792889836487814449463216052794675318347498363289600000⟩, + ⟨6, 0, 7, 6, 3, 4, 246385060107336832253251883947962980673195815731200000⟩, + ⟨6, 0, 8, 6, 4, 4, -101128368920721098239245382689224715329944210636800000⟩, + ⟨6, 0, 5, 7, 0, 4, 6654485910152521909610319994051665535774527533875200000⟩, + ⟨6, 0, 6, 7, 1, 4, 3554321785980183050729295330923460184183386459340800000⟩, + ⟨6, 0, 7, 7, 2, 4, -437533486288389647413872709941065701886419324108800000⟩, + ⟨6, 0, 8, 7, 3, 4, -484349117975964133029438511709082781587214644019200000⟩ +] + +def collectedFourData_11_2_46 : List CollectedFourTerm := [ + ⟨6, 1, 4, 0, 6, 5, -288602272369622751127947246288081713437889003520000000⟩, + ⟨6, 1, 5, 0, 7, 5, -3730834486690218134715980062568372352288030720000000⟩, + ⟨6, 1, 6, 0, 8, 5, -114918958983297649204460125541429964353317109760000000⟩, + ⟨6, 1, 4, 1, 5, 5, 447224106407977604014293236118454210661424562176000000⟩, + ⟨6, 1, 5, 1, 6, 5, 615558749633641984465745050626568247813854986240000000⟩, + ⟨6, 1, 6, 1, 7, 5, 384338034199636802042801816885458682790700646400000000⟩, + ⟨6, 1, 7, 1, 8, 5, 240842283640385348080440325633343067579073167360000000⟩, + ⟨6, 1, 4, 2, 4, 5, -119238594466890003546771792725151544419563864064000000⟩, + ⟨6, 1, 5, 2, 5, 5, -107674664225771697564848321353269249366672015360000000⟩, + ⟨6, 1, 6, 2, 6, 5, -26530707698291861185135126276739218439845969920000000⟩, + ⟨6, 1, 7, 2, 7, 5, -14219604290150615915350553008201372968104755200000000⟩, + ⟨6, 1, 8, 2, 8, 5, -57468080396225077658169138495823051018846863360000000⟩, + ⟨6, 1, 4, 3, 3, 5, 152086829136982532374026404130015757356163399680000000⟩, + ⟨6, 1, 5, 3, 4, 5, 145733163269709653628682215773608038014574919680000000⟩, + ⟨6, 1, 6, 3, 5, 5, 64632476780015297341802292628520186552223006720000000⟩, + ⟨6, 1, 7, 3, 6, 5, -11102966979684786007053809390849619045761679360000000⟩, + ⟨6, 1, 8, 3, 7, 5, -35202461204593413728089100699986943657430220800000000⟩, + ⟨6, 1, 4, 4, 2, 5, -507043345619350220024867097272538377499690663936000000⟩, + ⟨6, 1, 5, 4, 3, 5, -13593465887772066105060694816158339327464570880000000⟩, + ⟨6, 1, 6, 4, 4, 5, -29869207860832047753713209169167937336613273600000000⟩, + ⟨6, 1, 7, 4, 5, 5, -38226516304185721181375542154225237022159667200000000⟩, + ⟨6, 1, 8, 4, 6, 5, 44902086963582876546886263367485112614565969920000000⟩, + ⟨6, 1, 4, 5, 1, 5, 488853070961408701696516664144925706017520484352000000⟩, + ⟨6, 1, 5, 5, 2, 5, -1055814151787714961685238229648982362432397639680000000⟩, + ⟨6, 1, 6, 5, 3, 5, -11064331997484591931100466164928208700398632960000000⟩, + ⟨6, 1, 7, 5, 4, 5, 24222680030219702778872135174796858119474380800000000⟩, + ⟨6, 1, 8, 5, 5, 5, 15009410726484766810428085280966889202086051840000000⟩, + ⟨6, 1, 4, 6, 0, 5, 1525233122020288667778756863876494698355196166144000000⟩, + ⟨6, 1, 5, 6, 1, 5, 1348876004959874400437514236871992584306478284800000000⟩, + ⟨6, 1, 6, 6, 2, 5, -792792277147609769740311429270258366600613724160000000⟩, + ⟨6, 1, 7, 6, 3, 5, 72632152808039661835585049831752003732824391680000000⟩, + ⟨6, 1, 8, 6, 4, 5, -22358816545566087875904554760547611070578032640000000⟩, + ⟨6, 1, 5, 7, 0, 5, 5885052088076085978487884388486760728606109859840000000⟩, + ⟨6, 1, 6, 7, 1, 5, 1571674290899322823271026796848446648224506183680000000⟩, + ⟨6, 1, 7, 7, 2, 5, -128981030833964639487187238535576148183948984320000000⟩, + ⟨6, 1, 8, 7, 3, 5, -107086401060428653831833688802477158342758236160000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1108.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1108.lean new file mode 100644 index 0000000000000000000000000000000000000000..4da1a9a67c47de4d87f169db213a9d0329b5575d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1108.lean @@ -0,0 +1,633 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1105 +import OAI.Analysis.LaughlinFock.Sparse1106 +import OAI.Analysis.LaughlinFock.Sparse1107 + +namespace OAI + +/-! Sparse1108. -/ +namespace LaughlinFock +def collectedFourData_11_2_47 : List CollectedFourTerm := [ + ⟨6, 2, 3, 0, 5, 6, 323226926781177639383210877090443432483597844480000000⟩, + ⟨6, 2, 4, 0, 6, 6, 339247865423618657178127153800098248873337683968000000⟩, + ⟨6, 2, 5, 0, 7, 6, 2192771431538629910287201228367551033428148224000000⟩, + ⟨6, 2, 6, 0, 8, 6, 45028533803847302594390103433648333706628169728000000⟩, + ⟨6, 2, 3, 1, 4, 6, -309201808008306772052428530988323766235378692915200000⟩, + ⟨6, 2, 4, 1, 5, 6, -525705574731507850805627527710250057537912464998400000⟩, + ⟨6, 2, 5, 1, 6, 6, -361790276530797567063347922033337798591783108608000000⟩, + ⟨6, 2, 6, 1, 7, 6, -150594630495894509025916278263328377648625745920000000⟩, + ⟨6, 2, 7, 1, 8, 6, -70776669530262544737717876769426274853643616256000000⟩, + ⟨6, 2, 3, 2, 3, 6, 214486656488613344016173413308414045099209313484800000⟩, + ⟨6, 2, 4, 2, 4, 6, 140163271470009100126273024801156667007091448217600000⟩, + ⟨6, 2, 5, 2, 5, 6, 63285017991845119876729105822251333571011674112000000⟩, + ⟨6, 2, 6, 2, 6, 6, 10395489821711281355168688449730382499546136576000000⟩, + ⟨6, 2, 7, 2, 7, 6, 4178735637625111629625418694431212839024721920000000⟩, + ⟨6, 2, 8, 2, 8, 6, 13510582189348232097224036925124837600526126284800000⟩, + ⟨6, 2, 3, 3, 2, 6, -141435236506569235808233868424446222441152040140800000⟩, + ⟨6, 2, 4, 3, 3, 6, -178775904015365109482313984688361043852276006912000000⟩, + ⟨6, 2, 5, 3, 4, 6, -85653630088819337671404856835658876717373587456000000⟩, + ⟨6, 2, 6, 3, 5, 6, -25324852324308639480765326997737343564556271616000000⟩, + ⟨6, 2, 7, 3, 6, 6, 3262844932578094106764731440991834227349651456000000⟩, + ⟨6, 2, 8, 3, 7, 6, 8275998468938648225937725264009277935550726144000000⟩, + ⟨6, 2, 3, 4, 1, 6, 130592001456269609152623872697350039696016251289600000⟩, + ⟨6, 2, 4, 4, 2, 6, 596022239417128726437369870877920838930034746982400000⟩, + ⟨6, 2, 5, 4, 3, 6, 7989462883073343055322528483137893120130154496000000⟩, + ⟨6, 2, 6, 4, 4, 6, 11703609637214823996373556434027816255834030080000000⟩, + ⟨6, 2, 7, 4, 5, 6, 11233681523275798137107450639258771933752197120000000⟩, + ⟨6, 2, 8, 4, 6, 6, -10556352886890540087950906039442332616937281945600000⟩, + ⟨6, 2, 3, 5, 0, 6, -156859253448798292455295568034532256615380706918400000⟩, + ⟨6, 2, 4, 5, 1, 6, -574639830337297988853226668291331282657803553996800000⟩, + ⟨6, 2, 5, 5, 2, 6, 620547257540810416967151760029920547911768211456000000⟩, + ⟨6, 2, 6, 5, 3, 6, 4335321619456493322807865810446190801676402688000000⟩, + ⟨6, 2, 7, 5, 4, 6, -7118353944010986998720497622789045236719943680000000⟩, + ⟨6, 2, 8, 5, 5, 6, -3528669756075197770540459793672454202732000051200000⟩, + ⟨6, 2, 4, 6, 0, 6, -1792889836487814449463216052794675318347498363289600000⟩, + ⟨6, 2, 5, 6, 1, 6, -792792277147609769740311429270258366600613724160000000⟩, + ⟨6, 2, 6, 6, 2, 6, 310638681091416970744548364658313541330610946048000000⟩, + ⟨6, 2, 7, 6, 3, 6, -21344515584489119048076703781904849239883644928000000⟩, + ⟨6, 2, 8, 6, 4, 6, 5256494153148581739892929684395897136511922995200000⟩, + ⟨6, 2, 5, 7, 0, 6, -3458897503463949803092174563662668072701004873728000000⟩, + ⟨6, 2, 6, 7, 1, 6, -615826923272805264651974960472636462476247957504000000⟩, + ⟨6, 2, 7, 7, 2, 6, 37903841705133869768511787965109166682692124672000000⟩, + ⟨6, 2, 8, 7, 3, 6, 25175708200329331838059860863232645756961475788800000⟩ +] + +def collectedFourData_11_2_48 : List CollectedFourTerm := [ + ⟨6, 3, 2, 0, 4, 7, 12924605338373005099847469898281017759045674598400000⟩, + ⟨6, 3, 3, 0, 5, 7, -88837901986546827459642003304782466372463493120000000⟩, + ⟨6, 3, 4, 0, 6, 7, -46620603236517982908424478812721692040648196096000000⟩, + ⟨6, 3, 5, 0, 7, 7, -200892105384326303320568077075506707721879552000000⟩, + ⟨6, 3, 6, 0, 8, 7, -3093987645537520438083025089888888475676049408000000⟩, + ⟨6, 3, 2, 1, 3, 7, -7716577227623408635688711726181047231441377689600000⟩, + ⟨6, 3, 3, 1, 4, 7, 84983142300212007829930841652868803612061256908800000⟩, + ⟨6, 3, 4, 1, 5, 7, 72244260072732557365288886528315902343244467404800000⟩, + ⟨6, 3, 5, 1, 6, 7, 33145639036737480894273962279431861543353974784000000⟩, + ⟨6, 3, 6, 1, 7, 7, 10347614876120508288635025373389392798935941120000000⟩, + ⟨6, 3, 7, 1, 8, 7, 3890548905240419350555123610313944508538866892800000⟩, + ⟨6, 3, 2, 2, 2, 7, -1883968184148805987813478799731909548424193638400000⟩, + ⟨6, 3, 3, 2, 3, 7, -58950981455382779099337560147982477581511504691200000⟩, + ⟨6, 3, 4, 2, 4, 7, -19261716678382139133181928188656972324360368947200000⟩, + ⟨6, 3, 5, 2, 5, 7, -5797895905067460647335435154738742307665739776000000⟩, + ⟨6, 3, 6, 2, 6, 7, -714291902503333306922192928378583275993563136000000⟩, + ⟨6, 3, 7, 2, 7, 7, -229702463652943187396238109852419687444381696000000⟩, + ⟨6, 3, 8, 2, 8, 7, -618890154702914299226449829607759532235371315200000⟩, + ⟨6, 3, 2, 3, 1, 7, -10797142992364796370011452472137229574120407040000000⟩, + ⟨6, 3, 3, 3, 2, 7, 38873028937718903114201125624429683745399976755200000⟩, + ⟨6, 3, 4, 3, 3, 7, 24567996850747158111373193165420213014326411264000000⟩, + ⟨6, 3, 5, 3, 4, 7, 7847210080751209251657653608469910875786969088000000⟩, + ⟨6, 3, 6, 3, 5, 7, 1740113958802237182498781523315310451885080576000000⟩, + ⟨6, 3, 7, 3, 6, 7, -179356528989869591577140524366132818102504652800000⟩, + ⟨6, 3, 8, 3, 7, 7, -379105348754005883397401966344027595505401856000000⟩, + ⟨6, 3, 2, 4, 0, 7, 41348393995822513934104474768657570085825465548800000⟩, + ⟨6, 3, 3, 4, 1, 7, -35892799962959791751936210587137157212020303462400000⟩, + ⟨6, 3, 4, 4, 2, 7, -81907416895046274300429310616943213693048245452800000⟩, + ⟨6, 3, 5, 4, 3, 7, -731959563311310843696918733284488670250795008000000⟩, + ⟨6, 3, 6, 4, 4, 7, -804175054499389945969291791326557554742394880000000⟩, + ⟨6, 3, 7, 4, 5, 7, -617508391427104486034264996645054349318291456000000⟩, + ⟨6, 3, 8, 4, 6, 7, 483563386070590450406738280245372868387825254400000⟩, + ⟨6, 3, 3, 5, 0, 7, 43112271376453667536986107861301433178489723289600000⟩, + ⟨6, 3, 4, 5, 1, 7, 78968973026852943905396446251317845222217062809600000⟩, + ⟨6, 3, 5, 5, 2, 7, -56851819238801944834611875611248095858773721088000000⟩, + ⟨6, 3, 6, 5, 3, 7, -297887370449624612888166280927562489520979968000000⟩, + ⟨6, 3, 7, 5, 4, 7, 391291428768688987823648501993141569358659584000000⟩, + ⟨6, 3, 8, 5, 5, 7, 161640626630777795135558229555221074688134348800000⟩, + ⟨6, 3, 4, 6, 0, 7, 246385060107336832253251883947962980673195815731200000⟩, + ⟨6, 3, 5, 6, 1, 7, 72632152808039661835585049831752003732824391680000000⟩, + ⟨6, 3, 6, 6, 2, 7, -21344515584489119048076703781904849239883644928000000⟩, + ⟨6, 3, 7, 6, 3, 7, 1173294565727119052780631938447539079381149286400000⟩, + ⟨6, 3, 8, 6, 4, 7, -240788474844697158175863951106854903605939404800000⟩, + ⟨6, 3, 5, 7, 0, 7, 316889025360882244788528285891129039923177324544000000⟩, + ⟨6, 3, 6, 7, 1, 7, 42314522180436735427079655187431089641560735744000000⟩, + ⟨6, 3, 7, 7, 2, 7, -2083550283293016397884460633812945959202167193600000⟩, + ⟨6, 3, 8, 7, 3, 7, -1153244007141404744088348586140551304992469811200000⟩ +] + +def collectedFourData_11_2_49 : List CollectedFourTerm := [ + ⟨6, 4, 1, 0, 3, 8, -8506705894517651792398791776545472237343552307200000⟩, + ⟨6, 4, 2, 0, 4, 8, -15914653139816559303309208076840518599597411532800000⟩, + ⟨6, 4, 3, 0, 5, 8, 54695070324015418629254003584307443355111915520000000⟩, + ⟨6, 4, 4, 0, 6, 8, 19135354884566565234647955100672129344517177344000000⟩, + ⟨6, 4, 5, 0, 7, 8, 61841891725443848097535385372955047463223296000000⟩, + ⟨6, 4, 6, 0, 8, 8, 761953481881804454763767364246694116340216627200000⟩, + ⟨6, 4, 1, 1, 2, 8, -2496445762988384204048577509245842701131186176000000⟩, + ⟨6, 4, 2, 1, 3, 8, 9501771759298700170101693284869092423104672563200000⟩, + ⟨6, 4, 3, 1, 4, 8, -52321800048472547399931684448266246346322529484800000⟩, + ⟨6, 4, 4, 1, 5, 8, -29652545417554980846241240635121189434453865267200000⟩, + ⟨6, 4, 5, 1, 6, 8, -10203432417411907538008181656477905208561631232000000⟩, + ⟨6, 4, 6, 1, 7, 8, -2548297565248427466270461583150498768022929408000000⟩, + ⟨6, 4, 7, 1, 8, 8, -798434906771250192761726882786904990526577049600000⟩, + ⟨6, 4, 1, 2, 1, 8, -9145060543332943846232913682272059519966537318400000⟩, + ⟨6, 4, 2, 2, 2, 8, 2319815529543482759901814259087673006702251212800000⟩, + ⟨6, 4, 3, 2, 3, 8, 36294509486054344382058848655154848198846264115200000⟩, + ⟨6, 4, 4, 2, 4, 8, 7905941981422237114202278911332117188497427660800000⟩, + ⟨6, 4, 5, 2, 5, 8, 1784803091742352895530312514684276629882011648000000⟩, + ⟨6, 4, 6, 2, 6, 8, 175908007576364791736901878306146312742397542400000⟩, + ⟨6, 4, 7, 2, 7, 8, 47140511433959391053700907178832099249487872000000⟩, + ⟨6, 4, 8, 2, 8, 8, 108866790854467217916775218348246386030621491200000⟩, + ⟨6, 4, 1, 3, 0, 8, -8026064270894077554918607724359742355949171507200000⟩, + ⟨6, 4, 2, 3, 1, 8, 13295012197727786416559366559987250421752135680000000⟩, + ⟨6, 4, 3, 3, 2, 8, -23933062396926003595194576509561874066250609459200000⟩, + ⟨6, 4, 4, 3, 3, 8, -10083896515815931427100705068053197700460445696000000⟩, + ⟨6, 4, 5, 3, 4, 8, -2415656480040504495698275835712503374543847424000000⟩, + ⟨6, 4, 6, 3, 5, 8, -428536258602334675774899191721713040368232038400000⟩, + ⟨6, 4, 7, 3, 6, 8, 36808305714895551712555617186416392457001369600000⟩, + ⟨6, 4, 8, 3, 7, 8, 66687088816954913958078217424063092947419136000000⟩, + ⟨6, 4, 2, 4, 0, 8, -50914154135001696630968702819027507018758461849600000⟩, + ⟨6, 4, 3, 4, 1, 8, 22098216799370103835502856096703107041570743910400000⟩, + ⟨6, 4, 4, 4, 2, 8, 33618773270980842811175753716403556177987973939200000⟩, + ⟨6, 4, 5, 4, 3, 8, 225323757621552124740696001352020490226499584000000⟩, + ⟨6, 4, 6, 4, 4, 8, 198043448461103220080530105666014110382292992000000⟩, + ⟨6, 4, 7, 4, 5, 8, 126727684691344871920646709296233625463816192000000⟩, + ⟨6, 4, 8, 4, 6, 8, -85061934846088546109596766284602704497370726400000⟩, + ⟨6, 4, 3, 5, 0, 8, -26543048203910292287475081961535525899900393881600000⟩, + ⟨6, 4, 4, 5, 1, 8, -32412693505324479169315691266967835225677522534400000⟩, + ⟨6, 4, 5, 5, 2, 8, 17501056315948200577014246880986362316192743424000000⟩, + ⟨6, 4, 6, 5, 3, 8, 73360447786556587617389336486321638910145331200000⟩, + ⟨6, 4, 7, 5, 4, 8, -80302482518211966006652769210773695614681088000000⟩, + ⟨6, 4, 8, 5, 5, 8, -28433634239092293288572821399585443002764492800000⟩, + ⟨6, 4, 4, 6, 0, 8, -101128368920721098239245382689224715329944210636800000⟩, + ⟨6, 4, 5, 6, 1, 8, -22358816545566087875904554760547611070578032640000000⟩, + ⟨6, 4, 6, 6, 2, 8, 5256494153148581739892929684395897136511922995200000⟩, + ⟨6, 4, 7, 6, 3, 8, -240788474844697158175863951106854903605939404800000⟩, + ⟨6, 4, 8, 6, 4, 8, 42356253903678955295091486506239211202202828800000⟩, + ⟨6, 4, 5, 7, 0, 8, -97549959755054057510091137450743833415712243712000000⟩, + ⟨6, 4, 6, 7, 1, 8, -10420758323340765712634014919815729301400689049600000⟩, + ⟨6, 4, 7, 7, 2, 8, 427595004384469847054935813294854305339355955200000⟩, + ⟨6, 4, 8, 7, 3, 8, 202863098040230959213360208188620620931740467200000⟩ +] + +def collectedFourData_11_2_50 : List CollectedFourTerm := [ + ⟨7, 0, 4, 0, 6, 5, -1259151619116299632924388922916719925922277359616000000⟩, + ⟨7, 0, 5, 0, 7, 5, -16277371089283836663430378696738426983731429376000000⟩, + ⟨7, 0, 6, 0, 8, 5, -501383416294297724724333682610941401814907486208000000⟩, + ⟨7, 0, 4, 1, 5, 5, 1951207636266406591150729601785807371094952037580800000⟩, + ⟨7, 0, 5, 1, 6, 5, 2685639963602682886523569573128487124550750830592000000⟩, + ⟨7, 0, 6, 1, 7, 5, 1676840081947276480586786823513682252649327493120000000⟩, + ⟨7, 0, 7, 1, 8, 5, 1050778113794844957954896296324355077803016716288000000⟩, + ⟨7, 0, 4, 2, 4, 5, -520229685135145669226313366806078299091995145011200000⟩, + ⟨7, 0, 5, 2, 5, 5, -469777062683844873237388563283166524567808114688000000⟩, + ⟨7, 0, 6, 2, 6, 5, -115751630367695220529202917995517769047118708736000000⟩, + ⟨7, 0, 7, 2, 7, 5, -62039143413968513999235206259072722429710172160000000⟩, + ⟨7, 0, 8, 2, 8, 5, -250729233294938356126172916762215117628100313088000000⟩, + ⟨7, 0, 4, 3, 3, 5, 663544245794553277768509612446019425723895250944000000⟩, + ⟨7, 0, 5, 3, 4, 5, 635823644018228910150254672372737309799501266944000000⟩, + ⟨7, 0, 6, 3, 5, 5, 281986995864066145063561428158953644717219250176000000⟩, + ⟨7, 0, 7, 3, 6, 5, -48441471838308463853662062531259888740637605888000000⟩, + ⟨7, 0, 8, 3, 7, 5, -153585887105814892275386705695361030748257648640000000⟩, + ⟨7, 0, 4, 4, 2, 5, -2212194811761817349415141820919763225037691997388800000⟩, + ⟨7, 0, 5, 4, 3, 5, -59307345162095745217042886200723628379711995904000000⟩, + ⟨7, 0, 6, 4, 4, 5, -130317274118755891661382867065075198063416442880000000⟩, + ⟨7, 0, 7, 4, 5, 5, -166779628941886957268195392724685100249000181760000000⟩, + ⟨7, 0, 8, 4, 6, 5, 195904678912179329266457647243836586351694708736000000⟩, + ⟨7, 0, 4, 5, 1, 5, 2132831910008975562387939671228271000407183563161600000⟩, + ⟨7, 0, 5, 5, 2, 5, -4606443628436707073973408319170839770980044242944000000⟩, + ⟨7, 0, 6, 5, 3, 5, -48272910101103569174044970916415325347164192768000000⟩, + ⟨7, 0, 7, 5, 4, 5, 105681866358712429983336307357405986620587376640000000⟩, + ⟨7, 0, 8, 5, 5, 5, 65485013901865950209948416350711840605126787072000000⟩, + ⟨7, 0, 4, 6, 0, 5, 6654485910152521909610319994051665535774527533875200000⟩, + ⟨7, 0, 5, 6, 1, 5, 5885052088076085978487884388486760728606109859840000000⟩, + ⟨7, 0, 6, 6, 2, 5, -3458897503463949803092174563662668072701004873728000000⟩, + ⟨7, 0, 7, 6, 3, 5, 316889025360882244788528285891129039923177324544000000⟩, + ⟨7, 0, 8, 6, 4, 5, -97549959755054057510091137450743833415712243712000000⟩, + ⟨7, 0, 5, 7, 0, 5, 25676072487032614565705104896902147253973624553472000000⟩, + ⟨7, 0, 6, 7, 1, 5, 6857105496296308588028181247894566538159948038144000000⟩, + ⟨7, 0, 7, 7, 2, 5, -562735256643704415542179233504277093072037216256000000⟩, + ⟨7, 0, 8, 7, 3, 5, -467210511453924142500759448140220772202030563328000000⟩ +] + +def collectedFourData_11_2_51 : List CollectedFourTerm := [ + ⟨7, 1, 3, 0, 5, 6, -640782542403334916131861509151348409750299607040000000⟩, + ⟨7, 1, 4, 0, 6, 6, -672543317711331320278325254524449965732647665664000000⟩, + ⟨7, 1, 5, 0, 7, 6, -4347068688871825826594277826696858828749668352000000⟩, + ⟨7, 1, 6, 0, 8, 6, -89267000923649531553062760828211764250640646144000000⟩, + ⟨7, 1, 3, 1, 4, 6, 612978388355014846146587708607452993207286733209600000⟩, + ⟨7, 1, 4, 1, 5, 6, 1042187165799202854938116247536315469155001381683200000⟩, + ⟨7, 1, 5, 1, 6, 6, 717232612767922613666911510953086164403836944384000000⟩, + ⟨7, 1, 6, 1, 7, 6, 298546940882740326511599973797040518877843292160000000⟩, + ⟨7, 1, 7, 1, 8, 6, 140311497857186801136440189696333597794986098688000000⟩, + ⟨7, 1, 3, 2, 3, 6, -425209949013343975023735608469502850347890533990400000⟩, + ⟨7, 1, 4, 2, 4, 6, -277867250536725292647763223616319168386616315084800000⟩, + ⟨7, 1, 5, 2, 5, 6, -125459642637720847351230254852488848133299634176000000⟩, + ⟨7, 1, 6, 2, 6, 6, -20608581295560700857974420887951267290622722048000000⟩, + ⟨7, 1, 7, 2, 7, 6, -8284151548183352491807073355006323896520540160000000⟩, + ⟨7, 1, 8, 2, 8, 6, -26784108894803609465608244829148192766123468390400000⟩, + ⟨7, 1, 3, 3, 2, 6, 280388862823460734533269144119717050947572491878400000⟩, + ⟨7, 1, 4, 3, 3, 6, 354415021781196335380908982741704283614741528576000000⟩, + ⟨7, 1, 5, 3, 4, 6, 169804389136012291308689986448880961613136396288000000⟩, + ⟨7, 1, 6, 3, 5, 6, 50205357022577361961592510511864132911096659968000000⟩, + ⟨7, 1, 7, 3, 6, 6, -6468440275647790980936878043826062935917068288000000⟩, + ⟨7, 1, 8, 3, 7, 6, -16406786998419800779060757853578533856725696512000000⟩, + ⟨7, 1, 3, 4, 1, 6, -258892647169027338322210017620962740761768283340800000⟩, + ⟨7, 1, 4, 4, 2, 6, -1181586725171552678503461338498151348580306334515200000⟩, + ⟨7, 1, 5, 4, 3, 6, -15838743354815504239889130064927111393163870208000000⟩, + ⟨7, 1, 6, 4, 4, 6, -23201868771619311367804553108218765668872355840000000⟩, + ⟨7, 1, 7, 4, 5, 6, -22270257860995796581962269512310427418896629760000000⟩, + ⟨7, 1, 8, 4, 6, 6, 20927484936760563006053816439265273709874433228800000⟩, + ⟨7, 1, 3, 5, 0, 6, 310966268266555723599484108844519554176938881843200000⟩, + ⟨7, 1, 4, 5, 1, 6, 1139197080876360975114861039343851180590090315366400000⟩, + ⟨7, 1, 5, 5, 2, 6, -1230206447613240535226492705718034418031591948288000000⟩, + ⟨7, 1, 6, 5, 3, 6, -8594576068014780387670292633453471099963572224000000⟩, + ⟨7, 1, 7, 5, 4, 6, 14111809877331618989486833375669217563131248640000000⟩, + ⟨7, 1, 8, 5, 5, 6, 6995425783726169800815472422982518472670026137600000⟩, + ⟨7, 1, 4, 6, 0, 6, 3554321785980183050729295330923460184183386459340800000⟩, + ⟨7, 1, 5, 6, 1, 6, 1571674290899322823271026796848446648224506183680000000⟩, + ⟨7, 1, 6, 6, 2, 6, -615826923272805264651974960472636462476247957504000000⟩, + ⟨7, 1, 7, 6, 3, 6, 42314522180436735427079655187431089641560735744000000⟩, + ⟨7, 1, 8, 6, 4, 6, -10420758323340765712634014919815729301400689049600000⟩, + ⟨7, 1, 5, 7, 0, 6, 6857105496296308588028181247894566538159948038144000000⟩, + ⟨7, 1, 6, 7, 1, 6, 1220848601646114063920680677029518832397862305792000000⟩, + ⟨7, 1, 7, 7, 2, 6, -75142625945616607394048178994180457905369645056000000⟩, + ⟨7, 1, 8, 7, 3, 6, -49909685644268343640238394372588416339649390182400000⟩ +] + +def collectedFourData_11_2_52 : List CollectedFourTerm := [ + ⟨7, 2, 2, 0, 4, 7, -22951666104009365387618019715310762208066640281600000⟩, + ⟨7, 2, 3, 0, 5, 7, 157759390743037327389028766122547214491194490880000000⟩, + ⟨7, 2, 4, 0, 6, 7, 82789415308116252300122325501481856264363311104000000⟩, + ⟨7, 2, 5, 0, 7, 7, 356746562467411030363891406377588637300686848000000⟩, + ⟨7, 2, 6, 0, 8, 7, 5494339634454672923692298218408500432514056192000000⟩, + ⟨7, 2, 2, 1, 3, 7, 13703188558367985501504820438381224508365629030400000⟩, + ⟨7, 2, 3, 1, 4, 7, -150914063174753531262507846108225266717516051251200000⟩, + ⟨7, 2, 4, 1, 5, 7, -128292206354465270852512209852840123020990427955200000⟩, + ⟨7, 2, 5, 1, 6, 7, -58860415467895661758907267371792370234101334016000000⟩, + ⟨7, 2, 6, 1, 7, 7, -18375416145549775594830067174104425768555642880000000⟩, + ⟨7, 2, 7, 1, 8, 7, -6908882483961246730384438625224005814926390067200000⟩, + ⟨7, 2, 2, 2, 2, 7, 3345572849700914313521900037926088042109049241600000⟩, + ⟨7, 2, 3, 2, 3, 7, 104685845907455535164601138238905464008148307148800000⟩, + ⟨7, 2, 4, 2, 4, 7, 34205182921887722717701248590891730229089062092800000⟩, + ⟨7, 2, 5, 2, 5, 7, 10295971709389389477374460036839996740205543424000000⟩, + ⟨7, 2, 6, 2, 6, 7, 1268447957817323634155730254855920338352472064000000⟩, + ⟨7, 2, 7, 2, 7, 7, 407908335380890184148810405982006147761045504000000⟩, + ⟨7, 2, 8, 2, 8, 7, 1099032412512188212628553104398538041893637324800000⟩, + ⟨7, 2, 2, 3, 1, 7, 19173693459114694217255867777099445975342120960000000⟩, + ⟨7, 2, 3, 3, 2, 7, -69031181786347026468511655583689273673226439884800000⟩, + ⟨7, 2, 4, 3, 3, 7, -43628137633615754347334199870985613252845633536000000⟩, + ⟨7, 2, 5, 3, 4, 7, -13935167914697082079907421078091666578066112512000000⟩, + ⟨7, 2, 6, 3, 5, 7, -3090114825152754527672000429311582181076762624000000⟩, + ⟨7, 2, 7, 3, 6, 7, 318503432729789369996317004537594244043584307200000⟩, + ⟨7, 2, 8, 3, 7, 7, 673219735152183069483382131481547859604537344000000⟩, + ⟨7, 2, 2, 4, 0, 7, -73426964157391381562786290654592067299779490611200000⟩, + ⟨7, 2, 3, 4, 1, 7, 63738856136829293058192469281178017406960376217600000⟩, + ⟨7, 2, 4, 4, 2, 7, 145452153841445460074442440989690070878668403507200000⟩, + ⟨7, 2, 5, 4, 3, 7, 1299822397584521879728931828893348899525230592000000⟩, + ⟨7, 2, 6, 4, 4, 7, 1428063515815407047470083448537331392441221120000000⟩, + ⟨7, 2, 7, 4, 5, 7, 1096578661042732413023506027990681505438367744000000⟩, + ⟨7, 2, 8, 4, 6, 7, -858717545847592930692953085182335746630588825600000⟩, + ⟨7, 2, 3, 5, 0, 7, -76559278346395247338098298822227829538423203430400000⟩, + ⟨7, 2, 4, 5, 1, 7, -140234030675400926571349001322687427548262327910400000⟩, + ⟨7, 2, 5, 5, 2, 7, 100958128965099717242813614133848970960685760512000000⟩, + ⟨7, 2, 6, 5, 3, 7, 528991894465212151101330767891473548686917632000000⟩, + ⟨7, 2, 7, 5, 4, 7, -694859919304139281306701995576656482288009216000000⟩, + ⟨7, 2, 8, 5, 5, 7, -287043325048985541934496640582521266656981811200000⟩, + ⟨7, 2, 4, 6, 0, 7, -437533486288389647413872709941065701886419324108800000⟩, + ⟨7, 2, 5, 6, 1, 7, -128981030833964639487187238535576148183948984320000000⟩, + ⟨7, 2, 6, 6, 2, 7, 37903841705133869768511787965109166682692124672000000⟩, + ⟨7, 2, 7, 6, 3, 7, -2083550283293016397884460633812945959202167193600000⟩, + ⟨7, 2, 8, 6, 4, 7, 427595004384469847054935813294854305339355955200000⟩, + ⟨7, 2, 5, 7, 0, 7, -562735256643704415542179233504277093072037216256000000⟩, + ⟨7, 2, 6, 7, 1, 7, -75142625945616607394048178994180457905369645056000000⟩, + ⟨7, 2, 7, 7, 2, 7, 3699993087686444211342633087804615366747252326400000⟩, + ⟨7, 2, 8, 7, 3, 7, 2047944265638312221994125087531109092235726028800000⟩ +] + +def collectedFourData_11_2_53 : List CollectedFourTerm := [ + ⟨7, 3, 1, 0, 3, 8, -40742430050667332915479222317224372342837005516800000⟩, + ⟨7, 3, 2, 0, 4, 8, -76222412102843147956537354888656734648274203443200000⟩, + ⟨7, 3, 3, 0, 5, 8, 261959224219645413241650974691400103217730682880000000⟩, + ⟨7, 3, 4, 0, 6, 8, 91647797343222351004337338113233193105553883136000000⟩, + ⟨7, 3, 5, 0, 7, 8, 296188557482473647460479230269694792668545024000000⟩, + ⟨7, 3, 6, 0, 8, 8, 3649336984535785242160243347863925500712635596800000⟩, + ⟨7, 3, 1, 1, 2, 8, -11956598492418706886204199461846942175140511744000000⟩, + ⟨7, 3, 2, 1, 3, 8, 45508246795052081092232127893546640763960216780800000⟩, + ⟨7, 3, 3, 1, 4, 8, -250592568384635367407986096561067717388708033331200000⟩, + ⟨7, 3, 4, 1, 5, 8, -142019340092334618426372031504707640404157975756800000⟩, + ⟨7, 3, 5, 1, 6, 8, -48868814403355826402697979456197397295250014208000000⟩, + ⟨7, 3, 6, 1, 7, 8, -12204940030585947594745453415258624376755453952000000⟩, + ⟨7, 3, 7, 1, 8, 8, -3824062891383561122305953168089637441348462182400000⟩, + ⟨7, 3, 1, 2, 1, 8, -43799796785731830206083987994836001575602330009600000⟩, + ⟨7, 3, 2, 2, 2, 8, 11110637080305024453931411084823179328144749363200000⟩, + ⟨7, 3, 3, 2, 3, 8, 173830685143570255842370478545932264983870885068800000⟩, + ⟨7, 3, 4, 2, 4, 8, 37865102209577912606722222465404624461611873075200000⟩, + ⟨7, 3, 5, 2, 5, 8, 8548222545978924212303056280572852994951872512000000⟩, + ⟨7, 3, 6, 2, 6, 8, 842502348488525153351251252253200296019859865600000⟩, + ⟨7, 3, 7, 2, 7, 8, 225777053240851141054597121230373074520506368000000⟩, + ⟨7, 3, 8, 2, 8, 8, 521411891539276360539795638461714430534929612800000⟩, + ⟨7, 3, 1, 3, 0, 8, -38440421732436528667874095252827610246028250316800000⟩, + ⟨7, 3, 2, 3, 1, 8, 63675776640848261393851762260213237291071569920000000⟩, + ⟨7, 3, 3, 3, 2, 8, -114626170540753611502807603002027365246220160204800000⟩, + ⟨7, 3, 4, 3, 3, 8, -48296303355047900861113400704617437336514330624000000⟩, + ⟨7, 3, 5, 3, 4, 8, -11569662379878495678943976968803067616512966656000000⟩, + ⟨7, 3, 6, 3, 5, 8, -2052452354269420097255948289823002401827297689600000⟩, + ⟨7, 3, 7, 3, 6, 8, 176291485737058567349488796840550331509532262400000⟩, + ⟨7, 3, 8, 3, 7, 8, 319394379575113385514754141158193337921961984000000⟩, + ⟨7, 3, 2, 4, 0, 8, -243850720732108081256760945293514962768287393382400000⟩, + ⟨7, 3, 3, 4, 1, 8, 105838271988815373028979234508156104737960860057600000⟩, + ⟨7, 3, 4, 4, 2, 8, 161015384258779182714365375050781236099457797324800000⟩, + ⟨7, 3, 5, 4, 3, 8, 1079176539953735716228022167790484369960861696000000⟩, + ⟨7, 3, 6, 4, 4, 8, 948518903318327945403279927635474645042331648000000⟩, + ⟨7, 3, 7, 4, 5, 8, 606955723289750320581909628645131850453352448000000⟩, + ⟨7, 3, 8, 4, 6, 8, -407399758897823430444943026981780375985559961600000⟩, + ⟨7, 3, 3, 5, 0, 8, -127126563230105128684911691216894885106926642790400000⟩, + ⟨7, 3, 4, 5, 1, 8, -155238927296813659348395944714480526903626799513600000⟩, + ⟨7, 3, 5, 5, 2, 8, 83820408464437680685901157424216376727784390656000000⟩, + ⟨7, 3, 6, 5, 3, 8, 351356088889316294221780871923839582142778572800000⟩, + ⟨7, 3, 7, 5, 4, 8, -384604606937419071153812031545614873890127872000000⟩, + ⟨7, 3, 8, 5, 5, 8, -136181427739152406939626488726849239376933683200000⟩, + ⟨7, 3, 4, 6, 0, 8, -484349117975964133029438511709082781587214644019200000⟩, + ⟨7, 3, 5, 6, 1, 8, -107086401060428653831833688802477158342758236160000000⟩, + ⟨7, 3, 6, 6, 2, 8, 25175708200329331838059860863232645756961475788800000⟩, + ⟨7, 3, 7, 6, 3, 8, -1153244007141404744088348586140551304992469811200000⟩, + ⟨7, 3, 8, 6, 4, 8, 202863098040230959213360208188620620931740467200000⟩, + ⟨7, 3, 5, 7, 0, 8, -467210511453924142500759448140220772202030563328000000⟩, + ⟨7, 3, 6, 7, 1, 8, -49909685644268343640238394372588416339649390182400000⟩, + ⟨7, 3, 7, 7, 2, 8, 2047944265638312221994125087531109092235726028800000⟩, + ⟨7, 3, 8, 7, 3, 8, 971602366915311091101940312624757567648484556800000⟩ +] + +def collectedFourData_11_2 : List (List CollectedFourTerm) := [ + collectedFourData_11_2_0, + collectedFourData_11_2_1, + collectedFourData_11_2_2, + collectedFourData_11_2_3, + collectedFourData_11_2_4, + collectedFourData_11_2_5, + collectedFourData_11_2_6, + collectedFourData_11_2_7, + collectedFourData_11_2_8, + collectedFourData_11_2_9, + collectedFourData_11_2_10, + collectedFourData_11_2_11, + collectedFourData_11_2_12, + collectedFourData_11_2_13, + collectedFourData_11_2_14, + collectedFourData_11_2_15, + collectedFourData_11_2_16, + collectedFourData_11_2_17, + collectedFourData_11_2_18, + collectedFourData_11_2_19, + collectedFourData_11_2_20, + collectedFourData_11_2_21, + collectedFourData_11_2_22, + collectedFourData_11_2_23, + collectedFourData_11_2_24, + collectedFourData_11_2_25, + collectedFourData_11_2_26, + collectedFourData_11_2_27, + collectedFourData_11_2_28, + collectedFourData_11_2_29, + collectedFourData_11_2_30, + collectedFourData_11_2_31, + collectedFourData_11_2_32, + collectedFourData_11_2_33, + collectedFourData_11_2_34, + collectedFourData_11_2_35, + collectedFourData_11_2_36, + collectedFourData_11_2_37, + collectedFourData_11_2_38, + collectedFourData_11_2_39, + collectedFourData_11_2_40, + collectedFourData_11_2_41, + collectedFourData_11_2_42, + collectedFourData_11_2_43, + collectedFourData_11_2_44, + collectedFourData_11_2_45, + collectedFourData_11_2_46, + collectedFourData_11_2_47, + collectedFourData_11_2_48, + collectedFourData_11_2_49, + collectedFourData_11_2_50, + collectedFourData_11_2_51, + collectedFourData_11_2_52, + collectedFourData_11_2_53 +] + +theorem collectedFourChecked_11_2 : collectNumericRowParts 11 2 = collectedFourData_11_2 := by + decide +kernel + +def collectedFourData_11_3_0 : List CollectedFourTerm := [ + ⟨0, 3, 8, 3, 8, 0, -84885611736805918588385660890005403080012595200000000⟩, + ⟨0, 3, 8, 4, 7, 0, -30153615520174904903311449035998227125391222374400000⟩, + ⟨0, 3, 8, 5, 6, 0, -62787741534275616650945660052133779629588191641600000⟩, + ⟨0, 3, 8, 6, 5, 0, 65892933646157854939917283685909050594444915507200000⟩, + ⟨0, 3, 8, 7, 4, 0, -130284941275600969045107244457989411887768403968000000⟩ +] + +def collectedFourData_11_3_1 : List CollectedFourTerm := [ + ⟨0, 4, 7, 2, 8, 1, -929790988446526592902270314628075515820376064000000⟩, + ⟨0, 4, 7, 3, 7, 1, 519175870019602365866598049636661474975809536000000⟩, + ⟨0, 4, 8, 3, 8, 1, 2349347180779400705987286937564345547096064000000000⟩, + ⟨0, 4, 7, 4, 6, 1, -170510512078992745801025028747636566686433280000000⟩, + ⟨0, 4, 8, 4, 7, 1, 834550286711458135787229285925129760966443008000000⟩, + ⟨0, 4, 7, 5, 5, 1, -451587185162138497882361548596735511105634304000000⟩, + ⟨0, 4, 8, 5, 6, 1, 1737752730326340074918559730196198436070490112000000⟩, + ⟨0, 4, 7, 6, 4, 1, 161661700447080332894015412167433112894046208000000⟩, + ⟨0, 4, 8, 6, 5, 1, -1823693965649567695952698667026697669421563904000000⟩, + ⟨0, 4, 7, 7, 3, 1, 6773554710957348848321948303121094404275699712000000⟩, + ⟨0, 4, 8, 7, 4, 1, 3605847365898482298970123243479165705136373760000000⟩ +] + +def collectedFourData_11_3_2 : List CollectedFourTerm := [ + ⟨0, 5, 6, 1, 8, 2, 3648957292767572064238941888907412916305657856000000⟩, + ⟨0, 5, 6, 2, 7, 2, 4882722219099787632512236702580313038398685184000000⟩, + ⟨0, 5, 7, 2, 8, 2, 22899023706687303731418339310153992970306584576000000⟩, + ⟨0, 5, 6, 3, 6, 2, -12937786228784652311527062006586303816113586176000000⟩, + ⟨0, 5, 7, 3, 7, 2, -12786336610319395191957126039398924204139085824000000⟩, + ⟨0, 5, 8, 3, 8, 2, -28930026993373281993339503141268186923532288000000000⟩, + ⟨0, 5, 6, 4, 5, 2, 10293318978328948201547875646781503596998426624000000⟩, + ⟨0, 5, 7, 4, 6, 2, 4199356959632224555754280653274014564241899520000000⟩, + ⟨0, 5, 8, 4, 7, 2, -10276711130400156419205107860574577069744193536000000⟩, + ⟨0, 5, 6, 5, 4, 2, 11609639976980399229642424020811873833248096256000000⟩, + ⟨0, 5, 7, 5, 5, 2, 11121752939272239996170006319957081689985908736000000⟩, + ⟨0, 5, 8, 5, 6, 2, -21398809766154226907566169336231476025050005504000000⟩, + ⟨0, 5, 6, 6, 3, 2, -42988050544534406435103160768086869008623599616000000⟩, + ⟨0, 5, 7, 6, 4, 2, -3981427177721000796379930356027100142996815872000000⟩, + ⟨0, 5, 8, 6, 5, 2, 22457096203376328442906148839836042439654637568000000⟩, + ⟨0, 5, 6, 7, 2, 2, 42423940960097744392811153226807061875234177024000000⟩, + ⟨0, 5, 7, 7, 3, 2, -166820061532222771938409911992246476392426897408000000⟩, + ⟨0, 5, 8, 7, 4, 2, -44402658952611497277290798716354903112857681920000000⟩ +] + +def collectedFourData_11_3_3 : List CollectedFourTerm := [ + ⟨0, 6, 5, 0, 8, 3, -135000882856054810335128030481387264435604684800000⟩, + ⟨0, 6, 5, 1, 7, 3, 1070764430400104603533830993639283472758682419200000⟩, + ⟨0, 6, 6, 1, 8, 3, 585695756799598160948478233981966398729381478400000⟩, + ⟨0, 6, 5, 2, 6, 3, 748408661433858162797115735568779819397781913600000⟩, + ⟨0, 6, 6, 2, 7, 3, 783727913457940195410644857857525493591021977600000⟩, + ⟨0, 6, 7, 2, 8, 3, 1837766236185222500401193295907347457956328243200000⟩, + ⟨0, 6, 5, 3, 5, 3, -282793517334747371428879717739385812491960320000000⟩, + ⟨0, 6, 6, 3, 6, 3, -2076649817633839158908719177572891752237786726400000⟩, + ⟨0, 6, 7, 3, 7, 3, -1026170286031962075081919634788442383556857036800000⟩, + ⟨0, 6, 8, 3, 8, 3, -1547857163442358719455411941519322444621414400000000⟩, + ⟨0, 6, 5, 4, 4, 3, 1018794137735447285135455006908872246973746380800000⟩, + ⟨0, 6, 6, 4, 5, 3, 1652185203959868284259931517617386008161655193600000⟩, + ⟨0, 6, 7, 4, 6, 3, 337020325973450797329384287006008490500030464000000⟩, + ⟨0, 6, 8, 4, 7, 3, -549839823635883070752439577622545848563715276800000⟩, + ⟨0, 6, 5, 5, 3, 3, -2657073679998409891887023981594344178335717785600000⟩, + ⟨0, 6, 6, 5, 4, 3, 1863468472477276107508667124594789777888667238400000⟩, + ⟨0, 6, 7, 5, 5, 3, 892578753609453434283711565982128685150581555200000⟩, + ⟨0, 6, 8, 5, 6, 3, -1144910822007498517987803553528041500925178675200000⟩, + ⟨0, 6, 5, 6, 2, 3, -39324490127671663061870520023181106098890342400000⟩, + ⟨0, 6, 6, 6, 3, 3, -6900031098452271468689211150177573205088560742400000⟩, + ⟨0, 6, 7, 6, 4, 3, -319530322897961814333684895485169783600997990400000⟩, + ⟨0, 6, 8, 6, 5, 3, 1201532830801452979275519288502991598280664678400000⟩, + ⟨0, 6, 5, 7, 1, 3, 1833172420469079590352203595404265546507406540800000⟩, + ⟨0, 6, 6, 7, 2, 3, 6809485618342268193213729008422786601460537753600000⟩, + ⟨0, 6, 7, 7, 3, 3, -13388181108905941336107093910632121538430212505600000⟩, + ⟨0, 6, 8, 7, 4, 3, -2375696840913102500925681089565338205312516096000000⟩ +] + +def collectedFourData_11_3_4 : List CollectedFourTerm := [ + ⟨0, 7, 4, 0, 7, 4, 20544862290599082900808836194710801404751113093120000⟩, + ⟨0, 7, 5, 0, 8, 4, 1936713685057979716806310880676404998993398988800000⟩, + ⟨0, 7, 4, 1, 6, 4, 46031469357557177333696345540067082359835962900480000⟩, + ⟨0, 7, 5, 1, 7, 4, -15361115290189278861580477636645819676565386035200000⟩, + ⟨0, 7, 6, 1, 8, 4, -4201176182987078091462870855660685473470427955200000⟩, + ⟨0, 7, 4, 2, 5, 4, -5841152223214847651712911324067732340583788707840000⟩, + ⟨0, 7, 5, 2, 6, 4, -10736620872030609431404432911191177473998559641600000⟩, + ⟨0, 7, 6, 2, 7, 4, -5621654256047899135123292222956906688757419212800000⟩, + ⟨0, 7, 7, 2, 8, 4, -8788157391416110774039761284903038475301185126400000⟩, + ⟨0, 7, 4, 3, 4, 4, 4007613878551605664205826706428621725227643043840000⟩, + ⟨0, 7, 5, 3, 5, 4, 4056936987974092084317579394584390234191953920000000⟩, + ⟨0, 7, 6, 3, 6, 4, 14895740071466623096278142276451340897442018099200000⟩, + ⟨0, 7, 7, 3, 7, 4, 4907123553843799310044399877711723818714241433600000⟩, + ⟨0, 7, 8, 3, 8, 4, 5551363975430832407981166643568767990864281600000000⟩, + ⟨0, 7, 4, 4, 3, 4, 8957600593037070686195675972035029531710246092800000⟩, + ⟨0, 7, 5, 4, 4, 4, -14615552928738426108605463305246145447046466764800000⟩, + ⟨0, 7, 6, 4, 5, 4, -11851069515490484700898474745434792863780883660800000⟩, + ⟨0, 7, 7, 4, 6, 4, -1611623725827630074508200951328746594503753728000000⟩, + ⟨0, 7, 8, 4, 7, 4, 1971991383495090643792473917817381131486704435200000⟩, + ⟨0, 7, 4, 5, 2, 4, -61374447066043256532230714351577877876261445959680000⟩, + ⟨0, 7, 5, 5, 3, 4, 38118202262034237580870119120025042788762098073600000⟩, + ⟨0, 7, 6, 5, 4, 4, -13366597373177717109299870093970090535310013235200000⟩, + ⟨0, 7, 7, 5, 5, 4, -4268291808013886093021215759597512797161154150400000⟩, + ⟨0, 7, 8, 5, 6, 4, 4106203622974036760335489410806589605578329292800000⟩, + ⟨0, 7, 4, 6, 1, 4, 32933903262599434081860699114889533147752347729920000⟩, + ⟨0, 7, 5, 6, 2, 4, 564146519466804580702003119118192689036027494400000⟩, + ⟨0, 7, 6, 6, 3, 4, 49493693570681743386382595011563963225428144947200000⟩, + ⟨0, 7, 7, 6, 4, 4, 1527986918938194111950449740060915885880954060800000⟩, + ⟨0, 7, 8, 6, 5, 4, -4309277515875261188986452941269293712914618777600000⟩, + ⟨0, 7, 4, 7, 0, 4, 628419465697098731255525434860159315812092099952640000⟩, + ⟨0, 7, 5, 7, 1, 4, -26298569599569804063504939394642764432476523724800000⟩, + ⟨0, 7, 6, 7, 2, 4, -48844213853441051662660839187042220409598299340800000⟩, + ⟨0, 7, 7, 7, 3, 4, 64021985197681572000526495211095376538989966131200000⟩, + ⟨0, 7, 8, 7, 4, 4, 8520397211496936116188535742437427641050988544000000⟩ +] + +def collectedFourData_11_3_5 : List CollectedFourTerm := [ + ⟨0, 8, 3, 0, 6, 5, -135000882856054810335128030481387264435604684800000⟩, + ⟨0, 8, 4, 0, 7, 5, 1936713685057979716806310880676404998993398988800000⟩, + ⟨0, 8, 5, 0, 8, 5, 91284620087406907047790745383941209069715456000000⟩, + ⟨0, 8, 3, 1, 5, 5, 1809879596560614394431356399484804321826465382400000⟩, + ⟨0, 8, 4, 1, 6, 5, 4339273507270048024718728514232810543602938675200000⟩, + ⟨0, 8, 5, 1, 7, 5, -724027296446664354346916005054056487320551424000000⟩, + ⟨0, 8, 6, 1, 8, 5, -132011518530252522042401469642708063633801216000000⟩, + ⟨0, 8, 3, 2, 4, 5, -2356852186364271171110358116432408321110887628800000⟩, + ⟨0, 8, 4, 2, 5, 5, -550631067134651737644359110917144631198718361600000⟩, + ⟨0, 8, 5, 2, 6, 5, -506057433727741003796261376101793669517934592000000⟩, + ⟨0, 8, 6, 2, 7, 5, -176646511040935034006257844925958490343604224000000⟩, + ⟨0, 8, 7, 2, 8, 5, -207109500731322681214593577938660905434742784000000⟩, + ⟨0, 8, 3, 3, 3, 5, 3150267108134285169803884380219374125149742694400000⟩, + ⟨0, 8, 4, 3, 4, 5, 377787912775192259887497388417471083741551001600000⟩, + ⟨0, 8, 5, 3, 5, 5, 191218740551563289822726041311006068991590400000000⟩, + ⟨0, 8, 6, 3, 6, 5, 468061604849931472417944252591520567825268736000000⟩, + ⟨0, 8, 7, 3, 7, 5, 115645619894813479136884310052210248112930816000000⟩, + ⟨0, 8, 8, 3, 8, 5, 104662688217427377775274720569503773412556800000000⟩, + ⟨0, 8, 3, 4, 2, 5, -4312572767948833790515747869141092180070236160000000⟩, + ⟨0, 8, 4, 4, 3, 5, 844410997184274505363345553913618231692623872000000⟩, + ⟨0, 8, 5, 4, 4, 5, -688886130541971752657809625435296178242584576000000⟩, + ⟨0, 8, 6, 4, 5, 5, -372390400879385089599395700846028718881112064000000⟩, + ⟨0, 8, 7, 4, 6, 5, -37980952133258198243702179165862805299527680000000⟩, + ⟨0, 8, 8, 4, 7, 5, 37178956424341107586846493813869483864463769600000⟩, + ⟨0, 8, 3, 5, 1, 5, 3581256654944351350102700642664784227541922611200000⟩, + ⟨0, 8, 4, 5, 2, 5, -5785618314904094778671037661190969593003455283200000⟩, + ⟨0, 8, 5, 5, 3, 5, 1796654631373950579473575158106710442279698432000000⟩, + ⟨0, 8, 6, 5, 4, 5, -420012096603162678055881169208557894543343616000000⟩, + ⟨0, 8, 7, 5, 5, 5, -100590345161183268188878893629370474612916224000000⟩, + ⟨0, 8, 8, 5, 6, 5, 77416345145203500641676552585402623348598374400000⟩, + ⟨0, 8, 3, 6, 0, 5, 1950354204041596789510755352650894153434215219200000⟩, + ⟨0, 8, 4, 6, 1, 5, 3104598134991541935885642951809935593240841420800000⟩, + ⟨0, 8, 5, 6, 2, 5, 26590353081342769574417128426546659462217728000000⟩, + ⟨0, 8, 6, 6, 3, 5, 1555216292141107152195124314210141920953368576000000⟩, + ⟨0, 8, 7, 6, 4, 5, 36009893065227340711750671104993443392258048000000⟩, + ⟨0, 8, 8, 6, 5, 5, -81245000522852483278654828890046713146690764800000⟩, + ⟨0, 8, 4, 7, 0, 5, 59239558871577393936573517365437051136737122713600000⟩, + ⟨0, 8, 5, 7, 1, 5, -1239550767498753721784299038562770223707979776000000⟩, + ⟨0, 8, 6, 7, 2, 5, -1534808006462742289889671319732005537226686464000000⟩, + ⟨0, 8, 7, 7, 3, 5, 1508798807252965591332369794229960113727209472000000⟩, + ⟨0, 8, 8, 7, 4, 5, 160639381741553490794448359114290844990963712000000⟩ +] + +def collectedFourData_11_3_6 : List CollectedFourTerm := [ + ⟨1, 2, 8, 3, 8, 0, 33203204931090117028054315511679952693808332800000000⟩, + ⟨1, 2, 8, 4, 7, 0, 11794657010117931458477368938219558803101817241600000⟩, + ⟨1, 2, 8, 5, 6, 0, 24559571482936422267620414842482468066324538982400000⟩, + ⟨1, 2, 8, 6, 5, 0, -25774174616868081084513565981299759812172369100800000⟩, + ⟨1, 2, 8, 7, 4, 0, 50961258523075995984521619583782251530448535552000000⟩ +] + +def collectedFourData_11_3_7 : List CollectedFourTerm := [ + ⟨1, 3, 7, 2, 8, 1, 3755137995819161304600665644640666943878489702400000⟩, + ⟨1, 3, 7, 3, 7, 1, -2096790633861043880210885476445880197670607257600000⟩, + ⟨1, 3, 8, 3, 8, 1, -9488286048733549957925273100680569681241702400000000⟩, + ⟨1, 3, 7, 4, 6, 1, 688639178643998653631431478522883081920053248000000⟩, + ⟨1, 3, 8, 4, 7, 1, -3370490282217015645063808688767156412799044812800000⟩, + ⟨1, 3, 7, 5, 5, 1, 1823820857051568608261566743734723670972982886400000⟩, + ⟨1, 3, 8, 5, 6, 1, -7018245375651129630569951771491668193747088179200000⟩, + ⟨1, 3, 7, 6, 4, 1, -652901567514471265091428755511696913777609932800000⟩, + ⟨1, 3, 8, 6, 5, 1, 7365335422962819582084891104125955025001670246400000⟩, + ⟨1, 3, 7, 7, 3, 1, -27356290798616028394830284224880998817358623539200000⟩, + ⟨1, 3, 8, 7, 4, 1, -14562901360694954486668975236873908367724118016000000⟩ +] + +def collectedFourData_11_3_8 : List CollectedFourTerm := [ + ⟨1, 4, 6, 1, 8, 2, -12576293814378923143388113953205544649466105036800000⟩, + ⟨1, 4, 6, 2, 7, 2, -16828519578211080578549204818231542068527969075200000⟩, + ⟨1, 4, 7, 2, 8, 2, -78922505003971734156549198485039908343662824652800000⟩, + ⟨1, 4, 6, 3, 6, 2, 44590656416648105849740133776677487341074173132800000⟩, + ⟨1, 4, 7, 3, 7, 2, 44068678561859334199525544829241713389445788467200000⟩, + ⟨1, 4, 8, 3, 8, 2, 99708626419857293821356627909858794349684326400000000⟩, + ⟨1, 4, 6, 4, 5, 2, -35476382267659834298356719470542750503893414707200000⟩, + ⟨1, 4, 7, 4, 6, 2, -14473270778057258941341834360087234593691795456000000⟩, + ⟨1, 4, 8, 4, 7, 2, 35419142580149379786406601818462942206393896140800000⟩, + ⟨1, 4, 6, 5, 4, 2, -40013141211341941107161113068353243152642788556800000⟩, + ⟨1, 4, 7, 5, 5, 2, -38331616808026428627912343478420792291980266700800000⟩, + ⟨1, 4, 8, 5, 6, 2, 73751950846495891938227258146077424244994814771200000⟩, + ⟨1, 4, 6, 6, 3, 2, 148160230657397592889282668424860018631984860364800000⟩, + ⟨1, 4, 7, 6, 4, 2, 13722166079284439180947518599343942918158784921600000⟩, + ⟨1, 4, 8, 6, 5, 2, -77399382182745622346537634591992037887317534310400000⟩, + ⟨1, 4, 6, 7, 2, 2, -146216001852241623424209163678016873434801451827200000⟩, + ⟨1, 4, 7, 7, 3, 2, 574952771335611155451410642257515506918891087462400000⟩, + ⟨1, 4, 8, 7, 4, 2, 153035741534855685953185359100905738986298802176000000⟩ +] + +def collectedFourData_11_3_9 : List CollectedFourTerm := [ + ⟨1, 5, 5, 0, 8, 3, 1809879596560614394431356399484804321826465382400000⟩, + ⟨1, 5, 5, 1, 7, 3, -14355126087363063678906224543827239394921257369600000⟩, + ⟨1, 5, 6, 1, 8, 3, -7852087909336050253046287478920521955325195059200000⟩, + ⟨1, 5, 5, 2, 6, 3, -10033486726621282994015279745080199749489708236800000⟩, + ⟨1, 5, 6, 2, 7, 3, -10506991730824307504454611328829336112866315468800000⟩, + ⟨1, 5, 7, 2, 8, 3, -24637880462353225214797088897117411156438915481600000⟩, + ⟨1, 5, 5, 3, 5, 3, 3791250888407167040769499753858705752493916160000000⟩, + ⟨1, 5, 6, 3, 6, 3, 27840455963123633693431628733417009294494348083200000⟩, + ⟨1, 5, 7, 3, 7, 3, 13757277908073473673308017033162688328240621158400000⟩, + ⟨1, 5, 8, 3, 8, 3, 20751235393708896625012034676368269206827827200000000⟩, + ⟨1, 5, 5, 4, 4, 3, -13658390108078107166907508974141587536059197030400000⟩, + ⟨1, 5, 6, 4, 5, 3, -22149901742306934581240008806564700933656988876800000⟩, + ⟨1, 5, 7, 4, 6, 3, -4518238686304997030311150844733995370971922432000000⟩, + ⟨1, 5, 8, 4, 7, 3, 7371387928152642204346314257619755943852402278400000⟩, + ⟨1, 5, 5, 5, 3, 3, 35621866600049908353589412681239013443515501772800000⟩, + ⟨1, 5, 6, 5, 4, 3, -24982455638950903492394564157014822016567685939200000⟩, + ⟨1, 5, 7, 5, 5, 3, -11966292666424588410381945068518840876209379737600000⟩, + ⟨1, 5, 8, 5, 6, 3, 15349164337260306553611420273846028507417254297600000⟩, + ⟨1, 5, 5, 6, 2, 3, 527200939886521279018426224445954897636176691200000⟩, + ⟨1, 5, 6, 6, 3, 3, 92504769128347898316599416060939703769996931891200000⟩, + ⟨1, 5, 7, 6, 4, 3, 4283760221865161088159607851075032184861700915200000⟩, + ⟨1, 5, 8, 6, 5, 3, -16108263213241158415793485835729987451244196659200000⟩, + ⟨1, 5, 5, 7, 1, 3, -24576293803369138101516098464892463311413995110400000⟩, + ⟨1, 5, 6, 7, 2, 3, -91290877681529630484814718421149651727649918156800000⟩, + ⟨1, 5, 7, 7, 3, 3, 179487684165025149442489347606901648598103805132800000⟩, + ⟨1, 5, 8, 7, 4, 3, 31849608306389595834851530566169140099545038848000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1109.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1109.lean new file mode 100644 index 0000000000000000000000000000000000000000..c3135411c6b65f7e8af190b1ee94a558aa5ce9b3 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1109.lean @@ -0,0 +1,656 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1109. -/ +namespace LaughlinFock +def collectedFourData_11_3_10 : List CollectedFourTerm := [ + ⟨1, 6, 4, 0, 7, 4, 46031469357557177333696345540067082359835962900480000⟩, + ⟨1, 6, 5, 0, 8, 4, 4339273507270048024718728514232810543602938675200000⟩, + ⟨1, 6, 4, 1, 6, 4, 103135087558376567183336495763877292138351736913920000⟩, + ⟨1, 6, 5, 1, 7, 4, -34417106222308590517870682314151743553442467020800000⟩, + ⟨1, 6, 6, 1, 8, 4, -9412879482835882025891311802402893257339882700800000⟩, + ⟨1, 6, 4, 2, 5, 4, -13087302108555572236825956613011763100453814927360000⟩, + ⟨1, 6, 5, 2, 6, 4, -24055767699194172554548582772647079256498005606400000⟩, + ⟨1, 6, 6, 2, 7, 4, -12595509376787553293324670214750891610872165171200000⟩, + ⟨1, 6, 7, 2, 8, 4, -19690168371557591825033097464408394196735072665600000⟩, + ⟨1, 6, 4, 3, 4, 4, 8979196493903090756996940782218186199934550671360000⟩, + ⟨1, 6, 5, 3, 5, 4, 9089706614043419943373687484689232489537863680000000⟩, + ⟨1, 6, 6, 3, 6, 4, 33374417066382700842728154111957430224359836876800000⟩, + ⟨1, 6, 7, 3, 7, 4, 10994578805518061292326854016352164393353897574400000⟩, + ⟨1, 6, 8, 3, 8, 4, 12438021589690575189780029862613303465240166400000000⟩, + ⟨1, 6, 4, 4, 3, 4, 20069811682519602708417740727679706294020944691200000⟩, + ⟨1, 6, 5, 4, 4, 4, -32746648153043422708224045086357586808709264179200000⟩, + ⟨1, 6, 6, 4, 5, 4, -26552728148788820391981884384980043599417914163200000⟩, + ⟨1, 6, 7, 4, 6, 4, -3610898291846543013549164533984433880654938112000000⟩, + ⟨1, 6, 8, 4, 7, 4, 4418314401856918595206058539064937631984700620800000⟩, + ⟨1, 6, 4, 5, 2, 4, -137511555906136197677391643633510912041897657630720000⟩, + ⟨1, 6, 5, 5, 3, 4, 85405140933598875459576081223388875380652140134400000⟩, + ⟨1, 6, 6, 5, 4, 4, -29948320348673060747397979892816777652428655820800000⟩, + ⟨1, 6, 7, 5, 5, 4, -9563254345082998267018155137863442574754814361600000⟩, + ⟨1, 6, 8, 5, 6, 4, 9200090201301029075952945291888437483747357491200000⟩, + ⟨1, 6, 4, 6, 1, 4, 73789541025582223370834884515283399087763415367680000⟩, + ⟨1, 6, 5, 6, 2, 4, 1263989646496263475553661686742104430521981337600000⟩, + ⟨1, 6, 6, 6, 3, 4, 110892319781264771665506406267199798410486795468800000⟩, + ⟨1, 6, 7, 6, 4, 4, 3423507154391382407342932750729859412863955763200000⟩, + ⟨1, 6, 8, 6, 5, 4, -9655084230765997621254113509954801370000680550400000⟩, + ⟨1, 6, 4, 7, 0, 4, 1407995389298126466623597920441734233139209369026560000⟩, + ⟨1, 6, 5, 7, 1, 4, -58922848133380332929823389138355284943966516019200000⟩, + ⟨1, 6, 6, 7, 2, 4, -109437138175292175650923248183878375876007768883200000⟩, + ⟨1, 6, 7, 7, 3, 4, 143443455991698640209219149538636492705517849804800000⟩, + ⟨1, 6, 8, 7, 4, 4, 19090242495064209908654862704817041496946507776000000⟩ +] + +def collectedFourData_11_3_11 : List CollectedFourTerm := [ + ⟨1, 7, 3, 0, 6, 5, 1070764430400104603533830993639283472758682419200000⟩, + ⟨1, 7, 4, 0, 7, 5, -15361115290189278861580477636645819676565386035200000⟩, + ⟨1, 7, 5, 0, 8, 5, -724027296446664354346916005054056487320551424000000⟩, + ⟨1, 7, 3, 1, 5, 5, -14355126087363063678906224543827239394921257369600000⟩, + ⟨1, 7, 4, 1, 6, 5, -34417106222308590517870682314151743553442467020800000⟩, + ⟨1, 7, 5, 1, 7, 5, 5742648931418225811069906552900276768888324096000000⟩, + ⟨1, 7, 6, 1, 8, 5, 1047054178127243123766551701052021676875710464000000⟩, + ⟨1, 7, 3, 2, 4, 5, 18693459149896179014894860881990764913759564595200000⟩, + ⟨1, 7, 4, 2, 5, 5, 4367350409031740991483899915648401138648508006400000⟩, + ⟨1, 7, 5, 2, 6, 5, 4013813008563746614913298759118596457069805568000000⟩, + ⟨1, 7, 6, 2, 7, 5, 1401078250566635665142653123342637677513015296000000⟩, + ⟨1, 7, 7, 2, 8, 5, 1642696565306784306217688608752806652108865536000000⟩, + ⟨1, 7, 3, 3, 3, 5, -24986458564469338417173533965019273085475985817600000⟩, + ⟨1, 7, 4, 3, 4, 5, -2996438620820695424287130142808853809134462566400000⟩, + ⟨1, 7, 5, 3, 5, 5, -1516658420870000784080317835483646558575001600000000⟩, + ⟨1, 7, 6, 3, 6, 5, -3712447704832306174127440634115773848872812544000000⟩, + ⟨1, 7, 7, 3, 7, 5, -917247455684940363100819663928035880535588864000000⟩, + ⟨1, 7, 8, 3, 8, 5, -830135932168469148513428859503409750029107200000000⟩, + ⟨1, 7, 3, 4, 2, 5, 34205328333707476379558496832048031767084400640000000⟩, + ⟨1, 7, 4, 4, 3, 5, -6697476648265134453657695456604662908676210688000000⟩, + ⟨1, 7, 5, 4, 4, 5, 5463925491263729572093816333875760640141819904000000⟩, + ⟨1, 7, 6, 4, 5, 5, 2953628058190122645010487317966834332289990656000000⟩, + ⟨1, 7, 7, 4, 6, 5, 301247308288975809203027431547820231591198720000000⟩, + ⟨1, 7, 8, 4, 7, 5, -294886250047915412549345948003494373001422438400000⟩, + ⟨1, 7, 3, 5, 1, 5, -28404867887692382165317862097006626143946460364800000⟩, + ⟨1, 7, 4, 5, 2, 5, 45888842860947615146732444042126425638560386252800000⟩, + ⟨1, 7, 5, 5, 3, 5, -14250231793225311098857732483383106152513404928000000⟩, + ⟨1, 7, 6, 5, 4, 5, 3331341276189799042989651360781175432165720064000000⟩, + ⟨1, 7, 7, 5, 5, 5, 797835994562413151153958079736747183409463296000000⟩, + ⟨1, 7, 8, 5, 6, 5, -614030567499684251537231177152407532069296537600000⟩, + ⟨1, 7, 3, 6, 0, 5, -15469305564436803732799529802202147110033083596800000⟩, + ⟨1, 7, 4, 6, 1, 5, -24624233436902671326671146322420552200380166963200000⟩, + ⟨1, 7, 5, 6, 2, 5, -210902356110071047657072553202910164745715712000000⟩, + ⟨1, 7, 6, 6, 3, 5, -12335254792215217347841704330013413609679355904000000⟩, + ⟨1, 7, 7, 6, 4, 5, -285613781340004718426028270347275660261588992000000⟩, + ⟨1, 7, 8, 6, 5, 5, 644397687387469067782684535407708299433554739200000⟩, + ⟨1, 7, 4, 7, 0, 5, -469860723651061027632227313959186500398753408614400000⟩, + ⟨1, 7, 5, 7, 1, 5, 9831542160565118111172794289989839050667720704000000⟩, + ⟨1, 7, 6, 7, 2, 5, 12173385729379996950658338689295320228095328256000000⟩, + ⟨1, 7, 7, 7, 3, 5, -11967092816416499742428223203868505888247513088000000⟩, + ⟨1, 7, 8, 7, 4, 5, -1274117120209669425291781812894160180947714048000000⟩ +] + +def collectedFourData_11_3_12 : List CollectedFourTerm := [ + ⟨1, 8, 2, 0, 5, 6, 3648957292767572064238941888907412916305657856000000⟩, + ⟨1, 8, 3, 0, 6, 6, 585695756799598160948478233981966398729381478400000⟩, + ⟨1, 8, 4, 0, 7, 6, -4201176182987078091462870855660685473470427955200000⟩, + ⟨1, 8, 5, 0, 8, 6, -132011518530252522042401469642708063633801216000000⟩, + ⟨1, 8, 2, 1, 4, 6, -12576293814378923143388113953205544649466105036800000⟩, + ⟨1, 8, 3, 1, 5, 6, -7852087909336050253046287478920521955325195059200000⟩, + ⟨1, 8, 4, 1, 6, 6, -9412879482835882025891311802402893257339882700800000⟩, + ⟨1, 8, 5, 1, 7, 6, 1047054178127243123766551701052021676875710464000000⟩, + ⟨1, 8, 6, 1, 8, 6, 143181630771781054204689231544042198696722432000000⟩, + ⟨1, 8, 2, 2, 3, 6, 4687107476042822856985007318273163772007389593600000⟩, + ⟨1, 8, 3, 2, 4, 6, 10225105908598125081547192679990203115739965030400000⟩, + ⟨1, 8, 4, 2, 5, 6, 1194445076061722640563196668593817606754297446400000⟩, + ⟨1, 8, 5, 2, 6, 6, 731836427932264608473647271590417251447078912000000⟩, + ⟨1, 8, 6, 2, 7, 6, 191593398838074284285632895890106872598888448000000⟩, + ⟨1, 8, 7, 2, 8, 6, 179707203693710513216163496629949626816292454400000⟩, + ⟨1, 8, 2, 3, 2, 6, 2506333177319190138368090586555507241383886848000000⟩, + ⟨1, 8, 3, 3, 3, 6, -13667303790797681853549992234956826405990773555200000⟩, + ⟨1, 8, 4, 3, 4, 6, -819508631356638829277235674612261153015228006400000⟩, + ⟨1, 8, 5, 3, 5, 6, -276531537157995292500078212347142963881574400000000⟩, + ⟨1, 8, 6, 3, 6, 6, -507666487214234876317121741937212585486057472000000⟩, + ⟨1, 8, 7, 3, 7, 6, -100344749503708307045123677756263130501585305600000⟩, + ⟨1, 8, 8, 3, 8, 6, -75679125310546289412980122230587038000742400000000⟩, + ⟨1, 8, 2, 4, 1, 6, 5785713053011225150900075777029060010365576806400000⟩, + ⟨1, 8, 3, 4, 2, 6, 18709918910458777196614379550634791784446689280000000⟩, + ⟨1, 8, 4, 4, 3, 6, -1831721125013241201059013014186237693408575488000000⟩, + ⟨1, 8, 5, 4, 4, 6, 996234678965609649459644127850092155985985536000000⟩, + ⟨1, 8, 6, 4, 5, 6, 403900095046998873546014075284375581782704128000000⟩, + ⟨1, 8, 7, 4, 6, 6, 32955758559560069281023097812191390925324288000000⟩, + ⟨1, 8, 8, 4, 7, 6, -26883227920803074851031449223100591172799692800000⟩, + ⟨1, 8, 2, 5, 0, 6, -43167639905886888204242116413862500805963992268800000⟩, + ⟨1, 8, 3, 5, 1, 6, -15537134146357583147452636352812562092989716889600000⟩, + ⟨1, 8, 4, 5, 2, 6, 12550333100837902595612649253176431120611069132800000⟩, + ⟨1, 8, 5, 5, 3, 6, -2598237314620824447002363306502825517516849152000000⟩, + ⟨1, 8, 6, 5, 4, 6, 455551285259506342210277857461639570083807232000000⟩, + ⟨1, 8, 7, 5, 5, 6, 87281411927847506134237820385147440782009958400000⟩, + ⟨1, 8, 8, 5, 6, 6, -55977936216937422009802189373312887275336499200000⟩, + ⟨1, 8, 3, 6, 0, 6, -8461531194439799586113345679234360064746297753600000⟩, + ⟨1, 8, 4, 6, 1, 6, -6734585418123948558246923558896038433776677683200000⟩, + ⟨1, 8, 5, 6, 2, 6, -38453716356189222916581367175977051889860608000000⟩, + ⟨1, 8, 6, 6, 3, 6, -1686810419202746403774183166516953013291057152000000⟩, + ⟨1, 8, 7, 6, 4, 6, -31245486881147461201917812634788888383900876800000⟩, + ⟨1, 8, 8, 6, 5, 6, 58746346765442215216621462826553013233411686400000⟩, + ⟨1, 8, 4, 7, 0, 6, -128504190238363074471474229889953159717453194854400000⟩, + ⟨1, 8, 5, 7, 1, 6, 1792579943435888697297188028325098696512372736000000⟩, + ⟨1, 8, 6, 7, 2, 6, 1664675292986354751850214991843500538281852928000000⟩, + ⟨1, 8, 7, 7, 3, 6, -1309172266991175114252110006045778673732367155200000⟩, + ⟨1, 8, 8, 7, 4, 6, -116154554289419053537492736277281247766511616000000⟩ +] + +def collectedFourData_11_3_13 : List CollectedFourTerm := [ + ⟨2, 1, 8, 3, 8, 0, 34302619696437327819955230726096229402411008000000000⟩, + ⟨2, 1, 8, 4, 7, 0, 12185198227329998486681287515867601262792933376000000⟩, + ⟨2, 1, 8, 5, 6, 0, 25372780797367928357162235300478567070526603264000000⟩, + ⟨2, 1, 8, 6, 5, 0, -26627601513374957620807165502812411238692159488000000⟩, + ⟨2, 1, 8, 7, 4, 0, 52648672740987359011434158333796025979602206720000000⟩ +] + +def collectedFourData_11_3_14 : List CollectedFourTerm := [ + ⟨2, 2, 7, 2, 8, 1, 655565565655846292353573699104553123836434841600000⟩, + ⟨2, 2, 7, 3, 7, 1, -366054120908315209503239963700906808593245798400000⟩, + ⟨2, 2, 8, 3, 8, 1, -1656448742381193297707807966151412150802841600000000⟩, + ⟨2, 2, 7, 4, 6, 1, 120221449433591215853893526368210434373189632000000⟩, + ⟨2, 2, 8, 4, 7, 1, -588414426010228297913585652591220260512936755200000⟩, + ⟨2, 2, 7, 5, 5, 1, 318399524368776595667954304575450848719116697600000⟩, + ⟨2, 2, 8, 5, 6, 1, -1225233268317372865304312888365043867989101772800000⟩, + ⟨2, 2, 7, 6, 4, 1, -113982438435486328893687351902761550605398835200000⟩, + ⟨2, 2, 8, 6, 5, 1, 1285827654849302672078015626829439173675030937600000⟩, + ⟨2, 2, 7, 7, 3, 1, -4775814436541999139278775644581655077981048012800000⟩, + ⟨2, 2, 8, 7, 4, 1, -2542366400048015630112363092357054761946578944000000⟩ +] + +def collectedFourData_11_3_15 : List CollectedFourTerm := [ + ⟨2, 3, 6, 1, 8, 2, 4687107476042822856985007318273163772007389593600000⟩, + ⟨2, 3, 6, 2, 7, 2, 6271885906131041751311991745702308095984035430400000⟩, + ⟨2, 3, 7, 2, 8, 2, 29413932967215057469647751126379964348975651225600000⟩, + ⟨2, 3, 6, 3, 6, 2, -16618663823929567963978891547956456444307020185600000⟩, + ⟨2, 3, 7, 3, 7, 2, -16424125882814356383772803532090521141415143014400000⟩, + ⟨2, 3, 8, 3, 8, 2, -37160792775383623886708572114840998225169612800000000⟩, + ⟨2, 3, 6, 4, 5, 2, 13221829817587894427759696643123086525217531494400000⟩, + ⟨2, 3, 7, 4, 6, 2, 5394099141438868497339008349022976830510989312000000⟩, + ⟨2, 3, 8, 4, 7, 2, -13200496937550544911037426109771375495014357401600000⟩, + ⟨2, 3, 6, 5, 4, 2, 14912652016543228973338226748378061483816884633600000⟩, + ⟨2, 3, 7, 5, 5, 2, 14285958197342106052166579978570789048603482521600000⟩, + ⟨2, 3, 8, 5, 6, 2, -27486899184092032100291829055135422736385861222400000⟩, + ⟨2, 3, 6, 6, 3, 2, -55218408142829491620026164476919418893505239449600000⟩, + ⟨2, 3, 7, 6, 4, 2, -5114167032594221937380516237265611734534796083200000⟩, + ⟨2, 3, 8, 6, 5, 2, 28846274444945322775754445759028292214399487180800000⟩, + ⟨2, 3, 6, 7, 2, 2, 54493806006279107370347592539063952281440773734400000⟩, + ⟨2, 3, 7, 7, 3, 2, -214281367203551443905147224741013818456538926284800000⟩, + ⟨2, 3, 8, 7, 4, 2, -57035481107293344927874469863794051501105610752000000⟩ +] + +def collectedFourData_11_3_16 : List CollectedFourTerm := [ + ⟨2, 4, 5, 0, 8, 3, -2356852186364271171110358116432408321110887628800000⟩, + ⟨2, 4, 5, 1, 7, 3, 18693459149896179014894860881990764913759564595200000⟩, + ⟨2, 4, 6, 1, 8, 3, 10225105908598125081547192679990203115739965030400000⟩, + ⟨2, 4, 5, 2, 6, 3, 13065755961574702626024863293831232317975796121600000⟩, + ⟨2, 4, 6, 2, 7, 3, 13682361235500694736829878714962486676250270105600000⟩, + ⟨2, 4, 7, 2, 8, 3, 32083815158437816056382609296695097765133497139200000⟩, + ⟨2, 4, 5, 3, 5, 3, -4937023414363167784704599840670843001550929920000000⟩, + ⟨2, 4, 6, 3, 6, 3, -36254256708986893725992013308359108205151151718400000⟩, + ⟨2, 4, 7, 3, 7, 3, -17914932340074010241123640914516913295647886540800000⟩, + ⟨2, 4, 8, 3, 8, 3, -27022568020747618766032613969524726868371046400000000⟩, + ⟨2, 4, 5, 4, 4, 3, 17786159173026471337253543076169669412960128204800000⟩, + ⟨2, 4, 6, 4, 5, 3, 28843932186602513929104895043496281656872507801600000⟩, + ⟨2, 4, 7, 4, 6, 3, 5883717760325017632841010855304218367580176384000000⟩, + ⟨2, 4, 8, 4, 7, 3, -9599131228409261923965359818620210728529611980800000⟩, + ⟨2, 4, 5, 5, 3, 3, -46387325620029052371299989992103019006691744153600000⟩, + ⟨2, 4, 6, 5, 4, 3, 32532526089194968526913012358356899679080703590400000⟩, + ⟨2, 4, 7, 5, 5, 3, 15582684664290595226932803555578220951394005811200000⟩, + ⟨2, 4, 8, 5, 6, 3, -19987910574760102681322850789977595252825076531200000⟩, + ⟨2, 4, 5, 6, 2, 3, -686528921695169150068306006749001079413171814400000⟩, + ⟨2, 4, 6, 6, 3, 3, -120461089115309667689484608662257769073328154214400000⟩, + ⟨2, 4, 7, 6, 4, 3, -5578376409098918947174398295887759471880332902400000⟩, + ⟨2, 4, 8, 6, 5, 3, 20976420445207837470669355996339173440671344230400000⟩, + ⟨2, 4, 5, 7, 1, 3, 32003616093177700407154151429631879429493673164800000⟩, + ⟨2, 4, 6, 7, 2, 3, 118880341580567951577519282298703252445139147161600000⟩, + ⟨2, 4, 7, 7, 3, 3, -233731537530834748825373639863911391679588440473600000⟩, + ⟨2, 4, 8, 7, 4, 3, -41475034645624276873899224893250608119442046976000000⟩ +] + +def collectedFourData_11_3_17 : List CollectedFourTerm := [ + ⟨2, 5, 4, 0, 7, 4, -5841152223214847651712911324067732340583788707840000⟩, + ⟨2, 5, 5, 0, 8, 4, -550631067134651737644359110917144631198718361600000⟩, + ⟨2, 5, 4, 1, 6, 4, -13087302108555572236825956613011763100453814927360000⟩, + ⟨2, 5, 5, 1, 7, 4, 4367350409031740991483899915648401138648508006400000⟩, + ⟨2, 5, 6, 1, 8, 4, 1194445076061722640563196668593817606754297446400000⟩, + ⟨2, 5, 4, 2, 5, 4, 1660710050628081109972331819389446286633473146880000⟩, + ⟨2, 5, 5, 2, 6, 4, 3052550851371406275173154800756447016157131571200000⟩, + ⟨2, 5, 6, 2, 7, 4, 1598304130317043841742582039186067816248351129600000⟩, + ⟨2, 5, 7, 2, 8, 4, 2498579175598618990977312948024848578295680204800000⟩, + ⟨2, 5, 4, 3, 4, 4, -1139412977579310269723238657842409966563890298880000⟩, + ⟨2, 5, 5, 3, 5, 4, -1153436132672000098642323394774996379699773440000000⟩, + ⟨2, 5, 6, 3, 6, 4, -4235038619591575754618813807521964248713815654400000⟩, + ⟨2, 5, 7, 3, 7, 4, -1395154430859358139962720755705405763354833715200000⟩, + ⟨2, 5, 8, 3, 8, 4, -1578319755484575566800988676729630371296051200000000⟩, + ⟨2, 5, 4, 4, 3, 4, -2546753922153615296155199284169921092617083289600000⟩, + ⟨2, 5, 5, 4, 4, 4, 4155378034452881190287593975148454395483101593600000⟩, + ⟨2, 5, 6, 4, 5, 4, 3369402046542624985862401280054192334066784665600000⟩, + ⟨2, 5, 7, 4, 6, 4, 458204069511402661942535125627242775100522496000000⟩, + ⟨2, 5, 8, 4, 7, 4, -560660942426155807431213900761287289131656806400000⟩, + ⟨2, 5, 4, 5, 2, 4, 17449495784278963740020234633540131248364333301760000⟩, + ⟨2, 5, 5, 5, 3, 4, -10837464799640766136356664579994094831775462195200000⟩, + ⟨2, 5, 6, 5, 4, 4, 3800284901343969009464414614041813648436258406400000⟩, + ⟨2, 5, 7, 5, 5, 4, 1213526858007624506135945427644150146990394572800000⟩, + ⟨2, 5, 8, 5, 6, 4, -1167443231404996758543307608512011957561825689600000⟩, + ⟨2, 5, 4, 6, 1, 4, -9363506045474977606191978018783814453934099005440000⟩, + ⟨2, 5, 5, 6, 2, 4, -160393661918595162603545484533439617901055180800000⟩, + ⟨2, 5, 6, 6, 3, 4, -14071654224121450142529918163419102108252005990400000⟩, + ⟨2, 5, 7, 6, 4, 4, -434425116233708329187797741143891996778797465600000⟩, + ⟨2, 5, 8, 6, 5, 4, 1225179589245645593338354314110665092899222323200000⟩, + ⟨2, 5, 4, 7, 0, 4, -178667235985696084176847912678336546835251310100480000⟩, + ⟨2, 5, 5, 7, 1, 4, 7477000629699437306109225190503840081975548313600000⟩, + ⟨2, 5, 6, 7, 2, 4, 13886999304529735834899884517395833960693078425600000⟩, + ⟨2, 5, 7, 7, 3, 4, -18202222817681448740825079488655292897635493478400000⟩, + ⟨2, 5, 8, 7, 4, 4, -2422451725917977300702690316044145717053227008000000⟩ +] + +def collectedFourData_11_3_18 : List CollectedFourTerm := [ + ⟨2, 6, 3, 0, 6, 5, 748408661433858162797115735568779819397781913600000⟩, + ⟨2, 6, 4, 0, 7, 5, -10736620872030609431404432911191177473998559641600000⟩, + ⟨2, 6, 5, 0, 8, 5, -506057433727741003796261376101793669517934592000000⟩, + ⟨2, 6, 3, 1, 5, 5, -10033486726621282994015279745080199749489708236800000⟩, + ⟨2, 6, 4, 1, 6, 5, -24055767699194172554548582772647079256498005606400000⟩, + ⟨2, 6, 5, 1, 7, 5, 4013813008563746614913298759118596457069805568000000⟩, + ⟨2, 6, 6, 1, 8, 5, 731836427932264608473647271590417251447078912000000⟩, + ⟨2, 6, 3, 2, 4, 5, 13065755961574702626024863293831232317975796121600000⟩, + ⟨2, 6, 4, 2, 5, 5, 3052550851371406275173154800756447016157131571200000⟩, + ⟨2, 6, 5, 2, 6, 5, 2805446590957946351380581977750509235359186944000000⟩, + ⟨2, 6, 6, 2, 7, 5, 979280846748759435549617785067552353359495168000000⟩, + ⟨2, 6, 7, 2, 8, 5, 1148159485577852931590745688628845031706329088000000⟩, + ⟨2, 6, 3, 3, 3, 5, -17464235341866499796281628109942988942984662220800000⟩, + ⟨2, 6, 4, 3, 4, 5, -2094354793275278806488336726375808218705376051200000⟩, + ⟨2, 6, 5, 3, 5, 5, -1060065376089836436695575149715328737266892800000000⟩, + ⟨2, 6, 6, 3, 6, 5, -2594807913425505405117075984066875889970839552000000⟩, + ⟨2, 6, 7, 3, 7, 5, -641108278369190856879484916714208510043226112000000⟩, + ⟨2, 6, 8, 3, 8, 5, -580221852877763821360694655362938068113817600000000⟩, + ⟨2, 6, 3, 4, 2, 5, 23907745966654902096694554526412063798061957120000000⟩, + ⟨2, 6, 4, 4, 3, 5, -4681187935463701685023064285119437463464443904000000⟩, + ⟨2, 6, 5, 4, 4, 5, 3818999816386340284749481045376985299190546432000000⟩, + ⟨2, 6, 6, 4, 5, 5, 2064432435972463610668606832262646631705346048000000⟩, + ⟨2, 6, 7, 4, 6, 5, 210556204853443519116885023829311297956085760000000⟩, + ⟨2, 6, 8, 4, 7, 5, -206110155892220611231627326790193901875704627200000⟩, + ⟨2, 6, 3, 5, 1, 5, -19853525715352676477500216674356886459675731558400000⟩, + ⟨2, 6, 4, 5, 2, 5, 32073915125736425335388757791707362426337257062400000⟩, + ⟨2, 6, 5, 5, 3, 5, -9960171069097666084514854910608998807921229824000000⟩, + ⟨2, 6, 6, 5, 4, 5, 2328434335795923845343540525771305417768435712000000⟩, + ⟨2, 6, 7, 5, 5, 5, 557645875957132685184619077170784280057479168000000⟩, + ⟨2, 6, 8, 5, 6, 5, -429175439578428948590928441815341401239243980800000⟩, + ⟨2, 6, 3, 6, 0, 5, -10812240248273333934776033167663879953091815014400000⟩, + ⟨2, 6, 4, 6, 1, 5, -17211058811937707952991267352455044545847597465600000⟩, + ⟨2, 6, 5, 6, 2, 5, -147409780852176625085058436076567814834487296000000⟩, + ⟨2, 6, 6, 6, 3, 5, -8621701716443636882729062526556111980495634432000000⟩, + ⟨2, 6, 7, 6, 4, 5, -199629182396227929065772029720359921344577536000000⟩, + ⟨2, 6, 8, 6, 5, 5, 450400477412685631994839270057468321179736473600000⟩, + ⟨2, 6, 4, 7, 0, 5, -328408214976506911611607654651765890858609750835200000⟩, + ⟨2, 6, 5, 7, 1, 5, 6871736769841774023300770893220382882851192832000000⟩, + ⟨2, 6, 6, 7, 2, 5, 8508563658057822444238397731828711350859726848000000⟩, + ⟨2, 6, 7, 7, 3, 5, -8364375638292716816642324770203023930875183104000000⟩, + ⟨2, 6, 8, 7, 4, 5, -890541618094066727412562720599957041036918784000000⟩ +] + +def collectedFourData_11_3_19 : List CollectedFourTerm := [ + ⟨2, 7, 2, 0, 5, 6, 4882722219099787632512236702580313038398685184000000⟩, + ⟨2, 7, 3, 0, 6, 6, 783727913457940195410644857857525493591021977600000⟩, + ⟨2, 7, 4, 0, 7, 6, -5621654256047899135123292222956906688757419212800000⟩, + ⟨2, 7, 5, 0, 8, 6, -176646511040935034006257844925958490343604224000000⟩, + ⟨2, 7, 2, 1, 4, 6, -16828519578211080578549204818231542068527969075200000⟩, + ⟨2, 7, 3, 1, 5, 6, -10506991730824307504454611328829336112866315468800000⟩, + ⟨2, 7, 4, 1, 6, 6, -12595509376787553293324670214750891610872165171200000⟩, + ⟨2, 7, 5, 1, 7, 6, 1401078250566635665142653123342637677513015296000000⟩, + ⟨2, 7, 6, 1, 8, 6, 191593398838074284285632895890106872598888448000000⟩, + ⟨2, 7, 2, 2, 3, 6, 6271885906131041751311991745702308095984035430400000⟩, + ⟨2, 7, 3, 2, 4, 6, 13682361235500694736829878714962486676250270105600000⟩, + ⟨2, 7, 4, 2, 5, 6, 1598304130317043841742582039186067816248351129600000⟩, + ⟨2, 7, 5, 2, 6, 6, 979280846748759435549617785067552353359495168000000⟩, + ⟨2, 7, 6, 2, 7, 6, 256373881764447714200903528958396525415759872000000⟩, + ⟨2, 7, 7, 2, 8, 6, 240468793139000274684961908399531200999954841600000⟩, + ⟨2, 7, 2, 3, 2, 6, 3353760461274569710015571988057668604471017472000000⟩, + ⟨2, 7, 3, 3, 3, 6, -18288415714479378950897304615643550609941777612800000⟩, + ⟨2, 7, 4, 3, 4, 6, -1096596282724429507696465521426469147534530969600000⟩, + ⟨2, 7, 5, 3, 5, 6, -370030825912756895790384205624344630106521600000000⟩, + ⟨2, 7, 6, 3, 6, 6, -679315825900836284653986799515017049179947008000000⟩, + ⟨2, 7, 7, 3, 7, 6, -134272752093557505302973128715688313637725798400000⟩, + ⟨2, 7, 8, 3, 8, 6, -101267325711991784214444569832476485720473600000000⟩, + ⟨2, 7, 2, 4, 1, 6, 7741945824706318642978153194305564264208374169600000⟩, + ⟨2, 7, 3, 4, 2, 6, 25036011510116468192119406404260410962131025920000000⟩, + ⟨2, 7, 4, 4, 3, 6, -2451052374338190326393188929877309067920146432000000⟩, + ⟨2, 7, 5, 4, 4, 6, 1333075948042609816084309936240030585353928704000000⟩, + ⟨2, 7, 6, 4, 5, 6, 540464524561953139083592475822920983109435392000000⟩, + ⟨2, 7, 7, 4, 6, 6, 44098574374929441762557936779317157803589632000000⟩, + ⟨2, 7, 8, 4, 7, 6, -35972833814799610775878881604974188239729459200000⟩, + ⟨2, 7, 2, 5, 0, 6, -57763239633508740293677910190834451630819324723200000⟩, + ⟨2, 7, 3, 5, 1, 6, -20790462598156384421927507939227442862142940774400000⟩, + ⟨2, 7, 4, 5, 2, 6, 16793781174152017251427803792055793389382349619200000⟩, + ⟨2, 7, 5, 5, 3, 6, -3476738708819236443466704184174288630110486528000000⟩, + ⟨2, 7, 6, 5, 4, 6, 609579724839421555666783340758630246958235648000000⟩, + ⟨2, 7, 7, 5, 5, 6, 116792512255266916065774512012942811885836697600000⟩, + ⟨2, 7, 8, 5, 6, 6, -74904881317064251881010506187165984797543628800000⟩, + ⟨2, 7, 3, 6, 0, 6, -11322496553354108922398400212201258392475821670400000⟩, + ⟨2, 7, 4, 6, 1, 6, -9011645579594837816608773924440496906536013004800000⟩, + ⟨2, 7, 5, 6, 2, 6, -51455470753651742196617096039996149425242112000000⟩, + ⟨2, 7, 6, 6, 3, 6, -2257145275329727068641106957085351263262998528000000⟩, + ⟨2, 7, 7, 6, 4, 6, -41810035251318972994120911544156261706838835200000⟩, + ⟨2, 7, 8, 6, 5, 6, 78609331276938200400445140512126397494958489600000⟩, + ⟨2, 7, 4, 7, 0, 6, -171953304624288506427286108280962608468298668441600000⟩, + ⟨2, 7, 5, 7, 1, 6, 2398676996487548037685259742517999428125589504000000⟩, + ⟨2, 7, 6, 7, 2, 6, 2227525944675029243823768812088744216826478592000000⟩, + ⟨2, 7, 7, 7, 3, 6, -1751822234076835668254331738213867877305208012800000⟩, + ⟨2, 7, 8, 7, 4, 6, -155428079194761018238660458750865717617229824000000⟩ +] + +def collectedFourData_11_3_20 : List CollectedFourTerm := [ + ⟨2, 8, 1, 0, 4, 7, -929790988446526592902270314628075515820376064000000⟩, + ⟨2, 8, 2, 0, 5, 7, 22899023706687303731418339310153992970306584576000000⟩, + ⟨2, 8, 3, 0, 6, 7, 1837766236185222500401193295907347457956328243200000⟩, + ⟨2, 8, 4, 0, 7, 7, -8788157391416110774039761284903038475301185126400000⟩, + ⟨2, 8, 5, 0, 8, 7, -207109500731322681214593577938660905434742784000000⟩, + ⟨2, 8, 1, 1, 3, 7, 3755137995819161304600665644640666943878489702400000⟩, + ⟨2, 8, 2, 1, 4, 7, -78922505003971734156549198485039908343662824652800000⟩, + ⟨2, 8, 3, 1, 5, 7, -24637880462353225214797088897117411156438915481600000⟩, + ⟨2, 8, 4, 1, 6, 7, -19690168371557591825033097464408394196735072665600000⟩, + ⟨2, 8, 5, 1, 7, 7, 1642696565306784306217688608752806652108865536000000⟩, + ⟨2, 8, 6, 1, 8, 7, 179707203693710513216163496629949626816292454400000⟩, + ⟨2, 8, 1, 2, 2, 7, 655565565655846292353573699104553123836434841600000⟩, + ⟨2, 8, 2, 2, 3, 7, 29413932967215057469647751126379964348975651225600000⟩, + ⟨2, 8, 3, 2, 4, 7, 32083815158437816056382609296695097765133497139200000⟩, + ⟨2, 8, 4, 2, 5, 7, 2498579175598618990977312948024848578295680204800000⟩, + ⟨2, 8, 5, 2, 6, 7, 1148159485577852931590745688628845031706329088000000⟩, + ⟨2, 8, 6, 2, 7, 7, 240468793139000274684961908399531200999954841600000⟩, + ⟨2, 8, 7, 2, 8, 7, 187958695570428094649414479084405250589091430400000⟩, + ⟨2, 8, 1, 3, 1, 7, -3679047175465701104655411024886193948605808640000000⟩, + ⟨2, 8, 2, 3, 2, 7, 15728488507674290494537078402066136974762180608000000⟩, + ⟨2, 8, 3, 3, 3, 7, -42884567891804662112049110742177369238451886489600000⟩, + ⟨2, 8, 4, 3, 4, 7, -1714274889291949020525838300979716723535826124800000⟩, + ⟨2, 8, 5, 3, 5, 7, -433843267882209522514272489388762470128025600000000⟩, + ⟨2, 8, 6, 3, 6, 7, -637171991508419896323048329890647014472312422400000⟩, + ⟨2, 8, 7, 3, 7, 7, -104952210241967450187335732939354506956216729600000⟩, + ⟨2, 8, 8, 3, 8, 7, -67846312777876636289114511111829436183347200000000⟩, + ⟨2, 8, 1, 4, 0, 7, 29437908500239536178676746245867992716225491763200000⟩, + ⟨2, 8, 2, 4, 1, 7, 36308229921898751177491372297780383032482883174400000⟩, + ⟨2, 8, 3, 4, 2, 7, 58707028104985132002880089892926497031129661440000000⟩, + ⟨2, 8, 4, 4, 3, 7, -3831654004177634797301390023351577749556822016000000⟩, + ⟨2, 8, 5, 4, 4, 7, 1562967150662032950237589417486592255893438464000000⟩, + ⟨2, 8, 6, 4, 5, 7, 506934836970897456899563002224522618604198297600000⟩, + ⟨2, 8, 7, 4, 6, 7, 34468965423035365284621423583726150046711808000000⟩, + ⟨2, 8, 8, 4, 7, 7, -24100805638402080516405800861969685087151718400000⟩, + ⟨2, 8, 2, 5, 0, 7, -270898432142765312795126012251118410837592427724800000⟩, + ⟨2, 8, 3, 5, 1, 7, -48751626095570965614683046332754742136705699020800000⟩, + ⟨2, 8, 4, 5, 2, 7, 26253196200508435618189869459391328236097608089600000⟩, + ⟨2, 8, 5, 5, 3, 7, -4076308181314442777657361855627251833632718848000000⟩, + ⟨2, 8, 6, 5, 4, 7, 571762223769812356498118571669945116141184614400000⟩, + ⟨2, 8, 7, 5, 5, 7, 91289052393605199727711887290922531673237094400000⟩, + ⟨2, 8, 8, 5, 6, 7, -50184202759345417840484153949922234243586457600000⟩, + ⟨2, 8, 3, 6, 0, 7, -26550160480145294216903243896498252397708889292800000⟩, + ⟨2, 8, 4, 6, 1, 7, -14087625474999313170991384855036030660370654822400000⟩, + ⟨2, 8, 5, 6, 2, 7, -60329053740633555274419051728979545284411392000000⟩, + ⟨2, 8, 6, 6, 3, 7, -2117115037469484683567837337593017355624408678400000⟩, + ⟨2, 8, 7, 6, 4, 7, -32680164378123601730895102944391738256313548800000⟩, + ⟨2, 8, 8, 6, 5, 7, 52666081972413629693541542108131278705603379200000⟩, + ⟨2, 8, 4, 7, 0, 7, -268809257237162151016926275150902900050677779660800000⟩, + ⟨2, 8, 5, 7, 1, 7, 2812332902760370850113216093393941862771851264000000⟩, + ⟨2, 8, 6, 7, 2, 7, 2089333249999167233864608859867301927020239257600000⟩, + ⟨2, 8, 7, 7, 3, 7, -1369284628122303760440844083928507980524499763200000⟩, + ⟨2, 8, 8, 7, 4, 7, -104132522522648205945061945836707191506075648000000⟩ +] + +def collectedFourData_11_3_21 : List CollectedFourTerm := [ + ⟨3, 0, 8, 3, 8, 0, -191674600642127805457573931710934814511280947200000000⟩, + ⟨3, 0, 8, 4, 7, 0, -68087890214729458606980160945652105796531938918400000⟩, + ⟨3, 0, 8, 5, 6, 0, -141776857556475525939154281259800021259609807257600000⟩, + ⟨3, 0, 8, 6, 5, 0, 148788487039779867887319887745645098807160156979200000⟩, + ⟨3, 0, 8, 7, 4, 0, -294187832045227937384982317694364274789500059648000000⟩ +] + +def collectedFourData_11_3_22 : List CollectedFourTerm := [ + ⟨3, 1, 7, 2, 8, 1, -3679047175465701104655411024886193948605808640000000⟩, + ⟨3, 1, 7, 3, 7, 1, 2054303108870598224114920102311949904495247360000000⟩, + ⟨3, 1, 8, 3, 8, 1, 9296023748386600011827513919042140913008640000000000⟩, + ⟨3, 1, 7, 4, 6, 1, -674685198766589560694327469600862144089292800000000⟩, + ⟨3, 1, 8, 4, 7, 1, 3302193625515505444225443683107090255136686080000000⟩, + ⟨3, 1, 7, 5, 5, 1, -1786864552024879023862479621839385424602071040000000⟩, + ⟨3, 1, 8, 5, 6, 1, 6876033811476993683584417592985921342532485120000000⟩, + ⟨3, 1, 7, 6, 4, 1, 639671743221050368079189097698437976115118080000000⟩, + ⟨3, 1, 8, 6, 5, 1, -7216090730720987540976197464762876112708567040000000⟩, + ⟨3, 1, 7, 7, 3, 1, 26801966933284834934801583858367049946491781120000000⟩, + ⟨3, 1, 8, 7, 4, 1, 14267811509803849033097699294229991404444057600000000⟩ +] + +def collectedFourData_11_3_23 : List CollectedFourTerm := [ + ⟨3, 2, 6, 1, 8, 2, 2506333177319190138368090586555507241383886848000000⟩, + ⟨3, 2, 6, 2, 7, 2, 3353760461274569710015571988057668604471017472000000⟩, + ⟨3, 2, 7, 2, 8, 2, 15728488507674290494537078402066136974762180608000000⟩, + ⟨3, 2, 6, 3, 6, 2, -8886484621384075905668116546675756939144593408000000⟩, + ⟨3, 2, 7, 3, 7, 2, -8782459505989011919610692710796469999964782592000000⟩, + ⟨3, 2, 8, 3, 8, 2, -19870960566720384871986800699008670503010304000000000⟩, + ⟨3, 2, 6, 4, 5, 2, 7070098329528024203810142308457221773162708992000000⟩, + ⟨3, 2, 7, 4, 6, 2, 2884382256869263519032640760883949290557276160000000⟩, + ⟨3, 2, 8, 4, 7, 2, -7058691015896180604908077183426141432250892288000000⟩, + ⟨3, 2, 6, 5, 4, 2, 7974230311960685188897994408664862904756994048000000⟩, + ⟨3, 2, 7, 5, 5, 2, 7639118834548875554306707911144070315285413888000000⟩, + ⟨3, 2, 8, 5, 6, 2, -14698047296513118286100303580725578600946860032000000⟩, + ⟨3, 2, 6, 6, 3, 2, -29526894579334210866110782198088001706606460928000000⟩, + ⟨3, 2, 7, 6, 4, 2, -2734694387457187268533950711216895264844414976000000⟩, + ⟨3, 2, 8, 6, 5, 2, 15424944926686513331561591210340310117508972544000000⟩, + ⟨3, 2, 6, 7, 2, 2, 29139428666833764111700276834800199234530312192000000⟩, + ⟨3, 2, 7, 7, 3, 2, -114582501606513288592200836105171542183734411264000000⟩, + ⟨3, 2, 8, 7, 4, 2, -30498536531161278560457335362325937833493135360000000⟩ +] + +def collectedFourData_11_3_24 : List CollectedFourTerm := [ + ⟨3, 3, 5, 0, 8, 3, 3150267108134285169803884380219374125149742694400000⟩, + ⟨3, 3, 5, 1, 7, 3, -24986458564469338417173533965019273085475985817600000⟩, + ⟨3, 3, 6, 1, 8, 3, -13667303790797681853549992234956826405990773555200000⟩, + ⟨3, 3, 5, 2, 6, 3, -17464235341866499796281628109942988942984662220800000⟩, + ⟨3, 3, 6, 2, 7, 3, -18288415714479378950897304615643550609941777612800000⟩, + ⟨3, 3, 7, 2, 8, 3, -42884567891804662112049110742177369238451886489600000⟩, + ⟨3, 3, 5, 3, 5, 3, 6599031778208119765522408798733182880930856960000000⟩, + ⟨3, 3, 6, 3, 6, 3, 48458954320916393814567614225659251072758395699200000⟩, + ⟨3, 3, 7, 3, 7, 3, 23945847101445483994686874403295648372406773350400000⟩, + ⟨3, 3, 8, 3, 8, 3, 36119493494584952689083819844401017623098163200000000⟩, + ⟨3, 3, 5, 4, 4, 3, -23773723505868648806568290183794240925469140582400000⟩, + ⟨3, 3, 6, 4, 5, 3, -38554004940327478688072895655793886908593786060800000⟩, + ⟨3, 3, 7, 4, 6, 3, -7864422996543680530045864325484889642308206592000000⟩, + ⟨3, 3, 8, 4, 7, 3, 12830599878293995109664889713482843203976980070400000⟩, + ⟨3, 3, 5, 5, 3, 3, 62003237615219017222075292218029402739312479436800000⟩, + ⟨3, 3, 6, 5, 4, 3, -43484333670245423778329492178517382352858198835200000⟩, + ⟨3, 3, 7, 5, 5, 3, -20828467410198459317951445711207888677508848025600000⟩, + ⟨3, 3, 8, 5, 6, 3, 26716676424723434659987624025500103982569855385600000⟩, + ⟨3, 3, 5, 6, 2, 3, 917643241825653741027727460991819739936535347200000⟩, + ⟨3, 3, 6, 6, 3, 3, 161013324910881997388674736443023806530120266547200000⟩, + ⟨3, 3, 7, 6, 4, 3, 7456290988483932717218217480261029831797584691200000⟩, + ⟨3, 3, 8, 6, 5, 3, -28037960020255749826178548143108896689818383155200000⟩, + ⟨3, 3, 5, 7, 1, 3, -42777370470237975702618538072196396497221609062400000⟩, + ⟨3, 3, 6, 7, 2, 3, -158900431707917456271439450108893674753890241740800000⟩, + ⟨3, 3, 7, 7, 3, 3, 312415339017463109923320616661138691060700859596800000⟩, + ⟨3, 3, 8, 7, 4, 3, 55437264249649417963441706333348708652404441088000000⟩ +] + +def collectedFourData_11_3_25 : List CollectedFourTerm := [ + ⟨3, 4, 4, 0, 7, 4, 4007613878551605664205826706428621725227643043840000⟩, + ⟨3, 4, 5, 0, 8, 4, 377787912775192259887497388417471083741551001600000⟩, + ⟨3, 4, 4, 1, 6, 4, 8979196493903090756996940782218186199934550671360000⟩, + ⟨3, 4, 5, 1, 7, 4, -2996438620820695424287130142808853809134462566400000⟩, + ⟨3, 4, 6, 1, 8, 4, -819508631356638829277235674612261153015228006400000⟩, + ⟨3, 4, 4, 2, 5, 4, -1139412977579310269723238657842409966563890298880000⟩, + ⟨3, 4, 5, 2, 6, 4, -2094354793275278806488336726375808218705376051200000⟩, + ⟨3, 4, 6, 2, 7, 4, -1096596282724429507696465521426469147534530969600000⟩, + ⟨3, 4, 7, 2, 8, 4, -1714274889291949020525838300979716723535826124800000⟩, + ⟨3, 4, 4, 3, 4, 4, 781751114822931733013575882042896773236528250880000⟩, + ⟨3, 4, 5, 3, 5, 4, 791372399943218226870659581687455706188349440000000⟩, + ⟨3, 4, 6, 3, 6, 4, 2905659517076577795749502198580144432411469414400000⟩, + ⟨3, 4, 7, 3, 7, 4, 957215296943148125119291554214660991305855795200000⟩, + ⟨3, 4, 8, 3, 8, 4, 1082885005416080640467814324751457311732531200000000⟩, + ⟨3, 4, 4, 4, 3, 4, 1747327577445186360580777395153293542224927129600000⟩, + ⟨3, 4, 5, 4, 4, 4, -2851004398638375847705033972442380929768987033600000⟩, + ⟨3, 4, 6, 4, 5, 4, -2311746362383361189187998256479678552746858905600000⟩, + ⟨3, 4, 7, 4, 6, 4, -314373760177757908641537387415443569582800896000000⟩, + ⟨3, 4, 8, 4, 7, 4, 384669409076319399383513090644806786861131366400000⟩, + ⟨3, 4, 4, 5, 2, 4, -11972097080585179790864888739655828664393410805760000⟩, + ⟨3, 4, 5, 5, 3, 4, 7435583371160726746449501990518067546224276275200000⟩, + ⟨3, 4, 6, 5, 4, 4, -2607375040244011344365444129350726006694372966400000⟩, + ⟨3, 4, 7, 5, 5, 4, -832600639787777261094868955276210174094527692800000⟩, + ⟨3, 4, 8, 5, 6, 4, 800982668796938405299827381974162864298629529600000⟩, + ⟨3, 4, 4, 6, 1, 4, 6424300436925479602426039904770192009890040381440000⟩, + ⟨3, 4, 5, 6, 2, 4, 110046073269923236497782503601963094130871500800000⟩, + ⟨3, 4, 6, 6, 3, 4, 9654560368866831104991670068449643042670274150400000⟩, + ⟨3, 4, 7, 6, 4, 4, 298059023028060993759103302910514745767991705600000⟩, + ⟨3, 4, 8, 6, 5, 4, -840595577369941938284495292745952526507127603200000⟩, + ⟨3, 4, 4, 7, 0, 4, 122583570366985401466256178404280944575566556692480000⟩, + ⟨3, 4, 5, 7, 1, 4, -5129969284900863293448651879917607237329721753600000⟩, + ⟨3, 4, 6, 7, 2, 4, -9527868649456154545701342137138686312207456665600000⟩, + ⟨3, 4, 7, 7, 3, 4, 12488543012919482482832121626768769073868596838400000⟩, + ⟨3, 4, 8, 7, 4, 4, 1662043854691216800710029168531557566757470208000000⟩ +] + +def collectedFourData_11_3_26 : List CollectedFourTerm := [ + ⟨3, 5, 3, 0, 6, 5, -282793517334747371428879717739385812491960320000000⟩, + ⟨3, 5, 4, 0, 7, 5, 4056936987974092084317579394584390234191953920000000⟩, + ⟨3, 5, 5, 0, 8, 5, 191218740551563289822726041311006068991590400000000⟩, + ⟨3, 5, 3, 1, 5, 5, 3791250888407167040769499753858705752493916160000000⟩, + ⟨3, 5, 4, 1, 6, 5, 9089706614043419943373687484689232489537863680000000⟩, + ⟨3, 5, 5, 1, 7, 5, -1516658420870000784080317835483646558575001600000000⟩, + ⟨3, 5, 6, 1, 8, 5, -276531537157995292500078212347142963881574400000000⟩, + ⟨3, 5, 3, 2, 4, 5, -4937023414363167784704599840670843001550929920000000⟩, + ⟨3, 5, 4, 2, 5, 5, -1153436132672000098642323394774996379699773440000000⟩, + ⟨3, 5, 5, 2, 6, 5, -1060065376089836436695575149715328737266892800000000⟩, + ⟨3, 5, 6, 2, 7, 5, -370030825912756895790384205624344630106521600000000⟩, + ⟨3, 5, 7, 2, 8, 5, -433843267882209522514272489388762470128025600000000⟩, + ⟨3, 5, 3, 3, 3, 5, 6599031778208119765522408798733182880930856960000000⟩, + ⟨3, 5, 4, 3, 4, 5, 791372399943218226870659581687455706188349440000000⟩, + ⟨3, 5, 5, 3, 5, 5, 400556048796771127490319274687784665743360000000000⟩, + ⟨3, 5, 6, 3, 6, 5, 980473495910343145789282752004244753507942400000000⟩, + ⟨3, 5, 7, 3, 7, 5, 242249020321460580946569625711188623386214400000000⟩, + ⟨3, 5, 8, 3, 8, 5, 219242490186343525272303732723601763205120000000000⟩, + ⟨3, 5, 3, 4, 2, 5, -9033775157682979453530795868482135700537344000000000⟩, + ⟨3, 5, 4, 4, 3, 5, 1768832550706334144310992610732971377085644800000000⟩, + ⟨3, 5, 5, 4, 4, 5, -1443046354791677256638264583972953646327398400000000⟩, + ⟨3, 5, 6, 4, 5, 5, -780065945188407771793219654915824924858777600000000⟩, + ⟨3, 5, 7, 4, 6, 5, -79560717072784960601400618025300694925312000000000⟩, + ⟨3, 5, 8, 4, 7, 5, 77880734078496962096503120894526638144880640000000⟩, + ⟨3, 5, 3, 5, 1, 5, 7501848465761811420709432496133830449645486080000000⟩, + ⟨3, 5, 4, 5, 2, 5, -12119441877817927775343093366046840329213050880000000⟩, + ⟨3, 5, 5, 5, 3, 5, 3763547851637000411976435659734283545529548800000000⟩, + ⟨3, 5, 6, 5, 4, 5, -879821639745839033965994301889875022341734400000000⟩, + ⟨3, 5, 7, 5, 5, 5, -210711936961021741295010140371785719847321600000000⟩, + ⟨3, 5, 8, 5, 6, 5, 162168128679248814324355852548123957091368960000000⟩, + ⟨3, 5, 3, 6, 0, 5, 4085510507347009711171572817956253149199073280000000⟩, + ⟨3, 5, 4, 6, 1, 5, 6503366555323073750559656409627599599011102720000000⟩, + ⟨3, 5, 5, 6, 2, 5, 55700224442706341865901864812487329919795200000000⟩, + ⟨3, 5, 6, 6, 3, 5, 3257794143019283166071865869437691985552998400000000⟩, + ⟨3, 5, 7, 6, 4, 5, 75431834987492762751019363080582980645683200000000⟩, + ⟨3, 5, 8, 6, 5, 5, -170188216385359628141352085111535502171832320000000⟩, + ⟨3, 5, 4, 7, 0, 5, 124092249355988964571242267018450855990122250240000000⟩, + ⟨3, 5, 5, 7, 1, 5, -2596552807952519137883423530188099339839078400000000⟩, + ⟨3, 5, 6, 7, 2, 5, -3215043823409071038264465158676538004707737600000000⟩, + ⟨3, 5, 7, 7, 3, 5, 3160560972838120115691392963255246284180684800000000⟩, + ⟨3, 5, 8, 7, 4, 5, 336499842253703193235731544877477229546700800000000⟩ +] + +def collectedFourData_11_3_27 : List CollectedFourTerm := [ + ⟨3, 6, 2, 0, 5, 6, -12937786228784652311527062006586303816113586176000000⟩, + ⟨3, 6, 3, 0, 6, 6, -2076649817633839158908719177572891752237786726400000⟩, + ⟨3, 6, 4, 0, 7, 6, 14895740071466623096278142276451340897442018099200000⟩, + ⟨3, 6, 5, 0, 8, 6, 468061604849931472417944252591520567825268736000000⟩, + ⟨3, 6, 2, 1, 4, 6, 44590656416648105849740133776677487341074173132800000⟩, + ⟨3, 6, 3, 1, 5, 6, 27840455963123633693431628733417009294494348083200000⟩, + ⟨3, 6, 4, 1, 6, 6, 33374417066382700842728154111957430224359836876800000⟩, + ⟨3, 6, 5, 1, 7, 6, -3712447704832306174127440634115773848872812544000000⟩, + ⟨3, 6, 6, 1, 8, 6, -507666487214234876317121741937212585486057472000000⟩, + ⟨3, 6, 2, 2, 3, 6, -16618663823929567963978891547956456444307020185600000⟩, + ⟨3, 6, 3, 2, 4, 6, -36254256708986893725992013308359108205151151718400000⟩, + ⟨3, 6, 4, 2, 5, 6, -4235038619591575754618813807521964248713815654400000⟩, + ⟨3, 6, 5, 2, 6, 6, -2594807913425505405117075984066875889970839552000000⟩, + ⟨3, 6, 6, 2, 7, 6, -679315825900836284653986799515017049179947008000000⟩, + ⟨3, 6, 7, 2, 8, 6, -637171991508419896323048329890647014472312422400000⟩, + ⟨3, 6, 2, 3, 2, 6, -8886484621384075905668116546675756939144593408000000⟩, + ⟨3, 6, 3, 3, 3, 6, 48458954320916393814567614225659251072758395699200000⟩, + ⟨3, 6, 4, 3, 4, 6, 2905659517076577795749502198580144432411469414400000⟩, + ⟨3, 6, 5, 3, 5, 6, 980473495910343145789282752004244753507942400000000⟩, + ⟨3, 6, 6, 3, 6, 6, 1799988314501266847077886535690611118217101312000000⟩, + ⟨3, 6, 7, 3, 7, 6, 355783533239235678189083310072350032650672537600000⟩, + ⟨3, 6, 8, 3, 8, 6, 268328803735226647633564284942371143444070400000000⟩, + ⟨3, 6, 2, 4, 1, 6, -20513892779538277144963979590008219218198554214400000⟩, + ⟨3, 6, 3, 4, 2, 6, -66338110259935548094029070496716643405534330880000000⟩, + ⟨3, 6, 4, 4, 3, 6, 6494572132466928967677191548626210034808782848000000⟩, + ⟨3, 6, 5, 4, 4, 6, -3532261486234928071516497493881203424762003456000000⟩, + ⟨3, 6, 6, 4, 5, 6, -1432072964477068201491934042217662531699212288000000⟩, + ⟨3, 6, 7, 4, 6, 6, -116848328177511232365651773461102577370267648000000⟩, + ⟨3, 6, 8, 4, 7, 6, 95317491566267978035161003168140035776892108800000⟩, + ⟨3, 6, 2, 5, 0, 6, 153055695721756589542803891214884193787177651404800000⟩, + ⟨3, 6, 3, 5, 1, 6, 55088646992923044971180993050925728953932552601600000⟩, + ⟨3, 6, 4, 5, 2, 6, -44498609803001473319977895382420264821602438348800000⟩, + ⟨3, 6, 5, 5, 3, 6, 9212341019952004106407159587156924077118062592000000⟩, + ⟨3, 6, 6, 5, 4, 6, -1615208036722563362465991007875879472591798272000000⟩, + ⟨3, 6, 7, 5, 5, 6, -309466008688886702669882529830567050924680806400000⟩, + ⟨3, 6, 8, 5, 6, 6, 198476034164264468080256721260480513843606323200000⟩, + ⟨3, 6, 3, 6, 0, 6, 30001305298595099433454133491513724638357723545600000⟩, + ⟨3, 6, 4, 6, 1, 6, 23878225884384971896495904074994191211164807987200000⟩, + ⟨3, 6, 5, 6, 2, 6, 136341952509222131588594886920133032036794368000000⟩, + ⟨3, 6, 6, 6, 3, 6, 5980775016300487583796874168191842940818030592000000⟩, + ⟨3, 6, 7, 6, 4, 6, 110784368642467014480231724128688911955053772800000⟩, + ⟨3, 6, 8, 6, 5, 6, -208291743419360133109051876897881743126062694400000⟩, + ⟨3, 6, 4, 7, 0, 6, 455625980085406589630530542622537053142507742822400000⟩, + ⟨3, 6, 5, 7, 1, 6, -6355792695120938912369619836579890068933574656000000⟩, + ⟨3, 6, 6, 7, 2, 6, -5902292450417225112615850654418476589371097088000000⟩, + ⟨3, 6, 7, 7, 3, 6, 4641816707626810065744421240047067317570581299200000⟩, + ⟨3, 6, 8, 7, 4, 6, 411838964483048548761549778379108176034267136000000⟩ +] + +def collectedFourData_11_3_28 : List CollectedFourTerm := [ + ⟨3, 7, 1, 0, 4, 7, 519175870019602365866598049636661474975809536000000⟩, + ⟨3, 7, 2, 0, 5, 7, -12786336610319395191957126039398924204139085824000000⟩, + ⟨3, 7, 3, 0, 6, 7, -1026170286031962075081919634788442383556857036800000⟩, + ⟨3, 7, 4, 0, 7, 7, 4907123553843799310044399877711723818714241433600000⟩, + ⟨3, 7, 5, 0, 8, 7, 115645619894813479136884310052210248112930816000000⟩, + ⟨3, 7, 1, 1, 3, 7, -2096790633861043880210885476445880197670607257600000⟩, + ⟨3, 7, 2, 1, 4, 7, 44068678561859334199525544829241713389445788467200000⟩, + ⟨3, 7, 3, 1, 5, 7, 13757277908073473673308017033162688328240621158400000⟩, + ⟨3, 7, 4, 1, 6, 7, 10994578805518061292326854016352164393353897574400000⟩, + ⟨3, 7, 5, 1, 7, 7, -917247455684940363100819663928035880535588864000000⟩, + ⟨3, 7, 6, 1, 8, 7, -100344749503708307045123677756263130501585305600000⟩, + ⟨3, 7, 1, 2, 2, 7, -366054120908315209503239963700906808593245798400000⟩, + ⟨3, 7, 2, 2, 3, 7, -16424125882814356383772803532090521141415143014400000⟩, + ⟨3, 7, 3, 2, 4, 7, -17914932340074010241123640914516913295647886540800000⟩, + ⟨3, 7, 4, 2, 5, 7, -1395154430859358139962720755705405763354833715200000⟩, + ⟨3, 7, 5, 2, 6, 7, -641108278369190856879484916714208510043226112000000⟩, + ⟨3, 7, 6, 2, 7, 7, -134272752093557505302973128715688313637725798400000⟩, + ⟨3, 7, 7, 2, 8, 7, -104952210241967450187335732939354506956216729600000⟩, + ⟨3, 7, 1, 3, 1, 7, 2054303108870598224114920102311949904495247360000000⟩, + ⟨3, 7, 2, 3, 2, 7, -8782459505989011919610692710796469999964782592000000⟩, + ⟨3, 7, 3, 3, 3, 7, 23945847101445483994686874403295648372406773350400000⟩, + ⟨3, 7, 4, 3, 4, 7, 957215296943148125119291554214660991305855795200000⟩, + ⟨3, 7, 5, 3, 5, 7, 242249020321460580946569625711188623386214400000000⟩, + ⟨3, 7, 6, 3, 6, 7, 355783533239235678189083310072350032650672537600000⟩, + ⟨3, 7, 7, 3, 7, 7, 58603122357522592514763576802900503356139110400000⟩, + ⟨3, 7, 8, 3, 8, 7, 37883964140078297049212992668187778403532800000000⟩, + ⟨3, 7, 1, 4, 0, 7, -16437513319745708525063021367153836241669901516800000⟩, + ⟨3, 7, 2, 4, 1, 7, -20273757320522417904662346928497715808636082585600000⟩, + ⟨3, 7, 3, 4, 2, 7, -32780778445266469475251213857169560738264514560000000⟩, + ⟨3, 7, 4, 4, 3, 7, 2139515574953783122653661922122486494353424384000000⟩, + ⟨3, 7, 5, 4, 4, 7, -872728215631321574153057639448485419743707136000000⟩, + ⟨3, 7, 6, 4, 5, 7, -283061826042581885347286967521788274841904742400000⟩, + ⟨3, 7, 7, 4, 6, 7, -19246750435900967440967966280445586300731392000000⟩, + ⟨3, 7, 8, 4, 7, 7, 13457386542750248090612410537215026708191641600000⟩, + ⟨3, 7, 2, 5, 0, 7, 151264027014986496130787466392802788314033894195200000⟩, + ⟨3, 7, 3, 5, 1, 7, 27221889873687513836606068749035755337845781299200000⟩, + ⟨3, 7, 4, 5, 2, 7, -14659236481703291515209896224977091267993691750400000⟩, + ⟨3, 7, 5, 5, 3, 7, 2276125358063374083656004974631555245751140352000000⟩, + ⟨3, 7, 6, 5, 4, 7, -319260084963822841690213579998848083427957145600000⟩, + ⟨3, 7, 7, 5, 5, 7, -50973900358941574679550534166490381440096665600000⟩, + ⟨3, 7, 8, 5, 6, 7, 28021810764540130553961492219911131892180582400000⟩, + ⟨3, 7, 3, 6, 0, 7, 14825055133594944515232221752949560187643179827200000⟩, + ⟨3, 7, 4, 6, 1, 7, 7866235856633834095277418450338969676905290137600000⟩, + ⟨3, 7, 5, 6, 2, 7, 33686483685525742918518619335592091905425408000000⟩, + ⟨3, 7, 6, 6, 3, 7, 1182152822696470467813034259615813556200118681600000⟩, + ⟨3, 7, 7, 6, 4, 7, 18247921290077890401841830949897649448497971200000⟩, + ⟨3, 7, 8, 6, 5, 7, -29407640285087650883738207733370508479876300800000⟩, + ⟨3, 7, 4, 7, 0, 7, 150097475378417239735623624880727832787963556659200000⟩, + ⟨3, 7, 5, 7, 1, 7, -1570347959614948636231408681708403381382414336000000⟩, + ⟨3, 7, 6, 7, 2, 7, -1166640052773091854050956095059772208528647782400000⟩, + ⟨3, 7, 7, 7, 3, 7, 764579939947169571728605300274967207694093516800000⟩, + ⟨3, 7, 8, 7, 4, 7, 58145425853566395215827618426582199332503552000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1110.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1110.lean new file mode 100644 index 0000000000000000000000000000000000000000..5743f7e41872dbc66f0e0f68a14aa81aa94a9ba6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1110.lean @@ -0,0 +1,613 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1110. -/ +namespace LaughlinFock +def collectedFourData_11_3_29 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 3, 8, -84885611736805918588385660890005403080012595200000000⟩, + ⟨3, 8, 1, 0, 4, 8, 2349347180779400705987286937564345547096064000000000⟩, + ⟨3, 8, 2, 0, 5, 8, -28930026993373281993339503141268186923532288000000000⟩, + ⟨3, 8, 3, 0, 6, 8, -1547857163442358719455411941519322444621414400000000⟩, + ⟨3, 8, 4, 0, 7, 8, 5551363975430832407981166643568767990864281600000000⟩, + ⟨3, 8, 5, 0, 8, 8, 104662688217427377775274720569503773412556800000000⟩, + ⟨3, 8, 0, 1, 2, 8, 33203204931090117028054315511679952693808332800000000⟩, + ⟨3, 8, 1, 1, 3, 8, -9488286048733549957925273100680569681241702400000000⟩, + ⟨3, 8, 2, 1, 4, 8, 99708626419857293821356627909858794349684326400000000⟩, + ⟨3, 8, 3, 1, 5, 8, 20751235393708896625012034676368269206827827200000000⟩, + ⟨3, 8, 4, 1, 6, 8, 12438021589690575189780029862613303465240166400000000⟩, + ⟨3, 8, 5, 1, 7, 8, -830135932168469148513428859503409750029107200000000⟩, + ⟨3, 8, 6, 1, 8, 8, -75679125310546289412980122230587038000742400000000⟩, + ⟨3, 8, 0, 2, 1, 8, 34302619696437327819955230726096229402411008000000000⟩, + ⟨3, 8, 1, 2, 2, 8, -1656448742381193297707807966151412150802841600000000⟩, + ⟨3, 8, 2, 2, 3, 8, -37160792775383623886708572114840998225169612800000000⟩, + ⟨3, 8, 3, 2, 4, 8, -27022568020747618766032613969524726868371046400000000⟩, + ⟨3, 8, 4, 2, 5, 8, -1578319755484575566800988676729630371296051200000000⟩, + ⟨3, 8, 5, 2, 6, 8, -580221852877763821360694655362938068113817600000000⟩, + ⟨3, 8, 6, 2, 7, 8, -101267325711991784214444569832476485720473600000000⟩, + ⟨3, 8, 7, 2, 8, 8, -67846312777876636289114511111829436183347200000000⟩, + ⟨3, 8, 0, 3, 0, 8, -191674600642127805457573931710934814511280947200000000⟩, + ⟨3, 8, 1, 3, 1, 8, 9296023748386600011827513919042140913008640000000000⟩, + ⟨3, 8, 2, 3, 2, 8, -19870960566720384871986800699008670503010304000000000⟩, + ⟨3, 8, 3, 3, 3, 8, 36119493494584952689083819844401017623098163200000000⟩, + ⟨3, 8, 4, 3, 4, 8, 1082885005416080640467814324751457311732531200000000⟩, + ⟨3, 8, 5, 3, 5, 8, 219242490186343525272303732723601763205120000000000⟩, + ⟨3, 8, 6, 3, 6, 8, 268328803735226647633564284942371143444070400000000⟩, + ⟨3, 8, 7, 3, 7, 8, 37883964140078297049212992668187778403532800000000⟩, + ⟨3, 8, 8, 3, 8, 8, 21428813791432664465879844907529954918400000000000⟩, + ⟨3, 8, 1, 4, 0, 8, -74382165672126406223557875605501250972627763200000000⟩, + ⟨3, 8, 2, 4, 1, 8, -45870867036806549159519860032438017560097587200000000⟩, + ⟨3, 8, 3, 4, 2, 8, -49445948133935907290570801105176891993620480000000000⟩, + ⟨3, 8, 4, 4, 3, 8, 2420405672966612570485712967419904607125504000000000⟩, + ⟨3, 8, 5, 4, 4, 8, -789844710195282428042158011662148234431692800000000⟩, + ⟨3, 8, 6, 4, 5, 8, -213482733373278788759534223606625840241049600000000⟩, + ⟨3, 8, 7, 4, 6, 8, -12442053835943983312971894421769152364544000000000⟩, + ⟨3, 8, 8, 4, 7, 8, 7612081705009523767793689962877870197964800000000⟩, + ⟨3, 8, 2, 5, 0, 8, 342245986324036948970981639045710071235765862400000000⟩, + ⟨3, 8, 3, 5, 1, 8, 41061018640831925726403851012659674143627673600000000⟩, + ⟨3, 8, 4, 5, 2, 8, -16583800350432234982983355927379576820754022400000000⟩, + ⟨3, 8, 5, 5, 3, 8, 2059960411050995643334438013528584958351769600000000⟩, + ⟨3, 8, 6, 5, 4, 8, -240783141082433079758635915628278471616102400000000⟩, + ⟨3, 8, 7, 5, 5, 8, -32952056743614480024281978038964096021299200000000⟩, + ⟨3, 8, 8, 5, 6, 8, 15850351952393459566510838036551504704307200000000⟩, + ⟨3, 8, 3, 6, 0, 8, 22361851730959317632441192564167340644211097600000000⟩, + ⟨3, 8, 4, 6, 1, 8, 8898968586709725575344337286205995677751705600000000⟩, + ⟨3, 8, 5, 6, 2, 8, 30487258768005942998296190743758240114278400000000⟩, + ⟨3, 8, 6, 6, 3, 8, 891569235535896033330047785501836513273446400000000⟩, + ⟨3, 8, 7, 6, 4, 8, 11796361148930196517099399836686140991078400000000⟩, + ⟨3, 8, 8, 6, 5, 8, -16634237256282933810867579419120466552422400000000⟩, + ⟨3, 8, 4, 7, 0, 8, 169803288724240915005074537417728026817540915200000000⟩, + ⟨3, 8, 5, 7, 1, 8, -1421211101981595667291363592886525878914252800000000⟩, + ⟨3, 8, 6, 7, 2, 8, -879869641239717557310274227730350226381209600000000⟩, + ⟨3, 8, 7, 7, 3, 8, 494262385039346890448146364292741587376537600000000⟩, + ⟨3, 8, 8, 7, 4, 8, 32889575621825457129532490604509141139456000000000⟩ +] + +def collectedFourData_11_3_30 : List CollectedFourTerm := [ + ⟨4, 0, 7, 2, 8, 1, 29437908500239536178676746245867992716225491763200000⟩, + ⟨4, 0, 7, 3, 7, 1, -16437513319745708525063021367153836241669901516800000⟩, + ⟨4, 0, 8, 3, 8, 1, -74382165672126406223557875605501250972627763200000000⟩, + ⟨4, 0, 7, 4, 6, 1, 5398495914976328714245127399174677937063460864000000⟩, + ⟨4, 0, 8, 4, 7, 1, -26422513537270615644820504803168189643584071270400000⟩, + ⟨4, 0, 7, 5, 5, 1, 14297602796618526023202848904040620552025748275200000⟩, + ⟨4, 0, 8, 5, 6, 1, -55018607952802568310602377806134875941152332185600000⟩, + ⟨4, 0, 7, 6, 4, 1, -5118335631221251186301590582316965060936099430400000⟩, + ⟨4, 0, 8, 6, 5, 1, 57739574549897338951436046461905953077765288755200000⟩, + ⟨4, 0, 7, 7, 3, 1, -214456029667141249982071994847294135666365536665600000⟩, + ⟨4, 0, 8, 7, 4, 1, -114163942372145294319787379703507099556761305088000000⟩ +] + +def collectedFourData_11_3_31 : List CollectedFourTerm := [ + ⟨4, 1, 6, 1, 8, 2, 5785713053011225150900075777029060010365576806400000⟩, + ⟨4, 1, 6, 2, 7, 2, 7741945824706318642978153194305564264208374169600000⟩, + ⟨4, 1, 7, 2, 8, 2, 36308229921898751177491372297780383032482883174400000⟩, + ⟨4, 1, 6, 3, 6, 2, -20513892779538277144963979590008219218198554214400000⟩, + ⟨4, 1, 7, 3, 7, 2, -20273757320522417904662346928497715808636082585600000⟩, + ⟨4, 1, 8, 3, 8, 2, -45870867036806549159519860032438017560097587200000000⟩, + ⟨4, 1, 6, 4, 5, 2, 16320878868537470707380847724883507747053214105600000⟩, + ⟨4, 1, 7, 4, 6, 2, 6658415658564764658693728794366021414774898688000000⟩, + ⟨4, 1, 8, 4, 7, 2, -16294545799982656959390714016108764861267600998400000⟩, + ⟨4, 1, 6, 5, 4, 2, 18408010882646132213762527110232514531045041766400000⟩, + ⟨4, 1, 7, 5, 5, 2, 17634427040473474814316606659992165588505355878400000⟩, + ⟨4, 1, 8, 5, 6, 2, -33929520969822093672641345031784751723663956377600000⟩, + ⟨4, 1, 6, 6, 3, 2, -68160985510021845474906688165998520027075470950400000⟩, + ⟨4, 1, 7, 6, 4, 2, -6312870593857433973964383061240372919435840716800000⟩, + ⟨4, 1, 8, 6, 5, 2, 35607518590072857967116203631762136228041012019200000⟩, + ⟨4, 1, 6, 7, 2, 2, 67266544735811384890089356719676435510691731865600000⟩, + ⟨4, 1, 7, 7, 3, 2, -264506523390707098993387849197408952454820868915200000⟩, + ⟨4, 1, 8, 7, 4, 2, -70403960057225564762921966053069200540982837248000000⟩ +] + +def collectedFourData_11_3_32 : List CollectedFourTerm := [ + ⟨4, 2, 5, 0, 8, 3, -4312572767948833790515747869141092180070236160000000⟩, + ⟨4, 2, 5, 1, 7, 3, 34205328333707476379558496832048031767084400640000000⟩, + ⟨4, 2, 6, 1, 8, 3, 18709918910458777196614379550634791784446689280000000⟩, + ⟨4, 2, 5, 2, 6, 3, 23907745966654902096694554526412063798061957120000000⟩, + ⟨4, 2, 6, 2, 7, 3, 25036011510116468192119406404260410962131025920000000⟩, + ⟨4, 2, 7, 2, 8, 3, 58707028104985132002880089892926497031129661440000000⟩, + ⟨4, 2, 5, 3, 5, 3, -9033775157682979453530795868482135700537344000000000⟩, + ⟨4, 2, 6, 3, 6, 3, -66338110259935548094029070496716643405534330880000000⟩, + ⟨4, 2, 7, 3, 7, 3, -32780778445266469475251213857169560738264514560000000⟩, + ⟨4, 2, 8, 3, 8, 3, -49445948133935907290570801105176891993620480000000000⟩, + ⟨4, 2, 5, 4, 4, 3, 32545149050828956197976102080544365396476559360000000⟩, + ⟨4, 2, 6, 4, 5, 3, 52778683868331108123218062270742392973945733120000000⟩, + ⟨4, 2, 7, 4, 6, 3, 10766038334638614007955925228605750943468748800000000⟩, + ⟨4, 2, 8, 4, 7, 3, -17564509208982177312259359036521606986397122560000000⟩, + ⟨4, 2, 5, 5, 3, 3, -84879619691174533648466819273173532027671019520000000⟩, + ⟨4, 2, 6, 5, 4, 3, 59528080248967650260866915650698991270918881280000000⟩, + ⟨4, 2, 7, 5, 5, 3, 28513227059190291322467455466828008462839971840000000⟩, + ⟨4, 2, 8, 5, 6, 3, -36573918097884530361941550923177221735411875840000000⟩, + ⟨4, 2, 5, 6, 2, 3, -1256211971731290400495408851141688224204718080000000⟩, + ⟨4, 2, 6, 6, 3, 3, -220419937882285808540719856507347476007700398080000000⟩, + ⟨4, 2, 7, 6, 4, 3, -10207324129375827975400586180774613676122439680000000⟩, + ⟨4, 2, 8, 6, 5, 3, 38382695403820612213958977395786090338876129280000000⟩, + ⟨4, 2, 5, 7, 1, 3, 58560279697572589293257230060145636351001231360000000⟩, + ⟨4, 2, 6, 7, 2, 3, 217527482932938492956983245605362085743684485120000000⟩, + ⟨4, 2, 7, 7, 3, 3, -427682427263809900481106680411618176306532843520000000⟩, + ⟨4, 2, 8, 7, 4, 3, -75891100000790939131421594161307494764458803200000000⟩ +] + +def collectedFourData_11_3_33 : List CollectedFourTerm := [ + ⟨4, 3, 4, 0, 7, 4, 8957600593037070686195675972035029531710246092800000⟩, + ⟨4, 3, 5, 0, 8, 4, 844410997184274505363345553913618231692623872000000⟩, + ⟨4, 3, 4, 1, 6, 4, 20069811682519602708417740727679706294020944691200000⟩, + ⟨4, 3, 5, 1, 7, 4, -6697476648265134453657695456604662908676210688000000⟩, + ⟨4, 3, 6, 1, 8, 4, -1831721125013241201059013014186237693408575488000000⟩, + ⟨4, 3, 4, 2, 5, 4, -2546753922153615296155199284169921092617083289600000⟩, + ⟨4, 3, 5, 2, 6, 4, -4681187935463701685023064285119437463464443904000000⟩, + ⟨4, 3, 6, 2, 7, 4, -2451052374338190326393188929877309067920146432000000⟩, + ⟨4, 3, 7, 2, 8, 4, -3831654004177634797301390023351577749556822016000000⟩, + ⟨4, 3, 4, 3, 4, 4, 1747327577445186360580777395153293542224927129600000⟩, + ⟨4, 3, 5, 3, 5, 4, 1768832550706334144310992610732971377085644800000000⟩, + ⟨4, 3, 6, 3, 6, 4, 6494572132466928967677191548626210034808782848000000⟩, + ⟨4, 3, 7, 3, 7, 4, 2139515574953783122653661922122486494353424384000000⟩, + ⟨4, 3, 8, 3, 8, 4, 2420405672966612570485712967419904607125504000000000⟩, + ⟨4, 3, 4, 4, 3, 4, 3905531575214970363523409840856872684598853632000000⟩, + ⟨4, 3, 5, 4, 4, 4, -6372409984073659087550228513127845352871821312000000⟩, + ⟨4, 3, 6, 4, 5, 4, -5167089748207097892726833519121516612185751552000000⟩, + ⟨4, 3, 7, 4, 6, 4, -702671131985729864366022848548300468330168320000000⟩, + ⟨4, 3, 8, 4, 7, 4, 859792143476301230821046789580609192814706688000000⟩, + ⟨4, 3, 4, 5, 2, 4, -26759380309289008651945735398651564876155269939200000⟩, + ⟨4, 3, 5, 5, 3, 4, 16619611577739534740916285908316443978690985984000000⟩, + ⟨4, 3, 6, 5, 4, 4, -5827862891621898381814208843007253208459378688000000⟩, + ⟨4, 3, 7, 5, 5, 4, -1860983670268523042494699103671362338030616576000000⟩, + ⟨4, 3, 8, 5, 6, 4, 1790312901007556670649103059382004211758661632000000⟩, + ⟨4, 3, 4, 6, 1, 4, 14359246960300936070366759966700162023083003084800000⟩, + ⟨4, 3, 5, 6, 2, 4, 245968998275933064602046870452513937278631936000000⟩, + ⟨4, 3, 6, 6, 3, 4, 21579348287148145132966444821360057273148243968000000⟩, + ⟨4, 3, 7, 6, 4, 4, 666205318762180022197714636431062276927127552000000⟩, + ⟨4, 3, 8, 6, 5, 4, -1878853519959026476301783166197635528727199744000000⟩, + ⟨4, 3, 4, 7, 0, 4, 273992129953586887453153492424482744295312955801600000⟩, + ⟨4, 3, 5, 7, 1, 4, -11466228359628685255020200706883181570489843712000000⟩, + ⟨4, 3, 6, 7, 2, 4, -21296173845867861224029551954480470511952330752000000⟩, + ⟨4, 3, 7, 7, 3, 4, 27913712171075369268887177652190782046945148928000000⟩, + ⟨4, 3, 8, 7, 4, 4, 3714910036147573479921549444263694661173903360000000⟩ +] + +def collectedFourData_11_3_34 : List CollectedFourTerm := [ + ⟨4, 4, 3, 0, 6, 5, 1018794137735447285135455006908872246973746380800000⟩, + ⟨4, 4, 4, 0, 7, 5, -14615552928738426108605463305246145447046466764800000⟩, + ⟨4, 4, 5, 0, 8, 5, -688886130541971752657809625435296178242584576000000⟩, + ⟨4, 4, 3, 1, 5, 5, -13658390108078107166907508974141587536059197030400000⟩, + ⟨4, 4, 4, 1, 6, 5, -32746648153043422708224045086357586808709264179200000⟩, + ⟨4, 4, 5, 1, 7, 5, 5463925491263729572093816333875760640141819904000000⟩, + ⟨4, 4, 6, 1, 8, 5, 996234678965609649459644127850092155985985536000000⟩, + ⟨4, 4, 3, 2, 4, 5, 17786159173026471337253543076169669412960128204800000⟩, + ⟨4, 4, 4, 2, 5, 5, 4155378034452881190287593975148454395483101593600000⟩, + ⟨4, 4, 5, 2, 6, 5, 3818999816386340284749481045376985299190546432000000⟩, + ⟨4, 4, 6, 2, 7, 5, 1333075948042609816084309936240030585353928704000000⟩, + ⟨4, 4, 7, 2, 8, 5, 1562967150662032950237589417486592255893438464000000⟩, + ⟨4, 4, 3, 3, 3, 5, -23773723505868648806568290183794240925469140582400000⟩, + ⟨4, 4, 4, 3, 4, 5, -2851004398638375847705033972442380929768987033600000⟩, + ⟨4, 4, 5, 3, 5, 5, -1443046354791677256638264583972953646327398400000000⟩, + ⟨4, 4, 6, 3, 6, 5, -3532261486234928071516497493881203424762003456000000⟩, + ⟨4, 4, 7, 3, 7, 5, -872728215631321574153057639448485419743707136000000⟩, + ⟨4, 4, 8, 3, 8, 5, -789844710195282428042158011662148234431692800000000⟩, + ⟨4, 4, 3, 4, 2, 5, 32545149050828956197976102080544365396476559360000000⟩, + ⟨4, 4, 4, 4, 3, 5, -6372409984073659087550228513127845352871821312000000⟩, + ⟨4, 4, 5, 4, 4, 5, 5198730086170985094759054579190846312044036096000000⟩, + ⟨4, 4, 6, 4, 5, 5, 2810271676292634117364198583316724023079993344000000⟩, + ⟨4, 4, 7, 4, 6, 5, 286626061699407744061558698165674081286881280000000⟩, + ⟨4, 4, 8, 4, 7, 5, -280573741822322803219098605107178618949835161600000⟩, + ⟨4, 4, 3, 5, 1, 5, -27026217966838459657819441893835322629811286835200000⟩, + ⟨4, 4, 4, 5, 2, 5, 43661596114775082575873853248298845356118192947200000⟩, + ⟨4, 4, 5, 5, 3, 5, -13558586931099667275881747655273264232185987072000000⟩, + ⟨4, 4, 6, 5, 4, 5, 3169652321855796401514138056993905390110375936000000⟩, + ⟨4, 4, 7, 5, 5, 5, 759112472414490197753985770471379796129480704000000⟩, + ⟨4, 4, 8, 5, 6, 5, -584228168958970554112042137616215262921909862400000⟩, + ⟨4, 4, 3, 6, 0, 5, -14718492113150988475348976354854646405307511603200000⟩, + ⟨4, 4, 4, 6, 1, 5, -23429079225550613557699797153498154723995077836800000⟩, + ⟨4, 4, 5, 6, 2, 5, -200666064298798811553098248397731956195852288000000⟩, + ⟨4, 4, 6, 6, 3, 5, -11736554664116080858056996922177200352810500096000000⟩, + ⟨4, 4, 7, 6, 4, 5, -271751318800272191615641173986416216409899008000000⟩, + ⟨4, 4, 8, 6, 5, 5, 613121399667077256881451387839492509087354060800000⟩, + ⟨4, 4, 4, 7, 0, 5, -447055708255985824512833381831641344582841112985600000⟩, + ⟨4, 4, 5, 7, 1, 5, 9354361457767057920186703214360782461569335296000000⟩, + ⟨4, 4, 6, 7, 2, 5, 11582542028268967281490022445330656081681055744000000⟩, + ⟨4, 4, 7, 7, 3, 5, -11386261684603603701511292533350298443854118912000000⟩, + ⟨4, 4, 8, 7, 4, 5, -1212276964012470795409991763778953406895357952000000⟩ +] + +def collectedFourData_11_3_35 : List CollectedFourTerm := [ + ⟨4, 5, 2, 0, 5, 6, 10293318978328948201547875646781503596998426624000000⟩, + ⟨4, 5, 3, 0, 6, 6, 1652185203959868284259931517617386008161655193600000⟩, + ⟨4, 5, 4, 0, 7, 6, -11851069515490484700898474745434792863780883660800000⟩, + ⟨4, 5, 5, 0, 8, 6, -372390400879385089599395700846028718881112064000000⟩, + ⟨4, 5, 2, 1, 4, 6, -35476382267659834298356719470542750503893414707200000⟩, + ⟨4, 5, 3, 1, 5, 6, -22149901742306934581240008806564700933656988876800000⟩, + ⟨4, 5, 4, 1, 6, 6, -26552728148788820391981884384980043599417914163200000⟩, + ⟨4, 5, 5, 1, 7, 6, 2953628058190122645010487317966834332289990656000000⟩, + ⟨4, 5, 6, 1, 8, 6, 403900095046998873546014075284375581782704128000000⟩, + ⟨4, 5, 2, 2, 3, 6, 13221829817587894427759696643123086525217531494400000⟩, + ⟨4, 5, 3, 2, 4, 6, 28843932186602513929104895043496281656872507801600000⟩, + ⟨4, 5, 4, 2, 5, 6, 3369402046542624985862401280054192334066784665600000⟩, + ⟨4, 5, 5, 2, 6, 6, 2064432435972463610668606832262646631705346048000000⟩, + ⟨4, 5, 6, 2, 7, 6, 540464524561953139083592475822920983109435392000000⟩, + ⟨4, 5, 7, 2, 8, 6, 506934836970897456899563002224522618604198297600000⟩, + ⟨4, 5, 2, 3, 2, 6, 7070098329528024203810142308457221773162708992000000⟩, + ⟨4, 5, 3, 3, 3, 6, -38554004940327478688072895655793886908593786060800000⟩, + ⟨4, 5, 4, 3, 4, 6, -2311746362383361189187998256479678552746858905600000⟩, + ⟨4, 5, 5, 3, 5, 6, -780065945188407771793219654915824924858777600000000⟩, + ⟨4, 5, 6, 3, 6, 6, -1432072964477068201491934042217662531699212288000000⟩, + ⟨4, 5, 7, 3, 7, 6, -283061826042581885347286967521788274841904742400000⟩, + ⟨4, 5, 8, 3, 8, 6, -213482733373278788759534223606625840241049600000000⟩, + ⟨4, 5, 2, 4, 1, 6, 16320878868537470707380847724883507747053214105600000⟩, + ⟨4, 5, 3, 4, 2, 6, 52778683868331108123218062270742392973945733120000000⟩, + ⟨4, 5, 4, 4, 3, 6, -5167089748207097892726833519121516612185751552000000⟩, + ⟨4, 5, 5, 4, 4, 6, 2810271676292634117364198583316724023079993344000000⟩, + ⟨4, 5, 6, 4, 5, 6, 1139359049758261555217530078619400136254554112000000⟩, + ⟨4, 5, 7, 4, 6, 6, 92964676703316497235586896192830186037706752000000⟩, + ⟨4, 5, 8, 4, 7, 6, -75834716044611999066907552201566074690548531200000⟩, + ⟨4, 5, 2, 5, 0, 6, -121771303811540282273741177559387164436012938035200000⟩, + ⟨4, 5, 3, 5, 1, 6, -43828596759554413012601581583785512525206283878400000⟩, + ⟨4, 5, 4, 5, 2, 6, 35403149866197532675349460933437663055447274291200000⟩, + ⟨4, 5, 5, 5, 3, 6, -7329350089626417657822907847964504402331435008000000⟩, + ⟨4, 5, 6, 5, 4, 6, 1285061543323057265779802912674442343327203328000000⟩, + ⟨4, 5, 7, 5, 5, 6, 246211545318156127376354456937642638435785113600000⟩, + ⟨4, 5, 8, 5, 6, 6, -157907782141365695698905386379589107923602636800000⟩, + ⟨4, 5, 3, 6, 0, 6, -23869076188444566356839754317590159188195436134400000⟩, + ⟨4, 5, 4, 6, 1, 6, -18997546513616648988565134644065670202301140172800000⟩, + ⟨4, 5, 5, 6, 2, 6, -108473828712922994721485045099933594164396032000000⟩, + ⟨4, 5, 6, 6, 3, 6, -4758312117063356132985817932267313507501867008000000⟩, + ⟨4, 5, 7, 6, 4, 6, -88140182878629700719367276070461840899126067200000⟩, + ⟨4, 5, 8, 6, 5, 6, 165717172756929022778689405431147732775049625600000⟩, + ⟨4, 5, 4, 7, 0, 6, -362496602192924195824515900363770696749261887897600000⟩, + ⟨4, 5, 5, 7, 1, 6, 5056676653495647946760444544833064059371782144000000⟩, + ⟨4, 5, 6, 7, 2, 6, 4695871289043118783457149689608483592116109312000000⟩, + ⟨4, 5, 7, 7, 3, 6, -3693035204449174180581099858094284245933280460800000⟩, + ⟨4, 5, 8, 7, 4, 6, -327659597566787560646333645956582856315633664000000⟩ +] + +def collectedFourData_11_3_36 : List CollectedFourTerm := [ + ⟨4, 6, 1, 0, 4, 7, -170510512078992745801025028747636566686433280000000⟩, + ⟨4, 6, 2, 0, 5, 7, 4199356959632224555754280653274014564241899520000000⟩, + ⟨4, 6, 3, 0, 6, 7, 337020325973450797329384287006008490500030464000000⟩, + ⟨4, 6, 4, 0, 7, 7, -1611623725827630074508200951328746594503753728000000⟩, + ⟨4, 6, 5, 0, 8, 7, -37980952133258198243702179165862805299527680000000⟩, + ⟨4, 6, 1, 1, 3, 7, 688639178643998653631431478522883081920053248000000⟩, + ⟨4, 6, 2, 1, 4, 7, -14473270778057258941341834360087234593691795456000000⟩, + ⟨4, 6, 3, 1, 5, 7, -4518238686304997030311150844733995370971922432000000⟩, + ⟨4, 6, 4, 1, 6, 7, -3610898291846543013549164533984433880654938112000000⟩, + ⟨4, 6, 5, 1, 7, 7, 301247308288975809203027431547820231591198720000000⟩, + ⟨4, 6, 6, 1, 8, 7, 32955758559560069281023097812191390925324288000000⟩, + ⟨4, 6, 1, 2, 2, 7, 120221449433591215853893526368210434373189632000000⟩, + ⟨4, 6, 2, 2, 3, 7, 5394099141438868497339008349022976830510989312000000⟩, + ⟨4, 6, 3, 2, 4, 7, 5883717760325017632841010855304218367580176384000000⟩, + ⟨4, 6, 4, 2, 5, 7, 458204069511402661942535125627242775100522496000000⟩, + ⟨4, 6, 5, 2, 6, 7, 210556204853443519116885023829311297956085760000000⟩, + ⟨4, 6, 6, 2, 7, 7, 44098574374929441762557936779317157803589632000000⟩, + ⟨4, 6, 7, 2, 8, 7, 34468965423035365284621423583726150046711808000000⟩, + ⟨4, 6, 1, 3, 1, 7, -674685198766589560694327469600862144089292800000000⟩, + ⟨4, 6, 2, 3, 2, 7, 2884382256869263519032640760883949290557276160000000⟩, + ⟨4, 6, 3, 3, 3, 7, -7864422996543680530045864325484889642308206592000000⟩, + ⟨4, 6, 4, 3, 4, 7, -314373760177757908641537387415443569582800896000000⟩, + ⟨4, 6, 5, 3, 5, 7, -79560717072784960601400618025300694925312000000000⟩, + ⟨4, 6, 6, 3, 6, 7, -116848328177511232365651773461102577370267648000000⟩, + ⟨4, 6, 7, 3, 7, 7, -19246750435900967440967966280445586300731392000000⟩, + ⟨4, 6, 8, 3, 8, 7, -12442053835943983312971894421769152364544000000000⟩, + ⟨4, 6, 1, 4, 0, 7, 5398495914976328714245127399174677937063460864000000⟩, + ⟨4, 6, 2, 4, 1, 7, 6658415658564764658693728794366021414774898688000000⟩, + ⟨4, 6, 3, 4, 2, 7, 10766038334638614007955925228605750943468748800000000⟩, + ⟨4, 6, 4, 4, 3, 7, -702671131985729864366022848548300468330168320000000⟩, + ⟨4, 6, 5, 4, 4, 7, 286626061699407744061558698165674081286881280000000⟩, + ⟨4, 6, 6, 4, 5, 7, 92964676703316497235586896192830186037706752000000⟩, + ⟨4, 6, 7, 4, 6, 7, 6321120572414395696368407526998936817500160000000⟩, + ⟨4, 6, 8, 4, 7, 7, -4419746762426869167282651644049622007021568000000⟩, + ⟨4, 6, 2, 5, 0, 7, -49678939632695400910362162126501912405287632896000000⟩, + ⟨4, 6, 3, 5, 1, 7, -8940358460698785869569260360181005082549026816000000⟩, + ⟨4, 6, 4, 5, 2, 7, 4814464738293606191921302681679160894755438592000000⟩, + ⟨4, 6, 5, 5, 3, 7, -747537246568707318131588636754962000337960960000000⟩, + ⟨4, 6, 6, 5, 4, 7, 104853102228169417961835917967211141936447488000000⟩, + ⟨4, 6, 7, 5, 5, 7, 16741120600498082584634071556165318725337088000000⟩, + ⟨4, 6, 8, 5, 6, 7, -9203072751940429898504542116759324906749952000000⟩, + ⟨4, 6, 3, 6, 0, 7, -4868923785562552774528804244563421050234208256000000⟩, + ⟨4, 6, 4, 6, 1, 7, -2583471192523117590232265034943204618716315648000000⟩, + ⟨4, 6, 5, 6, 2, 7, -11063494886892101865947660550573534310563840000000⟩, + ⟨4, 6, 6, 6, 3, 7, -388248943746155420586619542630475817463840768000000⟩, + ⟨4, 6, 7, 6, 4, 7, -5993079769733628948988222533731501658341376000000⟩, + ⟨4, 6, 8, 6, 5, 7, 9658214284604151037848797127416708736221184000000⟩, + ⟨4, 6, 4, 7, 0, 7, -49295814513820941684171459303816385163339759616000000⟩, + ⟨4, 6, 5, 7, 1, 7, 515742063909935851566029530060222220237537280000000⟩, + ⟨4, 6, 6, 7, 2, 7, 383154156996341692495274922298060431742205952000000⟩, + ⟨4, 6, 7, 7, 3, 7, -251107427394102707052767216787285723907620864000000⟩, + ⟨4, 6, 8, 7, 4, 7, -19096431305577384952405342288713157139496960000000⟩ +] + +def collectedFourData_11_3_37 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 3, 8, -30153615520174904903311449035998227125391222374400000⟩, + ⟨4, 7, 1, 0, 4, 8, 834550286711458135787229285925129760966443008000000⟩, + ⟨4, 7, 2, 0, 5, 8, -10276711130400156419205107860574577069744193536000000⟩, + ⟨4, 7, 3, 0, 6, 8, -549839823635883070752439577622545848563715276800000⟩, + ⟨4, 7, 4, 0, 7, 8, 1971991383495090643792473917817381131486704435200000⟩, + ⟨4, 7, 5, 0, 8, 8, 37178956424341107586846493813869483864463769600000⟩, + ⟨4, 7, 0, 1, 2, 8, 11794657010117931458477368938219558803101817241600000⟩, + ⟨4, 7, 1, 1, 3, 8, -3370490282217015645063808688767156412799044812800000⟩, + ⟨4, 7, 2, 1, 4, 8, 35419142580149379786406601818462942206393896140800000⟩, + ⟨4, 7, 3, 1, 5, 8, 7371387928152642204346314257619755943852402278400000⟩, + ⟨4, 7, 4, 1, 6, 8, 4418314401856918595206058539064937631984700620800000⟩, + ⟨4, 7, 5, 1, 7, 8, -294886250047915412549345948003494373001422438400000⟩, + ⟨4, 7, 6, 1, 8, 8, -26883227920803074851031449223100591172799692800000⟩, + ⟨4, 7, 0, 2, 1, 8, 12185198227329998486681287515867601262792933376000000⟩, + ⟨4, 7, 1, 2, 2, 8, -588414426010228297913585652591220260512936755200000⟩, + ⟨4, 7, 2, 2, 3, 8, -13200496937550544911037426109771375495014357401600000⟩, + ⟨4, 7, 3, 2, 4, 8, -9599131228409261923965359818620210728529611980800000⟩, + ⟨4, 7, 4, 2, 5, 8, -560660942426155807431213900761287289131656806400000⟩, + ⟨4, 7, 5, 2, 6, 8, -206110155892220611231627326790193901875704627200000⟩, + ⟨4, 7, 6, 2, 7, 8, -35972833814799610775878881604974188239729459200000⟩, + ⟨4, 7, 7, 2, 8, 8, -24100805638402080516405800861969685087151718400000⟩, + ⟨4, 7, 0, 3, 0, 8, -68087890214729458606980160945652105796531938918400000⟩, + ⟨4, 7, 1, 3, 1, 8, 3302193625515505444225443683107090255136686080000000⟩, + ⟨4, 7, 2, 3, 2, 8, -7058691015896180604908077183426141432250892288000000⟩, + ⟨4, 7, 3, 3, 3, 8, 12830599878293995109664889713482843203976980070400000⟩, + ⟨4, 7, 4, 3, 4, 8, 384669409076319399383513090644806786861131366400000⟩, + ⟨4, 7, 5, 3, 5, 8, 77880734078496962096503120894526638144880640000000⟩, + ⟨4, 7, 6, 3, 6, 8, 95317491566267978035161003168140035776892108800000⟩, + ⟨4, 7, 7, 3, 7, 8, 13457386542750248090612410537215026708191641600000⟩, + ⟨4, 7, 8, 3, 8, 8, 7612081705009523767793689962877870197964800000000⟩, + ⟨4, 7, 1, 4, 0, 8, -26422513537270615644820504803168189643584071270400000⟩, + ⟨4, 7, 2, 4, 1, 8, -16294545799982656959390714016108764861267600998400000⟩, + ⟨4, 7, 3, 4, 2, 8, -17564509208982177312259359036521606986397122560000000⟩, + ⟨4, 7, 4, 4, 3, 8, 859792143476301230821046789580609192814706688000000⟩, + ⟨4, 7, 5, 4, 4, 8, -280573741822322803219098605107178618949835161600000⟩, + ⟨4, 7, 6, 4, 5, 8, -75834716044611999066907552201566074690548531200000⟩, + ⟨4, 7, 7, 4, 6, 8, -4419746762426869167282651644049622007021568000000⟩, + ⟨4, 7, 8, 4, 7, 8, 2704012851467629244567252101271671721793945600000⟩, + ⟨4, 7, 2, 5, 0, 8, 121574830808026980025574525384805023404862000332800000⟩, + ⟨4, 7, 3, 5, 1, 8, 14585960372192628786794516808850269845815767859200000⟩, + ⟨4, 7, 4, 5, 2, 8, -5891004722693794609961435093271572388084763852800000⟩, + ⟨4, 7, 5, 5, 3, 8, 731752448391443445019960132380827298647192371200000⟩, + ⟨4, 7, 6, 5, 4, 8, -85532543282498534913287758418753242375441612800000⟩, + ⟨4, 7, 7, 5, 5, 8, -11705442528078149636825939155469666229839462400000⟩, + ⟨4, 7, 8, 5, 6, 8, 5630464443300838131228176722767126261556838400000⟩, + ⟨4, 7, 3, 6, 0, 8, 7943521471049684826580670020805030163562836787200000⟩, + ⟨4, 7, 4, 6, 1, 8, 3161149125269369093012768864495732986398061363200000⟩, + ⟨4, 7, 5, 6, 2, 8, 10829881064000493413764336663622084958407884800000⟩, + ⟨4, 7, 6, 6, 3, 8, 316708985043561921565803390766852508924824780800000⟩, + ⟨4, 7, 7, 6, 4, 8, 4190379633769418602727609677893091013217484800000⟩, + ⟨4, 7, 8, 6, 5, 8, -5908921246306356366785128195104619514088652800000⟩, + ⟨4, 7, 4, 7, 0, 8, 60318621465879464371881112957511725592015693414400000⟩, + ⟨4, 7, 5, 7, 1, 8, -504851791314541339726897330944877307637635481600000⟩, + ⟨4, 7, 6, 7, 2, 8, -312552979556520924157286948314488438271456051200000⟩, + ⟨4, 7, 7, 7, 3, 8, 175575078268522544960892093025420109390492467200000⟩, + ⟨4, 7, 8, 7, 4, 8, 11683247580251926765458525254413673595666432000000⟩ +] + +def collectedFourData_11_3_38 : List CollectedFourTerm := [ + ⟨5, 0, 6, 1, 8, 2, -43167639905886888204242116413862500805963992268800000⟩, + ⟨5, 0, 6, 2, 7, 2, -57763239633508740293677910190834451630819324723200000⟩, + ⟨5, 0, 7, 2, 8, 2, -270898432142765312795126012251118410837592427724800000⟩, + ⟨5, 0, 6, 3, 6, 2, 153055695721756589542803891214884193787177651404800000⟩, + ⟨5, 0, 7, 3, 7, 2, 151264027014986496130787466392802788314033894195200000⟩, + ⟨5, 0, 8, 3, 8, 2, 342245986324036948970981639045710071235765862400000000⟩, + ⟨5, 0, 6, 4, 5, 2, -121771303811540282273741177559387164436012938035200000⟩, + ⟨5, 0, 7, 4, 6, 2, -49678939632695400910362162126501912405287632896000000⟩, + ⟨5, 0, 8, 4, 7, 2, 121574830808026980025574525384805023404862000332800000⟩, + ⟨5, 0, 6, 5, 4, 2, -137343552624363722408191064974040964070510480588800000⟩, + ⟨5, 0, 7, 5, 5, 2, -131571785440275389625948438870533468040234585292800000⟩, + ⟨5, 0, 8, 5, 6, 2, 253150705882695725978909400489029902577507185459200000⟩, + ⟨5, 0, 6, 6, 3, 2, 508554235436136201715124797294486999273315290316800000⟩, + ⟨5, 0, 7, 6, 4, 2, 47100801935946150274929844345970439373597546905600000⟩, + ⟨5, 0, 8, 6, 5, 2, -265670372235008271268397595345881999804073404006400000⟩, + ⟨5, 0, 6, 7, 2, 2, -501880745599275996257717741215428362945812443955200000⟩, + ⟨5, 0, 7, 7, 3, 2, 1973503049644923086834607355888261216998898689638400000⟩, + ⟨5, 0, 8, 7, 4, 2, 525289237100514802146742350186202297789543612416000000⟩ +] + +def collectedFourData_11_3_39 : List CollectedFourTerm := [ + ⟨5, 1, 5, 0, 8, 3, 3581256654944351350102700642664784227541922611200000⟩, + ⟨5, 1, 5, 1, 7, 3, -28404867887692382165317862097006626143946460364800000⟩, + ⟨5, 1, 6, 1, 8, 3, -15537134146357583147452636352812562092989716889600000⟩, + ⟨5, 1, 5, 2, 6, 3, -19853525715352676477500216674356886459675731558400000⟩, + ⟨5, 1, 6, 2, 7, 3, -20790462598156384421927507939227442862142940774400000⟩, + ⟨5, 1, 7, 2, 8, 3, -48751626095570965614683046332754742136705699020800000⟩, + ⟨5, 1, 5, 3, 5, 3, 7501848465761811420709432496133830449645486080000000⟩, + ⟨5, 1, 6, 3, 6, 3, 55088646992923044971180993050925728953932552601600000⟩, + ⟨5, 1, 7, 3, 7, 3, 27221889873687513836606068749035755337845781299200000⟩, + ⟨5, 1, 8, 3, 8, 3, 41061018640831925726403851012659674143627673600000000⟩, + ⟨5, 1, 5, 4, 4, 3, -27026217966838459657819441893835322629811286835200000⟩, + ⟨5, 1, 6, 4, 5, 3, -43828596759554413012601581583785512525206283878400000⟩, + ⟨5, 1, 7, 4, 6, 3, -8940358460698785869569260360181005082549026816000000⟩, + ⟨5, 1, 8, 4, 7, 3, 14585960372192628786794516808850269845815767859200000⟩, + ⟨5, 1, 5, 5, 3, 3, 70485930149937566229891661637834119313617217126400000⟩, + ⟨5, 1, 6, 5, 4, 3, -49433446116451969197040539681592233846384466329600000⟩, + ⟨5, 1, 7, 5, 5, 3, -23678019978833224791704089996893418333131295948800000⟩, + ⟨5, 1, 8, 5, 6, 3, 30371797679308778768211128439272203169844481228800000⟩, + ⟨5, 1, 5, 6, 2, 3, 1043186451766980367581445189728893243527633305600000⟩, + ⟨5, 1, 6, 6, 3, 3, 183041634749923397263094616532781966258744170905600000⟩, + ⟨5, 1, 7, 6, 4, 3, 8476389717798947493179017328424172680587614617600000⟩, + ⟨5, 1, 8, 6, 5, 3, -31873846714246422347399808833167860453206497689600000⟩, + ⟨5, 1, 5, 7, 1, 3, -48629762943590201441262339078530176164859949875200000⟩, + ⟨5, 1, 6, 7, 2, 3, -180639675619294369516130838225329231198670972518400000⟩, + ⟨5, 1, 7, 7, 3, 3, 355157030676553383115510489863083663747371656806400000⟩, + ⟨5, 1, 8, 7, 4, 3, 63021662834027429998475171946663539729523277824000000⟩ +] + +def collectedFourData_11_3_40 : List CollectedFourTerm := [ + ⟨5, 2, 4, 0, 7, 4, -61374447066043256532230714351577877876261445959680000⟩, + ⟨5, 2, 5, 0, 8, 4, -5785618314904094778671037661190969593003455283200000⟩, + ⟨5, 2, 4, 1, 6, 4, -137511555906136197677391643633510912041897657630720000⟩, + ⟨5, 2, 5, 1, 7, 4, 45888842860947615146732444042126425638560386252800000⟩, + ⟨5, 2, 6, 1, 8, 4, 12550333100837902595612649253176431120611069132800000⟩, + ⟨5, 2, 4, 2, 5, 4, 17449495784278963740020234633540131248364333301760000⟩, + ⟨5, 2, 5, 2, 6, 4, 32073915125736425335388757791707362426337257062400000⟩, + ⟨5, 2, 6, 2, 7, 4, 16793781174152017251427803792055793389382349619200000⟩, + ⟨5, 2, 7, 2, 8, 4, 26253196200508435618189869459391328236097608089600000⟩, + ⟨5, 2, 4, 3, 4, 4, -11972097080585179790864888739655828664393410805760000⟩, + ⟨5, 2, 5, 3, 5, 4, -12119441877817927775343093366046840329213050880000000⟩, + ⟨5, 2, 6, 3, 6, 4, -44498609803001473319977895382420264821602438348800000⟩, + ⟨5, 2, 7, 3, 7, 4, -14659236481703291515209896224977091267993691750400000⟩, + ⟨5, 2, 8, 3, 8, 4, -16583800350432234982983355927379576820754022400000000⟩, + ⟨5, 2, 4, 4, 3, 4, -26759380309289008651945735398651564876155269939200000⟩, + ⟨5, 2, 5, 4, 4, 4, 43661596114775082575873853248298845356118192947200000⟩, + ⟨5, 2, 6, 4, 5, 4, 35403149866197532675349460933437663055447274291200000⟩, + ⟨5, 2, 7, 4, 6, 4, 4814464738293606191921302681679160894755438592000000⟩, + ⟨5, 2, 8, 4, 7, 4, -5891004722693794609961435093271572388084763852800000⟩, + ⟨5, 2, 4, 5, 2, 4, 183346215680704186268312459908465959248105853419520000⟩, + ⟨5, 2, 5, 5, 3, 4, -113871952700040799221497169929785983122832516710400000⟩, + ⟨5, 2, 6, 5, 4, 4, 39930543769504474668018147898146483946696527052800000⟩, + ⟨5, 2, 7, 5, 5, 4, 12750830155393342078908321482539576376537225625600000⟩, + ⟨5, 2, 8, 5, 6, 4, -12266617966864276299522903083774200382592594739200000⟩, + ⟨5, 2, 4, 6, 1, 4, -98384699487302218364132876232929500348409582714880000⟩, + ⟨5, 2, 5, 6, 2, 4, -1685296314317534766004984879453342482218719641600000⟩, + ⟨5, 2, 6, 6, 3, 4, -147854389734543948498366919765169298801437756620800000⟩, + ⟨5, 2, 7, 6, 4, 4, -4564613329965724538821251347684568421211779891200000⟩, + ⟨5, 2, 8, 6, 5, 4, 12873268316429510707527490312893585356107441766400000⟩, + ⟨5, 2, 4, 7, 0, 4, -1877301326587432336284891449426530543295672572968960000⟩, + ⟨5, 2, 5, 7, 1, 4, 78562715338326356890405697550265671366105838387200000⟩, + ⟨5, 2, 6, 7, 2, 4, 145914174319009263688378121533629143991473877811200000⟩, + ⟨5, 2, 7, 7, 3, 4, -191255306849931422524683076787495016112939912396800000⟩, + ⟨5, 2, 8, 7, 4, 4, -25453306050046667638051004941092469100632866816000000⟩ +] + +def collectedFourData_11_3_41 : List CollectedFourTerm := [ + ⟨5, 3, 3, 0, 6, 5, -2657073679998409891887023981594344178335717785600000⟩, + ⟨5, 3, 4, 0, 7, 5, 38118202262034237580870119120025042788762098073600000⟩, + ⟨5, 3, 5, 0, 8, 5, 1796654631373950579473575158106710442279698432000000⟩, + ⟨5, 3, 3, 1, 5, 5, 35621866600049908353589412681239013443515501772800000⟩, + ⟨5, 3, 4, 1, 6, 5, 85405140933598875459576081223388875380652140134400000⟩, + ⟨5, 3, 5, 1, 7, 5, -14250231793225311098857732483383106152513404928000000⟩, + ⟨5, 3, 6, 1, 8, 5, -2598237314620824447002363306502825517516849152000000⟩, + ⟨5, 3, 3, 2, 4, 5, -46387325620029052371299989992103019006691744153600000⟩, + ⟨5, 3, 4, 2, 5, 5, -10837464799640766136356664579994094831775462195200000⟩, + ⟨5, 3, 5, 2, 6, 5, -9960171069097666084514854910608998807921229824000000⟩, + ⟨5, 3, 6, 2, 7, 5, -3476738708819236443466704184174288630110486528000000⟩, + ⟨5, 3, 7, 2, 8, 5, -4076308181314442777657361855627251833632718848000000⟩, + ⟨5, 3, 3, 3, 3, 5, 62003237615219017222075292218029402739312479436800000⟩, + ⟨5, 3, 4, 3, 4, 5, 7435583371160726746449501990518067546224276275200000⟩, + ⟨5, 3, 5, 3, 5, 5, 3763547851637000411976435659734283545529548800000000⟩, + ⟨5, 3, 6, 3, 6, 5, 9212341019952004106407159587156924077118062592000000⟩, + ⟨5, 3, 7, 3, 7, 5, 2276125358063374083656004974631555245751140352000000⟩, + ⟨5, 3, 8, 3, 8, 5, 2059960411050995643334438013528584958351769600000000⟩, + ⟨5, 3, 3, 4, 2, 5, -84879619691174533648466819273173532027671019520000000⟩, + ⟨5, 3, 4, 4, 3, 5, 16619611577739534740916285908316443978690985984000000⟩, + ⟨5, 3, 5, 4, 4, 5, -13558586931099667275881747655273264232185987072000000⟩, + ⟨5, 3, 6, 4, 5, 5, -7329350089626417657822907847964504402331435008000000⟩, + ⟨5, 3, 7, 4, 6, 5, -747537246568707318131588636754962000337960960000000⟩, + ⟨5, 3, 8, 4, 7, 5, 731752448391443445019960132380827298647192371200000⟩, + ⟨5, 3, 3, 5, 1, 5, 70485930149937566229891661637834119313617217126400000⟩, + ⟨5, 3, 4, 5, 2, 5, -113871952700040799221497169929785983122832516710400000⟩, + ⟨5, 3, 5, 5, 3, 5, 35361574176971108766651299005747388747354210304000000⟩, + ⟨5, 3, 6, 5, 4, 5, -8266635473452092184424147568089976907814141952000000⟩, + ⟨5, 3, 7, 5, 5, 5, -1979808968173337410400856768621926597712150528000000⟩, + ⟨5, 3, 8, 5, 6, 5, 1523700650952944349514217596035800166654856396800000⟩, + ⟨5, 3, 3, 6, 0, 5, 38386673572785091995113715529041537041823065702400000⟩, + ⟨5, 3, 4, 6, 1, 5, 61104385519121818015675167583453669593928276377600000⟩, + ⟨5, 3, 5, 6, 2, 5, 523348631650313047227124745829053987045769216000000⟩, + ⟨5, 3, 6, 6, 3, 5, 30609609279066417005262797655197600755400835072000000⟩, + ⟨5, 3, 7, 6, 4, 5, 708743061963476083904350681486338408113504256000000⟩, + ⟨5, 3, 8, 6, 5, 5, -1599055857663573816950451887112228574357723545600000⟩, + ⟨5, 3, 4, 7, 0, 5, 1165946987622422117647822711455888983166391890739200000⟩, + ⟨5, 3, 5, 7, 1, 5, -24396712448573809164141231506259747315721961472000000⟩, + ⟨5, 3, 6, 7, 2, 5, -30207935470846282754765541232654742221706231808000000⟩, + ⟨5, 3, 7, 7, 3, 5, 29696025050735770222121911068440653575103709184000000⟩, + ⟨5, 3, 8, 7, 4, 5, 3161688013935499144438767294726407831855038464000000⟩ +] + +def collectedFourData_11_3_42 : List CollectedFourTerm := [ + ⟨5, 4, 2, 0, 5, 6, 11609639976980399229642424020811873833248096256000000⟩, + ⟨5, 4, 3, 0, 6, 6, 1863468472477276107508667124594789777888667238400000⟩, + ⟨5, 4, 4, 0, 7, 6, -13366597373177717109299870093970090535310013235200000⟩, + ⟨5, 4, 5, 0, 8, 6, -420012096603162678055881169208557894543343616000000⟩, + ⟨5, 4, 2, 1, 4, 6, -40013141211341941107161113068353243152642788556800000⟩, + ⟨5, 4, 3, 1, 5, 6, -24982455638950903492394564157014822016567685939200000⟩, + ⟨5, 4, 4, 1, 6, 6, -29948320348673060747397979892816777652428655820800000⟩, + ⟨5, 4, 5, 1, 7, 6, 3331341276189799042989651360781175432165720064000000⟩, + ⟨5, 4, 6, 1, 8, 6, 455551285259506342210277857461639570083807232000000⟩, + ⟨5, 4, 2, 2, 3, 6, 14912652016543228973338226748378061483816884633600000⟩, + ⟨5, 4, 3, 2, 4, 6, 32532526089194968526913012358356899679080703590400000⟩, + ⟨5, 4, 4, 2, 5, 6, 3800284901343969009464414614041813648436258406400000⟩, + ⟨5, 4, 5, 2, 6, 6, 2328434335795923845343540525771305417768435712000000⟩, + ⟨5, 4, 6, 2, 7, 6, 609579724839421555666783340758630246958235648000000⟩, + ⟨5, 4, 7, 2, 8, 6, 571762223769812356498118571669945116141184614400000⟩, + ⟨5, 4, 2, 3, 2, 6, 7974230311960685188897994408664862904756994048000000⟩, + ⟨5, 4, 3, 3, 3, 6, -43484333670245423778329492178517382352858198835200000⟩, + ⟨5, 4, 4, 3, 4, 6, -2607375040244011344365444129350726006694372966400000⟩, + ⟨5, 4, 5, 3, 5, 6, -879821639745839033965994301889875022341734400000000⟩, + ⟨5, 4, 6, 3, 6, 6, -1615208036722563362465991007875879472591798272000000⟩, + ⟨5, 4, 7, 3, 7, 6, -319260084963822841690213579998848083427957145600000⟩, + ⟨5, 4, 8, 3, 8, 6, -240783141082433079758635915628278471616102400000000⟩, + ⟨5, 4, 2, 4, 1, 6, 18408010882646132213762527110232514531045041766400000⟩, + ⟨5, 4, 3, 4, 2, 6, 59528080248967650260866915650698991270918881280000000⟩, + ⟨5, 4, 4, 4, 3, 6, -5827862891621898381814208843007253208459378688000000⟩, + ⟨5, 4, 5, 4, 4, 6, 3169652321855796401514138056993905390110375936000000⟩, + ⟨5, 4, 6, 4, 5, 6, 1285061543323057265779802912674442343327203328000000⟩, + ⟨5, 4, 7, 4, 6, 6, 104853102228169417961835917967211141936447488000000⟩, + ⟨5, 4, 8, 4, 7, 6, -85532543282498534913287758418753242375441612800000⟩, + ⟨5, 4, 2, 5, 0, 6, -137343552624363722408191064974040964070510480588800000⟩, + ⟨5, 4, 3, 5, 1, 6, -49433446116451969197040539681592233846384466329600000⟩, + ⟨5, 4, 4, 5, 2, 6, 39930543769504474668018147898146483946696527052800000⟩, + ⟨5, 4, 5, 5, 3, 6, -8266635473452092184424147568089976907814141952000000⟩, + ⟨5, 4, 6, 5, 4, 6, 1449396632675373644366952548008839492541612032000000⟩, + ⟨5, 4, 7, 5, 5, 6, 277697349643762159977719925844300815336367718400000⟩, + ⟨5, 4, 8, 5, 6, 6, -178101203711295758246797363294058721301443379200000⟩, + ⟨5, 4, 3, 6, 0, 6, -26921480011877000855813258066160960637945616793600000⟩, + ⟨5, 4, 4, 6, 1, 6, -21426973742227702673524616901845545514668602163200000⟩, + ⟨5, 4, 5, 6, 2, 6, -122345581724712167601402298225825339888631808000000⟩, + ⟨5, 4, 6, 6, 3, 6, -5366810325562959933326331776909541545399549952000000⟩, + ⟨5, 4, 7, 6, 4, 6, -99411646805122589152291159276122682516360396800000⟩, + ⟨5, 4, 8, 6, 5, 6, 186909267823287195020840078764979158532908646400000⟩, + ⟨5, 4, 4, 7, 0, 6, -408853068014195364256328630278705809969417447014400000⟩, + ⟨5, 4, 5, 7, 1, 6, 5703330048421087245364899781293334123706843136000000⟩, + ⟨5, 4, 6, 7, 2, 6, 5296384495497292365743159021736984287146672128000000⟩, + ⟨5, 4, 7, 7, 3, 6, -4165304624896561233457476313109007402894832435200000⟩, + ⟨5, 4, 8, 7, 4, 6, -369561068763288447086811939603242577366614016000000⟩ +] + +def collectedFourData_11_3_43 : List CollectedFourTerm := [ + ⟨5, 5, 1, 0, 4, 7, -451587185162138497882361548596735511105634304000000⟩, + ⟨5, 5, 2, 0, 5, 7, 11121752939272239996170006319957081689985908736000000⟩, + ⟨5, 5, 3, 0, 6, 7, 892578753609453434283711565982128685150581555200000⟩, + ⟨5, 5, 4, 0, 7, 7, -4268291808013886093021215759597512797161154150400000⟩, + ⟨5, 5, 5, 0, 8, 7, -100590345161183268188878893629370474612916224000000⟩, + ⟨5, 5, 1, 1, 3, 7, 1823820857051568608261566743734723670972982886400000⟩, + ⟨5, 5, 2, 1, 4, 7, -38331616808026428627912343478420792291980266700800000⟩, + ⟨5, 5, 3, 1, 5, 7, -11966292666424588410381945068518840876209379737600000⟩, + ⟨5, 5, 4, 1, 6, 7, -9563254345082998267018155137863442574754814361600000⟩, + ⟨5, 5, 5, 1, 7, 7, 797835994562413151153958079736747183409463296000000⟩, + ⟨5, 5, 6, 1, 8, 7, 87281411927847506134237820385147440782009958400000⟩, + ⟨5, 5, 1, 2, 2, 7, 318399524368776595667954304575450848719116697600000⟩, + ⟨5, 5, 2, 2, 3, 7, 14285958197342106052166579978570789048603482521600000⟩, + ⟨5, 5, 3, 2, 4, 7, 15582684664290595226932803555578220951394005811200000⟩, + ⟨5, 5, 4, 2, 5, 7, 1213526858007624506135945427644150146990394572800000⟩, + ⟨5, 5, 5, 2, 6, 7, 557645875957132685184619077170784280057479168000000⟩, + ⟨5, 5, 6, 2, 7, 7, 116792512255266916065774512012942811885836697600000⟩, + ⟨5, 5, 7, 2, 8, 7, 91289052393605199727711887290922531673237094400000⟩, + ⟨5, 5, 1, 3, 1, 7, -1786864552024879023862479621839385424602071040000000⟩, + ⟨5, 5, 2, 3, 2, 7, 7639118834548875554306707911144070315285413888000000⟩, + ⟨5, 5, 3, 3, 3, 7, -20828467410198459317951445711207888677508848025600000⟩, + ⟨5, 5, 4, 3, 4, 7, -832600639787777261094868955276210174094527692800000⟩, + ⟨5, 5, 5, 3, 5, 7, -210711936961021741295010140371785719847321600000000⟩, + ⟨5, 5, 6, 3, 6, 7, -309466008688886702669882529830567050924680806400000⟩, + ⟨5, 5, 7, 3, 7, 7, -50973900358941574679550534166490381440096665600000⟩, + ⟨5, 5, 8, 3, 8, 7, -32952056743614480024281978038964096021299200000000⟩, + ⟨5, 5, 1, 4, 0, 7, 14297602796618526023202848904040620552025748275200000⟩, + ⟨5, 5, 2, 4, 1, 7, 17634427040473474814316606659992165588505355878400000⟩, + ⟨5, 5, 3, 4, 2, 7, 28513227059190291322467455466828008462839971840000000⟩, + ⟨5, 5, 4, 4, 3, 7, -1860983670268523042494699103671362338030616576000000⟩, + ⟨5, 5, 5, 4, 4, 7, 759112472414490197753985770471379796129480704000000⟩, + ⟨5, 5, 6, 4, 5, 7, 246211545318156127376354456937642638435785113600000⟩, + ⟨5, 5, 7, 4, 6, 7, 16741120600498082584634071556165318725337088000000⟩, + ⟨5, 5, 8, 4, 7, 7, -11705442528078149636825939155469666229839462400000⟩, + ⟨5, 5, 2, 5, 0, 7, -131571785440275389625948438870533468040234585292800000⟩, + ⟨5, 5, 3, 5, 1, 7, -23678019978833224791704089996893418333131295948800000⟩, + ⟨5, 5, 4, 5, 2, 7, 12750830155393342078908321482539576376537225625600000⟩, + ⟨5, 5, 5, 5, 3, 7, -1979808968173337410400856768621926597712150528000000⟩, + ⟨5, 5, 6, 5, 4, 7, 277697349643762159977719925844300815336367718400000⟩, + ⟨5, 5, 7, 5, 5, 7, 44337885308422788360411461096077059128976998400000⟩, + ⟨5, 5, 8, 5, 6, 7, -24373803516382618991159162902219344055998873600000⟩, + ⟨5, 5, 3, 6, 0, 7, -12895061778200281872500198061244575704815553740800000⟩, + ⟨5, 5, 4, 6, 1, 7, -6842173362534421322491820431913286843578607206400000⟩, + ⟨5, 5, 5, 6, 2, 7, -29301023456622708546248192195302300279898112000000⟩, + ⟨5, 5, 6, 6, 3, 7, -1028254771572529872581098034596509728576530022400000⟩, + ⟨5, 5, 7, 6, 4, 7, -15872323592649632215262453219153869691210956800000⟩, + ⟨5, 5, 8, 6, 5, 7, 25579219423472102324821341131736551429190451200000⟩, + ⟨5, 5, 4, 7, 0, 7, -130557100821198801447941460959952197344327158988800000⟩, + ⟨5, 5, 5, 7, 1, 7, 1365912893410949691481973156797568562971541504000000⟩, + ⟨5, 5, 6, 7, 2, 7, 1014761524855378069026528865829597330594699673600000⟩, + ⟨5, 5, 7, 7, 3, 7, -665043432968375001516099473110311891302036275200000⟩, + ⟨5, 5, 8, 7, 4, 7, -50575788875308240953523004517967260788195328000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1111.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1111.lean new file mode 100644 index 0000000000000000000000000000000000000000..78f03db2592c81b8b1666bdcbcd95984a8b27b30 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1111.lean @@ -0,0 +1,651 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1108 +import OAI.Analysis.LaughlinFock.Sparse1109 +import OAI.Analysis.LaughlinFock.Sparse1110 + +namespace OAI + +/-! Sparse1111. -/ +namespace LaughlinFock +def collectedFourData_11_3_44 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 3, 8, -62787741534275616650945660052133779629588191641600000⟩, + ⟨5, 6, 1, 0, 4, 8, 1737752730326340074918559730196198436070490112000000⟩, + ⟨5, 6, 2, 0, 5, 8, -21398809766154226907566169336231476025050005504000000⟩, + ⟨5, 6, 3, 0, 6, 8, -1144910822007498517987803553528041500925178675200000⟩, + ⟨5, 6, 4, 0, 7, 8, 4106203622974036760335489410806589605578329292800000⟩, + ⟨5, 6, 5, 0, 8, 8, 77416345145203500641676552585402623348598374400000⟩, + ⟨5, 6, 0, 1, 2, 8, 24559571482936422267620414842482468066324538982400000⟩, + ⟨5, 6, 1, 1, 3, 8, -7018245375651129630569951771491668193747088179200000⟩, + ⟨5, 6, 2, 1, 4, 8, 73751950846495891938227258146077424244994814771200000⟩, + ⟨5, 6, 3, 1, 5, 8, 15349164337260306553611420273846028507417254297600000⟩, + ⟨5, 6, 4, 1, 6, 8, 9200090201301029075952945291888437483747357491200000⟩, + ⟨5, 6, 5, 1, 7, 8, -614030567499684251537231177152407532069296537600000⟩, + ⟨5, 6, 6, 1, 8, 8, -55977936216937422009802189373312887275336499200000⟩, + ⟨5, 6, 0, 2, 1, 8, 25372780797367928357162235300478567070526603264000000⟩, + ⟨5, 6, 1, 2, 2, 8, -1225233268317372865304312888365043867989101772800000⟩, + ⟨5, 6, 2, 2, 3, 8, -27486899184092032100291829055135422736385861222400000⟩, + ⟨5, 6, 3, 2, 4, 8, -19987910574760102681322850789977595252825076531200000⟩, + ⟨5, 6, 4, 2, 5, 8, -1167443231404996758543307608512011957561825689600000⟩, + ⟨5, 6, 5, 2, 6, 8, -429175439578428948590928441815341401239243980800000⟩, + ⟨5, 6, 6, 2, 7, 8, -74904881317064251881010506187165984797543628800000⟩, + ⟨5, 6, 7, 2, 8, 8, -50184202759345417840484153949922234243586457600000⟩, + ⟨5, 6, 0, 3, 0, 8, -141776857556475525939154281259800021259609807257600000⟩, + ⟨5, 6, 1, 3, 1, 8, 6876033811476993683584417592985921342532485120000000⟩, + ⟨5, 6, 2, 3, 2, 8, -14698047296513118286100303580725578600946860032000000⟩, + ⟨5, 6, 3, 3, 3, 8, 26716676424723434659987624025500103982569855385600000⟩, + ⟨5, 6, 4, 3, 4, 8, 800982668796938405299827381974162864298629529600000⟩, + ⟨5, 6, 5, 3, 5, 8, 162168128679248814324355852548123957091368960000000⟩, + ⟨5, 6, 6, 3, 6, 8, 198476034164264468080256721260480513843606323200000⟩, + ⟨5, 6, 7, 3, 7, 8, 28021810764540130553961492219911131892180582400000⟩, + ⟨5, 6, 8, 3, 8, 8, 15850351952393459566510838036551504704307200000000⟩, + ⟨5, 6, 1, 4, 0, 8, -55018607952802568310602377806134875941152332185600000⟩, + ⟨5, 6, 2, 4, 1, 8, -33929520969822093672641345031784751723663956377600000⟩, + ⟨5, 6, 3, 4, 2, 8, -36573918097884530361941550923177221735411875840000000⟩, + ⟨5, 6, 4, 4, 3, 8, 1790312901007556670649103059382004211758661632000000⟩, + ⟨5, 6, 5, 4, 4, 8, -584228168958970554112042137616215262921909862400000⟩, + ⟨5, 6, 6, 4, 5, 8, -157907782141365695698905386379589107923602636800000⟩, + ⟨5, 6, 7, 4, 6, 8, -9203072751940429898504542116759324906749952000000⟩, + ⟨5, 6, 8, 4, 7, 8, 5630464443300838131228176722767126261556838400000⟩, + ⟨5, 6, 2, 5, 0, 8, 253150705882695725978909400489029902577507185459200000⟩, + ⟨5, 6, 3, 5, 1, 8, 30371797679308778768211128439272203169844481228800000⟩, + ⟨5, 6, 4, 5, 2, 8, -12266617966864276299522903083774200382592594739200000⟩, + ⟨5, 6, 5, 5, 3, 8, 1523700650952944349514217596035800166654856396800000⟩, + ⟨5, 6, 6, 5, 4, 8, -178101203711295758246797363294058721301443379200000⟩, + ⟨5, 6, 7, 5, 5, 8, -24373803516382618991159162902219344055998873600000⟩, + ⟨5, 6, 8, 5, 6, 8, 11724104724601578017964586339687788149578137600000⟩, + ⟨5, 6, 3, 6, 0, 8, 16540496533907633621014210860405793741456854220800000⟩, + ⟨5, 6, 4, 6, 1, 8, 6582342143877123898479109433659444923858734284800000⟩, + ⟨5, 6, 5, 6, 2, 8, 22550654751117705037715822639186080376763187200000⟩, + ⟨5, 6, 6, 6, 3, 8, 659471229285694068576001157082652953218855731200000⟩, + ⟨5, 6, 7, 6, 4, 8, 8725470191114270872093392010703648689697587200000⟩, + ⟨5, 6, 8, 6, 5, 8, -12303924871338985489380401403397913495941939200000⟩, + ⟨5, 6, 4, 7, 0, 8, 125599200923998546404643898224167774540248226201600000⟩, + ⟨5, 6, 5, 7, 1, 8, -1051233931299711926729669210220575209042634342400000⟩, + ⟨5, 6, 6, 7, 2, 8, -650817335089796734022020504209053787207027916800000⟩, + ⟨5, 6, 7, 7, 3, 8, 365593393827297202963063159425516978968513740800000⟩, + ⟨5, 6, 8, 7, 4, 8, 24327587809793562809600744556855422298882048000000⟩ +] + +def collectedFourData_11_3_45 : List CollectedFourTerm := [ + ⟨6, 0, 5, 0, 8, 3, 1950354204041596789510755352650894153434215219200000⟩, + ⟨6, 0, 5, 1, 7, 3, -15469305564436803732799529802202147110033083596800000⟩, + ⟨6, 0, 6, 1, 8, 3, -8461531194439799586113345679234360064746297753600000⟩, + ⟨6, 0, 5, 2, 6, 3, -10812240248273333934776033167663879953091815014400000⟩, + ⟨6, 0, 6, 2, 7, 3, -11322496553354108922398400212201258392475821670400000⟩, + ⟨6, 0, 7, 2, 8, 3, -26550160480145294216903243896498252397708889292800000⟩, + ⟨6, 0, 5, 3, 5, 3, 4085510507347009711171572817956253149199073280000000⟩, + ⟨6, 0, 6, 3, 6, 3, 30001305298595099433454133491513724638357723545600000⟩, + ⟨6, 0, 7, 3, 7, 3, 14825055133594944515232221752949560187643179827200000⟩, + ⟨6, 0, 8, 3, 8, 3, 22361851730959317632441192564167340644211097600000000⟩, + ⟨6, 0, 5, 4, 4, 3, -14718492113150988475348976354854646405307511603200000⟩, + ⟨6, 0, 6, 4, 5, 3, -23869076188444566356839754317590159188195436134400000⟩, + ⟨6, 0, 7, 4, 6, 3, -4868923785562552774528804244563421050234208256000000⟩, + ⟨6, 0, 8, 4, 7, 3, 7943521471049684826580670020805030163562836787200000⟩, + ⟨6, 0, 5, 5, 3, 3, 38386673572785091995113715529041537041823065702400000⟩, + ⟨6, 0, 6, 5, 4, 3, -26921480011877000855813258066160960637945616793600000⟩, + ⟨6, 0, 7, 5, 5, 3, -12895061778200281872500198061244575704815553740800000⟩, + ⟨6, 0, 8, 5, 6, 3, 16540496533907633621014210860405793741456854220800000⟩, + ⟨6, 0, 5, 6, 2, 3, 568119874623892796523180876962408240030259609600000⟩, + ⟨6, 0, 6, 6, 3, 3, 99684567805628787724071912598978600966699981209600000⟩, + ⟨6, 0, 7, 6, 4, 3, 4616246171125378149144710316821336824250735001600000⟩, + ⟨6, 0, 8, 6, 5, 3, -17358513205771319965339644408334582403231750553600000⟩, + ⟨6, 0, 5, 7, 1, 3, -26483793745313457187385121774678501126625768243200000⟩, + ⟨6, 0, 6, 7, 2, 3, -98376459635863664405184642782507664043560822374400000⟩, + ⟨6, 0, 7, 7, 3, 3, 193418700365587100536448756157700915868469716582400000⟩, + ⟨6, 0, 8, 7, 4, 3, 34321629778848509686562652273821733849592233984000000⟩ +] + +def collectedFourData_11_3_46 : List CollectedFourTerm := [ + ⟨6, 1, 4, 0, 7, 4, 32933903262599434081860699114889533147752347729920000⟩, + ⟨6, 1, 5, 0, 8, 4, 3104598134991541935885642951809935593240841420800000⟩, + ⟨6, 1, 4, 1, 6, 4, 73789541025582223370834884515283399087763415367680000⟩, + ⟨6, 1, 5, 1, 7, 4, -24624233436902671326671146322420552200380166963200000⟩, + ⟨6, 1, 6, 1, 8, 4, -6734585418123948558246923558896038433776677683200000⟩, + ⟨6, 1, 4, 2, 5, 4, -9363506045474977606191978018783814453934099005440000⟩, + ⟨6, 1, 5, 2, 6, 4, -17211058811937707952991267352455044545847597465600000⟩, + ⟨6, 1, 6, 2, 7, 4, -9011645579594837816608773924440496906536013004800000⟩, + ⟨6, 1, 7, 2, 8, 4, -14087625474999313170991384855036030660370654822400000⟩, + ⟨6, 1, 4, 3, 4, 4, 6424300436925479602426039904770192009890040381440000⟩, + ⟨6, 1, 5, 3, 5, 4, 6503366555323073750559656409627599599011102720000000⟩, + ⟨6, 1, 6, 3, 6, 4, 23878225884384971896495904074994191211164807987200000⟩, + ⟨6, 1, 7, 3, 7, 4, 7866235856633834095277418450338969676905290137600000⟩, + ⟨6, 1, 8, 3, 8, 4, 8898968586709725575344337286205995677751705600000000⟩, + ⟨6, 1, 4, 4, 3, 4, 14359246960300936070366759966700162023083003084800000⟩, + ⟨6, 1, 5, 4, 4, 4, -23429079225550613557699797153498154723995077836800000⟩, + ⟨6, 1, 6, 4, 5, 4, -18997546513616648988565134644065670202301140172800000⟩, + ⟨6, 1, 7, 4, 6, 4, -2583471192523117590232265034943204618716315648000000⟩, + ⟨6, 1, 8, 4, 7, 4, 3161149125269369093012768864495732986398061363200000⟩, + ⟨6, 1, 4, 5, 2, 4, -98384699487302218364132876232929500348409582714880000⟩, + ⟨6, 1, 5, 5, 3, 4, 61104385519121818015675167583453669593928276377600000⟩, + ⟨6, 1, 6, 5, 4, 4, -21426973742227702673524616901845545514668602163200000⟩, + ⟨6, 1, 7, 5, 5, 4, -6842173362534421322491820431913286843578607206400000⟩, + ⟨6, 1, 8, 5, 6, 4, 6582342143877123898479109433659444923858734284800000⟩, + ⟨6, 1, 4, 6, 1, 4, 52793830825849247756446787305250010016770655518720000⟩, + ⟨6, 1, 5, 6, 2, 4, 904340298574478092675568302916302816705668710400000⟩, + ⟨6, 1, 6, 6, 3, 4, 79339568847411394539264126611987262726697333555200000⟩, + ⟨6, 1, 7, 6, 4, 4, 2449399400348107895631118215230280679883066572800000⟩, + ⟨6, 1, 8, 6, 5, 4, -6907874427781927937062643880083503656648415641600000⟩, + ⟨6, 1, 4, 7, 0, 4, 1007371361212427678794095964056729716097615648522240000⟩, + ⟨6, 1, 5, 7, 1, 4, -42157233029168899107415015588492329853005909196800000⟩, + ⟨6, 1, 6, 7, 2, 4, -78298437401696474099639925775371180602339151052800000⟩, + ⟨6, 1, 7, 7, 3, 4, 102628766129273220839979759829725585740775240499200000⟩, + ⟨6, 1, 8, 7, 4, 4, 13658399533335570054418341262227677242095304704000000⟩ +] + +def collectedFourData_11_3_47 : List CollectedFourTerm := [ + ⟨6, 2, 3, 0, 6, 5, -39324490127671663061870520023181106098890342400000⟩, + ⟨6, 2, 4, 0, 7, 5, 564146519466804580702003119118192689036027494400000⟩, + ⟨6, 2, 5, 0, 8, 5, 26590353081342769574417128426546659462217728000000⟩, + ⟨6, 2, 3, 1, 5, 5, 527200939886521279018426224445954897636176691200000⟩, + ⟨6, 2, 4, 1, 6, 5, 1263989646496263475553661686742104430521981337600000⟩, + ⟨6, 2, 5, 1, 7, 5, -210902356110071047657072553202910164745715712000000⟩, + ⟨6, 2, 6, 1, 8, 5, -38453716356189222916581367175977051889860608000000⟩, + ⟨6, 2, 3, 2, 4, 5, -686528921695169150068306006749001079413171814400000⟩, + ⟨6, 2, 4, 2, 5, 5, -160393661918595162603545484533439617901055180800000⟩, + ⟨6, 2, 5, 2, 6, 5, -147409780852176625085058436076567814834487296000000⟩, + ⟨6, 2, 6, 2, 7, 5, -51455470753651742196617096039996149425242112000000⟩, + ⟨6, 2, 7, 2, 8, 5, -60329053740633555274419051728979545284411392000000⟩, + ⟨6, 2, 3, 3, 3, 5, 917643241825653741027727460991819739936535347200000⟩, + ⟨6, 2, 4, 3, 4, 5, 110046073269923236497782503601963094130871500800000⟩, + ⟨6, 2, 5, 3, 5, 5, 55700224442706341865901864812487329919795200000000⟩, + ⟨6, 2, 6, 3, 6, 5, 136341952509222131588594886920133032036794368000000⟩, + ⟨6, 2, 7, 3, 7, 5, 33686483685525742918518619335592091905425408000000⟩, + ⟨6, 2, 8, 3, 8, 5, 30487258768005942998296190743758240114278400000000⟩, + ⟨6, 2, 3, 4, 2, 5, -1256211971731290400495408851141688224204718080000000⟩, + ⟨6, 2, 4, 4, 3, 5, 245968998275933064602046870452513937278631936000000⟩, + ⟨6, 2, 5, 4, 4, 5, -200666064298798811553098248397731956195852288000000⟩, + ⟨6, 2, 6, 4, 5, 5, -108473828712922994721485045099933594164396032000000⟩, + ⟨6, 2, 7, 4, 6, 5, -11063494886892101865947660550573534310563840000000⟩, + ⟨6, 2, 8, 4, 7, 5, 10829881064000493413764336663622084958407884800000⟩, + ⟨6, 2, 3, 5, 1, 5, 1043186451766980367581445189728893243527633305600000⟩, + ⟨6, 2, 4, 5, 2, 5, -1685296314317534766004984879453342482218719641600000⟩, + ⟨6, 2, 5, 5, 3, 5, 523348631650313047227124745829053987045769216000000⟩, + ⟨6, 2, 6, 5, 4, 5, -122345581724712167601402298225825339888631808000000⟩, + ⟨6, 2, 7, 5, 5, 5, -29301023456622708546248192195302300279898112000000⟩, + ⟨6, 2, 8, 5, 6, 5, 22550654751117705037715822639186080376763187200000⟩, + ⟨6, 2, 3, 6, 0, 5, 568119874623892796523180876962408240030259609600000⟩, + ⟨6, 2, 4, 6, 1, 5, 904340298574478092675568302916302816705668710400000⟩, + ⟨6, 2, 5, 6, 2, 5, 7745520289326536590868502556176998794788864000000⟩, + ⟨6, 2, 6, 6, 3, 5, 453019909446867351388280263668725474591244288000000⟩, + ⟨6, 2, 7, 6, 4, 5, 10489343879713256661357642677128033179009024000000⟩, + ⟨6, 2, 8, 6, 5, 5, -23665906128852393718717079005418455619233382400000⟩, + ⟨6, 2, 4, 7, 0, 5, 17255927507502875149205508066924206198931377356800000⟩, + ⟨6, 2, 5, 7, 1, 5, -361069504791511563893762597175819302640549888000000⟩, + ⟨6, 2, 6, 7, 2, 5, -447075167370348644154387654882275537801183232000000⟩, + ⟨6, 2, 7, 7, 3, 5, 439498931749400356904500125059274153431924736000000⟩, + ⟨6, 2, 8, 7, 4, 5, 46792744223358822738643990766622224318201856000000⟩ +] + +def collectedFourData_11_3_48 : List CollectedFourTerm := [ + ⟨6, 3, 2, 0, 5, 6, -42988050544534406435103160768086869008623599616000000⟩, + ⟨6, 3, 3, 0, 6, 6, -6900031098452271468689211150177573205088560742400000⟩, + ⟨6, 3, 4, 0, 7, 6, 49493693570681743386382595011563963225428144947200000⟩, + ⟨6, 3, 5, 0, 8, 6, 1555216292141107152195124314210141920953368576000000⟩, + ⟨6, 3, 2, 1, 4, 6, 148160230657397592889282668424860018631984860364800000⟩, + ⟨6, 3, 3, 1, 5, 6, 92504769128347898316599416060939703769996931891200000⟩, + ⟨6, 3, 4, 1, 6, 6, 110892319781264771665506406267199798410486795468800000⟩, + ⟨6, 3, 5, 1, 7, 6, -12335254792215217347841704330013413609679355904000000⟩, + ⟨6, 3, 6, 1, 8, 6, -1686810419202746403774183166516953013291057152000000⟩, + ⟨6, 3, 2, 2, 3, 6, -55218408142829491620026164476919418893505239449600000⟩, + ⟨6, 3, 3, 2, 4, 6, -120461089115309667689484608662257769073328154214400000⟩, + ⟨6, 3, 4, 2, 5, 6, -14071654224121450142529918163419102108252005990400000⟩, + ⟨6, 3, 5, 2, 6, 6, -8621701716443636882729062526556111980495634432000000⟩, + ⟨6, 3, 6, 2, 7, 6, -2257145275329727068641106957085351263262998528000000⟩, + ⟨6, 3, 7, 2, 8, 6, -2117115037469484683567837337593017355624408678400000⟩, + ⟨6, 3, 2, 3, 2, 6, -29526894579334210866110782198088001706606460928000000⟩, + ⟨6, 3, 3, 3, 3, 6, 161013324910881997388674736443023806530120266547200000⟩, + ⟨6, 3, 4, 3, 4, 6, 9654560368866831104991670068449643042670274150400000⟩, + ⟨6, 3, 5, 3, 5, 6, 3257794143019283166071865869437691985552998400000000⟩, + ⟨6, 3, 6, 3, 6, 6, 5980775016300487583796874168191842940818030592000000⟩, + ⟨6, 3, 7, 3, 7, 6, 1182152822696470467813034259615813556200118681600000⟩, + ⟨6, 3, 8, 3, 8, 6, 891569235535896033330047785501836513273446400000000⟩, + ⟨6, 3, 2, 4, 1, 6, -68160985510021845474906688165998520027075470950400000⟩, + ⟨6, 3, 3, 4, 2, 6, -220419937882285808540719856507347476007700398080000000⟩, + ⟨6, 3, 4, 4, 3, 6, 21579348287148145132966444821360057273148243968000000⟩, + ⟨6, 3, 5, 4, 4, 6, -11736554664116080858056996922177200352810500096000000⟩, + ⟨6, 3, 6, 4, 5, 6, -4758312117063356132985817932267313507501867008000000⟩, + ⟨6, 3, 7, 4, 6, 6, -388248943746155420586619542630475817463840768000000⟩, + ⟨6, 3, 8, 4, 7, 6, 316708985043561921565803390766852508924824780800000⟩, + ⟨6, 3, 2, 5, 0, 6, 508554235436136201715124797294486999273315290316800000⟩, + ⟨6, 3, 3, 5, 1, 6, 183041634749923397263094616532781966258744170905600000⟩, + ⟨6, 3, 4, 5, 2, 6, -147854389734543948498366919765169298801437756620800000⟩, + ⟨6, 3, 5, 5, 3, 6, 30609609279066417005262797655197600755400835072000000⟩, + ⟨6, 3, 6, 5, 4, 6, -5366810325562959933326331776909541545399549952000000⟩, + ⟨6, 3, 7, 5, 5, 6, -1028254771572529872581098034596509728576530022400000⟩, + ⟨6, 3, 8, 5, 6, 6, 659471229285694068576001157082652953218855731200000⟩, + ⟨6, 3, 3, 6, 0, 6, 99684567805628787724071912598978600966699981209600000⟩, + ⟨6, 3, 4, 6, 1, 6, 79339568847411394539264126611987262726697333555200000⟩, + ⟨6, 3, 5, 6, 2, 6, 453019909446867351388280263668725474591244288000000⟩, + ⟨6, 3, 6, 6, 3, 6, 19872167784330870180203353292809344469614723072000000⟩, + ⟨6, 3, 7, 6, 4, 6, 368100380894458055200564560415295858482662604800000⟩, + ⟨6, 3, 8, 6, 5, 6, -692085634727771345676684244355213610136790630400000⟩, + ⟨6, 3, 4, 7, 0, 6, 1513896760617167524199268085201258921756247615078400000⟩, + ⟨6, 3, 5, 7, 1, 6, -21118229409337479211960624555203346286348599296000000⟩, + ⟨6, 3, 6, 7, 2, 6, -19611395775163783535461405969797362493903863808000000⟩, + ⟨6, 3, 7, 7, 3, 6, 15423245346408092854641512419635919033631716147200000⟩, + ⟨6, 3, 8, 7, 4, 6, 1368406766686010643645940322637526486248062976000000⟩ +] + +def collectedFourData_11_3_49 : List CollectedFourTerm := [ + ⟨6, 4, 1, 0, 4, 7, 161661700447080332894015412167433112894046208000000⟩, + ⟨6, 4, 2, 0, 5, 7, -3981427177721000796379930356027100142996815872000000⟩, + ⟨6, 4, 3, 0, 6, 7, -319530322897961814333684895485169783600997990400000⟩, + ⟨6, 4, 4, 0, 7, 7, 1527986918938194111950449740060915885880954060800000⟩, + ⟨6, 4, 5, 0, 8, 7, 36009893065227340711750671104993443392258048000000⟩, + ⟨6, 4, 1, 1, 3, 7, -652901567514471265091428755511696913777609932800000⟩, + ⟨6, 4, 2, 1, 4, 7, 13722166079284439180947518599343942918158784921600000⟩, + ⟨6, 4, 3, 1, 5, 7, 4283760221865161088159607851075032184861700915200000⟩, + ⟨6, 4, 4, 1, 6, 7, 3423507154391382407342932750729859412863955763200000⟩, + ⟨6, 4, 5, 1, 7, 7, -285613781340004718426028270347275660261588992000000⟩, + ⟨6, 4, 6, 1, 8, 7, -31245486881147461201917812634788888383900876800000⟩, + ⟨6, 4, 1, 2, 2, 7, -113982438435486328893687351902761550605398835200000⟩, + ⟨6, 4, 2, 2, 3, 7, -5114167032594221937380516237265611734534796083200000⟩, + ⟨6, 4, 3, 2, 4, 7, -5578376409098918947174398295887759471880332902400000⟩, + ⟨6, 4, 4, 2, 5, 7, -434425116233708329187797741143891996778797465600000⟩, + ⟨6, 4, 5, 2, 6, 7, -199629182396227929065772029720359921344577536000000⟩, + ⟨6, 4, 6, 2, 7, 7, -41810035251318972994120911544156261706838835200000⟩, + ⟨6, 4, 7, 2, 8, 7, -32680164378123601730895102944391738256313548800000⟩, + ⟨6, 4, 1, 3, 1, 7, 639671743221050368079189097698437976115118080000000⟩, + ⟨6, 4, 2, 3, 2, 7, -2734694387457187268533950711216895264844414976000000⟩, + ⟨6, 4, 3, 3, 3, 7, 7456290988483932717218217480261029831797584691200000⟩, + ⟨6, 4, 4, 3, 4, 7, 298059023028060993759103302910514745767991705600000⟩, + ⟨6, 4, 5, 3, 5, 7, 75431834987492762751019363080582980645683200000000⟩, + ⟨6, 4, 6, 3, 6, 7, 110784368642467014480231724128688911955053772800000⟩, + ⟨6, 4, 7, 3, 7, 7, 18247921290077890401841830949897649448497971200000⟩, + ⟨6, 4, 8, 3, 8, 7, 11796361148930196517099399836686140991078400000000⟩, + ⟨6, 4, 1, 4, 0, 7, -5118335631221251186301590582316965060936099430400000⟩, + ⟨6, 4, 2, 4, 1, 7, -6312870593857433973964383061240372919435840716800000⟩, + ⟨6, 4, 3, 4, 2, 7, -10207324129375827975400586180774613676122439680000000⟩, + ⟨6, 4, 4, 4, 3, 7, 666205318762180022197714636431062276927127552000000⟩, + ⟨6, 4, 5, 4, 4, 7, -271751318800272191615641173986416216409899008000000⟩, + ⟨6, 4, 6, 4, 5, 7, -88140182878629700719367276070461840899126067200000⟩, + ⟨6, 4, 7, 4, 6, 7, -5993079769733628948988222533731501658341376000000⟩, + ⟨6, 4, 8, 4, 7, 7, 4190379633769418602727609677893091013217484800000⟩, + ⟨6, 4, 2, 5, 0, 7, 47100801935946150274929844345970439373597546905600000⟩, + ⟨6, 4, 3, 5, 1, 7, 8476389717798947493179017328424172680587614617600000⟩, + ⟨6, 4, 4, 5, 2, 7, -4564613329965724538821251347684568421211779891200000⟩, + ⟨6, 4, 5, 5, 3, 7, 708743061963476083904350681486338408113504256000000⟩, + ⟨6, 4, 6, 5, 4, 7, -99411646805122589152291159276122682516360396800000⟩, + ⟨6, 4, 7, 5, 5, 7, -15872323592649632215262453219153869691210956800000⟩, + ⟨6, 4, 8, 5, 6, 7, 8725470191114270872093392010703648689697587200000⟩, + ⟨6, 4, 3, 6, 0, 7, 4616246171125378149144710316821336824250735001600000⟩, + ⟨6, 4, 4, 6, 1, 7, 2449399400348107895631118215230280679883066572800000⟩, + ⟨6, 4, 5, 6, 2, 7, 10489343879713256661357642677128033179009024000000⟩, + ⟨6, 4, 6, 6, 3, 7, 368100380894458055200564560415295858482662604800000⟩, + ⟨6, 4, 7, 6, 4, 7, 5682062968887767728061131941175305661159833600000⟩, + ⟨6, 4, 8, 6, 5, 7, -9156991703878366299148763348258357617518182400000⟩, + ⟨6, 4, 4, 7, 0, 7, 46737559473965030006463857515750050962895116697600000⟩, + ⟨6, 4, 5, 7, 1, 7, -488977119517073322557867172446747625529540608000000⟩, + ⟨6, 4, 6, 7, 2, 7, -363269993140953594837544215985522536818619187200000⟩, + ⟨6, 4, 7, 7, 3, 7, 238075959144478623735717603034702911635875430400000⟩, + ⟨6, 4, 8, 7, 4, 7, 18105403119663982311476484508121823870713856000000⟩ +] + +def collectedFourData_11_3_50 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 3, 8, 65892933646157854939917283685909050594444915507200000⟩, + ⟨6, 5, 1, 0, 4, 8, -1823693965649567695952698667026697669421563904000000⟩, + ⟨6, 5, 2, 0, 5, 8, 22457096203376328442906148839836042439654637568000000⟩, + ⟨6, 5, 3, 0, 6, 8, 1201532830801452979275519288502991598280664678400000⟩, + ⟨6, 5, 4, 0, 7, 8, -4309277515875261188986452941269293712914618777600000⟩, + ⟨6, 5, 5, 0, 8, 8, -81245000522852483278654828890046713146690764800000⟩, + ⟨6, 5, 0, 1, 2, 8, -25774174616868081084513565981299759812172369100800000⟩, + ⟨6, 5, 1, 1, 3, 8, 7365335422962819582084891104125955025001670246400000⟩, + ⟨6, 5, 2, 1, 4, 8, -77399382182745622346537634591992037887317534310400000⟩, + ⟨6, 5, 3, 1, 5, 8, -16108263213241158415793485835729987451244196659200000⟩, + ⟨6, 5, 4, 1, 6, 8, -9655084230765997621254113509954801370000680550400000⟩, + ⟨6, 5, 5, 1, 7, 8, 644397687387469067782684535407708299433554739200000⟩, + ⟨6, 5, 6, 1, 8, 8, 58746346765442215216621462826553013233411686400000⟩, + ⟨6, 5, 0, 2, 1, 8, -26627601513374957620807165502812411238692159488000000⟩, + ⟨6, 5, 1, 2, 2, 8, 1285827654849302672078015626829439173675030937600000⟩, + ⟨6, 5, 2, 2, 3, 8, 28846274444945322775754445759028292214399487180800000⟩, + ⟨6, 5, 3, 2, 4, 8, 20976420445207837470669355996339173440671344230400000⟩, + ⟨6, 5, 4, 2, 5, 8, 1225179589245645593338354314110665092899222323200000⟩, + ⟨6, 5, 5, 2, 6, 8, 450400477412685631994839270057468321179736473600000⟩, + ⟨6, 5, 6, 2, 7, 8, 78609331276938200400445140512126397494958489600000⟩, + ⟨6, 5, 7, 2, 8, 8, 52666081972413629693541542108131278705603379200000⟩, + ⟨6, 5, 0, 3, 0, 8, 148788487039779867887319887745645098807160156979200000⟩, + ⟨6, 5, 1, 3, 1, 8, -7216090730720987540976197464762876112708567040000000⟩, + ⟨6, 5, 2, 3, 2, 8, 15424944926686513331561591210340310117508972544000000⟩, + ⟨6, 5, 3, 3, 3, 8, -28037960020255749826178548143108896689818383155200000⟩, + ⟨6, 5, 4, 3, 4, 8, -840595577369941938284495292745952526507127603200000⟩, + ⟨6, 5, 5, 3, 5, 8, -170188216385359628141352085111535502171832320000000⟩, + ⟨6, 5, 6, 3, 6, 8, -208291743419360133109051876897881743126062694400000⟩, + ⟨6, 5, 7, 3, 7, 8, -29407640285087650883738207733370508479876300800000⟩, + ⟨6, 5, 8, 3, 8, 8, -16634237256282933810867579419120466552422400000000⟩, + ⟨6, 5, 1, 4, 0, 8, 57739574549897338951436046461905953077765288755200000⟩, + ⟨6, 5, 2, 4, 1, 8, 35607518590072857967116203631762136228041012019200000⟩, + ⟨6, 5, 3, 4, 2, 8, 38382695403820612213958977395786090338876129280000000⟩, + ⟨6, 5, 4, 4, 3, 8, -1878853519959026476301783166197635528727199744000000⟩, + ⟨6, 5, 5, 4, 4, 8, 613121399667077256881451387839492509087354060800000⟩, + ⟨6, 5, 6, 4, 5, 8, 165717172756929022778689405431147732775049625600000⟩, + ⟨6, 5, 7, 4, 6, 8, 9658214284604151037848797127416708736221184000000⟩, + ⟨6, 5, 8, 4, 7, 8, -5908921246306356366785128195104619514088652800000⟩, + ⟨6, 5, 2, 5, 0, 8, -265670372235008271268397595345881999804073404006400000⟩, + ⟨6, 5, 3, 5, 1, 8, -31873846714246422347399808833167860453206497689600000⟩, + ⟨6, 5, 4, 5, 2, 8, 12873268316429510707527490312893585356107441766400000⟩, + ⟨6, 5, 5, 5, 3, 8, -1599055857663573816950451887112228574357723545600000⟩, + ⟨6, 5, 6, 5, 4, 8, 186909267823287195020840078764979158532908646400000⟩, + ⟨6, 5, 7, 5, 5, 8, 25579219423472102324821341131736551429190451200000⟩, + ⟨6, 5, 8, 5, 6, 8, -12303924871338985489380401403397913495941939200000⟩, + ⟨6, 5, 3, 6, 0, 8, -17358513205771319965339644408334582403231750553600000⟩, + ⟨6, 5, 4, 6, 1, 8, -6907874427781927937062643880083503656648415641600000⟩, + ⟨6, 5, 5, 6, 2, 8, -23665906128852393718717079005418455619233382400000⟩, + ⟨6, 5, 6, 6, 3, 8, -692085634727771345676684244355213610136790630400000⟩, + ⟨6, 5, 7, 6, 4, 8, -9156991703878366299148763348258357617518182400000⟩, + ⟨6, 5, 8, 6, 5, 8, 12912420248335734880321302941397897483544166400000⟩, + ⟨6, 5, 4, 7, 0, 8, -131810758123503925454070151767773069364205663027200000⟩, + ⟨6, 5, 5, 7, 1, 8, 1103223113128028828524403294191326474388950220800000⟩, + ⟨6, 5, 6, 7, 2, 8, 683003758837716489114228213180777300351359385600000⟩, + ⟨6, 5, 7, 7, 3, 8, -383673956926529836003387781953045939904682393600000⟩, + ⟨6, 5, 8, 7, 4, 8, -25530718101187392233615287030020807711522816000000⟩ +] + +def collectedFourData_11_3_51 : List CollectedFourTerm := [ + ⟨7, 0, 4, 0, 7, 4, 628419465697098731255525434860159315812092099952640000⟩, + ⟨7, 0, 5, 0, 8, 4, 59239558871577393936573517365437051136737122713600000⟩, + ⟨7, 0, 4, 1, 6, 4, 1407995389298126466623597920441734233139209369026560000⟩, + ⟨7, 0, 5, 1, 7, 4, -469860723651061027632227313959186500398753408614400000⟩, + ⟨7, 0, 6, 1, 8, 4, -128504190238363074471474229889953159717453194854400000⟩, + ⟨7, 0, 4, 2, 5, 4, -178667235985696084176847912678336546835251310100480000⟩, + ⟨7, 0, 5, 2, 6, 4, -328408214976506911611607654651765890858609750835200000⟩, + ⟨7, 0, 6, 2, 7, 4, -171953304624288506427286108280962608468298668441600000⟩, + ⟨7, 0, 7, 2, 8, 4, -268809257237162151016926275150902900050677779660800000⟩, + ⟨7, 0, 4, 3, 4, 4, 122583570366985401466256178404280944575566556692480000⟩, + ⟨7, 0, 5, 3, 5, 4, 124092249355988964571242267018450855990122250240000000⟩, + ⟨7, 0, 6, 3, 6, 4, 455625980085406589630530542622537053142507742822400000⟩, + ⟨7, 0, 7, 3, 7, 4, 150097475378417239735623624880727832787963556659200000⟩, + ⟨7, 0, 8, 3, 8, 4, 169803288724240915005074537417728026817540915200000000⟩, + ⟨7, 0, 4, 4, 3, 4, 273992129953586887453153492424482744295312955801600000⟩, + ⟨7, 0, 5, 4, 4, 4, -447055708255985824512833381831641344582841112985600000⟩, + ⟨7, 0, 6, 4, 5, 4, -362496602192924195824515900363770696749261887897600000⟩, + ⟨7, 0, 7, 4, 6, 4, -49295814513820941684171459303816385163339759616000000⟩, + ⟨7, 0, 8, 4, 7, 4, 60318621465879464371881112957511725592015693414400000⟩, + ⟨7, 0, 4, 5, 2, 4, -1877301326587432336284891449426530543295672572968960000⟩, + ⟨7, 0, 5, 5, 3, 4, 1165946987622422117647822711455888983166391890739200000⟩, + ⟨7, 0, 6, 5, 4, 4, -408853068014195364256328630278705809969417447014400000⟩, + ⟨7, 0, 7, 5, 5, 4, -130557100821198801447941460959952197344327158988800000⟩, + ⟨7, 0, 8, 5, 6, 4, 125599200923998546404643898224167774540248226201600000⟩, + ⟨7, 0, 4, 6, 1, 4, 1007371361212427678794095964056729716097615648522240000⟩, + ⟨7, 0, 5, 6, 2, 4, 17255927507502875149205508066924206198931377356800000⟩, + ⟨7, 0, 6, 6, 3, 4, 1513896760617167524199268085201258921756247615078400000⟩, + ⟨7, 0, 7, 6, 4, 4, 46737559473965030006463857515750050962895116697600000⟩, + ⟨7, 0, 8, 6, 5, 4, -131810758123503925454070151767773069364205663027200000⟩, + ⟨7, 0, 4, 7, 0, 4, 19221887169705217092348377750122764618862963017646080000⟩, + ⟨7, 0, 5, 7, 1, 4, -804411965512264845056472603343390314911587998105600000⟩, + ⟨7, 0, 6, 7, 2, 4, -1494030689425429356916638133889326097781162088857600000⟩, + ⟨7, 0, 7, 7, 3, 4, 1958283348981330324671663475134649390790131213926400000⟩, + ⟨7, 0, 8, 7, 4, 4, 260619097243889196417629487263688618836930592768000000⟩ +] + +def collectedFourData_11_3_52 : List CollectedFourTerm := [ + ⟨7, 1, 3, 0, 6, 5, 1833172420469079590352203595404265546507406540800000⟩, + ⟨7, 1, 4, 0, 7, 5, -26298569599569804063504939394642764432476523724800000⟩, + ⟨7, 1, 5, 0, 8, 5, -1239550767498753721784299038562770223707979776000000⟩, + ⟨7, 1, 3, 1, 5, 5, -24576293803369138101516098464892463311413995110400000⟩, + ⟨7, 1, 4, 1, 6, 5, -58922848133380332929823389138355284943966516019200000⟩, + ⟨7, 1, 5, 1, 7, 5, 9831542160565118111172794289989839050667720704000000⟩, + ⟨7, 1, 6, 1, 8, 5, 1792579943435888697297188028325098696512372736000000⟩, + ⟨7, 1, 3, 2, 4, 5, 32003616093177700407154151429631879429493673164800000⟩, + ⟨7, 1, 4, 2, 5, 5, 7477000629699437306109225190503840081975548313600000⟩, + ⟨7, 1, 5, 2, 6, 5, 6871736769841774023300770893220382882851192832000000⟩, + ⟨7, 1, 6, 2, 7, 5, 2398676996487548037685259742517999428125589504000000⟩, + ⟨7, 1, 7, 2, 8, 5, 2812332902760370850113216093393941862771851264000000⟩, + ⟨7, 1, 3, 3, 3, 5, -42777370470237975702618538072196396497221609062400000⟩, + ⟨7, 1, 4, 3, 4, 5, -5129969284900863293448651879917607237329721753600000⟩, + ⟨7, 1, 5, 3, 5, 5, -2596552807952519137883423530188099339839078400000000⟩, + ⟨7, 1, 6, 3, 6, 5, -6355792695120938912369619836579890068933574656000000⟩, + ⟨7, 1, 7, 3, 7, 5, -1570347959614948636231408681708403381382414336000000⟩, + ⟨7, 1, 8, 3, 8, 5, -1421211101981595667291363592886525878914252800000000⟩, + ⟨7, 1, 3, 4, 2, 5, 58560279697572589293257230060145636351001231360000000⟩, + ⟨7, 1, 4, 4, 3, 5, -11466228359628685255020200706883181570489843712000000⟩, + ⟨7, 1, 5, 4, 4, 5, 9354361457767057920186703214360782461569335296000000⟩, + ⟨7, 1, 6, 4, 5, 5, 5056676653495647946760444544833064059371782144000000⟩, + ⟨7, 1, 7, 4, 6, 5, 515742063909935851566029530060222220237537280000000⟩, + ⟨7, 1, 8, 4, 7, 5, -504851791314541339726897330944877307637635481600000⟩, + ⟨7, 1, 3, 5, 1, 5, -48629762943590201441262339078530176164859949875200000⟩, + ⟨7, 1, 4, 5, 2, 5, 78562715338326356890405697550265671366105838387200000⟩, + ⟨7, 1, 5, 5, 3, 5, -24396712448573809164141231506259747315721961472000000⟩, + ⟨7, 1, 6, 5, 4, 5, 5703330048421087245364899781293334123706843136000000⟩, + ⟨7, 1, 7, 5, 5, 5, 1365912893410949691481973156797568562971541504000000⟩, + ⟨7, 1, 8, 5, 6, 5, -1051233931299711926729669210220575209042634342400000⟩, + ⟨7, 1, 3, 6, 0, 5, -26483793745313457187385121774678501126625768243200000⟩, + ⟨7, 1, 4, 6, 1, 5, -42157233029168899107415015588492329853005909196800000⟩, + ⟨7, 1, 5, 6, 2, 5, -361069504791511563893762597175819302640549888000000⟩, + ⟨7, 1, 6, 6, 3, 5, -21118229409337479211960624555203346286348599296000000⟩, + ⟨7, 1, 7, 6, 4, 5, -488977119517073322557867172446747625529540608000000⟩, + ⟨7, 1, 8, 6, 5, 5, 1103223113128028828524403294191326474388950220800000⟩, + ⟨7, 1, 4, 7, 0, 5, -804411965512264845056472603343390314911587998105600000⟩, + ⟨7, 1, 5, 7, 1, 5, 16831817930945347208291415662407053498170474496000000⟩, + ⟨7, 1, 6, 7, 2, 5, 20841105988637163126512966527984403752937324544000000⟩, + ⟨7, 1, 7, 7, 3, 5, -20487927952603968424765163475278815675979661312000000⟩, + ⟨7, 1, 8, 7, 4, 5, -2181316729341763883019373910290280208087908352000000⟩ +] + +def collectedFourData_11_3_53 : List CollectedFourTerm := [ + ⟨7, 2, 2, 0, 5, 6, 42423940960097744392811153226807061875234177024000000⟩, + ⟨7, 2, 3, 0, 6, 6, 6809485618342268193213729008422786601460537753600000⟩, + ⟨7, 2, 4, 0, 7, 6, -48844213853441051662660839187042220409598299340800000⟩, + ⟨7, 2, 5, 0, 8, 6, -1534808006462742289889671319732005537226686464000000⟩, + ⟨7, 2, 2, 1, 4, 6, -146216001852241623424209163678016873434801451827200000⟩, + ⟨7, 2, 3, 1, 5, 6, -91290877681529630484814718421149651727649918156800000⟩, + ⟨7, 2, 4, 1, 6, 6, -109437138175292175650923248183878375876007768883200000⟩, + ⟨7, 2, 5, 1, 7, 6, 12173385729379996950658338689295320228095328256000000⟩, + ⟨7, 2, 6, 1, 8, 6, 1664675292986354751850214991843500538281852928000000⟩, + ⟨7, 2, 2, 2, 3, 6, 54493806006279107370347592539063952281440773734400000⟩, + ⟨7, 2, 3, 2, 4, 6, 118880341580567951577519282298703252445139147161600000⟩, + ⟨7, 2, 4, 2, 5, 6, 13886999304529735834899884517395833960693078425600000⟩, + ⟨7, 2, 5, 2, 6, 6, 8508563658057822444238397731828711350859726848000000⟩, + ⟨7, 2, 6, 2, 7, 6, 2227525944675029243823768812088744216826478592000000⟩, + ⟨7, 2, 7, 2, 8, 6, 2089333249999167233864608859867301927020239257600000⟩, + ⟨7, 2, 2, 3, 2, 6, 29139428666833764111700276834800199234530312192000000⟩, + ⟨7, 2, 3, 3, 3, 6, -158900431707917456271439450108893674753890241740800000⟩, + ⟨7, 2, 4, 3, 4, 6, -9527868649456154545701342137138686312207456665600000⟩, + ⟨7, 2, 5, 3, 5, 6, -3215043823409071038264465158676538004707737600000000⟩, + ⟨7, 2, 6, 3, 6, 6, -5902292450417225112615850654418476589371097088000000⟩, + ⟨7, 2, 7, 3, 7, 6, -1166640052773091854050956095059772208528647782400000⟩, + ⟨7, 2, 8, 3, 8, 6, -879869641239717557310274227730350226381209600000000⟩, + ⟨7, 2, 2, 4, 1, 6, 67266544735811384890089356719676435510691731865600000⟩, + ⟨7, 2, 3, 4, 2, 6, 217527482932938492956983245605362085743684485120000000⟩, + ⟨7, 2, 4, 4, 3, 6, -21296173845867861224029551954480470511952330752000000⟩, + ⟨7, 2, 5, 4, 4, 6, 11582542028268967281490022445330656081681055744000000⟩, + ⟨7, 2, 6, 4, 5, 6, 4695871289043118783457149689608483592116109312000000⟩, + ⟨7, 2, 7, 4, 6, 6, 383154156996341692495274922298060431742205952000000⟩, + ⟨7, 2, 8, 4, 7, 6, -312552979556520924157286948314488438271456051200000⟩, + ⟨7, 2, 2, 5, 0, 6, -501880745599275996257717741215428362945812443955200000⟩, + ⟨7, 2, 3, 5, 1, 6, -180639675619294369516130838225329231198670972518400000⟩, + ⟨7, 2, 4, 5, 2, 6, 145914174319009263688378121533629143991473877811200000⟩, + ⟨7, 2, 5, 5, 3, 6, -30207935470846282754765541232654742221706231808000000⟩, + ⟨7, 2, 6, 5, 4, 6, 5296384495497292365743159021736984287146672128000000⟩, + ⟨7, 2, 7, 5, 5, 6, 1014761524855378069026528865829597330594699673600000⟩, + ⟨7, 2, 8, 5, 6, 6, -650817335089796734022020504209053787207027916800000⟩, + ⟨7, 2, 3, 6, 0, 6, -98376459635863664405184642782507664043560822374400000⟩, + ⟨7, 2, 4, 6, 1, 6, -78298437401696474099639925775371180602339151052800000⟩, + ⟨7, 2, 5, 6, 2, 6, -447075167370348644154387654882275537801183232000000⟩, + ⟨7, 2, 6, 6, 3, 6, -19611395775163783535461405969797362493903863808000000⟩, + ⟨7, 2, 7, 6, 4, 6, -363269993140953594837544215985522536818619187200000⟩, + ⟨7, 2, 8, 6, 5, 6, 683003758837716489114228213180777300351359385600000⟩, + ⟨7, 2, 4, 7, 0, 6, -1494030689425429356916638133889326097781162088857600000⟩, + ⟨7, 2, 5, 7, 1, 6, 20841105988637163126512966527984403752937324544000000⟩, + ⟨7, 2, 6, 7, 2, 6, 19354045739960637476776794620914229150075584512000000⟩, + ⟨7, 2, 7, 7, 3, 6, -15220854207177120244873531226480209191271976140800000⟩, + ⟨7, 2, 8, 7, 4, 6, -1350449884186864451549845334345150962612568064000000⟩ +] + +def collectedFourData_11_3_54 : List CollectedFourTerm := [ + ⟨7, 3, 1, 0, 4, 7, 6773554710957348848321948303121094404275699712000000⟩, + ⟨7, 3, 2, 0, 5, 7, -166820061532222771938409911992246476392426897408000000⟩, + ⟨7, 3, 3, 0, 6, 7, -13388181108905941336107093910632121538430212505600000⟩, + ⟨7, 3, 4, 0, 7, 7, 64021985197681572000526495211095376538989966131200000⟩, + ⟨7, 3, 5, 0, 8, 7, 1508798807252965591332369794229960113727209472000000⟩, + ⟨7, 3, 1, 1, 3, 7, -27356290798616028394830284224880998817358623539200000⟩, + ⟨7, 3, 2, 1, 4, 7, 574952771335611155451410642257515506918891087462400000⟩, + ⟨7, 3, 3, 1, 5, 7, 179487684165025149442489347606901648598103805132800000⟩, + ⟨7, 3, 4, 1, 6, 7, 143443455991698640209219149538636492705517849804800000⟩, + ⟨7, 3, 5, 1, 7, 7, -11967092816416499742428223203868505888247513088000000⟩, + ⟨7, 3, 6, 1, 8, 7, -1309172266991175114252110006045778673732367155200000⟩, + ⟨7, 3, 1, 2, 2, 7, -4775814436541999139278775644581655077981048012800000⟩, + ⟨7, 3, 2, 2, 3, 7, -214281367203551443905147224741013818456538926284800000⟩, + ⟨7, 3, 3, 2, 4, 7, -233731537530834748825373639863911391679588440473600000⟩, + ⟨7, 3, 4, 2, 5, 7, -18202222817681448740825079488655292897635493478400000⟩, + ⟨7, 3, 5, 2, 6, 7, -8364375638292716816642324770203023930875183104000000⟩, + ⟨7, 3, 6, 2, 7, 7, -1751822234076835668254331738213867877305208012800000⟩, + ⟨7, 3, 7, 2, 8, 7, -1369284628122303760440844083928507980524499763200000⟩, + ⟨7, 3, 1, 3, 1, 7, 26801966933284834934801583858367049946491781120000000⟩, + ⟨7, 3, 2, 3, 2, 7, -114582501606513288592200836105171542183734411264000000⟩, + ⟨7, 3, 3, 3, 3, 7, 312415339017463109923320616661138691060700859596800000⟩, + ⟨7, 3, 4, 3, 4, 7, 12488543012919482482832121626768769073868596838400000⟩, + ⟨7, 3, 5, 3, 5, 7, 3160560972838120115691392963255246284180684800000000⟩, + ⟨7, 3, 6, 3, 6, 7, 4641816707626810065744421240047067317570581299200000⟩, + ⟨7, 3, 7, 3, 7, 7, 764579939947169571728605300274967207694093516800000⟩, + ⟨7, 3, 8, 3, 8, 7, 494262385039346890448146364292741587376537600000000⟩, + ⟨7, 3, 1, 4, 0, 7, -214456029667141249982071994847294135666365536665600000⟩, + ⟨7, 3, 2, 4, 1, 7, -264506523390707098993387849197408952454820868915200000⟩, + ⟨7, 3, 3, 4, 2, 7, -427682427263809900481106680411618176306532843520000000⟩, + ⟨7, 3, 4, 4, 3, 7, 27913712171075369268887177652190782046945148928000000⟩, + ⟨7, 3, 5, 4, 4, 7, -11386261684603603701511292533350298443854118912000000⟩, + ⟨7, 3, 6, 4, 5, 7, -3693035204449174180581099858094284245933280460800000⟩, + ⟨7, 3, 7, 4, 6, 7, -251107427394102707052767216787285723907620864000000⟩, + ⟨7, 3, 8, 4, 7, 7, 175575078268522544960892093025420109390492467200000⟩, + ⟨7, 3, 2, 5, 0, 7, 1973503049644923086834607355888261216998898689638400000⟩, + ⟨7, 3, 3, 5, 1, 7, 355157030676553383115510489863083663747371656806400000⟩, + ⟨7, 3, 4, 5, 2, 7, -191255306849931422524683076787495016112939912396800000⟩, + ⟨7, 3, 5, 5, 3, 7, 29696025050735770222121911068440653575103709184000000⟩, + ⟨7, 3, 6, 5, 4, 7, -4165304624896561233457476313109007402894832435200000⟩, + ⟨7, 3, 7, 5, 5, 7, -665043432968375001516099473110311891302036275200000⟩, + ⟨7, 3, 8, 5, 6, 7, 365593393827297202963063159425516978968513740800000⟩, + ⟨7, 3, 3, 6, 0, 7, 193418700365587100536448756157700915868469716582400000⟩, + ⟨7, 3, 4, 6, 1, 7, 102628766129273220839979759829725585740775240499200000⟩, + ⟨7, 3, 5, 6, 2, 7, 439498931749400356904500125059274153431924736000000⟩, + ⟨7, 3, 6, 6, 3, 7, 15423245346408092854641512419635919033631716147200000⟩, + ⟨7, 3, 7, 6, 4, 7, 238075959144478623735717603034702911635875430400000⟩, + ⟨7, 3, 8, 6, 5, 7, -383673956926529836003387781953045939904682393600000⟩, + ⟨7, 3, 4, 7, 0, 7, 1958283348981330324671663475134649390790131213926400000⟩, + ⟨7, 3, 5, 7, 1, 7, -20487927952603968424765163475278815675979661312000000⟩, + ⟨7, 3, 6, 7, 2, 7, -15220854207177120244873531226480209191271976140800000⟩, + ⟨7, 3, 7, 7, 3, 7, 9975278808580025616141128639309841016444000665600000⟩, + ⟨7, 3, 8, 7, 4, 7, 758608490791714495325032522427496315784003584000000⟩ +] + +def collectedFourData_11_3_55 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 3, 8, -130284941275600969045107244457989411887768403968000000⟩, + ⟨7, 4, 1, 0, 4, 8, 3605847365898482298970123243479165705136373760000000⟩, + ⟨7, 4, 2, 0, 5, 8, -44402658952611497277290798716354903112857681920000000⟩, + ⟨7, 4, 3, 0, 6, 8, -2375696840913102500925681089565338205312516096000000⟩, + ⟨7, 4, 4, 0, 7, 8, 8520397211496936116188535742437427641050988544000000⟩, + ⟨7, 4, 5, 0, 8, 8, 160639381741553490794448359114290844990963712000000⟩, + ⟨7, 4, 0, 1, 2, 8, 50961258523075995984521619583782251530448535552000000⟩, + ⟨7, 4, 1, 1, 3, 8, -14562901360694954486668975236873908367724118016000000⟩, + ⟨7, 4, 2, 1, 4, 8, 153035741534855685953185359100905738986298802176000000⟩, + ⟨7, 4, 3, 1, 5, 8, 31849608306389595834851530566169140099545038848000000⟩, + ⟨7, 4, 4, 1, 6, 8, 19090242495064209908654862704817041496946507776000000⟩, + ⟨7, 4, 5, 1, 7, 8, -1274117120209669425291781812894160180947714048000000⟩, + ⟨7, 4, 6, 1, 8, 8, -116154554289419053537492736277281247766511616000000⟩, + ⟨7, 4, 0, 2, 1, 8, 52648672740987359011434158333796025979602206720000000⟩, + ⟨7, 4, 1, 2, 2, 8, -2542366400048015630112363092357054761946578944000000⟩, + ⟨7, 4, 2, 2, 3, 8, -57035481107293344927874469863794051501105610752000000⟩, + ⟨7, 4, 3, 2, 4, 8, -41475034645624276873899224893250608119442046976000000⟩, + ⟨7, 4, 4, 2, 5, 8, -2422451725917977300702690316044145717053227008000000⟩, + ⟨7, 4, 5, 2, 6, 8, -890541618094066727412562720599957041036918784000000⟩, + ⟨7, 4, 6, 2, 7, 8, -155428079194761018238660458750865717617229824000000⟩, + ⟨7, 4, 7, 2, 8, 8, -104132522522648205945061945836707191506075648000000⟩, + ⟨7, 4, 0, 3, 0, 8, -294187832045227937384982317694364274789500059648000000⟩, + ⟨7, 4, 1, 3, 1, 8, 14267811509803849033097699294229991404444057600000000⟩, + ⟨7, 4, 2, 3, 2, 8, -30498536531161278560457335362325937833493135360000000⟩, + ⟨7, 4, 3, 3, 3, 8, 55437264249649417963441706333348708652404441088000000⟩, + ⟨7, 4, 4, 3, 4, 8, 1662043854691216800710029168531557566757470208000000⟩, + ⟨7, 4, 5, 3, 5, 8, 336499842253703193235731544877477229546700800000000⟩, + ⟨7, 4, 6, 3, 6, 8, 411838964483048548761549778379108176034267136000000⟩, + ⟨7, 4, 7, 3, 7, 8, 58145425853566395215827618426582199332503552000000⟩, + ⟨7, 4, 8, 3, 8, 8, 32889575621825457129532490604509141139456000000000⟩, + ⟨7, 4, 1, 4, 0, 8, -114163942372145294319787379703507099556761305088000000⟩, + ⟨7, 4, 2, 4, 1, 8, -70403960057225564762921966053069200540982837248000000⟩, + ⟨7, 4, 3, 4, 2, 8, -75891100000790939131421594161307494764458803200000000⟩, + ⟨7, 4, 4, 4, 3, 8, 3714910036147573479921549444263694661173903360000000⟩, + ⟨7, 4, 5, 4, 4, 8, -1212276964012470795409991763778953406895357952000000⟩, + ⟨7, 4, 6, 4, 5, 8, -327659597566787560646333645956582856315633664000000⟩, + ⟨7, 4, 7, 4, 6, 8, -19096431305577384952405342288713157139496960000000⟩, + ⟨7, 4, 8, 4, 7, 8, 11683247580251926765458525254413673595666432000000⟩, + ⟨7, 4, 2, 5, 0, 8, 525289237100514802146742350186202297789543612416000000⟩, + ⟨7, 4, 3, 5, 1, 8, 63021662834027429998475171946663539729523277824000000⟩, + ⟨7, 4, 4, 5, 2, 8, -25453306050046667638051004941092469100632866816000000⟩, + ⟨7, 4, 5, 5, 3, 8, 3161688013935499144438767294726407831855038464000000⟩, + ⟨7, 4, 6, 5, 4, 8, -369561068763288447086811939603242577366614016000000⟩, + ⟨7, 4, 7, 5, 5, 8, -50575788875308240953523004517967260788195328000000⟩, + ⟨7, 4, 8, 5, 6, 8, 24327587809793562809600744556855422298882048000000⟩, + ⟨7, 4, 3, 6, 0, 8, 34321629778848509686562652273821733849592233984000000⟩, + ⟨7, 4, 4, 6, 1, 8, 13658399533335570054418341262227677242095304704000000⟩, + ⟨7, 4, 5, 6, 2, 8, 46792744223358822738643990766622224318201856000000⟩, + ⟨7, 4, 6, 6, 3, 8, 1368406766686010643645940322637526486248062976000000⟩, + ⟨7, 4, 7, 6, 4, 8, 18105403119663982311476484508121823870713856000000⟩, + ⟨7, 4, 8, 6, 5, 8, -25530718101187392233615287030020807711522816000000⟩, + ⟨7, 4, 4, 7, 0, 8, 260619097243889196417629487263688618836930592768000000⟩, + ⟨7, 4, 5, 7, 1, 8, -2181316729341763883019373910290280208087908352000000⟩, + ⟨7, 4, 6, 7, 2, 8, -1350449884186864451549845334345150962612568064000000⟩, + ⟨7, 4, 7, 7, 3, 8, 758608490791714495325032522427496315784003584000000⟩, + ⟨7, 4, 8, 7, 4, 8, 50479891006204625707511424826067957883863040000000⟩ +] + +def collectedFourData_11_3 : List (List CollectedFourTerm) := [ + collectedFourData_11_3_0, + collectedFourData_11_3_1, + collectedFourData_11_3_2, + collectedFourData_11_3_3, + collectedFourData_11_3_4, + collectedFourData_11_3_5, + collectedFourData_11_3_6, + collectedFourData_11_3_7, + collectedFourData_11_3_8, + collectedFourData_11_3_9, + collectedFourData_11_3_10, + collectedFourData_11_3_11, + collectedFourData_11_3_12, + collectedFourData_11_3_13, + collectedFourData_11_3_14, + collectedFourData_11_3_15, + collectedFourData_11_3_16, + collectedFourData_11_3_17, + collectedFourData_11_3_18, + collectedFourData_11_3_19, + collectedFourData_11_3_20, + collectedFourData_11_3_21, + collectedFourData_11_3_22, + collectedFourData_11_3_23, + collectedFourData_11_3_24, + collectedFourData_11_3_25, + collectedFourData_11_3_26, + collectedFourData_11_3_27, + collectedFourData_11_3_28, + collectedFourData_11_3_29, + collectedFourData_11_3_30, + collectedFourData_11_3_31, + collectedFourData_11_3_32, + collectedFourData_11_3_33, + collectedFourData_11_3_34, + collectedFourData_11_3_35, + collectedFourData_11_3_36, + collectedFourData_11_3_37, + collectedFourData_11_3_38, + collectedFourData_11_3_39, + collectedFourData_11_3_40, + collectedFourData_11_3_41, + collectedFourData_11_3_42, + collectedFourData_11_3_43, + collectedFourData_11_3_44, + collectedFourData_11_3_45, + collectedFourData_11_3_46, + collectedFourData_11_3_47, + collectedFourData_11_3_48, + collectedFourData_11_3_49, + collectedFourData_11_3_50, + collectedFourData_11_3_51, + collectedFourData_11_3_52, + collectedFourData_11_3_53, + collectedFourData_11_3_54, + collectedFourData_11_3_55 +] + +theorem collectedFourChecked_11_3 : collectNumericRowParts 11 3 = collectedFourData_11_3 := by + decide +kernel +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1112.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1112.lean new file mode 100644 index 0000000000000000000000000000000000000000..e34cc631c6093b7a0fca36857939841b996be1a5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1112.lean @@ -0,0 +1,634 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1112. -/ +namespace LaughlinFock +def collectedFourData_11_4_0 : List CollectedFourTerm := [ + ⟨0, 4, 7, 3, 8, 0, -5627721229070855875447475083812689295729229824000000⟩, + ⟨0, 4, 7, 4, 7, 0, -14885788875873215619758674354679717233466277888000000⟩, + ⟨0, 4, 8, 4, 8, 0, 15944821315269898563409065010842689621584773120000000⟩, + ⟨0, 4, 7, 5, 6, 0, 4715789059724708735847109524234139484175728640000000⟩, + ⟨0, 4, 8, 5, 7, 0, -26141570226225136425661656494358843480984256512000000⟩, + ⟨0, 4, 7, 6, 5, 0, 29462801208193070475604046074007697413684330496000000⟩, + ⟨0, 4, 8, 6, 6, 0, 39048617904700548378576521949428717109664284672000000⟩, + ⟨0, 4, 7, 7, 4, 0, 22909965838390926595435501683292694034430033920000000⟩, + ⟨0, 4, 8, 7, 5, 0, 100866713154367199640915316038494688896373227520000000⟩ +] + +def collectedFourData_11_4_1 : List CollectedFourTerm := [ + ⟨0, 5, 6, 2, 8, 1, -54972582611330638325610604320008643660517421875200000⟩, + ⟨0, 5, 6, 3, 7, 1, -116556581094916281596952323237876982856915353600000⟩, + ⟨0, 5, 7, 3, 8, 1, 18654828180426477355506987005352981383901452697600000⟩, + ⟨0, 5, 6, 4, 6, 1, -23554780372336282340677729248525363556818459033600000⟩, + ⟨0, 5, 7, 4, 7, 1, 49343565984586965965291216217924288346672280371200000⟩, + ⟨0, 5, 8, 4, 8, 1, -26427028800524889390600537033344708012402540544000000⟩, + ⟨0, 5, 6, 5, 5, 1, -19677222878988087588293360045151613880634232012800000⟩, + ⟨0, 5, 7, 5, 6, 1, -15631946051248119062203840164594397857171111936000000⟩, + ⟨0, 5, 8, 5, 7, 1, 43327172854410986339754560383162563473036437094400000⟩, + ⟨0, 5, 6, 6, 4, 1, 13119950955753738088834774798731008163231616204800000⟩, + ⟨0, 5, 7, 6, 5, 1, -97663596308526979440817133014041925590702253670400000⟩, + ⟨0, 5, 8, 6, 6, 1, -64719380015877310879806237665981038581940381286400000⟩, + ⟨0, 5, 6, 7, 3, 1, 66232012438838527101065134658901439623108073881600000⟩, + ⟨0, 5, 7, 7, 4, 1, -75942190264670271317689694924863265641498411008000000⟩, + ⟨0, 5, 8, 7, 5, 1, -167177008813009947723684334165196931786105421824000000⟩ +] + +def collectedFourData_11_4_2 : List CollectedFourTerm := [ + ⟨0, 6, 5, 1, 8, 2, -51628621673390639913576220328373351692208439296000000⟩, + ⟨0, 6, 5, 2, 7, 2, -26464233440485996120933182679601219228851293388800000⟩, + ⟨0, 6, 6, 2, 8, 2, 46910229335557301539525293005166159780464138649600000⟩, + ⟨0, 6, 5, 3, 6, 2, 18107224855352482944107617059998148474447278899200000⟩, + ⟨0, 6, 6, 3, 7, 2, 99462235354466222923393415570697440967052492800000⟩, + ⟨0, 6, 7, 3, 8, 2, -7959442931273634914346826264587686856435852902400000⟩, + ⟨0, 6, 5, 4, 5, 2, 10979349052646429597492879695006022464361516236800000⟩, + ⟨0, 6, 6, 4, 6, 2, 20100204442409272270563017272675497558800125132800000⟩, + ⟨0, 6, 7, 4, 7, 2, -21053385948198859867240995239594819804063386828800000⟩, + ⟨0, 6, 8, 4, 8, 2, 7517068344505252851159388300095594509635682304000000⟩, + ⟨0, 6, 5, 5, 4, 2, 7283004454527574489263671392850941966204639641600000⟩, + ⟨0, 6, 6, 5, 5, 2, 16791334772580790970362542683457368882250409574400000⟩, + ⟨0, 6, 7, 5, 6, 2, 6669671856329752976589747554039719794063704064000000⟩, + ⟨0, 6, 8, 5, 7, 2, -12324250371813696117456931249258700943330272870400000⟩, + ⟨0, 6, 5, 6, 3, 2, -66366766779565111194375847056055217538394069401600000⟩, + ⟨0, 6, 6, 6, 4, 2, -11195761213496579280356982131770559066286745190400000⟩, + ⟨0, 6, 7, 6, 5, 2, 41670060627859162307400885742609138819960248729600000⟩, + ⟨0, 6, 8, 6, 6, 2, 18409182752458892297583455223323361194711344742400000⟩, + ⟨0, 6, 5, 7, 2, 2, 3676700246887438272488690719129363481734466764800000⟩, + ⟨0, 6, 6, 7, 3, 2, -56518335964463316778279160232789458425874271436800000⟩, + ⟨0, 6, 7, 7, 4, 2, 32402202992241574157939468231324917280897236992000000⟩, + ⟨0, 6, 8, 7, 5, 2, 47552867572172652192387518275519232440516214784000000⟩ +] + +def collectedFourData_11_4_3 : List CollectedFourTerm := [ + ⟨0, 7, 4, 0, 8, 3, -2577713702312326923481165555391674628690631720960000⟩, + ⟨0, 7, 4, 1, 7, 3, 3006252746002733047816236617115364392921999605760000⟩, + ⟨0, 7, 5, 1, 8, 3, 14756736800969068233268528641685183520084852736000000⟩, + ⟨0, 7, 4, 2, 6, 3, -1982002022104522146560120982139336568569488998400000⟩, + ⟨0, 7, 5, 2, 7, 3, 7564132352615810355819194260411131036236041420800000⟩, + ⟨0, 7, 6, 2, 8, 3, -6704051794730540421239646039344657693762440396800000⟩, + ⟨0, 7, 4, 3, 5, 3, -5438008876681617106626386310839213721653933506560000⟩, + ⟨0, 7, 5, 3, 6, 3, -5175492638110041695433505831910209515104187187200000⟩, + ⟨0, 7, 6, 3, 7, 3, -14214383235397989839198007549351161193981542400000⟩, + ⟨0, 7, 7, 3, 8, 3, 758335206404029738862010992050431846517624012800000⟩, + ⟨0, 7, 4, 4, 4, 3, 4075601597852745847300673206901689552682247782400000⟩, + ⟨0, 7, 5, 4, 5, 3, -3138169468106818059950150511578903866275318988800000⟩, + ⟨0, 7, 6, 4, 6, 3, -2872567744290346195165950697436826621792642662400000⟩, + ⟨0, 7, 7, 4, 7, 3, 2005859444735832678570804836860008097417632153600000⟩, + ⟨0, 7, 8, 4, 8, 3, -537141005702715711049509974788293678612873216000000⟩, + ⟨0, 7, 4, 5, 3, 3, 3883575143695960057558051287497385800704846725120000⟩, + ⟨0, 7, 5, 5, 4, 3, -2081662774877843149845755706162655995778144665600000⟩, + ⟨0, 7, 6, 5, 5, 3, -2399689355871792860002339261473899549352473395200000⟩, + ⟨0, 7, 7, 5, 6, 3, -635452383727015059271223416898052563568427008000000⟩, + ⟨0, 7, 8, 5, 7, 3, 880643880813853744155794137032563224647145881600000⟩, + ⟨0, 7, 4, 6, 2, 3, -4918926725797211594166303422281323295768125112320000⟩, + ⟨0, 7, 5, 6, 3, 3, 18969263132625906282117958592094430236566460825600000⟩, + ⟨0, 7, 6, 6, 4, 3, 1600012707672357959174767250811031816905110323200000⟩, + ⟨0, 7, 7, 6, 5, 3, -3970111262804109154289709486231456226896720691200000⟩, + ⟨0, 7, 8, 6, 6, 3, -1315449918058670075062009455657384506608425369600000⟩, + ⟨0, 7, 4, 7, 1, 3, -4725206133776730471057412781414237287050085662720000⟩, + ⟨0, 7, 5, 7, 2, 3, -1050891851860912237444587685305104643000159436800000⟩, + ⟨0, 7, 6, 7, 3, 3, 8077169031670915605885075147679622398334101094400000⟩, + ⟨0, 7, 7, 7, 4, 3, -3087116963615809756776669460834359386648346624000000⟩, + ⟨0, 7, 8, 7, 5, 3, -3397946372329544099705843079760444382968283136000000⟩ +] + +def collectedFourData_11_4_4 : List CollectedFourTerm := [ + ⟨0, 8, 3, 0, 7, 4, -2577713702312326923481165555391674628690631720960000⟩, + ⟨0, 8, 4, 0, 8, 4, 9948743461078196484965625857064129733620148469760000⟩, + ⟨0, 8, 3, 1, 6, 4, 12222759366610190504428570370282563096701692805120000⟩, + ⟨0, 8, 4, 1, 7, 4, -11602699447310160309180470895322347831921538498560000⟩, + ⟨0, 8, 5, 1, 8, 4, -28476977218958963276424867854641106087898513408000000⟩, + ⟨0, 8, 3, 2, 5, 4, 5201386691122118124385599958957393632999002603520000⟩, + ⟨0, 8, 4, 2, 6, 4, 7649580959890074583744620718172263325704283750400000⟩, + ⟨0, 8, 5, 2, 7, 4, -14596968665354622352404916083078496170795230822400000⟩, + ⟨0, 8, 6, 2, 8, 4, 8624812418814503935558742390481538596222900633600000⟩, + ⟨0, 8, 3, 3, 4, 4, -566736284782889082298281315287928778088345763840000⟩, + ⟨0, 8, 4, 3, 5, 4, 20988116408986785499943765149776245463671227023360000⟩, + ⟨0, 8, 5, 3, 6, 4, 9987464568905975789350873812420174389582600601600000⟩, + ⟨0, 8, 6, 3, 7, 4, 18286909589632258200501515779279960455040204800000⟩, + ⟨0, 8, 7, 3, 8, 4, -731702905878349680485442804875277396459336499200000⟩, + ⟨0, 8, 3, 4, 3, 4, -8369544791905049647299673445810237540430847672320000⟩, + ⟨0, 8, 4, 4, 4, 4, -15729875164268530195174121135891681983934654054400000⟩, + ⟨0, 8, 5, 4, 5, 4, 6055917487573663812874984412709014850498881126400000⟩, + ⟨0, 8, 6, 4, 6, 4, 3695579734976846722457652330650017709985418444800000⟩, + ⟨0, 8, 7, 4, 7, 4, -1935414803509434577451265440068230946551653990400000⟩, + ⟨0, 8, 8, 4, 8, 4, 414621535616477227825355847849571889393644339200000⟩, + ⟨0, 8, 3, 5, 2, 4, -10450945606231726750953474436628607043113981050880000⟩, + ⟨0, 8, 4, 5, 3, 4, -14988744786433078972745338024253709476791289118720000⟩, + ⟨0, 8, 5, 5, 4, 4, 4017111927743970110484229929587149506983283916800000⟩, + ⟨0, 8, 6, 5, 5, 4, 3087218176638788514724818882179030043192616550400000⟩, + ⟨0, 8, 7, 5, 6, 4, 613135657943666674881860999946968973088653312000000⟩, + ⟨0, 8, 8, 5, 7, 4, -679772935444775558197371623144104636178151505920000⟩, + ⟨0, 8, 3, 6, 1, 4, -2544407480847059542114542195625450069966863728640000⟩, + ⟨0, 8, 4, 6, 2, 4, 18984707283395724611872645783344497881574717521920000⟩, + ⟨0, 8, 5, 6, 3, 4, -36606146831374821186812509490827120525271944396800000⟩, + ⟨0, 8, 6, 6, 4, 4, -2058428230259255724143593781145753628889736806400000⟩, + ⟨0, 8, 7, 6, 5, 4, 3830683216501517844181856693654645251660106956800000⟩, + ⟨0, 8, 8, 6, 6, 4, 1015401652939373397610067931904002480666071531520000⟩, + ⟨0, 8, 3, 7, 0, 4, 267442774183439550077862622687191903616735138283520000⟩, + ⟨0, 8, 4, 7, 1, 4, 18237038342732879238618186188641897152344563384320000⟩, + ⟨0, 8, 5, 7, 2, 4, 2027970257155196657679301916098992194076436070400000⟩, + ⟨0, 8, 6, 7, 3, 4, -10391337941030821006042569813849213652381256908800000⟩, + ⟨0, 8, 7, 7, 4, 4, 2978699174175690917458574571068907205045518336000000⟩, + ⟨0, 8, 8, 7, 5, 4, 2622889944875029021040211689540556473922433843200000⟩ +] + +def collectedFourData_11_4_5 : List CollectedFourTerm := [ + ⟨1, 3, 7, 3, 8, 0, -4423179003039954306993517385722787402485648588800000⟩, + ⟨1, 3, 7, 4, 7, 0, -11699674898487965117117266311569052406430407065600000⟩, + ⟨1, 3, 8, 4, 8, 0, 12532034899775906185959372285164029305887391744000000⟩, + ⟨1, 3, 7, 5, 6, 0, 3706434327981749089476940604397390373079482368000000⟩, + ⟨1, 3, 8, 5, 7, 0, -20546299261206284901705411102796223050661914214400000⟩, + ⟨1, 3, 7, 6, 5, 0, 23156662949407617339609657850968128937216127795200000⟩, + ⟨1, 3, 8, 6, 6, 0, 30690757374689225313831314351220444244346300006400000⟩, + ⟨1, 3, 7, 7, 4, 0, 18006378733415676070291663052507287941707464704000000⟩, + ⟨1, 3, 8, 7, 5, 0, 79277474766409343754038915947083182255609217024000000⟩ +] + +def collectedFourData_11_4_6 : List CollectedFourTerm := [ + ⟨1, 4, 6, 2, 8, 1, -24012869963624860411414032432585429502427922432000000⟩, + ⟨1, 4, 6, 3, 7, 1, -50913708112015017667045893079090625853259776000000⟩, + ⟨1, 4, 7, 3, 8, 1, 8148715996435928998138421713534121636649762816000000⟩, + ⟨1, 4, 6, 4, 6, 1, -10289090510840805154931243583013730615952408576000000⟩, + ⟨1, 4, 7, 4, 7, 1, 21554028885759658873416341796923185055548833792000000⟩, + ⟨1, 4, 8, 4, 8, 1, -11543732820389183928478644820220791170835415040000000⟩, + ⟨1, 4, 6, 5, 5, 1, -8595313732649965742515106114755088376448155648000000⟩, + ⟨1, 4, 7, 5, 6, 1, -6828274568450991633177229803801073050986741760000000⟩, + ⟨1, 4, 8, 5, 7, 1, 18925975790521156893011831466780690671053307904000000⟩, + ⟨1, 4, 6, 6, 4, 1, 5730996457945462602660372694954511721843130368000000⟩, + ⟨1, 4, 7, 6, 5, 1, -42660961645510090576152333674941021865392472064000000⟩, + ⟨1, 4, 8, 6, 6, 1, -28270421046715775069825955301706397680217882624000000⟩, + ⟨1, 4, 6, 7, 3, 1, 28931162164376924684442527315675894162449760256000000⟩, + ⟨1, 4, 7, 7, 4, 1, -33172717252009131275848356259643823469394657280000000⟩, + ⟨1, 4, 8, 7, 5, 1, -73025489850410443292045291828140029144559779840000000⟩ +] + +def collectedFourData_11_4_7 : List CollectedFourTerm := [ + ⟨1, 5, 5, 1, 8, 2, 25209615228664859299572750469346449931995447296000000⟩, + ⟨1, 5, 5, 2, 7, 2, 12922156755931137194231601277512051785024195788800000⟩, + ⟨1, 5, 6, 2, 8, 2, -22905682807475217468874533725314715042845399449600000⟩, + ⟨1, 5, 5, 3, 6, 2, -8841533178051513783114553875225254286966600499200000⟩, + ⟨1, 5, 6, 3, 7, 2, -48566175152440974538054750920876303196146892800000⟩, + ⟨1, 5, 7, 3, 8, 2, 3886497203068698178615912351049949066058688102400000⟩, + ⟨1, 5, 5, 4, 5, 2, -5361079883739709299274330906550394779941522636800000⟩, + ⟨1, 5, 6, 4, 6, 2, -9814680376636903544576353132683707784387939532800000⟩, + ⟨1, 5, 7, 4, 7, 2, 10280107076502098587734108035696734400433409228800000⟩, + ⟨1, 5, 8, 4, 8, 2, -3670491182417592735464009234772429339365474304000000⟩, + ⟨1, 5, 5, 5, 4, 2, -3556200689779804315884102640602130981555116441600000⟩, + ⟨1, 5, 6, 5, 5, 2, -8199000381422784592379131372468767713179100774400000⟩, + ⟨1, 5, 7, 5, 6, 2, -3256717993813635818680346451473939958085976064000000⟩, + ⟨1, 5, 8, 5, 7, 2, 6017778507057885361022817512409386197597972070400000⟩, + ⟨1, 5, 5, 6, 3, 2, 32406068576990085640998086184602607034021026201600000⟩, + ⟨1, 5, 6, 6, 4, 2, 5466751256110435401906881469158518891961804390400000⟩, + ⟨1, 5, 7, 6, 5, 2, -20346973460360384750341050350086150782409349529600000⟩, + ⟨1, 5, 8, 6, 6, 2, -8988975471775049288138786770903933631974499942400000⟩, + ⟨1, 5, 5, 7, 2, 2, -1795287101048851992832615732542580466914217164800000⟩, + ⟨1, 5, 6, 7, 3, 2, 27597202033438656082678272162856803874663877836800000⟩, + ⟨1, 5, 7, 7, 4, 2, -15821593595176408531700607937829928169994452992000000⟩, + ⟨1, 5, 8, 7, 5, 2, -23219475082984491555426308115793960002109046784000000⟩ +] + +def collectedFourData_11_4_8 : List CollectedFourTerm := [ + ⟨1, 6, 4, 0, 8, 3, 12222759366610190504428570370282563096701692805120000⟩, + ⟨1, 6, 4, 1, 7, 3, -14254765328143631174068890747713748079284552990720000⟩, + ⟨1, 6, 5, 1, 8, 3, -69972100777851165075320928392295892830589550592000000⟩, + ⟨1, 6, 4, 2, 6, 3, 9398069986820869847641484845481751970646379724800000⟩, + ⟨1, 6, 5, 2, 7, 3, -35866888351595485862215309665031165061845588377600000⟩, + ⟨1, 6, 6, 2, 8, 3, 31788639597476183613489232444234002555920292249600000⟩, + ⟨1, 6, 4, 3, 5, 3, 25785436867385713148598719097810723321502047928320000⟩, + ⟨1, 6, 5, 3, 6, 3, 24540662162184870762548040566584531076690372198400000⟩, + ⟨1, 6, 6, 3, 7, 3, 67400419866331873555362172810641918166617292800000⟩, + ⟨1, 6, 7, 3, 8, 3, -3595802256391179611596178560666306646357154201600000⟩, + ⟨1, 6, 4, 4, 4, 3, -19325302713035854377846207084516721535287610572800000⟩, + ⟨1, 6, 5, 4, 5, 3, 14880275581382318791179330732421609683894770073600000⟩, + ⟨1, 6, 6, 4, 6, 3, 13620870413673648148921750725261332091945929932800000⟩, + ⟨1, 6, 7, 4, 7, 3, -9511194860102354541823628367960752095262618419200000⟩, + ⟨1, 6, 8, 4, 8, 3, 2546964487465722687731907245939412586727473152000000⟩, + ⟨1, 6, 4, 5, 3, 3, -18414769809759456337211822245932730397053566320640000⟩, + ⟨1, 6, 5, 5, 4, 3, 9870631931287710407024478211309061702463730483200000⟩, + ⟨1, 6, 6, 5, 5, 3, 11378620335193020380890125148084930241620239974400000⟩, + ⟨1, 6, 7, 5, 6, 3, 3013128094197120920522562186588385272058085376000000⟩, + ⟨1, 6, 8, 5, 7, 3, -4175753976560612895821399657494635471485219635200000⟩, + ⟨1, 6, 4, 6, 2, 3, 23324102152024918375221088523950981013203624919040000⟩, + ⟨1, 6, 5, 6, 3, 3, -89946660260994297475635190160300491881906910003200000⟩, + ⟨1, 6, 6, 6, 4, 3, -7586789134826923985685483988857370374476031590400000⟩, + ⟨1, 6, 7, 6, 5, 3, 18825098605944389572533173368688451459750454886400000⟩, + ⟨1, 6, 8, 6, 6, 3, 6237476176208061100695779417521767294992331571200000⟩, + ⟨1, 6, 4, 7, 1, 3, 22405536145839056046922009206885616440951271587840000⟩, + ⟨1, 6, 5, 7, 2, 3, 4983019725621554921682839608750776506971167129600000⟩, + ⟨1, 6, 6, 7, 3, 3, -38299557219635504470898704267957450036663340236800000⟩, + ⟨1, 6, 7, 7, 4, 3, 14638199637534628556465128647262074413229539328000000⟩, + ⟨1, 6, 8, 7, 5, 3, 16112061169699994285117811637382448407371579392000000⟩ +] + +def collectedFourData_11_4_9 : List CollectedFourTerm := [ + ⟨1, 7, 3, 0, 7, 4, 3006252746002733047816236617115364392921999605760000⟩, + ⟨1, 7, 4, 0, 8, 4, -11602699447310160309180470895322347831921538498560000⟩, + ⟨1, 7, 3, 1, 6, 4, -14254765328143631174068890747713748079284552990720000⟩, + ⟨1, 7, 4, 1, 7, 4, 13531621856698449070566253518524596938247357071360000⟩, + ⟨1, 7, 5, 1, 8, 4, 33211209951499842910881844816449687973106024448000000⟩, + ⟨1, 7, 3, 2, 5, 4, -6066105405414541662130079578119077376166062981120000⟩, + ⟨1, 7, 4, 2, 6, 4, -8921306406452656961011279415066799040492889702400000⟩, + ⟨1, 7, 5, 2, 7, 4, 17023681526064692752556832044225334299228268134400000⟩, + ⟨1, 7, 6, 2, 8, 4, -10058667878655666063875631180020581746481928601600000⟩, + ⟨1, 7, 3, 3, 4, 4, 660954903897823647113444805744305113278751703040000⟩, + ⟨1, 7, 4, 3, 5, 4, -24477343054561072919886776737757262714239094620160000⟩, + ⟨1, 7, 5, 3, 6, 4, -11647857851298589459464084048045362328465152409600000⟩, + ⟨1, 7, 6, 3, 7, 4, -21327066741516149647833596376664035210087628800000⟩, + ⟨1, 7, 7, 3, 8, 4, 853346850770025837172388353166315105293644595200000⟩, + ⟨1, 7, 3, 4, 3, 4, 9760962589013237523589083347326356937433331793920000⟩, + ⟨1, 7, 4, 4, 4, 4, 18344931155249313475698277509726338321897383526400000⟩, + ⟨1, 7, 5, 4, 5, 4, -7062700004369386504881087595479193604512441958400000⟩, + ⟨1, 7, 6, 4, 6, 4, -4309961465612010350813136752244430672608677068800000⟩, + ⟨1, 7, 7, 4, 7, 4, 2257173115263054834674557541006651818049431142400000⟩, + ⟨1, 7, 8, 4, 8, 4, -483551423449693297649214214288516170168611635200000⟩, + ⟨1, 7, 3, 5, 2, 4, 12188391557555744161570609816568085485054098145280000⟩, + ⟨1, 7, 4, 5, 3, 4, 17480589536738604577821574967311242244944895672320000⟩, + ⟨1, 7, 5, 5, 4, 4, -4684947654562068740148693618558191792596765900800000⟩, + ⟨1, 7, 6, 5, 5, 4, -3600461181047555906428087052921208589173286502400000⟩, + ⟨1, 7, 7, 5, 6, 4, -715068067377641372439584473176781916441935872000000⟩, + ⟨1, 7, 8, 5, 7, 4, 792783640792233888512126734730730877759279595520000⟩, + ⟨1, 7, 3, 6, 1, 4, 2967409440926177487659198466646353481421385891840000⟩, + ⟨1, 7, 4, 6, 2, 4, -22140871715726051987181014064883510081914163691520000⟩, + ⟨1, 7, 5, 6, 3, 4, 42691835533822984600688434249479183561833368780800000⟩, + ⟨1, 7, 6, 6, 4, 4, 2400637244592126527170365308805238097715816038400000⟩, + ⟨1, 7, 7, 6, 5, 4, -4467525593840731909311788093798511801040424140800000⟩, + ⟨1, 7, 8, 6, 6, 4, -1184209869663347417007600721950501905466780549120000⟩, + ⟨1, 7, 3, 7, 0, 4, -311904527475773881559704029064522481092481117061120000⟩, + ⟨1, 7, 4, 7, 1, 4, -21268904513180493828551329239850162448028842065920000⟩, + ⟨1, 7, 5, 7, 2, 4, -2365115702692567418762229004973714955611563622400000⟩, + ⟨1, 7, 6, 7, 3, 4, 12118874253507475451928358667668257926904859852800000⟩, + ⟨1, 7, 7, 7, 4, 4, -3473901141096060782957370782791747209334358016000000⟩, + ⟨1, 7, 8, 7, 5, 4, -3058939436202804481094178870502581325549220659200000⟩ +] + +def collectedFourData_11_4_10 : List CollectedFourTerm := [ + ⟨1, 8, 2, 0, 6, 5, -51628621673390639913576220328373351692208439296000000⟩, + ⟨1, 8, 3, 0, 7, 5, 14756736800969068233268528641685183520084852736000000⟩, + ⟨1, 8, 4, 0, 8, 5, -28476977218958963276424867854641106087898513408000000⟩, + ⟨1, 8, 2, 1, 5, 5, 25209615228664859299572750469346449931995447296000000⟩, + ⟨1, 8, 3, 1, 6, 5, -69972100777851165075320928392295892830589550592000000⟩, + ⟨1, 8, 4, 1, 7, 5, 33211209951499842910881844816449687973106024448000000⟩, + ⟨1, 8, 5, 1, 8, 5, 54341082348853880575693391991502992433584537600000000⟩, + ⟨1, 8, 2, 2, 4, 5, 92875432767263995720276873175460306426494189568000000⟩, + ⟨1, 8, 3, 2, 5, 5, -29776578497487641192460235163427977949748396032000000⟩, + ⟨1, 8, 4, 2, 6, 5, -21895925207198355412485262641876323333906104320000000⟩, + ⟨1, 8, 5, 2, 7, 5, 27854609363509998521889539063826477319748321280000000⟩, + ⟨1, 8, 6, 2, 8, 5, -12343698866558024406922430063550582775810621440000000⟩, + ⟨1, 8, 2, 3, 3, 5, -105794169029092071682024458744117285422125547520000000⟩, + ⟨1, 8, 3, 3, 4, 5, 3244417012873847336662897817297133685067218944000000⟩, + ⟨1, 8, 4, 3, 5, 5, -60075738728798424931282333226662235967521292288000000⟩, + ⟨1, 8, 5, 3, 6, 5, -19058540884523722409072889720166616816701931520000000⟩, + ⟨1, 8, 6, 3, 7, 5, -26171943714622782376664351599184253466705920000000⟩, + ⟨1, 8, 7, 3, 8, 5, 837761555045089460448901855699643328620396544000000⟩, + ⟨1, 8, 2, 4, 2, 5, 25225094279440099324909143848593114286606254080000000⟩, + ⟨1, 8, 3, 4, 3, 5, 47913455061852942040987663238956837106312282112000000⟩, + ⟨1, 8, 4, 4, 4, 5, 45024710754919579538042620915263236109521387520000000⟩, + ⟨1, 8, 5, 4, 5, 5, -11556181274430052424402691835136267857774510080000000⟩, + ⟨1, 8, 6, 4, 6, 5, -5289056871126556421899303225461492665989201920000000⟩, + ⟨1, 8, 7, 4, 7, 5, 2215948716916700406615834235657666220185878528000000⟩, + ⟨1, 8, 8, 4, 8, 5, -395599976031566131657004916546088329145221120000000⟩, + ⟨1, 8, 2, 5, 1, 5, -26125683478872488458130699768515644728945934336000000⟩, + ⟨1, 8, 3, 5, 2, 5, 59828930378909676567154446104777942678013739008000000⟩, + ⟨1, 8, 4, 5, 3, 5, 42903321961604436653752795812977763997949362176000000⟩, + ⟨1, 8, 5, 5, 4, 5, -7665638399456445207748874527771325124009000960000000⟩, + ⟨1, 8, 6, 5, 5, 5, -4418379166677750852022274364414351009550172160000000⟩, + ⟨1, 8, 7, 5, 6, 5, -702008257895151479450557948463012411961507840000000⟩, + ⟨1, 8, 8, 5, 7, 5, 648587045940634554933250629117752567043981312000000⟩, + ⟨1, 8, 2, 6, 0, 5, 470316663465156096785530989132251396418362671104000000⟩, + ⟨1, 8, 3, 6, 1, 5, 14566067393595841685459370384826515700133658624000000⟩, + ⟨1, 8, 4, 6, 2, 5, -54341242080763616388315832494005463553708916736000000⟩, + ⟨1, 8, 5, 6, 3, 5, 69853539023573928514449044368558204675644456960000000⟩, + ⟨1, 8, 6, 6, 4, 5, 2945990820312202857608152418010673659311554560000000⟩, + ⟨1, 8, 7, 6, 5, 5, -4385931916573509832971770352451661420744933376000000⟩, + ⟨1, 8, 8, 6, 6, 5, -968818151155545791223189995649471926576873472000000⟩, + ⟨1, 8, 3, 7, 0, 5, -1531039938378632889079171429108296362711719084032000000⟩, + ⟨1, 8, 4, 7, 1, 5, -52201137506364270549653823885366600983333830656000000⟩, + ⟨1, 8, 5, 7, 2, 5, -3869866450282098982267931556233111782954106880000000⟩, + ⟨1, 8, 6, 7, 3, 5, 14871923021179647467311842998496227411644907520000000⟩, + ⟨1, 8, 7, 7, 4, 5, -3410454751677361132475991989790609273016811520000000⟩, + ⟨1, 8, 8, 7, 5, 5, -2502559829130018890879366687004087394259435520000000⟩ +] + +def collectedFourData_11_4_11 : List CollectedFourTerm := [ + ⟨2, 2, 7, 3, 8, 0, -3689808806938585534735573743683292908301267763200000⟩, + ⟨2, 2, 7, 4, 7, 0, -9759849974213048450056007351159563334061549158400000⟩, + ⟨2, 2, 8, 4, 8, 0, 10454203347925677946924845910224760738745942016000000⟩, + ⟨2, 2, 7, 5, 6, 0, 3091901552328611662002426075387666735512420352000000⟩, + ⟨2, 2, 8, 5, 7, 0, -17139689782369384037437169804369160086530660761600000⟩, + ⟨2, 2, 7, 6, 5, 0, 19317250970695309308664943216584346666745515212800000⟩, + ⟨2, 2, 8, 6, 6, 0, 25602180417051669708825717137584758559426058649600000⟩, + ⟨2, 2, 7, 7, 4, 0, 15020892165107039258993937220641316627814547456000000⟩, + ⟨2, 2, 8, 7, 5, 0, 66133141883678447362439658171001416824112807936000000⟩ +] + +def collectedFourData_11_4_12 : List CollectedFourTerm := [ + ⟨2, 3, 6, 2, 8, 1, -36269946895678324476681181913059481939905767014400000⟩, + ⟨2, 3, 6, 3, 7, 1, -76901990152871024708332216081946371758961459200000⟩, + ⟨2, 3, 7, 3, 8, 1, 12308128803695915184445325202684974634879890227200000⟩, + ⟨2, 3, 6, 4, 6, 1, -15541031413501632821125139896772157801002906419200000⟩, + ⟨2, 3, 7, 4, 7, 1, 32556020344867117463669120450645866630187738726400000⟩, + ⟨2, 3, 8, 4, 8, 1, -17436090605065321241531279963519562383169159168000000⟩, + ⟨2, 3, 6, 5, 5, 1, -12982686913607409089858077881436013750073792921600000⟩, + ⟨2, 3, 7, 5, 6, 1, -10313684135298695858211950990965460207394619392000000⟩, + ⟨2, 3, 8, 5, 7, 1, 28586509563868635162871313534500411321600494796800000⟩, + ⟨2, 3, 6, 6, 4, 1, 8656313781063118514641069251285609235061774745600000⟩, + ⟨2, 3, 7, 6, 5, 1, -64436729793028314221498422057928073908908248268800000⟩, + ⟨2, 3, 8, 6, 6, 1, -42700713060791666827908338671460839958260796620800000⟩, + ⟨2, 3, 6, 7, 3, 1, 43698721432371729262196874985230474229197255475200000⟩, + ⟨2, 3, 7, 7, 4, 1, -50105326641018405554975525684148192184501272576000000⟩, + ⟨2, 3, 8, 7, 5, 1, -110300461499082697447562231522962415103485411328000000⟩ +] + +def collectedFourData_11_4_13 : List CollectedFourTerm := [ + ⟨2, 4, 5, 1, 8, 2, 92875432767263995720276873175460306426494189568000000⟩, + ⟨2, 4, 5, 2, 7, 2, 47606871033433477206694793237081921301764269670400000⟩, + ⟨2, 4, 6, 2, 8, 2, -84387452338224699255058092524565209414795840716800000⟩, + ⟨2, 4, 5, 3, 6, 2, -32573334134189691855011069523556073127137614233600000⟩, + ⟨2, 4, 6, 3, 7, 2, -178923973817929138173602386394286516309747302400000⟩, + ⟨2, 4, 7, 3, 8, 2, 14318350613829795254128015891157533551188194099200000⟩, + ⟨2, 4, 5, 4, 5, 2, -19750900987018717043549456269265970610647230054400000⟩, + ⟨2, 4, 6, 4, 6, 2, -36158532337139630930087487254851954109938296422400000⟩, + ⟨2, 4, 7, 4, 7, 2, 37873223568216735905889352272892713214945945190400000⟩, + ⟨2, 4, 8, 4, 8, 2, -13522556926923591792996499844226067662196703232000000⟩, + ⟨2, 4, 5, 5, 4, 2, -13101496197966144140441742156100546311008079052800000⟩, + ⟨2, 4, 6, 5, 5, 2, -30206161489436313099606962635426693470261293875200000⟩, + ⟨2, 4, 7, 5, 6, 2, -11998163809039478618413917353976682028898189312000000⟩, + ⟨2, 4, 8, 5, 7, 2, 22170262341213105226247785993654382960315675443200000⟩, + ⟨2, 4, 5, 6, 3, 2, 119388083319548110960095061614763347694450429132800000⟩, + ⟨2, 4, 6, 6, 4, 2, 20140207779328758567235534424347263453692638003200000⟩, + ⟨2, 4, 7, 6, 5, 2, -74960841270050952598477492376714492523626417356800000⟩, + ⟨2, 4, 8, 6, 6, 2, -33116530319992669513267408965083343966363136819200000⟩, + ⟨2, 4, 5, 7, 2, 2, -6614066297283572053274539122785007551746827878400000⟩, + ⟨2, 4, 6, 7, 3, 2, 101671606598216970569017790504357887229479511654400000⟩, + ⟨2, 4, 7, 7, 4, 2, -58288765571833953071412652900704478397869326336000000⟩, + ⟨2, 4, 8, 7, 5, 2, -85543503040411154493254589528680114103697539072000000⟩ +] + +def collectedFourData_11_4_14 : List CollectedFourTerm := [ + ⟨2, 5, 4, 0, 8, 3, 5201386691122118124385599958957393632999002603520000⟩, + ⟨2, 5, 4, 1, 7, 3, -6066105405414541662130079578119077376166062981120000⟩, + ⟨2, 5, 5, 1, 8, 3, -29776578497487641192460235163427977949748396032000000⟩, + ⟨2, 5, 4, 2, 6, 3, 3999342103160564826167650922202069411247738060800000⟩, + ⟨2, 5, 5, 2, 7, 3, -15263129227070007048539781609904568211802266009600000⟩, + ⟨2, 5, 6, 2, 8, 3, 13527633324998223177715743151107136146323904921600000⟩, + ⟨2, 5, 4, 3, 5, 3, 10972974606141325273912805405114582328228414750720000⟩, + ⟨2, 5, 5, 3, 6, 3, 10443261601828720059545324392990194570107446886400000⟩, + ⟨2, 5, 6, 3, 7, 3, 28682201486063340368958316223895639088221388800000⟩, + ⟨2, 5, 7, 3, 8, 3, -1530191132731677133600639025411442510023727513600000⟩, + ⟨2, 5, 4, 4, 4, 3, -8223869039595451370487038070782967026086104268800000⟩, + ⟨2, 5, 5, 4, 5, 3, 6332290855751068537892989455295143140556118425600000⟩, + ⟨2, 5, 6, 4, 6, 3, 5796351868361265272105224425022655322515098828800000⟩, + ⟨2, 5, 7, 4, 7, 3, -4047482313785064482457574069580881281651258163200000⟩, + ⟨2, 5, 8, 4, 8, 3, 1083858954472647219306505718982282315187617792000000⟩, + ⟨2, 5, 4, 5, 3, 3, -7836392400084048502605698411907739523269200445440000⟩, + ⟨2, 5, 5, 5, 4, 3, 4200440507780658335889871520446469781289382707200000⟩, + ⟨2, 5, 6, 5, 5, 3, 4842163917297055004090305817934006621990970982400000⟩, + ⟨2, 5, 7, 5, 6, 3, 1282234550948996347154407685764319365558173696000000⟩, + ⟨2, 5, 8, 5, 7, 3, -1776989181216801449201572864512530921144136499200000⟩, + ⟨2, 5, 4, 6, 2, 3, 9925555341237230500232405222206381820691181731840000⟩, + ⟨2, 5, 5, 6, 3, 3, -38276738301047752175037663244446756619301368627200000⟩, + ⟨2, 5, 6, 6, 4, 3, -3228552804699682999747381946709549328565167718400000⟩, + ⟨2, 5, 7, 6, 5, 3, 8011007532023145485762060835181598648570373734400000⟩, + ⟨2, 5, 8, 6, 6, 3, 2654353619833852775318886203462598650877915955200000⟩, + ⟨2, 5, 4, 7, 1, 3, 9534660220406802048711934812380015427194600816640000⟩, + ⟨2, 5, 5, 7, 2, 3, 2120520555550714830917614379123195744282581401600000⟩, + ⟨2, 5, 6, 7, 3, 3, -16298349760716139149476218078214800716493278412800000⟩, + ⟨2, 5, 7, 7, 4, 3, 6229275607327716549294624454710042829718028288000000⟩, + ⟨2, 5, 8, 7, 5, 3, 6856476350467919427460246122689117402098040832000000⟩ +] + +def collectedFourData_11_4_15 : List CollectedFourTerm := [ + ⟨2, 6, 3, 0, 7, 4, -1982002022104522146560120982139336568569488998400000⟩, + ⟨2, 6, 4, 0, 8, 4, 7649580959890074583744620718172263325704283750400000⟩, + ⟨2, 6, 3, 1, 6, 4, 9398069986820869847641484845481751970646379724800000⟩, + ⟨2, 6, 4, 1, 7, 4, -8921306406452656961011279415066799040492889702400000⟩, + ⟨2, 6, 5, 1, 8, 4, -21895925207198355412485262641876323333906104320000000⟩, + ⟨2, 6, 3, 2, 5, 4, 3999342103160564826167650922202069411247738060800000⟩, + ⟨2, 6, 4, 2, 6, 4, 5881756735495425612267579127169203559429308416000000⟩, + ⟨2, 6, 5, 2, 7, 4, -11223597634359697261739029904722341962811703296000000⟩, + ⟨2, 6, 6, 2, 8, 4, 6631611431101944289893318218862363867762130944000000⟩, + ⟨2, 6, 3, 3, 4, 4, -435763080062795097394894456532410371747191193600000⟩, + ⟨2, 6, 4, 3, 5, 4, 16137746067556364422929099717706420822489851494400000⟩, + ⟨2, 6, 5, 3, 6, 4, 7679353589000879934429192858406392051913457664000000⟩, + ⟨2, 6, 6, 3, 7, 4, 14060790285663054469981751930703999236308992000000⟩, + ⟨2, 6, 7, 3, 8, 4, -562605784238069343741301272104912213841543168000000⟩, + ⟨2, 6, 3, 4, 3, 4, -6435336355146647552316066573235059200730385612800000⟩, + ⟨2, 6, 4, 4, 4, 4, -12094688543209843422685741958287026673812504576000000⟩, + ⟨2, 6, 5, 4, 5, 4, 4656390155082793998584109031513830315006099456000000⟩, + ⟨2, 6, 6, 4, 6, 4, 2841528328379548821202502628996294641914478592000000⟩, + ⟨2, 6, 7, 4, 7, 4, -1488138908027552507254856468366476727619158016000000⟩, + ⟨2, 6, 8, 4, 8, 4, 318802170024842236733596481967227415998496768000000⟩, + ⟨2, 6, 3, 5, 2, 4, -8035723791154321372983897192452335235419550515200000⟩, + ⟨2, 6, 4, 5, 3, 4, -11524833983258029222891791680826019962325617868800000⟩, + ⟨2, 6, 5, 5, 4, 4, 3088754176488465098601989401364572130060009472000000⟩, + ⟨2, 6, 6, 5, 5, 4, 2373759608480571918431026606186884448351420416000000⟩, + ⟨2, 6, 7, 5, 6, 4, 471439521300837897130968942284893342641684480000000⟩, + ⟨2, 6, 8, 5, 7, 4, -522676871141613651914827710401274655535844556800000⟩, + ⟨2, 6, 3, 6, 1, 4, -1956392894824947104574181349092311285435570585600000⟩, + ⟨2, 6, 4, 6, 2, 4, 14597326379185937044338691933420689019252821196800000⟩, + ⟨2, 6, 5, 6, 3, 4, -28146437277404459990900018252584910162516508672000000⟩, + ⟨2, 6, 6, 6, 4, 4, -1582723834330826899851527559894330907249606656000000⟩, + ⟨2, 6, 7, 6, 5, 4, 2945409288214247442611174295891473364336771072000000⟩, + ⟨2, 6, 8, 6, 6, 4, 780741525937803964480745101600982604521983180800000⟩, + ⟨2, 6, 3, 7, 0, 4, 205636537041845019078515411008634199908182445260800000⟩, + ⟨2, 6, 4, 7, 1, 4, 14022444323459891806119815337785516097884966092800000⟩, + ⟨2, 6, 5, 7, 2, 4, 1559304722958102466910347595576640844874121216000000⟩, + ⟨2, 6, 6, 7, 3, 4, -7989891504638116988576527718354865181427761152000000⟩, + ⟨2, 6, 7, 7, 4, 4, 2290319433520224656365323210092218513033789440000000⟩, + ⟨2, 6, 8, 7, 5, 4, 2016737999195398841652824982191165410721660928000000⟩ +] + +def collectedFourData_11_4_16 : List CollectedFourTerm := [ + ⟨2, 7, 2, 0, 6, 5, -26464233440485996120933182679601219228851293388800000⟩, + ⟨2, 7, 3, 0, 7, 5, 7564132352615810355819194260411131036236041420800000⟩, + ⟨2, 7, 4, 0, 8, 5, -14596968665354622352404916083078496170795230822400000⟩, + ⟨2, 7, 2, 1, 5, 5, 12922156755931137194231601277512051785024195788800000⟩, + ⟨2, 7, 3, 1, 6, 5, -35866888351595485862215309665031165061845588377600000⟩, + ⟨2, 7, 4, 1, 7, 5, 17023681526064692752556832044225334299228268134400000⟩, + ⟨2, 7, 5, 1, 8, 5, 27854609363509998521889539063826477319748321280000000⟩, + ⟨2, 7, 2, 2, 4, 5, 47606871033433477206694793237081921301764269670400000⟩, + ⟨2, 7, 3, 2, 5, 5, -15263129227070007048539781609904568211802266009600000⟩, + ⟨2, 7, 4, 2, 6, 5, -11223597634359697261739029904722341962811703296000000⟩, + ⟨2, 7, 5, 2, 7, 5, 14277950111718802025986196645704593248442384384000000⟩, + ⟨2, 7, 6, 2, 8, 5, -6327237058354739813150062954921675253121810432000000⟩, + ⟨2, 7, 2, 3, 3, 5, -54228865599778769686477794612073793544316256256000000⟩, + ⟨2, 7, 3, 3, 4, 5, 1663050579776187730196871160526552238279308083200000⟩, + ⟨2, 7, 4, 3, 5, 5, -30794127797682016740455341181856925070504912486400000⟩, + ⟨2, 7, 5, 3, 6, 5, -9769187296801961159546303530907411086055571456000000⟩, + ⟨2, 7, 6, 3, 7, 5, -13415435190903298183375266727255830247243776000000⟩, + ⟨2, 7, 7, 3, 8, 5, 429426869081120177631767758482119696762221363200000⟩, + ⟨2, 7, 2, 4, 2, 5, 12930091138060192105498032223684781747390644224000000⟩, + ⟨2, 7, 3, 4, 3, 5, 24559882069263809072113926520495752281287399833600000⟩, + ⟨2, 7, 4, 4, 4, 5, 23079145198692637211605198051283827491399008256000000⟩, + ⟨2, 7, 5, 4, 5, 5, -5923564662674543850689835975674029240718721024000000⟩, + ⟨2, 7, 6, 4, 6, 5, -2711109287460225367955420852688473925485592576000000⟩, + ⟨2, 7, 7, 4, 7, 5, 1135869644315020392121938367229382213320992358400000⟩, + ⟨2, 7, 8, 4, 8, 5, -202779965364558164981177946249640895720718336000000⟩, + ⟨2, 7, 2, 5, 1, 5, -13391722729903420909543336854786299612669725900800000⟩, + ⟨2, 7, 3, 5, 2, 5, 30667616696381720705479300148643036282667558502400000⟩, + ⟨2, 7, 4, 5, 3, 5, 21991745875900763423519054760515410151858818252800000⟩, + ⟨2, 7, 5, 5, 4, 5, -3929317450249217645579676272714164466287116288000000⟩, + ⟨2, 7, 6, 5, 5, 5, -2264809981472062564517592410042340690936987648000000⟩, + ⟨2, 7, 7, 5, 6, 5, -359841301431863168454656640412540729244516352000000⟩, + ⟨2, 7, 8, 5, 7, 5, 332458206977364808773235476211329478923229593600000⟩, + ⟨2, 7, 2, 6, 0, 5, 241078873877962480832101622649419397914627879731200000⟩, + ⟨2, 7, 3, 6, 1, 5, 7466397422975322721119933450302179505861767987200000⟩, + ⟨2, 7, 4, 6, 2, 5, -27854691240236708076298592698117994229017660620800000⟩, + ⟨2, 7, 5, 6, 3, 5, 35806114969688149990405117003873377502875353088000000⟩, + ⟨2, 7, 6, 6, 4, 5, 1510080770226202904616508933782768647424442368000000⟩, + ⟨2, 7, 7, 6, 5, 5, -2248177896914534331552179886987154407925009612800000⟩, + ⟨2, 7, 8, 6, 6, 5, -496604962180788794760033817342512355367033241600000⟩, + ⟨2, 7, 3, 7, 0, 5, -784793337933371246247973185759963298209558272409600000⟩, + ⟨2, 7, 4, 7, 1, 5, -26757698424851390605853683810082016003869166796800000⟩, + ⟨2, 7, 5, 7, 2, 5, -1983648716629481208657906093414293418817880064000000⟩, + ⟨2, 7, 6, 7, 3, 5, 7623175474860367478365390789780462810228064256000000⟩, + ⟨2, 7, 7, 7, 4, 5, -1748159601423599357404119574639866911398035456000000⟩, + ⟨2, 7, 8, 7, 5, 5, -1282783180535954651930811195100121055841222656000000⟩ +] + +def collectedFourData_11_4_17 : List CollectedFourTerm := [ + ⟨2, 8, 1, 0, 5, 6, -54972582611330638325610604320008643660517421875200000⟩, + ⟨2, 8, 2, 0, 6, 6, 46910229335557301539525293005166159780464138649600000⟩, + ⟨2, 8, 3, 0, 7, 6, -6704051794730540421239646039344657693762440396800000⟩, + ⟨2, 8, 4, 0, 8, 6, 8624812418814503935558742390481538596222900633600000⟩, + ⟨2, 8, 1, 1, 4, 6, -24012869963624860411414032432585429502427922432000000⟩, + ⟨2, 8, 2, 1, 5, 6, -22905682807475217468874533725314715042845399449600000⟩, + ⟨2, 8, 3, 1, 6, 6, 31788639597476183613489232444234002555920292249600000⟩, + ⟨2, 8, 4, 1, 7, 6, -10058667878655666063875631180020581746481928601600000⟩, + ⟨2, 8, 5, 1, 8, 6, -12343698866558024406922430063550582775810621440000000⟩, + ⟨2, 8, 1, 2, 3, 6, -36269946895678324476681181913059481939905767014400000⟩, + ⟨2, 8, 2, 2, 4, 6, -84387452338224699255058092524565209414795840716800000⟩, + ⟨2, 8, 3, 2, 5, 6, 13527633324998223177715743151107136146323904921600000⟩, + ⟨2, 8, 4, 2, 6, 6, 6631611431101944289893318218862363867762130944000000⟩, + ⟨2, 8, 5, 2, 7, 6, -6327237058354739813150062954921675253121810432000000⟩, + ⟨2, 8, 6, 2, 8, 6, 2243119130091886503496688658565129490272144588800000⟩, + ⟨2, 8, 1, 3, 2, 6, 93460801194751278525545284932073964915929802342400000⟩, + ⟨2, 8, 2, 3, 3, 6, 96125532130509335690179006802171818129754161152000000⟩, + ⟨2, 8, 3, 3, 4, 6, -1473953218206267246239110745689485593015431987200000⟩, + ⟨2, 8, 4, 3, 5, 6, 18195118585572190931778777023850992821400607129600000⟩, + ⟨2, 8, 5, 3, 6, 6, 4329190353704962768021993684968787862133669888000000⟩, + ⟨2, 8, 6, 3, 7, 6, 4756012622521838273559610155778463989392998400000⟩, + ⟨2, 8, 7, 3, 8, 6, -126866278825895396817099475744494047505835622400000⟩, + ⟨2, 8, 1, 4, 1, 6, -42076831473966310760465180799228444927604241203200000⟩, + ⟨2, 8, 2, 4, 2, 6, -22919747212028893369778910488086173384607531008000000⟩, + ⟨2, 8, 3, 4, 3, 6, -21767297792968857171914321272673254624466672025600000⟩, + ⟨2, 8, 4, 4, 4, 6, -13636618854827934202757973627095916851320848384000000⟩, + ⟨2, 8, 5, 4, 5, 6, 2625012523364468502373289607413284251371569152000000⟩, + ⟨2, 8, 6, 4, 6, 6, 961136914957495727255958712169042387023586918400000⟩, + ⟨2, 8, 7, 4, 7, 6, -335571817650558707379425174350062120608779468800000⟩, + ⟨2, 8, 8, 4, 8, 6, 51349384450741479032824915758847958729097216000000⟩, + ⟨2, 8, 1, 5, 0, 6, -221770626619755827290995928671061114291015699660800000⟩, + ⟨2, 8, 2, 5, 1, 6, 23738030646937505783616554332725796702869100953600000⟩, + ⟨2, 8, 3, 5, 2, 6, -27180551736695484038488395761949372760772208230400000⟩, + ⟨2, 8, 4, 5, 3, 6, -12994114551473112407816072046323261471498384179200000⟩, + ⟨2, 8, 5, 5, 4, 6, 1741266973951060637101356977624639194817101824000000⟩, + ⟨2, 8, 6, 5, 5, 6, 802915798571966255061007375284614881076261683200000⟩, + ⟨2, 8, 7, 5, 6, 6, 106308501324597042653055570385983666351243264000000⟩, + ⟨2, 8, 8, 5, 7, 6, -84187430711873697919620139876199698070608281600000⟩, + ⟨2, 8, 2, 6, 0, 6, -427333944397273717768357539951956677091876300390400000⟩, + ⟨2, 8, 3, 6, 1, 6, -6617429826747974968346750570846153877467902771200000⟩, + ⟨2, 8, 4, 6, 2, 6, 16458313533359951954999257178513917587689255731200000⟩, + ⟨2, 8, 5, 6, 3, 6, -15867388230049528084519395157189603462924468224000000⟩, + ⟨2, 8, 6, 6, 4, 6, -535350743529605870166385211847746307113562931200000⟩, + ⟨2, 8, 7, 6, 5, 6, 664182855000383778634258526552612953956915609600000⟩, + ⟨2, 8, 8, 6, 6, 6, 125753839031004209893012161123344193106319769600000⟩, + ⟨2, 8, 3, 7, 0, 6, 695558319236090621421066806168461889761812519321600000⟩, + ⟨2, 8, 4, 7, 1, 6, 15810140787744503585085139765867131287272370995200000⟩, + ⟨2, 8, 5, 7, 2, 6, 879048853120342117804427010285474845212803072000000⟩, + ⟨2, 8, 6, 7, 3, 6, -2702552564729255370605021848777897210020259430400000⟩, + ⟨2, 8, 7, 7, 4, 6, 516461636182520893650226930115327419421294592000000⟩, + ⟨2, 8, 8, 7, 5, 6, 324835476650093237827734908401936022567387136000000⟩ +] + +def collectedFourData_11_4_18 : List CollectedFourTerm := [ + ⟨3, 1, 7, 3, 8, 0, -11827827505585121510985314019824667016289687961600000⟩, + ⟨3, 1, 7, 4, 7, 0, -31285583621108940764677262470878266806657823539200000⟩, + ⟨3, 1, 8, 4, 8, 0, 33511360717404640276321593599416140350418321408000000⟩, + ⟨3, 1, 7, 5, 6, 0, 9911212243957977989209490002829879489096318976000000⟩, + ⟨3, 1, 8, 5, 7, 0, -54941950884795288067987123313205704472459529420800000⟩, + ⟨3, 1, 7, 6, 5, 0, 61922209067805443841648023777716281539608077926400000⟩, + ⟨3, 1, 8, 6, 6, 0, 82068798028319278122469795704090501146114575564800000⟩, + ⟨3, 1, 7, 7, 4, 0, 48150061644058024393174795083351756072579760128000000⟩, + ⟨3, 1, 8, 7, 5, 0, 211992391890768982486858932856165772450089402368000000⟩ +] + +def collectedFourData_11_4_19 : List CollectedFourTerm := [ + ⟨3, 2, 6, 2, 8, 1, 93460801194751278525545284932073964915929802342400000⟩, + ⟨3, 2, 6, 3, 7, 1, 198161900645478771242313209764790824519021363200000⟩, + ⟨3, 2, 7, 3, 8, 1, -31715722730729470049843175136104492267996394291200000⟩, + ⟨3, 2, 6, 4, 6, 1, 40046302010762736431100124145154918302438601523200000⟩, + ⟨3, 2, 7, 4, 7, 1, -83890714091628627895941798256915651947936507494400000⟩, + ⟨3, 2, 8, 4, 8, 1, 44929511541354125574484592091921963825210851328000000⟩, + ⟨3, 2, 6, 5, 5, 1, 33453931545483960036170514729018880252752533913600000⟩, + ⟨3, 2, 7, 5, 6, 1, 26576415601795830189808046320797963192926994432000000⟩, + ⟨3, 2, 8, 5, 7, 1, -73662034711137831846504539306489994228376849612800000⟩, + ⟨3, 2, 6, 6, 4, 1, -22305685301891737765865376170655763298724190617600000⟩, + ⟨3, 2, 7, 6, 5, 1, 166041279579146626978823281153232541662644587724800000⟩, + ⟨3, 2, 8, 6, 6, 1, 110031670730796976065885296516589736416779226316800000⟩, + ⟨3, 2, 6, 7, 3, 1, -112603349765101149238507603877437757173959701299200000⟩, + ⟨3, 2, 7, 7, 4, 1, 129111961080711592251034290305110505928781725696000000⟩, + ⟨3, 2, 8, 7, 5, 1, 284223451815514157878685874301459132216076402688000000⟩ +] + +def collectedFourData_11_4_20 : List CollectedFourTerm := [ + ⟨3, 3, 5, 1, 8, 2, -105794169029092071682024458744117285422125547520000000⟩, + ⟨3, 3, 5, 2, 7, 2, -54228865599778769686477794612073793544316256256000000⟩, + ⟨3, 3, 6, 2, 8, 2, 96125532130509335690179006802171818129754161152000000⟩, + ⟨3, 3, 5, 3, 6, 2, 37104201989228329333141316527369492582895714304000000⟩, + ⟨3, 3, 6, 3, 7, 2, 203811843083253173419806000779561434387316736000000⟩, + ⟨3, 3, 7, 3, 8, 2, -16309996733509032989905318606138160897838809088000000⟩, + ⟨3, 3, 5, 4, 5, 2, 22498201033783185661723940072994615042313814016000000⟩, + ⟨3, 3, 6, 4, 6, 2, 41188092135249519572600334319113116521422913536000000⟩, + ⟨3, 3, 7, 4, 7, 2, -43141292551422580929583379790899959975227949056000000⟩, + ⟨3, 3, 8, 4, 8, 2, 15403510170632805821457194617481532883316244480000000⟩, + ⟨3, 3, 5, 5, 4, 2, 14923880966185770573167022451257474807540744192000000⟩, + ⟨3, 3, 6, 5, 5, 2, 34407761655780402144252955717860003640642633728000000⟩, + ⟨3, 3, 7, 5, 6, 2, 13667077850749604143185912682473852312936775680000000⟩, + ⟨3, 3, 8, 5, 7, 2, -25254089393296821966678100383827473632747061248000000⟩, + ⟨3, 3, 5, 6, 3, 2, -135994661779056844001846260346819525422866235392000000⟩, + ⟨3, 3, 6, 6, 4, 2, -22941659409832220124562701149036272416769179648000000⟩, + ⟨3, 3, 7, 6, 5, 2, 85387703460391987657069825313786100955062730752000000⟩, + ⟨3, 3, 8, 6, 6, 2, 37722955381643786644020017883023915216051109888000000⟩, + ⟨3, 3, 5, 7, 2, 2, 7534066081585727728081678435594905220993253376000000⟩, + ⟨3, 3, 6, 7, 3, 2, -115813868247216418213243366386425269794442838016000000⟩, + ⟨3, 3, 7, 7, 4, 2, 66396584475214232228990735315897750477906903040000000⟩, + ⟨3, 3, 8, 7, 5, 2, 97442386542372953692498541670237810423056302080000000⟩ +] + +def collectedFourData_11_4_21 : List CollectedFourTerm := [ + ⟨3, 4, 4, 0, 8, 3, -566736284782889082298281315287928778088345763840000⟩, + ⟨3, 4, 4, 1, 7, 3, 660954903897823647113444805744305113278751703040000⟩, + ⟨3, 4, 5, 1, 8, 3, 3244417012873847336662897817297133685067218944000000⟩, + ⟨3, 4, 4, 2, 6, 3, -435763080062795097394894456532410371747191193600000⟩, + ⟨3, 4, 5, 2, 7, 3, 1663050579776187730196871160526552238279308083200000⟩, + ⟨3, 4, 6, 2, 8, 3, -1473953218206267246239110745689485593015431987200000⟩, + ⟨3, 4, 4, 3, 5, 3, -1195600948477052143615616933549179679747069706240000⟩, + ⟨3, 4, 5, 3, 6, 3, -1137884112968992027790689866887223699716230348800000⟩, + ⟨3, 4, 6, 3, 7, 3, -3125175126346736211972816079051302161193369600000⟩, + ⟨3, 4, 7, 3, 8, 3, 166727622664982693721194484622640876524614451200000⟩, + ⟨3, 4, 4, 4, 4, 3, 896062004772012988373815856521808720176978329600000⟩, + ⟨3, 4, 5, 4, 5, 3, -689958122105858558117989452678702559673922355200000⟩, + ⟨3, 4, 6, 4, 6, 3, -631562911632077301854738284617365294971197849600000⟩, + ⟨3, 4, 7, 4, 7, 3, 441008374392586382350732446707299291951949414400000⟩, + ⟨3, 4, 8, 4, 8, 3, -118095852810739035837165028854288594568740864000000⟩, + ⟨3, 4, 4, 5, 3, 3, 853843057372530828046359731940770456424394260480000⟩, + ⟨3, 4, 5, 5, 4, 3, -457674498974349003144882562956433697414735462400000⟩, + ⟨3, 4, 6, 5, 5, 3, -527595841601745761859611712686525412876799180800000⟩, + ⟨3, 4, 7, 5, 6, 3, -139710598111350667506316939192014793743532032000000⟩, + ⟨3, 4, 8, 5, 7, 3, 193618414947136981349124806257580682191988326400000⟩, + ⟨3, 4, 4, 6, 2, 3, -1081475516538880059764915944789508025570589409280000⟩, + ⟨3, 4, 5, 6, 3, 3, 4170583297598054527381788184325646022892480102400000⟩, + ⟨3, 4, 6, 6, 4, 3, 351778887134833914193656649347216761298930892800000⟩, + ⟨3, 4, 7, 6, 5, 3, -872868893561743013562475229728671193581276364800000⟩, + ⟨3, 4, 8, 6, 6, 3, -289214895630095445294673680918981454592370278400000⟩, + ⟨3, 4, 4, 7, 1, 3, -1038884095889975578465732118948895373409522810880000⟩, + ⟨3, 4, 5, 7, 2, 3, -231049143781174180819662900997872456467428147200000⟩, + ⟨3, 4, 6, 7, 3, 3, 1775846853925725723464974600234240111707527577600000⟩, + ⟨3, 4, 7, 7, 4, 3, -678733715493851449673543359153001102359658496000000⟩, + ⟨3, 4, 8, 7, 5, 3, -747072687404371197131283331992530584332140544000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1113.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1113.lean new file mode 100644 index 0000000000000000000000000000000000000000..0be64974ca94d6827ae44a43964397dbb65d216d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1113.lean @@ -0,0 +1,636 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1113. -/ +namespace LaughlinFock +def collectedFourData_11_4_22 : List CollectedFourTerm := [ + ⟨3, 5, 3, 0, 7, 4, -5438008876681617106626386310839213721653933506560000⟩, + ⟨3, 5, 4, 0, 8, 4, 20988116408986785499943765149776245463671227023360000⟩, + ⟨3, 5, 3, 1, 6, 4, 25785436867385713148598719097810723321502047928320000⟩, + ⟨3, 5, 4, 1, 7, 4, -24477343054561072919886776737757262714239094620160000⟩, + ⟨3, 5, 5, 1, 8, 4, -60075738728798424931282333226662235967521292288000000⟩, + ⟨3, 5, 3, 2, 5, 4, 10972974606141325273912805405114582328228414750720000⟩, + ⟨3, 5, 4, 2, 6, 4, 16137746067556364422929099717706420822489851494400000⟩, + ⟨3, 5, 5, 2, 7, 4, -30794127797682016740455341181856925070504912486400000⟩, + ⟨3, 5, 6, 2, 8, 4, 18195118585572190931778777023850992821400607129600000⟩, + ⟨3, 5, 3, 3, 4, 4, -1195600948477052143615616933549179679747069706240000⟩, + ⟨3, 5, 4, 3, 5, 4, 44277051883036593914256533204748724573192543272960000⟩, + ⟨3, 5, 5, 3, 6, 4, 21069803420191141837419289511650832070378887577600000⟩, + ⟨3, 5, 6, 3, 7, 4, 38578518858121544006308446848801142339325132800000⟩, + ⟨3, 5, 7, 3, 8, 4, -1543618631382860104049873920208711807109641011200000⟩, + ⟨3, 5, 3, 4, 3, 4, -17656599657027941881986556662945987570752311787520000⟩, + ⟨3, 5, 4, 4, 4, 4, -33184135497923375781258623228015021316330907238400000⟩, + ⟨3, 5, 5, 4, 5, 4, 12775714007469251921939839935951717020520048230400000⟩, + ⟨3, 5, 6, 4, 6, 4, 7796286835602117700012104271304543602488429772800000⟩, + ⟨3, 5, 7, 4, 7, 4, -4082999160110016924663855944976221607721068134400000⟩, + ⟨3, 5, 8, 4, 8, 4, 874695893932357019641024002600534930579731251200000⟩, + ⟨3, 5, 3, 5, 2, 4, -22047574532976130785999491676607591632581878087680000⟩, + ⟨3, 5, 4, 5, 3, 4, -31620628437448721405244151429717420062669715537920000⟩, + ⟨3, 5, 5, 5, 4, 4, 8474599138802446746165773243417114679710633164800000⟩, + ⟨3, 5, 6, 5, 5, 4, 6512872175740338746265575699966302311221192294400000⟩, + ⟨3, 5, 7, 5, 6, 4, 1293486219015214928542784678154847785301573632000000⟩, + ⟨3, 5, 8, 5, 7, 4, -1434065875415326465835794079601928261403274117120000⟩, + ⟨3, 5, 3, 6, 1, 4, -5367745244295144028959163936396719531943306199040000⟩, + ⟨3, 5, 4, 6, 2, 4, 40050610211559955170518896220349427024804309893120000⟩, + ⟨3, 5, 5, 6, 3, 4, -77225236934403124074294671628281074053058186444800000⟩, + ⟨3, 5, 6, 6, 4, 4, -4342511341783441044063925648048876386548868710400000⟩, + ⟨3, 5, 7, 6, 5, 4, 8081304497238744919093524941089507172097510604800000⟩, + ⟨3, 5, 8, 6, 6, 4, 2142116557447099487348922957914168854561129758720000⟩, + ⟨3, 5, 3, 7, 0, 4, 564203921757981724985700071741759632896223315230720000⟩, + ⟨3, 5, 4, 7, 1, 4, 38473309236476314620327728312007766585047011819520000⟩, + ⟨3, 5, 5, 7, 2, 4, 4278256444912223413276936425885482678258919014400000⟩, + ⟨3, 5, 6, 7, 3, 4, -21921824721354298348473152363612760192022531276800000⟩, + ⟨3, 5, 7, 7, 4, 4, 6283937791695443510257247879203807549294903296000000⟩, + ⟨3, 5, 8, 7, 5, 4, 5533313800518084962419046721499666751794918195200000⟩ +] + +def collectedFourData_11_4_23 : List CollectedFourTerm := [ + ⟨3, 6, 2, 0, 6, 5, 18107224855352482944107617059998148474447278899200000⟩, + ⟨3, 6, 3, 0, 7, 5, -5175492638110041695433505831910209515104187187200000⟩, + ⟨3, 6, 4, 0, 8, 5, 9987464568905975789350873812420174389582600601600000⟩, + ⟨3, 6, 2, 1, 5, 5, -8841533178051513783114553875225254286966600499200000⟩, + ⟨3, 6, 3, 1, 6, 5, 24540662162184870762548040566584531076690372198400000⟩, + ⟨3, 6, 4, 1, 7, 5, -11647857851298589459464084048045362328465152409600000⟩, + ⟨3, 6, 5, 1, 8, 5, -19058540884523722409072889720166616816701931520000000⟩, + ⟨3, 6, 2, 2, 4, 5, -32573334134189691855011069523556073127137614233600000⟩, + ⟨3, 6, 3, 2, 5, 5, 10443261601828720059545324392990194570107446886400000⟩, + ⟨3, 6, 4, 2, 6, 5, 7679353589000879934429192858406392051913457664000000⟩, + ⟨3, 6, 5, 2, 7, 5, -9769187296801961159546303530907411086055571456000000⟩, + ⟨3, 6, 6, 2, 8, 5, 4329190353704962768021993684968787862133669888000000⟩, + ⟨3, 6, 2, 3, 3, 5, 37104201989228329333141316527369492582895714304000000⟩, + ⟨3, 6, 3, 3, 4, 5, -1137884112968992027790689866887223699716230348800000⟩, + ⟨3, 6, 4, 3, 5, 5, 21069803420191141837419289511650832070378887577600000⟩, + ⟨3, 6, 5, 3, 6, 5, 6684224254409301264148254901468715112783151104000000⟩, + ⟨3, 6, 6, 3, 7, 5, 9179041670728007461764804166140925505961984000000⟩, + ⟨3, 6, 7, 3, 8, 5, -293820295035874669004193582489579285285489868800000⟩, + ⟨3, 6, 2, 4, 2, 5, -8846962001131622210935227484913961001619030016000000⟩, + ⟨3, 6, 3, 4, 3, 5, -16804239127091550462466962504746190614269683302400000⟩, + ⟨3, 6, 4, 4, 4, 5, -15791096784339045162538766561978981941776482304000000⟩, + ⟨3, 6, 5, 4, 5, 5, 4052991655075818001035905544492413137994121216000000⟩, + ⟨3, 6, 6, 4, 6, 5, 1854981576771310347815312556147862665569501184000000⟩, + ⟨3, 6, 7, 4, 7, 5, -777179021725090079940883385332110891842902425600000⟩, + ⟨3, 6, 8, 4, 8, 5, 138745089188920548045686077768021345277313024000000⟩, + ⟨3, 6, 2, 5, 1, 5, 9162817249787792646417290213398941619471987507200000⟩, + ⟨3, 6, 3, 5, 2, 5, -20983242630017705852924151843015080633435789721600000⟩, + ⟨3, 6, 4, 5, 3, 5, -15047081882504469809497041010952625911061754675200000⟩, + ⟨3, 6, 5, 5, 4, 5, 2688497845959761060635070987862289158443630592000000⟩, + ⟨3, 6, 6, 5, 5, 5, 1549616907717551475784532563381177672984952832000000⟩, + ⟨3, 6, 7, 5, 6, 5, 246208807518354525546685373584555866920583168000000⟩, + ⟨3, 6, 8, 5, 7, 5, -227472884196108776316491735027129804455831142400000⟩, + ⟨3, 6, 2, 6, 0, 5, -164949775968393351265635903861508150965117439180800000⟩, + ⟨3, 6, 3, 6, 1, 5, -5108620935545817926213231172688776097247841484800000⟩, + ⟨3, 6, 4, 6, 2, 5, 19058596905806344639448183416068065397044359987200000⟩, + ⟨3, 6, 5, 6, 3, 5, -24499080104125601607819201931580509515040161792000000⟩, + ⟨3, 6, 6, 6, 4, 5, -1033219878358493729698659731568301079173005312000000⟩, + ⟨3, 6, 7, 6, 5, 5, 1538236986376785490392782808413220298109956915200000⟩, + ⟨3, 6, 8, 6, 6, 5, 339784552411589695858096393225018474490127974400000⟩, + ⟨3, 6, 3, 7, 0, 5, 536967355086980232541147090040676199823946704486400000⟩, + ⟨3, 6, 4, 7, 1, 5, 18308017992664648149036005668981667403431883571200000⟩, + ⟨3, 6, 5, 7, 2, 5, 1357242159566658579254217851143849543861272576000000⟩, + ⟨3, 6, 6, 7, 3, 5, -5215890826595210470777308819461530011045986304000000⟩, + ⟨3, 6, 7, 7, 4, 5, 1196116980195409729520297388653389084417327104000000⟩, + ⟨3, 6, 8, 7, 5, 5, 877699463423497935716234692855263589935611904000000⟩ +] + +def collectedFourData_11_4_24 : List CollectedFourTerm := [ + ⟨3, 7, 1, 0, 5, 6, -116556581094916281596952323237876982856915353600000⟩, + ⟨3, 7, 2, 0, 6, 6, 99462235354466222923393415570697440967052492800000⟩, + ⟨3, 7, 3, 0, 7, 6, -14214383235397989839198007549351161193981542400000⟩, + ⟨3, 7, 4, 0, 8, 6, 18286909589632258200501515779279960455040204800000⟩, + ⟨3, 7, 1, 1, 4, 6, -50913708112015017667045893079090625853259776000000⟩, + ⟨3, 7, 2, 1, 5, 6, -48566175152440974538054750920876303196146892800000⟩, + ⟨3, 7, 3, 1, 6, 6, 67400419866331873555362172810641918166617292800000⟩, + ⟨3, 7, 4, 1, 7, 6, -21327066741516149647833596376664035210087628800000⟩, + ⟨3, 7, 5, 1, 8, 6, -26171943714622782376664351599184253466705920000000⟩, + ⟨3, 7, 1, 2, 3, 6, -76901990152871024708332216081946371758961459200000⟩, + ⟨3, 7, 2, 2, 4, 6, -178923973817929138173602386394286516309747302400000⟩, + ⟨3, 7, 3, 2, 5, 6, 28682201486063340368958316223895639088221388800000⟩, + ⟨3, 7, 4, 2, 6, 6, 14060790285663054469981751930703999236308992000000⟩, + ⟨3, 7, 5, 2, 7, 6, -13415435190903298183375266727255830247243776000000⟩, + ⟨3, 7, 6, 2, 8, 6, 4756012622521838273559610155778463989392998400000⟩, + ⟨3, 7, 1, 3, 2, 6, 198161900645478771242313209764790824519021363200000⟩, + ⟨3, 7, 2, 3, 3, 6, 203811843083253173419806000779561434387316736000000⟩, + ⟨3, 7, 3, 3, 4, 6, -3125175126346736211972816079051302161193369600000⟩, + ⟨3, 7, 4, 3, 5, 6, 38578518858121544006308446848801142339325132800000⟩, + ⟨3, 7, 5, 3, 6, 6, 9179041670728007461764804166140925505961984000000⟩, + ⟨3, 7, 6, 3, 7, 6, 10084019061734125758572616199782406501171200000⟩, + ⟨3, 7, 7, 3, 8, 6, -268990449670685540332857760503009601860403200000⟩, + ⟨3, 7, 1, 4, 1, 6, -89214138884237666052199150400898191419087257600000⟩, + ⟨3, 7, 2, 4, 2, 6, -48595995452525881808530994914804039516422144000000⟩, + ⟨3, 7, 3, 4, 3, 6, -46152494387273512898970909949892262521261260800000⟩, + ⟨3, 7, 4, 4, 4, 6, -28913279964503806869293272843731570536742912000000⟩, + ⟨3, 7, 5, 4, 5, 6, 5565728778251692209512397844295135564660736000000⟩, + ⟨3, 7, 6, 4, 6, 6, 2037867377700218620474874016910673645351731200000⟩, + ⟨3, 7, 7, 4, 7, 6, -711502023721440235069457665298018135860838400000⟩, + ⟨3, 7, 8, 4, 8, 6, 108874431736690237587476639061626887077888000000⟩, + ⟨3, 7, 1, 5, 0, 6, -470213055275815902175345048137380214409160294400000⟩, + ⟨3, 7, 2, 5, 1, 6, 50330975237155718408259777889747639001205964800000⟩, + ⟨3, 7, 3, 5, 2, 6, -57630040871496723358635029328345326270231347200000⟩, + ⟨3, 7, 4, 5, 3, 6, -27550998962221526168650326339253383259068825600000⟩, + ⟨3, 7, 5, 5, 4, 6, 3691951798811688084512607794837418600824832000000⟩, + ⟨3, 7, 6, 5, 5, 6, 1702396284531729724233317231327166047295897600000⟩, + ⟨3, 7, 7, 5, 6, 6, 225402461865880326479735592612415250890752000000⟩, + ⟨3, 7, 8, 5, 7, 6, -178499874461394409638322060506291931761868800000⟩, + ⟨3, 7, 2, 6, 0, 6, -906062280117161809860122142831279280737170227200000⟩, + ⟨3, 7, 3, 6, 1, 6, -14030721490648887818667774390195133886339481600000⟩, + ⟨3, 7, 4, 6, 2, 6, 34896027527024591659498209055533539830372761600000⟩, + ⟨3, 7, 5, 6, 3, 6, -33643107802963036649868174255226665704620032000000⟩, + ⟨3, 7, 6, 6, 4, 6, -1135086790329748425185195107046823445502361600000⟩, + ⟨3, 7, 7, 6, 5, 6, 1408245331096176938614007669862795588717772800000⟩, + ⟨3, 7, 8, 6, 6, 6, 266631779711822784856244678920036567272652800000⟩, + ⟨3, 7, 3, 7, 0, 6, 1474769708665187975946925612524290505838480588800000⟩, + ⟨3, 7, 4, 7, 1, 6, 33521727910759703683822211895935883430959513600000⟩, + ⟨3, 7, 5, 7, 2, 6, 1863818726864690751917261851057421650231296000000⟩, + ⟨3, 7, 6, 7, 3, 6, -5730134409024715465927945328763287064752947200000⟩, + ⟨3, 7, 7, 7, 4, 6, 1095036829645214433657056487414288567238656000000⟩, + ⟨3, 7, 8, 7, 5, 6, 688738108674350953567296408380678967656448000000⟩ +] + +def collectedFourData_11_4_25 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 4, 7, -5627721229070855875447475083812689295729229824000000⟩, + ⟨3, 8, 1, 0, 5, 7, 18654828180426477355506987005352981383901452697600000⟩, + ⟨3, 8, 2, 0, 6, 7, -7959442931273634914346826264587686856435852902400000⟩, + ⟨3, 8, 3, 0, 7, 7, 758335206404029738862010992050431846517624012800000⟩, + ⟨3, 8, 4, 0, 8, 7, -731702905878349680485442804875277396459336499200000⟩, + ⟨3, 8, 0, 1, 3, 7, -4423179003039954306993517385722787402485648588800000⟩, + ⟨3, 8, 1, 1, 4, 7, 8148715996435928998138421713534121636649762816000000⟩, + ⟨3, 8, 2, 1, 5, 7, 3886497203068698178615912351049949066058688102400000⟩, + ⟨3, 8, 3, 1, 6, 7, -3595802256391179611596178560666306646357154201600000⟩, + ⟨3, 8, 4, 1, 7, 7, 853346850770025837172388353166315105293644595200000⟩, + ⟨3, 8, 5, 1, 8, 7, 837761555045089460448901855699643328620396544000000⟩, + ⟨3, 8, 0, 2, 2, 7, -3689808806938585534735573743683292908301267763200000⟩, + ⟨3, 8, 1, 2, 3, 7, 12308128803695915184445325202684974634879890227200000⟩, + ⟨3, 8, 2, 2, 4, 7, 14318350613829795254128015891157533551188194099200000⟩, + ⟨3, 8, 3, 2, 5, 7, -1530191132731677133600639025411442510023727513600000⟩, + ⟨3, 8, 4, 2, 6, 7, -562605784238069343741301272104912213841543168000000⟩, + ⟨3, 8, 5, 2, 7, 7, 429426869081120177631767758482119696762221363200000⟩, + ⟨3, 8, 6, 2, 8, 7, -126866278825895396817099475744494047505835622400000⟩, + ⟨3, 8, 0, 3, 1, 7, -11827827505585121510985314019824667016289687961600000⟩, + ⟨3, 8, 1, 3, 2, 7, -31715722730729470049843175136104492267996394291200000⟩, + ⟨3, 8, 2, 3, 3, 7, -16309996733509032989905318606138160897838809088000000⟩, + ⟨3, 8, 3, 3, 4, 7, 166727622664982693721194484622640876524614451200000⟩, + ⟨3, 8, 4, 3, 5, 7, -1543618631382860104049873920208711807109641011200000⟩, + ⟨3, 8, 5, 3, 6, 7, -293820295035874669004193582489579285285489868800000⟩, + ⟨3, 8, 6, 3, 7, 7, -268990449670685540332857760503009601860403200000⟩, + ⟨3, 8, 7, 3, 8, 7, 6150257146289170553160849595208693544753561600000⟩, + ⟨3, 8, 0, 4, 0, 7, -37771310278015105387738218905586965755119796224000000⟩, + ⟨3, 8, 1, 4, 1, 7, 14278682649372487318685339111478988455848548761600000⟩, + ⟨3, 8, 2, 4, 2, 7, 3888883565851249654027521539478013219493117952000000⟩, + ⟨3, 8, 3, 4, 3, 7, 2462228629806176846142984748856977155872627097600000⟩, + ⟨3, 8, 4, 4, 4, 7, 1156889351085108042042744533707708725196750848000000⟩, + ⟨3, 8, 5, 4, 5, 7, -178158475620676615504081616602717835855344435200000⟩, + ⟨3, 8, 6, 4, 6, 7, -54359958954950207363108921062372286789792563200000⟩, + ⟨3, 8, 7, 4, 7, 7, 16267939666070905171362980018632725206610739200000⟩, + ⟨3, 8, 8, 4, 8, 7, -2178162955504398799473944390168264809906176000000⟩, + ⟨3, 8, 1, 5, 0, 7, 75257387201676514763644593334077761363577824870400000⟩, + ⟨3, 8, 2, 5, 1, 7, -4027724931455592166226847833358391547053631078400000⟩, + ⟨3, 8, 3, 5, 2, 7, 3074554007417367648128963683036737135285003878400000⟩, + ⟨3, 8, 4, 5, 3, 7, 1102381236244427604577384307330097969556252262400000⟩, + ⟨3, 8, 5, 5, 4, 7, -118179043706100003526731570281766503938680422400000⟩, + ⟨3, 8, 6, 5, 5, 7, -45411292788169860189249836727944033823463833600000⟩, + ⟨3, 8, 7, 5, 6, 7, -5153651750755369819660909884861228804734976000000⟩, + ⟨3, 8, 8, 5, 7, 7, 3571103039640209521563049345783908120762777600000⟩, + ⟨3, 8, 2, 6, 0, 7, 72507429428574383536181360433587527131005032857600000⟩, + ⟨3, 8, 3, 6, 1, 7, 748536879961979587436031764562893237361259315200000⟩, + ⟨3, 8, 4, 6, 2, 7, -1396273362646850731832071678936177380663125606400000⟩, + ⟨3, 8, 5, 6, 3, 7, 1076912842885736248539398534987151479650281062400000⟩, + ⟨3, 8, 6, 6, 4, 7, 30278354719169651133017023749628477484669337600000⟩, + ⟨3, 8, 7, 6, 5, 7, -32198432776725087464504757701685764629620326400000⟩, + ⟨3, 8, 8, 6, 6, 7, -5334286995252214555269739722445829466331545600000⟩, + ⟨3, 8, 3, 7, 0, 7, -78678742010694971188519302219466106911634069913600000⟩, + ⟨3, 8, 4, 7, 1, 7, -1341284354370754083453808641179778156943795814400000⟩, + ⟨3, 8, 5, 7, 2, 7, -59660669148845723608960261329111145551967027200000⟩, + ⟨3, 8, 6, 7, 3, 7, 152850904180258805204374783769668192461599539200000⟩, + ⟨3, 8, 7, 7, 4, 7, -25037164312786633719986903600599463916208128000000⟩, + ⟨3, 8, 8, 7, 5, 7, -13779027917103500002870802799454530406711296000000⟩ +] + +def collectedFourData_11_4_26 : List CollectedFourTerm := [ + ⟨4, 0, 7, 3, 8, 0, -37771310278015105387738218905586965755119796224000000⟩, + ⟨4, 0, 7, 4, 7, 0, -99908244825492550143643467244121818058025074688000000⟩, + ⟨4, 0, 8, 4, 8, 0, 107016102737200014747580664090888872500784005120000000⟩, + ⟨4, 0, 7, 5, 6, 0, 31650738288246587200867990358431970041150832640000000⟩, + ⟨4, 0, 8, 5, 7, 0, -175453139908334161258911563833499750728269299712000000⟩, + ⟨4, 0, 7, 6, 5, 0, 197744088734450612777113907218506014778086916096000000⟩, + ⟨4, 0, 8, 6, 6, 0, 262080761070251393974028429594590372378938703872000000⟩, + ⟨4, 0, 7, 7, 4, 0, 153763733653072013715609358118476210642008145920000000⟩, + ⟨4, 0, 8, 7, 5, 0, 676982345819955514790034518161639983719928299520000000⟩ +] + +def collectedFourData_11_4_27 : List CollectedFourTerm := [ + ⟨4, 1, 6, 2, 8, 1, -42076831473966310760465180799228444927604241203200000⟩, + ⟨4, 1, 6, 3, 7, 1, -89214138884237666052199150400898191419087257600000⟩, + ⟨4, 1, 7, 3, 8, 1, 14278682649372487318685339111478988455848548761600000⟩, + ⟨4, 1, 6, 4, 6, 1, -18029178857039928775865086720131083006081866137600000⟩, + ⟨4, 1, 7, 4, 7, 1, 37768298515959906357874805496643020814548153139200000⟩, + ⟨4, 1, 8, 4, 8, 1, -20227640477785152278675553174318382502016712704000000⟩, + ⟨4, 1, 6, 5, 5, 1, -15061238741659601372153853304077848320771149004800000⟩, + ⟨4, 1, 7, 5, 6, 1, -11964923755882082590995383456770467181652606976000000⟩, + ⟨4, 1, 8, 5, 7, 1, 33163261826863816014159532622390014664486839910400000⟩, + ⟨4, 1, 6, 6, 4, 1, 10042205388366976045835583691553868369904848076800000⟩, + ⟨4, 1, 7, 6, 5, 1, -74753167630300980341989118895348136848650561126400000⟩, + ⟨4, 1, 8, 6, 6, 1, -49537175018340231547511974303736096845885498982400000⟩, + ⟨4, 1, 6, 7, 3, 1, 50694966348483740372319792397796713248782391705600000⟩, + ⟨4, 1, 7, 7, 4, 1, -58127280723241786225400478945011209209410224128000000⟩, + ⟨4, 1, 8, 7, 5, 1, -127959766341720580726595197836427112837686493184000000⟩ +] + +def collectedFourData_11_4_28 : List CollectedFourTerm := [ + ⟨4, 2, 5, 1, 8, 2, 25225094279440099324909143848593114286606254080000000⟩, + ⟨4, 2, 5, 2, 7, 2, 12930091138060192105498032223684781747390644224000000⟩, + ⟨4, 2, 6, 2, 8, 2, -22919747212028893369778910488086173384607531008000000⟩, + ⟨4, 2, 5, 3, 6, 2, -8846962001131622210935227484913961001619030016000000⟩, + ⟨4, 2, 6, 3, 7, 2, -48595995452525881808530994914804039516422144000000⟩, + ⟨4, 2, 7, 3, 8, 2, 3888883565851249654027521539478013219493117952000000⟩, + ⟨4, 2, 5, 4, 5, 2, -5364371660586670713106859111544896428141707264000000⟩, + ⟨4, 2, 6, 4, 6, 2, -9820706725492873788962223106268783805248569344000000⟩, + ⟨4, 2, 7, 4, 7, 2, 10286419203758652033258444589620094581734375424000000⟩, + ⟨4, 2, 8, 4, 8, 2, -3672744914530017434520293298278047888095313920000000⟩, + ⟨4, 2, 5, 5, 4, 2, -3558384245956475107045762247406341194323591168000000⟩, + ⟨4, 2, 6, 5, 5, 2, -8204034680520929816823162785271129596611264512000000⟩, + ⟨4, 2, 7, 5, 6, 2, -3258717663492431980930708822692991341397278720000000⟩, + ⟨4, 2, 8, 5, 7, 2, 6021473505899398043087629571526274383549038592000000⟩, + ⟨4, 2, 5, 6, 3, 2, 32425966349184512986699569798084090942317395968000000⟩, + ⟨4, 2, 6, 6, 4, 2, 5470107916634659604097773463418754874256392192000000⟩, + ⟨4, 2, 7, 6, 5, 2, -20359466782152827672005868644937693298224529408000000⟩, + ⟨4, 2, 8, 6, 6, 2, -8994494826453131864500325078847071665784881152000000⟩, + ⟨4, 2, 5, 7, 2, 2, -1796389432042054558150675728932277929801416704000000⟩, + ⟨4, 2, 6, 7, 3, 2, 27614147095378531563868641771430785071934603264000000⟩, + ⟨4, 2, 7, 7, 4, 2, -15831308271437174232634970082425381027221340160000000⟩, + ⟨4, 2, 8, 7, 5, 2, -23233732160314861137185870286407331028999864320000000⟩ +] + +def collectedFourData_11_4_29 : List CollectedFourTerm := [ + ⟨4, 3, 4, 0, 8, 3, -8369544791905049647299673445810237540430847672320000⟩, + ⟨4, 3, 4, 1, 7, 3, 9760962589013237523589083347326356937433331793920000⟩, + ⟨4, 3, 5, 1, 8, 3, 47913455061852942040987663238956837106312282112000000⟩, + ⟨4, 3, 4, 2, 6, 3, -6435336355146647552316066573235059200730385612800000⟩, + ⟨4, 3, 5, 2, 7, 3, 24559882069263809072113926520495752281287399833600000⟩, + ⟨4, 3, 6, 2, 8, 3, -21767297792968857171914321272673254624466672025600000⟩, + ⟨4, 3, 4, 3, 5, 3, -17656599657027941881986556662945987570752311787520000⟩, + ⟨4, 3, 5, 3, 6, 3, -16804239127091550462466962504746190614269683302400000⟩, + ⟨4, 3, 6, 3, 7, 3, -46152494387273512898970909949892262521261260800000⟩, + ⟨4, 3, 7, 3, 8, 3, 2462228629806176846142984748856977155872627097600000⟩, + ⟨4, 3, 4, 4, 4, 3, 13233017342689874868414539975613534777094491340800000⟩, + ⟨4, 3, 5, 4, 5, 3, -10189281262829114614456700674793407180145531289600000⟩, + ⟨4, 3, 6, 4, 6, 3, -9326902511342844484044171388459901258763652300800000⟩, + ⟨4, 3, 7, 4, 7, 3, 6512798707599925992624430377887344414038373171200000⟩, + ⟨4, 3, 8, 4, 8, 3, -1744036082348874998411112631363759354278838272000000⟩, + ⟨4, 3, 4, 5, 3, 3, 12609529168710657631339012420389109807302353879040000⟩, + ⟨4, 3, 5, 5, 4, 3, -6758923545447512292935235837750821615027041075200000⟩, + ⟨4, 3, 6, 5, 5, 3, -7791519877715747102691550555484444107848705638400000⟩, + ⟨4, 3, 7, 5, 6, 3, -2063242005485402809524084986200766592829095936000000⟩, + ⟨4, 3, 8, 5, 7, 3, 2859351059652934474391894972840985727448855347200000⟩, + ⟨4, 3, 4, 6, 2, 3, -15971198633396710394287109394312972510936107581440000⟩, + ⟨4, 3, 5, 6, 3, 3, 61591051525825763464030034333778451237914751795200000⟩, + ⟨4, 3, 6, 6, 4, 3, 5195060263080575051148646306550051717759002214400000⟩, + ⟨4, 3, 7, 6, 5, 3, -12890502158202695833217633510442780923097671270400000⟩, + ⟨4, 3, 8, 6, 6, 3, -4271117075889245355519254642735066430573851443200000⟩, + ⟨4, 3, 4, 7, 1, 3, -15342209785420555069136763964218763797458048778240000⟩, + ⟨4, 3, 5, 7, 2, 3, -3412126962628936615911387035664077358823479705600000⟩, + ⟨4, 3, 6, 7, 3, 3, 26225654129749079034109115605978723090363632844800000⟩, + ⟨4, 3, 7, 7, 4, 3, -10023519555975039841255223876603796960741163008000000⟩, + ⟨4, 3, 8, 7, 5, 3, -11032747484017357503145309081134283325190438912000000⟩ +] + +def collectedFourData_11_4_30 : List CollectedFourTerm := [ + ⟨4, 4, 3, 0, 7, 4, 4075601597852745847300673206901689552682247782400000⟩, + ⟨4, 4, 4, 0, 8, 4, -15729875164268530195174121135891681983934654054400000⟩, + ⟨4, 4, 3, 1, 6, 4, -19325302713035854377846207084516721535287610572800000⟩, + ⟨4, 4, 4, 1, 7, 4, 18344931155249313475698277509726338321897383526400000⟩, + ⟨4, 4, 5, 1, 8, 4, 45024710754919579538042620915263236109521387520000000⟩, + ⟨4, 4, 3, 2, 5, 4, -8223869039595451370487038070782967026086104268800000⟩, + ⟨4, 4, 4, 2, 6, 4, -12094688543209843422685741958287026673812504576000000⟩, + ⟨4, 4, 5, 2, 7, 4, 23079145198692637211605198051283827491399008256000000⟩, + ⟨4, 4, 6, 2, 8, 4, -13636618854827934202757973627095916851320848384000000⟩, + ⟨4, 4, 3, 3, 4, 4, 896062004772012988373815856521808720176978329600000⟩, + ⟨4, 4, 4, 3, 5, 4, -33184135497923375781258623228015021316330907238400000⟩, + ⟨4, 4, 5, 3, 6, 4, -15791096784339045162538766561978981941776482304000000⟩, + ⟨4, 4, 6, 3, 7, 4, -28913279964503806869293272843731570536742912000000⟩, + ⟨4, 4, 7, 3, 8, 4, 1156889351085108042042744533707708725196750848000000⟩, + ⟨4, 4, 3, 4, 3, 4, 13233017342689874868414539975613534777094491340800000⟩, + ⟨4, 4, 4, 4, 4, 4, 24870374198658527853024531727031581122112782336000000⟩, + ⟨4, 4, 5, 4, 5, 4, -9574960542235226249888818228625960074022486016000000⟩, + ⟨4, 4, 6, 4, 6, 4, -5843050242295263877415930870647894329903808512000000⟩, + ⟨4, 4, 7, 4, 7, 4, 3060068175381552914624175038884453171568050176000000⟩, + ⟨4, 4, 8, 4, 8, 4, -655554645788171550885726491217962099118440448000000⟩, + ⟨4, 4, 3, 5, 2, 4, 16523902780057185514830996522136589089717302067200000⟩, + ⟨4, 4, 4, 5, 3, 4, 23698579150428850127941829218687523512487038156800000⟩, + ⟨4, 4, 5, 5, 4, 4, -6351422105868500588774575976759548457036808192000000⟩, + ⟨4, 4, 6, 5, 5, 4, -4881174865285549354599886673161985665139736576000000⟩, + ⟨4, 4, 7, 5, 6, 4, -969423666008400420557404317604866491185889280000000⟩, + ⟨4, 4, 8, 5, 7, 4, 1074783308709003772012266796681291038787947724800000⟩, + ⟨4, 4, 3, 6, 1, 4, 4022941409368464761334529827997677339459295641600000⟩, + ⟨4, 4, 4, 6, 2, 4, -30016562067993110518476488512960318503759170764800000⟩, + ⟨4, 4, 5, 6, 3, 4, 57877672909660739008079546775541828406992699392000000⟩, + ⟨4, 4, 6, 6, 4, 4, 3254563676634921583806726628230529116291465216000000⟩, + ⟨4, 4, 7, 6, 5, 4, -6056661228140387064565823706698920408532385792000000⟩, + ⟨4, 4, 8, 6, 6, 4, -1605443069751974500527912564198331616202640588800000⟩, + ⟨4, 4, 3, 7, 0, 4, -422851535769246338540704008504869409698358283468800000⟩, + ⟨4, 4, 4, 7, 1, 4, -28834428952706923306727194488504491225394236620800000⟩, + ⟨4, 4, 5, 7, 2, 4, -3206406829837348713264162674238080728355045376000000⟩, + ⟨4, 4, 6, 7, 3, 4, 16429657598631817252112575682133913841719836672000000⟩, + ⟨4, 4, 7, 7, 4, 4, -4709596377170581011866420316857554526105763840000000⟩, + ⟨4, 4, 8, 7, 5, 4, -4147029377519807987165260190729974508534366208000000⟩ +] + +def collectedFourData_11_4_31 : List CollectedFourTerm := [ + ⟨4, 5, 2, 0, 6, 5, 10979349052646429597492879695006022464361516236800000⟩, + ⟨4, 5, 3, 0, 7, 5, -3138169468106818059950150511578903866275318988800000⟩, + ⟨4, 5, 4, 0, 8, 5, 6055917487573663812874984412709014850498881126400000⟩, + ⟨4, 5, 2, 1, 5, 5, -5361079883739709299274330906550394779941522636800000⟩, + ⟨4, 5, 3, 1, 6, 5, 14880275581382318791179330732421609683894770073600000⟩, + ⟨4, 5, 4, 1, 7, 5, -7062700004369386504881087595479193604512441958400000⟩, + ⟨4, 5, 5, 1, 8, 5, -11556181274430052424402691835136267857774510080000000⟩, + ⟨4, 5, 2, 2, 4, 5, -19750900987018717043549456269265970610647230054400000⟩, + ⟨4, 5, 3, 2, 5, 5, 6332290855751068537892989455295143140556118425600000⟩, + ⟨4, 5, 4, 2, 6, 5, 4656390155082793998584109031513830315006099456000000⟩, + ⟨4, 5, 5, 2, 7, 5, -5923564662674543850689835975674029240718721024000000⟩, + ⟨4, 5, 6, 2, 8, 5, 2625012523364468502373289607413284251371569152000000⟩, + ⟨4, 5, 2, 3, 3, 5, 22498201033783185661723940072994615042313814016000000⟩, + ⟨4, 5, 3, 3, 4, 5, -689958122105858558117989452678702559673922355200000⟩, + ⟨4, 5, 4, 3, 5, 5, 12775714007469251921939839935951717020520048230400000⟩, + ⟨4, 5, 5, 3, 6, 5, 4052991655075818001035905544492413137994121216000000⟩, + ⟨4, 5, 6, 3, 7, 5, 5565728778251692209512397844295135564660736000000⟩, + ⟨4, 5, 7, 3, 8, 5, -178158475620676615504081616602717835855344435200000⟩, + ⟨4, 5, 2, 4, 2, 5, -5364371660586670713106859111544896428141707264000000⟩, + ⟨4, 5, 3, 4, 3, 5, -10189281262829114614456700674793407180145531289600000⟩, + ⟨4, 5, 4, 4, 4, 5, -9574960542235226249888818228625960074022486016000000⟩, + ⟨4, 5, 5, 4, 5, 5, 2457538935094553259908117472654644544289112064000000⟩, + ⟨4, 5, 6, 4, 6, 5, 1124771486536234528749946024658660424507457536000000⟩, + ⟨4, 5, 7, 4, 7, 5, -471243927442129355998962888347135704713029222400000⟩, + ⟨4, 5, 8, 4, 8, 5, 84128339693943972696583847639285235393232896000000⟩, + ⟨4, 5, 2, 5, 1, 5, 5555891070811557987830294998389311447298264268800000⟩, + ⟨4, 5, 3, 5, 2, 5, -12723227713341960033001700932334441418432341606400000⟩, + ⟨4, 5, 4, 5, 3, 5, -9123825739808692076636892221164336700384398540800000⟩, + ⟨4, 5, 5, 5, 4, 5, 1630175607465038027447786056687774715785248768000000⟩, + ⟨4, 5, 6, 5, 5, 5, 939613058523671320264815913981365377436745728000000⟩, + ⟨4, 5, 7, 5, 6, 5, 149289162705724350459021615807692659356598272000000⟩, + ⟨4, 5, 8, 5, 7, 5, -137928601182805624406613574067949131875850649600000⟩, + ⟨4, 5, 2, 6, 0, 5, -100017599658706278460083438943936104207370892083200000⟩, + ⟨4, 5, 3, 6, 1, 5, -3097621688418737765399941673171522711673058099200000⟩, + ⟨4, 5, 4, 6, 2, 5, 11556215243037677275682281256434493849577770188800000⟩, + ⟨4, 5, 5, 6, 3, 5, -14855062224094983202479500815354651599666413568000000⟩, + ⟨4, 5, 6, 6, 4, 5, -626494771189494826427776535584915209634971648000000⟩, + ⟨4, 5, 7, 6, 5, 5, 932712822314642496501276857500075374559415500800000⟩, + ⟨4, 5, 8, 6, 6, 5, 206028987513308081046198443961736384434772377600000⟩, + ⟨4, 5, 3, 7, 0, 5, 325591142125435878150602469823470356607067068825600000⟩, + ⟨4, 5, 4, 7, 1, 5, 11101100340297477560657403502012028228379397324800000⟩, + ⟨4, 5, 5, 7, 2, 5, 822966276604505419103476744652309169652629504000000⟩, + ⟨4, 5, 6, 7, 3, 5, -3162664983903218957012272039863993357897302016000000⟩, + ⟨4, 5, 7, 7, 4, 5, 725267728117972581643798517818919902790025216000000⟩, + ⟨4, 5, 8, 7, 5, 5, 532194681914412670917868137860164545115324416000000⟩ +] + +def collectedFourData_11_4_32 : List CollectedFourTerm := [ + ⟨4, 6, 1, 0, 5, 6, -23554780372336282340677729248525363556818459033600000⟩, + ⟨4, 6, 2, 0, 6, 6, 20100204442409272270563017272675497558800125132800000⟩, + ⟨4, 6, 3, 0, 7, 6, -2872567744290346195165950697436826621792642662400000⟩, + ⟨4, 6, 4, 0, 8, 6, 3695579734976846722457652330650017709985418444800000⟩, + ⟨4, 6, 1, 1, 4, 6, -10289090510840805154931243583013730615952408576000000⟩, + ⟨4, 6, 2, 1, 5, 6, -9814680376636903544576353132683707784387939532800000⟩, + ⟨4, 6, 3, 1, 6, 6, 13620870413673648148921750725261332091945929932800000⟩, + ⟨4, 6, 4, 1, 7, 6, -4309961465612010350813136752244430672608677068800000⟩, + ⟨4, 6, 5, 1, 8, 6, -5289056871126556421899303225461492665989201920000000⟩, + ⟨4, 6, 1, 2, 3, 6, -15541031413501632821125139896772157801002906419200000⟩, + ⟨4, 6, 2, 2, 4, 6, -36158532337139630930087487254851954109938296422400000⟩, + ⟨4, 6, 3, 2, 5, 6, 5796351868361265272105224425022655322515098828800000⟩, + ⟨4, 6, 4, 2, 6, 6, 2841528328379548821202502628996294641914478592000000⟩, + ⟨4, 6, 5, 2, 7, 6, -2711109287460225367955420852688473925485592576000000⟩, + ⟨4, 6, 6, 2, 8, 6, 961136914957495727255958712169042387023586918400000⟩, + ⟨4, 6, 1, 3, 2, 6, 40046302010762736431100124145154918302438601523200000⟩, + ⟨4, 6, 2, 3, 3, 6, 41188092135249519572600334319113116521422913536000000⟩, + ⟨4, 6, 3, 3, 4, 6, -631562911632077301854738284617365294971197849600000⟩, + ⟨4, 6, 4, 3, 5, 6, 7796286835602117700012104271304543602488429772800000⟩, + ⟨4, 6, 5, 3, 6, 6, 1854981576771310347815312556147862665569501184000000⟩, + ⟨4, 6, 6, 3, 7, 6, 2037867377700218620474874016910673645351731200000⟩, + ⟨4, 6, 7, 3, 8, 6, -54359958954950207363108921062372286789792563200000⟩, + ⟨4, 6, 1, 4, 1, 6, -18029178857039928775865086720131083006081866137600000⟩, + ⟨4, 6, 2, 4, 2, 6, -9820706725492873788962223106268783805248569344000000⟩, + ⟨4, 6, 3, 4, 3, 6, -9326902511342844484044171388459901258763652300800000⟩, + ⟨4, 6, 4, 4, 4, 6, -5843050242295263877415930870647894329903808512000000⟩, + ⟨4, 6, 5, 4, 5, 6, 1124771486536234528749946024658660424507457536000000⟩, + ⟨4, 6, 6, 4, 6, 6, 411830186324598256173311944302617903236330291200000⟩, + ⟨4, 6, 7, 4, 7, 6, -143786594852019857065624656709257247827846758400000⟩, + ⟨4, 6, 8, 4, 8, 6, 22002303976574954178619489282639247639052288000000⟩, + ⟨4, 6, 1, 5, 0, 6, -95024795178297685206248860904827972978511079014400000⟩, + ⟨4, 6, 2, 5, 1, 6, 10171326719606458498461001639494831357081472204800000⟩, + ⟨4, 6, 3, 5, 2, 6, -11646386182788229590875938397503386452195750707200000⟩, + ⟨4, 6, 4, 5, 3, 6, -5567748500319539263208966569302208555867806105600000⟩, + ⟨4, 6, 5, 5, 4, 6, 746102132967026044261306783528206972519186432000000⟩, + ⟨4, 6, 6, 5, 5, 6, 344035233464609391966492330483858327582906777600000⟩, + ⟨4, 6, 7, 5, 6, 6, 45551314518320967927193342843858798459748352000000⟩, + ⟨4, 6, 8, 5, 7, 6, -36072826604306837891216226946831058572463308800000⟩, + ⟨4, 6, 2, 6, 0, 6, -183105044874629014748261373608750119799590433587200000⟩, + ⟨4, 6, 3, 6, 1, 6, -2835451761479883751496272659135190520395569561600000⟩, + ⟨4, 6, 4, 6, 2, 6, 7052096557265236583435133643989774825026066841600000⟩, + ⟨4, 6, 5, 6, 3, 6, -6798895505491032563953164833543042836444741632000000⟩, + ⟨4, 6, 6, 6, 4, 6, -229388334820705314555139132062511241333676441600000⟩, + ⟨4, 6, 7, 6, 5, 6, 284590618330904494914335812016538171109854412800000⟩, + ⟨4, 6, 8, 6, 6, 6, 53883298157851184796949955324189341156953292800000⟩, + ⟨4, 6, 3, 7, 0, 6, 298034450402200329170151505669167274630650318028800000⟩, + ⟨4, 6, 4, 7, 1, 6, 6774365987933039759583847475224346032680311193600000⟩, + ⟨4, 6, 5, 7, 2, 6, 376656902190656600963746474460968106481156096000000⟩, + ⟨4, 6, 6, 7, 3, 6, -1157996024253932549762691952082950331372352307200000⟩, + ⟨4, 6, 7, 7, 4, 6, 221294686062453886457296729513325490346131456000000⟩, + ⟨4, 6, 8, 7, 5, 6, 139186262427100300456371853998917772638158848000000⟩ +] + +def collectedFourData_11_4_33 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 4, 7, -14885788875873215619758674354679717233466277888000000⟩, + ⟨4, 7, 1, 0, 5, 7, 49343565984586965965291216217924288346672280371200000⟩, + ⟨4, 7, 2, 0, 6, 7, -21053385948198859867240995239594819804063386828800000⟩, + ⟨4, 7, 3, 0, 7, 7, 2005859444735832678570804836860008097417632153600000⟩, + ⟨4, 7, 4, 0, 8, 7, -1935414803509434577451265440068230946551653990400000⟩, + ⟨4, 7, 0, 1, 3, 7, -11699674898487965117117266311569052406430407065600000⟩, + ⟨4, 7, 1, 1, 4, 7, 21554028885759658873416341796923185055548833792000000⟩, + ⟨4, 7, 2, 1, 5, 7, 10280107076502098587734108035696734400433409228800000⟩, + ⟨4, 7, 3, 1, 6, 7, -9511194860102354541823628367960752095262618419200000⟩, + ⟨4, 7, 4, 1, 7, 7, 2257173115263054834674557541006651818049431142400000⟩, + ⟨4, 7, 5, 1, 8, 7, 2215948716916700406615834235657666220185878528000000⟩, + ⟨4, 7, 0, 2, 2, 7, -9759849974213048450056007351159563334061549158400000⟩, + ⟨4, 7, 1, 2, 3, 7, 32556020344867117463669120450645866630187738726400000⟩, + ⟨4, 7, 2, 2, 4, 7, 37873223568216735905889352272892713214945945190400000⟩, + ⟨4, 7, 3, 2, 5, 7, -4047482313785064482457574069580881281651258163200000⟩, + ⟨4, 7, 4, 2, 6, 7, -1488138908027552507254856468366476727619158016000000⟩, + ⟨4, 7, 5, 2, 7, 7, 1135869644315020392121938367229382213320992358400000⟩, + ⟨4, 7, 6, 2, 8, 7, -335571817650558707379425174350062120608779468800000⟩, + ⟨4, 7, 0, 3, 1, 7, -31285583621108940764677262470878266806657823539200000⟩, + ⟨4, 7, 1, 3, 2, 7, -83890714091628627895941798256915651947936507494400000⟩, + ⟨4, 7, 2, 3, 3, 7, -43141292551422580929583379790899959975227949056000000⟩, + ⟨4, 7, 3, 3, 4, 7, 441008374392586382350732446707299291951949414400000⟩, + ⟨4, 7, 4, 3, 5, 7, -4082999160110016924663855944976221607721068134400000⟩, + ⟨4, 7, 5, 3, 6, 7, -777179021725090079940883385332110891842902425600000⟩, + ⟨4, 7, 6, 3, 7, 7, -711502023721440235069457665298018135860838400000⟩, + ⟨4, 7, 7, 3, 8, 7, 16267939666070905171362980018632725206610739200000⟩, + ⟨4, 7, 0, 4, 0, 7, -99908244825492550143643467244121818058025074688000000⟩, + ⟨4, 7, 1, 4, 1, 7, 37768298515959906357874805496643020814548153139200000⟩, + ⟨4, 7, 2, 4, 2, 7, 10286419203758652033258444589620094581734375424000000⟩, + ⟨4, 7, 3, 4, 3, 7, 6512798707599925992624430377887344414038373171200000⟩, + ⟨4, 7, 4, 4, 4, 7, 3060068175381552914624175038884453171568050176000000⟩, + ⟨4, 7, 5, 4, 5, 7, -471243927442129355998962888347135704713029222400000⟩, + ⟨4, 7, 6, 4, 6, 7, -143786594852019857065624656709257247827846758400000⟩, + ⟨4, 7, 7, 4, 7, 7, 43030048123857768017456452268475727154144870400000⟩, + ⟨4, 7, 8, 4, 8, 7, -5761421465831863260566520299753878283354112000000⟩, + ⟨4, 7, 1, 5, 0, 7, 199062023798744004357568774865927197537111690444800000⟩, + ⟨4, 7, 2, 5, 1, 7, -10653666118006640322744877277719401770601204940800000⟩, + ⟨4, 7, 3, 5, 2, 7, 8132450059087430240745850628370195568321678540800000⟩, + ⟨4, 7, 4, 5, 3, 7, 2915889695937896609388802805198136969200979148800000⟩, + ⟨4, 7, 5, 5, 4, 7, -312593361070239485519173475878878243306917068800000⟩, + ⟨4, 7, 6, 5, 5, 7, -120116631494336855950753772230882032681694003200000⟩, + ⟨4, 7, 7, 5, 6, 7, -13631835831744769327443319374596244045299712000000⟩, + ⟨4, 7, 8, 5, 7, 7, 9445863385605158398863100391549154142401331200000⟩, + ⟨4, 7, 2, 6, 0, 7, 191788157670388663749900680568170833526392042291200000⟩, + ⟨4, 7, 3, 6, 1, 7, 1979942059560496707967828163121083489926407782400000⟩, + ⟨4, 7, 4, 6, 2, 7, -3693258717578331172117770016258947768088579276800000⟩, + ⟨4, 7, 5, 6, 3, 7, 2848523685591331556828810314750953504153324748800000⟩, + ⟨4, 7, 6, 6, 4, 7, 80088756623215480773564622018896997658080051200000⟩, + ⟨4, 7, 7, 6, 5, 7, -85167522153093347723649876191981925152115916800000⟩, + ⟨4, 7, 8, 6, 6, 7, -14109631018050703398203509667183664097866547200000⟩, + ⟨4, 7, 3, 7, 0, 7, -208111790708557837927975916417878008505327366963200000⟩, + ⟨4, 7, 4, 7, 1, 7, -3547808235158688623663179539141623849956461772800000⟩, + ⟨4, 7, 5, 7, 2, 7, -157807412448833370849693376562305435116660326400000⟩, + ⟨4, 7, 6, 7, 3, 7, 404303304392587220239772991215489008838010470400000⟩, + ⟨4, 7, 7, 7, 4, 7, -66225373795251413401694607071148943695937536000000⟩, + ⟨4, 7, 8, 7, 5, 7, -36446670355530381271025752473987403902615552000000⟩ +] + +def collectedFourData_11_4_34 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 4, 8, 15944821315269898563409065010842689621584773120000000⟩, + ⟨4, 8, 1, 0, 5, 8, -26427028800524889390600537033344708012402540544000000⟩, + ⟨4, 8, 2, 0, 6, 8, 7517068344505252851159388300095594509635682304000000⟩, + ⟨4, 8, 3, 0, 7, 8, -537141005702715711049509974788293678612873216000000⟩, + ⟨4, 8, 4, 0, 8, 8, 414621535616477227825355847849571889393644339200000⟩, + ⟨4, 8, 0, 1, 3, 8, 12532034899775906185959372285164029305887391744000000⟩, + ⟨4, 8, 1, 1, 4, 8, -11543732820389183928478644820220791170835415040000000⟩, + ⟨4, 8, 2, 1, 5, 8, -3670491182417592735464009234772429339365474304000000⟩, + ⟨4, 8, 3, 1, 6, 8, 2546964487465722687731907245939412586727473152000000⟩, + ⟨4, 8, 4, 1, 7, 8, -483551423449693297649214214288516170168611635200000⟩, + ⟨4, 8, 5, 1, 8, 8, -395599976031566131657004916546088329145221120000000⟩, + ⟨4, 8, 0, 2, 2, 8, 10454203347925677946924845910224760738745942016000000⟩, + ⟨4, 8, 1, 2, 3, 8, -17436090605065321241531279963519562383169159168000000⟩, + ⟨4, 8, 2, 2, 4, 8, -13522556926923591792996499844226067662196703232000000⟩, + ⟨4, 8, 3, 2, 5, 8, 1083858954472647219306505718982282315187617792000000⟩, + ⟨4, 8, 4, 2, 6, 8, 318802170024842236733596481967227415998496768000000⟩, + ⟨4, 8, 5, 2, 7, 8, -202779965364558164981177946249640895720718336000000⟩, + ⟨4, 8, 6, 2, 8, 8, 51349384450741479032824915758847958729097216000000⟩, + ⟨4, 8, 0, 3, 1, 8, 33511360717404640276321593599416140350418321408000000⟩, + ⟨4, 8, 1, 3, 2, 8, 44929511541354125574484592091921963825210851328000000⟩, + ⟨4, 8, 2, 3, 3, 8, 15403510170632805821457194617481532883316244480000000⟩, + ⟨4, 8, 3, 3, 4, 8, -118095852810739035837165028854288594568740864000000⟩, + ⟨4, 8, 4, 3, 5, 8, 874695893932357019641024002600534930579731251200000⟩, + ⟨4, 8, 5, 3, 6, 8, 138745089188920548045686077768021345277313024000000⟩, + ⟨4, 8, 6, 3, 7, 8, 108874431736690237587476639061626887077888000000⟩, + ⟨4, 8, 7, 3, 8, 8, -2178162955504398799473944390168264809906176000000⟩, + ⟨4, 8, 0, 4, 0, 8, 107016102737200014747580664090888872500784005120000000⟩, + ⟨4, 8, 1, 4, 1, 8, -20227640477785152278675553174318382502016712704000000⟩, + ⟨4, 8, 2, 4, 2, 8, -3672744914530017434520293298278047888095313920000000⟩, + ⟨4, 8, 3, 4, 3, 8, -1744036082348874998411112631363759354278838272000000⟩, + ⟨4, 8, 4, 4, 4, 8, -655554645788171550885726491217962099118440448000000⟩, + ⟨4, 8, 5, 4, 5, 8, 84128339693943972696583847639285235393232896000000⟩, + ⟨4, 8, 6, 4, 6, 8, 22002303976574954178619489282639247639052288000000⟩, + ⟨4, 8, 7, 4, 7, 8, -5761421465831863260566520299753878283354112000000⟩, + ⟨4, 8, 8, 4, 8, 8, 685701245818892196826031646340507049656320000000⟩, + ⟨4, 8, 1, 5, 0, 8, -106612032005619407992529399794477241297195237376000000⟩, + ⟨4, 8, 2, 5, 1, 8, 3803869673298188971911415489681203745221771264000000⟩, + ⟨4, 8, 3, 5, 2, 8, -2177755981372176380261463025043122319888744448000000⟩, + ⟨4, 8, 4, 5, 3, 8, -624667467266347216224123986487046784588080742400000⟩, + ⟨4, 8, 5, 5, 4, 8, 55805409756539057089398648723021970645450752000000⟩, + ⟨4, 8, 6, 5, 5, 8, 18380313140460399330493100182324946952781824000000⟩, + ⟨4, 8, 7, 5, 6, 8, 1825207151840597105786012369816984601231360000000⟩, + ⟨4, 8, 8, 5, 7, 8, -1124208726918631715506261744761409300856832000000⟩, + ⟨4, 8, 2, 6, 0, 8, -68477568996373175861792929723615788750965047296000000⟩, + ⟨4, 8, 3, 6, 1, 8, -530200693720837029694296956864018113514962944000000⟩, + ⟨4, 8, 4, 6, 2, 8, 791202277741493150673510229816099022576182886400000⟩, + ⟨4, 8, 5, 6, 3, 8, -508529774693174682721087415795651517666557952000000⟩, + ⟨4, 8, 6, 6, 4, 8, -12255225670678464277215372899137855300829184000000⟩, + ⟨4, 8, 7, 6, 5, 8, 11403333524335165141196214344664866309013504000000⟩, + ⟨4, 8, 8, 6, 6, 8, 1679271621508656139879382517840164885102592000000⟩, + ⟨4, 8, 3, 7, 0, 8, 55729416561642351191118484896120071970506145792000000⟩, + ⟨4, 8, 4, 7, 1, 8, 760042599584833004314063123226139295968814694400000⟩, + ⟨4, 8, 5, 7, 2, 8, 28172406746499947237084785005709504655917056000000⟩, + ⟨4, 8, 6, 7, 3, 8, -61866714425878581927058108961731872584368128000000⟩, + ⟨4, 8, 7, 7, 4, 8, 8867112792168850576801503118387534972846080000000⟩, + ⟨4, 8, 8, 7, 5, 8, 4337736341100896275276302741886647108894720000000⟩ +] + +def collectedFourData_11_4_35 : List CollectedFourTerm := [ + ⟨5, 0, 6, 2, 8, 1, -221770626619755827290995928671061114291015699660800000⟩, + ⟨5, 0, 6, 3, 7, 1, -470213055275815902175345048137380214409160294400000⟩, + ⟨5, 0, 7, 3, 8, 1, 75257387201676514763644593334077761363577824870400000⟩, + ⟨5, 0, 6, 4, 6, 1, -95024795178297685206248860904827972978511079014400000⟩, + ⟨5, 0, 7, 4, 7, 1, 199062023798744004357568774865927197537111690444800000⟩, + ⟨5, 0, 8, 4, 8, 1, -106612032005619407992529399794477241297195237376000000⟩, + ⟨5, 0, 6, 5, 5, 1, -79381936243801941478915051838858297584387306291200000⟩, + ⟨5, 0, 7, 5, 6, 1, -63062463257037793596755097331365956489570156544000000⟩, + ⟨5, 0, 8, 5, 7, 1, 174790665039715804622799555404774229804033087897600000⟩, + ⟨5, 0, 6, 6, 4, 1, 52928561956961004480302231994488015063895716659200000⟩, + ⟨5, 0, 7, 6, 5, 1, -393994895681264329571138870923300538360824175001600000⟩, + ⟨5, 0, 8, 6, 6, 1, -261091198171302290972086893452720538827615738265600000⟩, + ⟨5, 0, 6, 7, 3, 1, 267193466326634070133495565157094198683292296806400000⟩, + ⟨5, 0, 7, 7, 4, 1, -306366307017951906947727041133924138537222930432000000⟩, + ⟨5, 0, 8, 7, 5, 1, -674426200111543951749322771147952413981588586496000000⟩ +] + +def collectedFourData_11_4_36 : List CollectedFourTerm := [ + ⟨5, 1, 5, 1, 8, 2, -26125683478872488458130699768515644728945934336000000⟩, + ⟨5, 1, 5, 2, 7, 2, -13391722729903420909543336854786299612669725900800000⟩, + ⟨5, 1, 6, 2, 8, 2, 23738030646937505783616554332725796702869100953600000⟩, + ⟨5, 1, 5, 3, 6, 2, 9162817249787792646417290213398941619471987507200000⟩, + ⟨5, 1, 6, 3, 7, 2, 50330975237155718408259777889747639001205964800000⟩, + ⟨5, 1, 7, 3, 8, 2, -4027724931455592166226847833358391547053631078400000⟩, + ⟨5, 1, 5, 4, 5, 2, 5555891070811557987830294998389311447298264268800000⟩, + ⟨5, 1, 6, 4, 6, 2, 10171326719606458498461001639494831357081472204800000⟩, + ⟨5, 1, 7, 4, 7, 2, -10653666118006640322744877277719401770601204940800000⟩, + ⟨5, 1, 8, 4, 8, 2, 3803869673298188971911415489681203745221771264000000⟩, + ⟨5, 1, 5, 5, 4, 2, 3685426087062723626402983703409353617315568025600000⟩, + ⟨5, 1, 6, 5, 5, 2, 8496936064483959199542836188169559491320637030400000⟩, + ⟨5, 1, 7, 5, 6, 2, 3375060774016813162840186627590363015674855424000000⟩, + ⟨5, 1, 8, 5, 7, 2, -6236452841318621199432980866595939290695755366400000⟩, + ⟨5, 1, 5, 6, 3, 2, -33583641906378975677266824144208716574139980185600000⟩, + ⟨5, 1, 6, 6, 4, 2, -5665402334759630337239618018050035557184464486400000⟩, + ⟨5, 1, 7, 6, 5, 2, 21086342792489638715726568269869625069654350233600000⟩, + ⟨5, 1, 8, 6, 6, 2, 9315617308903333773255223999328788749209724518400000⟩, + ⟨5, 1, 5, 7, 2, 2, 1860524332889190947627410714030119129665293516800000⟩, + ⟨5, 1, 6, 7, 3, 2, -28600030531536978392539521733252966936749067468800000⟩, + ⟨5, 1, 7, 7, 4, 2, 16396519449012896938799447529251234592243843072000000⟩, + ⟨5, 1, 8, 7, 5, 2, 24063225521738640425541391957445728140414418944000000⟩ +] + +def collectedFourData_11_4_37 : List CollectedFourTerm := [ + ⟨5, 2, 4, 0, 8, 3, -10450945606231726750953474436628607043113981050880000⟩, + ⟨5, 2, 4, 1, 7, 3, 12188391557555744161570609816568085485054098145280000⟩, + ⟨5, 2, 5, 1, 8, 3, 59828930378909676567154446104777942678013739008000000⟩, + ⟨5, 2, 4, 2, 6, 3, -8035723791154321372983897192452335235419550515200000⟩, + ⟨5, 2, 5, 2, 7, 3, 30667616696381720705479300148643036282667558502400000⟩, + ⟨5, 2, 6, 2, 8, 3, -27180551736695484038488395761949372760772208230400000⟩, + ⟨5, 2, 4, 3, 5, 3, -22047574532976130785999491676607591632581878087680000⟩, + ⟨5, 2, 5, 3, 6, 3, -20983242630017705852924151843015080633435789721600000⟩, + ⟨5, 2, 6, 3, 7, 3, -57630040871496723358635029328345326270231347200000⟩, + ⟨5, 2, 7, 3, 8, 3, 3074554007417367648128963683036737135285003878400000⟩, + ⟨5, 2, 4, 4, 4, 3, 16523902780057185514830996522136589089717302067200000⟩, + ⟨5, 2, 5, 4, 5, 3, -12723227713341960033001700932334441418432341606400000⟩, + ⟨5, 2, 6, 4, 6, 3, -11646386182788229590875938397503386452195750707200000⟩, + ⟨5, 2, 7, 4, 7, 3, 8132450059087430240745850628370195568321678540800000⟩, + ⟨5, 2, 8, 4, 8, 3, -2177755981372176380261463025043122319888744448000000⟩, + ⟨5, 2, 4, 5, 3, 3, 15745360917339896453406371384697830401637728911360000⟩, + ⟨5, 2, 5, 5, 4, 3, -8439783057075035685237717869334079776874089676800000⟩, + ⟨5, 2, 6, 5, 5, 3, -9729173145788970706521691313458608872856590745600000⟩, + ⟨5, 2, 7, 5, 6, 3, -2576344413937038353385096730995070077631463424000000⟩, + ⟨5, 2, 8, 5, 7, 3, 3570435804639741953123065477050508433649618124800000⟩, + ⟨5, 2, 4, 6, 2, 3, -19943035413991617665585054592837554012790152232960000⟩, + ⟨5, 2, 5, 6, 3, 3, 76907973531557759260532129213146551677455486156800000⟩, + ⟨5, 2, 6, 6, 4, 3, 6487006591214252247511177487699488458522859929600000⟩, + ⟨5, 2, 7, 6, 5, 3, -16096208365201302541785023638191839167972481433600000⟩, + ⟨5, 2, 8, 6, 6, 3, -5333290321970524579394821735353937752520182988800000⟩, + ⟨5, 2, 4, 7, 1, 3, -19157624928646821504671096698320758199636103004160000⟩, + ⟨5, 2, 5, 7, 2, 3, -4260680141467393381216756744868558261631477350400000⟩, + ⟨5, 2, 6, 7, 3, 3, 32747645375283090726503881320183226693753975603200000⟩, + ⟨5, 2, 7, 7, 4, 3, -12516243149067497456790351688963332583899267072000000⟩, + ⟨5, 2, 8, 7, 5, 3, -13776453404523869290919999766445387852397150208000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1114.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1114.lean new file mode 100644 index 0000000000000000000000000000000000000000..8c1ca4e7c9023e1704247c9f1193b1dab4f2b601 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1114.lean @@ -0,0 +1,622 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1114. -/ +namespace LaughlinFock +def collectedFourData_11_4_38 : List CollectedFourTerm := [ + ⟨5, 3, 3, 0, 7, 4, 3883575143695960057558051287497385800704846725120000⟩, + ⟨5, 3, 4, 0, 8, 4, -14988744786433078972745338024253709476791289118720000⟩, + ⟨5, 3, 3, 1, 6, 4, -18414769809759456337211822245932730397053566320640000⟩, + ⟨5, 3, 4, 1, 7, 4, 17480589536738604577821574967311242244944895672320000⟩, + ⟨5, 3, 5, 1, 8, 4, 42903321961604436653752795812977763997949362176000000⟩, + ⟨5, 3, 3, 2, 5, 4, -7836392400084048502605698411907739523269200445440000⟩, + ⟨5, 3, 4, 2, 6, 4, -11524833983258029222891791680826019962325617868800000⟩, + ⟨5, 3, 5, 2, 7, 4, 21991745875900763423519054760515410151858818252800000⟩, + ⟨5, 3, 6, 2, 8, 4, -12994114551473112407816072046323261471498384179200000⟩, + ⟨5, 3, 3, 3, 4, 4, 853843057372530828046359731940770456424394260480000⟩, + ⟨5, 3, 4, 3, 5, 4, -31620628437448721405244151429717420062669715537920000⟩, + ⟨5, 3, 5, 3, 6, 4, -15047081882504469809497041010952625911061754675200000⟩, + ⟨5, 3, 6, 3, 7, 4, -27550998962221526168650326339253383259068825600000⟩, + ⟨5, 3, 7, 3, 8, 4, 1102381236244427604577384307330097969556252262400000⟩, + ⟨5, 3, 3, 4, 3, 4, 12609529168710657631339012420389109807302353879040000⟩, + ⟨5, 3, 4, 4, 4, 4, 23698579150428850127941829218687523512487038156800000⟩, + ⟨5, 3, 5, 4, 5, 4, -9123825739808692076636892221164336700384398540800000⟩, + ⟨5, 3, 6, 4, 6, 4, -5567748500319539263208966569302208555867806105600000⟩, + ⟨5, 3, 7, 4, 7, 4, 2915889695937896609388802805198136969200979148800000⟩, + ⟨5, 3, 8, 4, 8, 4, -624667467266347216224123986487046784588080742400000⟩, + ⟨5, 3, 3, 5, 2, 4, 15745360917339896453406371384697830401637728911360000⟩, + ⟨5, 3, 4, 5, 3, 4, 22581994515363348114268854260206936452845367459840000⟩, + ⟨5, 3, 5, 5, 4, 4, -6052167864117901510952912586505665299579771289600000⟩, + ⟨5, 3, 6, 5, 5, 4, -4651192940164644445765548074028049518568459468800000⟩, + ⟨5, 3, 7, 5, 6, 4, -923748203211118628046088001286970629018353664000000⟩, + ⟨5, 3, 8, 5, 7, 4, 1024143710406013570561420644081287648300488458240000⟩, + ⟨5, 3, 3, 6, 1, 4, 3833396097940446215412951706210869946529957806080000⟩, + ⟨5, 3, 4, 6, 2, 4, -28602298715331118935320813060751213462974355210240000⟩, + ⟨5, 3, 5, 6, 3, 4, 55150702660766953879137600429285650132924733849600000⟩, + ⟨5, 3, 6, 6, 4, 4, 3101221327622952166502555448253808635953335500800000⟩, + ⟨5, 3, 7, 6, 5, 4, -5771294969504745190259658626335761309210614169600000⟩, + ⟨5, 3, 8, 6, 6, 4, -1529800852858772759033849612360429096626752061440000⟩, + ⟨5, 3, 3, 7, 0, 4, -402928420347145306647220799702103145987186297405440000⟩, + ⟨5, 3, 4, 7, 1, 4, -27475863102614691754385451758778673689028240343040000⟩, + ⟨5, 3, 5, 7, 2, 4, -3055333443655009533432615283221697862250056908800000⟩, + ⟨5, 3, 6, 7, 3, 4, 15655556201346677212852499601249675216990869913600000⟩, + ⟨5, 3, 7, 7, 4, 4, -4487698561325631392958600722010849871807905792000000⟩, + ⟨5, 3, 8, 7, 5, 4, -3951637524923443493278596268955453229892003430400000⟩ +] + +def collectedFourData_11_4_39 : List CollectedFourTerm := [ + ⟨5, 4, 2, 0, 6, 5, 7283004454527574489263671392850941966204639641600000⟩, + ⟨5, 4, 3, 0, 7, 5, -2081662774877843149845755706162655995778144665600000⟩, + ⟨5, 4, 4, 0, 8, 5, 4017111927743970110484229929587149506983283916800000⟩, + ⟨5, 4, 2, 1, 5, 5, -3556200689779804315884102640602130981555116441600000⟩, + ⟨5, 4, 3, 1, 6, 5, 9870631931287710407024478211309061702463730483200000⟩, + ⟨5, 4, 4, 1, 7, 5, -4684947654562068740148693618558191792596765900800000⟩, + ⟨5, 4, 5, 1, 8, 5, -7665638399456445207748874527771325124009000960000000⟩, + ⟨5, 4, 2, 2, 4, 5, -13101496197966144140441742156100546311008079052800000⟩, + ⟨5, 4, 3, 2, 5, 5, 4200440507780658335889871520446469781289382707200000⟩, + ⟨5, 4, 4, 2, 6, 5, 3088754176488465098601989401364572130060009472000000⟩, + ⟨5, 4, 5, 2, 7, 5, -3929317450249217645579676272714164466287116288000000⟩, + ⟨5, 4, 6, 2, 8, 5, 1741266973951060637101356977624639194817101824000000⟩, + ⟨5, 4, 2, 3, 3, 5, 14923880966185770573167022451257474807540744192000000⟩, + ⟨5, 4, 3, 3, 4, 5, -457674498974349003144882562956433697414735462400000⟩, + ⟨5, 4, 4, 3, 5, 5, 8474599138802446746165773243417114679710633164800000⟩, + ⟨5, 4, 5, 3, 6, 5, 2688497845959761060635070987862289158443630592000000⟩, + ⟨5, 4, 6, 3, 7, 5, 3691951798811688084512607794837418600824832000000⟩, + ⟨5, 4, 7, 3, 8, 5, -118179043706100003526731570281766503938680422400000⟩, + ⟨5, 4, 2, 4, 2, 5, -3558384245956475107045762247406341194323591168000000⟩, + ⟨5, 4, 3, 4, 3, 5, -6758923545447512292935235837750821615027041075200000⟩, + ⟨5, 4, 4, 4, 4, 5, -6351422105868500588774575976759548457036808192000000⟩, + ⟨5, 4, 5, 4, 5, 5, 1630175607465038027447786056687774715785248768000000⟩, + ⟨5, 4, 6, 4, 6, 5, 746102132967026044261306783528206972519186432000000⟩, + ⟨5, 4, 7, 4, 7, 5, -312593361070239485519173475878878243306917068800000⟩, + ⟨5, 4, 8, 4, 8, 5, 55805409756539057089398648723021970645450752000000⟩, + ⟨5, 4, 2, 5, 1, 5, 3685426087062723626402983703409353617315568025600000⟩, + ⟨5, 4, 3, 5, 2, 5, -8439783057075035685237717869334079776874089676800000⟩, + ⟨5, 4, 4, 5, 3, 5, -6052167864117901510952912586505665299579771289600000⟩, + ⟨5, 4, 5, 5, 4, 5, 1081355201833968130848682949514079351357833216000000⟩, + ⟨5, 4, 6, 5, 5, 5, 623279764396479475562313484257119379690356736000000⟩, + ⟨5, 4, 7, 5, 6, 5, 99028970823767470081398674782139535813771264000000⟩, + ⟨5, 4, 8, 5, 7, 5, -91493094172008367810337792695335900471833395200000⟩, + ⟨5, 4, 2, 6, 0, 5, -66345337993415481570688261760807153873891780198400000⟩, + ⟨5, 4, 3, 6, 1, 5, -2054765947144844632134248653200508154764748390400000⟩, + ⟨5, 4, 4, 6, 2, 5, 7665660932078321024713061011671252028930759065600000⟩, + ⟨5, 4, 5, 6, 3, 5, -9853906987708928840854690042268613044984610816000000⟩, + ⟨5, 4, 6, 6, 4, 5, -415576933334816353380032897472882392250187776000000⟩, + ⟨5, 4, 7, 6, 5, 5, 618702584929219874788183749658611812914534809600000⟩, + ⟨5, 4, 8, 6, 6, 5, 136666575279301308540452075750388554364302131200000⟩, + ⟨5, 4, 3, 7, 0, 5, 215976532587121220959397253162811509475395187507200000⟩, + ⟨5, 4, 4, 7, 1, 5, 7363766543978890294094124539048815869325580697600000⟩, + ⟨5, 4, 5, 7, 2, 5, 545903680600434988369125067601315455511298048000000⟩, + ⟨5, 4, 6, 7, 3, 5, -2097911547897600369957646924332477347310600192000000⟩, + ⟨5, 4, 7, 7, 4, 5, 481096654207846655157801287431680166138478592000000⟩, + ⟨5, 4, 8, 7, 5, 5, 353024229439567667007336756861259861293268992000000⟩ +] + +def collectedFourData_11_4_40 : List CollectedFourTerm := [ + ⟨5, 5, 1, 0, 5, 6, -19677222878988087588293360045151613880634232012800000⟩, + ⟨5, 5, 2, 0, 6, 6, 16791334772580790970362542683457368882250409574400000⟩, + ⟨5, 5, 3, 0, 7, 6, -2399689355871792860002339261473899549352473395200000⟩, + ⟨5, 5, 4, 0, 8, 6, 3087218176638788514724818882179030043192616550400000⟩, + ⟨5, 5, 1, 1, 4, 6, -8595313732649965742515106114755088376448155648000000⟩, + ⟨5, 5, 2, 1, 5, 6, -8199000381422784592379131372468767713179100774400000⟩, + ⟨5, 5, 3, 1, 6, 6, 11378620335193020380890125148084930241620239974400000⟩, + ⟨5, 5, 4, 1, 7, 6, -3600461181047555906428087052921208589173286502400000⟩, + ⟨5, 5, 5, 1, 8, 6, -4418379166677750852022274364414351009550172160000000⟩, + ⟨5, 5, 1, 2, 3, 6, -12982686913607409089858077881436013750073792921600000⟩, + ⟨5, 5, 2, 2, 4, 6, -30206161489436313099606962635426693470261293875200000⟩, + ⟨5, 5, 3, 2, 5, 6, 4842163917297055004090305817934006621990970982400000⟩, + ⟨5, 5, 4, 2, 6, 6, 2373759608480571918431026606186884448351420416000000⟩, + ⟨5, 5, 5, 2, 7, 6, -2264809981472062564517592410042340690936987648000000⟩, + ⟨5, 5, 6, 2, 8, 6, 802915798571966255061007375284614881076261683200000⟩, + ⟨5, 5, 1, 3, 2, 6, 33453931545483960036170514729018880252752533913600000⟩, + ⟨5, 5, 2, 3, 3, 6, 34407761655780402144252955717860003640642633728000000⟩, + ⟨5, 5, 3, 3, 4, 6, -527595841601745761859611712686525412876799180800000⟩, + ⟨5, 5, 4, 3, 5, 6, 6512872175740338746265575699966302311221192294400000⟩, + ⟨5, 5, 5, 3, 6, 6, 1549616907717551475784532563381177672984952832000000⟩, + ⟨5, 5, 6, 3, 7, 6, 1702396284531729724233317231327166047295897600000⟩, + ⟨5, 5, 7, 3, 8, 6, -45411292788169860189249836727944033823463833600000⟩, + ⟨5, 5, 1, 4, 1, 6, -15061238741659601372153853304077848320771149004800000⟩, + ⟨5, 5, 2, 4, 2, 6, -8204034680520929816823162785271129596611264512000000⟩, + ⟨5, 5, 3, 4, 3, 6, -7791519877715747102691550555484444107848705638400000⟩, + ⟨5, 5, 4, 4, 4, 6, -4881174865285549354599886673161985665139736576000000⟩, + ⟨5, 5, 5, 4, 5, 6, 939613058523671320264815913981365377436745728000000⟩, + ⟨5, 5, 6, 4, 6, 6, 344035233464609391966492330483858327582906777600000⟩, + ⟨5, 5, 7, 4, 7, 6, -120116631494336855950753772230882032681694003200000⟩, + ⟨5, 5, 8, 4, 8, 6, 18380313140460399330493100182324946952781824000000⟩, + ⟨5, 5, 1, 5, 0, 6, -79381936243801941478915051838858297584387306291200000⟩, + ⟨5, 5, 2, 5, 1, 6, 8496936064483959199542836188169559491320637030400000⟩, + ⟨5, 5, 3, 5, 2, 6, -9729173145788970706521691313458608872856590745600000⟩, + ⟨5, 5, 4, 5, 3, 6, -4651192940164644445765548074028049518568459468800000⟩, + ⟨5, 5, 5, 5, 4, 6, 623279764396479475562313484257119379690356736000000⟩, + ⟨5, 5, 6, 5, 5, 6, 287400598099330574782134463384962832337259724800000⟩, + ⟨5, 5, 7, 5, 6, 6, 38052716010910769545798046852992598745808896000000⟩, + ⟨5, 5, 8, 5, 7, 6, -30134564523542353249583100490612928877586022400000⟩, + ⟨5, 5, 2, 6, 0, 6, -152962529104992323790799625676843711565624088985600000⟩, + ⟨5, 5, 3, 6, 1, 6, -2368683358168163182244956785310379608424369356800000⟩, + ⟨5, 5, 4, 6, 2, 6, 5891189538936429378726995475934078363224558796800000⟩, + ⟨5, 5, 5, 6, 3, 6, -5679670116967773359849612165470276891585806336000000⟩, + ⟨5, 5, 6, 6, 4, 6, -191626723695036867780633244154477786732219596800000⟩, + ⟨5, 5, 7, 6, 5, 6, 237741678659125144455104480823773418261735014400000⟩, + ⟨5, 5, 8, 6, 6, 6, 45013099275263702999921480085035427849201254400000⟩, + ⟨5, 5, 3, 7, 0, 6, 248972404474987975789871304790694663173966292582400000⟩, + ⟨5, 5, 4, 7, 1, 6, 5659178616878494366332568898720569900330175692800000⟩, + ⟨5, 5, 5, 7, 2, 6, 314652129892886374720197714934008437022916608000000⟩, + ⟨5, 5, 6, 7, 3, 6, -967368215794859507281545922789786228123867545600000⟩, + ⟨5, 5, 7, 7, 4, 6, 184865440931925192008073951253293730929573888000000⟩, + ⟨5, 5, 8, 7, 5, 6, 116273599845912301312573040396922991310536704000000⟩ +] + +def collectedFourData_11_4_41 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 4, 7, 4715789059724708735847109524234139484175728640000000⟩, + ⟨5, 6, 1, 0, 5, 7, -15631946051248119062203840164594397857171111936000000⟩, + ⟨5, 6, 2, 0, 6, 7, 6669671856329752976589747554039719794063704064000000⟩, + ⟨5, 6, 3, 0, 7, 7, -635452383727015059271223416898052563568427008000000⟩, + ⟨5, 6, 4, 0, 8, 7, 613135657943666674881860999946968973088653312000000⟩, + ⟨5, 6, 0, 1, 3, 7, 3706434327981749089476940604397390373079482368000000⟩, + ⟨5, 6, 1, 1, 4, 7, -6828274568450991633177229803801073050986741760000000⟩, + ⟨5, 6, 2, 1, 5, 7, -3256717993813635818680346451473939958085976064000000⟩, + ⟨5, 6, 3, 1, 6, 7, 3013128094197120920522562186588385272058085376000000⟩, + ⟨5, 6, 4, 1, 7, 7, -715068067377641372439584473176781916441935872000000⟩, + ⟨5, 6, 5, 1, 8, 7, -702008257895151479450557948463012411961507840000000⟩, + ⟨5, 6, 0, 2, 2, 7, 3091901552328611662002426075387666735512420352000000⟩, + ⟨5, 6, 1, 2, 3, 7, -10313684135298695858211950990965460207394619392000000⟩, + ⟨5, 6, 2, 2, 4, 7, -11998163809039478618413917353976682028898189312000000⟩, + ⟨5, 6, 3, 2, 5, 7, 1282234550948996347154407685764319365558173696000000⟩, + ⟨5, 6, 4, 2, 6, 7, 471439521300837897130968942284893342641684480000000⟩, + ⟨5, 6, 5, 2, 7, 7, -359841301431863168454656640412540729244516352000000⟩, + ⟨5, 6, 6, 2, 8, 7, 106308501324597042653055570385983666351243264000000⟩, + ⟨5, 6, 0, 3, 1, 7, 9911212243957977989209490002829879489096318976000000⟩, + ⟨5, 6, 1, 3, 2, 7, 26576415601795830189808046320797963192926994432000000⟩, + ⟨5, 6, 2, 3, 3, 7, 13667077850749604143185912682473852312936775680000000⟩, + ⟨5, 6, 3, 3, 4, 7, -139710598111350667506316939192014793743532032000000⟩, + ⟨5, 6, 4, 3, 5, 7, 1293486219015214928542784678154847785301573632000000⟩, + ⟨5, 6, 5, 3, 6, 7, 246208807518354525546685373584555866920583168000000⟩, + ⟨5, 6, 6, 3, 7, 7, 225402461865880326479735592612415250890752000000⟩, + ⟨5, 6, 7, 3, 8, 7, -5153651750755369819660909884861228804734976000000⟩, + ⟨5, 6, 0, 4, 0, 7, 31650738288246587200867990358431970041150832640000000⟩, + ⟨5, 6, 1, 4, 1, 7, -11964923755882082590995383456770467181652606976000000⟩, + ⟨5, 6, 2, 4, 2, 7, -3258717663492431980930708822692991341397278720000000⟩, + ⟨5, 6, 3, 4, 3, 7, -2063242005485402809524084986200766592829095936000000⟩, + ⟨5, 6, 4, 4, 4, 7, -969423666008400420557404317604866491185889280000000⟩, + ⟨5, 6, 5, 4, 5, 7, 149289162705724350459021615807692659356598272000000⟩, + ⟨5, 6, 6, 4, 6, 7, 45551314518320967927193342843858798459748352000000⟩, + ⟨5, 6, 7, 4, 7, 7, -13631835831744769327443319374596244045299712000000⟩, + ⟨5, 6, 8, 4, 8, 7, 1825207151840597105786012369816984601231360000000⟩, + ⟨5, 6, 1, 5, 0, 7, -63062463257037793596755097331365956489570156544000000⟩, + ⟨5, 6, 2, 5, 1, 7, 3375060774016813162840186627590363015674855424000000⟩, + ⟨5, 6, 3, 5, 2, 7, -2576344413937038353385096730995070077631463424000000⟩, + ⟨5, 6, 4, 5, 3, 7, -923748203211118628046088001286970629018353664000000⟩, + ⟨5, 6, 5, 5, 4, 7, 99028970823767470081398674782139535813771264000000⟩, + ⟨5, 6, 6, 5, 5, 7, 38052716010910769545798046852992598745808896000000⟩, + ⟨5, 6, 7, 5, 6, 7, 4318539166137020919781426703935982649999360000000⟩, + ⟨5, 6, 8, 5, 7, 7, -2992431209721692771966353154931603051380736000000⟩, + ⟨5, 6, 2, 6, 0, 7, -60758116567988836646111500071014661963997249536000000⟩, + ⟨5, 6, 3, 6, 1, 7, -627241806344407171259791918084073668132995072000000⟩, + ⟨5, 6, 4, 6, 2, 7, 1170017202334338809226154971261527458005909504000000⟩, + ⟨5, 6, 5, 6, 3, 7, -902406781722565012730901250622050536379121664000000⟩, + ⟨5, 6, 6, 6, 4, 7, -25371962845909916678056669342642514046222336000000⟩, + ⟨5, 6, 7, 6, 5, 7, 26980905920571121295752464400454812333768704000000⟩, + ⟨5, 6, 8, 6, 6, 7, 4469903754951161207653606298565742707081216000000⟩, + ⟨5, 6, 3, 7, 0, 7, 65929411871063148494466735587522596825460637696000000⟩, + ⟨5, 6, 4, 7, 1, 7, 1123938771460046632597234172348865871173648384000000⟩, + ⟨5, 6, 5, 7, 2, 7, 49993082353589303983671814285943616036667392000000⟩, + ⟨5, 6, 6, 7, 3, 7, -128082503088252885638259784244571393031667712000000⟩, + ⟨5, 6, 7, 7, 4, 7, 20980070040225255010907216950164522616750080000000⟩, + ⟨5, 6, 8, 7, 5, 7, 11546234516638654141187991387372186564034560000000⟩ +] + +def collectedFourData_11_4_42 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 4, 8, -26141570226225136425661656494358843480984256512000000⟩, + ⟨5, 7, 1, 0, 5, 8, 43327172854410986339754560383162563473036437094400000⟩, + ⟨5, 7, 2, 0, 6, 8, -12324250371813696117456931249258700943330272870400000⟩, + ⟨5, 7, 3, 0, 7, 8, 880643880813853744155794137032563224647145881600000⟩, + ⟨5, 7, 4, 0, 8, 8, -679772935444775558197371623144104636178151505920000⟩, + ⟨5, 7, 0, 1, 3, 8, -20546299261206284901705411102796223050661914214400000⟩, + ⟨5, 7, 1, 1, 4, 8, 18925975790521156893011831466780690671053307904000000⟩, + ⟨5, 7, 2, 1, 5, 8, 6017778507057885361022817512409386197597972070400000⟩, + ⟨5, 7, 3, 1, 6, 8, -4175753976560612895821399657494635471485219635200000⟩, + ⟨5, 7, 4, 1, 7, 8, 792783640792233888512126734730730877759279595520000⟩, + ⟨5, 7, 5, 1, 8, 8, 648587045940634554933250629117752567043981312000000⟩, + ⟨5, 7, 0, 2, 2, 8, -17139689782369384037437169804369160086530660761600000⟩, + ⟨5, 7, 1, 2, 3, 8, 28586509563868635162871313534500411321600494796800000⟩, + ⟨5, 7, 2, 2, 4, 8, 22170262341213105226247785993654382960315675443200000⟩, + ⟨5, 7, 3, 2, 5, 8, -1776989181216801449201572864512530921144136499200000⟩, + ⟨5, 7, 4, 2, 6, 8, -522676871141613651914827710401274655535844556800000⟩, + ⟨5, 7, 5, 2, 7, 8, 332458206977364808773235476211329478923229593600000⟩, + ⟨5, 7, 6, 2, 8, 8, -84187430711873697919620139876199698070608281600000⟩, + ⟨5, 7, 0, 3, 1, 8, -54941950884795288067987123313205704472459529420800000⟩, + ⟨5, 7, 1, 3, 2, 8, -73662034711137831846504539306489994228376849612800000⟩, + ⟨5, 7, 2, 3, 3, 8, -25254089393296821966678100383827473632747061248000000⟩, + ⟨5, 7, 3, 3, 4, 8, 193618414947136981349124806257580682191988326400000⟩, + ⟨5, 7, 4, 3, 5, 8, -1434065875415326465835794079601928261403274117120000⟩, + ⟨5, 7, 5, 3, 6, 8, -227472884196108776316491735027129804455831142400000⟩, + ⟨5, 7, 6, 3, 7, 8, -178499874461394409638322060506291931761868800000⟩, + ⟨5, 7, 7, 3, 8, 8, 3571103039640209521563049345783908120762777600000⟩, + ⟨5, 7, 0, 4, 0, 8, -175453139908334161258911563833499750728269299712000000⟩, + ⟨5, 7, 1, 4, 1, 8, 33163261826863816014159532622390014664486839910400000⟩, + ⟨5, 7, 2, 4, 2, 8, 6021473505899398043087629571526274383549038592000000⟩, + ⟨5, 7, 3, 4, 3, 8, 2859351059652934474391894972840985727448855347200000⟩, + ⟨5, 7, 4, 4, 4, 8, 1074783308709003772012266796681291038787947724800000⟩, + ⟨5, 7, 5, 4, 5, 8, -137928601182805624406613574067949131875850649600000⟩, + ⟨5, 7, 6, 4, 6, 8, -36072826604306837891216226946831058572463308800000⟩, + ⟨5, 7, 7, 4, 7, 8, 9445863385605158398863100391549154142401331200000⟩, + ⟨5, 7, 8, 4, 8, 8, -1124208726918631715506261744761409300856832000000⟩, + ⟨5, 7, 1, 5, 0, 8, 174790665039715804622799555404774229804033087897600000⟩, + ⟨5, 7, 2, 5, 1, 8, -6236452841318621199432980866595939290695755366400000⟩, + ⟨5, 7, 3, 5, 2, 8, 3570435804639741953123065477050508433649618124800000⟩, + ⟨5, 7, 4, 5, 3, 8, 1024143710406013570561420644081287648300488458240000⟩, + ⟨5, 7, 5, 5, 4, 8, -91493094172008367810337792695335900471833395200000⟩, + ⟨5, 7, 6, 5, 5, 8, -30134564523542353249583100490612928877586022400000⟩, + ⟨5, 7, 7, 5, 6, 8, -2992431209721692771966353154931603051380736000000⟩, + ⟨5, 7, 8, 5, 7, 8, 1843142723432966005615063075357510193066803200000⟩, + ⟨5, 7, 2, 6, 0, 8, 112269127602297325271750893256995972765732936089600000⟩, + ⟨5, 7, 3, 6, 1, 8, 869265223789178129475964752036149551016863334400000⟩, + ⟨5, 7, 4, 6, 2, 8, -1297177904836145971712596215836651202359737712640000⟩, + ⟨5, 7, 5, 6, 3, 8, 833735703550155969772590148326514730755896115200000⟩, + ⟨5, 7, 6, 6, 4, 8, 20092469910683046867847468861793632338208358400000⟩, + ⟨5, 7, 7, 6, 5, 8, -18695790830468089078315575621326649751397990400000⟩, + ⟨5, 7, 8, 6, 6, 8, -2753169581181500699893045239687179234652979200000⟩, + ⟨5, 7, 3, 7, 0, 8, -91368503158924705420184001950087341301992469299200000⟩, + ⟨5, 7, 4, 7, 1, 8, -1246091542772068084709634034614745399479962173440000⟩, + ⟨5, 7, 5, 7, 2, 8, -46188723902481745380021033365608152061024665600000⟩, + ⟨5, 7, 6, 7, 3, 8, 101430616740815116146362111187828273088089292800000⟩, + ⟨5, 7, 7, 7, 4, 8, -14537651264762233498345317906244335103377408000000⟩, + ⟨5, 7, 8, 7, 5, 8, -7111728437818401936619811072815831210524672000000⟩ +] + +def collectedFourData_11_4_43 : List CollectedFourTerm := [ + ⟨6, 0, 5, 1, 8, 2, 470316663465156096785530989132251396418362671104000000⟩, + ⟨6, 0, 5, 2, 7, 2, 241078873877962480832101622649419397914627879731200000⟩, + ⟨6, 0, 6, 2, 8, 2, -427333944397273717768357539951956677091876300390400000⟩, + ⟨6, 0, 5, 3, 6, 2, -164949775968393351265635903861508150965117439180800000⟩, + ⟨6, 0, 6, 3, 7, 2, -906062280117161809860122142831279280737170227200000⟩, + ⟨6, 0, 7, 3, 8, 2, 72507429428574383536181360433587527131005032857600000⟩, + ⟨6, 0, 5, 4, 5, 2, -100017599658706278460083438943936104207370892083200000⟩, + ⟨6, 0, 6, 4, 6, 2, -183105044874629014748261373608750119799590433587200000⟩, + ⟨6, 0, 7, 4, 7, 2, 191788157670388663749900680568170833526392042291200000⟩, + ⟨6, 0, 8, 4, 8, 2, -68477568996373175861792929723615788750965047296000000⟩, + ⟨6, 0, 5, 5, 4, 2, -66345337993415481570688261760807153873891780198400000⟩, + ⟨6, 0, 6, 5, 5, 2, -152962529104992323790799625676843711565624088985600000⟩, + ⟨6, 0, 7, 5, 6, 2, -60758116567988836646111500071014661963997249536000000⟩, + ⟨6, 0, 8, 5, 7, 2, 112269127602297325271750893256995972765732936089600000⟩, + ⟨6, 0, 5, 6, 3, 2, 604575433258614209385432364690035858792941774438400000⟩, + ⟨6, 0, 6, 6, 4, 2, 101989030274619574961612322241673798685766031769600000⟩, + ⟨6, 0, 7, 6, 5, 2, -379598045535008924838435275137101415433508382310400000⟩, + ⟨6, 0, 8, 6, 6, 2, -167700494970199208737634778812413425002581957017600000⟩, + ⟨6, 0, 5, 7, 2, 2, -33493309265872793337992362031539191601341608755200000⟩, + ⟨6, 0, 6, 7, 3, 2, 514860058894603785023358225925181824736630616883200000⟩, + ⟨6, 0, 7, 7, 4, 2, -295171467033102651517703858220975477531825143808000000⟩, + ⟨6, 0, 8, 7, 5, 2, -433188128790808270095135024279255719733746466816000000⟩ +] + +def collectedFourData_11_4_44 : List CollectedFourTerm := [ + ⟨6, 1, 4, 0, 8, 3, -2544407480847059542114542195625450069966863728640000⟩, + ⟨6, 1, 4, 1, 7, 3, 2967409440926177487659198466646353481421385891840000⟩, + ⟨6, 1, 5, 1, 8, 3, 14566067393595841685459370384826515700133658624000000⟩, + ⟨6, 1, 4, 2, 6, 3, -1956392894824947104574181349092311285435570585600000⟩, + ⟨6, 1, 5, 2, 7, 3, 7466397422975322721119933450302179505861767987200000⟩, + ⟨6, 1, 6, 2, 8, 3, -6617429826747974968346750570846153877467902771200000⟩, + ⟨6, 1, 4, 3, 5, 3, -5367745244295144028959163936396719531943306199040000⟩, + ⟨6, 1, 5, 3, 6, 3, -5108620935545817926213231172688776097247841484800000⟩, + ⟨6, 1, 6, 3, 7, 3, -14030721490648887818667774390195133886339481600000⟩, + ⟨6, 1, 7, 3, 8, 3, 748536879961979587436031764562893237361259315200000⟩, + ⟨6, 1, 4, 4, 4, 3, 4022941409368464761334529827997677339459295641600000⟩, + ⟨6, 1, 5, 4, 5, 3, -3097621688418737765399941673171522711673058099200000⟩, + ⟨6, 1, 6, 4, 6, 3, -2835451761479883751496272659135190520395569561600000⟩, + ⟨6, 1, 7, 4, 7, 3, 1979942059560496707967828163121083489926407782400000⟩, + ⟨6, 1, 8, 4, 8, 3, -530200693720837029694296956864018113514962944000000⟩, + ⟨6, 1, 4, 5, 3, 3, 3833396097940446215412951706210869946529957806080000⟩, + ⟨6, 1, 5, 5, 4, 3, -2054765947144844632134248653200508154764748390400000⟩, + ⟨6, 1, 6, 5, 5, 3, -2368683358168163182244956785310379608424369356800000⟩, + ⟨6, 1, 7, 5, 6, 3, -627241806344407171259791918084073668132995072000000⟩, + ⟨6, 1, 8, 5, 7, 3, 869265223789178129475964752036149551016863334400000⟩, + ⟨6, 1, 4, 6, 2, 3, -4855370069852891353839167217661995991742420090880000⟩, + ⟨6, 1, 5, 6, 3, 3, 18724164354448398971885403668972109905946633830400000⟩, + ⟨6, 1, 6, 6, 4, 3, 1579339202487831931404299410110796593363733708800000⟩, + ⟨6, 1, 7, 6, 5, 3, -3918814097862133559953411414885667119469219020800000⟩, + ⟨6, 1, 8, 6, 6, 3, -1298453202613495565400376594252592119122650726400000⟩, + ⟨6, 1, 4, 7, 1, 3, -4664152510242265919570778495503166439925722644480000⟩, + ⟨6, 1, 5, 7, 2, 3, -1037313448362212286294525025296088908789134131200000⟩, + ⟨6, 1, 6, 7, 3, 3, 7972805238151135814564319467206160975794903449600000⟩, + ⟨6, 1, 7, 7, 4, 3, -3047228825073838424658202536233086398932975616000000⟩, + ⟨6, 1, 8, 7, 5, 3, -3354042057314890392575120586610553086462132224000000⟩ +] + +def collectedFourData_11_4_45 : List CollectedFourTerm := [ + ⟨6, 2, 3, 0, 7, 4, -4918926725797211594166303422281323295768125112320000⟩, + ⟨6, 2, 4, 0, 8, 4, 18984707283395724611872645783344497881574717521920000⟩, + ⟨6, 2, 3, 1, 6, 4, 23324102152024918375221088523950981013203624919040000⟩, + ⟨6, 2, 4, 1, 7, 4, -22140871715726051987181014064883510081914163691520000⟩, + ⟨6, 2, 5, 1, 8, 4, -54341242080763616388315832494005463553708916736000000⟩, + ⟨6, 2, 3, 2, 5, 4, 9925555341237230500232405222206381820691181731840000⟩, + ⟨6, 2, 4, 2, 6, 4, 14597326379185937044338691933420689019252821196800000⟩, + ⟨6, 2, 5, 2, 7, 4, -27854691240236708076298592698117994229017660620800000⟩, + ⟨6, 2, 6, 2, 8, 4, 16458313533359951954999257178513917587689255731200000⟩, + ⟨6, 2, 3, 3, 4, 4, -1081475516538880059764915944789508025570589409280000⟩, + ⟨6, 2, 4, 3, 5, 4, 40050610211559955170518896220349427024804309893120000⟩, + ⟨6, 2, 5, 3, 6, 4, 19058596905806344639448183416068065397044359987200000⟩, + ⟨6, 2, 6, 3, 7, 4, 34896027527024591659498209055533539830372761600000⟩, + ⟨6, 2, 7, 3, 8, 4, -1396273362646850731832071678936177380663125606400000⟩, + ⟨6, 2, 3, 4, 3, 4, -15971198633396710394287109394312972510936107581440000⟩, + ⟨6, 2, 4, 4, 4, 4, -30016562067993110518476488512960318503759170764800000⟩, + ⟨6, 2, 5, 4, 5, 4, 11556215243037677275682281256434493849577770188800000⟩, + ⟨6, 2, 6, 4, 6, 4, 7052096557265236583435133643989774825026066841600000⟩, + ⟨6, 2, 7, 4, 7, 4, -3693258717578331172117770016258947768088579276800000⟩, + ⟨6, 2, 8, 4, 8, 4, 791202277741493150673510229816099022576182886400000⟩, + ⟨6, 2, 3, 5, 2, 4, -19943035413991617665585054592837554012790152232960000⟩, + ⟨6, 2, 4, 5, 3, 4, -28602298715331118935320813060751213462974355210240000⟩, + ⟨6, 2, 5, 5, 4, 4, 7665660932078321024713061011671252028930759065600000⟩, + ⟨6, 2, 6, 5, 5, 4, 5891189538936429378726995475934078363224558796800000⟩, + ⟨6, 2, 7, 5, 6, 4, 1170017202334338809226154971261527458005909504000000⟩, + ⟨6, 2, 8, 5, 7, 4, -1297177904836145971712596215836651202359737712640000⟩, + ⟨6, 2, 3, 6, 1, 4, -4855370069852891353839167217661995991742420090880000⟩, + ⟨6, 2, 4, 6, 2, 4, 36227601208761915512222382257160881263918857584640000⟩, + ⟨6, 2, 5, 6, 3, 4, -69853744353293318542530067836196028327610915225600000⟩, + ⟨6, 2, 6, 6, 4, 4, -3927999306468709445606047040801309063945964748800000⟩, + ⟨6, 2, 7, 6, 5, 4, 7309908014535999513988483493923592246369294745600000⟩, + ⟨6, 2, 8, 6, 6, 4, 1937641997861006372040181059230059576510214307840000⟩, + ⟨6, 2, 3, 7, 0, 4, 510348146255411365785083712580185180516137136291840000⟩, + ⟨6, 2, 4, 7, 1, 4, 34800860632034612933682014332498944924568717885440000⟩, + ⟨6, 2, 5, 7, 2, 4, 3869877825490906157364399075352798436604562636800000⟩, + ⟨6, 2, 6, 7, 3, 4, -19829288981579015464444549318235099679749151129600000⟩, + ⟨6, 2, 7, 7, 4, 4, 5684107960794627247662982733351733859096461312000000⟩, + ⟨6, 2, 8, 7, 5, 4, 5005134370468313975499698584430342352272778854400000⟩ +] + +def collectedFourData_11_4_46 : List CollectedFourTerm := [ + ⟨6, 3, 2, 0, 6, 5, -66366766779565111194375847056055217538394069401600000⟩, + ⟨6, 3, 3, 0, 7, 5, 18969263132625906282117958592094430236566460825600000⟩, + ⟨6, 3, 4, 0, 8, 5, -36606146831374821186812509490827120525271944396800000⟩, + ⟨6, 3, 2, 1, 5, 5, 32406068576990085640998086184602607034021026201600000⟩, + ⟨6, 3, 3, 1, 6, 5, -89946660260994297475635190160300491881906910003200000⟩, + ⟨6, 3, 4, 1, 7, 5, 42691835533822984600688434249479183561833368780800000⟩, + ⟨6, 3, 5, 1, 8, 5, 69853539023573928514449044368558204675644456960000000⟩, + ⟨6, 3, 2, 2, 4, 5, 119388083319548110960095061614763347694450429132800000⟩, + ⟨6, 3, 3, 2, 5, 5, -38276738301047752175037663244446756619301368627200000⟩, + ⟨6, 3, 4, 2, 6, 5, -28146437277404459990900018252584910162516508672000000⟩, + ⟨6, 3, 5, 2, 7, 5, 35806114969688149990405117003873377502875353088000000⟩, + ⟨6, 3, 6, 2, 8, 5, -15867388230049528084519395157189603462924468224000000⟩, + ⟨6, 3, 2, 3, 3, 5, -135994661779056844001846260346819525422866235392000000⟩, + ⟨6, 3, 3, 3, 4, 5, 4170583297598054527381788184325646022892480102400000⟩, + ⟨6, 3, 4, 3, 5, 5, -77225236934403124074294671628281074053058186444800000⟩, + ⟨6, 3, 5, 3, 6, 5, -24499080104125601607819201931580509515040161792000000⟩, + ⟨6, 3, 6, 3, 7, 5, -33643107802963036649868174255226665704620032000000⟩, + ⟨6, 3, 7, 3, 8, 5, 1076912842885736248539398534987151479650281062400000⟩, + ⟨6, 3, 2, 4, 2, 5, 32425966349184512986699569798084090942317395968000000⟩, + ⟨6, 3, 3, 4, 3, 5, 61591051525825763464030034333778451237914751795200000⟩, + ⟨6, 3, 4, 4, 4, 5, 57877672909660739008079546775541828406992699392000000⟩, + ⟨6, 3, 5, 4, 5, 5, -14855062224094983202479500815354651599666413568000000⟩, + ⟨6, 3, 6, 4, 6, 5, -6798895505491032563953164833543042836444741632000000⟩, + ⟨6, 3, 7, 4, 7, 5, 2848523685591331556828810314750953504153324748800000⟩, + ⟨6, 3, 8, 4, 8, 5, -508529774693174682721087415795651517666557952000000⟩, + ⟨6, 3, 2, 5, 1, 5, -33583641906378975677266824144208716574139980185600000⟩, + ⟨6, 3, 3, 5, 2, 5, 76907973531557759260532129213146551677455486156800000⟩, + ⟨6, 3, 4, 5, 3, 5, 55150702660766953879137600429285650132924733849600000⟩, + ⟨6, 3, 5, 5, 4, 5, -9853906987708928840854690042268613044984610816000000⟩, + ⟨6, 3, 6, 5, 5, 5, -5679670116967773359849612165470276891585806336000000⟩, + ⟨6, 3, 7, 5, 6, 5, -902406781722565012730901250622050536379121664000000⟩, + ⟨6, 3, 8, 5, 7, 5, 833735703550155969772590148326514730755896115200000⟩, + ⟨6, 3, 2, 6, 0, 5, 604575433258614209385432364690035858792941774438400000⟩, + ⟨6, 3, 3, 6, 1, 5, 18724164354448398971885403668972109905946633830400000⟩, + ⟨6, 3, 4, 6, 2, 5, -69853744353293318542530067836196028327610915225600000⟩, + ⟨6, 3, 5, 6, 3, 5, 89794253320036799160506400464170201572930748416000000⟩, + ⟨6, 3, 6, 6, 4, 5, 3786966983996949186855351742718140934705381376000000⟩, + ⟨6, 3, 7, 6, 5, 5, -5637960324792239564154279955866644680592169369600000⟩, + ⟨6, 3, 8, 6, 6, 5, -1245381461010189443079276577743854334547014451200000⟩, + ⟨6, 3, 3, 7, 0, 5, -1968097679681894122664546461148331212050464453427200000⟩, + ⟨6, 3, 4, 7, 1, 5, -67102715629893465506247770016267530276058012057600000⟩, + ⟨6, 3, 5, 7, 2, 5, -4974576423881287966032501932113944273745870848000000⟩, + ⟨6, 3, 6, 7, 3, 5, 19117330943951482130785304397565807249317691392000000⟩, + ⟨6, 3, 7, 7, 4, 5, -4384018937183577961301596366214988345787809792000000⟩, + ⟨6, 3, 8, 7, 5, 5, -3216952131367499133087221245500543565868040192000000⟩ +] + +def collectedFourData_11_4_47 : List CollectedFourTerm := [ + ⟨6, 4, 1, 0, 5, 6, 13119950955753738088834774798731008163231616204800000⟩, + ⟨6, 4, 2, 0, 6, 6, -11195761213496579280356982131770559066286745190400000⟩, + ⟨6, 4, 3, 0, 7, 6, 1600012707672357959174767250811031816905110323200000⟩, + ⟨6, 4, 4, 0, 8, 6, -2058428230259255724143593781145753628889736806400000⟩, + ⟨6, 4, 1, 1, 4, 6, 5730996457945462602660372694954511721843130368000000⟩, + ⟨6, 4, 2, 1, 5, 6, 5466751256110435401906881469158518891961804390400000⟩, + ⟨6, 4, 3, 1, 6, 6, -7586789134826923985685483988857370374476031590400000⟩, + ⟨6, 4, 4, 1, 7, 6, 2400637244592126527170365308805238097715816038400000⟩, + ⟨6, 4, 5, 1, 8, 6, 2945990820312202857608152418010673659311554560000000⟩, + ⟨6, 4, 1, 2, 3, 6, 8656313781063118514641069251285609235061774745600000⟩, + ⟨6, 4, 2, 2, 4, 6, 20140207779328758567235534424347263453692638003200000⟩, + ⟨6, 4, 3, 2, 5, 6, -3228552804699682999747381946709549328565167718400000⟩, + ⟨6, 4, 4, 2, 6, 6, -1582723834330826899851527559894330907249606656000000⟩, + ⟨6, 4, 5, 2, 7, 6, 1510080770226202904616508933782768647424442368000000⟩, + ⟨6, 4, 6, 2, 8, 6, -535350743529605870166385211847746307113562931200000⟩, + ⟨6, 4, 1, 3, 2, 6, -22305685301891737765865376170655763298724190617600000⟩, + ⟨6, 4, 2, 3, 3, 6, -22941659409832220124562701149036272416769179648000000⟩, + ⟨6, 4, 3, 3, 4, 6, 351778887134833914193656649347216761298930892800000⟩, + ⟨6, 4, 4, 3, 5, 6, -4342511341783441044063925648048876386548868710400000⟩, + ⟨6, 4, 5, 3, 6, 6, -1033219878358493729698659731568301079173005312000000⟩, + ⟨6, 4, 6, 3, 7, 6, -1135086790329748425185195107046823445502361600000⟩, + ⟨6, 4, 7, 3, 8, 6, 30278354719169651133017023749628477484669337600000⟩, + ⟨6, 4, 1, 4, 1, 6, 10042205388366976045835583691553868369904848076800000⟩, + ⟨6, 4, 2, 4, 2, 6, 5470107916634659604097773463418754874256392192000000⟩, + ⟨6, 4, 3, 4, 3, 6, 5195060263080575051148646306550051717759002214400000⟩, + ⟨6, 4, 4, 4, 4, 6, 3254563676634921583806726628230529116291465216000000⟩, + ⟨6, 4, 5, 4, 5, 6, -626494771189494826427776535584915209634971648000000⟩, + ⟨6, 4, 6, 4, 6, 6, -229388334820705314555139132062511241333676441600000⟩, + ⟨6, 4, 7, 4, 7, 6, 80088756623215480773564622018896997658080051200000⟩, + ⟨6, 4, 8, 4, 8, 6, -12255225670678464277215372899137855300829184000000⟩, + ⟨6, 4, 1, 5, 0, 6, 52928561956961004480302231994488015063895716659200000⟩, + ⟨6, 4, 2, 5, 1, 6, -5665402334759630337239618018050035557184464486400000⟩, + ⟨6, 4, 3, 5, 2, 6, 6487006591214252247511177487699488458522859929600000⟩, + ⟨6, 4, 4, 5, 3, 6, 3101221327622952166502555448253808635953335500800000⟩, + ⟨6, 4, 5, 5, 4, 6, -415576933334816353380032897472882392250187776000000⟩, + ⟨6, 4, 6, 5, 5, 6, -191626723695036867780633244154477786732219596800000⟩, + ⟨6, 4, 7, 5, 6, 6, -25371962845909916678056669342642514046222336000000⟩, + ⟨6, 4, 8, 5, 7, 6, 20092469910683046867847468861793632338208358400000⟩, + ⟨6, 4, 2, 6, 0, 6, 101989030274619574961612322241673798685766031769600000⟩, + ⟨6, 4, 3, 6, 1, 6, 1579339202487831931404299410110796593363733708800000⟩, + ⟨6, 4, 4, 6, 2, 6, -3927999306468709445606047040801309063945964748800000⟩, + ⟨6, 4, 5, 6, 3, 6, 3786966983996949186855351742718140934705381376000000⟩, + ⟨6, 4, 6, 6, 4, 6, 127768701516072230289137675353513196612537548800000⟩, + ⟨6, 4, 7, 6, 5, 6, -158516228805692704353439289581751832727152230400000⟩, + ⟨6, 4, 8, 6, 6, 6, -30012855903998598041541445744660419329812070400000⟩, + ⟨6, 4, 3, 7, 0, 6, -166004408047641460256755342218555693673258313318400000⟩, + ⟨6, 4, 4, 7, 1, 6, -3773304106982518104942407249262649533189115084800000⟩, + ⟨6, 4, 5, 7, 2, 6, -209796907709286465611182871808739417132105728000000⟩, + ⟨6, 4, 6, 7, 3, 6, 645000751652625465051370860282356582223288729600000⟩, + ⟨6, 4, 7, 7, 4, 6, -123260560362437538641081931397935282109022208000000⟩, + ⟨6, 4, 8, 7, 5, 6, -77526383515037702367862462036846752263307264000000⟩ +] + +def collectedFourData_11_4_48 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 4, 7, 29462801208193070475604046074007697413684330496000000⟩, + ⟨6, 5, 1, 0, 5, 7, -97663596308526979440817133014041925590702253670400000⟩, + ⟨6, 5, 2, 0, 6, 7, 41670060627859162307400885742609138819960248729600000⟩, + ⟨6, 5, 3, 0, 7, 7, -3970111262804109154289709486231456226896720691200000⟩, + ⟨6, 5, 4, 0, 8, 7, 3830683216501517844181856693654645251660106956800000⟩, + ⟨6, 5, 0, 1, 3, 7, 23156662949407617339609657850968128937216127795200000⟩, + ⟨6, 5, 1, 1, 4, 7, -42660961645510090576152333674941021865392472064000000⟩, + ⟨6, 5, 2, 1, 5, 7, -20346973460360384750341050350086150782409349529600000⟩, + ⟨6, 5, 3, 1, 6, 7, 18825098605944389572533173368688451459750454886400000⟩, + ⟨6, 5, 4, 1, 7, 7, -4467525593840731909311788093798511801040424140800000⟩, + ⟨6, 5, 5, 1, 8, 7, -4385931916573509832971770352451661420744933376000000⟩, + ⟨6, 5, 0, 2, 2, 7, 19317250970695309308664943216584346666745515212800000⟩, + ⟨6, 5, 1, 2, 3, 7, -64436729793028314221498422057928073908908248268800000⟩, + ⟨6, 5, 2, 2, 4, 7, -74960841270050952598477492376714492523626417356800000⟩, + ⟨6, 5, 3, 2, 5, 7, 8011007532023145485762060835181598648570373734400000⟩, + ⟨6, 5, 4, 2, 6, 7, 2945409288214247442611174295891473364336771072000000⟩, + ⟨6, 5, 5, 2, 7, 7, -2248177896914534331552179886987154407925009612800000⟩, + ⟨6, 5, 6, 2, 8, 7, 664182855000383778634258526552612953956915609600000⟩, + ⟨6, 5, 0, 3, 1, 7, 61922209067805443841648023777716281539608077926400000⟩, + ⟨6, 5, 1, 3, 2, 7, 166041279579146626978823281153232541662644587724800000⟩, + ⟨6, 5, 2, 3, 3, 7, 85387703460391987657069825313786100955062730752000000⟩, + ⟨6, 5, 3, 3, 4, 7, -872868893561743013562475229728671193581276364800000⟩, + ⟨6, 5, 4, 3, 5, 7, 8081304497238744919093524941089507172097510604800000⟩, + ⟨6, 5, 5, 3, 6, 7, 1538236986376785490392782808413220298109956915200000⟩, + ⟨6, 5, 6, 3, 7, 7, 1408245331096176938614007669862795588717772800000⟩, + ⟨6, 5, 7, 3, 8, 7, -32198432776725087464504757701685764629620326400000⟩, + ⟨6, 5, 0, 4, 0, 7, 197744088734450612777113907218506014778086916096000000⟩, + ⟨6, 5, 1, 4, 1, 7, -74753167630300980341989118895348136848650561126400000⟩, + ⟨6, 5, 2, 4, 2, 7, -20359466782152827672005868644937693298224529408000000⟩, + ⟨6, 5, 3, 4, 3, 7, -12890502158202695833217633510442780923097671270400000⟩, + ⟨6, 5, 4, 4, 4, 7, -6056661228140387064565823706698920408532385792000000⟩, + ⟨6, 5, 5, 4, 5, 7, 932712822314642496501276857500075374559415500800000⟩, + ⟨6, 5, 6, 4, 6, 7, 284590618330904494914335812016538171109854412800000⟩, + ⟨6, 5, 7, 4, 7, 7, -85167522153093347723649876191981925152115916800000⟩, + ⟨6, 5, 8, 4, 8, 7, 11403333524335165141196214344664866309013504000000⟩, + ⟨6, 5, 1, 5, 0, 7, -393994895681264329571138870923300538360824175001600000⟩, + ⟨6, 5, 2, 5, 1, 7, 21086342792489638715726568269869625069654350233600000⟩, + ⟨6, 5, 3, 5, 2, 7, -16096208365201302541785023638191839167972481433600000⟩, + ⟨6, 5, 4, 5, 3, 7, -5771294969504745190259658626335761309210614169600000⟩, + ⟨6, 5, 5, 5, 4, 7, 618702584929219874788183749658611812914534809600000⟩, + ⟨6, 5, 6, 5, 5, 7, 237741678659125144455104480823773418261735014400000⟩, + ⟨6, 5, 7, 5, 6, 7, 26980905920571121295752464400454812333768704000000⟩, + ⟨6, 5, 8, 5, 7, 7, -18695790830468089078315575621326649751397990400000⟩, + ⟨6, 5, 2, 6, 0, 7, -379598045535008924838435275137101415433508382310400000⟩, + ⟨6, 5, 3, 6, 1, 7, -3918814097862133559953411414885667119469219020800000⟩, + ⟨6, 5, 4, 6, 2, 7, 7309908014535999513988483493923592246369294745600000⟩, + ⟨6, 5, 5, 6, 3, 7, -5637960324792239564154279955866644680592169369600000⟩, + ⟨6, 5, 6, 6, 4, 7, -158516228805692704353439289581751832727152230400000⟩, + ⟨6, 5, 7, 6, 5, 7, 168568410818857069873114694551443477737609625600000⟩, + ⟨6, 5, 8, 6, 6, 7, 27926585367575741363428516454574589353551462400000⟩, + ⟨6, 5, 3, 7, 0, 7, 411906709805975124228487824125843104554920863334400000⟩, + ⟨6, 5, 4, 7, 1, 7, 7022024135159514353862535097934824475782125977600000⟩, + ⟨6, 5, 5, 7, 2, 7, 312341419116530941875678906357169395344395468800000⟩, + ⟨6, 5, 6, 7, 3, 7, -800220128369622921623995136116140660025511116800000⟩, + ⟨6, 5, 7, 7, 4, 7, 131077031881745839971152618379872838365478912000000⟩, + ⟨6, 5, 8, 7, 5, 7, 72137325897855288709431939813188962546089984000000⟩ +] + +def collectedFourData_11_4_49 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 4, 8, 39048617904700548378576521949428717109664284672000000⟩, + ⟨6, 6, 1, 0, 5, 8, -64719380015877310879806237665981038581940381286400000⟩, + ⟨6, 6, 2, 0, 6, 8, 18409182752458892297583455223323361194711344742400000⟩, + ⟨6, 6, 3, 0, 7, 8, -1315449918058670075062009455657384506608425369600000⟩, + ⟨6, 6, 4, 0, 8, 8, 1015401652939373397610067931904002480666071531520000⟩, + ⟨6, 6, 0, 1, 3, 8, 30690757374689225313831314351220444244346300006400000⟩, + ⟨6, 6, 1, 1, 4, 8, -28270421046715775069825955301706397680217882624000000⟩, + ⟨6, 6, 2, 1, 5, 8, -8988975471775049288138786770903933631974499942400000⟩, + ⟨6, 6, 3, 1, 6, 8, 6237476176208061100695779417521767294992331571200000⟩, + ⟨6, 6, 4, 1, 7, 8, -1184209869663347417007600721950501905466780549120000⟩, + ⟨6, 6, 5, 1, 8, 8, -968818151155545791223189995649471926576873472000000⟩, + ⟨6, 6, 0, 2, 2, 8, 25602180417051669708825717137584758559426058649600000⟩, + ⟨6, 6, 1, 2, 3, 8, -42700713060791666827908338671460839958260796620800000⟩, + ⟨6, 6, 2, 2, 4, 8, -33116530319992669513267408965083343966363136819200000⟩, + ⟨6, 6, 3, 2, 5, 8, 2654353619833852775318886203462598650877915955200000⟩, + ⟨6, 6, 4, 2, 6, 8, 780741525937803964480745101600982604521983180800000⟩, + ⟨6, 6, 5, 2, 7, 8, -496604962180788794760033817342512355367033241600000⟩, + ⟨6, 6, 6, 2, 8, 8, 125753839031004209893012161123344193106319769600000⟩, + ⟨6, 6, 0, 3, 1, 8, 82068798028319278122469795704090501146114575564800000⟩, + ⟨6, 6, 1, 3, 2, 8, 110031670730796976065885296516589736416779226316800000⟩, + ⟨6, 6, 2, 3, 3, 8, 37722955381643786644020017883023915216051109888000000⟩, + ⟨6, 6, 3, 3, 4, 8, -289214895630095445294673680918981454592370278400000⟩, + ⟨6, 6, 4, 3, 5, 8, 2142116557447099487348922957914168854561129758720000⟩, + ⟨6, 6, 5, 3, 6, 8, 339784552411589695858096393225018474490127974400000⟩, + ⟨6, 6, 6, 3, 7, 8, 266631779711822784856244678920036567272652800000⟩, + ⟨6, 6, 7, 3, 8, 8, -5334286995252214555269739722445829466331545600000⟩, + ⟨6, 6, 0, 4, 0, 8, 262080761070251393974028429594590372378938703872000000⟩, + ⟨6, 6, 1, 4, 1, 8, -49537175018340231547511974303736096845885498982400000⟩, + ⟨6, 6, 2, 4, 2, 8, -8994494826453131864500325078847071665784881152000000⟩, + ⟨6, 6, 3, 4, 3, 8, -4271117075889245355519254642735066430573851443200000⟩, + ⟨6, 6, 4, 4, 4, 8, -1605443069751974500527912564198331616202640588800000⟩, + ⟨6, 6, 5, 4, 5, 8, 206028987513308081046198443961736384434772377600000⟩, + ⟨6, 6, 6, 4, 6, 8, 53883298157851184796949955324189341156953292800000⟩, + ⟨6, 6, 7, 4, 7, 8, -14109631018050703398203509667183664097866547200000⟩, + ⟨6, 6, 8, 4, 8, 8, 1679271621508656139879382517840164885102592000000⟩, + ⟨6, 6, 1, 5, 0, 8, -261091198171302290972086893452720538827615738265600000⟩, + ⟨6, 6, 2, 5, 1, 8, 9315617308903333773255223999328788749209724518400000⟩, + ⟨6, 6, 3, 5, 2, 8, -5333290321970524579394821735353937752520182988800000⟩, + ⟨6, 6, 4, 5, 3, 8, -1529800852858772759033849612360429096626752061440000⟩, + ⟨6, 6, 5, 5, 4, 8, 136666575279301308540452075750388554364302131200000⟩, + ⟨6, 6, 6, 5, 5, 8, 45013099275263702999921480085035427849201254400000⟩, + ⟨6, 6, 7, 5, 6, 8, 4469903754951161207653606298565742707081216000000⟩, + ⟨6, 6, 8, 5, 7, 8, -2753169581181500699893045239687179234652979200000⟩, + ⟨6, 6, 2, 6, 0, 8, -167700494970199208737634778812413425002581957017600000⟩, + ⟨6, 6, 3, 6, 1, 8, -1298453202613495565400376594252592119122650726400000⟩, + ⟨6, 6, 4, 6, 2, 8, 1937641997861006372040181059230059576510214307840000⟩, + ⟨6, 6, 5, 6, 3, 8, -1245381461010189443079276577743854334547014451200000⟩, + ⟨6, 6, 6, 6, 4, 8, -30012855903998598041541445744660419329812070400000⟩, + ⟨6, 6, 7, 6, 5, 8, 27926585367575741363428516454574589353551462400000⟩, + ⟨6, 6, 8, 6, 6, 8, 4112509924692653862181645344842078743638835200000⟩, + ⟨6, 6, 3, 7, 0, 8, 136480469134101858338996995067435393689232552755200000⟩, + ⟨6, 6, 4, 7, 1, 8, 1861332433626026412453033538937766606510112112640000⟩, + ⟨6, 6, 5, 7, 2, 8, 68993783294790283442478504125683011319077273600000⟩, + ⟨6, 6, 6, 7, 3, 8, -151510615570323536370235241907977585517448396800000⟩, + ⟨6, 6, 7, 7, 4, 8, 21715420479983151841437219930922437310414848000000⟩, + ⟨6, 6, 8, 7, 5, 8, 10623048424680045278814449997533787960901632000000⟩ +] + +def collectedFourData_11_4_50 : List CollectedFourTerm := [ + ⟨7, 0, 4, 0, 8, 3, 267442774183439550077862622687191903616735138283520000⟩, + ⟨7, 0, 4, 1, 7, 3, -311904527475773881559704029064522481092481117061120000⟩, + ⟨7, 0, 5, 1, 8, 3, -1531039938378632889079171429108296362711719084032000000⟩, + ⟨7, 0, 4, 2, 6, 3, 205636537041845019078515411008634199908182445260800000⟩, + ⟨7, 0, 5, 2, 7, 3, -784793337933371246247973185759963298209558272409600000⟩, + ⟨7, 0, 6, 2, 8, 3, 695558319236090621421066806168461889761812519321600000⟩, + ⟨7, 0, 4, 3, 5, 3, 564203921757981724985700071741759632896223315230720000⟩, + ⟨7, 0, 5, 3, 6, 3, 536967355086980232541147090040676199823946704486400000⟩, + ⟨7, 0, 6, 3, 7, 3, 1474769708665187975946925612524290505838480588800000⟩, + ⟨7, 0, 7, 3, 8, 3, -78678742010694971188519302219466106911634069913600000⟩, + ⟨7, 0, 4, 4, 4, 3, -422851535769246338540704008504869409698358283468800000⟩, + ⟨7, 0, 5, 4, 5, 3, 325591142125435878150602469823470356607067068825600000⟩, + ⟨7, 0, 6, 4, 6, 3, 298034450402200329170151505669167274630650318028800000⟩, + ⟨7, 0, 7, 4, 7, 3, -208111790708557837927975916417878008505327366963200000⟩, + ⟨7, 0, 8, 4, 8, 3, 55729416561642351191118484896120071970506145792000000⟩, + ⟨7, 0, 4, 5, 3, 3, -402928420347145306647220799702103145987186297405440000⟩, + ⟨7, 0, 5, 5, 4, 3, 215976532587121220959397253162811509475395187507200000⟩, + ⟨7, 0, 6, 5, 5, 3, 248972404474987975789871304790694663173966292582400000⟩, + ⟨7, 0, 7, 5, 6, 3, 65929411871063148494466735587522596825460637696000000⟩, + ⟨7, 0, 8, 5, 7, 3, -91368503158924705420184001950087341301992469299200000⟩, + ⟨7, 0, 4, 6, 2, 3, 510348146255411365785083712580185180516137136291840000⟩, + ⟨7, 0, 5, 6, 3, 3, -1968097679681894122664546461148331212050464453427200000⟩, + ⟨7, 0, 6, 6, 4, 3, -166004408047641460256755342218555693673258313318400000⟩, + ⟨7, 0, 7, 6, 5, 3, 411906709805975124228487824125843104554920863334400000⟩, + ⟨7, 0, 8, 6, 6, 3, 136480469134101858338996995067435393689232552755200000⟩, + ⟨7, 0, 4, 7, 1, 3, 490249260758569509160890377813146784967309278576640000⟩, + ⟨7, 0, 5, 7, 2, 3, 109032058904112118468401670400366618531155515801600000⟩, + ⟨7, 0, 6, 7, 3, 3, -838021884059837682071666381600423334750561553612800000⟩, + ⟨7, 0, 7, 7, 4, 3, 320294346202040722478319896416923974422430220288000000⟩, + ⟨7, 0, 8, 7, 5, 3, 352543497568086032511910903274643249319831928832000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1115.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1115.lean new file mode 100644 index 0000000000000000000000000000000000000000..94b143fbc73e209cdd2075d7837aedcd79d65d59 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1115.lean @@ -0,0 +1,615 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PartsTrace +import OAI.Analysis.LaughlinFock.Sparse1112 +import OAI.Analysis.LaughlinFock.Sparse1113 +import OAI.Analysis.LaughlinFock.Sparse1114 + +namespace OAI + +/-! Sparse1115. -/ +namespace LaughlinFock +def collectedFourData_11_4_51 : List CollectedFourTerm := [ + ⟨7, 1, 3, 0, 7, 4, -4725206133776730471057412781414237287050085662720000⟩, + ⟨7, 1, 4, 0, 8, 4, 18237038342732879238618186188641897152344563384320000⟩, + ⟨7, 1, 3, 1, 6, 4, 22405536145839056046922009206885616440951271587840000⟩, + ⟨7, 1, 4, 1, 7, 4, -21268904513180493828551329239850162448028842065920000⟩, + ⟨7, 1, 5, 1, 8, 4, -52201137506364270549653823885366600983333830656000000⟩, + ⟨7, 1, 3, 2, 5, 4, 9534660220406802048711934812380015427194600816640000⟩, + ⟨7, 1, 4, 2, 6, 4, 14022444323459891806119815337785516097884966092800000⟩, + ⟨7, 1, 5, 2, 7, 4, -26757698424851390605853683810082016003869166796800000⟩, + ⟨7, 1, 6, 2, 8, 4, 15810140787744503585085139765867131287272370995200000⟩, + ⟨7, 1, 3, 3, 4, 4, -1038884095889975578465732118948895373409522810880000⟩, + ⟨7, 1, 4, 3, 5, 4, 38473309236476314620327728312007766585047011819520000⟩, + ⟨7, 1, 5, 3, 6, 4, 18308017992664648149036005668981667403431883571200000⟩, + ⟨7, 1, 6, 3, 7, 4, 33521727910759703683822211895935883430959513600000⟩, + ⟨7, 1, 7, 3, 8, 4, -1341284354370754083453808641179778156943795814400000⟩, + ⟨7, 1, 3, 4, 3, 4, -15342209785420555069136763964218763797458048778240000⟩, + ⟨7, 1, 4, 4, 4, 4, -28834428952706923306727194488504491225394236620800000⟩, + ⟨7, 1, 5, 4, 5, 4, 11101100340297477560657403502012028228379397324800000⟩, + ⟨7, 1, 6, 4, 6, 4, 6774365987933039759583847475224346032680311193600000⟩, + ⟨7, 1, 7, 4, 7, 4, -3547808235158688623663179539141623849956461772800000⟩, + ⟨7, 1, 8, 4, 8, 4, 760042599584833004314063123226139295968814694400000⟩, + ⟨7, 1, 3, 5, 2, 4, -19157624928646821504671096698320758199636103004160000⟩, + ⟨7, 1, 4, 5, 3, 4, -27475863102614691754385451758778673689028240343040000⟩, + ⟨7, 1, 5, 5, 4, 4, 7363766543978890294094124539048815869325580697600000⟩, + ⟨7, 1, 6, 5, 5, 4, 5659178616878494366332568898720569900330175692800000⟩, + ⟨7, 1, 7, 5, 6, 4, 1123938771460046632597234172348865871173648384000000⟩, + ⟨7, 1, 8, 5, 7, 4, -1246091542772068084709634034614745399479962173440000⟩, + ⟨7, 1, 3, 6, 1, 4, -4664152510242265919570778495503166439925722644480000⟩, + ⟨7, 1, 4, 6, 2, 4, 34800860632034612933682014332498944924568717885440000⟩, + ⟨7, 1, 5, 6, 3, 4, -67102715629893465506247770016267530276058012057600000⟩, + ⟨7, 1, 6, 6, 4, 4, -3773304106982518104942407249262649533189115084800000⟩, + ⟨7, 1, 7, 6, 5, 4, 7022024135159514353862535097934824475782125977600000⟩, + ⟨7, 1, 8, 6, 6, 4, 1861332433626026412453033538937766606510112112640000⟩, + ⟨7, 1, 3, 7, 0, 4, 490249260758569509160890377813146784967309278576640000⟩, + ⟨7, 1, 4, 7, 1, 4, 33430308944589547283254301321527628893262173962240000⟩, + ⟨7, 1, 5, 7, 2, 4, 3717471606575431161985431042164368584813104332800000⟩, + ⟨7, 1, 6, 7, 3, 4, -19048358137313567912762968433042137272152594841600000⟩, + ⟨7, 1, 7, 7, 4, 4, 5460252469413018040504352035115299300234493952000000⟩, + ⟨7, 1, 8, 7, 5, 4, 4808018689052661871599487040162231555239339622400000⟩ +] + +def collectedFourData_11_4_52 : List CollectedFourTerm := [ + ⟨7, 2, 2, 0, 6, 5, 3676700246887438272488690719129363481734466764800000⟩, + ⟨7, 2, 3, 0, 7, 5, -1050891851860912237444587685305104643000159436800000⟩, + ⟨7, 2, 4, 0, 8, 5, 2027970257155196657679301916098992194076436070400000⟩, + ⟨7, 2, 2, 1, 5, 5, -1795287101048851992832615732542580466914217164800000⟩, + ⟨7, 2, 3, 1, 6, 5, 4983019725621554921682839608750776506971167129600000⟩, + ⟨7, 2, 4, 1, 7, 5, -2365115702692567418762229004973714955611563622400000⟩, + ⟨7, 2, 5, 1, 8, 5, -3869866450282098982267931556233111782954106880000000⟩, + ⟨7, 2, 2, 2, 4, 5, -6614066297283572053274539122785007551746827878400000⟩, + ⟨7, 2, 3, 2, 5, 5, 2120520555550714830917614379123195744282581401600000⟩, + ⟨7, 2, 4, 2, 6, 5, 1559304722958102466910347595576640844874121216000000⟩, + ⟨7, 2, 5, 2, 7, 5, -1983648716629481208657906093414293418817880064000000⟩, + ⟨7, 2, 6, 2, 8, 5, 879048853120342117804427010285474845212803072000000⟩, + ⟨7, 2, 2, 3, 3, 5, 7534066081585727728081678435594905220993253376000000⟩, + ⟨7, 2, 3, 3, 4, 5, -231049143781174180819662900997872456467428147200000⟩, + ⟨7, 2, 4, 3, 5, 5, 4278256444912223413276936425885482678258919014400000⟩, + ⟨7, 2, 5, 3, 6, 5, 1357242159566658579254217851143849543861272576000000⟩, + ⟨7, 2, 6, 3, 7, 5, 1863818726864690751917261851057421650231296000000⟩, + ⟨7, 2, 7, 3, 8, 5, -59660669148845723608960261329111145551967027200000⟩, + ⟨7, 2, 2, 4, 2, 5, -1796389432042054558150675728932277929801416704000000⟩, + ⟨7, 2, 3, 4, 3, 5, -3412126962628936615911387035664077358823479705600000⟩, + ⟨7, 2, 4, 4, 4, 5, -3206406829837348713264162674238080728355045376000000⟩, + ⟨7, 2, 5, 4, 5, 5, 822966276604505419103476744652309169652629504000000⟩, + ⟨7, 2, 6, 4, 6, 5, 376656902190656600963746474460968106481156096000000⟩, + ⟨7, 2, 7, 4, 7, 5, -157807412448833370849693376562305435116660326400000⟩, + ⟨7, 2, 8, 4, 8, 5, 28172406746499947237084785005709504655917056000000⟩, + ⟨7, 2, 2, 5, 1, 5, 1860524332889190947627410714030119129665293516800000⟩, + ⟨7, 2, 3, 5, 2, 5, -4260680141467393381216756744868558261631477350400000⟩, + ⟨7, 2, 4, 5, 3, 5, -3055333443655009533432615283221697862250056908800000⟩, + ⟨7, 2, 5, 5, 4, 5, 545903680600434988369125067601315455511298048000000⟩, + ⟨7, 2, 6, 5, 5, 5, 314652129892886374720197714934008437022916608000000⟩, + ⟨7, 2, 7, 5, 6, 5, 49993082353589303983671814285943616036667392000000⟩, + ⟨7, 2, 8, 5, 7, 5, -46188723902481745380021033365608152061024665600000⟩, + ⟨7, 2, 2, 6, 0, 5, -33493309265872793337992362031539191601341608755200000⟩, + ⟨7, 2, 3, 6, 1, 5, -1037313448362212286294525025296088908789134131200000⟩, + ⟨7, 2, 4, 6, 2, 5, 3869877825490906157364399075352798436604562636800000⟩, + ⟨7, 2, 5, 6, 3, 5, -4974576423881287966032501932113944273745870848000000⟩, + ⟨7, 2, 6, 6, 4, 5, -209796907709286465611182871808739417132105728000000⟩, + ⟨7, 2, 7, 6, 5, 5, 312341419116530941875678906357169395344395468800000⟩, + ⟨7, 2, 8, 6, 6, 5, 68993783294790283442478504125683011319077273600000⟩, + ⟨7, 2, 3, 7, 0, 5, 109032058904112118468401670400366618531155515801600000⟩, + ⟨7, 2, 4, 7, 1, 5, 3717471606575431161985431042164368584813104332800000⟩, + ⟨7, 2, 5, 7, 2, 5, 275590137253400372943595825104988903355449344000000⟩, + ⟨7, 2, 6, 7, 3, 5, -1059094767037796415733388014270935489237221376000000⟩, + ⟨7, 2, 7, 7, 4, 5, 242873418291414448206576724090218324821016576000000⟩, + ⟨7, 2, 8, 7, 5, 5, 178218244907266219860203229796315712534347776000000⟩ +] + +def collectedFourData_11_4_53 : List CollectedFourTerm := [ + ⟨7, 3, 1, 0, 5, 6, 66232012438838527101065134658901439623108073881600000⟩, + ⟨7, 3, 2, 0, 6, 6, -56518335964463316778279160232789458425874271436800000⟩, + ⟨7, 3, 3, 0, 7, 6, 8077169031670915605885075147679622398334101094400000⟩, + ⟨7, 3, 4, 0, 8, 6, -10391337941030821006042569813849213652381256908800000⟩, + ⟨7, 3, 1, 1, 4, 6, 28931162164376924684442527315675894162449760256000000⟩, + ⟨7, 3, 2, 1, 5, 6, 27597202033438656082678272162856803874663877836800000⟩, + ⟨7, 3, 3, 1, 6, 6, -38299557219635504470898704267957450036663340236800000⟩, + ⟨7, 3, 4, 1, 7, 6, 12118874253507475451928358667668257926904859852800000⟩, + ⟨7, 3, 5, 1, 8, 6, 14871923021179647467311842998496227411644907520000000⟩, + ⟨7, 3, 1, 2, 3, 6, 43698721432371729262196874985230474229197255475200000⟩, + ⟨7, 3, 2, 2, 4, 6, 101671606598216970569017790504357887229479511654400000⟩, + ⟨7, 3, 3, 2, 5, 6, -16298349760716139149476218078214800716493278412800000⟩, + ⟨7, 3, 4, 2, 6, 6, -7989891504638116988576527718354865181427761152000000⟩, + ⟨7, 3, 5, 2, 7, 6, 7623175474860367478365390789780462810228064256000000⟩, + ⟨7, 3, 6, 2, 8, 6, -2702552564729255370605021848777897210020259430400000⟩, + ⟨7, 3, 1, 3, 2, 6, -112603349765101149238507603877437757173959701299200000⟩, + ⟨7, 3, 2, 3, 3, 6, -115813868247216418213243366386425269794442838016000000⟩, + ⟨7, 3, 3, 3, 4, 6, 1775846853925725723464974600234240111707527577600000⟩, + ⟨7, 3, 4, 3, 5, 6, -21921824721354298348473152363612760192022531276800000⟩, + ⟨7, 3, 5, 3, 6, 6, -5215890826595210470777308819461530011045986304000000⟩, + ⟨7, 3, 6, 3, 7, 6, -5730134409024715465927945328763287064752947200000⟩, + ⟨7, 3, 7, 3, 8, 6, 152850904180258805204374783769668192461599539200000⟩, + ⟨7, 3, 1, 4, 1, 6, 50694966348483740372319792397796713248782391705600000⟩, + ⟨7, 3, 2, 4, 2, 6, 27614147095378531563868641771430785071934603264000000⟩, + ⟨7, 3, 3, 4, 3, 6, 26225654129749079034109115605978723090363632844800000⟩, + ⟨7, 3, 4, 4, 4, 6, 16429657598631817252112575682133913841719836672000000⟩, + ⟨7, 3, 5, 4, 5, 6, -3162664983903218957012272039863993357897302016000000⟩, + ⟨7, 3, 6, 4, 6, 6, -1157996024253932549762691952082950331372352307200000⟩, + ⟨7, 3, 7, 4, 7, 6, 404303304392587220239772991215489008838010470400000⟩, + ⟨7, 3, 8, 4, 8, 6, -61866714425878581927058108961731872584368128000000⟩, + ⟨7, 3, 1, 5, 0, 6, 267193466326634070133495565157094198683292296806400000⟩, + ⟨7, 3, 2, 5, 1, 6, -28600030531536978392539521733252966936749067468800000⟩, + ⟨7, 3, 3, 5, 2, 6, 32747645375283090726503881320183226693753975603200000⟩, + ⟨7, 3, 4, 5, 3, 6, 15655556201346677212852499601249675216990869913600000⟩, + ⟨7, 3, 5, 5, 4, 6, -2097911547897600369957646924332477347310600192000000⟩, + ⟨7, 3, 6, 5, 5, 6, -967368215794859507281545922789786228123867545600000⟩, + ⟨7, 3, 7, 5, 6, 6, -128082503088252885638259784244571393031667712000000⟩, + ⟨7, 3, 8, 5, 7, 6, 101430616740815116146362111187828273088089292800000⟩, + ⟨7, 3, 2, 6, 0, 6, 514860058894603785023358225925181824736630616883200000⟩, + ⟨7, 3, 3, 6, 1, 6, 7972805238151135814564319467206160975794903449600000⟩, + ⟨7, 3, 4, 6, 2, 6, -19829288981579015464444549318235099679749151129600000⟩, + ⟨7, 3, 5, 6, 3, 6, 19117330943951482130785304397565807249317691392000000⟩, + ⟨7, 3, 6, 6, 4, 6, 645000751652625465051370860282356582223288729600000⟩, + ⟨7, 3, 7, 6, 5, 6, -800220128369622921623995136116140660025511116800000⟩, + ⟨7, 3, 8, 6, 6, 6, -151510615570323536370235241907977585517448396800000⟩, + ⟨7, 3, 3, 7, 0, 6, -838021884059837682071666381600423334750561553612800000⟩, + ⟨7, 3, 4, 7, 1, 6, -19048358137313567912762968433042137272152594841600000⟩, + ⟨7, 3, 5, 7, 2, 6, -1059094767037796415733388014270935489237221376000000⟩, + ⟨7, 3, 6, 7, 3, 6, 3256086699606313650359560029201746485851665203200000⟩, + ⟨7, 3, 7, 7, 4, 6, -622242796080190230537484033403487592472641536000000⟩, + ⟨7, 3, 8, 7, 5, 6, -391367956680837630554416318468282516387135488000000⟩ +] + +def collectedFourData_11_4_54 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 4, 7, 22909965838390926595435501683292694034430033920000000⟩, + ⟨7, 4, 1, 0, 5, 7, -75942190264670271317689694924863265641498411008000000⟩, + ⟨7, 4, 2, 0, 6, 7, 32402202992241574157939468231324917280897236992000000⟩, + ⟨7, 4, 3, 0, 7, 7, -3087116963615809756776669460834359386648346624000000⟩, + ⟨7, 4, 4, 0, 8, 7, 2978699174175690917458574571068907205045518336000000⟩, + ⟨7, 4, 0, 1, 3, 7, 18006378733415676070291663052507287941707464704000000⟩, + ⟨7, 4, 1, 1, 4, 7, -33172717252009131275848356259643823469394657280000000⟩, + ⟨7, 4, 2, 1, 5, 7, -15821593595176408531700607937829928169994452992000000⟩, + ⟨7, 4, 3, 1, 6, 7, 14638199637534628556465128647262074413229539328000000⟩, + ⟨7, 4, 4, 1, 7, 7, -3473901141096060782957370782791747209334358016000000⟩, + ⟨7, 4, 5, 1, 8, 7, -3410454751677361132475991989790609273016811520000000⟩, + ⟨7, 4, 0, 2, 2, 7, 15020892165107039258993937220641316627814547456000000⟩, + ⟨7, 4, 1, 2, 3, 7, -50105326641018405554975525684148192184501272576000000⟩, + ⟨7, 4, 2, 2, 4, 7, -58288765571833953071412652900704478397869326336000000⟩, + ⟨7, 4, 3, 2, 5, 7, 6229275607327716549294624454710042829718028288000000⟩, + ⟨7, 4, 4, 2, 6, 7, 2290319433520224656365323210092218513033789440000000⟩, + ⟨7, 4, 5, 2, 7, 7, -1748159601423599357404119574639866911398035456000000⟩, + ⟨7, 4, 6, 2, 8, 7, 516461636182520893650226930115327419421294592000000⟩, + ⟨7, 4, 0, 3, 1, 7, 48150061644058024393174795083351756072579760128000000⟩, + ⟨7, 4, 1, 3, 2, 7, 129111961080711592251034290305110505928781725696000000⟩, + ⟨7, 4, 2, 3, 3, 7, 66396584475214232228990735315897750477906903040000000⟩, + ⟨7, 4, 3, 3, 4, 7, -678733715493851449673543359153001102359658496000000⟩, + ⟨7, 4, 4, 3, 5, 7, 6283937791695443510257247879203807549294903296000000⟩, + ⟨7, 4, 5, 3, 6, 7, 1196116980195409729520297388653389084417327104000000⟩, + ⟨7, 4, 6, 3, 7, 7, 1095036829645214433657056487414288567238656000000⟩, + ⟨7, 4, 7, 3, 8, 7, -25037164312786633719986903600599463916208128000000⟩, + ⟨7, 4, 0, 4, 0, 7, 153763733653072013715609358118476210642008145920000000⟩, + ⟨7, 4, 1, 4, 1, 7, -58127280723241786225400478945011209209410224128000000⟩, + ⟨7, 4, 2, 4, 2, 7, -15831308271437174232634970082425381027221340160000000⟩, + ⟨7, 4, 3, 4, 3, 7, -10023519555975039841255223876603796960741163008000000⟩, + ⟨7, 4, 4, 4, 4, 7, -4709596377170581011866420316857554526105763840000000⟩, + ⟨7, 4, 5, 4, 5, 7, 725267728117972581643798517818919902790025216000000⟩, + ⟨7, 4, 6, 4, 6, 7, 221294686062453886457296729513325490346131456000000⟩, + ⟨7, 4, 7, 4, 7, 7, -66225373795251413401694607071148943695937536000000⟩, + ⟨7, 4, 8, 4, 8, 7, 8867112792168850576801503118387534972846080000000⟩, + ⟨7, 4, 1, 5, 0, 7, -306366307017951906947727041133924138537222930432000000⟩, + ⟨7, 4, 2, 5, 1, 7, 16396519449012896938799447529251234592243843072000000⟩, + ⟨7, 4, 3, 5, 2, 7, -12516243149067497456790351688963332583899267072000000⟩, + ⟨7, 4, 4, 5, 3, 7, -4487698561325631392958600722010849871807905792000000⟩, + ⟨7, 4, 5, 5, 4, 7, 481096654207846655157801287431680166138478592000000⟩, + ⟨7, 4, 6, 5, 5, 7, 184865440931925192008073951253293730929573888000000⟩, + ⟨7, 4, 7, 5, 6, 7, 20980070040225255010907216950164522616750080000000⟩, + ⟨7, 4, 8, 5, 7, 7, -14537651264762233498345317906244335103377408000000⟩, + ⟨7, 4, 2, 6, 0, 7, -295171467033102651517703858220975477531825143808000000⟩, + ⟨7, 4, 3, 6, 1, 7, -3047228825073838424658202536233086398932975616000000⟩, + ⟨7, 4, 4, 6, 2, 7, 5684107960794627247662982733351733859096461312000000⟩, + ⟨7, 4, 5, 6, 3, 7, -4384018937183577961301596366214988345787809792000000⟩, + ⟨7, 4, 6, 6, 4, 7, -123260560362437538641081931397935282109022208000000⟩, + ⟨7, 4, 7, 6, 5, 7, 131077031881745839971152618379872838365478912000000⟩, + ⟨7, 4, 8, 6, 6, 7, 21715420479983151841437219930922437310414848000000⟩, + ⟨7, 4, 3, 7, 0, 7, 320294346202040722478319896416923974422430220288000000⟩, + ⟨7, 4, 4, 7, 1, 7, 5460252469413018040504352035115299300234493952000000⟩, + ⟨7, 4, 5, 7, 2, 7, 242873418291414448206576724090218324821016576000000⟩, + ⟨7, 4, 6, 7, 3, 7, -622242796080190230537484033403487592472641536000000⟩, + ⟨7, 4, 7, 7, 4, 7, 101924128034825282777159333341896269616906240000000⟩, + ⟨7, 4, 8, 7, 5, 7, 56093229571571149790525120889361572487495680000000⟩ +] + +def collectedFourData_11_4_55 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 4, 8, 100866713154367199640915316038494688896373227520000000⟩, + ⟨7, 5, 1, 0, 5, 8, -167177008813009947723684334165196931786105421824000000⟩, + ⟨7, 5, 2, 0, 6, 8, 47552867572172652192387518275519232440516214784000000⟩, + ⟨7, 5, 3, 0, 7, 8, -3397946372329544099705843079760444382968283136000000⟩, + ⟨7, 5, 4, 0, 8, 8, 2622889944875029021040211689540556473922433843200000⟩, + ⟨7, 5, 0, 1, 3, 8, 79277474766409343754038915947083182255609217024000000⟩, + ⟨7, 5, 1, 1, 4, 8, -73025489850410443292045291828140029144559779840000000⟩, + ⟨7, 5, 2, 1, 5, 8, -23219475082984491555426308115793960002109046784000000⟩, + ⟨7, 5, 3, 1, 6, 8, 16112061169699994285117811637382448407371579392000000⟩, + ⟨7, 5, 4, 1, 7, 8, -3058939436202804481094178870502581325549220659200000⟩, + ⟨7, 5, 5, 1, 8, 8, -2502559829130018890879366687004087394259435520000000⟩, + ⟨7, 5, 0, 2, 2, 8, 66133141883678447362439658171001416824112807936000000⟩, + ⟨7, 5, 1, 2, 3, 8, -110300461499082697447562231522962415103485411328000000⟩, + ⟨7, 5, 2, 2, 4, 8, -85543503040411154493254589528680114103697539072000000⟩, + ⟨7, 5, 3, 2, 5, 8, 6856476350467919427460246122689117402098040832000000⟩, + ⟨7, 5, 4, 2, 6, 8, 2016737999195398841652824982191165410721660928000000⟩, + ⟨7, 5, 5, 2, 7, 8, -1282783180535954651930811195100121055841222656000000⟩, + ⟨7, 5, 6, 2, 8, 8, 324835476650093237827734908401936022567387136000000⟩, + ⟨7, 5, 0, 3, 1, 8, 211992391890768982486858932856165772450089402368000000⟩, + ⟨7, 5, 1, 3, 2, 8, 284223451815514157878685874301459132216076402688000000⟩, + ⟨7, 5, 2, 3, 3, 8, 97442386542372953692498541670237810423056302080000000⟩, + ⟨7, 5, 3, 3, 4, 8, -747072687404371197131283331992530584332140544000000⟩, + ⟨7, 5, 4, 3, 5, 8, 5533313800518084962419046721499666751794918195200000⟩, + ⟨7, 5, 5, 3, 6, 8, 877699463423497935716234692855263589935611904000000⟩, + ⟨7, 5, 6, 3, 7, 8, 688738108674350953567296408380678967656448000000⟩, + ⟨7, 5, 7, 3, 8, 8, -13779027917103500002870802799454530406711296000000⟩, + ⟨7, 5, 0, 4, 0, 8, 676982345819955514790034518161639983719928299520000000⟩, + ⟨7, 5, 1, 4, 1, 8, -127959766341720580726595197836427112837686493184000000⟩, + ⟨7, 5, 2, 4, 2, 8, -23233732160314861137185870286407331028999864320000000⟩, + ⟨7, 5, 3, 4, 3, 8, -11032747484017357503145309081134283325190438912000000⟩, + ⟨7, 5, 4, 4, 4, 8, -4147029377519807987165260190729974508534366208000000⟩, + ⟨7, 5, 5, 4, 5, 8, 532194681914412670917868137860164545115324416000000⟩, + ⟨7, 5, 6, 4, 6, 8, 139186262427100300456371853998917772638158848000000⟩, + ⟨7, 5, 7, 4, 7, 8, -36446670355530381271025752473987403902615552000000⟩, + ⟨7, 5, 8, 4, 8, 8, 4337736341100896275276302741886647108894720000000⟩, + ⟨7, 5, 1, 5, 0, 8, -674426200111543951749322771147952413981588586496000000⟩, + ⟨7, 5, 2, 5, 1, 8, 24063225521738640425541391957445728140414418944000000⟩, + ⟨7, 5, 3, 5, 2, 8, -13776453404523869290919999766445387852397150208000000⟩, + ⟨7, 5, 4, 5, 3, 8, -3951637524923443493278596268955453229892003430400000⟩, + ⟨7, 5, 5, 5, 4, 8, 353024229439567667007336756861259861293268992000000⟩, + ⟨7, 5, 6, 5, 5, 8, 116273599845912301312573040396922991310536704000000⟩, + ⟨7, 5, 7, 5, 6, 8, 11546234516638654141187991387372186564034560000000⟩, + ⟨7, 5, 8, 5, 7, 8, -7111728437818401936619811072815831210524672000000⟩, + ⟨7, 5, 2, 6, 0, 8, -433188128790808270095135024279255719733746466816000000⟩, + ⟨7, 5, 3, 6, 1, 8, -3354042057314890392575120586610553086462132224000000⟩, + ⟨7, 5, 4, 6, 2, 8, 5005134370468313975499698584430342352272778854400000⟩, + ⟨7, 5, 5, 6, 3, 8, -3216952131367499133087221245500543565868040192000000⟩, + ⟨7, 5, 6, 6, 4, 8, -77526383515037702367862462036846752263307264000000⟩, + ⟨7, 5, 7, 6, 5, 8, 72137325897855288709431939813188962546089984000000⟩, + ⟨7, 5, 8, 6, 6, 8, 10623048424680045278814449997533787960901632000000⟩, + ⟨7, 5, 3, 7, 0, 8, 352543497568086032511910903274643249319831928832000000⟩, + ⟨7, 5, 4, 7, 1, 8, 4808018689052661871599487040162231555239339622400000⟩, + ⟨7, 5, 5, 7, 2, 8, 178218244907266219860203229796315712534347776000000⟩, + ⟨7, 5, 6, 7, 3, 8, -391367956680837630554416318468282516387135488000000⟩, + ⟨7, 5, 7, 7, 4, 8, 56093229571571149790525120889361572487495680000000⟩, + ⟨7, 5, 8, 7, 5, 8, 27440458479022615505218981860046261054341120000000⟩ +] + +def collectedFourData_11_4 : List (List CollectedFourTerm) := [ + collectedFourData_11_4_0, + collectedFourData_11_4_1, + collectedFourData_11_4_2, + collectedFourData_11_4_3, + collectedFourData_11_4_4, + collectedFourData_11_4_5, + collectedFourData_11_4_6, + collectedFourData_11_4_7, + collectedFourData_11_4_8, + collectedFourData_11_4_9, + collectedFourData_11_4_10, + collectedFourData_11_4_11, + collectedFourData_11_4_12, + collectedFourData_11_4_13, + collectedFourData_11_4_14, + collectedFourData_11_4_15, + collectedFourData_11_4_16, + collectedFourData_11_4_17, + collectedFourData_11_4_18, + collectedFourData_11_4_19, + collectedFourData_11_4_20, + collectedFourData_11_4_21, + collectedFourData_11_4_22, + collectedFourData_11_4_23, + collectedFourData_11_4_24, + collectedFourData_11_4_25, + collectedFourData_11_4_26, + collectedFourData_11_4_27, + collectedFourData_11_4_28, + collectedFourData_11_4_29, + collectedFourData_11_4_30, + collectedFourData_11_4_31, + collectedFourData_11_4_32, + collectedFourData_11_4_33, + collectedFourData_11_4_34, + collectedFourData_11_4_35, + collectedFourData_11_4_36, + collectedFourData_11_4_37, + collectedFourData_11_4_38, + collectedFourData_11_4_39, + collectedFourData_11_4_40, + collectedFourData_11_4_41, + collectedFourData_11_4_42, + collectedFourData_11_4_43, + collectedFourData_11_4_44, + collectedFourData_11_4_45, + collectedFourData_11_4_46, + collectedFourData_11_4_47, + collectedFourData_11_4_48, + collectedFourData_11_4_49, + collectedFourData_11_4_50, + collectedFourData_11_4_51, + collectedFourData_11_4_52, + collectedFourData_11_4_53, + collectedFourData_11_4_54, + collectedFourData_11_4_55 +] + +theorem collectedFourChecked_11_4 : collectNumericRowParts 11 4 = collectedFourData_11_4 := by + decide +kernel + +def collectedFourData_11_5_0 : List CollectedFourTerm := [ + ⟨0, 5, 6, 3, 8, 0, -112829666620571050438812066914287488011920736256000000⟩, + ⟨0, 5, 6, 4, 7, 0, 49233951595176293575180725874505508964125376512000000⟩, + ⟨0, 5, 7, 4, 8, 0, -288946732947821818327202068681453700797452779520000000⟩, + ⟨0, 5, 6, 5, 6, 0, 83386719381426899136786989569522965927740571648000000⟩, + ⟨0, 5, 7, 5, 7, 0, -131798990666905708012318491520935140919236100096000000⟩, + ⟨0, 5, 8, 5, 8, 0, -397811091076567400068049426630470388160424574976000000⟩, + ⟨0, 5, 6, 6, 5, 0, -7931546461872261972161148863606497845002108928000000⟩, + ⟨0, 5, 7, 6, 6, 0, -39846333220396327208479247225839455290410401792000000⟩, + ⟨0, 5, 8, 6, 7, 0, -107232979076579766510222896505113967534029144064000000⟩, + ⟨0, 5, 6, 7, 4, 0, -275253539659865902264032807818645387862658252800000000⟩, + ⟨0, 5, 7, 7, 5, 0, 143149413691076107478546521451396462670287732736000000⟩, + ⟨0, 5, 8, 7, 6, 0, -160320597432118694399372218762827386206996660224000000⟩ +] + +def collectedFourData_11_5_1 : List CollectedFourTerm := [ + ⟨0, 6, 5, 2, 8, 1, 132881483602370107876664950022927089543975796736000000⟩, + ⟨0, 6, 5, 3, 7, 1, -10468242825044282848982959259437453234201952256000000⟩, + ⟨0, 6, 6, 3, 8, 1, 135656643676949457052223960472504634484811890688000000⟩, + ⟨0, 6, 5, 4, 6, 1, -25636634285721618660471150958055933330356961280000000⟩, + ⟨0, 6, 6, 4, 7, 1, -59194650027773029412216715544175701576044773376000000⟩, + ⟨0, 6, 7, 4, 8, 1, 173702294649760396851650393515023317783260692480000000⟩, + ⟨0, 6, 5, 5, 5, 1, -7055235610152277620563165238641937012007895040000000⟩, + ⟨0, 6, 6, 5, 6, 1, -100256987522230368358245843363867257655005282304000000⟩, + ⟨0, 6, 7, 5, 7, 1, 79231860065703010501217456422345156600742805504000000⟩, + ⟨0, 6, 8, 5, 8, 1, 159431229537620524993746122252427280531027132416000000⟩, + ⟨0, 6, 5, 6, 4, 1, 58833931326005166522790904772563850494975410176000000⟩, + ⟨0, 6, 6, 6, 5, 1, 9536206251532120056035638681507377204632223744000000⟩, + ⟨0, 6, 7, 6, 6, 1, 23953894349833986746657299467510451846049169408000000⟩, + ⟨0, 6, 8, 6, 7, 1, 42975890025827599749258996782137203347605684224000000⟩, + ⟨0, 6, 5, 7, 3, 1, 82026064964347548803268233946619309787952709632000000⟩, + ⟨0, 6, 6, 7, 4, 1, 330941076658731337379776272447513216338519654400000000⟩, + ⟨0, 6, 7, 7, 5, 1, -86055244100641737337757099062493300777879076864000000⟩, + ⟨0, 6, 8, 7, 6, 1, 64251878698598104142085532275675882971971190784000000⟩ +] + +def collectedFourData_11_5_2 : List CollectedFourTerm := [ + ⟨0, 7, 4, 1, 8, 2, -7665888547106957144743388616748004193261846528000000⟩, + ⟨0, 7, 4, 2, 7, 2, 1039429302430695061022944824919915239907000320000000⟩, + ⟨0, 7, 5, 2, 8, 2, -12966394766872199656166243415442456401181409280000000⟩, + ⟨0, 7, 4, 3, 6, 2, 846539664336414332790205291465013249716518912000000⟩, + ⟨0, 7, 5, 3, 7, 2, 1021476922933607509354058417549079984608378880000000⟩, + ⟨0, 7, 6, 3, 8, 2, -6618595559663327471320334633284280899464069120000000⟩, + ⟨0, 7, 4, 4, 5, 2, -2189059624008749611959712451880148560443867136000000⟩, + ⟨0, 7, 5, 4, 6, 2, 2501587968699261083450627540116196204897894400000000⟩, + ⟨0, 7, 6, 4, 7, 2, 2888066792826120496819965845299218151102218240000000⟩, + ⟨0, 7, 7, 4, 8, 2, -5649878029859116838101073686744535973809356800000000⟩, + ⟨0, 7, 4, 5, 4, 2, -305699305027599108736493027257885389037240320000000⟩, + ⟨0, 7, 5, 5, 5, 2, 688440312483817009914572015030266095678259200000000⟩, + ⟨0, 7, 6, 5, 6, 2, 4891470365580086893641118659299575912684584960000000⟩, + ⟨0, 7, 7, 5, 7, 2, -2577112446054291919063165049395048696397168640000000⟩, + ⟨0, 7, 8, 5, 8, 2, -3889270732667623666880183695073418401462353920000000⟩, + ⟨0, 7, 4, 6, 3, 2, 7641341145783082700138606372667320794475397120000000⟩, + ⟨0, 7, 5, 6, 4, 2, -5740935144453979666119798509355123641658900480000000⟩, + ⟨0, 7, 6, 6, 5, 2, -465265029722600794945580558410609850906050560000000⟩, + ⟨0, 7, 7, 6, 6, 2, -779129496760969572901659921879525758368481280000000⟩, + ⟨0, 7, 8, 6, 7, 2, -1048382250908709440742129932453190048814202880000000⟩, + ⟨0, 7, 4, 7, 2, 2, -7852684054538956628017740327824293086300733440000000⟩, + ⟨0, 7, 5, 7, 3, 2, -8003992058693908309457846306020135454229135360000000⟩, + ⟨0, 7, 6, 7, 4, 2, -16146390483460436394259327597386344228192256000000000⟩, + ⟨0, 7, 7, 7, 5, 2, 2799051296234846758840511991964134537418506240000000⟩, + ⟨0, 7, 8, 7, 6, 2, -1567402773384504417434862244187811918989230080000000⟩ +] + +def collectedFourData_11_5_3 : List CollectedFourTerm := [ + ⟨0, 8, 3, 0, 8, 3, 224606823976919447167350414737878398481622630400000⟩, + ⟨0, 8, 3, 1, 7, 3, -3000460111153331043527666779387438810006762291200000⟩, + ⟨0, 8, 4, 1, 8, 3, 4670730136982745678504516156798333832242030182400000⟩, + ⟨0, 8, 3, 2, 6, 3, 976712383889646083155966122373923598719202099200000⟩, + ⟨0, 8, 4, 2, 7, 3, -633311290438496765254615460569127518161862656000000⟩, + ⟨0, 8, 5, 2, 8, 3, 3950131183977436210956671204744362541042368512000000⟩, + ⟨0, 8, 3, 3, 5, 3, 1950951479297977512529722562627521486084951244800000⟩, + ⟨0, 8, 4, 3, 6, 3, -515786043336038219688078035987822614832322969600000⟩, + ⟨0, 8, 5, 3, 7, 3, -311186564927229100498084565485406360910692352000000⟩, + ⟨0, 8, 6, 3, 8, 3, 1344209200497105682931169040780388673081311232000000⟩, + ⟨0, 8, 3, 4, 4, 3, -797870604199000017219880429876516497472566067200000⟩, + ⟨0, 8, 4, 4, 5, 3, 1333766685320311499348249057750155775986945228800000⟩, + ⟨0, 8, 5, 4, 6, 3, -762093150971169840445777715501064278255861760000000⟩, + ⟨0, 8, 6, 4, 7, 3, -586554340655998071078589560336007908990910464000000⟩, + ⟨0, 8, 7, 4, 8, 3, 860600027712987332486726984837150071440015360000000⟩, + ⟨0, 8, 3, 5, 3, 3, -2008789427021122518318913336154160170824787558400000⟩, + ⟨0, 8, 4, 5, 4, 3, 186258768057088794748580696306241796262854656000000⟩, + ⟨0, 8, 5, 5, 5, 3, -209729041537232697756699608721070877237575680000000⟩, + ⟨0, 8, 6, 5, 6, 3, -993437264764090962503805583817973631398445056000000⟩, + ⟨0, 8, 7, 5, 7, 3, 392550605654244887826745511312078979547004928000000⟩, + ⟨0, 8, 8, 5, 8, 3, 473936815290935350842528588589634856175219507200000⟩, + ⟨0, 8, 3, 6, 2, 3, -2246391228416124931187883766236264380263877836800000⟩, + ⟨0, 8, 4, 6, 3, 3, -4655773711978197432657012631531000202941956096000000⟩, + ⟨0, 8, 5, 6, 4, 3, 1748940036689165814333125393558780248684756992000000⟩, + ⟨0, 8, 6, 6, 5, 3, 94493390325015214481793251476874939351433216000000⟩, + ⟨0, 8, 7, 6, 6, 3, 118678467563522975079577951122928155708358656000000⟩, + ⟨0, 8, 8, 6, 7, 3, 127753242022937933700979526936391769832344780800000⟩, + ⟨0, 8, 3, 7, 1, 3, 20650820318309014207229231723371896065293811712000000⟩, + ⟨0, 8, 4, 7, 2, 3, 4784542306394586125691421616276718956474007552000000⟩, + ⟨0, 8, 5, 7, 3, 3, 2438366191667422736381740209481260043541151744000000⟩, + ⟨0, 8, 6, 7, 4, 3, 3279264678893669586450027299743480699001241600000000⟩, + ⟨0, 8, 7, 7, 5, 3, -426356747947326700598308117716565165445480448000000⟩, + ⟨0, 8, 8, 7, 6, 3, 190999786272660972487424388943599020196809932800000⟩ +] + +def collectedFourData_11_5_4 : List CollectedFourTerm := [ + ⟨1, 4, 6, 3, 8, 0, -81122626128754386653904471223273079448570691584000000⟩, + ⟨1, 4, 6, 4, 7, 0, 35398380299463680603998305717900765270972039168000000⟩, + ⟨1, 4, 7, 4, 8, 0, -207747824575931125557707955157752976577428193280000000⟩, + ⟨1, 4, 6, 5, 6, 0, 59953643958117856923607535307006811237433475072000000⟩, + ⟨1, 4, 7, 5, 7, 0, -94761249982008207761954609241877836852671545344000000⟩, + ⟨1, 4, 8, 5, 8, 0, -286019460819646850221162727501943479200502513664000000⟩, + ⟨1, 4, 6, 6, 5, 0, -5702648049232104236328689387121155150280916992000000⟩, + ⟨1, 4, 7, 6, 6, 0, -28648841118268803450039553582251339293380313088000000⟩, + ⟨1, 4, 8, 6, 7, 0, -77098702237199741183705207249486804030268112896000000⟩, + ⟨1, 4, 6, 7, 4, 0, -197902649695257577619077985999217152333394739200000000⟩, + ⟨1, 4, 7, 7, 5, 0, 102922012580814872780227458247990561478283362304000000⟩, + ⟨1, 4, 8, 7, 6, 0, -115267803900903537861840644693437175654447579136000000⟩ +] + +def collectedFourData_11_5_5 : List CollectedFourTerm := [ + ⟨1, 5, 5, 2, 8, 1, 28932796793744431012197328751232017540038262784000000⟩, + ⟨1, 5, 5, 3, 7, 1, -2279290795329268933832060164501614241895153664000000⟩, + ⟨1, 5, 6, 3, 8, 1, 29537043076455898428413546295273684980541161472000000⟩, + ⟨1, 5, 5, 4, 6, 1, -5581963040718903781949049898023246862032568320000000⟩, + ⟨1, 5, 6, 4, 7, 1, -12888678949847513894311162283227485648866770944000000⟩, + ⟨1, 5, 7, 4, 8, 1, 37820869074184527719856967428828803122719621120000000⟩, + ⟨1, 5, 5, 5, 5, 1, -1536163600124678912901078027335688819321077760000000⟩, + ⟨1, 5, 6, 5, 6, 1, -21829339713075903214459119159102239399504510976000000⟩, + ⟨1, 5, 7, 5, 7, 1, 17251457800780391567583879279585489932859211776000000⟩, + ⟨1, 5, 8, 5, 8, 1, 34713575147850957859756070962458209474737864704000000⟩, + ⟨1, 5, 5, 6, 4, 1, 12810138278754594766467209694626520786895110144000000⟩, + ⟨1, 5, 6, 6, 5, 1, 2076354885413793928301975059795156621470990336000000⟩, + ⟨1, 5, 7, 6, 6, 1, 5215573598774962364848425791597783888431153152000000⟩, + ⟨1, 5, 8, 6, 7, 1, 9357305919824936587653477881713295693715603456000000⟩, + ⟨1, 5, 5, 7, 3, 1, 17859850786325939191243733434073749553946820608000000⟩, + ⟨1, 5, 6, 7, 4, 1, 72057074184407201750801576372868066032851353600000000⟩, + ⟨1, 5, 7, 7, 5, 1, -18737139465197336026175297688146767520376815616000000⟩, + ⟨1, 5, 8, 7, 6, 1, 13989808810124527960638127773309449916012036096000000⟩ +] + +def collectedFourData_11_5_6 : List CollectedFourTerm := [ + ⟨1, 6, 4, 1, 8, 2, 17645497833408929300168958336879750313788466790400000⟩, + ⟨1, 6, 4, 2, 7, 2, -2392579463074038475352255782551906753158578176000000⟩, + ⟨1, 6, 5, 2, 8, 2, 29846310621397559146298834102029700689091887104000000⟩, + ⟨1, 6, 4, 3, 6, 2, -1948582179502238278305176951939702394959010201600000⟩, + ⟨1, 6, 5, 3, 7, 2, -2351256311612367026337829713639600991852560384000000⟩, + ⟨1, 6, 6, 3, 8, 2, 15234817580582251604441618371062541056806486016000000⟩, + ⟨1, 6, 4, 4, 5, 2, 5038821868500408119881235727656652826125061324800000⟩, + ⟨1, 6, 5, 4, 6, 2, -5758205954927872319651804689959631336683601920000000⟩, + ⟨1, 6, 6, 4, 7, 2, -6647810755712850236360180304807978799340716032000000⟩, + ⟨1, 6, 7, 4, 8, 2, 13005003910802719637442246237921699806041866240000000⟩, + ⟨1, 6, 4, 5, 4, 2, 703664864339157146961274750831072694476210176000000⟩, + ⟨1, 6, 5, 5, 5, 2, -1584665882854384260722002406735675675702722560000000⟩, + ⟨1, 6, 6, 5, 6, 2, -11259285757630927577142587359211915038559305728000000⟩, + ⟨1, 6, 7, 5, 7, 2, 5932049729638173298848287422942531813745098752000000⟩, + ⟨1, 6, 8, 5, 8, 2, 8952402303412954784392587829550364006763462656000000⟩, + ⟨1, 6, 4, 6, 3, 2, -17588994126863428630243476690371044703433916416000000⟩, + ⟨1, 6, 5, 6, 4, 2, 13214601025139386332263610304153022731086987264000000⟩, + ⟨1, 6, 6, 6, 5, 2, 1070956487755019140804524816717614309135351808000000⟩, + ⟨1, 6, 7, 6, 6, 2, 1793416087718769091228658784006531962533576704000000⟩, + ⟨1, 6, 8, 6, 7, 2, 2413187541576698752445114353414424264215363584000000⟩, + ⟨1, 6, 4, 7, 2, 2, 18075467523344714914029623055613079472561979392000000⟩, + ⟨1, 6, 5, 7, 3, 2, 18423751358034853896923109539826306988740968448000000⟩, + ⟨1, 6, 6, 7, 4, 2, 37166089298389131159404526481162225090088140800000000⟩, + ⟨1, 6, 7, 7, 5, 2, -6442913079130542183597444686735925386969874432000000⟩, + ⟨1, 6, 8, 7, 6, 2, 3607879513493992779476202244709036477638508544000000⟩ +] + +def collectedFourData_11_5_7 : List CollectedFourTerm := [ + ⟨1, 7, 3, 0, 8, 3, -3000460111153331043527666779387438810006762291200000⟩, + ⟨1, 7, 3, 1, 7, 3, 40082312367977660416287799418920842401104370073600000⟩, + ⟨1, 7, 4, 1, 8, 3, -62394985236150140223635731695499729965895856947200000⟩, + ⟨1, 7, 3, 2, 6, 3, -13047629168344007757421668948426614107618777497600000⟩, + ⟨1, 7, 4, 2, 7, 3, 8460229441199071923939964846101896341349203968000000⟩, + ⟨1, 7, 5, 2, 8, 3, -52768704180444260572778109679316971045609537536000000⟩, + ⟨1, 7, 3, 3, 5, 3, -26062218363546673200761382660950654424506066534400000⟩, + ⟨1, 7, 4, 3, 6, 3, 6890242342229177603334232923809397752776674508800000⟩, + ⟨1, 7, 5, 3, 7, 3, 4157054797617921962244721991869892073992749056000000⟩, + ⟨1, 7, 6, 3, 8, 3, -17956916961487027405094339127787403652624285696000000⟩, + ⟨1, 7, 3, 4, 4, 3, 10658531559160962050147347943106219772405717401600000⟩, + ⟨1, 7, 4, 4, 5, 3, -17817418304708442937133848355189049305707472486400000⟩, + ⟨1, 7, 5, 4, 6, 3, 10180590509160675423119564601920054277470945280000000⟩, + ⟨1, 7, 6, 4, 7, 3, 7835616349497088883789469761418005996101435392000000⟩, + ⟨1, 7, 7, 4, 8, 3, -11496516486407446392812375532606360251353006080000000⟩, + ⟨1, 7, 3, 5, 3, 3, 26834859425743880517472012037190677865677665075200000⟩, + ⟨1, 7, 4, 5, 4, 3, -2488179094528684933227662063630892667364179968000000⟩, + ⟨1, 7, 5, 5, 5, 3, 2801711952204764110264011780298774506677207040000000⟩, + ⟨1, 7, 6, 5, 6, 3, 13271052201709725222508049496498782481225351168000000⟩, + ⟨1, 7, 7, 5, 7, 3, -5243974394988448195272975715924239135522422784000000⟩, + ⟨1, 7, 8, 5, 8, 3, -6331190140659408349376664908101831585957517721600000⟩, + ⟨1, 7, 3, 6, 2, 3, 30008915827062923269167311278628455251056158310400000⟩, + ⟨1, 7, 4, 6, 3, 3, 62195186513043602933039419506892583840973324288000000⟩, + ⟨1, 7, 5, 6, 4, 3, -23363603669602354652953835893073248847161982976000000⟩, + ⟨1, 7, 6, 6, 5, 3, -1262310928126498421675676611475946019538075648000000⟩, + ⟨1, 7, 7, 6, 6, 3, -1585392650464381605180604579572998855844691968000000⟩, + ⟨1, 7, 8, 6, 7, 3, -1706620039290224276507591103706199057563543142400000⟩, + ⟨1, 7, 3, 7, 1, 3, -275868566816332040565712894239304321047919067136000000⟩, + ⟨1, 7, 4, 7, 2, 3, -63915370362646314092426319508155944213629894656000000⟩, + ⟨1, 7, 5, 7, 3, 3, -32573455983843006938809227527821658711478239232000000⟩, + ⟨1, 7, 6, 7, 4, 3, -43806785068763436577436658719669743690501324800000000⟩, + ⟨1, 7, 7, 7, 5, 3, 5695581250320630433156220750939584037696569344000000⟩, + ⟨1, 7, 8, 7, 6, 3, -2551513038663603318703279201685083646138410598400000⟩ +] + +def collectedFourData_11_5_8 : List CollectedFourTerm := [ + ⟨1, 8, 2, 0, 7, 4, -7665888547106957144743388616748004193261846528000000⟩, + ⟨1, 8, 3, 0, 8, 4, 4670730136982745678504516156798333832242030182400000⟩, + ⟨1, 8, 2, 1, 6, 4, 17645497833408929300168958336879750313788466790400000⟩, + ⟨1, 8, 3, 1, 7, 4, -62394985236150140223635731695499729965895856947200000⟩, + ⟨1, 8, 4, 1, 8, 4, 48564241340148768779734645622199016238882173747200000⟩, + ⟨1, 8, 2, 2, 5, 4, 37002205364466475465194630624020909790389600256000000⟩, + ⟨1, 8, 3, 2, 6, 4, 20310869838337667059310487007649163441555583795200000⟩, + ⟨1, 8, 4, 2, 7, 4, -6584898174434997598882238050849869550445395968000000⟩, + ⟨1, 8, 5, 2, 8, 4, 27381175750229601254505138787481457000682881024000000⟩, + ⟨1, 8, 2, 3, 4, 4, -2726362508785125109391125939595003302852008345600000⟩, + ⟨1, 8, 3, 3, 5, 4, 40570307298786781063791056364101432555925720268800000⟩, + ⟨1, 8, 4, 3, 6, 4, -5362921246534078071916164884254112978041621708800000⟩, + ⟨1, 8, 5, 3, 7, 4, -2157055963089089686964355585387613516625608704000000⟩, + ⟨1, 8, 6, 3, 8, 4, 6988254310359337711073921909728502908975054848000000⟩, + ⟨1, 8, 2, 4, 3, 4, -57989451122740755006380842521154124182158154137600000⟩, + ⟨1, 8, 3, 4, 4, 4, -16591830161081170100152218958938186593770615603200000⟩, + ⟨1, 8, 4, 4, 5, 4, 13867931843133404188590210416957879907208554086400000⟩, + ⟨1, 8, 5, 4, 6, 4, -5282611015408509493290715791357852159332843520000000⟩, + ⟨1, 8, 6, 4, 7, 4, -3049369769105432993746525559338124284784541696000000⟩, + ⟨1, 8, 7, 4, 8, 4, 3579259449161074896529791008619946685006610432000000⟩, + ⟨1, 8, 2, 5, 2, 4, 7887864084845923472618057315880669559987057459200000⟩, + ⟨1, 8, 3, 5, 3, 4, -41773055464263205097076926849968971981070427750400000⟩, + ⟨1, 8, 4, 5, 4, 4, 1936638490847725034977790313071768026604371968000000⟩, + ⟨1, 8, 5, 5, 5, 4, -1453781527446855429970533067736444462023311360000000⟩, + ⟨1, 8, 6, 5, 6, 4, -5164666515444072395497343149882486280719171584000000⟩, + ⟨1, 8, 7, 5, 7, 4, 1632628886029322859307166534137393938058287513600000⟩, + ⟨1, 8, 8, 5, 8, 4, 1642596996097551773721099830607297452145062707200000⟩, + ⟨1, 8, 2, 6, 1, 4, -132355768437017082504289609623318242978108434022400000⟩, + ⟨1, 8, 3, 6, 2, 4, -46714017963653102970869711653673524588404591820800000⟩, + ⟨1, 8, 4, 6, 3, 4, -48408730871291766629679898075845464662147596288000000⟩, + ⟨1, 8, 5, 6, 4, 4, 12123150419774160168306349204173214035669417984000000⟩, + ⟨1, 8, 6, 6, 5, 4, 491250797863198190167650197596075409302093824000000⟩, + ⟨1, 8, 7, 6, 6, 4, 493587047129821233531274216412173684805153587200000⟩, + ⟨1, 8, 8, 6, 7, 4, 442774405402084329257872247332783421360229580800000⟩, + ⟨1, 8, 2, 7, 0, 4, 1079754923764072841304422734578168233627638510387200000⟩, + ⟨1, 8, 3, 7, 1, 4, 429436680089707183725803838642924366300312502272000000⟩, + ⟨1, 8, 4, 7, 2, 4, 49747611284603115933936430166234147935701958656000000⟩, + ⟨1, 8, 5, 7, 3, 4, 16902054673089842837737642734836319803815231488000000⟩, + ⟨1, 8, 6, 7, 4, 4, 17048191247770855332622497833767472917276262400000000⟩, + ⟨1, 8, 7, 7, 5, 4, -1773229571999264641018359893322847886736202137600000⟩, + ⟨1, 8, 8, 7, 6, 4, 661977852457303954137603026714293858963606732800000⟩ +] + +def collectedFourData_11_5_9 : List CollectedFourTerm := [ + ⟨2, 3, 6, 3, 8, 0, -31752978061436931889586095055729041932854231040000000⟩, + ⟨2, 3, 6, 4, 7, 0, 13855616450030847666865841806359349675771822080000000⟩, + ⟨2, 3, 7, 4, 8, 0, -81316550398663459644897028058021506482752716800000000⟩, + ⟨2, 3, 6, 5, 6, 0, 23467025565516514337322671334880620417719992320000000⟩, + ⟨2, 3, 7, 5, 7, 0, -37091401441779841237281228145332083028016496640000000⟩, + ⟨2, 3, 8, 5, 8, 0, -111953595414129592218440136311077358584819875840000000⟩, + ⟨2, 3, 6, 6, 5, 0, -2232127669436722789142341169647253143966187520000000⟩, + ⟨2, 3, 7, 6, 6, 0, -11213715173251006387423511378990057926195937280000000⟩, + ⟨2, 3, 8, 6, 7, 0, -30177935768715379987234771014311569696499957760000000⟩, + ⟨2, 3, 6, 7, 4, 0, -77462956932632539142767789634197161510961152000000000⟩, + ⟨2, 3, 7, 7, 5, 0, 40285683088348152553101146067401358176409354240000000⟩, + ⟨2, 3, 8, 7, 6, 0, -45118066600140082288018151555157461691436892160000000⟩ +] + +def collectedFourData_11_5_10 : List CollectedFourTerm := [ + ⟨2, 4, 5, 2, 8, 1, -25155733070561865701332436379535760988070477824000000⟩, + ⟨2, 4, 5, 3, 7, 1, 1981738275986117176206806591485853758604181504000000⟩, + ⟨2, 4, 6, 3, 8, 1, -25681097358885882408942593657619909723964833792000000⟩, + ⟨2, 4, 5, 4, 6, 1, 4853259547048921932520727650160130888585707520000000⟩, + ⟨2, 4, 6, 4, 7, 1, 11206112205669459903490399377706071635036995584000000⟩, + ⟨2, 4, 7, 4, 8, 1, -32883502196806610584041118349615614325497528320000000⟩, + ⟨2, 4, 5, 5, 5, 1, 1335623436369789305639474149175000722424463360000000⟩, + ⟨2, 4, 6, 5, 6, 1, 18979604593479230914701124439520367733989441536000000⟩, + ⟨2, 4, 7, 5, 7, 1, -14999347301548228556228208041432905426283790336000000⟩, + ⟨2, 4, 8, 5, 8, 1, -30181853367629966323580558991318695742164434944000000⟩, + ⟨2, 4, 5, 6, 4, 1, -11137824712715324021971848603109532435988086784000000⟩, + ⟨2, 4, 6, 6, 5, 1, -1805294857236878519570908641521462725098602496000000⟩, + ⟨2, 4, 7, 6, 6, 1, -4534700817067910212107909213992006664975286272000000⟩, + ⟨2, 4, 8, 6, 7, 1, -8135746144997575777368128949282127579044642816000000⟩, + ⟨2, 4, 5, 7, 3, 1, -15528316956832124431456972651609437664431833088000000⟩, + ⟨2, 4, 6, 7, 4, 1, -62650304322482063771570984292589059387791769600000000⟩, + ⟨2, 4, 7, 7, 5, 1, 16291079021932109399931162960062237864494104576000000⟩, + ⟨2, 4, 8, 7, 6, 1, -12163493859389940053990890326513199505637113856000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1116.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1116.lean new file mode 100644 index 0000000000000000000000000000000000000000..1256857339d07109fdcb43282b4380db64cdc1f2 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1116.lean @@ -0,0 +1,615 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1116. -/ +namespace LaughlinFock +def collectedFourData_11_5_11 : List CollectedFourTerm := [ + ⟨2, 5, 4, 1, 8, 2, 37002205364466475465194630624020909790389600256000000⟩, + ⟨2, 5, 4, 2, 7, 2, -5017184410396840533850865737274934721920368640000000⟩, + ⟨2, 5, 5, 2, 8, 2, 62587030720869990043018096033025105003607490560000000⟩, + ⟨2, 5, 4, 3, 6, 2, -4086132261962493004822953938645566342639386624000000⟩, + ⟨2, 5, 5, 3, 7, 2, -4930530706935059335766661731105483551156469760000000⟩, + ⟨2, 5, 6, 3, 8, 2, 31947064011964091954121253259143841178703626240000000⟩, + ⟨2, 5, 4, 4, 5, 2, 10566294209064944291306126542183611423283740672000000⟩, + ⟨2, 5, 5, 4, 6, 2, -12074826184372531948365195700853259253894348800000000⟩, + ⟨2, 5, 6, 4, 7, 2, -13940307104357533444154149305140886525947412480000000⟩, + ⟨2, 5, 7, 4, 8, 2, 27271195747286338088537557509071664225819033600000000⟩, + ⟨2, 5, 4, 5, 4, 2, 1475569126122344402283150372404612311956848640000000⟩, + ⟨2, 5, 5, 5, 5, 2, -3323008111475515166124355874630531356714598400000000⟩, + ⟨2, 5, 6, 5, 6, 2, -23610464708582590778233588426044743887009873920000000⟩, + ⟨2, 5, 7, 5, 7, 2, 12439372603742207919921321238431934602050273280000000⟩, + ⟨2, 5, 8, 5, 8, 2, 18772982868696603710758845760569908540567715840000000⟩, + ⟨2, 5, 4, 6, 3, 2, -36883718384207316029913098857477116814153482240000000⟩, + ⟨2, 5, 5, 6, 4, 2, 27710716102093273437716700440074997434637352960000000⟩, + ⟨2, 5, 6, 6, 5, 2, 2245771259640526052937246669430407394618245120000000⟩, + ⟨2, 5, 7, 6, 6, 2, 3760752516489798426423790685643702620714434560000000⟩, + ⟨2, 5, 8, 6, 7, 2, 5060399079663849058033715459483670335465717760000000⟩, + ⟨2, 5, 4, 7, 2, 2, 37903841969888692568238689863957816254796922880000000⟩, + ⟨2, 5, 5, 7, 3, 2, 38634185205199879442273244949604659322651934720000000⟩, + ⟨2, 5, 6, 7, 4, 2, 77936439186732458613000237528238583722278912000000000⟩, + ⟨2, 5, 7, 7, 5, 2, -13510641363034785180181548816258530512711188480000000⟩, + ⟨2, 5, 8, 7, 6, 2, 7565640819484058876044835875926888446857052160000000⟩ +] + +def collectedFourData_11_5_12 : List CollectedFourTerm := [ + ⟨2, 6, 3, 0, 8, 3, 976712383889646083155966122373923598719202099200000⟩, + ⟨2, 6, 3, 1, 7, 3, -13047629168344007757421668948426614107618777497600000⟩, + ⟨2, 6, 4, 1, 8, 3, 20310869838337667059310487007649163441555583795200000⟩, + ⟨2, 6, 3, 2, 6, 3, 4247275590083695988929434777897757741271325081600000⟩, + ⟨2, 6, 4, 2, 7, 3, -2753981242760351791717345314292262015323865088000000⟩, + ⟨2, 6, 5, 2, 8, 3, 17177314460293930292766153560472132564629323776000000⟩, + ⟨2, 6, 3, 3, 5, 3, 8483795979386493736502642519669670750087177830400000⟩, + ⟨2, 6, 4, 3, 6, 3, -2242917677405553682036315156537605690323946700800000⟩, + ⟨2, 6, 5, 3, 7, 3, -1353208091735168544155908006730267632752132096000000⟩, + ⟨2, 6, 6, 3, 8, 3, 5845351220490243270671621062893892696943886336000000⟩, + ⟨2, 6, 3, 4, 4, 3, -3469574459335025669310424120295768734905768345600000⟩, + ⟨2, 6, 4, 4, 5, 3, 5799941496459870366205708706966828981034575462400000⟩, + ⟨2, 6, 5, 4, 6, 3, -3313994673231798491855531363074216028515860480000000⟩, + ⟨2, 6, 6, 4, 7, 3, -2550656646130261814522028214731193591290396672000000⟩, + ⟨2, 6, 7, 4, 8, 3, 3742356041370421531414089530117829602605793280000000⟩, + ⟨2, 6, 3, 5, 3, 3, -8735306769663118166184021563937436626586907443200000⟩, + ⟨2, 6, 4, 5, 4, 3, 809954221996754877891655037238214028414681088000000⟩, + ⟨2, 6, 5, 5, 5, 3, -912015710403219888667704874600188317678960640000000⟩, + ⟨2, 6, 6, 5, 6, 3, -4320004450141963982462031167024337194254860288000000⟩, + ⟨2, 6, 7, 5, 7, 3, 1707023104005428366478216571653207464916025344000000⟩, + ⟨2, 6, 8, 5, 8, 3, 2060934518727907591318201001788199246176557465600000⟩, + ⟨2, 6, 3, 6, 2, 3, -9768528368846740337136672248532074962161657446400000⟩, + ⟨2, 6, 4, 6, 3, 3, -20245831184293210440065762626040918432135774208000000⟩, + ⟨2, 6, 5, 6, 4, 3, 7605340578121774657827154309875455420390178816000000⟩, + ⟨2, 6, 6, 6, 5, 3, 410908550737730149059209796498198052070227968000000⟩, + ⟨2, 6, 7, 6, 6, 3, 516078393870392545702793612188638871277273088000000⟩, + ⟨2, 6, 8, 6, 7, 3, 555540438872314946728548338086898858593773158400000⟩, + ⟨2, 6, 3, 7, 1, 3, 89800975701633149716635503277456885199065317376000000⟩, + ⟨2, 6, 4, 7, 2, 3, 20805786926490402357866355850333289959649181696000000⟩, + ⟨2, 6, 5, 7, 3, 3, 10603339710213511048180606296322182852863066112000000⟩, + ⟨2, 6, 6, 7, 4, 3, 14260022759844910194309487186917311535434956800000000⟩, + ⟨2, 6, 7, 7, 5, 3, -1854030560166161653915812216535120541651042304000000⟩, + ⟨2, 6, 8, 7, 6, 3, 830570742552121345320819132346966247393879654400000⟩ +] + +def collectedFourData_11_5_13 : List CollectedFourTerm := [ + ⟨2, 7, 2, 0, 7, 4, 1039429302430695061022944824919915239907000320000000⟩, + ⟨2, 7, 3, 0, 8, 4, -633311290438496765254615460569127518161862656000000⟩, + ⟨2, 7, 2, 1, 6, 4, -2392579463074038475352255782551906753158578176000000⟩, + ⟨2, 7, 3, 1, 7, 4, 8460229441199071923939964846101896341349203968000000⟩, + ⟨2, 7, 4, 1, 8, 4, -6584898174434997598882238050849869550445395968000000⟩, + ⟨2, 7, 2, 2, 5, 4, -5017184410396840533850865737274934721920368640000000⟩, + ⟨2, 7, 3, 2, 6, 4, -2753981242760351791717345314292262015323865088000000⟩, + ⟨2, 7, 4, 2, 7, 4, 892856199769979459088549979843762407258193920000000⟩, + ⟨2, 7, 5, 2, 8, 4, -3712654604212095779697329666871162906932674560000000⟩, + ⟨2, 7, 2, 3, 4, 4, 369671573394997769923336337901356632101617664000000⟩, + ⟨2, 7, 3, 3, 5, 4, -5500988692418633753706592701794417161977987072000000⟩, + ⟨2, 7, 4, 3, 6, 4, 727166519056606201975255989139541063916060672000000⟩, + ⟨2, 7, 5, 3, 7, 4, 292478446724067790863061387091734211340533760000000⟩, + ⟨2, 7, 6, 3, 8, 4, -947547861984818570702645231135433296046981120000000⟩, + ⟨2, 7, 2, 4, 3, 4, 7862876476543211433129949039001345063223558144000000⟩, + ⟨2, 7, 3, 4, 4, 4, 2249711086249705272681009969205619096297668608000000⟩, + ⟨2, 7, 4, 4, 5, 4, -1880373636178754395461491568438770943620284416000000⟩, + ⟨2, 7, 5, 4, 6, 4, 716277134609658940029795084333177591614668800000000⟩, + ⟨2, 7, 6, 4, 7, 4, 413468611300211544515483346328499345676042240000000⟩, + ⟨2, 7, 7, 4, 8, 4, -485317146159659891529964463897522666031022080000000⟩, + ⟨2, 7, 2, 5, 2, 4, -1069527297846473312423628002951176954469941248000000⟩, + ⟨2, 7, 3, 5, 3, 4, 5664071116453191635006675948209468102542360576000000⟩, + ⟨2, 7, 4, 5, 4, 4, -262591711741227170579266479752284492183633920000000⟩, + ⟨2, 7, 5, 5, 5, 4, 197120413331732185013507962884844503328358400000000⟩, + ⟨2, 7, 6, 5, 6, 4, 700284863319745872198097551000262776151080960000000⟩, + ⟨2, 7, 7, 5, 7, 4, -221370594381273182652409640903856186231619584000000⟩, + ⟨2, 7, 8, 5, 8, 4, -222722185345725930826338040128590360365498368000000⟩, + ⟨2, 7, 2, 6, 1, 4, 17946316752946628248791101991109924379223392256000000⟩, + ⟨2, 7, 3, 6, 2, 4, 6334023617395207862754486174739812301985021952000000⟩, + ⟨2, 7, 4, 6, 3, 4, 6563812277194069607843610098846772159546654720000000⟩, + ⟨2, 7, 5, 6, 4, 4, -1643796111390611843263890480170779766905896960000000⟩, + ⟨2, 7, 6, 6, 5, 4, -66609430988162542106080625947486563399106560000000⟩, + ⟨2, 7, 7, 6, 6, 4, -66926206523129934513471935242576508976365568000000⟩, + ⟨2, 7, 8, 6, 7, 4, -60036444374728393320173707048638090263396352000000⟩, + ⟨2, 7, 2, 7, 0, 4, -146405586294071049897056343451995498937810157568000000⟩, + ⟨2, 7, 3, 7, 1, 4, -58227962235669847120759634456230513727955271680000000⟩, + ⟨2, 7, 4, 7, 2, 4, -6745353076475783899087075679228601226116464640000000⟩, + ⟨2, 7, 5, 7, 3, 4, -2291774892178082600826646460030044884141342720000000⟩, + ⟨2, 7, 6, 7, 4, 4, -2311589769076810965355377013066251796217856000000000⟩, + ⟨2, 7, 7, 7, 5, 4, 240434851843530120109496598873182823612678144000000⟩, + ⟨2, 7, 8, 7, 6, 4, -89758567865422516333367708698568379158495232000000⟩ +] + +def collectedFourData_11_5_14 : List CollectedFourTerm := [ + ⟨2, 8, 1, 0, 6, 5, 132881483602370107876664950022927089543975796736000000⟩, + ⟨2, 8, 2, 0, 7, 5, -12966394766872199656166243415442456401181409280000000⟩, + ⟨2, 8, 3, 0, 8, 5, 3950131183977436210956671204744362541042368512000000⟩, + ⟨2, 8, 1, 1, 5, 5, 28932796793744431012197328751232017540038262784000000⟩, + ⟨2, 8, 2, 1, 6, 5, 29846310621397559146298834102029700689091887104000000⟩, + ⟨2, 8, 3, 1, 7, 5, -52768704180444260572778109679316971045609537536000000⟩, + ⟨2, 8, 4, 1, 8, 5, 27381175750229601254505138787481457000682881024000000⟩, + ⟨2, 8, 1, 2, 4, 5, -25155733070561865701332436379535760988070477824000000⟩, + ⟨2, 8, 2, 2, 5, 5, 62587030720869990043018096033025105003607490560000000⟩, + ⟨2, 8, 3, 2, 6, 5, 17177314460293930292766153560472132564629323776000000⟩, + ⟨2, 8, 4, 2, 7, 5, -3712654604212095779697329666871162906932674560000000⟩, + ⟨2, 8, 5, 2, 8, 5, 11578407766330375248345451665310260279178690560000000⟩, + ⟨2, 8, 1, 3, 3, 5, 69667370371847004085033969614604442614854844416000000⟩, + ⟨2, 8, 2, 3, 4, 5, -4611480110788881383683426461256150257034592256000000⟩, + ⟨2, 8, 3, 3, 5, 5, 34311131515727101980029269427216355130337132544000000⟩, + ⟨2, 8, 4, 3, 6, 5, -3023687493797883617852536538312786956303466496000000⟩, + ⟨2, 8, 5, 3, 7, 5, -912132983012262956010720945025182049511669760000000⟩, + ⟨2, 8, 6, 3, 8, 5, 2364043347685032615442303248779680119307370496000000⟩, + ⟨2, 8, 1, 4, 2, 5, -120112366376010276889071049312112254992135487488000000⟩, + ⟨2, 8, 2, 4, 3, 5, -98085709301821651075081256359414075078188466176000000⟩, + ⟨2, 8, 3, 4, 4, 5, -14032047195276915238695456654733340288080674816000000⟩, + ⟨2, 8, 4, 4, 5, 5, 7818927437359573360493891405209789764036722688000000⟩, + ⟨2, 8, 5, 4, 6, 5, -2233805624902553402292510823906865985670348800000000⟩, + ⟨2, 8, 6, 4, 7, 5, -1031565537991255839050487671382393171310804992000000⟩, + ⟨2, 8, 7, 4, 8, 5, 1009017430610284950832058734988353950418206720000000⟩, + ⟨2, 8, 1, 5, 1, 5, -54460346640712027149454784969124946982278791168000000⟩, + ⟨2, 8, 2, 5, 2, 5, 13341853193279715425967219881138749607554056192000000⟩, + ⟨2, 8, 3, 5, 3, 5, -35328320027069611840047698174724611631954788352000000⟩, + ⟨2, 8, 4, 5, 4, 5, 1091902960269708173442566509445708505478594560000000⟩, + ⟨2, 8, 5, 5, 5, 5, -614746257848228448839202289147855575082598400000000⟩, + ⟨2, 8, 6, 5, 6, 5, -1747145277862588535800299539347339281923309568000000⟩, + ⟨2, 8, 7, 5, 7, 5, 460249117763048340716739775451357091679174656000000⟩, + ⟨2, 8, 8, 5, 8, 5, 396907881741290509624410074922974018688516096000000⟩, + ⟨2, 8, 1, 6, 0, 5, 593731529420671230856642490128764645943441096704000000⟩, + ⟨2, 8, 2, 6, 1, 5, -223871914218575222683255189854742747791621095424000000⟩, + ⟨2, 8, 3, 6, 2, 5, -39506992199363266639017285901952694491811938304000000⟩, + ⟨2, 8, 4, 6, 3, 5, -27293496845725558630375398233122137227353128960000000⟩, + ⟨2, 8, 5, 6, 4, 5, 5126397063921824383035865230523929377856552960000000⟩, + ⟨2, 8, 6, 6, 5, 5, 166184304284962696068290123305392062016258048000000⟩, + ⟨2, 8, 7, 6, 6, 5, 139145524696228019432712472202052691833126912000000⟩, + ⟨2, 8, 8, 6, 7, 5, 106989512190100031118348111118277534489247744000000⟩, + ⟨2, 8, 2, 7, 0, 5, 1826341265851386338249714960731597492146218729472000000⟩, + ⟨2, 8, 3, 7, 1, 5, 363183307923225671636315318302112917201732239360000000⟩, + ⟨2, 8, 4, 7, 2, 5, 28048375721494398160296517379121590102938091520000000⟩, + ⟨2, 8, 5, 7, 3, 5, 7147205177710567843798434748223212078466334720000000⟩, + ⟨2, 8, 6, 7, 4, 5, 5767200407920259784409603934554548501007564800000000⟩, + ⟨2, 8, 7, 7, 5, 5, -499885401445329620981377019189814377312157696000000⟩, + ⟨2, 8, 8, 7, 6, 5, 159956597876837347617154898660712016829743104000000⟩ +] + +def collectedFourData_11_5_15 : List CollectedFourTerm := [ + ⟨3, 2, 6, 3, 8, 0, 139524652890978256224757859710662153113696206848000000⟩, + ⟨3, 2, 6, 4, 7, 0, -60882480756313614743705215011383025443794845696000000⟩, + ⟨3, 2, 7, 4, 8, 0, 357310216594903801088822256744400071289900892160000000⟩, + ⟨3, 2, 6, 5, 6, 0, -103115638163995072893040223877573357553355587584000000⟩, + ⟨3, 2, 7, 5, 7, 0, 162982032784173715592560064784838064995269869568000000⟩, + ⟨3, 2, 8, 5, 8, 0, 491931387028665196005340980469465428807131332608000000⟩, + ⟨3, 2, 6, 6, 5, 0, 9808114302977394793144162404461387373896269824000000⟩, + ⟨3, 2, 7, 6, 6, 0, 49273794544212892610106250036321656064689831936000000⟩, + ⟨3, 2, 8, 6, 7, 0, 132603814513066426301838604556773742871903731712000000⟩, + ⟨3, 2, 6, 7, 4, 0, 340377276015579302019782820597501980869813862400000000⟩, + ⟨3, 2, 7, 7, 5, 0, -177017914304047052353945409450693663730526322688000000⟩, + ⟨3, 2, 8, 7, 6, 0, 198251722068922382346967878082158381448657108992000000⟩ +] + +def collectedFourData_11_5_16 : List CollectedFourTerm := [ + ⟨3, 3, 5, 2, 8, 1, 69667370371847004085033969614604442614854844416000000⟩, + ⟨3, 3, 5, 3, 7, 1, -5488311315195025127446619155467649665032257536000000⟩, + ⟨3, 3, 6, 3, 8, 1, 71122336854125454846112492942544298635195056128000000⟩, + ⟨3, 3, 5, 4, 6, 1, -13440825971024176393861315077348451294044487680000000⟩, + ⟨3, 3, 6, 4, 7, 1, -31034689677736045568324793084135728657524064256000000⟩, + ⟨3, 3, 7, 4, 8, 1, 91068986947920504130605806198328363926295674880000000⟩, + ⟨3, 3, 5, 5, 5, 1, -3698933056647147757393408451215356353304330240000000⟩, + ⟨3, 3, 6, 5, 6, 1, -52562934223232038944206198650883810786304589824000000⟩, + ⟨3, 3, 7, 5, 7, 1, 41539838289021269162698538581273988351366529024000000⟩, + ⟨3, 3, 8, 5, 8, 1, 83586924347360711343753011137721637457411178496000000⟩, + ⟨3, 3, 5, 6, 4, 1, 30845571354288418921201063807878464620311085056000000⟩, + ⟨3, 3, 6, 6, 5, 1, 4999661313654698412302316185841331202596798464000000⟩, + ⟨3, 3, 7, 6, 6, 1, 12558595707071202633716537266754246008476008448000000⟩, + ⟨3, 3, 8, 6, 7, 1, 22531485699303968714919855490221623692801081344000000⟩, + ⟨3, 3, 5, 7, 3, 1, 43004789629805563175631406715774898022008225792000000⟩, + ⟨3, 3, 6, 7, 4, 1, 173506450513699853747281749981260765878183526400000000⟩, + ⟨3, 3, 7, 7, 5, 1, -45117215737439111409723649633326195901080797184000000⟩, + ⟨3, 3, 8, 7, 6, 1, 33686103654417518136954596416190921230415560704000000⟩ +] + +def collectedFourData_11_5_17 : List CollectedFourTerm := [ + ⟨3, 4, 4, 1, 8, 2, -2726362508785125109391125939595003302852008345600000⟩, + ⟨3, 4, 4, 2, 7, 2, 369671573394997769923336337901356632101617664000000⟩, + ⟨3, 4, 5, 2, 8, 2, -4611480110788881383683426461256150257034592256000000⟩, + ⟨3, 4, 4, 3, 6, 2, 301070644174360525851271907880624296152163942400000⟩, + ⟨3, 4, 5, 3, 7, 2, 363286834808782140382312169635135204859314176000000⟩, + ⟨3, 4, 6, 3, 8, 2, -2353894226845721042753262372583820445219815424000000⟩, + ⟨3, 4, 4, 4, 5, 2, -778535984670042620275233785475612270046425907200000⟩, + ⟨3, 4, 5, 4, 6, 2, 889686252073610296327797892025994942747770880000000⟩, + ⟨3, 4, 6, 4, 7, 2, 1027136903757879851130095831155455479248846848000000⟩, + ⟨3, 4, 7, 4, 8, 2, -2009371196197453034762343841120610191524495360000000⟩, + ⟨3, 4, 4, 5, 4, 2, -108721529026592795740153741440727590490865664000000⟩, + ⟨3, 4, 5, 5, 5, 2, 244842831455009299921740258814644641951907840000000⟩, + ⟨3, 4, 6, 5, 6, 2, 1739644574220151568756942771728457582134689792000000⟩, + ⟨3, 4, 7, 5, 7, 2, -916546426506234271101897467783013048074108928000000⟩, + ⟨3, 4, 8, 5, 8, 2, -1383213680567004924188541853620111454853136384000000⟩, + ⟨3, 4, 4, 6, 3, 2, 2717632259937094228969066584002993575925121024000000⟩, + ⟨3, 4, 5, 6, 4, 2, -2041755531276688450987310132251779927424106496000000⟩, + ⟨3, 4, 6, 6, 5, 2, -165470855190454077278411996097271269175590912000000⟩, + ⟨3, 4, 7, 6, 6, 2, -277096312632849393583028906128653671680966656000000⟩, + ⟨3, 4, 8, 6, 7, 2, -372855676962842491574264364607342829660798976000000⟩, + ⟨3, 4, 4, 7, 2, 2, -2792796068984000128329863369607590650878885888000000⟩, + ⟨3, 4, 5, 7, 3, 2, -2846608548420952809999425737173619199937871872000000⟩, + ⟨3, 4, 6, 7, 4, 2, -5742441126792091538406677255623317904372531200000000⟩, + ⟨3, 4, 7, 7, 5, 2, 995478667257829578992050938423352075587944448000000⟩, + ⟨3, 4, 8, 7, 6, 2, -557444597747778565928128405728866948314300416000000⟩ +] + +def collectedFourData_11_5_18 : List CollectedFourTerm := [ + ⟨3, 5, 3, 0, 8, 3, 1950951479297977512529722562627521486084951244800000⟩, + ⟨3, 5, 3, 1, 7, 3, -26062218363546673200761382660950654424506066534400000⟩, + ⟨3, 5, 4, 1, 8, 3, 40570307298786781063791056364101432555925720268800000⟩, + ⟨3, 5, 3, 2, 6, 3, 8483795979386493736502642519669670750087177830400000⟩, + ⟨3, 5, 4, 2, 7, 3, -5500988692418633753706592701794417161977987072000000⟩, + ⟨3, 5, 5, 2, 8, 3, 34311131515727101980029269427216355130337132544000000⟩, + ⟨3, 5, 3, 3, 5, 3, 16946108792162487182185217415601380262074227097600000⟩, + ⟨3, 5, 4, 3, 6, 3, -4480155706894724495918625138345039227901915955200000⟩, + ⟨3, 5, 5, 3, 7, 3, -2702989510438116660872365311381832409624346624000000⟩, + ⟨3, 5, 6, 3, 8, 3, 11675900499199731436290212715562933017781469184000000⟩, + ⟨3, 5, 3, 4, 4, 3, -6930363058383154033621041633476852913973651046400000⟩, + ⟨3, 5, 4, 4, 5, 3, 11585196040310042035347565329882628061591607705600000⟩, + ⟨3, 5, 5, 4, 6, 3, -6619597454451538288073353457105917474630533120000000⟩, + ⟨3, 5, 6, 4, 7, 3, -5094854369647563895197651908987712531351994368000000⟩, + ⟨3, 5, 7, 4, 8, 3, 7475235468905724994983882182502514218573496320000000⟩, + ⟨3, 5, 3, 5, 3, 3, -17448493482316087126911993111250580026289867980800000⟩, + ⟨3, 5, 4, 5, 4, 3, 1617857430326949054931334813752091002716291072000000⟩, + ⟨3, 5, 5, 5, 5, 3, -1821721961042721717690754987604528586723164160000000⟩, + ⟨3, 5, 6, 5, 6, 3, -8629069531210696918130072272705975121055055872000000⟩, + ⟨3, 5, 7, 5, 7, 3, 3409723583817579758261036288911999589978996736000000⟩, + ⟨3, 5, 8, 5, 8, 3, 4116650217985528410241088501923674829825140326400000⟩, + ⟨3, 5, 3, 6, 2, 3, -19512320296247076499540865430888598464240392601600000⟩, + ⟨3, 5, 4, 6, 3, 3, -40440394685398725163854704270560194711206756352000000⟩, + ⟨3, 5, 5, 6, 4, 3, 15191422466010264849635999912202907527155810304000000⟩, + ⟨3, 5, 6, 6, 5, 3, 820776574701993942474853206598232330093985792000000⟩, + ⟨3, 5, 7, 6, 6, 3, 1030849943711704751347058534141949427499139072000000⟩, + ⟨3, 5, 8, 6, 7, 3, 1109674105606761078533449381851951408778680729600000⟩, + ⟨3, 5, 3, 7, 1, 3, 179374552096697498127993376222937592832871890944000000⟩, + ⟨3, 5, 4, 7, 2, 3, 41558888216964757445308397128790805827523969024000000⟩, + ⟨3, 5, 5, 7, 3, 3, 21179829020656007845912777919724933452270665728000000⟩, + ⟨3, 5, 6, 7, 4, 3, 28483935452266743562756300399923055012557619200000000⟩, + ⟨3, 5, 7, 7, 5, 3, -3703366235221721063482698272492398856399486976000000⟩, + ⟨3, 5, 8, 7, 6, 3, 1659038265073090491122219239364260259518060953600000⟩ +] + +def collectedFourData_11_5_19 : List CollectedFourTerm := [ + ⟨3, 6, 2, 0, 7, 4, 846539664336414332790205291465013249716518912000000⟩, + ⟨3, 6, 3, 0, 8, 4, -515786043336038219688078035987822614832322969600000⟩, + ⟨3, 6, 2, 1, 6, 4, -1948582179502238278305176951939702394959010201600000⟩, + ⟨3, 6, 3, 1, 7, 4, 6890242342229177603334232923809397752776674508800000⟩, + ⟨3, 6, 4, 1, 8, 4, -5362921246534078071916164884254112978041621708800000⟩, + ⟨3, 6, 2, 2, 5, 4, -4086132261962493004822953938645566342639386624000000⟩, + ⟨3, 6, 3, 2, 6, 4, -2242917677405553682036315156537605690323946700800000⟩, + ⟨3, 6, 4, 2, 7, 4, 727166519056606201975255989139541063916060672000000⟩, + ⟨3, 6, 5, 2, 8, 4, -3023687493797883617852536538312786956303466496000000⟩, + ⟨3, 6, 2, 3, 4, 4, 301070644174360525851271907880624296152163942400000⟩, + ⟨3, 6, 3, 3, 5, 4, -4480155706894724495918625138345039227901915955200000⟩, + ⟨3, 6, 4, 3, 6, 4, 592224309550771318735646726364466331386065715200000⟩, + ⟨3, 6, 5, 3, 7, 4, 238202449686987534335335763467239233175945216000000⟩, + ⟨3, 6, 6, 3, 8, 4, -771708905215127515903343772228398494821384192000000⟩, + ⟨3, 6, 2, 4, 3, 4, 6403741743287431866963579912159735289878046310400000⟩, + ⟨3, 6, 3, 4, 4, 4, 1832226264310763843533310820830025331216534732800000⟩, + ⟨3, 6, 4, 4, 5, 4, -1531427739313652010599118452475739197895448985600000⟩, + ⟨3, 6, 5, 4, 6, 4, 583355696906321125727564752450848859178926080000000⟩, + ⟨3, 6, 6, 4, 7, 4, 336740150200895655993024292196728809543696384000000⟩, + ⟨3, 6, 7, 4, 8, 4, -395255562880476117338219912079324896116604928000000⟩, + ⟨3, 6, 2, 5, 2, 4, -871052295331989623184405989487301742503447756800000⟩, + ⟨3, 6, 3, 5, 3, 4, 4612974495222647756592520382216715478836550041600000⟩, + ⟨3, 6, 4, 5, 4, 4, -213861874968417684785936249850743700609564672000000⟩, + ⟨3, 6, 5, 5, 5, 4, 160540258144998802901984634525969425041981440000000⟩, + ⟨3, 6, 6, 5, 6, 4, 570331153593869580244293209507227787367284736000000⟩, + ⟨3, 6, 7, 5, 7, 4, -180290269115220113627800922607150892512077414400000⟩, + ⟨3, 6, 8, 5, 8, 4, -181391041778346232239211887864122832415673548800000⟩, + ⟨3, 6, 2, 6, 1, 4, 14615971403333962552347031881597031500752722329600000⟩, + ⟨3, 6, 3, 6, 2, 4, 5158602142954476459156892299092998024512877363200000⟩, + ⟨3, 6, 4, 6, 3, 4, 5345748314877422687588911536790648290596093952000000⟩, + ⟨3, 6, 5, 6, 4, 4, -1338752529989305219730351210244094693616910336000000⟩, + ⟨3, 6, 6, 6, 5, 4, -54248543136601024990789646479826830749597696000000⟩, + ⟨3, 6, 7, 6, 6, 4, -54506533799760306549447080764297802005925068800000⟩, + ⟨3, 6, 8, 6, 7, 4, -48895322991265268785428783784973950740804403200000⟩, + ⟨3, 6, 2, 7, 0, 4, -119236715367298915150811997362711517417763032268800000⟩, + ⟨3, 6, 3, 7, 1, 4, -47422445654271875757512039319136320761823756288000000⟩, + ⟨3, 6, 4, 7, 2, 4, -5493600109057098167625775822302671944468660224000000⟩, + ⟨3, 6, 5, 7, 3, 4, -1866484178791383232567898000282616181662154752000000⟩, + ⟨3, 6, 6, 7, 4, 4, -1882621956704215652491042273370378830715289600000000⟩, + ⟨3, 6, 7, 7, 5, 4, 195816722020850056499314372145861693675038310400000⟩, + ⟨3, 6, 8, 7, 6, 4, -73101833606599099155904622876253809196348211200000⟩ +] + +def collectedFourData_11_5_20 : List CollectedFourTerm := [ + ⟨3, 7, 1, 0, 6, 5, -10468242825044282848982959259437453234201952256000000⟩, + ⟨3, 7, 2, 0, 7, 5, 1021476922933607509354058417549079984608378880000000⟩, + ⟨3, 7, 3, 0, 8, 5, -311186564927229100498084565485406360910692352000000⟩, + ⟨3, 7, 1, 1, 5, 5, -2279290795329268933832060164501614241895153664000000⟩, + ⟨3, 7, 2, 1, 6, 5, -2351256311612367026337829713639600991852560384000000⟩, + ⟨3, 7, 3, 1, 7, 5, 4157054797617921962244721991869892073992749056000000⟩, + ⟨3, 7, 4, 1, 8, 5, -2157055963089089686964355585387613516625608704000000⟩, + ⟨3, 7, 1, 2, 4, 5, 1981738275986117176206806591485853758604181504000000⟩, + ⟨3, 7, 2, 2, 5, 5, -4930530706935059335766661731105483551156469760000000⟩, + ⟨3, 7, 3, 2, 6, 5, -1353208091735168544155908006730267632752132096000000⟩, + ⟨3, 7, 4, 2, 7, 5, 292478446724067790863061387091734211340533760000000⟩, + ⟨3, 7, 5, 2, 8, 5, -912132983012262956010720945025182049511669760000000⟩, + ⟨3, 7, 1, 3, 3, 5, -5488311315195025127446619155467649665032257536000000⟩, + ⟨3, 7, 2, 3, 4, 5, 363286834808782140382312169635135204859314176000000⟩, + ⟨3, 7, 3, 3, 5, 5, -2702989510438116660872365311381832409624346624000000⟩, + ⟨3, 7, 4, 3, 6, 5, 238202449686987534335335763467239233175945216000000⟩, + ⟨3, 7, 5, 3, 7, 5, 71856735009647741544133664038447335037992960000000⟩, + ⟨3, 7, 6, 3, 8, 5, -186236480370362971037760345328412474229129216000000⟩, + ⟨3, 7, 1, 4, 2, 5, 9462307188541452002214931590303306064381083648000000⟩, + ⟨3, 7, 2, 4, 3, 5, 7727073741219576318841886313126257795316842496000000⟩, + ⟨3, 7, 3, 4, 4, 5, 1105427734477976116470052258065883610203815936000000⟩, + ⟨3, 7, 4, 4, 5, 5, -615965662233329626153829841142220808517582848000000⟩, + ⟨3, 7, 5, 4, 6, 5, 175976509830393193644443459365659009141964800000000⟩, + ⟨3, 7, 6, 4, 7, 5, 81265487477198076217473765961312132694802432000000⟩, + ⟨3, 7, 7, 4, 8, 5, -79489174804354269377984791803087346068357120000000⟩, + ⟨3, 7, 1, 5, 1, 5, 4290320347995344539892959497394974734237564928000000⟩, + ⟨3, 7, 2, 5, 2, 5, -1051055084403448220995634865920455677818437632000000⟩, + ⟨3, 7, 3, 5, 3, 5, 2783122393116051936336506877301213526325460992000000⟩, + ⟨3, 7, 4, 5, 4, 5, -86018796747420657167206469842853808580853760000000⟩, + ⟨3, 7, 5, 5, 5, 5, 48428967892918364707054125574146706794086400000000⟩, + ⟨3, 7, 6, 5, 6, 5, 137637995328408761455560581104739689407971328000000⟩, + ⟨3, 7, 7, 5, 7, 5, -36257869750861638651398973502478483850264576000000⟩, + ⟨3, 7, 8, 5, 8, 5, -31267923661018492295398196041865515096866816000000⟩, + ⟨3, 7, 1, 6, 0, 5, -46773452962483721196709480136844957166268841984000000⟩, + ⟨3, 7, 2, 6, 1, 5, 17636359078893736622737805715635664180272431104000000⟩, + ⟨3, 7, 3, 6, 2, 5, 3112313141141723750601788806595325736028995584000000⟩, + ⟨3, 7, 4, 6, 3, 5, 2150148724863719540995398920013354446786396160000000⟩, + ⟨3, 7, 5, 6, 4, 5, -403851370619183428586638094946258259185500160000000⟩, + ⟨3, 7, 6, 6, 5, 5, -13091798825573976639761998575037065260433408000000⟩, + ⟨3, 7, 7, 6, 6, 5, -10961716418647289838218115382246942024138752000000⟩, + ⟨3, 7, 8, 6, 7, 5, -8428504581499314492157588124925202293325824000000⟩, + ⟨3, 7, 2, 7, 0, 5, -143876959633750388311092640657269943823354560512000000⟩, + ⟨3, 7, 3, 7, 1, 5, -28611142457739266883389077545704657238160834560000000⟩, + ⟨3, 7, 4, 7, 2, 5, -2209617171187596243421710323243273645111377920000000⟩, + ⟨3, 7, 5, 7, 3, 5, -563048193716536104404119792878813227117445120000000⟩, + ⟨3, 7, 6, 7, 4, 5, -454333084295326924715961269580976819588300800000000⟩, + ⟨3, 7, 7, 7, 5, 5, 39380368318909385379564237081130936005820416000000⟩, + ⟨3, 7, 8, 7, 6, 5, -12601187634639187289181720398673470904336384000000⟩ +] + +def collectedFourData_11_5_21 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 5, 6, -112829666620571050438812066914287488011920736256000000⟩, + ⟨3, 8, 1, 0, 6, 6, 135656643676949457052223960472504634484811890688000000⟩, + ⟨3, 8, 2, 0, 7, 6, -6618595559663327471320334633284280899464069120000000⟩, + ⟨3, 8, 3, 0, 8, 6, 1344209200497105682931169040780388673081311232000000⟩, + ⟨3, 8, 0, 1, 4, 6, -81122626128754386653904471223273079448570691584000000⟩, + ⟨3, 8, 1, 1, 5, 6, 29537043076455898428413546295273684980541161472000000⟩, + ⟨3, 8, 2, 1, 6, 6, 15234817580582251604441618371062541056806486016000000⟩, + ⟨3, 8, 3, 1, 7, 6, -17956916961487027405094339127787403652624285696000000⟩, + ⟨3, 8, 4, 1, 8, 6, 6988254310359337711073921909728502908975054848000000⟩, + ⟨3, 8, 0, 2, 3, 6, -31752978061436931889586095055729041932854231040000000⟩, + ⟨3, 8, 1, 2, 4, 6, -25681097358885882408942593657619909723964833792000000⟩, + ⟨3, 8, 2, 2, 5, 6, 31947064011964091954121253259143841178703626240000000⟩, + ⟨3, 8, 3, 2, 6, 6, 5845351220490243270671621062893892696943886336000000⟩, + ⟨3, 8, 4, 2, 7, 6, -947547861984818570702645231135433296046981120000000⟩, + ⟨3, 8, 5, 2, 8, 6, 2364043347685032615442303248779680119307370496000000⟩, + ⟨3, 8, 0, 3, 2, 6, 139524652890978256224757859710662153113696206848000000⟩, + ⟨3, 8, 1, 3, 3, 6, 71122336854125454846112492942544298635195056128000000⟩, + ⟨3, 8, 2, 3, 4, 6, -2353894226845721042753262372583820445219815424000000⟩, + ⟨3, 8, 3, 3, 5, 6, 11675900499199731436290212715562933017781469184000000⟩, + ⟨3, 8, 4, 3, 6, 6, -771708905215127515903343772228398494821384192000000⟩, + ⟨3, 8, 5, 3, 7, 6, -186236480370362971037760345328412474229129216000000⟩, + ⟨3, 8, 6, 3, 8, 6, 402235858801588455920858322566003483505328128000000⟩, + ⟨3, 8, 0, 4, 1, 6, 115165017570162766617390214457026201036322242560000000⟩, + ⟨3, 8, 1, 4, 2, 6, -122620850136075741835102107890368393466351714304000000⟩, + ⟨3, 8, 2, 4, 3, 6, -50067088942107272733243919273160399170886959104000000⟩, + ⟨3, 8, 3, 4, 4, 6, -4775033046550228002185366874855897312081739776000000⟩, + ⟨3, 8, 4, 4, 5, 6, 1995555408757666186753913231300884661299838976000000⟩, + ⟨3, 8, 5, 4, 6, 6, -456091496702052431595745217797315845244846080000000⟩, + ⟨3, 8, 6, 4, 7, 6, -175518207181079966540293660285098957792608256000000⟩, + ⟨3, 8, 7, 4, 8, 6, 147155747187390754334910372520862626275655680000000⟩, + ⟨3, 8, 0, 5, 0, 6, -712668905028425984838251572827349045362988941312000000⟩, + ⟨3, 8, 1, 5, 1, 6, -55597722410065342033230309268277984727341727744000000⟩, + ⟨3, 8, 2, 5, 2, 6, 6810245399000928212916284850205713879760109568000000⟩, + ⟨3, 8, 3, 5, 3, 6, -12022044485792549011540705664383538942781161472000000⟩, + ⟨3, 8, 4, 5, 4, 6, 278676695193957268147717163202572417362821120000000⟩, + ⟨3, 8, 5, 5, 5, 6, -125516982188732541214891288728769861716541440000000⟩, + ⟨3, 8, 6, 5, 6, 6, -297272248404570817510856458977349651685965824000000⟩, + ⟨3, 8, 7, 5, 7, 6, 67123025591138306265224894088128353076772864000000⟩, + ⟨3, 8, 8, 5, 8, 6, 50649636828887985905147073159559494758301696000000⟩, + ⟨3, 8, 1, 6, 0, 6, 606131300937353726912748477294172132967115128832000000⟩, + ⟨3, 8, 2, 6, 1, 6, -114273680851212936899857478604181248267094327296000000⟩, + ⟨3, 8, 3, 6, 2, 6, -13444025001944045724654106265102052455343980544000000⟩, + ⟨3, 8, 4, 6, 3, 6, -6965876802252410538181491543777048270911569920000000⟩, + ⟨3, 8, 5, 6, 4, 6, 1046691835452383459806514006811100203592974336000000⟩, + ⟨3, 8, 6, 6, 5, 6, 28275829383105047212562153068476399001534464000000⟩, + ⟨3, 8, 7, 6, 6, 6, 20293072283271073420879249012580168528560128000000⟩, + ⟨3, 8, 8, 6, 7, 6, 13652991503103002438810820953493839642886144000000⟩, + ⟨3, 8, 2, 7, 0, 6, 932241722539329433533258258272152788858398834688000000⟩, + ⟨3, 8, 3, 7, 1, 6, 123589400260323600675525242299050472325995560960000000⟩, + ⟨3, 8, 4, 7, 2, 6, 7158537833521185351167851364871932591776727040000000⟩, + ⟨3, 8, 5, 7, 3, 6, 1459294161675716421442276611721735757472202752000000⟩, + ⟨3, 8, 6, 7, 4, 6, 981274227155053984567096831346745798977126400000000⟩, + ⟨3, 8, 7, 7, 5, 6, -72903606544501702571282881457661459377946624000000⟩, + ⟨3, 8, 8, 7, 6, 6, 20412150938658113877404573134646810461077504000000⟩ +] + +def collectedFourData_11_5_22 : List CollectedFourTerm := [ + ⟨4, 1, 6, 3, 8, 0, 115165017570162766617390214457026201036322242560000000⟩, + ⟨4, 1, 6, 4, 7, 0, -50252997020495176081509293643902576357403525120000000⟩, + ⟨4, 1, 7, 4, 8, 0, 294927358853952892106118775561463627571737395200000000⟩, + ⟨4, 1, 6, 5, 6, 0, -85112659554108831624772884326222716144692756480000000⟩, + ⟨4, 1, 7, 5, 7, 0, 134526969107578248305891392622012898579799080960000000⟩, + ⟨4, 1, 8, 5, 8, 0, 406044993888918689404909497284937008585386229760000000⟩, + ⟨4, 1, 6, 6, 5, 0, 8095713786976164294167832867627442585762529280000000⟩, + ⟨4, 1, 7, 6, 6, 0, 40671073511767840795786408251970042738948177920000000⟩, + ⟨4, 1, 8, 6, 7, 0, 109452489662888469878935660310362698990370160640000000⟩, + ⟨4, 1, 6, 7, 4, 0, 280950743546719818361450635619023033653526528000000000⟩, + ⟨4, 1, 7, 7, 5, 0, -146112323439991397090646209295634756267262607360000000⟩, + ⟨4, 1, 8, 7, 6, 0, 163638916724076509453123041290677594792122122240000000⟩ +] + +def collectedFourData_11_5_23 : List CollectedFourTerm := [ + ⟨4, 2, 5, 2, 8, 1, -120112366376010276889071049312112254992135487488000000⟩, + ⟨4, 2, 5, 3, 7, 1, 9462307188541452002214931590303306064381083648000000⟩, + ⟨4, 2, 6, 3, 8, 1, -122620850136075741835102107890368393466351714304000000⟩, + ⟨4, 2, 5, 4, 6, 1, 23173106790323786150190410797061133419403018240000000⟩, + ⟨4, 2, 6, 4, 7, 1, 53506397572376028819754073629467428625850564608000000⟩, + ⟨4, 2, 7, 4, 8, 1, -157010541195926101069405882385382131378253987840000000⟩, + ⟨4, 2, 5, 5, 5, 1, 6377269590182164128835610482485619295854264320000000⟩, + ⟨4, 2, 6, 5, 6, 1, 90622889589791114842997763401937366144182648832000000⟩, + ⟨4, 2, 7, 5, 7, 1, -71618151354646336457123698225563930040763154432000000⟩, + ⟨4, 2, 8, 5, 8, 1, -144110840237931462956709439467290981861506940928000000⟩, + ⟨4, 2, 5, 6, 4, 1, -53180341784234244813124997729878393639831339008000000⟩, + ⟨4, 2, 6, 6, 5, 1, -8619833765167231186256943463619020776749924352000000⟩, + ⟨4, 2, 7, 6, 6, 1, -21652068115742986521103789441640017708726616064000000⟩, + ⟨4, 2, 8, 6, 7, 1, -38846163575082637201099769837825000954702856192000000⟩, + ⟨4, 2, 5, 7, 3, 1, -74143849844888428156461630216455027241837920256000000⟩, + ⟨4, 2, 6, 7, 4, 1, -299139615023050872993544551366748986498298675200000000⟩, + ⟨4, 2, 7, 7, 5, 1, 77785848921759904995558846589477711051134861312000000⟩, + ⟨4, 2, 8, 7, 6, 1, -58077656761316710343945411035948908651239964672000000⟩ +] + +def collectedFourData_11_5_24 : List CollectedFourTerm := [ + ⟨4, 3, 4, 1, 8, 2, -57989451122740755006380842521154124182158154137600000⟩, + ⟨4, 3, 4, 2, 7, 2, 7862876476543211433129949039001345063223558144000000⟩, + ⟨4, 3, 5, 2, 8, 2, -98085709301821651075081256359414075078188466176000000⟩, + ⟨4, 3, 4, 3, 6, 2, 6403741743287431866963579912159735289878046310400000⟩, + ⟨4, 3, 5, 3, 7, 2, 7727073741219576318841886313126257795316842496000000⟩, + ⟨4, 3, 6, 3, 8, 2, -50067088942107272733243919273160399170886959104000000⟩, + ⟨4, 3, 4, 4, 5, 2, -16559380597716573628574830522772041359762338611200000⟩, + ⟨4, 3, 5, 4, 6, 2, 18923535393019603603937597623601678669819412480000000⟩, + ⟨4, 3, 6, 4, 7, 2, 21847096666309550202023137321728611682204254208000000⟩, + ⟨4, 3, 7, 4, 8, 2, -42739119392181639773867968935581796876744130560000000⟩, + ⟨4, 3, 4, 5, 4, 2, -2312495778958842945722178096061174651388166144000000⟩, + ⟨4, 3, 5, 5, 5, 2, 5207781929828736529743255407129370043235696640000000⟩, + ⟨4, 3, 6, 5, 6, 2, 37002061788413275554849299414771201813073887232000000⟩, + ⟨4, 3, 7, 5, 7, 2, -19494848550162089723781625832611130483448741888000000⟩, + ⟨4, 3, 8, 5, 8, 2, -29420813212872884974328783024853610312199307264000000⟩, + ⟨4, 3, 4, 6, 3, 2, 57803759624551894398745815601717297199085256704000000⟩, + ⟨4, 3, 5, 6, 4, 2, -43427930880077503191405532462675608039604617216000000⟩, + ⟨4, 3, 6, 6, 5, 2, -3519548129929633139305257627241001504842186752000000⟩, + ⟨4, 3, 7, 6, 6, 2, -5893810168653820546232360457500303566439448576000000⟩, + ⟨4, 3, 8, 6, 7, 2, -7930602033075880309876260096687333074635063296000000⟩, + ⟨4, 3, 4, 7, 2, 2, -59402486139048611756988550336360815163550466048000000⟩, + ⟨4, 3, 5, 7, 3, 2, -60547072061150800645567037678608914080870694912000000⟩, + ⟨4, 3, 6, 7, 4, 2, -122141134194114390158270189633797708919812915200000000⟩, + ⟨4, 3, 7, 7, 5, 2, 21173729220771322856896393845459500065313783808000000⟩, + ⟨4, 3, 8, 7, 6, 2, -11856789458689850494653538152541204915773505536000000⟩ +] + +def collectedFourData_11_5_25 : List CollectedFourTerm := [ + ⟨4, 4, 3, 0, 8, 3, -797870604199000017219880429876516497472566067200000⟩, + ⟨4, 4, 3, 1, 7, 3, 10658531559160962050147347943106219772405717401600000⟩, + ⟨4, 4, 4, 1, 8, 3, -16591830161081170100152218958938186593770615603200000⟩, + ⟨4, 4, 3, 2, 6, 3, -3469574459335025669310424120295768734905768345600000⟩, + ⟨4, 4, 4, 2, 7, 3, 2249711086249705272681009969205619096297668608000000⟩, + ⟨4, 4, 5, 2, 8, 3, -14032047195276915238695456654733340288080674816000000⟩, + ⟨4, 4, 3, 3, 5, 3, -6930363058383154033621041633476852913973651046400000⟩, + ⟨4, 4, 4, 3, 6, 3, 1832226264310763843533310820830025331216534732800000⟩, + ⟨4, 4, 5, 3, 7, 3, 1105427734477976116470052258065883610203815936000000⟩, + ⟨4, 4, 6, 3, 8, 3, -4775033046550228002185366874855897312081739776000000⟩, + ⟨4, 4, 3, 4, 4, 3, 2834274977817655162951998853541003681175542169600000⟩, + ⟨4, 4, 4, 4, 5, 3, -4737938109958621264614390305386428524845753958400000⟩, + ⟨4, 4, 5, 4, 6, 3, 2707182765220749892219605694495066185982279680000000⟩, + ⟨4, 4, 6, 4, 7, 3, 2083616418630443213597216761463278199271063552000000⟩, + ⟨4, 4, 7, 4, 8, 3, -3057108648469189518596241906866391727189524480000000⟩, + ⟨4, 4, 3, 5, 3, 3, 7135820744300292330880246788026761333578085171200000⟩, + ⟨4, 4, 4, 5, 4, 3, -661646842138429489991489640392135447421124608000000⟩, + ⟨4, 4, 5, 5, 5, 3, 745020271986858705922903494751420812613386240000000⟩, + ⟨4, 4, 6, 5, 6, 3, 3528986237535588677661508459885539904148471808000000⟩, + ⟨4, 4, 7, 5, 7, 3, -1394457137883845429125966070807261843086639104000000⟩, + ⟨4, 4, 8, 5, 8, 3, -1683565291886172061149422306502815659085896089600000⟩, + ⟨4, 4, 3, 6, 2, 3, 7979853394248996117706978245775396686761715302400000⟩, + ⟨4, 4, 4, 6, 3, 3, 16538700466961715371532541457034745809393942528000000⟩, + ⟨4, 4, 5, 6, 4, 3, -6212758005626756359553616867389163539011731456000000⟩, + ⟨4, 4, 6, 6, 5, 3, -335668779320699769945561603483192783890546688000000⟩, + ⟨4, 4, 7, 6, 6, 3, -421581405870597384409161637793819297587396608000000⟩, + ⟨4, 4, 8, 6, 7, 3, -453817718430927691696536395312242659179259494400000⟩, + ⟨4, 4, 3, 7, 1, 3, -73357889100766322479127370815114231462196412416000000⟩, + ⟨4, 4, 4, 7, 2, 3, -16996125020720677023099995672809320405622849536000000⟩, + ⟨4, 4, 5, 7, 3, 3, -8661805871063029358198163361934676993446510592000000⟩, + ⟨4, 4, 6, 7, 4, 3, -11648928756261633653162590787619149597953228800000000⟩, + ⟨4, 4, 7, 7, 5, 3, 1514546664548406104008897737233053469286334464000000⟩, + ⟨4, 4, 8, 7, 6, 3, -678488356573297015781004352624042516310025830400000⟩ +] + +def collectedFourData_11_5_26 : List CollectedFourTerm := [ + ⟨4, 5, 2, 0, 7, 4, -2189059624008749611959712451880148560443867136000000⟩, + ⟨4, 5, 3, 0, 8, 4, 1333766685320311499348249057750155775986945228800000⟩, + ⟨4, 5, 2, 1, 6, 4, 5038821868500408119881235727656652826125061324800000⟩, + ⟨4, 5, 3, 1, 7, 4, -17817418304708442937133848355189049305707472486400000⟩, + ⟨4, 5, 4, 1, 8, 4, 13867931843133404188590210416957879907208554086400000⟩, + ⟨4, 5, 2, 2, 5, 4, 10566294209064944291306126542183611423283740672000000⟩, + ⟨4, 5, 3, 2, 6, 4, 5799941496459870366205708706966828981034575462400000⟩, + ⟨4, 5, 4, 2, 7, 4, -1880373636178754395461491568438770943620284416000000⟩, + ⟨4, 5, 5, 2, 8, 4, 7818927437359573360493891405209789764036722688000000⟩, + ⟨4, 5, 2, 3, 4, 4, -778535984670042620275233785475612270046425907200000⟩, + ⟨4, 5, 3, 3, 5, 4, 11585196040310042035347565329882628061591607705600000⟩, + ⟨4, 5, 4, 3, 6, 4, -1531427739313652010599118452475739197895448985600000⟩, + ⟨4, 5, 5, 3, 7, 4, -615965662233329626153829841142220808517582848000000⟩, + ⟨4, 5, 6, 3, 8, 4, 1995555408757666186753913231300884661299838976000000⟩, + ⟨4, 5, 2, 4, 3, 4, -16559380597716573628574830522772041359762338611200000⟩, + ⟨4, 5, 3, 4, 4, 4, -4737938109958621264614390305386428524845753958400000⟩, + ⟨4, 5, 4, 4, 5, 4, 3960105795924378727914820586595580402117430476800000⟩, + ⟨4, 5, 5, 4, 6, 4, -1508494470290566635458137765160487387125514240000000⟩, + ⟨4, 5, 6, 4, 7, 4, -870773452966619464419623144927971532920061952000000⟩, + ⟨4, 5, 7, 4, 8, 4, 1022087954431225211815496306088967342217232384000000⟩, + ⟨4, 5, 2, 5, 2, 4, 2252446625293210361242050800441036267218953830400000⟩, + ⟨4, 5, 3, 5, 3, 4, -11928651000647113994736815091065328757306608844800000⟩, + ⟨4, 5, 4, 5, 4, 4, 553023579793097064779774710812350799377596416000000⟩, + ⟨4, 5, 5, 5, 5, 4, -415139670281887402184527094457503788113592320000000⟩, + ⟨4, 5, 6, 5, 6, 4, -1474814415961641060898925666184575909162385408000000⟩, + ⟨4, 5, 7, 5, 7, 4, 466211053478717973000636442102749774252028723200000⟩, + ⟨4, 5, 8, 5, 8, 4, 469057532023761522224338785477943574110037606400000⟩, + ⟨4, 5, 2, 6, 1, 4, -37795314516993494322120709740465822852551855308800000⟩, + ⟨4, 5, 3, 6, 2, 4, -13339584833651726828352065805592012122184325529600000⟩, + ⟨4, 5, 4, 6, 3, 4, -13823524507128759845205721093486316109227360256000000⟩, + ⟨4, 5, 5, 6, 4, 4, 3461868632270641659312706771089365295282782208000000⟩, + ⟨4, 5, 6, 6, 5, 4, 140280840277836986053921841770568390214156288000000⟩, + ⟨4, 5, 7, 6, 6, 4, 140947976110788093709255478801775711261976166400000⟩, + ⟨4, 5, 8, 6, 7, 4, 126437994428705193120689376836806890571274649600000⟩, + ⟨4, 5, 2, 7, 0, 4, 308333194894752095217677365405387629349711537766400000⟩, + ⟨4, 5, 3, 7, 1, 4, 122629293613655771179077631405907624978980798464000000⟩, + ⟨4, 5, 4, 7, 2, 4, 14205853187769716312655721431670118950184681472000000⟩, + ⟨4, 5, 5, 7, 3, 4, 4826525355839242588092939661473237672872902656000000⟩, + ⟨4, 5, 6, 7, 4, 4, 4868255896696880286646189052604162746666188800000000⟩, + ⟨4, 5, 7, 7, 5, 4, -506360774267560891449641447938077012599714611200000⟩, + ⟨4, 5, 8, 7, 6, 4, 189033401659509783938744813007662458919819673600000⟩ +] + +def collectedFourData_11_5_27 : List CollectedFourTerm := [ + ⟨4, 6, 1, 0, 6, 5, -25636634285721618660471150958055933330356961280000000⟩, + ⟨4, 6, 2, 0, 7, 5, 2501587968699261083450627540116196204897894400000000⟩, + ⟨4, 6, 3, 0, 8, 5, -762093150971169840445777715501064278255861760000000⟩, + ⟨4, 6, 1, 1, 5, 5, -5581963040718903781949049898023246862032568320000000⟩, + ⟨4, 6, 2, 1, 6, 5, -5758205954927872319651804689959631336683601920000000⟩, + ⟨4, 6, 3, 1, 7, 5, 10180590509160675423119564601920054277470945280000000⟩, + ⟨4, 6, 4, 1, 8, 5, -5282611015408509493290715791357852159332843520000000⟩, + ⟨4, 6, 1, 2, 4, 5, 4853259547048921932520727650160130888585707520000000⟩, + ⟨4, 6, 2, 2, 5, 5, -12074826184372531948365195700853259253894348800000000⟩, + ⟨4, 6, 3, 2, 6, 5, -3313994673231798491855531363074216028515860480000000⟩, + ⟨4, 6, 4, 2, 7, 5, 716277134609658940029795084333177591614668800000000⟩, + ⟨4, 6, 5, 2, 8, 5, -2233805624902553402292510823906865985670348800000000⟩, + ⟨4, 6, 1, 3, 3, 5, -13440825971024176393861315077348451294044487680000000⟩, + ⟨4, 6, 2, 3, 4, 5, 889686252073610296327797892025994942747770880000000⟩, + ⟨4, 6, 3, 3, 5, 5, -6619597454451538288073353457105917474630533120000000⟩, + ⟨4, 6, 4, 3, 6, 5, 583355696906321125727564752450848859178926080000000⟩, + ⟨4, 6, 5, 3, 7, 5, 175976509830393193644443459365659009141964800000000⟩, + ⟨4, 6, 6, 3, 8, 5, -456091496702052431595745217797315845244846080000000⟩, + ⟨4, 6, 1, 4, 2, 5, 23173106790323786150190410797061133419403018240000000⟩, + ⟨4, 6, 2, 4, 3, 5, 18923535393019603603937597623601678669819412480000000⟩, + ⟨4, 6, 3, 4, 4, 5, 2707182765220749892219605694495066185982279680000000⟩, + ⟨4, 6, 4, 4, 5, 5, -1508494470290566635458137765160487387125514240000000⟩, + ⟨4, 6, 5, 4, 6, 5, 430964919404265086110194207843029115469824000000000⟩, + ⟨4, 6, 6, 4, 7, 5, 199018461581684215873137164431606824472412160000000⟩, + ⟨4, 6, 7, 4, 8, 5, -194668287523642463374732146346960371685785600000000⟩, + ⟨4, 6, 1, 5, 1, 5, 10506956665831954284936677982356865429421424640000000⟩, + ⟨4, 6, 2, 5, 2, 5, -2574024625081763448006054864896973200330588160000000⟩, + ⟨4, 6, 3, 5, 3, 5, 6815842176876208753627427004853962589297704960000000⟩, + ⟨4, 6, 4, 5, 4, 5, -210659274031705992730966707048484761816268800000000⟩, + ⟨4, 6, 5, 5, 5, 5, 118602114935220789048629080342550053650432000000000⟩, + ⟨4, 6, 6, 5, 6, 5, 337074235765002845811078492562419108953456640000000⟩, + ⟨4, 6, 7, 5, 7, 5, -88795203007553098538072519654440254182522880000000⟩, + ⟨4, 6, 8, 5, 8, 5, -76574869074839402325772961875657278703534080000000⟩, + ⟨4, 6, 1, 6, 0, 5, -114547773482177041523097827716496482050685009920000000⟩, + ⟨4, 6, 2, 6, 1, 5, 43191287725535950272209147971745093120446955520000000⟩, + ⟨4, 6, 3, 6, 2, 5, 7622027413350371656062982956481199067805777920000000⟩, + ⟨4, 6, 4, 6, 3, 5, 5265695249957928998691606555274162859723980800000000⟩, + ⟨4, 6, 5, 6, 4, 5, -989028442250299944867364812816782606519500800000000⟩, + ⟨4, 6, 6, 6, 5, 5, -32061699775488351575287908718884577911767040000000⟩, + ⟨4, 6, 7, 6, 6, 5, -26845146761052700697868884692225335503093760000000⟩, + ⟨4, 6, 8, 6, 7, 5, -20641333330029341553114046012611861015429120000000⟩, + ⟨4, 6, 2, 7, 0, 5, -352353404283625540984837278131370706862667202560000000⟩, + ⟨4, 6, 3, 7, 1, 5, -70068435356785025411080283342906352638676172800000000⟩, + ⟨4, 6, 4, 7, 2, 5, -5411332950136023976329693774067995843860889600000000⟩, + ⟨4, 6, 5, 7, 3, 5, -1378900056943025251800387326807199402531225600000000⟩, + ⟨4, 6, 6, 7, 4, 5, -1112657713491085060080987988254685610901504000000000⟩, + ⟨4, 6, 7, 7, 5, 5, 96442174441499644656818042266909111568302080000000⟩, + ⟨4, 6, 8, 7, 6, 5, -30860197299028141062160456132541303142481920000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1117.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1117.lean new file mode 100644 index 0000000000000000000000000000000000000000..bb08480f0370bfe7379af5c70a8d1e4beb9fb077 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1117.lean @@ -0,0 +1,618 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1117. -/ +namespace LaughlinFock +def collectedFourData_11_5_28 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 5, 6, 49233951595176293575180725874505508964125376512000000⟩, + ⟨4, 7, 1, 0, 6, 6, -59194650027773029412216715544175701576044773376000000⟩, + ⟨4, 7, 2, 0, 7, 6, 2888066792826120496819965845299218151102218240000000⟩, + ⟨4, 7, 3, 0, 8, 6, -586554340655998071078589560336007908990910464000000⟩, + ⟨4, 7, 0, 1, 4, 6, 35398380299463680603998305717900765270972039168000000⟩, + ⟨4, 7, 1, 1, 5, 6, -12888678949847513894311162283227485648866770944000000⟩, + ⟨4, 7, 2, 1, 6, 6, -6647810755712850236360180304807978799340716032000000⟩, + ⟨4, 7, 3, 1, 7, 6, 7835616349497088883789469761418005996101435392000000⟩, + ⟨4, 7, 4, 1, 8, 6, -3049369769105432993746525559338124284784541696000000⟩, + ⟨4, 7, 0, 2, 3, 6, 13855616450030847666865841806359349675771822080000000⟩, + ⟨4, 7, 1, 2, 4, 6, 11206112205669459903490399377706071635036995584000000⟩, + ⟨4, 7, 2, 2, 5, 6, -13940307104357533444154149305140886525947412480000000⟩, + ⟨4, 7, 3, 2, 6, 6, -2550656646130261814522028214731193591290396672000000⟩, + ⟨4, 7, 4, 2, 7, 6, 413468611300211544515483346328499345676042240000000⟩, + ⟨4, 7, 5, 2, 8, 6, -1031565537991255839050487671382393171310804992000000⟩, + ⟨4, 7, 0, 3, 2, 6, -60882480756313614743705215011383025443794845696000000⟩, + ⟨4, 7, 1, 3, 3, 6, -31034689677736045568324793084135728657524064256000000⟩, + ⟨4, 7, 2, 3, 4, 6, 1027136903757879851130095831155455479248846848000000⟩, + ⟨4, 7, 3, 3, 5, 6, -5094854369647563895197651908987712531351994368000000⟩, + ⟨4, 7, 4, 3, 6, 6, 336740150200895655993024292196728809543696384000000⟩, + ⟨4, 7, 5, 3, 7, 6, 81265487477198076217473765961312132694802432000000⟩, + ⟨4, 7, 6, 3, 8, 6, -175518207181079966540293660285098957792608256000000⟩, + ⟨4, 7, 0, 4, 1, 6, -50252997020495176081509293643902576357403525120000000⟩, + ⟨4, 7, 1, 4, 2, 6, 53506397572376028819754073629467428625850564608000000⟩, + ⟨4, 7, 2, 4, 3, 6, 21847096666309550202023137321728611682204254208000000⟩, + ⟨4, 7, 3, 4, 4, 6, 2083616418630443213597216761463278199271063552000000⟩, + ⟨4, 7, 4, 4, 5, 6, -870773452966619464419623144927971532920061952000000⟩, + ⟨4, 7, 5, 4, 6, 6, 199018461581684215873137164431606824472412160000000⟩, + ⟨4, 7, 6, 4, 7, 6, 76588499950862296611626767110320873917120512000000⟩, + ⟨4, 7, 7, 4, 8, 6, -64212357892893753822771646109442395980431360000000⟩, + ⟨4, 7, 0, 5, 0, 6, 310977665932052649834932439934966379514244890624000000⟩, + ⟨4, 7, 1, 5, 1, 6, 24260424194501190717288668349425495930975551488000000⟩, + ⟨4, 7, 2, 5, 2, 6, -2971694434347933165002632004699520489159131136000000⟩, + ⟨4, 7, 3, 5, 3, 6, 5245896527187405784567665442794357733346770944000000⟩, + ⟨4, 7, 4, 5, 4, 6, -121602370483132329761850128625485494867722240000000⟩, + ⟨4, 7, 5, 5, 5, 6, 54770143443160573362901518943938514130042880000000⟩, + ⟨4, 7, 6, 5, 6, 6, 129716659872426272334322663058926171374747648000000⟩, + ⟨4, 7, 7, 5, 7, 6, -29289564454614509000455246248434943003721728000000⟩, + ⟨4, 7, 8, 5, 8, 6, -22101295188016471044092068937345040113467392000000⟩, + ⟨4, 7, 1, 6, 0, 6, -264489296339284635595696795775850265210376945664000000⟩, + ⟨4, 7, 2, 6, 1, 6, 49864056503429265886848554665602998014775918592000000⟩, + ⟨4, 7, 3, 6, 2, 6, 5866386882236655327406799633618278314135257088000000⟩, + ⟨4, 7, 4, 6, 3, 6, 3039605199343279233485451150583470009184419840000000⟩, + ⟨4, 7, 5, 6, 4, 6, -456730722559216057300272138991988491180572672000000⟩, + ⟨4, 7, 6, 6, 5, 6, -12338340233183360598963104419954229067644928000000⟩, + ⟨4, 7, 7, 6, 6, 6, -8855012767801839636462262428083764127072256000000⟩, + ⟨4, 7, 8, 6, 7, 6, -5957570760654653573578441808875826643468288000000⟩, + ⟨4, 7, 2, 7, 0, 6, -406789678789470277847722996522405541668114661376000000⟩, + ⟨4, 7, 3, 7, 1, 6, -53929030656058534894042050888348665693255761920000000⟩, + ⟨4, 7, 4, 7, 2, 6, -3123674080975818066806159705070326857680814080000000⟩, + ⟨4, 7, 5, 7, 3, 6, -636772404554517342809406298989386506388373504000000⟩, + ⟨4, 7, 6, 7, 4, 6, -428185327922769318895316296606599445531852800000000⟩, + ⟨4, 7, 7, 7, 5, 6, 31811958177596609852981766507388110265909248000000⟩, + ⟨4, 7, 8, 7, 6, 6, -8906973505885553354223105538930505058091008000000⟩ +] + +def collectedFourData_11_5_29 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 5, 7, -288946732947821818327202068681453700797452779520000000⟩, + ⟨4, 8, 1, 0, 6, 7, 173702294649760396851650393515023317783260692480000000⟩, + ⟨4, 8, 2, 0, 7, 7, -5649878029859116838101073686744535973809356800000000⟩, + ⟨4, 8, 3, 0, 8, 7, 860600027712987332486726984837150071440015360000000⟩, + ⟨4, 8, 0, 1, 4, 7, -207747824575931125557707955157752976577428193280000000⟩, + ⟨4, 8, 1, 1, 5, 7, 37820869074184527719856967428828803122719621120000000⟩, + ⟨4, 8, 2, 1, 6, 7, 13005003910802719637442246237921699806041866240000000⟩, + ⟨4, 8, 3, 1, 7, 7, -11496516486407446392812375532606360251353006080000000⟩, + ⟨4, 8, 4, 1, 8, 7, 3579259449161074896529791008619946685006610432000000⟩, + ⟨4, 8, 0, 2, 3, 7, -81316550398663459644897028058021506482752716800000000⟩, + ⟨4, 8, 1, 2, 4, 7, -32883502196806610584041118349615614325497528320000000⟩, + ⟨4, 8, 2, 2, 5, 7, 27271195747286338088537557509071664225819033600000000⟩, + ⟨4, 8, 3, 2, 6, 7, 3742356041370421531414089530117829602605793280000000⟩, + ⟨4, 8, 4, 2, 7, 7, -485317146159659891529964463897522666031022080000000⟩, + ⟨4, 8, 5, 2, 8, 7, 1009017430610284950832058734988353950418206720000000⟩, + ⟨4, 8, 0, 3, 2, 7, 357310216594903801088822256744400071289900892160000000⟩, + ⟨4, 8, 1, 3, 3, 7, 91068986947920504130605806198328363926295674880000000⟩, + ⟨4, 8, 2, 3, 4, 7, -2009371196197453034762343841120610191524495360000000⟩, + ⟨4, 8, 3, 3, 5, 7, 7475235468905724994983882182502514218573496320000000⟩, + ⟨4, 8, 4, 3, 6, 7, -395255562880476117338219912079324896116604928000000⟩, + ⟨4, 8, 5, 3, 7, 7, -79489174804354269377984791803087346068357120000000⟩, + ⟨4, 8, 6, 3, 8, 7, 147155747187390754334910372520862626275655680000000⟩, + ⟨4, 8, 0, 4, 1, 7, 294927358853952892106118775561463627571737395200000000⟩, + ⟨4, 8, 1, 4, 2, 7, -157010541195926101069405882385382131378253987840000000⟩, + ⟨4, 8, 2, 4, 3, 7, -42739119392181639773867968935581796876744130560000000⟩, + ⟨4, 8, 3, 4, 4, 7, -3057108648469189518596241906866391727189524480000000⟩, + ⟨4, 8, 4, 4, 5, 7, 1022087954431225211815496306088967342217232384000000⟩, + ⟨4, 8, 5, 4, 6, 7, -194668287523642463374732146346960371685785600000000⟩, + ⟨4, 8, 6, 4, 7, 7, -64212357892893753822771646109442395980431360000000⟩, + ⟨4, 8, 7, 4, 8, 7, 47106596228012696055950583858333538792243200000000⟩, + ⟨4, 8, 0, 5, 0, 7, -1825081629231024835823918172787236461962372055040000000⟩, + ⟨4, 8, 1, 5, 1, 7, -71190409095826202875545343039880301895735050240000000⟩, + ⟨4, 8, 2, 5, 2, 7, 5813477422953717616045417769611839204250091520000000⟩, + ⟨4, 8, 3, 5, 3, 7, -7696846453523520083032904113924279116559810560000000⟩, + ⟨4, 8, 4, 5, 4, 7, 142733242128199370443784996460229292017582080000000⟩, + ⟨4, 8, 5, 5, 5, 7, -53572969797720285786330748605195480779980800000000⟩, + ⟨4, 8, 6, 5, 6, 7, -108755395310562238179476291853414034770493440000000⟩, + ⟨4, 8, 7, 5, 7, 7, 21487011717577350694080275566416205562511360000000⟩, + ⟨4, 8, 8, 5, 8, 7, 14412134606717779731711956224733079907860480000000⟩, + ⟨4, 8, 1, 6, 0, 7, 776124154174049423604096705811011009723991326720000000⟩, + ⟨4, 8, 2, 6, 1, 7, -97548241618988159889354703014541242838485565440000000⟩, + ⟨4, 8, 3, 6, 2, 7, -8607237835426534415042542183848563457518469120000000⟩, + ⟨4, 8, 4, 6, 3, 7, -3567798087884959697252468861287328566770401280000000⟩, + ⟨4, 8, 5, 6, 4, 7, 446747436963511209313960445767757617189355520000000⟩, + ⟨4, 8, 6, 6, 5, 7, 10344554591952679308436387090883594252451840000000⟩, + ⟨4, 8, 7, 6, 6, 7, 6496093972168264600739947788124400878878720000000⟩, + ⟨4, 8, 8, 6, 7, 7, 3884899550056944435267766894411786192158720000000⟩, + ⟨4, 8, 2, 7, 0, 7, 795796023372804286507665520092687819021295288320000000⟩, + ⟨4, 8, 3, 7, 1, 7, 79125363261709789550575676301083201367755980800000000⟩, + ⟨4, 8, 4, 7, 2, 7, 3666475638247093126628204666519651085566607360000000⟩, + ⟨4, 8, 5, 7, 3, 7, 622853742068861487214007450444520351219056640000000⟩, + ⟨4, 8, 6, 7, 4, 7, 358993707132311809393171299628831928745984000000000⟩, + ⟨4, 8, 7, 7, 5, 7, -23337455877170207587414494945270438832373760000000⟩, + ⟨4, 8, 8, 7, 6, 7, 5808189068253980658386378821973417939435520000000⟩ +] + +def collectedFourData_11_5_30 : List CollectedFourTerm := [ + ⟨5, 0, 6, 3, 8, 0, -712668905028425984838251572827349045362988941312000000⟩, + ⟨5, 0, 6, 4, 7, 0, 310977665932052649834932439934966379514244890624000000⟩, + ⟨5, 0, 7, 4, 8, 0, -1825081629231024835823918172787236461962372055040000000⟩, + ⟨5, 0, 6, 5, 6, 0, 526697665387229026213591238547480758693916573696000000⟩, + ⟨5, 0, 7, 5, 7, 0, -832485330992818240272622108786687025762367700992000000⟩, + ⟨5, 0, 8, 5, 8, 0, -2512704354955629765062245886435797226725155274752000000⟩, + ⟨5, 0, 6, 6, 5, 0, -50098229494671023012774153570003349979325792256000000⟩, + ⟨5, 0, 7, 6, 6, 0, -251682412224731982370624725746522234743563485184000000⟩, + ⟨5, 0, 8, 6, 7, 0, -677318404550785629266741977297760015108253155328000000⟩, + ⟨5, 0, 6, 7, 4, 0, -1738590962732051674533334504100259250491201945600000000⟩, + ⟨5, 0, 7, 7, 5, 0, 904178297838562287137600099172382796945421238272000000⟩, + ⟨5, 0, 8, 7, 6, 0, -1012637084266808461018983190960661388878464155648000000⟩ +] + +def collectedFourData_11_5_31 : List CollectedFourTerm := [ + ⟨5, 1, 5, 2, 8, 1, -54460346640712027149454784969124946982278791168000000⟩, + ⟨5, 1, 5, 3, 7, 1, 4290320347995344539892959497394974734237564928000000⟩, + ⟨5, 1, 6, 3, 8, 1, -55597722410065342033230309268277984727341727744000000⟩, + ⟨5, 1, 5, 4, 6, 1, 10506956665831954284936677982356865429421424640000000⟩, + ⟨5, 1, 6, 4, 7, 1, 24260424194501190717288668349425495930975551488000000⟩, + ⟨5, 1, 7, 4, 8, 1, -71190409095826202875545343039880301895735050240000000⟩, + ⟨5, 1, 5, 5, 5, 1, 2891528349506892678799431306278615547138539520000000⟩, + ⟨5, 1, 6, 5, 6, 1, 41089474211114390186471024744616255786269540352000000⟩, + ⟨5, 1, 7, 5, 7, 1, -32472504424157490548560617060168950741521661952000000⟩, + ⟨5, 1, 8, 5, 8, 1, -65341534355196449587136582557087872612468523008000000⟩, + ⟨5, 1, 5, 6, 4, 1, -24112586700476439743857769828545752748825509888000000⟩, + ⟨5, 1, 6, 6, 5, 1, -3908333080098912713237616232694453298184323072000000⟩, + ⟨5, 1, 7, 6, 6, 1, -9817300005398826746076434895704588766469423104000000⟩, + ⟨5, 1, 8, 6, 7, 1, -17613303257534853463281340275347281052342157312000000⟩, + ⟨5, 1, 5, 7, 3, 1, -33617685552784225485227523389459709287429308416000000⟩, + ⟨5, 1, 6, 7, 4, 1, -135633387465907965583645255867345532571824947200000000⟩, + ⟨5, 1, 7, 7, 5, 1, 35269010376163849307925504082294329920697925632000000⟩, + ⟨5, 1, 8, 7, 6, 1, -26333086381797604043391928960574779841253998592000000⟩ +] + +def collectedFourData_11_5_32 : List CollectedFourTerm := [ + ⟨5, 2, 4, 1, 8, 2, 7887864084845923472618057315880669559987057459200000⟩, + ⟨5, 2, 4, 2, 7, 2, -1069527297846473312423628002951176954469941248000000⟩, + ⟨5, 2, 5, 2, 8, 2, 13341853193279715425967219881138749607554056192000000⟩, + ⟨5, 2, 4, 3, 6, 2, -871052295331989623184405989487301742503447756800000⟩, + ⟨5, 2, 5, 3, 7, 2, -1051055084403448220995634865920455677818437632000000⟩, + ⟨5, 2, 6, 3, 8, 2, 6810245399000928212916284850205713879760109568000000⟩, + ⟨5, 2, 4, 4, 5, 2, 2252446625293210361242050800441036267218953830400000⟩, + ⟨5, 2, 5, 4, 6, 2, -2574024625081763448006054864896973200330588160000000⟩, + ⟨5, 2, 6, 4, 7, 2, -2971694434347933165002632004699520489159131136000000⟩, + ⟨5, 2, 7, 4, 8, 2, 5813477422953717616045417769611839204250091520000000⟩, + ⟨5, 2, 4, 5, 4, 2, 314551216610052073619678863085425420557877248000000⟩, + ⟨5, 2, 5, 5, 5, 2, -708374975977254979353119704444890843583610880000000⟩, + ⟨5, 2, 6, 5, 6, 2, -5033109101658975613217368576971404661535801344000000⟩, + ⟨5, 2, 7, 5, 7, 2, 2651736009586607226201383820951343956750237696000000⟩, + ⟨5, 2, 8, 5, 8, 2, 4001889505689327752841316153823008234603020288000000⟩, + ⟨5, 2, 4, 6, 3, 2, -7862605882344145440822963711586830545760288768000000⟩, + ⟨5, 2, 5, 6, 4, 2, 5907171211934458564778997830276962917518671872000000⟩, + ⟨5, 2, 6, 6, 5, 2, 478737369494979369288322645818017594090717184000000⟩, + ⟨5, 2, 7, 6, 6, 2, 801690180750704261957634136222759261927636992000000⟩, + ⟨5, 2, 8, 6, 7, 2, 1078739490316954358785457074098521282269151232000000⟩, + ⟨5, 2, 4, 7, 2, 2, 8080068493405906267003442375814200712983740416000000⟩, + ⟨5, 2, 5, 7, 3, 2, 8235757812966125676231605713721032673700347904000000⟩, + ⟨5, 2, 6, 7, 4, 2, 16613929724095766258340831347886501940061798400000000⟩, + ⟨5, 2, 7, 7, 5, 2, -2880101381012711447990261294947642977168654336000000⟩, + ⟨5, 2, 8, 7, 6, 2, 1612788911121515554753737951233649836726157312000000⟩ +] + +def collectedFourData_11_5_33 : List CollectedFourTerm := [ + ⟨5, 3, 3, 0, 8, 3, -2008789427021122518318913336154160170824787558400000⟩, + ⟨5, 3, 3, 1, 7, 3, 26834859425743880517472012037190677865677665075200000⟩, + ⟨5, 3, 4, 1, 8, 3, -41773055464263205097076926849968971981070427750400000⟩, + ⟨5, 3, 3, 2, 6, 3, -8735306769663118166184021563937436626586907443200000⟩, + ⟨5, 3, 4, 2, 7, 3, 5664071116453191635006675948209468102542360576000000⟩, + ⟨5, 3, 5, 2, 8, 3, -35328320027069611840047698174724611631954788352000000⟩, + ⟨5, 3, 3, 3, 5, 3, -17448493482316087126911993111250580026289867980800000⟩, + ⟨5, 3, 4, 3, 6, 3, 4612974495222647756592520382216715478836550041600000⟩, + ⟨5, 3, 5, 3, 7, 3, 2783122393116051936336506877301213526325460992000000⟩, + ⟨5, 3, 6, 3, 8, 3, -12022044485792549011540705664383538942781161472000000⟩, + ⟨5, 3, 3, 4, 4, 3, 7135820744300292330880246788026761333578085171200000⟩, + ⟨5, 3, 4, 4, 5, 3, -11928651000647113994736815091065328757306608844800000⟩, + ⟨5, 3, 5, 4, 6, 3, 6815842176876208753627427004853962589297704960000000⟩, + ⟨5, 3, 6, 4, 7, 3, 5245896527187405784567665442794357733346770944000000⟩, + ⟨5, 3, 7, 4, 8, 3, -7696846453523520083032904113924279116559810560000000⟩, + ⟨5, 3, 3, 5, 3, 3, 17965771879337511397169836967949456995061753446400000⟩, + ⟨5, 3, 4, 5, 4, 3, -1665820465016270453047245993534793243296792576000000⟩, + ⟨5, 3, 5, 5, 5, 3, 1875728767806982269333512711424458995563233280000000⟩, + ⟨5, 3, 6, 5, 6, 3, 8884887104195719261798052282332621561424510976000000⟩, + ⟨5, 3, 7, 5, 7, 3, -3510808319385775218455022487129364015389605888000000⟩, + ⟨5, 3, 8, 5, 8, 3, -4238692515105084106047625884731455337525359411200000⟩, + ⟨5, 3, 3, 6, 2, 3, 20090782945486151102771381756366238106520440012800000⟩, + ⟨5, 3, 4, 6, 3, 3, 41639291458863893597419501512113041364867874816000000⟩, + ⟨5, 3, 5, 6, 4, 3, -15641787689211755642846430217564481206125330432000000⟩, + ⟨5, 3, 6, 6, 5, 3, -845109333934467571940555596948834834590990336000000⟩, + ⟨5, 3, 7, 6, 6, 3, -1061410542367012559764634899997412858135576576000000⟩, + ⟨5, 3, 8, 6, 7, 3, -1142571526988509776463533183507722897170681036800000⟩, + ⟨5, 3, 3, 7, 1, 3, -184692293761274678959394729480124159751253655552000000⟩, + ⟨5, 3, 4, 7, 2, 3, -42790943872695245103759367391998258230111240192000000⟩, + ⟨5, 3, 5, 7, 3, 3, -21807726667871022098832315409693380675920461824000000⟩, + ⟨5, 3, 6, 7, 4, 3, -29328370789136552958154901464748501744851353600000000⟩, + ⟨5, 3, 7, 7, 5, 3, 3813156306879212685433200768157055455548407808000000⟩, + ⟨5, 3, 8, 7, 6, 3, -1708222147637162656737314841836614460499610828800000⟩ +] + +def collectedFourData_11_5_34 : List CollectedFourTerm := [ + ⟨5, 4, 2, 0, 7, 4, -305699305027599108736493027257885389037240320000000⟩, + ⟨5, 4, 3, 0, 8, 4, 186258768057088794748580696306241796262854656000000⟩, + ⟨5, 4, 2, 1, 6, 4, 703664864339157146961274750831072694476210176000000⟩, + ⟨5, 4, 3, 1, 7, 4, -2488179094528684933227662063630892667364179968000000⟩, + ⟨5, 4, 4, 1, 8, 4, 1936638490847725034977790313071768026604371968000000⟩, + ⟨5, 4, 2, 2, 5, 4, 1475569126122344402283150372404612311956848640000000⟩, + ⟨5, 4, 3, 2, 6, 4, 809954221996754877891655037238214028414681088000000⟩, + ⟨5, 4, 4, 2, 7, 4, -262591711741227170579266479752284492183633920000000⟩, + ⟨5, 4, 5, 2, 8, 4, 1091902960269708173442566509445708505478594560000000⟩, + ⟨5, 4, 2, 3, 4, 4, -108721529026592795740153741440727590490865664000000⟩, + ⟨5, 4, 3, 3, 5, 4, 1617857430326949054931334813752091002716291072000000⟩, + ⟨5, 4, 4, 3, 6, 4, -213861874968417684785936249850743700609564672000000⟩, + ⟨5, 4, 5, 3, 7, 4, -86018796747420657167206469842853808580853760000000⟩, + ⟨5, 4, 6, 3, 8, 4, 278676695193957268147717163202572417362821120000000⟩, + ⟨5, 4, 2, 4, 3, 4, -2312495778958842945722178096061174651388166144000000⟩, + ⟨5, 4, 3, 4, 4, 4, -661646842138429489991489640392135447421124608000000⟩, + ⟨5, 4, 4, 4, 5, 4, 553023579793097064779774710812350799377596416000000⟩, + ⟨5, 4, 5, 4, 6, 4, -210659274031705992730966707048484761816268800000000⟩, + ⟨5, 4, 6, 4, 7, 4, -121602370483132329761850128625485494867722240000000⟩, + ⟨5, 4, 7, 4, 8, 4, 142733242128199370443784996460229292017582080000000⟩, + ⟨5, 4, 2, 5, 2, 4, 314551216610052073619678863085425420557877248000000⟩, + ⟨5, 4, 3, 5, 3, 4, -1665820465016270453047245993534793243296792576000000⟩, + ⟨5, 4, 4, 5, 4, 4, 77229017497948722148709516725371231189073920000000⟩, + ⟨5, 4, 5, 5, 5, 4, -57973710401801449683641225365059145197158400000000⟩, + ⟨5, 4, 6, 5, 6, 4, -205955898623963706259817929288140266101800960000000⟩, + ⟨5, 4, 7, 5, 7, 4, 65105762073139071355845397973726055402307584000000⟩, + ⟨5, 4, 8, 5, 8, 4, 65503269068130043073362401025086318201274368000000⟩, + ⟨5, 4, 2, 6, 1, 4, -5278066094876846473986364444037330699871584256000000⟩, + ⟨5, 4, 3, 6, 2, 4, -1862855524024655297752860815170221005919485952000000⟩, + ⟨5, 4, 4, 6, 3, 4, -1930437064625315025661905629796795648017694720000000⟩, + ⟨5, 4, 5, 6, 4, 4, 483445413443772994370525790560294466968616960000000⟩, + ⟨5, 4, 6, 6, 5, 4, 19590035333569787908621826343013999769026560000000⟩, + ⟨5, 4, 7, 6, 6, 4, 19683199977536263491987768240437089762541568000000⟩, + ⟨5, 4, 8, 6, 7, 4, 17656900068878221893298852108636092578660352000000⟩, + ⟨5, 4, 2, 7, 0, 4, 43058326215735931632297079375058694871940333568000000⟩, + ⟨5, 4, 3, 7, 1, 4, 17125019996061162419776020873311263523529031680000000⟩, + ⟨5, 4, 4, 7, 2, 4, 1983828763363070430363017905623886627224944640000000⟩, + ⟨5, 4, 5, 7, 3, 4, 674017934822703830399676436534178410628382720000000⟩, + ⟨5, 4, 6, 7, 4, 4, 679845550114079139577568628849712463609856000000000⟩, + ⟨5, 4, 7, 7, 5, 4, -70712617915523550245164452749490783617286144000000⟩, + ⟨5, 4, 8, 7, 6, 4, 26398266580099403637358170302498686717919232000000⟩ +] + +def collectedFourData_11_5_35 : List CollectedFourTerm := [ + ⟨5, 5, 1, 0, 6, 5, -7055235610152277620563165238641937012007895040000000⟩, + ⟨5, 5, 2, 0, 7, 5, 688440312483817009914572015030266095678259200000000⟩, + ⟨5, 5, 3, 0, 8, 5, -209729041537232697756699608721070877237575680000000⟩, + ⟨5, 5, 1, 1, 5, 5, -1536163600124678912901078027335688819321077760000000⟩, + ⟨5, 5, 2, 1, 6, 5, -1584665882854384260722002406735675675702722560000000⟩, + ⟨5, 5, 3, 1, 7, 5, 2801711952204764110264011780298774506677207040000000⟩, + ⟨5, 5, 4, 1, 8, 5, -1453781527446855429970533067736444462023311360000000⟩, + ⟨5, 5, 1, 2, 4, 5, 1335623436369789305639474149175000722424463360000000⟩, + ⟨5, 5, 2, 2, 5, 5, -3323008111475515166124355874630531356714598400000000⟩, + ⟨5, 5, 3, 2, 6, 5, -912015710403219888667704874600188317678960640000000⟩, + ⟨5, 5, 4, 2, 7, 5, 197120413331732185013507962884844503328358400000000⟩, + ⟨5, 5, 5, 2, 8, 5, -614746257848228448839202289147855575082598400000000⟩, + ⟨5, 5, 1, 3, 3, 5, -3698933056647147757393408451215356353304330240000000⟩, + ⟨5, 5, 2, 3, 4, 5, 244842831455009299921740258814644641951907840000000⟩, + ⟨5, 5, 3, 3, 5, 5, -1821721961042721717690754987604528586723164160000000⟩, + ⟨5, 5, 4, 3, 6, 5, 160540258144998802901984634525969425041981440000000⟩, + ⟨5, 5, 5, 3, 7, 5, 48428967892918364707054125574146706794086400000000⟩, + ⟨5, 5, 6, 3, 8, 5, -125516982188732541214891288728769861716541440000000⟩, + ⟨5, 5, 1, 4, 2, 5, 6377269590182164128835610482485619295854264320000000⟩, + ⟨5, 5, 2, 4, 3, 5, 5207781929828736529743255407129370043235696640000000⟩, + ⟨5, 5, 3, 4, 4, 5, 745020271986858705922903494751420812613386240000000⟩, + ⟨5, 5, 4, 4, 5, 5, -415139670281887402184527094457503788113592320000000⟩, + ⟨5, 5, 5, 4, 6, 5, 118602114935220789048629080342550053650432000000000⟩, + ⟨5, 5, 6, 4, 7, 5, 54770143443160573362901518943938514130042880000000⟩, + ⟨5, 5, 7, 4, 8, 5, -53572969797720285786330748605195480779980800000000⟩, + ⟨5, 5, 1, 5, 1, 5, 2891528349506892678799431306278615547138539520000000⟩, + ⟨5, 5, 2, 5, 2, 5, -708374975977254979353119704444890843583610880000000⟩, + ⟨5, 5, 3, 5, 3, 5, 1875728767806982269333512711424458995563233280000000⟩, + ⟨5, 5, 4, 5, 4, 5, -57973710401801449683641225365059145197158400000000⟩, + ⟨5, 5, 5, 5, 5, 5, 32639458651418280725914735439504606232576000000000⟩, + ⟨5, 5, 6, 5, 6, 5, 92763274809385643267728823444209749479915520000000⟩, + ⟨5, 5, 7, 5, 7, 5, -24436557127099313629050250240346885550243840000000⟩, + ⟨5, 5, 8, 5, 8, 5, -21073505091128552979717731519021163416125440000000⟩, + ⟨5, 5, 1, 6, 0, 5, -31523698529538240318151849469620859190179266560000000⟩, + ⟨5, 5, 2, 6, 1, 5, 11886299418767748504200836472766304632554127360000000⟩, + ⟨5, 5, 3, 6, 2, 5, 2097592009500896703876798101827273609508290560000000⟩, + ⟨5, 5, 4, 6, 3, 5, 1449126286456567231364579244536446105052774400000000⟩, + ⟨5, 5, 5, 6, 4, 5, -272181933378987624774905018785556232300134400000000⟩, + ⟨5, 5, 6, 6, 5, 5, -8823422117622549549815153301465059788062720000000⟩, + ⟨5, 5, 7, 6, 6, 5, -7387819839276998972351538230323991732551680000000⟩, + ⟨5, 5, 8, 6, 7, 5, -5680522190549590514674298020819286265692160000000⟩, + ⟨5, 5, 2, 7, 0, 5, -96968122162774105674296236909974369750566830080000000⟩, + ⟨5, 5, 3, 7, 1, 5, -19282925939781868750135501002625238014781030400000000⟩, + ⟨5, 5, 4, 7, 2, 5, -1489205973868945284886403936989677819317452800000000⟩, + ⟨5, 5, 5, 7, 3, 5, -379475116591405508360793872644591626013900800000000⟩, + ⟨5, 5, 6, 7, 4, 5, -306204872084360291170366251160683436572672000000000⟩, + ⟨5, 5, 7, 7, 5, 5, 26541013764008361085496058227116947737149440000000⟩, + ⟨5, 5, 8, 7, 6, 5, -8492767049444218314898430582091007194562560000000⟩ +] + +def collectedFourData_11_5_36 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 5, 6, 83386719381426899136786989569522965927740571648000000⟩, + ⟨5, 6, 1, 0, 6, 6, -100256987522230368358245843363867257655005282304000000⟩, + ⟨5, 6, 2, 0, 7, 6, 4891470365580086893641118659299575912684584960000000⟩, + ⟨5, 6, 3, 0, 8, 6, -993437264764090962503805583817973631398445056000000⟩, + ⟨5, 6, 0, 1, 4, 6, 59953643958117856923607535307006811237433475072000000⟩, + ⟨5, 6, 1, 1, 5, 6, -21829339713075903214459119159102239399504510976000000⟩, + ⟨5, 6, 2, 1, 6, 6, -11259285757630927577142587359211915038559305728000000⟩, + ⟨5, 6, 3, 1, 7, 6, 13271052201709725222508049496498782481225351168000000⟩, + ⟨5, 6, 4, 1, 8, 6, -5164666515444072395497343149882486280719171584000000⟩, + ⟨5, 6, 0, 2, 3, 6, 23467025565516514337322671334880620417719992320000000⟩, + ⟨5, 6, 1, 2, 4, 6, 18979604593479230914701124439520367733989441536000000⟩, + ⟨5, 6, 2, 2, 5, 6, -23610464708582590778233588426044743887009873920000000⟩, + ⟨5, 6, 3, 2, 6, 6, -4320004450141963982462031167024337194254860288000000⟩, + ⟨5, 6, 4, 2, 7, 6, 700284863319745872198097551000262776151080960000000⟩, + ⟨5, 6, 5, 2, 8, 6, -1747145277862588535800299539347339281923309568000000⟩, + ⟨5, 6, 0, 3, 2, 6, -103115638163995072893040223877573357553355587584000000⟩, + ⟨5, 6, 1, 3, 3, 6, -52562934223232038944206198650883810786304589824000000⟩, + ⟨5, 6, 2, 3, 4, 6, 1739644574220151568756942771728457582134689792000000⟩, + ⟨5, 6, 3, 3, 5, 6, -8629069531210696918130072272705975121055055872000000⟩, + ⟨5, 6, 4, 3, 6, 6, 570331153593869580244293209507227787367284736000000⟩, + ⟨5, 6, 5, 3, 7, 6, 137637995328408761455560581104739689407971328000000⟩, + ⟨5, 6, 6, 3, 8, 6, -297272248404570817510856458977349651685965824000000⟩, + ⟨5, 6, 0, 4, 1, 6, -85112659554108831624772884326222716144692756480000000⟩, + ⟨5, 6, 1, 4, 2, 6, 90622889589791114842997763401937366144182648832000000⟩, + ⟨5, 6, 2, 4, 3, 6, 37002061788413275554849299414771201813073887232000000⟩, + ⟨5, 6, 3, 4, 4, 6, 3528986237535588677661508459885539904148471808000000⟩, + ⟨5, 6, 4, 4, 5, 6, -1474814415961641060898925666184575909162385408000000⟩, + ⟨5, 6, 5, 4, 6, 6, 337074235765002845811078492562419108953456640000000⟩, + ⟨5, 6, 6, 4, 7, 6, 129716659872426272334322663058926171374747648000000⟩, + ⟨5, 6, 7, 4, 8, 6, -108755395310562238179476291853414034770493440000000⟩, + ⟨5, 6, 0, 5, 0, 6, 526697665387229026213591238547480758693916573696000000⟩, + ⟨5, 6, 1, 5, 1, 6, 41089474211114390186471024744616255786269540352000000⟩, + ⟨5, 6, 2, 5, 2, 6, -5033109101658975613217368576971404661535801344000000⟩, + ⟨5, 6, 3, 5, 3, 6, 8884887104195719261798052282332621561424510976000000⟩, + ⟨5, 6, 4, 5, 4, 6, -205955898623963706259817929288140266101800960000000⟩, + ⟨5, 6, 5, 5, 5, 6, 92763274809385643267728823444209749479915520000000⟩, + ⟨5, 6, 6, 5, 6, 6, 219698934686724839767986096673503970949332992000000⟩, + ⟨5, 6, 7, 5, 7, 6, -49607244855406789002514493644386947995533312000000⟩, + ⟨5, 6, 8, 5, 8, 6, -37432593568007934810759829800550938515079168000000⟩, + ⟨5, 6, 1, 6, 0, 6, -447961092267796386383112917981349269450948345856000000⟩, + ⟨5, 6, 2, 6, 1, 6, 84453917513264405245858402305510616563311443968000000⟩, + ⟨5, 6, 3, 6, 2, 6, 9935801228270273863922581870957281143005642752000000⟩, + ⟨5, 6, 4, 6, 3, 6, 5148128427148172602431903302612758885155471360000000⟩, + ⟨5, 6, 5, 6, 4, 6, -773557176723818085728860663317328711844364288000000⟩, + ⟨5, 6, 6, 6, 5, 6, -20897240244226757809264839445894057911386112000000⟩, + ⟨5, 6, 7, 6, 6, 6, -14997586845334353932108071164263563027021824000000⟩, + ⟨5, 6, 8, 6, 7, 6, -10090237836249080203537724211079926673047552000000⟩, + ⟨5, 6, 2, 7, 0, 6, -688972867166765197151791110477921874584539234304000000⟩, + ⟨5, 6, 3, 7, 1, 6, -91338696166523279615999490494438132141449543680000000⟩, + ⟨5, 6, 4, 7, 2, 6, -5290514484213917825368088544223321460645560320000000⟩, + ⟨5, 6, 5, 7, 3, 6, -1078490758674473417086149775962959324922249216000000⟩, + ⟨5, 6, 6, 7, 4, 6, -725210319828124916568660964657077431776051200000000⟩, + ⟨5, 6, 7, 7, 5, 6, 53879380865882710904746738510802686304059392000000⟩, + ⟨5, 6, 8, 7, 6, 6, -15085591877330667790891558641742139917074432000000⟩ +] + +def collectedFourData_11_5_37 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 5, 7, -131798990666905708012318491520935140919236100096000000⟩, + ⟨5, 7, 1, 0, 6, 7, 79231860065703010501217456422345156600742805504000000⟩, + ⟨5, 7, 2, 0, 7, 7, -2577112446054291919063165049395048696397168640000000⟩, + ⟨5, 7, 3, 0, 8, 7, 392550605654244887826745511312078979547004928000000⟩, + ⟨5, 7, 0, 1, 4, 7, -94761249982008207761954609241877836852671545344000000⟩, + ⟨5, 7, 1, 1, 5, 7, 17251457800780391567583879279585489932859211776000000⟩, + ⟨5, 7, 2, 1, 6, 7, 5932049729638173298848287422942531813745098752000000⟩, + ⟨5, 7, 3, 1, 7, 7, -5243974394988448195272975715924239135522422784000000⟩, + ⟨5, 7, 4, 1, 8, 7, 1632628886029322859307166534137393938058287513600000⟩, + ⟨5, 7, 0, 2, 3, 7, -37091401441779841237281228145332083028016496640000000⟩, + ⟨5, 7, 1, 2, 4, 7, -14999347301548228556228208041432905426283790336000000⟩, + ⟨5, 7, 2, 2, 5, 7, 12439372603742207919921321238431934602050273280000000⟩, + ⟨5, 7, 3, 2, 6, 7, 1707023104005428366478216571653207464916025344000000⟩, + ⟨5, 7, 4, 2, 7, 7, -221370594381273182652409640903856186231619584000000⟩, + ⟨5, 7, 5, 2, 8, 7, 460249117763048340716739775451357091679174656000000⟩, + ⟨5, 7, 0, 3, 2, 7, 162982032784173715592560064784838064995269869568000000⟩, + ⟨5, 7, 1, 3, 3, 7, 41539838289021269162698538581273988351366529024000000⟩, + ⟨5, 7, 2, 3, 4, 7, -916546426506234271101897467783013048074108928000000⟩, + ⟨5, 7, 3, 3, 5, 7, 3409723583817579758261036288911999589978996736000000⟩, + ⟨5, 7, 4, 3, 6, 7, -180290269115220113627800922607150892512077414400000⟩, + ⟨5, 7, 5, 3, 7, 7, -36257869750861638651398973502478483850264576000000⟩, + ⟨5, 7, 6, 3, 8, 7, 67123025591138306265224894088128353076772864000000⟩, + ⟨5, 7, 0, 4, 1, 7, 134526969107578248305891392622012898579799080960000000⟩, + ⟨5, 7, 1, 4, 2, 7, -71618151354646336457123698225563930040763154432000000⟩, + ⟨5, 7, 2, 4, 3, 7, -19494848550162089723781625832611130483448741888000000⟩, + ⟨5, 7, 3, 4, 4, 7, -1394457137883845429125966070807261843086639104000000⟩, + ⟨5, 7, 4, 4, 5, 7, 466211053478717973000636442102749774252028723200000⟩, + ⟨5, 7, 5, 4, 6, 7, -88795203007553098538072519654440254182522880000000⟩, + ⟨5, 7, 6, 4, 7, 7, -29289564454614509000455246248434943003721728000000⟩, + ⟨5, 7, 7, 4, 8, 7, 21487011717577350694080275566416205562511360000000⟩, + ⟨5, 7, 0, 5, 0, 7, -832485330992818240272622108786687025762367700992000000⟩, + ⟨5, 7, 1, 5, 1, 7, -32472504424157490548560617060168950741521661952000000⟩, + ⟨5, 7, 2, 5, 2, 7, 2651736009586607226201383820951343956750237696000000⟩, + ⟨5, 7, 3, 5, 3, 7, -3510808319385775218455022487129364015389605888000000⟩, + ⟨5, 7, 4, 5, 4, 7, 65105762073139071355845397973726055402307584000000⟩, + ⟨5, 7, 5, 5, 5, 7, -24436557127099313629050250240346885550243840000000⟩, + ⟨5, 7, 6, 5, 6, 7, -49607244855406789002514493644386947995533312000000⟩, + ⟨5, 7, 7, 5, 7, 7, 9800998363722870346945965180371586911305728000000⟩, + ⟨5, 7, 8, 5, 8, 7, 6573892617308115336356590458094323083771904000000⟩, + ⟨5, 7, 1, 6, 0, 7, 354018123370917811147977614668918228805700550656000000⟩, + ⟨5, 7, 2, 6, 1, 7, -44495259231865982569950068900481430347854118912000000⟩, + ⟨5, 7, 3, 6, 2, 7, -3926070551363786211272643280426463168273842176000000⟩, + ⟨5, 7, 4, 6, 3, 7, -1627400947189351528025152465947847870585503744000000⟩, + ⟨5, 7, 5, 6, 4, 7, 203777563684897599208669317517930084901584896000000⟩, + ⟨5, 7, 6, 6, 5, 7, 4718523169335407311980182389488214062661632000000⟩, + ⟨5, 7, 7, 6, 6, 7, 2963101953340849180980878216343369868640256000000⟩, + ⟨5, 7, 8, 6, 7, 7, 1772042321836126626988124496797985989984256000000⟩, + ⟨5, 7, 2, 7, 0, 7, 362991169989152042233071351469266815792852238336000000⟩, + ⟨5, 7, 3, 7, 1, 7, 36091922229585559005703307704117376440955043840000000⟩, + ⟨5, 7, 4, 7, 2, 7, 1672411324730323764879037200820978433579286528000000⟩, + ⟨5, 7, 5, 7, 3, 7, 284105979328049034252161921135605939722780672000000⟩, + ⟨5, 7, 6, 7, 4, 7, 163749933328900517592208693291278467806003200000000⟩, + ⟨5, 7, 7, 7, 5, 7, -10645052456432928189813549260635113152053248000000⟩, + ⟨5, 7, 8, 7, 6, 7, 2649323800925851117627849354963200975568896000000⟩ +] + +def collectedFourData_11_5_38 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 5, 8, -397811091076567400068049426630470388160424574976000000⟩, + ⟨5, 8, 1, 0, 6, 8, 159431229537620524993746122252427280531027132416000000⟩, + ⟨5, 8, 2, 0, 7, 8, -3889270732667623666880183695073418401462353920000000⟩, + ⟨5, 8, 3, 0, 8, 8, 473936815290935350842528588589634856175219507200000⟩, + ⟨5, 8, 0, 1, 4, 8, -286019460819646850221162727501943479200502513664000000⟩, + ⟨5, 8, 1, 1, 5, 8, 34713575147850957859756070962458209474737864704000000⟩, + ⟨5, 8, 2, 1, 6, 8, 8952402303412954784392587829550364006763462656000000⟩, + ⟨5, 8, 3, 1, 7, 8, -6331190140659408349376664908101831585957517721600000⟩, + ⟨5, 8, 4, 1, 8, 8, 1642596996097551773721099830607297452145062707200000⟩, + ⟨5, 8, 0, 2, 3, 8, -111953595414129592218440136311077358584819875840000000⟩, + ⟨5, 8, 1, 2, 4, 8, -30181853367629966323580558991318695742164434944000000⟩, + ⟨5, 8, 2, 2, 5, 8, 18772982868696603710758845760569908540567715840000000⟩, + ⟨5, 8, 3, 2, 6, 8, 2060934518727907591318201001788199246176557465600000⟩, + ⟨5, 8, 4, 2, 7, 8, -222722185345725930826338040128590360365498368000000⟩, + ⟨5, 8, 5, 2, 8, 8, 396907881741290509624410074922974018688516096000000⟩, + ⟨5, 8, 0, 3, 2, 8, 491931387028665196005340980469465428807131332608000000⟩, + ⟨5, 8, 1, 3, 3, 8, 83586924347360711343753011137721637457411178496000000⟩, + ⟨5, 8, 2, 3, 4, 8, -1383213680567004924188541853620111454853136384000000⟩, + ⟨5, 8, 3, 3, 5, 8, 4116650217985528410241088501923674829825140326400000⟩, + ⟨5, 8, 4, 3, 6, 8, -181391041778346232239211887864122832415673548800000⟩, + ⟨5, 8, 5, 3, 7, 8, -31267923661018492295398196041865515096866816000000⟩, + ⟨5, 8, 6, 3, 8, 8, 50649636828887985905147073159559494758301696000000⟩, + ⟨5, 8, 0, 4, 1, 8, 406044993888918689404909497284937008585386229760000000⟩, + ⟨5, 8, 1, 4, 2, 8, -144110840237931462956709439467290981861506940928000000⟩, + ⟨5, 8, 2, 4, 3, 8, -29420813212872884974328783024853610312199307264000000⟩, + ⟨5, 8, 3, 4, 4, 8, -1683565291886172061149422306502815659085896089600000⟩, + ⟨5, 8, 4, 4, 5, 8, 469057532023761522224338785477943574110037606400000⟩, + ⟨5, 8, 5, 4, 6, 8, -76574869074839402325772961875657278703534080000000⟩, + ⟨5, 8, 6, 4, 7, 8, -22101295188016471044092068937345040113467392000000⟩, + ⟨5, 8, 7, 4, 8, 8, 14412134606717779731711956224733079907860480000000⟩, + ⟨5, 8, 0, 5, 0, 8, -2512704354955629765062245886435797226725155274752000000⟩, + ⟨5, 8, 1, 5, 1, 8, -65341534355196449587136582557087872612468523008000000⟩, + ⟨5, 8, 2, 5, 2, 8, 4001889505689327752841316153823008234603020288000000⟩, + ⟨5, 8, 3, 5, 3, 8, -4238692515105084106047625884731455337525359411200000⟩, + ⟨5, 8, 4, 5, 4, 8, 65503269068130043073362401025086318201274368000000⟩, + ⟨5, 8, 5, 5, 5, 8, -21073505091128552979717731519021163416125440000000⟩, + ⟨5, 8, 6, 5, 6, 8, -37432593568007934810759829800550938515079168000000⟩, + ⟨5, 8, 7, 5, 7, 8, 6573892617308115336356590458094323083771904000000⟩, + ⟨5, 8, 8, 5, 8, 8, 3968417939285771209176729354488276839091404800000⟩, + ⟨5, 8, 1, 6, 0, 8, 712359202987564783140957724147323393212336308224000000⟩, + ⟨5, 8, 2, 6, 1, 8, -67150391414977292871732869005734550064527835136000000⟩, + ⟨5, 8, 3, 6, 2, 8, -4740049682561885705778277604397023401557255782400000⟩, + ⟨5, 8, 4, 6, 3, 8, -1637337137774694441824593746606684137154674688000000⟩, + ⟨5, 8, 5, 6, 4, 8, 175732919471263036070187454082996442482343936000000⟩, + ⟨5, 8, 6, 6, 5, 8, 3560499289041046486782591191048679113883648000000⟩, + ⟨5, 8, 7, 6, 6, 8, 1987462229102913539511174146442561960542208000000⟩, + ⟨5, 8, 8, 6, 7, 8, 1069716977218841418686432607818629038420787200000⟩, + ⟨5, 8, 2, 7, 0, 8, 547811150350497966851877727529773161289202270208000000⟩, + ⟨5, 8, 3, 7, 1, 8, 43574740257270380744683584566283787345242095616000000⟩, + ⟨5, 8, 4, 7, 2, 8, 1682622328778407831994311534215018498496659456000000⟩, + ⟨5, 8, 5, 7, 3, 8, 245006232696757597316657687320966507058429952000000⟩, + ⟨5, 8, 6, 7, 4, 8, 123562288511595387370457132929701081042124800000000⟩, + ⟨5, 8, 7, 7, 5, 8, -7140030959827712405028411697145923988619264000000⟩, + ⟨5, 8, 8, 7, 6, 8, 1599299640351600848716284703439192813941555200000⟩ +] + +def collectedFourData_11_5_39 : List CollectedFourTerm := [ + ⟨6, 0, 5, 2, 8, 1, 593731529420671230856642490128764645943441096704000000⟩, + ⟨6, 0, 5, 3, 7, 1, -46773452962483721196709480136844957166268841984000000⟩, + ⟨6, 0, 6, 3, 8, 1, 606131300937353726912748477294172132967115128832000000⟩, + ⟨6, 0, 5, 4, 6, 1, -114547773482177041523097827716496482050685009920000000⟩, + ⟨6, 0, 6, 4, 7, 1, -264489296339284635595696795775850265210376945664000000⟩, + ⟨6, 0, 7, 4, 8, 1, 776124154174049423604096705811011009723991326720000000⟩, + ⟨6, 0, 5, 5, 5, 1, -31523698529538240318151849469620859190179266560000000⟩, + ⟨6, 0, 6, 5, 6, 1, -447961092267796386383112917981349269450948345856000000⟩, + ⟨6, 0, 7, 5, 7, 1, 354018123370917811147977614668918228805700550656000000⟩, + ⟨6, 0, 8, 5, 8, 1, 712359202987564783140957724147323393212336308224000000⟩, + ⟨6, 0, 5, 6, 4, 1, 262877558867025918091516814285615953055122980864000000⟩, + ⟨6, 0, 6, 6, 5, 1, 42608993887634047630294376576935401446248022016000000⟩, + ⟨6, 0, 7, 6, 6, 1, 107029075401250544229869965834943426732765478912000000⟩, + ⟨6, 0, 8, 6, 7, 1, 192021794320138659835392331355142581481149300736000000⟩, + ⟨6, 0, 5, 7, 3, 1, 366502989606693063191819264460763831134635163648000000⟩, + ⟨6, 0, 6, 7, 4, 1, 1478687220114748252060023254370303169948916121600000000⟩, + ⟨6, 0, 7, 7, 5, 1, -384505879294923025943005156990497442004201373696000000⟩, + ⟨6, 0, 8, 7, 6, 1, 287085643339322827076086888735439859542787096576000000⟩ +] + +def collectedFourData_11_5_40 : List CollectedFourTerm := [ + ⟨6, 1, 4, 1, 8, 2, -132355768437017082504289609623318242978108434022400000⟩, + ⟨6, 1, 4, 2, 7, 2, 17946316752946628248791101991109924379223392256000000⟩, + ⟨6, 1, 5, 2, 8, 2, -223871914218575222683255189854742747791621095424000000⟩, + ⟨6, 1, 4, 3, 6, 2, 14615971403333962552347031881597031500752722329600000⟩, + ⟨6, 1, 5, 3, 7, 2, 17636359078893736622737805715635664180272431104000000⟩, + ⟨6, 1, 6, 3, 8, 2, -114273680851212936899857478604181248267094327296000000⟩, + ⟨6, 1, 4, 4, 5, 2, -37795314516993494322120709740465822852551855308800000⟩, + ⟨6, 1, 5, 4, 6, 2, 43191287725535950272209147971745093120446955520000000⟩, + ⟨6, 1, 6, 4, 7, 2, 49864056503429265886848554665602998014775918592000000⟩, + ⟨6, 1, 7, 4, 8, 2, -97548241618988159889354703014541242838485565440000000⟩, + ⟨6, 1, 4, 5, 4, 2, -5278066094876846473986364444037330699871584256000000⟩, + ⟨6, 1, 5, 5, 5, 2, 11886299418767748504200836472766304632554127360000000⟩, + ⟨6, 1, 6, 5, 6, 2, 84453917513264405245858402305510616563311443968000000⟩, + ⟨6, 1, 7, 5, 7, 2, -44495259231865982569950068900481430347854118912000000⟩, + ⟨6, 1, 8, 5, 8, 2, -67150391414977292871732869005734550064527835136000000⟩, + ⟨6, 1, 4, 6, 3, 2, 131931944095534920655762635782711518844940189696000000⟩, + ⟨6, 1, 5, 6, 4, 2, -99120392622723909901963246099420964785313808384000000⟩, + ⟨6, 1, 6, 6, 5, 2, -8033055810476972792860840107853828833775976448000000⟩, + ⟨6, 1, 7, 6, 6, 2, -13452097903857738127762572170552996446573953024000000⟩, + ⟨6, 1, 8, 6, 7, 2, -18100894316695818847555677397028839131451490304000000⟩, + ⟨6, 1, 4, 7, 2, 2, -135580895279759305418150317579735793509179850752000000⟩, + ⟨6, 1, 5, 7, 3, 2, -138193310923104111643800412937824325971149324288000000⟩, + ⟨6, 1, 6, 7, 4, 2, -278776283634994609231497629126571297335987404800000000⟩, + ⟨6, 1, 7, 7, 5, 2, 48327155153802022509397716512221936581441748992000000⟩, + ⟨6, 1, 8, 7, 6, 2, -27062068179938456266632044830729573795903832064000000⟩ +] + +def collectedFourData_11_5_41 : List CollectedFourTerm := [ + ⟨6, 2, 3, 0, 8, 3, -2246391228416124931187883766236264380263877836800000⟩, + ⟨6, 2, 3, 1, 7, 3, 30008915827062923269167311278628455251056158310400000⟩, + ⟨6, 2, 4, 1, 8, 3, -46714017963653102970869711653673524588404591820800000⟩, + ⟨6, 2, 3, 2, 6, 3, -9768528368846740337136672248532074962161657446400000⟩, + ⟨6, 2, 4, 2, 7, 3, 6334023617395207862754486174739812301985021952000000⟩, + ⟨6, 2, 5, 2, 8, 3, -39506992199363266639017285901952694491811938304000000⟩, + ⟨6, 2, 3, 3, 5, 3, -19512320296247076499540865430888598464240392601600000⟩, + ⟨6, 2, 4, 3, 6, 3, 5158602142954476459156892299092998024512877363200000⟩, + ⟨6, 2, 5, 3, 7, 3, 3112313141141723750601788806595325736028995584000000⟩, + ⟨6, 2, 6, 3, 8, 3, -13444025001944045724654106265102052455343980544000000⟩, + ⟨6, 2, 3, 4, 4, 3, 7979853394248996117706978245775396686761715302400000⟩, + ⟨6, 2, 4, 4, 5, 3, -13339584833651726828352065805592012122184325529600000⟩, + ⟨6, 2, 5, 4, 6, 3, 7622027413350371656062982956481199067805777920000000⟩, + ⟨6, 2, 6, 4, 7, 3, 5866386882236655327406799633618278314135257088000000⟩, + ⟨6, 2, 7, 4, 8, 3, -8607237835426534415042542183848563457518469120000000⟩, + ⟨6, 2, 3, 5, 3, 3, 20090782945486151102771381756366238106520440012800000⟩, + ⟨6, 2, 4, 5, 4, 3, -1862855524024655297752860815170221005919485952000000⟩, + ⟨6, 2, 5, 5, 5, 3, 2097592009500896703876798101827273609508290560000000⟩, + ⟨6, 2, 6, 5, 6, 3, 9935801228270273863922581870957281143005642752000000⟩, + ⟨6, 2, 7, 5, 7, 3, -3926070551363786211272643280426463168273842176000000⟩, + ⟨6, 2, 8, 5, 8, 3, -4740049682561885705778277604397023401557255782400000⟩, + ⟨6, 2, 3, 6, 2, 3, 22467142635094029231748778687055767194562042265600000⟩, + ⟨6, 2, 4, 6, 3, 3, 46564432205999839048296362756606392677729042432000000⟩, + ⟨6, 2, 5, 6, 4, 3, -17491915374076260823268781270099426130173886464000000⟩, + ⟨6, 2, 6, 6, 5, 3, -945069786442588384855460783072953727264489472000000⟩, + ⟨6, 2, 7, 6, 6, 3, -1186955337403111129510957893796958637184253952000000⟩, + ⟨6, 2, 8, 6, 7, 3, -1277716131685920872923503179772784263187503513600000⟩, + ⟨6, 2, 3, 7, 1, 3, -206537899433607001148810349775380510299551432704000000⟩, + ⟨6, 2, 4, 7, 2, 3, -47852303321715245536967758204420612844351913984000000⟩, + ⟨6, 2, 5, 7, 3, 3, -24387168331052129650333925919834457423214542848000000⟩, + ⟨6, 2, 6, 7, 4, 3, -32797362430442189721406650432476014808609587200000000⟩, + ⟨6, 2, 7, 7, 5, 3, 4264180588134397127790238767877819303005782016000000⟩, + ⟨6, 2, 8, 7, 6, 3, -1910272523849722142212310601943654916190476697600000⟩ +] + +def collectedFourData_11_5_42 : List CollectedFourTerm := [ + ⟨6, 3, 2, 0, 7, 4, 7641341145783082700138606372667320794475397120000000⟩, + ⟨6, 3, 3, 0, 8, 4, -4655773711978197432657012631531000202941956096000000⟩, + ⟨6, 3, 2, 1, 6, 4, -17588994126863428630243476690371044703433916416000000⟩, + ⟨6, 3, 3, 1, 7, 4, 62195186513043602933039419506892583840973324288000000⟩, + ⟨6, 3, 4, 1, 8, 4, -48408730871291766629679898075845464662147596288000000⟩, + ⟨6, 3, 2, 2, 5, 4, -36883718384207316029913098857477116814153482240000000⟩, + ⟨6, 3, 3, 2, 6, 4, -20245831184293210440065762626040918432135774208000000⟩, + ⟨6, 3, 4, 2, 7, 4, 6563812277194069607843610098846772159546654720000000⟩, + ⟨6, 3, 5, 2, 8, 4, -27293496845725558630375398233122137227353128960000000⟩, + ⟨6, 3, 2, 3, 4, 4, 2717632259937094228969066584002993575925121024000000⟩, + ⟨6, 3, 3, 3, 5, 4, -40440394685398725163854704270560194711206756352000000⟩, + ⟨6, 3, 4, 3, 6, 4, 5345748314877422687588911536790648290596093952000000⟩, + ⟨6, 3, 5, 3, 7, 4, 2150148724863719540995398920013354446786396160000000⟩, + ⟨6, 3, 6, 3, 8, 4, -6965876802252410538181491543777048270911569920000000⟩, + ⟨6, 3, 2, 4, 3, 4, 57803759624551894398745815601717297199085256704000000⟩, + ⟨6, 3, 3, 4, 4, 4, 16538700466961715371532541457034745809393942528000000⟩, + ⟨6, 3, 4, 4, 5, 4, -13823524507128759845205721093486316109227360256000000⟩, + ⟨6, 3, 5, 4, 6, 4, 5265695249957928998691606555274162859723980800000000⟩, + ⟨6, 3, 6, 4, 7, 4, 3039605199343279233485451150583470009184419840000000⟩, + ⟨6, 3, 7, 4, 8, 4, -3567798087884959697252468861287328566770401280000000⟩, + ⟨6, 3, 2, 5, 2, 4, -7862605882344145440822963711586830545760288768000000⟩, + ⟨6, 3, 3, 5, 3, 4, 41639291458863893597419501512113041364867874816000000⟩, + ⟨6, 3, 4, 5, 4, 4, -1930437064625315025661905629796795648017694720000000⟩, + ⟨6, 3, 5, 5, 5, 4, 1449126286456567231364579244536446105052774400000000⟩, + ⟨6, 3, 6, 5, 6, 4, 5148128427148172602431903302612758885155471360000000⟩, + ⟨6, 3, 7, 5, 7, 4, -1627400947189351528025152465947847870585503744000000⟩, + ⟨6, 3, 8, 5, 8, 4, -1637337137774694441824593746606684137154674688000000⟩, + ⟨6, 3, 2, 6, 1, 4, 131931944095534920655762635782711518844940189696000000⟩, + ⟨6, 3, 3, 6, 2, 4, 46564432205999839048296362756606392677729042432000000⟩, + ⟨6, 3, 4, 6, 3, 4, 48253718371830698021728314669781322588246507520000000⟩, + ⟨6, 3, 5, 6, 4, 4, -12084330152973359634405886523134156226282127360000000⟩, + ⟨6, 3, 6, 6, 5, 4, -489677734230493487078850481077983650995240960000000⟩, + ⟨6, 3, 7, 6, 6, 4, -492006502453270406932705756300139959720869888000000⟩, + ⟨6, 3, 8, 6, 7, 4, -441356570932074104443904477777656900151672832000000⟩, + ⟨6, 3, 2, 7, 0, 4, -1076297375786145483340638249441241694315256741888000000⟩, + ⟨6, 3, 3, 7, 1, 4, -428061555149581016635676937774612468527404154880000000⟩, + ⟨6, 3, 4, 7, 2, 4, -49588311475898211274017688149299435887908618240000000⟩, + ⟨6, 3, 5, 7, 3, 4, -16847931590461021649279934806075533669454315520000000⟩, + ⟨6, 3, 6, 7, 4, 4, -16993600212454651939796838794023818856759296000000000⟩, + ⟨6, 3, 7, 7, 5, 4, 1767551407273056191571444341684141649983176704000000⟩, + ⟨6, 3, 8, 7, 6, 4, -659858093487168843265192463312967814361382912000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1118.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1118.lean new file mode 100644 index 0000000000000000000000000000000000000000..220d16415a83b693c29b2f5df41b5cf8ca708654 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1118.lean @@ -0,0 +1,623 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1115 +import OAI.Analysis.LaughlinFock.Sparse1116 +import OAI.Analysis.LaughlinFock.Sparse1117 + +namespace OAI + +/-! Sparse1118. -/ +namespace LaughlinFock +def collectedFourData_11_5_43 : List CollectedFourTerm := [ + ⟨6, 4, 1, 0, 6, 5, 58833931326005166522790904772563850494975410176000000⟩, + ⟨6, 4, 2, 0, 7, 5, -5740935144453979666119798509355123641658900480000000⟩, + ⟨6, 4, 3, 0, 8, 5, 1748940036689165814333125393558780248684756992000000⟩, + ⟨6, 4, 1, 1, 5, 5, 12810138278754594766467209694626520786895110144000000⟩, + ⟨6, 4, 2, 1, 6, 5, 13214601025139386332263610304153022731086987264000000⟩, + ⟨6, 4, 3, 1, 7, 5, -23363603669602354652953835893073248847161982976000000⟩, + ⟨6, 4, 4, 1, 8, 5, 12123150419774160168306349204173214035669417984000000⟩, + ⟨6, 4, 1, 2, 4, 5, -11137824712715324021971848603109532435988086784000000⟩, + ⟨6, 4, 2, 2, 5, 5, 27710716102093273437716700440074997434637352960000000⟩, + ⟨6, 4, 3, 2, 6, 5, 7605340578121774657827154309875455420390178816000000⟩, + ⟨6, 4, 4, 2, 7, 5, -1643796111390611843263890480170779766905896960000000⟩, + ⟨6, 4, 5, 2, 8, 5, 5126397063921824383035865230523929377856552960000000⟩, + ⟨6, 4, 1, 3, 3, 5, 30845571354288418921201063807878464620311085056000000⟩, + ⟨6, 4, 2, 3, 4, 5, -2041755531276688450987310132251779927424106496000000⟩, + ⟨6, 4, 3, 3, 5, 5, 15191422466010264849635999912202907527155810304000000⟩, + ⟨6, 4, 4, 3, 6, 5, -1338752529989305219730351210244094693616910336000000⟩, + ⟨6, 4, 5, 3, 7, 5, -403851370619183428586638094946258259185500160000000⟩, + ⟨6, 4, 6, 3, 8, 5, 1046691835452383459806514006811100203592974336000000⟩, + ⟨6, 4, 1, 4, 2, 5, -53180341784234244813124997729878393639831339008000000⟩, + ⟨6, 4, 2, 4, 3, 5, -43427930880077503191405532462675608039604617216000000⟩, + ⟨6, 4, 3, 4, 4, 5, -6212758005626756359553616867389163539011731456000000⟩, + ⟨6, 4, 4, 4, 5, 5, 3461868632270641659312706771089365295282782208000000⟩, + ⟨6, 4, 5, 4, 6, 5, -989028442250299944867364812816782606519500800000000⟩, + ⟨6, 4, 6, 4, 7, 5, -456730722559216057300272138991988491180572672000000⟩, + ⟨6, 4, 7, 4, 8, 5, 446747436963511209313960445767757617189355520000000⟩, + ⟨6, 4, 1, 5, 1, 5, -24112586700476439743857769828545752748825509888000000⟩, + ⟨6, 4, 2, 5, 2, 5, 5907171211934458564778997830276962917518671872000000⟩, + ⟨6, 4, 3, 5, 3, 5, -15641787689211755642846430217564481206125330432000000⟩, + ⟨6, 4, 4, 5, 4, 5, 483445413443772994370525790560294466968616960000000⟩, + ⟨6, 4, 5, 5, 5, 5, -272181933378987624774905018785556232300134400000000⟩, + ⟨6, 4, 6, 5, 6, 5, -773557176723818085728860663317328711844364288000000⟩, + ⟨6, 4, 7, 5, 7, 5, 203777563684897599208669317517930084901584896000000⟩, + ⟨6, 4, 8, 5, 8, 5, 175732919471263036070187454082996442482343936000000⟩, + ⟨6, 4, 1, 6, 0, 5, 262877558867025918091516814285615953055122980864000000⟩, + ⟨6, 4, 2, 6, 1, 5, -99120392622723909901963246099420964785313808384000000⟩, + ⟨6, 4, 3, 6, 2, 5, -17491915374076260823268781270099426130173886464000000⟩, + ⟨6, 4, 4, 6, 3, 5, -12084330152973359634405886523134156226282127360000000⟩, + ⟨6, 4, 5, 6, 4, 5, 2269737548318820928563125733395183277818511360000000⟩, + ⟨6, 4, 6, 6, 5, 5, 73578919204564415429103006749137668793171968000000⟩, + ⟨6, 4, 7, 6, 6, 5, 61607366371644115965964256064194965659451392000000⟩, + ⟨6, 4, 8, 6, 7, 5, 47370133461415278217174446263877172413333504000000⟩, + ⟨6, 4, 2, 7, 0, 5, 808621590457869392568001042847159863348247396352000000⟩, + ⟨6, 4, 3, 7, 1, 5, 160801198314776574737052742903700664889387253760000000⟩, + ⟨6, 4, 4, 7, 2, 5, 12418556493110667809159445230961037083483832320000000⟩, + ⟨6, 4, 5, 7, 3, 5, 3164460293479083253989005467432623978074603520000000⟩, + ⟨6, 4, 6, 7, 4, 5, 2553456384925834617350316139002414809009356800000000⟩, + ⟨6, 4, 7, 7, 5, 5, -221326723499815579443816457733298589098049536000000⟩, + ⟨6, 4, 8, 7, 6, 5, 70821571519987285652873726303488436563083264000000⟩ +] + +def collectedFourData_11_5_44 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 5, 6, -7931546461872261972161148863606497845002108928000000⟩, + ⟨6, 5, 1, 0, 6, 6, 9536206251532120056035638681507377204632223744000000⟩, + ⟨6, 5, 2, 0, 7, 6, -465265029722600794945580558410609850906050560000000⟩, + ⟨6, 5, 3, 0, 8, 6, 94493390325015214481793251476874939351433216000000⟩, + ⟨6, 5, 0, 1, 4, 6, -5702648049232104236328689387121155150280916992000000⟩, + ⟨6, 5, 1, 1, 5, 6, 2076354885413793928301975059795156621470990336000000⟩, + ⟨6, 5, 2, 1, 6, 6, 1070956487755019140804524816717614309135351808000000⟩, + ⟨6, 5, 3, 1, 7, 6, -1262310928126498421675676611475946019538075648000000⟩, + ⟨6, 5, 4, 1, 8, 6, 491250797863198190167650197596075409302093824000000⟩, + ⟨6, 5, 0, 2, 3, 6, -2232127669436722789142341169647253143966187520000000⟩, + ⟨6, 5, 1, 2, 4, 6, -1805294857236878519570908641521462725098602496000000⟩, + ⟨6, 5, 2, 2, 5, 6, 2245771259640526052937246669430407394618245120000000⟩, + ⟨6, 5, 3, 2, 6, 6, 410908550737730149059209796498198052070227968000000⟩, + ⟨6, 5, 4, 2, 7, 6, -66609430988162542106080625947486563399106560000000⟩, + ⟨6, 5, 5, 2, 8, 6, 166184304284962696068290123305392062016258048000000⟩, + ⟨6, 5, 0, 3, 2, 6, 9808114302977394793144162404461387373896269824000000⟩, + ⟨6, 5, 1, 3, 3, 6, 4999661313654698412302316185841331202596798464000000⟩, + ⟨6, 5, 2, 3, 4, 6, -165470855190454077278411996097271269175590912000000⟩, + ⟨6, 5, 3, 3, 5, 6, 820776574701993942474853206598232330093985792000000⟩, + ⟨6, 5, 4, 3, 6, 6, -54248543136601024990789646479826830749597696000000⟩, + ⟨6, 5, 5, 3, 7, 6, -13091798825573976639761998575037065260433408000000⟩, + ⟨6, 5, 6, 3, 8, 6, 28275829383105047212562153068476399001534464000000⟩, + ⟨6, 5, 0, 4, 1, 6, 8095713786976164294167832867627442585762529280000000⟩, + ⟨6, 5, 1, 4, 2, 6, -8619833765167231186256943463619020776749924352000000⟩, + ⟨6, 5, 2, 4, 3, 6, -3519548129929633139305257627241001504842186752000000⟩, + ⟨6, 5, 3, 4, 4, 6, -335668779320699769945561603483192783890546688000000⟩, + ⟨6, 5, 4, 4, 5, 6, 140280840277836986053921841770568390214156288000000⟩, + ⟨6, 5, 5, 4, 6, 6, -32061699775488351575287908718884577911767040000000⟩, + ⟨6, 5, 6, 4, 7, 6, -12338340233183360598963104419954229067644928000000⟩, + ⟨6, 5, 7, 4, 8, 6, 10344554591952679308436387090883594252451840000000⟩, + ⟨6, 5, 0, 5, 0, 6, -50098229494671023012774153570003349979325792256000000⟩, + ⟨6, 5, 1, 5, 1, 6, -3908333080098912713237616232694453298184323072000000⟩, + ⟨6, 5, 2, 5, 2, 6, 478737369494979369288322645818017594090717184000000⟩, + ⟨6, 5, 3, 5, 3, 6, -845109333934467571940555596948834834590990336000000⟩, + ⟨6, 5, 4, 5, 4, 6, 19590035333569787908621826343013999769026560000000⟩, + ⟨6, 5, 5, 5, 5, 6, -8823422117622549549815153301465059788062720000000⟩, + ⟨6, 5, 6, 5, 6, 6, -20897240244226757809264839445894057911386112000000⟩, + ⟨6, 5, 7, 5, 7, 6, 4718523169335407311980182389488214062661632000000⟩, + ⟨6, 5, 8, 5, 8, 6, 3560499289041046486782591191048679113883648000000⟩, + ⟨6, 5, 1, 6, 0, 6, 42608993887634047630294376576935401446248022016000000⟩, + ⟨6, 5, 2, 6, 1, 6, -8033055810476972792860840107853828833775976448000000⟩, + ⟨6, 5, 3, 6, 2, 6, -945069786442588384855460783072953727264489472000000⟩, + ⟨6, 5, 4, 6, 3, 6, -489677734230493487078850481077983650995240960000000⟩, + ⟨6, 5, 5, 6, 4, 6, 73578919204564415429103006749137668793171968000000⟩, + ⟨6, 5, 6, 6, 5, 6, 1987695800380762540918356678197660123922432000000⟩, + ⟨6, 5, 7, 6, 6, 6, 1426534797892874637510325175983193890750464000000⟩, + ⟨6, 5, 8, 6, 7, 6, 959759429357964753358335185380431492022272000000⟩, + ⟨6, 5, 2, 7, 0, 6, 65533460812942162655242340591830846187444895744000000⟩, + ⟨6, 5, 3, 7, 1, 6, 8687919584626024550163279318994593610444308480000000⟩, + ⟨6, 5, 4, 7, 2, 6, 503221157398083611445541900742329789600235520000000⟩, + ⟨6, 5, 5, 7, 3, 6, 102583476416650400241464339025669543193214976000000⟩, + ⟨6, 5, 6, 7, 4, 6, 68980281140874255490655849881623218828083200000000⟩, + ⟨6, 5, 7, 7, 5, 6, -5124878587918701035451231866534154586816512000000⟩, + ⟨6, 5, 8, 7, 6, 6, 1434905627268766725342669180671389914365952000000⟩ +] + +def collectedFourData_11_5_45 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 5, 7, -39846333220396327208479247225839455290410401792000000⟩, + ⟨6, 6, 1, 0, 6, 7, 23953894349833986746657299467510451846049169408000000⟩, + ⟨6, 6, 2, 0, 7, 7, -779129496760969572901659921879525758368481280000000⟩, + ⟨6, 6, 3, 0, 8, 7, 118678467563522975079577951122928155708358656000000⟩, + ⟨6, 6, 0, 1, 4, 7, -28648841118268803450039553582251339293380313088000000⟩, + ⟨6, 6, 1, 1, 5, 7, 5215573598774962364848425791597783888431153152000000⟩, + ⟨6, 6, 2, 1, 6, 7, 1793416087718769091228658784006531962533576704000000⟩, + ⟨6, 6, 3, 1, 7, 7, -1585392650464381605180604579572998855844691968000000⟩, + ⟨6, 6, 4, 1, 8, 7, 493587047129821233531274216412173684805153587200000⟩, + ⟨6, 6, 0, 2, 3, 7, -11213715173251006387423511378990057926195937280000000⟩, + ⟨6, 6, 1, 2, 4, 7, -4534700817067910212107909213992006664975286272000000⟩, + ⟨6, 6, 2, 2, 5, 7, 3760752516489798426423790685643702620714434560000000⟩, + ⟨6, 6, 3, 2, 6, 7, 516078393870392545702793612188638871277273088000000⟩, + ⟨6, 6, 4, 2, 7, 7, -66926206523129934513471935242576508976365568000000⟩, + ⟨6, 6, 5, 2, 8, 7, 139145524696228019432712472202052691833126912000000⟩, + ⟨6, 6, 0, 3, 2, 7, 49273794544212892610106250036321656064689831936000000⟩, + ⟨6, 6, 1, 3, 3, 7, 12558595707071202633716537266754246008476008448000000⟩, + ⟨6, 6, 2, 3, 4, 7, -277096312632849393583028906128653671680966656000000⟩, + ⟨6, 6, 3, 3, 5, 7, 1030849943711704751347058534141949427499139072000000⟩, + ⟨6, 6, 4, 3, 6, 7, -54506533799760306549447080764297802005925068800000⟩, + ⟨6, 6, 5, 3, 7, 7, -10961716418647289838218115382246942024138752000000⟩, + ⟨6, 6, 6, 3, 8, 7, 20293072283271073420879249012580168528560128000000⟩, + ⟨6, 6, 0, 4, 1, 7, 40671073511767840795786408251970042738948177920000000⟩, + ⟨6, 6, 1, 4, 2, 7, -21652068115742986521103789441640017708726616064000000⟩, + ⟨6, 6, 2, 4, 3, 7, -5893810168653820546232360457500303566439448576000000⟩, + ⟨6, 6, 3, 4, 4, 7, -421581405870597384409161637793819297587396608000000⟩, + ⟨6, 6, 4, 4, 5, 7, 140947976110788093709255478801775711261976166400000⟩, + ⟨6, 6, 5, 4, 6, 7, -26845146761052700697868884692225335503093760000000⟩, + ⟨6, 6, 6, 4, 7, 7, -8855012767801839636462262428083764127072256000000⟩, + ⟨6, 6, 7, 4, 8, 7, 6496093972168264600739947788124400878878720000000⟩, + ⟨6, 6, 0, 5, 0, 7, -251682412224731982370624725746522234743563485184000000⟩, + ⟨6, 6, 1, 5, 1, 7, -9817300005398826746076434895704588766469423104000000⟩, + ⟨6, 6, 2, 5, 2, 7, 801690180750704261957634136222759261927636992000000⟩, + ⟨6, 6, 3, 5, 3, 7, -1061410542367012559764634899997412858135576576000000⟩, + ⟨6, 6, 4, 5, 4, 7, 19683199977536263491987768240437089762541568000000⟩, + ⟨6, 6, 5, 5, 5, 7, -7387819839276998972351538230323991732551680000000⟩, + ⟨6, 6, 6, 5, 6, 7, -14997586845334353932108071164263563027021824000000⟩, + ⟨6, 6, 7, 5, 7, 7, 2963101953340849180980878216343369868640256000000⟩, + ⟨6, 6, 8, 5, 8, 7, 1987462229102913539511174146442561960542208000000⟩, + ⟨6, 6, 1, 6, 0, 7, 107029075401250544229869965834943426732765478912000000⟩, + ⟨6, 6, 2, 6, 1, 7, -13452097903857738127762572170552996446573953024000000⟩, + ⟨6, 6, 3, 6, 2, 7, -1186955337403111129510957893796958637184253952000000⟩, + ⟨6, 6, 4, 6, 3, 7, -492006502453270406932705756300139959720869888000000⟩, + ⟨6, 6, 5, 6, 4, 7, 61607366371644115965964256064194965659451392000000⟩, + ⟨6, 6, 6, 6, 5, 7, 1426534797892874637510325175983193890750464000000⟩, + ⟨6, 6, 7, 6, 6, 7, 895824370136647790761255353503666889818112000000⟩, + ⟨6, 6, 8, 6, 7, 7, 535735429226294349177931272852545954906112000000⟩, + ⟨6, 6, 2, 7, 0, 7, 109741865565599575410616052375740216455852982272000000⟩, + ⟨6, 6, 3, 7, 1, 7, 10911546078218986159328364207966455852622151680000000⟩, + ⟨6, 6, 4, 7, 2, 7, 505614334294760861912446515416507840364281856000000⟩, + ⟨6, 6, 5, 7, 3, 7, 85892778578425283304676077223360130180972544000000⟩, + ⟨6, 6, 6, 7, 4, 7, 49505951261274847079258286751355865818726400000000⟩, + ⟨6, 6, 7, 7, 5, 7, -3218281909302448659502091947949911279927296000000⟩, + ⟨6, 6, 8, 7, 6, 7, 800960906045281584594621305194265173819392000000⟩ +] + +def collectedFourData_11_5_46 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 5, 8, -107232979076579766510222896505113967534029144064000000⟩, + ⟨6, 7, 1, 0, 6, 8, 42975890025827599749258996782137203347605684224000000⟩, + ⟨6, 7, 2, 0, 7, 8, -1048382250908709440742129932453190048814202880000000⟩, + ⟨6, 7, 3, 0, 8, 8, 127753242022937933700979526936391769832344780800000⟩, + ⟨6, 7, 0, 1, 4, 8, -77098702237199741183705207249486804030268112896000000⟩, + ⟨6, 7, 1, 1, 5, 8, 9357305919824936587653477881713295693715603456000000⟩, + ⟨6, 7, 2, 1, 6, 8, 2413187541576698752445114353414424264215363584000000⟩, + ⟨6, 7, 3, 1, 7, 8, -1706620039290224276507591103706199057563543142400000⟩, + ⟨6, 7, 4, 1, 8, 8, 442774405402084329257872247332783421360229580800000⟩, + ⟨6, 7, 0, 2, 3, 8, -30177935768715379987234771014311569696499957760000000⟩, + ⟨6, 7, 1, 2, 4, 8, -8135746144997575777368128949282127579044642816000000⟩, + ⟨6, 7, 2, 2, 5, 8, 5060399079663849058033715459483670335465717760000000⟩, + ⟨6, 7, 3, 2, 6, 8, 555540438872314946728548338086898858593773158400000⟩, + ⟨6, 7, 4, 2, 7, 8, -60036444374728393320173707048638090263396352000000⟩, + ⟨6, 7, 5, 2, 8, 8, 106989512190100031118348111118277534489247744000000⟩, + ⟨6, 7, 0, 3, 2, 8, 132603814513066426301838604556773742871903731712000000⟩, + ⟨6, 7, 1, 3, 3, 8, 22531485699303968714919855490221623692801081344000000⟩, + ⟨6, 7, 2, 3, 4, 8, -372855676962842491574264364607342829660798976000000⟩, + ⟨6, 7, 3, 3, 5, 8, 1109674105606761078533449381851951408778680729600000⟩, + ⟨6, 7, 4, 3, 6, 8, -48895322991265268785428783784973950740804403200000⟩, + ⟨6, 7, 5, 3, 7, 8, -8428504581499314492157588124925202293325824000000⟩, + ⟨6, 7, 6, 3, 8, 8, 13652991503103002438810820953493839642886144000000⟩, + ⟨6, 7, 0, 4, 1, 8, 109452489662888469878935660310362698990370160640000000⟩, + ⟨6, 7, 1, 4, 2, 8, -38846163575082637201099769837825000954702856192000000⟩, + ⟨6, 7, 2, 4, 3, 8, -7930602033075880309876260096687333074635063296000000⟩, + ⟨6, 7, 3, 4, 4, 8, -453817718430927691696536395312242659179259494400000⟩, + ⟨6, 7, 4, 4, 5, 8, 126437994428705193120689376836806890571274649600000⟩, + ⟨6, 7, 5, 4, 6, 8, -20641333330029341553114046012611861015429120000000⟩, + ⟨6, 7, 6, 4, 7, 8, -5957570760654653573578441808875826643468288000000⟩, + ⟨6, 7, 7, 4, 8, 8, 3884899550056944435267766894411786192158720000000⟩, + ⟨6, 7, 0, 5, 0, 8, -677318404550785629266741977297760015108253155328000000⟩, + ⟨6, 7, 1, 5, 1, 8, -17613303257534853463281340275347281052342157312000000⟩, + ⟨6, 7, 2, 5, 2, 8, 1078739490316954358785457074098521282269151232000000⟩, + ⟨6, 7, 3, 5, 3, 8, -1142571526988509776463533183507722897170681036800000⟩, + ⟨6, 7, 4, 5, 4, 8, 17656900068878221893298852108636092578660352000000⟩, + ⟨6, 7, 5, 5, 5, 8, -5680522190549590514674298020819286265692160000000⟩, + ⟨6, 7, 6, 5, 6, 8, -10090237836249080203537724211079926673047552000000⟩, + ⟨6, 7, 7, 5, 7, 8, 1772042321836126626988124496797985989984256000000⟩, + ⟨6, 7, 8, 5, 8, 8, 1069716977218841418686432607818629038420787200000⟩, + ⟨6, 7, 1, 6, 0, 8, 192021794320138659835392331355142581481149300736000000⟩, + ⟨6, 7, 2, 6, 1, 8, -18100894316695818847555677397028839131451490304000000⟩, + ⟨6, 7, 3, 6, 2, 8, -1277716131685920872923503179772784263187503513600000⟩, + ⟨6, 7, 4, 6, 3, 8, -441356570932074104443904477777656900151672832000000⟩, + ⟨6, 7, 5, 6, 4, 8, 47370133461415278217174446263877172413333504000000⟩, + ⟨6, 7, 6, 6, 5, 8, 959759429357964753358335185380431492022272000000⟩, + ⟨6, 7, 7, 6, 6, 8, 535735429226294349177931272852545954906112000000⟩, + ⟨6, 7, 8, 6, 7, 8, 288350276824966515567517760382897058794700800000⟩, + ⟨6, 7, 2, 7, 0, 8, 147666626047250129261099449434988805816542298112000000⟩, + ⟨6, 7, 3, 7, 1, 8, 11745899787836533099947025408158298557093249024000000⟩, + ⟨6, 7, 4, 7, 2, 8, 453563535615332421882328490911236741906038784000000⟩, + ⟨6, 7, 5, 7, 3, 8, 66043277358866494889337220581407651820208128000000⟩, + ⟨6, 7, 6, 7, 4, 8, 33307146522136505794893234470474352898867200000000⟩, + ⟨6, 7, 7, 7, 5, 8, -1924649180718723219094678328756895058231296000000⟩, + ⟨6, 7, 8, 7, 6, 8, 431103276700740106833753414149547641064652800000⟩ +] + +def collectedFourData_11_5_47 : List CollectedFourTerm := [ + ⟨7, 0, 4, 1, 8, 2, 1079754923764072841304422734578168233627638510387200000⟩, + ⟨7, 0, 4, 2, 7, 2, -146405586294071049897056343451995498937810157568000000⟩, + ⟨7, 0, 5, 2, 8, 2, 1826341265851386338249714960731597492146218729472000000⟩, + ⟨7, 0, 4, 3, 6, 2, -119236715367298915150811997362711517417763032268800000⟩, + ⟨7, 0, 5, 3, 7, 2, -143876959633750388311092640657269943823354560512000000⟩, + ⟨7, 0, 6, 3, 8, 2, 932241722539329433533258258272152788858398834688000000⟩, + ⟨7, 0, 4, 4, 5, 2, 308333194894752095217677365405387629349711537766400000⟩, + ⟨7, 0, 5, 4, 6, 2, -352353404283625540984837278131370706862667202560000000⟩, + ⟨7, 0, 6, 4, 7, 2, -406789678789470277847722996522405541668114661376000000⟩, + ⟨7, 0, 7, 4, 8, 2, 795796023372804286507665520092687819021295288320000000⟩, + ⟨7, 0, 4, 5, 4, 2, 43058326215735931632297079375058694871940333568000000⟩, + ⟨7, 0, 5, 5, 5, 2, -96968122162774105674296236909974369750566830080000000⟩, + ⟨7, 0, 6, 5, 6, 2, -688972867166765197151791110477921874584539234304000000⟩, + ⟨7, 0, 7, 5, 7, 2, 362991169989152042233071351469266815792852238336000000⟩, + ⟨7, 0, 8, 5, 8, 2, 547811150350497966851877727529773161289202270208000000⟩, + ⟨7, 0, 4, 6, 3, 2, -1076297375786145483340638249441241694315256741888000000⟩, + ⟨7, 0, 5, 6, 4, 2, 808621590457869392568001042847159863348247396352000000⟩, + ⟨7, 0, 6, 6, 5, 2, 65533460812942162655242340591830846187444895744000000⟩, + ⟨7, 0, 7, 6, 6, 2, 109741865565599575410616052375740216455852982272000000⟩, + ⟨7, 0, 8, 6, 7, 2, 147666626047250129261099449434988805816542298112000000⟩, + ⟨7, 0, 4, 7, 2, 2, 1106065424842623912995770272382966369281015545856000000⟩, + ⟨7, 0, 5, 7, 3, 2, 1127377443858720938545987804292844996958579851264000000⟩, + ⟨7, 0, 6, 7, 4, 2, 2274249686569377079286824432415421329964426854400000000⟩, + ⟨7, 0, 7, 7, 5, 2, -394251677467757240946406983481913277293134872576000000⟩, + ⟨7, 0, 8, 7, 6, 2, 220771649846394355863704229204840754136997691392000000⟩ +] + +def collectedFourData_11_5_48 : List CollectedFourTerm := [ + ⟨7, 1, 3, 0, 8, 3, 20650820318309014207229231723371896065293811712000000⟩, + ⟨7, 1, 3, 1, 7, 3, -275868566816332040565712894239304321047919067136000000⟩, + ⟨7, 1, 4, 1, 8, 3, 429436680089707183725803838642924366300312502272000000⟩, + ⟨7, 1, 3, 2, 6, 3, 89800975701633149716635503277456885199065317376000000⟩, + ⟨7, 1, 4, 2, 7, 3, -58227962235669847120759634456230513727955271680000000⟩, + ⟨7, 1, 5, 2, 8, 3, 363183307923225671636315318302112917201732239360000000⟩, + ⟨7, 1, 3, 3, 5, 3, 179374552096697498127993376222937592832871890944000000⟩, + ⟨7, 1, 4, 3, 6, 3, -47422445654271875757512039319136320761823756288000000⟩, + ⟨7, 1, 5, 3, 7, 3, -28611142457739266883389077545704657238160834560000000⟩, + ⟨7, 1, 6, 3, 8, 3, 123589400260323600675525242299050472325995560960000000⟩, + ⟨7, 1, 3, 4, 4, 3, -73357889100766322479127370815114231462196412416000000⟩, + ⟨7, 1, 4, 4, 5, 3, 122629293613655771179077631405907624978980798464000000⟩, + ⟨7, 1, 5, 4, 6, 3, -70068435356785025411080283342906352638676172800000000⟩, + ⟨7, 1, 6, 4, 7, 3, -53929030656058534894042050888348665693255761920000000⟩, + ⟨7, 1, 7, 4, 8, 3, 79125363261709789550575676301083201367755980800000000⟩, + ⟨7, 1, 3, 5, 3, 3, -184692293761274678959394729480124159751253655552000000⟩, + ⟨7, 1, 4, 5, 4, 3, 17125019996061162419776020873311263523529031680000000⟩, + ⟨7, 1, 5, 5, 5, 3, -19282925939781868750135501002625238014781030400000000⟩, + ⟨7, 1, 6, 5, 6, 3, -91338696166523279615999490494438132141449543680000000⟩, + ⟨7, 1, 7, 5, 7, 3, 36091922229585559005703307704117376440955043840000000⟩, + ⟨7, 1, 8, 5, 8, 3, 43574740257270380744683584566283787345242095616000000⟩, + ⟨7, 1, 3, 6, 2, 3, -206537899433607001148810349775380510299551432704000000⟩, + ⟨7, 1, 4, 6, 3, 3, -428061555149581016635676937774612468527404154880000000⟩, + ⟨7, 1, 5, 6, 4, 3, 160801198314776574737052742903700664889387253760000000⟩, + ⟨7, 1, 6, 6, 5, 3, 8687919584626024550163279318994593610444308480000000⟩, + ⟨7, 1, 7, 6, 6, 3, 10911546078218986159328364207966455852622151680000000⟩, + ⟨7, 1, 8, 6, 7, 3, 11745899787836533099947025408158298557093249024000000⟩, + ⟨7, 1, 3, 7, 1, 3, 1898679533721143700214633677666941747303137935360000000⟩, + ⟨7, 1, 4, 7, 2, 3, 439900808556268735140490591323749887391626690560000000⟩, + ⟨7, 1, 5, 7, 3, 3, 224188478349784152407779822789423507142155960320000000⟩, + ⟨7, 1, 6, 7, 4, 3, 301502440847341842328147204789275424821608448000000000⟩, + ⟨7, 1, 7, 7, 5, 3, -39200129530630689901218893469532974220773949440000000⟩, + ⟨7, 1, 8, 7, 6, 3, 17560919108839997075896540089256473510316867584000000⟩ +] + +def collectedFourData_11_5_49 : List CollectedFourTerm := [ + ⟨7, 2, 2, 0, 7, 4, -7852684054538956628017740327824293086300733440000000⟩, + ⟨7, 2, 3, 0, 8, 4, 4784542306394586125691421616276718956474007552000000⟩, + ⟨7, 2, 2, 1, 6, 4, 18075467523344714914029623055613079472561979392000000⟩, + ⟨7, 2, 3, 1, 7, 4, -63915370362646314092426319508155944213629894656000000⟩, + ⟨7, 2, 4, 1, 8, 4, 49747611284603115933936430166234147935701958656000000⟩, + ⟨7, 2, 2, 2, 5, 4, 37903841969888692568238689863957816254796922880000000⟩, + ⟨7, 2, 3, 2, 6, 4, 20805786926490402357866355850333289959649181696000000⟩, + ⟨7, 2, 4, 2, 7, 4, -6745353076475783899087075679228601226116464640000000⟩, + ⟨7, 2, 5, 2, 8, 4, 28048375721494398160296517379121590102938091520000000⟩, + ⟨7, 2, 2, 3, 4, 4, -2792796068984000128329863369607590650878885888000000⟩, + ⟨7, 2, 3, 3, 5, 4, 41558888216964757445308397128790805827523969024000000⟩, + ⟨7, 2, 4, 3, 6, 4, -5493600109057098167625775822302671944468660224000000⟩, + ⟨7, 2, 5, 3, 7, 4, -2209617171187596243421710323243273645111377920000000⟩, + ⟨7, 2, 6, 3, 8, 4, 7158537833521185351167851364871932591776727040000000⟩, + ⟨7, 2, 2, 4, 3, 4, -59402486139048611756988550336360815163550466048000000⟩, + ⟨7, 2, 3, 4, 4, 4, -16996125020720677023099995672809320405622849536000000⟩, + ⟨7, 2, 4, 4, 5, 4, 14205853187769716312655721431670118950184681472000000⟩, + ⟨7, 2, 5, 4, 6, 4, -5411332950136023976329693774067995843860889600000000⟩, + ⟨7, 2, 6, 4, 7, 4, -3123674080975818066806159705070326857680814080000000⟩, + ⟨7, 2, 7, 4, 8, 4, 3666475638247093126628204666519651085566607360000000⟩, + ⟨7, 2, 2, 5, 2, 4, 8080068493405906267003442375814200712983740416000000⟩, + ⟨7, 2, 3, 5, 3, 4, -42790943872695245103759367391998258230111240192000000⟩, + ⟨7, 2, 4, 5, 4, 4, 1983828763363070430363017905623886627224944640000000⟩, + ⟨7, 2, 5, 5, 5, 4, -1489205973868945284886403936989677819317452800000000⟩, + ⟨7, 2, 6, 5, 6, 4, -5290514484213917825368088544223321460645560320000000⟩, + ⟨7, 2, 7, 5, 7, 4, 1672411324730323764879037200820978433579286528000000⟩, + ⟨7, 2, 8, 5, 8, 4, 1682622328778407831994311534215018498496659456000000⟩, + ⟨7, 2, 2, 6, 1, 4, -135580895279759305418150317579735793509179850752000000⟩, + ⟨7, 2, 3, 6, 2, 4, -47852303321715245536967758204420612844351913984000000⟩, + ⟨7, 2, 4, 6, 3, 4, -49588311475898211274017688149299435887908618240000000⟩, + ⟨7, 2, 5, 6, 4, 4, 12418556493110667809159445230961037083483832320000000⟩, + ⟨7, 2, 6, 6, 5, 4, 503221157398083611445541900742329789600235520000000⟩, + ⟨7, 2, 7, 6, 6, 4, 505614334294760861912446515416507840364281856000000⟩, + ⟨7, 2, 8, 6, 7, 4, 453563535615332421882328490911236741906038784000000⟩, + ⟨7, 2, 2, 7, 0, 4, 1106065424842623912995770272382966369281015545856000000⟩, + ⟨7, 2, 3, 7, 1, 4, 439900808556268735140490591323749887391626690560000000⟩, + ⟨7, 2, 4, 7, 2, 4, 50959816528174556119139780608161846509048954880000000⟩, + ⟨7, 2, 5, 7, 3, 4, 17313908805836754086613878356203717689333514240000000⟩, + ⟨7, 2, 6, 7, 4, 4, 17463606305706564940193967670801242576125952000000000⟩, + ⟨7, 2, 7, 7, 5, 4, -1816438042310254729361929275046220471413506048000000⟩, + ⟨7, 2, 8, 7, 6, 4, 678108335975117888213112744671519301376671744000000⟩ +] + +def collectedFourData_11_5_50 : List CollectedFourTerm := [ + ⟨7, 3, 1, 0, 6, 5, 82026064964347548803268233946619309787952709632000000⟩, + ⟨7, 3, 2, 0, 7, 5, -8003992058693908309457846306020135454229135360000000⟩, + ⟨7, 3, 3, 0, 8, 5, 2438366191667422736381740209481260043541151744000000⟩, + ⟨7, 3, 1, 1, 5, 5, 17859850786325939191243733434073749553946820608000000⟩, + ⟨7, 3, 2, 1, 6, 5, 18423751358034853896923109539826306988740968448000000⟩, + ⟨7, 3, 3, 1, 7, 5, -32573455983843006938809227527821658711478239232000000⟩, + ⟨7, 3, 4, 1, 8, 5, 16902054673089842837737642734836319803815231488000000⟩, + ⟨7, 3, 1, 2, 4, 5, -15528316956832124431456972651609437664431833088000000⟩, + ⟨7, 3, 2, 2, 5, 5, 38634185205199879442273244949604659322651934720000000⟩, + ⟨7, 3, 3, 2, 6, 5, 10603339710213511048180606296322182852863066112000000⟩, + ⟨7, 3, 4, 2, 7, 5, -2291774892178082600826646460030044884141342720000000⟩, + ⟨7, 3, 5, 2, 8, 5, 7147205177710567843798434748223212078466334720000000⟩, + ⟨7, 3, 1, 3, 3, 5, 43004789629805563175631406715774898022008225792000000⟩, + ⟨7, 3, 2, 3, 4, 5, -2846608548420952809999425737173619199937871872000000⟩, + ⟨7, 3, 3, 3, 5, 5, 21179829020656007845912777919724933452270665728000000⟩, + ⟨7, 3, 4, 3, 6, 5, -1866484178791383232567898000282616181662154752000000⟩, + ⟨7, 3, 5, 3, 7, 5, -563048193716536104404119792878813227117445120000000⟩, + ⟨7, 3, 6, 3, 8, 5, 1459294161675716421442276611721735757472202752000000⟩, + ⟨7, 3, 1, 4, 2, 5, -74143849844888428156461630216455027241837920256000000⟩, + ⟨7, 3, 2, 4, 3, 5, -60547072061150800645567037678608914080870694912000000⟩, + ⟨7, 3, 3, 4, 4, 5, -8661805871063029358198163361934676993446510592000000⟩, + ⟨7, 3, 4, 4, 5, 5, 4826525355839242588092939661473237672872902656000000⟩, + ⟨7, 3, 5, 4, 6, 5, -1378900056943025251800387326807199402531225600000000⟩, + ⟨7, 3, 6, 4, 7, 5, -636772404554517342809406298989386506388373504000000⟩, + ⟨7, 3, 7, 4, 8, 5, 622853742068861487214007450444520351219056640000000⟩, + ⟨7, 3, 1, 5, 1, 5, -33617685552784225485227523389459709287429308416000000⟩, + ⟨7, 3, 2, 5, 2, 5, 8235757812966125676231605713721032673700347904000000⟩, + ⟨7, 3, 3, 5, 3, 5, -21807726667871022098832315409693380675920461824000000⟩, + ⟨7, 3, 4, 5, 4, 5, 674017934822703830399676436534178410628382720000000⟩, + ⟨7, 3, 5, 5, 5, 5, -379475116591405508360793872644591626013900800000000⟩, + ⟨7, 3, 6, 5, 6, 5, -1078490758674473417086149775962959324922249216000000⟩, + ⟨7, 3, 7, 5, 7, 5, 284105979328049034252161921135605939722780672000000⟩, + ⟨7, 3, 8, 5, 8, 5, 245006232696757597316657687320966507058429952000000⟩, + ⟨7, 3, 1, 6, 0, 5, 366502989606693063191819264460763831134635163648000000⟩, + ⟨7, 3, 2, 6, 1, 5, -138193310923104111643800412937824325971149324288000000⟩, + ⟨7, 3, 3, 6, 2, 5, -24387168331052129650333925919834457423214542848000000⟩, + ⟨7, 3, 4, 6, 3, 5, -16847931590461021649279934806075533669454315520000000⟩, + ⟨7, 3, 5, 6, 4, 5, 3164460293479083253989005467432623978074603520000000⟩, + ⟨7, 3, 6, 6, 5, 5, 102583476416650400241464339025669543193214976000000⟩, + ⟨7, 3, 7, 6, 6, 5, 85892778578425283304676077223360130180972544000000⟩, + ⟨7, 3, 8, 6, 7, 5, 66043277358866494889337220581407651820208128000000⟩, + ⟨7, 3, 2, 7, 0, 5, 1127377443858720938545987804292844996958579851264000000⟩, + ⟨7, 3, 3, 7, 1, 5, 224188478349784152407779822789423507142155960320000000⟩, + ⟨7, 3, 4, 7, 2, 5, 17313908805836754086613878356203717689333514240000000⟩, + ⟨7, 3, 5, 7, 3, 5, 4411879671472538966976965703849980570778992640000000⟩, + ⟨7, 3, 6, 7, 4, 5, 3560020120922560809503449090279734978910617600000000⟩, + ⟨7, 3, 7, 7, 5, 5, -308572957661892106994621658490557568911409152000000⟩, + ⟨7, 3, 8, 7, 6, 5, 98739191746106113873793130564365056840040448000000⟩ +] + +def collectedFourData_11_5_51 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 5, 6, -275253539659865902264032807818645387862658252800000000⟩, + ⟨7, 4, 1, 0, 6, 6, 330941076658731337379776272447513216338519654400000000⟩, + ⟨7, 4, 2, 0, 7, 6, -16146390483460436394259327597386344228192256000000000⟩, + ⟨7, 4, 3, 0, 8, 6, 3279264678893669586450027299743480699001241600000000⟩, + ⟨7, 4, 0, 1, 4, 6, -197902649695257577619077985999217152333394739200000000⟩, + ⟨7, 4, 1, 1, 5, 6, 72057074184407201750801576372868066032851353600000000⟩, + ⟨7, 4, 2, 1, 6, 6, 37166089298389131159404526481162225090088140800000000⟩, + ⟨7, 4, 3, 1, 7, 6, -43806785068763436577436658719669743690501324800000000⟩, + ⟨7, 4, 4, 1, 8, 6, 17048191247770855332622497833767472917276262400000000⟩, + ⟨7, 4, 0, 2, 3, 6, -77462956932632539142767789634197161510961152000000000⟩, + ⟨7, 4, 1, 2, 4, 6, -62650304322482063771570984292589059387791769600000000⟩, + ⟨7, 4, 2, 2, 5, 6, 77936439186732458613000237528238583722278912000000000⟩, + ⟨7, 4, 3, 2, 6, 6, 14260022759844910194309487186917311535434956800000000⟩, + ⟨7, 4, 4, 2, 7, 6, -2311589769076810965355377013066251796217856000000000⟩, + ⟨7, 4, 5, 2, 8, 6, 5767200407920259784409603934554548501007564800000000⟩, + ⟨7, 4, 0, 3, 2, 6, 340377276015579302019782820597501980869813862400000000⟩, + ⟨7, 4, 1, 3, 3, 6, 173506450513699853747281749981260765878183526400000000⟩, + ⟨7, 4, 2, 3, 4, 6, -5742441126792091538406677255623317904372531200000000⟩, + ⟨7, 4, 3, 3, 5, 6, 28483935452266743562756300399923055012557619200000000⟩, + ⟨7, 4, 4, 3, 6, 6, -1882621956704215652491042273370378830715289600000000⟩, + ⟨7, 4, 5, 3, 7, 6, -454333084295326924715961269580976819588300800000000⟩, + ⟨7, 4, 6, 3, 8, 6, 981274227155053984567096831346745798977126400000000⟩, + ⟨7, 4, 0, 4, 1, 6, 280950743546719818361450635619023033653526528000000000⟩, + ⟨7, 4, 1, 4, 2, 6, -299139615023050872993544551366748986498298675200000000⟩, + ⟨7, 4, 2, 4, 3, 6, -122141134194114390158270189633797708919812915200000000⟩, + ⟨7, 4, 3, 4, 4, 6, -11648928756261633653162590787619149597953228800000000⟩, + ⟨7, 4, 4, 4, 5, 6, 4868255896696880286646189052604162746666188800000000⟩, + ⟨7, 4, 5, 4, 6, 6, -1112657713491085060080987988254685610901504000000000⟩, + ⟨7, 4, 6, 4, 7, 6, -428185327922769318895316296606599445531852800000000⟩, + ⟨7, 4, 7, 4, 8, 6, 358993707132311809393171299628831928745984000000000⟩, + ⟨7, 4, 0, 5, 0, 6, -1738590962732051674533334504100259250491201945600000000⟩, + ⟨7, 4, 1, 5, 1, 6, -135633387465907965583645255867345532571824947200000000⟩, + ⟨7, 4, 2, 5, 2, 6, 16613929724095766258340831347886501940061798400000000⟩, + ⟨7, 4, 3, 5, 3, 6, -29328370789136552958154901464748501744851353600000000⟩, + ⟨7, 4, 4, 5, 4, 6, 679845550114079139577568628849712463609856000000000⟩, + ⟨7, 4, 5, 5, 5, 6, -306204872084360291170366251160683436572672000000000⟩, + ⟨7, 4, 6, 5, 6, 6, -725210319828124916568660964657077431776051200000000⟩, + ⟨7, 4, 7, 5, 7, 6, 163749933328900517592208693291278467806003200000000⟩, + ⟨7, 4, 8, 5, 8, 6, 123562288511595387370457132929701081042124800000000⟩, + ⟨7, 4, 1, 6, 0, 6, 1478687220114748252060023254370303169948916121600000000⟩, + ⟨7, 4, 2, 6, 1, 6, -278776283634994609231497629126571297335987404800000000⟩, + ⟨7, 4, 3, 6, 2, 6, -32797362430442189721406650432476014808609587200000000⟩, + ⟨7, 4, 4, 6, 3, 6, -16993600212454651939796838794023818856759296000000000⟩, + ⟨7, 4, 5, 6, 4, 6, 2553456384925834617350316139002414809009356800000000⟩, + ⟨7, 4, 6, 6, 5, 6, 68980281140874255490655849881623218828083200000000⟩, + ⟨7, 4, 7, 6, 6, 6, 49505951261274847079258286751355865818726400000000⟩, + ⟨7, 4, 8, 6, 7, 6, 33307146522136505794893234470474352898867200000000⟩, + ⟨7, 4, 2, 7, 0, 6, 2274249686569377079286824432415421329964426854400000000⟩, + ⟨7, 4, 3, 7, 1, 6, 301502440847341842328147204789275424821608448000000000⟩, + ⟨7, 4, 4, 7, 2, 6, 17463606305706564940193967670801242576125952000000000⟩, + ⟨7, 4, 5, 7, 3, 6, 3560020120922560809503449090279734978910617600000000⟩, + ⟨7, 4, 6, 7, 4, 6, 2393866901244424642206238356605552107192320000000000⟩, + ⟨7, 4, 7, 7, 5, 6, -177851945825794520134099072301746147767091200000000⟩, + ⟨7, 4, 8, 7, 6, 6, 49796449517406753353036569799549774934835200000000⟩ +] + +def collectedFourData_11_5_52 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 5, 7, 143149413691076107478546521451396462670287732736000000⟩, + ⟨7, 5, 1, 0, 6, 7, -86055244100641737337757099062493300777879076864000000⟩, + ⟨7, 5, 2, 0, 7, 7, 2799051296234846758840511991964134537418506240000000⟩, + ⟨7, 5, 3, 0, 8, 7, -426356747947326700598308117716565165445480448000000⟩, + ⟨7, 5, 0, 1, 4, 7, 102922012580814872780227458247990561478283362304000000⟩, + ⟨7, 5, 1, 1, 5, 7, -18737139465197336026175297688146767520376815616000000⟩, + ⟨7, 5, 2, 1, 6, 7, -6442913079130542183597444686735925386969874432000000⟩, + ⟨7, 5, 3, 1, 7, 7, 5695581250320630433156220750939584037696569344000000⟩, + ⟨7, 5, 4, 1, 8, 7, -1773229571999264641018359893322847886736202137600000⟩, + ⟨7, 5, 0, 2, 3, 7, 40285683088348152553101146067401358176409354240000000⟩, + ⟨7, 5, 1, 2, 4, 7, 16291079021932109399931162960062237864494104576000000⟩, + ⟨7, 5, 2, 2, 5, 7, -13510641363034785180181548816258530512711188480000000⟩, + ⟨7, 5, 3, 2, 6, 7, -1854030560166161653915812216535120541651042304000000⟩, + ⟨7, 5, 4, 2, 7, 7, 240434851843530120109496598873182823612678144000000⟩, + ⟨7, 5, 5, 2, 8, 7, -499885401445329620981377019189814377312157696000000⟩, + ⟨7, 5, 0, 3, 2, 7, -177017914304047052353945409450693663730526322688000000⟩, + ⟨7, 5, 1, 3, 3, 7, -45117215737439111409723649633326195901080797184000000⟩, + ⟨7, 5, 2, 3, 4, 7, 995478667257829578992050938423352075587944448000000⟩, + ⟨7, 5, 3, 3, 5, 7, -3703366235221721063482698272492398856399486976000000⟩, + ⟨7, 5, 4, 3, 6, 7, 195816722020850056499314372145861693675038310400000⟩, + ⟨7, 5, 5, 3, 7, 7, 39380368318909385379564237081130936005820416000000⟩, + ⟨7, 5, 6, 3, 8, 7, -72903606544501702571282881457661459377946624000000⟩, + ⟨7, 5, 0, 4, 1, 7, -146112323439991397090646209295634756267262607360000000⟩, + ⟨7, 5, 1, 4, 2, 7, 77785848921759904995558846589477711051134861312000000⟩, + ⟨7, 5, 2, 4, 3, 7, 21173729220771322856896393845459500065313783808000000⟩, + ⟨7, 5, 3, 4, 4, 7, 1514546664548406104008897737233053469286334464000000⟩, + ⟨7, 5, 4, 4, 5, 7, -506360774267560891449641447938077012599714611200000⟩, + ⟨7, 5, 5, 4, 6, 7, 96442174441499644656818042266909111568302080000000⟩, + ⟨7, 5, 6, 4, 7, 7, 31811958177596609852981766507388110265909248000000⟩, + ⟨7, 5, 7, 4, 8, 7, -23337455877170207587414494945270438832373760000000⟩, + ⟨7, 5, 0, 5, 0, 7, 904178297838562287137600099172382796945421238272000000⟩, + ⟨7, 5, 1, 5, 1, 7, 35269010376163849307925504082294329920697925632000000⟩, + ⟨7, 5, 2, 5, 2, 7, -2880101381012711447990261294947642977168654336000000⟩, + ⟨7, 5, 3, 5, 3, 7, 3813156306879212685433200768157055455548407808000000⟩, + ⟨7, 5, 4, 5, 4, 7, -70712617915523550245164452749490783617286144000000⟩, + ⟨7, 5, 5, 5, 5, 7, 26541013764008361085496058227116947737149440000000⟩, + ⟨7, 5, 6, 5, 6, 7, 53879380865882710904746738510802686304059392000000⟩, + ⟨7, 5, 7, 5, 7, 7, -10645052456432928189813549260635113152053248000000⟩, + ⟨7, 5, 8, 5, 8, 7, -7140030959827712405028411697145923988619264000000⟩, + ⟨7, 5, 1, 6, 0, 7, -384505879294923025943005156990497442004201373696000000⟩, + ⟨7, 5, 2, 6, 1, 7, 48327155153802022509397716512221936581441748992000000⟩, + ⟨7, 5, 3, 6, 2, 7, 4264180588134397127790238767877819303005782016000000⟩, + ⟨7, 5, 4, 6, 3, 7, 1767551407273056191571444341684141649983176704000000⟩, + ⟨7, 5, 5, 6, 4, 7, -221326723499815579443816457733298589098049536000000⟩, + ⟨7, 5, 6, 6, 5, 7, -5124878587918701035451231866534154586816512000000⟩, + ⟨7, 5, 7, 6, 6, 7, -3218281909302448659502091947949911279927296000000⟩, + ⟨7, 5, 8, 6, 7, 7, -1924649180718723219094678328756895058231296000000⟩, + ⟨7, 5, 2, 7, 0, 7, -394251677467757240946406983481913277293134872576000000⟩, + ⟨7, 5, 3, 7, 1, 7, -39200129530630689901218893469532974220773949440000000⟩, + ⟨7, 5, 4, 7, 2, 7, -1816438042310254729361929275046220471413506048000000⟩, + ⟨7, 5, 5, 7, 3, 7, -308572957661892106994621658490557568911409152000000⟩, + ⟨7, 5, 6, 7, 4, 7, -177851945825794520134099072301746147767091200000000⟩, + ⟨7, 5, 7, 7, 5, 7, 11561795808439014139779774613463616158957568000000⟩, + ⟨7, 5, 8, 7, 6, 7, -2877481434883074826179823668990440726593536000000⟩ +] + +def collectedFourData_11_5_53 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 5, 8, -160320597432118694399372218762827386206996660224000000⟩, + ⟨7, 6, 1, 0, 6, 8, 64251878698598104142085532275675882971971190784000000⟩, + ⟨7, 6, 2, 0, 7, 8, -1567402773384504417434862244187811918989230080000000⟩, + ⟨7, 6, 3, 0, 8, 8, 190999786272660972487424388943599020196809932800000⟩, + ⟨7, 6, 0, 1, 4, 8, -115267803900903537861840644693437175654447579136000000⟩, + ⟨7, 6, 1, 1, 5, 8, 13989808810124527960638127773309449916012036096000000⟩, + ⟨7, 6, 2, 1, 6, 8, 3607879513493992779476202244709036477638508544000000⟩, + ⟨7, 6, 3, 1, 7, 8, -2551513038663603318703279201685083646138410598400000⟩, + ⟨7, 6, 4, 1, 8, 8, 661977852457303954137603026714293858963606732800000⟩, + ⟨7, 6, 0, 2, 3, 8, -45118066600140082288018151555157461691436892160000000⟩, + ⟨7, 6, 1, 2, 4, 8, -12163493859389940053990890326513199505637113856000000⟩, + ⟨7, 6, 2, 2, 5, 8, 7565640819484058876044835875926888446857052160000000⟩, + ⟨7, 6, 3, 2, 6, 8, 830570742552121345320819132346966247393879654400000⟩, + ⟨7, 6, 4, 2, 7, 8, -89758567865422516333367708698568379158495232000000⟩, + ⟨7, 6, 5, 2, 8, 8, 159956597876837347617154898660712016829743104000000⟩, + ⟨7, 6, 0, 3, 2, 8, 198251722068922382346967878082158381448657108992000000⟩, + ⟨7, 6, 1, 3, 3, 8, 33686103654417518136954596416190921230415560704000000⟩, + ⟨7, 6, 2, 3, 4, 8, -557444597747778565928128405728866948314300416000000⟩, + ⟨7, 6, 3, 3, 5, 8, 1659038265073090491122219239364260259518060953600000⟩, + ⟨7, 6, 4, 3, 6, 8, -73101833606599099155904622876253809196348211200000⟩, + ⟨7, 6, 5, 3, 7, 8, -12601187634639187289181720398673470904336384000000⟩, + ⟨7, 6, 6, 3, 8, 8, 20412150938658113877404573134646810461077504000000⟩, + ⟨7, 6, 0, 4, 1, 8, 163638916724076509453123041290677594792122122240000000⟩, + ⟨7, 6, 1, 4, 2, 8, -58077656761316710343945411035948908651239964672000000⟩, + ⟨7, 6, 2, 4, 3, 8, -11856789458689850494653538152541204915773505536000000⟩, + ⟨7, 6, 3, 4, 4, 8, -678488356573297015781004352624042516310025830400000⟩, + ⟨7, 6, 4, 4, 5, 8, 189033401659509783938744813007662458919819673600000⟩, + ⟨7, 6, 5, 4, 6, 8, -30860197299028141062160456132541303142481920000000⟩, + ⟨7, 6, 6, 4, 7, 8, -8906973505885553354223105538930505058091008000000⟩, + ⟨7, 6, 7, 4, 8, 8, 5808189068253980658386378821973417939435520000000⟩, + ⟨7, 6, 0, 5, 0, 8, -1012637084266808461018983190960661388878464155648000000⟩, + ⟨7, 6, 1, 5, 1, 8, -26333086381797604043391928960574779841253998592000000⟩, + ⟨7, 6, 2, 5, 2, 8, 1612788911121515554753737951233649836726157312000000⟩, + ⟨7, 6, 3, 5, 3, 8, -1708222147637162656737314841836614460499610828800000⟩, + ⟨7, 6, 4, 5, 4, 8, 26398266580099403637358170302498686717919232000000⟩, + ⟨7, 6, 5, 5, 5, 8, -8492767049444218314898430582091007194562560000000⟩, + ⟨7, 6, 6, 5, 6, 8, -15085591877330667790891558641742139917074432000000⟩, + ⟨7, 6, 7, 5, 7, 8, 2649323800925851117627849354963200975568896000000⟩, + ⟨7, 6, 8, 5, 8, 8, 1599299640351600848716284703439192813941555200000⟩, + ⟨7, 6, 1, 6, 0, 8, 287085643339322827076086888735439859542787096576000000⟩, + ⟨7, 6, 2, 6, 1, 8, -27062068179938456266632044830729573795903832064000000⟩, + ⟨7, 6, 3, 6, 2, 8, -1910272523849722142212310601943654916190476697600000⟩, + ⟨7, 6, 4, 6, 3, 8, -659858093487168843265192463312967814361382912000000⟩, + ⟨7, 6, 5, 6, 4, 8, 70821571519987285652873726303488436563083264000000⟩, + ⟨7, 6, 6, 6, 5, 8, 1434905627268766725342669180671389914365952000000⟩, + ⟨7, 6, 7, 6, 6, 8, 800960906045281584594621305194265173819392000000⟩, + ⟨7, 6, 8, 6, 7, 8, 431103276700740106833753414149547641064652800000⟩, + ⟨7, 6, 2, 7, 0, 8, 220771649846394355863704229204840754136997691392000000⟩, + ⟨7, 6, 3, 7, 1, 8, 17560919108839997075896540089256473510316867584000000⟩, + ⟨7, 6, 4, 7, 2, 8, 678108335975117888213112744671519301376671744000000⟩, + ⟨7, 6, 5, 7, 3, 8, 98739191746106113873793130564365056840040448000000⟩, + ⟨7, 6, 6, 7, 4, 8, 49796449517406753353036569799549774934835200000000⟩, + ⟨7, 6, 7, 7, 5, 8, -2877481434883074826179823668990440726593536000000⟩, + ⟨7, 6, 8, 7, 6, 8, 644528721208507789095052263014599570017484800000⟩ +] + +def collectedFourData_11_5 : List (List CollectedFourTerm) := [ + collectedFourData_11_5_0, + collectedFourData_11_5_1, + collectedFourData_11_5_2, + collectedFourData_11_5_3, + collectedFourData_11_5_4, + collectedFourData_11_5_5, + collectedFourData_11_5_6, + collectedFourData_11_5_7, + collectedFourData_11_5_8, + collectedFourData_11_5_9, + collectedFourData_11_5_10, + collectedFourData_11_5_11, + collectedFourData_11_5_12, + collectedFourData_11_5_13, + collectedFourData_11_5_14, + collectedFourData_11_5_15, + collectedFourData_11_5_16, + collectedFourData_11_5_17, + collectedFourData_11_5_18, + collectedFourData_11_5_19, + collectedFourData_11_5_20, + collectedFourData_11_5_21, + collectedFourData_11_5_22, + collectedFourData_11_5_23, + collectedFourData_11_5_24, + collectedFourData_11_5_25, + collectedFourData_11_5_26, + collectedFourData_11_5_27, + collectedFourData_11_5_28, + collectedFourData_11_5_29, + collectedFourData_11_5_30, + collectedFourData_11_5_31, + collectedFourData_11_5_32, + collectedFourData_11_5_33, + collectedFourData_11_5_34, + collectedFourData_11_5_35, + collectedFourData_11_5_36, + collectedFourData_11_5_37, + collectedFourData_11_5_38, + collectedFourData_11_5_39, + collectedFourData_11_5_40, + collectedFourData_11_5_41, + collectedFourData_11_5_42, + collectedFourData_11_5_43, + collectedFourData_11_5_44, + collectedFourData_11_5_45, + collectedFourData_11_5_46, + collectedFourData_11_5_47, + collectedFourData_11_5_48, + collectedFourData_11_5_49, + collectedFourData_11_5_50, + collectedFourData_11_5_51, + collectedFourData_11_5_52, + collectedFourData_11_5_53 +] + +theorem collectedFourChecked_11_5 : collectNumericRowParts 11 5 = collectedFourData_11_5 := by + decide +kernel +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1119.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1119.lean new file mode 100644 index 0000000000000000000000000000000000000000..a141f2b570dc8a8887d39606b5e34f1d8c8ee138 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1119.lean @@ -0,0 +1,618 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1119. -/ +namespace LaughlinFock +def collectedFourData_11_6_0 : List CollectedFourTerm := [ + ⟨0, 6, 5, 3, 8, 0, -9895468244120475846761344712605676100208558080000000⟩, + ⟨0, 6, 5, 4, 7, 0, -5912862630054063518260945568252404177462886400000000⟩, + ⟨0, 6, 6, 4, 8, 0, 22442344999597305386056909477495182655173427200000000⟩, + ⟨0, 6, 5, 5, 6, 0, 13133782714751979712171784946873635918000947200000000⟩, + ⟨0, 6, 6, 5, 7, 0, -27202798382839871761347773027659617673496494080000000⟩, + ⟨0, 6, 7, 5, 8, 0, -5554572850582940588068782112419329502955438080000000⟩, + ⟨0, 6, 5, 6, 5, 0, -26621856869226726589979645951588321997178798080000000⟩, + ⟨0, 6, 6, 6, 6, 0, 17713232834733330934576522485995574324331806720000000⟩, + ⟨0, 6, 7, 6, 7, 0, 18354426238317640323472940319472246537983098880000000⟩, + ⟨0, 6, 8, 6, 8, 0, -72626599552649373996739091909441534358391357440000000⟩, + ⟨0, 6, 5, 7, 4, 0, -80505276987091341080482030835014423522584821760000000⟩, + ⟨0, 6, 6, 7, 5, 0, -18305565269104836760408768681711988314315161600000000⟩, + ⟨0, 6, 7, 7, 6, 0, -45966493252754710083610571716533654384877240320000000⟩, + ⟨0, 6, 8, 7, 7, 0, -54992684027705246341160299280616101912059576320000000⟩ +] + +def collectedFourData_11_6_1 : List CollectedFourTerm := [ + ⟨0, 7, 4, 2, 8, 1, -5267419670085787284983392285702091555679397478400000⟩, + ⟨0, 7, 4, 3, 7, 1, -31755374937291716429949761707814200660782061977600000⟩, + ⟨0, 7, 5, 3, 8, 1, 26261982596420540138348311053494220349016899584000000⟩, + ⟨0, 7, 4, 4, 6, 1, 37653423540435121299650967149496312908906653286400000⟩, + ⟨0, 7, 5, 4, 7, 1, 15692384802282494736018187200552563003589918720000000⟩, + ⟨0, 7, 6, 4, 8, 1, -29780322631648998537090696869830972339944161280000000⟩, + ⟨0, 7, 4, 5, 5, 1, 19534786910097798166712432878257225328952239718400000⟩, + ⟨0, 7, 5, 5, 6, 1, -34856276082228218313460266797659243116295618560000000⟩, + ⟨0, 7, 6, 5, 7, 1, 36097302324654896831986723991993572686343176192000000⟩, + ⟨0, 7, 7, 5, 8, 1, 4913835031479595058450377187467109122103574528000000⟩, + ⟨0, 7, 4, 6, 4, 1, -37913592548518625076724616883645140098104478924800000⟩, + ⟨0, 7, 5, 6, 5, 1, 70652820517051920790045667456536818502896451584000000⟩, + ⟨0, 7, 6, 6, 6, 1, -23504931800903268785645788602437645193317449728000000⟩, + ⟨0, 7, 7, 6, 7, 1, -16237184218960807028419193330791776008754167808000000⟩, + ⟨0, 7, 8, 6, 8, 1, 48186666018107336979387540576022405290318102528000000⟩, + ⟨0, 7, 4, 7, 3, 1, 137992134067811524574079201909823266684994270003200000⟩, + ⟨0, 7, 5, 7, 4, 1, 213656204132755883394165429350493178435152642048000000⟩, + ⟨0, 7, 6, 7, 5, 1, 24290939279225610816658958656719509801234595840000000⟩, + ⟨0, 7, 7, 7, 6, 1, 40664110615805817385532441319140044118176038912000000⟩, + ⟨0, 7, 8, 7, 7, 1, 36486825970164415676968824369403565314758672384000000⟩ +] + +def collectedFourData_11_6_2 : List CollectedFourTerm := [ + ⟨0, 8, 3, 1, 8, 2, 266476744145148747421620689624321792417149747200000⟩, + ⟨0, 8, 3, 2, 7, 2, -9574508007902905726931355366607929504660298137600000⟩, + ⟨0, 8, 4, 2, 8, 2, 3202370845095649207463998656163281487985953996800000⟩, + ⟨0, 8, 3, 3, 6, 2, 10513327902164747180968713589906174364585715302400000⟩, + ⟨0, 8, 4, 3, 7, 2, 19305939766255204845706311321861750124105118515200000⟩, + ⟨0, 8, 5, 3, 8, 2, -7983093494410782451160919420142223110422134784000000⟩, + ⟨0, 8, 3, 4, 5, 2, 19667474490916489321117805443298647009066273996800000⟩, + ⟨0, 8, 4, 4, 6, 2, -22891706626057348839247483824995682044506590412800000⟩, + ⟨0, 8, 5, 4, 7, 2, -4770156806210304974935609065461436761474334720000000⟩, + ⟨0, 8, 6, 4, 8, 2, 6035063524223407619176216785940291496989163520000000⟩, + ⟨0, 8, 3, 5, 4, 2, -20133577243627876450409208324029263052841104179200000⟩, + ⟨0, 8, 4, 5, 5, 2, -11876333382229723388887329276736564231056182476800000⟩, + ⟨0, 8, 5, 5, 6, 2, 10595578982271837117384962342961812429403586560000000⟩, + ⟨0, 8, 6, 5, 7, 2, -7315216670986307730971133587797184363813142528000000⟩, + ⟨0, 8, 7, 5, 8, 2, -746851543450478258036933892198611023470526464000000⟩, + ⟨0, 8, 3, 6, 3, 2, -26782438177518309471418272337386756470356102348800000⟩, + ⟨0, 8, 4, 6, 4, 2, 23049878501181644307592095836916468521799096729600000⟩, + ⟨0, 8, 5, 6, 5, 2, -21476979879970137180065682031462026066247286784000000⟩, + ⟨0, 8, 6, 6, 6, 2, 4763338473715366540954541236051116095283658752000000⟩, + ⟨0, 8, 7, 6, 7, 2, 2467882217765288045056591750141891102170415104000000⟩, + ⟨0, 8, 8, 6, 8, 2, -5859095498127834380894559405604067217853592371200000⟩, + ⟨0, 8, 3, 7, 2, 2, -98585480909683631960217572891174310523369527705600000⟩, + ⟨0, 8, 4, 7, 3, 2, -83893445874627401116379785909217031271529997926400000⟩, + ⟨0, 8, 5, 7, 4, 2, -64947017879951716512402138282844946887971176448000000⟩, + ⟨0, 8, 6, 7, 5, 2, -4922625030844493380952184731897673439311298560000000⟩, + ⟨0, 8, 7, 7, 6, 2, -6180519610832536708654432750981727179040096256000000⟩, + ⟨0, 8, 8, 7, 7, 2, -4436492819454058318393399520823129403203099033600000⟩ +] + +def collectedFourData_11_6_3 : List CollectedFourTerm := [ + ⟨1, 5, 5, 3, 8, 0, -15111182810206844116901112892679020497900404736000000⟩, + ⟨1, 5, 5, 4, 7, 0, -9029420935939650287845651465839280275723386880000000⟩, + ⟨1, 5, 6, 4, 8, 0, 34271281521230200760964491576803414883161866240000000⟩, + ⟨1, 5, 5, 5, 6, 0, 20056351725455104089986450372599617518032650240000000⟩, + ⟨1, 5, 6, 5, 7, 0, -41540880044411543184864218717909576365885095936000000⟩, + ⟨1, 5, 7, 5, 8, 0, -8482283375285687060773996128999797832586100736000000⟩, + ⟨1, 5, 5, 6, 5, 0, -40653735222390362525074704190403161307517812736000000⟩, + ⟨1, 5, 6, 6, 6, 0, 27049543581169309918744348846564729122585575424000000⟩, + ⟨1, 5, 7, 6, 7, 0, 28028697927303278580043791716813201642247684096000000⟩, + ⟨1, 5, 8, 6, 8, 0, -110906709581514747711461176816162619768489115648000000⟩, + ⟨1, 5, 5, 7, 4, 0, -122938089206753078410778029223770114671343828992000000⟩, + ⟨1, 5, 6, 7, 5, 0, -27954083263313298948991497857709483146052894720000000⟩, + ⟨1, 5, 7, 7, 6, 0, -70194564375387339102124072728585026318100332544000000⟩, + ⟨1, 5, 8, 7, 7, 0, -83978289967263386412390748700884803569785503744000000⟩ +] + +def collectedFourData_11_6_4 : List CollectedFourTerm := [ + ⟨1, 6, 4, 2, 8, 1, -2573171081873167710625491812796935383179224678400000⟩, + ⟨1, 6, 4, 3, 7, 1, -15512721142522560193675804102490254553757882777600000⟩, + ⟨1, 6, 5, 3, 8, 1, 12829160841984926623731787752437947447413571584000000⟩, + ⟨1, 6, 4, 4, 6, 1, 18393958836811663067335660092213365952852944486400000⟩, + ⟨1, 6, 5, 4, 7, 1, 7665838932139172129076206406972438378939678720000000⟩, + ⟨1, 6, 6, 4, 8, 1, -14547894377924933813240521215652629237234401280000000⟩, + ⟨1, 6, 4, 5, 5, 1, 9542879040583354279115110517222483691189986918400000⟩, + ⟨1, 6, 5, 5, 6, 1, -17027532882170419198452249997655308969244098560000000⟩, + ⟨1, 6, 6, 5, 7, 1, 17633782818357113799460802351651833633352712192000000⟩, + ⟨1, 6, 7, 5, 8, 1, 2400442530885847051434964771498036005099798528000000⟩, + ⟨1, 6, 4, 6, 4, 1, -18521053203680136877172390795698950684975877324800000⟩, + ⟨1, 6, 5, 6, 5, 1, 34514393383106369307264771533890506237709123584000000⟩, + ⟨1, 6, 6, 6, 6, 1, -11482322385468908564075615165888830747315273728000000⟩, + ⟨1, 6, 7, 6, 7, 1, -7931977229867625622152820257221687040496631808000000⟩, + ⟨1, 6, 8, 6, 8, 1, 23539520922139638653334747712244732289538326528000000⟩, + ⟨1, 6, 4, 7, 3, 1, 67410115606656200412933251785235244062514295603200000⟩, + ⟨1, 6, 5, 7, 4, 1, 104372539188289887265090404341223842606689026048000000⟩, + ⟨1, 6, 6, 7, 5, 1, 11866292496079472750899004626586149310001315840000000⟩, + ⟨1, 6, 7, 7, 6, 1, 19864700377097365486104181542947097584087334912000000⟩, + ⟨1, 6, 8, 7, 7, 1, 17824067823750387283958149373847559787337744384000000⟩ +] + +def collectedFourData_11_6_5 : List CollectedFourTerm := [ + ⟨1, 7, 3, 1, 8, 2, 122156229508946710419551501429918825227223040000000⟩, + ⟨1, 7, 3, 2, 7, 2, -4389072680246975377228307833018676886707896320000000⟩, + ⟨1, 7, 4, 2, 8, 2, 1468006332714664504625626996562024050993397760000000⟩, + ⟨1, 7, 3, 3, 6, 2, 4819439310696900906715435145314473717981511680000000⟩, + ⟨1, 7, 4, 3, 7, 2, 8850081145122343653273513113816512984661360640000000⟩, + ⟨1, 7, 5, 3, 8, 2, -3659548619235020508636955686134571481222348800000000⟩, + ⟨1, 7, 3, 4, 5, 2, 9015813126511015728631208402219966247217397760000000⟩, + ⟨1, 7, 4, 4, 6, 2, -10493840944487710291248640851812112460110888960000000⟩, + ⟨1, 7, 5, 4, 7, 2, -2186698773592391474915771637492631474274304000000000⟩, + ⟨1, 7, 6, 4, 8, 2, 2766547630004614710158497567052792504254464000000000⟩, + ⟨1, 7, 3, 5, 4, 2, -9229480382982561722684154007583370958539325440000000⟩, + ⟨1, 7, 4, 5, 5, 2, -5444257850787129926614623125208356452313333760000000⟩, + ⟨1, 7, 5, 5, 6, 2, 4857144221311718456790394855580661650030592000000000⟩, + ⟨1, 7, 6, 5, 7, 2, -3353385637592212545330265616923976216975769600000000⟩, + ⟨1, 7, 7, 5, 8, 2, -342365968345641888336815883891964761656524800000000⟩, + ⟨1, 7, 3, 6, 3, 2, -12277400323684733225236914888392288315281244160000000⟩, + ⟨1, 7, 4, 6, 4, 2, 10566348884876757747842365835709559327130910720000000⟩, + ⟨1, 7, 5, 6, 5, 2, -9845312737488371737109818594460631342828748800000000⟩, + ⟨1, 7, 6, 6, 6, 2, 2183573165795763899341947422791933620545126400000000⟩, + ⟨1, 7, 7, 6, 7, 2, 1131307677754337311862912038714450182458572800000000⟩, + ⟨1, 7, 8, 6, 8, 2, -2685881714294316884779778076131868993745059840000000⟩, + ⟨1, 7, 3, 7, 2, 2, -45192801611586486965637254405375418674624593920000000⟩, + ⟨1, 7, 4, 7, 3, 2, -38457791359741633437367162433015038221987348480000000⟩, + ⟨1, 7, 5, 7, 4, 2, -29772514849339363943969857985299895176239513600000000⟩, + ⟨1, 7, 6, 7, 5, 2, -2256592090177986779885586433520458889428992000000000⟩, + ⟨1, 7, 7, 7, 6, 2, -2833226495945800367486338537011033134019379200000000⟩, + ⟨1, 7, 8, 7, 7, 2, -2033743082558937181292292351898957475500523520000000⟩ +] + +def collectedFourData_11_6_6 : List CollectedFourTerm := [ + ⟨1, 8, 2, 0, 8, 3, 266476744145148747421620689624321792417149747200000⟩, + ⟨1, 8, 2, 1, 7, 3, 122156229508946710419551501429918825227223040000000⟩, + ⟨1, 8, 3, 1, 8, 3, 4634998277538153843939326264031060379356364800000⟩, + ⟨1, 8, 2, 2, 6, 3, 257332150782279852822019337659645716202940006400000⟩, + ⟨1, 8, 3, 2, 7, 3, -166535463600278809970155217066301861216544358400000⟩, + ⟨1, 8, 4, 2, 8, 3, 27850429122197294545741622072867582163655065600000⟩, + ⟨1, 8, 2, 3, 5, 3, -63772803586532485061861026060210106085566054400000⟩, + ⟨1, 8, 3, 3, 6, 3, 182864950838579733680395885246835647716104601600000⟩, + ⟨1, 8, 4, 3, 7, 3, 167900200540778176307828938035558003935438438400000⟩, + ⟨1, 8, 5, 3, 8, 3, -46284995356374502160079707628879436371197952000000⟩, + ⟨1, 8, 2, 4, 4, 3, -8056323130096737733693582324847497363587072000000⟩, + ⟨1, 8, 3, 4, 5, 3, 342088802838531177464254516354740057634190131200000⟩, + ⟨1, 8, 4, 4, 6, 3, -199084954152491993141424292907154248688048537600000⟩, + ⟨1, 8, 5, 4, 7, 3, -27656783147936569885717493669170270867292160000000⟩, + ⟨1, 8, 6, 4, 8, 3, 26242917678749039534283680656887759419473920000000⟩, + ⟨1, 8, 2, 5, 3, 3, -134342413806177553762652111421189711331118284800000⟩, + ⟨1, 8, 3, 5, 4, 3, -350196022336816246030462098683013750474984652800000⟩, + ⟨1, 8, 4, 5, 5, 3, -103286282911277044886170666044928527387171225600000⟩, + ⟨1, 8, 5, 5, 6, 3, 61431865270763434494807859467185058144583680000000⟩, + ⟨1, 8, 6, 5, 7, 3, -31809545687194621891840253196796606009049088000000⟩, + ⟨1, 8, 7, 5, 8, 3, -2598092098861827372529007528804533566386995200000⟩, + ⟨1, 8, 2, 6, 2, 3, 89904194055205480930684008922490240285383065600000⟩, + ⟨1, 8, 3, 6, 3, 3, -465843858980252340392742043701979630334587699200000⟩, + ⟨1, 8, 4, 6, 4, 3, 200460545803290530834948724875562378176181043200000⟩, + ⟨1, 8, 5, 6, 5, 3, -124520890893904820322641787194038042547453952000000⟩, + ⟨1, 8, 6, 6, 6, 3, 20712938470323055956627672781217041106337792000000⟩, + ⟨1, 8, 7, 6, 7, 3, 8585086751344106965528039403091706938340147200000⟩, + ⟨1, 8, 8, 6, 8, 3, -16985157953697338678509883904687658486254796800000⟩, + ⟨1, 8, 2, 7, 1, 3, -1326029642553843309662427240965171670257605017600000⟩, + ⟨1, 8, 3, 7, 2, 3, -1714759521220204437894412353293217859780372070400000⟩, + ⟨1, 8, 4, 7, 3, 3, -729605839288241219282118160199476403816418508800000⟩, + ⟨1, 8, 5, 7, 4, 3, -376554830917185653885928510733449013487468544000000⟩, + ⟨1, 8, 6, 7, 5, 3, -21405581387716196871234227538890009094389760000000⟩, + ⟨1, 8, 7, 7, 6, 3, -21500336055513988363844346139190542824426700800000⟩, + ⟨1, 8, 8, 7, 7, 3, -12861120171697043820732535341984752693831270400000⟩ +] + +def collectedFourData_11_6_7 : List CollectedFourTerm := [ + ⟨2, 4, 5, 3, 8, 0, -4305930128053736765925117316755934742304522240000000⟩, + ⟨2, 4, 5, 4, 7, 0, -2572932650955700671684179984187161165640499200000000⟩, + ⟨2, 4, 6, 4, 8, 0, 9765598463252028139751122864281315318536601600000000⟩, + ⟨2, 4, 5, 5, 6, 0, 5715055547812379027965927043102650339531161600000000⟩, + ⟨2, 4, 6, 5, 7, 0, -11837069882331036805942943224734052119729930240000000⟩, + ⟨2, 4, 7, 5, 8, 0, -2417025854234373690306013239105112982673162240000000⟩, + ⟨2, 4, 5, 6, 5, 0, -11584278048292230452101363883853093047359242240000000⟩, + ⟨2, 4, 6, 6, 6, 0, 7707764912855633318435916108917730632175452160000000⟩, + ⟨2, 4, 7, 6, 7, 0, 7986774852182500677424154177294356013792624640000000⟩, + ⟨2, 4, 8, 6, 8, 0, -31602856519463516899315808533499675769380536320000000⟩, + ⟨2, 4, 5, 7, 4, 0, -35031197018089016136884683478037638461815521280000000⟩, + ⟨2, 4, 6, 7, 5, 0, -7965513410659071597150070129833739062922444800000000⟩, + ⟨2, 4, 7, 7, 6, 0, -20001934551769914793054480720911027961551912960000000⟩, + ⟨2, 4, 8, 7, 7, 0, -23929605869649496536087652572175405457300520960000000⟩ +] + +def collectedFourData_11_6_8 : List CollectedFourTerm := [ + ⟨2, 5, 4, 2, 8, 1, -1531041733425247561123599238157155639761882316800000⟩, + ⟨2, 5, 4, 3, 7, 1, -9230098859536655539127694297267072763329458995200000⟩, + ⟨2, 5, 5, 3, 8, 1, 7633375329092117103870153496591493137346592768000000⟩, + ⟨2, 5, 4, 4, 6, 1, 10944440818744164418117325913763256313706237132800000⟩, + ⟨2, 5, 5, 4, 7, 1, 4561188880716487405152440111067805754264125440000000⟩, + ⟨2, 5, 6, 4, 8, 1, -8656025082425307502782487992772901661636034560000000⟩, + ⟨2, 5, 4, 5, 5, 1, 5678031348590431508524507464279090538990062796800000⟩, + ⟨2, 5, 5, 5, 6, 1, -10131414752607806109607748008079112753245061120000000⟩, + ⟨2, 5, 6, 5, 7, 1, 10492134628455522304306247771900159151449309184000000⟩, + ⟨2, 5, 7, 5, 8, 1, 1428267914001182652825809375594973689341280256000000⟩, + ⟨2, 5, 4, 6, 4, 1, -11020062211013675291132856283823162864906639769600000⟩, + ⟨2, 5, 5, 6, 5, 1, 20536130320151295179508464843878651407806496768000000⟩, + ⟨2, 5, 6, 6, 6, 1, -6832003861942344052365680113544403443207110656000000⟩, + ⟨2, 5, 7, 6, 7, 1, -4719541678770006144870081821971422885042978816000000⟩, + ⟨2, 5, 8, 6, 8, 1, 14006060137438220660953924777641638615901536256000000⟩, + ⟨2, 5, 4, 7, 3, 1, 40109148193007081898483565859226750558830749286400000⟩, + ⟨2, 5, 5, 7, 4, 1, 62101861180760172739571427623498117346855223296000000⟩, + ⟨2, 5, 6, 7, 5, 1, 7060466814862183648611928754975759685837127680000000⟩, + ⟨2, 5, 7, 7, 6, 1, 11819534858593369664197178810666286130736922624000000⟩, + ⟨2, 5, 8, 7, 7, 1, 10605354571954215004656763740834368116771258368000000⟩ +] + +def collectedFourData_11_6_9 : List CollectedFourTerm := [ + ⟨2, 6, 3, 1, 8, 2, 257332150782279852822019337659645716202940006400000⟩, + ⟨2, 6, 3, 2, 7, 2, -9245942816735179782304179120299800422966833971200000⟩, + ⟨2, 6, 4, 2, 8, 2, 3092476155150190214100549559037680075933325721600000⟩, + ⟨2, 6, 3, 3, 6, 2, 10152545542472477003957040700468316437058735308800000⟩, + ⟨2, 6, 4, 3, 7, 2, 18643424284025053038387670530779891410657502822400000⟩, + ⟨2, 6, 5, 3, 8, 2, -7709140343195505160852932525219854085110366208000000⟩, + ⟨2, 6, 3, 4, 5, 2, 18992552342377838175456485669514425677121165721600000⟩, + ⟨2, 6, 4, 4, 6, 2, -22106139580989574159133374815536296340796053913600000⟩, + ⟨2, 6, 5, 4, 7, 2, -4606460929446836312665936280418488504958320640000000⟩, + ⟨2, 6, 6, 4, 8, 2, 5827960266394481447806522005870467264796426240000000⟩, + ⟨2, 6, 3, 5, 4, 2, -19442660002712466885688096042015517623357695590400000⟩, + ⟨2, 6, 4, 5, 5, 2, -11468777219042740165280215444273039208624003481600000⟩, + ⟨2, 6, 5, 5, 6, 2, 10231974039754754287905987756383669538489630720000000⟩, + ⟨2, 6, 6, 5, 7, 2, -7064182825492413405633721508794935467034279936000000⟩, + ⟨2, 6, 7, 5, 8, 2, -721222088658109772527494522102786804173242368000000⟩, + ⟨2, 6, 3, 6, 3, 2, -25863354198219250871573406021921811043530152345600000⟩, + ⟨2, 6, 4, 6, 4, 2, 22258883524741868540159392665215910020786631475200000⟩, + ⟨2, 6, 5, 6, 5, 2, -20739961539796082756218905230665620763818590208000000⟩, + ⟨2, 6, 6, 6, 6, 2, 4599876579389198617606281519501194476256231424000000⟩, + ⟨2, 6, 7, 6, 7, 2, 2383192728551827647239661432344241024477954048000000⟩, + ⟨2, 6, 8, 6, 8, 2, -5658030876235687064183917371658437713004488294400000⟩, + ⟨2, 6, 3, 7, 2, 2, -95202355912063296661728569259767822849039086387200000⟩, + ⟨2, 6, 4, 7, 3, 2, -81014502532706938599181661246892424771442363596800000⟩, + ⟨2, 6, 5, 7, 4, 2, -62718252774957670842476742368942545606306430976000000⟩, + ⟨2, 6, 6, 7, 5, 2, -4753696952976530753699448841354791459980574720000000⟩, + ⟨2, 6, 7, 7, 6, 2, -5968424785096017801391355954632891251422134272000000⟩, + ⟨2, 6, 8, 7, 7, 2, -4284247178201788939545965662451556155898671923200000⟩ +] + +def collectedFourData_11_6_10 : List CollectedFourTerm := [ + ⟨2, 7, 2, 0, 8, 3, -9574508007902905726931355366607929504660298137600000⟩, + ⟨2, 7, 2, 1, 7, 3, -4389072680246975377228307833018676886707896320000000⟩, + ⟨2, 7, 3, 1, 8, 3, -166535463600278809970155217066301861216544358400000⟩, + ⟨2, 7, 2, 2, 6, 3, -9245942816735179782304179120299800422966833971200000⟩, + ⟨2, 7, 3, 2, 7, 3, 5983618326453949888323828748703377112849134387200000⟩, + ⟨2, 7, 4, 2, 8, 3, -1000665771076686927525641730806183710734208204800000⟩, + ⟨2, 7, 2, 3, 5, 3, 2291356495608813427775638715376473568355496755200000⟩, + ⟨2, 7, 3, 3, 6, 3, -6570336716569445517728606462987204495443545292800000⟩, + ⟨2, 7, 4, 3, 7, 3, -6032653317508834313233974424166223915554911027200000⟩, + ⟨2, 7, 5, 3, 8, 3, 1663019638381543941980715532808688974709129216000000⟩, + ⟨2, 7, 2, 4, 4, 3, 289463647459417068512268152607724608134578176000000⟩, + ⟨2, 7, 3, 4, 5, 3, -12291248876890268695359844736105994470387456409600000⟩, + ⟨2, 7, 4, 4, 6, 3, 7153121349860649860308190367775800145709157580800000⟩, + ⟨2, 7, 5, 4, 7, 3, 993708072245574044549603600494559766018785280000000⟩, + ⟨2, 7, 6, 4, 8, 3, -942907893414734584737276425896824621351567360000000⟩, + ⟨2, 7, 2, 5, 3, 3, 4826922217601214594445650370428464393552815718400000⟩, + ⟨2, 7, 3, 5, 4, 3, 12582541230589532772217695288257335553669097062400000⟩, + ⟨2, 7, 4, 5, 5, 3, 3711075598784294431567740710887755804389985484800000⟩, + ⟨2, 7, 5, 5, 6, 3, -2207246594303020420906538881762871660186173440000000⟩, + ⟨2, 7, 6, 5, 7, 3, 1142916808319698256700756828446288765050159104000000⟩, + ⟨2, 7, 7, 5, 8, 3, 93349435372387619623837075840806575461210521600000⟩, + ⟨2, 7, 2, 6, 2, 3, -3230257216955314869795911398744912566466432204800000⟩, + ⟨2, 7, 3, 6, 3, 3, 16737767389597615335863331583922699134811347353600000⟩, + ⟨2, 7, 4, 6, 4, 3, -7202546350599179597527794318948614046257617305600000⟩, + ⟨2, 7, 5, 6, 5, 3, 4474034951303274502946903400199396209475977216000000⟩, + ⟨2, 7, 6, 6, 6, 3, -744215769700662040198163582340362192799399936000000⟩, + ⟨2, 7, 7, 6, 7, 3, -308462121574528108066891386284275381218941337600000⟩, + ⟨2, 7, 8, 6, 8, 3, 610276635452247989057671165498559701119821414400000⟩, + ⟨2, 7, 2, 7, 1, 3, 47644238044400973997665496299010065380210953420800000⟩, + ⟨2, 7, 3, 7, 2, 3, 61611300529129089381235660590634785115989029683200000⟩, + ⟨2, 7, 4, 7, 3, 3, 26214733947188090189343519307639323207171204710400000⟩, + ⟨2, 7, 5, 7, 4, 3, 13529613083486611192637116233472101814791831552000000⟩, + ⟨2, 7, 6, 7, 5, 3, 769102426059633431384913678435379534972846080000000⟩, + ⟨2, 7, 7, 7, 6, 3, 772506960772508676835949724443828756117087846400000⟩, + ⟨2, 7, 8, 7, 7, 3, 462099979754487343378418988317220672470463283200000⟩ +] + +def collectedFourData_11_6_11 : List CollectedFourTerm := [ + ⟨2, 8, 1, 0, 7, 4, -5267419670085787284983392285702091555679397478400000⟩, + ⟨2, 8, 2, 0, 8, 4, 3202370845095649207463998656163281487985953996800000⟩, + ⟨2, 8, 1, 1, 6, 4, -2573171081873167710625491812796935383179224678400000⟩, + ⟨2, 8, 2, 1, 7, 4, 1468006332714664504625626996562024050993397760000000⟩, + ⟨2, 8, 3, 1, 8, 4, 27850429122197294545741622072867582163655065600000⟩, + ⟨2, 8, 1, 2, 5, 4, -1531041733425247561123599238157155639761882316800000⟩, + ⟨2, 8, 2, 2, 6, 4, 3092476155150190214100549559037680075933325721600000⟩, + ⟨2, 8, 3, 2, 7, 4, -1000665771076686927525641730806183710734208204800000⟩, + ⟨2, 8, 4, 2, 8, 4, 111563709534251679106391950372002844994489548800000⟩, + ⟨2, 8, 1, 3, 4, 4, -834812017552442027611795542814847310645480652800000⟩, + ⟨2, 8, 2, 3, 5, 4, -766386453612187820583712113203127506188212633600000⟩, + ⟨2, 8, 3, 3, 6, 4, 1098785166101290900785882353263352583631876915200000⟩, + ⟨2, 8, 4, 3, 7, 4, 672577399855738111660230861894630851690574643200000⟩, + ⟨2, 8, 5, 3, 8, 4, -139056899852680459806221945937149988565942272000000⟩, + ⟨2, 8, 1, 4, 3, 4, 2630934490261365906187473976106966135470659993600000⟩, + ⟨2, 8, 2, 4, 4, 4, -96816457260670853773543885024045183027642368000000⟩, + ⟨2, 8, 3, 4, 5, 4, 2055517475189269114146249669412552259158828646400000⟩, + ⟨2, 8, 4, 4, 6, 4, -797497801569101705059079534983760857577344204800000⟩, + ⟨2, 8, 5, 4, 7, 4, -83090999466207194353054295092579276695797760000000⟩, + ⟨2, 8, 6, 4, 8, 4, 63074588166609486358230205706944122659536896000000⟩, + ⟨2, 8, 1, 5, 2, 4, 532863154900085857195900884143451125015642112000000⟩, + ⟨2, 8, 2, 5, 3, 4, -1614453188449129228320448700286610330690466611200000⟩, + ⟨2, 8, 3, 5, 4, 4, -2104231526089631198379302849601593630871099801600000⟩, + ⟨2, 8, 4, 5, 5, 4, -413745900109029756968992497120378196610305228800000⟩, + ⟨2, 8, 5, 5, 6, 4, 184563586340371290746328241578149608402452480000000⟩, + ⟨2, 8, 6, 5, 7, 4, -76453922484826029997790044205117965026616934400000⟩, + ⟨2, 8, 7, 5, 8, 4, -5203740146855354931112066483143762378542284800000⟩, + ⟨2, 8, 1, 6, 1, 4, 11757480506618531634344471029824863074603814092800000⟩, + ⟨2, 8, 2, 6, 2, 4, 1080419121817962978801073673016949235008300646400000⟩, + ⟨2, 8, 3, 6, 3, 4, -2799127550794131224051451707640085380294141542400000⟩, + ⟨2, 8, 4, 6, 4, 4, 803008169351733627572018386434037361938110873600000⟩, + ⟨2, 8, 5, 6, 5, 4, -374105882938487408948697013275165118559158272000000⟩, + ⟨2, 8, 6, 6, 6, 4, 49783338869896040067637236872895104170957209600000⟩, + ⟨2, 8, 7, 6, 7, 4, 17195141239133279473696368172428498748361932800000⟩, + ⟨2, 8, 8, 6, 8, 4, -29159754261781348432488923466557325454186905600000⟩, + ⟨2, 8, 1, 7, 0, 4, -73644587429962989362777890580620394636832984268800000⟩, + ⟨2, 8, 2, 7, 1, 4, -15935494411227179316674052331651492262187525734400000⟩, + ⟨2, 8, 3, 7, 2, 4, -10303518070069693252923107811154267032003595468800000⟩, + ⟨2, 8, 4, 7, 3, 4, -2922667136355610116991769216268642480074155622400000⟩, + ⟨2, 8, 5, 7, 4, 4, -1131307176520707788402956260026068591479619584000000⟩, + ⟨2, 8, 6, 7, 5, 4, -51448099141444238865168612086539416489689088000000⟩, + ⟨2, 8, 7, 7, 6, 4, -43063200858804505370668248820552379955098419200000⟩, + ⟨2, 8, 8, 7, 7, 4, -22079694799440403887869166854411465645673676800000⟩ +] + +def collectedFourData_11_6_12 : List CollectedFourTerm := [ + ⟨3, 3, 5, 3, 8, 0, -765855693988738069105040618519644369651236864000000⟩, + ⟨3, 3, 5, 4, 7, 0, -457623570839180718992963804457514709412741120000000⟩, + ⟨3, 3, 6, 4, 8, 0, 1736916058986245529050126327695827623749877760000000⟩, + ⟨3, 3, 5, 5, 6, 0, 1016483710276177201918536918263625418549493760000000⟩, + ⟨3, 3, 6, 5, 7, 0, -2105349390242751194119538161118907829441265664000000⟩, + ⟨3, 3, 7, 5, 8, 0, -429893880749076478340031656420407123183140864000000⟩, + ⟨3, 3, 5, 6, 5, 0, -2060387660782458418798498156059717816878628864000000⟩, + ⟨3, 3, 6, 6, 6, 0, 1370908368433104328115055411729226016778878976000000⟩, + ⟨3, 3, 7, 6, 7, 0, 1420533268131492332656551425646575932359573504000000⟩, + ⟨3, 3, 8, 6, 8, 0, -5620905795487213200172367092703446008858673152000000⟩, + ⟨3, 3, 5, 7, 4, 0, -6230672794421609546794708688644465211587166208000000⟩, + ⟨3, 3, 6, 7, 5, 0, -1416751693519531155691959735910898871859937280000000⟩, + ⟨3, 3, 7, 7, 6, 0, -3557557835753133931202317797030565174214393856000000⟩, + ⟨3, 3, 8, 7, 7, 0, -4256136157615951948001781776900391454591942656000000⟩ +] + +def collectedFourData_11_6_13 : List CollectedFourTerm := [ + ⟨3, 4, 4, 2, 8, 1, -834812017552442027611795542814847310645480652800000⟩, + ⟨3, 4, 4, 3, 7, 1, -5032780807287185725005073964236126946600366899200000⟩, + ⟨3, 4, 5, 3, 8, 1, 4162155296027113595312000108743494803681968128000000⟩, + ⟨3, 4, 4, 4, 6, 1, 5967538651241608659991487737222209169343171788800000⟩, + ⟨3, 4, 5, 4, 7, 1, 2487022534278035530382651997566799578388234240000000⟩, + ⟨3, 4, 6, 4, 8, 1, -4719762763669190362627676809354268097915125760000000⟩, + ⟨3, 4, 4, 5, 5, 1, 3095989287789211093760029857750373857464470732800000⟩, + ⟨3, 4, 5, 5, 6, 1, -5524230075272502431661680136959247148143083520000000⟩, + ⟨3, 4, 6, 5, 7, 1, 5720915299948908067464370650607887155529252864000000⟩, + ⟨3, 4, 7, 5, 8, 1, 778773819721590427523043726329446112874725376000000⟩, + ⟨3, 4, 4, 6, 4, 1, -6008771783998480889312604370017891624882379161600000⟩, + ⟨3, 4, 5, 6, 5, 1, 11197479474926683210070381168234891317899952128000000⟩, + ⟨3, 4, 6, 6, 6, 1, -3725201477790175298299392256875987085113163776000000⟩, + ⟨3, 4, 7, 6, 7, 1, -2573365588123070870655838844898083187128795136000000⟩, + ⟨3, 4, 8, 6, 8, 1, 7636909606074112990580858266985345478480101376000000⟩, + ⟨3, 4, 4, 7, 3, 1, 21869814646008765032170206919363742791142631014400000⟩, + ⟨3, 4, 5, 7, 4, 1, 33861506772965643475364082218175804685173129216000000⟩, + ⟨3, 4, 6, 7, 5, 1, 3849772620757201328327865561291408964614881280000000⟩, + ⟨3, 4, 7, 7, 6, 1, 6444690256586989912634887875241828803730735104000000⟩, + ⟨3, 4, 8, 7, 7, 1, 5782649325479265639631330647832770251983945728000000⟩ +] + +def collectedFourData_11_6_14 : List CollectedFourTerm := [ + ⟨3, 5, 3, 1, 8, 2, -63772803586532485061861026060210106085566054400000⟩, + ⟨3, 5, 3, 2, 7, 2, 2291356495608813427775638715376473568355496755200000⟩, + ⟨3, 5, 4, 2, 8, 2, -766386453612187820583712113203127506188212633600000⟩, + ⟨3, 5, 3, 3, 6, 2, -2516033425342231501013310637162143995097042124800000⟩, + ⟨3, 5, 4, 3, 7, 2, -4620267741248722171835644176182695074002789990400000⟩, + ⟨3, 5, 5, 3, 8, 2, 1910501627694299574168016463088679803596832768000000⟩, + ⟨3, 5, 3, 4, 5, 2, -4706789674183239890496945881657428021884852633600000⟩, + ⟨3, 5, 4, 4, 6, 2, 5478407938025899546592224858318136215858682265600000⟩, + ⟨3, 5, 5, 4, 7, 2, 1141586572799429808038298837939211917003325440000000⟩, + ⟨3, 5, 6, 4, 8, 2, -1444302098470954253193272321118303845131223040000000⟩, + ⟨3, 5, 3, 5, 4, 2, 4818336666380106821965440590430344150503548518400000⟩, + ⟨3, 5, 4, 5, 5, 2, 2842225795510957115336510784343795479057373593600000⟩, + ⟨3, 5, 5, 5, 6, 2, -2535717627028486188266000871155113191926661120000000⟩, + ⟨3, 5, 6, 5, 7, 2, 1750666375965742060401251543336264017385619456000000⟩, + ⟨3, 5, 7, 5, 8, 2, 178735359971310548353442182466163318485680128000000⟩, + ⟨3, 5, 3, 6, 3, 2, 6409531814652421168255641508238220086757398937600000⟩, + ⟨3, 5, 4, 6, 4, 2, -5516261387329981623067933089627299965199135539200000⟩, + ⟨3, 5, 5, 6, 5, 2, 5139837714210454998360851355879861912776736768000000⟩, + ⟨3, 5, 6, 6, 6, 2, -1139954819978438667920011956485312070606127104000000⟩, + ⟨3, 5, 7, 6, 7, 2, -590609767667063797393335377230569727126929408000000⟩, + ⟨3, 5, 8, 6, 8, 2, 1402189701752423898815863214599683837444646502400000⟩, + ⟨3, 5, 3, 7, 2, 2, 23593325303886783256886628836690298987087082291200000⟩, + ⟨3, 5, 4, 7, 3, 2, 20077250129736723032922355107316660983103802572800000⟩, + ⟨3, 5, 5, 7, 4, 2, 15543020191409740240635734057375473430792503296000000⟩, + ⟨3, 5, 6, 7, 5, 2, 1178075033261432288217344729818513309559685120000000⟩, + ⟨3, 5, 7, 7, 6, 2, 1479112424871283477032572345667987513972621312000000⟩, + ⟨3, 5, 8, 7, 7, 2, 1061734621892542850122163246128295960491799347200000⟩ +] + +def collectedFourData_11_6_15 : List CollectedFourTerm := [ + ⟨3, 6, 2, 0, 8, 3, 10513327902164747180968713589906174364585715302400000⟩, + ⟨3, 6, 2, 1, 7, 3, 4819439310696900906715435145314473717981511680000000⟩, + ⟨3, 6, 3, 1, 8, 3, 182864950838579733680395885246835647716104601600000⟩, + ⟨3, 6, 2, 2, 6, 3, 10152545542472477003957040700468316437058735308800000⟩, + ⟨3, 6, 3, 2, 7, 3, -6570336716569445517728606462987204495443545292800000⟩, + ⟨3, 6, 4, 2, 8, 3, 1098785166101290900785882353263352583631876915200000⟩, + ⟨3, 6, 2, 3, 5, 3, -2516033425342231501013310637162143995097042124800000⟩, + ⟨3, 6, 3, 3, 6, 3, 7214585258261925790789703141274616572188767027200000⟩, + ⟨3, 6, 4, 3, 7, 3, 6624179790199359292869088298205261664766184652800000⟩, + ⟨3, 6, 5, 3, 8, 3, -1826085554642936415816834864230741519508701184000000⟩, + ⟨3, 6, 2, 4, 4, 3, -317846748781823181694824702334928688695476224000000⟩, + ⟨3, 6, 3, 4, 5, 3, 13496456388484959329964450362796488165320713830400000⟩, + ⟨3, 6, 4, 4, 6, 3, -7854514322092252087252937701384758811216261939200000⟩, + ⟨3, 6, 5, 4, 7, 3, -1091145236279766862743173352860292452418846720000000⟩, + ⟨3, 6, 6, 4, 8, 3, 1035363890951485900031373742414396054453616640000000⟩, + ⟨3, 6, 2, 5, 3, 3, -5300221796252991124490779365797638628202617241600000⟩, + ⟨3, 6, 3, 5, 4, 3, -13816311155675705158239654403530039584439769497600000⟩, + ⟨3, 6, 4, 5, 5, 3, -4074961826501960206660943192819894614538531635200000⟩, + ⟨3, 6, 5, 5, 6, 3, 2423676202233051760910523363316826594932162560000000⟩, + ⟨3, 6, 6, 5, 7, 3, -1254984502685938277680529856329419026906218496000000⟩, + ⟨3, 6, 7, 5, 8, 3, -102502731497198410017303731328936058278012518400000⟩, + ⟨3, 6, 2, 6, 2, 3, 3546997224520964460945850187169961895605252915200000⟩, + ⟨3, 6, 3, 6, 3, 3, -18378974331814492437033861559166151966700496486400000⟩, + ⟨3, 6, 4, 6, 4, 3, 7908785647459570883608332759134560712502175334400000⟩, + ⟨3, 6, 5, 6, 5, 3, -4912732481916788839213220069928474142713053184000000⟩, + ⟨3, 6, 6, 6, 6, 3, 817189187200722455677437974172985479307198464000000⟩, + ⟨3, 6, 7, 6, 7, 3, 338708101432850920529412963701308379913152102400000⟩, + ⟨3, 6, 8, 6, 8, 3, -670116769889739803738308868622306330988353945600000⟩, + ⟨3, 6, 2, 7, 1, 3, -52315951565984580666930101223184932307163362099200000⟩, + ⟨3, 6, 3, 7, 2, 3, -67652541979901092126630709301402991601738632396800000⟩, + ⟨3, 6, 4, 7, 3, 3, -28785196443233558604294569390204789679959153049600000⟩, + ⟨3, 6, 5, 7, 4, 3, -14856247299464942600333004851802765059055157248000000⟩, + ⟨3, 6, 6, 7, 5, 3, -844516082585257909972175109525827791796305920000000⟩, + ⟨3, 6, 7, 7, 6, 3, -848254445931052370747298265294111788701948313600000⟩, + ⟨3, 6, 8, 7, 7, 3, -507410783586226778266425860201781433453038796800000⟩ +] + +def collectedFourData_11_6_16 : List CollectedFourTerm := [ + ⟨3, 7, 1, 0, 7, 4, -31755374937291716429949761707814200660782061977600000⟩, + ⟨3, 7, 2, 0, 8, 4, 19305939766255204845706311321861750124105118515200000⟩, + ⟨3, 7, 1, 1, 6, 4, -15512721142522560193675804102490254553757882777600000⟩, + ⟨3, 7, 2, 1, 7, 4, 8850081145122343653273513113816512984661360640000000⟩, + ⟨3, 7, 3, 1, 8, 4, 167900200540778176307828938035558003935438438400000⟩, + ⟨3, 7, 1, 2, 5, 4, -9230098859536655539127694297267072763329458995200000⟩, + ⟨3, 7, 2, 2, 6, 4, 18643424284025053038387670530779891410657502822400000⟩, + ⟨3, 7, 3, 2, 7, 4, -6032653317508834313233974424166223915554911027200000⟩, + ⟨3, 7, 4, 2, 8, 4, 672577399855738111660230861894630851690574643200000⟩, + ⟨3, 7, 1, 3, 4, 4, -5032780807287185725005073964236126946600366899200000⟩, + ⟨3, 7, 2, 3, 5, 4, -4620267741248722171835644176182695074002789990400000⟩, + ⟨3, 7, 3, 3, 6, 4, 6624179790199359292869088298205261664766184652800000⟩, + ⟨3, 7, 4, 3, 7, 4, 4054726762718697772619031760467719918751370444800000⟩, + ⟨3, 7, 5, 3, 8, 4, -838323936389024365234531860930011847047774208000000⟩, + ⟨3, 7, 1, 4, 3, 4, 15860955915126745150432022900622200216591165030400000⟩, + ⟨3, 7, 2, 4, 4, 4, -583671530459772585592939608274660072202698752000000⟩, + ⟨3, 7, 3, 4, 5, 4, 12391974097960451699649939142613205545238763929600000⟩, + ⟨3, 7, 4, 4, 6, 4, -4807826846285867394763791871293414836050015027200000⟩, + ⟨3, 7, 5, 4, 7, 4, -500925691747804532282470666607946862574960640000000⟩, + ⟨3, 7, 6, 4, 8, 4, 380253961464461517281930576561681774615199744000000⟩, + ⟨3, 7, 1, 5, 2, 4, 3212439929595507928498481205071117050831699968000000⟩, + ⟨3, 7, 2, 5, 3, 4, -9732956462357064252518452174739105089885883596800000⟩, + ⟨3, 7, 3, 5, 4, 4, -12685653555445204787414334394528032735743075942400000⟩, + ⟨3, 7, 4, 5, 5, 4, -2494324927505824540714710290014122143355450163200000⟩, + ⟨3, 7, 5, 5, 6, 4, 1112667349688172758964317439637263930328350720000000⟩, + ⟨3, 7, 6, 5, 7, 4, -460913146472862613901220045243327382910769561600000⟩, + ⟨3, 7, 7, 5, 8, 4, -31371474040331777904048289954915661284324147200000⟩, + ⟨3, 7, 1, 6, 1, 4, 70881612856089230345572774198638764066518283059200000⟩, + ⟨3, 7, 2, 6, 2, 4, 6513457527903808664120769446607726245953771929600000⟩, + ⟨3, 7, 3, 6, 3, 4, -16874931264271761751913161589325180265094027673600000⟩, + ⟨3, 7, 4, 6, 4, 4, 4841046867840937379423750588269626480310773350400000⟩, + ⟨3, 7, 5, 6, 5, 4, -2255349549310687731264378323031321387579998208000000⟩, + ⟨3, 7, 6, 6, 6, 4, 300125809306941030979522232552350848672753254400000⟩, + ⟨3, 7, 7, 6, 7, 4, 103663309807906605990174220166925727751680819200000⟩, + ⟨3, 7, 8, 6, 8, 4, -175793649957470711357124493908077341225412198400000⟩, + ⟨3, 7, 1, 7, 0, 4, -443976677845102806777168933021560963903817724723200000⟩, + ⟨3, 7, 2, 7, 1, 4, -96069353029430111472120032969213358565796452761600000⟩, + ⟨3, 7, 3, 7, 2, 4, -62116197299862130133752595875772782692357321523200000⟩, + ⟨3, 7, 4, 7, 3, 4, -17619706904872750766380658348680157872178960793600000⟩, + ⟨3, 7, 5, 7, 4, 4, -6820243270853497363905756480770341955463806976000000⟩, + ⟨3, 7, 6, 7, 5, 4, -310162049043817671842901649584123902617976832000000⟩, + ⟨3, 7, 7, 7, 6, 4, -259612519017108856202635416643423174182882508800000⟩, + ⟨3, 7, 8, 7, 7, 4, -133110522945247091470324915999830094061450035200000⟩ +] + +def collectedFourData_11_6_17 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 6, 5, -9895468244120475846761344712605676100208558080000000⟩, + ⟨3, 8, 1, 0, 7, 5, 26261982596420540138348311053494220349016899584000000⟩, + ⟨3, 8, 2, 0, 8, 5, -7983093494410782451160919420142223110422134784000000⟩, + ⟨3, 8, 0, 1, 5, 5, -15111182810206844116901112892679020497900404736000000⟩, + ⟨3, 8, 1, 1, 6, 5, 12829160841984926623731787752437947447413571584000000⟩, + ⟨3, 8, 2, 1, 7, 5, -3659548619235020508636955686134571481222348800000000⟩, + ⟨3, 8, 3, 1, 8, 5, -46284995356374502160079707628879436371197952000000⟩, + ⟨3, 8, 0, 2, 4, 5, -4305930128053736765925117316755934742304522240000000⟩, + ⟨3, 8, 1, 2, 5, 5, 7633375329092117103870153496591493137346592768000000⟩, + ⟨3, 8, 2, 2, 6, 5, -7709140343195505160852932525219854085110366208000000⟩, + ⟨3, 8, 3, 2, 7, 5, 1663019638381543941980715532808688974709129216000000⟩, + ⟨3, 8, 4, 2, 8, 5, -139056899852680459806221945937149988565942272000000⟩, + ⟨3, 8, 0, 3, 3, 5, -765855693988738069105040618519644369651236864000000⟩, + ⟨3, 8, 1, 3, 4, 5, 4162155296027113595312000108743494803681968128000000⟩, + ⟨3, 8, 2, 3, 5, 5, 1910501627694299574168016463088679803596832768000000⟩, + ⟨3, 8, 3, 3, 6, 5, -1826085554642936415816834864230741519508701184000000⟩, + ⟨3, 8, 4, 3, 7, 5, -838323936389024365234531860930011847047774208000000⟩, + ⟨3, 8, 5, 3, 8, 5, 138660297169137911319564870335106023732281344000000⟩, + ⟨3, 8, 0, 4, 2, 5, 5676340554826631482316683733301006054702710784000000⟩, + ⟨3, 8, 1, 4, 3, 5, -13117154151957148201293411101983371761220059136000000⟩, + ⟨3, 8, 2, 4, 4, 5, 241350820219098029474633053068165520388259840000000⟩, + ⟨3, 8, 3, 4, 5, 5, -3416091593298071325305515018185514774154969088000000⟩, + ⟨3, 8, 4, 4, 6, 5, 994029083368550453869234974935958019387686912000000⟩, + ⟨3, 8, 5, 4, 7, 5, 82854016523243253294964013348672614453739520000000⟩, + ⟨3, 8, 6, 4, 8, 5, -52412244845267646641087043123400732217180160000000⟩, + ⟨3, 8, 0, 5, 1, 5, 4375263188133034075336797644862380775491764224000000⟩, + ⟨3, 8, 1, 5, 2, 5, -2656716908229923649683370051485477876394885120000000⟩, + ⟨3, 8, 2, 5, 3, 5, 4024621559828757642859993908954958513890656256000000⟩, + ⟨3, 8, 3, 5, 4, 5, 3497050116767154608237848302529509241569411072000000⟩, + ⟨3, 8, 4, 5, 5, 5, 515707324864943133202724359618048608511721472000000⟩, + ⟨3, 8, 5, 5, 6, 5, -184037194527348162088609895264453798091816960000000⟩, + ⟨3, 8, 6, 5, 7, 5, 63529890897918077976632112566380936795521024000000⟩, + ⟨3, 8, 7, 5, 8, 5, 3706356154096237010376257621169364285784064000000⟩, + ⟨3, 8, 0, 6, 0, 5, -100921615873559158512248953893063940148236910592000000⟩, + ⟨3, 8, 1, 6, 1, 5, -58619735616687782370321549860820094660040982528000000⟩, + ⟨3, 8, 2, 6, 2, 5, -2693344175247877853993822930604836120671813632000000⟩, + ⟨3, 8, 3, 6, 3, 5, 4651906982185295940321006501752666981199249408000000⟩, + ⟨3, 8, 4, 6, 4, 5, -1000897398021225505232316333125841840173481984000000⟩, + ⟨3, 8, 5, 6, 5, 5, 373038899586639020930718203894810897069113344000000⟩, + ⟨3, 8, 6, 6, 6, 5, -41367793621920357974120045528418111996297216000000⟩, + ⟨3, 8, 7, 6, 7, 5, -12247213687395356418608395136467061339848704000000⟩, + ⟨3, 8, 8, 6, 8, 5, 18172867525816711692246530350712933194924032000000⟩, + ⟨3, 8, 1, 7, 0, 5, 367172732484169074896600510811012775214252556288000000⟩, + ⟨3, 8, 2, 7, 1, 5, 39725112398931861277372117437580031520587907072000000⟩, + ⟨3, 8, 3, 7, 2, 5, 17123552528941106527768629455555809176868356096000000⟩, + ⟨3, 8, 4, 7, 3, 5, 3642914286192200615805017668192221178946912256000000⟩, + ⟨3, 8, 5, 7, 4, 5, 1128080587530198177466847442522287713202208768000000⟩, + ⟨3, 8, 6, 7, 5, 5, 42751137144205121790333867945718331190804480000000⟩, + ⟨3, 8, 7, 7, 6, 5, 30671700548799318727814464811501104876486656000000⟩, + ⟨3, 8, 8, 7, 7, 5, 13760450962599521273815832779285478869303296000000⟩ +] + +def collectedFourData_11_6_18 : List CollectedFourTerm := [ + ⟨4, 2, 5, 3, 8, 0, 5676340554826631482316683733301006054702710784000000⟩, + ⟨4, 2, 5, 4, 7, 0, 3391797246384666253142699747702907014448414720000000⟩, + ⟨4, 2, 6, 4, 8, 0, -12873609406236591642745696376779970475259330560000000⟩, + ⟨4, 2, 5, 5, 6, 0, -7533935901044766917932474450493794077439426560000000⟩, + ⟨4, 2, 6, 5, 7, 0, 15604349774658962976629036709250499210939203584000000⟩, + ⟨4, 2, 7, 5, 8, 0, 3186271367728017565522527402969868389039734784000000⟩, + ⟨4, 2, 5, 6, 5, 0, 15271104111861349587121763640715238063455862784000000⟩, + ⟨4, 2, 6, 6, 6, 0, -10160847310749993993984087483589226518340960256000000⟩, + ⟨4, 2, 7, 6, 7, 0, -10528655284103399565167379283303805669420826624000000⟩, + ⟨4, 2, 8, 6, 8, 0, 41660819097146122977010893958215601971592691712000000⟩, + ⟨4, 2, 5, 7, 4, 0, 46180267306794269928646902315515143789580648448000000⟩, + ⟨4, 2, 6, 7, 5, 0, 10500627150997564535882068944324472560345415680000000⟩, + ⟨4, 2, 7, 7, 6, 0, 26367773952365139197592170770152192643260481536000000⟩, + ⟨4, 2, 8, 7, 7, 0, 31545470599706324114125327240926797247950094336000000⟩ +] + +def collectedFourData_11_6_19 : List CollectedFourTerm := [ + ⟨4, 3, 4, 2, 8, 1, 2630934490261365906187473976106966135470659993600000⟩, + ⟨4, 3, 4, 3, 7, 1, 15860955915126745150432022900622200216591165030400000⟩, + ⟨4, 3, 5, 3, 8, 1, -13117154151957148201293411101983371761220059136000000⟩, + ⟨4, 3, 4, 4, 6, 1, -18806872600552938448487427555217812229514172825600000⟩, + ⟨4, 3, 5, 4, 7, 1, -7837924258293607020740826139436584578978938880000000⟩, + ⟨4, 3, 6, 4, 8, 1, 14874470395376800574081183397437266751253381120000000⟩, + ⟨4, 3, 4, 5, 5, 1, -9757100793308447087610201867823095794718316953600000⟩, + ⟨4, 3, 5, 5, 6, 1, 17409772657304330692951291498601619011131146240000000⟩, + ⟨4, 3, 6, 5, 7, 1, -18029631895606988228849088351119016826836615168000000⟩, + ⟨4, 3, 7, 5, 8, 1, -2454328470767862918430508562701631693848051712000000⟩, + ⟨4, 3, 4, 6, 4, 1, 18936820024440815291803777663579915755002737459200000⟩, + ⟨4, 3, 5, 6, 5, 1, -35289184073979510103365953270971570403080667136000000⟩, + ⟨4, 3, 6, 6, 6, 1, 11740081413568184722209494811909724257241792512000000⟩, + ⟨4, 3, 7, 6, 7, 1, 8110036917885414565481857766071535797725560832000000⟩, + ⟨4, 3, 8, 6, 8, 1, -24067943991195063719113519409785100968459763712000000⟩, + ⟨4, 3, 4, 7, 3, 1, -68923360514743840415949442251119242703371291852800000⟩, + ⟨4, 3, 5, 7, 4, 1, -106715528991073461264602650548232764186314145792000000⟩, + ⟨4, 3, 6, 7, 5, 1, -12132671014139717187148879975746495399182991360000000⟩, + ⟨4, 3, 7, 7, 6, 1, -20310629840736514247080533065528487201680130048000000⟩, + ⟨4, 3, 8, 7, 7, 1, -18224188482689529246845660658049350609546510336000000⟩ +] + +def collectedFourData_11_6_20 : List CollectedFourTerm := [ + ⟨4, 4, 3, 1, 8, 2, -8056323130096737733693582324847497363587072000000⟩, + ⟨4, 4, 3, 2, 7, 2, 289463647459417068512268152607724608134578176000000⟩, + ⟨4, 4, 4, 2, 8, 2, -96816457260670853773543885024045183027642368000000⟩, + ⟨4, 4, 3, 3, 6, 2, -317846748781823181694824702334928688695476224000000⟩, + ⟨4, 4, 4, 3, 7, 2, -583671530459772585592939608274660072202698752000000⟩, + ⟨4, 4, 5, 3, 8, 2, 241350820219098029474633053068165520388259840000000⟩, + ⟨4, 4, 3, 4, 5, 2, -594601717159424539746746977561256223590842368000000⟩, + ⟨4, 4, 4, 4, 6, 2, 692079101200816823713185568750353427388694528000000⟩, + ⟨4, 4, 5, 4, 7, 2, 144214928530978468938938799758631834432307200000000⟩, + ⟨4, 4, 6, 4, 8, 2, -182456529247148245622131642391535451058995200000000⟩, + ⟨4, 4, 3, 5, 4, 2, 608693282259098434908991897427791966101307392000000⟩, + ⟨4, 4, 4, 5, 5, 2, 359054144236620820445381444440772472018567168000000⟩, + ⟨4, 4, 5, 5, 6, 2, -320333424612646341380145173394664902465945600000000⟩, + ⟨4, 4, 6, 5, 7, 2, 221159071337329482617091190716073197730529280000000⟩, + ⟨4, 4, 7, 5, 8, 2, 22579371357716564021676255667006711938416640000000⟩, + ⟨4, 4, 3, 6, 3, 2, 809706591327905062720562070808538615421861888000000⟩, + ⟨4, 4, 4, 6, 4, 2, -696861070975261896759949142419250764207620096000000⟩, + ⟨4, 4, 5, 6, 5, 2, 649308029962192224149191600014358113775779840000000⟩, + ⟨4, 4, 6, 6, 6, 2, -144008791631625847792748366206346817196523520000000⟩, + ⟨4, 4, 7, 6, 7, 2, -74610850778435107217911290829573723300823040000000⟩, + ⟨4, 4, 8, 6, 8, 2, 177136533000049691210680042426966154844045312000000⟩, + ⟨4, 4, 3, 7, 2, 2, 2980509585150805460828615746899843148840697856000000⟩, + ⟨4, 4, 4, 7, 3, 2, 2536329054272497746725012933375198710374334464000000⟩, + ⟨4, 4, 5, 7, 4, 2, 1963526551090169372987004037749564204625428480000000⟩, + ⟨4, 4, 6, 7, 5, 2, 148824461301523463915449944002350594759065600000000⟩, + ⟨4, 4, 7, 7, 6, 2, 186854065845404580200852154392813731640770560000000⟩, + ⟨4, 4, 8, 7, 7, 2, 134127350709476558724698828779673589053915136000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1120.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1120.lean new file mode 100644 index 0000000000000000000000000000000000000000..3617312faf0632574ad73fb5608ef5260474e606 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1120.lean @@ -0,0 +1,620 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1120. -/ +namespace LaughlinFock +def collectedFourData_11_6_21 : List CollectedFourTerm := [ + ⟨4, 5, 2, 0, 8, 3, 19667474490916489321117805443298647009066273996800000⟩, + ⟨4, 5, 2, 1, 7, 3, 9015813126511015728631208402219966247217397760000000⟩, + ⟨4, 5, 3, 1, 8, 3, 342088802838531177464254516354740057634190131200000⟩, + ⟨4, 5, 2, 2, 6, 3, 18992552342377838175456485669514425677121165721600000⟩, + ⟨4, 5, 3, 2, 7, 3, -12291248876890268695359844736105994470387456409600000⟩, + ⟨4, 5, 4, 2, 8, 3, 2055517475189269114146249669412552259158828646400000⟩, + ⟨4, 5, 2, 3, 5, 3, -4706789674183239890496945881657428021884852633600000⟩, + ⟨4, 5, 3, 3, 6, 3, 13496456388484959329964450362796488165320713830400000⟩, + ⟨4, 5, 4, 3, 7, 3, 12391974097960451699649939142613205545238763929600000⟩, + ⟨4, 5, 5, 3, 8, 3, -3416091593298071325305515018185514774154969088000000⟩, + ⟨4, 5, 2, 4, 4, 3, -594601717159424539746746977561256223590842368000000⟩, + ⟨4, 5, 3, 4, 5, 3, 25248067425314409031214996646547148894668377292800000⟩, + ⟨4, 5, 4, 4, 6, 3, -14693583373964745897856174672853219005310592614400000⟩, + ⟨4, 5, 5, 4, 7, 3, -2041225318959054199959756649842364931679191040000000⟩, + ⟨4, 5, 6, 4, 8, 3, 1936874137627872130447734418552235772849684480000000⟩, + ⟨4, 5, 2, 5, 3, 3, -9915221701830619111121120174258643036349346611200000⟩, + ⟨4, 5, 3, 5, 4, 3, -25846425579179916440465062516387257885301879603200000⟩, + ⟨4, 5, 4, 5, 5, 3, -7623105501891905335893061005528001313302275686400000⟩, + ⟨4, 5, 5, 5, 6, 3, 4534015330373639634587634325514396364617809920000000⟩, + ⟨4, 5, 6, 5, 7, 3, -2347722426501030368168315781019978455865884672000000⟩, + ⟨4, 5, 7, 5, 8, 3, -191753731618635574405017560380754048580373708800000⟩, + ⟨4, 5, 2, 6, 2, 3, 6635432479781556354676401173043605675983660646400000⟩, + ⟨4, 5, 3, 6, 3, 3, -34381882901772936715676704100717033245559803084800000⟩, + ⟨4, 5, 4, 6, 4, 3, 14795109733380416029938729282287240855432252620800000⟩, + ⟨4, 5, 5, 6, 5, 3, -9190338365542706851763925018281328407727833088000000⟩, + ⟨4, 5, 6, 6, 6, 3, 1528730735223589194861227029416833895049986048000000⟩, + ⟨4, 5, 7, 6, 7, 3, 633627430513767870917011218773165451810491596800000⟩, + ⟨4, 5, 8, 6, 8, 3, -1253599678464141330191762103188962200465388339200000⟩, + ⟨4, 5, 2, 7, 1, 3, -97868405938348403180081041400917173577454085734400000⟩, + ⟨4, 5, 3, 7, 2, 3, -126558845687804881455792191057047730416273430937600000⟩, + ⟨4, 5, 4, 7, 3, 3, -53848992634077989435272906253311029627455746867200000⟩, + ⟨4, 5, 5, 7, 4, 3, -27791853113685477798277488411937663087684878336000000⟩, + ⟨4, 5, 6, 7, 5, 3, -1579851657437061745583382108968718221904445440000000⟩, + ⟨4, 5, 7, 7, 6, 3, -1586845082014454673661245112514620867399070515200000⟩, + ⟨4, 5, 8, 7, 7, 3, -949222618705085328265376193550222639305955737600000⟩ +] + +def collectedFourData_11_6_22 : List CollectedFourTerm := [ + ⟨4, 6, 1, 0, 7, 4, 37653423540435121299650967149496312908906653286400000⟩, + ⟨4, 6, 2, 0, 8, 4, -22891706626057348839247483824995682044506590412800000⟩, + ⟨4, 6, 1, 1, 6, 4, 18393958836811663067335660092213365952852944486400000⟩, + ⟨4, 6, 2, 1, 7, 4, -10493840944487710291248640851812112460110888960000000⟩, + ⟨4, 6, 3, 1, 8, 4, -199084954152491993141424292907154248688048537600000⟩, + ⟨4, 6, 1, 2, 5, 4, 10944440818744164418117325913763256313706237132800000⟩, + ⟨4, 6, 2, 2, 6, 4, -22106139580989574159133374815536296340796053913600000⟩, + ⟨4, 6, 3, 2, 7, 4, 7153121349860649860308190367775800145709157580800000⟩, + ⟨4, 6, 4, 2, 8, 4, -797497801569101705059079534983760857577344204800000⟩, + ⟨4, 6, 1, 3, 4, 4, 5967538651241608659991487737222209169343171788800000⟩, + ⟨4, 6, 2, 3, 5, 4, 5478407938025899546592224858318136215858682265600000⟩, + ⟨4, 6, 3, 3, 6, 4, -7854514322092252087252937701384758811216261939200000⟩, + ⟨4, 6, 4, 3, 7, 4, -4807826846285867394763791871293414836050015027200000⟩, + ⟨4, 6, 5, 3, 8, 4, 994029083368550453869234974935958019387686912000000⟩, + ⟨4, 6, 1, 4, 3, 4, -18806872600552938448487427555217812229514172825600000⟩, + ⟨4, 6, 2, 4, 4, 4, 692079101200816823713185568750353427388694528000000⟩, + ⟨4, 6, 3, 4, 5, 4, -14693583373964745897856174672853219005310592614400000⟩, + ⟨4, 6, 4, 4, 6, 4, 5700803121038999145445806920065086640064613580800000⟩, + ⟨4, 6, 5, 4, 7, 4, 593964557839799664805186497188771352501288960000000⟩, + ⟨4, 6, 6, 4, 8, 4, -450880000384929344602604025309801577936060416000000⟩, + ⟨4, 6, 1, 5, 2, 4, -3809098822045946269870821451776654992109207552000000⟩, + ⟨4, 6, 2, 5, 3, 4, 11540696108971878552012118987190899179850511155200000⟩, + ⟨4, 6, 3, 5, 4, 4, 15041809052913120839578799342456111148536797593600000⟩, + ⟨4, 6, 4, 5, 5, 4, 2957605543260260924261862095873586463322721484800000⟩, + ⟨4, 6, 5, 5, 6, 4, -1319327359861281918073909513149727683725230080000000⟩, + ⟨4, 6, 6, 5, 7, 4, 546520327779743049357236390405138718006863462400000⟩, + ⟨4, 6, 7, 5, 8, 4, 37198219245120372624245436346500833503661260800000⟩, + ⟨4, 6, 1, 6, 1, 4, -84046728951237548602437406031396257651562958028800000⟩, + ⟨4, 6, 2, 6, 2, 4, -7723227185794780901084116085931178538968704614400000⟩, + ⟨4, 6, 3, 6, 3, 4, 20009177512912259244715701261350500725791549030400000⟩, + ⟨4, 6, 4, 6, 4, 4, -5740193225678151419895789509970745490182609305600000⟩, + ⟨4, 6, 5, 6, 5, 4, 2674244343819654577182239284324317320982822912000000⟩, + ⟨4, 6, 6, 6, 6, 4, -355869336626195436474038646723535585926551961600000⟩, + ⟨4, 6, 7, 6, 7, 4, -122917097263325335663575675535259107809086668800000⟩, + ⟨4, 6, 8, 6, 8, 4, 208444484457791321415882709042749928382241177600000⟩, + ⟨4, 6, 1, 7, 0, 4, 526438183330822233713615387377096545004593925324800000⟩, + ⟨4, 6, 2, 7, 1, 4, 113912685522245757758832481458237281421945628262400000⟩, + ⟨4, 6, 3, 7, 2, 4, 73653278862920433055231661974771300628289080524800000⟩, + ⟨4, 6, 4, 7, 3, 4, 20892283213711760745087893638931120789683332710400000⟩, + ⟨4, 6, 5, 7, 4, 4, 8086993431296931116961082665192231361434353664000000⟩, + ⟨4, 6, 6, 7, 5, 4, 367769645985231797112103535134246736807067648000000⟩, + ⟨4, 6, 7, 7, 6, 4, 307831356242968101765460861441082651032367923200000⟩, + ⟨4, 6, 8, 7, 7, 4, 157833655185733873245425419692799810268351692800000⟩ +] + +def collectedFourData_11_6_23 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 6, 5, -5912862630054063518260945568252404177462886400000000⟩, + ⟨4, 7, 1, 0, 7, 5, 15692384802282494736018187200552563003589918720000000⟩, + ⟨4, 7, 2, 0, 8, 5, -4770156806210304974935609065461436761474334720000000⟩, + ⟨4, 7, 0, 1, 5, 5, -9029420935939650287845651465839280275723386880000000⟩, + ⟨4, 7, 1, 1, 6, 5, 7665838932139172129076206406972438378939678720000000⟩, + ⟨4, 7, 2, 1, 7, 5, -2186698773592391474915771637492631474274304000000000⟩, + ⟨4, 7, 3, 1, 8, 5, -27656783147936569885717493669170270867292160000000⟩, + ⟨4, 7, 0, 2, 4, 5, -2572932650955700671684179984187161165640499200000000⟩, + ⟨4, 7, 1, 2, 5, 5, 4561188880716487405152440111067805754264125440000000⟩, + ⟨4, 7, 2, 2, 6, 5, -4606460929446836312665936280418488504958320640000000⟩, + ⟨4, 7, 3, 2, 7, 5, 993708072245574044549603600494559766018785280000000⟩, + ⟨4, 7, 4, 2, 8, 5, -83090999466207194353054295092579276695797760000000⟩, + ⟨4, 7, 0, 3, 3, 5, -457623570839180718992963804457514709412741120000000⟩, + ⟨4, 7, 1, 3, 4, 5, 2487022534278035530382651997566799578388234240000000⟩, + ⟨4, 7, 2, 3, 5, 5, 1141586572799429808038298837939211917003325440000000⟩, + ⟨4, 7, 3, 3, 6, 5, -1091145236279766862743173352860292452418846720000000⟩, + ⟨4, 7, 4, 3, 7, 5, -500925691747804532282470666607946862574960640000000⟩, + ⟨4, 7, 5, 3, 8, 5, 82854016523243253294964013348672614453739520000000⟩, + ⟨4, 7, 0, 4, 2, 5, 3391797246384666253142699747702907014448414720000000⟩, + ⟨4, 7, 1, 4, 3, 5, -7837924258293607020740826139436584578978938880000000⟩, + ⟨4, 7, 2, 4, 4, 5, 144214928530978468938938799758631834432307200000000⟩, + ⟨4, 7, 3, 4, 5, 5, -2041225318959054199959756649842364931679191040000000⟩, + ⟨4, 7, 4, 4, 6, 5, 593964557839799664805186497188771352501288960000000⟩, + ⟨4, 7, 5, 4, 7, 5, 49507957174361119134193098667370481293721600000000⟩, + ⟨4, 7, 6, 4, 8, 5, -31318013080074488123809599700386062322892800000000⟩, + ⟨4, 7, 0, 5, 1, 5, 2614361398929678720776601373011017147005009920000000⟩, + ⟨4, 7, 1, 5, 2, 5, -1587474360764997685259933003760699021302169600000000⟩, + ⟨4, 7, 2, 5, 3, 5, 2404841674405926185086943681968482395074068480000000⟩, + ⟨4, 7, 3, 5, 4, 5, 2089600657669187636948712751956757692819701760000000⟩, + ⟨4, 7, 4, 5, 5, 5, 308151822027306194655183354301057326655733760000000⟩, + ⟨4, 7, 5, 5, 6, 5, -109968181718667809311862690415004800044236800000000⟩, + ⟨4, 7, 6, 5, 7, 5, 37961166517299996683806181810402062415953920000000⟩, + ⟨4, 7, 7, 5, 8, 5, 2214667791011075465230719373998359178117120000000⟩, + ⟨4, 7, 0, 6, 0, 5, -60303932703538042269981301480636877280494223360000000⟩, + ⟨4, 7, 1, 6, 1, 5, -35027189776239804539970883626957924810872586240000000⟩, + ⟨4, 7, 2, 6, 2, 5, -1609360338573086987934199246993016838747586560000000⟩, + ⟨4, 7, 3, 6, 3, 5, 2779665021894655484669628138508567590878576640000000⟩, + ⟨4, 7, 4, 6, 4, 5, -598068598198413808244743208518692410983710720000000⟩, + ⟨4, 7, 5, 6, 5, 5, 222902819200384036281913572947216213496299520000000⟩, + ⟨4, 7, 6, 6, 6, 5, -24718595922954459858981199873460088896225280000000⟩, + ⟨4, 7, 7, 6, 7, 5, -7318106667414512433102383642102846529208320000000⟩, + ⟨4, 7, 8, 6, 8, 5, 10858876671972517482414893259999901447618560000000⟩, + ⟨4, 7, 1, 7, 0, 5, 219397594446370387272502560183829407359607767040000000⟩, + ⟨4, 7, 2, 7, 1, 5, 23737040712338603885421949853069648634587381760000000⟩, + ⟨4, 7, 3, 7, 2, 5, 10231876990995569073273329738499372476981575680000000⟩, + ⟨4, 7, 4, 7, 3, 5, 2176759221082261084292721954531822621142548480000000⟩, + ⟨4, 7, 5, 7, 4, 5, 674064671336793013453520787101873610361405440000000⟩, + ⟨4, 7, 6, 7, 5, 5, 25545188461645583586366856574817291101798400000000⟩, + ⟨4, 7, 7, 7, 6, 5, 18327334038281635258686962390551058951700480000000⟩, + ⟨4, 7, 8, 7, 7, 5, 8222314928633061361817196964627135258951680000000⟩ +] + +def collectedFourData_11_6_24 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 6, 6, 22442344999597305386056909477495182655173427200000000⟩, + ⟨4, 8, 1, 0, 7, 6, -29780322631648998537090696869830972339944161280000000⟩, + ⟨4, 8, 2, 0, 8, 6, 6035063524223407619176216785940291496989163520000000⟩, + ⟨4, 8, 0, 1, 5, 6, 34271281521230200760964491576803414883161866240000000⟩, + ⟨4, 8, 1, 1, 6, 6, -14547894377924933813240521215652629237234401280000000⟩, + ⟨4, 8, 2, 1, 7, 6, 2766547630004614710158497567052792504254464000000000⟩, + ⟨4, 8, 3, 1, 8, 6, 26242917678749039534283680656887759419473920000000⟩, + ⟨4, 8, 0, 2, 4, 6, 9765598463252028139751122864281315318536601600000000⟩, + ⟨4, 8, 1, 2, 5, 6, -8656025082425307502782487992772901661636034560000000⟩, + ⟨4, 8, 2, 2, 6, 6, 5827960266394481447806522005870467264796426240000000⟩, + ⟨4, 8, 3, 2, 7, 6, -942907893414734584737276425896824621351567360000000⟩, + ⟨4, 8, 4, 2, 8, 6, 63074588166609486358230205706944122659536896000000⟩, + ⟨4, 8, 0, 3, 3, 6, 1736916058986245529050126327695827623749877760000000⟩, + ⟨4, 8, 1, 3, 4, 6, -4719762763669190362627676809354268097915125760000000⟩, + ⟨4, 8, 2, 3, 5, 6, -1444302098470954253193272321118303845131223040000000⟩, + ⟨4, 8, 3, 3, 6, 6, 1035363890951485900031373742414396054453616640000000⟩, + ⟨4, 8, 4, 3, 7, 6, 380253961464461517281930576561681774615199744000000⟩, + ⟨4, 8, 5, 3, 8, 6, -52412244845267646641087043123400732217180160000000⟩, + ⟨4, 8, 0, 4, 2, 6, -12873609406236591642745696376779970475259330560000000⟩, + ⟨4, 8, 1, 4, 3, 6, 14874470395376800574081183397437266751253381120000000⟩, + ⟨4, 8, 2, 4, 4, 6, -182456529247148245622131642391535451058995200000000⟩, + ⟨4, 8, 3, 4, 5, 6, 1936874137627872130447734418552235772849684480000000⟩, + ⟨4, 8, 4, 4, 6, 6, -450880000384929344602604025309801577936060416000000⟩, + ⟨4, 8, 5, 4, 7, 6, -31318013080074488123809599700386062322892800000000⟩, + ⟨4, 8, 6, 4, 8, 6, 16981130756058804905978357803187719844659200000000⟩, + ⟨4, 8, 0, 5, 1, 6, -9922841800888113579881131511971730809851740160000000⟩, + ⟨4, 8, 1, 5, 2, 6, 3012639520933494680092436664622458130032230400000000⟩, + ⟨4, 8, 2, 5, 3, 6, -3042535677620592049905616102268161922621767680000000⟩, + ⟨4, 8, 3, 5, 4, 6, -1982776440316547249417864968239138487790469120000000⟩, + ⟨4, 8, 4, 5, 5, 6, -233918828658060049934153966097696931757162496000000⟩, + ⟨4, 8, 5, 5, 6, 6, 69564271079251815998105290647627024983654400000000⟩, + ⟨4, 8, 6, 5, 7, 6, -20583155471408963405439998665881113465978880000000⟩, + ⟨4, 8, 7, 5, 8, 6, -1050724956232244070368373359918413743390720000000⟩, + ⟨4, 8, 0, 6, 0, 6, 228884340333968675953310985771360410934737633280000000⟩, + ⟨4, 8, 1, 6, 1, 6, 66473071209972765708891127193420850561558773760000000⟩, + ⟨4, 8, 2, 6, 2, 6, 2036115849275514478328466520708299973680168960000000⟩, + ⟨4, 8, 3, 6, 3, 6, -2637563448861261303794545099181579080229191680000000⟩, + ⟨4, 8, 4, 6, 4, 6, 453995387816801662934330078971182361935347712000000⟩, + ⟨4, 8, 5, 6, 5, 6, -141005078895041107075973896940321283149660160000000⟩, + ⟨4, 8, 6, 6, 6, 6, 13402820555718134608139937952383585138769920000000⟩, + ⟨4, 8, 7, 6, 7, 6, 3471995817626244206711321937191270004817920000000⟩, + ⟨4, 8, 8, 6, 8, 6, -4579444881961571380219611436440529215160320000000⟩, + ⟨4, 8, 1, 7, 0, 6, -416363174211114548014892060850021551215434792960000000⟩, + ⟨4, 8, 2, 7, 1, 6, -30031412885533760221561587965388927166222172160000000⟩, + ⟨4, 8, 3, 7, 2, 6, -9708804676867005292797119387373773992922972160000000⟩, + ⟨4, 8, 4, 7, 3, 6, -1652383438515166015571016910316603865833668608000000⟩, + ⟨4, 8, 5, 7, 4, 6, -426403499530259410875140334024058698486251520000000⟩, + ⟨4, 8, 6, 7, 5, 6, -13851012334219786087849410070637694261657600000000⟩, + ⟨4, 8, 7, 7, 6, 6, -8695203557566383893902675934461987525754880000000⟩, + ⟨4, 8, 8, 7, 7, 6, -3467544494265363431857516552974930762792960000000⟩ +] + +def collectedFourData_11_6_25 : List CollectedFourTerm := [ + ⟨5, 1, 5, 3, 8, 0, 4375263188133034075336797644862380775491764224000000⟩, + ⟨5, 1, 5, 4, 7, 0, 2614361398929678720776601373011017147005009920000000⟩, + ⟨5, 1, 6, 4, 8, 0, -9922841800888113579881131511971730809851740160000000⟩, + ⟨5, 1, 5, 5, 6, 0, -5807078009364047774062279539009192590479196160000000⟩, + ⟨5, 1, 6, 5, 7, 0, 12027667558769751281290992502317338092344705024000000⟩, + ⟨5, 1, 7, 5, 8, 0, 2455944228146909083077843700474892525160628224000000⟩, + ⟨5, 1, 5, 6, 5, 0, 11770805330902959062431344456054116204333236224000000⟩, + ⟨5, 1, 6, 6, 6, 0, -7831873505398370979177065515561710755266953216000000⟩, + ⟨5, 1, 7, 6, 7, 0, -8115375996232295532222905008201289239797694464000000⟩, + ⟨5, 1, 8, 6, 8, 0, 32111718178751926071763640279426824483878469632000000⟩, + ⟨5, 1, 5, 7, 4, 0, 35595260998523989775658300806200218373092016128000000⟩, + ⟨5, 1, 6, 7, 5, 0, 8093772208047709023540820159278258133118484480000000⟩, + ⟨5, 1, 7, 7, 6, 0, 20324000932026498788380615382471125789411639296000000⟩, + ⟨5, 1, 8, 7, 7, 0, 24314914676827987945614602162679754970256900096000000⟩ +] + +def collectedFourData_11_6_26 : List CollectedFourTerm := [ + ⟨5, 2, 4, 2, 8, 1, 532863154900085857195900884143451125015642112000000⟩, + ⟨5, 2, 4, 3, 7, 1, 3212439929595507928498481205071117050831699968000000⟩, + ⟨5, 2, 5, 3, 8, 1, -2656716908229923649683370051485477876394885120000000⟩, + ⟨5, 2, 4, 4, 6, 1, -3809098822045946269870821451776654992109207552000000⟩, + ⟨5, 2, 5, 4, 7, 1, -1587474360764997685259933003760699021302169600000000⟩, + ⟨5, 2, 6, 4, 8, 1, 3012639520933494680092436664622458130032230400000000⟩, + ⟨5, 2, 4, 5, 5, 1, -1976179768308850451576439502824638245672845312000000⟩, + ⟨5, 2, 5, 5, 6, 1, 3526133553915599717225702403914408007617740800000000⟩, + ⟨5, 2, 6, 5, 7, 1, -3651678355786780137267489917189857573664194560000000⟩, + ⟨5, 2, 7, 5, 8, 1, -497093795735120417849492386458552255947735040000000⟩, + ⟨5, 2, 4, 6, 4, 1, 3835418061282174414685058603173352979472318464000000⟩, + ⟨5, 2, 5, 6, 5, 1, -7147386614572263029869788841503468385594245120000000⟩, + ⟨5, 2, 6, 6, 6, 1, 2377807902087415574814838811112440440333271040000000⟩, + ⟨5, 2, 7, 6, 7, 1, 1642587405508251253094751814734646951217725440000000⟩, + ⟨5, 2, 8, 6, 8, 1, -4874663589906677993460983899801141438882775040000000⟩, + ⟨5, 2, 4, 7, 3, 1, -13959571956713316780987269819669819549942808576000000⟩, + ⟨5, 2, 5, 7, 4, 1, -21613907022582627060390336542038271040568688640000000⟩, + ⟨5, 2, 6, 7, 5, 1, -2457322057196891162643975478280326019756851200000000⟩, + ⟨5, 2, 7, 7, 6, 1, -4113666203018044451630812343024259550056284160000000⟩, + ⟨5, 2, 8, 7, 7, 1, -3691083379812709786252571968120921821145989120000000⟩ +] + +def collectedFourData_11_6_27 : List CollectedFourTerm := [ + ⟨5, 3, 3, 1, 8, 2, -134342413806177553762652111421189711331118284800000⟩, + ⟨5, 3, 3, 2, 7, 2, 4826922217601214594445650370428464393552815718400000⟩, + ⟨5, 3, 4, 2, 8, 2, -1614453188449129228320448700286610330690466611200000⟩, + ⟨5, 3, 3, 3, 6, 2, -5300221796252991124490779365797638628202617241600000⟩, + ⟨5, 3, 4, 3, 7, 2, -9732956462357064252518452174739105089885883596800000⟩, + ⟨5, 3, 5, 3, 8, 2, 4024621559828757642859993908954958513890656256000000⟩, + ⟨5, 3, 3, 4, 5, 2, -9915221701830619111121120174258643036349346611200000⟩, + ⟨5, 3, 4, 4, 6, 2, 11540696108971878552012118987190899179850511155200000⟩, + ⟨5, 3, 5, 4, 7, 2, 2404841674405926185086943681968482395074068480000000⟩, + ⟨5, 3, 6, 4, 8, 2, -3042535677620592049905616102268161922621767680000000⟩, + ⟨5, 3, 3, 5, 4, 2, 10150204191885526876023753403641428023719021772800000⟩, + ⟨5, 3, 4, 5, 5, 2, 5987371614186963587315293368106490015924826931200000⟩, + ⟨5, 3, 5, 5, 6, 2, -5341688111353767615981448397160324896170967040000000⟩, + ⟨5, 3, 6, 5, 7, 2, 3687916062799816986983530394142982745622577152000000⟩, + ⟨5, 3, 7, 5, 8, 2, 376520057777931761076692462455697541615845376000000⟩, + ⟨5, 3, 3, 6, 3, 2, 13502181602844516115485583750393005525947331379200000⟩, + ⟨5, 3, 4, 6, 4, 2, -11620437369578368097716278132742022267421484646400000⟩, + ⟨5, 3, 5, 6, 5, 2, 10827471371273974254470728134969397586486624256000000⟩, + ⟨5, 3, 6, 6, 6, 2, -2401404259075588054006352050486267003816378368000000⟩, + ⟨5, 3, 7, 6, 7, 2, -1244165809618802622619661289914653657201115136000000⟩, + ⟨5, 3, 8, 6, 8, 2, 2953822610166153475535268471515528998672977100800000⟩, + ⟨5, 3, 3, 7, 2, 2, 49701190676645577928348975356214279125126768230400000⟩, + ⟨5, 3, 4, 7, 3, 2, 42294302482082220598862291946671346131547036057600000⟩, + ⟨5, 3, 5, 7, 4, 2, 32742591401346227005698544734066409990030098432000000⟩, + ⟨5, 3, 6, 7, 5, 2, 2481707478931601408274743268277397494997975040000000⟩, + ⟨5, 3, 7, 7, 6, 2, 3115866361093769600205200703901818524327215104000000⟩, + ⟨5, 3, 8, 7, 7, 2, 2236627275341479022814417570537989881727444582400000⟩ +] + +def collectedFourData_11_6_28 : List CollectedFourTerm := [ + ⟨5, 4, 2, 0, 8, 3, -20133577243627876450409208324029263052841104179200000⟩, + ⟨5, 4, 2, 1, 7, 3, -9229480382982561722684154007583370958539325440000000⟩, + ⟨5, 4, 3, 1, 8, 3, -350196022336816246030462098683013750474984652800000⟩, + ⟨5, 4, 2, 2, 6, 3, -19442660002712466885688096042015517623357695590400000⟩, + ⟨5, 4, 3, 2, 7, 3, 12582541230589532772217695288257335553669097062400000⟩, + ⟨5, 4, 4, 2, 8, 3, -2104231526089631198379302849601593630871099801600000⟩, + ⟨5, 4, 2, 3, 5, 3, 4818336666380106821965440590430344150503548518400000⟩, + ⟨5, 4, 3, 3, 6, 3, -13816311155675705158239654403530039584439769497600000⟩, + ⟨5, 4, 4, 3, 7, 3, -12685653555445204787414334394528032735743075942400000⟩, + ⟨5, 4, 5, 3, 8, 3, 3497050116767154608237848302529509241569411072000000⟩, + ⟨5, 4, 2, 4, 4, 3, 608693282259098434908991897427791966101307392000000⟩, + ⟨5, 4, 3, 4, 5, 3, -25846425579179916440465062516387257885301879603200000⟩, + ⟨5, 4, 4, 4, 6, 3, 15041809052913120839578799342456111148536797593600000⟩, + ⟨5, 4, 5, 4, 7, 3, 2089600657669187636948712751956757692819701760000000⟩, + ⟨5, 4, 6, 4, 8, 3, -1982776440316547249417864968239138487790469120000000⟩, + ⟨5, 4, 2, 5, 3, 3, 10150204191885526876023753403641428023719021772800000⟩, + ⟨5, 4, 3, 5, 4, 3, 26458964322564064195074149815839383545038294220800000⟩, + ⟨5, 4, 4, 5, 5, 3, 7803766748473522908878545959991942509852465561600000⟩, + ⟨5, 4, 5, 5, 6, 3, -4641467714628609821625459672474604460813844480000000⟩, + ⟨5, 4, 6, 5, 7, 3, 2403361491196387443176788936025533236136378368000000⟩, + ⟨5, 4, 7, 5, 8, 3, 196298135232399290287153229125381968171840307200000⟩, + ⟨5, 4, 2, 6, 2, 3, -6792686698958764359616331046667889692200507801600000⟩, + ⟨5, 4, 3, 6, 3, 3, 35196704869449487383338783532964353405051155251200000⟩, + ⟨5, 4, 4, 6, 4, 3, -15145741502425323968358322498969571551498941235200000⟩, + ⟨5, 4, 5, 6, 5, 3, 9408141724713552361345812651316419320529027072000000⟩, + ⟨5, 4, 6, 6, 6, 3, -1564960379460387874251892595895114935474061312000000⟩, + ⟨5, 4, 7, 6, 7, 3, -648643872492239097023206761253040052700918579200000⟩, + ⟨5, 4, 8, 6, 8, 3, 1283308945975845007883927428854925574898765004800000⟩, + ⟨5, 4, 2, 7, 1, 3, 100187805586351401677782386935501454680264382873600000⟩, + ⟨5, 4, 3, 7, 2, 3, 129558184844558640117882839606749102687140603494400000⟩, + ⟨5, 4, 4, 7, 3, 3, 55125168876689674055557898061014665712764767436800000⟩, + ⟨5, 4, 5, 7, 4, 3, 28450496868135096342110722257871923440919773184000000⟩, + ⟨5, 4, 6, 7, 5, 3, 1617292824921334275153661238478368400589455360000000⟩, + ⟨5, 4, 7, 7, 6, 3, 1624451987832233510760676609644579050947923148800000⟩, + ⟨5, 4, 8, 7, 7, 3, 971718403596973323542741120333852075847214694400000⟩ +] + +def collectedFourData_11_6_29 : List CollectedFourTerm := [ + ⟨5, 5, 1, 0, 7, 4, 19534786910097798166712432878257225328952239718400000⟩, + ⟨5, 5, 2, 0, 8, 4, -11876333382229723388887329276736564231056182476800000⟩, + ⟨5, 5, 1, 1, 6, 4, 9542879040583354279115110517222483691189986918400000⟩, + ⟨5, 5, 2, 1, 7, 4, -5444257850787129926614623125208356452313333760000000⟩, + ⟨5, 5, 3, 1, 8, 4, -103286282911277044886170666044928527387171225600000⟩, + ⟨5, 5, 1, 2, 5, 4, 5678031348590431508524507464279090538990062796800000⟩, + ⟨5, 5, 2, 2, 6, 4, -11468777219042740165280215444273039208624003481600000⟩, + ⟨5, 5, 3, 2, 7, 4, 3711075598784294431567740710887755804389985484800000⟩, + ⟨5, 5, 4, 2, 8, 4, -413745900109029756968992497120378196610305228800000⟩, + ⟨5, 5, 1, 3, 4, 4, 3095989287789211093760029857750373857464470732800000⟩, + ⟨5, 5, 2, 3, 5, 4, 2842225795510957115336510784343795479057373593600000⟩, + ⟨5, 5, 3, 3, 6, 4, -4074961826501960206660943192819894614538531635200000⟩, + ⟨5, 5, 4, 3, 7, 4, -2494324927505824540714710290014122143355450163200000⟩, + ⟨5, 5, 5, 3, 8, 4, 515707324864943133202724359618048608511721472000000⟩, + ⟨5, 5, 1, 4, 3, 4, -9757100793308447087610201867823095794718316953600000⟩, + ⟨5, 5, 2, 4, 4, 4, 359054144236620820445381444440772472018567168000000⟩, + ⟨5, 5, 3, 4, 5, 4, -7623105501891905335893061005528001313302275686400000⟩, + ⟨5, 5, 4, 4, 6, 4, 2957605543260260924261862095873586463322721484800000⟩, + ⟨5, 5, 5, 4, 7, 4, 308151822027306194655183354301057326655733760000000⟩, + ⟨5, 5, 6, 4, 8, 4, -233918828658060049934153966097696931757162496000000⟩, + ⟨5, 5, 1, 5, 2, 4, -1976179768308850451576439502824638245672845312000000⟩, + ⟨5, 5, 2, 5, 3, 4, 5987371614186963587315293368106490015924826931200000⟩, + ⟨5, 5, 3, 5, 4, 4, 7803766748473522908878545959991942509852465561600000⟩, + ⟨5, 5, 4, 5, 5, 4, 1534420741042809651496315446210598069546568908800000⟩, + ⟨5, 5, 5, 5, 6, 4, -684473718887082853873180885080306629455380480000000⟩, + ⟨5, 5, 6, 5, 7, 4, 283537515088082462257035711154831858382300774400000⟩, + ⟨5, 5, 7, 5, 8, 4, 19298624615320389842497643333260273941007564800000⟩, + ⟨5, 5, 1, 6, 1, 4, -43603868816604290550513369979506917256895188172800000⟩, + ⟨5, 5, 2, 6, 2, 4, -4006849395002765154576726515383933260850947686400000⟩, + ⟨5, 5, 3, 6, 3, 4, 10380862673517858936563140457739241065128814182400000⟩, + ⟨5, 5, 4, 6, 4, 4, -2978041329123556221280645249676160294152935833600000⟩, + ⟨5, 5, 5, 6, 5, 4, 1387411515076474013699659861712815694882537472000000⟩, + ⟨5, 5, 6, 6, 6, 4, -184626814912731159441093204846778963669391769600000⟩, + ⟨5, 5, 7, 6, 7, 4, -63770012840088164957772741836248585603960012800000⟩, + ⟨5, 5, 8, 6, 8, 4, 108142054655280116666367464224890079984327065600000⟩, + ⟨5, 5, 1, 7, 0, 4, 273118796798464271970973517330316148826165791948800000⟩, + ⟨5, 5, 2, 7, 1, 4, 59098478406469447626435394812363808156254889574400000⟩, + ⟨5, 5, 3, 7, 2, 4, 38211694250645400771433219921139158590096723148800000⟩, + ⟨5, 5, 4, 7, 3, 4, 10839022385494250699032468178782436255263516262400000⟩, + ⟨5, 5, 5, 7, 4, 4, 4195573166251341197159554662159154370769321984000000⟩, + ⟨5, 5, 6, 7, 5, 4, 190800755703091796148935679920227605584805888000000⟩, + ⟨5, 5, 7, 7, 6, 4, 159704467297511895271398157675062245614367539200000⟩, + ⟨5, 5, 8, 7, 7, 4, 81884900000769854666737119046852763290750156800000⟩ +] + +def collectedFourData_11_6_30 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 6, 5, 13133782714751979712171784946873635918000947200000000⟩, + ⟨5, 6, 1, 0, 7, 5, -34856276082228218313460266797659243116295618560000000⟩, + ⟨5, 6, 2, 0, 8, 5, 10595578982271837117384962342961812429403586560000000⟩, + ⟨5, 6, 0, 1, 5, 5, 20056351725455104089986450372599617518032650240000000⟩, + ⟨5, 6, 1, 1, 6, 5, -17027532882170419198452249997655308969244098560000000⟩, + ⟨5, 6, 2, 1, 7, 5, 4857144221311718456790394855580661650030592000000000⟩, + ⟨5, 6, 3, 1, 8, 5, 61431865270763434494807859467185058144583680000000⟩, + ⟨5, 6, 0, 2, 4, 5, 5715055547812379027965927043102650339531161600000000⟩, + ⟨5, 6, 1, 2, 5, 5, -10131414752607806109607748008079112753245061120000000⟩, + ⟨5, 6, 2, 2, 6, 5, 10231974039754754287905987756383669538489630720000000⟩, + ⟨5, 6, 3, 2, 7, 5, -2207246594303020420906538881762871660186173440000000⟩, + ⟨5, 6, 4, 2, 8, 5, 184563586340371290746328241578149608402452480000000⟩, + ⟨5, 6, 0, 3, 3, 5, 1016483710276177201918536918263625418549493760000000⟩, + ⟨5, 6, 1, 3, 4, 5, -5524230075272502431661680136959247148143083520000000⟩, + ⟨5, 6, 2, 3, 5, 5, -2535717627028486188266000871155113191926661120000000⟩, + ⟨5, 6, 3, 3, 6, 5, 2423676202233051760910523363316826594932162560000000⟩, + ⟨5, 6, 4, 3, 7, 5, 1112667349688172758964317439637263930328350720000000⟩, + ⟨5, 6, 5, 3, 8, 5, -184037194527348162088609895264453798091816960000000⟩, + ⟨5, 6, 0, 4, 2, 5, -7533935901044766917932474450493794077439426560000000⟩, + ⟨5, 6, 1, 4, 3, 5, 17409772657304330692951291498601619011131146240000000⟩, + ⟨5, 6, 2, 4, 4, 5, -320333424612646341380145173394664902465945600000000⟩, + ⟨5, 6, 3, 4, 5, 5, 4534015330373639634587634325514396364617809920000000⟩, + ⟨5, 6, 4, 4, 6, 5, -1319327359861281918073909513149727683725230080000000⟩, + ⟨5, 6, 5, 4, 7, 5, -109968181718667809311862690415004800044236800000000⟩, + ⟨5, 6, 6, 4, 8, 5, 69564271079251815998105290647627024983654400000000⟩, + ⟨5, 6, 0, 5, 1, 5, -5807078009364047774062279539009192590479196160000000⟩, + ⟨5, 6, 1, 5, 2, 5, 3526133553915599717225702403914408007617740800000000⟩, + ⟨5, 6, 2, 5, 3, 5, -5341688111353767615981448397160324896170967040000000⟩, + ⟨5, 6, 3, 5, 4, 5, -4641467714628609821625459672474604460813844480000000⟩, + ⟨5, 6, 4, 5, 5, 5, -684473718887082853873180885080306629455380480000000⟩, + ⟨5, 6, 5, 5, 6, 5, 244263784666368643017578594383613433112166400000000⟩, + ⟨5, 6, 6, 5, 7, 5, -84320192067810251026547340695428961308508160000000⟩, + ⟨5, 6, 7, 5, 8, 5, -4919269628327769852562217928290677303541760000000⟩, + ⟨5, 6, 0, 6, 0, 5, 133948444015526340075831646940572247659936481280000000⟩, + ⟨5, 6, 1, 6, 1, 5, 77803177312324824866521066282943252105023979520000000⟩, + ⟨5, 6, 2, 6, 2, 5, 3574747177301722672124901649428918586709114880000000⟩, + ⟨5, 6, 3, 6, 3, 5, -6174254113701083486293301313893435330757918720000000⟩, + ⟨5, 6, 4, 6, 4, 5, 1328443346092492249930021131220585579869634560000000⟩, + ⟨5, 6, 5, 6, 5, 5, -495116727218254655018472128086240673094696960000000⟩, + ⟨5, 6, 6, 6, 6, 5, 54905498094223382787041807903223757343293440000000⟩, + ⟨5, 6, 7, 6, 7, 5, 16255142198749360770271539374223636415119360000000⟩, + ⟨5, 6, 8, 6, 8, 5, -24119979722017005895458698418223164822650880000000⟩, + ⟨5, 6, 1, 7, 0, 5, -487330843600463877572262769154181610386405457920000000⟩, + ⟨5, 6, 2, 7, 1, 5, -52725245707970432417060340979274126268542484480000000⟩, + ⟨5, 6, 3, 7, 2, 5, -22727274007814618596419720202951710080646512640000000⟩, + ⟨5, 6, 4, 7, 3, 5, -4835066264978623912347818621741020363138007040000000⟩, + ⟨5, 6, 5, 7, 4, 5, -1497247523395820856573251000299746122394501120000000⟩, + ⟨5, 6, 6, 7, 5, 5, -56741543927864739464026925027955083260723200000000⟩, + ⟨5, 6, 7, 7, 6, 5, -40709084255736897185303376932099572409303040000000⟩, + ⟨5, 6, 8, 7, 7, 5, -18263589811140372299650440915407939976560640000000⟩ +] + +def collectedFourData_11_6_31 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 6, 6, -27202798382839871761347773027659617673496494080000000⟩, + ⟨5, 7, 1, 0, 7, 6, 36097302324654896831986723991993572686343176192000000⟩, + ⟨5, 7, 2, 0, 8, 6, -7315216670986307730971133587797184363813142528000000⟩, + ⟨5, 7, 0, 1, 5, 6, -41540880044411543184864218717909576365885095936000000⟩, + ⟨5, 7, 1, 1, 6, 6, 17633782818357113799460802351651833633352712192000000⟩, + ⟨5, 7, 2, 1, 7, 6, -3353385637592212545330265616923976216975769600000000⟩, + ⟨5, 7, 3, 1, 8, 6, -31809545687194621891840253196796606009049088000000⟩, + ⟨5, 7, 0, 2, 4, 6, -11837069882331036805942943224734052119729930240000000⟩, + ⟨5, 7, 1, 2, 5, 6, 10492134628455522304306247771900159151449309184000000⟩, + ⟨5, 7, 2, 2, 6, 6, -7064182825492413405633721508794935467034279936000000⟩, + ⟨5, 7, 3, 2, 7, 6, 1142916808319698256700756828446288765050159104000000⟩, + ⟨5, 7, 4, 2, 8, 6, -76453922484826029997790044205117965026616934400000⟩, + ⟨5, 7, 0, 3, 3, 6, -2105349390242751194119538161118907829441265664000000⟩, + ⟨5, 7, 1, 3, 4, 6, 5720915299948908067464370650607887155529252864000000⟩, + ⟨5, 7, 2, 3, 5, 6, 1750666375965742060401251543336264017385619456000000⟩, + ⟨5, 7, 3, 3, 6, 6, -1254984502685938277680529856329419026906218496000000⟩, + ⟨5, 7, 4, 3, 7, 6, -460913146472862613901220045243327382910769561600000⟩, + ⟨5, 7, 5, 3, 8, 6, 63529890897918077976632112566380936795521024000000⟩, + ⟨5, 7, 0, 4, 2, 6, 15604349774658962976629036709250499210939203584000000⟩, + ⟨5, 7, 1, 4, 3, 6, -18029631895606988228849088351119016826836615168000000⟩, + ⟨5, 7, 2, 4, 4, 6, 221159071337329482617091190716073197730529280000000⟩, + ⟨5, 7, 3, 4, 5, 6, -2347722426501030368168315781019978455865884672000000⟩, + ⟨5, 7, 4, 4, 6, 6, 546520327779743049357236390405138718006863462400000⟩, + ⟨5, 7, 5, 4, 7, 6, 37961166517299996683806181810402062415953920000000⟩, + ⟨5, 7, 6, 4, 8, 6, -20583155471408963405439998665881113465978880000000⟩, + ⟨5, 7, 0, 5, 1, 6, 12027667558769751281290992502317338092344705024000000⟩, + ⟨5, 7, 1, 5, 2, 6, -3651678355786780137267489917189857573664194560000000⟩, + ⟨5, 7, 2, 5, 3, 6, 3687916062799816986983530394142982745622577152000000⟩, + ⟨5, 7, 3, 5, 4, 6, 2403361491196387443176788936025533236136378368000000⟩, + ⟨5, 7, 4, 5, 5, 6, 283537515088082462257035711154831858382300774400000⟩, + ⟨5, 7, 5, 5, 6, 6, -84320192067810251026547340695428961308508160000000⟩, + ⟨5, 7, 6, 5, 7, 6, 24949238966847374112624871296274797095288832000000⟩, + ⟨5, 7, 7, 5, 8, 6, 1273603945608930683603790189140003266756608000000⟩, + ⟨5, 7, 0, 6, 0, 6, -277435114877967322862324049115887317277046996992000000⟩, + ⟨5, 7, 1, 6, 1, 6, -80573289201529217124072337319153169702599000064000000⟩, + ⟨5, 7, 2, 6, 2, 6, -2468015215564169152660633844614784262648889344000000⟩, + ⟨5, 7, 3, 6, 3, 6, 3197041428719151459470977811843501043065290752000000⟩, + ⟨5, 7, 4, 6, 4, 6, -550296548856247159162300002752688950761802956800000⟩, + ⟨5, 7, 5, 6, 5, 6, 170914970436781864702529345729126321067393024000000⟩, + ⟨5, 7, 6, 6, 6, 6, -16245816796111296141130824347132083713343488000000⟩, + ⟨5, 7, 7, 6, 7, 6, -4208472965487551484746020073337626126450688000000⟩, + ⟨5, 7, 8, 6, 8, 6, 5550833294451353102253583716217940028162048000000⟩, + ⟨5, 7, 1, 7, 0, 6, 504681818335268229574040649113226326141193682944000000⟩, + ⟨5, 7, 2, 7, 1, 6, 36401653654805369459511424097380873251349069824000000⟩, + ⟨5, 7, 3, 7, 2, 6, 11768229040589339382445225497156605810074189824000000⟩, + ⟨5, 7, 4, 7, 3, 6, 2002885773740591550178595123619741271799837491200000⟩, + ⟨5, 7, 5, 7, 4, 6, 516851889928041663768657126392828356856905728000000⟩, + ⟨5, 7, 6, 7, 5, 6, 16789078678398803062041195845148213919088640000000⟩, + ⟨5, 7, 7, 7, 6, 6, 10539623612348646152418452384595040882655232000000⟩, + ⟨5, 7, 8, 7, 7, 6, 4203077430755105404006438994440133692882944000000⟩ +] + +def collectedFourData_11_6_32 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 6, 7, -5554572850582940588068782112419329502955438080000000⟩, + ⟨5, 8, 1, 0, 7, 7, 4913835031479595058450377187467109122103574528000000⟩, + ⟨5, 8, 2, 0, 8, 7, -746851543450478258036933892198611023470526464000000⟩, + ⟨5, 8, 0, 1, 5, 7, -8482283375285687060773996128999797832586100736000000⟩, + ⟨5, 8, 1, 1, 6, 7, 2400442530885847051434964771498036005099798528000000⟩, + ⟨5, 8, 2, 1, 7, 7, -342365968345641888336815883891964761656524800000000⟩, + ⟨5, 8, 3, 1, 8, 7, -2598092098861827372529007528804533566386995200000⟩, + ⟨5, 8, 0, 2, 4, 7, -2417025854234373690306013239105112982673162240000000⟩, + ⟨5, 8, 1, 2, 5, 7, 1428267914001182652825809375594973689341280256000000⟩, + ⟨5, 8, 2, 2, 6, 7, -721222088658109772527494522102786804173242368000000⟩, + ⟨5, 8, 3, 2, 7, 7, 93349435372387619623837075840806575461210521600000⟩, + ⟨5, 8, 4, 2, 8, 7, -5203740146855354931112066483143762378542284800000⟩, + ⟨5, 8, 0, 3, 3, 7, -429893880749076478340031656420407123183140864000000⟩, + ⟨5, 8, 1, 3, 4, 7, 778773819721590427523043726329446112874725376000000⟩, + ⟨5, 8, 2, 3, 5, 7, 178735359971310548353442182466163318485680128000000⟩, + ⟨5, 8, 3, 3, 6, 7, -102502731497198410017303731328936058278012518400000⟩, + ⟨5, 8, 4, 3, 7, 7, -31371474040331777904048289954915661284324147200000⟩, + ⟨5, 8, 5, 3, 8, 7, 3706356154096237010376257621169364285784064000000⟩, + ⟨5, 8, 0, 4, 2, 7, 3186271367728017565522527402969868389039734784000000⟩, + ⟨5, 8, 1, 4, 3, 7, -2454328470767862918430508562701631693848051712000000⟩, + ⟨5, 8, 2, 4, 4, 7, 22579371357716564021676255667006711938416640000000⟩, + ⟨5, 8, 3, 4, 5, 7, -191753731618635574405017560380754048580373708800000⟩, + ⟨5, 8, 4, 4, 6, 7, 37198219245120372624245436346500833503661260800000⟩, + ⟨5, 8, 5, 4, 7, 7, 2214667791011075465230719373998359178117120000000⟩, + ⟨5, 8, 6, 4, 8, 7, -1050724956232244070368373359918413743390720000000⟩, + ⟨5, 8, 0, 5, 1, 7, 2455944228146909083077843700474892525160628224000000⟩, + ⟨5, 8, 1, 5, 2, 7, -497093795735120417849492386458552255947735040000000⟩, + ⟨5, 8, 2, 5, 3, 7, 376520057777931761076692462455697541615845376000000⟩, + ⟨5, 8, 3, 5, 4, 7, 196298135232399290287153229125381968171840307200000⟩, + ⟨5, 8, 4, 5, 5, 7, 19298624615320389842497643333260273941007564800000⟩, + ⟨5, 8, 5, 5, 6, 7, -4919269628327769852562217928290677303541760000000⟩, + ⟨5, 8, 6, 5, 7, 7, 1273603945608930683603790189140003266756608000000⟩, + ⟨5, 8, 7, 5, 8, 7, 57790834597348060769848270838625126580224000000⟩, + ⟨5, 8, 0, 6, 0, 7, -56649817243494870453134190446791300844032622592000000⟩, + ⟨5, 8, 1, 6, 1, 7, -10968239330438552692008693817102043049860530176000000⟩, + ⟨5, 8, 2, 6, 2, 7, -251973530779210822867665413984665009517494272000000⟩, + ⟨5, 8, 3, 6, 3, 7, 261123128175732980417002560228837929916353740800000⟩, + ⟨5, 8, 4, 6, 4, 7, -37455242986748617445702198217895281474247065600000⟩, + ⟨5, 8, 5, 6, 5, 7, 9971239420565449466703658746984715794776064000000⟩, + ⟨5, 8, 6, 6, 6, 7, -829313326897910522313980950299880269545472000000⟩, + ⟨5, 8, 7, 6, 7, 7, -190962948799297871759010772527756255166464000000⟩, + ⟨5, 8, 8, 6, 8, 7, 226686295149113608002910948208875530721689600000⟩, + ⟨5, 8, 1, 7, 0, 7, 68701067364605922567900252324920024036693508096000000⟩, + ⟨5, 8, 2, 7, 1, 7, 3716449209777893084093187610456504062298816512000000⟩, + ⟨5, 8, 3, 7, 2, 7, 961187663244742199719289244775932849175501209600000⟩, + ⟨5, 8, 4, 7, 3, 7, 136323902968457136737536258067742807944488550400000⟩, + ⟨5, 8, 5, 7, 4, 7, 30153320837102916874359009267177437012164608000000⟩, + ⟨5, 8, 6, 7, 5, 7, 857045654833832846882241346723106688860160000000⟩, + ⟨5, 8, 7, 7, 6, 7, 478244156670170446707461549731803662647296000000⟩, + ⟨5, 8, 8, 7, 7, 7, 171646309745085427238624766702330019892428800000⟩ +] + +def collectedFourData_11_6_33 : List CollectedFourTerm := [ + ⟨6, 0, 5, 3, 8, 0, -100921615873559158512248953893063940148236910592000000⟩, + ⟨6, 0, 5, 4, 7, 0, -60303932703538042269981301480636877280494223360000000⟩, + ⟨6, 0, 6, 4, 8, 0, 228884340333968675953310985771360410934737633280000000⟩, + ⟨6, 0, 5, 5, 6, 0, 133948444015526340075831646940572247659936481280000000⟩, + ⟨6, 0, 6, 5, 7, 0, -277435114877967322862324049115887317277046996992000000⟩, + ⟨6, 0, 7, 5, 8, 0, -56649817243494870453134190446791300844032622592000000⟩, + ⟨6, 0, 5, 6, 5, 0, -271510225339091241192338657452971682179519086592000000⟩, + ⟨6, 0, 6, 6, 6, 0, 180653207703236026242550414077359897003245436928000000⟩, + ⟨6, 0, 7, 6, 7, 0, 187192592478245953943323512607452500307593920512000000⟩, + ⟨6, 0, 8, 6, 8, 0, -740702066990135533660135355411532697970153619456000000⟩, + ⟨6, 0, 5, 7, 4, 0, -821054894973072790277118324360525028888751898624000000⟩, + ⟨6, 0, 6, 7, 5, 0, -186694270635918355477240653505006971161243811840000000⟩, + ⟨6, 0, 7, 7, 6, 0, -468801744461702546089532837521409201496095981568000000⟩, + ⟨6, 0, 8, 7, 7, 0, -560857798376308060043615016325009155662668627968000000⟩ +] + +def collectedFourData_11_6_34 : List CollectedFourTerm := [ + ⟨6, 1, 4, 2, 8, 1, 11757480506618531634344471029824863074603814092800000⟩, + ⟨6, 1, 4, 3, 7, 1, 70881612856089230345572774198638764066518283059200000⟩, + ⟨6, 1, 5, 3, 8, 1, -58619735616687782370321549860820094660040982528000000⟩, + ⟨6, 1, 4, 4, 6, 1, -84046728951237548602437406031396257651562958028800000⟩, + ⟨6, 1, 5, 4, 7, 1, -35027189776239804539970883626957924810872586240000000⟩, + ⟨6, 1, 6, 4, 8, 1, 66473071209972765708891127193420850561558773760000000⟩, + ⟨6, 1, 4, 5, 5, 1, -43603868816604290550513369979506917256895188172800000⟩, + ⟨6, 1, 5, 5, 6, 1, 77803177312324824866521066282943252105023979520000000⟩, + ⟨6, 1, 6, 5, 7, 1, -80573289201529217124072337319153169702599000064000000⟩, + ⟨6, 1, 7, 5, 8, 1, -10968239330438552692008693817102043049860530176000000⟩, + ⟨6, 1, 4, 6, 4, 1, 84627455802819180005082476533834697563828754841600000⟩, + ⟨6, 1, 5, 6, 5, 1, -157705140656340888816904401368095042556582166528000000⟩, + ⟨6, 1, 6, 6, 6, 1, 52465684294719830290347239925624897640203288576000000⟩, + ⟨6, 1, 7, 6, 7, 1, 36243244110772841989162980625592443990689447936000000⟩, + ⟨6, 1, 8, 6, 8, 1, -107558125585540731229533257859677555625270706176000000⟩, + ⟨6, 1, 4, 7, 3, 1, -308014156453678065156883566222457990689749100134400000⟩, + ⟨6, 1, 5, 7, 4, 1, -476904976733717264841501626804115619581857366016000000⟩, + ⟨6, 1, 6, 7, 5, 1, -54220142489291749466657393280124401745165025280000000⟩, + ⟨6, 1, 7, 7, 6, 1, -90766925331493464256223422126742151078875234304000000⟩, + ⟨6, 1, 8, 7, 7, 1, -81442750333505163563988087719779745548235440128000000⟩ +] + +def collectedFourData_11_6_35 : List CollectedFourTerm := [ + ⟨6, 2, 3, 1, 8, 2, 89904194055205480930684008922490240285383065600000⟩, + ⟨6, 2, 3, 2, 7, 2, -3230257216955314869795911398744912566466432204800000⟩, + ⟨6, 2, 4, 2, 8, 2, 1080419121817962978801073673016949235008300646400000⟩, + ⟨6, 2, 3, 3, 6, 2, 3546997224520964460945850187169961895605252915200000⟩, + ⟨6, 2, 4, 3, 7, 2, 6513457527903808664120769446607726245953771929600000⟩, + ⟨6, 2, 5, 3, 8, 2, -2693344175247877853993822930604836120671813632000000⟩, + ⟨6, 2, 3, 4, 5, 2, 6635432479781556354676401173043605675983660646400000⟩, + ⟨6, 2, 4, 4, 6, 2, -7723227185794780901084116085931178538968704614400000⟩, + ⟨6, 2, 5, 4, 7, 2, -1609360338573086987934199246993016838747586560000000⟩, + ⟨6, 2, 6, 4, 8, 2, 2036115849275514478328466520708299973680168960000000⟩, + ⟨6, 2, 3, 5, 4, 2, -6792686698958764359616331046667889692200507801600000⟩, + ⟨6, 2, 4, 5, 5, 2, -4006849395002765154576726515383933260850947686400000⟩, + ⟨6, 2, 5, 5, 6, 2, 3574747177301722672124901649428918586709114880000000⟩, + ⟨6, 2, 6, 5, 7, 2, -2468015215564169152660633844614784262648889344000000⟩, + ⟨6, 2, 7, 5, 8, 2, -251973530779210822867665413984665009517494272000000⟩, + ⟨6, 2, 3, 6, 3, 2, -9035886140486624822392081303525712794707453542400000⟩, + ⟨6, 2, 4, 6, 4, 2, 7776591373355946251234311935707905202072636620800000⟩, + ⟨6, 2, 5, 6, 5, 2, -7245925242154872462889783123181829321111109632000000⟩, + ⟨6, 2, 6, 6, 6, 2, 1607059962644507037908292768713594035394052096000000⟩, + ⟨6, 2, 7, 6, 7, 2, 832616604211090444714309655154730711218388992000000⟩, + ⟨6, 2, 8, 6, 8, 2, -1976747578260499943738179883999559205097413017600000⟩, + ⟨6, 2, 3, 7, 2, 2, -33260869480986224709570496446653724176688139468800000⟩, + ⟨6, 2, 4, 7, 3, 2, -28304055808202464852286334052935820626233602867200000⟩, + ⟨6, 2, 5, 7, 4, 2, -21911890726215101519294023587281617594041237504000000⟩, + ⟨6, 2, 6, 7, 5, 2, -1660800222750365513968717653096204856071290880000000⟩, + ⟨6, 2, 7, 7, 6, 2, -2085189971218008903719209614721403109179916288000000⟩, + ⟨6, 2, 8, 7, 7, 2, -1496788444501057041634961822629976648138411212800000⟩ +] + +def collectedFourData_11_6_36 : List CollectedFourTerm := [ + ⟨6, 3, 2, 0, 8, 3, -26782438177518309471418272337386756470356102348800000⟩, + ⟨6, 3, 2, 1, 7, 3, -12277400323684733225236914888392288315281244160000000⟩, + ⟨6, 3, 3, 1, 8, 3, -465843858980252340392742043701979630334587699200000⟩, + ⟨6, 3, 2, 2, 6, 3, -25863354198219250871573406021921811043530152345600000⟩, + ⟨6, 3, 3, 2, 7, 3, 16737767389597615335863331583922699134811347353600000⟩, + ⟨6, 3, 4, 2, 8, 3, -2799127550794131224051451707640085380294141542400000⟩, + ⟨6, 3, 2, 3, 5, 3, 6409531814652421168255641508238220086757398937600000⟩, + ⟨6, 3, 3, 3, 6, 3, -18378974331814492437033861559166151966700496486400000⟩, + ⟨6, 3, 4, 3, 7, 3, -16874931264271761751913161589325180265094027673600000⟩, + ⟨6, 3, 5, 3, 8, 3, 4651906982185295940321006501752666981199249408000000⟩, + ⟨6, 3, 2, 4, 4, 3, 809706591327905062720562070808538615421861888000000⟩, + ⟨6, 3, 3, 4, 5, 3, -34381882901772936715676704100717033245559803084800000⟩, + ⟨6, 3, 4, 4, 6, 3, 20009177512912259244715701261350500725791549030400000⟩, + ⟨6, 3, 5, 4, 7, 3, 2779665021894655484669628138508567590878576640000000⟩, + ⟨6, 3, 6, 4, 8, 3, -2637563448861261303794545099181579080229191680000000⟩, + ⟨6, 3, 2, 5, 3, 3, 13502181602844516115485583750393005525947331379200000⟩, + ⟨6, 3, 3, 5, 4, 3, 35196704869449487383338783532964353405051155251200000⟩, + ⟨6, 3, 4, 5, 5, 3, 10380862673517858936563140457739241065128814182400000⟩, + ⟨6, 3, 5, 5, 6, 3, -6174254113701083486293301313893435330757918720000000⟩, + ⟨6, 3, 6, 5, 7, 3, 3197041428719151459470977811843501043065290752000000⟩, + ⟨6, 3, 7, 5, 8, 3, 261123128175732980417002560228837929916353740800000⟩, + ⟨6, 3, 2, 6, 2, 3, -9035886140486624822392081303525712794707453542400000⟩, + ⟨6, 3, 3, 6, 3, 3, 46819974454203422751216784837631185442252311756800000⟩, + ⟨6, 3, 4, 6, 4, 3, -20147432348107013329847925391868711087450672332800000⟩, + ⟨6, 3, 5, 6, 5, 3, 12515062328887367569350391458018039850397073408000000⟩, + ⟨6, 3, 6, 6, 6, 3, -2081768883193806067178895882215533801812000768000000⟩, + ⟨6, 3, 7, 6, 7, 3, -862850362061101283075712637131356533412383948800000⟩, + ⟨6, 3, 8, 6, 8, 3, 1707105602365428669707047032692568044116063027200000⟩, + ⟨6, 3, 2, 7, 1, 3, 133273569658711076331396644283033954853081998950400000⟩, + ⟨6, 3, 3, 7, 2, 3, 172343147668359491256390615243152162779385403801600000⟩, + ⟨6, 3, 4, 7, 3, 3, 73329563325983844540109791243984410492152263475200000⟩, + ⟨6, 3, 5, 7, 4, 3, 37845916017317059429645616169393414127931621376000000⟩, + ⟨6, 3, 6, 7, 5, 3, 2151383461282741472070368749390591928869847040000000⟩, + ⟨6, 3, 7, 7, 6, 3, 2160906847799890330679852635333381513966465843200000⟩, + ⟨6, 3, 8, 7, 7, 3, 1292616198074260918067550597734623034088200601600000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1121.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1121.lean new file mode 100644 index 0000000000000000000000000000000000000000..699604071db14f6e666ff5072e996dbaf6d997e6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1121.lean @@ -0,0 +1,616 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1121. -/ +namespace LaughlinFock +def collectedFourData_11_6_37 : List CollectedFourTerm := [ + ⟨6, 4, 1, 0, 7, 4, -37913592548518625076724616883645140098104478924800000⟩, + ⟨6, 4, 2, 0, 8, 4, 23049878501181644307592095836916468521799096729600000⟩, + ⟨6, 4, 1, 1, 6, 4, -18521053203680136877172390795698950684975877324800000⟩, + ⟨6, 4, 2, 1, 7, 4, 10566348884876757747842365835709559327130910720000000⟩, + ⟨6, 4, 3, 1, 8, 4, 200460545803290530834948724875562378176181043200000⟩, + ⟨6, 4, 1, 2, 5, 4, -11020062211013675291132856283823162864906639769600000⟩, + ⟨6, 4, 2, 2, 6, 4, 22258883524741868540159392665215910020786631475200000⟩, + ⟨6, 4, 3, 2, 7, 4, -7202546350599179597527794318948614046257617305600000⟩, + ⟨6, 4, 4, 2, 8, 4, 803008169351733627572018386434037361938110873600000⟩, + ⟨6, 4, 1, 3, 4, 4, -6008771783998480889312604370017891624882379161600000⟩, + ⟨6, 4, 2, 3, 5, 4, -5516261387329981623067933089627299965199135539200000⟩, + ⟨6, 4, 3, 3, 6, 4, 7908785647459570883608332759134560712502175334400000⟩, + ⟨6, 4, 4, 3, 7, 4, 4841046867840937379423750588269626480310773350400000⟩, + ⟨6, 4, 5, 3, 8, 4, -1000897398021225505232316333125841840173481984000000⟩, + ⟨6, 4, 1, 4, 3, 4, 18936820024440815291803777663579915755002737459200000⟩, + ⟨6, 4, 2, 4, 4, 4, -696861070975261896759949142419250764207620096000000⟩, + ⟨6, 4, 3, 4, 5, 4, 14795109733380416029938729282287240855432252620800000⟩, + ⟨6, 4, 4, 4, 6, 4, -5740193225678151419895789509970745490182609305600000⟩, + ⟨6, 4, 5, 4, 7, 4, -598068598198413808244743208518692410983710720000000⟩, + ⟨6, 4, 6, 4, 8, 4, 453995387816801662934330078971182361935347712000000⟩, + ⟨6, 4, 1, 5, 2, 4, 3835418061282174414685058603173352979472318464000000⟩, + ⟨6, 4, 2, 5, 3, 4, -11620437369578368097716278132742022267421484646400000⟩, + ⟨6, 4, 3, 5, 4, 4, -15145741502425323968358322498969571551498941235200000⟩, + ⟨6, 4, 4, 5, 5, 4, -2978041329123556221280645249676160294152935833600000⟩, + ⟨6, 4, 5, 5, 6, 4, 1328443346092492249930021131220585579869634560000000⟩, + ⟨6, 4, 6, 5, 7, 4, -550296548856247159162300002752688950761802956800000⟩, + ⟨6, 4, 7, 5, 8, 4, -37455242986748617445702198217895281474247065600000⟩, + ⟨6, 4, 1, 6, 1, 4, 84627455802819180005082476533834697563828754841600000⟩, + ⟨6, 4, 2, 6, 2, 4, 7776591373355946251234311935707905202072636620800000⟩, + ⟨6, 4, 3, 6, 3, 4, -20147432348107013329847925391868711087450672332800000⟩, + ⟨6, 4, 4, 6, 4, 4, 5779855499046961662687577709190456994356736819200000⟩, + ⟨6, 4, 5, 6, 5, 4, -2692722225321115515678384209663468210680233984000000⟩, + ⟨6, 4, 6, 6, 6, 4, 358328241119114803177549889074721289583932211200000⟩, + ⟨6, 4, 7, 6, 7, 4, 123766401689446407543234648671797247582247321600000⟩, + ⟨6, 4, 8, 6, 8, 4, -209884746448938652797605686803168839685321523200000⟩, + ⟨6, 4, 1, 7, 0, 4, -530075645401897404687291271980860345371164514713600000⟩, + ⟨6, 4, 2, 7, 1, 4, -114699773324995613676936925510514873521402596556800000⟩, + ⟨6, 4, 3, 7, 2, 4, -74162191431874110337013589951622890360137161113600000⟩, + ⟨6, 4, 4, 7, 3, 4, -21036639930557811781985793709299225168532262092800000⟩, + ⟨6, 4, 5, 7, 4, 4, -8142871087604568413423319743408196816205774848000000⟩, + ⟨6, 4, 6, 7, 5, 4, -370310776512086763507015609565113448384167936000000⟩, + ⟨6, 4, 7, 7, 6, 4, -309958338893688504319980836015574226401912422400000⟩, + ⟨6, 4, 8, 7, 7, 4, -158924218052288865306573929039084054243809689600000⟩ +] + +def collectedFourData_11_6_38 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 6, 5, -26621856869226726589979645951588321997178798080000000⟩, + ⟨6, 5, 1, 0, 7, 5, 70652820517051920790045667456536818502896451584000000⟩, + ⟨6, 5, 2, 0, 8, 5, -21476979879970137180065682031462026066247286784000000⟩, + ⟨6, 5, 0, 1, 5, 5, -40653735222390362525074704190403161307517812736000000⟩, + ⟨6, 5, 1, 1, 6, 5, 34514393383106369307264771533890506237709123584000000⟩, + ⟨6, 5, 2, 1, 7, 5, -9845312737488371737109818594460631342828748800000000⟩, + ⟨6, 5, 3, 1, 8, 5, -124520890893904820322641787194038042547453952000000⟩, + ⟨6, 5, 0, 2, 4, 5, -11584278048292230452101363883853093047359242240000000⟩, + ⟨6, 5, 1, 2, 5, 5, 20536130320151295179508464843878651407806496768000000⟩, + ⟨6, 5, 2, 2, 6, 5, -20739961539796082756218905230665620763818590208000000⟩, + ⟨6, 5, 3, 2, 7, 5, 4474034951303274502946903400199396209475977216000000⟩, + ⟨6, 5, 4, 2, 8, 5, -374105882938487408948697013275165118559158272000000⟩, + ⟨6, 5, 0, 3, 3, 5, -2060387660782458418798498156059717816878628864000000⟩, + ⟨6, 5, 1, 3, 4, 5, 11197479474926683210070381168234891317899952128000000⟩, + ⟨6, 5, 2, 3, 5, 5, 5139837714210454998360851355879861912776736768000000⟩, + ⟨6, 5, 3, 3, 6, 5, -4912732481916788839213220069928474142713053184000000⟩, + ⟨6, 5, 4, 3, 7, 5, -2255349549310687731264378323031321387579998208000000⟩, + ⟨6, 5, 5, 3, 8, 5, 373038899586639020930718203894810897069113344000000⟩, + ⟨6, 5, 0, 4, 2, 5, 15271104111861349587121763640715238063455862784000000⟩, + ⟨6, 5, 1, 4, 3, 5, -35289184073979510103365953270971570403080667136000000⟩, + ⟨6, 5, 2, 4, 4, 5, 649308029962192224149191600014358113775779840000000⟩, + ⟨6, 5, 3, 4, 5, 5, -9190338365542706851763925018281328407727833088000000⟩, + ⟨6, 5, 4, 4, 6, 5, 2674244343819654577182239284324317320982822912000000⟩, + ⟨6, 5, 5, 4, 7, 5, 222902819200384036281913572947216213496299520000000⟩, + ⟨6, 5, 6, 4, 8, 5, -141005078895041107075973896940321283149660160000000⟩, + ⟨6, 5, 0, 5, 1, 5, 11770805330902959062431344456054116204333236224000000⟩, + ⟨6, 5, 1, 5, 2, 5, -7147386614572263029869788841503468385594245120000000⟩, + ⟨6, 5, 2, 5, 3, 5, 10827471371273974254470728134969397586486624256000000⟩, + ⟨6, 5, 3, 5, 4, 5, 9408141724713552361345812651316419320529027072000000⟩, + ⟨6, 5, 4, 5, 5, 5, 1387411515076474013699659861712815694882537472000000⟩, + ⟨6, 5, 5, 5, 6, 5, -495116727218254655018472128086240673094696960000000⟩, + ⟨6, 5, 6, 5, 7, 5, 170914970436781864702529345729126321067393024000000⟩, + ⟨6, 5, 7, 5, 8, 5, 9971239420565449466703658746984715794776064000000⟩, + ⟨6, 5, 0, 6, 0, 5, -271510225339091241192338657452971682179519086592000000⟩, + ⟨6, 5, 1, 6, 1, 5, -157705140656340888816904401368095042556582166528000000⟩, + ⟨6, 5, 2, 6, 2, 5, -7245925242154872462889783123181829321111109632000000⟩, + ⟨6, 5, 3, 6, 3, 5, 12515062328887367569350391458018039850397073408000000⟩, + ⟨6, 5, 4, 6, 4, 5, -2692722225321115515678384209663468210680233984000000⟩, + ⟨6, 5, 5, 6, 5, 5, 1003589516579973253947833348826212619301945344000000⟩, + ⟨6, 5, 6, 6, 6, 5, -111292103984348458005296631626689169867145216000000⟩, + ⟨6, 5, 7, 6, 7, 5, -32948776327628233583133024401110465410760704000000⟩, + ⟨6, 5, 8, 6, 8, 5, 48890609947959203986036981332612843445420032000000⟩, + ⟨6, 5, 1, 7, 0, 5, 987807720598190297248012008067938403589227020288000000⟩, + ⟨6, 5, 2, 7, 1, 5, 106872785633632759433852255163059978770235523072000000⟩, + ⟨6, 5, 3, 7, 2, 5, 46067629471602945413593804985135884739171844096000000⟩, + ⟨6, 5, 4, 7, 3, 5, 9800561259088739938092229870109336047510880256000000⟩, + ⟨6, 5, 5, 7, 4, 5, 3034884170946210933062207556898080609710112768000000⟩, + ⟨6, 5, 6, 7, 5, 5, 115013724057569175988396792950587998580244480000000⟩, + ⟨6, 5, 7, 7, 6, 5, 82516319774061727518437982166151939443654656000000⟩, + ⟨6, 5, 8, 7, 7, 5, 37019850596761471431705467982392724654391296000000⟩ +] + +def collectedFourData_11_6_39 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 6, 6, 17713232834733330934576522485995574324331806720000000⟩, + ⟨6, 6, 1, 0, 7, 6, -23504931800903268785645788602437645193317449728000000⟩, + ⟨6, 6, 2, 0, 8, 6, 4763338473715366540954541236051116095283658752000000⟩, + ⟨6, 6, 0, 1, 5, 6, 27049543581169309918744348846564729122585575424000000⟩, + ⟨6, 6, 1, 1, 6, 6, -11482322385468908564075615165888830747315273728000000⟩, + ⟨6, 6, 2, 1, 7, 6, 2183573165795763899341947422791933620545126400000000⟩, + ⟨6, 6, 3, 1, 8, 6, 20712938470323055956627672781217041106337792000000⟩, + ⟨6, 6, 0, 2, 4, 6, 7707764912855633318435916108917730632175452160000000⟩, + ⟨6, 6, 1, 2, 5, 6, -6832003861942344052365680113544403443207110656000000⟩, + ⟨6, 6, 2, 2, 6, 6, 4599876579389198617606281519501194476256231424000000⟩, + ⟨6, 6, 3, 2, 7, 6, -744215769700662040198163582340362192799399936000000⟩, + ⟨6, 6, 4, 2, 8, 6, 49783338869896040067637236872895104170957209600000⟩, + ⟨6, 6, 0, 3, 3, 6, 1370908368433104328115055411729226016778878976000000⟩, + ⟨6, 6, 1, 3, 4, 6, -3725201477790175298299392256875987085113163776000000⟩, + ⟨6, 6, 2, 3, 5, 6, -1139954819978438667920011956485312070606127104000000⟩, + ⟨6, 6, 3, 3, 6, 6, 817189187200722455677437974172985479307198464000000⟩, + ⟨6, 6, 4, 3, 7, 6, 300125809306941030979522232552350848672753254400000⟩, + ⟨6, 6, 5, 3, 8, 6, -41367793621920357974120045528418111996297216000000⟩, + ⟨6, 6, 0, 4, 2, 6, -10160847310749993993984087483589226518340960256000000⟩, + ⟨6, 6, 1, 4, 3, 6, 11740081413568184722209494811909724257241792512000000⟩, + ⟨6, 6, 2, 4, 4, 6, -144008791631625847792748366206346817196523520000000⟩, + ⟨6, 6, 3, 4, 5, 6, 1528730735223589194861227029416833895049986048000000⟩, + ⟨6, 6, 4, 4, 6, 6, -355869336626195436474038646723535585926551961600000⟩, + ⟨6, 6, 5, 4, 7, 6, -24718595922954459858981199873460088896225280000000⟩, + ⟨6, 6, 6, 4, 8, 6, 13402820555718134608139937952383585138769920000000⟩, + ⟨6, 6, 0, 5, 1, 6, -7831873505398370979177065515561710755266953216000000⟩, + ⟨6, 6, 1, 5, 2, 6, 2377807902087415574814838811112440440333271040000000⟩, + ⟨6, 6, 2, 5, 3, 6, -2401404259075588054006352050486267003816378368000000⟩, + ⟨6, 6, 3, 5, 4, 6, -1564960379460387874251892595895114935474061312000000⟩, + ⟨6, 6, 4, 5, 5, 6, -184626814912731159441093204846778963669391769600000⟩, + ⟨6, 6, 5, 5, 6, 6, 54905498094223382787041807903223757343293440000000⟩, + ⟨6, 6, 6, 5, 7, 6, -16245816796111296141130824347132083713343488000000⟩, + ⟨6, 6, 7, 5, 8, 6, -829313326897910522313980950299880269545472000000⟩, + ⟨6, 6, 0, 6, 0, 6, 180653207703236026242550414077359897003245436928000000⟩, + ⟨6, 6, 1, 6, 1, 6, 52465684294719830290347239925624897640203288576000000⟩, + ⟨6, 6, 2, 6, 2, 6, 1607059962644507037908292768713594035394052096000000⟩, + ⟨6, 6, 3, 6, 3, 6, -2081768883193806067178895882215533801812000768000000⟩, + ⟨6, 6, 4, 6, 4, 6, 358328241119114803177549889074721289583932211200000⟩, + ⟨6, 6, 5, 6, 5, 6, -111292103984348458005296631626689169867145216000000⟩, + ⟨6, 6, 6, 6, 6, 6, 10578541643034416103007280630776044969787392000000⟩, + ⟨6, 6, 7, 6, 7, 6, 2740367386738663804832866794811483270152192000000⟩, + ⟨6, 6, 8, 6, 8, 6, -3614451762927124119638974111800748966674432000000⟩, + ⟨6, 6, 1, 7, 0, 6, -328625990231521891832956324111107180662668394496000000⟩, + ⟨6, 6, 2, 7, 1, 6, -23703111631472351246615960320867316184347836416000000⟩, + ⟨6, 6, 3, 7, 2, 6, -7662938868080808374529703399028888435913916416000000⟩, + ⟨6, 6, 4, 7, 3, 6, -1304188692367111927349851571062869710036847820800000⟩, + ⟨6, 6, 5, 7, 4, 6, -336550590807694853648577323299533875211927552000000⟩, + ⟨6, 6, 6, 7, 5, 6, -10932289227226506254738847487969078290677760000000⟩, + ⟨6, 6, 7, 7, 6, 6, -6862926541916123543669149272464332148441088000000⟩, + ⟨6, 6, 8, 7, 7, 6, -2736854058380357947587243515406441561194496000000⟩ +] + +def collectedFourData_11_6_40 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 6, 7, 18354426238317640323472940319472246537983098880000000⟩, + ⟨6, 7, 1, 0, 7, 7, -16237184218960807028419193330791776008754167808000000⟩, + ⟨6, 7, 2, 0, 8, 7, 2467882217765288045056591750141891102170415104000000⟩, + ⟨6, 7, 0, 1, 5, 7, 28028697927303278580043791716813201642247684096000000⟩, + ⟨6, 7, 1, 1, 6, 7, -7931977229867625622152820257221687040496631808000000⟩, + ⟨6, 7, 2, 1, 7, 7, 1131307677754337311862912038714450182458572800000000⟩, + ⟨6, 7, 3, 1, 8, 7, 8585086751344106965528039403091706938340147200000⟩, + ⟨6, 7, 0, 2, 4, 7, 7986774852182500677424154177294356013792624640000000⟩, + ⟨6, 7, 1, 2, 5, 7, -4719541678770006144870081821971422885042978816000000⟩, + ⟨6, 7, 2, 2, 6, 7, 2383192728551827647239661432344241024477954048000000⟩, + ⟨6, 7, 3, 2, 7, 7, -308462121574528108066891386284275381218941337600000⟩, + ⟨6, 7, 4, 2, 8, 7, 17195141239133279473696368172428498748361932800000⟩, + ⟨6, 7, 0, 3, 3, 7, 1420533268131492332656551425646575932359573504000000⟩, + ⟨6, 7, 1, 3, 4, 7, -2573365588123070870655838844898083187128795136000000⟩, + ⟨6, 7, 2, 3, 5, 7, -590609767667063797393335377230569727126929408000000⟩, + ⟨6, 7, 3, 3, 6, 7, 338708101432850920529412963701308379913152102400000⟩, + ⟨6, 7, 4, 3, 7, 7, 103663309807906605990174220166925727751680819200000⟩, + ⟨6, 7, 5, 3, 8, 7, -12247213687395356418608395136467061339848704000000⟩, + ⟨6, 7, 0, 4, 2, 7, -10528655284103399565167379283303805669420826624000000⟩, + ⟨6, 7, 1, 4, 3, 7, 8110036917885414565481857766071535797725560832000000⟩, + ⟨6, 7, 2, 4, 4, 7, -74610850778435107217911290829573723300823040000000⟩, + ⟨6, 7, 3, 4, 5, 7, 633627430513767870917011218773165451810491596800000⟩, + ⟨6, 7, 4, 4, 6, 7, -122917097263325335663575675535259107809086668800000⟩, + ⟨6, 7, 5, 4, 7, 7, -7318106667414512433102383642102846529208320000000⟩, + ⟨6, 7, 6, 4, 8, 7, 3471995817626244206711321937191270004817920000000⟩, + ⟨6, 7, 0, 5, 1, 7, -8115375996232295532222905008201289239797694464000000⟩, + ⟨6, 7, 1, 5, 2, 7, 1642587405508251253094751814734646951217725440000000⟩, + ⟨6, 7, 2, 5, 3, 7, -1244165809618802622619661289914653657201115136000000⟩, + ⟨6, 7, 3, 5, 4, 7, -648643872492239097023206761253040052700918579200000⟩, + ⟨6, 7, 4, 5, 5, 7, -63770012840088164957772741836248585603960012800000⟩, + ⟨6, 7, 5, 5, 6, 7, 16255142198749360770271539374223636415119360000000⟩, + ⟨6, 7, 6, 5, 7, 7, -4208472965487551484746020073337626126450688000000⟩, + ⟨6, 7, 7, 5, 8, 7, -190962948799297871759010772527756255166464000000⟩, + ⟨6, 7, 0, 6, 0, 7, 187192592478245953943323512607452500307593920512000000⟩, + ⟨6, 7, 1, 6, 1, 7, 36243244110772841989162980625592443990689447936000000⟩, + ⟨6, 7, 2, 6, 2, 7, 832616604211090444714309655154730711218388992000000⟩, + ⟨6, 7, 3, 6, 3, 7, -862850362061101283075712637131356533412383948800000⟩, + ⟨6, 7, 4, 6, 4, 7, 123766401689446407543234648671797247582247321600000⟩, + ⟨6, 7, 5, 6, 5, 7, -32948776327628233583133024401110465410760704000000⟩, + ⟨6, 7, 6, 6, 6, 7, 2740367386738663804832866794811483270152192000000⟩, + ⟨6, 7, 7, 6, 7, 7, 631014382612786704370786079871429041455104000000⟩, + ⟨6, 7, 8, 6, 8, 7, -749057937572148569923540563446695896652185600000⟩, + ⟨6, 7, 1, 7, 0, 7, -227014517111791001330695729467908033787834925056000000⟩, + ⟨6, 7, 2, 7, 1, 7, -12280564991088987396480187352924217754760773632000000⟩, + ⟨6, 7, 3, 7, 2, 7, -3176130467773956919779617586459239138077546905600000⟩, + ⟨6, 7, 4, 7, 3, 7, -450466145437542101157849670784530297886500454400000⟩, + ⟨6, 7, 5, 7, 4, 7, -99638067234431669837919620230082450253938688000000⟩, + ⟨6, 7, 6, 7, 5, 7, -2832005570485466654970828043119419468021760000000⟩, + ⟨6, 7, 7, 7, 6, 7, -1580301012090938223321598237554362082656256000000⟩, + ⟨6, 7, 8, 7, 7, 7, -567184843199051351099349571234106920717516800000⟩ +] + +def collectedFourData_11_6_41 : List CollectedFourTerm := [ + ⟨6, 8, 0, 0, 6, 8, -72626599552649373996739091909441534358391357440000000⟩, + ⟨6, 8, 1, 0, 7, 8, 48186666018107336979387540576022405290318102528000000⟩, + ⟨6, 8, 2, 0, 8, 8, -5859095498127834380894559405604067217853592371200000⟩, + ⟨6, 8, 0, 1, 5, 8, -110906709581514747711461176816162619768489115648000000⟩, + ⟨6, 8, 1, 1, 6, 8, 23539520922139638653334747712244732289538326528000000⟩, + ⟨6, 8, 2, 1, 7, 8, -2685881714294316884779778076131868993745059840000000⟩, + ⟨6, 8, 3, 1, 8, 8, -16985157953697338678509883904687658486254796800000⟩, + ⟨6, 8, 0, 2, 4, 8, -31602856519463516899315808533499675769380536320000000⟩, + ⟨6, 8, 1, 2, 5, 8, 14006060137438220660953924777641638615901536256000000⟩, + ⟨6, 8, 2, 2, 6, 8, -5658030876235687064183917371658437713004488294400000⟩, + ⟨6, 8, 3, 2, 7, 8, 610276635452247989057671165498559701119821414400000⟩, + ⟨6, 8, 4, 2, 8, 8, -29159754261781348432488923466557325454186905600000⟩, + ⟨6, 8, 0, 3, 3, 8, -5620905795487213200172367092703446008858673152000000⟩, + ⟨6, 8, 1, 3, 4, 8, 7636909606074112990580858266985345478480101376000000⟩, + ⟨6, 8, 2, 3, 5, 8, 1402189701752423898815863214599683837444646502400000⟩, + ⟨6, 8, 3, 3, 6, 8, -670116769889739803738308868622306330988353945600000⟩, + ⟨6, 8, 4, 3, 7, 8, -175793649957470711357124493908077341225412198400000⟩, + ⟨6, 8, 5, 3, 8, 8, 18172867525816711692246530350712933194924032000000⟩, + ⟨6, 8, 0, 4, 2, 8, 41660819097146122977010893958215601971592691712000000⟩, + ⟨6, 8, 1, 4, 3, 8, -24067943991195063719113519409785100968459763712000000⟩, + ⟨6, 8, 2, 4, 4, 8, 177136533000049691210680042426966154844045312000000⟩, + ⟨6, 8, 3, 4, 5, 8, -1253599678464141330191762103188962200465388339200000⟩, + ⟨6, 8, 4, 4, 6, 8, 208444484457791321415882709042749928382241177600000⟩, + ⟨6, 8, 5, 4, 7, 8, 10858876671972517482414893259999901447618560000000⟩, + ⟨6, 8, 6, 4, 8, 8, -4579444881961571380219611436440529215160320000000⟩, + ⟨6, 8, 0, 5, 1, 8, 32111718178751926071763640279426824483878469632000000⟩, + ⟨6, 8, 1, 5, 2, 8, -4874663589906677993460983899801141438882775040000000⟩, + ⟨6, 8, 2, 5, 3, 8, 2953822610166153475535268471515528998672977100800000⟩, + ⟨6, 8, 3, 5, 4, 8, 1283308945975845007883927428854925574898765004800000⟩, + ⟨6, 8, 4, 5, 5, 8, 108142054655280116666367464224890079984327065600000⟩, + ⟨6, 8, 5, 5, 6, 8, -24119979722017005895458698418223164822650880000000⟩, + ⟨6, 8, 6, 5, 7, 8, 5550833294451353102253583716217940028162048000000⟩, + ⟨6, 8, 7, 5, 8, 8, 226686295149113608002910948208875530721689600000⟩, + ⟨6, 8, 0, 6, 0, 8, -740702066990135533660135355411532697970153619456000000⟩, + ⟨6, 8, 1, 6, 1, 8, -107558125585540731229533257859677555625270706176000000⟩, + ⟨6, 8, 2, 6, 2, 8, -1976747578260499943738179883999559205097413017600000⟩, + ⟨6, 8, 3, 6, 3, 8, 1707105602365428669707047032692568044116063027200000⟩, + ⟨6, 8, 4, 6, 4, 8, -209884746448938652797605686803168839685321523200000⟩, + ⟨6, 8, 5, 6, 5, 8, 48890609947959203986036981332612843445420032000000⟩, + ⟨6, 8, 6, 6, 6, 8, -3614451762927124119638974111800748966674432000000⟩, + ⟨6, 8, 7, 6, 7, 8, -749057937572148569923540563446695896652185600000⟩, + ⟨6, 8, 8, 6, 8, 8, 808348948354600241926631429499137854695014400000⟩, + ⟨6, 8, 1, 7, 0, 8, 673705032215733248475833354728992571214681604096000000⟩, + ⟨6, 8, 2, 7, 1, 8, 29155768673154312609063459229678226249340262809600000⟩, + ⟨6, 8, 3, 7, 2, 8, 6283812760336423706400457933153539616749807206400000⟩, + ⟨6, 8, 4, 7, 3, 8, 763906613009750337584670315394660537591450828800000⟩, + ⟨6, 8, 5, 7, 4, 8, 147846640272415564568149418191100292108386304000000⟩, + ⟨6, 8, 6, 7, 5, 8, 3735319423372193629028377959347705044008960000000⟩, + ⟨6, 8, 7, 7, 6, 8, 1875927157093661909336945628304178715977318400000⟩, + ⟨6, 8, 8, 7, 7, 8, 612079851938637671639725246692616456844083200000⟩ +] + +def collectedFourData_11_6_42 : List CollectedFourTerm := [ + ⟨7, 0, 4, 2, 8, 1, -73644587429962989362777890580620394636832984268800000⟩, + ⟨7, 0, 4, 3, 7, 1, -443976677845102806777168933021560963903817724723200000⟩, + ⟨7, 0, 5, 3, 8, 1, 367172732484169074896600510811012775214252556288000000⟩, + ⟨7, 0, 4, 4, 6, 1, 526438183330822233713615387377096545004593925324800000⟩, + ⟨7, 0, 5, 4, 7, 1, 219397594446370387272502560183829407359607767040000000⟩, + ⟨7, 0, 6, 4, 8, 1, -416363174211114548014892060850021551215434792960000000⟩, + ⟨7, 0, 4, 5, 5, 1, 273118796798464271970973517330316148826165791948800000⟩, + ⟨7, 0, 5, 5, 6, 1, -487330843600463877572262769154181610386405457920000000⟩, + ⟨7, 0, 6, 5, 7, 1, 504681818335268229574040649113226326141193682944000000⟩, + ⟨7, 0, 7, 5, 8, 1, 68701067364605922567900252324920024036693508096000000⟩, + ⟨7, 0, 4, 6, 4, 1, -530075645401897404687291271980860345371164514713600000⟩, + ⟨7, 0, 5, 6, 5, 1, 987807720598190297248012008067938403589227020288000000⟩, + ⟨7, 0, 6, 6, 6, 1, -328625990231521891832956324111107180662668394496000000⟩, + ⟨7, 0, 7, 6, 7, 1, -227014517111791001330695729467908033787834925056000000⟩, + ⟨7, 0, 8, 6, 8, 1, 673705032215733248475833354728992571214681604096000000⟩, + ⟨7, 0, 4, 7, 3, 1, 1929288801444334460105607720362930803897901934182400000⟩, + ⟨7, 0, 5, 7, 4, 1, 2987159556427084557902525495603185029842768756736000000⟩, + ⟨7, 0, 6, 7, 5, 1, 339615279121232043887336439394007317025264762880000000⟩, + ⟨7, 0, 7, 7, 6, 1, 568531052597642161721736262775496056971129257984000000⟩, + ⟨7, 0, 8, 7, 7, 1, 510127807066843223743975765480676354074909605888000000⟩ +] + +def collectedFourData_11_6_43 : List CollectedFourTerm := [ + ⟨7, 1, 3, 1, 8, 2, -1326029642553843309662427240965171670257605017600000⟩, + ⟨7, 1, 3, 2, 7, 2, 47644238044400973997665496299010065380210953420800000⟩, + ⟨7, 1, 4, 2, 8, 2, -15935494411227179316674052331651492262187525734400000⟩, + ⟨7, 1, 3, 3, 6, 2, -52315951565984580666930101223184932307163362099200000⟩, + ⟨7, 1, 4, 3, 7, 2, -96069353029430111472120032969213358565796452761600000⟩, + ⟨7, 1, 5, 3, 8, 2, 39725112398931861277372117437580031520587907072000000⟩, + ⟨7, 1, 3, 4, 5, 2, -97868405938348403180081041400917173577454085734400000⟩, + ⟨7, 1, 4, 4, 6, 2, 113912685522245757758832481458237281421945628262400000⟩, + ⟨7, 1, 5, 4, 7, 2, 23737040712338603885421949853069648634587381760000000⟩, + ⟨7, 1, 6, 4, 8, 2, -30031412885533760221561587965388927166222172160000000⟩, + ⟨7, 1, 3, 5, 4, 2, 100187805586351401677782386935501454680264382873600000⟩, + ⟨7, 1, 4, 5, 5, 2, 59098478406469447626435394812363808156254889574400000⟩, + ⟨7, 1, 5, 5, 6, 2, -52725245707970432417060340979274126268542484480000000⟩, + ⟨7, 1, 6, 5, 7, 2, 36401653654805369459511424097380873251349069824000000⟩, + ⟨7, 1, 7, 5, 8, 2, 3716449209777893084093187610456504062298816512000000⟩, + ⟨7, 1, 3, 6, 3, 2, 133273569658711076331396644283033954853081998950400000⟩, + ⟨7, 1, 4, 6, 4, 2, -114699773324995613676936925510514873521402596556800000⟩, + ⟨7, 1, 5, 6, 5, 2, 106872785633632759433852255163059978770235523072000000⟩, + ⟨7, 1, 6, 6, 6, 2, -23703111631472351246615960320867316184347836416000000⟩, + ⟨7, 1, 7, 6, 7, 2, -12280564991088987396480187352924217754760773632000000⟩, + ⟨7, 1, 8, 6, 8, 2, 29155768673154312609063459229678226249340262809600000⟩, + ⟨7, 1, 3, 7, 2, 2, 490576655876806805843973856178256963760978447564800000⟩, + ⟨7, 1, 4, 7, 3, 2, 417466808980327337286653900847862928158596739891200000⟩, + ⟨7, 1, 5, 7, 4, 2, 323186442331269019376527077006253996043019485184000000⟩, + ⟨7, 1, 6, 7, 5, 2, 24495746264904071956901228808043351731842580480000000⟩, + ⟨7, 1, 7, 7, 6, 2, 30755224950831750751737346013450366057340469248000000⟩, + ⟨7, 1, 8, 7, 7, 2, 22076676921453811561978288797384968973927107788800000⟩ +] + +def collectedFourData_11_6_44 : List CollectedFourTerm := [ + ⟨7, 2, 2, 0, 8, 3, -98585480909683631960217572891174310523369527705600000⟩, + ⟨7, 2, 2, 1, 7, 3, -45192801611586486965637254405375418674624593920000000⟩, + ⟨7, 2, 3, 1, 8, 3, -1714759521220204437894412353293217859780372070400000⟩, + ⟨7, 2, 2, 2, 6, 3, -95202355912063296661728569259767822849039086387200000⟩, + ⟨7, 2, 3, 2, 7, 3, 61611300529129089381235660590634785115989029683200000⟩, + ⟨7, 2, 4, 2, 8, 3, -10303518070069693252923107811154267032003595468800000⟩, + ⟨7, 2, 2, 3, 5, 3, 23593325303886783256886628836690298987087082291200000⟩, + ⟨7, 2, 3, 3, 6, 3, -67652541979901092126630709301402991601738632396800000⟩, + ⟨7, 2, 4, 3, 7, 3, -62116197299862130133752595875772782692357321523200000⟩, + ⟨7, 2, 5, 3, 8, 3, 17123552528941106527768629455555809176868356096000000⟩, + ⟨7, 2, 2, 4, 4, 3, 2980509585150805460828615746899843148840697856000000⟩, + ⟨7, 2, 3, 4, 5, 3, -126558845687804881455792191057047730416273430937600000⟩, + ⟨7, 2, 4, 4, 6, 3, 73653278862920433055231661974771300628289080524800000⟩, + ⟨7, 2, 5, 4, 7, 3, 10231876990995569073273329738499372476981575680000000⟩, + ⟨7, 2, 6, 4, 8, 3, -9708804676867005292797119387373773992922972160000000⟩, + ⟨7, 2, 2, 5, 3, 3, 49701190676645577928348975356214279125126768230400000⟩, + ⟨7, 2, 3, 5, 4, 3, 129558184844558640117882839606749102687140603494400000⟩, + ⟨7, 2, 4, 5, 5, 3, 38211694250645400771433219921139158590096723148800000⟩, + ⟨7, 2, 5, 5, 6, 3, -22727274007814618596419720202951710080646512640000000⟩, + ⟨7, 2, 6, 5, 7, 3, 11768229040589339382445225497156605810074189824000000⟩, + ⟨7, 2, 7, 5, 8, 3, 961187663244742199719289244775932849175501209600000⟩, + ⟨7, 2, 2, 6, 2, 3, -33260869480986224709570496446653724176688139468800000⟩, + ⟨7, 2, 3, 6, 3, 3, 172343147668359491256390615243152162779385403801600000⟩, + ⟨7, 2, 4, 6, 4, 3, -74162191431874110337013589951622890360137161113600000⟩, + ⟨7, 2, 5, 6, 5, 3, 46067629471602945413593804985135884739171844096000000⟩, + ⟨7, 2, 6, 6, 6, 3, -7662938868080808374529703399028888435913916416000000⟩, + ⟨7, 2, 7, 6, 7, 3, -3176130467773956919779617586459239138077546905600000⟩, + ⟨7, 2, 8, 6, 8, 3, 6283812760336423706400457933153539616749807206400000⟩, + ⟨7, 2, 2, 7, 1, 3, 490576655876806805843973856178256963760978447564800000⟩, + ⟨7, 2, 3, 7, 2, 3, 634390789283554443946481660093301502649165886259200000⟩, + ⟨7, 2, 4, 7, 3, 3, 269924277150299607438803634572328002333129991782400000⟩, + ⟨7, 2, 5, 7, 4, 3, 139309864408335392434934207756427536248615206912000000⟩, + ⟨7, 2, 6, 7, 5, 3, 7919188378066920990488232470223997228264980480000000⟩, + ⟨7, 2, 7, 7, 6, 3, 7954243724165694803221757218736668269470967398400000⟩, + ⟨7, 2, 8, 7, 7, 3, 4758087694411920312070525182015269707678167859200000⟩ +] + +def collectedFourData_11_6_45 : List CollectedFourTerm := [ + ⟨7, 3, 1, 0, 7, 4, 137992134067811524574079201909823266684994270003200000⟩, + ⟨7, 3, 2, 0, 8, 4, -83893445874627401116379785909217031271529997926400000⟩, + ⟨7, 3, 1, 1, 6, 4, 67410115606656200412933251785235244062514295603200000⟩, + ⟨7, 3, 2, 1, 7, 4, -38457791359741633437367162433015038221987348480000000⟩, + ⟨7, 3, 3, 1, 8, 4, -729605839288241219282118160199476403816418508800000⟩, + ⟨7, 3, 1, 2, 5, 4, 40109148193007081898483565859226750558830749286400000⟩, + ⟨7, 3, 2, 2, 6, 4, -81014502532706938599181661246892424771442363596800000⟩, + ⟨7, 3, 3, 2, 7, 4, 26214733947188090189343519307639323207171204710400000⟩, + ⟨7, 3, 4, 2, 8, 4, -2922667136355610116991769216268642480074155622400000⟩, + ⟨7, 3, 1, 3, 4, 4, 21869814646008765032170206919363742791142631014400000⟩, + ⟨7, 3, 2, 3, 5, 4, 20077250129736723032922355107316660983103802572800000⟩, + ⟨7, 3, 3, 3, 6, 4, -28785196443233558604294569390204789679959153049600000⟩, + ⟨7, 3, 4, 3, 7, 4, -17619706904872750766380658348680157872178960793600000⟩, + ⟨7, 3, 5, 3, 8, 4, 3642914286192200615805017668192221178946912256000000⟩, + ⟨7, 3, 1, 4, 3, 4, -68923360514743840415949442251119242703371291852800000⟩, + ⟨7, 3, 2, 4, 4, 4, 2536329054272497746725012933375198710374334464000000⟩, + ⟨7, 3, 3, 4, 5, 4, -53848992634077989435272906253311029627455746867200000⟩, + ⟨7, 3, 4, 4, 6, 4, 20892283213711760745087893638931120789683332710400000⟩, + ⟨7, 3, 5, 4, 7, 4, 2176759221082261084292721954531822621142548480000000⟩, + ⟨7, 3, 6, 4, 8, 4, -1652383438515166015571016910316603865833668608000000⟩, + ⟨7, 3, 1, 5, 2, 4, -13959571956713316780987269819669819549942808576000000⟩, + ⟨7, 3, 2, 5, 3, 4, 42294302482082220598862291946671346131547036057600000⟩, + ⟨7, 3, 3, 5, 4, 4, 55125168876689674055557898061014665712764767436800000⟩, + ⟨7, 3, 4, 5, 5, 4, 10839022385494250699032468178782436255263516262400000⟩, + ⟨7, 3, 5, 5, 6, 4, -4835066264978623912347818621741020363138007040000000⟩, + ⟨7, 3, 6, 5, 7, 4, 2002885773740591550178595123619741271799837491200000⟩, + ⟨7, 3, 7, 5, 8, 4, 136323902968457136737536258067742807944488550400000⟩, + ⟨7, 3, 1, 6, 1, 4, -308014156453678065156883566222457990689749100134400000⟩, + ⟨7, 3, 2, 6, 2, 4, -28304055808202464852286334052935820626233602867200000⟩, + ⟨7, 3, 3, 6, 3, 4, 73329563325983844540109791243984410492152263475200000⟩, + ⟨7, 3, 4, 6, 4, 4, -21036639930557811781985793709299225168532262092800000⟩, + ⟨7, 3, 5, 6, 5, 4, 9800561259088739938092229870109336047510880256000000⟩, + ⟨7, 3, 6, 6, 6, 4, -1304188692367111927349851571062869710036847820800000⟩, + ⟨7, 3, 7, 6, 7, 4, -450466145437542101157849670784530297886500454400000⟩, + ⟨7, 3, 8, 6, 8, 4, 763906613009750337584670315394660537591450828800000⟩, + ⟨7, 3, 1, 7, 0, 4, 1929288801444334460105607720362930803897901934182400000⟩, + ⟨7, 3, 2, 7, 1, 4, 417466808980327337286653900847862928158596739891200000⟩, + ⟨7, 3, 3, 7, 2, 4, 269924277150299607438803634572328002333129991782400000⟩, + ⟨7, 3, 4, 7, 3, 4, 76565965990137586836723678976480384625646187315200000⟩, + ⟨7, 3, 5, 7, 4, 4, 29637185064424595899415622158791226976928530432000000⟩, + ⟨7, 3, 6, 7, 5, 4, 1347800904222352995457957755160314593383809024000000⟩, + ⟨7, 3, 7, 7, 6, 4, 1128139270930821367998575324351628376456927641600000⟩, + ⟨7, 3, 8, 7, 7, 4, 578428224020950151080872966560927117409150566400000⟩ +] + +def collectedFourData_11_6_46 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 6, 5, -80505276987091341080482030835014423522584821760000000⟩, + ⟨7, 4, 1, 0, 7, 5, 213656204132755883394165429350493178435152642048000000⟩, + ⟨7, 4, 2, 0, 8, 5, -64947017879951716512402138282844946887971176448000000⟩, + ⟨7, 4, 0, 1, 5, 5, -122938089206753078410778029223770114671343828992000000⟩, + ⟨7, 4, 1, 1, 6, 5, 104372539188289887265090404341223842606689026048000000⟩, + ⟨7, 4, 2, 1, 7, 5, -29772514849339363943969857985299895176239513600000000⟩, + ⟨7, 4, 3, 1, 8, 5, -376554830917185653885928510733449013487468544000000⟩, + ⟨7, 4, 0, 2, 4, 5, -35031197018089016136884683478037638461815521280000000⟩, + ⟨7, 4, 1, 2, 5, 5, 62101861180760172739571427623498117346855223296000000⟩, + ⟨7, 4, 2, 2, 6, 5, -62718252774957670842476742368942545606306430976000000⟩, + ⟨7, 4, 3, 2, 7, 5, 13529613083486611192637116233472101814791831552000000⟩, + ⟨7, 4, 4, 2, 8, 5, -1131307176520707788402956260026068591479619584000000⟩, + ⟨7, 4, 0, 3, 3, 5, -6230672794421609546794708688644465211587166208000000⟩, + ⟨7, 4, 1, 3, 4, 5, 33861506772965643475364082218175804685173129216000000⟩, + ⟨7, 4, 2, 3, 5, 5, 15543020191409740240635734057375473430792503296000000⟩, + ⟨7, 4, 3, 3, 6, 5, -14856247299464942600333004851802765059055157248000000⟩, + ⟨7, 4, 4, 3, 7, 5, -6820243270853497363905756480770341955463806976000000⟩, + ⟨7, 4, 5, 3, 8, 5, 1128080587530198177466847442522287713202208768000000⟩, + ⟨7, 4, 0, 4, 2, 5, 46180267306794269928646902315515143789580648448000000⟩, + ⟨7, 4, 1, 4, 3, 5, -106715528991073461264602650548232764186314145792000000⟩, + ⟨7, 4, 2, 4, 4, 5, 1963526551090169372987004037749564204625428480000000⟩, + ⟨7, 4, 3, 4, 5, 5, -27791853113685477798277488411937663087684878336000000⟩, + ⟨7, 4, 4, 4, 6, 5, 8086993431296931116961082665192231361434353664000000⟩, + ⟨7, 4, 5, 4, 7, 5, 674064671336793013453520787101873610361405440000000⟩, + ⟨7, 4, 6, 4, 8, 5, -426403499530259410875140334024058698486251520000000⟩, + ⟨7, 4, 0, 5, 1, 5, 35595260998523989775658300806200218373092016128000000⟩, + ⟨7, 4, 1, 5, 2, 5, -21613907022582627060390336542038271040568688640000000⟩, + ⟨7, 4, 2, 5, 3, 5, 32742591401346227005698544734066409990030098432000000⟩, + ⟨7, 4, 3, 5, 4, 5, 28450496868135096342110722257871923440919773184000000⟩, + ⟨7, 4, 4, 5, 5, 5, 4195573166251341197159554662159154370769321984000000⟩, + ⟨7, 4, 5, 5, 6, 5, -1497247523395820856573251000299746122394501120000000⟩, + ⟨7, 4, 6, 5, 7, 5, 516851889928041663768657126392828356856905728000000⟩, + ⟨7, 4, 7, 5, 8, 5, 30153320837102916874359009267177437012164608000000⟩, + ⟨7, 4, 0, 6, 0, 5, -821054894973072790277118324360525028888751898624000000⟩, + ⟨7, 4, 1, 6, 1, 5, -476904976733717264841501626804115619581857366016000000⟩, + ⟨7, 4, 2, 6, 2, 5, -21911890726215101519294023587281617594041237504000000⟩, + ⟨7, 4, 3, 6, 3, 5, 37845916017317059429645616169393414127931621376000000⟩, + ⟨7, 4, 4, 6, 4, 5, -8142871087604568413423319743408196816205774848000000⟩, + ⟨7, 4, 5, 6, 5, 5, 3034884170946210933062207556898080609710112768000000⟩, + ⟨7, 4, 6, 6, 6, 5, -336550590807694853648577323299533875211927552000000⟩, + ⟨7, 4, 7, 6, 7, 5, -99638067234431669837919620230082450253938688000000⟩, + ⟨7, 4, 8, 6, 8, 5, 147846640272415564568149418191100292108386304000000⟩, + ⟨7, 4, 1, 7, 0, 5, 2987159556427084557902525495603185029842768756736000000⟩, + ⟨7, 4, 2, 7, 1, 5, 323186442331269019376527077006253996043019485184000000⟩, + ⟨7, 4, 3, 7, 2, 5, 139309864408335392434934207756427536248615206912000000⟩, + ⟨7, 4, 4, 7, 3, 5, 29637185064424595899415622158791226976928530432000000⟩, + ⟨7, 4, 5, 7, 4, 5, 9177578859579397789170460960711328674187575296000000⟩, + ⟨7, 4, 6, 7, 5, 5, 347804879203395919604320264320702019597762560000000⟩, + ⟨7, 4, 7, 7, 6, 5, 249531774286005995182998766590480375173087232000000⟩, + ⟨7, 4, 8, 7, 7, 5, 111949115381131121306770703484265855621005312000000⟩ +] + +def collectedFourData_11_6_47 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 6, 6, -18305565269104836760408768681711988314315161600000000⟩, + ⟨7, 5, 1, 0, 7, 6, 24290939279225610816658958656719509801234595840000000⟩, + ⟨7, 5, 2, 0, 8, 6, -4922625030844493380952184731897673439311298560000000⟩, + ⟨7, 5, 0, 1, 5, 6, -27954083263313298948991497857709483146052894720000000⟩, + ⟨7, 5, 1, 1, 6, 6, 11866292496079472750899004626586149310001315840000000⟩, + ⟨7, 5, 2, 1, 7, 6, -2256592090177986779885586433520458889428992000000000⟩, + ⟨7, 5, 3, 1, 8, 6, -21405581387716196871234227538890009094389760000000⟩, + ⟨7, 5, 0, 2, 4, 6, -7965513410659071597150070129833739062922444800000000⟩, + ⟨7, 5, 1, 2, 5, 6, 7060466814862183648611928754975759685837127680000000⟩, + ⟨7, 5, 2, 2, 6, 6, -4753696952976530753699448841354791459980574720000000⟩, + ⟨7, 5, 3, 2, 7, 6, 769102426059633431384913678435379534972846080000000⟩, + ⟨7, 5, 4, 2, 8, 6, -51448099141444238865168612086539416489689088000000⟩, + ⟨7, 5, 0, 3, 3, 6, -1416751693519531155691959735910898871859937280000000⟩, + ⟨7, 5, 1, 3, 4, 6, 3849772620757201328327865561291408964614881280000000⟩, + ⟨7, 5, 2, 3, 5, 6, 1178075033261432288217344729818513309559685120000000⟩, + ⟨7, 5, 3, 3, 6, 6, -844516082585257909972175109525827791796305920000000⟩, + ⟨7, 5, 4, 3, 7, 6, -310162049043817671842901649584123902617976832000000⟩, + ⟨7, 5, 5, 3, 8, 6, 42751137144205121790333867945718331190804480000000⟩, + ⟨7, 5, 0, 4, 2, 6, 10500627150997564535882068944324472560345415680000000⟩, + ⟨7, 5, 1, 4, 3, 6, -12132671014139717187148879975746495399182991360000000⟩, + ⟨7, 5, 2, 4, 4, 6, 148824461301523463915449944002350594759065600000000⟩, + ⟨7, 5, 3, 4, 5, 6, -1579851657437061745583382108968718221904445440000000⟩, + ⟨7, 5, 4, 4, 6, 6, 367769645985231797112103535134246736807067648000000⟩, + ⟨7, 5, 5, 4, 7, 6, 25545188461645583586366856574817291101798400000000⟩, + ⟨7, 5, 6, 4, 8, 6, -13851012334219786087849410070637694261657600000000⟩, + ⟨7, 5, 0, 5, 1, 6, 8093772208047709023540820159278258133118484480000000⟩, + ⟨7, 5, 1, 5, 2, 6, -2457322057196891162643975478280326019756851200000000⟩, + ⟨7, 5, 2, 5, 3, 6, 2481707478931601408274743268277397494997975040000000⟩, + ⟨7, 5, 3, 5, 4, 6, 1617292824921334275153661238478368400589455360000000⟩, + ⟨7, 5, 4, 5, 5, 6, 190800755703091796148935679920227605584805888000000⟩, + ⟨7, 5, 5, 5, 6, 6, -56741543927864739464026925027955083260723200000000⟩, + ⟨7, 5, 6, 5, 7, 6, 16789078678398803062041195845148213919088640000000⟩, + ⟨7, 5, 7, 5, 8, 6, 857045654833832846882241346723106688860160000000⟩, + ⟨7, 5, 0, 6, 0, 6, -186694270635918355477240653505006971161243811840000000⟩, + ⟨7, 5, 1, 6, 1, 6, -54220142489291749466657393280124401745165025280000000⟩, + ⟨7, 5, 2, 6, 2, 6, -1660800222750365513968717653096204856071290880000000⟩, + ⟨7, 5, 3, 6, 3, 6, 2151383461282741472070368749390591928869847040000000⟩, + ⟨7, 5, 4, 6, 4, 6, -370310776512086763507015609565113448384167936000000⟩, + ⟨7, 5, 5, 6, 5, 6, 115013724057569175988396792950587998580244480000000⟩, + ⟨7, 5, 6, 6, 6, 6, -10932289227226506254738847487969078290677760000000⟩, + ⟨7, 5, 7, 6, 7, 6, -2832005570485466654970828043119419468021760000000⟩, + ⟨7, 5, 8, 6, 8, 6, 3735319423372193629028377959347705044008960000000⟩, + ⟨7, 5, 1, 7, 0, 6, 339615279121232043887336439394007317025264762880000000⟩, + ⟨7, 5, 2, 7, 1, 6, 24495746264904071956901228808043351731842580480000000⟩, + ⟨7, 5, 3, 7, 2, 6, 7919188378066920990488232470223997228264980480000000⟩, + ⟨7, 5, 4, 7, 3, 6, 1347800904222352995457957755160314593383809024000000⟩, + ⟨7, 5, 5, 7, 4, 6, 347804879203395919604320264320702019597762560000000⟩, + ⟨7, 5, 6, 7, 5, 6, 11297866169145248481796875163072203640012800000000⟩, + ⟨7, 5, 7, 7, 6, 6, 7092423552620730895397043103900765928816640000000⟩, + ⟨7, 5, 8, 7, 7, 6, 2828374756044375216569271997112062448762880000000⟩ +] + +def collectedFourData_11_6_48 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 6, 7, -45966493252754710083610571716533654384877240320000000⟩, + ⟨7, 6, 1, 0, 7, 7, 40664110615805817385532441319140044118176038912000000⟩, + ⟨7, 6, 2, 0, 8, 7, -6180519610832536708654432750981727179040096256000000⟩, + ⟨7, 6, 0, 1, 5, 7, -70194564375387339102124072728585026318100332544000000⟩, + ⟨7, 6, 1, 1, 6, 7, 19864700377097365486104181542947097584087334912000000⟩, + ⟨7, 6, 2, 1, 7, 7, -2833226495945800367486338537011033134019379200000000⟩, + ⟨7, 6, 3, 1, 8, 7, -21500336055513988363844346139190542824426700800000⟩, + ⟨7, 6, 0, 2, 4, 7, -20001934551769914793054480720911027961551912960000000⟩, + ⟨7, 6, 1, 2, 5, 7, 11819534858593369664197178810666286130736922624000000⟩, + ⟨7, 6, 2, 2, 6, 7, -5968424785096017801391355954632891251422134272000000⟩, + ⟨7, 6, 3, 2, 7, 7, 772506960772508676835949724443828756117087846400000⟩, + ⟨7, 6, 4, 2, 8, 7, -43063200858804505370668248820552379955098419200000⟩, + ⟨7, 6, 0, 3, 3, 7, -3557557835753133931202317797030565174214393856000000⟩, + ⟨7, 6, 1, 3, 4, 7, 6444690256586989912634887875241828803730735104000000⟩, + ⟨7, 6, 2, 3, 5, 7, 1479112424871283477032572345667987513972621312000000⟩, + ⟨7, 6, 3, 3, 6, 7, -848254445931052370747298265294111788701948313600000⟩, + ⟨7, 6, 4, 3, 7, 7, -259612519017108856202635416643423174182882508800000⟩, + ⟨7, 6, 5, 3, 8, 7, 30671700548799318727814464811501104876486656000000⟩, + ⟨7, 6, 0, 4, 2, 7, 26367773952365139197592170770152192643260481536000000⟩, + ⟨7, 6, 1, 4, 3, 7, -20310629840736514247080533065528487201680130048000000⟩, + ⟨7, 6, 2, 4, 4, 7, 186854065845404580200852154392813731640770560000000⟩, + ⟨7, 6, 3, 4, 5, 7, -1586845082014454673661245112514620867399070515200000⟩, + ⟨7, 6, 4, 4, 6, 7, 307831356242968101765460861441082651032367923200000⟩, + ⟨7, 6, 5, 4, 7, 7, 18327334038281635258686962390551058951700480000000⟩, + ⟨7, 6, 6, 4, 8, 7, -8695203557566383893902675934461987525754880000000⟩, + ⟨7, 6, 0, 5, 1, 7, 20324000932026498788380615382471125789411639296000000⟩, + ⟨7, 6, 1, 5, 2, 7, -4113666203018044451630812343024259550056284160000000⟩, + ⟨7, 6, 2, 5, 3, 7, 3115866361093769600205200703901818524327215104000000⟩, + ⟨7, 6, 3, 5, 4, 7, 1624451987832233510760676609644579050947923148800000⟩, + ⟨7, 6, 4, 5, 5, 7, 159704467297511895271398157675062245614367539200000⟩, + ⟨7, 6, 5, 5, 6, 7, -40709084255736897185303376932099572409303040000000⟩, + ⟨7, 6, 6, 5, 7, 7, 10539623612348646152418452384595040882655232000000⟩, + ⟨7, 6, 7, 5, 8, 7, 478244156670170446707461549731803662647296000000⟩, + ⟨7, 6, 0, 6, 0, 7, -468801744461702546089532837521409201496095981568000000⟩, + ⟨7, 6, 1, 6, 1, 7, -90766925331493464256223422126742151078875234304000000⟩, + ⟨7, 6, 2, 6, 2, 7, -2085189971218008903719209614721403109179916288000000⟩, + ⟨7, 6, 3, 6, 3, 7, 2160906847799890330679852635333381513966465843200000⟩, + ⟨7, 6, 4, 6, 4, 7, -309958338893688504319980836015574226401912422400000⟩, + ⟨7, 6, 5, 6, 5, 7, 82516319774061727518437982166151939443654656000000⟩, + ⟨7, 6, 6, 6, 6, 7, -6862926541916123543669149272464332148441088000000⟩, + ⟨7, 6, 7, 6, 7, 7, -1580301012090938223321598237554362082656256000000⟩, + ⟨7, 6, 8, 6, 8, 7, 1875927157093661909336945628304178715977318400000⟩, + ⟨7, 6, 1, 7, 0, 7, 568531052597642161721736262775496056971129257984000000⟩, + ⟨7, 6, 2, 7, 1, 7, 30755224950831750751737346013450366057340469248000000⟩, + ⟨7, 6, 3, 7, 2, 7, 7954243724165694803221757218736668269470967398400000⟩, + ⟨7, 6, 4, 7, 3, 7, 1128139270930821367998575324351628376456927641600000⟩, + ⟨7, 6, 5, 7, 4, 7, 249531774286005995182998766590480375173087232000000⟩, + ⟨7, 6, 6, 7, 5, 7, 7092423552620730895397043103900765928816640000000⟩, + ⟨7, 6, 7, 7, 6, 7, 3957677285381479080179572767263882722934784000000⟩, + ⟨7, 6, 8, 7, 7, 7, 1420447467518528963045444312425293210137395200000⟩ +] + +def collectedFourData_11_6_49 : List CollectedFourTerm := [ + ⟨7, 7, 0, 0, 6, 8, -54992684027705246341160299280616101912059576320000000⟩, + ⟨7, 7, 1, 0, 7, 8, 36486825970164415676968824369403565314758672384000000⟩, + ⟨7, 7, 2, 0, 8, 8, -4436492819454058318393399520823129403203099033600000⟩, + ⟨7, 7, 0, 1, 5, 8, -83978289967263386412390748700884803569785503744000000⟩, + ⟨7, 7, 1, 1, 6, 8, 17824067823750387283958149373847559787337744384000000⟩, + ⟨7, 7, 2, 1, 7, 8, -2033743082558937181292292351898957475500523520000000⟩, + ⟨7, 7, 3, 1, 8, 8, -12861120171697043820732535341984752693831270400000⟩, + ⟨7, 7, 0, 2, 4, 8, -23929605869649496536087652572175405457300520960000000⟩, + ⟨7, 7, 1, 2, 5, 8, 10605354571954215004656763740834368116771258368000000⟩, + ⟨7, 7, 2, 2, 6, 8, -4284247178201788939545965662451556155898671923200000⟩, + ⟨7, 7, 3, 2, 7, 8, 462099979754487343378418988317220672470463283200000⟩, + ⟨7, 7, 4, 2, 8, 8, -22079694799440403887869166854411465645673676800000⟩, + ⟨7, 7, 0, 3, 3, 8, -4256136157615951948001781776900391454591942656000000⟩, + ⟨7, 7, 1, 3, 4, 8, 5782649325479265639631330647832770251983945728000000⟩, + ⟨7, 7, 2, 3, 5, 8, 1061734621892542850122163246128295960491799347200000⟩, + ⟨7, 7, 3, 3, 6, 8, -507410783586226778266425860201781433453038796800000⟩, + ⟨7, 7, 4, 3, 7, 8, -133110522945247091470324915999830094061450035200000⟩, + ⟨7, 7, 5, 3, 8, 8, 13760450962599521273815832779285478869303296000000⟩, + ⟨7, 7, 0, 4, 2, 8, 31545470599706324114125327240926797247950094336000000⟩, + ⟨7, 7, 1, 4, 3, 8, -18224188482689529246845660658049350609546510336000000⟩, + ⟨7, 7, 2, 4, 4, 8, 134127350709476558724698828779673589053915136000000⟩, + ⟨7, 7, 3, 4, 5, 8, -949222618705085328265376193550222639305955737600000⟩, + ⟨7, 7, 4, 4, 6, 8, 157833655185733873245425419692799810268351692800000⟩, + ⟨7, 7, 5, 4, 7, 8, 8222314928633061361817196964627135258951680000000⟩, + ⟨7, 7, 6, 4, 8, 8, -3467544494265363431857516552974930762792960000000⟩, + ⟨7, 7, 0, 5, 1, 8, 24314914676827987945614602162679754970256900096000000⟩, + ⟨7, 7, 1, 5, 2, 8, -3691083379812709786252571968120921821145989120000000⟩, + ⟨7, 7, 2, 5, 3, 8, 2236627275341479022814417570537989881727444582400000⟩, + ⟨7, 7, 3, 5, 4, 8, 971718403596973323542741120333852075847214694400000⟩, + ⟨7, 7, 4, 5, 5, 8, 81884900000769854666737119046852763290750156800000⟩, + ⟨7, 7, 5, 5, 6, 8, -18263589811140372299650440915407939976560640000000⟩, + ⟨7, 7, 6, 5, 7, 8, 4203077430755105404006438994440133692882944000000⟩, + ⟨7, 7, 7, 5, 8, 8, 171646309745085427238624766702330019892428800000⟩, + ⟨7, 7, 0, 6, 0, 8, -560857798376308060043615016325009155662668627968000000⟩, + ⟨7, 7, 1, 6, 1, 8, -81442750333505163563988087719779745548235440128000000⟩, + ⟨7, 7, 2, 6, 2, 8, -1496788444501057041634961822629976648138411212800000⟩, + ⟨7, 7, 3, 6, 3, 8, 1292616198074260918067550597734623034088200601600000⟩, + ⟨7, 7, 4, 6, 4, 8, -158924218052288865306573929039084054243809689600000⟩, + ⟨7, 7, 5, 6, 5, 8, 37019850596761471431705467982392724654391296000000⟩, + ⟨7, 7, 6, 6, 6, 8, -2736854058380357947587243515406441561194496000000⟩, + ⟨7, 7, 7, 6, 7, 8, -567184843199051351099349571234106920717516800000⟩, + ⟨7, 7, 8, 6, 8, 8, 612079851938637671639725246692616456844083200000⟩, + ⟨7, 7, 1, 7, 0, 8, 510127807066843223743975765480676354074909605888000000⟩, + ⟨7, 7, 2, 7, 1, 8, 22076676921453811561978288797384968973927107788800000⟩, + ⟨7, 7, 3, 7, 2, 8, 4758087694411920312070525182015269707678167859200000⟩, + ⟨7, 7, 4, 7, 3, 8, 578428224020950151080872966560927117409150566400000⟩, + ⟨7, 7, 5, 7, 4, 8, 111949115381131121306770703484265855621005312000000⟩, + ⟨7, 7, 6, 7, 5, 8, 2828374756044375216569271997112062448762880000000⟩, + ⟨7, 7, 7, 7, 6, 8, 1420447467518528963045444312425293210137395200000⟩, + ⟨7, 7, 8, 7, 7, 8, 463465370879507449600851444719355480873369600000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1122.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1122.lean new file mode 100644 index 0000000000000000000000000000000000000000..ce89815a301972e5939ecafc617fa7eb75faa55a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1122.lean @@ -0,0 +1,613 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PartsTrace +import OAI.Analysis.LaughlinFock.Sparse1119 +import OAI.Analysis.LaughlinFock.Sparse1120 +import OAI.Analysis.LaughlinFock.Sparse1121 + +namespace OAI + +/-! Sparse1122. -/ +namespace LaughlinFock +def collectedFourData_11_6 : List (List CollectedFourTerm) := [ + collectedFourData_11_6_0, + collectedFourData_11_6_1, + collectedFourData_11_6_2, + collectedFourData_11_6_3, + collectedFourData_11_6_4, + collectedFourData_11_6_5, + collectedFourData_11_6_6, + collectedFourData_11_6_7, + collectedFourData_11_6_8, + collectedFourData_11_6_9, + collectedFourData_11_6_10, + collectedFourData_11_6_11, + collectedFourData_11_6_12, + collectedFourData_11_6_13, + collectedFourData_11_6_14, + collectedFourData_11_6_15, + collectedFourData_11_6_16, + collectedFourData_11_6_17, + collectedFourData_11_6_18, + collectedFourData_11_6_19, + collectedFourData_11_6_20, + collectedFourData_11_6_21, + collectedFourData_11_6_22, + collectedFourData_11_6_23, + collectedFourData_11_6_24, + collectedFourData_11_6_25, + collectedFourData_11_6_26, + collectedFourData_11_6_27, + collectedFourData_11_6_28, + collectedFourData_11_6_29, + collectedFourData_11_6_30, + collectedFourData_11_6_31, + collectedFourData_11_6_32, + collectedFourData_11_6_33, + collectedFourData_11_6_34, + collectedFourData_11_6_35, + collectedFourData_11_6_36, + collectedFourData_11_6_37, + collectedFourData_11_6_38, + collectedFourData_11_6_39, + collectedFourData_11_6_40, + collectedFourData_11_6_41, + collectedFourData_11_6_42, + collectedFourData_11_6_43, + collectedFourData_11_6_44, + collectedFourData_11_6_45, + collectedFourData_11_6_46, + collectedFourData_11_6_47, + collectedFourData_11_6_48, + collectedFourData_11_6_49 +] + +theorem collectedFourChecked_11_6 : collectNumericRowParts 11 6 = collectedFourData_11_6 := by + decide +kernel + +def collectedFourData_11_7_0 : List CollectedFourTerm := [ + ⟨0, 7, 4, 3, 8, 0, -4476483206440535204315781715193462300604786278400000⟩, + ⟨0, 7, 4, 4, 7, 0, -10200945527339497103013676689450706696499783270400000⟩, + ⟨0, 7, 5, 4, 8, 0, 44323025269908706618428424722394328280883789824000000⟩, + ⟨0, 7, 4, 5, 6, 0, 9357110990071021481897870172996494113622930227200000⟩, + ⟨0, 7, 5, 5, 7, 0, -1507800126167106800679382852884306231973380096000000⟩, + ⟨0, 7, 6, 5, 8, 0, 31215755665824406271008635639093874214729416704000000⟩, + ⟨0, 7, 4, 6, 5, 0, -15182695307648243970376619465547846713677027737600000⟩, + ⟨0, 7, 5, 6, 6, 0, 14341869879299160568481205883747832550616203264000000⟩, + ⟨0, 7, 6, 6, 7, 0, 29480058048995621043721251282880775332892246016000000⟩, + ⟨0, 7, 7, 6, 8, 0, 10780375570610719472427380798189423591405125632000000⟩, + ⟨0, 7, 4, 7, 4, 0, -62789757576380036488768176278326615203764187955200000⟩, + ⟨0, 7, 5, 7, 5, 0, -16219225721665369483761260206130291009623425024000000⟩, + ⟨0, 7, 6, 7, 6, 0, -31906851912427212304478530747215000627723632640000000⟩, + ⟨0, 7, 7, 7, 7, 0, -3810136604488897365825778377054292625930059776000000⟩, + ⟨0, 7, 8, 7, 8, 0, -25558804049397669493314211356709285704971059200000000⟩ +] + +def collectedFourData_11_7_1 : List CollectedFourTerm := [ + ⟨0, 8, 3, 2, 8, 1, -355116043312283124146546546335249845121449984000000⟩, + ⟨0, 8, 3, 3, 7, 1, -886685493624617133267533114222785770950964019200000⟩, + ⟨0, 8, 4, 3, 8, 1, -515093817309435334386908631177323214599199129600000⟩, + ⟨0, 8, 3, 4, 6, 1, -2036727707449979693264236063520984010771451084800000⟩, + ⟨0, 8, 4, 4, 7, 1, -1173788380191639504628464329616092994740001177600000⟩, + ⟨0, 8, 5, 4, 8, 1, 2550050478032896596813626444420563313023254528000000⟩, + ⟨0, 8, 3, 5, 5, 1, -669374586393787064852509065953679405745805721600000⟩, + ⟨0, 8, 4, 5, 6, 1, 1076691187387743313268883389394445289365753036800000⟩, + ⟨0, 8, 5, 5, 7, 1, -86748736330524671409963075587025273159155712000000⟩, + ⟨0, 8, 6, 5, 8, 1, 1197297223780073824554331655699875995259502592000000⟩, + ⟨0, 8, 3, 6, 4, 1, 3158115730299373588269343707440258120331716198400000⟩, + ⟨0, 8, 4, 6, 5, 1, -1747021517205924529148972286120232535504348774400000⟩, + ⟨0, 8, 5, 6, 6, 1, 825135286205786440311699519481827474127454208000000⟩, + ⟨0, 8, 6, 6, 7, 1, 1130723601145463444849453758506905450701651968000000⟩, + ⟨0, 8, 7, 6, 8, 1, 310115360016654483330347961779208605298327552000000⟩, + ⟨0, 8, 3, 7, 3, 1, -5628417887683198392180142470224211828913943347200000⟩, + ⟨0, 8, 4, 7, 4, 1, -7225005529210682440863709389874549602604862668800000⟩, + ⟨0, 8, 5, 7, 5, 1, -933145787161234036670170154170057009479548928000000⟩, + ⟨0, 8, 6, 7, 6, 1, -1223804594810283228815392578311874172126494720000000⟩, + ⟨0, 8, 7, 7, 7, 1, -109604890578665622335294800493061359152398336000000⟩, + ⟨0, 8, 8, 7, 8, 1, -588193067483273852897200535611515681594408960000000⟩ +] + +def collectedFourData_11_7_2 : List CollectedFourTerm := [ + ⟨1, 6, 4, 3, 8, 0, -563193259828491877985625398441568853757735731200000⟩, + ⟨1, 6, 4, 4, 7, 0, -1283396697793804716344802868478938778118075187200000⟩, + ⟨1, 6, 5, 4, 8, 0, 5576348203720688293701717420807367322901676032000000⟩, + ⟨1, 6, 4, 5, 6, 0, 1177232572545586200208651708641269991897405849600000⟩, + ⟨1, 6, 5, 5, 7, 0, -189698660547660117290751811258257496791318528000000⟩, + ⟨1, 6, 6, 5, 8, 0, 3927302389105678544443120084998334407216463872000000⟩, + ⟨1, 6, 4, 6, 5, 0, -1910158324953552815285964291148520331460529356800000⟩, + ⟨1, 6, 5, 6, 6, 0, 1804372780341815462002102376321633203311869952000000⟩, + ⟨1, 6, 6, 6, 7, 0, 3708931593591038083100115882978939357351641088000000⟩, + ⟨1, 6, 7, 6, 8, 0, 1356295685651723033607104110789973610621566976000000⟩, + ⟨1, 6, 4, 7, 4, 0, -7899676291067969402865966791573057548041427353600000⟩, + ⟨1, 6, 5, 7, 5, 0, -2040565815803018572975156041080603279603269632000000⟩, + ⟨1, 6, 6, 7, 6, 0, -4014250274315987994529684344313794910507499520000000⟩, + ⟨1, 6, 7, 7, 7, 0, -479359165602728897996289086498416163467296768000000⟩, + ⟨1, 6, 8, 7, 8, 0, -3215592577045256159947190644910395915606425600000000⟩ +] + +def collectedFourData_11_7_3 : List CollectedFourTerm := [ + ⟨1, 7, 3, 2, 8, 1, -3723993531935712220480332114333723517972905984000000⟩, + ⟨1, 7, 3, 3, 7, 1, -9298400073171475878189999374139682363465216819200000⟩, + ⟨1, 7, 4, 3, 8, 1, -5401631607822275143143838433782955716598405529600000⟩, + ⟨1, 7, 3, 4, 6, 1, -21358541670245136656500946932884130467282734284800000⟩, + ⟨1, 7, 4, 4, 7, 1, -12309160394229272045568280371977207909352839577600000⟩, + ⟨1, 7, 5, 4, 8, 1, 26741600851733773312526974013499536078461206528000000⟩, + ⟨1, 7, 3, 5, 5, 1, -7019526932441421206577885413946270948945140121600000⟩, + ⟨1, 7, 4, 5, 6, 1, 11290931776343797960662287720859553238799404236800000⟩, + ⟨1, 7, 5, 5, 7, 1, -909707514155827936734839589202566036389363712000000⟩, + ⟨1, 7, 6, 5, 8, 1, 12555690459866522252718508566886471962923630592000000⟩, + ⟨1, 7, 3, 6, 4, 1, 33118195514464667137683822885413370546637661798400000⟩, + ⟨1, 7, 4, 6, 5, 1, -18320481298295499392058078377275004559445878374400000⟩, + ⟨1, 7, 5, 6, 6, 1, 8652941838789591657127697309423174253394526208000000⟩, + ⟨1, 7, 6, 6, 7, 1, 11857553203727966159500202805790185449972563968000000⟩, + ⟨1, 7, 7, 6, 8, 1, 3252085104587529952454336427479680351891095552000000⟩, + ⟨1, 7, 3, 7, 3, 1, -59023500074119297922380323555241558231909348147200000⟩, + ⟨1, 7, 4, 7, 4, 1, -75766427244515568977695571273004958463462001868800000⟩, + ⟨1, 7, 5, 7, 5, 1, -9785614987508778653175986382274915932127100928000000⟩, + ⟨1, 7, 6, 7, 6, 1, -12833665167357597467138749721333119845106974720000000⟩, + ⟨1, 7, 7, 7, 7, 1, -1149393025942610581279716888456389870103822336000000⟩, + ⟨1, 7, 8, 7, 8, 1, -6168201127739285497731953233661924702379048960000000⟩ +] + +def collectedFourData_11_7_4 : List CollectedFourTerm := [ + ⟨1, 8, 2, 1, 8, 2, 4004854754722201678189844611307480703762117427200000⟩, + ⟨1, 8, 2, 2, 7, 2, 4868073851310512609812183075483861427652290150400000⟩, + ⟨1, 8, 3, 2, 8, 2, 2047788652559465822937491954747521228376899584000000⟩, + ⟨1, 8, 2, 3, 6, 2, 1933856391927163546379775480091075435472879616000000⟩, + ⟨1, 8, 3, 3, 7, 2, 5113101833692273170611443642198094893662024499200000⟩, + ⟨1, 8, 4, 3, 8, 2, 1485152943600218921326713809803941339751828684800000⟩, + ⟨1, 8, 2, 4, 5, 2, 898120098618748677189689250341685760582326681600000⟩, + ⟨1, 8, 3, 4, 6, 2, 11744859085405506527886307799271793064195968204800000⟩, + ⟨1, 8, 4, 4, 7, 2, 3384345160870199948806405543701880307553455308800000⟩, + ⟨1, 8, 5, 4, 8, 2, -4901650723955510526093163570631235530523672576000000⟩, + ⟨1, 8, 2, 5, 4, 2, -4762042305500330606248098751350229072017044275200000⟩, + ⟨1, 8, 3, 5, 5, 2, 3859971150679551552926740010508517699005028761600000⟩, + ⟨1, 8, 4, 5, 6, 2, -3104388040706601095704738118579985865452709478400000⟩, + ⟨1, 8, 5, 5, 7, 2, 166746505569077821490595853954620276294549504000000⟩, + ⟨1, 8, 6, 5, 8, 2, -1726063715489266363595094552791270812809166848000000⟩, + ⟨1, 8, 2, 6, 3, 2, -2402842043130837275196281413287456276379336704000000⟩, + ⟨1, 8, 3, 6, 4, 2, -18211380977483747942299093343557501528706541158400000⟩, + ⟨1, 8, 4, 6, 5, 2, 5037129279407820069348138899551961468451894067200000⟩, + ⟨1, 8, 5, 6, 6, 2, -1586056828220815561187680553933076548221403136000000⟩, + ⟨1, 8, 6, 6, 7, 2, -1630088954873448485552223195968666831570337792000000⟩, + ⟨1, 8, 7, 6, 8, 2, -357658138620363891890997814935834402058823270400000⟩, + ⟨1, 8, 2, 7, 2, 2, 11621570231269303040407902462696432301167240806400000⟩, + ⟨1, 8, 3, 7, 3, 2, 32456461766005785339607132353641422623905887027200000⟩, + ⟨1, 8, 4, 7, 4, 2, 20831619151019751964122321624289728916581934694400000⟩, + ⟨1, 8, 5, 7, 5, 2, 1793672228293785109660334515046427822051557376000000⟩, + ⟨1, 8, 6, 7, 6, 2, 1764277627974425542583449653155751274406215680000000⟩, + ⟨1, 8, 7, 7, 7, 2, 126408060361631054213523353888575192151831347200000⟩, + ⟨1, 8, 8, 7, 8, 2, 565305863529225491017525964044609519783772160000000⟩ +] + +def collectedFourData_11_7_5 : List CollectedFourTerm := [ + ⟨2, 5, 4, 3, 8, 0, 2723855208351876016987154416341265835072107315200000⟩, + ⟨2, 5, 4, 4, 7, 0, 6207082060484563668904217682855811459214160691200000⟩, + ⟨2, 5, 5, 4, 8, 0, -26969721020655948874294180151424075337429942272000000⟩, + ⟨2, 5, 4, 5, 6, 0, -5693624733979017403591589991814305798738778521600000⟩, + ⟨2, 5, 5, 5, 7, 0, 917467806179839105752377959042901849552191488000000⟩, + ⟨2, 5, 6, 5, 8, 0, -18994195830035194923711436891929365382181158912000000⟩, + ⟨2, 5, 4, 6, 5, 0, 9238382404977445422460435344527962581156809932800000⟩, + ⟨2, 5, 5, 6, 6, 0, -8726756064231164835512964879306192033354350592000000⟩, + ⟨2, 5, 6, 6, 7, 0, -17938056719109697800167316365835519196290613248000000⟩, + ⟨2, 5, 7, 6, 8, 0, -6559654262468727993314157447083930507381047296000000⟩, + ⟨2, 5, 4, 7, 4, 0, 38206377711750355569035271908865976448094673305600000⟩, + ⟨2, 5, 5, 7, 5, 0, 9869091521181337231503471896364751766654287872000000⟩, + ⟨2, 5, 6, 7, 6, 0, 19414714800836452142941484784238478797748305920000000⟩, + ⟨2, 5, 7, 7, 7, 0, 2318395927351521027264602947424666306664726528000000⟩, + ⟨2, 5, 8, 7, 8, 0, 15552047962345385118297968721849604372011417600000000⟩ +] + +def collectedFourData_11_7_6 : List CollectedFourTerm := [ + ⟨2, 6, 3, 2, 8, 1, -4415963985125208402577581788260561631204868096000000⟩, + ⟨2, 6, 3, 3, 7, 1, -11026173780991327526304164271833103646981934284800000⟩, + ⟨2, 6, 4, 3, 8, 1, -6405330846173157498115982145397379010230904422400000⟩, + ⟨2, 6, 3, 4, 6, 1, -25327259562014398192297877714922948259795383091200000⟩, + ⟨2, 6, 4, 4, 7, 1, -14596375778287588627275376874412360414689388134400000⟩, + ⟨2, 6, 5, 4, 8, 1, 31710566963435999549602652429710979701860728832000000⟩, + ⟨2, 6, 3, 5, 5, 1, -8323853911251334044885484309938508634721248870400000⟩, + ⟨2, 6, 4, 5, 6, 1, 13388945940763452407728329905917578254734275379200000⟩, + ⟨2, 6, 5, 5, 7, 1, -1078743984128720803199295010051755524361289728000000⟩, + ⟨2, 6, 6, 5, 8, 1, 14888714602662175225993834588094757944004968448000000⟩, + ⟨2, 6, 3, 6, 4, 1, 39272022733130757792734493068590215087825459609600000⟩, + ⟨2, 6, 4, 6, 5, 1, -21724684779830997071127558042828610269645216153600000⟩, + ⟨2, 6, 5, 6, 6, 1, 10260780314947543941800553047807108204306890752000000⟩, + ⟨2, 6, 6, 6, 7, 1, 14060853610599845867172063626166558237961224192000000⟩, + ⟨2, 6, 7, 6, 8, 1, 3856368324827852114473551290011914589005938688000000⟩, + ⟨2, 6, 3, 7, 3, 1, -69990897773623052517694164608578692136573914316800000⟩, + ⟨2, 6, 4, 7, 4, 1, -89844896647679264446218869029930223315291681587200000⟩, + ⟨2, 6, 5, 7, 5, 1, -11603920089162556279338646875545578617471762432000000⟩, + ⟨2, 6, 6, 7, 6, 1, -15218340926265976149379430181155049901318471680000000⟩, + ⟨2, 6, 7, 7, 7, 1, -1362966440137274318584795005380782529376681984000000⟩, + ⟨2, 6, 8, 7, 8, 1, -7314339780538480940826127343439038600435466240000000⟩ +] + +def collectedFourData_11_7_7 : List CollectedFourTerm := [ + ⟨2, 7, 2, 1, 8, 2, 4868073851310512609812183075483861427652290150400000⟩, + ⟨2, 7, 2, 2, 7, 2, 5917353929969676971434543572996702710700756172800000⟩, + ⟨2, 7, 3, 2, 8, 2, 2489175513988549823075210189156303401320972288000000⟩, + ⟨2, 7, 2, 3, 6, 2, 2350685932524745397202101700247999041201242112000000⟩, + ⟨2, 7, 3, 3, 7, 2, 6215196020863373214026753809496929043506161254400000⟩, + ⟨2, 7, 4, 3, 8, 2, 1805267519730203681924285867332085453279566233600000⟩, + ⟨2, 7, 2, 4, 5, 2, 1091703753367610641378733174288871485301011251200000⟩, + ⟨2, 7, 3, 4, 6, 2, 14276383265478801170397833263348599664414398873600000⟩, + ⟨2, 7, 4, 4, 7, 2, 4113817651442967814730871824316831473159739801600000⟩, + ⟨2, 7, 5, 4, 8, 2, -5958168068245020168910946406626609590626680832000000⟩, + ⟨2, 7, 2, 5, 4, 2, -5788468008460549970444656674681991464596432486400000⟩, + ⟨2, 7, 3, 5, 5, 2, 4691961575705008198914053277061823373006549811200000⟩, + ⟨2, 7, 4, 5, 6, 2, -3773517685620325791281783557124537025727089868800000⟩, + ⟨2, 7, 5, 5, 7, 2, 202687576272547436778144315325591878503497728000000⟩, + ⟨2, 7, 6, 5, 8, 2, -2098104963522457593505889753249897923095822336000000⟩, + ⟨2, 7, 2, 6, 3, 2, -2920758238535953497263991611930893898773168128000000⟩, + ⟨2, 7, 3, 6, 4, 2, -22136719796943512419829629721511491564909415628800000⟩, + ⟨2, 7, 4, 6, 5, 2, 6122848101255719754621737898651571194901718630400000⟩, + ⟨2, 7, 5, 6, 6, 2, -1927920547692825086008718296680357234581962752000000⟩, + ⟨2, 7, 6, 6, 7, 2, -1981443498586993934811303129335535886500102144000000⟩, + ⟨2, 7, 7, 6, 8, 2, -434748908252718033312081109137229657410424012800000⟩, + ⟨2, 7, 2, 7, 2, 2, 14126520340669654177330225849118132450785807564800000⟩, + ⟨2, 7, 3, 7, 3, 2, 39452230481729904432997209713509828728109557350400000⟩, + ⟨2, 7, 4, 7, 4, 2, 25321732417377740761816892992986339748946431180800000⟩, + ⟨2, 7, 5, 7, 5, 2, 2180286029620196621337993160045897197847314432000000⟩, + ⟨2, 7, 6, 7, 6, 2, 2144555623913055364886545668923150535764213760000000⟩, + ⟨2, 7, 7, 7, 7, 2, 153654454638023941292148093666103358558463590400000⟩, + ⟨2, 7, 8, 7, 8, 2, 687153682413638975012421026365148023090053120000000⟩ +] + +def collectedFourData_11_7_8 : List CollectedFourTerm := [ + ⟨2, 8, 1, 0, 8, 3, -355116043312283124146546546335249845121449984000000⟩, + ⟨2, 8, 1, 1, 7, 3, -3723993531935712220480332114333723517972905984000000⟩, + ⟨2, 8, 2, 1, 8, 3, 2047788652559465822937491954747521228376899584000000⟩, + ⟨2, 8, 1, 2, 6, 3, -4415963985125208402577581788260561631204868096000000⟩, + ⟨2, 8, 2, 2, 7, 3, 2489175513988549823075210189156303401320972288000000⟩, + ⟨2, 8, 3, 2, 8, 3, 523544375811226158823141208012750598690570240000000⟩, + ⟨2, 8, 1, 3, 5, 3, -3648267504035923614297364182114305467100430336000000⟩, + ⟨2, 8, 2, 3, 6, 3, 988832159368219682913679846601111843131883520000000⟩, + ⟨2, 8, 3, 3, 7, 3, 1307232416115716027613788232117043043040755712000000⟩, + ⟨2, 8, 4, 3, 8, 3, 253132721116688469513315537498341294160740352000000⟩, + ⟨2, 8, 1, 4, 4, 3, 4109096270007836046875589104855198481097162752000000⟩, + ⟨2, 8, 2, 4, 5, 3, 459232671152049303477406838894534662136266752000000⟩, + ⟨2, 8, 3, 4, 6, 3, 3002729266603783317710396318823832323492937728000000⟩, + ⟨2, 8, 4, 4, 7, 3, 576835203041403591407338458753006462264410112000000⟩, + ⟨2, 8, 5, 4, 8, 3, -626586065293037281065027662227149210444103680000000⟩, + ⟨2, 8, 1, 5, 3, 3, 7847326708248079159938165846052720511299878912000000⟩, + ⟨2, 8, 2, 5, 4, 3, -2434958767159614899498870035202173645979910144000000⟩, + ⟨2, 8, 3, 5, 5, 3, 986852907992262737914163530010879824207282176000000⟩, + ⟨2, 8, 4, 5, 6, 3, -529118698200350893406407711323165636025122816000000⟩, + ⟨2, 8, 5, 5, 7, 3, 21315479765881481633385723185394768119070720000000⟩, + ⟨2, 8, 6, 5, 8, 3, -176516448493210326676159357292953995011162112000000⟩, + ⟨2, 8, 1, 6, 2, 3, -19554899114328711004323479342688746132364853248000000⟩, + ⟨2, 8, 2, 6, 3, 3, -1228636984653253527768726293164656763475066880000000⟩, + ⟨2, 8, 3, 6, 4, 3, -4655981502095121486045861392745722552751489024000000⟩, + ⟨2, 8, 4, 6, 5, 3, 858539348831047703963914808914844962026160128000000⟩, + ⟨2, 8, 5, 6, 6, 3, -202748250190307871703488467143719742058004480000000⟩, + ⟨2, 8, 6, 6, 7, 3, -166701559426911802232372274658363755145986048000000⟩, + ⟨2, 8, 7, 6, 8, 3, -30480018320211856905284924056201692287336448000000⟩, + ⟨2, 8, 1, 7, 1, 3, 55957801593025836319859056045784979144859189248000000⟩, + ⟨2, 8, 2, 7, 2, 3, 5942417666072626229484653398145904610910404608000000⟩, + ⟨2, 8, 3, 7, 3, 3, 8297925664880586577573849058012215943513505792000000⟩, + ⟨2, 8, 4, 7, 4, 3, 3550586802313612029841026156944393103690694656000000⟩, + ⟨2, 8, 5, 7, 5, 3, 229288067886861988135432953415540944855367680000000⟩, + ⟨2, 8, 6, 7, 6, 3, 180424406266946746922361566217314137716817920000000⟩, + ⟨2, 8, 7, 7, 7, 3, 10772633360189354955313569656765242266353664000000⟩, + ⟨2, 8, 8, 7, 8, 3, 41293701322144352826881402399058741008793600000000⟩ +] + +def collectedFourData_11_7_9 : List CollectedFourTerm := [ + ⟨3, 4, 4, 3, 8, 0, -1729805102966253799139903774622796415423112806400000⟩, + ⟨3, 4, 4, 4, 7, 0, -3941854981804687475404272905785909680703694438400000⟩, + ⟨3, 4, 5, 4, 8, 0, 17127327805112982810817918194424685784050171904000000⟩, + ⟨3, 4, 4, 5, 6, 0, 3615779975753937850133137332903756109878342451200000⟩, + ⟨3, 4, 5, 5, 7, 0, -582644954133744388883521784521904700486844416000000⟩, + ⟨3, 4, 6, 5, 8, 0, 12062409474920498894475829843776914132129808384000000⟩, + ⟨3, 4, 4, 6, 5, 0, -5866905472171931267290513219624501830598891929600000⟩, + ⟨3, 4, 5, 6, 6, 0, 5541993247645003063963466891914579023331590144000000⟩, + ⟨3, 4, 6, 6, 7, 0, 11391700247088018305845832923392426603221876736000000⟩, + ⟨3, 4, 7, 6, 8, 0, 4165758657846732757091125402025125799968899072000000⟩, + ⟨3, 4, 4, 7, 4, 0, -24263252660786898671140224822969615273740677939200000⟩, + ⟨3, 4, 5, 7, 5, 0, -6267442124910151543938912770869655842905391104000000⟩, + ⟨3, 4, 6, 7, 6, 0, -12329463266677025328174938168690337281149501440000000⟩, + ⟨3, 4, 7, 7, 7, 0, -1472315082509616614743672275534622874922909696000000⟩, + ⟨3, 4, 8, 7, 8, 0, -9876447119639147727181998703810402617340723200000000⟩ +] + +def collectedFourData_11_7_10 : List CollectedFourTerm := [ + ⟨3, 5, 3, 2, 8, 1, -3648267504035923614297364182114305467100430336000000⟩, + ⟨3, 5, 3, 3, 7, 1, -9109320554819472708830108956651102233728699596800000⟩, + ⟨3, 5, 4, 3, 8, 1, -5291791431589286193033203267112965392824690278400000⟩, + ⟨3, 5, 3, 4, 6, 1, -20924223643495217452778573804785661303669863219200000⟩, + ⟨3, 5, 4, 4, 7, 1, -12058858180908330609781044650798793782555207270400000⟩, + ⟨3, 5, 5, 4, 8, 1, 26197820312155123766259551733006122032312614912000000⟩, + ⟨3, 5, 3, 5, 5, 1, -6876787454574209648570582131867407822583391846400000⟩, + ⟨3, 5, 4, 5, 6, 1, 11061334864486223755068065471470436649782162227200000⟩, + ⟨3, 5, 5, 5, 7, 1, -891208949105473602120391296209225209293570048000000⟩, + ⟨3, 5, 6, 5, 8, 1, 12300375149055349889634239800932413934107885568000000⟩, + ⟨3, 5, 3, 6, 4, 1, 32444749286373232413328524126991934538083047833600000⟩, + ⟨3, 5, 4, 6, 5, 1, -17947941102928632102107621248730308326266083737600000⟩, + ⟨3, 5, 5, 6, 6, 1, 8476987474347172304117876191567711806142021632000000⟩, + ⟨3, 5, 6, 6, 7, 1, 11616434255204445271233293326567027933207068672000000⟩, + ⟨3, 5, 7, 6, 8, 1, 3185955159610296413099624405665281723919761408000000⟩, + ⟨3, 5, 3, 7, 3, 1, -57823279081513907875754749540391118617443093708800000⟩, + ⟨3, 5, 4, 7, 4, 1, -74225745034897666617081847426161813491931099955200000⟩, + ⟨3, 5, 5, 7, 5, 1, -9586628134495771935575992920587392350538432512000000⟩, + ⟨3, 5, 6, 7, 6, 1, -12572697343921366085547275157579160580134010880000000⟩, + ⟨3, 5, 7, 7, 7, 1, -1126020544867137235638039589101043093491154944000000⟩, + ⟨3, 5, 8, 7, 8, 1, -6042773044504162367849112418818942130024611840000000⟩ +] + +def collectedFourData_11_7_11 : List CollectedFourTerm := [ + ⟨3, 6, 2, 1, 8, 2, 1933856391927163546379775480091075435472879616000000⟩, + ⟨3, 6, 2, 2, 7, 2, 2350685932524745397202101700247999041201242112000000⟩, + ⟨3, 6, 3, 2, 8, 2, 988832159368219682913679846601111843131883520000000⟩, + ⟨3, 6, 2, 3, 6, 2, 933816773301922135175808137027068914806292480000000⟩, + ⟨3, 6, 3, 3, 7, 2, 2469004563024705386995168024259274348246859776000000⟩, + ⟨3, 6, 4, 3, 8, 2, 717147734155454538363120756627565945232031744000000⟩, + ⟨3, 6, 2, 4, 5, 2, 433682467855840599463944447150180269291470848000000⟩, + ⟨3, 6, 3, 4, 6, 2, 5671334469199931328063427147846538517591097344000000⟩, + ⟨3, 6, 4, 4, 7, 2, 1634225938935602166992376301756211483287486464000000⟩, + ⟨3, 6, 5, 4, 8, 2, -2366899466788101632079715192741456873028321280000000⟩, + ⟨3, 6, 2, 5, 4, 2, -2299485628101929523283619344392622694052397056000000⟩, + ⟨3, 6, 3, 5, 5, 2, 1863895281993537936932421367401363539648053248000000⟩, + ⟨3, 6, 4, 5, 6, 2, -1499040795041051401916340089378880844518653952000000⟩, + ⟨3, 6, 5, 5, 7, 2, 80518224848493249851666915604537548073861120000000⟩, + ⟨3, 6, 6, 5, 8, 2, -833478254145575290691680114196567733766717440000000⟩, + ⟨3, 6, 2, 6, 3, 2, -1160279642706347936329410595250503651814277120000000⟩, + ⟨3, 6, 3, 6, 4, 2, -8793875849704972779133936516473600507591524352000000⟩, + ⟨3, 6, 4, 6, 5, 2, 2432319085345199826796671848878237644610338816000000⟩, + ⟨3, 6, 5, 6, 6, 2, -765872003622090250605284493198487812392878080000000⟩, + ⟨3, 6, 6, 6, 7, 2, -787134150389569509450809325424299988494581760000000⟩, + ⟨3, 6, 7, 6, 8, 2, -172705258956074039788659152534864643030515712000000⟩, + ⟨3, 6, 2, 7, 2, 2, 5611800989654001795176783835184318863787425792000000⟩, + ⟨3, 6, 3, 7, 3, 2, 15672512460413481431222213551665402515728367616000000⟩, + ⟨3, 6, 4, 7, 4, 2, 10059131308542616344728388658587797983101714432000000⟩, + ⟨3, 6, 5, 7, 5, 2, 866124919915799271815443922388993220836065280000000⟩, + ⟨3, 6, 6, 7, 6, 2, 851930913092278199333883595738508385740390400000000⟩, + ⟨3, 6, 7, 7, 7, 2, 61039675716881685110888375928194072592777216000000⟩, + ⟨3, 6, 8, 7, 8, 2, 272973784203000185821509205321821763456204800000000⟩ +] + +def collectedFourData_11_7_12 : List CollectedFourTerm := [ + ⟨3, 7, 1, 0, 8, 3, -886685493624617133267533114222785770950964019200000⟩, + ⟨3, 7, 1, 1, 7, 3, -9298400073171475878189999374139682363465216819200000⟩, + ⟨3, 7, 2, 1, 8, 3, 5113101833692273170611443642198094893662024499200000⟩, + ⟨3, 7, 1, 2, 6, 3, -11026173780991327526304164271833103646981934284800000⟩, + ⟨3, 7, 2, 2, 7, 3, 6215196020863373214026753809496929043506161254400000⟩, + ⟨3, 7, 3, 2, 8, 3, 1307232416115716027613788232117043043040755712000000⟩, + ⟨3, 7, 1, 3, 5, 3, -9109320554819472708830108956651102233728699596800000⟩, + ⟨3, 7, 2, 3, 6, 3, 2469004563024705386995168024259274348246859776000000⟩, + ⟨3, 7, 3, 3, 7, 3, 3264014797400656542764216181377422539227765145600000⟩, + ⟨3, 7, 4, 3, 8, 3, 632044414784484001106283942779339098719623577600000⟩, + ⟨3, 7, 1, 4, 4, 3, 10259959027868980542625529110134266417410316697600000⟩, + ⟨3, 7, 2, 4, 5, 3, 1146653200770560132994859077676075455587391897600000⟩, + ⟨3, 7, 3, 4, 6, 3, 7497482955559748655501080737617485185780442726400000⟩, + ⟨3, 7, 4, 4, 7, 3, 1440293719140826795731549973873260748965779865600000⟩, + ⟨3, 7, 5, 4, 8, 3, -1564516121041851552791316495389902160825155584000000⟩, + ⟨3, 7, 1, 5, 3, 3, 19593907081854207951945121384176109676696017305600000⟩, + ⟨3, 7, 2, 5, 4, 3, -6079822798982602579001191887732764388713771827200000⟩, + ⟨3, 7, 3, 5, 5, 3, 2464062591192263302589376169433421880679517388800000⟩, + ⟨3, 7, 4, 5, 6, 3, -1321150882747417367420575761331554725669948620800000⟩, + ⟨3, 7, 5, 5, 7, 3, 53222396042061394214950571150255318825435136000000⟩, + ⟨3, 7, 6, 5, 8, 3, -440742053795159567578361698542048740581677465600000⟩, + ⟨3, 7, 1, 6, 2, 3, -48826420829206170980037627592528006821731264102400000⟩, + ⟨3, 7, 2, 6, 3, 3, -3067770695633478413439452977060720195607199744000000⟩, + ⟨3, 7, 3, 6, 4, 3, -11625470981219118699305456044383808293837157171200000⟩, + ⟨3, 7, 4, 6, 5, 3, 2143677822083021145052111511187734903354975846400000⟩, + ⟨3, 7, 5, 6, 6, 3, -506239962083127607177462113071441666453274624000000⟩, + ⟨3, 7, 6, 6, 7, 3, -416235361066076814942472701486657467750704742400000⟩, + ⟨3, 7, 7, 6, 8, 3, -76105235454479433862094708612498901363484262400000⟩, + ⟨3, 7, 1, 7, 1, 3, 139720443111684943425504223067793606639954060902400000⟩, + ⟨3, 7, 2, 7, 2, 3, 14837559836551040609805618403326278887056762470400000⟩, + ⟨3, 7, 3, 7, 3, 3, 20719002852131992517907913190903759613176945049600000⟩, + ⟨3, 7, 4, 7, 4, 3, 8865422643544082555469072527206377736270302412800000⟩, + ⟨3, 7, 5, 7, 5, 3, 572506952263242824488181507222375199915638784000000⟩, + ⟨3, 7, 6, 7, 6, 3, 450499792238484305159802060997838331231338496000000⟩, + ⟨3, 7, 7, 7, 7, 3, 26898074329513469640517990525588872535159603200000⟩, + ⟨3, 7, 8, 7, 8, 3, 103105806200411135374697978038483882271047680000000⟩ +] + +def collectedFourData_11_7_13 : List CollectedFourTerm := [ + ⟨3, 8, 0, 0, 7, 4, -4476483206440535204315781715193462300604786278400000⟩, + ⟨3, 8, 1, 0, 8, 4, -515093817309435334386908631177323214599199129600000⟩, + ⟨3, 8, 0, 1, 6, 4, -563193259828491877985625398441568853757735731200000⟩, + ⟨3, 8, 1, 1, 7, 4, -5401631607822275143143838433782955716598405529600000⟩, + ⟨3, 8, 2, 1, 8, 4, 1485152943600218921326713809803941339751828684800000⟩, + ⟨3, 8, 0, 2, 5, 4, 2723855208351876016987154416341265835072107315200000⟩, + ⟨3, 8, 1, 2, 6, 4, -6405330846173157498115982145397379010230904422400000⟩, + ⟨3, 8, 2, 2, 7, 4, 1805267519730203681924285867332085453279566233600000⟩, + ⟨3, 8, 3, 2, 8, 4, 253132721116688469513315537498341294160740352000000⟩, + ⟨3, 8, 0, 3, 4, 4, -1729805102966253799139903774622796415423112806400000⟩, + ⟨3, 8, 1, 3, 5, 4, -5291791431589286193033203267112965392824690278400000⟩, + ⟨3, 8, 2, 3, 6, 4, 717147734155454538363120756627565945232031744000000⟩, + ⟨3, 8, 3, 3, 7, 4, 632044414784484001106283942779339098719623577600000⟩, + ⟨3, 8, 4, 3, 8, 4, 91791895960090103699923244349897497428308787200000⟩, + ⟨3, 8, 0, 4, 3, 4, -6638555413813750696631950510155079471166442700800000⟩, + ⟨3, 8, 1, 4, 4, 4, 5960220956700123082502298819382068841806613708800000⟩, + ⟨3, 8, 2, 4, 5, 4, 333057199289784540700503817018059930126935654400000⟩, + ⟨3, 8, 3, 4, 6, 4, 1451813953410127891907040474099603285375084134400000⟩, + ⟨3, 8, 4, 4, 7, 4, 209174051897011643323312764955971264009417523200000⟩, + ⟨3, 8, 5, 4, 8, 4, -181771910519327432789571202524532219585128038400000⟩, + ⟨3, 8, 0, 5, 2, 4, 11203944414787150753843167240948791198195751321600000⟩, + ⟨3, 8, 1, 5, 3, 4, 11382503116794486830605906927642887148591172812800000⟩, + ⟨3, 8, 2, 5, 4, 4, -1765946977034168643623564546186508301088115916800000⟩, + ⟨3, 8, 3, 5, 5, 4, 477141525118914289980236782125729049440210124800000⟩, + ⟨3, 8, 4, 5, 6, 4, -191870921631485957938140462085428528679590297600000⟩, + ⟨3, 8, 5, 5, 7, 4, 6183596628291308700691205323598411924609433600000⟩, + ⟨3, 8, 6, 5, 8, 4, -42672685443049327803557864416930213070163148800000⟩, + ⟨3, 8, 0, 6, 1, 4, -8143747560413963318052736286426101082524483584000000⟩, + ⟨3, 8, 1, 6, 2, 4, -28364270839328959233776484769741635898207056691200000⟩, + ⟨3, 8, 2, 6, 3, 4, -891065507220789003392253264576609022573019136000000⟩, + ⟨3, 8, 3, 6, 4, 4, -2251158300130922345277990805051913856137507635200000⟩, + ⟨3, 8, 4, 6, 5, 4, 311326620430137157871290373976227934771137740800000⟩, + ⟨3, 8, 5, 6, 6, 4, -58817038604756185454673029755601098021168742400000⟩, + ⟨3, 8, 6, 6, 7, 4, -40299945240310141241555854665835720207446835200000⟩, + ⟨3, 8, 7, 6, 8, 4, -6315870658495494160180971139570335703734681600000⟩, + ⟨3, 8, 0, 7, 0, 4, 79428327127344751806209713599442316935784772403200000⟩, + ⟨3, 8, 1, 7, 1, 4, 81166475504596561160060332979186485059178935091200000⟩, + ⟨3, 8, 2, 7, 2, 4, 4309721649174644243987161702952662377868925337600000⟩, + ⟨3, 8, 3, 7, 3, 4, 4012031453724556588245127512079094427304958361600000⟩, + ⟨3, 8, 4, 7, 4, 4, 1287526531210481411283134035036913317552167321600000⟩, + ⟨3, 8, 5, 7, 5, 4, 66516209771738894155711163373902571323680358400000⟩, + ⟨3, 8, 6, 7, 6, 4, 43617430560158275923210759569774647399415808000000⟩, + ⟨3, 8, 7, 7, 7, 4, 2232234844466351844369186662274464721194188800000⟩, + ⟨3, 8, 8, 7, 8, 4, 7487035099310626578768568839327166475796480000000⟩ +] + +def collectedFourData_11_7_14 : List CollectedFourTerm := [ + ⟨4, 3, 4, 3, 8, 0, -6638555413813750696631950510155079471166442700800000⟩, + ⟨4, 3, 4, 4, 7, 0, -15127844567607752667985299643142885046741683404800000⟩, + ⟨4, 3, 5, 4, 8, 0, 65730361489755488384419301787722162171163967488000000⟩, + ⟨4, 3, 4, 5, 6, 0, 13876450989790457247559232983088000230203221606400000⟩, + ⟨4, 3, 5, 5, 7, 0, -2236044284967802685265346700124776962354839552000000⟩, + ⟨4, 3, 6, 5, 8, 0, 46292483231814096013400919702572303573789442048000000⟩, + ⟨4, 3, 4, 6, 5, 0, -22515702501879087713226430912921832914787971891200000⟩, + ⟨4, 3, 5, 6, 6, 0, 21268771386085294540791539674471973854031904768000000⟩, + ⟨4, 3, 6, 6, 7, 0, 43718470490212756477262566220984183603532398592000000⟩, + ⟨4, 3, 7, 6, 8, 0, 15987130367038486295480472560972319369549840384000000⟩, + ⟨4, 3, 4, 7, 4, 0, -93116240108085793472235596371023267039241725542400000⟩, + ⟨4, 3, 5, 7, 5, 0, -24052861086916528045073712729147583947381669888000000⟩, + ⟨4, 3, 6, 7, 6, 0, -47317368285052006666307552593770543727698247680000000⟩, + ⟨4, 3, 7, 7, 7, 0, -5650373701102749650211482876649402937966067712000000⟩, + ⟨4, 3, 8, 7, 8, 0, -37903311409415342229413338338055177330124390400000000⟩ +] + +def collectedFourData_11_7_15 : List CollectedFourTerm := [ + ⟨4, 4, 3, 2, 8, 1, 4109096270007836046875589104855198481097162752000000⟩, + ⟨4, 4, 3, 3, 7, 1, 10259959027868980542625529110134266417410316697600000⟩, + ⟨4, 4, 4, 3, 8, 1, 5960220956700123082502298819382068841806613708800000⟩, + ⟨4, 4, 3, 4, 6, 1, 23567254657499849284350419972670464099021645414400000⟩, + ⟨4, 4, 4, 4, 7, 1, 13582065765985558992773654764100847459308981452800000⟩, + ⟨4, 4, 5, 4, 8, 1, -29506982590482801563684415571715289501803741184000000⟩, + ⟨4, 4, 3, 5, 5, 1, 7745424820950663074006273254986199626127559884800000⟩, + ⟨4, 4, 4, 5, 6, 1, -12458540878015730838697430536343424866441389670400000⟩, + ⟨4, 4, 5, 5, 7, 1, 1003781483818201262934029081513579539423297536000000⟩, + ⟨4, 4, 6, 5, 8, 1, -13854089808043508421577382308716035309542834176000000⟩, + ⟨4, 4, 3, 6, 4, 1, -36542988727249561215677635547752792126951469875200000⟩, + ⟨4, 4, 4, 6, 5, 1, 20215024736749175726868764580321376064622506803200000⟩, + ⟨4, 4, 5, 6, 6, 1, -9547753165909328196283567357465777799612596224000000⟩, + ⟨4, 4, 6, 6, 7, 1, -13083757322084193643930770792693663514968981504000000⟩, + ⟨4, 4, 7, 6, 8, 1, -3588387213460754247485224829671133555831341056000000⟩, + ⟨4, 4, 3, 7, 3, 1, 65127192600493948478707876980887885958413392281600000⟩, + ⟨4, 4, 4, 7, 4, 1, 83601526402337899714569566823002169793405412966400000⟩, + ⟨4, 4, 5, 7, 5, 1, 10797557433995900529248646063838635398617104384000000⟩, + ⟨4, 4, 6, 7, 6, 1, 14160810220931651649152602981119270569807708160000000⟩, + ⟨4, 4, 7, 7, 7, 1, 1268253168318159756483899309892795936389726208000000⟩, + ⟨4, 4, 8, 7, 8, 1, 6806062370757407782054882862631140629288058880000000⟩ +] + +def collectedFourData_11_7_16 : List CollectedFourTerm := [ + ⟨4, 5, 2, 1, 8, 2, 898120098618748677189689250341685760582326681600000⟩, + ⟨4, 5, 2, 2, 7, 2, 1091703753367610641378733174288871485301011251200000⟩, + ⟨4, 5, 3, 2, 8, 2, 459232671152049303477406838894534662136266752000000⟩, + ⟨4, 5, 2, 3, 6, 2, 433682467855840599463944447150180269291470848000000⟩, + ⟨4, 5, 3, 3, 7, 2, 1146653200770560132994859077676075455587391897600000⟩, + ⟨4, 5, 4, 3, 8, 2, 333057199289784540700503817018059930126935654400000⟩, + ⟨4, 5, 2, 4, 5, 2, 201410478268119449548092894309419695823703244800000⟩, + ⟨4, 5, 3, 4, 6, 2, 2633876793561614812806109085463288947130394214400000⟩, + ⟨4, 5, 4, 4, 7, 2, 758965954022836541816596731461124871575463526400000⟩, + ⟨4, 5, 5, 4, 8, 2, -1099233630483797463125191870150033436445769728000000⟩, + ⟨4, 5, 2, 5, 4, 2, -1067925347354895049041379428057815191341603225600000⟩, + ⟨4, 5, 3, 5, 5, 2, 865628813735671640493797708498930360463969484800000⟩, + ⟨4, 5, 4, 5, 6, 2, -696183373437640469886418296264409327489725235200000⟩, + ⟨4, 5, 5, 5, 7, 2, 37394212074594936942567354326898616421056512000000⟩, + ⟨4, 5, 6, 5, 8, 2, -387083329938389929095394885512898576901996544000000⟩, + ⟨4, 5, 2, 6, 3, 2, -538856179539933522127830167064706503369818112000000⟩, + ⟨4, 5, 3, 6, 4, 2, -4084045060609407356396086530873311353042580275200000⟩, + ⟨4, 5, 4, 6, 5, 2, 1129615759433688421835748058711247801948936601600000⟩, + ⟨4, 5, 5, 6, 6, 2, -355685687051945904794250438868183346376081408000000⟩, + ⟨4, 5, 6, 6, 7, 2, -365560236905477121680146415575037271789797376000000⟩, + ⟨4, 5, 7, 6, 8, 2, -80207643573281311751163788197846035538850611200000⟩, + ⟨4, 5, 2, 7, 2, 2, 2606228300765505830863667860597934066844775219200000⟩, + ⟨4, 5, 3, 7, 3, 2, 7278616186449625472982893527799555676712835481600000⟩, + ⟨4, 5, 4, 7, 4, 2, 4671654027962332650541202879765489154201432883200000⟩, + ⟨4, 5, 5, 7, 5, 2, 402245069353749379425527597893072900879024128000000⟩, + ⟨4, 5, 6, 7, 6, 2, 395653099618379250159912842524121250178007040000000⟩, + ⟨4, 5, 7, 7, 7, 2, 28347999263725569145417109579819994811308441600000⟩, + ⟨4, 5, 8, 7, 8, 2, 126774274973136337864337420694686867631636480000000⟩ +] + +def collectedFourData_11_7_17 : List CollectedFourTerm := [ + ⟨4, 6, 1, 0, 8, 3, -2036727707449979693264236063520984010771451084800000⟩, + ⟨4, 6, 1, 1, 7, 3, -21358541670245136656500946932884130467282734284800000⟩, + ⟨4, 6, 2, 1, 8, 3, 11744859085405506527886307799271793064195968204800000⟩, + ⟨4, 6, 1, 2, 6, 3, -25327259562014398192297877714922948259795383091200000⟩, + ⟨4, 6, 2, 2, 7, 3, 14276383265478801170397833263348599664414398873600000⟩, + ⟨4, 6, 3, 2, 8, 3, 3002729266603783317710396318823832323492937728000000⟩, + ⟨4, 6, 1, 3, 5, 3, -20924223643495217452778573804785661303669863219200000⟩, + ⟨4, 6, 2, 3, 6, 3, 5671334469199931328063427147846538517591097344000000⟩, + ⟨4, 6, 3, 3, 7, 3, 7497482955559748655501080737617485185780442726400000⟩, + ⟨4, 6, 4, 3, 8, 3, 1451813953410127891907040474099603285375084134400000⟩, + ⟨4, 6, 1, 4, 4, 3, 23567254657499849284350419972670464099021645414400000⟩, + ⟨4, 6, 2, 4, 5, 3, 2633876793561614812806109085463288947130394214400000⟩, + ⟨4, 6, 3, 4, 6, 3, 17221812448177119031945360303359377953596742041600000⟩, + ⟨4, 6, 4, 4, 7, 3, 3308372749675554681733245931872456046832674406400000⟩, + ⟨4, 6, 5, 4, 8, 3, -3593713165930200273294986715719860294564970496000000⟩, + ⟨4, 6, 1, 5, 3, 3, 45007450485829046794462524018454293153459889766400000⟩, + ⟨4, 6, 2, 5, 4, 3, -13965429275779195005641986585245648946910252236800000⟩, + ⟨4, 6, 3, 5, 5, 3, 5659982697875212439390871424917929745162908467200000⟩, + ⟨4, 6, 4, 5, 6, 3, -3034700159144408817074935717366328001282913075200000⟩, + ⟨4, 6, 5, 5, 7, 3, 122252511691179279337926239818546416067805184000000⟩, + ⟨4, 6, 6, 5, 8, 3, -1012390029223873644841433611900320495882888806400000⟩, + ⟨4, 6, 1, 6, 2, 3, -112154901454334663497228866368398012782493669785600000⟩, + ⟨4, 6, 2, 6, 3, 3, -7046707790784064963619705453730390652313665536000000⟩, + ⟨4, 6, 3, 6, 4, 3, -26703852752584729166941139644972141539400404172800000⟩, + ⟨4, 6, 4, 6, 5, 3, 4924054862152648388015207734838324300980263321600000⟩, + ⟨4, 6, 5, 6, 6, 3, -1162839546611149567501539368973835646854496256000000⟩, + ⟨4, 6, 6, 6, 7, 3, -956097848447070589054536369793711150124865945600000⟩, + ⟨4, 6, 7, 6, 8, 3, -174814681018978355838577967808547325797308825600000⟩, + ⟨4, 6, 1, 7, 1, 3, 320939611428032015655654478865389044574417688985600000⟩, + ⟨4, 6, 2, 7, 2, 3, 34082061167501538238678210980063576818615687577600000⟩, + ⟨4, 6, 3, 7, 3, 3, 47591809590986196564227357716544756183699187302400000⟩, + ⟨4, 6, 4, 7, 4, 3, 20363987080186708937726693308905874407694742323200000⟩, + ⟨4, 6, 5, 7, 5, 3, 1315055654757264905329101243991184646441271296000000⟩, + ⟨4, 6, 6, 7, 6, 3, 1034803676895415484341943723947623568348545024000000⟩, + ⟨4, 6, 7, 7, 7, 3, 61785214326695897833617208454004559022181580800000⟩, + ⟨4, 6, 8, 7, 8, 3, 236835330900596867905675268446346993907793920000000⟩ +] + +def collectedFourData_11_7_18 : List CollectedFourTerm := [ + ⟨4, 7, 0, 0, 7, 4, -10200945527339497103013676689450706696499783270400000⟩, + ⟨4, 7, 1, 0, 8, 4, -1173788380191639504628464329616092994740001177600000⟩, + ⟨4, 7, 0, 1, 6, 4, -1283396697793804716344802868478938778118075187200000⟩, + ⟨4, 7, 1, 1, 7, 4, -12309160394229272045568280371977207909352839577600000⟩, + ⟨4, 7, 2, 1, 8, 4, 3384345160870199948806405543701880307553455308800000⟩, + ⟨4, 7, 0, 2, 5, 4, 6207082060484563668904217682855811459214160691200000⟩, + ⟨4, 7, 1, 2, 6, 4, -14596375778287588627275376874412360414689388134400000⟩, + ⟨4, 7, 2, 2, 7, 4, 4113817651442967814730871824316831473159739801600000⟩, + ⟨4, 7, 3, 2, 8, 4, 576835203041403591407338458753006462264410112000000⟩, + ⟨4, 7, 0, 3, 4, 4, -3941854981804687475404272905785909680703694438400000⟩, + ⟨4, 7, 1, 3, 5, 4, -12058858180908330609781044650798793782555207270400000⟩, + ⟨4, 7, 2, 3, 6, 4, 1634225938935602166992376301756211483287486464000000⟩, + ⟨4, 7, 3, 3, 7, 4, 1440293719140826795731549973873260748965779865600000⟩, + ⟨4, 7, 4, 3, 8, 4, 209174051897011643323312764955971264009417523200000⟩, + ⟨4, 7, 0, 4, 3, 4, -15127844567607752667985299643142885046741683404800000⟩, + ⟨4, 7, 1, 4, 4, 4, 13582065765985558992773654764100847459308981452800000⟩, + ⟨4, 7, 2, 4, 5, 4, 758965954022836541816596731461124871575463526400000⟩, + ⟨4, 7, 3, 4, 6, 4, 3308372749675554681733245931872456046832674406400000⟩, + ⟨4, 7, 4, 4, 7, 4, 476662820060251113884231393379273393097093939200000⟩, + ⟨4, 7, 5, 4, 8, 4, -414219214525432604357515006831534662641673830400000⟩, + ⟨4, 7, 0, 5, 2, 4, 25531387340434456635411306790204996400981842329600000⟩, + ⟨4, 7, 1, 5, 3, 4, 25938284341631433444069568059786387776881872076800000⟩, + ⟨4, 7, 2, 5, 4, 4, -4024214564454818608952393304697255165785066700800000⟩, + ⟨4, 7, 3, 5, 5, 4, 1087303242770333690104462598800898494812703948800000⟩, + ⟨4, 7, 4, 5, 6, 4, -437232695752594643394698900912711693674060185600000⟩, + ⟨4, 7, 5, 5, 7, 4, 14091091032685133817005086300249281298799001600000⟩, + ⟨4, 7, 6, 5, 8, 4, -97241901652518078445180760889858323731238092800000⟩, + ⟨4, 7, 0, 6, 1, 4, -18557854775968832649893636371697683200164757504000000⟩, + ⟨4, 7, 1, 6, 2, 4, -64636092309786361348529452539900266271166640947200000⟩, + ⟨4, 7, 2, 6, 3, 4, -2030547258028935938930725972280301575592738816000000⟩, + ⟨4, 7, 3, 6, 4, 4, -5129907146756268393951001323484628565697442611200000⟩, + ⟨4, 7, 4, 6, 5, 4, 709446623556928123333366007176138262561213644800000⟩, + ⟨4, 7, 5, 6, 6, 4, -134031421367404675472106163799749062897854054400000⟩, + ⟨4, 7, 6, 6, 7, 4, -91834935415305982947314129707658396849877811200000⟩, + ⟨4, 7, 7, 6, 8, 4, -14392515189678110427567225337686360503982489600000⟩, + ⟨4, 7, 0, 7, 0, 4, 181000129116536880719373322028824624322135143219200000⟩, + ⟨4, 7, 1, 7, 1, 4, 184960996631748183835210990251687922818463511347200000⟩, + ⟨4, 7, 2, 7, 2, 4, 9820931689852925655909755828540476060761430425600000⟩, + ⟨4, 7, 3, 7, 3, 4, 9142559555352272829004875566058111731236444569600000⟩, + ⟨4, 7, 4, 7, 4, 4, 2933996935582375741379220701452674659264338329600000⟩, + ⟨4, 7, 5, 7, 5, 4, 151576181854176039017189172186299968331867750400000⟩, + ⟨4, 7, 6, 7, 6, 4, 99394773233267607119164114741834594645966848000000⟩, + ⟨4, 7, 7, 7, 7, 4, 5086784648241010757730368873338147252784332800000⟩, + ⟨4, 7, 8, 7, 8, 4, 17061347867777623321167481742735654655098880000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1123.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1123.lean new file mode 100644 index 0000000000000000000000000000000000000000..8221b819e76776b252143ea2a0f59f21f026769d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1123.lean @@ -0,0 +1,609 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1123. -/ +namespace LaughlinFock +def collectedFourData_11_7_19 : List CollectedFourTerm := [ + ⟨4, 8, 0, 0, 7, 5, 44323025269908706618428424722394328280883789824000000⟩, + ⟨4, 8, 1, 0, 8, 5, 2550050478032896596813626444420563313023254528000000⟩, + ⟨4, 8, 0, 1, 6, 5, 5576348203720688293701717420807367322901676032000000⟩, + ⟨4, 8, 1, 1, 7, 5, 26741600851733773312526974013499536078461206528000000⟩, + ⟨4, 8, 2, 1, 8, 5, -4901650723955510526093163570631235530523672576000000⟩, + ⟨4, 8, 0, 2, 5, 5, -26969721020655948874294180151424075337429942272000000⟩, + ⟨4, 8, 1, 2, 6, 5, 31710566963435999549602652429710979701860728832000000⟩, + ⟨4, 8, 2, 2, 7, 5, -5958168068245020168910946406626609590626680832000000⟩, + ⟨4, 8, 3, 2, 8, 5, -626586065293037281065027662227149210444103680000000⟩, + ⟨4, 8, 0, 3, 4, 5, 17127327805112982810817918194424685784050171904000000⟩, + ⟨4, 8, 1, 3, 5, 5, 26197820312155123766259551733006122032312614912000000⟩, + ⟨4, 8, 2, 3, 6, 5, -2366899466788101632079715192741456873028321280000000⟩, + ⟨4, 8, 3, 3, 7, 5, -1564516121041851552791316495389902160825155584000000⟩, + ⟨4, 8, 4, 3, 8, 5, -181771910519327432789571202524532219585128038400000⟩, + ⟨4, 8, 0, 4, 3, 5, 65730361489755488384419301787722162171163967488000000⟩, + ⟨4, 8, 1, 4, 4, 5, -29506982590482801563684415571715289501803741184000000⟩, + ⟨4, 8, 2, 4, 5, 5, -1099233630483797463125191870150033436445769728000000⟩, + ⟨4, 8, 3, 4, 6, 5, -3593713165930200273294986715719860294564970496000000⟩, + ⟨4, 8, 4, 4, 7, 5, -414219214525432604357515006831534662641673830400000⟩, + ⟨4, 8, 5, 4, 8, 5, 299963185822455199683720471500900235586043904000000⟩, + ⟨4, 8, 0, 5, 2, 5, -110933670141952323347963403005353177421684146176000000⟩, + ⟨4, 8, 1, 5, 3, 5, -56350817149792700070776976288115444616899067904000000⟩, + ⟨4, 8, 2, 5, 4, 5, 5828393173744844532814430931368106010047676416000000⟩, + ⟨4, 8, 3, 5, 5, 5, -1181080934512456375070679802211996322634924032000000⟩, + ⟨4, 8, 4, 5, 6, 5, 379954500702581593828626582137360823161664307200000⟩, + ⟨4, 8, 5, 5, 7, 5, -10204279303462735750685561010995976172732416000000⟩, + ⟨4, 8, 6, 5, 8, 5, 60359324432751019847577101790784798089805824000000⟩, + ⟨4, 8, 0, 6, 1, 5, 80633727921208576013796900080721795301496586240000000⟩, + ⟨4, 8, 1, 6, 2, 5, 140421647440264153363365676943936067294845730816000000⟩, + ⟨4, 8, 2, 6, 3, 5, 2940903768451394115488435535891251310436024320000000⟩, + ⟨4, 8, 3, 6, 4, 5, 5572351197459643282716443700247606202223034368000000⟩, + ⟨4, 8, 4, 6, 5, 5, -616507960743247705404267849914425499144788377600000⟩, + ⟨4, 8, 5, 6, 6, 5, 97060905780869055865150241060845568491782144000000⟩, + ⟨4, 8, 6, 6, 7, 5, 57003149535277027774098990110833456233578496000000⟩, + ⟨4, 8, 7, 6, 8, 5, 7816920166125317260735147783645012502249472000000⟩, + ⟨4, 8, 0, 7, 0, 5, -786444087480716074191215658065993733775086845952000000⟩, + ⟨4, 8, 1, 7, 1, 5, -401827012294349432829304228188226572093348642816000000⟩, + ⟨4, 8, 2, 7, 2, 5, -14223956079913410060718063545100846460999565312000000⟩, + ⟨4, 8, 3, 7, 3, 5, -9931086709498654607002495102577094453199110144000000⟩, + ⟨4, 8, 4, 7, 4, 5, -2549638559859439843982513931129504933499581235200000⟩, + ⟨4, 8, 5, 7, 5, 5, -109766212694584761878950451339807840066863104000000⟩, + ⟨4, 8, 6, 7, 6, 5, -61695640074426311875735573617459765014691840000000⟩, + ⟨4, 8, 7, 7, 7, 5, -2762754735606510572595312277785583231696896000000⟩, + ⟨4, 8, 8, 7, 8, 5, -8236824176472388462720117635189465887539200000000⟩ +] + +def collectedFourData_11_7_20 : List CollectedFourTerm := [ + ⟨5, 2, 4, 3, 8, 0, 11203944414787150753843167240948791198195751321600000⟩, + ⟨5, 2, 4, 4, 7, 0, 25531387340434456635411306790204996400981842329600000⟩, + ⟨5, 2, 5, 4, 8, 0, -110933670141952323347963403005353177421684146176000000⟩, + ⟨5, 2, 4, 5, 6, 0, -23419400136454486531351059597441181405741370572800000⟩, + ⟨5, 2, 5, 5, 7, 0, 3773790277573271879933596202260107873069563904000000⟩, + ⟨5, 2, 6, 5, 8, 0, -78128203595690087084673684707713551408662839296000000⟩, + ⟨5, 2, 4, 6, 5, 0, 37999935764039212861463183372796117352272258662400000⟩, + ⟨5, 2, 5, 6, 6, 0, -35895479893813026270538199637917724606763892736000000⟩, + ⟨5, 2, 6, 6, 7, 0, -73784021182171953796254386908311692525105577984000000⟩, + ⟨5, 2, 7, 6, 8, 0, -26981611031149585916790333100361418976020922368000000⟩, + ⟨5, 2, 4, 7, 4, 0, 157153042078114487998058814266769799685797104844800000⟩, + ⟨5, 2, 5, 7, 5, 0, 40594210914267782011028843652722808105757310976000000⟩, + ⟨5, 2, 6, 7, 6, 0, 79857910505137582346907052917327744168477327360000000⟩, + ⟨5, 2, 7, 7, 7, 0, 9536182034151573440868723536781264901556404224000000⟩, + ⟨5, 2, 8, 7, 8, 0, 63969729511302295545518526341111223818177740800000000⟩ +] + +def collectedFourData_11_7_21 : List CollectedFourTerm := [ + ⟨5, 3, 3, 2, 8, 1, 7847326708248079159938165846052720511299878912000000⟩, + ⟨5, 3, 3, 3, 7, 1, 19593907081854207951945121384176109676696017305600000⟩, + ⟨5, 3, 4, 3, 8, 1, 11382503116794486830605906927642887148591172812800000⟩, + ⟨5, 3, 3, 4, 6, 1, 45007450485829046794462524018454293153459889766400000⟩, + ⟨5, 3, 4, 4, 7, 1, 25938284341631433444069568059786387776881872076800000⟩, + ⟨5, 3, 5, 4, 8, 1, -56350817149792700070776976288115444616899067904000000⟩, + ⟨5, 3, 3, 5, 5, 1, 14791787553825752939407022868314463693553061068800000⟩, + ⟨5, 3, 4, 5, 6, 1, -23792638126160738205842158122632471950836262502400000⟩, + ⟨5, 3, 5, 5, 7, 1, 1916966829106789559952756138466222865085628416000000⟩, + ⟨5, 3, 6, 5, 8, 1, -26457780938999514706500752402802807952958816256000000⟩, + ⟨5, 3, 3, 6, 4, 1, -69787795806012377172870189165602201993164829491200000⟩, + ⟨5, 3, 4, 6, 5, 1, 38605545623851954013260037212864151008857764659200000⟩, + ⟨5, 3, 5, 6, 6, 1, -18233775384984480815557420082863846416810246144000000⟩, + ⟨5, 3, 6, 6, 7, 1, -24986642203355304214469082684741001153634893824000000⟩, + ⟨5, 3, 7, 6, 8, 1, -6852905108420051281957407827259086227202113536000000⟩, + ⟨5, 3, 3, 7, 3, 1, 124376340768014718789328718815591681259512371609600000⟩, + ⟨5, 3, 4, 7, 4, 1, 159657610306151835666727801692304489180245157478400000⟩, + ⟨5, 3, 5, 7, 5, 1, 20620583035275793747228910133023493136375087104000000⟩, + ⟨5, 3, 6, 7, 6, 1, 27043538762584751535931904241219004068224040960000000⟩, + ⟨5, 3, 7, 7, 7, 1, 2422040348191784384099904909342175170656206848000000⟩, + ⟨5, 3, 8, 7, 8, 1, 12997844662311840844832550823530097733303009280000000⟩ +] + +def collectedFourData_11_7_22 : List CollectedFourTerm := [ + ⟨5, 4, 2, 1, 8, 2, -4762042305500330606248098751350229072017044275200000⟩, + ⟨5, 4, 2, 2, 7, 2, -5788468008460549970444656674681991464596432486400000⟩, + ⟨5, 4, 3, 2, 8, 2, -2434958767159614899498870035202173645979910144000000⟩, + ⟨5, 4, 2, 3, 6, 2, -2299485628101929523283619344392622694052397056000000⟩, + ⟨5, 4, 3, 3, 7, 2, -6079822798982602579001191887732764388713771827200000⟩, + ⟨5, 4, 4, 3, 8, 2, -1765946977034168643623564546186508301088115916800000⟩, + ⟨5, 4, 2, 4, 5, 2, -1067925347354895049041379428057815191341603225600000⟩, + ⟨5, 4, 3, 4, 6, 2, -13965429275779195005641986585245648946910252236800000⟩, + ⟨5, 4, 4, 4, 7, 2, -4024214564454818608952393304697255165785066700800000⟩, + ⟨5, 4, 5, 4, 8, 2, 5828393173744844532814430931368106010047676416000000⟩, + ⟨5, 4, 2, 5, 4, 2, 5662389351982355802450620855280570978012443443200000⟩, + ⟨5, 4, 3, 5, 5, 2, -4589765932428139949588562342989643987797252505600000⟩, + ⟨5, 4, 4, 5, 6, 2, 3691326674232799040997014043750913807330207334400000⟩, + ⟨5, 4, 5, 5, 7, 2, -198272836955700014484898921133370647840292864000000⟩, + ⟨5, 4, 6, 5, 8, 2, 2052406126703370964003417455222652585711239168000000⟩, + ⟨5, 4, 2, 6, 3, 2, 2857141185790046510014030118666798449834328064000000⟩, + ⟨5, 4, 3, 6, 4, 2, 21654559770015222886631865294438797097549850214400000⟩, + ⟨5, 4, 4, 6, 5, 2, -5989486309966890100011563809790086926224798515200000⟩, + ⟨5, 4, 5, 6, 6, 2, 1885928498657650352257718587447008903221477376000000⟩, + ⟨5, 4, 6, 6, 7, 2, 1938285665836746059377665996475498884677763072000000⟩, + ⟨5, 4, 7, 6, 8, 2, 425279639669433272919049320423395994135586406400000⟩, + ⟨5, 4, 2, 7, 2, 2, -13818830516235920304291456256511620992312174182400000⟩, + ⟨5, 4, 3, 7, 3, 2, -38592921212518372741985001146120693369311277875200000⟩, + ⟨5, 4, 4, 7, 4, 2, -24770199611423375893609038369586263963793253990400000⟩, + ⟨5, 4, 5, 7, 5, 2, -2132797206506566368323411617373152153190793216000000⟩, + ⟨5, 4, 6, 7, 6, 2, -2097845044980854947375688198031084188734586880000000⟩, + ⟨5, 4, 7, 7, 7, 2, -150307706038163605994361173889724697443250995200000⟩, + ⟨5, 4, 8, 7, 8, 2, -672186783927523628267779738630682086798786560000000⟩ +] + +def collectedFourData_11_7_23 : List CollectedFourTerm := [ + ⟨5, 5, 1, 0, 8, 3, -669374586393787064852509065953679405745805721600000⟩, + ⟨5, 5, 1, 1, 7, 3, -7019526932441421206577885413946270948945140121600000⟩, + ⟨5, 5, 2, 1, 8, 3, 3859971150679551552926740010508517699005028761600000⟩, + ⟨5, 5, 1, 2, 6, 3, -8323853911251334044885484309938508634721248870400000⟩, + ⟨5, 5, 2, 2, 7, 3, 4691961575705008198914053277061823373006549811200000⟩, + ⟨5, 5, 3, 2, 8, 3, 986852907992262737914163530010879824207282176000000⟩, + ⟨5, 5, 1, 3, 5, 3, -6876787454574209648570582131867407822583391846400000⟩, + ⟨5, 5, 2, 3, 6, 3, 1863895281993537936932421367401363539648053248000000⟩, + ⟨5, 5, 3, 3, 7, 3, 2464062591192263302589376169433421880679517388800000⟩, + ⟨5, 5, 4, 3, 8, 3, 477141525118914289980236782125729049440210124800000⟩, + ⟨5, 5, 1, 4, 4, 3, 7745424820950663074006273254986199626127559884800000⟩, + ⟨5, 5, 2, 4, 5, 3, 865628813735671640493797708498930360463969484800000⟩, + ⟨5, 5, 3, 4, 6, 3, 5659982697875212439390871424917929745162908467200000⟩, + ⟨5, 5, 4, 4, 7, 3, 1087303242770333690104462598800898494812703948800000⟩, + ⟨5, 5, 5, 4, 8, 3, -1181080934512456375070679802211996322634924032000000⟩, + ⟨5, 5, 1, 5, 3, 3, 14791787553825752939407022868314463693553061068800000⟩, + ⟨5, 5, 2, 5, 4, 3, -4589765932428139949588562342989643987797252505600000⟩, + ⟨5, 5, 3, 5, 5, 3, 1860164499912297372650228063386924213896373862400000⟩, + ⟨5, 5, 4, 5, 6, 3, -997360205012253312168367523400789303983760998400000⟩, + ⟨5, 5, 5, 5, 7, 3, 40178529584271632481985322758350761285910528000000⟩, + ⟨5, 5, 6, 5, 8, 3, -332723983968076585005405948371991577534188748800000⟩, + ⟨5, 5, 1, 6, 2, 3, -36859930023255186526917590344596455183535518515200000⟩, + ⟨5, 5, 2, 6, 3, 3, -2315914442387386841698481515528414144298483712000000⟩, + ⟨5, 5, 3, 6, 4, 3, -8776273983998416846997202998410300127023045017600000⟩, + ⟨5, 5, 4, 6, 5, 3, 1618300362231750645234689347447814094834578227200000⟩, + ⟨5, 5, 5, 6, 6, 3, -382169515202263900590808063214869030687997952000000⟩, + ⟨5, 5, 6, 6, 7, 3, -314223447501248832075658825880225193546429235200000⟩, + ⟨5, 5, 7, 6, 8, 3, -57453190416478036459166896199521190391526195200000⟩, + ⟨5, 5, 1, 7, 1, 3, 105477437593261435333773537170475442332840964915200000⟩, + ⟨5, 5, 2, 7, 2, 3, 11201136761677003866635339636120707279659152179200000⟩, + ⟨5, 5, 3, 7, 3, 3, 15641142281401711819821989868295070965742488780800000⟩, + ⟨5, 5, 4, 7, 4, 3, 6692664600804607522680486228297996265098471014400000⟩, + ⟨5, 5, 5, 7, 5, 3, 432195639980791880783726803600299967886917632000000⟩, + ⟨5, 5, 6, 7, 6, 3, 340090273573130652544326789636937018987511808000000⟩, + ⟨5, 5, 7, 7, 7, 3, 20305832799301306478845932322884548174649753600000⟩, + ⟨5, 5, 8, 7, 8, 3, 77836399576213908799090935355637309783408640000000⟩ +] + +def collectedFourData_11_7_24 : List CollectedFourTerm := [ + ⟨5, 6, 0, 0, 7, 4, 9357110990071021481897870172996494113622930227200000⟩, + ⟨5, 6, 1, 0, 8, 4, 1076691187387743313268883389394445289365753036800000⟩, + ⟨5, 6, 0, 1, 6, 4, 1177232572545586200208651708641269991897405849600000⟩, + ⟨5, 6, 1, 1, 7, 4, 11290931776343797960662287720859553238799404236800000⟩, + ⟨5, 6, 2, 1, 8, 4, -3104388040706601095704738118579985865452709478400000⟩, + ⟨5, 6, 0, 2, 5, 4, -5693624733979017403591589991814305798738778521600000⟩, + ⟨5, 6, 1, 2, 6, 4, 13388945940763452407728329905917578254734275379200000⟩, + ⟨5, 6, 2, 2, 7, 4, -3773517685620325791281783557124537025727089868800000⟩, + ⟨5, 6, 3, 2, 8, 4, -529118698200350893406407711323165636025122816000000⟩, + ⟨5, 6, 0, 3, 4, 4, 3615779975753937850133137332903756109878342451200000⟩, + ⟨5, 6, 1, 3, 5, 4, 11061334864486223755068065471470436649782162227200000⟩, + ⟨5, 6, 2, 3, 6, 4, -1499040795041051401916340089378880844518653952000000⟩, + ⟨5, 6, 3, 3, 7, 4, -1321150882747417367420575761331554725669948620800000⟩, + ⟨5, 6, 4, 3, 8, 4, -191870921631485957938140462085428528679590297600000⟩, + ⟨5, 6, 0, 4, 3, 4, 13876450989790457247559232983088000230203221606400000⟩, + ⟨5, 6, 1, 4, 4, 4, -12458540878015730838697430536343424866441389670400000⟩, + ⟨5, 6, 2, 4, 5, 4, -696183373437640469886418296264409327489725235200000⟩, + ⟨5, 6, 3, 4, 6, 4, -3034700159144408817074935717366328001282913075200000⟩, + ⟨5, 6, 4, 4, 7, 4, -437232695752594643394698900912711693674060185600000⟩, + ⟨5, 6, 5, 4, 8, 4, 379954500702581593828626582137360823161664307200000⟩, + ⟨5, 6, 0, 5, 2, 4, -23419400136454486531351059597441181405741370572800000⟩, + ⟨5, 6, 1, 5, 3, 4, -23792638126160738205842158122632471950836262502400000⟩, + ⟨5, 6, 2, 5, 4, 4, 3691326674232799040997014043750913807330207334400000⟩, + ⟨5, 6, 3, 5, 5, 4, -997360205012253312168367523400789303983760998400000⟩, + ⟨5, 6, 4, 5, 6, 4, 401064278961208731085562871238528175461682380800000⟩, + ⟨5, 6, 5, 5, 7, 4, -12925458959726207460951654904880085607435468800000⟩, + ⟨5, 6, 6, 5, 8, 4, 89197934074792937254532471405677450373785190400000⟩, + ⟨5, 6, 0, 6, 1, 4, 17022726610093855848045707542135177851722268672000000⟩, + ⟨5, 6, 1, 6, 2, 4, 59289316670323049568141229354298187361507973529600000⟩, + ⟨5, 6, 2, 6, 3, 4, 1862577935843220670709456446358453824769753088000000⟩, + ⟨5, 6, 3, 6, 4, 4, 4705555030394922443849568026394179787933981081600000⟩, + ⟨5, 6, 4, 6, 5, 4, -650760341809673476282508318066344358624781926400000⟩, + ⟨5, 6, 5, 6, 6, 4, 122944180275303908479342091055862992128389939200000⟩, + ⟨5, 6, 6, 6, 7, 4, 84238238616605784221726034978130372813494681600000⟩, + ⟨5, 6, 7, 6, 8, 4, 13201948946317428558877373575852310861237452800000⟩, + ⟨5, 6, 0, 7, 0, 4, -166027579778904867036823969411075605633124899225600000⟩, + ⟨5, 6, 1, 7, 1, 4, -169660799548333944162766761429059079193923000729600000⟩, + ⟨5, 6, 2, 7, 2, 4, -9008532356296858463111513647376243132560362700800000⟩, + ⟨5, 6, 3, 7, 3, 4, -8386275984269204806624980838320291133399026892800000⟩, + ⟨5, 6, 4, 7, 4, 4, -2691293164657525641294999743289030834192698572800000⟩, + ⟨5, 6, 5, 7, 5, 4, -139037616979670740375240790398355076942082867200000⟩, + ⟨5, 6, 6, 7, 6, 4, -91172717517607468624074947067048464392126464000000⟩, + ⟨5, 6, 7, 7, 7, 4, -4665999677050958880260955571589188766033510400000⟩, + ⟨5, 6, 8, 7, 8, 4, -15650012561202617461704365222039224414371840000000⟩ +] + +def collectedFourData_11_7_25 : List CollectedFourTerm := [ + ⟨5, 7, 0, 0, 7, 5, -1507800126167106800679382852884306231973380096000000⟩, + ⟨5, 7, 1, 0, 8, 5, -86748736330524671409963075587025273159155712000000⟩, + ⟨5, 7, 0, 1, 6, 5, -189698660547660117290751811258257496791318528000000⟩, + ⟨5, 7, 1, 1, 7, 5, -909707514155827936734839589202566036389363712000000⟩, + ⟨5, 7, 2, 1, 8, 5, 166746505569077821490595853954620276294549504000000⟩, + ⟨5, 7, 0, 2, 5, 5, 917467806179839105752377959042901849552191488000000⟩, + ⟨5, 7, 1, 2, 6, 5, -1078743984128720803199295010051755524361289728000000⟩, + ⟨5, 7, 2, 2, 7, 5, 202687576272547436778144315325591878503497728000000⟩, + ⟨5, 7, 3, 2, 8, 5, 21315479765881481633385723185394768119070720000000⟩, + ⟨5, 7, 0, 3, 4, 5, -582644954133744388883521784521904700486844416000000⟩, + ⟨5, 7, 1, 3, 5, 5, -891208949105473602120391296209225209293570048000000⟩, + ⟨5, 7, 2, 3, 6, 5, 80518224848493249851666915604537548073861120000000⟩, + ⟨5, 7, 3, 3, 7, 5, 53222396042061394214950571150255318825435136000000⟩, + ⟨5, 7, 4, 3, 8, 5, 6183596628291308700691205323598411924609433600000⟩, + ⟨5, 7, 0, 4, 3, 5, -2236044284967802685265346700124776962354839552000000⟩, + ⟨5, 7, 1, 4, 4, 5, 1003781483818201262934029081513579539423297536000000⟩, + ⟨5, 7, 2, 4, 5, 5, 37394212074594936942567354326898616421056512000000⟩, + ⟨5, 7, 3, 4, 6, 5, 122252511691179279337926239818546416067805184000000⟩, + ⟨5, 7, 4, 4, 7, 5, 14091091032685133817005086300249281298799001600000⟩, + ⟨5, 7, 5, 4, 8, 5, -10204279303462735750685561010995976172732416000000⟩, + ⟨5, 7, 0, 5, 2, 5, 3773790277573271879933596202260107873069563904000000⟩, + ⟨5, 7, 1, 5, 3, 5, 1916966829106789559952756138466222865085628416000000⟩, + ⟨5, 7, 2, 5, 4, 5, -198272836955700014484898921133370647840292864000000⟩, + ⟨5, 7, 3, 5, 5, 5, 40178529584271632481985322758350761285910528000000⟩, + ⟨5, 7, 4, 5, 6, 5, -12925458959726207460951654904880085607435468800000⟩, + ⟨5, 7, 5, 5, 7, 5, 347133651809891465780803804971671815716864000000⟩, + ⟨5, 7, 6, 5, 8, 5, -2053329989116304183361081667864358704644096000000⟩, + ⟨5, 7, 0, 6, 1, 5, -2743033545037907880464029291376764540378152960000000⟩, + ⟨5, 7, 1, 6, 2, 5, -4776925231021338670962326241128554337836990464000000⟩, + ⟨5, 7, 2, 6, 3, 5, -100044955102079053872340061298106633059041280000000⟩, + ⟨5, 7, 3, 6, 4, 5, -189562688634461630044991647455891224707203072000000⟩, + ⟨5, 7, 4, 6, 5, 5, 20972638382217750630750911697200105652643430400000⟩, + ⟨5, 7, 5, 6, 6, 5, -3301860491044713976239006635972670705893376000000⟩, + ⟨5, 7, 6, 6, 7, 5, -1939158158492510097920746924183791215837184000000⟩, + ⟨5, 7, 7, 6, 8, 5, -265919420909290100468228858442144219660288000000⟩, + ⟨5, 7, 0, 7, 0, 5, 26753600123316702051288719829296217932282462208000000⟩, + ⟨5, 7, 1, 7, 1, 5, 13669527658485564105167556629826665824559038464000000⟩, + ⟨5, 7, 2, 7, 2, 5, 483876780551107907254076017774172276049051648000000⟩, + ⟨5, 7, 3, 7, 3, 5, 337840066249372050199879611869387089432805376000000⟩, + ⟨5, 7, 4, 7, 4, 5, 86734723517316943918136265508275308903320780800000⟩, + ⟨5, 7, 5, 7, 5, 5, 3734075197753785466203392543009508704649216000000⟩, + ⟨5, 7, 6, 7, 6, 5, 2098789361098410623689690595706937918095360000000⟩, + ⟨5, 7, 7, 7, 7, 5, 93984603116529292923482174714300841590784000000⟩, + ⟨5, 7, 8, 7, 8, 5, 280203899821184828998552060826995182796800000000⟩ +] + +def collectedFourData_11_7_26 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 7, 6, 31215755665824406271008635639093874214729416704000000⟩, + ⟨5, 8, 1, 0, 8, 6, 1197297223780073824554331655699875995259502592000000⟩, + ⟨5, 8, 0, 1, 6, 6, 3927302389105678544443120084998334407216463872000000⟩, + ⟨5, 8, 1, 1, 7, 6, 12555690459866522252718508566886471962923630592000000⟩, + ⟨5, 8, 2, 1, 8, 6, -1726063715489266363595094552791270812809166848000000⟩, + ⟨5, 8, 0, 2, 5, 6, -18994195830035194923711436891929365382181158912000000⟩, + ⟨5, 8, 1, 2, 6, 6, 14888714602662175225993834588094757944004968448000000⟩, + ⟨5, 8, 2, 2, 7, 6, -2098104963522457593505889753249897923095822336000000⟩, + ⟨5, 8, 3, 2, 8, 6, -176516448493210326676159357292953995011162112000000⟩, + ⟨5, 8, 0, 3, 4, 6, 12062409474920498894475829843776914132129808384000000⟩, + ⟨5, 8, 1, 3, 5, 6, 12300375149055349889634239800932413934107885568000000⟩, + ⟨5, 8, 2, 3, 6, 6, -833478254145575290691680114196567733766717440000000⟩, + ⟨5, 8, 3, 3, 7, 6, -440742053795159567578361698542048740581677465600000⟩, + ⟨5, 8, 4, 3, 8, 6, -42672685443049327803557864416930213070163148800000⟩, + ⟨5, 8, 0, 4, 3, 6, 46292483231814096013400919702572303573789442048000000⟩, + ⟨5, 8, 1, 4, 4, 6, -13854089808043508421577382308716035309542834176000000⟩, + ⟨5, 8, 2, 4, 5, 6, -387083329938389929095394885512898576901996544000000⟩, + ⟨5, 8, 3, 4, 6, 6, -1012390029223873644841433611900320495882888806400000⟩, + ⟨5, 8, 4, 4, 7, 6, -97241901652518078445180760889858323731238092800000⟩, + ⟨5, 8, 5, 4, 8, 6, 60359324432751019847577101790784798089805824000000⟩, + ⟨5, 8, 0, 5, 2, 6, -78128203595690087084673684707713551408662839296000000⟩, + ⟨5, 8, 1, 5, 3, 6, -26457780938999514706500752402802807952958816256000000⟩, + ⟨5, 8, 2, 5, 4, 6, 2052406126703370964003417455222652585711239168000000⟩, + ⟨5, 8, 3, 5, 5, 6, -332723983968076585005405948371991577534188748800000⟩, + ⟨5, 8, 4, 5, 6, 6, 89197934074792937254532471405677450373785190400000⟩, + ⟨5, 8, 5, 5, 7, 6, -2053329989116304183361081667864358704644096000000⟩, + ⟨5, 8, 6, 5, 8, 6, 10627444269503391381530141818942997372338176000000⟩, + ⟨5, 8, 0, 6, 1, 6, 56788604430434778736742513473858244650771415040000000⟩, + ⟨5, 8, 1, 6, 2, 6, 65930635525515149132981845558007171575210573824000000⟩, + ⟨5, 8, 2, 6, 3, 6, 1035607710818946564053597745580119822811791360000000⟩, + ⟨5, 8, 3, 6, 4, 6, 1569794953343648912951966208656335811925717811200000⟩, + ⟨5, 8, 4, 6, 5, 6, -144731109480940026822649893419549986414342963200000⟩, + ⟨5, 8, 5, 6, 6, 6, 19530832377649676127389573174886022999179264000000⟩, + ⟨5, 8, 6, 6, 7, 6, 10036523777652129699761352746302702306197504000000⟩, + ⟨5, 8, 7, 6, 8, 6, 1223397588143949803137663427329298201051136000000⟩, + ⟨5, 8, 0, 7, 0, 6, -553875696212846370853903315647968765928057864192000000⟩, + ⟨5, 8, 1, 7, 1, 6, -188665428549081340291882417114716490328728141824000000⟩, + ⟨5, 8, 2, 7, 2, 6, -5008813533013030773805530544531633302851813376000000⟩, + ⟨5, 8, 3, 7, 3, 6, -2797700511930462962015718388626765100455926169600000⟩, + ⟨5, 8, 4, 7, 4, 6, -598551910179668266244052699594866884509853286400000⟩, + ⟨5, 8, 5, 7, 5, 6, -22087425247271185741871513022435804026241024000000⟩, + ⟨5, 8, 6, 7, 6, 6, -10862728877835820276696049569936311488348160000000⟩, + ⟨5, 8, 7, 7, 7, 6, -432388640070971781749052414374940034203648000000⟩, + ⟨5, 8, 8, 7, 8, 6, -1160203706264958226637761925031700086128640000000⟩ +] + +def collectedFourData_11_7_27 : List CollectedFourTerm := [ + ⟨6, 1, 4, 3, 8, 0, -8143747560413963318052736286426101082524483584000000⟩, + ⟨6, 1, 4, 4, 7, 0, -18557854775968832649893636371697683200164757504000000⟩, + ⟨6, 1, 5, 4, 8, 0, 80633727921208576013796900080721795301496586240000000⟩, + ⟨6, 1, 4, 5, 6, 0, 17022726610093855848045707542135177851722268672000000⟩, + ⟨6, 1, 5, 5, 7, 0, -2743033545037907880464029291376764540378152960000000⟩, + ⟨6, 1, 6, 5, 8, 0, 56788604430434778736742513473858244650771415040000000⟩, + ⟨6, 1, 4, 6, 5, 0, -27620797883096309612243039885025759838209048576000000⟩, + ⟨6, 1, 5, 6, 6, 0, 26091143975091006739282988060593135039430000640000000⟩, + ⟨6, 1, 6, 6, 7, 0, 53630973187156815671337683875289057806421852160000000⟩, + ⟨6, 1, 7, 6, 8, 0, 19611970648565317315699275572076787265773240320000000⟩, + ⟨6, 1, 4, 7, 4, 0, -114228940777870802182968666894494099196925181952000000⟩, + ⟨6, 1, 5, 7, 5, 0, -29506483954318918856323725764650287948355338240000000⟩, + ⟨6, 1, 6, 7, 6, 0, -58045866685810920124417938902260647069116006400000000⟩, + ⟨6, 1, 7, 7, 7, 0, -6931510573525164104980138437794455269157109760000000⟩, + ⟨6, 1, 8, 7, 8, 0, -46497314638623731660471490876568507087060992000000000⟩ +] + +def collectedFourData_11_7_28 : List CollectedFourTerm := [ + ⟨6, 2, 3, 2, 8, 1, -19554899114328711004323479342688746132364853248000000⟩, + ⟨6, 2, 3, 3, 7, 1, -48826420829206170980037627592528006821731264102400000⟩, + ⟨6, 2, 4, 3, 8, 1, -28364270839328959233776484769741635898207056691200000⟩, + ⟨6, 2, 3, 4, 6, 1, -112154901454334663497228866368398012782493669785600000⟩, + ⟨6, 2, 4, 4, 7, 1, -64636092309786361348529452539900266271166640947200000⟩, + ⟨6, 2, 5, 4, 8, 1, 140421647440264153363365676943936067294845730816000000⟩, + ⟨6, 2, 3, 5, 5, 1, -36859930023255186526917590344596455183535518515200000⟩, + ⟨6, 2, 4, 5, 6, 1, 59289316670323049568141229354298187361507973529600000⟩, + ⟨6, 2, 5, 5, 7, 1, -4776925231021338670962326241128554337836990464000000⟩, + ⟨6, 2, 6, 5, 8, 1, 65930635525515149132981845558007171575210573824000000⟩, + ⟨6, 2, 3, 6, 4, 1, 173905504018783620058004873119578642156423531724800000⟩, + ⟨6, 2, 4, 6, 5, 1, -96201875873800250081838653858905189165287918796800000⟩, + ⟨6, 2, 5, 6, 6, 1, 45437083402164588703250330704447926191077195776000000⟩, + ⟨6, 2, 6, 6, 7, 1, 62264677597643161813394228046568268389203050496000000⟩, + ⟨6, 2, 7, 6, 8, 1, 17076881467719508851781865598816731227377106944000000⟩, + ⟨6, 2, 3, 7, 3, 1, -309935712676716095333577931946354439624052860518400000⟩, + ⟨6, 2, 4, 7, 4, 1, -397853763255463504539708995117873644778410318233600000⟩, + ⟨6, 2, 5, 7, 5, 1, -51384813698355422293031843893249150560937967616000000⟩, + ⟨6, 2, 6, 7, 6, 1, -67390296321031495258054897482728433824657571840000000⟩, + ⟨6, 2, 7, 7, 7, 1, -6035527310203922087702778304289846142059937792000000⟩, + ⟨6, 2, 8, 7, 8, 1, -32389570426330311884243277515849761425582981120000000⟩ +] + +def collectedFourData_11_7_29 : List CollectedFourTerm := [ + ⟨6, 3, 2, 1, 8, 2, -2402842043130837275196281413287456276379336704000000⟩, + ⟨6, 3, 2, 2, 7, 2, -2920758238535953497263991611930893898773168128000000⟩, + ⟨6, 3, 3, 2, 8, 2, -1228636984653253527768726293164656763475066880000000⟩, + ⟨6, 3, 2, 3, 6, 2, -1160279642706347936329410595250503651814277120000000⟩, + ⟨6, 3, 3, 3, 7, 2, -3067770695633478413439452977060720195607199744000000⟩, + ⟨6, 3, 4, 3, 8, 2, -891065507220789003392253264576609022573019136000000⟩, + ⟨6, 3, 2, 4, 5, 2, -538856179539933522127830167064706503369818112000000⟩, + ⟨6, 3, 3, 4, 6, 2, -7046707790784064963619705453730390652313665536000000⟩, + ⟨6, 3, 4, 4, 7, 2, -2030547258028935938930725972280301575592738816000000⟩, + ⟨6, 3, 5, 4, 8, 2, 2940903768451394115488435535891251310436024320000000⟩, + ⟨6, 3, 2, 5, 4, 2, 2857141185790046510014030118666798449834328064000000⟩, + ⟨6, 3, 3, 5, 5, 2, -2315914442387386841698481515528414144298483712000000⟩, + ⟨6, 3, 4, 5, 6, 2, 1862577935843220670709456446358453824769753088000000⟩, + ⟨6, 3, 5, 5, 7, 2, -100044955102079053872340061298106633059041280000000⟩, + ⟨6, 3, 6, 5, 8, 2, 1035607710818946564053597745580119822811791360000000⟩, + ⟨6, 3, 2, 6, 3, 2, 1441662741308996098769968451396801049950945280000000⟩, + ⟨6, 3, 3, 6, 4, 2, 10926506591674503452508140443874944395339890688000000⟩, + ⟨6, 3, 4, 6, 5, 2, -3022188506330988617985647823944614270419861504000000⟩, + ⟨6, 3, 5, 6, 6, 2, 951606053914950140728193107499936246157803520000000⟩, + ⟨6, 3, 6, 6, 7, 2, 978024551375976615592425524820405854341693440000000⟩, + ⟨6, 3, 7, 6, 8, 2, 214588559430675216433200960814998711359766528000000⟩, + ⟨6, 3, 2, 7, 2, 2, -6972736658168434307032608402454001972882178048000000⟩, + ⟨6, 3, 3, 7, 3, 2, -19473303197992481293799175219113383818065608704000000⟩, + ⟨6, 3, 4, 7, 4, 2, -12498603167452915434222920256998122443094622208000000⟩, + ⟨6, 3, 5, 7, 5, 2, -1076171623117812389909320891729005947199160320000000⟩, + ⟨6, 3, 6, 7, 6, 2, -1058535382651138181640170128088411246533017600000000⟩, + ⟨6, 3, 7, 7, 7, 2, -75842601200306630005210050837091948223791104000000⟩, + ⟨6, 3, 8, 7, 8, 2, -339173522963538357675741519744858116535091200000000⟩ +] + +def collectedFourData_11_7_30 : List CollectedFourTerm := [ + ⟨6, 4, 1, 0, 8, 3, 3158115730299373588269343707440258120331716198400000⟩, + ⟨6, 4, 1, 1, 7, 3, 33118195514464667137683822885413370546637661798400000⟩, + ⟨6, 4, 2, 1, 8, 3, -18211380977483747942299093343557501528706541158400000⟩, + ⟨6, 4, 1, 2, 6, 3, 39272022733130757792734493068590215087825459609600000⟩, + ⟨6, 4, 2, 2, 7, 3, -22136719796943512419829629721511491564909415628800000⟩, + ⟨6, 4, 3, 2, 8, 3, -4655981502095121486045861392745722552751489024000000⟩, + ⟨6, 4, 1, 3, 5, 3, 32444749286373232413328524126991934538083047833600000⟩, + ⟨6, 4, 2, 3, 6, 3, -8793875849704972779133936516473600507591524352000000⟩, + ⟨6, 4, 3, 3, 7, 3, -11625470981219118699305456044383808293837157171200000⟩, + ⟨6, 4, 4, 3, 8, 3, -2251158300130922345277990805051913856137507635200000⟩, + ⟨6, 4, 1, 4, 4, 3, -36542988727249561215677635547752792126951469875200000⟩, + ⟨6, 4, 2, 4, 5, 3, -4084045060609407356396086530873311353042580275200000⟩, + ⟨6, 4, 3, 4, 6, 3, -26703852752584729166941139644972141539400404172800000⟩, + ⟨6, 4, 4, 4, 7, 3, -5129907146756268393951001323484628565697442611200000⟩, + ⟨6, 4, 5, 4, 8, 3, 5572351197459643282716443700247606202223034368000000⟩, + ⟨6, 4, 1, 5, 3, 3, -69787795806012377172870189165602201993164829491200000⟩, + ⟨6, 4, 2, 5, 4, 3, 21654559770015222886631865294438797097549850214400000⟩, + ⟨6, 4, 3, 5, 5, 3, -8776273983998416846997202998410300127023045017600000⟩, + ⟨6, 4, 4, 5, 6, 3, 4705555030394922443849568026394179787933981081600000⟩, + ⟨6, 4, 5, 5, 7, 3, -189562688634461630044991647455891224707203072000000⟩, + ⟨6, 4, 6, 5, 8, 3, 1569794953343648912951966208656335811925717811200000⟩, + ⟨6, 4, 1, 6, 2, 3, 173905504018783620058004873119578642156423531724800000⟩, + ⟨6, 4, 2, 6, 3, 3, 10926506591674503452508140443874944395339890688000000⟩, + ⟨6, 4, 3, 6, 4, 3, 41406544983435016995271920735715120333740992102400000⟩, + ⟨6, 4, 4, 6, 5, 3, -7635156658467221930450346574392730149614046412800000⟩, + ⟨6, 4, 5, 6, 6, 3, 1803079444804505698539900281272132459925864448000000⟩, + ⟨6, 4, 6, 6, 7, 3, 1482509244530536102843152835462722485060685004800000⟩, + ⟨6, 4, 7, 6, 8, 3, 271064704424590645533170719008468642965540044800000⟩, + ⟨6, 4, 1, 7, 1, 3, -497643564046191382406662116364674860145877765324800000⟩, + ⟨6, 4, 2, 7, 2, 3, -52847070867844747652892915949930325143454534860800000⟩, + ⟨6, 4, 3, 7, 3, 3, -73795059571750513885129247915087838848786576179200000⟩, + ⟨6, 4, 4, 7, 4, 3, -31576055893141671083252980194525250461625850265600000⟩, + ⟨6, 4, 5, 7, 5, 3, -2039103182186201552459704645900731757539360768000000⟩, + ⟨6, 4, 6, 7, 6, 3, -1604549178479373211930691304282227549291937792000000⟩, + ⟨6, 4, 7, 7, 7, 3, -95803114255933809625907537065056522664830566400000⟩, + ⟨6, 4, 8, 7, 8, 3, -367232881092526394630010098237989293769359360000000⟩ +] + +def collectedFourData_11_7_31 : List CollectedFourTerm := [ + ⟨6, 5, 0, 0, 7, 4, -15182695307648243970376619465547846713677027737600000⟩, + ⟨6, 5, 1, 0, 8, 4, -1747021517205924529148972286120232535504348774400000⟩, + ⟨6, 5, 0, 1, 6, 4, -1910158324953552815285964291148520331460529356800000⟩, + ⟨6, 5, 1, 1, 7, 4, -18320481298295499392058078377275004559445878374400000⟩, + ⟨6, 5, 2, 1, 8, 4, 5037129279407820069348138899551961468451894067200000⟩, + ⟨6, 5, 0, 2, 5, 4, 9238382404977445422460435344527962581156809932800000⟩, + ⟨6, 5, 1, 2, 6, 4, -21724684779830997071127558042828610269645216153600000⟩, + ⟨6, 5, 2, 2, 7, 4, 6122848101255719754621737898651571194901718630400000⟩, + ⟨6, 5, 3, 2, 8, 4, 858539348831047703963914808914844962026160128000000⟩, + ⟨6, 5, 0, 3, 4, 4, -5866905472171931267290513219624501830598891929600000⟩, + ⟨6, 5, 1, 3, 5, 4, -17947941102928632102107621248730308326266083737600000⟩, + ⟨6, 5, 2, 3, 6, 4, 2432319085345199826796671848878237644610338816000000⟩, + ⟨6, 5, 3, 3, 7, 4, 2143677822083021145052111511187734903354975846400000⟩, + ⟨6, 5, 4, 3, 8, 4, 311326620430137157871290373976227934771137740800000⟩, + ⟨6, 5, 0, 4, 3, 4, -22515702501879087713226430912921832914787971891200000⟩, + ⟨6, 5, 1, 4, 4, 4, 20215024736749175726868764580321376064622506803200000⟩, + ⟨6, 5, 2, 4, 5, 4, 1129615759433688421835748058711247801948936601600000⟩, + ⟨6, 5, 3, 4, 6, 4, 4924054862152648388015207734838324300980263321600000⟩, + ⟨6, 5, 4, 4, 7, 4, 709446623556928123333366007176138262561213644800000⟩, + ⟨6, 5, 5, 4, 8, 4, -616507960743247705404267849914425499144788377600000⟩, + ⟨6, 5, 0, 5, 2, 4, 37999935764039212861463183372796117352272258662400000⟩, + ⟨6, 5, 1, 5, 3, 4, 38605545623851954013260037212864151008857764659200000⟩, + ⟨6, 5, 2, 5, 4, 4, -5989486309966890100011563809790086926224798515200000⟩, + ⟨6, 5, 3, 5, 5, 4, 1618300362231750645234689347447814094834578227200000⟩, + ⟨6, 5, 4, 5, 6, 4, -650760341809673476282508318066344358624781926400000⟩, + ⟨6, 5, 5, 5, 7, 4, 20972638382217750630750911697200105652643430400000⟩, + ⟨6, 5, 6, 5, 8, 4, -144731109480940026822649893419549986414342963200000⟩, + ⟨6, 5, 0, 6, 1, 4, -27620797883096309612243039885025759838209048576000000⟩, + ⟨6, 5, 1, 6, 2, 4, -96201875873800250081838653858905189165287918796800000⟩, + ⟨6, 5, 2, 6, 3, 4, -3022188506330988617985647823944614270419861504000000⟩, + ⟨6, 5, 3, 6, 4, 4, -7635156658467221930450346574392730149614046412800000⟩, + ⟨6, 5, 4, 6, 5, 4, 1055913090961669177637883853808664269198406451200000⟩, + ⟨6, 5, 5, 6, 6, 4, -199487216828914472998631738042323069056948633600000⟩, + ⟨6, 5, 6, 6, 7, 4, -136683588719426557919737087091453403283115212800000⟩, + ⟨6, 5, 7, 6, 8, 4, -21421266513965325019928450145258888099161702400000⟩, + ⟨6, 5, 0, 7, 0, 4, 269393636467941550471181829945348418281726069964800000⟩, + ⟨6, 5, 1, 7, 1, 4, 275288839464197449120631893686452419175474056396800000⟩, + ⟨6, 5, 2, 7, 2, 4, 14617097315600780723050842212417517592884176486400000⟩, + ⟨6, 5, 3, 7, 3, 4, 13607434299979463461945239957128963496757061222400000⟩, + ⟨6, 5, 4, 7, 4, 4, 4366848287458591676513641928708827740983682662400000⟩, + ⟨6, 5, 5, 7, 5, 4, 225600164104478395547158777225416130101352857600000⟩, + ⟨6, 5, 6, 7, 6, 4, 147935360808369676032968136992146096612442112000000⟩, + ⟨6, 5, 7, 7, 7, 4, 7570974788844747186086370682873409787081523200000⟩, + ⟨6, 5, 8, 7, 8, 4, 25393454510664469089641473182863117223198720000000⟩ +] + +def collectedFourData_11_7_32 : List CollectedFourTerm := [ + ⟨6, 6, 0, 0, 7, 5, 14341869879299160568481205883747832550616203264000000⟩, + ⟨6, 6, 1, 0, 8, 5, 825135286205786440311699519481827474127454208000000⟩, + ⟨6, 6, 0, 1, 6, 5, 1804372780341815462002102376321633203311869952000000⟩, + ⟨6, 6, 1, 1, 7, 5, 8652941838789591657127697309423174253394526208000000⟩, + ⟨6, 6, 2, 1, 8, 5, -1586056828220815561187680553933076548221403136000000⟩, + ⟨6, 6, 0, 2, 5, 5, -8726756064231164835512964879306192033354350592000000⟩, + ⟨6, 6, 1, 2, 6, 5, 10260780314947543941800553047807108204306890752000000⟩, + ⟨6, 6, 2, 2, 7, 5, -1927920547692825086008718296680357234581962752000000⟩, + ⟨6, 6, 3, 2, 8, 5, -202748250190307871703488467143719742058004480000000⟩, + ⟨6, 6, 0, 3, 4, 5, 5541993247645003063963466891914579023331590144000000⟩, + ⟨6, 6, 1, 3, 5, 5, 8476987474347172304117876191567711806142021632000000⟩, + ⟨6, 6, 2, 3, 6, 5, -765872003622090250605284493198487812392878080000000⟩, + ⟨6, 6, 3, 3, 7, 5, -506239962083127607177462113071441666453274624000000⟩, + ⟨6, 6, 4, 3, 8, 5, -58817038604756185454673029755601098021168742400000⟩, + ⟨6, 6, 0, 4, 3, 5, 21268771386085294540791539674471973854031904768000000⟩, + ⟨6, 6, 1, 4, 4, 5, -9547753165909328196283567357465777799612596224000000⟩, + ⟨6, 6, 2, 4, 5, 5, -355685687051945904794250438868183346376081408000000⟩, + ⟨6, 6, 3, 4, 6, 5, -1162839546611149567501539368973835646854496256000000⟩, + ⟨6, 6, 4, 4, 7, 5, -134031421367404675472106163799749062897854054400000⟩, + ⟨6, 6, 5, 4, 8, 5, 97060905780869055865150241060845568491782144000000⟩, + ⟨6, 6, 0, 5, 2, 5, -35895479893813026270538199637917724606763892736000000⟩, + ⟨6, 6, 1, 5, 3, 5, -18233775384984480815557420082863846416810246144000000⟩, + ⟨6, 6, 2, 5, 4, 5, 1885928498657650352257718587447008903221477376000000⟩, + ⟨6, 6, 3, 5, 5, 5, -382169515202263900590808063214869030687997952000000⟩, + ⟨6, 6, 4, 5, 6, 5, 122944180275303908479342091055862992128389939200000⟩, + ⟨6, 6, 5, 5, 7, 5, -3301860491044713976239006635972670705893376000000⟩, + ⟨6, 6, 6, 5, 8, 5, 19530832377649676127389573174886022999179264000000⟩, + ⟨6, 6, 0, 6, 1, 5, 26091143975091006739282988060593135039430000640000000⟩, + ⟨6, 6, 1, 6, 2, 5, 45437083402164588703250330704447926191077195776000000⟩, + ⟨6, 6, 2, 6, 3, 5, 951606053914950140728193107499936246157803520000000⟩, + ⟨6, 6, 3, 6, 4, 5, 1803079444804505698539900281272132459925864448000000⟩, + ⟨6, 6, 4, 6, 5, 5, -199487216828914472998631738042323069056948633600000⟩, + ⟨6, 6, 5, 6, 6, 5, 31406585462053386950513985211356342632054784000000⟩, + ⟨6, 6, 6, 6, 7, 5, 18444854528018986018023855449763415647584256000000⟩, + ⟨6, 6, 7, 6, 8, 5, 2529368227839601902257193049513287632289792000000⟩, + ⟨6, 6, 0, 7, 0, 5, -254474479151811465549110825998798695288193155072000000⟩, + ⟨6, 6, 1, 7, 1, 5, -130021601396094723786285788458862422260266827776000000⟩, + ⟨6, 6, 2, 7, 2, 5, -4602531664405146777661288319501062500916396032000000⟩, + ⟨6, 6, 3, 7, 3, 5, -3213461907898335456941766598952224911507062784000000⟩, + ⟨6, 6, 4, 7, 4, 5, -825001999346221687081560896487904172632650547200000⟩, + ⟨6, 6, 5, 7, 5, 5, -35517718612903087109868830945905662800953344000000⟩, + ⟨6, 6, 6, 7, 6, 5, -19963232127754068674861241929492683020042240000000⟩, + ⟨6, 6, 7, 7, 7, 5, -893961291793558630525309065163944971206656000000⟩, + ⟨6, 6, 8, 7, 8, 5, -2665239113040258866407298848000102839091200000000⟩ +] + +def collectedFourData_11_7_33 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 7, 6, 29480058048995621043721251282880775332892246016000000⟩, + ⟨6, 7, 1, 0, 8, 6, 1130723601145463444849453758506905450701651968000000⟩, + ⟨6, 7, 0, 1, 6, 6, 3708931593591038083100115882978939357351641088000000⟩, + ⟨6, 7, 1, 1, 7, 6, 11857553203727966159500202805790185449972563968000000⟩, + ⟨6, 7, 2, 1, 8, 6, -1630088954873448485552223195968666831570337792000000⟩, + ⟨6, 7, 0, 2, 5, 6, -17938056719109697800167316365835519196290613248000000⟩, + ⟨6, 7, 1, 2, 6, 6, 14060853610599845867172063626166558237961224192000000⟩, + ⟨6, 7, 2, 2, 7, 6, -1981443498586993934811303129335535886500102144000000⟩, + ⟨6, 7, 3, 2, 8, 6, -166701559426911802232372274658363755145986048000000⟩, + ⟨6, 7, 0, 3, 4, 6, 11391700247088018305845832923392426603221876736000000⟩, + ⟨6, 7, 1, 3, 5, 6, 11616434255204445271233293326567027933207068672000000⟩, + ⟨6, 7, 2, 3, 6, 6, -787134150389569509450809325424299988494581760000000⟩, + ⟨6, 7, 3, 3, 7, 6, -416235361066076814942472701486657467750704742400000⟩, + ⟨6, 7, 4, 3, 8, 6, -40299945240310141241555854665835720207446835200000⟩, + ⟨6, 7, 0, 4, 3, 6, 43718470490212756477262566220984183603532398592000000⟩, + ⟨6, 7, 1, 4, 4, 6, -13083757322084193643930770792693663514968981504000000⟩, + ⟨6, 7, 2, 4, 5, 6, -365560236905477121680146415575037271789797376000000⟩, + ⟨6, 7, 3, 4, 6, 6, -956097848447070589054536369793711150124865945600000⟩, + ⟨6, 7, 4, 4, 7, 6, -91834935415305982947314129707658396849877811200000⟩, + ⟨6, 7, 5, 4, 8, 6, 57003149535277027774098990110833456233578496000000⟩, + ⟨6, 7, 0, 5, 2, 6, -73784021182171953796254386908311692525105577984000000⟩, + ⟨6, 7, 1, 5, 3, 6, -24986642203355304214469082684741001153634893824000000⟩, + ⟨6, 7, 2, 5, 4, 6, 1938285665836746059377665996475498884677763072000000⟩, + ⟨6, 7, 3, 5, 5, 6, -314223447501248832075658825880225193546429235200000⟩, + ⟨6, 7, 4, 5, 6, 6, 84238238616605784221726034978130372813494681600000⟩, + ⟨6, 7, 5, 5, 7, 6, -1939158158492510097920746924183791215837184000000⟩, + ⟨6, 7, 6, 5, 8, 6, 10036523777652129699761352746302702306197504000000⟩, + ⟨6, 7, 0, 6, 1, 6, 53630973187156815671337683875289057806421852160000000⟩, + ⟨6, 7, 1, 6, 2, 6, 62264677597643161813394228046568268389203050496000000⟩, + ⟨6, 7, 2, 6, 3, 6, 978024551375976615592425524820405854341693440000000⟩, + ⟨6, 7, 3, 6, 4, 6, 1482509244530536102843152835462722485060685004800000⟩, + ⟨6, 7, 4, 6, 5, 6, -136683588719426557919737087091453403283115212800000⟩, + ⟨6, 7, 5, 6, 6, 6, 18444854528018986018023855449763415647584256000000⟩, + ⟨6, 7, 6, 6, 7, 6, 9478460388490342214973583049830990627209216000000⟩, + ⟨6, 7, 7, 6, 8, 6, 1155372700298600336978646200517323699257344000000⟩, + ⟨6, 7, 0, 7, 0, 6, -523078404735179617114727906296170034571790778368000000⟩, + ⟨6, 7, 1, 7, 1, 6, -178175016648877431514906298778249434412399722496000000⟩, + ⟨6, 7, 2, 7, 2, 6, -4730307197768082504374114964684732368425058304000000⟩, + ⟨6, 7, 3, 7, 3, 6, -2642139257442724412442353788400392591615878758400000⟩, + ⟨6, 7, 4, 7, 4, 6, -565270475792206677330599619139757502990227865600000⟩, + ⟨6, 7, 5, 7, 5, 6, -20859292512828216458606315779226773588279296000000⟩, + ⟨6, 7, 6, 7, 6, 6, -10258725795951148118873086890142149000560640000000⟩, + ⟨6, 7, 7, 7, 7, 6, -408346424333850219540663042750041127124992000000⟩, + ⟨6, 7, 8, 7, 8, 6, -1095692603937080988193134369609859265986560000000⟩ +] + +def collectedFourData_11_7_34 : List CollectedFourTerm := [ + ⟨6, 8, 0, 0, 7, 7, 10780375570610719472427380798189423591405125632000000⟩, + ⟨6, 8, 1, 0, 8, 7, 310115360016654483330347961779208605298327552000000⟩, + ⟨6, 8, 0, 1, 6, 7, 1356295685651723033607104110789973610621566976000000⟩, + ⟨6, 8, 1, 1, 7, 7, 3252085104587529952454336427479680351891095552000000⟩, + ⟨6, 8, 2, 1, 8, 7, -357658138620363891890997814935834402058823270400000⟩, + ⟨6, 8, 0, 2, 5, 7, -6559654262468727993314157447083930507381047296000000⟩, + ⟨6, 8, 1, 2, 6, 7, 3856368324827852114473551290011914589005938688000000⟩, + ⟨6, 8, 2, 2, 7, 7, -434748908252718033312081109137229657410424012800000⟩, + ⟨6, 8, 3, 2, 8, 7, -30480018320211856905284924056201692287336448000000⟩, + ⟨6, 8, 0, 3, 4, 7, 4165758657846732757091125402025125799968899072000000⟩, + ⟨6, 8, 1, 3, 5, 7, 3185955159610296413099624405665281723919761408000000⟩, + ⟨6, 8, 2, 3, 6, 7, -172705258956074039788659152534864643030515712000000⟩, + ⟨6, 8, 3, 3, 7, 7, -76105235454479433862094708612498901363484262400000⟩, + ⟨6, 8, 4, 3, 8, 7, -6315870658495494160180971139570335703734681600000⟩, + ⟨6, 8, 0, 4, 3, 7, 15987130367038486295480472560972319369549840384000000⟩, + ⟨6, 8, 1, 4, 4, 7, -3588387213460754247485224829671133555831341056000000⟩, + ⟨6, 8, 2, 4, 5, 7, -80207643573281311751163788197846035538850611200000⟩, + ⟨6, 8, 3, 4, 6, 7, -174814681018978355838577967808547325797308825600000⟩, + ⟨6, 8, 4, 4, 7, 7, -14392515189678110427567225337686360503982489600000⟩, + ⟨6, 8, 5, 4, 8, 7, 7816920166125317260735147783645012502249472000000⟩, + ⟨6, 8, 0, 5, 2, 7, -26981611031149585916790333100361418976020922368000000⟩, + ⟨6, 8, 1, 5, 3, 7, -6852905108420051281957407827259086227202113536000000⟩, + ⟨6, 8, 2, 5, 4, 7, 425279639669433272919049320423395994135586406400000⟩, + ⟨6, 8, 3, 5, 5, 7, -57453190416478036459166896199521190391526195200000⟩, + ⟨6, 8, 4, 5, 6, 7, 13201948946317428558877373575852310861237452800000⟩, + ⟨6, 8, 5, 5, 7, 7, -265919420909290100468228858442144219660288000000⟩, + ⟨6, 8, 6, 5, 8, 7, 1223397588143949803137663427329298201051136000000⟩, + ⟨6, 8, 0, 6, 1, 7, 19611970648565317315699275572076787265773240320000000⟩, + ⟨6, 8, 1, 6, 2, 7, 17076881467719508851781865598816731227377106944000000⟩, + ⟨6, 8, 2, 6, 3, 7, 214588559430675216433200960814998711359766528000000⟩, + ⟨6, 8, 3, 6, 4, 7, 271064704424590645533170719008468642965540044800000⟩, + ⟨6, 8, 4, 6, 5, 7, -21421266513965325019928450145258888099161702400000⟩, + ⟨6, 8, 5, 6, 6, 7, 2529368227839601902257193049513287632289792000000⟩, + ⟨6, 8, 6, 6, 7, 7, 1155372700298600336978646200517323699257344000000⟩, + ⟨6, 8, 7, 6, 8, 7, 126750275856467546031690387195127132481126400000⟩, + ⟨6, 8, 0, 7, 0, 7, -191281226331007026960099470176210513778008129536000000⟩, + ⟨6, 8, 1, 7, 1, 7, -48866769366151845718942861744215413772930514944000000⟩, + ⟨6, 8, 2, 7, 2, 7, -1037877633854397175378677120624167586989133004800000⟩, + ⟨6, 8, 3, 7, 3, 7, -483093579017859343612776445983544225613375078400000⟩, + ⟨6, 8, 4, 7, 4, 7, -88590076013272276147079983503143812742302924800000⟩, + ⟨6, 8, 5, 7, 5, 7, -2860463423932831653008941682091740545155072000000⟩, + ⟨6, 8, 6, 7, 6, 7, -1250482804030453636784264738548985112821760000000⟩, + ⟨6, 8, 7, 7, 7, 7, -44797684691650636518265865668210579419955200000⟩, + ⟨6, 8, 8, 7, 8, 7, -109275513643994450631655377407110293749760000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1124.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1124.lean new file mode 100644 index 0000000000000000000000000000000000000000..095e1a183afb87aad3c1214fd6dd291ef85447af --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1124.lean @@ -0,0 +1,426 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1102 +import OAI.Analysis.LaughlinFock.Sparse1111 +import OAI.Analysis.LaughlinFock.Sparse1118 +import OAI.Analysis.LaughlinFock.Sparse1122 +import OAI.Analysis.LaughlinFock.Sparse1123 + +namespace OAI + +/-! Sparse1124. -/ +namespace LaughlinFock +def collectedFourData_11_7_35 : List CollectedFourTerm := [ + ⟨7, 0, 4, 3, 8, 0, 79428327127344751806209713599442316935784772403200000⟩, + ⟨7, 0, 4, 4, 7, 0, 181000129116536880719373322028824624322135143219200000⟩, + ⟨7, 0, 5, 4, 8, 0, -786444087480716074191215658065993733775086845952000000⟩, + ⟨7, 0, 4, 5, 6, 0, -166027579778904867036823969411075605633124899225600000⟩, + ⟨7, 0, 5, 5, 7, 0, 26753600123316702051288719829296217932282462208000000⟩, + ⟨7, 0, 6, 5, 8, 0, -553875696212846370853903315647968765928057864192000000⟩, + ⟨7, 0, 4, 6, 5, 0, 269393636467941550471181829945348418281726069964800000⟩, + ⟨7, 0, 5, 6, 6, 0, -254474479151811465549110825998798695288193155072000000⟩, + ⟨7, 0, 6, 6, 7, 0, -523078404735179617114727906296170034571790778368000000⟩, + ⟨7, 0, 7, 6, 8, 0, -191281226331007026960099470176210513778008129536000000⟩, + ⟨7, 0, 4, 7, 4, 0, 1114107922453039880295335842380136138127598786969600000⟩, + ⟨7, 0, 5, 7, 5, 0, 287785278523817537912330451151716091216162455552000000⟩, + ⟨7, 0, 6, 7, 6, 0, 566138138898361442804780476010025674789848350720000000⟩, + ⟨7, 0, 7, 7, 7, 0, 67605028917745550649026257196902897599903694848000000⟩, + ⟨7, 0, 8, 7, 8, 0, 453501768106371470572801896922587896366078361600000000⟩ +] + +def collectedFourData_11_7_36 : List CollectedFourTerm := [ + ⟨7, 1, 3, 2, 8, 1, 55957801593025836319859056045784979144859189248000000⟩, + ⟨7, 1, 3, 3, 7, 1, 139720443111684943425504223067793606639954060902400000⟩, + ⟨7, 1, 4, 3, 8, 1, 81166475504596561160060332979186485059178935091200000⟩, + ⟨7, 1, 3, 4, 6, 1, 320939611428032015655654478865389044574417688985600000⟩, + ⟨7, 1, 4, 4, 7, 1, 184960996631748183835210990251687922818463511347200000⟩, + ⟨7, 1, 5, 4, 8, 1, -401827012294349432829304228188226572093348642816000000⟩, + ⟨7, 1, 3, 5, 5, 1, 105477437593261435333773537170475442332840964915200000⟩, + ⟨7, 1, 4, 5, 6, 1, -169660799548333944162766761429059079193923000729600000⟩, + ⟨7, 1, 5, 5, 7, 1, 13669527658485564105167556629826665824559038464000000⟩, + ⟨7, 1, 6, 5, 8, 1, -188665428549081340291882417114716490328728141824000000⟩, + ⟨7, 1, 3, 6, 4, 1, -497643564046191382406662116364674860145877765324800000⟩, + ⟨7, 1, 4, 6, 5, 1, 275288839464197449120631893686452419175474056396800000⟩, + ⟨7, 1, 5, 6, 6, 1, -130021601396094723786285788458862422260266827776000000⟩, + ⟨7, 1, 6, 6, 7, 1, -178175016648877431514906298778249434412399722496000000⟩, + ⟨7, 1, 7, 6, 8, 1, -48866769366151845718942861744215413772930514944000000⟩, + ⟨7, 1, 3, 7, 3, 1, 886904146892199950155717970302354583143357769318400000⟩, + ⟨7, 1, 4, 7, 4, 1, 1138488202732522981853898991418000891697235073433600000⟩, + ⟨7, 1, 5, 7, 5, 1, 147041475029664257597847047361440647607658479616000000⟩, + ⟨7, 1, 6, 7, 6, 1, 192842356730151420879819747282577572939788451840000000⟩, + ⟨7, 1, 7, 7, 7, 1, 17271111334254197677562182771895308087870881792000000⟩, + ⟨7, 1, 8, 7, 8, 1, 92685170350578276441324116728279755094354821120000000⟩ +] + +def collectedFourData_11_7_37 : List CollectedFourTerm := [ + ⟨7, 2, 2, 1, 8, 2, 11621570231269303040407902462696432301167240806400000⟩, + ⟨7, 2, 2, 2, 7, 2, 14126520340669654177330225849118132450785807564800000⟩, + ⟨7, 2, 3, 2, 8, 2, 5942417666072626229484653398145904610910404608000000⟩, + ⟨7, 2, 2, 3, 6, 2, 5611800989654001795176783835184318863787425792000000⟩, + ⟨7, 2, 3, 3, 7, 2, 14837559836551040609805618403326278887056762470400000⟩, + ⟨7, 2, 4, 3, 8, 2, 4309721649174644243987161702952662377868925337600000⟩, + ⟨7, 2, 2, 4, 5, 2, 2606228300765505830863667860597934066844775219200000⟩, + ⟨7, 2, 3, 4, 6, 2, 34082061167501538238678210980063576818615687577600000⟩, + ⟨7, 2, 4, 4, 7, 2, 9820931689852925655909755828540476060761430425600000⟩, + ⟨7, 2, 5, 4, 8, 2, -14223956079913410060718063545100846460999565312000000⟩, + ⟨7, 2, 2, 5, 4, 2, -13818830516235920304291456256511620992312174182400000⟩, + ⟨7, 2, 3, 5, 5, 2, 11201136761677003866635339636120707279659152179200000⟩, + ⟨7, 2, 4, 5, 6, 2, -9008532356296858463111513647376243132560362700800000⟩, + ⟨7, 2, 5, 5, 7, 2, 483876780551107907254076017774172276049051648000000⟩, + ⟨7, 2, 6, 5, 8, 2, -5008813533013030773805530544531633302851813376000000⟩, + ⟨7, 2, 2, 6, 3, 2, -6972736658168434307032608402454001972882178048000000⟩, + ⟨7, 2, 3, 6, 4, 2, -52847070867844747652892915949930325143454534860800000⟩, + ⟨7, 2, 4, 6, 5, 2, 14617097315600780723050842212417517592884176486400000⟩, + ⟨7, 2, 5, 6, 6, 2, -4602531664405146777661288319501062500916396032000000⟩, + ⟨7, 2, 6, 6, 7, 2, -4730307197768082504374114964684732368425058304000000⟩, + ⟨7, 2, 7, 6, 8, 2, -1037877633854397175378677120624167586989133004800000⟩, + ⟨7, 2, 2, 7, 2, 2, 33724292867568275573819586060518530997317061836800000⟩, + ⟨7, 2, 3, 7, 3, 2, 94184451864923483143824469497124449001014716006400000⟩, + ⟨7, 2, 4, 7, 4, 2, 60450662963287354928493381098536592253840575692800000⟩, + ⟨7, 2, 5, 7, 5, 2, 5205004687976373791026080771522066154795302912000000⟩, + ⟨7, 2, 6, 7, 6, 2, 5119705361795136463574479792970094092652380160000000⟩, + ⟨7, 2, 7, 7, 7, 2, 366819832744003362285094668707164075292255846400000⟩, + ⟨7, 2, 8, 7, 8, 2, 1640444459916236555423336466364454200588369920000000⟩ +] + +def collectedFourData_11_7_38 : List CollectedFourTerm := [ + ⟨7, 3, 1, 0, 8, 3, -5628417887683198392180142470224211828913943347200000⟩, + ⟨7, 3, 1, 1, 7, 3, -59023500074119297922380323555241558231909348147200000⟩, + ⟨7, 3, 2, 1, 8, 3, 32456461766005785339607132353641422623905887027200000⟩, + ⟨7, 3, 1, 2, 6, 3, -69990897773623052517694164608578692136573914316800000⟩, + ⟨7, 3, 2, 2, 7, 3, 39452230481729904432997209713509828728109557350400000⟩, + ⟨7, 3, 3, 2, 8, 3, 8297925664880586577573849058012215943513505792000000⟩, + ⟨7, 3, 1, 3, 5, 3, -57823279081513907875754749540391118617443093708800000⟩, + ⟨7, 3, 2, 3, 6, 3, 15672512460413481431222213551665402515728367616000000⟩, + ⟨7, 3, 3, 3, 7, 3, 20719002852131992517907913190903759613176945049600000⟩, + ⟨7, 3, 4, 3, 8, 3, 4012031453724556588245127512079094427304958361600000⟩, + ⟨7, 3, 1, 4, 4, 3, 65127192600493948478707876980887885958413392281600000⟩, + ⟨7, 3, 2, 4, 5, 3, 7278616186449625472982893527799555676712835481600000⟩, + ⟨7, 3, 3, 4, 6, 3, 47591809590986196564227357716544756183699187302400000⟩, + ⟨7, 3, 4, 4, 7, 3, 9142559555352272829004875566058111731236444569600000⟩, + ⟨7, 3, 5, 4, 8, 3, -9931086709498654607002495102577094453199110144000000⟩, + ⟨7, 3, 1, 5, 3, 3, 124376340768014718789328718815591681259512371609600000⟩, + ⟨7, 3, 2, 5, 4, 3, -38592921212518372741985001146120693369311277875200000⟩, + ⟨7, 3, 3, 5, 5, 3, 15641142281401711819821989868295070965742488780800000⟩, + ⟨7, 3, 4, 5, 6, 3, -8386275984269204806624980838320291133399026892800000⟩, + ⟨7, 3, 5, 5, 7, 3, 337840066249372050199879611869387089432805376000000⟩, + ⟨7, 3, 6, 5, 8, 3, -2797700511930462962015718388626765100455926169600000⟩, + ⟨7, 3, 1, 6, 2, 3, -309935712676716095333577931946354439624052860518400000⟩, + ⟨7, 3, 2, 6, 3, 3, -19473303197992481293799175219113383818065608704000000⟩, + ⟨7, 3, 3, 6, 4, 3, -73795059571750513885129247915087838848786576179200000⟩, + ⟨7, 3, 4, 6, 5, 3, 13607434299979463461945239957128963496757061222400000⟩, + ⟨7, 3, 5, 6, 6, 3, -3213461907898335456941766598952224911507062784000000⟩, + ⟨7, 3, 6, 6, 7, 3, -2642139257442724412442353788400392591615878758400000⟩, + ⟨7, 3, 7, 6, 8, 3, -483093579017859343612776445983544225613375078400000⟩, + ⟨7, 3, 1, 7, 1, 3, 886904146892199950155717970302354583143357769318400000⟩, + ⟨7, 3, 2, 7, 2, 3, 94184451864923483143824469497124449001014716006400000⟩, + ⟨7, 3, 3, 7, 3, 3, 131518116746441957581444399464829505292671228313600000⟩, + ⟨7, 3, 4, 7, 4, 3, 56275087105372094141316133338178313655214197964800000⟩, + ⟨7, 3, 5, 7, 5, 3, 3634105208791887269281944806365189433242681344000000⟩, + ⟨7, 3, 6, 7, 6, 3, 2859639756445715955585197915045007405808091136000000⟩, + ⟨7, 3, 7, 7, 7, 3, 170741039285073864603564000123747960305693491200000⟩, + ⟨7, 3, 8, 7, 8, 3, 654485235311714489357453443745512405472378880000000⟩ +] + +def collectedFourData_11_7_39 : List CollectedFourTerm := [ + ⟨7, 4, 0, 0, 7, 4, -62789757576380036488768176278326615203764187955200000⟩, + ⟨7, 4, 1, 0, 8, 4, -7225005529210682440863709389874549602604862668800000⟩, + ⟨7, 4, 0, 1, 6, 4, -7899676291067969402865966791573057548041427353600000⟩, + ⟨7, 4, 1, 1, 7, 4, -75766427244515568977695571273004958463462001868800000⟩, + ⟨7, 4, 2, 1, 8, 4, 20831619151019751964122321624289728916581934694400000⟩, + ⟨7, 4, 0, 2, 5, 4, 38206377711750355569035271908865976448094673305600000⟩, + ⟨7, 4, 1, 2, 6, 4, -89844896647679264446218869029930223315291681587200000⟩, + ⟨7, 4, 2, 2, 7, 4, 25321732417377740761816892992986339748946431180800000⟩, + ⟨7, 4, 3, 2, 8, 4, 3550586802313612029841026156944393103690694656000000⟩, + ⟨7, 4, 0, 3, 4, 4, -24263252660786898671140224822969615273740677939200000⟩, + ⟨7, 4, 1, 3, 5, 4, -74225745034897666617081847426161813491931099955200000⟩, + ⟨7, 4, 2, 3, 6, 4, 10059131308542616344728388658587797983101714432000000⟩, + ⟨7, 4, 3, 3, 7, 4, 8865422643544082555469072527206377736270302412800000⟩, + ⟨7, 4, 4, 3, 8, 4, 1287526531210481411283134035036913317552167321600000⟩, + ⟨7, 4, 0, 4, 3, 4, -93116240108085793472235596371023267039241725542400000⟩, + ⟨7, 4, 1, 4, 4, 4, 83601526402337899714569566823002169793405412966400000⟩, + ⟨7, 4, 2, 4, 5, 4, 4671654027962332650541202879765489154201432883200000⟩, + ⟨7, 4, 3, 4, 6, 4, 20363987080186708937726693308905874407694742323200000⟩, + ⟨7, 4, 4, 4, 7, 4, 2933996935582375741379220701452674659264338329600000⟩, + ⟨7, 4, 5, 4, 8, 4, -2549638559859439843982513931129504933499581235200000⟩, + ⟨7, 4, 0, 5, 2, 4, 157153042078114487998058814266769799685797104844800000⟩, + ⟨7, 4, 1, 5, 3, 4, 159657610306151835666727801692304489180245157478400000⟩, + ⟨7, 4, 2, 5, 4, 4, -24770199611423375893609038369586263963793253990400000⟩, + ⟨7, 4, 3, 5, 5, 4, 6692664600804607522680486228297996265098471014400000⟩, + ⟨7, 4, 4, 5, 6, 4, -2691293164657525641294999743289030834192698572800000⟩, + ⟨7, 4, 5, 5, 7, 4, 86734723517316943918136265508275308903320780800000⟩, + ⟨7, 4, 6, 5, 8, 4, -598551910179668266244052699594866884509853286400000⟩, + ⟨7, 4, 0, 6, 1, 4, -114228940777870802182968666894494099196925181952000000⟩, + ⟨7, 4, 1, 6, 2, 4, -397853763255463504539708995117873644778410318233600000⟩, + ⟨7, 4, 2, 6, 3, 4, -12498603167452915434222920256998122443094622208000000⟩, + ⟨7, 4, 3, 6, 4, 4, -31576055893141671083252980194525250461625850265600000⟩, + ⟨7, 4, 4, 6, 5, 4, 4366848287458591676513641928708827740983682662400000⟩, + ⟨7, 4, 5, 6, 6, 4, -825001999346221687081560896487904172632650547200000⟩, + ⟨7, 4, 6, 6, 7, 4, -565270475792206677330599619139757502990227865600000⟩, + ⟨7, 4, 7, 6, 8, 4, -88590076013272276147079983503143812742302924800000⟩, + ⟨7, 4, 0, 7, 0, 4, 1114107922453039880295335842380136138127598786969600000⟩, + ⟨7, 4, 1, 7, 1, 4, 1138488202732522981853898991418000891697235073433600000⟩, + ⟨7, 4, 2, 7, 2, 4, 60450662963287354928493381098536592253840575692800000⟩, + ⟨7, 4, 3, 7, 3, 4, 56275087105372094141316133338178313655214197964800000⟩, + ⟨7, 4, 4, 7, 4, 4, 18059596124821861967269165172290748404135152844800000⟩, + ⟨7, 4, 5, 7, 5, 4, 932995053004585957674708047073704002563814195200000⟩, + ⟨7, 4, 6, 7, 6, 4, 611803454782671038711344241399279461098061824000000⟩, + ⟨7, 4, 7, 7, 7, 4, 31310624495571311148139589882469598915618406400000⟩, + ⟨7, 4, 8, 7, 8, 4, 105017509766415230914257220844643581102653440000000⟩ +] + +def collectedFourData_11_7_40 : List CollectedFourTerm := [ + ⟨7, 5, 0, 0, 7, 5, -16219225721665369483761260206130291009623425024000000⟩, + ⟨7, 5, 1, 0, 8, 5, -933145787161234036670170154170057009479548928000000⟩, + ⟨7, 5, 0, 1, 6, 5, -2040565815803018572975156041080603279603269632000000⟩, + ⟨7, 5, 1, 1, 7, 5, -9785614987508778653175986382274915932127100928000000⟩, + ⟨7, 5, 2, 1, 8, 5, 1793672228293785109660334515046427822051557376000000⟩, + ⟨7, 5, 0, 2, 5, 5, 9869091521181337231503471896364751766654287872000000⟩, + ⟨7, 5, 1, 2, 6, 5, -11603920089162556279338646875545578617471762432000000⟩, + ⟨7, 5, 2, 2, 7, 5, 2180286029620196621337993160045897197847314432000000⟩, + ⟨7, 5, 3, 2, 8, 5, 229288067886861988135432953415540944855367680000000⟩, + ⟨7, 5, 0, 3, 4, 5, -6267442124910151543938912770869655842905391104000000⟩, + ⟨7, 5, 1, 3, 5, 5, -9586628134495771935575992920587392350538432512000000⟩, + ⟨7, 5, 2, 3, 6, 5, 866124919915799271815443922388993220836065280000000⟩, + ⟨7, 5, 3, 3, 7, 5, 572506952263242824488181507222375199915638784000000⟩, + ⟨7, 5, 4, 3, 8, 5, 66516209771738894155711163373902571323680358400000⟩, + ⟨7, 5, 0, 4, 3, 5, -24052861086916528045073712729147583947381669888000000⟩, + ⟨7, 5, 1, 4, 4, 5, 10797557433995900529248646063838635398617104384000000⟩, + ⟨7, 5, 2, 4, 5, 5, 402245069353749379425527597893072900879024128000000⟩, + ⟨7, 5, 3, 4, 6, 5, 1315055654757264905329101243991184646441271296000000⟩, + ⟨7, 5, 4, 4, 7, 5, 151576181854176039017189172186299968331867750400000⟩, + ⟨7, 5, 5, 4, 8, 5, -109766212694584761878950451339807840066863104000000⟩, + ⟨7, 5, 0, 5, 2, 5, 40594210914267782011028843652722808105757310976000000⟩, + ⟨7, 5, 1, 5, 3, 5, 20620583035275793747228910133023493136375087104000000⟩, + ⟨7, 5, 2, 5, 4, 5, -2132797206506566368323411617373152153190793216000000⟩, + ⟨7, 5, 3, 5, 5, 5, 432195639980791880783726803600299967886917632000000⟩, + ⟨7, 5, 4, 5, 6, 5, -139037616979670740375240790398355076942082867200000⟩, + ⟨7, 5, 5, 5, 7, 5, 3734075197753785466203392543009508704649216000000⟩, + ⟨7, 5, 6, 5, 8, 5, -22087425247271185741871513022435804026241024000000⟩, + ⟨7, 5, 0, 6, 1, 5, -29506483954318918856323725764650287948355338240000000⟩, + ⟨7, 5, 1, 6, 2, 5, -51384813698355422293031843893249150560937967616000000⟩, + ⟨7, 5, 2, 6, 3, 5, -1076171623117812389909320891729005947199160320000000⟩, + ⟨7, 5, 3, 6, 4, 5, -2039103182186201552459704645900731757539360768000000⟩, + ⟨7, 5, 4, 6, 5, 5, 225600164104478395547158777225416130101352857600000⟩, + ⟨7, 5, 5, 6, 6, 5, -35517718612903087109868830945905662800953344000000⟩, + ⟨7, 5, 6, 6, 7, 5, -20859292512828216458606315779226773588279296000000⟩, + ⟨7, 5, 7, 6, 8, 5, -2860463423932831653008941682091740545155072000000⟩, + ⟨7, 5, 0, 7, 0, 5, 287785278523817537912330451151716091216162455552000000⟩, + ⟨7, 5, 1, 7, 1, 5, 147041475029664257597847047361440647607658479616000000⟩, + ⟨7, 5, 2, 7, 2, 5, 5205004687976373791026080771522066154795302912000000⟩, + ⟨7, 5, 3, 7, 3, 5, 3634105208791887269281944806365189433242681344000000⟩, + ⟨7, 5, 4, 7, 4, 5, 932995053004585957674708047073704002563814195200000⟩, + ⟨7, 5, 5, 7, 5, 5, 40167000548008124646325004283073250463842304000000⟩, + ⟨7, 5, 6, 7, 6, 5, 22576426277677797745222148322177209692323840000000⟩, + ⟨7, 5, 7, 7, 7, 5, 1010981141235944777227394506196857122717696000000⟩, + ⟨7, 5, 8, 7, 8, 5, 3014119856086964856338870813808718459699200000000⟩ +] + +def collectedFourData_11_7_41 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 7, 6, -31906851912427212304478530747215000627723632640000000⟩, + ⟨7, 6, 1, 0, 8, 6, -1223804594810283228815392578311874172126494720000000⟩, + ⟨7, 6, 0, 1, 6, 6, -4014250274315987994529684344313794910507499520000000⟩, + ⟨7, 6, 1, 1, 7, 6, -12833665167357597467138749721333119845106974720000000⟩, + ⟨7, 6, 2, 1, 8, 6, 1764277627974425542583449653155751274406215680000000⟩, + ⟨7, 6, 0, 2, 5, 6, 19414714800836452142941484784238478797748305920000000⟩, + ⟨7, 6, 1, 2, 6, 6, -15218340926265976149379430181155049901318471680000000⟩, + ⟨7, 6, 2, 2, 7, 6, 2144555623913055364886545668923150535764213760000000⟩, + ⟨7, 6, 3, 2, 8, 6, 180424406266946746922361566217314137716817920000000⟩, + ⟨7, 6, 0, 3, 4, 6, -12329463266677025328174938168690337281149501440000000⟩, + ⟨7, 6, 1, 3, 5, 6, -12572697343921366085547275157579160580134010880000000⟩, + ⟨7, 6, 2, 3, 6, 6, 851930913092278199333883595738508385740390400000000⟩, + ⟨7, 6, 3, 3, 7, 6, 450499792238484305159802060997838331231338496000000⟩, + ⟨7, 6, 4, 3, 8, 6, 43617430560158275923210759569774647399415808000000⟩, + ⟨7, 6, 0, 4, 3, 6, -47317368285052006666307552593770543727698247680000000⟩, + ⟨7, 6, 1, 4, 4, 6, 14160810220931651649152602981119270569807708160000000⟩, + ⟨7, 6, 2, 4, 5, 6, 395653099618379250159912842524121250178007040000000⟩, + ⟨7, 6, 3, 4, 6, 6, 1034803676895415484341943723947623568348545024000000⟩, + ⟨7, 6, 4, 4, 7, 6, 99394773233267607119164114741834594645966848000000⟩, + ⟨7, 6, 5, 4, 8, 6, -61695640074426311875735573617459765014691840000000⟩, + ⟨7, 6, 0, 5, 2, 6, 79857910505137582346907052917327744168477327360000000⟩, + ⟨7, 6, 1, 5, 3, 6, 27043538762584751535931904241219004068224040960000000⟩, + ⟨7, 6, 2, 5, 4, 6, -2097845044980854947375688198031084188734586880000000⟩, + ⟨7, 6, 3, 5, 5, 6, 340090273573130652544326789636937018987511808000000⟩, + ⟨7, 6, 4, 5, 6, 6, -91172717517607468624074947067048464392126464000000⟩, + ⟨7, 6, 5, 5, 7, 6, 2098789361098410623689690595706937918095360000000⟩, + ⟨7, 6, 6, 5, 8, 6, -10862728877835820276696049569936311488348160000000⟩, + ⟨7, 6, 0, 6, 1, 6, -58045866685810920124417938902260647069116006400000000⟩, + ⟨7, 6, 1, 6, 2, 6, -67390296321031495258054897482728433824657571840000000⟩, + ⟨7, 6, 2, 6, 3, 6, -1058535382651138181640170128088411246533017600000000⟩, + ⟨7, 6, 3, 6, 4, 6, -1604549178479373211930691304282227549291937792000000⟩, + ⟨7, 6, 4, 6, 5, 6, 147935360808369676032968136992146096612442112000000⟩, + ⟨7, 6, 5, 6, 6, 6, -19963232127754068674861241929492683020042240000000⟩, + ⟨7, 6, 6, 6, 7, 6, -10258725795951148118873086890142149000560640000000⟩, + ⟨7, 6, 7, 6, 8, 6, -1250482804030453636784264738548985112821760000000⟩, + ⟨7, 6, 0, 7, 0, 6, 566138138898361442804780476010025674789848350720000000⟩, + ⟨7, 6, 1, 7, 1, 6, 192842356730151420879819747282577572939788451840000000⟩, + ⟨7, 6, 2, 7, 2, 6, 5119705361795136463574479792970094092652380160000000⟩, + ⟨7, 6, 3, 7, 3, 6, 2859639756445715955585197915045007405808091136000000⟩, + ⟨7, 6, 4, 7, 4, 6, 611803454782671038711344241399279461098061824000000⟩, + ⟨7, 6, 5, 7, 5, 6, 22576426277677797745222148322177209692323840000000⟩, + ⟨7, 6, 6, 7, 6, 6, 11103222532248782636363679513830842014105600000000⟩, + ⟨7, 6, 7, 7, 7, 6, 441961439442729305951987376453632844103680000000⟩, + ⟨7, 6, 8, 7, 8, 6, 1185889851277049552120681960371757934182400000000⟩ +] + +def collectedFourData_11_7_42 : List CollectedFourTerm := [ + ⟨7, 7, 0, 0, 7, 7, -3810136604488897365825778377054292625930059776000000⟩, + ⟨7, 7, 1, 0, 8, 7, -109604890578665622335294800493061359152398336000000⟩, + ⟨7, 7, 0, 1, 6, 7, -479359165602728897996289086498416163467296768000000⟩, + ⟨7, 7, 1, 1, 7, 7, -1149393025942610581279716888456389870103822336000000⟩, + ⟨7, 7, 2, 1, 8, 7, 126408060361631054213523353888575192151831347200000⟩, + ⟨7, 7, 0, 2, 5, 7, 2318395927351521027264602947424666306664726528000000⟩, + ⟨7, 7, 1, 2, 6, 7, -1362966440137274318584795005380782529376681984000000⟩, + ⟨7, 7, 2, 2, 7, 7, 153654454638023941292148093666103358558463590400000⟩, + ⟨7, 7, 3, 2, 8, 7, 10772633360189354955313569656765242266353664000000⟩, + ⟨7, 7, 0, 3, 4, 7, -1472315082509616614743672275534622874922909696000000⟩, + ⟨7, 7, 1, 3, 5, 7, -1126020544867137235638039589101043093491154944000000⟩, + ⟨7, 7, 2, 3, 6, 7, 61039675716881685110888375928194072592777216000000⟩, + ⟨7, 7, 3, 3, 7, 7, 26898074329513469640517990525588872535159603200000⟩, + ⟨7, 7, 4, 3, 8, 7, 2232234844466351844369186662274464721194188800000⟩, + ⟨7, 7, 0, 4, 3, 7, -5650373701102749650211482876649402937966067712000000⟩, + ⟨7, 7, 1, 4, 4, 7, 1268253168318159756483899309892795936389726208000000⟩, + ⟨7, 7, 2, 4, 5, 7, 28347999263725569145417109579819994811308441600000⟩, + ⟨7, 7, 3, 4, 6, 7, 61785214326695897833617208454004559022181580800000⟩, + ⟨7, 7, 4, 4, 7, 7, 5086784648241010757730368873338147252784332800000⟩, + ⟨7, 7, 5, 4, 8, 7, -2762754735606510572595312277785583231696896000000⟩, + ⟨7, 7, 0, 5, 2, 7, 9536182034151573440868723536781264901556404224000000⟩, + ⟨7, 7, 1, 5, 3, 7, 2422040348191784384099904909342175170656206848000000⟩, + ⟨7, 7, 2, 5, 4, 7, -150307706038163605994361173889724697443250995200000⟩, + ⟨7, 7, 3, 5, 5, 7, 20305832799301306478845932322884548174649753600000⟩, + ⟨7, 7, 4, 5, 6, 7, -4665999677050958880260955571589188766033510400000⟩, + ⟨7, 7, 5, 5, 7, 7, 93984603116529292923482174714300841590784000000⟩, + ⟨7, 7, 6, 5, 8, 7, -432388640070971781749052414374940034203648000000⟩, + ⟨7, 7, 0, 6, 1, 7, -6931510573525164104980138437794455269157109760000000⟩, + ⟨7, 7, 1, 6, 2, 7, -6035527310203922087702778304289846142059937792000000⟩, + ⟨7, 7, 2, 6, 3, 7, -75842601200306630005210050837091948223791104000000⟩, + ⟨7, 7, 3, 6, 4, 7, -95803114255933809625907537065056522664830566400000⟩, + ⟨7, 7, 4, 6, 5, 7, 7570974788844747186086370682873409787081523200000⟩, + ⟨7, 7, 5, 6, 6, 7, -893961291793558630525309065163944971206656000000⟩, + ⟨7, 7, 6, 6, 7, 7, -408346424333850219540663042750041127124992000000⟩, + ⟨7, 7, 7, 6, 8, 7, -44797684691650636518265865668210579419955200000⟩, + ⟨7, 7, 0, 7, 0, 7, 67605028917745550649026257196902897599903694848000000⟩, + ⟨7, 7, 1, 7, 1, 7, 17271111334254197677562182771895308087870881792000000⟩, + ⟨7, 7, 2, 7, 2, 7, 366819832744003362285094668707164075292255846400000⟩, + ⟨7, 7, 3, 7, 3, 7, 170741039285073864603564000123747960305693491200000⟩, + ⟨7, 7, 4, 7, 4, 7, 31310624495571311148139589882469598915618406400000⟩, + ⟨7, 7, 5, 7, 5, 7, 1010981141235944777227394506196857122717696000000⟩, + ⟨7, 7, 6, 7, 6, 7, 441961439442729305951987376453632844103680000000⟩, + ⟨7, 7, 7, 7, 7, 7, 15832963992954886821465957280426296449433600000⟩, + ⟨7, 7, 8, 7, 8, 7, 38621533339187947181055724954899374407680000000⟩ +] + +def collectedFourData_11_7_43 : List CollectedFourTerm := [ + ⟨7, 8, 0, 0, 7, 8, -25558804049397669493314211356709285704971059200000000⟩, + ⟨7, 8, 1, 0, 8, 8, -588193067483273852897200535611515681594408960000000⟩, + ⟨7, 8, 0, 1, 6, 8, -3215592577045256159947190644910395915606425600000000⟩, + ⟨7, 8, 1, 1, 7, 8, -6168201127739285497731953233661924702379048960000000⟩, + ⟨7, 8, 2, 1, 8, 8, 565305863529225491017525964044609519783772160000000⟩, + ⟨7, 8, 0, 2, 5, 8, 15552047962345385118297968721849604372011417600000000⟩, + ⟨7, 8, 1, 2, 6, 8, -7314339780538480940826127343439038600435466240000000⟩, + ⟨7, 8, 2, 2, 7, 8, 687153682413638975012421026365148023090053120000000⟩, + ⟨7, 8, 3, 2, 8, 8, 41293701322144352826881402399058741008793600000000⟩, + ⟨7, 8, 0, 3, 4, 8, -9876447119639147727181998703810402617340723200000000⟩, + ⟨7, 8, 1, 3, 5, 8, -6042773044504162367849112418818942130024611840000000⟩, + ⟨7, 8, 2, 3, 6, 8, 272973784203000185821509205321821763456204800000000⟩, + ⟨7, 8, 3, 3, 7, 8, 103105806200411135374697978038483882271047680000000⟩, + ⟨7, 8, 4, 3, 8, 8, 7487035099310626578768568839327166475796480000000⟩, + ⟨7, 8, 0, 4, 3, 8, -37903311409415342229413338338055177330124390400000000⟩, + ⟨7, 8, 1, 4, 4, 8, 6806062370757407782054882862631140629288058880000000⟩, + ⟨7, 8, 2, 4, 5, 8, 126774274973136337864337420694686867631636480000000⟩, + ⟨7, 8, 3, 4, 6, 8, 236835330900596867905675268446346993907793920000000⟩, + ⟨7, 8, 4, 4, 7, 8, 17061347867777623321167481742735654655098880000000⟩, + ⟨7, 8, 5, 4, 8, 8, -8236824176472388462720117635189465887539200000000⟩, + ⟨7, 8, 0, 5, 2, 8, 63969729511302295545518526341111223818177740800000000⟩, + ⟨7, 8, 1, 5, 3, 8, 12997844662311840844832550823530097733303009280000000⟩, + ⟨7, 8, 2, 5, 4, 8, -672186783927523628267779738630682086798786560000000⟩, + ⟨7, 8, 3, 5, 5, 8, 77836399576213908799090935355637309783408640000000⟩, + ⟨7, 8, 4, 5, 6, 8, -15650012561202617461704365222039224414371840000000⟩, + ⟨7, 8, 5, 5, 7, 8, 280203899821184828998552060826995182796800000000⟩, + ⟨7, 8, 6, 5, 8, 8, -1160203706264958226637761925031700086128640000000⟩, + ⟨7, 8, 0, 6, 1, 8, -46497314638623731660471490876568507087060992000000000⟩, + ⟨7, 8, 1, 6, 2, 8, -32389570426330311884243277515849761425582981120000000⟩, + ⟨7, 8, 2, 6, 3, 8, -339173522963538357675741519744858116535091200000000⟩, + ⟨7, 8, 3, 6, 4, 8, -367232881092526394630010098237989293769359360000000⟩, + ⟨7, 8, 4, 6, 5, 8, 25393454510664469089641473182863117223198720000000⟩, + ⟨7, 8, 5, 6, 6, 8, -2665239113040258866407298848000102839091200000000⟩, + ⟨7, 8, 6, 6, 7, 8, -1095692603937080988193134369609859265986560000000⟩, + ⟨7, 8, 7, 6, 8, 8, -109275513643994450631655377407110293749760000000⟩, + ⟨7, 8, 0, 7, 0, 8, 453501768106371470572801896922587896366078361600000000⟩, + ⟨7, 8, 1, 7, 1, 8, 92685170350578276441324116728279755094354821120000000⟩, + ⟨7, 8, 2, 7, 2, 8, 1640444459916236555423336466364454200588369920000000⟩, + ⟨7, 8, 3, 7, 3, 8, 654485235311714489357453443745512405472378880000000⟩, + ⟨7, 8, 4, 7, 4, 8, 105017509766415230914257220844643581102653440000000⟩, + ⟨7, 8, 5, 7, 5, 8, 3014119856086964856338870813808718459699200000000⟩, + ⟨7, 8, 6, 7, 6, 8, 1185889851277049552120681960371757934182400000000⟩, + ⟨7, 8, 7, 7, 7, 8, 38621533339187947181055724954899374407680000000⟩, + ⟨7, 8, 8, 7, 8, 8, 86359126121673453832721691702567370752000000000⟩ +] + +def collectedFourData_11_7 : List (List CollectedFourTerm) := [ + collectedFourData_11_7_0, + collectedFourData_11_7_1, + collectedFourData_11_7_2, + collectedFourData_11_7_3, + collectedFourData_11_7_4, + collectedFourData_11_7_5, + collectedFourData_11_7_6, + collectedFourData_11_7_7, + collectedFourData_11_7_8, + collectedFourData_11_7_9, + collectedFourData_11_7_10, + collectedFourData_11_7_11, + collectedFourData_11_7_12, + collectedFourData_11_7_13, + collectedFourData_11_7_14, + collectedFourData_11_7_15, + collectedFourData_11_7_16, + collectedFourData_11_7_17, + collectedFourData_11_7_18, + collectedFourData_11_7_19, + collectedFourData_11_7_20, + collectedFourData_11_7_21, + collectedFourData_11_7_22, + collectedFourData_11_7_23, + collectedFourData_11_7_24, + collectedFourData_11_7_25, + collectedFourData_11_7_26, + collectedFourData_11_7_27, + collectedFourData_11_7_28, + collectedFourData_11_7_29, + collectedFourData_11_7_30, + collectedFourData_11_7_31, + collectedFourData_11_7_32, + collectedFourData_11_7_33, + collectedFourData_11_7_34, + collectedFourData_11_7_35, + collectedFourData_11_7_36, + collectedFourData_11_7_37, + collectedFourData_11_7_38, + collectedFourData_11_7_39, + collectedFourData_11_7_40, + collectedFourData_11_7_41, + collectedFourData_11_7_42, + collectedFourData_11_7_43 +] + +theorem collectedFourChecked_11_7 : collectNumericRowParts 11 7 = collectedFourData_11_7 := by + decide +kernel + +def collectedFourData_11 : Fin 8 → List (List CollectedFourTerm) := + ![collectedFourData_11_0, collectedFourData_11_1, collectedFourData_11_2, collectedFourData_11_3, collectedFourData_11_4, collectedFourData_11_5, collectedFourData_11_6, collectedFourData_11_7] + +theorem collectedFourChecked_11 (t : Fin 8) : + collectNumericRowParts 11 t = collectedFourData_11 t := by + fin_cases t + · exact collectedFourChecked_11_0 + · exact collectedFourChecked_11_1 + · exact collectedFourChecked_11_2 + · exact collectedFourChecked_11_3 + · exact collectedFourChecked_11_4 + · exact collectedFourChecked_11_5 + · exact collectedFourChecked_11_6 + · exact collectedFourChecked_11_7 + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1301.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1301.lean new file mode 100644 index 0000000000000000000000000000000000000000..043aa8983a2dd98fe72a39cb1d11c1433eb3ca51 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1301.lean @@ -0,0 +1,617 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1301. -/ +namespace LaughlinFock + +def collectedFourData_13_0_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_1 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_2 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_3 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_4 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_5 : List CollectedFourTerm := [ + ⟨0, 5, 8, 0, 8, 5, 621918312905720022931676894936364425802544054272000000⟩, + ⟨0, 5, 8, 1, 7, 5, 519684129729633919541665970053511189745830461440000000⟩, + ⟨0, 5, 8, 2, 6, 5, 28279402217399611811951579243531324703847219200000000⟩, + ⟨0, 5, 8, 3, 5, 5, 449947019792929864986205423131617965516668272640000000⟩, + ⟨0, 5, 8, 4, 4, 5, -643736622497033665912167767125737609129917153280000000⟩, + ⟨0, 5, 8, 5, 3, 5, 900480788244852127070200221008251984453985894400000000⟩, + ⟨0, 5, 8, 6, 2, 5, -3211246469684236312830884044096923768578950299648000000⟩, + ⟨0, 5, 8, 7, 1, 5, 6004325892044116776726842441369818665055200215040000000⟩ +] + +def collectedFourData_13_0_6 : List CollectedFourTerm := [ + ⟨0, 6, 7, 0, 7, 6, -5331367908389622868070775308159533362595233792000000⟩, + ⟨0, 6, 8, 0, 8, 6, 718880864422981257768084119186312485537446887424000000⟩, + ⟨0, 6, 7, 1, 6, 6, -369006800945395780846569820655563467682027143168000000⟩, + ⟨0, 6, 8, 1, 7, 6, 600707470184398078389962935879808176802475540480000000⟩, + ⟨0, 6, 7, 2, 5, 6, 37424692814782933013726471737852335473421189120000000⟩, + ⟨0, 6, 8, 2, 6, 6, 32688410502700968839424046863129318131132006400000000⟩, + ⟨0, 6, 7, 3, 4, 6, -150368521360941211994747376403654514920214495232000000⟩, + ⟨0, 6, 8, 3, 5, 6, 520097729590928577163189073885648613660300410880000000⟩, + ⟨0, 6, 7, 4, 3, 6, 533325408667198103183395788119569509154075705344000000⟩, + ⟨0, 6, 8, 4, 4, 6, -744100840959722206580854800298213120740698357760000000⟩, + ⟨0, 6, 7, 5, 2, 6, -1035933392249336409762234615338449993839081947136000000⟩, + ⟨0, 6, 8, 5, 3, 6, 1040873687133056627683179656077368288613289164800000000⟩, + ⟨0, 6, 7, 6, 1, 6, 2846193449844367501734537195905979341670545620992000000⟩, + ⟨0, 6, 8, 6, 2, 6, -3711908123779286896940164073919929814697918857216000000⟩, + ⟨0, 6, 7, 7, 0, 6, -9647634505377938352995985031992201945149803069440000000⟩, + ⟨0, 6, 8, 7, 1, 6, 6940453268505551286821575362685942329440395591680000000⟩ +] + +def collectedFourData_13_0_7 : List CollectedFourTerm := [ + ⟨0, 7, 6, 0, 6, 7, -5331367908389622868070775308159533362595233792000000⟩, + ⟨0, 7, 7, 0, 7, 7, 97724779146254425344289686567581062564675584000000⟩, + ⟨0, 7, 8, 0, 8, 7, -6588597421465944834010773499816689600691175424000000⟩, + ⟨0, 7, 6, 1, 5, 7, 3352575509809075129335539303298299221776531456000000⟩, + ⟨0, 7, 7, 1, 6, 7, 6763950405506188828318470614578948459343118336000000⟩, + ⟨0, 7, 8, 1, 7, 7, -5505529337311057416638438921746945602465300480000000⟩, + ⟨0, 7, 6, 2, 4, 7, -1203286413439226750069383134784367061249294336000000⟩, + ⟨0, 7, 7, 2, 5, 7, -686000272872895045613647546458537040533258240000000⟩, + ⟨0, 7, 8, 2, 6, 7, -299591751301915607886817181440204001928806400000000⟩, + ⟨0, 7, 6, 3, 3, 7, -1826700056586950837783230601311875195658567680000000⟩, + ⟨0, 7, 7, 3, 4, 7, 2756277712033846010150770564298702145101758464000000⟩, + ⟨0, 7, 8, 3, 5, 7, -4766734976098688729512308529821612952654970880000000⟩, + ⟨0, 7, 6, 4, 2, 7, 5554437294147931577052260983832302959533752320000000⟩, + ⟨0, 7, 7, 4, 3, 7, -9775935307910641457123682815258718651902066688000000⟩, + ⟨0, 7, 8, 4, 4, 7, 6819740411358681625909821631860146108639477760000000⟩, + ⟨0, 7, 6, 5, 1, 7, -8583230362177209368644295922569374214431703040000000⟩, + ⟨0, 7, 7, 5, 2, 7, 18988815573670606214328176568886462540280758272000000⟩, + ⟨0, 7, 8, 5, 3, 7, -9539685962598524713554328643675911466306764800000000⟩, + ⟨0, 7, 6, 6, 0, 7, 12589921866507744646303007654822260383261130752000000⟩, + ⟨0, 7, 7, 6, 1, 7, -52171155897131102762426606947217349580878249984000000⟩, + ⟨0, 7, 8, 6, 2, 7, 34019918324965894480584020393567544223482249216000000⟩, + ⟨0, 7, 7, 7, 0, 7, 176842597907790207852980038031943025875096698880000000⟩, + ⟨0, 7, 8, 7, 1, 7, -63609778437188752306220739208424358774759751680000000⟩ +] + +def collectedFourData_13_0_8 : List CollectedFourTerm := [ + ⟨0, 8, 5, 0, 5, 8, 621918312905720022931676894936364425802544054272000000⟩, + ⟨0, 8, 6, 0, 6, 8, 718880864422981257768084119186312485537446887424000000⟩, + ⟨0, 8, 7, 0, 7, 8, -6588597421465944834010773499816689600691175424000000⟩, + ⟨0, 8, 8, 0, 8, 8, 296135169001378716547105457959100066191456075776000000⟩, + ⟨0, 8, 5, 1, 4, 8, 332818416994309293090050742114480328646527549440000000⟩, + ⟨0, 8, 6, 1, 5, 8, -452060788515878913707725632432296181219597484032000000⟩, + ⟨0, 8, 7, 1, 6, 8, -456025038787203884823508818702701148382949277696000000⟩, + ⟨0, 8, 8, 1, 7, 8, 247454921958777577511610007727142823148409323520000000⟩, + ⟨0, 8, 5, 2, 3, 8, 491037243604840835000320509383681741898041524224000000⟩, + ⟨0, 8, 6, 2, 4, 8, 162250962962131303855425180839903159376666427392000000⟩, + ⟨0, 8, 7, 2, 5, 8, 46250087935333277228530013585790829008141680640000000⟩, + ⟨0, 8, 8, 2, 6, 8, 13465635889993703895265505314538174958639513600000000⟩, + ⟨0, 8, 5, 3, 2, 8, -1334017663574852642180519680309327373946071285760000000⟩, + ⟨0, 8, 6, 3, 3, 8, 246311966888323630189831773406776138312670248960000000⟩, + ⟨0, 8, 7, 3, 4, 8, -185828040595232029719921040699796525574053167104000000⟩, + ⟨0, 8, 8, 3, 5, 8, 214248614300324252419145273273009846269111173120000000⟩, + ⟨0, 8, 5, 4, 1, 8, 369760620722884677581799130531465281269535866880000000⟩, + ⟨0, 8, 6, 4, 2, 8, -748959507580938516123936765375019925239800791040000000⟩, + ⟨0, 8, 7, 4, 3, 8, 659092839347558875419833867072483534198242541568000000⟩, + ⟨0, 8, 8, 4, 4, 8, -306524264585267000528069926251885238212089610240000000⟩, + ⟨0, 8, 5, 5, 0, 8, 4233029083091993187126971313481419367077963104256000000⟩, + ⟨0, 8, 6, 5, 1, 8, 1157361519281703312494325613286393670534042746880000000⟩, + ⟨0, 8, 7, 5, 2, 8, -1280224549171301030796532896148584451996743892992000000⟩, + ⟨0, 8, 8, 5, 3, 8, 428776617243314807219995520843617400400327475200000000⟩, + ⟨0, 8, 6, 6, 0, 8, -1697623212266117031114556599085337978418751340544000000⟩, + ⟨0, 8, 7, 6, 1, 8, 3517375492906503007788030656661880327375970893824000000⟩, + ⟨0, 8, 8, 6, 2, 8, -1529080260656649529616010504317306053170334531584000000⟩, + ⟨0, 8, 7, 7, 0, 8, -11922714942510697637256356090253795429094973767680000000⟩, + ⟨0, 8, 8, 7, 1, 8, 2859044388759443364393857116895203516783861432320000000⟩ +] + +def collectedFourData_13_0_9 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_10 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_11 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_12 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_13 : List CollectedFourTerm := [ + ⟨1, 4, 8, 0, 8, 5, 332818416994309293090050742114480328646527549440000000⟩, + ⟨1, 4, 8, 1, 7, 5, 278107985895411385893787228608027602503650508800000000⟩, + ⟨1, 4, 8, 2, 6, 5, 15133668979075553985764802385989779570294784000000000⟩, + ⟨1, 4, 8, 3, 5, 5, 240788302500897066332553768452723182008061132800000000⟩, + ⟨1, 4, 8, 4, 4, 5, -344494444390488536323359944627901160127830425600000000⟩, + ⟨1, 4, 8, 5, 3, 5, 481890602444556341653439185482069721573490688000000000⟩, + ⟨1, 4, 8, 6, 2, 5, -1718492516525865981479553058274437597219478568960000000⟩, + ⟨1, 4, 8, 7, 1, 5, 3213203723124660190351993754549331042941848780800000000⟩ +] + +def collectedFourData_13_0_14 : List CollectedFourTerm := [ + ⟨1, 5, 7, 0, 7, 6, 3352575509809075129335539303298299221776531456000000⟩, + ⟨1, 5, 8, 0, 8, 6, -452060788515878913707725632432296181219597484032000000⟩, + ⟨1, 5, 7, 1, 6, 6, 232046106188947652149302298127835524842414669824000000⟩, + ⟨1, 5, 8, 1, 7, 6, -377748673080769623793417494181876251176353136640000000⟩, + ⟨1, 5, 7, 2, 5, 6, -23534130592549511046321312082067786389688156160000000⟩, + ⟨1, 5, 8, 2, 6, 6, -20555768498641011244019326666945211363701555200000000⟩, + ⟨1, 5, 7, 3, 4, 6, 94557687787329579633397180278485678830047461376000000⟩, + ⟨1, 5, 8, 3, 5, 6, -327058072317604641671512478902997822960660643840000000⟩, + ⟨1, 5, 7, 4, 3, 6, -335376161349301274766154902270393461728547438592000000⟩, + ⟨1, 5, 8, 4, 4, 6, 467920109640947674440307180637083357234782535680000000⟩, + ⟨1, 5, 7, 5, 2, 6, 651435987972854274492415978604510687529478914048000000⟩, + ⟨1, 5, 8, 5, 3, 6, -654542641260152610379087673704947072018835046400000000⟩, + ⟨1, 5, 7, 6, 1, 6, -1789799282302669394358319262106299790960472621056000000⟩, + ⟨1, 5, 8, 6, 2, 6, 2334194991656976933997168048568841887027180863488000000⟩, + ⟨1, 5, 7, 7, 0, 6, 6066815069997472055676294718675159046590216273920000000⟩, + ⟨1, 5, 8, 7, 1, 6, -4364432178531539792902434002812959780419917578240000000⟩ +] + +def collectedFourData_13_0_15 : List CollectedFourTerm := [ + ⟨1, 6, 6, 0, 6, 7, -369006800945395780846569820655563467682027143168000000⟩, + ⟨1, 6, 7, 0, 7, 7, 6763950405506188828318470614578948459343118336000000⟩, + ⟨1, 6, 8, 0, 8, 7, -456025038787203884823508818702701148382949277696000000⟩, + ⟨1, 6, 6, 1, 5, 7, 232046106188947652149302298127835524842414669824000000⟩, + ⟨1, 6, 7, 1, 6, 7, 468161969644122464042888173684445707829294137344000000⟩, + ⟨1, 6, 8, 1, 7, 7, -381061259170506288766561826809799940251760721920000000⟩, + ⟨1, 6, 6, 2, 4, 7, -83284604940796062819713893577990332970742841344000000⟩, + ⟨1, 6, 7, 2, 5, 7, -47481016221399343245677217908621176902474792960000000⟩, + ⟨1, 6, 8, 2, 6, 7, -20736027908256159936284896587537490174908825600000000⟩, + ⟨1, 6, 6, 3, 3, 7, -126433732533669800393475482817889276439266590720000000⟩, + ⟨1, 6, 7, 3, 4, 7, 190773782359717520260287222675933891295608569856000000⟩, + ⟨1, 6, 8, 3, 5, 7, -329926138039873195510908600488241288518849003520000000⟩, + ⟨1, 6, 6, 4, 2, 7, 384446388278694541054116385518344365789182689280000000⟩, + ⟨1, 6, 7, 4, 3, 7, -676634341543854352806893769924515766185861578752000000⟩, + ⟨1, 6, 8, 4, 4, 7, 472023434832438775652227031063258557561480151040000000⟩, + ⟨1, 6, 6, 5, 1, 7, -594082125291011683631212543585626036371623772160000000⟩, + ⟨1, 6, 7, 5, 2, 7, 1314297232715049107903971416074759110374444761088000000⟩, + ⟨1, 6, 8, 5, 3, 7, -660282512775503427618059404035444189030462259200000000⟩, + ⟨1, 6, 6, 6, 0, 7, 871402400273628000106015007365387065153193771008000000⟩, + ⟨1, 6, 7, 6, 1, 7, -3610989087609022714810565959494225231835023015936000000⟩, + ⟨1, 6, 8, 6, 2, 7, 2354664214743943545509573503302777978509919780864000000⟩, + ⟨1, 6, 7, 7, 0, 7, 12240033410963317950082969513869561523686887915520000000⟩, + ⟨1, 6, 8, 7, 1, 7, -4402705131832189443205110865177734789414487326720000000⟩ +] + +def collectedFourData_13_0_16 : List CollectedFourTerm := [ + ⟨1, 7, 5, 0, 5, 8, 519684129729633919541665970053511189745830461440000000⟩, + ⟨1, 7, 6, 0, 6, 8, 600707470184398078389962935879808176802475540480000000⟩, + ⟨1, 7, 7, 0, 7, 8, -5505529337311057416638438921746945602465300480000000⟩, + ⟨1, 7, 8, 0, 8, 8, 247454921958777577511610007727142823148409323520000000⟩, + ⟨1, 7, 5, 1, 4, 8, 278107985895411385893787228608027602503650508800000000⟩, + ⟨1, 7, 6, 1, 5, 8, -377748673080769623793417494181876251176353136640000000⟩, + ⟨1, 7, 7, 1, 6, 8, -381061259170506288766561826809799940251760721920000000⟩, + ⟨1, 7, 8, 1, 7, 8, 206776988387149702111936960831688163669206630400000000⟩, + ⟨1, 7, 5, 2, 3, 8, 410317974743902946403004695115100994782342676480000000⟩, + ⟨1, 7, 6, 2, 4, 8, 135579301549772318931959656810180887137054883840000000⟩, + ⟨1, 7, 7, 2, 5, 8, 38647256721376490352798249153352432586902732800000000⟩, + ⟨1, 7, 8, 2, 6, 8, 11252084274624582031264999511152726294659072000000000⟩, + ⟨1, 7, 5, 3, 2, 8, -1114724866839470432429575498052813197363327795200000000⟩, + ⟨1, 7, 6, 3, 3, 8, 205821918245648697578106978878964105236132659200000000⟩, + ⟨1, 7, 7, 3, 4, 8, -155280655919093505158373669745545352931526574080000000⟩, + ⟨1, 7, 8, 3, 5, 8, 179029307158097608098186169738930965281400422400000000⟩, + ⟨1, 7, 5, 4, 1, 8, 308977437070247440532198940050570747531860377600000000⟩, + ⟨1, 7, 6, 4, 2, 8, -625841628752519987710807862760341116845608140800000000⟩, + ⟨1, 7, 7, 4, 3, 8, 550747713195726455371809095857198800005612175360000000⟩, + ⟨1, 7, 8, 4, 4, 8, -256136203704551538776572492858833730760658124800000000⟩, + ⟨1, 7, 5, 5, 0, 8, 3537181635460826366169458427523876096551545733120000000⟩, + ⟨1, 7, 6, 5, 1, 8, 967108382964850673883829157668505927085037977600000000⟩, + ⟨1, 7, 7, 5, 2, 8, -1069774545769741344366979590814408673767288995840000000⟩, + ⟨1, 7, 8, 5, 3, 8, 358292075593355568516095773446515305274671104000000000⟩, + ⟨1, 7, 6, 6, 0, 8, -1418559034792539284926600917324467764321981562880000000⟩, + ⟨1, 7, 7, 6, 1, 8, 2939170923305104747215349084504213734191246868480000000⟩, + ⟨1, 7, 8, 6, 2, 8, -1277722054578856417657610995115790273502437703680000000⟩, + ⟨1, 7, 7, 7, 0, 8, -9962796737668129187000981264879011610937104793600000000⟩, + ⟨1, 7, 8, 7, 1, 8, 2389059727295865904447677841006989561641199206400000000⟩ +] + +def collectedFourData_13_0_17 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_18 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_19 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_20 : List CollectedFourTerm := [ + ⟨2, 3, 8, 0, 8, 5, 491037243604840835000320509383681741898041524224000000⟩, + ⟨2, 3, 8, 1, 7, 5, 410317974743902946403004695115100994782342676480000000⟩, + ⟨2, 3, 8, 2, 6, 5, 22328076577686529406984808790504966304720486400000000⟩, + ⟨2, 3, 8, 3, 5, 5, 355256855735693139437712138293549516278600826880000000⟩, + ⟨2, 3, 8, 4, 4, 5, -508263947465320090310271421705612708489734389760000000⟩, + ⟨2, 3, 8, 5, 3, 5, 710976980422021183822727702743376223131192524800000000⟩, + ⟨2, 3, 8, 6, 2, 5, -2535448116396864271144926251879788177052103868416000000⟩, + ⟨2, 3, 8, 7, 1, 5, 4740731338106579061960782219596659184853770567680000000⟩ +] + +def collectedFourData_13_0_21 : List CollectedFourTerm := [ + ⟨2, 4, 7, 0, 7, 6, -1203286413439226750069383134784367061249294336000000⟩, + ⟨2, 4, 8, 0, 8, 6, 162250962962131303855425180839903159376666427392000000⟩, + ⟨2, 4, 7, 1, 6, 6, -83284604940796062819713893577990332970742841344000000⟩, + ⟨2, 4, 8, 1, 7, 6, 135579301549772318931959656810180887137054883840000000⟩, + ⟨2, 4, 7, 2, 5, 6, 8446729838377891202109197548985835345370152960000000⟩, + ⟨2, 4, 8, 2, 6, 6, 7377753873059037495430907816967266957996851200000000⟩, + ⟨2, 4, 7, 3, 4, 6, -33938081533979112808781271356367386392035065856000000⟩, + ⟨2, 4, 8, 3, 5, 6, 117385733348571050134083972498024990799602647040000000⟩, + ⟨2, 4, 7, 4, 3, 6, 120371212270174344411499918878794752157131210752000000⟩, + ⟨2, 4, 8, 4, 4, 6, -167943095944768202408039385448334564257777582080000000⟩, + ⟨2, 4, 7, 5, 2, 6, -233809520847372390944046256982006991095844569088000000⟩, + ⟨2, 4, 8, 5, 3, 6, 234924542322932022293833242373694584141538918400000000⟩, + ⟨2, 4, 7, 6, 1, 6, 642384087361160809977090583051533595223770791936000000⟩, + ⟨2, 4, 8, 6, 2, 6, -837775349596430635447339056829606973661121609728000000⟩, + ⟨2, 4, 7, 7, 0, 6, -2177465093692115461643683218889547253968032235520000000⟩, + ⟨2, 4, 8, 7, 1, 6, 1566455976140875315016915697302654486519941693440000000⟩ +] + +def collectedFourData_13_0_22 : List CollectedFourTerm := [ + ⟨2, 5, 6, 0, 6, 7, 37424692814782933013726471737852335473421189120000000⟩, + ⟨2, 5, 7, 0, 7, 7, -686000272872895045613647546458537040533258240000000⟩, + ⟨2, 5, 8, 0, 8, 7, 46250087935333277228530013585790829008141680640000000⟩, + ⟨2, 5, 6, 1, 5, 7, -23534130592549511046321312082067786389688156160000000⟩, + ⟨2, 5, 7, 1, 6, 7, -47481016221399343245677217908621176902474792960000000⟩, + ⟨2, 5, 8, 1, 7, 7, 38647256721376490352798249153352432586902732800000000⟩, + ⟨2, 5, 6, 2, 4, 7, 8446729838377891202109197548985835345370152960000000⟩, + ⟨2, 5, 7, 2, 5, 7, 4815527632734725709061056283166662581446246400000000⟩, + ⟨2, 5, 8, 2, 6, 7, 2103049246455726009249265701606039805231104000000000⟩, + ⟨2, 5, 6, 3, 3, 7, 12822917055664794395422449451800238138117324800000000⟩, + ⟨2, 5, 7, 3, 4, 7, -19348288930271454657851663718781353970410455040000000⟩, + ⟨2, 5, 8, 3, 5, 7, 33461129540365960197070924301091748516252876800000000⟩, + ⟨2, 5, 6, 4, 2, 7, -38990576727099290470273682533919907418157875200000000⟩, + ⟨2, 5, 7, 4, 3, 7, 68624297208979742331686161881949255749001543680000000⟩, + ⟨2, 5, 8, 4, 4, 7, -47872646262139704952435979134731258789730713600000000⟩, + ⟨2, 5, 6, 5, 1, 7, 60251846277108329346082188175643269130511974400000000⟩, + ⟨2, 5, 7, 5, 2, 7, -133296107485451252203364105982909723283732561920000000⟩, + ⟨2, 5, 8, 5, 3, 7, 66965893713305364354449412443254233055100928000000000⟩, + ⟨2, 5, 6, 6, 0, 7, -88377685898344300938121983389242649205245214720000000⟩, + ⟨2, 5, 7, 6, 1, 7, 366226738951888576489959821650718546863576842240000000⟩, + ⟨2, 5, 8, 6, 2, 7, -238810191825689969486876326396085438332545269760000000⟩, + ⟨2, 5, 7, 7, 0, 7, -1241384953541186294849777616941940648335690956800000000⟩, + ⟨2, 5, 8, 7, 1, 7, 446522629639203060737637556237073229707791564800000000⟩ +] + +def collectedFourData_13_0_23 : List CollectedFourTerm := [ + ⟨2, 6, 5, 0, 5, 8, 28279402217399611811951579243531324703847219200000000⟩, + ⟨2, 6, 6, 0, 6, 8, 32688410502700968839424046863129318131132006400000000⟩, + ⟨2, 6, 7, 0, 7, 8, -299591751301915607886817181440204001928806400000000⟩, + ⟨2, 6, 8, 0, 8, 8, 13465635889993703895265505314538174958639513600000000⟩, + ⟨2, 6, 5, 1, 4, 8, 15133668979075553985764802385989779570294784000000000⟩, + ⟨2, 6, 6, 1, 5, 8, -20555768498641011244019326666945211363701555200000000⟩, + ⟨2, 6, 7, 1, 6, 8, -20736027908256159936284896587537490174908825600000000⟩, + ⟨2, 6, 8, 1, 7, 8, 11252084274624582031264999511152726294659072000000000⟩, + ⟨2, 6, 5, 2, 3, 8, 22328076577686529406984808790504966304720486400000000⟩, + ⟨2, 6, 6, 2, 4, 8, 7377753873059037495430907816967266957996851200000000⟩, + ⟨2, 6, 7, 2, 5, 8, 2103049246455726009249265701606039805231104000000000⟩, + ⟨2, 6, 8, 2, 6, 8, 612299277162322935196648706246557260840960000000000⟩, + ⟨2, 6, 5, 3, 2, 8, -60659448822289155866016757214381242828455936000000000⟩, + ⟨2, 6, 6, 3, 3, 8, 11200112680472982626377565450470940743827456000000000⟩, + ⟨2, 6, 7, 3, 4, 8, -8449833031465146461030984912829669152548454400000000⟩, + ⟨2, 6, 8, 3, 5, 8, 9742152003872369830297499334778746549829632000000000⟩, + ⟨2, 6, 5, 4, 1, 8, 16813477108790292273855260078342834768314368000000000⟩, + ⟨2, 6, 6, 4, 2, 8, -34056123963401805523009611396924835620716544000000000⟩, + ⟨2, 6, 7, 4, 3, 8, 29969774350965465487769786653759259483622604800000000⟩, + ⟨2, 6, 8, 4, 4, 8, -13938041038057458048343220587390745563889664000000000⟩, + ⟨2, 6, 5, 5, 0, 8, 192481117784444262125672597032766716952287641600000000⟩, + ⟨2, 6, 6, 5, 1, 8, 52626673367744399890318942777882366986682368000000000⟩, + ⟨2, 6, 7, 5, 2, 8, -58213408744071936624804159504653016336905011200000000⟩, + ⟨2, 6, 8, 5, 3, 8, 19497008158172500816387039886909563962654720000000000⟩, + ⟨2, 6, 6, 6, 0, 8, -77193047120555269071015615817476273978369638400000000⟩, + ⟨2, 6, 7, 6, 1, 8, 159939455470908929353733031974517216553363046400000000⟩, + ⟨2, 6, 8, 6, 2, 8, -69529188667500841754995083237568494543726182400000000⟩, + ⟨2, 6, 7, 7, 0, 8, -542140735183293314779247624378029893639733248000000000⟩, + ⟨2, 6, 8, 7, 1, 8, 130004318170615639361750650940465913110986752000000000⟩ +] + +def collectedFourData_13_0_24 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_25 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_26 : List CollectedFourTerm := [ + ⟨3, 2, 8, 0, 8, 5, -1334017663574852642180519680309327373946071285760000000⟩, + ⟨3, 2, 8, 1, 7, 5, -1114724866839470432429575498052813197363327795200000000⟩, + ⟨3, 2, 8, 2, 6, 5, -60659448822289155866016757214381242828455936000000000⟩, + ⟨3, 2, 8, 3, 5, 5, -965138442816083317098715196342469476274615091200000000⟩, + ⟨3, 2, 8, 4, 4, 5, 1380818038769093565466263095670768017334494822400000000⟩, + ⟨3, 2, 8, 5, 3, 5, -1931535464225097333584889673164073753066340352000000000⟩, + ⟨3, 2, 8, 6, 2, 5, 6888138560571012381986747111308157256875208867840000000⟩, + ⟨3, 2, 8, 7, 1, 5, -12879306866561021037143781311738659053862335283200000000⟩ +] + +def collectedFourData_13_0_27 : List CollectedFourTerm := [ + ⟨3, 3, 7, 0, 7, 6, -1826700056586950837783230601311875195658567680000000⟩, + ⟨3, 3, 8, 0, 8, 6, 246311966888323630189831773406776138312670248960000000⟩, + ⟨3, 3, 7, 1, 6, 6, -126433732533669800393475482817889276439266590720000000⟩, + ⟨3, 3, 8, 1, 7, 6, 205821918245648697578106978878964105236132659200000000⟩, + ⟨3, 3, 7, 2, 5, 6, 12822917055664794395422449451800238138117324800000000⟩, + ⟨3, 3, 8, 2, 6, 6, 11200112680472982626377565450470940743827456000000000⟩, + ⟨3, 3, 7, 3, 4, 6, -51521146392220362393514219949051309582482145280000000⟩, + ⟨3, 3, 8, 3, 5, 6, 178202399159030642769723259364307188407546675200000000⟩, + ⟨3, 3, 7, 4, 3, 6, 182734632261741832947766685345657051135355125760000000⟩, + ⟨3, 3, 8, 4, 4, 6, -254953151169432796630753561901339702838322790400000000⟩, + ⟨3, 3, 7, 5, 2, 6, -354944475556512329437925452611420230008638013440000000⟩, + ⟨3, 3, 8, 5, 3, 6, 356637181274578941045091503176057776339156992000000000⟩, + ⟨3, 3, 7, 6, 1, 6, 975198452859831281867130860159482881847779655680000000⟩, + ⟨3, 3, 8, 6, 2, 6, -1271820458888813860197761986354574670764326256640000000⟩, + ⟨3, 3, 7, 7, 0, 6, -3305593386112299168374601386751028518429759897600000000⟩, + ⟨3, 3, 8, 7, 1, 6, 2378025039008740174239319360839105902613312307200000000⟩ +] + +def collectedFourData_13_0_28 : List CollectedFourTerm := [ + ⟨3, 4, 6, 0, 6, 7, -150368521360941211994747376403654514920214495232000000⟩, + ⟨3, 4, 7, 0, 7, 7, 2756277712033846010150770564298702145101758464000000⟩, + ⟨3, 4, 8, 0, 8, 7, -185828040595232029719921040699796525574053167104000000⟩, + ⟨3, 4, 6, 1, 5, 7, 94557687787329579633397180278485678830047461376000000⟩, + ⟨3, 4, 7, 1, 6, 7, 190773782359717520260287222675933891295608569856000000⟩, + ⟨3, 4, 8, 1, 7, 7, -155280655919093505158373669745545352931526574080000000⟩, + ⟨3, 4, 6, 2, 4, 7, -33938081533979112808781271356367386392035065856000000⟩, + ⟨3, 4, 7, 2, 5, 7, -19348288930271454657851663718781353970410455040000000⟩, + ⟨3, 4, 8, 2, 6, 7, -8449833031465146461030984912829669152548454400000000⟩, + ⟨3, 4, 6, 3, 3, 7, -51521146392220362393514219949051309582482145280000000⟩, + ⟨3, 4, 7, 3, 4, 7, 77739411561982657297567609139914006056816082944000000⟩, + ⟨3, 4, 8, 3, 5, 7, -134443336567996439130818552346164416853028372480000000⟩, + ⟨3, 4, 6, 4, 2, 7, 156660079976617776811744039478451635592332574720000000⟩, + ⟨3, 4, 7, 4, 3, 7, -275725285223236898784321110668271055281584078848000000⟩, + ⟨3, 4, 8, 4, 4, 7, 192347311110857783094600986205661770095221800960000000⟩, + ⟨3, 4, 6, 5, 1, 7, -242085648606226478732821890490988043024822435840000000⟩, + ⟨3, 4, 7, 5, 2, 7, 535569889242727427399339926018481627094488973312000000⟩, + ⟨3, 4, 8, 5, 3, 7, -269061992549105201636908473940323056579562700800000000⟩, + ⟨3, 4, 6, 6, 0, 7, 355092345463058325641523795434019457936121659392000000⟩, + ⟨3, 4, 7, 6, 1, 7, -1471460927991435379129045793603123220297352740864000000⟩, + ⟨3, 4, 8, 6, 2, 7, 959514500452153130423450644302717206786092302336000000⟩, + ⟨3, 4, 7, 7, 0, 7, 4987755566292189551383335345448400201391255060480000000⟩, + ⟨3, 4, 8, 7, 1, 7, -1794081461278537493395223432400124658721258209280000000⟩ +] + +def collectedFourData_13_0_29 : List CollectedFourTerm := [ + ⟨3, 5, 5, 0, 5, 8, 449947019792929864986205423131617965516668272640000000⟩, + ⟨3, 5, 6, 0, 6, 8, 520097729590928577163189073885648613660300410880000000⟩, + ⟨3, 5, 7, 0, 7, 8, -4766734976098688729512308529821612952654970880000000⟩, + ⟨3, 5, 8, 0, 8, 8, 214248614300324252419145273273009846269111173120000000⟩, + ⟨3, 5, 5, 1, 4, 8, 240788302500897066332553768452723182008061132800000000⟩, + ⟨3, 5, 6, 1, 5, 8, -327058072317604641671512478902997822960660643840000000⟩, + ⟨3, 5, 7, 1, 6, 8, -329926138039873195510908600488241288518849003520000000⟩, + ⟨3, 5, 8, 1, 7, 8, 179029307158097608098186169738930965281400422400000000⟩, + ⟨3, 5, 5, 2, 3, 8, 355256855735693139437712138293549516278600826880000000⟩, + ⟨3, 5, 6, 2, 4, 8, 117385733348571050134083972498024990799602647040000000⟩, + ⟨3, 5, 7, 2, 5, 8, 33461129540365960197070924301091748516252876800000000⟩, + ⟨3, 5, 8, 2, 6, 8, 9742152003872369830297499334778746549829632000000000⟩, + ⟨3, 5, 5, 3, 2, 8, -965138442816083317098715196342469476274615091200000000⟩, + ⟨3, 5, 6, 3, 3, 8, 178202399159030642769723259364307188407546675200000000⟩, + ⟨3, 5, 7, 3, 4, 8, -134443336567996439130818552346164416853028372480000000⟩, + ⟨3, 5, 8, 3, 5, 8, 155005124465292393633206938158480563785590374400000000⟩, + ⟨3, 5, 5, 4, 1, 8, 267515340646139109602424177299767285415254425600000000⟩, + ⟨3, 5, 6, 4, 2, 8, -541859101731757513730053984905197768372178124800000000⟩, + ⟨3, 5, 7, 4, 3, 8, 476842139357055856631728769871329398574190428160000000⟩, + ⟨3, 5, 8, 4, 4, 8, -221764943212515428372507324031897882296372428800000000⟩, + ⟨3, 5, 5, 5, 0, 8, 3062522490671174956777011883478602911125832990720000000⟩, + ⟨3, 5, 6, 5, 1, 8, 837330812773097211804351239065850159306480025600000000⟩, + ⟨3, 5, 7, 5, 2, 8, -926220065580699670807284447803920036398146519040000000⟩, + ⟨3, 5, 8, 5, 3, 8, 310212381726038828901024797883812578301313024000000000⟩, + ⟨3, 5, 6, 6, 0, 8, -1228200696521754410628064248668114395971484385280000000⟩, + ⟨3, 5, 7, 6, 1, 8, 2544759637534404987100029771579759182251693178880000000⟩, + ⟨3, 5, 8, 6, 2, 8, -1106262819456410308766569277760165416349550510080000000⟩, + ⟨3, 5, 7, 7, 0, 8, -8625875689620622072499576308749382035755866521600000000⟩, + ⟨3, 5, 8, 7, 1, 8, 2068468600269414326245908700956701040520357478400000000⟩ +] + +def collectedFourData_13_0_30 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_0_31 : List CollectedFourTerm := [ + ⟨4, 1, 8, 0, 8, 5, 369760620722884677581799130531465281269535866880000000⟩, + ⟨4, 1, 8, 1, 7, 5, 308977437070247440532198940050570747531860377600000000⟩, + ⟨4, 1, 8, 2, 6, 5, 16813477108790292273855260078342834768314368000000000⟩, + ⟨4, 1, 8, 3, 5, 5, 267515340646139109602424177299767285415254425600000000⟩, + ⟨4, 1, 8, 4, 4, 5, -382732664687814851530165380193236291819877171200000000⟩, + ⟨4, 1, 8, 5, 3, 5, 535379531846852962148022710648474515040894976000000000⟩, + ⟨4, 1, 8, 6, 2, 5, -1909241878369673562969702190989143977005856849920000000⟩, + ⟨4, 1, 8, 7, 1, 5, 3569863152110279617058466390650868552278055321600000000⟩ +] + +def collectedFourData_13_0_32 : List CollectedFourTerm := [ + ⟨4, 2, 7, 0, 7, 6, 5554437294147931577052260983832302959533752320000000⟩, + ⟨4, 2, 8, 0, 8, 6, -748959507580938516123936765375019925239800791040000000⟩, + ⟨4, 2, 7, 1, 6, 6, 384446388278694541054116385518344365789182689280000000⟩, + ⟨4, 2, 8, 1, 7, 6, -625841628752519987710807862760341116845608140800000000⟩, + ⟨4, 2, 7, 2, 5, 6, -38990576727099290470273682533919907418157875200000000⟩, + ⟨4, 2, 8, 2, 6, 6, -34056123963401805523009611396924835620716544000000000⟩, + ⟨4, 2, 7, 3, 4, 6, 156660079976617776811744039478451635592332574720000000⟩, + ⟨4, 2, 8, 3, 5, 6, -541859101731757513730053984905197768372178124800000000⟩, + ⟨4, 2, 7, 4, 3, 6, -555640239188175250573246583615732222269839114240000000⟩, + ⟨4, 2, 8, 4, 4, 6, 775234711363586993203669379937961513571686809600000000⟩, + ⟨4, 2, 7, 5, 2, 6, 1079277807691372824817272594139885074167428546560000000⟩, + ⟨4, 2, 8, 5, 3, 6, -1084424809102219447643043979271430479447851008000000000⟩, + ⟨4, 2, 7, 6, 1, 6, -2965280827702310206497675273640848035802324664320000000⟩, + ⟨4, 2, 8, 6, 2, 6, 3867217807783598808051107936534339017025897103360000000⟩, + ⟨4, 2, 7, 7, 0, 6, 10051300495066760193505874499935534919893542502400000000⟩, + ⟨4, 2, 8, 7, 1, 6, -7230848280459889444456170978978360023824780492800000000⟩ +] + +def collectedFourData_13_0_33 : List CollectedFourTerm := [ + ⟨4, 3, 6, 0, 6, 7, 533325408667198103183395788119569509154075705344000000⟩, + ⟨4, 3, 7, 0, 7, 7, -9775935307910641457123682815258718651902066688000000⟩, + ⟨4, 3, 8, 0, 8, 7, 659092839347558875419833867072483534198242541568000000⟩, + ⟨4, 3, 6, 1, 5, 7, -335376161349301274766154902270393461728547438592000000⟩, + ⟨4, 3, 7, 1, 6, 7, -676634341543854352806893769924515766185861578752000000⟩, + ⟨4, 3, 8, 1, 7, 7, 550747713195726455371809095857198800005612175360000000⟩, + ⟨4, 3, 6, 2, 4, 7, 120371212270174344411499918878794752157131210752000000⟩, + ⟨4, 3, 7, 2, 5, 7, 68624297208979742331686161881949255749001543680000000⟩, + ⟨4, 3, 8, 2, 6, 7, 29969774350965465487769786653759259483622604800000000⟩, + ⟨4, 3, 6, 3, 3, 7, 182734632261741832947766685345657051135355125760000000⟩, + ⟨4, 3, 7, 3, 4, 7, -275725285223236898784321110668271055281584078848000000⟩, + ⟨4, 3, 8, 3, 5, 7, 476842139357055856631728769871329398574190428160000000⟩, + ⟨4, 3, 6, 4, 2, 7, -555640239188175250573246583615732222269839114240000000⟩, + ⟨4, 3, 7, 4, 3, 7, 977939392438287983569145128857876301540560470016000000⟩, + ⟨4, 3, 8, 4, 4, 7, -682215315917054863870165631894973504463118008320000000⟩, + ⟨4, 3, 6, 5, 1, 7, 858626701299174788389425382494091319916657377280000000⟩, + ⟨4, 3, 7, 5, 2, 7, -1899553360404446209338964415483963685797263048704000000⟩, + ⟨4, 3, 8, 5, 3, 7, 954306099669715728178686128674544383115762073600000000⟩, + ⟨4, 3, 6, 6, 0, 7, -1259437603992238073431200768406931190347741528064000000⟩, + ⟨4, 3, 7, 6, 1, 7, 5218961346804153246109056925129284564903933247488000000⟩, + ⟨4, 3, 8, 6, 2, 7, -3403195419122287757337410678944928453683065126912000000⟩, + ⟨4, 3, 7, 7, 0, 7, -17690516283921138682650985026764514654213541724160000000⟩, + ⟨4, 3, 8, 7, 1, 7, 6363228286470069279407713478132635925502241013760000000⟩ +] + +def collectedFourData_13_0_34 : List CollectedFourTerm := [ + ⟨4, 4, 5, 0, 5, 8, -643736622497033665912167767125737609129917153280000000⟩, + ⟨4, 4, 6, 0, 6, 8, -744100840959722206580854800298213120740698357760000000⟩, + ⟨4, 4, 7, 0, 7, 8, 6819740411358681625909821631860146108639477760000000⟩, + ⟨4, 4, 8, 0, 8, 8, -306524264585267000528069926251885238212089610240000000⟩, + ⟨4, 4, 5, 1, 4, 8, -344494444390488536323359944627901160127830425600000000⟩, + ⟨4, 4, 6, 1, 5, 8, 467920109640947674440307180637083357234782535680000000⟩, + ⟨4, 4, 7, 1, 6, 8, 472023434832438775652227031063258557561480151040000000⟩, + ⟨4, 4, 8, 1, 7, 8, -256136203704551538776572492858833730760658124800000000⟩, + ⟨4, 4, 5, 2, 3, 8, -508263947465320090310271421705612708489734389760000000⟩, + ⟨4, 4, 6, 2, 4, 8, -167943095944768202408039385448334564257777582080000000⟩, + ⟨4, 4, 7, 2, 5, 8, -47872646262139704952435979134731258789730713600000000⟩, + ⟨4, 4, 8, 2, 6, 8, -13938041038057458048343220587390745563889664000000000⟩, + ⟨4, 4, 5, 3, 2, 8, 1380818038769093565466263095670768017334494822400000000⟩, + ⟨4, 4, 6, 3, 3, 8, -254953151169432796630753561901339702838322790400000000⟩, + ⟨4, 4, 7, 3, 4, 8, 192347311110857783094600986205661770095221800960000000⟩, + ⟨4, 4, 8, 3, 5, 8, -221764943212515428372507324031897882296372428800000000⟩, + ⟨4, 4, 5, 4, 1, 8, -382732664687814851530165380193236291819877171200000000⟩, + ⟨4, 4, 6, 4, 2, 8, 775234711363586993203669379937961513571686809600000000⟩, + ⟨4, 4, 7, 4, 3, 8, -682215315917054863870165631894973504463118008320000000⟩, + ⟨4, 4, 8, 4, 4, 8, 317277833282616065451075968985161288434424217600000000⟩, + ⟨4, 4, 5, 5, 0, 8, -4381533375580863203788665571807164360889403965440000000⟩, + ⟨4, 4, 6, 5, 1, 8, -1197964394953237614648641818850400125930648371200000000⟩, + ⟨4, 4, 7, 5, 2, 8, 1325137739506080248626550494697384554623223726080000000⟩, + ⟨4, 4, 8, 5, 3, 8, -443819076657030506798974840356365126596558848000000000⟩, + ⟨4, 4, 6, 6, 0, 8, 1757179697492557825325032872766816962986177986560000000⟩, + ⟨4, 4, 7, 6, 1, 8, -3640773028982542987729462781087706409076533493760000000⟩, + ⟨4, 4, 8, 6, 2, 8, 1582723875621290167990389786125795568883240796160000000⟩, + ⟨4, 4, 7, 7, 0, 8, 12340990912821471702882389329301030749468832563200000000⟩, + ⟨4, 4, 8, 7, 1, 8, -2959346171670148656240368852520134220056415436800000000⟩ +] + +def collectedFourData_13_0_35 : List CollectedFourTerm := [ + ⟨5, 0, 8, 0, 8, 5, 4233029083091993187126971313481419367077963104256000000⟩, + ⟨5, 0, 8, 1, 7, 5, 3537181635460826366169458427523876096551545733120000000⟩, + ⟨5, 0, 8, 2, 6, 5, 192481117784444262125672597032766716952287641600000000⟩, + ⟨5, 0, 8, 3, 5, 5, 3062522490671174956777011883478602911125832990720000000⟩, + ⟨5, 0, 8, 4, 4, 5, -4381533375580863203788665571807164360889403965440000000⟩, + ⟨5, 0, 8, 5, 3, 5, 6129038631451116793539247570600188312269566771200000000⟩, + ⟨5, 0, 8, 6, 2, 5, -21857050061187931468427903461241858596503923195904000000⟩, + ⟨5, 0, 8, 7, 1, 5, 40867885054926891943927122960508573323993462865920000000⟩ +] + +def collectedFourData_13_0_36 : List CollectedFourTerm := [ + ⟨5, 1, 7, 0, 7, 6, -8583230362177209368644295922569374214431703040000000⟩, + ⟨5, 1, 8, 0, 8, 6, 1157361519281703312494325613286393670534042746880000000⟩, + ⟨5, 1, 7, 1, 6, 6, -594082125291011683631212543585626036371623772160000000⟩, + ⟨5, 1, 8, 1, 7, 6, 967108382964850673883829157668505927085037977600000000⟩, + ⟨5, 1, 7, 2, 5, 6, 60251846277108329346082188175643269130511974400000000⟩, + ⟨5, 1, 8, 2, 6, 6, 52626673367744399890318942777882366986682368000000000⟩, + ⟨5, 1, 7, 3, 4, 6, -242085648606226478732821890490988043024822435840000000⟩, + ⟨5, 1, 8, 3, 5, 6, 837330812773097211804351239065850159306480025600000000⟩, + ⟨5, 1, 7, 4, 3, 6, 858626701299174788389425382494091319916657377280000000⟩, + ⟨5, 1, 8, 4, 4, 6, -1197964394953237614648641818850400125930648371200000000⟩, + ⟨5, 1, 7, 5, 2, 6, -1667799915206662916854230751822324064107962040320000000⟩, + ⟨5, 1, 8, 5, 3, 6, 1675753537949022941429961351841487626463870976000000000⟩, + ⟨5, 1, 7, 6, 1, 6, 4582226260710862072813645324328356603860394967040000000⟩, + ⟨5, 1, 8, 6, 2, 6, -5975982722838987169668091558408628791364466769920000000⟩, + ⟨5, 1, 7, 7, 0, 6, -15532199396601222873185631014001564570283199692800000000⟩, + ⟨5, 1, 8, 7, 1, 6, 11173775707312402003930434969271853629258176921600000000⟩ +] + +def collectedFourData_13_0_37 : List CollectedFourTerm := [ + ⟨5, 2, 6, 0, 6, 7, -1035933392249336409762234615338449993839081947136000000⟩, + ⟨5, 2, 7, 0, 7, 7, 18988815573670606214328176568886462540280758272000000⟩, + ⟨5, 2, 8, 0, 8, 7, -1280224549171301030796532896148584451996743892992000000⟩, + ⟨5, 2, 6, 1, 5, 7, 651435987972854274492415978604510687529478914048000000⟩, + ⟨5, 2, 7, 1, 6, 7, 1314297232715049107903971416074759110374444761088000000⟩, + ⟨5, 2, 8, 1, 7, 7, -1069774545769741344366979590814408673767288995840000000⟩, + ⟨5, 2, 6, 2, 4, 7, -233809520847372390944046256982006991095844569088000000⟩, + ⟨5, 2, 7, 2, 5, 7, -133296107485451252203364105982909723283732561920000000⟩, + ⟨5, 2, 8, 2, 6, 7, -58213408744071936624804159504653016336905011200000000⟩, + ⟨5, 2, 6, 3, 3, 7, -354944475556512329437925452611420230008638013440000000⟩, + ⟨5, 2, 7, 3, 4, 7, 535569889242727427399339926018481627094488973312000000⟩, + ⟨5, 2, 8, 3, 5, 7, -926220065580699670807284447803920036398146519040000000⟩, + ⟨5, 2, 6, 4, 2, 7, 1079277807691372824817272594139885074167428546560000000⟩, + ⟨5, 2, 7, 4, 3, 7, -1899553360404446209338964415483963685797263048704000000⟩, + ⟨5, 2, 8, 4, 4, 7, 1325137739506080248626550494697384554623223726080000000⟩, + ⟨5, 2, 6, 5, 1, 7, -1667799915206662916854230751822324064107962040320000000⟩, + ⟨5, 2, 7, 5, 2, 7, 3689699992580596183018388895451957362704542334976000000⟩, + ⟨5, 2, 8, 5, 3, 7, -1853647958655537275075775732107507279864424038400000000⟩, + ⟨5, 2, 6, 6, 0, 7, 2446336604682941408235958785815535714418940706816000000⟩, + ⟨5, 2, 7, 6, 1, 7, -10137331250584978196083865156551116010596411113472000000⟩, + ⟨5, 2, 8, 6, 2, 7, 6610380300141861137818348528175600158126928560128000000⟩, + ⟨5, 2, 7, 7, 0, 7, 34362129099460048069923530363380169214761411543040000000⟩, + ⟨5, 2, 8, 7, 1, 7, -12359959899404097526575224244121484999983041085440000000⟩ +] + +def collectedFourData_13_0_38 : List CollectedFourTerm := [ + ⟨5, 3, 5, 0, 5, 8, 900480788244852127070200221008251984453985894400000000⟩, + ⟨5, 3, 6, 0, 6, 8, 1040873687133056627683179656077368288613289164800000000⟩, + ⟨5, 3, 7, 0, 7, 8, -9539685962598524713554328643675911466306764800000000⟩, + ⟨5, 3, 8, 0, 8, 8, 428776617243314807219995520843617400400327475200000000⟩, + ⟨5, 3, 5, 1, 4, 8, 481890602444556341653439185482069721573490688000000000⟩, + ⟨5, 3, 6, 1, 5, 8, -654542641260152610379087673704947072018835046400000000⟩, + ⟨5, 3, 7, 1, 6, 8, -660282512775503427618059404035444189030462259200000000⟩, + ⟨5, 3, 8, 1, 7, 8, 358292075593355568516095773446515305274671104000000000⟩, + ⟨5, 3, 5, 2, 3, 8, 710976980422021183822727702743376223131192524800000000⟩, + ⟨5, 3, 6, 2, 4, 8, 234924542322932022293833242373694584141538918400000000⟩, + ⟨5, 3, 7, 2, 5, 8, 66965893713305364354449412443254233055100928000000000⟩, + ⟨5, 3, 8, 2, 6, 8, 19497008158172500816387039886909563962654720000000000⟩, + ⟨5, 3, 5, 3, 2, 8, -1931535464225097333584889673164073753066340352000000000⟩, + ⟨5, 3, 6, 3, 3, 8, 356637181274578941045091503176057776339156992000000000⟩, + ⟨5, 3, 7, 3, 4, 8, -269061992549105201636908473940323056579562700800000000⟩, + ⟨5, 3, 8, 3, 5, 8, 310212381726038828901024797883812578301313024000000000⟩, + ⟨5, 3, 5, 4, 1, 8, 535379531846852962148022710648474515040894976000000000⟩, + ⟨5, 3, 6, 4, 2, 8, -1084424809102219447643043979271430479447851008000000000⟩, + ⟨5, 3, 7, 4, 3, 8, 954306099669715728178686128674544383115762073600000000⟩, + ⟨5, 3, 8, 4, 4, 8, -443819076657030506798974840356365126596558848000000000⟩, + ⟨5, 3, 5, 5, 0, 8, 6129038631451116793539247570600188312269566771200000000⟩, + ⟨5, 3, 6, 5, 1, 8, 1675753537949022941429961351841487626463870976000000000⟩, + ⟨5, 3, 7, 5, 2, 8, -1853647958655537275075775732107507279864424038400000000⟩, + ⟨5, 3, 8, 5, 3, 8, 620829292632122803530019494220724270310359040000000000⟩, + ⟨5, 3, 6, 6, 0, 8, -2458003015190021349751354686578809917122858188800000000⟩, + ⟨5, 3, 7, 6, 1, 8, 5092837741997357353019910939109011545689738444800000000⟩, + ⟨5, 3, 8, 6, 2, 8, -2213968249258607369423753015847208622895189196800000000⟩, + ⟨5, 3, 7, 7, 0, 8, -17262999861331089396636734834045922354067931136000000000⟩, + ⟨5, 3, 8, 7, 1, 8, 4139634565170634644203099497255792541763108864000000000⟩ +] + +def collectedFourData_13_0_39 : List CollectedFourTerm := [ + ⟨6, 0, 7, 0, 7, 6, 12589921866507744646303007654822260383261130752000000⟩, + ⟨6, 0, 8, 0, 8, 6, -1697623212266117031114556599085337978418751340544000000⟩, + ⟨6, 0, 7, 1, 6, 6, 871402400273628000106015007365387065153193771008000000⟩, + ⟨6, 0, 8, 1, 7, 6, -1418559034792539284926600917324467764321981562880000000⟩, + ⟨6, 0, 7, 2, 5, 6, -88377685898344300938121983389242649205245214720000000⟩, + ⟨6, 0, 8, 2, 6, 6, -77193047120555269071015615817476273978369638400000000⟩, + ⟨6, 0, 7, 3, 4, 6, 355092345463058325641523795434019457936121659392000000⟩, + ⟨6, 0, 8, 3, 5, 6, -1228200696521754410628064248668114395971484385280000000⟩, + ⟨6, 0, 7, 4, 3, 6, -1259437603992238073431200768406931190347741528064000000⟩, + ⟨6, 0, 8, 4, 4, 6, 1757179697492557825325032872766816962986177986560000000⟩, + ⟨6, 0, 7, 5, 2, 6, 2446336604682941408235958785815535714418940706816000000⟩, + ⟨6, 0, 8, 5, 3, 6, -2458003015190021349751354686578809917122858188800000000⟩, + ⟨6, 0, 7, 6, 1, 6, -6721230604648035302759032455862445529697408253952000000⟩, + ⟨6, 0, 8, 6, 2, 6, 8765599008932868849926885405852776202684696887296000000⟩, + ⟨6, 0, 7, 7, 0, 6, 22782701683032240261936560195116039137854635376640000000⟩, + ⟨6, 0, 8, 7, 1, 6, -16389745721943031124837751533222941776658122670080000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1302.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1302.lean new file mode 100644 index 0000000000000000000000000000000000000000..883432a3b13351b587d1c30d7a21630fa36e92ac --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1302.lean @@ -0,0 +1,621 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PartsTrace +import OAI.Analysis.LaughlinFock.Sparse1301 + +namespace OAI + +/-! Sparse1302. -/ +namespace LaughlinFock +def collectedFourData_13_0_40 : List CollectedFourTerm := [ + ⟨6, 1, 6, 0, 6, 7, 2846193449844367501734537195905979341670545620992000000⟩, + ⟨6, 1, 7, 0, 7, 7, -52171155897131102762426606947217349580878249984000000⟩, + ⟨6, 1, 8, 0, 8, 7, 3517375492906503007788030656661880327375970893824000000⟩, + ⟨6, 1, 6, 1, 5, 7, -1789799282302669394358319262106299790960472621056000000⟩, + ⟨6, 1, 7, 1, 6, 7, -3610989087609022714810565959494225231835023015936000000⟩, + ⟨6, 1, 8, 1, 7, 7, 2939170923305104747215349084504213734191246868480000000⟩, + ⟨6, 1, 6, 2, 4, 7, 642384087361160809977090583051533595223770791936000000⟩, + ⟨6, 1, 7, 2, 5, 7, 366226738951888576489959821650718546863576842240000000⟩, + ⟨6, 1, 8, 2, 6, 7, 159939455470908929353733031974517216553363046400000000⟩, + ⟨6, 1, 6, 3, 3, 7, 975198452859831281867130860159482881847779655680000000⟩, + ⟨6, 1, 7, 3, 4, 7, -1471460927991435379129045793603123220297352740864000000⟩, + ⟨6, 1, 8, 3, 5, 7, 2544759637534404987100029771579759182251693178880000000⟩, + ⟨6, 1, 6, 4, 2, 7, -2965280827702310206497675273640848035802324664320000000⟩, + ⟨6, 1, 7, 4, 3, 7, 5218961346804153246109056925129284564903933247488000000⟩, + ⟨6, 1, 8, 4, 4, 7, -3640773028982542987729462781087706409076533493760000000⟩, + ⟨6, 1, 6, 5, 1, 7, 4582226260710862072813645324328356603860394967040000000⟩, + ⟨6, 1, 7, 5, 2, 7, -10137331250584978196083865156551116010596411113472000000⟩, + ⟨6, 1, 8, 5, 3, 7, 5092837741997357353019910939109011545689738444800000000⟩, + ⟨6, 1, 6, 6, 0, 7, -6721230604648035302759032455862445529697408253952000000⟩, + ⟨6, 1, 7, 6, 1, 7, 27851989346215669041289288913573180647587534864384000000⟩, + ⟨6, 1, 8, 6, 2, 7, -18161805818800761065740035199208401577346456354816000000⟩, + ⟨6, 1, 7, 7, 0, 7, -94408836994077861417079175936591038336163779706880000000⟩, + ⟨6, 1, 8, 7, 1, 7, 33958589586188256626527410728666316200197415239680000000⟩ +] + +def collectedFourData_13_0_41 : List CollectedFourTerm := [ + ⟨6, 2, 5, 0, 5, 8, -3211246469684236312830884044096923768578950299648000000⟩, + ⟨6, 2, 6, 0, 6, 8, -3711908123779286896940164073919929814697918857216000000⟩, + ⟨6, 2, 7, 0, 7, 8, 34019918324965894480584020393567544223482249216000000⟩, + ⟨6, 2, 8, 0, 8, 8, -1529080260656649529616010504317306053170334531584000000⟩, + ⟨6, 2, 5, 1, 4, 8, -1718492516525865981479553058274437597219478568960000000⟩, + ⟨6, 2, 6, 1, 5, 8, 2334194991656976933997168048568841887027180863488000000⟩, + ⟨6, 2, 7, 1, 6, 8, 2354664214743943545509573503302777978509919780864000000⟩, + ⟨6, 2, 8, 1, 7, 8, -1277722054578856417657610995115790273502437703680000000⟩, + ⟨6, 2, 5, 2, 3, 8, -2535448116396864271144926251879788177052103868416000000⟩, + ⟨6, 2, 6, 2, 4, 8, -837775349596430635447339056829606973661121609728000000⟩, + ⟨6, 2, 7, 2, 5, 8, -238810191825689969486876326396085438332545269760000000⟩, + ⟨6, 2, 8, 2, 6, 8, -69529188667500841754995083237568494543726182400000000⟩, + ⟨6, 2, 5, 3, 2, 8, 6888138560571012381986747111308157256875208867840000000⟩, + ⟨6, 2, 6, 3, 3, 8, -1271820458888813860197761986354574670764326256640000000⟩, + ⟨6, 2, 7, 3, 4, 8, 959514500452153130423450644302717206786092302336000000⟩, + ⟨6, 2, 8, 3, 5, 8, -1106262819456410308766569277760165416349550510080000000⟩, + ⟨6, 2, 5, 4, 1, 8, -1909241878369673562969702190989143977005856849920000000⟩, + ⟨6, 2, 6, 4, 2, 8, 3867217807783598808051107936534339017025897103360000000⟩, + ⟨6, 2, 7, 4, 3, 8, -3403195419122287757337410678944928453683065126912000000⟩, + ⟨6, 2, 8, 4, 4, 8, 1582723875621290167990389786125795568883240796160000000⟩, + ⟨6, 2, 5, 5, 0, 8, -21857050061187931468427903461241858596503923195904000000⟩, + ⟨6, 2, 6, 5, 1, 8, -5975982722838987169668091558408628791364466769920000000⟩, + ⟨6, 2, 7, 5, 2, 8, 6610380300141861137818348528175600158126928560128000000⟩, + ⟨6, 2, 8, 5, 3, 8, -2213968249258607369423753015847208622895189196800000000⟩, + ⟨6, 2, 6, 6, 0, 8, 8765599008932868849926885405852776202684696887296000000⟩, + ⟨6, 2, 7, 6, 1, 8, -18161805818800761065740035199208401577346456354816000000⟩, + ⟨6, 2, 8, 6, 2, 8, 7895335266710323885922120520621157852187675590656000000⟩, + ⟨6, 2, 7, 7, 0, 8, 61562387653944306331832374201916238163432565637120000000⟩, + ⟨6, 2, 8, 7, 1, 8, -14762543584186272475444932408254346598774871162880000000⟩ +] + +def collectedFourData_13_0_42 : List CollectedFourTerm := [ + ⟨7, 0, 6, 0, 6, 7, -9647634505377938352995985031992201945149803069440000000⟩, + ⟨7, 0, 7, 0, 7, 7, 176842597907790207852980038031943025875096698880000000⟩, + ⟨7, 0, 8, 0, 8, 7, -11922714942510697637256356090253795429094973767680000000⟩, + ⟨7, 0, 6, 1, 5, 7, 6066815069997472055676294718675159046590216273920000000⟩, + ⟨7, 0, 7, 1, 6, 7, 12240033410963317950082969513869561523686887915520000000⟩, + ⟨7, 0, 8, 1, 7, 7, -9962796737668129187000981264879011610937104793600000000⟩, + ⟨7, 0, 6, 2, 4, 7, -2177465093692115461643683218889547253968032235520000000⟩, + ⟨7, 0, 7, 2, 5, 7, -1241384953541186294849777616941940648335690956800000000⟩, + ⟨7, 0, 8, 2, 6, 7, -542140735183293314779247624378029893639733248000000000⟩, + ⟨7, 0, 6, 3, 3, 7, -3305593386112299168374601386751028518429759897600000000⟩, + ⟨7, 0, 7, 3, 4, 7, 4987755566292189551383335345448400201391255060480000000⟩, + ⟨7, 0, 8, 3, 5, 7, -8625875689620622072499576308749382035755866521600000000⟩, + ⟨7, 0, 6, 4, 2, 7, 10051300495066760193505874499935534919893542502400000000⟩, + ⟨7, 0, 7, 4, 3, 7, -17690516283921138682650985026764514654213541724160000000⟩, + ⟨7, 0, 8, 4, 4, 7, 12340990912821471702882389329301030749468832563200000000⟩, + ⟨7, 0, 6, 5, 1, 7, -15532199396601222873185631014001564570283199692800000000⟩, + ⟨7, 0, 7, 5, 2, 7, 34362129099460048069923530363380169214761411543040000000⟩, + ⟨7, 0, 8, 5, 3, 7, -17262999861331089396636734834045922354067931136000000000⟩, + ⟨7, 0, 6, 6, 0, 7, 22782701683032240261936560195116039137854635376640000000⟩, + ⟨7, 0, 7, 6, 1, 7, -94408836994077861417079175936591038336163779706880000000⟩, + ⟨7, 0, 8, 6, 2, 7, 61562387653944306331832374201916238163432565637120000000⟩, + ⟨7, 0, 7, 7, 0, 7, 320014071231339305559734377165695341956968323481600000000⟩, + ⟨7, 0, 8, 7, 1, 7, -115108149329622102223949109973891712593803450777600000000⟩ +] + +def collectedFourData_13_0_43 : List CollectedFourTerm := [ + ⟨7, 1, 5, 0, 5, 8, 6004325892044116776726842441369818665055200215040000000⟩, + ⟨7, 1, 6, 0, 6, 8, 6940453268505551286821575362685942329440395591680000000⟩, + ⟨7, 1, 7, 0, 7, 8, -63609778437188752306220739208424358774759751680000000⟩, + ⟨7, 1, 8, 0, 8, 8, 2859044388759443364393857116895203516783861432320000000⟩, + ⟨7, 1, 5, 1, 4, 8, 3213203723124660190351993754549331042941848780800000000⟩, + ⟨7, 1, 6, 1, 5, 8, -4364432178531539792902434002812959780419917578240000000⟩, + ⟨7, 1, 7, 1, 6, 8, -4402705131832189443205110865177734789414487326720000000⟩, + ⟨7, 1, 8, 1, 7, 8, 2389059727295865904447677841006989561641199206400000000⟩, + ⟨7, 1, 5, 2, 3, 8, 4740731338106579061960782219596659184853770567680000000⟩, + ⟨7, 1, 6, 2, 4, 8, 1566455976140875315016915697302654486519941693440000000⟩, + ⟨7, 1, 7, 2, 5, 8, 446522629639203060737637556237073229707791564800000000⟩, + ⟨7, 1, 8, 2, 6, 8, 130004318170615639361750650940465913110986752000000000⟩, + ⟨7, 1, 5, 3, 2, 8, -12879306866561021037143781311738659053862335283200000000⟩, + ⟨7, 1, 6, 3, 3, 8, 2378025039008740174239319360839105902613312307200000000⟩, + ⟨7, 1, 7, 3, 4, 8, -1794081461278537493395223432400124658721258209280000000⟩, + ⟨7, 1, 8, 3, 5, 8, 2068468600269414326245908700956701040520357478400000000⟩, + ⟨7, 1, 5, 4, 1, 8, 3569863152110279617058466390650868552278055321600000000⟩, + ⟨7, 1, 6, 4, 2, 8, -7230848280459889444456170978978360023824780492800000000⟩, + ⟨7, 1, 7, 4, 3, 8, 6363228286470069279407713478132635925502241013760000000⟩, + ⟨7, 1, 8, 4, 4, 8, -2959346171670148656240368852520134220056415436800000000⟩, + ⟨7, 1, 5, 5, 0, 8, 40867885054926891943927122960508573323993462865920000000⟩, + ⟨7, 1, 6, 5, 1, 8, 11173775707312402003930434969271853629258176921600000000⟩, + ⟨7, 1, 7, 5, 2, 8, -12359959899404097526575224244121484999983041085440000000⟩, + ⟨7, 1, 8, 5, 3, 8, 4139634565170634644203099497255792541763108864000000000⟩, + ⟨7, 1, 6, 6, 0, 8, -16389745721943031124837751533222941776658122670080000000⟩, + ⟨7, 1, 7, 6, 1, 8, 33958589586188256626527410728666316200197415239680000000⟩, + ⟨7, 1, 8, 6, 2, 8, -14762543584186272475444932408254346598774871162880000000⟩, + ⟨7, 1, 7, 7, 0, 8, -115108149329622102223949109973891712593803450777600000000⟩, + ⟨7, 1, 8, 7, 1, 8, 27602715491245157720298066956593452779980613222400000000⟩ +] + +def collectedFourData_13_0 : List (List CollectedFourTerm) := [ + collectedFourData_13_0_0, + collectedFourData_13_0_1, + collectedFourData_13_0_2, + collectedFourData_13_0_3, + collectedFourData_13_0_4, + collectedFourData_13_0_5, + collectedFourData_13_0_6, + collectedFourData_13_0_7, + collectedFourData_13_0_8, + collectedFourData_13_0_9, + collectedFourData_13_0_10, + collectedFourData_13_0_11, + collectedFourData_13_0_12, + collectedFourData_13_0_13, + collectedFourData_13_0_14, + collectedFourData_13_0_15, + collectedFourData_13_0_16, + collectedFourData_13_0_17, + collectedFourData_13_0_18, + collectedFourData_13_0_19, + collectedFourData_13_0_20, + collectedFourData_13_0_21, + collectedFourData_13_0_22, + collectedFourData_13_0_23, + collectedFourData_13_0_24, + collectedFourData_13_0_25, + collectedFourData_13_0_26, + collectedFourData_13_0_27, + collectedFourData_13_0_28, + collectedFourData_13_0_29, + collectedFourData_13_0_30, + collectedFourData_13_0_31, + collectedFourData_13_0_32, + collectedFourData_13_0_33, + collectedFourData_13_0_34, + collectedFourData_13_0_35, + collectedFourData_13_0_36, + collectedFourData_13_0_37, + collectedFourData_13_0_38, + collectedFourData_13_0_39, + collectedFourData_13_0_40, + collectedFourData_13_0_41, + collectedFourData_13_0_42, + collectedFourData_13_0_43 +] + +theorem collectedFourChecked_13_0 : collectNumericRowParts 13 0 = collectedFourData_13_0 := by + decide +kernel + +def collectedFourData_13_1_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_1 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_2 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_3 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_4 : List CollectedFourTerm := [ + ⟨0, 5, 8, 1, 8, 4, -1473291397320698563721013237154249730983677709516800000⟩, + ⟨0, 5, 8, 2, 7, 4, -632597943329587644778594219209322163404621322649600000⟩, + ⟨0, 5, 8, 3, 6, 4, 33969832345143450995864240311266805959761068032000000⟩, + ⟨0, 5, 8, 4, 5, 4, 462367905706368197519230931663497128012023228006400000⟩, + ⟨0, 5, 8, 5, 4, 4, 231462436885259661751579783305880420260206818099200000⟩, + ⟨0, 5, 8, 6, 3, 4, -1228926842606995982214404035579599850430618035814400000⟩, + ⟨0, 5, 8, 7, 2, 4, 483369648897650136264088739570794639046395664793600000⟩ +] + +def collectedFourData_13_1_5 : List CollectedFourTerm := [ + ⟨0, 6, 7, 0, 8, 5, 2247969292798250488804325507396097955581740974080000000⟩, + ⟨0, 6, 7, 1, 7, 5, -177836011356471642848994524927038842907027046400000000⟩, + ⟨0, 6, 8, 1, 8, 5, -2569983217398187879639508278742126344703953600512000000⟩, + ⟨0, 6, 7, 2, 6, 5, -111538242610512642548086684234388803052453756928000000⟩, + ⟨0, 6, 8, 2, 7, 5, -1103492561399760688898220643699760270438735806464000000⟩, + ⟨0, 6, 7, 3, 5, 5, -267522957412081842493476948599917763336173780992000000⟩, + ⟨0, 6, 8, 3, 6, 5, 59256369231242693210590787632952809343554682880000000⟩, + ⟨0, 6, 7, 4, 4, 5, 138310675636318606746364728245223220459352358912000000⟩, + ⟨0, 6, 8, 4, 5, 5, 806546322126019885089482488385846732383454232576000000⟩, + ⟨0, 6, 7, 5, 3, 5, 157768789128778606731362662527098924319935299584000000⟩, + ⟨0, 6, 8, 5, 4, 5, 403758943638031512264346494993718296924471164928000000⟩, + ⟨0, 6, 7, 6, 2, 5, 1116608060584631538148860505393713718219279171584000000⟩, + ⟨0, 6, 8, 6, 3, 5, -2143718049704078109949280320115852398571915575296000000⟩, + ⟨0, 6, 7, 7, 1, 5, -5776811856253007210677491066001779383547967045632000000⟩, + ⟨0, 6, 8, 7, 2, 5, 843181388098615413549179789953892948072070119424000000⟩ +] + +def collectedFourData_13_1_6 : List CollectedFourTerm := [ + ⟨0, 7, 6, 0, 7, 6, 1055278715479481142192276613696004181140982202368000000⟩, + ⟨0, 7, 7, 0, 8, 6, 3095450102873909644399632757240610874958156922880000000⟩, + ⟨0, 7, 6, 1, 6, 6, -388875818196282706743446877698285119039988563968000000⟩, + ⟨0, 7, 7, 1, 7, 6, -244879901790313428071746960476868398515906150400000000⟩, + ⟨0, 7, 8, 1, 8, 6, -1769431379726903991606956448445188507876684988416000000⟩, + ⟨0, 7, 6, 2, 5, 6, -6986557252418132867146537293321777751032594432000000⟩, + ⟨0, 7, 7, 2, 6, 6, -153587980791903437995393782162038070344845099008000000⟩, + ⟨0, 7, 8, 2, 7, 6, -759753741665554675167067096968558106829496778752000000⟩, + ⟨0, 7, 6, 3, 4, 6, 113131312717740461252531772453750288038240452608000000⟩, + ⟨0, 7, 7, 3, 5, 6, -368378682349146086426705723780218148408222810112000000⟩, + ⟨0, 7, 8, 3, 6, 6, 40797962592375701741925223119229824450523299840000000⟩, + ⟨0, 7, 6, 4, 3, 6, -142840700180164589448072358020435642145176551424000000⟩, + ⟨0, 7, 7, 4, 4, 6, 190453578035341204188609913471086786190856159232000000⟩, + ⟨0, 7, 8, 4, 5, 6, 555306494576220029221796015576103704395637587968000000⟩, + ⟨0, 7, 6, 5, 2, 6, 310069525175929955667569988310547542883702931456000000⟩, + ⟨0, 7, 7, 5, 3, 6, 217247369038149688933005815609722403137020493824000000⟩, + ⟨0, 7, 8, 5, 4, 6, 277987708200597182061134507415212719914828693504000000⟩, + ⟨0, 7, 6, 6, 1, 6, -580699005126251704693839223750365932063966625792000000⟩, + ⟨0, 7, 7, 6, 2, 6, 1537567504627269799651792103303040542174110285824000000⟩, + ⟨0, 7, 8, 6, 3, 6, -1475948154351565951561600103480884996815011708928000000⟩, + ⟨0, 7, 6, 7, 0, 6, -172312498602233687768599004356174228596556038144000000⟩, + ⟨0, 7, 7, 7, 1, 6, -7954660640609756318023919034299979323782465585152000000⟩, + ⟨0, 7, 8, 7, 2, 6, 580529708055373375742261282268303288197323948032000000⟩ +] + +def collectedFourData_13_1_7 : List CollectedFourTerm := [ + ⟨0, 8, 5, 0, 6, 7, 2247969292798250488804325507396097955581740974080000000⟩, + ⟨0, 8, 6, 0, 7, 7, 3095450102873909644399632757240610874958156922880000000⟩, + ⟨0, 8, 7, 0, 8, 7, 4539943428608082595165545548282804100053493350400000000⟩, + ⟨0, 8, 5, 1, 5, 7, -736845703366731737212836452860515263423132467200000000⟩, + ⟨0, 8, 6, 1, 6, 7, -1140689823251025990101449466199566751296787578880000000⟩, + ⟨0, 8, 7, 1, 7, 7, -359153229412081996797286359890003219428933632000000000⟩, + ⟨0, 8, 8, 1, 8, 7, -1730091607099055956101376266949573862340710891520000000⟩, + ⟨0, 8, 5, 2, 4, 7, 553518087890711077909828668644291897841124638720000000⟩, + ⟨0, 8, 6, 2, 5, 7, -20493675318662935454721584513031320173144965120000000⟩, + ⟨0, 8, 7, 2, 6, 7, -225259888202368328173922334414919802148240752640000000⟩, + ⟨0, 8, 8, 2, 7, 7, -742862134682246429673068574249085759240211005440000000⟩, + ⟨0, 8, 5, 3, 3, 7, -165283582000758824557906252051799416782150696960000000⟩, + ⟨0, 8, 6, 3, 4, 7, 331848191812790617326591485571557131975686881280000000⟩, + ⟨0, 8, 7, 3, 5, 7, -540282777169493430903942100045570253022780456960000000⟩, + ⟨0, 8, 8, 3, 6, 7, 39890901380252728932705849825048252545551564800000000⟩, + ⟨0, 8, 5, 4, 2, 7, -341357679787317168268127728558740652225147699200000000⟩, + ⟨0, 8, 6, 4, 3, 7, -418994767525820581511679630017321232542560419840000000⟩, + ⟨0, 8, 7, 4, 4, 7, 279328834683420716660361036144462813844796866560000000⟩, + ⟨0, 8, 8, 4, 5, 7, 542960363787713552450694424593374657737874472960000000⟩, + ⟨0, 8, 5, 5, 1, 7, -115247584921241889689372332564151674235560919040000000⟩, + ⟨0, 8, 6, 5, 2, 7, 909527245764447674894648158973979664212515880960000000⟩, + ⟨0, 8, 7, 5, 3, 7, 318625961546413066605372220105358406569605201920000000⟩, + ⟨0, 8, 8, 5, 4, 7, 271807206735976423399995462394654776502391930880000000⟩, + ⟨0, 8, 5, 6, 0, 7, 6119511022185254760034287447074268382170835845120000000⟩, + ⟨0, 8, 6, 6, 1, 7, -1703364967747029222454909141422118773235352862720000000⟩, + ⟨0, 8, 7, 6, 2, 7, 2255074143237851524687957997010093846139156561920000000⟩, + ⟨0, 8, 8, 6, 3, 7, -1443133395063390480539325601987701366390427484160000000⟩, + ⟨0, 8, 6, 7, 0, 7, -505444423071106490877517386019013528740996055040000000⟩, + ⟨0, 8, 7, 7, 1, 7, -11666706973765967703503572217162701403322486620160000000⟩, + ⟨0, 8, 8, 7, 2, 7, 567622789493697241869461487690886518227903447040000000⟩ +] + +def collectedFourData_13_1_8 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_9 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_10 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_11 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_12 : List CollectedFourTerm := [ + ⟨1, 4, 8, 1, 8, 4, -453380649476523768531151918143517911287368935014400000⟩, + ⟨1, 4, 8, 2, 7, 4, -194671377926909045756018488049347841050538724556800000⟩, + ⟨1, 4, 8, 3, 6, 4, 10453644594177517978869414829539866590845075456000000⟩, + ⟨1, 4, 8, 4, 5, 4, 142285946804196546137500902706303508459816170291200000⟩, + ⟨1, 4, 8, 5, 4, 4, 71228672179380807049358773510697759740939311513600000⟩, + ⟨1, 4, 8, 6, 3, 4, -378181567525308270780465795599109607841821045555200000⟩, + ⟨1, 4, 8, 7, 2, 4, 148748880060658039565051974537734930300035452108800000⟩ +] + +def collectedFourData_13_1_13 : List CollectedFourTerm := [ + ⟨1, 5, 7, 0, 8, 5, -736845703366731737212836452860515263423132467200000000⟩, + ⟨1, 5, 7, 1, 7, 5, 58291588453496611057002198872502523895218176000000000⟩, + ⟨1, 5, 8, 1, 8, 5, 842396334118616022245097416289952615503054766080000000⟩, + ⟨1, 5, 7, 2, 6, 5, 36560319169808332114356618481643228359053803520000000⟩, + ⟨1, 5, 8, 2, 7, 5, 361705898372134508102340421150046179641010421760000000⟩, + ⟨1, 5, 7, 3, 5, 5, 87689428121892483565303653198918438861699809280000000⟩, + ⟨1, 5, 8, 3, 6, 5, -19423219527524216994272923722722093688894259200000000⟩, + ⟨1, 5, 7, 4, 4, 5, -45335862637834332107138456330769049254447022080000000⟩, + ⟨1, 5, 8, 4, 5, 5, -264372024088024158482225389671872019262435491840000000⟩, + ⟨1, 5, 7, 5, 3, 5, -51713897857654457621765620336282919030552002560000000⟩, + ⟨1, 5, 8, 5, 4, 5, -132345243224047239748347716617957658685100523520000000⟩, + ⟨1, 5, 7, 6, 2, 5, -366004933618230854997719873855743997803820482560000000⟩, + ⟨1, 5, 8, 6, 3, 5, 702673937413042743354768922708985990976519536640000000⟩, + ⟨1, 5, 7, 7, 1, 5, 1893539653355061639227254073955723645582972026880000000⟩, + ⟨1, 5, 8, 7, 2, 5, -276380369149028712887366748615835468395876188160000000⟩ +] + +def collectedFourData_13_1_14 : List CollectedFourTerm := [ + ⟨1, 6, 6, 0, 7, 6, -388875818196282706743446877698285119039988563968000000⟩, + ⟨1, 6, 7, 0, 8, 6, -1140689823251025990101449466199566751296787578880000000⟩, + ⟨1, 6, 6, 1, 6, 6, 143302806888431675418115940692858103555652845568000000⟩, + ⟨1, 6, 7, 1, 7, 6, 90239545981239021001442234058624914633942630400000000⟩, + ⟨1, 6, 8, 1, 8, 6, 652044872544249096036277801967279019781433327616000000⟩, + ⟨1, 6, 6, 2, 5, 6, 2574583499179939423122733730699766984534392832000000⟩, + ⟨1, 6, 7, 2, 6, 6, 56597987640098221881702334834912177700217028608000000⟩, + ⟨1, 6, 8, 2, 7, 6, 279973293864491394461996540651093463277504561152000000⟩, + ⟨1, 6, 6, 3, 4, 6, -41689490322697848427286817609479094343940702208000000⟩, + ⟨1, 6, 7, 3, 5, 6, 135749503333347706087723827166045310428498624512000000⟩, + ⟨1, 6, 8, 3, 6, 6, -15034266162226904191825133680945932512620707840000000⟩, + ⟨1, 6, 6, 4, 3, 6, 52637557585014585580521867667284765022013620224000000⟩, + ⟨1, 6, 7, 4, 4, 6, -70183156260525341466065711030566578786907717632000000⟩, + ⟨1, 6, 8, 4, 5, 6, -204633396144941040078672064613915836729490669568000000⟩, + ⟨1, 6, 6, 5, 2, 6, -114262268850685610505381194262902007810968518656000000⟩, + ⟨1, 6, 7, 5, 3, 6, -80056810723520093051421384136354820356124442624000000⟩, + ⟨1, 6, 8, 5, 4, 6, -102439948697248852841748265839738070396047458304000000⟩, + ⟨1, 6, 6, 6, 1, 6, 213990671309649229462641001311505989039336456192000000⟩, + ⟨1, 6, 7, 6, 2, 6, -566601801612450186726219750289790620279844634624000000⟩, + ⟨1, 6, 8, 6, 3, 6, 543894743369263630945608537181802001821784342528000000⟩, + ⟨1, 6, 6, 7, 0, 6, 63498072022558815174396294688919436946197970944000000⟩, + ⟨1, 6, 7, 7, 1, 6, 2931334745707787346679106610000459411739537047552000000⟩, + ⟨1, 6, 8, 7, 2, 6, -213928284438777745137544546967676589296354066432000000⟩ +] + +def collectedFourData_13_1_15 : List CollectedFourTerm := [ + ⟨1, 7, 5, 0, 6, 7, -177836011356471642848994524927038842907027046400000000⟩, + ⟨1, 7, 6, 0, 7, 7, -244879901790313428071746960476868398515906150400000000⟩, + ⟨1, 7, 7, 0, 8, 7, -359153229412081996797286359890003219428933632000000000⟩, + ⟨1, 7, 5, 1, 5, 7, 58291588453496611057002198872502523895218176000000000⟩, + ⟨1, 7, 6, 1, 6, 7, 90239545981239021001442234058624914633942630400000000⟩, + ⟨1, 7, 7, 1, 7, 7, 28412477870164876296001323430086638630338560000000000⟩, + ⟨1, 7, 8, 1, 8, 7, 136866901017502831583325129708059840355080601600000000⟩, + ⟨1, 7, 5, 2, 4, 7, -43788609248133219361452966807955972562721177600000000⟩, + ⟨1, 7, 6, 2, 5, 7, 1621247002074894531876458480768918297876889600000000⟩, + ⟨1, 7, 7, 2, 6, 7, 17820225643139658520045625196416986126693171200000000⟩, + ⟨1, 7, 8, 2, 7, 7, 58767546088317971890565940632175812285772595200000000⟩, + ⟨1, 7, 5, 3, 3, 7, 13075522454818175582655309309673550262357196800000000⟩, + ⟨1, 7, 6, 3, 4, 7, -26252386541447485167235855884984881871480422400000000⟩, + ⟨1, 7, 7, 3, 5, 7, 42741568759072529923640259041802568793377996800000000⟩, + ⟨1, 7, 8, 3, 6, 7, -3155754312839355375069881297322596980752384000000000⟩, + ⟨1, 7, 5, 4, 2, 7, 27004678584248048807263631756116857754484736000000000⟩, + ⟨1, 7, 6, 4, 3, 7, 33146519605377598443477506552084462417687347200000000⟩, + ⟨1, 7, 7, 4, 4, 7, -22097599809789295302690174604562459005865164800000000⟩, + ⟨1, 7, 8, 4, 5, 7, -42953391636623048670198098253201911019523276800000000⟩, + ⟨1, 7, 5, 5, 1, 7, 9117193409411616937749393506592885459596083200000000⟩, + ⟨1, 7, 6, 5, 2, 7, -71952360792902986177225297659209754981747916800000000⟩, + ⟨1, 7, 7, 5, 3, 7, -25206380842284924442742433012420735573531033600000000⟩, + ⟨1, 7, 8, 5, 4, 7, -21502566631459796883542880307623421396018790400000000⟩, + ⟨1, 7, 5, 6, 0, 7, -484112231925874337647840636937066427417467289600000000⟩, + ⟨1, 7, 6, 6, 1, 7, 134752566558151338093696270881809511929715097600000000⟩, + ⟨1, 7, 7, 6, 2, 7, -178398073421781321484516662057344923560679833600000000⟩, + ⟨1, 7, 8, 6, 3, 7, 114165744014204143505236408298197524637600972800000000⟩, + ⟨1, 7, 6, 7, 0, 7, 39985519575069040137489278332568098856710963200000000⟩, + ⟨1, 7, 7, 7, 1, 7, 922948832319959995690765092727039698500635852800000000⟩, + ⟨1, 7, 8, 7, 2, 7, -44904426925218102437753848509770905821590323200000000⟩ +] + +def collectedFourData_13_1_16 : List CollectedFourTerm := [ + ⟨1, 8, 4, 0, 5, 8, -1473291397320698563721013237154249730983677709516800000⟩, + ⟨1, 8, 5, 0, 6, 8, -2569983217398187879639508278742126344703953600512000000⟩, + ⟨1, 8, 6, 0, 7, 8, -1769431379726903991606956448445188507876684988416000000⟩, + ⟨1, 8, 7, 0, 8, 8, -1730091607099055956101376266949573862340710891520000000⟩, + ⟨1, 8, 4, 1, 4, 8, -453380649476523768531151918143517911287368935014400000⟩, + ⟨1, 8, 5, 1, 5, 8, 842396334118616022245097416289952615503054766080000000⟩, + ⟨1, 8, 6, 1, 6, 8, 652044872544249096036277801967279019781433327616000000⟩, + ⟨1, 8, 7, 1, 7, 8, 136866901017502831583325129708059840355080601600000000⟩, + ⟨1, 8, 8, 1, 8, 8, 494480330430950200726183511143399172302367096832000000⟩, + ⟨1, 8, 4, 2, 3, 8, -711857898563046315707809735668071268520000330137600000⟩, + ⟨1, 8, 5, 2, 4, 8, -632807663771380186299684046538708667252665745408000000⟩, + ⟨1, 8, 6, 2, 5, 8, 11714662162090765456420361455753370712548573184000000⟩, + ⟨1, 8, 7, 2, 6, 8, 85842532649019111447989782128331370257849516032000000⟩, + ⟨1, 8, 8, 2, 7, 8, 212318649668639666950407760545116238906082197504000000⟩, + ⟨1, 8, 4, 3, 2, 8, 1899106543275257335061909489898738651801887283609600000⟩, + ⟨1, 8, 5, 3, 3, 8, 188959890695237332593725815104979012338365497344000000⟩, + ⟨1, 8, 6, 3, 4, 8, -189692156030564430810085232639465193763604791296000000⟩, + ⟨1, 8, 7, 3, 5, 8, 205892146662209597348228040230011960954818920448000000⟩, + ⟨1, 8, 8, 3, 6, 8, -11401284194870064898422963461668440525955399680000000⟩, + ⟨1, 8, 4, 4, 1, 8, -24381081986271967533555274264629920563608944640000000⟩, + ⟨1, 8, 5, 4, 2, 8, 390256001714042852899954504629478365871346810880000000⟩, + ⟨1, 8, 6, 4, 3, 8, 239507168574044898013359890365346196978388697088000000⟩, + ⟨1, 8, 7, 4, 4, 8, -106447245457133734016314596975383280887349116928000000⟩, + ⟨1, 8, 8, 4, 5, 8, -155184395436053685485589500798761125685216935936000000⟩, + ⟨1, 8, 4, 5, 0, 8, -7825562215269521510674289329935241680351754872422400000⟩, + ⟨1, 8, 5, 5, 1, 8, 131756407902074446024720292454715631201006125056000000⟩, + ⟨1, 8, 6, 5, 2, 8, -519906958887184749205705383219515958047614697472000000⟩, + ⟨1, 8, 7, 5, 3, 8, -121422680820568314774044329752500886067841335296000000⟩, + ⟨1, 8, 8, 5, 4, 8, -77685665226525769263706293140420973951354667008000000⟩, + ⟨1, 8, 5, 6, 0, 8, -6996110078586734638789406789436755800461429178368000000⟩, + ⟨1, 8, 6, 6, 1, 8, 973683091276716755295604217527568964311008149504000000⟩, + ⟨1, 8, 7, 6, 2, 8, -859368604466966094033152511797218418979080503296000000⟩, + ⟨1, 8, 8, 6, 3, 8, 412464331437004233328416878165309865708912377856000000⟩, + ⟨1, 8, 6, 7, 0, 8, 288923805316595486801455266761347397551524937728000000⟩, + ⟨1, 8, 7, 7, 1, 8, 4445974302368114690983820725942830822543335620608000000⟩, + ⟨1, 8, 8, 7, 2, 8, -162233203928207331637710233436918745176226136064000000⟩ +] + +def collectedFourData_13_1_17 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_18 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_19 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_20 : List CollectedFourTerm := [ + ⟨2, 3, 8, 1, 8, 4, -711857898563046315707809735668071268520000330137600000⟩, + ⟨2, 3, 8, 2, 7, 4, -305655651959177220905474989830133564653171847987200000⟩, + ⟨2, 3, 8, 3, 6, 4, 16413381298315603123929581772333050170152321024000000⟩, + ⟨2, 3, 8, 4, 5, 4, 223404715671116108923676055631544180842267725004800000⟩, + ⟨2, 3, 8, 5, 4, 4, 111836914419691506884080813308056228032774825574400000⟩, + ⟨2, 3, 8, 6, 3, 4, -593787000492143030401373243525397648411984710860800000⟩, + ⟨2, 3, 8, 7, 2, 4, 233552237608388665506018828113323843188954444595200000⟩ +] + +def collectedFourData_13_1_21 : List CollectedFourTerm := [ + ⟨2, 4, 7, 0, 8, 5, 553518087890711077909828668644291897841124638720000000⟩, + ⟨2, 4, 7, 1, 7, 5, -43788609248133219361452966807955972562721177600000000⟩, + ⟨2, 4, 8, 1, 8, 5, -632807663771380186299684046538708667252665745408000000⟩, + ⟨2, 4, 7, 2, 6, 5, -27464091691221361968331184000444710213807767552000000⟩, + ⟨2, 4, 8, 2, 7, 5, -271713272305110907704706441590551950400239435776000000⟩, + ⟨2, 4, 7, 3, 5, 5, -65872250269609607251791829993331326172925001728000000⟩, + ⟨2, 4, 8, 3, 6, 5, 14590711847044384726288708831567698747897937920000000⟩, + ⟨2, 4, 7, 4, 4, 5, 34056275127223577591492432769855274916153131008000000⟩, + ⟨2, 4, 8, 4, 5, 5, 198596119372590875373911644274294785802275651584000000⟩, + ⟨2, 4, 7, 5, 3, 5, 38847451683243163258895959575184986516127481856000000⟩, + ⟨2, 4, 8, 5, 4, 5, 99417674061330718614903819428664744535551639552000000⟩, + ⟨2, 4, 7, 6, 2, 5, 274942705222099346633530809641505499868987129856000000⟩, + ⟨2, 4, 8, 6, 3, 5, -527848276064284645896106228083780314239088984064000000⟩, + ⟨2, 4, 7, 7, 1, 5, -1422425948175319490172955681558963691034916159488000000⟩, + ⟨2, 4, 8, 7, 2, 5, 207616781590649493949832098838870479233840316416000000⟩ +] + +def collectedFourData_13_1_22 : List CollectedFourTerm := [ + ⟨2, 5, 6, 0, 7, 6, -6986557252418132867146537293321777751032594432000000⟩, + ⟨2, 5, 7, 0, 8, 6, -20493675318662935454721584513031320173144965120000000⟩, + ⟨2, 5, 6, 1, 6, 6, 2574583499179939423122733730699766984534392832000000⟩, + ⟨2, 5, 7, 1, 7, 6, 1621247002074894531876458480768918297876889600000000⟩, + ⟨2, 5, 8, 1, 8, 6, 11714662162090765456420361455753370712548573184000000⟩, + ⟨2, 5, 6, 2, 5, 6, 46255061838462249333076859178921653088288768000000⟩, + ⟨2, 5, 7, 2, 6, 6, 1016841527594322333411938117728736374048161792000000⟩, + ⟨2, 5, 8, 2, 7, 6, 5030010494880016989061222411330945490456936448000000⟩, + ⟨2, 5, 6, 3, 4, 6, -748994916461083393241236866240575828700168192000000⟩, + ⟨2, 5, 7, 3, 5, 6, 2438880569701687747532286829484186493505241088000000⟩, + ⟨2, 5, 8, 3, 6, 6, -270106178825122355329476100464342531739484160000000⟩, + ⟨2, 5, 6, 4, 3, 6, 945688295561588491207127220476749442476670976000000⟩, + ⟨2, 5, 7, 4, 4, 6, -1260913166686216937193309728662114772837203968000000⟩, + ⟨2, 5, 8, 4, 5, 6, -3676451121477979990991385308684168183867768832000000⟩, + ⟨2, 5, 6, 5, 2, 6, -2052840124693922343978575546440667207401734144000000⟩, + ⟨2, 5, 7, 5, 3, 6, -1438303605917611806836976440473033930834968576000000⟩, + ⟨2, 5, 8, 5, 4, 6, -1840439885996868317245830642140638665712336896000000⟩, + ⟨2, 5, 6, 6, 1, 6, 3844564271244125581516097723320490702728593408000000⟩, + ⟨2, 5, 7, 6, 2, 6, -10179588807166628028265492691497163515364376576000000⟩, + ⟨2, 5, 8, 6, 3, 6, 9771632963612629252643415399866713968708943872000000⟩, + ⟨2, 5, 6, 7, 0, 6, 1140808697392071341565636639963025465468256256000000⟩, + ⟨2, 5, 7, 7, 1, 6, 52664467854755835349651617591580864973056770048000000⟩, + ⟨2, 5, 8, 7, 2, 6, -3843443426427483267392449033500559964444295168000000⟩ +] + +def collectedFourData_13_1_23 : List CollectedFourTerm := [ + ⟨2, 6, 5, 0, 6, 7, -111538242610512642548086684234388803052453756928000000⟩, + ⟨2, 6, 6, 0, 7, 7, -153587980791903437995393782162038070344845099008000000⟩, + ⟨2, 6, 7, 0, 8, 7, -225259888202368328173922334414919802148240752640000000⟩, + ⟨2, 6, 5, 1, 5, 7, 36560319169808332114356618481643228359053803520000000⟩, + ⟨2, 6, 6, 1, 6, 7, 56597987640098221881702334834912177700217028608000000⟩, + ⟨2, 6, 7, 1, 7, 7, 17820225643139658520045625196416986126693171200000000⟩, + ⟨2, 6, 8, 1, 8, 7, 85842532649019111447989782128331370257849516032000000⟩, + ⟨2, 6, 5, 2, 4, 7, -27464091691221361968331184000444710213807767552000000⟩, + ⟨2, 6, 6, 2, 5, 7, 1016841527594322333411938117728736374048161792000000⟩, + ⟨2, 6, 7, 2, 6, 7, 11176795048413335290725635704857829080431591424000000⟩, + ⟨2, 6, 8, 2, 7, 7, 36858838450240331156898042729775139088607739904000000⟩, + ⟨2, 6, 5, 3, 3, 7, 8200930647850149314217225264529098968647335936000000⟩, + ⟨2, 6, 6, 3, 4, 7, -16465422480126763019858449328077660406780264448000000⟩, + ⟨2, 6, 7, 3, 5, 7, 26807390862176193137801959675540758070019751936000000⟩, + ⟨2, 6, 8, 3, 6, 7, -1979280166484899276712397908141968354632007680000000⟩, + ⟨2, 6, 5, 4, 2, 7, 16937257918538904833761020619422493374645534720000000⟩, + ⟨2, 6, 6, 4, 3, 7, 20789403210511101915221236288044630980840914944000000⟩, + ⟨2, 6, 7, 4, 4, 7, -13859552010271750686495237940439126221359415296000000⟩, + ⟨2, 6, 8, 4, 5, 7, -26940245570997387601002643641022463173025857536000000⟩, + ⟨2, 6, 5, 5, 1, 7, 5718277882354861961145596836589988175794929664000000⟩, + ⟨2, 6, 6, 5, 2, 7, -45128316887579005694641038748770968712391950336000000⟩, + ⟨2, 6, 7, 5, 3, 7, -15809370668374706054213726118211480182872604672000000⟩, + ⟨2, 6, 8, 5, 4, 7, -13486348886227410208262546402032293509288951808000000⟩, + ⟨2, 6, 5, 6, 0, 7, -303633820638431262774859395158562773877015969792000000⟩, + ⟨2, 6, 6, 6, 1, 7, 84516428064868293522732878827403894962312445952000000⟩, + ⟨2, 6, 7, 6, 2, 7, -111890766345860102755551480615527242025687580672000000⟩, + ⟨2, 6, 8, 6, 3, 7, 71604431276526068782878818258460312879765651456000000⟩, + ⟨2, 6, 6, 7, 0, 7, 25078804620350882146649178257475960348044427264000000⟩, + ⟨2, 6, 7, 7, 1, 7, 578870893421254211615585214274599257106133549056000000⟩, + ⟨2, 6, 8, 7, 2, 7, -28163929377787105123059174815192845160980414464000000⟩ +] + +def collectedFourData_13_1_24 : List CollectedFourTerm := [ + ⟨2, 7, 4, 0, 5, 8, -632597943329587644778594219209322163404621322649600000⟩, + ⟨2, 7, 5, 0, 6, 8, -1103492561399760688898220643699760270438735806464000000⟩, + ⟨2, 7, 6, 0, 7, 8, -759753741665554675167067096968558106829496778752000000⟩, + ⟨2, 7, 7, 0, 8, 8, -742862134682246429673068574249085759240211005440000000⟩, + ⟨2, 7, 4, 1, 4, 8, -194671377926909045756018488049347841050538724556800000⟩, + ⟨2, 7, 5, 1, 5, 8, 361705898372134508102340421150046179641010421760000000⟩, + ⟨2, 7, 6, 1, 6, 8, 279973293864491394461996540651093463277504561152000000⟩, + ⟨2, 7, 7, 1, 7, 8, 58767546088317971890565940632175812285772595200000000⟩, + ⟨2, 7, 8, 1, 8, 8, 212318649668639666950407760545116238906082197504000000⟩, + ⟨2, 7, 4, 2, 3, 8, -305655651959177220905474989830133564653171847987200000⟩, + ⟨2, 7, 5, 2, 4, 8, -271713272305110907704706441590551950400239435776000000⟩, + ⟨2, 7, 6, 2, 5, 8, 5030010494880016989061222411330945490456936448000000⟩, + ⟨2, 7, 7, 2, 6, 8, 36858838450240331156898042729775139088607739904000000⟩, + ⟨2, 7, 8, 2, 7, 8, 91164817330200064032687579057331910301594943488000000⟩, + ⟨2, 7, 4, 3, 2, 8, 815433318639124607363541546466217123205644235571200000⟩, + ⟨2, 7, 5, 3, 3, 8, 81135095503154501371348732553030728551883603968000000⟩, + ⟨2, 7, 6, 3, 4, 8, -81449513646056777291049099966892874693043290112000000⟩, + ⟨2, 7, 7, 3, 5, 8, 88405422554623199755056293235387410672995270656000000⟩, + ⟨2, 7, 8, 3, 6, 8, -4895453096452834194796764542258128815610920960000000⟩, + ⟨2, 7, 4, 4, 1, 8, -10468684164391691152819313321390513103914926080000000⟩, + ⟨2, 7, 5, 4, 2, 8, 167567084492106768271904125910874659881337487360000000⟩, + ⟨2, 7, 6, 4, 3, 8, 102838951295154644343500581153944450356515700736000000⟩, + ⟨2, 7, 7, 4, 4, 8, -45706035256666018445379259968815061190853001216000000⟩, + ⟨2, 7, 8, 4, 5, 8, -66632663143368649906619534305811626951748616192000000⟩, + ⟨2, 7, 4, 5, 0, 8, -3360119099168028162191947164144500074569345584332800000⟩, + ⟨2, 7, 5, 5, 1, 8, 56573216141031722179755417878755013133003128832000000⟩, + ⟨2, 7, 6, 5, 2, 8, -223236267796642812432920162515946689708985155584000000⟩, + ⟨2, 7, 7, 5, 3, 8, -52136147879737124174908219104532640613229658112000000⟩, + ⟨2, 7, 8, 5, 4, 8, -33356464401993447521129986426274789250067070976000000⟩, + ⟨2, 7, 5, 6, 0, 8, -3003971145877802808520598884676844313372205776896000000⟩, + ⟨2, 7, 6, 6, 1, 8, 418077457125319343722499340299975753652385087488000000⟩, + ⟨2, 7, 7, 6, 2, 8, -368993406692298075864151539867675109720024154112000000⟩, + ⟨2, 7, 8, 6, 3, 8, 177102838066097547327655773525459364810359570432000000⟩, + ⟨2, 7, 6, 7, 0, 8, 124057335401960183947225884059880525913512738816000000⟩, + ⟨2, 7, 7, 7, 1, 8, 1909000626005863945505350936240691674560306610176000000⟩, + ⟨2, 7, 8, 7, 2, 8, -69659261793961260775574949597237762603570167808000000⟩ +] + +def collectedFourData_13_1_25 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_26 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_27 : List CollectedFourTerm := [ + ⟨3, 2, 8, 1, 8, 4, 1899106543275257335061909489898738651801887283609600000⟩, + ⟨3, 2, 8, 2, 7, 4, 815433318639124607363541546466217123205644235571200000⟩, + ⟨3, 2, 8, 3, 6, 4, -43787896269499965146186443001900319907516514304000000⟩, + ⟨3, 2, 8, 4, 5, 4, -596002879487596553713887353829065745265643539660800000⟩, + ⟨3, 2, 8, 5, 4, 4, -298360412075052075938162250929984672405035312742400000⟩, + ⟨3, 2, 8, 6, 3, 4, 1584115004164057416589811673390735163009560005836800000⟩, + ⟨3, 2, 8, 7, 2, 4, -623074610163064720548982775808196837568203141939200000⟩ +] + +def collectedFourData_13_1_28 : List CollectedFourTerm := [ + ⟨3, 3, 7, 0, 8, 5, -165283582000758824557906252051799416782150696960000000⟩, + ⟨3, 3, 7, 1, 7, 5, 13075522454818175582655309309673550262357196800000000⟩, + ⟨3, 3, 8, 1, 8, 5, 188959890695237332593725815104979012338365497344000000⟩, + ⟨3, 3, 7, 2, 6, 5, 8200930647850149314217225264529098968647335936000000⟩, + ⟨3, 3, 8, 2, 7, 5, 81135095503154501371348732553030728551883603968000000⟩, + ⟨3, 3, 7, 3, 5, 5, 19669820584365836656725231233715103852715311104000000⟩, + ⟨3, 3, 8, 3, 6, 5, -4356867771404357780337157810799624984262082560000000⟩, + ⟨3, 3, 7, 4, 4, 5, -10169393314825627506471727651375107804594438144000000⟩, + ⟨3, 3, 8, 4, 5, 5, -59301906657534836641678901730905909130021568512000000⟩, + ⟨3, 3, 7, 5, 3, 5, -11600065302790243114707358287236571919609233408000000⟩, + ⟨3, 3, 8, 5, 4, 5, -29686670846942753728367999041089853750757031936000000⟩, + ⟨3, 3, 7, 6, 2, 5, -82099422147627949240440214244826093635562897408000000⟩, + ⟨3, 3, 8, 6, 3, 5, 157618433307741013612152578695461961229666353152000000⟩, + ⟨3, 3, 7, 7, 1, 5, 424744305540494619550603514538941469612293750784000000⟩, + ⟨3, 3, 8, 7, 2, 5, -61995526606073937472139807538418332567745855488000000⟩ +] + +def collectedFourData_13_1_29 : List CollectedFourTerm := [ + ⟨3, 4, 6, 0, 7, 6, 113131312717740461252531772453750288038240452608000000⟩, + ⟨3, 4, 7, 0, 8, 6, 331848191812790617326591485571557131975686881280000000⟩, + ⟨3, 4, 6, 1, 6, 6, -41689490322697848427286817609479094343940702208000000⟩, + ⟨3, 4, 7, 1, 7, 6, -26252386541447485167235855884984881871480422400000000⟩, + ⟨3, 4, 8, 1, 8, 6, -189692156030564430810085232639465193763604791296000000⟩, + ⟨3, 4, 6, 2, 5, 6, -748994916461083393241236866240575828700168192000000⟩, + ⟨3, 4, 7, 2, 6, 6, -16465422480126763019858449328077660406780264448000000⟩, + ⟨3, 4, 8, 2, 7, 6, -81449513646056777291049099966892874693043290112000000⟩, + ⟨3, 4, 6, 3, 4, 6, 12128259320973713562577573484483777663544066048000000⟩, + ⟨3, 4, 7, 3, 5, 6, -39492091804822113687620671025687370257003446272000000⟩, + ⟨3, 4, 8, 3, 6, 6, 4373751689085855738738816263522574635410391040000000⟩, + ⟨3, 4, 6, 4, 3, 6, -15313258652772872106712028880825153628347039744000000⟩, + ⟨3, 4, 7, 4, 4, 6, 20417604353120033779639146707037697386051796992000000⟩, + ⟨3, 4, 8, 4, 5, 6, 59531715906494200748368981977216928304446046208000000⟩, + ⟨3, 4, 6, 5, 2, 6, 33241049878449385915558960777674121418203201536000000⟩, + ⟨3, 4, 7, 5, 3, 6, 23290036729864437574473299294005034409623814144000000⟩, + ⟨3, 4, 8, 5, 4, 6, 29801713885454786684884998078637082123094196224000000⟩, + ⟨3, 4, 6, 6, 1, 6, -62253923802461201249281094058521607228308324352000000⟩, + ⟨3, 4, 7, 6, 2, 6, 164835154579601432782994699126412360423932166144000000⟩, + ⟨3, 4, 8, 6, 3, 6, -158229242905985208208266765675875804165563219968000000⟩, + ⟨3, 4, 6, 7, 0, 6, -18472787215922536957867076439543959516363096064000000⟩, + ⟨3, 4, 7, 7, 1, 6, -852780585162690219278929409749988113287072448512000000⟩, + ⟨3, 4, 8, 7, 2, 6, 62235774284625971006000165111319775887639969792000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1303.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1303.lean new file mode 100644 index 0000000000000000000000000000000000000000..bfd00cbc314bfed873ad7acaf124eece8ef41110 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1303.lean @@ -0,0 +1,611 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1302 + +namespace OAI + +/-! Sparse1303. -/ +namespace LaughlinFock +def collectedFourData_13_1_30 : List CollectedFourTerm := [ + ⟨3, 5, 5, 0, 6, 7, -267522957412081842493476948599917763336173780992000000⟩, + ⟨3, 5, 6, 0, 7, 7, -368378682349146086426705723780218148408222810112000000⟩, + ⟨3, 5, 7, 0, 8, 7, -540282777169493430903942100045570253022780456960000000⟩, + ⟨3, 5, 5, 1, 5, 7, 87689428121892483565303653198918438861699809280000000⟩, + ⟨3, 5, 6, 1, 6, 7, 135749503333347706087723827166045310428498624512000000⟩, + ⟨3, 5, 7, 1, 7, 7, 42741568759072529923640259041802568793377996800000000⟩, + ⟨3, 5, 8, 1, 8, 7, 205892146662209597348228040230011960954818920448000000⟩, + ⟨3, 5, 5, 2, 4, 7, -65872250269609607251791829993331326172925001728000000⟩, + ⟨3, 5, 6, 2, 5, 7, 2438880569701687747532286829484186493505241088000000⟩, + ⟨3, 5, 7, 2, 6, 7, 26807390862176193137801959675540758070019751936000000⟩, + ⟨3, 5, 8, 2, 7, 7, 88405422554623199755056293235387410672995270656000000⟩, + ⟨3, 5, 5, 3, 3, 7, 19669820584365836656725231233715103852715311104000000⟩, + ⟨3, 5, 6, 3, 4, 7, -39492091804822113687620671025687370257003446272000000⟩, + ⟨3, 5, 7, 3, 5, 7, 64297162265626915825204052736959823497977135104000000⟩, + ⟨3, 5, 8, 3, 6, 7, -4747276551004323845349278992838696279495147520000000⟩, + ⟨3, 5, 5, 4, 2, 7, 40623782684484093567876882545792757803337646080000000⟩, + ⟨3, 5, 6, 4, 3, 7, 49863100758447543357678645008006837713256841216000000⟩, + ⟨3, 5, 7, 4, 4, 7, -33241946936009929028630792078794695919370502144000000⟩, + ⟨3, 5, 8, 4, 5, 7, -64615812477232608494508885661737569764459413504000000⟩, + ⟨3, 5, 5, 5, 1, 7, 13715211703070944410928510212936197990353207296000000⟩, + ⟨3, 5, 6, 5, 2, 7, -108239654079477556277609463040366516188903112704000000⟩, + ⟨3, 5, 7, 5, 3, 7, -37918560459987004217523699458295110364360081408000000⟩, + ⟨3, 5, 8, 5, 4, 7, -32346824320456365602322206894370430385035149312000000⟩, + ⟨3, 5, 5, 6, 0, 7, -728261587831999692600618622841345597372878553088000000⟩, + ⟨3, 5, 6, 6, 1, 7, 202711502858912764748389316223174146011145699328000000⟩, + ⟨3, 5, 7, 6, 2, 7, -268368480795191143181282505062351090925497745408000000⟩, + ⟨3, 5, 8, 6, 3, 7, 171742254231114805554370502468765273078454288384000000⟩, + ⟨3, 5, 6, 7, 0, 7, 60151171682202052358449350364242126182018973696000000⟩, + ⟨3, 5, 7, 7, 1, 7, 1388413962272990465539502802237024209502977654784000000⟩, + ⟨3, 5, 8, 7, 2, 7, -67550801439474024485619280856220834140044394496000000⟩ +] + +def collectedFourData_13_1_31 : List CollectedFourTerm := [ + ⟨3, 6, 4, 0, 5, 8, 33969832345143450995864240311266805959761068032000000⟩, + ⟨3, 6, 5, 0, 6, 8, 59256369231242693210590787632952809343554682880000000⟩, + ⟨3, 6, 6, 0, 7, 8, 40797962592375701741925223119229824450523299840000000⟩, + ⟨3, 6, 7, 0, 8, 8, 39890901380252728932705849825048252545551564800000000⟩, + ⟨3, 6, 4, 1, 4, 8, 10453644594177517978869414829539866590845075456000000⟩, + ⟨3, 6, 5, 1, 5, 8, -19423219527524216994272923722722093688894259200000000⟩, + ⟨3, 6, 6, 1, 6, 8, -15034266162226904191825133680945932512620707840000000⟩, + ⟨3, 6, 7, 1, 7, 8, -3155754312839355375069881297322596980752384000000000⟩, + ⟨3, 6, 8, 1, 8, 8, -11401284194870064898422963461668440525955399680000000⟩, + ⟨3, 6, 4, 2, 3, 8, 16413381298315603123929581772333050170152321024000000⟩, + ⟨3, 6, 5, 2, 4, 8, 14590711847044384726288708831567698747897937920000000⟩, + ⟨3, 6, 6, 2, 5, 8, -270106178825122355329476100464342531739484160000000⟩, + ⟨3, 6, 7, 2, 6, 8, -1979280166484899276712397908141968354632007680000000⟩, + ⟨3, 6, 8, 2, 7, 8, -4895453096452834194796764542258128815610920960000000⟩, + ⟨3, 6, 4, 3, 2, 8, -43787896269499965146186443001900319907516514304000000⟩, + ⟨3, 6, 5, 3, 3, 8, -4356867771404357780337157810799624984262082560000000⟩, + ⟨3, 6, 6, 3, 4, 8, 4373751689085855738738816263522574635410391040000000⟩, + ⟨3, 6, 7, 3, 5, 8, -4747276551004323845349278992838696279495147520000000⟩, + ⟨3, 6, 8, 3, 6, 8, 262880590576586738463483856025669214614323200000000⟩, + ⟨3, 6, 4, 4, 1, 8, 562157132643986269170405473708493550229913600000000⟩, + ⟨3, 6, 5, 4, 2, 8, -8998173052541315954742999354936926374409011200000000⟩, + ⟨3, 6, 6, 4, 3, 8, -5522341592923391263539487247601858392484741120000000⟩, + ⟨3, 6, 7, 4, 4, 8, 2454365163848204028610677528119047229244702720000000⟩, + ⟨3, 6, 8, 4, 5, 8, 3578102678894347626781805010286500922408304640000000⟩, + ⟨3, 6, 4, 5, 0, 8, 180434798535194221773785019789044173760549093376000000⟩, + ⟨3, 6, 5, 5, 1, 8, -3037921143754256069679513642250107140639293440000000⟩, + ⟨3, 6, 6, 5, 2, 8, 11987548600765137877043191234073000806742753280000000⟩, + ⟨3, 6, 7, 5, 3, 8, 2799655328113427816573227708298978690900951040000000⟩, + ⟨3, 6, 8, 5, 4, 8, 1791206429471591888683236546886519916247121920000000⟩, + ⟨3, 6, 5, 6, 0, 8, 161310034708651633247660934565278042611326648320000000⟩, + ⟨3, 6, 6, 6, 1, 8, -22450311885430288175230278019154215875599400960000000⟩, + ⟨3, 6, 7, 6, 2, 8, 19814550922860126879226475504078575216141271040000000⟩, + ⟨3, 6, 8, 6, 3, 8, -9510232811205913225812794589272021996603965440000000⟩, + ⟨3, 6, 6, 7, 0, 8, -6661746104656852437178210114267812169745694720000000⟩, + ⟨3, 6, 7, 7, 1, 8, -102511289984397939509945222081523909102843985920000000⟩, + ⟨3, 6, 8, 7, 2, 8, 3740627786382884192115237442764733167288975360000000⟩ +] + +def collectedFourData_13_1_32 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_1_33 : List CollectedFourTerm := [ + ⟨4, 1, 8, 1, 8, 4, -24381081986271967533555274264629920563608944640000000⟩, + ⟨4, 1, 8, 2, 7, 4, -10468684164391691152819313321390513103914926080000000⟩, + ⟨4, 1, 8, 3, 6, 4, 562157132643986269170405473708493550229913600000000⟩, + ⟨4, 1, 8, 4, 5, 4, 7651595493836969469442844126593357739427102720000000⟩, + ⟨4, 1, 8, 5, 4, 4, 3830406300277480516074285012307084858003292160000000⟩, + ⟨4, 1, 8, 6, 3, 4, -20337162192910990381910057068367357219564421120000000⟩, + ⟨4, 1, 8, 7, 2, 4, 7999147392621195266776329943520681039002337280000000⟩ +] + +def collectedFourData_13_1_34 : List CollectedFourTerm := [ + ⟨4, 2, 7, 0, 8, 5, -341357679787317168268127728558740652225147699200000000⟩, + ⟨4, 2, 7, 1, 7, 5, 27004678584248048807263631756116857754484736000000000⟩, + ⟨4, 2, 8, 1, 8, 5, 390256001714042852899954504629478365871346810880000000⟩, + ⟨4, 2, 7, 2, 6, 5, 16937257918538904833761020619422493374645534720000000⟩, + ⟨4, 2, 8, 2, 7, 5, 167567084492106768271904125910874659881337487360000000⟩, + ⟨4, 2, 7, 3, 5, 5, 40623782684484093567876882545792757803337646080000000⟩, + ⟨4, 2, 8, 3, 6, 5, -8998173052541315954742999354936926374409011200000000⟩, + ⟨4, 2, 7, 4, 4, 5, -21002694065388739475177149469578135266530426880000000⟩, + ⟨4, 2, 8, 4, 5, 5, -122475330087456669664569509013219367855576842240000000⟩, + ⟨4, 2, 7, 5, 3, 5, -23957439264134901711787910100816473247354716160000000⟩, + ⟨4, 2, 8, 5, 4, 5, -61311431893311966489848972546807497470215454720000000⟩, + ⟨4, 2, 7, 6, 2, 5, -169558693712634394438347055965886649125211996160000000⟩, + ⟨4, 2, 8, 6, 3, 5, 325526964229244776796665680202060410553148375040000000⟩, + ⟨4, 2, 7, 7, 1, 5, 877217984309614691003039496699738400765960519680000000⟩, + ⟨4, 2, 8, 7, 2, 5, -128038422590243296828170267983819044653115637760000000⟩ +] + +def collectedFourData_13_1_35 : List CollectedFourTerm := [ + ⟨4, 3, 6, 0, 7, 6, -142840700180164589448072358020435642145176551424000000⟩, + ⟨4, 3, 7, 0, 8, 6, -418994767525820581511679630017321232542560419840000000⟩, + ⟨4, 3, 6, 1, 6, 6, 52637557585014585580521867667284765022013620224000000⟩, + ⟨4, 3, 7, 1, 7, 6, 33146519605377598443477506552084462417687347200000000⟩, + ⟨4, 3, 8, 1, 8, 6, 239507168574044898013359890365346196978388697088000000⟩, + ⟨4, 3, 6, 2, 5, 6, 945688295561588491207127220476749442476670976000000⟩, + ⟨4, 3, 7, 2, 6, 6, 20789403210511101915221236288044630980840914944000000⟩, + ⟨4, 3, 8, 2, 7, 6, 102838951295154644343500581153944450356515700736000000⟩, + ⟨4, 3, 6, 3, 4, 6, -15313258652772872106712028880825153628347039744000000⟩, + ⟨4, 3, 7, 3, 5, 6, 49863100758447543357678645008006837713256841216000000⟩, + ⟨4, 3, 8, 3, 6, 6, -5522341592923391263539487247601858392484741120000000⟩, + ⟨4, 3, 6, 4, 3, 6, 19334669911056684739012968103642493080968364032000000⟩, + ⟨4, 3, 7, 4, 4, 6, -25779466636949068884238420279316297933836517376000000⟩, + ⟨4, 3, 8, 4, 5, 6, -75165325838889570187861967692601406554294452224000000⟩, + ⟨4, 3, 6, 5, 2, 6, -41970474179929759906188049543503618121094135808000000⟩, + ⟨4, 3, 7, 5, 3, 6, -29406227805521671710821054312503089407283167232000000⟩, + ⟨4, 3, 8, 5, 4, 6, -37627934969588293065928201406656051336521449472000000⟩, + ⟨4, 3, 6, 6, 1, 6, 78602412111070017543235102528406179467761811456000000⟩, + ⟨4, 3, 7, 6, 2, 6, -208122475810039315607449533704896842939846623232000000⟩, + ⟨4, 3, 8, 6, 3, 6, 199781787223300263727552467426169837079708565504000000⟩, + ⟨4, 3, 6, 7, 0, 6, 23323921528118106274119245216358666517182676992000000⟩, + ⟨4, 3, 7, 7, 1, 6, 1076729094345490415602407850487361489500620455936000000⟩, + ⟨4, 3, 8, 7, 2, 6, -78579496352618731253899882171607426915710795776000000⟩ +] + +def collectedFourData_13_1_36 : List CollectedFourTerm := [ + ⟨4, 4, 5, 0, 6, 7, 138310675636318606746364728245223220459352358912000000⟩, + ⟨4, 4, 6, 0, 7, 7, 190453578035341204188609913471086786190856159232000000⟩, + ⟨4, 4, 7, 0, 8, 7, 279328834683420716660361036144462813844796866560000000⟩, + ⟨4, 4, 5, 1, 5, 7, -45335862637834332107138456330769049254447022080000000⟩, + ⟨4, 4, 6, 1, 6, 7, -70183156260525341466065711030566578786907717632000000⟩, + ⟨4, 4, 7, 1, 7, 7, -22097599809789295302690174604562459005865164800000000⟩, + ⟨4, 4, 8, 1, 8, 7, -106447245457133734016314596975383280887349116928000000⟩, + ⟨4, 4, 5, 2, 4, 7, 34056275127223577591492432769855274916153131008000000⟩, + ⟨4, 4, 6, 2, 5, 7, -1260913166686216937193309728662114772837203968000000⟩, + ⟨4, 4, 7, 2, 6, 7, -13859552010271750686495237940439126221359415296000000⟩, + ⟨4, 4, 8, 2, 7, 7, -45706035256666018445379259968815061190853001216000000⟩, + ⟨4, 4, 5, 3, 3, 7, -10169393314825627506471727651375107804594438144000000⟩, + ⟨4, 4, 6, 3, 4, 7, 20417604353120033779639146707037697386051796992000000⟩, + ⟨4, 4, 7, 3, 5, 7, -33241946936009929028630792078794695919370502144000000⟩, + ⟨4, 4, 8, 3, 6, 7, 2454365163848204028610677528119047229244702720000000⟩, + ⟨4, 4, 5, 4, 2, 7, -21002694065388739475177149469578135266530426880000000⟩, + ⟨4, 4, 6, 4, 3, 7, -25779466636949068884238420279316297933836517376000000⟩, + ⟨4, 4, 7, 4, 4, 7, 17186248928550992827436517594631814425381699584000000⟩, + ⟨4, 4, 8, 4, 5, 7, 33406690651783642428812812281595295275149164544000000⟩, + ⟨4, 4, 5, 5, 1, 7, -7090831439280492896851318136613086134592864256000000⟩, + ⟨4, 4, 6, 5, 2, 7, 55960429830751584071662458773039992590506655744000000⟩, + ⟨4, 4, 7, 5, 3, 7, 19604080962288828180637223479398341350929727488000000⟩, + ⟨4, 4, 8, 5, 4, 7, 16723466164289540463282308449771497912828690432000000⟩, + ⟨4, 4, 5, 6, 0, 7, 376514797935143754187661089123952618383991635968000000⟩, + ⟨4, 4, 6, 6, 1, 7, -104802837075707148109946889839969464474411204608000000⟩, + ⟨4, 4, 7, 6, 2, 7, 138747815355150347594895606067937451779700031488000000⟩, + ⟨4, 4, 8, 6, 3, 7, -88791584272973205231953382988674030567344308224000000⟩, + ⟨4, 4, 6, 7, 0, 7, -31098449554243132547535770947764911676541894656000000⟩, + ⟨4, 4, 7, 7, 1, 7, -717816799883369314542122489719406797141126938624000000⟩, + ⟨4, 4, 8, 7, 2, 7, 34924094280540083554766153609011461292824723456000000⟩ +] + +def collectedFourData_13_1_37 : List CollectedFourTerm := [ + ⟨4, 5, 4, 0, 5, 8, 462367905706368197519230931663497128012023228006400000⟩, + ⟨4, 5, 5, 0, 6, 8, 806546322126019885089482488385846732383454232576000000⟩, + ⟨4, 5, 6, 0, 7, 8, 555306494576220029221796015576103704395637587968000000⟩, + ⟨4, 5, 7, 0, 8, 8, 542960363787713552450694424593374657737874472960000000⟩, + ⟨4, 5, 4, 1, 4, 8, 142285946804196546137500902706303508459816170291200000⟩, + ⟨4, 5, 5, 1, 5, 8, -264372024088024158482225389671872019262435491840000000⟩, + ⟨4, 5, 6, 1, 6, 8, -204633396144941040078672064613915836729490669568000000⟩, + ⟨4, 5, 7, 1, 7, 8, -42953391636623048670198098253201911019523276800000000⟩, + ⟨4, 5, 8, 1, 8, 8, -155184395436053685485589500798761125685216935936000000⟩, + ⟨4, 5, 4, 2, 3, 8, 223404715671116108923676055631544180842267725004800000⟩, + ⟨4, 5, 5, 2, 4, 8, 198596119372590875373911644274294785802275651584000000⟩, + ⟨4, 5, 6, 2, 5, 8, -3676451121477979990991385308684168183867768832000000⟩, + ⟨4, 5, 7, 2, 6, 8, -26940245570997387601002643641022463173025857536000000⟩, + ⟨4, 5, 8, 2, 7, 8, -66632663143368649906619534305811626951748616192000000⟩, + ⟨4, 5, 4, 3, 2, 8, -596002879487596553713887353829065745265643539660800000⟩, + ⟨4, 5, 5, 3, 3, 8, -59301906657534836641678901730905909130021568512000000⟩, + ⟨4, 5, 6, 3, 4, 8, 59531715906494200748368981977216928304446046208000000⟩, + ⟨4, 5, 7, 3, 5, 8, -64615812477232608494508885661737569764459413504000000⟩, + ⟨4, 5, 8, 3, 6, 8, 3578102678894347626781805010286500922408304640000000⟩, + ⟨4, 5, 4, 4, 1, 8, 7651595493836969469442844126593357739427102720000000⟩, + ⟨4, 5, 5, 4, 2, 8, -122475330087456669664569509013219367855576842240000000⟩, + ⟨4, 5, 6, 4, 3, 8, -75165325838889570187861967692601406554294452224000000⟩, + ⟨4, 5, 7, 4, 4, 8, 33406690651783642428812812281595295275149164544000000⟩, + ⟨4, 5, 8, 4, 5, 8, 48702031415213886698357592377497073736826748928000000⟩, + ⟨4, 5, 4, 5, 0, 8, 2455922038932156526616243508243969983935189037875200000⟩, + ⟨4, 5, 5, 5, 1, 8, -41349548701542714733428627220079687087777906688000000⟩, + ⟨4, 5, 6, 5, 2, 8, 163164118232143581095779634481244718289603526656000000⟩, + ⟨4, 5, 7, 5, 3, 8, 38106480997824138571392793687269226918296158208000000⟩, + ⟨4, 5, 8, 5, 4, 8, 24380348924535266799634387622415747037878288384000000⟩, + ⟨4, 5, 5, 6, 0, 8, 2195612335081892695825280469172644270104761073664000000⟩, + ⟨4, 5, 6, 6, 1, 8, -305574180745264251814050235068262744814562312192000000⟩, + ⟨4, 5, 7, 6, 2, 8, 269698487753202762430783453626258490485488222208000000⟩, + ⟨4, 5, 8, 6, 3, 8, -129445043561597701793485903692071173841473241088000000⟩, + ⟨4, 5, 6, 7, 0, 8, -90673912177788757660371121683985809191095762944000000⟩, + ⟨4, 5, 7, 7, 1, 8, -1395294800980099352340670788935410075784586461184000000⟩, + ⟨4, 5, 8, 7, 2, 8, 50914182267495630428425150088535524260888707072000000⟩ +] + +def collectedFourData_13_1_38 : List CollectedFourTerm := [ + ⟨5, 0, 8, 1, 8, 4, -7825562215269521510674289329935241680351754872422400000⟩, + ⟨5, 0, 8, 2, 7, 4, -3360119099168028162191947164144500074569345584332800000⟩, + ⟨5, 0, 8, 3, 6, 4, 180434798535194221773785019789044173760549093376000000⟩, + ⟨5, 0, 8, 4, 5, 4, 2455922038932156526616243508243969983935189037875200000⟩, + ⟨5, 0, 8, 5, 4, 4, 1229440220473380455254129225084227487658457799065600000⟩, + ⟨5, 0, 8, 6, 3, 4, -6527590863779674305414358353603960579294210765619200000⟩, + ⟨5, 0, 8, 7, 2, 4, 2567475291921602246425391010416574638202410552524800000⟩ +] + +def collectedFourData_13_1_39 : List CollectedFourTerm := [ + ⟨5, 1, 7, 0, 8, 5, -115247584921241889689372332564151674235560919040000000⟩, + ⟨5, 1, 7, 1, 7, 5, 9117193409411616937749393506592885459596083200000000⟩, + ⟨5, 1, 8, 1, 8, 5, 131756407902074446024720292454715631201006125056000000⟩, + ⟨5, 1, 7, 2, 6, 5, 5718277882354861961145596836589988175794929664000000⟩, + ⟨5, 1, 8, 2, 7, 5, 56573216141031722179755417878755013133003128832000000⟩, + ⟨5, 1, 7, 3, 5, 5, 13715211703070944410928510212936197990353207296000000⟩, + ⟨5, 1, 8, 3, 6, 5, -3037921143754256069679513642250107140639293440000000⟩, + ⟨5, 1, 7, 4, 4, 5, -7090831439280492896851318136613086134592864256000000⟩, + ⟨5, 1, 8, 4, 5, 5, -41349548701542714733428627220079687087777906688000000⟩, + ⟨5, 1, 7, 5, 3, 5, -8088398707798651061613897690745198280171323392000000⟩, + ⟨5, 1, 8, 5, 4, 5, -20699679169866269465472202637821077948846833664000000⟩, + ⟨5, 1, 7, 6, 2, 5, -57245613940652616693841140630974923510112059392000000⟩, + ⟨5, 1, 8, 6, 3, 5, 109902892700519926128217890223955589259012866048000000⟩, + ⟨5, 1, 7, 7, 1, 5, 296162237229147965588001886405260207758682095616000000⟩, + ⟨5, 1, 8, 7, 2, 5, -43227733999846487086399007090967049057245069312000000⟩ +] + +def collectedFourData_13_1_40 : List CollectedFourTerm := [ + ⟨5, 2, 6, 0, 7, 6, 310069525175929955667569988310547542883702931456000000⟩, + ⟨5, 2, 7, 0, 8, 6, 909527245764447674894648158973979664212515880960000000⟩, + ⟨5, 2, 6, 1, 6, 6, -114262268850685610505381194262902007810968518656000000⟩, + ⟨5, 2, 7, 1, 7, 6, -71952360792902986177225297659209754981747916800000000⟩, + ⟨5, 2, 8, 1, 8, 6, -519906958887184749205705383219515958047614697472000000⟩, + ⟨5, 2, 6, 2, 5, 6, -2052840124693922343978575546440667207401734144000000⟩, + ⟨5, 2, 7, 2, 6, 6, -45128316887579005694641038748770968712391950336000000⟩, + ⟨5, 2, 8, 2, 7, 6, -223236267796642812432920162515946689708985155584000000⟩, + ⟨5, 2, 6, 3, 4, 6, 33241049878449385915558960777674121418203201536000000⟩, + ⟨5, 2, 7, 3, 5, 6, -108239654079477556277609463040366516188903112704000000⟩, + ⟨5, 2, 8, 3, 6, 6, 11987548600765137877043191234073000806742753280000000⟩, + ⟨5, 2, 6, 4, 3, 6, -41970474179929759906188049543503618121094135808000000⟩, + ⟨5, 2, 7, 4, 4, 6, 55960429830751584071662458773039992590506655744000000⟩, + ⟨5, 2, 8, 4, 5, 6, 163164118232143581095779634481244718289603526656000000⟩, + ⟨5, 2, 6, 5, 2, 6, 91106841285188480546798181555219061315209265152000000⟩, + ⟨5, 2, 7, 5, 3, 6, 63833172767795566066802756078877192437637316608000000⟩, + ⟨5, 2, 8, 5, 4, 6, 81680332808892064944228586236747383473510023168000000⟩, + ⟨5, 2, 6, 6, 1, 6, -170625126943662699175423884144740411116055691264000000⟩, + ⟨5, 2, 7, 6, 2, 6, 451779059970045441556032625643589005388816580608000000⟩, + ⟨5, 2, 8, 6, 3, 6, -433673622608925554859117154154034292512811646976000000⟩, + ⟨5, 2, 6, 7, 0, 6, -50630088373569177070734472154102565328857858048000000⟩, + ⟨5, 2, 7, 7, 1, 6, -2337295172914424779807068091305149672122308624384000000⟩, + ⟨5, 2, 8, 7, 2, 6, 170575382869788274567489677791783404238844985344000000⟩ +] + +def collectedFourData_13_1_41 : List CollectedFourTerm := [ + ⟨5, 3, 5, 0, 6, 7, 157768789128778606731362662527098924319935299584000000⟩, + ⟨5, 3, 6, 0, 7, 7, 217247369038149688933005815609722403137020493824000000⟩, + ⟨5, 3, 7, 0, 8, 7, 318625961546413066605372220105358406569605201920000000⟩, + ⟨5, 3, 5, 1, 5, 7, -51713897857654457621765620336282919030552002560000000⟩, + ⟨5, 3, 6, 1, 6, 7, -80056810723520093051421384136354820356124442624000000⟩, + ⟨5, 3, 7, 1, 7, 7, -25206380842284924442742433012420735573531033600000000⟩, + ⟨5, 3, 8, 1, 8, 7, -121422680820568314774044329752500886067841335296000000⟩, + ⟨5, 3, 5, 2, 4, 7, 38847451683243163258895959575184986516127481856000000⟩, + ⟨5, 3, 6, 2, 5, 7, -1438303605917611806836976440473033930834968576000000⟩, + ⟨5, 3, 7, 2, 6, 7, -15809370668374706054213726118211480182872604672000000⟩, + ⟨5, 3, 8, 2, 7, 7, -52136147879737124174908219104532640613229658112000000⟩, + ⟨5, 3, 5, 3, 3, 7, -11600065302790243114707358287236571919609233408000000⟩, + ⟨5, 3, 6, 3, 4, 7, 23290036729864437574473299294005034409623814144000000⟩, + ⟨5, 3, 7, 3, 5, 7, -37918560459987004217523699458295110364360081408000000⟩, + ⟨5, 3, 8, 3, 6, 7, 2799655328113427816573227708298978690900951040000000⟩, + ⟨5, 3, 5, 4, 2, 7, -23957439264134901711787910100816473247354716160000000⟩, + ⟨5, 3, 6, 4, 3, 7, -29406227805521671710821054312503089407283167232000000⟩, + ⟨5, 3, 7, 4, 4, 7, 19604080962288828180637223479398341350929727488000000⟩, + ⟨5, 3, 8, 4, 5, 7, 38106480997824138571392793687269226918296158208000000⟩, + ⟨5, 3, 5, 5, 1, 7, -8088398707798651061613897690745198280171323392000000⟩, + ⟨5, 3, 6, 5, 2, 7, 63833172767795566066802756078877192437637316608000000⟩, + ⟨5, 3, 7, 5, 3, 7, 22362063529611522854071063529975741696459145216000000⟩, + ⟨5, 3, 8, 5, 4, 7, 19076192019433963349412474279312804556490932224000000⟩, + ⟨5, 3, 5, 6, 0, 7, 429484444971477711951321736087818539057415192576000000⟩, + ⟨5, 3, 6, 6, 1, 7, -119546930319189355952042070770113775142810157056000000⟩, + ⟨5, 3, 7, 6, 2, 7, 158267427457330510956240145565070715724513673216000000⟩, + ⟨5, 3, 8, 6, 3, 7, -101283148760025445795658373254713177167749971968000000⟩, + ⟨5, 3, 6, 7, 0, 7, -35473507069377625724829336745387789259680776192000000⟩, + ⟨5, 3, 7, 7, 1, 7, -818802213298972633928468677511710909702254624768000000⟩, + ⟨5, 3, 8, 7, 2, 7, 39837359196684265699002359414324726324413857792000000⟩ +] + +def collectedFourData_13_1_42 : List CollectedFourTerm := [ + ⟨5, 4, 4, 0, 5, 8, 231462436885259661751579783305880420260206818099200000⟩, + ⟨5, 4, 5, 0, 6, 8, 403758943638031512264346494993718296924471164928000000⟩, + ⟨5, 4, 6, 0, 7, 8, 277987708200597182061134507415212719914828693504000000⟩, + ⟨5, 4, 7, 0, 8, 8, 271807206735976423399995462394654776502391930880000000⟩, + ⟨5, 4, 4, 1, 4, 8, 71228672179380807049358773510697759740939311513600000⟩, + ⟨5, 4, 5, 1, 5, 8, -132345243224047239748347716617957658685100523520000000⟩, + ⟨5, 4, 6, 1, 6, 8, -102439948697248852841748265839738070396047458304000000⟩, + ⟨5, 4, 7, 1, 7, 8, -21502566631459796883542880307623421396018790400000000⟩, + ⟨5, 4, 8, 1, 8, 8, -77685665226525769263706293140420973951354667008000000⟩, + ⟨5, 4, 4, 2, 3, 8, 111836914419691506884080813308056228032774825574400000⟩, + ⟨5, 4, 5, 2, 4, 8, 99417674061330718614903819428664744535551639552000000⟩, + ⟨5, 4, 6, 2, 5, 8, -1840439885996868317245830642140638665712336896000000⟩, + ⟨5, 4, 7, 2, 6, 8, -13486348886227410208262546402032293509288951808000000⟩, + ⟨5, 4, 8, 2, 7, 8, -33356464401993447521129986426274789250067070976000000⟩, + ⟨5, 4, 4, 3, 2, 8, -298360412075052075938162250929984672405035312742400000⟩, + ⟨5, 4, 5, 3, 3, 8, -29686670846942753728367999041089853750757031936000000⟩, + ⟨5, 4, 6, 3, 4, 8, 29801713885454786684884998078637082123094196224000000⟩, + ⟨5, 4, 7, 3, 5, 8, -32346824320456365602322206894370430385035149312000000⟩, + ⟨5, 4, 8, 3, 6, 8, 1791206429471591888683236546886519916247121920000000⟩, + ⟨5, 4, 4, 4, 1, 8, 3830406300277480516074285012307084858003292160000000⟩, + ⟨5, 4, 5, 4, 2, 8, -61311431893311966489848972546807497470215454720000000⟩, + ⟨5, 4, 6, 4, 3, 8, -37627934969588293065928201406656051336521449472000000⟩, + ⟨5, 4, 7, 4, 4, 8, 16723466164289540463282308449771497912828690432000000⟩, + ⟨5, 4, 8, 4, 5, 8, 24380348924535266799634387622415747037878288384000000⟩, + ⟨5, 4, 4, 5, 0, 8, 1229440220473380455254129225084227487658457799065600000⟩, + ⟨5, 4, 5, 5, 1, 8, -20699679169866269465472202637821077948846833664000000⟩, + ⟨5, 4, 6, 5, 2, 8, 81680332808892064944228586236747383473510023168000000⟩, + ⟨5, 4, 7, 5, 3, 8, 19076192019433963349412474279312804556490932224000000⟩, + ⟨5, 4, 8, 5, 4, 8, 12204858738118357059950738313489272402400509952000000⟩, + ⟨5, 4, 5, 6, 0, 8, 1099128584102308526722474237581545615723480481792000000⟩, + ⟨5, 4, 6, 6, 1, 8, -152971137597584132354287135221181321041439358976000000⟩, + ⟨5, 4, 7, 6, 2, 8, 135011683183887322245758667810474935035807924224000000⟩, + ⟨5, 4, 8, 6, 3, 8, -64800486486433336565800583016412215045588516864000000⟩, + ⟨5, 4, 6, 7, 0, 8, -45391568955305941964452633545119343964304965632000000⟩, + ⟨5, 4, 7, 7, 1, 8, -698487786073295093301043285922890886959545188352000000⟩, + ⟨5, 4, 8, 7, 2, 8, 25487756728380775546619078689276066710071279616000000⟩ +] + +def collectedFourData_13_1_43 : List CollectedFourTerm := [ + ⟨6, 0, 7, 0, 8, 5, 6119511022185254760034287447074268382170835845120000000⟩, + ⟨6, 0, 7, 1, 7, 5, -484112231925874337647840636937066427417467289600000000⟩, + ⟨6, 0, 8, 1, 8, 5, -6996110078586734638789406789436755800461429178368000000⟩, + ⟨6, 0, 7, 2, 6, 5, -303633820638431262774859395158562773877015969792000000⟩, + ⟨6, 0, 8, 2, 7, 5, -3003971145877802808520598884676844313372205776896000000⟩, + ⟨6, 0, 7, 3, 5, 5, -728261587831999692600618622841345597372878553088000000⟩, + ⟨6, 0, 8, 3, 6, 5, 161310034708651633247660934565278042611326648320000000⟩, + ⟨6, 0, 7, 4, 4, 5, 376514797935143754187661089123952618383991635968000000⟩, + ⟨6, 0, 8, 4, 5, 5, 2195612335081892695825280469172644270104761073664000000⟩, + ⟨6, 0, 7, 5, 3, 5, 429484444971477711951321736087818539057415192576000000⟩, + ⟨6, 0, 8, 5, 4, 5, 1099128584102308526722474237581545615723480481792000000⟩, + ⟨6, 0, 7, 6, 2, 5, 3039674677096136962278664758796586911542936600576000000⟩, + ⟨6, 0, 8, 6, 3, 5, -5835714160175112447301411371305008972839197343744000000⟩, + ⟨6, 0, 7, 7, 1, 5, -15725865980769615839823091565896336085992549122048000000⟩, + ⟨6, 0, 8, 7, 2, 5, 2295341762319181328090229010626958168134135054336000000⟩ +] + +def collectedFourData_13_1_44 : List CollectedFourTerm := [ + ⟨6, 1, 6, 0, 7, 6, -580699005126251704693839223750365932063966625792000000⟩, + ⟨6, 1, 7, 0, 8, 6, -1703364967747029222454909141422118773235352862720000000⟩, + ⟨6, 1, 6, 1, 6, 6, 213990671309649229462641001311505989039336456192000000⟩, + ⟨6, 1, 7, 1, 7, 6, 134752566558151338093696270881809511929715097600000000⟩, + ⟨6, 1, 8, 1, 8, 6, 973683091276716755295604217527568964311008149504000000⟩, + ⟨6, 1, 6, 2, 5, 6, 3844564271244125581516097723320490702728593408000000⟩, + ⟨6, 1, 7, 2, 6, 6, 84516428064868293522732878827403894962312445952000000⟩, + ⟨6, 1, 8, 2, 7, 6, 418077457125319343722499340299975753652385087488000000⟩, + ⟨6, 1, 6, 3, 4, 6, -62253923802461201249281094058521607228308324352000000⟩, + ⟨6, 1, 7, 3, 5, 6, 202711502858912764748389316223174146011145699328000000⟩, + ⟨6, 1, 8, 3, 6, 6, -22450311885430288175230278019154215875599400960000000⟩, + ⟨6, 1, 6, 4, 3, 6, 78602412111070017543235102528406179467761811456000000⟩, + ⟨6, 1, 7, 4, 4, 6, -104802837075707148109946889839969464474411204608000000⟩, + ⟨6, 1, 8, 4, 5, 6, -305574180745264251814050235068262744814562312192000000⟩, + ⟨6, 1, 6, 5, 2, 6, -170625126943662699175423884144740411116055691264000000⟩, + ⟨6, 1, 7, 5, 3, 6, -119546930319189355952042070770113775142810157056000000⟩, + ⟨6, 1, 8, 5, 4, 6, -152971137597584132354287135221181321041439358976000000⟩, + ⟨6, 1, 6, 6, 1, 6, 319547177071037254987307707985490965696241205248000000⟩, + ⟨6, 1, 7, 6, 2, 6, -846092986766840412743045744651287877281231405056000000⟩, + ⟨6, 1, 8, 6, 3, 6, 812185077058485265071214482389710512515482386432000000⟩, + ⟨6, 1, 6, 7, 0, 6, 94820159869965027576613067061495606122838491136000000⟩, + ⟨6, 1, 7, 7, 1, 6, 4377292417975291376010116197249881407089004249088000000⟩, + ⟨6, 1, 8, 7, 2, 6, -319454016241402625920576958548249666931348471808000000⟩ +] + +def collectedFourData_13_1_45 : List CollectedFourTerm := [ + ⟨6, 2, 5, 0, 6, 7, 1116608060584631538148860505393713718219279171584000000⟩, + ⟨6, 2, 6, 0, 7, 7, 1537567504627269799651792103303040542174110285824000000⟩, + ⟨6, 2, 7, 0, 8, 7, 2255074143237851524687957997010093846139156561920000000⟩, + ⟨6, 2, 5, 1, 5, 7, -366004933618230854997719873855743997803820482560000000⟩, + ⟨6, 2, 6, 1, 6, 7, -566601801612450186726219750289790620279844634624000000⟩, + ⟨6, 2, 7, 1, 7, 7, -178398073421781321484516662057344923560679833600000000⟩, + ⟨6, 2, 8, 1, 8, 7, -859368604466966094033152511797218418979080503296000000⟩, + ⟨6, 2, 5, 2, 4, 7, 274942705222099346633530809641505499868987129856000000⟩, + ⟨6, 2, 6, 2, 5, 7, -10179588807166628028265492691497163515364376576000000⟩, + ⟨6, 2, 7, 2, 6, 7, -111890766345860102755551480615527242025687580672000000⟩, + ⟨6, 2, 8, 2, 7, 7, -368993406692298075864151539867675109720024154112000000⟩, + ⟨6, 2, 5, 3, 3, 7, -82099422147627949240440214244826093635562897408000000⟩, + ⟨6, 2, 6, 3, 4, 7, 164835154579601432782994699126412360423932166144000000⟩, + ⟨6, 2, 7, 3, 5, 7, -268368480795191143181282505062351090925497745408000000⟩, + ⟨6, 2, 8, 3, 6, 7, 19814550922860126879226475504078575216141271040000000⟩, + ⟨6, 2, 5, 4, 2, 7, -169558693712634394438347055965886649125211996160000000⟩, + ⟨6, 2, 6, 4, 3, 7, -208122475810039315607449533704896842939846623232000000⟩, + ⟨6, 2, 7, 4, 4, 7, 138747815355150347594895606067937451779700031488000000⟩, + ⟨6, 2, 8, 4, 5, 7, 269698487753202762430783453626258490485488222208000000⟩, + ⟨6, 2, 5, 5, 1, 7, -57245613940652616693841140630974923510112059392000000⟩, + ⟨6, 2, 6, 5, 2, 7, 451779059970045441556032625643589005388816580608000000⟩, + ⟨6, 2, 7, 5, 3, 7, 158267427457330510956240145565070715724513673216000000⟩, + ⟨6, 2, 8, 5, 4, 7, 135011683183887322245758667810474935035807924224000000⟩, + ⟨6, 2, 5, 6, 0, 7, 3039674677096136962278664758796586911542936600576000000⟩, + ⟨6, 2, 6, 6, 1, 7, -846092986766840412743045744651287877281231405056000000⟩, + ⟨6, 2, 7, 6, 2, 7, 1120137171634111863911487695721514043571192201216000000⟩, + ⟨6, 2, 8, 6, 3, 7, -716831135811812732473679141309587466475660115968000000⟩, + ⟨6, 2, 6, 7, 0, 7, -251063623861252705614248433519290006703483912192000000⟩, + ⟨6, 2, 7, 7, 1, 7, -5795069838863304011320443759229197711345627168768000000⟩, + ⟨6, 2, 8, 7, 2, 7, 281948772232218774779023611581102227170149793792000000⟩ +] + +def collectedFourData_13_1_46 : List CollectedFourTerm := [ + ⟨6, 3, 4, 0, 5, 8, -1228926842606995982214404035579599850430618035814400000⟩, + ⟨6, 3, 5, 0, 6, 8, -2143718049704078109949280320115852398571915575296000000⟩, + ⟨6, 3, 6, 0, 7, 8, -1475948154351565951561600103480884996815011708928000000⟩, + ⟨6, 3, 7, 0, 8, 8, -1443133395063390480539325601987701366390427484160000000⟩, + ⟨6, 3, 4, 1, 4, 8, -378181567525308270780465795599109607841821045555200000⟩, + ⟨6, 3, 5, 1, 5, 8, 702673937413042743354768922708985990976519536640000000⟩, + ⟨6, 3, 6, 1, 6, 8, 543894743369263630945608537181802001821784342528000000⟩, + ⟨6, 3, 7, 1, 7, 8, 114165744014204143505236408298197524637600972800000000⟩, + ⟨6, 3, 8, 1, 8, 8, 412464331437004233328416878165309865708912377856000000⟩, + ⟨6, 3, 4, 2, 3, 8, -593787000492143030401373243525397648411984710860800000⟩, + ⟨6, 3, 5, 2, 4, 8, -527848276064284645896106228083780314239088984064000000⟩, + ⟨6, 3, 6, 2, 5, 8, 9771632963612629252643415399866713968708943872000000⟩, + ⟨6, 3, 7, 2, 6, 8, 71604431276526068782878818258460312879765651456000000⟩, + ⟨6, 3, 8, 2, 7, 8, 177102838066097547327655773525459364810359570432000000⟩, + ⟨6, 3, 4, 3, 2, 8, 1584115004164057416589811673390735163009560005836800000⟩, + ⟨6, 3, 5, 3, 3, 8, 157618433307741013612152578695461961229666353152000000⟩, + ⟨6, 3, 6, 3, 4, 8, -158229242905985208208266765675875804165563219968000000⟩, + ⟨6, 3, 7, 3, 5, 8, 171742254231114805554370502468765273078454288384000000⟩, + ⟨6, 3, 8, 3, 6, 8, -9510232811205913225812794589272021996603965440000000⟩, + ⟨6, 3, 4, 4, 1, 8, -20337162192910990381910057068367357219564421120000000⟩, + ⟨6, 3, 5, 4, 2, 8, 325526964229244776796665680202060410553148375040000000⟩, + ⟨6, 3, 6, 4, 3, 8, 199781787223300263727552467426169837079708565504000000⟩, + ⟨6, 3, 7, 4, 4, 8, -88791584272973205231953382988674030567344308224000000⟩, + ⟨6, 3, 8, 4, 5, 8, -129445043561597701793485903692071173841473241088000000⟩, + ⟨6, 3, 4, 5, 0, 8, -6527590863779674305414358353603960579294210765619200000⟩, + ⟨6, 3, 5, 5, 1, 8, 109902892700519926128217890223955589259012866048000000⟩, + ⟨6, 3, 6, 5, 2, 8, -433673622608925554859117154154034292512811646976000000⟩, + ⟨6, 3, 7, 5, 3, 8, -101283148760025445795658373254713177167749971968000000⟩, + ⟨6, 3, 8, 5, 4, 8, -64800486486433336565800583016412215045588516864000000⟩, + ⟨6, 3, 5, 6, 0, 8, -5835714160175112447301411371305008972839197343744000000⟩, + ⟨6, 3, 6, 6, 1, 8, 812185077058485265071214482389710512515482386432000000⟩, + ⟨6, 3, 7, 6, 2, 8, -716831135811812732473679141309587466475660115968000000⟩, + ⟨6, 3, 8, 6, 3, 8, 344051753402416849402184531376672149630456168448000000⟩, + ⟨6, 3, 6, 7, 0, 8, 241002031551558082848972366406589703733980954624000000⟩, + ⟨6, 3, 7, 7, 1, 8, 3708551595195231888797965234222966906905547505664000000⟩, + ⟨6, 3, 8, 7, 2, 8, -135324715417523266706902027678661259154698534912000000⟩ +] + +def collectedFourData_13_1_47 : List CollectedFourTerm := [ + ⟨7, 0, 6, 0, 7, 6, -172312498602233687768599004356174228596556038144000000⟩, + ⟨7, 0, 7, 0, 8, 6, -505444423071106490877517386019013528740996055040000000⟩, + ⟨7, 0, 6, 1, 6, 6, 63498072022558815174396294688919436946197970944000000⟩, + ⟨7, 0, 7, 1, 7, 6, 39985519575069040137489278332568098856710963200000000⟩, + ⟨7, 0, 8, 1, 8, 6, 288923805316595486801455266761347397551524937728000000⟩, + ⟨7, 0, 6, 2, 5, 6, 1140808697392071341565636639963025465468256256000000⟩, + ⟨7, 0, 7, 2, 6, 6, 25078804620350882146649178257475960348044427264000000⟩, + ⟨7, 0, 8, 2, 7, 6, 124057335401960183947225884059880525913512738816000000⟩, + ⟨7, 0, 6, 3, 4, 6, -18472787215922536957867076439543959516363096064000000⟩, + ⟨7, 0, 7, 3, 5, 6, 60151171682202052358449350364242126182018973696000000⟩, + ⟨7, 0, 8, 3, 6, 6, -6661746104656852437178210114267812169745694720000000⟩, + ⟨7, 0, 6, 4, 3, 6, 23323921528118106274119245216358666517182676992000000⟩, + ⟨7, 0, 7, 4, 4, 6, -31098449554243132547535770947764911676541894656000000⟩, + ⟨7, 0, 8, 4, 5, 6, -90673912177788757660371121683985809191095762944000000⟩, + ⟨7, 0, 6, 5, 2, 6, -50630088373569177070734472154102565328857858048000000⟩, + ⟨7, 0, 7, 5, 3, 6, -35473507069377625724829336745387789259680776192000000⟩, + ⟨7, 0, 8, 5, 4, 6, -45391568955305941964452633545119343964304965632000000⟩, + ⟨7, 0, 6, 6, 1, 6, 94820159869965027576613067061495606122838491136000000⟩, + ⟨7, 0, 7, 6, 2, 6, -251063623861252705614248433519290006703483912192000000⟩, + ⟨7, 0, 8, 6, 3, 6, 241002031551558082848972366406589703733980954624000000⟩, + ⟨7, 0, 6, 7, 0, 6, 28136260818123276680427073271848821630280138752000000⟩, + ⟨7, 0, 7, 7, 1, 6, 1298886664167693655754898717501750568878411350016000000⟩, + ⟨7, 0, 8, 7, 2, 6, -94792515987016218555609862687792455399354925056000000⟩ +] + +def collectedFourData_13_1_48 : List CollectedFourTerm := [ + ⟨7, 1, 5, 0, 6, 7, -5776811856253007210677491066001779383547967045632000000⟩, + ⟨7, 1, 6, 0, 7, 7, -7954660640609756318023919034299979323782465585152000000⟩, + ⟨7, 1, 7, 0, 8, 7, -11666706973765967703503572217162701403322486620160000000⟩, + ⟨7, 1, 5, 1, 5, 7, 1893539653355061639227254073955723645582972026880000000⟩, + ⟨7, 1, 6, 1, 6, 7, 2931334745707787346679106610000459411739537047552000000⟩, + ⟨7, 1, 7, 1, 7, 7, 922948832319959995690765092727039698500635852800000000⟩, + ⟨7, 1, 8, 1, 8, 7, 4445974302368114690983820725942830822543335620608000000⟩, + ⟨7, 1, 5, 2, 4, 7, -1422425948175319490172955681558963691034916159488000000⟩, + ⟨7, 1, 6, 2, 5, 7, 52664467854755835349651617591580864973056770048000000⟩, + ⟨7, 1, 7, 2, 6, 7, 578870893421254211615585214274599257106133549056000000⟩, + ⟨7, 1, 8, 2, 7, 7, 1909000626005863945505350936240691674560306610176000000⟩, + ⟨7, 1, 5, 3, 3, 7, 424744305540494619550603514538941469612293750784000000⟩, + ⟨7, 1, 6, 3, 4, 7, -852780585162690219278929409749988113287072448512000000⟩, + ⟨7, 1, 7, 3, 5, 7, 1388413962272990465539502802237024209502977654784000000⟩, + ⟨7, 1, 8, 3, 6, 7, -102511289984397939509945222081523909102843985920000000⟩, + ⟨7, 1, 5, 4, 2, 7, 877217984309614691003039496699738400765960519680000000⟩, + ⟨7, 1, 6, 4, 3, 7, 1076729094345490415602407850487361489500620455936000000⟩, + ⟨7, 1, 7, 4, 4, 7, -717816799883369314542122489719406797141126938624000000⟩, + ⟨7, 1, 8, 4, 5, 7, -1395294800980099352340670788935410075784586461184000000⟩, + ⟨7, 1, 5, 5, 1, 7, 296162237229147965588001886405260207758682095616000000⟩, + ⟨7, 1, 6, 5, 2, 7, -2337295172914424779807068091305149672122308624384000000⟩, + ⟨7, 1, 7, 5, 3, 7, -818802213298972633928468677511710909702254624768000000⟩, + ⟨7, 1, 8, 5, 4, 7, -698487786073295093301043285922890886959545188352000000⟩, + ⟨7, 1, 5, 6, 0, 7, -15725865980769615839823091565896336085992549122048000000⟩, + ⟨7, 1, 6, 6, 1, 7, 4377292417975291376010116197249881407089004249088000000⟩, + ⟨7, 1, 7, 6, 2, 7, -5795069838863304011320443759229197711345627168768000000⟩, + ⟨7, 1, 8, 6, 3, 7, 3708551595195231888797965234222966906905547505664000000⟩, + ⟨7, 1, 6, 7, 0, 7, 1298886664167693655754898717501750568878411350016000000⟩, + ⟨7, 1, 7, 7, 1, 7, 29981001691347185419281736617447583200272726360064000000⟩, + ⟨7, 1, 8, 7, 2, 7, -1458672087172892491719052632144699152777468706816000000⟩ +] + +def collectedFourData_13_1_49 : List CollectedFourTerm := [ + ⟨7, 2, 4, 0, 5, 8, 483369648897650136264088739570794639046395664793600000⟩, + ⟨7, 2, 5, 0, 6, 8, 843181388098615413549179789953892948072070119424000000⟩, + ⟨7, 2, 6, 0, 7, 8, 580529708055373375742261282268303288197323948032000000⟩, + ⟨7, 2, 7, 0, 8, 8, 567622789493697241869461487690886518227903447040000000⟩, + ⟨7, 2, 4, 1, 4, 8, 148748880060658039565051974537734930300035452108800000⟩, + ⟨7, 2, 5, 1, 5, 8, -276380369149028712887366748615835468395876188160000000⟩, + ⟨7, 2, 6, 1, 6, 8, -213928284438777745137544546967676589296354066432000000⟩, + ⟨7, 2, 7, 1, 7, 8, -44904426925218102437753848509770905821590323200000000⟩, + ⟨7, 2, 8, 1, 8, 8, -162233203928207331637710233436918745176226136064000000⟩, + ⟨7, 2, 4, 2, 3, 8, 233552237608388665506018828113323843188954444595200000⟩, + ⟨7, 2, 5, 2, 4, 8, 207616781590649493949832098838870479233840316416000000⟩, + ⟨7, 2, 6, 2, 5, 8, -3843443426427483267392449033500559964444295168000000⟩, + ⟨7, 2, 7, 2, 6, 8, -28163929377787105123059174815192845160980414464000000⟩, + ⟨7, 2, 8, 2, 7, 8, -69659261793961260775574949597237762603570167808000000⟩, + ⟨7, 2, 4, 3, 2, 8, -623074610163064720548982775808196837568203141939200000⟩, + ⟨7, 2, 5, 3, 3, 8, -61995526606073937472139807538418332567745855488000000⟩, + ⟨7, 2, 6, 3, 4, 8, 62235774284625971006000165111319775887639969792000000⟩, + ⟨7, 2, 7, 3, 5, 8, -67550801439474024485619280856220834140044394496000000⟩, + ⟨7, 2, 8, 3, 6, 8, 3740627786382884192115237442764733167288975360000000⟩, + ⟨7, 2, 4, 4, 1, 8, 7999147392621195266776329943520681039002337280000000⟩, + ⟨7, 2, 5, 4, 2, 8, -128038422590243296828170267983819044653115637760000000⟩, + ⟨7, 2, 6, 4, 3, 8, -78579496352618731253899882171607426915710795776000000⟩, + ⟨7, 2, 7, 4, 4, 8, 34924094280540083554766153609011461292824723456000000⟩, + ⟨7, 2, 8, 4, 5, 8, 50914182267495630428425150088535524260888707072000000⟩, + ⟨7, 2, 4, 5, 0, 8, 2567475291921602246425391010416574638202410552524800000⟩, + ⟨7, 2, 5, 5, 1, 8, -43227733999846487086399007090967049057245069312000000⟩, + ⟨7, 2, 6, 5, 2, 8, 170575382869788274567489677791783404238844985344000000⟩, + ⟨7, 2, 7, 5, 3, 8, 39837359196684265699002359414324726324413857792000000⟩, + ⟨7, 2, 8, 5, 4, 8, 25487756728380775546619078689276066710071279616000000⟩, + ⟨7, 2, 5, 6, 0, 8, 2295341762319181328090229010626958168134135054336000000⟩, + ⟨7, 2, 6, 6, 1, 8, -319454016241402625920576958548249666931348471808000000⟩, + ⟨7, 2, 7, 6, 2, 8, 281948772232218774779023611581102227170149793792000000⟩, + ⟨7, 2, 8, 6, 3, 8, -135324715417523266706902027678661259154698534912000000⟩, + ⟨7, 2, 6, 7, 0, 8, -94792515987016218555609862687792455399354925056000000⟩, + ⟨7, 2, 7, 7, 1, 8, -1458672087172892491719052632144699152777468706816000000⟩, + ⟨7, 2, 8, 7, 2, 8, 53226813761981595316775550234649699527507836928000000⟩ +] + +def collectedFourData_13_1 : List (List CollectedFourTerm) := [ + collectedFourData_13_1_0, + collectedFourData_13_1_1, + collectedFourData_13_1_2, + collectedFourData_13_1_3, + collectedFourData_13_1_4, + collectedFourData_13_1_5, + collectedFourData_13_1_6, + collectedFourData_13_1_7, + collectedFourData_13_1_8, + collectedFourData_13_1_9, + collectedFourData_13_1_10, + collectedFourData_13_1_11, + collectedFourData_13_1_12, + collectedFourData_13_1_13, + collectedFourData_13_1_14, + collectedFourData_13_1_15, + collectedFourData_13_1_16, + collectedFourData_13_1_17, + collectedFourData_13_1_18, + collectedFourData_13_1_19, + collectedFourData_13_1_20, + collectedFourData_13_1_21, + collectedFourData_13_1_22, + collectedFourData_13_1_23, + collectedFourData_13_1_24, + collectedFourData_13_1_25, + collectedFourData_13_1_26, + collectedFourData_13_1_27, + collectedFourData_13_1_28, + collectedFourData_13_1_29, + collectedFourData_13_1_30, + collectedFourData_13_1_31, + collectedFourData_13_1_32, + collectedFourData_13_1_33, + collectedFourData_13_1_34, + collectedFourData_13_1_35, + collectedFourData_13_1_36, + collectedFourData_13_1_37, + collectedFourData_13_1_38, + collectedFourData_13_1_39, + collectedFourData_13_1_40, + collectedFourData_13_1_41, + collectedFourData_13_1_42, + collectedFourData_13_1_43, + collectedFourData_13_1_44, + collectedFourData_13_1_45, + collectedFourData_13_1_46, + collectedFourData_13_1_47, + collectedFourData_13_1_48, + collectedFourData_13_1_49 +] + +theorem collectedFourChecked_13_1 : collectNumericRowParts 13 1 = collectedFourData_13_1 := by + decide +kernel + +def collectedFourData_13_2_0 : List CollectedFourTerm := [ + +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1304.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1304.lean new file mode 100644 index 0000000000000000000000000000000000000000..201607364f4887af7ea8cb3ceed09fc569f56116 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1304.lean @@ -0,0 +1,609 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1304. -/ +namespace LaughlinFock +def collectedFourData_13_2_1 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_2_2 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_2_3 : List CollectedFourTerm := [ + ⟨0, 5, 8, 2, 8, 3, 281161634136760737892115900351924291809270824960000000⟩, + ⟨0, 5, 8, 3, 7, 3, 172227460003510964079989981926747803021528268800000000⟩, + ⟨0, 5, 8, 4, 6, 3, -219682718820397345545713347635745715421047685120000000⟩, + ⟨0, 5, 8, 5, 5, 3, -73433294068501497767484970227854273931368202240000000⟩, + ⟨0, 5, 8, 6, 4, 3, 109390140648030837258508007168614886710223831040000000⟩, + ⟨0, 5, 8, 7, 3, 3, 523918448439290826483301949382800206435461365760000000⟩ +] + +def collectedFourData_13_2_4 : List CollectedFourTerm := [ + ⟨0, 6, 7, 1, 8, 4, -309180221543219327290219798534090734961881513984000000⟩, + ⟨0, 6, 7, 2, 7, 4, 18254354419136021560386873720411162053317754880000000⟩, + ⟨0, 6, 8, 2, 8, 4, 295097581039362050254200554902279604587028545536000000⟩, + ⟨0, 6, 7, 3, 6, 4, 14253384989870453908484928629225225835232886784000000⟩, + ⟨0, 6, 8, 3, 7, 4, 180764018503563478322590112975958293780449198080000000⟩, + ⟨0, 6, 7, 4, 5, 4, 49073122049453079741307369244394238961705287680000000⟩, + ⟨0, 6, 8, 4, 6, 4, -230571426002298997844909431083493633433788219392000000⟩, + ⟨0, 6, 7, 5, 4, 4, -31095758871379632148040644779247223721972203520000000⟩, + ⟨0, 6, 8, 5, 5, 4, -77073059821619747610051417172601017233240489984000000⟩, + ⟨0, 6, 7, 6, 3, 4, -93241206473035965816848957625443384081296392192000000⟩, + ⟨0, 6, 8, 6, 4, 4, 114812129307399391407887730604032776067103064064000000⟩, + ⟨0, 6, 7, 7, 2, 4, 165578830616232504600244651002963712528726622208000000⟩, + ⟨0, 6, 8, 7, 3, 4, 549886784059334106026024028679399158633323298816000000⟩ +] + +def collectedFourData_13_2_5 : List CollectedFourTerm := [ + ⟨0, 7, 6, 0, 8, 5, 635705007388250693140394658944576165278384128000000⟩, + ⟨0, 7, 6, 1, 7, 5, -2126068796933465153301091117446182991738961920000000⟩, + ⟨0, 7, 7, 1, 8, 5, -3996850834419756751791771189712040723138740224000000⟩, + ⟨0, 7, 6, 2, 6, 5, 146761716974911100929630573403521776013541376000000⟩, + ⟨0, 7, 7, 2, 7, 5, 235978651311364505525383486157994900250951680000000⟩, + ⟨0, 7, 8, 2, 8, 5, 1907400491411370677282270408249104087539253248000000⟩, + ⟨0, 7, 6, 3, 5, 5, -357531859777220819661095477772597750625468416000000⟩, + ⟨0, 7, 7, 3, 6, 5, 184257108704174634776360767729183322510721024000000⟩, + ⟨0, 7, 8, 3, 7, 5, 1168391067486252327521787140794879600691773440000000⟩, + ⟨0, 7, 6, 4, 4, 5, 165229524978651730447671533004760419485614080000000⟩, + ⟨0, 7, 7, 4, 5, 5, 634380646446110397570618134658774913756692480000000⟩, + ⟨0, 7, 8, 4, 6, 5, -1490327537464779326231702385454396528977248256000000⟩, + ⟨0, 7, 6, 5, 3, 5, 61205316480714672411226245535340844011225088000000⟩, + ⟨0, 7, 7, 5, 4, 5, -401982730886347505280723560087359907923230720000000⟩, + ⟨0, 7, 8, 5, 5, 5, -498171457931152698481287850354168748008538112000000⟩, + ⟨0, 7, 6, 6, 2, 5, 4385542863077259820574402456735102066856296448000000⟩, + ⟨0, 7, 7, 6, 3, 5, -1205352632305957819923408462453040246331277312000000⟩, + ⟨0, 7, 8, 6, 4, 5, 742102700705326177170424624475460569558679552000000⟩, + ⟨0, 7, 6, 7, 1, 5, -8694137377743651653188555653393717657499336704000000⟩, + ⟨0, 7, 7, 7, 2, 5, 2140479374804466182183348438265531823804121088000000⟩, + ⟨0, 7, 8, 7, 3, 5, 3554262689789683769525750763236337512022540288000000⟩ +] + +def collectedFourData_13_2_6 : List CollectedFourTerm := [ + ⟨0, 8, 5, 0, 7, 6, 635705007388250693140394658944576165278384128000000⟩, + ⟨0, 8, 6, 0, 8, 6, 39162583025406261856675116877545879950220853248000000⟩, + ⟨0, 8, 5, 1, 6, 6, -104886394955276567179526155128243196835477323776000000⟩, + ⟨0, 8, 6, 1, 7, 6, -130976388120191039570135132747159554726003998720000000⟩, + ⟨0, 8, 7, 1, 8, 6, -123112922522199565218798918116716327483937390592000000⟩, + ⟨0, 8, 5, 2, 5, 6, 18346920363625113239348068617220145380866392064000000⟩, + ⟨0, 8, 6, 2, 6, 6, 9041250043938791760001046913486573322597564416000000⟩, + ⟨0, 8, 7, 2, 7, 6, 7268727960923964659395826817098648315693629440000000⟩, + ⟨0, 8, 8, 2, 8, 6, 39168445132799874123092025100864585721557549056000000⟩, + ⟨0, 8, 5, 3, 4, 6, -24831790840250254818080179483572255263746424832000000⟩, + ⟨0, 8, 6, 3, 5, 6, -22025736748997813621410632191793708335477293056000000⟩, + ⟨0, 8, 7, 3, 6, 6, 5675576119256091693070092543527307381930196992000000⟩, + ⟨0, 8, 8, 3, 7, 6, 23992895894991554451210872198753566576009543680000000⟩, + ⟨0, 8, 5, 4, 3, 6, 2316220235297615355116388328035364415798771712000000⟩, + ⟨0, 8, 6, 4, 4, 6, 10178958660102072225113336351253469794171617280000000⟩, + ⟨0, 8, 7, 4, 5, 6, 19540497909735254434540545984463769895268515840000000⟩, + ⟨0, 8, 8, 4, 6, 6, -30603857262245209501062333058122567484107128832000000⟩, + ⟨0, 8, 5, 5, 2, 6, 179902471030889101335867027990061718195071352832000000⟩, + ⟨0, 8, 6, 5, 3, 6, 3770551215445020762962594047121653287100612608000000⟩, + ⟨0, 8, 7, 5, 4, 6, -12382065494335044024427901969554607720638709760000000⟩, + ⟨0, 8, 8, 5, 5, 6, -10229944631221643064227588080888220676589092864000000⟩, + ⟨0, 8, 5, 6, 1, 6, -229837917966595298408920251082859928706634219520000000⟩, + ⟨0, 8, 6, 6, 2, 6, 270171202823083815566340620601890002239769018368000000⟩, + ⟨0, 8, 7, 6, 3, 6, -37127851746450245256996301078666661708112592896000000⟩, + ⟨0, 8, 8, 6, 4, 6, 15239069637636089095275347284933882326804332544000000⟩, + ⟨0, 8, 5, 7, 0, 6, -1002766832588595449448667365221882803629814972416000000⟩, + ⟨0, 8, 6, 7, 1, 6, -535602005541897189318376564969270585503843876864000000⟩, + ⟨0, 8, 7, 7, 2, 6, 65932075613456075084307578620902005190168674304000000⟩, + ⟨0, 8, 8, 7, 3, 6, 72986739690715704843204866957278510014252711936000000⟩ +] + +def collectedFourData_13_2_7 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_2_8 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_2_9 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_2_10 : List CollectedFourTerm := [ + ⟨1, 4, 8, 2, 8, 3, -268961767769154127320678512756590568425694586470400000⟩, + ⟨1, 4, 8, 3, 7, 3, -164754349373299169300094890898006573033468198912000000⟩, + ⟨1, 4, 8, 4, 6, 3, 210150480109700034157705729576134147110368758988800000⟩, + ⟨1, 4, 8, 5, 5, 3, 70246954732697554792673310188500402055138613657600000⟩, + ⟨1, 4, 8, 6, 4, 3, -104643600096945094799863368896532492692645058969600000⟩, + ⟨1, 4, 8, 7, 3, 3, -501185136769270734815972193122135434777416066662400000⟩ +] + +def collectedFourData_13_2_11 : List CollectedFourTerm := [ + ⟨1, 5, 7, 1, 8, 4, 479112126052826319651064384762080266483620066099200000⟩, + ⟨1, 5, 7, 2, 7, 4, -28287328703694280189060863384396507602950815744000000⟩, + ⟨1, 5, 8, 2, 8, 4, -457289372325038009187127408285923966934389148876800000⟩, + ⟨1, 5, 7, 3, 6, 4, -22087342947943632948155123888149490928031314739200000⟩, + ⟨1, 5, 8, 3, 7, 4, -280115696880009908768973681475206521480653307904000000⟩, + ⟨1, 5, 7, 4, 5, 4, -76044734426444197168320714105206522594809872384000000⟩, + ⟨1, 5, 8, 4, 6, 4, 357298295368325174803530860853483125239289846169600000⟩, + ⟨1, 5, 7, 5, 4, 4, 48186637132641217699065987339591765105548722176000000⟩, + ⟨1, 5, 8, 5, 5, 4, 119434022552348310628855058864414056538973614899200000⟩, + ⟨1, 5, 7, 6, 3, 4, 144488520145465114730577773056631804686488934809600000⟩, + ⟨1, 5, 8, 6, 4, 4, -177915272505329885077447443810727136606723191603200000⟩, + ⟨1, 5, 7, 7, 2, 4, -256584412708930541705024419705680246041980855910400000⟩, + ⟨1, 5, 8, 7, 3, 4, -852116040554007710558232189028245842424947854540800000⟩ +] + +def collectedFourData_13_2_12 : List CollectedFourTerm := [ + ⟨1, 6, 6, 0, 8, 5, -104886394955276567179526155128243196835477323776000000⟩, + ⟨1, 6, 6, 1, 7, 5, 350784859243779174814587040130654837217574256640000000⟩, + ⟨1, 6, 7, 1, 8, 5, 659449383478342860463342726765783620527333572608000000⟩, + ⟨1, 6, 6, 2, 6, 5, -24214544847125498904981285160903047861441134592000000⟩, + ⟨1, 6, 7, 2, 7, 5, -38934646942840370759878096102383436423558594560000000⟩, + ⟨1, 6, 8, 2, 8, 5, -314706285077091899156067108485888546539428642816000000⟩, + ⟨1, 6, 6, 3, 5, 5, 58989983432339460597210025574746617030767542272000000⟩, + ⟨1, 6, 7, 3, 6, 5, -30400993624799594542635165416758256098458206208000000⟩, + ⟨1, 6, 8, 3, 7, 5, -192775462741848519449168654533847132311891476480000000⟩, + ⟨1, 6, 6, 4, 4, 5, -27261589910049692636981990970242781700014735360000000⟩, + ⟨1, 6, 7, 4, 5, 5, -104667885673099664585679403951726096208269148160000000⟩, + ⟨1, 6, 8, 4, 6, 5, 245892482976443903552653444862740161363078807552000000⟩, + ⟨1, 6, 6, 5, 3, 5, -10098402440045946351937265348046144089773572096000000⟩, + ⟨1, 6, 7, 5, 4, 5, 66324032352942825497450212084271316077893386240000000⟩, + ⟨1, 6, 8, 5, 5, 5, 82194426164242535336549084474485198695174242304000000⟩, + ⟨1, 6, 6, 6, 2, 5, -723580553061595134126695844066675597183566217216000000⟩, + ⟨1, 6, 7, 6, 3, 5, 198873834220424885365643773676591169260123848704000000⟩, + ⟨1, 6, 8, 6, 4, 5, -122441189008942890456098179877734862502739574784000000⟩, + ⟨1, 6, 6, 7, 1, 5, 1434465225535845227333823021906172328807673888768000000⟩, + ⟨1, 6, 7, 7, 2, 5, -353162492807373970553443604230754221404608004096000000⟩, + ⟨1, 6, 8, 7, 3, 5, -586425772840269916832375753474368767543000170496000000⟩ +] + +def collectedFourData_13_2_13 : List CollectedFourTerm := [ + ⟨1, 7, 5, 0, 7, 6, -2126068796933465153301091117446182991738961920000000⟩, + ⟨1, 7, 6, 0, 8, 6, -130976388120191039570135132747159554726003998720000000⟩, + ⟨1, 7, 5, 1, 6, 6, 350784859243779174814587040130654837217574256640000000⟩, + ⟨1, 7, 6, 1, 7, 6, 438040928860130036305495237290124454260427980800000000⟩, + ⟨1, 7, 7, 1, 8, 6, 411742144598015668856755559645675497731265658880000000⟩, + ⟨1, 7, 5, 2, 5, 6, -61359930237427722642195675606402910649277480960000000⟩, + ⟨1, 7, 6, 2, 6, 6, -30237798004242775956289530654123847695193866240000000⟩, + ⟨1, 7, 7, 2, 7, 6, -24309727832110632047333796179616793856940441600000000⟩, + ⟨1, 7, 8, 2, 8, 6, -130995993508647922050960081981399646924009635840000000⟩, + ⟨1, 7, 5, 3, 4, 6, 83048104173876382624906008076311227171057172480000000⟩, + ⟨1, 7, 6, 3, 5, 6, 73663461963128919287199704255476888206405795840000000⟩, + ⟨1, 7, 7, 3, 6, 6, -18981548283450132611362537556950025669317754880000000⟩, + ⟨1, 7, 8, 3, 7, 6, -80242481524548334689769948062104314776335155200000000⟩, + ⟨1, 7, 5, 4, 3, 6, -7746428786716465662412528101825719482114375680000000⟩, + ⟨1, 7, 6, 4, 4, 6, -34042781071412193221009050063595219052606259200000000⟩, + ⟨1, 7, 7, 4, 5, 6, -65351762845339451178238426301103272170723737600000000⟩, + ⟨1, 7, 8, 4, 6, 6, 102352357201626995370689040987589820774067732480000000⟩, + ⟨1, 7, 5, 5, 2, 6, -601670626634534153281711240928371263224131092480000000⟩, + ⟨1, 7, 6, 5, 3, 6, -12610332140267757670614559224403391608384389120000000⟩, + ⟨1, 7, 7, 5, 4, 6, 41410910380031761926729548315905828340524646400000000⟩, + ⟨1, 7, 8, 5, 5, 6, 34213299914301323264237542807982932608637992960000000⟩, + ⟨1, 7, 5, 6, 1, 6, 768676068399273604085603633770917365581401292800000000⟩, + ⟨1, 7, 6, 6, 2, 6, -903567782975367054155497669579970265891754475520000000⟩, + ⟨1, 7, 7, 6, 3, 6, 124171378513446099463620304480672713587231293440000000⟩, + ⟨1, 7, 8, 6, 4, 6, -50965951304968549325409231663009975360458588160000000⟩, + ⟨1, 7, 5, 7, 0, 6, 3353680163894552961173573647027364505298654986240000000⟩, + ⟨1, 7, 6, 7, 1, 6, 1791281645296441959069599842782243113267059752960000000⟩, + ⟨1, 7, 7, 7, 2, 6, -220504993746597307137960806089253109222667714560000000⟩, + ⟨1, 7, 8, 7, 3, 6, -244098800611718951894909068305172487535109079040000000⟩ +] + +def collectedFourData_13_2_14 : List CollectedFourTerm := [ + ⟨1, 8, 4, 0, 6, 7, -309180221543219327290219798534090734961881513984000000⟩, + ⟨1, 8, 5, 0, 7, 7, -3996850834419756751791771189712040723138740224000000⟩, + ⟨1, 8, 6, 0, 8, 7, -123112922522199565218798918116716327483937390592000000⟩, + ⟨1, 8, 4, 1, 5, 7, 479112126052826319651064384762080266483620066099200000⟩, + ⟨1, 8, 5, 1, 6, 7, 659449383478342860463342726765783620527333572608000000⟩, + ⟨1, 8, 6, 1, 7, 7, 411742144598015668856755559645675497731265658880000000⟩, + ⟨1, 8, 7, 1, 8, 7, 258014845141416810654287395801151369577089728512000000⟩, + ⟨1, 8, 4, 2, 4, 7, -127740557103304167354153986136403265004816354508800000⟩, + ⟨1, 8, 5, 2, 5, 7, -115352094308110947820378107855869784316666970112000000⟩, + ⟨1, 8, 6, 2, 6, 7, -28422402971764218723927186344554072855610916864000000⟩, + ⟨1, 8, 7, 2, 7, 7, -15233491990856656214670946186219064903168163840000000⟩, + ⟨1, 8, 8, 2, 8, 7, -61565675428266672560174308419943928096423411712000000⟩, + ⟨1, 8, 4, 3, 3, 7, 162930940010600544944617350599159831557576851456000000⟩, + ⟨1, 8, 5, 3, 4, 7, 156124244400320977019121368062052601430284435456000000⟩, + ⟨1, 8, 6, 3, 5, 7, 69240908346484166068638172194006883042458599424000000⟩, + ⟨1, 8, 7, 3, 6, 7, -11894631883457467518518881869486579283144998912000000⟩, + ⟨1, 8, 8, 3, 7, 7, -37712470746465183673168121410675665779671695360000000⟩, + ⟨1, 8, 4, 4, 2, 7, -543196602866064773264512004171912476000047543091200000⟩, + ⟨1, 8, 5, 4, 3, 7, -14562708603135506754852558316722417323785322496000000⟩, + ⟨1, 8, 6, 4, 4, 7, -31998945219339723715216315767445472255536005120000000⟩, + ⟨1, 8, 7, 4, 5, 7, -40952147336583620548092506219181124570306314240000000⟩, + ⟨1, 8, 8, 4, 6, 7, 48103700227880507396709593765796159640634916864000000⟩, + ⟨1, 8, 4, 5, 1, 7, 523709323356804967643389315852353183975125444198400000⟩, + ⟨1, 8, 5, 5, 2, 7, -1131095922003389923887951940846541709586471059456000000⟩, + ⟨1, 8, 6, 5, 3, 7, -11853242145747170660683125061397492987993260032000000⟩, + ⟨1, 8, 7, 5, 4, 7, 25949808075392431016064269121223463173210767360000000⟩, + ⟨1, 8, 8, 5, 5, 7, 16079613287674817241152634404113049218216624128000000⟩, + ⟨1, 8, 4, 6, 0, 7, 1633985452364459310584567130555041636570507300044800000⟩, + ⟨1, 8, 5, 6, 1, 7, 1445053701842312088482641953800058405474439004160000000⟩, + ⟨1, 8, 6, 6, 2, 7, -849320034363150536852614521233115298243723395072000000⟩, + ⟨1, 8, 7, 6, 3, 7, 77810978104808387011102472206278890170777337856000000⟩, + ⟨1, 8, 8, 6, 4, 7, -23953047203137505782851806483607149715797311488000000⟩, + ⟨1, 8, 5, 7, 0, 7, 6304668682769069747729377777946130466818100297728000000⟩, + ⟨1, 8, 6, 7, 1, 7, 1683737974286241613637282276356003173539833184256000000⟩, + ⟨1, 8, 7, 7, 2, 7, -138177649679224934607688772504480116298527801344000000⟩, + ⟨1, 8, 8, 7, 3, 7, -114721886741506833669178595042689123240453865472000000⟩ +] + +def collectedFourData_13_2_15 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_2_16 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_2_17 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_2_18 : List CollectedFourTerm := [ + ⟨2, 3, 8, 2, 8, 3, 186573004419569687836198925490444067500205906329600000⟩, + ⟨2, 3, 8, 3, 7, 3, 114286555329865521793680492820569849180180185088000000⟩, + ⟨2, 3, 8, 4, 6, 3, -145776876689529147376143572730357061298758562611200000⟩, + ⟨2, 3, 8, 5, 5, 3, -48728804485899037092634538770361580470625789542400000⟩, + ⟨2, 3, 8, 6, 4, 3, 72589018972108688764117697310309696397692528230400000⟩, + ⟨2, 3, 8, 7, 3, 3, 347661370287140511684740957091864529967741770137600000⟩ +] + +def collectedFourData_13_2_19 : List CollectedFourTerm := [ + ⟨2, 4, 7, 1, 8, 4, -127740557103304167354153986136403265004816354508800000⟩, + ⟨2, 4, 7, 2, 7, 4, 7541948807147871788564876430359045489679138816000000⟩, + ⟨2, 4, 8, 2, 8, 4, 121922188986258172183542220328278573630530728755200000⟩, + ⟨2, 4, 7, 3, 6, 4, 5888912719339035606030198576323628393571339468800000⟩, + ⟨2, 4, 8, 3, 7, 4, 74684261213809170183477306914839869416911405056000000⟩, + ⟨2, 4, 7, 4, 5, 4, 20274996628525619479870876982109188188092235776000000⟩, + ⟨2, 4, 8, 4, 6, 4, -95262634403409790782067984834322826810311992934400000⟩, + ⟨2, 4, 7, 5, 4, 4, -12847489215039543550675913260157813029878104064000000⟩, + ⟨2, 4, 8, 5, 5, 4, -31843419834970731749505644963700499802749717708800000⟩, + ⟨2, 4, 7, 6, 3, 4, -38523433356764278266363856377313944648720737894400000⟩, + ⟨2, 4, 8, 6, 4, 4, 47435651888533422685213673467992703130984565964800000⟩, + ⟨2, 4, 7, 7, 2, 4, 68410365843775445435402497181783460458178124185600000⟩, + ⟨2, 4, 8, 7, 3, 4, 227190613257467475640333334792427746769671238451200000⟩ +] + +def collectedFourData_13_2_20 : List CollectedFourTerm := [ + ⟨2, 5, 6, 0, 8, 5, 18346920363625113239348068617220145380866392064000000⟩, + ⟨2, 5, 6, 1, 7, 5, -61359930237427722642195675606402910649277480960000000⟩, + ⟨2, 5, 7, 1, 8, 5, -115352094308110947820378107855869784316666970112000000⟩, + ⟨2, 5, 6, 2, 6, 5, 4235652547130381329127725114837318312749170688000000⟩, + ⟨2, 5, 7, 2, 7, 5, 6810519773806145994459218867066908073357475840000000⟩, + ⟨2, 5, 8, 2, 8, 5, 55048999946119682211225581013695504240684826624000000⟩, + ⟨2, 5, 6, 3, 5, 5, -10318635975106034722839380148144681622551134208000000⟩, + ⟨2, 5, 7, 3, 6, 5, 5317797501259368155546506039447495922272960512000000⟩, + ⟨2, 5, 8, 3, 7, 5, 33720637118796747248018361243433797170201886720000000⟩, + ⟨2, 5, 6, 4, 4, 5, 4768647251902955573759636726219033478734807040000000⟩, + ⟨2, 5, 7, 4, 5, 5, 18308698319664865189752684447966413810030346240000000⟩, + ⟨2, 5, 8, 4, 6, 5, -43011963611739185192211184364829733212943024128000000⟩, + ⟨2, 5, 6, 5, 3, 5, 1766431055680399402536639535433387760936812544000000⟩, + ⟨2, 5, 7, 5, 4, 5, -11601521248707207593382876089185755624489615360000000⟩, + ⟨2, 5, 8, 5, 5, 5, -14377599609675189888028319425213614274753069056000000⟩, + ⟨2, 5, 6, 6, 2, 5, 126570035983690239753458211644502667142023348224000000⟩, + ⟨2, 5, 7, 6, 3, 5, -34787375430404763884012610928432453845994438656000000⟩, + ⟨2, 5, 8, 6, 4, 5, 21417637100908234746363750176211319558584139776000000⟩, + ⟨2, 5, 6, 7, 1, 5, -250919285275441694702460509704977696266599268352000000⟩, + ⟨2, 5, 7, 7, 2, 5, 61775830256336336864246760221039980441233260544000000⟩, + ⟨2, 5, 8, 7, 3, 5, 102578670551747090547636675366874235939422470144000000⟩ +] + +def collectedFourData_13_2_21 : List CollectedFourTerm := [ + ⟨2, 6, 5, 0, 7, 6, 146761716974911100929630573403521776013541376000000⟩, + ⟨2, 6, 6, 0, 8, 6, 9041250043938791760001046913486573322597564416000000⟩, + ⟨2, 6, 5, 1, 6, 6, -24214544847125498904981285160903047861441134592000000⟩, + ⟨2, 6, 6, 1, 7, 6, -30237798004242775956289530654123847695193866240000000⟩, + ⟨2, 6, 7, 1, 8, 6, -28422402971764218723927186344554072855610916864000000⟩, + ⟨2, 6, 5, 2, 5, 6, 4235652547130381329127725114837318312749170688000000⟩, + ⟨2, 6, 6, 2, 6, 6, 2087303646544269587946734656748248743618281472000000⟩, + ⟨2, 6, 7, 2, 7, 6, 1678091226859293080410993859238888431136276480000000⟩, + ⟨2, 6, 8, 2, 8, 6, 9042603396415457744784992536509099968248676352000000⟩, + ⟨2, 6, 5, 3, 4, 6, -5732778909905994223622292095606865002646994944000000⟩, + ⟨2, 6, 6, 3, 5, 6, -5084960642674434961573463456413474678061924352000000⟩, + ⟨2, 6, 7, 3, 6, 6, 1310289027777165517768920708335700296979185664000000⟩, + ⟨2, 6, 8, 3, 7, 6, 5539107850064006851650649935781586495141314560000000⟩, + ⟨2, 6, 5, 4, 3, 6, 534733020305910779204370962917857864821243904000000⟩, + ⟨2, 6, 6, 4, 4, 6, 2349960174312182162853174881829083795958005760000000⟩, + ⟨2, 6, 7, 4, 5, 6, 4511207227326318736220872489756390461831905280000000⟩, + ⟨2, 6, 8, 4, 6, 6, -7065344122921285064511936702166584753540562944000000⟩, + ⟨2, 6, 5, 5, 2, 6, 41533093541289721593720622390783430388501970944000000⟩, + ⟨2, 6, 6, 5, 3, 6, 870486410975495486318469165061729048420417536000000⟩, + ⟨2, 6, 7, 5, 4, 6, -2858579326141074484339366767461571604953169920000000⟩, + ⟨2, 6, 8, 5, 5, 6, -2361731024905107264458610976189588108411404288000000⟩, + ⟨2, 6, 5, 6, 1, 6, -53061415396583722370270252553478436879691939840000000⟩, + ⟨2, 6, 6, 6, 2, 6, 62372938930267688131012130698382294997276819456000000⟩, + ⟨2, 6, 7, 6, 3, 6, -8571502830039999683066315140542999311922757632000000⟩, + ⟨2, 6, 8, 6, 4, 6, 3518160151527295834738037566122926254847950848000000⟩, + ⟨2, 6, 5, 7, 0, 6, -231503260735390441058405835991035538094237417472000000⟩, + ⟨2, 6, 6, 7, 1, 6, -123651487773364205147846525327707603743736332288000000⟩, + ⟨2, 6, 7, 7, 2, 6, 15221375493807883609868763058271044060229664768000000⟩, + ⟨2, 6, 8, 7, 3, 6, 16850046969770503067025025045064005920397197312000000⟩ +] + +def collectedFourData_13_2_22 : List CollectedFourTerm := [ + ⟨2, 7, 4, 0, 6, 7, 18254354419136021560386873720411162053317754880000000⟩, + ⟨2, 7, 5, 0, 7, 7, 235978651311364505525383486157994900250951680000000⟩, + ⟨2, 7, 6, 0, 8, 7, 7268727960923964659395826817098648315693629440000000⟩, + ⟨2, 7, 4, 1, 5, 7, -28287328703694280189060863384396507602950815744000000⟩, + ⟨2, 7, 5, 1, 6, 7, -38934646942840370759878096102383436423558594560000000⟩, + ⟨2, 7, 6, 1, 7, 7, -24309727832110632047333796179616793856940441600000000⟩, + ⟨2, 7, 7, 1, 8, 7, -15233491990856656214670946186219064903168163840000000⟩, + ⟨2, 7, 4, 2, 4, 7, 7541948807147871788564876430359045489679138816000000⟩, + ⟨2, 7, 5, 2, 5, 7, 6810519773806145994459218867066908073357475840000000⟩, + ⟨2, 7, 6, 2, 6, 7, 1678091226859293080410993859238888431136276480000000⟩, + ⟨2, 7, 7, 2, 7, 7, 899402815788770656072705863784876756225228800000000⟩, + ⟨2, 7, 8, 2, 8, 7, 3634907995445547711635463298044887364890787840000000⟩, + ⟨2, 7, 4, 3, 3, 7, -9619629321537109310502963373326736264443985920000000⟩, + ⟨2, 7, 5, 3, 4, 7, -9217754216224618232421874473773792076150865920000000⟩, + ⟨2, 7, 6, 3, 5, 7, -4088062538253120966733054851712058591469895680000000⟩, + ⟨2, 7, 7, 3, 6, 7, 702272690672214581873225446192918470422691840000000⟩, + ⟨2, 7, 8, 3, 7, 7, 2226587469247424194491092421066941661393715200000000⟩, + ⟨2, 7, 4, 4, 2, 7, 32070949617977872948940990213854393207760093184000000⟩, + ⟨2, 7, 5, 4, 3, 7, 859798996253312610784291728531223210591518720000000⟩, + ⟨2, 7, 6, 4, 4, 7, 1889254377776209895868051703424701178472038400000000⟩, + ⟨2, 7, 7, 4, 5, 7, 2417861685897577098254704811955607879601356800000000⟩, + ⟨2, 7, 8, 4, 6, 7, -2840097560085543445996188623373329718816276480000000⟩, + ⟨2, 7, 4, 5, 1, 7, -30920398314756591308881562405944670040241471488000000⟩, + ⟨2, 7, 5, 5, 2, 7, 66781198807709228367502862911634681397950545920000000⟩, + ⟨2, 7, 6, 5, 3, 7, 699828993149431018816919666588788816336650240000000⟩, + ⟨2, 7, 7, 5, 4, 7, -1532106392033731155285612587721404884136755200000000⟩, + ⟨2, 7, 8, 5, 5, 7, -949358786311738392778808965571302128573480960000000⟩, + ⟨2, 7, 4, 6, 0, 7, -96472372696723965622591982264807514753346830336000000⟩, + ⟨2, 7, 5, 6, 1, 7, -85317625740903695492103318049208237808628531200000000⟩, + ⟨2, 7, 6, 6, 2, 7, 50144827651501339555505024333174554068296663040000000⟩, + ⟨2, 7, 7, 6, 3, 7, -4594049273058863747924762197048393748887633920000000⟩, + ⟨2, 7, 8, 6, 4, 7, 1414215343018781731611027215364962977484636160000000⟩, + ⟨2, 7, 5, 7, 0, 7, -372234860483811083995411237554436334578261032960000000⟩, + ⟨2, 7, 6, 7, 1, 7, -99409818578200229901684880260075886758246481920000000⟩, + ⟨2, 7, 7, 7, 2, 7, 8158166707617803682976208119640122955220910080000000⟩, + ⟨2, 7, 8, 7, 3, 7, 6773311597225534231637913636911192235615191040000000⟩ +] + +def collectedFourData_13_2_23 : List CollectedFourTerm := [ + ⟨2, 8, 3, 0, 5, 8, 281161634136760737892115900351924291809270824960000000⟩, + ⟨2, 8, 4, 0, 6, 8, 295097581039362050254200554902279604587028545536000000⟩, + ⟨2, 8, 5, 0, 7, 8, 1907400491411370677282270408249104087539253248000000⟩, + ⟨2, 8, 6, 0, 8, 8, 39168445132799874123092025100864585721557549056000000⟩, + ⟨2, 8, 3, 1, 4, 8, -268961767769154127320678512756590568425694586470400000⟩, + ⟨2, 8, 4, 1, 5, 8, -457289372325038009187127408285923966934389148876800000⟩, + ⟨2, 8, 5, 1, 6, 8, -314706285077091899156067108485888546539428642816000000⟩, + ⟨2, 8, 6, 1, 7, 8, -130995993508647922050960081981399646924009635840000000⟩, + ⟨2, 8, 7, 1, 8, 8, -61565675428266672560174308419943928096423411712000000⟩, + ⟨2, 8, 3, 2, 3, 8, 186573004419569687836198925490444067500205906329600000⟩, + ⟨2, 8, 4, 2, 4, 8, 121922188986258172183542220328278573630530728755200000⟩, + ⟨2, 8, 5, 2, 5, 8, 55048999946119682211225581013695504240684826624000000⟩, + ⟨2, 8, 6, 2, 6, 8, 9042603396415457744784992536509099968248676352000000⟩, + ⟨2, 8, 7, 2, 7, 8, 3634907995445547711635463298044887364890787840000000⟩, + ⟨2, 8, 8, 2, 8, 8, 11752292435301431103806498956058354154848491929600000⟩, + ⟨2, 8, 3, 3, 2, 8, -123028618366401318034115014257111580710924818841600000⟩, + ⟨2, 8, 4, 3, 3, 8, -155509708976893937602734212191783182434486452224000000⟩, + ⟨2, 8, 5, 3, 4, 8, -74506523467402074181345467638273681531823194112000000⟩, + ⟨2, 8, 6, 3, 5, 8, -22029033702984793852289870960366018017395474432000000⟩, + ⟨2, 8, 7, 3, 6, 8, 2838212838002727060593274393781520786220122112000000⟩, + ⟨2, 8, 8, 3, 7, 8, 7198946191804776951661235332091447631924953088000000⟩, + ⟨2, 8, 3, 4, 1, 8, 113596540054017419125419952561504033245400085299200000⟩, + ⟨2, 8, 4, 4, 2, 8, 518454908708212569719356264075053458708218301644800000⟩, + ⟨2, 8, 5, 4, 3, 8, 6949700826133977553432307702989327024565256192000000⟩, + ⟨2, 8, 6, 4, 4, 8, 10180482312124257474334973327256739427553116160000000⟩, + ⟨2, 8, 7, 4, 5, 8, 9771711428591554110595415329122045363738378240000000⟩, + ⟨2, 8, 8, 4, 6, 8, -9182531473350298114141874969112575942088405811200000⟩, + ⟨2, 8, 3, 5, 0, 8, -136445327956831205615027954991530700502630976716800000⟩, + ⟨2, 8, 4, 5, 1, 8, -499855242094620244778794617604200301716972345753600000⟩, + ⟨2, 8, 5, 5, 2, 8, 539788199970658099000466799422491118096049242112000000⟩, + ⟨2, 8, 6, 5, 3, 8, 3771115615810127290037535746548859527785086976000000⟩, + ⟨2, 8, 7, 5, 4, 8, -6191959460781323279185947665570576100344463360000000⟩, + ⟨2, 8, 8, 5, 5, 8, -3069442774545606546452628553947872787024995942400000⟩, + ⟨2, 8, 4, 6, 0, 8, -1559560155690154810305280102935039683475442709299200000⟩, + ⟨2, 8, 5, 6, 1, 8, -689616964754700931898029661949876612226162360320000000⟩, + ⟨2, 8, 6, 6, 2, 8, 270211643786964641944480738502496752010522525696000000⟩, + ⟨2, 8, 7, 6, 3, 8, -18566704641087428976793494888232785967061139456000000⟩, + ⟨2, 8, 8, 6, 4, 8, 4572405215887623152504559170626348213286102630400000⟩, + ⟨2, 8, 5, 7, 0, 8, -3008750799539260273514075001146581411537203757056000000⟩, + ⟨2, 8, 6, 7, 1, 8, -535682177896072189312164896582963855322469367808000000⟩, + ⟨2, 8, 7, 7, 2, 8, 32970972375365646378856593131956141256809119744000000⟩, + ⟨2, 8, 8, 7, 3, 8, 21899299444649607142671416815392006082467043737600000⟩ +] + +def collectedFourData_13_2_24 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_2_25 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_2_26 : List CollectedFourTerm := [ + ⟨3, 2, 8, 2, 8, 3, -123028618366401318034115014257111580710924818841600000⟩, + ⟨3, 2, 8, 3, 7, 3, -75362012011496678931081562744444918864646504448000000⟩, + ⟨3, 2, 8, 4, 6, 3, 96127131492989174774945960175597001771303777075200000⟩, + ⟨3, 2, 8, 5, 5, 3, 32132395086830880607392825738095805957606368870400000⟩, + ⟨3, 2, 8, 6, 4, 3, -47866124793852007190389153019123748132501218918400000⟩, + ⟨3, 2, 8, 7, 3, 3, -229252341081507223005615206004054730492440320409600000⟩ +] + +def collectedFourData_13_2_27 : List CollectedFourTerm := [ + ⟨3, 3, 7, 1, 8, 4, 162930940010600544944617350599159831557576851456000000⟩, + ⟨3, 3, 7, 2, 7, 4, -9619629321537109310502963373326736264443985920000000⟩, + ⟨3, 3, 8, 2, 8, 4, -155509708976893937602734212191783182434486452224000000⟩, + ⟨3, 3, 7, 3, 6, 4, -7511209491801039285957768884169072707062726656000000⟩, + ⟨3, 3, 8, 3, 7, 4, -95258523678760540195907690366267519801197854720000000⟩, + ⟨3, 3, 7, 4, 5, 4, -25860418447415623949487315427888363415399301120000000⟩, + ⟨3, 3, 8, 4, 6, 4, 121505893846084192841508574864023848442635747328000000⟩, + ⟨3, 3, 7, 5, 4, 4, 16386757205776275470246121128588474259792199680000000⟩, + ⟨3, 3, 8, 5, 5, 4, 40615748392800633634325225938242143623846035456000000⟩, + ⟨3, 3, 7, 6, 3, 4, 49135993701494316222746386330840426028652822528000000⟩, + ⟨3, 3, 8, 6, 4, 4, -60503379094895588562604230408319186202762674176000000⟩, + ⟨3, 3, 7, 7, 2, 4, -87256275267231508694668399741971226505691267072000000⟩, + ⟨3, 3, 8, 7, 3, 4, -289777820130287405166680404227704624019085983744000000⟩ +] + +def collectedFourData_13_2_28 : List CollectedFourTerm := [ + ⟨3, 4, 6, 0, 8, 5, -24831790840250254818080179483572255263746424832000000⟩, + ⟨3, 4, 6, 1, 7, 5, 83048104173876382624906008076311227171057172480000000⟩, + ⟨3, 4, 7, 1, 8, 5, 156124244400320977019121368062052601430284435456000000⟩, + ⟨3, 4, 6, 2, 6, 5, -5732778909905994223622292095606865002646994944000000⟩, + ⟨3, 4, 7, 2, 7, 5, -9217754216224618232421874473773792076150865920000000⟩, + ⟨3, 4, 8, 2, 8, 5, -74506523467402074181345467638273681531823194112000000⟩, + ⟨3, 4, 6, 3, 5, 5, 13965843052249834199462481371797937637455560704000000⟩, + ⟨3, 4, 7, 3, 6, 5, -7197416932374290835189209689316052000263110656000000⟩, + ⟨3, 4, 8, 3, 7, 5, -45639474709557825106095372947212447100813967360000000⟩, + ⟨3, 4, 6, 4, 4, 5, -6454164993540707927774738076837745564078571520000000⟩, + ⟨3, 4, 7, 4, 5, 5, -24780058899287046977097020967394222147758981120000000⟩, + ⟨3, 4, 8, 4, 6, 5, 58214897261598336804664293037639060685705969664000000⟩, + ⟨3, 4, 6, 5, 3, 5, -2390790696150993851526923113703770537246851072000000⟩, + ⟨3, 4, 7, 5, 4, 5, 15702174717440926118139005554919552281403719680000000⟩, + ⟨3, 4, 8, 5, 5, 5, 19459480894687613795767209838844003422964809728000000⟩, + ⟨3, 4, 6, 6, 2, 5, -171307260177638675342809713671317753434747174912000000⟩, + ⟨3, 4, 7, 6, 3, 5, 47083260484507255509945921650819465254721814528000000⟩, + ⟨3, 4, 8, 6, 4, 5, -28987877760486053948379310028550040494526169088000000⟩, + ⟨3, 4, 6, 7, 1, 5, 339608778272024582617379972897761923226272792576000000⟩, + ⟨3, 4, 7, 7, 2, 5, -83611007488182492479444526468549999468396675072000000⟩, + ⟨3, 4, 8, 7, 3, 5, -138835948558541948147327723625636811398155599872000000⟩ +] + +def collectedFourData_13_2_29 : List CollectedFourTerm := [ + ⟨3, 5, 5, 0, 7, 6, -357531859777220819661095477772597750625468416000000⟩, + ⟨3, 5, 6, 0, 8, 6, -22025736748997813621410632191793708335477293056000000⟩, + ⟨3, 5, 5, 1, 6, 6, 58989983432339460597210025574746617030767542272000000⟩, + ⟨3, 5, 6, 1, 7, 6, 73663461963128919287199704255476888206405795840000000⟩, + ⟨3, 5, 7, 1, 8, 6, 69240908346484166068638172194006883042458599424000000⟩, + ⟨3, 5, 5, 2, 5, 6, -10318635975106034722839380148144681622551134208000000⟩, + ⟨3, 5, 6, 2, 6, 6, -5084960642674434961573463456413474678061924352000000⟩, + ⟨3, 5, 7, 2, 7, 6, -4088062538253120966733054851712058591469895680000000⟩, + ⟨3, 5, 8, 2, 8, 6, -22029033702984793852289870960366018017395474432000000⟩, + ⟨3, 5, 5, 3, 4, 6, 13965843052249834199462481371797937637455560704000000⟩, + ⟨3, 5, 6, 3, 5, 6, 12387668071368745952935379526663084691194642432000000⟩, + ⟨3, 5, 7, 3, 6, 6, -3192045463919868448751143800683742048471220224000000⟩, + ⟨3, 5, 8, 3, 7, 6, -13494033539267859802949982654577822699314216960000000⟩, + ⟨3, 5, 5, 4, 3, 6, -1302683664207509679728070414131316013676888064000000⟩, + ⟨3, 5, 6, 4, 4, 6, -5724828305653211643995067373188359792004956160000000⟩, + ⟨3, 5, 7, 4, 5, 6, -10989925322978768662745407584770878561824276480000000⟩, + ⟨3, 5, 8, 4, 6, 6, 17212156387254164957552975229693025962587848704000000⟩, + ⟨3, 5, 5, 5, 2, 6, -101180365576242859056104958898596019426981576704000000⟩, + ⟨3, 5, 6, 5, 3, 6, -2120625404512480753081173987486847616182910976000000⟩, + ⟨3, 5, 7, 5, 4, 6, 6963894971129626956056070776838650680018206720000000⟩, + ⟨3, 5, 8, 5, 5, 6, 5753503727216777493583114841639342789841911808000000⟩, + ⟨3, 5, 5, 6, 1, 6, 129264953560030594683604585257040373104446013440000000⟩, + ⟨3, 5, 6, 6, 2, 6, -151949113945851836884591961986424061387337629696000000⟩, + ⟨3, 5, 7, 6, 3, 6, 20881367505626846189985378279783725422620966912000000⟩, + ⟨3, 5, 8, 6, 4, 6, -8570725172046693515497983834434260807364640768000000⟩, + ⟨3, 5, 5, 7, 0, 6, 563973991728132290127122856317907289434438500352000000⟩, + ⟨3, 5, 6, 7, 1, 6, 301232142135464171769555063071184797466579959808000000⟩, + ⟨3, 5, 7, 7, 2, 6, -37081377901833054332064005151738986172921151488000000⟩, + ⟨3, 5, 8, 7, 3, 6, -41049047085388401945118965796460048036545953792000000⟩ +] + +def collectedFourData_13_2_30 : List CollectedFourTerm := [ + ⟨3, 6, 4, 0, 6, 7, 14253384989870453908484928629225225835232886784000000⟩, + ⟨3, 6, 5, 0, 7, 7, 184257108704174634776360767729183322510721024000000⟩, + ⟨3, 6, 6, 0, 8, 7, 5675576119256091693070092543527307381930196992000000⟩, + ⟨3, 6, 4, 1, 5, 7, -22087342947943632948155123888149490928031314739200000⟩, + ⟨3, 6, 5, 1, 6, 7, -30400993624799594542635165416758256098458206208000000⟩, + ⟨3, 6, 6, 1, 7, 7, -18981548283450132611362537556950025669317754880000000⟩, + ⟨3, 6, 7, 1, 8, 7, -11894631883457467518518881869486579283144998912000000⟩, + ⟨3, 6, 4, 2, 4, 7, 5888912719339035606030198576323628393571339468800000⟩, + ⟨3, 6, 5, 2, 5, 7, 5317797501259368155546506039447495922272960512000000⟩, + ⟨3, 6, 6, 2, 6, 7, 1310289027777165517768920708335700296979185664000000⟩, + ⟨3, 6, 7, 2, 7, 7, 702272690672214581873225446192918470422691840000000⟩, + ⟨3, 6, 8, 2, 8, 7, 2838212838002727060593274393781520786220122112000000⟩, + ⟨3, 6, 4, 3, 3, 7, -7511209491801039285957768884169072707062726656000000⟩, + ⟨3, 6, 5, 3, 4, 7, -7197416932374290835189209689316052000263110656000000⟩, + ⟨3, 6, 6, 3, 5, 7, -3192045463919868448751143800683742048471220224000000⟩, + ⟨3, 6, 7, 3, 6, 7, 548349330696135440114586577898963781719949312000000⟩, + ⟨3, 6, 8, 3, 7, 7, 1738566463875360695800902732736674603057807360000000⟩, + ⟨3, 6, 4, 4, 2, 7, 25041673969942172771192859380784903616558478131200000⟩, + ⟨3, 6, 5, 4, 3, 7, 671349192971497034900694303590015799127965696000000⟩, + ⟨3, 6, 6, 4, 4, 7, 1475169670312393823799637665476503409912709120000000⟩, + ⟨3, 6, 7, 4, 5, 7, 1887917406995679198268457793022666802976522240000000⟩, + ⟨3, 6, 8, 4, 6, 7, -2217608084252751684166682487091555222803185664000000⟩, + ⟨3, 6, 4, 5, 1, 7, -24143299242528159882330325245731459305778341478400000⟩, + ⟨3, 6, 5, 5, 2, 7, 52144168719192031888386494712116634147310534656000000⟩, + ⟨3, 6, 6, 5, 3, 7, 546441240122715128582210301876326430180114432000000⟩, + ⟨3, 6, 7, 5, 4, 7, -1196300989324811142219214764179597313819279360000000⟩, + ⟨3, 6, 8, 5, 5, 7, -741279366233419124026396501656911818656841728000000⟩, + ⟨3, 6, 4, 6, 0, 7, -75327663600702404473952360253499566058420096204800000⟩, + ⟨3, 6, 5, 6, 1, 7, -66617801878108716042322856345097714274570076160000000⟩, + ⟨3, 6, 6, 6, 2, 7, 39154139190937129281176777291902010728195817472000000⟩, + ⟨3, 6, 7, 6, 3, 7, -3587130579797391831542810487322656362050093056000000⟩, + ⟨3, 6, 8, 6, 4, 7, 1104249171446866551376668515592491773710041088000000⟩, + ⟨3, 6, 5, 7, 0, 7, -290648831029850783121972375187559332443825635328000000⟩, + ⟨3, 6, 6, 7, 1, 7, -77621283307773491771242536525912755231004819456000000⟩, + ⟨3, 6, 7, 7, 2, 7, 6370068654595787399926340090751884880871686144000000⟩, + ⟨3, 6, 8, 7, 3, 7, 5288744572111757020484663905216509945285967872000000⟩ +] + +def collectedFourData_13_2_31 : List CollectedFourTerm := [ + ⟨3, 7, 3, 0, 5, 8, 172227460003510964079989981926747803021528268800000000⟩, + ⟨3, 7, 4, 0, 6, 8, 180764018503563478322590112975958293780449198080000000⟩, + ⟨3, 7, 5, 0, 7, 8, 1168391067486252327521787140794879600691773440000000⟩, + ⟨3, 7, 6, 0, 8, 8, 23992895894991554451210872198753566576009543680000000⟩, + ⟨3, 7, 3, 1, 4, 8, -164754349373299169300094890898006573033468198912000000⟩, + ⟨3, 7, 4, 1, 5, 8, -280115696880009908768973681475206521480653307904000000⟩, + ⟨3, 7, 5, 1, 6, 8, -192775462741848519449168654533847132311891476480000000⟩, + ⟨3, 7, 6, 1, 7, 8, -80242481524548334689769948062104314776335155200000000⟩, + ⟨3, 7, 7, 1, 8, 8, -37712470746465183673168121410675665779671695360000000⟩, + ⟨3, 7, 3, 2, 3, 8, 114286555329865521793680492820569849180180185088000000⟩, + ⟨3, 7, 4, 2, 4, 8, 74684261213809170183477306914839869416911405056000000⟩, + ⟨3, 7, 5, 2, 5, 8, 33720637118796747248018361243433797170201886720000000⟩, + ⟨3, 7, 6, 2, 6, 8, 5539107850064006851650649935781586495141314560000000⟩, + ⟨3, 7, 7, 2, 7, 8, 2226587469247424194491092421066941661393715200000000⟩, + ⟨3, 7, 8, 2, 8, 8, 7198946191804776951661235332091447631924953088000000⟩, + ⟨3, 7, 3, 3, 2, 8, -75362012011496678931081562744444918864646504448000000⟩, + ⟨3, 7, 4, 3, 3, 8, -95258523678760540195907690366267519801197854720000000⟩, + ⟨3, 7, 5, 3, 4, 8, -45639474709557825106095372947212447100813967360000000⟩, + ⟨3, 7, 6, 3, 5, 8, -13494033539267859802949982654577822699314216960000000⟩, + ⟨3, 7, 7, 3, 6, 8, 1738566463875360695800902732736674603057807360000000⟩, + ⟨3, 7, 8, 3, 7, 8, 4409763163893841673721284362831778294676848640000000⟩, + ⟨3, 7, 3, 4, 1, 8, 69584328668306544729577793829870456726016229376000000⟩, + ⟨3, 7, 4, 4, 2, 8, 317583059748951078407462164864099813070884306944000000⟩, + ⟨3, 7, 5, 4, 3, 8, 4257086229934040252503827084233268629612789760000000⟩, + ⟨3, 7, 6, 4, 4, 8, 6236123273401429145375476788777509448371404800000000⟩, + ⟨3, 7, 7, 4, 5, 8, 5985727904878338787338351649067041278866227200000000⟩, + ⟨3, 7, 8, 4, 6, 8, -5624821739683602425560704569953370481660788736000000⟩, + ⟨3, 7, 3, 5, 0, 8, -83580508185268801163452818920663978351058223104000000⟩, + ⟨3, 7, 4, 5, 1, 8, -306189708207207843277897461398446346130904055808000000⟩, + ⟨3, 7, 5, 5, 2, 8, 330650911552155914884193528199090000935371407360000000⟩, + ⟨3, 7, 6, 5, 3, 8, 2310022368039851245522437665109774691498721280000000⟩, + ⟨3, 7, 7, 5, 4, 8, -3792926633284373450205493525280084313558220800000000⟩, + ⟨3, 7, 8, 5, 5, 8, -1880207924915461793695081583527511200546947072000000⟩, + ⟨3, 7, 4, 6, 0, 8, -955319117993692276570028903411859534276382949376000000⟩, + ⟨3, 7, 5, 6, 1, 8, -422429534455120964737069208399843323889162649600000000⟩, + ⟨3, 7, 6, 6, 2, 8, 165519969378772964518754505280185558711014522880000000⟩, + ⟨3, 7, 7, 6, 3, 8, -11373160462620176501922058990320827865162055680000000⟩, + ⟨3, 7, 8, 6, 4, 8, 2800857730312106386239285131810649903791603712000000⟩, + ⟨3, 7, 5, 7, 0, 8, -1843030645269778707304640468344332368979091783680000000⟩, + ⟨3, 7, 6, 7, 1, 8, -328135739968396015581215157071570677134513930240000000⟩, + ⟨3, 7, 7, 7, 2, 8, 20196592054565492084501463944446435788136120320000000⟩, + ⟨3, 7, 8, 7, 3, 8, 13414563942154762191619673928644120192722403328000000⟩ +] + +def collectedFourData_13_2_32 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_2_33 : List CollectedFourTerm := [ + ⟨4, 1, 8, 2, 8, 3, 113596540054017419125419952561504033245400085299200000⟩, + ⟨4, 1, 8, 3, 7, 3, 69584328668306544729577793829870456726016229376000000⟩, + ⟨4, 1, 8, 4, 6, 3, -88757475194919999558731404886249577506901747302400000⟩, + ⟨4, 1, 8, 5, 5, 3, -29668941698117403157323289996248470747437911244800000⟩, + ⟨4, 1, 8, 6, 4, 3, 44196433598740207671005712193406214083141487820800000⟩, + ⟨4, 1, 8, 7, 3, 3, 211676543977630746057958469016312209475921720115200000⟩ +] + +def collectedFourData_13_2_34 : List CollectedFourTerm := [ + ⟨4, 2, 7, 1, 8, 4, -543196602866064773264512004171912476000047543091200000⟩, + ⟨4, 2, 7, 2, 7, 4, 32070949617977872948940990213854393207760093184000000⟩, + ⟨4, 2, 8, 2, 8, 4, 518454908708212569719356264075053458708218301644800000⟩, + ⟨4, 2, 7, 3, 6, 4, 25041673969942172771192859380784903616558478131200000⟩, + ⟨4, 2, 8, 3, 7, 4, 317583059748951078407462164864099813070884306944000000⟩, + ⟨4, 2, 7, 4, 5, 4, 86216230314617598264959132594609515602036916224000000⟩, + ⟨4, 2, 8, 4, 6, 4, -405089351114671351484586052343843388735719315865600000⟩, + ⟨4, 2, 7, 5, 4, 4, -54631924701284805687661060485800300141856423936000000⟩, + ⟨4, 2, 8, 5, 5, 4, -135409128237992881073376388382743363461160579891200000⟩, + ⟨4, 2, 7, 6, 3, 4, -163814833790092548600858621233886427386096490905600000⟩, + ⟨4, 2, 8, 6, 4, 4, 201712639625885056867054522298421337067927843635200000⟩, + ⟨4, 2, 7, 7, 2, 4, 290904307682890920148884881979380141757336807014400000⟩, + ⟨4, 2, 8, 7, 3, 4, 966092305552675096286192250304687416596746783948800000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1305.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1305.lean new file mode 100644 index 0000000000000000000000000000000000000000..6e22151b5173afd9e5e17ab34a724b947d498d66 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1305.lean @@ -0,0 +1,610 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1305. -/ +namespace LaughlinFock +def collectedFourData_13_2_35 : List CollectedFourTerm := [ + ⟨4, 3, 6, 0, 8, 5, 2316220235297615355116388328035364415798771712000000⟩, + ⟨4, 3, 6, 1, 7, 5, -7746428786716465662412528101825719482114375680000000⟩, + ⟨4, 3, 7, 1, 8, 5, -14562708603135506754852558316722417323785322496000000⟩, + ⟨4, 3, 6, 2, 6, 5, 534733020305910779204370962917857864821243904000000⟩, + ⟨4, 3, 7, 2, 7, 5, 859798996253312610784291728531223210591518720000000⟩, + ⟨4, 3, 8, 2, 8, 5, 6949700826133977553432307702989327024565256192000000⟩, + ⟨4, 3, 6, 3, 5, 5, -1302683664207509679728070414131316013676888064000000⟩, + ⟨4, 3, 7, 3, 6, 5, 671349192971497034900694303590015799127965696000000⟩, + ⟨4, 3, 8, 3, 7, 5, 4257086229934040252503827084233268629612789760000000⟩, + ⟨4, 3, 6, 4, 4, 5, 602021322431444572708219403920483532742328320000000⟩, + ⟨4, 3, 7, 4, 5, 5, 2311394865704215701634661702509934661253201920000000⟩, + ⟨4, 3, 8, 4, 6, 5, -5430076465307683006921473050659032926911463424000000⟩, + ⟨4, 3, 6, 5, 3, 5, 223004366636747842352050645954595327733399552000000⟩, + ⟨4, 3, 7, 5, 4, 5, -1464642443740427179286500098089227989685370880000000⟩, + ⟨4, 3, 8, 5, 5, 5, -1815110464912749533101416332561673336020533248000000⟩, + ⟨4, 3, 6, 6, 2, 5, 15978925766146686110645056966275786240260308992000000⟩, + ⟨4, 3, 7, 6, 3, 5, -4391757379867865062181512399706932021504770048000000⟩, + ⟨4, 3, 8, 6, 4, 5, 2703885091458625496888352016224245882717995008000000⟩, + ⟨4, 3, 6, 7, 1, 5, -31677486709631008479778260129854222786327740416000000⟩, + ⟨4, 3, 7, 7, 2, 5, 7798934385507131278373590973360093397151383552000000⟩, + ⟨4, 3, 8, 7, 3, 5, 12950118479444828594736266013485812439530340352000000⟩ +] + +def collectedFourData_13_2_36 : List CollectedFourTerm := [ + ⟨4, 4, 5, 0, 7, 6, 165229524978651730447671533004760419485614080000000⟩, + ⟨4, 4, 6, 0, 8, 6, 10178958660102072225113336351253469794171617280000000⟩, + ⟨4, 4, 5, 1, 6, 6, -27261589910049692636981990970242781700014735360000000⟩, + ⟨4, 4, 6, 1, 7, 6, -34042781071412193221009050063595219052606259200000000⟩, + ⟨4, 4, 7, 1, 8, 6, -31998945219339723715216315767445472255536005120000000⟩, + ⟨4, 4, 5, 2, 5, 6, 4768647251902955573759636726219033478734807040000000⟩, + ⟨4, 4, 6, 2, 6, 6, 2349960174312182162853174881829083795958005760000000⟩, + ⟨4, 4, 7, 2, 7, 6, 1889254377776209895868051703424701178472038400000000⟩, + ⟨4, 4, 8, 2, 8, 6, 10180482312124257474334973327256739427553116160000000⟩, + ⟨4, 4, 5, 3, 4, 6, -6454164993540707927774738076837745564078571520000000⟩, + ⟨4, 4, 6, 3, 5, 6, -5724828305653211643995067373188359792004956160000000⟩, + ⟨4, 4, 7, 3, 6, 6, 1475169670312393823799637665476503409912709120000000⟩, + ⟨4, 4, 8, 3, 7, 6, 6236123273401429145375476788777509448371404800000000⟩, + ⟨4, 4, 5, 4, 3, 6, 602021322431444572708219403920483532742328320000000⟩, + ⟨4, 4, 6, 4, 4, 6, 2645668170989907258709055171993368936631500800000000⟩, + ⟨4, 4, 7, 4, 5, 6, 5078876444180682455411218609868679636477542400000000⟩, + ⟨4, 4, 8, 4, 6, 6, -7954413980047399978920681982140601312236011520000000⟩, + ⟨4, 4, 5, 5, 2, 6, 46759423766446881876669480490477704569180651520000000⟩, + ⟨4, 4, 6, 5, 3, 6, 980024349336552524033975690696528338228346880000000⟩, + ⟨4, 4, 7, 5, 4, 6, -3218289577879682618080064887288315933989273600000000⟩, + ⟨4, 4, 8, 5, 5, 6, -2658920210364699900892954717251679737127895040000000⟩, + ⟨4, 4, 5, 6, 1, 6, -59738415721664095507426418338335874673226547200000000⟩, + ⟨4, 4, 6, 6, 2, 6, 70221657823288943978241338604166897535004180480000000⟩, + ⟨4, 4, 7, 6, 3, 6, -9650100653992679351631501495918690656908738560000000⟩, + ⟨4, 4, 8, 6, 4, 6, 3960868969222064401610602113320282207645859840000000⟩, + ⟨4, 4, 5, 7, 0, 6, -260634548237511783322765734130150396126832885760000000⟩, + ⟨4, 4, 6, 7, 1, 6, -139211212629715868206827318649312594013234135040000000⟩, + ⟨4, 4, 7, 7, 2, 6, 17136762189784884569641001382447976709294653440000000⟩, + ⟨4, 4, 8, 7, 3, 6, 18970378066366558908065598552709492900846632960000000⟩ +] + +def collectedFourData_13_2_37 : List CollectedFourTerm := [ + ⟨4, 5, 4, 0, 6, 7, 49073122049453079741307369244394238961705287680000000⟩, + ⟨4, 5, 5, 0, 7, 7, 634380646446110397570618134658774913756692480000000⟩, + ⟨4, 5, 6, 0, 8, 7, 19540497909735254434540545984463769895268515840000000⟩, + ⟨4, 5, 4, 1, 5, 7, -76044734426444197168320714105206522594809872384000000⟩, + ⟨4, 5, 5, 1, 6, 7, -104667885673099664585679403951726096208269148160000000⟩, + ⟨4, 5, 6, 1, 7, 7, -65351762845339451178238426301103272170723737600000000⟩, + ⟨4, 5, 7, 1, 8, 7, -40952147336583620548092506219181124570306314240000000⟩, + ⟨4, 5, 4, 2, 4, 7, 20274996628525619479870876982109188188092235776000000⟩, + ⟨4, 5, 5, 2, 5, 7, 18308698319664865189752684447966413810030346240000000⟩, + ⟨4, 5, 6, 2, 6, 7, 4511207227326318736220872489756390461831905280000000⟩, + ⟨4, 5, 7, 2, 7, 7, 2417861685897577098254704811955607879601356800000000⟩, + ⟨4, 5, 8, 2, 8, 7, 9771711428591554110595415329122045363738378240000000⟩, + ⟨4, 5, 4, 3, 3, 7, -25860418447415623949487315427888363415399301120000000⟩, + ⟨4, 5, 5, 3, 4, 7, -24780058899287046977097020967394222147758981120000000⟩, + ⟨4, 5, 6, 3, 5, 7, -10989925322978768662745407584770878561824276480000000⟩, + ⟨4, 5, 7, 3, 6, 7, 1887917406995679198268457793022666802976522240000000⟩, + ⟨4, 5, 8, 3, 7, 7, 5985727904878338787338351649067041278866227200000000⟩, + ⟨4, 5, 4, 4, 2, 7, 86216230314617598264959132594609515602036916224000000⟩, + ⟨4, 5, 5, 4, 3, 7, 2311394865704215701634661702509934661253201920000000⟩, + ⟨4, 5, 6, 4, 4, 7, 5078876444180682455411218609868679636477542400000000⟩, + ⟨4, 5, 7, 4, 5, 7, 6499929763956231237580062769042299032489164800000000⟩, + ⟨4, 5, 8, 4, 6, 7, -7635025101316525887148670619645485650311905280000000⟩, + ⟨4, 5, 4, 5, 1, 7, -83123206960806351416461910148276381180669984768000000⟩, + ⟨4, 5, 5, 5, 2, 7, 179527681146809545724085776241800314730179461120000000⟩, + ⟨4, 5, 6, 5, 3, 7, 1881348022834835248565461812732941457571184640000000⟩, + ⟨4, 5, 7, 5, 4, 7, -4118756667187412571033305757168996636111667200000000⟩, + ⟨4, 5, 8, 5, 5, 7, -2552158160167988760260492369794203665364418560000000⟩, + ⟨4, 5, 4, 6, 0, 7, -259346368052534490864500083305763349856566378496000000⟩, + ⟨4, 5, 5, 6, 1, 7, -229359097825114327088253252925351422132958003200000000⟩, + ⟨4, 5, 6, 6, 2, 7, 134804178279309577645289407671105263205026365440000000⟩, + ⟨4, 5, 7, 6, 3, 7, -12350167828542089720685299932901086986365829120000000⟩, + ⟨4, 5, 8, 6, 4, 7, 3801830540740346157619401278887008763914485760000000⟩, + ⟨4, 5, 5, 7, 0, 7, -1000677773651321743609172356348110601494001090560000000⟩, + ⟨4, 5, 6, 7, 1, 7, -267243094331949558983547234147725129026759557120000000⟩, + ⟨4, 5, 7, 7, 2, 7, 21931573220854648260470120559813630108767354880000000⟩, + ⟨4, 5, 8, 7, 3, 7, 18208671698692509617457288859353955513600573440000000⟩ +] + +def collectedFourData_13_2_38 : List CollectedFourTerm := [ + ⟨4, 6, 3, 0, 5, 8, -219682718820397345545713347635745715421047685120000000⟩, + ⟨4, 6, 4, 0, 6, 8, -230571426002298997844909431083493633433788219392000000⟩, + ⟨4, 6, 5, 0, 7, 8, -1490327537464779326231702385454396528977248256000000⟩, + ⟨4, 6, 6, 0, 8, 8, -30603857262245209501062333058122567484107128832000000⟩, + ⟨4, 6, 3, 1, 4, 8, 210150480109700034157705729576134147110368758988800000⟩, + ⟨4, 6, 4, 1, 5, 8, 357298295368325174803530860853483125239289846169600000⟩, + ⟨4, 6, 5, 1, 6, 8, 245892482976443903552653444862740161363078807552000000⟩, + ⟨4, 6, 6, 1, 7, 8, 102352357201626995370689040987589820774067732480000000⟩, + ⟨4, 6, 7, 1, 8, 8, 48103700227880507396709593765796159640634916864000000⟩, + ⟨4, 6, 3, 2, 3, 8, -145776876689529147376143572730357061298758562611200000⟩, + ⟨4, 6, 4, 2, 4, 8, -95262634403409790782067984834322826810311992934400000⟩, + ⟨4, 6, 5, 2, 5, 8, -43011963611739185192211184364829733212943024128000000⟩, + ⟨4, 6, 6, 2, 6, 8, -7065344122921285064511936702166584753540562944000000⟩, + ⟨4, 6, 7, 2, 7, 8, -2840097560085543445996188623373329718816276480000000⟩, + ⟨4, 6, 8, 2, 8, 8, -9182531473350298114141874969112575942088405811200000⟩, + ⟨4, 6, 3, 3, 2, 8, 96127131492989174774945960175597001771303777075200000⟩, + ⟨4, 6, 4, 3, 3, 8, 121505893846084192841508574864023848442635747328000000⟩, + ⟨4, 6, 5, 3, 4, 8, 58214897261598336804664293037639060685705969664000000⟩, + ⟨4, 6, 6, 3, 5, 8, 17212156387254164957552975229693025962587848704000000⟩, + ⟨4, 6, 7, 3, 6, 8, -2217608084252751684166682487091555222803185664000000⟩, + ⟨4, 6, 8, 3, 7, 8, -5624821739683602425560704569953370481660788736000000⟩, + ⟨4, 6, 3, 4, 1, 8, -88757475194919999558731404886249577506901747302400000⟩, + ⟨4, 6, 4, 4, 2, 8, -405089351114671351484586052343843388735719315865600000⟩, + ⟨4, 6, 5, 4, 3, 8, -5430076465307683006921473050659032926911463424000000⟩, + ⟨4, 6, 6, 4, 4, 8, -7954413980047399978920681982140601312236011520000000⟩, + ⟨4, 6, 7, 4, 5, 8, -7635025101316525887148670619645485650311905280000000⟩, + ⟨4, 6, 8, 4, 6, 8, 7174675470616480307030582950682841611906737766400000⟩, + ⟨4, 6, 3, 5, 0, 8, 106610138000966979886140102086440666783893002649600000⟩, + ⟨4, 6, 4, 5, 1, 8, 390556695038133405215044632375484299565805548339200000⟩, + ⟨4, 6, 5, 5, 2, 8, -421757896381561705993618247805637311496835825664000000⟩, + ⟨4, 6, 6, 5, 3, 8, -2946521967731405549577082111966083067592835072000000⟩, + ⟨4, 6, 7, 5, 4, 8, 4838023129814614015891426116890140979673169920000000⟩, + ⟨4, 6, 8, 5, 5, 8, 2398277190435636063315749647591879329251642572800000⟩, + ⟨4, 6, 4, 6, 0, 8, 1218546108603587506350556200597416716950277875302400000⟩, + ⟨4, 6, 5, 6, 1, 8, 538825043562994518562635160409821351374791639040000000⟩, + ⟨4, 6, 6, 6, 2, 8, -211127057737810801759018120788846652338745638912000000⟩, + ⟨4, 6, 7, 6, 3, 8, 14506901582117713512202148407361186051634757632000000⟩, + ⟨4, 6, 8, 6, 4, 8, -3572601263535718936603064183953313588889570508800000⟩, + ⟨4, 6, 5, 7, 0, 8, 2350856146946151951197491766926039036220336504832000000⟩, + ⟨4, 6, 6, 7, 1, 8, 418549698735211260121076328785305474197488664576000000⟩, + ⟨4, 6, 7, 7, 2, 8, -25761526375427787920788592555470072398917664768000000⟩, + ⟨4, 6, 8, 7, 3, 8, -17110789873708584078687607133234775791393518387200000⟩ +] + +def collectedFourData_13_2_39 : List CollectedFourTerm := [ + ⟨5, 0, 8, 2, 8, 3, -136445327956831205615027954991530700502630976716800000⟩, + ⟨5, 0, 8, 3, 7, 3, -83580508185268801163452818920663978351058223104000000⟩, + ⟨5, 0, 8, 4, 6, 3, 106610138000966979886140102086440666783893002649600000⟩, + ⟨5, 0, 8, 5, 5, 3, 35636547364970264915876659444294929385488855859200000⟩, + ⟨5, 0, 8, 6, 4, 3, -53086096407820584574950163923071051799800787763200000⟩, + ⟨5, 0, 8, 7, 3, 3, -254253126460210257369823382433789770213853285580800000⟩ +] + +def collectedFourData_13_2_40 : List CollectedFourTerm := [ + ⟨5, 1, 7, 1, 8, 4, 523709323356804967643389315852353183975125444198400000⟩, + ⟨5, 1, 7, 2, 7, 4, -30920398314756591308881562405944670040241471488000000⟩, + ⟨5, 1, 8, 2, 8, 4, -499855242094620244778794617604200301716972345753600000⟩, + ⟨5, 1, 7, 3, 6, 4, -24143299242528159882330325245731459305778341478400000⟩, + ⟨5, 1, 8, 3, 7, 4, -306189708207207843277897461398446346130904055808000000⟩, + ⟨5, 1, 7, 4, 5, 4, -83123206960806351416461910148276381180669984768000000⟩, + ⟨5, 1, 8, 4, 6, 4, 390556695038133405215044632375484299565805548339200000⟩, + ⟨5, 1, 7, 5, 4, 4, 52671994206201654815627517359525353683368804352000000⟩, + ⟨5, 1, 8, 5, 5, 4, 130551300489888192980949231618504274697800541798400000⟩, + ⟨5, 1, 7, 6, 3, 4, 157937946053705887810792892502635690444434125619200000⟩, + ⟨5, 1, 8, 6, 4, 4, -194476161031946875015894147601807011354065135206400000⟩, + ⟨5, 1, 7, 7, 2, 4, -280468061350801853142698002645374855096524655820800000⟩, + ⟨5, 1, 8, 7, 3, 4, -931433563780881956090375668286883161421760797081600000⟩ +] + +def collectedFourData_13_2_41 : List CollectedFourTerm := [ + ⟨5, 2, 6, 0, 8, 5, 179902471030889101335867027990061718195071352832000000⟩, + ⟨5, 2, 6, 1, 7, 5, -601670626634534153281711240928371263224131092480000000⟩, + ⟨5, 2, 7, 1, 8, 5, -1131095922003389923887951940846541709586471059456000000⟩, + ⟨5, 2, 6, 2, 6, 5, 41533093541289721593720622390783430388501970944000000⟩, + ⟨5, 2, 7, 2, 7, 5, 66781198807709228367502862911634681397950545920000000⟩, + ⟨5, 2, 8, 2, 8, 5, 539788199970658099000466799422491118096049242112000000⟩, + ⟨5, 2, 6, 3, 5, 5, -101180365576242859056104958898596019426981576704000000⟩, + ⟨5, 2, 7, 3, 6, 5, 52144168719192031888386494712116634147310534656000000⟩, + ⟨5, 2, 8, 3, 7, 5, 330650911552155914884193528199090000935371407360000000⟩, + ⟨5, 2, 6, 4, 4, 5, 46759423766446881876669480490477704569180651520000000⟩, + ⟨5, 2, 7, 4, 5, 5, 179527681146809545724085776241800314730179461120000000⟩, + ⟨5, 2, 8, 4, 6, 5, -421757896381561705993618247805637311496835825664000000⟩, + ⟨5, 2, 6, 5, 3, 5, 17320907570550748022839940131551632054468739072000000⟩, + ⟨5, 2, 7, 5, 4, 5, -113759819031960987973813388795735991054426439680000000⟩, + ⟨5, 2, 8, 5, 5, 5, -140980919195653035629608252490452529425026121728000000⟩, + ⟨5, 2, 6, 6, 2, 5, 1241094515081620833934303520059841095823536422912000000⟩, + ⟨5, 2, 7, 6, 3, 5, -341110915432811669007671253667488575152642326528000000⟩, + ⟨5, 2, 8, 6, 4, 5, 210012675791378406924170962571836347794312921088000000⟩, + ⟨5, 2, 6, 7, 1, 5, -2460412895226481070452985411436068836063183896576000000⟩, + ⟨5, 2, 7, 7, 2, 5, 605748773790598303456881684803093825764114563072000000⟩, + ⟨5, 2, 8, 7, 3, 5, 1005844901573252168230813889090596520733412687872000000⟩ +] + +def collectedFourData_13_2_42 : List CollectedFourTerm := [ + ⟨5, 3, 5, 0, 7, 6, 61205316480714672411226245535340844011225088000000⟩, + ⟨5, 3, 6, 0, 8, 6, 3770551215445020762962594047121653287100612608000000⟩, + ⟨5, 3, 5, 1, 6, 6, -10098402440045946351937265348046144089773572096000000⟩, + ⟨5, 3, 6, 1, 7, 6, -12610332140267757670614559224403391608384389120000000⟩, + ⟨5, 3, 7, 1, 8, 6, -11853242145747170660683125061397492987993260032000000⟩, + ⟨5, 3, 5, 2, 5, 6, 1766431055680399402536639535433387760936812544000000⟩, + ⟨5, 3, 6, 2, 6, 6, 870486410975495486318469165061729048420417536000000⟩, + ⟨5, 3, 7, 2, 7, 6, 699828993149431018816919666588788816336650240000000⟩, + ⟨5, 3, 8, 2, 8, 6, 3771115615810127290037535746548859527785086976000000⟩, + ⟨5, 3, 5, 3, 4, 6, -2390790696150993851526923113703770537246851072000000⟩, + ⟨5, 3, 6, 3, 5, 6, -2120625404512480753081173987486847616182910976000000⟩, + ⟨5, 3, 7, 3, 6, 6, 546441240122715128582210301876326430180114432000000⟩, + ⟨5, 3, 8, 3, 7, 6, 2310022368039851245522437665109774691498721280000000⟩, + ⟨5, 3, 5, 4, 3, 6, 223004366636747842352050645954595327733399552000000⟩, + ⟨5, 3, 6, 4, 4, 6, 980024349336552524033975690696528338228346880000000⟩, + ⟨5, 3, 7, 4, 5, 6, 1881348022834835248565461812732941457571184640000000⟩, + ⟨5, 3, 8, 4, 6, 6, -2946521967731405549577082111966083067592835072000000⟩, + ⟨5, 3, 5, 5, 2, 6, 17320907570550748022839940131551632054468739072000000⟩, + ⟨5, 3, 6, 5, 3, 6, 363026526086667378387649858204521832453767168000000⟩, + ⟨5, 3, 7, 5, 4, 6, -1192138222065104241402814464282833034632232960000000⟩, + ⟨5, 3, 8, 5, 5, 6, -984933249631786516826019233179556165235769344000000⟩, + ⟨5, 3, 5, 6, 1, 6, -22128663994969183862200932329856417400797265920000000⟩, + ⟨5, 3, 6, 6, 2, 6, 26011929716738959936847194862677144810058416128000000⟩, + ⟨5, 3, 7, 6, 3, 6, -3574648445395495354657995371130749874251759616000000⟩, + ⟨5, 3, 8, 6, 4, 6, 1467208955731131752347786729726432778202906624000000⟩, + ⟨5, 3, 5, 7, 0, 6, -96545820202207138348089941832830650694328385536000000⟩, + ⟨5, 3, 6, 7, 1, 6, -51567456408088682326021755800720826599781433344000000⟩, + ⟨5, 3, 7, 7, 2, 6, 6347902733582545813215969214697682584243011584000000⟩, + ⟨5, 3, 8, 7, 3, 6, 7027121777786325884435617438476791642855571456000000⟩ +] + +def collectedFourData_13_2_43 : List CollectedFourTerm := [ + ⟨5, 4, 4, 0, 6, 7, -31095758871379632148040644779247223721972203520000000⟩, + ⟨5, 4, 5, 0, 7, 7, -401982730886347505280723560087359907923230720000000⟩, + ⟨5, 4, 6, 0, 8, 7, -12382065494335044024427901969554607720638709760000000⟩, + ⟨5, 4, 4, 1, 5, 7, 48186637132641217699065987339591765105548722176000000⟩, + ⟨5, 4, 5, 1, 6, 7, 66324032352942825497450212084271316077893386240000000⟩, + ⟨5, 4, 6, 1, 7, 7, 41410910380031761926729548315905828340524646400000000⟩, + ⟨5, 4, 7, 1, 8, 7, 25949808075392431016064269121223463173210767360000000⟩, + ⟨5, 4, 4, 2, 4, 7, -12847489215039543550675913260157813029878104064000000⟩, + ⟨5, 4, 5, 2, 5, 7, -11601521248707207593382876089185755624489615360000000⟩, + ⟨5, 4, 6, 2, 6, 7, -2858579326141074484339366767461571604953169920000000⟩, + ⟨5, 4, 7, 2, 7, 7, -1532106392033731155285612587721404884136755200000000⟩, + ⟨5, 4, 8, 2, 8, 7, -6191959460781323279185947665570576100344463360000000⟩, + ⟨5, 4, 4, 3, 3, 7, 16386757205776275470246121128588474259792199680000000⟩, + ⟨5, 4, 5, 3, 4, 7, 15702174717440926118139005554919552281403719680000000⟩, + ⟨5, 4, 6, 3, 5, 7, 6963894971129626956056070776838650680018206720000000⟩, + ⟨5, 4, 7, 3, 6, 7, -1196300989324811142219214764179597313819279360000000⟩, + ⟨5, 4, 8, 3, 7, 7, -3792926633284373450205493525280084313558220800000000⟩, + ⟨5, 4, 4, 4, 2, 7, -54631924701284805687661060485800300141856423936000000⟩, + ⟨5, 4, 5, 4, 3, 7, -1464642443740427179286500098089227989685370880000000⟩, + ⟨5, 4, 6, 4, 4, 7, -3218289577879682618080064887288315933989273600000000⟩, + ⟨5, 4, 7, 4, 5, 7, -4118756667187412571033305757168996636111667200000000⟩, + ⟨5, 4, 8, 4, 6, 7, 4838023129814614015891426116890140979673169920000000⟩, + ⟨5, 4, 4, 5, 1, 7, 52671994206201654815627517359525353683368804352000000⟩, + ⟨5, 4, 5, 5, 2, 7, -113759819031960987973813388795735991054426439680000000⟩, + ⟨5, 4, 6, 5, 3, 7, -1192138222065104241402814464282833034632232960000000⟩, + ⟨5, 4, 7, 5, 4, 7, 2609898429606322507054525182970290001202380800000000⟩, + ⟨5, 4, 8, 5, 5, 7, 1617204926766874388492037410824996702220451840000000⟩, + ⟨5, 4, 4, 6, 0, 7, 164337865379803490920751130384637912595923206144000000⟩, + ⟨5, 4, 5, 6, 1, 7, 145336080181318216673232811048781148716846284800000000⟩, + ⟨5, 4, 6, 6, 2, 7, -85420247328131843984645971473468542840639324160000000⟩, + ⟨5, 4, 7, 6, 3, 7, 7825828575373779756472970039862831387173191680000000⟩, + ⟨5, 4, 8, 6, 4, 7, -2409074475546358980199583076323210868440432640000000⟩, + ⟨5, 4, 5, 7, 0, 7, 634091198152274579900017844144435919723524259840000000⟩, + ⟨5, 4, 6, 7, 1, 7, 169341718527979427873842000508030610757574983680000000⟩, + ⟨5, 4, 7, 7, 2, 7, -13897198386082785626134039911533129645760184320000000⟩, + ⟨5, 4, 8, 7, 3, 7, -11538138208122572134614360946368446216703836160000000⟩ +] + +def collectedFourData_13_2_44 : List CollectedFourTerm := [ + ⟨5, 5, 3, 0, 5, 8, -73433294068501497767484970227854273931368202240000000⟩, + ⟨5, 5, 4, 0, 6, 8, -77073059821619747610051417172601017233240489984000000⟩, + ⟨5, 5, 5, 0, 7, 8, -498171457931152698481287850354168748008538112000000⟩, + ⟨5, 5, 6, 0, 8, 8, -10229944631221643064227588080888220676589092864000000⟩, + ⟨5, 5, 3, 1, 4, 8, 70246954732697554792673310188500402055138613657600000⟩, + ⟨5, 5, 4, 1, 5, 8, 119434022552348310628855058864414056538973614899200000⟩, + ⟨5, 5, 5, 1, 6, 8, 82194426164242535336549084474485198695174242304000000⟩, + ⟨5, 5, 6, 1, 7, 8, 34213299914301323264237542807982932608637992960000000⟩, + ⟨5, 5, 7, 1, 8, 8, 16079613287674817241152634404113049218216624128000000⟩, + ⟨5, 5, 3, 2, 3, 8, -48728804485899037092634538770361580470625789542400000⟩, + ⟨5, 5, 4, 2, 4, 8, -31843419834970731749505644963700499802749717708800000⟩, + ⟨5, 5, 5, 2, 5, 8, -14377599609675189888028319425213614274753069056000000⟩, + ⟨5, 5, 6, 2, 6, 8, -2361731024905107264458610976189588108411404288000000⟩, + ⟨5, 5, 7, 2, 7, 8, -949358786311738392778808965571302128573480960000000⟩, + ⟨5, 5, 8, 2, 8, 8, -3069442774545606546452628553947872787024995942400000⟩, + ⟨5, 5, 3, 3, 2, 8, 32132395086830880607392825738095805957606368870400000⟩, + ⟨5, 5, 4, 3, 3, 8, 40615748392800633634325225938242143623846035456000000⟩, + ⟨5, 5, 5, 3, 4, 8, 19459480894687613795767209838844003422964809728000000⟩, + ⟨5, 5, 6, 3, 5, 8, 5753503727216777493583114841639342789841911808000000⟩, + ⟨5, 5, 7, 3, 6, 8, -741279366233419124026396501656911818656841728000000⟩, + ⟨5, 5, 8, 3, 7, 8, -1880207924915461793695081583527511200546947072000000⟩, + ⟨5, 5, 3, 4, 1, 8, -29668941698117403157323289996248470747437911244800000⟩, + ⟨5, 5, 4, 4, 2, 8, -135409128237992881073376388382743363461160579891200000⟩, + ⟨5, 5, 5, 4, 3, 8, -1815110464912749533101416332561673336020533248000000⟩, + ⟨5, 5, 6, 4, 4, 8, -2658920210364699900892954717251679737127895040000000⟩, + ⟨5, 5, 7, 4, 5, 8, -2552158160167988760260492369794203665364418560000000⟩, + ⟨5, 5, 8, 4, 6, 8, 2398277190435636063315749647591879329251642572800000⟩, + ⟨5, 5, 3, 5, 0, 8, 35636547364970264915876659444294929385488855859200000⟩, + ⟨5, 5, 4, 5, 1, 8, 130551300489888192980949231618504274697800541798400000⟩, + ⟨5, 5, 5, 5, 2, 8, -140980919195653035629608252490452529425026121728000000⟩, + ⟨5, 5, 6, 5, 3, 8, -984933249631786516826019233179556165235769344000000⟩, + ⟨5, 5, 7, 5, 4, 8, 1617204926766874388492037410824996702220451840000000⟩, + ⟨5, 5, 8, 5, 5, 8, 801671588592373422111003653106297380489763225600000⟩, + ⟨5, 5, 4, 6, 0, 8, 407323139524104858816120185051830925208410967244800000⟩, + ⟨5, 5, 5, 6, 1, 8, 180112928717817201725137023371602670425032622080000000⟩, + ⟨5, 5, 6, 6, 2, 8, -70573395121503955410809195873449084054640001024000000⟩, + ⟨5, 5, 7, 6, 3, 8, 4849218798923333854066746886656632240644030464000000⟩, + ⟨5, 5, 8, 6, 4, 8, -1194212638041876318120058498782588606116108697600000⟩, + ⟨5, 5, 5, 7, 0, 8, 785820166822391402519380996208542087261521444864000000⟩, + ⟨5, 5, 6, 7, 1, 8, 139908515674523396016309448459650369453400522752000000⟩, + ⟨5, 5, 7, 7, 2, 8, -8611299751469566258034899217475637999709454336000000⟩, + ⟨5, 5, 8, 7, 3, 8, -5719619965044401091464312526527668053831214694400000⟩ +] + +def collectedFourData_13_2_45 : List CollectedFourTerm := [ + ⟨6, 0, 7, 1, 8, 4, 1633985452364459310584567130555041636570507300044800000⟩, + ⟨6, 0, 7, 2, 7, 4, -96472372696723965622591982264807514753346830336000000⟩, + ⟨6, 0, 8, 2, 8, 4, -1559560155690154810305280102935039683475442709299200000⟩, + ⟨6, 0, 7, 3, 6, 4, -75327663600702404473952360253499566058420096204800000⟩, + ⟨6, 0, 8, 3, 7, 4, -955319117993692276570028903411859534276382949376000000⟩, + ⟨6, 0, 7, 4, 5, 4, -259346368052534490864500083305763349856566378496000000⟩, + ⟨6, 0, 8, 4, 6, 4, 1218546108603587506350556200597416716950277875302400000⟩, + ⟨6, 0, 7, 5, 4, 4, 164337865379803490920751130384637912595923206144000000⟩, + ⟨6, 0, 8, 5, 5, 4, 407323139524104858816120185051830925208410967244800000⟩, + ⟨6, 0, 7, 6, 3, 4, 492770120214673664506503767895925961346391631462400000⟩, + ⟨6, 0, 8, 6, 4, 4, -606770213524326589435472296135348291979665263820800000⟩, + ⟨6, 0, 7, 7, 2, 4, -875066972576779294827745419882131403772838648217600000⟩, + ⟨6, 0, 8, 7, 3, 4, -2906094707855784798176631070254496689523287864115200000⟩ +] + +def collectedFourData_13_2_46 : List CollectedFourTerm := [ + ⟨6, 1, 6, 0, 8, 5, -229837917966595298408920251082859928706634219520000000⟩, + ⟨6, 1, 6, 1, 7, 5, 768676068399273604085603633770917365581401292800000000⟩, + ⟨6, 1, 7, 1, 8, 5, 1445053701842312088482641953800058405474439004160000000⟩, + ⟨6, 1, 6, 2, 6, 5, -53061415396583722370270252553478436879691939840000000⟩, + ⟨6, 1, 7, 2, 7, 5, -85317625740903695492103318049208237808628531200000000⟩, + ⟨6, 1, 8, 2, 8, 5, -689616964754700931898029661949876612226162360320000000⟩, + ⟨6, 1, 6, 3, 5, 5, 129264953560030594683604585257040373104446013440000000⟩, + ⟨6, 1, 7, 3, 6, 5, -66617801878108716042322856345097714274570076160000000⟩, + ⟨6, 1, 8, 3, 7, 5, -422429534455120964737069208399843323889162649600000000⟩, + ⟨6, 1, 6, 4, 4, 5, -59738415721664095507426418338335874673226547200000000⟩, + ⟨6, 1, 7, 4, 5, 5, -229359097825114327088253252925351422132958003200000000⟩, + ⟨6, 1, 8, 4, 6, 5, 538825043562994518562635160409821351374791639040000000⟩, + ⟨6, 1, 6, 5, 3, 5, -22128663994969183862200932329856417400797265920000000⟩, + ⟨6, 1, 7, 5, 4, 5, 145336080181318216673232811048781148716846284800000000⟩, + ⟨6, 1, 8, 5, 5, 5, 180112928717817201725137023371602670425032622080000000⟩, + ⟨6, 1, 6, 6, 2, 5, -1585584554295219539480622858540516733201227448320000000⟩, + ⟨6, 1, 7, 6, 3, 5, 435792916848237971013510298990512022396946350080000000⟩, + ⟨6, 1, 8, 6, 4, 5, -268305798546793054510854657126571332846936391680000000⟩, + ⟨6, 1, 6, 7, 1, 5, 3143348581798645646542053593696893296449012367360000000⟩, + ⟨6, 1, 7, 7, 2, 5, -773886185003787836923123431213456889103693905920000000⟩, + ⟨6, 1, 8, 7, 3, 5, -1285036812725143845982004265629725900113098833920000000⟩ +] + +def collectedFourData_13_2_47 : List CollectedFourTerm := [ + ⟨6, 2, 5, 0, 7, 6, 4385542863077259820574402456735102066856296448000000⟩, + ⟨6, 2, 6, 0, 8, 6, 270171202823083815566340620601890002239769018368000000⟩, + ⟨6, 2, 5, 1, 6, 6, -723580553061595134126695844066675597183566217216000000⟩, + ⟨6, 2, 6, 1, 7, 6, -903567782975367054155497669579970265891754475520000000⟩, + ⟨6, 2, 7, 1, 8, 6, -849320034363150536852614521233115298243723395072000000⟩, + ⟨6, 2, 5, 2, 5, 6, 126570035983690239753458211644502667142023348224000000⟩, + ⟨6, 2, 6, 2, 6, 6, 62372938930267688131012130698382294997276819456000000⟩, + ⟨6, 2, 7, 2, 7, 6, 50144827651501339555505024333174554068296663040000000⟩, + ⟨6, 2, 8, 2, 8, 6, 270211643786964641944480738502496752010522525696000000⟩, + ⟨6, 2, 5, 3, 4, 6, -171307260177638675342809713671317753434747174912000000⟩, + ⟨6, 2, 6, 3, 5, 6, -151949113945851836884591961986424061387337629696000000⟩, + ⟨6, 2, 7, 3, 6, 6, 39154139190937129281176777291902010728195817472000000⟩, + ⟨6, 2, 8, 3, 7, 6, 165519969378772964518754505280185558711014522880000000⟩, + ⟨6, 2, 5, 4, 3, 6, 15978925766146686110645056966275786240260308992000000⟩, + ⟨6, 2, 6, 4, 4, 6, 70221657823288943978241338604166897535004180480000000⟩, + ⟨6, 2, 7, 4, 5, 6, 134804178279309577645289407671105263205026365440000000⟩, + ⟨6, 2, 8, 4, 6, 6, -211127057737810801759018120788846652338745638912000000⟩, + ⟨6, 2, 5, 5, 2, 6, 1241094515081620833934303520059841095823536422912000000⟩, + ⟨6, 2, 6, 5, 3, 6, 26011929716738959936847194862677144810058416128000000⟩, + ⟨6, 2, 7, 5, 4, 6, -85420247328131843984645971473468542840639324160000000⟩, + ⟨6, 2, 8, 5, 5, 6, -70573395121503955410809195873449084054640001024000000⟩, + ⟨6, 2, 5, 6, 1, 6, -1585584554295219539480622858540516733201227448320000000⟩, + ⟨6, 2, 6, 6, 2, 6, 1863832086548501824467290187949881247983665676288000000⟩, + ⟨6, 2, 7, 6, 3, 6, -256134187013869428576920445382858190878603739136000000⟩, + ⟨6, 2, 8, 6, 4, 6, 105129883062971634797858593687917942730238459904000000⟩, + ⟨6, 2, 5, 7, 0, 6, -6917795006927899606184349127325336145402009747456000000⟩, + ⟨6, 2, 6, 7, 1, 6, -3694961539636831587911849762835818774857487745024000000⟩, + ⟨6, 2, 7, 7, 2, 6, 454846100461606437222141455581310000192305496064000000⟩, + ⟨6, 2, 8, 7, 3, 6, 503514164006586636761197217264652915139229515776000000⟩ +] + +def collectedFourData_13_2_48 : List CollectedFourTerm := [ + ⟨6, 3, 4, 0, 6, 7, -93241206473035965816848957625443384081296392192000000⟩, + ⟨6, 3, 5, 0, 7, 7, -1205352632305957819923408462453040246331277312000000⟩, + ⟨6, 3, 6, 0, 8, 7, -37127851746450245256996301078666661708112592896000000⟩, + ⟨6, 3, 4, 1, 5, 7, 144488520145465114730577773056631804686488934809600000⟩, + ⟨6, 3, 5, 1, 6, 7, 198873834220424885365643773676591169260123848704000000⟩, + ⟨6, 3, 6, 1, 7, 7, 124171378513446099463620304480672713587231293440000000⟩, + ⟨6, 3, 7, 1, 8, 7, 77810978104808387011102472206278890170777337856000000⟩, + ⟨6, 3, 4, 2, 4, 7, -38523433356764278266363856377313944648720737894400000⟩, + ⟨6, 3, 5, 2, 5, 7, -34787375430404763884012610928432453845994438656000000⟩, + ⟨6, 3, 6, 2, 6, 7, -8571502830039999683066315140542999311922757632000000⟩, + ⟨6, 3, 7, 2, 7, 7, -4594049273058863747924762197048393748887633920000000⟩, + ⟨6, 3, 8, 2, 8, 7, -18566704641087428976793494888232785967061139456000000⟩, + ⟨6, 3, 4, 3, 3, 7, 49135993701494316222746386330840426028652822528000000⟩, + ⟨6, 3, 5, 3, 4, 7, 47083260484507255509945921650819465254721814528000000⟩, + ⟨6, 3, 6, 3, 5, 7, 20881367505626846189985378279783725422620966912000000⟩, + ⟨6, 3, 7, 3, 6, 7, -3587130579797391831542810487322656362050093056000000⟩, + ⟨6, 3, 8, 3, 7, 7, -11373160462620176501922058990320827865162055680000000⟩, + ⟨6, 3, 4, 4, 2, 7, -163814833790092548600858621233886427386096490905600000⟩, + ⟨6, 3, 5, 4, 3, 7, -4391757379867865062181512399706932021504770048000000⟩, + ⟨6, 3, 6, 4, 4, 7, -9650100653992679351631501495918690656908738560000000⟩, + ⟨6, 3, 7, 4, 5, 7, -12350167828542089720685299932901086986365829120000000⟩, + ⟨6, 3, 8, 4, 6, 7, 14506901582117713512202148407361186051634757632000000⟩, + ⟨6, 3, 4, 5, 1, 7, 157937946053705887810792892502635690444434125619200000⟩, + ⟨6, 3, 5, 5, 2, 7, -341110915432811669007671253667488575152642326528000000⟩, + ⟨6, 3, 6, 5, 3, 7, -3574648445395495354657995371130749874251759616000000⟩, + ⟨6, 3, 7, 5, 4, 7, 7825828575373779756472970039862831387173191680000000⟩, + ⟨6, 3, 8, 5, 5, 7, 4849218798923333854066746886656632240644030464000000⟩, + ⟨6, 3, 4, 6, 0, 7, 492770120214673664506503767895925961346391631462400000⟩, + ⟨6, 3, 5, 6, 1, 7, 435792916848237971013510298990512022396946350080000000⟩, + ⟨6, 3, 6, 6, 2, 7, -256134187013869428576920445382858190878603739136000000⟩, + ⟨6, 3, 7, 6, 3, 7, 23465891314542381055612638768950781587622985728000000⟩, + ⟨6, 3, 8, 6, 4, 7, -7223654245340914745275918533205647108178182144000000⟩, + ⟨6, 3, 5, 7, 0, 7, 1901334152165293468731169715346774239539063947264000000⟩, + ⟨6, 3, 6, 7, 1, 7, 507774266165240825124955862249173075698728828928000000⟩, + ⟨6, 3, 7, 7, 2, 7, -41671005665860327957689212676258919184043343872000000⟩, + ⟨6, 3, 8, 7, 3, 7, -34597320214242142322650457584216539149774094336000000⟩ +] + +def collectedFourData_13_2_49 : List CollectedFourTerm := [ + ⟨6, 4, 3, 0, 5, 8, 109390140648030837258508007168614886710223831040000000⟩, + ⟨6, 4, 4, 0, 6, 8, 114812129307399391407887730604032776067103064064000000⟩, + ⟨6, 4, 5, 0, 7, 8, 742102700705326177170424624475460569558679552000000⟩, + ⟨6, 4, 6, 0, 8, 8, 15239069637636089095275347284933882326804332544000000⟩, + ⟨6, 4, 3, 1, 4, 8, -104643600096945094799863368896532492692645058969600000⟩, + ⟨6, 4, 4, 1, 5, 8, -177915272505329885077447443810727136606723191603200000⟩, + ⟨6, 4, 5, 1, 6, 8, -122441189008942890456098179877734862502739574784000000⟩, + ⟨6, 4, 6, 1, 7, 8, -50965951304968549325409231663009975360458588160000000⟩, + ⟨6, 4, 7, 1, 8, 8, -23953047203137505782851806483607149715797311488000000⟩, + ⟨6, 4, 3, 2, 3, 8, 72589018972108688764117697310309696397692528230400000⟩, + ⟨6, 4, 4, 2, 4, 8, 47435651888533422685213673467992703130984565964800000⟩, + ⟨6, 4, 5, 2, 5, 8, 21417637100908234746363750176211319558584139776000000⟩, + ⟨6, 4, 6, 2, 6, 8, 3518160151527295834738037566122926254847950848000000⟩, + ⟨6, 4, 7, 2, 7, 8, 1414215343018781731611027215364962977484636160000000⟩, + ⟨6, 4, 8, 2, 8, 8, 4572405215887623152504559170626348213286102630400000⟩, + ⟨6, 4, 3, 3, 2, 8, -47866124793852007190389153019123748132501218918400000⟩, + ⟨6, 4, 4, 3, 3, 8, -60503379094895588562604230408319186202762674176000000⟩, + ⟨6, 4, 5, 3, 4, 8, -28987877760486053948379310028550040494526169088000000⟩, + ⟨6, 4, 6, 3, 5, 8, -8570725172046693515497983834434260807364640768000000⟩, + ⟨6, 4, 7, 3, 6, 8, 1104249171446866551376668515592491773710041088000000⟩, + ⟨6, 4, 8, 3, 7, 8, 2800857730312106386239285131810649903791603712000000⟩, + ⟨6, 4, 3, 4, 1, 8, 44196433598740207671005712193406214083141487820800000⟩, + ⟨6, 4, 4, 4, 2, 8, 201712639625885056867054522298421337067927843635200000⟩, + ⟨6, 4, 5, 4, 3, 8, 2703885091458625496888352016224245882717995008000000⟩, + ⟨6, 4, 6, 4, 4, 8, 3960868969222064401610602113320282207645859840000000⟩, + ⟨6, 4, 7, 4, 5, 8, 3801830540740346157619401278887008763914485760000000⟩, + ⟨6, 4, 8, 4, 6, 8, -3572601263535718936603064183953313588889570508800000⟩, + ⟨6, 4, 3, 5, 0, 8, -53086096407820584574950163923071051799800787763200000⟩, + ⟨6, 4, 4, 5, 1, 8, -194476161031946875015894147601807011354065135206400000⟩, + ⟨6, 4, 5, 5, 2, 8, 210012675791378406924170962571836347794312921088000000⟩, + ⟨6, 4, 6, 5, 3, 8, 1467208955731131752347786729726432778202906624000000⟩, + ⟨6, 4, 7, 5, 4, 8, -2409074475546358980199583076323210868440432640000000⟩, + ⟨6, 4, 8, 5, 5, 8, -1194212638041876318120058498782588606116108697600000⟩, + ⟨6, 4, 4, 6, 0, 8, -606770213524326589435472296135348291979665263820800000⟩, + ⟨6, 4, 5, 6, 1, 8, -268305798546793054510854657126571332846936391680000000⟩, + ⟨6, 4, 6, 6, 2, 8, 105129883062971634797858593687917942730238459904000000⟩, + ⟨6, 4, 7, 6, 3, 8, -7223654245340914745275918533205647108178182144000000⟩, + ⟨6, 4, 8, 6, 4, 8, 1778962663954516122393842433262046870492518809600000⟩, + ⟨6, 4, 5, 7, 0, 8, -1170599517060648690121093649408926000988546924544000000⟩, + ⟨6, 4, 6, 7, 1, 8, -208415166466815314252680298396314586028013780992000000⟩, + ⟨6, 4, 7, 7, 2, 8, 12827850131534095411648074398845629160180678656000000⟩, + ⟨6, 4, 8, 7, 3, 8, 8520250117689700286961128743922066079133099622400000⟩ +] + +def collectedFourData_13_2_50 : List CollectedFourTerm := [ + ⟨7, 0, 6, 0, 8, 5, -1002766832588595449448667365221882803629814972416000000⟩, + ⟨7, 0, 6, 1, 7, 5, 3353680163894552961173573647027364505298654986240000000⟩, + ⟨7, 0, 7, 1, 8, 5, 6304668682769069747729377777946130466818100297728000000⟩, + ⟨7, 0, 6, 2, 6, 5, -231503260735390441058405835991035538094237417472000000⟩, + ⟨7, 0, 7, 2, 7, 5, -372234860483811083995411237554436334578261032960000000⟩, + ⟨7, 0, 8, 2, 8, 5, -3008750799539260273514075001146581411537203757056000000⟩, + ⟨7, 0, 6, 3, 5, 5, 563973991728132290127122856317907289434438500352000000⟩, + ⟨7, 0, 7, 3, 6, 5, -290648831029850783121972375187559332443825635328000000⟩, + ⟨7, 0, 8, 3, 7, 5, -1843030645269778707304640468344332368979091783680000000⟩, + ⟨7, 0, 6, 4, 4, 5, -260634548237511783322765734130150396126832885760000000⟩, + ⟨7, 0, 7, 4, 5, 5, -1000677773651321743609172356348110601494001090560000000⟩, + ⟨7, 0, 8, 4, 6, 5, 2350856146946151951197491766926039036220336504832000000⟩, + ⟨7, 0, 6, 5, 3, 5, -96545820202207138348089941832830650694328385536000000⟩, + ⟨7, 0, 7, 5, 4, 5, 634091198152274579900017844144435919723524259840000000⟩, + ⟨7, 0, 8, 5, 5, 5, 785820166822391402519380996208542087261521444864000000⟩, + ⟨7, 0, 6, 6, 2, 5, -6917795006927899606184349127325336145402009747456000000⟩, + ⟨7, 0, 7, 6, 3, 5, 1901334152165293468731169715346774239539063947264000000⟩, + ⟨7, 0, 8, 6, 4, 5, -1170599517060648690121093649408926000988546924544000000⟩, + ⟨7, 0, 6, 7, 1, 5, 13714210992592617176056362495789133076319896076288000000⟩, + ⟨7, 0, 7, 7, 2, 5, -3376411539862226493253075401025662558432223297536000000⟩, + ⟨7, 0, 8, 7, 3, 5, -5606526137447089710009113377682649266424366759936000000⟩ +] + +def collectedFourData_13_2_51 : List CollectedFourTerm := [ + ⟨7, 1, 5, 0, 7, 6, -8694137377743651653188555653393717657499336704000000⟩, + ⟨7, 1, 6, 0, 8, 6, -535602005541897189318376564969270585503843876864000000⟩, + ⟨7, 1, 5, 1, 6, 6, 1434465225535845227333823021906172328807673888768000000⟩, + ⟨7, 1, 6, 1, 7, 6, 1791281645296441959069599842782243113267059752960000000⟩, + ⟨7, 1, 7, 1, 8, 6, 1683737974286241613637282276356003173539833184256000000⟩, + ⟨7, 1, 5, 2, 5, 6, -250919285275441694702460509704977696266599268352000000⟩, + ⟨7, 1, 6, 2, 6, 6, -123651487773364205147846525327707603743736332288000000⟩, + ⟨7, 1, 7, 2, 7, 6, -99409818578200229901684880260075886758246481920000000⟩, + ⟨7, 1, 8, 2, 8, 6, -535682177896072189312164896582963855322469367808000000⟩, + ⟨7, 1, 5, 3, 4, 6, 339608778272024582617379972897761923226272792576000000⟩, + ⟨7, 1, 6, 3, 5, 6, 301232142135464171769555063071184797466579959808000000⟩, + ⟨7, 1, 7, 3, 6, 6, -77621283307773491771242536525912755231004819456000000⟩, + ⟨7, 1, 8, 3, 7, 6, -328135739968396015581215157071570677134513930240000000⟩, + ⟨7, 1, 5, 4, 3, 6, -31677486709631008479778260129854222786327740416000000⟩, + ⟨7, 1, 6, 4, 4, 6, -139211212629715868206827318649312594013234135040000000⟩, + ⟨7, 1, 7, 4, 5, 6, -267243094331949558983547234147725129026759557120000000⟩, + ⟨7, 1, 8, 4, 6, 6, 418549698735211260121076328785305474197488664576000000⟩, + ⟨7, 1, 5, 5, 2, 6, -2460412895226481070452985411436068836063183896576000000⟩, + ⟨7, 1, 6, 5, 3, 6, -51567456408088682326021755800720826599781433344000000⟩, + ⟨7, 1, 7, 5, 4, 6, 169341718527979427873842000508030610757574983680000000⟩, + ⟨7, 1, 8, 5, 5, 6, 139908515674523396016309448459650369453400522752000000⟩, + ⟨7, 1, 5, 6, 1, 6, 3143348581798645646542053593696893296449012367360000000⟩, + ⟨7, 1, 6, 6, 2, 6, -3694961539636831587911849762835818774857487745024000000⟩, + ⟨7, 1, 7, 6, 3, 6, 507774266165240825124955862249173075698728828928000000⟩, + ⟨7, 1, 8, 6, 4, 6, -208415166466815314252680298396314586028013780992000000⟩, + ⟨7, 1, 5, 7, 0, 6, 13714210992592617176056362495789133076319896076288000000⟩, + ⟨7, 1, 6, 7, 1, 6, 7325091609876684383524084062177112994387173834752000000⟩, + ⟨7, 1, 7, 7, 2, 6, -901711511347399288728578147930165494864435740672000000⟩, + ⟨7, 1, 8, 7, 3, 6, -998193712885366872804767887451768326792987803648000000⟩ +] + +def collectedFourData_13_2_52 : List CollectedFourTerm := [ + ⟨7, 2, 4, 0, 6, 7, 165578830616232504600244651002963712528726622208000000⟩, + ⟨7, 2, 5, 0, 7, 7, 2140479374804466182183348438265531823804121088000000⟩, + ⟨7, 2, 6, 0, 8, 7, 65932075613456075084307578620902005190168674304000000⟩, + ⟨7, 2, 4, 1, 5, 7, -256584412708930541705024419705680246041980855910400000⟩, + ⟨7, 2, 5, 1, 6, 7, -353162492807373970553443604230754221404608004096000000⟩, + ⟨7, 2, 6, 1, 7, 7, -220504993746597307137960806089253109222667714560000000⟩, + ⟨7, 2, 7, 1, 8, 7, -138177649679224934607688772504480116298527801344000000⟩, + ⟨7, 2, 4, 2, 4, 7, 68410365843775445435402497181783460458178124185600000⟩, + ⟨7, 2, 5, 2, 5, 7, 61775830256336336864246760221039980441233260544000000⟩, + ⟨7, 2, 6, 2, 6, 7, 15221375493807883609868763058271044060229664768000000⟩, + ⟨7, 2, 7, 2, 7, 7, 8158166707617803682976208119640122955220910080000000⟩, + ⟨7, 2, 8, 2, 8, 7, 32970972375365646378856593131956141256809119744000000⟩, + ⟨7, 2, 4, 3, 3, 7, -87256275267231508694668399741971226505691267072000000⟩, + ⟨7, 2, 5, 3, 4, 7, -83611007488182492479444526468549999468396675072000000⟩, + ⟨7, 2, 6, 3, 5, 7, -37081377901833054332064005151738986172921151488000000⟩, + ⟨7, 2, 7, 3, 6, 7, 6370068654595787399926340090751884880871686144000000⟩, + ⟨7, 2, 8, 3, 7, 7, 20196592054565492084501463944446435788136120320000000⟩, + ⟨7, 2, 4, 4, 2, 7, 290904307682890920148884881979380141757336807014400000⟩, + ⟨7, 2, 5, 4, 3, 7, 7798934385507131278373590973360093397151383552000000⟩, + ⟨7, 2, 6, 4, 4, 7, 17136762189784884569641001382447976709294653440000000⟩, + ⟨7, 2, 7, 4, 5, 7, 21931573220854648260470120559813630108767354880000000⟩, + ⟨7, 2, 8, 4, 6, 7, -25761526375427787920788592555470072398917664768000000⟩, + ⟨7, 2, 4, 5, 1, 7, -280468061350801853142698002645374855096524655820800000⟩, + ⟨7, 2, 5, 5, 2, 7, 605748773790598303456881684803093825764114563072000000⟩, + ⟨7, 2, 6, 5, 3, 7, 6347902733582545813215969214697682584243011584000000⟩, + ⟨7, 2, 7, 5, 4, 7, -13897198386082785626134039911533129645760184320000000⟩, + ⟨7, 2, 8, 5, 5, 7, -8611299751469566258034899217475637999709454336000000⟩, + ⟨7, 2, 4, 6, 0, 7, -875066972576779294827745419882131403772838648217600000⟩, + ⟨7, 2, 5, 6, 1, 7, -773886185003787836923123431213456889103693905920000000⟩, + ⟨7, 2, 6, 6, 2, 7, 454846100461606437222141455581310000192305496064000000⟩, + ⟨7, 2, 7, 6, 3, 7, -41671005665860327957689212676258919184043343872000000⟩, + ⟨7, 2, 8, 6, 4, 7, 12827850131534095411648074398845629160180678656000000⟩, + ⟨7, 2, 5, 7, 0, 7, -3376411539862226493253075401025662558432223297536000000⟩, + ⟨7, 2, 6, 7, 1, 7, -901711511347399288728578147930165494864435740672000000⟩, + ⟨7, 2, 7, 7, 2, 7, 73999861753728884226852661756092307334945046528000000⟩, + ⟨7, 2, 8, 7, 3, 7, 61438327969149366659823752625933272767071780864000000⟩ +] + +def collectedFourData_13_2_53 : List CollectedFourTerm := [ + ⟨7, 3, 3, 0, 5, 8, 523918448439290826483301949382800206435461365760000000⟩, + ⟨7, 3, 4, 0, 6, 8, 549886784059334106026024028679399158633323298816000000⟩, + ⟨7, 3, 5, 0, 7, 8, 3554262689789683769525750763236337512022540288000000⟩, + ⟨7, 3, 6, 0, 8, 8, 72986739690715704843204866957278510014252711936000000⟩, + ⟨7, 3, 3, 1, 4, 8, -501185136769270734815972193122135434777416066662400000⟩, + ⟨7, 3, 4, 1, 5, 8, -852116040554007710558232189028245842424947854540800000⟩, + ⟨7, 3, 5, 1, 6, 8, -586425772840269916832375753474368767543000170496000000⟩, + ⟨7, 3, 6, 1, 7, 8, -244098800611718951894909068305172487535109079040000000⟩, + ⟨7, 3, 7, 1, 8, 8, -114721886741506833669178595042689123240453865472000000⟩, + ⟨7, 3, 3, 2, 3, 8, 347661370287140511684740957091864529967741770137600000⟩, + ⟨7, 3, 4, 2, 4, 8, 227190613257467475640333334792427746769671238451200000⟩, + ⟨7, 3, 5, 2, 5, 8, 102578670551747090547636675366874235939422470144000000⟩, + ⟨7, 3, 6, 2, 6, 8, 16850046969770503067025025045064005920397197312000000⟩, + ⟨7, 3, 7, 2, 7, 8, 6773311597225534231637913636911192235615191040000000⟩, + ⟨7, 3, 8, 2, 8, 8, 21899299444649607142671416815392006082467043737600000⟩, + ⟨7, 3, 3, 3, 2, 8, -229252341081507223005615206004054730492440320409600000⟩, + ⟨7, 3, 4, 3, 3, 8, -289777820130287405166680404227704624019085983744000000⟩, + ⟨7, 3, 5, 3, 4, 8, -138835948558541948147327723625636811398155599872000000⟩, + ⟨7, 3, 6, 3, 5, 8, -41049047085388401945118965796460048036545953792000000⟩, + ⟨7, 3, 7, 3, 6, 8, 5288744572111757020484663905216509945285967872000000⟩, + ⟨7, 3, 8, 3, 7, 8, 13414563942154762191619673928644120192722403328000000⟩, + ⟨7, 3, 3, 4, 1, 8, 211676543977630746057958469016312209475921720115200000⟩, + ⟨7, 3, 4, 4, 2, 8, 966092305552675096286192250304687416596746783948800000⟩, + ⟨7, 3, 5, 4, 3, 8, 12950118479444828594736266013485812439530340352000000⟩, + ⟨7, 3, 6, 4, 4, 8, 18970378066366558908065598552709492900846632960000000⟩, + ⟨7, 3, 7, 4, 5, 8, 18208671698692509617457288859353955513600573440000000⟩, + ⟨7, 3, 8, 4, 6, 8, -17110789873708584078687607133234775791393518387200000⟩, + ⟨7, 3, 3, 5, 0, 8, -254253126460210257369823382433789770213853285580800000⟩, + ⟨7, 3, 4, 5, 1, 8, -931433563780881956090375668286883161421760797081600000⟩, + ⟨7, 3, 5, 5, 2, 8, 1005844901573252168230813889090596520733412687872000000⟩, + ⟨7, 3, 6, 5, 3, 8, 7027121777786325884435617438476791642855571456000000⟩, + ⟨7, 3, 7, 5, 4, 8, -11538138208122572134614360946368446216703836160000000⟩, + ⟨7, 3, 8, 5, 5, 8, -5719619965044401091464312526527668053831214694400000⟩, + ⟨7, 3, 4, 6, 0, 8, -2906094707855784798176631070254496689523287864115200000⟩, + ⟨7, 3, 5, 6, 1, 8, -1285036812725143845982004265629725900113098833920000000⟩, + ⟨7, 3, 6, 6, 2, 8, 503514164006586636761197217264652915139229515776000000⟩, + ⟨7, 3, 7, 6, 3, 8, -34597320214242142322650457584216539149774094336000000⟩, + ⟨7, 3, 8, 6, 4, 8, 8520250117689700286961128743922066079133099622400000⟩, + ⟨7, 3, 5, 7, 0, 8, -5606526137447089710009113377682649266424366759936000000⟩, + ⟨7, 3, 6, 7, 1, 8, -998193712885366872804767887451768326792987803648000000⟩, + ⟨7, 3, 7, 7, 2, 8, 61438327969149366659823752625933272767071780864000000⟩, + ⟨7, 3, 8, 7, 3, 8, 40807299410443065826281493130239817841236351385600000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1306.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1306.lean new file mode 100644 index 0000000000000000000000000000000000000000..074ed7b78893e50de12295f5379946ba8c16b76b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1306.lean @@ -0,0 +1,640 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1303 +import OAI.Analysis.LaughlinFock.Sparse1304 +import OAI.Analysis.LaughlinFock.Sparse1305 + +namespace OAI + +/-! Sparse1306. -/ +namespace LaughlinFock +def collectedFourData_13_2 : List (List CollectedFourTerm) := [ + collectedFourData_13_2_0, + collectedFourData_13_2_1, + collectedFourData_13_2_2, + collectedFourData_13_2_3, + collectedFourData_13_2_4, + collectedFourData_13_2_5, + collectedFourData_13_2_6, + collectedFourData_13_2_7, + collectedFourData_13_2_8, + collectedFourData_13_2_9, + collectedFourData_13_2_10, + collectedFourData_13_2_11, + collectedFourData_13_2_12, + collectedFourData_13_2_13, + collectedFourData_13_2_14, + collectedFourData_13_2_15, + collectedFourData_13_2_16, + collectedFourData_13_2_17, + collectedFourData_13_2_18, + collectedFourData_13_2_19, + collectedFourData_13_2_20, + collectedFourData_13_2_21, + collectedFourData_13_2_22, + collectedFourData_13_2_23, + collectedFourData_13_2_24, + collectedFourData_13_2_25, + collectedFourData_13_2_26, + collectedFourData_13_2_27, + collectedFourData_13_2_28, + collectedFourData_13_2_29, + collectedFourData_13_2_30, + collectedFourData_13_2_31, + collectedFourData_13_2_32, + collectedFourData_13_2_33, + collectedFourData_13_2_34, + collectedFourData_13_2_35, + collectedFourData_13_2_36, + collectedFourData_13_2_37, + collectedFourData_13_2_38, + collectedFourData_13_2_39, + collectedFourData_13_2_40, + collectedFourData_13_2_41, + collectedFourData_13_2_42, + collectedFourData_13_2_43, + collectedFourData_13_2_44, + collectedFourData_13_2_45, + collectedFourData_13_2_46, + collectedFourData_13_2_47, + collectedFourData_13_2_48, + collectedFourData_13_2_49, + collectedFourData_13_2_50, + collectedFourData_13_2_51, + collectedFourData_13_2_52, + collectedFourData_13_2_53 +] + +theorem collectedFourChecked_13_2 : collectNumericRowParts 13 2 = collectedFourData_13_2 := by + decide +kernel + +def collectedFourData_13_3_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_3_1 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_3_2 : List CollectedFourTerm := [ + ⟨0, 5, 8, 3, 8, 2, -57860053986746563986679006282536373847064576000000000⟩, + ⟨0, 5, 8, 4, 7, 2, -20553422260800312838410215721149154139488387072000000⟩, + ⟨0, 5, 8, 5, 6, 2, -42797619532308453815132338672462952050100011008000000⟩, + ⟨0, 5, 8, 6, 5, 2, 44914192406752656885812297679672084879309275136000000⟩, + ⟨0, 5, 8, 7, 4, 2, -88805317905222994554581597432709806225715363840000000⟩ +] + +def collectedFourData_13_3_3 : List CollectedFourTerm := [ + ⟨0, 6, 7, 2, 8, 3, 3675532472370445000802386591814694915912656486400000⟩, + ⟨0, 6, 7, 3, 7, 3, -2052340572063924150163839269576884767113714073600000⟩, + ⟨0, 6, 8, 3, 8, 3, -9287142980654152316732471649115934667728486400000000⟩, + ⟨0, 6, 7, 4, 6, 3, 674040651946901594658768574012016981000060928000000⟩, + ⟨0, 6, 8, 4, 7, 3, -3299038941815298424514637465735275091382291660800000⟩, + ⟨0, 6, 7, 5, 5, 3, 1785157507218906868567423131964257370301163110400000⟩, + ⟨0, 6, 8, 5, 6, 3, -6869464932044991107926821321168249005551072051200000⟩, + ⟨0, 6, 7, 6, 4, 3, -639060645795923628667369790970339567201995980800000⟩, + ⟨0, 6, 8, 6, 5, 3, 7209196984808717875653115731017949589683988070400000⟩, + ⟨0, 6, 7, 7, 3, 3, -26776362217811882672214187821264243076860425011200000⟩, + ⟨0, 6, 8, 7, 4, 3, -14254181045478615005554086537392029231875096576000000⟩ +] + +def collectedFourData_13_3_4 : List CollectedFourTerm := [ + ⟨0, 7, 6, 1, 8, 4, -8402352365974156182925741711321370946940855910400000⟩, + ⟨0, 7, 6, 2, 7, 4, -11243308512095798270246584445913813377514838425600000⟩, + ⟨0, 7, 7, 2, 8, 4, -52728944348496664644238567709418230851807110758400000⟩, + ⟨0, 7, 6, 3, 6, 4, 29791480142933246192556284552902681794884036198400000⟩, + ⟨0, 7, 7, 3, 7, 4, 29442741323062795860266399266270342912285448601600000⟩, + ⟨0, 7, 8, 3, 8, 4, 66616367705169988895773999722825215890371379200000000⟩, + ⟨0, 7, 6, 4, 5, 4, -23702139030980969401796949490869585727561767321600000⟩, + ⟨0, 7, 7, 4, 6, 4, -9669742354965780447049205707972479567022522368000000⟩, + ⟨0, 7, 8, 4, 7, 4, 23663896601941087725509687013808573577840453222400000⟩, + ⟨0, 7, 6, 5, 4, 4, -26733194746355434218599740187940181070620026470400000⟩, + ⟨0, 7, 7, 5, 5, 4, -25609750848083316558127294557585076782966924902400000⟩, + ⟨0, 7, 8, 5, 6, 4, 49274443475688441124025872929679075266939951513600000⟩, + ⟨0, 7, 6, 6, 3, 4, 98987387141363486772765190023127926450856289894400000⟩, + ⟨0, 7, 7, 6, 4, 4, 9167921513629164671702698440365495315285724364800000⟩, + ⟨0, 7, 8, 6, 5, 4, -51711330190503134267837435295231524554975425331200000⟩, + ⟨0, 7, 6, 7, 2, 4, -97688427706882103325321678374084440819196598681600000⟩, + ⟨0, 7, 7, 7, 3, 4, 384131911186089432003158971266572259233939796787200000⟩, + ⟨0, 7, 8, 7, 4, 4, 102244766537963233394262428909249131692611862528000000⟩ +] + +def collectedFourData_13_3_5 : List CollectedFourTerm := [ + ⟨0, 8, 5, 0, 8, 5, 182569240174813814095581490767882418139430912000000⟩, + ⟨0, 8, 5, 1, 7, 5, -1448054592893328708693832010108112974641102848000000⟩, + ⟨0, 8, 6, 1, 8, 5, -792069111181515132254408817856248381802807296000000⟩, + ⟨0, 8, 5, 2, 6, 5, -1012114867455482007592522752203587339035869184000000⟩, + ⟨0, 8, 6, 2, 7, 5, -1059879066245610204037547069555750942061625344000000⟩, + ⟨0, 8, 7, 2, 8, 5, -2485314008775872174575122935263930865216913408000000⟩, + ⟨0, 8, 5, 3, 5, 5, 382437481103126579645452082622012137983180800000000⟩, + ⟨0, 8, 6, 3, 6, 5, 2808369629099588834507665515549123406951612416000000⟩, + ⟨0, 8, 7, 3, 7, 5, 1387747438737761749642611720626522977355169792000000⟩, + ⟨0, 8, 8, 3, 8, 5, 2093253764348547555505494411390075468251136000000000⟩, + ⟨0, 8, 5, 4, 4, 5, -1377772261083943505315619250870592356485169152000000⟩, + ⟨0, 8, 6, 4, 5, 5, -2234342405276310537596374205076172313286672384000000⟩, + ⟨0, 8, 7, 4, 6, 5, -455771425599098378924426149990353663594332160000000⟩, + ⟨0, 8, 8, 4, 7, 5, 743579128486822151736929876277389677289275392000000⟩, + ⟨0, 8, 5, 5, 3, 5, 3593309262747901158947150316213420884559396864000000⟩, + ⟨0, 8, 6, 5, 4, 5, -2520072579618976068335287015251347367260061696000000⟩, + ⟨0, 8, 7, 5, 5, 5, -1207084141934199218266546723552445695354994688000000⟩, + ⟨0, 8, 8, 5, 6, 5, 1548326902904070012833531051708052466971967488000000⟩, + ⟨0, 8, 5, 6, 2, 5, 53180706162685539148834256853093318924435456000000⟩, + ⟨0, 8, 6, 6, 3, 5, 9331297752846642913170745885260851525720211456000000⟩, + ⟨0, 8, 7, 6, 4, 5, 432118716782728088541008053259921320707096576000000⟩, + ⟨0, 8, 8, 6, 5, 5, -1624900010457049665573096577800934262933815296000000⟩, + ⟨0, 8, 5, 7, 1, 5, -2479101534997507443568598077125540447415959552000000⟩, + ⟨0, 8, 6, 7, 2, 5, -9208848038776453739338027918392033223360118784000000⟩, + ⟨0, 8, 7, 7, 3, 5, 18105585687035587095988437530759521364726513664000000⟩, + ⟨0, 8, 8, 7, 4, 5, 3212787634831069815888967182285816899819274240000000⟩ +] + +def collectedFourData_13_3_6 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_3_7 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_3_8 : List CollectedFourTerm := [ + ⟨1, 4, 8, 3, 8, 2, 199417252839714587642713255819717588699368652800000000⟩, + ⟨1, 4, 8, 4, 7, 2, 70838285160298759572813203636925884412787792281600000⟩, + ⟨1, 4, 8, 5, 6, 2, 147503901692991783876454516292154848489989629542400000⟩, + ⟨1, 4, 8, 6, 5, 2, -154798764365491244693075269183984075774635068620800000⟩, + ⟨1, 4, 8, 7, 4, 2, 306071483069711371906370718201811477972597604352000000⟩ +] + +def collectedFourData_13_3_9 : List CollectedFourTerm := [ + ⟨1, 5, 7, 2, 8, 3, -49275760924706450429594177794234822312877830963200000⟩, + ⟨1, 5, 7, 3, 7, 3, 27514555816146947346616034066325376656481242316800000⟩, + ⟨1, 5, 8, 3, 8, 3, 124507412362253379750072208058209615240966963200000000⟩, + ⟨1, 5, 7, 4, 6, 3, -9036477372609994060622301689467990741943844864000000⟩, + ⟨1, 5, 8, 4, 7, 3, 44228327568915853226077885545718535663114413670400000⟩, + ⟨1, 5, 7, 5, 5, 3, -23932585332849176820763890137037681752418759475200000⟩, + ⟨1, 5, 8, 5, 6, 3, 92094986023561839321668521643076171044503525785600000⟩, + ⟨1, 5, 7, 6, 4, 3, 8567520443730322176319215702150064369723401830400000⟩, + ⟨1, 5, 8, 6, 5, 3, -96649579279446950494760915014379924707465179955200000⟩, + ⟨1, 5, 7, 7, 3, 3, 358975368330050298884978695213803297196207610265600000⟩, + ⟨1, 5, 8, 7, 4, 3, 191097649838337575009109183397014840597270233088000000⟩ +] + +def collectedFourData_13_3_10 : List CollectedFourTerm := [ + ⟨1, 6, 6, 1, 8, 4, -18825758965671764051782623604805786514679765401600000⟩, + ⟨1, 6, 6, 2, 7, 4, -25191018753575106586649340429501783221744330342400000⟩, + ⟨1, 6, 7, 2, 8, 4, -118141010229345550950198584786450365180410435993600000⟩, + ⟨1, 6, 6, 3, 6, 4, 66748834132765401685456308223914860448719673753600000⟩, + ⟨1, 6, 7, 3, 7, 4, 65967472833108367753961124098112986360123385446400000⟩, + ⟨1, 6, 8, 3, 8, 4, 149256259076286902277360358351359641582881996800000000⟩, + ⟨1, 6, 6, 4, 5, 4, -53105456297577640783963768769960087198835828326400000⟩, + ⟨1, 6, 7, 4, 6, 4, -21665389751079258081294987203906603283929628672000000⟩, + ⟨1, 6, 8, 4, 7, 4, 53019772822283023142472702468779251583816407449600000⟩, + ⟨1, 6, 6, 5, 4, 4, -59896640697346121494795959785633555304857311641600000⟩, + ⟨1, 6, 7, 5, 5, 4, -57379526070497989602108930827180655448528886169600000⟩, + ⟨1, 6, 8, 5, 6, 4, 110401082415612348911435343502661249804968289894400000⟩, + ⟨1, 6, 6, 6, 3, 4, 221784639562529543331012812534399596820973590937600000⟩, + ⟨1, 6, 7, 6, 4, 4, 20541042926348294444057596504379156477183734579200000⟩, + ⟨1, 6, 8, 6, 5, 4, -115861010769191971455049362119457616440008166604800000⟩, + ⟨1, 6, 6, 7, 2, 4, -218874276350584351301846496367756751752015537766400000⟩, + ⟨1, 6, 7, 7, 3, 4, 860660735950191841255314897231818956233107098828800000⟩, + ⟨1, 6, 8, 7, 4, 4, 229082909940770518903858352457804497963358093312000000⟩ +] + +def collectedFourData_13_3_11 : List CollectedFourTerm := [ + ⟨1, 7, 5, 0, 8, 5, -1448054592893328708693832010108112974641102848000000⟩, + ⟨1, 7, 5, 1, 7, 5, 11485297862836451622139813105800553537776648192000000⟩, + ⟨1, 7, 6, 1, 8, 5, 6282325068763458742599310206312130061254262784000000⟩, + ⟨1, 7, 5, 2, 6, 5, 8027626017127493229826597518237192914139611136000000⟩, + ⟨1, 7, 6, 2, 7, 5, 8406469503399813990855918740055826065078091776000000⟩, + ⟨1, 7, 7, 2, 8, 5, 19712358783681411674612263305033679825306386432000000⟩, + ⟨1, 7, 5, 3, 5, 5, -3033316841740001568160635670967293117150003200000000⟩, + ⟨1, 7, 6, 3, 6, 5, -22274686228993837044764643804694643093236875264000000⟩, + ⟨1, 7, 7, 3, 7, 5, -11006969468219284357209835967136430566427066368000000⟩, + ⟨1, 7, 8, 3, 8, 5, -16602718643369382970268577190068195000582144000000000⟩, + ⟨1, 7, 5, 4, 4, 5, 10927850982527459144187632667751521280283639808000000⟩, + ⟨1, 7, 6, 4, 5, 5, 17721768349140735870062923907801005993739943936000000⟩, + ⟨1, 7, 7, 4, 6, 5, 3614967699467709710436329178573842779094384640000000⟩, + ⟨1, 7, 8, 4, 7, 5, -5897725000958308250986918960069887460028448768000000⟩, + ⟨1, 7, 5, 5, 3, 5, -28500463586450622197715464966766212305026809856000000⟩, + ⟨1, 7, 6, 5, 4, 5, 19988047657138794257937908164687052592994320384000000⟩, + ⟨1, 7, 7, 5, 5, 5, 9574031934748957813847496956840966200913559552000000⟩, + ⟨1, 7, 8, 5, 6, 5, -12280611349993685030744623543048150641385930752000000⟩, + ⟨1, 7, 5, 6, 2, 5, -421804712220142095314145106405820329491431424000000⟩, + ⟨1, 7, 6, 6, 3, 5, -74011528753291304087050225980080481658076135424000000⟩, + ⟨1, 7, 7, 6, 4, 5, -3427365376080056621112339244167307923139067904000000⟩, + ⟨1, 7, 8, 6, 5, 5, 12887953747749381355653690708154165988671094784000000⟩, + ⟨1, 7, 5, 7, 1, 5, 19663084321130236222345588579979678101335441408000000⟩, + ⟨1, 7, 6, 7, 2, 5, 73040314376279981703950032135771921368571969536000000⟩, + ⟨1, 7, 7, 7, 3, 5, -143605113796997996909138678446422070658970157056000000⟩, + ⟨1, 7, 8, 7, 4, 5, -25482342404193388505835636257883203618954280960000000⟩ +] + +def collectedFourData_13_3_12 : List CollectedFourTerm := [ + ⟨1, 8, 4, 0, 7, 6, -8402352365974156182925741711321370946940855910400000⟩, + ⟨1, 8, 5, 0, 8, 6, -792069111181515132254408817856248381802807296000000⟩, + ⟨1, 8, 4, 1, 6, 6, -18825758965671764051782623604805786514679765401600000⟩, + ⟨1, 8, 5, 1, 7, 6, 6282325068763458742599310206312130061254262784000000⟩, + ⟨1, 8, 6, 1, 8, 6, 1718179569261372650456270778528506384360669184000000⟩, + ⟨1, 8, 4, 2, 5, 6, 2388890152123445281126393337187635213508594892800000⟩, + ⟨1, 8, 5, 2, 6, 6, 4391018567593587650841883629542503508682473472000000⟩, + ⟨1, 8, 6, 2, 7, 6, 2299120786056891411427594750681282471186661376000000⟩, + ⟨1, 8, 7, 2, 8, 6, 3594144073874210264323269932598992536325849088000000⟩, + ⟨1, 8, 4, 3, 4, 6, -1639017262713277658554471349224522306030456012800000⟩, + ⟨1, 8, 5, 3, 5, 6, -1659189222947971755000469274082857783289446400000000⟩, + ⟨1, 8, 6, 3, 6, 6, -6091997846570818515805460903246551025832689664000000⟩, + ⟨1, 8, 7, 3, 7, 6, -2006894990074166140902473555125262610031706112000000⟩, + ⟨1, 8, 8, 3, 8, 6, -2270373759316388682389403666917611140022272000000000⟩, + ⟨1, 8, 4, 4, 3, 6, -3663442250026482402118026028372475386817150976000000⟩, + ⟨1, 8, 5, 4, 4, 6, 5977408073793657896757864767100552935915913216000000⟩, + ⟨1, 8, 6, 4, 5, 6, 4846801140563986482552168903412506981392449536000000⟩, + ⟨1, 8, 7, 4, 6, 6, 659115171191201385620461956243827818506485760000000⟩, + ⟨1, 8, 8, 4, 7, 6, -806496837624092245530943476693017735183990784000000⟩, + ⟨1, 8, 4, 5, 2, 6, 25100666201675805191225298506352862241222138265600000⟩, + ⟨1, 8, 5, 5, 3, 6, -15589423887724946682014179839016953105101094912000000⟩, + ⟨1, 8, 6, 5, 4, 6, 5466615423114076106523334289539674841005686784000000⟩, + ⟨1, 8, 7, 5, 5, 6, 1745628238556950122684756407702948815640199168000000⟩, + ⟨1, 8, 8, 5, 6, 6, -1679338086508122660294065681199386618260094976000000⟩, + ⟨1, 8, 4, 6, 1, 6, -13469170836247897116493847117792076867553355366400000⟩, + ⟨1, 8, 5, 6, 2, 6, -230722298137135337499488203055862311339163648000000⟩, + ⟨1, 8, 6, 6, 3, 6, -20241725030432956845290197998203436159492685824000000⟩, + ⟨1, 8, 7, 6, 4, 6, -624909737622949224038356252695777767678017536000000⟩, + ⟨1, 8, 8, 6, 5, 6, 1762390402963266456498643884796590397002350592000000⟩, + ⟨1, 8, 4, 7, 0, 6, -257008380476726148942948459779906319434906389708800000⟩, + ⟨1, 8, 5, 7, 1, 6, 10755479660615332183783128169950592179074236416000000⟩, + ⟨1, 8, 6, 7, 2, 6, 19976103515836257022202579902122006459382235136000000⟩, + ⟨1, 8, 7, 7, 3, 6, -26183445339823502285042200120915573474647343104000000⟩, + ⟨1, 8, 8, 7, 4, 6, -3484636628682571606124782088318437432995348480000000⟩ +] + +def collectedFourData_13_3_13 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_3_14 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_3_15 : List CollectedFourTerm := [ + ⟨2, 3, 8, 3, 8, 2, -74321585550767247773417144229681996450339225600000000⟩, + ⟨2, 3, 8, 4, 7, 2, -26400993875101089822074852219542750990028714803200000⟩, + ⟨2, 3, 8, 5, 6, 2, -54973798368184064200583658110270845472771722444800000⟩, + ⟨2, 3, 8, 6, 5, 2, 57692548889890645551508891518056584428798974361600000⟩, + ⟨2, 3, 8, 7, 4, 2, -114070962214586689855748939727588103002211221504000000⟩ +] + +def collectedFourData_13_3_16 : List CollectedFourTerm := [ + ⟨2, 4, 7, 2, 8, 3, 64167630316875632112765218593390195530266994278400000⟩, + ⟨2, 4, 7, 3, 7, 3, -35829864680148020482247281829033826591295773081600000⟩, + ⟨2, 4, 8, 3, 8, 3, -162135408124485712596195683817148361210226278400000000⟩, + ⟨2, 4, 7, 4, 6, 3, 11767435520650035265682021710608436735160352768000000⟩, + ⟨2, 4, 8, 4, 7, 3, -57594787370455571543792158911721264371177671884800000⟩, + ⟨2, 4, 7, 5, 5, 3, 31165369328581190453865607111156441902788011622400000⟩, + ⟨2, 4, 8, 5, 6, 3, -119927463448560616087937104739865571516950459187200000⟩, + ⟨2, 4, 7, 6, 4, 3, -11156752818197837894348796591775518943760665804800000⟩, + ⟨2, 4, 8, 6, 5, 3, 125858522671247024824016135978035040644028065382400000⟩, + ⟨2, 4, 7, 7, 3, 3, -467463075061669497650747279727822783359176880947200000⟩, + ⟨2, 4, 8, 7, 4, 3, -248850207873745661243395349359503648716652281856000000⟩ +] + +def collectedFourData_13_3_17 : List CollectedFourTerm := [ + ⟨2, 5, 6, 1, 8, 4, 2388890152123445281126393337187635213508594892800000⟩, + ⟨2, 5, 6, 2, 7, 4, 3196608260634087683485164078372135632496702259200000⟩, + ⟨2, 5, 7, 2, 8, 4, 14991475053591713945863877688149091469774081228800000⟩, + ⟨2, 5, 6, 3, 6, 4, -8470077239183151509237627615043928497427631308800000⟩, + ⟨2, 5, 7, 3, 7, 4, -8370926585156148839776324534232434580129002291200000⟩, + ⟨2, 5, 8, 3, 8, 4, -18939837065814906801611864120755564455552614400000000⟩, + ⟨2, 5, 6, 4, 5, 4, 6738804093085249971724802560108384668133569331200000⟩, + ⟨2, 5, 7, 4, 6, 4, 2749224417068415971655210753763456650603134976000000⟩, + ⟨2, 5, 8, 4, 7, 4, -6727931309113869689174566809135447469579881676800000⟩, + ⟨2, 5, 6, 5, 4, 4, 7600569802687938018928829228083627296872516812800000⟩, + ⟨2, 5, 7, 5, 5, 4, 7281161148045747036815672565864900881942367436800000⟩, + ⟨2, 5, 8, 5, 6, 4, -14009318776859961102519691302144143490741908275200000⟩, + ⟨2, 5, 6, 6, 3, 4, -28143308448242900285059836326838204216504011980800000⟩, + ⟨2, 5, 7, 6, 4, 4, -2606550697402249975126786446863351980672784793600000⟩, + ⟨2, 5, 8, 6, 5, 4, 14702155070947747120060251769327981114790667878400000⟩, + ⟨2, 5, 6, 7, 2, 4, 27773998609059471669799769034791667921386156851200000⟩, + ⟨2, 5, 7, 7, 3, 4, -109213336906088692444950476931931757385812960870400000⟩, + ⟨2, 5, 8, 7, 4, 4, -29069420711015727608432283792529748604638724096000000⟩ +] + +def collectedFourData_13_3_18 : List CollectedFourTerm := [ + ⟨2, 6, 5, 0, 8, 5, -1012114867455482007592522752203587339035869184000000⟩, + ⟨2, 6, 5, 1, 7, 5, 8027626017127493229826597518237192914139611136000000⟩, + ⟨2, 6, 6, 1, 8, 5, 4391018567593587650841883629542503508682473472000000⟩, + ⟨2, 6, 5, 2, 6, 5, 5610893181915892702761163955501018470718373888000000⟩, + ⟨2, 6, 6, 2, 7, 5, 5875685080492556613297706710405314120156971008000000⟩, + ⟨2, 6, 7, 2, 8, 5, 13777913826934235179088948263546140380475949056000000⟩, + ⟨2, 6, 5, 3, 5, 5, -2120130752179672873391150299430657474533785600000000⟩, + ⟨2, 6, 6, 3, 6, 5, -15568847480553032430702455904401255339825037312000000⟩, + ⟨2, 6, 7, 3, 7, 5, -7693299340430290282553819000570502120518713344000000⟩, + ⟨2, 6, 8, 3, 8, 5, -11604437057555276427213893107258761362276352000000000⟩, + ⟨2, 6, 5, 4, 4, 5, 7637999632772680569498962090753970598381092864000000⟩, + ⟨2, 6, 6, 4, 5, 5, 12386594615834781664011640993575879790232076288000000⟩, + ⟨2, 6, 7, 4, 6, 5, 2526674458241322229402620285951735575473029120000000⟩, + ⟨2, 6, 8, 4, 7, 5, -4122203117844412224632546535803878037514092544000000⟩, + ⟨2, 6, 5, 5, 3, 5, -19920342138195332169029709821217997615842459648000000⟩, + ⟨2, 6, 6, 5, 4, 5, 13970606014775543072061243154627832506610614272000000⟩, + ⟨2, 6, 7, 5, 5, 5, 6691750511485592222215428926049411360689750016000000⟩, + ⟨2, 6, 8, 5, 6, 5, -8583508791568578971818568836306828024784879616000000⟩, + ⟨2, 6, 5, 6, 2, 5, -294819561704353250170116872153135629668974592000000⟩, + ⟨2, 6, 6, 6, 3, 5, -51730210298661821296374375159336671882973806592000000⟩, + ⟨2, 6, 7, 6, 4, 5, -2395550188754735148789264356644319056134930432000000⟩, + ⟨2, 6, 8, 6, 5, 5, 9008009548253712639896785401149366423594729472000000⟩, + ⟨2, 6, 5, 7, 1, 5, 13743473539683548046601541786440765765702385664000000⟩, + ⟨2, 6, 6, 7, 2, 5, 51051381948346934665430386390972268105158361088000000⟩, + ⟨2, 6, 7, 7, 3, 5, -100372507659512601799707897242436287170502197248000000⟩, + ⟨2, 6, 8, 7, 4, 5, -17810832361881334548251254411999140820738375680000000⟩ +] + +def collectedFourData_13_3_19 : List CollectedFourTerm := [ + ⟨2, 7, 4, 0, 7, 6, -11243308512095798270246584445913813377514838425600000⟩, + ⟨2, 7, 5, 0, 8, 6, -1059879066245610204037547069555750942061625344000000⟩, + ⟨2, 7, 4, 1, 6, 6, -25191018753575106586649340429501783221744330342400000⟩, + ⟨2, 7, 5, 1, 7, 6, 8406469503399813990855918740055826065078091776000000⟩, + ⟨2, 7, 6, 1, 8, 6, 2299120786056891411427594750681282471186661376000000⟩, + ⟨2, 7, 4, 2, 5, 6, 3196608260634087683485164078372135632496702259200000⟩, + ⟨2, 7, 5, 2, 6, 6, 5875685080492556613297706710405314120156971008000000⟩, + ⟨2, 7, 6, 2, 7, 6, 3076486581173372570410842347500758304989118464000000⟩, + ⟨2, 7, 7, 2, 8, 6, 4809375862780005493699238167990624019999096832000000⟩, + ⟨2, 7, 4, 3, 4, 6, -2193192565448859015392931042852938295069061939200000⟩, + ⟨2, 7, 5, 3, 5, 6, -2220184955476541374742305233746067780639129600000000⟩, + ⟨2, 7, 6, 3, 6, 6, -8151789910810035415847841594180204590159364096000000⟩, + ⟨2, 7, 7, 3, 7, 6, -2685455041871150106059462574313766272754515968000000⟩, + ⟨2, 7, 8, 3, 8, 6, -3038019771359753526433337094974294571614208000000000⟩, + ⟨2, 7, 4, 4, 3, 6, -4902104748676380652786377859754618135840292864000000⟩, + ⟨2, 7, 5, 4, 4, 6, 7998455688255658896505859617440183512123572224000000⟩, + ⟨2, 7, 6, 4, 5, 6, 6485574294743437669003109709875051797313224704000000⟩, + ⟨2, 7, 7, 4, 6, 6, 881971487498588835251158735586343156071792640000000⟩, + ⟨2, 7, 8, 4, 7, 6, -1079185014443988323276366448149225647191883776000000⟩, + ⟨2, 7, 4, 5, 2, 6, 33587562348304034502855607584111586778764699238400000⟩, + ⟨2, 7, 5, 5, 3, 6, -20860432252915418660800225105045731780662919168000000⟩, + ⟨2, 7, 6, 5, 4, 6, 7314956698073058668001400089103562963498827776000000⟩, + ⟨2, 7, 7, 5, 5, 6, 2335850245105338321315490240258856237716733952000000⟩, + ⟨2, 7, 8, 5, 6, 6, -2247146439511927556430315185614979543926308864000000⟩, + ⟨2, 7, 4, 6, 1, 6, -18023291159189675633217547848880993813072026009600000⟩, + ⟨2, 7, 5, 6, 2, 6, -308732824521910453179702576239976896551452672000000⟩, + ⟨2, 7, 6, 6, 3, 6, -27085743303956724823693283485024215159155982336000000⟩, + ⟨2, 7, 7, 6, 4, 6, -836200705026379459882418230883125234136776704000000⟩, + ⟨2, 7, 8, 6, 5, 6, 2358279938308146012013354215363791924848754688000000⟩, + ⟨2, 7, 4, 7, 0, 6, -343906609248577012854572216561925216936597336883200000⟩, + ⟨2, 7, 5, 7, 1, 6, 14392061978925288226111558455107996568753537024000000⟩, + ⟨2, 7, 6, 7, 2, 6, 26730311336100350925885225745064930601917743104000000⟩, + ⟨2, 7, 7, 7, 3, 6, -35036444681536713365086634764277357546104160256000000⟩, + ⟨2, 7, 8, 7, 4, 6, -4662842375842830547159813762525971528516894720000000⟩ +] + +def collectedFourData_13_3_20 : List CollectedFourTerm := [ + ⟨2, 8, 3, 0, 6, 7, 3675532472370445000802386591814694915912656486400000⟩, + ⟨2, 8, 4, 0, 7, 7, -52728944348496664644238567709418230851807110758400000⟩, + ⟨2, 8, 5, 0, 8, 7, -2485314008775872174575122935263930865216913408000000⟩, + ⟨2, 8, 3, 1, 5, 7, -49275760924706450429594177794234822312877830963200000⟩, + ⟨2, 8, 4, 1, 6, 7, -118141010229345550950198584786450365180410435993600000⟩, + ⟨2, 8, 5, 1, 7, 7, 19712358783681411674612263305033679825306386432000000⟩, + ⟨2, 8, 6, 1, 8, 7, 3594144073874210264323269932598992536325849088000000⟩, + ⟨2, 8, 3, 2, 4, 7, 64167630316875632112765218593390195530266994278400000⟩, + ⟨2, 8, 4, 2, 5, 7, 14991475053591713945863877688149091469774081228800000⟩, + ⟨2, 8, 5, 2, 6, 7, 13777913826934235179088948263546140380475949056000000⟩, + ⟨2, 8, 6, 2, 7, 7, 4809375862780005493699238167990624019999096832000000⟩, + ⟨2, 8, 7, 2, 8, 7, 5638760867112842839482434372532157517672742912000000⟩, + ⟨2, 8, 3, 3, 3, 7, -85769135783609324224098221484354738476903772979200000⟩, + ⟨2, 8, 4, 3, 4, 7, -10285649335751694123155029805878300341214956748800000⟩, + ⟨2, 8, 5, 3, 5, 7, -5206119214586514270171269872665149641536307200000000⟩, + ⟨2, 8, 6, 3, 6, 7, -12743439830168397926460966597812940289446248448000000⟩, + ⟨2, 8, 7, 3, 7, 7, -3148566307259023505620071988180635208686501888000000⟩, + ⟨2, 8, 8, 3, 8, 7, -2849545136670818724142809466696836319700582400000000⟩, + ⟨2, 8, 3, 4, 2, 7, 117414056209970264005760179785852994062259322880000000⟩, + ⟨2, 8, 4, 4, 3, 7, -22989924025065808783808340140109466497340932096000000⟩, + ⟨2, 8, 5, 4, 4, 7, 18755605807944395402851073009839107070721261568000000⟩, + ⟨2, 8, 6, 4, 5, 7, 10138696739417949137991260044490452372083965952000000⟩, + ⟨2, 8, 7, 4, 6, 7, 1034068962691060958538642707511784501401354240000000⟩, + ⟨2, 8, 8, 4, 7, 7, -1012233836812887381689043636202726773660372172800000⟩, + ⟨2, 8, 3, 5, 1, 7, -97503252191141931229366092665509484273411398041600000⟩, + ⟨2, 8, 4, 5, 2, 7, 157519177203050613709139216756347969416585648537600000⟩, + ⟨2, 8, 5, 5, 3, 7, -48915698175773313331888342267527022003592626176000000⟩, + ⟨2, 8, 6, 5, 4, 7, 11435244475396247129962371433398902322823692288000000⟩, + ⟨2, 8, 7, 5, 5, 7, 2738671571808155991831356618727675950197112832000000⟩, + ⟨2, 8, 8, 5, 6, 7, -2107736515892507549300334465896733838230631219200000⟩, + ⟨2, 8, 3, 6, 0, 7, -53100320960290588433806487792996504795417778585600000⟩, + ⟨2, 8, 4, 6, 1, 7, -84525752849995879025948309130216183962223928934400000⟩, + ⟨2, 8, 5, 6, 2, 7, -723948644887602663293028620747754543412936704000000⟩, + ⟨2, 8, 6, 6, 3, 7, -42342300749389693671356746751860347112488173568000000⟩, + ⟨2, 8, 7, 6, 4, 7, -980404931343708051926853088331752147689406464000000⟩, + ⟨2, 8, 8, 6, 5, 7, 2211975442841372447128744768541513705635341926400000⟩, + ⟨2, 8, 4, 7, 0, 7, -1612855543422972906101557650905417400304066677964800000⟩, + ⟨2, 8, 5, 7, 1, 7, 33747994833124450201358593120727302353262215168000000⟩, + ⟨2, 8, 6, 7, 2, 7, 41786664999983344677292177197346038540404785152000000⟩, + ⟨2, 8, 7, 7, 3, 7, -41078538843669112813225322517855239415734992896000000⟩, + ⟨2, 8, 8, 7, 4, 7, -4373565945951224649692601725141702043255177216000000⟩ +] + +def collectedFourData_13_3_21 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_3_22 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_3_23 : List CollectedFourTerm := [ + ⟨3, 2, 8, 3, 8, 2, -39741921133440769743973601398017341006020608000000000⟩, + ⟨3, 2, 8, 4, 7, 2, -14117382031792361209816154366852282864501784576000000⟩, + ⟨3, 2, 8, 5, 6, 2, -29396094593026236572200607161451157201893720064000000⟩, + ⟨3, 2, 8, 6, 5, 2, 30849889853373026663123182420680620235017945088000000⟩, + ⟨3, 2, 8, 7, 4, 2, -60997073062322557120914670724651875666986270720000000⟩ +] + +def collectedFourData_13_3_24 : List CollectedFourTerm := [ + ⟨3, 3, 7, 2, 8, 3, -85769135783609324224098221484354738476903772979200000⟩, + ⟨3, 3, 7, 3, 7, 3, 47891694202890967989373748806591296744813546700800000⟩, + ⟨3, 3, 8, 3, 8, 3, 216716960967509716134502919066406105738588979200000000⟩, + ⟨3, 3, 7, 4, 6, 3, -15728845993087361060091728650969779284616413184000000⟩, + ⟨3, 3, 8, 4, 7, 3, 76983599269763970657989338280897059223861880422400000⟩, + ⟨3, 3, 7, 5, 5, 3, -41656934820396918635902891422415777355017696051200000⟩, + ⟨3, 3, 8, 5, 6, 3, 160300058548340607959925744153000623895419132313600000⟩, + ⟨3, 3, 7, 6, 4, 3, 14912581976967865434436434960522059663595169382400000⟩, + ⟨3, 3, 8, 6, 5, 3, -168227760121534498957071288858653380138910298931200000⟩, + ⟨3, 3, 7, 7, 3, 3, 624830678034926219846641233322277382121401719193600000⟩, + ⟨3, 3, 8, 7, 4, 3, 332623585497896507780650238000092251914426646528000000⟩ +] + +def collectedFourData_13_3_25 : List CollectedFourTerm := [ + ⟨3, 4, 6, 1, 8, 4, -1639017262713277658554471349224522306030456012800000⟩, + ⟨3, 4, 6, 2, 7, 4, -2193192565448859015392931042852938295069061939200000⟩, + ⟨3, 4, 7, 2, 8, 4, -10285649335751694123155029805878300341214956748800000⟩, + ⟨3, 4, 6, 3, 6, 4, 5811319034153155591499004397160288864822938828800000⟩, + ⟨3, 4, 7, 3, 7, 4, 5743291781658888750715749325287965947835134771200000⟩, + ⟨3, 4, 8, 3, 8, 4, 12994620064992967685613771897017487740790374400000000⟩, + ⟨3, 4, 6, 4, 5, 4, -4623492724766722378375996512959357105493717811200000⟩, + ⟨3, 4, 7, 4, 6, 4, -1886242561066547451849224324492661417496805376000000⟩, + ⟨3, 4, 8, 4, 7, 4, 4616032908915832792602157087737681442333576396800000⟩, + ⟨3, 4, 6, 5, 4, 4, -5214750080488022688730888258701452013388745932800000⟩, + ⟨3, 4, 7, 5, 5, 4, -4995603838726663566569213731657261044567166156800000⟩, + ⟨3, 4, 8, 5, 6, 4, 9611792025563260863597928583689954371583554355200000⟩, + ⟨3, 4, 6, 6, 3, 4, 19309120737733662209983340136899286085340548300800000⟩, + ⟨3, 4, 7, 6, 4, 4, 1788354138168365962554619817463088474607950233600000⟩, + ⟨3, 4, 8, 6, 5, 4, -10087146928439303259413943512951430318085531238400000⟩, + ⟨3, 4, 6, 7, 2, 4, -19055737298912309091402684274277372624414913331200000⟩, + ⟨3, 4, 7, 7, 3, 4, 74931258077516894896992729760612614443211581030400000⟩, + ⟨3, 4, 8, 7, 4, 4, 19944526256294601608520350022378690801089642496000000⟩ +] + +def collectedFourData_13_3_26 : List CollectedFourTerm := [ + ⟨3, 5, 5, 0, 8, 5, 382437481103126579645452082622012137983180800000000⟩, + ⟨3, 5, 5, 1, 7, 5, -3033316841740001568160635670967293117150003200000000⟩, + ⟨3, 5, 6, 1, 8, 5, -1659189222947971755000469274082857783289446400000000⟩, + ⟨3, 5, 5, 2, 6, 5, -2120130752179672873391150299430657474533785600000000⟩, + ⟨3, 5, 6, 2, 7, 5, -2220184955476541374742305233746067780639129600000000⟩, + ⟨3, 5, 7, 2, 8, 5, -5206119214586514270171269872665149641536307200000000⟩, + ⟨3, 5, 5, 3, 5, 5, 801112097593542254980638549375569331486720000000000⟩, + ⟨3, 5, 6, 3, 6, 5, 5882840975462058874735696512025468521047654400000000⟩, + ⟨3, 5, 7, 3, 7, 5, 2906988243857526971358835508534263480634572800000000⟩, + ⟨3, 5, 8, 3, 8, 5, 4384849803726870505446074654472035264102400000000000⟩, + ⟨3, 5, 5, 4, 4, 5, -2886092709583354513276529167945907292654796800000000⟩, + ⟨3, 5, 6, 4, 5, 5, -4680395671130446630759317929494949549152665600000000⟩, + ⟨3, 5, 7, 4, 6, 5, -954728604873419527216807416303608339103744000000000⟩, + ⟨3, 5, 8, 4, 7, 5, 1557614681569939241930062417890532762897612800000000⟩, + ⟨3, 5, 5, 5, 3, 5, 7527095703274000823952871319468567091059097600000000⟩, + ⟨3, 5, 6, 5, 4, 5, -5278929838475034203795965811339250134050406400000000⟩, + ⟨3, 5, 7, 5, 5, 5, -2528543243532260895540121684461428638167859200000000⟩, + ⟨3, 5, 8, 5, 6, 5, 3243362573584976286487117050962479141827379200000000⟩, + ⟨3, 5, 5, 6, 2, 5, 111400448885412683731803729624974659839590400000000⟩, + ⟨3, 5, 6, 6, 3, 5, 19546764858115698996431195216626151913317990400000000⟩, + ⟨3, 5, 7, 6, 4, 5, 905182019849913153012232356966995767748198400000000⟩, + ⟨3, 5, 8, 6, 5, 5, -3403764327707192562827041702230710043436646400000000⟩, + ⟨3, 5, 5, 7, 1, 5, -5193105615905038275766847060376198679678156800000000⟩, + ⟨3, 5, 6, 7, 2, 5, -19290262940454426229586790952059228028246425600000000⟩, + ⟨3, 5, 7, 7, 3, 5, 37926731674057441388296715559062955410168217600000000⟩, + ⟨3, 5, 8, 7, 4, 5, 6729996845074063864714630897549544590934016000000000⟩ +] + +def collectedFourData_13_3_27 : List CollectedFourTerm := [ + ⟨3, 6, 4, 0, 7, 6, 29791480142933246192556284552902681794884036198400000⟩, + ⟨3, 6, 5, 0, 8, 6, 2808369629099588834507665515549123406951612416000000⟩, + ⟨3, 6, 4, 1, 6, 6, 66748834132765401685456308223914860448719673753600000⟩, + ⟨3, 6, 5, 1, 7, 6, -22274686228993837044764643804694643093236875264000000⟩, + ⟨3, 6, 6, 1, 8, 6, -6091997846570818515805460903246551025832689664000000⟩, + ⟨3, 6, 4, 2, 5, 6, -8470077239183151509237627615043928497427631308800000⟩, + ⟨3, 6, 5, 2, 6, 6, -15568847480553032430702455904401255339825037312000000⟩, + ⟨3, 6, 6, 2, 7, 6, -8151789910810035415847841594180204590159364096000000⟩, + ⟨3, 6, 7, 2, 8, 6, -12743439830168397926460966597812940289446248448000000⟩, + ⟨3, 6, 4, 3, 4, 6, 5811319034153155591499004397160288864822938828800000⟩, + ⟨3, 6, 5, 3, 5, 6, 5882840975462058874735696512025468521047654400000000⟩, + ⟨3, 6, 6, 3, 6, 6, 21599859774015202164934638428287333418605215744000000⟩, + ⟨3, 6, 7, 3, 7, 6, 7115670664784713563781666201447000653013450752000000⟩, + ⟨3, 6, 8, 3, 8, 6, 8049864112056799429006928548271134303322112000000000⟩, + ⟨3, 6, 4, 4, 3, 6, 12989144264933857935354383097252420069617565696000000⟩, + ⟨3, 6, 5, 4, 4, 6, -21193568917409568429098984963287220548572020736000000⟩, + ⟨3, 6, 6, 4, 5, 6, -17184875573724818417903208506611950380390547456000000⟩, + ⟨3, 6, 7, 4, 6, 6, -2336966563550224647313035469222051547405352960000000⟩, + ⟨3, 6, 8, 4, 7, 6, 2859524746988039341054830095044201073306763264000000⟩, + ⟨3, 6, 4, 5, 2, 6, -88997219606002946639955790764840529643204876697600000⟩, + ⟨3, 6, 5, 5, 3, 6, 55274046119712024638442957522941544462708375552000000⟩, + ⟨3, 6, 6, 5, 4, 6, -19382496440670760349591892094510553671101579264000000⟩, + ⟨3, 6, 7, 5, 5, 6, -6189320173777734053397650596611341018493616128000000⟩, + ⟨3, 6, 8, 5, 6, 6, 5954281024927934042407701637814415415308189696000000⟩, + ⟨3, 6, 4, 6, 1, 6, 47756451768769943792991808149988382422329615974400000⟩, + ⟨3, 6, 5, 6, 2, 6, 818051715055332789531569321520798192220766208000000⟩, + ⟨3, 6, 6, 6, 3, 6, 71769300195605851005562490018302115289816367104000000⟩, + ⟨3, 6, 7, 6, 4, 6, 2215687372849340289604634482573778239101075456000000⟩, + ⟨3, 6, 8, 6, 5, 6, -6248752302580803993271556306936452293781880832000000⟩, + ⟨3, 6, 4, 7, 0, 6, 911251960170813179261061085245074106285015485644800000⟩, + ⟨3, 6, 5, 7, 1, 6, -38134756170725633474217719019479340413601447936000000⟩, + ⟨3, 6, 6, 7, 2, 6, -70827509405006701351390207853021719072453165056000000⟩, + ⟨3, 6, 7, 7, 3, 6, 92836334152536201314888424800941346351411625984000000⟩, + ⟨3, 6, 8, 7, 4, 6, 12355168934491456462846493351373245281028014080000000⟩ +] + +def collectedFourData_13_3_28 : List CollectedFourTerm := [ + ⟨3, 7, 3, 0, 6, 7, -2052340572063924150163839269576884767113714073600000⟩, + ⟨3, 7, 4, 0, 7, 7, 29442741323062795860266399266270342912285448601600000⟩, + ⟨3, 7, 5, 0, 8, 7, 1387747438737761749642611720626522977355169792000000⟩, + ⟨3, 7, 3, 1, 5, 7, 27514555816146947346616034066325376656481242316800000⟩, + ⟨3, 7, 4, 1, 6, 7, 65967472833108367753961124098112986360123385446400000⟩, + ⟨3, 7, 5, 1, 7, 7, -11006969468219284357209835967136430566427066368000000⟩, + ⟨3, 7, 6, 1, 8, 7, -2006894990074166140902473555125262610031706112000000⟩, + ⟨3, 7, 3, 2, 4, 7, -35829864680148020482247281829033826591295773081600000⟩, + ⟨3, 7, 4, 2, 5, 7, -8370926585156148839776324534232434580129002291200000⟩, + ⟨3, 7, 5, 2, 6, 7, -7693299340430290282553819000570502120518713344000000⟩, + ⟨3, 7, 6, 2, 7, 7, -2685455041871150106059462574313766272754515968000000⟩, + ⟨3, 7, 7, 2, 8, 7, -3148566307259023505620071988180635208686501888000000⟩, + ⟨3, 7, 3, 3, 3, 7, 47891694202890967989373748806591296744813546700800000⟩, + ⟨3, 7, 4, 3, 4, 7, 5743291781658888750715749325287965947835134771200000⟩, + ⟨3, 7, 5, 3, 5, 7, 2906988243857526971358835508534263480634572800000000⟩, + ⟨3, 7, 6, 3, 6, 7, 7115670664784713563781666201447000653013450752000000⟩, + ⟨3, 7, 7, 3, 7, 7, 1758093670725677775442907304087015100684173312000000⟩, + ⟨3, 7, 8, 3, 8, 7, 1591126493883288476066945692063886692948377600000000⟩, + ⟨3, 7, 3, 4, 2, 7, -65561556890532938950502427714339121476529029120000000⟩, + ⟨3, 7, 4, 4, 3, 7, 12837093449722698735921971532734918966120546304000000⟩, + ⟨3, 7, 5, 4, 4, 7, -10472738587575858889836691673381825036924485632000000⟩, + ⟨3, 7, 6, 4, 5, 7, -5661236520851637706945739350435765496838094848000000⟩, + ⟨3, 7, 7, 4, 6, 7, -577402513077029023229038988413367589021941760000000⟩, + ⟨3, 7, 8, 4, 7, 7, 565210234795510419805721242563031121744048947200000⟩, + ⟨3, 7, 3, 5, 1, 7, 54443779747375027673212137498071510675691562598400000⟩, + ⟨3, 7, 4, 5, 2, 7, -87955418890219749091259377349862547607962150502400000⟩, + ⟨3, 7, 5, 5, 3, 7, 27313504296760489003872059695578662949013684224000000⟩, + ⟨3, 7, 6, 5, 4, 7, -6385201699276456833804271599976961668559142912000000⟩, + ⟨3, 7, 7, 5, 5, 7, -1529217010768247240386516024994711443202899968000000⟩, + ⟨3, 7, 8, 5, 6, 7, 1176916052110685483266382673236267539471584460800000⟩, + ⟨3, 7, 3, 6, 0, 7, 29650110267189889030464443505899120375286359654400000⟩, + ⟨3, 7, 4, 6, 1, 7, 47197415139803004571664510702033818061431740825600000⟩, + ⟨3, 7, 5, 6, 2, 7, 404237804226308915022223432027105102865104896000000⟩, + ⟨3, 7, 6, 6, 3, 7, 23643056453929409356260685192316271124002373632000000⟩, + ⟨3, 7, 7, 6, 4, 7, 547437638702336712055254928496929483454939136000000⟩, + ⟨3, 7, 8, 6, 5, 7, -1235120891973681337117004724801561356154804633600000⟩, + ⟨3, 7, 4, 7, 0, 7, 900584852270503438413741749284366996727781339955200000⟩, + ⟨3, 7, 5, 7, 1, 7, -18844175515379383634776904180500840576588972032000000⟩, + ⟨3, 7, 6, 7, 2, 7, -23332801055461837081019121901195444170572955648000000⟩, + ⟨3, 7, 7, 7, 3, 7, 22937398198415087151858159008249016230822805504000000⟩, + ⟨3, 7, 8, 7, 4, 7, 2442107885849788599064759973916452371965149184000000⟩ +] + +def collectedFourData_13_3_29 : List CollectedFourTerm := [ + ⟨3, 8, 2, 0, 5, 8, -57860053986746563986679006282536373847064576000000000⟩, + ⟨3, 8, 3, 0, 6, 8, -9287142980654152316732471649115934667728486400000000⟩, + ⟨3, 8, 4, 0, 7, 8, 66616367705169988895773999722825215890371379200000000⟩, + ⟨3, 8, 5, 0, 8, 8, 2093253764348547555505494411390075468251136000000000⟩, + ⟨3, 8, 2, 1, 4, 8, 199417252839714587642713255819717588699368652800000000⟩, + ⟨3, 8, 3, 1, 5, 8, 124507412362253379750072208058209615240966963200000000⟩, + ⟨3, 8, 4, 1, 6, 8, 149256259076286902277360358351359641582881996800000000⟩, + ⟨3, 8, 5, 1, 7, 8, -16602718643369382970268577190068195000582144000000000⟩, + ⟨3, 8, 6, 1, 8, 8, -2270373759316388682389403666917611140022272000000000⟩, + ⟨3, 8, 2, 2, 3, 8, -74321585550767247773417144229681996450339225600000000⟩, + ⟨3, 8, 3, 2, 4, 8, -162135408124485712596195683817148361210226278400000000⟩, + ⟨3, 8, 4, 2, 5, 8, -18939837065814906801611864120755564455552614400000000⟩, + ⟨3, 8, 5, 2, 6, 8, -11604437057555276427213893107258761362276352000000000⟩, + ⟨3, 8, 6, 2, 7, 8, -3038019771359753526433337094974294571614208000000000⟩, + ⟨3, 8, 7, 2, 8, 8, -2849545136670818724142809466696836319700582400000000⟩, + ⟨3, 8, 2, 3, 2, 8, -39741921133440769743973601398017341006020608000000000⟩, + ⟨3, 8, 3, 3, 3, 8, 216716960967509716134502919066406105738588979200000000⟩, + ⟨3, 8, 4, 3, 4, 8, 12994620064992967685613771897017487740790374400000000⟩, + ⟨3, 8, 5, 3, 5, 8, 4384849803726870505446074654472035264102400000000000⟩, + ⟨3, 8, 6, 3, 6, 8, 8049864112056799429006928548271134303322112000000000⟩, + ⟨3, 8, 7, 3, 7, 8, 1591126493883288476066945692063886692948377600000000⟩, + ⟨3, 8, 8, 3, 8, 8, 1200013572320229210089271314821677475430400000000000⟩, + ⟨3, 8, 2, 4, 1, 8, -91741734073613098319039720064876035120195174400000000⟩, + ⟨3, 8, 3, 4, 2, 8, -296675688803615443743424806631061351961722880000000000⟩, + ⟨3, 8, 4, 4, 3, 8, 29044868075599350845828555609038855285506048000000000⟩, + ⟨3, 8, 5, 4, 4, 8, -15796894203905648560843160233242964688633856000000000⟩, + ⟨3, 8, 6, 4, 5, 8, -6404482001198363662786026708198775207231488000000000⟩, + ⟨3, 8, 7, 4, 6, 8, -522566261109647299144819565714304399310848000000000⟩, + ⟨3, 8, 8, 4, 7, 8, 426276575480533330996446637921160731086028800000000⟩, + ⟨3, 8, 2, 5, 0, 8, 684491972648073897941963278091420142471531724800000000⟩, + ⟨3, 8, 3, 5, 1, 8, 246366111844991554358423106075958044861766041600000000⟩, + ⟨3, 8, 4, 5, 2, 8, -199005604205186819795800271128554921849048268800000000⟩, + ⟨3, 8, 5, 5, 3, 8, 41199208221019912866688760270571699167035392000000000⟩, + ⟨3, 8, 6, 5, 4, 8, -7223494232472992392759077468848354148483072000000000⟩, + ⟨3, 8, 7, 5, 5, 8, -1383986383231808161019843077636492032894566400000000⟩, + ⟨3, 8, 8, 5, 6, 8, 887619709334033735724606930046884263441203200000000⟩, + ⟨3, 8, 3, 6, 0, 8, 134171110385755905794647155385004043865266585600000000⟩, + ⟨3, 8, 4, 6, 1, 8, 106787623040516706904132047434471948133020467200000000⟩, + ⟨3, 8, 5, 6, 2, 8, 609745175360118859965923814875164802285568000000000⟩, + ⟨3, 8, 6, 6, 3, 8, 26747077066076880999901433565055095398203392000000000⟩, + ⟨3, 8, 7, 6, 4, 8, 495447168255068253718174793140817921625292800000000⟩, + ⟨3, 8, 8, 6, 5, 8, -931517286351844293408584447470746126935654400000000⟩, + ⟨3, 8, 4, 7, 0, 8, 2037639464690890980060894449012736321810490982400000000⟩, + ⟨3, 8, 5, 7, 1, 8, -28424222039631913345827271857730517578285056000000000⟩, + ⟨3, 8, 6, 7, 2, 8, -26396089237191526719308226831910506791436288000000000⟩, + ⟨3, 8, 7, 7, 3, 8, 20759020171652569398822147300295146669814579200000000⟩, + ⟨3, 8, 8, 7, 4, 8, 1841816234822225599253819473852511903809536000000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1307.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1307.lean new file mode 100644 index 0000000000000000000000000000000000000000..e7bab342ed174a4d60e1524332528185190f9c06 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1307.lean @@ -0,0 +1,614 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1307. -/ +namespace LaughlinFock +def collectedFourData_13_3_30 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_3_31 : List CollectedFourTerm := [ + ⟨4, 1, 8, 3, 8, 2, -91741734073613098319039720064876035120195174400000000⟩, + ⟨4, 1, 8, 4, 7, 2, -32589091599965313918781428032217529722535201996800000⟩, + ⟨4, 1, 8, 5, 6, 2, -67859041939644187345282690063569503447327912755200000⟩, + ⟨4, 1, 8, 6, 5, 2, 71215037180145715934232407263524272456082024038400000⟩, + ⟨4, 1, 8, 7, 4, 2, -140807920114451129525843932106138401081965674496000000⟩ +] + +def collectedFourData_13_3_32 : List CollectedFourTerm := [ + ⟨4, 2, 7, 2, 8, 3, 117414056209970264005760179785852994062259322880000000⟩, + ⟨4, 2, 7, 3, 7, 3, -65561556890532938950502427714339121476529029120000000⟩, + ⟨4, 2, 8, 3, 8, 3, -296675688803615443743424806631061351961722880000000000⟩, + ⟨4, 2, 7, 4, 6, 3, 21532076669277228015911850457211501886937497600000000⟩, + ⟨4, 2, 8, 4, 7, 3, -105387055253893063873556154219129641918382735360000000⟩, + ⟨4, 2, 7, 5, 5, 3, 57026454118380582644934910933656016925679943680000000⟩, + ⟨4, 2, 8, 5, 6, 3, -219443508587307182171649305539063330412471255040000000⟩, + ⟨4, 2, 7, 6, 4, 3, -20414648258751655950801172361549227352244879360000000⟩, + ⟨4, 2, 8, 6, 5, 3, 230296172422923673283753864374716542033256775680000000⟩, + ⟨4, 2, 7, 7, 3, 3, -855364854527619800962213360823236352613065687040000000⟩, + ⟨4, 2, 8, 7, 4, 3, -455346600004745634788529564967844968586752819200000000⟩ +] + +def collectedFourData_13_3_33 : List CollectedFourTerm := [ + ⟨4, 3, 6, 1, 8, 4, -3663442250026482402118026028372475386817150976000000⟩, + ⟨4, 3, 6, 2, 7, 4, -4902104748676380652786377859754618135840292864000000⟩, + ⟨4, 3, 7, 2, 8, 4, -22989924025065808783808340140109466497340932096000000⟩, + ⟨4, 3, 6, 3, 6, 4, 12989144264933857935354383097252420069617565696000000⟩, + ⟨4, 3, 7, 3, 7, 4, 12837093449722698735921971532734918966120546304000000⟩, + ⟨4, 3, 8, 3, 8, 4, 29044868075599350845828555609038855285506048000000000⟩, + ⟨4, 3, 6, 4, 5, 4, -10334179496414195785453667038243033224371503104000000⟩, + ⟨4, 3, 7, 4, 6, 4, -4216026791914379186196137091289802809981009920000000⟩, + ⟨4, 3, 8, 4, 7, 4, 10317505721715614769852561474967310313776480256000000⟩, + ⟨4, 3, 6, 5, 4, 4, -11655725783243796763628417686014506416918757376000000⟩, + ⟨4, 3, 7, 5, 5, 4, -11165902021611138254968194622028174028183699456000000⟩, + ⟨4, 3, 8, 5, 6, 4, 21483754812090680047789236712584050541103939584000000⟩, + ⟨4, 3, 6, 6, 3, 4, 43158696574296290265932889642720114546296487936000000⟩, + ⟨4, 3, 7, 6, 4, 4, 3997231912573080133186287818586373661562765312000000⟩, + ⟨4, 3, 8, 6, 5, 4, -22546242239508317715621397994371626344726396928000000⟩, + ⟨4, 3, 6, 7, 2, 4, -42592347691735722448059103908960941023904661504000000⟩, + ⟨4, 3, 7, 7, 3, 4, 167482273026452215613323065913144692281670893568000000⟩, + ⟨4, 3, 8, 7, 4, 4, 44578920433770881759058593331164335934086840320000000⟩ +] + +def collectedFourData_13_3_34 : List CollectedFourTerm := [ + ⟨4, 4, 5, 0, 8, 5, -1377772261083943505315619250870592356485169152000000⟩, + ⟨4, 4, 5, 1, 7, 5, 10927850982527459144187632667751521280283639808000000⟩, + ⟨4, 4, 6, 1, 8, 5, 5977408073793657896757864767100552935915913216000000⟩, + ⟨4, 4, 5, 2, 6, 5, 7637999632772680569498962090753970598381092864000000⟩, + ⟨4, 4, 6, 2, 7, 5, 7998455688255658896505859617440183512123572224000000⟩, + ⟨4, 4, 7, 2, 8, 5, 18755605807944395402851073009839107070721261568000000⟩, + ⟨4, 4, 5, 3, 5, 5, -2886092709583354513276529167945907292654796800000000⟩, + ⟨4, 4, 6, 3, 6, 5, -21193568917409568429098984963287220548572020736000000⟩, + ⟨4, 4, 7, 3, 7, 5, -10472738587575858889836691673381825036924485632000000⟩, + ⟨4, 4, 8, 3, 8, 5, -15796894203905648560843160233242964688633856000000000⟩, + ⟨4, 4, 5, 4, 4, 5, 10397460172341970189518109158381692624088072192000000⟩, + ⟨4, 4, 6, 4, 5, 5, 16861630057755804704185191499900344138479960064000000⟩, + ⟨4, 4, 7, 4, 6, 5, 3439512740392892928738704377988088975442575360000000⟩, + ⟨4, 4, 8, 4, 7, 5, -5611474836446456064381972102143572378996703232000000⟩, + ⟨4, 4, 5, 5, 3, 5, -27117173862199334551763495310546528464371974144000000⟩, + ⟨4, 4, 6, 5, 4, 5, 19017913931134778409084828341963432340662255616000000⟩, + ⟨4, 4, 7, 5, 5, 5, 9109349668973882373047829245656557553553768448000000⟩, + ⟨4, 4, 8, 5, 6, 5, -11684563379179411082240842752324305258438197248000000⟩, + ⟨4, 4, 5, 6, 2, 5, -401332128597597623106196496795463912391704576000000⟩, + ⟨4, 4, 6, 6, 3, 5, -70419327984696485148341981533063202116863000576000000⟩, + ⟨4, 4, 7, 6, 4, 5, -3261015825603266299387694087836994596918788096000000⟩, + ⟨4, 4, 8, 6, 5, 5, 12262427993341545137629027756789850181747081216000000⟩, + ⟨4, 4, 5, 7, 1, 5, 18708722915534115840373406428721564923138670592000000⟩, + ⟨4, 4, 6, 7, 2, 5, 69495252169613803688940134671983936490086334464000000⟩, + ⟨4, 4, 7, 7, 3, 5, -136635140215243244418135510400203581326249426944000000⟩, + ⟨4, 4, 8, 7, 4, 5, -24245539280249415908199835275579068137907159040000000⟩ +] + +def collectedFourData_13_3_35 : List CollectedFourTerm := [ + ⟨4, 5, 4, 0, 7, 6, -23702139030980969401796949490869585727561767321600000⟩, + ⟨4, 5, 5, 0, 8, 6, -2234342405276310537596374205076172313286672384000000⟩, + ⟨4, 5, 4, 1, 6, 6, -53105456297577640783963768769960087198835828326400000⟩, + ⟨4, 5, 5, 1, 7, 6, 17721768349140735870062923907801005993739943936000000⟩, + ⟨4, 5, 6, 1, 8, 6, 4846801140563986482552168903412506981392449536000000⟩, + ⟨4, 5, 4, 2, 5, 6, 6738804093085249971724802560108384668133569331200000⟩, + ⟨4, 5, 5, 2, 6, 6, 12386594615834781664011640993575879790232076288000000⟩, + ⟨4, 5, 6, 2, 7, 6, 6485574294743437669003109709875051797313224704000000⟩, + ⟨4, 5, 7, 2, 8, 6, 10138696739417949137991260044490452372083965952000000⟩, + ⟨4, 5, 4, 3, 4, 6, -4623492724766722378375996512959357105493717811200000⟩, + ⟨4, 5, 5, 3, 5, 6, -4680395671130446630759317929494949549152665600000000⟩, + ⟨4, 5, 6, 3, 6, 6, -17184875573724818417903208506611950380390547456000000⟩, + ⟨4, 5, 7, 3, 7, 6, -5661236520851637706945739350435765496838094848000000⟩, + ⟨4, 5, 8, 3, 8, 6, -6404482001198363662786026708198775207231488000000000⟩, + ⟨4, 5, 4, 4, 3, 6, -10334179496414195785453667038243033224371503104000000⟩, + ⟨4, 5, 5, 4, 4, 6, 16861630057755804704185191499900344138479960064000000⟩, + ⟨4, 5, 6, 4, 5, 6, 13672308597099138662610360943432801635054649344000000⟩, + ⟨4, 5, 7, 4, 6, 6, 1859293534066329944711737923856603720754135040000000⟩, + ⟨4, 5, 8, 4, 7, 6, -2275041481338359972007226566046982240716455936000000⟩, + ⟨4, 5, 4, 5, 2, 6, 70806299732395065350698921866875326110894548582400000⟩, + ⟨4, 5, 5, 5, 3, 6, -43976100537758505946937447087787026413988610048000000⟩, + ⟨4, 5, 6, 5, 4, 6, 15420738519876687189357634952093308119926439936000000⟩, + ⟨4, 5, 7, 5, 5, 6, 4924230906363122547527089138752852768715702272000000⟩, + ⟨4, 5, 8, 5, 6, 6, -4737233464240970870967161591387673237708079104000000⟩, + ⟨4, 5, 4, 6, 1, 6, -37995093027233297977130269288131340404602280345600000⟩, + ⟨4, 5, 5, 6, 2, 6, -650842972277537968328910270599601564986376192000000⟩, + ⟨4, 5, 6, 6, 3, 6, -57099745404760273595829815187207762090022404096000000⟩, + ⟨4, 5, 7, 6, 4, 6, -1762803657572594014387345521409236817982521344000000⟩, + ⟨4, 5, 8, 6, 5, 6, 4971515182707870683360682162934431983251488768000000⟩, + ⟨4, 5, 4, 7, 0, 6, -724993204385848391649031800727541393498523775795200000⟩, + ⟨4, 5, 5, 7, 1, 6, 30340059920973887680562667268998384356230692864000000⟩, + ⟨4, 5, 6, 7, 2, 6, 56350455468517425401485796275301803105393311744000000⟩, + ⟨4, 5, 7, 7, 3, 6, -73860704088983483611621997161885684918665609216000000⟩, + ⟨4, 5, 8, 7, 4, 6, -9829787927003626819390009378697485689469009920000000⟩ +] + +def collectedFourData_13_3_36 : List CollectedFourTerm := [ + ⟨4, 6, 3, 0, 6, 7, 674040651946901594658768574012016981000060928000000⟩, + ⟨4, 6, 4, 0, 7, 7, -9669742354965780447049205707972479567022522368000000⟩, + ⟨4, 6, 5, 0, 8, 7, -455771425599098378924426149990353663594332160000000⟩, + ⟨4, 6, 3, 1, 5, 7, -9036477372609994060622301689467990741943844864000000⟩, + ⟨4, 6, 4, 1, 6, 7, -21665389751079258081294987203906603283929628672000000⟩, + ⟨4, 6, 5, 1, 7, 7, 3614967699467709710436329178573842779094384640000000⟩, + ⟨4, 6, 6, 1, 8, 7, 659115171191201385620461956243827818506485760000000⟩, + ⟨4, 6, 3, 2, 4, 7, 11767435520650035265682021710608436735160352768000000⟩, + ⟨4, 6, 4, 2, 5, 7, 2749224417068415971655210753763456650603134976000000⟩, + ⟨4, 6, 5, 2, 6, 7, 2526674458241322229402620285951735575473029120000000⟩, + ⟨4, 6, 6, 2, 7, 7, 881971487498588835251158735586343156071792640000000⟩, + ⟨4, 6, 7, 2, 8, 7, 1034068962691060958538642707511784501401354240000000⟩, + ⟨4, 6, 3, 3, 3, 7, -15728845993087361060091728650969779284616413184000000⟩, + ⟨4, 6, 4, 3, 4, 7, -1886242561066547451849224324492661417496805376000000⟩, + ⟨4, 6, 5, 3, 5, 7, -954728604873419527216807416303608339103744000000000⟩, + ⟨4, 6, 6, 3, 6, 7, -2336966563550224647313035469222051547405352960000000⟩, + ⟨4, 6, 7, 3, 7, 7, -577402513077029023229038988413367589021941760000000⟩, + ⟨4, 6, 8, 3, 8, 7, -522566261109647299144819565714304399310848000000000⟩, + ⟨4, 6, 3, 4, 2, 7, 21532076669277228015911850457211501886937497600000000⟩, + ⟨4, 6, 4, 4, 3, 7, -4216026791914379186196137091289802809981009920000000⟩, + ⟨4, 6, 5, 4, 4, 7, 3439512740392892928738704377988088975442575360000000⟩, + ⟨4, 6, 6, 4, 5, 7, 1859293534066329944711737923856603720754135040000000⟩, + ⟨4, 6, 7, 4, 6, 7, 189633617172431870891052225809968104525004800000000⟩, + ⟨4, 6, 8, 4, 7, 7, -185629364021928505025871369050084124294905856000000⟩, + ⟨4, 6, 3, 5, 1, 7, -17880716921397571739138520720362010165098053632000000⟩, + ⟨4, 6, 4, 5, 2, 7, 28886788429761637151527816090074965368532631552000000⟩, + ⟨4, 6, 5, 5, 3, 7, -8970446958824487817579063641059544004055531520000000⟩, + ⟨4, 6, 6, 5, 4, 7, 2097062044563388359236718359344222838728949760000000⟩, + ⟨4, 6, 7, 5, 5, 7, 502233618014942477539022146684959561760112640000000⟩, + ⟨4, 6, 8, 5, 6, 7, -386529055581498055737190768903891646083497984000000⟩, + ⟨4, 6, 3, 6, 0, 7, -9737847571125105549057608489126842100468416512000000⟩, + ⟨4, 6, 4, 6, 1, 7, -15500827155138705541393590209659227712297893888000000⟩, + ⟨4, 6, 5, 6, 2, 7, -132761938642705222391371926606882411726766080000000⟩, + ⟨4, 6, 6, 6, 3, 7, -7764978874923108411732390852609516349276815360000000⟩, + ⟨4, 6, 7, 6, 4, 7, -179792393092008868469646676011945049750241280000000⟩, + ⟨4, 6, 8, 6, 5, 7, 405644999953374343589649479351501766921289728000000⟩, + ⟨4, 6, 4, 7, 0, 7, -295774887082925650105028755822898310980038557696000000⟩, + ⟨4, 6, 5, 7, 1, 7, 6188904766919230218792354360722666642850447360000000⟩, + ⟨4, 6, 6, 7, 2, 7, 7663083139926833849905498445961208634844119040000000⟩, + ⟨4, 6, 7, 7, 3, 7, -7533222821823081211583016503618571717228625920000000⟩, + ⟨4, 6, 8, 7, 4, 7, -802050114834250168001024376125952599858872320000000⟩ +] + +def collectedFourData_13_3_37 : List CollectedFourTerm := [ + ⟨4, 7, 2, 0, 5, 8, -20553422260800312838410215721149154139488387072000000⟩, + ⟨4, 7, 3, 0, 6, 8, -3299038941815298424514637465735275091382291660800000⟩, + ⟨4, 7, 4, 0, 7, 8, 23663896601941087725509687013808573577840453222400000⟩, + ⟨4, 7, 5, 0, 8, 8, 743579128486822151736929876277389677289275392000000⟩, + ⟨4, 7, 2, 1, 4, 8, 70838285160298759572813203636925884412787792281600000⟩, + ⟨4, 7, 3, 1, 5, 8, 44228327568915853226077885545718535663114413670400000⟩, + ⟨4, 7, 4, 1, 6, 8, 53019772822283023142472702468779251583816407449600000⟩, + ⟨4, 7, 5, 1, 7, 8, -5897725000958308250986918960069887460028448768000000⟩, + ⟨4, 7, 6, 1, 8, 8, -806496837624092245530943476693017735183990784000000⟩, + ⟨4, 7, 2, 2, 3, 8, -26400993875101089822074852219542750990028714803200000⟩, + ⟨4, 7, 3, 2, 4, 8, -57594787370455571543792158911721264371177671884800000⟩, + ⟨4, 7, 4, 2, 5, 8, -6727931309113869689174566809135447469579881676800000⟩, + ⟨4, 7, 5, 2, 6, 8, -4122203117844412224632546535803878037514092544000000⟩, + ⟨4, 7, 6, 2, 7, 8, -1079185014443988323276366448149225647191883776000000⟩, + ⟨4, 7, 7, 2, 8, 8, -1012233836812887381689043636202726773660372172800000⟩, + ⟨4, 7, 2, 3, 2, 8, -14117382031792361209816154366852282864501784576000000⟩, + ⟨4, 7, 3, 3, 3, 8, 76983599269763970657989338280897059223861880422400000⟩, + ⟨4, 7, 4, 3, 4, 8, 4616032908915832792602157087737681442333576396800000⟩, + ⟨4, 7, 5, 3, 5, 8, 1557614681569939241930062417890532762897612800000000⟩, + ⟨4, 7, 6, 3, 6, 8, 2859524746988039341054830095044201073306763264000000⟩, + ⟨4, 7, 7, 3, 7, 8, 565210234795510419805721242563031121744048947200000⟩, + ⟨4, 7, 8, 3, 8, 8, 426276575480533330996446637921160731086028800000000⟩, + ⟨4, 7, 2, 4, 1, 8, -32589091599965313918781428032217529722535201996800000⟩, + ⟨4, 7, 3, 4, 2, 8, -105387055253893063873556154219129641918382735360000000⟩, + ⟨4, 7, 4, 4, 3, 8, 10317505721715614769852561474967310313776480256000000⟩, + ⟨4, 7, 5, 4, 4, 8, -5611474836446456064381972102143572378996703232000000⟩, + ⟨4, 7, 6, 4, 5, 8, -2275041481338359972007226566046982240716455936000000⟩, + ⟨4, 7, 7, 4, 6, 8, -185629364021928505025871369050084124294905856000000⟩, + ⟨4, 7, 8, 4, 7, 8, 151424719682187237695766117671213616420460953600000⟩, + ⟨4, 7, 2, 5, 0, 8, 243149661616053960051149050769610046809724000665600000⟩, + ⟨4, 7, 3, 5, 1, 8, 87515762233155772720767100853101619074894607155200000⟩, + ⟨4, 7, 4, 5, 2, 8, -70692056672325535319537221119258868657017166233600000⟩, + ⟨4, 7, 5, 5, 3, 8, 14635048967828868900399202647616545972943847424000000⟩, + ⟨4, 7, 6, 5, 4, 8, -2565976298474956047398632752562597271263248384000000⟩, + ⟨4, 7, 7, 5, 5, 8, -491628586179282284746689444529725981653257420800000⟩, + ⟨4, 7, 8, 5, 6, 8, 315306008824846935348777896474959070647182950400000⟩, + ⟨4, 7, 3, 6, 0, 8, 47661128826298108959484020124830180981377020723200000⟩, + ⟨4, 7, 4, 6, 1, 8, 37933789503232429116153226373948795836776736358400000⟩, + ⟨4, 7, 5, 6, 2, 8, 216597621280009868275286733272441699168157696000000⟩, + ⟨4, 7, 6, 6, 3, 8, 9501269551306857646974101723005575267744743424000000⟩, + ⟨4, 7, 7, 6, 4, 8, 175995944618315581314559606471509822555134361600000⟩, + ⟨4, 7, 8, 6, 5, 8, -330899589793155956539967178925858692788964556800000⟩, + ⟨4, 7, 4, 7, 0, 8, 723823457590553572462573355490140707104188320972800000⟩, + ⟨4, 7, 5, 7, 1, 8, -10097035826290826794537946618897546152752709632000000⟩, + ⟨4, 7, 6, 7, 2, 8, -9376589386695627724718608449434653148143681536000000⟩, + ⟨4, 7, 7, 7, 3, 8, 7374153287277946888357467907067644594400683622400000⟩, + ⟨4, 7, 8, 7, 4, 8, 654261864494107898865677414247165721357320192000000⟩ +] + +def collectedFourData_13_3_38 : List CollectedFourTerm := [ + ⟨5, 0, 8, 3, 8, 2, 684491972648073897941963278091420142471531724800000000⟩, + ⟨5, 0, 8, 4, 7, 2, 243149661616053960051149050769610046809724000665600000⟩, + ⟨5, 0, 8, 5, 6, 2, 506301411765391451957818800978059805155014370918400000⟩, + ⟨5, 0, 8, 6, 5, 2, -531340744470016542536795190691763999608146808012800000⟩, + ⟨5, 0, 8, 7, 4, 2, 1050578474201029604293484700372404595579087224832000000⟩ +] + +def collectedFourData_13_3_39 : List CollectedFourTerm := [ + ⟨5, 1, 7, 2, 8, 3, -97503252191141931229366092665509484273411398041600000⟩, + ⟨5, 1, 7, 3, 7, 3, 54443779747375027673212137498071510675691562598400000⟩, + ⟨5, 1, 8, 3, 8, 3, 246366111844991554358423106075958044861766041600000000⟩, + ⟨5, 1, 7, 4, 6, 3, -17880716921397571739138520720362010165098053632000000⟩, + ⟨5, 1, 8, 4, 7, 3, 87515762233155772720767100853101619074894607155200000⟩, + ⟨5, 1, 7, 5, 5, 3, -47356039957666449583408179993786836666262591897600000⟩, + ⟨5, 1, 8, 5, 6, 3, 182230786075852672609266770635633219019066887372800000⟩, + ⟨5, 1, 7, 6, 4, 3, 16952779435597894986358034656848345361175229235200000⟩, + ⟨5, 1, 8, 6, 5, 3, -191243080285478534084398852999007162719238986137600000⟩, + ⟨5, 1, 7, 7, 3, 3, 710314061353106766231020979726167327494743313612800000⟩, + ⟨5, 1, 8, 7, 4, 3, 378129977004164579990851031679981238377139666944000000⟩ +] + +def collectedFourData_13_3_40 : List CollectedFourTerm := [ + ⟨5, 2, 6, 1, 8, 4, 25100666201675805191225298506352862241222138265600000⟩, + ⟨5, 2, 6, 2, 7, 4, 33587562348304034502855607584111586778764699238400000⟩, + ⟨5, 2, 7, 2, 8, 4, 157519177203050613709139216756347969416585648537600000⟩, + ⟨5, 2, 6, 3, 6, 4, -88997219606002946639955790764840529643204876697600000⟩, + ⟨5, 2, 7, 3, 7, 4, -87955418890219749091259377349862547607962150502400000⟩, + ⟨5, 2, 8, 3, 8, 4, -199005604205186819795800271128554921849048268800000000⟩, + ⟨5, 2, 6, 4, 5, 4, 70806299732395065350698921866875326110894548582400000⟩, + ⟨5, 2, 7, 4, 6, 4, 28886788429761637151527816090074965368532631552000000⟩, + ⟨5, 2, 8, 4, 7, 4, -70692056672325535319537221119258868657017166233600000⟩, + ⟨5, 2, 6, 5, 4, 4, 79861087539008949336036295796292967893393054105600000⟩, + ⟨5, 2, 7, 5, 5, 4, 76504980932360052473449928895237458259223353753600000⟩, + ⟨5, 2, 8, 5, 6, 4, -147199415602371315594274837005290404591111136870400000⟩, + ⟨5, 2, 6, 6, 3, 4, -295708779469087896996733839530338597602875513241600000⟩, + ⟨5, 2, 7, 6, 4, 4, -27387679979794347232927508086107410527270679347200000⟩, + ⟨5, 2, 8, 6, 5, 4, 154479219797154128490329883754723024273289301196800000⟩, + ⟨5, 2, 6, 7, 2, 4, 291828348638018527376756243067258287982947755622400000⟩, + ⟨5, 2, 7, 7, 3, 4, -1147531841099588535148098460724970096677639474380800000⟩, + ⟨5, 2, 8, 7, 4, 4, -305439672600560011656612059293109629207594401792000000⟩ +] + +def collectedFourData_13_3_41 : List CollectedFourTerm := [ + ⟨5, 3, 5, 0, 8, 5, 3593309262747901158947150316213420884559396864000000⟩, + ⟨5, 3, 5, 1, 7, 5, -28500463586450622197715464966766212305026809856000000⟩, + ⟨5, 3, 6, 1, 8, 5, -15589423887724946682014179839016953105101094912000000⟩, + ⟨5, 3, 5, 2, 6, 5, -19920342138195332169029709821217997615842459648000000⟩, + ⟨5, 3, 6, 2, 7, 5, -20860432252915418660800225105045731780662919168000000⟩, + ⟨5, 3, 7, 2, 8, 5, -48915698175773313331888342267527022003592626176000000⟩, + ⟨5, 3, 5, 3, 5, 5, 7527095703274000823952871319468567091059097600000000⟩, + ⟨5, 3, 6, 3, 6, 5, 55274046119712024638442957522941544462708375552000000⟩, + ⟨5, 3, 7, 3, 7, 5, 27313504296760489003872059695578662949013684224000000⟩, + ⟨5, 3, 8, 3, 8, 5, 41199208221019912866688760270571699167035392000000000⟩, + ⟨5, 3, 5, 4, 4, 5, -27117173862199334551763495310546528464371974144000000⟩, + ⟨5, 3, 6, 4, 5, 5, -43976100537758505946937447087787026413988610048000000⟩, + ⟨5, 3, 7, 4, 6, 5, -8970446958824487817579063641059544004055531520000000⟩, + ⟨5, 3, 8, 4, 7, 5, 14635048967828868900399202647616545972943847424000000⟩, + ⟨5, 3, 5, 5, 3, 5, 70723148353942217533302598011494777494708420608000000⟩, + ⟨5, 3, 6, 5, 4, 5, -49599812840712553106544885408539861446884851712000000⟩, + ⟨5, 3, 7, 5, 5, 5, -23757707618080048924810281223463119172545806336000000⟩, + ⟨5, 3, 8, 5, 6, 5, 30474013019058886990284351920716003333097127936000000⟩, + ⟨5, 3, 5, 6, 2, 5, 1046697263300626094454249491658107974091538432000000⟩, + ⟨5, 3, 6, 6, 3, 5, 183657655674398502031576785931185604532405010432000000⟩, + ⟨5, 3, 7, 6, 4, 5, 8504916743561713006852208177836060897362051072000000⟩, + ⟨5, 3, 8, 6, 5, 5, -31981117153271476339009037742244571487154470912000000⟩, + ⟨5, 3, 5, 7, 1, 5, -48793424897147618328282463012519494631443922944000000⟩, + ⟨5, 3, 6, 7, 2, 5, -181247612825077696528593247395928453330237390848000000⟩, + ⟨5, 3, 7, 7, 3, 5, 356352300608829242665462932821287842901244510208000000⟩, + ⟨5, 3, 8, 7, 4, 5, 63233760278709982888775345894528156637100769280000000⟩ +] + +def collectedFourData_13_3_42 : List CollectedFourTerm := [ + ⟨5, 4, 4, 0, 7, 6, -26733194746355434218599740187940181070620026470400000⟩, + ⟨5, 4, 5, 0, 8, 6, -2520072579618976068335287015251347367260061696000000⟩, + ⟨5, 4, 4, 1, 6, 6, -59896640697346121494795959785633555304857311641600000⟩, + ⟨5, 4, 5, 1, 7, 6, 19988047657138794257937908164687052592994320384000000⟩, + ⟨5, 4, 6, 1, 8, 6, 5466615423114076106523334289539674841005686784000000⟩, + ⟨5, 4, 4, 2, 5, 6, 7600569802687938018928829228083627296872516812800000⟩, + ⟨5, 4, 5, 2, 6, 6, 13970606014775543072061243154627832506610614272000000⟩, + ⟨5, 4, 6, 2, 7, 6, 7314956698073058668001400089103562963498827776000000⟩, + ⟨5, 4, 7, 2, 8, 6, 11435244475396247129962371433398902322823692288000000⟩, + ⟨5, 4, 4, 3, 4, 6, -5214750080488022688730888258701452013388745932800000⟩, + ⟨5, 4, 5, 3, 5, 6, -5278929838475034203795965811339250134050406400000000⟩, + ⟨5, 4, 6, 3, 6, 6, -19382496440670760349591892094510553671101579264000000⟩, + ⟨5, 4, 7, 3, 7, 6, -6385201699276456833804271599976961668559142912000000⟩, + ⟨5, 4, 8, 3, 8, 6, -7223494232472992392759077468848354148483072000000000⟩, + ⟨5, 4, 4, 4, 3, 6, -11655725783243796763628417686014506416918757376000000⟩, + ⟨5, 4, 5, 4, 4, 6, 19017913931134778409084828341963432340662255616000000⟩, + ⟨5, 4, 6, 4, 5, 6, 15420738519876687189357634952093308119926439936000000⟩, + ⟨5, 4, 7, 4, 6, 6, 2097062044563388359236718359344222838728949760000000⟩, + ⟨5, 4, 8, 4, 7, 6, -2565976298474956047398632752562597271263248384000000⟩, + ⟨5, 4, 4, 5, 2, 6, 79861087539008949336036295796292967893393054105600000⟩, + ⟨5, 4, 5, 5, 3, 6, -49599812840712553106544885408539861446884851712000000⟩, + ⟨5, 4, 6, 5, 4, 6, 17392759592104483732403430576106073910499344384000000⟩, + ⟨5, 4, 7, 5, 5, 6, 5553946992875243199554398516886016306727354368000000⟩, + ⟨5, 4, 8, 5, 6, 6, -5343036111338872747403920898821761639043301376000000⟩, + ⟨5, 4, 4, 6, 1, 6, -42853947484455405347049233803691091029337204326400000⟩, + ⟨5, 4, 5, 6, 2, 6, -734073490348273005608413789354952039331790848000000⟩, + ⟨5, 4, 6, 6, 3, 6, -64401723906755519199915981322914498544794599424000000⟩, + ⟨5, 4, 7, 6, 4, 6, -1988232936102451783045823185522453650327207936000000⟩, + ⟨5, 4, 8, 6, 5, 6, 5607278034698615850625202362949374755987259392000000⟩, + ⟨5, 4, 4, 7, 0, 6, -817706136028390728512657260557411619938834894028800000⟩, + ⟨5, 4, 5, 7, 1, 6, 34219980290526523472189398687760004742241058816000000⟩, + ⟨5, 4, 6, 7, 2, 6, 63556613945967508388917908260843811445760065536000000⟩, + ⟨5, 4, 7, 7, 3, 6, -83306092497931224669149526262180148057896648704000000⟩, + ⟨5, 4, 8, 7, 4, 6, -11086832062898653412604358188097277320998420480000000⟩ +] + +def collectedFourData_13_3_43 : List CollectedFourTerm := [ + ⟨5, 5, 3, 0, 6, 7, 1785157507218906868567423131964257370301163110400000⟩, + ⟨5, 5, 4, 0, 7, 7, -25609750848083316558127294557585076782966924902400000⟩, + ⟨5, 5, 5, 0, 8, 7, -1207084141934199218266546723552445695354994688000000⟩, + ⟨5, 5, 3, 1, 5, 7, -23932585332849176820763890137037681752418759475200000⟩, + ⟨5, 5, 4, 1, 6, 7, -57379526070497989602108930827180655448528886169600000⟩, + ⟨5, 5, 5, 1, 7, 7, 9574031934748957813847496956840966200913559552000000⟩, + ⟨5, 5, 6, 1, 8, 7, 1745628238556950122684756407702948815640199168000000⟩, + ⟨5, 5, 3, 2, 4, 7, 31165369328581190453865607111156441902788011622400000⟩, + ⟨5, 5, 4, 2, 5, 7, 7281161148045747036815672565864900881942367436800000⟩, + ⟨5, 5, 5, 2, 6, 7, 6691750511485592222215428926049411360689750016000000⟩, + ⟨5, 5, 6, 2, 7, 7, 2335850245105338321315490240258856237716733952000000⟩, + ⟨5, 5, 7, 2, 8, 7, 2738671571808155991831356618727675950197112832000000⟩, + ⟨5, 5, 3, 3, 3, 7, -41656934820396918635902891422415777355017696051200000⟩, + ⟨5, 5, 4, 3, 4, 7, -4995603838726663566569213731657261044567166156800000⟩, + ⟨5, 5, 5, 3, 5, 7, -2528543243532260895540121684461428638167859200000000⟩, + ⟨5, 5, 6, 3, 6, 7, -6189320173777734053397650596611341018493616128000000⟩, + ⟨5, 5, 7, 3, 7, 7, -1529217010768247240386516024994711443202899968000000⟩, + ⟨5, 5, 8, 3, 8, 7, -1383986383231808161019843077636492032894566400000000⟩, + ⟨5, 5, 3, 4, 2, 7, 57026454118380582644934910933656016925679943680000000⟩, + ⟨5, 5, 4, 4, 3, 7, -11165902021611138254968194622028174028183699456000000⟩, + ⟨5, 5, 5, 4, 4, 7, 9109349668973882373047829245656557553553768448000000⟩, + ⟨5, 5, 6, 4, 5, 7, 4924230906363122547527089138752852768715702272000000⟩, + ⟨5, 5, 7, 4, 6, 7, 502233618014942477539022146684959561760112640000000⟩, + ⟨5, 5, 8, 4, 7, 7, -491628586179282284746689444529725981653257420800000⟩, + ⟨5, 5, 3, 5, 1, 7, -47356039957666449583408179993786836666262591897600000⟩, + ⟨5, 5, 4, 5, 2, 7, 76504980932360052473449928895237458259223353753600000⟩, + ⟨5, 5, 5, 5, 3, 7, -23757707618080048924810281223463119172545806336000000⟩, + ⟨5, 5, 6, 5, 4, 7, 5553946992875243199554398516886016306727354368000000⟩, + ⟨5, 5, 7, 5, 5, 7, 1330136559252683650812343832882311773869309952000000⟩, + ⟨5, 5, 8, 5, 6, 7, -1023699747688069997628684841893212450351952691200000⟩, + ⟨5, 5, 3, 6, 0, 7, -25790123556400563745000396122489151409631107481600000⟩, + ⟨5, 5, 4, 6, 1, 7, -41053040175206527934950922591479721061471643238400000⟩, + ⟨5, 5, 5, 6, 2, 7, -351612281479472502554978306343627603358777344000000⟩, + ⟨5, 5, 6, 6, 3, 7, -20565095431450597451621960691930194571530600448000000⟩, + ⟨5, 5, 7, 6, 4, 7, -476169707779488966457873596574616090736328704000000⟩, + ⟨5, 5, 8, 6, 5, 7, 1074327215785828297642496327532935160025998950400000⟩, + ⟨5, 5, 4, 7, 0, 7, -783342604927192808687648765759713184065962953932800000⟩, + ⟨5, 5, 5, 7, 1, 7, 16390954720931396297783677881570822755658498048000000⟩, + ⟨5, 5, 6, 7, 2, 7, 20295230497107561380530577316591946611893993472000000⟩, + ⟨5, 5, 7, 7, 3, 7, -19951302989051250045482984193309356739061088256000000⟩, + ⟨5, 5, 8, 7, 4, 7, -2124183132762946120047966189754624953104203776000000⟩ +] + +def collectedFourData_13_3_44 : List CollectedFourTerm := [ + ⟨5, 6, 2, 0, 5, 8, -42797619532308453815132338672462952050100011008000000⟩, + ⟨5, 6, 3, 0, 6, 8, -6869464932044991107926821321168249005551072051200000⟩, + ⟨5, 6, 4, 0, 7, 8, 49274443475688441124025872929679075266939951513600000⟩, + ⟨5, 6, 5, 0, 8, 8, 1548326902904070012833531051708052466971967488000000⟩, + ⟨5, 6, 2, 1, 4, 8, 147503901692991783876454516292154848489989629542400000⟩, + ⟨5, 6, 3, 1, 5, 8, 92094986023561839321668521643076171044503525785600000⟩, + ⟨5, 6, 4, 1, 6, 8, 110401082415612348911435343502661249804968289894400000⟩, + ⟨5, 6, 5, 1, 7, 8, -12280611349993685030744623543048150641385930752000000⟩, + ⟨5, 6, 6, 1, 8, 8, -1679338086508122660294065681199386618260094976000000⟩, + ⟨5, 6, 2, 2, 3, 8, -54973798368184064200583658110270845472771722444800000⟩, + ⟨5, 6, 3, 2, 4, 8, -119927463448560616087937104739865571516950459187200000⟩, + ⟨5, 6, 4, 2, 5, 8, -14009318776859961102519691302144143490741908275200000⟩, + ⟨5, 6, 5, 2, 6, 8, -8583508791568578971818568836306828024784879616000000⟩, + ⟨5, 6, 6, 2, 7, 8, -2247146439511927556430315185614979543926308864000000⟩, + ⟨5, 6, 7, 2, 8, 8, -2107736515892507549300334465896733838230631219200000⟩, + ⟨5, 6, 2, 3, 2, 8, -29396094593026236572200607161451157201893720064000000⟩, + ⟨5, 6, 3, 3, 3, 8, 160300058548340607959925744153000623895419132313600000⟩, + ⟨5, 6, 4, 3, 4, 8, 9611792025563260863597928583689954371583554355200000⟩, + ⟨5, 6, 5, 3, 5, 8, 3243362573584976286487117050962479141827379200000000⟩, + ⟨5, 6, 6, 3, 6, 8, 5954281024927934042407701637814415415308189696000000⟩, + ⟨5, 6, 7, 3, 7, 8, 1176916052110685483266382673236267539471584460800000⟩, + ⟨5, 6, 8, 3, 8, 8, 887619709334033735724606930046884263441203200000000⟩, + ⟨5, 6, 2, 4, 1, 8, -67859041939644187345282690063569503447327912755200000⟩, + ⟨5, 6, 3, 4, 2, 8, -219443508587307182171649305539063330412471255040000000⟩, + ⟨5, 6, 4, 4, 3, 8, 21483754812090680047789236712584050541103939584000000⟩, + ⟨5, 6, 5, 4, 4, 8, -11684563379179411082240842752324305258438197248000000⟩, + ⟨5, 6, 6, 4, 5, 8, -4737233464240970870967161591387673237708079104000000⟩, + ⟨5, 6, 7, 4, 6, 8, -386529055581498055737190768903891646083497984000000⟩, + ⟨5, 6, 8, 4, 7, 8, 315306008824846935348777896474959070647182950400000⟩, + ⟨5, 6, 2, 5, 0, 8, 506301411765391451957818800978059805155014370918400000⟩, + ⟨5, 6, 3, 5, 1, 8, 182230786075852672609266770635633219019066887372800000⟩, + ⟨5, 6, 4, 5, 2, 8, -147199415602371315594274837005290404591111136870400000⟩, + ⟨5, 6, 5, 5, 3, 8, 30474013019058886990284351920716003333097127936000000⟩, + ⟨5, 6, 6, 5, 4, 8, -5343036111338872747403920898821761639043301376000000⟩, + ⟨5, 6, 7, 5, 5, 8, -1023699747688069997628684841893212450351952691200000⟩, + ⟨5, 6, 8, 5, 6, 8, 656549864577688369006016835022516136376375705600000⟩, + ⟨5, 6, 3, 6, 0, 8, 99242979203445801726085265162434762448741125324800000⟩, + ⟨5, 6, 4, 6, 1, 8, 78988105726525486781749313203913339086304811417600000⟩, + ⟨5, 6, 5, 6, 2, 8, 451013095022354100754316452783721607535263744000000⟩, + ⟨5, 6, 6, 6, 3, 8, 19784136878570822057280034712479588596565671936000000⟩, + ⟨5, 6, 7, 6, 4, 8, 366469748026799376627922464449553244967298662400000⟩, + ⟨5, 6, 8, 6, 5, 8, -689019792794983187405302478590283155772748595200000⟩, + ⟨5, 6, 4, 7, 0, 8, 1507190411087982556855726778690013294482978714419200000⟩, + ⟨5, 6, 5, 7, 1, 8, -21024678625994238534593384204411504180852686848000000⟩, + ⟨5, 6, 6, 7, 2, 8, -19524520052693902020660615126271613616210837504000000⟩, + ⟨5, 6, 7, 7, 3, 8, 15354922540746482524448652695871713116677577113600000⟩, + ⟨5, 6, 8, 7, 4, 8, 1362344917348439517337641695183903648737394688000000⟩ +] + +def collectedFourData_13_3_45 : List CollectedFourTerm := [ + ⟨6, 0, 7, 2, 8, 3, -53100320960290588433806487792996504795417778585600000⟩, + ⟨6, 0, 7, 3, 7, 3, 29650110267189889030464443505899120375286359654400000⟩, + ⟨6, 0, 8, 3, 8, 3, 134171110385755905794647155385004043865266585600000000⟩, + ⟨6, 0, 7, 4, 6, 3, -9737847571125105549057608489126842100468416512000000⟩, + ⟨6, 0, 8, 4, 7, 3, 47661128826298108959484020124830180981377020723200000⟩, + ⟨6, 0, 7, 5, 5, 3, -25790123556400563745000396122489151409631107481600000⟩, + ⟨6, 0, 8, 5, 6, 3, 99242979203445801726085265162434762448741125324800000⟩, + ⟨6, 0, 7, 6, 4, 3, 9232492342250756298289420633642673648501470003200000⟩, + ⟨6, 0, 8, 6, 5, 3, -104151079234627919792037866450007494419390503321600000⟩, + ⟨6, 0, 7, 7, 3, 3, 386837400731174201072897512315401831736939433164800000⟩, + ⟨6, 0, 8, 7, 4, 3, 205929778673091058119375913642930403097553403904000000⟩ +] + +def collectedFourData_13_3_46 : List CollectedFourTerm := [ + ⟨6, 1, 6, 1, 8, 4, -13469170836247897116493847117792076867553355366400000⟩, + ⟨6, 1, 6, 2, 7, 4, -18023291159189675633217547848880993813072026009600000⟩, + ⟨6, 1, 7, 2, 8, 4, -84525752849995879025948309130216183962223928934400000⟩, + ⟨6, 1, 6, 3, 6, 4, 47756451768769943792991808149988382422329615974400000⟩, + ⟨6, 1, 7, 3, 7, 4, 47197415139803004571664510702033818061431740825600000⟩, + ⟨6, 1, 8, 3, 8, 4, 106787623040516706904132047434471948133020467200000000⟩, + ⟨6, 1, 6, 4, 5, 4, -37995093027233297977130269288131340404602280345600000⟩, + ⟨6, 1, 7, 4, 6, 4, -15500827155138705541393590209659227712297893888000000⟩, + ⟨6, 1, 8, 4, 7, 4, 37933789503232429116153226373948795836776736358400000⟩, + ⟨6, 1, 6, 5, 4, 4, -42853947484455405347049233803691091029337204326400000⟩, + ⟨6, 1, 7, 5, 5, 4, -41053040175206527934950922591479721061471643238400000⟩, + ⟨6, 1, 8, 5, 6, 4, 78988105726525486781749313203913339086304811417600000⟩, + ⟨6, 1, 6, 6, 3, 4, 158679137694822789078528253223974525453394667110400000⟩, + ⟨6, 1, 7, 6, 4, 4, 14696396402088647373786709291381684079298399436800000⟩, + ⟨6, 1, 8, 6, 5, 4, -82894493133383135244751726561002043879780987699200000⟩, + ⟨6, 1, 6, 7, 2, 4, -156596874803392948199279851550742361204678302105600000⟩, + ⟨6, 1, 7, 7, 3, 4, 615772596775639325039878558978353514444651442995200000⟩, + ⟨6, 1, 8, 7, 4, 4, 163900794400026840653020095146732126905143656448000000⟩ +] + +def collectedFourData_13_3_47 : List CollectedFourTerm := [ + ⟨6, 2, 5, 0, 8, 5, 53180706162685539148834256853093318924435456000000⟩, + ⟨6, 2, 5, 1, 7, 5, -421804712220142095314145106405820329491431424000000⟩, + ⟨6, 2, 6, 1, 8, 5, -230722298137135337499488203055862311339163648000000⟩, + ⟨6, 2, 5, 2, 6, 5, -294819561704353250170116872153135629668974592000000⟩, + ⟨6, 2, 6, 2, 7, 5, -308732824521910453179702576239976896551452672000000⟩, + ⟨6, 2, 7, 2, 8, 5, -723948644887602663293028620747754543412936704000000⟩, + ⟨6, 2, 5, 3, 5, 5, 111400448885412683731803729624974659839590400000000⟩, + ⟨6, 2, 6, 3, 6, 5, 818051715055332789531569321520798192220766208000000⟩, + ⟨6, 2, 7, 3, 7, 5, 404237804226308915022223432027105102865104896000000⟩, + ⟨6, 2, 8, 3, 8, 5, 609745175360118859965923814875164802285568000000000⟩, + ⟨6, 2, 5, 4, 4, 5, -401332128597597623106196496795463912391704576000000⟩, + ⟨6, 2, 6, 4, 5, 5, -650842972277537968328910270599601564986376192000000⟩, + ⟨6, 2, 7, 4, 6, 5, -132761938642705222391371926606882411726766080000000⟩, + ⟨6, 2, 8, 4, 7, 5, 216597621280009868275286733272441699168157696000000⟩, + ⟨6, 2, 5, 5, 3, 5, 1046697263300626094454249491658107974091538432000000⟩, + ⟨6, 2, 6, 5, 4, 5, -734073490348273005608413789354952039331790848000000⟩, + ⟨6, 2, 7, 5, 5, 5, -351612281479472502554978306343627603358777344000000⟩, + ⟨6, 2, 8, 5, 6, 5, 451013095022354100754316452783721607535263744000000⟩, + ⟨6, 2, 5, 6, 2, 5, 15491040578653073181737005112353997589577728000000⟩, + ⟨6, 2, 6, 6, 3, 5, 2718119456681204108329681582012352847547465728000000⟩, + ⟨6, 2, 7, 6, 4, 5, 125872126556559079936291712125536398148108288000000⟩, + ⟨6, 2, 8, 6, 5, 5, -473318122577047874374341580108369112384667648000000⟩, + ⟨6, 2, 5, 7, 1, 5, -722139009583023127787525194351638605281099776000000⟩, + ⟨6, 2, 6, 7, 2, 5, -2682451004222091864926325929293653226807099392000000⟩, + ⟨6, 2, 7, 7, 3, 5, 5273987180992804282854001500711289841183096832000000⟩, + ⟨6, 2, 8, 7, 4, 5, 935854884467176454772879815332444486364037120000000⟩ +] + +def collectedFourData_13_3_48 : List CollectedFourTerm := [ + ⟨6, 3, 4, 0, 7, 6, 98987387141363486772765190023127926450856289894400000⟩, + ⟨6, 3, 5, 0, 8, 6, 9331297752846642913170745885260851525720211456000000⟩, + ⟨6, 3, 4, 1, 6, 6, 221784639562529543331012812534399596820973590937600000⟩, + ⟨6, 3, 5, 1, 7, 6, -74011528753291304087050225980080481658076135424000000⟩, + ⟨6, 3, 6, 1, 8, 6, -20241725030432956845290197998203436159492685824000000⟩, + ⟨6, 3, 4, 2, 5, 6, -28143308448242900285059836326838204216504011980800000⟩, + ⟨6, 3, 5, 2, 6, 6, -51730210298661821296374375159336671882973806592000000⟩, + ⟨6, 3, 6, 2, 7, 6, -27085743303956724823693283485024215159155982336000000⟩, + ⟨6, 3, 7, 2, 8, 6, -42342300749389693671356746751860347112488173568000000⟩, + ⟨6, 3, 4, 3, 4, 6, 19309120737733662209983340136899286085340548300800000⟩, + ⟨6, 3, 5, 3, 5, 6, 19546764858115698996431195216626151913317990400000000⟩, + ⟨6, 3, 6, 3, 6, 6, 71769300195605851005562490018302115289816367104000000⟩, + ⟨6, 3, 7, 3, 7, 6, 23643056453929409356260685192316271124002373632000000⟩, + ⟨6, 3, 8, 3, 8, 6, 26747077066076880999901433565055095398203392000000000⟩, + ⟨6, 3, 4, 4, 3, 6, 43158696574296290265932889642720114546296487936000000⟩, + ⟨6, 3, 5, 4, 4, 6, -70419327984696485148341981533063202116863000576000000⟩, + ⟨6, 3, 6, 4, 5, 6, -57099745404760273595829815187207762090022404096000000⟩, + ⟨6, 3, 7, 4, 6, 6, -7764978874923108411732390852609516349276815360000000⟩, + ⟨6, 3, 8, 4, 7, 6, 9501269551306857646974101723005575267744743424000000⟩, + ⟨6, 3, 4, 5, 2, 6, -295708779469087896996733839530338597602875513241600000⟩, + ⟨6, 3, 5, 5, 3, 6, 183657655674398502031576785931185604532405010432000000⟩, + ⟨6, 3, 6, 5, 4, 6, -64401723906755519199915981322914498544794599424000000⟩, + ⟨6, 3, 7, 5, 5, 6, -20565095431450597451621960691930194571530600448000000⟩, + ⟨6, 3, 8, 5, 6, 6, 19784136878570822057280034712479588596565671936000000⟩, + ⟨6, 3, 4, 6, 1, 6, 158679137694822789078528253223974525453394667110400000⟩, + ⟨6, 3, 5, 6, 2, 6, 2718119456681204108329681582012352847547465728000000⟩, + ⟨6, 3, 6, 6, 3, 6, 238466013411970442162440239513712133635376676864000000⟩, + ⟨6, 3, 7, 6, 4, 6, 7362007617889161104011291208305917169653252096000000⟩, + ⟨6, 3, 8, 6, 5, 6, -20762569041833140370300527330656408304103718912000000⟩, + ⟨6, 3, 4, 7, 0, 6, 3027793521234335048398536170402517843512495230156800000⟩, + ⟨6, 3, 5, 7, 1, 6, -126709376456024875271763747331220077718091595776000000⟩, + ⟨6, 3, 6, 7, 2, 6, -235336749301965402425536871637568349926846365696000000⟩, + ⟨6, 3, 7, 7, 3, 6, 308464906928161857092830248392718380672634322944000000⟩, + ⟨6, 3, 8, 7, 4, 6, 41052203000580319309378209679125794587441889280000000⟩ +] + +def collectedFourData_13_3_49 : List CollectedFourTerm := [ + ⟨6, 4, 3, 0, 6, 7, -639060645795923628667369790970339567201995980800000⟩, + ⟨6, 4, 4, 0, 7, 7, 9167921513629164671702698440365495315285724364800000⟩, + ⟨6, 4, 5, 0, 8, 7, 432118716782728088541008053259921320707096576000000⟩, + ⟨6, 4, 3, 1, 5, 7, 8567520443730322176319215702150064369723401830400000⟩, + ⟨6, 4, 4, 1, 6, 7, 20541042926348294444057596504379156477183734579200000⟩, + ⟨6, 4, 5, 1, 7, 7, -3427365376080056621112339244167307923139067904000000⟩, + ⟨6, 4, 6, 1, 8, 7, -624909737622949224038356252695777767678017536000000⟩, + ⟨6, 4, 3, 2, 4, 7, -11156752818197837894348796591775518943760665804800000⟩, + ⟨6, 4, 4, 2, 5, 7, -2606550697402249975126786446863351980672784793600000⟩, + ⟨6, 4, 5, 2, 6, 7, -2395550188754735148789264356644319056134930432000000⟩, + ⟨6, 4, 6, 2, 7, 7, -836200705026379459882418230883125234136776704000000⟩, + ⟨6, 4, 7, 2, 8, 7, -980404931343708051926853088331752147689406464000000⟩, + ⟨6, 4, 3, 3, 3, 7, 14912581976967865434436434960522059663595169382400000⟩, + ⟨6, 4, 4, 3, 4, 7, 1788354138168365962554619817463088474607950233600000⟩, + ⟨6, 4, 5, 3, 5, 7, 905182019849913153012232356966995767748198400000000⟩, + ⟨6, 4, 6, 3, 6, 7, 2215687372849340289604634482573778239101075456000000⟩, + ⟨6, 4, 7, 3, 7, 7, 547437638702336712055254928496929483454939136000000⟩, + ⟨6, 4, 8, 3, 8, 7, 495447168255068253718174793140817921625292800000000⟩, + ⟨6, 4, 3, 4, 2, 7, -20414648258751655950801172361549227352244879360000000⟩, + ⟨6, 4, 4, 4, 3, 7, 3997231912573080133186287818586373661562765312000000⟩, + ⟨6, 4, 5, 4, 4, 7, -3261015825603266299387694087836994596918788096000000⟩, + ⟨6, 4, 6, 4, 5, 7, -1762803657572594014387345521409236817982521344000000⟩, + ⟨6, 4, 7, 4, 6, 7, -179792393092008868469646676011945049750241280000000⟩, + ⟨6, 4, 8, 4, 7, 7, 175995944618315581314559606471509822555134361600000⟩, + ⟨6, 4, 3, 5, 1, 7, 16952779435597894986358034656848345361175229235200000⟩, + ⟨6, 4, 4, 5, 2, 7, -27387679979794347232927508086107410527270679347200000⟩, + ⟨6, 4, 5, 5, 3, 7, 8504916743561713006852208177836060897362051072000000⟩, + ⟨6, 4, 6, 5, 4, 7, -1988232936102451783045823185522453650327207936000000⟩, + ⟨6, 4, 7, 5, 5, 7, -476169707779488966457873596574616090736328704000000⟩, + ⟨6, 4, 8, 5, 6, 7, 366469748026799376627922464449553244967298662400000⟩, + ⟨6, 4, 3, 6, 0, 7, 9232492342250756298289420633642673648501470003200000⟩, + ⟨6, 4, 4, 6, 1, 7, 14696396402088647373786709291381684079298399436800000⟩, + ⟨6, 4, 5, 6, 2, 7, 125872126556559079936291712125536398148108288000000⟩, + ⟨6, 4, 6, 6, 3, 7, 7362007617889161104011291208305917169653252096000000⟩, + ⟨6, 4, 7, 6, 4, 7, 170461889066633031841833958235259169834795008000000⟩, + ⟨6, 4, 8, 6, 5, 7, -384593651562891384564248060626851019935763660800000⟩, + ⟨6, 4, 4, 7, 0, 7, 280425356843790180038783145094500305777370700185600000⟩, + ⟨6, 4, 5, 7, 1, 7, -5867725434204879870694406069360971506354487296000000⟩, + ⟨6, 4, 6, 7, 2, 7, -7265399862819071896750884319710450736372383744000000⟩, + ⟨6, 4, 7, 7, 3, 7, 7142278774334358712071528091041087349076262912000000⟩, + ⟨6, 4, 8, 7, 4, 7, 760426931025887257082012349341116602569981952000000⟩ +] + +def collectedFourData_13_3_50 : List CollectedFourTerm := [ + ⟨6, 5, 2, 0, 5, 8, 44914192406752656885812297679672084879309275136000000⟩, + ⟨6, 5, 3, 0, 6, 8, 7209196984808717875653115731017949589683988070400000⟩, + ⟨6, 5, 4, 0, 7, 8, -51711330190503134267837435295231524554975425331200000⟩, + ⟨6, 5, 5, 0, 8, 8, -1624900010457049665573096577800934262933815296000000⟩, + ⟨6, 5, 2, 1, 4, 8, -154798764365491244693075269183984075774635068620800000⟩, + ⟨6, 5, 3, 1, 5, 8, -96649579279446950494760915014379924707465179955200000⟩, + ⟨6, 5, 4, 1, 6, 8, -115861010769191971455049362119457616440008166604800000⟩, + ⟨6, 5, 5, 1, 7, 8, 12887953747749381355653690708154165988671094784000000⟩, + ⟨6, 5, 6, 1, 8, 8, 1762390402963266456498643884796590397002350592000000⟩, + ⟨6, 5, 2, 2, 3, 8, 57692548889890645551508891518056584428798974361600000⟩, + ⟨6, 5, 3, 2, 4, 8, 125858522671247024824016135978035040644028065382400000⟩, + ⟨6, 5, 4, 2, 5, 8, 14702155070947747120060251769327981114790667878400000⟩, + ⟨6, 5, 5, 2, 6, 8, 9008009548253712639896785401149366423594729472000000⟩, + ⟨6, 5, 6, 2, 7, 8, 2358279938308146012013354215363791924848754688000000⟩, + ⟨6, 5, 7, 2, 8, 8, 2211975442841372447128744768541513705635341926400000⟩, + ⟨6, 5, 2, 3, 2, 8, 30849889853373026663123182420680620235017945088000000⟩, + ⟨6, 5, 3, 3, 3, 8, -168227760121534498957071288858653380138910298931200000⟩, + ⟨6, 5, 4, 3, 4, 8, -10087146928439303259413943512951430318085531238400000⟩, + ⟨6, 5, 5, 3, 5, 8, -3403764327707192562827041702230710043436646400000000⟩, + ⟨6, 5, 6, 3, 6, 8, -6248752302580803993271556306936452293781880832000000⟩, + ⟨6, 5, 7, 3, 7, 8, -1235120891973681337117004724801561356154804633600000⟩, + ⟨6, 5, 8, 3, 8, 8, -931517286351844293408584447470746126935654400000000⟩, + ⟨6, 5, 2, 4, 1, 8, 71215037180145715934232407263524272456082024038400000⟩, + ⟨6, 5, 3, 4, 2, 8, 230296172422923673283753864374716542033256775680000000⟩, + ⟨6, 5, 4, 4, 3, 8, -22546242239508317715621397994371626344726396928000000⟩, + ⟨6, 5, 5, 4, 4, 8, 12262427993341545137629027756789850181747081216000000⟩, + ⟨6, 5, 6, 4, 5, 8, 4971515182707870683360682162934431983251488768000000⟩, + ⟨6, 5, 7, 4, 6, 8, 405644999953374343589649479351501766921289728000000⟩, + ⟨6, 5, 8, 4, 7, 8, -330899589793155956539967178925858692788964556800000⟩, + ⟨6, 5, 2, 5, 0, 8, -531340744470016542536795190691763999608146808012800000⟩, + ⟨6, 5, 3, 5, 1, 8, -191243080285478534084398852999007162719238986137600000⟩, + ⟨6, 5, 4, 5, 2, 8, 154479219797154128490329883754723024273289301196800000⟩, + ⟨6, 5, 5, 5, 3, 8, -31981117153271476339009037742244571487154470912000000⟩, + ⟨6, 5, 6, 5, 4, 8, 5607278034698615850625202362949374755987259392000000⟩, + ⟨6, 5, 7, 5, 5, 8, 1074327215785828297642496327532935160025998950400000⟩, + ⟨6, 5, 8, 5, 6, 8, -689019792794983187405302478590283155772748595200000⟩, + ⟨6, 5, 3, 6, 0, 8, -104151079234627919792037866450007494419390503321600000⟩, + ⟨6, 5, 4, 6, 1, 8, -82894493133383135244751726561002043879780987699200000⟩, + ⟨6, 5, 5, 6, 2, 8, -473318122577047874374341580108369112384667648000000⟩, + ⟨6, 5, 6, 6, 3, 8, -20762569041833140370300527330656408304103718912000000⟩, + ⟨6, 5, 7, 6, 4, 8, -384593651562891384564248060626851019935763660800000⟩, + ⟨6, 5, 8, 6, 5, 8, 723095533906801153297992964718282259078473318400000⟩, + ⟨6, 5, 4, 7, 0, 8, -1581729097482047105448841821213276832370467956326400000⟩, + ⟨6, 5, 5, 7, 1, 8, 22064462262560576570488065883826529487779004416000000⟩, + ⟨6, 5, 6, 7, 2, 8, 20490112765131494673426846395423319010540781568000000⟩, + ⟨6, 5, 7, 7, 3, 8, -16114306190914253112142286842027929475996660531200000⟩, + ⟨6, 5, 8, 7, 4, 8, -1429720213666493965082456073681165231845277696000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1308.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1308.lean new file mode 100644 index 0000000000000000000000000000000000000000..89112771f9025f1482f37872bf65b79451044558 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1308.lean @@ -0,0 +1,624 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1306 +import OAI.Analysis.LaughlinFock.Sparse1307 + +namespace OAI + +/-! Sparse1308. -/ +namespace LaughlinFock +def collectedFourData_13_3_51 : List CollectedFourTerm := [ + ⟨7, 0, 6, 1, 8, 4, -257008380476726148942948459779906319434906389708800000⟩, + ⟨7, 0, 6, 2, 7, 4, -343906609248577012854572216561925216936597336883200000⟩, + ⟨7, 0, 7, 2, 8, 4, -1612855543422972906101557650905417400304066677964800000⟩, + ⟨7, 0, 6, 3, 6, 4, 911251960170813179261061085245074106285015485644800000⟩, + ⟨7, 0, 7, 3, 7, 4, 900584852270503438413741749284366996727781339955200000⟩, + ⟨7, 0, 8, 3, 8, 4, 2037639464690890980060894449012736321810490982400000000⟩, + ⟨7, 0, 6, 4, 5, 4, -724993204385848391649031800727541393498523775795200000⟩, + ⟨7, 0, 7, 4, 6, 4, -295774887082925650105028755822898310980038557696000000⟩, + ⟨7, 0, 8, 4, 7, 4, 723823457590553572462573355490140707104188320972800000⟩, + ⟨7, 0, 6, 5, 4, 4, -817706136028390728512657260557411619938834894028800000⟩, + ⟨7, 0, 7, 5, 5, 4, -783342604927192808687648765759713184065962953932800000⟩, + ⟨7, 0, 8, 5, 6, 4, 1507190411087982556855726778690013294482978714419200000⟩, + ⟨7, 0, 6, 6, 3, 4, 3027793521234335048398536170402517843512495230156800000⟩, + ⟨7, 0, 7, 6, 4, 4, 280425356843790180038783145094500305777370700185600000⟩, + ⟨7, 0, 8, 6, 5, 4, -1581729097482047105448841821213276832370467956326400000⟩, + ⟨7, 0, 6, 7, 2, 4, -2988061378850858713833276267778652195562324177715200000⟩, + ⟨7, 0, 7, 7, 3, 4, 11749700093887981948029980850807896344740787283558400000⟩, + ⟨7, 0, 8, 7, 4, 4, 3127429166926670357011553847164263426043167113216000000⟩ +] + +def collectedFourData_13_3_52 : List CollectedFourTerm := [ + ⟨7, 1, 5, 0, 8, 5, -2479101534997507443568598077125540447415959552000000⟩, + ⟨7, 1, 5, 1, 7, 5, 19663084321130236222345588579979678101335441408000000⟩, + ⟨7, 1, 6, 1, 8, 5, 10755479660615332183783128169950592179074236416000000⟩, + ⟨7, 1, 5, 2, 6, 5, 13743473539683548046601541786440765765702385664000000⟩, + ⟨7, 1, 6, 2, 7, 5, 14392061978925288226111558455107996568753537024000000⟩, + ⟨7, 1, 7, 2, 8, 5, 33747994833124450201358593120727302353262215168000000⟩, + ⟨7, 1, 5, 3, 5, 5, -5193105615905038275766847060376198679678156800000000⟩, + ⟨7, 1, 6, 3, 6, 5, -38134756170725633474217719019479340413601447936000000⟩, + ⟨7, 1, 7, 3, 7, 5, -18844175515379383634776904180500840576588972032000000⟩, + ⟨7, 1, 8, 3, 8, 5, -28424222039631913345827271857730517578285056000000000⟩, + ⟨7, 1, 5, 4, 4, 5, 18708722915534115840373406428721564923138670592000000⟩, + ⟨7, 1, 6, 4, 5, 5, 30340059920973887680562667268998384356230692864000000⟩, + ⟨7, 1, 7, 4, 6, 5, 6188904766919230218792354360722666642850447360000000⟩, + ⟨7, 1, 8, 4, 7, 5, -10097035826290826794537946618897546152752709632000000⟩, + ⟨7, 1, 5, 5, 3, 5, -48793424897147618328282463012519494631443922944000000⟩, + ⟨7, 1, 6, 5, 4, 5, 34219980290526523472189398687760004742241058816000000⟩, + ⟨7, 1, 7, 5, 5, 5, 16390954720931396297783677881570822755658498048000000⟩, + ⟨7, 1, 8, 5, 6, 5, -21024678625994238534593384204411504180852686848000000⟩, + ⟨7, 1, 5, 6, 2, 5, -722139009583023127787525194351638605281099776000000⟩, + ⟨7, 1, 6, 6, 3, 5, -126709376456024875271763747331220077718091595776000000⟩, + ⟨7, 1, 7, 6, 4, 5, -5867725434204879870694406069360971506354487296000000⟩, + ⟨7, 1, 8, 6, 5, 5, 22064462262560576570488065883826529487779004416000000⟩, + ⟨7, 1, 5, 7, 1, 5, 33663635861890694416582831324814106996340948992000000⟩, + ⟨7, 1, 6, 7, 2, 5, 125046635931822978759077799167906422517623947264000000⟩, + ⟨7, 1, 7, 7, 3, 5, -245855135431247621097181961703345788111755935744000000⟩, + ⟨7, 1, 8, 7, 4, 5, -43626334586835277660387478205805604161758167040000000⟩ +] + +def collectedFourData_13_3_53 : List CollectedFourTerm := [ + ⟨7, 2, 4, 0, 7, 6, -97688427706882103325321678374084440819196598681600000⟩, + ⟨7, 2, 5, 0, 8, 6, -9208848038776453739338027918392033223360118784000000⟩, + ⟨7, 2, 4, 1, 6, 6, -218874276350584351301846496367756751752015537766400000⟩, + ⟨7, 2, 5, 1, 7, 6, 73040314376279981703950032135771921368571969536000000⟩, + ⟨7, 2, 6, 1, 8, 6, 19976103515836257022202579902122006459382235136000000⟩, + ⟨7, 2, 4, 2, 5, 6, 27773998609059471669799769034791667921386156851200000⟩, + ⟨7, 2, 5, 2, 6, 6, 51051381948346934665430386390972268105158361088000000⟩, + ⟨7, 2, 6, 2, 7, 6, 26730311336100350925885225745064930601917743104000000⟩, + ⟨7, 2, 7, 2, 8, 6, 41786664999983344677292177197346038540404785152000000⟩, + ⟨7, 2, 4, 3, 4, 6, -19055737298912309091402684274277372624414913331200000⟩, + ⟨7, 2, 5, 3, 5, 6, -19290262940454426229586790952059228028246425600000000⟩, + ⟨7, 2, 6, 3, 6, 6, -70827509405006701351390207853021719072453165056000000⟩, + ⟨7, 2, 7, 3, 7, 6, -23332801055461837081019121901195444170572955648000000⟩, + ⟨7, 2, 8, 3, 8, 6, -26396089237191526719308226831910506791436288000000000⟩, + ⟨7, 2, 4, 4, 3, 6, -42592347691735722448059103908960941023904661504000000⟩, + ⟨7, 2, 5, 4, 4, 6, 69495252169613803688940134671983936490086334464000000⟩, + ⟨7, 2, 6, 4, 5, 6, 56350455468517425401485796275301803105393311744000000⟩, + ⟨7, 2, 7, 4, 6, 6, 7663083139926833849905498445961208634844119040000000⟩, + ⟨7, 2, 8, 4, 7, 6, -9376589386695627724718608449434653148143681536000000⟩, + ⟨7, 2, 4, 5, 2, 6, 291828348638018527376756243067258287982947755622400000⟩, + ⟨7, 2, 5, 5, 3, 6, -181247612825077696528593247395928453330237390848000000⟩, + ⟨7, 2, 6, 5, 4, 6, 63556613945967508388917908260843811445760065536000000⟩, + ⟨7, 2, 7, 5, 5, 6, 20295230497107561380530577316591946611893993472000000⟩, + ⟨7, 2, 8, 5, 6, 6, -19524520052693902020660615126271613616210837504000000⟩, + ⟨7, 2, 4, 6, 1, 6, -156596874803392948199279851550742361204678302105600000⟩, + ⟨7, 2, 5, 6, 2, 6, -2682451004222091864926325929293653226807099392000000⟩, + ⟨7, 2, 6, 6, 3, 6, -235336749301965402425536871637568349926846365696000000⟩, + ⟨7, 2, 7, 6, 4, 6, -7265399862819071896750884319710450736372383744000000⟩, + ⟨7, 2, 8, 6, 5, 6, 20490112765131494673426846395423319010540781568000000⟩, + ⟨7, 2, 4, 7, 0, 6, -2988061378850858713833276267778652195562324177715200000⟩, + ⟨7, 2, 5, 7, 1, 6, 125046635931822978759077799167906422517623947264000000⟩, + ⟨7, 2, 6, 7, 2, 6, 232248548879527649721321535450970749800907014144000000⟩, + ⟨7, 2, 7, 7, 3, 6, -304417084143542404897470624529604183825439522816000000⟩, + ⟨7, 2, 8, 7, 4, 6, -40513496525605933546495360030354528878377041920000000⟩ +] + +def collectedFourData_13_3_54 : List CollectedFourTerm := [ + ⟨7, 3, 3, 0, 6, 7, -26776362217811882672214187821264243076860425011200000⟩, + ⟨7, 3, 4, 0, 7, 7, 384131911186089432003158971266572259233939796787200000⟩, + ⟨7, 3, 5, 0, 8, 7, 18105585687035587095988437530759521364726513664000000⟩, + ⟨7, 3, 3, 1, 5, 7, 358975368330050298884978695213803297196207610265600000⟩, + ⟨7, 3, 4, 1, 6, 7, 860660735950191841255314897231818956233107098828800000⟩, + ⟨7, 3, 5, 1, 7, 7, -143605113796997996909138678446422070658970157056000000⟩, + ⟨7, 3, 6, 1, 8, 7, -26183445339823502285042200120915573474647343104000000⟩, + ⟨7, 3, 3, 2, 4, 7, -467463075061669497650747279727822783359176880947200000⟩, + ⟨7, 3, 4, 2, 5, 7, -109213336906088692444950476931931757385812960870400000⟩, + ⟨7, 3, 5, 2, 6, 7, -100372507659512601799707897242436287170502197248000000⟩, + ⟨7, 3, 6, 2, 7, 7, -35036444681536713365086634764277357546104160256000000⟩, + ⟨7, 3, 7, 2, 8, 7, -41078538843669112813225322517855239415734992896000000⟩, + ⟨7, 3, 3, 3, 3, 7, 624830678034926219846641233322277382121401719193600000⟩, + ⟨7, 3, 4, 3, 4, 7, 74931258077516894896992729760612614443211581030400000⟩, + ⟨7, 3, 5, 3, 5, 7, 37926731674057441388296715559062955410168217600000000⟩, + ⟨7, 3, 6, 3, 6, 7, 92836334152536201314888424800941346351411625984000000⟩, + ⟨7, 3, 7, 3, 7, 7, 22937398198415087151858159008249016230822805504000000⟩, + ⟨7, 3, 8, 3, 8, 7, 20759020171652569398822147300295146669814579200000000⟩, + ⟨7, 3, 3, 4, 2, 7, -855364854527619800962213360823236352613065687040000000⟩, + ⟨7, 3, 4, 4, 3, 7, 167482273026452215613323065913144692281670893568000000⟩, + ⟨7, 3, 5, 4, 4, 7, -136635140215243244418135510400203581326249426944000000⟩, + ⟨7, 3, 6, 4, 5, 7, -73860704088983483611621997161885684918665609216000000⟩, + ⟨7, 3, 7, 4, 6, 7, -7533222821823081211583016503618571717228625920000000⟩, + ⟨7, 3, 8, 4, 7, 7, 7374153287277946888357467907067644594400683622400000⟩, + ⟨7, 3, 3, 5, 1, 7, 710314061353106766231020979726167327494743313612800000⟩, + ⟨7, 3, 4, 5, 2, 7, -1147531841099588535148098460724970096677639474380800000⟩, + ⟨7, 3, 5, 5, 3, 7, 356352300608829242665462932821287842901244510208000000⟩, + ⟨7, 3, 6, 5, 4, 7, -83306092497931224669149526262180148057896648704000000⟩, + ⟨7, 3, 7, 5, 5, 7, -19951302989051250045482984193309356739061088256000000⟩, + ⟨7, 3, 8, 5, 6, 7, 15354922540746482524448652695871713116677577113600000⟩, + ⟨7, 3, 3, 6, 0, 7, 386837400731174201072897512315401831736939433164800000⟩, + ⟨7, 3, 4, 6, 1, 7, 615772596775639325039878558978353514444651442995200000⟩, + ⟨7, 3, 5, 6, 2, 7, 5273987180992804282854001500711289841183096832000000⟩, + ⟨7, 3, 6, 6, 3, 7, 308464906928161857092830248392718380672634322944000000⟩, + ⟨7, 3, 7, 6, 4, 7, 7142278774334358712071528091041087349076262912000000⟩, + ⟨7, 3, 8, 6, 5, 7, -16114306190914253112142286842027929475996660531200000⟩, + ⟨7, 3, 4, 7, 0, 7, 11749700093887981948029980850807896344740787283558400000⟩, + ⟨7, 3, 5, 7, 1, 7, -245855135431247621097181961703345788111755935744000000⟩, + ⟨7, 3, 6, 7, 2, 7, -304417084143542404897470624529604183825439522816000000⟩, + ⟨7, 3, 7, 7, 3, 7, 299258364257400768484233859179295230493320019968000000⟩, + ⟨7, 3, 8, 7, 4, 7, 31861556613252008803651365941954845262928150528000000⟩ +] + +def collectedFourData_13_3_55 : List CollectedFourTerm := [ + ⟨7, 4, 2, 0, 5, 8, -88805317905222994554581597432709806225715363840000000⟩, + ⟨7, 4, 3, 0, 6, 8, -14254181045478615005554086537392029231875096576000000⟩, + ⟨7, 4, 4, 0, 7, 8, 102244766537963233394262428909249131692611862528000000⟩, + ⟨7, 4, 5, 0, 8, 8, 3212787634831069815888967182285816899819274240000000⟩, + ⟨7, 4, 2, 1, 4, 8, 306071483069711371906370718201811477972597604352000000⟩, + ⟨7, 4, 3, 1, 5, 8, 191097649838337575009109183397014840597270233088000000⟩, + ⟨7, 4, 4, 1, 6, 8, 229082909940770518903858352457804497963358093312000000⟩, + ⟨7, 4, 5, 1, 7, 8, -25482342404193388505835636257883203618954280960000000⟩, + ⟨7, 4, 6, 1, 8, 8, -3484636628682571606124782088318437432995348480000000⟩, + ⟨7, 4, 2, 2, 3, 8, -114070962214586689855748939727588103002211221504000000⟩, + ⟨7, 4, 3, 2, 4, 8, -248850207873745661243395349359503648716652281856000000⟩, + ⟨7, 4, 4, 2, 5, 8, -29069420711015727608432283792529748604638724096000000⟩, + ⟨7, 4, 5, 2, 6, 8, -17810832361881334548251254411999140820738375680000000⟩, + ⟨7, 4, 6, 2, 7, 8, -4662842375842830547159813762525971528516894720000000⟩, + ⟨7, 4, 7, 2, 8, 8, -4373565945951224649692601725141702043255177216000000⟩, + ⟨7, 4, 2, 3, 2, 8, -60997073062322557120914670724651875666986270720000000⟩, + ⟨7, 4, 3, 3, 3, 8, 332623585497896507780650238000092251914426646528000000⟩, + ⟨7, 4, 4, 3, 4, 8, 19944526256294601608520350022378690801089642496000000⟩, + ⟨7, 4, 5, 3, 5, 8, 6729996845074063864714630897549544590934016000000000⟩, + ⟨7, 4, 6, 3, 6, 8, 12355168934491456462846493351373245281028014080000000⟩, + ⟨7, 4, 7, 3, 7, 8, 2442107885849788599064759973916452371965149184000000⟩, + ⟨7, 4, 8, 3, 8, 8, 1841816234822225599253819473852511903809536000000000⟩, + ⟨7, 4, 2, 4, 1, 8, -140807920114451129525843932106138401081965674496000000⟩, + ⟨7, 4, 3, 4, 2, 8, -455346600004745634788529564967844968586752819200000000⟩, + ⟨7, 4, 4, 4, 3, 8, 44578920433770881759058593331164335934086840320000000⟩, + ⟨7, 4, 5, 4, 4, 8, -24245539280249415908199835275579068137907159040000000⟩, + ⟨7, 4, 6, 4, 5, 8, -9829787927003626819390009378697485689469009920000000⟩, + ⟨7, 4, 7, 4, 6, 8, -802050114834250168001024376125952599858872320000000⟩, + ⟨7, 4, 8, 4, 7, 8, 654261864494107898865677414247165721357320192000000⟩, + ⟨7, 4, 2, 5, 0, 8, 1050578474201029604293484700372404595579087224832000000⟩, + ⟨7, 4, 3, 5, 1, 8, 378129977004164579990851031679981238377139666944000000⟩, + ⟨7, 4, 4, 5, 2, 8, -305439672600560011656612059293109629207594401792000000⟩, + ⟨7, 4, 5, 5, 3, 8, 63233760278709982888775345894528156637100769280000000⟩, + ⟨7, 4, 6, 5, 4, 8, -11086832062898653412604358188097277320998420480000000⟩, + ⟨7, 4, 7, 5, 5, 8, -2124183132762946120047966189754624953104203776000000⟩, + ⟨7, 4, 8, 5, 6, 8, 1362344917348439517337641695183903648737394688000000⟩, + ⟨7, 4, 3, 6, 0, 8, 205929778673091058119375913642930403097553403904000000⟩, + ⟨7, 4, 4, 6, 1, 8, 163900794400026840653020095146732126905143656448000000⟩, + ⟨7, 4, 5, 6, 2, 8, 935854884467176454772879815332444486364037120000000⟩, + ⟨7, 4, 6, 6, 3, 8, 41052203000580319309378209679125794587441889280000000⟩, + ⟨7, 4, 7, 6, 4, 8, 760426931025887257082012349341116602569981952000000⟩, + ⟨7, 4, 8, 6, 5, 8, -1429720213666493965082456073681165231845277696000000⟩, + ⟨7, 4, 4, 7, 0, 8, 3127429166926670357011553847164263426043167113216000000⟩, + ⟨7, 4, 5, 7, 1, 8, -43626334586835277660387478205805604161758167040000000⟩, + ⟨7, 4, 6, 7, 2, 8, -40513496525605933546495360030354528878377041920000000⟩, + ⟨7, 4, 7, 7, 3, 8, 31861556613252008803651365941954845262928150528000000⟩, + ⟨7, 4, 8, 7, 4, 8, 2826873896347459039620639790259805641496330240000000⟩ +] + +def collectedFourData_13_3 : List (List CollectedFourTerm) := [ + collectedFourData_13_3_0, + collectedFourData_13_3_1, + collectedFourData_13_3_2, + collectedFourData_13_3_3, + collectedFourData_13_3_4, + collectedFourData_13_3_5, + collectedFourData_13_3_6, + collectedFourData_13_3_7, + collectedFourData_13_3_8, + collectedFourData_13_3_9, + collectedFourData_13_3_10, + collectedFourData_13_3_11, + collectedFourData_13_3_12, + collectedFourData_13_3_13, + collectedFourData_13_3_14, + collectedFourData_13_3_15, + collectedFourData_13_3_16, + collectedFourData_13_3_17, + collectedFourData_13_3_18, + collectedFourData_13_3_19, + collectedFourData_13_3_20, + collectedFourData_13_3_21, + collectedFourData_13_3_22, + collectedFourData_13_3_23, + collectedFourData_13_3_24, + collectedFourData_13_3_25, + collectedFourData_13_3_26, + collectedFourData_13_3_27, + collectedFourData_13_3_28, + collectedFourData_13_3_29, + collectedFourData_13_3_30, + collectedFourData_13_3_31, + collectedFourData_13_3_32, + collectedFourData_13_3_33, + collectedFourData_13_3_34, + collectedFourData_13_3_35, + collectedFourData_13_3_36, + collectedFourData_13_3_37, + collectedFourData_13_3_38, + collectedFourData_13_3_39, + collectedFourData_13_3_40, + collectedFourData_13_3_41, + collectedFourData_13_3_42, + collectedFourData_13_3_43, + collectedFourData_13_3_44, + collectedFourData_13_3_45, + collectedFourData_13_3_46, + collectedFourData_13_3_47, + collectedFourData_13_3_48, + collectedFourData_13_3_49, + collectedFourData_13_3_50, + collectedFourData_13_3_51, + collectedFourData_13_3_52, + collectedFourData_13_3_53, + collectedFourData_13_3_54, + collectedFourData_13_3_55 +] + +theorem collectedFourChecked_13_3 : collectNumericRowParts 13 3 = collectedFourData_13_3 := by + decide +kernel + +def collectedFourData_13_4_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_4_1 : List CollectedFourTerm := [ + ⟨0, 5, 8, 4, 8, 1, -52854057601049778781201074066689416024805081088000000⟩, + ⟨0, 5, 8, 5, 7, 1, 86654345708821972679509120766325126946072874188800000⟩, + ⟨0, 5, 8, 6, 6, 1, -129438760031754621759612475331962077163880762572800000⟩, + ⟨0, 5, 8, 7, 5, 1, -334354017626019895447368668330393863572210843648000000⟩ +] + +def collectedFourData_13_4_2 : List CollectedFourTerm := [ + ⟨0, 6, 7, 3, 8, 2, -15918885862547269828693652529175373712871705804800000⟩, + ⟨0, 6, 7, 4, 7, 2, -42106771896397719734481990479189639608126773657600000⟩, + ⟨0, 6, 8, 4, 8, 2, 45102410067031517106956329800573567057814093824000000⟩, + ⟨0, 6, 7, 5, 6, 2, 13339343712659505953179495108079439588127408128000000⟩, + ⟨0, 6, 8, 5, 7, 2, -73945502230882176704741587495552205659981637222400000⟩, + ⟨0, 6, 7, 6, 5, 2, 83340121255718324614801771485218277639920497459200000⟩, + ⟨0, 6, 8, 6, 6, 2, 110455096514753353785500731339940167168268068454400000⟩, + ⟨0, 6, 7, 7, 4, 2, 64804405984483148315878936462649834561794473984000000⟩, + ⟨0, 6, 8, 7, 5, 2, 285317205433035913154325109653115394643097288704000000⟩ +] + +def collectedFourData_13_4_3 : List CollectedFourTerm := [ + ⟨0, 7, 6, 2, 8, 3, -13408103589461080842479292078689315387524880793600000⟩, + ⟨0, 7, 6, 3, 7, 3, -28428766470795979678396015098702322387963084800000⟩, + ⟨0, 7, 7, 3, 8, 3, 4550011238424178433172065952302591079105744076800000⟩, + ⟨0, 7, 6, 4, 6, 3, -5745135488580692390331901394873653243585285324800000⟩, + ⟨0, 7, 7, 4, 7, 3, 12035156668414996071424829021160048584505792921600000⟩, + ⟨0, 7, 8, 4, 8, 3, -6445692068432588532594119697459524143354478592000000⟩, + ⟨0, 7, 6, 5, 5, 3, -4799378711743585720004678522947799098704946790400000⟩, + ⟨0, 7, 7, 5, 6, 3, -3812714302362090355627340501388315381410562048000000⟩, + ⟨0, 7, 8, 5, 7, 3, 10567726569766244929869529644390758695765750579200000⟩, + ⟨0, 7, 6, 6, 4, 3, 3200025415344715918349534501622063633810220646400000⟩, + ⟨0, 7, 7, 6, 5, 3, -23820667576824654925738256917388737361380324147200000⟩, + ⟨0, 7, 8, 6, 6, 3, -15785399016704040900744113467888614079301104435200000⟩, + ⟨0, 7, 6, 7, 3, 3, 16154338063341831211770150295359244796668202188800000⟩, + ⟨0, 7, 7, 7, 4, 3, -18522701781694858540660016765006156319890079744000000⟩, + ⟨0, 7, 8, 7, 5, 3, -40775356467954529196470116957125332595619397632000000⟩ +] + +def collectedFourData_13_4_4 : List CollectedFourTerm := [ + ⟨0, 8, 5, 1, 8, 4, -56953954437917926552849735709282212175797026816000000⟩, + ⟨0, 8, 5, 2, 7, 4, -29193937330709244704809832166156992341590461644800000⟩, + ⟨0, 8, 6, 2, 8, 4, 51748874512887023613352454342889231577337403801600000⟩, + ⟨0, 8, 5, 3, 6, 4, 19974929137811951578701747624840348779165201203200000⟩, + ⟨0, 8, 6, 3, 7, 4, 109721457537793549203009094675679762730241228800000⟩, + ⟨0, 8, 7, 3, 8, 4, -8780434870540196165825313658503328757512037990400000⟩, + ⟨0, 8, 5, 4, 5, 4, 12111834975147327625749968825418029700997762252800000⟩, + ⟨0, 8, 6, 4, 6, 4, 22173478409861080334745913983900106259912510668800000⟩, + ⟨0, 8, 7, 4, 7, 4, -23224977642113214929415185280818771358619847884800000⟩, + ⟨0, 8, 8, 4, 8, 4, 8292430712329544556507116956991437787872886784000000⟩, + ⟨0, 8, 5, 5, 4, 4, 8034223855487940220968459859174299013966567833600000⟩, + ⟨0, 8, 6, 5, 5, 4, 18523309059832731088348913293074180259155699302400000⟩, + ⟨0, 8, 7, 5, 6, 4, 7357627895324000098582331999363627677063839744000000⟩, + ⟨0, 8, 8, 5, 7, 4, -13595458708895511163947432462882092723563030118400000⟩, + ⟨0, 8, 5, 6, 3, 4, -73212293662749642373625018981654241050543888793600000⟩, + ⟨0, 8, 6, 6, 4, 4, -12350569381555534344861562686874521773338420838400000⟩, + ⟨0, 8, 7, 6, 5, 4, 45968198598018214130182280323855743019921283481600000⟩, + ⟨0, 8, 8, 6, 6, 4, 20308033058787467952201358638080049613321430630400000⟩, + ⟨0, 8, 5, 7, 2, 4, 4055940514310393315358603832197984388152872140800000⟩, + ⟨0, 8, 6, 7, 3, 4, -62348027646184926036255418883095281914287541452800000⟩, + ⟨0, 8, 7, 7, 4, 4, 35744390090108291009502894852826886460546220032000000⟩, + ⟨0, 8, 8, 7, 5, 4, 52457798897500580420804233790811129478448676864000000⟩ +] + +def collectedFourData_13_4_5 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_4_6 : List CollectedFourTerm := [ + ⟨1, 4, 8, 4, 8, 1, -23087465640778367856957289640441582341670830080000000⟩, + ⟨1, 4, 8, 5, 7, 1, 37851951581042313786023662933561381342106615808000000⟩, + ⟨1, 4, 8, 6, 6, 1, -56540842093431550139651910603412795360435765248000000⟩, + ⟨1, 4, 8, 7, 5, 1, -146050979700820886584090583656280058289119559680000000⟩ +] + +def collectedFourData_13_4_7 : List CollectedFourTerm := [ + ⟨1, 5, 7, 3, 8, 2, 7772994406137396357231824702099898132117376204800000⟩, + ⟨1, 5, 7, 4, 7, 2, 20560214153004197175468216071393468800866818457600000⟩, + ⟨1, 5, 8, 4, 8, 2, -22022947094505556412784055408634576036192845824000000⟩, + ⟨1, 5, 7, 5, 6, 2, -6513435987627271637360692902947879916171952128000000⟩, + ⟨1, 5, 8, 5, 7, 2, 36106671042347312166136905074456317185587832422400000⟩, + ⟨1, 5, 7, 6, 5, 2, -40693946920720769500682100700172301564818699059200000⟩, + ⟨1, 5, 8, 6, 6, 2, -53933852830650295728832720625423601791846999654400000⟩, + ⟨1, 5, 7, 7, 4, 2, -31643187190352817063401215875659856339988905984000000⟩, + ⟨1, 5, 8, 7, 5, 2, -139316850497906949332557848694763760012654280704000000⟩ +] + +def collectedFourData_13_4_8 : List CollectedFourTerm := [ + ⟨1, 6, 6, 2, 8, 3, 63577279194952367226978464888468005111840584499200000⟩, + ⟨1, 6, 6, 3, 7, 3, 134800839732663747110724345621283836333234585600000⟩, + ⟨1, 6, 7, 3, 8, 3, -21574813538347077669577071363997839878142925209600000⟩, + ⟨1, 6, 6, 4, 6, 3, 27241740827347296297843501450522664183891859865600000⟩, + ⟨1, 6, 7, 4, 7, 3, -57067169160614127250941770207764512571575710515200000⟩, + ⟨1, 6, 8, 4, 8, 3, 30563573849588672252782886951272951040729677824000000⟩, + ⟨1, 6, 6, 5, 5, 3, 22757240670386040761780250296169860483240479948800000⟩, + ⟨1, 6, 7, 5, 6, 3, 18078768565182725523135373119530311632348512256000000⟩, + ⟨1, 6, 8, 5, 7, 3, -50109047718727354749856795889935625657822635622400000⟩, + ⟨1, 6, 6, 6, 4, 3, -15173578269653847971370967977714740748952063180800000⟩, + ⟨1, 6, 7, 6, 5, 3, 112950591635666337435199040212130708758502729318400000⟩, + ⟨1, 6, 8, 6, 6, 3, 74849714114496733208349353010261207539907978854400000⟩, + ⟨1, 6, 6, 7, 3, 3, -76599114439271008941797408535914900073326680473600000⟩, + ⟨1, 6, 7, 7, 4, 3, 87829197825207771338790771883572446479377235968000000⟩, + ⟨1, 6, 8, 7, 5, 3, 193344734036399931421413739648589380888458952704000000⟩ +] + +def collectedFourData_13_4_9 : List CollectedFourTerm := [ + ⟨1, 7, 5, 1, 8, 4, 66422419902999685821763689632899375946212048896000000⟩, + ⟨1, 7, 5, 2, 7, 4, 34047363052129385505113664088450668598456536268800000⟩, + ⟨1, 7, 6, 2, 8, 4, -60352007271933996383253787080123490478891571609600000⟩, + ⟨1, 7, 5, 3, 6, 4, -23295715702597178918928168096090724656930304819200000⟩, + ⟨1, 7, 6, 3, 7, 4, -127962400449096897887001578259984211260525772800000⟩, + ⟨1, 7, 7, 3, 8, 4, 10240162209240310046068660237995781263523735142400000⟩, + ⟨1, 7, 5, 4, 5, 4, -14125400008738773009762175190958387209024883916800000⟩, + ⟨1, 7, 6, 4, 6, 4, -25859768793672062104878820513466584035652062412800000⟩, + ⟨1, 7, 7, 4, 7, 4, 27086077383156658016094690492079821816593173708800000⟩, + ⟨1, 7, 8, 4, 8, 4, -9671028468993865952984284285770323403372232704000000⟩, + ⟨1, 7, 5, 5, 4, 4, -9369895309124137480297387237116383585193531801600000⟩, + ⟨1, 7, 6, 5, 5, 4, -21602767086285335438568522317527251535039719014400000⟩, + ⟨1, 7, 7, 5, 6, 4, -8580816808531696469275013678121382997303230464000000⟩, + ⟨1, 7, 8, 5, 7, 4, 15855672815844677770242534694614617555185591910400000⟩, + ⟨1, 7, 5, 6, 3, 4, 85383671067645969201376868498958367123666737561600000⟩, + ⟨1, 7, 6, 6, 4, 4, 14403823467552759163022191852831428586294896230400000⟩, + ⟨1, 7, 7, 6, 5, 4, -53610307126088782911741457125582141612485089689600000⟩, + ⟨1, 7, 8, 6, 6, 4, -23684197393266948340152014439010038109335610982400000⟩, + ⟨1, 7, 5, 7, 2, 4, -4730231405385134837524458009947429911223127244800000⟩, + ⟨1, 7, 6, 7, 3, 4, 72713245521044852711570152006009547561429159116800000⟩, + ⟨1, 7, 7, 7, 4, 4, -41686813693152729395488449393500966512012296192000000⟩, + ⟨1, 7, 8, 7, 5, 4, -61178788724056089621883577410051626510984413184000000⟩ +] + +def collectedFourData_13_4_10 : List CollectedFourTerm := [ + ⟨1, 8, 4, 0, 8, 5, -56953954437917926552849735709282212175797026816000000⟩, + ⟨1, 8, 4, 1, 7, 5, 66422419902999685821763689632899375946212048896000000⟩, + ⟨1, 8, 5, 1, 8, 5, 326046494093123283454160351949017954601507225600000000⟩, + ⟨1, 8, 4, 2, 6, 5, -43791850414396710824970525283752646667812208640000000⟩, + ⟨1, 8, 5, 2, 7, 5, 167127656181059991131337234382958863918489927680000000⟩, + ⟨1, 8, 6, 2, 8, 5, -148124386398696292883069160762606993309727457280000000⟩, + ⟨1, 8, 4, 3, 5, 5, -120151477457596849862564666453324471935042584576000000⟩, + ⟨1, 8, 5, 3, 6, 5, -114351245307142334454437338320999700900211589120000000⟩, + ⟨1, 8, 6, 3, 7, 5, -314063324575473388519972219190211041600471040000000⟩, + ⟨1, 8, 7, 3, 8, 5, 16755231100901789208978037113992866572407930880000000⟩, + ⟨1, 8, 4, 4, 4, 5, 90049421509839159076085241830526472219042775040000000⟩, + ⟨1, 8, 5, 4, 5, 5, -69337087646580314546416151010817607146647060480000000⟩, + ⟨1, 8, 6, 4, 6, 5, -63468682453518677062791638705537911991870423040000000⟩, + ⟨1, 8, 7, 4, 7, 5, 44318974338334008132316684713153324403717570560000000⟩, + ⟨1, 8, 8, 4, 8, 5, -11867999280946983949710147496382649874356633600000000⟩, + ⟨1, 8, 4, 5, 3, 5, 85806643923208873307505591625955527995898724352000000⟩, + ⟨1, 8, 5, 5, 4, 5, -45993830396738671246493247166627950744054005760000000⟩, + ⟨1, 8, 6, 5, 5, 5, -53020550000133010224267292372972212114602065920000000⟩, + ⟨1, 8, 7, 5, 6, 5, -14040165157903029589011158969260248239230156800000000⟩, + ⟨1, 8, 8, 5, 7, 5, 19457611378219036647997518873532577011319439360000000⟩, + ⟨1, 8, 4, 6, 2, 5, -108682484161527232776631664988010927107417833472000000⟩, + ⟨1, 8, 5, 6, 3, 5, 419121234141443571086694266211349228053866741760000000⟩, + ⟨1, 8, 6, 6, 4, 5, 35351889843746434291297829016128083911738654720000000⟩, + ⟨1, 8, 7, 6, 5, 5, -87718638331470196659435407049033228414898667520000000⟩, + ⟨1, 8, 8, 6, 6, 5, -29064544534666373736695699869484157797306204160000000⟩, + ⟨1, 8, 4, 7, 1, 5, -104402275012728541099307647770733201966667661312000000⟩, + ⟨1, 8, 5, 7, 2, 5, -23219198701692593893607589337398670697724641280000000⟩, + ⟨1, 8, 6, 7, 3, 5, 178463076254155769607742115981954728939738890240000000⟩, + ⟨1, 8, 7, 7, 4, 5, -68209095033547222649519839795812185460336230400000000⟩, + ⟨1, 8, 8, 7, 5, 5, -75076794873900566726381000610122621827783065600000000⟩ +] + +def collectedFourData_13_4_11 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_4_12 : List CollectedFourTerm := [ + ⟨2, 3, 8, 4, 8, 1, -34872181210130642483062559927039124766338318336000000⟩, + ⟨2, 3, 8, 5, 7, 1, 57173019127737270325742627069000822643200989593600000⟩, + ⟨2, 3, 8, 6, 6, 1, -85401426121583333655816677342921679916521593241600000⟩, + ⟨2, 3, 8, 7, 5, 1, -220600922998165394895124463045924830206970822656000000⟩ +] + +def collectedFourData_13_4_13 : List CollectedFourTerm := [ + ⟨2, 4, 7, 3, 8, 2, 28636701227659590508256031782315067102376388198400000⟩, + ⟨2, 4, 7, 4, 7, 2, 75746447136433471811778704545785426429891890380800000⟩, + ⟨2, 4, 8, 4, 8, 2, -81135341561541550757978999065356405973180219392000000⟩, + ⟨2, 4, 7, 5, 6, 2, -23996327618078957236827834707953364057796378624000000⟩, + ⟨2, 4, 8, 5, 7, 2, 133021574047278631357486715961926297761894052659200000⟩, + ⟨2, 4, 7, 6, 5, 2, -149921682540101905196954984753428985047252834713600000⟩, + ⟨2, 4, 8, 6, 6, 2, -198699181919956017079604453790500063798178820915200000⟩, + ⟨2, 4, 7, 7, 4, 2, -116577531143667906142825305801408956795738652672000000⟩, + ⟨2, 4, 8, 7, 5, 2, -513261018242466926959527537172080684622185234432000000⟩ +] + +def collectedFourData_13_4_14 : List CollectedFourTerm := [ + ⟨2, 5, 6, 2, 8, 3, 27055266649996446355431486302214272292647809843200000⟩, + ⟨2, 5, 6, 3, 7, 3, 57364402972126680737916632447791278176442777600000⟩, + ⟨2, 5, 7, 3, 8, 3, -9181146796390062801603834152468655060142365081600000⟩, + ⟨2, 5, 6, 4, 6, 3, 11592703736722530544210448850045310645030197657600000⟩, + ⟨2, 5, 7, 4, 7, 3, -24284893882710386894745444417485287689907548979200000⟩, + ⟨2, 5, 8, 4, 8, 3, 13006307453671766631678068627787387782251413504000000⟩, + ⟨2, 5, 6, 5, 5, 3, 9684327834594110008180611635868013243981941964800000⟩, + ⟨2, 5, 7, 5, 6, 3, 7693407305693978082926446114585916193349042176000000⟩, + ⟨2, 5, 8, 5, 7, 3, -21323870174601617390418874374150371053729637990400000⟩, + ⟨2, 5, 6, 6, 4, 3, -6457105609399365999494763893419098657130335436800000⟩, + ⟨2, 5, 7, 6, 5, 3, 48066045192138872914572365011089591891422242406400000⟩, + ⟨2, 5, 8, 6, 6, 3, 31852243438006233303826634441551183810534991462400000⟩, + ⟨2, 5, 6, 7, 3, 3, -32596699521432278298952436156429601432986556825600000⟩, + ⟨2, 5, 7, 7, 4, 3, 37375653643966299295767746728260256978308169728000000⟩, + ⟨2, 5, 8, 7, 5, 3, 82277716205615033129522953472269408825176489984000000⟩ +] + +def collectedFourData_13_4_15 : List CollectedFourTerm := [ + ⟨2, 6, 5, 1, 8, 4, -43791850414396710824970525283752646667812208640000000⟩, + ⟨2, 6, 5, 2, 7, 4, -22447195268719394523478059809444683925623406592000000⟩, + ⟨2, 6, 6, 2, 8, 4, 39789668586611665739359909313174183206572785664000000⟩, + ⟨2, 6, 5, 3, 6, 4, 15358707178001759868858385716812784103826915328000000⟩, + ⟨2, 6, 6, 3, 7, 4, 84364741713978326819890511584223995417853952000000⟩, + ⟨2, 6, 7, 3, 8, 4, -6751269410856832124895615265258946566098518016000000⟩, + ⟨2, 6, 5, 4, 5, 4, 9312780310165587997168218063027660630012198912000000⟩, + ⟨2, 6, 6, 4, 6, 4, 17049169970277292927215015773977767851486871552000000⟩, + ⟨2, 6, 7, 4, 7, 4, -17857666896330630087058277620397720731429896192000000⟩, + ⟨2, 6, 8, 4, 8, 4, 6376043400496844734671929639344548319969935360000000⟩, + ⟨2, 6, 5, 5, 4, 4, 6177508352976930197203978802729144260120018944000000⟩, + ⟨2, 6, 6, 5, 5, 4, 14242557650883431510586159637121306690108522496000000⟩, + ⟨2, 6, 7, 5, 6, 4, 5657274255610054765571627307418720111700213760000000⟩, + ⟨2, 6, 8, 5, 7, 4, -10453537422832273038296554208025493110716891136000000⟩, + ⟨2, 6, 5, 6, 3, 4, -56292874554808919981800036505169820325033017344000000⟩, + ⟨2, 6, 6, 6, 4, 4, -9496343005984961399109165359365985443497639936000000⟩, + ⟨2, 6, 7, 6, 5, 4, 35344911458570969311334091550697680372041252864000000⟩, + ⟨2, 6, 8, 6, 6, 4, 15614830518756079289614902032019652090439663616000000⟩, + ⟨2, 6, 5, 7, 2, 4, 3118609445916204933820695191153281689748242432000000⟩, + ⟨2, 6, 6, 7, 3, 4, -47939349027828701931459166310129191088566566912000000⟩, + ⟨2, 6, 7, 7, 4, 4, 27483833202242695876383878521106622156405473280000000⟩, + ⟨2, 6, 8, 7, 5, 4, 40334759983907976833056499643823308214433218560000000⟩ +] + +def collectedFourData_13_4_16 : List CollectedFourTerm := [ + ⟨2, 7, 4, 0, 8, 5, -29193937330709244704809832166156992341590461644800000⟩, + ⟨2, 7, 4, 1, 7, 5, 34047363052129385505113664088450668598456536268800000⟩, + ⟨2, 7, 5, 1, 8, 5, 167127656181059991131337234382958863918489927680000000⟩, + ⟨2, 7, 4, 2, 6, 5, -22447195268719394523478059809444683925623406592000000⟩, + ⟨2, 7, 5, 2, 7, 5, 85667700670312812155917179874227559490654306304000000⟩, + ⟨2, 7, 6, 2, 8, 5, -75926844700256877757800755459060103037461725184000000⟩, + ⟨2, 7, 4, 3, 5, 5, -61588255595364033480910682363713850141009824972800000⟩, + ⟨2, 7, 5, 3, 6, 5, -58615123780811766957277821185444466516333428736000000⟩, + ⟨2, 7, 6, 3, 7, 5, -160985222290839578200503200727069962966925312000000⟩, + ⟨2, 7, 7, 3, 8, 5, 8588537381622403552635355169642393935244427264000000⟩, + ⟨2, 7, 4, 4, 4, 5, 46158290397385274423210396102567654982798016512000000⟩, + ⟨2, 7, 5, 4, 5, 5, -35541387976047263104139015854044175444312326144000000⟩, + ⟨2, 7, 6, 4, 6, 5, -32533311449522704415465050232261687105827110912000000⟩, + ⟨2, 7, 7, 4, 7, 5, 22717392886300407842438767344587644266419847168000000⟩, + ⟨2, 7, 8, 4, 8, 5, -6083398960936744949435338387489226871621550080000000⟩, + ⟨2, 7, 4, 5, 3, 5, 43983491751801526847038109521030820303717636505600000⟩, + ⟨2, 7, 5, 5, 4, 5, -23575904701495305873478057636284986797722697728000000⟩, + ⟨2, 7, 6, 5, 5, 5, -27177719777664750774211108920508088291243851776000000⟩, + ⟨2, 7, 7, 5, 6, 5, -7196826028637263369093132808250814584890327040000000⟩, + ⟨2, 7, 8, 5, 7, 5, 9973746209320944263197064286339884367696887808000000⟩, + ⟨2, 7, 4, 6, 2, 5, -55709382480473416152597185396235988458035321241600000⟩, + ⟨2, 7, 5, 6, 3, 5, 214836689818128899942430702023240265017252118528000000⟩, + ⟨2, 7, 6, 6, 4, 5, 18120969242714434855398107205393223769093308416000000⟩, + ⟨2, 7, 7, 6, 5, 5, -44963557938290686631043597739743088158500192256000000⟩, + ⟨2, 7, 8, 6, 6, 5, -14898148865423663842801014520275370661010997248000000⟩, + ⟨2, 7, 4, 7, 1, 5, -53515396849702781211707367620164032007738333593600000⟩, + ⟨2, 7, 5, 7, 2, 5, -11901892299776887251947436560485760512907280384000000⟩, + ⟨2, 7, 6, 7, 3, 5, 91478105698324409740384689477365553722736771072000000⟩, + ⟨2, 7, 7, 7, 4, 5, -34963192028471987148082391492797338227960709120000000⟩, + ⟨2, 7, 8, 7, 5, 5, -38483495416078639557924335853003631675236679680000000⟩ +] + +def collectedFourData_13_4_17 : List CollectedFourTerm := [ + ⟨2, 8, 3, 0, 7, 6, -13408103589461080842479292078689315387524880793600000⟩, + ⟨2, 8, 4, 0, 8, 6, 51748874512887023613352454342889231577337403801600000⟩, + ⟨2, 8, 3, 1, 6, 6, 63577279194952367226978464888468005111840584499200000⟩, + ⟨2, 8, 4, 1, 7, 6, -60352007271933996383253787080123490478891571609600000⟩, + ⟨2, 8, 5, 1, 8, 6, -148124386398696292883069160762606993309727457280000000⟩, + ⟨2, 8, 3, 2, 5, 6, 27055266649996446355431486302214272292647809843200000⟩, + ⟨2, 8, 4, 2, 6, 6, 39789668586611665739359909313174183206572785664000000⟩, + ⟨2, 8, 5, 2, 7, 6, -75926844700256877757800755459060103037461725184000000⟩, + ⟨2, 8, 6, 2, 8, 6, 44862382601837730069933773171302589805442891776000000⟩, + ⟨2, 8, 3, 3, 4, 6, -2947906436412534492478221491378971186030863974400000⟩, + ⟨2, 8, 4, 3, 5, 6, 109170711513433145590672662143105956928403642777600000⟩, + ⟨2, 8, 5, 3, 6, 6, 51950284244459553216263924219625454345604038656000000⟩, + ⟨2, 8, 6, 3, 7, 6, 95120252450436765471192203115569279787859968000000⟩, + ⟨2, 8, 7, 3, 8, 6, -3805988364776861904512984272334821425175068672000000⟩, + ⟨2, 8, 3, 4, 3, 6, -43534595585937714343828642545346509248933344051200000⟩, + ⟨2, 8, 4, 4, 4, 6, -81819713128967605216547841762575501107925090304000000⟩, + ⟨2, 8, 5, 4, 5, 6, 31500150280373622028479475288959411016458829824000000⟩, + ⟨2, 8, 6, 4, 6, 6, 19222738299149914545119174243380847740471738368000000⟩, + ⟨2, 8, 7, 4, 7, 6, -10067154529516761221382755230501863618263384064000000⟩, + ⟨2, 8, 8, 4, 8, 6, 2156674146931142119378646461871614266622083072000000⟩, + ⟨2, 8, 3, 5, 2, 6, -54361103473390968076976791523898745521544416460800000⟩, + ⟨2, 8, 4, 5, 3, 6, -77964687308838674446896432277939568828990305075200000⟩, + ⟨2, 8, 5, 5, 4, 6, 20895203687412727645216283731495670337805221888000000⟩, + ⟨2, 8, 6, 5, 5, 6, 16058315971439325101220147505692297621525233664000000⟩, + ⟨2, 8, 7, 5, 6, 6, 3189255039737911279591667111579509990537297920000000⟩, + ⟨2, 8, 8, 5, 7, 6, -3535872089898695312624045874800387318965547827200000⟩, + ⟨2, 8, 3, 6, 1, 6, -13234859653495949936693501141692307754935805542400000⟩, + ⟨2, 8, 4, 6, 2, 6, 98749881200159711729995543071083505526135534387200000⟩, + ⟨2, 8, 5, 6, 3, 6, -190408658760594337014232741886275241555093618688000000⟩, + ⟨2, 8, 6, 6, 4, 6, -10707014870592117403327704236954926142271258624000000⟩, + ⟨2, 8, 7, 6, 5, 6, 19925485650011513359027755796578388618707468288000000⟩, + ⟨2, 8, 8, 6, 6, 6, 5281661239302176815506510767180456110465430323200000⟩, + ⟨2, 8, 3, 7, 0, 6, 1391116638472181242842133612336923779523625038643200000⟩, + ⟨2, 8, 4, 7, 1, 6, 94860844726467021510510838595202787723634225971200000⟩, + ⟨2, 8, 5, 7, 2, 6, 10548586237444105413653124123425698142553636864000000⟩, + ⟨2, 8, 6, 7, 3, 6, -54051051294585107412100436975557944200405188608000000⟩, + ⟨2, 8, 7, 7, 4, 6, 15493849085475626809506807903459822582638837760000000⟩, + ⟨2, 8, 8, 7, 5, 6, 13643090019303915988764866152881312947830259712000000⟩ +] + +def collectedFourData_13_4_18 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_4_19 : List CollectedFourTerm := [ + ⟨3, 2, 8, 4, 8, 1, 89859023082708251148969184183843927650421702656000000⟩, + ⟨3, 2, 8, 5, 7, 1, -147324069422275663693009078612979988456753699225600000⟩, + ⟨3, 2, 8, 6, 6, 1, 220063341461593952131770593033179472833558452633600000⟩, + ⟨3, 2, 8, 7, 5, 1, 568446903631028315757371748602918264432152805376000000⟩ +] + +def collectedFourData_13_4_20 : List CollectedFourTerm := [ + ⟨3, 3, 7, 3, 8, 2, -32619993467018065979810637212276321795677618176000000⟩, + ⟨3, 3, 7, 4, 7, 2, -86282585102845161859166759581799919950455898112000000⟩, + ⟨3, 3, 8, 4, 8, 2, 92421061023796834928743167704889197299897466880000000⟩, + ⟨3, 3, 7, 5, 6, 2, 27334155701499208286371825364947704625873551360000000⟩, + ⟨3, 3, 8, 5, 7, 2, -151524536359780931800068602302964841796482367488000000⟩, + ⟨3, 3, 7, 6, 5, 2, 170775406920783975314139650627572201910125461504000000⟩, + ⟨3, 3, 8, 6, 6, 2, 226337732289862719864120107298143491296306659328000000⟩, + ⟨3, 3, 7, 7, 4, 2, 132793168950428464457981470631795500955813806080000000⟩, + ⟨3, 3, 8, 7, 5, 2, 584654319254237722154991250021426862538337812480000000⟩ +] + +def collectedFourData_13_4_21 : List CollectedFourTerm := [ + ⟨3, 4, 6, 2, 8, 3, -2947906436412534492478221491378971186030863974400000⟩, + ⟨3, 4, 6, 3, 7, 3, -6250350252693472423945632158102604322386739200000⟩, + ⟨3, 4, 7, 3, 8, 3, 1000365735989896162327166907735845259147686707200000⟩, + ⟨3, 4, 6, 4, 6, 3, -1263125823264154603709476569234730589942395699200000⟩, + ⟨3, 4, 7, 4, 7, 3, 2646050246355518294104394680243795751711696486400000⟩, + ⟨3, 4, 8, 4, 8, 3, -1417150233728868430045980346251463134824890368000000⟩, + ⟨3, 4, 6, 5, 5, 3, -1055191683203491523719223425373050825753598361600000⟩, + ⟨3, 4, 7, 5, 6, 3, -838263588668104005037901635152088762461192192000000⟩, + ⟨3, 4, 8, 5, 7, 3, 2323420979365643776189497675090968186303859916800000⟩, + ⟨3, 4, 6, 6, 4, 3, 703557774269667828387313298694433522597861785600000⟩, + ⟨3, 4, 7, 6, 5, 3, -5237213361370458081374851378372027161487658188800000⟩, + ⟨3, 4, 8, 6, 6, 3, -3470578747561145343536084171027777455108443340800000⟩, + ⟨3, 4, 6, 7, 3, 3, 3551693707851451446929949200468480223415055155200000⟩, + ⟨3, 4, 7, 7, 4, 3, -4072402292963108698041260154918006614157950976000000⟩, + ⟨3, 4, 8, 7, 5, 3, -8964872248852454365575399983910367011985686528000000⟩ +] + +def collectedFourData_13_4_22 : List CollectedFourTerm := [ + ⟨3, 5, 5, 1, 8, 4, -120151477457596849862564666453324471935042584576000000⟩, + ⟨3, 5, 5, 2, 7, 4, -61588255595364033480910682363713850141009824972800000⟩, + ⟨3, 5, 6, 2, 8, 4, 109170711513433145590672662143105956928403642777600000⟩, + ⟨3, 5, 5, 3, 6, 4, 42139606840382283674838579023301664140757775155200000⟩, + ⟨3, 5, 6, 3, 7, 4, 231471113148729264037850681092806854035950796800000⟩, + ⟨3, 5, 7, 3, 8, 4, -18523423576594321248598487042504541685315692134400000⟩, + ⟨3, 5, 5, 4, 5, 4, 25551428014938503843879679871903434041040096460800000⟩, + ⟨3, 5, 6, 4, 6, 4, 46777721013612706200072625627827261614930578636800000⟩, + ⟨3, 5, 7, 4, 7, 4, -48995989921320203095966271339714659292652817612800000⟩, + ⟨3, 5, 8, 4, 8, 4, 17493917878647140392820480052010698611594625024000000⟩, + ⟨3, 5, 5, 5, 4, 4, 16949198277604893492331546486834229359421266329600000⟩, + ⟨3, 5, 6, 5, 5, 4, 39077233054442032477593454199797813867327153766400000⟩, + ⟨3, 5, 7, 5, 6, 4, 15521834628182579142513416137858173423618883584000000⟩, + ⟨3, 5, 8, 5, 7, 4, -28681317508306529316715881592038565228065482342400000⟩, + ⟨3, 5, 5, 6, 3, 4, -154450473868806248148589343256562148106116372889600000⟩, + ⟨3, 5, 6, 6, 4, 4, -26055068050700646264383553888293258319293212262400000⟩, + ⟨3, 5, 7, 6, 5, 4, 96975653966864939029122299293074086065170127257600000⟩, + ⟨3, 5, 8, 6, 6, 4, 42842331148941989746978459158283377091222595174400000⟩, + ⟨3, 5, 5, 7, 2, 4, 8556512889824446826553872851770965356517838028800000⟩, + ⟨3, 5, 6, 7, 3, 4, -131530948328125790090838914181676561152135187660800000⟩, + ⟨3, 5, 7, 7, 4, 4, 75407253500345322123086974550445690591538839552000000⟩, + ⟨3, 5, 8, 7, 5, 4, 110666276010361699248380934429993335035898363904000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1309.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1309.lean new file mode 100644 index 0000000000000000000000000000000000000000..9edf88f0087e38270626f63c278ed45dd69671d1 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1309.lean @@ -0,0 +1,611 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1309. -/ +namespace LaughlinFock +def collectedFourData_13_4_23 : List CollectedFourTerm := [ + ⟨3, 6, 4, 0, 8, 5, 19974929137811951578701747624840348779165201203200000⟩, + ⟨3, 6, 4, 1, 7, 5, -23295715702597178918928168096090724656930304819200000⟩, + ⟨3, 6, 5, 1, 8, 5, -114351245307142334454437338320999700900211589120000000⟩, + ⟨3, 6, 4, 2, 6, 5, 15358707178001759868858385716812784103826915328000000⟩, + ⟨3, 6, 5, 2, 7, 5, -58615123780811766957277821185444466516333428736000000⟩, + ⟨3, 6, 6, 2, 8, 5, 51950284244459553216263924219625454345604038656000000⟩, + ⟨3, 6, 4, 3, 5, 5, 42139606840382283674838579023301664140757775155200000⟩, + ⟨3, 6, 5, 3, 6, 5, 40105345526455807584889529408812290676698906624000000⟩, + ⟨3, 6, 6, 3, 7, 5, 110148500048736089541177649993691106071543808000000⟩, + ⟨3, 6, 7, 3, 8, 5, -5876405900717493380083871649791585705709797376000000⟩, + ⟨3, 6, 4, 4, 4, 5, -31582193568678090325077533123957963883552964608000000⟩, + ⟨3, 6, 5, 4, 5, 5, 24317949930454908006215433266954478827964727296000000⟩, + ⟨3, 6, 6, 4, 6, 5, 22259778921255724173783750673774351986834014208000000⟩, + ⟨3, 6, 7, 4, 7, 5, -15543580434501801598817667706642217836858048512000000⟩, + ⟨3, 6, 8, 4, 8, 5, 4162352675667616441370582333040640358319390720000000⟩, + ⟨3, 6, 4, 5, 3, 5, -30094163765008939618994082021905251822123509350400000⟩, + ⟨3, 6, 5, 5, 4, 5, 16130987075758566363810425927173734950661783552000000⟩, + ⟨3, 6, 6, 5, 5, 5, 18595402892610617709414390760574132075819433984000000⟩, + ⟨3, 6, 7, 5, 6, 5, 4924176150367090510933707471691117338411663360000000⟩, + ⟨3, 6, 8, 5, 7, 5, -6824186525883263289494752050813894133674934272000000⟩, + ⟨3, 6, 4, 6, 2, 5, 38117193811612689278896366832136130794088719974400000⟩, + ⟨3, 6, 5, 6, 3, 5, -146994480624753609646915211589483057090240970752000000⟩, + ⟨3, 6, 6, 6, 4, 5, -12398638540301924756383916778819612950076063744000000⟩, + ⟨3, 6, 7, 6, 5, 5, 30764739727535709807855656168264405962199138304000000⟩, + ⟨3, 6, 8, 6, 6, 5, 10193536572347690875742891796750554234703839232000000⟩, + ⟨3, 6, 4, 7, 1, 5, 36616035985329296298072011337963334806863767142400000⟩, + ⟨3, 6, 5, 7, 2, 5, 8143452957399951475525307106863097263167635456000000⟩, + ⟨3, 6, 6, 7, 3, 5, -62590689919142525649327705833538360132551835648000000⟩, + ⟨3, 6, 7, 7, 4, 5, 23922339603908194590405947773067781688346542080000000⟩, + ⟨3, 6, 8, 7, 5, 5, 26330983902704938071487040785657907698068357120000000⟩ +] + +def collectedFourData_13_4_24 : List CollectedFourTerm := [ + ⟨3, 7, 3, 0, 7, 6, -28428766470795979678396015098702322387963084800000⟩, + ⟨3, 7, 4, 0, 8, 6, 109721457537793549203009094675679762730241228800000⟩, + ⟨3, 7, 3, 1, 6, 6, 134800839732663747110724345621283836333234585600000⟩, + ⟨3, 7, 4, 1, 7, 6, -127962400449096897887001578259984211260525772800000⟩, + ⟨3, 7, 5, 1, 8, 6, -314063324575473388519972219190211041600471040000000⟩, + ⟨3, 7, 3, 2, 5, 6, 57364402972126680737916632447791278176442777600000⟩, + ⟨3, 7, 4, 2, 6, 6, 84364741713978326819890511584223995417853952000000⟩, + ⟨3, 7, 5, 2, 7, 6, -160985222290839578200503200727069962966925312000000⟩, + ⟨3, 7, 6, 2, 8, 6, 95120252450436765471192203115569279787859968000000⟩, + ⟨3, 7, 3, 3, 4, 6, -6250350252693472423945632158102604322386739200000⟩, + ⟨3, 7, 4, 3, 5, 6, 231471113148729264037850681092806854035950796800000⟩, + ⟨3, 7, 5, 3, 6, 6, 110148500048736089541177649993691106071543808000000⟩, + ⟨3, 7, 6, 3, 7, 6, 201680381234682515171452323995648130023424000000⟩, + ⟨3, 7, 7, 3, 8, 6, -8069713490120566209985732815090288055812096000000⟩, + ⟨3, 7, 3, 4, 3, 6, -92304988774547025797941819899784525042522521600000⟩, + ⟨3, 7, 4, 4, 4, 6, -173479679787022841215759637062389423220457472000000⟩, + ⟨3, 7, 5, 4, 5, 6, 66788745339020306514148774131541626775928832000000⟩, + ⟨3, 7, 6, 4, 6, 6, 40757347554004372409497480338213472907034624000000⟩, + ⟨3, 7, 7, 4, 7, 6, -21345060711643207052083729958940544075825152000000⟩, + ⟨3, 7, 8, 4, 8, 6, 4572726132940989978674018840588329257271296000000⟩, + ⟨3, 7, 3, 5, 2, 6, -115260081742993446717270058656690652540462694400000⟩, + ⟨3, 7, 4, 5, 3, 6, -165305993773329157011901958035520299554412953600000⟩, + ⟨3, 7, 5, 5, 4, 6, 44303421585740257014151293538049023209897984000000⟩, + ⟨3, 7, 6, 5, 5, 6, 34047925690634594484666344626543320945917952000000⟩, + ⟨3, 7, 7, 5, 6, 6, 6762073855976409794392067778372457526722560000000⟩, + ⟨3, 7, 8, 5, 7, 6, -7496994727378565204809526541264261133998489600000⟩, + ⟨3, 7, 3, 6, 1, 6, -28061442981297775637335548780390267772678963200000⟩, + ⟨3, 7, 4, 6, 2, 6, 209376165162147549956989254333201238982236569600000⟩, + ⟨3, 7, 5, 6, 3, 6, -403717293635556439798418091062719988455440384000000⟩, + ⟨3, 7, 6, 6, 4, 6, -22701735806594968503703902140936468910047232000000⟩, + ⟨3, 7, 7, 6, 5, 6, 42247359932885308158420230095883867661533184000000⟩, + ⟨3, 7, 8, 6, 6, 6, 11198534747896556963962276514641535825451417600000⟩, + ⟨3, 7, 3, 7, 0, 6, 2949539417330375951893851225048581011676961177600000⟩, + ⟨3, 7, 4, 7, 1, 6, 201130367464558222102933271375615300585757081600000⟩, + ⟨3, 7, 5, 7, 2, 6, 22365824722376289023007142212689059802775552000000⟩, + ⟨3, 7, 6, 7, 3, 6, -114602688180494309318558906575265741295058944000000⟩, + ⟨3, 7, 7, 7, 4, 6, 32851104889356433009711694622428657017159680000000⟩, + ⟨3, 7, 8, 7, 5, 6, 28927000564322740049826449151988516641570816000000⟩ +] + +def collectedFourData_13_4_25 : List CollectedFourTerm := [ + ⟨3, 8, 2, 0, 6, 7, -15918885862547269828693652529175373712871705804800000⟩, + ⟨3, 8, 3, 0, 7, 7, 4550011238424178433172065952302591079105744076800000⟩, + ⟨3, 8, 4, 0, 8, 7, -8780434870540196165825313658503328757512037990400000⟩, + ⟨3, 8, 2, 1, 5, 7, 7772994406137396357231824702099898132117376204800000⟩, + ⟨3, 8, 3, 1, 6, 7, -21574813538347077669577071363997839878142925209600000⟩, + ⟨3, 8, 4, 1, 7, 7, 10240162209240310046068660237995781263523735142400000⟩, + ⟨3, 8, 5, 1, 8, 7, 16755231100901789208978037113992866572407930880000000⟩, + ⟨3, 8, 2, 2, 4, 7, 28636701227659590508256031782315067102376388198400000⟩, + ⟨3, 8, 3, 2, 5, 7, -9181146796390062801603834152468655060142365081600000⟩, + ⟨3, 8, 4, 2, 6, 7, -6751269410856832124895615265258946566098518016000000⟩, + ⟨3, 8, 5, 2, 7, 7, 8588537381622403552635355169642393935244427264000000⟩, + ⟨3, 8, 6, 2, 8, 7, -3805988364776861904512984272334821425175068672000000⟩, + ⟨3, 8, 2, 3, 3, 7, -32619993467018065979810637212276321795677618176000000⟩, + ⟨3, 8, 3, 3, 4, 7, 1000365735989896162327166907735845259147686707200000⟩, + ⟨3, 8, 4, 3, 5, 7, -18523423576594321248598487042504541685315692134400000⟩, + ⟨3, 8, 5, 3, 6, 7, -5876405900717493380083871649791585705709797376000000⟩, + ⟨3, 8, 6, 3, 7, 7, -8069713490120566209985732815090288055812096000000⟩, + ⟨3, 8, 7, 3, 8, 7, 258310800144145163232755682998765128879649587200000⟩, + ⟨3, 8, 2, 4, 2, 7, 7777767131702499308055043078956026438986235904000000⟩, + ⟨3, 8, 3, 4, 3, 7, 14773371778837061076857908493141862935235762585600000⟩, + ⟨3, 8, 4, 4, 4, 7, 13882672213021296504512934404492504702361010176000000⟩, + ⟨3, 8, 5, 4, 5, 7, -3563169512413532310081632332054356717106888704000000⟩, + ⟨3, 8, 6, 4, 6, 7, -1630798768648506220893267631871168603693776896000000⟩, + ⟨3, 8, 7, 4, 7, 7, 683253465974978017197245160782574458677651046400000⟩, + ⟨3, 8, 8, 4, 8, 7, -121977125508246332770540885849422829354745856000000⟩, + ⟨3, 8, 2, 5, 1, 7, -8055449862911184332453695666716783094107262156800000⟩, + ⟨3, 8, 3, 5, 2, 7, 18447324044504205888773782098220422811710023270400000⟩, + ⟨3, 8, 4, 5, 3, 7, 13228574834933131254928611687961175634675027148800000⟩, + ⟨3, 8, 5, 5, 4, 7, -2363580874122000070534631405635330078773608448000000⟩, + ⟨3, 8, 6, 5, 5, 7, -1362338783645095805677495101838321014703915008000000⟩, + ⟨3, 8, 7, 5, 6, 7, -216453373531725532425758215164171609798868992000000⟩, + ⟨3, 8, 8, 5, 7, 7, 199981770219851733207530763363898854762715545600000⟩, + ⟨3, 8, 2, 6, 0, 7, 145014858857148767072362720867175054262010065715200000⟩, + ⟨3, 8, 3, 6, 1, 7, 4491221279771877524616190587377359424167555891200000⟩, + ⟨3, 8, 4, 6, 2, 7, -16755280351762208781984860147234128567957507276800000⟩, + ⟨3, 8, 5, 6, 3, 7, 21538256857714724970787970699743029593005621248000000⟩, + ⟨3, 8, 6, 6, 4, 7, 908350641575089533990510712488854324540080128000000⟩, + ⟨3, 8, 7, 6, 5, 7, -1352334176622453673509199823470802114444053708800000⟩, + ⟨3, 8, 8, 6, 6, 7, -298720071734124015095105424456966450114566553600000⟩, + ⟨3, 8, 3, 7, 0, 7, -472072452064169827131115813316796641469804419481600000⟩, + ⟨3, 8, 4, 7, 1, 7, -16095412252449049001445703694157337883325549772800000⟩, + ⟨3, 8, 5, 7, 2, 7, -1193213382976914472179205226582222911039340544000000⟩, + ⟨3, 8, 6, 7, 3, 7, 4585527125407764156131243513090045773847986176000000⟩, + ⟨3, 8, 7, 7, 4, 7, -1051560901137038616239449951225177484480741376000000⟩, + ⟨3, 8, 8, 7, 5, 7, -771625563357796000160764956769453702775832576000000⟩ +] + +def collectedFourData_13_4_26 : List CollectedFourTerm := [ + +] + +def collectedFourData_13_4_27 : List CollectedFourTerm := [ + ⟨4, 1, 8, 4, 8, 1, -40455280955570304557351106348636765004033425408000000⟩, + ⟨4, 1, 8, 5, 7, 1, 66326523653727632028319065244780029328973679820800000⟩, + ⟨4, 1, 8, 6, 6, 1, -99074350036680463095023948607472193691770997964800000⟩, + ⟨4, 1, 8, 7, 5, 1, -255919532683441161453190395672854225675372986368000000⟩ +] + +def collectedFourData_13_4_28 : List CollectedFourTerm := [ + ⟨4, 2, 7, 3, 8, 2, 7777767131702499308055043078956026438986235904000000⟩, + ⟨4, 2, 7, 4, 7, 2, 20572838407517304066516889179240189163468750848000000⟩, + ⟨4, 2, 8, 4, 8, 2, -22036469487180104607121759789668287328571883520000000⟩, + ⟨4, 2, 7, 5, 6, 2, -6517435326984863961861417645385982682794557440000000⟩, + ⟨4, 2, 8, 5, 7, 2, 36128841035396388258525777429157646301294231552000000⟩, + ⟨4, 2, 7, 6, 5, 2, -40718933564305655344011737289875386596449058816000000⟩, + ⟨4, 2, 8, 6, 6, 2, -53966968958718791187001950473082429994709286912000000⟩, + ⟨4, 2, 7, 7, 4, 2, -31662616542874348465269940164850762054442680320000000⟩, + ⟨4, 2, 8, 7, 5, 2, -139402392961889166823115221718443986173999185920000000⟩ +] + +def collectedFourData_13_4_29 : List CollectedFourTerm := [ + ⟨4, 3, 6, 2, 8, 3, -43534595585937714343828642545346509248933344051200000⟩, + ⟨4, 3, 6, 3, 7, 3, -92304988774547025797941819899784525042522521600000⟩, + ⟨4, 3, 7, 3, 8, 3, 14773371778837061076857908493141862935235762585600000⟩, + ⟨4, 3, 6, 4, 6, 3, -18653805022685688968088342776919802517527304601600000⟩, + ⟨4, 3, 7, 4, 7, 3, 39076792245599555955746582267324066484230239027200000⟩, + ⟨4, 3, 8, 4, 8, 3, -20928432988186499980933351576365112251346059264000000⟩, + ⟨4, 3, 6, 5, 5, 3, -15583039755431494205383101110968888215697411276800000⟩, + ⟨4, 3, 7, 5, 6, 3, -12379452032912416857144509917204599556974575616000000⟩, + ⟨4, 3, 8, 5, 7, 3, 34312212715835213692702739674091828729386264166400000⟩, + ⟨4, 3, 6, 6, 4, 3, 10390120526161150102297292613100103435518004428800000⟩, + ⟨4, 3, 7, 6, 5, 3, -77343012949216174999305801062656685538586027622400000⟩, + ⟨4, 3, 8, 6, 6, 3, -51253404910670944266231055712820797166886217318400000⟩, + ⟨4, 3, 6, 7, 3, 3, 52451308259498158068218231211957446180727265689600000⟩, + ⟨4, 3, 7, 7, 4, 3, -60141117335850239047531343259622781764446978048000000⟩, + ⟨4, 3, 8, 7, 5, 3, -132392969808208290037743708973611399902285266944000000⟩ +] + +def collectedFourData_13_4_30 : List CollectedFourTerm := [ + ⟨4, 4, 5, 1, 8, 4, 90049421509839159076085241830526472219042775040000000⟩, + ⟨4, 4, 5, 2, 7, 4, 46158290397385274423210396102567654982798016512000000⟩, + ⟨4, 4, 6, 2, 8, 4, -81819713128967605216547841762575501107925090304000000⟩, + ⟨4, 4, 5, 3, 6, 4, -31582193568678090325077533123957963883552964608000000⟩, + ⟨4, 4, 6, 3, 7, 4, -173479679787022841215759637062389423220457472000000⟩, + ⟨4, 4, 7, 3, 8, 4, 13882672213021296504512934404492504702361010176000000⟩, + ⟨4, 4, 5, 4, 5, 4, -19149921084470452499777636457251920148044972032000000⟩, + ⟨4, 4, 6, 4, 6, 4, -35058301453771583264495585223887365979422851072000000⟩, + ⟨4, 4, 7, 4, 7, 4, 36720818104578634975490100466613438058816602112000000⟩, + ⟨4, 4, 8, 4, 8, 4, -13111092915763431017714529824359241982368808960000000⟩, + ⟨4, 4, 5, 5, 4, 4, -12702844211737001177549151953519096914073616384000000⟩, + ⟨4, 4, 6, 5, 5, 4, -29287049191713296127599320038971913990838419456000000⟩, + ⟨4, 4, 7, 5, 6, 4, -11633083992100805046688851811258397894230671360000000⟩, + ⟨4, 4, 8, 5, 7, 4, 21495666174180075440245335933625820775758954496000000⟩, + ⟨4, 4, 5, 6, 3, 4, 115755345819321478016159093551083656813985398784000000⟩, + ⟨4, 4, 6, 6, 4, 4, 19527382059809529502840359769383174697748791296000000⟩, + ⟨4, 4, 7, 6, 5, 4, -72679934737684644774789884480387044902388629504000000⟩, + ⟨4, 4, 8, 6, 6, 4, -32108861395039490010558251283966632324052811776000000⟩, + ⟨4, 4, 5, 7, 2, 4, -6412813659674697426528325348476161456710090752000000⟩, + ⟨4, 4, 6, 7, 3, 4, 98577945591790903512675454092803483050319020032000000⟩, + ⟨4, 4, 7, 7, 4, 4, -56515156526046972142397043802290654313269166080000000⟩, + ⟨4, 4, 8, 7, 5, 4, -82940587550396159743305203814599490170687324160000000⟩ +] + +def collectedFourData_13_4_31 : List CollectedFourTerm := [ + ⟨4, 5, 4, 0, 8, 5, 12111834975147327625749968825418029700997762252800000⟩, + ⟨4, 5, 4, 1, 7, 5, -14125400008738773009762175190958387209024883916800000⟩, + ⟨4, 5, 5, 1, 8, 5, -69337087646580314546416151010817607146647060480000000⟩, + ⟨4, 5, 4, 2, 6, 5, 9312780310165587997168218063027660630012198912000000⟩, + ⟨4, 5, 5, 2, 7, 5, -35541387976047263104139015854044175444312326144000000⟩, + ⟨4, 5, 6, 2, 8, 5, 31500150280373622028479475288959411016458829824000000⟩, + ⟨4, 5, 4, 3, 5, 5, 25551428014938503843879679871903434041040096460800000⟩, + ⟨4, 5, 5, 3, 6, 5, 24317949930454908006215433266954478827964727296000000⟩, + ⟨4, 5, 6, 3, 7, 5, 66788745339020306514148774131541626775928832000000⟩, + ⟨4, 5, 7, 3, 8, 5, -3563169512413532310081632332054356717106888704000000⟩, + ⟨4, 5, 4, 4, 4, 5, -19149921084470452499777636457251920148044972032000000⟩, + ⟨4, 5, 5, 4, 5, 5, 14745233610567319559448704835927867265734672384000000⟩, + ⟨4, 5, 6, 4, 6, 5, 13497257838434814344999352295903925094089490432000000⟩, + ⟨4, 5, 7, 4, 7, 5, -9424878548842587119979257766942714094260584448000000⟩, + ⟨4, 5, 8, 4, 8, 5, 2523850190818319180897515429178557061796986880000000⟩, + ⟨4, 5, 4, 5, 3, 5, -18247651479617384153273784442328673400768797081600000⟩, + ⟨4, 5, 5, 5, 4, 5, 9781053644790228164686716340126648294711492608000000⟩, + ⟨4, 5, 6, 5, 5, 5, 11275356702284055843177790967776384529240948736000000⟩, + ⟨4, 5, 7, 5, 6, 5, 2985783254114487009180432316153853187131965440000000⟩, + ⟨4, 5, 8, 5, 7, 5, -4137858035484168732198407222038473956275519488000000⟩, + ⟨4, 5, 4, 6, 2, 5, 23112430486075354551364562512868987699155540377600000⟩, + ⟨4, 5, 5, 6, 3, 5, -89130373344569899214877004892127909597998481408000000⟩, + ⟨4, 5, 6, 6, 4, 5, -7517937254273937917133318427018982515619659776000000⟩, + ⟨4, 5, 7, 6, 5, 5, 18654256446292849930025537150001507491188310016000000⟩, + ⟨4, 5, 8, 6, 6, 5, 6180869625399242431385953318852091533043171328000000⟩, + ⟨4, 5, 4, 7, 1, 5, 22202200680594955121314807004024056456758794649600000⟩, + ⟨4, 5, 5, 7, 2, 5, 4937797659627032514620860467913855017915777024000000⟩, + ⟨4, 5, 6, 7, 3, 5, -37951979806838627484147264478367920294767624192000000⟩, + ⟨4, 5, 7, 7, 4, 5, 14505354562359451632875970356378398055800504320000000⟩, + ⟨4, 5, 8, 7, 5, 5, 15965840457432380127536044135804936353459732480000000⟩ +] + +def collectedFourData_13_4_32 : List CollectedFourTerm := [ + ⟨4, 6, 3, 0, 7, 6, -5745135488580692390331901394873653243585285324800000⟩, + ⟨4, 6, 4, 0, 8, 6, 22173478409861080334745913983900106259912510668800000⟩, + ⟨4, 6, 3, 1, 6, 6, 27241740827347296297843501450522664183891859865600000⟩, + ⟨4, 6, 4, 1, 7, 6, -25859768793672062104878820513466584035652062412800000⟩, + ⟨4, 6, 5, 1, 8, 6, -63468682453518677062791638705537911991870423040000000⟩, + ⟨4, 6, 3, 2, 5, 6, 11592703736722530544210448850045310645030197657600000⟩, + ⟨4, 6, 4, 2, 6, 6, 17049169970277292927215015773977767851486871552000000⟩, + ⟨4, 6, 5, 2, 7, 6, -32533311449522704415465050232261687105827110912000000⟩, + ⟨4, 6, 6, 2, 8, 6, 19222738299149914545119174243380847740471738368000000⟩, + ⟨4, 6, 3, 3, 4, 6, -1263125823264154603709476569234730589942395699200000⟩, + ⟨4, 6, 4, 3, 5, 6, 46777721013612706200072625627827261614930578636800000⟩, + ⟨4, 6, 5, 3, 6, 6, 22259778921255724173783750673774351986834014208000000⟩, + ⟨4, 6, 6, 3, 7, 6, 40757347554004372409497480338213472907034624000000⟩, + ⟨4, 6, 7, 3, 8, 6, -1630798768648506220893267631871168603693776896000000⟩, + ⟨4, 6, 3, 4, 3, 6, -18653805022685688968088342776919802517527304601600000⟩, + ⟨4, 6, 4, 4, 4, 6, -35058301453771583264495585223887365979422851072000000⟩, + ⟨4, 6, 5, 4, 5, 6, 13497257838434814344999352295903925094089490432000000⟩, + ⟨4, 6, 6, 4, 6, 6, 8236603726491965123466238886052358064726605824000000⟩, + ⟨4, 6, 7, 4, 7, 6, -4313597845560595711968739701277717434835402752000000⟩, + ⟨4, 6, 8, 4, 8, 6, 924096767016148075502018549870848400840196096000000⟩, + ⟨4, 6, 3, 5, 2, 6, -23292772365576459181751876795006772904391501414400000⟩, + ⟨4, 6, 4, 5, 3, 6, -33406491001917235579253799415813251335206836633600000⟩, + ⟨4, 6, 5, 5, 4, 6, 8953225595604312531135681402338483670230237184000000⟩, + ⟨4, 6, 6, 5, 5, 6, 6880704669292187839329846609677166551658135552000000⟩, + ⟨4, 6, 7, 5, 6, 6, 1366539435549629037815800285315763953792450560000000⟩, + ⟨4, 6, 8, 5, 7, 6, -1515058717380887191431081531766904460043458969600000⟩, + ⟨4, 6, 3, 6, 1, 6, -5670903522959767502992545318270381040791139123200000⟩, + ⟨4, 6, 4, 6, 2, 6, 42312579343591419500610801863938648950156401049600000⟩, + ⟨4, 6, 5, 6, 3, 6, -81586746065892390767437978002516514037336899584000000⟩, + ⟨4, 6, 6, 6, 4, 6, -4587766696414106291102782641250224826673528832000000⟩, + ⟨4, 6, 7, 6, 5, 6, 8537718549927134847430074360496145133295632384000000⟩, + ⟨4, 6, 8, 6, 6, 6, 2263098522629749761471898123615952328592038297600000⟩, + ⟨4, 6, 3, 7, 0, 6, 596068900804400658340303011338334549261300636057600000⟩, + ⟨4, 6, 4, 7, 1, 6, 40646195927598238557503084851346076196081867161600000⟩, + ⟨4, 6, 5, 7, 2, 6, 4519882826287879211564957693531617277773873152000000⟩, + ⟨4, 6, 6, 7, 3, 6, -23159920485078650995253839041659006627447046144000000⟩, + ⟨4, 6, 7, 7, 4, 6, 6638840581873616593718901885399764710383943680000000⟩, + ⟨4, 6, 8, 7, 5, 6, 5845823021938212619167617867954546450802671616000000⟩ +] + +def collectedFourData_13_4_33 : List CollectedFourTerm := [ + ⟨4, 7, 2, 0, 6, 7, -42106771896397719734481990479189639608126773657600000⟩, + ⟨4, 7, 3, 0, 7, 7, 12035156668414996071424829021160048584505792921600000⟩, + ⟨4, 7, 4, 0, 8, 7, -23224977642113214929415185280818771358619847884800000⟩, + ⟨4, 7, 2, 1, 5, 7, 20560214153004197175468216071393468800866818457600000⟩, + ⟨4, 7, 3, 1, 6, 7, -57067169160614127250941770207764512571575710515200000⟩, + ⟨4, 7, 4, 1, 7, 7, 27086077383156658016094690492079821816593173708800000⟩, + ⟨4, 7, 5, 1, 8, 7, 44318974338334008132316684713153324403717570560000000⟩, + ⟨4, 7, 2, 2, 4, 7, 75746447136433471811778704545785426429891890380800000⟩, + ⟨4, 7, 3, 2, 5, 7, -24284893882710386894745444417485287689907548979200000⟩, + ⟨4, 7, 4, 2, 6, 7, -17857666896330630087058277620397720731429896192000000⟩, + ⟨4, 7, 5, 2, 7, 7, 22717392886300407842438767344587644266419847168000000⟩, + ⟨4, 7, 6, 2, 8, 7, -10067154529516761221382755230501863618263384064000000⟩, + ⟨4, 7, 2, 3, 3, 7, -86282585102845161859166759581799919950455898112000000⟩, + ⟨4, 7, 3, 3, 4, 7, 2646050246355518294104394680243795751711696486400000⟩, + ⟨4, 7, 4, 3, 5, 7, -48995989921320203095966271339714659292652817612800000⟩, + ⟨4, 7, 5, 3, 6, 7, -15543580434501801598817667706642217836858048512000000⟩, + ⟨4, 7, 6, 3, 7, 7, -21345060711643207052083729958940544075825152000000⟩, + ⟨4, 7, 7, 3, 8, 7, 683253465974978017197245160782574458677651046400000⟩, + ⟨4, 7, 2, 4, 2, 7, 20572838407517304066516889179240189163468750848000000⟩, + ⟨4, 7, 3, 4, 3, 7, 39076792245599555955746582267324066484230239027200000⟩, + ⟨4, 7, 4, 4, 4, 7, 36720818104578634975490100466613438058816602112000000⟩, + ⟨4, 7, 5, 4, 5, 7, -9424878548842587119979257766942714094260584448000000⟩, + ⟨4, 7, 6, 4, 6, 7, -4313597845560595711968739701277717434835402752000000⟩, + ⟨4, 7, 7, 4, 7, 7, 1807262021202026256733170995275980540474084556800000⟩, + ⟨4, 7, 8, 4, 8, 7, -322639602086584342591725136786217183867830272000000⟩, + ⟨4, 7, 2, 5, 1, 7, -21307332236013280645489754555438803541202409881600000⟩, + ⟨4, 7, 3, 5, 2, 7, 48794700354524581444475103770221173409930071244800000⟩, + ⟨4, 7, 4, 5, 3, 7, 34990676351254759312665633662377643630411749785600000⟩, + ⟨4, 7, 5, 5, 4, 7, -6251867221404789710383469517577564866138341376000000⟩, + ⟨4, 7, 6, 5, 5, 7, -3603498944830105678522613166926460980450820096000000⟩, + ⟨4, 7, 7, 5, 6, 7, -572537104933280311752619413733042249902587904000000⟩, + ⟨4, 7, 8, 5, 7, 7, 528968349593888870336333621926752631974474547200000⟩, + ⟨4, 7, 2, 6, 0, 7, 383576315340777327499801361136341667052784084582400000⟩, + ⟨4, 7, 3, 6, 1, 7, 11879652357362980247806968978726500939558446694400000⟩, + ⟨4, 7, 4, 6, 2, 7, -44319104610939974065413240195107373217062951321600000⟩, + ⟨4, 7, 5, 6, 3, 7, 56970473711826631136576206295019070083066494976000000⟩, + ⟨4, 7, 6, 6, 4, 7, 2402662698696464423206938660566909929742401536000000⟩, + ⟨4, 7, 7, 6, 5, 7, -3577035930429920604393294800063240856388868505600000⟩, + ⟨4, 7, 8, 6, 6, 7, -790139337010839390299396541362285189480526643200000⟩, + ⟨4, 7, 3, 7, 0, 7, -1248670744251347027567855498507268051031964201779200000⟩, + ⟨4, 7, 4, 7, 1, 7, -42573698821904263483958154469699486199477541273600000⟩, + ⟨4, 7, 5, 7, 2, 7, -3156148248976667416993867531246108702333206528000000⟩, + ⟨4, 7, 6, 7, 3, 7, 12129099131777616607193189736464670265140314112000000⟩, + ⟨4, 7, 7, 7, 4, 7, -2781465699400559362871173496988255635229376512000000⟩, + ⟨4, 7, 8, 7, 5, 7, -2041013539909701351177442138543294618546470912000000⟩ +] + +def collectedFourData_13_4_34 : List CollectedFourTerm := [ + ⟨4, 8, 1, 0, 5, 8, -52854057601049778781201074066689416024805081088000000⟩, + ⟨4, 8, 2, 0, 6, 8, 45102410067031517106956329800573567057814093824000000⟩, + ⟨4, 8, 3, 0, 7, 8, -6445692068432588532594119697459524143354478592000000⟩, + ⟨4, 8, 4, 0, 8, 8, 8292430712329544556507116956991437787872886784000000⟩, + ⟨4, 8, 1, 1, 4, 8, -23087465640778367856957289640441582341670830080000000⟩, + ⟨4, 8, 2, 1, 5, 8, -22022947094505556412784055408634576036192845824000000⟩, + ⟨4, 8, 3, 1, 6, 8, 30563573849588672252782886951272951040729677824000000⟩, + ⟨4, 8, 4, 1, 7, 8, -9671028468993865952984284285770323403372232704000000⟩, + ⟨4, 8, 5, 1, 8, 8, -11867999280946983949710147496382649874356633600000000⟩, + ⟨4, 8, 1, 2, 3, 8, -34872181210130642483062559927039124766338318336000000⟩, + ⟨4, 8, 2, 2, 4, 8, -81135341561541550757978999065356405973180219392000000⟩, + ⟨4, 8, 3, 2, 5, 8, 13006307453671766631678068627787387782251413504000000⟩, + ⟨4, 8, 4, 2, 6, 8, 6376043400496844734671929639344548319969935360000000⟩, + ⟨4, 8, 5, 2, 7, 8, -6083398960936744949435338387489226871621550080000000⟩, + ⟨4, 8, 6, 2, 8, 8, 2156674146931142119378646461871614266622083072000000⟩, + ⟨4, 8, 1, 3, 2, 8, 89859023082708251148969184183843927650421702656000000⟩, + ⟨4, 8, 2, 3, 3, 8, 92421061023796834928743167704889197299897466880000000⟩, + ⟨4, 8, 3, 3, 4, 8, -1417150233728868430045980346251463134824890368000000⟩, + ⟨4, 8, 4, 3, 5, 8, 17493917878647140392820480052010698611594625024000000⟩, + ⟨4, 8, 5, 3, 6, 8, 4162352675667616441370582333040640358319390720000000⟩, + ⟨4, 8, 6, 3, 7, 8, 4572726132940989978674018840588329257271296000000⟩, + ⟨4, 8, 7, 3, 8, 8, -121977125508246332770540885849422829354745856000000⟩, + ⟨4, 8, 1, 4, 1, 8, -40455280955570304557351106348636765004033425408000000⟩, + ⟨4, 8, 2, 4, 2, 8, -22036469487180104607121759789668287328571883520000000⟩, + ⟨4, 8, 3, 4, 3, 8, -20928432988186499980933351576365112251346059264000000⟩, + ⟨4, 8, 4, 4, 4, 8, -13111092915763431017714529824359241982368808960000000⟩, + ⟨4, 8, 5, 4, 5, 8, 2523850190818319180897515429178557061796986880000000⟩, + ⟨4, 8, 6, 4, 6, 8, 924096767016148075502018549870848400840196096000000⟩, + ⟨4, 8, 7, 4, 7, 8, -322639602086584342591725136786217183867830272000000⟩, + ⟨4, 8, 8, 4, 8, 8, 49370489698960238171474278536516507575255040000000⟩, + ⟨4, 8, 1, 5, 0, 8, -213224064011238815985058799588954482594390474752000000⟩, + ⟨4, 8, 2, 5, 1, 8, 22823218039789133831468492938087222471330627584000000⟩, + ⟨4, 8, 3, 5, 2, 8, -26133071776466116563137556300517467838664933376000000⟩, + ⟨4, 8, 4, 5, 3, 8, -12493349345326944324482479729740935691761614848000000⟩, + ⟨4, 8, 5, 5, 4, 8, 1674162292696171712681959461690659119363522560000000⟩, + ⟨4, 8, 6, 5, 5, 8, 771973151899336771880710207657647772016836608000000⟩, + ⟨4, 8, 7, 5, 6, 8, 102211600503073437924016692709751137668956160000000⟩, + ⟨4, 8, 8, 5, 7, 8, -80943028338141483516450845622821469661691904000000⟩, + ⟨4, 8, 2, 6, 0, 8, -410865413978239055170757578341694732505790283776000000⟩, + ⟨4, 8, 3, 6, 1, 8, -6362408324650044356331563482368217362179555328000000⟩, + ⟨4, 8, 4, 6, 2, 8, 15824045554829863013470204596321980451523657728000000⟩, + ⟨4, 8, 5, 6, 3, 8, -15255893240795240481632622473869545529996738560000000⟩, + ⟨4, 8, 6, 6, 4, 8, -514719478168495499643045661763789922634825728000000⟩, + ⟨4, 8, 7, 6, 5, 8, 638586677362769247906988003301232513304756224000000⟩, + ⟨4, 8, 8, 6, 6, 8, 120907556748623242071315541284491871727386624000000⟩, + ⟨4, 8, 3, 7, 0, 8, 668752998739708214293421818753440863646073749504000000⟩, + ⟨4, 8, 4, 7, 1, 8, 15200851991696660086281262464522785919376293888000000⟩, + ⟨4, 8, 5, 7, 2, 8, 845172202394998417112543550171285139677511680000000⟩, + ⟨4, 8, 6, 7, 3, 8, -2598402005886900440936440576392738648543461376000000⟩, + ⟨4, 8, 7, 7, 4, 8, 496558316361455632300884174629701958479380480000000⟩, + ⟨4, 8, 8, 7, 5, 8, 312317016559264531819893797415838591840419840000000⟩ +] + +def collectedFourData_13_4_35 : List CollectedFourTerm := [ + ⟨5, 0, 8, 4, 8, 1, -213224064011238815985058799588954482594390474752000000⟩, + ⟨5, 0, 8, 5, 7, 1, 349581330079431609245599110809548459608066175795200000⟩, + ⟨5, 0, 8, 6, 6, 1, -522182396342604581944173786905441077655231476531200000⟩, + ⟨5, 0, 8, 7, 5, 1, -1348852400223087903498645542295904827963177172992000000⟩ +] + +def collectedFourData_13_4_36 : List CollectedFourTerm := [ + ⟨5, 1, 7, 3, 8, 2, -8055449862911184332453695666716783094107262156800000⟩, + ⟨5, 1, 7, 4, 7, 2, -21307332236013280645489754555438803541202409881600000⟩, + ⟨5, 1, 8, 4, 8, 2, 22823218039789133831468492938087222471330627584000000⟩, + ⟨5, 1, 7, 5, 6, 2, 6750121548033626325680373255180726031349710848000000⟩, + ⟨5, 1, 8, 5, 7, 2, -37418717047911727196597885199575635744174532198400000⟩, + ⟨5, 1, 7, 6, 5, 2, 42172685584979277431453136539739250139308700467200000⟩, + ⟨5, 1, 8, 6, 6, 2, 55893703853420002639531343995972732495258347110400000⟩, + ⟨5, 1, 7, 7, 4, 2, 32793038898025793877598895058502469184487686144000000⟩, + ⟨5, 1, 8, 7, 5, 2, 144379353130431842553248351744674368842486513664000000⟩ +] + +def collectedFourData_13_4_37 : List CollectedFourTerm := [ + ⟨5, 2, 6, 2, 8, 3, -54361103473390968076976791523898745521544416460800000⟩, + ⟨5, 2, 6, 3, 7, 3, -115260081742993446717270058656690652540462694400000⟩, + ⟨5, 2, 7, 3, 8, 3, 18447324044504205888773782098220422811710023270400000⟩, + ⟨5, 2, 6, 4, 6, 3, -23292772365576459181751876795006772904391501414400000⟩, + ⟨5, 2, 7, 4, 7, 3, 48794700354524581444475103770221173409930071244800000⟩, + ⟨5, 2, 8, 4, 8, 3, -26133071776466116563137556300517467838664933376000000⟩, + ⟨5, 2, 6, 5, 5, 3, -19458346291577941413043382626917217745713181491200000⟩, + ⟨5, 2, 7, 5, 6, 3, -15458066483622230120310580385970420465788780544000000⟩, + ⟨5, 2, 8, 5, 7, 3, 42845229655676903437476785724606101203795417497600000⟩, + ⟨5, 2, 6, 6, 4, 3, 12974013182428504495022354975398976917045719859200000⟩, + ⟨5, 2, 7, 6, 5, 3, -96577250191207815250710141829151035007834888601600000⟩, + ⟨5, 2, 8, 6, 6, 3, -63999483863646294952737860824247253030242195865600000⟩, + ⟨5, 2, 6, 7, 3, 3, 65495290750566181453007762640366453387507951206400000⟩, + ⟨5, 2, 7, 7, 4, 3, -75097458894404984740742110133779995503395602432000000⟩, + ⟨5, 2, 8, 7, 5, 3, -165317440854286431491039997197344654228765802496000000⟩ +] + +def collectedFourData_13_4_38 : List CollectedFourTerm := [ + ⟨5, 3, 5, 1, 8, 4, 85806643923208873307505591625955527995898724352000000⟩, + ⟨5, 3, 5, 2, 7, 4, 43983491751801526847038109521030820303717636505600000⟩, + ⟨5, 3, 6, 2, 8, 4, -77964687308838674446896432277939568828990305075200000⟩, + ⟨5, 3, 5, 3, 6, 4, -30094163765008939618994082021905251822123509350400000⟩, + ⟨5, 3, 6, 3, 7, 4, -165305993773329157011901958035520299554412953600000⟩, + ⟨5, 3, 7, 3, 8, 4, 13228574834933131254928611687961175634675027148800000⟩, + ⟨5, 3, 5, 4, 5, 4, -18247651479617384153273784442328673400768797081600000⟩, + ⟨5, 3, 6, 4, 6, 4, -33406491001917235579253799415813251335206836633600000⟩, + ⟨5, 3, 7, 4, 7, 4, 34990676351254759312665633662377643630411749785600000⟩, + ⟨5, 3, 8, 4, 8, 4, -12493349345326944324482479729740935691761614848000000⟩, + ⟨5, 3, 5, 5, 4, 4, -12104335728235803021905825173011330599159542579200000⟩, + ⟨5, 3, 6, 5, 5, 4, -27907157640987866674593288444168297111410756812800000⟩, + ⟨5, 3, 7, 5, 6, 4, -11084978438533423536553056015443647548220243968000000⟩, + ⟨5, 3, 8, 5, 7, 4, 20482874208120271411228412881625752966009769164800000⟩, + ⟨5, 3, 5, 6, 3, 4, 110301405321533907758275200858571300265849467699200000⟩, + ⟨5, 3, 6, 6, 4, 4, 18607327965737712999015332689522851815720013004800000⟩, + ⟨5, 3, 7, 6, 5, 4, -69255539634056942283115903516029135710527370035200000⟩, + ⟨5, 3, 8, 6, 6, 4, -30596017057175455180676992247208581932535041228800000⟩, + ⟨5, 3, 5, 7, 2, 4, -6110666887310019066865230566443395724500113817600000⟩, + ⟨5, 3, 6, 7, 3, 4, 93933337208080063277114997607498051301945219481600000⟩, + ⟨5, 3, 7, 7, 4, 4, -53852382735907576715503208664130198461694869504000000⟩, + ⟨5, 3, 8, 7, 5, 4, -79032750498468869865571925379109064597840068608000000⟩ +] + +def collectedFourData_13_4_39 : List CollectedFourTerm := [ + ⟨5, 4, 4, 0, 8, 5, 8034223855487940220968459859174299013966567833600000⟩, + ⟨5, 4, 4, 1, 7, 5, -9369895309124137480297387237116383585193531801600000⟩, + ⟨5, 4, 5, 1, 8, 5, -45993830396738671246493247166627950744054005760000000⟩, + ⟨5, 4, 4, 2, 6, 5, 6177508352976930197203978802729144260120018944000000⟩, + ⟨5, 4, 5, 2, 7, 5, -23575904701495305873478057636284986797722697728000000⟩, + ⟨5, 4, 6, 2, 8, 5, 20895203687412727645216283731495670337805221888000000⟩, + ⟨5, 4, 4, 3, 5, 5, 16949198277604893492331546486834229359421266329600000⟩, + ⟨5, 4, 5, 3, 6, 5, 16130987075758566363810425927173734950661783552000000⟩, + ⟨5, 4, 6, 3, 7, 5, 44303421585740257014151293538049023209897984000000⟩, + ⟨5, 4, 7, 3, 8, 5, -2363580874122000070534631405635330078773608448000000⟩, + ⟨5, 4, 4, 4, 4, 5, -12702844211737001177549151953519096914073616384000000⟩, + ⟨5, 4, 5, 4, 5, 5, 9781053644790228164686716340126648294711492608000000⟩, + ⟨5, 4, 6, 4, 6, 5, 8953225595604312531135681402338483670230237184000000⟩, + ⟨5, 4, 7, 4, 7, 5, -6251867221404789710383469517577564866138341376000000⟩, + ⟨5, 4, 8, 4, 8, 5, 1674162292696171712681959461690659119363522560000000⟩, + ⟨5, 4, 4, 5, 3, 5, -12104335728235803021905825173011330599159542579200000⟩, + ⟨5, 4, 5, 5, 4, 5, 6488131211003808785092097697084476108146999296000000⟩, + ⟨5, 4, 6, 5, 5, 5, 7479357172757753706747761811085432556284280832000000⟩, + ⟨5, 4, 7, 5, 6, 5, 1980579416475349401627973495642790716275425280000000⟩, + ⟨5, 4, 8, 5, 7, 5, -2744792825160251034310133780860077014155001856000000⟩, + ⟨5, 4, 4, 6, 2, 5, 15331321864156642049426122023342504057861518131200000⟩, + ⟨5, 4, 5, 6, 3, 5, -59123441926253573045128140253611678269907664896000000⟩, + ⟨5, 4, 6, 6, 4, 5, -4986923200017796240560394769674588707002253312000000⟩, + ⟨5, 4, 7, 6, 5, 5, 12374051698584397495763674993172236258290696192000000⟩, + ⟨5, 4, 8, 6, 6, 5, 4099997258379039256213562272511656630929063936000000⟩, + ⟨5, 4, 4, 7, 1, 5, 14727533087957780588188249078097631738651161395200000⟩, + ⟨5, 4, 5, 7, 2, 5, 3275422083602609930214750405607892733067788288000000⟩, + ⟨5, 4, 6, 7, 3, 5, -25174938574771204439491763091989728167727202304000000⟩, + ⟨5, 4, 7, 7, 4, 5, 9621933084156933103156025748633603322769571840000000⟩, + ⟨5, 4, 8, 7, 5, 5, 10590726883187030010220102705837795838798069760000000⟩ +] + +def collectedFourData_13_4_40 : List CollectedFourTerm := [ + ⟨5, 5, 3, 0, 7, 6, -4799378711743585720004678522947799098704946790400000⟩, + ⟨5, 5, 4, 0, 8, 6, 18523309059832731088348913293074180259155699302400000⟩, + ⟨5, 5, 3, 1, 6, 6, 22757240670386040761780250296169860483240479948800000⟩, + ⟨5, 5, 4, 1, 7, 6, -21602767086285335438568522317527251535039719014400000⟩, + ⟨5, 5, 5, 1, 8, 6, -53020550000133010224267292372972212114602065920000000⟩, + ⟨5, 5, 3, 2, 5, 6, 9684327834594110008180611635868013243981941964800000⟩, + ⟨5, 5, 4, 2, 6, 6, 14242557650883431510586159637121306690108522496000000⟩, + ⟨5, 5, 5, 2, 7, 6, -27177719777664750774211108920508088291243851776000000⟩, + ⟨5, 5, 6, 2, 8, 6, 16058315971439325101220147505692297621525233664000000⟩, + ⟨5, 5, 3, 3, 4, 6, -1055191683203491523719223425373050825753598361600000⟩, + ⟨5, 5, 4, 3, 5, 6, 39077233054442032477593454199797813867327153766400000⟩, + ⟨5, 5, 5, 3, 6, 6, 18595402892610617709414390760574132075819433984000000⟩, + ⟨5, 5, 6, 3, 7, 6, 34047925690634594484666344626543320945917952000000⟩, + ⟨5, 5, 7, 3, 8, 6, -1362338783645095805677495101838321014703915008000000⟩, + ⟨5, 5, 3, 4, 3, 6, -15583039755431494205383101110968888215697411276800000⟩, + ⟨5, 5, 4, 4, 4, 6, -29287049191713296127599320038971913990838419456000000⟩, + ⟨5, 5, 5, 4, 5, 6, 11275356702284055843177790967776384529240948736000000⟩, + ⟨5, 5, 6, 4, 6, 6, 6880704669292187839329846609677166551658135552000000⟩, + ⟨5, 5, 7, 4, 7, 6, -3603498944830105678522613166926460980450820096000000⟩, + ⟨5, 5, 8, 4, 8, 6, 771973151899336771880710207657647772016836608000000⟩, + ⟨5, 5, 3, 5, 2, 6, -19458346291577941413043382626917217745713181491200000⟩, + ⟨5, 5, 4, 5, 3, 6, -27907157640987866674593288444168297111410756812800000⟩, + ⟨5, 5, 5, 5, 4, 6, 7479357172757753706747761811085432556284280832000000⟩, + ⟨5, 5, 6, 5, 5, 6, 5748011961986611495642689267699256646745194496000000⟩, + ⟨5, 5, 7, 5, 6, 6, 1141581480327323086373941405589777962374266880000000⟩, + ⟨5, 5, 8, 5, 7, 6, -1265651709988778836482490220605743012858612940800000⟩, + ⟨5, 5, 3, 6, 1, 6, -4737366716336326364489913570620759216848738713600000⟩, + ⟨5, 5, 4, 6, 2, 6, 35347137233618576272361972855604470179347352780800000⟩, + ⟨5, 5, 5, 6, 3, 6, -68156041403613280318195345985643322699029676032000000⟩, + ⟨5, 5, 6, 6, 4, 6, -3832534473900737355612664883089555734644391936000000⟩, + ⟨5, 5, 7, 6, 5, 6, 7132250359773754333653134424713202547852050432000000⟩, + ⟨5, 5, 8, 6, 6, 6, 1890550169561075525996702163571487969666452684800000⟩, + ⟨5, 5, 3, 7, 0, 6, 497944808949975951579742609581389326347932585164800000⟩, + ⟨5, 5, 4, 7, 1, 6, 33955071701270966197995413392323419401981054156800000⟩, + ⟨5, 5, 5, 7, 2, 6, 3775825558714636496642372579208101244274999296000000⟩, + ⟨5, 5, 6, 7, 3, 6, -19347364315897190145630918455795724562477350912000000⟩, + ⟨5, 5, 7, 7, 4, 6, 5545963227957755760242218537598811927887216640000000⟩, + ⟨5, 5, 8, 7, 5, 6, 4883491193528316655128067696670765635042541568000000⟩ +] + +def collectedFourData_13_4_41 : List CollectedFourTerm := [ + ⟨5, 6, 2, 0, 6, 7, 13339343712659505953179495108079439588127408128000000⟩, + ⟨5, 6, 3, 0, 7, 7, -3812714302362090355627340501388315381410562048000000⟩, + ⟨5, 6, 4, 0, 8, 7, 7357627895324000098582331999363627677063839744000000⟩, + ⟨5, 6, 2, 1, 5, 7, -6513435987627271637360692902947879916171952128000000⟩, + ⟨5, 6, 3, 1, 6, 7, 18078768565182725523135373119530311632348512256000000⟩, + ⟨5, 6, 4, 1, 7, 7, -8580816808531696469275013678121382997303230464000000⟩, + ⟨5, 6, 5, 1, 8, 7, -14040165157903029589011158969260248239230156800000000⟩, + ⟨5, 6, 2, 2, 4, 7, -23996327618078957236827834707953364057796378624000000⟩, + ⟨5, 6, 3, 2, 5, 7, 7693407305693978082926446114585916193349042176000000⟩, + ⟨5, 6, 4, 2, 6, 7, 5657274255610054765571627307418720111700213760000000⟩, + ⟨5, 6, 5, 2, 7, 7, -7196826028637263369093132808250814584890327040000000⟩, + ⟨5, 6, 6, 2, 8, 7, 3189255039737911279591667111579509990537297920000000⟩, + ⟨5, 6, 2, 3, 3, 7, 27334155701499208286371825364947704625873551360000000⟩, + ⟨5, 6, 3, 3, 4, 7, -838263588668104005037901635152088762461192192000000⟩, + ⟨5, 6, 4, 3, 5, 7, 15521834628182579142513416137858173423618883584000000⟩, + ⟨5, 6, 5, 3, 6, 7, 4924176150367090510933707471691117338411663360000000⟩, + ⟨5, 6, 6, 3, 7, 7, 6762073855976409794392067778372457526722560000000⟩, + ⟨5, 6, 7, 3, 8, 7, -216453373531725532425758215164171609798868992000000⟩, + ⟨5, 6, 2, 4, 2, 7, -6517435326984863961861417645385982682794557440000000⟩, + ⟨5, 6, 3, 4, 3, 7, -12379452032912416857144509917204599556974575616000000⟩, + ⟨5, 6, 4, 4, 4, 7, -11633083992100805046688851811258397894230671360000000⟩, + ⟨5, 6, 5, 4, 5, 7, 2985783254114487009180432316153853187131965440000000⟩, + ⟨5, 6, 6, 4, 6, 7, 1366539435549629037815800285315763953792450560000000⟩, + ⟨5, 6, 7, 4, 7, 7, -572537104933280311752619413733042249902587904000000⟩, + ⟨5, 6, 8, 4, 8, 7, 102211600503073437924016692709751137668956160000000⟩, + ⟨5, 6, 2, 5, 1, 7, 6750121548033626325680373255180726031349710848000000⟩, + ⟨5, 6, 3, 5, 2, 7, -15458066483622230120310580385970420465788780544000000⟩, + ⟨5, 6, 4, 5, 3, 7, -11084978438533423536553056015443647548220243968000000⟩, + ⟨5, 6, 5, 5, 4, 7, 1980579416475349401627973495642790716275425280000000⟩, + ⟨5, 6, 6, 5, 5, 7, 1141581480327323086373941405589777962374266880000000⟩, + ⟨5, 6, 7, 5, 6, 7, 181378644977754878630819921565311271299973120000000⟩, + ⟨5, 6, 8, 5, 7, 7, -167576147744414795230115776676169770877321216000000⟩, + ⟨5, 6, 2, 6, 0, 7, -121516233135977673292223000142029323927994499072000000⟩, + ⟨5, 6, 3, 6, 1, 7, -3763450838066443027558751508504442008797970432000000⟩, + ⟨5, 6, 4, 6, 2, 7, 14040206428012065710713859655138329496070914048000000⟩, + ⟨5, 6, 5, 6, 3, 7, -18048135634451300254618025012441010727582433280000000⟩, + ⟨5, 6, 6, 6, 4, 7, -761158885377297500341700080279275421386670080000000⟩, + ⟨5, 6, 7, 6, 5, 7, 1133198048663987094421603504819102118018285568000000⟩, + ⟨5, 6, 8, 6, 6, 7, 250314610277265027628601952719681591596548096000000⟩, + ⟨5, 6, 3, 7, 0, 7, 395576471226378890966800413525135580952763826176000000⟩, + ⟨5, 6, 4, 7, 1, 7, 13487265257520559591166810068186390454083780608000000⟩, + ⟨5, 6, 5, 7, 2, 7, 999861647071786079673436285718872320733347840000000⟩, + ⟨5, 6, 6, 7, 3, 7, -3842475092647586569147793527337141790950031360000000⟩, + ⟨5, 6, 7, 7, 4, 7, 881162941689460710458103111906909949903503360000000⟩, + ⟨5, 6, 8, 7, 5, 7, 646589132931764631906527517692842447585935360000000⟩ +] + +def collectedFourData_13_4_42 : List CollectedFourTerm := [ + ⟨5, 7, 1, 0, 5, 8, 86654345708821972679509120766325126946072874188800000⟩, + ⟨5, 7, 2, 0, 6, 8, -73945502230882176704741587495552205659981637222400000⟩, + ⟨5, 7, 3, 0, 7, 8, 10567726569766244929869529644390758695765750579200000⟩, + ⟨5, 7, 4, 0, 8, 8, -13595458708895511163947432462882092723563030118400000⟩, + ⟨5, 7, 1, 1, 4, 8, 37851951581042313786023662933561381342106615808000000⟩, + ⟨5, 7, 2, 1, 5, 8, 36106671042347312166136905074456317185587832422400000⟩, + ⟨5, 7, 3, 1, 6, 8, -50109047718727354749856795889935625657822635622400000⟩, + ⟨5, 7, 4, 1, 7, 8, 15855672815844677770242534694614617555185591910400000⟩, + ⟨5, 7, 5, 1, 8, 8, 19457611378219036647997518873532577011319439360000000⟩, + ⟨5, 7, 1, 2, 3, 8, 57173019127737270325742627069000822643200989593600000⟩, + ⟨5, 7, 2, 2, 4, 8, 133021574047278631357486715961926297761894052659200000⟩, + ⟨5, 7, 3, 2, 5, 8, -21323870174601617390418874374150371053729637990400000⟩, + ⟨5, 7, 4, 2, 6, 8, -10453537422832273038296554208025493110716891136000000⟩, + ⟨5, 7, 5, 2, 7, 8, 9973746209320944263197064286339884367696887808000000⟩, + ⟨5, 7, 6, 2, 8, 8, -3535872089898695312624045874800387318965547827200000⟩, + ⟨5, 7, 1, 3, 2, 8, -147324069422275663693009078612979988456753699225600000⟩, + ⟨5, 7, 2, 3, 3, 8, -151524536359780931800068602302964841796482367488000000⟩, + ⟨5, 7, 3, 3, 4, 8, 2323420979365643776189497675090968186303859916800000⟩, + ⟨5, 7, 4, 3, 5, 8, -28681317508306529316715881592038565228065482342400000⟩, + ⟨5, 7, 5, 3, 6, 8, -6824186525883263289494752050813894133674934272000000⟩, + ⟨5, 7, 6, 3, 7, 8, -7496994727378565204809526541264261133998489600000⟩, + ⟨5, 7, 7, 3, 8, 8, 199981770219851733207530763363898854762715545600000⟩, + ⟨5, 7, 1, 4, 1, 8, 66326523653727632028319065244780029328973679820800000⟩, + ⟨5, 7, 2, 4, 2, 8, 36128841035396388258525777429157646301294231552000000⟩, + ⟨5, 7, 3, 4, 3, 8, 34312212715835213692702739674091828729386264166400000⟩, + ⟨5, 7, 4, 4, 4, 8, 21495666174180075440245335933625820775758954496000000⟩, + ⟨5, 7, 5, 4, 5, 8, -4137858035484168732198407222038473956275519488000000⟩, + ⟨5, 7, 6, 4, 6, 8, -1515058717380887191431081531766904460043458969600000⟩, + ⟨5, 7, 7, 4, 7, 8, 528968349593888870336333621926752631974474547200000⟩, + ⟨5, 7, 8, 4, 8, 8, -80943028338141483516450845622821469661691904000000⟩, + ⟨5, 7, 1, 5, 0, 8, 349581330079431609245599110809548459608066175795200000⟩, + ⟨5, 7, 2, 5, 1, 8, -37418717047911727196597885199575635744174532198400000⟩, + ⟨5, 7, 3, 5, 2, 8, 42845229655676903437476785724606101203795417497600000⟩, + ⟨5, 7, 4, 5, 3, 8, 20482874208120271411228412881625752966009769164800000⟩, + ⟨5, 7, 5, 5, 4, 8, -2744792825160251034310133780860077014155001856000000⟩, + ⟨5, 7, 6, 5, 5, 8, -1265651709988778836482490220605743012858612940800000⟩, + ⟨5, 7, 7, 5, 6, 8, -167576147744414795230115776676169770877321216000000⟩, + ⟨5, 7, 8, 5, 7, 8, 132706276087173552404284541425740733900809830400000⟩, + ⟨5, 7, 2, 6, 0, 8, 673614765613783951630505359541975836594397616537600000⟩, + ⟨5, 7, 3, 6, 1, 8, 10431182685470137553711577024433794612202360012800000⟩, + ⟨5, 7, 4, 6, 2, 8, -25943558096722919434251924316733024047194754252800000⟩, + ⟨5, 7, 5, 6, 3, 8, 25012071106504679093177704449795441922676883456000000⟩, + ⟨5, 7, 6, 6, 4, 8, 843883736248687968449593692195332558204751052800000⟩, + ⟨5, 7, 7, 6, 5, 8, -1046964286506212988385672234794292386078287462400000⟩, + ⟨5, 7, 8, 6, 6, 8, -198228209845068050392299257257476904895014502400000⟩, + ⟨5, 7, 3, 7, 0, 8, -1096422037907096465042208023401048095623909631590400000⟩, + ⟨5, 7, 4, 7, 1, 8, -24921830855441361694192680692294907989599243468800000⟩, + ⟨5, 7, 5, 7, 2, 8, -1385661717074452361400631000968244561830739968000000⟩, + ⟨5, 7, 6, 7, 3, 8, 4260085903114234878147208669888787469699750297600000⟩, + ⟨5, 7, 7, 7, 4, 8, -814108470826685075907337802749682765789134848000000⟩, + ⟨5, 7, 8, 7, 5, 8, -512044447522924939436626397242739847157776384000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1310.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1310.lean new file mode 100644 index 0000000000000000000000000000000000000000..f75a9b9f27a56faf51e048edf57f6afb8751841b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1310.lean @@ -0,0 +1,626 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1308 +import OAI.Analysis.LaughlinFock.Sparse1309 + +namespace OAI + +/-! Sparse1310. -/ +namespace LaughlinFock +def collectedFourData_13_4_43 : List CollectedFourTerm := [ + ⟨6, 0, 7, 3, 8, 2, 145014858857148767072362720867175054262010065715200000⟩, + ⟨6, 0, 7, 4, 7, 2, 383576315340777327499801361136341667052784084582400000⟩, + ⟨6, 0, 8, 4, 8, 2, -410865413978239055170757578341694732505790283776000000⟩, + ⟨6, 0, 7, 5, 6, 2, -121516233135977673292223000142029323927994499072000000⟩, + ⟨6, 0, 8, 5, 7, 2, 673614765613783951630505359541975836594397616537600000⟩, + ⟨6, 0, 7, 6, 5, 2, -759196091070017849676870550274202830867016764620800000⟩, + ⟨6, 0, 8, 6, 6, 2, -1006202969821195252425808672874480550015491742105600000⟩, + ⟨6, 0, 7, 7, 4, 2, -590342934066205303035407716441950955063650287616000000⟩, + ⟨6, 0, 8, 7, 5, 2, -2599128772744849620570810145675534318402478800896000000⟩ +] + +def collectedFourData_13_4_44 : List CollectedFourTerm := [ + ⟨6, 1, 6, 2, 8, 3, -13234859653495949936693501141692307754935805542400000⟩, + ⟨6, 1, 6, 3, 7, 3, -28061442981297775637335548780390267772678963200000⟩, + ⟨6, 1, 7, 3, 8, 3, 4491221279771877524616190587377359424167555891200000⟩, + ⟨6, 1, 6, 4, 6, 3, -5670903522959767502992545318270381040791139123200000⟩, + ⟨6, 1, 7, 4, 7, 3, 11879652357362980247806968978726500939558446694400000⟩, + ⟨6, 1, 8, 4, 8, 3, -6362408324650044356331563482368217362179555328000000⟩, + ⟨6, 1, 6, 5, 5, 3, -4737366716336326364489913570620759216848738713600000⟩, + ⟨6, 1, 7, 5, 6, 3, -3763450838066443027558751508504442008797970432000000⟩, + ⟨6, 1, 8, 5, 7, 3, 10431182685470137553711577024433794612202360012800000⟩, + ⟨6, 1, 6, 6, 4, 3, 3158678404975663862808598820221593186727467417600000⟩, + ⟨6, 1, 7, 6, 5, 3, -23512884587172801359720468489314002716815314124800000⟩, + ⟨6, 1, 8, 6, 6, 3, -15581438431361946784804519131031105429471808716800000⟩, + ⟨6, 1, 6, 7, 3, 3, 15945610476302271629128638934412321951589806899200000⟩, + ⟨6, 1, 7, 7, 4, 3, -18283372950443030547949215217398518393597853696000000⟩, + ⟨6, 1, 8, 7, 5, 3, -40248504687778684710901447039326637037545586688000000⟩ +] + +def collectedFourData_13_4_45 : List CollectedFourTerm := [ + ⟨6, 2, 5, 1, 8, 4, -108682484161527232776631664988010927107417833472000000⟩, + ⟨6, 2, 5, 2, 7, 4, -55709382480473416152597185396235988458035321241600000⟩, + ⟨6, 2, 6, 2, 8, 4, 98749881200159711729995543071083505526135534387200000⟩, + ⟨6, 2, 5, 3, 6, 4, 38117193811612689278896366832136130794088719974400000⟩, + ⟨6, 2, 6, 3, 7, 4, 209376165162147549956989254333201238982236569600000⟩, + ⟨6, 2, 7, 3, 8, 4, -16755280351762208781984860147234128567957507276800000⟩, + ⟨6, 2, 5, 4, 5, 4, 23112430486075354551364562512868987699155540377600000⟩, + ⟨6, 2, 6, 4, 6, 4, 42312579343591419500610801863938648950156401049600000⟩, + ⟨6, 2, 7, 4, 7, 4, -44319104610939974065413240195107373217062951321600000⟩, + ⟨6, 2, 8, 4, 8, 4, 15824045554829863013470204596321980451523657728000000⟩, + ⟨6, 2, 5, 5, 4, 4, 15331321864156642049426122023342504057861518131200000⟩, + ⟨6, 2, 6, 5, 5, 4, 35347137233618576272361972855604470179347352780800000⟩, + ⟨6, 2, 7, 5, 6, 4, 14040206428012065710713859655138329496070914048000000⟩, + ⟨6, 2, 8, 5, 7, 4, -25943558096722919434251924316733024047194754252800000⟩, + ⟨6, 2, 5, 6, 3, 4, -139707488706586637085060135672392056655221830451200000⟩, + ⟨6, 2, 6, 6, 4, 4, -23567995838812256673636282244807854383675788492800000⟩, + ⟨6, 2, 7, 6, 5, 4, 87718896174431994167861801927083106956431536947200000⟩, + ⟨6, 2, 8, 6, 6, 4, 38752839957220127440803621184601191530204286156800000⟩, + ⟨6, 2, 5, 7, 2, 4, 7739755650981812314728798150705596873209125273600000⟩, + ⟨6, 2, 6, 7, 3, 4, -118975733889474092786667295909410598078494906777600000⟩, + ⟨6, 2, 7, 7, 4, 4, 68209295529535526971955792800220806309157535744000000⟩, + ⟨6, 2, 8, 7, 5, 4, 100102687409366279509993971688606847045455577088000000⟩ +] + +def collectedFourData_13_4_46 : List CollectedFourTerm := [ + ⟨6, 3, 4, 0, 8, 5, -73212293662749642373625018981654241050543888793600000⟩, + ⟨6, 3, 4, 1, 7, 5, 85383671067645969201376868498958367123666737561600000⟩, + ⟨6, 3, 5, 1, 8, 5, 419121234141443571086694266211349228053866741760000000⟩, + ⟨6, 3, 4, 2, 6, 5, -56292874554808919981800036505169820325033017344000000⟩, + ⟨6, 3, 5, 2, 7, 5, 214836689818128899942430702023240265017252118528000000⟩, + ⟨6, 3, 6, 2, 8, 5, -190408658760594337014232741886275241555093618688000000⟩, + ⟨6, 3, 4, 3, 5, 5, -154450473868806248148589343256562148106116372889600000⟩, + ⟨6, 3, 5, 3, 6, 5, -146994480624753609646915211589483057090240970752000000⟩, + ⟨6, 3, 6, 3, 7, 5, -403717293635556439798418091062719988455440384000000⟩, + ⟨6, 3, 7, 3, 8, 5, 21538256857714724970787970699743029593005621248000000⟩, + ⟨6, 3, 4, 4, 4, 5, 115755345819321478016159093551083656813985398784000000⟩, + ⟨6, 3, 5, 4, 5, 5, -89130373344569899214877004892127909597998481408000000⟩, + ⟨6, 3, 6, 4, 6, 5, -81586746065892390767437978002516514037336899584000000⟩, + ⟨6, 3, 7, 4, 7, 5, 56970473711826631136576206295019070083066494976000000⟩, + ⟨6, 3, 8, 4, 8, 5, -15255893240795240481632622473869545529996738560000000⟩, + ⟨6, 3, 4, 5, 3, 5, 110301405321533907758275200858571300265849467699200000⟩, + ⟨6, 3, 5, 5, 4, 5, -59123441926253573045128140253611678269907664896000000⟩, + ⟨6, 3, 6, 5, 5, 5, -68156041403613280318195345985643322699029676032000000⟩, + ⟨6, 3, 7, 5, 6, 5, -18048135634451300254618025012441010727582433280000000⟩, + ⟨6, 3, 8, 5, 7, 5, 25012071106504679093177704449795441922676883456000000⟩, + ⟨6, 3, 4, 6, 2, 5, -139707488706586637085060135672392056655221830451200000⟩, + ⟨6, 3, 5, 6, 3, 5, 538765519920220794963038402785021209437584490496000000⟩, + ⟨6, 3, 6, 6, 4, 5, 45443603807963390242264220912617691216464576512000000⟩, + ⟨6, 3, 7, 6, 5, 5, -112759206495844791283085599117332893611843387392000000⟩, + ⟨6, 3, 8, 6, 6, 5, -37361443830305683292378297332315630036410433536000000⟩, + ⟨6, 3, 4, 7, 1, 5, -134205431259786931012495540032535060552116024115200000⟩, + ⟨6, 3, 5, 7, 2, 5, -29847458543287727796195011592683665642475225088000000⟩, + ⟨6, 3, 6, 7, 3, 5, 229407971327417785569423652770789686991812296704000000⟩, + ⟨6, 3, 7, 7, 4, 5, -87680378743671559226031927324299766915756195840000000⟩, + ⟨6, 3, 8, 7, 5, 5, -96508563941024973992616637365016306976041205760000000⟩ +] + +def collectedFourData_13_4_47 : List CollectedFourTerm := [ + ⟨6, 4, 3, 0, 7, 6, 3200025415344715918349534501622063633810220646400000⟩, + ⟨6, 4, 4, 0, 8, 6, -12350569381555534344861562686874521773338420838400000⟩, + ⟨6, 4, 3, 1, 6, 6, -15173578269653847971370967977714740748952063180800000⟩, + ⟨6, 4, 4, 1, 7, 6, 14403823467552759163022191852831428586294896230400000⟩, + ⟨6, 4, 5, 1, 8, 6, 35351889843746434291297829016128083911738654720000000⟩, + ⟨6, 4, 3, 2, 5, 6, -6457105609399365999494763893419098657130335436800000⟩, + ⟨6, 4, 4, 2, 6, 6, -9496343005984961399109165359365985443497639936000000⟩, + ⟨6, 4, 5, 2, 7, 6, 18120969242714434855398107205393223769093308416000000⟩, + ⟨6, 4, 6, 2, 8, 6, -10707014870592117403327704236954926142271258624000000⟩, + ⟨6, 4, 3, 3, 4, 6, 703557774269667828387313298694433522597861785600000⟩, + ⟨6, 4, 4, 3, 5, 6, -26055068050700646264383553888293258319293212262400000⟩, + ⟨6, 4, 5, 3, 6, 6, -12398638540301924756383916778819612950076063744000000⟩, + ⟨6, 4, 6, 3, 7, 6, -22701735806594968503703902140936468910047232000000⟩, + ⟨6, 4, 7, 3, 8, 6, 908350641575089533990510712488854324540080128000000⟩, + ⟨6, 4, 3, 4, 3, 6, 10390120526161150102297292613100103435518004428800000⟩, + ⟨6, 4, 4, 4, 4, 6, 19527382059809529502840359769383174697748791296000000⟩, + ⟨6, 4, 5, 4, 5, 6, -7517937254273937917133318427018982515619659776000000⟩, + ⟨6, 4, 6, 4, 6, 6, -4587766696414106291102782641250224826673528832000000⟩, + ⟨6, 4, 7, 4, 7, 6, 2402662698696464423206938660566909929742401536000000⟩, + ⟨6, 4, 8, 4, 8, 6, -514719478168495499643045661763789922634825728000000⟩, + ⟨6, 4, 3, 5, 2, 6, 12974013182428504495022354975398976917045719859200000⟩, + ⟨6, 4, 4, 5, 3, 6, 18607327965737712999015332689522851815720013004800000⟩, + ⟨6, 4, 5, 5, 4, 6, -4986923200017796240560394769674588707002253312000000⟩, + ⟨6, 4, 6, 5, 5, 6, -3832534473900737355612664883089555734644391936000000⟩, + ⟨6, 4, 7, 5, 6, 6, -761158885377297500341700080279275421386670080000000⟩, + ⟨6, 4, 8, 5, 7, 6, 843883736248687968449593692195332558204751052800000⟩, + ⟨6, 4, 3, 6, 1, 6, 3158678404975663862808598820221593186727467417600000⟩, + ⟨6, 4, 4, 6, 2, 6, -23567995838812256673636282244807854383675788492800000⟩, + ⟨6, 4, 5, 6, 3, 6, 45443603807963390242264220912617691216464576512000000⟩, + ⟨6, 4, 6, 6, 4, 6, 2555374030321444605782753507070263932250750976000000⟩, + ⟨6, 4, 7, 6, 5, 6, -4755486864170781130603178687452554981814566912000000⟩, + ⟨6, 4, 8, 6, 6, 6, -1260539947967941117744740721275737611852106956800000⟩, + ⟨6, 4, 3, 7, 0, 6, -332008816095282920513510684437111387346516626636800000⟩, + ⟨6, 4, 4, 7, 1, 6, -22639824641895108629654443495575897199134690508800000⟩, + ⟨6, 4, 5, 7, 2, 6, -2517562892511437587334194461704873005585268736000000⟩, + ⟨6, 4, 6, 7, 3, 6, 12900015033052509301027417205647131644465774592000000⟩, + ⟨6, 4, 7, 7, 4, 6, -3697816810873126159232457941938058463270666240000000⟩, + ⟨6, 4, 8, 7, 5, 6, -3256108107631583499450223405547563595058905088000000⟩ +] + +def collectedFourData_13_4_48 : List CollectedFourTerm := [ + ⟨6, 5, 2, 0, 6, 7, 83340121255718324614801771485218277639920497459200000⟩, + ⟨6, 5, 3, 0, 7, 7, -23820667576824654925738256917388737361380324147200000⟩, + ⟨6, 5, 4, 0, 8, 7, 45968198598018214130182280323855743019921283481600000⟩, + ⟨6, 5, 2, 1, 5, 7, -40693946920720769500682100700172301564818699059200000⟩, + ⟨6, 5, 3, 1, 6, 7, 112950591635666337435199040212130708758502729318400000⟩, + ⟨6, 5, 4, 1, 7, 7, -53610307126088782911741457125582141612485089689600000⟩, + ⟨6, 5, 5, 1, 8, 7, -87718638331470196659435407049033228414898667520000000⟩, + ⟨6, 5, 2, 2, 4, 7, -149921682540101905196954984753428985047252834713600000⟩, + ⟨6, 5, 3, 2, 5, 7, 48066045192138872914572365011089591891422242406400000⟩, + ⟨6, 5, 4, 2, 6, 7, 35344911458570969311334091550697680372041252864000000⟩, + ⟨6, 5, 5, 2, 7, 7, -44963557938290686631043597739743088158500192256000000⟩, + ⟨6, 5, 6, 2, 8, 7, 19925485650011513359027755796578388618707468288000000⟩, + ⟨6, 5, 2, 3, 3, 7, 170775406920783975314139650627572201910125461504000000⟩, + ⟨6, 5, 3, 3, 4, 7, -5237213361370458081374851378372027161487658188800000⟩, + ⟨6, 5, 4, 3, 5, 7, 96975653966864939029122299293074086065170127257600000⟩, + ⟨6, 5, 5, 3, 6, 7, 30764739727535709807855656168264405962199138304000000⟩, + ⟨6, 5, 6, 3, 7, 7, 42247359932885308158420230095883867661533184000000⟩, + ⟨6, 5, 7, 3, 8, 7, -1352334176622453673509199823470802114444053708800000⟩, + ⟨6, 5, 2, 4, 2, 7, -40718933564305655344011737289875386596449058816000000⟩, + ⟨6, 5, 3, 4, 3, 7, -77343012949216174999305801062656685538586027622400000⟩, + ⟨6, 5, 4, 4, 4, 7, -72679934737684644774789884480387044902388629504000000⟩, + ⟨6, 5, 5, 4, 5, 7, 18654256446292849930025537150001507491188310016000000⟩, + ⟨6, 5, 6, 4, 6, 7, 8537718549927134847430074360496145133295632384000000⟩, + ⟨6, 5, 7, 4, 7, 7, -3577035930429920604393294800063240856388868505600000⟩, + ⟨6, 5, 8, 4, 8, 7, 638586677362769247906988003301232513304756224000000⟩, + ⟨6, 5, 2, 5, 1, 7, 42172685584979277431453136539739250139308700467200000⟩, + ⟨6, 5, 3, 5, 2, 7, -96577250191207815250710141829151035007834888601600000⟩, + ⟨6, 5, 4, 5, 3, 7, -69255539634056942283115903516029135710527370035200000⟩, + ⟨6, 5, 5, 5, 4, 7, 12374051698584397495763674993172236258290696192000000⟩, + ⟨6, 5, 6, 5, 5, 7, 7132250359773754333653134424713202547852050432000000⟩, + ⟨6, 5, 7, 5, 6, 7, 1133198048663987094421603504819102118018285568000000⟩, + ⟨6, 5, 8, 5, 7, 7, -1046964286506212988385672234794292386078287462400000⟩, + ⟨6, 5, 2, 6, 0, 7, -759196091070017849676870550274202830867016764620800000⟩, + ⟨6, 5, 3, 6, 1, 7, -23512884587172801359720468489314002716815314124800000⟩, + ⟨6, 5, 4, 6, 2, 7, 87718896174431994167861801927083106956431536947200000⟩, + ⟨6, 5, 5, 6, 3, 7, -112759206495844791283085599117332893611843387392000000⟩, + ⟨6, 5, 6, 6, 4, 7, -4755486864170781130603178687452554981814566912000000⟩, + ⟨6, 5, 7, 6, 5, 7, 7079873254391996934670817171160626064979604275200000⟩, + ⟨6, 5, 8, 6, 6, 7, 1563888780584241516351996921456177003798881894400000⟩, + ⟨6, 5, 3, 7, 0, 7, 2471440258835850745370926944755058627329525180006400000⟩, + ⟨6, 5, 4, 7, 1, 7, 84264289621914172246350421175217893709385511731200000⟩, + ⟨6, 5, 5, 7, 2, 7, 6246828382330618837513578127143387906887909376000000⟩, + ⟨6, 5, 6, 7, 3, 7, -24006603851088687648719854083484219800765333504000000⟩, + ⟨6, 5, 7, 7, 4, 7, 5505235339033325278788409971954659211350114304000000⟩, + ⟨6, 5, 8, 7, 5, 7, 4039690250279896167728188629538581902581039104000000⟩ +] + +def collectedFourData_13_4_49 : List CollectedFourTerm := [ + ⟨6, 6, 1, 0, 5, 8, -129438760031754621759612475331962077163880762572800000⟩, + ⟨6, 6, 2, 0, 6, 8, 110455096514753353785500731339940167168268068454400000⟩, + ⟨6, 6, 3, 0, 7, 8, -15785399016704040900744113467888614079301104435200000⟩, + ⟨6, 6, 4, 0, 8, 8, 20308033058787467952201358638080049613321430630400000⟩, + ⟨6, 6, 1, 1, 4, 8, -56540842093431550139651910603412795360435765248000000⟩, + ⟨6, 6, 2, 1, 5, 8, -53933852830650295728832720625423601791846999654400000⟩, + ⟨6, 6, 3, 1, 6, 8, 74849714114496733208349353010261207539907978854400000⟩, + ⟨6, 6, 4, 1, 7, 8, -23684197393266948340152014439010038109335610982400000⟩, + ⟨6, 6, 5, 1, 8, 8, -29064544534666373736695699869484157797306204160000000⟩, + ⟨6, 6, 1, 2, 3, 8, -85401426121583333655816677342921679916521593241600000⟩, + ⟨6, 6, 2, 2, 4, 8, -198699181919956017079604453790500063798178820915200000⟩, + ⟨6, 6, 3, 2, 5, 8, 31852243438006233303826634441551183810534991462400000⟩, + ⟨6, 6, 4, 2, 6, 8, 15614830518756079289614902032019652090439663616000000⟩, + ⟨6, 6, 5, 2, 7, 8, -14898148865423663842801014520275370661010997248000000⟩, + ⟨6, 6, 6, 2, 8, 8, 5281661239302176815506510767180456110465430323200000⟩, + ⟨6, 6, 1, 3, 2, 8, 220063341461593952131770593033179472833558452633600000⟩, + ⟨6, 6, 2, 3, 3, 8, 226337732289862719864120107298143491296306659328000000⟩, + ⟨6, 6, 3, 3, 4, 8, -3470578747561145343536084171027777455108443340800000⟩, + ⟨6, 6, 4, 3, 5, 8, 42842331148941989746978459158283377091222595174400000⟩, + ⟨6, 6, 5, 3, 6, 8, 10193536572347690875742891796750554234703839232000000⟩, + ⟨6, 6, 6, 3, 7, 8, 11198534747896556963962276514641535825451417600000⟩, + ⟨6, 6, 7, 3, 8, 8, -298720071734124015095105424456966450114566553600000⟩, + ⟨6, 6, 1, 4, 1, 8, -99074350036680463095023948607472193691770997964800000⟩, + ⟨6, 6, 2, 4, 2, 8, -53966968958718791187001950473082429994709286912000000⟩, + ⟨6, 6, 3, 4, 3, 8, -51253404910670944266231055712820797166886217318400000⟩, + ⟨6, 6, 4, 4, 4, 8, -32108861395039490010558251283966632324052811776000000⟩, + ⟨6, 6, 5, 4, 5, 8, 6180869625399242431385953318852091533043171328000000⟩, + ⟨6, 6, 6, 4, 6, 8, 2263098522629749761471898123615952328592038297600000⟩, + ⟨6, 6, 7, 4, 7, 8, -790139337010839390299396541362285189480526643200000⟩, + ⟨6, 6, 8, 4, 8, 8, 120907556748623242071315541284491871727386624000000⟩, + ⟨6, 6, 1, 5, 0, 8, -522182396342604581944173786905441077655231476531200000⟩, + ⟨6, 6, 2, 5, 1, 8, 55893703853420002639531343995972732495258347110400000⟩, + ⟨6, 6, 3, 5, 2, 8, -63999483863646294952737860824247253030242195865600000⟩, + ⟨6, 6, 4, 5, 3, 8, -30596017057175455180676992247208581932535041228800000⟩, + ⟨6, 6, 5, 5, 4, 8, 4099997258379039256213562272511656630929063936000000⟩, + ⟨6, 6, 6, 5, 5, 8, 1890550169561075525996702163571487969666452684800000⟩, + ⟨6, 6, 7, 5, 6, 8, 250314610277265027628601952719681591596548096000000⟩, + ⟨6, 6, 8, 5, 7, 8, -198228209845068050392299257257476904895014502400000⟩, + ⟨6, 6, 2, 6, 0, 8, -1006202969821195252425808672874480550015491742105600000⟩, + ⟨6, 6, 3, 6, 1, 8, -15581438431361946784804519131031105429471808716800000⟩, + ⟨6, 6, 4, 6, 2, 8, 38752839957220127440803621184601191530204286156800000⟩, + ⟨6, 6, 5, 6, 3, 8, -37361443830305683292378297332315630036410433536000000⟩, + ⟨6, 6, 6, 6, 4, 8, -1260539947967941117744740721275737611852106956800000⟩, + ⟨6, 6, 7, 6, 5, 8, 1563888780584241516351996921456177003798881894400000⟩, + ⟨6, 6, 8, 6, 6, 8, 296100714577871078077078464828629669541996134400000⟩, + ⟨6, 6, 3, 7, 0, 8, 1637765629609222300067963940809224724270790633062400000⟩, + ⟨6, 6, 4, 7, 1, 8, 37226648672520528249060670778755332130202242252800000⟩, + ⟨6, 6, 5, 7, 2, 8, 2069813498843708503274355123770490339572318208000000⟩, + ⟨6, 6, 6, 7, 3, 8, -6363445853953588527549880160135058591732832665600000⟩, + ⟨6, 6, 7, 7, 4, 8, 1216063546879056503120484316131656489383231488000000⟩, + ⟨6, 6, 8, 7, 5, 8, 764859486576963260074640399822432733184917504000000⟩ +] + +def collectedFourData_13_4_50 : List CollectedFourTerm := [ + ⟨7, 0, 6, 2, 8, 3, 1391116638472181242842133612336923779523625038643200000⟩, + ⟨7, 0, 6, 3, 7, 3, 2949539417330375951893851225048581011676961177600000⟩, + ⟨7, 0, 7, 3, 8, 3, -472072452064169827131115813316796641469804419481600000⟩, + ⟨7, 0, 6, 4, 6, 3, 596068900804400658340303011338334549261300636057600000⟩, + ⟨7, 0, 7, 4, 7, 3, -1248670744251347027567855498507268051031964201779200000⟩, + ⟨7, 0, 8, 4, 8, 3, 668752998739708214293421818753440863646073749504000000⟩, + ⟨7, 0, 6, 5, 5, 3, 497944808949975951579742609581389326347932585164800000⟩, + ⟨7, 0, 7, 5, 6, 3, 395576471226378890966800413525135580952763826176000000⟩, + ⟨7, 0, 8, 5, 7, 3, -1096422037907096465042208023401048095623909631590400000⟩, + ⟨7, 0, 6, 6, 4, 3, -332008816095282920513510684437111387346516626636800000⟩, + ⟨7, 0, 7, 6, 5, 3, 2471440258835850745370926944755058627329525180006400000⟩, + ⟨7, 0, 8, 6, 6, 3, 1637765629609222300067963940809224724270790633062400000⟩, + ⟨7, 0, 6, 7, 3, 3, -1676043768119675364143332763200846669501123107225600000⟩, + ⟨7, 0, 7, 7, 4, 3, 1921766077212244334869919378501543846534581321728000000⟩, + ⟨7, 0, 8, 7, 5, 3, 4230521970817032390142930839295718991837983145984000000⟩ +] + +def collectedFourData_13_4_51 : List CollectedFourTerm := [ + ⟨7, 1, 5, 1, 8, 4, -104402275012728541099307647770733201966667661312000000⟩, + ⟨7, 1, 5, 2, 7, 4, -53515396849702781211707367620164032007738333593600000⟩, + ⟨7, 1, 6, 2, 8, 4, 94860844726467021510510838595202787723634225971200000⟩, + ⟨7, 1, 5, 3, 6, 4, 36616035985329296298072011337963334806863767142400000⟩, + ⟨7, 1, 6, 3, 7, 4, 201130367464558222102933271375615300585757081600000⟩, + ⟨7, 1, 7, 3, 8, 4, -16095412252449049001445703694157337883325549772800000⟩, + ⟨7, 1, 5, 4, 5, 4, 22202200680594955121314807004024056456758794649600000⟩, + ⟨7, 1, 6, 4, 6, 4, 40646195927598238557503084851346076196081867161600000⟩, + ⟨7, 1, 7, 4, 7, 4, -42573698821904263483958154469699486199477541273600000⟩, + ⟨7, 1, 8, 4, 8, 4, 15200851991696660086281262464522785919376293888000000⟩, + ⟨7, 1, 5, 5, 4, 4, 14727533087957780588188249078097631738651161395200000⟩, + ⟨7, 1, 6, 5, 5, 4, 33955071701270966197995413392323419401981054156800000⟩, + ⟨7, 1, 7, 5, 6, 4, 13487265257520559591166810068186390454083780608000000⟩, + ⟨7, 1, 8, 5, 7, 4, -24921830855441361694192680692294907989599243468800000⟩, + ⟨7, 1, 5, 6, 3, 4, -134205431259786931012495540032535060552116024115200000⟩, + ⟨7, 1, 6, 6, 4, 4, -22639824641895108629654443495575897199134690508800000⟩, + ⟨7, 1, 7, 6, 5, 4, 84264289621914172246350421175217893709385511731200000⟩, + ⟨7, 1, 8, 6, 6, 4, 37226648672520528249060670778755332130202242252800000⟩, + ⟨7, 1, 5, 7, 2, 4, 7434943213150862323970862084328737169626208665600000⟩, + ⟨7, 1, 6, 7, 3, 4, -114290148823881407476577810598252823632915569049600000⟩, + ⟨7, 1, 7, 7, 4, 4, 65523029632956216486052224421383591602813927424000000⟩, + ⟨7, 1, 8, 7, 5, 4, 96160373781053237431989740803244631104786792448000000⟩ +] + +def collectedFourData_13_4_52 : List CollectedFourTerm := [ + ⟨7, 2, 4, 0, 8, 5, 4055940514310393315358603832197984388152872140800000⟩, + ⟨7, 2, 4, 1, 7, 5, -4730231405385134837524458009947429911223127244800000⟩, + ⟨7, 2, 5, 1, 8, 5, -23219198701692593893607589337398670697724641280000000⟩, + ⟨7, 2, 4, 2, 6, 5, 3118609445916204933820695191153281689748242432000000⟩, + ⟨7, 2, 5, 2, 7, 5, -11901892299776887251947436560485760512907280384000000⟩, + ⟨7, 2, 6, 2, 8, 5, 10548586237444105413653124123425698142553636864000000⟩, + ⟨7, 2, 4, 3, 5, 5, 8556512889824446826553872851770965356517838028800000⟩, + ⟨7, 2, 5, 3, 6, 5, 8143452957399951475525307106863097263167635456000000⟩, + ⟨7, 2, 6, 3, 7, 5, 22365824722376289023007142212689059802775552000000⟩, + ⟨7, 2, 7, 3, 8, 5, -1193213382976914472179205226582222911039340544000000⟩, + ⟨7, 2, 4, 4, 4, 5, -6412813659674697426528325348476161456710090752000000⟩, + ⟨7, 2, 5, 4, 5, 5, 4937797659627032514620860467913855017915777024000000⟩, + ⟨7, 2, 6, 4, 6, 5, 4519882826287879211564957693531617277773873152000000⟩, + ⟨7, 2, 7, 4, 7, 5, -3156148248976667416993867531246108702333206528000000⟩, + ⟨7, 2, 8, 4, 8, 5, 845172202394998417112543550171285139677511680000000⟩, + ⟨7, 2, 4, 5, 3, 5, -6110666887310019066865230566443395724500113817600000⟩, + ⟨7, 2, 5, 5, 4, 5, 3275422083602609930214750405607892733067788288000000⟩, + ⟨7, 2, 6, 5, 5, 5, 3775825558714636496642372579208101244274999296000000⟩, + ⟨7, 2, 7, 5, 6, 5, 999861647071786079673436285718872320733347840000000⟩, + ⟨7, 2, 8, 5, 7, 5, -1385661717074452361400631000968244561830739968000000⟩, + ⟨7, 2, 4, 6, 2, 5, 7739755650981812314728798150705596873209125273600000⟩, + ⟨7, 2, 5, 6, 3, 5, -29847458543287727796195011592683665642475225088000000⟩, + ⟨7, 2, 6, 6, 4, 5, -2517562892511437587334194461704873005585268736000000⟩, + ⟨7, 2, 7, 6, 5, 5, 6246828382330618837513578127143387906887909376000000⟩, + ⟨7, 2, 8, 6, 6, 5, 2069813498843708503274355123770490339572318208000000⟩, + ⟨7, 2, 4, 7, 1, 5, 7434943213150862323970862084328737169626208665600000⟩, + ⟨7, 2, 5, 7, 2, 5, 1653540823520402237661574950629933420132696064000000⟩, + ⟨7, 2, 6, 7, 3, 5, -12709137204453556988800656171251225870846656512000000⟩, + ⟨7, 2, 7, 7, 4, 5, 4857468365828288964131534481804366496420331520000000⟩, + ⟨7, 2, 8, 7, 5, 5, 5346547347217986595806096893889471376030433280000000⟩ +] + +def collectedFourData_13_4_53 : List CollectedFourTerm := [ + ⟨7, 3, 3, 0, 7, 6, 16154338063341831211770150295359244796668202188800000⟩, + ⟨7, 3, 4, 0, 8, 6, -62348027646184926036255418883095281914287541452800000⟩, + ⟨7, 3, 3, 1, 6, 6, -76599114439271008941797408535914900073326680473600000⟩, + ⟨7, 3, 4, 1, 7, 6, 72713245521044852711570152006009547561429159116800000⟩, + ⟨7, 3, 5, 1, 8, 6, 178463076254155769607742115981954728939738890240000000⟩, + ⟨7, 3, 3, 2, 5, 6, -32596699521432278298952436156429601432986556825600000⟩, + ⟨7, 3, 4, 2, 6, 6, -47939349027828701931459166310129191088566566912000000⟩, + ⟨7, 3, 5, 2, 7, 6, 91478105698324409740384689477365553722736771072000000⟩, + ⟨7, 3, 6, 2, 8, 6, -54051051294585107412100436975557944200405188608000000⟩, + ⟨7, 3, 3, 3, 4, 6, 3551693707851451446929949200468480223415055155200000⟩, + ⟨7, 3, 4, 3, 5, 6, -131530948328125790090838914181676561152135187660800000⟩, + ⟨7, 3, 5, 3, 6, 6, -62590689919142525649327705833538360132551835648000000⟩, + ⟨7, 3, 6, 3, 7, 6, -114602688180494309318558906575265741295058944000000⟩, + ⟨7, 3, 7, 3, 8, 6, 4585527125407764156131243513090045773847986176000000⟩, + ⟨7, 3, 3, 4, 3, 6, 52451308259498158068218231211957446180727265689600000⟩, + ⟨7, 3, 4, 4, 4, 6, 98577945591790903512675454092803483050319020032000000⟩, + ⟨7, 3, 5, 4, 5, 6, -37951979806838627484147264478367920294767624192000000⟩, + ⟨7, 3, 6, 4, 6, 6, -23159920485078650995253839041659006627447046144000000⟩, + ⟨7, 3, 7, 4, 7, 6, 12129099131777616607193189736464670265140314112000000⟩, + ⟨7, 3, 8, 4, 8, 6, -2598402005886900440936440576392738648543461376000000⟩, + ⟨7, 3, 3, 5, 2, 6, 65495290750566181453007762640366453387507951206400000⟩, + ⟨7, 3, 4, 5, 3, 6, 93933337208080063277114997607498051301945219481600000⟩, + ⟨7, 3, 5, 5, 4, 6, -25174938574771204439491763091989728167727202304000000⟩, + ⟨7, 3, 6, 5, 5, 6, -19347364315897190145630918455795724562477350912000000⟩, + ⟨7, 3, 7, 5, 6, 6, -3842475092647586569147793527337141790950031360000000⟩, + ⟨7, 3, 8, 5, 7, 6, 4260085903114234878147208669888787469699750297600000⟩, + ⟨7, 3, 3, 6, 1, 6, 15945610476302271629128638934412321951589806899200000⟩, + ⟨7, 3, 4, 6, 2, 6, -118975733889474092786667295909410598078494906777600000⟩, + ⟨7, 3, 5, 6, 3, 6, 229407971327417785569423652770789686991812296704000000⟩, + ⟨7, 3, 6, 6, 4, 6, 12900015033052509301027417205647131644465774592000000⟩, + ⟨7, 3, 7, 6, 5, 6, -24006603851088687648719854083484219800765333504000000⟩, + ⟨7, 3, 8, 6, 6, 6, -6363445853953588527549880160135058591732832665600000⟩, + ⟨7, 3, 3, 7, 0, 6, -1676043768119675364143332763200846669501123107225600000⟩, + ⟨7, 3, 4, 7, 1, 6, -114290148823881407476577810598252823632915569049600000⟩, + ⟨7, 3, 5, 7, 2, 6, -12709137204453556988800656171251225870846656512000000⟩, + ⟨7, 3, 6, 7, 3, 6, 65121733992126273007191200584034929717033304064000000⟩, + ⟨7, 3, 7, 7, 4, 6, -18667283882405706916124521002104627774179246080000000⟩, + ⟨7, 3, 8, 7, 5, 6, -16437454180595180483285485375667865688259690496000000⟩ +] + +def collectedFourData_13_4_54 : List CollectedFourTerm := [ + ⟨7, 4, 2, 0, 6, 7, 64804405984483148315878936462649834561794473984000000⟩, + ⟨7, 4, 3, 0, 7, 7, -18522701781694858540660016765006156319890079744000000⟩, + ⟨7, 4, 4, 0, 8, 7, 35744390090108291009502894852826886460546220032000000⟩, + ⟨7, 4, 2, 1, 5, 7, -31643187190352817063401215875659856339988905984000000⟩, + ⟨7, 4, 3, 1, 6, 7, 87829197825207771338790771883572446479377235968000000⟩, + ⟨7, 4, 4, 1, 7, 7, -41686813693152729395488449393500966512012296192000000⟩, + ⟨7, 4, 5, 1, 8, 7, -68209095033547222649519839795812185460336230400000000⟩, + ⟨7, 4, 2, 2, 4, 7, -116577531143667906142825305801408956795738652672000000⟩, + ⟨7, 4, 3, 2, 5, 7, 37375653643966299295767746728260256978308169728000000⟩, + ⟨7, 4, 4, 2, 6, 7, 27483833202242695876383878521106622156405473280000000⟩, + ⟨7, 4, 5, 2, 7, 7, -34963192028471987148082391492797338227960709120000000⟩, + ⟨7, 4, 6, 2, 8, 7, 15493849085475626809506807903459822582638837760000000⟩, + ⟨7, 4, 2, 3, 3, 7, 132793168950428464457981470631795500955813806080000000⟩, + ⟨7, 4, 3, 3, 4, 7, -4072402292963108698041260154918006614157950976000000⟩, + ⟨7, 4, 4, 3, 5, 7, 75407253500345322123086974550445690591538839552000000⟩, + ⟨7, 4, 5, 3, 6, 7, 23922339603908194590405947773067781688346542080000000⟩, + ⟨7, 4, 6, 3, 7, 7, 32851104889356433009711694622428657017159680000000⟩, + ⟨7, 4, 7, 3, 8, 7, -1051560901137038616239449951225177484480741376000000⟩, + ⟨7, 4, 2, 4, 2, 7, -31662616542874348465269940164850762054442680320000000⟩, + ⟨7, 4, 3, 4, 3, 7, -60141117335850239047531343259622781764446978048000000⟩, + ⟨7, 4, 4, 4, 4, 7, -56515156526046972142397043802290654313269166080000000⟩, + ⟨7, 4, 5, 4, 5, 7, 14505354562359451632875970356378398055800504320000000⟩, + ⟨7, 4, 6, 4, 6, 7, 6638840581873616593718901885399764710383943680000000⟩, + ⟨7, 4, 7, 4, 7, 7, -2781465699400559362871173496988255635229376512000000⟩, + ⟨7, 4, 8, 4, 8, 7, 496558316361455632300884174629701958479380480000000⟩, + ⟨7, 4, 2, 5, 1, 7, 32793038898025793877598895058502469184487686144000000⟩, + ⟨7, 4, 3, 5, 2, 7, -75097458894404984740742110133779995503395602432000000⟩, + ⟨7, 4, 4, 5, 3, 7, -53852382735907576715503208664130198461694869504000000⟩, + ⟨7, 4, 5, 5, 4, 7, 9621933084156933103156025748633603322769571840000000⟩, + ⟨7, 4, 6, 5, 5, 7, 5545963227957755760242218537598811927887216640000000⟩, + ⟨7, 4, 7, 5, 6, 7, 881162941689460710458103111906909949903503360000000⟩, + ⟨7, 4, 8, 5, 7, 7, -814108470826685075907337802749682765789134848000000⟩, + ⟨7, 4, 2, 6, 0, 7, -590342934066205303035407716441950955063650287616000000⟩, + ⟨7, 4, 3, 6, 1, 7, -18283372950443030547949215217398518393597853696000000⟩, + ⟨7, 4, 4, 6, 2, 7, 68209295529535526971955792800220806309157535744000000⟩, + ⟨7, 4, 5, 6, 3, 7, -87680378743671559226031927324299766915756195840000000⟩, + ⟨7, 4, 6, 6, 4, 7, -3697816810873126159232457941938058463270666240000000⟩, + ⟨7, 4, 7, 6, 5, 7, 5505235339033325278788409971954659211350114304000000⟩, + ⟨7, 4, 8, 6, 6, 7, 1216063546879056503120484316131656489383231488000000⟩, + ⟨7, 4, 3, 7, 0, 7, 1921766077212244334869919378501543846534581321728000000⟩, + ⟨7, 4, 4, 7, 1, 7, 65523029632956216486052224421383591602813927424000000⟩, + ⟨7, 4, 5, 7, 2, 7, 4857468365828288964131534481804366496420331520000000⟩, + ⟨7, 4, 6, 7, 3, 7, -18667283882405706916124521002104627774179246080000000⟩, + ⟨7, 4, 7, 7, 4, 7, 4280813377462661876640692000359643323910062080000000⟩, + ⟨7, 4, 8, 7, 5, 7, 3141220856007984388269406769804248059299758080000000⟩ +] + +def collectedFourData_13_4_55 : List CollectedFourTerm := [ + ⟨7, 5, 1, 0, 5, 8, -334354017626019895447368668330393863572210843648000000⟩, + ⟨7, 5, 2, 0, 6, 8, 285317205433035913154325109653115394643097288704000000⟩, + ⟨7, 5, 3, 0, 7, 8, -40775356467954529196470116957125332595619397632000000⟩, + ⟨7, 5, 4, 0, 8, 8, 52457798897500580420804233790811129478448676864000000⟩, + ⟨7, 5, 1, 1, 4, 8, -146050979700820886584090583656280058289119559680000000⟩, + ⟨7, 5, 2, 1, 5, 8, -139316850497906949332557848694763760012654280704000000⟩, + ⟨7, 5, 3, 1, 6, 8, 193344734036399931421413739648589380888458952704000000⟩, + ⟨7, 5, 4, 1, 7, 8, -61178788724056089621883577410051626510984413184000000⟩, + ⟨7, 5, 5, 1, 8, 8, -75076794873900566726381000610122621827783065600000000⟩, + ⟨7, 5, 1, 2, 3, 8, -220600922998165394895124463045924830206970822656000000⟩, + ⟨7, 5, 2, 2, 4, 8, -513261018242466926959527537172080684622185234432000000⟩, + ⟨7, 5, 3, 2, 5, 8, 82277716205615033129522953472269408825176489984000000⟩, + ⟨7, 5, 4, 2, 6, 8, 40334759983907976833056499643823308214433218560000000⟩, + ⟨7, 5, 5, 2, 7, 8, -38483495416078639557924335853003631675236679680000000⟩, + ⟨7, 5, 6, 2, 8, 8, 13643090019303915988764866152881312947830259712000000⟩, + ⟨7, 5, 1, 3, 2, 8, 568446903631028315757371748602918264432152805376000000⟩, + ⟨7, 5, 2, 3, 3, 8, 584654319254237722154991250021426862538337812480000000⟩, + ⟨7, 5, 3, 3, 4, 8, -8964872248852454365575399983910367011985686528000000⟩, + ⟨7, 5, 4, 3, 5, 8, 110666276010361699248380934429993335035898363904000000⟩, + ⟨7, 5, 5, 3, 6, 8, 26330983902704938071487040785657907698068357120000000⟩, + ⟨7, 5, 6, 3, 7, 8, 28927000564322740049826449151988516641570816000000⟩, + ⟨7, 5, 7, 3, 8, 8, -771625563357796000160764956769453702775832576000000⟩, + ⟨7, 5, 1, 4, 1, 8, -255919532683441161453190395672854225675372986368000000⟩, + ⟨7, 5, 2, 4, 2, 8, -139402392961889166823115221718443986173999185920000000⟩, + ⟨7, 5, 3, 4, 3, 8, -132392969808208290037743708973611399902285266944000000⟩, + ⟨7, 5, 4, 4, 4, 8, -82940587550396159743305203814599490170687324160000000⟩, + ⟨7, 5, 5, 4, 5, 8, 15965840457432380127536044135804936353459732480000000⟩, + ⟨7, 5, 6, 4, 6, 8, 5845823021938212619167617867954546450802671616000000⟩, + ⟨7, 5, 7, 4, 7, 8, -2041013539909701351177442138543294618546470912000000⟩, + ⟨7, 5, 8, 4, 8, 8, 312317016559264531819893797415838591840419840000000⟩, + ⟨7, 5, 1, 5, 0, 8, -1348852400223087903498645542295904827963177172992000000⟩, + ⟨7, 5, 2, 5, 1, 8, 144379353130431842553248351744674368842486513664000000⟩, + ⟨7, 5, 3, 5, 2, 8, -165317440854286431491039997197344654228765802496000000⟩, + ⟨7, 5, 4, 5, 3, 8, -79032750498468869865571925379109064597840068608000000⟩, + ⟨7, 5, 5, 5, 4, 8, 10590726883187030010220102705837795838798069760000000⟩, + ⟨7, 5, 6, 5, 5, 8, 4883491193528316655128067696670765635042541568000000⟩, + ⟨7, 5, 7, 5, 6, 8, 646589132931764631906527517692842447585935360000000⟩, + ⟨7, 5, 8, 5, 7, 8, -512044447522924939436626397242739847157776384000000⟩, + ⟨7, 5, 2, 6, 0, 8, -2599128772744849620570810145675534318402478800896000000⟩, + ⟨7, 5, 3, 6, 1, 8, -40248504687778684710901447039326637037545586688000000⟩, + ⟨7, 5, 4, 6, 2, 8, 100102687409366279509993971688606847045455577088000000⟩, + ⟨7, 5, 5, 6, 3, 8, -96508563941024973992616637365016306976041205760000000⟩, + ⟨7, 5, 6, 6, 4, 8, -3256108107631583499450223405547563595058905088000000⟩, + ⟨7, 5, 7, 6, 5, 8, 4039690250279896167728188629538581902581039104000000⟩, + ⟨7, 5, 8, 6, 6, 8, 764859486576963260074640399822432733184917504000000⟩, + ⟨7, 5, 3, 7, 0, 8, 4230521970817032390142930839295718991837983145984000000⟩, + ⟨7, 5, 4, 7, 1, 8, 96160373781053237431989740803244631104786792448000000⟩, + ⟨7, 5, 5, 7, 2, 8, 5346547347217986595806096893889471376030433280000000⟩, + ⟨7, 5, 6, 7, 3, 8, -16437454180595180483285485375667865688259690496000000⟩, + ⟨7, 5, 7, 7, 4, 8, 3141220856007984388269406769804248059299758080000000⟩, + ⟨7, 5, 8, 7, 5, 8, 1975713010489628316375766693923330795912560640000000⟩ +] + +def collectedFourData_13_4 : List (List CollectedFourTerm) := [ + collectedFourData_13_4_0, + collectedFourData_13_4_1, + collectedFourData_13_4_2, + collectedFourData_13_4_3, + collectedFourData_13_4_4, + collectedFourData_13_4_5, + collectedFourData_13_4_6, + collectedFourData_13_4_7, + collectedFourData_13_4_8, + collectedFourData_13_4_9, + collectedFourData_13_4_10, + collectedFourData_13_4_11, + collectedFourData_13_4_12, + collectedFourData_13_4_13, + collectedFourData_13_4_14, + collectedFourData_13_4_15, + collectedFourData_13_4_16, + collectedFourData_13_4_17, + collectedFourData_13_4_18, + collectedFourData_13_4_19, + collectedFourData_13_4_20, + collectedFourData_13_4_21, + collectedFourData_13_4_22, + collectedFourData_13_4_23, + collectedFourData_13_4_24, + collectedFourData_13_4_25, + collectedFourData_13_4_26, + collectedFourData_13_4_27, + collectedFourData_13_4_28, + collectedFourData_13_4_29, + collectedFourData_13_4_30, + collectedFourData_13_4_31, + collectedFourData_13_4_32, + collectedFourData_13_4_33, + collectedFourData_13_4_34, + collectedFourData_13_4_35, + collectedFourData_13_4_36, + collectedFourData_13_4_37, + collectedFourData_13_4_38, + collectedFourData_13_4_39, + collectedFourData_13_4_40, + collectedFourData_13_4_41, + collectedFourData_13_4_42, + collectedFourData_13_4_43, + collectedFourData_13_4_44, + collectedFourData_13_4_45, + collectedFourData_13_4_46, + collectedFourData_13_4_47, + collectedFourData_13_4_48, + collectedFourData_13_4_49, + collectedFourData_13_4_50, + collectedFourData_13_4_51, + collectedFourData_13_4_52, + collectedFourData_13_4_53, + collectedFourData_13_4_54, + collectedFourData_13_4_55 +] + +theorem collectedFourChecked_13_4 : collectNumericRowParts 13 4 = collectedFourData_13_4 := by + decide +kernel + +def collectedFourData_13_5_0 : List CollectedFourTerm := [ + ⟨0, 5, 8, 5, 8, 0, -795622182153134800136098853260940776320849149952000000⟩, + ⟨0, 5, 8, 6, 7, 0, -214465958153159533020445793010227935068058288128000000⟩, + ⟨0, 5, 8, 7, 6, 0, -320641194864237388798744437525654772413993320448000000⟩ +] + +def collectedFourData_13_5_1 : List CollectedFourTerm := [ + ⟨0, 6, 7, 4, 8, 1, 347404589299520793703300787030046635566521384960000000⟩, + ⟨0, 6, 7, 5, 7, 1, 158463720131406021002434912844690313201485611008000000⟩, + ⟨0, 6, 8, 5, 8, 1, 956587377225723149962476733514563683186162794496000000⟩, + ⟨0, 6, 7, 6, 6, 1, 47907788699667973493314598935020903692098338816000000⟩, + ⟨0, 6, 8, 6, 7, 1, 257855340154965598495553980692823220085634105344000000⟩, + ⟨0, 6, 7, 7, 5, 1, -172110488201283474675514198124986601555758153728000000⟩, + ⟨0, 6, 8, 7, 6, 1, 385511272191588624852513193654055297831827144704000000⟩ +] + +def collectedFourData_13_5_2 : List CollectedFourTerm := [ + ⟨0, 7, 6, 3, 8, 2, -13237191119326654942640669266568561798928138240000000⟩, + ⟨0, 7, 6, 4, 7, 2, 5776133585652240993639931690598436302204436480000000⟩, + ⟨0, 7, 7, 4, 8, 2, -33899268179154701028606442120467215842856140800000000⟩, + ⟨0, 7, 6, 5, 6, 2, 9782940731160173787282237318599151825369169920000000⟩, + ⟨0, 7, 7, 5, 7, 2, -15462674676325751514378990296370292178383011840000000⟩, + ⟨0, 7, 8, 5, 8, 2, -46671248792011484002562204340881020817548247040000000⟩, + ⟨0, 7, 6, 6, 5, 2, -930530059445201589891161116821219701812101120000000⟩, + ⟨0, 7, 7, 6, 6, 2, -4674776980565817437409959531277154550210887680000000⟩, + ⟨0, 7, 8, 6, 7, 2, -12580587010904513288905559189438280585770434560000000⟩, + ⟨0, 7, 6, 7, 4, 2, -32292780966920872788518655194772688456384512000000000⟩, + ⟨0, 7, 7, 7, 5, 2, 16794307777409080553043071951784807224511037440000000⟩, + ⟨0, 7, 8, 7, 6, 2, -18808833280614053009218346930253743027870760960000000⟩ +] + +def collectedFourData_13_5_3 : List CollectedFourTerm := [ + ⟨0, 8, 5, 2, 8, 3, 7900262367954872421913342409488725082084737024000000⟩, + ⟨0, 8, 5, 3, 7, 3, -622373129854458200996169130970812721821384704000000⟩, + ⟨0, 8, 6, 3, 8, 3, 8065255202982634097587014244682332038487867392000000⟩, + ⟨0, 8, 5, 4, 6, 3, -1524186301942339680891555431002128556511723520000000⟩, + ⟨0, 8, 6, 4, 7, 3, -3519326043935988426471537362016047453945462784000000⟩, + ⟨0, 8, 7, 4, 8, 3, 10327200332555847989840723818045800857280184320000000⟩, + ⟨0, 8, 5, 5, 5, 3, -419458083074465395513399217442141754475151360000000⟩, + ⟨0, 8, 6, 5, 6, 3, -5960623588584545775022833502907841788390670336000000⟩, + ⟨0, 8, 7, 5, 7, 3, 4710607267850938653920946135744947754564059136000000⟩, + ⟨0, 8, 8, 5, 8, 3, 9478736305818707016850571771792697123504390144000000⟩, + ⟨0, 8, 5, 6, 4, 3, 3497880073378331628666250787117560497369513984000000⟩, + ⟨0, 8, 6, 6, 5, 3, 566960341950091286890759508861249636108599296000000⟩, + ⟨0, 8, 7, 6, 6, 3, 1424141610762275700954935413475137868500303872000000⟩, + ⟨0, 8, 8, 6, 7, 3, 2555064840458758674019590538727835396646895616000000⟩, + ⟨0, 8, 5, 7, 3, 3, 4876732383334845472763480418962520087082303488000000⟩, + ⟨0, 8, 6, 7, 4, 3, 19675588073362017518700163798460884194007449600000000⟩, + ⟨0, 8, 7, 7, 5, 3, -5116280975367920407179697412598781985345765376000000⟩, + ⟨0, 8, 8, 7, 6, 3, 3819995725453219449748487778871980403936198656000000⟩ +] + +def collectedFourData_13_5_4 : List CollectedFourTerm := [ + ⟨1, 4, 8, 5, 8, 0, -572038921639293700442325455003886958401005027328000000⟩, + ⟨1, 4, 8, 6, 7, 0, -154197404474399482367410414498973608060536225792000000⟩, + ⟨1, 4, 8, 7, 6, 0, -230535607801807075723681289386874351308895158272000000⟩ +] + +def collectedFourData_13_5_5 : List CollectedFourTerm := [ + ⟨1, 5, 7, 4, 8, 1, 75641738148369055439713934857657606245439242240000000⟩, + ⟨1, 5, 7, 5, 7, 1, 34502915601560783135167758559170979865718423552000000⟩, + ⟨1, 5, 8, 5, 8, 1, 208281450887105747158536425774749256848427188224000000⟩, + ⟨1, 5, 7, 6, 6, 1, 10431147197549924729696851583195567776862306304000000⟩, + ⟨1, 5, 8, 6, 7, 1, 56143835518949619525920867290279774162293620736000000⟩, + ⟨1, 5, 7, 7, 5, 1, -37474278930394672052350595376293535040753631232000000⟩, + ⟨1, 5, 8, 7, 6, 1, 83938852860747167763828766639856699496072216576000000⟩ +] + +def collectedFourData_13_5_6 : List CollectedFourTerm := [ + ⟨1, 6, 6, 3, 8, 2, 30469635161164503208883236742125082113612972032000000⟩, + ⟨1, 6, 6, 4, 7, 2, -13295621511425700472720360609615957598681432064000000⟩, + ⟨1, 6, 7, 4, 8, 2, 78030023464816317824653477427530198836251197440000000⟩, + ⟨1, 6, 6, 5, 6, 2, -22518571515261855154285174718423830077118611456000000⟩, + ⟨1, 6, 7, 5, 7, 2, 35592298377829039793089724537655190882470592512000000⟩, + ⟨1, 6, 8, 5, 8, 2, 107428827640955457412711053954604368081161551872000000⟩, + ⟨1, 6, 6, 6, 5, 2, 2141912975510038281609049633435228618270703616000000⟩, + ⟨1, 6, 7, 6, 6, 2, 10760496526312614547371952704039191775201460224000000⟩, + ⟨1, 6, 8, 6, 7, 2, 28958250498920385029341372240973091170584363008000000⟩, + ⟨1, 6, 6, 7, 4, 2, 74332178596778262318809052962324450180176281600000000⟩, + ⟨1, 6, 7, 7, 5, 2, -38657478474783253101584668120415552321819246592000000⟩, + ⟨1, 6, 8, 7, 6, 2, 43294554161927913353714426936508437731662102528000000⟩ +] + +def collectedFourData_13_5_7 : List CollectedFourTerm := [ + ⟨1, 7, 5, 2, 8, 3, -105537408360888521145556219358633942091219075072000000⟩, + ⟨1, 7, 5, 3, 7, 3, 8314109595235843924489443983739784147985498112000000⟩, + ⟨1, 7, 6, 3, 8, 3, -107741501768922164430566034766724421915745714176000000⟩, + ⟨1, 7, 5, 4, 6, 3, 20361181018321350846239129203840108554941890560000000⟩, + ⟨1, 7, 6, 4, 7, 3, 47013698096982533302736818568508035976608612352000000⟩, + ⟨1, 7, 7, 4, 8, 3, -137958197836889356713748506391276323016236072960000000⟩, + ⟨1, 7, 5, 5, 5, 3, 5603423904409528220528023560597549013354414080000000⟩, + ⟨1, 7, 6, 5, 6, 3, 79626313210258351335048296978992694887352107008000000⟩, + ⟨1, 7, 7, 5, 7, 3, -62927692739861378343275708591090869626269073408000000⟩, + ⟨1, 7, 8, 5, 8, 3, -126623802813188166987533298162036631719150354432000000⟩, + ⟨1, 7, 5, 6, 4, 3, -46727207339204709305907671786146497694323965952000000⟩, + ⟨1, 7, 6, 6, 5, 3, -7573865568758990530054059668855676117228453888000000⟩, + ⟨1, 7, 7, 6, 6, 3, -19024711805572579262167254954875986270136303616000000⟩, + ⟨1, 7, 8, 6, 7, 3, -34132400785804485530151822074123981151270862848000000⟩, + ⟨1, 7, 5, 7, 3, 3, -65146911967686013877618455055643317422956478464000000⟩, + ⟨1, 7, 6, 7, 4, 3, -262840710412580619464619952318018462143007948800000000⟩, + ⟨1, 7, 7, 7, 5, 3, 68346975003847565197874649011275008452358832128000000⟩, + ⟨1, 7, 8, 7, 6, 3, -51030260773272066374065584033701672922768211968000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1311.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1311.lean new file mode 100644 index 0000000000000000000000000000000000000000..d230ed4bfd8c3dce5b08c2d2dd6f62b6089e8ff0 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1311.lean @@ -0,0 +1,640 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1311. -/ +namespace LaughlinFock +def collectedFourData_13_5_8 : List CollectedFourTerm := [ + ⟨1, 8, 4, 1, 8, 4, 97128482680297537559469291244398032477764347494400000⟩, + ⟨1, 8, 4, 2, 7, 4, -13169796348869995197764476101699739100890791936000000⟩, + ⟨1, 8, 5, 2, 8, 4, 164287054501377607527030832724888742004097286144000000⟩, + ⟨1, 8, 4, 3, 6, 4, -10725842493068156143832329768508225956083243417600000⟩, + ⟨1, 8, 5, 3, 7, 4, -12942335778534538121786133512325681099753652224000000⟩, + ⟨1, 8, 6, 3, 8, 4, 83859051724312052532887062916742034907700658176000000⟩, + ⟨1, 8, 4, 4, 5, 4, 27735863686266808377180420833915759814417108172800000⟩, + ⟨1, 8, 5, 4, 6, 4, -31695666092451056959744294748147112955997061120000000⟩, + ⟨1, 8, 6, 4, 7, 4, -36592437229265195924958306712057491417414500352000000⟩, + ⟨1, 8, 7, 4, 8, 4, 71585188983221497930595820172398933700132208640000000⟩, + ⟨1, 8, 4, 5, 4, 4, 3873276981695450069955580626143536053208743936000000⟩, + ⟨1, 8, 5, 5, 5, 4, -8722689164681132579823198406418666772139868160000000⟩, + ⟨1, 8, 6, 5, 6, 4, -61975998185328868745968117798589835368630059008000000⟩, + ⟨1, 8, 7, 5, 7, 4, 32652577720586457186143330682747878761165750272000000⟩, + ⟨1, 8, 8, 5, 8, 4, 49277909882926553211632994918218923564351881216000000⟩, + ⟨1, 8, 4, 6, 3, 4, -96817461742583533259359796151690929324295192576000000⟩, + ⟨1, 8, 5, 6, 4, 4, 72738902518644961009838095225039284214016507904000000⟩, + ⟨1, 8, 6, 6, 5, 4, 5895009574358378282011802371152904911625125888000000⟩, + ⟨1, 8, 7, 6, 6, 4, 9871740942596424670625484328243473696103071744000000⟩, + ⟨1, 8, 8, 6, 7, 4, 13283232162062529877736167419983502640806887424000000⟩, + ⟨1, 8, 4, 7, 2, 4, 99495222569206231867872860332468295871403917312000000⟩, + ⟨1, 8, 5, 7, 3, 4, 101412328038539057026425856409017918822891388928000000⟩, + ⟨1, 8, 6, 7, 4, 4, 204578294973250263991469974005209675007315148800000000⟩, + ⟨1, 8, 7, 7, 5, 4, -35464591439985292820367197866456957734724042752000000⟩, + ⟨1, 8, 8, 7, 6, 4, 19859335573719118624128090801428815768908201984000000⟩ +] + +def collectedFourData_13_5_9 : List CollectedFourTerm := [ + ⟨2, 3, 8, 5, 8, 0, -223907190828259184436880272622154717169639751680000000⟩, + ⟨2, 3, 8, 6, 7, 0, -60355871537430759974469542028623139392999915520000000⟩, + ⟨2, 3, 8, 7, 6, 0, -90236133200280164576036303110314923382873784320000000⟩ +] + +def collectedFourData_13_5_10 : List CollectedFourTerm := [ + ⟨2, 4, 7, 4, 8, 1, -65767004393613221168082236699231228650995056640000000⟩, + ⟨2, 4, 7, 5, 7, 1, -29998694603096457112456416082865810852567580672000000⟩, + ⟨2, 4, 8, 5, 8, 1, -181091120205779797941483353947912174452986609664000000⟩, + ⟨2, 4, 7, 6, 6, 1, -9069401634135820424215818427984013329950572544000000⟩, + ⟨2, 4, 8, 6, 7, 1, -48814476869985454664208773695692765474267856896000000⟩, + ⟨2, 4, 7, 7, 5, 1, 32582158043864218799862325920124475728988209152000000⟩, + ⟨2, 4, 8, 7, 6, 1, -72980963156339640323945341959079197033822683136000000⟩ +] + +def collectedFourData_13_5_11 : List CollectedFourTerm := [ + ⟨2, 5, 6, 3, 8, 2, 63894128023928183908242506518287682357407252480000000⟩, + ⟨2, 5, 6, 4, 7, 2, -27880614208715066888308298610281773051894824960000000⟩, + ⟨2, 5, 7, 4, 8, 2, 163627174483718028531225345054429985354914201600000000⟩, + ⟨2, 5, 6, 5, 6, 2, -47220929417165181556467176852089487774019747840000000⟩, + ⟨2, 5, 7, 5, 7, 2, 74636235622453247519527927430591607612301639680000000⟩, + ⟨2, 5, 8, 5, 8, 2, 225275794424359244529106149126838902486812590080000000⟩, + ⟨2, 5, 6, 6, 5, 2, 4491542519281052105874493338860814789236490240000000⟩, + ⟨2, 5, 7, 6, 6, 2, 22564515098938790558542744113862215724286607360000000⟩, + ⟨2, 5, 8, 6, 7, 2, 60724788955966188696404585513804044025588613120000000⟩, + ⟨2, 5, 6, 7, 4, 2, 155872878373464917226000475056477167444557824000000000⟩, + ⟨2, 5, 7, 7, 5, 2, -81063848178208711081089292897551183076267130880000000⟩, + ⟨2, 5, 8, 7, 6, 2, 90787689833808706512538030511122661362284625920000000⟩ +] + +def collectedFourData_13_5_12 : List CollectedFourTerm := [ + ⟨2, 6, 5, 2, 8, 3, 34354628920587860585532307120944265129258647552000000⟩, + ⟨2, 6, 5, 3, 7, 3, -2706416183470337088311816013460535265504264192000000⟩, + ⟨2, 6, 6, 3, 8, 3, 35072107322941459624029726377363356181663318016000000⟩, + ⟨2, 6, 5, 4, 6, 3, -6627989346463596983711062726148432057031720960000000⟩, + ⟨2, 6, 6, 4, 7, 3, -15303939876781570887132169288387161547742380032000000⟩, + ⟨2, 6, 7, 4, 8, 3, 44908272496445058376969074361413955231269519360000000⟩, + ⟨2, 6, 5, 5, 5, 3, -1824031420806439777335409749200376635357921280000000⟩, + ⟨2, 6, 6, 5, 6, 3, -25920026700851783894772187002146023165529161728000000⟩, + ⟨2, 6, 7, 5, 7, 3, 20484277248065140397738598859838489578992304128000000⟩, + ⟨2, 6, 8, 5, 8, 3, 41218690374558151826364020035763984923531149312000000⟩, + ⟨2, 6, 5, 6, 4, 3, 15210681156243549315654308619750910840780357632000000⟩, + ⟨2, 6, 6, 6, 5, 3, 2465451304426380894355258778989188312421367808000000⟩, + ⟨2, 6, 7, 6, 6, 3, 6192940726444710548433523346263666455327277056000000⟩, + ⟨2, 6, 8, 6, 7, 3, 11110808777446298934570966761737977171875463168000000⟩, + ⟨2, 6, 5, 7, 3, 3, 21206679420427022096361212592644365705726132224000000⟩, + ⟨2, 6, 6, 7, 4, 3, 85560136559069461165856923121503869212609740800000000⟩, + ⟨2, 6, 7, 7, 5, 3, -22248366721993939846989746598421446499812507648000000⟩, + ⟨2, 6, 8, 7, 6, 3, 16611414851042426906416382646939324947877593088000000⟩ +] + +def collectedFourData_13_5_13 : List CollectedFourTerm := [ + ⟨2, 7, 4, 1, 8, 4, -13169796348869995197764476101699739100890791936000000⟩, + ⟨2, 7, 4, 2, 7, 4, 1785712399539958918177099959687524814516387840000000⟩, + ⟨2, 7, 5, 2, 8, 4, -22275927625272574678183978001226977441596047360000000⟩, + ⟨2, 7, 4, 3, 6, 4, 1454333038113212403950511978279082127832121344000000⟩, + ⟨2, 7, 5, 3, 7, 4, 1754870680344406745178368322550405268043202560000000⟩, + ⟨2, 7, 6, 3, 8, 4, -11370574343817822848431742773625199552563773440000000⟩, + ⟨2, 7, 4, 4, 5, 4, -3760747272357508790922983136877541887240568832000000⟩, + ⟨2, 7, 5, 4, 6, 4, 4297662807657953640178770505999065549688012800000000⟩, + ⟨2, 7, 6, 4, 7, 4, 4961623335602538534185800155941992148112506880000000⟩, + ⟨2, 7, 7, 4, 8, 4, -9706342923193197830599289277950453320620441600000000⟩, + ⟨2, 7, 4, 5, 4, 4, -525183423482454341158532959504568984367267840000000⟩, + ⟨2, 7, 5, 5, 5, 4, 1182722479990393110081047777309067019970150400000000⟩, + ⟨2, 7, 6, 5, 6, 4, 8403418359836950466377170612003153313812971520000000⟩, + ⟨2, 7, 7, 5, 7, 4, -4427411887625463653048192818077123724632391680000000⟩, + ⟨2, 7, 8, 5, 8, 4, -6681665560371777924790141203857710810964951040000000⟩, + ⟨2, 7, 4, 6, 3, 4, 13127624554388139215687220197693544319093309440000000⟩, + ⟨2, 7, 5, 6, 4, 4, -9862776668343671059583342881024678601435381760000000⟩, + ⟨2, 7, 6, 6, 5, 4, -799313171857950505272967511369838760789278720000000⟩, + ⟨2, 7, 7, 6, 6, 4, -1338524130462598690269438704851530179527311360000000⟩, + ⟨2, 7, 8, 6, 7, 4, -1801093331241851799605211211459142707901890560000000⟩, + ⟨2, 7, 4, 7, 2, 4, -13490706152951567798174151358457202452232929280000000⟩, + ⟨2, 7, 5, 7, 3, 4, -13750649353068495604959878760180269304848056320000000⟩, + ⟨2, 7, 6, 7, 4, 4, -27739077228921731584264524156795021554614272000000000⟩, + ⟨2, 7, 7, 7, 5, 4, 4808697036870602402189931977463656472253562880000000⟩, + ⟨2, 7, 8, 7, 6, 4, -2692757035962675490001031260957051374754856960000000⟩ +] + +def collectedFourData_13_5_14 : List CollectedFourTerm := [ + ⟨2, 8, 3, 0, 8, 5, 7900262367954872421913342409488725082084737024000000⟩, + ⟨2, 8, 3, 1, 7, 5, -105537408360888521145556219358633942091219075072000000⟩, + ⟨2, 8, 4, 1, 8, 5, 164287054501377607527030832724888742004097286144000000⟩, + ⟨2, 8, 3, 2, 6, 5, 34354628920587860585532307120944265129258647552000000⟩, + ⟨2, 8, 4, 2, 7, 5, -22275927625272574678183978001226977441596047360000000⟩, + ⟨2, 8, 5, 2, 8, 5, 138940893195964502980145419983723123350144286720000000⟩, + ⟨2, 8, 3, 3, 5, 5, 68622263031454203960058538854432710260674265088000000⟩, + ⟨2, 8, 4, 3, 6, 5, -18142124962787301707115219229876721737820798976000000⟩, + ⟨2, 8, 5, 3, 7, 5, -10945595796147155472128651340302184594140037120000000⟩, + ⟨2, 8, 6, 3, 8, 5, 47280866953700652308846064975593602386147409920000000⟩, + ⟨2, 8, 3, 4, 4, 5, -28064094390553830477390913309466680576161349632000000⟩, + ⟨2, 8, 4, 4, 5, 5, 46913564624157440162963348431258738584220336128000000⟩, + ⟨2, 8, 5, 4, 6, 5, -26805667498830640827510129886882391828044185600000000⟩, + ⟨2, 8, 6, 4, 7, 5, -20631310759825116781009753427647863426216099840000000⟩, + ⟨2, 8, 7, 4, 8, 5, 30270522918308548524961762049650618512546201600000000⟩, + ⟨2, 8, 3, 5, 3, 5, -70656640054139223680095396349449223263909576704000000⟩, + ⟨2, 8, 4, 5, 4, 5, 6551417761618249040655399056674251032871567360000000⟩, + ⟨2, 8, 5, 5, 5, 5, -7376955094178741386070427469774266900991180800000000⟩, + ⟨2, 8, 6, 5, 6, 5, -34942905557251770716005990786946785638466191360000000⟩, + ⟨2, 8, 7, 5, 7, 5, 13807473532891450221502193263540712750375239680000000⟩, + ⟨2, 8, 8, 5, 8, 5, 16670131033134201404225223146764908784917676032000000⟩, + ⟨2, 8, 3, 6, 2, 5, -79013984398726533278034571803905388983623876608000000⟩, + ⟨2, 8, 4, 6, 3, 5, -163760981074353351782252389398732823364118773760000000⟩, + ⟨2, 8, 5, 6, 4, 5, 61516764767061892596430382766287152534278635520000000⟩, + ⟨2, 8, 6, 6, 5, 5, 3323686085699253921365802466107841240325160960000000⟩, + ⟨2, 8, 7, 6, 6, 5, 4174365740886840582981374166061580754993807360000000⟩, + ⟨2, 8, 8, 6, 7, 5, 4493559511984201306970620666967656448548405248000000⟩, + ⟨2, 8, 3, 7, 1, 5, 726366615846451343272630636604225834403464478720000000⟩, + ⟨2, 8, 4, 7, 2, 5, 168290254328966388961779104274729540617628549120000000⟩, + ⟨2, 8, 5, 7, 3, 5, 85766462132526814125581216978678544941596016640000000⟩, + ⟨2, 8, 6, 7, 4, 5, 115344008158405195688192078691090970020151296000000000⟩, + ⟨2, 8, 7, 7, 5, 5, -14996562043359888629441310575694431319364730880000000⟩, + ⟨2, 8, 8, 7, 6, 5, 6718177110827168599920505743749904706849210368000000⟩ +] + +def collectedFourData_13_5_15 : List CollectedFourTerm := [ + ⟨3, 2, 8, 5, 8, 0, 983862774057330392010681960938930857614262665216000000⟩, + ⟨3, 2, 8, 6, 7, 0, 265207629026132852603677209113547485743807463424000000⟩, + ⟨3, 2, 8, 7, 6, 0, 396503444137844764693935756164316762897314217984000000⟩ +] + +def collectedFourData_13_5_16 : List CollectedFourTerm := [ + ⟨3, 3, 7, 4, 8, 1, 182137973895841008261211612396656727852591349760000000⟩, + ⟨3, 3, 7, 5, 7, 1, 83079676578042538325397077162547976702733058048000000⟩, + ⟨3, 3, 8, 5, 8, 1, 501521546084164268062518066826329824744467070976000000⟩, + ⟨3, 3, 7, 6, 6, 1, 25117191414142405267433074533508492016952016896000000⟩, + ⟨3, 3, 8, 6, 7, 1, 135188914195823812289519132941329742156806488064000000⟩, + ⟨3, 3, 7, 7, 5, 1, -90234431474878222819447299266652391802161594368000000⟩, + ⟨3, 3, 8, 7, 6, 1, 202116621926505108821727578497145527382493364224000000⟩ +] + +def collectedFourData_13_5_17 : List CollectedFourTerm := [ + ⟨3, 4, 6, 3, 8, 2, -4707788453691442085506524745167640890439630848000000⟩, + ⟨3, 4, 6, 4, 7, 2, 2054273807515759702260191662310910958497693696000000⟩, + ⟨3, 4, 7, 4, 8, 2, -12056227177184718208574063046723661149146972160000000⟩, + ⟨3, 4, 6, 5, 6, 2, 3479289148440303137513885543456915164269379584000000⟩, + ⟨3, 4, 7, 5, 7, 2, -5499278559037405626611384806698078288444653568000000⟩, + ⟨3, 4, 8, 5, 8, 2, -16598564166804059090262502243441337458237636608000000⟩, + ⟨3, 4, 6, 6, 5, 2, -330941710380908154556823992194542538351181824000000⟩, + ⟨3, 4, 7, 6, 6, 2, -1662577875797096361498173436771922030085799936000000⟩, + ⟨3, 4, 8, 6, 7, 2, -4474268123554109898891172375288113955929587712000000⟩, + ⟨3, 4, 6, 7, 4, 2, -11484882253584183076813354511246635808745062400000000⟩, + ⟨3, 4, 7, 7, 5, 2, 5972872003546977473952305630540112453527666688000000⟩, + ⟨3, 4, 8, 7, 6, 2, -6689335172973342791137540868746403379771604992000000⟩ +] + +def collectedFourData_13_5_18 : List CollectedFourTerm := [ + ⟨3, 5, 5, 2, 8, 3, 68622263031454203960058538854432710260674265088000000⟩, + ⟨3, 5, 5, 3, 7, 3, -5405979020876233321744730622763664819248693248000000⟩, + ⟨3, 5, 6, 3, 8, 3, 70055402995198388617741276293377598106688815104000000⟩, + ⟨3, 5, 5, 4, 6, 3, -13239194908903076576146706914211834949261066240000000⟩, + ⟨3, 5, 6, 4, 7, 3, -30569126217885383371185911453926275188111966208000000⟩, + ⟨3, 5, 7, 4, 8, 3, 89702825626868699939806586190030170622881955840000000⟩, + ⟨3, 5, 5, 5, 5, 3, -3643443922085443435381509975209057173446328320000000⟩, + ⟨3, 5, 6, 5, 6, 3, -51774417187264181508780433636235850726330335232000000⟩, + ⟨3, 5, 7, 5, 7, 3, 40916683005810957099132435466943995079747960832000000⟩, + ⟨3, 5, 8, 5, 8, 3, 82333004359710568204821770038473496596502806528000000⟩, + ⟨3, 5, 5, 6, 4, 3, 30382844932020529699271999824405815054311620608000000⟩, + ⟨3, 5, 6, 6, 5, 3, 4924659448211963654849119239589393980563914752000000⟩, + ⟨3, 5, 7, 6, 6, 3, 12370199324540457016164702409703393129989668864000000⟩, + ⟨3, 5, 8, 6, 7, 3, 22193482112135221570668987637039028175573614592000000⟩, + ⟨3, 5, 5, 7, 3, 3, 42359658041312015691825555839449866904541331456000000⟩, + ⟨3, 5, 6, 7, 4, 3, 170903612713600461376537802399538330075345715200000000⟩, + ⟨3, 5, 7, 7, 5, 3, -44440394822660652761792379269908786276793843712000000⟩, + ⟨3, 5, 8, 7, 6, 3, 33180765301461809822444384787285205190361219072000000⟩ +] + +def collectedFourData_13_5_19 : List CollectedFourTerm := [ + ⟨3, 6, 4, 1, 8, 4, -10725842493068156143832329768508225956083243417600000⟩, + ⟨3, 6, 4, 2, 7, 4, 1454333038113212403950511978279082127832121344000000⟩, + ⟨3, 6, 5, 2, 8, 4, -18142124962787301707115219229876721737820798976000000⟩, + ⟨3, 6, 4, 3, 6, 4, 1184448619101542637471293452728932662772131430400000⟩, + ⟨3, 6, 5, 3, 7, 4, 1429214698121925206012014580803435399055671296000000⟩, + ⟨3, 6, 6, 3, 8, 4, -9260506862581530190840125266740781937856610304000000⟩, + ⟨3, 6, 4, 4, 5, 4, -3062855478627304021198236904951478395790897971200000⟩, + ⟨3, 6, 5, 4, 6, 4, 3500134181437926754365388514705093155073556480000000⟩, + ⟨3, 6, 6, 4, 7, 4, 4040881802410747871916291506360745714524356608000000⟩, + ⟨3, 6, 7, 4, 8, 4, -7905111257609522346764398241586497922332098560000000⟩, + ⟨3, 6, 4, 5, 4, 4, -427723749936835369571872499701487401219129344000000⟩, + ⟨3, 6, 5, 5, 5, 4, 963241548869992817411907807155816550251888640000000⟩, + ⟨3, 6, 6, 5, 6, 4, 6843973843126434962931518514086733448407416832000000⟩, + ⟨3, 6, 7, 5, 7, 4, -3605805382304402272556018452143017850241548288000000⟩, + ⟨3, 6, 8, 5, 8, 4, -5441731253350386967176356635923684972470206464000000⟩, + ⟨3, 6, 4, 6, 3, 4, 10691496629754845375177823073581296581192187904000000⟩, + ⟨3, 6, 5, 6, 4, 4, -8032515179935831318382107261464568161701462016000000⟩, + ⟨3, 6, 6, 6, 5, 4, -650982517639212299889475757757921968995172352000000⟩, + ⟨3, 6, 7, 6, 6, 4, -1090130675995206130988941615285956040118501376000000⟩, + ⟨3, 6, 8, 6, 7, 4, -1466859689737958063562863513549218522224132096000000⟩, + ⟨3, 6, 4, 7, 2, 4, -10987200218114196335251551644605343888937320448000000⟩, + ⟨3, 6, 5, 7, 3, 4, -11198905072748299395407388001695697089972928512000000⟩, + ⟨3, 6, 6, 7, 4, 4, -22591463480450587829892507280444545968583475200000000⟩, + ⟨3, 6, 7, 7, 5, 4, 3916334440417001129986287442917233873500766208000000⟩, + ⟨3, 6, 8, 7, 6, 4, -2193055008197972974677138686287614275890446336000000⟩ +] + +def collectedFourData_13_5_20 : List CollectedFourTerm := [ + ⟨3, 7, 3, 0, 8, 5, -622373129854458200996169130970812721821384704000000⟩, + ⟨3, 7, 3, 1, 7, 5, 8314109595235843924489443983739784147985498112000000⟩, + ⟨3, 7, 4, 1, 8, 5, -12942335778534538121786133512325681099753652224000000⟩, + ⟨3, 7, 3, 2, 6, 5, -2706416183470337088311816013460535265504264192000000⟩, + ⟨3, 7, 4, 2, 7, 5, 1754870680344406745178368322550405268043202560000000⟩, + ⟨3, 7, 5, 2, 8, 5, -10945595796147155472128651340302184594140037120000000⟩, + ⟨3, 7, 3, 3, 5, 5, -5405979020876233321744730622763664819248693248000000⟩, + ⟨3, 7, 4, 3, 6, 5, 1429214698121925206012014580803435399055671296000000⟩, + ⟨3, 7, 5, 3, 7, 5, 862280820115772898529603968461368020455915520000000⟩, + ⟨3, 7, 6, 3, 8, 5, -3724729607407259420755206906568249484582584320000000⟩, + ⟨3, 7, 3, 4, 4, 5, 2210855468955952232940104516131767220407631872000000⟩, + ⟨3, 7, 4, 4, 5, 5, -3695793973399977756922979046853324851105497088000000⟩, + ⟨3, 7, 5, 4, 6, 5, 2111718117964718323733321512387908109703577600000000⟩, + ⟨3, 7, 6, 4, 7, 5, 1625309749543961524349475319226242653896048640000000⟩, + ⟨3, 7, 7, 4, 8, 5, -2384675244130628081339543754092620382050713600000000⟩, + ⟨3, 7, 3, 5, 3, 5, 5566244786232103872673013754602427052650921984000000⟩, + ⟨3, 7, 4, 5, 4, 5, -516112780484523943003238819057122851485122560000000⟩, + ⟨3, 7, 5, 5, 5, 5, 581147614715020376484649506889760481529036800000000⟩, + ⟨3, 7, 6, 5, 6, 5, 2752759906568175229111211622094793788159426560000000⟩, + ⟨3, 7, 7, 5, 7, 5, -1087736092525849159541969205074354515507937280000000⟩, + ⟨3, 7, 8, 5, 8, 5, -1313252793762776676406724233758351634068406272000000⟩, + ⟨3, 7, 3, 6, 2, 5, 6224626282283447501203577613190651472057991168000000⟩, + ⟨3, 7, 4, 6, 3, 5, 12900892349182317245972393520080126680718376960000000⟩, + ⟨3, 7, 5, 6, 4, 5, -4846216447430201143039657139355099110226001920000000⟩, + ⟨3, 7, 6, 6, 5, 5, -261835976511479532795239971500741305208668160000000⟩, + ⟨3, 7, 7, 6, 6, 5, -328851492559418695146543461467408260724162560000000⟩, + ⟨3, 7, 8, 6, 7, 5, -353997192422971208670618701246858496319684608000000⟩, + ⟨3, 7, 3, 7, 1, 5, -57222284915478533766778155091409314476321669120000000⟩, + ⟨3, 7, 4, 7, 2, 5, -13257703027125577460530261939459641870668267520000000⟩, + ⟨3, 7, 5, 7, 3, 5, -6756578324598433252849437514545758725409341440000000⟩, + ⟨3, 7, 6, 7, 4, 5, -9086661685906538494319225391619536391766016000000000⟩, + ⟨3, 7, 7, 7, 5, 5, 1181411049567281561386927112433928080174612480000000⟩, + ⟨3, 7, 8, 7, 6, 5, -529249880654845866145632256744285777982128128000000⟩ +] + +def collectedFourData_13_5_21 : List CollectedFourTerm := [ + ⟨3, 8, 2, 0, 7, 6, -13237191119326654942640669266568561798928138240000000⟩, + ⟨3, 8, 3, 0, 8, 6, 8065255202982634097587014244682332038487867392000000⟩, + ⟨3, 8, 2, 1, 6, 6, 30469635161164503208883236742125082113612972032000000⟩, + ⟨3, 8, 3, 1, 7, 6, -107741501768922164430566034766724421915745714176000000⟩, + ⟨3, 8, 4, 1, 8, 6, 83859051724312052532887062916742034907700658176000000⟩, + ⟨3, 8, 2, 2, 5, 6, 63894128023928183908242506518287682357407252480000000⟩, + ⟨3, 8, 3, 2, 6, 6, 35072107322941459624029726377363356181663318016000000⟩, + ⟨3, 8, 4, 2, 7, 6, -11370574343817822848431742773625199552563773440000000⟩, + ⟨3, 8, 5, 2, 8, 6, 47280866953700652308846064975593602386147409920000000⟩, + ⟨3, 8, 2, 3, 4, 6, -4707788453691442085506524745167640890439630848000000⟩, + ⟨3, 8, 3, 3, 5, 6, 70055402995198388617741276293377598106688815104000000⟩, + ⟨3, 8, 4, 3, 6, 6, -9260506862581530190840125266740781937856610304000000⟩, + ⟨3, 8, 5, 3, 7, 6, -3724729607407259420755206906568249484582584320000000⟩, + ⟨3, 8, 6, 3, 8, 6, 12067075764047653677625749676980104505159843840000000⟩, + ⟨3, 8, 2, 4, 3, 6, -100134177884214545466487838546320798341773918208000000⟩, + ⟨3, 8, 3, 4, 4, 6, -28650198279301368013112201249135383872490438656000000⟩, + ⟨3, 8, 4, 4, 5, 6, 23946664905091994241046958775610615935598067712000000⟩, + ⟨3, 8, 5, 4, 6, 6, -9121829934041048631914904355946316904896921600000000⟩, + ⟨3, 8, 6, 4, 7, 6, -5265546215432398996208809808552968733778247680000000⟩, + ⟨3, 8, 7, 4, 8, 6, 6180541381870411682066235645876230303577538560000000⟩, + ⟨3, 8, 2, 5, 2, 6, 13620490798001856425832569700411427759520219136000000⟩, + ⟨3, 8, 3, 5, 3, 6, -72132266914755294069244233986301233656686968832000000⟩, + ⟨3, 8, 4, 5, 4, 6, 3344120342327487217772605958430869008353853440000000⟩, + ⟨3, 8, 5, 5, 5, 6, -2510339643774650824297825774575397234330828800000000⟩, + ⟨3, 8, 6, 5, 6, 6, -8918167452137124525325693769320489550578974720000000⟩, + ⟨3, 8, 7, 5, 7, 6, 2819167074827808863139445551701390829224460288000000⟩, + ⟨3, 8, 8, 5, 8, 6, 2836379662417727210688236096935331706464894976000000⟩, + ⟨3, 8, 2, 6, 1, 6, -228547361702425873799714957208362496534188654592000000⟩, + ⟨3, 8, 3, 6, 2, 6, -80664150011664274347924637590612314732063883264000000⟩, + ⟨3, 8, 4, 6, 3, 6, -83590521627028926458177898525324579250938839040000000⟩, + ⟨3, 8, 5, 6, 4, 6, 20933836709047669196130280136222004071859486720000000⟩, + ⟨3, 8, 6, 6, 5, 6, 848274881493151416376864592054291970046033920000000⟩, + ⟨3, 8, 7, 6, 6, 6, 852309035897385083676928458528367078199525376000000⟩, + ⟨3, 8, 8, 6, 7, 6, 764567524173768136573405973395655020001624064000000⟩, + ⟨3, 8, 2, 7, 0, 6, 1864483445078658867066516516544305577716797669376000000⟩, + ⟨3, 8, 3, 7, 1, 6, 741536401561941604053151453794302833955973365760000000⟩, + ⟨3, 8, 4, 7, 2, 6, 85902454002254224214014216378463191101320724480000000⟩, + ⟨3, 8, 5, 7, 3, 6, 29185883233514328428845532234434715149444055040000000⟩, + ⟨3, 8, 6, 7, 4, 6, 29438226814651619537012904940402373969313792000000000⟩, + ⟨3, 8, 7, 7, 5, 6, -3061951474869071507993881021221781293873758208000000⟩, + ⟨3, 8, 8, 7, 6, 6, 1143080452564854377134656095540221385820340224000000⟩ +] + +def collectedFourData_13_5_22 : List CollectedFourTerm := [ + ⟨4, 1, 8, 5, 8, 0, 812089987777837378809818994569874017170772459520000000⟩, + ⟨4, 1, 8, 6, 7, 0, 218904979325776939757871320620725397980740321280000000⟩, + ⟨4, 1, 8, 7, 6, 0, 327277833448153018906246082581355189584244244480000000⟩ +] + +def collectedFourData_13_5_23 : List CollectedFourTerm := [ + ⟨4, 2, 7, 4, 8, 1, -314021082391852202138811764770764262756507975680000000⟩, + ⟨4, 2, 7, 5, 7, 1, -143236302709292672914247396451127860081526308864000000⟩, + ⟨4, 2, 8, 5, 8, 1, -864665041427588777740256636803745891169041645568000000⟩, + ⟨4, 2, 7, 6, 6, 1, -43304136231485973042207578883280035417453232128000000⟩, + ⟨4, 2, 8, 6, 7, 1, -233076981450495823206598619026950005728217137152000000⟩, + ⟨4, 2, 7, 7, 5, 1, 155571697843519809991117693178955422102269722624000000⟩, + ⟨4, 2, 8, 7, 6, 1, -348465940567900262063672466215693451907439788032000000⟩ +] + +def collectedFourData_13_5_24 : List CollectedFourTerm := [ + ⟨4, 3, 6, 3, 8, 2, -100134177884214545466487838546320798341773918208000000⟩, + ⟨4, 3, 6, 4, 7, 2, 43694193332619100404046274643457223364408508416000000⟩, + ⟨4, 3, 7, 4, 8, 2, -256434716353089838643207813613490781260464783360000000⟩, + ⟨4, 3, 6, 5, 6, 2, 74004123576826551109698598829542403626147774464000000⟩, + ⟨4, 3, 7, 5, 7, 2, -116969091300972538342689754995666782900692451328000000⟩, + ⟨4, 3, 8, 5, 8, 2, -353049758554474619691945396298243323746391687168000000⟩, + ⟨4, 3, 6, 6, 5, 2, -7039096259859266278610515254482003009684373504000000⟩, + ⟨4, 3, 7, 6, 6, 2, -35362861011922923277394162745001821398636691456000000⟩, + ⟨4, 3, 8, 6, 7, 2, -95167224396910563718515121160247996895620759552000000⟩, + ⟨4, 3, 6, 7, 4, 2, -244282268388228780316540379267595417839625830400000000⟩, + ⟨4, 3, 7, 7, 5, 2, 127042375324627937141378363072757000391882702848000000⟩, + ⟨4, 3, 8, 7, 6, 2, -142281473504278205935842457830494458989282066432000000⟩ +] + +def collectedFourData_13_5_25 : List CollectedFourTerm := [ + ⟨4, 4, 5, 2, 8, 3, -28064094390553830477390913309466680576161349632000000⟩, + ⟨4, 4, 5, 3, 7, 3, 2210855468955952232940104516131767220407631872000000⟩, + ⟨4, 4, 6, 3, 8, 3, -28650198279301368013112201249135383872490438656000000⟩, + ⟨4, 4, 5, 4, 6, 3, 5414365530441499784439211388990132371964559360000000⟩, + ⟨4, 4, 6, 4, 7, 3, 12501698511782659281583300568779669195626381312000000⟩, + ⟨4, 4, 7, 4, 8, 3, -36685303781630274223154902882396700726274293760000000⟩, + ⟨4, 4, 5, 5, 5, 3, 1490040543973717411845806989502841625226772480000000⟩, + ⟨4, 4, 6, 5, 6, 3, 21173917425213532065969050759313239424890830848000000⟩, + ⟨4, 4, 7, 5, 7, 3, -16733485654606145149511592849687142117039669248000000⟩, + ⟨4, 4, 8, 5, 8, 3, -33671305837723441222988446130056313181717921792000000⟩, + ⟨4, 4, 5, 6, 4, 3, -12425516011253512719107233734778327078023462912000000⟩, + ⟨4, 4, 6, 6, 5, 3, -2014012675924198619673369620899156703343280128000000⟩, + ⟨4, 4, 7, 6, 6, 3, -5058976870447168612909939653525831571048759296000000⟩, + ⟨4, 4, 8, 6, 7, 3, -9076354368618553833930727906244853183585189888000000⟩, + ⟨4, 4, 5, 7, 3, 3, -17323611742126058716396326723869353986893021184000000⟩, + ⟨4, 4, 6, 7, 4, 3, -69893572537569801918975544725714897587719372800000000⟩, + ⟨4, 4, 7, 7, 5, 3, 18174559974580873248106772846796641631436013568000000⟩, + ⟨4, 4, 8, 7, 6, 3, -13569767131465940315620087052480850326200516608000000⟩ +] + +def collectedFourData_13_5_26 : List CollectedFourTerm := [ + ⟨4, 5, 4, 1, 8, 4, 27735863686266808377180420833915759814417108172800000⟩, + ⟨4, 5, 4, 2, 7, 4, -3760747272357508790922983136877541887240568832000000⟩, + ⟨4, 5, 5, 2, 8, 4, 46913564624157440162963348431258738584220336128000000⟩, + ⟨4, 5, 4, 3, 6, 4, -3062855478627304021198236904951478395790897971200000⟩, + ⟨4, 5, 5, 3, 7, 4, -3695793973399977756922979046853324851105497088000000⟩, + ⟨4, 5, 6, 3, 8, 4, 23946664905091994241046958775610615935598067712000000⟩, + ⟨4, 5, 4, 4, 5, 4, 7920211591848757455829641173191160804234860953600000⟩, + ⟨4, 5, 5, 4, 6, 4, -9050966821743399812748826590962924322753085440000000⟩, + ⟨4, 5, 6, 4, 7, 4, -10449281435599433573035477739135658395040743424000000⟩, + ⟨4, 5, 7, 4, 8, 4, 20441759088624504236309926121779346844344647680000000⟩, + ⟨4, 5, 4, 5, 4, 4, 1106047159586194129559549421624701598755192832000000⟩, + ⟨4, 5, 5, 5, 5, 4, -2490838021691324413107162566745022728681553920000000⟩, + ⟨4, 5, 6, 5, 6, 4, -17697772991539692730787107994214910909948624896000000⟩, + ⟨4, 5, 7, 5, 7, 4, 9324221069574359460012728842054995485040574464000000⟩, + ⟨4, 5, 8, 5, 8, 4, 14071725960712845666730163564338307223301128192000000⟩, + ⟨4, 5, 4, 6, 3, 4, -27647049014257519690411442186972632218454720512000000⟩, + ⟨4, 5, 5, 6, 4, 4, 20771211793623849955876240626536191771696693248000000⟩, + ⟨4, 5, 6, 6, 5, 4, 1683370083334043832647062101246820682569875456000000⟩, + ⟨4, 5, 7, 6, 6, 4, 2818959522215761874185109576035514225239523328000000⟩, + ⟨4, 5, 8, 6, 7, 4, 3793139832861155793620681305104206717138239488000000⟩, + ⟨4, 5, 4, 7, 2, 4, 28411706375539432625311442863340237900369362944000000⟩, + ⟨4, 5, 5, 7, 3, 4, 28959152135035455528557637968839426037237415936000000⟩, + ⟨4, 5, 6, 7, 4, 4, 58419070760362563439754268631249952959994265600000000⟩, + ⟨4, 5, 7, 7, 5, 4, -10127215485351217828992828958761540251994292224000000⟩, + ⟨4, 5, 8, 7, 6, 4, 5671002049785293518162344390229873767594590208000000⟩ +] + +def collectedFourData_13_5_27 : List CollectedFourTerm := [ + ⟨4, 6, 3, 0, 8, 5, -1524186301942339680891555431002128556511723520000000⟩, + ⟨4, 6, 3, 1, 7, 5, 20361181018321350846239129203840108554941890560000000⟩, + ⟨4, 6, 4, 1, 8, 5, -31695666092451056959744294748147112955997061120000000⟩, + ⟨4, 6, 3, 2, 6, 5, -6627989346463596983711062726148432057031720960000000⟩, + ⟨4, 6, 4, 2, 7, 5, 4297662807657953640178770505999065549688012800000000⟩, + ⟨4, 6, 5, 2, 8, 5, -26805667498830640827510129886882391828044185600000000⟩, + ⟨4, 6, 3, 3, 5, 5, -13239194908903076576146706914211834949261066240000000⟩, + ⟨4, 6, 4, 3, 6, 5, 3500134181437926754365388514705093155073556480000000⟩, + ⟨4, 6, 5, 3, 7, 5, 2111718117964718323733321512387908109703577600000000⟩, + ⟨4, 6, 6, 3, 8, 5, -9121829934041048631914904355946316904896921600000000⟩, + ⟨4, 6, 3, 4, 4, 5, 5414365530441499784439211388990132371964559360000000⟩, + ⟨4, 6, 4, 4, 5, 5, -9050966821743399812748826590962924322753085440000000⟩, + ⟨4, 6, 5, 4, 6, 5, 5171579032851181033322330494116349385637888000000000⟩, + ⟨4, 6, 6, 4, 7, 5, 3980369231633684317462743288632136489448243200000000⟩, + ⟨4, 6, 7, 4, 8, 5, -5840048625709273901241964390408811150573568000000000⟩, + ⟨4, 6, 3, 5, 3, 5, 13631684353752417507254854009707925178595409920000000⟩, + ⟨4, 6, 4, 5, 4, 5, -1263955644190235956385800242290908570897612800000000⟩, + ⟨4, 6, 5, 5, 5, 5, 1423225379222649468583548964110600643805184000000000⟩, + ⟨4, 6, 6, 5, 6, 5, 6741484715300056916221569851248382179069132800000000⟩, + ⟨4, 6, 7, 5, 7, 5, -2663856090226592956142175589633207625475686400000000⟩, + ⟨4, 6, 8, 5, 8, 5, -3216144501143254897682464398777605705548431360000000⟩, + ⟨4, 6, 3, 6, 2, 5, 15244054826700743312125965912962398135611555840000000⟩, + ⟨4, 6, 4, 6, 3, 5, 31594171499747573992149639331644977158343884800000000⟩, + ⟨4, 6, 5, 6, 4, 5, -11868341307003599338408377753801391278234009600000000⟩, + ⟨4, 6, 6, 6, 5, 5, -641233995509767031505758174377691558235340800000000⟩, + ⟨4, 6, 7, 6, 6, 5, -805354402831581020936066540766760065092812800000000⟩, + ⟨4, 6, 8, 6, 7, 5, -866935999861232345230789932529698162648023040000000⟩, + ⟨4, 6, 3, 7, 1, 5, -140136870713570050822160566685812705277352345600000000⟩, + ⟨4, 6, 4, 7, 2, 5, -32467997700816143857978162644407975063165337600000000⟩, + ⟨4, 6, 5, 7, 3, 5, -16546800683316303021604647921686392830374707200000000⟩, + ⟨4, 6, 6, 7, 4, 5, -22253154269821701201619759765093712218030080000000000⟩, + ⟨4, 6, 7, 7, 5, 5, 2893265233244989339704541268007273347049062400000000⟩, + ⟨4, 6, 8, 7, 6, 5, -1296128286559181924610739157566734731984240640000000⟩ +] + +def collectedFourData_13_5_28 : List CollectedFourTerm := [ + ⟨4, 7, 2, 0, 7, 6, 5776133585652240993639931690598436302204436480000000⟩, + ⟨4, 7, 3, 0, 8, 6, -3519326043935988426471537362016047453945462784000000⟩, + ⟨4, 7, 2, 1, 6, 6, -13295621511425700472720360609615957598681432064000000⟩, + ⟨4, 7, 3, 1, 7, 6, 47013698096982533302736818568508035976608612352000000⟩, + ⟨4, 7, 4, 1, 8, 6, -36592437229265195924958306712057491417414500352000000⟩, + ⟨4, 7, 2, 2, 5, 6, -27880614208715066888308298610281773051894824960000000⟩, + ⟨4, 7, 3, 2, 6, 6, -15303939876781570887132169288387161547742380032000000⟩, + ⟨4, 7, 4, 2, 7, 6, 4961623335602538534185800155941992148112506880000000⟩, + ⟨4, 7, 5, 2, 8, 6, -20631310759825116781009753427647863426216099840000000⟩, + ⟨4, 7, 2, 3, 4, 6, 2054273807515759702260191662310910958497693696000000⟩, + ⟨4, 7, 3, 3, 5, 6, -30569126217885383371185911453926275188111966208000000⟩, + ⟨4, 7, 4, 3, 6, 6, 4040881802410747871916291506360745714524356608000000⟩, + ⟨4, 7, 5, 3, 7, 6, 1625309749543961524349475319226242653896048640000000⟩, + ⟨4, 7, 6, 3, 8, 6, -5265546215432398996208809808552968733778247680000000⟩, + ⟨4, 7, 2, 4, 3, 6, 43694193332619100404046274643457223364408508416000000⟩, + ⟨4, 7, 3, 4, 4, 6, 12501698511782659281583300568779669195626381312000000⟩, + ⟨4, 7, 4, 4, 5, 6, -10449281435599433573035477739135658395040743424000000⟩, + ⟨4, 7, 5, 4, 6, 6, 3980369231633684317462743288632136489448243200000000⟩, + ⟨4, 7, 6, 4, 7, 6, 2297654998525868898348803013309626217513615360000000⟩, + ⟨4, 7, 7, 4, 8, 6, -2696919031501537660556409136596580631178117120000000⟩, + ⟨4, 7, 2, 5, 2, 6, -5943388868695866330005264009399040978318262272000000⟩, + ⟨4, 7, 3, 5, 3, 6, 31475379163124434707405992656766146400080625664000000⟩, + ⟨4, 7, 4, 5, 4, 6, -1459228445797587957142201543505825938412666880000000⟩, + ⟨4, 7, 5, 5, 5, 6, 1095402868863211467258030378878770282600857600000000⟩, + ⟨4, 7, 6, 5, 6, 6, 3891499796172788170029679891767785141242429440000000⟩, + ⟨4, 7, 7, 5, 7, 6, -1230161707093809378019120342434267606156312576000000⟩, + ⟨4, 7, 8, 5, 8, 6, -1237672530528922378469155860491322246354173952000000⟩, + ⟨4, 7, 2, 6, 1, 6, 99728113006858531773697109331205996029551837184000000⟩, + ⟨4, 7, 3, 6, 2, 6, 35198321293419931964440797801709669884811542528000000⟩, + ⟨4, 7, 4, 6, 3, 6, 36475262392119350801825413807001640110213038080000000⟩, + ⟨4, 7, 5, 6, 4, 6, -9134614451184321146005442779839769823611453440000000⟩, + ⟨4, 7, 6, 6, 5, 6, -370150206995500817968893132598626872029347840000000⟩, + ⟨4, 7, 7, 6, 6, 6, -371910536247677264731415021979518093337034752000000⟩, + ⟨4, 7, 8, 6, 7, 6, -333623962596660600120392741297046292034224128000000⟩, + ⟨4, 7, 2, 7, 0, 6, -813579357578940555695445993044811083336229322752000000⟩, + ⟨4, 7, 3, 7, 1, 6, -323574183936351209364252305330091994159534571520000000⟩, + ⟨4, 7, 4, 7, 2, 6, -37484088971709816801673916460843922292169768960000000⟩, + ⟨4, 7, 5, 7, 3, 6, -12735448091090346856188125979787730127767470080000000⟩, + ⟨4, 7, 6, 7, 4, 6, -12845559837683079566859488898197983365955584000000000⟩, + ⟨4, 7, 7, 7, 5, 6, 1336102243459057613825234193310300631168188416000000⟩, + ⟨4, 7, 8, 7, 6, 6, -498790516329590987836493910180108283253096448000000⟩ +] + +def collectedFourData_13_5_29 : List CollectedFourTerm := [ + ⟨4, 8, 1, 0, 6, 7, 347404589299520793703300787030046635566521384960000000⟩, + ⟨4, 8, 2, 0, 7, 7, -33899268179154701028606442120467215842856140800000000⟩, + ⟨4, 8, 3, 0, 8, 7, 10327200332555847989840723818045800857280184320000000⟩, + ⟨4, 8, 1, 1, 5, 7, 75641738148369055439713934857657606245439242240000000⟩, + ⟨4, 8, 2, 1, 6, 7, 78030023464816317824653477427530198836251197440000000⟩, + ⟨4, 8, 3, 1, 7, 7, -137958197836889356713748506391276323016236072960000000⟩, + ⟨4, 8, 4, 1, 8, 7, 71585188983221497930595820172398933700132208640000000⟩, + ⟨4, 8, 1, 2, 4, 7, -65767004393613221168082236699231228650995056640000000⟩, + ⟨4, 8, 2, 2, 5, 7, 163627174483718028531225345054429985354914201600000000⟩, + ⟨4, 8, 3, 2, 6, 7, 44908272496445058376969074361413955231269519360000000⟩, + ⟨4, 8, 4, 2, 7, 7, -9706342923193197830599289277950453320620441600000000⟩, + ⟨4, 8, 5, 2, 8, 7, 30270522918308548524961762049650618512546201600000000⟩, + ⟨4, 8, 1, 3, 3, 7, 182137973895841008261211612396656727852591349760000000⟩, + ⟨4, 8, 2, 3, 4, 7, -12056227177184718208574063046723661149146972160000000⟩, + ⟨4, 8, 3, 3, 5, 7, 89702825626868699939806586190030170622881955840000000⟩, + ⟨4, 8, 4, 3, 6, 7, -7905111257609522346764398241586497922332098560000000⟩, + ⟨4, 8, 5, 3, 7, 7, -2384675244130628081339543754092620382050713600000000⟩, + ⟨4, 8, 6, 3, 8, 7, 6180541381870411682066235645876230303577538560000000⟩, + ⟨4, 8, 1, 4, 2, 7, -314021082391852202138811764770764262756507975680000000⟩, + ⟨4, 8, 2, 4, 3, 7, -256434716353089838643207813613490781260464783360000000⟩, + ⟨4, 8, 3, 4, 4, 7, -36685303781630274223154902882396700726274293760000000⟩, + ⟨4, 8, 4, 4, 5, 7, 20441759088624504236309926121779346844344647680000000⟩, + ⟨4, 8, 5, 4, 6, 7, -5840048625709273901241964390408811150573568000000000⟩, + ⟨4, 8, 6, 4, 7, 7, -2696919031501537660556409136596580631178117120000000⟩, + ⟨4, 8, 7, 4, 8, 7, 2637969388768710979133232696066678172365619200000000⟩, + ⟨4, 8, 1, 5, 1, 7, -142380818191652405751090686079760603791470100480000000⟩, + ⟨4, 8, 2, 5, 2, 7, 34880864537722305696272506617671035225500549120000000⟩, + ⟨4, 8, 3, 5, 3, 7, -92362157442282240996394849367091349398717726720000000⟩, + ⟨4, 8, 4, 5, 4, 7, 2854664842563987408875699929204585840351641600000000⟩, + ⟨4, 8, 5, 5, 5, 7, -1607189093931608573589922458155864423399424000000000⟩, + ⟨4, 8, 6, 5, 6, 7, -4567726603043614003538004257843389460360724480000000⟩, + ⟨4, 8, 7, 5, 7, 7, 1203272656184331638868495431719307511500636160000000⟩, + ⟨4, 8, 8, 5, 8, 7, 1037673691683680140683260848180781753365954560000000⟩, + ⟨4, 8, 1, 6, 0, 7, 1552248308348098847208193411622022019447982653440000000⟩, + ⟨4, 8, 2, 6, 1, 7, -585289449713928959336128218087247457030913392640000000⟩, + ⟨4, 8, 3, 6, 2, 7, -103286854025118412980510506206182761490221629440000000⟩, + ⟨4, 8, 4, 6, 3, 7, -71355961757699193945049377225746571335408025600000000⟩, + ⟨4, 8, 5, 6, 4, 7, 13402423108905336279418813373032728515680665600000000⟩, + ⟨4, 8, 6, 6, 5, 7, 434471292862012530954328257817110958602977280000000⟩, + ⟨4, 8, 7, 6, 6, 7, 363781262441422817641437076134966449217208320000000⟩, + ⟨4, 8, 8, 6, 7, 7, 279712767604099999339279216397648605835427840000000⟩, + ⟨4, 8, 2, 7, 0, 7, 4774776140236825719045993120556126914127771729920000000⟩, + ⟨4, 8, 3, 7, 1, 7, 949504359140517474606908115612998416413071769600000000⟩, + ⟨4, 8, 4, 7, 2, 7, 73329512764941862532564093330393021711332147200000000⟩, + ⟨4, 8, 5, 7, 3, 7, 18685612262065844616420223513335610536571699200000000⟩, + ⟨4, 8, 6, 7, 4, 7, 15077735699557095994513194584410941007331328000000000⟩, + ⟨4, 8, 7, 7, 5, 7, -1306897529121531624895211716935144574612930560000000⟩, + ⟨4, 8, 8, 7, 6, 7, 418189612914286607403819275182086091639357440000000⟩ +] + +def collectedFourData_13_5_30 : List CollectedFourTerm := [ + ⟨5, 0, 8, 5, 8, 0, -5025408709911259530124491772871594453450310549504000000⟩, + ⟨5, 0, 8, 6, 7, 0, -1354636809101571258533483954595520030216506310656000000⟩, + ⟨5, 0, 8, 7, 6, 0, -2025274168533616922037966381921322777756928311296000000⟩ +] + +def collectedFourData_13_5_31 : List CollectedFourTerm := [ + ⟨5, 1, 7, 4, 8, 1, -142380818191652405751090686079760603791470100480000000⟩, + ⟨5, 1, 7, 5, 7, 1, -64945008848314981097121234120337901483043323904000000⟩, + ⟨5, 1, 8, 5, 8, 1, -392049206131178697522819495342527235674811138048000000⟩, + ⟨5, 1, 7, 6, 6, 1, -19634600010797653492152869791409177532938846208000000⟩, + ⟨5, 1, 8, 6, 7, 1, -105679819545209120779688041652083686314052943872000000⟩, + ⟨5, 1, 7, 7, 5, 1, 70538020752327698615851008164588659841395851264000000⟩, + ⟨5, 1, 8, 7, 6, 1, -157998518290785624260351573763448679047523991552000000⟩ +] + +def collectedFourData_13_5_32 : List CollectedFourTerm := [ + ⟨5, 2, 6, 3, 8, 2, 13620490798001856425832569700411427759520219136000000⟩, + ⟨5, 2, 6, 4, 7, 2, -5943388868695866330005264009399040978318262272000000⟩, + ⟨5, 2, 7, 4, 8, 2, 34880864537722305696272506617671035225500549120000000⟩, + ⟨5, 2, 6, 5, 6, 2, -10066218203317951226434737153942809323071602688000000⟩, + ⟨5, 2, 7, 5, 7, 2, 15910416057519643357208302925708063740501426176000000⟩, + ⟨5, 2, 8, 5, 8, 2, 48022674068271933034095793845876098815236243456000000⟩, + ⟨5, 2, 6, 6, 5, 2, 957474738989958738576645291636035188181434368000000⟩, + ⟨5, 2, 7, 6, 6, 2, 4810141084504225571745804817336555571565821952000000⟩, + ⟨5, 2, 8, 6, 7, 2, 12944873883803452305425484889182255387229814784000000⟩, + ⟨5, 2, 6, 7, 4, 2, 33227859448191532516681662695773003880123596800000000⟩, + ⟨5, 2, 7, 7, 5, 2, -17280608286076268687941567769685857863011926016000000⟩, + ⟨5, 2, 8, 7, 6, 2, 19353466933458186657044855414803798040713887744000000⟩ +] + +def collectedFourData_13_5_33 : List CollectedFourTerm := [ + ⟨5, 3, 5, 2, 8, 3, -70656640054139223680095396349449223263909576704000000⟩, + ⟨5, 3, 5, 3, 7, 3, 5566244786232103872673013754602427052650921984000000⟩, + ⟨5, 3, 6, 3, 8, 3, -72132266914755294069244233986301233656686968832000000⟩, + ⟨5, 3, 5, 4, 6, 3, 13631684353752417507254854009707925178595409920000000⟩, + ⟨5, 3, 6, 4, 7, 3, 31475379163124434707405992656766146400080625664000000⟩, + ⟨5, 3, 7, 4, 8, 3, -92362157442282240996394849367091349398717726720000000⟩, + ⟨5, 3, 5, 5, 5, 3, 3751457535613964538667025422848917991126466560000000⟩, + ⟨5, 3, 6, 5, 6, 3, 53309322625174315570788313693995729368547065856000000⟩, + ⟨5, 3, 7, 5, 7, 3, -42129699832629302621460269845552368184675270656000000⟩, + ⟨5, 3, 8, 5, 8, 3, -84773850302101682120952517694629106750507188224000000⟩, + ⟨5, 3, 5, 6, 4, 3, -31283575378423511285692860435128962412250660864000000⟩, + ⟨5, 3, 6, 6, 5, 3, -5070656003606805431643333581693009007545942016000000⟩, + ⟨5, 3, 7, 6, 6, 3, -12736926508404150717175618799968954297626918912000000⟩, + ⟨5, 3, 8, 6, 7, 3, -22851430539770195529270663670154457943413620736000000⟩, + ⟨5, 3, 5, 7, 3, 3, -43615453335742044197664630819386761351840923648000000⟩, + ⟨5, 3, 6, 7, 4, 3, -175970224734819317748929408788491010469108121600000000⟩, + ⟨5, 3, 7, 7, 5, 3, 45757875682550552225198409217884665466580893696000000⟩, + ⟨5, 3, 8, 7, 6, 3, -34164442952743253134746296836732289209992216576000000⟩ +] + +def collectedFourData_13_5_34 : List CollectedFourTerm := [ + ⟨5, 4, 4, 1, 8, 4, 3873276981695450069955580626143536053208743936000000⟩, + ⟨5, 4, 4, 2, 7, 4, -525183423482454341158532959504568984367267840000000⟩, + ⟨5, 4, 5, 2, 8, 4, 6551417761618249040655399056674251032871567360000000⟩, + ⟨5, 4, 4, 3, 6, 4, -427723749936835369571872499701487401219129344000000⟩, + ⟨5, 4, 5, 3, 7, 4, -516112780484523943003238819057122851485122560000000⟩, + ⟨5, 4, 6, 3, 8, 4, 3344120342327487217772605958430869008353853440000000⟩, + ⟨5, 4, 4, 4, 5, 4, 1106047159586194129559549421624701598755192832000000⟩, + ⟨5, 4, 5, 4, 6, 4, -1263955644190235956385800242290908570897612800000000⟩, + ⟨5, 4, 6, 4, 7, 4, -1459228445797587957142201543505825938412666880000000⟩, + ⟨5, 4, 7, 4, 8, 4, 2854664842563987408875699929204585840351641600000000⟩, + ⟨5, 4, 4, 5, 4, 4, 154458034995897444297419033450742462378147840000000⟩, + ⟨5, 4, 5, 5, 5, 4, -347842262410808698101847352190354871182950400000000⟩, + ⟨5, 4, 6, 5, 6, 4, -2471470783487564475117815151457683193221611520000000⟩, + ⟨5, 4, 7, 5, 7, 4, 1302115241462781427116907959474521108046151680000000⟩, + ⟨5, 4, 8, 5, 8, 4, 1965098072043901292200872030752589546038231040000000⟩, + ⟨5, 4, 4, 6, 3, 4, -3860874129250630051323811259593591296035389440000000⟩, + ⟨5, 4, 5, 6, 4, 4, 2900672480662637966223154743361766801811701760000000⟩, + ⟨5, 4, 6, 6, 5, 4, 235080424002837454903461916116167997228318720000000⟩, + ⟨5, 4, 7, 6, 6, 4, 393663999550725269839755364808741795250831360000000⟩, + ⟨5, 4, 8, 6, 7, 4, 529707002066346656798965563259082777359810560000000⟩, + ⟨5, 4, 4, 7, 2, 4, 3967657526726140860726035811247773254449889280000000⟩, + ⟨5, 4, 5, 7, 3, 4, 4044107608936222982398058619205070463770296320000000⟩, + ⟨5, 4, 6, 7, 4, 4, 8158146601368949674930823546196549563318272000000000⟩, + ⟨5, 4, 7, 7, 5, 4, -1414252358310471004903289054989815672345722880000000⟩, + ⟨5, 4, 8, 7, 6, 4, 791947997402982109120745109074960601537576960000000⟩ +] + +def collectedFourData_13_5_35 : List CollectedFourTerm := [ + ⟨5, 5, 3, 0, 8, 5, -419458083074465395513399217442141754475151360000000⟩, + ⟨5, 5, 3, 1, 7, 5, 5603423904409528220528023560597549013354414080000000⟩, + ⟨5, 5, 4, 1, 8, 5, -8722689164681132579823198406418666772139868160000000⟩, + ⟨5, 5, 3, 2, 6, 5, -1824031420806439777335409749200376635357921280000000⟩, + ⟨5, 5, 4, 2, 7, 5, 1182722479990393110081047777309067019970150400000000⟩, + ⟨5, 5, 5, 2, 8, 5, -7376955094178741386070427469774266900991180800000000⟩, + ⟨5, 5, 3, 3, 5, 5, -3643443922085443435381509975209057173446328320000000⟩, + ⟨5, 5, 4, 3, 6, 5, 963241548869992817411907807155816550251888640000000⟩, + ⟨5, 5, 5, 3, 7, 5, 581147614715020376484649506889760481529036800000000⟩, + ⟨5, 5, 6, 3, 8, 5, -2510339643774650824297825774575397234330828800000000⟩, + ⟨5, 5, 3, 4, 4, 5, 1490040543973717411845806989502841625226772480000000⟩, + ⟨5, 5, 4, 4, 5, 5, -2490838021691324413107162566745022728681553920000000⟩, + ⟨5, 5, 5, 4, 6, 5, 1423225379222649468583548964110600643805184000000000⟩, + ⟨5, 5, 6, 4, 7, 5, 1095402868863211467258030378878770282600857600000000⟩, + ⟨5, 5, 7, 4, 8, 5, -1607189093931608573589922458155864423399424000000000⟩, + ⟨5, 5, 3, 5, 3, 5, 3751457535613964538667025422848917991126466560000000⟩, + ⟨5, 5, 4, 5, 4, 5, -347842262410808698101847352190354871182950400000000⟩, + ⟨5, 5, 5, 5, 5, 5, 391673503817019368710976825274055274790912000000000⟩, + ⟨5, 5, 6, 5, 6, 5, 1855265496187712865354576468884194989598310400000000⟩, + ⟨5, 5, 7, 5, 7, 5, -733096713812979408871507507210406566507315200000000⟩, + ⟨5, 5, 8, 5, 8, 5, -885087213827399225148144723798888863477268480000000⟩, + ⟨5, 5, 3, 6, 2, 5, 4195184019001793407753596203654547219016581120000000⟩, + ⟨5, 5, 4, 6, 3, 5, 8694757718739403388187475467218676630316646400000000⟩, + ⟨5, 5, 5, 6, 4, 5, -3266183200547851497298860225426674787601612800000000⟩, + ⟨5, 5, 6, 6, 5, 5, -176468442352450990996303066029301195761254400000000⟩, + ⟨5, 5, 7, 6, 6, 5, -221634595178309969170546146909719751976550400000000⟩, + ⟨5, 5, 8, 6, 7, 5, -238581932003082801616320516874410023159070720000000⟩, + ⟨5, 5, 3, 7, 1, 5, -38565851879563737500271002005250476029562060800000000⟩, + ⟨5, 5, 4, 7, 2, 5, -8935235843213671709318423621938066915904716800000000⟩, + ⟨5, 5, 5, 7, 3, 5, -4553701399096866100329526471735099512166809600000000⟩, + ⟨5, 5, 6, 7, 4, 5, -6124097441687205823407325023213668731453440000000000⟩, + ⟨5, 5, 7, 7, 5, 5, 796230412920250832564881746813508432114483200000000⟩, + ⟨5, 5, 8, 7, 6, 5, -356696216076657169225734084447822302171627520000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1312.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1312.lean new file mode 100644 index 0000000000000000000000000000000000000000..625cdb32cb3fc9ef6e5cf107025612121340023d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1312.lean @@ -0,0 +1,618 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1312. -/ +namespace LaughlinFock +def collectedFourData_13_5_36 : List CollectedFourTerm := [ + ⟨5, 6, 2, 0, 7, 6, 9782940731160173787282237318599151825369169920000000⟩, + ⟨5, 6, 3, 0, 8, 6, -5960623588584545775022833502907841788390670336000000⟩, + ⟨5, 6, 2, 1, 6, 6, -22518571515261855154285174718423830077118611456000000⟩, + ⟨5, 6, 3, 1, 7, 6, 79626313210258351335048296978992694887352107008000000⟩, + ⟨5, 6, 4, 1, 8, 6, -61975998185328868745968117798589835368630059008000000⟩, + ⟨5, 6, 2, 2, 5, 6, -47220929417165181556467176852089487774019747840000000⟩, + ⟨5, 6, 3, 2, 6, 6, -25920026700851783894772187002146023165529161728000000⟩, + ⟨5, 6, 4, 2, 7, 6, 8403418359836950466377170612003153313812971520000000⟩, + ⟨5, 6, 5, 2, 8, 6, -34942905557251770716005990786946785638466191360000000⟩, + ⟨5, 6, 2, 3, 4, 6, 3479289148440303137513885543456915164269379584000000⟩, + ⟨5, 6, 3, 3, 5, 6, -51774417187264181508780433636235850726330335232000000⟩, + ⟨5, 6, 4, 3, 6, 6, 6843973843126434962931518514086733448407416832000000⟩, + ⟨5, 6, 5, 3, 7, 6, 2752759906568175229111211622094793788159426560000000⟩, + ⟨5, 6, 6, 3, 8, 6, -8918167452137124525325693769320489550578974720000000⟩, + ⟨5, 6, 2, 4, 3, 6, 74004123576826551109698598829542403626147774464000000⟩, + ⟨5, 6, 3, 4, 4, 6, 21173917425213532065969050759313239424890830848000000⟩, + ⟨5, 6, 4, 4, 5, 6, -17697772991539692730787107994214910909948624896000000⟩, + ⟨5, 6, 5, 4, 6, 6, 6741484715300056916221569851248382179069132800000000⟩, + ⟨5, 6, 6, 4, 7, 6, 3891499796172788170029679891767785141242429440000000⟩, + ⟨5, 6, 7, 4, 8, 6, -4567726603043614003538004257843389460360724480000000⟩, + ⟨5, 6, 2, 5, 2, 6, -10066218203317951226434737153942809323071602688000000⟩, + ⟨5, 6, 3, 5, 3, 6, 53309322625174315570788313693995729368547065856000000⟩, + ⟨5, 6, 4, 5, 4, 6, -2471470783487564475117815151457683193221611520000000⟩, + ⟨5, 6, 5, 5, 5, 6, 1855265496187712865354576468884194989598310400000000⟩, + ⟨5, 6, 6, 5, 6, 6, 6590968040601745193039582900205119128479989760000000⟩, + ⟨5, 6, 7, 5, 7, 6, -2083504283927085138105608733064251815812399104000000⟩, + ⟨5, 6, 8, 5, 8, 6, -2096225239808444349402550468830852556844433408000000⟩, + ⟨5, 6, 2, 6, 1, 6, 168907835026528810491716804611021233126622887936000000⟩, + ⟨5, 6, 3, 6, 2, 6, 59614807369621643183535491225743686858033856512000000⟩, + ⟨5, 6, 4, 6, 3, 6, 61777541125778071229182839631353106621865656320000000⟩, + ⟨5, 6, 5, 6, 4, 6, -15471143534476361714577213266346574236887285760000000⟩, + ⟨5, 6, 6, 6, 5, 6, -626917207326802734277945183376821737341583360000000⟩, + ⟨5, 6, 7, 6, 6, 6, -629898647504042865148538988899069647134916608000000⟩, + ⟨5, 6, 8, 6, 7, 6, -565053318829948491398112555820475893690662912000000⟩, + ⟨5, 6, 2, 7, 0, 6, -1377945734333530394303582220955843749169078468608000000⟩, + ⟨5, 6, 3, 7, 1, 6, -548032176999139677695996942966628792848697262080000000⟩, + ⟨5, 6, 4, 7, 2, 6, -63486173810567013904417062530679857527746723840000000⟩, + ⟨5, 6, 5, 7, 3, 6, -21569815173489468341722995519259186498444984320000000⟩, + ⟨5, 6, 6, 7, 4, 6, -21756309594843747497059828939712322953281536000000000⟩, + ⟨5, 6, 7, 7, 5, 6, 2262933996367073857999363017453712824770494464000000⟩, + ⟨5, 6, 8, 7, 6, 6, -844793145130517396289927283937559835356168192000000⟩ +] + +def collectedFourData_13_5_37 : List CollectedFourTerm := [ + ⟨5, 7, 1, 0, 6, 7, 158463720131406021002434912844690313201485611008000000⟩, + ⟨5, 7, 2, 0, 7, 7, -15462674676325751514378990296370292178383011840000000⟩, + ⟨5, 7, 3, 0, 8, 7, 4710607267850938653920946135744947754564059136000000⟩, + ⟨5, 7, 1, 1, 5, 7, 34502915601560783135167758559170979865718423552000000⟩, + ⟨5, 7, 2, 1, 6, 7, 35592298377829039793089724537655190882470592512000000⟩, + ⟨5, 7, 3, 1, 7, 7, -62927692739861378343275708591090869626269073408000000⟩, + ⟨5, 7, 4, 1, 8, 7, 32652577720586457186143330682747878761165750272000000⟩, + ⟨5, 7, 1, 2, 4, 7, -29998694603096457112456416082865810852567580672000000⟩, + ⟨5, 7, 2, 2, 5, 7, 74636235622453247519527927430591607612301639680000000⟩, + ⟨5, 7, 3, 2, 6, 7, 20484277248065140397738598859838489578992304128000000⟩, + ⟨5, 7, 4, 2, 7, 7, -4427411887625463653048192818077123724632391680000000⟩, + ⟨5, 7, 5, 2, 8, 7, 13807473532891450221502193263540712750375239680000000⟩, + ⟨5, 7, 1, 3, 3, 7, 83079676578042538325397077162547976702733058048000000⟩, + ⟨5, 7, 2, 3, 4, 7, -5499278559037405626611384806698078288444653568000000⟩, + ⟨5, 7, 3, 3, 5, 7, 40916683005810957099132435466943995079747960832000000⟩, + ⟨5, 7, 4, 3, 6, 7, -3605805382304402272556018452143017850241548288000000⟩, + ⟨5, 7, 5, 3, 7, 7, -1087736092525849159541969205074354515507937280000000⟩, + ⟨5, 7, 6, 3, 8, 7, 2819167074827808863139445551701390829224460288000000⟩, + ⟨5, 7, 1, 4, 2, 7, -143236302709292672914247396451127860081526308864000000⟩, + ⟨5, 7, 2, 4, 3, 7, -116969091300972538342689754995666782900692451328000000⟩, + ⟨5, 7, 3, 4, 4, 7, -16733485654606145149511592849687142117039669248000000⟩, + ⟨5, 7, 4, 4, 5, 7, 9324221069574359460012728842054995485040574464000000⟩, + ⟨5, 7, 5, 4, 6, 7, -2663856090226592956142175589633207625475686400000000⟩, + ⟨5, 7, 6, 4, 7, 7, -1230161707093809378019120342434267606156312576000000⟩, + ⟨5, 7, 7, 4, 8, 7, 1203272656184331638868495431719307511500636160000000⟩, + ⟨5, 7, 1, 5, 1, 7, -64945008848314981097121234120337901483043323904000000⟩, + ⟨5, 7, 2, 5, 2, 7, 15910416057519643357208302925708063740501426176000000⟩, + ⟨5, 7, 3, 5, 3, 7, -42129699832629302621460269845552368184675270656000000⟩, + ⟨5, 7, 4, 5, 4, 7, 1302115241462781427116907959474521108046151680000000⟩, + ⟨5, 7, 5, 5, 5, 7, -733096713812979408871507507210406566507315200000000⟩, + ⟨5, 7, 6, 5, 6, 7, -2083504283927085138105608733064251815812399104000000⟩, + ⟨5, 7, 7, 5, 7, 7, 548855908368480739428974050100808867033120768000000⟩, + ⟨5, 7, 8, 5, 8, 7, 473320268446184304217674512982791262031577088000000⟩, + ⟨5, 7, 1, 6, 0, 7, 708036246741835622295955229337836457611401101312000000⟩, + ⟨5, 7, 2, 6, 1, 7, -266971555391195895419700413402888582087124713472000000⟩, + ⟨5, 7, 3, 6, 2, 7, -47112846616365434535271719365117558019286106112000000⟩, + ⟨5, 7, 4, 6, 3, 7, -32548018943787030560503049318956957411710074880000000⟩, + ⟨5, 7, 5, 6, 4, 7, 6113326910546927976260079525537902547047546880000000⟩, + ⟨5, 7, 6, 6, 5, 7, 198177973112087107103167660358504990631788544000000⟩, + ⟨5, 7, 7, 6, 6, 7, 165933709387087554134929180115228712643854336000000⟩, + ⟨5, 7, 8, 6, 7, 7, 127587047172201117143144963769454991278866432000000⟩, + ⟨5, 7, 2, 7, 0, 7, 2177947019934912253398428108815600894757113430016000000⟩, + ⟨5, 7, 3, 7, 1, 7, 433103066755026708068439692449408517291460526080000000⟩, + ⟨5, 7, 4, 7, 2, 7, 33448226494606475297580744016419568671585730560000000⟩, + ⟨5, 7, 5, 7, 3, 7, 8523179379841471027564857634068178191683420160000000⟩, + ⟨5, 7, 6, 7, 4, 7, 6877497199813821738872765118233695647852134400000000⟩, + ⟨5, 7, 7, 7, 5, 7, -596122937560243978629558758595566336514981888000000⟩, + ⟨5, 7, 8, 7, 6, 7, 190751313666661280469205153557350470240960512000000⟩ +] + +def collectedFourData_13_5_38 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 5, 8, -795622182153134800136098853260940776320849149952000000⟩, + ⟨5, 8, 1, 0, 6, 8, 956587377225723149962476733514563683186162794496000000⟩, + ⟨5, 8, 2, 0, 7, 8, -46671248792011484002562204340881020817548247040000000⟩, + ⟨5, 8, 3, 0, 8, 8, 9478736305818707016850571771792697123504390144000000⟩, + ⟨5, 8, 0, 1, 4, 8, -572038921639293700442325455003886958401005027328000000⟩, + ⟨5, 8, 1, 1, 5, 8, 208281450887105747158536425774749256848427188224000000⟩, + ⟨5, 8, 2, 1, 6, 8, 107428827640955457412711053954604368081161551872000000⟩, + ⟨5, 8, 3, 1, 7, 8, -126623802813188166987533298162036631719150354432000000⟩, + ⟨5, 8, 4, 1, 8, 8, 49277909882926553211632994918218923564351881216000000⟩, + ⟨5, 8, 0, 2, 3, 8, -223907190828259184436880272622154717169639751680000000⟩, + ⟨5, 8, 1, 2, 4, 8, -181091120205779797941483353947912174452986609664000000⟩, + ⟨5, 8, 2, 2, 5, 8, 225275794424359244529106149126838902486812590080000000⟩, + ⟨5, 8, 3, 2, 6, 8, 41218690374558151826364020035763984923531149312000000⟩, + ⟨5, 8, 4, 2, 7, 8, -6681665560371777924790141203857710810964951040000000⟩, + ⟨5, 8, 5, 2, 8, 8, 16670131033134201404225223146764908784917676032000000⟩, + ⟨5, 8, 0, 3, 2, 8, 983862774057330392010681960938930857614262665216000000⟩, + ⟨5, 8, 1, 3, 3, 8, 501521546084164268062518066826329824744467070976000000⟩, + ⟨5, 8, 2, 3, 4, 8, -16598564166804059090262502243441337458237636608000000⟩, + ⟨5, 8, 3, 3, 5, 8, 82333004359710568204821770038473496596502806528000000⟩, + ⟨5, 8, 4, 3, 6, 8, -5441731253350386967176356635923684972470206464000000⟩, + ⟨5, 8, 5, 3, 7, 8, -1313252793762776676406724233758351634068406272000000⟩, + ⟨5, 8, 6, 3, 8, 8, 2836379662417727210688236096935331706464894976000000⟩, + ⟨5, 8, 0, 4, 1, 8, 812089987777837378809818994569874017170772459520000000⟩, + ⟨5, 8, 1, 4, 2, 8, -864665041427588777740256636803745891169041645568000000⟩, + ⟨5, 8, 2, 4, 3, 8, -353049758554474619691945396298243323746391687168000000⟩, + ⟨5, 8, 3, 4, 4, 8, -33671305837723441222988446130056313181717921792000000⟩, + ⟨5, 8, 4, 4, 5, 8, 14071725960712845666730163564338307223301128192000000⟩, + ⟨5, 8, 5, 4, 6, 8, -3216144501143254897682464398777605705548431360000000⟩, + ⟨5, 8, 6, 4, 7, 8, -1237672530528922378469155860491322246354173952000000⟩, + ⟨5, 8, 7, 4, 8, 8, 1037673691683680140683260848180781753365954560000000⟩, + ⟨5, 8, 0, 5, 0, 8, -5025408709911259530124491772871594453450310549504000000⟩, + ⟨5, 8, 1, 5, 1, 8, -392049206131178697522819495342527235674811138048000000⟩, + ⟨5, 8, 2, 5, 2, 8, 48022674068271933034095793845876098815236243456000000⟩, + ⟨5, 8, 3, 5, 3, 8, -84773850302101682120952517694629106750507188224000000⟩, + ⟨5, 8, 4, 5, 4, 8, 1965098072043901292200872030752589546038231040000000⟩, + ⟨5, 8, 5, 5, 5, 8, -885087213827399225148144723798888863477268480000000⟩, + ⟨5, 8, 6, 5, 6, 8, -2096225239808444349402550468830852556844433408000000⟩, + ⟨5, 8, 7, 5, 7, 8, 473320268446184304217674512982791262031577088000000⟩, + ⟨5, 8, 8, 5, 8, 8, 357157614535719408825905641903944915518226432000000⟩, + ⟨5, 8, 1, 6, 0, 8, 4274155217925388698845746344883940359274017849344000000⟩, + ⟨5, 8, 2, 6, 1, 8, -805804696979727514460794428068814600774334021632000000⟩, + ⟨5, 8, 3, 6, 2, 8, -94800993651237714115565552087940468031145115648000000⟩, + ⟨5, 8, 4, 6, 3, 8, -49120114133240833254737812398200524114640240640000000⟩, + ⟨5, 8, 5, 6, 4, 8, 7380782617793047514947873071485850584258445312000000⟩, + ⟨5, 8, 6, 6, 5, 8, 199387960186298603259825106698726030377484288000000⟩, + ⟨5, 8, 7, 6, 6, 8, 143097280495409774844804538543864461159038976000000⟩, + ⟨5, 8, 8, 6, 7, 8, 96274527949695727681778934703676613457870848000000⟩, + ⟨5, 8, 2, 7, 0, 8, 6573733804205975602222532730357277935470427242496000000⟩, + ⟨5, 8, 3, 7, 1, 8, 871494805145407614893671691325675746904841912320000000⟩, + ⟨5, 8, 4, 7, 2, 8, 50478669863352234959829346026450554954899783680000000⟩, + ⟨5, 8, 5, 7, 3, 8, 10290261773263819087299622867480593296454057984000000⟩, + ⟨5, 8, 6, 7, 4, 8, 6919488156649341692745599444063260538358988800000000⟩, + ⟨5, 8, 7, 7, 5, 8, -514082229107595293162045642194506527180587008000000⟩, + ⟨5, 8, 8, 7, 6, 8, 143936967631644076384465623309527353254739968000000⟩ +] + +def collectedFourData_13_5_39 : List CollectedFourTerm := [ + ⟨6, 0, 7, 4, 8, 1, 1552248308348098847208193411622022019447982653440000000⟩, + ⟨6, 0, 7, 5, 7, 1, 708036246741835622295955229337836457611401101312000000⟩, + ⟨6, 0, 8, 5, 8, 1, 4274155217925388698845746344883940359274017849344000000⟩, + ⟨6, 0, 7, 6, 6, 1, 214058150802501088459739931669886853465530957824000000⟩, + ⟨6, 0, 8, 6, 7, 1, 1152130765920831959012353988130855488886895804416000000⟩, + ⟨6, 0, 7, 7, 5, 1, -769011758589846051886010313980994884008402747392000000⟩, + ⟨6, 0, 8, 7, 6, 1, 1722513860035936962456521332412639157256722579456000000⟩ +] + +def collectedFourData_13_5_40 : List CollectedFourTerm := [ + ⟨6, 1, 6, 3, 8, 2, -228547361702425873799714957208362496534188654592000000⟩, + ⟨6, 1, 6, 4, 7, 2, 99728113006858531773697109331205996029551837184000000⟩, + ⟨6, 1, 7, 4, 8, 2, -585289449713928959336128218087247457030913392640000000⟩, + ⟨6, 1, 6, 5, 6, 2, 168907835026528810491716804611021233126622887936000000⟩, + ⟨6, 1, 7, 5, 7, 2, -266971555391195895419700413402888582087124713472000000⟩, + ⟨6, 1, 8, 5, 8, 2, -805804696979727514460794428068814600774334021632000000⟩, + ⟨6, 1, 6, 6, 5, 2, -16066111620953945585721680215707657667551952896000000⟩, + ⟨6, 1, 7, 6, 6, 2, -80712587423146428766575433023317978679443718144000000⟩, + ⟨6, 1, 8, 6, 7, 2, -217210731800349826170668128764346069577417883648000000⟩, + ⟨6, 1, 6, 7, 4, 2, -557552567269989218462995258253142594671974809600000000⟩, + ⟨6, 1, 7, 7, 5, 2, 289962930922812135056386299073331619488650493952000000⟩, + ⟨6, 1, 8, 7, 6, 2, -324744818159261475199584537968754885550845984768000000⟩ +] + +def collectedFourData_13_5_41 : List CollectedFourTerm := [ + ⟨6, 2, 5, 2, 8, 3, -79013984398726533278034571803905388983623876608000000⟩, + ⟨6, 2, 5, 3, 7, 3, 6224626282283447501203577613190651472057991168000000⟩, + ⟨6, 2, 6, 3, 8, 3, -80664150011664274347924637590612314732063883264000000⟩, + ⟨6, 2, 5, 4, 6, 3, 15244054826700743312125965912962398135611555840000000⟩, + ⟨6, 2, 6, 4, 7, 3, 35198321293419931964440797801709669884811542528000000⟩, + ⟨6, 2, 7, 4, 8, 3, -103286854025118412980510506206182761490221629440000000⟩, + ⟨6, 2, 5, 5, 5, 3, 4195184019001793407753596203654547219016581120000000⟩, + ⟨6, 2, 6, 5, 6, 3, 59614807369621643183535491225743686858033856512000000⟩, + ⟨6, 2, 7, 5, 7, 3, -47112846616365434535271719365117558019286106112000000⟩, + ⟨6, 2, 8, 5, 8, 3, -94800993651237714115565552087940468031145115648000000⟩, + ⟨6, 2, 5, 6, 4, 3, -34983830748152521646537562540198852260347772928000000⟩, + ⟨6, 2, 6, 6, 5, 3, -5670418718655530309132764698437722363586936832000000⟩, + ⟨6, 2, 7, 6, 6, 3, -14243464048837333554131494725563503646211047424000000⟩, + ⟨6, 2, 8, 6, 7, 3, -25554322633718417458470063595455685263750070272000000⟩, + ⟨6, 2, 5, 7, 3, 3, -48774336662104259300667851839668914846429085696000000⟩, + ⟨6, 2, 6, 7, 4, 3, -196784174582653138328439902594856088851657523200000000⟩, + ⟨6, 2, 7, 7, 5, 3, 51170167057612765533482865214533831636069384192000000⟩, + ⟨6, 2, 8, 7, 6, 3, -38205450476994442844246212038873098323809533952000000⟩ +] + +def collectedFourData_13_5_42 : List CollectedFourTerm := [ + ⟨6, 3, 4, 1, 8, 4, -96817461742583533259359796151690929324295192576000000⟩, + ⟨6, 3, 4, 2, 7, 4, 13127624554388139215687220197693544319093309440000000⟩, + ⟨6, 3, 5, 2, 8, 4, -163760981074353351782252389398732823364118773760000000⟩, + ⟨6, 3, 4, 3, 6, 4, 10691496629754845375177823073581296581192187904000000⟩, + ⟨6, 3, 5, 3, 7, 4, 12900892349182317245972393520080126680718376960000000⟩, + ⟨6, 3, 6, 3, 8, 4, -83590521627028926458177898525324579250938839040000000⟩, + ⟨6, 3, 4, 4, 5, 4, -27647049014257519690411442186972632218454720512000000⟩, + ⟨6, 3, 5, 4, 6, 4, 31594171499747573992149639331644977158343884800000000⟩, + ⟨6, 3, 6, 4, 7, 4, 36475262392119350801825413807001640110213038080000000⟩, + ⟨6, 3, 7, 4, 8, 4, -71355961757699193945049377225746571335408025600000000⟩, + ⟨6, 3, 4, 5, 4, 4, -3860874129250630051323811259593591296035389440000000⟩, + ⟨6, 3, 5, 5, 5, 4, 8694757718739403388187475467218676630316646400000000⟩, + ⟨6, 3, 6, 5, 6, 4, 61777541125778071229182839631353106621865656320000000⟩, + ⟨6, 3, 7, 5, 7, 4, -32548018943787030560503049318956957411710074880000000⟩, + ⟨6, 3, 8, 5, 8, 4, -49120114133240833254737812398200524114640240640000000⟩, + ⟨6, 3, 4, 6, 3, 4, 96507436743661396043456629339562645176493015040000000⟩, + ⟨6, 3, 5, 6, 4, 4, -72505980917840157806435319138804937357692764160000000⟩, + ⟨6, 3, 6, 6, 5, 4, -5876132810765921844946205772935803811942891520000000⟩, + ⟨6, 3, 7, 6, 6, 4, -9840130049065408138654115126002799194417397760000000⟩, + ⟨6, 3, 8, 6, 7, 4, -13240697127962223133317134333329707004550184960000000⟩, + ⟨6, 3, 4, 7, 2, 4, -99176622951796422548035376298598871775817236480000000⟩, + ⟨6, 3, 5, 7, 3, 4, -101087589542766129895679608836453202016725893120000000⟩, + ⟨6, 3, 6, 7, 4, 4, -203923202549455823277562065528285826281111552000000000⟩, + ⟨6, 3, 7, 7, 5, 4, 35351028145461123831428886833682832999663534080000000⟩, + ⟨6, 3, 8, 7, 6, 4, -19795742804615065297955773899389034430841487360000000⟩ +] + +def collectedFourData_13_5_43 : List CollectedFourTerm := [ + ⟨6, 4, 3, 0, 8, 5, 3497880073378331628666250787117560497369513984000000⟩, + ⟨6, 4, 3, 1, 7, 5, -46727207339204709305907671786146497694323965952000000⟩, + ⟨6, 4, 4, 1, 8, 5, 72738902518644961009838095225039284214016507904000000⟩, + ⟨6, 4, 3, 2, 6, 5, 15210681156243549315654308619750910840780357632000000⟩, + ⟨6, 4, 4, 2, 7, 5, -9862776668343671059583342881024678601435381760000000⟩, + ⟨6, 4, 5, 2, 8, 5, 61516764767061892596430382766287152534278635520000000⟩, + ⟨6, 4, 3, 3, 5, 5, 30382844932020529699271999824405815054311620608000000⟩, + ⟨6, 4, 4, 3, 6, 5, -8032515179935831318382107261464568161701462016000000⟩, + ⟨6, 4, 5, 3, 7, 5, -4846216447430201143039657139355099110226001920000000⟩, + ⟨6, 4, 6, 3, 8, 5, 20933836709047669196130280136222004071859486720000000⟩, + ⟨6, 4, 3, 4, 4, 5, -12425516011253512719107233734778327078023462912000000⟩, + ⟨6, 4, 4, 4, 5, 5, 20771211793623849955876240626536191771696693248000000⟩, + ⟨6, 4, 5, 4, 6, 5, -11868341307003599338408377753801391278234009600000000⟩, + ⟨6, 4, 6, 4, 7, 5, -9134614451184321146005442779839769823611453440000000⟩, + ⟨6, 4, 7, 4, 8, 5, 13402423108905336279418813373032728515680665600000000⟩, + ⟨6, 4, 3, 5, 3, 5, -31283575378423511285692860435128962412250660864000000⟩, + ⟨6, 4, 4, 5, 4, 5, 2900672480662637966223154743361766801811701760000000⟩, + ⟨6, 4, 5, 5, 5, 5, -3266183200547851497298860225426674787601612800000000⟩, + ⟨6, 4, 6, 5, 6, 5, -15471143534476361714577213266346574236887285760000000⟩, + ⟨6, 4, 7, 5, 7, 5, 6113326910546927976260079525537902547047546880000000⟩, + ⟨6, 4, 8, 5, 8, 5, 7380782617793047514947873071485850584258445312000000⟩, + ⟨6, 4, 3, 6, 2, 5, -34983830748152521646537562540198852260347772928000000⟩, + ⟨6, 4, 4, 6, 3, 5, -72505980917840157806435319138804937357692764160000000⟩, + ⟨6, 4, 5, 6, 4, 5, 27236850579825851142757508800742199333822136320000000⟩, + ⟨6, 4, 6, 6, 5, 5, 1471578384091288308582060134982753375863439360000000⟩, + ⟨6, 4, 7, 6, 6, 5, 1848220991149323478978927681925848969783541760000000⟩, + ⟨6, 4, 8, 6, 7, 5, 1989545605379441685121326743082841241360007168000000⟩, + ⟨6, 4, 3, 7, 1, 5, 321602396629553149474105485807401329778774507520000000⟩, + ⟨6, 4, 4, 7, 2, 5, 74511338958664006854956671385766222500902993920000000⟩, + ⟨6, 4, 5, 7, 3, 5, 37973523521748999047868065609191487736895242240000000⟩, + ⟨6, 4, 6, 7, 4, 5, 51069127698516692347006322780048296180187136000000000⟩, + ⟨6, 4, 7, 7, 5, 5, -6639801704994467383314493731998957672941486080000000⟩, + ⟨6, 4, 8, 7, 6, 5, 2974506003839465997420696504746514335649497088000000⟩ +] + +def collectedFourData_13_5_44 : List CollectedFourTerm := [ + ⟨6, 5, 2, 0, 7, 6, -930530059445201589891161116821219701812101120000000⟩, + ⟨6, 5, 3, 0, 8, 6, 566960341950091286890759508861249636108599296000000⟩, + ⟨6, 5, 2, 1, 6, 6, 2141912975510038281609049633435228618270703616000000⟩, + ⟨6, 5, 3, 1, 7, 6, -7573865568758990530054059668855676117228453888000000⟩, + ⟨6, 5, 4, 1, 8, 6, 5895009574358378282011802371152904911625125888000000⟩, + ⟨6, 5, 2, 2, 5, 6, 4491542519281052105874493338860814789236490240000000⟩, + ⟨6, 5, 3, 2, 6, 6, 2465451304426380894355258778989188312421367808000000⟩, + ⟨6, 5, 4, 2, 7, 6, -799313171857950505272967511369838760789278720000000⟩, + ⟨6, 5, 5, 2, 8, 6, 3323686085699253921365802466107841240325160960000000⟩, + ⟨6, 5, 2, 3, 4, 6, -330941710380908154556823992194542538351181824000000⟩, + ⟨6, 5, 3, 3, 5, 6, 4924659448211963654849119239589393980563914752000000⟩, + ⟨6, 5, 4, 3, 6, 6, -650982517639212299889475757757921968995172352000000⟩, + ⟨6, 5, 5, 3, 7, 6, -261835976511479532795239971500741305208668160000000⟩, + ⟨6, 5, 6, 3, 8, 6, 848274881493151416376864592054291970046033920000000⟩, + ⟨6, 5, 2, 4, 3, 6, -7039096259859266278610515254482003009684373504000000⟩, + ⟨6, 5, 3, 4, 4, 6, -2014012675924198619673369620899156703343280128000000⟩, + ⟨6, 5, 4, 4, 5, 6, 1683370083334043832647062101246820682569875456000000⟩, + ⟨6, 5, 5, 4, 6, 6, -641233995509767031505758174377691558235340800000000⟩, + ⟨6, 5, 6, 4, 7, 6, -370150206995500817968893132598626872029347840000000⟩, + ⟨6, 5, 7, 4, 8, 6, 434471292862012530954328257817110958602977280000000⟩, + ⟨6, 5, 2, 5, 2, 6, 957474738989958738576645291636035188181434368000000⟩, + ⟨6, 5, 3, 5, 3, 6, -5070656003606805431643333581693009007545942016000000⟩, + ⟨6, 5, 4, 5, 4, 6, 235080424002837454903461916116167997228318720000000⟩, + ⟨6, 5, 5, 5, 5, 6, -176468442352450990996303066029301195761254400000000⟩, + ⟨6, 5, 6, 5, 6, 6, -626917207326802734277945183376821737341583360000000⟩, + ⟨6, 5, 7, 5, 7, 6, 198177973112087107103167660358504990631788544000000⟩, + ⟨6, 5, 8, 5, 8, 6, 199387960186298603259825106698726030377484288000000⟩, + ⟨6, 5, 2, 6, 1, 6, -16066111620953945585721680215707657667551952896000000⟩, + ⟨6, 5, 3, 6, 2, 6, -5670418718655530309132764698437722363586936832000000⟩, + ⟨6, 5, 4, 6, 3, 6, -5876132810765921844946205772935803811942891520000000⟩, + ⟨6, 5, 5, 6, 4, 6, 1471578384091288308582060134982753375863439360000000⟩, + ⟨6, 5, 6, 6, 5, 6, 59630874011422876227550700345929803717672960000000⟩, + ⟨6, 5, 7, 6, 6, 6, 59914461511500734775433657391294143411519488000000⟩, + ⟨6, 5, 8, 6, 7, 6, 53746528044046026188066770381304163553247232000000⟩, + ⟨6, 5, 2, 7, 0, 6, 131066921625884325310484681183661692374889791488000000⟩, + ⟨6, 5, 3, 7, 1, 6, 52127517507756147300979675913967561662665850880000000⟩, + ⟨6, 5, 4, 7, 2, 6, 6038653888777003337346502808907957475202826240000000⟩, + ⟨6, 5, 5, 7, 3, 6, 2051669528333008004829286780513390863864299520000000⟩, + ⟨6, 5, 6, 7, 4, 6, 2069408434226227664719675496448696564842496000000000⟩, + ⟨6, 5, 7, 7, 5, 6, -215244900692585443488951738394434492646293504000000⟩, + ⟨6, 5, 8, 7, 6, 6, 80354715127050936619189474117597835204493312000000⟩ +] + +def collectedFourData_13_5_45 : List CollectedFourTerm := [ + ⟨6, 6, 1, 0, 6, 7, 47907788699667973493314598935020903692098338816000000⟩, + ⟨6, 6, 2, 0, 7, 7, -4674776980565817437409959531277154550210887680000000⟩, + ⟨6, 6, 3, 0, 8, 7, 1424141610762275700954935413475137868500303872000000⟩, + ⟨6, 6, 1, 1, 5, 7, 10431147197549924729696851583195567776862306304000000⟩, + ⟨6, 6, 2, 1, 6, 7, 10760496526312614547371952704039191775201460224000000⟩, + ⟨6, 6, 3, 1, 7, 7, -19024711805572579262167254954875986270136303616000000⟩, + ⟨6, 6, 4, 1, 8, 7, 9871740942596424670625484328243473696103071744000000⟩, + ⟨6, 6, 1, 2, 4, 7, -9069401634135820424215818427984013329950572544000000⟩, + ⟨6, 6, 2, 2, 5, 7, 22564515098938790558542744113862215724286607360000000⟩, + ⟨6, 6, 3, 2, 6, 7, 6192940726444710548433523346263666455327277056000000⟩, + ⟨6, 6, 4, 2, 7, 7, -1338524130462598690269438704851530179527311360000000⟩, + ⟨6, 6, 5, 2, 8, 7, 4174365740886840582981374166061580754993807360000000⟩, + ⟨6, 6, 1, 3, 3, 7, 25117191414142405267433074533508492016952016896000000⟩, + ⟨6, 6, 2, 3, 4, 7, -1662577875797096361498173436771922030085799936000000⟩, + ⟨6, 6, 3, 3, 5, 7, 12370199324540457016164702409703393129989668864000000⟩, + ⟨6, 6, 4, 3, 6, 7, -1090130675995206130988941615285956040118501376000000⟩, + ⟨6, 6, 5, 3, 7, 7, -328851492559418695146543461467408260724162560000000⟩, + ⟨6, 6, 6, 3, 8, 7, 852309035897385083676928458528367078199525376000000⟩, + ⟨6, 6, 1, 4, 2, 7, -43304136231485973042207578883280035417453232128000000⟩, + ⟨6, 6, 2, 4, 3, 7, -35362861011922923277394162745001821398636691456000000⟩, + ⟨6, 6, 3, 4, 4, 7, -5058976870447168612909939653525831571048759296000000⟩, + ⟨6, 6, 4, 4, 5, 7, 2818959522215761874185109576035514225239523328000000⟩, + ⟨6, 6, 5, 4, 6, 7, -805354402831581020936066540766760065092812800000000⟩, + ⟨6, 6, 6, 4, 7, 7, -371910536247677264731415021979518093337034752000000⟩, + ⟨6, 6, 7, 4, 8, 7, 363781262441422817641437076134966449217208320000000⟩, + ⟨6, 6, 1, 5, 1, 7, -19634600010797653492152869791409177532938846208000000⟩, + ⟨6, 6, 2, 5, 2, 7, 4810141084504225571745804817336555571565821952000000⟩, + ⟨6, 6, 3, 5, 3, 7, -12736926508404150717175618799968954297626918912000000⟩, + ⟨6, 6, 4, 5, 4, 7, 393663999550725269839755364808741795250831360000000⟩, + ⟨6, 6, 5, 5, 5, 7, -221634595178309969170546146909719751976550400000000⟩, + ⟨6, 6, 6, 5, 6, 7, -629898647504042865148538988899069647134916608000000⟩, + ⟨6, 6, 7, 5, 7, 7, 165933709387087554134929180115228712643854336000000⟩, + ⟨6, 6, 8, 5, 8, 7, 143097280495409774844804538543864461159038976000000⟩, + ⟨6, 6, 1, 6, 0, 7, 214058150802501088459739931669886853465530957824000000⟩, + ⟨6, 6, 2, 6, 1, 7, -80712587423146428766575433023317978679443718144000000⟩, + ⟨6, 6, 3, 6, 2, 7, -14243464048837333554131494725563503646211047424000000⟩, + ⟨6, 6, 4, 6, 3, 7, -9840130049065408138654115126002799194417397760000000⟩, + ⟨6, 6, 5, 6, 4, 7, 1848220991149323478978927681925848969783541760000000⟩, + ⟨6, 6, 6, 6, 5, 7, 59914461511500734775433657391294143411519488000000⟩, + ⟨6, 6, 7, 6, 6, 7, 50166164727652276282630299796205345829814272000000⟩, + ⟨6, 6, 8, 6, 7, 7, 38572950904293193140811051645383308753240064000000⟩, + ⟨6, 6, 2, 7, 0, 7, 658451193393597452463696314254441298735117893632000000⟩, + ⟨6, 6, 3, 7, 1, 7, 130938552938627833911940370495597470231465820160000000⟩, + ⟨6, 6, 4, 7, 2, 7, 10112286685895217238248930308330156807285637120000000⟩, + ⟨6, 6, 5, 7, 3, 7, 2576783357352758499140282316700803905429176320000000⟩, + ⟨6, 6, 6, 7, 4, 7, 2079249952973543577328848043556946364386508800000000⟩, + ⟨6, 6, 7, 7, 5, 7, -180223786920937124932117149085195031675928576000000⟩, + ⟨6, 6, 8, 7, 6, 7, 57669185235260274090812733973987092514996224000000⟩ +] + +def collectedFourData_13_5_46 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 5, 8, -214465958153159533020445793010227935068058288128000000⟩, + ⟨6, 7, 1, 0, 6, 8, 257855340154965598495553980692823220085634105344000000⟩, + ⟨6, 7, 2, 0, 7, 8, -12580587010904513288905559189438280585770434560000000⟩, + ⟨6, 7, 3, 0, 8, 8, 2555064840458758674019590538727835396646895616000000⟩, + ⟨6, 7, 0, 1, 4, 8, -154197404474399482367410414498973608060536225792000000⟩, + ⟨6, 7, 1, 1, 5, 8, 56143835518949619525920867290279774162293620736000000⟩, + ⟨6, 7, 2, 1, 6, 8, 28958250498920385029341372240973091170584363008000000⟩, + ⟨6, 7, 3, 1, 7, 8, -34132400785804485530151822074123981151270862848000000⟩, + ⟨6, 7, 4, 1, 8, 8, 13283232162062529877736167419983502640806887424000000⟩, + ⟨6, 7, 0, 2, 3, 8, -60355871537430759974469542028623139392999915520000000⟩, + ⟨6, 7, 1, 2, 4, 8, -48814476869985454664208773695692765474267856896000000⟩, + ⟨6, 7, 2, 2, 5, 8, 60724788955966188696404585513804044025588613120000000⟩, + ⟨6, 7, 3, 2, 6, 8, 11110808777446298934570966761737977171875463168000000⟩, + ⟨6, 7, 4, 2, 7, 8, -1801093331241851799605211211459142707901890560000000⟩, + ⟨6, 7, 5, 2, 8, 8, 4493559511984201306970620666967656448548405248000000⟩, + ⟨6, 7, 0, 3, 2, 8, 265207629026132852603677209113547485743807463424000000⟩, + ⟨6, 7, 1, 3, 3, 8, 135188914195823812289519132941329742156806488064000000⟩, + ⟨6, 7, 2, 3, 4, 8, -4474268123554109898891172375288113955929587712000000⟩, + ⟨6, 7, 3, 3, 5, 8, 22193482112135221570668987637039028175573614592000000⟩, + ⟨6, 7, 4, 3, 6, 8, -1466859689737958063562863513549218522224132096000000⟩, + ⟨6, 7, 5, 3, 7, 8, -353997192422971208670618701246858496319684608000000⟩, + ⟨6, 7, 6, 3, 8, 8, 764567524173768136573405973395655020001624064000000⟩, + ⟨6, 7, 0, 4, 1, 8, 218904979325776939757871320620725397980740321280000000⟩, + ⟨6, 7, 1, 4, 2, 8, -233076981450495823206598619026950005728217137152000000⟩, + ⟨6, 7, 2, 4, 3, 8, -95167224396910563718515121160247996895620759552000000⟩, + ⟨6, 7, 3, 4, 4, 8, -9076354368618553833930727906244853183585189888000000⟩, + ⟨6, 7, 4, 4, 5, 8, 3793139832861155793620681305104206717138239488000000⟩, + ⟨6, 7, 5, 4, 6, 8, -866935999861232345230789932529698162648023040000000⟩, + ⟨6, 7, 6, 4, 7, 8, -333623962596660600120392741297046292034224128000000⟩, + ⟨6, 7, 7, 4, 8, 8, 279712767604099999339279216397648605835427840000000⟩, + ⟨6, 7, 0, 5, 0, 8, -1354636809101571258533483954595520030216506310656000000⟩, + ⟨6, 7, 1, 5, 1, 8, -105679819545209120779688041652083686314052943872000000⟩, + ⟨6, 7, 2, 5, 2, 8, 12944873883803452305425484889182255387229814784000000⟩, + ⟨6, 7, 3, 5, 3, 8, -22851430539770195529270663670154457943413620736000000⟩, + ⟨6, 7, 4, 5, 4, 8, 529707002066346656798965563259082777359810560000000⟩, + ⟨6, 7, 5, 5, 5, 8, -238581932003082801616320516874410023159070720000000⟩, + ⟨6, 7, 6, 5, 6, 8, -565053318829948491398112555820475893690662912000000⟩, + ⟨6, 7, 7, 5, 7, 8, 127587047172201117143144963769454991278866432000000⟩, + ⟨6, 7, 8, 5, 8, 8, 96274527949695727681778934703676613457870848000000⟩, + ⟨6, 7, 1, 6, 0, 8, 1152130765920831959012353988130855488886895804416000000⟩, + ⟨6, 7, 2, 6, 1, 8, -217210731800349826170668128764346069577417883648000000⟩, + ⟨6, 7, 3, 6, 2, 8, -25554322633718417458470063595455685263750070272000000⟩, + ⟨6, 7, 4, 6, 3, 8, -13240697127962223133317134333329707004550184960000000⟩, + ⟨6, 7, 5, 6, 4, 8, 1989545605379441685121326743082841241360007168000000⟩, + ⟨6, 7, 6, 6, 5, 8, 53746528044046026188066770381304163553247232000000⟩, + ⟨6, 7, 7, 6, 6, 8, 38572950904293193140811051645383308753240064000000⟩, + ⟨6, 7, 8, 6, 7, 8, 25951524914246986401076598434460735291523072000000⟩, + ⟨6, 7, 2, 7, 0, 8, 1771999512567001551133193393219865669798507577344000000⟩, + ⟨6, 7, 3, 7, 1, 8, 234917995756730661998940508163165971141864980480000000⟩, + ⟨6, 7, 4, 7, 2, 8, 13606906068459972656469854727337102257181163520000000⟩, + ⟨6, 7, 5, 7, 3, 8, 2773817649072392785352163264419121376448741376000000⟩, + ⟨6, 7, 6, 7, 4, 8, 1865200205239644324514021130346563762336563200000000⟩, + ⟨6, 7, 7, 7, 5, 8, -138574741011748071774816839670496444192653312000000⟩, + ⟨6, 7, 8, 7, 6, 8, 38799294903066609615037807273459287695818752000000⟩ +] + +def collectedFourData_13_5_47 : List CollectedFourTerm := [ + ⟨7, 0, 6, 3, 8, 2, 1864483445078658867066516516544305577716797669376000000⟩, + ⟨7, 0, 6, 4, 7, 2, -813579357578940555695445993044811083336229322752000000⟩, + ⟨7, 0, 7, 4, 8, 2, 4774776140236825719045993120556126914127771729920000000⟩, + ⟨7, 0, 6, 5, 6, 2, -1377945734333530394303582220955843749169078468608000000⟩, + ⟨7, 0, 7, 5, 7, 2, 2177947019934912253398428108815600894757113430016000000⟩, + ⟨7, 0, 8, 5, 8, 2, 6573733804205975602222532730357277935470427242496000000⟩, + ⟨7, 0, 6, 6, 5, 2, 131066921625884325310484681183661692374889791488000000⟩, + ⟨7, 0, 7, 6, 6, 2, 658451193393597452463696314254441298735117893632000000⟩, + ⟨7, 0, 8, 6, 7, 2, 1771999512567001551133193393219865669798507577344000000⟩, + ⟨7, 0, 6, 7, 4, 2, 4548499373138754158573648864830842659928853708800000000⟩, + ⟨7, 0, 7, 7, 5, 2, -2365510064806543445678441900891479663758809235456000000⟩, + ⟨7, 0, 8, 7, 6, 2, 2649259798156732270364450750458089049643972296704000000⟩ +] + +def collectedFourData_13_5_48 : List CollectedFourTerm := [ + ⟨7, 1, 5, 2, 8, 3, 726366615846451343272630636604225834403464478720000000⟩, + ⟨7, 1, 5, 3, 7, 3, -57222284915478533766778155091409314476321669120000000⟩, + ⟨7, 1, 6, 3, 8, 3, 741536401561941604053151453794302833955973365760000000⟩, + ⟨7, 1, 5, 4, 6, 3, -140136870713570050822160566685812705277352345600000000⟩, + ⟨7, 1, 6, 4, 7, 3, -323574183936351209364252305330091994159534571520000000⟩, + ⟨7, 1, 7, 4, 8, 3, 949504359140517474606908115612998416413071769600000000⟩, + ⟨7, 1, 5, 5, 5, 3, -38565851879563737500271002005250476029562060800000000⟩, + ⟨7, 1, 6, 5, 6, 3, -548032176999139677695996942966628792848697262080000000⟩, + ⟨7, 1, 7, 5, 7, 3, 433103066755026708068439692449408517291460526080000000⟩, + ⟨7, 1, 8, 5, 8, 3, 871494805145407614893671691325675746904841912320000000⟩, + ⟨7, 1, 5, 6, 4, 3, 321602396629553149474105485807401329778774507520000000⟩, + ⟨7, 1, 6, 6, 5, 3, 52127517507756147300979675913967561662665850880000000⟩, + ⟨7, 1, 7, 6, 6, 3, 130938552938627833911940370495597470231465820160000000⟩, + ⟨7, 1, 8, 6, 7, 3, 234917995756730661998940508163165971141864980480000000⟩, + ⟨7, 1, 5, 7, 3, 3, 448376956699568304815559645578847014284311920640000000⟩, + ⟨7, 1, 6, 7, 4, 3, 1809014645084051053968883228735652548929650688000000000⟩, + ⟨7, 1, 7, 7, 5, 3, -470401554367568278814626721634395690649287393280000000⟩, + ⟨7, 1, 8, 7, 6, 3, 351218382176799941517930801785129470206337351680000000⟩ +] + +def collectedFourData_13_5_49 : List CollectedFourTerm := [ + ⟨7, 2, 4, 1, 8, 4, 99495222569206231867872860332468295871403917312000000⟩, + ⟨7, 2, 4, 2, 7, 4, -13490706152951567798174151358457202452232929280000000⟩, + ⟨7, 2, 5, 2, 8, 4, 168290254328966388961779104274729540617628549120000000⟩, + ⟨7, 2, 4, 3, 6, 4, -10987200218114196335251551644605343888937320448000000⟩, + ⟨7, 2, 5, 3, 7, 4, -13257703027125577460530261939459641870668267520000000⟩, + ⟨7, 2, 6, 3, 8, 4, 85902454002254224214014216378463191101320724480000000⟩, + ⟨7, 2, 4, 4, 5, 4, 28411706375539432625311442863340237900369362944000000⟩, + ⟨7, 2, 5, 4, 6, 4, -32467997700816143857978162644407975063165337600000000⟩, + ⟨7, 2, 6, 4, 7, 4, -37484088971709816801673916460843922292169768960000000⟩, + ⟨7, 2, 7, 4, 8, 4, 73329512764941862532564093330393021711332147200000000⟩, + ⟨7, 2, 4, 5, 4, 4, 3967657526726140860726035811247773254449889280000000⟩, + ⟨7, 2, 5, 5, 5, 4, -8935235843213671709318423621938066915904716800000000⟩, + ⟨7, 2, 6, 5, 6, 4, -63486173810567013904417062530679857527746723840000000⟩, + ⟨7, 2, 7, 5, 7, 4, 33448226494606475297580744016419568671585730560000000⟩, + ⟨7, 2, 8, 5, 8, 4, 50478669863352234959829346026450554954899783680000000⟩, + ⟨7, 2, 4, 6, 3, 4, -99176622951796422548035376298598871775817236480000000⟩, + ⟨7, 2, 5, 6, 4, 4, 74511338958664006854956671385766222500902993920000000⟩, + ⟨7, 2, 6, 6, 5, 4, 6038653888777003337346502808907957475202826240000000⟩, + ⟨7, 2, 7, 6, 6, 4, 10112286685895217238248930308330156807285637120000000⟩, + ⟨7, 2, 8, 6, 7, 4, 13606906068459972656469854727337102257181163520000000⟩, + ⟨7, 2, 4, 7, 2, 4, 101919633056349112238279561216323693018097909760000000⟩, + ⟨7, 2, 5, 7, 3, 4, 103883452835020524519683270137222306136001085440000000⟩, + ⟨7, 2, 6, 7, 4, 4, 209563275668478779282327612049614910913511424000000000⟩, + ⟨7, 2, 7, 7, 5, 4, -36328760846205094587238585500924409428270120960000000⟩, + ⟨7, 2, 8, 7, 6, 4, 20343250079253536646393382340145579041300152320000000⟩ +] + +def collectedFourData_13_5_50 : List CollectedFourTerm := [ + ⟨7, 3, 3, 0, 8, 5, 4876732383334845472763480418962520087082303488000000⟩, + ⟨7, 3, 3, 1, 7, 5, -65146911967686013877618455055643317422956478464000000⟩, + ⟨7, 3, 4, 1, 8, 5, 101412328038539057026425856409017918822891388928000000⟩, + ⟨7, 3, 3, 2, 6, 5, 21206679420427022096361212592644365705726132224000000⟩, + ⟨7, 3, 4, 2, 7, 5, -13750649353068495604959878760180269304848056320000000⟩, + ⟨7, 3, 5, 2, 8, 5, 85766462132526814125581216978678544941596016640000000⟩, + ⟨7, 3, 3, 3, 5, 5, 42359658041312015691825555839449866904541331456000000⟩, + ⟨7, 3, 4, 3, 6, 5, -11198905072748299395407388001695697089972928512000000⟩, + ⟨7, 3, 5, 3, 7, 5, -6756578324598433252849437514545758725409341440000000⟩, + ⟨7, 3, 6, 3, 8, 5, 29185883233514328428845532234434715149444055040000000⟩, + ⟨7, 3, 3, 4, 4, 5, -17323611742126058716396326723869353986893021184000000⟩, + ⟨7, 3, 4, 4, 5, 5, 28959152135035455528557637968839426037237415936000000⟩, + ⟨7, 3, 5, 4, 6, 5, -16546800683316303021604647921686392830374707200000000⟩, + ⟨7, 3, 6, 4, 7, 5, -12735448091090346856188125979787730127767470080000000⟩, + ⟨7, 3, 7, 4, 8, 5, 18685612262065844616420223513335610536571699200000000⟩, + ⟨7, 3, 3, 5, 3, 5, -43615453335742044197664630819386761351840923648000000⟩, + ⟨7, 3, 4, 5, 4, 5, 4044107608936222982398058619205070463770296320000000⟩, + ⟨7, 3, 5, 5, 5, 5, -4553701399096866100329526471735099512166809600000000⟩, + ⟨7, 3, 6, 5, 6, 5, -21569815173489468341722995519259186498444984320000000⟩, + ⟨7, 3, 7, 5, 7, 5, 8523179379841471027564857634068178191683420160000000⟩, + ⟨7, 3, 8, 5, 8, 5, 10290261773263819087299622867480593296454057984000000⟩, + ⟨7, 3, 3, 6, 2, 5, -48774336662104259300667851839668914846429085696000000⟩, + ⟨7, 3, 4, 6, 3, 5, -101087589542766129895679608836453202016725893120000000⟩, + ⟨7, 3, 5, 6, 4, 5, 37973523521748999047868065609191487736895242240000000⟩, + ⟨7, 3, 6, 6, 5, 5, 2051669528333008004829286780513390863864299520000000⟩, + ⟨7, 3, 7, 6, 6, 5, 2576783357352758499140282316700803905429176320000000⟩, + ⟨7, 3, 8, 6, 7, 5, 2773817649072392785352163264419121376448741376000000⟩, + ⟨7, 3, 3, 7, 1, 5, 448376956699568304815559645578847014284311920640000000⟩, + ⟨7, 3, 4, 7, 2, 5, 103883452835020524519683270137222306136001085440000000⟩, + ⟨7, 3, 5, 7, 3, 5, 52942556057670467603723588446199766849347911680000000⟩, + ⟨7, 3, 6, 7, 4, 5, 71200402418451216190068981805594699578212352000000000⟩, + ⟨7, 3, 7, 7, 5, 5, -9257188729856763209838649754716727067342274560000000⟩, + ⟨7, 3, 8, 7, 6, 5, 4147046053336456782699311483703332387281698816000000⟩ +] + +def collectedFourData_13_5_51 : List CollectedFourTerm := [ + ⟨7, 4, 2, 0, 7, 6, -32292780966920872788518655194772688456384512000000000⟩, + ⟨7, 4, 3, 0, 8, 6, 19675588073362017518700163798460884194007449600000000⟩, + ⟨7, 4, 2, 1, 6, 6, 74332178596778262318809052962324450180176281600000000⟩, + ⟨7, 4, 3, 1, 7, 6, -262840710412580619464619952318018462143007948800000000⟩, + ⟨7, 4, 4, 1, 8, 6, 204578294973250263991469974005209675007315148800000000⟩, + ⟨7, 4, 2, 2, 5, 6, 155872878373464917226000475056477167444557824000000000⟩, + ⟨7, 4, 3, 2, 6, 6, 85560136559069461165856923121503869212609740800000000⟩, + ⟨7, 4, 4, 2, 7, 6, -27739077228921731584264524156795021554614272000000000⟩, + ⟨7, 4, 5, 2, 8, 6, 115344008158405195688192078691090970020151296000000000⟩, + ⟨7, 4, 2, 3, 4, 6, -11484882253584183076813354511246635808745062400000000⟩, + ⟨7, 4, 3, 3, 5, 6, 170903612713600461376537802399538330075345715200000000⟩, + ⟨7, 4, 4, 3, 6, 6, -22591463480450587829892507280444545968583475200000000⟩, + ⟨7, 4, 5, 3, 7, 6, -9086661685906538494319225391619536391766016000000000⟩, + ⟨7, 4, 6, 3, 8, 6, 29438226814651619537012904940402373969313792000000000⟩, + ⟨7, 4, 2, 4, 3, 6, -244282268388228780316540379267595417839625830400000000⟩, + ⟨7, 4, 3, 4, 4, 6, -69893572537569801918975544725714897587719372800000000⟩, + ⟨7, 4, 4, 4, 5, 6, 58419070760362563439754268631249952959994265600000000⟩, + ⟨7, 4, 5, 4, 6, 6, -22253154269821701201619759765093712218030080000000000⟩, + ⟨7, 4, 6, 4, 7, 6, -12845559837683079566859488898197983365955584000000000⟩, + ⟨7, 4, 7, 4, 8, 6, 15077735699557095994513194584410941007331328000000000⟩, + ⟨7, 4, 2, 5, 2, 6, 33227859448191532516681662695773003880123596800000000⟩, + ⟨7, 4, 3, 5, 3, 6, -175970224734819317748929408788491010469108121600000000⟩, + ⟨7, 4, 4, 5, 4, 6, 8158146601368949674930823546196549563318272000000000⟩, + ⟨7, 4, 5, 5, 5, 6, -6124097441687205823407325023213668731453440000000000⟩, + ⟨7, 4, 6, 5, 6, 6, -21756309594843747497059828939712322953281536000000000⟩, + ⟨7, 4, 7, 5, 7, 6, 6877497199813821738872765118233695647852134400000000⟩, + ⟨7, 4, 8, 5, 8, 6, 6919488156649341692745599444063260538358988800000000⟩, + ⟨7, 4, 2, 6, 1, 6, -557552567269989218462995258253142594671974809600000000⟩, + ⟨7, 4, 3, 6, 2, 6, -196784174582653138328439902594856088851657523200000000⟩, + ⟨7, 4, 4, 6, 3, 6, -203923202549455823277562065528285826281111552000000000⟩, + ⟨7, 4, 5, 6, 4, 6, 51069127698516692347006322780048296180187136000000000⟩, + ⟨7, 4, 6, 6, 5, 6, 2069408434226227664719675496448696564842496000000000⟩, + ⟨7, 4, 7, 6, 6, 6, 2079249952973543577328848043556946364386508800000000⟩, + ⟨7, 4, 8, 6, 7, 6, 1865200205239644324514021130346563762336563200000000⟩, + ⟨7, 4, 2, 7, 0, 6, 4548499373138754158573648864830842659928853708800000000⟩, + ⟨7, 4, 3, 7, 1, 6, 1809014645084051053968883228735652548929650688000000000⟩, + ⟨7, 4, 4, 7, 2, 6, 209563275668478779282327612049614910913511424000000000⟩, + ⟨7, 4, 5, 7, 3, 6, 71200402418451216190068981805594699578212352000000000⟩, + ⟨7, 4, 6, 7, 4, 6, 71816007037332739266187150698166563215769600000000000⟩, + ⟨7, 4, 7, 7, 5, 6, -7469781724683369845632161036673338206217830400000000⟩, + ⟨7, 4, 8, 7, 6, 6, 2788601172974778187770047908774787396350771200000000⟩ +] + +def collectedFourData_13_5_52 : List CollectedFourTerm := [ + ⟨7, 5, 1, 0, 6, 7, -172110488201283474675514198124986601555758153728000000⟩, + ⟨7, 5, 2, 0, 7, 7, 16794307777409080553043071951784807224511037440000000⟩, + ⟨7, 5, 3, 0, 8, 7, -5116280975367920407179697412598781985345765376000000⟩, + ⟨7, 5, 1, 1, 5, 7, -37474278930394672052350595376293535040753631232000000⟩, + ⟨7, 5, 2, 1, 6, 7, -38657478474783253101584668120415552321819246592000000⟩, + ⟨7, 5, 3, 1, 7, 7, 68346975003847565197874649011275008452358832128000000⟩, + ⟨7, 5, 4, 1, 8, 7, -35464591439985292820367197866456957734724042752000000⟩, + ⟨7, 5, 1, 2, 4, 7, 32582158043864218799862325920124475728988209152000000⟩, + ⟨7, 5, 2, 2, 5, 7, -81063848178208711081089292897551183076267130880000000⟩, + ⟨7, 5, 3, 2, 6, 7, -22248366721993939846989746598421446499812507648000000⟩, + ⟨7, 5, 4, 2, 7, 7, 4808697036870602402189931977463656472253562880000000⟩, + ⟨7, 5, 5, 2, 8, 7, -14996562043359888629441310575694431319364730880000000⟩, + ⟨7, 5, 1, 3, 3, 7, -90234431474878222819447299266652391802161594368000000⟩, + ⟨7, 5, 2, 3, 4, 7, 5972872003546977473952305630540112453527666688000000⟩, + ⟨7, 5, 3, 3, 5, 7, -44440394822660652761792379269908786276793843712000000⟩, + ⟨7, 5, 4, 3, 6, 7, 3916334440417001129986287442917233873500766208000000⟩, + ⟨7, 5, 5, 3, 7, 7, 1181411049567281561386927112433928080174612480000000⟩, + ⟨7, 5, 6, 3, 8, 7, -3061951474869071507993881021221781293873758208000000⟩, + ⟨7, 5, 1, 4, 2, 7, 155571697843519809991117693178955422102269722624000000⟩, + ⟨7, 5, 2, 4, 3, 7, 127042375324627937141378363072757000391882702848000000⟩, + ⟨7, 5, 3, 4, 4, 7, 18174559974580873248106772846796641631436013568000000⟩, + ⟨7, 5, 4, 4, 5, 7, -10127215485351217828992828958761540251994292224000000⟩, + ⟨7, 5, 5, 4, 6, 7, 2893265233244989339704541268007273347049062400000000⟩, + ⟨7, 5, 6, 4, 7, 7, 1336102243459057613825234193310300631168188416000000⟩, + ⟨7, 5, 7, 4, 8, 7, -1306897529121531624895211716935144574612930560000000⟩, + ⟨7, 5, 1, 5, 1, 7, 70538020752327698615851008164588659841395851264000000⟩, + ⟨7, 5, 2, 5, 2, 7, -17280608286076268687941567769685857863011926016000000⟩, + ⟨7, 5, 3, 5, 3, 7, 45757875682550552225198409217884665466580893696000000⟩, + ⟨7, 5, 4, 5, 4, 7, -1414252358310471004903289054989815672345722880000000⟩, + ⟨7, 5, 5, 5, 5, 7, 796230412920250832564881746813508432114483200000000⟩, + ⟨7, 5, 6, 5, 6, 7, 2262933996367073857999363017453712824770494464000000⟩, + ⟨7, 5, 7, 5, 7, 7, -596122937560243978629558758595566336514981888000000⟩, + ⟨7, 5, 8, 5, 8, 7, -514082229107595293162045642194506527180587008000000⟩, + ⟨7, 5, 1, 6, 0, 7, -769011758589846051886010313980994884008402747392000000⟩, + ⟨7, 5, 2, 6, 1, 7, 289962930922812135056386299073331619488650493952000000⟩, + ⟨7, 5, 3, 6, 2, 7, 51170167057612765533482865214533831636069384192000000⟩, + ⟨7, 5, 4, 6, 3, 7, 35351028145461123831428886833682832999663534080000000⟩, + ⟨7, 5, 5, 6, 4, 7, -6639801704994467383314493731998957672941486080000000⟩, + ⟨7, 5, 6, 6, 5, 7, -215244900692585443488951738394434492646293504000000⟩, + ⟨7, 5, 7, 6, 6, 7, -180223786920937124932117149085195031675928576000000⟩, + ⟨7, 5, 8, 6, 7, 7, -138574741011748071774816839670496444192653312000000⟩, + ⟨7, 5, 2, 7, 0, 7, -2365510064806543445678441900891479663758809235456000000⟩, + ⟨7, 5, 3, 7, 1, 7, -470401554367568278814626721634395690649287393280000000⟩, + ⟨7, 5, 4, 7, 2, 7, -36328760846205094587238585500924409428270120960000000⟩, + ⟨7, 5, 5, 7, 3, 7, -9257188729856763209838649754716727067342274560000000⟩, + ⟨7, 5, 6, 7, 4, 7, -7469781724683369845632161036673338206217830400000000⟩, + ⟨7, 5, 7, 7, 5, 7, 647460565272584791827667378353962504901623808000000⟩, + ⟨7, 5, 8, 7, 6, 7, -207178663311581387484947304167311732314734592000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1313.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1313.lean new file mode 100644 index 0000000000000000000000000000000000000000..bd58b2577969a6405e6c931c7aca41845ff3771f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1313.lean @@ -0,0 +1,617 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1310 +import OAI.Analysis.LaughlinFock.Sparse1311 +import OAI.Analysis.LaughlinFock.Sparse1312 + +namespace OAI + +/-! Sparse1313. -/ +namespace LaughlinFock +def collectedFourData_13_5_53 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 5, 8, -320641194864237388798744437525654772413993320448000000⟩, + ⟨7, 6, 1, 0, 6, 8, 385511272191588624852513193654055297831827144704000000⟩, + ⟨7, 6, 2, 0, 7, 8, -18808833280614053009218346930253743027870760960000000⟩, + ⟨7, 6, 3, 0, 8, 8, 3819995725453219449748487778871980403936198656000000⟩, + ⟨7, 6, 0, 1, 4, 8, -230535607801807075723681289386874351308895158272000000⟩, + ⟨7, 6, 1, 1, 5, 8, 83938852860747167763828766639856699496072216576000000⟩, + ⟨7, 6, 2, 1, 6, 8, 43294554161927913353714426936508437731662102528000000⟩, + ⟨7, 6, 3, 1, 7, 8, -51030260773272066374065584033701672922768211968000000⟩, + ⟨7, 6, 4, 1, 8, 8, 19859335573719118624128090801428815768908201984000000⟩, + ⟨7, 6, 0, 2, 3, 8, -90236133200280164576036303110314923382873784320000000⟩, + ⟨7, 6, 1, 2, 4, 8, -72980963156339640323945341959079197033822683136000000⟩, + ⟨7, 6, 2, 2, 5, 8, 90787689833808706512538030511122661362284625920000000⟩, + ⟨7, 6, 3, 2, 6, 8, 16611414851042426906416382646939324947877593088000000⟩, + ⟨7, 6, 4, 2, 7, 8, -2692757035962675490001031260957051374754856960000000⟩, + ⟨7, 6, 5, 2, 8, 8, 6718177110827168599920505743749904706849210368000000⟩, + ⟨7, 6, 0, 3, 2, 8, 396503444137844764693935756164316762897314217984000000⟩, + ⟨7, 6, 1, 3, 3, 8, 202116621926505108821727578497145527382493364224000000⟩, + ⟨7, 6, 2, 3, 4, 8, -6689335172973342791137540868746403379771604992000000⟩, + ⟨7, 6, 3, 3, 5, 8, 33180765301461809822444384787285205190361219072000000⟩, + ⟨7, 6, 4, 3, 6, 8, -2193055008197972974677138686287614275890446336000000⟩, + ⟨7, 6, 5, 3, 7, 8, -529249880654845866145632256744285777982128128000000⟩, + ⟨7, 6, 6, 3, 8, 8, 1143080452564854377134656095540221385820340224000000⟩, + ⟨7, 6, 0, 4, 1, 8, 327277833448153018906246082581355189584244244480000000⟩, + ⟨7, 6, 1, 4, 2, 8, -348465940567900262063672466215693451907439788032000000⟩, + ⟨7, 6, 2, 4, 3, 8, -142281473504278205935842457830494458989282066432000000⟩, + ⟨7, 6, 3, 4, 4, 8, -13569767131465940315620087052480850326200516608000000⟩, + ⟨7, 6, 4, 4, 5, 8, 5671002049785293518162344390229873767594590208000000⟩, + ⟨7, 6, 5, 4, 6, 8, -1296128286559181924610739157566734731984240640000000⟩, + ⟨7, 6, 6, 4, 7, 8, -498790516329590987836493910180108283253096448000000⟩, + ⟨7, 6, 7, 4, 8, 8, 418189612914286607403819275182086091639357440000000⟩, + ⟨7, 6, 0, 5, 0, 8, -2025274168533616922037966381921322777756928311296000000⟩, + ⟨7, 6, 1, 5, 1, 8, -157998518290785624260351573763448679047523991552000000⟩, + ⟨7, 6, 2, 5, 2, 8, 19353466933458186657044855414803798040713887744000000⟩, + ⟨7, 6, 3, 5, 3, 8, -34164442952743253134746296836732289209992216576000000⟩, + ⟨7, 6, 4, 5, 4, 8, 791947997402982109120745109074960601537576960000000⟩, + ⟨7, 6, 5, 5, 5, 8, -356696216076657169225734084447822302171627520000000⟩, + ⟨7, 6, 6, 5, 6, 8, -844793145130517396289927283937559835356168192000000⟩, + ⟨7, 6, 7, 5, 7, 8, 190751313666661280469205153557350470240960512000000⟩, + ⟨7, 6, 8, 5, 8, 8, 143936967631644076384465623309527353254739968000000⟩, + ⟨7, 6, 1, 6, 0, 8, 1722513860035936962456521332412639157256722579456000000⟩, + ⟨7, 6, 2, 6, 1, 8, -324744818159261475199584537968754885550845984768000000⟩, + ⟨7, 6, 3, 6, 2, 8, -38205450476994442844246212038873098323809533952000000⟩, + ⟨7, 6, 4, 6, 3, 8, -19795742804615065297955773899389034430841487360000000⟩, + ⟨7, 6, 5, 6, 4, 8, 2974506003839465997420696504746514335649497088000000⟩, + ⟨7, 6, 6, 6, 5, 8, 80354715127050936619189474117597835204493312000000⟩, + ⟨7, 6, 7, 6, 6, 8, 57669185235260274090812733973987092514996224000000⟩, + ⟨7, 6, 8, 6, 7, 8, 38799294903066609615037807273459287695818752000000⟩, + ⟨7, 6, 2, 7, 0, 8, 2649259798156732270364450750458089049643972296704000000⟩, + ⟨7, 6, 3, 7, 1, 8, 351218382176799941517930801785129470206337351680000000⟩, + ⟨7, 6, 4, 7, 2, 8, 20343250079253536646393382340145579041300152320000000⟩, + ⟨7, 6, 5, 7, 3, 8, 4147046053336456782699311483703332387281698816000000⟩, + ⟨7, 6, 6, 7, 4, 8, 2788601172974778187770047908774787396350771200000000⟩, + ⟨7, 6, 7, 7, 5, 8, -207178663311581387484947304167311732314734592000000⟩, + ⟨7, 6, 8, 7, 6, 8, 58007584908765701018554703671313961301573632000000⟩ +] + +def collectedFourData_13_5 : List (List CollectedFourTerm) := [ + collectedFourData_13_5_0, + collectedFourData_13_5_1, + collectedFourData_13_5_2, + collectedFourData_13_5_3, + collectedFourData_13_5_4, + collectedFourData_13_5_5, + collectedFourData_13_5_6, + collectedFourData_13_5_7, + collectedFourData_13_5_8, + collectedFourData_13_5_9, + collectedFourData_13_5_10, + collectedFourData_13_5_11, + collectedFourData_13_5_12, + collectedFourData_13_5_13, + collectedFourData_13_5_14, + collectedFourData_13_5_15, + collectedFourData_13_5_16, + collectedFourData_13_5_17, + collectedFourData_13_5_18, + collectedFourData_13_5_19, + collectedFourData_13_5_20, + collectedFourData_13_5_21, + collectedFourData_13_5_22, + collectedFourData_13_5_23, + collectedFourData_13_5_24, + collectedFourData_13_5_25, + collectedFourData_13_5_26, + collectedFourData_13_5_27, + collectedFourData_13_5_28, + collectedFourData_13_5_29, + collectedFourData_13_5_30, + collectedFourData_13_5_31, + collectedFourData_13_5_32, + collectedFourData_13_5_33, + collectedFourData_13_5_34, + collectedFourData_13_5_35, + collectedFourData_13_5_36, + collectedFourData_13_5_37, + collectedFourData_13_5_38, + collectedFourData_13_5_39, + collectedFourData_13_5_40, + collectedFourData_13_5_41, + collectedFourData_13_5_42, + collectedFourData_13_5_43, + collectedFourData_13_5_44, + collectedFourData_13_5_45, + collectedFourData_13_5_46, + collectedFourData_13_5_47, + collectedFourData_13_5_48, + collectedFourData_13_5_49, + collectedFourData_13_5_50, + collectedFourData_13_5_51, + collectedFourData_13_5_52, + collectedFourData_13_5_53 +] + +theorem collectedFourChecked_13_5 : collectNumericRowParts 13 5 = collectedFourData_13_5 := by + decide +kernel + +def collectedFourData_13_6_0 : List CollectedFourTerm := [ + ⟨0, 6, 7, 5, 8, 0, -11109145701165881176137564224838659005910876160000000⟩, + ⟨0, 6, 7, 6, 7, 0, 36708852476635280646945880638944493075966197760000000⟩, + ⟨0, 6, 8, 6, 8, 0, -435759597315896243980434551456649206150348144640000000⟩, + ⟨0, 6, 7, 7, 6, 0, -91932986505509420167221143433067308769754480640000000⟩, + ⟨0, 6, 8, 7, 7, 0, -329956104166231478046961795683696611472357457920000000⟩ +] + +def collectedFourData_13_6_1 : List CollectedFourTerm := [ + ⟨0, 7, 6, 4, 8, 1, -59560645263297997074181393739661944679888322560000000⟩, + ⟨0, 7, 6, 5, 7, 1, 72194604649309793663973447983987145372686352384000000⟩, + ⟨0, 7, 7, 5, 8, 1, 29483010188877570350702263124802654732621447168000000⟩, + ⟨0, 7, 6, 6, 6, 1, -47009863601806537571291577204875290386634899456000000⟩, + ⟨0, 7, 7, 6, 7, 1, -97423105313764842170515159984750656052525006848000000⟩, + ⟨0, 7, 8, 6, 8, 1, 578239992217288043752650486912268863483817230336000000⟩, + ⟨0, 7, 6, 7, 5, 1, 48581878558451221633317917313439019602469191680000000⟩, + ⟨0, 7, 7, 7, 6, 1, 243984663694834904313194647914840264709056233472000000⟩, + ⟨0, 7, 8, 7, 7, 1, 437841911641972988123625892432842783777104068608000000⟩ +] + +def collectedFourData_13_6_2 : List CollectedFourTerm := [ + ⟨0, 8, 5, 3, 8, 2, -15966186988821564902321838840284446220844269568000000⟩, + ⟨0, 8, 5, 4, 7, 2, -9540313612420609949871218130922873522948669440000000⟩, + ⟨0, 8, 6, 4, 8, 2, 36210381145340445715057300715641748981934981120000000⟩, + ⟨0, 8, 5, 5, 6, 2, 21191157964543674234769924685923624858807173120000000⟩, + ⟨0, 8, 6, 5, 7, 2, -43891300025917846385826801526783106182878855168000000⟩, + ⟨0, 8, 7, 5, 8, 2, -8962218521405739096443206706383332281646317568000000⟩, + ⟨0, 8, 5, 6, 5, 2, -42953959759940274360131364062924052132494573568000000⟩, + ⟨0, 8, 6, 6, 6, 2, 28580030842292199245727247416306696571701952512000000⟩, + ⟨0, 8, 7, 6, 7, 2, 29614586613183456540679101001702693226044981248000000⟩, + ⟨0, 8, 8, 6, 8, 2, -117181909962556687617891188112081344357071847424000000⟩, + ⟨0, 8, 5, 7, 4, 2, -129894035759903433024804276565689893775942352896000000⟩, + ⟨0, 8, 6, 7, 5, 2, -29535750185066960285713108391386040635867791360000000⟩, + ⟨0, 8, 7, 7, 6, 2, -74166235329990440503853193011780726148481155072000000⟩, + ⟨0, 8, 8, 7, 7, 2, -88729856389081166367867990416462588064061980672000000⟩ +] + +def collectedFourData_13_6_3 : List CollectedFourTerm := [ + ⟨1, 5, 7, 5, 8, 0, -16964566750571374121547992257999595665172201472000000⟩, + ⟨1, 5, 7, 6, 7, 0, 56057395854606557160087583433626403284495368192000000⟩, + ⟨1, 5, 8, 6, 8, 0, -665440257489088486268767060896975718610934693888000000⟩, + ⟨1, 5, 7, 7, 6, 0, -140389128750774678204248145457170052636200665088000000⟩, + ⟨1, 5, 8, 7, 7, 0, -503869739803580318474344492205308821418713022464000000⟩ +] + +def collectedFourData_13_6_4 : List CollectedFourTerm := [ + ⟨1, 6, 6, 4, 8, 1, -29095788755849867626481042431305258474468802560000000⟩, + ⟨1, 6, 6, 5, 7, 1, 35267565636714227598921604703303667266705424384000000⟩, + ⟨1, 6, 7, 5, 8, 1, 14402655185315082308609788628988216030598791168000000⟩, + ⟨1, 6, 6, 6, 6, 1, -22964644770937817128151230331777661494630547456000000⟩, + ⟨1, 6, 7, 6, 7, 1, -47591863379205753732916921543330122242979790848000000⟩, + ⟨1, 6, 8, 6, 8, 1, 282474251065675663840016972546936787474459918336000000⟩, + ⟨1, 6, 6, 7, 5, 1, 23732584992158945501798009253172298620002631680000000⟩, + ⟨1, 6, 7, 7, 6, 1, 119188202262584192916625089257682585504524009472000000⟩, + ⟨1, 6, 8, 7, 7, 1, 213888813885004647407497792486170717448052932608000000⟩ +] + +def collectedFourData_13_6_5 : List CollectedFourTerm := [ + ⟨1, 7, 5, 3, 8, 2, -7319097238470041017273911372269142962444697600000000⟩, + ⟨1, 7, 5, 4, 7, 2, -4373397547184782949831543274985262948548608000000000⟩, + ⟨1, 7, 6, 4, 8, 2, 16599285780027688260950985402316755025526784000000000⟩, + ⟨1, 7, 5, 5, 6, 2, 9714288442623436913580789711161323300061184000000000⟩, + ⟨1, 7, 6, 5, 7, 2, -20120313825553275271981593701543857301854617600000000⟩, + ⟨1, 7, 7, 5, 8, 2, -4108391620147702660041790606703577139878297600000000⟩, + ⟨1, 7, 5, 6, 5, 2, -19690625474976743474219637188921262685657497600000000⟩, + ⟨1, 7, 6, 6, 6, 2, 13101438994774583396051684536751601723270758400000000⟩, + ⟨1, 7, 7, 6, 7, 2, 13575692133052047742354944464573402189502873600000000⟩, + ⟨1, 7, 8, 6, 8, 2, -53717634285886337695595561522637379874901196800000000⟩, + ⟨1, 7, 5, 7, 4, 2, -59545029698678727887939715970599790352479027200000000⟩, + ⟨1, 7, 6, 7, 5, 2, -13539552541067920679313518601122753336573952000000000⟩, + ⟨1, 7, 7, 7, 6, 2, -33998717951349604409836062444132397608232550400000000⟩, + ⟨1, 7, 8, 7, 7, 2, -40674861651178743625845847037979149510010470400000000⟩ +] + +def collectedFourData_13_6_6 : List CollectedFourTerm := [ + ⟨1, 8, 4, 2, 8, 3, 55700858244394589091483244145735164327310131200000⟩, + ⟨1, 8, 4, 3, 7, 3, 335800401081556352615657876071116007870876876800000⟩, + ⟨1, 8, 5, 3, 8, 3, -277709972138247012960478245773276618227187712000000⟩, + ⟨1, 8, 4, 4, 6, 3, -398169908304983986282848585814308497376097075200000⟩, + ⟨1, 8, 5, 4, 7, 3, -165940698887619419314304962015021625203752960000000⟩, + ⟨1, 8, 6, 4, 8, 3, 314915012144988474411404167882653113033687040000000⟩, + ⟨1, 8, 4, 5, 5, 3, -206572565822554089772341332089857054774342451200000⟩, + ⟨1, 8, 5, 5, 6, 3, 368591191624580606968847156803110348867502080000000⟩, + ⟨1, 8, 6, 5, 7, 3, -381714548246335462702083038361559272108589056000000⟩, + ⟨1, 8, 7, 5, 8, 3, -51961841977236547450580150576090671327739904000000⟩, + ⟨1, 8, 4, 6, 4, 3, 400921091606581061669897449751124756352362086400000⟩, + ⟨1, 8, 5, 6, 5, 3, -747125345363428921935850723164228255284723712000000⟩, + ⟨1, 8, 6, 6, 6, 3, 248555261643876671479532073374604493276053504000000⟩, + ⟨1, 8, 7, 6, 7, 3, 171701735026882139310560788061834138766802944000000⟩, + ⟨1, 8, 8, 6, 8, 3, -509554738610920160355296517140629754587643904000000⟩, + ⟨1, 8, 4, 7, 3, 3, -1459211678576482438564236320398952807632837017600000⟩, + ⟨1, 8, 5, 7, 4, 3, -2259328985503113923315571064400694080924811264000000⟩, + ⟨1, 8, 6, 7, 5, 3, -256866976652594362454810730466680109132677120000000⟩, + ⟨1, 8, 7, 7, 6, 3, -430006721110279767276886922783810856488534016000000⟩, + ⟨1, 8, 8, 7, 7, 3, -385833605150911314621976060259542580814938112000000⟩ +] + +def collectedFourData_13_6_7 : List CollectedFourTerm := [ + ⟨2, 4, 7, 5, 8, 0, -4834051708468747380612026478210225965346324480000000⟩, + ⟨2, 4, 7, 6, 7, 0, 15973549704365001354848308354588712027585249280000000⟩, + ⟨2, 4, 8, 6, 8, 0, -189617139116781101395894851200998054616283217920000000⟩, + ⟨2, 4, 7, 7, 6, 0, -40003869103539829586108961441822055923103825920000000⟩, + ⟨2, 4, 8, 7, 7, 0, -143577635217896979216525915433052432743803125760000000⟩ +] + +def collectedFourData_13_6_8 : List CollectedFourTerm := [ + ⟨2, 5, 6, 4, 8, 1, -17312050164850615005564975985545803323272069120000000⟩, + ⟨2, 5, 6, 5, 7, 1, 20984269256911044608612495543800318302898618368000000⟩, + ⟨2, 5, 7, 5, 8, 1, 8569607484007095916954856253569842136047681536000000⟩, + ⟨2, 5, 6, 6, 6, 1, -13664007723884688104731360227088806886414221312000000⟩, + ⟨2, 5, 7, 6, 7, 1, -28317250072620036869220490931828537310257872896000000⟩, + ⟨2, 5, 8, 6, 8, 1, 168072721649258647931447097331699663390818435072000000⟩, + ⟨2, 5, 6, 7, 5, 1, 14120933629724367297223857509951519371674255360000000⟩, + ⟨2, 5, 7, 7, 6, 1, 70917209151560217985183072863997716784421535744000000⟩, + ⟨2, 5, 8, 7, 7, 1, 127264254863450580055881164890012417401255100416000000⟩ +] + +def collectedFourData_13_6_9 : List CollectedFourTerm := [ + ⟨2, 6, 5, 3, 8, 2, -15418280686391010321705865050439708170220732416000000⟩, + ⟨2, 6, 5, 4, 7, 2, -9212921858893672625331872560836977009916641280000000⟩, + ⟨2, 6, 6, 4, 8, 2, 34967761598366888686839132035222803588778557440000000⟩, + ⟨2, 6, 5, 5, 6, 2, 20463948079509508575811975512767339076979261440000000⟩, + ⟨2, 6, 6, 5, 7, 2, -42385096952954480433802329052769612802205679616000000⟩, + ⟨2, 6, 7, 5, 8, 2, -8654665063897317270329934265233441650078908416000000⟩, + ⟨2, 6, 5, 6, 5, 2, -41479923079592165512437810461331241527637180416000000⟩, + ⟨2, 6, 6, 6, 6, 2, 27599259476335191705637689117007166857537388544000000⟩, + ⟨2, 6, 7, 6, 7, 2, 28598312742621931766875937188130892293735448576000000⟩, + ⟨2, 6, 8, 6, 8, 2, -113160617524713741283678347433168754260089765888000000⟩, + ⟨2, 6, 5, 7, 4, 2, -125436505549915341684953484737885091212612861952000000⟩, + ⟨2, 6, 6, 7, 5, 2, -28522181717859184522196693048128748759883448320000000⟩, + ⟨2, 6, 7, 7, 6, 2, -71621097421152213616696271455594695017065611264000000⟩, + ⟨2, 6, 8, 7, 7, 2, -85684943564035778790919313249031123117973438464000000⟩ +] + +def collectedFourData_13_6_10 : List CollectedFourTerm := [ + ⟨2, 7, 4, 2, 8, 3, -2001331542153373855051283461612367421468416409600000⟩, + ⟨2, 7, 4, 3, 7, 3, -12065306635017668626467948848332447831109822054400000⟩, + ⟨2, 7, 5, 3, 8, 3, 9978117830289263651884293196852133848254775296000000⟩, + ⟨2, 7, 4, 4, 6, 3, 14306242699721299720616380735551600291418315161600000⟩, + ⟨2, 7, 5, 4, 7, 3, 5962248433473444267297621602967358596112711680000000⟩, + ⟨2, 7, 6, 4, 8, 3, -11314894720976815016847317110761895456218808320000000⟩, + ⟨2, 7, 4, 5, 5, 3, 7422151197568588863135481421775511608779970969600000⟩, + ⟨2, 7, 5, 5, 6, 3, -13243479565818122525439233290577229961117040640000000⟩, + ⟨2, 7, 6, 5, 7, 3, 13715001699836379080409081941355465180601909248000000⟩, + ⟨2, 7, 7, 5, 8, 3, 1866988707447752392476741516816131509224210432000000⟩, + ⟨2, 7, 4, 6, 4, 3, -14405092701198359195055588637897228092515234611200000⟩, + ⟨2, 7, 5, 6, 5, 3, 26844209707819647017681420401196377256855863296000000⟩, + ⟨2, 7, 6, 6, 6, 3, -8930589236407944482377962988084346313592799232000000⟩, + ⟨2, 7, 7, 6, 7, 3, -6169242431490562161337827725685507624378826752000000⟩, + ⟨2, 7, 8, 6, 8, 3, 18308299063567439671730134964956791033594642432000000⟩, + ⟨2, 7, 4, 7, 3, 3, 52429467894376180378687038615278646414342409420800000⟩, + ⟨2, 7, 5, 7, 4, 3, 81177678500919667155822697400832610888750989312000000⟩, + ⟨2, 7, 6, 7, 5, 3, 9229229112715601176618964141224554419674152960000000⟩, + ⟨2, 7, 7, 7, 6, 3, 15450139215450173536718994488876575122341756928000000⟩, + ⟨2, 7, 8, 7, 7, 3, 13862999392634620301352569649516620174113898496000000⟩ +] + +def collectedFourData_13_6_11 : List CollectedFourTerm := [ + ⟨2, 8, 3, 1, 8, 4, 55700858244394589091483244145735164327310131200000⟩, + ⟨2, 8, 3, 2, 7, 4, -2001331542153373855051283461612367421468416409600000⟩, + ⟨2, 8, 4, 2, 8, 4, 669382257205510074638351702232017069966937292800000⟩, + ⟨2, 8, 3, 3, 6, 4, 2197570332202581801571764706526705167263753830400000⟩, + ⟨2, 8, 4, 3, 7, 4, 4035464399134428669961385171367785110143447859200000⟩, + ⟨2, 8, 5, 3, 8, 4, -1668682798232165517674663351245799862791307264000000⟩, + ⟨2, 8, 3, 4, 5, 4, 4111034950378538228292499338825104518317657292800000⟩, + ⟨2, 8, 4, 4, 6, 4, -4784986809414610230354477209902565145464065228800000⟩, + ⟨2, 8, 5, 4, 7, 4, -997091993594486332236651541110951320349573120000000⟩, + ⟨2, 8, 6, 4, 8, 4, 1261491763332189727164604114138882453190737920000000⟩, + ⟨2, 8, 3, 5, 4, 4, -4208463052179262396758605699203187261742199603200000⟩, + ⟨2, 8, 4, 5, 5, 4, -2482475400654178541813954982722269179661831372800000⟩, + ⟨2, 8, 5, 5, 6, 4, 2214763036084455488955938898937795300829429760000000⟩, + ⟨2, 8, 6, 5, 7, 4, -1529078449696520599955800884102359300532338688000000⟩, + ⟨2, 8, 7, 5, 8, 4, -156112204405660647933361994494312871356268544000000⟩, + ⟨2, 8, 3, 6, 3, 4, -5598255101588262448102903415280170760588283084800000⟩, + ⟨2, 8, 4, 6, 4, 4, 4818049016110401765432110318604224171628665241600000⟩, + ⟨2, 8, 5, 6, 5, 4, -4489270595261848907384364159301981422709899264000000⟩, + ⟨2, 8, 6, 6, 6, 4, 995666777397920801352744737457902083419144192000000⟩, + ⟨2, 8, 7, 6, 7, 4, 515854237173998384210891045172854962450857984000000⟩, + ⟨2, 8, 8, 6, 8, 4, -1224709678994816634164534785595407669075850035200000⟩, + ⟨2, 8, 3, 7, 2, 4, -20607036140139386505846215622308534064007190937600000⟩, + ⟨2, 8, 4, 7, 3, 4, -17536002818133660701950615297611854880444933734400000⟩, + ⟨2, 8, 5, 7, 4, 4, -13575686118248493460835475120312823097755435008000000⟩, + ⟨2, 8, 6, 7, 5, 4, -1028961982828884777303372241730788329793781760000000⟩, + ⟨2, 8, 7, 7, 6, 4, -1291896025764135161120047464616571398652952576000000⟩, + ⟨2, 8, 8, 7, 7, 4, -927347181576496963290505007885281557118294425600000⟩ +] + +def collectedFourData_13_6_12 : List CollectedFourTerm := [ + ⟨3, 3, 7, 5, 8, 0, -859787761498152956680063312840814246366281728000000⟩, + ⟨3, 3, 7, 6, 7, 0, 2841066536262984665313102851293151864719147008000000⟩, + ⟨3, 3, 8, 6, 8, 0, -33725434772923279201034202556220676053152038912000000⟩, + ⟨3, 3, 7, 7, 6, 0, -7115115671506267862404635594061130348428787712000000⟩, + ⟨3, 3, 8, 7, 7, 0, -25536816945695711688010690661402348727551655936000000⟩ +] + +def collectedFourData_13_6_13 : List CollectedFourTerm := [ + ⟨3, 4, 6, 4, 8, 1, -9439525527338380725255353618708536195830251520000000⟩, + ⟨3, 4, 6, 5, 7, 1, 11441830599897816134928741301215774311058505728000000⟩, + ⟨3, 4, 7, 5, 8, 1, 4672642918329542565138262357976676677248352256000000⟩, + ⟨3, 4, 6, 6, 6, 1, -7450402955580350596598784513751974170226327552000000⟩, + ⟨3, 4, 7, 6, 7, 1, -15440193528738425223935033069388499122772770816000000⟩, + ⟨3, 4, 8, 6, 8, 1, 91642915272889355886970299203824145741761216512000000⟩, + ⟨3, 4, 6, 7, 5, 1, 7699545241514402656655731122582817929229762560000000⟩, + ⟨3, 4, 7, 7, 6, 1, 38668141539521939475809327251450972822384410624000000⟩, + ⟨3, 4, 8, 7, 7, 1, 69391791905751187675575967773993243023807348736000000⟩ +] + +def collectedFourData_13_6_14 : List CollectedFourTerm := [ + ⟨3, 5, 5, 3, 8, 2, 3821003255388599148336032926177359607193665536000000⟩, + ⟨3, 5, 5, 4, 7, 2, 2283173145598859616076597675878423834006650880000000⟩, + ⟨3, 5, 6, 4, 8, 2, -8665812590825725519159633926709823070787338240000000⟩, + ⟨3, 5, 5, 5, 6, 2, -5071435254056972376532001742310226383853322240000000⟩, + ⟨3, 5, 6, 5, 7, 2, 10503998255794452362407509260017584104313716736000000⟩, + ⟨3, 5, 7, 5, 8, 2, 2144824319655726580241306189593959821828161536000000⟩, + ⟨3, 5, 5, 6, 5, 2, 10279675428420909996721702711759723825553473536000000⟩, + ⟨3, 5, 6, 6, 6, 2, -6839728919870632007520071738911872423636762624000000⟩, + ⟨3, 5, 7, 6, 7, 2, -7087317212004765568720024526766836725523152896000000⟩, + ⟨3, 5, 8, 6, 8, 2, 28043794035048477976317264291993676748892930048000000⟩, + ⟨3, 5, 5, 7, 4, 2, 31086040382819480481271468114750946861585006592000000⟩, + ⟨3, 5, 6, 7, 5, 2, 7068450199568593729304068378911079857358110720000000⟩, + ⟨3, 5, 7, 7, 6, 2, 17749349098455401724390868148015850167671455744000000⟩, + ⟨3, 5, 8, 7, 7, 2, 21234692437850857002443264922565919209835986944000000⟩ +] + +def collectedFourData_13_6_15 : List CollectedFourTerm := [ + ⟨3, 6, 4, 2, 8, 3, 2197570332202581801571764706526705167263753830400000⟩, + ⟨3, 6, 4, 3, 7, 3, 13248359580398718585738176596410523329532369305600000⟩, + ⟨3, 6, 5, 3, 8, 3, -10956513327857618494901009185384449117052207104000000⟩, + ⟨3, 6, 4, 4, 6, 3, -15709028644184504174505875402769517622432523878400000⟩, + ⟨3, 6, 5, 4, 7, 3, -6546871417678601176459040117161754714513080320000000⟩, + ⟨3, 6, 6, 4, 8, 3, 12424366691417830800376484908972752653443399680000000⟩, + ⟨3, 6, 4, 5, 5, 3, -8149923653003920413321886385639789229077063270400000⟩, + ⟨3, 6, 5, 5, 6, 3, 14542057213398310565463140179900959569592975360000000⟩, + ⟨3, 6, 6, 5, 7, 3, -15059814032231259332166358275953028322874621952000000⟩, + ⟨3, 6, 7, 5, 8, 3, -2050054629943968200346074626578721165560250368000000⟩, + ⟨3, 6, 4, 6, 4, 3, 15817571294919141767216665518269121425004350668800000⟩, + ⟨3, 6, 5, 6, 5, 3, -29476394891500733035279320419570844856278319104000000⟩, + ⟨3, 6, 6, 6, 6, 3, 9806270246408669468129255690075825751686381568000000⟩, + ⟨3, 6, 7, 6, 7, 3, 6774162028657018410588259274026167598263042048000000⟩, + ⟨3, 6, 8, 6, 8, 3, -20103503096692194112149266058669189929650618368000000⟩, + ⟨3, 6, 4, 7, 3, 3, -57570392886467117208589138780409579359918306099200000⟩, + ⟨3, 6, 5, 7, 4, 3, -89137483796789655601998029110816590354330943488000000⟩, + ⟨3, 6, 6, 7, 5, 3, -10134192991023094919666101314309933501555671040000000⟩, + ⟨3, 6, 7, 7, 6, 3, -16965088918621047414945965305882235774038966272000000⟩, + ⟨3, 6, 8, 7, 7, 3, -15222323507586803347992775806053443003591163904000000⟩ +] + +def collectedFourData_13_6_16 : List CollectedFourTerm := [ + ⟨3, 7, 3, 1, 8, 4, 335800401081556352615657876071116007870876876800000⟩, + ⟨3, 7, 3, 2, 7, 4, -12065306635017668626467948848332447831109822054400000⟩, + ⟨3, 7, 4, 2, 8, 4, 4035464399134428669961385171367785110143447859200000⟩, + ⟨3, 7, 3, 3, 6, 4, 13248359580398718585738176596410523329532369305600000⟩, + ⟨3, 7, 4, 3, 7, 4, 24328360576312186635714190562806319512508222668800000⟩, + ⟨3, 7, 5, 3, 8, 4, -10059887236668292382814382331160142164573290496000000⟩, + ⟨3, 7, 3, 4, 5, 4, 24783948195920903399299878285226411090477527859200000⟩, + ⟨3, 7, 4, 4, 6, 4, -28846961077715204368582751227760489016300090163200000⟩, + ⟨3, 7, 5, 4, 7, 4, -6011108300973654387389647999295362350899527680000000⟩, + ⟨3, 7, 6, 4, 8, 4, 7605079229289230345638611531233635492303994880000000⟩, + ⟨3, 7, 3, 5, 4, 4, -25371307110890409574828668789056065471486151884800000⟩, + ⟨3, 7, 4, 5, 5, 4, -14965949565034947244288261740084732860132700979200000⟩, + ⟨3, 7, 5, 5, 6, 4, 13352008196258073107571809275647167163940208640000000⟩, + ⟨3, 7, 6, 5, 7, 4, -9218262929457252278024400904866547658215391232000000⟩, + ⟨3, 7, 7, 5, 8, 4, -941144221209953337121448698647469838529724416000000⟩, + ⟨3, 7, 3, 6, 3, 4, -33749862528543523503826323178650360530188055347200000⟩, + ⟨3, 7, 4, 6, 4, 4, 29046281207045624276542503529617758881864640102400000⟩, + ⟨3, 7, 5, 6, 5, 4, -27064194591728252775172539876375856650959978496000000⟩, + ⟨3, 7, 6, 6, 6, 4, 6002516186138820619590444651047016973455065088000000⟩, + ⟨3, 7, 7, 6, 7, 4, 3109899294237198179705226605007771832550424576000000⟩, + ⟨3, 7, 8, 6, 8, 4, -7383333298213769876999228744139248331467312332800000⟩, + ⟨3, 7, 3, 7, 2, 4, -124232394599724260267505191751545565384714643046400000⟩, + ⟨3, 7, 4, 7, 3, 4, -105718241429236504598283950092080947233073764761600000⟩, + ⟨3, 7, 5, 7, 4, 4, -81842919250241968366869077769244103465565683712000000⟩, + ⟨3, 7, 6, 7, 5, 4, -6203240980876353436858032991682478052359536640000000⟩, + ⟨3, 7, 7, 7, 6, 4, -7788375570513265686079062499302695225486475264000000⟩, + ⟨3, 7, 8, 7, 7, 4, -5590641963700377841753646471992863950580901478400000⟩ +] + +def collectedFourData_13_6_17 : List CollectedFourTerm := [ + ⟨3, 8, 2, 0, 8, 5, -15966186988821564902321838840284446220844269568000000⟩, + ⟨3, 8, 2, 1, 7, 5, -7319097238470041017273911372269142962444697600000000⟩, + ⟨3, 8, 3, 1, 8, 5, -277709972138247012960478245773276618227187712000000⟩, + ⟨3, 8, 2, 2, 6, 5, -15418280686391010321705865050439708170220732416000000⟩, + ⟨3, 8, 3, 2, 7, 5, 9978117830289263651884293196852133848254775296000000⟩, + ⟨3, 8, 4, 2, 8, 5, -1668682798232165517674663351245799862791307264000000⟩, + ⟨3, 8, 2, 3, 5, 5, 3821003255388599148336032926177359607193665536000000⟩, + ⟨3, 8, 3, 3, 6, 5, -10956513327857618494901009185384449117052207104000000⟩, + ⟨3, 8, 4, 3, 7, 5, -10059887236668292382814382331160142164573290496000000⟩, + ⟨3, 8, 5, 3, 8, 5, 2773205943382758226391297406702120474645626880000000⟩, + ⟨3, 8, 2, 4, 4, 5, 482701640438196058949266106136331040776519680000000⟩, + ⟨3, 8, 3, 4, 5, 5, -20496549559788427951833090109113088644929814528000000⟩, + ⟨3, 8, 4, 4, 6, 5, 11928349000422605446430819699231496232652242944000000⟩, + ⟨3, 8, 5, 4, 7, 5, 1657080330464865065899280266973452289074790400000000⟩, + ⟨3, 8, 6, 4, 8, 5, -1572367345358029399232611293702021966515404800000000⟩, + ⟨3, 8, 2, 5, 3, 5, 8049243119657515285719987817909917027781312512000000⟩, + ⟨3, 8, 3, 5, 4, 5, 20982300700602927649427089815177055449416466432000000⟩, + ⟨3, 8, 4, 5, 5, 5, 6188487898379317598432692315416583302140657664000000⟩, + ⟨3, 8, 5, 5, 6, 5, -3680743890546963241772197905289075961836339200000000⟩, + ⟨3, 8, 6, 5, 7, 5, 1905896726937542339298963376991428103865630720000000⟩, + ⟨3, 8, 7, 5, 8, 5, 155666958472041954435802820089113300002930688000000⟩, + ⟨3, 8, 2, 6, 2, 5, -5386688350495755707987645861209672241343627264000000⟩, + ⟨3, 8, 3, 6, 3, 5, 27911441893111775641926039010516001887195496448000000⟩, + ⟨3, 8, 4, 6, 4, 5, -12010768776254706062787795997510102082081783808000000⟩, + ⟨3, 8, 5, 6, 5, 5, 7460777991732780418614364077896217941382266880000000⟩, + ⟨3, 8, 6, 6, 6, 5, -1241033808657610739223601365852543359888916480000000⟩, + ⟨3, 8, 7, 6, 7, 5, -514382974870604969581552595731616576273645568000000⟩, + ⟨3, 8, 8, 6, 8, 5, 1017680581445735854765805699639924258915745792000000⟩, + ⟨3, 8, 2, 7, 1, 5, 79450224797863722554744234875160063041175814144000000⟩, + ⟨3, 8, 3, 7, 2, 5, 102741315173646639166611776733334855061210136576000000⟩, + ⟨3, 8, 4, 7, 3, 5, 43714971434306407389660212018306654147362947072000000⟩, + ⟨3, 8, 5, 7, 4, 5, 22561611750603963549336948850445754264044175360000000⟩, + ⟨3, 8, 6, 7, 5, 5, 1282534114326153653710016038371549935724134400000000⟩, + ⟨3, 8, 7, 7, 6, 5, 1288211423049571386568207522083046404812439552000000⟩, + ⟨3, 8, 8, 7, 7, 5, 770585253905573191333686635639986816680984576000000⟩ +] + +def collectedFourData_13_6_18 : List CollectedFourTerm := [ + ⟨4, 2, 7, 5, 8, 0, 6372542735456035131045054805939736778079469568000000⟩, + ⟨4, 2, 7, 6, 7, 0, -21057310568206799130334758566607611338841653248000000⟩, + ⟨4, 2, 8, 6, 8, 0, 249964914582876737862065363749293611829556150272000000⟩, + ⟨4, 2, 7, 7, 6, 0, 52735547904730278395184341540304385286520963072000000⟩, + ⟨4, 2, 8, 7, 7, 0, 189272823598237944684751963445560783487700566016000000⟩ +] + +def collectedFourData_13_6_19 : List CollectedFourTerm := [ + ⟨4, 3, 6, 4, 8, 1, 29748940790753601148162366794874533502506762240000000⟩, + ⟨4, 3, 6, 5, 7, 1, -36059263791213976457698176702238033653673230336000000⟩, + ⟨4, 3, 7, 5, 8, 1, -14725970824607177510583051376209790163088310272000000⟩, + ⟨4, 3, 6, 6, 6, 1, 23480162827136369444418989623819448514483585024000000⟩, + ⟨4, 3, 7, 6, 7, 1, 48660221507312487392891146596429214786353364992000000⟩, + ⟨4, 3, 8, 6, 8, 1, -288815327894340764629362232917421211621517164544000000⟩, + ⟨4, 3, 6, 7, 5, 1, -24265342028279434374297759951492990798365982720000000⟩, + ⟨4, 3, 7, 7, 6, 1, -121863779044419085482483198393170923210080780288000000⟩, + ⟨4, 3, 8, 7, 7, 1, -218690261792274350962147927896592207314558124032000000⟩ +] + +def collectedFourData_13_6_20 : List CollectedFourTerm := [ + ⟨4, 4, 5, 3, 8, 2, 482701640438196058949266106136331040776519680000000⟩, + ⟨4, 4, 5, 4, 7, 2, 288429857061956937877877599517263668864614400000000⟩, + ⟨4, 4, 6, 4, 8, 2, -1094739175482889473732789854349212706353971200000000⟩, + ⟨4, 4, 5, 5, 6, 2, -640666849225292682760290346789329804931891200000000⟩, + ⟨4, 4, 6, 5, 7, 2, 1326954428023976895702547144296439186383175680000000⟩, + ⟨4, 4, 7, 5, 8, 2, 270952456292598768260115068004080543260999680000000⟩, + ⟨4, 4, 5, 6, 5, 2, 1298616059924384448298383200028716227551559680000000⟩, + ⟨4, 4, 6, 6, 6, 2, -864052749789755086756490197238080903179141120000000⟩, + ⟨4, 4, 7, 6, 7, 2, -895330209341221286614935489954884679609876480000000⟩, + ⟨4, 4, 8, 6, 8, 2, 3542730660000993824213600848539323096880906240000000⟩, + ⟨4, 4, 5, 7, 4, 2, 3927053102180338745974008075499128409250856960000000⟩, + ⟨4, 4, 6, 7, 5, 2, 892946767809140783492699664014103568554393600000000⟩, + ⟨4, 4, 7, 7, 6, 2, 2242248790144854962410225852713764779689246720000000⟩, + ⟨4, 4, 8, 7, 7, 2, 2682547014189531174493976575593471781078302720000000⟩ +] + +def collectedFourData_13_6_21 : List CollectedFourTerm := [ + ⟨4, 5, 4, 2, 8, 3, 4111034950378538228292499338825104518317657292800000⟩, + ⟨4, 5, 4, 3, 7, 3, 24783948195920903399299878285226411090477527859200000⟩, + ⟨4, 5, 5, 3, 8, 3, -20496549559788427951833090109113088644929814528000000⟩, + ⟨4, 5, 4, 4, 6, 3, -29387166747929491795712349345706438010621185228800000⟩, + ⟨4, 5, 5, 4, 7, 3, -12247351913754325199758539899054189590075146240000000⟩, + ⟨4, 5, 6, 4, 8, 3, 23242489651534465565372813022626829274196213760000000⟩, + ⟨4, 5, 4, 5, 5, 3, -15246211003783810671786122011056002626604551372800000⟩, + ⟨4, 5, 5, 5, 6, 3, 27204091982241837807525805953086378187706859520000000⟩, + ⟨4, 5, 6, 5, 7, 3, -28172669118012364418019789372239741470390616064000000⟩, + ⟨4, 5, 7, 5, 8, 3, -3835074632372711488100351207615080971607474176000000⟩, + ⟨4, 5, 4, 6, 4, 3, 29590219466760832059877458564574481710864505241600000⟩, + ⟨4, 5, 5, 6, 5, 3, -55142030193256241110583550109687970446366998528000000⟩, + ⟨4, 5, 6, 6, 6, 3, 18344768822683070338334724353002006740599832576000000⟩, + ⟨4, 5, 7, 6, 7, 3, 12672548610275357418340224375463309036209831936000000⟩, + ⟨4, 5, 8, 6, 8, 3, -37607990353924239905752863095668866013961650176000000⟩, + ⟨4, 5, 4, 7, 3, 3, -107697985268155978870545812506622059254911493734400000⟩, + ⟨4, 5, 5, 7, 4, 3, -166751118682112866789664930471625978526109270016000000⟩, + ⟨4, 5, 6, 7, 5, 3, -18958219889244740947000585307624618662853345280000000⟩, + ⟨4, 5, 7, 7, 6, 3, -31736901640289093473224902250292417347981410304000000⟩, + ⟨4, 5, 8, 7, 7, 3, -28476678561152559847961285806506679179178672128000000⟩ +] + +def collectedFourData_13_6_22 : List CollectedFourTerm := [ + ⟨4, 6, 3, 1, 8, 4, -398169908304983986282848585814308497376097075200000⟩, + ⟨4, 6, 3, 2, 7, 4, 14306242699721299720616380735551600291418315161600000⟩, + ⟨4, 6, 4, 2, 8, 4, -4784986809414610230354477209902565145464065228800000⟩, + ⟨4, 6, 3, 3, 6, 4, -15709028644184504174505875402769517622432523878400000⟩, + ⟨4, 6, 4, 3, 7, 4, -28846961077715204368582751227760489016300090163200000⟩, + ⟨4, 6, 5, 3, 8, 4, 11928349000422605446430819699231496232652242944000000⟩, + ⟨4, 6, 3, 4, 5, 4, -29387166747929491795712349345706438010621185228800000⟩, + ⟨4, 6, 4, 4, 6, 4, 34204818726233994872674841520390519840387681484800000⟩, + ⟨4, 6, 5, 4, 7, 4, 7127574694077595977662237966265256230015467520000000⟩, + ⟨4, 6, 6, 4, 8, 4, -9017600007698586892052080506196031558721208320000000⟩, + ⟨4, 6, 3, 5, 4, 4, 30083618105826241679157598684912222297073595187200000⟩, + ⟨4, 6, 4, 5, 5, 4, 17745633259561565545571172575241518779936328908800000⟩, + ⟨4, 6, 5, 5, 6, 4, -15831928318335383016886914157796732204702760960000000⟩, + ⟨4, 6, 6, 5, 7, 4, 10930406555594860987144727808102774360137269248000000⟩, + ⟨4, 6, 7, 5, 8, 4, 1115946577353611178727363090395025005109837824000000⟩, + ⟨4, 6, 3, 6, 3, 4, 40018355025824518489431402522701001451583098060800000⟩, + ⟨4, 6, 4, 6, 4, 4, -34441159354068908519374737059824472941095655833600000⟩, + ⟨4, 6, 5, 6, 5, 4, 32090932125835854926186871411891807851793874944000000⟩, + ⟨4, 6, 6, 6, 6, 4, -7117386732523908729480772934470711718531039232000000⟩, + ⟨4, 6, 7, 6, 7, 4, -3687512917899760069907270266057773234272600064000000⟩, + ⟨4, 6, 8, 6, 8, 4, 8754668347227235499467073779795496992054129459200000⟩, + ⟨4, 6, 3, 7, 2, 4, 147306557725840866110463323949542601256578161049600000⟩, + ⟨4, 6, 4, 7, 3, 4, 125353699282270564470527361833586724738099996262400000⟩, + ⟨4, 6, 5, 7, 4, 4, 97043921175563173403532991982306776337212243968000000⟩, + ⟨4, 6, 6, 7, 5, 4, 7355392919704635942242070702684934736141352960000000⟩, + ⟨4, 6, 7, 7, 6, 4, 9234940687289043052963825843232479530971037696000000⟩, + ⟨4, 6, 8, 7, 7, 4, 6629013517800822676307867627097592031270771097600000⟩ +] + +def collectedFourData_13_6_23 : List CollectedFourTerm := [ + ⟨4, 7, 2, 0, 8, 5, -9540313612420609949871218130922873522948669440000000⟩, + ⟨4, 7, 2, 1, 7, 5, -4373397547184782949831543274985262948548608000000000⟩, + ⟨4, 7, 3, 1, 8, 5, -165940698887619419314304962015021625203752960000000⟩, + ⟨4, 7, 2, 2, 6, 5, -9212921858893672625331872560836977009916641280000000⟩, + ⟨4, 7, 3, 2, 7, 5, 5962248433473444267297621602967358596112711680000000⟩, + ⟨4, 7, 4, 2, 8, 5, -997091993594486332236651541110951320349573120000000⟩, + ⟨4, 7, 2, 3, 5, 5, 2283173145598859616076597675878423834006650880000000⟩, + ⟨4, 7, 3, 3, 6, 5, -6546871417678601176459040117161754714513080320000000⟩, + ⟨4, 7, 4, 3, 7, 5, -6011108300973654387389647999295362350899527680000000⟩, + ⟨4, 7, 5, 3, 8, 5, 1657080330464865065899280266973452289074790400000000⟩, + ⟨4, 7, 2, 4, 4, 5, 288429857061956937877877599517263668864614400000000⟩, + ⟨4, 7, 3, 4, 5, 5, -12247351913754325199758539899054189590075146240000000⟩, + ⟨4, 7, 4, 4, 6, 5, 7127574694077595977662237966265256230015467520000000⟩, + ⟨4, 7, 5, 4, 7, 5, 990159143487222382683861973347409625874432000000000⟩, + ⟨4, 7, 6, 4, 8, 5, -939540392402234643714287991011581869686784000000000⟩, + ⟨4, 7, 2, 5, 3, 5, 4809683348811852370173887363936964790148136960000000⟩, + ⟨4, 7, 3, 5, 4, 5, 12537603946015125821692276511740546156918210560000000⟩, + ⟨4, 7, 4, 5, 5, 5, 3697821864327674335862200251612687919868805120000000⟩, + ⟨4, 7, 5, 5, 6, 5, -2199363634373356186237253808300096000884736000000000⟩, + ⟨4, 7, 6, 5, 7, 5, 1138834995518999900514185454312061872478617600000000⟩, + ⟨4, 7, 7, 5, 8, 5, 93016047222465169539690213707931085480919040000000⟩, + ⟨4, 7, 2, 6, 2, 5, -3218720677146173975868398493986033677495173120000000⟩, + ⟨4, 7, 3, 6, 3, 5, 16677990131367932908017768831051405545271459840000000⟩, + ⟨4, 7, 4, 6, 4, 5, -7176823178380965698936918502224308931804528640000000⟩, + ⟨4, 7, 5, 6, 5, 5, 4458056384007680725638271458944324269925990400000000⟩, + ⟨4, 7, 6, 6, 6, 5, -741557877688633795769435996203802666886758400000000⟩, + ⟨4, 7, 7, 6, 7, 5, -307360480031409522190300112968319554226749440000000⟩, + ⟨4, 7, 8, 6, 8, 5, 608097093630460979015234022559994481066639360000000⟩, + ⟨4, 7, 2, 7, 1, 5, 47474081424677207770843899706139297269174763520000000⟩, + ⟨4, 7, 3, 7, 2, 5, 61391261945973414439639978430996234861889454080000000⟩, + ⟨4, 7, 4, 7, 3, 5, 26121110652987133011512663454381871453710581760000000⟩, + ⟨4, 7, 5, 7, 4, 5, 13481293426735860269070415742037472207228108800000000⟩, + ⟨4, 7, 6, 7, 5, 5, 766355653849367507591005697244518733053952000000000⟩, + ⟨4, 7, 7, 7, 6, 5, 769748029607828680864852420403144475971420160000000⟩, + ⟨4, 7, 8, 7, 7, 5, 460449636003451436261763030019119574501294080000000⟩ +] + +def collectedFourData_13_6_24 : List CollectedFourTerm := [ + ⟨4, 8, 1, 0, 7, 6, -59560645263297997074181393739661944679888322560000000⟩, + ⟨4, 8, 2, 0, 8, 6, 36210381145340445715057300715641748981934981120000000⟩, + ⟨4, 8, 1, 1, 6, 6, -29095788755849867626481042431305258474468802560000000⟩, + ⟨4, 8, 2, 1, 7, 6, 16599285780027688260950985402316755025526784000000000⟩, + ⟨4, 8, 3, 1, 8, 6, 314915012144988474411404167882653113033687040000000⟩, + ⟨4, 8, 1, 2, 5, 6, -17312050164850615005564975985545803323272069120000000⟩, + ⟨4, 8, 2, 2, 6, 6, 34967761598366888686839132035222803588778557440000000⟩, + ⟨4, 8, 3, 2, 7, 6, -11314894720976815016847317110761895456218808320000000⟩, + ⟨4, 8, 4, 2, 8, 6, 1261491763332189727164604114138882453190737920000000⟩, + ⟨4, 8, 1, 3, 4, 6, -9439525527338380725255353618708536195830251520000000⟩, + ⟨4, 8, 2, 3, 5, 6, -8665812590825725519159633926709823070787338240000000⟩, + ⟨4, 8, 3, 3, 6, 6, 12424366691417830800376484908972752653443399680000000⟩, + ⟨4, 8, 4, 3, 7, 6, 7605079229289230345638611531233635492303994880000000⟩, + ⟨4, 8, 5, 3, 8, 6, -1572367345358029399232611293702021966515404800000000⟩, + ⟨4, 8, 1, 4, 3, 6, 29748940790753601148162366794874533502506762240000000⟩, + ⟨4, 8, 2, 4, 4, 6, -1094739175482889473732789854349212706353971200000000⟩, + ⟨4, 8, 3, 4, 5, 6, 23242489651534465565372813022626829274196213760000000⟩, + ⟨4, 8, 4, 4, 6, 6, -9017600007698586892052080506196031558721208320000000⟩, + ⟨4, 8, 5, 4, 7, 6, -939540392402234643714287991011581869686784000000000⟩, + ⟨4, 8, 6, 4, 8, 6, 713207491754469806051091027733884233475686400000000⟩, + ⟨4, 8, 1, 5, 2, 6, 6025279041866989360184873329244916260064460800000000⟩, + ⟨4, 8, 2, 5, 3, 6, -18255214065723552299433696613608971535730606080000000⟩, + ⟨4, 8, 3, 5, 4, 6, -23793317283798566993014379618869661853485629440000000⟩, + ⟨4, 8, 4, 5, 5, 6, -4678376573161200998683079321953938635143249920000000⟩, + ⟨4, 8, 5, 5, 6, 6, 2086928132377554479943158719428810749509632000000000⟩, + ⟨4, 8, 6, 5, 7, 6, -864492529799176463028479943967006765571112960000000⟩, + ⟨4, 8, 7, 5, 8, 6, -58840597549005667940628908155431169629880320000000⟩, + ⟨4, 8, 1, 6, 1, 6, 132946142419945531417782254386841701123117547520000000⟩, + ⟨4, 8, 2, 6, 2, 6, 12216695095653086869970799124249799842081013760000000⟩, + ⟨4, 8, 3, 6, 3, 6, -31650761386335135645534541190178948962750300160000000⟩, + ⟨4, 8, 4, 6, 4, 6, 9079907756336033258686601579423647238706954240000000⟩, + ⟨4, 8, 5, 6, 5, 6, -4230152366851233212279216908209638494489804800000000⟩, + ⟨4, 8, 6, 6, 6, 6, 562918463340161653541877394000110575828336640000000⟩, + ⟨4, 8, 7, 6, 7, 6, 194431765787069675575834028482711120269803520000000⟩, + ⟨4, 8, 8, 6, 8, 6, -329720031501233139375812023423718103491543040000000⟩, + ⟨4, 8, 1, 7, 0, 6, -832726348422229096029784121700043102430869585920000000⟩, + ⟨4, 8, 2, 7, 1, 6, -180188477313202561329369527792333562997333032960000000⟩, + ⟨4, 8, 3, 7, 2, 6, -116505656122404063513565432648485287915075665920000000⟩, + ⟨4, 8, 4, 7, 3, 6, -33047668770303320311420338206332077316673372160000000⟩, + ⟨4, 8, 5, 7, 4, 6, -12792104985907782326254210020721760954587545600000000⟩, + ⟨4, 8, 6, 7, 5, 6, -581742518037231015689675222966783158989619200000000⟩, + ⟨4, 8, 7, 7, 6, 6, -486931399223717498058549852329871301442273280000000⟩, + ⟨4, 8, 8, 7, 7, 6, -249663203587106167093741191814195014921093120000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1314.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1314.lean new file mode 100644 index 0000000000000000000000000000000000000000..b01be9081d070a6b6eb2cfde6e3dfc23a01cd46d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1314.lean @@ -0,0 +1,636 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1314. -/ +namespace LaughlinFock +def collectedFourData_13_6_25 : List CollectedFourTerm := [ + ⟨5, 1, 7, 5, 8, 0, 4911888456293818166155687400949785050321256448000000⟩, + ⟨5, 1, 7, 6, 7, 0, -16230751992464591064445810016402578479595388928000000⟩, + ⟨5, 1, 8, 6, 8, 0, 192670309072511556430581841676560946903270817792000000⟩, + ⟨5, 1, 7, 7, 6, 0, 40648001864052997576761230764942251578823278592000000⟩, + ⟨5, 1, 8, 7, 7, 0, 145889488060967927673687612976078529821541400576000000⟩ +] + +def collectedFourData_13_6_26 : List CollectedFourTerm := [ + ⟨5, 2, 6, 4, 8, 1, 6025279041866989360184873329244916260064460800000000⟩, + ⟨5, 2, 6, 5, 7, 1, -7303356711573560274534979834379715147328389120000000⟩, + ⟨5, 2, 7, 5, 8, 1, -2982562774410722507096954318751313535686410240000000⟩, + ⟨5, 2, 6, 6, 6, 1, 4755615804174831149629677622224880880666542080000000⟩, + ⟨5, 2, 7, 6, 7, 1, 9855524433049507518568510888407881707306352640000000⟩, + ⟨5, 2, 8, 6, 8, 1, -58495963078880135921531806797613697266593300480000000⟩, + ⟨5, 2, 6, 7, 5, 1, -4914644114393782325287950956560652039513702400000000⟩, + ⟨5, 2, 7, 7, 6, 1, -24681997218108266709784874058145557300337704960000000⟩, + ⟨5, 2, 8, 7, 7, 1, -44293000557752517435030863617451061853751869440000000⟩ +] + +def collectedFourData_13_6_27 : List CollectedFourTerm := [ + ⟨5, 3, 5, 3, 8, 2, 8049243119657515285719987817909917027781312512000000⟩, + ⟨5, 3, 5, 4, 7, 2, 4809683348811852370173887363936964790148136960000000⟩, + ⟨5, 3, 6, 4, 8, 2, -18255214065723552299433696613608971535730606080000000⟩, + ⟨5, 3, 5, 5, 6, 2, -10683376222707535231962896794320649792341934080000000⟩, + ⟨5, 3, 6, 5, 7, 2, 22127496376798901921901182364857896473735462912000000⟩, + ⟨5, 3, 7, 5, 8, 2, 4518240693335181132920309549468370499390144512000000⟩, + ⟨5, 3, 5, 6, 5, 2, 21654942742547948508941456269938795172973248512000000⟩, + ⟨5, 3, 6, 6, 6, 2, -14408425554453528324038112302917602022898270208000000⟩, + ⟨5, 3, 7, 6, 7, 2, -14929989715425631471435935478975843886413381632000000⟩, + ⟨5, 3, 8, 6, 8, 2, 59076452203323069510705369430310579973459542016000000⟩, + ⟨5, 3, 5, 7, 4, 2, 65485182802692454011397089468132819980060196864000000⟩, + ⟨5, 3, 6, 7, 5, 2, 14890244873589608449648459609664384969987850240000000⟩, + ⟨5, 3, 7, 7, 6, 2, 37390396333125235202462408446821822291926581248000000⟩, + ⟨5, 3, 8, 7, 7, 2, 44732545506829580456288351410759797634548891648000000⟩ +] + +def collectedFourData_13_6_28 : List CollectedFourTerm := [ + ⟨5, 4, 4, 2, 8, 3, -4208463052179262396758605699203187261742199603200000⟩, + ⟨5, 4, 4, 3, 7, 3, -25371307110890409574828668789056065471486151884800000⟩, + ⟨5, 4, 5, 3, 8, 3, 20982300700602927649427089815177055449416466432000000⟩, + ⟨5, 4, 4, 4, 6, 3, 30083618105826241679157598684912222297073595187200000⟩, + ⟨5, 4, 5, 4, 7, 3, 12537603946015125821692276511740546156918210560000000⟩, + ⟨5, 4, 6, 4, 8, 3, -23793317283798566993014379618869661853485629440000000⟩, + ⟨5, 4, 4, 5, 5, 3, 15607533496947045817757091919983885019704931123200000⟩, + ⟨5, 4, 5, 5, 6, 3, -27848806287771658929752758034847626764883066880000000⟩, + ⟨5, 4, 6, 5, 7, 3, 28840337894356649318121467232306398833636540416000000⟩, + ⟨5, 4, 7, 5, 8, 3, 3925962704647985805743064582507639363436806144000000⟩, + ⟨5, 4, 4, 6, 4, 3, -30291483004850647936716644997939143102997882470400000⟩, + ⟨5, 4, 5, 6, 5, 3, 56448850348281314168074875907898515923174162432000000⟩, + ⟨5, 4, 6, 6, 6, 3, -18779524553524654491022711150741379225688735744000000⟩, + ⟨5, 4, 7, 6, 7, 3, -12972877449844781940464135225060801054018371584000000⟩, + ⟨5, 4, 8, 6, 8, 3, 38499268379275350236517822865647767246962950144000000⟩, + ⟨5, 4, 4, 7, 3, 3, 110250337753379348111115796122029331425529534873600000⟩, + ⟨5, 4, 5, 7, 4, 3, 170702981208810578052664333547231540645518639104000000⟩, + ⟨5, 4, 6, 7, 5, 3, 19407513899056011301843934861740420807073464320000000⟩, + ⟨5, 4, 7, 7, 6, 3, 32489039756644670215213532192891581018958462976000000⟩, + ⟨5, 4, 8, 7, 7, 3, 29151552107909199706282233610015562275416440832000000⟩ +] + +def collectedFourData_13_6_29 : List CollectedFourTerm := [ + ⟨5, 5, 3, 1, 8, 4, -206572565822554089772341332089857054774342451200000⟩, + ⟨5, 5, 3, 2, 7, 4, 7422151197568588863135481421775511608779970969600000⟩, + ⟨5, 5, 4, 2, 8, 4, -2482475400654178541813954982722269179661831372800000⟩, + ⟨5, 5, 3, 3, 6, 4, -8149923653003920413321886385639789229077063270400000⟩, + ⟨5, 5, 4, 3, 7, 4, -14965949565034947244288261740084732860132700979200000⟩, + ⟨5, 5, 5, 3, 8, 4, 6188487898379317598432692315416583302140657664000000⟩, + ⟨5, 5, 3, 4, 5, 4, -15246211003783810671786122011056002626604551372800000⟩, + ⟨5, 5, 4, 4, 6, 4, 17745633259561565545571172575241518779936328908800000⟩, + ⟨5, 5, 5, 4, 7, 4, 3697821864327674335862200251612687919868805120000000⟩, + ⟨5, 5, 6, 4, 8, 4, -4678376573161200998683079321953938635143249920000000⟩, + ⟨5, 5, 3, 5, 4, 4, 15607533496947045817757091919983885019704931123200000⟩, + ⟨5, 5, 4, 5, 5, 4, 9206524446256857908977892677263588417279413452800000⟩, + ⟨5, 5, 5, 5, 6, 4, -8213684626644994246478170620963679553464565760000000⟩, + ⟨5, 5, 6, 5, 7, 4, 5670750301761649245140714223096637167646015488000000⟩, + ⟨5, 5, 7, 5, 8, 4, 578958738459611695274929299997808218230226944000000⟩, + ⟨5, 5, 3, 6, 3, 4, 20761725347035717873126280915478482130257628364800000⟩, + ⟨5, 5, 4, 6, 4, 4, -17868247974741337327683871498056961764917615001600000⟩, + ⟨5, 5, 5, 6, 5, 4, 16648938180917688164395918340553788338590449664000000⟩, + ⟨5, 5, 6, 6, 6, 4, -3692536298254623188821864096935579273387835392000000⟩, + ⟨5, 5, 7, 6, 7, 4, -1913100385202644948733182255087457568118800384000000⟩, + ⟨5, 5, 8, 6, 8, 4, 4541966295521764899987433497445383359341736755200000⟩, + ⟨5, 5, 3, 7, 2, 4, 76423388501290801542866439842278317180193446297600000⟩, + ⟨5, 5, 4, 7, 3, 4, 65034134312965504194194809072694617531581097574400000⟩, + ⟨5, 5, 5, 7, 4, 4, 50346877995016094365914655945909852449231863808000000⟩, + ⟨5, 5, 6, 7, 5, 4, 3816015114061835922978713598404552111696117760000000⟩, + ⟨5, 5, 7, 7, 6, 4, 4791134018925356858141944730251867368431026176000000⟩, + ⟨5, 5, 8, 7, 7, 4, 3439165800032333896002958999967816058211506585600000⟩ +] + +def collectedFourData_13_6_30 : List CollectedFourTerm := [ + ⟨5, 6, 2, 0, 8, 5, 21191157964543674234769924685923624858807173120000000⟩, + ⟨5, 6, 2, 1, 7, 5, 9714288442623436913580789711161323300061184000000000⟩, + ⟨5, 6, 3, 1, 8, 5, 368591191624580606968847156803110348867502080000000⟩, + ⟨5, 6, 2, 2, 6, 5, 20463948079509508575811975512767339076979261440000000⟩, + ⟨5, 6, 3, 2, 7, 5, -13243479565818122525439233290577229961117040640000000⟩, + ⟨5, 6, 4, 2, 8, 5, 2214763036084455488955938898937795300829429760000000⟩, + ⟨5, 6, 2, 3, 5, 5, -5071435254056972376532001742310226383853322240000000⟩, + ⟨5, 6, 3, 3, 6, 5, 14542057213398310565463140179900959569592975360000000⟩, + ⟨5, 6, 4, 3, 7, 5, 13352008196258073107571809275647167163940208640000000⟩, + ⟨5, 6, 5, 3, 8, 5, -3680743890546963241772197905289075961836339200000000⟩, + ⟨5, 6, 2, 4, 4, 5, -640666849225292682760290346789329804931891200000000⟩, + ⟨5, 6, 3, 4, 5, 5, 27204091982241837807525805953086378187706859520000000⟩, + ⟨5, 6, 4, 4, 6, 5, -15831928318335383016886914157796732204702760960000000⟩, + ⟨5, 6, 5, 4, 7, 5, -2199363634373356186237253808300096000884736000000000⟩, + ⟨5, 6, 6, 4, 8, 5, 2086928132377554479943158719428810749509632000000000⟩, + ⟨5, 6, 2, 5, 3, 5, -10683376222707535231962896794320649792341934080000000⟩, + ⟨5, 6, 3, 5, 4, 5, -27848806287771658929752758034847626764883066880000000⟩, + ⟨5, 6, 4, 5, 5, 5, -8213684626644994246478170620963679553464565760000000⟩, + ⟨5, 6, 5, 5, 6, 5, 4885275693327372860351571887672268662243328000000000⟩, + ⟨5, 6, 6, 5, 7, 5, -2529605762034307530796420220862868839255244800000000⟩, + ⟨5, 6, 7, 5, 8, 5, -206609324389766333807613152988208446748753920000000⟩, + ⟨5, 6, 2, 6, 2, 5, 7149494354603445344249803298857837173418229760000000⟩, + ⟨5, 6, 3, 6, 3, 5, -37045524682206500917759807883360611984547512320000000⟩, + ⟨5, 6, 4, 6, 4, 5, 15941320153109906999160253574647026958435614720000000⟩, + ⟨5, 6, 5, 6, 5, 5, -9902334544365093100369442561724813461893939200000000⟩, + ⟨5, 6, 6, 6, 6, 5, 1647164942826701483611254237096712720298803200000000⟩, + ⟨5, 6, 7, 6, 7, 5, 682715972347473152351404653717392729435013120000000⟩, + ⟨5, 6, 8, 6, 8, 5, -1350718864432952330145687111420497230068449280000000⟩, + ⟨5, 6, 2, 7, 1, 5, -105450491415940864834120681958548252537084968960000000⟩, + ⟨5, 6, 3, 7, 2, 5, -136363644046887711578518321217710260483879075840000000⟩, + ⟨5, 6, 4, 7, 3, 5, -58020795179743486948173823460892244357656084480000000⟩, + ⟨5, 6, 5, 7, 4, 5, -29944950467916417131465020005994922447890022400000000⟩, + ⟨5, 6, 6, 7, 5, 5, -1702246317835942183920807750838652497821696000000000⟩, + ⟨5, 6, 7, 7, 6, 5, -1709781538740949681782741831148182041190727680000000⟩, + ⟨5, 6, 8, 7, 7, 5, -1022761029423860848780424691262844638687395840000000⟩ +] + +def collectedFourData_13_6_31 : List CollectedFourTerm := [ + ⟨5, 7, 1, 0, 7, 6, 72194604649309793663973447983987145372686352384000000⟩, + ⟨5, 7, 2, 0, 8, 6, -43891300025917846385826801526783106182878855168000000⟩, + ⟨5, 7, 1, 1, 6, 6, 35267565636714227598921604703303667266705424384000000⟩, + ⟨5, 7, 2, 1, 7, 6, -20120313825553275271981593701543857301854617600000000⟩, + ⟨5, 7, 3, 1, 8, 6, -381714548246335462702083038361559272108589056000000⟩, + ⟨5, 7, 1, 2, 5, 6, 20984269256911044608612495543800318302898618368000000⟩, + ⟨5, 7, 2, 2, 6, 6, -42385096952954480433802329052769612802205679616000000⟩, + ⟨5, 7, 3, 2, 7, 6, 13715001699836379080409081941355465180601909248000000⟩, + ⟨5, 7, 4, 2, 8, 6, -1529078449696520599955800884102359300532338688000000⟩, + ⟨5, 7, 1, 3, 4, 6, 11441830599897816134928741301215774311058505728000000⟩, + ⟨5, 7, 2, 3, 5, 6, 10503998255794452362407509260017584104313716736000000⟩, + ⟨5, 7, 3, 3, 6, 6, -15059814032231259332166358275953028322874621952000000⟩, + ⟨5, 7, 4, 3, 7, 6, -9218262929457252278024400904866547658215391232000000⟩, + ⟨5, 7, 5, 3, 8, 6, 1905896726937542339298963376991428103865630720000000⟩, + ⟨5, 7, 1, 4, 3, 6, -36059263791213976457698176702238033653673230336000000⟩, + ⟨5, 7, 2, 4, 4, 6, 1326954428023976895702547144296439186383175680000000⟩, + ⟨5, 7, 3, 4, 5, 6, -28172669118012364418019789372239741470390616064000000⟩, + ⟨5, 7, 4, 4, 6, 6, 10930406555594860987144727808102774360137269248000000⟩, + ⟨5, 7, 5, 4, 7, 6, 1138834995518999900514185454312061872478617600000000⟩, + ⟨5, 7, 6, 4, 8, 6, -864492529799176463028479943967006765571112960000000⟩, + ⟨5, 7, 1, 5, 2, 6, -7303356711573560274534979834379715147328389120000000⟩, + ⟨5, 7, 2, 5, 3, 6, 22127496376798901921901182364857896473735462912000000⟩, + ⟨5, 7, 3, 5, 4, 6, 28840337894356649318121467232306398833636540416000000⟩, + ⟨5, 7, 4, 5, 5, 6, 5670750301761649245140714223096637167646015488000000⟩, + ⟨5, 7, 5, 5, 6, 6, -2529605762034307530796420220862868839255244800000000⟩, + ⟨5, 7, 6, 5, 7, 6, 1047868036607589712730244594443541478002130944000000⟩, + ⟨5, 7, 7, 5, 8, 6, 71321820954100118281812250591840182938370048000000⟩, + ⟨5, 7, 1, 6, 1, 6, -161146578403058434248144674638306339405198000128000000⟩, + ⟨5, 7, 2, 6, 2, 6, -14808091293385014915963803067688705575893336064000000⟩, + ⟨5, 7, 3, 6, 3, 6, 38364497144629817513651733742122012516783489024000000⟩, + ⟨5, 7, 4, 6, 4, 6, -11005930977124943183246000055053779015236059136000000⟩, + ⟨5, 7, 5, 6, 5, 6, 5127449113103455941075880371873789632021790720000000⟩, + ⟨5, 7, 6, 6, 6, 6, -682324305436674437927494622579547515960426496000000⟩, + ⟨5, 7, 7, 6, 7, 6, -235674486067302883145777124106907063081238528000000⟩, + ⟨5, 7, 8, 6, 8, 6, 399659997200497423362258027567691682027667456000000⟩, + ⟨5, 7, 1, 7, 0, 6, 1009363636670536459148081298226452652282387365888000000⟩, + ⟨5, 7, 2, 7, 1, 6, 218409921928832216757068544584285239508094418944000000⟩, + ⟨5, 7, 3, 7, 2, 6, 141218748487072072589342705965879269720890277888000000⟩, + ⟨5, 7, 4, 7, 3, 6, 40057715474811831003571902472394825435996749824000000⟩, + ⟨5, 7, 5, 7, 4, 6, 15505556697841249913059713791784850705707171840000000⟩, + ⟨5, 7, 6, 7, 5, 6, 705141304492749728605730225496224984601722880000000⟩, + ⟨5, 7, 7, 7, 6, 6, 590218922291524184535433333537322289428692992000000⟩, + ⟨5, 7, 8, 7, 7, 6, 302621575014367589088463607599689625887571968000000⟩ +] + +def collectedFourData_13_6_32 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 6, 7, -11109145701165881176137564224838659005910876160000000⟩, + ⟨5, 8, 1, 0, 7, 7, 29483010188877570350702263124802654732621447168000000⟩, + ⟨5, 8, 2, 0, 8, 7, -8962218521405739096443206706383332281646317568000000⟩, + ⟨5, 8, 0, 1, 5, 7, -16964566750571374121547992257999595665172201472000000⟩, + ⟨5, 8, 1, 1, 6, 7, 14402655185315082308609788628988216030598791168000000⟩, + ⟨5, 8, 2, 1, 7, 7, -4108391620147702660041790606703577139878297600000000⟩, + ⟨5, 8, 3, 1, 8, 7, -51961841977236547450580150576090671327739904000000⟩, + ⟨5, 8, 0, 2, 4, 7, -4834051708468747380612026478210225965346324480000000⟩, + ⟨5, 8, 1, 2, 5, 7, 8569607484007095916954856253569842136047681536000000⟩, + ⟨5, 8, 2, 2, 6, 7, -8654665063897317270329934265233441650078908416000000⟩, + ⟨5, 8, 3, 2, 7, 7, 1866988707447752392476741516816131509224210432000000⟩, + ⟨5, 8, 4, 2, 8, 7, -156112204405660647933361994494312871356268544000000⟩, + ⟨5, 8, 0, 3, 3, 7, -859787761498152956680063312840814246366281728000000⟩, + ⟨5, 8, 1, 3, 4, 7, 4672642918329542565138262357976676677248352256000000⟩, + ⟨5, 8, 2, 3, 5, 7, 2144824319655726580241306189593959821828161536000000⟩, + ⟨5, 8, 3, 3, 6, 7, -2050054629943968200346074626578721165560250368000000⟩, + ⟨5, 8, 4, 3, 7, 7, -941144221209953337121448698647469838529724416000000⟩, + ⟨5, 8, 5, 3, 8, 7, 155666958472041954435802820089113300002930688000000⟩, + ⟨5, 8, 0, 4, 2, 7, 6372542735456035131045054805939736778079469568000000⟩, + ⟨5, 8, 1, 4, 3, 7, -14725970824607177510583051376209790163088310272000000⟩, + ⟨5, 8, 2, 4, 4, 7, 270952456292598768260115068004080543260999680000000⟩, + ⟨5, 8, 3, 4, 5, 7, -3835074632372711488100351207615080971607474176000000⟩, + ⟨5, 8, 4, 4, 6, 7, 1115946577353611178727363090395025005109837824000000⟩, + ⟨5, 8, 5, 4, 7, 7, 93016047222465169539690213707931085480919040000000⟩, + ⟨5, 8, 6, 4, 8, 7, -58840597549005667940628908155431169629880320000000⟩, + ⟨5, 8, 0, 5, 1, 7, 4911888456293818166155687400949785050321256448000000⟩, + ⟨5, 8, 1, 5, 2, 7, -2982562774410722507096954318751313535686410240000000⟩, + ⟨5, 8, 2, 5, 3, 7, 4518240693335181132920309549468370499390144512000000⟩, + ⟨5, 8, 3, 5, 4, 7, 3925962704647985805743064582507639363436806144000000⟩, + ⟨5, 8, 4, 5, 5, 7, 578958738459611695274929299997808218230226944000000⟩, + ⟨5, 8, 5, 5, 6, 7, -206609324389766333807613152988208446748753920000000⟩, + ⟨5, 8, 6, 5, 7, 7, 71321820954100118281812250591840182938370048000000⟩, + ⟨5, 8, 7, 5, 8, 7, 4160940091009060375429075500381009113776128000000⟩, + ⟨5, 8, 0, 6, 0, 7, -113299634486989740906268380893582601688065245184000000⟩, + ⟨5, 8, 1, 6, 1, 7, -65809435982631316152052162902612258299163181056000000⟩, + ⟨5, 8, 2, 6, 2, 7, -3023682369350529874411984967815980114209931264000000⟩, + ⟨5, 8, 3, 6, 3, 7, 5222462563514659608340051204576758598327074816000000⟩, + ⟨5, 8, 4, 6, 4, 7, -1123657289602458523371065946536858444227411968000000⟩, + ⟨5, 8, 5, 6, 5, 7, 418792055663748877601553667373358063380594688000000⟩, + ⟨5, 8, 6, 6, 6, 7, -46441546306282989249582933216793295094546432000000⟩, + ⟨5, 8, 7, 6, 7, 7, -13749332313549446766648775621998450371985408000000⟩, + ⟨5, 8, 8, 6, 8, 7, 20401766563420224720261985338798797764952064000000⟩, + ⟨5, 8, 1, 7, 0, 7, 412206404187635535407401513949520144220161048576000000⟩, + ⟨5, 8, 2, 7, 1, 7, 44597390517334717009118251325478048747585798144000000⟩, + ⟨5, 8, 3, 7, 2, 7, 19223753264894843994385784895518656983510024192000000⟩, + ⟨5, 8, 4, 7, 3, 7, 4089717089053714102126087742032284238334656512000000⟩, + ⟨5, 8, 5, 7, 4, 7, 1266439475158322508723078389221452354510913536000000⟩, + ⟨5, 8, 6, 7, 5, 7, 47994556670694639425405515416493974576168960000000⟩, + ⟨5, 8, 7, 7, 6, 7, 34433579280252272162937231580689863710605312000000⟩, + ⟨5, 8, 8, 7, 7, 7, 15448167877057688451476229003209701790318592000000⟩ +] + +def collectedFourData_13_6_33 : List CollectedFourTerm := [ + ⟨6, 0, 7, 5, 8, 0, -113299634486989740906268380893582601688065245184000000⟩, + ⟨6, 0, 7, 6, 7, 0, 374385184956491907886647025214905000615187841024000000⟩, + ⟨6, 0, 8, 6, 8, 0, -4444212401940813201960812132469196187820921716736000000⟩, + ⟨6, 0, 7, 7, 6, 0, -937603488923405092179065675042818402992191963136000000⟩, + ⟨6, 0, 8, 7, 7, 0, -3365146790257848360261690097950054933976011767808000000⟩ +] + +def collectedFourData_13_6_34 : List CollectedFourTerm := [ + ⟨6, 1, 6, 4, 8, 1, 132946142419945531417782254386841701123117547520000000⟩, + ⟨6, 1, 6, 5, 7, 1, -161146578403058434248144674638306339405198000128000000⟩, + ⟨6, 1, 7, 5, 8, 1, -65809435982631316152052162902612258299163181056000000⟩, + ⟨6, 1, 6, 6, 6, 1, 104931368589439660580694479851249795280406577152000000⟩, + ⟨6, 1, 7, 6, 7, 1, 217459464664637051934977883753554663944136687616000000⟩, + ⟨6, 1, 8, 6, 8, 1, -1290697507026488774754399094316130667503248474112000000⟩, + ⟨6, 1, 6, 7, 5, 1, -108440284978583498933314786560248803490330050560000000⟩, + ⟨6, 1, 7, 7, 6, 1, -544601551988960785537340532760452906473251405824000000⟩, + ⟨6, 1, 8, 7, 7, 1, -977313004002061962767857052637356946578825281536000000⟩ +] + +def collectedFourData_13_6_35 : List CollectedFourTerm := [ + ⟨6, 2, 5, 3, 8, 2, -5386688350495755707987645861209672241343627264000000⟩, + ⟨6, 2, 5, 4, 7, 2, -3218720677146173975868398493986033677495173120000000⟩, + ⟨6, 2, 6, 4, 8, 2, 12216695095653086869970799124249799842081013760000000⟩, + ⟨6, 2, 5, 5, 6, 2, 7149494354603445344249803298857837173418229760000000⟩, + ⟨6, 2, 6, 5, 7, 2, -14808091293385014915963803067688705575893336064000000⟩, + ⟨6, 2, 7, 5, 8, 2, -3023682369350529874411984967815980114209931264000000⟩, + ⟨6, 2, 5, 6, 5, 2, -14491850484309744925779566246363658642222219264000000⟩, + ⟨6, 2, 6, 6, 6, 2, 9642359775867042227449756612281564212364312576000000⟩, + ⟨6, 2, 7, 6, 7, 2, 9991399250533085336571715861856768534620667904000000⟩, + ⟨6, 2, 8, 6, 8, 2, -39534951565209998874763597679991184101948260352000000⟩, + ⟨6, 2, 5, 7, 4, 2, -43823781452430203038588047174563235188082475008000000⟩, + ⟨6, 2, 6, 7, 5, 2, -9964801336502193083812305918577229136427745280000000⟩, + ⟨6, 2, 7, 7, 6, 2, -25022279654616106844630515376656837310158995456000000⟩, + ⟨6, 2, 8, 7, 7, 2, -29935768890021140832699236452599532962768224256000000⟩ +] + +def collectedFourData_13_6_36 : List CollectedFourTerm := [ + ⟨6, 3, 4, 2, 8, 3, -5598255101588262448102903415280170760588283084800000⟩, + ⟨6, 3, 4, 3, 7, 3, -33749862528543523503826323178650360530188055347200000⟩, + ⟨6, 3, 5, 3, 8, 3, 27911441893111775641926039010516001887195496448000000⟩, + ⟨6, 3, 4, 4, 6, 3, 40018355025824518489431402522701001451583098060800000⟩, + ⟨6, 3, 5, 4, 7, 3, 16677990131367932908017768831051405545271459840000000⟩, + ⟨6, 3, 6, 4, 8, 3, -31650761386335135645534541190178948962750300160000000⟩, + ⟨6, 3, 4, 5, 5, 3, 20761725347035717873126280915478482130257628364800000⟩, + ⟨6, 3, 5, 5, 6, 3, -37045524682206500917759807883360611984547512320000000⟩, + ⟨6, 3, 6, 5, 7, 3, 38364497144629817513651733742122012516783489024000000⟩, + ⟨6, 3, 7, 5, 8, 3, 5222462563514659608340051204576758598327074816000000⟩, + ⟨6, 3, 4, 6, 4, 3, -40294864696214026659695850783737422174901344665600000⟩, + ⟨6, 3, 5, 6, 5, 3, 75090373973324205416102348748108239102382440448000000⟩, + ⟨6, 3, 6, 6, 6, 3, -24981226598325672806146750586586405621744009216000000⟩, + ⟨6, 3, 7, 6, 7, 3, -17257007241222025661514252742627130668247678976000000⟩, + ⟨6, 3, 8, 6, 8, 3, 51213168070962860091211410980777041323481890816000000⟩, + ⟨6, 3, 4, 7, 3, 3, 146659126651967689080219582487968820984304526950400000⟩, + ⟨6, 3, 5, 7, 4, 3, 227075496103902356577873697016360484767589728256000000⟩, + ⟨6, 3, 6, 7, 5, 3, 25816601535392897664844424992687103146438164480000000⟩, + ⟨6, 3, 7, 7, 6, 3, 43218136955997806613597052706667630279329316864000000⟩, + ⟨6, 3, 8, 7, 7, 3, 38778485942227827542026517932038691022646018048000000⟩ +] + +def collectedFourData_13_6_37 : List CollectedFourTerm := [ + ⟨6, 4, 3, 1, 8, 4, 400921091606581061669897449751124756352362086400000⟩, + ⟨6, 4, 3, 2, 7, 4, -14405092701198359195055588637897228092515234611200000⟩, + ⟨6, 4, 4, 2, 8, 4, 4818049016110401765432110318604224171628665241600000⟩, + ⟨6, 4, 3, 3, 6, 4, 15817571294919141767216665518269121425004350668800000⟩, + ⟨6, 4, 4, 3, 7, 4, 29046281207045624276542503529617758881864640102400000⟩, + ⟨6, 4, 5, 3, 8, 4, -12010768776254706062787795997510102082081783808000000⟩, + ⟨6, 4, 3, 4, 5, 4, 29590219466760832059877458564574481710864505241600000⟩, + ⟨6, 4, 4, 4, 6, 4, -34441159354068908519374737059824472941095655833600000⟩, + ⟨6, 4, 5, 4, 7, 4, -7176823178380965698936918502224308931804528640000000⟩, + ⟨6, 4, 6, 4, 8, 4, 9079907756336033258686601579423647238706954240000000⟩, + ⟨6, 4, 3, 5, 4, 4, -30291483004850647936716644997939143102997882470400000⟩, + ⟨6, 4, 4, 5, 5, 4, -17868247974741337327683871498056961764917615001600000⟩, + ⟨6, 4, 5, 5, 6, 4, 15941320153109906999160253574647026958435614720000000⟩, + ⟨6, 4, 6, 5, 7, 4, -11005930977124943183246000055053779015236059136000000⟩, + ⟨6, 4, 7, 5, 8, 4, -1123657289602458523371065946536858444227411968000000⟩, + ⟨6, 4, 3, 6, 3, 4, -40294864696214026659695850783737422174901344665600000⟩, + ⟨6, 4, 4, 6, 4, 4, 34679132994281769976125466255142741966140420915200000⟩, + ⟨6, 4, 5, 6, 5, 4, -32312666703853386188140610515961618528162807808000000⟩, + ⟨6, 4, 6, 6, 6, 4, 7166564822382296063550997781494425791678644224000000⟩, + ⟨6, 4, 7, 6, 7, 4, 3712992050683392226297039460153917427467419648000000⟩, + ⟨6, 4, 8, 6, 8, 4, -8815159350855423417499438845733091266783503974400000⟩, + ⟨6, 4, 3, 7, 2, 4, -148324382863748220674027179903245780720274322227200000⟩, + ⟨6, 4, 4, 7, 3, 4, -126219839583346870691914762255795351011193572556800000⟩, + ⟨6, 4, 5, 7, 4, 4, -97714453051254820961079836920898361794469298176000000⟩, + ⟨6, 4, 6, 7, 5, 4, -7406215530241735270140312191302268967683358720000000⟩, + ⟨6, 4, 7, 7, 6, 4, -9298750166810655129599425080467226792057372672000000⟩, + ⟨6, 4, 8, 7, 7, 4, -6674817158196132342876105019641530278240006963200000⟩ +] + +def collectedFourData_13_6_38 : List CollectedFourTerm := [ + ⟨6, 5, 2, 0, 8, 5, -42953959759940274360131364062924052132494573568000000⟩, + ⟨6, 5, 2, 1, 7, 5, -19690625474976743474219637188921262685657497600000000⟩, + ⟨6, 5, 3, 1, 8, 5, -747125345363428921935850723164228255284723712000000⟩, + ⟨6, 5, 2, 2, 6, 5, -41479923079592165512437810461331241527637180416000000⟩, + ⟨6, 5, 3, 2, 7, 5, 26844209707819647017681420401196377256855863296000000⟩, + ⟨6, 5, 4, 2, 8, 5, -4489270595261848907384364159301981422709899264000000⟩, + ⟨6, 5, 2, 3, 5, 5, 10279675428420909996721702711759723825553473536000000⟩, + ⟨6, 5, 3, 3, 6, 5, -29476394891500733035279320419570844856278319104000000⟩, + ⟨6, 5, 4, 3, 7, 5, -27064194591728252775172539876375856650959978496000000⟩, + ⟨6, 5, 5, 3, 8, 5, 7460777991732780418614364077896217941382266880000000⟩, + ⟨6, 5, 2, 4, 4, 5, 1298616059924384448298383200028716227551559680000000⟩, + ⟨6, 5, 3, 4, 5, 5, -55142030193256241110583550109687970446366998528000000⟩, + ⟨6, 5, 4, 4, 6, 5, 32090932125835854926186871411891807851793874944000000⟩, + ⟨6, 5, 5, 4, 7, 5, 4458056384007680725638271458944324269925990400000000⟩, + ⟨6, 5, 6, 4, 8, 5, -4230152366851233212279216908209638494489804800000000⟩, + ⟨6, 5, 2, 5, 3, 5, 21654942742547948508941456269938795172973248512000000⟩, + ⟨6, 5, 3, 5, 4, 5, 56448850348281314168074875907898515923174162432000000⟩, + ⟨6, 5, 4, 5, 5, 5, 16648938180917688164395918340553788338590449664000000⟩, + ⟨6, 5, 5, 5, 6, 5, -9902334544365093100369442561724813461893939200000000⟩, + ⟨6, 5, 6, 5, 7, 5, 5127449113103455941075880371873789632021790720000000⟩, + ⟨6, 5, 7, 5, 8, 5, 418792055663748877601553667373358063380594688000000⟩, + ⟨6, 5, 2, 6, 2, 5, -14491850484309744925779566246363658642222219264000000⟩, + ⟨6, 5, 3, 6, 3, 5, 75090373973324205416102348748108239102382440448000000⟩, + ⟨6, 5, 4, 6, 4, 5, -32312666703853386188140610515961618528162807808000000⟩, + ⟨6, 5, 5, 6, 5, 5, 20071790331599465078956666976524252386038906880000000⟩, + ⟨6, 5, 6, 6, 6, 5, -3338763119530453740158898948800675096014356480000000⟩, + ⟨6, 5, 7, 6, 7, 5, -1383848605760385810491587024846639547251949568000000⟩, + ⟨6, 5, 8, 6, 8, 5, 2737874157085715423218070954626319232943521792000000⟩, + ⟨6, 5, 2, 7, 1, 5, 213745571267265518867704510326119957540471046144000000⟩, + ⟨6, 5, 3, 7, 2, 5, 276405776829617672481562829910815308435031064576000000⟩, + ⟨6, 5, 4, 7, 3, 5, 117606735109064879257106758441312032570130563072000000⟩, + ⟨6, 5, 5, 7, 4, 5, 60697683418924218661244151137961612194202255360000000⟩, + ⟨6, 5, 6, 7, 5, 5, 3450411721727075279651903788517639957407334400000000⟩, + ⟨6, 5, 7, 7, 6, 5, 3465685430510592555774395250978381456633495552000000⟩, + ⟨6, 5, 8, 7, 7, 5, 2073111633418642400175506207013992580645912576000000⟩ +] + +def collectedFourData_13_6_39 : List CollectedFourTerm := [ + ⟨6, 6, 1, 0, 7, 6, -47009863601806537571291577204875290386634899456000000⟩, + ⟨6, 6, 2, 0, 8, 6, 28580030842292199245727247416306696571701952512000000⟩, + ⟨6, 6, 1, 1, 6, 6, -22964644770937817128151230331777661494630547456000000⟩, + ⟨6, 6, 2, 1, 7, 6, 13101438994774583396051684536751601723270758400000000⟩, + ⟨6, 6, 3, 1, 8, 6, 248555261643876671479532073374604493276053504000000⟩, + ⟨6, 6, 1, 2, 5, 6, -13664007723884688104731360227088806886414221312000000⟩, + ⟨6, 6, 2, 2, 6, 6, 27599259476335191705637689117007166857537388544000000⟩, + ⟨6, 6, 3, 2, 7, 6, -8930589236407944482377962988084346313592799232000000⟩, + ⟨6, 6, 4, 2, 8, 6, 995666777397920801352744737457902083419144192000000⟩, + ⟨6, 6, 1, 3, 4, 6, -7450402955580350596598784513751974170226327552000000⟩, + ⟨6, 6, 2, 3, 5, 6, -6839728919870632007520071738911872423636762624000000⟩, + ⟨6, 6, 3, 3, 6, 6, 9806270246408669468129255690075825751686381568000000⟩, + ⟨6, 6, 4, 3, 7, 6, 6002516186138820619590444651047016973455065088000000⟩, + ⟨6, 6, 5, 3, 8, 6, -1241033808657610739223601365852543359888916480000000⟩, + ⟨6, 6, 1, 4, 3, 6, 23480162827136369444418989623819448514483585024000000⟩, + ⟨6, 6, 2, 4, 4, 6, -864052749789755086756490197238080903179141120000000⟩, + ⟨6, 6, 3, 4, 5, 6, 18344768822683070338334724353002006740599832576000000⟩, + ⟨6, 6, 4, 4, 6, 6, -7117386732523908729480772934470711718531039232000000⟩, + ⟨6, 6, 5, 4, 7, 6, -741557877688633795769435996203802666886758400000000⟩, + ⟨6, 6, 6, 4, 8, 6, 562918463340161653541877394000110575828336640000000⟩, + ⟨6, 6, 1, 5, 2, 6, 4755615804174831149629677622224880880666542080000000⟩, + ⟨6, 6, 2, 5, 3, 6, -14408425554453528324038112302917602022898270208000000⟩, + ⟨6, 6, 3, 5, 4, 6, -18779524553524654491022711150741379225688735744000000⟩, + ⟨6, 6, 4, 5, 5, 6, -3692536298254623188821864096935579273387835392000000⟩, + ⟨6, 6, 5, 5, 6, 6, 1647164942826701483611254237096712720298803200000000⟩, + ⟨6, 6, 6, 5, 7, 6, -682324305436674437927494622579547515960426496000000⟩, + ⟨6, 6, 7, 5, 8, 6, -46441546306282989249582933216793295094546432000000⟩, + ⟨6, 6, 1, 6, 1, 6, 104931368589439660580694479851249795280406577152000000⟩, + ⟨6, 6, 2, 6, 2, 6, 9642359775867042227449756612281564212364312576000000⟩, + ⟨6, 6, 3, 6, 3, 6, -24981226598325672806146750586586405621744009216000000⟩, + ⟨6, 6, 4, 6, 4, 6, 7166564822382296063550997781494425791678644224000000⟩, + ⟨6, 6, 5, 6, 5, 6, -3338763119530453740158898948800675096014356480000000⟩, + ⟨6, 6, 6, 6, 6, 6, 444298749007445476326305786492593888731070464000000⟩, + ⟨6, 6, 7, 6, 7, 6, 153460573657365173070640540509443063128522752000000⟩, + ⟨6, 6, 8, 6, 8, 6, -260240526930752936614006136049653925600559104000000⟩, + ⟨6, 6, 1, 7, 0, 6, -657251980463043783665912648222214361325336788992000000⟩, + ⟨6, 6, 2, 7, 1, 6, -142218669788834107479695761925203897106087018496000000⟩, + ⟨6, 6, 3, 7, 2, 6, -91955266416969700494356440788346661230966996992000000⟩, + ⟨6, 6, 4, 7, 3, 6, -26083773847342238546997031421257394200736956416000000⟩, + ⟨6, 6, 5, 7, 4, 6, -10096517724230845609457319698986016256357826560000000⟩, + ⟨6, 6, 6, 7, 5, 6, -459156147543513262699031594494701288208465920000000⟩, + ⟨6, 6, 7, 7, 6, 6, -384323886347302918445472359258002600312700928000000⟩, + ⟨6, 6, 8, 7, 7, 6, -197053492203385772226281533109263792406003712000000⟩ +] + +def collectedFourData_13_6_40 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 6, 7, 36708852476635280646945880638944493075966197760000000⟩, + ⟨6, 7, 1, 0, 7, 7, -97423105313764842170515159984750656052525006848000000⟩, + ⟨6, 7, 2, 0, 8, 7, 29614586613183456540679101001702693226044981248000000⟩, + ⟨6, 7, 0, 1, 5, 7, 56057395854606557160087583433626403284495368192000000⟩, + ⟨6, 7, 1, 1, 6, 7, -47591863379205753732916921543330122242979790848000000⟩, + ⟨6, 7, 2, 1, 7, 7, 13575692133052047742354944464573402189502873600000000⟩, + ⟨6, 7, 3, 1, 8, 7, 171701735026882139310560788061834138766802944000000⟩, + ⟨6, 7, 0, 2, 4, 7, 15973549704365001354848308354588712027585249280000000⟩, + ⟨6, 7, 1, 2, 5, 7, -28317250072620036869220490931828537310257872896000000⟩, + ⟨6, 7, 2, 2, 6, 7, 28598312742621931766875937188130892293735448576000000⟩, + ⟨6, 7, 3, 2, 7, 7, -6169242431490562161337827725685507624378826752000000⟩, + ⟨6, 7, 4, 2, 8, 7, 515854237173998384210891045172854962450857984000000⟩, + ⟨6, 7, 0, 3, 3, 7, 2841066536262984665313102851293151864719147008000000⟩, + ⟨6, 7, 1, 3, 4, 7, -15440193528738425223935033069388499122772770816000000⟩, + ⟨6, 7, 2, 3, 5, 7, -7087317212004765568720024526766836725523152896000000⟩, + ⟨6, 7, 3, 3, 6, 7, 6774162028657018410588259274026167598263042048000000⟩, + ⟨6, 7, 4, 3, 7, 7, 3109899294237198179705226605007771832550424576000000⟩, + ⟨6, 7, 5, 3, 8, 7, -514382974870604969581552595731616576273645568000000⟩, + ⟨6, 7, 0, 4, 2, 7, -21057310568206799130334758566607611338841653248000000⟩, + ⟨6, 7, 1, 4, 3, 7, 48660221507312487392891146596429214786353364992000000⟩, + ⟨6, 7, 2, 4, 4, 7, -895330209341221286614935489954884679609876480000000⟩, + ⟨6, 7, 3, 4, 5, 7, 12672548610275357418340224375463309036209831936000000⟩, + ⟨6, 7, 4, 4, 6, 7, -3687512917899760069907270266057773234272600064000000⟩, + ⟨6, 7, 5, 4, 7, 7, -307360480031409522190300112968319554226749440000000⟩, + ⟨6, 7, 6, 4, 8, 7, 194431765787069675575834028482711120269803520000000⟩, + ⟨6, 7, 0, 5, 1, 7, -16230751992464591064445810016402578479595388928000000⟩, + ⟨6, 7, 1, 5, 2, 7, 9855524433049507518568510888407881707306352640000000⟩, + ⟨6, 7, 2, 5, 3, 7, -14929989715425631471435935478975843886413381632000000⟩, + ⟨6, 7, 3, 5, 4, 7, -12972877449844781940464135225060801054018371584000000⟩, + ⟨6, 7, 4, 5, 5, 7, -1913100385202644948733182255087457568118800384000000⟩, + ⟨6, 7, 5, 5, 6, 7, 682715972347473152351404653717392729435013120000000⟩, + ⟨6, 7, 6, 5, 7, 7, -235674486067302883145777124106907063081238528000000⟩, + ⟨6, 7, 7, 5, 8, 7, -13749332313549446766648775621998450371985408000000⟩, + ⟨6, 7, 0, 6, 0, 7, 374385184956491907886647025214905000615187841024000000⟩, + ⟨6, 7, 1, 6, 1, 7, 217459464664637051934977883753554663944136687616000000⟩, + ⟨6, 7, 2, 6, 2, 7, 9991399250533085336571715861856768534620667904000000⟩, + ⟨6, 7, 3, 6, 3, 7, -17257007241222025661514252742627130668247678976000000⟩, + ⟨6, 7, 4, 6, 4, 7, 3712992050683392226297039460153917427467419648000000⟩, + ⟨6, 7, 5, 6, 5, 7, -1383848605760385810491587024846639547251949568000000⟩, + ⟨6, 7, 6, 6, 6, 7, 153460573657365173070640540509443063128522752000000⟩, + ⟨6, 7, 7, 6, 7, 7, 45433035548120642714696597750742890984767488000000⟩, + ⟨6, 7, 8, 6, 8, 7, -67415214381493371293118650710202630698696704000000⟩, + ⟨6, 7, 1, 7, 0, 7, -1362087102670746007984174376807448202727009550336000000⟩, + ⟨6, 7, 2, 7, 1, 7, -147366779893067848757762248235090613057129283584000000⟩, + ⟨6, 7, 3, 7, 2, 7, -63522609355479138395592351729184782761550938112000000⟩, + ⟨6, 7, 4, 7, 3, 7, -13513984363126263034735490123535908936595013632000000⟩, + ⟨6, 7, 5, 7, 4, 7, -4184798823846130133192624049663462910665424896000000⟩, + ⟨6, 7, 6, 7, 5, 7, -158592311947186132678366370414687490209218560000000⟩, + ⟨6, 7, 7, 7, 6, 7, -113781672870547552079155073103914069951250432000000⟩, + ⟨6, 7, 8, 7, 7, 7, -51046635887914621598941461411069622864576512000000⟩ +] + +def collectedFourData_13_6_41 : List CollectedFourTerm := [ + ⟨6, 8, 0, 0, 6, 8, -435759597315896243980434551456649206150348144640000000⟩, + ⟨6, 8, 1, 0, 7, 8, 578239992217288043752650486912268863483817230336000000⟩, + ⟨6, 8, 2, 0, 8, 8, -117181909962556687617891188112081344357071847424000000⟩, + ⟨6, 8, 0, 1, 5, 8, -665440257489088486268767060896975718610934693888000000⟩, + ⟨6, 8, 1, 1, 6, 8, 282474251065675663840016972546936787474459918336000000⟩, + ⟨6, 8, 2, 1, 7, 8, -53717634285886337695595561522637379874901196800000000⟩, + ⟨6, 8, 3, 1, 8, 8, -509554738610920160355296517140629754587643904000000⟩, + ⟨6, 8, 0, 2, 4, 8, -189617139116781101395894851200998054616283217920000000⟩, + ⟨6, 8, 1, 2, 5, 8, 168072721649258647931447097331699663390818435072000000⟩, + ⟨6, 8, 2, 2, 6, 8, -113160617524713741283678347433168754260089765888000000⟩, + ⟨6, 8, 3, 2, 7, 8, 18308299063567439671730134964956791033594642432000000⟩, + ⟨6, 8, 4, 2, 8, 8, -1224709678994816634164534785595407669075850035200000⟩, + ⟨6, 8, 0, 3, 3, 8, -33725434772923279201034202556220676053152038912000000⟩, + ⟨6, 8, 1, 3, 4, 8, 91642915272889355886970299203824145741761216512000000⟩, + ⟨6, 8, 2, 3, 5, 8, 28043794035048477976317264291993676748892930048000000⟩, + ⟨6, 8, 3, 3, 6, 8, -20103503096692194112149266058669189929650618368000000⟩, + ⟨6, 8, 4, 3, 7, 8, -7383333298213769876999228744139248331467312332800000⟩, + ⟨6, 8, 5, 3, 8, 8, 1017680581445735854765805699639924258915745792000000⟩, + ⟨6, 8, 0, 4, 2, 8, 249964914582876737862065363749293611829556150272000000⟩, + ⟨6, 8, 1, 4, 3, 8, -288815327894340764629362232917421211621517164544000000⟩, + ⟨6, 8, 2, 4, 4, 8, 3542730660000993824213600848539323096880906240000000⟩, + ⟨6, 8, 3, 4, 5, 8, -37607990353924239905752863095668866013961650176000000⟩, + ⟨6, 8, 4, 4, 6, 8, 8754668347227235499467073779795496992054129459200000⟩, + ⟨6, 8, 5, 4, 7, 8, 608097093630460979015234022559994481066639360000000⟩, + ⟨6, 8, 6, 4, 8, 8, -329720031501233139375812023423718103491543040000000⟩, + ⟨6, 8, 0, 5, 1, 8, 192670309072511556430581841676560946903270817792000000⟩, + ⟨6, 8, 1, 5, 2, 8, -58495963078880135921531806797613697266593300480000000⟩, + ⟨6, 8, 2, 5, 3, 8, 59076452203323069510705369430310579973459542016000000⟩, + ⟨6, 8, 3, 5, 4, 8, 38499268379275350236517822865647767246962950144000000⟩, + ⟨6, 8, 4, 5, 5, 8, 4541966295521764899987433497445383359341736755200000⟩, + ⟨6, 8, 5, 5, 6, 8, -1350718864432952330145687111420497230068449280000000⟩, + ⟨6, 8, 6, 5, 7, 8, 399659997200497423362258027567691682027667456000000⟩, + ⟨6, 8, 7, 5, 8, 8, 20401766563420224720261985338798797764952064000000⟩, + ⟨6, 8, 0, 6, 0, 8, -4444212401940813201960812132469196187820921716736000000⟩, + ⟨6, 8, 1, 6, 1, 8, -1290697507026488774754399094316130667503248474112000000⟩, + ⟨6, 8, 2, 6, 2, 8, -39534951565209998874763597679991184101948260352000000⟩, + ⟨6, 8, 3, 6, 3, 8, 51213168070962860091211410980777041323481890816000000⟩, + ⟨6, 8, 4, 6, 4, 8, -8815159350855423417499438845733091266783503974400000⟩, + ⟨6, 8, 5, 6, 5, 8, 2737874157085715423218070954626319232943521792000000⟩, + ⟨6, 8, 6, 6, 6, 8, -260240526930752936614006136049653925600559104000000⟩, + ⟨6, 8, 7, 6, 7, 8, -67415214381493371293118650710202630698696704000000⟩, + ⟨6, 8, 8, 6, 8, 8, 88918384319006026611929457244905164016451584000000⟩, + ⟨6, 8, 1, 7, 0, 8, 8084460386588798981710000256747910854576179249152000000⟩, + ⟨6, 8, 2, 7, 1, 8, 583115373463086252181269184593564524986805256192000000⟩, + ⟨6, 8, 3, 7, 2, 8, 188514382810092711192013737994606188502494216192000000⟩, + ⟨6, 8, 4, 7, 3, 8, 32084077746409514178556153246575742578840934809600000⟩, + ⟨6, 8, 5, 7, 4, 8, 8279411855255271615816367418701616358069633024000000⟩, + ⟨6, 8, 6, 7, 5, 8, 268942998482797941290043213073034763168645120000000⟩, + ⟨6, 8, 7, 7, 6, 8, 168833444138429571840325106547376084437958656000000⟩, + ⟨6, 8, 8, 7, 7, 8, 67328783713250143880369777136187810252849152000000⟩ +] + +def collectedFourData_13_6_42 : List CollectedFourTerm := [ + ⟨7, 0, 6, 4, 8, 1, -832726348422229096029784121700043102430869585920000000⟩, + ⟨7, 0, 6, 5, 7, 1, 1009363636670536459148081298226452652282387365888000000⟩, + ⟨7, 0, 7, 5, 8, 1, 412206404187635535407401513949520144220161048576000000⟩, + ⟨7, 0, 6, 6, 6, 1, -657251980463043783665912648222214361325336788992000000⟩, + ⟨7, 0, 7, 6, 7, 1, -1362087102670746007984174376807448202727009550336000000⟩, + ⟨7, 0, 8, 6, 8, 1, 8084460386588798981710000256747910854576179249152000000⟩, + ⟨7, 0, 6, 7, 5, 1, 679230558242464087774672878788014634050529525760000000⟩, + ⟨7, 0, 7, 7, 6, 1, 3411186315585852970330417576652976341826775547904000000⟩, + ⟨7, 0, 8, 7, 7, 1, 6121533684802118684927709185768116248898915270656000000⟩ +] + +def collectedFourData_13_6_43 : List CollectedFourTerm := [ + ⟨7, 1, 5, 3, 8, 2, 79450224797863722554744234875160063041175814144000000⟩, + ⟨7, 1, 5, 4, 7, 2, 47474081424677207770843899706139297269174763520000000⟩, + ⟨7, 1, 6, 4, 8, 2, -180188477313202561329369527792333562997333032960000000⟩, + ⟨7, 1, 5, 5, 6, 2, -105450491415940864834120681958548252537084968960000000⟩, + ⟨7, 1, 6, 5, 7, 2, 218409921928832216757068544584285239508094418944000000⟩, + ⟨7, 1, 7, 5, 8, 2, 44597390517334717009118251325478048747585798144000000⟩, + ⟨7, 1, 5, 6, 5, 2, 213745571267265518867704510326119957540471046144000000⟩, + ⟨7, 1, 6, 6, 6, 2, -142218669788834107479695761925203897106087018496000000⟩, + ⟨7, 1, 7, 6, 7, 2, -147366779893067848757762248235090613057129283584000000⟩, + ⟨7, 1, 8, 6, 8, 2, 583115373463086252181269184593564524986805256192000000⟩, + ⟨7, 1, 5, 7, 4, 2, 646372884662538038753054154012507992086038970368000000⟩, + ⟨7, 1, 6, 7, 5, 2, 146974477589424431741407372848260110391055482880000000⟩, + ⟨7, 1, 7, 7, 6, 2, 369062699409981009020848152161404392688085630976000000⟩, + ⟨7, 1, 8, 7, 7, 2, 441533538429076231239565775947699379478542155776000000⟩ +] + +def collectedFourData_13_6_44 : List CollectedFourTerm := [ + ⟨7, 2, 4, 2, 8, 3, -20607036140139386505846215622308534064007190937600000⟩, + ⟨7, 2, 4, 3, 7, 3, -124232394599724260267505191751545565384714643046400000⟩, + ⟨7, 2, 5, 3, 8, 3, 102741315173646639166611776733334855061210136576000000⟩, + ⟨7, 2, 4, 4, 6, 3, 147306557725840866110463323949542601256578161049600000⟩, + ⟨7, 2, 5, 4, 7, 3, 61391261945973414439639978430996234861889454080000000⟩, + ⟨7, 2, 6, 4, 8, 3, -116505656122404063513565432648485287915075665920000000⟩, + ⟨7, 2, 4, 5, 5, 3, 76423388501290801542866439842278317180193446297600000⟩, + ⟨7, 2, 5, 5, 6, 3, -136363644046887711578518321217710260483879075840000000⟩, + ⟨7, 2, 6, 5, 7, 3, 141218748487072072589342705965879269720890277888000000⟩, + ⟨7, 2, 7, 5, 8, 3, 19223753264894843994385784895518656983510024192000000⟩, + ⟨7, 2, 4, 6, 4, 3, -148324382863748220674027179903245780720274322227200000⟩, + ⟨7, 2, 5, 6, 5, 3, 276405776829617672481562829910815308435031064576000000⟩, + ⟨7, 2, 6, 6, 6, 3, -91955266416969700494356440788346661230966996992000000⟩, + ⟨7, 2, 7, 6, 7, 3, -63522609355479138395592351729184782761550938112000000⟩, + ⟨7, 2, 8, 6, 8, 3, 188514382810092711192013737994606188502494216192000000⟩, + ⟨7, 2, 4, 7, 3, 3, 539848554300599214877607269144656004666259983564800000⟩, + ⟨7, 2, 5, 7, 4, 3, 835859186450012354609605246538565217491691241472000000⟩, + ⟨7, 2, 6, 7, 5, 3, 95030260536803051885858789642687966739179765760000000⟩, + ⟨7, 2, 7, 7, 6, 3, 159084874483313896064435144374733365389419347968000000⟩, + ⟨7, 2, 8, 7, 7, 3, 142742630832357609362115755460458091230345035776000000⟩ +] + +def collectedFourData_13_6_45 : List CollectedFourTerm := [ + ⟨7, 3, 3, 1, 8, 4, -1459211678576482438564236320398952807632837017600000⟩, + ⟨7, 3, 3, 2, 7, 4, 52429467894376180378687038615278646414342409420800000⟩, + ⟨7, 3, 4, 2, 8, 4, -17536002818133660701950615297611854880444933734400000⟩, + ⟨7, 3, 3, 3, 6, 4, -57570392886467117208589138780409579359918306099200000⟩, + ⟨7, 3, 4, 3, 7, 4, -105718241429236504598283950092080947233073764761600000⟩, + ⟨7, 3, 5, 3, 8, 4, 43714971434306407389660212018306654147362947072000000⟩, + ⟨7, 3, 3, 4, 5, 4, -107697985268155978870545812506622059254911493734400000⟩, + ⟨7, 3, 4, 4, 6, 4, 125353699282270564470527361833586724738099996262400000⟩, + ⟨7, 3, 5, 4, 7, 4, 26121110652987133011512663454381871453710581760000000⟩, + ⟨7, 3, 6, 4, 8, 4, -33047668770303320311420338206332077316673372160000000⟩, + ⟨7, 3, 3, 5, 4, 4, 110250337753379348111115796122029331425529534873600000⟩, + ⟨7, 3, 4, 5, 5, 4, 65034134312965504194194809072694617531581097574400000⟩, + ⟨7, 3, 5, 5, 6, 4, -58020795179743486948173823460892244357656084480000000⟩, + ⟨7, 3, 6, 5, 7, 4, 40057715474811831003571902472394825435996749824000000⟩, + ⟨7, 3, 7, 5, 8, 4, 4089717089053714102126087742032284238334656512000000⟩, + ⟨7, 3, 3, 6, 3, 4, 146659126651967689080219582487968820984304526950400000⟩, + ⟨7, 3, 4, 6, 4, 4, -126219839583346870691914762255795351011193572556800000⟩, + ⟨7, 3, 5, 6, 5, 4, 117606735109064879257106758441312032570130563072000000⟩, + ⟨7, 3, 6, 6, 6, 4, -26083773847342238546997031421257394200736956416000000⟩, + ⟨7, 3, 7, 6, 7, 4, -13513984363126263034735490123535908936595013632000000⟩, + ⟨7, 3, 8, 6, 8, 4, 32084077746409514178556153246575742578840934809600000⟩, + ⟨7, 3, 3, 7, 2, 4, 539848554300599214877607269144656004666259983564800000⟩, + ⟨7, 3, 4, 7, 3, 4, 459395795940825521020342073858882307753877123891200000⟩, + ⟨7, 3, 5, 7, 4, 4, 355646220773095150792987465905494723723142365184000000⟩, + ⟨7, 3, 6, 7, 5, 4, 26956018084447059909159155103206291867676180480000000⟩, + ⟨7, 3, 7, 7, 6, 4, 33844178127924641039957259730548851293707829248000000⟩, + ⟨7, 3, 8, 7, 7, 4, 24293985408879906345396664595558938931184323788800000⟩ +] + +def collectedFourData_13_6_46 : List CollectedFourTerm := [ + ⟨7, 4, 2, 0, 8, 5, -129894035759903433024804276565689893775942352896000000⟩, + ⟨7, 4, 2, 1, 7, 5, -59545029698678727887939715970599790352479027200000000⟩, + ⟨7, 4, 3, 1, 8, 5, -2259328985503113923315571064400694080924811264000000⟩, + ⟨7, 4, 2, 2, 6, 5, -125436505549915341684953484737885091212612861952000000⟩, + ⟨7, 4, 3, 2, 7, 5, 81177678500919667155822697400832610888750989312000000⟩, + ⟨7, 4, 4, 2, 8, 5, -13575686118248493460835475120312823097755435008000000⟩, + ⟨7, 4, 2, 3, 5, 5, 31086040382819480481271468114750946861585006592000000⟩, + ⟨7, 4, 3, 3, 6, 5, -89137483796789655601998029110816590354330943488000000⟩, + ⟨7, 4, 4, 3, 7, 5, -81842919250241968366869077769244103465565683712000000⟩, + ⟨7, 4, 5, 3, 8, 5, 22561611750603963549336948850445754264044175360000000⟩, + ⟨7, 4, 2, 4, 4, 5, 3927053102180338745974008075499128409250856960000000⟩, + ⟨7, 4, 3, 4, 5, 5, -166751118682112866789664930471625978526109270016000000⟩, + ⟨7, 4, 4, 4, 6, 5, 97043921175563173403532991982306776337212243968000000⟩, + ⟨7, 4, 5, 4, 7, 5, 13481293426735860269070415742037472207228108800000000⟩, + ⟨7, 4, 6, 4, 8, 5, -12792104985907782326254210020721760954587545600000000⟩, + ⟨7, 4, 2, 5, 3, 5, 65485182802692454011397089468132819980060196864000000⟩, + ⟨7, 4, 3, 5, 4, 5, 170702981208810578052664333547231540645518639104000000⟩, + ⟨7, 4, 4, 5, 5, 5, 50346877995016094365914655945909852449231863808000000⟩, + ⟨7, 4, 5, 5, 6, 5, -29944950467916417131465020005994922447890022400000000⟩, + ⟨7, 4, 6, 5, 7, 5, 15505556697841249913059713791784850705707171840000000⟩, + ⟨7, 4, 7, 5, 8, 5, 1266439475158322508723078389221452354510913536000000⟩, + ⟨7, 4, 2, 6, 2, 5, -43823781452430203038588047174563235188082475008000000⟩, + ⟨7, 4, 3, 6, 3, 5, 227075496103902356577873697016360484767589728256000000⟩, + ⟨7, 4, 4, 6, 4, 5, -97714453051254820961079836920898361794469298176000000⟩, + ⟨7, 4, 5, 6, 5, 5, 60697683418924218661244151137961612194202255360000000⟩, + ⟨7, 4, 6, 6, 6, 5, -10096517724230845609457319698986016256357826560000000⟩, + ⟨7, 4, 7, 6, 7, 5, -4184798823846130133192624049663462910665424896000000⟩, + ⟨7, 4, 8, 6, 8, 5, 8279411855255271615816367418701616358069633024000000⟩, + ⟨7, 4, 2, 7, 1, 5, 646372884662538038753054154012507992086038970368000000⟩, + ⟨7, 4, 3, 7, 2, 5, 835859186450012354609605246538565217491691241472000000⟩, + ⟨7, 4, 4, 7, 3, 5, 355646220773095150792987465905494723723142365184000000⟩, + ⟨7, 4, 5, 7, 4, 5, 183551577191587955783409219214226573483751505920000000⟩, + ⟨7, 4, 6, 7, 5, 5, 10434146376101877588129607929621060587932876800000000⟩, + ⟨7, 4, 7, 7, 6, 5, 10480334520012251797685948196800175757269663744000000⟩, + ⟨7, 4, 8, 7, 7, 5, 6269150461343342793179159395118887914776297472000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1315.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1315.lean new file mode 100644 index 0000000000000000000000000000000000000000..284eb0918573ed3f3891b662558c2e26aa18fa93 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1315.lean @@ -0,0 +1,613 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1313 +import OAI.Analysis.LaughlinFock.Sparse1314 + +namespace OAI + +/-! Sparse1315. -/ +namespace LaughlinFock +def collectedFourData_13_6_47 : List CollectedFourTerm := [ + ⟨7, 5, 1, 0, 7, 6, 48581878558451221633317917313439019602469191680000000⟩, + ⟨7, 5, 2, 0, 8, 6, -29535750185066960285713108391386040635867791360000000⟩, + ⟨7, 5, 1, 1, 6, 6, 23732584992158945501798009253172298620002631680000000⟩, + ⟨7, 5, 2, 1, 7, 6, -13539552541067920679313518601122753336573952000000000⟩, + ⟨7, 5, 3, 1, 8, 6, -256866976652594362454810730466680109132677120000000⟩, + ⟨7, 5, 1, 2, 5, 6, 14120933629724367297223857509951519371674255360000000⟩, + ⟨7, 5, 2, 2, 6, 6, -28522181717859184522196693048128748759883448320000000⟩, + ⟨7, 5, 3, 2, 7, 6, 9229229112715601176618964141224554419674152960000000⟩, + ⟨7, 5, 4, 2, 8, 6, -1028961982828884777303372241730788329793781760000000⟩, + ⟨7, 5, 1, 3, 4, 6, 7699545241514402656655731122582817929229762560000000⟩, + ⟨7, 5, 2, 3, 5, 6, 7068450199568593729304068378911079857358110720000000⟩, + ⟨7, 5, 3, 3, 6, 6, -10134192991023094919666101314309933501555671040000000⟩, + ⟨7, 5, 4, 3, 7, 6, -6203240980876353436858032991682478052359536640000000⟩, + ⟨7, 5, 5, 3, 8, 6, 1282534114326153653710016038371549935724134400000000⟩, + ⟨7, 5, 1, 4, 3, 6, -24265342028279434374297759951492990798365982720000000⟩, + ⟨7, 5, 2, 4, 4, 6, 892946767809140783492699664014103568554393600000000⟩, + ⟨7, 5, 3, 4, 5, 6, -18958219889244740947000585307624618662853345280000000⟩, + ⟨7, 5, 4, 4, 6, 6, 7355392919704635942242070702684934736141352960000000⟩, + ⟨7, 5, 5, 4, 7, 6, 766355653849367507591005697244518733053952000000000⟩, + ⟨7, 5, 6, 4, 8, 6, -581742518037231015689675222966783158989619200000000⟩, + ⟨7, 5, 1, 5, 2, 6, -4914644114393782325287950956560652039513702400000000⟩, + ⟨7, 5, 2, 5, 3, 6, 14890244873589608449648459609664384969987850240000000⟩, + ⟨7, 5, 3, 5, 4, 6, 19407513899056011301843934861740420807073464320000000⟩, + ⟨7, 5, 4, 5, 5, 6, 3816015114061835922978713598404552111696117760000000⟩, + ⟨7, 5, 5, 5, 6, 6, -1702246317835942183920807750838652497821696000000000⟩, + ⟨7, 5, 6, 5, 7, 6, 705141304492749728605730225496224984601722880000000⟩, + ⟨7, 5, 7, 5, 8, 6, 47994556670694639425405515416493974576168960000000⟩, + ⟨7, 5, 1, 6, 1, 6, -108440284978583498933314786560248803490330050560000000⟩, + ⟨7, 5, 2, 6, 2, 6, -9964801336502193083812305918577229136427745280000000⟩, + ⟨7, 5, 3, 6, 3, 6, 25816601535392897664844424992687103146438164480000000⟩, + ⟨7, 5, 4, 6, 4, 6, -7406215530241735270140312191302268967683358720000000⟩, + ⟨7, 5, 5, 6, 5, 6, 3450411721727075279651903788517639957407334400000000⟩, + ⟨7, 5, 6, 6, 6, 6, -459156147543513262699031594494701288208465920000000⟩, + ⟨7, 5, 7, 6, 7, 6, -158592311947186132678366370414687490209218560000000⟩, + ⟨7, 5, 8, 6, 8, 6, 268942998482797941290043213073034763168645120000000⟩, + ⟨7, 5, 1, 7, 0, 6, 679230558242464087774672878788014634050529525760000000⟩, + ⟨7, 5, 2, 7, 1, 6, 146974477589424431741407372848260110391055482880000000⟩, + ⟨7, 5, 3, 7, 2, 6, 95030260536803051885858789642687966739179765760000000⟩, + ⟨7, 5, 4, 7, 3, 6, 26956018084447059909159155103206291867676180480000000⟩, + ⟨7, 5, 5, 7, 4, 6, 10434146376101877588129607929621060587932876800000000⟩, + ⟨7, 5, 6, 7, 5, 6, 474510379104100436235468756849032552880537600000000⟩, + ⟨7, 5, 7, 7, 6, 6, 397175718946760930142234413818442892013731840000000⟩, + ⟨7, 5, 8, 7, 7, 6, 203642982435195015592987583792068496310927360000000⟩ +] + +def collectedFourData_13_6_48 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 6, 7, -91932986505509420167221143433067308769754480640000000⟩, + ⟨7, 6, 1, 0, 7, 7, 243984663694834904313194647914840264709056233472000000⟩, + ⟨7, 6, 2, 0, 8, 7, -74166235329990440503853193011780726148481155072000000⟩, + ⟨7, 6, 0, 1, 5, 7, -140389128750774678204248145457170052636200665088000000⟩, + ⟨7, 6, 1, 1, 6, 7, 119188202262584192916625089257682585504524009472000000⟩, + ⟨7, 6, 2, 1, 7, 7, -33998717951349604409836062444132397608232550400000000⟩, + ⟨7, 6, 3, 1, 8, 7, -430006721110279767276886922783810856488534016000000⟩, + ⟨7, 6, 0, 2, 4, 7, -40003869103539829586108961441822055923103825920000000⟩, + ⟨7, 6, 1, 2, 5, 7, 70917209151560217985183072863997716784421535744000000⟩, + ⟨7, 6, 2, 2, 6, 7, -71621097421152213616696271455594695017065611264000000⟩, + ⟨7, 6, 3, 2, 7, 7, 15450139215450173536718994488876575122341756928000000⟩, + ⟨7, 6, 4, 2, 8, 7, -1291896025764135161120047464616571398652952576000000⟩, + ⟨7, 6, 0, 3, 3, 7, -7115115671506267862404635594061130348428787712000000⟩, + ⟨7, 6, 1, 3, 4, 7, 38668141539521939475809327251450972822384410624000000⟩, + ⟨7, 6, 2, 3, 5, 7, 17749349098455401724390868148015850167671455744000000⟩, + ⟨7, 6, 3, 3, 6, 7, -16965088918621047414945965305882235774038966272000000⟩, + ⟨7, 6, 4, 3, 7, 7, -7788375570513265686079062499302695225486475264000000⟩, + ⟨7, 6, 5, 3, 8, 7, 1288211423049571386568207522083046404812439552000000⟩, + ⟨7, 6, 0, 4, 2, 7, 52735547904730278395184341540304385286520963072000000⟩, + ⟨7, 6, 1, 4, 3, 7, -121863779044419085482483198393170923210080780288000000⟩, + ⟨7, 6, 2, 4, 4, 7, 2242248790144854962410225852713764779689246720000000⟩, + ⟨7, 6, 3, 4, 5, 7, -31736901640289093473224902250292417347981410304000000⟩, + ⟨7, 6, 4, 4, 6, 7, 9234940687289043052963825843232479530971037696000000⟩, + ⟨7, 6, 5, 4, 7, 7, 769748029607828680864852420403144475971420160000000⟩, + ⟨7, 6, 6, 4, 8, 7, -486931399223717498058549852329871301442273280000000⟩, + ⟨7, 6, 0, 5, 1, 7, 40648001864052997576761230764942251578823278592000000⟩, + ⟨7, 6, 1, 5, 2, 7, -24681997218108266709784874058145557300337704960000000⟩, + ⟨7, 6, 2, 5, 3, 7, 37390396333125235202462408446821822291926581248000000⟩, + ⟨7, 6, 3, 5, 4, 7, 32489039756644670215213532192891581018958462976000000⟩, + ⟨7, 6, 4, 5, 5, 7, 4791134018925356858141944730251867368431026176000000⟩, + ⟨7, 6, 5, 5, 6, 7, -1709781538740949681782741831148182041190727680000000⟩, + ⟨7, 6, 6, 5, 7, 7, 590218922291524184535433333537322289428692992000000⟩, + ⟨7, 6, 7, 5, 8, 7, 34433579280252272162937231580689863710605312000000⟩, + ⟨7, 6, 0, 6, 0, 7, -937603488923405092179065675042818402992191963136000000⟩, + ⟨7, 6, 1, 6, 1, 7, -544601551988960785537340532760452906473251405824000000⟩, + ⟨7, 6, 2, 6, 2, 7, -25022279654616106844630515376656837310158995456000000⟩, + ⟨7, 6, 3, 6, 3, 7, 43218136955997806613597052706667630279329316864000000⟩, + ⟨7, 6, 4, 6, 4, 7, -9298750166810655129599425080467226792057372672000000⟩, + ⟨7, 6, 5, 6, 5, 7, 3465685430510592555774395250978381456633495552000000⟩, + ⟨7, 6, 6, 6, 6, 7, -384323886347302918445472359258002600312700928000000⟩, + ⟨7, 6, 7, 6, 7, 7, -113781672870547552079155073103914069951250432000000⟩, + ⟨7, 6, 8, 6, 8, 7, 168833444138429571840325106547376084437958656000000⟩, + ⟨7, 6, 1, 7, 0, 7, 3411186315585852970330417576652976341826775547904000000⟩, + ⟨7, 6, 2, 7, 1, 7, 369062699409981009020848152161404392688085630976000000⟩, + ⟨7, 6, 3, 7, 2, 7, 159084874483313896064435144374733365389419347968000000⟩, + ⟨7, 6, 4, 7, 3, 7, 33844178127924641039957259730548851293707829248000000⟩, + ⟨7, 6, 5, 7, 4, 7, 10480334520012251797685948196800175757269663744000000⟩, + ⟨7, 6, 6, 7, 5, 7, 397175718946760930142234413818442892013731840000000⟩, + ⟨7, 6, 7, 7, 6, 7, 284952764547466493772929239242999556051304448000000⟩, + ⟨7, 6, 8, 7, 7, 7, 127840272076667606674089988118276388912365568000000⟩ +] + +def collectedFourData_13_6_49 : List CollectedFourTerm := [ + ⟨7, 7, 0, 0, 6, 8, -329956104166231478046961795683696611472357457920000000⟩, + ⟨7, 7, 1, 0, 7, 8, 437841911641972988123625892432842783777104068608000000⟩, + ⟨7, 7, 2, 0, 8, 8, -88729856389081166367867990416462588064061980672000000⟩, + ⟨7, 7, 0, 1, 5, 8, -503869739803580318474344492205308821418713022464000000⟩, + ⟨7, 7, 1, 1, 6, 8, 213888813885004647407497792486170717448052932608000000⟩, + ⟨7, 7, 2, 1, 7, 8, -40674861651178743625845847037979149510010470400000000⟩, + ⟨7, 7, 3, 1, 8, 8, -385833605150911314621976060259542580814938112000000⟩, + ⟨7, 7, 0, 2, 4, 8, -143577635217896979216525915433052432743803125760000000⟩, + ⟨7, 7, 1, 2, 5, 8, 127264254863450580055881164890012417401255100416000000⟩, + ⟨7, 7, 2, 2, 6, 8, -85684943564035778790919313249031123117973438464000000⟩, + ⟨7, 7, 3, 2, 7, 8, 13862999392634620301352569649516620174113898496000000⟩, + ⟨7, 7, 4, 2, 8, 8, -927347181576496963290505007885281557118294425600000⟩, + ⟨7, 7, 0, 3, 3, 8, -25536816945695711688010690661402348727551655936000000⟩, + ⟨7, 7, 1, 3, 4, 8, 69391791905751187675575967773993243023807348736000000⟩, + ⟨7, 7, 2, 3, 5, 8, 21234692437850857002443264922565919209835986944000000⟩, + ⟨7, 7, 3, 3, 6, 8, -15222323507586803347992775806053443003591163904000000⟩, + ⟨7, 7, 4, 3, 7, 8, -5590641963700377841753646471992863950580901478400000⟩, + ⟨7, 7, 5, 3, 8, 8, 770585253905573191333686635639986816680984576000000⟩, + ⟨7, 7, 0, 4, 2, 8, 189272823598237944684751963445560783487700566016000000⟩, + ⟨7, 7, 1, 4, 3, 8, -218690261792274350962147927896592207314558124032000000⟩, + ⟨7, 7, 2, 4, 4, 8, 2682547014189531174493976575593471781078302720000000⟩, + ⟨7, 7, 3, 4, 5, 8, -28476678561152559847961285806506679179178672128000000⟩, + ⟨7, 7, 4, 4, 6, 8, 6629013517800822676307867627097592031270771097600000⟩, + ⟨7, 7, 5, 4, 7, 8, 460449636003451436261763030019119574501294080000000⟩, + ⟨7, 7, 6, 4, 8, 8, -249663203587106167093741191814195014921093120000000⟩, + ⟨7, 7, 0, 5, 1, 8, 145889488060967927673687612976078529821541400576000000⟩, + ⟨7, 7, 1, 5, 2, 8, -44293000557752517435030863617451061853751869440000000⟩, + ⟨7, 7, 2, 5, 3, 8, 44732545506829580456288351410759797634548891648000000⟩, + ⟨7, 7, 3, 5, 4, 8, 29151552107909199706282233610015562275416440832000000⟩, + ⟨7, 7, 4, 5, 5, 8, 3439165800032333896002958999967816058211506585600000⟩, + ⟨7, 7, 5, 5, 6, 8, -1022761029423860848780424691262844638687395840000000⟩, + ⟨7, 7, 6, 5, 7, 8, 302621575014367589088463607599689625887571968000000⟩, + ⟨7, 7, 7, 5, 8, 8, 15448167877057688451476229003209701790318592000000⟩, + ⟨7, 7, 0, 6, 0, 8, -3365146790257848360261690097950054933976011767808000000⟩, + ⟨7, 7, 1, 6, 1, 8, -977313004002061962767857052637356946578825281536000000⟩, + ⟨7, 7, 2, 6, 2, 8, -29935768890021140832699236452599532962768224256000000⟩, + ⟨7, 7, 3, 6, 3, 8, 38778485942227827542026517932038691022646018048000000⟩, + ⟨7, 7, 4, 6, 4, 8, -6674817158196132342876105019641530278240006963200000⟩, + ⟨7, 7, 5, 6, 5, 8, 2073111633418642400175506207013992580645912576000000⟩, + ⟨7, 7, 6, 6, 6, 8, -197053492203385772226281533109263792406003712000000⟩, + ⟨7, 7, 7, 6, 7, 8, -51046635887914621598941461411069622864576512000000⟩, + ⟨7, 7, 8, 6, 8, 8, 67328783713250143880369777136187810252849152000000⟩, + ⟨7, 7, 1, 7, 0, 8, 6121533684802118684927709185768116248898915270656000000⟩, + ⟨7, 7, 2, 7, 1, 8, 441533538429076231239565775947699379478542155776000000⟩, + ⟨7, 7, 3, 7, 2, 8, 142742630832357609362115755460458091230345035776000000⟩, + ⟨7, 7, 4, 7, 3, 8, 24293985408879906345396664595558938931184323788800000⟩, + ⟨7, 7, 5, 7, 4, 8, 6269150461343342793179159395118887914776297472000000⟩, + ⟨7, 7, 6, 7, 5, 8, 203642982435195015592987583792068496310927360000000⟩, + ⟨7, 7, 7, 7, 6, 8, 127840272076667606674089988118276388912365568000000⟩, + ⟨7, 7, 8, 7, 7, 8, 50981190796745819456093658919129102896070656000000⟩ +] + +def collectedFourData_13_6 : List (List CollectedFourTerm) := [ + collectedFourData_13_6_0, + collectedFourData_13_6_1, + collectedFourData_13_6_2, + collectedFourData_13_6_3, + collectedFourData_13_6_4, + collectedFourData_13_6_5, + collectedFourData_13_6_6, + collectedFourData_13_6_7, + collectedFourData_13_6_8, + collectedFourData_13_6_9, + collectedFourData_13_6_10, + collectedFourData_13_6_11, + collectedFourData_13_6_12, + collectedFourData_13_6_13, + collectedFourData_13_6_14, + collectedFourData_13_6_15, + collectedFourData_13_6_16, + collectedFourData_13_6_17, + collectedFourData_13_6_18, + collectedFourData_13_6_19, + collectedFourData_13_6_20, + collectedFourData_13_6_21, + collectedFourData_13_6_22, + collectedFourData_13_6_23, + collectedFourData_13_6_24, + collectedFourData_13_6_25, + collectedFourData_13_6_26, + collectedFourData_13_6_27, + collectedFourData_13_6_28, + collectedFourData_13_6_29, + collectedFourData_13_6_30, + collectedFourData_13_6_31, + collectedFourData_13_6_32, + collectedFourData_13_6_33, + collectedFourData_13_6_34, + collectedFourData_13_6_35, + collectedFourData_13_6_36, + collectedFourData_13_6_37, + collectedFourData_13_6_38, + collectedFourData_13_6_39, + collectedFourData_13_6_40, + collectedFourData_13_6_41, + collectedFourData_13_6_42, + collectedFourData_13_6_43, + collectedFourData_13_6_44, + collectedFourData_13_6_45, + collectedFourData_13_6_46, + collectedFourData_13_6_47, + collectedFourData_13_6_48, + collectedFourData_13_6_49 +] + +theorem collectedFourChecked_13_6 : collectNumericRowParts 13 6 = collectedFourData_13_6 := by + decide +kernel + +def collectedFourData_13_7_0 : List CollectedFourTerm := [ + ⟨0, 7, 6, 5, 8, 0, 62431511331648812542017271278187748429458833408000000⟩, + ⟨0, 7, 6, 6, 7, 0, 58960116097991242087442502565761550665784492032000000⟩, + ⟨0, 7, 7, 6, 8, 0, 64682253423664316834564284789136541548430753792000000⟩, + ⟨0, 7, 6, 7, 6, 0, -63813703824854424608957061494430001255447265280000000⟩, + ⟨0, 7, 7, 7, 7, 0, -22860819626933384194954670262325755755580358656000000⟩, + ⟨0, 7, 8, 7, 8, 0, -306705648592772033919770536280511428459652710400000000⟩ +] + +def collectedFourData_13_7_1 : List CollectedFourTerm := [ + ⟨0, 8, 5, 4, 8, 1, 5100100956065793193627252888841126626046509056000000⟩, + ⟨0, 8, 5, 5, 7, 1, -173497472661049342819926151174050546318311424000000⟩, + ⟨0, 8, 6, 5, 8, 1, 7183783342680442947325989934199255971557015552000000⟩, + ⟨0, 8, 5, 6, 6, 1, 1650270572411572880623399038963654948254908416000000⟩, + ⟨0, 8, 6, 6, 7, 1, 6784341606872780669096722551041432704209911808000000⟩, + ⟨0, 8, 7, 6, 8, 1, 3721384320199853799964175541350503263579930624000000⟩, + ⟨0, 8, 5, 7, 5, 1, -1866291574322468073340340308340114018959097856000000⟩, + ⟨0, 8, 6, 7, 6, 1, -7342827568861699372892355469871245032758968320000000⟩, + ⟨0, 8, 7, 7, 7, 1, -1315258686943987468023537605916736309828780032000000⟩, + ⟨0, 8, 8, 7, 8, 1, -11763861349665477057944010712230313631888179200000000⟩ +] + +def collectedFourData_13_7_2 : List CollectedFourTerm := [ + ⟨1, 6, 6, 5, 8, 0, 7854604778211357088886240169996668814432927744000000⟩, + ⟨1, 6, 6, 6, 7, 0, 7417863187182076166200231765957878714703282176000000⟩, + ⟨1, 6, 7, 6, 8, 0, 8137774113910338201642624664739841663729401856000000⟩, + ⟨1, 6, 6, 7, 6, 0, -8028500548631975989059368688627589821014999040000000⟩, + ⟨1, 6, 7, 7, 7, 0, -2876154993616373387977734518990496980803780608000000⟩, + ⟨1, 6, 8, 7, 8, 0, -38587110924543073919366287738924750987277107200000000⟩ +] + +def collectedFourData_13_7_3 : List CollectedFourTerm := [ + ⟨1, 7, 5, 4, 8, 1, 53483201703467546625053948026999072156922413056000000⟩, + ⟨1, 7, 5, 5, 7, 1, -1819415028311655873469679178405132072778727424000000⟩, + ⟨1, 7, 6, 5, 8, 1, 75334142759199133516311051401318831777541783552000000⟩, + ⟨1, 7, 5, 6, 6, 1, 17305883677579183314255394618846348506789052416000000⟩, + ⟨1, 7, 6, 6, 7, 1, 71145319222367796957001216834741112699835383808000000⟩, + ⟨1, 7, 7, 6, 8, 1, 39025021255050359429452037129756164222693146624000000⟩, + ⟨1, 7, 5, 7, 5, 1, -19571229975017557306351972764549831864254201856000000⟩, + ⟨1, 7, 6, 7, 6, 1, -77001991004145584802832498327998719070641848320000000⟩, + ⟨1, 7, 7, 7, 7, 1, -13792716311311326975356602661476678441245868032000000⟩, + ⟨1, 7, 8, 7, 8, 1, -123364022554785709954639064673238494047580979200000000⟩ +] + +def collectedFourData_13_7_4 : List CollectedFourTerm := [ + ⟨1, 8, 4, 3, 8, 2, 2970305887200437842653427619607882679503657369600000⟩, + ⟨1, 8, 4, 4, 7, 2, 6768690321740399897612811087403760615106910617600000⟩, + ⟨1, 8, 5, 4, 8, 2, -29409904343733063156558981423787413183142035456000000⟩, + ⟨1, 8, 4, 5, 6, 2, -6208776081413202191409476237159971730905418956800000⟩, + ⟨1, 8, 5, 5, 7, 2, 1000479033414466928943575123727721657767297024000000⟩, + ⟨1, 8, 6, 5, 8, 2, -20712764585871196363141134633495249753710002176000000⟩, + ⟨1, 8, 4, 6, 5, 2, 10074258558815640138696277799103922936903788134400000⟩, + ⟨1, 8, 5, 6, 6, 2, -9516340969324893367126083323598459289328418816000000⟩, + ⟨1, 8, 6, 6, 7, 2, -19561067458481381826626678351624001978844053504000000⟩, + ⟨1, 8, 7, 6, 8, 2, -7153162772407277837819956298716688041176465408000000⟩, + ⟨1, 8, 4, 7, 4, 2, 41663238302039503928244643248579457833163869388800000⟩, + ⟨1, 8, 5, 7, 5, 2, 10762033369762710657962007090278566932309344256000000⟩, + ⟨1, 8, 6, 7, 6, 2, 21171331535693106511001395837869015292874588160000000⟩, + ⟨1, 8, 7, 7, 7, 2, 2528161207232621084270467077771503843036626944000000⟩, + ⟨1, 8, 8, 7, 8, 2, 16959175905876764730525778921338285593513164800000000⟩ +] + +def collectedFourData_13_7_5 : List CollectedFourTerm := [ + ⟨2, 5, 6, 5, 8, 0, -37988391660070389847422873783858730764362317824000000⟩, + ⟨2, 5, 6, 6, 7, 0, -35876113438219395600334632731671038392581226496000000⟩, + ⟨2, 5, 7, 6, 8, 0, -39357925574812367959884944682503583044286283776000000⟩, + ⟨2, 5, 6, 7, 6, 0, 38829429601672904285882969568476957595496611840000000⟩, + ⟨2, 5, 7, 7, 7, 0, 13910375564109126163587617684547997839988359168000000⟩, + ⟨2, 5, 8, 7, 8, 0, 186624575548144621419575624662195252464137011200000000⟩ +] + +def collectedFourData_13_7_6 : List CollectedFourTerm := [ + ⟨2, 6, 5, 4, 8, 1, 63421133926871999099205304859421959403721457664000000⟩, + ⟨2, 6, 5, 5, 7, 1, -2157487968257441606398590020103511048722579456000000⟩, + ⟨2, 6, 6, 5, 8, 1, 89332287615973051355963007528568547664029810688000000⟩, + ⟨2, 6, 5, 6, 6, 1, 20521560629895087883601106095614216408613781504000000⟩, + ⟨2, 6, 6, 6, 7, 1, 84365121663599075203032381756999349427767345152000000⟩, + ⟨2, 6, 7, 6, 8, 1, 46276419897934225373682615480142975068071264256000000⟩, + ⟨2, 6, 5, 7, 5, 1, -23207840178325112558677293751091157234943524864000000⟩, + ⟨2, 6, 6, 7, 6, 1, -91310045557595856896276581086930299407910830080000000⟩, + ⟨2, 6, 7, 7, 7, 1, -16355597281647291823017540064569390352520183808000000⟩, + ⟨2, 6, 8, 7, 8, 1, -146286795610769618816522546868780772008709324800000000⟩ +] + +def collectedFourData_13_7_7 : List CollectedFourTerm := [ + ⟨2, 7, 4, 3, 8, 2, 3610535039460407363848571734664170906559132467200000⟩, + ⟨2, 7, 4, 4, 7, 2, 8227635302885935629461743648633662946319479603200000⟩, + ⟨2, 7, 5, 4, 8, 2, -35749008409470121013465678439759657543760084992000000⟩, + ⟨2, 7, 4, 5, 6, 2, -7547035371240651582563567114249074051454179737600000⟩, + ⟨2, 7, 5, 5, 7, 2, 1216125457635284620668865891953551271020986368000000⟩, + ⟨2, 7, 6, 5, 8, 2, -25177259562269491122070677038998775077149868032000000⟩, + ⟨2, 7, 4, 6, 5, 2, 12245696202511439509243475797303142389803437260800000⟩, + ⟨2, 7, 5, 6, 6, 2, -11567523286156950516052309780082143407491776512000000⟩, + ⟨2, 7, 6, 6, 7, 2, -23777321983043927217735637552026430638001225728000000⟩, + ⟨2, 7, 7, 6, 8, 2, -8694978165054360666241622182744593148208480256000000⟩, + ⟨2, 7, 4, 7, 4, 2, 50643464834755481523633785985972679497892862361600000⟩, + ⟨2, 7, 5, 7, 5, 2, 13081716177721179728027958960275383187083886592000000⟩, + ⟨2, 7, 6, 7, 6, 2, 25734667486956664378638548027077806429170565120000000⟩, + ⟨2, 7, 7, 7, 7, 2, 3073089092760478825842961873322067171169271808000000⟩, + ⟨2, 7, 8, 7, 8, 2, 20614610472409169250372630790954440692701593600000000⟩ +] + +def collectedFourData_13_7_8 : List CollectedFourTerm := [ + ⟨2, 8, 3, 2, 8, 3, 1047088751622452317646282416025501197381140480000000⟩, + ⟨2, 8, 3, 3, 7, 3, 2614464832231432055227576464234086086081511424000000⟩, + ⟨2, 8, 4, 3, 8, 3, 1518796326700130817079893224990047764964442112000000⟩, + ⟨2, 8, 3, 4, 6, 3, 6005458533207566635420792637647664646985875456000000⟩, + ⟨2, 8, 4, 4, 7, 3, 3461011218248421548444030752518038773586460672000000⟩, + ⟨2, 8, 5, 4, 8, 3, -7519032783516447372780331946725790525329244160000000⟩, + ⟨2, 8, 3, 5, 5, 3, 1973705815984525475828327060021759648414564352000000⟩, + ⟨2, 8, 4, 5, 6, 3, -3174712189202105360438446267938993816150736896000000⟩, + ⟨2, 8, 5, 5, 7, 3, 255785757190577779600628678224737217428848640000000⟩, + ⟨2, 8, 6, 5, 8, 3, -3530328969864206533523187145859079900223242240000000⟩, + ⟨2, 8, 3, 6, 4, 3, -9311963004190242972091722785491445105502978048000000⟩, + ⟨2, 8, 4, 6, 5, 3, 5151236092986286223783488853489069772156960768000000⟩, + ⟨2, 8, 5, 6, 6, 3, -2432979002283694460441861605724636904696053760000000⟩, + ⟨2, 8, 6, 6, 7, 3, -3334031188538236044647445493167275102919720960000000⟩, + ⟨2, 8, 7, 6, 8, 3, -914400549606355707158547721686050768620093440000000⟩, + ⟨2, 8, 3, 7, 3, 3, 16595851329761173155147698116024431887027011584000000⟩, + ⟨2, 8, 4, 7, 4, 3, 21303520813881672179046156941666358622144167936000000⟩, + ⟨2, 8, 5, 7, 5, 3, 2751456814642343857625195440986491338264412160000000⟩, + ⟨2, 8, 6, 7, 6, 3, 3608488125338934938447231324346282754336358400000000⟩, + ⟨2, 8, 7, 7, 7, 3, 323179000805680648659407089702957267990609920000000⟩, + ⟨2, 8, 8, 7, 8, 3, 1734335455530062818729018900760467122369331200000000⟩ +] + +def collectedFourData_13_7_9 : List CollectedFourTerm := [ + ⟨3, 4, 6, 5, 8, 0, 24124818949840997788951659687553828264259616768000000⟩, + ⟨3, 4, 6, 6, 7, 0, 22783400494176036611691665846784853206443753472000000⟩, + ⟨3, 4, 7, 6, 8, 0, 24994551947080396542546752412150754799813394432000000⟩, + ⟨3, 4, 6, 7, 6, 0, -24658926533354050656349876337380674562299002880000000⟩, + ⟨3, 4, 7, 7, 7, 0, -8833890495057699688462033653207737249537458176000000⟩, + ⟨3, 4, 8, 7, 8, 0, -118517365435669772726183984445724831408088678400000000⟩ +] + +def collectedFourData_13_7_10 : List CollectedFourTerm := [ + ⟨3, 5, 5, 4, 8, 1, 52395640624310247532519103466012244064625229824000000⟩, + ⟨3, 5, 5, 5, 7, 1, -1782417898210947204240782592418450418587140096000000⟩, + ⟨3, 5, 6, 5, 8, 1, 73802250894332099337805438805594483604647313408000000⟩, + ⟨3, 5, 5, 6, 6, 1, 16953974948694344608235752383135423612284043264000000⟩, + ⟨3, 5, 6, 6, 7, 1, 69698605531226671627399759959402167599242412032000000⟩, + ⟨3, 5, 7, 6, 8, 1, 38231461915323556957195492867983380687037136896000000⟩, + ⟨3, 5, 5, 7, 5, 1, -19173256268991543871151985841174784701076865024000000⟩, + ⟨3, 5, 6, 7, 6, 1, -75436184063528196513283650945474963480804065280000000⟩, + ⟨3, 5, 7, 7, 7, 1, -13512246538405646827656475069212517121893859328000000⟩, + ⟨3, 5, 8, 7, 8, 1, -120855460890083247356982248376378842600492236800000000⟩ +] + +def collectedFourData_13_7_11 : List CollectedFourTerm := [ + ⟨3, 6, 4, 3, 8, 2, 1434295468310909076726241513255131890464063488000000⟩, + ⟨3, 6, 4, 4, 7, 2, 3268451877871204333984752603512422966574972928000000⟩, + ⟨3, 6, 5, 4, 8, 2, -14201396800728609792478291156448741238169927680000000⟩, + ⟨3, 6, 4, 5, 6, 2, -2998081590082102803832680178757761689037307904000000⟩, + ⟨3, 6, 5, 5, 7, 2, 483109349090959499110001493627225288443166720000000⟩, + ⟨3, 6, 6, 5, 8, 2, -10001739049746903488300161370358812805200609280000000⟩, + ⟨3, 6, 4, 6, 5, 2, 4864638170690399653593343697756475289220677632000000⟩, + ⟨3, 6, 5, 6, 6, 2, -4595232021732541503631706959190926874357268480000000⟩, + ⟨3, 6, 6, 6, 7, 2, -9445609804674834113409711905091599861934981120000000⟩, + ⟨3, 6, 7, 6, 8, 2, -3454105179121480795773183050697292860610314240000000⟩, + ⟨3, 6, 4, 7, 4, 2, 20118262617085232689456777317175595966203428864000000⟩, + ⟨3, 6, 5, 7, 5, 2, 5196749519494795630892663534333959325016391680000000⟩, + ⟨3, 6, 6, 7, 6, 2, 10223170957107338392006603148862100628884684800000000⟩, + ⟨3, 6, 7, 7, 7, 2, 1220793514337633702217767518563881451855544320000000⟩, + ⟨3, 6, 8, 7, 8, 2, 8189213526090005574645276159654652903686144000000000⟩ +] + +def collectedFourData_13_7_12 : List CollectedFourTerm := [ + ⟨3, 7, 3, 2, 8, 3, 2614464832231432055227576464234086086081511424000000⟩, + ⟨3, 7, 3, 3, 7, 3, 6528029594801313085528432362754845078455530291200000⟩, + ⟨3, 7, 4, 3, 8, 3, 3792266488706904006637703656676034592317741465600000⟩, + ⟨3, 7, 3, 4, 6, 3, 14994965911119497311002161475234970371560885452800000⟩, + ⟨3, 7, 4, 4, 7, 3, 8641762314844960774389299843239564493794679193600000⟩, + ⟨3, 7, 5, 4, 8, 3, -18774193452502218633495797944678825929901867008000000⟩, + ⟨3, 7, 3, 5, 5, 3, 4928125182384526605178752338866843761359034777600000⟩, + ⟨3, 7, 4, 5, 6, 3, -7926905296484504204523454567989328354019691724800000⟩, + ⟨3, 7, 5, 5, 7, 3, 638668752504736730579406853803063825905221632000000⟩, + ⟨3, 7, 6, 5, 8, 3, -8814841075903191351567233970840974811633549312000000⟩, + ⟨3, 7, 3, 6, 4, 3, -23250941962438237398610912088767616587674314342400000⟩, + ⟨3, 7, 4, 6, 5, 3, 12862066932498126870312669067126409420129855078400000⟩, + ⟨3, 7, 5, 6, 6, 3, -6074879544997531286129545356857299997439295488000000⟩, + ⟨3, 7, 6, 6, 7, 3, -8324707221321536298849454029733149355014094848000000⟩, + ⟨3, 7, 7, 6, 8, 3, -2283157063634383015862841258374967040904527872000000⟩, + ⟨3, 7, 3, 7, 3, 3, 41438005704263985035815826381807519226353890099200000⟩, + ⟨3, 7, 4, 7, 4, 3, 53192535861264495332814435163238266417621814476800000⟩, + ⟨3, 7, 5, 7, 5, 3, 6870083427158913893858178086668502398987665408000000⟩, + ⟨3, 7, 6, 7, 6, 3, 9009995844769686103196041219956766624626769920000000⟩, + ⟨3, 7, 7, 7, 7, 3, 806942229885404089215539715767666176054788096000000⟩, + ⟨3, 7, 8, 7, 8, 3, 4330443860417267685737315077616323055384002560000000⟩ +] + +def collectedFourData_13_7_13 : List CollectedFourTerm := [ + ⟨3, 8, 2, 1, 8, 4, 2970305887200437842653427619607882679503657369600000⟩, + ⟨3, 8, 2, 2, 7, 4, 3610535039460407363848571734664170906559132467200000⟩, + ⟨3, 8, 3, 2, 8, 4, 1518796326700130817079893224990047764964442112000000⟩, + ⟨3, 8, 2, 3, 6, 4, 1434295468310909076726241513255131890464063488000000⟩, + ⟨3, 8, 3, 3, 7, 4, 3792266488706904006637703656676034592317741465600000⟩, + ⟨3, 8, 4, 3, 8, 4, 1101502751521081244399078932198769969139705446400000⟩, + ⟨3, 8, 2, 4, 5, 4, 666114398579569081401007634036119860253871308800000⟩, + ⟨3, 8, 3, 4, 6, 4, 8710883720460767351442242844597619712250504806400000⟩, + ⟨3, 8, 4, 4, 7, 4, 2510088622764139719879753179471655168113010278400000⟩, + ⟨3, 8, 5, 4, 8, 4, -3635438210386548655791424050490644391702560768000000⟩, + ⟨3, 8, 2, 5, 4, 4, -3531893954068337287247129092373016602176231833600000⟩, + ⟨3, 8, 3, 5, 5, 4, 2862849150713485739881420692754374296641260748800000⟩, + ⟨3, 8, 4, 5, 6, 4, -2302451059577831495257685545025142344155083571200000⟩, + ⟨3, 8, 5, 5, 7, 4, 123671932565826174013824106471968238492188672000000⟩, + ⟨3, 8, 6, 5, 8, 4, -1280180563291479834106735932507906392104894464000000⟩, + ⟨3, 8, 2, 6, 3, 4, -1782131014441578006784506529153218045146038272000000⟩, + ⟨3, 8, 3, 6, 4, 4, -13506949800785534071667944830311483136825045811200000⟩, + ⟨3, 8, 4, 6, 5, 4, 3735919445161645894455484487714735217253652889600000⟩, + ⟨3, 8, 5, 6, 6, 4, -1176340772095123709093460595112021960423374848000000⟩, + ⟨3, 8, 6, 6, 7, 4, -1208998357209304237246675639975071606223405056000000⟩, + ⟨3, 8, 7, 6, 8, 4, -265266567656810754727600787861954099556856627200000⟩, + ⟨3, 8, 2, 7, 2, 4, 8619443298349288487974323405905324755737850675200000⟩, + ⟨3, 8, 3, 7, 3, 4, 24072188722347339529470765072474566563829750169600000⟩, + ⟨3, 8, 4, 7, 4, 4, 15450318374525776935397608420442959810626007859200000⟩, + ⟨3, 8, 5, 7, 5, 4, 1330324195434777883114223267478051426473607168000000⟩, + ⟨3, 8, 6, 7, 6, 4, 1308522916804748277696322787093239421982474240000000⟩, + ⟨3, 8, 7, 7, 7, 4, 93753863467586777463505839815527518290155929600000⟩, + ⟨3, 8, 8, 7, 8, 4, 419273965561395088411039855002321322644602880000000⟩ +] + +def collectedFourData_13_7_14 : List CollectedFourTerm := [ + ⟨4, 3, 6, 5, 8, 0, 92584966463628192026801839405144607147578884096000000⟩, + ⟨4, 3, 6, 6, 7, 0, 87436940980425512954525132441968367207064797184000000⟩, + ⟨4, 3, 7, 6, 8, 0, 95922782202230917772882835365833916217299042304000000⟩, + ⟨4, 3, 6, 7, 6, 0, -94634736570104013332615105187541087455396495360000000⟩, + ⟨4, 3, 7, 7, 7, 0, -33902242206616497901268897259896417627796406272000000⟩, + ⟨4, 3, 8, 7, 8, 0, -454839736912984106752960060056662127961492684800000000⟩ +] + +def collectedFourData_13_7_15 : List CollectedFourTerm := [ + ⟨4, 4, 5, 4, 8, 1, -59013965180965603127368831143430579003607482368000000⟩, + ⟨4, 4, 5, 5, 7, 1, 2007562967636402525868058163027159078846595072000000⟩, + ⟨4, 4, 6, 5, 8, 1, -83124538848261050529464293852296211857257005056000000⟩, + ⟨4, 4, 5, 6, 6, 1, -19095506331818656392567134714931555599225192448000000⟩, + ⟨4, 4, 6, 6, 7, 1, -78502543932505161863584624756161981089813889024000000⟩, + ⟨4, 4, 7, 6, 8, 1, -43060646561529050969822697956053602669976092672000000⟩, + ⟨4, 4, 5, 7, 5, 1, 21595114867991801058497292127677270797234208768000000⟩, + ⟨4, 4, 6, 7, 6, 1, 84964861325589909894915617886715623418846248960000000⟩, + ⟨4, 4, 7, 7, 7, 1, 15219038019817917077806791718713551236676714496000000⟩, + ⟨4, 4, 8, 7, 8, 1, 136121247415148155641097657252622812585761177600000000⟩ +] + +def collectedFourData_13_7_16 : List CollectedFourTerm := [ + ⟨4, 5, 4, 3, 8, 2, 666114398579569081401007634036119860253871308800000⟩, + ⟨4, 5, 4, 4, 7, 2, 1517931908045673083633193462922249743150927052800000⟩, + ⟨4, 5, 5, 4, 8, 2, -6595401782902784778751151220900200618674618368000000⟩, + ⟨4, 5, 4, 5, 6, 2, -1392366746875280939772836592528818654979450470400000⟩, + ⟨4, 5, 5, 5, 7, 2, 224365272447569621655404125961391698526339072000000⟩, + ⟨4, 5, 6, 5, 8, 2, -4644999959260679149144738626154782922823958528000000⟩, + ⟨4, 5, 4, 6, 5, 2, 2259231518867376843671496117422495603897873203200000⟩, + ⟨4, 5, 5, 6, 6, 2, -2134114122311675428765502633209100078256488448000000⟩, + ⟨4, 5, 6, 6, 7, 2, -4386722842865725460161756986900447261477568512000000⟩, + ⟨4, 5, 7, 6, 8, 2, -1604152871465626235023275763956920710777012224000000⟩, + ⟨4, 5, 4, 7, 4, 2, 9343308055924665301082405759530978308402865766400000⟩, + ⟨4, 5, 5, 7, 5, 2, 2413470416122496276553165587358437405274144768000000⟩, + ⟨4, 5, 6, 7, 6, 2, 4747837195420551001918954110289455002136084480000000⟩, + ⟨4, 5, 7, 7, 7, 2, 566959985274511382908342191596399896226168832000000⟩, + ⟨4, 5, 8, 7, 8, 2, 3803228249194090135930122620840606028949094400000000⟩ +] + +def collectedFourData_13_7_17 : List CollectedFourTerm := [ + ⟨4, 6, 3, 2, 8, 3, 6005458533207566635420792637647664646985875456000000⟩, + ⟨4, 6, 3, 3, 7, 3, 14994965911119497311002161475234970371560885452800000⟩, + ⟨4, 6, 4, 3, 8, 3, 8710883720460767351442242844597619712250504806400000⟩, + ⟨4, 6, 3, 4, 6, 3, 34443624896354238063890720606718755907193484083200000⟩, + ⟨4, 6, 4, 4, 7, 3, 19850236498053328090399475591234736280996046438400000⟩, + ⟨4, 6, 5, 4, 8, 3, -43124557991162403279539840588638323534779645952000000⟩, + ⟨4, 6, 3, 5, 5, 3, 11319965395750424878781742849835859490325816934400000⟩, + ⟨4, 6, 4, 5, 6, 3, -18208200954866452902449614304197968007697478451200000⟩, + ⟨4, 6, 5, 5, 7, 3, 1467030140294151352055114877822556992813662208000000⟩, + ⟨4, 6, 6, 5, 8, 3, -20247800584477472896828672238006409917657776128000000⟩, + ⟨4, 6, 3, 6, 4, 3, -53407705505169458333882279289944283078800808345600000⟩, + ⟨4, 6, 4, 6, 5, 3, 29544329172915890328091246409029945805881579929600000⟩, + ⟨4, 6, 5, 6, 6, 3, -13954074559333794810018472427686027762253955072000000⟩, + ⟨4, 6, 6, 6, 7, 3, -19121956968941411781090727395874223002497318912000000⟩, + ⟨4, 6, 7, 6, 8, 3, -5244440430569350675157339034256419773919264768000000⟩, + ⟨4, 6, 3, 7, 3, 3, 95183619181972393128454715433089512367398374604800000⟩, + ⟨4, 6, 4, 7, 4, 3, 122183922481120253626360159853435246446168453939200000⟩, + ⟨4, 6, 5, 7, 5, 3, 15780667857087178863949214927894215757295255552000000⟩, + ⟨4, 6, 6, 7, 6, 3, 20696073537908309686838874478952471366970900480000000⟩, + ⟨4, 6, 7, 7, 7, 3, 1853556429800876935008516253620136770665447424000000⟩, + ⟨4, 6, 8, 7, 8, 3, 9947083897825068452038361274746573744127344640000000⟩ +] + +def collectedFourData_13_7_18 : List CollectedFourTerm := [ + ⟨4, 7, 2, 1, 8, 4, 6768690321740399897612811087403760615106910617600000⟩, + ⟨4, 7, 2, 2, 7, 4, 8227635302885935629461743648633662946319479603200000⟩, + ⟨4, 7, 3, 2, 8, 4, 3461011218248421548444030752518038773586460672000000⟩, + ⟨4, 7, 2, 3, 6, 4, 3268451877871204333984752603512422966574972928000000⟩, + ⟨4, 7, 3, 3, 7, 4, 8641762314844960774389299843239564493794679193600000⟩, + ⟨4, 7, 4, 3, 8, 4, 2510088622764139719879753179471655168113010278400000⟩, + ⟨4, 7, 2, 4, 5, 4, 1517931908045673083633193462922249743150927052800000⟩, + ⟨4, 7, 3, 4, 6, 4, 19850236498053328090399475591234736280996046438400000⟩, + ⟨4, 7, 4, 4, 7, 4, 5719953840723013366610776720551280717165127270400000⟩, + ⟨4, 7, 5, 4, 8, 4, -8284384290508652087150300136630693252833476608000000⟩, + ⟨4, 7, 2, 5, 4, 4, -8048429128909637217904786609394510331570133401600000⟩, + ⟨4, 7, 3, 5, 5, 4, 6523819456622002140626775592805390968876223692800000⟩, + ⟨4, 7, 4, 5, 6, 4, -5246792349031135720736386810952540324088722227200000⟩, + ⟨4, 7, 5, 5, 7, 4, 281821820653702676340101726004985625975980032000000⟩, + ⟨4, 7, 6, 5, 8, 4, -2917257049575542353355422826695749711937142784000000⟩, + ⟨4, 7, 2, 6, 3, 4, -4061094516057871877861451944560603151185477632000000⟩, + ⟨4, 7, 3, 6, 4, 4, -30779442880537610363706007940907771394184655667200000⟩, + ⟨4, 7, 4, 6, 5, 4, 8513359482683137480000392086113659150734563737600000⟩, + ⟨4, 7, 5, 6, 6, 4, -2680628427348093509442123275994981257957081088000000⟩, + ⟨4, 7, 6, 6, 7, 4, -2755048062459179488419423891229751905496334336000000⟩, + ⟨4, 7, 7, 6, 8, 4, -604485637966480637957823464182827141167264563200000⟩, + ⟨4, 7, 2, 7, 2, 4, 19641863379705851311819511657080952121522860851200000⟩, + ⟨4, 7, 3, 7, 3, 4, 54855357332113636974029253396348670387418667417600000⟩, + ⟨4, 7, 4, 7, 4, 4, 35207963226988508896550648417432095911172059955200000⟩, + ⟨4, 7, 5, 7, 5, 4, 3031523637083520780343783443725999366637355008000000⟩, + ⟨4, 7, 6, 7, 6, 4, 2981843196998028213574923442255037839379005440000000⟩, + ⟨4, 7, 7, 7, 7, 4, 213644955226122451824675492680202184616941977600000⟩, + ⟨4, 7, 8, 7, 8, 4, 955435480595546905985378977593196660685537280000000⟩ +] + +def collectedFourData_13_7_19 : List CollectedFourTerm := [ + ⟨4, 8, 1, 0, 8, 5, 5100100956065793193627252888841126626046509056000000⟩, + ⟨4, 8, 1, 1, 7, 5, 53483201703467546625053948026999072156922413056000000⟩, + ⟨4, 8, 2, 1, 8, 5, -29409904343733063156558981423787413183142035456000000⟩, + ⟨4, 8, 1, 2, 6, 5, 63421133926871999099205304859421959403721457664000000⟩, + ⟨4, 8, 2, 2, 7, 5, -35749008409470121013465678439759657543760084992000000⟩, + ⟨4, 8, 3, 2, 8, 5, -7519032783516447372780331946725790525329244160000000⟩, + ⟨4, 8, 1, 3, 5, 5, 52395640624310247532519103466012244064625229824000000⟩, + ⟨4, 8, 2, 3, 6, 5, -14201396800728609792478291156448741238169927680000000⟩, + ⟨4, 8, 3, 3, 7, 5, -18774193452502218633495797944678825929901867008000000⟩, + ⟨4, 8, 4, 3, 8, 5, -3635438210386548655791424050490644391702560768000000⟩, + ⟨4, 8, 1, 4, 4, 5, -59013965180965603127368831143430579003607482368000000⟩, + ⟨4, 8, 2, 4, 5, 5, -6595401782902784778751151220900200618674618368000000⟩, + ⟨4, 8, 3, 4, 6, 5, -43124557991162403279539840588638323534779645952000000⟩, + ⟨4, 8, 4, 4, 7, 5, -8284384290508652087150300136630693252833476608000000⟩, + ⟨4, 8, 5, 4, 8, 5, 8998895574673655990511614145027007067581317120000000⟩, + ⟨4, 8, 1, 5, 3, 5, -112701634299585400141553952576230889233798135808000000⟩, + ⟨4, 8, 2, 5, 4, 5, 34970359042469067196886585588208636060286058496000000⟩, + ⟨4, 8, 3, 5, 5, 5, -14172971214149476500848157626543955871619088384000000⟩, + ⟨4, 8, 4, 5, 6, 5, 7599090014051631876572531642747216463233286144000000⟩, + ⟨4, 8, 5, 5, 7, 5, -306128379103882072520566830329879285181972480000000⟩, + ⟨4, 8, 6, 5, 8, 5, 2535091626175542833598238275212961519771844608000000⟩, + ⟨4, 8, 1, 6, 2, 5, 280843294880528306726731353887872134589691461632000000⟩, + ⟨4, 8, 2, 6, 3, 5, 17645422610708364692930613215347507862616145920000000⟩, + ⟨4, 8, 3, 6, 4, 5, 66868214369515719392597324402971274426676412416000000⟩, + ⟨4, 8, 4, 6, 5, 5, -12330159214864954108085356998288509982895767552000000⟩, + ⟨4, 8, 5, 6, 6, 5, 2911827173426071675954507231825367054753464320000000⟩, + ⟨4, 8, 6, 6, 7, 5, 2394132280481635166512157584655005161810296832000000⟩, + ⟨4, 8, 7, 6, 8, 5, 437747529303017766601168275884120700125970432000000⟩, + ⟨4, 8, 1, 7, 1, 5, -803654024588698865658608456376453144186697285632000000⟩, + ⟨4, 8, 2, 7, 2, 5, -85343736479480460364308381270605078765997391872000000⟩, + ⟨4, 8, 3, 7, 3, 5, -119173040513983855284029941230925133438389321728000000⟩, + ⟨4, 8, 4, 7, 4, 5, -50992771197188796879650278622590098669991624704000000⟩, + ⟨4, 8, 5, 7, 5, 5, -3292986380837542856368513540194235202005893120000000⟩, + ⟨4, 8, 6, 7, 6, 5, -2591216883125905098780894091933310130617057280000000⟩, + ⟨4, 8, 7, 7, 7, 5, -154714265193964592065337487555992660975026176000000⟩, + ⟨4, 8, 8, 7, 8, 5, -593051340706011969315848469733641543902822400000000⟩ +] + +def collectedFourData_13_7_20 : List CollectedFourTerm := [ + ⟨5, 2, 6, 5, 8, 0, -156256407191380174169347369415427102817325678592000000⟩, + ⟨5, 2, 6, 6, 7, 0, -147568042364343907592508773816623385050211155968000000⟩, + ⟨5, 2, 7, 6, 8, 0, -161889666186897515500741998602168513856125534208000000⟩, + ⟨5, 2, 6, 7, 6, 0, 159715821010275164693814105834655488336954654720000000⟩, + ⟨5, 2, 7, 7, 7, 0, 57217092204909440645212341220687589409338425344000000⟩, + ⟨5, 2, 8, 7, 8, 0, 767636754135627546546222316093334685818132889600000000⟩ +] + +def collectedFourData_13_7_21 : List CollectedFourTerm := [ + ⟨5, 3, 5, 4, 8, 1, -112701634299585400141553952576230889233798135808000000⟩, + ⟨5, 3, 5, 5, 7, 1, 3833933658213579119905512276932445730171256832000000⟩, + ⟨5, 3, 6, 5, 8, 1, -158746685633997088239004514416816847717752897536000000⟩, + ⟨5, 3, 5, 6, 6, 1, -36467550769968961631114840165727692833620492288000000⟩, + ⟨5, 3, 6, 6, 7, 1, -149919853220131825286814496108446006921809362944000000⟩, + ⟨5, 3, 7, 6, 8, 1, -82234861301040615383488893927109034726425362432000000⟩, + ⟨5, 3, 5, 7, 5, 1, 41241166070551587494457820266046986272750174208000000⟩, + ⟨5, 3, 6, 7, 6, 1, 162261232575508509215591425447314024409344245760000000⟩, + ⟨5, 3, 7, 7, 7, 1, 29064484178301412609198858912106102047874482176000000⟩, + ⟨5, 3, 8, 7, 8, 1, 259956893246236816896651016470601954666060185600000000⟩ +] + +def collectedFourData_13_7_22 : List CollectedFourTerm := [ + ⟨5, 4, 4, 3, 8, 2, -3531893954068337287247129092373016602176231833600000⟩, + ⟨5, 4, 4, 4, 7, 2, -8048429128909637217904786609394510331570133401600000⟩, + ⟨5, 4, 5, 4, 8, 2, 34970359042469067196886585588208636060286058496000000⟩, + ⟨5, 4, 4, 5, 6, 2, 7382653348465598081994028087501827614660414668800000⟩, + ⟨5, 4, 5, 5, 7, 2, -1189637021734200086909393526800223887041757184000000⟩, + ⟨5, 4, 6, 5, 8, 2, 24628873520440451568041009462671831028534870016000000⟩, + ⟨5, 4, 4, 6, 5, 2, -11978972619933780200023127619580173852449597030400000⟩, + ⟨5, 4, 5, 6, 6, 2, 11315570991945902113546311524682053419328864256000000⟩, + ⟨5, 4, 6, 6, 7, 2, 23259427990040952712531991957705986616133156864000000⟩, + ⟨5, 4, 7, 6, 8, 2, 8505592793388665458380986408467919882711728128000000⟩, + ⟨5, 4, 4, 7, 4, 2, -49540399222846751787218076739172527927586507980800000⟩, + ⟨5, 4, 5, 7, 5, 2, -12796783239039398209940469704238912919144759296000000⟩, + ⟨5, 4, 6, 7, 6, 2, -25174140539770259368508258376373010264815042560000000⟩, + ⟨5, 4, 7, 7, 7, 2, -3006154120763272119887223477794493948865019904000000⟩, + ⟨5, 4, 8, 7, 8, 2, -20165603517825708848033392158920462603963596800000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1316.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1316.lean new file mode 100644 index 0000000000000000000000000000000000000000..0f494aa18105c6df7ece43be41695a1dc66b1865 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1316.lean @@ -0,0 +1,653 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1316. -/ +namespace LaughlinFock +def collectedFourData_13_7_23 : List CollectedFourTerm := [ + ⟨5, 5, 3, 2, 8, 3, 1973705815984525475828327060021759648414564352000000⟩, + ⟨5, 5, 3, 3, 7, 3, 4928125182384526605178752338866843761359034777600000⟩, + ⟨5, 5, 4, 3, 8, 3, 2862849150713485739881420692754374296641260748800000⟩, + ⟨5, 5, 3, 4, 6, 3, 11319965395750424878781742849835859490325816934400000⟩, + ⟨5, 5, 4, 4, 7, 3, 6523819456622002140626775592805390968876223692800000⟩, + ⟨5, 5, 5, 4, 8, 3, -14172971214149476500848157626543955871619088384000000⟩, + ⟨5, 5, 3, 5, 5, 3, 3720328999824594745300456126773848427792747724800000⟩, + ⟨5, 5, 4, 5, 6, 3, -5984161230073519873010205140404735823902565990400000⟩, + ⟨5, 5, 5, 5, 7, 3, 482142355011259589783823873100209135430926336000000⟩, + ⟨5, 5, 6, 5, 8, 3, -6654479679361531700108118967439831550683774976000000⟩, + ⟨5, 5, 3, 6, 4, 3, -17552547967996833693994405996820600254046090035200000⟩, + ⟨5, 5, 4, 6, 5, 3, 9709802173390503871408136084686884569007469363200000⟩, + ⟨5, 5, 5, 6, 6, 3, -4586034182427166807089696758578428368255975424000000⟩, + ⟨5, 5, 6, 6, 7, 3, -6284468950024976641513176517604503870928584704000000⟩, + ⟨5, 5, 7, 6, 8, 3, -1723595712494341093775006885985635711745785856000000⟩, + ⟨5, 5, 3, 7, 3, 3, 31282284562803423639643979736590141931484977561600000⟩, + ⟨5, 5, 4, 7, 4, 3, 40155987604827645136082917369787977590590826086400000⟩, + ⟨5, 5, 5, 7, 5, 3, 5186347679769502569404721643203599614643011584000000⟩, + ⟨5, 5, 6, 7, 6, 3, 6801805471462613050886535792738740379750236160000000⟩, + ⟨5, 5, 7, 7, 7, 3, 609174983979039194365377969686536445239492608000000⟩, + ⟨5, 5, 8, 7, 8, 3, 3269128782200984169561819284936767010903162880000000⟩ +] + +def collectedFourData_13_7_24 : List CollectedFourTerm := [ + ⟨5, 6, 2, 1, 8, 4, -6208776081413202191409476237159971730905418956800000⟩, + ⟨5, 6, 2, 2, 7, 4, -7547035371240651582563567114249074051454179737600000⟩, + ⟨5, 6, 3, 2, 8, 4, -3174712189202105360438446267938993816150736896000000⟩, + ⟨5, 6, 2, 3, 6, 4, -2998081590082102803832680178757761689037307904000000⟩, + ⟨5, 6, 3, 3, 7, 4, -7926905296484504204523454567989328354019691724800000⟩, + ⟨5, 6, 4, 3, 8, 4, -2302451059577831495257685545025142344155083571200000⟩, + ⟨5, 6, 2, 4, 5, 4, -1392366746875280939772836592528818654979450470400000⟩, + ⟨5, 6, 3, 4, 6, 4, -18208200954866452902449614304197968007697478451200000⟩, + ⟨5, 6, 4, 4, 7, 4, -5246792349031135720736386810952540324088722227200000⟩, + ⟨5, 6, 5, 4, 8, 4, 7599090014051631876572531642747216463233286144000000⟩, + ⟨5, 6, 2, 5, 4, 4, 7382653348465598081994028087501827614660414668800000⟩, + ⟨5, 6, 3, 5, 5, 4, -5984161230073519873010205140404735823902565990400000⟩, + ⟨5, 6, 4, 5, 6, 4, 4812771347534504773026754454862338105540188569600000⟩, + ⟨5, 6, 5, 5, 7, 4, -258509179194524149219033098097601712148709376000000⟩, + ⟨5, 6, 6, 5, 8, 4, 2675938022243788117635974142170323511213555712000000⟩, + ⟨5, 6, 2, 6, 3, 4, 3725155871686441341418912892716907649539506176000000⟩, + ⟨5, 6, 3, 6, 4, 4, 28233330182369534663097408158365078727603886489600000⟩, + ⟨5, 6, 4, 6, 5, 4, -7809124101716081715390099816796132303497383116800000⟩, + ⟨5, 6, 5, 6, 6, 4, 2458883605506078169586841821117259842567798784000000⟩, + ⟨5, 6, 6, 6, 7, 4, 2527147158498173526651781049343911184404840448000000⟩, + ⟨5, 6, 7, 6, 8, 4, 554481855745331999472849690185797056171973017600000⟩, + ⟨5, 6, 2, 7, 2, 4, -18017064712593716926223027294752486265120725401600000⟩, + ⟨5, 6, 3, 7, 3, 4, -50317655905615228839749885029921746800394161356800000⟩, + ⟨5, 6, 4, 7, 4, 4, -32295517975890307695539996919468370010312382873600000⟩, + ⟨5, 6, 5, 7, 5, 4, -2780752339593414807504815807967101538841657344000000⟩, + ⟨5, 6, 6, 7, 6, 4, -2735181525528224058722248412011453931763793920000000⟩, + ⟨5, 6, 7, 7, 7, 4, -195971986436140272970960134006745928173407436800000⟩, + ⟨5, 6, 8, 7, 8, 4, -876400703427346577855444452434196567204823040000000⟩ +] + +def collectedFourData_13_7_25 : List CollectedFourTerm := [ + ⟨5, 7, 1, 0, 8, 5, -173497472661049342819926151174050546318311424000000⟩, + ⟨5, 7, 1, 1, 7, 5, -1819415028311655873469679178405132072778727424000000⟩, + ⟨5, 7, 2, 1, 8, 5, 1000479033414466928943575123727721657767297024000000⟩, + ⟨5, 7, 1, 2, 6, 5, -2157487968257441606398590020103511048722579456000000⟩, + ⟨5, 7, 2, 2, 7, 5, 1216125457635284620668865891953551271020986368000000⟩, + ⟨5, 7, 3, 2, 8, 5, 255785757190577779600628678224737217428848640000000⟩, + ⟨5, 7, 1, 3, 5, 5, -1782417898210947204240782592418450418587140096000000⟩, + ⟨5, 7, 2, 3, 6, 5, 483109349090959499110001493627225288443166720000000⟩, + ⟨5, 7, 3, 3, 7, 5, 638668752504736730579406853803063825905221632000000⟩, + ⟨5, 7, 4, 3, 8, 5, 123671932565826174013824106471968238492188672000000⟩, + ⟨5, 7, 1, 4, 4, 5, 2007562967636402525868058163027159078846595072000000⟩, + ⟨5, 7, 2, 4, 5, 5, 224365272447569621655404125961391698526339072000000⟩, + ⟨5, 7, 3, 4, 6, 5, 1467030140294151352055114877822556992813662208000000⟩, + ⟨5, 7, 4, 4, 7, 5, 281821820653702676340101726004985625975980032000000⟩, + ⟨5, 7, 5, 4, 8, 5, -306128379103882072520566830329879285181972480000000⟩, + ⟨5, 7, 1, 5, 3, 5, 3833933658213579119905512276932445730171256832000000⟩, + ⟨5, 7, 2, 5, 4, 5, -1189637021734200086909393526800223887041757184000000⟩, + ⟨5, 7, 3, 5, 5, 5, 482142355011259589783823873100209135430926336000000⟩, + ⟨5, 7, 4, 5, 6, 5, -258509179194524149219033098097601712148709376000000⟩, + ⟨5, 7, 5, 5, 7, 5, 10414009554296743973424114149150154471505920000000⟩, + ⟨5, 7, 6, 5, 8, 5, -86239859542884775701165430050303065595052032000000⟩, + ⟨5, 7, 1, 6, 2, 5, -9553850462042677341924652482257108675673980928000000⟩, + ⟨5, 7, 2, 6, 3, 5, -600269730612474323234040367788639798354247680000000⟩, + ⟨5, 7, 3, 6, 4, 5, -2274752263613539560539899769470694696486436864000000⟩, + ⟨5, 7, 4, 6, 5, 5, 419452767644355012615018233944002113052868608000000⟩, + ⟨5, 7, 5, 6, 6, 5, -99055814731341419287170199079180121176801280000000⟩, + ⟨5, 7, 6, 6, 7, 5, -81444642656685424112671370815719231065161728000000⟩, + ⟨5, 7, 7, 6, 8, 5, -14891487570920245626220816072760076300976128000000⟩, + ⟨5, 7, 1, 7, 1, 5, 27339055316971128210335113259653331649118076928000000⟩, + ⟨5, 7, 2, 7, 2, 5, 2903260683306647443524456106645033656294309888000000⟩, + ⟨5, 7, 3, 7, 3, 5, 4054080794992464602398555342432645073193664512000000⟩, + ⟨5, 7, 4, 7, 4, 5, 1734694470346338878362725310165506178066415616000000⟩, + ⟨5, 7, 5, 7, 5, 5, 112022255932613563986101776290285261139476480000000⟩, + ⟨5, 7, 6, 7, 6, 5, 88149153166133246194967005019691392560005120000000⟩, + ⟨5, 7, 7, 7, 7, 5, 5263137774525640403715001784000847129083904000000⟩, + ⟨5, 7, 8, 7, 8, 5, 20174680787125307687895748379543653161369600000000⟩ +] + +def collectedFourData_13_7_26 : List CollectedFourTerm := [ + ⟨5, 8, 0, 0, 7, 6, 62431511331648812542017271278187748429458833408000000⟩, + ⟨5, 8, 1, 0, 8, 6, 7183783342680442947325989934199255971557015552000000⟩, + ⟨5, 8, 0, 1, 6, 6, 7854604778211357088886240169996668814432927744000000⟩, + ⟨5, 8, 1, 1, 7, 6, 75334142759199133516311051401318831777541783552000000⟩, + ⟨5, 8, 2, 1, 8, 6, -20712764585871196363141134633495249753710002176000000⟩, + ⟨5, 8, 0, 2, 5, 6, -37988391660070389847422873783858730764362317824000000⟩, + ⟨5, 8, 1, 2, 6, 6, 89332287615973051355963007528568547664029810688000000⟩, + ⟨5, 8, 2, 2, 7, 6, -25177259562269491122070677038998775077149868032000000⟩, + ⟨5, 8, 3, 2, 8, 6, -3530328969864206533523187145859079900223242240000000⟩, + ⟨5, 8, 0, 3, 4, 6, 24124818949840997788951659687553828264259616768000000⟩, + ⟨5, 8, 1, 3, 5, 6, 73802250894332099337805438805594483604647313408000000⟩, + ⟨5, 8, 2, 3, 6, 6, -10001739049746903488300161370358812805200609280000000⟩, + ⟨5, 8, 3, 3, 7, 6, -8814841075903191351567233970840974811633549312000000⟩, + ⟨5, 8, 4, 3, 8, 6, -1280180563291479834106735932507906392104894464000000⟩, + ⟨5, 8, 0, 4, 3, 6, 92584966463628192026801839405144607147578884096000000⟩, + ⟨5, 8, 1, 4, 4, 6, -83124538848261050529464293852296211857257005056000000⟩, + ⟨5, 8, 2, 4, 5, 6, -4644999959260679149144738626154782922823958528000000⟩, + ⟨5, 8, 3, 4, 6, 6, -20247800584477472896828672238006409917657776128000000⟩, + ⟨5, 8, 4, 4, 7, 6, -2917257049575542353355422826695749711937142784000000⟩, + ⟨5, 8, 5, 4, 8, 6, 2535091626175542833598238275212961519771844608000000⟩, + ⟨5, 8, 0, 5, 2, 6, -156256407191380174169347369415427102817325678592000000⟩, + ⟨5, 8, 1, 5, 3, 6, -158746685633997088239004514416816847717752897536000000⟩, + ⟨5, 8, 2, 5, 4, 6, 24628873520440451568041009462671831028534870016000000⟩, + ⟨5, 8, 3, 5, 5, 6, -6654479679361531700108118967439831550683774976000000⟩, + ⟨5, 8, 4, 5, 6, 6, 2675938022243788117635974142170323511213555712000000⟩, + ⟨5, 8, 5, 5, 7, 6, -86239859542884775701165430050303065595052032000000⟩, + ⟨5, 8, 6, 5, 8, 6, 595136879092189917365687941860807852850937856000000⟩, + ⟨5, 8, 0, 6, 1, 6, 113577208860869557473485026947716489301542830080000000⟩, + ⟨5, 8, 1, 6, 2, 6, 395583813153090894797891073348043029451263442944000000⟩, + ⟨5, 8, 2, 6, 3, 6, 12427292529827358768643172946961437873741496320000000⟩, + ⟨5, 8, 3, 6, 4, 6, 31395899066872978259039324173126716238514356224000000⟩, + ⟨5, 8, 4, 6, 5, 6, -4341933284428200804679496802586499592430288896000000⟩, + ⟨5, 8, 5, 6, 6, 6, 820294959861286397350362073345212965965529088000000⟩, + ⟨5, 8, 6, 6, 7, 6, 562045331548519263186635753792951329147060224000000⟩, + ⟨5, 8, 7, 6, 8, 6, 88084626346364385825911766767709470475681792000000⟩, + ⟨5, 8, 0, 7, 0, 6, -1107751392425692741707806631295937531856115728384000000⟩, + ⟨5, 8, 1, 7, 1, 6, -1131992571294488041751294502688298941972368850944000000⟩, + ⟨5, 8, 2, 7, 2, 6, -60105762396156369285666366534379599634221760512000000⟩, + ⟨5, 8, 3, 7, 3, 6, -55954010238609259240314367772535302009118523392000000⟩, + ⟨5, 8, 4, 7, 4, 6, -17956557305390047987321580987846006535295598592000000⟩, + ⟨5, 8, 5, 7, 5, 6, -927671860385389801158603546942303769102123008000000⟩, + ⟨5, 8, 6, 7, 6, 6, -608312817158805935494978775916433443347496960000000⟩, + ⟨5, 8, 7, 7, 7, 6, -31131982085109968285931773834995682462662656000000⟩, + ⟨5, 8, 8, 7, 8, 6, -104418333563846240397398573252853007751577600000000⟩ +] + +def collectedFourData_13_7_27 : List CollectedFourTerm := [ + ⟨6, 1, 6, 5, 8, 0, 113577208860869557473485026947716489301542830080000000⟩, + ⟨6, 1, 6, 6, 7, 0, 107261946374313631342675367750578115612843704320000000⟩, + ⟨6, 1, 7, 6, 8, 0, 117671823891391903894195653432460723594639441920000000⟩, + ⟨6, 1, 6, 7, 6, 0, -116091733371621840248835877804521294138232012800000000⟩, + ⟨6, 1, 7, 7, 7, 0, -41589063441150984629880830626766731614942658560000000⟩, + ⟨6, 1, 8, 7, 8, 0, -557967775663484779925657890518822085044731904000000000⟩ +] + +def collectedFourData_13_7_28 : List CollectedFourTerm := [ + ⟨6, 2, 5, 4, 8, 1, 280843294880528306726731353887872134589691461632000000⟩, + ⟨6, 2, 5, 5, 7, 1, -9553850462042677341924652482257108675673980928000000⟩, + ⟨6, 2, 6, 5, 8, 1, 395583813153090894797891073348043029451263442944000000⟩, + ⟨6, 2, 5, 6, 6, 1, 90874166804329177406500661408895852382154391552000000⟩, + ⟨6, 2, 6, 6, 7, 1, 373588065585858970880365368279409610335218302976000000⟩, + ⟨6, 2, 7, 6, 8, 1, 204922577612634106221382387185800774728525283328000000⟩, + ⟨6, 2, 5, 7, 5, 1, -102769627396710844586063687786498301121875935232000000⟩, + ⟨6, 2, 6, 7, 6, 1, -404341777926188971548329384896370602947945431040000000⟩, + ⟨6, 2, 7, 7, 7, 1, -72426327722447065052433339651478153704719253504000000⟩, + ⟨6, 2, 8, 7, 8, 1, -647791408526606237684865550316995228511659622400000000⟩ +] + +def collectedFourData_13_7_29 : List CollectedFourTerm := [ + ⟨6, 3, 4, 3, 8, 2, -1782131014441578006784506529153218045146038272000000⟩, + ⟨6, 3, 4, 4, 7, 2, -4061094516057871877861451944560603151185477632000000⟩, + ⟨6, 3, 5, 4, 8, 2, 17645422610708364692930613215347507862616145920000000⟩, + ⟨6, 3, 4, 5, 6, 2, 3725155871686441341418912892716907649539506176000000⟩, + ⟨6, 3, 5, 5, 7, 2, -600269730612474323234040367788639798354247680000000⟩, + ⟨6, 3, 6, 5, 8, 2, 12427292529827358768643172946961437873741496320000000⟩, + ⟨6, 3, 4, 6, 5, 2, -6044377012661977235971295647889228540839723008000000⟩, + ⟨6, 3, 5, 6, 6, 2, 5709636323489700844369158644999617476946821120000000⟩, + ⟨6, 3, 6, 6, 7, 2, 11736294616511719387109106297844870252100321280000000⟩, + ⟨6, 3, 7, 6, 8, 2, 4291771188613504328664019216299974227195330560000000⟩, + ⟨6, 3, 4, 7, 4, 2, -24997206334905830868445840513996244886189244416000000⟩, + ⟨6, 3, 5, 7, 5, 2, -6457029738706874339455925350374035683194961920000000⟩, + ⟨6, 3, 6, 7, 6, 2, -12702424591813658179682041537060934958396211200000000⟩, + ⟨6, 3, 7, 7, 7, 2, -1516852024006132600104201016741838964475822080000000⟩, + ⟨6, 3, 8, 7, 8, 2, -10175205688906150730272245592345743496052736000000000⟩ +] + +def collectedFourData_13_7_30 : List CollectedFourTerm := [ + ⟨6, 4, 3, 2, 8, 3, -9311963004190242972091722785491445105502978048000000⟩, + ⟨6, 4, 3, 3, 7, 3, -23250941962438237398610912088767616587674314342400000⟩, + ⟨6, 4, 4, 3, 8, 3, -13506949800785534071667944830311483136825045811200000⟩, + ⟨6, 4, 3, 4, 6, 3, -53407705505169458333882279289944283078800808345600000⟩, + ⟨6, 4, 4, 4, 7, 3, -30779442880537610363706007940907771394184655667200000⟩, + ⟨6, 4, 5, 4, 8, 3, 66868214369515719392597324402971274426676412416000000⟩, + ⟨6, 4, 3, 5, 5, 3, -17552547967996833693994405996820600254046090035200000⟩, + ⟨6, 4, 4, 5, 6, 3, 28233330182369534663097408158365078727603886489600000⟩, + ⟨6, 4, 5, 5, 7, 3, -2274752263613539560539899769470694696486436864000000⟩, + ⟨6, 4, 6, 5, 8, 3, 31395899066872978259039324173126716238514356224000000⟩, + ⟨6, 4, 3, 6, 4, 3, 82813089966870033990543841471430240667481984204800000⟩, + ⟨6, 4, 4, 6, 5, 3, -45810939950803331582702079446356380897684278476800000⟩, + ⟨6, 4, 5, 6, 6, 3, 21636953337654068382478803375265589519110373376000000⟩, + ⟨6, 4, 6, 6, 7, 3, 29650184890610722056863056709254449701213700096000000⟩, + ⟨6, 4, 7, 6, 8, 3, 8131941132737719365995121570254059288966201344000000⟩, + ⟨6, 4, 3, 7, 3, 3, -147590119143501027770258495830175677697573152358400000⟩, + ⟨6, 4, 4, 7, 4, 3, -189456335358850026499517881167151502769755101593600000⟩, + ⟨6, 4, 5, 7, 5, 3, -24469238186234418629516455750808781090472329216000000⟩, + ⟨6, 4, 6, 7, 6, 3, -32090983569587464238613826085644550985838755840000000⟩, + ⟨6, 4, 7, 7, 7, 3, -2874093427678014288777226111951695679944916992000000⟩, + ⟨6, 4, 8, 7, 8, 3, -15423781005886108574460424125995550338313093120000000⟩ +] + +def collectedFourData_13_7_31 : List CollectedFourTerm := [ + ⟨6, 5, 2, 1, 8, 4, 10074258558815640138696277799103922936903788134400000⟩, + ⟨6, 5, 2, 2, 7, 4, 12245696202511439509243475797303142389803437260800000⟩, + ⟨6, 5, 3, 2, 8, 4, 5151236092986286223783488853489069772156960768000000⟩, + ⟨6, 5, 2, 3, 6, 4, 4864638170690399653593343697756475289220677632000000⟩, + ⟨6, 5, 3, 3, 7, 4, 12862066932498126870312669067126409420129855078400000⟩, + ⟨6, 5, 4, 3, 8, 4, 3735919445161645894455484487714735217253652889600000⟩, + ⟨6, 5, 2, 4, 5, 4, 2259231518867376843671496117422495603897873203200000⟩, + ⟨6, 5, 3, 4, 6, 4, 29544329172915890328091246409029945805881579929600000⟩, + ⟨6, 5, 4, 4, 7, 4, 8513359482683137480000392086113659150734563737600000⟩, + ⟨6, 5, 5, 4, 8, 4, -12330159214864954108085356998288509982895767552000000⟩, + ⟨6, 5, 2, 5, 4, 4, -11978972619933780200023127619580173852449597030400000⟩, + ⟨6, 5, 3, 5, 5, 4, 9709802173390503871408136084686884569007469363200000⟩, + ⟨6, 5, 4, 5, 6, 4, -7809124101716081715390099816796132303497383116800000⟩, + ⟨6, 5, 5, 5, 7, 4, 419452767644355012615018233944002113052868608000000⟩, + ⟨6, 5, 6, 5, 8, 4, -4341933284428200804679496802586499592430288896000000⟩, + ⟨6, 5, 2, 6, 3, 4, -6044377012661977235971295647889228540839723008000000⟩, + ⟨6, 5, 3, 6, 4, 4, -45810939950803331582702079446356380897684278476800000⟩, + ⟨6, 5, 4, 6, 5, 4, 12670957091540030131654606245703971230380877414400000⟩, + ⟨6, 5, 5, 6, 6, 4, -3989744336578289459972634760846461381138972672000000⟩, + ⟨6, 5, 6, 6, 7, 4, -4100507661582796737592112612743602098493456384000000⟩, + ⟨6, 5, 7, 6, 8, 4, -899693193586543650836994906100873300164791500800000⟩, + ⟨6, 5, 2, 7, 2, 4, 29234194631201561446101684424835035185768352972800000⟩, + ⟨6, 5, 3, 7, 3, 4, 81644605799876780771671439742773780980542367334400000⟩, + ⟨6, 5, 4, 7, 4, 4, 52402179449503100118163703144505932891804191948800000⟩, + ⟨6, 5, 5, 7, 5, 4, 4512003282089567910943175544508322602027057152000000⟩, + ⟨6, 5, 6, 7, 6, 4, 4438060824251090280989044109764382898373263360000000⟩, + ⟨6, 5, 7, 7, 7, 4, 317980941131479381815627568680683211057423974400000⟩, + ⟨6, 5, 8, 7, 8, 4, 1422033452597210269019922498240334564499128320000000⟩ +] + +def collectedFourData_13_7_32 : List CollectedFourTerm := [ + ⟨6, 6, 1, 0, 8, 5, 1650270572411572880623399038963654948254908416000000⟩, + ⟨6, 6, 1, 1, 7, 5, 17305883677579183314255394618846348506789052416000000⟩, + ⟨6, 6, 2, 1, 8, 5, -9516340969324893367126083323598459289328418816000000⟩, + ⟨6, 6, 1, 2, 6, 5, 20521560629895087883601106095614216408613781504000000⟩, + ⟨6, 6, 2, 2, 7, 5, -11567523286156950516052309780082143407491776512000000⟩, + ⟨6, 6, 3, 2, 8, 5, -2432979002283694460441861605724636904696053760000000⟩, + ⟨6, 6, 1, 3, 5, 5, 16953974948694344608235752383135423612284043264000000⟩, + ⟨6, 6, 2, 3, 6, 5, -4595232021732541503631706959190926874357268480000000⟩, + ⟨6, 6, 3, 3, 7, 5, -6074879544997531286129545356857299997439295488000000⟩, + ⟨6, 6, 4, 3, 8, 5, -1176340772095123709093460595112021960423374848000000⟩, + ⟨6, 6, 1, 4, 4, 5, -19095506331818656392567134714931555599225192448000000⟩, + ⟨6, 6, 2, 4, 5, 5, -2134114122311675428765502633209100078256488448000000⟩, + ⟨6, 6, 3, 4, 6, 5, -13954074559333794810018472427686027762253955072000000⟩, + ⟨6, 6, 4, 4, 7, 5, -2680628427348093509442123275994981257957081088000000⟩, + ⟨6, 6, 5, 4, 8, 5, 2911827173426071675954507231825367054753464320000000⟩, + ⟨6, 6, 1, 5, 3, 5, -36467550769968961631114840165727692833620492288000000⟩, + ⟨6, 6, 2, 5, 4, 5, 11315570991945902113546311524682053419328864256000000⟩, + ⟨6, 6, 3, 5, 5, 5, -4586034182427166807089696758578428368255975424000000⟩, + ⟨6, 6, 4, 5, 6, 5, 2458883605506078169586841821117259842567798784000000⟩, + ⟨6, 6, 5, 5, 7, 5, -99055814731341419287170199079180121176801280000000⟩, + ⟨6, 6, 6, 5, 8, 5, 820294959861286397350362073345212965965529088000000⟩, + ⟨6, 6, 1, 6, 2, 5, 90874166804329177406500661408895852382154391552000000⟩, + ⟨6, 6, 2, 6, 3, 5, 5709636323489700844369158644999617476946821120000000⟩, + ⟨6, 6, 3, 6, 4, 5, 21636953337654068382478803375265589519110373376000000⟩, + ⟨6, 6, 4, 6, 5, 5, -3989744336578289459972634760846461381138972672000000⟩, + ⟨6, 6, 5, 6, 6, 5, 942197563861601608515419556340690278961643520000000⟩, + ⟨6, 6, 6, 6, 7, 5, 774683890176797412757001928890063457198538752000000⟩, + ⟨6, 6, 7, 6, 8, 5, 141644620759017706526402810772744107408228352000000⟩, + ⟨6, 6, 1, 7, 1, 5, -260043202792189447572571576917724844520533655552000000⟩, + ⟨6, 6, 2, 7, 2, 5, -27615189986430880665967729917006375005498376192000000⟩, + ⟨6, 6, 3, 7, 3, 5, -38561542894780025483301199187426698938084753408000000⟩, + ⟨6, 6, 4, 7, 4, 5, -16500039986924433741631217929758083452653010944000000⟩, + ⟨6, 6, 5, 7, 5, 5, -1065531558387092613296064928377169884028600320000000⟩, + ⟨6, 6, 6, 7, 6, 5, -838455749365670884344172161038692686841774080000000⟩, + ⟨6, 6, 7, 7, 7, 5, -50061832340439283309417307649180918387572736000000⟩, + ⟨6, 6, 8, 7, 8, 5, -191897216138898638381325517056007404414566400000000⟩ +] + +def collectedFourData_13_7_33 : List CollectedFourTerm := [ + ⟨6, 7, 0, 0, 7, 6, 58960116097991242087442502565761550665784492032000000⟩, + ⟨6, 7, 1, 0, 8, 6, 6784341606872780669096722551041432704209911808000000⟩, + ⟨6, 7, 0, 1, 6, 6, 7417863187182076166200231765957878714703282176000000⟩, + ⟨6, 7, 1, 1, 7, 6, 71145319222367796957001216834741112699835383808000000⟩, + ⟨6, 7, 2, 1, 8, 6, -19561067458481381826626678351624001978844053504000000⟩, + ⟨6, 7, 0, 2, 5, 6, -35876113438219395600334632731671038392581226496000000⟩, + ⟨6, 7, 1, 2, 6, 6, 84365121663599075203032381756999349427767345152000000⟩, + ⟨6, 7, 2, 2, 7, 6, -23777321983043927217735637552026430638001225728000000⟩, + ⟨6, 7, 3, 2, 8, 6, -3334031188538236044647445493167275102919720960000000⟩, + ⟨6, 7, 0, 3, 4, 6, 22783400494176036611691665846784853206443753472000000⟩, + ⟨6, 7, 1, 3, 5, 6, 69698605531226671627399759959402167599242412032000000⟩, + ⟨6, 7, 2, 3, 6, 6, -9445609804674834113409711905091599861934981120000000⟩, + ⟨6, 7, 3, 3, 7, 6, -8324707221321536298849454029733149355014094848000000⟩, + ⟨6, 7, 4, 3, 8, 6, -1208998357209304237246675639975071606223405056000000⟩, + ⟨6, 7, 0, 4, 3, 6, 87436940980425512954525132441968367207064797184000000⟩, + ⟨6, 7, 1, 4, 4, 6, -78502543932505161863584624756161981089813889024000000⟩, + ⟨6, 7, 2, 4, 5, 6, -4386722842865725460161756986900447261477568512000000⟩, + ⟨6, 7, 3, 4, 6, 6, -19121956968941411781090727395874223002497318912000000⟩, + ⟨6, 7, 4, 4, 7, 6, -2755048062459179488419423891229751905496334336000000⟩, + ⟨6, 7, 5, 4, 8, 6, 2394132280481635166512157584655005161810296832000000⟩, + ⟨6, 7, 0, 5, 2, 6, -147568042364343907592508773816623385050211155968000000⟩, + ⟨6, 7, 1, 5, 3, 6, -149919853220131825286814496108446006921809362944000000⟩, + ⟨6, 7, 2, 5, 4, 6, 23259427990040952712531991957705986616133156864000000⟩, + ⟨6, 7, 3, 5, 5, 6, -6284468950024976641513176517604503870928584704000000⟩, + ⟨6, 7, 4, 5, 6, 6, 2527147158498173526651781049343911184404840448000000⟩, + ⟨6, 7, 5, 5, 7, 6, -81444642656685424112671370815719231065161728000000⟩, + ⟨6, 7, 6, 5, 8, 6, 562045331548519263186635753792951329147060224000000⟩, + ⟨6, 7, 0, 6, 1, 6, 107261946374313631342675367750578115612843704320000000⟩, + ⟨6, 7, 1, 6, 2, 6, 373588065585858970880365368279409610335218302976000000⟩, + ⟨6, 7, 2, 6, 3, 6, 11736294616511719387109106297844870252100321280000000⟩, + ⟨6, 7, 3, 6, 4, 6, 29650184890610722056863056709254449701213700096000000⟩, + ⟨6, 7, 4, 6, 5, 6, -4100507661582796737592112612743602098493456384000000⟩, + ⟨6, 7, 5, 6, 6, 6, 774683890176797412757001928890063457198538752000000⟩, + ⟨6, 7, 6, 6, 7, 6, 530793781755459164038520650790535475123716096000000⟩, + ⟨6, 7, 7, 6, 8, 6, 83186834421499224262462526437247306346528768000000⟩, + ⟨6, 7, 0, 7, 0, 6, -1046156809470359234229455812592340069143581556736000000⟩, + ⟨6, 7, 1, 7, 1, 6, -1069050099893264589089437792669496606474398334976000000⟩, + ⟨6, 7, 2, 7, 2, 6, -56763686373216990052489379576216788421100699648000000⟩, + ⟨6, 7, 3, 7, 3, 6, -52842785148854488248847075768007851832317575168000000⟩, + ⟨6, 7, 4, 7, 4, 6, -16958114273766200319917988574192725089706835968000000⟩, + ⟨6, 7, 5, 7, 5, 6, -876090285538785091261465262727524490707730432000000⟩, + ⟨6, 7, 6, 7, 6, 6, -574488644573264294656892865847960344031395840000000⟩, + ⟨6, 7, 7, 7, 7, 6, -29400942552037215806927739078002961152999424000000⟩, + ⟨6, 7, 8, 7, 8, 6, -98612334354337288937382093264887333938790400000000⟩ +] + +def collectedFourData_13_7_34 : List CollectedFourTerm := [ + ⟨6, 8, 0, 0, 7, 7, 64682253423664316834564284789136541548430753792000000⟩, + ⟨6, 8, 1, 0, 8, 7, 3721384320199853799964175541350503263579930624000000⟩, + ⟨6, 8, 0, 1, 6, 7, 8137774113910338201642624664739841663729401856000000⟩, + ⟨6, 8, 1, 1, 7, 7, 39025021255050359429452037129756164222693146624000000⟩, + ⟨6, 8, 2, 1, 8, 7, -7153162772407277837819956298716688041176465408000000⟩, + ⟨6, 8, 0, 2, 5, 7, -39357925574812367959884944682503583044286283776000000⟩, + ⟨6, 8, 1, 2, 6, 7, 46276419897934225373682615480142975068071264256000000⟩, + ⟨6, 8, 2, 2, 7, 7, -8694978165054360666241622182744593148208480256000000⟩, + ⟨6, 8, 3, 2, 8, 7, -914400549606355707158547721686050768620093440000000⟩, + ⟨6, 8, 0, 3, 4, 7, 24994551947080396542546752412150754799813394432000000⟩, + ⟨6, 8, 1, 3, 5, 7, 38231461915323556957195492867983380687037136896000000⟩, + ⟨6, 8, 2, 3, 6, 7, -3454105179121480795773183050697292860610314240000000⟩, + ⟨6, 8, 3, 3, 7, 7, -2283157063634383015862841258374967040904527872000000⟩, + ⟨6, 8, 4, 3, 8, 7, -265266567656810754727600787861954099556856627200000⟩, + ⟨6, 8, 0, 4, 3, 7, 95922782202230917772882835365833916217299042304000000⟩, + ⟨6, 8, 1, 4, 4, 7, -43060646561529050969822697956053602669976092672000000⟩, + ⟨6, 8, 2, 4, 5, 7, -1604152871465626235023275763956920710777012224000000⟩, + ⟨6, 8, 3, 4, 6, 7, -5244440430569350675157339034256419773919264768000000⟩, + ⟨6, 8, 4, 4, 7, 7, -604485637966480637957823464182827141167264563200000⟩, + ⟨6, 8, 5, 4, 8, 7, 437747529303017766601168275884120700125970432000000⟩, + ⟨6, 8, 0, 5, 2, 7, -161889666186897515500741998602168513856125534208000000⟩, + ⟨6, 8, 1, 5, 3, 7, -82234861301040615383488893927109034726425362432000000⟩, + ⟨6, 8, 2, 5, 4, 7, 8505592793388665458380986408467919882711728128000000⟩, + ⟨6, 8, 3, 5, 5, 7, -1723595712494341093775006885985635711745785856000000⟩, + ⟨6, 8, 4, 5, 6, 7, 554481855745331999472849690185797056171973017600000⟩, + ⟨6, 8, 5, 5, 7, 7, -14891487570920245626220816072760076300976128000000⟩, + ⟨6, 8, 6, 5, 8, 7, 88084626346364385825911766767709470475681792000000⟩, + ⟨6, 8, 0, 6, 1, 7, 117671823891391903894195653432460723594639441920000000⟩, + ⟨6, 8, 1, 6, 2, 7, 204922577612634106221382387185800774728525283328000000⟩, + ⟨6, 8, 2, 6, 3, 7, 4291771188613504328664019216299974227195330560000000⟩, + ⟨6, 8, 3, 6, 4, 7, 8131941132737719365995121570254059288966201344000000⟩, + ⟨6, 8, 4, 6, 5, 7, -899693193586543650836994906100873300164791500800000⟩, + ⟨6, 8, 5, 6, 6, 7, 141644620759017706526402810772744107408228352000000⟩, + ⟨6, 8, 6, 6, 7, 7, 83186834421499224262462526437247306346528768000000⟩, + ⟨6, 8, 7, 6, 8, 7, 11407524827082079142852134847561441923301376000000⟩, + ⟨6, 8, 0, 7, 0, 7, -1147687357986042161760596821057263082668048777216000000⟩, + ⟨6, 8, 1, 7, 1, 7, -586401232393822148627314340930584965275166179328000000⟩, + ⟨6, 8, 2, 7, 2, 7, -20757552677087943507573542412483351739782660096000000⟩, + ⟨6, 8, 3, 7, 3, 7, -14492807370535780308383293379506326768401252352000000⟩, + ⟨6, 8, 4, 7, 4, 7, -3720783192557435598177359307132040135176722841600000⟩, + ⟨6, 8, 5, 7, 5, 7, -160185951740238572568500734197137470528684032000000⟩, + ⟨6, 8, 6, 7, 6, 7, -90034761890192661848467061175526928123166720000000⟩, + ⟨6, 8, 7, 7, 7, 7, -4031791622248557286643927910138952147795968000000⟩, + ⟨6, 8, 8, 7, 8, 7, -12020306500839389569482091514782132312473600000000⟩ +] + +def collectedFourData_13_7_35 : List CollectedFourTerm := [ + ⟨7, 0, 6, 5, 8, 0, -1107751392425692741707806631295937531856115728384000000⟩, + ⟨7, 0, 6, 6, 7, 0, -1046156809470359234229455812592340069143581556736000000⟩, + ⟨7, 0, 7, 6, 8, 0, -1147687357986042161760596821057263082668048777216000000⟩, + ⟨7, 0, 6, 7, 6, 0, 1132276277796722885609560952020051349579696701440000000⟩, + ⟨7, 0, 7, 7, 7, 0, 405630173506473303894157543181417385599422169088000000⟩, + ⟨7, 0, 8, 7, 8, 0, 5442021217276457646873622763071054756392940339200000000⟩ +] + +def collectedFourData_13_7_36 : List CollectedFourTerm := [ + ⟨7, 1, 5, 4, 8, 1, -803654024588698865658608456376453144186697285632000000⟩, + ⟨7, 1, 5, 5, 7, 1, 27339055316971128210335113259653331649118076928000000⟩, + ⟨7, 1, 6, 5, 8, 1, -1131992571294488041751294502688298941972368850944000000⟩, + ⟨7, 1, 5, 6, 6, 1, -260043202792189447572571576917724844520533655552000000⟩, + ⟨7, 1, 6, 6, 7, 1, -1069050099893264589089437792669496606474398334976000000⟩, + ⟨7, 1, 7, 6, 8, 1, -586401232393822148627314340930584965275166179328000000⟩, + ⟨7, 1, 5, 7, 5, 1, 294082950059328515195694094722881295215316959232000000⟩, + ⟨7, 1, 6, 7, 6, 1, 1157054140380908525278918483695465437638730711040000000⟩, + ⟨7, 1, 7, 7, 7, 1, 207253336011050372130746193262743697054450581504000000⟩, + ⟨7, 1, 8, 7, 8, 1, 1853703407011565528826482334565595101887096422400000000⟩ +] + +def collectedFourData_13_7_37 : List CollectedFourTerm := [ + ⟨7, 2, 4, 3, 8, 2, 8619443298349288487974323405905324755737850675200000⟩, + ⟨7, 2, 4, 4, 7, 2, 19641863379705851311819511657080952121522860851200000⟩, + ⟨7, 2, 5, 4, 8, 2, -85343736479480460364308381270605078765997391872000000⟩, + ⟨7, 2, 4, 5, 6, 2, -18017064712593716926223027294752486265120725401600000⟩, + ⟨7, 2, 5, 5, 7, 2, 2903260683306647443524456106645033656294309888000000⟩, + ⟨7, 2, 6, 5, 8, 2, -60105762396156369285666366534379599634221760512000000⟩, + ⟨7, 2, 4, 6, 5, 2, 29234194631201561446101684424835035185768352972800000⟩, + ⟨7, 2, 5, 6, 6, 2, -27615189986430880665967729917006375005498376192000000⟩, + ⟨7, 2, 6, 6, 7, 2, -56763686373216990052489379576216788421100699648000000⟩, + ⟨7, 2, 7, 6, 8, 2, -20757552677087943507573542412483351739782660096000000⟩, + ⟨7, 2, 4, 7, 4, 2, 120901325926574709856986762197073184507681151385600000⟩, + ⟨7, 2, 5, 7, 5, 2, 31230028127858242746156484629132396928771817472000000⟩, + ⟨7, 2, 6, 7, 6, 2, 61436464341541637562893757515641129111828561920000000⟩, + ⟨7, 2, 7, 7, 7, 2, 7336396654880067245701893374143281505845116928000000⟩, + ⟨7, 2, 8, 7, 8, 2, 49213333797487096662700093990933626017651097600000000⟩ +] + +def collectedFourData_13_7_38 : List CollectedFourTerm := [ + ⟨7, 3, 3, 2, 8, 3, 16595851329761173155147698116024431887027011584000000⟩, + ⟨7, 3, 3, 3, 7, 3, 41438005704263985035815826381807519226353890099200000⟩, + ⟨7, 3, 4, 3, 8, 3, 24072188722347339529470765072474566563829750169600000⟩, + ⟨7, 3, 3, 4, 6, 3, 95183619181972393128454715433089512367398374604800000⟩, + ⟨7, 3, 4, 4, 7, 3, 54855357332113636974029253396348670387418667417600000⟩, + ⟨7, 3, 5, 4, 8, 3, -119173040513983855284029941230925133438389321728000000⟩, + ⟨7, 3, 3, 5, 5, 3, 31282284562803423639643979736590141931484977561600000⟩, + ⟨7, 3, 4, 5, 6, 3, -50317655905615228839749885029921746800394161356800000⟩, + ⟨7, 3, 5, 5, 7, 3, 4054080794992464602398555342432645073193664512000000⟩, + ⟨7, 3, 6, 5, 8, 3, -55954010238609259240314367772535302009118523392000000⟩, + ⟨7, 3, 3, 6, 4, 3, -147590119143501027770258495830175677697573152358400000⟩, + ⟨7, 3, 4, 6, 5, 3, 81644605799876780771671439742773780980542367334400000⟩, + ⟨7, 3, 5, 6, 6, 3, -38561542894780025483301199187426698938084753408000000⟩, + ⟨7, 3, 6, 6, 7, 3, -52842785148854488248847075768007851832317575168000000⟩, + ⟨7, 3, 7, 6, 8, 3, -14492807370535780308383293379506326768401252352000000⟩, + ⟨7, 3, 3, 7, 3, 3, 263036233492883915162888798929659010585342456627200000⟩, + ⟨7, 3, 4, 7, 4, 3, 337650522632232564847896800029069881931285187788800000⟩, + ⟨7, 3, 5, 7, 5, 3, 43609262505502647231383337676382273198912176128000000⟩, + ⟨7, 3, 6, 7, 6, 3, 57192795128914319111703958300900148116161822720000000⟩, + ⟨7, 3, 7, 7, 7, 3, 5122231178552215938106920003712438809170804736000000⟩, + ⟨7, 3, 8, 7, 8, 3, 27488379883092008553013044637311521029839912960000000⟩ +] + +def collectedFourData_13_7_39 : List CollectedFourTerm := [ + ⟨7, 4, 2, 1, 8, 4, 41663238302039503928244643248579457833163869388800000⟩, + ⟨7, 4, 2, 2, 7, 4, 50643464834755481523633785985972679497892862361600000⟩, + ⟨7, 4, 3, 2, 8, 4, 21303520813881672179046156941666358622144167936000000⟩, + ⟨7, 4, 2, 3, 6, 4, 20118262617085232689456777317175595966203428864000000⟩, + ⟨7, 4, 3, 3, 7, 4, 53192535861264495332814435163238266417621814476800000⟩, + ⟨7, 4, 4, 3, 8, 4, 15450318374525776935397608420442959810626007859200000⟩, + ⟨7, 4, 2, 4, 5, 4, 9343308055924665301082405759530978308402865766400000⟩, + ⟨7, 4, 3, 4, 6, 4, 122183922481120253626360159853435246446168453939200000⟩, + ⟨7, 4, 4, 4, 7, 4, 35207963226988508896550648417432095911172059955200000⟩, + ⟨7, 4, 5, 4, 8, 4, -50992771197188796879650278622590098669991624704000000⟩, + ⟨7, 4, 2, 5, 4, 4, -49540399222846751787218076739172527927586507980800000⟩, + ⟨7, 4, 3, 5, 5, 4, 40155987604827645136082917369787977590590826086400000⟩, + ⟨7, 4, 4, 5, 6, 4, -32295517975890307695539996919468370010312382873600000⟩, + ⟨7, 4, 5, 5, 7, 4, 1734694470346338878362725310165506178066415616000000⟩, + ⟨7, 4, 6, 5, 8, 4, -17956557305390047987321580987846006535295598592000000⟩, + ⟨7, 4, 2, 6, 3, 4, -24997206334905830868445840513996244886189244416000000⟩, + ⟨7, 4, 3, 6, 4, 4, -189456335358850026499517881167151502769755101593600000⟩, + ⟨7, 4, 4, 6, 5, 4, 52402179449503100118163703144505932891804191948800000⟩, + ⟨7, 4, 5, 6, 6, 4, -16500039986924433741631217929758083452653010944000000⟩, + ⟨7, 4, 6, 6, 7, 4, -16958114273766200319917988574192725089706835968000000⟩, + ⟨7, 4, 7, 6, 8, 4, -3720783192557435598177359307132040135176722841600000⟩, + ⟨7, 4, 2, 7, 2, 4, 120901325926574709856986762197073184507681151385600000⟩, + ⟨7, 4, 3, 7, 3, 4, 337650522632232564847896800029069881931285187788800000⟩, + ⟨7, 4, 4, 7, 4, 4, 216715153497862343607229982067488980849621834137600000⟩, + ⟨7, 4, 5, 7, 5, 4, 18659901060091719153494160941474080051276283904000000⟩, + ⟨7, 4, 6, 7, 6, 4, 18354103643480131161340327241978383832941854720000000⟩, + ⟨7, 4, 7, 7, 7, 4, 1315046228813995068221862775063723154455973068800000⟩, + ⟨7, 4, 8, 7, 8, 4, 5880980546919252931198404367300040541748592640000000⟩ +] + +def collectedFourData_13_7_40 : List CollectedFourTerm := [ + ⟨7, 5, 1, 0, 8, 5, -1866291574322468073340340308340114018959097856000000⟩, + ⟨7, 5, 1, 1, 7, 5, -19571229975017557306351972764549831864254201856000000⟩, + ⟨7, 5, 2, 1, 8, 5, 10762033369762710657962007090278566932309344256000000⟩, + ⟨7, 5, 1, 2, 6, 5, -23207840178325112558677293751091157234943524864000000⟩, + ⟨7, 5, 2, 2, 7, 5, 13081716177721179728027958960275383187083886592000000⟩, + ⟨7, 5, 3, 2, 8, 5, 2751456814642343857625195440986491338264412160000000⟩, + ⟨7, 5, 1, 3, 5, 5, -19173256268991543871151985841174784701076865024000000⟩, + ⟨7, 5, 2, 3, 6, 5, 5196749519494795630892663534333959325016391680000000⟩, + ⟨7, 5, 3, 3, 7, 5, 6870083427158913893858178086668502398987665408000000⟩, + ⟨7, 5, 4, 3, 8, 5, 1330324195434777883114223267478051426473607168000000⟩, + ⟨7, 5, 1, 4, 4, 5, 21595114867991801058497292127677270797234208768000000⟩, + ⟨7, 5, 2, 4, 5, 5, 2413470416122496276553165587358437405274144768000000⟩, + ⟨7, 5, 3, 4, 6, 5, 15780667857087178863949214927894215757295255552000000⟩, + ⟨7, 5, 4, 4, 7, 5, 3031523637083520780343783443725999366637355008000000⟩, + ⟨7, 5, 5, 4, 8, 5, -3292986380837542856368513540194235202005893120000000⟩, + ⟨7, 5, 1, 5, 3, 5, 41241166070551587494457820266046986272750174208000000⟩, + ⟨7, 5, 2, 5, 4, 5, -12796783239039398209940469704238912919144759296000000⟩, + ⟨7, 5, 3, 5, 5, 5, 5186347679769502569404721643203599614643011584000000⟩, + ⟨7, 5, 4, 5, 6, 5, -2780752339593414807504815807967101538841657344000000⟩, + ⟨7, 5, 5, 5, 7, 5, 112022255932613563986101776290285261139476480000000⟩, + ⟨7, 5, 6, 5, 8, 5, -927671860385389801158603546942303769102123008000000⟩, + ⟨7, 5, 1, 6, 2, 5, -102769627396710844586063687786498301121875935232000000⟩, + ⟨7, 5, 2, 6, 3, 5, -6457029738706874339455925350374035683194961920000000⟩, + ⟨7, 5, 3, 6, 4, 5, -24469238186234418629516455750808781090472329216000000⟩, + ⟨7, 5, 4, 6, 5, 5, 4512003282089567910943175544508322602027057152000000⟩, + ⟨7, 5, 5, 6, 6, 5, -1065531558387092613296064928377169884028600320000000⟩, + ⟨7, 5, 6, 6, 7, 5, -876090285538785091261465262727524490707730432000000⟩, + ⟨7, 5, 7, 6, 8, 5, -160185951740238572568500734197137470528684032000000⟩, + ⟨7, 5, 1, 7, 1, 5, 294082950059328515195694094722881295215316959232000000⟩, + ⟨7, 5, 2, 7, 2, 5, 31230028127858242746156484629132396928771817472000000⟩, + ⟨7, 5, 3, 7, 3, 5, 43609262505502647231383337676382273198912176128000000⟩, + ⟨7, 5, 4, 7, 4, 5, 18659901060091719153494160941474080051276283904000000⟩, + ⟨7, 5, 5, 7, 5, 5, 1205010016440243739389750128492197513915269120000000⟩, + ⟨7, 5, 6, 7, 6, 5, 948209903662467505299330229531442807077601280000000⟩, + ⟨7, 5, 7, 7, 7, 5, 56614943909212907524734092347023998872190976000000⟩, + ⟨7, 5, 8, 7, 8, 5, 217016629638261469656398698594227729098342400000000⟩ +] + +def collectedFourData_13_7_41 : List CollectedFourTerm := [ + ⟨7, 6, 0, 0, 7, 6, -63813703824854424608957061494430001255447265280000000⟩, + ⟨7, 6, 1, 0, 8, 6, -7342827568861699372892355469871245032758968320000000⟩, + ⟨7, 6, 0, 1, 6, 6, -8028500548631975989059368688627589821014999040000000⟩, + ⟨7, 6, 1, 1, 7, 6, -77001991004145584802832498327998719070641848320000000⟩, + ⟨7, 6, 2, 1, 8, 6, 21171331535693106511001395837869015292874588160000000⟩, + ⟨7, 6, 0, 2, 5, 6, 38829429601672904285882969568476957595496611840000000⟩, + ⟨7, 6, 1, 2, 6, 6, -91310045557595856896276581086930299407910830080000000⟩, + ⟨7, 6, 2, 2, 7, 6, 25734667486956664378638548027077806429170565120000000⟩, + ⟨7, 6, 3, 2, 8, 6, 3608488125338934938447231324346282754336358400000000⟩, + ⟨7, 6, 0, 3, 4, 6, -24658926533354050656349876337380674562299002880000000⟩, + ⟨7, 6, 1, 3, 5, 6, -75436184063528196513283650945474963480804065280000000⟩, + ⟨7, 6, 2, 3, 6, 6, 10223170957107338392006603148862100628884684800000000⟩, + ⟨7, 6, 3, 3, 7, 6, 9009995844769686103196041219956766624626769920000000⟩, + ⟨7, 6, 4, 3, 8, 6, 1308522916804748277696322787093239421982474240000000⟩, + ⟨7, 6, 0, 4, 3, 6, -94634736570104013332615105187541087455396495360000000⟩, + ⟨7, 6, 1, 4, 4, 6, 84964861325589909894915617886715623418846248960000000⟩, + ⟨7, 6, 2, 4, 5, 6, 4747837195420551001918954110289455002136084480000000⟩, + ⟨7, 6, 3, 4, 6, 6, 20696073537908309686838874478952471366970900480000000⟩, + ⟨7, 6, 4, 4, 7, 6, 2981843196998028213574923442255037839379005440000000⟩, + ⟨7, 6, 5, 4, 8, 6, -2591216883125905098780894091933310130617057280000000⟩, + ⟨7, 6, 0, 5, 2, 6, 159715821010275164693814105834655488336954654720000000⟩, + ⟨7, 6, 1, 5, 3, 6, 162261232575508509215591425447314024409344245760000000⟩, + ⟨7, 6, 2, 5, 4, 6, -25174140539770259368508258376373010264815042560000000⟩, + ⟨7, 6, 3, 5, 5, 6, 6801805471462613050886535792738740379750236160000000⟩, + ⟨7, 6, 4, 5, 6, 6, -2735181525528224058722248412011453931763793920000000⟩, + ⟨7, 6, 5, 5, 7, 6, 88149153166133246194967005019691392560005120000000⟩, + ⟨7, 6, 6, 5, 8, 6, -608312817158805935494978775916433443347496960000000⟩, + ⟨7, 6, 0, 6, 1, 6, -116091733371621840248835877804521294138232012800000000⟩, + ⟨7, 6, 1, 6, 2, 6, -404341777926188971548329384896370602947945431040000000⟩, + ⟨7, 6, 2, 6, 3, 6, -12702424591813658179682041537060934958396211200000000⟩, + ⟨7, 6, 3, 6, 4, 6, -32090983569587464238613826085644550985838755840000000⟩, + ⟨7, 6, 4, 6, 5, 6, 4438060824251090280989044109764382898373263360000000⟩, + ⟨7, 6, 5, 6, 6, 6, -838455749365670884344172161038692686841774080000000⟩, + ⟨7, 6, 6, 6, 7, 6, -574488644573264294656892865847960344031395840000000⟩, + ⟨7, 6, 7, 6, 8, 6, -90034761890192661848467061175526928123166720000000⟩, + ⟨7, 6, 0, 7, 0, 6, 1132276277796722885609560952020051349579696701440000000⟩, + ⟨7, 6, 1, 7, 1, 6, 1157054140380908525278918483695465437638730711040000000⟩, + ⟨7, 6, 2, 7, 2, 6, 61436464341541637562893757515641129111828561920000000⟩, + ⟨7, 6, 3, 7, 3, 6, 57192795128914319111703958300900148116161822720000000⟩, + ⟨7, 6, 4, 7, 4, 6, 18354103643480131161340327241978383832941854720000000⟩, + ⟨7, 6, 5, 7, 5, 6, 948209903662467505299330229531442807077601280000000⟩, + ⟨7, 6, 6, 7, 6, 6, 621780461805931827636366052774527152789913600000000⟩, + ⟨7, 6, 7, 7, 7, 6, 31821223639876510028543091104661564775464960000000⟩, + ⟨7, 6, 8, 7, 8, 6, 106730086614934459690861376433458214076416000000000⟩ +] + +def collectedFourData_13_7_42 : List CollectedFourTerm := [ + ⟨7, 7, 0, 0, 7, 7, -22860819626933384194954670262325755755580358656000000⟩, + ⟨7, 7, 1, 0, 8, 7, -1315258686943987468023537605916736309828780032000000⟩, + ⟨7, 7, 0, 1, 6, 7, -2876154993616373387977734518990496980803780608000000⟩, + ⟨7, 7, 1, 1, 7, 7, -13792716311311326975356602661476678441245868032000000⟩, + ⟨7, 7, 2, 1, 8, 7, 2528161207232621084270467077771503843036626944000000⟩, + ⟨7, 7, 0, 2, 5, 7, 13910375564109126163587617684547997839988359168000000⟩, + ⟨7, 7, 1, 2, 6, 7, -16355597281647291823017540064569390352520183808000000⟩, + ⟨7, 7, 2, 2, 7, 7, 3073089092760478825842961873322067171169271808000000⟩, + ⟨7, 7, 3, 2, 8, 7, 323179000805680648659407089702957267990609920000000⟩, + ⟨7, 7, 0, 3, 4, 7, -8833890495057699688462033653207737249537458176000000⟩, + ⟨7, 7, 1, 3, 5, 7, -13512246538405646827656475069212517121893859328000000⟩, + ⟨7, 7, 2, 3, 6, 7, 1220793514337633702217767518563881451855544320000000⟩, + ⟨7, 7, 3, 3, 7, 7, 806942229885404089215539715767666176054788096000000⟩, + ⟨7, 7, 4, 3, 8, 7, 93753863467586777463505839815527518290155929600000⟩, + ⟨7, 7, 0, 4, 3, 7, -33902242206616497901268897259896417627796406272000000⟩, + ⟨7, 7, 1, 4, 4, 7, 15219038019817917077806791718713551236676714496000000⟩, + ⟨7, 7, 2, 4, 5, 7, 566959985274511382908342191596399896226168832000000⟩, + ⟨7, 7, 3, 4, 6, 7, 1853556429800876935008516253620136770665447424000000⟩, + ⟨7, 7, 4, 4, 7, 7, 213644955226122451824675492680202184616941977600000⟩, + ⟨7, 7, 5, 4, 8, 7, -154714265193964592065337487555992660975026176000000⟩, + ⟨7, 7, 0, 5, 2, 7, 57217092204909440645212341220687589409338425344000000⟩, + ⟨7, 7, 1, 5, 3, 7, 29064484178301412609198858912106102047874482176000000⟩, + ⟨7, 7, 2, 5, 4, 7, -3006154120763272119887223477794493948865019904000000⟩, + ⟨7, 7, 3, 5, 5, 7, 609174983979039194365377969686536445239492608000000⟩, + ⟨7, 7, 4, 5, 6, 7, -195971986436140272970960134006745928173407436800000⟩, + ⟨7, 7, 5, 5, 7, 7, 5263137774525640403715001784000847129083904000000⟩, + ⟨7, 7, 6, 5, 8, 7, -31131982085109968285931773834995682462662656000000⟩, + ⟨7, 7, 0, 6, 1, 7, -41589063441150984629880830626766731614942658560000000⟩, + ⟨7, 7, 1, 6, 2, 7, -72426327722447065052433339651478153704719253504000000⟩, + ⟨7, 7, 2, 6, 3, 7, -1516852024006132600104201016741838964475822080000000⟩, + ⟨7, 7, 3, 6, 4, 7, -2874093427678014288777226111951695679944916992000000⟩, + ⟨7, 7, 4, 6, 5, 7, 317980941131479381815627568680683211057423974400000⟩, + ⟨7, 7, 5, 6, 6, 7, -50061832340439283309417307649180918387572736000000⟩, + ⟨7, 7, 6, 6, 7, 7, -29400942552037215806927739078002961152999424000000⟩, + ⟨7, 7, 7, 6, 8, 7, -4031791622248557286643927910138952147795968000000⟩, + ⟨7, 7, 0, 7, 0, 7, 405630173506473303894157543181417385599422169088000000⟩, + ⟨7, 7, 1, 7, 1, 7, 207253336011050372130746193262743697054450581504000000⟩, + ⟨7, 7, 2, 7, 2, 7, 7336396654880067245701893374143281505845116928000000⟩, + ⟨7, 7, 3, 7, 3, 7, 5122231178552215938106920003712438809170804736000000⟩, + ⟨7, 7, 4, 7, 4, 7, 1315046228813995068221862775063723154455973068800000⟩, + ⟨7, 7, 5, 7, 5, 7, 56614943909212907524734092347023998872190976000000⟩, + ⟨7, 7, 6, 7, 6, 7, 31821223639876510028543091104661564775464960000000⟩, + ⟨7, 7, 7, 7, 7, 7, 1424966759365939813931936155238366680449024000000⟩, + ⟨7, 7, 8, 7, 8, 7, 4248368667310674189916129745038931184844800000000⟩ +] + +def collectedFourData_13_7_43 : List CollectedFourTerm := [ + ⟨7, 8, 0, 0, 7, 8, -306705648592772033919770536280511428459652710400000000⟩, + ⟨7, 8, 1, 0, 8, 8, -11763861349665477057944010712230313631888179200000000⟩, + ⟨7, 8, 0, 1, 6, 8, -38587110924543073919366287738924750987277107200000000⟩, + ⟨7, 8, 1, 1, 7, 8, -123364022554785709954639064673238494047580979200000000⟩, + ⟨7, 8, 2, 1, 8, 8, 16959175905876764730525778921338285593513164800000000⟩, + ⟨7, 8, 0, 2, 5, 8, 186624575548144621419575624662195252464137011200000000⟩, + ⟨7, 8, 1, 2, 6, 8, -146286795610769618816522546868780772008709324800000000⟩, + ⟨7, 8, 2, 2, 7, 8, 20614610472409169250372630790954440692701593600000000⟩, + ⟨7, 8, 3, 2, 8, 8, 1734335455530062818729018900760467122369331200000000⟩, + ⟨7, 8, 0, 3, 4, 8, -118517365435669772726183984445724831408088678400000000⟩, + ⟨7, 8, 1, 3, 5, 8, -120855460890083247356982248376378842600492236800000000⟩, + ⟨7, 8, 2, 3, 6, 8, 8189213526090005574645276159654652903686144000000000⟩, + ⟨7, 8, 3, 3, 7, 8, 4330443860417267685737315077616323055384002560000000⟩, + ⟨7, 8, 4, 3, 8, 8, 419273965561395088411039855002321322644602880000000⟩, + ⟨7, 8, 0, 4, 3, 8, -454839736912984106752960060056662127961492684800000000⟩, + ⟨7, 8, 1, 4, 4, 8, 136121247415148155641097657252622812585761177600000000⟩, + ⟨7, 8, 2, 4, 5, 8, 3803228249194090135930122620840606028949094400000000⟩, + ⟨7, 8, 3, 4, 6, 8, 9947083897825068452038361274746573744127344640000000⟩, + ⟨7, 8, 4, 4, 7, 8, 955435480595546905985378977593196660685537280000000⟩, + ⟨7, 8, 5, 4, 8, 8, -593051340706011969315848469733641543902822400000000⟩, + ⟨7, 8, 0, 5, 2, 8, 767636754135627546546222316093334685818132889600000000⟩, + ⟨7, 8, 1, 5, 3, 8, 259956893246236816896651016470601954666060185600000000⟩, + ⟨7, 8, 2, 5, 4, 8, -20165603517825708848033392158920462603963596800000000⟩, + ⟨7, 8, 3, 5, 5, 8, 3269128782200984169561819284936767010903162880000000⟩, + ⟨7, 8, 4, 5, 6, 8, -876400703427346577855444452434196567204823040000000⟩, + ⟨7, 8, 5, 5, 7, 8, 20174680787125307687895748379543653161369600000000⟩, + ⟨7, 8, 6, 5, 8, 8, -104418333563846240397398573252853007751577600000000⟩, + ⟨7, 8, 0, 6, 1, 8, -557967775663484779925657890518822085044731904000000000⟩, + ⟨7, 8, 1, 6, 2, 8, -647791408526606237684865550316995228511659622400000000⟩, + ⟨7, 8, 2, 6, 3, 8, -10175205688906150730272245592345743496052736000000000⟩, + ⟨7, 8, 3, 6, 4, 8, -15423781005886108574460424125995550338313093120000000⟩, + ⟨7, 8, 4, 6, 5, 8, 1422033452597210269019922498240334564499128320000000⟩, + ⟨7, 8, 5, 6, 6, 8, -191897216138898638381325517056007404414566400000000⟩, + ⟨7, 8, 6, 6, 7, 8, -98612334354337288937382093264887333938790400000000⟩, + ⟨7, 8, 7, 6, 8, 8, -12020306500839389569482091514782132312473600000000⟩, + ⟨7, 8, 0, 7, 0, 8, 5442021217276457646873622763071054756392940339200000000⟩, + ⟨7, 8, 1, 7, 1, 8, 1853703407011565528826482334565595101887096422400000000⟩, + ⟨7, 8, 2, 7, 2, 8, 49213333797487096662700093990933626017651097600000000⟩, + ⟨7, 8, 3, 7, 3, 8, 27488379883092008553013044637311521029839912960000000⟩, + ⟨7, 8, 4, 7, 4, 8, 5880980546919252931198404367300040541748592640000000⟩, + ⟨7, 8, 5, 7, 5, 8, 217016629638261469656398698594227729098342400000000⟩, + ⟨7, 8, 6, 7, 6, 8, 106730086614934459690861376433458214076416000000000⟩, + ⟨7, 8, 7, 7, 7, 8, 4248368667310674189916129745038931184844800000000⟩, + ⟨7, 8, 8, 7, 8, 8, 11399404648060895905919263304738892939264000000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1317.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1317.lean new file mode 100644 index 0000000000000000000000000000000000000000..1268d01b70852cb4a15af5482d82198b505caf79 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1317.lean @@ -0,0 +1,76 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1315 +import OAI.Analysis.LaughlinFock.Sparse1316 + +namespace OAI + +/-! Sparse1317. -/ +namespace LaughlinFock +def collectedFourData_13_7 : List (List CollectedFourTerm) := [ + collectedFourData_13_7_0, + collectedFourData_13_7_1, + collectedFourData_13_7_2, + collectedFourData_13_7_3, + collectedFourData_13_7_4, + collectedFourData_13_7_5, + collectedFourData_13_7_6, + collectedFourData_13_7_7, + collectedFourData_13_7_8, + collectedFourData_13_7_9, + collectedFourData_13_7_10, + collectedFourData_13_7_11, + collectedFourData_13_7_12, + collectedFourData_13_7_13, + collectedFourData_13_7_14, + collectedFourData_13_7_15, + collectedFourData_13_7_16, + collectedFourData_13_7_17, + collectedFourData_13_7_18, + collectedFourData_13_7_19, + collectedFourData_13_7_20, + collectedFourData_13_7_21, + collectedFourData_13_7_22, + collectedFourData_13_7_23, + collectedFourData_13_7_24, + collectedFourData_13_7_25, + collectedFourData_13_7_26, + collectedFourData_13_7_27, + collectedFourData_13_7_28, + collectedFourData_13_7_29, + collectedFourData_13_7_30, + collectedFourData_13_7_31, + collectedFourData_13_7_32, + collectedFourData_13_7_33, + collectedFourData_13_7_34, + collectedFourData_13_7_35, + collectedFourData_13_7_36, + collectedFourData_13_7_37, + collectedFourData_13_7_38, + collectedFourData_13_7_39, + collectedFourData_13_7_40, + collectedFourData_13_7_41, + collectedFourData_13_7_42, + collectedFourData_13_7_43 +] + +theorem collectedFourChecked_13_7 : collectNumericRowParts 13 7 = collectedFourData_13_7 := by + decide +kernel + +def collectedFourData_13 : Fin 8 → List (List CollectedFourTerm) := + ![collectedFourData_13_0, collectedFourData_13_1, collectedFourData_13_2, collectedFourData_13_3, collectedFourData_13_4, collectedFourData_13_5, collectedFourData_13_6, collectedFourData_13_7] + +theorem collectedFourChecked_13 (t : Fin 8) : + collectNumericRowParts 13 t = collectedFourData_13 t := by + fin_cases t + · exact collectedFourChecked_13_0 + · exact collectedFourChecked_13_1 + · exact collectedFourChecked_13_2 + · exact collectedFourChecked_13_3 + · exact collectedFourChecked_13_4 + · exact collectedFourChecked_13_5 + · exact collectedFourChecked_13_6 + · exact collectedFourChecked_13_7 + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1401.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1401.lean new file mode 100644 index 0000000000000000000000000000000000000000..0f3eaeb3d164092bb7b9d3cff3c1c9e05f0f8ed3 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1401.lean @@ -0,0 +1,611 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PartsTrace + +namespace OAI + +/-! Sparse1401. -/ +namespace LaughlinFock + +def collectedFourData_14_0_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_1 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_2 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_3 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_4 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_5 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_6 : List CollectedFourTerm := [ + ⟨0, 6, 8, 0, 8, 6, 718880864422981257768084119186312485537446887424000000⟩, + ⟨0, 6, 8, 1, 7, 6, 600707470184398078389962935879808176802475540480000000⟩, + ⟨0, 6, 8, 2, 6, 6, 32688410502700968839424046863129318131132006400000000⟩, + ⟨0, 6, 8, 3, 5, 6, 520097729590928577163189073885648613660300410880000000⟩, + ⟨0, 6, 8, 4, 4, 6, -744100840959722206580854800298213120740698357760000000⟩, + ⟨0, 6, 8, 5, 3, 6, 1040873687133056627683179656077368288613289164800000000⟩, + ⟨0, 6, 8, 6, 2, 6, -3711908123779286896940164073919929814697918857216000000⟩, + ⟨0, 6, 8, 7, 1, 6, 6940453268505551286821575362685942329440395591680000000⟩ +] + +def collectedFourData_14_0_7 : List CollectedFourTerm := [ + ⟨0, 7, 7, 0, 7, 7, 97724779146254425344289686567581062564675584000000⟩, + ⟨0, 7, 8, 0, 8, 7, -13177194842931889668021546999633379201382350848000000⟩, + ⟨0, 7, 7, 1, 6, 7, 6763950405506188828318470614578948459343118336000000⟩, + ⟨0, 7, 8, 1, 7, 7, -11011058674622114833276877843493891204930600960000000⟩, + ⟨0, 7, 7, 2, 5, 7, -686000272872895045613647546458537040533258240000000⟩, + ⟨0, 7, 8, 2, 6, 7, -599183502603831215773634362880408003857612800000000⟩, + ⟨0, 7, 7, 3, 4, 7, 2756277712033846010150770564298702145101758464000000⟩, + ⟨0, 7, 8, 3, 5, 7, -9533469952197377459024617059643225905309941760000000⟩, + ⟨0, 7, 7, 4, 3, 7, -9775935307910641457123682815258718651902066688000000⟩, + ⟨0, 7, 8, 4, 4, 7, 13639480822717363251819643263720292217278955520000000⟩, + ⟨0, 7, 7, 5, 2, 7, 18988815573670606214328176568886462540280758272000000⟩, + ⟨0, 7, 8, 5, 3, 7, -19079371925197049427108657287351822932613529600000000⟩, + ⟨0, 7, 7, 6, 1, 7, -52171155897131102762426606947217349580878249984000000⟩, + ⟨0, 7, 8, 6, 2, 7, 68039836649931788961168040787135088446964498432000000⟩, + ⟨0, 7, 7, 7, 0, 7, 176842597907790207852980038031943025875096698880000000⟩, + ⟨0, 7, 8, 7, 1, 7, -127219556874377504612441478416848717549519503360000000⟩ +] + +def collectedFourData_14_0_8 : List CollectedFourTerm := [ + ⟨0, 8, 6, 0, 6, 8, 718880864422981257768084119186312485537446887424000000⟩, + ⟨0, 8, 7, 0, 7, 8, -13177194842931889668021546999633379201382350848000000⟩, + ⟨0, 8, 8, 0, 8, 8, 888405507004136149641316373877300198574368227328000000⟩, + ⟨0, 8, 6, 1, 5, 8, -452060788515878913707725632432296181219597484032000000⟩, + ⟨0, 8, 7, 1, 6, 8, -912050077574407769647017637405402296765898555392000000⟩, + ⟨0, 8, 8, 1, 7, 8, 742364765876332732534830023181428469445227970560000000⟩, + ⟨0, 8, 6, 2, 4, 8, 162250962962131303855425180839903159376666427392000000⟩, + ⟨0, 8, 7, 2, 5, 8, 92500175870666554457060027171581658016283361280000000⟩, + ⟨0, 8, 8, 2, 6, 8, 40396907669981111685796515943614524875918540800000000⟩, + ⟨0, 8, 6, 3, 3, 8, 246311966888323630189831773406776138312670248960000000⟩, + ⟨0, 8, 7, 3, 4, 8, -371656081190464059439842081399593051148106334208000000⟩, + ⟨0, 8, 8, 3, 5, 8, 642745842900972757257435819819029538807333519360000000⟩, + ⟨0, 8, 6, 4, 2, 8, -748959507580938516123936765375019925239800791040000000⟩, + ⟨0, 8, 7, 4, 3, 8, 1318185678695117750839667734144967068396485083136000000⟩, + ⟨0, 8, 8, 4, 4, 8, -919572793755801001584209778755655714636268830720000000⟩, + ⟨0, 8, 6, 5, 1, 8, 1157361519281703312494325613286393670534042746880000000⟩, + ⟨0, 8, 7, 5, 2, 8, -2560449098342602061593065792297168903993487785984000000⟩, + ⟨0, 8, 8, 5, 3, 8, 1286329851729944421659986562530852201200982425600000000⟩, + ⟨0, 8, 6, 6, 0, 8, -1697623212266117031114556599085337978418751340544000000⟩, + ⟨0, 8, 7, 6, 1, 8, 7034750985813006015576061313323760654751941787648000000⟩, + ⟨0, 8, 8, 6, 2, 8, -4587240781969948588848031512951918159511003594752000000⟩, + ⟨0, 8, 7, 7, 0, 8, -23845429885021395274512712180507590858189947535360000000⟩, + ⟨0, 8, 8, 7, 1, 8, 8577133166278330093181571350685610550351584296960000000⟩ +] + +def collectedFourData_14_0_9 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_10 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_11 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_12 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_13 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_14 : List CollectedFourTerm := [ + ⟨1, 5, 8, 0, 8, 6, -452060788515878913707725632432296181219597484032000000⟩, + ⟨1, 5, 8, 1, 7, 6, -377748673080769623793417494181876251176353136640000000⟩, + ⟨1, 5, 8, 2, 6, 6, -20555768498641011244019326666945211363701555200000000⟩, + ⟨1, 5, 8, 3, 5, 6, -327058072317604641671512478902997822960660643840000000⟩, + ⟨1, 5, 8, 4, 4, 6, 467920109640947674440307180637083357234782535680000000⟩, + ⟨1, 5, 8, 5, 3, 6, -654542641260152610379087673704947072018835046400000000⟩, + ⟨1, 5, 8, 6, 2, 6, 2334194991656976933997168048568841887027180863488000000⟩, + ⟨1, 5, 8, 7, 1, 6, -4364432178531539792902434002812959780419917578240000000⟩ +] + +def collectedFourData_14_0_15 : List CollectedFourTerm := [ + ⟨1, 6, 7, 0, 7, 7, 6763950405506188828318470614578948459343118336000000⟩, + ⟨1, 6, 8, 0, 8, 7, -912050077574407769647017637405402296765898555392000000⟩, + ⟨1, 6, 7, 1, 6, 7, 468161969644122464042888173684445707829294137344000000⟩, + ⟨1, 6, 8, 1, 7, 7, -762122518341012577533123653619599880503521443840000000⟩, + ⟨1, 6, 7, 2, 5, 7, -47481016221399343245677217908621176902474792960000000⟩, + ⟨1, 6, 8, 2, 6, 7, -41472055816512319872569793175074980349817651200000000⟩, + ⟨1, 6, 7, 3, 4, 7, 190773782359717520260287222675933891295608569856000000⟩, + ⟨1, 6, 8, 3, 5, 7, -659852276079746391021817200976482577037698007040000000⟩, + ⟨1, 6, 7, 4, 3, 7, -676634341543854352806893769924515766185861578752000000⟩, + ⟨1, 6, 8, 4, 4, 7, 944046869664877551304454062126517115122960302080000000⟩, + ⟨1, 6, 7, 5, 2, 7, 1314297232715049107903971416074759110374444761088000000⟩, + ⟨1, 6, 8, 5, 3, 7, -1320565025551006855236118808070888378060924518400000000⟩, + ⟨1, 6, 7, 6, 1, 7, -3610989087609022714810565959494225231835023015936000000⟩, + ⟨1, 6, 8, 6, 2, 7, 4709328429487887091019147006605555957019839561728000000⟩, + ⟨1, 6, 7, 7, 0, 7, 12240033410963317950082969513869561523686887915520000000⟩, + ⟨1, 6, 8, 7, 1, 7, -8805410263664378886410221730355469578828974653440000000⟩ +] + +def collectedFourData_14_0_16 : List CollectedFourTerm := [ + ⟨1, 7, 6, 0, 6, 8, 600707470184398078389962935879808176802475540480000000⟩, + ⟨1, 7, 7, 0, 7, 8, -11011058674622114833276877843493891204930600960000000⟩, + ⟨1, 7, 8, 0, 8, 8, 742364765876332732534830023181428469445227970560000000⟩, + ⟨1, 7, 6, 1, 5, 8, -377748673080769623793417494181876251176353136640000000⟩, + ⟨1, 7, 7, 1, 6, 8, -762122518341012577533123653619599880503521443840000000⟩, + ⟨1, 7, 8, 1, 7, 8, 620330965161449106335810882495064491007619891200000000⟩, + ⟨1, 7, 6, 2, 4, 8, 135579301549772318931959656810180887137054883840000000⟩, + ⟨1, 7, 7, 2, 5, 8, 77294513442752980705596498306704865173805465600000000⟩, + ⟨1, 7, 8, 2, 6, 8, 33756252823873746093794998533458178883977216000000000⟩, + ⟨1, 7, 6, 3, 3, 8, 205821918245648697578106978878964105236132659200000000⟩, + ⟨1, 7, 7, 3, 4, 8, -310561311838187010316747339491090705863053148160000000⟩, + ⟨1, 7, 8, 3, 5, 8, 537087921474292824294558509216792895844201267200000000⟩, + ⟨1, 7, 6, 4, 2, 8, -625841628752519987710807862760341116845608140800000000⟩, + ⟨1, 7, 7, 4, 3, 8, 1101495426391452910743618191714397600011224350720000000⟩, + ⟨1, 7, 8, 4, 4, 8, -768408611113654616329717478576501192281974374400000000⟩, + ⟨1, 7, 6, 5, 1, 8, 967108382964850673883829157668505927085037977600000000⟩, + ⟨1, 7, 7, 5, 2, 8, -2139549091539482688733959181628817347534577991680000000⟩, + ⟨1, 7, 8, 5, 3, 8, 1074876226780066705548287320339545915824013312000000000⟩, + ⟨1, 7, 6, 6, 0, 8, -1418559034792539284926600917324467764321981562880000000⟩, + ⟨1, 7, 7, 6, 1, 8, 5878341846610209494430698169008427468382493736960000000⟩, + ⟨1, 7, 8, 6, 2, 8, -3833166163736569252972832985347370820507313111040000000⟩, + ⟨1, 7, 7, 7, 0, 8, -19925593475336258374001962529758023221874209587200000000⟩, + ⟨1, 7, 8, 7, 1, 8, 7167179181887597713343033523020968684923597619200000000⟩ +] + +def collectedFourData_14_0_17 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_18 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_19 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_20 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_21 : List CollectedFourTerm := [ + ⟨2, 4, 8, 0, 8, 6, 162250962962131303855425180839903159376666427392000000⟩, + ⟨2, 4, 8, 1, 7, 6, 135579301549772318931959656810180887137054883840000000⟩, + ⟨2, 4, 8, 2, 6, 6, 7377753873059037495430907816967266957996851200000000⟩, + ⟨2, 4, 8, 3, 5, 6, 117385733348571050134083972498024990799602647040000000⟩, + ⟨2, 4, 8, 4, 4, 6, -167943095944768202408039385448334564257777582080000000⟩, + ⟨2, 4, 8, 5, 3, 6, 234924542322932022293833242373694584141538918400000000⟩, + ⟨2, 4, 8, 6, 2, 6, -837775349596430635447339056829606973661121609728000000⟩, + ⟨2, 4, 8, 7, 1, 6, 1566455976140875315016915697302654486519941693440000000⟩ +] + +def collectedFourData_14_0_22 : List CollectedFourTerm := [ + ⟨2, 5, 7, 0, 7, 7, -686000272872895045613647546458537040533258240000000⟩, + ⟨2, 5, 8, 0, 8, 7, 92500175870666554457060027171581658016283361280000000⟩, + ⟨2, 5, 7, 1, 6, 7, -47481016221399343245677217908621176902474792960000000⟩, + ⟨2, 5, 8, 1, 7, 7, 77294513442752980705596498306704865173805465600000000⟩, + ⟨2, 5, 7, 2, 5, 7, 4815527632734725709061056283166662581446246400000000⟩, + ⟨2, 5, 8, 2, 6, 7, 4206098492911452018498531403212079610462208000000000⟩, + ⟨2, 5, 7, 3, 4, 7, -19348288930271454657851663718781353970410455040000000⟩, + ⟨2, 5, 8, 3, 5, 7, 66922259080731920394141848602183497032505753600000000⟩, + ⟨2, 5, 7, 4, 3, 7, 68624297208979742331686161881949255749001543680000000⟩, + ⟨2, 5, 8, 4, 4, 7, -95745292524279409904871958269462517579461427200000000⟩, + ⟨2, 5, 7, 5, 2, 7, -133296107485451252203364105982909723283732561920000000⟩, + ⟨2, 5, 8, 5, 3, 7, 133931787426610728708898824886508466110201856000000000⟩, + ⟨2, 5, 7, 6, 1, 7, 366226738951888576489959821650718546863576842240000000⟩, + ⟨2, 5, 8, 6, 2, 7, -477620383651379938973752652792170876665090539520000000⟩, + ⟨2, 5, 7, 7, 0, 7, -1241384953541186294849777616941940648335690956800000000⟩, + ⟨2, 5, 8, 7, 1, 7, 893045259278406121475275112474146459415583129600000000⟩ +] + +def collectedFourData_14_0_23 : List CollectedFourTerm := [ + ⟨2, 6, 6, 0, 6, 8, 32688410502700968839424046863129318131132006400000000⟩, + ⟨2, 6, 7, 0, 7, 8, -599183502603831215773634362880408003857612800000000⟩, + ⟨2, 6, 8, 0, 8, 8, 40396907669981111685796515943614524875918540800000000⟩, + ⟨2, 6, 6, 1, 5, 8, -20555768498641011244019326666945211363701555200000000⟩, + ⟨2, 6, 7, 1, 6, 8, -41472055816512319872569793175074980349817651200000000⟩, + ⟨2, 6, 8, 1, 7, 8, 33756252823873746093794998533458178883977216000000000⟩, + ⟨2, 6, 6, 2, 4, 8, 7377753873059037495430907816967266957996851200000000⟩, + ⟨2, 6, 7, 2, 5, 8, 4206098492911452018498531403212079610462208000000000⟩, + ⟨2, 6, 8, 2, 6, 8, 1836897831486968805589946118739671782522880000000000⟩, + ⟨2, 6, 6, 3, 3, 8, 11200112680472982626377565450470940743827456000000000⟩, + ⟨2, 6, 7, 3, 4, 8, -16899666062930292922061969825659338305096908800000000⟩, + ⟨2, 6, 8, 3, 5, 8, 29226456011617109490892498004336239649488896000000000⟩, + ⟨2, 6, 6, 4, 2, 8, -34056123963401805523009611396924835620716544000000000⟩, + ⟨2, 6, 7, 4, 3, 8, 59939548701930930975539573307518518967245209600000000⟩, + ⟨2, 6, 8, 4, 4, 8, -41814123114172374145029661762172236691668992000000000⟩, + ⟨2, 6, 6, 5, 1, 8, 52626673367744399890318942777882366986682368000000000⟩, + ⟨2, 6, 7, 5, 2, 8, -116426817488143873249608319009306032673810022400000000⟩, + ⟨2, 6, 8, 5, 3, 8, 58491024474517502449161119660728691887964160000000000⟩, + ⟨2, 6, 6, 6, 0, 8, -77193047120555269071015615817476273978369638400000000⟩, + ⟨2, 6, 7, 6, 1, 8, 319878910941817858707466063949034433106726092800000000⟩, + ⟨2, 6, 8, 6, 2, 8, -208587566002502525264985249712705483631178547200000000⟩, + ⟨2, 6, 7, 7, 0, 8, -1084281470366586629558495248756059787279466496000000000⟩, + ⟨2, 6, 8, 7, 1, 8, 390012954511846918085251952821397739332960256000000000⟩ +] + +def collectedFourData_14_0_24 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_25 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_26 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_27 : List CollectedFourTerm := [ + ⟨3, 3, 8, 0, 8, 6, 246311966888323630189831773406776138312670248960000000⟩, + ⟨3, 3, 8, 1, 7, 6, 205821918245648697578106978878964105236132659200000000⟩, + ⟨3, 3, 8, 2, 6, 6, 11200112680472982626377565450470940743827456000000000⟩, + ⟨3, 3, 8, 3, 5, 6, 178202399159030642769723259364307188407546675200000000⟩, + ⟨3, 3, 8, 4, 4, 6, -254953151169432796630753561901339702838322790400000000⟩, + ⟨3, 3, 8, 5, 3, 6, 356637181274578941045091503176057776339156992000000000⟩, + ⟨3, 3, 8, 6, 2, 6, -1271820458888813860197761986354574670764326256640000000⟩, + ⟨3, 3, 8, 7, 1, 6, 2378025039008740174239319360839105902613312307200000000⟩ +] + +def collectedFourData_14_0_28 : List CollectedFourTerm := [ + ⟨3, 4, 7, 0, 7, 7, 2756277712033846010150770564298702145101758464000000⟩, + ⟨3, 4, 8, 0, 8, 7, -371656081190464059439842081399593051148106334208000000⟩, + ⟨3, 4, 7, 1, 6, 7, 190773782359717520260287222675933891295608569856000000⟩, + ⟨3, 4, 8, 1, 7, 7, -310561311838187010316747339491090705863053148160000000⟩, + ⟨3, 4, 7, 2, 5, 7, -19348288930271454657851663718781353970410455040000000⟩, + ⟨3, 4, 8, 2, 6, 7, -16899666062930292922061969825659338305096908800000000⟩, + ⟨3, 4, 7, 3, 4, 7, 77739411561982657297567609139914006056816082944000000⟩, + ⟨3, 4, 8, 3, 5, 7, -268886673135992878261637104692328833706056744960000000⟩, + ⟨3, 4, 7, 4, 3, 7, -275725285223236898784321110668271055281584078848000000⟩, + ⟨3, 4, 8, 4, 4, 7, 384694622221715566189201972411323540190443601920000000⟩, + ⟨3, 4, 7, 5, 2, 7, 535569889242727427399339926018481627094488973312000000⟩, + ⟨3, 4, 8, 5, 3, 7, -538123985098210403273816947880646113159125401600000000⟩, + ⟨3, 4, 7, 6, 1, 7, -1471460927991435379129045793603123220297352740864000000⟩, + ⟨3, 4, 8, 6, 2, 7, 1919029000904306260846901288605434413572184604672000000⟩, + ⟨3, 4, 7, 7, 0, 7, 4987755566292189551383335345448400201391255060480000000⟩, + ⟨3, 4, 8, 7, 1, 7, -3588162922557074986790446864800249317442516418560000000⟩ +] + +def collectedFourData_14_0_29 : List CollectedFourTerm := [ + ⟨3, 5, 6, 0, 6, 8, 520097729590928577163189073885648613660300410880000000⟩, + ⟨3, 5, 7, 0, 7, 8, -9533469952197377459024617059643225905309941760000000⟩, + ⟨3, 5, 8, 0, 8, 8, 642745842900972757257435819819029538807333519360000000⟩, + ⟨3, 5, 6, 1, 5, 8, -327058072317604641671512478902997822960660643840000000⟩, + ⟨3, 5, 7, 1, 6, 8, -659852276079746391021817200976482577037698007040000000⟩, + ⟨3, 5, 8, 1, 7, 8, 537087921474292824294558509216792895844201267200000000⟩, + ⟨3, 5, 6, 2, 4, 8, 117385733348571050134083972498024990799602647040000000⟩, + ⟨3, 5, 7, 2, 5, 8, 66922259080731920394141848602183497032505753600000000⟩, + ⟨3, 5, 8, 2, 6, 8, 29226456011617109490892498004336239649488896000000000⟩, + ⟨3, 5, 6, 3, 3, 8, 178202399159030642769723259364307188407546675200000000⟩, + ⟨3, 5, 7, 3, 4, 8, -268886673135992878261637104692328833706056744960000000⟩, + ⟨3, 5, 8, 3, 5, 8, 465015373395877180899620814475441691356771123200000000⟩, + ⟨3, 5, 6, 4, 2, 8, -541859101731757513730053984905197768372178124800000000⟩, + ⟨3, 5, 7, 4, 3, 8, 953684278714111713263457539742658797148380856320000000⟩, + ⟨3, 5, 8, 4, 4, 8, -665294829637546285117521972095693646889117286400000000⟩, + ⟨3, 5, 6, 5, 1, 8, 837330812773097211804351239065850159306480025600000000⟩, + ⟨3, 5, 7, 5, 2, 8, -1852440131161399341614568895607840072796293038080000000⟩, + ⟨3, 5, 8, 5, 3, 8, 930637145178116486703074393651437734903939072000000000⟩, + ⟨3, 5, 6, 6, 0, 8, -1228200696521754410628064248668114395971484385280000000⟩, + ⟨3, 5, 7, 6, 1, 8, 5089519275068809974200059543159518364503386357760000000⟩, + ⟨3, 5, 8, 6, 2, 8, -3318788458369230926299707833280496249048651530240000000⟩, + ⟨3, 5, 7, 7, 0, 8, -17251751379241244144999152617498764071511733043200000000⟩, + ⟨3, 5, 8, 7, 1, 8, 6205405800808242978737726102870103121561072435200000000⟩ +] + +def collectedFourData_14_0_30 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_31 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_32 : List CollectedFourTerm := [ + ⟨4, 2, 8, 0, 8, 6, -748959507580938516123936765375019925239800791040000000⟩, + ⟨4, 2, 8, 1, 7, 6, -625841628752519987710807862760341116845608140800000000⟩, + ⟨4, 2, 8, 2, 6, 6, -34056123963401805523009611396924835620716544000000000⟩, + ⟨4, 2, 8, 3, 5, 6, -541859101731757513730053984905197768372178124800000000⟩, + ⟨4, 2, 8, 4, 4, 6, 775234711363586993203669379937961513571686809600000000⟩, + ⟨4, 2, 8, 5, 3, 6, -1084424809102219447643043979271430479447851008000000000⟩, + ⟨4, 2, 8, 6, 2, 6, 3867217807783598808051107936534339017025897103360000000⟩, + ⟨4, 2, 8, 7, 1, 6, -7230848280459889444456170978978360023824780492800000000⟩ +] + +def collectedFourData_14_0_33 : List CollectedFourTerm := [ + ⟨4, 3, 7, 0, 7, 7, -9775935307910641457123682815258718651902066688000000⟩, + ⟨4, 3, 8, 0, 8, 7, 1318185678695117750839667734144967068396485083136000000⟩, + ⟨4, 3, 7, 1, 6, 7, -676634341543854352806893769924515766185861578752000000⟩, + ⟨4, 3, 8, 1, 7, 7, 1101495426391452910743618191714397600011224350720000000⟩, + ⟨4, 3, 7, 2, 5, 7, 68624297208979742331686161881949255749001543680000000⟩, + ⟨4, 3, 8, 2, 6, 7, 59939548701930930975539573307518518967245209600000000⟩, + ⟨4, 3, 7, 3, 4, 7, -275725285223236898784321110668271055281584078848000000⟩, + ⟨4, 3, 8, 3, 5, 7, 953684278714111713263457539742658797148380856320000000⟩, + ⟨4, 3, 7, 4, 3, 7, 977939392438287983569145128857876301540560470016000000⟩, + ⟨4, 3, 8, 4, 4, 7, -1364430631834109727740331263789947008926236016640000000⟩, + ⟨4, 3, 7, 5, 2, 7, -1899553360404446209338964415483963685797263048704000000⟩, + ⟨4, 3, 8, 5, 3, 7, 1908612199339431456357372257349088766231524147200000000⟩, + ⟨4, 3, 7, 6, 1, 7, 5218961346804153246109056925129284564903933247488000000⟩, + ⟨4, 3, 8, 6, 2, 7, -6806390838244575514674821357889856907366130253824000000⟩, + ⟨4, 3, 7, 7, 0, 7, -17690516283921138682650985026764514654213541724160000000⟩, + ⟨4, 3, 8, 7, 1, 7, 12726456572940138558815426956265271851004482027520000000⟩ +] + +def collectedFourData_14_0_34 : List CollectedFourTerm := [ + ⟨4, 4, 6, 0, 6, 8, -744100840959722206580854800298213120740698357760000000⟩, + ⟨4, 4, 7, 0, 7, 8, 13639480822717363251819643263720292217278955520000000⟩, + ⟨4, 4, 8, 0, 8, 8, -919572793755801001584209778755655714636268830720000000⟩, + ⟨4, 4, 6, 1, 5, 8, 467920109640947674440307180637083357234782535680000000⟩, + ⟨4, 4, 7, 1, 6, 8, 944046869664877551304454062126517115122960302080000000⟩, + ⟨4, 4, 8, 1, 7, 8, -768408611113654616329717478576501192281974374400000000⟩, + ⟨4, 4, 6, 2, 4, 8, -167943095944768202408039385448334564257777582080000000⟩, + ⟨4, 4, 7, 2, 5, 8, -95745292524279409904871958269462517579461427200000000⟩, + ⟨4, 4, 8, 2, 6, 8, -41814123114172374145029661762172236691668992000000000⟩, + ⟨4, 4, 6, 3, 3, 8, -254953151169432796630753561901339702838322790400000000⟩, + ⟨4, 4, 7, 3, 4, 8, 384694622221715566189201972411323540190443601920000000⟩, + ⟨4, 4, 8, 3, 5, 8, -665294829637546285117521972095693646889117286400000000⟩, + ⟨4, 4, 6, 4, 2, 8, 775234711363586993203669379937961513571686809600000000⟩, + ⟨4, 4, 7, 4, 3, 8, -1364430631834109727740331263789947008926236016640000000⟩, + ⟨4, 4, 8, 4, 4, 8, 951833499847848196353227906955483865303272652800000000⟩, + ⟨4, 4, 6, 5, 1, 8, -1197964394953237614648641818850400125930648371200000000⟩, + ⟨4, 4, 7, 5, 2, 8, 2650275479012160497253100989394769109246447452160000000⟩, + ⟨4, 4, 8, 5, 3, 8, -1331457229971091520396924521069095379789676544000000000⟩, + ⟨4, 4, 6, 6, 0, 8, 1757179697492557825325032872766816962986177986560000000⟩, + ⟨4, 4, 7, 6, 1, 8, -7281546057965085975458925562175412818153066987520000000⟩, + ⟨4, 4, 8, 6, 2, 8, 4748171626863870503971169358377386706649722388480000000⟩, + ⟨4, 4, 7, 7, 0, 8, 24681981825642943405764778658602061498937665126400000000⟩, + ⟨4, 4, 8, 7, 1, 8, -8878038515010445968721106557560402660169246310400000000⟩ +] + +def collectedFourData_14_0_35 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_0_36 : List CollectedFourTerm := [ + ⟨5, 1, 8, 0, 8, 6, 1157361519281703312494325613286393670534042746880000000⟩, + ⟨5, 1, 8, 1, 7, 6, 967108382964850673883829157668505927085037977600000000⟩, + ⟨5, 1, 8, 2, 6, 6, 52626673367744399890318942777882366986682368000000000⟩, + ⟨5, 1, 8, 3, 5, 6, 837330812773097211804351239065850159306480025600000000⟩, + ⟨5, 1, 8, 4, 4, 6, -1197964394953237614648641818850400125930648371200000000⟩, + ⟨5, 1, 8, 5, 3, 6, 1675753537949022941429961351841487626463870976000000000⟩, + ⟨5, 1, 8, 6, 2, 6, -5975982722838987169668091558408628791364466769920000000⟩, + ⟨5, 1, 8, 7, 1, 6, 11173775707312402003930434969271853629258176921600000000⟩ +] + +def collectedFourData_14_0_37 : List CollectedFourTerm := [ + ⟨5, 2, 7, 0, 7, 7, 18988815573670606214328176568886462540280758272000000⟩, + ⟨5, 2, 8, 0, 8, 7, -2560449098342602061593065792297168903993487785984000000⟩, + ⟨5, 2, 7, 1, 6, 7, 1314297232715049107903971416074759110374444761088000000⟩, + ⟨5, 2, 8, 1, 7, 7, -2139549091539482688733959181628817347534577991680000000⟩, + ⟨5, 2, 7, 2, 5, 7, -133296107485451252203364105982909723283732561920000000⟩, + ⟨5, 2, 8, 2, 6, 7, -116426817488143873249608319009306032673810022400000000⟩, + ⟨5, 2, 7, 3, 4, 7, 535569889242727427399339926018481627094488973312000000⟩, + ⟨5, 2, 8, 3, 5, 7, -1852440131161399341614568895607840072796293038080000000⟩, + ⟨5, 2, 7, 4, 3, 7, -1899553360404446209338964415483963685797263048704000000⟩, + ⟨5, 2, 8, 4, 4, 7, 2650275479012160497253100989394769109246447452160000000⟩, + ⟨5, 2, 7, 5, 2, 7, 3689699992580596183018388895451957362704542334976000000⟩, + ⟨5, 2, 8, 5, 3, 7, -3707295917311074550151551464215014559728848076800000000⟩, + ⟨5, 2, 7, 6, 1, 7, -10137331250584978196083865156551116010596411113472000000⟩, + ⟨5, 2, 8, 6, 2, 7, 13220760600283722275636697056351200316253857120256000000⟩, + ⟨5, 2, 7, 7, 0, 7, 34362129099460048069923530363380169214761411543040000000⟩, + ⟨5, 2, 8, 7, 1, 7, -24719919798808195053150448488242969999966082170880000000⟩ +] + +def collectedFourData_14_0_38 : List CollectedFourTerm := [ + ⟨5, 3, 6, 0, 6, 8, 1040873687133056627683179656077368288613289164800000000⟩, + ⟨5, 3, 7, 0, 7, 8, -19079371925197049427108657287351822932613529600000000⟩, + ⟨5, 3, 8, 0, 8, 8, 1286329851729944421659986562530852201200982425600000000⟩, + ⟨5, 3, 6, 1, 5, 8, -654542641260152610379087673704947072018835046400000000⟩, + ⟨5, 3, 7, 1, 6, 8, -1320565025551006855236118808070888378060924518400000000⟩, + ⟨5, 3, 8, 1, 7, 8, 1074876226780066705548287320339545915824013312000000000⟩, + ⟨5, 3, 6, 2, 4, 8, 234924542322932022293833242373694584141538918400000000⟩, + ⟨5, 3, 7, 2, 5, 8, 133931787426610728708898824886508466110201856000000000⟩, + ⟨5, 3, 8, 2, 6, 8, 58491024474517502449161119660728691887964160000000000⟩, + ⟨5, 3, 6, 3, 3, 8, 356637181274578941045091503176057776339156992000000000⟩, + ⟨5, 3, 7, 3, 4, 8, -538123985098210403273816947880646113159125401600000000⟩, + ⟨5, 3, 8, 3, 5, 8, 930637145178116486703074393651437734903939072000000000⟩, + ⟨5, 3, 6, 4, 2, 8, -1084424809102219447643043979271430479447851008000000000⟩, + ⟨5, 3, 7, 4, 3, 8, 1908612199339431456357372257349088766231524147200000000⟩, + ⟨5, 3, 8, 4, 4, 8, -1331457229971091520396924521069095379789676544000000000⟩, + ⟨5, 3, 6, 5, 1, 8, 1675753537949022941429961351841487626463870976000000000⟩, + ⟨5, 3, 7, 5, 2, 8, -3707295917311074550151551464215014559728848076800000000⟩, + ⟨5, 3, 8, 5, 3, 8, 1862487877896368410590058482662172810931077120000000000⟩, + ⟨5, 3, 6, 6, 0, 8, -2458003015190021349751354686578809917122858188800000000⟩, + ⟨5, 3, 7, 6, 1, 8, 10185675483994714706039821878218023091379476889600000000⟩, + ⟨5, 3, 8, 6, 2, 8, -6641904747775822108271259047541625868685567590400000000⟩, + ⟨5, 3, 7, 7, 0, 8, -34525999722662178793273469668091844708135862272000000000⟩, + ⟨5, 3, 8, 7, 1, 8, 12418903695511903932609298491767377625289326592000000000⟩ +] + +def collectedFourData_14_0_39 : List CollectedFourTerm := [ + ⟨6, 0, 8, 0, 8, 6, -1697623212266117031114556599085337978418751340544000000⟩, + ⟨6, 0, 8, 1, 7, 6, -1418559034792539284926600917324467764321981562880000000⟩, + ⟨6, 0, 8, 2, 6, 6, -77193047120555269071015615817476273978369638400000000⟩, + ⟨6, 0, 8, 3, 5, 6, -1228200696521754410628064248668114395971484385280000000⟩, + ⟨6, 0, 8, 4, 4, 6, 1757179697492557825325032872766816962986177986560000000⟩, + ⟨6, 0, 8, 5, 3, 6, -2458003015190021349751354686578809917122858188800000000⟩, + ⟨6, 0, 8, 6, 2, 6, 8765599008932868849926885405852776202684696887296000000⟩, + ⟨6, 0, 8, 7, 1, 6, -16389745721943031124837751533222941776658122670080000000⟩ +] + +def collectedFourData_14_0_40 : List CollectedFourTerm := [ + ⟨6, 1, 7, 0, 7, 7, -52171155897131102762426606947217349580878249984000000⟩, + ⟨6, 1, 8, 0, 8, 7, 7034750985813006015576061313323760654751941787648000000⟩, + ⟨6, 1, 7, 1, 6, 7, -3610989087609022714810565959494225231835023015936000000⟩, + ⟨6, 1, 8, 1, 7, 7, 5878341846610209494430698169008427468382493736960000000⟩, + ⟨6, 1, 7, 2, 5, 7, 366226738951888576489959821650718546863576842240000000⟩, + ⟨6, 1, 8, 2, 6, 7, 319878910941817858707466063949034433106726092800000000⟩, + ⟨6, 1, 7, 3, 4, 7, -1471460927991435379129045793603123220297352740864000000⟩, + ⟨6, 1, 8, 3, 5, 7, 5089519275068809974200059543159518364503386357760000000⟩, + ⟨6, 1, 7, 4, 3, 7, 5218961346804153246109056925129284564903933247488000000⟩, + ⟨6, 1, 8, 4, 4, 7, -7281546057965085975458925562175412818153066987520000000⟩, + ⟨6, 1, 7, 5, 2, 7, -10137331250584978196083865156551116010596411113472000000⟩, + ⟨6, 1, 8, 5, 3, 7, 10185675483994714706039821878218023091379476889600000000⟩, + ⟨6, 1, 7, 6, 1, 7, 27851989346215669041289288913573180647587534864384000000⟩, + ⟨6, 1, 8, 6, 2, 7, -36323611637601522131480070398416803154692912709632000000⟩, + ⟨6, 1, 7, 7, 0, 7, -94408836994077861417079175936591038336163779706880000000⟩, + ⟨6, 1, 8, 7, 1, 7, 67917179172376513253054821457332632400394830479360000000⟩ +] + +def collectedFourData_14_0_41 : List CollectedFourTerm := [ + ⟨6, 2, 6, 0, 6, 8, -3711908123779286896940164073919929814697918857216000000⟩, + ⟨6, 2, 7, 0, 7, 8, 68039836649931788961168040787135088446964498432000000⟩, + ⟨6, 2, 8, 0, 8, 8, -4587240781969948588848031512951918159511003594752000000⟩, + ⟨6, 2, 6, 1, 5, 8, 2334194991656976933997168048568841887027180863488000000⟩, + ⟨6, 2, 7, 1, 6, 8, 4709328429487887091019147006605555957019839561728000000⟩, + ⟨6, 2, 8, 1, 7, 8, -3833166163736569252972832985347370820507313111040000000⟩, + ⟨6, 2, 6, 2, 4, 8, -837775349596430635447339056829606973661121609728000000⟩, + ⟨6, 2, 7, 2, 5, 8, -477620383651379938973752652792170876665090539520000000⟩, + ⟨6, 2, 8, 2, 6, 8, -208587566002502525264985249712705483631178547200000000⟩, + ⟨6, 2, 6, 3, 3, 8, -1271820458888813860197761986354574670764326256640000000⟩, + ⟨6, 2, 7, 3, 4, 8, 1919029000904306260846901288605434413572184604672000000⟩, + ⟨6, 2, 8, 3, 5, 8, -3318788458369230926299707833280496249048651530240000000⟩, + ⟨6, 2, 6, 4, 2, 8, 3867217807783598808051107936534339017025897103360000000⟩, + ⟨6, 2, 7, 4, 3, 8, -6806390838244575514674821357889856907366130253824000000⟩, + ⟨6, 2, 8, 4, 4, 8, 4748171626863870503971169358377386706649722388480000000⟩, + ⟨6, 2, 6, 5, 1, 8, -5975982722838987169668091558408628791364466769920000000⟩, + ⟨6, 2, 7, 5, 2, 8, 13220760600283722275636697056351200316253857120256000000⟩, + ⟨6, 2, 8, 5, 3, 8, -6641904747775822108271259047541625868685567590400000000⟩, + ⟨6, 2, 6, 6, 0, 8, 8765599008932868849926885405852776202684696887296000000⟩, + ⟨6, 2, 7, 6, 1, 8, -36323611637601522131480070398416803154692912709632000000⟩, + ⟨6, 2, 8, 6, 2, 8, 23686005800130971657766361561863473556563026771968000000⟩, + ⟨6, 2, 7, 7, 0, 8, 123124775307888612663664748403832476326865131274240000000⟩, + ⟨6, 2, 8, 7, 1, 8, -44287630752558817426334797224763039796324613488640000000⟩ +] + +def collectedFourData_14_0_42 : List CollectedFourTerm := [ + ⟨7, 0, 7, 0, 7, 7, 176842597907790207852980038031943025875096698880000000⟩, + ⟨7, 0, 8, 0, 8, 7, -23845429885021395274512712180507590858189947535360000000⟩, + ⟨7, 0, 7, 1, 6, 7, 12240033410963317950082969513869561523686887915520000000⟩, + ⟨7, 0, 8, 1, 7, 7, -19925593475336258374001962529758023221874209587200000000⟩, + ⟨7, 0, 7, 2, 5, 7, -1241384953541186294849777616941940648335690956800000000⟩, + ⟨7, 0, 8, 2, 6, 7, -1084281470366586629558495248756059787279466496000000000⟩, + ⟨7, 0, 7, 3, 4, 7, 4987755566292189551383335345448400201391255060480000000⟩, + ⟨7, 0, 8, 3, 5, 7, -17251751379241244144999152617498764071511733043200000000⟩, + ⟨7, 0, 7, 4, 3, 7, -17690516283921138682650985026764514654213541724160000000⟩, + ⟨7, 0, 8, 4, 4, 7, 24681981825642943405764778658602061498937665126400000000⟩, + ⟨7, 0, 7, 5, 2, 7, 34362129099460048069923530363380169214761411543040000000⟩, + ⟨7, 0, 8, 5, 3, 7, -34525999722662178793273469668091844708135862272000000000⟩, + ⟨7, 0, 7, 6, 1, 7, -94408836994077861417079175936591038336163779706880000000⟩, + ⟨7, 0, 8, 6, 2, 7, 123124775307888612663664748403832476326865131274240000000⟩, + ⟨7, 0, 7, 7, 0, 7, 320014071231339305559734377165695341956968323481600000000⟩, + ⟨7, 0, 8, 7, 1, 7, -230216298659244204447898219947783425187606901555200000000⟩ +] + +def collectedFourData_14_0_43 : List CollectedFourTerm := [ + ⟨7, 1, 6, 0, 6, 8, 6940453268505551286821575362685942329440395591680000000⟩, + ⟨7, 1, 7, 0, 7, 8, -127219556874377504612441478416848717549519503360000000⟩, + ⟨7, 1, 8, 0, 8, 8, 8577133166278330093181571350685610550351584296960000000⟩, + ⟨7, 1, 6, 1, 5, 8, -4364432178531539792902434002812959780419917578240000000⟩, + ⟨7, 1, 7, 1, 6, 8, -8805410263664378886410221730355469578828974653440000000⟩, + ⟨7, 1, 8, 1, 7, 8, 7167179181887597713343033523020968684923597619200000000⟩, + ⟨7, 1, 6, 2, 4, 8, 1566455976140875315016915697302654486519941693440000000⟩, + ⟨7, 1, 7, 2, 5, 8, 893045259278406121475275112474146459415583129600000000⟩, + ⟨7, 1, 8, 2, 6, 8, 390012954511846918085251952821397739332960256000000000⟩, + ⟨7, 1, 6, 3, 3, 8, 2378025039008740174239319360839105902613312307200000000⟩, + ⟨7, 1, 7, 3, 4, 8, -3588162922557074986790446864800249317442516418560000000⟩, + ⟨7, 1, 8, 3, 5, 8, 6205405800808242978737726102870103121561072435200000000⟩, + ⟨7, 1, 6, 4, 2, 8, -7230848280459889444456170978978360023824780492800000000⟩, + ⟨7, 1, 7, 4, 3, 8, 12726456572940138558815426956265271851004482027520000000⟩, + ⟨7, 1, 8, 4, 4, 8, -8878038515010445968721106557560402660169246310400000000⟩, + ⟨7, 1, 6, 5, 1, 8, 11173775707312402003930434969271853629258176921600000000⟩, + ⟨7, 1, 7, 5, 2, 8, -24719919798808195053150448488242969999966082170880000000⟩, + ⟨7, 1, 8, 5, 3, 8, 12418903695511903932609298491767377625289326592000000000⟩, + ⟨7, 1, 6, 6, 0, 8, -16389745721943031124837751533222941776658122670080000000⟩, + ⟨7, 1, 7, 6, 1, 8, 67917179172376513253054821457332632400394830479360000000⟩, + ⟨7, 1, 8, 6, 2, 8, -44287630752558817426334797224763039796324613488640000000⟩, + ⟨7, 1, 7, 7, 0, 8, -230216298659244204447898219947783425187606901555200000000⟩, + ⟨7, 1, 8, 7, 1, 8, 82808146473735473160894200869780358339941839667200000000⟩ +] + +def collectedFourData_14_0 : List (List CollectedFourTerm) := [ + collectedFourData_14_0_0, + collectedFourData_14_0_1, + collectedFourData_14_0_2, + collectedFourData_14_0_3, + collectedFourData_14_0_4, + collectedFourData_14_0_5, + collectedFourData_14_0_6, + collectedFourData_14_0_7, + collectedFourData_14_0_8, + collectedFourData_14_0_9, + collectedFourData_14_0_10, + collectedFourData_14_0_11, + collectedFourData_14_0_12, + collectedFourData_14_0_13, + collectedFourData_14_0_14, + collectedFourData_14_0_15, + collectedFourData_14_0_16, + collectedFourData_14_0_17, + collectedFourData_14_0_18, + collectedFourData_14_0_19, + collectedFourData_14_0_20, + collectedFourData_14_0_21, + collectedFourData_14_0_22, + collectedFourData_14_0_23, + collectedFourData_14_0_24, + collectedFourData_14_0_25, + collectedFourData_14_0_26, + collectedFourData_14_0_27, + collectedFourData_14_0_28, + collectedFourData_14_0_29, + collectedFourData_14_0_30, + collectedFourData_14_0_31, + collectedFourData_14_0_32, + collectedFourData_14_0_33, + collectedFourData_14_0_34, + collectedFourData_14_0_35, + collectedFourData_14_0_36, + collectedFourData_14_0_37, + collectedFourData_14_0_38, + collectedFourData_14_0_39, + collectedFourData_14_0_40, + collectedFourData_14_0_41, + collectedFourData_14_0_42, + collectedFourData_14_0_43 +] + +theorem collectedFourChecked_14_0 : collectNumericRowParts 14 0 = collectedFourData_14_0 := by + decide +kernel + +def collectedFourData_14_1_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_1 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_2 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_3 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_4 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_5 : List CollectedFourTerm := [ + ⟨0, 6, 8, 1, 8, 5, -2569983217398187879639508278742126344703953600512000000⟩, + ⟨0, 6, 8, 2, 7, 5, -1103492561399760688898220643699760270438735806464000000⟩, + ⟨0, 6, 8, 3, 6, 5, 59256369231242693210590787632952809343554682880000000⟩, + ⟨0, 6, 8, 4, 5, 5, 806546322126019885089482488385846732383454232576000000⟩, + ⟨0, 6, 8, 5, 4, 5, 403758943638031512264346494993718296924471164928000000⟩, + ⟨0, 6, 8, 6, 3, 5, -2143718049704078109949280320115852398571915575296000000⟩, + ⟨0, 6, 8, 7, 2, 5, 843181388098615413549179789953892948072070119424000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1402.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1402.lean new file mode 100644 index 0000000000000000000000000000000000000000..62dabac144c2fb8e46388549fefcc84053f67596 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1402.lean @@ -0,0 +1,635 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1402. -/ +namespace LaughlinFock +def collectedFourData_14_1_6 : List CollectedFourTerm := [ + ⟨0, 7, 7, 0, 8, 6, 3095450102873909644399632757240610874958156922880000000⟩, + ⟨0, 7, 7, 1, 7, 6, -244879901790313428071746960476868398515906150400000000⟩, + ⟨0, 7, 8, 1, 8, 6, -3538862759453807983213912896890377015753369976832000000⟩, + ⟨0, 7, 7, 2, 6, 6, -153587980791903437995393782162038070344845099008000000⟩, + ⟨0, 7, 8, 2, 7, 6, -1519507483331109350334134193937116213658993557504000000⟩, + ⟨0, 7, 7, 3, 5, 6, -368378682349146086426705723780218148408222810112000000⟩, + ⟨0, 7, 8, 3, 6, 6, 81595925184751403483850446238459648901046599680000000⟩, + ⟨0, 7, 7, 4, 4, 6, 190453578035341204188609913471086786190856159232000000⟩, + ⟨0, 7, 8, 4, 5, 6, 1110612989152440058443592031152207408791275175936000000⟩, + ⟨0, 7, 7, 5, 3, 6, 217247369038149688933005815609722403137020493824000000⟩, + ⟨0, 7, 8, 5, 4, 6, 555975416401194364122269014830425439829657387008000000⟩, + ⟨0, 7, 7, 6, 2, 6, 1537567504627269799651792103303040542174110285824000000⟩, + ⟨0, 7, 8, 6, 3, 6, -2951896308703131903123200206961769993630023417856000000⟩, + ⟨0, 7, 7, 7, 1, 6, -7954660640609756318023919034299979323782465585152000000⟩, + ⟨0, 7, 8, 7, 2, 6, 1161059416110746751484522564536606576394647896064000000⟩ +] + +def collectedFourData_14_1_7 : List CollectedFourTerm := [ + ⟨0, 8, 6, 0, 7, 7, 3095450102873909644399632757240610874958156922880000000⟩, + ⟨0, 8, 7, 0, 8, 7, 9079886857216165190331091096565608200106986700800000000⟩, + ⟨0, 8, 6, 1, 6, 7, -1140689823251025990101449466199566751296787578880000000⟩, + ⟨0, 8, 7, 1, 7, 7, -718306458824163993594572719780006438857867264000000000⟩, + ⟨0, 8, 8, 1, 8, 7, -5190274821297167868304128800848721587022132674560000000⟩, + ⟨0, 8, 6, 2, 5, 7, -20493675318662935454721584513031320173144965120000000⟩, + ⟨0, 8, 7, 2, 6, 7, -450519776404736656347844668829839604296481505280000000⟩, + ⟨0, 8, 8, 2, 7, 7, -2228586404046739289019205722747257277720633016320000000⟩, + ⟨0, 8, 6, 3, 4, 7, 331848191812790617326591485571557131975686881280000000⟩, + ⟨0, 8, 7, 3, 5, 7, -1080565554338986861807884200091140506045560913920000000⟩, + ⟨0, 8, 8, 3, 6, 7, 119672704140758186798117549475144757636654694400000000⟩, + ⟨0, 8, 6, 4, 3, 7, -418994767525820581511679630017321232542560419840000000⟩, + ⟨0, 8, 7, 4, 4, 7, 558657669366841433320722072288925627689593733120000000⟩, + ⟨0, 8, 8, 4, 5, 7, 1628881091363140657352083273780123973213623418880000000⟩, + ⟨0, 8, 6, 5, 2, 7, 909527245764447674894648158973979664212515880960000000⟩, + ⟨0, 8, 7, 5, 3, 7, 637251923092826133210744440210716813139210403840000000⟩, + ⟨0, 8, 8, 5, 4, 7, 815421620207929270199986387183964329507175792640000000⟩, + ⟨0, 8, 6, 6, 1, 7, -1703364967747029222454909141422118773235352862720000000⟩, + ⟨0, 8, 7, 6, 2, 7, 4510148286475703049375915994020187692278313123840000000⟩, + ⟨0, 8, 8, 6, 3, 7, -4329400185190171441617976805963104099171282452480000000⟩, + ⟨0, 8, 6, 7, 0, 7, -505444423071106490877517386019013528740996055040000000⟩, + ⟨0, 8, 7, 7, 1, 7, -23333413947531935407007144434325402806644973240320000000⟩, + ⟨0, 8, 8, 7, 2, 7, 1702868368481091725608384463072659554683710341120000000⟩ +] + +def collectedFourData_14_1_8 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_9 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_10 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_11 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_12 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_13 : List CollectedFourTerm := [ + ⟨1, 5, 8, 1, 8, 5, 842396334118616022245097416289952615503054766080000000⟩, + ⟨1, 5, 8, 2, 7, 5, 361705898372134508102340421150046179641010421760000000⟩, + ⟨1, 5, 8, 3, 6, 5, -19423219527524216994272923722722093688894259200000000⟩, + ⟨1, 5, 8, 4, 5, 5, -264372024088024158482225389671872019262435491840000000⟩, + ⟨1, 5, 8, 5, 4, 5, -132345243224047239748347716617957658685100523520000000⟩, + ⟨1, 5, 8, 6, 3, 5, 702673937413042743354768922708985990976519536640000000⟩, + ⟨1, 5, 8, 7, 2, 5, -276380369149028712887366748615835468395876188160000000⟩ +] + +def collectedFourData_14_1_14 : List CollectedFourTerm := [ + ⟨1, 6, 7, 0, 8, 6, -1140689823251025990101449466199566751296787578880000000⟩, + ⟨1, 6, 7, 1, 7, 6, 90239545981239021001442234058624914633942630400000000⟩, + ⟨1, 6, 8, 1, 8, 6, 1304089745088498192072555603934558039562866655232000000⟩, + ⟨1, 6, 7, 2, 6, 6, 56597987640098221881702334834912177700217028608000000⟩, + ⟨1, 6, 8, 2, 7, 6, 559946587728982788923993081302186926555009122304000000⟩, + ⟨1, 6, 7, 3, 5, 6, 135749503333347706087723827166045310428498624512000000⟩, + ⟨1, 6, 8, 3, 6, 6, -30068532324453808383650267361891865025241415680000000⟩, + ⟨1, 6, 7, 4, 4, 6, -70183156260525341466065711030566578786907717632000000⟩, + ⟨1, 6, 8, 4, 5, 6, -409266792289882080157344129227831673458981339136000000⟩, + ⟨1, 6, 7, 5, 3, 6, -80056810723520093051421384136354820356124442624000000⟩, + ⟨1, 6, 8, 5, 4, 6, -204879897394497705683496531679476140792094916608000000⟩, + ⟨1, 6, 7, 6, 2, 6, -566601801612450186726219750289790620279844634624000000⟩, + ⟨1, 6, 8, 6, 3, 6, 1087789486738527261891217074363604003643568685056000000⟩, + ⟨1, 6, 7, 7, 1, 6, 2931334745707787346679106610000459411739537047552000000⟩, + ⟨1, 6, 8, 7, 2, 6, -427856568877555490275089093935353178592708132864000000⟩ +] + +def collectedFourData_14_1_15 : List CollectedFourTerm := [ + ⟨1, 7, 6, 0, 7, 7, -244879901790313428071746960476868398515906150400000000⟩, + ⟨1, 7, 7, 0, 8, 7, -718306458824163993594572719780006438857867264000000000⟩, + ⟨1, 7, 6, 1, 6, 7, 90239545981239021001442234058624914633942630400000000⟩, + ⟨1, 7, 7, 1, 7, 7, 56824955740329752592002646860173277260677120000000000⟩, + ⟨1, 7, 8, 1, 8, 7, 410600703052508494749975389124179521065241804800000000⟩, + ⟨1, 7, 6, 2, 5, 7, 1621247002074894531876458480768918297876889600000000⟩, + ⟨1, 7, 7, 2, 6, 7, 35640451286279317040091250392833972253386342400000000⟩, + ⟨1, 7, 8, 2, 7, 7, 176302638264953915671697821896527436857317785600000000⟩, + ⟨1, 7, 6, 3, 4, 7, -26252386541447485167235855884984881871480422400000000⟩, + ⟨1, 7, 7, 3, 5, 7, 85483137518145059847280518083605137586755993600000000⟩, + ⟨1, 7, 8, 3, 6, 7, -9467262938518066125209643891967790942257152000000000⟩, + ⟨1, 7, 6, 4, 3, 7, 33146519605377598443477506552084462417687347200000000⟩, + ⟨1, 7, 7, 4, 4, 7, -44195199619578590605380349209124918011730329600000000⟩, + ⟨1, 7, 8, 4, 5, 7, -128860174909869146010594294759605733058569830400000000⟩, + ⟨1, 7, 6, 5, 2, 7, -71952360792902986177225297659209754981747916800000000⟩, + ⟨1, 7, 7, 5, 3, 7, -50412761684569848885484866024841471147062067200000000⟩, + ⟨1, 7, 8, 5, 4, 7, -64507699894379390650628640922870264188056371200000000⟩, + ⟨1, 7, 6, 6, 1, 7, 134752566558151338093696270881809511929715097600000000⟩, + ⟨1, 7, 7, 6, 2, 7, -356796146843562642969033324114689847121359667200000000⟩, + ⟨1, 7, 8, 6, 3, 7, 342497232042612430515709224894592573912802918400000000⟩, + ⟨1, 7, 6, 7, 0, 7, 39985519575069040137489278332568098856710963200000000⟩, + ⟨1, 7, 7, 7, 1, 7, 1845897664639919991381530185454079397001271705600000000⟩, + ⟨1, 7, 8, 7, 2, 7, -134713280775654307313261545529312717464770969600000000⟩ +] + +def collectedFourData_14_1_16 : List CollectedFourTerm := [ + ⟨1, 8, 5, 0, 6, 8, -2569983217398187879639508278742126344703953600512000000⟩, + ⟨1, 8, 6, 0, 7, 8, -3538862759453807983213912896890377015753369976832000000⟩, + ⟨1, 8, 7, 0, 8, 8, -5190274821297167868304128800848721587022132674560000000⟩, + ⟨1, 8, 5, 1, 5, 8, 842396334118616022245097416289952615503054766080000000⟩, + ⟨1, 8, 6, 1, 6, 8, 1304089745088498192072555603934558039562866655232000000⟩, + ⟨1, 8, 7, 1, 7, 8, 410600703052508494749975389124179521065241804800000000⟩, + ⟨1, 8, 8, 1, 8, 8, 1977921321723800802904734044573596689209468387328000000⟩, + ⟨1, 8, 5, 2, 4, 8, -632807663771380186299684046538708667252665745408000000⟩, + ⟨1, 8, 6, 2, 5, 8, 23429324324181530912840722911506741425097146368000000⟩, + ⟨1, 8, 7, 2, 6, 8, 257527597947057334343969346384994110773548548096000000⟩, + ⟨1, 8, 8, 2, 7, 8, 849274598674558667801631042180464955624328790016000000⟩, + ⟨1, 8, 5, 3, 3, 8, 188959890695237332593725815104979012338365497344000000⟩, + ⟨1, 8, 6, 3, 4, 8, -379384312061128861620170465278930387527209582592000000⟩, + ⟨1, 8, 7, 3, 5, 8, 617676439986628792044684120690035882864456761344000000⟩, + ⟨1, 8, 8, 3, 6, 8, -45605136779480259593691853846673762103821598720000000⟩, + ⟨1, 8, 5, 4, 2, 8, 390256001714042852899954504629478365871346810880000000⟩, + ⟨1, 8, 6, 4, 3, 8, 479014337148089796026719780730692393956777394176000000⟩, + ⟨1, 8, 7, 4, 4, 8, -319341736371401202048943790926149842662047350784000000⟩, + ⟨1, 8, 8, 4, 5, 8, -620737581744214741942358003195044502740867743744000000⟩, + ⟨1, 8, 5, 5, 1, 8, 131756407902074446024720292454715631201006125056000000⟩, + ⟨1, 8, 6, 5, 2, 8, -1039813917774369498411410766439031916095229394944000000⟩, + ⟨1, 8, 7, 5, 3, 8, -364268042461704944322132989257502658203524005888000000⟩, + ⟨1, 8, 8, 5, 4, 8, -310742660906103077054825172561683895805418668032000000⟩, + ⟨1, 8, 5, 6, 0, 8, -6996110078586734638789406789436755800461429178368000000⟩, + ⟨1, 8, 6, 6, 1, 8, 1947366182553433510591208435055137928622016299008000000⟩, + ⟨1, 8, 7, 6, 2, 8, -2578105813400898282099457535391655256937241509888000000⟩, + ⟨1, 8, 8, 6, 3, 8, 1649857325748016933313667512661239462835649511424000000⟩, + ⟨1, 8, 6, 7, 0, 8, 577847610633190973602910533522694795103049875456000000⟩, + ⟨1, 8, 7, 7, 1, 8, 13337922907104344072951462177828492467630006861824000000⟩, + ⟨1, 8, 8, 7, 2, 8, -648932815712829326550840933747674980704904544256000000⟩ +] + +def collectedFourData_14_1_17 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_18 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_19 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_20 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_21 : List CollectedFourTerm := [ + ⟨2, 4, 8, 1, 8, 5, -632807663771380186299684046538708667252665745408000000⟩, + ⟨2, 4, 8, 2, 7, 5, -271713272305110907704706441590551950400239435776000000⟩, + ⟨2, 4, 8, 3, 6, 5, 14590711847044384726288708831567698747897937920000000⟩, + ⟨2, 4, 8, 4, 5, 5, 198596119372590875373911644274294785802275651584000000⟩, + ⟨2, 4, 8, 5, 4, 5, 99417674061330718614903819428664744535551639552000000⟩, + ⟨2, 4, 8, 6, 3, 5, -527848276064284645896106228083780314239088984064000000⟩, + ⟨2, 4, 8, 7, 2, 5, 207616781590649493949832098838870479233840316416000000⟩ +] + +def collectedFourData_14_1_22 : List CollectedFourTerm := [ + ⟨2, 5, 7, 0, 8, 6, -20493675318662935454721584513031320173144965120000000⟩, + ⟨2, 5, 7, 1, 7, 6, 1621247002074894531876458480768918297876889600000000⟩, + ⟨2, 5, 8, 1, 8, 6, 23429324324181530912840722911506741425097146368000000⟩, + ⟨2, 5, 7, 2, 6, 6, 1016841527594322333411938117728736374048161792000000⟩, + ⟨2, 5, 8, 2, 7, 6, 10060020989760033978122444822661890980913872896000000⟩, + ⟨2, 5, 7, 3, 5, 6, 2438880569701687747532286829484186493505241088000000⟩, + ⟨2, 5, 8, 3, 6, 6, -540212357650244710658952200928685063478968320000000⟩, + ⟨2, 5, 7, 4, 4, 6, -1260913166686216937193309728662114772837203968000000⟩, + ⟨2, 5, 8, 4, 5, 6, -7352902242955959981982770617368336367735537664000000⟩, + ⟨2, 5, 7, 5, 3, 6, -1438303605917611806836976440473033930834968576000000⟩, + ⟨2, 5, 8, 5, 4, 6, -3680879771993736634491661284281277331424673792000000⟩, + ⟨2, 5, 7, 6, 2, 6, -10179588807166628028265492691497163515364376576000000⟩, + ⟨2, 5, 8, 6, 3, 6, 19543265927225258505286830799733427937417887744000000⟩, + ⟨2, 5, 7, 7, 1, 6, 52664467854755835349651617591580864973056770048000000⟩, + ⟨2, 5, 8, 7, 2, 6, -7686886852854966534784898067001119928888590336000000⟩ +] + +def collectedFourData_14_1_23 : List CollectedFourTerm := [ + ⟨2, 6, 6, 0, 7, 7, -153587980791903437995393782162038070344845099008000000⟩, + ⟨2, 6, 7, 0, 8, 7, -450519776404736656347844668829839604296481505280000000⟩, + ⟨2, 6, 6, 1, 6, 7, 56597987640098221881702334834912177700217028608000000⟩, + ⟨2, 6, 7, 1, 7, 7, 35640451286279317040091250392833972253386342400000000⟩, + ⟨2, 6, 8, 1, 8, 7, 257527597947057334343969346384994110773548548096000000⟩, + ⟨2, 6, 6, 2, 5, 7, 1016841527594322333411938117728736374048161792000000⟩, + ⟨2, 6, 7, 2, 6, 7, 22353590096826670581451271409715658160863182848000000⟩, + ⟨2, 6, 8, 2, 7, 7, 110576515350720993470694128189325417265823219712000000⟩, + ⟨2, 6, 6, 3, 4, 7, -16465422480126763019858449328077660406780264448000000⟩, + ⟨2, 6, 7, 3, 5, 7, 53614781724352386275603919351081516140039503872000000⟩, + ⟨2, 6, 8, 3, 6, 7, -5937840499454697830137193724425905063896023040000000⟩, + ⟨2, 6, 6, 4, 3, 7, 20789403210511101915221236288044630980840914944000000⟩, + ⟨2, 6, 7, 4, 4, 7, -27719104020543501372990475880878252442718830592000000⟩, + ⟨2, 6, 8, 4, 5, 7, -80820736712992162803007930923067389519077572608000000⟩, + ⟨2, 6, 6, 5, 2, 7, -45128316887579005694641038748770968712391950336000000⟩, + ⟨2, 6, 7, 5, 3, 7, -31618741336749412108427452236422960365745209344000000⟩, + ⟨2, 6, 8, 5, 4, 7, -40459046658682230624787639206096880527866855424000000⟩, + ⟨2, 6, 6, 6, 1, 7, 84516428064868293522732878827403894962312445952000000⟩, + ⟨2, 6, 7, 6, 2, 7, -223781532691720205511102961231054484051375161344000000⟩, + ⟨2, 6, 8, 6, 3, 7, 214813293829578206348636454775380938639296954368000000⟩, + ⟨2, 6, 6, 7, 0, 7, 25078804620350882146649178257475960348044427264000000⟩, + ⟨2, 6, 7, 7, 1, 7, 1157741786842508423231170428549198514212267098112000000⟩, + ⟨2, 6, 8, 7, 2, 7, -84491788133361315369177524445578535482941243392000000⟩ +] + +def collectedFourData_14_1_24 : List CollectedFourTerm := [ + ⟨2, 7, 5, 0, 6, 8, -1103492561399760688898220643699760270438735806464000000⟩, + ⟨2, 7, 6, 0, 7, 8, -1519507483331109350334134193937116213658993557504000000⟩, + ⟨2, 7, 7, 0, 8, 8, -2228586404046739289019205722747257277720633016320000000⟩, + ⟨2, 7, 5, 1, 5, 8, 361705898372134508102340421150046179641010421760000000⟩, + ⟨2, 7, 6, 1, 6, 8, 559946587728982788923993081302186926555009122304000000⟩, + ⟨2, 7, 7, 1, 7, 8, 176302638264953915671697821896527436857317785600000000⟩, + ⟨2, 7, 8, 1, 8, 8, 849274598674558667801631042180464955624328790016000000⟩, + ⟨2, 7, 5, 2, 4, 8, -271713272305110907704706441590551950400239435776000000⟩, + ⟨2, 7, 6, 2, 5, 8, 10060020989760033978122444822661890980913872896000000⟩, + ⟨2, 7, 7, 2, 6, 8, 110576515350720993470694128189325417265823219712000000⟩, + ⟨2, 7, 8, 2, 7, 8, 364659269320800256130750316229327641206379773952000000⟩, + ⟨2, 7, 5, 3, 3, 8, 81135095503154501371348732553030728551883603968000000⟩, + ⟨2, 7, 6, 3, 4, 8, -162899027292113554582098199933785749386086580224000000⟩, + ⟨2, 7, 7, 3, 5, 8, 265216267663869599265168879706162232018985811968000000⟩, + ⟨2, 7, 8, 3, 6, 8, -19581812385811336779187058169032515262443683840000000⟩, + ⟨2, 7, 5, 4, 2, 8, 167567084492106768271904125910874659881337487360000000⟩, + ⟨2, 7, 6, 4, 3, 8, 205677902590309288687001162307888900713031401472000000⟩, + ⟨2, 7, 7, 4, 4, 8, -137118105769998055336137779906445183572559003648000000⟩, + ⟨2, 7, 8, 4, 5, 8, -266530652573474599626478137223246507806994464768000000⟩, + ⟨2, 7, 5, 5, 1, 8, 56573216141031722179755417878755013133003128832000000⟩, + ⟨2, 7, 6, 5, 2, 8, -446472535593285624865840325031893379417970311168000000⟩, + ⟨2, 7, 7, 5, 3, 8, -156408443639211372524724657313597921839688974336000000⟩, + ⟨2, 7, 8, 5, 4, 8, -133425857607973790084519945705099157000268283904000000⟩, + ⟨2, 7, 5, 6, 0, 8, -3003971145877802808520598884676844313372205776896000000⟩, + ⟨2, 7, 6, 6, 1, 8, 836154914250638687444998680599951507304770174976000000⟩, + ⟨2, 7, 7, 6, 2, 8, -1106980220076894227592454619603025329160072462336000000⟩, + ⟨2, 7, 8, 6, 3, 8, 708411352264390189310623094101837459241438281728000000⟩, + ⟨2, 7, 6, 7, 0, 8, 248114670803920367894451768119761051827025477632000000⟩, + ⟨2, 7, 7, 7, 1, 8, 5727001878017591836516052808722075023680919830528000000⟩, + ⟨2, 7, 8, 7, 2, 8, -278637047175845043102299798388951050414280671232000000⟩ +] + +def collectedFourData_14_1_25 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_26 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_27 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_28 : List CollectedFourTerm := [ + ⟨3, 3, 8, 1, 8, 5, 188959890695237332593725815104979012338365497344000000⟩, + ⟨3, 3, 8, 2, 7, 5, 81135095503154501371348732553030728551883603968000000⟩, + ⟨3, 3, 8, 3, 6, 5, -4356867771404357780337157810799624984262082560000000⟩, + ⟨3, 3, 8, 4, 5, 5, -59301906657534836641678901730905909130021568512000000⟩, + ⟨3, 3, 8, 5, 4, 5, -29686670846942753728367999041089853750757031936000000⟩, + ⟨3, 3, 8, 6, 3, 5, 157618433307741013612152578695461961229666353152000000⟩, + ⟨3, 3, 8, 7, 2, 5, -61995526606073937472139807538418332567745855488000000⟩ +] + +def collectedFourData_14_1_29 : List CollectedFourTerm := [ + ⟨3, 4, 7, 0, 8, 6, 331848191812790617326591485571557131975686881280000000⟩, + ⟨3, 4, 7, 1, 7, 6, -26252386541447485167235855884984881871480422400000000⟩, + ⟨3, 4, 8, 1, 8, 6, -379384312061128861620170465278930387527209582592000000⟩, + ⟨3, 4, 7, 2, 6, 6, -16465422480126763019858449328077660406780264448000000⟩, + ⟨3, 4, 8, 2, 7, 6, -162899027292113554582098199933785749386086580224000000⟩, + ⟨3, 4, 7, 3, 5, 6, -39492091804822113687620671025687370257003446272000000⟩, + ⟨3, 4, 8, 3, 6, 6, 8747503378171711477477632527045149270820782080000000⟩, + ⟨3, 4, 7, 4, 4, 6, 20417604353120033779639146707037697386051796992000000⟩, + ⟨3, 4, 8, 4, 5, 6, 119063431812988401496737963954433856608892092416000000⟩, + ⟨3, 4, 7, 5, 3, 6, 23290036729864437574473299294005034409623814144000000⟩, + ⟨3, 4, 8, 5, 4, 6, 59603427770909573369769996157274164246188392448000000⟩, + ⟨3, 4, 7, 6, 2, 6, 164835154579601432782994699126412360423932166144000000⟩, + ⟨3, 4, 8, 6, 3, 6, -316458485811970416416533531351751608331126439936000000⟩, + ⟨3, 4, 7, 7, 1, 6, -852780585162690219278929409749988113287072448512000000⟩, + ⟨3, 4, 8, 7, 2, 6, 124471548569251942012000330222639551775279939584000000⟩ +] + +def collectedFourData_14_1_30 : List CollectedFourTerm := [ + ⟨3, 5, 6, 0, 7, 7, -368378682349146086426705723780218148408222810112000000⟩, + ⟨3, 5, 7, 0, 8, 7, -1080565554338986861807884200091140506045560913920000000⟩, + ⟨3, 5, 6, 1, 6, 7, 135749503333347706087723827166045310428498624512000000⟩, + ⟨3, 5, 7, 1, 7, 7, 85483137518145059847280518083605137586755993600000000⟩, + ⟨3, 5, 8, 1, 8, 7, 617676439986628792044684120690035882864456761344000000⟩, + ⟨3, 5, 6, 2, 5, 7, 2438880569701687747532286829484186493505241088000000⟩, + ⟨3, 5, 7, 2, 6, 7, 53614781724352386275603919351081516140039503872000000⟩, + ⟨3, 5, 8, 2, 7, 7, 265216267663869599265168879706162232018985811968000000⟩, + ⟨3, 5, 6, 3, 4, 7, -39492091804822113687620671025687370257003446272000000⟩, + ⟨3, 5, 7, 3, 5, 7, 128594324531253831650408105473919646995954270208000000⟩, + ⟨3, 5, 8, 3, 6, 7, -14241829653012971536047836978516088838485442560000000⟩, + ⟨3, 5, 6, 4, 3, 7, 49863100758447543357678645008006837713256841216000000⟩, + ⟨3, 5, 7, 4, 4, 7, -66483893872019858057261584157589391838741004288000000⟩, + ⟨3, 5, 8, 4, 5, 7, -193847437431697825483526656985212709293378240512000000⟩, + ⟨3, 5, 6, 5, 2, 7, -108239654079477556277609463040366516188903112704000000⟩, + ⟨3, 5, 7, 5, 3, 7, -75837120919974008435047398916590220728720162816000000⟩, + ⟨3, 5, 8, 5, 4, 7, -97040472961369096806966620683111291155105447936000000⟩, + ⟨3, 5, 6, 6, 1, 7, 202711502858912764748389316223174146011145699328000000⟩, + ⟨3, 5, 7, 6, 2, 7, -536736961590382286362565010124702181850995490816000000⟩, + ⟨3, 5, 8, 6, 3, 7, 515226762693344416663111507406295819235362865152000000⟩, + ⟨3, 5, 6, 7, 0, 7, 60151171682202052358449350364242126182018973696000000⟩, + ⟨3, 5, 7, 7, 1, 7, 2776827924545980931079005604474048419005955309568000000⟩, + ⟨3, 5, 8, 7, 2, 7, -202652404318422073456857842568662502420133183488000000⟩ +] + +def collectedFourData_14_1_31 : List CollectedFourTerm := [ + ⟨3, 6, 5, 0, 6, 8, 59256369231242693210590787632952809343554682880000000⟩, + ⟨3, 6, 6, 0, 7, 8, 81595925184751403483850446238459648901046599680000000⟩, + ⟨3, 6, 7, 0, 8, 8, 119672704140758186798117549475144757636654694400000000⟩, + ⟨3, 6, 5, 1, 5, 8, -19423219527524216994272923722722093688894259200000000⟩, + ⟨3, 6, 6, 1, 6, 8, -30068532324453808383650267361891865025241415680000000⟩, + ⟨3, 6, 7, 1, 7, 8, -9467262938518066125209643891967790942257152000000000⟩, + ⟨3, 6, 8, 1, 8, 8, -45605136779480259593691853846673762103821598720000000⟩, + ⟨3, 6, 5, 2, 4, 8, 14590711847044384726288708831567698747897937920000000⟩, + ⟨3, 6, 6, 2, 5, 8, -540212357650244710658952200928685063478968320000000⟩, + ⟨3, 6, 7, 2, 6, 8, -5937840499454697830137193724425905063896023040000000⟩, + ⟨3, 6, 8, 2, 7, 8, -19581812385811336779187058169032515262443683840000000⟩, + ⟨3, 6, 5, 3, 3, 8, -4356867771404357780337157810799624984262082560000000⟩, + ⟨3, 6, 6, 3, 4, 8, 8747503378171711477477632527045149270820782080000000⟩, + ⟨3, 6, 7, 3, 5, 8, -14241829653012971536047836978516088838485442560000000⟩, + ⟨3, 6, 8, 3, 6, 8, 1051522362306346953853935424102676858457292800000000⟩, + ⟨3, 6, 5, 4, 2, 8, -8998173052541315954742999354936926374409011200000000⟩, + ⟨3, 6, 6, 4, 3, 8, -11044683185846782527078974495203716784969482240000000⟩, + ⟨3, 6, 7, 4, 4, 8, 7363095491544612085832032584357141687734108160000000⟩, + ⟨3, 6, 8, 4, 5, 8, 14312410715577390507127220041146003689633218560000000⟩, + ⟨3, 6, 5, 5, 1, 8, -3037921143754256069679513642250107140639293440000000⟩, + ⟨3, 6, 6, 5, 2, 8, 23975097201530275754086382468146001613485506560000000⟩, + ⟨3, 6, 7, 5, 3, 8, 8398965984340283449719683124896936072702853120000000⟩, + ⟨3, 6, 8, 5, 4, 8, 7164825717886367554732946187546079664988487680000000⟩, + ⟨3, 6, 5, 6, 0, 8, 161310034708651633247660934565278042611326648320000000⟩, + ⟨3, 6, 6, 6, 1, 8, -44900623770860576350460556038308431751198801920000000⟩, + ⟨3, 6, 7, 6, 2, 8, 59443652768580380637679426512235725648423813120000000⟩, + ⟨3, 6, 8, 6, 3, 8, -38040931244823652903251178357088087986415861760000000⟩, + ⟨3, 6, 6, 7, 0, 8, -13323492209313704874356420228535624339491389440000000⟩, + ⟨3, 6, 7, 7, 1, 8, -307533869953193818529835666244571727308531957760000000⟩, + ⟨3, 6, 8, 7, 2, 8, 14962511145531536768460949771058932669155901440000000⟩ +] + +def collectedFourData_14_1_32 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_33 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_34 : List CollectedFourTerm := [ + ⟨4, 2, 8, 1, 8, 5, 390256001714042852899954504629478365871346810880000000⟩, + ⟨4, 2, 8, 2, 7, 5, 167567084492106768271904125910874659881337487360000000⟩, + ⟨4, 2, 8, 3, 6, 5, -8998173052541315954742999354936926374409011200000000⟩, + ⟨4, 2, 8, 4, 5, 5, -122475330087456669664569509013219367855576842240000000⟩, + ⟨4, 2, 8, 5, 4, 5, -61311431893311966489848972546807497470215454720000000⟩, + ⟨4, 2, 8, 6, 3, 5, 325526964229244776796665680202060410553148375040000000⟩, + ⟨4, 2, 8, 7, 2, 5, -128038422590243296828170267983819044653115637760000000⟩ +] + +def collectedFourData_14_1_35 : List CollectedFourTerm := [ + ⟨4, 3, 7, 0, 8, 6, -418994767525820581511679630017321232542560419840000000⟩, + ⟨4, 3, 7, 1, 7, 6, 33146519605377598443477506552084462417687347200000000⟩, + ⟨4, 3, 8, 1, 8, 6, 479014337148089796026719780730692393956777394176000000⟩, + ⟨4, 3, 7, 2, 6, 6, 20789403210511101915221236288044630980840914944000000⟩, + ⟨4, 3, 8, 2, 7, 6, 205677902590309288687001162307888900713031401472000000⟩, + ⟨4, 3, 7, 3, 5, 6, 49863100758447543357678645008006837713256841216000000⟩, + ⟨4, 3, 8, 3, 6, 6, -11044683185846782527078974495203716784969482240000000⟩, + ⟨4, 3, 7, 4, 4, 6, -25779466636949068884238420279316297933836517376000000⟩, + ⟨4, 3, 8, 4, 5, 6, -150330651677779140375723935385202813108588904448000000⟩, + ⟨4, 3, 7, 5, 3, 6, -29406227805521671710821054312503089407283167232000000⟩, + ⟨4, 3, 8, 5, 4, 6, -75255869939176586131856402813312102673042898944000000⟩, + ⟨4, 3, 7, 6, 2, 6, -208122475810039315607449533704896842939846623232000000⟩, + ⟨4, 3, 8, 6, 3, 6, 399563574446600527455104934852339674159417131008000000⟩, + ⟨4, 3, 7, 7, 1, 6, 1076729094345490415602407850487361489500620455936000000⟩, + ⟨4, 3, 8, 7, 2, 6, -157158992705237462507799764343214853831421591552000000⟩ +] + +def collectedFourData_14_1_36 : List CollectedFourTerm := [ + ⟨4, 4, 6, 0, 7, 7, 190453578035341204188609913471086786190856159232000000⟩, + ⟨4, 4, 7, 0, 8, 7, 558657669366841433320722072288925627689593733120000000⟩, + ⟨4, 4, 6, 1, 6, 7, -70183156260525341466065711030566578786907717632000000⟩, + ⟨4, 4, 7, 1, 7, 7, -44195199619578590605380349209124918011730329600000000⟩, + ⟨4, 4, 8, 1, 8, 7, -319341736371401202048943790926149842662047350784000000⟩, + ⟨4, 4, 6, 2, 5, 7, -1260913166686216937193309728662114772837203968000000⟩, + ⟨4, 4, 7, 2, 6, 7, -27719104020543501372990475880878252442718830592000000⟩, + ⟨4, 4, 8, 2, 7, 7, -137118105769998055336137779906445183572559003648000000⟩, + ⟨4, 4, 6, 3, 4, 7, 20417604353120033779639146707037697386051796992000000⟩, + ⟨4, 4, 7, 3, 5, 7, -66483893872019858057261584157589391838741004288000000⟩, + ⟨4, 4, 8, 3, 6, 7, 7363095491544612085832032584357141687734108160000000⟩, + ⟨4, 4, 6, 4, 3, 7, -25779466636949068884238420279316297933836517376000000⟩, + ⟨4, 4, 7, 4, 4, 7, 34372497857101985654873035189263628850763399168000000⟩, + ⟨4, 4, 8, 4, 5, 7, 100220071955350927286438436844785885825447493632000000⟩, + ⟨4, 4, 6, 5, 2, 7, 55960429830751584071662458773039992590506655744000000⟩, + ⟨4, 4, 7, 5, 3, 7, 39208161924577656361274446958796682701859454976000000⟩, + ⟨4, 4, 8, 5, 4, 7, 50170398492868621389846925349314493738486071296000000⟩, + ⟨4, 4, 6, 6, 1, 7, -104802837075707148109946889839969464474411204608000000⟩, + ⟨4, 4, 7, 6, 2, 7, 277495630710300695189791212135874903559400062976000000⟩, + ⟨4, 4, 8, 6, 3, 7, -266374752818919615695860148966022091702032924672000000⟩, + ⟨4, 4, 6, 7, 0, 7, -31098449554243132547535770947764911676541894656000000⟩, + ⟨4, 4, 7, 7, 1, 7, -1435633599766738629084244979438813594282253877248000000⟩, + ⟨4, 4, 8, 7, 2, 7, 104772282841620250664298460827034383878474170368000000⟩ +] + +def collectedFourData_14_1_37 : List CollectedFourTerm := [ + ⟨4, 5, 5, 0, 6, 8, 806546322126019885089482488385846732383454232576000000⟩, + ⟨4, 5, 6, 0, 7, 8, 1110612989152440058443592031152207408791275175936000000⟩, + ⟨4, 5, 7, 0, 8, 8, 1628881091363140657352083273780123973213623418880000000⟩, + ⟨4, 5, 5, 1, 5, 8, -264372024088024158482225389671872019262435491840000000⟩, + ⟨4, 5, 6, 1, 6, 8, -409266792289882080157344129227831673458981339136000000⟩, + ⟨4, 5, 7, 1, 7, 8, -128860174909869146010594294759605733058569830400000000⟩, + ⟨4, 5, 8, 1, 8, 8, -620737581744214741942358003195044502740867743744000000⟩, + ⟨4, 5, 5, 2, 4, 8, 198596119372590875373911644274294785802275651584000000⟩, + ⟨4, 5, 6, 2, 5, 8, -7352902242955959981982770617368336367735537664000000⟩, + ⟨4, 5, 7, 2, 6, 8, -80820736712992162803007930923067389519077572608000000⟩, + ⟨4, 5, 8, 2, 7, 8, -266530652573474599626478137223246507806994464768000000⟩, + ⟨4, 5, 5, 3, 3, 8, -59301906657534836641678901730905909130021568512000000⟩, + ⟨4, 5, 6, 3, 4, 8, 119063431812988401496737963954433856608892092416000000⟩, + ⟨4, 5, 7, 3, 5, 8, -193847437431697825483526656985212709293378240512000000⟩, + ⟨4, 5, 8, 3, 6, 8, 14312410715577390507127220041146003689633218560000000⟩, + ⟨4, 5, 5, 4, 2, 8, -122475330087456669664569509013219367855576842240000000⟩, + ⟨4, 5, 6, 4, 3, 8, -150330651677779140375723935385202813108588904448000000⟩, + ⟨4, 5, 7, 4, 4, 8, 100220071955350927286438436844785885825447493632000000⟩, + ⟨4, 5, 8, 4, 5, 8, 194808125660855546793430369509988294947306995712000000⟩, + ⟨4, 5, 5, 5, 1, 8, -41349548701542714733428627220079687087777906688000000⟩, + ⟨4, 5, 6, 5, 2, 8, 326328236464287162191559268962489436579207053312000000⟩, + ⟨4, 5, 7, 5, 3, 8, 114319442993472415714178381061807680754888474624000000⟩, + ⟨4, 5, 8, 5, 4, 8, 97521395698141067198537550489662988151513153536000000⟩, + ⟨4, 5, 5, 6, 0, 8, 2195612335081892695825280469172644270104761073664000000⟩, + ⟨4, 5, 6, 6, 1, 8, -611148361490528503628100470136525489629124624384000000⟩, + ⟨4, 5, 7, 6, 2, 8, 809095463259608287292350360878775471456464666624000000⟩, + ⟨4, 5, 8, 6, 3, 8, -517780174246390807173943614768284695365892964352000000⟩, + ⟨4, 5, 6, 7, 0, 8, -181347824355577515320742243367971618382191525888000000⟩, + ⟨4, 5, 7, 7, 1, 8, -4185884402940298057022012366806230227353759383552000000⟩, + ⟨4, 5, 8, 7, 2, 8, 203656729069982521713700600354142097043554828288000000⟩ +] + +def collectedFourData_14_1_38 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_1_39 : List CollectedFourTerm := [ + ⟨5, 1, 8, 1, 8, 5, 131756407902074446024720292454715631201006125056000000⟩, + ⟨5, 1, 8, 2, 7, 5, 56573216141031722179755417878755013133003128832000000⟩, + ⟨5, 1, 8, 3, 6, 5, -3037921143754256069679513642250107140639293440000000⟩, + ⟨5, 1, 8, 4, 5, 5, -41349548701542714733428627220079687087777906688000000⟩, + ⟨5, 1, 8, 5, 4, 5, -20699679169866269465472202637821077948846833664000000⟩, + ⟨5, 1, 8, 6, 3, 5, 109902892700519926128217890223955589259012866048000000⟩, + ⟨5, 1, 8, 7, 2, 5, -43227733999846487086399007090967049057245069312000000⟩ +] + +def collectedFourData_14_1_40 : List CollectedFourTerm := [ + ⟨5, 2, 7, 0, 8, 6, 909527245764447674894648158973979664212515880960000000⟩, + ⟨5, 2, 7, 1, 7, 6, -71952360792902986177225297659209754981747916800000000⟩, + ⟨5, 2, 8, 1, 8, 6, -1039813917774369498411410766439031916095229394944000000⟩, + ⟨5, 2, 7, 2, 6, 6, -45128316887579005694641038748770968712391950336000000⟩, + ⟨5, 2, 8, 2, 7, 6, -446472535593285624865840325031893379417970311168000000⟩, + ⟨5, 2, 7, 3, 5, 6, -108239654079477556277609463040366516188903112704000000⟩, + ⟨5, 2, 8, 3, 6, 6, 23975097201530275754086382468146001613485506560000000⟩, + ⟨5, 2, 7, 4, 4, 6, 55960429830751584071662458773039992590506655744000000⟩, + ⟨5, 2, 8, 4, 5, 6, 326328236464287162191559268962489436579207053312000000⟩, + ⟨5, 2, 7, 5, 3, 6, 63833172767795566066802756078877192437637316608000000⟩, + ⟨5, 2, 8, 5, 4, 6, 163360665617784129888457172473494766947020046336000000⟩, + ⟨5, 2, 7, 6, 2, 6, 451779059970045441556032625643589005388816580608000000⟩, + ⟨5, 2, 8, 6, 3, 6, -867347245217851109718234308308068585025623293952000000⟩, + ⟨5, 2, 7, 7, 1, 6, -2337295172914424779807068091305149672122308624384000000⟩, + ⟨5, 2, 8, 7, 2, 6, 341150765739576549134979355583566808477689970688000000⟩ +] + +def collectedFourData_14_1_41 : List CollectedFourTerm := [ + ⟨5, 3, 6, 0, 7, 7, 217247369038149688933005815609722403137020493824000000⟩, + ⟨5, 3, 7, 0, 8, 7, 637251923092826133210744440210716813139210403840000000⟩, + ⟨5, 3, 6, 1, 6, 7, -80056810723520093051421384136354820356124442624000000⟩, + ⟨5, 3, 7, 1, 7, 7, -50412761684569848885484866024841471147062067200000000⟩, + ⟨5, 3, 8, 1, 8, 7, -364268042461704944322132989257502658203524005888000000⟩, + ⟨5, 3, 6, 2, 5, 7, -1438303605917611806836976440473033930834968576000000⟩, + ⟨5, 3, 7, 2, 6, 7, -31618741336749412108427452236422960365745209344000000⟩, + ⟨5, 3, 8, 2, 7, 7, -156408443639211372524724657313597921839688974336000000⟩, + ⟨5, 3, 6, 3, 4, 7, 23290036729864437574473299294005034409623814144000000⟩, + ⟨5, 3, 7, 3, 5, 7, -75837120919974008435047398916590220728720162816000000⟩, + ⟨5, 3, 8, 3, 6, 7, 8398965984340283449719683124896936072702853120000000⟩, + ⟨5, 3, 6, 4, 3, 7, -29406227805521671710821054312503089407283167232000000⟩, + ⟨5, 3, 7, 4, 4, 7, 39208161924577656361274446958796682701859454976000000⟩, + ⟨5, 3, 8, 4, 5, 7, 114319442993472415714178381061807680754888474624000000⟩, + ⟨5, 3, 6, 5, 2, 7, 63833172767795566066802756078877192437637316608000000⟩, + ⟨5, 3, 7, 5, 3, 7, 44724127059223045708142127059951483392918290432000000⟩, + ⟨5, 3, 8, 5, 4, 7, 57228576058301890048237422837938413669472796672000000⟩, + ⟨5, 3, 6, 6, 1, 7, -119546930319189355952042070770113775142810157056000000⟩, + ⟨5, 3, 7, 6, 2, 7, 316534854914661021912480291130141431449027346432000000⟩, + ⟨5, 3, 8, 6, 3, 7, -303849446280076337386975119764139531503249915904000000⟩, + ⟨5, 3, 6, 7, 0, 7, -35473507069377625724829336745387789259680776192000000⟩, + ⟨5, 3, 7, 7, 1, 7, -1637604426597945267856937355023421819404509249536000000⟩, + ⟨5, 3, 8, 7, 2, 7, 119512077590052797097007078242974178973241573376000000⟩ +] + +def collectedFourData_14_1_42 : List CollectedFourTerm := [ + ⟨5, 4, 5, 0, 6, 8, 403758943638031512264346494993718296924471164928000000⟩, + ⟨5, 4, 6, 0, 7, 8, 555975416401194364122269014830425439829657387008000000⟩, + ⟨5, 4, 7, 0, 8, 8, 815421620207929270199986387183964329507175792640000000⟩, + ⟨5, 4, 5, 1, 5, 8, -132345243224047239748347716617957658685100523520000000⟩, + ⟨5, 4, 6, 1, 6, 8, -204879897394497705683496531679476140792094916608000000⟩, + ⟨5, 4, 7, 1, 7, 8, -64507699894379390650628640922870264188056371200000000⟩, + ⟨5, 4, 8, 1, 8, 8, -310742660906103077054825172561683895805418668032000000⟩, + ⟨5, 4, 5, 2, 4, 8, 99417674061330718614903819428664744535551639552000000⟩, + ⟨5, 4, 6, 2, 5, 8, -3680879771993736634491661284281277331424673792000000⟩, + ⟨5, 4, 7, 2, 6, 8, -40459046658682230624787639206096880527866855424000000⟩, + ⟨5, 4, 8, 2, 7, 8, -133425857607973790084519945705099157000268283904000000⟩, + ⟨5, 4, 5, 3, 3, 8, -29686670846942753728367999041089853750757031936000000⟩, + ⟨5, 4, 6, 3, 4, 8, 59603427770909573369769996157274164246188392448000000⟩, + ⟨5, 4, 7, 3, 5, 8, -97040472961369096806966620683111291155105447936000000⟩, + ⟨5, 4, 8, 3, 6, 8, 7164825717886367554732946187546079664988487680000000⟩, + ⟨5, 4, 5, 4, 2, 8, -61311431893311966489848972546807497470215454720000000⟩, + ⟨5, 4, 6, 4, 3, 8, -75255869939176586131856402813312102673042898944000000⟩, + ⟨5, 4, 7, 4, 4, 8, 50170398492868621389846925349314493738486071296000000⟩, + ⟨5, 4, 8, 4, 5, 8, 97521395698141067198537550489662988151513153536000000⟩, + ⟨5, 4, 5, 5, 1, 8, -20699679169866269465472202637821077948846833664000000⟩, + ⟨5, 4, 6, 5, 2, 8, 163360665617784129888457172473494766947020046336000000⟩, + ⟨5, 4, 7, 5, 3, 8, 57228576058301890048237422837938413669472796672000000⟩, + ⟨5, 4, 8, 5, 4, 8, 48819434952473428239802953253957089609602039808000000⟩, + ⟨5, 4, 5, 6, 0, 8, 1099128584102308526722474237581545615723480481792000000⟩, + ⟨5, 4, 6, 6, 1, 8, -305942275195168264708574270442362642082878717952000000⟩, + ⟨5, 4, 7, 6, 2, 8, 405035049551661966737276003431424805107423772672000000⟩, + ⟨5, 4, 8, 6, 3, 8, -259201945945733346263202332065648860182354067456000000⟩, + ⟨5, 4, 6, 7, 0, 8, -90783137910611883928905267090238687928609931264000000⟩, + ⟨5, 4, 7, 7, 1, 8, -2095463358219885279903129857768672660878635565056000000⟩, + ⟨5, 4, 8, 7, 2, 8, 101951026913523102186476314757104266840285118464000000⟩ +] + +def collectedFourData_14_1_43 : List CollectedFourTerm := [ + ⟨6, 0, 8, 1, 8, 5, -6996110078586734638789406789436755800461429178368000000⟩, + ⟨6, 0, 8, 2, 7, 5, -3003971145877802808520598884676844313372205776896000000⟩, + ⟨6, 0, 8, 3, 6, 5, 161310034708651633247660934565278042611326648320000000⟩, + ⟨6, 0, 8, 4, 5, 5, 2195612335081892695825280469172644270104761073664000000⟩, + ⟨6, 0, 8, 5, 4, 5, 1099128584102308526722474237581545615723480481792000000⟩, + ⟨6, 0, 8, 6, 3, 5, -5835714160175112447301411371305008972839197343744000000⟩, + ⟨6, 0, 8, 7, 2, 5, 2295341762319181328090229010626958168134135054336000000⟩ +] + +def collectedFourData_14_1_44 : List CollectedFourTerm := [ + ⟨6, 1, 7, 0, 8, 6, -1703364967747029222454909141422118773235352862720000000⟩, + ⟨6, 1, 7, 1, 7, 6, 134752566558151338093696270881809511929715097600000000⟩, + ⟨6, 1, 8, 1, 8, 6, 1947366182553433510591208435055137928622016299008000000⟩, + ⟨6, 1, 7, 2, 6, 6, 84516428064868293522732878827403894962312445952000000⟩, + ⟨6, 1, 8, 2, 7, 6, 836154914250638687444998680599951507304770174976000000⟩, + ⟨6, 1, 7, 3, 5, 6, 202711502858912764748389316223174146011145699328000000⟩, + ⟨6, 1, 8, 3, 6, 6, -44900623770860576350460556038308431751198801920000000⟩, + ⟨6, 1, 7, 4, 4, 6, -104802837075707148109946889839969464474411204608000000⟩, + ⟨6, 1, 8, 4, 5, 6, -611148361490528503628100470136525489629124624384000000⟩, + ⟨6, 1, 7, 5, 3, 6, -119546930319189355952042070770113775142810157056000000⟩, + ⟨6, 1, 8, 5, 4, 6, -305942275195168264708574270442362642082878717952000000⟩, + ⟨6, 1, 7, 6, 2, 6, -846092986766840412743045744651287877281231405056000000⟩, + ⟨6, 1, 8, 6, 3, 6, 1624370154116970530142428964779421025030964772864000000⟩, + ⟨6, 1, 7, 7, 1, 6, 4377292417975291376010116197249881407089004249088000000⟩, + ⟨6, 1, 8, 7, 2, 6, -638908032482805251841153917096499333862696943616000000⟩ +] + +def collectedFourData_14_1_45 : List CollectedFourTerm := [ + ⟨6, 2, 6, 0, 7, 7, 1537567504627269799651792103303040542174110285824000000⟩, + ⟨6, 2, 7, 0, 8, 7, 4510148286475703049375915994020187692278313123840000000⟩, + ⟨6, 2, 6, 1, 6, 7, -566601801612450186726219750289790620279844634624000000⟩, + ⟨6, 2, 7, 1, 7, 7, -356796146843562642969033324114689847121359667200000000⟩, + ⟨6, 2, 8, 1, 8, 7, -2578105813400898282099457535391655256937241509888000000⟩, + ⟨6, 2, 6, 2, 5, 7, -10179588807166628028265492691497163515364376576000000⟩, + ⟨6, 2, 7, 2, 6, 7, -223781532691720205511102961231054484051375161344000000⟩, + ⟨6, 2, 8, 2, 7, 7, -1106980220076894227592454619603025329160072462336000000⟩, + ⟨6, 2, 6, 3, 4, 7, 164835154579601432782994699126412360423932166144000000⟩, + ⟨6, 2, 7, 3, 5, 7, -536736961590382286362565010124702181850995490816000000⟩, + ⟨6, 2, 8, 3, 6, 7, 59443652768580380637679426512235725648423813120000000⟩, + ⟨6, 2, 6, 4, 3, 7, -208122475810039315607449533704896842939846623232000000⟩, + ⟨6, 2, 7, 4, 4, 7, 277495630710300695189791212135874903559400062976000000⟩, + ⟨6, 2, 8, 4, 5, 7, 809095463259608287292350360878775471456464666624000000⟩, + ⟨6, 2, 6, 5, 2, 7, 451779059970045441556032625643589005388816580608000000⟩, + ⟨6, 2, 7, 5, 3, 7, 316534854914661021912480291130141431449027346432000000⟩, + ⟨6, 2, 8, 5, 4, 7, 405035049551661966737276003431424805107423772672000000⟩, + ⟨6, 2, 6, 6, 1, 7, -846092986766840412743045744651287877281231405056000000⟩, + ⟨6, 2, 7, 6, 2, 7, 2240274343268223727822975391443028087142384402432000000⟩, + ⟨6, 2, 8, 6, 3, 7, -2150493407435438197421037423928762399426980347904000000⟩, + ⟨6, 2, 6, 7, 0, 7, -251063623861252705614248433519290006703483912192000000⟩, + ⟨6, 2, 7, 7, 1, 7, -11590139677726608022640887518458395422691254337536000000⟩, + ⟨6, 2, 8, 7, 2, 7, 845846316696656324337070834743306681510449381376000000⟩ +] + +def collectedFourData_14_1_46 : List CollectedFourTerm := [ + ⟨6, 3, 5, 0, 6, 8, -2143718049704078109949280320115852398571915575296000000⟩, + ⟨6, 3, 6, 0, 7, 8, -2951896308703131903123200206961769993630023417856000000⟩, + ⟨6, 3, 7, 0, 8, 8, -4329400185190171441617976805963104099171282452480000000⟩, + ⟨6, 3, 5, 1, 5, 8, 702673937413042743354768922708985990976519536640000000⟩, + ⟨6, 3, 6, 1, 6, 8, 1087789486738527261891217074363604003643568685056000000⟩, + ⟨6, 3, 7, 1, 7, 8, 342497232042612430515709224894592573912802918400000000⟩, + ⟨6, 3, 8, 1, 8, 8, 1649857325748016933313667512661239462835649511424000000⟩, + ⟨6, 3, 5, 2, 4, 8, -527848276064284645896106228083780314239088984064000000⟩, + ⟨6, 3, 6, 2, 5, 8, 19543265927225258505286830799733427937417887744000000⟩, + ⟨6, 3, 7, 2, 6, 8, 214813293829578206348636454775380938639296954368000000⟩, + ⟨6, 3, 8, 2, 7, 8, 708411352264390189310623094101837459241438281728000000⟩, + ⟨6, 3, 5, 3, 3, 8, 157618433307741013612152578695461961229666353152000000⟩, + ⟨6, 3, 6, 3, 4, 8, -316458485811970416416533531351751608331126439936000000⟩, + ⟨6, 3, 7, 3, 5, 8, 515226762693344416663111507406295819235362865152000000⟩, + ⟨6, 3, 8, 3, 6, 8, -38040931244823652903251178357088087986415861760000000⟩, + ⟨6, 3, 5, 4, 2, 8, 325526964229244776796665680202060410553148375040000000⟩, + ⟨6, 3, 6, 4, 3, 8, 399563574446600527455104934852339674159417131008000000⟩, + ⟨6, 3, 7, 4, 4, 8, -266374752818919615695860148966022091702032924672000000⟩, + ⟨6, 3, 8, 4, 5, 8, -517780174246390807173943614768284695365892964352000000⟩, + ⟨6, 3, 5, 5, 1, 8, 109902892700519926128217890223955589259012866048000000⟩, + ⟨6, 3, 6, 5, 2, 8, -867347245217851109718234308308068585025623293952000000⟩, + ⟨6, 3, 7, 5, 3, 8, -303849446280076337386975119764139531503249915904000000⟩, + ⟨6, 3, 8, 5, 4, 8, -259201945945733346263202332065648860182354067456000000⟩, + ⟨6, 3, 5, 6, 0, 8, -5835714160175112447301411371305008972839197343744000000⟩, + ⟨6, 3, 6, 6, 1, 8, 1624370154116970530142428964779421025030964772864000000⟩, + ⟨6, 3, 7, 6, 2, 8, -2150493407435438197421037423928762399426980347904000000⟩, + ⟨6, 3, 8, 6, 3, 8, 1376207013609667397608738125506688598521824673792000000⟩, + ⟨6, 3, 6, 7, 0, 8, 482004063103116165697944732813179407467961909248000000⟩, + ⟨6, 3, 7, 7, 1, 8, 11125654785585695666393895702668900720716642516992000000⟩, + ⟨6, 3, 8, 7, 2, 8, -541298861670093066827608110714645036618794139648000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1403.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1403.lean new file mode 100644 index 0000000000000000000000000000000000000000..e12d948db53022ca82959356878d5073dcf5d83a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1403.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1401 +import OAI.Analysis.LaughlinFock.Sparse1402 + +namespace OAI + +/-! Sparse1403. -/ +namespace LaughlinFock +def collectedFourData_14_1_47 : List CollectedFourTerm := [ + ⟨7, 0, 7, 0, 8, 6, -505444423071106490877517386019013528740996055040000000⟩, + ⟨7, 0, 7, 1, 7, 6, 39985519575069040137489278332568098856710963200000000⟩, + ⟨7, 0, 8, 1, 8, 6, 577847610633190973602910533522694795103049875456000000⟩, + ⟨7, 0, 7, 2, 6, 6, 25078804620350882146649178257475960348044427264000000⟩, + ⟨7, 0, 8, 2, 7, 6, 248114670803920367894451768119761051827025477632000000⟩, + ⟨7, 0, 7, 3, 5, 6, 60151171682202052358449350364242126182018973696000000⟩, + ⟨7, 0, 8, 3, 6, 6, -13323492209313704874356420228535624339491389440000000⟩, + ⟨7, 0, 7, 4, 4, 6, -31098449554243132547535770947764911676541894656000000⟩, + ⟨7, 0, 8, 4, 5, 6, -181347824355577515320742243367971618382191525888000000⟩, + ⟨7, 0, 7, 5, 3, 6, -35473507069377625724829336745387789259680776192000000⟩, + ⟨7, 0, 8, 5, 4, 6, -90783137910611883928905267090238687928609931264000000⟩, + ⟨7, 0, 7, 6, 2, 6, -251063623861252705614248433519290006703483912192000000⟩, + ⟨7, 0, 8, 6, 3, 6, 482004063103116165697944732813179407467961909248000000⟩, + ⟨7, 0, 7, 7, 1, 6, 1298886664167693655754898717501750568878411350016000000⟩, + ⟨7, 0, 8, 7, 2, 6, -189585031974032437111219725375584910798709850112000000⟩ +] + +def collectedFourData_14_1_48 : List CollectedFourTerm := [ + ⟨7, 1, 6, 0, 7, 7, -7954660640609756318023919034299979323782465585152000000⟩, + ⟨7, 1, 7, 0, 8, 7, -23333413947531935407007144434325402806644973240320000000⟩, + ⟨7, 1, 6, 1, 6, 7, 2931334745707787346679106610000459411739537047552000000⟩, + ⟨7, 1, 7, 1, 7, 7, 1845897664639919991381530185454079397001271705600000000⟩, + ⟨7, 1, 8, 1, 8, 7, 13337922907104344072951462177828492467630006861824000000⟩, + ⟨7, 1, 6, 2, 5, 7, 52664467854755835349651617591580864973056770048000000⟩, + ⟨7, 1, 7, 2, 6, 7, 1157741786842508423231170428549198514212267098112000000⟩, + ⟨7, 1, 8, 2, 7, 7, 5727001878017591836516052808722075023680919830528000000⟩, + ⟨7, 1, 6, 3, 4, 7, -852780585162690219278929409749988113287072448512000000⟩, + ⟨7, 1, 7, 3, 5, 7, 2776827924545980931079005604474048419005955309568000000⟩, + ⟨7, 1, 8, 3, 6, 7, -307533869953193818529835666244571727308531957760000000⟩, + ⟨7, 1, 6, 4, 3, 7, 1076729094345490415602407850487361489500620455936000000⟩, + ⟨7, 1, 7, 4, 4, 7, -1435633599766738629084244979438813594282253877248000000⟩, + ⟨7, 1, 8, 4, 5, 7, -4185884402940298057022012366806230227353759383552000000⟩, + ⟨7, 1, 6, 5, 2, 7, -2337295172914424779807068091305149672122308624384000000⟩, + ⟨7, 1, 7, 5, 3, 7, -1637604426597945267856937355023421819404509249536000000⟩, + ⟨7, 1, 8, 5, 4, 7, -2095463358219885279903129857768672660878635565056000000⟩, + ⟨7, 1, 6, 6, 1, 7, 4377292417975291376010116197249881407089004249088000000⟩, + ⟨7, 1, 7, 6, 2, 7, -11590139677726608022640887518458395422691254337536000000⟩, + ⟨7, 1, 8, 6, 3, 7, 11125654785585695666393895702668900720716642516992000000⟩, + ⟨7, 1, 6, 7, 0, 7, 1298886664167693655754898717501750568878411350016000000⟩, + ⟨7, 1, 7, 7, 1, 7, 59962003382694370838563473234895166400545452720128000000⟩, + ⟨7, 1, 8, 7, 2, 7, -4376016261518677475157157896434097458332406120448000000⟩ +] + +def collectedFourData_14_1_49 : List CollectedFourTerm := [ + ⟨7, 2, 5, 0, 6, 8, 843181388098615413549179789953892948072070119424000000⟩, + ⟨7, 2, 6, 0, 7, 8, 1161059416110746751484522564536606576394647896064000000⟩, + ⟨7, 2, 7, 0, 8, 8, 1702868368481091725608384463072659554683710341120000000⟩, + ⟨7, 2, 5, 1, 5, 8, -276380369149028712887366748615835468395876188160000000⟩, + ⟨7, 2, 6, 1, 6, 8, -427856568877555490275089093935353178592708132864000000⟩, + ⟨7, 2, 7, 1, 7, 8, -134713280775654307313261545529312717464770969600000000⟩, + ⟨7, 2, 8, 1, 8, 8, -648932815712829326550840933747674980704904544256000000⟩, + ⟨7, 2, 5, 2, 4, 8, 207616781590649493949832098838870479233840316416000000⟩, + ⟨7, 2, 6, 2, 5, 8, -7686886852854966534784898067001119928888590336000000⟩, + ⟨7, 2, 7, 2, 6, 8, -84491788133361315369177524445578535482941243392000000⟩, + ⟨7, 2, 8, 2, 7, 8, -278637047175845043102299798388951050414280671232000000⟩, + ⟨7, 2, 5, 3, 3, 8, -61995526606073937472139807538418332567745855488000000⟩, + ⟨7, 2, 6, 3, 4, 8, 124471548569251942012000330222639551775279939584000000⟩, + ⟨7, 2, 7, 3, 5, 8, -202652404318422073456857842568662502420133183488000000⟩, + ⟨7, 2, 8, 3, 6, 8, 14962511145531536768460949771058932669155901440000000⟩, + ⟨7, 2, 5, 4, 2, 8, -128038422590243296828170267983819044653115637760000000⟩, + ⟨7, 2, 6, 4, 3, 8, -157158992705237462507799764343214853831421591552000000⟩, + ⟨7, 2, 7, 4, 4, 8, 104772282841620250664298460827034383878474170368000000⟩, + ⟨7, 2, 8, 4, 5, 8, 203656729069982521713700600354142097043554828288000000⟩, + ⟨7, 2, 5, 5, 1, 8, -43227733999846487086399007090967049057245069312000000⟩, + ⟨7, 2, 6, 5, 2, 8, 341150765739576549134979355583566808477689970688000000⟩, + ⟨7, 2, 7, 5, 3, 8, 119512077590052797097007078242974178973241573376000000⟩, + ⟨7, 2, 8, 5, 4, 8, 101951026913523102186476314757104266840285118464000000⟩, + ⟨7, 2, 5, 6, 0, 8, 2295341762319181328090229010626958168134135054336000000⟩, + ⟨7, 2, 6, 6, 1, 8, -638908032482805251841153917096499333862696943616000000⟩, + ⟨7, 2, 7, 6, 2, 8, 845846316696656324337070834743306681510449381376000000⟩, + ⟨7, 2, 8, 6, 3, 8, -541298861670093066827608110714645036618794139648000000⟩, + ⟨7, 2, 6, 7, 0, 8, -189585031974032437111219725375584910798709850112000000⟩, + ⟨7, 2, 7, 7, 1, 8, -4376016261518677475157157896434097458332406120448000000⟩, + ⟨7, 2, 8, 7, 2, 8, 212907255047926381267102200938598798110031347712000000⟩ +] + +def collectedFourData_14_1 : List (List CollectedFourTerm) := [ + collectedFourData_14_1_0, + collectedFourData_14_1_1, + collectedFourData_14_1_2, + collectedFourData_14_1_3, + collectedFourData_14_1_4, + collectedFourData_14_1_5, + collectedFourData_14_1_6, + collectedFourData_14_1_7, + collectedFourData_14_1_8, + collectedFourData_14_1_9, + collectedFourData_14_1_10, + collectedFourData_14_1_11, + collectedFourData_14_1_12, + collectedFourData_14_1_13, + collectedFourData_14_1_14, + collectedFourData_14_1_15, + collectedFourData_14_1_16, + collectedFourData_14_1_17, + collectedFourData_14_1_18, + collectedFourData_14_1_19, + collectedFourData_14_1_20, + collectedFourData_14_1_21, + collectedFourData_14_1_22, + collectedFourData_14_1_23, + collectedFourData_14_1_24, + collectedFourData_14_1_25, + collectedFourData_14_1_26, + collectedFourData_14_1_27, + collectedFourData_14_1_28, + collectedFourData_14_1_29, + collectedFourData_14_1_30, + collectedFourData_14_1_31, + collectedFourData_14_1_32, + collectedFourData_14_1_33, + collectedFourData_14_1_34, + collectedFourData_14_1_35, + collectedFourData_14_1_36, + collectedFourData_14_1_37, + collectedFourData_14_1_38, + collectedFourData_14_1_39, + collectedFourData_14_1_40, + collectedFourData_14_1_41, + collectedFourData_14_1_42, + collectedFourData_14_1_43, + collectedFourData_14_1_44, + collectedFourData_14_1_45, + collectedFourData_14_1_46, + collectedFourData_14_1_47, + collectedFourData_14_1_48, + collectedFourData_14_1_49 +] + +theorem collectedFourChecked_14_1 : collectNumericRowParts 14 1 = collectedFourData_14_1 := by + decide +kernel + +def collectedFourData_14_2_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_1 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_2 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_3 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_4 : List CollectedFourTerm := [ + ⟨0, 6, 8, 2, 8, 4, 295097581039362050254200554902279604587028545536000000⟩, + ⟨0, 6, 8, 3, 7, 4, 180764018503563478322590112975958293780449198080000000⟩, + ⟨0, 6, 8, 4, 6, 4, -230571426002298997844909431083493633433788219392000000⟩, + ⟨0, 6, 8, 5, 5, 4, -77073059821619747610051417172601017233240489984000000⟩, + ⟨0, 6, 8, 6, 4, 4, 114812129307399391407887730604032776067103064064000000⟩, + ⟨0, 6, 8, 7, 3, 4, 549886784059334106026024028679399158633323298816000000⟩ +] + +def collectedFourData_14_2_5 : List CollectedFourTerm := [ + ⟨0, 7, 7, 1, 8, 5, -3996850834419756751791771189712040723138740224000000⟩, + ⟨0, 7, 7, 2, 7, 5, 235978651311364505525383486157994900250951680000000⟩, + ⟨0, 7, 8, 2, 8, 5, 3814800982822741354564540816498208175078506496000000⟩, + ⟨0, 7, 7, 3, 6, 5, 184257108704174634776360767729183322510721024000000⟩, + ⟨0, 7, 8, 3, 7, 5, 2336782134972504655043574281589759201383546880000000⟩, + ⟨0, 7, 7, 4, 5, 5, 634380646446110397570618134658774913756692480000000⟩, + ⟨0, 7, 8, 4, 6, 5, -2980655074929558652463404770908793057954496512000000⟩, + ⟨0, 7, 7, 5, 4, 5, -401982730886347505280723560087359907923230720000000⟩, + ⟨0, 7, 8, 5, 5, 5, -996342915862305396962575700708337496017076224000000⟩, + ⟨0, 7, 7, 6, 3, 5, -1205352632305957819923408462453040246331277312000000⟩, + ⟨0, 7, 8, 6, 4, 5, 1484205401410652354340849248950921139117359104000000⟩, + ⟨0, 7, 7, 7, 2, 5, 2140479374804466182183348438265531823804121088000000⟩, + ⟨0, 7, 8, 7, 3, 5, 7108525379579367539051501526472675024045080576000000⟩ +] + +def collectedFourData_14_2_6 : List CollectedFourTerm := [ + ⟨0, 8, 6, 0, 8, 6, 39162583025406261856675116877545879950220853248000000⟩, + ⟨0, 8, 6, 1, 7, 6, -130976388120191039570135132747159554726003998720000000⟩, + ⟨0, 8, 7, 1, 8, 6, -246225845044399130437597836233432654967874781184000000⟩, + ⟨0, 8, 6, 2, 6, 6, 9041250043938791760001046913486573322597564416000000⟩, + ⟨0, 8, 7, 2, 7, 6, 14537455921847929318791653634197296631387258880000000⟩, + ⟨0, 8, 8, 2, 8, 6, 117505335398399622369276075302593757164672647168000000⟩, + ⟨0, 8, 6, 3, 5, 6, -22025736748997813621410632191793708335477293056000000⟩, + ⟨0, 8, 7, 3, 6, 6, 11351152238512183386140185087054614763860393984000000⟩, + ⟨0, 8, 8, 3, 7, 6, 71978687684974663353632616596260699728028631040000000⟩, + ⟨0, 8, 6, 4, 4, 6, 10178958660102072225113336351253469794171617280000000⟩, + ⟨0, 8, 7, 4, 5, 6, 39080995819470508869081091968927539790537031680000000⟩, + ⟨0, 8, 8, 4, 6, 6, -91811571786735628503186999174367702452321386496000000⟩, + ⟨0, 8, 6, 5, 3, 6, 3770551215445020762962594047121653287100612608000000⟩, + ⟨0, 8, 7, 5, 4, 6, -24764130988670088048855803939109215441277419520000000⟩, + ⟨0, 8, 8, 5, 5, 6, -30689833893664929192682764242664662029767278592000000⟩, + ⟨0, 8, 6, 6, 2, 6, 270171202823083815566340620601890002239769018368000000⟩, + ⟨0, 8, 7, 6, 3, 6, -74255703492900490513992602157333323416225185792000000⟩, + ⟨0, 8, 8, 6, 4, 6, 45717208912908267285826041854801646980412997632000000⟩, + ⟨0, 8, 6, 7, 1, 6, -535602005541897189318376564969270585503843876864000000⟩, + ⟨0, 8, 7, 7, 2, 6, 131864151226912150168615157241804010380337348608000000⟩, + ⟨0, 8, 8, 7, 3, 6, 218960219072147114529614600871835530042758135808000000⟩ +] + +def collectedFourData_14_2_7 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_8 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_9 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_10 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_11 : List CollectedFourTerm := [ + ⟨1, 5, 8, 2, 8, 4, -457289372325038009187127408285923966934389148876800000⟩, + ⟨1, 5, 8, 3, 7, 4, -280115696880009908768973681475206521480653307904000000⟩, + ⟨1, 5, 8, 4, 6, 4, 357298295368325174803530860853483125239289846169600000⟩, + ⟨1, 5, 8, 5, 5, 4, 119434022552348310628855058864414056538973614899200000⟩, + ⟨1, 5, 8, 6, 4, 4, -177915272505329885077447443810727136606723191603200000⟩, + ⟨1, 5, 8, 7, 3, 4, -852116040554007710558232189028245842424947854540800000⟩ +] + +def collectedFourData_14_2_12 : List CollectedFourTerm := [ + ⟨1, 6, 7, 1, 8, 5, 659449383478342860463342726765783620527333572608000000⟩, + ⟨1, 6, 7, 2, 7, 5, -38934646942840370759878096102383436423558594560000000⟩, + ⟨1, 6, 8, 2, 8, 5, -629412570154183798312134216971777093078857285632000000⟩, + ⟨1, 6, 7, 3, 6, 5, -30400993624799594542635165416758256098458206208000000⟩, + ⟨1, 6, 8, 3, 7, 5, -385550925483697038898337309067694264623782952960000000⟩, + ⟨1, 6, 7, 4, 5, 5, -104667885673099664585679403951726096208269148160000000⟩, + ⟨1, 6, 8, 4, 6, 5, 491784965952887807105306889725480322726157615104000000⟩, + ⟨1, 6, 7, 5, 4, 5, 66324032352942825497450212084271316077893386240000000⟩, + ⟨1, 6, 8, 5, 5, 5, 164388852328485070673098168948970397390348484608000000⟩, + ⟨1, 6, 7, 6, 3, 5, 198873834220424885365643773676591169260123848704000000⟩, + ⟨1, 6, 8, 6, 4, 5, -244882378017885780912196359755469725005479149568000000⟩, + ⟨1, 6, 7, 7, 2, 5, -353162492807373970553443604230754221404608004096000000⟩, + ⟨1, 6, 8, 7, 3, 5, -1172851545680539833664751506948737535086000340992000000⟩ +] + +def collectedFourData_14_2_13 : List CollectedFourTerm := [ + ⟨1, 7, 6, 0, 8, 6, -130976388120191039570135132747159554726003998720000000⟩, + ⟨1, 7, 6, 1, 7, 6, 438040928860130036305495237290124454260427980800000000⟩, + ⟨1, 7, 7, 1, 8, 6, 823484289196031337713511119291350995462531317760000000⟩, + ⟨1, 7, 6, 2, 6, 6, -30237798004242775956289530654123847695193866240000000⟩, + ⟨1, 7, 7, 2, 7, 6, -48619455664221264094667592359233587713880883200000000⟩, + ⟨1, 7, 8, 2, 8, 6, -392987980525943766152880245944198940772028907520000000⟩, + ⟨1, 7, 6, 3, 5, 6, 73663461963128919287199704255476888206405795840000000⟩, + ⟨1, 7, 7, 3, 6, 6, -37963096566900265222725075113900051338635509760000000⟩, + ⟨1, 7, 8, 3, 7, 6, -240727444573645004069309844186312944329005465600000000⟩, + ⟨1, 7, 6, 4, 4, 6, -34042781071412193221009050063595219052606259200000000⟩, + ⟨1, 7, 7, 4, 5, 6, -130703525690678902356476852602206544341447475200000000⟩, + ⟨1, 7, 8, 4, 6, 6, 307057071604880986112067122962769462322203197440000000⟩, + ⟨1, 7, 6, 5, 3, 6, -12610332140267757670614559224403391608384389120000000⟩, + ⟨1, 7, 7, 5, 4, 6, 82821820760063523853459096631811656681049292800000000⟩, + ⟨1, 7, 8, 5, 5, 6, 102639899742903969792712628423948797825913978880000000⟩, + ⟨1, 7, 6, 6, 2, 6, -903567782975367054155497669579970265891754475520000000⟩, + ⟨1, 7, 7, 6, 3, 6, 248342757026892198927240608961345427174462586880000000⟩, + ⟨1, 7, 8, 6, 4, 6, -152897853914905647976227694989029926081375764480000000⟩, + ⟨1, 7, 6, 7, 1, 6, 1791281645296441959069599842782243113267059752960000000⟩, + ⟨1, 7, 7, 7, 2, 6, -441009987493194614275921612178506218445335429120000000⟩, + ⟨1, 7, 8, 7, 3, 6, -732296401835156855684727204915517462605327237120000000⟩ +] + +def collectedFourData_14_2_14 : List CollectedFourTerm := [ + ⟨1, 8, 5, 0, 7, 7, -3996850834419756751791771189712040723138740224000000⟩, + ⟨1, 8, 6, 0, 8, 7, -246225845044399130437597836233432654967874781184000000⟩, + ⟨1, 8, 5, 1, 6, 7, 659449383478342860463342726765783620527333572608000000⟩, + ⟨1, 8, 6, 1, 7, 7, 823484289196031337713511119291350995462531317760000000⟩, + ⟨1, 8, 7, 1, 8, 7, 774044535424250431962862187403454108731269185536000000⟩, + ⟨1, 8, 5, 2, 5, 7, -115352094308110947820378107855869784316666970112000000⟩, + ⟨1, 8, 6, 2, 6, 7, -56844805943528437447854372689108145711221833728000000⟩, + ⟨1, 8, 7, 2, 7, 7, -45700475972569968644012838558657194709504491520000000⟩, + ⟨1, 8, 8, 2, 8, 7, -246262701713066690240697233679775712385693646848000000⟩, + ⟨1, 8, 5, 3, 4, 7, 156124244400320977019121368062052601430284435456000000⟩, + ⟨1, 8, 6, 3, 5, 7, 138481816692968332137276344388013766084917198848000000⟩, + ⟨1, 8, 7, 3, 6, 7, -35683895650372402555556645608459737849434996736000000⟩, + ⟨1, 8, 8, 3, 7, 7, -150849882985860734692672485642702663118686781440000000⟩, + ⟨1, 8, 5, 4, 3, 7, -14562708603135506754852558316722417323785322496000000⟩, + ⟨1, 8, 6, 4, 4, 7, -63997890438679447430432631534890944511072010240000000⟩, + ⟨1, 8, 7, 4, 5, 7, -122856442009750861644277518657543373710918942720000000⟩, + ⟨1, 8, 8, 4, 6, 7, 192414800911522029586838375063184638562539667456000000⟩, + ⟨1, 8, 5, 5, 2, 7, -1131095922003389923887951940846541709586471059456000000⟩, + ⟨1, 8, 6, 5, 3, 7, -23706484291494341321366250122794985975986520064000000⟩, + ⟨1, 8, 7, 5, 4, 7, 77849424226177293048192807363670389519632302080000000⟩, + ⟨1, 8, 8, 5, 5, 7, 64318453150699268964610537616452196872866496512000000⟩, + ⟨1, 8, 5, 6, 1, 7, 1445053701842312088482641953800058405474439004160000000⟩, + ⟨1, 8, 6, 6, 2, 7, -1698640068726301073705229042466230596487446790144000000⟩, + ⟨1, 8, 7, 6, 3, 7, 233432934314425161033307416618836670512332013568000000⟩, + ⟨1, 8, 8, 6, 4, 7, -95812188812550023131407225934428598863189245952000000⟩, + ⟨1, 8, 5, 7, 0, 7, 6304668682769069747729377777946130466818100297728000000⟩, + ⟨1, 8, 6, 7, 1, 7, 3367475948572483227274564552712006347079666368512000000⟩, + ⟨1, 8, 7, 7, 2, 7, -414532949037674803823066317513440348895583404032000000⟩, + ⟨1, 8, 8, 7, 3, 7, -458887546966027334676714380170756492961815461888000000⟩ +] + +def collectedFourData_14_2_15 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_16 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_17 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_18 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_19 : List CollectedFourTerm := [ + ⟨2, 4, 8, 2, 8, 4, 121922188986258172183542220328278573630530728755200000⟩, + ⟨2, 4, 8, 3, 7, 4, 74684261213809170183477306914839869416911405056000000⟩, + ⟨2, 4, 8, 4, 6, 4, -95262634403409790782067984834322826810311992934400000⟩, + ⟨2, 4, 8, 5, 5, 4, -31843419834970731749505644963700499802749717708800000⟩, + ⟨2, 4, 8, 6, 4, 4, 47435651888533422685213673467992703130984565964800000⟩, + ⟨2, 4, 8, 7, 3, 4, 227190613257467475640333334792427746769671238451200000⟩ +] + +def collectedFourData_14_2_20 : List CollectedFourTerm := [ + ⟨2, 5, 7, 1, 8, 5, -115352094308110947820378107855869784316666970112000000⟩, + ⟨2, 5, 7, 2, 7, 5, 6810519773806145994459218867066908073357475840000000⟩, + ⟨2, 5, 8, 2, 8, 5, 110097999892239364422451162027391008481369653248000000⟩, + ⟨2, 5, 7, 3, 6, 5, 5317797501259368155546506039447495922272960512000000⟩, + ⟨2, 5, 8, 3, 7, 5, 67441274237593494496036722486867594340403773440000000⟩, + ⟨2, 5, 7, 4, 5, 5, 18308698319664865189752684447966413810030346240000000⟩, + ⟨2, 5, 8, 4, 6, 5, -86023927223478370384422368729659466425886048256000000⟩, + ⟨2, 5, 7, 5, 4, 5, -11601521248707207593382876089185755624489615360000000⟩, + ⟨2, 5, 8, 5, 5, 5, -28755199219350379776056638850427228549506138112000000⟩, + ⟨2, 5, 7, 6, 3, 5, -34787375430404763884012610928432453845994438656000000⟩, + ⟨2, 5, 8, 6, 4, 5, 42835274201816469492727500352422639117168279552000000⟩, + ⟨2, 5, 7, 7, 2, 5, 61775830256336336864246760221039980441233260544000000⟩, + ⟨2, 5, 8, 7, 3, 5, 205157341103494181095273350733748471878844940288000000⟩ +] + +def collectedFourData_14_2_21 : List CollectedFourTerm := [ + ⟨2, 6, 6, 0, 8, 6, 9041250043938791760001046913486573322597564416000000⟩, + ⟨2, 6, 6, 1, 7, 6, -30237798004242775956289530654123847695193866240000000⟩, + ⟨2, 6, 7, 1, 8, 6, -56844805943528437447854372689108145711221833728000000⟩, + ⟨2, 6, 6, 2, 6, 6, 2087303646544269587946734656748248743618281472000000⟩, + ⟨2, 6, 7, 2, 7, 6, 3356182453718586160821987718477776862272552960000000⟩, + ⟨2, 6, 8, 2, 8, 6, 27127810189246373234354977609527299904746029056000000⟩, + ⟨2, 6, 6, 3, 5, 6, -5084960642674434961573463456413474678061924352000000⟩, + ⟨2, 6, 7, 3, 6, 6, 2620578055554331035537841416671400593958371328000000⟩, + ⟨2, 6, 8, 3, 7, 6, 16617323550192020554951949807344759485423943680000000⟩, + ⟨2, 6, 6, 4, 4, 6, 2349960174312182162853174881829083795958005760000000⟩, + ⟨2, 6, 7, 4, 5, 6, 9022414454652637472441744979512780923663810560000000⟩, + ⟨2, 6, 8, 4, 6, 6, -21196032368763855193535810106499754260621688832000000⟩, + ⟨2, 6, 6, 5, 3, 6, 870486410975495486318469165061729048420417536000000⟩, + ⟨2, 6, 7, 5, 4, 6, -5717158652282148968678733534923143209906339840000000⟩, + ⟨2, 6, 8, 5, 5, 6, -7085193074715321793375832928568764325234212864000000⟩, + ⟨2, 6, 6, 6, 2, 6, 62372938930267688131012130698382294997276819456000000⟩, + ⟨2, 6, 7, 6, 3, 6, -17143005660079999366132630281085998623845515264000000⟩, + ⟨2, 6, 8, 6, 4, 6, 10554480454581887504214112698368778764543852544000000⟩, + ⟨2, 6, 6, 7, 1, 6, -123651487773364205147846525327707603743736332288000000⟩, + ⟨2, 6, 7, 7, 2, 6, 30442750987615767219737526116542088120459329536000000⟩, + ⟨2, 6, 8, 7, 3, 6, 50550140909311509201075075135192017761191591936000000⟩ +] + +def collectedFourData_14_2_22 : List CollectedFourTerm := [ + ⟨2, 7, 5, 0, 7, 7, 235978651311364505525383486157994900250951680000000⟩, + ⟨2, 7, 6, 0, 8, 7, 14537455921847929318791653634197296631387258880000000⟩, + ⟨2, 7, 5, 1, 6, 7, -38934646942840370759878096102383436423558594560000000⟩, + ⟨2, 7, 6, 1, 7, 7, -48619455664221264094667592359233587713880883200000000⟩, + ⟨2, 7, 7, 1, 8, 7, -45700475972569968644012838558657194709504491520000000⟩, + ⟨2, 7, 5, 2, 5, 7, 6810519773806145994459218867066908073357475840000000⟩, + ⟨2, 7, 6, 2, 6, 7, 3356182453718586160821987718477776862272552960000000⟩, + ⟨2, 7, 7, 2, 7, 7, 2698208447366311968218117591354630268675686400000000⟩, + ⟨2, 7, 8, 2, 8, 7, 14539631981782190846541853192179549459563151360000000⟩, + ⟨2, 7, 5, 3, 4, 7, -9217754216224618232421874473773792076150865920000000⟩, + ⟨2, 7, 6, 3, 5, 7, -8176125076506241933466109703424117182939791360000000⟩, + ⟨2, 7, 7, 3, 6, 7, 2106818072016643745619676338578755411268075520000000⟩, + ⟨2, 7, 8, 3, 7, 7, 8906349876989696777964369684267766645574860800000000⟩, + ⟨2, 7, 5, 4, 3, 7, 859798996253312610784291728531223210591518720000000⟩, + ⟨2, 7, 6, 4, 4, 7, 3778508755552419791736103406849402356944076800000000⟩, + ⟨2, 7, 7, 4, 5, 7, 7253585057692731294764114435866823638804070400000000⟩, + ⟨2, 7, 8, 4, 6, 7, -11360390240342173783984754493493318875265105920000000⟩, + ⟨2, 7, 5, 5, 2, 7, 66781198807709228367502862911634681397950545920000000⟩, + ⟨2, 7, 6, 5, 3, 7, 1399657986298862037633839333177577632673300480000000⟩, + ⟨2, 7, 7, 5, 4, 7, -4596319176101193465856837763164214652410265600000000⟩, + ⟨2, 7, 8, 5, 5, 7, -3797435145246953571115235862285208514293923840000000⟩, + ⟨2, 7, 5, 6, 1, 7, -85317625740903695492103318049208237808628531200000000⟩, + ⟨2, 7, 6, 6, 2, 7, 100289655303002679111010048666349108136593326080000000⟩, + ⟨2, 7, 7, 6, 3, 7, -13782147819176591243774286591145181246662901760000000⟩, + ⟨2, 7, 8, 6, 4, 7, 5656861372075126926444108861459851909938544640000000⟩, + ⟨2, 7, 5, 7, 0, 7, -372234860483811083995411237554436334578261032960000000⟩, + ⟨2, 7, 6, 7, 1, 7, -198819637156400459803369760520151773516492963840000000⟩, + ⟨2, 7, 7, 7, 2, 7, 24474500122853411048928624358920368865662730240000000⟩, + ⟨2, 7, 8, 7, 3, 7, 27093246388902136926551654547644768942460764160000000⟩ +] + +def collectedFourData_14_2_23 : List CollectedFourTerm := [ + ⟨2, 8, 4, 0, 6, 8, 295097581039362050254200554902279604587028545536000000⟩, + ⟨2, 8, 5, 0, 7, 8, 3814800982822741354564540816498208175078506496000000⟩, + ⟨2, 8, 6, 0, 8, 8, 117505335398399622369276075302593757164672647168000000⟩, + ⟨2, 8, 4, 1, 5, 8, -457289372325038009187127408285923966934389148876800000⟩, + ⟨2, 8, 5, 1, 6, 8, -629412570154183798312134216971777093078857285632000000⟩, + ⟨2, 8, 6, 1, 7, 8, -392987980525943766152880245944198940772028907520000000⟩, + ⟨2, 8, 7, 1, 8, 8, -246262701713066690240697233679775712385693646848000000⟩, + ⟨2, 8, 4, 2, 4, 8, 121922188986258172183542220328278573630530728755200000⟩, + ⟨2, 8, 5, 2, 5, 8, 110097999892239364422451162027391008481369653248000000⟩, + ⟨2, 8, 6, 2, 6, 8, 27127810189246373234354977609527299904746029056000000⟩, + ⟨2, 8, 7, 2, 7, 8, 14539631981782190846541853192179549459563151360000000⟩, + ⟨2, 8, 8, 2, 8, 8, 58761462176507155519032494780291770774242459648000000⟩, + ⟨2, 8, 4, 3, 3, 8, -155509708976893937602734212191783182434486452224000000⟩, + ⟨2, 8, 5, 3, 4, 8, -149013046934804148362690935276547363063646388224000000⟩, + ⟨2, 8, 6, 3, 5, 8, -66087101108954381556869612881098054052186423296000000⟩, + ⟨2, 8, 7, 3, 6, 8, 11352851352010908242373097575126083144880488448000000⟩, + ⟨2, 8, 8, 3, 7, 8, 35994730959023884758306176660457238159624765440000000⟩, + ⟨2, 8, 4, 4, 2, 8, 518454908708212569719356264075053458708218301644800000⟩, + ⟨2, 8, 5, 4, 3, 8, 13899401652267955106864615405978654049130512384000000⟩, + ⟨2, 8, 6, 4, 4, 8, 30541446936372772423004919981770218282659348480000000⟩, + ⟨2, 8, 7, 4, 5, 8, 39086845714366216442381661316488181454953512960000000⟩, + ⟨2, 8, 8, 4, 6, 8, -45912657366751490570709374845562879710442029056000000⟩, + ⟨2, 8, 4, 5, 1, 8, -499855242094620244778794617604200301716972345753600000⟩, + ⟨2, 8, 5, 5, 2, 8, 1079576399941316198000933598844982236192098484224000000⟩, + ⟨2, 8, 6, 5, 3, 8, 11313346847430381870112607239646578583355260928000000⟩, + ⟨2, 8, 7, 5, 4, 8, -24767837843125293116743790662282304401377853440000000⟩, + ⟨2, 8, 8, 5, 5, 8, -15347213872728032732263142769739363935124979712000000⟩, + ⟨2, 8, 4, 6, 0, 8, -1559560155690154810305280102935039683475442709299200000⟩, + ⟨2, 8, 5, 6, 1, 8, -1379233929509401863796059323899753224452324720640000000⟩, + ⟨2, 8, 6, 6, 2, 8, 810634931360893925833442215507490256031567577088000000⟩, + ⟨2, 8, 7, 6, 3, 8, -74266818564349715907173979552931143868244557824000000⟩, + ⟨2, 8, 8, 6, 4, 8, 22862026079438115762522795853131741066430513152000000⟩, + ⟨2, 8, 5, 7, 0, 8, -6017501599078520547028150002293162823074407514112000000⟩, + ⟨2, 8, 6, 7, 1, 8, -1607046533688216567936494689748891565967408103424000000⟩, + ⟨2, 8, 7, 7, 2, 8, 131883889501462585515426372527824565027236478976000000⟩, + ⟨2, 8, 8, 7, 3, 8, 109496497223248035713357084076960030412335218688000000⟩ +] + +def collectedFourData_14_2_24 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_25 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_26 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_27 : List CollectedFourTerm := [ + ⟨3, 3, 8, 2, 8, 4, -155509708976893937602734212191783182434486452224000000⟩, + ⟨3, 3, 8, 3, 7, 4, -95258523678760540195907690366267519801197854720000000⟩, + ⟨3, 3, 8, 4, 6, 4, 121505893846084192841508574864023848442635747328000000⟩, + ⟨3, 3, 8, 5, 5, 4, 40615748392800633634325225938242143623846035456000000⟩, + ⟨3, 3, 8, 6, 4, 4, -60503379094895588562604230408319186202762674176000000⟩, + ⟨3, 3, 8, 7, 3, 4, -289777820130287405166680404227704624019085983744000000⟩ +] + +def collectedFourData_14_2_28 : List CollectedFourTerm := [ + ⟨3, 4, 7, 1, 8, 5, 156124244400320977019121368062052601430284435456000000⟩, + ⟨3, 4, 7, 2, 7, 5, -9217754216224618232421874473773792076150865920000000⟩, + ⟨3, 4, 8, 2, 8, 5, -149013046934804148362690935276547363063646388224000000⟩, + ⟨3, 4, 7, 3, 6, 5, -7197416932374290835189209689316052000263110656000000⟩, + ⟨3, 4, 8, 3, 7, 5, -91278949419115650212190745894424894201627934720000000⟩, + ⟨3, 4, 7, 4, 5, 5, -24780058899287046977097020967394222147758981120000000⟩, + ⟨3, 4, 8, 4, 6, 5, 116429794523196673609328586075278121371411939328000000⟩, + ⟨3, 4, 7, 5, 4, 5, 15702174717440926118139005554919552281403719680000000⟩, + ⟨3, 4, 8, 5, 5, 5, 38918961789375227591534419677688006845929619456000000⟩, + ⟨3, 4, 7, 6, 3, 5, 47083260484507255509945921650819465254721814528000000⟩, + ⟨3, 4, 8, 6, 4, 5, -57975755520972107896758620057100080989052338176000000⟩, + ⟨3, 4, 7, 7, 2, 5, -83611007488182492479444526468549999468396675072000000⟩, + ⟨3, 4, 8, 7, 3, 5, -277671897117083896294655447251273622796311199744000000⟩ +] + +def collectedFourData_14_2_29 : List CollectedFourTerm := [ + ⟨3, 5, 6, 0, 8, 6, -22025736748997813621410632191793708335477293056000000⟩, + ⟨3, 5, 6, 1, 7, 6, 73663461963128919287199704255476888206405795840000000⟩, + ⟨3, 5, 7, 1, 8, 6, 138481816692968332137276344388013766084917198848000000⟩, + ⟨3, 5, 6, 2, 6, 6, -5084960642674434961573463456413474678061924352000000⟩, + ⟨3, 5, 7, 2, 7, 6, -8176125076506241933466109703424117182939791360000000⟩, + ⟨3, 5, 8, 2, 8, 6, -66087101108954381556869612881098054052186423296000000⟩, + ⟨3, 5, 6, 3, 5, 6, 12387668071368745952935379526663084691194642432000000⟩, + ⟨3, 5, 7, 3, 6, 6, -6384090927839736897502287601367484096942440448000000⟩, + ⟨3, 5, 8, 3, 7, 6, -40482100617803579408849947963733468097942650880000000⟩, + ⟨3, 5, 6, 4, 4, 6, -5724828305653211643995067373188359792004956160000000⟩, + ⟨3, 5, 7, 4, 5, 6, -21979850645957537325490815169541757123648552960000000⟩, + ⟨3, 5, 8, 4, 6, 6, 51636469161762494872658925689079077887763546112000000⟩, + ⟨3, 5, 6, 5, 3, 6, -2120625404512480753081173987486847616182910976000000⟩, + ⟨3, 5, 7, 5, 4, 6, 13927789942259253912112141553677301360036413440000000⟩, + ⟨3, 5, 8, 5, 5, 6, 17260511181650332480749344524918028369525735424000000⟩, + ⟨3, 5, 6, 6, 2, 6, -151949113945851836884591961986424061387337629696000000⟩, + ⟨3, 5, 7, 6, 3, 6, 41762735011253692379970756559567450845241933824000000⟩, + ⟨3, 5, 8, 6, 4, 6, -25712175516140080546493951503302782422093922304000000⟩, + ⟨3, 5, 6, 7, 1, 6, 301232142135464171769555063071184797466579959808000000⟩, + ⟨3, 5, 7, 7, 2, 6, -74162755803666108664128010303477972345842302976000000⟩, + ⟨3, 5, 8, 7, 3, 6, -123147141256165205835356897389380144109637861376000000⟩ +] + +def collectedFourData_14_2_30 : List CollectedFourTerm := [ + ⟨3, 6, 5, 0, 7, 7, 184257108704174634776360767729183322510721024000000⟩, + ⟨3, 6, 6, 0, 8, 7, 11351152238512183386140185087054614763860393984000000⟩, + ⟨3, 6, 5, 1, 6, 7, -30400993624799594542635165416758256098458206208000000⟩, + ⟨3, 6, 6, 1, 7, 7, -37963096566900265222725075113900051338635509760000000⟩, + ⟨3, 6, 7, 1, 8, 7, -35683895650372402555556645608459737849434996736000000⟩, + ⟨3, 6, 5, 2, 5, 7, 5317797501259368155546506039447495922272960512000000⟩, + ⟨3, 6, 6, 2, 6, 7, 2620578055554331035537841416671400593958371328000000⟩, + ⟨3, 6, 7, 2, 7, 7, 2106818072016643745619676338578755411268075520000000⟩, + ⟨3, 6, 8, 2, 8, 7, 11352851352010908242373097575126083144880488448000000⟩, + ⟨3, 6, 5, 3, 4, 7, -7197416932374290835189209689316052000263110656000000⟩, + ⟨3, 6, 6, 3, 5, 7, -6384090927839736897502287601367484096942440448000000⟩, + ⟨3, 6, 7, 3, 6, 7, 1645047992088406320343759733696891345159847936000000⟩, + ⟨3, 6, 8, 3, 7, 7, 6954265855501442783203610930946698412231229440000000⟩, + ⟨3, 6, 5, 4, 3, 7, 671349192971497034900694303590015799127965696000000⟩, + ⟨3, 6, 6, 4, 4, 7, 2950339340624787647599275330953006819825418240000000⟩, + ⟨3, 6, 7, 4, 5, 7, 5663752220987037594805373379068000408929566720000000⟩, + ⟨3, 6, 8, 4, 6, 7, -8870432337011006736666729948366220891212742656000000⟩, + ⟨3, 6, 5, 5, 2, 7, 52144168719192031888386494712116634147310534656000000⟩, + ⟨3, 6, 6, 5, 3, 7, 1092882480245430257164420603752652860360228864000000⟩, + ⟨3, 6, 7, 5, 4, 7, -3588902967974433426657644292538791941457838080000000⟩, + ⟨3, 6, 8, 5, 5, 7, -2965117464933676496105586006627647274627366912000000⟩, + ⟨3, 6, 5, 6, 1, 7, -66617801878108716042322856345097714274570076160000000⟩, + ⟨3, 6, 6, 6, 2, 7, 78308278381874258562353554583804021456391634944000000⟩, + ⟨3, 6, 7, 6, 3, 7, -10761391739392175494628431461967969086150279168000000⟩, + ⟨3, 6, 8, 6, 4, 7, 4416996685787466205506674062369967094840164352000000⟩, + ⟨3, 6, 5, 7, 0, 7, -290648831029850783121972375187559332443825635328000000⟩, + ⟨3, 6, 6, 7, 1, 7, -155242566615546983542485073051825510462009638912000000⟩, + ⟨3, 6, 7, 7, 2, 7, 19110205963787362199779020272255654642615058432000000⟩, + ⟨3, 6, 8, 7, 3, 7, 21154978288447028081938655620866039781143871488000000⟩ +] + +def collectedFourData_14_2_31 : List CollectedFourTerm := [ + ⟨3, 7, 4, 0, 6, 8, 180764018503563478322590112975958293780449198080000000⟩, + ⟨3, 7, 5, 0, 7, 8, 2336782134972504655043574281589759201383546880000000⟩, + ⟨3, 7, 6, 0, 8, 8, 71978687684974663353632616596260699728028631040000000⟩, + ⟨3, 7, 4, 1, 5, 8, -280115696880009908768973681475206521480653307904000000⟩, + ⟨3, 7, 5, 1, 6, 8, -385550925483697038898337309067694264623782952960000000⟩, + ⟨3, 7, 6, 1, 7, 8, -240727444573645004069309844186312944329005465600000000⟩, + ⟨3, 7, 7, 1, 8, 8, -150849882985860734692672485642702663118686781440000000⟩, + ⟨3, 7, 4, 2, 4, 8, 74684261213809170183477306914839869416911405056000000⟩, + ⟨3, 7, 5, 2, 5, 8, 67441274237593494496036722486867594340403773440000000⟩, + ⟨3, 7, 6, 2, 6, 8, 16617323550192020554951949807344759485423943680000000⟩, + ⟨3, 7, 7, 2, 7, 8, 8906349876989696777964369684267766645574860800000000⟩, + ⟨3, 7, 8, 2, 8, 8, 35994730959023884758306176660457238159624765440000000⟩, + ⟨3, 7, 4, 3, 3, 8, -95258523678760540195907690366267519801197854720000000⟩, + ⟨3, 7, 5, 3, 4, 8, -91278949419115650212190745894424894201627934720000000⟩, + ⟨3, 7, 6, 3, 5, 8, -40482100617803579408849947963733468097942650880000000⟩, + ⟨3, 7, 7, 3, 6, 8, 6954265855501442783203610930946698412231229440000000⟩, + ⟨3, 7, 8, 3, 7, 8, 22048815819469208368606421814158891473384243200000000⟩, + ⟨3, 7, 4, 4, 2, 8, 317583059748951078407462164864099813070884306944000000⟩, + ⟨3, 7, 5, 4, 3, 8, 8514172459868080505007654168466537259225579520000000⟩, + ⟨3, 7, 6, 4, 4, 8, 18708369820204287436126430366332528345114214400000000⟩, + ⟨3, 7, 7, 4, 5, 8, 23942911619513355149353406596268165115464908800000000⟩, + ⟨3, 7, 8, 4, 6, 8, -28124108698418012127803522849766852408303943680000000⟩, + ⟨3, 7, 4, 5, 1, 8, -306189708207207843277897461398446346130904055808000000⟩, + ⟨3, 7, 5, 5, 2, 8, 661301823104311829768387056398180001870742814720000000⟩, + ⟨3, 7, 6, 5, 3, 8, 6930067104119553736567312995329324074496163840000000⟩, + ⟨3, 7, 7, 5, 4, 8, -15171706533137493800821974101120337254232883200000000⟩, + ⟨3, 7, 8, 5, 5, 8, -9401039624577308968475407917637556002734735360000000⟩, + ⟨3, 7, 4, 6, 0, 8, -955319117993692276570028903411859534276382949376000000⟩, + ⟨3, 7, 5, 6, 1, 8, -844859068910241929474138416799686647778325299200000000⟩, + ⟨3, 7, 6, 6, 2, 8, 496559908136318893556263515840556676133043568640000000⟩, + ⟨3, 7, 7, 6, 3, 8, -45492641850480706007688235961283311460648222720000000⟩, + ⟨3, 7, 8, 6, 4, 8, 14004288651560531931196425659053249518958018560000000⟩, + ⟨3, 7, 5, 7, 0, 8, -3686061290539557414609280936688664737958183567360000000⟩, + ⟨3, 7, 6, 7, 1, 8, -984407219905188046743645471214712031403541790720000000⟩, + ⟨3, 7, 7, 7, 2, 8, 80786368218261968338005855777785743152544481280000000⟩, + ⟨3, 7, 8, 7, 3, 8, 67072819710773810958098369643220600963612016640000000⟩ +] + +def collectedFourData_14_2_32 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_33 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_34 : List CollectedFourTerm := [ + ⟨4, 2, 8, 2, 8, 4, 518454908708212569719356264075053458708218301644800000⟩, + ⟨4, 2, 8, 3, 7, 4, 317583059748951078407462164864099813070884306944000000⟩, + ⟨4, 2, 8, 4, 6, 4, -405089351114671351484586052343843388735719315865600000⟩, + ⟨4, 2, 8, 5, 5, 4, -135409128237992881073376388382743363461160579891200000⟩, + ⟨4, 2, 8, 6, 4, 4, 201712639625885056867054522298421337067927843635200000⟩, + ⟨4, 2, 8, 7, 3, 4, 966092305552675096286192250304687416596746783948800000⟩ +] + +def collectedFourData_14_2_35 : List CollectedFourTerm := [ + ⟨4, 3, 7, 1, 8, 5, -14562708603135506754852558316722417323785322496000000⟩, + ⟨4, 3, 7, 2, 7, 5, 859798996253312610784291728531223210591518720000000⟩, + ⟨4, 3, 8, 2, 8, 5, 13899401652267955106864615405978654049130512384000000⟩, + ⟨4, 3, 7, 3, 6, 5, 671349192971497034900694303590015799127965696000000⟩, + ⟨4, 3, 8, 3, 7, 5, 8514172459868080505007654168466537259225579520000000⟩, + ⟨4, 3, 7, 4, 5, 5, 2311394865704215701634661702509934661253201920000000⟩, + ⟨4, 3, 8, 4, 6, 5, -10860152930615366013842946101318065853822926848000000⟩, + ⟨4, 3, 7, 5, 4, 5, -1464642443740427179286500098089227989685370880000000⟩, + ⟨4, 3, 8, 5, 5, 5, -3630220929825499066202832665123346672041066496000000⟩, + ⟨4, 3, 7, 6, 3, 5, -4391757379867865062181512399706932021504770048000000⟩, + ⟨4, 3, 8, 6, 4, 5, 5407770182917250993776704032448491765435990016000000⟩, + ⟨4, 3, 7, 7, 2, 5, 7798934385507131278373590973360093397151383552000000⟩, + ⟨4, 3, 8, 7, 3, 5, 25900236958889657189472532026971624879060680704000000⟩ +] + +def collectedFourData_14_2_36 : List CollectedFourTerm := [ + ⟨4, 4, 6, 0, 8, 6, 10178958660102072225113336351253469794171617280000000⟩, + ⟨4, 4, 6, 1, 7, 6, -34042781071412193221009050063595219052606259200000000⟩, + ⟨4, 4, 7, 1, 8, 6, -63997890438679447430432631534890944511072010240000000⟩, + ⟨4, 4, 6, 2, 6, 6, 2349960174312182162853174881829083795958005760000000⟩, + ⟨4, 4, 7, 2, 7, 6, 3778508755552419791736103406849402356944076800000000⟩, + ⟨4, 4, 8, 2, 8, 6, 30541446936372772423004919981770218282659348480000000⟩, + ⟨4, 4, 6, 3, 5, 6, -5724828305653211643995067373188359792004956160000000⟩, + ⟨4, 4, 7, 3, 6, 6, 2950339340624787647599275330953006819825418240000000⟩, + ⟨4, 4, 8, 3, 7, 6, 18708369820204287436126430366332528345114214400000000⟩, + ⟨4, 4, 6, 4, 4, 6, 2645668170989907258709055171993368936631500800000000⟩, + ⟨4, 4, 7, 4, 5, 6, 10157752888361364910822437219737359272955084800000000⟩, + ⟨4, 4, 8, 4, 6, 6, -23863241940142199936762045946421803936708034560000000⟩, + ⟨4, 4, 6, 5, 3, 6, 980024349336552524033975690696528338228346880000000⟩, + ⟨4, 4, 7, 5, 4, 6, -6436579155759365236160129774576631867978547200000000⟩, + ⟨4, 4, 8, 5, 5, 6, -7976760631094099702678864151755039211383685120000000⟩, + ⟨4, 4, 6, 6, 2, 6, 70221657823288943978241338604166897535004180480000000⟩, + ⟨4, 4, 7, 6, 3, 6, -19300201307985358703263002991837381313817477120000000⟩, + ⟨4, 4, 8, 6, 4, 6, 11882606907666193204831806339960846622937579520000000⟩, + ⟨4, 4, 6, 7, 1, 6, -139211212629715868206827318649312594013234135040000000⟩, + ⟨4, 4, 7, 7, 2, 6, 34273524379569769139282002764895953418589306880000000⟩, + ⟨4, 4, 8, 7, 3, 6, 56911134199099676724196795658128478702539898880000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1404.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1404.lean new file mode 100644 index 0000000000000000000000000000000000000000..76ac570ae8c1c98d85ac264a40ff2164748c8c11 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1404.lean @@ -0,0 +1,634 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1403 + +namespace OAI + +/-! Sparse1404. -/ +namespace LaughlinFock +def collectedFourData_14_2_37 : List CollectedFourTerm := [ + ⟨4, 5, 5, 0, 7, 7, 634380646446110397570618134658774913756692480000000⟩, + ⟨4, 5, 6, 0, 8, 7, 39080995819470508869081091968927539790537031680000000⟩, + ⟨4, 5, 5, 1, 6, 7, -104667885673099664585679403951726096208269148160000000⟩, + ⟨4, 5, 6, 1, 7, 7, -130703525690678902356476852602206544341447475200000000⟩, + ⟨4, 5, 7, 1, 8, 7, -122856442009750861644277518657543373710918942720000000⟩, + ⟨4, 5, 5, 2, 5, 7, 18308698319664865189752684447966413810030346240000000⟩, + ⟨4, 5, 6, 2, 6, 7, 9022414454652637472441744979512780923663810560000000⟩, + ⟨4, 5, 7, 2, 7, 7, 7253585057692731294764114435866823638804070400000000⟩, + ⟨4, 5, 8, 2, 8, 7, 39086845714366216442381661316488181454953512960000000⟩, + ⟨4, 5, 5, 3, 4, 7, -24780058899287046977097020967394222147758981120000000⟩, + ⟨4, 5, 6, 3, 5, 7, -21979850645957537325490815169541757123648552960000000⟩, + ⟨4, 5, 7, 3, 6, 7, 5663752220987037594805373379068000408929566720000000⟩, + ⟨4, 5, 8, 3, 7, 7, 23942911619513355149353406596268165115464908800000000⟩, + ⟨4, 5, 5, 4, 3, 7, 2311394865704215701634661702509934661253201920000000⟩, + ⟨4, 5, 6, 4, 4, 7, 10157752888361364910822437219737359272955084800000000⟩, + ⟨4, 5, 7, 4, 5, 7, 19499789291868693712740188307126897097467494400000000⟩, + ⟨4, 5, 8, 4, 6, 7, -30540100405266103548594682478581942601247621120000000⟩, + ⟨4, 5, 5, 5, 2, 7, 179527681146809545724085776241800314730179461120000000⟩, + ⟨4, 5, 6, 5, 3, 7, 3762696045669670497130923625465882915142369280000000⟩, + ⟨4, 5, 7, 5, 4, 7, -12356270001562237713099917271506989908335001600000000⟩, + ⟨4, 5, 8, 5, 5, 7, -10208632640671955041041969479176814661457674240000000⟩, + ⟨4, 5, 5, 6, 1, 7, -229359097825114327088253252925351422132958003200000000⟩, + ⟨4, 5, 6, 6, 2, 7, 269608356558619155290578815342210526410052730880000000⟩, + ⟨4, 5, 7, 6, 3, 7, -37050503485626269162055899798703260959097487360000000⟩, + ⟨4, 5, 8, 6, 4, 7, 15207322162961384630477605115548035055657943040000000⟩, + ⟨4, 5, 5, 7, 0, 7, -1000677773651321743609172356348110601494001090560000000⟩, + ⟨4, 5, 6, 7, 1, 7, -534486188663899117967094468295450258053519114240000000⟩, + ⟨4, 5, 7, 7, 2, 7, 65794719662563944781410361679440890326302064640000000⟩, + ⟨4, 5, 8, 7, 3, 7, 72834686794770038469829155437415822054402293760000000⟩ +] + +def collectedFourData_14_2_38 : List CollectedFourTerm := [ + ⟨4, 6, 4, 0, 6, 8, -230571426002298997844909431083493633433788219392000000⟩, + ⟨4, 6, 5, 0, 7, 8, -2980655074929558652463404770908793057954496512000000⟩, + ⟨4, 6, 6, 0, 8, 8, -91811571786735628503186999174367702452321386496000000⟩, + ⟨4, 6, 4, 1, 5, 8, 357298295368325174803530860853483125239289846169600000⟩, + ⟨4, 6, 5, 1, 6, 8, 491784965952887807105306889725480322726157615104000000⟩, + ⟨4, 6, 6, 1, 7, 8, 307057071604880986112067122962769462322203197440000000⟩, + ⟨4, 6, 7, 1, 8, 8, 192414800911522029586838375063184638562539667456000000⟩, + ⟨4, 6, 4, 2, 4, 8, -95262634403409790782067984834322826810311992934400000⟩, + ⟨4, 6, 5, 2, 5, 8, -86023927223478370384422368729659466425886048256000000⟩, + ⟨4, 6, 6, 2, 6, 8, -21196032368763855193535810106499754260621688832000000⟩, + ⟨4, 6, 7, 2, 7, 8, -11360390240342173783984754493493318875265105920000000⟩, + ⟨4, 6, 8, 2, 8, 8, -45912657366751490570709374845562879710442029056000000⟩, + ⟨4, 6, 4, 3, 3, 8, 121505893846084192841508574864023848442635747328000000⟩, + ⟨4, 6, 5, 3, 4, 8, 116429794523196673609328586075278121371411939328000000⟩, + ⟨4, 6, 6, 3, 5, 8, 51636469161762494872658925689079077887763546112000000⟩, + ⟨4, 6, 7, 3, 6, 8, -8870432337011006736666729948366220891212742656000000⟩, + ⟨4, 6, 8, 3, 7, 8, -28124108698418012127803522849766852408303943680000000⟩, + ⟨4, 6, 4, 4, 2, 8, -405089351114671351484586052343843388735719315865600000⟩, + ⟨4, 6, 5, 4, 3, 8, -10860152930615366013842946101318065853822926848000000⟩, + ⟨4, 6, 6, 4, 4, 8, -23863241940142199936762045946421803936708034560000000⟩, + ⟨4, 6, 7, 4, 5, 8, -30540100405266103548594682478581942601247621120000000⟩, + ⟨4, 6, 8, 4, 6, 8, 35873377353082401535152914753414208059533688832000000⟩, + ⟨4, 6, 4, 5, 1, 8, 390556695038133405215044632375484299565805548339200000⟩, + ⟨4, 6, 5, 5, 2, 8, -843515792763123411987236495611274622993671651328000000⟩, + ⟨4, 6, 6, 5, 3, 8, -8839565903194216648731246335898249202778505216000000⟩, + ⟨4, 6, 7, 5, 4, 8, 19352092519258456063565704467560563918692679680000000⟩, + ⟨4, 6, 8, 5, 5, 8, 11991385952178180316578748237959396646258212864000000⟩, + ⟨4, 6, 4, 6, 0, 8, 1218546108603587506350556200597416716950277875302400000⟩, + ⟨4, 6, 5, 6, 1, 8, 1077650087125989037125270320819642702749583278080000000⟩, + ⟨4, 6, 6, 6, 2, 8, -633381173213432405277054362366539957016236916736000000⟩, + ⟨4, 6, 7, 6, 3, 8, 58027606328470854048808593629444744206539030528000000⟩, + ⟨4, 6, 8, 6, 4, 8, -17863006317678594683015320919766567944447852544000000⟩, + ⟨4, 6, 5, 7, 0, 8, 4701712293892303902394983533852078072440673009664000000⟩, + ⟨4, 6, 6, 7, 1, 8, 1255649096205633780363228986355916422592465993728000000⟩, + ⟨4, 6, 7, 7, 2, 8, -103046105501711151683154370221880289595670659072000000⟩, + ⟨4, 6, 8, 7, 3, 8, -85553949368542920393438035666173878956967591936000000⟩ +] + +def collectedFourData_14_2_39 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_2_40 : List CollectedFourTerm := [ + ⟨5, 1, 8, 2, 8, 4, -499855242094620244778794617604200301716972345753600000⟩, + ⟨5, 1, 8, 3, 7, 4, -306189708207207843277897461398446346130904055808000000⟩, + ⟨5, 1, 8, 4, 6, 4, 390556695038133405215044632375484299565805548339200000⟩, + ⟨5, 1, 8, 5, 5, 4, 130551300489888192980949231618504274697800541798400000⟩, + ⟨5, 1, 8, 6, 4, 4, -194476161031946875015894147601807011354065135206400000⟩, + ⟨5, 1, 8, 7, 3, 4, -931433563780881956090375668286883161421760797081600000⟩ +] + +def collectedFourData_14_2_41 : List CollectedFourTerm := [ + ⟨5, 2, 7, 1, 8, 5, -1131095922003389923887951940846541709586471059456000000⟩, + ⟨5, 2, 7, 2, 7, 5, 66781198807709228367502862911634681397950545920000000⟩, + ⟨5, 2, 8, 2, 8, 5, 1079576399941316198000933598844982236192098484224000000⟩, + ⟨5, 2, 7, 3, 6, 5, 52144168719192031888386494712116634147310534656000000⟩, + ⟨5, 2, 8, 3, 7, 5, 661301823104311829768387056398180001870742814720000000⟩, + ⟨5, 2, 7, 4, 5, 5, 179527681146809545724085776241800314730179461120000000⟩, + ⟨5, 2, 8, 4, 6, 5, -843515792763123411987236495611274622993671651328000000⟩, + ⟨5, 2, 7, 5, 4, 5, -113759819031960987973813388795735991054426439680000000⟩, + ⟨5, 2, 8, 5, 5, 5, -281961838391306071259216504980905058850052243456000000⟩, + ⟨5, 2, 7, 6, 3, 5, -341110915432811669007671253667488575152642326528000000⟩, + ⟨5, 2, 8, 6, 4, 5, 420025351582756813848341925143672695588625842176000000⟩, + ⟨5, 2, 7, 7, 2, 5, 605748773790598303456881684803093825764114563072000000⟩, + ⟨5, 2, 8, 7, 3, 5, 2011689803146504336461627778181193041466825375744000000⟩ +] + +def collectedFourData_14_2_42 : List CollectedFourTerm := [ + ⟨5, 3, 6, 0, 8, 6, 3770551215445020762962594047121653287100612608000000⟩, + ⟨5, 3, 6, 1, 7, 6, -12610332140267757670614559224403391608384389120000000⟩, + ⟨5, 3, 7, 1, 8, 6, -23706484291494341321366250122794985975986520064000000⟩, + ⟨5, 3, 6, 2, 6, 6, 870486410975495486318469165061729048420417536000000⟩, + ⟨5, 3, 7, 2, 7, 6, 1399657986298862037633839333177577632673300480000000⟩, + ⟨5, 3, 8, 2, 8, 6, 11313346847430381870112607239646578583355260928000000⟩, + ⟨5, 3, 6, 3, 5, 6, -2120625404512480753081173987486847616182910976000000⟩, + ⟨5, 3, 7, 3, 6, 6, 1092882480245430257164420603752652860360228864000000⟩, + ⟨5, 3, 8, 3, 7, 6, 6930067104119553736567312995329324074496163840000000⟩, + ⟨5, 3, 6, 4, 4, 6, 980024349336552524033975690696528338228346880000000⟩, + ⟨5, 3, 7, 4, 5, 6, 3762696045669670497130923625465882915142369280000000⟩, + ⟨5, 3, 8, 4, 6, 6, -8839565903194216648731246335898249202778505216000000⟩, + ⟨5, 3, 6, 5, 3, 6, 363026526086667378387649858204521832453767168000000⟩, + ⟨5, 3, 7, 5, 4, 6, -2384276444130208482805628928565666069264465920000000⟩, + ⟨5, 3, 8, 5, 5, 6, -2954799748895359550478057699538668495707308032000000⟩, + ⟨5, 3, 6, 6, 2, 6, 26011929716738959936847194862677144810058416128000000⟩, + ⟨5, 3, 7, 6, 3, 6, -7149296890790990709315990742261499748503519232000000⟩, + ⟨5, 3, 8, 6, 4, 6, 4401626867193395257043360189179298334608719872000000⟩, + ⟨5, 3, 6, 7, 1, 6, -51567456408088682326021755800720826599781433344000000⟩, + ⟨5, 3, 7, 7, 2, 6, 12695805467165091626431938429395365168486023168000000⟩, + ⟨5, 3, 8, 7, 3, 6, 21081365333358977653306852315430374928566714368000000⟩ +] + +def collectedFourData_14_2_43 : List CollectedFourTerm := [ + ⟨5, 4, 5, 0, 7, 7, -401982730886347505280723560087359907923230720000000⟩, + ⟨5, 4, 6, 0, 8, 7, -24764130988670088048855803939109215441277419520000000⟩, + ⟨5, 4, 5, 1, 6, 7, 66324032352942825497450212084271316077893386240000000⟩, + ⟨5, 4, 6, 1, 7, 7, 82821820760063523853459096631811656681049292800000000⟩, + ⟨5, 4, 7, 1, 8, 7, 77849424226177293048192807363670389519632302080000000⟩, + ⟨5, 4, 5, 2, 5, 7, -11601521248707207593382876089185755624489615360000000⟩, + ⟨5, 4, 6, 2, 6, 7, -5717158652282148968678733534923143209906339840000000⟩, + ⟨5, 4, 7, 2, 7, 7, -4596319176101193465856837763164214652410265600000000⟩, + ⟨5, 4, 8, 2, 8, 7, -24767837843125293116743790662282304401377853440000000⟩, + ⟨5, 4, 5, 3, 4, 7, 15702174717440926118139005554919552281403719680000000⟩, + ⟨5, 4, 6, 3, 5, 7, 13927789942259253912112141553677301360036413440000000⟩, + ⟨5, 4, 7, 3, 6, 7, -3588902967974433426657644292538791941457838080000000⟩, + ⟨5, 4, 8, 3, 7, 7, -15171706533137493800821974101120337254232883200000000⟩, + ⟨5, 4, 5, 4, 3, 7, -1464642443740427179286500098089227989685370880000000⟩, + ⟨5, 4, 6, 4, 4, 7, -6436579155759365236160129774576631867978547200000000⟩, + ⟨5, 4, 7, 4, 5, 7, -12356270001562237713099917271506989908335001600000000⟩, + ⟨5, 4, 8, 4, 6, 7, 19352092519258456063565704467560563918692679680000000⟩, + ⟨5, 4, 5, 5, 2, 7, -113759819031960987973813388795735991054426439680000000⟩, + ⟨5, 4, 6, 5, 3, 7, -2384276444130208482805628928565666069264465920000000⟩, + ⟨5, 4, 7, 5, 4, 7, 7829695288818967521163575548910870003607142400000000⟩, + ⟨5, 4, 8, 5, 5, 7, 6468819707067497553968149643299986808881807360000000⟩, + ⟨5, 4, 5, 6, 1, 7, 145336080181318216673232811048781148716846284800000000⟩, + ⟨5, 4, 6, 6, 2, 7, -170840494656263687969291942946937085681278648320000000⟩, + ⟨5, 4, 7, 6, 3, 7, 23477485726121339269418910119588494161519575040000000⟩, + ⟨5, 4, 8, 6, 4, 7, -9636297902185435920798332305292843473761730560000000⟩, + ⟨5, 4, 5, 7, 0, 7, 634091198152274579900017844144435919723524259840000000⟩, + ⟨5, 4, 6, 7, 1, 7, 338683437055958855747684001016061221515149967360000000⟩, + ⟨5, 4, 7, 7, 2, 7, -41691595158248356878402119734599388937280552960000000⟩, + ⟨5, 4, 8, 7, 3, 7, -46152552832490288538457443785473784866815344640000000⟩ +] + +def collectedFourData_14_2_44 : List CollectedFourTerm := [ + ⟨5, 5, 4, 0, 6, 8, -77073059821619747610051417172601017233240489984000000⟩, + ⟨5, 5, 5, 0, 7, 8, -996342915862305396962575700708337496017076224000000⟩, + ⟨5, 5, 6, 0, 8, 8, -30689833893664929192682764242664662029767278592000000⟩, + ⟨5, 5, 4, 1, 5, 8, 119434022552348310628855058864414056538973614899200000⟩, + ⟨5, 5, 5, 1, 6, 8, 164388852328485070673098168948970397390348484608000000⟩, + ⟨5, 5, 6, 1, 7, 8, 102639899742903969792712628423948797825913978880000000⟩, + ⟨5, 5, 7, 1, 8, 8, 64318453150699268964610537616452196872866496512000000⟩, + ⟨5, 5, 4, 2, 4, 8, -31843419834970731749505644963700499802749717708800000⟩, + ⟨5, 5, 5, 2, 5, 8, -28755199219350379776056638850427228549506138112000000⟩, + ⟨5, 5, 6, 2, 6, 8, -7085193074715321793375832928568764325234212864000000⟩, + ⟨5, 5, 7, 2, 7, 8, -3797435145246953571115235862285208514293923840000000⟩, + ⟨5, 5, 8, 2, 8, 8, -15347213872728032732263142769739363935124979712000000⟩, + ⟨5, 5, 4, 3, 3, 8, 40615748392800633634325225938242143623846035456000000⟩, + ⟨5, 5, 5, 3, 4, 8, 38918961789375227591534419677688006845929619456000000⟩, + ⟨5, 5, 6, 3, 5, 8, 17260511181650332480749344524918028369525735424000000⟩, + ⟨5, 5, 7, 3, 6, 8, -2965117464933676496105586006627647274627366912000000⟩, + ⟨5, 5, 8, 3, 7, 8, -9401039624577308968475407917637556002734735360000000⟩, + ⟨5, 5, 4, 4, 2, 8, -135409128237992881073376388382743363461160579891200000⟩, + ⟨5, 5, 5, 4, 3, 8, -3630220929825499066202832665123346672041066496000000⟩, + ⟨5, 5, 6, 4, 4, 8, -7976760631094099702678864151755039211383685120000000⟩, + ⟨5, 5, 7, 4, 5, 8, -10208632640671955041041969479176814661457674240000000⟩, + ⟨5, 5, 8, 4, 6, 8, 11991385952178180316578748237959396646258212864000000⟩, + ⟨5, 5, 4, 5, 1, 8, 130551300489888192980949231618504274697800541798400000⟩, + ⟨5, 5, 5, 5, 2, 8, -281961838391306071259216504980905058850052243456000000⟩, + ⟨5, 5, 6, 5, 3, 8, -2954799748895359550478057699538668495707308032000000⟩, + ⟨5, 5, 7, 5, 4, 8, 6468819707067497553968149643299986808881807360000000⟩, + ⟨5, 5, 8, 5, 5, 8, 4008357942961867110555018265531486902448816128000000⟩, + ⟨5, 5, 4, 6, 0, 8, 407323139524104858816120185051830925208410967244800000⟩, + ⟨5, 5, 5, 6, 1, 8, 360225857435634403450274046743205340850065244160000000⟩, + ⟨5, 5, 6, 6, 2, 8, -211720185364511866232427587620347252163920003072000000⟩, + ⟨5, 5, 7, 6, 3, 8, 19396875195693335416266987546626528962576121856000000⟩, + ⟨5, 5, 8, 6, 4, 8, -5971063190209381590600292493912943030580543488000000⟩, + ⟨5, 5, 5, 7, 0, 8, 1571640333644782805038761992417084174523042889728000000⟩, + ⟨5, 5, 6, 7, 1, 8, 419725547023570188048928345378951108360201568256000000⟩, + ⟨5, 5, 7, 7, 2, 8, -34445199005878265032139596869902551998837817344000000⟩, + ⟨5, 5, 8, 7, 3, 8, -28598099825222005457321562632638340269156073472000000⟩ +] + +def collectedFourData_14_2_45 : List CollectedFourTerm := [ + ⟨6, 0, 8, 2, 8, 4, -1559560155690154810305280102935039683475442709299200000⟩, + ⟨6, 0, 8, 3, 7, 4, -955319117993692276570028903411859534276382949376000000⟩, + ⟨6, 0, 8, 4, 6, 4, 1218546108603587506350556200597416716950277875302400000⟩, + ⟨6, 0, 8, 5, 5, 4, 407323139524104858816120185051830925208410967244800000⟩, + ⟨6, 0, 8, 6, 4, 4, -606770213524326589435472296135348291979665263820800000⟩, + ⟨6, 0, 8, 7, 3, 4, -2906094707855784798176631070254496689523287864115200000⟩ +] + +def collectedFourData_14_2_46 : List CollectedFourTerm := [ + ⟨6, 1, 7, 1, 8, 5, 1445053701842312088482641953800058405474439004160000000⟩, + ⟨6, 1, 7, 2, 7, 5, -85317625740903695492103318049208237808628531200000000⟩, + ⟨6, 1, 8, 2, 8, 5, -1379233929509401863796059323899753224452324720640000000⟩, + ⟨6, 1, 7, 3, 6, 5, -66617801878108716042322856345097714274570076160000000⟩, + ⟨6, 1, 8, 3, 7, 5, -844859068910241929474138416799686647778325299200000000⟩, + ⟨6, 1, 7, 4, 5, 5, -229359097825114327088253252925351422132958003200000000⟩, + ⟨6, 1, 8, 4, 6, 5, 1077650087125989037125270320819642702749583278080000000⟩, + ⟨6, 1, 7, 5, 4, 5, 145336080181318216673232811048781148716846284800000000⟩, + ⟨6, 1, 8, 5, 5, 5, 360225857435634403450274046743205340850065244160000000⟩, + ⟨6, 1, 7, 6, 3, 5, 435792916848237971013510298990512022396946350080000000⟩, + ⟨6, 1, 8, 6, 4, 5, -536611597093586109021709314253142665693872783360000000⟩, + ⟨6, 1, 7, 7, 2, 5, -773886185003787836923123431213456889103693905920000000⟩, + ⟨6, 1, 8, 7, 3, 5, -2570073625450287691964008531259451800226197667840000000⟩ +] + +def collectedFourData_14_2_47 : List CollectedFourTerm := [ + ⟨6, 2, 6, 0, 8, 6, 270171202823083815566340620601890002239769018368000000⟩, + ⟨6, 2, 6, 1, 7, 6, -903567782975367054155497669579970265891754475520000000⟩, + ⟨6, 2, 7, 1, 8, 6, -1698640068726301073705229042466230596487446790144000000⟩, + ⟨6, 2, 6, 2, 6, 6, 62372938930267688131012130698382294997276819456000000⟩, + ⟨6, 2, 7, 2, 7, 6, 100289655303002679111010048666349108136593326080000000⟩, + ⟨6, 2, 8, 2, 8, 6, 810634931360893925833442215507490256031567577088000000⟩, + ⟨6, 2, 6, 3, 5, 6, -151949113945851836884591961986424061387337629696000000⟩, + ⟨6, 2, 7, 3, 6, 6, 78308278381874258562353554583804021456391634944000000⟩, + ⟨6, 2, 8, 3, 7, 6, 496559908136318893556263515840556676133043568640000000⟩, + ⟨6, 2, 6, 4, 4, 6, 70221657823288943978241338604166897535004180480000000⟩, + ⟨6, 2, 7, 4, 5, 6, 269608356558619155290578815342210526410052730880000000⟩, + ⟨6, 2, 8, 4, 6, 6, -633381173213432405277054362366539957016236916736000000⟩, + ⟨6, 2, 6, 5, 3, 6, 26011929716738959936847194862677144810058416128000000⟩, + ⟨6, 2, 7, 5, 4, 6, -170840494656263687969291942946937085681278648320000000⟩, + ⟨6, 2, 8, 5, 5, 6, -211720185364511866232427587620347252163920003072000000⟩, + ⟨6, 2, 6, 6, 2, 6, 1863832086548501824467290187949881247983665676288000000⟩, + ⟨6, 2, 7, 6, 3, 6, -512268374027738857153840890765716381757207478272000000⟩, + ⟨6, 2, 8, 6, 4, 6, 315389649188914904393575781063753828190715379712000000⟩, + ⟨6, 2, 6, 7, 1, 6, -3694961539636831587911849762835818774857487745024000000⟩, + ⟨6, 2, 7, 7, 2, 6, 909692200923212874444282911162620000384610992128000000⟩, + ⟨6, 2, 8, 7, 3, 6, 1510542492019759910283591651793958745417688547328000000⟩ +] + +def collectedFourData_14_2_48 : List CollectedFourTerm := [ + ⟨6, 3, 5, 0, 7, 7, -1205352632305957819923408462453040246331277312000000⟩, + ⟨6, 3, 6, 0, 8, 7, -74255703492900490513992602157333323416225185792000000⟩, + ⟨6, 3, 5, 1, 6, 7, 198873834220424885365643773676591169260123848704000000⟩, + ⟨6, 3, 6, 1, 7, 7, 248342757026892198927240608961345427174462586880000000⟩, + ⟨6, 3, 7, 1, 8, 7, 233432934314425161033307416618836670512332013568000000⟩, + ⟨6, 3, 5, 2, 5, 7, -34787375430404763884012610928432453845994438656000000⟩, + ⟨6, 3, 6, 2, 6, 7, -17143005660079999366132630281085998623845515264000000⟩, + ⟨6, 3, 7, 2, 7, 7, -13782147819176591243774286591145181246662901760000000⟩, + ⟨6, 3, 8, 2, 8, 7, -74266818564349715907173979552931143868244557824000000⟩, + ⟨6, 3, 5, 3, 4, 7, 47083260484507255509945921650819465254721814528000000⟩, + ⟨6, 3, 6, 3, 5, 7, 41762735011253692379970756559567450845241933824000000⟩, + ⟨6, 3, 7, 3, 6, 7, -10761391739392175494628431461967969086150279168000000⟩, + ⟨6, 3, 8, 3, 7, 7, -45492641850480706007688235961283311460648222720000000⟩, + ⟨6, 3, 5, 4, 3, 7, -4391757379867865062181512399706932021504770048000000⟩, + ⟨6, 3, 6, 4, 4, 7, -19300201307985358703263002991837381313817477120000000⟩, + ⟨6, 3, 7, 4, 5, 7, -37050503485626269162055899798703260959097487360000000⟩, + ⟨6, 3, 8, 4, 6, 7, 58027606328470854048808593629444744206539030528000000⟩, + ⟨6, 3, 5, 5, 2, 7, -341110915432811669007671253667488575152642326528000000⟩, + ⟨6, 3, 6, 5, 3, 7, -7149296890790990709315990742261499748503519232000000⟩, + ⟨6, 3, 7, 5, 4, 7, 23477485726121339269418910119588494161519575040000000⟩, + ⟨6, 3, 8, 5, 5, 7, 19396875195693335416266987546626528962576121856000000⟩, + ⟨6, 3, 5, 6, 1, 7, 435792916848237971013510298990512022396946350080000000⟩, + ⟨6, 3, 6, 6, 2, 7, -512268374027738857153840890765716381757207478272000000⟩, + ⟨6, 3, 7, 6, 3, 7, 70397673943627143166837916306852344762868957184000000⟩, + ⟨6, 3, 8, 6, 4, 7, -28894616981363658981103674132822588432712728576000000⟩, + ⟨6, 3, 5, 7, 0, 7, 1901334152165293468731169715346774239539063947264000000⟩, + ⟨6, 3, 6, 7, 1, 7, 1015548532330481650249911724498346151397457657856000000⟩, + ⟨6, 3, 7, 7, 2, 7, -125013016997580983873067638028776757552130031616000000⟩, + ⟨6, 3, 8, 7, 3, 7, -138389280856968569290601830336866156599096377344000000⟩ +] + +def collectedFourData_14_2_49 : List CollectedFourTerm := [ + ⟨6, 4, 4, 0, 6, 8, 114812129307399391407887730604032776067103064064000000⟩, + ⟨6, 4, 5, 0, 7, 8, 1484205401410652354340849248950921139117359104000000⟩, + ⟨6, 4, 6, 0, 8, 8, 45717208912908267285826041854801646980412997632000000⟩, + ⟨6, 4, 4, 1, 5, 8, -177915272505329885077447443810727136606723191603200000⟩, + ⟨6, 4, 5, 1, 6, 8, -244882378017885780912196359755469725005479149568000000⟩, + ⟨6, 4, 6, 1, 7, 8, -152897853914905647976227694989029926081375764480000000⟩, + ⟨6, 4, 7, 1, 8, 8, -95812188812550023131407225934428598863189245952000000⟩, + ⟨6, 4, 4, 2, 4, 8, 47435651888533422685213673467992703130984565964800000⟩, + ⟨6, 4, 5, 2, 5, 8, 42835274201816469492727500352422639117168279552000000⟩, + ⟨6, 4, 6, 2, 6, 8, 10554480454581887504214112698368778764543852544000000⟩, + ⟨6, 4, 7, 2, 7, 8, 5656861372075126926444108861459851909938544640000000⟩, + ⟨6, 4, 8, 2, 8, 8, 22862026079438115762522795853131741066430513152000000⟩, + ⟨6, 4, 4, 3, 3, 8, -60503379094895588562604230408319186202762674176000000⟩, + ⟨6, 4, 5, 3, 4, 8, -57975755520972107896758620057100080989052338176000000⟩, + ⟨6, 4, 6, 3, 5, 8, -25712175516140080546493951503302782422093922304000000⟩, + ⟨6, 4, 7, 3, 6, 8, 4416996685787466205506674062369967094840164352000000⟩, + ⟨6, 4, 8, 3, 7, 8, 14004288651560531931196425659053249518958018560000000⟩, + ⟨6, 4, 4, 4, 2, 8, 201712639625885056867054522298421337067927843635200000⟩, + ⟨6, 4, 5, 4, 3, 8, 5407770182917250993776704032448491765435990016000000⟩, + ⟨6, 4, 6, 4, 4, 8, 11882606907666193204831806339960846622937579520000000⟩, + ⟨6, 4, 7, 4, 5, 8, 15207322162961384630477605115548035055657943040000000⟩, + ⟨6, 4, 8, 4, 6, 8, -17863006317678594683015320919766567944447852544000000⟩, + ⟨6, 4, 4, 5, 1, 8, -194476161031946875015894147601807011354065135206400000⟩, + ⟨6, 4, 5, 5, 2, 8, 420025351582756813848341925143672695588625842176000000⟩, + ⟨6, 4, 6, 5, 3, 8, 4401626867193395257043360189179298334608719872000000⟩, + ⟨6, 4, 7, 5, 4, 8, -9636297902185435920798332305292843473761730560000000⟩, + ⟨6, 4, 8, 5, 5, 8, -5971063190209381590600292493912943030580543488000000⟩, + ⟨6, 4, 4, 6, 0, 8, -606770213524326589435472296135348291979665263820800000⟩, + ⟨6, 4, 5, 6, 1, 8, -536611597093586109021709314253142665693872783360000000⟩, + ⟨6, 4, 6, 6, 2, 8, 315389649188914904393575781063753828190715379712000000⟩, + ⟨6, 4, 7, 6, 3, 8, -28894616981363658981103674132822588432712728576000000⟩, + ⟨6, 4, 8, 6, 4, 8, 8894813319772580611969212166310234352462594048000000⟩, + ⟨6, 4, 5, 7, 0, 8, -2341199034121297380242187298817852001977093849088000000⟩, + ⟨6, 4, 6, 7, 1, 8, -625245499400445942758040895188943758084041342976000000⟩, + ⟨6, 4, 7, 7, 2, 8, 51311400526136381646592297595382516640722714624000000⟩, + ⟨6, 4, 8, 7, 3, 8, 42601250588448501434805643719610330395665498112000000⟩ +] + +def collectedFourData_14_2_50 : List CollectedFourTerm := [ + ⟨7, 0, 7, 1, 8, 5, 6304668682769069747729377777946130466818100297728000000⟩, + ⟨7, 0, 7, 2, 7, 5, -372234860483811083995411237554436334578261032960000000⟩, + ⟨7, 0, 8, 2, 8, 5, -6017501599078520547028150002293162823074407514112000000⟩, + ⟨7, 0, 7, 3, 6, 5, -290648831029850783121972375187559332443825635328000000⟩, + ⟨7, 0, 8, 3, 7, 5, -3686061290539557414609280936688664737958183567360000000⟩, + ⟨7, 0, 7, 4, 5, 5, -1000677773651321743609172356348110601494001090560000000⟩, + ⟨7, 0, 8, 4, 6, 5, 4701712293892303902394983533852078072440673009664000000⟩, + ⟨7, 0, 7, 5, 4, 5, 634091198152274579900017844144435919723524259840000000⟩, + ⟨7, 0, 8, 5, 5, 5, 1571640333644782805038761992417084174523042889728000000⟩, + ⟨7, 0, 7, 6, 3, 5, 1901334152165293468731169715346774239539063947264000000⟩, + ⟨7, 0, 8, 6, 4, 5, -2341199034121297380242187298817852001977093849088000000⟩, + ⟨7, 0, 7, 7, 2, 5, -3376411539862226493253075401025662558432223297536000000⟩, + ⟨7, 0, 8, 7, 3, 5, -11213052274894179420018226755365298532848733519872000000⟩ +] + +def collectedFourData_14_2_51 : List CollectedFourTerm := [ + ⟨7, 1, 6, 0, 8, 6, -535602005541897189318376564969270585503843876864000000⟩, + ⟨7, 1, 6, 1, 7, 6, 1791281645296441959069599842782243113267059752960000000⟩, + ⟨7, 1, 7, 1, 8, 6, 3367475948572483227274564552712006347079666368512000000⟩, + ⟨7, 1, 6, 2, 6, 6, -123651487773364205147846525327707603743736332288000000⟩, + ⟨7, 1, 7, 2, 7, 6, -198819637156400459803369760520151773516492963840000000⟩, + ⟨7, 1, 8, 2, 8, 6, -1607046533688216567936494689748891565967408103424000000⟩, + ⟨7, 1, 6, 3, 5, 6, 301232142135464171769555063071184797466579959808000000⟩, + ⟨7, 1, 7, 3, 6, 6, -155242566615546983542485073051825510462009638912000000⟩, + ⟨7, 1, 8, 3, 7, 6, -984407219905188046743645471214712031403541790720000000⟩, + ⟨7, 1, 6, 4, 4, 6, -139211212629715868206827318649312594013234135040000000⟩, + ⟨7, 1, 7, 4, 5, 6, -534486188663899117967094468295450258053519114240000000⟩, + ⟨7, 1, 8, 4, 6, 6, 1255649096205633780363228986355916422592465993728000000⟩, + ⟨7, 1, 6, 5, 3, 6, -51567456408088682326021755800720826599781433344000000⟩, + ⟨7, 1, 7, 5, 4, 6, 338683437055958855747684001016061221515149967360000000⟩, + ⟨7, 1, 8, 5, 5, 6, 419725547023570188048928345378951108360201568256000000⟩, + ⟨7, 1, 6, 6, 2, 6, -3694961539636831587911849762835818774857487745024000000⟩, + ⟨7, 1, 7, 6, 3, 6, 1015548532330481650249911724498346151397457657856000000⟩, + ⟨7, 1, 8, 6, 4, 6, -625245499400445942758040895188943758084041342976000000⟩, + ⟨7, 1, 6, 7, 1, 6, 7325091609876684383524084062177112994387173834752000000⟩, + ⟨7, 1, 7, 7, 2, 6, -1803423022694798577457156295860330989728871481344000000⟩, + ⟨7, 1, 8, 7, 3, 6, -2994581138656100618414303662355304980378963410944000000⟩ +] + +def collectedFourData_14_2_52 : List CollectedFourTerm := [ + ⟨7, 2, 5, 0, 7, 7, 2140479374804466182183348438265531823804121088000000⟩, + ⟨7, 2, 6, 0, 8, 7, 131864151226912150168615157241804010380337348608000000⟩, + ⟨7, 2, 5, 1, 6, 7, -353162492807373970553443604230754221404608004096000000⟩, + ⟨7, 2, 6, 1, 7, 7, -441009987493194614275921612178506218445335429120000000⟩, + ⟨7, 2, 7, 1, 8, 7, -414532949037674803823066317513440348895583404032000000⟩, + ⟨7, 2, 5, 2, 5, 7, 61775830256336336864246760221039980441233260544000000⟩, + ⟨7, 2, 6, 2, 6, 7, 30442750987615767219737526116542088120459329536000000⟩, + ⟨7, 2, 7, 2, 7, 7, 24474500122853411048928624358920368865662730240000000⟩, + ⟨7, 2, 8, 2, 8, 7, 131883889501462585515426372527824565027236478976000000⟩, + ⟨7, 2, 5, 3, 4, 7, -83611007488182492479444526468549999468396675072000000⟩, + ⟨7, 2, 6, 3, 5, 7, -74162755803666108664128010303477972345842302976000000⟩, + ⟨7, 2, 7, 3, 6, 7, 19110205963787362199779020272255654642615058432000000⟩, + ⟨7, 2, 8, 3, 7, 7, 80786368218261968338005855777785743152544481280000000⟩, + ⟨7, 2, 5, 4, 3, 7, 7798934385507131278373590973360093397151383552000000⟩, + ⟨7, 2, 6, 4, 4, 7, 34273524379569769139282002764895953418589306880000000⟩, + ⟨7, 2, 7, 4, 5, 7, 65794719662563944781410361679440890326302064640000000⟩, + ⟨7, 2, 8, 4, 6, 7, -103046105501711151683154370221880289595670659072000000⟩, + ⟨7, 2, 5, 5, 2, 7, 605748773790598303456881684803093825764114563072000000⟩, + ⟨7, 2, 6, 5, 3, 7, 12695805467165091626431938429395365168486023168000000⟩, + ⟨7, 2, 7, 5, 4, 7, -41691595158248356878402119734599388937280552960000000⟩, + ⟨7, 2, 8, 5, 5, 7, -34445199005878265032139596869902551998837817344000000⟩, + ⟨7, 2, 5, 6, 1, 7, -773886185003787836923123431213456889103693905920000000⟩, + ⟨7, 2, 6, 6, 2, 7, 909692200923212874444282911162620000384610992128000000⟩, + ⟨7, 2, 7, 6, 3, 7, -125013016997580983873067638028776757552130031616000000⟩, + ⟨7, 2, 8, 6, 4, 7, 51311400526136381646592297595382516640722714624000000⟩, + ⟨7, 2, 5, 7, 0, 7, -3376411539862226493253075401025662558432223297536000000⟩, + ⟨7, 2, 6, 7, 1, 7, -1803423022694798577457156295860330989728871481344000000⟩, + ⟨7, 2, 7, 7, 2, 7, 221999585261186652680557985268276922004835139584000000⟩, + ⟨7, 2, 8, 7, 3, 7, 245753311876597466639295010503733091068287123456000000⟩ +] + +def collectedFourData_14_2_53 : List CollectedFourTerm := [ + ⟨7, 3, 4, 0, 6, 8, 549886784059334106026024028679399158633323298816000000⟩, + ⟨7, 3, 5, 0, 7, 8, 7108525379579367539051501526472675024045080576000000⟩, + ⟨7, 3, 6, 0, 8, 8, 218960219072147114529614600871835530042758135808000000⟩, + ⟨7, 3, 4, 1, 5, 8, -852116040554007710558232189028245842424947854540800000⟩, + ⟨7, 3, 5, 1, 6, 8, -1172851545680539833664751506948737535086000340992000000⟩, + ⟨7, 3, 6, 1, 7, 8, -732296401835156855684727204915517462605327237120000000⟩, + ⟨7, 3, 7, 1, 8, 8, -458887546966027334676714380170756492961815461888000000⟩, + ⟨7, 3, 4, 2, 4, 8, 227190613257467475640333334792427746769671238451200000⟩, + ⟨7, 3, 5, 2, 5, 8, 205157341103494181095273350733748471878844940288000000⟩, + ⟨7, 3, 6, 2, 6, 8, 50550140909311509201075075135192017761191591936000000⟩, + ⟨7, 3, 7, 2, 7, 8, 27093246388902136926551654547644768942460764160000000⟩, + ⟨7, 3, 8, 2, 8, 8, 109496497223248035713357084076960030412335218688000000⟩, + ⟨7, 3, 4, 3, 3, 8, -289777820130287405166680404227704624019085983744000000⟩, + ⟨7, 3, 5, 3, 4, 8, -277671897117083896294655447251273622796311199744000000⟩, + ⟨7, 3, 6, 3, 5, 8, -123147141256165205835356897389380144109637861376000000⟩, + ⟨7, 3, 7, 3, 6, 8, 21154978288447028081938655620866039781143871488000000⟩, + ⟨7, 3, 8, 3, 7, 8, 67072819710773810958098369643220600963612016640000000⟩, + ⟨7, 3, 4, 4, 2, 8, 966092305552675096286192250304687416596746783948800000⟩, + ⟨7, 3, 5, 4, 3, 8, 25900236958889657189472532026971624879060680704000000⟩, + ⟨7, 3, 6, 4, 4, 8, 56911134199099676724196795658128478702539898880000000⟩, + ⟨7, 3, 7, 4, 5, 8, 72834686794770038469829155437415822054402293760000000⟩, + ⟨7, 3, 8, 4, 6, 8, -85553949368542920393438035666173878956967591936000000⟩, + ⟨7, 3, 4, 5, 1, 8, -931433563780881956090375668286883161421760797081600000⟩, + ⟨7, 3, 5, 5, 2, 8, 2011689803146504336461627778181193041466825375744000000⟩, + ⟨7, 3, 6, 5, 3, 8, 21081365333358977653306852315430374928566714368000000⟩, + ⟨7, 3, 7, 5, 4, 8, -46152552832490288538457443785473784866815344640000000⟩, + ⟨7, 3, 8, 5, 5, 8, -28598099825222005457321562632638340269156073472000000⟩, + ⟨7, 3, 4, 6, 0, 8, -2906094707855784798176631070254496689523287864115200000⟩, + ⟨7, 3, 5, 6, 1, 8, -2570073625450287691964008531259451800226197667840000000⟩, + ⟨7, 3, 6, 6, 2, 8, 1510542492019759910283591651793958745417688547328000000⟩, + ⟨7, 3, 7, 6, 3, 8, -138389280856968569290601830336866156599096377344000000⟩, + ⟨7, 3, 8, 6, 4, 8, 42601250588448501434805643719610330395665498112000000⟩, + ⟨7, 3, 5, 7, 0, 8, -11213052274894179420018226755365298532848733519872000000⟩, + ⟨7, 3, 6, 7, 1, 8, -2994581138656100618414303662355304980378963410944000000⟩, + ⟨7, 3, 7, 7, 2, 8, 245753311876597466639295010503733091068287123456000000⟩, + ⟨7, 3, 8, 7, 3, 8, 204036497052215329131407465651199089206181756928000000⟩ +] + +def collectedFourData_14_2 : List (List CollectedFourTerm) := [ + collectedFourData_14_2_0, + collectedFourData_14_2_1, + collectedFourData_14_2_2, + collectedFourData_14_2_3, + collectedFourData_14_2_4, + collectedFourData_14_2_5, + collectedFourData_14_2_6, + collectedFourData_14_2_7, + collectedFourData_14_2_8, + collectedFourData_14_2_9, + collectedFourData_14_2_10, + collectedFourData_14_2_11, + collectedFourData_14_2_12, + collectedFourData_14_2_13, + collectedFourData_14_2_14, + collectedFourData_14_2_15, + collectedFourData_14_2_16, + collectedFourData_14_2_17, + collectedFourData_14_2_18, + collectedFourData_14_2_19, + collectedFourData_14_2_20, + collectedFourData_14_2_21, + collectedFourData_14_2_22, + collectedFourData_14_2_23, + collectedFourData_14_2_24, + collectedFourData_14_2_25, + collectedFourData_14_2_26, + collectedFourData_14_2_27, + collectedFourData_14_2_28, + collectedFourData_14_2_29, + collectedFourData_14_2_30, + collectedFourData_14_2_31, + collectedFourData_14_2_32, + collectedFourData_14_2_33, + collectedFourData_14_2_34, + collectedFourData_14_2_35, + collectedFourData_14_2_36, + collectedFourData_14_2_37, + collectedFourData_14_2_38, + collectedFourData_14_2_39, + collectedFourData_14_2_40, + collectedFourData_14_2_41, + collectedFourData_14_2_42, + collectedFourData_14_2_43, + collectedFourData_14_2_44, + collectedFourData_14_2_45, + collectedFourData_14_2_46, + collectedFourData_14_2_47, + collectedFourData_14_2_48, + collectedFourData_14_2_49, + collectedFourData_14_2_50, + collectedFourData_14_2_51, + collectedFourData_14_2_52, + collectedFourData_14_2_53 +] + +theorem collectedFourChecked_14_2 : collectNumericRowParts 14 2 = collectedFourData_14_2 := by + decide +kernel + +def collectedFourData_14_3_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_1 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_2 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_3 : List CollectedFourTerm := [ + ⟨0, 6, 8, 3, 8, 3, -9287142980654152316732471649115934667728486400000000⟩, + ⟨0, 6, 8, 4, 7, 3, -3299038941815298424514637465735275091382291660800000⟩, + ⟨0, 6, 8, 5, 6, 3, -6869464932044991107926821321168249005551072051200000⟩, + ⟨0, 6, 8, 6, 5, 3, 7209196984808717875653115731017949589683988070400000⟩, + ⟨0, 6, 8, 7, 4, 3, -14254181045478615005554086537392029231875096576000000⟩ +] + +def collectedFourData_14_3_4 : List CollectedFourTerm := [ + ⟨0, 7, 7, 2, 8, 4, -52728944348496664644238567709418230851807110758400000⟩, + ⟨0, 7, 7, 3, 7, 4, 29442741323062795860266399266270342912285448601600000⟩, + ⟨0, 7, 8, 3, 8, 4, 133232735410339977791547999445650431780742758400000000⟩, + ⟨0, 7, 7, 4, 6, 4, -9669742354965780447049205707972479567022522368000000⟩, + ⟨0, 7, 8, 4, 7, 4, 47327793203882175451019374027617147155680906444800000⟩, + ⟨0, 7, 7, 5, 5, 4, -25609750848083316558127294557585076782966924902400000⟩, + ⟨0, 7, 8, 5, 6, 4, 98548886951376882248051745859358150533879903027200000⟩, + ⟨0, 7, 7, 6, 4, 4, 9167921513629164671702698440365495315285724364800000⟩, + ⟨0, 7, 8, 6, 5, 4, -103422660381006268535674870590463049109950850662400000⟩, + ⟨0, 7, 7, 7, 3, 4, 384131911186089432003158971266572259233939796787200000⟩, + ⟨0, 7, 8, 7, 4, 4, 204489533075926466788524857818498263385223725056000000⟩ +] + +def collectedFourData_14_3_5 : List CollectedFourTerm := [ + ⟨0, 8, 6, 1, 8, 5, -792069111181515132254408817856248381802807296000000⟩, + ⟨0, 8, 6, 2, 7, 5, -1059879066245610204037547069555750942061625344000000⟩, + ⟨0, 8, 7, 2, 8, 5, -4970628017551744349150245870527861730433826816000000⟩, + ⟨0, 8, 6, 3, 6, 5, 2808369629099588834507665515549123406951612416000000⟩, + ⟨0, 8, 7, 3, 7, 5, 2775494877475523499285223441253045954710339584000000⟩, + ⟨0, 8, 8, 3, 8, 5, 6279761293045642666516483234170226404753408000000000⟩, + ⟨0, 8, 6, 4, 5, 5, -2234342405276310537596374205076172313286672384000000⟩, + ⟨0, 8, 7, 4, 6, 5, -911542851198196757848852299980707327188664320000000⟩, + ⟨0, 8, 8, 4, 7, 5, 2230737385460466455210789628832169031867826176000000⟩, + ⟨0, 8, 6, 5, 4, 5, -2520072579618976068335287015251347367260061696000000⟩, + ⟨0, 8, 7, 5, 5, 5, -2414168283868398436533093447104891390709989376000000⟩, + ⟨0, 8, 8, 5, 6, 5, 4644980708712210038500593155124157400915902464000000⟩, + ⟨0, 8, 6, 6, 3, 5, 9331297752846642913170745885260851525720211456000000⟩, + ⟨0, 8, 7, 6, 4, 5, 864237433565456177082016106519842641414193152000000⟩, + ⟨0, 8, 8, 6, 5, 5, -4874700031371148996719289733402802788801445888000000⟩, + ⟨0, 8, 6, 7, 2, 5, -9208848038776453739338027918392033223360118784000000⟩, + ⟨0, 8, 7, 7, 3, 5, 36211171374071174191976875061519042729453027328000000⟩, + ⟨0, 8, 8, 7, 4, 5, 9638362904493209447666901546857450699457822720000000⟩ +] + +def collectedFourData_14_3_6 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_7 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_8 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_9 : List CollectedFourTerm := [ + ⟨1, 5, 8, 3, 8, 3, 124507412362253379750072208058209615240966963200000000⟩, + ⟨1, 5, 8, 4, 7, 3, 44228327568915853226077885545718535663114413670400000⟩, + ⟨1, 5, 8, 5, 6, 3, 92094986023561839321668521643076171044503525785600000⟩, + ⟨1, 5, 8, 6, 5, 3, -96649579279446950494760915014379924707465179955200000⟩, + ⟨1, 5, 8, 7, 4, 3, 191097649838337575009109183397014840597270233088000000⟩ +] + +def collectedFourData_14_3_10 : List CollectedFourTerm := [ + ⟨1, 6, 7, 2, 8, 4, -118141010229345550950198584786450365180410435993600000⟩, + ⟨1, 6, 7, 3, 7, 4, 65967472833108367753961124098112986360123385446400000⟩, + ⟨1, 6, 8, 3, 8, 4, 298512518152573804554720716702719283165763993600000000⟩, + ⟨1, 6, 7, 4, 6, 4, -21665389751079258081294987203906603283929628672000000⟩, + ⟨1, 6, 8, 4, 7, 4, 106039545644566046284945404937558503167632814899200000⟩, + ⟨1, 6, 7, 5, 5, 4, -57379526070497989602108930827180655448528886169600000⟩, + ⟨1, 6, 8, 5, 6, 4, 220802164831224697822870687005322499609936579788800000⟩, + ⟨1, 6, 7, 6, 4, 4, 20541042926348294444057596504379156477183734579200000⟩, + ⟨1, 6, 8, 6, 5, 4, -231722021538383942910098724238915232880016333209600000⟩, + ⟨1, 6, 7, 7, 3, 4, 860660735950191841255314897231818956233107098828800000⟩, + ⟨1, 6, 8, 7, 4, 4, 458165819881541037807716704915608995926716186624000000⟩ +] + +def collectedFourData_14_3_11 : List CollectedFourTerm := [ + ⟨1, 7, 6, 1, 8, 5, 6282325068763458742599310206312130061254262784000000⟩, + ⟨1, 7, 6, 2, 7, 5, 8406469503399813990855918740055826065078091776000000⟩, + ⟨1, 7, 7, 2, 8, 5, 39424717567362823349224526610067359650612772864000000⟩, + ⟨1, 7, 6, 3, 6, 5, -22274686228993837044764643804694643093236875264000000⟩, + ⟨1, 7, 7, 3, 7, 5, -22013938936438568714419671934272861132854132736000000⟩, + ⟨1, 7, 8, 3, 8, 5, -49808155930108148910805731570204585001746432000000000⟩, + ⟨1, 7, 6, 4, 5, 5, 17721768349140735870062923907801005993739943936000000⟩, + ⟨1, 7, 7, 4, 6, 5, 7229935398935419420872658357147685558188769280000000⟩, + ⟨1, 7, 8, 4, 7, 5, -17693175002874924752960756880209662380085346304000000⟩, + ⟨1, 7, 6, 5, 4, 5, 19988047657138794257937908164687052592994320384000000⟩, + ⟨1, 7, 7, 5, 5, 5, 19148063869497915627694993913681932401827119104000000⟩, + ⟨1, 7, 8, 5, 6, 5, -36841834049981055092233870629144451924157792256000000⟩, + ⟨1, 7, 6, 6, 3, 5, -74011528753291304087050225980080481658076135424000000⟩, + ⟨1, 7, 7, 6, 4, 5, -6854730752160113242224678488334615846278135808000000⟩, + ⟨1, 7, 8, 6, 5, 5, 38663861243248144066961072124462497966013284352000000⟩, + ⟨1, 7, 6, 7, 2, 5, 73040314376279981703950032135771921368571969536000000⟩, + ⟨1, 7, 7, 7, 3, 5, -287210227593995993818277356892844141317940314112000000⟩, + ⟨1, 7, 8, 7, 4, 5, -76447027212580165517506908773649610856862842880000000⟩ +] + +def collectedFourData_14_3_12 : List CollectedFourTerm := [ + ⟨1, 8, 5, 0, 8, 6, -792069111181515132254408817856248381802807296000000⟩, + ⟨1, 8, 5, 1, 7, 6, 6282325068763458742599310206312130061254262784000000⟩, + ⟨1, 8, 6, 1, 8, 6, 3436359138522745300912541557057012768721338368000000⟩, + ⟨1, 8, 5, 2, 6, 6, 4391018567593587650841883629542503508682473472000000⟩, + ⟨1, 8, 6, 2, 7, 6, 4598241572113782822855189501362564942373322752000000⟩, + ⟨1, 8, 7, 2, 8, 6, 10782432221622630792969809797796977608977547264000000⟩, + ⟨1, 8, 5, 3, 5, 6, -1659189222947971755000469274082857783289446400000000⟩, + ⟨1, 8, 6, 3, 6, 6, -12183995693141637031610921806493102051665379328000000⟩, + ⟨1, 8, 7, 3, 7, 6, -6020684970222498422707420665375787830095118336000000⟩, + ⟨1, 8, 8, 3, 8, 6, -9081495037265554729557614667670444560089088000000000⟩, + ⟨1, 8, 5, 4, 4, 6, 5977408073793657896757864767100552935915913216000000⟩, + ⟨1, 8, 6, 4, 5, 6, 9693602281127972965104337806825013962784899072000000⟩, + ⟨1, 8, 7, 4, 6, 6, 1977345513573604156861385868731483455519457280000000⟩, + ⟨1, 8, 8, 4, 7, 6, -3225987350496368982123773906772070940735963136000000⟩, + ⟨1, 8, 5, 5, 3, 6, -15589423887724946682014179839016953105101094912000000⟩, + ⟨1, 8, 6, 5, 4, 6, 10933230846228152213046668579079349682011373568000000⟩, + ⟨1, 8, 7, 5, 5, 6, 5236884715670850368054269223108846446920597504000000⟩, + ⟨1, 8, 8, 5, 6, 6, -6717352346032490641176262724797546473040379904000000⟩, + ⟨1, 8, 5, 6, 2, 6, -230722298137135337499488203055862311339163648000000⟩, + ⟨1, 8, 6, 6, 3, 6, -40483450060865913690580395996406872318985371648000000⟩, + ⟨1, 8, 7, 6, 4, 6, -1874729212868847672115068758087333303034052608000000⟩, + ⟨1, 8, 8, 6, 5, 6, 7049561611853065825994575539186361588009402368000000⟩, + ⟨1, 8, 5, 7, 1, 6, 10755479660615332183783128169950592179074236416000000⟩, + ⟨1, 8, 6, 7, 2, 6, 39952207031672514044405159804244012918764470272000000⟩, + ⟨1, 8, 7, 7, 3, 6, -78550336019470506855126600362746720423942029312000000⟩, + ⟨1, 8, 8, 7, 4, 6, -13938546514730286424499128353273749731981393920000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1405.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1405.lean new file mode 100644 index 0000000000000000000000000000000000000000..4f6205df339da6a4fa2f13a8625a7f80a9b80118 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1405.lean @@ -0,0 +1,613 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1405. -/ +namespace LaughlinFock +def collectedFourData_14_3_13 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_14 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_15 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_16 : List CollectedFourTerm := [ + ⟨2, 4, 8, 3, 8, 3, -162135408124485712596195683817148361210226278400000000⟩, + ⟨2, 4, 8, 4, 7, 3, -57594787370455571543792158911721264371177671884800000⟩, + ⟨2, 4, 8, 5, 6, 3, -119927463448560616087937104739865571516950459187200000⟩, + ⟨2, 4, 8, 6, 5, 3, 125858522671247024824016135978035040644028065382400000⟩, + ⟨2, 4, 8, 7, 4, 3, -248850207873745661243395349359503648716652281856000000⟩ +] + +def collectedFourData_14_3_17 : List CollectedFourTerm := [ + ⟨2, 5, 7, 2, 8, 4, 14991475053591713945863877688149091469774081228800000⟩, + ⟨2, 5, 7, 3, 7, 4, -8370926585156148839776324534232434580129002291200000⟩, + ⟨2, 5, 8, 3, 8, 4, -37879674131629813603223728241511128911105228800000000⟩, + ⟨2, 5, 7, 4, 6, 4, 2749224417068415971655210753763456650603134976000000⟩, + ⟨2, 5, 8, 4, 7, 4, -13455862618227739378349133618270894939159763353600000⟩, + ⟨2, 5, 7, 5, 5, 4, 7281161148045747036815672565864900881942367436800000⟩, + ⟨2, 5, 8, 5, 6, 4, -28018637553719922205039382604288286981483816550400000⟩, + ⟨2, 5, 7, 6, 4, 4, -2606550697402249975126786446863351980672784793600000⟩, + ⟨2, 5, 8, 6, 5, 4, 29404310141895494240120503538655962229581335756800000⟩, + ⟨2, 5, 7, 7, 3, 4, -109213336906088692444950476931931757385812960870400000⟩, + ⟨2, 5, 8, 7, 4, 4, -58138841422031455216864567585059497209277448192000000⟩ +] + +def collectedFourData_14_3_18 : List CollectedFourTerm := [ + ⟨2, 6, 6, 1, 8, 5, 4391018567593587650841883629542503508682473472000000⟩, + ⟨2, 6, 6, 2, 7, 5, 5875685080492556613297706710405314120156971008000000⟩, + ⟨2, 6, 7, 2, 8, 5, 27555827653868470358177896527092280760951898112000000⟩, + ⟨2, 6, 6, 3, 6, 5, -15568847480553032430702455904401255339825037312000000⟩, + ⟨2, 6, 7, 3, 7, 5, -15386598680860580565107638001141004241037426688000000⟩, + ⟨2, 6, 8, 3, 8, 5, -34813311172665829281641679321776284086829056000000000⟩, + ⟨2, 6, 6, 4, 5, 5, 12386594615834781664011640993575879790232076288000000⟩, + ⟨2, 6, 7, 4, 6, 5, 5053348916482644458805240571903471150946058240000000⟩, + ⟨2, 6, 8, 4, 7, 5, -12366609353533236673897639607411634112542277632000000⟩, + ⟨2, 6, 6, 5, 4, 5, 13970606014775543072061243154627832506610614272000000⟩, + ⟨2, 6, 7, 5, 5, 5, 13383501022971184444430857852098822721379500032000000⟩, + ⟨2, 6, 8, 5, 6, 5, -25750526374705736915455706508920484074354638848000000⟩, + ⟨2, 6, 6, 6, 3, 5, -51730210298661821296374375159336671882973806592000000⟩, + ⟨2, 6, 7, 6, 4, 5, -4791100377509470297578528713288638112269860864000000⟩, + ⟨2, 6, 8, 6, 5, 5, 27024028644761137919690356203448099270784188416000000⟩, + ⟨2, 6, 6, 7, 2, 5, 51051381948346934665430386390972268105158361088000000⟩, + ⟨2, 6, 7, 7, 3, 5, -200745015319025203599415794484872574341004394496000000⟩, + ⟨2, 6, 8, 7, 4, 5, -53432497085644003644753763235997422462215127040000000⟩ +] + +def collectedFourData_14_3_19 : List CollectedFourTerm := [ + ⟨2, 7, 5, 0, 8, 6, -1059879066245610204037547069555750942061625344000000⟩, + ⟨2, 7, 5, 1, 7, 6, 8406469503399813990855918740055826065078091776000000⟩, + ⟨2, 7, 6, 1, 8, 6, 4598241572113782822855189501362564942373322752000000⟩, + ⟨2, 7, 5, 2, 6, 6, 5875685080492556613297706710405314120156971008000000⟩, + ⟨2, 7, 6, 2, 7, 6, 6152973162346745140821684695001516609978236928000000⟩, + ⟨2, 7, 7, 2, 8, 6, 14428127588340016481097714503971872059997290496000000⟩, + ⟨2, 7, 5, 3, 5, 6, -2220184955476541374742305233746067780639129600000000⟩, + ⟨2, 7, 6, 3, 6, 6, -16303579821620070831695683188360409180318728192000000⟩, + ⟨2, 7, 7, 3, 7, 6, -8056365125613450318178387722941298818263547904000000⟩, + ⟨2, 7, 8, 3, 8, 6, -12152079085439014105733348379897178286456832000000000⟩, + ⟨2, 7, 5, 4, 4, 6, 7998455688255658896505859617440183512123572224000000⟩, + ⟨2, 7, 6, 4, 5, 6, 12971148589486875338006219419750103594626449408000000⟩, + ⟨2, 7, 7, 4, 6, 6, 2645914462495766505753476206759029468215377920000000⟩, + ⟨2, 7, 8, 4, 7, 6, -4316740057775953293105465792596902588767535104000000⟩, + ⟨2, 7, 5, 5, 3, 6, -20860432252915418660800225105045731780662919168000000⟩, + ⟨2, 7, 6, 5, 4, 6, 14629913396146117336002800178207125926997655552000000⟩, + ⟨2, 7, 7, 5, 5, 6, 7007550735316014963946470720776568713150201856000000⟩, + ⟨2, 7, 8, 5, 6, 6, -8988585758047710225721260742459918175705235456000000⟩, + ⟨2, 7, 5, 6, 2, 6, -308732824521910453179702576239976896551452672000000⟩, + ⟨2, 7, 6, 6, 3, 6, -54171486607913449647386566970048430318311964672000000⟩, + ⟨2, 7, 7, 6, 4, 6, -2508602115079138379647254692649375702410330112000000⟩, + ⟨2, 7, 8, 6, 5, 6, 9433119753232584048053416861455167699395018752000000⟩, + ⟨2, 7, 5, 7, 1, 6, 14392061978925288226111558455107996568753537024000000⟩, + ⟨2, 7, 6, 7, 2, 6, 53460622672200701851770451490129861203835486208000000⟩, + ⟨2, 7, 7, 7, 3, 6, -105109334044610140095259904292832072638312480768000000⟩, + ⟨2, 7, 8, 7, 4, 6, -18651369503371322188639255050103886114067578880000000⟩ +] + +def collectedFourData_14_3_20 : List CollectedFourTerm := [ + ⟨2, 8, 4, 0, 7, 7, -52728944348496664644238567709418230851807110758400000⟩, + ⟨2, 8, 5, 0, 8, 7, -4970628017551744349150245870527861730433826816000000⟩, + ⟨2, 8, 4, 1, 6, 7, -118141010229345550950198584786450365180410435993600000⟩, + ⟨2, 8, 5, 1, 7, 7, 39424717567362823349224526610067359650612772864000000⟩, + ⟨2, 8, 6, 1, 8, 7, 10782432221622630792969809797796977608977547264000000⟩, + ⟨2, 8, 4, 2, 5, 7, 14991475053591713945863877688149091469774081228800000⟩, + ⟨2, 8, 5, 2, 6, 7, 27555827653868470358177896527092280760951898112000000⟩, + ⟨2, 8, 6, 2, 7, 7, 14428127588340016481097714503971872059997290496000000⟩, + ⟨2, 8, 7, 2, 8, 7, 22555043468451371357929737490128630070690971648000000⟩, + ⟨2, 8, 4, 3, 4, 7, -10285649335751694123155029805878300341214956748800000⟩, + ⟨2, 8, 5, 3, 5, 7, -10412238429173028540342539745330299283072614400000000⟩, + ⟨2, 8, 6, 3, 6, 7, -38230319490505193779382899793438820868338745344000000⟩, + ⟨2, 8, 7, 3, 7, 7, -12594265229036094022480287952722540834746007552000000⟩, + ⟨2, 8, 8, 3, 8, 7, -14247725683354093620714047333484181598502912000000000⟩, + ⟨2, 8, 4, 4, 3, 7, -22989924025065808783808340140109466497340932096000000⟩, + ⟨2, 8, 5, 4, 4, 7, 37511211615888790805702146019678214141442523136000000⟩, + ⟨2, 8, 6, 4, 5, 7, 30416090218253847413973780133471357116251897856000000⟩, + ⟨2, 8, 7, 4, 6, 7, 4136275850764243834154570830047138005605416960000000⟩, + ⟨2, 8, 8, 4, 7, 7, -5061169184064436908445218181013633868301860864000000⟩, + ⟨2, 8, 4, 5, 2, 7, 157519177203050613709139216756347969416585648537600000⟩, + ⟨2, 8, 5, 5, 3, 7, -97831396351546626663776684535054044007185252352000000⟩, + ⟨2, 8, 6, 5, 4, 7, 34305733426188741389887114300196706968471076864000000⟩, + ⟨2, 8, 7, 5, 5, 7, 10954686287232623967325426474910703800788451328000000⟩, + ⟨2, 8, 8, 5, 6, 7, -10538682579462537746501672329483669191153156096000000⟩, + ⟨2, 8, 4, 6, 1, 7, -84525752849995879025948309130216183962223928934400000⟩, + ⟨2, 8, 5, 6, 2, 7, -1447897289775205326586057241495509086825873408000000⟩, + ⟨2, 8, 6, 6, 3, 7, -127026902248169081014070240255581041337464520704000000⟩, + ⟨2, 8, 7, 6, 4, 7, -3921619725374832207707412353327008590757625856000000⟩, + ⟨2, 8, 8, 6, 5, 7, 11059877214206862235643723842707568528176709632000000⟩, + ⟨2, 8, 4, 7, 0, 7, -1612855543422972906101557650905417400304066677964800000⟩, + ⟨2, 8, 5, 7, 1, 7, 67495989666248900402717186241454604706524430336000000⟩, + ⟨2, 8, 6, 7, 2, 7, 125359994999950034031876531592038115621214355456000000⟩, + ⟨2, 8, 7, 7, 3, 7, -164314155374676451252901290071420957662939971584000000⟩, + ⟨2, 8, 8, 7, 4, 7, -21867829729756123248463008625708510216275886080000000⟩ +] + +def collectedFourData_14_3_21 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_22 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_23 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_24 : List CollectedFourTerm := [ + ⟨3, 3, 8, 3, 8, 3, 216716960967509716134502919066406105738588979200000000⟩, + ⟨3, 3, 8, 4, 7, 3, 76983599269763970657989338280897059223861880422400000⟩, + ⟨3, 3, 8, 5, 6, 3, 160300058548340607959925744153000623895419132313600000⟩, + ⟨3, 3, 8, 6, 5, 3, -168227760121534498957071288858653380138910298931200000⟩, + ⟨3, 3, 8, 7, 4, 3, 332623585497896507780650238000092251914426646528000000⟩ +] + +def collectedFourData_14_3_25 : List CollectedFourTerm := [ + ⟨3, 4, 7, 2, 8, 4, -10285649335751694123155029805878300341214956748800000⟩, + ⟨3, 4, 7, 3, 7, 4, 5743291781658888750715749325287965947835134771200000⟩, + ⟨3, 4, 8, 3, 8, 4, 25989240129985935371227543794034975481580748800000000⟩, + ⟨3, 4, 7, 4, 6, 4, -1886242561066547451849224324492661417496805376000000⟩, + ⟨3, 4, 8, 4, 7, 4, 9232065817831665585204314175475362884667152793600000⟩, + ⟨3, 4, 7, 5, 5, 4, -4995603838726663566569213731657261044567166156800000⟩, + ⟨3, 4, 8, 5, 6, 4, 19223584051126521727195857167379908743167108710400000⟩, + ⟨3, 4, 7, 6, 4, 4, 1788354138168365962554619817463088474607950233600000⟩, + ⟨3, 4, 8, 6, 5, 4, -20174293856878606518827887025902860636171062476800000⟩, + ⟨3, 4, 7, 7, 3, 4, 74931258077516894896992729760612614443211581030400000⟩, + ⟨3, 4, 8, 7, 4, 4, 39889052512589203217040700044757381602179284992000000⟩ +] + +def collectedFourData_14_3_26 : List CollectedFourTerm := [ + ⟨3, 5, 6, 1, 8, 5, -1659189222947971755000469274082857783289446400000000⟩, + ⟨3, 5, 6, 2, 7, 5, -2220184955476541374742305233746067780639129600000000⟩, + ⟨3, 5, 7, 2, 8, 5, -10412238429173028540342539745330299283072614400000000⟩, + ⟨3, 5, 6, 3, 6, 5, 5882840975462058874735696512025468521047654400000000⟩, + ⟨3, 5, 7, 3, 7, 5, 5813976487715053942717671017068526961269145600000000⟩, + ⟨3, 5, 8, 3, 8, 5, 13154549411180611516338223963416105792307200000000000⟩, + ⟨3, 5, 6, 4, 5, 5, -4680395671130446630759317929494949549152665600000000⟩, + ⟨3, 5, 7, 4, 6, 5, -1909457209746839054433614832607216678207488000000000⟩, + ⟨3, 5, 8, 4, 7, 5, 4672844044709817725790187253671598288692838400000000⟩, + ⟨3, 5, 6, 5, 4, 5, -5278929838475034203795965811339250134050406400000000⟩, + ⟨3, 5, 7, 5, 5, 5, -5057086487064521791080243368922857276335718400000000⟩, + ⟨3, 5, 8, 5, 6, 5, 9730087720754928859461351152887437425482137600000000⟩, + ⟨3, 5, 6, 6, 3, 5, 19546764858115698996431195216626151913317990400000000⟩, + ⟨3, 5, 7, 6, 4, 5, 1810364039699826306024464713933991535496396800000000⟩, + ⟨3, 5, 8, 6, 5, 5, -10211292983121577688481125106692130130309939200000000⟩, + ⟨3, 5, 6, 7, 2, 5, -19290262940454426229586790952059228028246425600000000⟩, + ⟨3, 5, 7, 7, 3, 5, 75853463348114882776593431118125910820336435200000000⟩, + ⟨3, 5, 8, 7, 4, 5, 20189990535222191594143892692648633772802048000000000⟩ +] + +def collectedFourData_14_3_27 : List CollectedFourTerm := [ + ⟨3, 6, 5, 0, 8, 6, 2808369629099588834507665515549123406951612416000000⟩, + ⟨3, 6, 5, 1, 7, 6, -22274686228993837044764643804694643093236875264000000⟩, + ⟨3, 6, 6, 1, 8, 6, -12183995693141637031610921806493102051665379328000000⟩, + ⟨3, 6, 5, 2, 6, 6, -15568847480553032430702455904401255339825037312000000⟩, + ⟨3, 6, 6, 2, 7, 6, -16303579821620070831695683188360409180318728192000000⟩, + ⟨3, 6, 7, 2, 8, 6, -38230319490505193779382899793438820868338745344000000⟩, + ⟨3, 6, 5, 3, 5, 6, 5882840975462058874735696512025468521047654400000000⟩, + ⟨3, 6, 6, 3, 6, 6, 43199719548030404329869276856574666837210431488000000⟩, + ⟨3, 6, 7, 3, 7, 6, 21347011994354140691344998604341001959040352256000000⟩, + ⟨3, 6, 8, 3, 8, 6, 32199456448227197716027714193084537213288448000000000⟩, + ⟨3, 6, 5, 4, 4, 6, -21193568917409568429098984963287220548572020736000000⟩, + ⟨3, 6, 6, 4, 5, 6, -34369751147449636835806417013223900760781094912000000⟩, + ⟨3, 6, 7, 4, 6, 6, -7010899690650673941939106407666154642216058880000000⟩, + ⟨3, 6, 8, 4, 7, 6, 11438098987952157364219320380176804293227053056000000⟩, + ⟨3, 6, 5, 5, 3, 6, 55274046119712024638442957522941544462708375552000000⟩, + ⟨3, 6, 6, 5, 4, 6, -38764992881341520699183784189021107342203158528000000⟩, + ⟨3, 6, 7, 5, 5, 6, -18567960521333202160192951789834023055480848384000000⟩, + ⟨3, 6, 8, 5, 6, 6, 23817124099711736169630806551257661661232758784000000⟩, + ⟨3, 6, 5, 6, 2, 6, 818051715055332789531569321520798192220766208000000⟩, + ⟨3, 6, 6, 6, 3, 6, 143538600391211702011124980036604230579632734208000000⟩, + ⟨3, 6, 7, 6, 4, 6, 6647062118548020868813903447721334717303226368000000⟩, + ⟨3, 6, 8, 6, 5, 6, -24995009210323215973086225227745809175127523328000000⟩, + ⟨3, 6, 5, 7, 1, 6, -38134756170725633474217719019479340413601447936000000⟩, + ⟨3, 6, 6, 7, 2, 6, -141655018810013402702780415706043438144906330112000000⟩, + ⟨3, 6, 7, 7, 3, 6, 278509002457608603944665274402824039054234877952000000⟩, + ⟨3, 6, 8, 7, 4, 6, 49420675737965825851385973405492981124112056320000000⟩ +] + +def collectedFourData_14_3_28 : List CollectedFourTerm := [ + ⟨3, 7, 4, 0, 7, 7, 29442741323062795860266399266270342912285448601600000⟩, + ⟨3, 7, 5, 0, 8, 7, 2775494877475523499285223441253045954710339584000000⟩, + ⟨3, 7, 4, 1, 6, 7, 65967472833108367753961124098112986360123385446400000⟩, + ⟨3, 7, 5, 1, 7, 7, -22013938936438568714419671934272861132854132736000000⟩, + ⟨3, 7, 6, 1, 8, 7, -6020684970222498422707420665375787830095118336000000⟩, + ⟨3, 7, 4, 2, 5, 7, -8370926585156148839776324534232434580129002291200000⟩, + ⟨3, 7, 5, 2, 6, 7, -15386598680860580565107638001141004241037426688000000⟩, + ⟨3, 7, 6, 2, 7, 7, -8056365125613450318178387722941298818263547904000000⟩, + ⟨3, 7, 7, 2, 8, 7, -12594265229036094022480287952722540834746007552000000⟩, + ⟨3, 7, 4, 3, 4, 7, 5743291781658888750715749325287965947835134771200000⟩, + ⟨3, 7, 5, 3, 5, 7, 5813976487715053942717671017068526961269145600000000⟩, + ⟨3, 7, 6, 3, 6, 7, 21347011994354140691344998604341001959040352256000000⟩, + ⟨3, 7, 7, 3, 7, 7, 7032374682902711101771629216348060402736693248000000⟩, + ⟨3, 7, 8, 3, 8, 7, 7955632469416442380334728460319433464741888000000000⟩, + ⟨3, 7, 4, 4, 3, 7, 12837093449722698735921971532734918966120546304000000⟩, + ⟨3, 7, 5, 4, 4, 7, -20945477175151717779673383346763650073848971264000000⟩, + ⟨3, 7, 6, 4, 5, 7, -16983709562554913120837218051307296490514284544000000⟩, + ⟨3, 7, 7, 4, 6, 7, -2309610052308116092916155953653470356087767040000000⟩, + ⟨3, 7, 8, 4, 7, 7, 2826051173977552099028606212815155608720244736000000⟩, + ⟨3, 7, 4, 5, 2, 7, -87955418890219749091259377349862547607962150502400000⟩, + ⟨3, 7, 5, 5, 3, 7, 54627008593520978007744119391157325898027368448000000⟩, + ⟨3, 7, 6, 5, 4, 7, -19155605097829370501412814799930885005677428736000000⟩, + ⟨3, 7, 7, 5, 5, 7, -6116868043072988961546064099978845772811599872000000⟩, + ⟨3, 7, 8, 5, 6, 7, 5884580260553427416331913366181337697357922304000000⟩, + ⟨3, 7, 4, 6, 1, 7, 47197415139803004571664510702033818061431740825600000⟩, + ⟨3, 7, 5, 6, 2, 7, 808475608452617830044446864054210205730209792000000⟩, + ⟨3, 7, 6, 6, 3, 7, 70929169361788228068782055576948813372007120896000000⟩, + ⟨3, 7, 7, 6, 4, 7, 2189750554809346848221019713987717933819756544000000⟩, + ⟨3, 7, 8, 6, 5, 7, -6175604459868406685585023624007806780774023168000000⟩, + ⟨3, 7, 4, 7, 0, 7, 900584852270503438413741749284366996727781339955200000⟩, + ⟨3, 7, 5, 7, 1, 7, -37688351030758767269553808361001681153177944064000000⟩, + ⟨3, 7, 6, 7, 2, 7, -69998403166385511243057365703586332511718866944000000⟩, + ⟨3, 7, 7, 7, 3, 7, 91749592793660348607432636032996064923291222016000000⟩, + ⟨3, 7, 8, 7, 4, 7, 12210539429248942995323799869582261859825745920000000⟩ +] + +def collectedFourData_14_3_29 : List CollectedFourTerm := [ + ⟨3, 8, 3, 0, 6, 8, -9287142980654152316732471649115934667728486400000000⟩, + ⟨3, 8, 4, 0, 7, 8, 133232735410339977791547999445650431780742758400000000⟩, + ⟨3, 8, 5, 0, 8, 8, 6279761293045642666516483234170226404753408000000000⟩, + ⟨3, 8, 3, 1, 5, 8, 124507412362253379750072208058209615240966963200000000⟩, + ⟨3, 8, 4, 1, 6, 8, 298512518152573804554720716702719283165763993600000000⟩, + ⟨3, 8, 5, 1, 7, 8, -49808155930108148910805731570204585001746432000000000⟩, + ⟨3, 8, 6, 1, 8, 8, -9081495037265554729557614667670444560089088000000000⟩, + ⟨3, 8, 3, 2, 4, 8, -162135408124485712596195683817148361210226278400000000⟩, + ⟨3, 8, 4, 2, 5, 8, -37879674131629813603223728241511128911105228800000000⟩, + ⟨3, 8, 5, 2, 6, 8, -34813311172665829281641679321776284086829056000000000⟩, + ⟨3, 8, 6, 2, 7, 8, -12152079085439014105733348379897178286456832000000000⟩, + ⟨3, 8, 7, 2, 8, 8, -14247725683354093620714047333484181598502912000000000⟩, + ⟨3, 8, 3, 3, 3, 8, 216716960967509716134502919066406105738588979200000000⟩, + ⟨3, 8, 4, 3, 4, 8, 25989240129985935371227543794034975481580748800000000⟩, + ⟨3, 8, 5, 3, 5, 8, 13154549411180611516338223963416105792307200000000000⟩, + ⟨3, 8, 6, 3, 6, 8, 32199456448227197716027714193084537213288448000000000⟩, + ⟨3, 8, 7, 3, 7, 8, 7955632469416442380334728460319433464741888000000000⟩, + ⟨3, 8, 8, 3, 8, 8, 7200081433921375260535627888930064852582400000000000⟩, + ⟨3, 8, 3, 4, 2, 8, -296675688803615443743424806631061351961722880000000000⟩, + ⟨3, 8, 4, 4, 3, 8, 58089736151198701691657111218077710571012096000000000⟩, + ⟨3, 8, 5, 4, 4, 8, -47390682611716945682529480699728894065901568000000000⟩, + ⟨3, 8, 6, 4, 5, 8, -25617928004793454651144106832795100828925952000000000⟩, + ⟨3, 8, 7, 4, 6, 8, -2612831305548236495724097828571521996554240000000000⟩, + ⟨3, 8, 8, 4, 7, 8, 2557659452883199985978679827526964386516172800000000⟩, + ⟨3, 8, 3, 5, 1, 8, 246366111844991554358423106075958044861766041600000000⟩, + ⟨3, 8, 4, 5, 2, 8, -398011208410373639591600542257109843698096537600000000⟩, + ⟨3, 8, 5, 5, 3, 8, 123597624663059738600066280811715097501106176000000000⟩, + ⟨3, 8, 6, 5, 4, 8, -28893976929891969571036309875393416593932288000000000⟩, + ⟨3, 8, 7, 5, 5, 8, -6919931916159040805099215388182460164472832000000000⟩, + ⟨3, 8, 8, 5, 6, 8, 5325718256004202414347641580281305580647219200000000⟩, + ⟨3, 8, 3, 6, 0, 8, 134171110385755905794647155385004043865266585600000000⟩, + ⟨3, 8, 4, 6, 1, 8, 213575246081033413808264094868943896266040934400000000⟩, + ⟨3, 8, 5, 6, 2, 8, 1829235526080356579897771444625494406856704000000000⟩, + ⟨3, 8, 6, 6, 3, 8, 106988308264307523999605734260220381592813568000000000⟩, + ⟨3, 8, 7, 6, 4, 8, 2477235841275341268590873965704089608126464000000000⟩, + ⟨3, 8, 8, 6, 5, 8, -5589103718111065760451506684824476761613926400000000⟩, + ⟨3, 8, 4, 7, 0, 8, 4075278929381781960121788898025472643620981964800000000⟩, + ⟨3, 8, 5, 7, 1, 8, -85272666118895740037481815573191552734855168000000000⟩, + ⟨3, 8, 6, 7, 2, 8, -105584356948766106877232907327642027165745152000000000⟩, + ⟨3, 8, 7, 7, 3, 8, 103795100858262846994110736501475733349072896000000000⟩, + ⟨3, 8, 8, 7, 4, 8, 11050897408933353595522916843115071422857216000000000⟩ +] + +def collectedFourData_14_3_30 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_31 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_32 : List CollectedFourTerm := [ + ⟨4, 2, 8, 3, 8, 3, -296675688803615443743424806631061351961722880000000000⟩, + ⟨4, 2, 8, 4, 7, 3, -105387055253893063873556154219129641918382735360000000⟩, + ⟨4, 2, 8, 5, 6, 3, -219443508587307182171649305539063330412471255040000000⟩, + ⟨4, 2, 8, 6, 5, 3, 230296172422923673283753864374716542033256775680000000⟩, + ⟨4, 2, 8, 7, 4, 3, -455346600004745634788529564967844968586752819200000000⟩ +] + +def collectedFourData_14_3_33 : List CollectedFourTerm := [ + ⟨4, 3, 7, 2, 8, 4, -22989924025065808783808340140109466497340932096000000⟩, + ⟨4, 3, 7, 3, 7, 4, 12837093449722698735921971532734918966120546304000000⟩, + ⟨4, 3, 8, 3, 8, 4, 58089736151198701691657111218077710571012096000000000⟩, + ⟨4, 3, 7, 4, 6, 4, -4216026791914379186196137091289802809981009920000000⟩, + ⟨4, 3, 8, 4, 7, 4, 20635011443431229539705122949934620627552960512000000⟩, + ⟨4, 3, 7, 5, 5, 4, -11165902021611138254968194622028174028183699456000000⟩, + ⟨4, 3, 8, 5, 6, 4, 42967509624181360095578473425168101082207879168000000⟩, + ⟨4, 3, 7, 6, 4, 4, 3997231912573080133186287818586373661562765312000000⟩, + ⟨4, 3, 8, 6, 5, 4, -45092484479016635431242795988743252689452793856000000⟩, + ⟨4, 3, 7, 7, 3, 4, 167482273026452215613323065913144692281670893568000000⟩, + ⟨4, 3, 8, 7, 4, 4, 89157840867541763518117186662328671868173680640000000⟩ +] + +def collectedFourData_14_3_34 : List CollectedFourTerm := [ + ⟨4, 4, 6, 1, 8, 5, 5977408073793657896757864767100552935915913216000000⟩, + ⟨4, 4, 6, 2, 7, 5, 7998455688255658896505859617440183512123572224000000⟩, + ⟨4, 4, 7, 2, 8, 5, 37511211615888790805702146019678214141442523136000000⟩, + ⟨4, 4, 6, 3, 6, 5, -21193568917409568429098984963287220548572020736000000⟩, + ⟨4, 4, 7, 3, 7, 5, -20945477175151717779673383346763650073848971264000000⟩, + ⟨4, 4, 8, 3, 8, 5, -47390682611716945682529480699728894065901568000000000⟩, + ⟨4, 4, 6, 4, 5, 5, 16861630057755804704185191499900344138479960064000000⟩, + ⟨4, 4, 7, 4, 6, 5, 6879025480785785857477408755976177950885150720000000⟩, + ⟨4, 4, 8, 4, 7, 5, -16834424509339368193145916306430717136990109696000000⟩, + ⟨4, 4, 6, 5, 4, 5, 19017913931134778409084828341963432340662255616000000⟩, + ⟨4, 4, 7, 5, 5, 5, 18218699337947764746095658491313115107107536896000000⟩, + ⟨4, 4, 8, 5, 6, 5, -35053690137538233246722528256972915775314591744000000⟩, + ⟨4, 4, 6, 6, 3, 5, -70419327984696485148341981533063202116863000576000000⟩, + ⟨4, 4, 7, 6, 4, 5, -6522031651206532598775388175673989193837576192000000⟩, + ⟨4, 4, 8, 6, 5, 5, 36787283980024635412887083270369550545241243648000000⟩, + ⟨4, 4, 6, 7, 2, 5, 69495252169613803688940134671983936490086334464000000⟩, + ⟨4, 4, 7, 7, 3, 5, -273270280430486488836271020800407162652498853888000000⟩, + ⟨4, 4, 8, 7, 4, 5, -72736617840748247724599505826737204413721477120000000⟩ +] + +def collectedFourData_14_3_35 : List CollectedFourTerm := [ + ⟨4, 5, 5, 0, 8, 6, -2234342405276310537596374205076172313286672384000000⟩, + ⟨4, 5, 5, 1, 7, 6, 17721768349140735870062923907801005993739943936000000⟩, + ⟨4, 5, 6, 1, 8, 6, 9693602281127972965104337806825013962784899072000000⟩, + ⟨4, 5, 5, 2, 6, 6, 12386594615834781664011640993575879790232076288000000⟩, + ⟨4, 5, 6, 2, 7, 6, 12971148589486875338006219419750103594626449408000000⟩, + ⟨4, 5, 7, 2, 8, 6, 30416090218253847413973780133471357116251897856000000⟩, + ⟨4, 5, 5, 3, 5, 6, -4680395671130446630759317929494949549152665600000000⟩, + ⟨4, 5, 6, 3, 6, 6, -34369751147449636835806417013223900760781094912000000⟩, + ⟨4, 5, 7, 3, 7, 6, -16983709562554913120837218051307296490514284544000000⟩, + ⟨4, 5, 8, 3, 8, 6, -25617928004793454651144106832795100828925952000000000⟩, + ⟨4, 5, 5, 4, 4, 6, 16861630057755804704185191499900344138479960064000000⟩, + ⟨4, 5, 6, 4, 5, 6, 27344617194198277325220721886865603270109298688000000⟩, + ⟨4, 5, 7, 4, 6, 6, 5577880602198989834135213771569811162262405120000000⟩, + ⟨4, 5, 8, 4, 7, 6, -9100165925353439888028906264187928962865823744000000⟩, + ⟨4, 5, 5, 5, 3, 6, -43976100537758505946937447087787026413988610048000000⟩, + ⟨4, 5, 6, 5, 4, 6, 30841477039753374378715269904186616239852879872000000⟩, + ⟨4, 5, 7, 5, 5, 6, 14772692719089367642581267416258558306147106816000000⟩, + ⟨4, 5, 8, 5, 6, 6, -18948933856963883483868646365550692950832316416000000⟩, + ⟨4, 5, 5, 6, 2, 6, -650842972277537968328910270599601564986376192000000⟩, + ⟨4, 5, 6, 6, 3, 6, -114199490809520547191659630374415524180044808192000000⟩, + ⟨4, 5, 7, 6, 4, 6, -5288410972717782043162036564227710453947564032000000⟩, + ⟨4, 5, 8, 6, 5, 6, 19886060730831482733442728651737727933005955072000000⟩, + ⟨4, 5, 5, 7, 1, 6, 30340059920973887680562667268998384356230692864000000⟩, + ⟨4, 5, 6, 7, 2, 6, 112700910937034850802971592550603606210786623488000000⟩, + ⟨4, 5, 7, 7, 3, 6, -221582112266950450834865991485657054755996827648000000⟩, + ⟨4, 5, 8, 7, 4, 6, -39319151708014507277560037514789942757876039680000000⟩ +] + +def collectedFourData_14_3_36 : List CollectedFourTerm := [ + ⟨4, 6, 4, 0, 7, 7, -9669742354965780447049205707972479567022522368000000⟩, + ⟨4, 6, 5, 0, 8, 7, -911542851198196757848852299980707327188664320000000⟩, + ⟨4, 6, 4, 1, 6, 7, -21665389751079258081294987203906603283929628672000000⟩, + ⟨4, 6, 5, 1, 7, 7, 7229935398935419420872658357147685558188769280000000⟩, + ⟨4, 6, 6, 1, 8, 7, 1977345513573604156861385868731483455519457280000000⟩, + ⟨4, 6, 4, 2, 5, 7, 2749224417068415971655210753763456650603134976000000⟩, + ⟨4, 6, 5, 2, 6, 7, 5053348916482644458805240571903471150946058240000000⟩, + ⟨4, 6, 6, 2, 7, 7, 2645914462495766505753476206759029468215377920000000⟩, + ⟨4, 6, 7, 2, 8, 7, 4136275850764243834154570830047138005605416960000000⟩, + ⟨4, 6, 4, 3, 4, 7, -1886242561066547451849224324492661417496805376000000⟩, + ⟨4, 6, 5, 3, 5, 7, -1909457209746839054433614832607216678207488000000000⟩, + ⟨4, 6, 6, 3, 6, 7, -7010899690650673941939106407666154642216058880000000⟩, + ⟨4, 6, 7, 3, 7, 7, -2309610052308116092916155953653470356087767040000000⟩, + ⟨4, 6, 8, 3, 8, 7, -2612831305548236495724097828571521996554240000000000⟩, + ⟨4, 6, 4, 4, 3, 7, -4216026791914379186196137091289802809981009920000000⟩, + ⟨4, 6, 5, 4, 4, 7, 6879025480785785857477408755976177950885150720000000⟩, + ⟨4, 6, 6, 4, 5, 7, 5577880602198989834135213771569811162262405120000000⟩, + ⟨4, 6, 7, 4, 6, 7, 758534468689727483564208903239872418100019200000000⟩, + ⟨4, 6, 8, 4, 7, 7, -928146820109642525129356845250420621474529280000000⟩, + ⟨4, 6, 4, 5, 2, 7, 28886788429761637151527816090074965368532631552000000⟩, + ⟨4, 6, 5, 5, 3, 7, -17940893917648975635158127282119088008111063040000000⟩, + ⟨4, 6, 6, 5, 4, 7, 6291186133690165077710155078032668516186849280000000⟩, + ⟨4, 6, 7, 5, 5, 7, 2008934472059769910156088586739838247040450560000000⟩, + ⟨4, 6, 8, 5, 6, 7, -1932645277907490278685953844519458230417489920000000⟩, + ⟨4, 6, 4, 6, 1, 7, -15500827155138705541393590209659227712297893888000000⟩, + ⟨4, 6, 5, 6, 2, 7, -265523877285410444782743853213764823453532160000000⟩, + ⟨4, 6, 6, 6, 3, 7, -23294936624769325235197172557828549047830446080000000⟩, + ⟨4, 6, 7, 6, 4, 7, -719169572368035473878586704047780199000965120000000⟩, + ⟨4, 6, 8, 6, 5, 7, 2028224999766871717948247396757508834606448640000000⟩, + ⟨4, 6, 4, 7, 0, 7, -295774887082925650105028755822898310980038557696000000⟩, + ⟨4, 6, 5, 7, 1, 7, 12377809533838460437584708721445333285700894720000000⟩, + ⟨4, 6, 6, 7, 2, 7, 22989249419780501549716495337883625904532357120000000⟩, + ⟨4, 6, 7, 7, 3, 7, -30132891287292324846332066014474286868914503680000000⟩, + ⟨4, 6, 8, 7, 4, 7, -4010250574171250840005121880629762999294361600000000⟩ +] + +def collectedFourData_14_3_37 : List CollectedFourTerm := [ + ⟨4, 7, 3, 0, 6, 8, -3299038941815298424514637465735275091382291660800000⟩, + ⟨4, 7, 4, 0, 7, 8, 47327793203882175451019374027617147155680906444800000⟩, + ⟨4, 7, 5, 0, 8, 8, 2230737385460466455210789628832169031867826176000000⟩, + ⟨4, 7, 3, 1, 5, 8, 44228327568915853226077885545718535663114413670400000⟩, + ⟨4, 7, 4, 1, 6, 8, 106039545644566046284945404937558503167632814899200000⟩, + ⟨4, 7, 5, 1, 7, 8, -17693175002874924752960756880209662380085346304000000⟩, + ⟨4, 7, 6, 1, 8, 8, -3225987350496368982123773906772070940735963136000000⟩, + ⟨4, 7, 3, 2, 4, 8, -57594787370455571543792158911721264371177671884800000⟩, + ⟨4, 7, 4, 2, 5, 8, -13455862618227739378349133618270894939159763353600000⟩, + ⟨4, 7, 5, 2, 6, 8, -12366609353533236673897639607411634112542277632000000⟩, + ⟨4, 7, 6, 2, 7, 8, -4316740057775953293105465792596902588767535104000000⟩, + ⟨4, 7, 7, 2, 8, 8, -5061169184064436908445218181013633868301860864000000⟩, + ⟨4, 7, 3, 3, 3, 8, 76983599269763970657989338280897059223861880422400000⟩, + ⟨4, 7, 4, 3, 4, 8, 9232065817831665585204314175475362884667152793600000⟩, + ⟨4, 7, 5, 3, 5, 8, 4672844044709817725790187253671598288692838400000000⟩, + ⟨4, 7, 6, 3, 6, 8, 11438098987952157364219320380176804293227053056000000⟩, + ⟨4, 7, 7, 3, 7, 8, 2826051173977552099028606212815155608720244736000000⟩, + ⟨4, 7, 8, 3, 8, 8, 2557659452883199985978679827526964386516172800000000⟩, + ⟨4, 7, 3, 4, 2, 8, -105387055253893063873556154219129641918382735360000000⟩, + ⟨4, 7, 4, 4, 3, 8, 20635011443431229539705122949934620627552960512000000⟩, + ⟨4, 7, 5, 4, 4, 8, -16834424509339368193145916306430717136990109696000000⟩, + ⟨4, 7, 6, 4, 5, 8, -9100165925353439888028906264187928962865823744000000⟩, + ⟨4, 7, 7, 4, 6, 8, -928146820109642525129356845250420621474529280000000⟩, + ⟨4, 7, 8, 4, 7, 8, 908548318093123426174596706027281698522765721600000⟩, + ⟨4, 7, 3, 5, 1, 8, 87515762233155772720767100853101619074894607155200000⟩, + ⟨4, 7, 4, 5, 2, 8, -141384113344651070639074442238517737314034332467200000⟩, + ⟨4, 7, 5, 5, 3, 8, 43905146903486606701197607942849637918831542272000000⟩, + ⟨4, 7, 6, 5, 4, 8, -10263905193899824189594531010250389085052993536000000⟩, + ⟨4, 7, 7, 5, 5, 8, -2458142930896411423733447222648629908266287104000000⟩, + ⟨4, 7, 8, 5, 6, 8, 1891836052949081612092667378849754423883097702400000⟩, + ⟨4, 7, 3, 6, 0, 8, 47661128826298108959484020124830180981377020723200000⟩, + ⟨4, 7, 4, 6, 1, 8, 75867579006464858232306452747897591673553472716800000⟩, + ⟨4, 7, 5, 6, 2, 8, 649792863840029604825860199817325097504473088000000⟩, + ⟨4, 7, 6, 6, 3, 8, 38005078205227430587896406892022301070978973696000000⟩, + ⟨4, 7, 7, 6, 4, 8, 879979723091577906572798032357549112775671808000000⟩, + ⟨4, 7, 8, 6, 5, 8, -1985397538758935739239803073555152156733787340800000⟩, + ⟨4, 7, 4, 7, 0, 8, 1447646915181107144925146710980281414208376641945600000⟩, + ⟨4, 7, 5, 7, 1, 8, -30291107478872480383613839856692638458258128896000000⟩, + ⟨4, 7, 6, 7, 2, 8, -37506357546782510898874433797738612592574726144000000⟩, + ⟨4, 7, 7, 7, 3, 8, 36870766436389734441787339535338222972003418112000000⟩, + ⟨4, 7, 8, 7, 4, 8, 3925571186964647393194064485482994328143921152000000⟩ +] + +def collectedFourData_14_3_38 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_3_39 : List CollectedFourTerm := [ + ⟨5, 1, 8, 3, 8, 3, 246366111844991554358423106075958044861766041600000000⟩, + ⟨5, 1, 8, 4, 7, 3, 87515762233155772720767100853101619074894607155200000⟩, + ⟨5, 1, 8, 5, 6, 3, 182230786075852672609266770635633219019066887372800000⟩, + ⟨5, 1, 8, 6, 5, 3, -191243080285478534084398852999007162719238986137600000⟩, + ⟨5, 1, 8, 7, 4, 3, 378129977004164579990851031679981238377139666944000000⟩ +] + +def collectedFourData_14_3_40 : List CollectedFourTerm := [ + ⟨5, 2, 7, 2, 8, 4, 157519177203050613709139216756347969416585648537600000⟩, + ⟨5, 2, 7, 3, 7, 4, -87955418890219749091259377349862547607962150502400000⟩, + ⟨5, 2, 8, 3, 8, 4, -398011208410373639591600542257109843698096537600000000⟩, + ⟨5, 2, 7, 4, 6, 4, 28886788429761637151527816090074965368532631552000000⟩, + ⟨5, 2, 8, 4, 7, 4, -141384113344651070639074442238517737314034332467200000⟩, + ⟨5, 2, 7, 5, 5, 4, 76504980932360052473449928895237458259223353753600000⟩, + ⟨5, 2, 8, 5, 6, 4, -294398831204742631188549674010580809182222273740800000⟩, + ⟨5, 2, 7, 6, 4, 4, -27387679979794347232927508086107410527270679347200000⟩, + ⟨5, 2, 8, 6, 5, 4, 308958439594308256980659767509446048546578602393600000⟩, + ⟨5, 2, 7, 7, 3, 4, -1147531841099588535148098460724970096677639474380800000⟩, + ⟨5, 2, 8, 7, 4, 4, -610879345201120023313224118586219258415188803584000000⟩ +] + +def collectedFourData_14_3_41 : List CollectedFourTerm := [ + ⟨5, 3, 6, 1, 8, 5, -15589423887724946682014179839016953105101094912000000⟩, + ⟨5, 3, 6, 2, 7, 5, -20860432252915418660800225105045731780662919168000000⟩, + ⟨5, 3, 7, 2, 8, 5, -97831396351546626663776684535054044007185252352000000⟩, + ⟨5, 3, 6, 3, 6, 5, 55274046119712024638442957522941544462708375552000000⟩, + ⟨5, 3, 7, 3, 7, 5, 54627008593520978007744119391157325898027368448000000⟩, + ⟨5, 3, 8, 3, 8, 5, 123597624663059738600066280811715097501106176000000000⟩, + ⟨5, 3, 6, 4, 5, 5, -43976100537758505946937447087787026413988610048000000⟩, + ⟨5, 3, 7, 4, 6, 5, -17940893917648975635158127282119088008111063040000000⟩, + ⟨5, 3, 8, 4, 7, 5, 43905146903486606701197607942849637918831542272000000⟩, + ⟨5, 3, 6, 5, 4, 5, -49599812840712553106544885408539861446884851712000000⟩, + ⟨5, 3, 7, 5, 5, 5, -47515415236160097849620562446926238345091612672000000⟩, + ⟨5, 3, 8, 5, 6, 5, 91422039057176660970853055762148009999291383808000000⟩, + ⟨5, 3, 6, 6, 3, 5, 183657655674398502031576785931185604532405010432000000⟩, + ⟨5, 3, 7, 6, 4, 5, 17009833487123426013704416355672121794724102144000000⟩, + ⟨5, 3, 8, 6, 5, 5, -95943351459814429017027113226733714461463412736000000⟩, + ⟨5, 3, 6, 7, 2, 5, -181247612825077696528593247395928453330237390848000000⟩, + ⟨5, 3, 7, 7, 3, 5, 712704601217658485330925865642575685802489020416000000⟩, + ⟨5, 3, 8, 7, 4, 5, 189701280836129948666326037683584469911302307840000000⟩ +] + +def collectedFourData_14_3_42 : List CollectedFourTerm := [ + ⟨5, 4, 5, 0, 8, 6, -2520072579618976068335287015251347367260061696000000⟩, + ⟨5, 4, 5, 1, 7, 6, 19988047657138794257937908164687052592994320384000000⟩, + ⟨5, 4, 6, 1, 8, 6, 10933230846228152213046668579079349682011373568000000⟩, + ⟨5, 4, 5, 2, 6, 6, 13970606014775543072061243154627832506610614272000000⟩, + ⟨5, 4, 6, 2, 7, 6, 14629913396146117336002800178207125926997655552000000⟩, + ⟨5, 4, 7, 2, 8, 6, 34305733426188741389887114300196706968471076864000000⟩, + ⟨5, 4, 5, 3, 5, 6, -5278929838475034203795965811339250134050406400000000⟩, + ⟨5, 4, 6, 3, 6, 6, -38764992881341520699183784189021107342203158528000000⟩, + ⟨5, 4, 7, 3, 7, 6, -19155605097829370501412814799930885005677428736000000⟩, + ⟨5, 4, 8, 3, 8, 6, -28893976929891969571036309875393416593932288000000000⟩, + ⟨5, 4, 5, 4, 4, 6, 19017913931134778409084828341963432340662255616000000⟩, + ⟨5, 4, 6, 4, 5, 6, 30841477039753374378715269904186616239852879872000000⟩, + ⟨5, 4, 7, 4, 6, 6, 6291186133690165077710155078032668516186849280000000⟩, + ⟨5, 4, 8, 4, 7, 6, -10263905193899824189594531010250389085052993536000000⟩, + ⟨5, 4, 5, 5, 3, 6, -49599812840712553106544885408539861446884851712000000⟩, + ⟨5, 4, 6, 5, 4, 6, 34785519184208967464806861152212147820998688768000000⟩, + ⟨5, 4, 7, 5, 5, 6, 16661840978625729598663195550658048920182063104000000⟩, + ⟨5, 4, 8, 5, 6, 6, -21372144445355490989615683595287046556173205504000000⟩, + ⟨5, 4, 5, 6, 2, 6, -734073490348273005608413789354952039331790848000000⟩, + ⟨5, 4, 6, 6, 3, 6, -128803447813511038399831962645828997089589198848000000⟩, + ⟨5, 4, 7, 6, 4, 6, -5964698808307355349137469556567360950981623808000000⟩, + ⟨5, 4, 8, 6, 5, 6, 22429112138794463402500809451797499023949037568000000⟩, + ⟨5, 4, 5, 7, 1, 6, 34219980290526523472189398687760004742241058816000000⟩, + ⟨5, 4, 6, 7, 2, 6, 127113227891935016777835816521687622891520131072000000⟩, + ⟨5, 4, 7, 7, 3, 6, -249918277493793674007448578786540444173689946112000000⟩, + ⟨5, 4, 8, 7, 4, 6, -44347328251594613650417432752389109283993681920000000⟩ +] + +def collectedFourData_14_3_43 : List CollectedFourTerm := [ + ⟨5, 5, 4, 0, 7, 7, -25609750848083316558127294557585076782966924902400000⟩, + ⟨5, 5, 5, 0, 8, 7, -2414168283868398436533093447104891390709989376000000⟩, + ⟨5, 5, 4, 1, 6, 7, -57379526070497989602108930827180655448528886169600000⟩, + ⟨5, 5, 5, 1, 7, 7, 19148063869497915627694993913681932401827119104000000⟩, + ⟨5, 5, 6, 1, 8, 7, 5236884715670850368054269223108846446920597504000000⟩, + ⟨5, 5, 4, 2, 5, 7, 7281161148045747036815672565864900881942367436800000⟩, + ⟨5, 5, 5, 2, 6, 7, 13383501022971184444430857852098822721379500032000000⟩, + ⟨5, 5, 6, 2, 7, 7, 7007550735316014963946470720776568713150201856000000⟩, + ⟨5, 5, 7, 2, 8, 7, 10954686287232623967325426474910703800788451328000000⟩, + ⟨5, 5, 4, 3, 4, 7, -4995603838726663566569213731657261044567166156800000⟩, + ⟨5, 5, 5, 3, 5, 7, -5057086487064521791080243368922857276335718400000000⟩, + ⟨5, 5, 6, 3, 6, 7, -18567960521333202160192951789834023055480848384000000⟩, + ⟨5, 5, 7, 3, 7, 7, -6116868043072988961546064099978845772811599872000000⟩, + ⟨5, 5, 8, 3, 8, 7, -6919931916159040805099215388182460164472832000000000⟩, + ⟨5, 5, 4, 4, 3, 7, -11165902021611138254968194622028174028183699456000000⟩, + ⟨5, 5, 5, 4, 4, 7, 18218699337947764746095658491313115107107536896000000⟩, + ⟨5, 5, 6, 4, 5, 7, 14772692719089367642581267416258558306147106816000000⟩, + ⟨5, 5, 7, 4, 6, 7, 2008934472059769910156088586739838247040450560000000⟩, + ⟨5, 5, 8, 4, 7, 7, -2458142930896411423733447222648629908266287104000000⟩, + ⟨5, 5, 4, 5, 2, 7, 76504980932360052473449928895237458259223353753600000⟩, + ⟨5, 5, 5, 5, 3, 7, -47515415236160097849620562446926238345091612672000000⟩, + ⟨5, 5, 6, 5, 4, 7, 16661840978625729598663195550658048920182063104000000⟩, + ⟨5, 5, 7, 5, 5, 7, 5320546237010734603249375331529247095477239808000000⟩, + ⟨5, 5, 8, 5, 6, 7, -5118498738440349988143424209466062251759763456000000⟩, + ⟨5, 5, 4, 6, 1, 7, -41053040175206527934950922591479721061471643238400000⟩, + ⟨5, 5, 5, 6, 2, 7, -703224562958945005109956612687255206717554688000000⟩, + ⟨5, 5, 6, 6, 3, 7, -61695286294351792354865882075790583714591801344000000⟩, + ⟨5, 5, 7, 6, 4, 7, -1904678831117955865831494386298464362945314816000000⟩, + ⟨5, 5, 8, 6, 5, 7, 5371636078929141488212481637664675800129994752000000⟩, + ⟨5, 5, 4, 7, 0, 7, -783342604927192808687648765759713184065962953932800000⟩, + ⟨5, 5, 5, 7, 1, 7, 32781909441862792595567355763141645511316996096000000⟩, + ⟨5, 5, 6, 7, 2, 7, 60885691491322684141591731949775839835681980416000000⟩, + ⟨5, 5, 7, 7, 3, 7, -79805211956205000181931936773237426956244353024000000⟩, + ⟨5, 5, 8, 7, 4, 7, -10620915663814730600239830948773124765521018880000000⟩ +] + +def collectedFourData_14_3_44 : List CollectedFourTerm := [ + ⟨5, 6, 3, 0, 6, 8, -6869464932044991107926821321168249005551072051200000⟩, + ⟨5, 6, 4, 0, 7, 8, 98548886951376882248051745859358150533879903027200000⟩, + ⟨5, 6, 5, 0, 8, 8, 4644980708712210038500593155124157400915902464000000⟩, + ⟨5, 6, 3, 1, 5, 8, 92094986023561839321668521643076171044503525785600000⟩, + ⟨5, 6, 4, 1, 6, 8, 220802164831224697822870687005322499609936579788800000⟩, + ⟨5, 6, 5, 1, 7, 8, -36841834049981055092233870629144451924157792256000000⟩, + ⟨5, 6, 6, 1, 8, 8, -6717352346032490641176262724797546473040379904000000⟩, + ⟨5, 6, 3, 2, 4, 8, -119927463448560616087937104739865571516950459187200000⟩, + ⟨5, 6, 4, 2, 5, 8, -28018637553719922205039382604288286981483816550400000⟩, + ⟨5, 6, 5, 2, 6, 8, -25750526374705736915455706508920484074354638848000000⟩, + ⟨5, 6, 6, 2, 7, 8, -8988585758047710225721260742459918175705235456000000⟩, + ⟨5, 6, 7, 2, 8, 8, -10538682579462537746501672329483669191153156096000000⟩, + ⟨5, 6, 3, 3, 3, 8, 160300058548340607959925744153000623895419132313600000⟩, + ⟨5, 6, 4, 3, 4, 8, 19223584051126521727195857167379908743167108710400000⟩, + ⟨5, 6, 5, 3, 5, 8, 9730087720754928859461351152887437425482137600000000⟩, + ⟨5, 6, 6, 3, 6, 8, 23817124099711736169630806551257661661232758784000000⟩, + ⟨5, 6, 7, 3, 7, 8, 5884580260553427416331913366181337697357922304000000⟩, + ⟨5, 6, 8, 3, 8, 8, 5325718256004202414347641580281305580647219200000000⟩, + ⟨5, 6, 3, 4, 2, 8, -219443508587307182171649305539063330412471255040000000⟩, + ⟨5, 6, 4, 4, 3, 8, 42967509624181360095578473425168101082207879168000000⟩, + ⟨5, 6, 5, 4, 4, 8, -35053690137538233246722528256972915775314591744000000⟩, + ⟨5, 6, 6, 4, 5, 8, -18948933856963883483868646365550692950832316416000000⟩, + ⟨5, 6, 7, 4, 6, 8, -1932645277907490278685953844519458230417489920000000⟩, + ⟨5, 6, 8, 4, 7, 8, 1891836052949081612092667378849754423883097702400000⟩, + ⟨5, 6, 3, 5, 1, 8, 182230786075852672609266770635633219019066887372800000⟩, + ⟨5, 6, 4, 5, 2, 8, -294398831204742631188549674010580809182222273740800000⟩, + ⟨5, 6, 5, 5, 3, 8, 91422039057176660970853055762148009999291383808000000⟩, + ⟨5, 6, 6, 5, 4, 8, -21372144445355490989615683595287046556173205504000000⟩, + ⟨5, 6, 7, 5, 5, 8, -5118498738440349988143424209466062251759763456000000⟩, + ⟨5, 6, 8, 5, 6, 8, 3939299187466130214036101010135096818258254233600000⟩, + ⟨5, 6, 3, 6, 0, 8, 99242979203445801726085265162434762448741125324800000⟩, + ⟨5, 6, 4, 6, 1, 8, 157976211453050973563498626407826678172609622835200000⟩, + ⟨5, 6, 5, 6, 2, 8, 1353039285067062302262949358351164822605791232000000⟩, + ⟨5, 6, 6, 6, 3, 8, 79136547514283288229120138849918354386262687744000000⟩, + ⟨5, 6, 7, 6, 4, 8, 1832348740133996883139612322247766224836493312000000⟩, + ⟨5, 6, 8, 6, 5, 8, -4134118756769899124431814871541698934636491571200000⟩, + ⟨5, 6, 4, 7, 0, 8, 3014380822175965113711453557380026588965957428838400000⟩, + ⟨5, 6, 5, 7, 1, 8, -63074035877982715603780152613234512542558060544000000⟩, + ⟨5, 6, 6, 7, 2, 8, -78098080210775608082642460505086454464843350016000000⟩, + ⟨5, 6, 7, 7, 3, 8, 76774612703732412622243263479358565583387885568000000⟩, + ⟨5, 6, 8, 7, 4, 8, 8174069504090637104025850171103421892424368128000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1406.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1406.lean new file mode 100644 index 0000000000000000000000000000000000000000..5a6381b5f0454607058b44bae304e0044cc0ba23 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1406.lean @@ -0,0 +1,615 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1404 +import OAI.Analysis.LaughlinFock.Sparse1405 + +namespace OAI + +/-! Sparse1406. -/ +namespace LaughlinFock +def collectedFourData_14_3_45 : List CollectedFourTerm := [ + ⟨6, 0, 8, 3, 8, 3, 134171110385755905794647155385004043865266585600000000⟩, + ⟨6, 0, 8, 4, 7, 3, 47661128826298108959484020124830180981377020723200000⟩, + ⟨6, 0, 8, 5, 6, 3, 99242979203445801726085265162434762448741125324800000⟩, + ⟨6, 0, 8, 6, 5, 3, -104151079234627919792037866450007494419390503321600000⟩, + ⟨6, 0, 8, 7, 4, 3, 205929778673091058119375913642930403097553403904000000⟩ +] + +def collectedFourData_14_3_46 : List CollectedFourTerm := [ + ⟨6, 1, 7, 2, 8, 4, -84525752849995879025948309130216183962223928934400000⟩, + ⟨6, 1, 7, 3, 7, 4, 47197415139803004571664510702033818061431740825600000⟩, + ⟨6, 1, 8, 3, 8, 4, 213575246081033413808264094868943896266040934400000000⟩, + ⟨6, 1, 7, 4, 6, 4, -15500827155138705541393590209659227712297893888000000⟩, + ⟨6, 1, 8, 4, 7, 4, 75867579006464858232306452747897591673553472716800000⟩, + ⟨6, 1, 7, 5, 5, 4, -41053040175206527934950922591479721061471643238400000⟩, + ⟨6, 1, 8, 5, 6, 4, 157976211453050973563498626407826678172609622835200000⟩, + ⟨6, 1, 7, 6, 4, 4, 14696396402088647373786709291381684079298399436800000⟩, + ⟨6, 1, 8, 6, 5, 4, -165788986266766270489503453122004087759561975398400000⟩, + ⟨6, 1, 7, 7, 3, 4, 615772596775639325039878558978353514444651442995200000⟩, + ⟨6, 1, 8, 7, 4, 4, 327801588800053681306040190293464253810287312896000000⟩ +] + +def collectedFourData_14_3_47 : List CollectedFourTerm := [ + ⟨6, 2, 6, 1, 8, 5, -230722298137135337499488203055862311339163648000000⟩, + ⟨6, 2, 6, 2, 7, 5, -308732824521910453179702576239976896551452672000000⟩, + ⟨6, 2, 7, 2, 8, 5, -1447897289775205326586057241495509086825873408000000⟩, + ⟨6, 2, 6, 3, 6, 5, 818051715055332789531569321520798192220766208000000⟩, + ⟨6, 2, 7, 3, 7, 5, 808475608452617830044446864054210205730209792000000⟩, + ⟨6, 2, 8, 3, 8, 5, 1829235526080356579897771444625494406856704000000000⟩, + ⟨6, 2, 6, 4, 5, 5, -650842972277537968328910270599601564986376192000000⟩, + ⟨6, 2, 7, 4, 6, 5, -265523877285410444782743853213764823453532160000000⟩, + ⟨6, 2, 8, 4, 7, 5, 649792863840029604825860199817325097504473088000000⟩, + ⟨6, 2, 6, 5, 4, 5, -734073490348273005608413789354952039331790848000000⟩, + ⟨6, 2, 7, 5, 5, 5, -703224562958945005109956612687255206717554688000000⟩, + ⟨6, 2, 8, 5, 6, 5, 1353039285067062302262949358351164822605791232000000⟩, + ⟨6, 2, 6, 6, 3, 5, 2718119456681204108329681582012352847547465728000000⟩, + ⟨6, 2, 7, 6, 4, 5, 251744253113118159872583424251072796296216576000000⟩, + ⟨6, 2, 8, 6, 5, 5, -1419954367731143623123024740325107337154002944000000⟩, + ⟨6, 2, 6, 7, 2, 5, -2682451004222091864926325929293653226807099392000000⟩, + ⟨6, 2, 7, 7, 3, 5, 10547974361985608565708003001422579682366193664000000⟩, + ⟨6, 2, 8, 7, 4, 5, 2807564653401529364318639445997333459092111360000000⟩ +] + +def collectedFourData_14_3_48 : List CollectedFourTerm := [ + ⟨6, 3, 5, 0, 8, 6, 9331297752846642913170745885260851525720211456000000⟩, + ⟨6, 3, 5, 1, 7, 6, -74011528753291304087050225980080481658076135424000000⟩, + ⟨6, 3, 6, 1, 8, 6, -40483450060865913690580395996406872318985371648000000⟩, + ⟨6, 3, 5, 2, 6, 6, -51730210298661821296374375159336671882973806592000000⟩, + ⟨6, 3, 6, 2, 7, 6, -54171486607913449647386566970048430318311964672000000⟩, + ⟨6, 3, 7, 2, 8, 6, -127026902248169081014070240255581041337464520704000000⟩, + ⟨6, 3, 5, 3, 5, 6, 19546764858115698996431195216626151913317990400000000⟩, + ⟨6, 3, 6, 3, 6, 6, 143538600391211702011124980036604230579632734208000000⟩, + ⟨6, 3, 7, 3, 7, 6, 70929169361788228068782055576948813372007120896000000⟩, + ⟨6, 3, 8, 3, 8, 6, 106988308264307523999605734260220381592813568000000000⟩, + ⟨6, 3, 5, 4, 4, 6, -70419327984696485148341981533063202116863000576000000⟩, + ⟨6, 3, 6, 4, 5, 6, -114199490809520547191659630374415524180044808192000000⟩, + ⟨6, 3, 7, 4, 6, 6, -23294936624769325235197172557828549047830446080000000⟩, + ⟨6, 3, 8, 4, 7, 6, 38005078205227430587896406892022301070978973696000000⟩, + ⟨6, 3, 5, 5, 3, 6, 183657655674398502031576785931185604532405010432000000⟩, + ⟨6, 3, 6, 5, 4, 6, -128803447813511038399831962645828997089589198848000000⟩, + ⟨6, 3, 7, 5, 5, 6, -61695286294351792354865882075790583714591801344000000⟩, + ⟨6, 3, 8, 5, 6, 6, 79136547514283288229120138849918354386262687744000000⟩, + ⟨6, 3, 5, 6, 2, 6, 2718119456681204108329681582012352847547465728000000⟩, + ⟨6, 3, 6, 6, 3, 6, 476932026823940884324880479027424267270753353728000000⟩, + ⟨6, 3, 7, 6, 4, 6, 22086022853667483312033873624917751508959756288000000⟩, + ⟨6, 3, 8, 6, 5, 6, -83050276167332561481202109322625633216414875648000000⟩, + ⟨6, 3, 5, 7, 1, 6, -126709376456024875271763747331220077718091595776000000⟩, + ⟨6, 3, 6, 7, 2, 6, -470673498603930804851073743275136699853692731392000000⟩, + ⟨6, 3, 7, 7, 3, 6, 925394720784485571278490745178155142017902968832000000⟩, + ⟨6, 3, 8, 7, 4, 6, 164208812002321277237512838716503178349767557120000000⟩ +] + +def collectedFourData_14_3_49 : List CollectedFourTerm := [ + ⟨6, 4, 4, 0, 7, 7, 9167921513629164671702698440365495315285724364800000⟩, + ⟨6, 4, 5, 0, 8, 7, 864237433565456177082016106519842641414193152000000⟩, + ⟨6, 4, 4, 1, 6, 7, 20541042926348294444057596504379156477183734579200000⟩, + ⟨6, 4, 5, 1, 7, 7, -6854730752160113242224678488334615846278135808000000⟩, + ⟨6, 4, 6, 1, 8, 7, -1874729212868847672115068758087333303034052608000000⟩, + ⟨6, 4, 4, 2, 5, 7, -2606550697402249975126786446863351980672784793600000⟩, + ⟨6, 4, 5, 2, 6, 7, -4791100377509470297578528713288638112269860864000000⟩, + ⟨6, 4, 6, 2, 7, 7, -2508602115079138379647254692649375702410330112000000⟩, + ⟨6, 4, 7, 2, 8, 7, -3921619725374832207707412353327008590757625856000000⟩, + ⟨6, 4, 4, 3, 4, 7, 1788354138168365962554619817463088474607950233600000⟩, + ⟨6, 4, 5, 3, 5, 7, 1810364039699826306024464713933991535496396800000000⟩, + ⟨6, 4, 6, 3, 6, 7, 6647062118548020868813903447721334717303226368000000⟩, + ⟨6, 4, 7, 3, 7, 7, 2189750554809346848221019713987717933819756544000000⟩, + ⟨6, 4, 8, 3, 8, 7, 2477235841275341268590873965704089608126464000000000⟩, + ⟨6, 4, 4, 4, 3, 7, 3997231912573080133186287818586373661562765312000000⟩, + ⟨6, 4, 5, 4, 4, 7, -6522031651206532598775388175673989193837576192000000⟩, + ⟨6, 4, 6, 4, 5, 7, -5288410972717782043162036564227710453947564032000000⟩, + ⟨6, 4, 7, 4, 6, 7, -719169572368035473878586704047780199000965120000000⟩, + ⟨6, 4, 8, 4, 7, 7, 879979723091577906572798032357549112775671808000000⟩, + ⟨6, 4, 4, 5, 2, 7, -27387679979794347232927508086107410527270679347200000⟩, + ⟨6, 4, 5, 5, 3, 7, 17009833487123426013704416355672121794724102144000000⟩, + ⟨6, 4, 6, 5, 4, 7, -5964698808307355349137469556567360950981623808000000⟩, + ⟨6, 4, 7, 5, 5, 7, -1904678831117955865831494386298464362945314816000000⟩, + ⟨6, 4, 8, 5, 6, 7, 1832348740133996883139612322247766224836493312000000⟩, + ⟨6, 4, 4, 6, 1, 7, 14696396402088647373786709291381684079298399436800000⟩, + ⟨6, 4, 5, 6, 2, 7, 251744253113118159872583424251072796296216576000000⟩, + ⟨6, 4, 6, 6, 3, 7, 22086022853667483312033873624917751508959756288000000⟩, + ⟨6, 4, 7, 6, 4, 7, 681847556266532127367335832941036679339180032000000⟩, + ⟨6, 4, 8, 6, 5, 7, -1922968257814456922821240303134255099678818304000000⟩, + ⟨6, 4, 4, 7, 0, 7, 280425356843790180038783145094500305777370700185600000⟩, + ⟨6, 4, 5, 7, 1, 7, -11735450868409759741388812138721943012708974592000000⟩, + ⟨6, 4, 6, 7, 2, 7, -21796199588457215690252652959131352209117151232000000⟩, + ⟨6, 4, 7, 7, 3, 7, 28569115097337434848286112364164349396305051648000000⟩, + ⟨6, 4, 8, 7, 4, 7, 3802134655129436285410061746705583012849909760000000⟩ +] + +def collectedFourData_14_3_50 : List CollectedFourTerm := [ + ⟨6, 5, 3, 0, 6, 8, 7209196984808717875653115731017949589683988070400000⟩, + ⟨6, 5, 4, 0, 7, 8, -103422660381006268535674870590463049109950850662400000⟩, + ⟨6, 5, 5, 0, 8, 8, -4874700031371148996719289733402802788801445888000000⟩, + ⟨6, 5, 3, 1, 5, 8, -96649579279446950494760915014379924707465179955200000⟩, + ⟨6, 5, 4, 1, 6, 8, -231722021538383942910098724238915232880016333209600000⟩, + ⟨6, 5, 5, 1, 7, 8, 38663861243248144066961072124462497966013284352000000⟩, + ⟨6, 5, 6, 1, 8, 8, 7049561611853065825994575539186361588009402368000000⟩, + ⟨6, 5, 3, 2, 4, 8, 125858522671247024824016135978035040644028065382400000⟩, + ⟨6, 5, 4, 2, 5, 8, 29404310141895494240120503538655962229581335756800000⟩, + ⟨6, 5, 5, 2, 6, 8, 27024028644761137919690356203448099270784188416000000⟩, + ⟨6, 5, 6, 2, 7, 8, 9433119753232584048053416861455167699395018752000000⟩, + ⟨6, 5, 7, 2, 8, 8, 11059877214206862235643723842707568528176709632000000⟩, + ⟨6, 5, 3, 3, 3, 8, -168227760121534498957071288858653380138910298931200000⟩, + ⟨6, 5, 4, 3, 4, 8, -20174293856878606518827887025902860636171062476800000⟩, + ⟨6, 5, 5, 3, 5, 8, -10211292983121577688481125106692130130309939200000000⟩, + ⟨6, 5, 6, 3, 6, 8, -24995009210323215973086225227745809175127523328000000⟩, + ⟨6, 5, 7, 3, 7, 8, -6175604459868406685585023624007806780774023168000000⟩, + ⟨6, 5, 8, 3, 8, 8, -5589103718111065760451506684824476761613926400000000⟩, + ⟨6, 5, 3, 4, 2, 8, 230296172422923673283753864374716542033256775680000000⟩, + ⟨6, 5, 4, 4, 3, 8, -45092484479016635431242795988743252689452793856000000⟩, + ⟨6, 5, 5, 4, 4, 8, 36787283980024635412887083270369550545241243648000000⟩, + ⟨6, 5, 6, 4, 5, 8, 19886060730831482733442728651737727933005955072000000⟩, + ⟨6, 5, 7, 4, 6, 8, 2028224999766871717948247396757508834606448640000000⟩, + ⟨6, 5, 8, 4, 7, 8, -1985397538758935739239803073555152156733787340800000⟩, + ⟨6, 5, 3, 5, 1, 8, -191243080285478534084398852999007162719238986137600000⟩, + ⟨6, 5, 4, 5, 2, 8, 308958439594308256980659767509446048546578602393600000⟩, + ⟨6, 5, 5, 5, 3, 8, -95943351459814429017027113226733714461463412736000000⟩, + ⟨6, 5, 6, 5, 4, 8, 22429112138794463402500809451797499023949037568000000⟩, + ⟨6, 5, 7, 5, 5, 8, 5371636078929141488212481637664675800129994752000000⟩, + ⟨6, 5, 8, 5, 6, 8, -4134118756769899124431814871541698934636491571200000⟩, + ⟨6, 5, 3, 6, 0, 8, -104151079234627919792037866450007494419390503321600000⟩, + ⟨6, 5, 4, 6, 1, 8, -165788986266766270489503453122004087759561975398400000⟩, + ⟨6, 5, 5, 6, 2, 8, -1419954367731143623123024740325107337154002944000000⟩, + ⟨6, 5, 6, 6, 3, 8, -83050276167332561481202109322625633216414875648000000⟩, + ⟨6, 5, 7, 6, 4, 8, -1922968257814456922821240303134255099678818304000000⟩, + ⟨6, 5, 8, 6, 5, 8, 4338573203440806919787957788309693554470839910400000⟩, + ⟨6, 5, 4, 7, 0, 8, -3163458194964094210897683642426553664740935912652800000⟩, + ⟨6, 5, 5, 7, 1, 8, 66193386787681729711464197651479588463337013248000000⟩, + ⟨6, 5, 6, 7, 2, 8, 81960451060525978693707385581693276042163126272000000⟩, + ⟨6, 5, 7, 7, 3, 8, -80571530954571265560711434210139647379983302656000000⟩, + ⟨6, 5, 8, 7, 4, 8, -8578321281998963790494736442086991391071666176000000⟩ +] + +def collectedFourData_14_3_51 : List CollectedFourTerm := [ + ⟨7, 0, 7, 2, 8, 4, -1612855543422972906101557650905417400304066677964800000⟩, + ⟨7, 0, 7, 3, 7, 4, 900584852270503438413741749284366996727781339955200000⟩, + ⟨7, 0, 8, 3, 8, 4, 4075278929381781960121788898025472643620981964800000000⟩, + ⟨7, 0, 7, 4, 6, 4, -295774887082925650105028755822898310980038557696000000⟩, + ⟨7, 0, 8, 4, 7, 4, 1447646915181107144925146710980281414208376641945600000⟩, + ⟨7, 0, 7, 5, 5, 4, -783342604927192808687648765759713184065962953932800000⟩, + ⟨7, 0, 8, 5, 6, 4, 3014380822175965113711453557380026588965957428838400000⟩, + ⟨7, 0, 7, 6, 4, 4, 280425356843790180038783145094500305777370700185600000⟩, + ⟨7, 0, 8, 6, 5, 4, -3163458194964094210897683642426553664740935912652800000⟩, + ⟨7, 0, 7, 7, 3, 4, 11749700093887981948029980850807896344740787283558400000⟩, + ⟨7, 0, 8, 7, 4, 4, 6254858333853340714023107694328526852086334226432000000⟩ +] + +def collectedFourData_14_3_52 : List CollectedFourTerm := [ + ⟨7, 1, 6, 1, 8, 5, 10755479660615332183783128169950592179074236416000000⟩, + ⟨7, 1, 6, 2, 7, 5, 14392061978925288226111558455107996568753537024000000⟩, + ⟨7, 1, 7, 2, 8, 5, 67495989666248900402717186241454604706524430336000000⟩, + ⟨7, 1, 6, 3, 6, 5, -38134756170725633474217719019479340413601447936000000⟩, + ⟨7, 1, 7, 3, 7, 5, -37688351030758767269553808361001681153177944064000000⟩, + ⟨7, 1, 8, 3, 8, 5, -85272666118895740037481815573191552734855168000000000⟩, + ⟨7, 1, 6, 4, 5, 5, 30340059920973887680562667268998384356230692864000000⟩, + ⟨7, 1, 7, 4, 6, 5, 12377809533838460437584708721445333285700894720000000⟩, + ⟨7, 1, 8, 4, 7, 5, -30291107478872480383613839856692638458258128896000000⟩, + ⟨7, 1, 6, 5, 4, 5, 34219980290526523472189398687760004742241058816000000⟩, + ⟨7, 1, 7, 5, 5, 5, 32781909441862792595567355763141645511316996096000000⟩, + ⟨7, 1, 8, 5, 6, 5, -63074035877982715603780152613234512542558060544000000⟩, + ⟨7, 1, 6, 6, 3, 5, -126709376456024875271763747331220077718091595776000000⟩, + ⟨7, 1, 7, 6, 4, 5, -11735450868409759741388812138721943012708974592000000⟩, + ⟨7, 1, 8, 6, 5, 5, 66193386787681729711464197651479588463337013248000000⟩, + ⟨7, 1, 6, 7, 2, 5, 125046635931822978759077799167906422517623947264000000⟩, + ⟨7, 1, 7, 7, 3, 5, -491710270862495242194363923406691576223511871488000000⟩, + ⟨7, 1, 8, 7, 4, 5, -130879003760505832981162434617416812485274501120000000⟩ +] + +def collectedFourData_14_3_53 : List CollectedFourTerm := [ + ⟨7, 2, 5, 0, 8, 6, -9208848038776453739338027918392033223360118784000000⟩, + ⟨7, 2, 5, 1, 7, 6, 73040314376279981703950032135771921368571969536000000⟩, + ⟨7, 2, 6, 1, 8, 6, 39952207031672514044405159804244012918764470272000000⟩, + ⟨7, 2, 5, 2, 6, 6, 51051381948346934665430386390972268105158361088000000⟩, + ⟨7, 2, 6, 2, 7, 6, 53460622672200701851770451490129861203835486208000000⟩, + ⟨7, 2, 7, 2, 8, 6, 125359994999950034031876531592038115621214355456000000⟩, + ⟨7, 2, 5, 3, 5, 6, -19290262940454426229586790952059228028246425600000000⟩, + ⟨7, 2, 6, 3, 6, 6, -141655018810013402702780415706043438144906330112000000⟩, + ⟨7, 2, 7, 3, 7, 6, -69998403166385511243057365703586332511718866944000000⟩, + ⟨7, 2, 8, 3, 8, 6, -105584356948766106877232907327642027165745152000000000⟩, + ⟨7, 2, 5, 4, 4, 6, 69495252169613803688940134671983936490086334464000000⟩, + ⟨7, 2, 6, 4, 5, 6, 112700910937034850802971592550603606210786623488000000⟩, + ⟨7, 2, 7, 4, 6, 6, 22989249419780501549716495337883625904532357120000000⟩, + ⟨7, 2, 8, 4, 7, 6, -37506357546782510898874433797738612592574726144000000⟩, + ⟨7, 2, 5, 5, 3, 6, -181247612825077696528593247395928453330237390848000000⟩, + ⟨7, 2, 6, 5, 4, 6, 127113227891935016777835816521687622891520131072000000⟩, + ⟨7, 2, 7, 5, 5, 6, 60885691491322684141591731949775839835681980416000000⟩, + ⟨7, 2, 8, 5, 6, 6, -78098080210775608082642460505086454464843350016000000⟩, + ⟨7, 2, 5, 6, 2, 6, -2682451004222091864926325929293653226807099392000000⟩, + ⟨7, 2, 6, 6, 3, 6, -470673498603930804851073743275136699853692731392000000⟩, + ⟨7, 2, 7, 6, 4, 6, -21796199588457215690252652959131352209117151232000000⟩, + ⟨7, 2, 8, 6, 5, 6, 81960451060525978693707385581693276042163126272000000⟩, + ⟨7, 2, 5, 7, 1, 6, 125046635931822978759077799167906422517623947264000000⟩, + ⟨7, 2, 6, 7, 2, 6, 464497097759055299442643070901941499601814028288000000⟩, + ⟨7, 2, 7, 7, 3, 6, -913251252430627214692411873588812551476318568448000000⟩, + ⟨7, 2, 8, 7, 4, 6, -162053986102423734185981440121418115513508167680000000⟩ +] + +def collectedFourData_14_3_54 : List CollectedFourTerm := [ + ⟨7, 3, 4, 0, 7, 7, 384131911186089432003158971266572259233939796787200000⟩, + ⟨7, 3, 5, 0, 8, 7, 36211171374071174191976875061519042729453027328000000⟩, + ⟨7, 3, 4, 1, 6, 7, 860660735950191841255314897231818956233107098828800000⟩, + ⟨7, 3, 5, 1, 7, 7, -287210227593995993818277356892844141317940314112000000⟩, + ⟨7, 3, 6, 1, 8, 7, -78550336019470506855126600362746720423942029312000000⟩, + ⟨7, 3, 4, 2, 5, 7, -109213336906088692444950476931931757385812960870400000⟩, + ⟨7, 3, 5, 2, 6, 7, -200745015319025203599415794484872574341004394496000000⟩, + ⟨7, 3, 6, 2, 7, 7, -105109334044610140095259904292832072638312480768000000⟩, + ⟨7, 3, 7, 2, 8, 7, -164314155374676451252901290071420957662939971584000000⟩, + ⟨7, 3, 4, 3, 4, 7, 74931258077516894896992729760612614443211581030400000⟩, + ⟨7, 3, 5, 3, 5, 7, 75853463348114882776593431118125910820336435200000000⟩, + ⟨7, 3, 6, 3, 6, 7, 278509002457608603944665274402824039054234877952000000⟩, + ⟨7, 3, 7, 3, 7, 7, 91749592793660348607432636032996064923291222016000000⟩, + ⟨7, 3, 8, 3, 8, 7, 103795100858262846994110736501475733349072896000000000⟩, + ⟨7, 3, 4, 4, 3, 7, 167482273026452215613323065913144692281670893568000000⟩, + ⟨7, 3, 5, 4, 4, 7, -273270280430486488836271020800407162652498853888000000⟩, + ⟨7, 3, 6, 4, 5, 7, -221582112266950450834865991485657054755996827648000000⟩, + ⟨7, 3, 7, 4, 6, 7, -30132891287292324846332066014474286868914503680000000⟩, + ⟨7, 3, 8, 4, 7, 7, 36870766436389734441787339535338222972003418112000000⟩, + ⟨7, 3, 4, 5, 2, 7, -1147531841099588535148098460724970096677639474380800000⟩, + ⟨7, 3, 5, 5, 3, 7, 712704601217658485330925865642575685802489020416000000⟩, + ⟨7, 3, 6, 5, 4, 7, -249918277493793674007448578786540444173689946112000000⟩, + ⟨7, 3, 7, 5, 5, 7, -79805211956205000181931936773237426956244353024000000⟩, + ⟨7, 3, 8, 5, 6, 7, 76774612703732412622243263479358565583387885568000000⟩, + ⟨7, 3, 4, 6, 1, 7, 615772596775639325039878558978353514444651442995200000⟩, + ⟨7, 3, 5, 6, 2, 7, 10547974361985608565708003001422579682366193664000000⟩, + ⟨7, 3, 6, 6, 3, 7, 925394720784485571278490745178155142017902968832000000⟩, + ⟨7, 3, 7, 6, 4, 7, 28569115097337434848286112364164349396305051648000000⟩, + ⟨7, 3, 8, 6, 5, 7, -80571530954571265560711434210139647379983302656000000⟩, + ⟨7, 3, 4, 7, 0, 7, 11749700093887981948029980850807896344740787283558400000⟩, + ⟨7, 3, 5, 7, 1, 7, -491710270862495242194363923406691576223511871488000000⟩, + ⟨7, 3, 6, 7, 2, 7, -913251252430627214692411873588812551476318568448000000⟩, + ⟨7, 3, 7, 7, 3, 7, 1197033457029603073936935436717180921973280079872000000⟩, + ⟨7, 3, 8, 7, 4, 7, 159307783066260044018256829709774226314640752640000000⟩ +] + +def collectedFourData_14_3_55 : List CollectedFourTerm := [ + ⟨7, 4, 3, 0, 6, 8, -14254181045478615005554086537392029231875096576000000⟩, + ⟨7, 4, 4, 0, 7, 8, 204489533075926466788524857818498263385223725056000000⟩, + ⟨7, 4, 5, 0, 8, 8, 9638362904493209447666901546857450699457822720000000⟩, + ⟨7, 4, 3, 1, 5, 8, 191097649838337575009109183397014840597270233088000000⟩, + ⟨7, 4, 4, 1, 6, 8, 458165819881541037807716704915608995926716186624000000⟩, + ⟨7, 4, 5, 1, 7, 8, -76447027212580165517506908773649610856862842880000000⟩, + ⟨7, 4, 6, 1, 8, 8, -13938546514730286424499128353273749731981393920000000⟩, + ⟨7, 4, 3, 2, 4, 8, -248850207873745661243395349359503648716652281856000000⟩, + ⟨7, 4, 4, 2, 5, 8, -58138841422031455216864567585059497209277448192000000⟩, + ⟨7, 4, 5, 2, 6, 8, -53432497085644003644753763235997422462215127040000000⟩, + ⟨7, 4, 6, 2, 7, 8, -18651369503371322188639255050103886114067578880000000⟩, + ⟨7, 4, 7, 2, 8, 8, -21867829729756123248463008625708510216275886080000000⟩, + ⟨7, 4, 3, 3, 3, 8, 332623585497896507780650238000092251914426646528000000⟩, + ⟨7, 4, 4, 3, 4, 8, 39889052512589203217040700044757381602179284992000000⟩, + ⟨7, 4, 5, 3, 5, 8, 20189990535222191594143892692648633772802048000000000⟩, + ⟨7, 4, 6, 3, 6, 8, 49420675737965825851385973405492981124112056320000000⟩, + ⟨7, 4, 7, 3, 7, 8, 12210539429248942995323799869582261859825745920000000⟩, + ⟨7, 4, 8, 3, 8, 8, 11050897408933353595522916843115071422857216000000000⟩, + ⟨7, 4, 3, 4, 2, 8, -455346600004745634788529564967844968586752819200000000⟩, + ⟨7, 4, 4, 4, 3, 8, 89157840867541763518117186662328671868173680640000000⟩, + ⟨7, 4, 5, 4, 4, 8, -72736617840748247724599505826737204413721477120000000⟩, + ⟨7, 4, 6, 4, 5, 8, -39319151708014507277560037514789942757876039680000000⟩, + ⟨7, 4, 7, 4, 6, 8, -4010250574171250840005121880629762999294361600000000⟩, + ⟨7, 4, 8, 4, 7, 8, 3925571186964647393194064485482994328143921152000000⟩, + ⟨7, 4, 3, 5, 1, 8, 378129977004164579990851031679981238377139666944000000⟩, + ⟨7, 4, 4, 5, 2, 8, -610879345201120023313224118586219258415188803584000000⟩, + ⟨7, 4, 5, 5, 3, 8, 189701280836129948666326037683584469911302307840000000⟩, + ⟨7, 4, 6, 5, 4, 8, -44347328251594613650417432752389109283993681920000000⟩, + ⟨7, 4, 7, 5, 5, 8, -10620915663814730600239830948773124765521018880000000⟩, + ⟨7, 4, 8, 5, 6, 8, 8174069504090637104025850171103421892424368128000000⟩, + ⟨7, 4, 3, 6, 0, 8, 205929778673091058119375913642930403097553403904000000⟩, + ⟨7, 4, 4, 6, 1, 8, 327801588800053681306040190293464253810287312896000000⟩, + ⟨7, 4, 5, 6, 2, 8, 2807564653401529364318639445997333459092111360000000⟩, + ⟨7, 4, 6, 6, 3, 8, 164208812002321277237512838716503178349767557120000000⟩, + ⟨7, 4, 7, 6, 4, 8, 3802134655129436285410061746705583012849909760000000⟩, + ⟨7, 4, 8, 6, 5, 8, -8578321281998963790494736442086991391071666176000000⟩, + ⟨7, 4, 4, 7, 0, 8, 6254858333853340714023107694328526852086334226432000000⟩, + ⟨7, 4, 5, 7, 1, 8, -130879003760505832981162434617416812485274501120000000⟩, + ⟨7, 4, 6, 7, 2, 8, -162053986102423734185981440121418115513508167680000000⟩, + ⟨7, 4, 7, 7, 3, 8, 159307783066260044018256829709774226314640752640000000⟩, + ⟨7, 4, 8, 7, 4, 8, 16961243378084754237723838741558833848977981440000000⟩ +] + +def collectedFourData_14_3 : List (List CollectedFourTerm) := [ + collectedFourData_14_3_0, + collectedFourData_14_3_1, + collectedFourData_14_3_2, + collectedFourData_14_3_3, + collectedFourData_14_3_4, + collectedFourData_14_3_5, + collectedFourData_14_3_6, + collectedFourData_14_3_7, + collectedFourData_14_3_8, + collectedFourData_14_3_9, + collectedFourData_14_3_10, + collectedFourData_14_3_11, + collectedFourData_14_3_12, + collectedFourData_14_3_13, + collectedFourData_14_3_14, + collectedFourData_14_3_15, + collectedFourData_14_3_16, + collectedFourData_14_3_17, + collectedFourData_14_3_18, + collectedFourData_14_3_19, + collectedFourData_14_3_20, + collectedFourData_14_3_21, + collectedFourData_14_3_22, + collectedFourData_14_3_23, + collectedFourData_14_3_24, + collectedFourData_14_3_25, + collectedFourData_14_3_26, + collectedFourData_14_3_27, + collectedFourData_14_3_28, + collectedFourData_14_3_29, + collectedFourData_14_3_30, + collectedFourData_14_3_31, + collectedFourData_14_3_32, + collectedFourData_14_3_33, + collectedFourData_14_3_34, + collectedFourData_14_3_35, + collectedFourData_14_3_36, + collectedFourData_14_3_37, + collectedFourData_14_3_38, + collectedFourData_14_3_39, + collectedFourData_14_3_40, + collectedFourData_14_3_41, + collectedFourData_14_3_42, + collectedFourData_14_3_43, + collectedFourData_14_3_44, + collectedFourData_14_3_45, + collectedFourData_14_3_46, + collectedFourData_14_3_47, + collectedFourData_14_3_48, + collectedFourData_14_3_49, + collectedFourData_14_3_50, + collectedFourData_14_3_51, + collectedFourData_14_3_52, + collectedFourData_14_3_53, + collectedFourData_14_3_54, + collectedFourData_14_3_55 +] + +theorem collectedFourChecked_14_3 : collectNumericRowParts 14 3 = collectedFourData_14_3 := by + decide +kernel + +def collectedFourData_14_4_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_4_1 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_4_2 : List CollectedFourTerm := [ + ⟨0, 6, 8, 4, 8, 2, 45102410067031517106956329800573567057814093824000000⟩, + ⟨0, 6, 8, 5, 7, 2, -73945502230882176704741587495552205659981637222400000⟩, + ⟨0, 6, 8, 6, 6, 2, 110455096514753353785500731339940167168268068454400000⟩, + ⟨0, 6, 8, 7, 5, 2, 285317205433035913154325109653115394643097288704000000⟩ +] + +def collectedFourData_14_4_3 : List CollectedFourTerm := [ + ⟨0, 7, 7, 3, 8, 3, 4550011238424178433172065952302591079105744076800000⟩, + ⟨0, 7, 7, 4, 7, 3, 12035156668414996071424829021160048584505792921600000⟩, + ⟨0, 7, 8, 4, 8, 3, -12891384136865177065188239394919048286708957184000000⟩, + ⟨0, 7, 7, 5, 6, 3, -3812714302362090355627340501388315381410562048000000⟩, + ⟨0, 7, 8, 5, 7, 3, 21135453139532489859739059288781517391531501158400000⟩, + ⟨0, 7, 7, 6, 5, 3, -23820667576824654925738256917388737361380324147200000⟩, + ⟨0, 7, 8, 6, 6, 3, -31570798033408081801488226935777228158602208870400000⟩, + ⟨0, 7, 7, 7, 4, 3, -18522701781694858540660016765006156319890079744000000⟩, + ⟨0, 7, 8, 7, 5, 3, -81550712935909058392940233914250665191238795264000000⟩ +] + +def collectedFourData_14_4_4 : List CollectedFourTerm := [ + ⟨0, 8, 6, 2, 8, 4, 51748874512887023613352454342889231577337403801600000⟩, + ⟨0, 8, 6, 3, 7, 4, 109721457537793549203009094675679762730241228800000⟩, + ⟨0, 8, 7, 3, 8, 4, -17560869741080392331650627317006657515024075980800000⟩, + ⟨0, 8, 6, 4, 6, 4, 22173478409861080334745913983900106259912510668800000⟩, + ⟨0, 8, 7, 4, 7, 4, -46449955284226429858830370561637542717239695769600000⟩, + ⟨0, 8, 8, 4, 8, 4, 24877292136988633669521350870974313363618660352000000⟩, + ⟨0, 8, 6, 5, 5, 4, 18523309059832731088348913293074180259155699302400000⟩, + ⟨0, 8, 7, 5, 6, 4, 14715255790648000197164663998727255354127679488000000⟩, + ⟨0, 8, 8, 5, 7, 4, -40786376126686533491842297388646278170689090355200000⟩, + ⟨0, 8, 6, 6, 4, 4, -12350569381555534344861562686874521773338420838400000⟩, + ⟨0, 8, 7, 6, 5, 4, 91936397196036428260364560647711486039842566963200000⟩, + ⟨0, 8, 8, 6, 6, 4, 60924099176362403856604075914240148839964291891200000⟩, + ⟨0, 8, 6, 7, 3, 4, -62348027646184926036255418883095281914287541452800000⟩, + ⟨0, 8, 7, 7, 4, 4, 71488780180216582019005789705653772921092440064000000⟩, + ⟨0, 8, 8, 7, 5, 4, 157373396692501741262412701372433388435346030592000000⟩ +] + +def collectedFourData_14_4_5 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_4_6 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_4_7 : List CollectedFourTerm := [ + ⟨1, 5, 8, 4, 8, 2, -22022947094505556412784055408634576036192845824000000⟩, + ⟨1, 5, 8, 5, 7, 2, 36106671042347312166136905074456317185587832422400000⟩, + ⟨1, 5, 8, 6, 6, 2, -53933852830650295728832720625423601791846999654400000⟩, + ⟨1, 5, 8, 7, 5, 2, -139316850497906949332557848694763760012654280704000000⟩ +] + +def collectedFourData_14_4_8 : List CollectedFourTerm := [ + ⟨1, 6, 7, 3, 8, 3, -21574813538347077669577071363997839878142925209600000⟩, + ⟨1, 6, 7, 4, 7, 3, -57067169160614127250941770207764512571575710515200000⟩, + ⟨1, 6, 8, 4, 8, 3, 61127147699177344505565773902545902081459355648000000⟩, + ⟨1, 6, 7, 5, 6, 3, 18078768565182725523135373119530311632348512256000000⟩, + ⟨1, 6, 8, 5, 7, 3, -100218095437454709499713591779871251315645271244800000⟩, + ⟨1, 6, 7, 6, 5, 3, 112950591635666337435199040212130708758502729318400000⟩, + ⟨1, 6, 8, 6, 6, 3, 149699428228993466416698706020522415079815957708800000⟩, + ⟨1, 6, 7, 7, 4, 3, 87829197825207771338790771883572446479377235968000000⟩, + ⟨1, 6, 8, 7, 5, 3, 386689468072799862842827479297178761776917905408000000⟩ +] + +def collectedFourData_14_4_9 : List CollectedFourTerm := [ + ⟨1, 7, 6, 2, 8, 4, -60352007271933996383253787080123490478891571609600000⟩, + ⟨1, 7, 6, 3, 7, 4, -127962400449096897887001578259984211260525772800000⟩, + ⟨1, 7, 7, 3, 8, 4, 20480324418480620092137320475991562527047470284800000⟩, + ⟨1, 7, 6, 4, 6, 4, -25859768793672062104878820513466584035652062412800000⟩, + ⟨1, 7, 7, 4, 7, 4, 54172154766313316032189380984159643633186347417600000⟩, + ⟨1, 7, 8, 4, 8, 4, -29013085406981597858952852857310970210116698112000000⟩, + ⟨1, 7, 6, 5, 5, 4, -21602767086285335438568522317527251535039719014400000⟩, + ⟨1, 7, 7, 5, 6, 4, -17161633617063392938550027356242765994606460928000000⟩, + ⟨1, 7, 8, 5, 7, 4, 47567018447534033310727604083843852665556775731200000⟩, + ⟨1, 7, 6, 6, 4, 4, 14403823467552759163022191852831428586294896230400000⟩, + ⟨1, 7, 7, 6, 5, 4, -107220614252177565823482914251164283224970179379200000⟩, + ⟨1, 7, 8, 6, 6, 4, -71052592179800845020456043317030114328006832947200000⟩, + ⟨1, 7, 6, 7, 3, 4, 72713245521044852711570152006009547561429159116800000⟩, + ⟨1, 7, 7, 7, 4, 4, -83373627386305458790976898787001933024024592384000000⟩, + ⟨1, 7, 8, 7, 5, 4, -183536366172168268865650732230154879532953239552000000⟩ +] + +def collectedFourData_14_4_10 : List CollectedFourTerm := [ + ⟨1, 8, 5, 1, 8, 5, 326046494093123283454160351949017954601507225600000000⟩, + ⟨1, 8, 5, 2, 7, 5, 167127656181059991131337234382958863918489927680000000⟩, + ⟨1, 8, 6, 2, 8, 5, -296248772797392585766138321525213986619454914560000000⟩, + ⟨1, 8, 5, 3, 6, 5, -114351245307142334454437338320999700900211589120000000⟩, + ⟨1, 8, 6, 3, 7, 5, -628126649150946777039944438380422083200942080000000⟩, + ⟨1, 8, 7, 3, 8, 5, 50265693302705367626934111341978599717223792640000000⟩, + ⟨1, 8, 5, 4, 5, 5, -69337087646580314546416151010817607146647060480000000⟩, + ⟨1, 8, 6, 4, 6, 5, -126937364907037354125583277411075823983740846080000000⟩, + ⟨1, 8, 7, 4, 7, 5, 132956923015002024396950054139459973211152711680000000⟩, + ⟨1, 8, 8, 4, 8, 5, -47471997123787935798840589985530599497426534400000000⟩, + ⟨1, 8, 5, 5, 4, 5, -45993830396738671246493247166627950744054005760000000⟩, + ⟨1, 8, 6, 5, 5, 5, -106041100000266020448534584745944424229204131840000000⟩, + ⟨1, 8, 7, 5, 6, 5, -42120495473709088767033476907780744717690470400000000⟩, + ⟨1, 8, 8, 5, 7, 5, 77830445512876146591990075494130308045277757440000000⟩, + ⟨1, 8, 5, 6, 3, 5, 419121234141443571086694266211349228053866741760000000⟩, + ⟨1, 8, 6, 6, 4, 5, 70703779687492868582595658032256167823477309440000000⟩, + ⟨1, 8, 7, 6, 5, 5, -263155914994410589978306221147099685244696002560000000⟩, + ⟨1, 8, 8, 6, 6, 5, -116258178138665494946782799477936631189224816640000000⟩, + ⟨1, 8, 5, 7, 2, 5, -23219198701692593893607589337398670697724641280000000⟩, + ⟨1, 8, 6, 7, 3, 5, 356926152508311539215484231963909457879477780480000000⟩, + ⟨1, 8, 7, 7, 4, 5, -204627285100641667948559519387436556381008691200000000⟩, + ⟨1, 8, 8, 7, 5, 5, -300307179495602266905524002440490487311132262400000000⟩ +] + +def collectedFourData_14_4_11 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_4_12 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_4_13 : List CollectedFourTerm := [ + ⟨2, 4, 8, 4, 8, 2, -81135341561541550757978999065356405973180219392000000⟩, + ⟨2, 4, 8, 5, 7, 2, 133021574047278631357486715961926297761894052659200000⟩, + ⟨2, 4, 8, 6, 6, 2, -198699181919956017079604453790500063798178820915200000⟩, + ⟨2, 4, 8, 7, 5, 2, -513261018242466926959527537172080684622185234432000000⟩ +] + +def collectedFourData_14_4_14 : List CollectedFourTerm := [ + ⟨2, 5, 7, 3, 8, 3, -9181146796390062801603834152468655060142365081600000⟩, + ⟨2, 5, 7, 4, 7, 3, -24284893882710386894745444417485287689907548979200000⟩, + ⟨2, 5, 8, 4, 8, 3, 26012614907343533263356137255574775564502827008000000⟩, + ⟨2, 5, 7, 5, 6, 3, 7693407305693978082926446114585916193349042176000000⟩, + ⟨2, 5, 8, 5, 7, 3, -42647740349203234780837748748300742107459275980800000⟩, + ⟨2, 5, 7, 6, 5, 3, 48066045192138872914572365011089591891422242406400000⟩, + ⟨2, 5, 8, 6, 6, 3, 63704486876012466607653268883102367621069982924800000⟩, + ⟨2, 5, 7, 7, 4, 3, 37375653643966299295767746728260256978308169728000000⟩, + ⟨2, 5, 8, 7, 5, 3, 164555432411230066259045906944538817650352979968000000⟩ +] + +def collectedFourData_14_4_15 : List CollectedFourTerm := [ + ⟨2, 6, 6, 2, 8, 4, 39789668586611665739359909313174183206572785664000000⟩, + ⟨2, 6, 6, 3, 7, 4, 84364741713978326819890511584223995417853952000000⟩, + ⟨2, 6, 7, 3, 8, 4, -13502538821713664249791230530517893132197036032000000⟩, + ⟨2, 6, 6, 4, 6, 4, 17049169970277292927215015773977767851486871552000000⟩, + ⟨2, 6, 7, 4, 7, 4, -35715333792661260174116555240795441462859792384000000⟩, + ⟨2, 6, 8, 4, 8, 4, 19128130201490534204015788918033644959909806080000000⟩, + ⟨2, 6, 6, 5, 5, 4, 14242557650883431510586159637121306690108522496000000⟩, + ⟨2, 6, 7, 5, 6, 4, 11314548511220109531143254614837440223400427520000000⟩, + ⟨2, 6, 8, 5, 7, 4, -31360612268496819114889662624076479332150673408000000⟩, + ⟨2, 6, 6, 6, 4, 4, -9496343005984961399109165359365985443497639936000000⟩, + ⟨2, 6, 7, 6, 5, 4, 70689822917141938622668183101395360744082505728000000⟩, + ⟨2, 6, 8, 6, 6, 4, 46844491556268237868844706096058956271318990848000000⟩, + ⟨2, 6, 6, 7, 3, 4, -47939349027828701931459166310129191088566566912000000⟩, + ⟨2, 6, 7, 7, 4, 4, 54967666404485391752767757042213244312810946560000000⟩, + ⟨2, 6, 8, 7, 5, 4, 121004279951723930499169498931469924643299655680000000⟩ +] + +def collectedFourData_14_4_16 : List CollectedFourTerm := [ + ⟨2, 7, 5, 1, 8, 5, 167127656181059991131337234382958863918489927680000000⟩, + ⟨2, 7, 5, 2, 7, 5, 85667700670312812155917179874227559490654306304000000⟩, + ⟨2, 7, 6, 2, 8, 5, -151853689400513755515601510918120206074923450368000000⟩, + ⟨2, 7, 5, 3, 6, 5, -58615123780811766957277821185444466516333428736000000⟩, + ⟨2, 7, 6, 3, 7, 5, -321970444581679156401006401454139925933850624000000⟩, + ⟨2, 7, 7, 3, 8, 5, 25765612144867210657906065508927181805733281792000000⟩, + ⟨2, 7, 5, 4, 5, 5, -35541387976047263104139015854044175444312326144000000⟩, + ⟨2, 7, 6, 4, 6, 5, -65066622899045408830930100464523374211654221824000000⟩, + ⟨2, 7, 7, 4, 7, 5, 68152178658901223527316302033762932799259541504000000⟩, + ⟨2, 7, 8, 4, 8, 5, -24333595843746979797741353549956907486486200320000000⟩, + ⟨2, 7, 5, 5, 4, 5, -23575904701495305873478057636284986797722697728000000⟩, + ⟨2, 7, 6, 5, 5, 5, -54355439555329501548422217841016176582487703552000000⟩, + ⟨2, 7, 7, 5, 6, 5, -21590478085911790107279398424752443754670981120000000⟩, + ⟨2, 7, 8, 5, 7, 5, 39894984837283777052788257145359537470787551232000000⟩, + ⟨2, 7, 5, 6, 3, 5, 214836689818128899942430702023240265017252118528000000⟩, + ⟨2, 7, 6, 6, 4, 5, 36241938485428869710796214410786447538186616832000000⟩, + ⟨2, 7, 7, 6, 5, 5, -134890673814872059893130793219229264475500576768000000⟩, + ⟨2, 7, 8, 6, 6, 5, -59592595461694655371204058081101482644043988992000000⟩, + ⟨2, 7, 5, 7, 2, 5, -11901892299776887251947436560485760512907280384000000⟩, + ⟨2, 7, 6, 7, 3, 5, 182956211396648819480769378954731107445473542144000000⟩, + ⟨2, 7, 7, 7, 4, 5, -104889576085415961444247174478392014683882127360000000⟩, + ⟨2, 7, 8, 7, 5, 5, -153933981664314558231697343412014526700946718720000000⟩ +] + +def collectedFourData_14_4_17 : List CollectedFourTerm := [ + ⟨2, 8, 4, 0, 8, 6, 51748874512887023613352454342889231577337403801600000⟩, + ⟨2, 8, 4, 1, 7, 6, -60352007271933996383253787080123490478891571609600000⟩, + ⟨2, 8, 5, 1, 8, 6, -296248772797392585766138321525213986619454914560000000⟩, + ⟨2, 8, 4, 2, 6, 6, 39789668586611665739359909313174183206572785664000000⟩, + ⟨2, 8, 5, 2, 7, 6, -151853689400513755515601510918120206074923450368000000⟩, + ⟨2, 8, 6, 2, 8, 6, 134587147805513190209801319513907769416328675328000000⟩, + ⟨2, 8, 4, 3, 5, 6, 109170711513433145590672662143105956928403642777600000⟩, + ⟨2, 8, 5, 3, 6, 6, 103900568488919106432527848439250908691208077312000000⟩, + ⟨2, 8, 6, 3, 7, 6, 285360757351310296413576609346707839363579904000000⟩, + ⟨2, 8, 7, 3, 8, 6, -15223953459107447618051937089339285700700274688000000⟩, + ⟨2, 8, 4, 4, 4, 6, -81819713128967605216547841762575501107925090304000000⟩, + ⟨2, 8, 5, 4, 5, 6, 63000300560747244056958950577918822032917659648000000⟩, + ⟨2, 8, 6, 4, 6, 6, 57668214897449743635357522730142543221415215104000000⟩, + ⟨2, 8, 7, 4, 7, 6, -40268618118067044885531020922007454473053536256000000⟩, + ⟨2, 8, 8, 4, 8, 6, 10783370734655710596893232309358071333110415360000000⟩, + ⟨2, 8, 4, 5, 3, 6, -77964687308838674446896432277939568828990305075200000⟩, + ⟨2, 8, 5, 5, 4, 6, 41790407374825455290432567462991340675610443776000000⟩, + ⟨2, 8, 6, 5, 5, 6, 48174947914317975303660442517076892864575700992000000⟩, + ⟨2, 8, 7, 5, 6, 6, 12757020158951645118366668446318039962149191680000000⟩, + ⟨2, 8, 8, 5, 7, 6, -17679360449493476563120229374001936594827739136000000⟩, + ⟨2, 8, 4, 6, 2, 6, 98749881200159711729995543071083505526135534387200000⟩, + ⟨2, 8, 5, 6, 3, 6, -380817317521188674028465483772550483110187237376000000⟩, + ⟨2, 8, 6, 6, 4, 6, -32121044611776352209983112710864778426813775872000000⟩, + ⟨2, 8, 7, 6, 5, 6, 79701942600046053436111023186313554474829873152000000⟩, + ⟨2, 8, 8, 6, 6, 6, 26408306196510884077532553835902280552327151616000000⟩, + ⟨2, 8, 4, 7, 1, 6, 94860844726467021510510838595202787723634225971200000⟩, + ⟨2, 8, 5, 7, 2, 6, 21097172474888210827306248246851396285107273728000000⟩, + ⟨2, 8, 6, 7, 3, 6, -162153153883755322236301310926673832601215565824000000⟩, + ⟨2, 8, 7, 7, 4, 6, 61975396341902507238027231613839290330555351040000000⟩, + ⟨2, 8, 8, 7, 5, 6, 68215450096519579943824330764406564739151298560000000⟩ +] + +def collectedFourData_14_4_18 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_4_19 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_4_20 : List CollectedFourTerm := [ + ⟨3, 3, 8, 4, 8, 2, 92421061023796834928743167704889197299897466880000000⟩, + ⟨3, 3, 8, 5, 7, 2, -151524536359780931800068602302964841796482367488000000⟩, + ⟨3, 3, 8, 6, 6, 2, 226337732289862719864120107298143491296306659328000000⟩, + ⟨3, 3, 8, 7, 5, 2, 584654319254237722154991250021426862538337812480000000⟩ +] + +def collectedFourData_14_4_21 : List CollectedFourTerm := [ + ⟨3, 4, 7, 3, 8, 3, 1000365735989896162327166907735845259147686707200000⟩, + ⟨3, 4, 7, 4, 7, 3, 2646050246355518294104394680243795751711696486400000⟩, + ⟨3, 4, 8, 4, 8, 3, -2834300467457736860091960692502926269649780736000000⟩, + ⟨3, 4, 7, 5, 6, 3, -838263588668104005037901635152088762461192192000000⟩, + ⟨3, 4, 8, 5, 7, 3, 4646841958731287552378995350181936372607719833600000⟩, + ⟨3, 4, 7, 6, 5, 3, -5237213361370458081374851378372027161487658188800000⟩, + ⟨3, 4, 8, 6, 6, 3, -6941157495122290687072168342055554910216886681600000⟩, + ⟨3, 4, 7, 7, 4, 3, -4072402292963108698041260154918006614157950976000000⟩, + ⟨3, 4, 8, 7, 5, 3, -17929744497704908731150799967820734023971373056000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1407.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1407.lean new file mode 100644 index 0000000000000000000000000000000000000000..df682853ab9f97f3efa6b873e5ce63d8b32a98f8 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1407.lean @@ -0,0 +1,642 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1407. -/ +namespace LaughlinFock +def collectedFourData_14_4_22 : List CollectedFourTerm := [ + ⟨3, 5, 6, 2, 8, 4, 109170711513433145590672662143105956928403642777600000⟩, + ⟨3, 5, 6, 3, 7, 4, 231471113148729264037850681092806854035950796800000⟩, + ⟨3, 5, 7, 3, 8, 4, -37046847153188642497196974085009083370631384268800000⟩, + ⟨3, 5, 6, 4, 6, 4, 46777721013612706200072625627827261614930578636800000⟩, + ⟨3, 5, 7, 4, 7, 4, -97991979842640406191932542679429318585305635225600000⟩, + ⟨3, 5, 8, 4, 8, 4, 52481753635941421178461440156032095834783875072000000⟩, + ⟨3, 5, 6, 5, 5, 4, 39077233054442032477593454199797813867327153766400000⟩, + ⟨3, 5, 7, 5, 6, 4, 31043669256365158285026832275716346847237767168000000⟩, + ⟨3, 5, 8, 5, 7, 4, -86043952524919587950147644776115695684196447027200000⟩, + ⟨3, 5, 6, 6, 4, 4, -26055068050700646264383553888293258319293212262400000⟩, + ⟨3, 5, 7, 6, 5, 4, 193951307933729878058244598586148172130340254515200000⟩, + ⟨3, 5, 8, 6, 6, 4, 128526993446825969240935377474850131273667785523200000⟩, + ⟨3, 5, 6, 7, 3, 4, -131530948328125790090838914181676561152135187660800000⟩, + ⟨3, 5, 7, 7, 4, 4, 150814507000690644246173949100891381183077679104000000⟩, + ⟨3, 5, 8, 7, 5, 4, 331998828031085097745142803289980005107695091712000000⟩ +] + +def collectedFourData_14_4_23 : List CollectedFourTerm := [ + ⟨3, 6, 5, 1, 8, 5, -114351245307142334454437338320999700900211589120000000⟩, + ⟨3, 6, 5, 2, 7, 5, -58615123780811766957277821185444466516333428736000000⟩, + ⟨3, 6, 6, 2, 8, 5, 103900568488919106432527848439250908691208077312000000⟩, + ⟨3, 6, 5, 3, 6, 5, 40105345526455807584889529408812290676698906624000000⟩, + ⟨3, 6, 6, 3, 7, 5, 220297000097472179082355299987382212143087616000000⟩, + ⟨3, 6, 7, 3, 8, 5, -17629217702152480140251614949374757117129392128000000⟩, + ⟨3, 6, 5, 4, 5, 5, 24317949930454908006215433266954478827964727296000000⟩, + ⟨3, 6, 6, 4, 6, 5, 44519557842511448347567501347548703973668028416000000⟩, + ⟨3, 6, 7, 4, 7, 5, -46630741303505404796453003119926653510574145536000000⟩, + ⟨3, 6, 8, 4, 8, 5, 16649410702670465765482329332162561433277562880000000⟩, + ⟨3, 6, 5, 5, 4, 5, 16130987075758566363810425927173734950661783552000000⟩, + ⟨3, 6, 6, 5, 5, 5, 37190805785221235418828781521148264151638867968000000⟩, + ⟨3, 6, 7, 5, 6, 5, 14772528451101271532801122415073352015234990080000000⟩, + ⟨3, 6, 8, 5, 7, 5, -27296746103533053157979008203255576534699737088000000⟩, + ⟨3, 6, 5, 6, 3, 5, -146994480624753609646915211589483057090240970752000000⟩, + ⟨3, 6, 6, 6, 4, 5, -24797277080603849512767833557639225900152127488000000⟩, + ⟨3, 6, 7, 6, 5, 5, 92294219182607129423566968504793217886597414912000000⟩, + ⟨3, 6, 8, 6, 6, 5, 40774146289390763502971567187002216938815356928000000⟩, + ⟨3, 6, 5, 7, 2, 5, 8143452957399951475525307106863097263167635456000000⟩, + ⟨3, 6, 6, 7, 3, 5, -125181379838285051298655411667076720265103671296000000⟩, + ⟨3, 6, 7, 7, 4, 5, 71767018811724583771217843319203345065039626240000000⟩, + ⟨3, 6, 8, 7, 5, 5, 105323935610819752285948163142631630792273428480000000⟩ +] + +def collectedFourData_14_4_24 : List CollectedFourTerm := [ + ⟨3, 7, 4, 0, 8, 6, 109721457537793549203009094675679762730241228800000⟩, + ⟨3, 7, 4, 1, 7, 6, -127962400449096897887001578259984211260525772800000⟩, + ⟨3, 7, 5, 1, 8, 6, -628126649150946777039944438380422083200942080000000⟩, + ⟨3, 7, 4, 2, 6, 6, 84364741713978326819890511584223995417853952000000⟩, + ⟨3, 7, 5, 2, 7, 6, -321970444581679156401006401454139925933850624000000⟩, + ⟨3, 7, 6, 2, 8, 6, 285360757351310296413576609346707839363579904000000⟩, + ⟨3, 7, 4, 3, 5, 6, 231471113148729264037850681092806854035950796800000⟩, + ⟨3, 7, 5, 3, 6, 6, 220297000097472179082355299987382212143087616000000⟩, + ⟨3, 7, 6, 3, 7, 6, 605041143704047545514356971986944390070272000000⟩, + ⟨3, 7, 7, 3, 8, 6, -32278853960482264839942931260361152223248384000000⟩, + ⟨3, 7, 4, 4, 4, 6, -173479679787022841215759637062389423220457472000000⟩, + ⟨3, 7, 5, 4, 5, 6, 133577490678040613028297548263083253551857664000000⟩, + ⟨3, 7, 6, 4, 6, 6, 122272042662013117228492441014640418721103872000000⟩, + ⟨3, 7, 7, 4, 7, 6, -85380242846572828208334919835762176303300608000000⟩, + ⟨3, 7, 8, 4, 8, 6, 22863630664704949893370094202941646286356480000000⟩, + ⟨3, 7, 4, 5, 3, 6, -165305993773329157011901958035520299554412953600000⟩, + ⟨3, 7, 5, 5, 4, 6, 88606843171480514028302587076098046419795968000000⟩, + ⟨3, 7, 6, 5, 5, 6, 102143777071903783453999033879629962837753856000000⟩, + ⟨3, 7, 7, 5, 6, 6, 27048295423905639177568271113489830106890240000000⟩, + ⟨3, 7, 8, 5, 7, 6, -37484973636892826024047632706321305669992448000000⟩, + ⟨3, 7, 4, 6, 2, 6, 209376165162147549956989254333201238982236569600000⟩, + ⟨3, 7, 5, 6, 3, 6, -807434587271112879596836182125439976910880768000000⟩, + ⟨3, 7, 6, 6, 4, 6, -68105207419784905511111706422809406730141696000000⟩, + ⟨3, 7, 7, 6, 5, 6, 168989439731541232633680920383535470646132736000000⟩, + ⟨3, 7, 8, 6, 6, 6, 55992673739482784819811382573207679127257088000000⟩, + ⟨3, 7, 4, 7, 1, 6, 201130367464558222102933271375615300585757081600000⟩, + ⟨3, 7, 5, 7, 2, 6, 44731649444752578046014284425378119605551104000000⟩, + ⟨3, 7, 6, 7, 3, 6, -343808064541482927955676719725797223885176832000000⟩, + ⟨3, 7, 7, 7, 4, 6, 131404419557425732038846778489714628068638720000000⟩, + ⟨3, 7, 8, 7, 5, 6, 144635002821613700249132245759942583207854080000000⟩ +] + +def collectedFourData_14_4_25 : List CollectedFourTerm := [ + ⟨3, 8, 3, 0, 7, 7, 4550011238424178433172065952302591079105744076800000⟩, + ⟨3, 8, 4, 0, 8, 7, -17560869741080392331650627317006657515024075980800000⟩, + ⟨3, 8, 3, 1, 6, 7, -21574813538347077669577071363997839878142925209600000⟩, + ⟨3, 8, 4, 1, 7, 7, 20480324418480620092137320475991562527047470284800000⟩, + ⟨3, 8, 5, 1, 8, 7, 50265693302705367626934111341978599717223792640000000⟩, + ⟨3, 8, 3, 2, 5, 7, -9181146796390062801603834152468655060142365081600000⟩, + ⟨3, 8, 4, 2, 6, 7, -13502538821713664249791230530517893132197036032000000⟩, + ⟨3, 8, 5, 2, 7, 7, 25765612144867210657906065508927181805733281792000000⟩, + ⟨3, 8, 6, 2, 8, 7, -15223953459107447618051937089339285700700274688000000⟩, + ⟨3, 8, 3, 3, 4, 7, 1000365735989896162327166907735845259147686707200000⟩, + ⟨3, 8, 4, 3, 5, 7, -37046847153188642497196974085009083370631384268800000⟩, + ⟨3, 8, 5, 3, 6, 7, -17629217702152480140251614949374757117129392128000000⟩, + ⟨3, 8, 6, 3, 7, 7, -32278853960482264839942931260361152223248384000000⟩, + ⟨3, 8, 7, 3, 8, 7, 1291554000720725816163778414993825644398247936000000⟩, + ⟨3, 8, 3, 4, 3, 7, 14773371778837061076857908493141862935235762585600000⟩, + ⟨3, 8, 4, 4, 4, 7, 27765344426042593009025868808985009404722020352000000⟩, + ⟨3, 8, 5, 4, 5, 7, -10689508537240596930244896996163070151320666112000000⟩, + ⟨3, 8, 6, 4, 6, 7, -6523195074594024883573070527484674414775107584000000⟩, + ⟨3, 8, 7, 4, 7, 7, 3416267329874890085986225803912872293388255232000000⟩, + ⟨3, 8, 8, 4, 8, 7, -731862753049477996623245315096536976128475136000000⟩, + ⟨3, 8, 3, 5, 2, 7, 18447324044504205888773782098220422811710023270400000⟩, + ⟨3, 8, 4, 5, 3, 7, 26457149669866262509857223375922351269350054297600000⟩, + ⟨3, 8, 5, 5, 4, 7, -7090742622366000211603894216905990236320825344000000⟩, + ⟨3, 8, 6, 5, 5, 7, -5449355134580383222709980407353284058815660032000000⟩, + ⟨3, 8, 7, 5, 6, 7, -1082266867658627662128791075820858048994344960000000⟩, + ⟨3, 8, 8, 5, 7, 7, 1199890621319110399245184580183393128576293273600000⟩, + ⟨3, 8, 3, 6, 1, 7, 4491221279771877524616190587377359424167555891200000⟩, + ⟨3, 8, 4, 6, 2, 7, -33510560703524417563969720294468257135915014553600000⟩, + ⟨3, 8, 5, 6, 3, 7, 64614770573144174912363912099229088779016863744000000⟩, + ⟨3, 8, 6, 6, 4, 7, 3633402566300358135962042849955417298160320512000000⟩, + ⟨3, 8, 7, 6, 5, 7, -6761670883112268367545999117354010572220268544000000⟩, + ⟨3, 8, 8, 6, 6, 7, -1792320430404744090570632546741798700687399321600000⟩, + ⟨3, 8, 3, 7, 0, 7, -472072452064169827131115813316796641469804419481600000⟩, + ⟨3, 8, 4, 7, 1, 7, -32190824504898098002891407388314675766651099545600000⟩, + ⟨3, 8, 5, 7, 2, 7, -3579640148930743416537615679746668733118021632000000⟩, + ⟨3, 8, 6, 7, 3, 7, 18342108501631056624524974052360183095391944704000000⟩, + ⟨3, 8, 7, 7, 4, 7, -5257804505685193081197249756125887422403706880000000⟩, + ⟨3, 8, 8, 7, 5, 7, -4629753380146776000964589740616722216654995456000000⟩ +] + +def collectedFourData_14_4_26 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_4_27 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_4_28 : List CollectedFourTerm := [ + ⟨4, 2, 8, 4, 8, 2, -22036469487180104607121759789668287328571883520000000⟩, + ⟨4, 2, 8, 5, 7, 2, 36128841035396388258525777429157646301294231552000000⟩, + ⟨4, 2, 8, 6, 6, 2, -53966968958718791187001950473082429994709286912000000⟩, + ⟨4, 2, 8, 7, 5, 2, -139402392961889166823115221718443986173999185920000000⟩ +] + +def collectedFourData_14_4_29 : List CollectedFourTerm := [ + ⟨4, 3, 7, 3, 8, 3, 14773371778837061076857908493141862935235762585600000⟩, + ⟨4, 3, 7, 4, 7, 3, 39076792245599555955746582267324066484230239027200000⟩, + ⟨4, 3, 8, 4, 8, 3, -41856865976372999961866703152730224502692118528000000⟩, + ⟨4, 3, 7, 5, 6, 3, -12379452032912416857144509917204599556974575616000000⟩, + ⟨4, 3, 8, 5, 7, 3, 68624425431670427385405479348183657458772528332800000⟩, + ⟨4, 3, 7, 6, 5, 3, -77343012949216174999305801062656685538586027622400000⟩, + ⟨4, 3, 8, 6, 6, 3, -102506809821341888532462111425641594333772434636800000⟩, + ⟨4, 3, 7, 7, 4, 3, -60141117335850239047531343259622781764446978048000000⟩, + ⟨4, 3, 8, 7, 5, 3, -264785939616416580075487417947222799804570533888000000⟩ +] + +def collectedFourData_14_4_30 : List CollectedFourTerm := [ + ⟨4, 4, 6, 2, 8, 4, -81819713128967605216547841762575501107925090304000000⟩, + ⟨4, 4, 6, 3, 7, 4, -173479679787022841215759637062389423220457472000000⟩, + ⟨4, 4, 7, 3, 8, 4, 27765344426042593009025868808985009404722020352000000⟩, + ⟨4, 4, 6, 4, 6, 4, -35058301453771583264495585223887365979422851072000000⟩, + ⟨4, 4, 7, 4, 7, 4, 73441636209157269950980200933226876117633204224000000⟩, + ⟨4, 4, 8, 4, 8, 4, -39333278747290293053143589473077725947106426880000000⟩, + ⟨4, 4, 6, 5, 5, 4, -29287049191713296127599320038971913990838419456000000⟩, + ⟨4, 4, 7, 5, 6, 4, -23266167984201610093377703622516795788461342720000000⟩, + ⟨4, 4, 8, 5, 7, 4, 64486998522540226320736007800877462327276863488000000⟩, + ⟨4, 4, 6, 6, 4, 4, 19527382059809529502840359769383174697748791296000000⟩, + ⟨4, 4, 7, 6, 5, 4, -145359869475369289549579768960774089804777259008000000⟩, + ⟨4, 4, 8, 6, 6, 4, -96326584185118470031674753851899896972158435328000000⟩, + ⟨4, 4, 6, 7, 3, 4, 98577945591790903512675454092803483050319020032000000⟩, + ⟨4, 4, 7, 7, 4, 4, -113030313052093944284794087604581308626538332160000000⟩, + ⟨4, 4, 8, 7, 5, 4, -248821762651188479229915611443798470512061972480000000⟩ +] + +def collectedFourData_14_4_31 : List CollectedFourTerm := [ + ⟨4, 5, 5, 1, 8, 5, -69337087646580314546416151010817607146647060480000000⟩, + ⟨4, 5, 5, 2, 7, 5, -35541387976047263104139015854044175444312326144000000⟩, + ⟨4, 5, 6, 2, 8, 5, 63000300560747244056958950577918822032917659648000000⟩, + ⟨4, 5, 5, 3, 6, 5, 24317949930454908006215433266954478827964727296000000⟩, + ⟨4, 5, 6, 3, 7, 5, 133577490678040613028297548263083253551857664000000⟩, + ⟨4, 5, 7, 3, 8, 5, -10689508537240596930244896996163070151320666112000000⟩, + ⟨4, 5, 5, 4, 5, 5, 14745233610567319559448704835927867265734672384000000⟩, + ⟨4, 5, 6, 4, 6, 5, 26994515676869628689998704591807850188178980864000000⟩, + ⟨4, 5, 7, 4, 7, 5, -28274635646527761359937773300828142282781753344000000⟩, + ⟨4, 5, 8, 4, 8, 5, 10095400763273276723590061716714228247187947520000000⟩, + ⟨4, 5, 5, 5, 4, 5, 9781053644790228164686716340126648294711492608000000⟩, + ⟨4, 5, 6, 5, 5, 5, 22550713404568111686355581935552769058481897472000000⟩, + ⟨4, 5, 7, 5, 6, 5, 8957349762343461027541296948461559561395896320000000⟩, + ⟨4, 5, 8, 5, 7, 5, -16551432141936674928793628888153895825102077952000000⟩, + ⟨4, 5, 5, 6, 3, 5, -89130373344569899214877004892127909597998481408000000⟩, + ⟨4, 5, 6, 6, 4, 5, -15035874508547875834266636854037965031239319552000000⟩, + ⟨4, 5, 7, 6, 5, 5, 55962769338878549790076611450004522473564930048000000⟩, + ⟨4, 5, 8, 6, 6, 5, 24723478501596969725543813275408366132172685312000000⟩, + ⟨4, 5, 5, 7, 2, 5, 4937797659627032514620860467913855017915777024000000⟩, + ⟨4, 5, 6, 7, 3, 5, -75903959613677254968294528956735840589535248384000000⟩, + ⟨4, 5, 7, 7, 4, 5, 43516063687078354898627911069135194167401512960000000⟩, + ⟨4, 5, 8, 7, 5, 5, 63863361829729520510144176543219745413838929920000000⟩ +] + +def collectedFourData_14_4_32 : List CollectedFourTerm := [ + ⟨4, 6, 4, 0, 8, 6, 22173478409861080334745913983900106259912510668800000⟩, + ⟨4, 6, 4, 1, 7, 6, -25859768793672062104878820513466584035652062412800000⟩, + ⟨4, 6, 5, 1, 8, 6, -126937364907037354125583277411075823983740846080000000⟩, + ⟨4, 6, 4, 2, 6, 6, 17049169970277292927215015773977767851486871552000000⟩, + ⟨4, 6, 5, 2, 7, 6, -65066622899045408830930100464523374211654221824000000⟩, + ⟨4, 6, 6, 2, 8, 6, 57668214897449743635357522730142543221415215104000000⟩, + ⟨4, 6, 4, 3, 5, 6, 46777721013612706200072625627827261614930578636800000⟩, + ⟨4, 6, 5, 3, 6, 6, 44519557842511448347567501347548703973668028416000000⟩, + ⟨4, 6, 6, 3, 7, 6, 122272042662013117228492441014640418721103872000000⟩, + ⟨4, 6, 7, 3, 8, 6, -6523195074594024883573070527484674414775107584000000⟩, + ⟨4, 6, 4, 4, 4, 6, -35058301453771583264495585223887365979422851072000000⟩, + ⟨4, 6, 5, 4, 5, 6, 26994515676869628689998704591807850188178980864000000⟩, + ⟨4, 6, 6, 4, 6, 6, 24709811179475895370398716658157074194179817472000000⟩, + ⟨4, 6, 7, 4, 7, 6, -17254391382242382847874958805110869739341611008000000⟩, + ⟨4, 6, 8, 4, 8, 6, 4620483835080740377510092749354242004200980480000000⟩, + ⟨4, 6, 4, 5, 3, 6, -33406491001917235579253799415813251335206836633600000⟩, + ⟨4, 6, 5, 5, 4, 6, 17906451191208625062271362804676967340460474368000000⟩, + ⟨4, 6, 6, 5, 5, 6, 20642114007876563517989539829031499654974406656000000⟩, + ⟨4, 6, 7, 5, 6, 6, 5466157742198516151263201141263055815169802240000000⟩, + ⟨4, 6, 8, 5, 7, 6, -7575293586904435957155407658834522300217294848000000⟩, + ⟨4, 6, 4, 6, 2, 6, 42312579343591419500610801863938648950156401049600000⟩, + ⟨4, 6, 5, 6, 3, 6, -163173492131784781534875956005033028074673799168000000⟩, + ⟨4, 6, 6, 6, 4, 6, -13763300089242318873308347923750674480020586496000000⟩, + ⟨4, 6, 7, 6, 5, 6, 34150874199708539389720297441984580533182529536000000⟩, + ⟨4, 6, 8, 6, 6, 6, 11315492613148748807359490618079761642960191488000000⟩, + ⟨4, 6, 4, 7, 1, 6, 40646195927598238557503084851346076196081867161600000⟩, + ⟨4, 6, 5, 7, 2, 6, 9039765652575758423129915387063234555547746304000000⟩, + ⟨4, 6, 6, 7, 3, 6, -69479761455235952985761517124977019882341138432000000⟩, + ⟨4, 6, 7, 7, 4, 6, 26555362327494466374875607541599058841535774720000000⟩, + ⟨4, 6, 8, 7, 5, 6, 29229115109691063095838089339772732254013358080000000⟩ +] + +def collectedFourData_14_4_33 : List CollectedFourTerm := [ + ⟨4, 7, 3, 0, 7, 7, 12035156668414996071424829021160048584505792921600000⟩, + ⟨4, 7, 4, 0, 8, 7, -46449955284226429858830370561637542717239695769600000⟩, + ⟨4, 7, 3, 1, 6, 7, -57067169160614127250941770207764512571575710515200000⟩, + ⟨4, 7, 4, 1, 7, 7, 54172154766313316032189380984159643633186347417600000⟩, + ⟨4, 7, 5, 1, 8, 7, 132956923015002024396950054139459973211152711680000000⟩, + ⟨4, 7, 3, 2, 5, 7, -24284893882710386894745444417485287689907548979200000⟩, + ⟨4, 7, 4, 2, 6, 7, -35715333792661260174116555240795441462859792384000000⟩, + ⟨4, 7, 5, 2, 7, 7, 68152178658901223527316302033762932799259541504000000⟩, + ⟨4, 7, 6, 2, 8, 7, -40268618118067044885531020922007454473053536256000000⟩, + ⟨4, 7, 3, 3, 4, 7, 2646050246355518294104394680243795751711696486400000⟩, + ⟨4, 7, 4, 3, 5, 7, -97991979842640406191932542679429318585305635225600000⟩, + ⟨4, 7, 5, 3, 6, 7, -46630741303505404796453003119926653510574145536000000⟩, + ⟨4, 7, 6, 3, 7, 7, -85380242846572828208334919835762176303300608000000⟩, + ⟨4, 7, 7, 3, 8, 7, 3416267329874890085986225803912872293388255232000000⟩, + ⟨4, 7, 3, 4, 3, 7, 39076792245599555955746582267324066484230239027200000⟩, + ⟨4, 7, 4, 4, 4, 7, 73441636209157269950980200933226876117633204224000000⟩, + ⟨4, 7, 5, 4, 5, 7, -28274635646527761359937773300828142282781753344000000⟩, + ⟨4, 7, 6, 4, 6, 7, -17254391382242382847874958805110869739341611008000000⟩, + ⟨4, 7, 7, 4, 7, 7, 9036310106010131283665854976379902702370422784000000⟩, + ⟨4, 7, 8, 4, 8, 7, -1935837612519506055550350820717303103206981632000000⟩, + ⟨4, 7, 3, 5, 2, 7, 48794700354524581444475103770221173409930071244800000⟩, + ⟨4, 7, 4, 5, 3, 7, 69981352702509518625331267324755287260823499571200000⟩, + ⟨4, 7, 5, 5, 4, 7, -18755601664214369131150408552732694598415024128000000⟩, + ⟨4, 7, 6, 5, 5, 7, -14413995779320422714090452667705843921803280384000000⟩, + ⟨4, 7, 7, 5, 6, 7, -2862685524666401558763097068665211249512939520000000⟩, + ⟨4, 7, 8, 5, 7, 7, 3173810097563333222018001731560515791846847283200000⟩, + ⟨4, 7, 3, 6, 1, 7, 11879652357362980247806968978726500939558446694400000⟩, + ⟨4, 7, 4, 6, 2, 7, -88638209221879948130826480390214746434125902643200000⟩, + ⟨4, 7, 5, 6, 3, 7, 170911421135479893409728618885057210249199484928000000⟩, + ⟨4, 7, 6, 6, 4, 7, 9610650794785857692827754642267639718969606144000000⟩, + ⟨4, 7, 7, 6, 5, 7, -17885179652149603021966474000316204281944342528000000⟩, + ⟨4, 7, 8, 6, 6, 7, -4740836022065036341796379248173711136883159859200000⟩, + ⟨4, 7, 3, 7, 0, 7, -1248670744251347027567855498507268051031964201779200000⟩, + ⟨4, 7, 4, 7, 1, 7, -85147397643808526967916308939398972398955082547200000⟩, + ⟨4, 7, 5, 7, 2, 7, -9468444746930002250981602593738326106999619584000000⟩, + ⟨4, 7, 6, 7, 3, 7, 48516396527110466428772758945858681060561256448000000⟩, + ⟨4, 7, 7, 7, 4, 7, -13907328497002796814355867484941278176146882560000000⟩, + ⟨4, 7, 8, 7, 5, 7, -12246081239458208107064652831259767711278825472000000⟩ +] + +def collectedFourData_14_4_34 : List CollectedFourTerm := [ + ⟨4, 8, 2, 0, 6, 8, 45102410067031517106956329800573567057814093824000000⟩, + ⟨4, 8, 3, 0, 7, 8, -12891384136865177065188239394919048286708957184000000⟩, + ⟨4, 8, 4, 0, 8, 8, 24877292136988633669521350870974313363618660352000000⟩, + ⟨4, 8, 2, 1, 5, 8, -22022947094505556412784055408634576036192845824000000⟩, + ⟨4, 8, 3, 1, 6, 8, 61127147699177344505565773902545902081459355648000000⟩, + ⟨4, 8, 4, 1, 7, 8, -29013085406981597858952852857310970210116698112000000⟩, + ⟨4, 8, 5, 1, 8, 8, -47471997123787935798840589985530599497426534400000000⟩, + ⟨4, 8, 2, 2, 4, 8, -81135341561541550757978999065356405973180219392000000⟩, + ⟨4, 8, 3, 2, 5, 8, 26012614907343533263356137255574775564502827008000000⟩, + ⟨4, 8, 4, 2, 6, 8, 19128130201490534204015788918033644959909806080000000⟩, + ⟨4, 8, 5, 2, 7, 8, -24333595843746979797741353549956907486486200320000000⟩, + ⟨4, 8, 6, 2, 8, 8, 10783370734655710596893232309358071333110415360000000⟩, + ⟨4, 8, 2, 3, 3, 8, 92421061023796834928743167704889197299897466880000000⟩, + ⟨4, 8, 3, 3, 4, 8, -2834300467457736860091960692502926269649780736000000⟩, + ⟨4, 8, 4, 3, 5, 8, 52481753635941421178461440156032095834783875072000000⟩, + ⟨4, 8, 5, 3, 6, 8, 16649410702670465765482329332162561433277562880000000⟩, + ⟨4, 8, 6, 3, 7, 8, 22863630664704949893370094202941646286356480000000⟩, + ⟨4, 8, 7, 3, 8, 8, -731862753049477996623245315096536976128475136000000⟩, + ⟨4, 8, 2, 4, 2, 8, -22036469487180104607121759789668287328571883520000000⟩, + ⟨4, 8, 3, 4, 3, 8, -41856865976372999961866703152730224502692118528000000⟩, + ⟨4, 8, 4, 4, 4, 8, -39333278747290293053143589473077725947106426880000000⟩, + ⟨4, 8, 5, 4, 5, 8, 10095400763273276723590061716714228247187947520000000⟩, + ⟨4, 8, 6, 4, 6, 8, 4620483835080740377510092749354242004200980480000000⟩, + ⟨4, 8, 7, 4, 7, 8, -1935837612519506055550350820717303103206981632000000⟩, + ⟨4, 8, 8, 4, 8, 8, 345593427892721667200319949755615553026785280000000⟩, + ⟨4, 8, 2, 5, 1, 8, 22823218039789133831468492938087222471330627584000000⟩, + ⟨4, 8, 3, 5, 2, 8, -52266143552932233126275112601034935677329866752000000⟩, + ⟨4, 8, 4, 5, 3, 8, -37480048035980832973447439189222807075284844544000000⟩, + ⟨4, 8, 5, 5, 4, 8, 6696649170784686850727837846762636477454090240000000⟩, + ⟨4, 8, 6, 5, 5, 8, 3859865759496683859403551038288238860084183040000000⟩, + ⟨4, 8, 7, 5, 6, 8, 613269603018440627544100156258506826013736960000000⟩, + ⟨4, 8, 8, 5, 7, 8, -566601198366990384615155919359750287631843328000000⟩, + ⟨4, 8, 2, 6, 0, 8, -410865413978239055170757578341694732505790283776000000⟩, + ⟨4, 8, 3, 6, 1, 8, -12724816649300088712663126964736434724359110656000000⟩, + ⟨4, 8, 4, 6, 2, 8, 47472136664489589040410613788965941354570973184000000⟩, + ⟨4, 8, 5, 6, 3, 8, -61023572963180961926530489895478182119986954240000000⟩, + ⟨4, 8, 6, 6, 4, 8, -2573597390842477498215228308818949613174128640000000⟩, + ⟨4, 8, 7, 6, 5, 8, 3831520064176615487441928019807395079828537344000000⟩, + ⟨4, 8, 8, 6, 6, 8, 846352897240362694499208788991443102091706368000000⟩, + ⟨4, 8, 3, 7, 0, 8, 1337505997479416428586843637506881727292147499008000000⟩, + ⟨4, 8, 4, 7, 1, 8, 45602555975089980258843787393568357758128881664000000⟩, + ⟨4, 8, 5, 7, 2, 8, 3380688809579993668450174200685140558710046720000000⟩, + ⟨4, 8, 6, 7, 3, 8, -12992010029434502204682202881963693242717306880000000⟩, + ⟨4, 8, 7, 7, 4, 8, 2979349898168733793805305047778211750876282880000000⟩, + ⟨4, 8, 8, 7, 5, 8, 2186219115914851722739256581910870142882938880000000⟩ +] + +def collectedFourData_14_4_35 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_4_36 : List CollectedFourTerm := [ + ⟨5, 1, 8, 4, 8, 2, 22823218039789133831468492938087222471330627584000000⟩, + ⟨5, 1, 8, 5, 7, 2, -37418717047911727196597885199575635744174532198400000⟩, + ⟨5, 1, 8, 6, 6, 2, 55893703853420002639531343995972732495258347110400000⟩, + ⟨5, 1, 8, 7, 5, 2, 144379353130431842553248351744674368842486513664000000⟩ +] + +def collectedFourData_14_4_37 : List CollectedFourTerm := [ + ⟨5, 2, 7, 3, 8, 3, 18447324044504205888773782098220422811710023270400000⟩, + ⟨5, 2, 7, 4, 7, 3, 48794700354524581444475103770221173409930071244800000⟩, + ⟨5, 2, 8, 4, 8, 3, -52266143552932233126275112601034935677329866752000000⟩, + ⟨5, 2, 7, 5, 6, 3, -15458066483622230120310580385970420465788780544000000⟩, + ⟨5, 2, 8, 5, 7, 3, 85690459311353806874953571449212202407590834995200000⟩, + ⟨5, 2, 7, 6, 5, 3, -96577250191207815250710141829151035007834888601600000⟩, + ⟨5, 2, 8, 6, 6, 3, -127998967727292589905475721648494506060484391731200000⟩, + ⟨5, 2, 7, 7, 4, 3, -75097458894404984740742110133779995503395602432000000⟩, + ⟨5, 2, 8, 7, 5, 3, -330634881708572862982079994394689308457531604992000000⟩ +] + +def collectedFourData_14_4_38 : List CollectedFourTerm := [ + ⟨5, 3, 6, 2, 8, 4, -77964687308838674446896432277939568828990305075200000⟩, + ⟨5, 3, 6, 3, 7, 4, -165305993773329157011901958035520299554412953600000⟩, + ⟨5, 3, 7, 3, 8, 4, 26457149669866262509857223375922351269350054297600000⟩, + ⟨5, 3, 6, 4, 6, 4, -33406491001917235579253799415813251335206836633600000⟩, + ⟨5, 3, 7, 4, 7, 4, 69981352702509518625331267324755287260823499571200000⟩, + ⟨5, 3, 8, 4, 8, 4, -37480048035980832973447439189222807075284844544000000⟩, + ⟨5, 3, 6, 5, 5, 4, -27907157640987866674593288444168297111410756812800000⟩, + ⟨5, 3, 7, 5, 6, 4, -22169956877066847073106112030887295096440487936000000⟩, + ⟨5, 3, 8, 5, 7, 4, 61448622624360814233685238644877258898029307494400000⟩, + ⟨5, 3, 6, 6, 4, 4, 18607327965737712999015332689522851815720013004800000⟩, + ⟨5, 3, 7, 6, 5, 4, -138511079268113884566231807032058271421054740070400000⟩, + ⟨5, 3, 8, 6, 6, 4, -91788051171526365542030976741625745797605123686400000⟩, + ⟨5, 3, 6, 7, 3, 4, 93933337208080063277114997607498051301945219481600000⟩, + ⟨5, 3, 7, 7, 4, 4, -107704765471815153431006417328260396923389739008000000⟩, + ⟨5, 3, 8, 7, 5, 4, -237098251495406609596715776137327193793520205824000000⟩ +] + +def collectedFourData_14_4_39 : List CollectedFourTerm := [ + ⟨5, 4, 5, 1, 8, 5, -45993830396738671246493247166627950744054005760000000⟩, + ⟨5, 4, 5, 2, 7, 5, -23575904701495305873478057636284986797722697728000000⟩, + ⟨5, 4, 6, 2, 8, 5, 41790407374825455290432567462991340675610443776000000⟩, + ⟨5, 4, 5, 3, 6, 5, 16130987075758566363810425927173734950661783552000000⟩, + ⟨5, 4, 6, 3, 7, 5, 88606843171480514028302587076098046419795968000000⟩, + ⟨5, 4, 7, 3, 8, 5, -7090742622366000211603894216905990236320825344000000⟩, + ⟨5, 4, 5, 4, 5, 5, 9781053644790228164686716340126648294711492608000000⟩, + ⟨5, 4, 6, 4, 6, 5, 17906451191208625062271362804676967340460474368000000⟩, + ⟨5, 4, 7, 4, 7, 5, -18755601664214369131150408552732694598415024128000000⟩, + ⟨5, 4, 8, 4, 8, 5, 6696649170784686850727837846762636477454090240000000⟩, + ⟨5, 4, 5, 5, 4, 5, 6488131211003808785092097697084476108146999296000000⟩, + ⟨5, 4, 6, 5, 5, 5, 14958714345515507413495523622170865112568561664000000⟩, + ⟨5, 4, 7, 5, 6, 5, 5941738249426048204883920486928372148826275840000000⟩, + ⟨5, 4, 8, 5, 7, 5, -10979171300641004137240535123440308056620007424000000⟩, + ⟨5, 4, 5, 6, 3, 5, -59123441926253573045128140253611678269907664896000000⟩, + ⟨5, 4, 6, 6, 4, 5, -9973846400035592481120789539349177414004506624000000⟩, + ⟨5, 4, 7, 6, 5, 5, 37122155095753192487291024979516708774872088576000000⟩, + ⟨5, 4, 8, 6, 6, 5, 16399989033516157024854249090046626523716255744000000⟩, + ⟨5, 4, 5, 7, 2, 5, 3275422083602609930214750405607892733067788288000000⟩, + ⟨5, 4, 6, 7, 3, 5, -50349877149542408878983526183979456335454404608000000⟩, + ⟨5, 4, 7, 7, 4, 5, 28865799252470799309468077245900809968308715520000000⟩, + ⟨5, 4, 8, 7, 5, 5, 42362907532748120040880410823351183355192279040000000⟩ +] + +def collectedFourData_14_4_40 : List CollectedFourTerm := [ + ⟨5, 5, 4, 0, 8, 6, 18523309059832731088348913293074180259155699302400000⟩, + ⟨5, 5, 4, 1, 7, 6, -21602767086285335438568522317527251535039719014400000⟩, + ⟨5, 5, 5, 1, 8, 6, -106041100000266020448534584745944424229204131840000000⟩, + ⟨5, 5, 4, 2, 6, 6, 14242557650883431510586159637121306690108522496000000⟩, + ⟨5, 5, 5, 2, 7, 6, -54355439555329501548422217841016176582487703552000000⟩, + ⟨5, 5, 6, 2, 8, 6, 48174947914317975303660442517076892864575700992000000⟩, + ⟨5, 5, 4, 3, 5, 6, 39077233054442032477593454199797813867327153766400000⟩, + ⟨5, 5, 5, 3, 6, 6, 37190805785221235418828781521148264151638867968000000⟩, + ⟨5, 5, 6, 3, 7, 6, 102143777071903783453999033879629962837753856000000⟩, + ⟨5, 5, 7, 3, 8, 6, -5449355134580383222709980407353284058815660032000000⟩, + ⟨5, 5, 4, 4, 4, 6, -29287049191713296127599320038971913990838419456000000⟩, + ⟨5, 5, 5, 4, 5, 6, 22550713404568111686355581935552769058481897472000000⟩, + ⟨5, 5, 6, 4, 6, 6, 20642114007876563517989539829031499654974406656000000⟩, + ⟨5, 5, 7, 4, 7, 6, -14413995779320422714090452667705843921803280384000000⟩, + ⟨5, 5, 8, 4, 8, 6, 3859865759496683859403551038288238860084183040000000⟩, + ⟨5, 5, 4, 5, 3, 6, -27907157640987866674593288444168297111410756812800000⟩, + ⟨5, 5, 5, 5, 4, 6, 14958714345515507413495523622170865112568561664000000⟩, + ⟨5, 5, 6, 5, 5, 6, 17244035885959834486928067803097769940235583488000000⟩, + ⟨5, 5, 7, 5, 6, 6, 4566325921309292345495765622359111849497067520000000⟩, + ⟨5, 5, 8, 5, 7, 6, -6328258549943894182412451103028715064293064704000000⟩, + ⟨5, 5, 4, 6, 2, 6, 35347137233618576272361972855604470179347352780800000⟩, + ⟨5, 5, 5, 6, 3, 6, -136312082807226560636390691971286645398059352064000000⟩, + ⟨5, 5, 6, 6, 4, 6, -11497603421702212066837994649268667203933175808000000⟩, + ⟨5, 5, 7, 6, 5, 6, 28529001439095017334612537698852810191408201728000000⟩, + ⟨5, 5, 8, 6, 6, 6, 9452750847805377629983510817857439848332263424000000⟩, + ⟨5, 5, 4, 7, 1, 6, 33955071701270966197995413392323419401981054156800000⟩, + ⟨5, 5, 5, 7, 2, 6, 7551651117429272993284745158416202488549998592000000⟩, + ⟨5, 5, 6, 7, 3, 6, -58042092947691570436892755367387173687432052736000000⟩, + ⟨5, 5, 7, 7, 4, 6, 22183852911831023040968874150395247711548866560000000⟩, + ⟨5, 5, 8, 7, 5, 6, 24417455967641583275640338483353828175212707840000000⟩ +] + +def collectedFourData_14_4_41 : List CollectedFourTerm := [ + ⟨5, 6, 3, 0, 7, 7, -3812714302362090355627340501388315381410562048000000⟩, + ⟨5, 6, 4, 0, 8, 7, 14715255790648000197164663998727255354127679488000000⟩, + ⟨5, 6, 3, 1, 6, 7, 18078768565182725523135373119530311632348512256000000⟩, + ⟨5, 6, 4, 1, 7, 7, -17161633617063392938550027356242765994606460928000000⟩, + ⟨5, 6, 5, 1, 8, 7, -42120495473709088767033476907780744717690470400000000⟩, + ⟨5, 6, 3, 2, 5, 7, 7693407305693978082926446114585916193349042176000000⟩, + ⟨5, 6, 4, 2, 6, 7, 11314548511220109531143254614837440223400427520000000⟩, + ⟨5, 6, 5, 2, 7, 7, -21590478085911790107279398424752443754670981120000000⟩, + ⟨5, 6, 6, 2, 8, 7, 12757020158951645118366668446318039962149191680000000⟩, + ⟨5, 6, 3, 3, 4, 7, -838263588668104005037901635152088762461192192000000⟩, + ⟨5, 6, 4, 3, 5, 7, 31043669256365158285026832275716346847237767168000000⟩, + ⟨5, 6, 5, 3, 6, 7, 14772528451101271532801122415073352015234990080000000⟩, + ⟨5, 6, 6, 3, 7, 7, 27048295423905639177568271113489830106890240000000⟩, + ⟨5, 6, 7, 3, 8, 7, -1082266867658627662128791075820858048994344960000000⟩, + ⟨5, 6, 3, 4, 3, 7, -12379452032912416857144509917204599556974575616000000⟩, + ⟨5, 6, 4, 4, 4, 7, -23266167984201610093377703622516795788461342720000000⟩, + ⟨5, 6, 5, 4, 5, 7, 8957349762343461027541296948461559561395896320000000⟩, + ⟨5, 6, 6, 4, 6, 7, 5466157742198516151263201141263055815169802240000000⟩, + ⟨5, 6, 7, 4, 7, 7, -2862685524666401558763097068665211249512939520000000⟩, + ⟨5, 6, 8, 4, 8, 7, 613269603018440627544100156258506826013736960000000⟩, + ⟨5, 6, 3, 5, 2, 7, -15458066483622230120310580385970420465788780544000000⟩, + ⟨5, 6, 4, 5, 3, 7, -22169956877066847073106112030887295096440487936000000⟩, + ⟨5, 6, 5, 5, 4, 7, 5941738249426048204883920486928372148826275840000000⟩, + ⟨5, 6, 6, 5, 5, 7, 4566325921309292345495765622359111849497067520000000⟩, + ⟨5, 6, 7, 5, 6, 7, 906893224888774393154099607826556356499865600000000⟩, + ⟨5, 6, 8, 5, 7, 7, -1005456886466488771380694660057018625263927296000000⟩, + ⟨5, 6, 3, 6, 1, 7, -3763450838066443027558751508504442008797970432000000⟩, + ⟨5, 6, 4, 6, 2, 7, 28080412856024131421427719310276658992141828096000000⟩, + ⟨5, 6, 5, 6, 3, 7, -54144406903353900763854075037323032182747299840000000⟩, + ⟨5, 6, 6, 6, 4, 7, -3044635541509190001366800321117101685546680320000000⟩, + ⟨5, 6, 7, 6, 5, 7, 5665990243319935472108017524095510590091427840000000⟩, + ⟨5, 6, 8, 6, 6, 7, 1501887661663590165771611716318089549579288576000000⟩, + ⟨5, 6, 3, 7, 0, 7, 395576471226378890966800413525135580952763826176000000⟩, + ⟨5, 6, 4, 7, 1, 7, 26974530515041119182333620136372780908167561216000000⟩, + ⟨5, 6, 5, 7, 2, 7, 2999584941215358239020308857156616962200043520000000⟩, + ⟨5, 6, 6, 7, 3, 7, -15369900370590346276591174109348567163800125440000000⟩, + ⟨5, 6, 7, 7, 4, 7, 4405814708447303552290515559534549749517516800000000⟩, + ⟨5, 6, 8, 7, 5, 7, 3879534797590587791439165106157054685515612160000000⟩ +] + +def collectedFourData_14_4_42 : List CollectedFourTerm := [ + ⟨5, 7, 2, 0, 6, 8, -73945502230882176704741587495552205659981637222400000⟩, + ⟨5, 7, 3, 0, 7, 8, 21135453139532489859739059288781517391531501158400000⟩, + ⟨5, 7, 4, 0, 8, 8, -40786376126686533491842297388646278170689090355200000⟩, + ⟨5, 7, 2, 1, 5, 8, 36106671042347312166136905074456317185587832422400000⟩, + ⟨5, 7, 3, 1, 6, 8, -100218095437454709499713591779871251315645271244800000⟩, + ⟨5, 7, 4, 1, 7, 8, 47567018447534033310727604083843852665556775731200000⟩, + ⟨5, 7, 5, 1, 8, 8, 77830445512876146591990075494130308045277757440000000⟩, + ⟨5, 7, 2, 2, 4, 8, 133021574047278631357486715961926297761894052659200000⟩, + ⟨5, 7, 3, 2, 5, 8, -42647740349203234780837748748300742107459275980800000⟩, + ⟨5, 7, 4, 2, 6, 8, -31360612268496819114889662624076479332150673408000000⟩, + ⟨5, 7, 5, 2, 7, 8, 39894984837283777052788257145359537470787551232000000⟩, + ⟨5, 7, 6, 2, 8, 8, -17679360449493476563120229374001936594827739136000000⟩, + ⟨5, 7, 2, 3, 3, 8, -151524536359780931800068602302964841796482367488000000⟩, + ⟨5, 7, 3, 3, 4, 8, 4646841958731287552378995350181936372607719833600000⟩, + ⟨5, 7, 4, 3, 5, 8, -86043952524919587950147644776115695684196447027200000⟩, + ⟨5, 7, 5, 3, 6, 8, -27296746103533053157979008203255576534699737088000000⟩, + ⟨5, 7, 6, 3, 7, 8, -37484973636892826024047632706321305669992448000000⟩, + ⟨5, 7, 7, 3, 8, 8, 1199890621319110399245184580183393128576293273600000⟩, + ⟨5, 7, 2, 4, 2, 8, 36128841035396388258525777429157646301294231552000000⟩, + ⟨5, 7, 3, 4, 3, 8, 68624425431670427385405479348183657458772528332800000⟩, + ⟨5, 7, 4, 4, 4, 8, 64486998522540226320736007800877462327276863488000000⟩, + ⟨5, 7, 5, 4, 5, 8, -16551432141936674928793628888153895825102077952000000⟩, + ⟨5, 7, 6, 4, 6, 8, -7575293586904435957155407658834522300217294848000000⟩, + ⟨5, 7, 7, 4, 7, 8, 3173810097563333222018001731560515791846847283200000⟩, + ⟨5, 7, 8, 4, 8, 8, -566601198366990384615155919359750287631843328000000⟩, + ⟨5, 7, 2, 5, 1, 8, -37418717047911727196597885199575635744174532198400000⟩, + ⟨5, 7, 3, 5, 2, 8, 85690459311353806874953571449212202407590834995200000⟩, + ⟨5, 7, 4, 5, 3, 8, 61448622624360814233685238644877258898029307494400000⟩, + ⟨5, 7, 5, 5, 4, 8, -10979171300641004137240535123440308056620007424000000⟩, + ⟨5, 7, 6, 5, 5, 8, -6328258549943894182412451103028715064293064704000000⟩, + ⟨5, 7, 7, 5, 6, 8, -1005456886466488771380694660057018625263927296000000⟩, + ⟨5, 7, 8, 5, 7, 8, 928943932610214866829991789980185137305668812800000⟩, + ⟨5, 7, 2, 6, 0, 8, 673614765613783951630505359541975836594397616537600000⟩, + ⟨5, 7, 3, 6, 1, 8, 20862365370940275107423154048867589224404720025600000⟩, + ⟨5, 7, 4, 6, 2, 8, -77830674290168758302755772950199072141584262758400000⟩, + ⟨5, 7, 5, 6, 3, 8, 100048284426018716372710817799181767690707533824000000⟩, + ⟨5, 7, 6, 6, 4, 8, 4219418681243439842247968460976662791023755264000000⟩, + ⟨5, 7, 7, 6, 5, 8, -6281785719037277930314033408765754316469724774400000⟩, + ⟨5, 7, 8, 6, 6, 8, -1387597468915476352746094800802338334265101516800000⟩, + ⟨5, 7, 3, 7, 0, 8, -2192844075814192930084416046802096191247819263180800000⟩, + ⟨5, 7, 4, 7, 1, 8, -74765492566324085082578042076884723968797730406400000⟩, + ⟨5, 7, 5, 7, 2, 8, -5542646868297809445602524003872978247322959872000000⟩, + ⟨5, 7, 6, 7, 3, 8, 21300429515571174390736043349443937348498751488000000⟩, + ⟨5, 7, 7, 7, 4, 8, -4884650824960110455444026816498096594734809088000000⟩, + ⟨5, 7, 8, 7, 5, 8, -3584311132660474576056384780699178930104434688000000⟩ +] + +def collectedFourData_14_4_43 : List CollectedFourTerm := [ + ⟨6, 0, 8, 4, 8, 2, -410865413978239055170757578341694732505790283776000000⟩, + ⟨6, 0, 8, 5, 7, 2, 673614765613783951630505359541975836594397616537600000⟩, + ⟨6, 0, 8, 6, 6, 2, -1006202969821195252425808672874480550015491742105600000⟩, + ⟨6, 0, 8, 7, 5, 2, -2599128772744849620570810145675534318402478800896000000⟩ +] + +def collectedFourData_14_4_44 : List CollectedFourTerm := [ + ⟨6, 1, 7, 3, 8, 3, 4491221279771877524616190587377359424167555891200000⟩, + ⟨6, 1, 7, 4, 7, 3, 11879652357362980247806968978726500939558446694400000⟩, + ⟨6, 1, 8, 4, 8, 3, -12724816649300088712663126964736434724359110656000000⟩, + ⟨6, 1, 7, 5, 6, 3, -3763450838066443027558751508504442008797970432000000⟩, + ⟨6, 1, 8, 5, 7, 3, 20862365370940275107423154048867589224404720025600000⟩, + ⟨6, 1, 7, 6, 5, 3, -23512884587172801359720468489314002716815314124800000⟩, + ⟨6, 1, 8, 6, 6, 3, -31162876862723893569609038262062210858943617433600000⟩, + ⟨6, 1, 7, 7, 4, 3, -18283372950443030547949215217398518393597853696000000⟩, + ⟨6, 1, 8, 7, 5, 3, -80497009375557369421802894078653274075091173376000000⟩ +] + +def collectedFourData_14_4_45 : List CollectedFourTerm := [ + ⟨6, 2, 6, 2, 8, 4, 98749881200159711729995543071083505526135534387200000⟩, + ⟨6, 2, 6, 3, 7, 4, 209376165162147549956989254333201238982236569600000⟩, + ⟨6, 2, 7, 3, 8, 4, -33510560703524417563969720294468257135915014553600000⟩, + ⟨6, 2, 6, 4, 6, 4, 42312579343591419500610801863938648950156401049600000⟩, + ⟨6, 2, 7, 4, 7, 4, -88638209221879948130826480390214746434125902643200000⟩, + ⟨6, 2, 8, 4, 8, 4, 47472136664489589040410613788965941354570973184000000⟩, + ⟨6, 2, 6, 5, 5, 4, 35347137233618576272361972855604470179347352780800000⟩, + ⟨6, 2, 7, 5, 6, 4, 28080412856024131421427719310276658992141828096000000⟩, + ⟨6, 2, 8, 5, 7, 4, -77830674290168758302755772950199072141584262758400000⟩, + ⟨6, 2, 6, 6, 4, 4, -23567995838812256673636282244807854383675788492800000⟩, + ⟨6, 2, 7, 6, 5, 4, 175437792348863988335723603854166213912863073894400000⟩, + ⟨6, 2, 8, 6, 6, 4, 116258519871660382322410863553803574590612858470400000⟩, + ⟨6, 2, 6, 7, 3, 4, -118975733889474092786667295909410598078494906777600000⟩, + ⟨6, 2, 7, 7, 4, 4, 136418591059071053943911585600441612618315071488000000⟩, + ⟨6, 2, 8, 7, 5, 4, 300308062228098838529981915065820541136366731264000000⟩ +] + +def collectedFourData_14_4_46 : List CollectedFourTerm := [ + ⟨6, 3, 5, 1, 8, 5, 419121234141443571086694266211349228053866741760000000⟩, + ⟨6, 3, 5, 2, 7, 5, 214836689818128899942430702023240265017252118528000000⟩, + ⟨6, 3, 6, 2, 8, 5, -380817317521188674028465483772550483110187237376000000⟩, + ⟨6, 3, 5, 3, 6, 5, -146994480624753609646915211589483057090240970752000000⟩, + ⟨6, 3, 6, 3, 7, 5, -807434587271112879596836182125439976910880768000000⟩, + ⟨6, 3, 7, 3, 8, 5, 64614770573144174912363912099229088779016863744000000⟩, + ⟨6, 3, 5, 4, 5, 5, -89130373344569899214877004892127909597998481408000000⟩, + ⟨6, 3, 6, 4, 6, 5, -163173492131784781534875956005033028074673799168000000⟩, + ⟨6, 3, 7, 4, 7, 5, 170911421135479893409728618885057210249199484928000000⟩, + ⟨6, 3, 8, 4, 8, 5, -61023572963180961926530489895478182119986954240000000⟩, + ⟨6, 3, 5, 5, 4, 5, -59123441926253573045128140253611678269907664896000000⟩, + ⟨6, 3, 6, 5, 5, 5, -136312082807226560636390691971286645398059352064000000⟩, + ⟨6, 3, 7, 5, 6, 5, -54144406903353900763854075037323032182747299840000000⟩, + ⟨6, 3, 8, 5, 7, 5, 100048284426018716372710817799181767690707533824000000⟩, + ⟨6, 3, 5, 6, 3, 5, 538765519920220794963038402785021209437584490496000000⟩, + ⟨6, 3, 6, 6, 4, 5, 90887207615926780484528441825235382432929153024000000⟩, + ⟨6, 3, 7, 6, 5, 5, -338277619487534373849256797351998680835530162176000000⟩, + ⟨6, 3, 8, 6, 6, 5, -149445775321222733169513189329262520145641734144000000⟩, + ⟨6, 3, 5, 7, 2, 5, -29847458543287727796195011592683665642475225088000000⟩, + ⟨6, 3, 6, 7, 3, 5, 458815942654835571138847305541579373983624593408000000⟩, + ⟨6, 3, 7, 7, 4, 5, -263041136231014677678095781972899300747268587520000000⟩, + ⟨6, 3, 8, 7, 5, 5, -386034255764099895970466549460065227904164823040000000⟩ +] + +def collectedFourData_14_4_47 : List CollectedFourTerm := [ + ⟨6, 4, 4, 0, 8, 6, -12350569381555534344861562686874521773338420838400000⟩, + ⟨6, 4, 4, 1, 7, 6, 14403823467552759163022191852831428586294896230400000⟩, + ⟨6, 4, 5, 1, 8, 6, 70703779687492868582595658032256167823477309440000000⟩, + ⟨6, 4, 4, 2, 6, 6, -9496343005984961399109165359365985443497639936000000⟩, + ⟨6, 4, 5, 2, 7, 6, 36241938485428869710796214410786447538186616832000000⟩, + ⟨6, 4, 6, 2, 8, 6, -32121044611776352209983112710864778426813775872000000⟩, + ⟨6, 4, 4, 3, 5, 6, -26055068050700646264383553888293258319293212262400000⟩, + ⟨6, 4, 5, 3, 6, 6, -24797277080603849512767833557639225900152127488000000⟩, + ⟨6, 4, 6, 3, 7, 6, -68105207419784905511111706422809406730141696000000⟩, + ⟨6, 4, 7, 3, 8, 6, 3633402566300358135962042849955417298160320512000000⟩, + ⟨6, 4, 4, 4, 4, 6, 19527382059809529502840359769383174697748791296000000⟩, + ⟨6, 4, 5, 4, 5, 6, -15035874508547875834266636854037965031239319552000000⟩, + ⟨6, 4, 6, 4, 6, 6, -13763300089242318873308347923750674480020586496000000⟩, + ⟨6, 4, 7, 4, 7, 6, 9610650794785857692827754642267639718969606144000000⟩, + ⟨6, 4, 8, 4, 8, 6, -2573597390842477498215228308818949613174128640000000⟩, + ⟨6, 4, 4, 5, 3, 6, 18607327965737712999015332689522851815720013004800000⟩, + ⟨6, 4, 5, 5, 4, 6, -9973846400035592481120789539349177414004506624000000⟩, + ⟨6, 4, 6, 5, 5, 6, -11497603421702212066837994649268667203933175808000000⟩, + ⟨6, 4, 7, 5, 6, 6, -3044635541509190001366800321117101685546680320000000⟩, + ⟨6, 4, 8, 5, 7, 6, 4219418681243439842247968460976662791023755264000000⟩, + ⟨6, 4, 4, 6, 2, 6, -23567995838812256673636282244807854383675788492800000⟩, + ⟨6, 4, 5, 6, 3, 6, 90887207615926780484528441825235382432929153024000000⟩, + ⟨6, 4, 6, 6, 4, 6, 7666122090964333817348260521210791796752252928000000⟩, + ⟨6, 4, 7, 6, 5, 6, -19021947456683124522412714749810219927258267648000000⟩, + ⟨6, 4, 8, 6, 6, 6, -6302699739839705588723703606378688059260534784000000⟩, + ⟨6, 4, 4, 7, 1, 6, -22639824641895108629654443495575897199134690508800000⟩, + ⟨6, 4, 5, 7, 2, 6, -5035125785022875174668388923409746011170537472000000⟩, + ⟨6, 4, 6, 7, 3, 6, 38700045099157527903082251616941394933397323776000000⟩, + ⟨6, 4, 7, 7, 4, 6, -14791267243492504636929831767752233853082664960000000⟩, + ⟨6, 4, 8, 7, 5, 6, -16280540538157917497251117027737817975294525440000000⟩ +] + +def collectedFourData_14_4_48 : List CollectedFourTerm := [ + ⟨6, 5, 3, 0, 7, 7, -23820667576824654925738256917388737361380324147200000⟩, + ⟨6, 5, 4, 0, 8, 7, 91936397196036428260364560647711486039842566963200000⟩, + ⟨6, 5, 3, 1, 6, 7, 112950591635666337435199040212130708758502729318400000⟩, + ⟨6, 5, 4, 1, 7, 7, -107220614252177565823482914251164283224970179379200000⟩, + ⟨6, 5, 5, 1, 8, 7, -263155914994410589978306221147099685244696002560000000⟩, + ⟨6, 5, 3, 2, 5, 7, 48066045192138872914572365011089591891422242406400000⟩, + ⟨6, 5, 4, 2, 6, 7, 70689822917141938622668183101395360744082505728000000⟩, + ⟨6, 5, 5, 2, 7, 7, -134890673814872059893130793219229264475500576768000000⟩, + ⟨6, 5, 6, 2, 8, 7, 79701942600046053436111023186313554474829873152000000⟩, + ⟨6, 5, 3, 3, 4, 7, -5237213361370458081374851378372027161487658188800000⟩, + ⟨6, 5, 4, 3, 5, 7, 193951307933729878058244598586148172130340254515200000⟩, + ⟨6, 5, 5, 3, 6, 7, 92294219182607129423566968504793217886597414912000000⟩, + ⟨6, 5, 6, 3, 7, 7, 168989439731541232633680920383535470646132736000000⟩, + ⟨6, 5, 7, 3, 8, 7, -6761670883112268367545999117354010572220268544000000⟩, + ⟨6, 5, 3, 4, 3, 7, -77343012949216174999305801062656685538586027622400000⟩, + ⟨6, 5, 4, 4, 4, 7, -145359869475369289549579768960774089804777259008000000⟩, + ⟨6, 5, 5, 4, 5, 7, 55962769338878549790076611450004522473564930048000000⟩, + ⟨6, 5, 6, 4, 6, 7, 34150874199708539389720297441984580533182529536000000⟩, + ⟨6, 5, 7, 4, 7, 7, -17885179652149603021966474000316204281944342528000000⟩, + ⟨6, 5, 8, 4, 8, 7, 3831520064176615487441928019807395079828537344000000⟩, + ⟨6, 5, 3, 5, 2, 7, -96577250191207815250710141829151035007834888601600000⟩, + ⟨6, 5, 4, 5, 3, 7, -138511079268113884566231807032058271421054740070400000⟩, + ⟨6, 5, 5, 5, 4, 7, 37122155095753192487291024979516708774872088576000000⟩, + ⟨6, 5, 6, 5, 5, 7, 28529001439095017334612537698852810191408201728000000⟩, + ⟨6, 5, 7, 5, 6, 7, 5665990243319935472108017524095510590091427840000000⟩, + ⟨6, 5, 8, 5, 7, 7, -6281785719037277930314033408765754316469724774400000⟩, + ⟨6, 5, 3, 6, 1, 7, -23512884587172801359720468489314002716815314124800000⟩, + ⟨6, 5, 4, 6, 2, 7, 175437792348863988335723603854166213912863073894400000⟩, + ⟨6, 5, 5, 6, 3, 7, -338277619487534373849256797351998680835530162176000000⟩, + ⟨6, 5, 6, 6, 4, 7, -19021947456683124522412714749810219927258267648000000⟩, + ⟨6, 5, 7, 6, 5, 7, 35399366271959984673354085855803130324898021376000000⟩, + ⟨6, 5, 8, 6, 6, 7, 9383332683505449098111981528737062022793291366400000⟩, + ⟨6, 5, 3, 7, 0, 7, 2471440258835850745370926944755058627329525180006400000⟩, + ⟨6, 5, 4, 7, 1, 7, 168528579243828344492700842350435787418771023462400000⟩, + ⟨6, 5, 5, 7, 2, 7, 18740485146991856512540734381430163720663728128000000⟩, + ⟨6, 5, 6, 7, 3, 7, -96026415404354750594879416333936879203061334016000000⟩, + ⟨6, 5, 7, 7, 4, 7, 27526176695166626393942049859773296056750571520000000⟩, + ⟨6, 5, 8, 7, 5, 7, 24238141501679377006369131777231491415486234624000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1408.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1408.lean new file mode 100644 index 0000000000000000000000000000000000000000..4f8245a6fc63b23a644edf7bb1fa94e834aff770 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1408.lean @@ -0,0 +1,612 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1406 +import OAI.Analysis.LaughlinFock.Sparse1407 + +namespace OAI + +/-! Sparse1408. -/ +namespace LaughlinFock +def collectedFourData_14_4_49 : List CollectedFourTerm := [ + ⟨6, 6, 2, 0, 6, 8, 110455096514753353785500731339940167168268068454400000⟩, + ⟨6, 6, 3, 0, 7, 8, -31570798033408081801488226935777228158602208870400000⟩, + ⟨6, 6, 4, 0, 8, 8, 60924099176362403856604075914240148839964291891200000⟩, + ⟨6, 6, 2, 1, 5, 8, -53933852830650295728832720625423601791846999654400000⟩, + ⟨6, 6, 3, 1, 6, 8, 149699428228993466416698706020522415079815957708800000⟩, + ⟨6, 6, 4, 1, 7, 8, -71052592179800845020456043317030114328006832947200000⟩, + ⟨6, 6, 5, 1, 8, 8, -116258178138665494946782799477936631189224816640000000⟩, + ⟨6, 6, 2, 2, 4, 8, -198699181919956017079604453790500063798178820915200000⟩, + ⟨6, 6, 3, 2, 5, 8, 63704486876012466607653268883102367621069982924800000⟩, + ⟨6, 6, 4, 2, 6, 8, 46844491556268237868844706096058956271318990848000000⟩, + ⟨6, 6, 5, 2, 7, 8, -59592595461694655371204058081101482644043988992000000⟩, + ⟨6, 6, 6, 2, 8, 8, 26408306196510884077532553835902280552327151616000000⟩, + ⟨6, 6, 2, 3, 3, 8, 226337732289862719864120107298143491296306659328000000⟩, + ⟨6, 6, 3, 3, 4, 8, -6941157495122290687072168342055554910216886681600000⟩, + ⟨6, 6, 4, 3, 5, 8, 128526993446825969240935377474850131273667785523200000⟩, + ⟨6, 6, 5, 3, 6, 8, 40774146289390763502971567187002216938815356928000000⟩, + ⟨6, 6, 6, 3, 7, 8, 55992673739482784819811382573207679127257088000000⟩, + ⟨6, 6, 7, 3, 8, 8, -1792320430404744090570632546741798700687399321600000⟩, + ⟨6, 6, 2, 4, 2, 8, -53966968958718791187001950473082429994709286912000000⟩, + ⟨6, 6, 3, 4, 3, 8, -102506809821341888532462111425641594333772434636800000⟩, + ⟨6, 6, 4, 4, 4, 8, -96326584185118470031674753851899896972158435328000000⟩, + ⟨6, 6, 5, 4, 5, 8, 24723478501596969725543813275408366132172685312000000⟩, + ⟨6, 6, 6, 4, 6, 8, 11315492613148748807359490618079761642960191488000000⟩, + ⟨6, 6, 7, 4, 7, 8, -4740836022065036341796379248173711136883159859200000⟩, + ⟨6, 6, 8, 4, 8, 8, 846352897240362694499208788991443102091706368000000⟩, + ⟨6, 6, 2, 5, 1, 8, 55893703853420002639531343995972732495258347110400000⟩, + ⟨6, 6, 3, 5, 2, 8, -127998967727292589905475721648494506060484391731200000⟩, + ⟨6, 6, 4, 5, 3, 8, -91788051171526365542030976741625745797605123686400000⟩, + ⟨6, 6, 5, 5, 4, 8, 16399989033516157024854249090046626523716255744000000⟩, + ⟨6, 6, 6, 5, 5, 8, 9452750847805377629983510817857439848332263424000000⟩, + ⟨6, 6, 7, 5, 6, 8, 1501887661663590165771611716318089549579288576000000⟩, + ⟨6, 6, 8, 5, 7, 8, -1387597468915476352746094800802338334265101516800000⟩, + ⟨6, 6, 2, 6, 0, 8, -1006202969821195252425808672874480550015491742105600000⟩, + ⟨6, 6, 3, 6, 1, 8, -31162876862723893569609038262062210858943617433600000⟩, + ⟨6, 6, 4, 6, 2, 8, 116258519871660382322410863553803574590612858470400000⟩, + ⟨6, 6, 5, 6, 3, 8, -149445775321222733169513189329262520145641734144000000⟩, + ⟨6, 6, 6, 6, 4, 8, -6302699739839705588723703606378688059260534784000000⟩, + ⟨6, 6, 7, 6, 5, 8, 9383332683505449098111981528737062022793291366400000⟩, + ⟨6, 6, 8, 6, 6, 8, 2072705002045097546539549253800407686793972940800000⟩, + ⟨6, 6, 3, 7, 0, 8, 3275531259218444600135927881618449448541581266124800000⟩, + ⟨6, 6, 4, 7, 1, 8, 111679946017561584747182012336265996390606726758400000⟩, + ⟨6, 6, 5, 7, 2, 8, 8279253995374834013097420495081961358289272832000000⟩, + ⟨6, 6, 6, 7, 3, 8, -31817229269767942637749400800675292958664163328000000⟩, + ⟨6, 6, 7, 7, 4, 8, 7296381281274339018722905896789938936299388928000000⟩, + ⟨6, 6, 8, 7, 5, 8, 5354016406038742820522482798757029132294422528000000⟩ +] + +def collectedFourData_14_4_50 : List CollectedFourTerm := [ + ⟨7, 0, 7, 3, 8, 3, -472072452064169827131115813316796641469804419481600000⟩, + ⟨7, 0, 7, 4, 7, 3, -1248670744251347027567855498507268051031964201779200000⟩, + ⟨7, 0, 8, 4, 8, 3, 1337505997479416428586843637506881727292147499008000000⟩, + ⟨7, 0, 7, 5, 6, 3, 395576471226378890966800413525135580952763826176000000⟩, + ⟨7, 0, 8, 5, 7, 3, -2192844075814192930084416046802096191247819263180800000⟩, + ⟨7, 0, 7, 6, 5, 3, 2471440258835850745370926944755058627329525180006400000⟩, + ⟨7, 0, 8, 6, 6, 3, 3275531259218444600135927881618449448541581266124800000⟩, + ⟨7, 0, 7, 7, 4, 3, 1921766077212244334869919378501543846534581321728000000⟩, + ⟨7, 0, 8, 7, 5, 3, 8461043941634064780285861678591437983675966291968000000⟩ +] + +def collectedFourData_14_4_51 : List CollectedFourTerm := [ + ⟨7, 1, 6, 2, 8, 4, 94860844726467021510510838595202787723634225971200000⟩, + ⟨7, 1, 6, 3, 7, 4, 201130367464558222102933271375615300585757081600000⟩, + ⟨7, 1, 7, 3, 8, 4, -32190824504898098002891407388314675766651099545600000⟩, + ⟨7, 1, 6, 4, 6, 4, 40646195927598238557503084851346076196081867161600000⟩, + ⟨7, 1, 7, 4, 7, 4, -85147397643808526967916308939398972398955082547200000⟩, + ⟨7, 1, 8, 4, 8, 4, 45602555975089980258843787393568357758128881664000000⟩, + ⟨7, 1, 6, 5, 5, 4, 33955071701270966197995413392323419401981054156800000⟩, + ⟨7, 1, 7, 5, 6, 4, 26974530515041119182333620136372780908167561216000000⟩, + ⟨7, 1, 8, 5, 7, 4, -74765492566324085082578042076884723968797730406400000⟩, + ⟨7, 1, 6, 6, 4, 4, -22639824641895108629654443495575897199134690508800000⟩, + ⟨7, 1, 7, 6, 5, 4, 168528579243828344492700842350435787418771023462400000⟩, + ⟨7, 1, 8, 6, 6, 4, 111679946017561584747182012336265996390606726758400000⟩, + ⟨7, 1, 6, 7, 3, 4, -114290148823881407476577810598252823632915569049600000⟩, + ⟨7, 1, 7, 7, 4, 4, 131046059265912432972104448842767183205627854848000000⟩, + ⟨7, 1, 8, 7, 5, 4, 288481121343159712295969222409733893314360377344000000⟩ +] + +def collectedFourData_14_4_52 : List CollectedFourTerm := [ + ⟨7, 2, 5, 1, 8, 5, -23219198701692593893607589337398670697724641280000000⟩, + ⟨7, 2, 5, 2, 7, 5, -11901892299776887251947436560485760512907280384000000⟩, + ⟨7, 2, 6, 2, 8, 5, 21097172474888210827306248246851396285107273728000000⟩, + ⟨7, 2, 5, 3, 6, 5, 8143452957399951475525307106863097263167635456000000⟩, + ⟨7, 2, 6, 3, 7, 5, 44731649444752578046014284425378119605551104000000⟩, + ⟨7, 2, 7, 3, 8, 5, -3579640148930743416537615679746668733118021632000000⟩, + ⟨7, 2, 5, 4, 5, 5, 4937797659627032514620860467913855017915777024000000⟩, + ⟨7, 2, 6, 4, 6, 5, 9039765652575758423129915387063234555547746304000000⟩, + ⟨7, 2, 7, 4, 7, 5, -9468444746930002250981602593738326106999619584000000⟩, + ⟨7, 2, 8, 4, 8, 5, 3380688809579993668450174200685140558710046720000000⟩, + ⟨7, 2, 5, 5, 4, 5, 3275422083602609930214750405607892733067788288000000⟩, + ⟨7, 2, 6, 5, 5, 5, 7551651117429272993284745158416202488549998592000000⟩, + ⟨7, 2, 7, 5, 6, 5, 2999584941215358239020308857156616962200043520000000⟩, + ⟨7, 2, 8, 5, 7, 5, -5542646868297809445602524003872978247322959872000000⟩, + ⟨7, 2, 5, 6, 3, 5, -29847458543287727796195011592683665642475225088000000⟩, + ⟨7, 2, 6, 6, 4, 5, -5035125785022875174668388923409746011170537472000000⟩, + ⟨7, 2, 7, 6, 5, 5, 18740485146991856512540734381430163720663728128000000⟩, + ⟨7, 2, 8, 6, 6, 5, 8279253995374834013097420495081961358289272832000000⟩, + ⟨7, 2, 5, 7, 2, 5, 1653540823520402237661574950629933420132696064000000⟩, + ⟨7, 2, 6, 7, 3, 5, -25418274408907113977601312342502451741693313024000000⟩, + ⟨7, 2, 7, 7, 4, 5, 14572405097484866892394603445413099489260994560000000⟩, + ⟨7, 2, 8, 7, 5, 5, 21386189388871946383224387575557885504121733120000000⟩ +] + +def collectedFourData_14_4_53 : List CollectedFourTerm := [ + ⟨7, 3, 4, 0, 8, 6, -62348027646184926036255418883095281914287541452800000⟩, + ⟨7, 3, 4, 1, 7, 6, 72713245521044852711570152006009547561429159116800000⟩, + ⟨7, 3, 5, 1, 8, 6, 356926152508311539215484231963909457879477780480000000⟩, + ⟨7, 3, 4, 2, 6, 6, -47939349027828701931459166310129191088566566912000000⟩, + ⟨7, 3, 5, 2, 7, 6, 182956211396648819480769378954731107445473542144000000⟩, + ⟨7, 3, 6, 2, 8, 6, -162153153883755322236301310926673832601215565824000000⟩, + ⟨7, 3, 4, 3, 5, 6, -131530948328125790090838914181676561152135187660800000⟩, + ⟨7, 3, 5, 3, 6, 6, -125181379838285051298655411667076720265103671296000000⟩, + ⟨7, 3, 6, 3, 7, 6, -343808064541482927955676719725797223885176832000000⟩, + ⟨7, 3, 7, 3, 8, 6, 18342108501631056624524974052360183095391944704000000⟩, + ⟨7, 3, 4, 4, 4, 6, 98577945591790903512675454092803483050319020032000000⟩, + ⟨7, 3, 5, 4, 5, 6, -75903959613677254968294528956735840589535248384000000⟩, + ⟨7, 3, 6, 4, 6, 6, -69479761455235952985761517124977019882341138432000000⟩, + ⟨7, 3, 7, 4, 7, 6, 48516396527110466428772758945858681060561256448000000⟩, + ⟨7, 3, 8, 4, 8, 6, -12992010029434502204682202881963693242717306880000000⟩, + ⟨7, 3, 4, 5, 3, 6, 93933337208080063277114997607498051301945219481600000⟩, + ⟨7, 3, 5, 5, 4, 6, -50349877149542408878983526183979456335454404608000000⟩, + ⟨7, 3, 6, 5, 5, 6, -58042092947691570436892755367387173687432052736000000⟩, + ⟨7, 3, 7, 5, 6, 6, -15369900370590346276591174109348567163800125440000000⟩, + ⟨7, 3, 8, 5, 7, 6, 21300429515571174390736043349443937348498751488000000⟩, + ⟨7, 3, 4, 6, 2, 6, -118975733889474092786667295909410598078494906777600000⟩, + ⟨7, 3, 5, 6, 3, 6, 458815942654835571138847305541579373983624593408000000⟩, + ⟨7, 3, 6, 6, 4, 6, 38700045099157527903082251616941394933397323776000000⟩, + ⟨7, 3, 7, 6, 5, 6, -96026415404354750594879416333936879203061334016000000⟩, + ⟨7, 3, 8, 6, 6, 6, -31817229269767942637749400800675292958664163328000000⟩, + ⟨7, 3, 4, 7, 1, 6, -114290148823881407476577810598252823632915569049600000⟩, + ⟨7, 3, 5, 7, 2, 6, -25418274408907113977601312342502451741693313024000000⟩, + ⟨7, 3, 6, 7, 3, 6, 195365201976378819021573601752104789151099912192000000⟩, + ⟨7, 3, 7, 7, 4, 6, -74669135529622827664498084008418511096716984320000000⟩, + ⟨7, 3, 8, 7, 5, 6, -82187270902975902416427426878339328441298452480000000⟩ +] + +def collectedFourData_14_4_54 : List CollectedFourTerm := [ + ⟨7, 4, 3, 0, 7, 7, -18522701781694858540660016765006156319890079744000000⟩, + ⟨7, 4, 4, 0, 8, 7, 71488780180216582019005789705653772921092440064000000⟩, + ⟨7, 4, 3, 1, 6, 7, 87829197825207771338790771883572446479377235968000000⟩, + ⟨7, 4, 4, 1, 7, 7, -83373627386305458790976898787001933024024592384000000⟩, + ⟨7, 4, 5, 1, 8, 7, -204627285100641667948559519387436556381008691200000000⟩, + ⟨7, 4, 3, 2, 5, 7, 37375653643966299295767746728260256978308169728000000⟩, + ⟨7, 4, 4, 2, 6, 7, 54967666404485391752767757042213244312810946560000000⟩, + ⟨7, 4, 5, 2, 7, 7, -104889576085415961444247174478392014683882127360000000⟩, + ⟨7, 4, 6, 2, 8, 7, 61975396341902507238027231613839290330555351040000000⟩, + ⟨7, 4, 3, 3, 4, 7, -4072402292963108698041260154918006614157950976000000⟩, + ⟨7, 4, 4, 3, 5, 7, 150814507000690644246173949100891381183077679104000000⟩, + ⟨7, 4, 5, 3, 6, 7, 71767018811724583771217843319203345065039626240000000⟩, + ⟨7, 4, 6, 3, 7, 7, 131404419557425732038846778489714628068638720000000⟩, + ⟨7, 4, 7, 3, 8, 7, -5257804505685193081197249756125887422403706880000000⟩, + ⟨7, 4, 3, 4, 3, 7, -60141117335850239047531343259622781764446978048000000⟩, + ⟨7, 4, 4, 4, 4, 7, -113030313052093944284794087604581308626538332160000000⟩, + ⟨7, 4, 5, 4, 5, 7, 43516063687078354898627911069135194167401512960000000⟩, + ⟨7, 4, 6, 4, 6, 7, 26555362327494466374875607541599058841535774720000000⟩, + ⟨7, 4, 7, 4, 7, 7, -13907328497002796814355867484941278176146882560000000⟩, + ⟨7, 4, 8, 4, 8, 7, 2979349898168733793805305047778211750876282880000000⟩, + ⟨7, 4, 3, 5, 2, 7, -75097458894404984740742110133779995503395602432000000⟩, + ⟨7, 4, 4, 5, 3, 7, -107704765471815153431006417328260396923389739008000000⟩, + ⟨7, 4, 5, 5, 4, 7, 28865799252470799309468077245900809968308715520000000⟩, + ⟨7, 4, 6, 5, 5, 7, 22183852911831023040968874150395247711548866560000000⟩, + ⟨7, 4, 7, 5, 6, 7, 4405814708447303552290515559534549749517516800000000⟩, + ⟨7, 4, 8, 5, 7, 7, -4884650824960110455444026816498096594734809088000000⟩, + ⟨7, 4, 3, 6, 1, 7, -18283372950443030547949215217398518393597853696000000⟩, + ⟨7, 4, 4, 6, 2, 7, 136418591059071053943911585600441612618315071488000000⟩, + ⟨7, 4, 5, 6, 3, 7, -263041136231014677678095781972899300747268587520000000⟩, + ⟨7, 4, 6, 6, 4, 7, -14791267243492504636929831767752233853082664960000000⟩, + ⟨7, 4, 7, 6, 5, 7, 27526176695166626393942049859773296056750571520000000⟩, + ⟨7, 4, 8, 6, 6, 7, 7296381281274339018722905896789938936299388928000000⟩, + ⟨7, 4, 3, 7, 0, 7, 1921766077212244334869919378501543846534581321728000000⟩, + ⟨7, 4, 4, 7, 1, 7, 131046059265912432972104448842767183205627854848000000⟩, + ⟨7, 4, 5, 7, 2, 7, 14572405097484866892394603445413099489260994560000000⟩, + ⟨7, 4, 6, 7, 3, 7, -74669135529622827664498084008418511096716984320000000⟩, + ⟨7, 4, 7, 7, 4, 7, 21404066887313309383203460001798216619550310400000000⟩, + ⟨7, 4, 8, 7, 5, 7, 18847325136047906329616440618825488355798548480000000⟩ +] + +def collectedFourData_14_4_55 : List CollectedFourTerm := [ + ⟨7, 5, 2, 0, 6, 8, 285317205433035913154325109653115394643097288704000000⟩, + ⟨7, 5, 3, 0, 7, 8, -81550712935909058392940233914250665191238795264000000⟩, + ⟨7, 5, 4, 0, 8, 8, 157373396692501741262412701372433388435346030592000000⟩, + ⟨7, 5, 2, 1, 5, 8, -139316850497906949332557848694763760012654280704000000⟩, + ⟨7, 5, 3, 1, 6, 8, 386689468072799862842827479297178761776917905408000000⟩, + ⟨7, 5, 4, 1, 7, 8, -183536366172168268865650732230154879532953239552000000⟩, + ⟨7, 5, 5, 1, 8, 8, -300307179495602266905524002440490487311132262400000000⟩, + ⟨7, 5, 2, 2, 4, 8, -513261018242466926959527537172080684622185234432000000⟩, + ⟨7, 5, 3, 2, 5, 8, 164555432411230066259045906944538817650352979968000000⟩, + ⟨7, 5, 4, 2, 6, 8, 121004279951723930499169498931469924643299655680000000⟩, + ⟨7, 5, 5, 2, 7, 8, -153933981664314558231697343412014526700946718720000000⟩, + ⟨7, 5, 6, 2, 8, 8, 68215450096519579943824330764406564739151298560000000⟩, + ⟨7, 5, 2, 3, 3, 8, 584654319254237722154991250021426862538337812480000000⟩, + ⟨7, 5, 3, 3, 4, 8, -17929744497704908731150799967820734023971373056000000⟩, + ⟨7, 5, 4, 3, 5, 8, 331998828031085097745142803289980005107695091712000000⟩, + ⟨7, 5, 5, 3, 6, 8, 105323935610819752285948163142631630792273428480000000⟩, + ⟨7, 5, 6, 3, 7, 8, 144635002821613700249132245759942583207854080000000⟩, + ⟨7, 5, 7, 3, 8, 8, -4629753380146776000964589740616722216654995456000000⟩, + ⟨7, 5, 2, 4, 2, 8, -139402392961889166823115221718443986173999185920000000⟩, + ⟨7, 5, 3, 4, 3, 8, -264785939616416580075487417947222799804570533888000000⟩, + ⟨7, 5, 4, 4, 4, 8, -248821762651188479229915611443798470512061972480000000⟩, + ⟨7, 5, 5, 4, 5, 8, 63863361829729520510144176543219745413838929920000000⟩, + ⟨7, 5, 6, 4, 6, 8, 29229115109691063095838089339772732254013358080000000⟩, + ⟨7, 5, 7, 4, 7, 8, -12246081239458208107064652831259767711278825472000000⟩, + ⟨7, 5, 8, 4, 8, 8, 2186219115914851722739256581910870142882938880000000⟩, + ⟨7, 5, 2, 5, 1, 8, 144379353130431842553248351744674368842486513664000000⟩, + ⟨7, 5, 3, 5, 2, 8, -330634881708572862982079994394689308457531604992000000⟩, + ⟨7, 5, 4, 5, 3, 8, -237098251495406609596715776137327193793520205824000000⟩, + ⟨7, 5, 5, 5, 4, 8, 42362907532748120040880410823351183355192279040000000⟩, + ⟨7, 5, 6, 5, 5, 8, 24417455967641583275640338483353828175212707840000000⟩, + ⟨7, 5, 7, 5, 6, 8, 3879534797590587791439165106157054685515612160000000⟩, + ⟨7, 5, 8, 5, 7, 8, -3584311132660474576056384780699178930104434688000000⟩, + ⟨7, 5, 2, 6, 0, 8, -2599128772744849620570810145675534318402478800896000000⟩, + ⟨7, 5, 3, 6, 1, 8, -80497009375557369421802894078653274075091173376000000⟩, + ⟨7, 5, 4, 6, 2, 8, 300308062228098838529981915065820541136366731264000000⟩, + ⟨7, 5, 5, 6, 3, 8, -386034255764099895970466549460065227904164823040000000⟩, + ⟨7, 5, 6, 6, 4, 8, -16280540538157917497251117027737817975294525440000000⟩, + ⟨7, 5, 7, 6, 5, 8, 24238141501679377006369131777231491415486234624000000⟩, + ⟨7, 5, 8, 6, 6, 8, 5354016406038742820522482798757029132294422528000000⟩, + ⟨7, 5, 3, 7, 0, 8, 8461043941634064780285861678591437983675966291968000000⟩, + ⟨7, 5, 4, 7, 1, 8, 288481121343159712295969222409733893314360377344000000⟩, + ⟨7, 5, 5, 7, 2, 8, 21386189388871946383224387575557885504121733120000000⟩, + ⟨7, 5, 6, 7, 3, 8, -82187270902975902416427426878339328441298452480000000⟩, + ⟨7, 5, 7, 7, 4, 8, 18847325136047906329616440618825488355798548480000000⟩, + ⟨7, 5, 8, 7, 5, 8, 13829991073427398214630366857463315571387924480000000⟩ +] + +def collectedFourData_14_4 : List (List CollectedFourTerm) := [ + collectedFourData_14_4_0, + collectedFourData_14_4_1, + collectedFourData_14_4_2, + collectedFourData_14_4_3, + collectedFourData_14_4_4, + collectedFourData_14_4_5, + collectedFourData_14_4_6, + collectedFourData_14_4_7, + collectedFourData_14_4_8, + collectedFourData_14_4_9, + collectedFourData_14_4_10, + collectedFourData_14_4_11, + collectedFourData_14_4_12, + collectedFourData_14_4_13, + collectedFourData_14_4_14, + collectedFourData_14_4_15, + collectedFourData_14_4_16, + collectedFourData_14_4_17, + collectedFourData_14_4_18, + collectedFourData_14_4_19, + collectedFourData_14_4_20, + collectedFourData_14_4_21, + collectedFourData_14_4_22, + collectedFourData_14_4_23, + collectedFourData_14_4_24, + collectedFourData_14_4_25, + collectedFourData_14_4_26, + collectedFourData_14_4_27, + collectedFourData_14_4_28, + collectedFourData_14_4_29, + collectedFourData_14_4_30, + collectedFourData_14_4_31, + collectedFourData_14_4_32, + collectedFourData_14_4_33, + collectedFourData_14_4_34, + collectedFourData_14_4_35, + collectedFourData_14_4_36, + collectedFourData_14_4_37, + collectedFourData_14_4_38, + collectedFourData_14_4_39, + collectedFourData_14_4_40, + collectedFourData_14_4_41, + collectedFourData_14_4_42, + collectedFourData_14_4_43, + collectedFourData_14_4_44, + collectedFourData_14_4_45, + collectedFourData_14_4_46, + collectedFourData_14_4_47, + collectedFourData_14_4_48, + collectedFourData_14_4_49, + collectedFourData_14_4_50, + collectedFourData_14_4_51, + collectedFourData_14_4_52, + collectedFourData_14_4_53, + collectedFourData_14_4_54, + collectedFourData_14_4_55 +] + +theorem collectedFourChecked_14_4 : collectNumericRowParts 14 4 = collectedFourData_14_4 := by + decide +kernel + +def collectedFourData_14_5_0 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_5_1 : List CollectedFourTerm := [ + ⟨0, 6, 8, 5, 8, 1, 956587377225723149962476733514563683186162794496000000⟩, + ⟨0, 6, 8, 6, 7, 1, 257855340154965598495553980692823220085634105344000000⟩, + ⟨0, 6, 8, 7, 6, 1, 385511272191588624852513193654055297831827144704000000⟩ +] + +def collectedFourData_14_5_2 : List CollectedFourTerm := [ + ⟨0, 7, 7, 4, 8, 2, -33899268179154701028606442120467215842856140800000000⟩, + ⟨0, 7, 7, 5, 7, 2, -15462674676325751514378990296370292178383011840000000⟩, + ⟨0, 7, 8, 5, 8, 2, -93342497584022968005124408681762041635096494080000000⟩, + ⟨0, 7, 7, 6, 6, 2, -4674776980565817437409959531277154550210887680000000⟩, + ⟨0, 7, 8, 6, 7, 2, -25161174021809026577811118378876561171540869120000000⟩, + ⟨0, 7, 7, 7, 5, 2, 16794307777409080553043071951784807224511037440000000⟩, + ⟨0, 7, 8, 7, 6, 2, -37617666561228106018436693860507486055741521920000000⟩ +] + +def collectedFourData_14_5_3 : List CollectedFourTerm := [ + ⟨0, 8, 6, 3, 8, 3, 8065255202982634097587014244682332038487867392000000⟩, + ⟨0, 8, 6, 4, 7, 3, -3519326043935988426471537362016047453945462784000000⟩, + ⟨0, 8, 7, 4, 8, 3, 20654400665111695979681447636091601714560368640000000⟩, + ⟨0, 8, 6, 5, 6, 3, -5960623588584545775022833502907841788390670336000000⟩, + ⟨0, 8, 7, 5, 7, 3, 9421214535701877307841892271489895509128118272000000⟩, + ⟨0, 8, 8, 5, 8, 3, 28436208917456121050551715315378091370513170432000000⟩, + ⟨0, 8, 6, 6, 5, 3, 566960341950091286890759508861249636108599296000000⟩, + ⟨0, 8, 7, 6, 6, 3, 2848283221524551401909870826950275737000607744000000⟩, + ⟨0, 8, 8, 6, 7, 3, 7665194521376276022058771616183506189940686848000000⟩, + ⟨0, 8, 6, 7, 4, 3, 19675588073362017518700163798460884194007449600000000⟩, + ⟨0, 8, 7, 7, 5, 3, -10232561950735840814359394825197563970691530752000000⟩, + ⟨0, 8, 8, 7, 6, 3, 11459987176359658349245463336615941211808595968000000⟩ +] + +def collectedFourData_14_5_4 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_5_5 : List CollectedFourTerm := [ + ⟨1, 5, 8, 5, 8, 1, 208281450887105747158536425774749256848427188224000000⟩, + ⟨1, 5, 8, 6, 7, 1, 56143835518949619525920867290279774162293620736000000⟩, + ⟨1, 5, 8, 7, 6, 1, 83938852860747167763828766639856699496072216576000000⟩ +] + +def collectedFourData_14_5_6 : List CollectedFourTerm := [ + ⟨1, 6, 7, 4, 8, 2, 78030023464816317824653477427530198836251197440000000⟩, + ⟨1, 6, 7, 5, 7, 2, 35592298377829039793089724537655190882470592512000000⟩, + ⟨1, 6, 8, 5, 8, 2, 214857655281910914825422107909208736162323103744000000⟩, + ⟨1, 6, 7, 6, 6, 2, 10760496526312614547371952704039191775201460224000000⟩, + ⟨1, 6, 8, 6, 7, 2, 57916500997840770058682744481946182341168726016000000⟩, + ⟨1, 6, 7, 7, 5, 2, -38657478474783253101584668120415552321819246592000000⟩, + ⟨1, 6, 8, 7, 6, 2, 86589108323855826707428853873016875463324205056000000⟩ +] + +def collectedFourData_14_5_7 : List CollectedFourTerm := [ + ⟨1, 7, 6, 3, 8, 3, -107741501768922164430566034766724421915745714176000000⟩, + ⟨1, 7, 6, 4, 7, 3, 47013698096982533302736818568508035976608612352000000⟩, + ⟨1, 7, 7, 4, 8, 3, -275916395673778713427497012782552646032472145920000000⟩, + ⟨1, 7, 6, 5, 6, 3, 79626313210258351335048296978992694887352107008000000⟩, + ⟨1, 7, 7, 5, 7, 3, -125855385479722756686551417182181739252538146816000000⟩, + ⟨1, 7, 8, 5, 8, 3, -379871408439564500962599894486109895157451063296000000⟩, + ⟨1, 7, 6, 6, 5, 3, -7573865568758990530054059668855676117228453888000000⟩, + ⟨1, 7, 7, 6, 6, 3, -38049423611145158524334509909751972540272607232000000⟩, + ⟨1, 7, 8, 6, 7, 3, -102397202357413456590455466222371943453812588544000000⟩, + ⟨1, 7, 6, 7, 4, 3, -262840710412580619464619952318018462143007948800000000⟩, + ⟨1, 7, 7, 7, 5, 3, 136693950007695130395749298022550016904717664256000000⟩, + ⟨1, 7, 8, 7, 6, 3, -153090782319816199122196752101105018768304635904000000⟩ +] + +def collectedFourData_14_5_8 : List CollectedFourTerm := [ + ⟨1, 8, 5, 2, 8, 4, 164287054501377607527030832724888742004097286144000000⟩, + ⟨1, 8, 5, 3, 7, 4, -12942335778534538121786133512325681099753652224000000⟩, + ⟨1, 8, 6, 3, 8, 4, 167718103448624105065774125833484069815401316352000000⟩, + ⟨1, 8, 5, 4, 6, 4, -31695666092451056959744294748147112955997061120000000⟩, + ⟨1, 8, 6, 4, 7, 4, -73184874458530391849916613424114982834829000704000000⟩, + ⟨1, 8, 7, 4, 8, 4, 214755566949664493791787460517196801100396625920000000⟩, + ⟨1, 8, 5, 5, 5, 4, -8722689164681132579823198406418666772139868160000000⟩, + ⟨1, 8, 6, 5, 6, 4, -123951996370657737491936235597179670737260118016000000⟩, + ⟨1, 8, 7, 5, 7, 4, 97957733161759371558429992048243636283497250816000000⟩, + ⟨1, 8, 8, 5, 8, 4, 197111639531706212846531979672875694257407524864000000⟩, + ⟨1, 8, 5, 6, 4, 4, 72738902518644961009838095225039284214016507904000000⟩, + ⟨1, 8, 6, 6, 5, 4, 11790019148716756564023604742305809823250251776000000⟩, + ⟨1, 8, 7, 6, 6, 4, 29615222827789274011876452984730421088309215232000000⟩, + ⟨1, 8, 8, 6, 7, 4, 53132928648250119510944669679934010563227549696000000⟩, + ⟨1, 8, 5, 7, 3, 4, 101412328038539057026425856409017918822891388928000000⟩, + ⟨1, 8, 6, 7, 4, 4, 409156589946500527982939948010419350014630297600000000⟩, + ⟨1, 8, 7, 7, 5, 4, -106393774319955878461101593599370873204172128256000000⟩, + ⟨1, 8, 8, 7, 6, 4, 79437342294876474496512363205715263075632807936000000⟩ +] + +def collectedFourData_14_5_9 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_5_10 : List CollectedFourTerm := [ + ⟨2, 4, 8, 5, 8, 1, -181091120205779797941483353947912174452986609664000000⟩, + ⟨2, 4, 8, 6, 7, 1, -48814476869985454664208773695692765474267856896000000⟩, + ⟨2, 4, 8, 7, 6, 1, -72980963156339640323945341959079197033822683136000000⟩ +] + +def collectedFourData_14_5_11 : List CollectedFourTerm := [ + ⟨2, 5, 7, 4, 8, 2, 163627174483718028531225345054429985354914201600000000⟩, + ⟨2, 5, 7, 5, 7, 2, 74636235622453247519527927430591607612301639680000000⟩, + ⟨2, 5, 8, 5, 8, 2, 450551588848718489058212298253677804973625180160000000⟩, + ⟨2, 5, 7, 6, 6, 2, 22564515098938790558542744113862215724286607360000000⟩, + ⟨2, 5, 8, 6, 7, 2, 121449577911932377392809171027608088051177226240000000⟩, + ⟨2, 5, 7, 7, 5, 2, -81063848178208711081089292897551183076267130880000000⟩, + ⟨2, 5, 8, 7, 6, 2, 181575379667617413025076061022245322724569251840000000⟩ +] + +def collectedFourData_14_5_12 : List CollectedFourTerm := [ + ⟨2, 6, 6, 3, 8, 3, 35072107322941459624029726377363356181663318016000000⟩, + ⟨2, 6, 6, 4, 7, 3, -15303939876781570887132169288387161547742380032000000⟩, + ⟨2, 6, 7, 4, 8, 3, 89816544992890116753938148722827910462539038720000000⟩, + ⟨2, 6, 6, 5, 6, 3, -25920026700851783894772187002146023165529161728000000⟩, + ⟨2, 6, 7, 5, 7, 3, 40968554496130280795477197719676979157984608256000000⟩, + ⟨2, 6, 8, 5, 8, 3, 123656071123674455479092060107291954770593447936000000⟩, + ⟨2, 6, 6, 6, 5, 3, 2465451304426380894355258778989188312421367808000000⟩, + ⟨2, 6, 7, 6, 6, 3, 12385881452889421096867046692527332910654554112000000⟩, + ⟨2, 6, 8, 6, 7, 3, 33332426332338896803712900285213931515626389504000000⟩, + ⟨2, 6, 6, 7, 4, 3, 85560136559069461165856923121503869212609740800000000⟩, + ⟨2, 6, 7, 7, 5, 3, -44496733443987879693979493196842892999625015296000000⟩, + ⟨2, 6, 8, 7, 6, 3, 49834244553127280719249147940817974843632779264000000⟩ +] + +def collectedFourData_14_5_13 : List CollectedFourTerm := [ + ⟨2, 7, 5, 2, 8, 4, -22275927625272574678183978001226977441596047360000000⟩, + ⟨2, 7, 5, 3, 7, 4, 1754870680344406745178368322550405268043202560000000⟩, + ⟨2, 7, 6, 3, 8, 4, -22741148687635645696863485547250399105127546880000000⟩, + ⟨2, 7, 5, 4, 6, 4, 4297662807657953640178770505999065549688012800000000⟩, + ⟨2, 7, 6, 4, 7, 4, 9923246671205077068371600311883984296225013760000000⟩, + ⟨2, 7, 7, 4, 8, 4, -29119028769579593491797867833851359961861324800000000⟩, + ⟨2, 7, 5, 5, 5, 4, 1182722479990393110081047777309067019970150400000000⟩, + ⟨2, 7, 6, 5, 6, 4, 16806836719673900932754341224006306627625943040000000⟩, + ⟨2, 7, 7, 5, 7, 4, -13282235662876390959144578454231371173897175040000000⟩, + ⟨2, 7, 8, 5, 8, 4, -26726662241487111699160564815430843243859804160000000⟩, + ⟨2, 7, 5, 6, 4, 4, -9862776668343671059583342881024678601435381760000000⟩, + ⟨2, 7, 6, 6, 5, 4, -1598626343715901010545935022739677521578557440000000⟩, + ⟨2, 7, 7, 6, 6, 4, -4015572391387796070808316114554590538581934080000000⟩, + ⟨2, 7, 8, 6, 7, 4, -7204373324967407198420844845836570831607562240000000⟩, + ⟨2, 7, 5, 7, 3, 4, -13750649353068495604959878760180269304848056320000000⟩, + ⟨2, 7, 6, 7, 4, 4, -55478154457843463168529048313590043109228544000000000⟩, + ⟨2, 7, 7, 7, 5, 4, 14426091110611807206569795932390969416760688640000000⟩, + ⟨2, 7, 8, 7, 6, 4, -10771028143850701960004125043828205499019427840000000⟩ +] + +def collectedFourData_14_5_14 : List CollectedFourTerm := [ + ⟨2, 8, 4, 1, 8, 5, 164287054501377607527030832724888742004097286144000000⟩, + ⟨2, 8, 4, 2, 7, 5, -22275927625272574678183978001226977441596047360000000⟩, + ⟨2, 8, 5, 2, 8, 5, 277881786391929005960290839967446246700288573440000000⟩, + ⟨2, 8, 4, 3, 6, 5, -18142124962787301707115219229876721737820798976000000⟩, + ⟨2, 8, 5, 3, 7, 5, -21891191592294310944257302680604369188280074240000000⟩, + ⟨2, 8, 6, 3, 8, 5, 141842600861101956926538194926780807158442229760000000⟩, + ⟨2, 8, 4, 4, 5, 5, 46913564624157440162963348431258738584220336128000000⟩, + ⟨2, 8, 5, 4, 6, 5, -53611334997661281655020259773764783656088371200000000⟩, + ⟨2, 8, 6, 4, 7, 5, -61893932279475350343029260282943590278648299520000000⟩, + ⟨2, 8, 7, 4, 8, 5, 121082091673234194099847048198602474050184806400000000⟩, + ⟨2, 8, 4, 5, 4, 5, 6551417761618249040655399056674251032871567360000000⟩, + ⟨2, 8, 5, 5, 5, 5, -14753910188357482772140854939548533801982361600000000⟩, + ⟨2, 8, 6, 5, 6, 5, -104828716671755312148017972360840356915398574080000000⟩, + ⟨2, 8, 7, 5, 7, 5, 55229894131565800886008773054162851001500958720000000⟩, + ⟨2, 8, 8, 5, 8, 5, 83350655165671007021126115733824543924588380160000000⟩, + ⟨2, 8, 4, 6, 3, 5, -163760981074353351782252389398732823364118773760000000⟩, + ⟨2, 8, 5, 6, 4, 5, 123033529534123785192860765532574305068557271040000000⟩, + ⟨2, 8, 6, 6, 5, 5, 9971058257097761764097407398323523720975482880000000⟩, + ⟨2, 8, 7, 6, 6, 5, 16697462963547362331925496664246323019975229440000000⟩, + ⟨2, 8, 8, 6, 7, 5, 22467797559921006534853103334838282242742026240000000⟩, + ⟨2, 8, 4, 7, 2, 5, 168290254328966388961779104274729540617628549120000000⟩, + ⟨2, 8, 5, 7, 3, 5, 171532924265053628251162433957357089883192033280000000⟩, + ⟨2, 8, 6, 7, 4, 5, 346032024475215587064576236073272910060453888000000000⟩, + ⟨2, 8, 7, 7, 5, 5, -59986248173439554517765242302777725277458923520000000⟩, + ⟨2, 8, 8, 7, 6, 5, 33590885554135842999602528718749523534246051840000000⟩ +] + +def collectedFourData_14_5_15 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_5_16 : List CollectedFourTerm := [ + ⟨3, 3, 8, 5, 8, 1, 501521546084164268062518066826329824744467070976000000⟩, + ⟨3, 3, 8, 6, 7, 1, 135188914195823812289519132941329742156806488064000000⟩, + ⟨3, 3, 8, 7, 6, 1, 202116621926505108821727578497145527382493364224000000⟩ +] + +def collectedFourData_14_5_17 : List CollectedFourTerm := [ + ⟨3, 4, 7, 4, 8, 2, -12056227177184718208574063046723661149146972160000000⟩, + ⟨3, 4, 7, 5, 7, 2, -5499278559037405626611384806698078288444653568000000⟩, + ⟨3, 4, 8, 5, 8, 2, -33197128333608118180525004486882674916475273216000000⟩, + ⟨3, 4, 7, 6, 6, 2, -1662577875797096361498173436771922030085799936000000⟩, + ⟨3, 4, 8, 6, 7, 2, -8948536247108219797782344750576227911859175424000000⟩, + ⟨3, 4, 7, 7, 5, 2, 5972872003546977473952305630540112453527666688000000⟩, + ⟨3, 4, 8, 7, 6, 2, -13378670345946685582275081737492806759543209984000000⟩ +] + +def collectedFourData_14_5_18 : List CollectedFourTerm := [ + ⟨3, 5, 6, 3, 8, 3, 70055402995198388617741276293377598106688815104000000⟩, + ⟨3, 5, 6, 4, 7, 3, -30569126217885383371185911453926275188111966208000000⟩, + ⟨3, 5, 7, 4, 8, 3, 179405651253737399879613172380060341245763911680000000⟩, + ⟨3, 5, 6, 5, 6, 3, -51774417187264181508780433636235850726330335232000000⟩, + ⟨3, 5, 7, 5, 7, 3, 81833366011621914198264870933887990159495921664000000⟩, + ⟨3, 5, 8, 5, 8, 3, 246999013079131704614465310115420489789508419584000000⟩, + ⟨3, 5, 6, 6, 5, 3, 4924659448211963654849119239589393980563914752000000⟩, + ⟨3, 5, 7, 6, 6, 3, 24740398649080914032329404819406786259979337728000000⟩, + ⟨3, 5, 8, 6, 7, 3, 66580446336405664712006962911117084526720843776000000⟩, + ⟨3, 5, 6, 7, 4, 3, 170903612713600461376537802399538330075345715200000000⟩, + ⟨3, 5, 7, 7, 5, 3, -88880789645321305523584758539817572553587687424000000⟩, + ⟨3, 5, 8, 7, 6, 3, 99542295904385429467333154361855615571083657216000000⟩ +] + +def collectedFourData_14_5_19 : List CollectedFourTerm := [ + ⟨3, 6, 5, 2, 8, 4, -18142124962787301707115219229876721737820798976000000⟩, + ⟨3, 6, 5, 3, 7, 4, 1429214698121925206012014580803435399055671296000000⟩, + ⟨3, 6, 6, 3, 8, 4, -18521013725163060381680250533481563875713220608000000⟩, + ⟨3, 6, 5, 4, 6, 4, 3500134181437926754365388514705093155073556480000000⟩, + ⟨3, 6, 6, 4, 7, 4, 8081763604821495743832583012721491429048713216000000⟩, + ⟨3, 6, 7, 4, 8, 4, -23715333772828567040293194724759493766996295680000000⟩, + ⟨3, 6, 5, 5, 5, 4, 963241548869992817411907807155816550251888640000000⟩, + ⟨3, 6, 6, 5, 6, 4, 13687947686252869925863037028173466896814833664000000⟩, + ⟨3, 6, 7, 5, 7, 4, -10817416146913206817668055356429053550724644864000000⟩, + ⟨3, 6, 8, 5, 8, 4, -21766925013401547868705426543694739889880825856000000⟩, + ⟨3, 6, 5, 6, 4, 4, -8032515179935831318382107261464568161701462016000000⟩, + ⟨3, 6, 6, 6, 5, 4, -1301965035278424599778951515515843937990344704000000⟩, + ⟨3, 6, 7, 6, 6, 4, -3270392027985618392966824845857868120355504128000000⟩, + ⟨3, 6, 8, 6, 7, 4, -5867438758951832254251454054196874088896528384000000⟩, + ⟨3, 6, 5, 7, 3, 4, -11198905072748299395407388001695697089972928512000000⟩, + ⟨3, 6, 6, 7, 4, 4, -45182926960901175659785014560889091937166950400000000⟩, + ⟨3, 6, 7, 7, 5, 4, 11749003321251003389958862328751701620502298624000000⟩, + ⟨3, 6, 8, 7, 6, 4, -8772220032791891898708554745150457103561785344000000⟩ +] + +def collectedFourData_14_5_20 : List CollectedFourTerm := [ + ⟨3, 7, 4, 1, 8, 5, -12942335778534538121786133512325681099753652224000000⟩, + ⟨3, 7, 4, 2, 7, 5, 1754870680344406745178368322550405268043202560000000⟩, + ⟨3, 7, 5, 2, 8, 5, -21891191592294310944257302680604369188280074240000000⟩, + ⟨3, 7, 4, 3, 6, 5, 1429214698121925206012014580803435399055671296000000⟩, + ⟨3, 7, 5, 3, 7, 5, 1724561640231545797059207936922736040911831040000000⟩, + ⟨3, 7, 6, 3, 8, 5, -11174188822221778262265620719704748453747752960000000⟩, + ⟨3, 7, 4, 4, 5, 5, -3695793973399977756922979046853324851105497088000000⟩, + ⟨3, 7, 5, 4, 6, 5, 4223436235929436647466643024775816219407155200000000⟩, + ⟨3, 7, 6, 4, 7, 5, 4875929248631884573048425957678727961688145920000000⟩, + ⟨3, 7, 7, 4, 8, 5, -9538700976522512325358175016370481528202854400000000⟩, + ⟨3, 7, 4, 5, 4, 5, -516112780484523943003238819057122851485122560000000⟩, + ⟨3, 7, 5, 5, 5, 5, 1162295229430040752969299013779520963058073600000000⟩, + ⟨3, 7, 6, 5, 6, 5, 8258279719704525687333634866284381364478279680000000⟩, + ⟨3, 7, 7, 5, 7, 5, -4350944370103396638167876820297418062031749120000000⟩, + ⟨3, 7, 8, 5, 8, 5, -6566263968813883382033621168791758170342031360000000⟩, + ⟨3, 7, 4, 6, 3, 5, 12900892349182317245972393520080126680718376960000000⟩, + ⟨3, 7, 5, 6, 4, 5, -9692432894860402286079314278710198220452003840000000⟩, + ⟨3, 7, 6, 6, 5, 5, -785507929534438598385719914502223915626004480000000⟩, + ⟨3, 7, 7, 6, 6, 5, -1315405970237674780586173845869633042896650240000000⟩, + ⟨3, 7, 8, 6, 7, 5, -1769985962114856043353093506234292481598423040000000⟩, + ⟨3, 7, 4, 7, 2, 5, -13257703027125577460530261939459641870668267520000000⟩, + ⟨3, 7, 5, 7, 3, 5, -13513156649196866505698875029091517450818682880000000⟩, + ⟨3, 7, 6, 7, 4, 5, -27259985057719615482957676174858609175298048000000000⟩, + ⟨3, 7, 7, 7, 5, 5, 4725644198269126245547708449735712320698449920000000⟩, + ⟨3, 7, 8, 7, 6, 5, -2646249403274229330728161283721428889910640640000000⟩ +] + +def collectedFourData_14_5_21 : List CollectedFourTerm := [ + ⟨3, 8, 3, 0, 8, 6, 8065255202982634097587014244682332038487867392000000⟩, + ⟨3, 8, 3, 1, 7, 6, -107741501768922164430566034766724421915745714176000000⟩, + ⟨3, 8, 4, 1, 8, 6, 167718103448624105065774125833484069815401316352000000⟩, + ⟨3, 8, 3, 2, 6, 6, 35072107322941459624029726377363356181663318016000000⟩, + ⟨3, 8, 4, 2, 7, 6, -22741148687635645696863485547250399105127546880000000⟩, + ⟨3, 8, 5, 2, 8, 6, 141842600861101956926538194926780807158442229760000000⟩, + ⟨3, 8, 3, 3, 5, 6, 70055402995198388617741276293377598106688815104000000⟩, + ⟨3, 8, 4, 3, 6, 6, -18521013725163060381680250533481563875713220608000000⟩, + ⟨3, 8, 5, 3, 7, 6, -11174188822221778262265620719704748453747752960000000⟩, + ⟨3, 8, 6, 3, 8, 6, 48268303056190614710502998707920418020639375360000000⟩, + ⟨3, 8, 3, 4, 4, 6, -28650198279301368013112201249135383872490438656000000⟩, + ⟨3, 8, 4, 4, 5, 6, 47893329810183988482093917551221231871196135424000000⟩, + ⟨3, 8, 5, 4, 6, 6, -27365489802123145895744713067838950714690764800000000⟩, + ⟨3, 8, 6, 4, 7, 6, -21062184861729595984835239234211874935112990720000000⟩, + ⟨3, 8, 7, 4, 8, 6, 30902706909352058410331178229381151517887692800000000⟩, + ⟨3, 8, 3, 5, 3, 6, -72132266914755294069244233986301233656686968832000000⟩, + ⟨3, 8, 4, 5, 4, 6, 6688240684654974435545211916861738016707706880000000⟩, + ⟨3, 8, 5, 5, 5, 6, -7531018931323952472893477323726191702992486400000000⟩, + ⟨3, 8, 6, 5, 6, 6, -35672669808548498101302775077281958202315898880000000⟩, + ⟨3, 8, 7, 5, 7, 6, 14095835374139044315697227758506954146122301440000000⟩, + ⟨3, 8, 8, 5, 8, 6, 17018277974506363264129416581611990238789369856000000⟩, + ⟨3, 8, 3, 6, 2, 6, -80664150011664274347924637590612314732063883264000000⟩, + ⟨3, 8, 4, 6, 3, 6, -167181043254057852916355797050649158501877678080000000⟩, + ⟨3, 8, 5, 6, 4, 6, 62801510127143007588390840408666012215578460160000000⟩, + ⟨3, 8, 6, 6, 5, 6, 3393099525972605665507458368217167880184135680000000⟩, + ⟨3, 8, 7, 6, 6, 6, 4261545179486925418384642292641835390997626880000000⟩, + ⟨3, 8, 8, 6, 7, 6, 4587405145042608819440435840373930120009744384000000⟩, + ⟨3, 8, 3, 7, 1, 6, 741536401561941604053151453794302833955973365760000000⟩, + ⟨3, 8, 4, 7, 2, 6, 171804908004508448428028432756926382202641448960000000⟩, + ⟨3, 8, 5, 7, 3, 6, 87557649700542985286536596703304145448332165120000000⟩, + ⟨3, 8, 6, 7, 4, 6, 117752907258606478148051619761609495877255168000000000⟩, + ⟨3, 8, 7, 7, 5, 6, -15309757374345357539969405106108906469368791040000000⟩, + ⟨3, 8, 8, 7, 6, 6, 6858482715389126262807936573241328314922041344000000⟩ +] + +def collectedFourData_14_5_22 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_5_23 : List CollectedFourTerm := [ + ⟨4, 2, 8, 5, 8, 1, -864665041427588777740256636803745891169041645568000000⟩, + ⟨4, 2, 8, 6, 7, 1, -233076981450495823206598619026950005728217137152000000⟩, + ⟨4, 2, 8, 7, 6, 1, -348465940567900262063672466215693451907439788032000000⟩ +] + +def collectedFourData_14_5_24 : List CollectedFourTerm := [ + ⟨4, 3, 7, 4, 8, 2, -256434716353089838643207813613490781260464783360000000⟩, + ⟨4, 3, 7, 5, 7, 2, -116969091300972538342689754995666782900692451328000000⟩, + ⟨4, 3, 8, 5, 8, 2, -706099517108949239383890792596486647492783374336000000⟩, + ⟨4, 3, 7, 6, 6, 2, -35362861011922923277394162745001821398636691456000000⟩, + ⟨4, 3, 8, 6, 7, 2, -190334448793821127437030242320495993791241519104000000⟩, + ⟨4, 3, 7, 7, 5, 2, 127042375324627937141378363072757000391882702848000000⟩, + ⟨4, 3, 8, 7, 6, 2, -284562947008556411871684915660988917978564132864000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1409.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1409.lean new file mode 100644 index 0000000000000000000000000000000000000000..00e4aff6c629d936730ab99c3f600d70a6b3bc76 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1409.lean @@ -0,0 +1,625 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1409. -/ +namespace LaughlinFock +def collectedFourData_14_5_25 : List CollectedFourTerm := [ + ⟨4, 4, 6, 3, 8, 3, -28650198279301368013112201249135383872490438656000000⟩, + ⟨4, 4, 6, 4, 7, 3, 12501698511782659281583300568779669195626381312000000⟩, + ⟨4, 4, 7, 4, 8, 3, -73370607563260548446309805764793401452548587520000000⟩, + ⟨4, 4, 6, 5, 6, 3, 21173917425213532065969050759313239424890830848000000⟩, + ⟨4, 4, 7, 5, 7, 3, -33466971309212290299023185699374284234079338496000000⟩, + ⟨4, 4, 8, 5, 8, 3, -101013917513170323668965338390168939545153765376000000⟩, + ⟨4, 4, 6, 6, 5, 3, -2014012675924198619673369620899156703343280128000000⟩, + ⟨4, 4, 7, 6, 6, 3, -10117953740894337225819879307051663142097518592000000⟩, + ⟨4, 4, 8, 6, 7, 3, -27229063105855661501792183718734559550755569664000000⟩, + ⟨4, 4, 6, 7, 4, 3, -69893572537569801918975544725714897587719372800000000⟩, + ⟨4, 4, 7, 7, 5, 3, 36349119949161746496213545693593283262872027136000000⟩, + ⟨4, 4, 8, 7, 6, 3, -40709301394397820946860261157442550978601549824000000⟩ +] + +def collectedFourData_14_5_26 : List CollectedFourTerm := [ + ⟨4, 5, 5, 2, 8, 4, 46913564624157440162963348431258738584220336128000000⟩, + ⟨4, 5, 5, 3, 7, 4, -3695793973399977756922979046853324851105497088000000⟩, + ⟨4, 5, 6, 3, 8, 4, 47893329810183988482093917551221231871196135424000000⟩, + ⟨4, 5, 5, 4, 6, 4, -9050966821743399812748826590962924322753085440000000⟩, + ⟨4, 5, 6, 4, 7, 4, -20898562871198867146070955478271316790081486848000000⟩, + ⟨4, 5, 7, 4, 8, 4, 61325277265873512708929778365338040533033943040000000⟩, + ⟨4, 5, 5, 5, 5, 4, -2490838021691324413107162566745022728681553920000000⟩, + ⟨4, 5, 6, 5, 6, 4, -35395545983079385461574215988429821819897249792000000⟩, + ⟨4, 5, 7, 5, 7, 4, 27972663208723078380038186526164986455121723392000000⟩, + ⟨4, 5, 8, 5, 8, 4, 56286903842851382666920654257353228893204512768000000⟩, + ⟨4, 5, 5, 6, 4, 4, 20771211793623849955876240626536191771696693248000000⟩, + ⟨4, 5, 6, 6, 5, 4, 3366740166668087665294124202493641365139750912000000⟩, + ⟨4, 5, 7, 6, 6, 4, 8456878566647285622555328728106542675718569984000000⟩, + ⟨4, 5, 8, 6, 7, 4, 15172559331444623174482725220416826868552957952000000⟩, + ⟨4, 5, 5, 7, 3, 4, 28959152135035455528557637968839426037237415936000000⟩, + ⟨4, 5, 6, 7, 4, 4, 116838141520725126879508537262499905919988531200000000⟩, + ⟨4, 5, 7, 7, 5, 4, -30381646456053653486978486876284620755982876672000000⟩, + ⟨4, 5, 8, 7, 6, 4, 22684008199141174072649377560919495070378360832000000⟩ +] + +def collectedFourData_14_5_27 : List CollectedFourTerm := [ + ⟨4, 6, 4, 1, 8, 5, -31695666092451056959744294748147112955997061120000000⟩, + ⟨4, 6, 4, 2, 7, 5, 4297662807657953640178770505999065549688012800000000⟩, + ⟨4, 6, 5, 2, 8, 5, -53611334997661281655020259773764783656088371200000000⟩, + ⟨4, 6, 4, 3, 6, 5, 3500134181437926754365388514705093155073556480000000⟩, + ⟨4, 6, 5, 3, 7, 5, 4223436235929436647466643024775816219407155200000000⟩, + ⟨4, 6, 6, 3, 8, 5, -27365489802123145895744713067838950714690764800000000⟩, + ⟨4, 6, 4, 4, 5, 5, -9050966821743399812748826590962924322753085440000000⟩, + ⟨4, 6, 5, 4, 6, 5, 10343158065702362066644660988232698771275776000000000⟩, + ⟨4, 6, 6, 4, 7, 5, 11941107694901052952388229865896409468344729600000000⟩, + ⟨4, 6, 7, 4, 8, 5, -23360194502837095604967857561635244602294272000000000⟩, + ⟨4, 6, 4, 5, 4, 5, -1263955644190235956385800242290908570897612800000000⟩, + ⟨4, 6, 5, 5, 5, 5, 2846450758445298937167097928221201287610368000000000⟩, + ⟨4, 6, 6, 5, 6, 5, 20224454145900170748664709553745146537207398400000000⟩, + ⟨4, 6, 7, 5, 7, 5, -10655424360906371824568702358532830501902745600000000⟩, + ⟨4, 6, 8, 5, 8, 5, -16080722505716274488412321993888028527742156800000000⟩, + ⟨4, 6, 4, 6, 3, 5, 31594171499747573992149639331644977158343884800000000⟩, + ⟨4, 6, 5, 6, 4, 5, -23736682614007198676816755507602782556468019200000000⟩, + ⟨4, 6, 6, 6, 5, 5, -1923701986529301094517274523133074674706022400000000⟩, + ⟨4, 6, 7, 6, 6, 5, -3221417611326324083744266163067040260371251200000000⟩, + ⟨4, 6, 8, 6, 7, 5, -4334679999306161726153949662648490813240115200000000⟩, + ⟨4, 6, 4, 7, 2, 5, -32467997700816143857978162644407975063165337600000000⟩, + ⟨4, 6, 5, 7, 3, 5, -33093601366632606043209295843372785660749414400000000⟩, + ⟨4, 6, 6, 7, 4, 5, -66759462809465103604859279295281136654090240000000000⟩, + ⟨4, 6, 7, 7, 5, 5, 11573060932979957358818165072029093388196249600000000⟩, + ⟨4, 6, 8, 7, 6, 5, -6480641432795909623053695787833673659921203200000000⟩ +] + +def collectedFourData_14_5_28 : List CollectedFourTerm := [ + ⟨4, 7, 3, 0, 8, 6, -3519326043935988426471537362016047453945462784000000⟩, + ⟨4, 7, 3, 1, 7, 6, 47013698096982533302736818568508035976608612352000000⟩, + ⟨4, 7, 4, 1, 8, 6, -73184874458530391849916613424114982834829000704000000⟩, + ⟨4, 7, 3, 2, 6, 6, -15303939876781570887132169288387161547742380032000000⟩, + ⟨4, 7, 4, 2, 7, 6, 9923246671205077068371600311883984296225013760000000⟩, + ⟨4, 7, 5, 2, 8, 6, -61893932279475350343029260282943590278648299520000000⟩, + ⟨4, 7, 3, 3, 5, 6, -30569126217885383371185911453926275188111966208000000⟩, + ⟨4, 7, 4, 3, 6, 6, 8081763604821495743832583012721491429048713216000000⟩, + ⟨4, 7, 5, 3, 7, 6, 4875929248631884573048425957678727961688145920000000⟩, + ⟨4, 7, 6, 3, 8, 6, -21062184861729595984835239234211874935112990720000000⟩, + ⟨4, 7, 3, 4, 4, 6, 12501698511782659281583300568779669195626381312000000⟩, + ⟨4, 7, 4, 4, 5, 6, -20898562871198867146070955478271316790081486848000000⟩, + ⟨4, 7, 5, 4, 6, 6, 11941107694901052952388229865896409468344729600000000⟩, + ⟨4, 7, 6, 4, 7, 6, 9190619994103475593395212053238504870054461440000000⟩, + ⟨4, 7, 7, 4, 8, 6, -13484595157507688302782045682982903155890585600000000⟩, + ⟨4, 7, 3, 5, 3, 6, 31475379163124434707405992656766146400080625664000000⟩, + ⟨4, 7, 4, 5, 4, 6, -2918456891595175914284403087011651876825333760000000⟩, + ⟨4, 7, 5, 5, 5, 6, 3286208606589634401774091136636310847802572800000000⟩, + ⟨4, 7, 6, 5, 6, 6, 15565999184691152680118719567071140564969717760000000⟩, + ⟨4, 7, 7, 5, 7, 6, -6150808535469046890095601712171338030781562880000000⟩, + ⟨4, 7, 8, 5, 8, 6, -7426035183173534270814935162947933478125043712000000⟩, + ⟨4, 7, 3, 6, 2, 6, 35198321293419931964440797801709669884811542528000000⟩, + ⟨4, 7, 4, 6, 3, 6, 72950524784238701603650827614003280220426076160000000⟩, + ⟨4, 7, 5, 6, 4, 6, -27403843353552963438016328339519309470834360320000000⟩, + ⟨4, 7, 6, 6, 5, 6, -1480600827982003271875572530394507488117391360000000⟩, + ⟨4, 7, 7, 6, 6, 6, -1859552681238386323657075109897590466685173760000000⟩, + ⟨4, 7, 8, 6, 7, 6, -2001743775579963600722356447782277752205344768000000⟩, + ⟨4, 7, 3, 7, 1, 6, -323574183936351209364252305330091994159534571520000000⟩, + ⟨4, 7, 4, 7, 2, 6, -74968177943419633603347832921687844584339537920000000⟩, + ⟨4, 7, 5, 7, 3, 6, -38206344273271040568564377939363190383302410240000000⟩, + ⟨4, 7, 6, 7, 4, 6, -51382239350732318267437955592791933463822336000000000⟩, + ⟨4, 7, 7, 7, 5, 6, 6680511217295288069126170966551503155840942080000000⟩, + ⟨4, 7, 8, 7, 6, 6, -2992743097977545927018963461080649699518578688000000⟩ +] + +def collectedFourData_14_5_29 : List CollectedFourTerm := [ + ⟨4, 8, 2, 0, 7, 7, -33899268179154701028606442120467215842856140800000000⟩, + ⟨4, 8, 3, 0, 8, 7, 20654400665111695979681447636091601714560368640000000⟩, + ⟨4, 8, 2, 1, 6, 7, 78030023464816317824653477427530198836251197440000000⟩, + ⟨4, 8, 3, 1, 7, 7, -275916395673778713427497012782552646032472145920000000⟩, + ⟨4, 8, 4, 1, 8, 7, 214755566949664493791787460517196801100396625920000000⟩, + ⟨4, 8, 2, 2, 5, 7, 163627174483718028531225345054429985354914201600000000⟩, + ⟨4, 8, 3, 2, 6, 7, 89816544992890116753938148722827910462539038720000000⟩, + ⟨4, 8, 4, 2, 7, 7, -29119028769579593491797867833851359961861324800000000⟩, + ⟨4, 8, 5, 2, 8, 7, 121082091673234194099847048198602474050184806400000000⟩, + ⟨4, 8, 2, 3, 4, 7, -12056227177184718208574063046723661149146972160000000⟩, + ⟨4, 8, 3, 3, 5, 7, 179405651253737399879613172380060341245763911680000000⟩, + ⟨4, 8, 4, 3, 6, 7, -23715333772828567040293194724759493766996295680000000⟩, + ⟨4, 8, 5, 3, 7, 7, -9538700976522512325358175016370481528202854400000000⟩, + ⟨4, 8, 6, 3, 8, 7, 30902706909352058410331178229381151517887692800000000⟩, + ⟨4, 8, 2, 4, 3, 7, -256434716353089838643207813613490781260464783360000000⟩, + ⟨4, 8, 3, 4, 4, 7, -73370607563260548446309805764793401452548587520000000⟩, + ⟨4, 8, 4, 4, 5, 7, 61325277265873512708929778365338040533033943040000000⟩, + ⟨4, 8, 5, 4, 6, 7, -23360194502837095604967857561635244602294272000000000⟩, + ⟨4, 8, 6, 4, 7, 7, -13484595157507688302782045682982903155890585600000000⟩, + ⟨4, 8, 7, 4, 8, 7, 15827816332612265874799396176400069034193715200000000⟩, + ⟨4, 8, 2, 5, 2, 7, 34880864537722305696272506617671035225500549120000000⟩, + ⟨4, 8, 3, 5, 3, 7, -184724314884564481992789698734182698797435453440000000⟩, + ⟨4, 8, 4, 5, 4, 7, 8563994527691962226627099787613757521054924800000000⟩, + ⟨4, 8, 5, 5, 5, 7, -6428756375726434294359689832623457693597696000000000⟩, + ⟨4, 8, 6, 5, 6, 7, -22838633015218070017690021289216947301803622400000000⟩, + ⟨4, 8, 7, 5, 7, 7, 7219635937105989833210972590315845069003816960000000⟩, + ⟨4, 8, 8, 5, 8, 7, 7263715841785760984782825937265472273561681920000000⟩, + ⟨4, 8, 2, 6, 1, 7, -585289449713928959336128218087247457030913392640000000⟩, + ⟨4, 8, 3, 6, 2, 7, -206573708050236825961021012412365522980443258880000000⟩, + ⟨4, 8, 4, 6, 3, 7, -214067885273097581835148131677239714006224076800000000⟩, + ⟨4, 8, 5, 6, 4, 7, 53609692435621345117675253492130914062722662400000000⟩, + ⟨4, 8, 6, 6, 5, 7, 2172356464310062654771641289085554793014886400000000⟩, + ⟨4, 8, 7, 6, 6, 7, 2182687574648536905848622456809798695303249920000000⟩, + ⟨4, 8, 8, 6, 7, 7, 1957989373228699995374954514783540240847994880000000⟩, + ⟨4, 8, 2, 7, 0, 7, 4774776140236825719045993120556126914127771729920000000⟩, + ⟨4, 8, 3, 7, 1, 7, 1899008718281034949213816231225996832826143539200000000⟩, + ⟨4, 8, 4, 7, 2, 7, 219988538294825587597692279991179065133996441600000000⟩, + ⟨4, 8, 5, 7, 3, 7, 74742449048263378465680894053342442146286796800000000⟩, + ⟨4, 8, 6, 7, 4, 7, 75388678497785479972565972922054705036656640000000000⟩, + ⟨4, 8, 7, 7, 5, 7, -7841385174729189749371270301610867447677583360000000⟩, + ⟨4, 8, 8, 7, 6, 7, 2927327290400006251826734926274602641475502080000000⟩ +] + +def collectedFourData_14_5_30 : List CollectedFourTerm := [ + +] + +def collectedFourData_14_5_31 : List CollectedFourTerm := [ + ⟨5, 1, 8, 5, 8, 1, -392049206131178697522819495342527235674811138048000000⟩, + ⟨5, 1, 8, 6, 7, 1, -105679819545209120779688041652083686314052943872000000⟩, + ⟨5, 1, 8, 7, 6, 1, -157998518290785624260351573763448679047523991552000000⟩ +] + +def collectedFourData_14_5_32 : List CollectedFourTerm := [ + ⟨5, 2, 7, 4, 8, 2, 34880864537722305696272506617671035225500549120000000⟩, + ⟨5, 2, 7, 5, 7, 2, 15910416057519643357208302925708063740501426176000000⟩, + ⟨5, 2, 8, 5, 8, 2, 96045348136543866068191587691752197630472486912000000⟩, + ⟨5, 2, 7, 6, 6, 2, 4810141084504225571745804817336555571565821952000000⟩, + ⟨5, 2, 8, 6, 7, 2, 25889747767606904610850969778364510774459629568000000⟩, + ⟨5, 2, 7, 7, 5, 2, -17280608286076268687941567769685857863011926016000000⟩, + ⟨5, 2, 8, 7, 6, 2, 38706933866916373314089710829607596081427775488000000⟩ +] + +def collectedFourData_14_5_33 : List CollectedFourTerm := [ + ⟨5, 3, 6, 3, 8, 3, -72132266914755294069244233986301233656686968832000000⟩, + ⟨5, 3, 6, 4, 7, 3, 31475379163124434707405992656766146400080625664000000⟩, + ⟨5, 3, 7, 4, 8, 3, -184724314884564481992789698734182698797435453440000000⟩, + ⟨5, 3, 6, 5, 6, 3, 53309322625174315570788313693995729368547065856000000⟩, + ⟨5, 3, 7, 5, 7, 3, -84259399665258605242920539691104736369350541312000000⟩, + ⟨5, 3, 8, 5, 8, 3, -254321550906305046362857553083887320251521564672000000⟩, + ⟨5, 3, 6, 6, 5, 3, -5070656003606805431643333581693009007545942016000000⟩, + ⟨5, 3, 7, 6, 6, 3, -25473853016808301434351237599937908595253837824000000⟩, + ⟨5, 3, 8, 6, 7, 3, -68554291619310586587811991010463373830240862208000000⟩, + ⟨5, 3, 6, 7, 4, 3, -175970224734819317748929408788491010469108121600000000⟩, + ⟨5, 3, 7, 7, 5, 3, 91515751365101104450396818435769330933161787392000000⟩, + ⟨5, 3, 8, 7, 6, 3, -102493328858229759404238890510196867629976649728000000⟩ +] + +def collectedFourData_14_5_34 : List CollectedFourTerm := [ + ⟨5, 4, 5, 2, 8, 4, 6551417761618249040655399056674251032871567360000000⟩, + ⟨5, 4, 5, 3, 7, 4, -516112780484523943003238819057122851485122560000000⟩, + ⟨5, 4, 6, 3, 8, 4, 6688240684654974435545211916861738016707706880000000⟩, + ⟨5, 4, 5, 4, 6, 4, -1263955644190235956385800242290908570897612800000000⟩, + ⟨5, 4, 6, 4, 7, 4, -2918456891595175914284403087011651876825333760000000⟩, + ⟨5, 4, 7, 4, 8, 4, 8563994527691962226627099787613757521054924800000000⟩, + ⟨5, 4, 5, 5, 5, 4, -347842262410808698101847352190354871182950400000000⟩, + ⟨5, 4, 6, 5, 6, 4, -4942941566975128950235630302915366386443223040000000⟩, + ⟨5, 4, 7, 5, 7, 4, 3906345724388344281350723878423563324138455040000000⟩, + ⟨5, 4, 8, 5, 8, 4, 7860392288175605168803488123010358184152924160000000⟩, + ⟨5, 4, 5, 6, 4, 4, 2900672480662637966223154743361766801811701760000000⟩, + ⟨5, 4, 6, 6, 5, 4, 470160848005674909806923832232335994456637440000000⟩, + ⟨5, 4, 7, 6, 6, 4, 1180991998652175809519266094426225385752494080000000⟩, + ⟨5, 4, 8, 6, 7, 4, 2118828008265386627195862253036331109439242240000000⟩, + ⟨5, 4, 5, 7, 3, 4, 4044107608936222982398058619205070463770296320000000⟩, + ⟨5, 4, 6, 7, 4, 4, 16316293202737899349861647092393099126636544000000000⟩, + ⟨5, 4, 7, 7, 5, 4, -4242757074931413014709867164969447017037168640000000⟩, + ⟨5, 4, 8, 7, 6, 4, 3167791989611928436482980436299842406150307840000000⟩ +] + +def collectedFourData_14_5_35 : List CollectedFourTerm := [ + ⟨5, 5, 4, 1, 8, 5, -8722689164681132579823198406418666772139868160000000⟩, + ⟨5, 5, 4, 2, 7, 5, 1182722479990393110081047777309067019970150400000000⟩, + ⟨5, 5, 5, 2, 8, 5, -14753910188357482772140854939548533801982361600000000⟩, + ⟨5, 5, 4, 3, 6, 5, 963241548869992817411907807155816550251888640000000⟩, + ⟨5, 5, 5, 3, 7, 5, 1162295229430040752969299013779520963058073600000000⟩, + ⟨5, 5, 6, 3, 8, 5, -7531018931323952472893477323726191702992486400000000⟩, + ⟨5, 5, 4, 4, 5, 5, -2490838021691324413107162566745022728681553920000000⟩, + ⟨5, 5, 5, 4, 6, 5, 2846450758445298937167097928221201287610368000000000⟩, + ⟨5, 5, 6, 4, 7, 5, 3286208606589634401774091136636310847802572800000000⟩, + ⟨5, 5, 7, 4, 8, 5, -6428756375726434294359689832623457693597696000000000⟩, + ⟨5, 5, 4, 5, 4, 5, -347842262410808698101847352190354871182950400000000⟩, + ⟨5, 5, 5, 5, 5, 5, 783347007634038737421953650548110549581824000000000⟩, + ⟨5, 5, 6, 5, 6, 5, 5565796488563138596063729406652584968794931200000000⟩, + ⟨5, 5, 7, 5, 7, 5, -2932386855251917635486030028841626266029260800000000⟩, + ⟨5, 5, 8, 5, 8, 5, -4425436069136996125740723618994444317386342400000000⟩, + ⟨5, 5, 4, 6, 3, 5, 8694757718739403388187475467218676630316646400000000⟩, + ⟨5, 5, 5, 6, 4, 5, -6532366401095702994597720450853349575203225600000000⟩, + ⟨5, 5, 6, 6, 5, 5, -529405327057352972988909198087903587283763200000000⟩, + ⟨5, 5, 7, 6, 6, 5, -886538380713239876682184587638879007906201600000000⟩, + ⟨5, 5, 8, 6, 7, 5, -1192909660015414008081602584372050115795353600000000⟩, + ⟨5, 5, 4, 7, 2, 5, -8935235843213671709318423621938066915904716800000000⟩, + ⟨5, 5, 5, 7, 3, 5, -9107402798193732200659052943470199024333619200000000⟩, + ⟨5, 5, 6, 7, 4, 5, -18372292325061617470221975069641006194360320000000000⟩, + ⟨5, 5, 7, 7, 5, 5, 3184921651681003330259526987254033728457932800000000⟩, + ⟨5, 5, 8, 7, 6, 5, -1783481080383285846128670422239111510858137600000000⟩ +] + +def collectedFourData_14_5_36 : List CollectedFourTerm := [ + ⟨5, 6, 3, 0, 8, 6, -5960623588584545775022833502907841788390670336000000⟩, + ⟨5, 6, 3, 1, 7, 6, 79626313210258351335048296978992694887352107008000000⟩, + ⟨5, 6, 4, 1, 8, 6, -123951996370657737491936235597179670737260118016000000⟩, + ⟨5, 6, 3, 2, 6, 6, -25920026700851783894772187002146023165529161728000000⟩, + ⟨5, 6, 4, 2, 7, 6, 16806836719673900932754341224006306627625943040000000⟩, + ⟨5, 6, 5, 2, 8, 6, -104828716671755312148017972360840356915398574080000000⟩, + ⟨5, 6, 3, 3, 5, 6, -51774417187264181508780433636235850726330335232000000⟩, + ⟨5, 6, 4, 3, 6, 6, 13687947686252869925863037028173466896814833664000000⟩, + ⟨5, 6, 5, 3, 7, 6, 8258279719704525687333634866284381364478279680000000⟩, + ⟨5, 6, 6, 3, 8, 6, -35672669808548498101302775077281958202315898880000000⟩, + ⟨5, 6, 3, 4, 4, 6, 21173917425213532065969050759313239424890830848000000⟩, + ⟨5, 6, 4, 4, 5, 6, -35395545983079385461574215988429821819897249792000000⟩, + ⟨5, 6, 5, 4, 6, 6, 20224454145900170748664709553745146537207398400000000⟩, + ⟨5, 6, 6, 4, 7, 6, 15565999184691152680118719567071140564969717760000000⟩, + ⟨5, 6, 7, 4, 8, 6, -22838633015218070017690021289216947301803622400000000⟩, + ⟨5, 6, 3, 5, 3, 6, 53309322625174315570788313693995729368547065856000000⟩, + ⟨5, 6, 4, 5, 4, 6, -4942941566975128950235630302915366386443223040000000⟩, + ⟨5, 6, 5, 5, 5, 6, 5565796488563138596063729406652584968794931200000000⟩, + ⟨5, 6, 6, 5, 6, 6, 26363872162406980772158331600820476513919959040000000⟩, + ⟨5, 6, 7, 5, 7, 6, -10417521419635425690528043665321259079061995520000000⟩, + ⟨5, 6, 8, 5, 8, 6, -12577351438850666096415302812985115341066600448000000⟩, + ⟨5, 6, 3, 6, 2, 6, 59614807369621643183535491225743686858033856512000000⟩, + ⟨5, 6, 4, 6, 3, 6, 123555082251556142458365679262706213243731312640000000⟩, + ⟨5, 6, 5, 6, 4, 6, -46413430603429085143731639799039722710661857280000000⟩, + ⟨5, 6, 6, 6, 5, 6, -2507668829307210937111780733507286949366333440000000⟩, + ⟨5, 6, 7, 6, 6, 6, -3149493237520214325742694944495348235674583040000000⟩, + ⟨5, 6, 8, 6, 7, 6, -3390319912979690948388675334922855362143977472000000⟩, + ⟨5, 6, 3, 7, 1, 6, -548032176999139677695996942966628792848697262080000000⟩, + ⟨5, 6, 4, 7, 2, 6, -126972347621134027808834125061359715055493447680000000⟩, + ⟨5, 6, 5, 7, 3, 6, -64709445520468405025168986557777559495334952960000000⟩, + ⟨5, 6, 6, 7, 4, 6, -87025238379374989988239315758849291813126144000000000⟩, + ⟨5, 6, 7, 7, 5, 6, 11314669981835369289996815087268564123852472320000000⟩, + ⟨5, 6, 8, 7, 6, 6, -5068758870783104377739563703625359012137009152000000⟩ +] + +def collectedFourData_14_5_37 : List CollectedFourTerm := [ + ⟨5, 7, 2, 0, 7, 7, -15462674676325751514378990296370292178383011840000000⟩, + ⟨5, 7, 3, 0, 8, 7, 9421214535701877307841892271489895509128118272000000⟩, + ⟨5, 7, 2, 1, 6, 7, 35592298377829039793089724537655190882470592512000000⟩, + ⟨5, 7, 3, 1, 7, 7, -125855385479722756686551417182181739252538146816000000⟩, + ⟨5, 7, 4, 1, 8, 7, 97957733161759371558429992048243636283497250816000000⟩, + ⟨5, 7, 2, 2, 5, 7, 74636235622453247519527927430591607612301639680000000⟩, + ⟨5, 7, 3, 2, 6, 7, 40968554496130280795477197719676979157984608256000000⟩, + ⟨5, 7, 4, 2, 7, 7, -13282235662876390959144578454231371173897175040000000⟩, + ⟨5, 7, 5, 2, 8, 7, 55229894131565800886008773054162851001500958720000000⟩, + ⟨5, 7, 2, 3, 4, 7, -5499278559037405626611384806698078288444653568000000⟩, + ⟨5, 7, 3, 3, 5, 7, 81833366011621914198264870933887990159495921664000000⟩, + ⟨5, 7, 4, 3, 6, 7, -10817416146913206817668055356429053550724644864000000⟩, + ⟨5, 7, 5, 3, 7, 7, -4350944370103396638167876820297418062031749120000000⟩, + ⟨5, 7, 6, 3, 8, 7, 14095835374139044315697227758506954146122301440000000⟩, + ⟨5, 7, 2, 4, 3, 7, -116969091300972538342689754995666782900692451328000000⟩, + ⟨5, 7, 3, 4, 4, 7, -33466971309212290299023185699374284234079338496000000⟩, + ⟨5, 7, 4, 4, 5, 7, 27972663208723078380038186526164986455121723392000000⟩, + ⟨5, 7, 5, 4, 6, 7, -10655424360906371824568702358532830501902745600000000⟩, + ⟨5, 7, 6, 4, 7, 7, -6150808535469046890095601712171338030781562880000000⟩, + ⟨5, 7, 7, 4, 8, 7, 7219635937105989833210972590315845069003816960000000⟩, + ⟨5, 7, 2, 5, 2, 7, 15910416057519643357208302925708063740501426176000000⟩, + ⟨5, 7, 3, 5, 3, 7, -84259399665258605242920539691104736369350541312000000⟩, + ⟨5, 7, 4, 5, 4, 7, 3906345724388344281350723878423563324138455040000000⟩, + ⟨5, 7, 5, 5, 5, 7, -2932386855251917635486030028841626266029260800000000⟩, + ⟨5, 7, 6, 5, 6, 7, -10417521419635425690528043665321259079061995520000000⟩, + ⟨5, 7, 7, 5, 7, 7, 3293135450210884436573844300604853202198724608000000⟩, + ⟨5, 7, 8, 5, 8, 7, 3313241879123290129523721590879538834221039616000000⟩, + ⟨5, 7, 2, 6, 1, 7, -266971555391195895419700413402888582087124713472000000⟩, + ⟨5, 7, 3, 6, 2, 7, -94225693232730869070543438730235116038572212224000000⟩, + ⟨5, 7, 4, 6, 3, 7, -97644056831361091681509147956870872235130224640000000⟩, + ⟨5, 7, 5, 6, 4, 7, 24453307642187711905040318102151610188190187520000000⟩, + ⟨5, 7, 6, 6, 5, 7, 990889865560435535515838301792524953158942720000000⟩, + ⟨5, 7, 7, 6, 6, 7, 995602256322525324809575080691372275863126016000000⟩, + ⟨5, 7, 8, 6, 7, 7, 893109330205407820002014746386184938952065024000000⟩, + ⟨5, 7, 2, 7, 0, 7, 2177947019934912253398428108815600894757113430016000000⟩, + ⟨5, 7, 3, 7, 1, 7, 866206133510053416136879384898817034582921052160000000⟩, + ⟨5, 7, 4, 7, 2, 7, 100344679483819425892742232049258706014757191680000000⟩, + ⟨5, 7, 5, 7, 3, 7, 34092717519365884110259430536272712766733680640000000⟩, + ⟨5, 7, 6, 7, 4, 7, 34387485999069108694363825591168478239260672000000000⟩, + ⟨5, 7, 7, 7, 5, 7, -3576737625361463871777352551573398019089891328000000⟩, + ⟨5, 7, 8, 7, 6, 7, 1335259195666628963284436074901453291686723584000000⟩ +] + +def collectedFourData_14_5_38 : List CollectedFourTerm := [ + ⟨5, 8, 1, 0, 6, 8, 956587377225723149962476733514563683186162794496000000⟩, + ⟨5, 8, 2, 0, 7, 8, -93342497584022968005124408681762041635096494080000000⟩, + ⟨5, 8, 3, 0, 8, 8, 28436208917456121050551715315378091370513170432000000⟩, + ⟨5, 8, 1, 1, 5, 8, 208281450887105747158536425774749256848427188224000000⟩, + ⟨5, 8, 2, 1, 6, 8, 214857655281910914825422107909208736162323103744000000⟩, + ⟨5, 8, 3, 1, 7, 8, -379871408439564500962599894486109895157451063296000000⟩, + ⟨5, 8, 4, 1, 8, 8, 197111639531706212846531979672875694257407524864000000⟩, + ⟨5, 8, 1, 2, 4, 8, -181091120205779797941483353947912174452986609664000000⟩, + ⟨5, 8, 2, 2, 5, 8, 450551588848718489058212298253677804973625180160000000⟩, + ⟨5, 8, 3, 2, 6, 8, 123656071123674455479092060107291954770593447936000000⟩, + ⟨5, 8, 4, 2, 7, 8, -26726662241487111699160564815430843243859804160000000⟩, + ⟨5, 8, 5, 2, 8, 8, 83350655165671007021126115733824543924588380160000000⟩, + ⟨5, 8, 1, 3, 3, 8, 501521546084164268062518066826329824744467070976000000⟩, + ⟨5, 8, 2, 3, 4, 8, -33197128333608118180525004486882674916475273216000000⟩, + ⟨5, 8, 3, 3, 5, 8, 246999013079131704614465310115420489789508419584000000⟩, + ⟨5, 8, 4, 3, 6, 8, -21766925013401547868705426543694739889880825856000000⟩, + ⟨5, 8, 5, 3, 7, 8, -6566263968813883382033621168791758170342031360000000⟩, + ⟨5, 8, 6, 3, 8, 8, 17018277974506363264129416581611990238789369856000000⟩, + ⟨5, 8, 1, 4, 2, 8, -864665041427588777740256636803745891169041645568000000⟩, + ⟨5, 8, 2, 4, 3, 8, -706099517108949239383890792596486647492783374336000000⟩, + ⟨5, 8, 3, 4, 4, 8, -101013917513170323668965338390168939545153765376000000⟩, + ⟨5, 8, 4, 4, 5, 8, 56286903842851382666920654257353228893204512768000000⟩, + ⟨5, 8, 5, 4, 6, 8, -16080722505716274488412321993888028527742156800000000⟩, + ⟨5, 8, 6, 4, 7, 8, -7426035183173534270814935162947933478125043712000000⟩, + ⟨5, 8, 7, 4, 8, 8, 7263715841785760984782825937265472273561681920000000⟩, + ⟨5, 8, 1, 5, 1, 8, -392049206131178697522819495342527235674811138048000000⟩, + ⟨5, 8, 2, 5, 2, 8, 96045348136543866068191587691752197630472486912000000⟩, + ⟨5, 8, 3, 5, 3, 8, -254321550906305046362857553083887320251521564672000000⟩, + ⟨5, 8, 4, 5, 4, 8, 7860392288175605168803488123010358184152924160000000⟩, + ⟨5, 8, 5, 5, 5, 8, -4425436069136996125740723618994444317386342400000000⟩, + ⟨5, 8, 6, 5, 6, 8, -12577351438850666096415302812985115341066600448000000⟩, + ⟨5, 8, 7, 5, 7, 8, 3313241879123290129523721590879538834221039616000000⟩, + ⟨5, 8, 8, 5, 8, 8, 2857260916285755270607245135231559324145811456000000⟩, + ⟨5, 8, 1, 6, 0, 8, 4274155217925388698845746344883940359274017849344000000⟩, + ⟨5, 8, 2, 6, 1, 8, -1611609393959455028921588856137629201548668043264000000⟩, + ⟨5, 8, 3, 6, 2, 8, -284402980953713142346696656263821404093435346944000000⟩, + ⟨5, 8, 4, 6, 3, 8, -196480456532963333018951249592802096458560962560000000⟩, + ⟨5, 8, 5, 6, 4, 8, 36903913088965237574739365357429252921292226560000000⟩, + ⟨5, 8, 6, 6, 5, 8, 1196327761117791619558950640192356182264905728000000⟩, + ⟨5, 8, 7, 6, 6, 8, 1001680963467868423913631769807051228113272832000000⟩, + ⟨5, 8, 8, 6, 7, 8, 770196223597565821454231477629412907662966784000000⟩, + ⟨5, 8, 2, 7, 0, 8, 13147467608411951204445065460714555870940854484992000000⟩, + ⟨5, 8, 3, 7, 1, 8, 2614484415436222844681015073977027240714525736960000000⟩, + ⟨5, 8, 4, 7, 2, 8, 201914679453408939839317384105802219819599134720000000⟩, + ⟨5, 8, 5, 7, 3, 8, 51451308866319095436498114337402966482270289920000000⟩, + ⟨5, 8, 6, 7, 4, 8, 41516928939896050156473596664379563230153932800000000⟩, + ⟨5, 8, 7, 7, 5, 8, -3598575603753167052134319495361545690264109056000000⟩, + ⟨5, 8, 8, 7, 6, 8, 1151495741053152611075724986476218826037919744000000⟩ +] + +def collectedFourData_14_5_39 : List CollectedFourTerm := [ + ⟨6, 0, 8, 5, 8, 1, 4274155217925388698845746344883940359274017849344000000⟩, + ⟨6, 0, 8, 6, 7, 1, 1152130765920831959012353988130855488886895804416000000⟩, + ⟨6, 0, 8, 7, 6, 1, 1722513860035936962456521332412639157256722579456000000⟩ +] + +def collectedFourData_14_5_40 : List CollectedFourTerm := [ + ⟨6, 1, 7, 4, 8, 2, -585289449713928959336128218087247457030913392640000000⟩, + ⟨6, 1, 7, 5, 7, 2, -266971555391195895419700413402888582087124713472000000⟩, + ⟨6, 1, 8, 5, 8, 2, -1611609393959455028921588856137629201548668043264000000⟩, + ⟨6, 1, 7, 6, 6, 2, -80712587423146428766575433023317978679443718144000000⟩, + ⟨6, 1, 8, 6, 7, 2, -434421463600699652341336257528692139154835767296000000⟩, + ⟨6, 1, 7, 7, 5, 2, 289962930922812135056386299073331619488650493952000000⟩, + ⟨6, 1, 8, 7, 6, 2, -649489636318522950399169075937509771101691969536000000⟩ +] + +def collectedFourData_14_5_41 : List CollectedFourTerm := [ + ⟨6, 2, 6, 3, 8, 3, -80664150011664274347924637590612314732063883264000000⟩, + ⟨6, 2, 6, 4, 7, 3, 35198321293419931964440797801709669884811542528000000⟩, + ⟨6, 2, 7, 4, 8, 3, -206573708050236825961021012412365522980443258880000000⟩, + ⟨6, 2, 6, 5, 6, 3, 59614807369621643183535491225743686858033856512000000⟩, + ⟨6, 2, 7, 5, 7, 3, -94225693232730869070543438730235116038572212224000000⟩, + ⟨6, 2, 8, 5, 8, 3, -284402980953713142346696656263821404093435346944000000⟩, + ⟨6, 2, 6, 6, 5, 3, -5670418718655530309132764698437722363586936832000000⟩, + ⟨6, 2, 7, 6, 6, 3, -28486928097674667108262989451127007292422094848000000⟩, + ⟨6, 2, 8, 6, 7, 3, -76662967901155252375410190786367055791250210816000000⟩, + ⟨6, 2, 6, 7, 4, 3, -196784174582653138328439902594856088851657523200000000⟩, + ⟨6, 2, 7, 7, 5, 3, 102340334115225531066965730429067663272138768384000000⟩, + ⟨6, 2, 8, 7, 6, 3, -114616351430983328532738636116619294971428601856000000⟩ +] + +def collectedFourData_14_5_42 : List CollectedFourTerm := [ + ⟨6, 3, 5, 2, 8, 4, -163760981074353351782252389398732823364118773760000000⟩, + ⟨6, 3, 5, 3, 7, 4, 12900892349182317245972393520080126680718376960000000⟩, + ⟨6, 3, 6, 3, 8, 4, -167181043254057852916355797050649158501877678080000000⟩, + ⟨6, 3, 5, 4, 6, 4, 31594171499747573992149639331644977158343884800000000⟩, + ⟨6, 3, 6, 4, 7, 4, 72950524784238701603650827614003280220426076160000000⟩, + ⟨6, 3, 7, 4, 8, 4, -214067885273097581835148131677239714006224076800000000⟩, + ⟨6, 3, 5, 5, 5, 4, 8694757718739403388187475467218676630316646400000000⟩, + ⟨6, 3, 6, 5, 6, 4, 123555082251556142458365679262706213243731312640000000⟩, + ⟨6, 3, 7, 5, 7, 4, -97644056831361091681509147956870872235130224640000000⟩, + ⟨6, 3, 8, 5, 8, 4, -196480456532963333018951249592802096458560962560000000⟩, + ⟨6, 3, 5, 6, 4, 4, -72505980917840157806435319138804937357692764160000000⟩, + ⟨6, 3, 6, 6, 5, 4, -11752265621531843689892411545871607623885783040000000⟩, + ⟨6, 3, 7, 6, 6, 4, -29520390147196224415962345378008397583252193280000000⟩, + ⟨6, 3, 8, 6, 7, 4, -52962788511848892533268537333318828018200739840000000⟩, + ⟨6, 3, 5, 7, 3, 4, -101087589542766129895679608836453202016725893120000000⟩, + ⟨6, 3, 6, 7, 4, 4, -407846405098911646555124131056571652562223104000000000⟩, + ⟨6, 3, 7, 7, 5, 4, 106053084436383371494286660501048498998990602240000000⟩, + ⟨6, 3, 8, 7, 6, 4, -79182971218460261191823095597556137723365949440000000⟩ +] + +def collectedFourData_14_5_43 : List CollectedFourTerm := [ + ⟨6, 4, 4, 1, 8, 5, 72738902518644961009838095225039284214016507904000000⟩, + ⟨6, 4, 4, 2, 7, 5, -9862776668343671059583342881024678601435381760000000⟩, + ⟨6, 4, 5, 2, 8, 5, 123033529534123785192860765532574305068557271040000000⟩, + ⟨6, 4, 4, 3, 6, 5, -8032515179935831318382107261464568161701462016000000⟩, + ⟨6, 4, 5, 3, 7, 5, -9692432894860402286079314278710198220452003840000000⟩, + ⟨6, 4, 6, 3, 8, 5, 62801510127143007588390840408666012215578460160000000⟩, + ⟨6, 4, 4, 4, 5, 5, 20771211793623849955876240626536191771696693248000000⟩, + ⟨6, 4, 5, 4, 6, 5, -23736682614007198676816755507602782556468019200000000⟩, + ⟨6, 4, 6, 4, 7, 5, -27403843353552963438016328339519309470834360320000000⟩, + ⟨6, 4, 7, 4, 8, 5, 53609692435621345117675253492130914062722662400000000⟩, + ⟨6, 4, 4, 5, 4, 5, 2900672480662637966223154743361766801811701760000000⟩, + ⟨6, 4, 5, 5, 5, 5, -6532366401095702994597720450853349575203225600000000⟩, + ⟨6, 4, 6, 5, 6, 5, -46413430603429085143731639799039722710661857280000000⟩, + ⟨6, 4, 7, 5, 7, 5, 24453307642187711905040318102151610188190187520000000⟩, + ⟨6, 4, 8, 5, 8, 5, 36903913088965237574739365357429252921292226560000000⟩, + ⟨6, 4, 4, 6, 3, 5, -72505980917840157806435319138804937357692764160000000⟩, + ⟨6, 4, 5, 6, 4, 5, 54473701159651702285515017601484398667644272640000000⟩, + ⟨6, 4, 6, 6, 5, 5, 4414735152273864925746180404948260127590318080000000⟩, + ⟨6, 4, 7, 6, 6, 5, 7392883964597293915915710727703395879134167040000000⟩, + ⟨6, 4, 8, 6, 7, 5, 9947728026897208425606633715414206206800035840000000⟩, + ⟨6, 4, 4, 7, 2, 5, 74511338958664006854956671385766222500902993920000000⟩, + ⟨6, 4, 5, 7, 3, 5, 75947047043497998095736131218382975473790484480000000⟩, + ⟨6, 4, 6, 7, 4, 5, 153207383095550077041018968340144888540561408000000000⟩, + ⟨6, 4, 7, 7, 5, 5, -26559206819977869533257974927995830691765944320000000⟩, + ⟨6, 4, 8, 7, 6, 5, 14872530019197329987103482523732571678247485440000000⟩ +] + +def collectedFourData_14_5_44 : List CollectedFourTerm := [ + ⟨6, 5, 3, 0, 8, 6, 566960341950091286890759508861249636108599296000000⟩, + ⟨6, 5, 3, 1, 7, 6, -7573865568758990530054059668855676117228453888000000⟩, + ⟨6, 5, 4, 1, 8, 6, 11790019148716756564023604742305809823250251776000000⟩, + ⟨6, 5, 3, 2, 6, 6, 2465451304426380894355258778989188312421367808000000⟩, + ⟨6, 5, 4, 2, 7, 6, -1598626343715901010545935022739677521578557440000000⟩, + ⟨6, 5, 5, 2, 8, 6, 9971058257097761764097407398323523720975482880000000⟩, + ⟨6, 5, 3, 3, 5, 6, 4924659448211963654849119239589393980563914752000000⟩, + ⟨6, 5, 4, 3, 6, 6, -1301965035278424599778951515515843937990344704000000⟩, + ⟨6, 5, 5, 3, 7, 6, -785507929534438598385719914502223915626004480000000⟩, + ⟨6, 5, 6, 3, 8, 6, 3393099525972605665507458368217167880184135680000000⟩, + ⟨6, 5, 3, 4, 4, 6, -2014012675924198619673369620899156703343280128000000⟩, + ⟨6, 5, 4, 4, 5, 6, 3366740166668087665294124202493641365139750912000000⟩, + ⟨6, 5, 5, 4, 6, 6, -1923701986529301094517274523133074674706022400000000⟩, + ⟨6, 5, 6, 4, 7, 6, -1480600827982003271875572530394507488117391360000000⟩, + ⟨6, 5, 7, 4, 8, 6, 2172356464310062654771641289085554793014886400000000⟩, + ⟨6, 5, 3, 5, 3, 6, -5070656003606805431643333581693009007545942016000000⟩, + ⟨6, 5, 4, 5, 4, 6, 470160848005674909806923832232335994456637440000000⟩, + ⟨6, 5, 5, 5, 5, 6, -529405327057352972988909198087903587283763200000000⟩, + ⟨6, 5, 6, 5, 6, 6, -2507668829307210937111780733507286949366333440000000⟩, + ⟨6, 5, 7, 5, 7, 6, 990889865560435535515838301792524953158942720000000⟩, + ⟨6, 5, 8, 5, 8, 6, 1196327761117791619558950640192356182264905728000000⟩, + ⟨6, 5, 3, 6, 2, 6, -5670418718655530309132764698437722363586936832000000⟩, + ⟨6, 5, 4, 6, 3, 6, -11752265621531843689892411545871607623885783040000000⟩, + ⟨6, 5, 5, 6, 4, 6, 4414735152273864925746180404948260127590318080000000⟩, + ⟨6, 5, 6, 6, 5, 6, 238523496045691504910202801383719214870691840000000⟩, + ⟨6, 5, 7, 6, 6, 6, 299572307557503673877168286956470717057597440000000⟩, + ⟨6, 5, 8, 6, 7, 6, 322479168264276157128400622287824981319483392000000⟩, + ⟨6, 5, 3, 7, 1, 6, 52127517507756147300979675913967561662665850880000000⟩, + ⟨6, 5, 4, 7, 2, 6, 12077307777554006674693005617815914950405652480000000⟩, + ⟨6, 5, 5, 7, 3, 6, 6155008584999024014487860341540172591592898560000000⟩, + ⟨6, 5, 6, 7, 4, 6, 8277633736904910658878701985794786259369984000000000⟩, + ⟨6, 5, 7, 7, 5, 6, -1076224503462927217444758691972172463231467520000000⟩, + ⟨6, 5, 8, 7, 6, 6, 482128290762305619715136844705587011226959872000000⟩ +] + +def collectedFourData_14_5_45 : List CollectedFourTerm := [ + ⟨6, 6, 2, 0, 7, 7, -4674776980565817437409959531277154550210887680000000⟩, + ⟨6, 6, 3, 0, 8, 7, 2848283221524551401909870826950275737000607744000000⟩, + ⟨6, 6, 2, 1, 6, 7, 10760496526312614547371952704039191775201460224000000⟩, + ⟨6, 6, 3, 1, 7, 7, -38049423611145158524334509909751972540272607232000000⟩, + ⟨6, 6, 4, 1, 8, 7, 29615222827789274011876452984730421088309215232000000⟩, + ⟨6, 6, 2, 2, 5, 7, 22564515098938790558542744113862215724286607360000000⟩, + ⟨6, 6, 3, 2, 6, 7, 12385881452889421096867046692527332910654554112000000⟩, + ⟨6, 6, 4, 2, 7, 7, -4015572391387796070808316114554590538581934080000000⟩, + ⟨6, 6, 5, 2, 8, 7, 16697462963547362331925496664246323019975229440000000⟩, + ⟨6, 6, 2, 3, 4, 7, -1662577875797096361498173436771922030085799936000000⟩, + ⟨6, 6, 3, 3, 5, 7, 24740398649080914032329404819406786259979337728000000⟩, + ⟨6, 6, 4, 3, 6, 7, -3270392027985618392966824845857868120355504128000000⟩, + ⟨6, 6, 5, 3, 7, 7, -1315405970237674780586173845869633042896650240000000⟩, + ⟨6, 6, 6, 3, 8, 7, 4261545179486925418384642292641835390997626880000000⟩, + ⟨6, 6, 2, 4, 3, 7, -35362861011922923277394162745001821398636691456000000⟩, + ⟨6, 6, 3, 4, 4, 7, -10117953740894337225819879307051663142097518592000000⟩, + ⟨6, 6, 4, 4, 5, 7, 8456878566647285622555328728106542675718569984000000⟩, + ⟨6, 6, 5, 4, 6, 7, -3221417611326324083744266163067040260371251200000000⟩, + ⟨6, 6, 6, 4, 7, 7, -1859552681238386323657075109897590466685173760000000⟩, + ⟨6, 6, 7, 4, 8, 7, 2182687574648536905848622456809798695303249920000000⟩, + ⟨6, 6, 2, 5, 2, 7, 4810141084504225571745804817336555571565821952000000⟩, + ⟨6, 6, 3, 5, 3, 7, -25473853016808301434351237599937908595253837824000000⟩, + ⟨6, 6, 4, 5, 4, 7, 1180991998652175809519266094426225385752494080000000⟩, + ⟨6, 6, 5, 5, 5, 7, -886538380713239876682184587638879007906201600000000⟩, + ⟨6, 6, 6, 5, 6, 7, -3149493237520214325742694944495348235674583040000000⟩, + ⟨6, 6, 7, 5, 7, 7, 995602256322525324809575080691372275863126016000000⟩, + ⟨6, 6, 8, 5, 8, 7, 1001680963467868423913631769807051228113272832000000⟩, + ⟨6, 6, 2, 6, 1, 7, -80712587423146428766575433023317978679443718144000000⟩, + ⟨6, 6, 3, 6, 2, 7, -28486928097674667108262989451127007292422094848000000⟩, + ⟨6, 6, 4, 6, 3, 7, -29520390147196224415962345378008397583252193280000000⟩, + ⟨6, 6, 5, 6, 4, 7, 7392883964597293915915710727703395879134167040000000⟩, + ⟨6, 6, 6, 6, 5, 7, 299572307557503673877168286956470717057597440000000⟩, + ⟨6, 6, 7, 6, 6, 7, 300996988365913657695781798777232074978885632000000⟩, + ⟨6, 6, 8, 6, 7, 7, 270010656330052351985677361517683161272680448000000⟩, + ⟨6, 6, 2, 7, 0, 7, 658451193393597452463696314254441298735117893632000000⟩, + ⟨6, 6, 3, 7, 1, 7, 261877105877255667823880740991194940462931640320000000⟩, + ⟨6, 6, 4, 7, 2, 7, 30336860057685651714746790924990470421856911360000000⟩, + ⟨6, 6, 5, 7, 3, 7, 10307133429411033996561129266803215621716705280000000⟩, + ⟨6, 6, 6, 7, 4, 7, 10396249764867717886644240217784731821932544000000000⟩, + ⟨6, 6, 7, 7, 5, 7, -1081342721525622749592702894511170190055571456000000⟩, + ⟨6, 6, 8, 7, 6, 7, 403684296646821918635689137817909647604973568000000⟩ +] + +def collectedFourData_14_5_46 : List CollectedFourTerm := [ + ⟨6, 7, 1, 0, 6, 8, 257855340154965598495553980692823220085634105344000000⟩, + ⟨6, 7, 2, 0, 7, 8, -25161174021809026577811118378876561171540869120000000⟩, + ⟨6, 7, 3, 0, 8, 8, 7665194521376276022058771616183506189940686848000000⟩, + ⟨6, 7, 1, 1, 5, 8, 56143835518949619525920867290279774162293620736000000⟩, + ⟨6, 7, 2, 1, 6, 8, 57916500997840770058682744481946182341168726016000000⟩, + ⟨6, 7, 3, 1, 7, 8, -102397202357413456590455466222371943453812588544000000⟩, + ⟨6, 7, 4, 1, 8, 8, 53132928648250119510944669679934010563227549696000000⟩, + ⟨6, 7, 1, 2, 4, 8, -48814476869985454664208773695692765474267856896000000⟩, + ⟨6, 7, 2, 2, 5, 8, 121449577911932377392809171027608088051177226240000000⟩, + ⟨6, 7, 3, 2, 6, 8, 33332426332338896803712900285213931515626389504000000⟩, + ⟨6, 7, 4, 2, 7, 8, -7204373324967407198420844845836570831607562240000000⟩, + ⟨6, 7, 5, 2, 8, 8, 22467797559921006534853103334838282242742026240000000⟩, + ⟨6, 7, 1, 3, 3, 8, 135188914195823812289519132941329742156806488064000000⟩, + ⟨6, 7, 2, 3, 4, 8, -8948536247108219797782344750576227911859175424000000⟩, + ⟨6, 7, 3, 3, 5, 8, 66580446336405664712006962911117084526720843776000000⟩, + ⟨6, 7, 4, 3, 6, 8, -5867438758951832254251454054196874088896528384000000⟩, + ⟨6, 7, 5, 3, 7, 8, -1769985962114856043353093506234292481598423040000000⟩, + ⟨6, 7, 6, 3, 8, 8, 4587405145042608819440435840373930120009744384000000⟩, + ⟨6, 7, 1, 4, 2, 8, -233076981450495823206598619026950005728217137152000000⟩, + ⟨6, 7, 2, 4, 3, 8, -190334448793821127437030242320495993791241519104000000⟩, + ⟨6, 7, 3, 4, 4, 8, -27229063105855661501792183718734559550755569664000000⟩, + ⟨6, 7, 4, 4, 5, 8, 15172559331444623174482725220416826868552957952000000⟩, + ⟨6, 7, 5, 4, 6, 8, -4334679999306161726153949662648490813240115200000000⟩, + ⟨6, 7, 6, 4, 7, 8, -2001743775579963600722356447782277752205344768000000⟩, + ⟨6, 7, 7, 4, 8, 8, 1957989373228699995374954514783540240847994880000000⟩, + ⟨6, 7, 1, 5, 1, 8, -105679819545209120779688041652083686314052943872000000⟩, + ⟨6, 7, 2, 5, 2, 8, 25889747767606904610850969778364510774459629568000000⟩, + ⟨6, 7, 3, 5, 3, 8, -68554291619310586587811991010463373830240862208000000⟩, + ⟨6, 7, 4, 5, 4, 8, 2118828008265386627195862253036331109439242240000000⟩, + ⟨6, 7, 5, 5, 5, 8, -1192909660015414008081602584372050115795353600000000⟩, + ⟨6, 7, 6, 5, 6, 8, -3390319912979690948388675334922855362143977472000000⟩, + ⟨6, 7, 7, 5, 7, 8, 893109330205407820002014746386184938952065024000000⟩, + ⟨6, 7, 8, 5, 8, 8, 770196223597565821454231477629412907662966784000000⟩, + ⟨6, 7, 1, 6, 0, 8, 1152130765920831959012353988130855488886895804416000000⟩, + ⟨6, 7, 2, 6, 1, 8, -434421463600699652341336257528692139154835767296000000⟩, + ⟨6, 7, 3, 6, 2, 8, -76662967901155252375410190786367055791250210816000000⟩, + ⟨6, 7, 4, 6, 3, 8, -52962788511848892533268537333318828018200739840000000⟩, + ⟨6, 7, 5, 6, 4, 8, 9947728026897208425606633715414206206800035840000000⟩, + ⟨6, 7, 6, 6, 5, 8, 322479168264276157128400622287824981319483392000000⟩, + ⟨6, 7, 7, 6, 6, 8, 270010656330052351985677361517683161272680448000000⟩, + ⟨6, 7, 8, 6, 7, 8, 207612199313975891208612787475685882332184576000000⟩, + ⟨6, 7, 2, 7, 0, 8, 3543999025134003102266386786439731339597015154688000000⟩, + ⟨6, 7, 3, 7, 1, 8, 704753987270191985996821524489497913425594941440000000⟩, + ⟨6, 7, 4, 7, 2, 8, 54427624273839890625879418909348409028724654080000000⟩, + ⟨6, 7, 5, 7, 3, 8, 13869088245361963926760816322095606882243706880000000⟩, + ⟨6, 7, 6, 7, 4, 8, 11191201231437865947084126782079382574019379200000000⟩, + ⟨6, 7, 7, 7, 5, 8, -970023187082236502423717877693475109348573184000000⟩, + ⟨6, 7, 8, 7, 6, 8, 310394359224532876920302458187674301566550016000000⟩ +] + +def collectedFourData_14_5_47 : List CollectedFourTerm := [ + ⟨7, 0, 7, 4, 8, 2, 4774776140236825719045993120556126914127771729920000000⟩, + ⟨7, 0, 7, 5, 7, 2, 2177947019934912253398428108815600894757113430016000000⟩, + ⟨7, 0, 8, 5, 8, 2, 13147467608411951204445065460714555870940854484992000000⟩, + ⟨7, 0, 7, 6, 6, 2, 658451193393597452463696314254441298735117893632000000⟩, + ⟨7, 0, 8, 6, 7, 2, 3543999025134003102266386786439731339597015154688000000⟩, + ⟨7, 0, 7, 7, 5, 2, -2365510064806543445678441900891479663758809235456000000⟩, + ⟨7, 0, 8, 7, 6, 2, 5298519596313464540728901500916178099287944593408000000⟩ +] + +def collectedFourData_14_5_48 : List CollectedFourTerm := [ + ⟨7, 1, 6, 3, 8, 3, 741536401561941604053151453794302833955973365760000000⟩, + ⟨7, 1, 6, 4, 7, 3, -323574183936351209364252305330091994159534571520000000⟩, + ⟨7, 1, 7, 4, 8, 3, 1899008718281034949213816231225996832826143539200000000⟩, + ⟨7, 1, 6, 5, 6, 3, -548032176999139677695996942966628792848697262080000000⟩, + ⟨7, 1, 7, 5, 7, 3, 866206133510053416136879384898817034582921052160000000⟩, + ⟨7, 1, 8, 5, 8, 3, 2614484415436222844681015073977027240714525736960000000⟩, + ⟨7, 1, 6, 6, 5, 3, 52127517507756147300979675913967561662665850880000000⟩, + ⟨7, 1, 7, 6, 6, 3, 261877105877255667823880740991194940462931640320000000⟩, + ⟨7, 1, 8, 6, 7, 3, 704753987270191985996821524489497913425594941440000000⟩, + ⟨7, 1, 6, 7, 4, 3, 1809014645084051053968883228735652548929650688000000000⟩, + ⟨7, 1, 7, 7, 5, 3, -940803108735136557629253443268791381298574786560000000⟩, + ⟨7, 1, 8, 7, 6, 3, 1053655146530399824553792405355388410619012055040000000⟩ +] + +def collectedFourData_14_5_49 : List CollectedFourTerm := [ + ⟨7, 2, 5, 2, 8, 4, 168290254328966388961779104274729540617628549120000000⟩, + ⟨7, 2, 5, 3, 7, 4, -13257703027125577460530261939459641870668267520000000⟩, + ⟨7, 2, 6, 3, 8, 4, 171804908004508448428028432756926382202641448960000000⟩, + ⟨7, 2, 5, 4, 6, 4, -32467997700816143857978162644407975063165337600000000⟩, + ⟨7, 2, 6, 4, 7, 4, -74968177943419633603347832921687844584339537920000000⟩, + ⟨7, 2, 7, 4, 8, 4, 219988538294825587597692279991179065133996441600000000⟩, + ⟨7, 2, 5, 5, 5, 4, -8935235843213671709318423621938066915904716800000000⟩, + ⟨7, 2, 6, 5, 6, 4, -126972347621134027808834125061359715055493447680000000⟩, + ⟨7, 2, 7, 5, 7, 4, 100344679483819425892742232049258706014757191680000000⟩, + ⟨7, 2, 8, 5, 8, 4, 201914679453408939839317384105802219819599134720000000⟩, + ⟨7, 2, 5, 6, 4, 4, 74511338958664006854956671385766222500902993920000000⟩, + ⟨7, 2, 6, 6, 5, 4, 12077307777554006674693005617815914950405652480000000⟩, + ⟨7, 2, 7, 6, 6, 4, 30336860057685651714746790924990470421856911360000000⟩, + ⟨7, 2, 8, 6, 7, 4, 54427624273839890625879418909348409028724654080000000⟩, + ⟨7, 2, 5, 7, 3, 4, 103883452835020524519683270137222306136001085440000000⟩, + ⟨7, 2, 6, 7, 4, 4, 419126551336957558564655224099229821827022848000000000⟩, + ⟨7, 2, 7, 7, 5, 4, -108986282538615283761715756502773228284810362880000000⟩, + ⟨7, 2, 8, 7, 6, 4, 81373000317014146585573529360582316165200609280000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1410.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1410.lean new file mode 100644 index 0000000000000000000000000000000000000000..d25004b949515ab6fe5ffd7fa858cbdcd2e6fa2f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1410.lean @@ -0,0 +1,614 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1408 +import OAI.Analysis.LaughlinFock.Sparse1409 + +namespace OAI + +/-! Sparse1410. -/ +namespace LaughlinFock +def collectedFourData_14_5_50 : List CollectedFourTerm := [ + ⟨7, 3, 4, 1, 8, 5, 101412328038539057026425856409017918822891388928000000⟩, + ⟨7, 3, 4, 2, 7, 5, -13750649353068495604959878760180269304848056320000000⟩, + ⟨7, 3, 5, 2, 8, 5, 171532924265053628251162433957357089883192033280000000⟩, + ⟨7, 3, 4, 3, 6, 5, -11198905072748299395407388001695697089972928512000000⟩, + ⟨7, 3, 5, 3, 7, 5, -13513156649196866505698875029091517450818682880000000⟩, + ⟨7, 3, 6, 3, 8, 5, 87557649700542985286536596703304145448332165120000000⟩, + ⟨7, 3, 4, 4, 5, 5, 28959152135035455528557637968839426037237415936000000⟩, + ⟨7, 3, 5, 4, 6, 5, -33093601366632606043209295843372785660749414400000000⟩, + ⟨7, 3, 6, 4, 7, 5, -38206344273271040568564377939363190383302410240000000⟩, + ⟨7, 3, 7, 4, 8, 5, 74742449048263378465680894053342442146286796800000000⟩, + ⟨7, 3, 4, 5, 4, 5, 4044107608936222982398058619205070463770296320000000⟩, + ⟨7, 3, 5, 5, 5, 5, -9107402798193732200659052943470199024333619200000000⟩, + ⟨7, 3, 6, 5, 6, 5, -64709445520468405025168986557777559495334952960000000⟩, + ⟨7, 3, 7, 5, 7, 5, 34092717519365884110259430536272712766733680640000000⟩, + ⟨7, 3, 8, 5, 8, 5, 51451308866319095436498114337402966482270289920000000⟩, + ⟨7, 3, 4, 6, 3, 5, -101087589542766129895679608836453202016725893120000000⟩, + ⟨7, 3, 5, 6, 4, 5, 75947047043497998095736131218382975473790484480000000⟩, + ⟨7, 3, 6, 6, 5, 5, 6155008584999024014487860341540172591592898560000000⟩, + ⟨7, 3, 7, 6, 6, 5, 10307133429411033996561129266803215621716705280000000⟩, + ⟨7, 3, 8, 6, 7, 5, 13869088245361963926760816322095606882243706880000000⟩, + ⟨7, 3, 4, 7, 2, 5, 103883452835020524519683270137222306136001085440000000⟩, + ⟨7, 3, 5, 7, 3, 5, 105885112115340935207447176892399533698695823360000000⟩, + ⟨7, 3, 6, 7, 4, 5, 213601207255353648570206945416784098734637056000000000⟩, + ⟨7, 3, 7, 7, 5, 5, -37028754919427052839354599018866908269369098240000000⟩, + ⟨7, 3, 8, 7, 6, 5, 20735230266682283913496557418516661936408494080000000⟩ +] + +def collectedFourData_14_5_51 : List CollectedFourTerm := [ + ⟨7, 4, 3, 0, 8, 6, 19675588073362017518700163798460884194007449600000000⟩, + ⟨7, 4, 3, 1, 7, 6, -262840710412580619464619952318018462143007948800000000⟩, + ⟨7, 4, 4, 1, 8, 6, 409156589946500527982939948010419350014630297600000000⟩, + ⟨7, 4, 3, 2, 6, 6, 85560136559069461165856923121503869212609740800000000⟩, + ⟨7, 4, 4, 2, 7, 6, -55478154457843463168529048313590043109228544000000000⟩, + ⟨7, 4, 5, 2, 8, 6, 346032024475215587064576236073272910060453888000000000⟩, + ⟨7, 4, 3, 3, 5, 6, 170903612713600461376537802399538330075345715200000000⟩, + ⟨7, 4, 4, 3, 6, 6, -45182926960901175659785014560889091937166950400000000⟩, + ⟨7, 4, 5, 3, 7, 6, -27259985057719615482957676174858609175298048000000000⟩, + ⟨7, 4, 6, 3, 8, 6, 117752907258606478148051619761609495877255168000000000⟩, + ⟨7, 4, 3, 4, 4, 6, -69893572537569801918975544725714897587719372800000000⟩, + ⟨7, 4, 4, 4, 5, 6, 116838141520725126879508537262499905919988531200000000⟩, + ⟨7, 4, 5, 4, 6, 6, -66759462809465103604859279295281136654090240000000000⟩, + ⟨7, 4, 6, 4, 7, 6, -51382239350732318267437955592791933463822336000000000⟩, + ⟨7, 4, 7, 4, 8, 6, 75388678497785479972565972922054705036656640000000000⟩, + ⟨7, 4, 3, 5, 3, 6, -175970224734819317748929408788491010469108121600000000⟩, + ⟨7, 4, 4, 5, 4, 6, 16316293202737899349861647092393099126636544000000000⟩, + ⟨7, 4, 5, 5, 5, 6, -18372292325061617470221975069641006194360320000000000⟩, + ⟨7, 4, 6, 5, 6, 6, -87025238379374989988239315758849291813126144000000000⟩, + ⟨7, 4, 7, 5, 7, 6, 34387485999069108694363825591168478239260672000000000⟩, + ⟨7, 4, 8, 5, 8, 6, 41516928939896050156473596664379563230153932800000000⟩, + ⟨7, 4, 3, 6, 2, 6, -196784174582653138328439902594856088851657523200000000⟩, + ⟨7, 4, 4, 6, 3, 6, -407846405098911646555124131056571652562223104000000000⟩, + ⟨7, 4, 5, 6, 4, 6, 153207383095550077041018968340144888540561408000000000⟩, + ⟨7, 4, 6, 6, 5, 6, 8277633736904910658878701985794786259369984000000000⟩, + ⟨7, 4, 7, 6, 6, 6, 10396249764867717886644240217784731821932544000000000⟩, + ⟨7, 4, 8, 6, 7, 6, 11191201231437865947084126782079382574019379200000000⟩, + ⟨7, 4, 3, 7, 1, 6, 1809014645084051053968883228735652548929650688000000000⟩, + ⟨7, 4, 4, 7, 2, 6, 419126551336957558564655224099229821827022848000000000⟩, + ⟨7, 4, 5, 7, 3, 6, 213601207255353648570206945416784098734637056000000000⟩, + ⟨7, 4, 6, 7, 4, 6, 287264028149330957064748602792666252863078400000000000⟩, + ⟨7, 4, 7, 7, 5, 6, -37348908623416849228160805183366691031089152000000000⟩, + ⟨7, 4, 8, 7, 6, 6, 16731607037848669126620287452648724378104627200000000⟩ +] + +def collectedFourData_14_5_52 : List CollectedFourTerm := [ + ⟨7, 5, 2, 0, 7, 7, 16794307777409080553043071951784807224511037440000000⟩, + ⟨7, 5, 3, 0, 8, 7, -10232561950735840814359394825197563970691530752000000⟩, + ⟨7, 5, 2, 1, 6, 7, -38657478474783253101584668120415552321819246592000000⟩, + ⟨7, 5, 3, 1, 7, 7, 136693950007695130395749298022550016904717664256000000⟩, + ⟨7, 5, 4, 1, 8, 7, -106393774319955878461101593599370873204172128256000000⟩, + ⟨7, 5, 2, 2, 5, 7, -81063848178208711081089292897551183076267130880000000⟩, + ⟨7, 5, 3, 2, 6, 7, -44496733443987879693979493196842892999625015296000000⟩, + ⟨7, 5, 4, 2, 7, 7, 14426091110611807206569795932390969416760688640000000⟩, + ⟨7, 5, 5, 2, 8, 7, -59986248173439554517765242302777725277458923520000000⟩, + ⟨7, 5, 2, 3, 4, 7, 5972872003546977473952305630540112453527666688000000⟩, + ⟨7, 5, 3, 3, 5, 7, -88880789645321305523584758539817572553587687424000000⟩, + ⟨7, 5, 4, 3, 6, 7, 11749003321251003389958862328751701620502298624000000⟩, + ⟨7, 5, 5, 3, 7, 7, 4725644198269126245547708449735712320698449920000000⟩, + ⟨7, 5, 6, 3, 8, 7, -15309757374345357539969405106108906469368791040000000⟩, + ⟨7, 5, 2, 4, 3, 7, 127042375324627937141378363072757000391882702848000000⟩, + ⟨7, 5, 3, 4, 4, 7, 36349119949161746496213545693593283262872027136000000⟩, + ⟨7, 5, 4, 4, 5, 7, -30381646456053653486978486876284620755982876672000000⟩, + ⟨7, 5, 5, 4, 6, 7, 11573060932979957358818165072029093388196249600000000⟩, + ⟨7, 5, 6, 4, 7, 7, 6680511217295288069126170966551503155840942080000000⟩, + ⟨7, 5, 7, 4, 8, 7, -7841385174729189749371270301610867447677583360000000⟩, + ⟨7, 5, 2, 5, 2, 7, -17280608286076268687941567769685857863011926016000000⟩, + ⟨7, 5, 3, 5, 3, 7, 91515751365101104450396818435769330933161787392000000⟩, + ⟨7, 5, 4, 5, 4, 7, -4242757074931413014709867164969447017037168640000000⟩, + ⟨7, 5, 5, 5, 5, 7, 3184921651681003330259526987254033728457932800000000⟩, + ⟨7, 5, 6, 5, 6, 7, 11314669981835369289996815087268564123852472320000000⟩, + ⟨7, 5, 7, 5, 7, 7, -3576737625361463871777352551573398019089891328000000⟩, + ⟨7, 5, 8, 5, 8, 7, -3598575603753167052134319495361545690264109056000000⟩, + ⟨7, 5, 2, 6, 1, 7, 289962930922812135056386299073331619488650493952000000⟩, + ⟨7, 5, 3, 6, 2, 7, 102340334115225531066965730429067663272138768384000000⟩, + ⟨7, 5, 4, 6, 3, 7, 106053084436383371494286660501048498998990602240000000⟩, + ⟨7, 5, 5, 6, 4, 7, -26559206819977869533257974927995830691765944320000000⟩, + ⟨7, 5, 6, 6, 5, 7, -1076224503462927217444758691972172463231467520000000⟩, + ⟨7, 5, 7, 6, 6, 7, -1081342721525622749592702894511170190055571456000000⟩, + ⟨7, 5, 8, 6, 7, 7, -970023187082236502423717877693475109348573184000000⟩, + ⟨7, 5, 2, 7, 0, 7, -2365510064806543445678441900891479663758809235456000000⟩, + ⟨7, 5, 3, 7, 1, 7, -940803108735136557629253443268791381298574786560000000⟩, + ⟨7, 5, 4, 7, 2, 7, -108986282538615283761715756502773228284810362880000000⟩, + ⟨7, 5, 5, 7, 3, 7, -37028754919427052839354599018866908269369098240000000⟩, + ⟨7, 5, 6, 7, 4, 7, -37348908623416849228160805183366691031089152000000000⟩, + ⟨7, 5, 7, 7, 5, 7, 3884763391635508750966004270123775029409742848000000⟩, + ⟨7, 5, 8, 7, 6, 7, -1450250643181069712394631129171182126203142144000000⟩ +] + +def collectedFourData_14_5_53 : List CollectedFourTerm := [ + ⟨7, 6, 1, 0, 6, 8, 385511272191588624852513193654055297831827144704000000⟩, + ⟨7, 6, 2, 0, 7, 8, -37617666561228106018436693860507486055741521920000000⟩, + ⟨7, 6, 3, 0, 8, 8, 11459987176359658349245463336615941211808595968000000⟩, + ⟨7, 6, 1, 1, 5, 8, 83938852860747167763828766639856699496072216576000000⟩, + ⟨7, 6, 2, 1, 6, 8, 86589108323855826707428853873016875463324205056000000⟩, + ⟨7, 6, 3, 1, 7, 8, -153090782319816199122196752101105018768304635904000000⟩, + ⟨7, 6, 4, 1, 8, 8, 79437342294876474496512363205715263075632807936000000⟩, + ⟨7, 6, 1, 2, 4, 8, -72980963156339640323945341959079197033822683136000000⟩, + ⟨7, 6, 2, 2, 5, 8, 181575379667617413025076061022245322724569251840000000⟩, + ⟨7, 6, 3, 2, 6, 8, 49834244553127280719249147940817974843632779264000000⟩, + ⟨7, 6, 4, 2, 7, 8, -10771028143850701960004125043828205499019427840000000⟩, + ⟨7, 6, 5, 2, 8, 8, 33590885554135842999602528718749523534246051840000000⟩, + ⟨7, 6, 1, 3, 3, 8, 202116621926505108821727578497145527382493364224000000⟩, + ⟨7, 6, 2, 3, 4, 8, -13378670345946685582275081737492806759543209984000000⟩, + ⟨7, 6, 3, 3, 5, 8, 99542295904385429467333154361855615571083657216000000⟩, + ⟨7, 6, 4, 3, 6, 8, -8772220032791891898708554745150457103561785344000000⟩, + ⟨7, 6, 5, 3, 7, 8, -2646249403274229330728161283721428889910640640000000⟩, + ⟨7, 6, 6, 3, 8, 8, 6858482715389126262807936573241328314922041344000000⟩, + ⟨7, 6, 1, 4, 2, 8, -348465940567900262063672466215693451907439788032000000⟩, + ⟨7, 6, 2, 4, 3, 8, -284562947008556411871684915660988917978564132864000000⟩, + ⟨7, 6, 3, 4, 4, 8, -40709301394397820946860261157442550978601549824000000⟩, + ⟨7, 6, 4, 4, 5, 8, 22684008199141174072649377560919495070378360832000000⟩, + ⟨7, 6, 5, 4, 6, 8, -6480641432795909623053695787833673659921203200000000⟩, + ⟨7, 6, 6, 4, 7, 8, -2992743097977545927018963461080649699518578688000000⟩, + ⟨7, 6, 7, 4, 8, 8, 2927327290400006251826734926274602641475502080000000⟩, + ⟨7, 6, 1, 5, 1, 8, -157998518290785624260351573763448679047523991552000000⟩, + ⟨7, 6, 2, 5, 2, 8, 38706933866916373314089710829607596081427775488000000⟩, + ⟨7, 6, 3, 5, 3, 8, -102493328858229759404238890510196867629976649728000000⟩, + ⟨7, 6, 4, 5, 4, 8, 3167791989611928436482980436299842406150307840000000⟩, + ⟨7, 6, 5, 5, 5, 8, -1783481080383285846128670422239111510858137600000000⟩, + ⟨7, 6, 6, 5, 6, 8, -5068758870783104377739563703625359012137009152000000⟩, + ⟨7, 6, 7, 5, 7, 8, 1335259195666628963284436074901453291686723584000000⟩, + ⟨7, 6, 8, 5, 8, 8, 1151495741053152611075724986476218826037919744000000⟩, + ⟨7, 6, 1, 6, 0, 8, 1722513860035936962456521332412639157256722579456000000⟩, + ⟨7, 6, 2, 6, 1, 8, -649489636318522950399169075937509771101691969536000000⟩, + ⟨7, 6, 3, 6, 2, 8, -114616351430983328532738636116619294971428601856000000⟩, + ⟨7, 6, 4, 6, 3, 8, -79182971218460261191823095597556137723365949440000000⟩, + ⟨7, 6, 5, 6, 4, 8, 14872530019197329987103482523732571678247485440000000⟩, + ⟨7, 6, 6, 6, 5, 8, 482128290762305619715136844705587011226959872000000⟩, + ⟨7, 6, 7, 6, 6, 8, 403684296646821918635689137817909647604973568000000⟩, + ⟨7, 6, 8, 6, 7, 8, 310394359224532876920302458187674301566550016000000⟩, + ⟨7, 6, 2, 7, 0, 8, 5298519596313464540728901500916178099287944593408000000⟩, + ⟨7, 6, 3, 7, 1, 8, 1053655146530399824553792405355388410619012055040000000⟩, + ⟨7, 6, 4, 7, 2, 8, 81373000317014146585573529360582316165200609280000000⟩, + ⟨7, 6, 5, 7, 3, 8, 20735230266682283913496557418516661936408494080000000⟩, + ⟨7, 6, 6, 7, 4, 8, 16731607037848669126620287452648724378104627200000000⟩, + ⟨7, 6, 7, 7, 5, 8, -1450250643181069712394631129171182126203142144000000⟩, + ⟨7, 6, 8, 7, 6, 8, 464060679270125608148437629370511690412589056000000⟩ +] + +def collectedFourData_14_5 : List (List CollectedFourTerm) := [ + collectedFourData_14_5_0, + collectedFourData_14_5_1, + collectedFourData_14_5_2, + collectedFourData_14_5_3, + collectedFourData_14_5_4, + collectedFourData_14_5_5, + collectedFourData_14_5_6, + collectedFourData_14_5_7, + collectedFourData_14_5_8, + collectedFourData_14_5_9, + collectedFourData_14_5_10, + collectedFourData_14_5_11, + collectedFourData_14_5_12, + collectedFourData_14_5_13, + collectedFourData_14_5_14, + collectedFourData_14_5_15, + collectedFourData_14_5_16, + collectedFourData_14_5_17, + collectedFourData_14_5_18, + collectedFourData_14_5_19, + collectedFourData_14_5_20, + collectedFourData_14_5_21, + collectedFourData_14_5_22, + collectedFourData_14_5_23, + collectedFourData_14_5_24, + collectedFourData_14_5_25, + collectedFourData_14_5_26, + collectedFourData_14_5_27, + collectedFourData_14_5_28, + collectedFourData_14_5_29, + collectedFourData_14_5_30, + collectedFourData_14_5_31, + collectedFourData_14_5_32, + collectedFourData_14_5_33, + collectedFourData_14_5_34, + collectedFourData_14_5_35, + collectedFourData_14_5_36, + collectedFourData_14_5_37, + collectedFourData_14_5_38, + collectedFourData_14_5_39, + collectedFourData_14_5_40, + collectedFourData_14_5_41, + collectedFourData_14_5_42, + collectedFourData_14_5_43, + collectedFourData_14_5_44, + collectedFourData_14_5_45, + collectedFourData_14_5_46, + collectedFourData_14_5_47, + collectedFourData_14_5_48, + collectedFourData_14_5_49, + collectedFourData_14_5_50, + collectedFourData_14_5_51, + collectedFourData_14_5_52, + collectedFourData_14_5_53 +] + +theorem collectedFourChecked_14_5 : collectNumericRowParts 14 5 = collectedFourData_14_5 := by + decide +kernel + +def collectedFourData_14_6_0 : List CollectedFourTerm := [ + ⟨0, 6, 8, 6, 8, 0, -435759597315896243980434551456649206150348144640000000⟩, + ⟨0, 6, 8, 7, 7, 0, -329956104166231478046961795683696611472357457920000000⟩ +] + +def collectedFourData_14_6_1 : List CollectedFourTerm := [ + ⟨0, 7, 7, 5, 8, 1, 29483010188877570350702263124802654732621447168000000⟩, + ⟨0, 7, 7, 6, 7, 1, -97423105313764842170515159984750656052525006848000000⟩, + ⟨0, 7, 8, 6, 8, 1, 1156479984434576087505300973824537726967634460672000000⟩, + ⟨0, 7, 7, 7, 6, 1, 243984663694834904313194647914840264709056233472000000⟩, + ⟨0, 7, 8, 7, 7, 1, 875683823283945976247251784865685567554208137216000000⟩ +] + +def collectedFourData_14_6_2 : List CollectedFourTerm := [ + ⟨0, 8, 6, 4, 8, 2, 36210381145340445715057300715641748981934981120000000⟩, + ⟨0, 8, 6, 5, 7, 2, -43891300025917846385826801526783106182878855168000000⟩, + ⟨0, 8, 7, 5, 8, 2, -17924437042811478192886413412766664563292635136000000⟩, + ⟨0, 8, 6, 6, 6, 2, 28580030842292199245727247416306696571701952512000000⟩, + ⟨0, 8, 7, 6, 7, 2, 59229173226366913081358202003405386452089962496000000⟩, + ⟨0, 8, 8, 6, 8, 2, -351545729887670062853673564336244033071215542272000000⟩, + ⟨0, 8, 6, 7, 5, 2, -29535750185066960285713108391386040635867791360000000⟩, + ⟨0, 8, 7, 7, 6, 2, -148332470659980881007706386023561452296962310144000000⟩, + ⟨0, 8, 8, 7, 7, 2, -266189569167243499103603971249387764192185942016000000⟩ +] + +def collectedFourData_14_6_3 : List CollectedFourTerm := [ + ⟨1, 5, 8, 6, 8, 0, -665440257489088486268767060896975718610934693888000000⟩, + ⟨1, 5, 8, 7, 7, 0, -503869739803580318474344492205308821418713022464000000⟩ +] + +def collectedFourData_14_6_4 : List CollectedFourTerm := [ + ⟨1, 6, 7, 5, 8, 1, 14402655185315082308609788628988216030598791168000000⟩, + ⟨1, 6, 7, 6, 7, 1, -47591863379205753732916921543330122242979790848000000⟩, + ⟨1, 6, 8, 6, 8, 1, 564948502131351327680033945093873574948919836672000000⟩, + ⟨1, 6, 7, 7, 6, 1, 119188202262584192916625089257682585504524009472000000⟩, + ⟨1, 6, 8, 7, 7, 1, 427777627770009294814995584972341434896105865216000000⟩ +] + +def collectedFourData_14_6_5 : List CollectedFourTerm := [ + ⟨1, 7, 6, 4, 8, 2, 16599285780027688260950985402316755025526784000000000⟩, + ⟨1, 7, 6, 5, 7, 2, -20120313825553275271981593701543857301854617600000000⟩, + ⟨1, 7, 7, 5, 8, 2, -8216783240295405320083581213407154279756595200000000⟩, + ⟨1, 7, 6, 6, 6, 2, 13101438994774583396051684536751601723270758400000000⟩, + ⟨1, 7, 7, 6, 7, 2, 27151384266104095484709888929146804379005747200000000⟩, + ⟨1, 7, 8, 6, 8, 2, -161152902857659013086786684567912139624703590400000000⟩, + ⟨1, 7, 6, 7, 5, 2, -13539552541067920679313518601122753336573952000000000⟩, + ⟨1, 7, 7, 7, 6, 2, -67997435902699208819672124888264795216465100800000000⟩, + ⟨1, 7, 8, 7, 7, 2, -122024584953536230877537541113937448530031411200000000⟩ +] + +def collectedFourData_14_6_6 : List CollectedFourTerm := [ + ⟨1, 8, 5, 3, 8, 3, -277709972138247012960478245773276618227187712000000⟩, + ⟨1, 8, 5, 4, 7, 3, -165940698887619419314304962015021625203752960000000⟩, + ⟨1, 8, 6, 4, 8, 3, 629830024289976948822808335765306226067374080000000⟩, + ⟨1, 8, 5, 5, 6, 3, 368591191624580606968847156803110348867502080000000⟩, + ⟨1, 8, 6, 5, 7, 3, -763429096492670925404166076723118544217178112000000⟩, + ⟨1, 8, 7, 5, 8, 3, -155885525931709642351740451728272013983219712000000⟩, + ⟨1, 8, 5, 6, 5, 3, -747125345363428921935850723164228255284723712000000⟩, + ⟨1, 8, 6, 6, 6, 3, 497110523287753342959064146749208986552107008000000⟩, + ⟨1, 8, 7, 6, 7, 3, 515105205080646417931682364185502416300408832000000⟩, + ⟨1, 8, 8, 6, 8, 3, -2038218954443680641421186068562519018350575616000000⟩, + ⟨1, 8, 5, 7, 4, 3, -2259328985503113923315571064400694080924811264000000⟩, + ⟨1, 8, 6, 7, 5, 3, -513733953305188724909621460933360218265354240000000⟩, + ⟨1, 8, 7, 7, 6, 3, -1290020163330839301830660768351432569465602048000000⟩, + ⟨1, 8, 8, 7, 7, 3, -1543334420603645258487904241038170323259752448000000⟩ +] + +def collectedFourData_14_6_7 : List CollectedFourTerm := [ + ⟨2, 4, 8, 6, 8, 0, -189617139116781101395894851200998054616283217920000000⟩, + ⟨2, 4, 8, 7, 7, 0, -143577635217896979216525915433052432743803125760000000⟩ +] + +def collectedFourData_14_6_8 : List CollectedFourTerm := [ + ⟨2, 5, 7, 5, 8, 1, 8569607484007095916954856253569842136047681536000000⟩, + ⟨2, 5, 7, 6, 7, 1, -28317250072620036869220490931828537310257872896000000⟩, + ⟨2, 5, 8, 6, 8, 1, 336145443298517295862894194663399326781636870144000000⟩, + ⟨2, 5, 7, 7, 6, 1, 70917209151560217985183072863997716784421535744000000⟩, + ⟨2, 5, 8, 7, 7, 1, 254528509726901160111762329780024834802510200832000000⟩ +] + +def collectedFourData_14_6_9 : List CollectedFourTerm := [ + ⟨2, 6, 6, 4, 8, 2, 34967761598366888686839132035222803588778557440000000⟩, + ⟨2, 6, 6, 5, 7, 2, -42385096952954480433802329052769612802205679616000000⟩, + ⟨2, 6, 7, 5, 8, 2, -17309330127794634540659868530466883300157816832000000⟩, + ⟨2, 6, 6, 6, 6, 2, 27599259476335191705637689117007166857537388544000000⟩, + ⟨2, 6, 7, 6, 7, 2, 57196625485243863533751874376261784587470897152000000⟩, + ⟨2, 6, 8, 6, 8, 2, -339481852574141223851035042299506262780269297664000000⟩, + ⟨2, 6, 6, 7, 5, 2, -28522181717859184522196693048128748759883448320000000⟩, + ⟨2, 6, 7, 7, 6, 2, -143242194842304427233392542911189390034131222528000000⟩, + ⟨2, 6, 8, 7, 7, 2, -257054830692107336372757939747093369353920315392000000⟩ +] + +def collectedFourData_14_6_10 : List CollectedFourTerm := [ + ⟨2, 7, 5, 3, 8, 3, 9978117830289263651884293196852133848254775296000000⟩, + ⟨2, 7, 5, 4, 7, 3, 5962248433473444267297621602967358596112711680000000⟩, + ⟨2, 7, 6, 4, 8, 3, -22629789441953630033694634221523790912437616640000000⟩, + ⟨2, 7, 5, 5, 6, 3, -13243479565818122525439233290577229961117040640000000⟩, + ⟨2, 7, 6, 5, 7, 3, 27430003399672758160818163882710930361203818496000000⟩, + ⟨2, 7, 7, 5, 8, 3, 5600966122343257177430224550448394527672631296000000⟩, + ⟨2, 7, 5, 6, 5, 3, 26844209707819647017681420401196377256855863296000000⟩, + ⟨2, 7, 6, 6, 6, 3, -17861178472815888964755925976168692627185598464000000⟩, + ⟨2, 7, 7, 6, 7, 3, -18507727294471686484013483177056522873136480256000000⟩, + ⟨2, 7, 8, 6, 8, 3, 73233196254269758686920539859827164134378569728000000⟩, + ⟨2, 7, 5, 7, 4, 3, 81177678500919667155822697400832610888750989312000000⟩, + ⟨2, 7, 6, 7, 5, 3, 18458458225431202353237928282449108839348305920000000⟩, + ⟨2, 7, 7, 7, 6, 3, 46350417646350520610156983466629725367025270784000000⟩, + ⟨2, 7, 8, 7, 7, 3, 55451997570538481205410278598066480696455593984000000⟩ +] + +def collectedFourData_14_6_11 : List CollectedFourTerm := [ + ⟨2, 8, 4, 2, 8, 4, 669382257205510074638351702232017069966937292800000⟩, + ⟨2, 8, 4, 3, 7, 4, 4035464399134428669961385171367785110143447859200000⟩, + ⟨2, 8, 5, 3, 8, 4, -3337365596464331035349326702491599725582614528000000⟩, + ⟨2, 8, 4, 4, 6, 4, -4784986809414610230354477209902565145464065228800000⟩, + ⟨2, 8, 5, 4, 7, 4, -1994183987188972664473303082221902640699146240000000⟩, + ⟨2, 8, 6, 4, 8, 4, 3784475289996569181493812342416647359572213760000000⟩, + ⟨2, 8, 4, 5, 5, 4, -2482475400654178541813954982722269179661831372800000⟩, + ⟨2, 8, 5, 5, 6, 4, 4429526072168910977911877797875590601658859520000000⟩, + ⟨2, 8, 6, 5, 7, 4, -4587235349089561799867402652307077901597016064000000⟩, + ⟨2, 8, 7, 5, 8, 4, -624448817622642591733447977977251485425074176000000⟩, + ⟨2, 8, 4, 6, 4, 4, 4818049016110401765432110318604224171628665241600000⟩, + ⟨2, 8, 5, 6, 5, 4, -8978541190523697814768728318603962845419798528000000⟩, + ⟨2, 8, 6, 6, 6, 4, 2987000332193762404058234212373706250257432576000000⟩, + ⟨2, 8, 7, 6, 7, 4, 2063416948695993536843564180691419849803431936000000⟩, + ⟨2, 8, 8, 6, 8, 4, -6123548394974083170822673927977038345379250176000000⟩, + ⟨2, 8, 4, 7, 3, 4, -17536002818133660701950615297611854880444933734400000⟩, + ⟨2, 8, 5, 7, 4, 4, -27151372236496986921670950240625646195510870016000000⟩, + ⟨2, 8, 6, 7, 5, 4, -3086885948486654331910116725192364989381345280000000⟩, + ⟨2, 8, 7, 7, 6, 4, -5167584103056540644480189858466285594611810304000000⟩, + ⟨2, 8, 8, 7, 7, 4, -4636735907882484816452525039426407785591472128000000⟩ +] + +def collectedFourData_14_6_12 : List CollectedFourTerm := [ + ⟨3, 3, 8, 6, 8, 0, -33725434772923279201034202556220676053152038912000000⟩, + ⟨3, 3, 8, 7, 7, 0, -25536816945695711688010690661402348727551655936000000⟩ +] + +def collectedFourData_14_6_13 : List CollectedFourTerm := [ + ⟨3, 4, 7, 5, 8, 1, 4672642918329542565138262357976676677248352256000000⟩, + ⟨3, 4, 7, 6, 7, 1, -15440193528738425223935033069388499122772770816000000⟩, + ⟨3, 4, 8, 6, 8, 1, 183285830545778711773940598407648291483522433024000000⟩, + ⟨3, 4, 7, 7, 6, 1, 38668141539521939475809327251450972822384410624000000⟩, + ⟨3, 4, 8, 7, 7, 1, 138783583811502375351151935547986486047614697472000000⟩ +] + +def collectedFourData_14_6_14 : List CollectedFourTerm := [ + ⟨3, 5, 6, 4, 8, 2, -8665812590825725519159633926709823070787338240000000⟩, + ⟨3, 5, 6, 5, 7, 2, 10503998255794452362407509260017584104313716736000000⟩, + ⟨3, 5, 7, 5, 8, 2, 4289648639311453160482612379187919643656323072000000⟩, + ⟨3, 5, 6, 6, 6, 2, -6839728919870632007520071738911872423636762624000000⟩, + ⟨3, 5, 7, 6, 7, 2, -14174634424009531137440049053533673451046305792000000⟩, + ⟨3, 5, 8, 6, 8, 2, 84131382105145433928951792875981030246678790144000000⟩, + ⟨3, 5, 6, 7, 5, 2, 7068450199568593729304068378911079857358110720000000⟩, + ⟨3, 5, 7, 7, 6, 2, 35498698196910803448781736296031700335342911488000000⟩, + ⟨3, 5, 8, 7, 7, 2, 63704077313552571007329794767697757629507960832000000⟩ +] + +def collectedFourData_14_6_15 : List CollectedFourTerm := [ + ⟨3, 6, 5, 3, 8, 3, -10956513327857618494901009185384449117052207104000000⟩, + ⟨3, 6, 5, 4, 7, 3, -6546871417678601176459040117161754714513080320000000⟩, + ⟨3, 6, 6, 4, 8, 3, 24848733382835661600752969817945505306886799360000000⟩, + ⟨3, 6, 5, 5, 6, 3, 14542057213398310565463140179900959569592975360000000⟩, + ⟨3, 6, 6, 5, 7, 3, -30119628064462518664332716551906056645749243904000000⟩, + ⟨3, 6, 7, 5, 8, 3, -6150163889831904601038223879736163496680751104000000⟩, + ⟨3, 6, 5, 6, 5, 3, -29476394891500733035279320419570844856278319104000000⟩, + ⟨3, 6, 6, 6, 6, 3, 19612540492817338936258511380151651503372763136000000⟩, + ⟨3, 6, 7, 6, 7, 3, 20322486085971055231764777822078502794789126144000000⟩, + ⟨3, 6, 8, 6, 8, 3, -80414012386768776448597064234676759718602473472000000⟩, + ⟨3, 6, 5, 7, 4, 3, -89137483796789655601998029110816590354330943488000000⟩, + ⟨3, 6, 6, 7, 5, 3, -20268385982046189839332202628619867003111342080000000⟩, + ⟨3, 6, 7, 7, 6, 3, -50895266755863142244837895917646707322116898816000000⟩, + ⟨3, 6, 8, 7, 7, 3, -60889294030347213391971103224213772014364655616000000⟩ +] + +def collectedFourData_14_6_16 : List CollectedFourTerm := [ + ⟨3, 7, 4, 2, 8, 4, 4035464399134428669961385171367785110143447859200000⟩, + ⟨3, 7, 4, 3, 7, 4, 24328360576312186635714190562806319512508222668800000⟩, + ⟨3, 7, 5, 3, 8, 4, -20119774473336584765628764662320284329146580992000000⟩, + ⟨3, 7, 4, 4, 6, 4, -28846961077715204368582751227760489016300090163200000⟩, + ⟨3, 7, 5, 4, 7, 4, -12022216601947308774779295998590724701799055360000000⟩, + ⟨3, 7, 6, 4, 8, 4, 22815237687867691036915834593700906476911984640000000⟩, + ⟨3, 7, 4, 5, 5, 4, -14965949565034947244288261740084732860132700979200000⟩, + ⟨3, 7, 5, 5, 6, 4, 26704016392516146215143618551294334327880417280000000⟩, + ⟨3, 7, 6, 5, 7, 4, -27654788788371756834073202714599642974646173696000000⟩, + ⟨3, 7, 7, 5, 8, 4, -3764576884839813348485794794589879354118897664000000⟩, + ⟨3, 7, 4, 6, 4, 4, 29046281207045624276542503529617758881864640102400000⟩, + ⟨3, 7, 5, 6, 5, 4, -54128389183456505550345079752751713301919956992000000⟩, + ⟨3, 7, 6, 6, 6, 4, 18007548558416461858771333953141050920365195264000000⟩, + ⟨3, 7, 7, 6, 7, 4, 12439597176948792718820906420031087330201698304000000⟩, + ⟨3, 7, 8, 6, 8, 4, -36916666491068849384996143720696241657336561664000000⟩, + ⟨3, 7, 4, 7, 3, 4, -105718241429236504598283950092080947233073764761600000⟩, + ⟨3, 7, 5, 7, 4, 4, -163685838500483936733738155538488206931131367424000000⟩, + ⟨3, 7, 6, 7, 5, 4, -18609722942629060310574098975047434157078609920000000⟩, + ⟨3, 7, 7, 7, 6, 4, -31153502282053062744316249997210780901945901056000000⟩, + ⟨3, 7, 8, 7, 7, 4, -27953209818501889208768232359964319752904507392000000⟩ +] + +def collectedFourData_14_6_17 : List CollectedFourTerm := [ + ⟨3, 8, 3, 1, 8, 5, -277709972138247012960478245773276618227187712000000⟩, + ⟨3, 8, 3, 2, 7, 5, 9978117830289263651884293196852133848254775296000000⟩, + ⟨3, 8, 4, 2, 8, 5, -3337365596464331035349326702491599725582614528000000⟩, + ⟨3, 8, 3, 3, 6, 5, -10956513327857618494901009185384449117052207104000000⟩, + ⟨3, 8, 4, 3, 7, 5, -20119774473336584765628764662320284329146580992000000⟩, + ⟨3, 8, 5, 3, 8, 5, 8319617830148274679173892220106361423936880640000000⟩, + ⟨3, 8, 3, 4, 5, 5, -20496549559788427951833090109113088644929814528000000⟩, + ⟨3, 8, 4, 4, 6, 5, 23856698000845210892861639398462992465304485888000000⟩, + ⟨3, 8, 5, 4, 7, 5, 4971240991394595197697840800920356867224371200000000⟩, + ⟨3, 8, 6, 4, 8, 5, -6289469381432117596930445174808087866061619200000000⟩, + ⟨3, 8, 3, 5, 4, 5, 20982300700602927649427089815177055449416466432000000⟩, + ⟨3, 8, 4, 5, 5, 5, 12376975796758635196865384630833166604281315328000000⟩, + ⟨3, 8, 5, 5, 6, 5, -11042231671640889725316593715867227885509017600000000⟩, + ⟨3, 8, 6, 5, 7, 5, 7623586907750169357195853507965712415462522880000000⟩, + ⟨3, 8, 7, 5, 8, 5, 778334792360209772179014100445566500014653440000000⟩, + ⟨3, 8, 3, 6, 3, 5, 27911441893111775641926039010516001887195496448000000⟩, + ⟨3, 8, 4, 6, 4, 5, -24021537552509412125575591995020204164163567616000000⟩, + ⟨3, 8, 5, 6, 5, 5, 22382333975198341255843092233688653824146800640000000⟩, + ⟨3, 8, 6, 6, 6, 5, -4964135234630442956894405463410173439555665920000000⟩, + ⟨3, 8, 7, 6, 7, 5, -2571914874353024847907762978658082881368227840000000⟩, + ⟨3, 8, 8, 6, 8, 5, 6106083488674415128594834197839545553494474752000000⟩, + ⟨3, 8, 3, 7, 2, 5, 102741315173646639166611776733334855061210136576000000⟩, + ⟨3, 8, 4, 7, 3, 5, 87429942868612814779320424036613308294725894144000000⟩, + ⟨3, 8, 5, 7, 4, 5, 67684835251811890648010846551337262792132526080000000⟩, + ⟨3, 8, 6, 7, 5, 5, 5130136457304614614840064153486199742896537600000000⟩, + ⟨3, 8, 7, 7, 6, 5, 6441057115247856932841037610415232024062197760000000⟩, + ⟨3, 8, 8, 7, 7, 5, 4623511523433439148002119813839920900085907456000000⟩ +] + +def collectedFourData_14_6_18 : List CollectedFourTerm := [ + ⟨4, 2, 8, 6, 8, 0, 249964914582876737862065363749293611829556150272000000⟩, + ⟨4, 2, 8, 7, 7, 0, 189272823598237944684751963445560783487700566016000000⟩ +] + +def collectedFourData_14_6_19 : List CollectedFourTerm := [ + ⟨4, 3, 7, 5, 8, 1, -14725970824607177510583051376209790163088310272000000⟩, + ⟨4, 3, 7, 6, 7, 1, 48660221507312487392891146596429214786353364992000000⟩, + ⟨4, 3, 8, 6, 8, 1, -577630655788681529258724465834842423243034329088000000⟩, + ⟨4, 3, 7, 7, 6, 1, -121863779044419085482483198393170923210080780288000000⟩, + ⟨4, 3, 8, 7, 7, 1, -437380523584548701924295855793184414629116248064000000⟩ +] + +def collectedFourData_14_6_20 : List CollectedFourTerm := [ + ⟨4, 4, 6, 4, 8, 2, -1094739175482889473732789854349212706353971200000000⟩, + ⟨4, 4, 6, 5, 7, 2, 1326954428023976895702547144296439186383175680000000⟩, + ⟨4, 4, 7, 5, 8, 2, 541904912585197536520230136008161086521999360000000⟩, + ⟨4, 4, 6, 6, 6, 2, -864052749789755086756490197238080903179141120000000⟩, + ⟨4, 4, 7, 6, 7, 2, -1790660418682442573229870979909769359219752960000000⟩, + ⟨4, 4, 8, 6, 8, 2, 10628191980002981472640802545617969290642718720000000⟩, + ⟨4, 4, 6, 7, 5, 2, 892946767809140783492699664014103568554393600000000⟩, + ⟨4, 4, 7, 7, 6, 2, 4484497580289709924820451705427529559378493440000000⟩, + ⟨4, 4, 8, 7, 7, 2, 8047641042568593523481929726780415343234908160000000⟩ +] + +def collectedFourData_14_6_21 : List CollectedFourTerm := [ + ⟨4, 5, 5, 3, 8, 3, -20496549559788427951833090109113088644929814528000000⟩, + ⟨4, 5, 5, 4, 7, 3, -12247351913754325199758539899054189590075146240000000⟩, + ⟨4, 5, 6, 4, 8, 3, 46484979303068931130745626045253658548392427520000000⟩, + ⟨4, 5, 5, 5, 6, 3, 27204091982241837807525805953086378187706859520000000⟩, + ⟨4, 5, 6, 5, 7, 3, -56345338236024728836039578744479482940781232128000000⟩, + ⟨4, 5, 7, 5, 8, 3, -11505223897118134464301053622845242914822422528000000⟩, + ⟨4, 5, 5, 6, 5, 3, -55142030193256241110583550109687970446366998528000000⟩, + ⟨4, 5, 6, 6, 6, 3, 36689537645366140676669448706004013481199665152000000⟩, + ⟨4, 5, 7, 6, 7, 3, 38017645830826072255020673126389927108629495808000000⟩, + ⟨4, 5, 8, 6, 8, 3, -150431961415696959623011452382675464055846600704000000⟩, + ⟨4, 5, 5, 7, 4, 3, -166751118682112866789664930471625978526109270016000000⟩, + ⟨4, 5, 6, 7, 5, 3, -37916439778489481894001170615249237325706690560000000⟩, + ⟨4, 5, 7, 7, 6, 3, -95210704920867280419674706750877252043944230912000000⟩, + ⟨4, 5, 8, 7, 7, 3, -113906714244610239391845143226026716716714688512000000⟩ +] + +def collectedFourData_14_6_22 : List CollectedFourTerm := [ + ⟨4, 6, 4, 2, 8, 4, -4784986809414610230354477209902565145464065228800000⟩, + ⟨4, 6, 4, 3, 7, 4, -28846961077715204368582751227760489016300090163200000⟩, + ⟨4, 6, 5, 3, 8, 4, 23856698000845210892861639398462992465304485888000000⟩, + ⟨4, 6, 4, 4, 6, 4, 34204818726233994872674841520390519840387681484800000⟩, + ⟨4, 6, 5, 4, 7, 4, 14255149388155191955324475932530512460030935040000000⟩, + ⟨4, 6, 6, 4, 8, 4, -27052800023095760676156241518588094676163624960000000⟩, + ⟨4, 6, 4, 5, 5, 4, 17745633259561565545571172575241518779936328908800000⟩, + ⟨4, 6, 5, 5, 6, 4, -31663856636670766033773828315593464409405521920000000⟩, + ⟨4, 6, 6, 5, 7, 4, 32791219666784582961434183424308323080411807744000000⟩, + ⟨4, 6, 7, 5, 8, 4, 4463786309414444714909452361580100020439351296000000⟩, + ⟨4, 6, 4, 6, 4, 4, -34441159354068908519374737059824472941095655833600000⟩, + ⟨4, 6, 5, 6, 5, 4, 64181864251671709852373742823783615703587749888000000⟩, + ⟨4, 6, 6, 6, 6, 4, -21352160197571726188442318803412135155593117696000000⟩, + ⟨4, 6, 7, 6, 7, 4, -14750051671599040279629081064231092937090400256000000⟩, + ⟨4, 6, 8, 6, 8, 4, 43773341736136177497335368898977484960270647296000000⟩, + ⟨4, 6, 4, 7, 3, 4, 125353699282270564470527361833586724738099996262400000⟩, + ⟨4, 6, 5, 7, 4, 4, 194087842351126346807065983964613552674424487936000000⟩, + ⟨4, 6, 6, 7, 5, 4, 22066178759113907826726212108054804208424058880000000⟩, + ⟨4, 6, 7, 7, 6, 4, 36939762749156172211855303372929918123884150784000000⟩, + ⟨4, 6, 8, 7, 7, 4, 33145067589004113381539338135487960156353855488000000⟩ +] + +def collectedFourData_14_6_23 : List CollectedFourTerm := [ + ⟨4, 7, 3, 1, 8, 5, -165940698887619419314304962015021625203752960000000⟩, + ⟨4, 7, 3, 2, 7, 5, 5962248433473444267297621602967358596112711680000000⟩, + ⟨4, 7, 4, 2, 8, 5, -1994183987188972664473303082221902640699146240000000⟩, + ⟨4, 7, 3, 3, 6, 5, -6546871417678601176459040117161754714513080320000000⟩, + ⟨4, 7, 4, 3, 7, 5, -12022216601947308774779295998590724701799055360000000⟩, + ⟨4, 7, 5, 3, 8, 5, 4971240991394595197697840800920356867224371200000000⟩, + ⟨4, 7, 3, 4, 5, 5, -12247351913754325199758539899054189590075146240000000⟩, + ⟨4, 7, 4, 4, 6, 5, 14255149388155191955324475932530512460030935040000000⟩, + ⟨4, 7, 5, 4, 7, 5, 2970477430461667148051585920042228877623296000000000⟩, + ⟨4, 7, 6, 4, 8, 5, -3758161569608938574857151964046327478747136000000000⟩, + ⟨4, 7, 3, 5, 4, 5, 12537603946015125821692276511740546156918210560000000⟩, + ⟨4, 7, 4, 5, 5, 5, 7395643728655348671724400503225375839737610240000000⟩, + ⟨4, 7, 5, 5, 6, 5, -6598090903120068558711761424900288002654208000000000⟩, + ⟨4, 7, 6, 5, 7, 5, 4555339982075999602056741817248247489914470400000000⟩, + ⟨4, 7, 7, 5, 8, 5, 465080236112325847698451068539655427404595200000000⟩, + ⟨4, 7, 3, 6, 3, 5, 16677990131367932908017768831051405545271459840000000⟩, + ⟨4, 7, 4, 6, 4, 5, -14353646356761931397873837004448617863609057280000000⟩, + ⟨4, 7, 5, 6, 5, 5, 13374169152023042176914814376832972809777971200000000⟩, + ⟨4, 7, 6, 6, 6, 5, -2966231510754535183077743984815210667547033600000000⟩, + ⟨4, 7, 7, 6, 7, 5, -1536802400157047610951500564841597771133747200000000⟩, + ⟨4, 7, 8, 6, 8, 5, 3648582561782765874091404135359966886399836160000000⟩, + ⟨4, 7, 3, 7, 2, 5, 61391261945973414439639978430996234861889454080000000⟩, + ⟨4, 7, 4, 7, 3, 5, 52242221305974266023025326908763742907421163520000000⟩, + ⟨4, 7, 5, 7, 4, 5, 40443880280207580807211247226112416621684326400000000⟩, + ⟨4, 7, 6, 7, 5, 5, 3065422615397470030364022788978074932215808000000000⟩, + ⟨4, 7, 7, 7, 6, 5, 3848740148039143404324262102015722379857100800000000⟩, + ⟨4, 7, 8, 7, 7, 5, 2762697816020708617570578180114717447007764480000000⟩ +] + +def collectedFourData_14_6_24 : List CollectedFourTerm := [ + ⟨4, 8, 2, 0, 8, 6, 36210381145340445715057300715641748981934981120000000⟩, + ⟨4, 8, 2, 1, 7, 6, 16599285780027688260950985402316755025526784000000000⟩, + ⟨4, 8, 3, 1, 8, 6, 629830024289976948822808335765306226067374080000000⟩, + ⟨4, 8, 2, 2, 6, 6, 34967761598366888686839132035222803588778557440000000⟩, + ⟨4, 8, 3, 2, 7, 6, -22629789441953630033694634221523790912437616640000000⟩, + ⟨4, 8, 4, 2, 8, 6, 3784475289996569181493812342416647359572213760000000⟩, + ⟨4, 8, 2, 3, 5, 6, -8665812590825725519159633926709823070787338240000000⟩, + ⟨4, 8, 3, 3, 6, 6, 24848733382835661600752969817945505306886799360000000⟩, + ⟨4, 8, 4, 3, 7, 6, 22815237687867691036915834593700906476911984640000000⟩, + ⟨4, 8, 5, 3, 8, 6, -6289469381432117596930445174808087866061619200000000⟩, + ⟨4, 8, 2, 4, 4, 6, -1094739175482889473732789854349212706353971200000000⟩, + ⟨4, 8, 3, 4, 5, 6, 46484979303068931130745626045253658548392427520000000⟩, + ⟨4, 8, 4, 4, 6, 6, -27052800023095760676156241518588094676163624960000000⟩, + ⟨4, 8, 5, 4, 7, 6, -3758161569608938574857151964046327478747136000000000⟩, + ⟨4, 8, 6, 4, 8, 6, 3566037458772349030255455138669421167378432000000000⟩, + ⟨4, 8, 2, 5, 3, 6, -18255214065723552299433696613608971535730606080000000⟩, + ⟨4, 8, 3, 5, 4, 6, -47586634567597133986028759237739323706971258880000000⟩, + ⟨4, 8, 4, 5, 5, 6, -14035129719483602996049237965861815905429749760000000⟩, + ⟨4, 8, 5, 5, 6, 6, 8347712529510217919772634877715242998038528000000000⟩, + ⟨4, 8, 6, 5, 7, 6, -4322462648995882315142399719835033827855564800000000⟩, + ⟨4, 8, 7, 5, 8, 6, -353043585294034007643773448932587017779281920000000⟩, + ⟨4, 8, 2, 6, 2, 6, 12216695095653086869970799124249799842081013760000000⟩, + ⟨4, 8, 3, 6, 3, 6, -63301522772670271291069082380357897925500600320000000⟩, + ⟨4, 8, 4, 6, 4, 6, 27239723269008099776059804738270941716120862720000000⟩, + ⟨4, 8, 5, 6, 5, 6, -16920609467404932849116867632838553977959219200000000⟩, + ⟨4, 8, 6, 6, 6, 6, 2814592316700808267709386970000552879141683200000000⟩, + ⟨4, 8, 7, 6, 7, 6, 1166590594722418053455004170896266721618821120000000⟩, + ⟨4, 8, 8, 6, 8, 6, -2308040220508631975630684163966026724440801280000000⟩, + ⟨4, 8, 2, 7, 1, 6, -180188477313202561329369527792333562997333032960000000⟩, + ⟨4, 8, 3, 7, 2, 6, -233011312244808127027130865296970575830151331840000000⟩, + ⟨4, 8, 4, 7, 3, 6, -99143006310909960934261014618996231950020116480000000⟩, + ⟨4, 8, 5, 7, 4, 6, -51168419943631129305016840082887043818350182400000000⟩, + ⟨4, 8, 6, 7, 5, 6, -2908712590186155078448376114833915794948096000000000⟩, + ⟨4, 8, 7, 7, 6, 6, -2921588395342304988351299113979227808653639680000000⟩, + ⟨4, 8, 8, 7, 7, 6, -1747642425109743169656188342699365104447651840000000⟩ +] + +def collectedFourData_14_6_25 : List CollectedFourTerm := [ + ⟨5, 1, 8, 6, 8, 0, 192670309072511556430581841676560946903270817792000000⟩, + ⟨5, 1, 8, 7, 7, 0, 145889488060967927673687612976078529821541400576000000⟩ +] + +def collectedFourData_14_6_26 : List CollectedFourTerm := [ + ⟨5, 2, 7, 5, 8, 1, -2982562774410722507096954318751313535686410240000000⟩, + ⟨5, 2, 7, 6, 7, 1, 9855524433049507518568510888407881707306352640000000⟩, + ⟨5, 2, 8, 6, 8, 1, -116991926157760271843063613595227394533186600960000000⟩, + ⟨5, 2, 7, 7, 6, 1, -24681997218108266709784874058145557300337704960000000⟩, + ⟨5, 2, 8, 7, 7, 1, -88586001115505034870061727234902123707503738880000000⟩ +] + +def collectedFourData_14_6_27 : List CollectedFourTerm := [ + ⟨5, 3, 6, 4, 8, 2, -18255214065723552299433696613608971535730606080000000⟩, + ⟨5, 3, 6, 5, 7, 2, 22127496376798901921901182364857896473735462912000000⟩, + ⟨5, 3, 7, 5, 8, 2, 9036481386670362265840619098936740998780289024000000⟩, + ⟨5, 3, 6, 6, 6, 2, -14408425554453528324038112302917602022898270208000000⟩, + ⟨5, 3, 7, 6, 7, 2, -29859979430851262942871870957951687772826763264000000⟩, + ⟨5, 3, 8, 6, 8, 2, 177229356609969208532116108290931739920378626048000000⟩, + ⟨5, 3, 6, 7, 5, 2, 14890244873589608449648459609664384969987850240000000⟩, + ⟨5, 3, 7, 7, 6, 2, 74780792666250470404924816893643644583853162496000000⟩, + ⟨5, 3, 8, 7, 7, 2, 134197636520488741368865054232279392903646674944000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1411.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1411.lean new file mode 100644 index 0000000000000000000000000000000000000000..6c433b131b87179c554e104937a56faf32c4ccbe --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1411.lean @@ -0,0 +1,622 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1411. -/ +namespace LaughlinFock +def collectedFourData_14_6_28 : List CollectedFourTerm := [ + ⟨5, 4, 5, 3, 8, 3, 20982300700602927649427089815177055449416466432000000⟩, + ⟨5, 4, 5, 4, 7, 3, 12537603946015125821692276511740546156918210560000000⟩, + ⟨5, 4, 6, 4, 8, 3, -47586634567597133986028759237739323706971258880000000⟩, + ⟨5, 4, 5, 5, 6, 3, -27848806287771658929752758034847626764883066880000000⟩, + ⟨5, 4, 6, 5, 7, 3, 57680675788713298636242934464612797667273080832000000⟩, + ⟨5, 4, 7, 5, 8, 3, 11777888113943957417229193747522918090310418432000000⟩, + ⟨5, 4, 5, 6, 5, 3, 56448850348281314168074875907898515923174162432000000⟩, + ⟨5, 4, 6, 6, 6, 3, -37559049107049308982045422301482758451377471488000000⟩, + ⟨5, 4, 7, 6, 7, 3, -38918632349534345821392405675182403162055114752000000⟩, + ⟨5, 4, 8, 6, 8, 3, 153997073517101400946071291462591068987851800576000000⟩, + ⟨5, 4, 5, 7, 4, 3, 170702981208810578052664333547231540645518639104000000⟩, + ⟨5, 4, 6, 7, 5, 3, 38815027798112022603687869723480841614146928640000000⟩, + ⟨5, 4, 7, 7, 6, 3, 97467119269934010645640596578674743056875388928000000⟩, + ⟨5, 4, 8, 7, 7, 3, 116606208431636798825128934440062249101665763328000000⟩ +] + +def collectedFourData_14_6_29 : List CollectedFourTerm := [ + ⟨5, 5, 4, 2, 8, 4, -2482475400654178541813954982722269179661831372800000⟩, + ⟨5, 5, 4, 3, 7, 4, -14965949565034947244288261740084732860132700979200000⟩, + ⟨5, 5, 5, 3, 8, 4, 12376975796758635196865384630833166604281315328000000⟩, + ⟨5, 5, 4, 4, 6, 4, 17745633259561565545571172575241518779936328908800000⟩, + ⟨5, 5, 5, 4, 7, 4, 7395643728655348671724400503225375839737610240000000⟩, + ⟨5, 5, 6, 4, 8, 4, -14035129719483602996049237965861815905429749760000000⟩, + ⟨5, 5, 4, 5, 5, 4, 9206524446256857908977892677263588417279413452800000⟩, + ⟨5, 5, 5, 5, 6, 4, -16427369253289988492956341241927359106929131520000000⟩, + ⟨5, 5, 6, 5, 7, 4, 17012250905284947735422142669289911502938046464000000⟩, + ⟨5, 5, 7, 5, 8, 4, 2315834953838446781099717199991232872920907776000000⟩, + ⟨5, 5, 4, 6, 4, 4, -17868247974741337327683871498056961764917615001600000⟩, + ⟨5, 5, 5, 6, 5, 4, 33297876361835376328791836681107576677180899328000000⟩, + ⟨5, 5, 6, 6, 6, 4, -11077608894763869566465592290806737820163506176000000⟩, + ⟨5, 5, 7, 6, 7, 4, -7652401540810579794932729020349830272475201536000000⟩, + ⟨5, 5, 8, 6, 8, 4, 22709831477608824499937167487226916796708683776000000⟩, + ⟨5, 5, 4, 7, 3, 4, 65034134312965504194194809072694617531581097574400000⟩, + ⟨5, 5, 5, 7, 4, 4, 100693755990032188731829311891819704898463727616000000⟩, + ⟨5, 5, 6, 7, 5, 4, 11448045342185507768936140795213656335088353280000000⟩, + ⟨5, 5, 7, 7, 6, 4, 19164536075701427432567778921007469473724104704000000⟩, + ⟨5, 5, 8, 7, 7, 4, 17195829000161669480014794999839080291057532928000000⟩ +] + +def collectedFourData_14_6_30 : List CollectedFourTerm := [ + ⟨5, 6, 3, 1, 8, 5, 368591191624580606968847156803110348867502080000000⟩, + ⟨5, 6, 3, 2, 7, 5, -13243479565818122525439233290577229961117040640000000⟩, + ⟨5, 6, 4, 2, 8, 5, 4429526072168910977911877797875590601658859520000000⟩, + ⟨5, 6, 3, 3, 6, 5, 14542057213398310565463140179900959569592975360000000⟩, + ⟨5, 6, 4, 3, 7, 5, 26704016392516146215143618551294334327880417280000000⟩, + ⟨5, 6, 5, 3, 8, 5, -11042231671640889725316593715867227885509017600000000⟩, + ⟨5, 6, 3, 4, 5, 5, 27204091982241837807525805953086378187706859520000000⟩, + ⟨5, 6, 4, 4, 6, 5, -31663856636670766033773828315593464409405521920000000⟩, + ⟨5, 6, 5, 4, 7, 5, -6598090903120068558711761424900288002654208000000000⟩, + ⟨5, 6, 6, 4, 8, 5, 8347712529510217919772634877715242998038528000000000⟩, + ⟨5, 6, 3, 5, 4, 5, -27848806287771658929752758034847626764883066880000000⟩, + ⟨5, 6, 4, 5, 5, 5, -16427369253289988492956341241927359106929131520000000⟩, + ⟨5, 6, 5, 5, 6, 5, 14655827079982118581054715663016805986729984000000000⟩, + ⟨5, 6, 6, 5, 7, 5, -10118423048137230123185680883451475357020979200000000⟩, + ⟨5, 6, 7, 5, 8, 5, -1033046621948831669038065764941042233743769600000000⟩, + ⟨5, 6, 3, 6, 3, 5, -37045524682206500917759807883360611984547512320000000⟩, + ⟨5, 6, 4, 6, 4, 5, 31882640306219813998320507149294053916871229440000000⟩, + ⟨5, 6, 5, 6, 5, 5, -29707003633095279301108327685174440385681817600000000⟩, + ⟨5, 6, 6, 6, 6, 5, 6588659771306805934445016948386850881195212800000000⟩, + ⟨5, 6, 7, 6, 7, 5, 3413579861737365761757023268586963647175065600000000⟩, + ⟨5, 6, 8, 6, 8, 5, -8104313186597713980874122668522983380410695680000000⟩, + ⟨5, 6, 3, 7, 2, 5, -136363644046887711578518321217710260483879075840000000⟩, + ⟨5, 6, 4, 7, 3, 5, -116041590359486973896347646921784488715312168960000000⟩, + ⟨5, 6, 5, 7, 4, 5, -89834851403749251394395060017984767343670067200000000⟩, + ⟨5, 6, 6, 7, 5, 5, -6808985271343768735683231003354609991286784000000000⟩, + ⟨5, 6, 7, 7, 6, 5, -8548907693704748408913709155740910205953638400000000⟩, + ⟨5, 6, 8, 7, 7, 5, -6136566176543165092682548147577067832124375040000000⟩ +] + +def collectedFourData_14_6_31 : List CollectedFourTerm := [ + ⟨5, 7, 2, 0, 8, 6, -43891300025917846385826801526783106182878855168000000⟩, + ⟨5, 7, 2, 1, 7, 6, -20120313825553275271981593701543857301854617600000000⟩, + ⟨5, 7, 3, 1, 8, 6, -763429096492670925404166076723118544217178112000000⟩, + ⟨5, 7, 2, 2, 6, 6, -42385096952954480433802329052769612802205679616000000⟩, + ⟨5, 7, 3, 2, 7, 6, 27430003399672758160818163882710930361203818496000000⟩, + ⟨5, 7, 4, 2, 8, 6, -4587235349089561799867402652307077901597016064000000⟩, + ⟨5, 7, 2, 3, 5, 6, 10503998255794452362407509260017584104313716736000000⟩, + ⟨5, 7, 3, 3, 6, 6, -30119628064462518664332716551906056645749243904000000⟩, + ⟨5, 7, 4, 3, 7, 6, -27654788788371756834073202714599642974646173696000000⟩, + ⟨5, 7, 5, 3, 8, 6, 7623586907750169357195853507965712415462522880000000⟩, + ⟨5, 7, 2, 4, 4, 6, 1326954428023976895702547144296439186383175680000000⟩, + ⟨5, 7, 3, 4, 5, 6, -56345338236024728836039578744479482940781232128000000⟩, + ⟨5, 7, 4, 4, 6, 6, 32791219666784582961434183424308323080411807744000000⟩, + ⟨5, 7, 5, 4, 7, 6, 4555339982075999602056741817248247489914470400000000⟩, + ⟨5, 7, 6, 4, 8, 6, -4322462648995882315142399719835033827855564800000000⟩, + ⟨5, 7, 2, 5, 3, 6, 22127496376798901921901182364857896473735462912000000⟩, + ⟨5, 7, 3, 5, 4, 6, 57680675788713298636242934464612797667273080832000000⟩, + ⟨5, 7, 4, 5, 5, 6, 17012250905284947735422142669289911502938046464000000⟩, + ⟨5, 7, 5, 5, 6, 6, -10118423048137230123185680883451475357020979200000000⟩, + ⟨5, 7, 6, 5, 7, 6, 5239340183037948563651222972217707390010654720000000⟩, + ⟨5, 7, 7, 5, 8, 6, 427930925724600709690873503551041097630220288000000⟩, + ⟨5, 7, 2, 6, 2, 6, -14808091293385014915963803067688705575893336064000000⟩, + ⟨5, 7, 3, 6, 3, 6, 76728994289259635027303467484244025033566978048000000⟩, + ⟨5, 7, 4, 6, 4, 6, -33017792931374829549738000165161337045708177408000000⟩, + ⟨5, 7, 5, 6, 5, 6, 20509796452413823764303521487495158528087162880000000⟩, + ⟨5, 7, 6, 6, 6, 6, -3411621527183372189637473112897737579802132480000000⟩, + ⟨5, 7, 7, 6, 7, 6, -1414046916403817298874662744641442378487431168000000⟩, + ⟨5, 7, 8, 6, 8, 6, 2797619980403481963535806192973841774193672192000000⟩, + ⟨5, 7, 2, 7, 1, 6, 218409921928832216757068544584285239508094418944000000⟩, + ⟨5, 7, 3, 7, 2, 6, 282437496974144145178685411931758539441780555776000000⟩, + ⟨5, 7, 4, 7, 3, 6, 120173146424435493010715707417184476307990249472000000⟩, + ⟨5, 7, 5, 7, 4, 6, 62022226791364999652238855167139402822828687360000000⟩, + ⟨5, 7, 6, 7, 5, 6, 3525706522463748643028651127481124923008614400000000⟩, + ⟨5, 7, 7, 7, 6, 6, 3541313533749145107212600001223933736572157952000000⟩, + ⟨5, 7, 8, 7, 7, 6, 2118351025100573123619245253197827381213003776000000⟩ +] + +def collectedFourData_14_6_32 : List CollectedFourTerm := [ + ⟨5, 8, 1, 0, 7, 7, 29483010188877570350702263124802654732621447168000000⟩, + ⟨5, 8, 2, 0, 8, 7, -17924437042811478192886413412766664563292635136000000⟩, + ⟨5, 8, 1, 1, 6, 7, 14402655185315082308609788628988216030598791168000000⟩, + ⟨5, 8, 2, 1, 7, 7, -8216783240295405320083581213407154279756595200000000⟩, + ⟨5, 8, 3, 1, 8, 7, -155885525931709642351740451728272013983219712000000⟩, + ⟨5, 8, 1, 2, 5, 7, 8569607484007095916954856253569842136047681536000000⟩, + ⟨5, 8, 2, 2, 6, 7, -17309330127794634540659868530466883300157816832000000⟩, + ⟨5, 8, 3, 2, 7, 7, 5600966122343257177430224550448394527672631296000000⟩, + ⟨5, 8, 4, 2, 8, 7, -624448817622642591733447977977251485425074176000000⟩, + ⟨5, 8, 1, 3, 4, 7, 4672642918329542565138262357976676677248352256000000⟩, + ⟨5, 8, 2, 3, 5, 7, 4289648639311453160482612379187919643656323072000000⟩, + ⟨5, 8, 3, 3, 6, 7, -6150163889831904601038223879736163496680751104000000⟩, + ⟨5, 8, 4, 3, 7, 7, -3764576884839813348485794794589879354118897664000000⟩, + ⟨5, 8, 5, 3, 8, 7, 778334792360209772179014100445566500014653440000000⟩, + ⟨5, 8, 1, 4, 3, 7, -14725970824607177510583051376209790163088310272000000⟩, + ⟨5, 8, 2, 4, 4, 7, 541904912585197536520230136008161086521999360000000⟩, + ⟨5, 8, 3, 4, 5, 7, -11505223897118134464301053622845242914822422528000000⟩, + ⟨5, 8, 4, 4, 6, 7, 4463786309414444714909452361580100020439351296000000⟩, + ⟨5, 8, 5, 4, 7, 7, 465080236112325847698451068539655427404595200000000⟩, + ⟨5, 8, 6, 4, 8, 7, -353043585294034007643773448932587017779281920000000⟩, + ⟨5, 8, 1, 5, 2, 7, -2982562774410722507096954318751313535686410240000000⟩, + ⟨5, 8, 2, 5, 3, 7, 9036481386670362265840619098936740998780289024000000⟩, + ⟨5, 8, 3, 5, 4, 7, 11777888113943957417229193747522918090310418432000000⟩, + ⟨5, 8, 4, 5, 5, 7, 2315834953838446781099717199991232872920907776000000⟩, + ⟨5, 8, 5, 5, 6, 7, -1033046621948831669038065764941042233743769600000000⟩, + ⟨5, 8, 6, 5, 7, 7, 427930925724600709690873503551041097630220288000000⟩, + ⟨5, 8, 7, 5, 8, 7, 29126580637063422628003528502667063796432896000000⟩, + ⟨5, 8, 1, 6, 1, 7, -65809435982631316152052162902612258299163181056000000⟩, + ⟨5, 8, 2, 6, 2, 7, -6047364738701059748823969935631960228419862528000000⟩, + ⟨5, 8, 3, 6, 3, 7, 15667387690543978825020153613730275794981224448000000⟩, + ⟨5, 8, 4, 6, 4, 7, -4494629158409834093484263786147433776909647872000000⟩, + ⟨5, 8, 5, 6, 5, 7, 2093960278318744388007768336866790316902973440000000⟩, + ⟨5, 8, 6, 6, 6, 7, -278649277837697935497497599300759770567278592000000⟩, + ⟨5, 8, 7, 6, 7, 7, -96245326194846127366541429353989152603897856000000⟩, + ⟨5, 8, 8, 6, 8, 7, 163214132507361797762095882710390382119616512000000⟩, + ⟨5, 8, 1, 7, 0, 7, 412206404187635535407401513949520144220161048576000000⟩, + ⟨5, 8, 2, 7, 1, 7, 89194781034669434018236502650956097495171596288000000⟩, + ⟨5, 8, 3, 7, 2, 7, 57671259794684531983157354686555970950530072576000000⟩, + ⟨5, 8, 4, 7, 3, 7, 16358868356214856408504350968129136953338626048000000⟩, + ⟨5, 8, 5, 7, 4, 7, 6332197375791612543615391946107261772554567680000000⟩, + ⟨5, 8, 6, 7, 5, 7, 287967340024167836552433092498963847457013760000000⟩, + ⟨5, 8, 7, 7, 6, 7, 241035054961765905140560621064829045974237184000000⟩, + ⟨5, 8, 8, 7, 7, 7, 123585343016461507611809832025677614322548736000000⟩ +] + +def collectedFourData_14_6_33 : List CollectedFourTerm := [ + ⟨6, 0, 8, 6, 8, 0, -4444212401940813201960812132469196187820921716736000000⟩, + ⟨6, 0, 8, 7, 7, 0, -3365146790257848360261690097950054933976011767808000000⟩ +] + +def collectedFourData_14_6_34 : List CollectedFourTerm := [ + ⟨6, 1, 7, 5, 8, 1, -65809435982631316152052162902612258299163181056000000⟩, + ⟨6, 1, 7, 6, 7, 1, 217459464664637051934977883753554663944136687616000000⟩, + ⟨6, 1, 8, 6, 8, 1, -2581395014052977549508798188632261335006496948224000000⟩, + ⟨6, 1, 7, 7, 6, 1, -544601551988960785537340532760452906473251405824000000⟩, + ⟨6, 1, 8, 7, 7, 1, -1954626008004123925535714105274713893157650563072000000⟩ +] + +def collectedFourData_14_6_35 : List CollectedFourTerm := [ + ⟨6, 2, 6, 4, 8, 2, 12216695095653086869970799124249799842081013760000000⟩, + ⟨6, 2, 6, 5, 7, 2, -14808091293385014915963803067688705575893336064000000⟩, + ⟨6, 2, 7, 5, 8, 2, -6047364738701059748823969935631960228419862528000000⟩, + ⟨6, 2, 6, 6, 6, 2, 9642359775867042227449756612281564212364312576000000⟩, + ⟨6, 2, 7, 6, 7, 2, 19982798501066170673143431723713537069241335808000000⟩, + ⟨6, 2, 8, 6, 8, 2, -118604854695629996624290793039973552305844781056000000⟩, + ⟨6, 2, 6, 7, 5, 2, -9964801336502193083812305918577229136427745280000000⟩, + ⟨6, 2, 7, 7, 6, 2, -50044559309232213689261030753313674620317990912000000⟩, + ⟨6, 2, 8, 7, 7, 2, -89807306670063422498097709357798598888304672768000000⟩ +] + +def collectedFourData_14_6_36 : List CollectedFourTerm := [ + ⟨6, 3, 5, 3, 8, 3, 27911441893111775641926039010516001887195496448000000⟩, + ⟨6, 3, 5, 4, 7, 3, 16677990131367932908017768831051405545271459840000000⟩, + ⟨6, 3, 6, 4, 8, 3, -63301522772670271291069082380357897925500600320000000⟩, + ⟨6, 3, 5, 5, 6, 3, -37045524682206500917759807883360611984547512320000000⟩, + ⟨6, 3, 6, 5, 7, 3, 76728994289259635027303467484244025033566978048000000⟩, + ⟨6, 3, 7, 5, 8, 3, 15667387690543978825020153613730275794981224448000000⟩, + ⟨6, 3, 5, 6, 5, 3, 75090373973324205416102348748108239102382440448000000⟩, + ⟨6, 3, 6, 6, 6, 3, -49962453196651345612293501173172811243488018432000000⟩, + ⟨6, 3, 7, 6, 7, 3, -51771021723666076984542758227881392004743036928000000⟩, + ⟨6, 3, 8, 6, 8, 3, 204852672283851440364845643923108165293927563264000000⟩, + ⟨6, 3, 5, 7, 4, 3, 227075496103902356577873697016360484767589728256000000⟩, + ⟨6, 3, 6, 7, 5, 3, 51633203070785795329688849985374206292876328960000000⟩, + ⟨6, 3, 7, 7, 6, 3, 129654410867993419840791158120002890837987950592000000⟩, + ⟨6, 3, 8, 7, 7, 3, 155113943768911310168106071728154764090584072192000000⟩ +] + +def collectedFourData_14_6_37 : List CollectedFourTerm := [ + ⟨6, 4, 4, 2, 8, 4, 4818049016110401765432110318604224171628665241600000⟩, + ⟨6, 4, 4, 3, 7, 4, 29046281207045624276542503529617758881864640102400000⟩, + ⟨6, 4, 5, 3, 8, 4, -24021537552509412125575591995020204164163567616000000⟩, + ⟨6, 4, 4, 4, 6, 4, -34441159354068908519374737059824472941095655833600000⟩, + ⟨6, 4, 5, 4, 7, 4, -14353646356761931397873837004448617863609057280000000⟩, + ⟨6, 4, 6, 4, 8, 4, 27239723269008099776059804738270941716120862720000000⟩, + ⟨6, 4, 4, 5, 5, 4, -17868247974741337327683871498056961764917615001600000⟩, + ⟨6, 4, 5, 5, 6, 4, 31882640306219813998320507149294053916871229440000000⟩, + ⟨6, 4, 6, 5, 7, 4, -33017792931374829549738000165161337045708177408000000⟩, + ⟨6, 4, 7, 5, 8, 4, -4494629158409834093484263786147433776909647872000000⟩, + ⟨6, 4, 4, 6, 4, 4, 34679132994281769976125466255142741966140420915200000⟩, + ⟨6, 4, 5, 6, 5, 4, -64625333407706772376281221031923237056325615616000000⟩, + ⟨6, 4, 6, 6, 6, 4, 21499694467146888190652993344483277375035932672000000⟩, + ⟨6, 4, 7, 6, 7, 4, 14851968202733568905188157840615669709869678592000000⟩, + ⟨6, 4, 8, 6, 8, 4, -44075796754277117087497194228665456333917519872000000⟩, + ⟨6, 4, 4, 7, 3, 4, -126219839583346870691914762255795351011193572556800000⟩, + ⟨6, 4, 5, 7, 4, 4, -195428906102509641922159673841796723588938596352000000⟩, + ⟨6, 4, 6, 7, 5, 4, -22218646590725205810420936573906806903050076160000000⟩, + ⟨6, 4, 7, 7, 6, 4, -37195000667242620518397700321868907168229490688000000⟩, + ⟨6, 4, 8, 7, 7, 4, -33374085790980661714380525098207651391200034816000000⟩ +] + +def collectedFourData_14_6_38 : List CollectedFourTerm := [ + ⟨6, 5, 3, 1, 8, 5, -747125345363428921935850723164228255284723712000000⟩, + ⟨6, 5, 3, 2, 7, 5, 26844209707819647017681420401196377256855863296000000⟩, + ⟨6, 5, 4, 2, 8, 5, -8978541190523697814768728318603962845419798528000000⟩, + ⟨6, 5, 3, 3, 6, 5, -29476394891500733035279320419570844856278319104000000⟩, + ⟨6, 5, 4, 3, 7, 5, -54128389183456505550345079752751713301919956992000000⟩, + ⟨6, 5, 5, 3, 8, 5, 22382333975198341255843092233688653824146800640000000⟩, + ⟨6, 5, 3, 4, 5, 5, -55142030193256241110583550109687970446366998528000000⟩, + ⟨6, 5, 4, 4, 6, 5, 64181864251671709852373742823783615703587749888000000⟩, + ⟨6, 5, 5, 4, 7, 5, 13374169152023042176914814376832972809777971200000000⟩, + ⟨6, 5, 6, 4, 8, 5, -16920609467404932849116867632838553977959219200000000⟩, + ⟨6, 5, 3, 5, 4, 5, 56448850348281314168074875907898515923174162432000000⟩, + ⟨6, 5, 4, 5, 5, 5, 33297876361835376328791836681107576677180899328000000⟩, + ⟨6, 5, 5, 5, 6, 5, -29707003633095279301108327685174440385681817600000000⟩, + ⟨6, 5, 6, 5, 7, 5, 20509796452413823764303521487495158528087162880000000⟩, + ⟨6, 5, 7, 5, 8, 5, 2093960278318744388007768336866790316902973440000000⟩, + ⟨6, 5, 3, 6, 3, 5, 75090373973324205416102348748108239102382440448000000⟩, + ⟨6, 5, 4, 6, 4, 5, -64625333407706772376281221031923237056325615616000000⟩, + ⟨6, 5, 5, 6, 5, 5, 60215370994798395236870000929572757158116720640000000⟩, + ⟨6, 5, 6, 6, 6, 5, -13355052478121814960635595795202700384057425920000000⟩, + ⟨6, 5, 7, 6, 7, 5, -6919243028801929052457935124233197736259747840000000⟩, + ⟨6, 5, 8, 6, 8, 5, 16427244942514292539308425727757915397661130752000000⟩, + ⟨6, 5, 3, 7, 2, 5, 276405776829617672481562829910815308435031064576000000⟩, + ⟨6, 5, 4, 7, 3, 5, 235213470218129758514213516882624065140261126144000000⟩, + ⟨6, 5, 5, 7, 4, 5, 182093050256772655983732453413884836582606766080000000⟩, + ⟨6, 5, 6, 7, 5, 5, 13801646886908301118607615154070559829629337600000000⟩, + ⟨6, 5, 7, 7, 6, 5, 17328427152552962778871976254891907283167477760000000⟩, + ⟨6, 5, 8, 7, 7, 5, 12438669800511854401053037242083955483875475456000000⟩ +] + +def collectedFourData_14_6_39 : List CollectedFourTerm := [ + ⟨6, 6, 2, 0, 8, 6, 28580030842292199245727247416306696571701952512000000⟩, + ⟨6, 6, 2, 1, 7, 6, 13101438994774583396051684536751601723270758400000000⟩, + ⟨6, 6, 3, 1, 8, 6, 497110523287753342959064146749208986552107008000000⟩, + ⟨6, 6, 2, 2, 6, 6, 27599259476335191705637689117007166857537388544000000⟩, + ⟨6, 6, 3, 2, 7, 6, -17861178472815888964755925976168692627185598464000000⟩, + ⟨6, 6, 4, 2, 8, 6, 2987000332193762404058234212373706250257432576000000⟩, + ⟨6, 6, 2, 3, 5, 6, -6839728919870632007520071738911872423636762624000000⟩, + ⟨6, 6, 3, 3, 6, 6, 19612540492817338936258511380151651503372763136000000⟩, + ⟨6, 6, 4, 3, 7, 6, 18007548558416461858771333953141050920365195264000000⟩, + ⟨6, 6, 5, 3, 8, 6, -4964135234630442956894405463410173439555665920000000⟩, + ⟨6, 6, 2, 4, 4, 6, -864052749789755086756490197238080903179141120000000⟩, + ⟨6, 6, 3, 4, 5, 6, 36689537645366140676669448706004013481199665152000000⟩, + ⟨6, 6, 4, 4, 6, 6, -21352160197571726188442318803412135155593117696000000⟩, + ⟨6, 6, 5, 4, 7, 6, -2966231510754535183077743984815210667547033600000000⟩, + ⟨6, 6, 6, 4, 8, 6, 2814592316700808267709386970000552879141683200000000⟩, + ⟨6, 6, 2, 5, 3, 6, -14408425554453528324038112302917602022898270208000000⟩, + ⟨6, 6, 3, 5, 4, 6, -37559049107049308982045422301482758451377471488000000⟩, + ⟨6, 6, 4, 5, 5, 6, -11077608894763869566465592290806737820163506176000000⟩, + ⟨6, 6, 5, 5, 6, 6, 6588659771306805934445016948386850881195212800000000⟩, + ⟨6, 6, 6, 5, 7, 6, -3411621527183372189637473112897737579802132480000000⟩, + ⟨6, 6, 7, 5, 8, 6, -278649277837697935497497599300759770567278592000000⟩, + ⟨6, 6, 2, 6, 2, 6, 9642359775867042227449756612281564212364312576000000⟩, + ⟨6, 6, 3, 6, 3, 6, -49962453196651345612293501173172811243488018432000000⟩, + ⟨6, 6, 4, 6, 4, 6, 21499694467146888190652993344483277375035932672000000⟩, + ⟨6, 6, 5, 6, 5, 6, -13355052478121814960635595795202700384057425920000000⟩, + ⟨6, 6, 6, 6, 6, 6, 2221493745037227381631528932462969443655352320000000⟩, + ⟨6, 6, 7, 6, 7, 6, 920763441944191038423843243056658378771136512000000⟩, + ⟨6, 6, 8, 6, 8, 6, -1821683688515270556298042952347577479203913728000000⟩, + ⟨6, 6, 2, 7, 1, 6, -142218669788834107479695761925203897106087018496000000⟩, + ⟨6, 6, 3, 7, 2, 6, -183910532833939400988712881576693322461933993984000000⟩, + ⟨6, 6, 4, 7, 3, 6, -78251321542026715640991094263772182602210869248000000⟩, + ⟨6, 6, 5, 7, 4, 6, -40386070896923382437829278795944065025431306240000000⟩, + ⟨6, 6, 6, 7, 5, 6, -2295780737717566313495157972473506441042329600000000⟩, + ⟨6, 6, 7, 7, 6, 6, -2305943318083817510672834155548015601876205568000000⟩, + ⟨6, 6, 8, 7, 7, 6, -1379374445423700405583970731764846546842025984000000⟩ +] + +def collectedFourData_14_6_40 : List CollectedFourTerm := [ + ⟨6, 7, 1, 0, 7, 7, -97423105313764842170515159984750656052525006848000000⟩, + ⟨6, 7, 2, 0, 8, 7, 59229173226366913081358202003405386452089962496000000⟩, + ⟨6, 7, 1, 1, 6, 7, -47591863379205753732916921543330122242979790848000000⟩, + ⟨6, 7, 2, 1, 7, 7, 27151384266104095484709888929146804379005747200000000⟩, + ⟨6, 7, 3, 1, 8, 7, 515105205080646417931682364185502416300408832000000⟩, + ⟨6, 7, 1, 2, 5, 7, -28317250072620036869220490931828537310257872896000000⟩, + ⟨6, 7, 2, 2, 6, 7, 57196625485243863533751874376261784587470897152000000⟩, + ⟨6, 7, 3, 2, 7, 7, -18507727294471686484013483177056522873136480256000000⟩, + ⟨6, 7, 4, 2, 8, 7, 2063416948695993536843564180691419849803431936000000⟩, + ⟨6, 7, 1, 3, 4, 7, -15440193528738425223935033069388499122772770816000000⟩, + ⟨6, 7, 2, 3, 5, 7, -14174634424009531137440049053533673451046305792000000⟩, + ⟨6, 7, 3, 3, 6, 7, 20322486085971055231764777822078502794789126144000000⟩, + ⟨6, 7, 4, 3, 7, 7, 12439597176948792718820906420031087330201698304000000⟩, + ⟨6, 7, 5, 3, 8, 7, -2571914874353024847907762978658082881368227840000000⟩, + ⟨6, 7, 1, 4, 3, 7, 48660221507312487392891146596429214786353364992000000⟩, + ⟨6, 7, 2, 4, 4, 7, -1790660418682442573229870979909769359219752960000000⟩, + ⟨6, 7, 3, 4, 5, 7, 38017645830826072255020673126389927108629495808000000⟩, + ⟨6, 7, 4, 4, 6, 7, -14750051671599040279629081064231092937090400256000000⟩, + ⟨6, 7, 5, 4, 7, 7, -1536802400157047610951500564841597771133747200000000⟩, + ⟨6, 7, 6, 4, 8, 7, 1166590594722418053455004170896266721618821120000000⟩, + ⟨6, 7, 1, 5, 2, 7, 9855524433049507518568510888407881707306352640000000⟩, + ⟨6, 7, 2, 5, 3, 7, -29859979430851262942871870957951687772826763264000000⟩, + ⟨6, 7, 3, 5, 4, 7, -38918632349534345821392405675182403162055114752000000⟩, + ⟨6, 7, 4, 5, 5, 7, -7652401540810579794932729020349830272475201536000000⟩, + ⟨6, 7, 5, 5, 6, 7, 3413579861737365761757023268586963647175065600000000⟩, + ⟨6, 7, 6, 5, 7, 7, -1414046916403817298874662744641442378487431168000000⟩, + ⟨6, 7, 7, 5, 8, 7, -96245326194846127366541429353989152603897856000000⟩, + ⟨6, 7, 1, 6, 1, 7, 217459464664637051934977883753554663944136687616000000⟩, + ⟨6, 7, 2, 6, 2, 7, 19982798501066170673143431723713537069241335808000000⟩, + ⟨6, 7, 3, 6, 3, 7, -51771021723666076984542758227881392004743036928000000⟩, + ⟨6, 7, 4, 6, 4, 7, 14851968202733568905188157840615669709869678592000000⟩, + ⟨6, 7, 5, 6, 5, 7, -6919243028801929052457935124233197736259747840000000⟩, + ⟨6, 7, 6, 6, 6, 7, 920763441944191038423843243056658378771136512000000⟩, + ⟨6, 7, 7, 6, 7, 7, 318031248836844499002876184255200236893372416000000⟩, + ⟨6, 7, 8, 6, 8, 7, -539321715051946970344949205681621045589573632000000⟩, + ⟨6, 7, 1, 7, 0, 7, -1362087102670746007984174376807448202727009550336000000⟩, + ⟨6, 7, 2, 7, 1, 7, -294733559786135697515524496470181226114258567168000000⟩, + ⟨6, 7, 3, 7, 2, 7, -190567828066437415186777055187554348284652814336000000⟩, + ⟨6, 7, 4, 7, 3, 7, -54055937452505052138941960494143635746380054528000000⟩, + ⟨6, 7, 5, 7, 4, 7, -20923994119230650665963120248317314553327124480000000⟩, + ⟨6, 7, 6, 7, 5, 7, -951553871683116796070198222488124941255311360000000⟩, + ⟨6, 7, 7, 7, 6, 7, -796471710093832864554085511727398489658753024000000⟩, + ⟨6, 7, 8, 7, 7, 7, -408373087103316972791531691288556982916612096000000⟩ +] + +def collectedFourData_14_6_41 : List CollectedFourTerm := [ + ⟨6, 8, 0, 0, 6, 8, -435759597315896243980434551456649206150348144640000000⟩, + ⟨6, 8, 1, 0, 7, 8, 1156479984434576087505300973824537726967634460672000000⟩, + ⟨6, 8, 2, 0, 8, 8, -351545729887670062853673564336244033071215542272000000⟩, + ⟨6, 8, 0, 1, 5, 8, -665440257489088486268767060896975718610934693888000000⟩, + ⟨6, 8, 1, 1, 6, 8, 564948502131351327680033945093873574948919836672000000⟩, + ⟨6, 8, 2, 1, 7, 8, -161152902857659013086786684567912139624703590400000000⟩, + ⟨6, 8, 3, 1, 8, 8, -2038218954443680641421186068562519018350575616000000⟩, + ⟨6, 8, 0, 2, 4, 8, -189617139116781101395894851200998054616283217920000000⟩, + ⟨6, 8, 1, 2, 5, 8, 336145443298517295862894194663399326781636870144000000⟩, + ⟨6, 8, 2, 2, 6, 8, -339481852574141223851035042299506262780269297664000000⟩, + ⟨6, 8, 3, 2, 7, 8, 73233196254269758686920539859827164134378569728000000⟩, + ⟨6, 8, 4, 2, 8, 8, -6123548394974083170822673927977038345379250176000000⟩, + ⟨6, 8, 0, 3, 3, 8, -33725434772923279201034202556220676053152038912000000⟩, + ⟨6, 8, 1, 3, 4, 8, 183285830545778711773940598407648291483522433024000000⟩, + ⟨6, 8, 2, 3, 5, 8, 84131382105145433928951792875981030246678790144000000⟩, + ⟨6, 8, 3, 3, 6, 8, -80414012386768776448597064234676759718602473472000000⟩, + ⟨6, 8, 4, 3, 7, 8, -36916666491068849384996143720696241657336561664000000⟩, + ⟨6, 8, 5, 3, 8, 8, 6106083488674415128594834197839545553494474752000000⟩, + ⟨6, 8, 0, 4, 2, 8, 249964914582876737862065363749293611829556150272000000⟩, + ⟨6, 8, 1, 4, 3, 8, -577630655788681529258724465834842423243034329088000000⟩, + ⟨6, 8, 2, 4, 4, 8, 10628191980002981472640802545617969290642718720000000⟩, + ⟨6, 8, 3, 4, 5, 8, -150431961415696959623011452382675464055846600704000000⟩, + ⟨6, 8, 4, 4, 6, 8, 43773341736136177497335368898977484960270647296000000⟩, + ⟨6, 8, 5, 4, 7, 8, 3648582561782765874091404135359966886399836160000000⟩, + ⟨6, 8, 6, 4, 8, 8, -2308040220508631975630684163966026724440801280000000⟩, + ⟨6, 8, 0, 5, 1, 8, 192670309072511556430581841676560946903270817792000000⟩, + ⟨6, 8, 1, 5, 2, 8, -116991926157760271843063613595227394533186600960000000⟩, + ⟨6, 8, 2, 5, 3, 8, 177229356609969208532116108290931739920378626048000000⟩, + ⟨6, 8, 3, 5, 4, 8, 153997073517101400946071291462591068987851800576000000⟩, + ⟨6, 8, 4, 5, 5, 8, 22709831477608824499937167487226916796708683776000000⟩, + ⟨6, 8, 5, 5, 6, 8, -8104313186597713980874122668522983380410695680000000⟩, + ⟨6, 8, 6, 5, 7, 8, 2797619980403481963535806192973841774193672192000000⟩, + ⟨6, 8, 7, 5, 8, 8, 163214132507361797762095882710390382119616512000000⟩, + ⟨6, 8, 0, 6, 0, 8, -4444212401940813201960812132469196187820921716736000000⟩, + ⟨6, 8, 1, 6, 1, 8, -2581395014052977549508798188632261335006496948224000000⟩, + ⟨6, 8, 2, 6, 2, 8, -118604854695629996624290793039973552305844781056000000⟩, + ⟨6, 8, 3, 6, 3, 8, 204852672283851440364845643923108165293927563264000000⟩, + ⟨6, 8, 4, 6, 4, 8, -44075796754277117087497194228665456333917519872000000⟩, + ⟨6, 8, 5, 6, 5, 8, 16427244942514292539308425727757915397661130752000000⟩, + ⟨6, 8, 6, 6, 6, 8, -1821683688515270556298042952347577479203913728000000⟩, + ⟨6, 8, 7, 6, 7, 8, -539321715051946970344949205681621045589573632000000⟩, + ⟨6, 8, 8, 6, 8, 8, 800265458871054239507365115204146476148064256000000⟩, + ⟨6, 8, 1, 7, 0, 8, 16168920773177597963420000513495821709152358498304000000⟩, + ⟨6, 8, 2, 7, 1, 8, 1749346120389258756543807553780693574960415768576000000⟩, + ⟨6, 8, 3, 7, 2, 8, 754057531240370844768054951978424754009976864768000000⟩, + ⟨6, 8, 4, 7, 3, 8, 160420388732047570892780766232878712894204674048000000⟩, + ⟨6, 8, 5, 7, 4, 8, 49676471131531629694898204512209698148417798144000000⟩, + ⟨6, 8, 6, 7, 5, 8, 1882600989379585589030302491511243342180515840000000⟩, + ⟨6, 8, 7, 7, 6, 8, 1350667553107436574722600852379008675503669248000000⟩, + ⟨6, 8, 8, 7, 7, 8, 605959053419251294923327994225690292275642368000000⟩ +] + +def collectedFourData_14_6_42 : List CollectedFourTerm := [ + ⟨7, 0, 7, 5, 8, 1, 412206404187635535407401513949520144220161048576000000⟩, + ⟨7, 0, 7, 6, 7, 1, -1362087102670746007984174376807448202727009550336000000⟩, + ⟨7, 0, 8, 6, 8, 1, 16168920773177597963420000513495821709152358498304000000⟩, + ⟨7, 0, 7, 7, 6, 1, 3411186315585852970330417576652976341826775547904000000⟩, + ⟨7, 0, 8, 7, 7, 1, 12243067369604237369855418371536232497797830541312000000⟩ +] + +def collectedFourData_14_6_43 : List CollectedFourTerm := [ + ⟨7, 1, 6, 4, 8, 2, -180188477313202561329369527792333562997333032960000000⟩, + ⟨7, 1, 6, 5, 7, 2, 218409921928832216757068544584285239508094418944000000⟩, + ⟨7, 1, 7, 5, 8, 2, 89194781034669434018236502650956097495171596288000000⟩, + ⟨7, 1, 6, 6, 6, 2, -142218669788834107479695761925203897106087018496000000⟩, + ⟨7, 1, 7, 6, 7, 2, -294733559786135697515524496470181226114258567168000000⟩, + ⟨7, 1, 8, 6, 8, 2, 1749346120389258756543807553780693574960415768576000000⟩, + ⟨7, 1, 6, 7, 5, 2, 146974477589424431741407372848260110391055482880000000⟩, + ⟨7, 1, 7, 7, 6, 2, 738125398819962018041696304322808785376171261952000000⟩, + ⟨7, 1, 8, 7, 7, 2, 1324600615287228693718697327843098138435626467328000000⟩ +] + +def collectedFourData_14_6_44 : List CollectedFourTerm := [ + ⟨7, 2, 5, 3, 8, 3, 102741315173646639166611776733334855061210136576000000⟩, + ⟨7, 2, 5, 4, 7, 3, 61391261945973414439639978430996234861889454080000000⟩, + ⟨7, 2, 6, 4, 8, 3, -233011312244808127027130865296970575830151331840000000⟩, + ⟨7, 2, 5, 5, 6, 3, -136363644046887711578518321217710260483879075840000000⟩, + ⟨7, 2, 6, 5, 7, 3, 282437496974144145178685411931758539441780555776000000⟩, + ⟨7, 2, 7, 5, 8, 3, 57671259794684531983157354686555970950530072576000000⟩, + ⟨7, 2, 5, 6, 5, 3, 276405776829617672481562829910815308435031064576000000⟩, + ⟨7, 2, 6, 6, 6, 3, -183910532833939400988712881576693322461933993984000000⟩, + ⟨7, 2, 7, 6, 7, 3, -190567828066437415186777055187554348284652814336000000⟩, + ⟨7, 2, 8, 6, 8, 3, 754057531240370844768054951978424754009976864768000000⟩, + ⟨7, 2, 5, 7, 4, 3, 835859186450012354609605246538565217491691241472000000⟩, + ⟨7, 2, 6, 7, 5, 3, 190060521073606103771717579285375933478359531520000000⟩, + ⟨7, 2, 7, 7, 6, 3, 477254623449941688193305433124200096168258043904000000⟩, + ⟨7, 2, 8, 7, 7, 3, 570970523329430437448463021841832364921380143104000000⟩ +] + +def collectedFourData_14_6_45 : List CollectedFourTerm := [ + ⟨7, 3, 4, 2, 8, 4, -17536002818133660701950615297611854880444933734400000⟩, + ⟨7, 3, 4, 3, 7, 4, -105718241429236504598283950092080947233073764761600000⟩, + ⟨7, 3, 5, 3, 8, 4, 87429942868612814779320424036613308294725894144000000⟩, + ⟨7, 3, 4, 4, 6, 4, 125353699282270564470527361833586724738099996262400000⟩, + ⟨7, 3, 5, 4, 7, 4, 52242221305974266023025326908763742907421163520000000⟩, + ⟨7, 3, 6, 4, 8, 4, -99143006310909960934261014618996231950020116480000000⟩, + ⟨7, 3, 4, 5, 5, 4, 65034134312965504194194809072694617531581097574400000⟩, + ⟨7, 3, 5, 5, 6, 4, -116041590359486973896347646921784488715312168960000000⟩, + ⟨7, 3, 6, 5, 7, 4, 120173146424435493010715707417184476307990249472000000⟩, + ⟨7, 3, 7, 5, 8, 4, 16358868356214856408504350968129136953338626048000000⟩, + ⟨7, 3, 4, 6, 4, 4, -126219839583346870691914762255795351011193572556800000⟩, + ⟨7, 3, 5, 6, 5, 4, 235213470218129758514213516882624065140261126144000000⟩, + ⟨7, 3, 6, 6, 6, 4, -78251321542026715640991094263772182602210869248000000⟩, + ⟨7, 3, 7, 6, 7, 4, -54055937452505052138941960494143635746380054528000000⟩, + ⟨7, 3, 8, 6, 8, 4, 160420388732047570892780766232878712894204674048000000⟩, + ⟨7, 3, 4, 7, 3, 4, 459395795940825521020342073858882307753877123891200000⟩, + ⟨7, 3, 5, 7, 4, 4, 711292441546190301585974931810989447446284730368000000⟩, + ⟨7, 3, 6, 7, 5, 4, 80868054253341179727477465309618875603028541440000000⟩, + ⟨7, 3, 7, 7, 6, 4, 135376712511698564159829038922195405174831316992000000⟩, + ⟨7, 3, 8, 7, 7, 4, 121469927044399531726983322977794694655921618944000000⟩ +] + +def collectedFourData_14_6_46 : List CollectedFourTerm := [ + ⟨7, 4, 3, 1, 8, 5, -2259328985503113923315571064400694080924811264000000⟩, + ⟨7, 4, 3, 2, 7, 5, 81177678500919667155822697400832610888750989312000000⟩, + ⟨7, 4, 4, 2, 8, 5, -27151372236496986921670950240625646195510870016000000⟩, + ⟨7, 4, 3, 3, 6, 5, -89137483796789655601998029110816590354330943488000000⟩, + ⟨7, 4, 4, 3, 7, 5, -163685838500483936733738155538488206931131367424000000⟩, + ⟨7, 4, 5, 3, 8, 5, 67684835251811890648010846551337262792132526080000000⟩, + ⟨7, 4, 3, 4, 5, 5, -166751118682112866789664930471625978526109270016000000⟩, + ⟨7, 4, 4, 4, 6, 5, 194087842351126346807065983964613552674424487936000000⟩, + ⟨7, 4, 5, 4, 7, 5, 40443880280207580807211247226112416621684326400000000⟩, + ⟨7, 4, 6, 4, 8, 5, -51168419943631129305016840082887043818350182400000000⟩, + ⟨7, 4, 3, 5, 4, 5, 170702981208810578052664333547231540645518639104000000⟩, + ⟨7, 4, 4, 5, 5, 5, 100693755990032188731829311891819704898463727616000000⟩, + ⟨7, 4, 5, 5, 6, 5, -89834851403749251394395060017984767343670067200000000⟩, + ⟨7, 4, 6, 5, 7, 5, 62022226791364999652238855167139402822828687360000000⟩, + ⟨7, 4, 7, 5, 8, 5, 6332197375791612543615391946107261772554567680000000⟩, + ⟨7, 4, 3, 6, 3, 5, 227075496103902356577873697016360484767589728256000000⟩, + ⟨7, 4, 4, 6, 4, 5, -195428906102509641922159673841796723588938596352000000⟩, + ⟨7, 4, 5, 6, 5, 5, 182093050256772655983732453413884836582606766080000000⟩, + ⟨7, 4, 6, 6, 6, 5, -40386070896923382437829278795944065025431306240000000⟩, + ⟨7, 4, 7, 6, 7, 5, -20923994119230650665963120248317314553327124480000000⟩, + ⟨7, 4, 8, 6, 8, 5, 49676471131531629694898204512209698148417798144000000⟩, + ⟨7, 4, 3, 7, 2, 5, 835859186450012354609605246538565217491691241472000000⟩, + ⟨7, 4, 4, 7, 3, 5, 711292441546190301585974931810989447446284730368000000⟩, + ⟨7, 4, 5, 7, 4, 5, 550654731574763867350227657642679720451254517760000000⟩, + ⟨7, 4, 6, 7, 5, 5, 41736585504407510352518431718484242351731507200000000⟩, + ⟨7, 4, 7, 7, 6, 5, 52401672600061258988429740984000878786348318720000000⟩, + ⟨7, 4, 8, 7, 7, 5, 37614902768060056759074956370713327488657784832000000⟩ +] + +def collectedFourData_14_6_47 : List CollectedFourTerm := [ + ⟨7, 5, 2, 0, 8, 6, -29535750185066960285713108391386040635867791360000000⟩, + ⟨7, 5, 2, 1, 7, 6, -13539552541067920679313518601122753336573952000000000⟩, + ⟨7, 5, 3, 1, 8, 6, -513733953305188724909621460933360218265354240000000⟩, + ⟨7, 5, 2, 2, 6, 6, -28522181717859184522196693048128748759883448320000000⟩, + ⟨7, 5, 3, 2, 7, 6, 18458458225431202353237928282449108839348305920000000⟩, + ⟨7, 5, 4, 2, 8, 6, -3086885948486654331910116725192364989381345280000000⟩, + ⟨7, 5, 2, 3, 5, 6, 7068450199568593729304068378911079857358110720000000⟩, + ⟨7, 5, 3, 3, 6, 6, -20268385982046189839332202628619867003111342080000000⟩, + ⟨7, 5, 4, 3, 7, 6, -18609722942629060310574098975047434157078609920000000⟩, + ⟨7, 5, 5, 3, 8, 6, 5130136457304614614840064153486199742896537600000000⟩, + ⟨7, 5, 2, 4, 4, 6, 892946767809140783492699664014103568554393600000000⟩, + ⟨7, 5, 3, 4, 5, 6, -37916439778489481894001170615249237325706690560000000⟩, + ⟨7, 5, 4, 4, 6, 6, 22066178759113907826726212108054804208424058880000000⟩, + ⟨7, 5, 5, 4, 7, 6, 3065422615397470030364022788978074932215808000000000⟩, + ⟨7, 5, 6, 4, 8, 6, -2908712590186155078448376114833915794948096000000000⟩, + ⟨7, 5, 2, 5, 3, 6, 14890244873589608449648459609664384969987850240000000⟩, + ⟨7, 5, 3, 5, 4, 6, 38815027798112022603687869723480841614146928640000000⟩, + ⟨7, 5, 4, 5, 5, 6, 11448045342185507768936140795213656335088353280000000⟩, + ⟨7, 5, 5, 5, 6, 6, -6808985271343768735683231003354609991286784000000000⟩, + ⟨7, 5, 6, 5, 7, 6, 3525706522463748643028651127481124923008614400000000⟩, + ⟨7, 5, 7, 5, 8, 6, 287967340024167836552433092498963847457013760000000⟩, + ⟨7, 5, 2, 6, 2, 6, -9964801336502193083812305918577229136427745280000000⟩, + ⟨7, 5, 3, 6, 3, 6, 51633203070785795329688849985374206292876328960000000⟩, + ⟨7, 5, 4, 6, 4, 6, -22218646590725205810420936573906806903050076160000000⟩, + ⟨7, 5, 5, 6, 5, 6, 13801646886908301118607615154070559829629337600000000⟩, + ⟨7, 5, 6, 6, 6, 6, -2295780737717566313495157972473506441042329600000000⟩, + ⟨7, 5, 7, 6, 7, 6, -951553871683116796070198222488124941255311360000000⟩, + ⟨7, 5, 8, 6, 8, 6, 1882600989379585589030302491511243342180515840000000⟩, + ⟨7, 5, 2, 7, 1, 6, 146974477589424431741407372848260110391055482880000000⟩, + ⟨7, 5, 3, 7, 2, 6, 190060521073606103771717579285375933478359531520000000⟩, + ⟨7, 5, 4, 7, 3, 6, 80868054253341179727477465309618875603028541440000000⟩, + ⟨7, 5, 5, 7, 4, 6, 41736585504407510352518431718484242351731507200000000⟩, + ⟨7, 5, 6, 7, 5, 6, 2372551895520502181177343784245162764402688000000000⟩, + ⟨7, 5, 7, 7, 6, 6, 2383054313680565580853406482910657352082391040000000⟩, + ⟨7, 5, 8, 7, 7, 6, 1425500877046365109150913086544479474176491520000000⟩ +] + +def collectedFourData_14_6_48 : List CollectedFourTerm := [ + ⟨7, 6, 1, 0, 7, 7, 243984663694834904313194647914840264709056233472000000⟩, + ⟨7, 6, 2, 0, 8, 7, -148332470659980881007706386023561452296962310144000000⟩, + ⟨7, 6, 1, 1, 6, 7, 119188202262584192916625089257682585504524009472000000⟩, + ⟨7, 6, 2, 1, 7, 7, -67997435902699208819672124888264795216465100800000000⟩, + ⟨7, 6, 3, 1, 8, 7, -1290020163330839301830660768351432569465602048000000⟩, + ⟨7, 6, 1, 2, 5, 7, 70917209151560217985183072863997716784421535744000000⟩, + ⟨7, 6, 2, 2, 6, 7, -143242194842304427233392542911189390034131222528000000⟩, + ⟨7, 6, 3, 2, 7, 7, 46350417646350520610156983466629725367025270784000000⟩, + ⟨7, 6, 4, 2, 8, 7, -5167584103056540644480189858466285594611810304000000⟩, + ⟨7, 6, 1, 3, 4, 7, 38668141539521939475809327251450972822384410624000000⟩, + ⟨7, 6, 2, 3, 5, 7, 35498698196910803448781736296031700335342911488000000⟩, + ⟨7, 6, 3, 3, 6, 7, -50895266755863142244837895917646707322116898816000000⟩, + ⟨7, 6, 4, 3, 7, 7, -31153502282053062744316249997210780901945901056000000⟩, + ⟨7, 6, 5, 3, 8, 7, 6441057115247856932841037610415232024062197760000000⟩, + ⟨7, 6, 1, 4, 3, 7, -121863779044419085482483198393170923210080780288000000⟩, + ⟨7, 6, 2, 4, 4, 7, 4484497580289709924820451705427529559378493440000000⟩, + ⟨7, 6, 3, 4, 5, 7, -95210704920867280419674706750877252043944230912000000⟩, + ⟨7, 6, 4, 4, 6, 7, 36939762749156172211855303372929918123884150784000000⟩, + ⟨7, 6, 5, 4, 7, 7, 3848740148039143404324262102015722379857100800000000⟩, + ⟨7, 6, 6, 4, 8, 7, -2921588395342304988351299113979227808653639680000000⟩, + ⟨7, 6, 1, 5, 2, 7, -24681997218108266709784874058145557300337704960000000⟩, + ⟨7, 6, 2, 5, 3, 7, 74780792666250470404924816893643644583853162496000000⟩, + ⟨7, 6, 3, 5, 4, 7, 97467119269934010645640596578674743056875388928000000⟩, + ⟨7, 6, 4, 5, 5, 7, 19164536075701427432567778921007469473724104704000000⟩, + ⟨7, 6, 5, 5, 6, 7, -8548907693704748408913709155740910205953638400000000⟩, + ⟨7, 6, 6, 5, 7, 7, 3541313533749145107212600001223933736572157952000000⟩, + ⟨7, 6, 7, 5, 8, 7, 241035054961765905140560621064829045974237184000000⟩, + ⟨7, 6, 1, 6, 1, 7, -544601551988960785537340532760452906473251405824000000⟩, + ⟨7, 6, 2, 6, 2, 7, -50044559309232213689261030753313674620317990912000000⟩, + ⟨7, 6, 3, 6, 3, 7, 129654410867993419840791158120002890837987950592000000⟩, + ⟨7, 6, 4, 6, 4, 7, -37195000667242620518397700321868907168229490688000000⟩, + ⟨7, 6, 5, 6, 5, 7, 17328427152552962778871976254891907283167477760000000⟩, + ⟨7, 6, 6, 6, 6, 7, -2305943318083817510672834155548015601876205568000000⟩, + ⟨7, 6, 7, 6, 7, 7, -796471710093832864554085511727398489658753024000000⟩, + ⟨7, 6, 8, 6, 8, 7, 1350667553107436574722600852379008675503669248000000⟩, + ⟨7, 6, 1, 7, 0, 7, 3411186315585852970330417576652976341826775547904000000⟩, + ⟨7, 6, 2, 7, 1, 7, 738125398819962018041696304322808785376171261952000000⟩, + ⟨7, 6, 3, 7, 2, 7, 477254623449941688193305433124200096168258043904000000⟩, + ⟨7, 6, 4, 7, 3, 7, 135376712511698564159829038922195405174831316992000000⟩, + ⟨7, 6, 5, 7, 4, 7, 52401672600061258988429740984000878786348318720000000⟩, + ⟨7, 6, 6, 7, 5, 7, 2383054313680565580853406482910657352082391040000000⟩, + ⟨7, 6, 7, 7, 6, 7, 1994669351832265456410504674700996892359131136000000⟩, + ⟨7, 6, 8, 7, 7, 7, 1022722176613340853392719904946211111298924544000000⟩ +] + +def collectedFourData_14_6_49 : List CollectedFourTerm := [ + ⟨7, 7, 0, 0, 6, 8, -329956104166231478046961795683696611472357457920000000⟩, + ⟨7, 7, 1, 0, 7, 8, 875683823283945976247251784865685567554208137216000000⟩, + ⟨7, 7, 2, 0, 8, 8, -266189569167243499103603971249387764192185942016000000⟩, + ⟨7, 7, 0, 1, 5, 8, -503869739803580318474344492205308821418713022464000000⟩, + ⟨7, 7, 1, 1, 6, 8, 427777627770009294814995584972341434896105865216000000⟩, + ⟨7, 7, 2, 1, 7, 8, -122024584953536230877537541113937448530031411200000000⟩, + ⟨7, 7, 3, 1, 8, 8, -1543334420603645258487904241038170323259752448000000⟩, + ⟨7, 7, 0, 2, 4, 8, -143577635217896979216525915433052432743803125760000000⟩, + ⟨7, 7, 1, 2, 5, 8, 254528509726901160111762329780024834802510200832000000⟩, + ⟨7, 7, 2, 2, 6, 8, -257054830692107336372757939747093369353920315392000000⟩, + ⟨7, 7, 3, 2, 7, 8, 55451997570538481205410278598066480696455593984000000⟩, + ⟨7, 7, 4, 2, 8, 8, -4636735907882484816452525039426407785591472128000000⟩, + ⟨7, 7, 0, 3, 3, 8, -25536816945695711688010690661402348727551655936000000⟩, + ⟨7, 7, 1, 3, 4, 8, 138783583811502375351151935547986486047614697472000000⟩, + ⟨7, 7, 2, 3, 5, 8, 63704077313552571007329794767697757629507960832000000⟩, + ⟨7, 7, 3, 3, 6, 8, -60889294030347213391971103224213772014364655616000000⟩, + ⟨7, 7, 4, 3, 7, 8, -27953209818501889208768232359964319752904507392000000⟩, + ⟨7, 7, 5, 3, 8, 8, 4623511523433439148002119813839920900085907456000000⟩, + ⟨7, 7, 0, 4, 2, 8, 189272823598237944684751963445560783487700566016000000⟩, + ⟨7, 7, 1, 4, 3, 8, -437380523584548701924295855793184414629116248064000000⟩, + ⟨7, 7, 2, 4, 4, 8, 8047641042568593523481929726780415343234908160000000⟩, + ⟨7, 7, 3, 4, 5, 8, -113906714244610239391845143226026716716714688512000000⟩, + ⟨7, 7, 4, 4, 6, 8, 33145067589004113381539338135487960156353855488000000⟩, + ⟨7, 7, 5, 4, 7, 8, 2762697816020708617570578180114717447007764480000000⟩, + ⟨7, 7, 6, 4, 8, 8, -1747642425109743169656188342699365104447651840000000⟩, + ⟨7, 7, 0, 5, 1, 8, 145889488060967927673687612976078529821541400576000000⟩, + ⟨7, 7, 1, 5, 2, 8, -88586001115505034870061727234902123707503738880000000⟩, + ⟨7, 7, 2, 5, 3, 8, 134197636520488741368865054232279392903646674944000000⟩, + ⟨7, 7, 3, 5, 4, 8, 116606208431636798825128934440062249101665763328000000⟩, + ⟨7, 7, 4, 5, 5, 8, 17195829000161669480014794999839080291057532928000000⟩, + ⟨7, 7, 5, 5, 6, 8, -6136566176543165092682548147577067832124375040000000⟩, + ⟨7, 7, 6, 5, 7, 8, 2118351025100573123619245253197827381213003776000000⟩, + ⟨7, 7, 7, 5, 8, 8, 123585343016461507611809832025677614322548736000000⟩, + ⟨7, 7, 0, 6, 0, 8, -3365146790257848360261690097950054933976011767808000000⟩, + ⟨7, 7, 1, 6, 1, 8, -1954626008004123925535714105274713893157650563072000000⟩, + ⟨7, 7, 2, 6, 2, 8, -89807306670063422498097709357798598888304672768000000⟩, + ⟨7, 7, 3, 6, 3, 8, 155113943768911310168106071728154764090584072192000000⟩, + ⟨7, 7, 4, 6, 4, 8, -33374085790980661714380525098207651391200034816000000⟩, + ⟨7, 7, 5, 6, 5, 8, 12438669800511854401053037242083955483875475456000000⟩, + ⟨7, 7, 6, 6, 6, 8, -1379374445423700405583970731764846546842025984000000⟩, + ⟨7, 7, 7, 6, 7, 8, -408373087103316972791531691288556982916612096000000⟩, + ⟨7, 7, 8, 6, 8, 8, 605959053419251294923327994225690292275642368000000⟩, + ⟨7, 7, 1, 7, 0, 8, 12243067369604237369855418371536232497797830541312000000⟩, + ⟨7, 7, 2, 7, 1, 8, 1324600615287228693718697327843098138435626467328000000⟩, + ⟨7, 7, 3, 7, 2, 8, 570970523329430437448463021841832364921380143104000000⟩, + ⟨7, 7, 4, 7, 3, 8, 121469927044399531726983322977794694655921618944000000⟩, + ⟨7, 7, 5, 7, 4, 8, 37614902768060056759074956370713327488657784832000000⟩, + ⟨7, 7, 6, 7, 5, 8, 1425500877046365109150913086544479474176491520000000⟩, + ⟨7, 7, 7, 7, 6, 8, 1022722176613340853392719904946211111298924544000000⟩, + ⟨7, 7, 8, 7, 7, 8, 458830717170712375104842930272161926064635904000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1412.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1412.lean new file mode 100644 index 0000000000000000000000000000000000000000..5a6904378abe3fe03cd003957654cf7073885426 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1412.lean @@ -0,0 +1,653 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1410 +import OAI.Analysis.LaughlinFock.Sparse1411 + +namespace OAI + +/-! Sparse1412. -/ +namespace LaughlinFock +def collectedFourData_14_6 : List (List CollectedFourTerm) := [ + collectedFourData_14_6_0, + collectedFourData_14_6_1, + collectedFourData_14_6_2, + collectedFourData_14_6_3, + collectedFourData_14_6_4, + collectedFourData_14_6_5, + collectedFourData_14_6_6, + collectedFourData_14_6_7, + collectedFourData_14_6_8, + collectedFourData_14_6_9, + collectedFourData_14_6_10, + collectedFourData_14_6_11, + collectedFourData_14_6_12, + collectedFourData_14_6_13, + collectedFourData_14_6_14, + collectedFourData_14_6_15, + collectedFourData_14_6_16, + collectedFourData_14_6_17, + collectedFourData_14_6_18, + collectedFourData_14_6_19, + collectedFourData_14_6_20, + collectedFourData_14_6_21, + collectedFourData_14_6_22, + collectedFourData_14_6_23, + collectedFourData_14_6_24, + collectedFourData_14_6_25, + collectedFourData_14_6_26, + collectedFourData_14_6_27, + collectedFourData_14_6_28, + collectedFourData_14_6_29, + collectedFourData_14_6_30, + collectedFourData_14_6_31, + collectedFourData_14_6_32, + collectedFourData_14_6_33, + collectedFourData_14_6_34, + collectedFourData_14_6_35, + collectedFourData_14_6_36, + collectedFourData_14_6_37, + collectedFourData_14_6_38, + collectedFourData_14_6_39, + collectedFourData_14_6_40, + collectedFourData_14_6_41, + collectedFourData_14_6_42, + collectedFourData_14_6_43, + collectedFourData_14_6_44, + collectedFourData_14_6_45, + collectedFourData_14_6_46, + collectedFourData_14_6_47, + collectedFourData_14_6_48, + collectedFourData_14_6_49 +] + +theorem collectedFourChecked_14_6 : collectNumericRowParts 14 6 = collectedFourData_14_6 := by + decide +kernel + +def collectedFourData_14_7_0 : List CollectedFourTerm := [ + ⟨0, 7, 7, 6, 8, 0, 64682253423664316834564284789136541548430753792000000⟩, + ⟨0, 7, 7, 7, 7, 0, -22860819626933384194954670262325755755580358656000000⟩, + ⟨0, 7, 8, 7, 8, 0, -613411297185544067839541072561022856919305420800000000⟩ +] + +def collectedFourData_14_7_1 : List CollectedFourTerm := [ + ⟨0, 8, 6, 5, 8, 1, 7183783342680442947325989934199255971557015552000000⟩, + ⟨0, 8, 6, 6, 7, 1, 6784341606872780669096722551041432704209911808000000⟩, + ⟨0, 8, 7, 6, 8, 1, 7442768640399707599928351082701006527159861248000000⟩, + ⟨0, 8, 6, 7, 6, 1, -7342827568861699372892355469871245032758968320000000⟩, + ⟨0, 8, 7, 7, 7, 1, -2630517373887974936047075211833472619657560064000000⟩, + ⟨0, 8, 8, 7, 8, 1, -35291584048996431173832032136690940895664537600000000⟩ +] + +def collectedFourData_14_7_2 : List CollectedFourTerm := [ + ⟨1, 6, 7, 6, 8, 0, 8137774113910338201642624664739841663729401856000000⟩, + ⟨1, 6, 7, 7, 7, 0, -2876154993616373387977734518990496980803780608000000⟩, + ⟨1, 6, 8, 7, 8, 0, -77174221849086147838732575477849501974554214400000000⟩ +] + +def collectedFourData_14_7_3 : List CollectedFourTerm := [ + ⟨1, 7, 6, 5, 8, 1, 75334142759199133516311051401318831777541783552000000⟩, + ⟨1, 7, 6, 6, 7, 1, 71145319222367796957001216834741112699835383808000000⟩, + ⟨1, 7, 7, 6, 8, 1, 78050042510100718858904074259512328445386293248000000⟩, + ⟨1, 7, 6, 7, 6, 1, -77001991004145584802832498327998719070641848320000000⟩, + ⟨1, 7, 7, 7, 7, 1, -27585432622622653950713205322953356882491736064000000⟩, + ⟨1, 7, 8, 7, 8, 1, -370092067664357129863917194019715482142742937600000000⟩ +] + +def collectedFourData_14_7_4 : List CollectedFourTerm := [ + ⟨1, 8, 5, 4, 8, 2, -29409904343733063156558981423787413183142035456000000⟩, + ⟨1, 8, 5, 5, 7, 2, 1000479033414466928943575123727721657767297024000000⟩, + ⟨1, 8, 6, 5, 8, 2, -41425529171742392726282269266990499507420004352000000⟩, + ⟨1, 8, 5, 6, 6, 2, -9516340969324893367126083323598459289328418816000000⟩, + ⟨1, 8, 6, 6, 7, 2, -39122134916962763653253356703248003957688107008000000⟩, + ⟨1, 8, 7, 6, 8, 2, -21459488317221833513459868896150064123529396224000000⟩, + ⟨1, 8, 5, 7, 5, 2, 10762033369762710657962007090278566932309344256000000⟩, + ⟨1, 8, 6, 7, 6, 2, 42342663071386213022002791675738030585749176320000000⟩, + ⟨1, 8, 7, 7, 7, 2, 7584483621697863252811401233314511529109880832000000⟩, + ⟨1, 8, 8, 7, 8, 2, 67836703623507058922103115685353142374052659200000000⟩ +] + +def collectedFourData_14_7_5 : List CollectedFourTerm := [ + ⟨2, 5, 7, 6, 8, 0, -39357925574812367959884944682503583044286283776000000⟩, + ⟨2, 5, 7, 7, 7, 0, 13910375564109126163587617684547997839988359168000000⟩, + ⟨2, 5, 8, 7, 8, 0, 373249151096289242839151249324390504928274022400000000⟩ +] + +def collectedFourData_14_7_6 : List CollectedFourTerm := [ + ⟨2, 6, 6, 5, 8, 1, 89332287615973051355963007528568547664029810688000000⟩, + ⟨2, 6, 6, 6, 7, 1, 84365121663599075203032381756999349427767345152000000⟩, + ⟨2, 6, 7, 6, 8, 1, 92552839795868450747365230960285950136142528512000000⟩, + ⟨2, 6, 6, 7, 6, 1, -91310045557595856896276581086930299407910830080000000⟩, + ⟨2, 6, 7, 7, 7, 1, -32711194563294583646035080129138780705040367616000000⟩, + ⟨2, 6, 8, 7, 8, 1, -438860386832308856449567640606342316026127974400000000⟩ +] + +def collectedFourData_14_7_7 : List CollectedFourTerm := [ + ⟨2, 7, 5, 4, 8, 2, -35749008409470121013465678439759657543760084992000000⟩, + ⟨2, 7, 5, 5, 7, 2, 1216125457635284620668865891953551271020986368000000⟩, + ⟨2, 7, 6, 5, 8, 2, -50354519124538982244141354077997550154299736064000000⟩, + ⟨2, 7, 5, 6, 6, 2, -11567523286156950516052309780082143407491776512000000⟩, + ⟨2, 7, 6, 6, 7, 2, -47554643966087854435471275104052861276002451456000000⟩, + ⟨2, 7, 7, 6, 8, 2, -26084934495163081998724866548233779444625440768000000⟩, + ⟨2, 7, 5, 7, 5, 2, 13081716177721179728027958960275383187083886592000000⟩, + ⟨2, 7, 6, 7, 6, 2, 51469334973913328757277096054155612858341130240000000⟩, + ⟨2, 7, 7, 7, 7, 2, 9219267278281436477528885619966201513507815424000000⟩, + ⟨2, 7, 8, 7, 8, 2, 82458441889636677001490523163817762770806374400000000⟩ +] + +def collectedFourData_14_7_8 : List CollectedFourTerm := [ + ⟨2, 8, 4, 3, 8, 3, 1518796326700130817079893224990047764964442112000000⟩, + ⟨2, 8, 4, 4, 7, 3, 3461011218248421548444030752518038773586460672000000⟩, + ⟨2, 8, 5, 4, 8, 3, -15038065567032894745560663893451581050658488320000000⟩, + ⟨2, 8, 4, 5, 6, 3, -3174712189202105360438446267938993816150736896000000⟩, + ⟨2, 8, 5, 5, 7, 3, 511571514381155559201257356449474434857697280000000⟩, + ⟨2, 8, 6, 5, 8, 3, -10590986909592619600569561437577239700669726720000000⟩, + ⟨2, 8, 4, 6, 5, 3, 5151236092986286223783488853489069772156960768000000⟩, + ⟨2, 8, 5, 6, 6, 3, -4865958004567388920883723211449273809392107520000000⟩, + ⟨2, 8, 6, 6, 7, 3, -10002093565614708133942336479501825308759162880000000⟩, + ⟨2, 8, 7, 6, 8, 3, -3657602198425422828634190886744203074480373760000000⟩, + ⟨2, 8, 4, 7, 4, 3, 21303520813881672179046156941666358622144167936000000⟩, + ⟨2, 8, 5, 7, 5, 3, 5502913629284687715250390881972982676528824320000000⟩, + ⟨2, 8, 6, 7, 6, 3, 10825464376016804815341693973038848263009075200000000⟩, + ⟨2, 8, 7, 7, 7, 3, 1292716003222722594637628358811829071962439680000000⟩, + ⟨2, 8, 8, 7, 8, 3, 8671677277650314093645094503802335611846656000000000⟩ +] + +def collectedFourData_14_7_9 : List CollectedFourTerm := [ + ⟨3, 4, 7, 6, 8, 0, 24994551947080396542546752412150754799813394432000000⟩, + ⟨3, 4, 7, 7, 7, 0, -8833890495057699688462033653207737249537458176000000⟩, + ⟨3, 4, 8, 7, 8, 0, -237034730871339545452367968891449662816177356800000000⟩ +] + +def collectedFourData_14_7_10 : List CollectedFourTerm := [ + ⟨3, 5, 6, 5, 8, 1, 73802250894332099337805438805594483604647313408000000⟩, + ⟨3, 5, 6, 6, 7, 1, 69698605531226671627399759959402167599242412032000000⟩, + ⟨3, 5, 7, 6, 8, 1, 76462923830647113914390985735966761374074273792000000⟩, + ⟨3, 5, 6, 7, 6, 1, -75436184063528196513283650945474963480804065280000000⟩, + ⟨3, 5, 7, 7, 7, 1, -27024493076811293655312950138425034243787718656000000⟩, + ⟨3, 5, 8, 7, 8, 1, -362566382670249742070946745129136527801476710400000000⟩ +] + +def collectedFourData_14_7_11 : List CollectedFourTerm := [ + ⟨3, 6, 5, 4, 8, 2, -14201396800728609792478291156448741238169927680000000⟩, + ⟨3, 6, 5, 5, 7, 2, 483109349090959499110001493627225288443166720000000⟩, + ⟨3, 6, 6, 5, 8, 2, -20003478099493806976600322740717625610401218560000000⟩, + ⟨3, 6, 5, 6, 6, 2, -4595232021732541503631706959190926874357268480000000⟩, + ⟨3, 6, 6, 6, 7, 2, -18891219609349668226819423810183199723869962240000000⟩, + ⟨3, 6, 7, 6, 8, 2, -10362315537364442387319549152091878581830942720000000⟩, + ⟨3, 6, 5, 7, 5, 2, 5196749519494795630892663534333959325016391680000000⟩, + ⟨3, 6, 6, 7, 6, 2, 20446341914214676784013206297724201257769369600000000⟩, + ⟨3, 6, 7, 7, 7, 2, 3662380543012901106653302555691644355566632960000000⟩, + ⟨3, 6, 8, 7, 8, 2, 32756854104360022298581104638618611614744576000000000⟩ +] + +def collectedFourData_14_7_12 : List CollectedFourTerm := [ + ⟨3, 7, 4, 3, 8, 3, 3792266488706904006637703656676034592317741465600000⟩, + ⟨3, 7, 4, 4, 7, 3, 8641762314844960774389299843239564493794679193600000⟩, + ⟨3, 7, 5, 4, 8, 3, -37548386905004437266991595889357651859803734016000000⟩, + ⟨3, 7, 4, 5, 6, 3, -7926905296484504204523454567989328354019691724800000⟩, + ⟨3, 7, 5, 5, 7, 3, 1277337505009473461158813707606127651810443264000000⟩, + ⟨3, 7, 6, 5, 8, 3, -26444523227709574054701701912522924434900647936000000⟩, + ⟨3, 7, 4, 6, 5, 3, 12862066932498126870312669067126409420129855078400000⟩, + ⟨3, 7, 5, 6, 6, 3, -12149759089995062572259090713714599994878590976000000⟩, + ⟨3, 7, 6, 6, 7, 3, -24974121663964608896548362089199448065042284544000000⟩, + ⟨3, 7, 7, 6, 8, 3, -9132628254537532063451365033499868163618111488000000⟩, + ⟨3, 7, 4, 7, 4, 3, 53192535861264495332814435163238266417621814476800000⟩, + ⟨3, 7, 5, 7, 5, 3, 13740166854317827787716356173337004797975330816000000⟩, + ⟨3, 7, 6, 7, 6, 3, 27029987534309058309588123659870299873880309760000000⟩, + ⟨3, 7, 7, 7, 7, 3, 3227768919541616356862158863070664704219152384000000⟩, + ⟨3, 7, 8, 7, 8, 3, 21652219302086338428686575388081615276920012800000000⟩ +] + +def collectedFourData_14_7_13 : List CollectedFourTerm := [ + ⟨3, 8, 3, 2, 8, 4, 1518796326700130817079893224990047764964442112000000⟩, + ⟨3, 8, 3, 3, 7, 4, 3792266488706904006637703656676034592317741465600000⟩, + ⟨3, 8, 4, 3, 8, 4, 2203005503042162488798157864397539938279410892800000⟩, + ⟨3, 8, 3, 4, 6, 4, 8710883720460767351442242844597619712250504806400000⟩, + ⟨3, 8, 4, 4, 7, 4, 5020177245528279439759506358943310336226020556800000⟩, + ⟨3, 8, 5, 4, 8, 4, -10906314631159645967374272151471933175107682304000000⟩, + ⟨3, 8, 3, 5, 5, 4, 2862849150713485739881420692754374296641260748800000⟩, + ⟨3, 8, 4, 5, 6, 4, -4604902119155662990515371090050284688310167142400000⟩, + ⟨3, 8, 5, 5, 7, 4, 371015797697478522041472319415904715476566016000000⟩, + ⟨3, 8, 6, 5, 8, 4, -5120722253165919336426943730031625568419577856000000⟩, + ⟨3, 8, 3, 6, 4, 4, -13506949800785534071667944830311483136825045811200000⟩, + ⟨3, 8, 4, 6, 5, 4, 7471838890323291788910968975429470434507305779200000⟩, + ⟨3, 8, 5, 6, 6, 4, -3529022316285371127280381785336065881270124544000000⟩, + ⟨3, 8, 6, 6, 7, 4, -4835993428837216948986702559900286424893620224000000⟩, + ⟨3, 8, 7, 6, 8, 4, -1326332838284053773638003939309770497784283136000000⟩, + ⟨3, 8, 3, 7, 3, 4, 24072188722347339529470765072474566563829750169600000⟩, + ⟨3, 8, 4, 7, 4, 4, 30900636749051553870795216840885919621252015718400000⟩, + ⟨3, 8, 5, 7, 5, 4, 3990972586304333649342669802434154279420821504000000⟩, + ⟨3, 8, 6, 7, 6, 4, 5234091667218993110785291148372957687929896960000000⟩, + ⟨3, 8, 7, 7, 7, 4, 468769317337933887317529199077637591450779648000000⟩, + ⟨3, 8, 8, 7, 8, 4, 2515643793368370530466239130013927935867617280000000⟩ +] + +def collectedFourData_14_7_14 : List CollectedFourTerm := [ + ⟨4, 3, 7, 6, 8, 0, 95922782202230917772882835365833916217299042304000000⟩, + ⟨4, 3, 7, 7, 7, 0, -33902242206616497901268897259896417627796406272000000⟩, + ⟨4, 3, 8, 7, 8, 0, -909679473825968213505920120113324255922985369600000000⟩ +] + +def collectedFourData_14_7_15 : List CollectedFourTerm := [ + ⟨4, 4, 6, 5, 8, 1, -83124538848261050529464293852296211857257005056000000⟩, + ⟨4, 4, 6, 6, 7, 1, -78502543932505161863584624756161981089813889024000000⟩, + ⟨4, 4, 7, 6, 8, 1, -86121293123058101939645395912107205339952185344000000⟩, + ⟨4, 4, 6, 7, 6, 1, 84964861325589909894915617886715623418846248960000000⟩, + ⟨4, 4, 7, 7, 7, 1, 30438076039635834155613583437427102473353428992000000⟩, + ⟨4, 4, 8, 7, 8, 1, 408363742245444466923292971757868437757283532800000000⟩ +] + +def collectedFourData_14_7_16 : List CollectedFourTerm := [ + ⟨4, 5, 5, 4, 8, 2, -6595401782902784778751151220900200618674618368000000⟩, + ⟨4, 5, 5, 5, 7, 2, 224365272447569621655404125961391698526339072000000⟩, + ⟨4, 5, 6, 5, 8, 2, -9289999918521358298289477252309565845647917056000000⟩, + ⟨4, 5, 5, 6, 6, 2, -2134114122311675428765502633209100078256488448000000⟩, + ⟨4, 5, 6, 6, 7, 2, -8773445685731450920323513973800894522955137024000000⟩, + ⟨4, 5, 7, 6, 8, 2, -4812458614396878705069827291870762132331036672000000⟩, + ⟨4, 5, 5, 7, 5, 2, 2413470416122496276553165587358437405274144768000000⟩, + ⟨4, 5, 6, 7, 6, 2, 9495674390841102003837908220578910004272168960000000⟩, + ⟨4, 5, 7, 7, 7, 2, 1700879955823534148725026574789199688678506496000000⟩, + ⟨4, 5, 8, 7, 8, 2, 15212912996776360543720490483362424115796377600000000⟩ +] + +def collectedFourData_14_7_17 : List CollectedFourTerm := [ + ⟨4, 6, 4, 3, 8, 3, 8710883720460767351442242844597619712250504806400000⟩, + ⟨4, 6, 4, 4, 7, 3, 19850236498053328090399475591234736280996046438400000⟩, + ⟨4, 6, 5, 4, 8, 3, -86249115982324806559079681177276647069559291904000000⟩, + ⟨4, 6, 4, 5, 6, 3, -18208200954866452902449614304197968007697478451200000⟩, + ⟨4, 6, 5, 5, 7, 3, 2934060280588302704110229755645113985627324416000000⟩, + ⟨4, 6, 6, 5, 8, 3, -60743401753432418690486016714019229752973328384000000⟩, + ⟨4, 6, 4, 6, 5, 3, 29544329172915890328091246409029945805881579929600000⟩, + ⟨4, 6, 5, 6, 6, 3, -27908149118667589620036944855372055524507910144000000⟩, + ⟨4, 6, 6, 6, 7, 3, -57365870906824235343272182187622669007491956736000000⟩, + ⟨4, 6, 7, 6, 8, 3, -20977761722277402700629356137025679095677059072000000⟩, + ⟨4, 6, 4, 7, 4, 3, 122183922481120253626360159853435246446168453939200000⟩, + ⟨4, 6, 5, 7, 5, 3, 31561335714174357727898429855788431514590511104000000⟩, + ⟨4, 6, 6, 7, 6, 3, 62088220613724929060516623436857414100912701440000000⟩, + ⟨4, 6, 7, 7, 7, 3, 7414225719203507740034065014480547082661789696000000⟩, + ⟨4, 6, 8, 7, 8, 3, 49735419489125342260191806373732868720636723200000000⟩ +] + +def collectedFourData_14_7_18 : List CollectedFourTerm := [ + ⟨4, 7, 3, 2, 8, 4, 3461011218248421548444030752518038773586460672000000⟩, + ⟨4, 7, 3, 3, 7, 4, 8641762314844960774389299843239564493794679193600000⟩, + ⟨4, 7, 4, 3, 8, 4, 5020177245528279439759506358943310336226020556800000⟩, + ⟨4, 7, 3, 4, 6, 4, 19850236498053328090399475591234736280996046438400000⟩, + ⟨4, 7, 4, 4, 7, 4, 11439907681446026733221553441102561434330254540800000⟩, + ⟨4, 7, 5, 4, 8, 4, -24853152871525956261450900409892079758500429824000000⟩, + ⟨4, 7, 3, 5, 5, 4, 6523819456622002140626775592805390968876223692800000⟩, + ⟨4, 7, 4, 5, 6, 4, -10493584698062271441472773621905080648177444454400000⟩, + ⟨4, 7, 5, 5, 7, 4, 845465461961108029020305178014956877927940096000000⟩, + ⟨4, 7, 6, 5, 8, 4, -11669028198302169413421691306782998847748571136000000⟩, + ⟨4, 7, 3, 6, 4, 4, -30779442880537610363706007940907771394184655667200000⟩, + ⟨4, 7, 4, 6, 5, 4, 17026718965366274960000784172227318301469127475200000⟩, + ⟨4, 7, 5, 6, 6, 4, -8041885282044280528326369827984943773871243264000000⟩, + ⟨4, 7, 6, 6, 7, 4, -11020192249836717953677695564919007621985337344000000⟩, + ⟨4, 7, 7, 6, 8, 4, -3022428189832403189789117320914135705836322816000000⟩, + ⟨4, 7, 3, 7, 3, 4, 54855357332113636974029253396348670387418667417600000⟩, + ⟨4, 7, 4, 7, 4, 4, 70415926453977017793101296834864191822344119910400000⟩, + ⟨4, 7, 5, 7, 5, 4, 9094570911250562341031350331177998099912065024000000⟩, + ⟨4, 7, 6, 7, 6, 4, 11927372787992112854299693769020151357516021760000000⟩, + ⟨4, 7, 7, 7, 7, 4, 1068224776130612259123377463401010923084709888000000⟩, + ⟨4, 7, 8, 7, 8, 4, 5732612883573281435912273865559179964113223680000000⟩ +] + +def collectedFourData_14_7_19 : List CollectedFourTerm := [ + ⟨4, 8, 2, 1, 8, 5, -29409904343733063156558981423787413183142035456000000⟩, + ⟨4, 8, 2, 2, 7, 5, -35749008409470121013465678439759657543760084992000000⟩, + ⟨4, 8, 3, 2, 8, 5, -15038065567032894745560663893451581050658488320000000⟩, + ⟨4, 8, 2, 3, 6, 5, -14201396800728609792478291156448741238169927680000000⟩, + ⟨4, 8, 3, 3, 7, 5, -37548386905004437266991595889357651859803734016000000⟩, + ⟨4, 8, 4, 3, 8, 5, -10906314631159645967374272151471933175107682304000000⟩, + ⟨4, 8, 2, 4, 5, 5, -6595401782902784778751151220900200618674618368000000⟩, + ⟨4, 8, 3, 4, 6, 5, -86249115982324806559079681177276647069559291904000000⟩, + ⟨4, 8, 4, 4, 7, 5, -24853152871525956261450900409892079758500429824000000⟩, + ⟨4, 8, 5, 4, 8, 5, 35995582298694623962046456580108028270325268480000000⟩, + ⟨4, 8, 2, 5, 4, 5, 34970359042469067196886585588208636060286058496000000⟩, + ⟨4, 8, 3, 5, 5, 5, -28345942428298953001696315253087911743238176768000000⟩, + ⟨4, 8, 4, 5, 6, 5, 22797270042154895629717594928241649389699858432000000⟩, + ⟨4, 8, 5, 5, 7, 5, -1224513516415528290082267321319517140727889920000000⟩, + ⟨4, 8, 6, 5, 8, 5, 12675458130877714167991191376064807598859223040000000⟩, + ⟨4, 8, 2, 6, 3, 5, 17645422610708364692930613215347507862616145920000000⟩, + ⟨4, 8, 3, 6, 4, 5, 133736428739031438785194648805942548853352824832000000⟩, + ⟨4, 8, 4, 6, 5, 5, -36990477644594862324256070994865529948687302656000000⟩, + ⟨4, 8, 5, 6, 6, 5, 11647308693704286703818028927301468219013857280000000⟩, + ⟨4, 8, 6, 6, 7, 5, 11970661402408175832560787923275025809051484160000000⟩, + ⟨4, 8, 7, 6, 8, 5, 2626485175818106599607009655304724200755822592000000⟩, + ⟨4, 8, 2, 7, 2, 5, -85343736479480460364308381270605078765997391872000000⟩, + ⟨4, 8, 3, 7, 3, 5, -238346081027967710568059882461850266876778643456000000⟩, + ⟨4, 8, 4, 7, 4, 5, -152978313591566390638950835867770296009974874112000000⟩, + ⟨4, 8, 5, 7, 5, 5, -13171945523350171425474054160776940808023572480000000⟩, + ⟨4, 8, 6, 7, 6, 5, -12956084415629525493904470459666550653085286400000000⟩, + ⟨4, 8, 7, 7, 7, 5, -928285591163787552392024925335955965850157056000000⟩, + ⟨4, 8, 8, 7, 8, 5, -4151359384942083785210939288135490807319756800000000⟩ +] + +def collectedFourData_14_7_20 : List CollectedFourTerm := [ + ⟨5, 2, 7, 6, 8, 0, -161889666186897515500741998602168513856125534208000000⟩, + ⟨5, 2, 7, 7, 7, 0, 57217092204909440645212341220687589409338425344000000⟩, + ⟨5, 2, 8, 7, 8, 0, 1535273508271255093092444632186669371636265779200000000⟩ +] + +def collectedFourData_14_7_21 : List CollectedFourTerm := [ + ⟨5, 3, 6, 5, 8, 1, -158746685633997088239004514416816847717752897536000000⟩, + ⟨5, 3, 6, 6, 7, 1, -149919853220131825286814496108446006921809362944000000⟩, + ⟨5, 3, 7, 6, 8, 1, -164469722602081230766977787854218069452850724864000000⟩, + ⟨5, 3, 6, 7, 6, 1, 162261232575508509215591425447314024409344245760000000⟩, + ⟨5, 3, 7, 7, 7, 1, 58128968356602825218397717824212204095748964352000000⟩, + ⟨5, 3, 8, 7, 8, 1, 779870679738710450689953049411805863998180556800000000⟩ +] + +def collectedFourData_14_7_22 : List CollectedFourTerm := [ + ⟨5, 4, 5, 4, 8, 2, 34970359042469067196886585588208636060286058496000000⟩, + ⟨5, 4, 5, 5, 7, 2, -1189637021734200086909393526800223887041757184000000⟩, + ⟨5, 4, 6, 5, 8, 2, 49257747040880903136082018925343662057069740032000000⟩, + ⟨5, 4, 5, 6, 6, 2, 11315570991945902113546311524682053419328864256000000⟩, + ⟨5, 4, 6, 6, 7, 2, 46518855980081905425063983915411973232266313728000000⟩, + ⟨5, 4, 7, 6, 8, 2, 25516778380165996375142959225403759648135184384000000⟩, + ⟨5, 4, 5, 7, 5, 2, -12796783239039398209940469704238912919144759296000000⟩, + ⟨5, 4, 6, 7, 6, 2, -50348281079540518737016516752746020529630085120000000⟩, + ⟨5, 4, 7, 7, 7, 2, -9018462362289816359661670433383481846595059712000000⟩, + ⟨5, 4, 8, 7, 8, 2, -80662414071302835392133568635681850415854387200000000⟩ +] + +def collectedFourData_14_7_23 : List CollectedFourTerm := [ + ⟨5, 5, 4, 3, 8, 3, 2862849150713485739881420692754374296641260748800000⟩, + ⟨5, 5, 4, 4, 7, 3, 6523819456622002140626775592805390968876223692800000⟩, + ⟨5, 5, 5, 4, 8, 3, -28345942428298953001696315253087911743238176768000000⟩, + ⟨5, 5, 4, 5, 6, 3, -5984161230073519873010205140404735823902565990400000⟩, + ⟨5, 5, 5, 5, 7, 3, 964284710022519179567647746200418270861852672000000⟩, + ⟨5, 5, 6, 5, 8, 3, -19963439038084595100324356902319494652051324928000000⟩, + ⟨5, 5, 4, 6, 5, 3, 9709802173390503871408136084686884569007469363200000⟩, + ⟨5, 5, 5, 6, 6, 3, -9172068364854333614179393517156856736511950848000000⟩, + ⟨5, 5, 6, 6, 7, 3, -18853406850074929924539529552813511612785754112000000⟩, + ⟨5, 5, 7, 6, 8, 3, -6894382849977364375100027543942542846983143424000000⟩, + ⟨5, 5, 4, 7, 4, 3, 40155987604827645136082917369787977590590826086400000⟩, + ⟨5, 5, 5, 7, 5, 3, 10372695359539005138809443286407199229286023168000000⟩, + ⟨5, 5, 6, 7, 6, 3, 20405416414387839152659607378216221139250708480000000⟩, + ⟨5, 5, 7, 7, 7, 3, 2436699935916156777461511878746145780957970432000000⟩, + ⟨5, 5, 8, 7, 8, 3, 16345643911004920847809096424683835054515814400000000⟩ +] + +def collectedFourData_14_7_24 : List CollectedFourTerm := [ + ⟨5, 6, 3, 2, 8, 4, -3174712189202105360438446267938993816150736896000000⟩, + ⟨5, 6, 3, 3, 7, 4, -7926905296484504204523454567989328354019691724800000⟩, + ⟨5, 6, 4, 3, 8, 4, -4604902119155662990515371090050284688310167142400000⟩, + ⟨5, 6, 3, 4, 6, 4, -18208200954866452902449614304197968007697478451200000⟩, + ⟨5, 6, 4, 4, 7, 4, -10493584698062271441472773621905080648177444454400000⟩, + ⟨5, 6, 5, 4, 8, 4, 22797270042154895629717594928241649389699858432000000⟩, + ⟨5, 6, 3, 5, 5, 4, -5984161230073519873010205140404735823902565990400000⟩, + ⟨5, 6, 4, 5, 6, 4, 9625542695069009546053508909724676211080377139200000⟩, + ⟨5, 6, 5, 5, 7, 4, -775527537583572447657099294292805136446128128000000⟩, + ⟨5, 6, 6, 5, 8, 4, 10703752088975152470543896568681294044854222848000000⟩, + ⟨5, 6, 3, 6, 4, 4, 28233330182369534663097408158365078727603886489600000⟩, + ⟨5, 6, 4, 6, 5, 4, -15618248203432163430780199633592264606994766233600000⟩, + ⟨5, 6, 5, 6, 6, 4, 7376650816518234508760525463351779527703396352000000⟩, + ⟨5, 6, 6, 6, 7, 4, 10108588633992694106607124197375644737619361792000000⟩, + ⟨5, 6, 7, 6, 8, 4, 2772409278726659997364248450928985280859865088000000⟩, + ⟨5, 6, 3, 7, 3, 4, -50317655905615228839749885029921746800394161356800000⟩, + ⟨5, 6, 4, 7, 4, 4, -64591035951780615391079993838936740020624765747200000⟩, + ⟨5, 6, 5, 7, 5, 4, -8342257018780244422514447423901304616524972032000000⟩, + ⟨5, 6, 6, 7, 6, 4, -10940726102112896234888993648045815727055175680000000⟩, + ⟨5, 6, 7, 7, 7, 4, -979859932180701364854800670033729640867037184000000⟩, + ⟨5, 6, 8, 7, 8, 4, -5258404220564079467132666714605179403228938240000000⟩ +] + +def collectedFourData_14_7_25 : List CollectedFourTerm := [ + ⟨5, 7, 2, 1, 8, 5, 1000479033414466928943575123727721657767297024000000⟩, + ⟨5, 7, 2, 2, 7, 5, 1216125457635284620668865891953551271020986368000000⟩, + ⟨5, 7, 3, 2, 8, 5, 511571514381155559201257356449474434857697280000000⟩, + ⟨5, 7, 2, 3, 6, 5, 483109349090959499110001493627225288443166720000000⟩, + ⟨5, 7, 3, 3, 7, 5, 1277337505009473461158813707606127651810443264000000⟩, + ⟨5, 7, 4, 3, 8, 5, 371015797697478522041472319415904715476566016000000⟩, + ⟨5, 7, 2, 4, 5, 5, 224365272447569621655404125961391698526339072000000⟩, + ⟨5, 7, 3, 4, 6, 5, 2934060280588302704110229755645113985627324416000000⟩, + ⟨5, 7, 4, 4, 7, 5, 845465461961108029020305178014956877927940096000000⟩, + ⟨5, 7, 5, 4, 8, 5, -1224513516415528290082267321319517140727889920000000⟩, + ⟨5, 7, 2, 5, 4, 5, -1189637021734200086909393526800223887041757184000000⟩, + ⟨5, 7, 3, 5, 5, 5, 964284710022519179567647746200418270861852672000000⟩, + ⟨5, 7, 4, 5, 6, 5, -775527537583572447657099294292805136446128128000000⟩, + ⟨5, 7, 5, 5, 7, 5, 41656038217186975893696456596600617886023680000000⟩, + ⟨5, 7, 6, 5, 8, 5, -431199297714423878505827150251515327975260160000000⟩, + ⟨5, 7, 2, 6, 3, 5, -600269730612474323234040367788639798354247680000000⟩, + ⟨5, 7, 3, 6, 4, 5, -4549504527227079121079799538941389392972873728000000⟩, + ⟨5, 7, 4, 6, 5, 5, 1258358302933065037845054701832006339158605824000000⟩, + ⟨5, 7, 5, 6, 6, 5, -396223258925365677148680796316720484707205120000000⟩, + ⟨5, 7, 6, 6, 7, 5, -407223213283427120563356854078596155325808640000000⟩, + ⟨5, 7, 7, 6, 8, 5, -89348925425521473757324896436560457805856768000000⟩, + ⟨5, 7, 2, 7, 2, 5, 2903260683306647443524456106645033656294309888000000⟩, + ⟨5, 7, 3, 7, 3, 5, 8108161589984929204797110684865290146387329024000000⟩, + ⟨5, 7, 4, 7, 4, 5, 5204083411039016635088175930496518534199246848000000⟩, + ⟨5, 7, 5, 7, 5, 5, 448089023730454255944407105161141044557905920000000⟩, + ⟨5, 7, 6, 7, 6, 5, 440745765830666230974835025098456962800025600000000⟩, + ⟨5, 7, 7, 7, 7, 5, 31578826647153842422290010704005082774503424000000⟩, + ⟨5, 7, 8, 7, 8, 5, 141222765509877153815270238656805572129587200000000⟩ +] + +def collectedFourData_14_7_26 : List CollectedFourTerm := [ + ⟨5, 8, 1, 0, 8, 6, 7183783342680442947325989934199255971557015552000000⟩, + ⟨5, 8, 1, 1, 7, 6, 75334142759199133516311051401318831777541783552000000⟩, + ⟨5, 8, 2, 1, 8, 6, -41425529171742392726282269266990499507420004352000000⟩, + ⟨5, 8, 1, 2, 6, 6, 89332287615973051355963007528568547664029810688000000⟩, + ⟨5, 8, 2, 2, 7, 6, -50354519124538982244141354077997550154299736064000000⟩, + ⟨5, 8, 3, 2, 8, 6, -10590986909592619600569561437577239700669726720000000⟩, + ⟨5, 8, 1, 3, 5, 6, 73802250894332099337805438805594483604647313408000000⟩, + ⟨5, 8, 2, 3, 6, 6, -20003478099493806976600322740717625610401218560000000⟩, + ⟨5, 8, 3, 3, 7, 6, -26444523227709574054701701912522924434900647936000000⟩, + ⟨5, 8, 4, 3, 8, 6, -5120722253165919336426943730031625568419577856000000⟩, + ⟨5, 8, 1, 4, 4, 6, -83124538848261050529464293852296211857257005056000000⟩, + ⟨5, 8, 2, 4, 5, 6, -9289999918521358298289477252309565845647917056000000⟩, + ⟨5, 8, 3, 4, 6, 6, -60743401753432418690486016714019229752973328384000000⟩, + ⟨5, 8, 4, 4, 7, 6, -11669028198302169413421691306782998847748571136000000⟩, + ⟨5, 8, 5, 4, 8, 6, 12675458130877714167991191376064807598859223040000000⟩, + ⟨5, 8, 1, 5, 3, 6, -158746685633997088239004514416816847717752897536000000⟩, + ⟨5, 8, 2, 5, 4, 6, 49257747040880903136082018925343662057069740032000000⟩, + ⟨5, 8, 3, 5, 5, 6, -19963439038084595100324356902319494652051324928000000⟩, + ⟨5, 8, 4, 5, 6, 6, 10703752088975152470543896568681294044854222848000000⟩, + ⟨5, 8, 5, 5, 7, 6, -431199297714423878505827150251515327975260160000000⟩, + ⟨5, 8, 6, 5, 8, 6, 3570821274553139504194127651164847117105627136000000⟩, + ⟨5, 8, 1, 6, 2, 6, 395583813153090894797891073348043029451263442944000000⟩, + ⟨5, 8, 2, 6, 3, 6, 24854585059654717537286345893922875747482992640000000⟩, + ⟨5, 8, 3, 6, 4, 6, 94187697200618934777117972519380148715543068672000000⟩, + ⟨5, 8, 4, 6, 5, 6, -17367733137712803218717987210345998369721155584000000⟩, + ⟨5, 8, 5, 6, 6, 6, 4101474799306431986751810366726064829827645440000000⟩, + ⟨5, 8, 6, 6, 7, 6, 3372271989291115579119814522757707974882361344000000⟩, + ⟨5, 8, 7, 6, 8, 6, 616592384424550700781382367373966293329772544000000⟩, + ⟨5, 8, 1, 7, 1, 6, -1131992571294488041751294502688298941972368850944000000⟩, + ⟨5, 8, 2, 7, 2, 6, -120211524792312738571332733068759199268443521024000000⟩, + ⟨5, 8, 3, 7, 3, 6, -167862030715827777720943103317605906027355570176000000⟩, + ⟨5, 8, 4, 7, 4, 6, -71826229221560191949286323951384026141182394368000000⟩, + ⟨5, 8, 5, 7, 5, 6, -4638359301926949005793017734711518845510615040000000⟩, + ⟨5, 8, 6, 7, 6, 6, -3649876902952835612969872655498600660084981760000000⟩, + ⟨5, 8, 7, 7, 7, 6, -217923874595769778001522416844969777238638592000000⟩, + ⟨5, 8, 8, 7, 8, 6, -835346668510769923179188586022824062012620800000000⟩ +] + +def collectedFourData_14_7_27 : List CollectedFourTerm := [ + ⟨6, 1, 7, 6, 8, 0, 117671823891391903894195653432460723594639441920000000⟩, + ⟨6, 1, 7, 7, 7, 0, -41589063441150984629880830626766731614942658560000000⟩, + ⟨6, 1, 8, 7, 8, 0, -1115935551326969559851315781037644170089463808000000000⟩ +] + +def collectedFourData_14_7_28 : List CollectedFourTerm := [ + ⟨6, 2, 6, 5, 8, 1, 395583813153090894797891073348043029451263442944000000⟩, + ⟨6, 2, 6, 6, 7, 1, 373588065585858970880365368279409610335218302976000000⟩, + ⟨6, 2, 7, 6, 8, 1, 409845155225268212442764774371601549457050566656000000⟩, + ⟨6, 2, 6, 7, 6, 1, -404341777926188971548329384896370602947945431040000000⟩, + ⟨6, 2, 7, 7, 7, 1, -144852655444894130104866679302956307409438507008000000⟩, + ⟨6, 2, 8, 7, 8, 1, -1943374225579818713054596650950985685534978867200000000⟩ +] + +def collectedFourData_14_7_29 : List CollectedFourTerm := [ + ⟨6, 3, 5, 4, 8, 2, 17645422610708364692930613215347507862616145920000000⟩, + ⟨6, 3, 5, 5, 7, 2, -600269730612474323234040367788639798354247680000000⟩, + ⟨6, 3, 6, 5, 8, 2, 24854585059654717537286345893922875747482992640000000⟩, + ⟨6, 3, 5, 6, 6, 2, 5709636323489700844369158644999617476946821120000000⟩, + ⟨6, 3, 6, 6, 7, 2, 23472589233023438774218212595689740504200642560000000⟩, + ⟨6, 3, 7, 6, 8, 2, 12875313565840512985992057648899922681585991680000000⟩, + ⟨6, 3, 5, 7, 5, 2, -6457029738706874339455925350374035683194961920000000⟩, + ⟨6, 3, 6, 7, 6, 2, -25404849183627316359364083074121869916792422400000000⟩, + ⟨6, 3, 7, 7, 7, 2, -4550556072018397800312603050225516893427466240000000⟩, + ⟨6, 3, 8, 7, 8, 2, -40700822755624602921088982369382973984210944000000000⟩ +] + +def collectedFourData_14_7_30 : List CollectedFourTerm := [ + ⟨6, 4, 4, 3, 8, 3, -13506949800785534071667944830311483136825045811200000⟩, + ⟨6, 4, 4, 4, 7, 3, -30779442880537610363706007940907771394184655667200000⟩, + ⟨6, 4, 5, 4, 8, 3, 133736428739031438785194648805942548853352824832000000⟩, + ⟨6, 4, 4, 5, 6, 3, 28233330182369534663097408158365078727603886489600000⟩, + ⟨6, 4, 5, 5, 7, 3, -4549504527227079121079799538941389392972873728000000⟩, + ⟨6, 4, 6, 5, 8, 3, 94187697200618934777117972519380148715543068672000000⟩, + ⟨6, 4, 4, 6, 5, 3, -45810939950803331582702079446356380897684278476800000⟩, + ⟨6, 4, 5, 6, 6, 3, 43273906675308136764957606750531179038220746752000000⟩, + ⟨6, 4, 6, 6, 7, 3, 88950554671832166170589170127763349103641100288000000⟩, + ⟨6, 4, 7, 6, 8, 3, 32527764530950877463980486281016237155864805376000000⟩, + ⟨6, 4, 4, 7, 4, 3, -189456335358850026499517881167151502769755101593600000⟩, + ⟨6, 4, 5, 7, 5, 3, -48938476372468837259032911501617562180944658432000000⟩, + ⟨6, 4, 6, 7, 6, 3, -96272950708762392715841478256933652957516267520000000⟩, + ⟨6, 4, 7, 7, 7, 3, -11496373710712057155108904447806782719779667968000000⟩, + ⟨6, 4, 8, 7, 8, 3, -77118905029430542872302120629977751691565465600000000⟩ +] + +def collectedFourData_14_7_31 : List CollectedFourTerm := [ + ⟨6, 5, 3, 2, 8, 4, 5151236092986286223783488853489069772156960768000000⟩, + ⟨6, 5, 3, 3, 7, 4, 12862066932498126870312669067126409420129855078400000⟩, + ⟨6, 5, 4, 3, 8, 4, 7471838890323291788910968975429470434507305779200000⟩, + ⟨6, 5, 3, 4, 6, 4, 29544329172915890328091246409029945805881579929600000⟩, + ⟨6, 5, 4, 4, 7, 4, 17026718965366274960000784172227318301469127475200000⟩, + ⟨6, 5, 5, 4, 8, 4, -36990477644594862324256070994865529948687302656000000⟩, + ⟨6, 5, 3, 5, 5, 4, 9709802173390503871408136084686884569007469363200000⟩, + ⟨6, 5, 4, 5, 6, 4, -15618248203432163430780199633592264606994766233600000⟩, + ⟨6, 5, 5, 5, 7, 4, 1258358302933065037845054701832006339158605824000000⟩, + ⟨6, 5, 6, 5, 8, 4, -17367733137712803218717987210345998369721155584000000⟩, + ⟨6, 5, 3, 6, 4, 4, -45810939950803331582702079446356380897684278476800000⟩, + ⟨6, 5, 4, 6, 5, 4, 25341914183080060263309212491407942460761754828800000⟩, + ⟨6, 5, 5, 6, 6, 4, -11969233009734868379917904282539384143416918016000000⟩, + ⟨6, 5, 6, 6, 7, 4, -16402030646331186950368450450974408393973825536000000⟩, + ⟨6, 5, 7, 6, 8, 4, -4498465967932718254184974530504366500823957504000000⟩, + ⟨6, 5, 3, 7, 3, 4, 81644605799876780771671439742773780980542367334400000⟩, + ⟨6, 5, 4, 7, 4, 4, 104804358899006200236327406289011865783608383897600000⟩, + ⟨6, 5, 5, 7, 5, 4, 13536009846268703732829526633524967806081171456000000⟩, + ⟨6, 5, 6, 7, 6, 4, 17752243297004361123956176439057531593493053440000000⟩, + ⟨6, 5, 7, 7, 7, 4, 1589904705657396909078137843403416055287119872000000⟩, + ⟨6, 5, 8, 7, 8, 4, 8532200715583261614119534989442007386994769920000000⟩ +] + +def collectedFourData_14_7_32 : List CollectedFourTerm := [ + ⟨6, 6, 2, 1, 8, 5, -9516340969324893367126083323598459289328418816000000⟩, + ⟨6, 6, 2, 2, 7, 5, -11567523286156950516052309780082143407491776512000000⟩, + ⟨6, 6, 3, 2, 8, 5, -4865958004567388920883723211449273809392107520000000⟩, + ⟨6, 6, 2, 3, 6, 5, -4595232021732541503631706959190926874357268480000000⟩, + ⟨6, 6, 3, 3, 7, 5, -12149759089995062572259090713714599994878590976000000⟩, + ⟨6, 6, 4, 3, 8, 5, -3529022316285371127280381785336065881270124544000000⟩, + ⟨6, 6, 2, 4, 5, 5, -2134114122311675428765502633209100078256488448000000⟩, + ⟨6, 6, 3, 4, 6, 5, -27908149118667589620036944855372055524507910144000000⟩, + ⟨6, 6, 4, 4, 7, 5, -8041885282044280528326369827984943773871243264000000⟩, + ⟨6, 6, 5, 4, 8, 5, 11647308693704286703818028927301468219013857280000000⟩, + ⟨6, 6, 2, 5, 4, 5, 11315570991945902113546311524682053419328864256000000⟩, + ⟨6, 6, 3, 5, 5, 5, -9172068364854333614179393517156856736511950848000000⟩, + ⟨6, 6, 4, 5, 6, 5, 7376650816518234508760525463351779527703396352000000⟩, + ⟨6, 6, 5, 5, 7, 5, -396223258925365677148680796316720484707205120000000⟩, + ⟨6, 6, 6, 5, 8, 5, 4101474799306431986751810366726064829827645440000000⟩, + ⟨6, 6, 2, 6, 3, 5, 5709636323489700844369158644999617476946821120000000⟩, + ⟨6, 6, 3, 6, 4, 5, 43273906675308136764957606750531179038220746752000000⟩, + ⟨6, 6, 4, 6, 5, 5, -11969233009734868379917904282539384143416918016000000⟩, + ⟨6, 6, 5, 6, 6, 5, 3768790255446406434061678225362761115846574080000000⟩, + ⟨6, 6, 6, 6, 7, 5, 3873419450883987063785009644450317285992693760000000⟩, + ⟨6, 6, 7, 6, 8, 5, 849867724554106239158416864636464644449370112000000⟩, + ⟨6, 6, 2, 7, 2, 5, -27615189986430880665967729917006375005498376192000000⟩, + ⟨6, 6, 3, 7, 3, 5, -77123085789560050966602398374853397876169506816000000⟩, + ⟨6, 6, 4, 7, 4, 5, -49500119960773301224893653789274250357959032832000000⟩, + ⟨6, 6, 5, 7, 5, 5, -4262126233548370453184259713508679536114401280000000⟩, + ⟨6, 6, 6, 7, 6, 5, -4192278746828354421720860805193463434208870400000000⟩, + ⟨6, 6, 7, 7, 7, 5, -300370994042635699856503845895085510325436416000000⟩, + ⟨6, 6, 8, 7, 8, 5, -1343280512972290468669278619392051830901964800000000⟩ +] + +def collectedFourData_14_7_33 : List CollectedFourTerm := [ + ⟨6, 7, 1, 0, 8, 6, 6784341606872780669096722551041432704209911808000000⟩, + ⟨6, 7, 1, 1, 7, 6, 71145319222367796957001216834741112699835383808000000⟩, + ⟨6, 7, 2, 1, 8, 6, -39122134916962763653253356703248003957688107008000000⟩, + ⟨6, 7, 1, 2, 6, 6, 84365121663599075203032381756999349427767345152000000⟩, + ⟨6, 7, 2, 2, 7, 6, -47554643966087854435471275104052861276002451456000000⟩, + ⟨6, 7, 3, 2, 8, 6, -10002093565614708133942336479501825308759162880000000⟩, + ⟨6, 7, 1, 3, 5, 6, 69698605531226671627399759959402167599242412032000000⟩, + ⟨6, 7, 2, 3, 6, 6, -18891219609349668226819423810183199723869962240000000⟩, + ⟨6, 7, 3, 3, 7, 6, -24974121663964608896548362089199448065042284544000000⟩, + ⟨6, 7, 4, 3, 8, 6, -4835993428837216948986702559900286424893620224000000⟩, + ⟨6, 7, 1, 4, 4, 6, -78502543932505161863584624756161981089813889024000000⟩, + ⟨6, 7, 2, 4, 5, 6, -8773445685731450920323513973800894522955137024000000⟩, + ⟨6, 7, 3, 4, 6, 6, -57365870906824235343272182187622669007491956736000000⟩, + ⟨6, 7, 4, 4, 7, 6, -11020192249836717953677695564919007621985337344000000⟩, + ⟨6, 7, 5, 4, 8, 6, 11970661402408175832560787923275025809051484160000000⟩, + ⟨6, 7, 1, 5, 3, 6, -149919853220131825286814496108446006921809362944000000⟩, + ⟨6, 7, 2, 5, 4, 6, 46518855980081905425063983915411973232266313728000000⟩, + ⟨6, 7, 3, 5, 5, 6, -18853406850074929924539529552813511612785754112000000⟩, + ⟨6, 7, 4, 5, 6, 6, 10108588633992694106607124197375644737619361792000000⟩, + ⟨6, 7, 5, 5, 7, 6, -407223213283427120563356854078596155325808640000000⟩, + ⟨6, 7, 6, 5, 8, 6, 3372271989291115579119814522757707974882361344000000⟩, + ⟨6, 7, 1, 6, 2, 6, 373588065585858970880365368279409610335218302976000000⟩, + ⟨6, 7, 2, 6, 3, 6, 23472589233023438774218212595689740504200642560000000⟩, + ⟨6, 7, 3, 6, 4, 6, 88950554671832166170589170127763349103641100288000000⟩, + ⟨6, 7, 4, 6, 5, 6, -16402030646331186950368450450974408393973825536000000⟩, + ⟨6, 7, 5, 6, 6, 6, 3873419450883987063785009644450317285992693760000000⟩, + ⟨6, 7, 6, 6, 7, 6, 3184762690532754984231123904743212850742296576000000⟩, + ⟨6, 7, 7, 6, 8, 6, 582307840950494569837237685060731144425701376000000⟩, + ⟨6, 7, 1, 7, 1, 6, -1069050099893264589089437792669496606474398334976000000⟩, + ⟨6, 7, 2, 7, 2, 6, -113527372746433980104978759152433576842201399296000000⟩, + ⟨6, 7, 3, 7, 3, 6, -158528355446563464746541227304023555496952725504000000⟩, + ⟨6, 7, 4, 7, 4, 6, -67832457095064801279671954296770900358827343872000000⟩, + ⟨6, 7, 5, 7, 5, 6, -4380451427693925456307326313637622453538652160000000⟩, + ⟨6, 7, 6, 7, 6, 6, -3446931867439585767941357195087762064188375040000000⟩, + ⟨6, 7, 7, 7, 7, 6, -205806597864260510648494173546020728070995968000000⟩, + ⟨6, 7, 8, 7, 8, 6, -788898674834698311499056746119098671510323200000000⟩ +] + +def collectedFourData_14_7_34 : List CollectedFourTerm := [ + ⟨6, 8, 0, 0, 7, 7, 64682253423664316834564284789136541548430753792000000⟩, + ⟨6, 8, 1, 0, 8, 7, 7442768640399707599928351082701006527159861248000000⟩, + ⟨6, 8, 0, 1, 6, 7, 8137774113910338201642624664739841663729401856000000⟩, + ⟨6, 8, 1, 1, 7, 7, 78050042510100718858904074259512328445386293248000000⟩, + ⟨6, 8, 2, 1, 8, 7, -21459488317221833513459868896150064123529396224000000⟩, + ⟨6, 8, 0, 2, 5, 7, -39357925574812367959884944682503583044286283776000000⟩, + ⟨6, 8, 1, 2, 6, 7, 92552839795868450747365230960285950136142528512000000⟩, + ⟨6, 8, 2, 2, 7, 7, -26084934495163081998724866548233779444625440768000000⟩, + ⟨6, 8, 3, 2, 8, 7, -3657602198425422828634190886744203074480373760000000⟩, + ⟨6, 8, 0, 3, 4, 7, 24994551947080396542546752412150754799813394432000000⟩, + ⟨6, 8, 1, 3, 5, 7, 76462923830647113914390985735966761374074273792000000⟩, + ⟨6, 8, 2, 3, 6, 7, -10362315537364442387319549152091878581830942720000000⟩, + ⟨6, 8, 3, 3, 7, 7, -9132628254537532063451365033499868163618111488000000⟩, + ⟨6, 8, 4, 3, 8, 7, -1326332838284053773638003939309770497784283136000000⟩, + ⟨6, 8, 0, 4, 3, 7, 95922782202230917772882835365833916217299042304000000⟩, + ⟨6, 8, 1, 4, 4, 7, -86121293123058101939645395912107205339952185344000000⟩, + ⟨6, 8, 2, 4, 5, 7, -4812458614396878705069827291870762132331036672000000⟩, + ⟨6, 8, 3, 4, 6, 7, -20977761722277402700629356137025679095677059072000000⟩, + ⟨6, 8, 4, 4, 7, 7, -3022428189832403189789117320914135705836322816000000⟩, + ⟨6, 8, 5, 4, 8, 7, 2626485175818106599607009655304724200755822592000000⟩, + ⟨6, 8, 0, 5, 2, 7, -161889666186897515500741998602168513856125534208000000⟩, + ⟨6, 8, 1, 5, 3, 7, -164469722602081230766977787854218069452850724864000000⟩, + ⟨6, 8, 2, 5, 4, 7, 25516778380165996375142959225403759648135184384000000⟩, + ⟨6, 8, 3, 5, 5, 7, -6894382849977364375100027543942542846983143424000000⟩, + ⟨6, 8, 4, 5, 6, 7, 2772409278726659997364248450928985280859865088000000⟩, + ⟨6, 8, 5, 5, 7, 7, -89348925425521473757324896436560457805856768000000⟩, + ⟨6, 8, 6, 5, 8, 7, 616592384424550700781382367373966293329772544000000⟩, + ⟨6, 8, 0, 6, 1, 7, 117671823891391903894195653432460723594639441920000000⟩, + ⟨6, 8, 1, 6, 2, 7, 409845155225268212442764774371601549457050566656000000⟩, + ⟨6, 8, 2, 6, 3, 7, 12875313565840512985992057648899922681585991680000000⟩, + ⟨6, 8, 3, 6, 4, 7, 32527764530950877463980486281016237155864805376000000⟩, + ⟨6, 8, 4, 6, 5, 7, -4498465967932718254184974530504366500823957504000000⟩, + ⟨6, 8, 5, 6, 6, 7, 849867724554106239158416864636464644449370112000000⟩, + ⟨6, 8, 6, 6, 7, 7, 582307840950494569837237685060731144425701376000000⟩, + ⟨6, 8, 7, 6, 8, 7, 91260198616656633142817078780491535386411008000000⟩, + ⟨6, 8, 0, 7, 0, 7, -1147687357986042161760596821057263082668048777216000000⟩, + ⟨6, 8, 1, 7, 1, 7, -1172802464787644297254628681861169930550332358656000000⟩, + ⟨6, 8, 2, 7, 2, 7, -62272658031263830522720627237450055219347980288000000⟩, + ⟨6, 8, 3, 7, 3, 7, -57971229482143121233533173518025307073605009408000000⟩, + ⟨6, 8, 4, 7, 4, 7, -18603915962787177990886796535660200675883614208000000⟩, + ⟨6, 8, 5, 7, 5, 7, -961115710441431435411004405182824823172104192000000⟩, + ⟨6, 8, 6, 7, 6, 7, -630243333231348632939269428228688496862167040000000⟩, + ⟨6, 8, 7, 7, 7, 7, -32254332977988458293151423281111617182367744000000⟩, + ⟨6, 8, 8, 7, 8, 7, -108182758507554506125338823633039190812262400000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1413.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1413.lean new file mode 100644 index 0000000000000000000000000000000000000000..76e41e0d98b6f307dae5b494bfe33cd82574f589 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1413.lean @@ -0,0 +1,309 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1412 + +namespace OAI + +/-! Sparse1413. -/ +namespace LaughlinFock +def collectedFourData_14_7_35 : List CollectedFourTerm := [ + ⟨7, 0, 7, 6, 8, 0, -1147687357986042161760596821057263082668048777216000000⟩, + ⟨7, 0, 7, 7, 7, 0, 405630173506473303894157543181417385599422169088000000⟩, + ⟨7, 0, 8, 7, 8, 0, 10884042434552915293747245526142109512785880678400000000⟩ +] + +def collectedFourData_14_7_36 : List CollectedFourTerm := [ + ⟨7, 1, 6, 5, 8, 1, -1131992571294488041751294502688298941972368850944000000⟩, + ⟨7, 1, 6, 6, 7, 1, -1069050099893264589089437792669496606474398334976000000⟩, + ⟨7, 1, 7, 6, 8, 1, -1172802464787644297254628681861169930550332358656000000⟩, + ⟨7, 1, 6, 7, 6, 1, 1157054140380908525278918483695465437638730711040000000⟩, + ⟨7, 1, 7, 7, 7, 1, 414506672022100744261492386525487394108901163008000000⟩, + ⟨7, 1, 8, 7, 8, 1, 5561110221034696586479447003696785305661289267200000000⟩ +] + +def collectedFourData_14_7_37 : List CollectedFourTerm := [ + ⟨7, 2, 5, 4, 8, 2, -85343736479480460364308381270605078765997391872000000⟩, + ⟨7, 2, 5, 5, 7, 2, 2903260683306647443524456106645033656294309888000000⟩, + ⟨7, 2, 6, 5, 8, 2, -120211524792312738571332733068759199268443521024000000⟩, + ⟨7, 2, 5, 6, 6, 2, -27615189986430880665967729917006375005498376192000000⟩, + ⟨7, 2, 6, 6, 7, 2, -113527372746433980104978759152433576842201399296000000⟩, + ⟨7, 2, 7, 6, 8, 2, -62272658031263830522720627237450055219347980288000000⟩, + ⟨7, 2, 5, 7, 5, 2, 31230028127858242746156484629132396928771817472000000⟩, + ⟨7, 2, 6, 7, 6, 2, 122872928683083275125787515031282258223657123840000000⟩, + ⟨7, 2, 7, 7, 7, 2, 22009189964640201737105680122429844517535350784000000⟩, + ⟨7, 2, 8, 7, 8, 2, 196853335189948386650800375963734504070604390400000000⟩ +] + +def collectedFourData_14_7_38 : List CollectedFourTerm := [ + ⟨7, 3, 4, 3, 8, 3, 24072188722347339529470765072474566563829750169600000⟩, + ⟨7, 3, 4, 4, 7, 3, 54855357332113636974029253396348670387418667417600000⟩, + ⟨7, 3, 5, 4, 8, 3, -238346081027967710568059882461850266876778643456000000⟩, + ⟨7, 3, 4, 5, 6, 3, -50317655905615228839749885029921746800394161356800000⟩, + ⟨7, 3, 5, 5, 7, 3, 8108161589984929204797110684865290146387329024000000⟩, + ⟨7, 3, 6, 5, 8, 3, -167862030715827777720943103317605906027355570176000000⟩, + ⟨7, 3, 4, 6, 5, 3, 81644605799876780771671439742773780980542367334400000⟩, + ⟨7, 3, 5, 6, 6, 3, -77123085789560050966602398374853397876169506816000000⟩, + ⟨7, 3, 6, 6, 7, 3, -158528355446563464746541227304023555496952725504000000⟩, + ⟨7, 3, 7, 6, 8, 3, -57971229482143121233533173518025307073605009408000000⟩, + ⟨7, 3, 4, 7, 4, 3, 337650522632232564847896800029069881931285187788800000⟩, + ⟨7, 3, 5, 7, 5, 3, 87218525011005294462766675352764546397824352256000000⟩, + ⟨7, 3, 6, 7, 6, 3, 171578385386742957335111874902700444348485468160000000⟩, + ⟨7, 3, 7, 7, 7, 3, 20488924714208863752427680014849755236683218944000000⟩, + ⟨7, 3, 8, 7, 8, 3, 137441899415460042765065223186557605149199564800000000⟩ +] + +def collectedFourData_14_7_39 : List CollectedFourTerm := [ + ⟨7, 4, 3, 2, 8, 4, 21303520813881672179046156941666358622144167936000000⟩, + ⟨7, 4, 3, 3, 7, 4, 53192535861264495332814435163238266417621814476800000⟩, + ⟨7, 4, 4, 3, 8, 4, 30900636749051553870795216840885919621252015718400000⟩, + ⟨7, 4, 3, 4, 6, 4, 122183922481120253626360159853435246446168453939200000⟩, + ⟨7, 4, 4, 4, 7, 4, 70415926453977017793101296834864191822344119910400000⟩, + ⟨7, 4, 5, 4, 8, 4, -152978313591566390638950835867770296009974874112000000⟩, + ⟨7, 4, 3, 5, 5, 4, 40155987604827645136082917369787977590590826086400000⟩, + ⟨7, 4, 4, 5, 6, 4, -64591035951780615391079993838936740020624765747200000⟩, + ⟨7, 4, 5, 5, 7, 4, 5204083411039016635088175930496518534199246848000000⟩, + ⟨7, 4, 6, 5, 8, 4, -71826229221560191949286323951384026141182394368000000⟩, + ⟨7, 4, 3, 6, 4, 4, -189456335358850026499517881167151502769755101593600000⟩, + ⟨7, 4, 4, 6, 5, 4, 104804358899006200236327406289011865783608383897600000⟩, + ⟨7, 4, 5, 6, 6, 4, -49500119960773301224893653789274250357959032832000000⟩, + ⟨7, 4, 6, 6, 7, 4, -67832457095064801279671954296770900358827343872000000⟩, + ⟨7, 4, 7, 6, 8, 4, -18603915962787177990886796535660200675883614208000000⟩, + ⟨7, 4, 3, 7, 3, 4, 337650522632232564847896800029069881931285187788800000⟩, + ⟨7, 4, 4, 7, 4, 4, 433430306995724687214459964134977961699243668275200000⟩, + ⟨7, 4, 5, 7, 5, 4, 55979703180275157460482482824422240153828851712000000⟩, + ⟨7, 4, 6, 7, 6, 4, 73416414573920524645361308967913535331767418880000000⟩, + ⟨7, 4, 7, 7, 7, 4, 6575231144069975341109313875318615772279865344000000⟩, + ⟨7, 4, 8, 7, 8, 4, 35285883281515517587190426203800243250491555840000000⟩ +] + +def collectedFourData_14_7_40 : List CollectedFourTerm := [ + ⟨7, 5, 2, 1, 8, 5, 10762033369762710657962007090278566932309344256000000⟩, + ⟨7, 5, 2, 2, 7, 5, 13081716177721179728027958960275383187083886592000000⟩, + ⟨7, 5, 3, 2, 8, 5, 5502913629284687715250390881972982676528824320000000⟩, + ⟨7, 5, 2, 3, 6, 5, 5196749519494795630892663534333959325016391680000000⟩, + ⟨7, 5, 3, 3, 7, 5, 13740166854317827787716356173337004797975330816000000⟩, + ⟨7, 5, 4, 3, 8, 5, 3990972586304333649342669802434154279420821504000000⟩, + ⟨7, 5, 2, 4, 5, 5, 2413470416122496276553165587358437405274144768000000⟩, + ⟨7, 5, 3, 4, 6, 5, 31561335714174357727898429855788431514590511104000000⟩, + ⟨7, 5, 4, 4, 7, 5, 9094570911250562341031350331177998099912065024000000⟩, + ⟨7, 5, 5, 4, 8, 5, -13171945523350171425474054160776940808023572480000000⟩, + ⟨7, 5, 2, 5, 4, 5, -12796783239039398209940469704238912919144759296000000⟩, + ⟨7, 5, 3, 5, 5, 5, 10372695359539005138809443286407199229286023168000000⟩, + ⟨7, 5, 4, 5, 6, 5, -8342257018780244422514447423901304616524972032000000⟩, + ⟨7, 5, 5, 5, 7, 5, 448089023730454255944407105161141044557905920000000⟩, + ⟨7, 5, 6, 5, 8, 5, -4638359301926949005793017734711518845510615040000000⟩, + ⟨7, 5, 2, 6, 3, 5, -6457029738706874339455925350374035683194961920000000⟩, + ⟨7, 5, 3, 6, 4, 5, -48938476372468837259032911501617562180944658432000000⟩, + ⟨7, 5, 4, 6, 5, 5, 13536009846268703732829526633524967806081171456000000⟩, + ⟨7, 5, 5, 6, 6, 5, -4262126233548370453184259713508679536114401280000000⟩, + ⟨7, 5, 6, 6, 7, 5, -4380451427693925456307326313637622453538652160000000⟩, + ⟨7, 5, 7, 6, 8, 5, -961115710441431435411004405182824823172104192000000⟩, + ⟨7, 5, 2, 7, 2, 5, 31230028127858242746156484629132396928771817472000000⟩, + ⟨7, 5, 3, 7, 3, 5, 87218525011005294462766675352764546397824352256000000⟩, + ⟨7, 5, 4, 7, 4, 5, 55979703180275157460482482824422240153828851712000000⟩, + ⟨7, 5, 5, 7, 5, 5, 4820040065760974957559000513968790055661076480000000⟩, + ⟨7, 5, 6, 7, 6, 5, 4741049518312337526496651147657214035388006400000000⟩, + ⟨7, 5, 7, 7, 7, 5, 339689663455277445148404554082143993233145856000000⟩, + ⟨7, 5, 8, 7, 8, 5, 1519116407467830287594790890159594103688396800000000⟩ +] + +def collectedFourData_14_7_41 : List CollectedFourTerm := [ + ⟨7, 6, 1, 0, 8, 6, -7342827568861699372892355469871245032758968320000000⟩, + ⟨7, 6, 1, 1, 7, 6, -77001991004145584802832498327998719070641848320000000⟩, + ⟨7, 6, 2, 1, 8, 6, 42342663071386213022002791675738030585749176320000000⟩, + ⟨7, 6, 1, 2, 6, 6, -91310045557595856896276581086930299407910830080000000⟩, + ⟨7, 6, 2, 2, 7, 6, 51469334973913328757277096054155612858341130240000000⟩, + ⟨7, 6, 3, 2, 8, 6, 10825464376016804815341693973038848263009075200000000⟩, + ⟨7, 6, 1, 3, 5, 6, -75436184063528196513283650945474963480804065280000000⟩, + ⟨7, 6, 2, 3, 6, 6, 20446341914214676784013206297724201257769369600000000⟩, + ⟨7, 6, 3, 3, 7, 6, 27029987534309058309588123659870299873880309760000000⟩, + ⟨7, 6, 4, 3, 8, 6, 5234091667218993110785291148372957687929896960000000⟩, + ⟨7, 6, 1, 4, 4, 6, 84964861325589909894915617886715623418846248960000000⟩, + ⟨7, 6, 2, 4, 5, 6, 9495674390841102003837908220578910004272168960000000⟩, + ⟨7, 6, 3, 4, 6, 6, 62088220613724929060516623436857414100912701440000000⟩, + ⟨7, 6, 4, 4, 7, 6, 11927372787992112854299693769020151357516021760000000⟩, + ⟨7, 6, 5, 4, 8, 6, -12956084415629525493904470459666550653085286400000000⟩, + ⟨7, 6, 1, 5, 3, 6, 162261232575508509215591425447314024409344245760000000⟩, + ⟨7, 6, 2, 5, 4, 6, -50348281079540518737016516752746020529630085120000000⟩, + ⟨7, 6, 3, 5, 5, 6, 20405416414387839152659607378216221139250708480000000⟩, + ⟨7, 6, 4, 5, 6, 6, -10940726102112896234888993648045815727055175680000000⟩, + ⟨7, 6, 5, 5, 7, 6, 440745765830666230974835025098456962800025600000000⟩, + ⟨7, 6, 6, 5, 8, 6, -3649876902952835612969872655498600660084981760000000⟩, + ⟨7, 6, 1, 6, 2, 6, -404341777926188971548329384896370602947945431040000000⟩, + ⟨7, 6, 2, 6, 3, 6, -25404849183627316359364083074121869916792422400000000⟩, + ⟨7, 6, 3, 6, 4, 6, -96272950708762392715841478256933652957516267520000000⟩, + ⟨7, 6, 4, 6, 5, 6, 17752243297004361123956176439057531593493053440000000⟩, + ⟨7, 6, 5, 6, 6, 6, -4192278746828354421720860805193463434208870400000000⟩, + ⟨7, 6, 6, 6, 7, 6, -3446931867439585767941357195087762064188375040000000⟩, + ⟨7, 6, 7, 6, 8, 6, -630243333231348632939269428228688496862167040000000⟩, + ⟨7, 6, 1, 7, 1, 6, 1157054140380908525278918483695465437638730711040000000⟩, + ⟨7, 6, 2, 7, 2, 6, 122872928683083275125787515031282258223657123840000000⟩, + ⟨7, 6, 3, 7, 3, 6, 171578385386742957335111874902700444348485468160000000⟩, + ⟨7, 6, 4, 7, 4, 6, 73416414573920524645361308967913535331767418880000000⟩, + ⟨7, 6, 5, 7, 5, 6, 4741049518312337526496651147657214035388006400000000⟩, + ⟨7, 6, 6, 7, 6, 6, 3730682770835590965818196316647162916739481600000000⟩, + ⟨7, 6, 7, 7, 7, 6, 222748565479135570199801637732630953428254720000000⟩, + ⟨7, 6, 8, 7, 8, 6, 853840692919475677526891011467665712611328000000000⟩ +] + +def collectedFourData_14_7_42 : List CollectedFourTerm := [ + ⟨7, 7, 0, 0, 7, 7, -22860819626933384194954670262325755755580358656000000⟩, + ⟨7, 7, 1, 0, 8, 7, -2630517373887974936047075211833472619657560064000000⟩, + ⟨7, 7, 0, 1, 6, 7, -2876154993616373387977734518990496980803780608000000⟩, + ⟨7, 7, 1, 1, 7, 7, -27585432622622653950713205322953356882491736064000000⟩, + ⟨7, 7, 2, 1, 8, 7, 7584483621697863252811401233314511529109880832000000⟩, + ⟨7, 7, 0, 2, 5, 7, 13910375564109126163587617684547997839988359168000000⟩, + ⟨7, 7, 1, 2, 6, 7, -32711194563294583646035080129138780705040367616000000⟩, + ⟨7, 7, 2, 2, 7, 7, 9219267278281436477528885619966201513507815424000000⟩, + ⟨7, 7, 3, 2, 8, 7, 1292716003222722594637628358811829071962439680000000⟩, + ⟨7, 7, 0, 3, 4, 7, -8833890495057699688462033653207737249537458176000000⟩, + ⟨7, 7, 1, 3, 5, 7, -27024493076811293655312950138425034243787718656000000⟩, + ⟨7, 7, 2, 3, 6, 7, 3662380543012901106653302555691644355566632960000000⟩, + ⟨7, 7, 3, 3, 7, 7, 3227768919541616356862158863070664704219152384000000⟩, + ⟨7, 7, 4, 3, 8, 7, 468769317337933887317529199077637591450779648000000⟩, + ⟨7, 7, 0, 4, 3, 7, -33902242206616497901268897259896417627796406272000000⟩, + ⟨7, 7, 1, 4, 4, 7, 30438076039635834155613583437427102473353428992000000⟩, + ⟨7, 7, 2, 4, 5, 7, 1700879955823534148725026574789199688678506496000000⟩, + ⟨7, 7, 3, 4, 6, 7, 7414225719203507740034065014480547082661789696000000⟩, + ⟨7, 7, 4, 4, 7, 7, 1068224776130612259123377463401010923084709888000000⟩, + ⟨7, 7, 5, 4, 8, 7, -928285591163787552392024925335955965850157056000000⟩, + ⟨7, 7, 0, 5, 2, 7, 57217092204909440645212341220687589409338425344000000⟩, + ⟨7, 7, 1, 5, 3, 7, 58128968356602825218397717824212204095748964352000000⟩, + ⟨7, 7, 2, 5, 4, 7, -9018462362289816359661670433383481846595059712000000⟩, + ⟨7, 7, 3, 5, 5, 7, 2436699935916156777461511878746145780957970432000000⟩, + ⟨7, 7, 4, 5, 6, 7, -979859932180701364854800670033729640867037184000000⟩, + ⟨7, 7, 5, 5, 7, 7, 31578826647153842422290010704005082774503424000000⟩, + ⟨7, 7, 6, 5, 8, 7, -217923874595769778001522416844969777238638592000000⟩, + ⟨7, 7, 0, 6, 1, 7, -41589063441150984629880830626766731614942658560000000⟩, + ⟨7, 7, 1, 6, 2, 7, -144852655444894130104866679302956307409438507008000000⟩, + ⟨7, 7, 2, 6, 3, 7, -4550556072018397800312603050225516893427466240000000⟩, + ⟨7, 7, 3, 6, 4, 7, -11496373710712057155108904447806782719779667968000000⟩, + ⟨7, 7, 4, 6, 5, 7, 1589904705657396909078137843403416055287119872000000⟩, + ⟨7, 7, 5, 6, 6, 7, -300370994042635699856503845895085510325436416000000⟩, + ⟨7, 7, 6, 6, 7, 7, -205806597864260510648494173546020728070995968000000⟩, + ⟨7, 7, 7, 6, 8, 7, -32254332977988458293151423281111617182367744000000⟩, + ⟨7, 7, 0, 7, 0, 7, 405630173506473303894157543181417385599422169088000000⟩, + ⟨7, 7, 1, 7, 1, 7, 414506672022100744261492386525487394108901163008000000⟩, + ⟨7, 7, 2, 7, 2, 7, 22009189964640201737105680122429844517535350784000000⟩, + ⟨7, 7, 3, 7, 3, 7, 20488924714208863752427680014849755236683218944000000⟩, + ⟨7, 7, 4, 7, 4, 7, 6575231144069975341109313875318615772279865344000000⟩, + ⟨7, 7, 5, 7, 5, 7, 339689663455277445148404554082143993233145856000000⟩, + ⟨7, 7, 6, 7, 6, 7, 222748565479135570199801637732630953428254720000000⟩, + ⟨7, 7, 7, 7, 7, 7, 11399734074927518511455489241906933443592192000000⟩, + ⟨7, 7, 8, 7, 8, 7, 38235318005796067709245167705350380663603200000000⟩ +] + +def collectedFourData_14_7_43 : List CollectedFourTerm := [ + ⟨7, 8, 0, 0, 7, 8, -613411297185544067839541072561022856919305420800000000⟩, + ⟨7, 8, 1, 0, 8, 8, -35291584048996431173832032136690940895664537600000000⟩, + ⟨7, 8, 0, 1, 6, 8, -77174221849086147838732575477849501974554214400000000⟩, + ⟨7, 8, 1, 1, 7, 8, -370092067664357129863917194019715482142742937600000000⟩, + ⟨7, 8, 2, 1, 8, 8, 67836703623507058922103115685353142374052659200000000⟩, + ⟨7, 8, 0, 2, 5, 8, 373249151096289242839151249324390504928274022400000000⟩, + ⟨7, 8, 1, 2, 6, 8, -438860386832308856449567640606342316026127974400000000⟩, + ⟨7, 8, 2, 2, 7, 8, 82458441889636677001490523163817762770806374400000000⟩, + ⟨7, 8, 3, 2, 8, 8, 8671677277650314093645094503802335611846656000000000⟩, + ⟨7, 8, 0, 3, 4, 8, -237034730871339545452367968891449662816177356800000000⟩, + ⟨7, 8, 1, 3, 5, 8, -362566382670249742070946745129136527801476710400000000⟩, + ⟨7, 8, 2, 3, 6, 8, 32756854104360022298581104638618611614744576000000000⟩, + ⟨7, 8, 3, 3, 7, 8, 21652219302086338428686575388081615276920012800000000⟩, + ⟨7, 8, 4, 3, 8, 8, 2515643793368370530466239130013927935867617280000000⟩, + ⟨7, 8, 0, 4, 3, 8, -909679473825968213505920120113324255922985369600000000⟩, + ⟨7, 8, 1, 4, 4, 8, 408363742245444466923292971757868437757283532800000000⟩, + ⟨7, 8, 2, 4, 5, 8, 15212912996776360543720490483362424115796377600000000⟩, + ⟨7, 8, 3, 4, 6, 8, 49735419489125342260191806373732868720636723200000000⟩, + ⟨7, 8, 4, 4, 7, 8, 5732612883573281435912273865559179964113223680000000⟩, + ⟨7, 8, 5, 4, 8, 8, -4151359384942083785210939288135490807319756800000000⟩, + ⟨7, 8, 0, 5, 2, 8, 1535273508271255093092444632186669371636265779200000000⟩, + ⟨7, 8, 1, 5, 3, 8, 779870679738710450689953049411805863998180556800000000⟩, + ⟨7, 8, 2, 5, 4, 8, -80662414071302835392133568635681850415854387200000000⟩, + ⟨7, 8, 3, 5, 5, 8, 16345643911004920847809096424683835054515814400000000⟩, + ⟨7, 8, 4, 5, 6, 8, -5258404220564079467132666714605179403228938240000000⟩, + ⟨7, 8, 5, 5, 7, 8, 141222765509877153815270238656805572129587200000000⟩, + ⟨7, 8, 6, 5, 8, 8, -835346668510769923179188586022824062012620800000000⟩, + ⟨7, 8, 0, 6, 1, 8, -1115935551326969559851315781037644170089463808000000000⟩, + ⟨7, 8, 1, 6, 2, 8, -1943374225579818713054596650950985685534978867200000000⟩, + ⟨7, 8, 2, 6, 3, 8, -40700822755624602921088982369382973984210944000000000⟩, + ⟨7, 8, 3, 6, 4, 8, -77118905029430542872302120629977751691565465600000000⟩, + ⟨7, 8, 4, 6, 5, 8, 8532200715583261614119534989442007386994769920000000⟩, + ⟨7, 8, 5, 6, 6, 8, -1343280512972290468669278619392051830901964800000000⟩, + ⟨7, 8, 6, 6, 7, 8, -788898674834698311499056746119098671510323200000000⟩, + ⟨7, 8, 7, 6, 8, 8, -108182758507554506125338823633039190812262400000000⟩, + ⟨7, 8, 0, 7, 0, 8, 10884042434552915293747245526142109512785880678400000000⟩, + ⟨7, 8, 1, 7, 1, 8, 5561110221034696586479447003696785305661289267200000000⟩, + ⟨7, 8, 2, 7, 2, 8, 196853335189948386650800375963734504070604390400000000⟩, + ⟨7, 8, 3, 7, 3, 8, 137441899415460042765065223186557605149199564800000000⟩, + ⟨7, 8, 4, 7, 4, 8, 35285883281515517587190426203800243250491555840000000⟩, + ⟨7, 8, 5, 7, 5, 8, 1519116407467830287594790890159594103688396800000000⟩, + ⟨7, 8, 6, 7, 6, 8, 853840692919475677526891011467665712611328000000000⟩, + ⟨7, 8, 7, 7, 7, 8, 38235318005796067709245167705350380663603200000000⟩, + ⟨7, 8, 8, 7, 8, 8, 113994046480608959059192633047388929392640000000000⟩ +] + +def collectedFourData_14_7 : List (List CollectedFourTerm) := [ + collectedFourData_14_7_0, + collectedFourData_14_7_1, + collectedFourData_14_7_2, + collectedFourData_14_7_3, + collectedFourData_14_7_4, + collectedFourData_14_7_5, + collectedFourData_14_7_6, + collectedFourData_14_7_7, + collectedFourData_14_7_8, + collectedFourData_14_7_9, + collectedFourData_14_7_10, + collectedFourData_14_7_11, + collectedFourData_14_7_12, + collectedFourData_14_7_13, + collectedFourData_14_7_14, + collectedFourData_14_7_15, + collectedFourData_14_7_16, + collectedFourData_14_7_17, + collectedFourData_14_7_18, + collectedFourData_14_7_19, + collectedFourData_14_7_20, + collectedFourData_14_7_21, + collectedFourData_14_7_22, + collectedFourData_14_7_23, + collectedFourData_14_7_24, + collectedFourData_14_7_25, + collectedFourData_14_7_26, + collectedFourData_14_7_27, + collectedFourData_14_7_28, + collectedFourData_14_7_29, + collectedFourData_14_7_30, + collectedFourData_14_7_31, + collectedFourData_14_7_32, + collectedFourData_14_7_33, + collectedFourData_14_7_34, + collectedFourData_14_7_35, + collectedFourData_14_7_36, + collectedFourData_14_7_37, + collectedFourData_14_7_38, + collectedFourData_14_7_39, + collectedFourData_14_7_40, + collectedFourData_14_7_41, + collectedFourData_14_7_42, + collectedFourData_14_7_43 +] + +theorem collectedFourChecked_14_7 : collectNumericRowParts 14 7 = collectedFourData_14_7 := by + decide +kernel + +def collectedFourData_14 : Fin 8 → List (List CollectedFourTerm) := + ![collectedFourData_14_0, collectedFourData_14_1, collectedFourData_14_2, collectedFourData_14_3, collectedFourData_14_4, collectedFourData_14_5, collectedFourData_14_6, collectedFourData_14_7] + +theorem collectedFourChecked_14 (t : Fin 8) : + collectNumericRowParts 14 t = collectedFourData_14 t := by + fin_cases t + · exact collectedFourChecked_14_0 + · exact collectedFourChecked_14_1 + · exact collectedFourChecked_14_2 + · exact collectedFourChecked_14_3 + · exact collectedFourChecked_14_4 + · exact collectedFourChecked_14_5 + · exact collectedFourChecked_14_6 + · exact collectedFourChecked_14_7 + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1501.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1501.lean new file mode 100644 index 0000000000000000000000000000000000000000..6ff0fd4221781f80fdf99cefe0e48b31e6d20c34 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1501.lean @@ -0,0 +1,631 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1501. -/ +namespace LaughlinFock + +def collectedFourData_15_0 : List CollectedFourTerm := [ + ⟨0, 7, 8, 0, 8, 7, -13177194842931889668021546999633379201382350848000000⟩, + ⟨0, 7, 8, 1, 7, 7, -11011058674622114833276877843493891204930600960000000⟩, + ⟨0, 7, 8, 2, 6, 7, -599183502603831215773634362880408003857612800000000⟩, + ⟨0, 7, 8, 3, 5, 7, -9533469952197377459024617059643225905309941760000000⟩, + ⟨0, 7, 8, 4, 4, 7, 13639480822717363251819643263720292217278955520000000⟩, + ⟨0, 7, 8, 5, 3, 7, -19079371925197049427108657287351822932613529600000000⟩, + ⟨0, 7, 8, 6, 2, 7, 68039836649931788961168040787135088446964498432000000⟩, + ⟨0, 7, 8, 7, 1, 7, -127219556874377504612441478416848717549519503360000000⟩, + ⟨0, 8, 7, 0, 7, 8, -13177194842931889668021546999633379201382350848000000⟩, + ⟨0, 8, 8, 0, 8, 8, 1776811014008272299282632747754600397148736454656000000⟩, + ⟨0, 8, 7, 1, 6, 8, -912050077574407769647017637405402296765898555392000000⟩, + ⟨0, 8, 8, 1, 7, 8, 1484729531752665465069660046362856938890455941120000000⟩, + ⟨0, 8, 7, 2, 5, 8, 92500175870666554457060027171581658016283361280000000⟩, + ⟨0, 8, 8, 2, 6, 8, 80793815339962223371593031887229049751837081600000000⟩, + ⟨0, 8, 7, 3, 4, 8, -371656081190464059439842081399593051148106334208000000⟩, + ⟨0, 8, 8, 3, 5, 8, 1285491685801945514514871639638059077614667038720000000⟩, + ⟨0, 8, 7, 4, 3, 8, 1318185678695117750839667734144967068396485083136000000⟩, + ⟨0, 8, 8, 4, 4, 8, -1839145587511602003168419557511311429272537661440000000⟩, + ⟨0, 8, 7, 5, 2, 8, -2560449098342602061593065792297168903993487785984000000⟩, + ⟨0, 8, 8, 5, 3, 8, 2572659703459888843319973125061704402401964851200000000⟩, + ⟨0, 8, 7, 6, 1, 8, 7034750985813006015576061313323760654751941787648000000⟩, + ⟨0, 8, 8, 6, 2, 8, -9174481563939897177696063025903836319022007189504000000⟩, + ⟨0, 8, 7, 7, 0, 8, -23845429885021395274512712180507590858189947535360000000⟩, + ⟨0, 8, 8, 7, 1, 8, 17154266332556660186363142701371221100703168593920000000⟩ +] + +def collectedFourData_15_1 : List CollectedFourTerm := [ + ⟨1, 6, 8, 0, 8, 7, -912050077574407769647017637405402296765898555392000000⟩, + ⟨1, 6, 8, 1, 7, 7, -762122518341012577533123653619599880503521443840000000⟩, + ⟨1, 6, 8, 2, 6, 7, -41472055816512319872569793175074980349817651200000000⟩, + ⟨1, 6, 8, 3, 5, 7, -659852276079746391021817200976482577037698007040000000⟩, + ⟨1, 6, 8, 4, 4, 7, 944046869664877551304454062126517115122960302080000000⟩, + ⟨1, 6, 8, 5, 3, 7, -1320565025551006855236118808070888378060924518400000000⟩, + ⟨1, 6, 8, 6, 2, 7, 4709328429487887091019147006605555957019839561728000000⟩, + ⟨1, 6, 8, 7, 1, 7, -8805410263664378886410221730355469578828974653440000000⟩, + ⟨1, 7, 7, 0, 7, 8, -11011058674622114833276877843493891204930600960000000⟩, + ⟨1, 7, 8, 0, 8, 8, 1484729531752665465069660046362856938890455941120000000⟩, + ⟨1, 7, 7, 1, 6, 8, -762122518341012577533123653619599880503521443840000000⟩, + ⟨1, 7, 8, 1, 7, 8, 1240661930322898212671621764990128982015239782400000000⟩, + ⟨1, 7, 7, 2, 5, 8, 77294513442752980705596498306704865173805465600000000⟩, + ⟨1, 7, 8, 2, 6, 8, 67512505647747492187589997066916357767954432000000000⟩, + ⟨1, 7, 7, 3, 4, 8, -310561311838187010316747339491090705863053148160000000⟩, + ⟨1, 7, 8, 3, 5, 8, 1074175842948585648589117018433585791688402534400000000⟩, + ⟨1, 7, 7, 4, 3, 8, 1101495426391452910743618191714397600011224350720000000⟩, + ⟨1, 7, 8, 4, 4, 8, -1536817222227309232659434957153002384563948748800000000⟩, + ⟨1, 7, 7, 5, 2, 8, -2139549091539482688733959181628817347534577991680000000⟩, + ⟨1, 7, 8, 5, 3, 8, 2149752453560133411096574640679091831648026624000000000⟩, + ⟨1, 7, 7, 6, 1, 8, 5878341846610209494430698169008427468382493736960000000⟩, + ⟨1, 7, 8, 6, 2, 8, -7666332327473138505945665970694741641014626222080000000⟩, + ⟨1, 7, 7, 7, 0, 8, -19925593475336258374001962529758023221874209587200000000⟩, + ⟨1, 7, 8, 7, 1, 8, 14334358363775195426686067046041937369847195238400000000⟩ +] + +def collectedFourData_15_2 : List CollectedFourTerm := [ + ⟨2, 5, 8, 0, 8, 7, 92500175870666554457060027171581658016283361280000000⟩, + ⟨2, 5, 8, 1, 7, 7, 77294513442752980705596498306704865173805465600000000⟩, + ⟨2, 5, 8, 2, 6, 7, 4206098492911452018498531403212079610462208000000000⟩, + ⟨2, 5, 8, 3, 5, 7, 66922259080731920394141848602183497032505753600000000⟩, + ⟨2, 5, 8, 4, 4, 7, -95745292524279409904871958269462517579461427200000000⟩, + ⟨2, 5, 8, 5, 3, 7, 133931787426610728708898824886508466110201856000000000⟩, + ⟨2, 5, 8, 6, 2, 7, -477620383651379938973752652792170876665090539520000000⟩, + ⟨2, 5, 8, 7, 1, 7, 893045259278406121475275112474146459415583129600000000⟩, + ⟨2, 6, 7, 0, 7, 8, -599183502603831215773634362880408003857612800000000⟩, + ⟨2, 6, 8, 0, 8, 8, 80793815339962223371593031887229049751837081600000000⟩, + ⟨2, 6, 7, 1, 6, 8, -41472055816512319872569793175074980349817651200000000⟩, + ⟨2, 6, 8, 1, 7, 8, 67512505647747492187589997066916357767954432000000000⟩, + ⟨2, 6, 7, 2, 5, 8, 4206098492911452018498531403212079610462208000000000⟩, + ⟨2, 6, 8, 2, 6, 8, 3673795662973937611179892237479343565045760000000000⟩, + ⟨2, 6, 7, 3, 4, 8, -16899666062930292922061969825659338305096908800000000⟩, + ⟨2, 6, 8, 3, 5, 8, 58452912023234218981784996008672479298977792000000000⟩, + ⟨2, 6, 7, 4, 3, 8, 59939548701930930975539573307518518967245209600000000⟩, + ⟨2, 6, 8, 4, 4, 8, -83628246228344748290059323524344473383337984000000000⟩, + ⟨2, 6, 7, 5, 2, 8, -116426817488143873249608319009306032673810022400000000⟩, + ⟨2, 6, 8, 5, 3, 8, 116982048949035004898322239321457383775928320000000000⟩, + ⟨2, 6, 7, 6, 1, 8, 319878910941817858707466063949034433106726092800000000⟩, + ⟨2, 6, 8, 6, 2, 8, -417175132005005050529970499425410967262357094400000000⟩, + ⟨2, 6, 7, 7, 0, 8, -1084281470366586629558495248756059787279466496000000000⟩, + ⟨2, 6, 8, 7, 1, 8, 780025909023693836170503905642795478665920512000000000⟩ +] + +def collectedFourData_15_3 : List CollectedFourTerm := [ + ⟨3, 4, 8, 0, 8, 7, -371656081190464059439842081399593051148106334208000000⟩, + ⟨3, 4, 8, 1, 7, 7, -310561311838187010316747339491090705863053148160000000⟩, + ⟨3, 4, 8, 2, 6, 7, -16899666062930292922061969825659338305096908800000000⟩, + ⟨3, 4, 8, 3, 5, 7, -268886673135992878261637104692328833706056744960000000⟩, + ⟨3, 4, 8, 4, 4, 7, 384694622221715566189201972411323540190443601920000000⟩, + ⟨3, 4, 8, 5, 3, 7, -538123985098210403273816947880646113159125401600000000⟩, + ⟨3, 4, 8, 6, 2, 7, 1919029000904306260846901288605434413572184604672000000⟩, + ⟨3, 4, 8, 7, 1, 7, -3588162922557074986790446864800249317442516418560000000⟩, + ⟨3, 5, 7, 0, 7, 8, -9533469952197377459024617059643225905309941760000000⟩, + ⟨3, 5, 8, 0, 8, 8, 1285491685801945514514871639638059077614667038720000000⟩, + ⟨3, 5, 7, 1, 6, 8, -659852276079746391021817200976482577037698007040000000⟩, + ⟨3, 5, 8, 1, 7, 8, 1074175842948585648589117018433585791688402534400000000⟩, + ⟨3, 5, 7, 2, 5, 8, 66922259080731920394141848602183497032505753600000000⟩, + ⟨3, 5, 8, 2, 6, 8, 58452912023234218981784996008672479298977792000000000⟩, + ⟨3, 5, 7, 3, 4, 8, -268886673135992878261637104692328833706056744960000000⟩, + ⟨3, 5, 8, 3, 5, 8, 930030746791754361799241628950883382713542246400000000⟩, + ⟨3, 5, 7, 4, 3, 8, 953684278714111713263457539742658797148380856320000000⟩, + ⟨3, 5, 8, 4, 4, 8, -1330589659275092570235043944191387293778234572800000000⟩, + ⟨3, 5, 7, 5, 2, 8, -1852440131161399341614568895607840072796293038080000000⟩, + ⟨3, 5, 8, 5, 3, 8, 1861274290356232973406148787302875469807878144000000000⟩, + ⟨3, 5, 7, 6, 1, 8, 5089519275068809974200059543159518364503386357760000000⟩, + ⟨3, 5, 8, 6, 2, 8, -6637576916738461852599415666560992498097303060480000000⟩, + ⟨3, 5, 7, 7, 0, 8, -17251751379241244144999152617498764071511733043200000000⟩, + ⟨3, 5, 8, 7, 1, 8, 12410811601616485957475452205740206243122144870400000000⟩ +] + +def collectedFourData_15_4 : List CollectedFourTerm := [ + ⟨4, 3, 8, 0, 8, 7, 1318185678695117750839667734144967068396485083136000000⟩, + ⟨4, 3, 8, 1, 7, 7, 1101495426391452910743618191714397600011224350720000000⟩, + ⟨4, 3, 8, 2, 6, 7, 59939548701930930975539573307518518967245209600000000⟩, + ⟨4, 3, 8, 3, 5, 7, 953684278714111713263457539742658797148380856320000000⟩, + ⟨4, 3, 8, 4, 4, 7, -1364430631834109727740331263789947008926236016640000000⟩, + ⟨4, 3, 8, 5, 3, 7, 1908612199339431456357372257349088766231524147200000000⟩, + ⟨4, 3, 8, 6, 2, 7, -6806390838244575514674821357889856907366130253824000000⟩, + ⟨4, 3, 8, 7, 1, 7, 12726456572940138558815426956265271851004482027520000000⟩, + ⟨4, 4, 7, 0, 7, 8, 13639480822717363251819643263720292217278955520000000⟩, + ⟨4, 4, 8, 0, 8, 8, -1839145587511602003168419557511311429272537661440000000⟩, + ⟨4, 4, 7, 1, 6, 8, 944046869664877551304454062126517115122960302080000000⟩, + ⟨4, 4, 8, 1, 7, 8, -1536817222227309232659434957153002384563948748800000000⟩, + ⟨4, 4, 7, 2, 5, 8, -95745292524279409904871958269462517579461427200000000⟩, + ⟨4, 4, 8, 2, 6, 8, -83628246228344748290059323524344473383337984000000000⟩, + ⟨4, 4, 7, 3, 4, 8, 384694622221715566189201972411323540190443601920000000⟩, + ⟨4, 4, 8, 3, 5, 8, -1330589659275092570235043944191387293778234572800000000⟩, + ⟨4, 4, 7, 4, 3, 8, -1364430631834109727740331263789947008926236016640000000⟩, + ⟨4, 4, 8, 4, 4, 8, 1903666999695696392706455813910967730606545305600000000⟩, + ⟨4, 4, 7, 5, 2, 8, 2650275479012160497253100989394769109246447452160000000⟩, + ⟨4, 4, 8, 5, 3, 8, -2662914459942183040793849042138190759579353088000000000⟩, + ⟨4, 4, 7, 6, 1, 8, -7281546057965085975458925562175412818153066987520000000⟩, + ⟨4, 4, 8, 6, 2, 8, 9496343253727741007942338716754773413299444776960000000⟩, + ⟨4, 4, 7, 7, 0, 8, 24681981825642943405764778658602061498937665126400000000⟩, + ⟨4, 4, 8, 7, 1, 8, -17756077030020891937442213115120805320338492620800000000⟩ +] + +def collectedFourData_15_5 : List CollectedFourTerm := [ + ⟨5, 2, 8, 0, 8, 7, -2560449098342602061593065792297168903993487785984000000⟩, + ⟨5, 2, 8, 1, 7, 7, -2139549091539482688733959181628817347534577991680000000⟩, + ⟨5, 2, 8, 2, 6, 7, -116426817488143873249608319009306032673810022400000000⟩, + ⟨5, 2, 8, 3, 5, 7, -1852440131161399341614568895607840072796293038080000000⟩, + ⟨5, 2, 8, 4, 4, 7, 2650275479012160497253100989394769109246447452160000000⟩, + ⟨5, 2, 8, 5, 3, 7, -3707295917311074550151551464215014559728848076800000000⟩, + ⟨5, 2, 8, 6, 2, 7, 13220760600283722275636697056351200316253857120256000000⟩, + ⟨5, 2, 8, 7, 1, 7, -24719919798808195053150448488242969999966082170880000000⟩, + ⟨5, 3, 7, 0, 7, 8, -19079371925197049427108657287351822932613529600000000⟩, + ⟨5, 3, 8, 0, 8, 8, 2572659703459888843319973125061704402401964851200000000⟩, + ⟨5, 3, 7, 1, 6, 8, -1320565025551006855236118808070888378060924518400000000⟩, + ⟨5, 3, 8, 1, 7, 8, 2149752453560133411096574640679091831648026624000000000⟩, + ⟨5, 3, 7, 2, 5, 8, 133931787426610728708898824886508466110201856000000000⟩, + ⟨5, 3, 8, 2, 6, 8, 116982048949035004898322239321457383775928320000000000⟩, + ⟨5, 3, 7, 3, 4, 8, -538123985098210403273816947880646113159125401600000000⟩, + ⟨5, 3, 8, 3, 5, 8, 1861274290356232973406148787302875469807878144000000000⟩, + ⟨5, 3, 7, 4, 3, 8, 1908612199339431456357372257349088766231524147200000000⟩, + ⟨5, 3, 8, 4, 4, 8, -2662914459942183040793849042138190759579353088000000000⟩, + ⟨5, 3, 7, 5, 2, 8, -3707295917311074550151551464215014559728848076800000000⟩, + ⟨5, 3, 8, 5, 3, 8, 3724975755792736821180116965324345621862154240000000000⟩, + ⟨5, 3, 7, 6, 1, 8, 10185675483994714706039821878218023091379476889600000000⟩, + ⟨5, 3, 8, 6, 2, 8, -13283809495551644216542518095083251737371135180800000000⟩, + ⟨5, 3, 7, 7, 0, 8, -34525999722662178793273469668091844708135862272000000000⟩, + ⟨5, 3, 8, 7, 1, 8, 24837807391023807865218596983534755250578653184000000000⟩ +] + +def collectedFourData_15_6 : List CollectedFourTerm := [ + ⟨6, 1, 8, 0, 8, 7, 7034750985813006015576061313323760654751941787648000000⟩, + ⟨6, 1, 8, 1, 7, 7, 5878341846610209494430698169008427468382493736960000000⟩, + ⟨6, 1, 8, 2, 6, 7, 319878910941817858707466063949034433106726092800000000⟩, + ⟨6, 1, 8, 3, 5, 7, 5089519275068809974200059543159518364503386357760000000⟩, + ⟨6, 1, 8, 4, 4, 7, -7281546057965085975458925562175412818153066987520000000⟩, + ⟨6, 1, 8, 5, 3, 7, 10185675483994714706039821878218023091379476889600000000⟩, + ⟨6, 1, 8, 6, 2, 7, -36323611637601522131480070398416803154692912709632000000⟩, + ⟨6, 1, 8, 7, 1, 7, 67917179172376513253054821457332632400394830479360000000⟩, + ⟨6, 2, 7, 0, 7, 8, 68039836649931788961168040787135088446964498432000000⟩, + ⟨6, 2, 8, 0, 8, 8, -9174481563939897177696063025903836319022007189504000000⟩, + ⟨6, 2, 7, 1, 6, 8, 4709328429487887091019147006605555957019839561728000000⟩, + ⟨6, 2, 8, 1, 7, 8, -7666332327473138505945665970694741641014626222080000000⟩, + ⟨6, 2, 7, 2, 5, 8, -477620383651379938973752652792170876665090539520000000⟩, + ⟨6, 2, 8, 2, 6, 8, -417175132005005050529970499425410967262357094400000000⟩, + ⟨6, 2, 7, 3, 4, 8, 1919029000904306260846901288605434413572184604672000000⟩, + ⟨6, 2, 8, 3, 5, 8, -6637576916738461852599415666560992498097303060480000000⟩, + ⟨6, 2, 7, 4, 3, 8, -6806390838244575514674821357889856907366130253824000000⟩, + ⟨6, 2, 8, 4, 4, 8, 9496343253727741007942338716754773413299444776960000000⟩, + ⟨6, 2, 7, 5, 2, 8, 13220760600283722275636697056351200316253857120256000000⟩, + ⟨6, 2, 8, 5, 3, 8, -13283809495551644216542518095083251737371135180800000000⟩, + ⟨6, 2, 7, 6, 1, 8, -36323611637601522131480070398416803154692912709632000000⟩, + ⟨6, 2, 8, 6, 2, 8, 47372011600261943315532723123726947113126053543936000000⟩, + ⟨6, 2, 7, 7, 0, 8, 123124775307888612663664748403832476326865131274240000000⟩, + ⟨6, 2, 8, 7, 1, 8, -88575261505117634852669594449526079592649226977280000000⟩ +] + +def collectedFourData_15_7 : List CollectedFourTerm := [ + ⟨7, 0, 8, 0, 8, 7, -23845429885021395274512712180507590858189947535360000000⟩, + ⟨7, 0, 8, 1, 7, 7, -19925593475336258374001962529758023221874209587200000000⟩, + ⟨7, 0, 8, 2, 6, 7, -1084281470366586629558495248756059787279466496000000000⟩, + ⟨7, 0, 8, 3, 5, 7, -17251751379241244144999152617498764071511733043200000000⟩, + ⟨7, 0, 8, 4, 4, 7, 24681981825642943405764778658602061498937665126400000000⟩, + ⟨7, 0, 8, 5, 3, 7, -34525999722662178793273469668091844708135862272000000000⟩, + ⟨7, 0, 8, 6, 2, 7, 123124775307888612663664748403832476326865131274240000000⟩, + ⟨7, 0, 8, 7, 1, 7, -230216298659244204447898219947783425187606901555200000000⟩, + ⟨7, 1, 7, 0, 7, 8, -127219556874377504612441478416848717549519503360000000⟩, + ⟨7, 1, 8, 0, 8, 8, 17154266332556660186363142701371221100703168593920000000⟩, + ⟨7, 1, 7, 1, 6, 8, -8805410263664378886410221730355469578828974653440000000⟩, + ⟨7, 1, 8, 1, 7, 8, 14334358363775195426686067046041937369847195238400000000⟩, + ⟨7, 1, 7, 2, 5, 8, 893045259278406121475275112474146459415583129600000000⟩, + ⟨7, 1, 8, 2, 6, 8, 780025909023693836170503905642795478665920512000000000⟩, + ⟨7, 1, 7, 3, 4, 8, -3588162922557074986790446864800249317442516418560000000⟩, + ⟨7, 1, 8, 3, 5, 8, 12410811601616485957475452205740206243122144870400000000⟩, + ⟨7, 1, 7, 4, 3, 8, 12726456572940138558815426956265271851004482027520000000⟩, + ⟨7, 1, 8, 4, 4, 8, -17756077030020891937442213115120805320338492620800000000⟩, + ⟨7, 1, 7, 5, 2, 8, -24719919798808195053150448488242969999966082170880000000⟩, + ⟨7, 1, 8, 5, 3, 8, 24837807391023807865218596983534755250578653184000000000⟩, + ⟨7, 1, 7, 6, 1, 8, 67917179172376513253054821457332632400394830479360000000⟩, + ⟨7, 1, 8, 6, 2, 8, -88575261505117634852669594449526079592649226977280000000⟩, + ⟨7, 1, 7, 7, 0, 8, -230216298659244204447898219947783425187606901555200000000⟩, + ⟨7, 1, 8, 7, 1, 8, 165616292947470946321788401739560716679883679334400000000⟩ +] + +def collectedFourData_15_8 : List CollectedFourTerm := [ + ⟨0, 7, 8, 1, 8, 6, -3538862759453807983213912896890377015753369976832000000⟩, + ⟨0, 7, 8, 2, 7, 6, -1519507483331109350334134193937116213658993557504000000⟩, + ⟨0, 7, 8, 3, 6, 6, 81595925184751403483850446238459648901046599680000000⟩, + ⟨0, 7, 8, 4, 5, 6, 1110612989152440058443592031152207408791275175936000000⟩, + ⟨0, 7, 8, 5, 4, 6, 555975416401194364122269014830425439829657387008000000⟩, + ⟨0, 7, 8, 6, 3, 6, -2951896308703131903123200206961769993630023417856000000⟩, + ⟨0, 7, 8, 7, 2, 6, 1161059416110746751484522564536606576394647896064000000⟩, + ⟨0, 8, 7, 0, 8, 7, 9079886857216165190331091096565608200106986700800000000⟩, + ⟨0, 8, 7, 1, 7, 7, -718306458824163993594572719780006438857867264000000000⟩, + ⟨0, 8, 8, 1, 8, 7, -10380549642594335736608257601697443174044265349120000000⟩, + ⟨0, 8, 7, 2, 6, 7, -450519776404736656347844668829839604296481505280000000⟩, + ⟨0, 8, 8, 2, 7, 7, -4457172808093478578038411445494514555441266032640000000⟩, + ⟨0, 8, 7, 3, 5, 7, -1080565554338986861807884200091140506045560913920000000⟩, + ⟨0, 8, 8, 3, 6, 7, 239345408281516373596235098950289515273309388800000000⟩, + ⟨0, 8, 7, 4, 4, 7, 558657669366841433320722072288925627689593733120000000⟩, + ⟨0, 8, 8, 4, 5, 7, 3257762182726281314704166547560247946427246837760000000⟩, + ⟨0, 8, 7, 5, 3, 7, 637251923092826133210744440210716813139210403840000000⟩, + ⟨0, 8, 8, 5, 4, 7, 1630843240415858540399972774367928659014351585280000000⟩, + ⟨0, 8, 7, 6, 2, 7, 4510148286475703049375915994020187692278313123840000000⟩, + ⟨0, 8, 8, 6, 3, 7, -8658800370380342883235953611926208198342564904960000000⟩, + ⟨0, 8, 7, 7, 1, 7, -23333413947531935407007144434325402806644973240320000000⟩, + ⟨0, 8, 8, 7, 2, 7, 3405736736962183451216768926145319109367420682240000000⟩, + ⟨1, 6, 8, 1, 8, 6, 1304089745088498192072555603934558039562866655232000000⟩, + ⟨1, 6, 8, 2, 7, 6, 559946587728982788923993081302186926555009122304000000⟩ +] + +def collectedFourData_15_9 : List CollectedFourTerm := [ + ⟨1, 6, 8, 3, 6, 6, -30068532324453808383650267361891865025241415680000000⟩, + ⟨1, 6, 8, 4, 5, 6, -409266792289882080157344129227831673458981339136000000⟩, + ⟨1, 6, 8, 5, 4, 6, -204879897394497705683496531679476140792094916608000000⟩, + ⟨1, 6, 8, 6, 3, 6, 1087789486738527261891217074363604003643568685056000000⟩, + ⟨1, 6, 8, 7, 2, 6, -427856568877555490275089093935353178592708132864000000⟩, + ⟨1, 7, 7, 0, 8, 7, -718306458824163993594572719780006438857867264000000000⟩, + ⟨1, 7, 7, 1, 7, 7, 56824955740329752592002646860173277260677120000000000⟩, + ⟨1, 7, 8, 1, 8, 7, 821201406105016989499950778248359042130483609600000000⟩, + ⟨1, 7, 7, 2, 6, 7, 35640451286279317040091250392833972253386342400000000⟩, + ⟨1, 7, 8, 2, 7, 7, 352605276529907831343395643793054873714635571200000000⟩, + ⟨1, 7, 7, 3, 5, 7, 85483137518145059847280518083605137586755993600000000⟩, + ⟨1, 7, 8, 3, 6, 7, -18934525877036132250419287783935581884514304000000000⟩, + ⟨1, 7, 7, 4, 4, 7, -44195199619578590605380349209124918011730329600000000⟩, + ⟨1, 7, 8, 4, 5, 7, -257720349819738292021188589519211466117139660800000000⟩, + ⟨1, 7, 7, 5, 3, 7, -50412761684569848885484866024841471147062067200000000⟩, + ⟨1, 7, 8, 5, 4, 7, -129015399788758781301257281845740528376112742400000000⟩, + ⟨1, 7, 7, 6, 2, 7, -356796146843562642969033324114689847121359667200000000⟩, + ⟨1, 7, 8, 6, 3, 7, 684994464085224861031418449789185147825605836800000000⟩, + ⟨1, 7, 7, 7, 1, 7, 1845897664639919991381530185454079397001271705600000000⟩, + ⟨1, 7, 8, 7, 2, 7, -269426561551308614626523091058625434929541939200000000⟩, + ⟨1, 8, 6, 0, 7, 8, -3538862759453807983213912896890377015753369976832000000⟩, + ⟨1, 8, 7, 0, 8, 8, -10380549642594335736608257601697443174044265349120000000⟩, + ⟨1, 8, 6, 1, 6, 8, 1304089745088498192072555603934558039562866655232000000⟩, + ⟨1, 8, 7, 1, 7, 8, 821201406105016989499950778248359042130483609600000000⟩ +] + +def collectedFourData_15_10 : List CollectedFourTerm := [ + ⟨1, 8, 8, 1, 8, 8, 5933763965171402408714202133720790067628405161984000000⟩, + ⟨1, 8, 6, 2, 5, 8, 23429324324181530912840722911506741425097146368000000⟩, + ⟨1, 8, 7, 2, 6, 8, 515055195894114668687938692769988221547097096192000000⟩, + ⟨1, 8, 8, 2, 7, 8, 2547823796023676003404893126541394866872986370048000000⟩, + ⟨1, 8, 6, 3, 4, 8, -379384312061128861620170465278930387527209582592000000⟩, + ⟨1, 8, 7, 3, 5, 8, 1235352879973257584089368241380071765728913522688000000⟩, + ⟨1, 8, 8, 3, 6, 8, -136815410338440778781075561540021286311464796160000000⟩, + ⟨1, 8, 6, 4, 3, 8, 479014337148089796026719780730692393956777394176000000⟩, + ⟨1, 8, 7, 4, 4, 8, -638683472742802404097887581852299685324094701568000000⟩, + ⟨1, 8, 8, 4, 5, 8, -1862212745232644225827074009585133508222603231232000000⟩, + ⟨1, 8, 6, 5, 2, 8, -1039813917774369498411410766439031916095229394944000000⟩, + ⟨1, 8, 7, 5, 3, 8, -728536084923409888644265978515005316407048011776000000⟩, + ⟨1, 8, 8, 5, 4, 8, -932227982718309231164475517685051687416256004096000000⟩, + ⟨1, 8, 6, 6, 1, 8, 1947366182553433510591208435055137928622016299008000000⟩, + ⟨1, 8, 7, 6, 2, 8, -5156211626801796564198915070783310513874483019776000000⟩, + ⟨1, 8, 8, 6, 3, 8, 4949571977244050799941002537983718388506948534272000000⟩, + ⟨1, 8, 6, 7, 0, 8, 577847610633190973602910533522694795103049875456000000⟩, + ⟨1, 8, 7, 7, 1, 8, 26675845814208688145902924355656984935260013723648000000⟩, + ⟨1, 8, 8, 7, 2, 8, -1946798447138487979652522801243024942114713632768000000⟩, + ⟨2, 5, 8, 1, 8, 6, 23429324324181530912840722911506741425097146368000000⟩, + ⟨2, 5, 8, 2, 7, 6, 10060020989760033978122444822661890980913872896000000⟩, + ⟨2, 5, 8, 3, 6, 6, -540212357650244710658952200928685063478968320000000⟩, + ⟨2, 5, 8, 4, 5, 6, -7352902242955959981982770617368336367735537664000000⟩, + ⟨2, 5, 8, 5, 4, 6, -3680879771993736634491661284281277331424673792000000⟩ +] + +def collectedFourData_15_11 : List CollectedFourTerm := [ + ⟨2, 5, 8, 6, 3, 6, 19543265927225258505286830799733427937417887744000000⟩, + ⟨2, 5, 8, 7, 2, 6, -7686886852854966534784898067001119928888590336000000⟩, + ⟨2, 6, 7, 0, 8, 7, -450519776404736656347844668829839604296481505280000000⟩, + ⟨2, 6, 7, 1, 7, 7, 35640451286279317040091250392833972253386342400000000⟩, + ⟨2, 6, 8, 1, 8, 7, 515055195894114668687938692769988221547097096192000000⟩, + ⟨2, 6, 7, 2, 6, 7, 22353590096826670581451271409715658160863182848000000⟩, + ⟨2, 6, 8, 2, 7, 7, 221153030701441986941388256378650834531646439424000000⟩, + ⟨2, 6, 7, 3, 5, 7, 53614781724352386275603919351081516140039503872000000⟩, + ⟨2, 6, 8, 3, 6, 7, -11875680998909395660274387448851810127792046080000000⟩, + ⟨2, 6, 7, 4, 4, 7, -27719104020543501372990475880878252442718830592000000⟩, + ⟨2, 6, 8, 4, 5, 7, -161641473425984325606015861846134779038155145216000000⟩, + ⟨2, 6, 7, 5, 3, 7, -31618741336749412108427452236422960365745209344000000⟩, + ⟨2, 6, 8, 5, 4, 7, -80918093317364461249575278412193761055733710848000000⟩, + ⟨2, 6, 7, 6, 2, 7, -223781532691720205511102961231054484051375161344000000⟩, + ⟨2, 6, 8, 6, 3, 7, 429626587659156412697272909550761877278593908736000000⟩, + ⟨2, 6, 7, 7, 1, 7, 1157741786842508423231170428549198514212267098112000000⟩, + ⟨2, 6, 8, 7, 2, 7, -168983576266722630738355048891157070965882486784000000⟩, + ⟨2, 7, 6, 0, 7, 8, -1519507483331109350334134193937116213658993557504000000⟩, + ⟨2, 7, 7, 0, 8, 8, -4457172808093478578038411445494514555441266032640000000⟩, + ⟨2, 7, 6, 1, 6, 8, 559946587728982788923993081302186926555009122304000000⟩, + ⟨2, 7, 7, 1, 7, 8, 352605276529907831343395643793054873714635571200000000⟩, + ⟨2, 7, 8, 1, 8, 8, 2547823796023676003404893126541394866872986370048000000⟩, + ⟨2, 7, 6, 2, 5, 8, 10060020989760033978122444822661890980913872896000000⟩, + ⟨2, 7, 7, 2, 6, 8, 221153030701441986941388256378650834531646439424000000⟩ +] + +def collectedFourData_15_12 : List CollectedFourTerm := [ + ⟨2, 7, 8, 2, 7, 8, 1093977807962400768392250948687982923619139321856000000⟩, + ⟨2, 7, 6, 3, 4, 8, -162899027292113554582098199933785749386086580224000000⟩, + ⟨2, 7, 7, 3, 5, 8, 530432535327739198530337759412324464037971623936000000⟩, + ⟨2, 7, 8, 3, 6, 8, -58745437157434010337561174507097545787331051520000000⟩, + ⟨2, 7, 6, 4, 3, 8, 205677902590309288687001162307888900713031401472000000⟩, + ⟨2, 7, 7, 4, 4, 8, -274236211539996110672275559812890367145118007296000000⟩, + ⟨2, 7, 8, 4, 5, 8, -799591957720423798879434411669739523420983394304000000⟩, + ⟨2, 7, 6, 5, 2, 8, -446472535593285624865840325031893379417970311168000000⟩, + ⟨2, 7, 7, 5, 3, 8, -312816887278422745049449314627195843679377948672000000⟩, + ⟨2, 7, 8, 5, 4, 8, -400277572823921370253559837115297471000804851712000000⟩, + ⟨2, 7, 6, 6, 1, 8, 836154914250638687444998680599951507304770174976000000⟩, + ⟨2, 7, 7, 6, 2, 8, -2213960440153788455184909239206050658320144924672000000⟩, + ⟨2, 7, 8, 6, 3, 8, 2125234056793170567931869282305512377724314845184000000⟩, + ⟨2, 7, 6, 7, 0, 8, 248114670803920367894451768119761051827025477632000000⟩, + ⟨2, 7, 7, 7, 1, 8, 11454003756035183673032105617444150047361839661056000000⟩, + ⟨2, 7, 8, 7, 2, 8, -835911141527535129306899395166853151242842013696000000⟩, + ⟨3, 4, 8, 1, 8, 6, -379384312061128861620170465278930387527209582592000000⟩, + ⟨3, 4, 8, 2, 7, 6, -162899027292113554582098199933785749386086580224000000⟩, + ⟨3, 4, 8, 3, 6, 6, 8747503378171711477477632527045149270820782080000000⟩, + ⟨3, 4, 8, 4, 5, 6, 119063431812988401496737963954433856608892092416000000⟩, + ⟨3, 4, 8, 5, 4, 6, 59603427770909573369769996157274164246188392448000000⟩, + ⟨3, 4, 8, 6, 3, 6, -316458485811970416416533531351751608331126439936000000⟩, + ⟨3, 4, 8, 7, 2, 6, 124471548569251942012000330222639551775279939584000000⟩, + ⟨3, 5, 7, 0, 8, 7, -1080565554338986861807884200091140506045560913920000000⟩ +] + +def collectedFourData_15_13 : List CollectedFourTerm := [ + ⟨3, 5, 7, 1, 7, 7, 85483137518145059847280518083605137586755993600000000⟩, + ⟨3, 5, 8, 1, 8, 7, 1235352879973257584089368241380071765728913522688000000⟩, + ⟨3, 5, 7, 2, 6, 7, 53614781724352386275603919351081516140039503872000000⟩, + ⟨3, 5, 8, 2, 7, 7, 530432535327739198530337759412324464037971623936000000⟩, + ⟨3, 5, 7, 3, 5, 7, 128594324531253831650408105473919646995954270208000000⟩, + ⟨3, 5, 8, 3, 6, 7, -28483659306025943072095673957032177676970885120000000⟩, + ⟨3, 5, 7, 4, 4, 7, -66483893872019858057261584157589391838741004288000000⟩, + ⟨3, 5, 8, 4, 5, 7, -387694874863395650967053313970425418586756481024000000⟩, + ⟨3, 5, 7, 5, 3, 7, -75837120919974008435047398916590220728720162816000000⟩, + ⟨3, 5, 8, 5, 4, 7, -194080945922738193613933241366222582310210895872000000⟩, + ⟨3, 5, 7, 6, 2, 7, -536736961590382286362565010124702181850995490816000000⟩, + ⟨3, 5, 8, 6, 3, 7, 1030453525386688833326223014812591638470725730304000000⟩, + ⟨3, 5, 7, 7, 1, 7, 2776827924545980931079005604474048419005955309568000000⟩, + ⟨3, 5, 8, 7, 2, 7, -405304808636844146913715685137325004840266366976000000⟩, + ⟨3, 6, 6, 0, 7, 8, 81595925184751403483850446238459648901046599680000000⟩, + ⟨3, 6, 7, 0, 8, 8, 239345408281516373596235098950289515273309388800000000⟩, + ⟨3, 6, 6, 1, 6, 8, -30068532324453808383650267361891865025241415680000000⟩, + ⟨3, 6, 7, 1, 7, 8, -18934525877036132250419287783935581884514304000000000⟩, + ⟨3, 6, 8, 1, 8, 8, -136815410338440778781075561540021286311464796160000000⟩, + ⟨3, 6, 6, 2, 5, 8, -540212357650244710658952200928685063478968320000000⟩, + ⟨3, 6, 7, 2, 6, 8, -11875680998909395660274387448851810127792046080000000⟩, + ⟨3, 6, 8, 2, 7, 8, -58745437157434010337561174507097545787331051520000000⟩, + ⟨3, 6, 6, 3, 4, 8, 8747503378171711477477632527045149270820782080000000⟩, + ⟨3, 6, 7, 3, 5, 8, -28483659306025943072095673957032177676970885120000000⟩ +] + +def collectedFourData_15_14 : List CollectedFourTerm := [ + ⟨3, 6, 8, 3, 6, 8, 3154567086919040861561806272308030575371878400000000⟩, + ⟨3, 6, 6, 4, 3, 8, -11044683185846782527078974495203716784969482240000000⟩, + ⟨3, 6, 7, 4, 4, 8, 14726190983089224171664065168714283375468216320000000⟩, + ⟨3, 6, 8, 4, 5, 8, 42937232146732171521381660123438011068899655680000000⟩, + ⟨3, 6, 6, 5, 2, 8, 23975097201530275754086382468146001613485506560000000⟩, + ⟨3, 6, 7, 5, 3, 8, 16797931968680566899439366249793872145405706240000000⟩, + ⟨3, 6, 8, 5, 4, 8, 21494477153659102664198838562638238994965463040000000⟩, + ⟨3, 6, 6, 6, 1, 8, -44900623770860576350460556038308431751198801920000000⟩, + ⟨3, 6, 7, 6, 2, 8, 118887305537160761275358853024471451296847626240000000⟩, + ⟨3, 6, 8, 6, 3, 8, -114122793734470958709753535071264263959247585280000000⟩, + ⟨3, 6, 6, 7, 0, 8, -13323492209313704874356420228535624339491389440000000⟩, + ⟨3, 6, 7, 7, 1, 8, -615067739906387637059671332489143454617063915520000000⟩, + ⟨3, 6, 8, 7, 2, 8, 44887533436594610305382849313176798007467704320000000⟩, + ⟨4, 3, 8, 1, 8, 6, 479014337148089796026719780730692393956777394176000000⟩, + ⟨4, 3, 8, 2, 7, 6, 205677902590309288687001162307888900713031401472000000⟩, + ⟨4, 3, 8, 3, 6, 6, -11044683185846782527078974495203716784969482240000000⟩, + ⟨4, 3, 8, 4, 5, 6, -150330651677779140375723935385202813108588904448000000⟩, + ⟨4, 3, 8, 5, 4, 6, -75255869939176586131856402813312102673042898944000000⟩, + ⟨4, 3, 8, 6, 3, 6, 399563574446600527455104934852339674159417131008000000⟩, + ⟨4, 3, 8, 7, 2, 6, -157158992705237462507799764343214853831421591552000000⟩, + ⟨4, 4, 7, 0, 8, 7, 558657669366841433320722072288925627689593733120000000⟩, + ⟨4, 4, 7, 1, 7, 7, -44195199619578590605380349209124918011730329600000000⟩, + ⟨4, 4, 8, 1, 8, 7, -638683472742802404097887581852299685324094701568000000⟩, + ⟨4, 4, 7, 2, 6, 7, -27719104020543501372990475880878252442718830592000000⟩ +] + +def collectedFourData_15_15 : List CollectedFourTerm := [ + ⟨4, 4, 8, 2, 7, 7, -274236211539996110672275559812890367145118007296000000⟩, + ⟨4, 4, 7, 3, 5, 7, -66483893872019858057261584157589391838741004288000000⟩, + ⟨4, 4, 8, 3, 6, 7, 14726190983089224171664065168714283375468216320000000⟩, + ⟨4, 4, 7, 4, 4, 7, 34372497857101985654873035189263628850763399168000000⟩, + ⟨4, 4, 8, 4, 5, 7, 200440143910701854572876873689571771650894987264000000⟩, + ⟨4, 4, 7, 5, 3, 7, 39208161924577656361274446958796682701859454976000000⟩, + ⟨4, 4, 8, 5, 4, 7, 100340796985737242779693850698628987476972142592000000⟩, + ⟨4, 4, 7, 6, 2, 7, 277495630710300695189791212135874903559400062976000000⟩, + ⟨4, 4, 8, 6, 3, 7, -532749505637839231391720297932044183404065849344000000⟩, + ⟨4, 4, 7, 7, 1, 7, -1435633599766738629084244979438813594282253877248000000⟩, + ⟨4, 4, 8, 7, 2, 7, 209544565683240501328596921654068767756948340736000000⟩, + ⟨4, 5, 6, 0, 7, 8, 1110612989152440058443592031152207408791275175936000000⟩, + ⟨4, 5, 7, 0, 8, 8, 3257762182726281314704166547560247946427246837760000000⟩, + ⟨4, 5, 6, 1, 6, 8, -409266792289882080157344129227831673458981339136000000⟩, + ⟨4, 5, 7, 1, 7, 8, -257720349819738292021188589519211466117139660800000000⟩, + ⟨4, 5, 8, 1, 8, 8, -1862212745232644225827074009585133508222603231232000000⟩, + ⟨4, 5, 6, 2, 5, 8, -7352902242955959981982770617368336367735537664000000⟩, + ⟨4, 5, 7, 2, 6, 8, -161641473425984325606015861846134779038155145216000000⟩, + ⟨4, 5, 8, 2, 7, 8, -799591957720423798879434411669739523420983394304000000⟩, + ⟨4, 5, 6, 3, 4, 8, 119063431812988401496737963954433856608892092416000000⟩, + ⟨4, 5, 7, 3, 5, 8, -387694874863395650967053313970425418586756481024000000⟩, + ⟨4, 5, 8, 3, 6, 8, 42937232146732171521381660123438011068899655680000000⟩, + ⟨4, 5, 6, 4, 3, 8, -150330651677779140375723935385202813108588904448000000⟩, + ⟨4, 5, 7, 4, 4, 8, 200440143910701854572876873689571771650894987264000000⟩ +] + +def collectedFourData_15_16 : List CollectedFourTerm := [ + ⟨4, 5, 8, 4, 5, 8, 584424376982566640380291108529964884841920987136000000⟩, + ⟨4, 5, 6, 5, 2, 8, 326328236464287162191559268962489436579207053312000000⟩, + ⟨4, 5, 7, 5, 3, 8, 228638885986944831428356762123615361509776949248000000⟩, + ⟨4, 5, 8, 5, 4, 8, 292564187094423201595612651468988964454539460608000000⟩, + ⟨4, 5, 6, 6, 1, 8, -611148361490528503628100470136525489629124624384000000⟩, + ⟨4, 5, 7, 6, 2, 8, 1618190926519216574584700721757550942912929333248000000⟩, + ⟨4, 5, 8, 6, 3, 8, -1553340522739172421521830844304854086097678893056000000⟩, + ⟨4, 5, 6, 7, 0, 8, -181347824355577515320742243367971618382191525888000000⟩, + ⟨4, 5, 7, 7, 1, 8, -8371768805880596114044024733612460454707518767104000000⟩, + ⟨4, 5, 8, 7, 2, 8, 610970187209947565141101801062426291130664484864000000⟩, + ⟨5, 2, 8, 1, 8, 6, -1039813917774369498411410766439031916095229394944000000⟩, + ⟨5, 2, 8, 2, 7, 6, -446472535593285624865840325031893379417970311168000000⟩, + ⟨5, 2, 8, 3, 6, 6, 23975097201530275754086382468146001613485506560000000⟩, + ⟨5, 2, 8, 4, 5, 6, 326328236464287162191559268962489436579207053312000000⟩, + ⟨5, 2, 8, 5, 4, 6, 163360665617784129888457172473494766947020046336000000⟩, + ⟨5, 2, 8, 6, 3, 6, -867347245217851109718234308308068585025623293952000000⟩, + ⟨5, 2, 8, 7, 2, 6, 341150765739576549134979355583566808477689970688000000⟩, + ⟨5, 3, 7, 0, 8, 7, 637251923092826133210744440210716813139210403840000000⟩, + ⟨5, 3, 7, 1, 7, 7, -50412761684569848885484866024841471147062067200000000⟩, + ⟨5, 3, 8, 1, 8, 7, -728536084923409888644265978515005316407048011776000000⟩, + ⟨5, 3, 7, 2, 6, 7, -31618741336749412108427452236422960365745209344000000⟩, + ⟨5, 3, 8, 2, 7, 7, -312816887278422745049449314627195843679377948672000000⟩, + ⟨5, 3, 7, 3, 5, 7, -75837120919974008435047398916590220728720162816000000⟩, + ⟨5, 3, 8, 3, 6, 7, 16797931968680566899439366249793872145405706240000000⟩ +] + +def collectedFourData_15_17 : List CollectedFourTerm := [ + ⟨5, 3, 7, 4, 4, 7, 39208161924577656361274446958796682701859454976000000⟩, + ⟨5, 3, 8, 4, 5, 7, 228638885986944831428356762123615361509776949248000000⟩, + ⟨5, 3, 7, 5, 3, 7, 44724127059223045708142127059951483392918290432000000⟩, + ⟨5, 3, 8, 5, 4, 7, 114457152116603780096474845675876827338945593344000000⟩, + ⟨5, 3, 7, 6, 2, 7, 316534854914661021912480291130141431449027346432000000⟩, + ⟨5, 3, 8, 6, 3, 7, -607698892560152674773950239528279063006499831808000000⟩, + ⟨5, 3, 7, 7, 1, 7, -1637604426597945267856937355023421819404509249536000000⟩, + ⟨5, 3, 8, 7, 2, 7, 239024155180105594194014156485948357946483146752000000⟩, + ⟨5, 4, 6, 0, 7, 8, 555975416401194364122269014830425439829657387008000000⟩, + ⟨5, 4, 7, 0, 8, 8, 1630843240415858540399972774367928659014351585280000000⟩, + ⟨5, 4, 6, 1, 6, 8, -204879897394497705683496531679476140792094916608000000⟩, + ⟨5, 4, 7, 1, 7, 8, -129015399788758781301257281845740528376112742400000000⟩, + ⟨5, 4, 8, 1, 8, 8, -932227982718309231164475517685051687416256004096000000⟩, + ⟨5, 4, 6, 2, 5, 8, -3680879771993736634491661284281277331424673792000000⟩, + ⟨5, 4, 7, 2, 6, 8, -80918093317364461249575278412193761055733710848000000⟩, + ⟨5, 4, 8, 2, 7, 8, -400277572823921370253559837115297471000804851712000000⟩, + ⟨5, 4, 6, 3, 4, 8, 59603427770909573369769996157274164246188392448000000⟩, + ⟨5, 4, 7, 3, 5, 8, -194080945922738193613933241366222582310210895872000000⟩, + ⟨5, 4, 8, 3, 6, 8, 21494477153659102664198838562638238994965463040000000⟩, + ⟨5, 4, 6, 4, 3, 8, -75255869939176586131856402813312102673042898944000000⟩, + ⟨5, 4, 7, 4, 4, 8, 100340796985737242779693850698628987476972142592000000⟩, + ⟨5, 4, 8, 4, 5, 8, 292564187094423201595612651468988964454539460608000000⟩, + ⟨5, 4, 6, 5, 2, 8, 163360665617784129888457172473494766947020046336000000⟩, + ⟨5, 4, 7, 5, 3, 8, 114457152116603780096474845675876827338945593344000000⟩ +] + +def collectedFourData_15_18 : List CollectedFourTerm := [ + ⟨5, 4, 8, 5, 4, 8, 146458304857420284719408859761871268828806119424000000⟩, + ⟨5, 4, 6, 6, 1, 8, -305942275195168264708574270442362642082878717952000000⟩, + ⟨5, 4, 7, 6, 2, 8, 810070099103323933474552006862849610214847545344000000⟩, + ⟨5, 4, 8, 6, 3, 8, -777605837837200038789606996196946580547062202368000000⟩, + ⟨5, 4, 6, 7, 0, 8, -90783137910611883928905267090238687928609931264000000⟩, + ⟨5, 4, 7, 7, 1, 8, -4190926716439770559806259715537345321757271130112000000⟩, + ⟨5, 4, 8, 7, 2, 8, 305853080740569306559428944271312800520855355392000000⟩, + ⟨6, 1, 8, 1, 8, 6, 1947366182553433510591208435055137928622016299008000000⟩, + ⟨6, 1, 8, 2, 7, 6, 836154914250638687444998680599951507304770174976000000⟩, + ⟨6, 1, 8, 3, 6, 6, -44900623770860576350460556038308431751198801920000000⟩, + ⟨6, 1, 8, 4, 5, 6, -611148361490528503628100470136525489629124624384000000⟩, + ⟨6, 1, 8, 5, 4, 6, -305942275195168264708574270442362642082878717952000000⟩, + ⟨6, 1, 8, 6, 3, 6, 1624370154116970530142428964779421025030964772864000000⟩, + ⟨6, 1, 8, 7, 2, 6, -638908032482805251841153917096499333862696943616000000⟩, + ⟨6, 2, 7, 0, 8, 7, 4510148286475703049375915994020187692278313123840000000⟩, + ⟨6, 2, 7, 1, 7, 7, -356796146843562642969033324114689847121359667200000000⟩, + ⟨6, 2, 8, 1, 8, 7, -5156211626801796564198915070783310513874483019776000000⟩, + ⟨6, 2, 7, 2, 6, 7, -223781532691720205511102961231054484051375161344000000⟩, + ⟨6, 2, 8, 2, 7, 7, -2213960440153788455184909239206050658320144924672000000⟩, + ⟨6, 2, 7, 3, 5, 7, -536736961590382286362565010124702181850995490816000000⟩, + ⟨6, 2, 8, 3, 6, 7, 118887305537160761275358853024471451296847626240000000⟩, + ⟨6, 2, 7, 4, 4, 7, 277495630710300695189791212135874903559400062976000000⟩, + ⟨6, 2, 8, 4, 5, 7, 1618190926519216574584700721757550942912929333248000000⟩, + ⟨6, 2, 7, 5, 3, 7, 316534854914661021912480291130141431449027346432000000⟩ +] + +def collectedFourData_15_19 : List CollectedFourTerm := [ + ⟨6, 2, 8, 5, 4, 7, 810070099103323933474552006862849610214847545344000000⟩, + ⟨6, 2, 7, 6, 2, 7, 2240274343268223727822975391443028087142384402432000000⟩, + ⟨6, 2, 8, 6, 3, 7, -4300986814870876394842074847857524798853960695808000000⟩, + ⟨6, 2, 7, 7, 1, 7, -11590139677726608022640887518458395422691254337536000000⟩, + ⟨6, 2, 8, 7, 2, 7, 1691692633393312648674141669486613363020898762752000000⟩, + ⟨6, 3, 6, 0, 7, 8, -2951896308703131903123200206961769993630023417856000000⟩, + ⟨6, 3, 7, 0, 8, 8, -8658800370380342883235953611926208198342564904960000000⟩, + ⟨6, 3, 6, 1, 6, 8, 1087789486738527261891217074363604003643568685056000000⟩, + ⟨6, 3, 7, 1, 7, 8, 684994464085224861031418449789185147825605836800000000⟩, + ⟨6, 3, 8, 1, 8, 8, 4949571977244050799941002537983718388506948534272000000⟩, + ⟨6, 3, 6, 2, 5, 8, 19543265927225258505286830799733427937417887744000000⟩, + ⟨6, 3, 7, 2, 6, 8, 429626587659156412697272909550761877278593908736000000⟩, + ⟨6, 3, 8, 2, 7, 8, 2125234056793170567931869282305512377724314845184000000⟩, + ⟨6, 3, 6, 3, 4, 8, -316458485811970416416533531351751608331126439936000000⟩, + ⟨6, 3, 7, 3, 5, 8, 1030453525386688833326223014812591638470725730304000000⟩, + ⟨6, 3, 8, 3, 6, 8, -114122793734470958709753535071264263959247585280000000⟩, + ⟨6, 3, 6, 4, 3, 8, 399563574446600527455104934852339674159417131008000000⟩, + ⟨6, 3, 7, 4, 4, 8, -532749505637839231391720297932044183404065849344000000⟩, + ⟨6, 3, 8, 4, 5, 8, -1553340522739172421521830844304854086097678893056000000⟩, + ⟨6, 3, 6, 5, 2, 8, -867347245217851109718234308308068585025623293952000000⟩, + ⟨6, 3, 7, 5, 3, 8, -607698892560152674773950239528279063006499831808000000⟩, + ⟨6, 3, 8, 5, 4, 8, -777605837837200038789606996196946580547062202368000000⟩, + ⟨6, 3, 6, 6, 1, 8, 1624370154116970530142428964779421025030964772864000000⟩, + ⟨6, 3, 7, 6, 2, 8, -4300986814870876394842074847857524798853960695808000000⟩ +] + +def collectedFourData_15_20 : List CollectedFourTerm := [ + ⟨6, 3, 8, 6, 3, 8, 4128621040829002192826214376520065795565474021376000000⟩, + ⟨6, 3, 6, 7, 0, 8, 482004063103116165697944732813179407467961909248000000⟩, + ⟨6, 3, 7, 7, 1, 8, 22251309571171391332787791405337801441433285033984000000⟩, + ⟨6, 3, 8, 7, 2, 8, -1623896585010279200482824332143935109856382418944000000⟩, + ⟨7, 0, 8, 1, 8, 6, 577847610633190973602910533522694795103049875456000000⟩, + ⟨7, 0, 8, 2, 7, 6, 248114670803920367894451768119761051827025477632000000⟩, + ⟨7, 0, 8, 3, 6, 6, -13323492209313704874356420228535624339491389440000000⟩, + ⟨7, 0, 8, 4, 5, 6, -181347824355577515320742243367971618382191525888000000⟩, + ⟨7, 0, 8, 5, 4, 6, -90783137910611883928905267090238687928609931264000000⟩, + ⟨7, 0, 8, 6, 3, 6, 482004063103116165697944732813179407467961909248000000⟩, + ⟨7, 0, 8, 7, 2, 6, -189585031974032437111219725375584910798709850112000000⟩, + ⟨7, 1, 7, 0, 8, 7, -23333413947531935407007144434325402806644973240320000000⟩, + ⟨7, 1, 7, 1, 7, 7, 1845897664639919991381530185454079397001271705600000000⟩, + ⟨7, 1, 8, 1, 8, 7, 26675845814208688145902924355656984935260013723648000000⟩, + ⟨7, 1, 7, 2, 6, 7, 1157741786842508423231170428549198514212267098112000000⟩, + ⟨7, 1, 8, 2, 7, 7, 11454003756035183673032105617444150047361839661056000000⟩, + ⟨7, 1, 7, 3, 5, 7, 2776827924545980931079005604474048419005955309568000000⟩, + ⟨7, 1, 8, 3, 6, 7, -615067739906387637059671332489143454617063915520000000⟩, + ⟨7, 1, 7, 4, 4, 7, -1435633599766738629084244979438813594282253877248000000⟩, + ⟨7, 1, 8, 4, 5, 7, -8371768805880596114044024733612460454707518767104000000⟩, + ⟨7, 1, 7, 5, 3, 7, -1637604426597945267856937355023421819404509249536000000⟩, + ⟨7, 1, 8, 5, 4, 7, -4190926716439770559806259715537345321757271130112000000⟩, + ⟨7, 1, 7, 6, 2, 7, -11590139677726608022640887518458395422691254337536000000⟩, + ⟨7, 1, 8, 6, 3, 7, 22251309571171391332787791405337801441433285033984000000⟩ +] + +def collectedFourData_15_21 : List CollectedFourTerm := [ + ⟨7, 1, 7, 7, 1, 7, 59962003382694370838563473234895166400545452720128000000⟩, + ⟨7, 1, 8, 7, 2, 7, -8752032523037354950314315792868194916664812240896000000⟩, + ⟨7, 2, 6, 0, 7, 8, 1161059416110746751484522564536606576394647896064000000⟩, + ⟨7, 2, 7, 0, 8, 8, 3405736736962183451216768926145319109367420682240000000⟩, + ⟨7, 2, 6, 1, 6, 8, -427856568877555490275089093935353178592708132864000000⟩, + ⟨7, 2, 7, 1, 7, 8, -269426561551308614626523091058625434929541939200000000⟩, + ⟨7, 2, 8, 1, 8, 8, -1946798447138487979652522801243024942114713632768000000⟩, + ⟨7, 2, 6, 2, 5, 8, -7686886852854966534784898067001119928888590336000000⟩, + ⟨7, 2, 7, 2, 6, 8, -168983576266722630738355048891157070965882486784000000⟩, + ⟨7, 2, 8, 2, 7, 8, -835911141527535129306899395166853151242842013696000000⟩, + ⟨7, 2, 6, 3, 4, 8, 124471548569251942012000330222639551775279939584000000⟩, + ⟨7, 2, 7, 3, 5, 8, -405304808636844146913715685137325004840266366976000000⟩, + ⟨7, 2, 8, 3, 6, 8, 44887533436594610305382849313176798007467704320000000⟩, + ⟨7, 2, 6, 4, 3, 8, -157158992705237462507799764343214853831421591552000000⟩, + ⟨7, 2, 7, 4, 4, 8, 209544565683240501328596921654068767756948340736000000⟩, + ⟨7, 2, 8, 4, 5, 8, 610970187209947565141101801062426291130664484864000000⟩, + ⟨7, 2, 6, 5, 2, 8, 341150765739576549134979355583566808477689970688000000⟩, + ⟨7, 2, 7, 5, 3, 8, 239024155180105594194014156485948357946483146752000000⟩, + ⟨7, 2, 8, 5, 4, 8, 305853080740569306559428944271312800520855355392000000⟩, + ⟨7, 2, 6, 6, 1, 8, -638908032482805251841153917096499333862696943616000000⟩, + ⟨7, 2, 7, 6, 2, 8, 1691692633393312648674141669486613363020898762752000000⟩, + ⟨7, 2, 8, 6, 3, 8, -1623896585010279200482824332143935109856382418944000000⟩, + ⟨7, 2, 6, 7, 0, 8, -189585031974032437111219725375584910798709850112000000⟩, + ⟨7, 2, 7, 7, 1, 8, -8752032523037354950314315792868194916664812240896000000⟩ +] + +def collectedFourData_15_22 : List CollectedFourTerm := [ + ⟨7, 2, 8, 7, 2, 8, 638721765143779143801306602815796394330094043136000000⟩, + ⟨0, 7, 8, 2, 8, 5, 3814800982822741354564540816498208175078506496000000⟩, + ⟨0, 7, 8, 3, 7, 5, 2336782134972504655043574281589759201383546880000000⟩, + ⟨0, 7, 8, 4, 6, 5, -2980655074929558652463404770908793057954496512000000⟩, + ⟨0, 7, 8, 5, 5, 5, -996342915862305396962575700708337496017076224000000⟩, + ⟨0, 7, 8, 6, 4, 5, 1484205401410652354340849248950921139117359104000000⟩, + ⟨0, 7, 8, 7, 3, 5, 7108525379579367539051501526472675024045080576000000⟩, + ⟨0, 8, 7, 1, 8, 6, -246225845044399130437597836233432654967874781184000000⟩, + ⟨0, 8, 7, 2, 7, 6, 14537455921847929318791653634197296631387258880000000⟩, + ⟨0, 8, 8, 2, 8, 6, 235010670796799244738552150605187514329345294336000000⟩, + ⟨0, 8, 7, 3, 6, 6, 11351152238512183386140185087054614763860393984000000⟩, + ⟨0, 8, 8, 3, 7, 6, 143957375369949326707265233192521399456057262080000000⟩, + ⟨0, 8, 7, 4, 5, 6, 39080995819470508869081091968927539790537031680000000⟩, + ⟨0, 8, 8, 4, 6, 6, -183623143573471257006373998348735404904642772992000000⟩, + ⟨0, 8, 7, 5, 4, 6, -24764130988670088048855803939109215441277419520000000⟩, + ⟨0, 8, 8, 5, 5, 6, -61379667787329858385365528485329324059534557184000000⟩, + ⟨0, 8, 7, 6, 3, 6, -74255703492900490513992602157333323416225185792000000⟩, + ⟨0, 8, 8, 6, 4, 6, 91434417825816534571652083709603293960825995264000000⟩, + ⟨0, 8, 7, 7, 2, 6, 131864151226912150168615157241804010380337348608000000⟩, + ⟨0, 8, 8, 7, 3, 6, 437920438144294229059229201743671060085516271616000000⟩, + ⟨1, 6, 8, 2, 8, 5, -629412570154183798312134216971777093078857285632000000⟩, + ⟨1, 6, 8, 3, 7, 5, -385550925483697038898337309067694264623782952960000000⟩, + ⟨1, 6, 8, 4, 6, 5, 491784965952887807105306889725480322726157615104000000⟩, + ⟨1, 6, 8, 5, 5, 5, 164388852328485070673098168948970397390348484608000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1502.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1502.lean new file mode 100644 index 0000000000000000000000000000000000000000..c6e76362a4a281c56fdaeb8307ea68b40a7799ac --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1502.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1502. -/ +namespace LaughlinFock +def collectedFourData_15_23 : List CollectedFourTerm := [ + ⟨1, 6, 8, 6, 4, 5, -244882378017885780912196359755469725005479149568000000⟩, + ⟨1, 6, 8, 7, 3, 5, -1172851545680539833664751506948737535086000340992000000⟩, + ⟨1, 7, 7, 1, 8, 6, 823484289196031337713511119291350995462531317760000000⟩, + ⟨1, 7, 7, 2, 7, 6, -48619455664221264094667592359233587713880883200000000⟩, + ⟨1, 7, 8, 2, 8, 6, -785975961051887532305760491888397881544057815040000000⟩, + ⟨1, 7, 7, 3, 6, 6, -37963096566900265222725075113900051338635509760000000⟩, + ⟨1, 7, 8, 3, 7, 6, -481454889147290008138619688372625888658010931200000000⟩, + ⟨1, 7, 7, 4, 5, 6, -130703525690678902356476852602206544341447475200000000⟩, + ⟨1, 7, 8, 4, 6, 6, 614114143209761972224134245925538924644406394880000000⟩, + ⟨1, 7, 7, 5, 4, 6, 82821820760063523853459096631811656681049292800000000⟩, + ⟨1, 7, 8, 5, 5, 6, 205279799485807939585425256847897595651827957760000000⟩, + ⟨1, 7, 7, 6, 3, 6, 248342757026892198927240608961345427174462586880000000⟩, + ⟨1, 7, 8, 6, 4, 6, -305795707829811295952455389978059852162751528960000000⟩, + ⟨1, 7, 7, 7, 2, 6, -441009987493194614275921612178506218445335429120000000⟩, + ⟨1, 7, 8, 7, 3, 6, -1464592803670313711369454409831034925210654474240000000⟩, + ⟨1, 8, 6, 0, 8, 7, -246225845044399130437597836233432654967874781184000000⟩, + ⟨1, 8, 6, 1, 7, 7, 823484289196031337713511119291350995462531317760000000⟩, + ⟨1, 8, 7, 1, 8, 7, 1548089070848500863925724374806908217462538371072000000⟩, + ⟨1, 8, 6, 2, 6, 7, -56844805943528437447854372689108145711221833728000000⟩, + ⟨1, 8, 7, 2, 7, 7, -91400951945139937288025677117314389419008983040000000⟩, + ⟨1, 8, 8, 2, 8, 7, -738788105139200070722091701039327137157080940544000000⟩, + ⟨1, 8, 6, 3, 5, 7, 138481816692968332137276344388013766084917198848000000⟩, + ⟨1, 8, 7, 3, 6, 7, -71367791300744805111113291216919475698869993472000000⟩, + ⟨1, 8, 8, 3, 7, 7, -452549648957582204078017456928107989356060344320000000⟩ +] + +def collectedFourData_15_24 : List CollectedFourTerm := [ + ⟨1, 8, 6, 4, 4, 7, -63997890438679447430432631534890944511072010240000000⟩, + ⟨1, 8, 7, 4, 5, 7, -245712884019501723288555037315086747421837885440000000⟩, + ⟨1, 8, 8, 4, 6, 7, 577244402734566088760515125189553915687619002368000000⟩, + ⟨1, 8, 6, 5, 3, 7, -23706484291494341321366250122794985975986520064000000⟩, + ⟨1, 8, 7, 5, 4, 7, 155698848452354586096385614727340779039264604160000000⟩, + ⟨1, 8, 8, 5, 5, 7, 192955359452097806893831612849356590618599489536000000⟩, + ⟨1, 8, 6, 6, 2, 7, -1698640068726301073705229042466230596487446790144000000⟩, + ⟨1, 8, 7, 6, 3, 7, 466865868628850322066614833237673341024664027136000000⟩, + ⟨1, 8, 8, 6, 4, 7, -287436566437650069394221677803285796589567737856000000⟩, + ⟨1, 8, 6, 7, 1, 7, 3367475948572483227274564552712006347079666368512000000⟩, + ⟨1, 8, 7, 7, 2, 7, -829065898075349607646132635026880697791166808064000000⟩, + ⟨1, 8, 8, 7, 3, 7, -1376662640898082004030143140512269478885446385664000000⟩, + ⟨2, 5, 8, 2, 8, 5, 110097999892239364422451162027391008481369653248000000⟩, + ⟨2, 5, 8, 3, 7, 5, 67441274237593494496036722486867594340403773440000000⟩, + ⟨2, 5, 8, 4, 6, 5, -86023927223478370384422368729659466425886048256000000⟩, + ⟨2, 5, 8, 5, 5, 5, -28755199219350379776056638850427228549506138112000000⟩, + ⟨2, 5, 8, 6, 4, 5, 42835274201816469492727500352422639117168279552000000⟩, + ⟨2, 5, 8, 7, 3, 5, 205157341103494181095273350733748471878844940288000000⟩, + ⟨2, 6, 7, 1, 8, 6, -56844805943528437447854372689108145711221833728000000⟩, + ⟨2, 6, 7, 2, 7, 6, 3356182453718586160821987718477776862272552960000000⟩, + ⟨2, 6, 8, 2, 8, 6, 54255620378492746468709955219054599809492058112000000⟩, + ⟨2, 6, 7, 3, 6, 6, 2620578055554331035537841416671400593958371328000000⟩, + ⟨2, 6, 8, 3, 7, 6, 33234647100384041109903899614689518970847887360000000⟩, + ⟨2, 6, 7, 4, 5, 6, 9022414454652637472441744979512780923663810560000000⟩ +] + +def collectedFourData_15_25 : List CollectedFourTerm := [ + ⟨2, 6, 8, 4, 6, 6, -42392064737527710387071620212999508521243377664000000⟩, + ⟨2, 6, 7, 5, 4, 6, -5717158652282148968678733534923143209906339840000000⟩, + ⟨2, 6, 8, 5, 5, 6, -14170386149430643586751665857137528650468425728000000⟩, + ⟨2, 6, 7, 6, 3, 6, -17143005660079999366132630281085998623845515264000000⟩, + ⟨2, 6, 8, 6, 4, 6, 21108960909163775008428225396737557529087705088000000⟩, + ⟨2, 6, 7, 7, 2, 6, 30442750987615767219737526116542088120459329536000000⟩, + ⟨2, 6, 8, 7, 3, 6, 101100281818623018402150150270384035522383183872000000⟩, + ⟨2, 7, 6, 0, 8, 7, 14537455921847929318791653634197296631387258880000000⟩, + ⟨2, 7, 6, 1, 7, 7, -48619455664221264094667592359233587713880883200000000⟩, + ⟨2, 7, 7, 1, 8, 7, -91400951945139937288025677117314389419008983040000000⟩, + ⟨2, 7, 6, 2, 6, 7, 3356182453718586160821987718477776862272552960000000⟩, + ⟨2, 7, 7, 2, 7, 7, 5396416894732623936436235182709260537351372800000000⟩, + ⟨2, 7, 8, 2, 8, 7, 43618895945346572539625559576538648378689454080000000⟩, + ⟨2, 7, 6, 3, 5, 7, -8176125076506241933466109703424117182939791360000000⟩, + ⟨2, 7, 7, 3, 6, 7, 4213636144033287491239352677157510822536151040000000⟩, + ⟨2, 7, 8, 3, 7, 7, 26719049630969090333893109052803299936724582400000000⟩, + ⟨2, 7, 6, 4, 4, 7, 3778508755552419791736103406849402356944076800000000⟩, + ⟨2, 7, 7, 4, 5, 7, 14507170115385462589528228871733647277608140800000000⟩, + ⟨2, 7, 8, 4, 6, 7, -34081170721026521351954263480479956625795317760000000⟩, + ⟨2, 7, 6, 5, 3, 7, 1399657986298862037633839333177577632673300480000000⟩, + ⟨2, 7, 7, 5, 4, 7, -9192638352202386931713675526328429304820531200000000⟩, + ⟨2, 7, 8, 5, 5, 7, -11392305435740860713345707586855625542881771520000000⟩, + ⟨2, 7, 6, 6, 2, 7, 100289655303002679111010048666349108136593326080000000⟩, + ⟨2, 7, 7, 6, 3, 7, -27564295638353182487548573182290362493325803520000000⟩ +] + +def collectedFourData_15_26 : List CollectedFourTerm := [ + ⟨2, 7, 8, 6, 4, 7, 16970584116225380779332326584379555729815633920000000⟩, + ⟨2, 7, 6, 7, 1, 7, -198819637156400459803369760520151773516492963840000000⟩, + ⟨2, 7, 7, 7, 2, 7, 48949000245706822097857248717840737731325460480000000⟩, + ⟨2, 7, 8, 7, 3, 7, 81279739166706410779654963642934306827382292480000000⟩, + ⟨2, 8, 5, 0, 7, 8, 3814800982822741354564540816498208175078506496000000⟩, + ⟨2, 8, 6, 0, 8, 8, 235010670796799244738552150605187514329345294336000000⟩, + ⟨2, 8, 5, 1, 6, 8, -629412570154183798312134216971777093078857285632000000⟩, + ⟨2, 8, 6, 1, 7, 8, -785975961051887532305760491888397881544057815040000000⟩, + ⟨2, 8, 7, 1, 8, 8, -738788105139200070722091701039327137157080940544000000⟩, + ⟨2, 8, 5, 2, 5, 8, 110097999892239364422451162027391008481369653248000000⟩, + ⟨2, 8, 6, 2, 6, 8, 54255620378492746468709955219054599809492058112000000⟩, + ⟨2, 8, 7, 2, 7, 8, 43618895945346572539625559576538648378689454080000000⟩, + ⟨2, 8, 8, 2, 8, 8, 235045848706028622076129979121167083096969838592000000⟩, + ⟨2, 8, 5, 3, 4, 8, -149013046934804148362690935276547363063646388224000000⟩, + ⟨2, 8, 6, 3, 5, 8, -132174202217908763113739225762196108104372846592000000⟩, + ⟨2, 8, 7, 3, 6, 8, 34058554056032724727119292725378249434641465344000000⟩, + ⟨2, 8, 8, 3, 7, 8, 143978923836095539033224706641828952638499061760000000⟩, + ⟨2, 8, 5, 4, 3, 8, 13899401652267955106864615405978654049130512384000000⟩, + ⟨2, 8, 6, 4, 4, 8, 61082893872745544846009839963540436565318696960000000⟩, + ⟨2, 8, 7, 4, 5, 8, 117260537143098649327144983949464544364860538880000000⟩, + ⟨2, 8, 8, 4, 6, 8, -183650629467005962282837499382251518841768116224000000⟩, + ⟨2, 8, 5, 5, 2, 8, 1079576399941316198000933598844982236192098484224000000⟩, + ⟨2, 8, 6, 5, 3, 8, 22626693694860763740225214479293157166710521856000000⟩, + ⟨2, 8, 7, 5, 4, 8, -74303513529375879350231371986846913204133560320000000⟩ +] + +def collectedFourData_15_27 : List CollectedFourTerm := [ + ⟨2, 8, 8, 5, 5, 8, -61388855490912130929052571078957455740499918848000000⟩, + ⟨2, 8, 5, 6, 1, 8, -1379233929509401863796059323899753224452324720640000000⟩, + ⟨2, 8, 6, 6, 2, 8, 1621269862721787851666884431014980512063135154176000000⟩, + ⟨2, 8, 7, 6, 3, 8, -222800455693049147721521938658793431604733673472000000⟩, + ⟨2, 8, 8, 6, 4, 8, 91448104317752463050091183412526964265722052608000000⟩, + ⟨2, 8, 5, 7, 0, 8, -6017501599078520547028150002293162823074407514112000000⟩, + ⟨2, 8, 6, 7, 1, 8, -3214093067376433135872989379497783131934816206848000000⟩, + ⟨2, 8, 7, 7, 2, 8, 395651668504387756546279117583473695081709436928000000⟩, + ⟨2, 8, 8, 7, 3, 8, 437985988892992142853428336307840121649340874752000000⟩, + ⟨3, 4, 8, 2, 8, 5, -149013046934804148362690935276547363063646388224000000⟩, + ⟨3, 4, 8, 3, 7, 5, -91278949419115650212190745894424894201627934720000000⟩, + ⟨3, 4, 8, 4, 6, 5, 116429794523196673609328586075278121371411939328000000⟩, + ⟨3, 4, 8, 5, 5, 5, 38918961789375227591534419677688006845929619456000000⟩, + ⟨3, 4, 8, 6, 4, 5, -57975755520972107896758620057100080989052338176000000⟩, + ⟨3, 4, 8, 7, 3, 5, -277671897117083896294655447251273622796311199744000000⟩, + ⟨3, 5, 7, 1, 8, 6, 138481816692968332137276344388013766084917198848000000⟩, + ⟨3, 5, 7, 2, 7, 6, -8176125076506241933466109703424117182939791360000000⟩, + ⟨3, 5, 8, 2, 8, 6, -132174202217908763113739225762196108104372846592000000⟩, + ⟨3, 5, 7, 3, 6, 6, -6384090927839736897502287601367484096942440448000000⟩, + ⟨3, 5, 8, 3, 7, 6, -80964201235607158817699895927466936195885301760000000⟩, + ⟨3, 5, 7, 4, 5, 6, -21979850645957537325490815169541757123648552960000000⟩, + ⟨3, 5, 8, 4, 6, 6, 103272938323524989745317851378158155775527092224000000⟩, + ⟨3, 5, 7, 5, 4, 6, 13927789942259253912112141553677301360036413440000000⟩, + ⟨3, 5, 8, 5, 5, 6, 34521022363300664961498689049836056739051470848000000⟩ +] + +def collectedFourData_15_28 : List CollectedFourTerm := [ + ⟨3, 5, 7, 6, 3, 6, 41762735011253692379970756559567450845241933824000000⟩, + ⟨3, 5, 8, 6, 4, 6, -51424351032280161092987903006605564844187844608000000⟩, + ⟨3, 5, 7, 7, 2, 6, -74162755803666108664128010303477972345842302976000000⟩, + ⟨3, 5, 8, 7, 3, 6, -246294282512330411670713794778760288219275722752000000⟩, + ⟨3, 6, 6, 0, 8, 7, 11351152238512183386140185087054614763860393984000000⟩, + ⟨3, 6, 6, 1, 7, 7, -37963096566900265222725075113900051338635509760000000⟩, + ⟨3, 6, 7, 1, 8, 7, -71367791300744805111113291216919475698869993472000000⟩, + ⟨3, 6, 6, 2, 6, 7, 2620578055554331035537841416671400593958371328000000⟩, + ⟨3, 6, 7, 2, 7, 7, 4213636144033287491239352677157510822536151040000000⟩, + ⟨3, 6, 8, 2, 8, 7, 34058554056032724727119292725378249434641465344000000⟩, + ⟨3, 6, 6, 3, 5, 7, -6384090927839736897502287601367484096942440448000000⟩, + ⟨3, 6, 7, 3, 6, 7, 3290095984176812640687519467393782690319695872000000⟩, + ⟨3, 6, 8, 3, 7, 7, 20862797566504328349610832792840095236693688320000000⟩, + ⟨3, 6, 6, 4, 4, 7, 2950339340624787647599275330953006819825418240000000⟩, + ⟨3, 6, 7, 4, 5, 7, 11327504441974075189610746758136000817859133440000000⟩, + ⟨3, 6, 8, 4, 6, 7, -26611297011033020210000189845098662673638227968000000⟩, + ⟨3, 6, 6, 5, 3, 7, 1092882480245430257164420603752652860360228864000000⟩, + ⟨3, 6, 7, 5, 4, 7, -7177805935948866853315288585077583882915676160000000⟩, + ⟨3, 6, 8, 5, 5, 7, -8895352394801029488316758019882941823882100736000000⟩, + ⟨3, 6, 6, 6, 2, 7, 78308278381874258562353554583804021456391634944000000⟩, + ⟨3, 6, 7, 6, 3, 7, -21522783478784350989256862923935938172300558336000000⟩, + ⟨3, 6, 8, 6, 4, 7, 13250990057362398616520022187109901284520493056000000⟩, + ⟨3, 6, 6, 7, 1, 7, -155242566615546983542485073051825510462009638912000000⟩, + ⟨3, 6, 7, 7, 2, 7, 38220411927574724399558040544511309285230116864000000⟩ +] + +def collectedFourData_15_29 : List CollectedFourTerm := [ + ⟨3, 6, 8, 7, 3, 7, 63464934865341084245815966862598119343431614464000000⟩, + ⟨3, 7, 5, 0, 7, 8, 2336782134972504655043574281589759201383546880000000⟩, + ⟨3, 7, 6, 0, 8, 8, 143957375369949326707265233192521399456057262080000000⟩, + ⟨3, 7, 5, 1, 6, 8, -385550925483697038898337309067694264623782952960000000⟩, + ⟨3, 7, 6, 1, 7, 8, -481454889147290008138619688372625888658010931200000000⟩, + ⟨3, 7, 7, 1, 8, 8, -452549648957582204078017456928107989356060344320000000⟩, + ⟨3, 7, 5, 2, 5, 8, 67441274237593494496036722486867594340403773440000000⟩, + ⟨3, 7, 6, 2, 6, 8, 33234647100384041109903899614689518970847887360000000⟩, + ⟨3, 7, 7, 2, 7, 8, 26719049630969090333893109052803299936724582400000000⟩, + ⟨3, 7, 8, 2, 8, 8, 143978923836095539033224706641828952638499061760000000⟩, + ⟨3, 7, 5, 3, 4, 8, -91278949419115650212190745894424894201627934720000000⟩, + ⟨3, 7, 6, 3, 5, 8, -80964201235607158817699895927466936195885301760000000⟩, + ⟨3, 7, 7, 3, 6, 8, 20862797566504328349610832792840095236693688320000000⟩, + ⟨3, 7, 8, 3, 7, 8, 88195263277876833474425687256635565893536972800000000⟩, + ⟨3, 7, 5, 4, 3, 8, 8514172459868080505007654168466537259225579520000000⟩, + ⟨3, 7, 6, 4, 4, 8, 37416739640408574872252860732665056690228428800000000⟩, + ⟨3, 7, 7, 4, 5, 8, 71828734858540065448060219788804495346394726400000000⟩, + ⟨3, 7, 8, 4, 6, 8, -112496434793672048511214091399067409633215774720000000⟩, + ⟨3, 7, 5, 5, 2, 8, 661301823104311829768387056398180001870742814720000000⟩, + ⟨3, 7, 6, 5, 3, 8, 13860134208239107473134625990658648148992327680000000⟩, + ⟨3, 7, 7, 5, 4, 8, -45515119599412481402465922303361011762698649600000000⟩, + ⟨3, 7, 8, 5, 5, 8, -37604158498309235873901631670550224010938941440000000⟩, + ⟨3, 7, 5, 6, 1, 8, -844859068910241929474138416799686647778325299200000000⟩, + ⟨3, 7, 6, 6, 2, 8, 993119816272637787112527031681113352266087137280000000⟩ +] + +def collectedFourData_15_30 : List CollectedFourTerm := [ + ⟨3, 7, 7, 6, 3, 8, -136477925551442118023064707883849934381944668160000000⟩, + ⟨3, 7, 8, 6, 4, 8, 56017154606242127724785702636212998075832074240000000⟩, + ⟨3, 7, 5, 7, 0, 8, -3686061290539557414609280936688664737958183567360000000⟩, + ⟨3, 7, 6, 7, 1, 8, -1968814439810376093487290942429424062807083581440000000⟩, + ⟨3, 7, 7, 7, 2, 8, 242359104654785905014017567333357229457633443840000000⟩, + ⟨3, 7, 8, 7, 3, 8, 268291278843095243832393478572882403854448066560000000⟩, + ⟨4, 3, 8, 2, 8, 5, 13899401652267955106864615405978654049130512384000000⟩, + ⟨4, 3, 8, 3, 7, 5, 8514172459868080505007654168466537259225579520000000⟩, + ⟨4, 3, 8, 4, 6, 5, -10860152930615366013842946101318065853822926848000000⟩, + ⟨4, 3, 8, 5, 5, 5, -3630220929825499066202832665123346672041066496000000⟩, + ⟨4, 3, 8, 6, 4, 5, 5407770182917250993776704032448491765435990016000000⟩, + ⟨4, 3, 8, 7, 3, 5, 25900236958889657189472532026971624879060680704000000⟩, + ⟨4, 4, 7, 1, 8, 6, -63997890438679447430432631534890944511072010240000000⟩, + ⟨4, 4, 7, 2, 7, 6, 3778508755552419791736103406849402356944076800000000⟩, + ⟨4, 4, 8, 2, 8, 6, 61082893872745544846009839963540436565318696960000000⟩, + ⟨4, 4, 7, 3, 6, 6, 2950339340624787647599275330953006819825418240000000⟩, + ⟨4, 4, 8, 3, 7, 6, 37416739640408574872252860732665056690228428800000000⟩, + ⟨4, 4, 7, 4, 5, 6, 10157752888361364910822437219737359272955084800000000⟩, + ⟨4, 4, 8, 4, 6, 6, -47726483880284399873524091892843607873416069120000000⟩, + ⟨4, 4, 7, 5, 4, 6, -6436579155759365236160129774576631867978547200000000⟩, + ⟨4, 4, 8, 5, 5, 6, -15953521262188199405357728303510078422767370240000000⟩, + ⟨4, 4, 7, 6, 3, 6, -19300201307985358703263002991837381313817477120000000⟩, + ⟨4, 4, 8, 6, 4, 6, 23765213815332386409663612679921693245875159040000000⟩, + ⟨4, 4, 7, 7, 2, 6, 34273524379569769139282002764895953418589306880000000⟩ +] + +def collectedFourData_15_31 : List CollectedFourTerm := [ + ⟨4, 4, 8, 7, 3, 6, 113822268398199353448393591316256957405079797760000000⟩, + ⟨4, 5, 6, 0, 8, 7, 39080995819470508869081091968927539790537031680000000⟩, + ⟨4, 5, 6, 1, 7, 7, -130703525690678902356476852602206544341447475200000000⟩, + ⟨4, 5, 7, 1, 8, 7, -245712884019501723288555037315086747421837885440000000⟩, + ⟨4, 5, 6, 2, 6, 7, 9022414454652637472441744979512780923663810560000000⟩, + ⟨4, 5, 7, 2, 7, 7, 14507170115385462589528228871733647277608140800000000⟩, + ⟨4, 5, 8, 2, 8, 7, 117260537143098649327144983949464544364860538880000000⟩, + ⟨4, 5, 6, 3, 5, 7, -21979850645957537325490815169541757123648552960000000⟩, + ⟨4, 5, 7, 3, 6, 7, 11327504441974075189610746758136000817859133440000000⟩, + ⟨4, 5, 8, 3, 7, 7, 71828734858540065448060219788804495346394726400000000⟩, + ⟨4, 5, 6, 4, 4, 7, 10157752888361364910822437219737359272955084800000000⟩, + ⟨4, 5, 7, 4, 5, 7, 38999578583737387425480376614253794194934988800000000⟩, + ⟨4, 5, 8, 4, 6, 7, -91620301215798310645784047435745827803742863360000000⟩, + ⟨4, 5, 6, 5, 3, 7, 3762696045669670497130923625465882915142369280000000⟩, + ⟨4, 5, 7, 5, 4, 7, -24712540003124475426199834543013979816670003200000000⟩, + ⟨4, 5, 8, 5, 5, 7, -30625897922015865123125908437530443984373022720000000⟩, + ⟨4, 5, 6, 6, 2, 7, 269608356558619155290578815342210526410052730880000000⟩, + ⟨4, 5, 7, 6, 3, 7, -74101006971252538324111799597406521918194974720000000⟩, + ⟨4, 5, 8, 6, 4, 7, 45621966488884153891432815346644105166973829120000000⟩, + ⟨4, 5, 6, 7, 1, 7, -534486188663899117967094468295450258053519114240000000⟩, + ⟨4, 5, 7, 7, 2, 7, 131589439325127889562820723358881780652604129280000000⟩, + ⟨4, 5, 8, 7, 3, 7, 218504060384310115409487466312247466163206881280000000⟩, + ⟨4, 6, 5, 0, 7, 8, -2980655074929558652463404770908793057954496512000000⟩, + ⟨4, 6, 6, 0, 8, 8, -183623143573471257006373998348735404904642772992000000⟩ +] + +def collectedFourData_15_32 : List CollectedFourTerm := [ + ⟨4, 6, 5, 1, 6, 8, 491784965952887807105306889725480322726157615104000000⟩, + ⟨4, 6, 6, 1, 7, 8, 614114143209761972224134245925538924644406394880000000⟩, + ⟨4, 6, 7, 1, 8, 8, 577244402734566088760515125189553915687619002368000000⟩, + ⟨4, 6, 5, 2, 5, 8, -86023927223478370384422368729659466425886048256000000⟩, + ⟨4, 6, 6, 2, 6, 8, -42392064737527710387071620212999508521243377664000000⟩, + ⟨4, 6, 7, 2, 7, 8, -34081170721026521351954263480479956625795317760000000⟩, + ⟨4, 6, 8, 2, 8, 8, -183650629467005962282837499382251518841768116224000000⟩, + ⟨4, 6, 5, 3, 4, 8, 116429794523196673609328586075278121371411939328000000⟩, + ⟨4, 6, 6, 3, 5, 8, 103272938323524989745317851378158155775527092224000000⟩, + ⟨4, 6, 7, 3, 6, 8, -26611297011033020210000189845098662673638227968000000⟩, + ⟨4, 6, 8, 3, 7, 8, -112496434793672048511214091399067409633215774720000000⟩, + ⟨4, 6, 5, 4, 3, 8, -10860152930615366013842946101318065853822926848000000⟩, + ⟨4, 6, 6, 4, 4, 8, -47726483880284399873524091892843607873416069120000000⟩, + ⟨4, 6, 7, 4, 5, 8, -91620301215798310645784047435745827803742863360000000⟩, + ⟨4, 6, 8, 4, 6, 8, 143493509412329606140611659013656832238134755328000000⟩, + ⟨4, 6, 5, 5, 2, 8, -843515792763123411987236495611274622993671651328000000⟩, + ⟨4, 6, 6, 5, 3, 8, -17679131806388433297462492671796498405557010432000000⟩, + ⟨4, 6, 7, 5, 4, 8, 58056277557775368190697113402681691756078039040000000⟩, + ⟨4, 6, 8, 5, 5, 8, 47965543808712721266314992951837586585032851456000000⟩, + ⟨4, 6, 5, 6, 1, 8, 1077650087125989037125270320819642702749583278080000000⟩, + ⟨4, 6, 6, 6, 2, 8, -1266762346426864810554108724733079914032473833472000000⟩, + ⟨4, 6, 7, 6, 3, 8, 174082818985412562146425780888334232619617091584000000⟩, + ⟨4, 6, 8, 6, 4, 8, -71452025270714378732061283679066271777791410176000000⟩, + ⟨4, 6, 5, 7, 0, 8, 4701712293892303902394983533852078072440673009664000000⟩ +] + +def collectedFourData_15_33 : List CollectedFourTerm := [ + ⟨4, 6, 6, 7, 1, 8, 2511298192411267560726457972711832845184931987456000000⟩, + ⟨4, 6, 7, 7, 2, 8, -309138316505133455049463110665640868787011977216000000⟩, + ⟨4, 6, 8, 7, 3, 8, -342215797474171681573752142664695515827870367744000000⟩, + ⟨5, 2, 8, 2, 8, 5, 1079576399941316198000933598844982236192098484224000000⟩, + ⟨5, 2, 8, 3, 7, 5, 661301823104311829768387056398180001870742814720000000⟩, + ⟨5, 2, 8, 4, 6, 5, -843515792763123411987236495611274622993671651328000000⟩, + ⟨5, 2, 8, 5, 5, 5, -281961838391306071259216504980905058850052243456000000⟩, + ⟨5, 2, 8, 6, 4, 5, 420025351582756813848341925143672695588625842176000000⟩, + ⟨5, 2, 8, 7, 3, 5, 2011689803146504336461627778181193041466825375744000000⟩, + ⟨5, 3, 7, 1, 8, 6, -23706484291494341321366250122794985975986520064000000⟩, + ⟨5, 3, 7, 2, 7, 6, 1399657986298862037633839333177577632673300480000000⟩, + ⟨5, 3, 8, 2, 8, 6, 22626693694860763740225214479293157166710521856000000⟩, + ⟨5, 3, 7, 3, 6, 6, 1092882480245430257164420603752652860360228864000000⟩, + ⟨5, 3, 8, 3, 7, 6, 13860134208239107473134625990658648148992327680000000⟩, + ⟨5, 3, 7, 4, 5, 6, 3762696045669670497130923625465882915142369280000000⟩, + ⟨5, 3, 8, 4, 6, 6, -17679131806388433297462492671796498405557010432000000⟩, + ⟨5, 3, 7, 5, 4, 6, -2384276444130208482805628928565666069264465920000000⟩, + ⟨5, 3, 8, 5, 5, 6, -5909599497790719100956115399077336991414616064000000⟩, + ⟨5, 3, 7, 6, 3, 6, -7149296890790990709315990742261499748503519232000000⟩, + ⟨5, 3, 8, 6, 4, 6, 8803253734386790514086720378358596669217439744000000⟩, + ⟨5, 3, 7, 7, 2, 6, 12695805467165091626431938429395365168486023168000000⟩, + ⟨5, 3, 8, 7, 3, 6, 42162730666717955306613704630860749857133428736000000⟩, + ⟨5, 4, 6, 0, 8, 7, -24764130988670088048855803939109215441277419520000000⟩, + ⟨5, 4, 6, 1, 7, 7, 82821820760063523853459096631811656681049292800000000⟩ +] + +def collectedFourData_15_34 : List CollectedFourTerm := [ + ⟨5, 4, 7, 1, 8, 7, 155698848452354586096385614727340779039264604160000000⟩, + ⟨5, 4, 6, 2, 6, 7, -5717158652282148968678733534923143209906339840000000⟩, + ⟨5, 4, 7, 2, 7, 7, -9192638352202386931713675526328429304820531200000000⟩, + ⟨5, 4, 8, 2, 8, 7, -74303513529375879350231371986846913204133560320000000⟩, + ⟨5, 4, 6, 3, 5, 7, 13927789942259253912112141553677301360036413440000000⟩, + ⟨5, 4, 7, 3, 6, 7, -7177805935948866853315288585077583882915676160000000⟩, + ⟨5, 4, 8, 3, 7, 7, -45515119599412481402465922303361011762698649600000000⟩, + ⟨5, 4, 6, 4, 4, 7, -6436579155759365236160129774576631867978547200000000⟩, + ⟨5, 4, 7, 4, 5, 7, -24712540003124475426199834543013979816670003200000000⟩, + ⟨5, 4, 8, 4, 6, 7, 58056277557775368190697113402681691756078039040000000⟩, + ⟨5, 4, 6, 5, 3, 7, -2384276444130208482805628928565666069264465920000000⟩, + ⟨5, 4, 7, 5, 4, 7, 15659390577637935042327151097821740007214284800000000⟩, + ⟨5, 4, 8, 5, 5, 7, 19406459121202492661904448929899960426645422080000000⟩, + ⟨5, 4, 6, 6, 2, 7, -170840494656263687969291942946937085681278648320000000⟩, + ⟨5, 4, 7, 6, 3, 7, 46954971452242678538837820239176988323039150080000000⟩, + ⟨5, 4, 8, 6, 4, 7, -28908893706556307762394996915878530421285191680000000⟩, + ⟨5, 4, 6, 7, 1, 7, 338683437055958855747684001016061221515149967360000000⟩, + ⟨5, 4, 7, 7, 2, 7, -83383190316496713756804239469198777874561105920000000⟩, + ⟨5, 4, 8, 7, 3, 7, -138457658497470865615372331356421354600446033920000000⟩, + ⟨5, 5, 5, 0, 7, 8, -996342915862305396962575700708337496017076224000000⟩, + ⟨5, 5, 6, 0, 8, 8, -61379667787329858385365528485329324059534557184000000⟩, + ⟨5, 5, 5, 1, 6, 8, 164388852328485070673098168948970397390348484608000000⟩, + ⟨5, 5, 6, 1, 7, 8, 205279799485807939585425256847897595651827957760000000⟩, + ⟨5, 5, 7, 1, 8, 8, 192955359452097806893831612849356590618599489536000000⟩ +] + +def collectedFourData_15_35 : List CollectedFourTerm := [ + ⟨5, 5, 5, 2, 5, 8, -28755199219350379776056638850427228549506138112000000⟩, + ⟨5, 5, 6, 2, 6, 8, -14170386149430643586751665857137528650468425728000000⟩, + ⟨5, 5, 7, 2, 7, 8, -11392305435740860713345707586855625542881771520000000⟩, + ⟨5, 5, 8, 2, 8, 8, -61388855490912130929052571078957455740499918848000000⟩, + ⟨5, 5, 5, 3, 4, 8, 38918961789375227591534419677688006845929619456000000⟩, + ⟨5, 5, 6, 3, 5, 8, 34521022363300664961498689049836056739051470848000000⟩, + ⟨5, 5, 7, 3, 6, 8, -8895352394801029488316758019882941823882100736000000⟩, + ⟨5, 5, 8, 3, 7, 8, -37604158498309235873901631670550224010938941440000000⟩, + ⟨5, 5, 5, 4, 3, 8, -3630220929825499066202832665123346672041066496000000⟩, + ⟨5, 5, 6, 4, 4, 8, -15953521262188199405357728303510078422767370240000000⟩, + ⟨5, 5, 7, 4, 5, 8, -30625897922015865123125908437530443984373022720000000⟩, + ⟨5, 5, 8, 4, 6, 8, 47965543808712721266314992951837586585032851456000000⟩, + ⟨5, 5, 5, 5, 2, 8, -281961838391306071259216504980905058850052243456000000⟩, + ⟨5, 5, 6, 5, 3, 8, -5909599497790719100956115399077336991414616064000000⟩, + ⟨5, 5, 7, 5, 4, 8, 19406459121202492661904448929899960426645422080000000⟩, + ⟨5, 5, 8, 5, 5, 8, 16033431771847468442220073062125947609795264512000000⟩, + ⟨5, 5, 5, 6, 1, 8, 360225857435634403450274046743205340850065244160000000⟩, + ⟨5, 5, 6, 6, 2, 8, -423440370729023732464855175240694504327840006144000000⟩, + ⟨5, 5, 7, 6, 3, 8, 58190625587080006248800962639879586887728365568000000⟩, + ⟨5, 5, 8, 6, 4, 8, -23884252760837526362401169975651772122322173952000000⟩, + ⟨5, 5, 5, 7, 0, 8, 1571640333644782805038761992417084174523042889728000000⟩, + ⟨5, 5, 6, 7, 1, 8, 839451094047140376097856690757902216720403136512000000⟩, + ⟨5, 5, 7, 7, 2, 8, -103335597017634795096418790609707655996513452032000000⟩, + ⟨5, 5, 8, 7, 3, 8, -114392399300888021829286250530553361076624293888000000⟩ +] + +def collectedFourData_15_36 : List CollectedFourTerm := [ + ⟨6, 1, 8, 2, 8, 5, -1379233929509401863796059323899753224452324720640000000⟩, + ⟨6, 1, 8, 3, 7, 5, -844859068910241929474138416799686647778325299200000000⟩, + ⟨6, 1, 8, 4, 6, 5, 1077650087125989037125270320819642702749583278080000000⟩, + ⟨6, 1, 8, 5, 5, 5, 360225857435634403450274046743205340850065244160000000⟩, + ⟨6, 1, 8, 6, 4, 5, -536611597093586109021709314253142665693872783360000000⟩, + ⟨6, 1, 8, 7, 3, 5, -2570073625450287691964008531259451800226197667840000000⟩, + ⟨6, 2, 7, 1, 8, 6, -1698640068726301073705229042466230596487446790144000000⟩, + ⟨6, 2, 7, 2, 7, 6, 100289655303002679111010048666349108136593326080000000⟩, + ⟨6, 2, 8, 2, 8, 6, 1621269862721787851666884431014980512063135154176000000⟩, + ⟨6, 2, 7, 3, 6, 6, 78308278381874258562353554583804021456391634944000000⟩, + ⟨6, 2, 8, 3, 7, 6, 993119816272637787112527031681113352266087137280000000⟩, + ⟨6, 2, 7, 4, 5, 6, 269608356558619155290578815342210526410052730880000000⟩, + ⟨6, 2, 8, 4, 6, 6, -1266762346426864810554108724733079914032473833472000000⟩, + ⟨6, 2, 7, 5, 4, 6, -170840494656263687969291942946937085681278648320000000⟩, + ⟨6, 2, 8, 5, 5, 6, -423440370729023732464855175240694504327840006144000000⟩, + ⟨6, 2, 7, 6, 3, 6, -512268374027738857153840890765716381757207478272000000⟩, + ⟨6, 2, 8, 6, 4, 6, 630779298377829808787151562127507656381430759424000000⟩, + ⟨6, 2, 7, 7, 2, 6, 909692200923212874444282911162620000384610992128000000⟩, + ⟨6, 2, 8, 7, 3, 6, 3021084984039519820567183303587917490835377094656000000⟩, + ⟨6, 3, 6, 0, 8, 7, -74255703492900490513992602157333323416225185792000000⟩, + ⟨6, 3, 6, 1, 7, 7, 248342757026892198927240608961345427174462586880000000⟩, + ⟨6, 3, 7, 1, 8, 7, 466865868628850322066614833237673341024664027136000000⟩, + ⟨6, 3, 6, 2, 6, 7, -17143005660079999366132630281085998623845515264000000⟩, + ⟨6, 3, 7, 2, 7, 7, -27564295638353182487548573182290362493325803520000000⟩ +] + +def collectedFourData_15_37 : List CollectedFourTerm := [ + ⟨6, 3, 8, 2, 8, 7, -222800455693049147721521938658793431604733673472000000⟩, + ⟨6, 3, 6, 3, 5, 7, 41762735011253692379970756559567450845241933824000000⟩, + ⟨6, 3, 7, 3, 6, 7, -21522783478784350989256862923935938172300558336000000⟩, + ⟨6, 3, 8, 3, 7, 7, -136477925551442118023064707883849934381944668160000000⟩, + ⟨6, 3, 6, 4, 4, 7, -19300201307985358703263002991837381313817477120000000⟩, + ⟨6, 3, 7, 4, 5, 7, -74101006971252538324111799597406521918194974720000000⟩, + ⟨6, 3, 8, 4, 6, 7, 174082818985412562146425780888334232619617091584000000⟩, + ⟨6, 3, 6, 5, 3, 7, -7149296890790990709315990742261499748503519232000000⟩, + ⟨6, 3, 7, 5, 4, 7, 46954971452242678538837820239176988323039150080000000⟩, + ⟨6, 3, 8, 5, 5, 7, 58190625587080006248800962639879586887728365568000000⟩, + ⟨6, 3, 6, 6, 2, 7, -512268374027738857153840890765716381757207478272000000⟩, + ⟨6, 3, 7, 6, 3, 7, 140795347887254286333675832613704689525737914368000000⟩, + ⟨6, 3, 8, 6, 4, 7, -86683850944090976943311022398467765298138185728000000⟩, + ⟨6, 3, 6, 7, 1, 7, 1015548532330481650249911724498346151397457657856000000⟩, + ⟨6, 3, 7, 7, 2, 7, -250026033995161967746135276057553515104260063232000000⟩, + ⟨6, 3, 8, 7, 3, 7, -415167842570905707871805491010598469797289132032000000⟩, + ⟨6, 4, 5, 0, 7, 8, 1484205401410652354340849248950921139117359104000000⟩, + ⟨6, 4, 6, 0, 8, 8, 91434417825816534571652083709603293960825995264000000⟩, + ⟨6, 4, 5, 1, 6, 8, -244882378017885780912196359755469725005479149568000000⟩, + ⟨6, 4, 6, 1, 7, 8, -305795707829811295952455389978059852162751528960000000⟩, + ⟨6, 4, 7, 1, 8, 8, -287436566437650069394221677803285796589567737856000000⟩, + ⟨6, 4, 5, 2, 5, 8, 42835274201816469492727500352422639117168279552000000⟩, + ⟨6, 4, 6, 2, 6, 8, 21108960909163775008428225396737557529087705088000000⟩, + ⟨6, 4, 7, 2, 7, 8, 16970584116225380779332326584379555729815633920000000⟩ +] + +def collectedFourData_15_38 : List CollectedFourTerm := [ + ⟨6, 4, 8, 2, 8, 8, 91448104317752463050091183412526964265722052608000000⟩, + ⟨6, 4, 5, 3, 4, 8, -57975755520972107896758620057100080989052338176000000⟩, + ⟨6, 4, 6, 3, 5, 8, -51424351032280161092987903006605564844187844608000000⟩, + ⟨6, 4, 7, 3, 6, 8, 13250990057362398616520022187109901284520493056000000⟩, + ⟨6, 4, 8, 3, 7, 8, 56017154606242127724785702636212998075832074240000000⟩, + ⟨6, 4, 5, 4, 3, 8, 5407770182917250993776704032448491765435990016000000⟩, + ⟨6, 4, 6, 4, 4, 8, 23765213815332386409663612679921693245875159040000000⟩, + ⟨6, 4, 7, 4, 5, 8, 45621966488884153891432815346644105166973829120000000⟩, + ⟨6, 4, 8, 4, 6, 8, -71452025270714378732061283679066271777791410176000000⟩, + ⟨6, 4, 5, 5, 2, 8, 420025351582756813848341925143672695588625842176000000⟩, + ⟨6, 4, 6, 5, 3, 8, 8803253734386790514086720378358596669217439744000000⟩, + ⟨6, 4, 7, 5, 4, 8, -28908893706556307762394996915878530421285191680000000⟩, + ⟨6, 4, 8, 5, 5, 8, -23884252760837526362401169975651772122322173952000000⟩, + ⟨6, 4, 5, 6, 1, 8, -536611597093586109021709314253142665693872783360000000⟩, + ⟨6, 4, 6, 6, 2, 8, 630779298377829808787151562127507656381430759424000000⟩, + ⟨6, 4, 7, 6, 3, 8, -86683850944090976943311022398467765298138185728000000⟩, + ⟨6, 4, 8, 6, 4, 8, 35579253279090322447876848665240937409850376192000000⟩, + ⟨6, 4, 5, 7, 0, 8, -2341199034121297380242187298817852001977093849088000000⟩, + ⟨6, 4, 6, 7, 1, 8, -1250490998800891885516081790377887516168082685952000000⟩, + ⟨6, 4, 7, 7, 2, 8, 153934201578409144939776892786147549922168143872000000⟩, + ⟨6, 4, 8, 7, 3, 8, 170405002353794005739222574878441321582661992448000000⟩, + ⟨7, 0, 8, 2, 8, 5, -6017501599078520547028150002293162823074407514112000000⟩, + ⟨7, 0, 8, 3, 7, 5, -3686061290539557414609280936688664737958183567360000000⟩, + ⟨7, 0, 8, 4, 6, 5, 4701712293892303902394983533852078072440673009664000000⟩ +] + +def collectedFourData_15_39 : List CollectedFourTerm := [ + ⟨7, 0, 8, 5, 5, 5, 1571640333644782805038761992417084174523042889728000000⟩, + ⟨7, 0, 8, 6, 4, 5, -2341199034121297380242187298817852001977093849088000000⟩, + ⟨7, 0, 8, 7, 3, 5, -11213052274894179420018226755365298532848733519872000000⟩, + ⟨7, 1, 7, 1, 8, 6, 3367475948572483227274564552712006347079666368512000000⟩, + ⟨7, 1, 7, 2, 7, 6, -198819637156400459803369760520151773516492963840000000⟩, + ⟨7, 1, 8, 2, 8, 6, -3214093067376433135872989379497783131934816206848000000⟩, + ⟨7, 1, 7, 3, 6, 6, -155242566615546983542485073051825510462009638912000000⟩, + ⟨7, 1, 8, 3, 7, 6, -1968814439810376093487290942429424062807083581440000000⟩, + ⟨7, 1, 7, 4, 5, 6, -534486188663899117967094468295450258053519114240000000⟩, + ⟨7, 1, 8, 4, 6, 6, 2511298192411267560726457972711832845184931987456000000⟩, + ⟨7, 1, 7, 5, 4, 6, 338683437055958855747684001016061221515149967360000000⟩, + ⟨7, 1, 8, 5, 5, 6, 839451094047140376097856690757902216720403136512000000⟩, + ⟨7, 1, 7, 6, 3, 6, 1015548532330481650249911724498346151397457657856000000⟩, + ⟨7, 1, 8, 6, 4, 6, -1250490998800891885516081790377887516168082685952000000⟩, + ⟨7, 1, 7, 7, 2, 6, -1803423022694798577457156295860330989728871481344000000⟩, + ⟨7, 1, 8, 7, 3, 6, -5989162277312201236828607324710609960757926821888000000⟩, + ⟨7, 2, 6, 0, 8, 7, 131864151226912150168615157241804010380337348608000000⟩, + ⟨7, 2, 6, 1, 7, 7, -441009987493194614275921612178506218445335429120000000⟩, + ⟨7, 2, 7, 1, 8, 7, -829065898075349607646132635026880697791166808064000000⟩, + ⟨7, 2, 6, 2, 6, 7, 30442750987615767219737526116542088120459329536000000⟩, + ⟨7, 2, 7, 2, 7, 7, 48949000245706822097857248717840737731325460480000000⟩, + ⟨7, 2, 8, 2, 8, 7, 395651668504387756546279117583473695081709436928000000⟩, + ⟨7, 2, 6, 3, 5, 7, -74162755803666108664128010303477972345842302976000000⟩, + ⟨7, 2, 7, 3, 6, 7, 38220411927574724399558040544511309285230116864000000⟩ +] + +def collectedFourData_15_40 : List CollectedFourTerm := [ + ⟨7, 2, 8, 3, 7, 7, 242359104654785905014017567333357229457633443840000000⟩, + ⟨7, 2, 6, 4, 4, 7, 34273524379569769139282002764895953418589306880000000⟩, + ⟨7, 2, 7, 4, 5, 7, 131589439325127889562820723358881780652604129280000000⟩, + ⟨7, 2, 8, 4, 6, 7, -309138316505133455049463110665640868787011977216000000⟩, + ⟨7, 2, 6, 5, 3, 7, 12695805467165091626431938429395365168486023168000000⟩, + ⟨7, 2, 7, 5, 4, 7, -83383190316496713756804239469198777874561105920000000⟩, + ⟨7, 2, 8, 5, 5, 7, -103335597017634795096418790609707655996513452032000000⟩, + ⟨7, 2, 6, 6, 2, 7, 909692200923212874444282911162620000384610992128000000⟩, + ⟨7, 2, 7, 6, 3, 7, -250026033995161967746135276057553515104260063232000000⟩, + ⟨7, 2, 8, 6, 4, 7, 153934201578409144939776892786147549922168143872000000⟩, + ⟨7, 2, 6, 7, 1, 7, -1803423022694798577457156295860330989728871481344000000⟩, + ⟨7, 2, 7, 7, 2, 7, 443999170522373305361115970536553844009670279168000000⟩, + ⟨7, 2, 8, 7, 3, 7, 737259935629792399917885031511199273204861370368000000⟩, + ⟨7, 3, 5, 0, 7, 8, 7108525379579367539051501526472675024045080576000000⟩, + ⟨7, 3, 6, 0, 8, 8, 437920438144294229059229201743671060085516271616000000⟩, + ⟨7, 3, 5, 1, 6, 8, -1172851545680539833664751506948737535086000340992000000⟩, + ⟨7, 3, 6, 1, 7, 8, -1464592803670313711369454409831034925210654474240000000⟩, + ⟨7, 3, 7, 1, 8, 8, -1376662640898082004030143140512269478885446385664000000⟩, + ⟨7, 3, 5, 2, 5, 8, 205157341103494181095273350733748471878844940288000000⟩, + ⟨7, 3, 6, 2, 6, 8, 101100281818623018402150150270384035522383183872000000⟩, + ⟨7, 3, 7, 2, 7, 8, 81279739166706410779654963642934306827382292480000000⟩, + ⟨7, 3, 8, 2, 8, 8, 437985988892992142853428336307840121649340874752000000⟩, + ⟨7, 3, 5, 3, 4, 8, -277671897117083896294655447251273622796311199744000000⟩, + ⟨7, 3, 6, 3, 5, 8, -246294282512330411670713794778760288219275722752000000⟩ +] + +def collectedFourData_15_41 : List CollectedFourTerm := [ + ⟨7, 3, 7, 3, 6, 8, 63464934865341084245815966862598119343431614464000000⟩, + ⟨7, 3, 8, 3, 7, 8, 268291278843095243832393478572882403854448066560000000⟩, + ⟨7, 3, 5, 4, 3, 8, 25900236958889657189472532026971624879060680704000000⟩, + ⟨7, 3, 6, 4, 4, 8, 113822268398199353448393591316256957405079797760000000⟩, + ⟨7, 3, 7, 4, 5, 8, 218504060384310115409487466312247466163206881280000000⟩, + ⟨7, 3, 8, 4, 6, 8, -342215797474171681573752142664695515827870367744000000⟩, + ⟨7, 3, 5, 5, 2, 8, 2011689803146504336461627778181193041466825375744000000⟩, + ⟨7, 3, 6, 5, 3, 8, 42162730666717955306613704630860749857133428736000000⟩, + ⟨7, 3, 7, 5, 4, 8, -138457658497470865615372331356421354600446033920000000⟩, + ⟨7, 3, 8, 5, 5, 8, -114392399300888021829286250530553361076624293888000000⟩, + ⟨7, 3, 5, 6, 1, 8, -2570073625450287691964008531259451800226197667840000000⟩, + ⟨7, 3, 6, 6, 2, 8, 3021084984039519820567183303587917490835377094656000000⟩, + ⟨7, 3, 7, 6, 3, 8, -415167842570905707871805491010598469797289132032000000⟩, + ⟨7, 3, 8, 6, 4, 8, 170405002353794005739222574878441321582661992448000000⟩, + ⟨7, 3, 5, 7, 0, 8, -11213052274894179420018226755365298532848733519872000000⟩, + ⟨7, 3, 6, 7, 1, 8, -5989162277312201236828607324710609960757926821888000000⟩, + ⟨7, 3, 7, 7, 2, 8, 737259935629792399917885031511199273204861370368000000⟩, + ⟨7, 3, 8, 7, 3, 8, 816145988208861316525629862604796356824727027712000000⟩, + ⟨0, 7, 8, 3, 8, 4, 133232735410339977791547999445650431780742758400000000⟩, + ⟨0, 7, 8, 4, 7, 4, 47327793203882175451019374027617147155680906444800000⟩, + ⟨0, 7, 8, 5, 6, 4, 98548886951376882248051745859358150533879903027200000⟩, + ⟨0, 7, 8, 6, 5, 4, -103422660381006268535674870590463049109950850662400000⟩, + ⟨0, 7, 8, 7, 4, 4, 204489533075926466788524857818498263385223725056000000⟩, + ⟨0, 8, 7, 2, 8, 5, -4970628017551744349150245870527861730433826816000000⟩ +] + +def collectedFourData_15_42 : List CollectedFourTerm := [ + ⟨0, 8, 7, 3, 7, 5, 2775494877475523499285223441253045954710339584000000⟩, + ⟨0, 8, 8, 3, 8, 5, 12559522586091285333032966468340452809506816000000000⟩, + ⟨0, 8, 7, 4, 6, 5, -911542851198196757848852299980707327188664320000000⟩, + ⟨0, 8, 8, 4, 7, 5, 4461474770920932910421579257664338063735652352000000⟩, + ⟨0, 8, 7, 5, 5, 5, -2414168283868398436533093447104891390709989376000000⟩, + ⟨0, 8, 8, 5, 6, 5, 9289961417424420077001186310248314801831804928000000⟩, + ⟨0, 8, 7, 6, 4, 5, 864237433565456177082016106519842641414193152000000⟩, + ⟨0, 8, 8, 6, 5, 5, -9749400062742297993438579466805605577602891776000000⟩, + ⟨0, 8, 7, 7, 3, 5, 36211171374071174191976875061519042729453027328000000⟩, + ⟨0, 8, 8, 7, 4, 5, 19276725808986418895333803093714901398915645440000000⟩, + ⟨1, 6, 8, 3, 8, 4, 298512518152573804554720716702719283165763993600000000⟩, + ⟨1, 6, 8, 4, 7, 4, 106039545644566046284945404937558503167632814899200000⟩, + ⟨1, 6, 8, 5, 6, 4, 220802164831224697822870687005322499609936579788800000⟩, + ⟨1, 6, 8, 6, 5, 4, -231722021538383942910098724238915232880016333209600000⟩, + ⟨1, 6, 8, 7, 4, 4, 458165819881541037807716704915608995926716186624000000⟩, + ⟨1, 7, 7, 2, 8, 5, 39424717567362823349224526610067359650612772864000000⟩, + ⟨1, 7, 7, 3, 7, 5, -22013938936438568714419671934272861132854132736000000⟩, + ⟨1, 7, 8, 3, 8, 5, -99616311860216297821611463140409170003492864000000000⟩, + ⟨1, 7, 7, 4, 6, 5, 7229935398935419420872658357147685558188769280000000⟩, + ⟨1, 7, 8, 4, 7, 5, -35386350005749849505921513760419324760170692608000000⟩, + ⟨1, 7, 7, 5, 5, 5, 19148063869497915627694993913681932401827119104000000⟩, + ⟨1, 7, 8, 5, 6, 5, -73683668099962110184467741258288903848315584512000000⟩, + ⟨1, 7, 7, 6, 4, 5, -6854730752160113242224678488334615846278135808000000⟩, + ⟨1, 7, 8, 6, 5, 5, 77327722486496288133922144248924995932026568704000000⟩ +] + +def collectedFourData_15_43 : List CollectedFourTerm := [ + ⟨1, 7, 7, 7, 3, 5, -287210227593995993818277356892844141317940314112000000⟩, + ⟨1, 7, 8, 7, 4, 5, -152894054425160331035013817547299221713725685760000000⟩, + ⟨1, 8, 6, 1, 8, 6, 3436359138522745300912541557057012768721338368000000⟩, + ⟨1, 8, 6, 2, 7, 6, 4598241572113782822855189501362564942373322752000000⟩, + ⟨1, 8, 7, 2, 8, 6, 21564864443245261585939619595593955217955094528000000⟩, + ⟨1, 8, 6, 3, 6, 6, -12183995693141637031610921806493102051665379328000000⟩, + ⟨1, 8, 7, 3, 7, 6, -12041369940444996845414841330751575660190236672000000⟩, + ⟨1, 8, 8, 3, 8, 6, -27244485111796664188672844003011333680267264000000000⟩, + ⟨1, 8, 6, 4, 5, 6, 9693602281127972965104337806825013962784899072000000⟩, + ⟨1, 8, 7, 4, 6, 6, 3954691027147208313722771737462966911038914560000000⟩, + ⟨1, 8, 8, 4, 7, 6, -9677962051489106946371321720316212822207889408000000⟩, + ⟨1, 8, 6, 5, 4, 6, 10933230846228152213046668579079349682011373568000000⟩, + ⟨1, 8, 7, 5, 5, 6, 10473769431341700736108538446217692893841195008000000⟩, + ⟨1, 8, 8, 5, 6, 6, -20152057038097471923528788174392639419121139712000000⟩, + ⟨1, 8, 6, 6, 3, 6, -40483450060865913690580395996406872318985371648000000⟩, + ⟨1, 8, 7, 6, 4, 6, -3749458425737695344230137516174666606068105216000000⟩, + ⟨1, 8, 8, 6, 5, 6, 21148684835559197477983726617559084764028207104000000⟩, + ⟨1, 8, 6, 7, 2, 6, 39952207031672514044405159804244012918764470272000000⟩, + ⟨1, 8, 7, 7, 3, 6, -157100672038941013710253200725493440847884058624000000⟩, + ⟨1, 8, 8, 7, 4, 6, -41815639544190859273497385059821249195944181760000000⟩, + ⟨2, 5, 8, 3, 8, 4, -37879674131629813603223728241511128911105228800000000⟩, + ⟨2, 5, 8, 4, 7, 4, -13455862618227739378349133618270894939159763353600000⟩, + ⟨2, 5, 8, 5, 6, 4, -28018637553719922205039382604288286981483816550400000⟩, + ⟨2, 5, 8, 6, 5, 4, 29404310141895494240120503538655962229581335756800000⟩ +] + +def collectedFourData_15_44 : List CollectedFourTerm := [ + ⟨2, 5, 8, 7, 4, 4, -58138841422031455216864567585059497209277448192000000⟩, + ⟨2, 6, 7, 2, 8, 5, 27555827653868470358177896527092280760951898112000000⟩, + ⟨2, 6, 7, 3, 7, 5, -15386598680860580565107638001141004241037426688000000⟩, + ⟨2, 6, 8, 3, 8, 5, -69626622345331658563283358643552568173658112000000000⟩, + ⟨2, 6, 7, 4, 6, 5, 5053348916482644458805240571903471150946058240000000⟩, + ⟨2, 6, 8, 4, 7, 5, -24733218707066473347795279214823268225084555264000000⟩, + ⟨2, 6, 7, 5, 5, 5, 13383501022971184444430857852098822721379500032000000⟩, + ⟨2, 6, 8, 5, 6, 5, -51501052749411473830911413017840968148709277696000000⟩, + ⟨2, 6, 7, 6, 4, 5, -4791100377509470297578528713288638112269860864000000⟩, + ⟨2, 6, 8, 6, 5, 5, 54048057289522275839380712406896198541568376832000000⟩, + ⟨2, 6, 7, 7, 3, 5, -200745015319025203599415794484872574341004394496000000⟩, + ⟨2, 6, 8, 7, 4, 5, -106864994171288007289507526471994844924430254080000000⟩, + ⟨2, 7, 6, 1, 8, 6, 4598241572113782822855189501362564942373322752000000⟩, + ⟨2, 7, 6, 2, 7, 6, 6152973162346745140821684695001516609978236928000000⟩, + ⟨2, 7, 7, 2, 8, 6, 28856255176680032962195429007943744119994580992000000⟩, + ⟨2, 7, 6, 3, 6, 6, -16303579821620070831695683188360409180318728192000000⟩, + ⟨2, 7, 7, 3, 7, 6, -16112730251226900636356775445882597636527095808000000⟩, + ⟨2, 7, 8, 3, 8, 6, -36456237256317042317200045139691534859370496000000000⟩, + ⟨2, 7, 6, 4, 5, 6, 12971148589486875338006219419750103594626449408000000⟩, + ⟨2, 7, 7, 4, 6, 6, 5291828924991533011506952413518058936430755840000000⟩, + ⟨2, 7, 8, 4, 7, 6, -12950220173327859879316397377790707766302605312000000⟩, + ⟨2, 7, 6, 5, 4, 6, 14629913396146117336002800178207125926997655552000000⟩, + ⟨2, 7, 7, 5, 5, 6, 14015101470632029927892941441553137426300403712000000⟩, + ⟨2, 7, 8, 5, 6, 6, -26965757274143130677163782227379754527115706368000000⟩ +] + +def collectedFourData_15_45 : List CollectedFourTerm := [ + ⟨2, 7, 6, 6, 3, 6, -54171486607913449647386566970048430318311964672000000⟩, + ⟨2, 7, 7, 6, 4, 6, -5017204230158276759294509385298751404820660224000000⟩, + ⟨2, 7, 8, 6, 5, 6, 28299359259697752144160250584365503098185056256000000⟩, + ⟨2, 7, 6, 7, 2, 6, 53460622672200701851770451490129861203835486208000000⟩, + ⟨2, 7, 7, 7, 3, 6, -210218668089220280190519808585664145276624961536000000⟩, + ⟨2, 7, 8, 7, 4, 6, -55954108510113966565917765150311658342202736640000000⟩, + ⟨2, 8, 5, 0, 8, 7, -4970628017551744349150245870527861730433826816000000⟩, + ⟨2, 8, 5, 1, 7, 7, 39424717567362823349224526610067359650612772864000000⟩, + ⟨2, 8, 6, 1, 8, 7, 21564864443245261585939619595593955217955094528000000⟩, + ⟨2, 8, 5, 2, 6, 7, 27555827653868470358177896527092280760951898112000000⟩, + ⟨2, 8, 6, 2, 7, 7, 28856255176680032962195429007943744119994580992000000⟩, + ⟨2, 8, 7, 2, 8, 7, 67665130405354114073789212470385890212072914944000000⟩, + ⟨2, 8, 5, 3, 5, 7, -10412238429173028540342539745330299283072614400000000⟩, + ⟨2, 8, 6, 3, 6, 7, -76460638981010387558765799586877641736677490688000000⟩, + ⟨2, 8, 7, 3, 7, 7, -37782795687108282067440863858167622504238022656000000⟩, + ⟨2, 8, 8, 3, 8, 7, -56990902733416374482856189333936726394011648000000000⟩, + ⟨2, 8, 5, 4, 4, 7, 37511211615888790805702146019678214141442523136000000⟩, + ⟨2, 8, 6, 4, 5, 7, 60832180436507694827947560266942714232503795712000000⟩, + ⟨2, 8, 7, 4, 6, 7, 12408827552292731502463712490141414016816250880000000⟩, + ⟨2, 8, 8, 4, 7, 7, -20244676736257747633780872724054535473207443456000000⟩, + ⟨2, 8, 5, 5, 3, 7, -97831396351546626663776684535054044007185252352000000⟩, + ⟨2, 8, 6, 5, 4, 7, 68611466852377482779774228600393413936942153728000000⟩, + ⟨2, 8, 7, 5, 5, 7, 32864058861697871901976279424732111402365353984000000⟩, + ⟨2, 8, 8, 5, 6, 7, -42154730317850150986006689317934676764612624384000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1503.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1503.lean new file mode 100644 index 0000000000000000000000000000000000000000..1e562a6b808f08207d1523bb1b1fc170cbd9adb8 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1503.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1503. -/ +namespace LaughlinFock +def collectedFourData_15_46 : List CollectedFourTerm := [ + ⟨2, 8, 5, 6, 2, 7, -1447897289775205326586057241495509086825873408000000⟩, + ⟨2, 8, 6, 6, 3, 7, -254053804496338162028140480511162082674929041408000000⟩, + ⟨2, 8, 7, 6, 4, 7, -11764859176124496623122237059981025772272877568000000⟩, + ⟨2, 8, 8, 6, 5, 7, 44239508856827448942574895370830274112706838528000000⟩, + ⟨2, 8, 5, 7, 1, 7, 67495989666248900402717186241454604706524430336000000⟩, + ⟨2, 8, 6, 7, 2, 7, 250719989999900068063753063184076231242428710912000000⟩, + ⟨2, 8, 7, 7, 3, 7, -492942466124029353758703870214262872988819914752000000⟩, + ⟨2, 8, 8, 7, 4, 7, -87471318919024492993852034502834040865103544320000000⟩, + ⟨3, 4, 8, 3, 8, 4, 25989240129985935371227543794034975481580748800000000⟩, + ⟨3, 4, 8, 4, 7, 4, 9232065817831665585204314175475362884667152793600000⟩, + ⟨3, 4, 8, 5, 6, 4, 19223584051126521727195857167379908743167108710400000⟩, + ⟨3, 4, 8, 6, 5, 4, -20174293856878606518827887025902860636171062476800000⟩, + ⟨3, 4, 8, 7, 4, 4, 39889052512589203217040700044757381602179284992000000⟩, + ⟨3, 5, 7, 2, 8, 5, -10412238429173028540342539745330299283072614400000000⟩, + ⟨3, 5, 7, 3, 7, 5, 5813976487715053942717671017068526961269145600000000⟩, + ⟨3, 5, 8, 3, 8, 5, 26309098822361223032676447926832211584614400000000000⟩, + ⟨3, 5, 7, 4, 6, 5, -1909457209746839054433614832607216678207488000000000⟩, + ⟨3, 5, 8, 4, 7, 5, 9345688089419635451580374507343196577385676800000000⟩, + ⟨3, 5, 7, 5, 5, 5, -5057086487064521791080243368922857276335718400000000⟩, + ⟨3, 5, 8, 5, 6, 5, 19460175441509857718922702305774874850964275200000000⟩, + ⟨3, 5, 7, 6, 4, 5, 1810364039699826306024464713933991535496396800000000⟩, + ⟨3, 5, 8, 6, 5, 5, -20422585966243155376962250213384260260619878400000000⟩, + ⟨3, 5, 7, 7, 3, 5, 75853463348114882776593431118125910820336435200000000⟩, + ⟨3, 5, 8, 7, 4, 5, 40379981070444383188287785385297267545604096000000000⟩ +] + +def collectedFourData_15_47 : List CollectedFourTerm := [ + ⟨3, 6, 6, 1, 8, 6, -12183995693141637031610921806493102051665379328000000⟩, + ⟨3, 6, 6, 2, 7, 6, -16303579821620070831695683188360409180318728192000000⟩, + ⟨3, 6, 7, 2, 8, 6, -76460638981010387558765799586877641736677490688000000⟩, + ⟨3, 6, 6, 3, 6, 6, 43199719548030404329869276856574666837210431488000000⟩, + ⟨3, 6, 7, 3, 7, 6, 42694023988708281382689997208682003918080704512000000⟩, + ⟨3, 6, 8, 3, 8, 6, 96598369344681593148083142579253611639865344000000000⟩, + ⟨3, 6, 6, 4, 5, 6, -34369751147449636835806417013223900760781094912000000⟩, + ⟨3, 6, 7, 4, 6, 6, -14021799381301347883878212815332309284432117760000000⟩, + ⟨3, 6, 8, 4, 7, 6, 34314296963856472092657961140530412879681159168000000⟩, + ⟨3, 6, 6, 5, 4, 6, -38764992881341520699183784189021107342203158528000000⟩, + ⟨3, 6, 7, 5, 5, 6, -37135921042666404320385903579668046110961696768000000⟩, + ⟨3, 6, 8, 5, 6, 6, 71451372299135208508892419653772984983698276352000000⟩, + ⟨3, 6, 6, 6, 3, 6, 143538600391211702011124980036604230579632734208000000⟩, + ⟨3, 6, 7, 6, 4, 6, 13294124237096041737627806895442669434606452736000000⟩, + ⟨3, 6, 8, 6, 5, 6, -74985027630969647919258675683237427525382569984000000⟩, + ⟨3, 6, 6, 7, 2, 6, -141655018810013402702780415706043438144906330112000000⟩, + ⟨3, 6, 7, 7, 3, 6, 557018004915217207889330548805648078108469755904000000⟩, + ⟨3, 6, 8, 7, 4, 6, 148262027213897477554157920216478943372336168960000000⟩, + ⟨3, 7, 5, 0, 8, 7, 2775494877475523499285223441253045954710339584000000⟩, + ⟨3, 7, 5, 1, 7, 7, -22013938936438568714419671934272861132854132736000000⟩, + ⟨3, 7, 6, 1, 8, 7, -12041369940444996845414841330751575660190236672000000⟩, + ⟨3, 7, 5, 2, 6, 7, -15386598680860580565107638001141004241037426688000000⟩, + ⟨3, 7, 6, 2, 7, 7, -16112730251226900636356775445882597636527095808000000⟩, + ⟨3, 7, 7, 2, 8, 7, -37782795687108282067440863858167622504238022656000000⟩ +] + +def collectedFourData_15_48 : List CollectedFourTerm := [ + ⟨3, 7, 5, 3, 5, 7, 5813976487715053942717671017068526961269145600000000⟩, + ⟨3, 7, 6, 3, 6, 7, 42694023988708281382689997208682003918080704512000000⟩, + ⟨3, 7, 7, 3, 7, 7, 21097124048708133305314887649044181208210079744000000⟩, + ⟨3, 7, 8, 3, 8, 7, 31822529877665769521338913841277733858967552000000000⟩, + ⟨3, 7, 5, 4, 4, 7, -20945477175151717779673383346763650073848971264000000⟩, + ⟨3, 7, 6, 4, 5, 7, -33967419125109826241674436102614592981028569088000000⟩, + ⟨3, 7, 7, 4, 6, 7, -6928830156924348278748467860960411068263301120000000⟩, + ⟨3, 7, 8, 4, 7, 7, 11304204695910208396114424851260622434880978944000000⟩, + ⟨3, 7, 5, 5, 3, 7, 54627008593520978007744119391157325898027368448000000⟩, + ⟨3, 7, 6, 5, 4, 7, -38311210195658741002825629599861770011354857472000000⟩, + ⟨3, 7, 7, 5, 5, 7, -18350604129218966884638192299936537318434799616000000⟩, + ⟨3, 7, 8, 5, 6, 7, 23538321042213709665327653464725350789431689216000000⟩, + ⟨3, 7, 5, 6, 2, 7, 808475608452617830044446864054210205730209792000000⟩, + ⟨3, 7, 6, 6, 3, 7, 141858338723576456137564111153897626744014241792000000⟩, + ⟨3, 7, 7, 6, 4, 7, 6569251664428040544663059141963153801459269632000000⟩, + ⟨3, 7, 8, 6, 5, 7, -24702417839473626742340094496031227123096092672000000⟩, + ⟨3, 7, 5, 7, 1, 7, -37688351030758767269553808361001681153177944064000000⟩, + ⟨3, 7, 6, 7, 2, 7, -139996806332771022486114731407172665023437733888000000⟩, + ⟨3, 7, 7, 7, 3, 7, 275248778380981045822297908098988194769873666048000000⟩, + ⟨3, 7, 8, 7, 4, 7, 48842157716995771981295199478329047439302983680000000⟩, + ⟨3, 8, 4, 0, 7, 8, 133232735410339977791547999445650431780742758400000000⟩, + ⟨3, 8, 5, 0, 8, 8, 12559522586091285333032966468340452809506816000000000⟩, + ⟨3, 8, 4, 1, 6, 8, 298512518152573804554720716702719283165763993600000000⟩, + ⟨3, 8, 5, 1, 7, 8, -99616311860216297821611463140409170003492864000000000⟩ +] + +def collectedFourData_15_49 : List CollectedFourTerm := [ + ⟨3, 8, 6, 1, 8, 8, -27244485111796664188672844003011333680267264000000000⟩, + ⟨3, 8, 4, 2, 5, 8, -37879674131629813603223728241511128911105228800000000⟩, + ⟨3, 8, 5, 2, 6, 8, -69626622345331658563283358643552568173658112000000000⟩, + ⟨3, 8, 6, 2, 7, 8, -36456237256317042317200045139691534859370496000000000⟩, + ⟨3, 8, 7, 2, 8, 8, -56990902733416374482856189333936726394011648000000000⟩, + ⟨3, 8, 4, 3, 4, 8, 25989240129985935371227543794034975481580748800000000⟩, + ⟨3, 8, 5, 3, 5, 8, 26309098822361223032676447926832211584614400000000000⟩, + ⟨3, 8, 6, 3, 6, 8, 96598369344681593148083142579253611639865344000000000⟩, + ⟨3, 8, 7, 3, 7, 8, 31822529877665769521338913841277733858967552000000000⟩, + ⟨3, 8, 8, 3, 8, 8, 36000407169606876302678139444650324262912000000000000⟩, + ⟨3, 8, 4, 4, 3, 8, 58089736151198701691657111218077710571012096000000000⟩, + ⟨3, 8, 5, 4, 4, 8, -94781365223433891365058961399457788131803136000000000⟩, + ⟨3, 8, 6, 4, 5, 8, -76853784014380363953432320498385302486777856000000000⟩, + ⟨3, 8, 7, 4, 6, 8, -10451325222192945982896391314286087986216960000000000⟩, + ⟨3, 8, 8, 4, 7, 8, 12788297264415999929893399137634821932580864000000000⟩, + ⟨3, 8, 4, 5, 2, 8, -398011208410373639591600542257109843698096537600000000⟩, + ⟨3, 8, 5, 5, 3, 8, 247195249326119477200132561623430195002212352000000000⟩, + ⟨3, 8, 6, 5, 4, 8, -86681930789675908713108929626180249781796864000000000⟩, + ⟨3, 8, 7, 5, 5, 8, -27679727664636163220396861552729840657891328000000000⟩, + ⟨3, 8, 8, 5, 6, 8, 26628591280021012071738207901406527903236096000000000⟩, + ⟨3, 8, 4, 6, 1, 8, 213575246081033413808264094868943896266040934400000000⟩, + ⟨3, 8, 5, 6, 2, 8, 3658471052160713159795542889250988813713408000000000⟩, + ⟨3, 8, 6, 6, 3, 8, 320964924792922571998817202780661144778440704000000000⟩, + ⟨3, 8, 7, 6, 4, 8, 9908943365101365074363495862816358432505856000000000⟩ +] + +def collectedFourData_15_50 : List CollectedFourTerm := [ + ⟨3, 8, 8, 6, 5, 8, -27945518590555328802257533424122383808069632000000000⟩, + ⟨3, 8, 4, 7, 0, 8, 4075278929381781960121788898025472643620981964800000000⟩, + ⟨3, 8, 5, 7, 1, 8, -170545332237791480074963631146383105469710336000000000⟩, + ⟨3, 8, 6, 7, 2, 8, -316753070846298320631698721982926081497235456000000000⟩, + ⟨3, 8, 7, 7, 3, 8, 415180403433051387976442946005902933396291584000000000⟩, + ⟨3, 8, 8, 7, 4, 8, 55254487044666767977614584215575357114286080000000000⟩, + ⟨4, 3, 8, 3, 8, 4, 58089736151198701691657111218077710571012096000000000⟩, + ⟨4, 3, 8, 4, 7, 4, 20635011443431229539705122949934620627552960512000000⟩, + ⟨4, 3, 8, 5, 6, 4, 42967509624181360095578473425168101082207879168000000⟩, + ⟨4, 3, 8, 6, 5, 4, -45092484479016635431242795988743252689452793856000000⟩, + ⟨4, 3, 8, 7, 4, 4, 89157840867541763518117186662328671868173680640000000⟩, + ⟨4, 4, 7, 2, 8, 5, 37511211615888790805702146019678214141442523136000000⟩, + ⟨4, 4, 7, 3, 7, 5, -20945477175151717779673383346763650073848971264000000⟩, + ⟨4, 4, 8, 3, 8, 5, -94781365223433891365058961399457788131803136000000000⟩, + ⟨4, 4, 7, 4, 6, 5, 6879025480785785857477408755976177950885150720000000⟩, + ⟨4, 4, 8, 4, 7, 5, -33668849018678736386291832612861434273980219392000000⟩, + ⟨4, 4, 7, 5, 5, 5, 18218699337947764746095658491313115107107536896000000⟩, + ⟨4, 4, 8, 5, 6, 5, -70107380275076466493445056513945831550629183488000000⟩, + ⟨4, 4, 7, 6, 4, 5, -6522031651206532598775388175673989193837576192000000⟩, + ⟨4, 4, 8, 6, 5, 5, 73574567960049270825774166540739101090482487296000000⟩, + ⟨4, 4, 7, 7, 3, 5, -273270280430486488836271020800407162652498853888000000⟩, + ⟨4, 4, 8, 7, 4, 5, -145473235681496495449199011653474408827442954240000000⟩, + ⟨4, 5, 6, 1, 8, 6, 9693602281127972965104337806825013962784899072000000⟩, + ⟨4, 5, 6, 2, 7, 6, 12971148589486875338006219419750103594626449408000000⟩ +] + +def collectedFourData_15_51 : List CollectedFourTerm := [ + ⟨4, 5, 7, 2, 8, 6, 60832180436507694827947560266942714232503795712000000⟩, + ⟨4, 5, 6, 3, 6, 6, -34369751147449636835806417013223900760781094912000000⟩, + ⟨4, 5, 7, 3, 7, 6, -33967419125109826241674436102614592981028569088000000⟩, + ⟨4, 5, 8, 3, 8, 6, -76853784014380363953432320498385302486777856000000000⟩, + ⟨4, 5, 6, 4, 5, 6, 27344617194198277325220721886865603270109298688000000⟩, + ⟨4, 5, 7, 4, 6, 6, 11155761204397979668270427543139622324524810240000000⟩, + ⟨4, 5, 8, 4, 7, 6, -27300497776060319664086718792563786888597471232000000⟩, + ⟨4, 5, 6, 5, 4, 6, 30841477039753374378715269904186616239852879872000000⟩, + ⟨4, 5, 7, 5, 5, 6, 29545385438178735285162534832517116612294213632000000⟩, + ⟨4, 5, 8, 5, 6, 6, -56846801570891650451605939096652078852496949248000000⟩, + ⟨4, 5, 6, 6, 3, 6, -114199490809520547191659630374415524180044808192000000⟩, + ⟨4, 5, 7, 6, 4, 6, -10576821945435564086324073128455420907895128064000000⟩, + ⟨4, 5, 8, 6, 5, 6, 59658182192494448200328185955213183799017865216000000⟩, + ⟨4, 5, 6, 7, 2, 6, 112700910937034850802971592550603606210786623488000000⟩, + ⟨4, 5, 7, 7, 3, 6, -443164224533900901669731982971314109511993655296000000⟩, + ⟨4, 5, 8, 7, 4, 6, -117957455124043521832680112544369828273628119040000000⟩, + ⟨4, 6, 5, 0, 8, 7, -911542851198196757848852299980707327188664320000000⟩, + ⟨4, 6, 5, 1, 7, 7, 7229935398935419420872658357147685558188769280000000⟩, + ⟨4, 6, 6, 1, 8, 7, 3954691027147208313722771737462966911038914560000000⟩, + ⟨4, 6, 5, 2, 6, 7, 5053348916482644458805240571903471150946058240000000⟩, + ⟨4, 6, 6, 2, 7, 7, 5291828924991533011506952413518058936430755840000000⟩, + ⟨4, 6, 7, 2, 8, 7, 12408827552292731502463712490141414016816250880000000⟩, + ⟨4, 6, 5, 3, 5, 7, -1909457209746839054433614832607216678207488000000000⟩, + ⟨4, 6, 6, 3, 6, 7, -14021799381301347883878212815332309284432117760000000⟩ +] + +def collectedFourData_15_52 : List CollectedFourTerm := [ + ⟨4, 6, 7, 3, 7, 7, -6928830156924348278748467860960411068263301120000000⟩, + ⟨4, 6, 8, 3, 8, 7, -10451325222192945982896391314286087986216960000000000⟩, + ⟨4, 6, 5, 4, 4, 7, 6879025480785785857477408755976177950885150720000000⟩, + ⟨4, 6, 6, 4, 5, 7, 11155761204397979668270427543139622324524810240000000⟩, + ⟨4, 6, 7, 4, 6, 7, 2275603406069182450692626709719617254300057600000000⟩, + ⟨4, 6, 8, 4, 7, 7, -3712587280438570100517427381001682485898117120000000⟩, + ⟨4, 6, 5, 5, 3, 7, -17940893917648975635158127282119088008111063040000000⟩, + ⟨4, 6, 6, 5, 4, 7, 12582372267380330155420310156065337032373698560000000⟩, + ⟨4, 6, 7, 5, 5, 7, 6026803416179309730468265760219514741121351680000000⟩, + ⟨4, 6, 8, 5, 6, 7, -7730581111629961114743815378077832921669959680000000⟩, + ⟨4, 6, 5, 6, 2, 7, -265523877285410444782743853213764823453532160000000⟩, + ⟨4, 6, 6, 6, 3, 7, -46589873249538650470394345115657098095660892160000000⟩, + ⟨4, 6, 7, 6, 4, 7, -2157508717104106421635760112143340597002895360000000⟩, + ⟨4, 6, 8, 6, 5, 7, 8112899999067486871792989587030035338425794560000000⟩, + ⟨4, 6, 5, 7, 1, 7, 12377809533838460437584708721445333285700894720000000⟩, + ⟨4, 6, 6, 7, 2, 7, 45978498839561003099432990675767251809064714240000000⟩, + ⟨4, 6, 7, 7, 3, 7, -90398673861876974538996198043422860606743511040000000⟩, + ⟨4, 6, 8, 7, 4, 7, -16041002296685003360020487522519051997177446400000000⟩, + ⟨4, 7, 4, 0, 7, 8, 47327793203882175451019374027617147155680906444800000⟩, + ⟨4, 7, 5, 0, 8, 8, 4461474770920932910421579257664338063735652352000000⟩, + ⟨4, 7, 4, 1, 6, 8, 106039545644566046284945404937558503167632814899200000⟩, + ⟨4, 7, 5, 1, 7, 8, -35386350005749849505921513760419324760170692608000000⟩, + ⟨4, 7, 6, 1, 8, 8, -9677962051489106946371321720316212822207889408000000⟩, + ⟨4, 7, 4, 2, 5, 8, -13455862618227739378349133618270894939159763353600000⟩ +] + +def collectedFourData_15_53 : List CollectedFourTerm := [ + ⟨4, 7, 5, 2, 6, 8, -24733218707066473347795279214823268225084555264000000⟩, + ⟨4, 7, 6, 2, 7, 8, -12950220173327859879316397377790707766302605312000000⟩, + ⟨4, 7, 7, 2, 8, 8, -20244676736257747633780872724054535473207443456000000⟩, + ⟨4, 7, 4, 3, 4, 8, 9232065817831665585204314175475362884667152793600000⟩, + ⟨4, 7, 5, 3, 5, 8, 9345688089419635451580374507343196577385676800000000⟩, + ⟨4, 7, 6, 3, 6, 8, 34314296963856472092657961140530412879681159168000000⟩, + ⟨4, 7, 7, 3, 7, 8, 11304204695910208396114424851260622434880978944000000⟩, + ⟨4, 7, 8, 3, 8, 8, 12788297264415999929893399137634821932580864000000000⟩, + ⟨4, 7, 4, 4, 3, 8, 20635011443431229539705122949934620627552960512000000⟩, + ⟨4, 7, 5, 4, 4, 8, -33668849018678736386291832612861434273980219392000000⟩, + ⟨4, 7, 6, 4, 5, 8, -27300497776060319664086718792563786888597471232000000⟩, + ⟨4, 7, 7, 4, 6, 8, -3712587280438570100517427381001682485898117120000000⟩, + ⟨4, 7, 8, 4, 7, 8, 4542741590465617130872983530136408492613828608000000⟩, + ⟨4, 7, 4, 5, 2, 8, -141384113344651070639074442238517737314034332467200000⟩, + ⟨4, 7, 5, 5, 3, 8, 87810293806973213402395215885699275837663084544000000⟩, + ⟨4, 7, 6, 5, 4, 8, -30791715581699472568783593030751167255158980608000000⟩, + ⟨4, 7, 7, 5, 5, 8, -9832571723585645694933788890594519633065148416000000⟩, + ⟨4, 7, 8, 5, 6, 8, 9459180264745408060463336894248772119415488512000000⟩, + ⟨4, 7, 4, 6, 1, 8, 75867579006464858232306452747897591673553472716800000⟩, + ⟨4, 7, 5, 6, 2, 8, 1299585727680059209651720399634650195008946176000000⟩, + ⟨4, 7, 6, 6, 3, 8, 114015234615682291763689220676066903212936921088000000⟩, + ⟨4, 7, 7, 6, 4, 8, 3519918892366311626291192129430196451102687232000000⟩, + ⟨4, 7, 8, 6, 5, 8, -9926987693794678696199015367775760783668936704000000⟩, + ⟨4, 7, 4, 7, 0, 8, 1447646915181107144925146710980281414208376641945600000⟩ +] + +def collectedFourData_15_54 : List CollectedFourTerm := [ + ⟨4, 7, 5, 7, 1, 8, -60582214957744960767227679713385276916516257792000000⟩, + ⟨4, 7, 6, 7, 2, 8, -112519072640347532696623301393215837777724178432000000⟩, + ⟨4, 7, 7, 7, 3, 8, 147483065745558937767149358141352891888013672448000000⟩, + ⟨4, 7, 8, 7, 4, 8, 19627855934823236965970322427414971640719605760000000⟩, + ⟨5, 2, 8, 3, 8, 4, -398011208410373639591600542257109843698096537600000000⟩, + ⟨5, 2, 8, 4, 7, 4, -141384113344651070639074442238517737314034332467200000⟩, + ⟨5, 2, 8, 5, 6, 4, -294398831204742631188549674010580809182222273740800000⟩, + ⟨5, 2, 8, 6, 5, 4, 308958439594308256980659767509446048546578602393600000⟩, + ⟨5, 2, 8, 7, 4, 4, -610879345201120023313224118586219258415188803584000000⟩, + ⟨5, 3, 7, 2, 8, 5, -97831396351546626663776684535054044007185252352000000⟩, + ⟨5, 3, 7, 3, 7, 5, 54627008593520978007744119391157325898027368448000000⟩, + ⟨5, 3, 8, 3, 8, 5, 247195249326119477200132561623430195002212352000000000⟩, + ⟨5, 3, 7, 4, 6, 5, -17940893917648975635158127282119088008111063040000000⟩, + ⟨5, 3, 8, 4, 7, 5, 87810293806973213402395215885699275837663084544000000⟩, + ⟨5, 3, 7, 5, 5, 5, -47515415236160097849620562446926238345091612672000000⟩, + ⟨5, 3, 8, 5, 6, 5, 182844078114353321941706111524296019998582767616000000⟩, + ⟨5, 3, 7, 6, 4, 5, 17009833487123426013704416355672121794724102144000000⟩, + ⟨5, 3, 8, 6, 5, 5, -191886702919628858034054226453467428922926825472000000⟩, + ⟨5, 3, 7, 7, 3, 5, 712704601217658485330925865642575685802489020416000000⟩, + ⟨5, 3, 8, 7, 4, 5, 379402561672259897332652075367168939822604615680000000⟩, + ⟨5, 4, 6, 1, 8, 6, 10933230846228152213046668579079349682011373568000000⟩, + ⟨5, 4, 6, 2, 7, 6, 14629913396146117336002800178207125926997655552000000⟩, + ⟨5, 4, 7, 2, 8, 6, 68611466852377482779774228600393413936942153728000000⟩, + ⟨5, 4, 6, 3, 6, 6, -38764992881341520699183784189021107342203158528000000⟩ +] + +def collectedFourData_15_55 : List CollectedFourTerm := [ + ⟨5, 4, 7, 3, 7, 6, -38311210195658741002825629599861770011354857472000000⟩, + ⟨5, 4, 8, 3, 8, 6, -86681930789675908713108929626180249781796864000000000⟩, + ⟨5, 4, 6, 4, 5, 6, 30841477039753374378715269904186616239852879872000000⟩, + ⟨5, 4, 7, 4, 6, 6, 12582372267380330155420310156065337032373698560000000⟩, + ⟨5, 4, 8, 4, 7, 6, -30791715581699472568783593030751167255158980608000000⟩, + ⟨5, 4, 6, 5, 4, 6, 34785519184208967464806861152212147820998688768000000⟩, + ⟨5, 4, 7, 5, 5, 6, 33323681957251459197326391101316097840364126208000000⟩, + ⟨5, 4, 8, 5, 6, 6, -64116433336066472968847050785861139668519616512000000⟩, + ⟨5, 4, 6, 6, 3, 6, -128803447813511038399831962645828997089589198848000000⟩, + ⟨5, 4, 7, 6, 4, 6, -11929397616614710698274939113134721901963247616000000⟩, + ⟨5, 4, 8, 6, 5, 6, 67287336416383390207502428355392497071847112704000000⟩, + ⟨5, 4, 6, 7, 2, 6, 127113227891935016777835816521687622891520131072000000⟩, + ⟨5, 4, 7, 7, 3, 6, -499836554987587348014897157573080888347379892224000000⟩, + ⟨5, 4, 8, 7, 4, 6, -133041984754783840951252298257167327851981045760000000⟩, + ⟨5, 5, 5, 0, 8, 7, -2414168283868398436533093447104891390709989376000000⟩, + ⟨5, 5, 5, 1, 7, 7, 19148063869497915627694993913681932401827119104000000⟩, + ⟨5, 5, 6, 1, 8, 7, 10473769431341700736108538446217692893841195008000000⟩, + ⟨5, 5, 5, 2, 6, 7, 13383501022971184444430857852098822721379500032000000⟩, + ⟨5, 5, 6, 2, 7, 7, 14015101470632029927892941441553137426300403712000000⟩, + ⟨5, 5, 7, 2, 8, 7, 32864058861697871901976279424732111402365353984000000⟩, + ⟨5, 5, 5, 3, 5, 7, -5057086487064521791080243368922857276335718400000000⟩, + ⟨5, 5, 6, 3, 6, 7, -37135921042666404320385903579668046110961696768000000⟩, + ⟨5, 5, 7, 3, 7, 7, -18350604129218966884638192299936537318434799616000000⟩, + ⟨5, 5, 8, 3, 8, 7, -27679727664636163220396861552729840657891328000000000⟩ +] + +def collectedFourData_15_56 : List CollectedFourTerm := [ + ⟨5, 5, 5, 4, 4, 7, 18218699337947764746095658491313115107107536896000000⟩, + ⟨5, 5, 6, 4, 5, 7, 29545385438178735285162534832517116612294213632000000⟩, + ⟨5, 5, 7, 4, 6, 7, 6026803416179309730468265760219514741121351680000000⟩, + ⟨5, 5, 8, 4, 7, 7, -9832571723585645694933788890594519633065148416000000⟩, + ⟨5, 5, 5, 5, 3, 7, -47515415236160097849620562446926238345091612672000000⟩, + ⟨5, 5, 6, 5, 4, 7, 33323681957251459197326391101316097840364126208000000⟩, + ⟨5, 5, 7, 5, 5, 7, 15961638711032203809748125994587741286431719424000000⟩, + ⟨5, 5, 8, 5, 6, 7, -20473994953761399952573696837864249007039053824000000⟩, + ⟨5, 5, 5, 6, 2, 7, -703224562958945005109956612687255206717554688000000⟩, + ⟨5, 5, 6, 6, 3, 7, -123390572588703584709731764151581167429183602688000000⟩, + ⟨5, 5, 7, 6, 4, 7, -5714036493353867597494483158895393088835944448000000⟩, + ⟨5, 5, 8, 6, 5, 7, 21486544315716565952849926550658703200519979008000000⟩, + ⟨5, 5, 5, 7, 1, 7, 32781909441862792595567355763141645511316996096000000⟩, + ⟨5, 5, 6, 7, 2, 7, 121771382982645368283183463899551679671363960832000000⟩, + ⟨5, 5, 7, 7, 3, 7, -239415635868615000545795810319712280868733059072000000⟩, + ⟨5, 5, 8, 7, 4, 7, -42483662655258922400959323795092499062084075520000000⟩, + ⟨5, 6, 4, 0, 7, 8, 98548886951376882248051745859358150533879903027200000⟩, + ⟨5, 6, 5, 0, 8, 8, 9289961417424420077001186310248314801831804928000000⟩, + ⟨5, 6, 4, 1, 6, 8, 220802164831224697822870687005322499609936579788800000⟩, + ⟨5, 6, 5, 1, 7, 8, -73683668099962110184467741258288903848315584512000000⟩, + ⟨5, 6, 6, 1, 8, 8, -20152057038097471923528788174392639419121139712000000⟩, + ⟨5, 6, 4, 2, 5, 8, -28018637553719922205039382604288286981483816550400000⟩, + ⟨5, 6, 5, 2, 6, 8, -51501052749411473830911413017840968148709277696000000⟩, + ⟨5, 6, 6, 2, 7, 8, -26965757274143130677163782227379754527115706368000000⟩ +] + +def collectedFourData_15_57 : List CollectedFourTerm := [ + ⟨5, 6, 7, 2, 8, 8, -42154730317850150986006689317934676764612624384000000⟩, + ⟨5, 6, 4, 3, 4, 8, 19223584051126521727195857167379908743167108710400000⟩, + ⟨5, 6, 5, 3, 5, 8, 19460175441509857718922702305774874850964275200000000⟩, + ⟨5, 6, 6, 3, 6, 8, 71451372299135208508892419653772984983698276352000000⟩, + ⟨5, 6, 7, 3, 7, 8, 23538321042213709665327653464725350789431689216000000⟩, + ⟨5, 6, 8, 3, 8, 8, 26628591280021012071738207901406527903236096000000000⟩, + ⟨5, 6, 4, 4, 3, 8, 42967509624181360095578473425168101082207879168000000⟩, + ⟨5, 6, 5, 4, 4, 8, -70107380275076466493445056513945831550629183488000000⟩, + ⟨5, 6, 6, 4, 5, 8, -56846801570891650451605939096652078852496949248000000⟩, + ⟨5, 6, 7, 4, 6, 8, -7730581111629961114743815378077832921669959680000000⟩, + ⟨5, 6, 8, 4, 7, 8, 9459180264745408060463336894248772119415488512000000⟩, + ⟨5, 6, 4, 5, 2, 8, -294398831204742631188549674010580809182222273740800000⟩, + ⟨5, 6, 5, 5, 3, 8, 182844078114353321941706111524296019998582767616000000⟩, + ⟨5, 6, 6, 5, 4, 8, -64116433336066472968847050785861139668519616512000000⟩, + ⟨5, 6, 7, 5, 5, 8, -20473994953761399952573696837864249007039053824000000⟩, + ⟨5, 6, 8, 5, 6, 8, 19696495937330651070180505050675484091291271168000000⟩, + ⟨5, 6, 4, 6, 1, 8, 157976211453050973563498626407826678172609622835200000⟩, + ⟨5, 6, 5, 6, 2, 8, 2706078570134124604525898716702329645211582464000000⟩, + ⟨5, 6, 6, 6, 3, 8, 237409642542849864687360416549755063158788063232000000⟩, + ⟨5, 6, 7, 6, 4, 8, 7329394960535987532558449288991064899345973248000000⟩, + ⟨5, 6, 8, 6, 5, 8, -20670593783849495622159074357708494673182457856000000⟩, + ⟨5, 6, 4, 7, 0, 8, 3014380822175965113711453557380026588965957428838400000⟩, + ⟨5, 6, 5, 7, 1, 8, -126148071755965431207560305226469025085116121088000000⟩, + ⟨5, 6, 6, 7, 2, 8, -234294240632326824247927381515259363394530050048000000⟩ +] + +def collectedFourData_15_58 : List CollectedFourTerm := [ + ⟨5, 6, 7, 7, 3, 8, 307098450814929650488973053917434262333551542272000000⟩, + ⟨5, 6, 8, 7, 4, 8, 40870347520453185520129250855517109462121840640000000⟩, + ⟨6, 1, 8, 3, 8, 4, 213575246081033413808264094868943896266040934400000000⟩, + ⟨6, 1, 8, 4, 7, 4, 75867579006464858232306452747897591673553472716800000⟩, + ⟨6, 1, 8, 5, 6, 4, 157976211453050973563498626407826678172609622835200000⟩, + ⟨6, 1, 8, 6, 5, 4, -165788986266766270489503453122004087759561975398400000⟩, + ⟨6, 1, 8, 7, 4, 4, 327801588800053681306040190293464253810287312896000000⟩, + ⟨6, 2, 7, 2, 8, 5, -1447897289775205326586057241495509086825873408000000⟩, + ⟨6, 2, 7, 3, 7, 5, 808475608452617830044446864054210205730209792000000⟩, + ⟨6, 2, 8, 3, 8, 5, 3658471052160713159795542889250988813713408000000000⟩, + ⟨6, 2, 7, 4, 6, 5, -265523877285410444782743853213764823453532160000000⟩, + ⟨6, 2, 8, 4, 7, 5, 1299585727680059209651720399634650195008946176000000⟩, + ⟨6, 2, 7, 5, 5, 5, -703224562958945005109956612687255206717554688000000⟩, + ⟨6, 2, 8, 5, 6, 5, 2706078570134124604525898716702329645211582464000000⟩, + ⟨6, 2, 7, 6, 4, 5, 251744253113118159872583424251072796296216576000000⟩, + ⟨6, 2, 8, 6, 5, 5, -2839908735462287246246049480650214674308005888000000⟩, + ⟨6, 2, 7, 7, 3, 5, 10547974361985608565708003001422579682366193664000000⟩, + ⟨6, 2, 8, 7, 4, 5, 5615129306803058728637278891994666918184222720000000⟩, + ⟨6, 3, 6, 1, 8, 6, -40483450060865913690580395996406872318985371648000000⟩, + ⟨6, 3, 6, 2, 7, 6, -54171486607913449647386566970048430318311964672000000⟩, + ⟨6, 3, 7, 2, 8, 6, -254053804496338162028140480511162082674929041408000000⟩, + ⟨6, 3, 6, 3, 6, 6, 143538600391211702011124980036604230579632734208000000⟩, + ⟨6, 3, 7, 3, 7, 6, 141858338723576456137564111153897626744014241792000000⟩, + ⟨6, 3, 8, 3, 8, 6, 320964924792922571998817202780661144778440704000000000⟩ +] + +def collectedFourData_15_59 : List CollectedFourTerm := [ + ⟨6, 3, 6, 4, 5, 6, -114199490809520547191659630374415524180044808192000000⟩, + ⟨6, 3, 7, 4, 6, 6, -46589873249538650470394345115657098095660892160000000⟩, + ⟨6, 3, 8, 4, 7, 6, 114015234615682291763689220676066903212936921088000000⟩, + ⟨6, 3, 6, 5, 4, 6, -128803447813511038399831962645828997089589198848000000⟩, + ⟨6, 3, 7, 5, 5, 6, -123390572588703584709731764151581167429183602688000000⟩, + ⟨6, 3, 8, 5, 6, 6, 237409642542849864687360416549755063158788063232000000⟩, + ⟨6, 3, 6, 6, 3, 6, 476932026823940884324880479027424267270753353728000000⟩, + ⟨6, 3, 7, 6, 4, 6, 44172045707334966624067747249835503017919512576000000⟩, + ⟨6, 3, 8, 6, 5, 6, -249150828501997684443606327967876899649244626944000000⟩, + ⟨6, 3, 6, 7, 2, 6, -470673498603930804851073743275136699853692731392000000⟩, + ⟨6, 3, 7, 7, 3, 6, 1850789441568971142556981490356310284035805937664000000⟩, + ⟨6, 3, 8, 7, 4, 6, 492626436006963831712538516149509535049302671360000000⟩, + ⟨6, 4, 5, 0, 8, 7, 864237433565456177082016106519842641414193152000000⟩, + ⟨6, 4, 5, 1, 7, 7, -6854730752160113242224678488334615846278135808000000⟩, + ⟨6, 4, 6, 1, 8, 7, -3749458425737695344230137516174666606068105216000000⟩, + ⟨6, 4, 5, 2, 6, 7, -4791100377509470297578528713288638112269860864000000⟩, + ⟨6, 4, 6, 2, 7, 7, -5017204230158276759294509385298751404820660224000000⟩, + ⟨6, 4, 7, 2, 8, 7, -11764859176124496623122237059981025772272877568000000⟩, + ⟨6, 4, 5, 3, 5, 7, 1810364039699826306024464713933991535496396800000000⟩, + ⟨6, 4, 6, 3, 6, 7, 13294124237096041737627806895442669434606452736000000⟩, + ⟨6, 4, 7, 3, 7, 7, 6569251664428040544663059141963153801459269632000000⟩, + ⟨6, 4, 8, 3, 8, 7, 9908943365101365074363495862816358432505856000000000⟩, + ⟨6, 4, 5, 4, 4, 7, -6522031651206532598775388175673989193837576192000000⟩, + ⟨6, 4, 6, 4, 5, 7, -10576821945435564086324073128455420907895128064000000⟩ +] + +def collectedFourData_15_60 : List CollectedFourTerm := [ + ⟨6, 4, 7, 4, 6, 7, -2157508717104106421635760112143340597002895360000000⟩, + ⟨6, 4, 8, 4, 7, 7, 3519918892366311626291192129430196451102687232000000⟩, + ⟨6, 4, 5, 5, 3, 7, 17009833487123426013704416355672121794724102144000000⟩, + ⟨6, 4, 6, 5, 4, 7, -11929397616614710698274939113134721901963247616000000⟩, + ⟨6, 4, 7, 5, 5, 7, -5714036493353867597494483158895393088835944448000000⟩, + ⟨6, 4, 8, 5, 6, 7, 7329394960535987532558449288991064899345973248000000⟩, + ⟨6, 4, 5, 6, 2, 7, 251744253113118159872583424251072796296216576000000⟩, + ⟨6, 4, 6, 6, 3, 7, 44172045707334966624067747249835503017919512576000000⟩, + ⟨6, 4, 7, 6, 4, 7, 2045542668799596382102007498823110038017540096000000⟩, + ⟨6, 4, 8, 6, 5, 7, -7691873031257827691284961212537020398715273216000000⟩, + ⟨6, 4, 5, 7, 1, 7, -11735450868409759741388812138721943012708974592000000⟩, + ⟨6, 4, 6, 7, 2, 7, -43592399176914431380505305918262704418234302464000000⟩, + ⟨6, 4, 7, 7, 3, 7, 85707345292012304544858337092493048188915154944000000⟩, + ⟨6, 4, 8, 7, 4, 7, 15208538620517745141640246986822332051399639040000000⟩, + ⟨6, 5, 4, 0, 7, 8, -103422660381006268535674870590463049109950850662400000⟩, + ⟨6, 5, 5, 0, 8, 8, -9749400062742297993438579466805605577602891776000000⟩, + ⟨6, 5, 4, 1, 6, 8, -231722021538383942910098724238915232880016333209600000⟩, + ⟨6, 5, 5, 1, 7, 8, 77327722486496288133922144248924995932026568704000000⟩, + ⟨6, 5, 6, 1, 8, 8, 21148684835559197477983726617559084764028207104000000⟩, + ⟨6, 5, 4, 2, 5, 8, 29404310141895494240120503538655962229581335756800000⟩, + ⟨6, 5, 5, 2, 6, 8, 54048057289522275839380712406896198541568376832000000⟩, + ⟨6, 5, 6, 2, 7, 8, 28299359259697752144160250584365503098185056256000000⟩, + ⟨6, 5, 7, 2, 8, 8, 44239508856827448942574895370830274112706838528000000⟩, + ⟨6, 5, 4, 3, 4, 8, -20174293856878606518827887025902860636171062476800000⟩ +] + +def collectedFourData_15_61 : List CollectedFourTerm := [ + ⟨6, 5, 5, 3, 5, 8, -20422585966243155376962250213384260260619878400000000⟩, + ⟨6, 5, 6, 3, 6, 8, -74985027630969647919258675683237427525382569984000000⟩, + ⟨6, 5, 7, 3, 7, 8, -24702417839473626742340094496031227123096092672000000⟩, + ⟨6, 5, 8, 3, 8, 8, -27945518590555328802257533424122383808069632000000000⟩, + ⟨6, 5, 4, 4, 3, 8, -45092484479016635431242795988743252689452793856000000⟩, + ⟨6, 5, 5, 4, 4, 8, 73574567960049270825774166540739101090482487296000000⟩, + ⟨6, 5, 6, 4, 5, 8, 59658182192494448200328185955213183799017865216000000⟩, + ⟨6, 5, 7, 4, 6, 8, 8112899999067486871792989587030035338425794560000000⟩, + ⟨6, 5, 8, 4, 7, 8, -9926987693794678696199015367775760783668936704000000⟩, + ⟨6, 5, 4, 5, 2, 8, 308958439594308256980659767509446048546578602393600000⟩, + ⟨6, 5, 5, 5, 3, 8, -191886702919628858034054226453467428922926825472000000⟩, + ⟨6, 5, 6, 5, 4, 8, 67287336416383390207502428355392497071847112704000000⟩, + ⟨6, 5, 7, 5, 5, 8, 21486544315716565952849926550658703200519979008000000⟩, + ⟨6, 5, 8, 5, 6, 8, -20670593783849495622159074357708494673182457856000000⟩, + ⟨6, 5, 4, 6, 1, 8, -165788986266766270489503453122004087759561975398400000⟩, + ⟨6, 5, 5, 6, 2, 8, -2839908735462287246246049480650214674308005888000000⟩, + ⟨6, 5, 6, 6, 3, 8, -249150828501997684443606327967876899649244626944000000⟩, + ⟨6, 5, 7, 6, 4, 8, -7691873031257827691284961212537020398715273216000000⟩, + ⟨6, 5, 8, 6, 5, 8, 21692866017204034598939788941548467772354199552000000⟩, + ⟨6, 5, 4, 7, 0, 8, -3163458194964094210897683642426553664740935912652800000⟩, + ⟨6, 5, 5, 7, 1, 8, 132386773575363459422928395302959176926674026496000000⟩, + ⟨6, 5, 6, 7, 2, 8, 245881353181577936081122156745079828126489378816000000⟩, + ⟨6, 5, 7, 7, 3, 8, -322286123818285062242845736840558589519933210624000000⟩, + ⟨6, 5, 8, 7, 4, 8, -42891606409994818952473682210434956955358330880000000⟩ +] + +def collectedFourData_15_62 : List CollectedFourTerm := [ + ⟨7, 0, 8, 3, 8, 4, 4075278929381781960121788898025472643620981964800000000⟩, + ⟨7, 0, 8, 4, 7, 4, 1447646915181107144925146710980281414208376641945600000⟩, + ⟨7, 0, 8, 5, 6, 4, 3014380822175965113711453557380026588965957428838400000⟩, + ⟨7, 0, 8, 6, 5, 4, -3163458194964094210897683642426553664740935912652800000⟩, + ⟨7, 0, 8, 7, 4, 4, 6254858333853340714023107694328526852086334226432000000⟩, + ⟨7, 1, 7, 2, 8, 5, 67495989666248900402717186241454604706524430336000000⟩, + ⟨7, 1, 7, 3, 7, 5, -37688351030758767269553808361001681153177944064000000⟩, + ⟨7, 1, 8, 3, 8, 5, -170545332237791480074963631146383105469710336000000000⟩, + ⟨7, 1, 7, 4, 6, 5, 12377809533838460437584708721445333285700894720000000⟩, + ⟨7, 1, 8, 4, 7, 5, -60582214957744960767227679713385276916516257792000000⟩, + ⟨7, 1, 7, 5, 5, 5, 32781909441862792595567355763141645511316996096000000⟩, + ⟨7, 1, 8, 5, 6, 5, -126148071755965431207560305226469025085116121088000000⟩, + ⟨7, 1, 7, 6, 4, 5, -11735450868409759741388812138721943012708974592000000⟩, + ⟨7, 1, 8, 6, 5, 5, 132386773575363459422928395302959176926674026496000000⟩, + ⟨7, 1, 7, 7, 3, 5, -491710270862495242194363923406691576223511871488000000⟩, + ⟨7, 1, 8, 7, 4, 5, -261758007521011665962324869234833624970549002240000000⟩, + ⟨7, 2, 6, 1, 8, 6, 39952207031672514044405159804244012918764470272000000⟩, + ⟨7, 2, 6, 2, 7, 6, 53460622672200701851770451490129861203835486208000000⟩, + ⟨7, 2, 7, 2, 8, 6, 250719989999900068063753063184076231242428710912000000⟩, + ⟨7, 2, 6, 3, 6, 6, -141655018810013402702780415706043438144906330112000000⟩, + ⟨7, 2, 7, 3, 7, 6, -139996806332771022486114731407172665023437733888000000⟩, + ⟨7, 2, 8, 3, 8, 6, -316753070846298320631698721982926081497235456000000000⟩, + ⟨7, 2, 6, 4, 5, 6, 112700910937034850802971592550603606210786623488000000⟩, + ⟨7, 2, 7, 4, 6, 6, 45978498839561003099432990675767251809064714240000000⟩ +] + +def collectedFourData_15_63 : List CollectedFourTerm := [ + ⟨7, 2, 8, 4, 7, 6, -112519072640347532696623301393215837777724178432000000⟩, + ⟨7, 2, 6, 5, 4, 6, 127113227891935016777835816521687622891520131072000000⟩, + ⟨7, 2, 7, 5, 5, 6, 121771382982645368283183463899551679671363960832000000⟩, + ⟨7, 2, 8, 5, 6, 6, -234294240632326824247927381515259363394530050048000000⟩, + ⟨7, 2, 6, 6, 3, 6, -470673498603930804851073743275136699853692731392000000⟩, + ⟨7, 2, 7, 6, 4, 6, -43592399176914431380505305918262704418234302464000000⟩, + ⟨7, 2, 8, 6, 5, 6, 245881353181577936081122156745079828126489378816000000⟩, + ⟨7, 2, 6, 7, 2, 6, 464497097759055299442643070901941499601814028288000000⟩, + ⟨7, 2, 7, 7, 3, 6, -1826502504861254429384823747177625102952637136896000000⟩, + ⟨7, 2, 8, 7, 4, 6, -486161958307271202557944320364254346540524503040000000⟩, + ⟨7, 3, 5, 0, 8, 7, 36211171374071174191976875061519042729453027328000000⟩, + ⟨7, 3, 5, 1, 7, 7, -287210227593995993818277356892844141317940314112000000⟩, + ⟨7, 3, 6, 1, 8, 7, -157100672038941013710253200725493440847884058624000000⟩, + ⟨7, 3, 5, 2, 6, 7, -200745015319025203599415794484872574341004394496000000⟩, + ⟨7, 3, 6, 2, 7, 7, -210218668089220280190519808585664145276624961536000000⟩, + ⟨7, 3, 7, 2, 8, 7, -492942466124029353758703870214262872988819914752000000⟩, + ⟨7, 3, 5, 3, 5, 7, 75853463348114882776593431118125910820336435200000000⟩, + ⟨7, 3, 6, 3, 6, 7, 557018004915217207889330548805648078108469755904000000⟩, + ⟨7, 3, 7, 3, 7, 7, 275248778380981045822297908098988194769873666048000000⟩, + ⟨7, 3, 8, 3, 8, 7, 415180403433051387976442946005902933396291584000000000⟩, + ⟨7, 3, 5, 4, 4, 7, -273270280430486488836271020800407162652498853888000000⟩, + ⟨7, 3, 6, 4, 5, 7, -443164224533900901669731982971314109511993655296000000⟩, + ⟨7, 3, 7, 4, 6, 7, -90398673861876974538996198043422860606743511040000000⟩, + ⟨7, 3, 8, 4, 7, 7, 147483065745558937767149358141352891888013672448000000⟩ +] + +def collectedFourData_15_64 : List CollectedFourTerm := [ + ⟨7, 3, 5, 5, 3, 7, 712704601217658485330925865642575685802489020416000000⟩, + ⟨7, 3, 6, 5, 4, 7, -499836554987587348014897157573080888347379892224000000⟩, + ⟨7, 3, 7, 5, 5, 7, -239415635868615000545795810319712280868733059072000000⟩, + ⟨7, 3, 8, 5, 6, 7, 307098450814929650488973053917434262333551542272000000⟩, + ⟨7, 3, 5, 6, 2, 7, 10547974361985608565708003001422579682366193664000000⟩, + ⟨7, 3, 6, 6, 3, 7, 1850789441568971142556981490356310284035805937664000000⟩, + ⟨7, 3, 7, 6, 4, 7, 85707345292012304544858337092493048188915154944000000⟩, + ⟨7, 3, 8, 6, 5, 7, -322286123818285062242845736840558589519933210624000000⟩, + ⟨7, 3, 5, 7, 1, 7, -491710270862495242194363923406691576223511871488000000⟩, + ⟨7, 3, 6, 7, 2, 7, -1826502504861254429384823747177625102952637136896000000⟩, + ⟨7, 3, 7, 7, 3, 7, 3591100371088809221810806310151542765919840239616000000⟩, + ⟨7, 3, 8, 7, 4, 7, 637231132265040176073027318839096905258563010560000000⟩, + ⟨7, 4, 4, 0, 7, 8, 204489533075926466788524857818498263385223725056000000⟩, + ⟨7, 4, 5, 0, 8, 8, 19276725808986418895333803093714901398915645440000000⟩, + ⟨7, 4, 4, 1, 6, 8, 458165819881541037807716704915608995926716186624000000⟩, + ⟨7, 4, 5, 1, 7, 8, -152894054425160331035013817547299221713725685760000000⟩, + ⟨7, 4, 6, 1, 8, 8, -41815639544190859273497385059821249195944181760000000⟩, + ⟨7, 4, 4, 2, 5, 8, -58138841422031455216864567585059497209277448192000000⟩, + ⟨7, 4, 5, 2, 6, 8, -106864994171288007289507526471994844924430254080000000⟩, + ⟨7, 4, 6, 2, 7, 8, -55954108510113966565917765150311658342202736640000000⟩, + ⟨7, 4, 7, 2, 8, 8, -87471318919024492993852034502834040865103544320000000⟩, + ⟨7, 4, 4, 3, 4, 8, 39889052512589203217040700044757381602179284992000000⟩, + ⟨7, 4, 5, 3, 5, 8, 40379981070444383188287785385297267545604096000000000⟩, + ⟨7, 4, 6, 3, 6, 8, 148262027213897477554157920216478943372336168960000000⟩ +] + +def collectedFourData_15_65 : List CollectedFourTerm := [ + ⟨7, 4, 7, 3, 7, 8, 48842157716995771981295199478329047439302983680000000⟩, + ⟨7, 4, 8, 3, 8, 8, 55254487044666767977614584215575357114286080000000000⟩, + ⟨7, 4, 4, 4, 3, 8, 89157840867541763518117186662328671868173680640000000⟩, + ⟨7, 4, 5, 4, 4, 8, -145473235681496495449199011653474408827442954240000000⟩, + ⟨7, 4, 6, 4, 5, 8, -117957455124043521832680112544369828273628119040000000⟩, + ⟨7, 4, 7, 4, 6, 8, -16041002296685003360020487522519051997177446400000000⟩, + ⟨7, 4, 8, 4, 7, 8, 19627855934823236965970322427414971640719605760000000⟩, + ⟨7, 4, 4, 5, 2, 8, -610879345201120023313224118586219258415188803584000000⟩, + ⟨7, 4, 5, 5, 3, 8, 379402561672259897332652075367168939822604615680000000⟩, + ⟨7, 4, 6, 5, 4, 8, -133041984754783840951252298257167327851981045760000000⟩, + ⟨7, 4, 7, 5, 5, 8, -42483662655258922400959323795092499062084075520000000⟩, + ⟨7, 4, 8, 5, 6, 8, 40870347520453185520129250855517109462121840640000000⟩, + ⟨7, 4, 4, 6, 1, 8, 327801588800053681306040190293464253810287312896000000⟩, + ⟨7, 4, 5, 6, 2, 8, 5615129306803058728637278891994666918184222720000000⟩, + ⟨7, 4, 6, 6, 3, 8, 492626436006963831712538516149509535049302671360000000⟩, + ⟨7, 4, 7, 6, 4, 8, 15208538620517745141640246986822332051399639040000000⟩, + ⟨7, 4, 8, 6, 5, 8, -42891606409994818952473682210434956955358330880000000⟩, + ⟨7, 4, 4, 7, 0, 8, 6254858333853340714023107694328526852086334226432000000⟩, + ⟨7, 4, 5, 7, 1, 8, -261758007521011665962324869234833624970549002240000000⟩, + ⟨7, 4, 6, 7, 2, 8, -486161958307271202557944320364254346540524503040000000⟩, + ⟨7, 4, 7, 7, 3, 8, 637231132265040176073027318839096905258563010560000000⟩, + ⟨7, 4, 8, 7, 4, 8, 84806216890423771188619193707794169244889907200000000⟩, + ⟨0, 7, 8, 4, 8, 3, -12891384136865177065188239394919048286708957184000000⟩, + ⟨0, 7, 8, 5, 7, 3, 21135453139532489859739059288781517391531501158400000⟩ +] + +def collectedFourData_15_66 : List CollectedFourTerm := [ + ⟨0, 7, 8, 6, 6, 3, -31570798033408081801488226935777228158602208870400000⟩, + ⟨0, 7, 8, 7, 5, 3, -81550712935909058392940233914250665191238795264000000⟩, + ⟨0, 8, 7, 3, 8, 4, -17560869741080392331650627317006657515024075980800000⟩, + ⟨0, 8, 7, 4, 7, 4, -46449955284226429858830370561637542717239695769600000⟩, + ⟨0, 8, 8, 4, 8, 4, 49754584273977267339042701741948626727237320704000000⟩, + ⟨0, 8, 7, 5, 6, 4, 14715255790648000197164663998727255354127679488000000⟩, + ⟨0, 8, 8, 5, 7, 4, -81572752253373066983684594777292556341378180710400000⟩, + ⟨0, 8, 7, 6, 5, 4, 91936397196036428260364560647711486039842566963200000⟩, + ⟨0, 8, 8, 6, 6, 4, 121848198352724807713208151828480297679928583782400000⟩, + ⟨0, 8, 7, 7, 4, 4, 71488780180216582019005789705653772921092440064000000⟩, + ⟨0, 8, 8, 7, 5, 4, 314746793385003482524825402744866776870692061184000000⟩, + ⟨1, 6, 8, 4, 8, 3, 61127147699177344505565773902545902081459355648000000⟩, + ⟨1, 6, 8, 5, 7, 3, -100218095437454709499713591779871251315645271244800000⟩, + ⟨1, 6, 8, 6, 6, 3, 149699428228993466416698706020522415079815957708800000⟩, + ⟨1, 6, 8, 7, 5, 3, 386689468072799862842827479297178761776917905408000000⟩, + ⟨1, 7, 7, 3, 8, 4, 20480324418480620092137320475991562527047470284800000⟩, + ⟨1, 7, 7, 4, 7, 4, 54172154766313316032189380984159643633186347417600000⟩, + ⟨1, 7, 8, 4, 8, 4, -58026170813963195717905705714621940420233396224000000⟩, + ⟨1, 7, 7, 5, 6, 4, -17161633617063392938550027356242765994606460928000000⟩, + ⟨1, 7, 8, 5, 7, 4, 95134036895068066621455208167687705331113551462400000⟩, + ⟨1, 7, 7, 6, 5, 4, -107220614252177565823482914251164283224970179379200000⟩, + ⟨1, 7, 8, 6, 6, 4, -142105184359601690040912086634060228656013665894400000⟩, + ⟨1, 7, 7, 7, 4, 4, -83373627386305458790976898787001933024024592384000000⟩, + ⟨1, 7, 8, 7, 5, 4, -367072732344336537731301464460309759065906479104000000⟩ +] + +def collectedFourData_15_67 : List CollectedFourTerm := [ + ⟨1, 8, 6, 2, 8, 5, -296248772797392585766138321525213986619454914560000000⟩, + ⟨1, 8, 6, 3, 7, 5, -628126649150946777039944438380422083200942080000000⟩, + ⟨1, 8, 7, 3, 8, 5, 100531386605410735253868222683957199434447585280000000⟩, + ⟨1, 8, 6, 4, 6, 5, -126937364907037354125583277411075823983740846080000000⟩, + ⟨1, 8, 7, 4, 7, 5, 265913846030004048793900108278919946422305423360000000⟩, + ⟨1, 8, 8, 4, 8, 5, -142415991371363807396521769956591798492279603200000000⟩, + ⟨1, 8, 6, 5, 5, 5, -106041100000266020448534584745944424229204131840000000⟩, + ⟨1, 8, 7, 5, 6, 5, -84240990947418177534066953815561489435380940800000000⟩, + ⟨1, 8, 8, 5, 7, 5, 233491336538628439775970226482390924135833272320000000⟩, + ⟨1, 8, 6, 6, 4, 5, 70703779687492868582595658032256167823477309440000000⟩, + ⟨1, 8, 7, 6, 5, 5, -526311829988821179956612442294199370489392005120000000⟩, + ⟨1, 8, 8, 6, 6, 5, -348774534415996484840348398433809893567674449920000000⟩, + ⟨1, 8, 6, 7, 3, 5, 356926152508311539215484231963909457879477780480000000⟩, + ⟨1, 8, 7, 7, 4, 5, -409254570201283335897119038774873112762017382400000000⟩, + ⟨1, 8, 8, 7, 5, 5, -900921538486806800716572007321471461933396787200000000⟩, + ⟨2, 5, 8, 4, 8, 3, 26012614907343533263356137255574775564502827008000000⟩, + ⟨2, 5, 8, 5, 7, 3, -42647740349203234780837748748300742107459275980800000⟩, + ⟨2, 5, 8, 6, 6, 3, 63704486876012466607653268883102367621069982924800000⟩, + ⟨2, 5, 8, 7, 5, 3, 164555432411230066259045906944538817650352979968000000⟩, + ⟨2, 6, 7, 3, 8, 4, -13502538821713664249791230530517893132197036032000000⟩, + ⟨2, 6, 7, 4, 7, 4, -35715333792661260174116555240795441462859792384000000⟩, + ⟨2, 6, 8, 4, 8, 4, 38256260402981068408031577836067289919819612160000000⟩, + ⟨2, 6, 7, 5, 6, 4, 11314548511220109531143254614837440223400427520000000⟩, + ⟨2, 6, 8, 5, 7, 4, -62721224536993638229779325248152958664301346816000000⟩ +] + +def collectedFourData_15_68 : List CollectedFourTerm := [ + ⟨2, 6, 7, 6, 5, 4, 70689822917141938622668183101395360744082505728000000⟩, + ⟨2, 6, 8, 6, 6, 4, 93688983112536475737689412192117912542637981696000000⟩, + ⟨2, 6, 7, 7, 4, 4, 54967666404485391752767757042213244312810946560000000⟩, + ⟨2, 6, 8, 7, 5, 4, 242008559903447860998338997862939849286599311360000000⟩, + ⟨2, 7, 6, 2, 8, 5, -151853689400513755515601510918120206074923450368000000⟩, + ⟨2, 7, 6, 3, 7, 5, -321970444581679156401006401454139925933850624000000⟩, + ⟨2, 7, 7, 3, 8, 5, 51531224289734421315812131017854363611466563584000000⟩, + ⟨2, 7, 6, 4, 6, 5, -65066622899045408830930100464523374211654221824000000⟩, + ⟨2, 7, 7, 4, 7, 5, 136304357317802447054632604067525865598519083008000000⟩, + ⟨2, 7, 8, 4, 8, 5, -73000787531240939393224060649870722459458600960000000⟩, + ⟨2, 7, 6, 5, 5, 5, -54355439555329501548422217841016176582487703552000000⟩, + ⟨2, 7, 7, 5, 6, 5, -43180956171823580214558796849504887509341962240000000⟩, + ⟨2, 7, 8, 5, 7, 5, 119684954511851331158364771436078612412362653696000000⟩, + ⟨2, 7, 6, 6, 4, 5, 36241938485428869710796214410786447538186616832000000⟩, + ⟨2, 7, 7, 6, 5, 5, -269781347629744119786261586438458528951001153536000000⟩, + ⟨2, 7, 8, 6, 6, 5, -178777786385083966113612174243304447932131966976000000⟩, + ⟨2, 7, 6, 7, 3, 5, 182956211396648819480769378954731107445473542144000000⟩, + ⟨2, 7, 7, 7, 4, 5, -209779152170831922888494348956784029367764254720000000⟩, + ⟨2, 7, 8, 7, 5, 5, -461801944992943674695092030236043580102840156160000000⟩, + ⟨2, 8, 5, 1, 8, 6, -296248772797392585766138321525213986619454914560000000⟩, + ⟨2, 8, 5, 2, 7, 6, -151853689400513755515601510918120206074923450368000000⟩, + ⟨2, 8, 6, 2, 8, 6, 269174295611026380419602639027815538832657350656000000⟩, + ⟨2, 8, 5, 3, 6, 6, 103900568488919106432527848439250908691208077312000000⟩, + ⟨2, 8, 6, 3, 7, 6, 570721514702620592827153218693415678727159808000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1504.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1504.lean new file mode 100644 index 0000000000000000000000000000000000000000..aed70438526e5ab15ac36473eec49f8dcb108869 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1504.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1504. -/ +namespace LaughlinFock +def collectedFourData_15_69 : List CollectedFourTerm := [ + ⟨2, 8, 7, 3, 8, 6, -45671860377322342854155811268017857102100824064000000⟩, + ⟨2, 8, 5, 4, 5, 6, 63000300560747244056958950577918822032917659648000000⟩, + ⟨2, 8, 6, 4, 6, 6, 115336429794899487270715045460285086442830430208000000⟩, + ⟨2, 8, 7, 4, 7, 6, -120805854354201134656593062766022363419160608768000000⟩, + ⟨2, 8, 8, 4, 8, 6, 43133482938622842387572929237432285332441661440000000⟩, + ⟨2, 8, 5, 5, 4, 6, 41790407374825455290432567462991340675610443776000000⟩, + ⟨2, 8, 6, 5, 5, 6, 96349895828635950607320885034153785729151401984000000⟩, + ⟨2, 8, 7, 5, 6, 6, 38271060476854935355100005338954119886447575040000000⟩, + ⟨2, 8, 8, 5, 7, 6, -70717441797973906252480917496007746379310956544000000⟩, + ⟨2, 8, 5, 6, 3, 6, -380817317521188674028465483772550483110187237376000000⟩, + ⟨2, 8, 6, 6, 4, 6, -64242089223552704419966225421729556853627551744000000⟩, + ⟨2, 8, 7, 6, 5, 6, 239105827800138160308333069558940663424489619456000000⟩, + ⟨2, 8, 8, 6, 6, 6, 105633224786043536310130215343609122209308606464000000⟩, + ⟨2, 8, 5, 7, 2, 6, 21097172474888210827306248246851396285107273728000000⟩, + ⟨2, 8, 6, 7, 3, 6, -324306307767510644472602621853347665202431131648000000⟩, + ⟨2, 8, 7, 7, 4, 6, 185926189025707521714081694841517870991666053120000000⟩, + ⟨2, 8, 8, 7, 5, 6, 272861800386078319775297323057626258956605194240000000⟩, + ⟨3, 4, 8, 4, 8, 3, -2834300467457736860091960692502926269649780736000000⟩, + ⟨3, 4, 8, 5, 7, 3, 4646841958731287552378995350181936372607719833600000⟩, + ⟨3, 4, 8, 6, 6, 3, -6941157495122290687072168342055554910216886681600000⟩, + ⟨3, 4, 8, 7, 5, 3, -17929744497704908731150799967820734023971373056000000⟩, + ⟨3, 5, 7, 3, 8, 4, -37046847153188642497196974085009083370631384268800000⟩, + ⟨3, 5, 7, 4, 7, 4, -97991979842640406191932542679429318585305635225600000⟩, + ⟨3, 5, 8, 4, 8, 4, 104963507271882842356922880312064191669567750144000000⟩ +] + +def collectedFourData_15_70 : List CollectedFourTerm := [ + ⟨3, 5, 7, 5, 6, 4, 31043669256365158285026832275716346847237767168000000⟩, + ⟨3, 5, 8, 5, 7, 4, -172087905049839175900295289552231391368392894054400000⟩, + ⟨3, 5, 7, 6, 5, 4, 193951307933729878058244598586148172130340254515200000⟩, + ⟨3, 5, 8, 6, 6, 4, 257053986893651938481870754949700262547335571046400000⟩, + ⟨3, 5, 7, 7, 4, 4, 150814507000690644246173949100891381183077679104000000⟩, + ⟨3, 5, 8, 7, 5, 4, 663997656062170195490285606579960010215390183424000000⟩, + ⟨3, 6, 6, 2, 8, 5, 103900568488919106432527848439250908691208077312000000⟩, + ⟨3, 6, 6, 3, 7, 5, 220297000097472179082355299987382212143087616000000⟩, + ⟨3, 6, 7, 3, 8, 5, -35258435404304960280503229898749514234258784256000000⟩, + ⟨3, 6, 6, 4, 6, 5, 44519557842511448347567501347548703973668028416000000⟩, + ⟨3, 6, 7, 4, 7, 5, -93261482607010809592906006239853307021148291072000000⟩, + ⟨3, 6, 8, 4, 8, 5, 49948232108011397296446987996487684299832688640000000⟩, + ⟨3, 6, 6, 5, 5, 5, 37190805785221235418828781521148264151638867968000000⟩, + ⟨3, 6, 7, 5, 6, 5, 29545056902202543065602244830146704030469980160000000⟩, + ⟨3, 6, 8, 5, 7, 5, -81890238310599159473937024609766729604099211264000000⟩, + ⟨3, 6, 6, 6, 4, 5, -24797277080603849512767833557639225900152127488000000⟩, + ⟨3, 6, 7, 6, 5, 5, 184588438365214258847133937009586435773194829824000000⟩, + ⟨3, 6, 8, 6, 6, 5, 122322438868172290508914701561006650816446070784000000⟩, + ⟨3, 6, 6, 7, 3, 5, -125181379838285051298655411667076720265103671296000000⟩, + ⟨3, 6, 7, 7, 4, 5, 143534037623449167542435686638406690130079252480000000⟩, + ⟨3, 6, 8, 7, 5, 5, 315971806832459256857844489427894892376820285440000000⟩, + ⟨3, 7, 5, 1, 8, 6, -628126649150946777039944438380422083200942080000000⟩, + ⟨3, 7, 5, 2, 7, 6, -321970444581679156401006401454139925933850624000000⟩, + ⟨3, 7, 6, 2, 8, 6, 570721514702620592827153218693415678727159808000000⟩ +] + +def collectedFourData_15_71 : List CollectedFourTerm := [ + ⟨3, 7, 5, 3, 6, 6, 220297000097472179082355299987382212143087616000000⟩, + ⟨3, 7, 6, 3, 7, 6, 1210082287408095091028713943973888780140544000000⟩, + ⟨3, 7, 7, 3, 8, 6, -96836561881446794519828793781083456669745152000000⟩, + ⟨3, 7, 5, 4, 5, 6, 133577490678040613028297548263083253551857664000000⟩, + ⟨3, 7, 6, 4, 6, 6, 244544085324026234456984882029280837442207744000000⟩, + ⟨3, 7, 7, 4, 7, 6, -256140728539718484625004759507286528909901824000000⟩, + ⟨3, 7, 8, 4, 8, 6, 91454522658819799573480376811766585145425920000000⟩, + ⟨3, 7, 5, 5, 4, 6, 88606843171480514028302587076098046419795968000000⟩, + ⟨3, 7, 6, 5, 5, 6, 204287554143807566907998067759259925675507712000000⟩, + ⟨3, 7, 7, 5, 6, 6, 81144886271716917532704813340469490320670720000000⟩, + ⟨3, 7, 8, 5, 7, 6, -149939894547571304096190530825285222679969792000000⟩, + ⟨3, 7, 5, 6, 3, 6, -807434587271112879596836182125439976910880768000000⟩, + ⟨3, 7, 6, 6, 4, 6, -136210414839569811022223412845618813460283392000000⟩, + ⟨3, 7, 7, 6, 5, 6, 506968319194623697901042761150606411938398208000000⟩, + ⟨3, 7, 8, 6, 6, 6, 223970694957931139279245530292830716509028352000000⟩, + ⟨3, 7, 5, 7, 2, 6, 44731649444752578046014284425378119605551104000000⟩, + ⟨3, 7, 6, 7, 3, 6, -687616129082965855911353439451594447770353664000000⟩, + ⟨3, 7, 7, 7, 4, 6, 394213258672277196116540335469143884205916160000000⟩, + ⟨3, 7, 8, 7, 5, 6, 578540011286454800996528983039770332831416320000000⟩, + ⟨3, 8, 4, 0, 8, 7, -17560869741080392331650627317006657515024075980800000⟩, + ⟨3, 8, 4, 1, 7, 7, 20480324418480620092137320475991562527047470284800000⟩, + ⟨3, 8, 5, 1, 8, 7, 100531386605410735253868222683957199434447585280000000⟩, + ⟨3, 8, 4, 2, 6, 7, -13502538821713664249791230530517893132197036032000000⟩, + ⟨3, 8, 5, 2, 7, 7, 51531224289734421315812131017854363611466563584000000⟩ +] + +def collectedFourData_15_72 : List CollectedFourTerm := [ + ⟨3, 8, 6, 2, 8, 7, -45671860377322342854155811268017857102100824064000000⟩, + ⟨3, 8, 4, 3, 5, 7, -37046847153188642497196974085009083370631384268800000⟩, + ⟨3, 8, 5, 3, 6, 7, -35258435404304960280503229898749514234258784256000000⟩, + ⟨3, 8, 6, 3, 7, 7, -96836561881446794519828793781083456669745152000000⟩, + ⟨3, 8, 7, 3, 8, 7, 5166216002882903264655113659975302577592991744000000⟩, + ⟨3, 8, 4, 4, 4, 7, 27765344426042593009025868808985009404722020352000000⟩, + ⟨3, 8, 5, 4, 5, 7, -21379017074481193860489793992326140302641332224000000⟩, + ⟨3, 8, 6, 4, 6, 7, -19569585223782074650719211582454023244325322752000000⟩, + ⟨3, 8, 7, 4, 7, 7, 13665069319499560343944903215651489173553020928000000⟩, + ⟨3, 8, 8, 4, 8, 7, -3659313765247389983116226575482684880642375680000000⟩, + ⟨3, 8, 4, 5, 3, 7, 26457149669866262509857223375922351269350054297600000⟩, + ⟨3, 8, 5, 5, 4, 7, -14181485244732000423207788433811980472641650688000000⟩, + ⟨3, 8, 6, 5, 5, 7, -16348065403741149668129941222059852176446980096000000⟩, + ⟨3, 8, 7, 5, 6, 7, -4329067470634510648515164303283432195977379840000000⟩, + ⟨3, 8, 8, 5, 7, 7, 5999453106595551996225922900916965642881466368000000⟩, + ⟨3, 8, 4, 6, 2, 7, -33510560703524417563969720294468257135915014553600000⟩, + ⟨3, 8, 5, 6, 3, 7, 129229541146288349824727824198458177558033727488000000⟩, + ⟨3, 8, 6, 6, 4, 7, 10900207698901074407886128549866251894480961536000000⟩, + ⟨3, 8, 7, 6, 5, 7, -27046683532449073470183996469416042288881074176000000⟩, + ⟨3, 8, 8, 6, 6, 7, -8961602152023720452853162733708993503436996608000000⟩, + ⟨3, 8, 4, 7, 1, 7, -32190824504898098002891407388314675766651099545600000⟩, + ⟨3, 8, 5, 7, 2, 7, -7159280297861486833075231359493337466236043264000000⟩, + ⟨3, 8, 6, 7, 3, 7, 55026325504893169873574922157080549286175834112000000⟩, + ⟨3, 8, 7, 7, 4, 7, -21031218022740772324788999024503549689614827520000000⟩ +] + +def collectedFourData_15_73 : List CollectedFourTerm := [ + ⟨3, 8, 8, 7, 5, 7, -23148766900733880004822948703083611083274977280000000⟩, + ⟨4, 3, 8, 4, 8, 3, -41856865976372999961866703152730224502692118528000000⟩, + ⟨4, 3, 8, 5, 7, 3, 68624425431670427385405479348183657458772528332800000⟩, + ⟨4, 3, 8, 6, 6, 3, -102506809821341888532462111425641594333772434636800000⟩, + ⟨4, 3, 8, 7, 5, 3, -264785939616416580075487417947222799804570533888000000⟩, + ⟨4, 4, 7, 3, 8, 4, 27765344426042593009025868808985009404722020352000000⟩, + ⟨4, 4, 7, 4, 7, 4, 73441636209157269950980200933226876117633204224000000⟩, + ⟨4, 4, 8, 4, 8, 4, -78666557494580586106287178946155451894212853760000000⟩, + ⟨4, 4, 7, 5, 6, 4, -23266167984201610093377703622516795788461342720000000⟩, + ⟨4, 4, 8, 5, 7, 4, 128973997045080452641472015601754924654553726976000000⟩, + ⟨4, 4, 7, 6, 5, 4, -145359869475369289549579768960774089804777259008000000⟩, + ⟨4, 4, 8, 6, 6, 4, -192653168370236940063349507703799793944316870656000000⟩, + ⟨4, 4, 7, 7, 4, 4, -113030313052093944284794087604581308626538332160000000⟩, + ⟨4, 4, 8, 7, 5, 4, -497643525302376958459831222887596941024123944960000000⟩, + ⟨4, 5, 6, 2, 8, 5, 63000300560747244056958950577918822032917659648000000⟩, + ⟨4, 5, 6, 3, 7, 5, 133577490678040613028297548263083253551857664000000⟩, + ⟨4, 5, 7, 3, 8, 5, -21379017074481193860489793992326140302641332224000000⟩, + ⟨4, 5, 6, 4, 6, 5, 26994515676869628689998704591807850188178980864000000⟩, + ⟨4, 5, 7, 4, 7, 5, -56549271293055522719875546601656284565563506688000000⟩, + ⟨4, 5, 8, 4, 8, 5, 30286202289819830170770185150142684741563842560000000⟩, + ⟨4, 5, 6, 5, 5, 5, 22550713404568111686355581935552769058481897472000000⟩, + ⟨4, 5, 7, 5, 6, 5, 17914699524686922055082593896923119122791792640000000⟩, + ⟨4, 5, 8, 5, 7, 5, -49654296425810024786380886664461687475306233856000000⟩, + ⟨4, 5, 6, 6, 4, 5, -15035874508547875834266636854037965031239319552000000⟩ +] + +def collectedFourData_15_74 : List CollectedFourTerm := [ + ⟨4, 5, 7, 6, 5, 5, 111925538677757099580153222900009044947129860096000000⟩, + ⟨4, 5, 8, 6, 6, 5, 74170435504790909176631439826225098396518055936000000⟩, + ⟨4, 5, 6, 7, 3, 5, -75903959613677254968294528956735840589535248384000000⟩, + ⟨4, 5, 7, 7, 4, 5, 87032127374156709797255822138270388334803025920000000⟩, + ⟨4, 5, 8, 7, 5, 5, 191590085489188561530432529629659236241516789760000000⟩, + ⟨4, 6, 5, 1, 8, 6, -126937364907037354125583277411075823983740846080000000⟩, + ⟨4, 6, 5, 2, 7, 6, -65066622899045408830930100464523374211654221824000000⟩, + ⟨4, 6, 6, 2, 8, 6, 115336429794899487270715045460285086442830430208000000⟩, + ⟨4, 6, 5, 3, 6, 6, 44519557842511448347567501347548703973668028416000000⟩, + ⟨4, 6, 6, 3, 7, 6, 244544085324026234456984882029280837442207744000000⟩, + ⟨4, 6, 7, 3, 8, 6, -19569585223782074650719211582454023244325322752000000⟩, + ⟨4, 6, 5, 4, 5, 6, 26994515676869628689998704591807850188178980864000000⟩, + ⟨4, 6, 6, 4, 6, 6, 49419622358951790740797433316314148388359634944000000⟩, + ⟨4, 6, 7, 4, 7, 6, -51763174146727148543624876415332609218024833024000000⟩, + ⟨4, 6, 8, 4, 8, 6, 18481935340322961510040370997416968016803921920000000⟩, + ⟨4, 6, 5, 5, 4, 6, 17906451191208625062271362804676967340460474368000000⟩, + ⟨4, 6, 6, 5, 5, 6, 41284228015753127035979079658062999309948813312000000⟩, + ⟨4, 6, 7, 5, 6, 6, 16398473226595548453789603423789167445509406720000000⟩, + ⟨4, 6, 8, 5, 7, 6, -30301174347617743828621630635338089200869179392000000⟩, + ⟨4, 6, 5, 6, 3, 6, -163173492131784781534875956005033028074673799168000000⟩, + ⟨4, 6, 6, 6, 4, 6, -27526600178484637746616695847501348960041172992000000⟩, + ⟨4, 6, 7, 6, 5, 6, 102452622599125618169160892325953741599547588608000000⟩, + ⟨4, 6, 8, 6, 6, 6, 45261970452594995229437962472319046571840765952000000⟩, + ⟨4, 6, 5, 7, 2, 6, 9039765652575758423129915387063234555547746304000000⟩ +] + +def collectedFourData_15_75 : List CollectedFourTerm := [ + ⟨4, 6, 6, 7, 3, 6, -138959522910471905971523034249954039764682276864000000⟩, + ⟨4, 6, 7, 7, 4, 6, 79666086982483399124626822624797176524607324160000000⟩, + ⟨4, 6, 8, 7, 5, 6, 116916460438764252383352357359090929016053432320000000⟩, + ⟨4, 7, 4, 0, 8, 7, -46449955284226429858830370561637542717239695769600000⟩, + ⟨4, 7, 4, 1, 7, 7, 54172154766313316032189380984159643633186347417600000⟩, + ⟨4, 7, 5, 1, 8, 7, 265913846030004048793900108278919946422305423360000000⟩, + ⟨4, 7, 4, 2, 6, 7, -35715333792661260174116555240795441462859792384000000⟩, + ⟨4, 7, 5, 2, 7, 7, 136304357317802447054632604067525865598519083008000000⟩, + ⟨4, 7, 6, 2, 8, 7, -120805854354201134656593062766022363419160608768000000⟩, + ⟨4, 7, 4, 3, 5, 7, -97991979842640406191932542679429318585305635225600000⟩, + ⟨4, 7, 5, 3, 6, 7, -93261482607010809592906006239853307021148291072000000⟩, + ⟨4, 7, 6, 3, 7, 7, -256140728539718484625004759507286528909901824000000⟩, + ⟨4, 7, 7, 3, 8, 7, 13665069319499560343944903215651489173553020928000000⟩, + ⟨4, 7, 4, 4, 4, 7, 73441636209157269950980200933226876117633204224000000⟩, + ⟨4, 7, 5, 4, 5, 7, -56549271293055522719875546601656284565563506688000000⟩, + ⟨4, 7, 6, 4, 6, 7, -51763174146727148543624876415332609218024833024000000⟩, + ⟨4, 7, 7, 4, 7, 7, 36145240424040525134663419905519610809481691136000000⟩, + ⟨4, 7, 8, 4, 8, 7, -9679188062597530277751754103586515516034908160000000⟩, + ⟨4, 7, 4, 5, 3, 7, 69981352702509518625331267324755287260823499571200000⟩, + ⟨4, 7, 5, 5, 4, 7, -37511203328428738262300817105465389196830048256000000⟩, + ⟨4, 7, 6, 5, 5, 7, -43241987337961268142271358003117531765409841152000000⟩, + ⟨4, 7, 7, 5, 6, 7, -11450742098665606235052388274660844998051758080000000⟩, + ⟨4, 7, 8, 5, 7, 7, 15869050487816666110090008657802578959234236416000000⟩, + ⟨4, 7, 4, 6, 2, 7, -88638209221879948130826480390214746434125902643200000⟩ +] + +def collectedFourData_15_76 : List CollectedFourTerm := [ + ⟨4, 7, 5, 6, 3, 7, 341822842270959786819457237770114420498398969856000000⟩, + ⟨4, 7, 6, 6, 4, 7, 28831952384357573078483263926802919156908818432000000⟩, + ⟨4, 7, 7, 6, 5, 7, -71540718608598412087865896001264817127777370112000000⟩, + ⟨4, 7, 8, 6, 6, 7, -23704180110325181708981896240868555684415799296000000⟩, + ⟨4, 7, 4, 7, 1, 7, -85147397643808526967916308939398972398955082547200000⟩, + ⟨4, 7, 5, 7, 2, 7, -18936889493860004501963205187476652213999239168000000⟩, + ⟨4, 7, 6, 7, 3, 7, 145549189581331399286318276837576043181683769344000000⟩, + ⟨4, 7, 7, 7, 4, 7, -55629313988011187257423469939765112704587530240000000⟩, + ⟨4, 7, 8, 7, 5, 7, -61230406197291040535323264156298838556394127360000000⟩, + ⟨4, 8, 3, 0, 7, 8, -12891384136865177065188239394919048286708957184000000⟩, + ⟨4, 8, 4, 0, 8, 8, 49754584273977267339042701741948626727237320704000000⟩, + ⟨4, 8, 3, 1, 6, 8, 61127147699177344505565773902545902081459355648000000⟩, + ⟨4, 8, 4, 1, 7, 8, -58026170813963195717905705714621940420233396224000000⟩, + ⟨4, 8, 5, 1, 8, 8, -142415991371363807396521769956591798492279603200000000⟩, + ⟨4, 8, 3, 2, 5, 8, 26012614907343533263356137255574775564502827008000000⟩, + ⟨4, 8, 4, 2, 6, 8, 38256260402981068408031577836067289919819612160000000⟩, + ⟨4, 8, 5, 2, 7, 8, -73000787531240939393224060649870722459458600960000000⟩, + ⟨4, 8, 6, 2, 8, 8, 43133482938622842387572929237432285332441661440000000⟩, + ⟨4, 8, 3, 3, 4, 8, -2834300467457736860091960692502926269649780736000000⟩, + ⟨4, 8, 4, 3, 5, 8, 104963507271882842356922880312064191669567750144000000⟩, + ⟨4, 8, 5, 3, 6, 8, 49948232108011397296446987996487684299832688640000000⟩, + ⟨4, 8, 6, 3, 7, 8, 91454522658819799573480376811766585145425920000000⟩, + ⟨4, 8, 7, 3, 8, 8, -3659313765247389983116226575482684880642375680000000⟩, + ⟨4, 8, 3, 4, 3, 8, -41856865976372999961866703152730224502692118528000000⟩ +] + +def collectedFourData_15_77 : List CollectedFourTerm := [ + ⟨4, 8, 4, 4, 4, 8, -78666557494580586106287178946155451894212853760000000⟩, + ⟨4, 8, 5, 4, 5, 8, 30286202289819830170770185150142684741563842560000000⟩, + ⟨4, 8, 6, 4, 6, 8, 18481935340322961510040370997416968016803921920000000⟩, + ⟨4, 8, 7, 4, 7, 8, -9679188062597530277751754103586515516034908160000000⟩, + ⟨4, 8, 8, 4, 8, 8, 2073560567356330003201919698533693318160711680000000⟩, + ⟨4, 8, 3, 5, 2, 8, -52266143552932233126275112601034935677329866752000000⟩, + ⟨4, 8, 4, 5, 3, 8, -74960096071961665946894878378445614150569689088000000⟩, + ⟨4, 8, 5, 5, 4, 8, 20089947512354060552183513540287909432362270720000000⟩, + ⟨4, 8, 6, 5, 5, 8, 15439463037986735437614204153152955440336732160000000⟩, + ⟨4, 8, 7, 5, 6, 8, 3066348015092203137720500781292534130068684800000000⟩, + ⟨4, 8, 8, 5, 7, 8, -3399607190201942307690935516158501725791059968000000⟩, + ⟨4, 8, 3, 6, 1, 8, -12724816649300088712663126964736434724359110656000000⟩, + ⟨4, 8, 4, 6, 2, 8, 94944273328979178080821227577931882709141946368000000⟩, + ⟨4, 8, 5, 6, 3, 8, -183070718889542885779591469686434546359960862720000000⟩, + ⟨4, 8, 6, 6, 4, 8, -10294389563369909992860913235275798452696514560000000⟩, + ⟨4, 8, 7, 6, 5, 8, 19157600320883077437209640099036975399142686720000000⟩, + ⟨4, 8, 8, 6, 6, 8, 5078117383442176166995252733948658612550238208000000⟩, + ⟨4, 8, 3, 7, 0, 8, 1337505997479416428586843637506881727292147499008000000⟩, + ⟨4, 8, 4, 7, 1, 8, 91205111950179960517687574787136715516257763328000000⟩, + ⟨4, 8, 5, 7, 2, 8, 10142066428739981005350522602055421676130140160000000⟩, + ⟨4, 8, 6, 7, 3, 8, -51968040117738008818728811527854772970869227520000000⟩, + ⟨4, 8, 7, 7, 4, 8, 14896749490843668969026525238891058754381414400000000⟩, + ⟨4, 8, 8, 7, 5, 8, 13117314695489110336435539491465220857297633280000000⟩, + ⟨5, 2, 8, 4, 8, 3, -52266143552932233126275112601034935677329866752000000⟩ +] + +def collectedFourData_15_78 : List CollectedFourTerm := [ + ⟨5, 2, 8, 5, 7, 3, 85690459311353806874953571449212202407590834995200000⟩, + ⟨5, 2, 8, 6, 6, 3, -127998967727292589905475721648494506060484391731200000⟩, + ⟨5, 2, 8, 7, 5, 3, -330634881708572862982079994394689308457531604992000000⟩, + ⟨5, 3, 7, 3, 8, 4, 26457149669866262509857223375922351269350054297600000⟩, + ⟨5, 3, 7, 4, 7, 4, 69981352702509518625331267324755287260823499571200000⟩, + ⟨5, 3, 8, 4, 8, 4, -74960096071961665946894878378445614150569689088000000⟩, + ⟨5, 3, 7, 5, 6, 4, -22169956877066847073106112030887295096440487936000000⟩, + ⟨5, 3, 8, 5, 7, 4, 122897245248721628467370477289754517796058614988800000⟩, + ⟨5, 3, 7, 6, 5, 4, -138511079268113884566231807032058271421054740070400000⟩, + ⟨5, 3, 8, 6, 6, 4, -183576102343052731084061953483251491595210247372800000⟩, + ⟨5, 3, 7, 7, 4, 4, -107704765471815153431006417328260396923389739008000000⟩, + ⟨5, 3, 8, 7, 5, 4, -474196502990813219193431552274654387587040411648000000⟩, + ⟨5, 4, 6, 2, 8, 5, 41790407374825455290432567462991340675610443776000000⟩, + ⟨5, 4, 6, 3, 7, 5, 88606843171480514028302587076098046419795968000000⟩, + ⟨5, 4, 7, 3, 8, 5, -14181485244732000423207788433811980472641650688000000⟩, + ⟨5, 4, 6, 4, 6, 5, 17906451191208625062271362804676967340460474368000000⟩, + ⟨5, 4, 7, 4, 7, 5, -37511203328428738262300817105465389196830048256000000⟩, + ⟨5, 4, 8, 4, 8, 5, 20089947512354060552183513540287909432362270720000000⟩, + ⟨5, 4, 6, 5, 5, 5, 14958714345515507413495523622170865112568561664000000⟩, + ⟨5, 4, 7, 5, 6, 5, 11883476498852096409767840973856744297652551680000000⟩, + ⟨5, 4, 8, 5, 7, 5, -32937513901923012411721605370320924169860022272000000⟩, + ⟨5, 4, 6, 6, 4, 5, -9973846400035592481120789539349177414004506624000000⟩, + ⟨5, 4, 7, 6, 5, 5, 74244310191506384974582049959033417549744177152000000⟩, + ⟨5, 4, 8, 6, 6, 5, 49199967100548471074562747270139879571148767232000000⟩ +] + +def collectedFourData_15_79 : List CollectedFourTerm := [ + ⟨5, 4, 6, 7, 3, 5, -50349877149542408878983526183979456335454404608000000⟩, + ⟨5, 4, 7, 7, 4, 5, 57731598504941598618936154491801619936617431040000000⟩, + ⟨5, 4, 8, 7, 5, 5, 127088722598244360122641232470053550065576837120000000⟩, + ⟨5, 5, 5, 1, 8, 6, -106041100000266020448534584745944424229204131840000000⟩, + ⟨5, 5, 5, 2, 7, 6, -54355439555329501548422217841016176582487703552000000⟩, + ⟨5, 5, 6, 2, 8, 6, 96349895828635950607320885034153785729151401984000000⟩, + ⟨5, 5, 5, 3, 6, 6, 37190805785221235418828781521148264151638867968000000⟩, + ⟨5, 5, 6, 3, 7, 6, 204287554143807566907998067759259925675507712000000⟩, + ⟨5, 5, 7, 3, 8, 6, -16348065403741149668129941222059852176446980096000000⟩, + ⟨5, 5, 5, 4, 5, 6, 22550713404568111686355581935552769058481897472000000⟩, + ⟨5, 5, 6, 4, 6, 6, 41284228015753127035979079658062999309948813312000000⟩, + ⟨5, 5, 7, 4, 7, 6, -43241987337961268142271358003117531765409841152000000⟩, + ⟨5, 5, 8, 4, 8, 6, 15439463037986735437614204153152955440336732160000000⟩, + ⟨5, 5, 5, 5, 4, 6, 14958714345515507413495523622170865112568561664000000⟩, + ⟨5, 5, 6, 5, 5, 6, 34488071771919668973856135606195539880471166976000000⟩, + ⟨5, 5, 7, 5, 6, 6, 13698977763927877036487296867077335548491202560000000⟩, + ⟨5, 5, 8, 5, 7, 6, -25313034199775576729649804412114860257172258816000000⟩, + ⟨5, 5, 5, 6, 3, 6, -136312082807226560636390691971286645398059352064000000⟩, + ⟨5, 5, 6, 6, 4, 6, -22995206843404424133675989298537334407866351616000000⟩, + ⟨5, 5, 7, 6, 5, 6, 85587004317285052003837613096558430574224605184000000⟩, + ⟨5, 5, 8, 6, 6, 6, 37811003391221510519934043271429759393329053696000000⟩, + ⟨5, 5, 5, 7, 2, 6, 7551651117429272993284745158416202488549998592000000⟩, + ⟨5, 5, 6, 7, 3, 6, -116084185895383140873785510734774347374864105472000000⟩, + ⟨5, 5, 7, 7, 4, 6, 66551558735493069122906622451185743134646599680000000⟩ +] + +def collectedFourData_15_80 : List CollectedFourTerm := [ + ⟨5, 5, 8, 7, 5, 6, 97669823870566333102561353933415312700850831360000000⟩, + ⟨5, 6, 4, 0, 8, 7, 14715255790648000197164663998727255354127679488000000⟩, + ⟨5, 6, 4, 1, 7, 7, -17161633617063392938550027356242765994606460928000000⟩, + ⟨5, 6, 5, 1, 8, 7, -84240990947418177534066953815561489435380940800000000⟩, + ⟨5, 6, 4, 2, 6, 7, 11314548511220109531143254614837440223400427520000000⟩, + ⟨5, 6, 5, 2, 7, 7, -43180956171823580214558796849504887509341962240000000⟩, + ⟨5, 6, 6, 2, 8, 7, 38271060476854935355100005338954119886447575040000000⟩, + ⟨5, 6, 4, 3, 5, 7, 31043669256365158285026832275716346847237767168000000⟩, + ⟨5, 6, 5, 3, 6, 7, 29545056902202543065602244830146704030469980160000000⟩, + ⟨5, 6, 6, 3, 7, 7, 81144886271716917532704813340469490320670720000000⟩, + ⟨5, 6, 7, 3, 8, 7, -4329067470634510648515164303283432195977379840000000⟩, + ⟨5, 6, 4, 4, 4, 7, -23266167984201610093377703622516795788461342720000000⟩, + ⟨5, 6, 5, 4, 5, 7, 17914699524686922055082593896923119122791792640000000⟩, + ⟨5, 6, 6, 4, 6, 7, 16398473226595548453789603423789167445509406720000000⟩, + ⟨5, 6, 7, 4, 7, 7, -11450742098665606235052388274660844998051758080000000⟩, + ⟨5, 6, 8, 4, 8, 7, 3066348015092203137720500781292534130068684800000000⟩, + ⟨5, 6, 4, 5, 3, 7, -22169956877066847073106112030887295096440487936000000⟩, + ⟨5, 6, 5, 5, 4, 7, 11883476498852096409767840973856744297652551680000000⟩, + ⟨5, 6, 6, 5, 5, 7, 13698977763927877036487296867077335548491202560000000⟩, + ⟨5, 6, 7, 5, 6, 7, 3627572899555097572616398431306225425999462400000000⟩, + ⟨5, 6, 8, 5, 7, 7, -5027284432332443856903473300285093126319636480000000⟩, + ⟨5, 6, 4, 6, 2, 7, 28080412856024131421427719310276658992141828096000000⟩, + ⟨5, 6, 5, 6, 3, 7, -108288813806707801527708150074646064365494599680000000⟩, + ⟨5, 6, 6, 6, 4, 7, -9133906624527570004100400963351305056640040960000000⟩ +] + +def collectedFourData_15_81 : List CollectedFourTerm := [ + ⟨5, 6, 7, 6, 5, 7, 22663960973279741888432070096382042360365711360000000⟩, + ⟨5, 6, 8, 6, 6, 7, 7509438308317950828858058581590447747896442880000000⟩, + ⟨5, 6, 4, 7, 1, 7, 26974530515041119182333620136372780908167561216000000⟩, + ⟨5, 6, 5, 7, 2, 7, 5999169882430716478040617714313233924400087040000000⟩, + ⟨5, 6, 6, 7, 3, 7, -46109701111771038829773522328045701491400376320000000⟩, + ⟨5, 6, 7, 7, 4, 7, 17623258833789214209162062238138198998070067200000000⟩, + ⟨5, 6, 8, 7, 5, 7, 19397673987952938957195825530785273427578060800000000⟩, + ⟨5, 7, 3, 0, 7, 8, 21135453139532489859739059288781517391531501158400000⟩, + ⟨5, 7, 4, 0, 8, 8, -81572752253373066983684594777292556341378180710400000⟩, + ⟨5, 7, 3, 1, 6, 8, -100218095437454709499713591779871251315645271244800000⟩, + ⟨5, 7, 4, 1, 7, 8, 95134036895068066621455208167687705331113551462400000⟩, + ⟨5, 7, 5, 1, 8, 8, 233491336538628439775970226482390924135833272320000000⟩, + ⟨5, 7, 3, 2, 5, 8, -42647740349203234780837748748300742107459275980800000⟩, + ⟨5, 7, 4, 2, 6, 8, -62721224536993638229779325248152958664301346816000000⟩, + ⟨5, 7, 5, 2, 7, 8, 119684954511851331158364771436078612412362653696000000⟩, + ⟨5, 7, 6, 2, 8, 8, -70717441797973906252480917496007746379310956544000000⟩, + ⟨5, 7, 3, 3, 4, 8, 4646841958731287552378995350181936372607719833600000⟩, + ⟨5, 7, 4, 3, 5, 8, -172087905049839175900295289552231391368392894054400000⟩, + ⟨5, 7, 5, 3, 6, 8, -81890238310599159473937024609766729604099211264000000⟩, + ⟨5, 7, 6, 3, 7, 8, -149939894547571304096190530825285222679969792000000⟩, + ⟨5, 7, 7, 3, 8, 8, 5999453106595551996225922900916965642881466368000000⟩, + ⟨5, 7, 3, 4, 3, 8, 68624425431670427385405479348183657458772528332800000⟩, + ⟨5, 7, 4, 4, 4, 8, 128973997045080452641472015601754924654553726976000000⟩, + ⟨5, 7, 5, 4, 5, 8, -49654296425810024786380886664461687475306233856000000⟩ +] + +def collectedFourData_15_82 : List CollectedFourTerm := [ + ⟨5, 7, 6, 4, 6, 8, -30301174347617743828621630635338089200869179392000000⟩, + ⟨5, 7, 7, 4, 7, 8, 15869050487816666110090008657802578959234236416000000⟩, + ⟨5, 7, 8, 4, 8, 8, -3399607190201942307690935516158501725791059968000000⟩, + ⟨5, 7, 3, 5, 2, 8, 85690459311353806874953571449212202407590834995200000⟩, + ⟨5, 7, 4, 5, 3, 8, 122897245248721628467370477289754517796058614988800000⟩, + ⟨5, 7, 5, 5, 4, 8, -32937513901923012411721605370320924169860022272000000⟩, + ⟨5, 7, 6, 5, 5, 8, -25313034199775576729649804412114860257172258816000000⟩, + ⟨5, 7, 7, 5, 6, 8, -5027284432332443856903473300285093126319636480000000⟩, + ⟨5, 7, 8, 5, 7, 8, 5573663595661289200979950739881110823834012876800000⟩, + ⟨5, 7, 3, 6, 1, 8, 20862365370940275107423154048867589224404720025600000⟩, + ⟨5, 7, 4, 6, 2, 8, -155661348580337516605511545900398144283168525516800000⟩, + ⟨5, 7, 5, 6, 3, 8, 300144853278056149118132453397545303072122601472000000⟩, + ⟨5, 7, 6, 6, 4, 8, 16877674724973759368991873843906651164095021056000000⟩, + ⟨5, 7, 7, 6, 5, 8, -31408928595186389651570167043828771582348623872000000⟩, + ⟨5, 7, 8, 6, 6, 8, -8325584813492858116476568804814030005590609100800000⟩, + ⟨5, 7, 3, 7, 0, 8, -2192844075814192930084416046802096191247819263180800000⟩, + ⟨5, 7, 4, 7, 1, 8, -149530985132648170165156084153769447937595460812800000⟩, + ⟨5, 7, 5, 7, 2, 8, -16627940604893428336807572011618934741968879616000000⟩, + ⟨5, 7, 6, 7, 3, 8, 85201718062284697562944173397775749393995005952000000⟩, + ⟨5, 7, 7, 7, 4, 8, -24423254124800552277220134082490482973674045440000000⟩, + ⟨5, 7, 8, 7, 5, 8, -21505866795962847456338308684195073580626608128000000⟩, + ⟨6, 1, 8, 4, 8, 3, -12724816649300088712663126964736434724359110656000000⟩, + ⟨6, 1, 8, 5, 7, 3, 20862365370940275107423154048867589224404720025600000⟩, + ⟨6, 1, 8, 6, 6, 3, -31162876862723893569609038262062210858943617433600000⟩ +] + +def collectedFourData_15_83 : List CollectedFourTerm := [ + ⟨6, 1, 8, 7, 5, 3, -80497009375557369421802894078653274075091173376000000⟩, + ⟨6, 2, 7, 3, 8, 4, -33510560703524417563969720294468257135915014553600000⟩, + ⟨6, 2, 7, 4, 7, 4, -88638209221879948130826480390214746434125902643200000⟩, + ⟨6, 2, 8, 4, 8, 4, 94944273328979178080821227577931882709141946368000000⟩, + ⟨6, 2, 7, 5, 6, 4, 28080412856024131421427719310276658992141828096000000⟩, + ⟨6, 2, 8, 5, 7, 4, -155661348580337516605511545900398144283168525516800000⟩, + ⟨6, 2, 7, 6, 5, 4, 175437792348863988335723603854166213912863073894400000⟩, + ⟨6, 2, 8, 6, 6, 4, 232517039743320764644821727107607149181225716940800000⟩, + ⟨6, 2, 7, 7, 4, 4, 136418591059071053943911585600441612618315071488000000⟩, + ⟨6, 2, 8, 7, 5, 4, 600616124456197677059963830131641082272733462528000000⟩, + ⟨6, 3, 6, 2, 8, 5, -380817317521188674028465483772550483110187237376000000⟩, + ⟨6, 3, 6, 3, 7, 5, -807434587271112879596836182125439976910880768000000⟩, + ⟨6, 3, 7, 3, 8, 5, 129229541146288349824727824198458177558033727488000000⟩, + ⟨6, 3, 6, 4, 6, 5, -163173492131784781534875956005033028074673799168000000⟩, + ⟨6, 3, 7, 4, 7, 5, 341822842270959786819457237770114420498398969856000000⟩, + ⟨6, 3, 8, 4, 8, 5, -183070718889542885779591469686434546359960862720000000⟩, + ⟨6, 3, 6, 5, 5, 5, -136312082807226560636390691971286645398059352064000000⟩, + ⟨6, 3, 7, 5, 6, 5, -108288813806707801527708150074646064365494599680000000⟩, + ⟨6, 3, 8, 5, 7, 5, 300144853278056149118132453397545303072122601472000000⟩, + ⟨6, 3, 6, 6, 4, 5, 90887207615926780484528441825235382432929153024000000⟩, + ⟨6, 3, 7, 6, 5, 5, -676555238975068747698513594703997361671060324352000000⟩, + ⟨6, 3, 8, 6, 6, 5, -448337325963668199508539567987787560436925202432000000⟩, + ⟨6, 3, 6, 7, 3, 5, 458815942654835571138847305541579373983624593408000000⟩, + ⟨6, 3, 7, 7, 4, 5, -526082272462029355356191563945798601494537175040000000⟩ +] + +def collectedFourData_15_84 : List CollectedFourTerm := [ + ⟨6, 3, 8, 7, 5, 5, -1158102767292299687911399648380195683712494469120000000⟩, + ⟨6, 4, 5, 1, 8, 6, 70703779687492868582595658032256167823477309440000000⟩, + ⟨6, 4, 5, 2, 7, 6, 36241938485428869710796214410786447538186616832000000⟩, + ⟨6, 4, 6, 2, 8, 6, -64242089223552704419966225421729556853627551744000000⟩, + ⟨6, 4, 5, 3, 6, 6, -24797277080603849512767833557639225900152127488000000⟩, + ⟨6, 4, 6, 3, 7, 6, -136210414839569811022223412845618813460283392000000⟩, + ⟨6, 4, 7, 3, 8, 6, 10900207698901074407886128549866251894480961536000000⟩, + ⟨6, 4, 5, 4, 5, 6, -15035874508547875834266636854037965031239319552000000⟩, + ⟨6, 4, 6, 4, 6, 6, -27526600178484637746616695847501348960041172992000000⟩, + ⟨6, 4, 7, 4, 7, 6, 28831952384357573078483263926802919156908818432000000⟩, + ⟨6, 4, 8, 4, 8, 6, -10294389563369909992860913235275798452696514560000000⟩, + ⟨6, 4, 5, 5, 4, 6, -9973846400035592481120789539349177414004506624000000⟩, + ⟨6, 4, 6, 5, 5, 6, -22995206843404424133675989298537334407866351616000000⟩, + ⟨6, 4, 7, 5, 6, 6, -9133906624527570004100400963351305056640040960000000⟩, + ⟨6, 4, 8, 5, 7, 6, 16877674724973759368991873843906651164095021056000000⟩, + ⟨6, 4, 5, 6, 3, 6, 90887207615926780484528441825235382432929153024000000⟩, + ⟨6, 4, 6, 6, 4, 6, 15332244181928667634696521042421583593504505856000000⟩, + ⟨6, 4, 7, 6, 5, 6, -57065842370049373567238144249430659781774802944000000⟩, + ⟨6, 4, 8, 6, 6, 6, -25210798959358822354894814425514752237042139136000000⟩, + ⟨6, 4, 5, 7, 2, 6, -5035125785022875174668388923409746011170537472000000⟩, + ⟨6, 4, 6, 7, 3, 6, 77400090198315055806164503233882789866794647552000000⟩, + ⟨6, 4, 7, 7, 4, 6, -44373801730477513910789495303256701559247994880000000⟩, + ⟨6, 4, 8, 7, 5, 6, -65122162152631669989004468110951271901178101760000000⟩, + ⟨6, 5, 4, 0, 8, 7, 91936397196036428260364560647711486039842566963200000⟩ +] + +def collectedFourData_15_85 : List CollectedFourTerm := [ + ⟨6, 5, 4, 1, 7, 7, -107220614252177565823482914251164283224970179379200000⟩, + ⟨6, 5, 5, 1, 8, 7, -526311829988821179956612442294199370489392005120000000⟩, + ⟨6, 5, 4, 2, 6, 7, 70689822917141938622668183101395360744082505728000000⟩, + ⟨6, 5, 5, 2, 7, 7, -269781347629744119786261586438458528951001153536000000⟩, + ⟨6, 5, 6, 2, 8, 7, 239105827800138160308333069558940663424489619456000000⟩, + ⟨6, 5, 4, 3, 5, 7, 193951307933729878058244598586148172130340254515200000⟩, + ⟨6, 5, 5, 3, 6, 7, 184588438365214258847133937009586435773194829824000000⟩, + ⟨6, 5, 6, 3, 7, 7, 506968319194623697901042761150606411938398208000000⟩, + ⟨6, 5, 7, 3, 8, 7, -27046683532449073470183996469416042288881074176000000⟩, + ⟨6, 5, 4, 4, 4, 7, -145359869475369289549579768960774089804777259008000000⟩, + ⟨6, 5, 5, 4, 5, 7, 111925538677757099580153222900009044947129860096000000⟩, + ⟨6, 5, 6, 4, 6, 7, 102452622599125618169160892325953741599547588608000000⟩, + ⟨6, 5, 7, 4, 7, 7, -71540718608598412087865896001264817127777370112000000⟩, + ⟨6, 5, 8, 4, 8, 7, 19157600320883077437209640099036975399142686720000000⟩, + ⟨6, 5, 4, 5, 3, 7, -138511079268113884566231807032058271421054740070400000⟩, + ⟨6, 5, 5, 5, 4, 7, 74244310191506384974582049959033417549744177152000000⟩, + ⟨6, 5, 6, 5, 5, 7, 85587004317285052003837613096558430574224605184000000⟩, + ⟨6, 5, 7, 5, 6, 7, 22663960973279741888432070096382042360365711360000000⟩, + ⟨6, 5, 8, 5, 7, 7, -31408928595186389651570167043828771582348623872000000⟩, + ⟨6, 5, 4, 6, 2, 7, 175437792348863988335723603854166213912863073894400000⟩, + ⟨6, 5, 5, 6, 3, 7, -676555238975068747698513594703997361671060324352000000⟩, + ⟨6, 5, 6, 6, 4, 7, -57065842370049373567238144249430659781774802944000000⟩, + ⟨6, 5, 7, 6, 5, 7, 141597465087839938693416343423212521299592085504000000⟩, + ⟨6, 5, 8, 6, 6, 7, 46916663417527245490559907643685310113966456832000000⟩ +] + +def collectedFourData_15_86 : List CollectedFourTerm := [ + ⟨6, 5, 4, 7, 1, 7, 168528579243828344492700842350435787418771023462400000⟩, + ⟨6, 5, 5, 7, 2, 7, 37480970293983713025081468762860327441327456256000000⟩, + ⟨6, 5, 6, 7, 3, 7, -288079246213064251784638249001810637609184002048000000⟩, + ⟨6, 5, 7, 7, 4, 7, 110104706780666505575768199439093184227002286080000000⟩, + ⟨6, 5, 8, 7, 5, 7, 121190707508396885031845658886157457077431173120000000⟩, + ⟨6, 6, 3, 0, 7, 8, -31570798033408081801488226935777228158602208870400000⟩, + ⟨6, 6, 4, 0, 8, 8, 121848198352724807713208151828480297679928583782400000⟩, + ⟨6, 6, 3, 1, 6, 8, 149699428228993466416698706020522415079815957708800000⟩, + ⟨6, 6, 4, 1, 7, 8, -142105184359601690040912086634060228656013665894400000⟩, + ⟨6, 6, 5, 1, 8, 8, -348774534415996484840348398433809893567674449920000000⟩, + ⟨6, 6, 3, 2, 5, 8, 63704486876012466607653268883102367621069982924800000⟩, + ⟨6, 6, 4, 2, 6, 8, 93688983112536475737689412192117912542637981696000000⟩, + ⟨6, 6, 5, 2, 7, 8, -178777786385083966113612174243304447932131966976000000⟩, + ⟨6, 6, 6, 2, 8, 8, 105633224786043536310130215343609122209308606464000000⟩, + ⟨6, 6, 3, 3, 4, 8, -6941157495122290687072168342055554910216886681600000⟩, + ⟨6, 6, 4, 3, 5, 8, 257053986893651938481870754949700262547335571046400000⟩, + ⟨6, 6, 5, 3, 6, 8, 122322438868172290508914701561006650816446070784000000⟩, + ⟨6, 6, 6, 3, 7, 8, 223970694957931139279245530292830716509028352000000⟩, + ⟨6, 6, 7, 3, 8, 8, -8961602152023720452853162733708993503436996608000000⟩, + ⟨6, 6, 3, 4, 3, 8, -102506809821341888532462111425641594333772434636800000⟩, + ⟨6, 6, 4, 4, 4, 8, -192653168370236940063349507703799793944316870656000000⟩, + ⟨6, 6, 5, 4, 5, 8, 74170435504790909176631439826225098396518055936000000⟩, + ⟨6, 6, 6, 4, 6, 8, 45261970452594995229437962472319046571840765952000000⟩, + ⟨6, 6, 7, 4, 7, 8, -23704180110325181708981896240868555684415799296000000⟩ +] + +def collectedFourData_15_87 : List CollectedFourTerm := [ + ⟨6, 6, 8, 4, 8, 8, 5078117383442176166995252733948658612550238208000000⟩, + ⟨6, 6, 3, 5, 2, 8, -127998967727292589905475721648494506060484391731200000⟩, + ⟨6, 6, 4, 5, 3, 8, -183576102343052731084061953483251491595210247372800000⟩, + ⟨6, 6, 5, 5, 4, 8, 49199967100548471074562747270139879571148767232000000⟩, + ⟨6, 6, 6, 5, 5, 8, 37811003391221510519934043271429759393329053696000000⟩, + ⟨6, 6, 7, 5, 6, 8, 7509438308317950828858058581590447747896442880000000⟩, + ⟨6, 6, 8, 5, 7, 8, -8325584813492858116476568804814030005590609100800000⟩, + ⟨6, 6, 3, 6, 1, 8, -31162876862723893569609038262062210858943617433600000⟩, + ⟨6, 6, 4, 6, 2, 8, 232517039743320764644821727107607149181225716940800000⟩, + ⟨6, 6, 5, 6, 3, 8, -448337325963668199508539567987787560436925202432000000⟩, + ⟨6, 6, 6, 6, 4, 8, -25210798959358822354894814425514752237042139136000000⟩, + ⟨6, 6, 7, 6, 5, 8, 46916663417527245490559907643685310113966456832000000⟩, + ⟨6, 6, 8, 6, 6, 8, 12436230012270585279237295522802446120763837644800000⟩, + ⟨6, 6, 3, 7, 0, 8, 3275531259218444600135927881618449448541581266124800000⟩, + ⟨6, 6, 4, 7, 1, 8, 223359892035123169494364024672531992781213453516800000⟩, + ⟨6, 6, 5, 7, 2, 8, 24837761986124502039292261485245884074867818496000000⟩, + ⟨6, 6, 6, 7, 3, 8, -127268917079071770550997603202701171834656653312000000⟩, + ⟨6, 6, 7, 7, 4, 8, 36481906406371695093614529483949694681496944640000000⟩, + ⟨6, 6, 8, 7, 5, 8, 32124098436232456923134896792542174793766535168000000⟩, + ⟨7, 0, 8, 4, 8, 3, 1337505997479416428586843637506881727292147499008000000⟩, + ⟨7, 0, 8, 5, 7, 3, -2192844075814192930084416046802096191247819263180800000⟩, + ⟨7, 0, 8, 6, 6, 3, 3275531259218444600135927881618449448541581266124800000⟩, + ⟨7, 0, 8, 7, 5, 3, 8461043941634064780285861678591437983675966291968000000⟩, + ⟨7, 1, 7, 3, 8, 4, -32190824504898098002891407388314675766651099545600000⟩ +] + +def collectedFourData_15_88 : List CollectedFourTerm := [ + ⟨7, 1, 7, 4, 7, 4, -85147397643808526967916308939398972398955082547200000⟩, + ⟨7, 1, 8, 4, 8, 4, 91205111950179960517687574787136715516257763328000000⟩, + ⟨7, 1, 7, 5, 6, 4, 26974530515041119182333620136372780908167561216000000⟩, + ⟨7, 1, 8, 5, 7, 4, -149530985132648170165156084153769447937595460812800000⟩, + ⟨7, 1, 7, 6, 5, 4, 168528579243828344492700842350435787418771023462400000⟩, + ⟨7, 1, 8, 6, 6, 4, 223359892035123169494364024672531992781213453516800000⟩, + ⟨7, 1, 7, 7, 4, 4, 131046059265912432972104448842767183205627854848000000⟩, + ⟨7, 1, 8, 7, 5, 4, 576962242686319424591938444819467786628720754688000000⟩, + ⟨7, 2, 6, 2, 8, 5, 21097172474888210827306248246851396285107273728000000⟩, + ⟨7, 2, 6, 3, 7, 5, 44731649444752578046014284425378119605551104000000⟩, + ⟨7, 2, 7, 3, 8, 5, -7159280297861486833075231359493337466236043264000000⟩, + ⟨7, 2, 6, 4, 6, 5, 9039765652575758423129915387063234555547746304000000⟩, + ⟨7, 2, 7, 4, 7, 5, -18936889493860004501963205187476652213999239168000000⟩, + ⟨7, 2, 8, 4, 8, 5, 10142066428739981005350522602055421676130140160000000⟩, + ⟨7, 2, 6, 5, 5, 5, 7551651117429272993284745158416202488549998592000000⟩, + ⟨7, 2, 7, 5, 6, 5, 5999169882430716478040617714313233924400087040000000⟩, + ⟨7, 2, 8, 5, 7, 5, -16627940604893428336807572011618934741968879616000000⟩, + ⟨7, 2, 6, 6, 4, 5, -5035125785022875174668388923409746011170537472000000⟩, + ⟨7, 2, 7, 6, 5, 5, 37480970293983713025081468762860327441327456256000000⟩, + ⟨7, 2, 8, 6, 6, 5, 24837761986124502039292261485245884074867818496000000⟩, + ⟨7, 2, 6, 7, 3, 5, -25418274408907113977601312342502451741693313024000000⟩, + ⟨7, 2, 7, 7, 4, 5, 29144810194969733784789206890826198978521989120000000⟩, + ⟨7, 2, 8, 7, 5, 5, 64158568166615839149673162726673656512365199360000000⟩, + ⟨7, 3, 5, 1, 8, 6, 356926152508311539215484231963909457879477780480000000⟩ +] + +def collectedFourData_15_89 : List CollectedFourTerm := [ + ⟨7, 3, 5, 2, 7, 6, 182956211396648819480769378954731107445473542144000000⟩, + ⟨7, 3, 6, 2, 8, 6, -324306307767510644472602621853347665202431131648000000⟩, + ⟨7, 3, 5, 3, 6, 6, -125181379838285051298655411667076720265103671296000000⟩, + ⟨7, 3, 6, 3, 7, 6, -687616129082965855911353439451594447770353664000000⟩, + ⟨7, 3, 7, 3, 8, 6, 55026325504893169873574922157080549286175834112000000⟩, + ⟨7, 3, 5, 4, 5, 6, -75903959613677254968294528956735840589535248384000000⟩, + ⟨7, 3, 6, 4, 6, 6, -138959522910471905971523034249954039764682276864000000⟩, + ⟨7, 3, 7, 4, 7, 6, 145549189581331399286318276837576043181683769344000000⟩, + ⟨7, 3, 8, 4, 8, 6, -51968040117738008818728811527854772970869227520000000⟩, + ⟨7, 3, 5, 5, 4, 6, -50349877149542408878983526183979456335454404608000000⟩, + ⟨7, 3, 6, 5, 5, 6, -116084185895383140873785510734774347374864105472000000⟩, + ⟨7, 3, 7, 5, 6, 6, -46109701111771038829773522328045701491400376320000000⟩, + ⟨7, 3, 8, 5, 7, 6, 85201718062284697562944173397775749393995005952000000⟩, + ⟨7, 3, 5, 6, 3, 6, 458815942654835571138847305541579373983624593408000000⟩, + ⟨7, 3, 6, 6, 4, 6, 77400090198315055806164503233882789866794647552000000⟩, + ⟨7, 3, 7, 6, 5, 6, -288079246213064251784638249001810637609184002048000000⟩, + ⟨7, 3, 8, 6, 6, 6, -127268917079071770550997603202701171834656653312000000⟩, + ⟨7, 3, 5, 7, 2, 6, -25418274408907113977601312342502451741693313024000000⟩, + ⟨7, 3, 6, 7, 3, 6, 390730403952757638043147203504209578302199824384000000⟩, + ⟨7, 3, 7, 7, 4, 6, -224007406588868482993494252025255533290150952960000000⟩, + ⟨7, 3, 8, 7, 5, 6, -328749083611903609665709707513357313765193809920000000⟩, + ⟨7, 4, 4, 0, 8, 7, 71488780180216582019005789705653772921092440064000000⟩, + ⟨7, 4, 4, 1, 7, 7, -83373627386305458790976898787001933024024592384000000⟩, + ⟨7, 4, 5, 1, 8, 7, -409254570201283335897119038774873112762017382400000000⟩ +] + +def collectedFourData_15_90 : List CollectedFourTerm := [ + ⟨7, 4, 4, 2, 6, 7, 54967666404485391752767757042213244312810946560000000⟩, + ⟨7, 4, 5, 2, 7, 7, -209779152170831922888494348956784029367764254720000000⟩, + ⟨7, 4, 6, 2, 8, 7, 185926189025707521714081694841517870991666053120000000⟩, + ⟨7, 4, 4, 3, 5, 7, 150814507000690644246173949100891381183077679104000000⟩, + ⟨7, 4, 5, 3, 6, 7, 143534037623449167542435686638406690130079252480000000⟩, + ⟨7, 4, 6, 3, 7, 7, 394213258672277196116540335469143884205916160000000⟩, + ⟨7, 4, 7, 3, 8, 7, -21031218022740772324788999024503549689614827520000000⟩, + ⟨7, 4, 4, 4, 4, 7, -113030313052093944284794087604581308626538332160000000⟩, + ⟨7, 4, 5, 4, 5, 7, 87032127374156709797255822138270388334803025920000000⟩, + ⟨7, 4, 6, 4, 6, 7, 79666086982483399124626822624797176524607324160000000⟩, + ⟨7, 4, 7, 4, 7, 7, -55629313988011187257423469939765112704587530240000000⟩, + ⟨7, 4, 8, 4, 8, 7, 14896749490843668969026525238891058754381414400000000⟩, + ⟨7, 4, 4, 5, 3, 7, -107704765471815153431006417328260396923389739008000000⟩, + ⟨7, 4, 5, 5, 4, 7, 57731598504941598618936154491801619936617431040000000⟩, + ⟨7, 4, 6, 5, 5, 7, 66551558735493069122906622451185743134646599680000000⟩, + ⟨7, 4, 7, 5, 6, 7, 17623258833789214209162062238138198998070067200000000⟩, + ⟨7, 4, 8, 5, 7, 7, -24423254124800552277220134082490482973674045440000000⟩, + ⟨7, 4, 4, 6, 2, 7, 136418591059071053943911585600441612618315071488000000⟩, + ⟨7, 4, 5, 6, 3, 7, -526082272462029355356191563945798601494537175040000000⟩, + ⟨7, 4, 6, 6, 4, 7, -44373801730477513910789495303256701559247994880000000⟩, + ⟨7, 4, 7, 6, 5, 7, 110104706780666505575768199439093184227002286080000000⟩, + ⟨7, 4, 8, 6, 6, 7, 36481906406371695093614529483949694681496944640000000⟩, + ⟨7, 4, 4, 7, 1, 7, 131046059265912432972104448842767183205627854848000000⟩, + ⟨7, 4, 5, 7, 2, 7, 29144810194969733784789206890826198978521989120000000⟩ +] + +def collectedFourData_15_91 : List CollectedFourTerm := [ + ⟨7, 4, 6, 7, 3, 7, -224007406588868482993494252025255533290150952960000000⟩, + ⟨7, 4, 7, 7, 4, 7, 85616267549253237532813840007192866478201241600000000⟩, + ⟨7, 4, 8, 7, 5, 7, 94236625680239531648082203094127441778992742400000000⟩, + ⟨7, 5, 3, 0, 7, 8, -81550712935909058392940233914250665191238795264000000⟩, + ⟨7, 5, 4, 0, 8, 8, 314746793385003482524825402744866776870692061184000000⟩, + ⟨7, 5, 3, 1, 6, 8, 386689468072799862842827479297178761776917905408000000⟩, + ⟨7, 5, 4, 1, 7, 8, -367072732344336537731301464460309759065906479104000000⟩, + ⟨7, 5, 5, 1, 8, 8, -900921538486806800716572007321471461933396787200000000⟩, + ⟨7, 5, 3, 2, 5, 8, 164555432411230066259045906944538817650352979968000000⟩, + ⟨7, 5, 4, 2, 6, 8, 242008559903447860998338997862939849286599311360000000⟩, + ⟨7, 5, 5, 2, 7, 8, -461801944992943674695092030236043580102840156160000000⟩, + ⟨7, 5, 6, 2, 8, 8, 272861800386078319775297323057626258956605194240000000⟩, + ⟨7, 5, 3, 3, 4, 8, -17929744497704908731150799967820734023971373056000000⟩, + ⟨7, 5, 4, 3, 5, 8, 663997656062170195490285606579960010215390183424000000⟩, + ⟨7, 5, 5, 3, 6, 8, 315971806832459256857844489427894892376820285440000000⟩, + ⟨7, 5, 6, 3, 7, 8, 578540011286454800996528983039770332831416320000000⟩, + ⟨7, 5, 7, 3, 8, 8, -23148766900733880004822948703083611083274977280000000⟩, + ⟨7, 5, 3, 4, 3, 8, -264785939616416580075487417947222799804570533888000000⟩, + ⟨7, 5, 4, 4, 4, 8, -497643525302376958459831222887596941024123944960000000⟩, + ⟨7, 5, 5, 4, 5, 8, 191590085489188561530432529629659236241516789760000000⟩, + ⟨7, 5, 6, 4, 6, 8, 116916460438764252383352357359090929016053432320000000⟩, + ⟨7, 5, 7, 4, 7, 8, -61230406197291040535323264156298838556394127360000000⟩, + ⟨7, 5, 8, 4, 8, 8, 13117314695489110336435539491465220857297633280000000⟩, + ⟨7, 5, 3, 5, 2, 8, -330634881708572862982079994394689308457531604992000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1505.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1505.lean new file mode 100644 index 0000000000000000000000000000000000000000..22f0ca113a7862ff5e3cb80e2f441d4de3e5ed71 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1505.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1505. -/ +namespace LaughlinFock +def collectedFourData_15_92 : List CollectedFourTerm := [ + ⟨7, 5, 4, 5, 3, 8, -474196502990813219193431552274654387587040411648000000⟩, + ⟨7, 5, 5, 5, 4, 8, 127088722598244360122641232470053550065576837120000000⟩, + ⟨7, 5, 6, 5, 5, 8, 97669823870566333102561353933415312700850831360000000⟩, + ⟨7, 5, 7, 5, 6, 8, 19397673987952938957195825530785273427578060800000000⟩, + ⟨7, 5, 8, 5, 7, 8, -21505866795962847456338308684195073580626608128000000⟩, + ⟨7, 5, 3, 6, 1, 8, -80497009375557369421802894078653274075091173376000000⟩, + ⟨7, 5, 4, 6, 2, 8, 600616124456197677059963830131641082272733462528000000⟩, + ⟨7, 5, 5, 6, 3, 8, -1158102767292299687911399648380195683712494469120000000⟩, + ⟨7, 5, 6, 6, 4, 8, -65122162152631669989004468110951271901178101760000000⟩, + ⟨7, 5, 7, 6, 5, 8, 121190707508396885031845658886157457077431173120000000⟩, + ⟨7, 5, 8, 6, 6, 8, 32124098436232456923134896792542174793766535168000000⟩, + ⟨7, 5, 3, 7, 0, 8, 8461043941634064780285861678591437983675966291968000000⟩, + ⟨7, 5, 4, 7, 1, 8, 576962242686319424591938444819467786628720754688000000⟩, + ⟨7, 5, 5, 7, 2, 8, 64158568166615839149673162726673656512365199360000000⟩, + ⟨7, 5, 6, 7, 3, 8, -328749083611903609665709707513357313765193809920000000⟩, + ⟨7, 5, 7, 7, 4, 8, 94236625680239531648082203094127441778992742400000000⟩, + ⟨7, 5, 8, 7, 5, 8, 82979946440564389287782201144779893428327546880000000⟩, + ⟨0, 7, 8, 5, 8, 2, -93342497584022968005124408681762041635096494080000000⟩, + ⟨0, 7, 8, 6, 7, 2, -25161174021809026577811118378876561171540869120000000⟩, + ⟨0, 7, 8, 7, 6, 2, -37617666561228106018436693860507486055741521920000000⟩, + ⟨0, 8, 7, 4, 8, 3, 20654400665111695979681447636091601714560368640000000⟩, + ⟨0, 8, 7, 5, 7, 3, 9421214535701877307841892271489895509128118272000000⟩, + ⟨0, 8, 8, 5, 8, 3, 56872417834912242101103430630756182741026340864000000⟩, + ⟨0, 8, 7, 6, 6, 3, 2848283221524551401909870826950275737000607744000000⟩ +] + +def collectedFourData_15_93 : List CollectedFourTerm := [ + ⟨0, 8, 8, 6, 7, 3, 15330389042752552044117543232367012379881373696000000⟩, + ⟨0, 8, 7, 7, 5, 3, -10232561950735840814359394825197563970691530752000000⟩, + ⟨0, 8, 8, 7, 6, 3, 22919974352719316698490926673231882423617191936000000⟩, + ⟨1, 6, 8, 5, 8, 2, 214857655281910914825422107909208736162323103744000000⟩, + ⟨1, 6, 8, 6, 7, 2, 57916500997840770058682744481946182341168726016000000⟩, + ⟨1, 6, 8, 7, 6, 2, 86589108323855826707428853873016875463324205056000000⟩, + ⟨1, 7, 7, 4, 8, 3, -275916395673778713427497012782552646032472145920000000⟩, + ⟨1, 7, 7, 5, 7, 3, -125855385479722756686551417182181739252538146816000000⟩, + ⟨1, 7, 8, 5, 8, 3, -759742816879129001925199788972219790314902126592000000⟩, + ⟨1, 7, 7, 6, 6, 3, -38049423611145158524334509909751972540272607232000000⟩, + ⟨1, 7, 8, 6, 7, 3, -204794404714826913180910932444743886907625177088000000⟩, + ⟨1, 7, 7, 7, 5, 3, 136693950007695130395749298022550016904717664256000000⟩, + ⟨1, 7, 8, 7, 6, 3, -306181564639632398244393504202210037536609271808000000⟩, + ⟨1, 8, 6, 3, 8, 4, 167718103448624105065774125833484069815401316352000000⟩, + ⟨1, 8, 6, 4, 7, 4, -73184874458530391849916613424114982834829000704000000⟩, + ⟨1, 8, 7, 4, 8, 4, 429511133899328987583574921034393602200793251840000000⟩, + ⟨1, 8, 6, 5, 6, 4, -123951996370657737491936235597179670737260118016000000⟩, + ⟨1, 8, 7, 5, 7, 4, 195915466323518743116859984096487272566994501632000000⟩, + ⟨1, 8, 8, 5, 8, 4, 591334918595118638539595939018627082772222574592000000⟩, + ⟨1, 8, 6, 6, 5, 4, 11790019148716756564023604742305809823250251776000000⟩, + ⟨1, 8, 7, 6, 6, 4, 59230445655578548023752905969460842176618430464000000⟩, + ⟨1, 8, 8, 6, 7, 4, 159398785944750358532834009039802031689682649088000000⟩, + ⟨1, 8, 6, 7, 4, 4, 409156589946500527982939948010419350014630297600000000⟩, + ⟨1, 8, 7, 7, 5, 4, -212787548639911756922203187198741746408344256512000000⟩ +] + +def collectedFourData_15_94 : List CollectedFourTerm := [ + ⟨1, 8, 8, 7, 6, 4, 238312026884629423489537089617145789226898423808000000⟩, + ⟨2, 5, 8, 5, 8, 2, 450551588848718489058212298253677804973625180160000000⟩, + ⟨2, 5, 8, 6, 7, 2, 121449577911932377392809171027608088051177226240000000⟩, + ⟨2, 5, 8, 7, 6, 2, 181575379667617413025076061022245322724569251840000000⟩, + ⟨2, 6, 7, 4, 8, 3, 89816544992890116753938148722827910462539038720000000⟩, + ⟨2, 6, 7, 5, 7, 3, 40968554496130280795477197719676979157984608256000000⟩, + ⟨2, 6, 8, 5, 8, 3, 247312142247348910958184120214583909541186895872000000⟩, + ⟨2, 6, 7, 6, 6, 3, 12385881452889421096867046692527332910654554112000000⟩, + ⟨2, 6, 8, 6, 7, 3, 66664852664677793607425800570427863031252779008000000⟩, + ⟨2, 6, 7, 7, 5, 3, -44496733443987879693979493196842892999625015296000000⟩, + ⟨2, 6, 8, 7, 6, 3, 99668489106254561438498295881635949687265558528000000⟩, + ⟨2, 7, 6, 3, 8, 4, -22741148687635645696863485547250399105127546880000000⟩, + ⟨2, 7, 6, 4, 7, 4, 9923246671205077068371600311883984296225013760000000⟩, + ⟨2, 7, 7, 4, 8, 4, -58238057539159186983595735667702719923722649600000000⟩, + ⟨2, 7, 6, 5, 6, 4, 16806836719673900932754341224006306627625943040000000⟩, + ⟨2, 7, 7, 5, 7, 4, -26564471325752781918289156908462742347794350080000000⟩, + ⟨2, 7, 8, 5, 8, 4, -80179986724461335097481694446292529731579412480000000⟩, + ⟨2, 7, 6, 6, 5, 4, -1598626343715901010545935022739677521578557440000000⟩, + ⟨2, 7, 7, 6, 6, 4, -8031144782775592141616632229109181077163868160000000⟩, + ⟨2, 7, 8, 6, 7, 4, -21613119974902221595262534537509712494822686720000000⟩, + ⟨2, 7, 6, 7, 4, 4, -55478154457843463168529048313590043109228544000000000⟩, + ⟨2, 7, 7, 7, 5, 4, 28852182221223614413139591864781938833521377280000000⟩, + ⟨2, 7, 8, 7, 6, 4, -32313084431552105880012375131484616497058283520000000⟩, + ⟨2, 8, 5, 2, 8, 5, 277881786391929005960290839967446246700288573440000000⟩ +] + +def collectedFourData_15_95 : List CollectedFourTerm := [ + ⟨2, 8, 5, 3, 7, 5, -21891191592294310944257302680604369188280074240000000⟩, + ⟨2, 8, 6, 3, 8, 5, 283685201722203913853076389853561614316884459520000000⟩, + ⟨2, 8, 5, 4, 6, 5, -53611334997661281655020259773764783656088371200000000⟩, + ⟨2, 8, 6, 4, 7, 5, -123787864558950700686058520565887180557296599040000000⟩, + ⟨2, 8, 7, 4, 8, 5, 363246275019702582299541144595807422150554419200000000⟩, + ⟨2, 8, 5, 5, 5, 5, -14753910188357482772140854939548533801982361600000000⟩, + ⟨2, 8, 6, 5, 6, 5, -209657433343510624296035944721680713830797148160000000⟩, + ⟨2, 8, 7, 5, 7, 5, 165689682394697402658026319162488553004502876160000000⟩, + ⟨2, 8, 8, 5, 8, 5, 333402620662684028084504462935298175698353520640000000⟩, + ⟨2, 8, 5, 6, 4, 5, 123033529534123785192860765532574305068557271040000000⟩, + ⟨2, 8, 6, 6, 5, 5, 19942116514195523528194814796647047441950965760000000⟩, + ⟨2, 8, 7, 6, 6, 5, 50092388890642086995776489992738969059925688320000000⟩, + ⟨2, 8, 8, 6, 7, 5, 89871190239684026139412413339353128970968104960000000⟩, + ⟨2, 8, 5, 7, 3, 5, 171532924265053628251162433957357089883192033280000000⟩, + ⟨2, 8, 6, 7, 4, 5, 692064048950431174129152472146545820120907776000000000⟩, + ⟨2, 8, 7, 7, 5, 5, -179958744520318663553295726908333175832376770560000000⟩, + ⟨2, 8, 8, 7, 6, 5, 134363542216543371998410114874998094136984207360000000⟩, + ⟨3, 4, 8, 5, 8, 2, -33197128333608118180525004486882674916475273216000000⟩, + ⟨3, 4, 8, 6, 7, 2, -8948536247108219797782344750576227911859175424000000⟩, + ⟨3, 4, 8, 7, 6, 2, -13378670345946685582275081737492806759543209984000000⟩, + ⟨3, 5, 7, 4, 8, 3, 179405651253737399879613172380060341245763911680000000⟩, + ⟨3, 5, 7, 5, 7, 3, 81833366011621914198264870933887990159495921664000000⟩, + ⟨3, 5, 8, 5, 8, 3, 493998026158263409228930620230840979579016839168000000⟩, + ⟨3, 5, 7, 6, 6, 3, 24740398649080914032329404819406786259979337728000000⟩ +] + +def collectedFourData_15_96 : List CollectedFourTerm := [ + ⟨3, 5, 8, 6, 7, 3, 133160892672811329424013925822234169053441687552000000⟩, + ⟨3, 5, 7, 7, 5, 3, -88880789645321305523584758539817572553587687424000000⟩, + ⟨3, 5, 8, 7, 6, 3, 199084591808770858934666308723711231142167314432000000⟩, + ⟨3, 6, 6, 3, 8, 4, -18521013725163060381680250533481563875713220608000000⟩, + ⟨3, 6, 6, 4, 7, 4, 8081763604821495743832583012721491429048713216000000⟩, + ⟨3, 6, 7, 4, 8, 4, -47430667545657134080586389449518987533992591360000000⟩, + ⟨3, 6, 6, 5, 6, 4, 13687947686252869925863037028173466896814833664000000⟩, + ⟨3, 6, 7, 5, 7, 4, -21634832293826413635336110712858107101449289728000000⟩, + ⟨3, 6, 8, 5, 8, 4, -65300775040204643606116279631084219669642477568000000⟩, + ⟨3, 6, 6, 6, 5, 4, -1301965035278424599778951515515843937990344704000000⟩, + ⟨3, 6, 7, 6, 6, 4, -6540784055971236785933649691715736240711008256000000⟩, + ⟨3, 6, 8, 6, 7, 4, -17602316276855496762754362162590622266689585152000000⟩, + ⟨3, 6, 6, 7, 4, 4, -45182926960901175659785014560889091937166950400000000⟩, + ⟨3, 6, 7, 7, 5, 4, 23498006642502006779917724657503403241004597248000000⟩, + ⟨3, 6, 8, 7, 6, 4, -26316660098375675696125664235451371310685356032000000⟩, + ⟨3, 7, 5, 2, 8, 5, -21891191592294310944257302680604369188280074240000000⟩, + ⟨3, 7, 5, 3, 7, 5, 1724561640231545797059207936922736040911831040000000⟩, + ⟨3, 7, 6, 3, 8, 5, -22348377644443556524531241439409496907495505920000000⟩, + ⟨3, 7, 5, 4, 6, 5, 4223436235929436647466643024775816219407155200000000⟩, + ⟨3, 7, 6, 4, 7, 5, 9751858497263769146096851915357455923376291840000000⟩, + ⟨3, 7, 7, 4, 8, 5, -28616102929567536976074525049111444584608563200000000⟩, + ⟨3, 7, 5, 5, 5, 5, 1162295229430040752969299013779520963058073600000000⟩, + ⟨3, 7, 6, 5, 6, 5, 16516559439409051374667269732568762728956559360000000⟩, + ⟨3, 7, 7, 5, 7, 5, -13052833110310189914503630460892254186095247360000000⟩ +] + +def collectedFourData_15_97 : List CollectedFourTerm := [ + ⟨3, 7, 8, 5, 8, 5, -26265055875255533528134484675167032681368125440000000⟩, + ⟨3, 7, 5, 6, 4, 5, -9692432894860402286079314278710198220452003840000000⟩, + ⟨3, 7, 6, 6, 5, 5, -1571015859068877196771439829004447831252008960000000⟩, + ⟨3, 7, 7, 6, 6, 5, -3946217910713024341758521537608899128689950720000000⟩, + ⟨3, 7, 8, 6, 7, 5, -7079943848459424173412374024937169926393692160000000⟩, + ⟨3, 7, 5, 7, 3, 5, -13513156649196866505698875029091517450818682880000000⟩, + ⟨3, 7, 6, 7, 4, 5, -54519970115439230965915352349717218350596096000000000⟩, + ⟨3, 7, 7, 7, 5, 5, 14176932594807378736643125349207136962095349760000000⟩, + ⟨3, 7, 8, 7, 6, 5, -10584997613096917322912645134885715559642562560000000⟩, + ⟨3, 8, 4, 1, 8, 6, 167718103448624105065774125833484069815401316352000000⟩, + ⟨3, 8, 4, 2, 7, 6, -22741148687635645696863485547250399105127546880000000⟩, + ⟨3, 8, 5, 2, 8, 6, 283685201722203913853076389853561614316884459520000000⟩, + ⟨3, 8, 4, 3, 6, 6, -18521013725163060381680250533481563875713220608000000⟩, + ⟨3, 8, 5, 3, 7, 6, -22348377644443556524531241439409496907495505920000000⟩, + ⟨3, 8, 6, 3, 8, 6, 144804909168571844131508996123761254061918126080000000⟩, + ⟨3, 8, 4, 4, 5, 6, 47893329810183988482093917551221231871196135424000000⟩, + ⟨3, 8, 5, 4, 6, 6, -54730979604246291791489426135677901429381529600000000⟩, + ⟨3, 8, 6, 4, 7, 6, -63186554585188787954505717702635624805338972160000000⟩, + ⟨3, 8, 7, 4, 8, 6, 123610827637408233641324712917524606071550771200000000⟩, + ⟨3, 8, 4, 5, 4, 6, 6688240684654974435545211916861738016707706880000000⟩, + ⟨3, 8, 5, 5, 5, 6, -15062037862647904945786954647452383405984972800000000⟩, + ⟨3, 8, 6, 5, 6, 6, -107018009425645494303908325231845874606947696640000000⟩, + ⟨3, 8, 7, 5, 7, 6, 56383341496556177262788911034027816584489205760000000⟩, + ⟨3, 8, 8, 5, 8, 6, 85091389872531816320647082908059951193946849280000000⟩ +] + +def collectedFourData_15_98 : List CollectedFourTerm := [ + ⟨3, 8, 4, 6, 3, 6, -167181043254057852916355797050649158501877678080000000⟩, + ⟨3, 8, 5, 6, 4, 6, 125603020254286015176781680817332024431156920320000000⟩, + ⟨3, 8, 6, 6, 5, 6, 10179298577917816996522375104651503640552407040000000⟩, + ⟨3, 8, 7, 6, 6, 6, 17046180717947701673538569170567341563990507520000000⟩, + ⟨3, 8, 8, 6, 7, 6, 22937025725213044097202179201869650600048721920000000⟩, + ⟨3, 8, 4, 7, 2, 6, 171804908004508448428028432756926382202641448960000000⟩, + ⟨3, 8, 5, 7, 3, 6, 175115299401085970573073193406608290896664330240000000⟩, + ⟨3, 8, 6, 7, 4, 6, 353258721775819434444154859284828487631765504000000000⟩, + ⟨3, 8, 7, 7, 5, 6, -61239029497381430159877620424435625877475164160000000⟩, + ⟨3, 8, 8, 7, 6, 6, 34292413576945631314039682866206641574610206720000000⟩, + ⟨4, 3, 8, 5, 8, 2, -706099517108949239383890792596486647492783374336000000⟩, + ⟨4, 3, 8, 6, 7, 2, -190334448793821127437030242320495993791241519104000000⟩, + ⟨4, 3, 8, 7, 6, 2, -284562947008556411871684915660988917978564132864000000⟩, + ⟨4, 4, 7, 4, 8, 3, -73370607563260548446309805764793401452548587520000000⟩, + ⟨4, 4, 7, 5, 7, 3, -33466971309212290299023185699374284234079338496000000⟩, + ⟨4, 4, 8, 5, 8, 3, -202027835026340647337930676780337879090307530752000000⟩, + ⟨4, 4, 7, 6, 6, 3, -10117953740894337225819879307051663142097518592000000⟩, + ⟨4, 4, 8, 6, 7, 3, -54458126211711323003584367437469119101511139328000000⟩, + ⟨4, 4, 7, 7, 5, 3, 36349119949161746496213545693593283262872027136000000⟩, + ⟨4, 4, 8, 7, 6, 3, -81418602788795641893720522314885101957203099648000000⟩, + ⟨4, 5, 6, 3, 8, 4, 47893329810183988482093917551221231871196135424000000⟩, + ⟨4, 5, 6, 4, 7, 4, -20898562871198867146070955478271316790081486848000000⟩, + ⟨4, 5, 7, 4, 8, 4, 122650554531747025417859556730676081066067886080000000⟩, + ⟨4, 5, 6, 5, 6, 4, -35395545983079385461574215988429821819897249792000000⟩ +] + +def collectedFourData_15_99 : List CollectedFourTerm := [ + ⟨4, 5, 7, 5, 7, 4, 55945326417446156760076373052329972910243446784000000⟩, + ⟨4, 5, 8, 5, 8, 4, 168860711528554148000761962772059686679613538304000000⟩, + ⟨4, 5, 6, 6, 5, 4, 3366740166668087665294124202493641365139750912000000⟩, + ⟨4, 5, 7, 6, 6, 4, 16913757133294571245110657456213085351437139968000000⟩, + ⟨4, 5, 8, 6, 7, 4, 45517677994333869523448175661250480605658873856000000⟩, + ⟨4, 5, 6, 7, 4, 4, 116838141520725126879508537262499905919988531200000000⟩, + ⟨4, 5, 7, 7, 5, 4, -60763292912107306973956973752569241511965753344000000⟩, + ⟨4, 5, 8, 7, 6, 4, 68052024597423522217948132682758485211135082496000000⟩, + ⟨4, 6, 5, 2, 8, 5, -53611334997661281655020259773764783656088371200000000⟩, + ⟨4, 6, 5, 3, 7, 5, 4223436235929436647466643024775816219407155200000000⟩, + ⟨4, 6, 6, 3, 8, 5, -54730979604246291791489426135677901429381529600000000⟩, + ⟨4, 6, 5, 4, 6, 5, 10343158065702362066644660988232698771275776000000000⟩, + ⟨4, 6, 6, 4, 7, 5, 23882215389802105904776459731792818936689459200000000⟩, + ⟨4, 6, 7, 4, 8, 5, -70080583508511286814903572684905733806882816000000000⟩, + ⟨4, 6, 5, 5, 5, 5, 2846450758445298937167097928221201287610368000000000⟩, + ⟨4, 6, 6, 5, 6, 5, 40448908291800341497329419107490293074414796800000000⟩, + ⟨4, 6, 7, 5, 7, 5, -31966273082719115473706107075598491505708236800000000⟩, + ⟨4, 6, 8, 5, 8, 5, -64322890022865097953649287975552114110968627200000000⟩, + ⟨4, 6, 5, 6, 4, 5, -23736682614007198676816755507602782556468019200000000⟩, + ⟨4, 6, 6, 6, 5, 5, -3847403973058602189034549046266149349412044800000000⟩, + ⟨4, 6, 7, 6, 6, 5, -9664252833978972251232798489201120781113753600000000⟩, + ⟨4, 6, 8, 6, 7, 5, -17338719997224646904615798650593963252960460800000000⟩, + ⟨4, 6, 5, 7, 3, 5, -33093601366632606043209295843372785660749414400000000⟩, + ⟨4, 6, 6, 7, 4, 5, -133518925618930207209718558590562273308180480000000000⟩ +] + +def collectedFourData_15_100 : List CollectedFourTerm := [ + ⟨4, 6, 7, 7, 5, 5, 34719182798939872076454495216087280164588748800000000⟩, + ⟨4, 6, 8, 7, 6, 5, -25922565731183638492214783151334694639684812800000000⟩, + ⟨4, 7, 4, 1, 8, 6, -73184874458530391849916613424114982834829000704000000⟩, + ⟨4, 7, 4, 2, 7, 6, 9923246671205077068371600311883984296225013760000000⟩, + ⟨4, 7, 5, 2, 8, 6, -123787864558950700686058520565887180557296599040000000⟩, + ⟨4, 7, 4, 3, 6, 6, 8081763604821495743832583012721491429048713216000000⟩, + ⟨4, 7, 5, 3, 7, 6, 9751858497263769146096851915357455923376291840000000⟩, + ⟨4, 7, 6, 3, 8, 6, -63186554585188787954505717702635624805338972160000000⟩, + ⟨4, 7, 4, 4, 5, 6, -20898562871198867146070955478271316790081486848000000⟩, + ⟨4, 7, 5, 4, 6, 6, 23882215389802105904776459731792818936689459200000000⟩, + ⟨4, 7, 6, 4, 7, 6, 27571859982310426780185636159715514610163384320000000⟩, + ⟨4, 7, 7, 4, 8, 6, -53938380630030753211128182731931612623562342400000000⟩, + ⟨4, 7, 4, 5, 4, 6, -2918456891595175914284403087011651876825333760000000⟩, + ⟨4, 7, 5, 5, 5, 6, 6572417213179268803548182273272621695605145600000000⟩, + ⟨4, 7, 6, 5, 6, 6, 46697997554073458040356158701213421694909153280000000⟩, + ⟨4, 7, 7, 5, 7, 6, -24603234141876187560382406848685352123126251520000000⟩, + ⟨4, 7, 8, 5, 8, 6, -37130175915867671354074675814739667390625218560000000⟩, + ⟨4, 7, 4, 6, 3, 6, 72950524784238701603650827614003280220426076160000000⟩, + ⟨4, 7, 5, 6, 4, 6, -54807686707105926876032656679038618941668720640000000⟩, + ⟨4, 7, 6, 6, 5, 6, -4441802483946009815626717591183522464352174080000000⟩, + ⟨4, 7, 7, 6, 6, 6, -7438210724953545294628300439590361866740695040000000⟩, + ⟨4, 7, 8, 6, 7, 6, -10008718877899818003611782238911388761026723840000000⟩, + ⟨4, 7, 4, 7, 2, 6, -74968177943419633603347832921687844584339537920000000⟩, + ⟨4, 7, 5, 7, 3, 6, -76412688546542081137128755878726380766604820480000000⟩ +] + +def collectedFourData_15_101 : List CollectedFourTerm := [ + ⟨4, 7, 6, 7, 4, 6, -154146718052196954802313866778375800391467008000000000⟩, + ⟨4, 7, 7, 7, 5, 6, 26722044869181152276504683866206012623363768320000000⟩, + ⟨4, 7, 8, 7, 6, 6, -14963715489887729635094817305403248497592893440000000⟩, + ⟨4, 8, 3, 0, 8, 7, 20654400665111695979681447636091601714560368640000000⟩, + ⟨4, 8, 3, 1, 7, 7, -275916395673778713427497012782552646032472145920000000⟩, + ⟨4, 8, 4, 1, 8, 7, 429511133899328987583574921034393602200793251840000000⟩, + ⟨4, 8, 3, 2, 6, 7, 89816544992890116753938148722827910462539038720000000⟩, + ⟨4, 8, 4, 2, 7, 7, -58238057539159186983595735667702719923722649600000000⟩, + ⟨4, 8, 5, 2, 8, 7, 363246275019702582299541144595807422150554419200000000⟩, + ⟨4, 8, 3, 3, 5, 7, 179405651253737399879613172380060341245763911680000000⟩, + ⟨4, 8, 4, 3, 6, 7, -47430667545657134080586389449518987533992591360000000⟩, + ⟨4, 8, 5, 3, 7, 7, -28616102929567536976074525049111444584608563200000000⟩, + ⟨4, 8, 6, 3, 8, 7, 123610827637408233641324712917524606071550771200000000⟩, + ⟨4, 8, 3, 4, 4, 7, -73370607563260548446309805764793401452548587520000000⟩, + ⟨4, 8, 4, 4, 5, 7, 122650554531747025417859556730676081066067886080000000⟩, + ⟨4, 8, 5, 4, 6, 7, -70080583508511286814903572684905733806882816000000000⟩, + ⟨4, 8, 6, 4, 7, 7, -53938380630030753211128182731931612623562342400000000⟩, + ⟨4, 8, 7, 4, 8, 7, 79139081663061329373996980882000345170968576000000000⟩, + ⟨4, 8, 3, 5, 3, 7, -184724314884564481992789698734182698797435453440000000⟩, + ⟨4, 8, 4, 5, 4, 7, 17127989055383924453254199575227515042109849600000000⟩, + ⟨4, 8, 5, 5, 5, 7, -19286269127179302883079069497870373080793088000000000⟩, + ⟨4, 8, 6, 5, 6, 7, -91354532060872280070760085156867789207214489600000000⟩, + ⟨4, 8, 7, 5, 7, 7, 36098179685529949166054862951579225345019084800000000⟩, + ⟨4, 8, 8, 5, 8, 7, 43582295050714565908696955623592833641370091520000000⟩ +] + +def collectedFourData_15_102 : List CollectedFourTerm := [ + ⟨4, 8, 3, 6, 2, 7, -206573708050236825961021012412365522980443258880000000⟩, + ⟨4, 8, 4, 6, 3, 7, -428135770546195163670296263354479428012448153600000000⟩, + ⟨4, 8, 5, 6, 4, 7, 160829077306864035353025760476392742188167987200000000⟩, + ⟨4, 8, 6, 6, 5, 7, 8689425857240250619086565156342219172059545600000000⟩, + ⟨4, 8, 7, 6, 6, 7, 10913437873242684529243112284048993476516249600000000⟩, + ⟨4, 8, 8, 6, 7, 7, 11747936239372199972249727088701241445087969280000000⟩, + ⟨4, 8, 3, 7, 1, 7, 1899008718281034949213816231225996832826143539200000000⟩, + ⟨4, 8, 4, 7, 2, 7, 439977076589651175195384559982358130267992883200000000⟩, + ⟨4, 8, 5, 7, 3, 7, 224227347144790135397042682160027326438860390400000000⟩, + ⟨4, 8, 6, 7, 4, 7, 301554713991141919890263891688218820146626560000000000⟩, + ⟨4, 8, 7, 7, 5, 7, -39206925873645948746856351508054337238387916800000000⟩, + ⟨4, 8, 8, 7, 6, 7, 17563963742400037510960409557647615848853012480000000⟩, + ⟨5, 2, 8, 5, 8, 2, 96045348136543866068191587691752197630472486912000000⟩, + ⟨5, 2, 8, 6, 7, 2, 25889747767606904610850969778364510774459629568000000⟩, + ⟨5, 2, 8, 7, 6, 2, 38706933866916373314089710829607596081427775488000000⟩, + ⟨5, 3, 7, 4, 8, 3, -184724314884564481992789698734182698797435453440000000⟩, + ⟨5, 3, 7, 5, 7, 3, -84259399665258605242920539691104736369350541312000000⟩, + ⟨5, 3, 8, 5, 8, 3, -508643101812610092725715106167774640503043129344000000⟩, + ⟨5, 3, 7, 6, 6, 3, -25473853016808301434351237599937908595253837824000000⟩, + ⟨5, 3, 8, 6, 7, 3, -137108583238621173175623982020926747660481724416000000⟩, + ⟨5, 3, 7, 7, 5, 3, 91515751365101104450396818435769330933161787392000000⟩, + ⟨5, 3, 8, 7, 6, 3, -204986657716459518808477781020393735259953299456000000⟩, + ⟨5, 4, 6, 3, 8, 4, 6688240684654974435545211916861738016707706880000000⟩, + ⟨5, 4, 6, 4, 7, 4, -2918456891595175914284403087011651876825333760000000⟩ +] + +def collectedFourData_15_103 : List CollectedFourTerm := [ + ⟨5, 4, 7, 4, 8, 4, 17127989055383924453254199575227515042109849600000000⟩, + ⟨5, 4, 6, 5, 6, 4, -4942941566975128950235630302915366386443223040000000⟩, + ⟨5, 4, 7, 5, 7, 4, 7812691448776688562701447756847126648276910080000000⟩, + ⟨5, 4, 8, 5, 8, 4, 23581176864526815506410464369031074552458772480000000⟩, + ⟨5, 4, 6, 6, 5, 4, 470160848005674909806923832232335994456637440000000⟩, + ⟨5, 4, 7, 6, 6, 4, 2361983997304351619038532188852450771504988160000000⟩, + ⟨5, 4, 8, 6, 7, 4, 6356484024796159881587586759108993328317726720000000⟩, + ⟨5, 4, 6, 7, 4, 4, 16316293202737899349861647092393099126636544000000000⟩, + ⟨5, 4, 7, 7, 5, 4, -8485514149862826029419734329938894034074337280000000⟩, + ⟨5, 4, 8, 7, 6, 4, 9503375968835785309448941308899527218450923520000000⟩, + ⟨5, 5, 5, 2, 8, 5, -14753910188357482772140854939548533801982361600000000⟩, + ⟨5, 5, 5, 3, 7, 5, 1162295229430040752969299013779520963058073600000000⟩, + ⟨5, 5, 6, 3, 8, 5, -15062037862647904945786954647452383405984972800000000⟩, + ⟨5, 5, 5, 4, 6, 5, 2846450758445298937167097928221201287610368000000000⟩, + ⟨5, 5, 6, 4, 7, 5, 6572417213179268803548182273272621695605145600000000⟩, + ⟨5, 5, 7, 4, 8, 5, -19286269127179302883079069497870373080793088000000000⟩, + ⟨5, 5, 5, 5, 5, 5, 783347007634038737421953650548110549581824000000000⟩, + ⟨5, 5, 6, 5, 6, 5, 11131592977126277192127458813305169937589862400000000⟩, + ⟨5, 5, 7, 5, 7, 5, -8797160565755752906458090086524878798087782400000000⟩, + ⟨5, 5, 8, 5, 8, 5, -17701744276547984502962894475977777269545369600000000⟩, + ⟨5, 5, 5, 6, 4, 5, -6532366401095702994597720450853349575203225600000000⟩, + ⟨5, 5, 6, 6, 5, 5, -1058810654114705945977818396175807174567526400000000⟩, + ⟨5, 5, 7, 6, 6, 5, -2659615142139719630046553762916637023718604800000000⟩, + ⟨5, 5, 8, 6, 7, 5, -4771638640061656032326410337488200463181414400000000⟩ +] + +def collectedFourData_15_104 : List CollectedFourTerm := [ + ⟨5, 5, 5, 7, 3, 5, -9107402798193732200659052943470199024333619200000000⟩, + ⟨5, 5, 6, 7, 4, 5, -36744584650123234940443950139282012388720640000000000⟩, + ⟨5, 5, 7, 7, 5, 5, 9554764955043009990778580961762101185373798400000000⟩, + ⟨5, 5, 8, 7, 6, 5, -7133924321533143384514681688956446043432550400000000⟩, + ⟨5, 6, 4, 1, 8, 6, -123951996370657737491936235597179670737260118016000000⟩, + ⟨5, 6, 4, 2, 7, 6, 16806836719673900932754341224006306627625943040000000⟩, + ⟨5, 6, 5, 2, 8, 6, -209657433343510624296035944721680713830797148160000000⟩, + ⟨5, 6, 4, 3, 6, 6, 13687947686252869925863037028173466896814833664000000⟩, + ⟨5, 6, 5, 3, 7, 6, 16516559439409051374667269732568762728956559360000000⟩, + ⟨5, 6, 6, 3, 8, 6, -107018009425645494303908325231845874606947696640000000⟩, + ⟨5, 6, 4, 4, 5, 6, -35395545983079385461574215988429821819897249792000000⟩, + ⟨5, 6, 5, 4, 6, 6, 40448908291800341497329419107490293074414796800000000⟩, + ⟨5, 6, 6, 4, 7, 6, 46697997554073458040356158701213421694909153280000000⟩, + ⟨5, 6, 7, 4, 8, 6, -91354532060872280070760085156867789207214489600000000⟩, + ⟨5, 6, 4, 5, 4, 6, -4942941566975128950235630302915366386443223040000000⟩, + ⟨5, 6, 5, 5, 5, 6, 11131592977126277192127458813305169937589862400000000⟩, + ⟨5, 6, 6, 5, 6, 6, 79091616487220942316474994802461429541759877120000000⟩, + ⟨5, 6, 7, 5, 7, 6, -41670085678541702762112174661285036316247982080000000⟩, + ⟨5, 6, 8, 5, 8, 6, -62886757194253330482076514064925576705333002240000000⟩, + ⟨5, 6, 4, 6, 3, 6, 123555082251556142458365679262706213243731312640000000⟩, + ⟨5, 6, 5, 6, 4, 6, -92826861206858170287463279598079445421323714560000000⟩, + ⟨5, 6, 6, 6, 5, 6, -7523006487921632811335342200521860848099000320000000⟩, + ⟨5, 6, 7, 6, 6, 6, -12597972950080857302970779777981392942698332160000000⟩, + ⟨5, 6, 8, 6, 7, 6, -16951599564898454741943376674614276810719887360000000⟩ +] + +def collectedFourData_15_105 : List CollectedFourTerm := [ + ⟨5, 6, 4, 7, 2, 6, -126972347621134027808834125061359715055493447680000000⟩, + ⟨5, 6, 5, 7, 3, 6, -129418891040936810050337973115555118990669905920000000⟩, + ⟨5, 6, 6, 7, 4, 6, -261075715138124969964717947276547875439378432000000000⟩, + ⟨5, 6, 7, 7, 5, 6, 45258679927341477159987260349074256495409889280000000⟩, + ⟨5, 6, 8, 7, 6, 6, -25343794353915521888697818518126795060685045760000000⟩, + ⟨5, 7, 3, 0, 8, 7, 9421214535701877307841892271489895509128118272000000⟩, + ⟨5, 7, 3, 1, 7, 7, -125855385479722756686551417182181739252538146816000000⟩, + ⟨5, 7, 4, 1, 8, 7, 195915466323518743116859984096487272566994501632000000⟩, + ⟨5, 7, 3, 2, 6, 7, 40968554496130280795477197719676979157984608256000000⟩, + ⟨5, 7, 4, 2, 7, 7, -26564471325752781918289156908462742347794350080000000⟩, + ⟨5, 7, 5, 2, 8, 7, 165689682394697402658026319162488553004502876160000000⟩, + ⟨5, 7, 3, 3, 5, 7, 81833366011621914198264870933887990159495921664000000⟩, + ⟨5, 7, 4, 3, 6, 7, -21634832293826413635336110712858107101449289728000000⟩, + ⟨5, 7, 5, 3, 7, 7, -13052833110310189914503630460892254186095247360000000⟩, + ⟨5, 7, 6, 3, 8, 7, 56383341496556177262788911034027816584489205760000000⟩, + ⟨5, 7, 3, 4, 4, 7, -33466971309212290299023185699374284234079338496000000⟩, + ⟨5, 7, 4, 4, 5, 7, 55945326417446156760076373052329972910243446784000000⟩, + ⟨5, 7, 5, 4, 6, 7, -31966273082719115473706107075598491505708236800000000⟩, + ⟨5, 7, 6, 4, 7, 7, -24603234141876187560382406848685352123126251520000000⟩, + ⟨5, 7, 7, 4, 8, 7, 36098179685529949166054862951579225345019084800000000⟩, + ⟨5, 7, 3, 5, 3, 7, -84259399665258605242920539691104736369350541312000000⟩, + ⟨5, 7, 4, 5, 4, 7, 7812691448776688562701447756847126648276910080000000⟩, + ⟨5, 7, 5, 5, 5, 7, -8797160565755752906458090086524878798087782400000000⟩, + ⟨5, 7, 6, 5, 6, 7, -41670085678541702762112174661285036316247982080000000⟩ +] + +def collectedFourData_15_106 : List CollectedFourTerm := [ + ⟨5, 7, 7, 5, 7, 7, 16465677251054422182869221503024266010993623040000000⟩, + ⟨5, 7, 8, 5, 8, 7, 19879451274739740777142329545277233005326237696000000⟩, + ⟨5, 7, 3, 6, 2, 7, -94225693232730869070543438730235116038572212224000000⟩, + ⟨5, 7, 4, 6, 3, 7, -195288113662722183363018295913741744470260449280000000⟩, + ⟨5, 7, 5, 6, 4, 7, 73359922926563135715120954306454830564570562560000000⟩, + ⟨5, 7, 6, 6, 5, 7, 3963559462241742142063353207170099812635770880000000⟩, + ⟨5, 7, 7, 6, 6, 7, 4978011281612626624047875403456861379315630080000000⟩, + ⟨5, 7, 8, 6, 7, 7, 5358655981232446920012088478317109633712390144000000⟩, + ⟨5, 7, 3, 7, 1, 7, 866206133510053416136879384898817034582921052160000000⟩, + ⟨5, 7, 4, 7, 2, 7, 200689358967638851785484464098517412029514383360000000⟩, + ⟨5, 7, 5, 7, 3, 7, 102278152558097652330778291608818138300201041920000000⟩, + ⟨5, 7, 6, 7, 4, 7, 137549943996276434777455302364673912957042688000000000⟩, + ⟨5, 7, 7, 7, 5, 7, -17883688126807319358886762757866990095449456640000000⟩, + ⟨5, 7, 8, 7, 6, 7, 8011555173999773779706616449408719750120341504000000⟩, + ⟨5, 8, 2, 0, 7, 8, -93342497584022968005124408681762041635096494080000000⟩, + ⟨5, 8, 3, 0, 8, 8, 56872417834912242101103430630756182741026340864000000⟩, + ⟨5, 8, 2, 1, 6, 8, 214857655281910914825422107909208736162323103744000000⟩, + ⟨5, 8, 3, 1, 7, 8, -759742816879129001925199788972219790314902126592000000⟩, + ⟨5, 8, 4, 1, 8, 8, 591334918595118638539595939018627082772222574592000000⟩, + ⟨5, 8, 2, 2, 5, 8, 450551588848718489058212298253677804973625180160000000⟩, + ⟨5, 8, 3, 2, 6, 8, 247312142247348910958184120214583909541186895872000000⟩, + ⟨5, 8, 4, 2, 7, 8, -80179986724461335097481694446292529731579412480000000⟩, + ⟨5, 8, 5, 2, 8, 8, 333402620662684028084504462935298175698353520640000000⟩, + ⟨5, 8, 2, 3, 4, 8, -33197128333608118180525004486882674916475273216000000⟩ +] + +def collectedFourData_15_107 : List CollectedFourTerm := [ + ⟨5, 8, 3, 3, 5, 8, 493998026158263409228930620230840979579016839168000000⟩, + ⟨5, 8, 4, 3, 6, 8, -65300775040204643606116279631084219669642477568000000⟩, + ⟨5, 8, 5, 3, 7, 8, -26265055875255533528134484675167032681368125440000000⟩, + ⟨5, 8, 6, 3, 8, 8, 85091389872531816320647082908059951193946849280000000⟩, + ⟨5, 8, 2, 4, 3, 8, -706099517108949239383890792596486647492783374336000000⟩, + ⟨5, 8, 3, 4, 4, 8, -202027835026340647337930676780337879090307530752000000⟩, + ⟨5, 8, 4, 4, 5, 8, 168860711528554148000761962772059686679613538304000000⟩, + ⟨5, 8, 5, 4, 6, 8, -64322890022865097953649287975552114110968627200000000⟩, + ⟨5, 8, 6, 4, 7, 8, -37130175915867671354074675814739667390625218560000000⟩, + ⟨5, 8, 7, 4, 8, 8, 43582295050714565908696955623592833641370091520000000⟩, + ⟨5, 8, 2, 5, 2, 8, 96045348136543866068191587691752197630472486912000000⟩, + ⟨5, 8, 3, 5, 3, 8, -508643101812610092725715106167774640503043129344000000⟩, + ⟨5, 8, 4, 5, 4, 8, 23581176864526815506410464369031074552458772480000000⟩, + ⟨5, 8, 5, 5, 5, 8, -17701744276547984502962894475977777269545369600000000⟩, + ⟨5, 8, 6, 5, 6, 8, -62886757194253330482076514064925576705333002240000000⟩, + ⟨5, 8, 7, 5, 7, 8, 19879451274739740777142329545277233005326237696000000⟩, + ⟨5, 8, 8, 5, 8, 8, 20000826414000286894250715946620915269020680192000000⟩, + ⟨5, 8, 2, 6, 1, 8, -1611609393959455028921588856137629201548668043264000000⟩, + ⟨5, 8, 3, 6, 2, 8, -568805961907426284693393312527642808186870693888000000⟩, + ⟨5, 8, 4, 6, 3, 8, -589441369598889999056853748778406289375682887680000000⟩, + ⟨5, 8, 5, 6, 4, 8, 147615652355860950298957461429717011685168906240000000⟩, + ⟨5, 8, 6, 6, 5, 8, 5981638805588958097794753200961780911324528640000000⟩, + ⟨5, 8, 7, 6, 6, 8, 6010085780807210543481790618842307368679636992000000⟩, + ⟨5, 8, 8, 6, 7, 8, 5391373565182960750179620343405890353640767488000000⟩ +] + +def collectedFourData_15_108 : List CollectedFourTerm := [ + ⟨5, 8, 2, 7, 0, 8, 13147467608411951204445065460714555870940854484992000000⟩, + ⟨5, 8, 3, 7, 1, 8, 5228968830872445689362030147954054481429051473920000000⟩, + ⟨5, 8, 4, 7, 2, 8, 605744038360226819517952152317406659458797404160000000⟩, + ⟨5, 8, 5, 7, 3, 8, 205805235465276381745992457349611865929081159680000000⟩, + ⟨5, 8, 6, 7, 4, 8, 207584644699480250782367983321897816150769664000000000⟩, + ⟨5, 8, 7, 7, 5, 8, -21591453622519002312805916972169274141584654336000000⟩, + ⟨5, 8, 8, 7, 6, 8, 8060470187372068277530074905333531782265438208000000⟩, + ⟨6, 1, 8, 5, 8, 2, -1611609393959455028921588856137629201548668043264000000⟩, + ⟨6, 1, 8, 6, 7, 2, -434421463600699652341336257528692139154835767296000000⟩, + ⟨6, 1, 8, 7, 6, 2, -649489636318522950399169075937509771101691969536000000⟩, + ⟨6, 2, 7, 4, 8, 3, -206573708050236825961021012412365522980443258880000000⟩, + ⟨6, 2, 7, 5, 7, 3, -94225693232730869070543438730235116038572212224000000⟩, + ⟨6, 2, 8, 5, 8, 3, -568805961907426284693393312527642808186870693888000000⟩, + ⟨6, 2, 7, 6, 6, 3, -28486928097674667108262989451127007292422094848000000⟩, + ⟨6, 2, 8, 6, 7, 3, -153325935802310504750820381572734111582500421632000000⟩, + ⟨6, 2, 7, 7, 5, 3, 102340334115225531066965730429067663272138768384000000⟩, + ⟨6, 2, 8, 7, 6, 3, -229232702861966657065477272233238589942857203712000000⟩, + ⟨6, 3, 6, 3, 8, 4, -167181043254057852916355797050649158501877678080000000⟩, + ⟨6, 3, 6, 4, 7, 4, 72950524784238701603650827614003280220426076160000000⟩, + ⟨6, 3, 7, 4, 8, 4, -428135770546195163670296263354479428012448153600000000⟩, + ⟨6, 3, 6, 5, 6, 4, 123555082251556142458365679262706213243731312640000000⟩, + ⟨6, 3, 7, 5, 7, 4, -195288113662722183363018295913741744470260449280000000⟩, + ⟨6, 3, 8, 5, 8, 4, -589441369598889999056853748778406289375682887680000000⟩, + ⟨6, 3, 6, 6, 5, 4, -11752265621531843689892411545871607623885783040000000⟩ +] + +def collectedFourData_15_109 : List CollectedFourTerm := [ + ⟨6, 3, 7, 6, 6, 4, -59040780294392448831924690756016795166504386560000000⟩, + ⟨6, 3, 8, 6, 7, 4, -158888365535546677599805611999956484054602219520000000⟩, + ⟨6, 3, 6, 7, 4, 4, -407846405098911646555124131056571652562223104000000000⟩, + ⟨6, 3, 7, 7, 5, 4, 212106168872766742988573321002096997997981204480000000⟩, + ⟨6, 3, 8, 7, 6, 4, -237548913655380783575469286792668413170097848320000000⟩, + ⟨6, 4, 5, 2, 8, 5, 123033529534123785192860765532574305068557271040000000⟩, + ⟨6, 4, 5, 3, 7, 5, -9692432894860402286079314278710198220452003840000000⟩, + ⟨6, 4, 6, 3, 8, 5, 125603020254286015176781680817332024431156920320000000⟩, + ⟨6, 4, 5, 4, 6, 5, -23736682614007198676816755507602782556468019200000000⟩, + ⟨6, 4, 6, 4, 7, 5, -54807686707105926876032656679038618941668720640000000⟩, + ⟨6, 4, 7, 4, 8, 5, 160829077306864035353025760476392742188167987200000000⟩, + ⟨6, 4, 5, 5, 5, 5, -6532366401095702994597720450853349575203225600000000⟩, + ⟨6, 4, 6, 5, 6, 5, -92826861206858170287463279598079445421323714560000000⟩, + ⟨6, 4, 7, 5, 7, 5, 73359922926563135715120954306454830564570562560000000⟩, + ⟨6, 4, 8, 5, 8, 5, 147615652355860950298957461429717011685168906240000000⟩, + ⟨6, 4, 5, 6, 4, 5, 54473701159651702285515017601484398667644272640000000⟩, + ⟨6, 4, 6, 6, 5, 5, 8829470304547729851492360809896520255180636160000000⟩, + ⟨6, 4, 7, 6, 6, 5, 22178651893791881747747132183110187637402501120000000⟩, + ⟨6, 4, 8, 6, 7, 5, 39790912107588833702426534861656824827200143360000000⟩, + ⟨6, 4, 5, 7, 3, 5, 75947047043497998095736131218382975473790484480000000⟩, + ⟨6, 4, 6, 7, 4, 5, 306414766191100154082037936680289777081122816000000000⟩, + ⟨6, 4, 7, 7, 5, 5, -79677620459933608599773924783987492075297832960000000⟩, + ⟨6, 4, 8, 7, 6, 5, 59490120076789319948413930094930286712989941760000000⟩, + ⟨6, 5, 4, 1, 8, 6, 11790019148716756564023604742305809823250251776000000⟩ +] + +def collectedFourData_15_110 : List CollectedFourTerm := [ + ⟨6, 5, 4, 2, 7, 6, -1598626343715901010545935022739677521578557440000000⟩, + ⟨6, 5, 5, 2, 8, 6, 19942116514195523528194814796647047441950965760000000⟩, + ⟨6, 5, 4, 3, 6, 6, -1301965035278424599778951515515843937990344704000000⟩, + ⟨6, 5, 5, 3, 7, 6, -1571015859068877196771439829004447831252008960000000⟩, + ⟨6, 5, 6, 3, 8, 6, 10179298577917816996522375104651503640552407040000000⟩, + ⟨6, 5, 4, 4, 5, 6, 3366740166668087665294124202493641365139750912000000⟩, + ⟨6, 5, 5, 4, 6, 6, -3847403973058602189034549046266149349412044800000000⟩, + ⟨6, 5, 6, 4, 7, 6, -4441802483946009815626717591183522464352174080000000⟩, + ⟨6, 5, 7, 4, 8, 6, 8689425857240250619086565156342219172059545600000000⟩, + ⟨6, 5, 4, 5, 4, 6, 470160848005674909806923832232335994456637440000000⟩, + ⟨6, 5, 5, 5, 5, 6, -1058810654114705945977818396175807174567526400000000⟩, + ⟨6, 5, 6, 5, 6, 6, -7523006487921632811335342200521860848099000320000000⟩, + ⟨6, 5, 7, 5, 7, 6, 3963559462241742142063353207170099812635770880000000⟩, + ⟨6, 5, 8, 5, 8, 6, 5981638805588958097794753200961780911324528640000000⟩, + ⟨6, 5, 4, 6, 3, 6, -11752265621531843689892411545871607623885783040000000⟩, + ⟨6, 5, 5, 6, 4, 6, 8829470304547729851492360809896520255180636160000000⟩, + ⟨6, 5, 6, 6, 5, 6, 715570488137074514730608404151157644612075520000000⟩, + ⟨6, 5, 7, 6, 6, 6, 1198289230230014695508673147825882868230389760000000⟩, + ⟨6, 5, 8, 6, 7, 6, 1612395841321380785642003111439124906597416960000000⟩, + ⟨6, 5, 4, 7, 2, 6, 12077307777554006674693005617815914950405652480000000⟩, + ⟨6, 5, 5, 7, 3, 6, 12310017169998048028975720683080345183185797120000000⟩, + ⟨6, 5, 6, 7, 4, 6, 24832901210714731976636105957384358778109952000000000⟩, + ⟨6, 5, 7, 7, 5, 6, -4304898013851708869779034767888689852925870080000000⟩, + ⟨6, 5, 8, 7, 6, 6, 2410641453811528098575684223527935056134799360000000⟩ +] + +def collectedFourData_15_111 : List CollectedFourTerm := [ + ⟨6, 6, 3, 0, 8, 7, 2848283221524551401909870826950275737000607744000000⟩, + ⟨6, 6, 3, 1, 7, 7, -38049423611145158524334509909751972540272607232000000⟩, + ⟨6, 6, 4, 1, 8, 7, 59230445655578548023752905969460842176618430464000000⟩, + ⟨6, 6, 3, 2, 6, 7, 12385881452889421096867046692527332910654554112000000⟩, + ⟨6, 6, 4, 2, 7, 7, -8031144782775592141616632229109181077163868160000000⟩, + ⟨6, 6, 5, 2, 8, 7, 50092388890642086995776489992738969059925688320000000⟩, + ⟨6, 6, 3, 3, 5, 7, 24740398649080914032329404819406786259979337728000000⟩, + ⟨6, 6, 4, 3, 6, 7, -6540784055971236785933649691715736240711008256000000⟩, + ⟨6, 6, 5, 3, 7, 7, -3946217910713024341758521537608899128689950720000000⟩, + ⟨6, 6, 6, 3, 8, 7, 17046180717947701673538569170567341563990507520000000⟩, + ⟨6, 6, 3, 4, 4, 7, -10117953740894337225819879307051663142097518592000000⟩, + ⟨6, 6, 4, 4, 5, 7, 16913757133294571245110657456213085351437139968000000⟩, + ⟨6, 6, 5, 4, 6, 7, -9664252833978972251232798489201120781113753600000000⟩, + ⟨6, 6, 6, 4, 7, 7, -7438210724953545294628300439590361866740695040000000⟩, + ⟨6, 6, 7, 4, 8, 7, 10913437873242684529243112284048993476516249600000000⟩, + ⟨6, 6, 3, 5, 3, 7, -25473853016808301434351237599937908595253837824000000⟩, + ⟨6, 6, 4, 5, 4, 7, 2361983997304351619038532188852450771504988160000000⟩, + ⟨6, 6, 5, 5, 5, 7, -2659615142139719630046553762916637023718604800000000⟩, + ⟨6, 6, 6, 5, 6, 7, -12597972950080857302970779777981392942698332160000000⟩, + ⟨6, 6, 7, 5, 7, 7, 4978011281612626624047875403456861379315630080000000⟩, + ⟨6, 6, 8, 5, 8, 7, 6010085780807210543481790618842307368679636992000000⟩, + ⟨6, 6, 3, 6, 2, 7, -28486928097674667108262989451127007292422094848000000⟩, + ⟨6, 6, 4, 6, 3, 7, -59040780294392448831924690756016795166504386560000000⟩, + ⟨6, 6, 5, 6, 4, 7, 22178651893791881747747132183110187637402501120000000⟩ +] + +def collectedFourData_15_112 : List CollectedFourTerm := [ + ⟨6, 6, 6, 6, 5, 7, 1198289230230014695508673147825882868230389760000000⟩, + ⟨6, 6, 7, 6, 6, 7, 1504984941829568288478908993886160374894428160000000⟩, + ⟨6, 6, 8, 6, 7, 7, 1620063937980314111914064169106098967636082688000000⟩, + ⟨6, 6, 3, 7, 1, 7, 261877105877255667823880740991194940462931640320000000⟩, + ⟨6, 6, 4, 7, 2, 7, 60673720115371303429493581849980940843713822720000000⟩, + ⟨6, 6, 5, 7, 3, 7, 30921400288233101989683387800409646865150115840000000⟩, + ⟨6, 6, 6, 7, 4, 7, 41584999059470871546576960871138927287730176000000000⟩, + ⟨6, 6, 7, 7, 5, 7, -5406713607628113747963514472555850950277857280000000⟩, + ⟨6, 6, 8, 7, 6, 7, 2422105779880931511814134826907457885629841408000000⟩, + ⟨6, 7, 2, 0, 7, 8, -25161174021809026577811118378876561171540869120000000⟩, + ⟨6, 7, 3, 0, 8, 8, 15330389042752552044117543232367012379881373696000000⟩, + ⟨6, 7, 2, 1, 6, 8, 57916500997840770058682744481946182341168726016000000⟩, + ⟨6, 7, 3, 1, 7, 8, -204794404714826913180910932444743886907625177088000000⟩, + ⟨6, 7, 4, 1, 8, 8, 159398785944750358532834009039802031689682649088000000⟩, + ⟨6, 7, 2, 2, 5, 8, 121449577911932377392809171027608088051177226240000000⟩, + ⟨6, 7, 3, 2, 6, 8, 66664852664677793607425800570427863031252779008000000⟩, + ⟨6, 7, 4, 2, 7, 8, -21613119974902221595262534537509712494822686720000000⟩, + ⟨6, 7, 5, 2, 8, 8, 89871190239684026139412413339353128970968104960000000⟩, + ⟨6, 7, 2, 3, 4, 8, -8948536247108219797782344750576227911859175424000000⟩, + ⟨6, 7, 3, 3, 5, 8, 133160892672811329424013925822234169053441687552000000⟩, + ⟨6, 7, 4, 3, 6, 8, -17602316276855496762754362162590622266689585152000000⟩, + ⟨6, 7, 5, 3, 7, 8, -7079943848459424173412374024937169926393692160000000⟩, + ⟨6, 7, 6, 3, 8, 8, 22937025725213044097202179201869650600048721920000000⟩, + ⟨6, 7, 2, 4, 3, 8, -190334448793821127437030242320495993791241519104000000⟩ +] + +def collectedFourData_15_113 : List CollectedFourTerm := [ + ⟨6, 7, 3, 4, 4, 8, -54458126211711323003584367437469119101511139328000000⟩, + ⟨6, 7, 4, 4, 5, 8, 45517677994333869523448175661250480605658873856000000⟩, + ⟨6, 7, 5, 4, 6, 8, -17338719997224646904615798650593963252960460800000000⟩, + ⟨6, 7, 6, 4, 7, 8, -10008718877899818003611782238911388761026723840000000⟩, + ⟨6, 7, 7, 4, 8, 8, 11747936239372199972249727088701241445087969280000000⟩, + ⟨6, 7, 2, 5, 2, 8, 25889747767606904610850969778364510774459629568000000⟩, + ⟨6, 7, 3, 5, 3, 8, -137108583238621173175623982020926747660481724416000000⟩, + ⟨6, 7, 4, 5, 4, 8, 6356484024796159881587586759108993328317726720000000⟩, + ⟨6, 7, 5, 5, 5, 8, -4771638640061656032326410337488200463181414400000000⟩, + ⟨6, 7, 6, 5, 6, 8, -16951599564898454741943376674614276810719887360000000⟩, + ⟨6, 7, 7, 5, 7, 8, 5358655981232446920012088478317109633712390144000000⟩, + ⟨6, 7, 8, 5, 8, 8, 5391373565182960750179620343405890353640767488000000⟩, + ⟨6, 7, 2, 6, 1, 8, -434421463600699652341336257528692139154835767296000000⟩, + ⟨6, 7, 3, 6, 2, 8, -153325935802310504750820381572734111582500421632000000⟩, + ⟨6, 7, 4, 6, 3, 8, -158888365535546677599805611999956484054602219520000000⟩, + ⟨6, 7, 5, 6, 4, 8, 39790912107588833702426534861656824827200143360000000⟩, + ⟨6, 7, 6, 6, 5, 8, 1612395841321380785642003111439124906597416960000000⟩, + ⟨6, 7, 7, 6, 6, 8, 1620063937980314111914064169106098967636082688000000⟩, + ⟨6, 7, 8, 6, 7, 8, 1453285395197831238460289512329801176325292032000000⟩, + ⟨6, 7, 2, 7, 0, 8, 3543999025134003102266386786439731339597015154688000000⟩, + ⟨6, 7, 3, 7, 1, 8, 1409507974540383971993643048978995826851189882880000000⟩, + ⟨6, 7, 4, 7, 2, 8, 163282872821519671877638256728045227086173962240000000⟩, + ⟨6, 7, 5, 7, 3, 8, 55476352981447855707043265288382427528974827520000000⟩, + ⟨6, 7, 6, 7, 4, 8, 55956006157189329735420633910396912870096896000000000⟩ +] + +def collectedFourData_15_114 : List CollectedFourTerm := [ + ⟨6, 7, 7, 7, 5, 8, -5820139122493419014542307266160850656091439104000000⟩, + ⟨6, 7, 8, 7, 6, 8, 2172760514571730138442117207313720110965850112000000⟩, + ⟨7, 0, 8, 5, 8, 2, 13147467608411951204445065460714555870940854484992000000⟩, + ⟨7, 0, 8, 6, 7, 2, 3543999025134003102266386786439731339597015154688000000⟩, + ⟨7, 0, 8, 7, 6, 2, 5298519596313464540728901500916178099287944593408000000⟩, + ⟨7, 1, 7, 4, 8, 3, 1899008718281034949213816231225996832826143539200000000⟩, + ⟨7, 1, 7, 5, 7, 3, 866206133510053416136879384898817034582921052160000000⟩, + ⟨7, 1, 8, 5, 8, 3, 5228968830872445689362030147954054481429051473920000000⟩, + ⟨7, 1, 7, 6, 6, 3, 261877105877255667823880740991194940462931640320000000⟩, + ⟨7, 1, 8, 6, 7, 3, 1409507974540383971993643048978995826851189882880000000⟩, + ⟨7, 1, 7, 7, 5, 3, -940803108735136557629253443268791381298574786560000000⟩, + ⟨7, 1, 8, 7, 6, 3, 2107310293060799649107584810710776821238024110080000000⟩, + ⟨7, 2, 6, 3, 8, 4, 171804908004508448428028432756926382202641448960000000⟩, + ⟨7, 2, 6, 4, 7, 4, -74968177943419633603347832921687844584339537920000000⟩, + ⟨7, 2, 7, 4, 8, 4, 439977076589651175195384559982358130267992883200000000⟩, + ⟨7, 2, 6, 5, 6, 4, -126972347621134027808834125061359715055493447680000000⟩, + ⟨7, 2, 7, 5, 7, 4, 200689358967638851785484464098517412029514383360000000⟩, + ⟨7, 2, 8, 5, 8, 4, 605744038360226819517952152317406659458797404160000000⟩, + ⟨7, 2, 6, 6, 5, 4, 12077307777554006674693005617815914950405652480000000⟩, + ⟨7, 2, 7, 6, 6, 4, 60673720115371303429493581849980940843713822720000000⟩, + ⟨7, 2, 8, 6, 7, 4, 163282872821519671877638256728045227086173962240000000⟩, + ⟨7, 2, 6, 7, 4, 4, 419126551336957558564655224099229821827022848000000000⟩, + ⟨7, 2, 7, 7, 5, 4, -217972565077230567523431513005546456569620725760000000⟩, + ⟨7, 2, 8, 7, 6, 4, 244119000951042439756720588081746948495601827840000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1506.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1506.lean new file mode 100644 index 0000000000000000000000000000000000000000..7cb9c5fa01f849678415c3f398e5ef3ee46e3183 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1506.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1506. -/ +namespace LaughlinFock +def collectedFourData_15_115 : List CollectedFourTerm := [ + ⟨7, 3, 5, 2, 8, 5, 171532924265053628251162433957357089883192033280000000⟩, + ⟨7, 3, 5, 3, 7, 5, -13513156649196866505698875029091517450818682880000000⟩, + ⟨7, 3, 6, 3, 8, 5, 175115299401085970573073193406608290896664330240000000⟩, + ⟨7, 3, 5, 4, 6, 5, -33093601366632606043209295843372785660749414400000000⟩, + ⟨7, 3, 6, 4, 7, 5, -76412688546542081137128755878726380766604820480000000⟩, + ⟨7, 3, 7, 4, 8, 5, 224227347144790135397042682160027326438860390400000000⟩, + ⟨7, 3, 5, 5, 5, 5, -9107402798193732200659052943470199024333619200000000⟩, + ⟨7, 3, 6, 5, 6, 5, -129418891040936810050337973115555118990669905920000000⟩, + ⟨7, 3, 7, 5, 7, 5, 102278152558097652330778291608818138300201041920000000⟩, + ⟨7, 3, 8, 5, 8, 5, 205805235465276381745992457349611865929081159680000000⟩, + ⟨7, 3, 5, 6, 4, 5, 75947047043497998095736131218382975473790484480000000⟩, + ⟨7, 3, 6, 6, 5, 5, 12310017169998048028975720683080345183185797120000000⟩, + ⟨7, 3, 7, 6, 6, 5, 30921400288233101989683387800409646865150115840000000⟩, + ⟨7, 3, 8, 6, 7, 5, 55476352981447855707043265288382427528974827520000000⟩, + ⟨7, 3, 5, 7, 3, 5, 105885112115340935207447176892399533698695823360000000⟩, + ⟨7, 3, 6, 7, 4, 5, 427202414510707297140413890833568197469274112000000000⟩, + ⟨7, 3, 7, 7, 5, 5, -111086264758281158518063797056600724808107294720000000⟩, + ⟨7, 3, 8, 7, 6, 5, 82940921066729135653986229674066647745633976320000000⟩, + ⟨7, 4, 4, 1, 8, 6, 409156589946500527982939948010419350014630297600000000⟩, + ⟨7, 4, 4, 2, 7, 6, -55478154457843463168529048313590043109228544000000000⟩, + ⟨7, 4, 5, 2, 8, 6, 692064048950431174129152472146545820120907776000000000⟩, + ⟨7, 4, 4, 3, 6, 6, -45182926960901175659785014560889091937166950400000000⟩, + ⟨7, 4, 5, 3, 7, 6, -54519970115439230965915352349717218350596096000000000⟩, + ⟨7, 4, 6, 3, 8, 6, 353258721775819434444154859284828487631765504000000000⟩ +] + +def collectedFourData_15_116 : List CollectedFourTerm := [ + ⟨7, 4, 4, 4, 5, 6, 116838141520725126879508537262499905919988531200000000⟩, + ⟨7, 4, 5, 4, 6, 6, -133518925618930207209718558590562273308180480000000000⟩, + ⟨7, 4, 6, 4, 7, 6, -154146718052196954802313866778375800391467008000000000⟩, + ⟨7, 4, 7, 4, 8, 6, 301554713991141919890263891688218820146626560000000000⟩, + ⟨7, 4, 4, 5, 4, 6, 16316293202737899349861647092393099126636544000000000⟩, + ⟨7, 4, 5, 5, 5, 6, -36744584650123234940443950139282012388720640000000000⟩, + ⟨7, 4, 6, 5, 6, 6, -261075715138124969964717947276547875439378432000000000⟩, + ⟨7, 4, 7, 5, 7, 6, 137549943996276434777455302364673912957042688000000000⟩, + ⟨7, 4, 8, 5, 8, 6, 207584644699480250782367983321897816150769664000000000⟩, + ⟨7, 4, 4, 6, 3, 6, -407846405098911646555124131056571652562223104000000000⟩, + ⟨7, 4, 5, 6, 4, 6, 306414766191100154082037936680289777081122816000000000⟩, + ⟨7, 4, 6, 6, 5, 6, 24832901210714731976636105957384358778109952000000000⟩, + ⟨7, 4, 7, 6, 6, 6, 41584999059470871546576960871138927287730176000000000⟩, + ⟨7, 4, 8, 6, 7, 6, 55956006157189329735420633910396912870096896000000000⟩, + ⟨7, 4, 4, 7, 2, 6, 419126551336957558564655224099229821827022848000000000⟩, + ⟨7, 4, 5, 7, 3, 6, 427202414510707297140413890833568197469274112000000000⟩, + ⟨7, 4, 6, 7, 4, 6, 861792084447992871194245808377998758589235200000000000⟩, + ⟨7, 4, 7, 7, 5, 6, -149395634493667396912643220733466764124356608000000000⟩, + ⟨7, 4, 8, 7, 6, 6, 83658035189243345633101437263243621890523136000000000⟩, + ⟨7, 5, 3, 0, 8, 7, -10232561950735840814359394825197563970691530752000000⟩, + ⟨7, 5, 3, 1, 7, 7, 136693950007695130395749298022550016904717664256000000⟩, + ⟨7, 5, 4, 1, 8, 7, -212787548639911756922203187198741746408344256512000000⟩, + ⟨7, 5, 3, 2, 6, 7, -44496733443987879693979493196842892999625015296000000⟩, + ⟨7, 5, 4, 2, 7, 7, 28852182221223614413139591864781938833521377280000000⟩ +] + +def collectedFourData_15_117 : List CollectedFourTerm := [ + ⟨7, 5, 5, 2, 8, 7, -179958744520318663553295726908333175832376770560000000⟩, + ⟨7, 5, 3, 3, 5, 7, -88880789645321305523584758539817572553587687424000000⟩, + ⟨7, 5, 4, 3, 6, 7, 23498006642502006779917724657503403241004597248000000⟩, + ⟨7, 5, 5, 3, 7, 7, 14176932594807378736643125349207136962095349760000000⟩, + ⟨7, 5, 6, 3, 8, 7, -61239029497381430159877620424435625877475164160000000⟩, + ⟨7, 5, 3, 4, 4, 7, 36349119949161746496213545693593283262872027136000000⟩, + ⟨7, 5, 4, 4, 5, 7, -60763292912107306973956973752569241511965753344000000⟩, + ⟨7, 5, 5, 4, 6, 7, 34719182798939872076454495216087280164588748800000000⟩, + ⟨7, 5, 6, 4, 7, 7, 26722044869181152276504683866206012623363768320000000⟩, + ⟨7, 5, 7, 4, 8, 7, -39206925873645948746856351508054337238387916800000000⟩, + ⟨7, 5, 3, 5, 3, 7, 91515751365101104450396818435769330933161787392000000⟩, + ⟨7, 5, 4, 5, 4, 7, -8485514149862826029419734329938894034074337280000000⟩, + ⟨7, 5, 5, 5, 5, 7, 9554764955043009990778580961762101185373798400000000⟩, + ⟨7, 5, 6, 5, 6, 7, 45258679927341477159987260349074256495409889280000000⟩, + ⟨7, 5, 7, 5, 7, 7, -17883688126807319358886762757866990095449456640000000⟩, + ⟨7, 5, 8, 5, 8, 7, -21591453622519002312805916972169274141584654336000000⟩, + ⟨7, 5, 3, 6, 2, 7, 102340334115225531066965730429067663272138768384000000⟩, + ⟨7, 5, 4, 6, 3, 7, 212106168872766742988573321002096997997981204480000000⟩, + ⟨7, 5, 5, 6, 4, 7, -79677620459933608599773924783987492075297832960000000⟩, + ⟨7, 5, 6, 6, 5, 7, -4304898013851708869779034767888689852925870080000000⟩, + ⟨7, 5, 7, 6, 6, 7, -5406713607628113747963514472555850950277857280000000⟩, + ⟨7, 5, 8, 6, 7, 7, -5820139122493419014542307266160850656091439104000000⟩, + ⟨7, 5, 3, 7, 1, 7, -940803108735136557629253443268791381298574786560000000⟩, + ⟨7, 5, 4, 7, 2, 7, -217972565077230567523431513005546456569620725760000000⟩ +] + +def collectedFourData_15_118 : List CollectedFourTerm := [ + ⟨7, 5, 5, 7, 3, 7, -111086264758281158518063797056600724808107294720000000⟩, + ⟨7, 5, 6, 7, 4, 7, -149395634493667396912643220733466764124356608000000000⟩, + ⟨7, 5, 7, 7, 5, 7, 19423816958177543754830021350618875147048714240000000⟩, + ⟨7, 5, 8, 7, 6, 7, -8701503859086418274367786775027092757218852864000000⟩, + ⟨7, 6, 2, 0, 7, 8, -37617666561228106018436693860507486055741521920000000⟩, + ⟨7, 6, 3, 0, 8, 8, 22919974352719316698490926673231882423617191936000000⟩, + ⟨7, 6, 2, 1, 6, 8, 86589108323855826707428853873016875463324205056000000⟩, + ⟨7, 6, 3, 1, 7, 8, -306181564639632398244393504202210037536609271808000000⟩, + ⟨7, 6, 4, 1, 8, 8, 238312026884629423489537089617145789226898423808000000⟩, + ⟨7, 6, 2, 2, 5, 8, 181575379667617413025076061022245322724569251840000000⟩, + ⟨7, 6, 3, 2, 6, 8, 99668489106254561438498295881635949687265558528000000⟩, + ⟨7, 6, 4, 2, 7, 8, -32313084431552105880012375131484616497058283520000000⟩, + ⟨7, 6, 5, 2, 8, 8, 134363542216543371998410114874998094136984207360000000⟩, + ⟨7, 6, 2, 3, 4, 8, -13378670345946685582275081737492806759543209984000000⟩, + ⟨7, 6, 3, 3, 5, 8, 199084591808770858934666308723711231142167314432000000⟩, + ⟨7, 6, 4, 3, 6, 8, -26316660098375675696125664235451371310685356032000000⟩, + ⟨7, 6, 5, 3, 7, 8, -10584997613096917322912645134885715559642562560000000⟩, + ⟨7, 6, 6, 3, 8, 8, 34292413576945631314039682866206641574610206720000000⟩, + ⟨7, 6, 2, 4, 3, 8, -284562947008556411871684915660988917978564132864000000⟩, + ⟨7, 6, 3, 4, 4, 8, -81418602788795641893720522314885101957203099648000000⟩, + ⟨7, 6, 4, 4, 5, 8, 68052024597423522217948132682758485211135082496000000⟩, + ⟨7, 6, 5, 4, 6, 8, -25922565731183638492214783151334694639684812800000000⟩, + ⟨7, 6, 6, 4, 7, 8, -14963715489887729635094817305403248497592893440000000⟩, + ⟨7, 6, 7, 4, 8, 8, 17563963742400037510960409557647615848853012480000000⟩ +] + +def collectedFourData_15_119 : List CollectedFourTerm := [ + ⟨7, 6, 2, 5, 2, 8, 38706933866916373314089710829607596081427775488000000⟩, + ⟨7, 6, 3, 5, 3, 8, -204986657716459518808477781020393735259953299456000000⟩, + ⟨7, 6, 4, 5, 4, 8, 9503375968835785309448941308899527218450923520000000⟩, + ⟨7, 6, 5, 5, 5, 8, -7133924321533143384514681688956446043432550400000000⟩, + ⟨7, 6, 6, 5, 6, 8, -25343794353915521888697818518126795060685045760000000⟩, + ⟨7, 6, 7, 5, 7, 8, 8011555173999773779706616449408719750120341504000000⟩, + ⟨7, 6, 8, 5, 8, 8, 8060470187372068277530074905333531782265438208000000⟩, + ⟨7, 6, 2, 6, 1, 8, -649489636318522950399169075937509771101691969536000000⟩, + ⟨7, 6, 3, 6, 2, 8, -229232702861966657065477272233238589942857203712000000⟩, + ⟨7, 6, 4, 6, 3, 8, -237548913655380783575469286792668413170097848320000000⟩, + ⟨7, 6, 5, 6, 4, 8, 59490120076789319948413930094930286712989941760000000⟩, + ⟨7, 6, 6, 6, 5, 8, 2410641453811528098575684223527935056134799360000000⟩, + ⟨7, 6, 7, 6, 6, 8, 2422105779880931511814134826907457885629841408000000⟩, + ⟨7, 6, 8, 6, 7, 8, 2172760514571730138442117207313720110965850112000000⟩, + ⟨7, 6, 2, 7, 0, 8, 5298519596313464540728901500916178099287944593408000000⟩, + ⟨7, 6, 3, 7, 1, 8, 2107310293060799649107584810710776821238024110080000000⟩, + ⟨7, 6, 4, 7, 2, 8, 244119000951042439756720588081746948495601827840000000⟩, + ⟨7, 6, 5, 7, 3, 8, 82940921066729135653986229674066647745633976320000000⟩, + ⟨7, 6, 6, 7, 4, 8, 83658035189243345633101437263243621890523136000000000⟩, + ⟨7, 6, 7, 7, 5, 8, -8701503859086418274367786775027092757218852864000000⟩, + ⟨7, 6, 8, 7, 6, 8, 3248424754890879257039063405593581832888123392000000⟩, + ⟨0, 7, 8, 6, 8, 1, 1156479984434576087505300973824537726967634460672000000⟩, + ⟨0, 7, 8, 7, 7, 1, 875683823283945976247251784865685567554208137216000000⟩, + ⟨0, 8, 7, 5, 8, 2, -17924437042811478192886413412766664563292635136000000⟩ +] + +def collectedFourData_15_120 : List CollectedFourTerm := [ + ⟨0, 8, 7, 6, 7, 2, 59229173226366913081358202003405386452089962496000000⟩, + ⟨0, 8, 8, 6, 8, 2, -703091459775340125707347128672488066142431084544000000⟩, + ⟨0, 8, 7, 7, 6, 2, -148332470659980881007706386023561452296962310144000000⟩, + ⟨0, 8, 8, 7, 7, 2, -532379138334486998207207942498775528384371884032000000⟩, + ⟨1, 6, 8, 6, 8, 1, 564948502131351327680033945093873574948919836672000000⟩, + ⟨1, 6, 8, 7, 7, 1, 427777627770009294814995584972341434896105865216000000⟩, + ⟨1, 7, 7, 5, 8, 2, -8216783240295405320083581213407154279756595200000000⟩, + ⟨1, 7, 7, 6, 7, 2, 27151384266104095484709888929146804379005747200000000⟩, + ⟨1, 7, 8, 6, 8, 2, -322305805715318026173573369135824279249407180800000000⟩, + ⟨1, 7, 7, 7, 6, 2, -67997435902699208819672124888264795216465100800000000⟩, + ⟨1, 7, 8, 7, 7, 2, -244049169907072461755075082227874897060062822400000000⟩, + ⟨1, 8, 6, 4, 8, 3, 629830024289976948822808335765306226067374080000000⟩, + ⟨1, 8, 6, 5, 7, 3, -763429096492670925404166076723118544217178112000000⟩, + ⟨1, 8, 7, 5, 8, 3, -311771051863419284703480903456544027966439424000000⟩, + ⟨1, 8, 6, 6, 6, 3, 497110523287753342959064146749208986552107008000000⟩, + ⟨1, 8, 7, 6, 7, 3, 1030210410161292835863364728371004832600817664000000⟩, + ⟨1, 8, 8, 6, 8, 3, -6114656863331041924263558205687557055051726848000000⟩, + ⟨1, 8, 6, 7, 5, 3, -513733953305188724909621460933360218265354240000000⟩, + ⟨1, 8, 7, 7, 6, 3, -2580040326661678603661321536702865138931204096000000⟩, + ⟨1, 8, 8, 7, 7, 3, -4630003261810935775463712723114510969779257344000000⟩, + ⟨2, 5, 8, 6, 8, 1, 336145443298517295862894194663399326781636870144000000⟩, + ⟨2, 5, 8, 7, 7, 1, 254528509726901160111762329780024834802510200832000000⟩, + ⟨2, 6, 7, 5, 8, 2, -17309330127794634540659868530466883300157816832000000⟩, + ⟨2, 6, 7, 6, 7, 2, 57196625485243863533751874376261784587470897152000000⟩ +] + +def collectedFourData_15_121 : List CollectedFourTerm := [ + ⟨2, 6, 8, 6, 8, 2, -678963705148282447702070084599012525560538595328000000⟩, + ⟨2, 6, 7, 7, 6, 2, -143242194842304427233392542911189390034131222528000000⟩, + ⟨2, 6, 8, 7, 7, 2, -514109661384214672745515879494186738707840630784000000⟩, + ⟨2, 7, 6, 4, 8, 3, -22629789441953630033694634221523790912437616640000000⟩, + ⟨2, 7, 6, 5, 7, 3, 27430003399672758160818163882710930361203818496000000⟩, + ⟨2, 7, 7, 5, 8, 3, 11201932244686514354860449100896789055345262592000000⟩, + ⟨2, 7, 6, 6, 6, 3, -17861178472815888964755925976168692627185598464000000⟩, + ⟨2, 7, 7, 6, 7, 3, -37015454588943372968026966354113045746272960512000000⟩, + ⟨2, 7, 8, 6, 8, 3, 219699588762809276060761619579481492403135709184000000⟩, + ⟨2, 7, 6, 7, 5, 3, 18458458225431202353237928282449108839348305920000000⟩, + ⟨2, 7, 7, 7, 6, 3, 92700835292701041220313966933259450734050541568000000⟩, + ⟨2, 7, 8, 7, 7, 3, 166355992711615443616230835794199442089366781952000000⟩, + ⟨2, 8, 5, 3, 8, 4, -3337365596464331035349326702491599725582614528000000⟩, + ⟨2, 8, 5, 4, 7, 4, -1994183987188972664473303082221902640699146240000000⟩, + ⟨2, 8, 6, 4, 8, 4, 7568950579993138362987624684833294719144427520000000⟩, + ⟨2, 8, 5, 5, 6, 4, 4429526072168910977911877797875590601658859520000000⟩, + ⟨2, 8, 6, 5, 7, 4, -9174470698179123599734805304614155803194032128000000⟩, + ⟨2, 8, 7, 5, 8, 4, -1873346452867927775200343933931754456275222528000000⟩, + ⟨2, 8, 5, 6, 5, 4, -8978541190523697814768728318603962845419798528000000⟩, + ⟨2, 8, 6, 6, 6, 4, 5974000664387524808116468424747412500514865152000000⟩, + ⟨2, 8, 7, 6, 7, 4, 6190250846087980610530692542074259549410295808000000⟩, + ⟨2, 8, 8, 6, 8, 4, -24494193579896332683290695711908153381517000704000000⟩, + ⟨2, 8, 5, 7, 4, 4, -27151372236496986921670950240625646195510870016000000⟩, + ⟨2, 8, 6, 7, 5, 4, -6173771896973308663820233450384729978762690560000000⟩ +] + +def collectedFourData_15_122 : List CollectedFourTerm := [ + ⟨2, 8, 7, 7, 6, 4, -15502752309169621933440569575398856783835430912000000⟩, + ⟨2, 8, 8, 7, 7, 4, -18546943631529939265810100157705631142365888512000000⟩, + ⟨3, 4, 8, 6, 8, 1, 183285830545778711773940598407648291483522433024000000⟩, + ⟨3, 4, 8, 7, 7, 1, 138783583811502375351151935547986486047614697472000000⟩, + ⟨3, 5, 7, 5, 8, 2, 4289648639311453160482612379187919643656323072000000⟩, + ⟨3, 5, 7, 6, 7, 2, -14174634424009531137440049053533673451046305792000000⟩, + ⟨3, 5, 8, 6, 8, 2, 168262764210290867857903585751962060493357580288000000⟩, + ⟨3, 5, 7, 7, 6, 2, 35498698196910803448781736296031700335342911488000000⟩, + ⟨3, 5, 8, 7, 7, 2, 127408154627105142014659589535395515259015921664000000⟩, + ⟨3, 6, 6, 4, 8, 3, 24848733382835661600752969817945505306886799360000000⟩, + ⟨3, 6, 6, 5, 7, 3, -30119628064462518664332716551906056645749243904000000⟩, + ⟨3, 6, 7, 5, 8, 3, -12300327779663809202076447759472326993361502208000000⟩, + ⟨3, 6, 6, 6, 6, 3, 19612540492817338936258511380151651503372763136000000⟩, + ⟨3, 6, 7, 6, 7, 3, 40644972171942110463529555644157005589578252288000000⟩, + ⟨3, 6, 8, 6, 8, 3, -241242037160306329345791192704030279155807420416000000⟩, + ⟨3, 6, 6, 7, 5, 3, -20268385982046189839332202628619867003111342080000000⟩, + ⟨3, 6, 7, 7, 6, 3, -101790533511726284489675791835293414644233797632000000⟩, + ⟨3, 6, 8, 7, 7, 3, -182667882091041640175913309672641316043093966848000000⟩, + ⟨3, 7, 5, 3, 8, 4, -20119774473336584765628764662320284329146580992000000⟩, + ⟨3, 7, 5, 4, 7, 4, -12022216601947308774779295998590724701799055360000000⟩, + ⟨3, 7, 6, 4, 8, 4, 45630475375735382073831669187401812953823969280000000⟩, + ⟨3, 7, 5, 5, 6, 4, 26704016392516146215143618551294334327880417280000000⟩, + ⟨3, 7, 6, 5, 7, 4, -55309577576743513668146405429199285949292347392000000⟩, + ⟨3, 7, 7, 5, 8, 4, -11293730654519440045457384383769638062356692992000000⟩ +] + +def collectedFourData_15_123 : List CollectedFourTerm := [ + ⟨3, 7, 5, 6, 5, 4, -54128389183456505550345079752751713301919956992000000⟩, + ⟨3, 7, 6, 6, 6, 4, 36015097116832923717542667906282101840730390528000000⟩, + ⟨3, 7, 7, 6, 7, 4, 37318791530846378156462719260093261990605094912000000⟩, + ⟨3, 7, 8, 6, 8, 4, -147666665964275397539984574882784966629346246656000000⟩, + ⟨3, 7, 5, 7, 4, 4, -163685838500483936733738155538488206931131367424000000⟩, + ⟨3, 7, 6, 7, 5, 4, -37219445885258120621148197950094868314157219840000000⟩, + ⟨3, 7, 7, 7, 6, 4, -93460506846159188232948749991632342705837703168000000⟩, + ⟨3, 7, 8, 7, 7, 4, -111812839274007556835072929439857279011618029568000000⟩, + ⟨3, 8, 4, 2, 8, 5, -3337365596464331035349326702491599725582614528000000⟩, + ⟨3, 8, 4, 3, 7, 5, -20119774473336584765628764662320284329146580992000000⟩, + ⟨3, 8, 5, 3, 8, 5, 16639235660296549358347784440212722847873761280000000⟩, + ⟨3, 8, 4, 4, 6, 5, 23856698000845210892861639398462992465304485888000000⟩, + ⟨3, 8, 5, 4, 7, 5, 9942481982789190395395681601840713734448742400000000⟩, + ⟨3, 8, 6, 4, 8, 5, -18868408144296352790791335524424263598184857600000000⟩, + ⟨3, 8, 4, 5, 5, 5, 12376975796758635196865384630833166604281315328000000⟩, + ⟨3, 8, 5, 5, 6, 5, -22084463343281779450633187431734455771018035200000000⟩, + ⟨3, 8, 6, 5, 7, 5, 22870760723250508071587560523897137246387568640000000⟩, + ⟨3, 8, 7, 5, 8, 5, 3113339169440839088716056401782266000058613760000000⟩, + ⟨3, 8, 4, 6, 4, 5, -24021537552509412125575591995020204164163567616000000⟩, + ⟨3, 8, 5, 6, 5, 5, 44764667950396682511686184467377307648293601280000000⟩, + ⟨3, 8, 6, 6, 6, 5, -14892405703891328870683216390230520318666997760000000⟩, + ⟨3, 8, 7, 6, 7, 5, -10287659497412099391631051914632331525472911360000000⟩, + ⟨3, 8, 8, 6, 8, 5, 30530417443372075642974170989197727767472373760000000⟩, + ⟨3, 8, 4, 7, 3, 5, 87429942868612814779320424036613308294725894144000000⟩ +] + +def collectedFourData_15_124 : List CollectedFourTerm := [ + ⟨3, 8, 5, 7, 4, 5, 135369670503623781296021693102674525584265052160000000⟩, + ⟨3, 8, 6, 7, 5, 5, 15390409371913843844520192460458599228689612800000000⟩, + ⟨3, 8, 7, 7, 6, 5, 25764228460991427731364150441660928096248791040000000⟩, + ⟨3, 8, 8, 7, 7, 5, 23117557617167195740010599069199604500429537280000000⟩, + ⟨4, 3, 8, 6, 8, 1, -577630655788681529258724465834842423243034329088000000⟩, + ⟨4, 3, 8, 7, 7, 1, -437380523584548701924295855793184414629116248064000000⟩, + ⟨4, 4, 7, 5, 8, 2, 541904912585197536520230136008161086521999360000000⟩, + ⟨4, 4, 7, 6, 7, 2, -1790660418682442573229870979909769359219752960000000⟩, + ⟨4, 4, 8, 6, 8, 2, 21256383960005962945281605091235938581285437440000000⟩, + ⟨4, 4, 7, 7, 6, 2, 4484497580289709924820451705427529559378493440000000⟩, + ⟨4, 4, 8, 7, 7, 2, 16095282085137187046963859453560830686469816320000000⟩, + ⟨4, 5, 6, 4, 8, 3, 46484979303068931130745626045253658548392427520000000⟩, + ⟨4, 5, 6, 5, 7, 3, -56345338236024728836039578744479482940781232128000000⟩, + ⟨4, 5, 7, 5, 8, 3, -23010447794236268928602107245690485829644845056000000⟩, + ⟨4, 5, 6, 6, 6, 3, 36689537645366140676669448706004013481199665152000000⟩, + ⟨4, 5, 7, 6, 7, 3, 76035291661652144510041346252779854217258991616000000⟩, + ⟨4, 5, 8, 6, 8, 3, -451295884247090878869034357148026392167539802112000000⟩, + ⟨4, 5, 6, 7, 5, 3, -37916439778489481894001170615249237325706690560000000⟩, + ⟨4, 5, 7, 7, 6, 3, -190421409841734560839349413501754504087888461824000000⟩, + ⟨4, 5, 8, 7, 7, 3, -341720142733830718175535429678080150150144065536000000⟩, + ⟨4, 6, 5, 3, 8, 4, 23856698000845210892861639398462992465304485888000000⟩, + ⟨4, 6, 5, 4, 7, 4, 14255149388155191955324475932530512460030935040000000⟩, + ⟨4, 6, 6, 4, 8, 4, -54105600046191521352312483037176189352327249920000000⟩, + ⟨4, 6, 5, 5, 6, 4, -31663856636670766033773828315593464409405521920000000⟩ +] + +def collectedFourData_15_125 : List CollectedFourTerm := [ + ⟨4, 6, 6, 5, 7, 4, 65582439333569165922868366848616646160823615488000000⟩, + ⟨4, 6, 7, 5, 8, 4, 13391358928243334144728357084740300061318053888000000⟩, + ⟨4, 6, 5, 6, 5, 4, 64181864251671709852373742823783615703587749888000000⟩, + ⟨4, 6, 6, 6, 6, 4, -42704320395143452376884637606824270311186235392000000⟩, + ⟨4, 6, 7, 6, 7, 4, -44250155014797120838887243192693278811271200768000000⟩, + ⟨4, 6, 8, 6, 8, 4, 175093366944544709989341475595909939841082589184000000⟩, + ⟨4, 6, 5, 7, 4, 4, 194087842351126346807065983964613552674424487936000000⟩, + ⟨4, 6, 6, 7, 5, 4, 44132357518227815653452424216109608416848117760000000⟩, + ⟨4, 6, 7, 7, 6, 4, 110819288247468516635565910118789754371652452352000000⟩, + ⟨4, 6, 8, 7, 7, 4, 132580270356016453526157352541951840625415421952000000⟩, + ⟨4, 7, 4, 2, 8, 5, -1994183987188972664473303082221902640699146240000000⟩, + ⟨4, 7, 4, 3, 7, 5, -12022216601947308774779295998590724701799055360000000⟩, + ⟨4, 7, 5, 3, 8, 5, 9942481982789190395395681601840713734448742400000000⟩, + ⟨4, 7, 4, 4, 6, 5, 14255149388155191955324475932530512460030935040000000⟩, + ⟨4, 7, 5, 4, 7, 5, 5940954860923334296103171840084457755246592000000000⟩, + ⟨4, 7, 6, 4, 8, 5, -11274484708826815724571455892138982436241408000000000⟩, + ⟨4, 7, 4, 5, 5, 5, 7395643728655348671724400503225375839737610240000000⟩, + ⟨4, 7, 5, 5, 6, 5, -13196181806240137117423522849800576005308416000000000⟩, + ⟨4, 7, 6, 5, 7, 5, 13666019946227998806170225451744742469743411200000000⟩, + ⟨4, 7, 7, 5, 8, 5, 1860320944449303390793804274158621709618380800000000⟩, + ⟨4, 7, 4, 6, 4, 5, -14353646356761931397873837004448617863609057280000000⟩, + ⟨4, 7, 5, 6, 5, 5, 26748338304046084353829628753665945619555942400000000⟩, + ⟨4, 7, 6, 6, 6, 5, -8898694532263605549233231954445632002641100800000000⟩, + ⟨4, 7, 7, 6, 7, 5, -6147209600628190443806002259366391084534988800000000⟩ +] + +def collectedFourData_15_126 : List CollectedFourTerm := [ + ⟨4, 7, 8, 6, 8, 5, 18242912808913829370457020676799834431999180800000000⟩, + ⟨4, 7, 4, 7, 3, 5, 52242221305974266023025326908763742907421163520000000⟩, + ⟨4, 7, 5, 7, 4, 5, 80887760560415161614422494452224833243368652800000000⟩, + ⟨4, 7, 6, 7, 5, 5, 9196267846192410091092068366934224796647424000000000⟩, + ⟨4, 7, 7, 7, 6, 5, 15394960592156573617297048408062889519428403200000000⟩, + ⟨4, 7, 8, 7, 7, 5, 13813489080103543087852890900573587235038822400000000⟩, + ⟨4, 8, 3, 1, 8, 6, 629830024289976948822808335765306226067374080000000⟩, + ⟨4, 8, 3, 2, 7, 6, -22629789441953630033694634221523790912437616640000000⟩, + ⟨4, 8, 4, 2, 8, 6, 7568950579993138362987624684833294719144427520000000⟩, + ⟨4, 8, 3, 3, 6, 6, 24848733382835661600752969817945505306886799360000000⟩, + ⟨4, 8, 4, 3, 7, 6, 45630475375735382073831669187401812953823969280000000⟩, + ⟨4, 8, 5, 3, 8, 6, -18868408144296352790791335524424263598184857600000000⟩, + ⟨4, 8, 3, 4, 5, 6, 46484979303068931130745626045253658548392427520000000⟩, + ⟨4, 8, 4, 4, 6, 6, -54105600046191521352312483037176189352327249920000000⟩, + ⟨4, 8, 5, 4, 7, 6, -11274484708826815724571455892138982436241408000000000⟩, + ⟨4, 8, 6, 4, 8, 6, 14264149835089396121021820554677684669513728000000000⟩, + ⟨4, 8, 3, 5, 4, 6, -47586634567597133986028759237739323706971258880000000⟩, + ⟨4, 8, 4, 5, 5, 6, -28070259438967205992098475931723631810859499520000000⟩, + ⟨4, 8, 5, 5, 6, 6, 25043137588530653759317904633145728994115584000000000⟩, + ⟨4, 8, 6, 5, 7, 6, -17289850595983529260569598879340135311422259200000000⟩, + ⟨4, 8, 7, 5, 8, 6, -1765217926470170038218867244662935088896409600000000⟩, + ⟨4, 8, 3, 6, 3, 6, -63301522772670271291069082380357897925500600320000000⟩, + ⟨4, 8, 4, 6, 4, 6, 54479446538016199552119609476541883432241725440000000⟩, + ⟨4, 8, 5, 6, 5, 6, -50761828402214798547350602898515661933877657600000000⟩ +] + +def collectedFourData_15_127 : List CollectedFourTerm := [ + ⟨4, 8, 6, 6, 6, 6, 11258369266803233070837547880002211516566732800000000⟩, + ⟨4, 8, 7, 6, 7, 6, 5832952973612090267275020854481333608094105600000000⟩, + ⟨4, 8, 8, 6, 8, 6, -13848241323051791853784104983796160346644807680000000⟩, + ⟨4, 8, 3, 7, 2, 6, -233011312244808127027130865296970575830151331840000000⟩, + ⟨4, 8, 4, 7, 3, 6, -198286012621819921868522029237992463900040232960000000⟩, + ⟨4, 8, 5, 7, 4, 6, -153505259830893387915050520248661131455050547200000000⟩, + ⟨4, 8, 6, 7, 5, 6, -11634850360744620313793504459335663179792384000000000⟩, + ⟨4, 8, 7, 7, 6, 6, -14607941976711524941756495569896139043268198400000000⟩, + ⟨4, 8, 8, 7, 7, 6, -10485854550658459017937130056196190626685911040000000⟩, + ⟨5, 2, 8, 6, 8, 1, -116991926157760271843063613595227394533186600960000000⟩, + ⟨5, 2, 8, 7, 7, 1, -88586001115505034870061727234902123707503738880000000⟩, + ⟨5, 3, 7, 5, 8, 2, 9036481386670362265840619098936740998780289024000000⟩, + ⟨5, 3, 7, 6, 7, 2, -29859979430851262942871870957951687772826763264000000⟩, + ⟨5, 3, 8, 6, 8, 2, 354458713219938417064232216581863479840757252096000000⟩, + ⟨5, 3, 7, 7, 6, 2, 74780792666250470404924816893643644583853162496000000⟩, + ⟨5, 3, 8, 7, 7, 2, 268395273040977482737730108464558785807293349888000000⟩, + ⟨5, 4, 6, 4, 8, 3, -47586634567597133986028759237739323706971258880000000⟩, + ⟨5, 4, 6, 5, 7, 3, 57680675788713298636242934464612797667273080832000000⟩, + ⟨5, 4, 7, 5, 8, 3, 23555776227887914834458387495045836180620836864000000⟩, + ⟨5, 4, 6, 6, 6, 3, -37559049107049308982045422301482758451377471488000000⟩, + ⟨5, 4, 7, 6, 7, 3, -77837264699068691642784811350364806324110229504000000⟩, + ⟨5, 4, 8, 6, 8, 3, 461991220551304202838213874387773206963555401728000000⟩, + ⟨5, 4, 6, 7, 5, 3, 38815027798112022603687869723480841614146928640000000⟩, + ⟨5, 4, 7, 7, 6, 3, 194934238539868021291281193157349486113750777856000000⟩ +] + +def collectedFourData_15_128 : List CollectedFourTerm := [ + ⟨5, 4, 8, 7, 7, 3, 349818625294910396475386803320186747304997289984000000⟩, + ⟨5, 5, 5, 3, 8, 4, 12376975796758635196865384630833166604281315328000000⟩, + ⟨5, 5, 5, 4, 7, 4, 7395643728655348671724400503225375839737610240000000⟩, + ⟨5, 5, 6, 4, 8, 4, -28070259438967205992098475931723631810859499520000000⟩, + ⟨5, 5, 5, 5, 6, 4, -16427369253289988492956341241927359106929131520000000⟩, + ⟨5, 5, 6, 5, 7, 4, 34024501810569895470844285338579823005876092928000000⟩, + ⟨5, 5, 7, 5, 8, 4, 6947504861515340343299151599973698618762723328000000⟩, + ⟨5, 5, 5, 6, 5, 4, 33297876361835376328791836681107576677180899328000000⟩, + ⟨5, 5, 6, 6, 6, 4, -22155217789527739132931184581613475640327012352000000⟩, + ⟨5, 5, 7, 6, 7, 4, -22957204622431739384798187061049490817425604608000000⟩, + ⟨5, 5, 8, 6, 8, 4, 90839325910435297999748669948907667186834735104000000⟩, + ⟨5, 5, 5, 7, 4, 4, 100693755990032188731829311891819704898463727616000000⟩, + ⟨5, 5, 6, 7, 5, 4, 22896090684371015537872281590427312670176706560000000⟩, + ⟨5, 5, 7, 7, 6, 4, 57493608227104282297703336763022408421172314112000000⟩, + ⟨5, 5, 8, 7, 7, 4, 68783316000646677920059179999356321164230131712000000⟩, + ⟨5, 6, 4, 2, 8, 5, 4429526072168910977911877797875590601658859520000000⟩, + ⟨5, 6, 4, 3, 7, 5, 26704016392516146215143618551294334327880417280000000⟩, + ⟨5, 6, 5, 3, 8, 5, -22084463343281779450633187431734455771018035200000000⟩, + ⟨5, 6, 4, 4, 6, 5, -31663856636670766033773828315593464409405521920000000⟩, + ⟨5, 6, 5, 4, 7, 5, -13196181806240137117423522849800576005308416000000000⟩, + ⟨5, 6, 6, 4, 8, 5, 25043137588530653759317904633145728994115584000000000⟩, + ⟨5, 6, 4, 5, 5, 5, -16427369253289988492956341241927359106929131520000000⟩, + ⟨5, 6, 5, 5, 6, 5, 29311654159964237162109431326033611973459968000000000⟩, + ⟨5, 6, 6, 5, 7, 5, -30355269144411690369557042650354426071062937600000000⟩ +] + +def collectedFourData_15_129 : List CollectedFourTerm := [ + ⟨5, 6, 7, 5, 8, 5, -4132186487795326676152263059764168934975078400000000⟩, + ⟨5, 6, 4, 6, 4, 5, 31882640306219813998320507149294053916871229440000000⟩, + ⟨5, 6, 5, 6, 5, 5, -59414007266190558602216655370348880771363635200000000⟩, + ⟨5, 6, 6, 6, 6, 5, 19765979313920417803335050845160552643585638400000000⟩, + ⟨5, 6, 7, 6, 7, 5, 13654319446949463047028093074347854588700262400000000⟩, + ⟨5, 6, 8, 6, 8, 5, -40521565932988569904370613342614916902053478400000000⟩, + ⟨5, 6, 4, 7, 3, 5, -116041590359486973896347646921784488715312168960000000⟩, + ⟨5, 6, 5, 7, 4, 5, -179669702807498502788790120035969534687340134400000000⟩, + ⟨5, 6, 6, 7, 5, 5, -20426955814031306207049693010063829973860352000000000⟩, + ⟨5, 6, 7, 7, 6, 5, -34195630774818993635654836622963640823814553600000000⟩, + ⟨5, 6, 8, 7, 7, 5, -30682830882715825463412740737885339160621875200000000⟩, + ⟨5, 7, 3, 1, 8, 6, -763429096492670925404166076723118544217178112000000⟩, + ⟨5, 7, 3, 2, 7, 6, 27430003399672758160818163882710930361203818496000000⟩, + ⟨5, 7, 4, 2, 8, 6, -9174470698179123599734805304614155803194032128000000⟩, + ⟨5, 7, 3, 3, 6, 6, -30119628064462518664332716551906056645749243904000000⟩, + ⟨5, 7, 4, 3, 7, 6, -55309577576743513668146405429199285949292347392000000⟩, + ⟨5, 7, 5, 3, 8, 6, 22870760723250508071587560523897137246387568640000000⟩, + ⟨5, 7, 3, 4, 5, 6, -56345338236024728836039578744479482940781232128000000⟩, + ⟨5, 7, 4, 4, 6, 6, 65582439333569165922868366848616646160823615488000000⟩, + ⟨5, 7, 5, 4, 7, 6, 13666019946227998806170225451744742469743411200000000⟩, + ⟨5, 7, 6, 4, 8, 6, -17289850595983529260569598879340135311422259200000000⟩, + ⟨5, 7, 3, 5, 4, 6, 57680675788713298636242934464612797667273080832000000⟩, + ⟨5, 7, 4, 5, 5, 6, 34024501810569895470844285338579823005876092928000000⟩, + ⟨5, 7, 5, 5, 6, 6, -30355269144411690369557042650354426071062937600000000⟩ +] + +def collectedFourData_15_130 : List CollectedFourTerm := [ + ⟨5, 7, 6, 5, 7, 6, 20957360732151794254604891888870829560042618880000000⟩, + ⟨5, 7, 7, 5, 8, 6, 2139654628623003548454367517755205488151101440000000⟩, + ⟨5, 7, 3, 6, 3, 6, 76728994289259635027303467484244025033566978048000000⟩, + ⟨5, 7, 4, 6, 4, 6, -66035585862749659099476000330322674091416354816000000⟩, + ⟨5, 7, 5, 6, 5, 6, 61529389357241471292910564462485475584261488640000000⟩, + ⟨5, 7, 6, 6, 6, 6, -13646486108733488758549892451590950319208529920000000⟩, + ⟨5, 7, 7, 6, 7, 6, -7070234582019086494373313723207211892437155840000000⟩, + ⟨5, 7, 8, 6, 8, 6, 16785719882420891781214837157843050645162033152000000⟩, + ⟨5, 7, 3, 7, 2, 6, 282437496974144145178685411931758539441780555776000000⟩, + ⟨5, 7, 4, 7, 3, 6, 240346292848870986021431414834368952615980498944000000⟩, + ⟨5, 7, 5, 7, 4, 6, 186066680374094998956716565501418208468486062080000000⟩, + ⟨5, 7, 6, 7, 5, 6, 14102826089854994572114604509924499692034457600000000⟩, + ⟨5, 7, 7, 7, 6, 6, 17706567668745725536063000006119668682860789760000000⟩, + ⟨5, 7, 8, 7, 7, 6, 12710106150603438741715471519186964287278022656000000⟩, + ⟨5, 8, 2, 0, 8, 7, -17924437042811478192886413412766664563292635136000000⟩, + ⟨5, 8, 2, 1, 7, 7, -8216783240295405320083581213407154279756595200000000⟩, + ⟨5, 8, 3, 1, 8, 7, -311771051863419284703480903456544027966439424000000⟩, + ⟨5, 8, 2, 2, 6, 7, -17309330127794634540659868530466883300157816832000000⟩, + ⟨5, 8, 3, 2, 7, 7, 11201932244686514354860449100896789055345262592000000⟩, + ⟨5, 8, 4, 2, 8, 7, -1873346452867927775200343933931754456275222528000000⟩, + ⟨5, 8, 2, 3, 5, 7, 4289648639311453160482612379187919643656323072000000⟩, + ⟨5, 8, 3, 3, 6, 7, -12300327779663809202076447759472326993361502208000000⟩, + ⟨5, 8, 4, 3, 7, 7, -11293730654519440045457384383769638062356692992000000⟩, + ⟨5, 8, 5, 3, 8, 7, 3113339169440839088716056401782266000058613760000000⟩ +] + +def collectedFourData_15_131 : List CollectedFourTerm := [ + ⟨5, 8, 2, 4, 4, 7, 541904912585197536520230136008161086521999360000000⟩, + ⟨5, 8, 3, 4, 5, 7, -23010447794236268928602107245690485829644845056000000⟩, + ⟨5, 8, 4, 4, 6, 7, 13391358928243334144728357084740300061318053888000000⟩, + ⟨5, 8, 5, 4, 7, 7, 1860320944449303390793804274158621709618380800000000⟩, + ⟨5, 8, 6, 4, 8, 7, -1765217926470170038218867244662935088896409600000000⟩, + ⟨5, 8, 2, 5, 3, 7, 9036481386670362265840619098936740998780289024000000⟩, + ⟨5, 8, 3, 5, 4, 7, 23555776227887914834458387495045836180620836864000000⟩, + ⟨5, 8, 4, 5, 5, 7, 6947504861515340343299151599973698618762723328000000⟩, + ⟨5, 8, 5, 5, 6, 7, -4132186487795326676152263059764168934975078400000000⟩, + ⟨5, 8, 6, 5, 7, 7, 2139654628623003548454367517755205488151101440000000⟩, + ⟨5, 8, 7, 5, 8, 7, 174759483822380535768021171016002382778597376000000⟩, + ⟨5, 8, 2, 6, 2, 7, -6047364738701059748823969935631960228419862528000000⟩, + ⟨5, 8, 3, 6, 3, 7, 31334775381087957650040307227460551589962448896000000⟩, + ⟨5, 8, 4, 6, 4, 7, -13483887475229502280452791358442301330728943616000000⟩, + ⟨5, 8, 5, 6, 5, 7, 8375841113274977552031073347467161267611893760000000⟩, + ⟨5, 8, 6, 6, 6, 7, -1393246389188489677487487996503798852836392960000000⟩, + ⟨5, 8, 7, 6, 7, 7, -577471957169076764199248576123934915623387136000000⟩, + ⟨5, 8, 8, 6, 8, 7, 1142498927551532584334671178972732674837315584000000⟩, + ⟨5, 8, 2, 7, 1, 7, 89194781034669434018236502650956097495171596288000000⟩, + ⟨5, 8, 3, 7, 2, 7, 115342519589369063966314709373111941901060145152000000⟩, + ⟨5, 8, 4, 7, 3, 7, 49076605068644569225513052904387410860015878144000000⟩, + ⟨5, 8, 5, 7, 4, 7, 25328789503166450174461567784429047090218270720000000⟩, + ⟨5, 8, 6, 7, 5, 7, 1439836700120839182762165462494819237285068800000000⟩, + ⟨5, 8, 7, 7, 6, 7, 1446210329770595430843363726388974275845423104000000⟩ +] + +def collectedFourData_15_132 : List CollectedFourTerm := [ + ⟨5, 8, 8, 7, 7, 7, 865097401115230553282668824179743300257841152000000⟩, + ⟨6, 1, 8, 6, 8, 1, -2581395014052977549508798188632261335006496948224000000⟩, + ⟨6, 1, 8, 7, 7, 1, -1954626008004123925535714105274713893157650563072000000⟩, + ⟨6, 2, 7, 5, 8, 2, -6047364738701059748823969935631960228419862528000000⟩, + ⟨6, 2, 7, 6, 7, 2, 19982798501066170673143431723713537069241335808000000⟩, + ⟨6, 2, 8, 6, 8, 2, -237209709391259993248581586079947104611689562112000000⟩, + ⟨6, 2, 7, 7, 6, 2, -50044559309232213689261030753313674620317990912000000⟩, + ⟨6, 2, 8, 7, 7, 2, -179614613340126844996195418715597197776609345536000000⟩, + ⟨6, 3, 6, 4, 8, 3, -63301522772670271291069082380357897925500600320000000⟩, + ⟨6, 3, 6, 5, 7, 3, 76728994289259635027303467484244025033566978048000000⟩, + ⟨6, 3, 7, 5, 8, 3, 31334775381087957650040307227460551589962448896000000⟩, + ⟨6, 3, 6, 6, 6, 3, -49962453196651345612293501173172811243488018432000000⟩, + ⟨6, 3, 7, 6, 7, 3, -103542043447332153969085516455762784009486073856000000⟩, + ⟨6, 3, 8, 6, 8, 3, 614558016851554321094536931769324495881782689792000000⟩, + ⟨6, 3, 6, 7, 5, 3, 51633203070785795329688849985374206292876328960000000⟩, + ⟨6, 3, 7, 7, 6, 3, 259308821735986839681582316240005781675975901184000000⟩, + ⟨6, 3, 8, 7, 7, 3, 465341831306733930504318215184464292271752216576000000⟩, + ⟨6, 4, 5, 3, 8, 4, -24021537552509412125575591995020204164163567616000000⟩, + ⟨6, 4, 5, 4, 7, 4, -14353646356761931397873837004448617863609057280000000⟩, + ⟨6, 4, 6, 4, 8, 4, 54479446538016199552119609476541883432241725440000000⟩, + ⟨6, 4, 5, 5, 6, 4, 31882640306219813998320507149294053916871229440000000⟩, + ⟨6, 4, 6, 5, 7, 4, -66035585862749659099476000330322674091416354816000000⟩, + ⟨6, 4, 7, 5, 8, 4, -13483887475229502280452791358442301330728943616000000⟩, + ⟨6, 4, 5, 6, 5, 4, -64625333407706772376281221031923237056325615616000000⟩ +] + +def collectedFourData_15_133 : List CollectedFourTerm := [ + ⟨6, 4, 6, 6, 6, 4, 42999388934293776381305986688966554750071865344000000⟩, + ⟨6, 4, 7, 6, 7, 4, 44555904608200706715564473521847009129609035776000000⟩, + ⟨6, 4, 8, 6, 8, 4, -176303187017108468349988776914661825335670079488000000⟩, + ⟨6, 4, 5, 7, 4, 4, -195428906102509641922159673841796723588938596352000000⟩, + ⟨6, 4, 6, 7, 5, 4, -44437293181450411620841873147813613806100152320000000⟩, + ⟨6, 4, 7, 7, 6, 4, -111585002001727861555193100965606721504688472064000000⟩, + ⟨6, 4, 8, 7, 7, 4, -133496343163922646857522100392830605564800139264000000⟩, + ⟨6, 5, 4, 2, 8, 5, -8978541190523697814768728318603962845419798528000000⟩, + ⟨6, 5, 4, 3, 7, 5, -54128389183456505550345079752751713301919956992000000⟩, + ⟨6, 5, 5, 3, 8, 5, 44764667950396682511686184467377307648293601280000000⟩, + ⟨6, 5, 4, 4, 6, 5, 64181864251671709852373742823783615703587749888000000⟩, + ⟨6, 5, 5, 4, 7, 5, 26748338304046084353829628753665945619555942400000000⟩, + ⟨6, 5, 6, 4, 8, 5, -50761828402214798547350602898515661933877657600000000⟩, + ⟨6, 5, 4, 5, 5, 5, 33297876361835376328791836681107576677180899328000000⟩, + ⟨6, 5, 5, 5, 6, 5, -59414007266190558602216655370348880771363635200000000⟩, + ⟨6, 5, 6, 5, 7, 5, 61529389357241471292910564462485475584261488640000000⟩, + ⟨6, 5, 7, 5, 8, 5, 8375841113274977552031073347467161267611893760000000⟩, + ⟨6, 5, 4, 6, 4, 5, -64625333407706772376281221031923237056325615616000000⟩, + ⟨6, 5, 5, 6, 5, 5, 120430741989596790473740001859145514316233441280000000⟩, + ⟨6, 5, 6, 6, 6, 5, -40065157434365444881906787385608101152172277760000000⟩, + ⟨6, 5, 7, 6, 7, 5, -27676972115207716209831740496932790945038991360000000⟩, + ⟨6, 5, 8, 6, 8, 5, 82136224712571462696542128638789576988305653760000000⟩, + ⟨6, 5, 4, 7, 3, 5, 235213470218129758514213516882624065140261126144000000⟩, + ⟨6, 5, 5, 7, 4, 5, 364186100513545311967464906827769673165213532160000000⟩ +] + +def collectedFourData_15_134 : List CollectedFourTerm := [ + ⟨6, 5, 6, 7, 5, 5, 41404940660724903355822845462211679488888012800000000⟩, + ⟨6, 5, 7, 7, 6, 5, 69313708610211851115487905019567629132669911040000000⟩, + ⟨6, 5, 8, 7, 7, 5, 62193349002559272005265186210419777419377377280000000⟩, + ⟨6, 6, 3, 1, 8, 6, 497110523287753342959064146749208986552107008000000⟩, + ⟨6, 6, 3, 2, 7, 6, -17861178472815888964755925976168692627185598464000000⟩, + ⟨6, 6, 4, 2, 8, 6, 5974000664387524808116468424747412500514865152000000⟩, + ⟨6, 6, 3, 3, 6, 6, 19612540492817338936258511380151651503372763136000000⟩, + ⟨6, 6, 4, 3, 7, 6, 36015097116832923717542667906282101840730390528000000⟩, + ⟨6, 6, 5, 3, 8, 6, -14892405703891328870683216390230520318666997760000000⟩, + ⟨6, 6, 3, 4, 5, 6, 36689537645366140676669448706004013481199665152000000⟩, + ⟨6, 6, 4, 4, 6, 6, -42704320395143452376884637606824270311186235392000000⟩, + ⟨6, 6, 5, 4, 7, 6, -8898694532263605549233231954445632002641100800000000⟩, + ⟨6, 6, 6, 4, 8, 6, 11258369266803233070837547880002211516566732800000000⟩, + ⟨6, 6, 3, 5, 4, 6, -37559049107049308982045422301482758451377471488000000⟩, + ⟨6, 6, 4, 5, 5, 6, -22155217789527739132931184581613475640327012352000000⟩, + ⟨6, 6, 5, 5, 6, 6, 19765979313920417803335050845160552643585638400000000⟩, + ⟨6, 6, 6, 5, 7, 6, -13646486108733488758549892451590950319208529920000000⟩, + ⟨6, 6, 7, 5, 8, 6, -1393246389188489677487487996503798852836392960000000⟩, + ⟨6, 6, 3, 6, 3, 6, -49962453196651345612293501173172811243488018432000000⟩, + ⟨6, 6, 4, 6, 4, 6, 42999388934293776381305986688966554750071865344000000⟩, + ⟨6, 6, 5, 6, 5, 6, -40065157434365444881906787385608101152172277760000000⟩, + ⟨6, 6, 6, 6, 6, 6, 8885974980148909526526115729851877774621409280000000⟩, + ⟨6, 6, 7, 6, 7, 6, 4603817209720955192119216215283291893855682560000000⟩, + ⟨6, 6, 8, 6, 8, 6, -10930102131091623337788257714085464875223482368000000⟩ +] + +def collectedFourData_15_135 : List CollectedFourTerm := [ + ⟨6, 6, 3, 7, 2, 6, -183910532833939400988712881576693322461933993984000000⟩, + ⟨6, 6, 4, 7, 3, 6, -156502643084053431281982188527544365204421738496000000⟩, + ⟨6, 6, 5, 7, 4, 6, -121158212690770147313487836387832195076293918720000000⟩, + ⟨6, 6, 6, 7, 5, 6, -9183122950870265253980631889894025764169318400000000⟩, + ⟨6, 6, 7, 7, 6, 6, -11529716590419087553364170777740078009381027840000000⟩, + ⟨6, 6, 8, 7, 7, 6, -8276246672542202433503824390589079281052155904000000⟩, + ⟨6, 7, 2, 0, 8, 7, 59229173226366913081358202003405386452089962496000000⟩, + ⟨6, 7, 2, 1, 7, 7, 27151384266104095484709888929146804379005747200000000⟩, + ⟨6, 7, 3, 1, 8, 7, 1030210410161292835863364728371004832600817664000000⟩, + ⟨6, 7, 2, 2, 6, 7, 57196625485243863533751874376261784587470897152000000⟩, + ⟨6, 7, 3, 2, 7, 7, -37015454588943372968026966354113045746272960512000000⟩, + ⟨6, 7, 4, 2, 8, 7, 6190250846087980610530692542074259549410295808000000⟩, + ⟨6, 7, 2, 3, 5, 7, -14174634424009531137440049053533673451046305792000000⟩, + ⟨6, 7, 3, 3, 6, 7, 40644972171942110463529555644157005589578252288000000⟩, + ⟨6, 7, 4, 3, 7, 7, 37318791530846378156462719260093261990605094912000000⟩, + ⟨6, 7, 5, 3, 8, 7, -10287659497412099391631051914632331525472911360000000⟩, + ⟨6, 7, 2, 4, 4, 7, -1790660418682442573229870979909769359219752960000000⟩, + ⟨6, 7, 3, 4, 5, 7, 76035291661652144510041346252779854217258991616000000⟩, + ⟨6, 7, 4, 4, 6, 7, -44250155014797120838887243192693278811271200768000000⟩, + ⟨6, 7, 5, 4, 7, 7, -6147209600628190443806002259366391084534988800000000⟩, + ⟨6, 7, 6, 4, 8, 7, 5832952973612090267275020854481333608094105600000000⟩, + ⟨6, 7, 2, 5, 3, 7, -29859979430851262942871870957951687772826763264000000⟩, + ⟨6, 7, 3, 5, 4, 7, -77837264699068691642784811350364806324110229504000000⟩, + ⟨6, 7, 4, 5, 5, 7, -22957204622431739384798187061049490817425604608000000⟩ +] + +def collectedFourData_15_136 : List CollectedFourTerm := [ + ⟨6, 7, 5, 5, 6, 7, 13654319446949463047028093074347854588700262400000000⟩, + ⟨6, 7, 6, 5, 7, 7, -7070234582019086494373313723207211892437155840000000⟩, + ⟨6, 7, 7, 5, 8, 7, -577471957169076764199248576123934915623387136000000⟩, + ⟨6, 7, 2, 6, 2, 7, 19982798501066170673143431723713537069241335808000000⟩, + ⟨6, 7, 3, 6, 3, 7, -103542043447332153969085516455762784009486073856000000⟩, + ⟨6, 7, 4, 6, 4, 7, 44555904608200706715564473521847009129609035776000000⟩, + ⟨6, 7, 5, 6, 5, 7, -27676972115207716209831740496932790945038991360000000⟩, + ⟨6, 7, 6, 6, 6, 7, 4603817209720955192119216215283291893855682560000000⟩, + ⟨6, 7, 7, 6, 7, 7, 1908187493021066994017257105531201421360234496000000⟩, + ⟨6, 7, 8, 6, 8, 7, -3775252005363628792414644439771347319127015424000000⟩, + ⟨6, 7, 2, 7, 1, 7, -294733559786135697515524496470181226114258567168000000⟩, + ⟨6, 7, 3, 7, 2, 7, -381135656132874830373554110375108696569305628672000000⟩, + ⟨6, 7, 4, 7, 3, 7, -162167812357515156416825881482430907239140163584000000⟩, + ⟨6, 7, 5, 7, 4, 7, -83695976476922602663852480993269258213308497920000000⟩, + ⟨6, 7, 6, 7, 5, 7, -4757769358415583980350991112440624706276556800000000⟩, + ⟨6, 7, 7, 7, 6, 7, -4778830260562997187324513070364390937952518144000000⟩, + ⟨6, 7, 8, 7, 7, 7, -2858611609723218809540721839019898880416284672000000⟩, + ⟨6, 8, 1, 0, 7, 8, 1156479984434576087505300973824537726967634460672000000⟩, + ⟨6, 8, 2, 0, 8, 8, -703091459775340125707347128672488066142431084544000000⟩, + ⟨6, 8, 1, 1, 6, 8, 564948502131351327680033945093873574948919836672000000⟩, + ⟨6, 8, 2, 1, 7, 8, -322305805715318026173573369135824279249407180800000000⟩, + ⟨6, 8, 3, 1, 8, 8, -6114656863331041924263558205687557055051726848000000⟩, + ⟨6, 8, 1, 2, 5, 8, 336145443298517295862894194663399326781636870144000000⟩, + ⟨6, 8, 2, 2, 6, 8, -678963705148282447702070084599012525560538595328000000⟩ +] + +def collectedFourData_15_137 : List CollectedFourTerm := [ + ⟨6, 8, 3, 2, 7, 8, 219699588762809276060761619579481492403135709184000000⟩, + ⟨6, 8, 4, 2, 8, 8, -24494193579896332683290695711908153381517000704000000⟩, + ⟨6, 8, 1, 3, 4, 8, 183285830545778711773940598407648291483522433024000000⟩, + ⟨6, 8, 2, 3, 5, 8, 168262764210290867857903585751962060493357580288000000⟩, + ⟨6, 8, 3, 3, 6, 8, -241242037160306329345791192704030279155807420416000000⟩, + ⟨6, 8, 4, 3, 7, 8, -147666665964275397539984574882784966629346246656000000⟩, + ⟨6, 8, 5, 3, 8, 8, 30530417443372075642974170989197727767472373760000000⟩, + ⟨6, 8, 1, 4, 3, 8, -577630655788681529258724465834842423243034329088000000⟩, + ⟨6, 8, 2, 4, 4, 8, 21256383960005962945281605091235938581285437440000000⟩, + ⟨6, 8, 3, 4, 5, 8, -451295884247090878869034357148026392167539802112000000⟩, + ⟨6, 8, 4, 4, 6, 8, 175093366944544709989341475595909939841082589184000000⟩, + ⟨6, 8, 5, 4, 7, 8, 18242912808913829370457020676799834431999180800000000⟩, + ⟨6, 8, 6, 4, 8, 8, -13848241323051791853784104983796160346644807680000000⟩, + ⟨6, 8, 1, 5, 2, 8, -116991926157760271843063613595227394533186600960000000⟩, + ⟨6, 8, 2, 5, 3, 8, 354458713219938417064232216581863479840757252096000000⟩, + ⟨6, 8, 3, 5, 4, 8, 461991220551304202838213874387773206963555401728000000⟩, + ⟨6, 8, 4, 5, 5, 8, 90839325910435297999748669948907667186834735104000000⟩, + ⟨6, 8, 5, 5, 6, 8, -40521565932988569904370613342614916902053478400000000⟩, + ⟨6, 8, 6, 5, 7, 8, 16785719882420891781214837157843050645162033152000000⟩, + ⟨6, 8, 7, 5, 8, 8, 1142498927551532584334671178972732674837315584000000⟩, + ⟨6, 8, 1, 6, 1, 8, -2581395014052977549508798188632261335006496948224000000⟩, + ⟨6, 8, 2, 6, 2, 8, -237209709391259993248581586079947104611689562112000000⟩, + ⟨6, 8, 3, 6, 3, 8, 614558016851554321094536931769324495881782689792000000⟩, + ⟨6, 8, 4, 6, 4, 8, -176303187017108468349988776914661825335670079488000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1507.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1507.lean new file mode 100644 index 0000000000000000000000000000000000000000..6ad1851d768a6c9c2d743a8781bfc0c273c6d5a6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1507.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1507. -/ +namespace LaughlinFock +def collectedFourData_15_138 : List CollectedFourTerm := [ + ⟨6, 8, 5, 6, 5, 8, 82136224712571462696542128638789576988305653760000000⟩, + ⟨6, 8, 6, 6, 6, 8, -10930102131091623337788257714085464875223482368000000⟩, + ⟨6, 8, 7, 6, 7, 8, -3775252005363628792414644439771347319127015424000000⟩, + ⟨6, 8, 8, 6, 8, 8, 6402123670968433916058920921633171809184514048000000⟩, + ⟨6, 8, 1, 7, 0, 8, 16168920773177597963420000513495821709152358498304000000⟩, + ⟨6, 8, 2, 7, 1, 8, 3498692240778517513087615107561387149920831537152000000⟩, + ⟨6, 8, 3, 7, 2, 8, 2262172593721112534304164855935274262029930594304000000⟩, + ⟨6, 8, 4, 7, 3, 8, 641681554928190283571123064931514851576818696192000000⟩, + ⟨6, 8, 5, 7, 4, 8, 248382355657658148474491022561048490742088990720000000⟩, + ⟨6, 8, 6, 7, 5, 8, 11295605936277513534181814949067460053083095040000000⟩, + ⟨6, 8, 7, 7, 6, 8, 9454672871752056023058205966653060728525684736000000⟩, + ⟨6, 8, 8, 7, 7, 8, 4847672427354010359386623953805522338205138944000000⟩, + ⟨7, 0, 8, 6, 8, 1, 16168920773177597963420000513495821709152358498304000000⟩, + ⟨7, 0, 8, 7, 7, 1, 12243067369604237369855418371536232497797830541312000000⟩, + ⟨7, 1, 7, 5, 8, 2, 89194781034669434018236502650956097495171596288000000⟩, + ⟨7, 1, 7, 6, 7, 2, -294733559786135697515524496470181226114258567168000000⟩, + ⟨7, 1, 8, 6, 8, 2, 3498692240778517513087615107561387149920831537152000000⟩, + ⟨7, 1, 7, 7, 6, 2, 738125398819962018041696304322808785376171261952000000⟩, + ⟨7, 1, 8, 7, 7, 2, 2649201230574457387437394655686196276871252934656000000⟩, + ⟨7, 2, 6, 4, 8, 3, -233011312244808127027130865296970575830151331840000000⟩, + ⟨7, 2, 6, 5, 7, 3, 282437496974144145178685411931758539441780555776000000⟩, + ⟨7, 2, 7, 5, 8, 3, 115342519589369063966314709373111941901060145152000000⟩, + ⟨7, 2, 6, 6, 6, 3, -183910532833939400988712881576693322461933993984000000⟩, + ⟨7, 2, 7, 6, 7, 3, -381135656132874830373554110375108696569305628672000000⟩ +] + +def collectedFourData_15_139 : List CollectedFourTerm := [ + ⟨7, 2, 8, 6, 8, 3, 2262172593721112534304164855935274262029930594304000000⟩, + ⟨7, 2, 6, 7, 5, 3, 190060521073606103771717579285375933478359531520000000⟩, + ⟨7, 2, 7, 7, 6, 3, 954509246899883376386610866248400192336516087808000000⟩, + ⟨7, 2, 8, 7, 7, 3, 1712911569988291312345389065525497094764140429312000000⟩, + ⟨7, 3, 5, 3, 8, 4, 87429942868612814779320424036613308294725894144000000⟩, + ⟨7, 3, 5, 4, 7, 4, 52242221305974266023025326908763742907421163520000000⟩, + ⟨7, 3, 6, 4, 8, 4, -198286012621819921868522029237992463900040232960000000⟩, + ⟨7, 3, 5, 5, 6, 4, -116041590359486973896347646921784488715312168960000000⟩, + ⟨7, 3, 6, 5, 7, 4, 240346292848870986021431414834368952615980498944000000⟩, + ⟨7, 3, 7, 5, 8, 4, 49076605068644569225513052904387410860015878144000000⟩, + ⟨7, 3, 5, 6, 5, 4, 235213470218129758514213516882624065140261126144000000⟩, + ⟨7, 3, 6, 6, 6, 4, -156502643084053431281982188527544365204421738496000000⟩, + ⟨7, 3, 7, 6, 7, 4, -162167812357515156416825881482430907239140163584000000⟩, + ⟨7, 3, 8, 6, 8, 4, 641681554928190283571123064931514851576818696192000000⟩, + ⟨7, 3, 5, 7, 4, 4, 711292441546190301585974931810989447446284730368000000⟩, + ⟨7, 3, 6, 7, 5, 4, 161736108506682359454954930619237751206057082880000000⟩, + ⟨7, 3, 7, 7, 6, 4, 406130137535095692479487116766586215524493950976000000⟩, + ⟨7, 3, 8, 7, 7, 4, 485879708177598126907933291911178778623686475776000000⟩, + ⟨7, 4, 4, 2, 8, 5, -27151372236496986921670950240625646195510870016000000⟩, + ⟨7, 4, 4, 3, 7, 5, -163685838500483936733738155538488206931131367424000000⟩, + ⟨7, 4, 5, 3, 8, 5, 135369670503623781296021693102674525584265052160000000⟩, + ⟨7, 4, 4, 4, 6, 5, 194087842351126346807065983964613552674424487936000000⟩, + ⟨7, 4, 5, 4, 7, 5, 80887760560415161614422494452224833243368652800000000⟩, + ⟨7, 4, 6, 4, 8, 5, -153505259830893387915050520248661131455050547200000000⟩ +] + +def collectedFourData_15_140 : List CollectedFourTerm := [ + ⟨7, 4, 4, 5, 5, 5, 100693755990032188731829311891819704898463727616000000⟩, + ⟨7, 4, 5, 5, 6, 5, -179669702807498502788790120035969534687340134400000000⟩, + ⟨7, 4, 6, 5, 7, 5, 186066680374094998956716565501418208468486062080000000⟩, + ⟨7, 4, 7, 5, 8, 5, 25328789503166450174461567784429047090218270720000000⟩, + ⟨7, 4, 4, 6, 4, 5, -195428906102509641922159673841796723588938596352000000⟩, + ⟨7, 4, 5, 6, 5, 5, 364186100513545311967464906827769673165213532160000000⟩, + ⟨7, 4, 6, 6, 6, 5, -121158212690770147313487836387832195076293918720000000⟩, + ⟨7, 4, 7, 6, 7, 5, -83695976476922602663852480993269258213308497920000000⟩, + ⟨7, 4, 8, 6, 8, 5, 248382355657658148474491022561048490742088990720000000⟩, + ⟨7, 4, 4, 7, 3, 5, 711292441546190301585974931810989447446284730368000000⟩, + ⟨7, 4, 5, 7, 4, 5, 1101309463149527734700455315285359440902509035520000000⟩, + ⟨7, 4, 6, 7, 5, 5, 125209756513222531057555295155452727055194521600000000⟩, + ⟨7, 4, 7, 7, 6, 5, 209606690400245035953718963936003515145393274880000000⟩, + ⟨7, 4, 8, 7, 7, 5, 188074513840300283795374781853566637443288924160000000⟩, + ⟨7, 5, 3, 1, 8, 6, -513733953305188724909621460933360218265354240000000⟩, + ⟨7, 5, 3, 2, 7, 6, 18458458225431202353237928282449108839348305920000000⟩, + ⟨7, 5, 4, 2, 8, 6, -6173771896973308663820233450384729978762690560000000⟩, + ⟨7, 5, 3, 3, 6, 6, -20268385982046189839332202628619867003111342080000000⟩, + ⟨7, 5, 4, 3, 7, 6, -37219445885258120621148197950094868314157219840000000⟩, + ⟨7, 5, 5, 3, 8, 6, 15390409371913843844520192460458599228689612800000000⟩, + ⟨7, 5, 3, 4, 5, 6, -37916439778489481894001170615249237325706690560000000⟩, + ⟨7, 5, 4, 4, 6, 6, 44132357518227815653452424216109608416848117760000000⟩, + ⟨7, 5, 5, 4, 7, 6, 9196267846192410091092068366934224796647424000000000⟩, + ⟨7, 5, 6, 4, 8, 6, -11634850360744620313793504459335663179792384000000000⟩ +] + +def collectedFourData_15_141 : List CollectedFourTerm := [ + ⟨7, 5, 3, 5, 4, 6, 38815027798112022603687869723480841614146928640000000⟩, + ⟨7, 5, 4, 5, 5, 6, 22896090684371015537872281590427312670176706560000000⟩, + ⟨7, 5, 5, 5, 6, 6, -20426955814031306207049693010063829973860352000000000⟩, + ⟨7, 5, 6, 5, 7, 6, 14102826089854994572114604509924499692034457600000000⟩, + ⟨7, 5, 7, 5, 8, 6, 1439836700120839182762165462494819237285068800000000⟩, + ⟨7, 5, 3, 6, 3, 6, 51633203070785795329688849985374206292876328960000000⟩, + ⟨7, 5, 4, 6, 4, 6, -44437293181450411620841873147813613806100152320000000⟩, + ⟨7, 5, 5, 6, 5, 6, 41404940660724903355822845462211679488888012800000000⟩, + ⟨7, 5, 6, 6, 6, 6, -9183122950870265253980631889894025764169318400000000⟩, + ⟨7, 5, 7, 6, 7, 6, -4757769358415583980350991112440624706276556800000000⟩, + ⟨7, 5, 8, 6, 8, 6, 11295605936277513534181814949067460053083095040000000⟩, + ⟨7, 5, 3, 7, 2, 6, 190060521073606103771717579285375933478359531520000000⟩, + ⟨7, 5, 4, 7, 3, 6, 161736108506682359454954930619237751206057082880000000⟩, + ⟨7, 5, 5, 7, 4, 6, 125209756513222531057555295155452727055194521600000000⟩, + ⟨7, 5, 6, 7, 5, 6, 9490207582082008724709375136980651057610752000000000⟩, + ⟨7, 5, 7, 7, 6, 6, 11915271568402827904267032414553286760411955200000000⟩, + ⟨7, 5, 8, 7, 7, 6, 8553005262278190654905478519266876845058949120000000⟩, + ⟨7, 6, 2, 0, 8, 7, -148332470659980881007706386023561452296962310144000000⟩, + ⟨7, 6, 2, 1, 7, 7, -67997435902699208819672124888264795216465100800000000⟩, + ⟨7, 6, 3, 1, 8, 7, -2580040326661678603661321536702865138931204096000000⟩, + ⟨7, 6, 2, 2, 6, 7, -143242194842304427233392542911189390034131222528000000⟩, + ⟨7, 6, 3, 2, 7, 7, 92700835292701041220313966933259450734050541568000000⟩, + ⟨7, 6, 4, 2, 8, 7, -15502752309169621933440569575398856783835430912000000⟩, + ⟨7, 6, 2, 3, 5, 7, 35498698196910803448781736296031700335342911488000000⟩ +] + +def collectedFourData_15_142 : List CollectedFourTerm := [ + ⟨7, 6, 3, 3, 6, 7, -101790533511726284489675791835293414644233797632000000⟩, + ⟨7, 6, 4, 3, 7, 7, -93460506846159188232948749991632342705837703168000000⟩, + ⟨7, 6, 5, 3, 8, 7, 25764228460991427731364150441660928096248791040000000⟩, + ⟨7, 6, 2, 4, 4, 7, 4484497580289709924820451705427529559378493440000000⟩, + ⟨7, 6, 3, 4, 5, 7, -190421409841734560839349413501754504087888461824000000⟩, + ⟨7, 6, 4, 4, 6, 7, 110819288247468516635565910118789754371652452352000000⟩, + ⟨7, 6, 5, 4, 7, 7, 15394960592156573617297048408062889519428403200000000⟩, + ⟨7, 6, 6, 4, 8, 7, -14607941976711524941756495569896139043268198400000000⟩, + ⟨7, 6, 2, 5, 3, 7, 74780792666250470404924816893643644583853162496000000⟩, + ⟨7, 6, 3, 5, 4, 7, 194934238539868021291281193157349486113750777856000000⟩, + ⟨7, 6, 4, 5, 5, 7, 57493608227104282297703336763022408421172314112000000⟩, + ⟨7, 6, 5, 5, 6, 7, -34195630774818993635654836622963640823814553600000000⟩, + ⟨7, 6, 6, 5, 7, 7, 17706567668745725536063000006119668682860789760000000⟩, + ⟨7, 6, 7, 5, 8, 7, 1446210329770595430843363726388974275845423104000000⟩, + ⟨7, 6, 2, 6, 2, 7, -50044559309232213689261030753313674620317990912000000⟩, + ⟨7, 6, 3, 6, 3, 7, 259308821735986839681582316240005781675975901184000000⟩, + ⟨7, 6, 4, 6, 4, 7, -111585002001727861555193100965606721504688472064000000⟩, + ⟨7, 6, 5, 6, 5, 7, 69313708610211851115487905019567629132669911040000000⟩, + ⟨7, 6, 6, 6, 6, 7, -11529716590419087553364170777740078009381027840000000⟩, + ⟨7, 6, 7, 6, 7, 7, -4778830260562997187324513070364390937952518144000000⟩, + ⟨7, 6, 8, 6, 8, 7, 9454672871752056023058205966653060728525684736000000⟩, + ⟨7, 6, 2, 7, 1, 7, 738125398819962018041696304322808785376171261952000000⟩, + ⟨7, 6, 3, 7, 2, 7, 954509246899883376386610866248400192336516087808000000⟩, + ⟨7, 6, 4, 7, 3, 7, 406130137535095692479487116766586215524493950976000000⟩ +] + +def collectedFourData_15_143 : List CollectedFourTerm := [ + ⟨7, 6, 5, 7, 4, 7, 209606690400245035953718963936003515145393274880000000⟩, + ⟨7, 6, 6, 7, 5, 7, 11915271568402827904267032414553286760411955200000000⟩, + ⟨7, 6, 7, 7, 6, 7, 11968016110993592738463028048205981354154786816000000⟩, + ⟨7, 6, 8, 7, 7, 7, 7159055236293385973749039334623477779092471808000000⟩, + ⟨7, 7, 1, 0, 7, 8, 875683823283945976247251784865685567554208137216000000⟩, + ⟨7, 7, 2, 0, 8, 8, -532379138334486998207207942498775528384371884032000000⟩, + ⟨7, 7, 1, 1, 6, 8, 427777627770009294814995584972341434896105865216000000⟩, + ⟨7, 7, 2, 1, 7, 8, -244049169907072461755075082227874897060062822400000000⟩, + ⟨7, 7, 3, 1, 8, 8, -4630003261810935775463712723114510969779257344000000⟩, + ⟨7, 7, 1, 2, 5, 8, 254528509726901160111762329780024834802510200832000000⟩, + ⟨7, 7, 2, 2, 6, 8, -514109661384214672745515879494186738707840630784000000⟩, + ⟨7, 7, 3, 2, 7, 8, 166355992711615443616230835794199442089366781952000000⟩, + ⟨7, 7, 4, 2, 8, 8, -18546943631529939265810100157705631142365888512000000⟩, + ⟨7, 7, 1, 3, 4, 8, 138783583811502375351151935547986486047614697472000000⟩, + ⟨7, 7, 2, 3, 5, 8, 127408154627105142014659589535395515259015921664000000⟩, + ⟨7, 7, 3, 3, 6, 8, -182667882091041640175913309672641316043093966848000000⟩, + ⟨7, 7, 4, 3, 7, 8, -111812839274007556835072929439857279011618029568000000⟩, + ⟨7, 7, 5, 3, 8, 8, 23117557617167195740010599069199604500429537280000000⟩, + ⟨7, 7, 1, 4, 3, 8, -437380523584548701924295855793184414629116248064000000⟩, + ⟨7, 7, 2, 4, 4, 8, 16095282085137187046963859453560830686469816320000000⟩, + ⟨7, 7, 3, 4, 5, 8, -341720142733830718175535429678080150150144065536000000⟩, + ⟨7, 7, 4, 4, 6, 8, 132580270356016453526157352541951840625415421952000000⟩, + ⟨7, 7, 5, 4, 7, 8, 13813489080103543087852890900573587235038822400000000⟩, + ⟨7, 7, 6, 4, 8, 8, -10485854550658459017937130056196190626685911040000000⟩ +] + +def collectedFourData_15_144 : List CollectedFourTerm := [ + ⟨7, 7, 1, 5, 2, 8, -88586001115505034870061727234902123707503738880000000⟩, + ⟨7, 7, 2, 5, 3, 8, 268395273040977482737730108464558785807293349888000000⟩, + ⟨7, 7, 3, 5, 4, 8, 349818625294910396475386803320186747304997289984000000⟩, + ⟨7, 7, 4, 5, 5, 8, 68783316000646677920059179999356321164230131712000000⟩, + ⟨7, 7, 5, 5, 6, 8, -30682830882715825463412740737885339160621875200000000⟩, + ⟨7, 7, 6, 5, 7, 8, 12710106150603438741715471519186964287278022656000000⟩, + ⟨7, 7, 7, 5, 8, 8, 865097401115230553282668824179743300257841152000000⟩, + ⟨7, 7, 1, 6, 1, 8, -1954626008004123925535714105274713893157650563072000000⟩, + ⟨7, 7, 2, 6, 2, 8, -179614613340126844996195418715597197776609345536000000⟩, + ⟨7, 7, 3, 6, 3, 8, 465341831306733930504318215184464292271752216576000000⟩, + ⟨7, 7, 4, 6, 4, 8, -133496343163922646857522100392830605564800139264000000⟩, + ⟨7, 7, 5, 6, 5, 8, 62193349002559272005265186210419777419377377280000000⟩, + ⟨7, 7, 6, 6, 6, 8, -8276246672542202433503824390589079281052155904000000⟩, + ⟨7, 7, 7, 6, 7, 8, -2858611609723218809540721839019898880416284672000000⟩, + ⟨7, 7, 8, 6, 8, 8, 4847672427354010359386623953805522338205138944000000⟩, + ⟨7, 7, 1, 7, 0, 8, 12243067369604237369855418371536232497797830541312000000⟩, + ⟨7, 7, 2, 7, 1, 8, 2649201230574457387437394655686196276871252934656000000⟩, + ⟨7, 7, 3, 7, 2, 8, 1712911569988291312345389065525497094764140429312000000⟩, + ⟨7, 7, 4, 7, 3, 8, 485879708177598126907933291911178778623686475776000000⟩, + ⟨7, 7, 5, 7, 4, 8, 188074513840300283795374781853566637443288924160000000⟩, + ⟨7, 7, 6, 7, 5, 8, 8553005262278190654905478519266876845058949120000000⟩, + ⟨7, 7, 7, 7, 6, 8, 7159055236293385973749039334623477779092471808000000⟩, + ⟨7, 7, 8, 7, 7, 8, 3670645737365699000838743442177295408517087232000000⟩, + ⟨0, 7, 8, 7, 8, 0, -613411297185544067839541072561022856919305420800000000⟩ +] + +def collectedFourData_15_145 : List CollectedFourTerm := [ + ⟨0, 8, 7, 6, 8, 1, 7442768640399707599928351082701006527159861248000000⟩, + ⟨0, 8, 7, 7, 7, 1, -2630517373887974936047075211833472619657560064000000⟩, + ⟨0, 8, 8, 7, 8, 1, -70583168097992862347664064273381881791329075200000000⟩, + ⟨1, 6, 8, 7, 8, 0, -77174221849086147838732575477849501974554214400000000⟩, + ⟨1, 7, 7, 6, 8, 1, 78050042510100718858904074259512328445386293248000000⟩, + ⟨1, 7, 7, 7, 7, 1, -27585432622622653950713205322953356882491736064000000⟩, + ⟨1, 7, 8, 7, 8, 1, -740184135328714259727834388039430964285485875200000000⟩, + ⟨1, 8, 6, 5, 8, 2, -41425529171742392726282269266990499507420004352000000⟩, + ⟨1, 8, 6, 6, 7, 2, -39122134916962763653253356703248003957688107008000000⟩, + ⟨1, 8, 7, 6, 8, 2, -42918976634443667026919737792300128247058792448000000⟩, + ⟨1, 8, 6, 7, 6, 2, 42342663071386213022002791675738030585749176320000000⟩, + ⟨1, 8, 7, 7, 7, 2, 15168967243395726505622802466629023058219761664000000⟩, + ⟨1, 8, 8, 7, 8, 2, 203510110870521176766309347056059427122157977600000000⟩, + ⟨2, 5, 8, 7, 8, 0, 373249151096289242839151249324390504928274022400000000⟩, + ⟨2, 6, 7, 6, 8, 1, 92552839795868450747365230960285950136142528512000000⟩, + ⟨2, 6, 7, 7, 7, 1, -32711194563294583646035080129138780705040367616000000⟩, + ⟨2, 6, 8, 7, 8, 1, -877720773664617712899135281212684632052255948800000000⟩, + ⟨2, 7, 6, 5, 8, 2, -50354519124538982244141354077997550154299736064000000⟩, + ⟨2, 7, 6, 6, 7, 2, -47554643966087854435471275104052861276002451456000000⟩, + ⟨2, 7, 7, 6, 8, 2, -52169868990326163997449733096467558889250881536000000⟩, + ⟨2, 7, 6, 7, 6, 2, 51469334973913328757277096054155612858341130240000000⟩, + ⟨2, 7, 7, 7, 7, 2, 18438534556562872955057771239932403027015630848000000⟩, + ⟨2, 7, 8, 7, 8, 2, 247375325668910031004471569491453288312419123200000000⟩, + ⟨2, 8, 5, 4, 8, 3, -15038065567032894745560663893451581050658488320000000⟩ +] + +def collectedFourData_15_146 : List CollectedFourTerm := [ + ⟨2, 8, 5, 5, 7, 3, 511571514381155559201257356449474434857697280000000⟩, + ⟨2, 8, 6, 5, 8, 3, -21181973819185239201139122875154479401339453440000000⟩, + ⟨2, 8, 5, 6, 6, 3, -4865958004567388920883723211449273809392107520000000⟩, + ⟨2, 8, 6, 6, 7, 3, -20004187131229416267884672959003650617518325760000000⟩, + ⟨2, 8, 7, 6, 8, 3, -10972806595276268485902572660232609223441121280000000⟩, + ⟨2, 8, 5, 7, 5, 3, 5502913629284687715250390881972982676528824320000000⟩, + ⟨2, 8, 6, 7, 6, 3, 21650928752033609630683387946077696526018150400000000⟩, + ⟨2, 8, 7, 7, 7, 3, 3878148009668167783912885076435487215887319040000000⟩, + ⟨2, 8, 8, 7, 8, 3, 34686709110601256374580378015209342447386624000000000⟩, + ⟨3, 4, 8, 7, 8, 0, -237034730871339545452367968891449662816177356800000000⟩, + ⟨3, 5, 7, 6, 8, 1, 76462923830647113914390985735966761374074273792000000⟩, + ⟨3, 5, 7, 7, 7, 1, -27024493076811293655312950138425034243787718656000000⟩, + ⟨3, 5, 8, 7, 8, 1, -725132765340499484141893490258273055602953420800000000⟩, + ⟨3, 6, 6, 5, 8, 2, -20003478099493806976600322740717625610401218560000000⟩, + ⟨3, 6, 6, 6, 7, 2, -18891219609349668226819423810183199723869962240000000⟩, + ⟨3, 6, 7, 6, 8, 2, -20724631074728884774639098304183757163661885440000000⟩, + ⟨3, 6, 6, 7, 6, 2, 20446341914214676784013206297724201257769369600000000⟩, + ⟨3, 6, 7, 7, 7, 2, 7324761086025802213306605111383288711133265920000000⟩, + ⟨3, 6, 8, 7, 8, 2, 98270562313080066895743313915855834844233728000000000⟩, + ⟨3, 7, 5, 4, 8, 3, -37548386905004437266991595889357651859803734016000000⟩, + ⟨3, 7, 5, 5, 7, 3, 1277337505009473461158813707606127651810443264000000⟩, + ⟨3, 7, 6, 5, 8, 3, -52889046455419148109403403825045848869801295872000000⟩, + ⟨3, 7, 5, 6, 6, 3, -12149759089995062572259090713714599994878590976000000⟩, + ⟨3, 7, 6, 6, 7, 3, -49948243327929217793096724178398896130084569088000000⟩ +] + +def collectedFourData_15_147 : List CollectedFourTerm := [ + ⟨3, 7, 7, 6, 8, 3, -27397884763612596190354095100499604490854334464000000⟩, + ⟨3, 7, 5, 7, 5, 3, 13740166854317827787716356173337004797975330816000000⟩, + ⟨3, 7, 6, 7, 6, 3, 54059975068618116619176247319740599747760619520000000⟩, + ⟨3, 7, 7, 7, 7, 3, 9683306758624849070586476589211994112657457152000000⟩, + ⟨3, 7, 8, 7, 8, 3, 86608877208345353714746301552326461107680051200000000⟩, + ⟨3, 8, 4, 3, 8, 4, 2203005503042162488798157864397539938279410892800000⟩, + ⟨3, 8, 4, 4, 7, 4, 5020177245528279439759506358943310336226020556800000⟩, + ⟨3, 8, 5, 4, 8, 4, -21812629262319291934748544302943866350215364608000000⟩, + ⟨3, 8, 4, 5, 6, 4, -4604902119155662990515371090050284688310167142400000⟩, + ⟨3, 8, 5, 5, 7, 4, 742031595394957044082944638831809430953132032000000⟩, + ⟨3, 8, 6, 5, 8, 4, -15362166759497758009280831190094876705258733568000000⟩, + ⟨3, 8, 4, 6, 5, 4, 7471838890323291788910968975429470434507305779200000⟩, + ⟨3, 8, 5, 6, 6, 4, -7058044632570742254560763570672131762540249088000000⟩, + ⟨3, 8, 6, 6, 7, 4, -14507980286511650846960107679700859274680860672000000⟩, + ⟨3, 8, 7, 6, 8, 4, -5305331353136215094552015757239081991137132544000000⟩, + ⟨3, 8, 4, 7, 4, 4, 30900636749051553870795216840885919621252015718400000⟩, + ⟨3, 8, 5, 7, 5, 4, 7981945172608667298685339604868308558841643008000000⟩, + ⟨3, 8, 6, 7, 6, 4, 15702275001656979332355873445118873063789690880000000⟩, + ⟨3, 8, 7, 7, 7, 4, 1875077269351735549270116796310550365803118592000000⟩, + ⟨3, 8, 8, 7, 8, 4, 12578218966841852652331195650069639679338086400000000⟩, + ⟨4, 3, 8, 7, 8, 0, -909679473825968213505920120113324255922985369600000000⟩, + ⟨4, 4, 7, 6, 8, 1, -86121293123058101939645395912107205339952185344000000⟩, + ⟨4, 4, 7, 7, 7, 1, 30438076039635834155613583437427102473353428992000000⟩, + ⟨4, 4, 8, 7, 8, 1, 816727484490888933846585943515736875514567065600000000⟩ +] + +def collectedFourData_15_148 : List CollectedFourTerm := [ + ⟨4, 5, 6, 5, 8, 2, -9289999918521358298289477252309565845647917056000000⟩, + ⟨4, 5, 6, 6, 7, 2, -8773445685731450920323513973800894522955137024000000⟩, + ⟨4, 5, 7, 6, 8, 2, -9624917228793757410139654583741524264662073344000000⟩, + ⟨4, 5, 6, 7, 6, 2, 9495674390841102003837908220578910004272168960000000⟩, + ⟨4, 5, 7, 7, 7, 2, 3401759911647068297450053149578399377357012992000000⟩, + ⟨4, 5, 8, 7, 8, 2, 45638738990329081631161471450087272347389132800000000⟩, + ⟨4, 6, 5, 4, 8, 3, -86249115982324806559079681177276647069559291904000000⟩, + ⟨4, 6, 5, 5, 7, 3, 2934060280588302704110229755645113985627324416000000⟩, + ⟨4, 6, 6, 5, 8, 3, -121486803506864837380972033428038459505946656768000000⟩, + ⟨4, 6, 5, 6, 6, 3, -27908149118667589620036944855372055524507910144000000⟩, + ⟨4, 6, 6, 6, 7, 3, -114731741813648470686544364375245338014983913472000000⟩, + ⟨4, 6, 7, 6, 8, 3, -62933285166832208101888068411077037287031177216000000⟩, + ⟨4, 6, 5, 7, 5, 3, 31561335714174357727898429855788431514590511104000000⟩, + ⟨4, 6, 6, 7, 6, 3, 124176441227449858121033246873714828201825402880000000⟩, + ⟨4, 6, 7, 7, 7, 3, 22242677157610523220102195043441641247985369088000000⟩, + ⟨4, 6, 8, 7, 8, 3, 198941677956501369040767225494931474882546892800000000⟩, + ⟨4, 7, 4, 3, 8, 4, 5020177245528279439759506358943310336226020556800000⟩, + ⟨4, 7, 4, 4, 7, 4, 11439907681446026733221553441102561434330254540800000⟩, + ⟨4, 7, 5, 4, 8, 4, -49706305743051912522901800819784159517000859648000000⟩, + ⟨4, 7, 4, 5, 6, 4, -10493584698062271441472773621905080648177444454400000⟩, + ⟨4, 7, 5, 5, 7, 4, 1690930923922216058040610356029913755855880192000000⟩, + ⟨4, 7, 6, 5, 8, 4, -35007084594906508240265073920348996543245713408000000⟩, + ⟨4, 7, 4, 6, 5, 4, 17026718965366274960000784172227318301469127475200000⟩, + ⟨4, 7, 5, 6, 6, 4, -16083770564088561056652739655969887547742486528000000⟩ +] + +def collectedFourData_15_149 : List CollectedFourTerm := [ + ⟨4, 7, 6, 6, 7, 4, -33060576749510153861033086694757022865956012032000000⟩, + ⟨4, 7, 7, 6, 8, 4, -12089712759329612759156469283656542823345291264000000⟩, + ⟨4, 7, 4, 7, 4, 4, 70415926453977017793101296834864191822344119910400000⟩, + ⟨4, 7, 5, 7, 5, 4, 18189141822501124682062700662355996199824130048000000⟩, + ⟨4, 7, 6, 7, 6, 4, 35782118363976338562899081307060454072548065280000000⟩, + ⟨4, 7, 7, 7, 7, 4, 4272899104522449036493509853604043692338839552000000⟩, + ⟨4, 7, 8, 7, 8, 4, 28663064417866407179561369327795899820566118400000000⟩, + ⟨4, 8, 3, 2, 8, 5, -15038065567032894745560663893451581050658488320000000⟩, + ⟨4, 8, 3, 3, 7, 5, -37548386905004437266991595889357651859803734016000000⟩, + ⟨4, 8, 4, 3, 8, 5, -21812629262319291934748544302943866350215364608000000⟩, + ⟨4, 8, 3, 4, 6, 5, -86249115982324806559079681177276647069559291904000000⟩, + ⟨4, 8, 4, 4, 7, 5, -49706305743051912522901800819784159517000859648000000⟩, + ⟨4, 8, 5, 4, 8, 5, 107986746896083871886139369740324084810975805440000000⟩, + ⟨4, 8, 3, 5, 5, 5, -28345942428298953001696315253087911743238176768000000⟩, + ⟨4, 8, 4, 5, 6, 5, 45594540084309791259435189856483298779399716864000000⟩, + ⟨4, 8, 5, 5, 7, 5, -3673540549246584870246801963958551422183669760000000⟩, + ⟨4, 8, 6, 5, 8, 5, 50701832523510856671964765504259230395436892160000000⟩, + ⟨4, 8, 3, 6, 4, 5, 133736428739031438785194648805942548853352824832000000⟩, + ⟨4, 8, 4, 6, 5, 5, -73980955289189724648512141989731059897374605312000000⟩, + ⟨4, 8, 5, 6, 6, 5, 34941926081112860111454086781904404657041571840000000⟩, + ⟨4, 8, 6, 6, 7, 5, 47882645609632703330243151693100103236205936640000000⟩, + ⟨4, 8, 7, 6, 8, 5, 13132425879090532998035048276523621003779112960000000⟩, + ⟨4, 8, 3, 7, 3, 5, -238346081027967710568059882461850266876778643456000000⟩, + ⟨4, 8, 4, 7, 4, 5, -305956627183132781277901671735540592019949748224000000⟩ +] + +def collectedFourData_15_150 : List CollectedFourTerm := [ + ⟨4, 8, 5, 7, 5, 5, -39515836570050514276422162482330822424070717440000000⟩, + ⟨4, 8, 6, 7, 6, 5, -51824337662518101975617881838666202612341145600000000⟩, + ⟨4, 8, 7, 7, 7, 5, -4641427955818937761960124626679779829250785280000000⟩, + ⟨4, 8, 8, 7, 8, 5, -24908156309652502711265635728812944843918540800000000⟩, + ⟨5, 2, 8, 7, 8, 0, 1535273508271255093092444632186669371636265779200000000⟩, + ⟨5, 3, 7, 6, 8, 1, -164469722602081230766977787854218069452850724864000000⟩, + ⟨5, 3, 7, 7, 7, 1, 58128968356602825218397717824212204095748964352000000⟩, + ⟨5, 3, 8, 7, 8, 1, 1559741359477420901379906098823611727996361113600000000⟩, + ⟨5, 4, 6, 5, 8, 2, 49257747040880903136082018925343662057069740032000000⟩, + ⟨5, 4, 6, 6, 7, 2, 46518855980081905425063983915411973232266313728000000⟩, + ⟨5, 4, 7, 6, 8, 2, 51033556760331992750285918450807519296270368768000000⟩, + ⟨5, 4, 6, 7, 6, 2, -50348281079540518737016516752746020529630085120000000⟩, + ⟨5, 4, 7, 7, 7, 2, -18036924724579632719323340866766963693190119424000000⟩, + ⟨5, 4, 8, 7, 8, 2, -241987242213908506176400705907045551247563161600000000⟩, + ⟨5, 5, 5, 4, 8, 3, -28345942428298953001696315253087911743238176768000000⟩, + ⟨5, 5, 5, 5, 7, 3, 964284710022519179567647746200418270861852672000000⟩, + ⟨5, 5, 6, 5, 8, 3, -39926878076169190200648713804638989304102649856000000⟩, + ⟨5, 5, 5, 6, 6, 3, -9172068364854333614179393517156856736511950848000000⟩, + ⟨5, 5, 6, 6, 7, 3, -37706813700149859849079059105627023225571508224000000⟩, + ⟨5, 5, 7, 6, 8, 3, -20683148549932093125300082631827628540949430272000000⟩, + ⟨5, 5, 5, 7, 5, 3, 10372695359539005138809443286407199229286023168000000⟩, + ⟨5, 5, 6, 7, 6, 3, 40810832828775678305319214756432442278501416960000000⟩, + ⟨5, 5, 7, 7, 7, 3, 7310099807748470332384535636238437342873911296000000⟩, + ⟨5, 5, 8, 7, 8, 3, 65382575644019683391236385698735340218063257600000000⟩ +] + +def collectedFourData_15_151 : List CollectedFourTerm := [ + ⟨5, 6, 4, 3, 8, 4, -4604902119155662990515371090050284688310167142400000⟩, + ⟨5, 6, 4, 4, 7, 4, -10493584698062271441472773621905080648177444454400000⟩, + ⟨5, 6, 5, 4, 8, 4, 45594540084309791259435189856483298779399716864000000⟩, + ⟨5, 6, 4, 5, 6, 4, 9625542695069009546053508909724676211080377139200000⟩, + ⟨5, 6, 5, 5, 7, 4, -1551055075167144895314198588585610272892256256000000⟩, + ⟨5, 6, 6, 5, 8, 4, 32111256266925457411631689706043882134562668544000000⟩, + ⟨5, 6, 4, 6, 5, 4, -15618248203432163430780199633592264606994766233600000⟩, + ⟨5, 6, 5, 6, 6, 4, 14753301633036469017521050926703559055406792704000000⟩, + ⟨5, 6, 6, 6, 7, 4, 30325765901978082319821372592126934212858085376000000⟩, + ⟨5, 6, 7, 6, 8, 4, 11089637114906639989456993803715941123439460352000000⟩, + ⟨5, 6, 4, 7, 4, 4, -64591035951780615391079993838936740020624765747200000⟩, + ⟨5, 6, 5, 7, 5, 4, -16684514037560488845028894847802609233049944064000000⟩, + ⟨5, 6, 6, 7, 6, 4, -32822178306338688704666980944137447181165527040000000⟩, + ⟨5, 6, 7, 7, 7, 4, -3919439728722805459419202680134918563468148736000000⟩, + ⟨5, 6, 8, 7, 8, 4, -26292021102820397335663333573025897016144691200000000⟩, + ⟨5, 7, 3, 2, 8, 5, 511571514381155559201257356449474434857697280000000⟩, + ⟨5, 7, 3, 3, 7, 5, 1277337505009473461158813707606127651810443264000000⟩, + ⟨5, 7, 4, 3, 8, 5, 742031595394957044082944638831809430953132032000000⟩, + ⟨5, 7, 3, 4, 6, 5, 2934060280588302704110229755645113985627324416000000⟩, + ⟨5, 7, 4, 4, 7, 5, 1690930923922216058040610356029913755855880192000000⟩, + ⟨5, 7, 5, 4, 8, 5, -3673540549246584870246801963958551422183669760000000⟩, + ⟨5, 7, 3, 5, 5, 5, 964284710022519179567647746200418270861852672000000⟩, + ⟨5, 7, 4, 5, 6, 5, -1551055075167144895314198588585610272892256256000000⟩, + ⟨5, 7, 5, 5, 7, 5, 124968114651560927681089369789801853658071040000000⟩ +] + +def collectedFourData_15_152 : List CollectedFourTerm := [ + ⟨5, 7, 6, 5, 8, 5, -1724797190857695514023308601006061311901040640000000⟩, + ⟨5, 7, 3, 6, 4, 5, -4549504527227079121079799538941389392972873728000000⟩, + ⟨5, 7, 4, 6, 5, 5, 2516716605866130075690109403664012678317211648000000⟩, + ⟨5, 7, 5, 6, 6, 5, -1188669776776097031446042388950161454121615360000000⟩, + ⟨5, 7, 6, 6, 7, 5, -1628892853133708482253427416314384621303234560000000⟩, + ⟨5, 7, 7, 6, 8, 5, -446744627127607368786624482182802289029283840000000⟩, + ⟨5, 7, 3, 7, 3, 5, 8108161589984929204797110684865290146387329024000000⟩, + ⟨5, 7, 4, 7, 4, 5, 10408166822078033270176351860993037068398493696000000⟩, + ⟨5, 7, 5, 7, 5, 5, 1344267071191362767833221315483423133673717760000000⟩, + ⟨5, 7, 6, 7, 6, 5, 1762983063322664923899340100393827851200102400000000⟩, + ⟨5, 7, 7, 7, 7, 5, 157894133235769212111450053520025413872517120000000⟩, + ⟨5, 7, 8, 7, 8, 5, 847336593059262922891621431940833432777523200000000⟩, + ⟨5, 8, 2, 1, 8, 6, -41425529171742392726282269266990499507420004352000000⟩, + ⟨5, 8, 2, 2, 7, 6, -50354519124538982244141354077997550154299736064000000⟩, + ⟨5, 8, 3, 2, 8, 6, -21181973819185239201139122875154479401339453440000000⟩, + ⟨5, 8, 2, 3, 6, 6, -20003478099493806976600322740717625610401218560000000⟩, + ⟨5, 8, 3, 3, 7, 6, -52889046455419148109403403825045848869801295872000000⟩, + ⟨5, 8, 4, 3, 8, 6, -15362166759497758009280831190094876705258733568000000⟩, + ⟨5, 8, 2, 4, 5, 6, -9289999918521358298289477252309565845647917056000000⟩, + ⟨5, 8, 3, 4, 6, 6, -121486803506864837380972033428038459505946656768000000⟩, + ⟨5, 8, 4, 4, 7, 6, -35007084594906508240265073920348996543245713408000000⟩, + ⟨5, 8, 5, 4, 8, 6, 50701832523510856671964765504259230395436892160000000⟩, + ⟨5, 8, 2, 5, 4, 6, 49257747040880903136082018925343662057069740032000000⟩, + ⟨5, 8, 3, 5, 5, 6, -39926878076169190200648713804638989304102649856000000⟩ +] + +def collectedFourData_15_153 : List CollectedFourTerm := [ + ⟨5, 8, 4, 5, 6, 6, 32111256266925457411631689706043882134562668544000000⟩, + ⟨5, 8, 5, 5, 7, 6, -1724797190857695514023308601006061311901040640000000⟩, + ⟨5, 8, 6, 5, 8, 6, 17854106372765697520970638255824235585528135680000000⟩, + ⟨5, 8, 2, 6, 3, 6, 24854585059654717537286345893922875747482992640000000⟩, + ⟨5, 8, 3, 6, 4, 6, 188375394401237869554235945038760297431086137344000000⟩, + ⟨5, 8, 4, 6, 5, 6, -52103199413138409656153961631037995109163466752000000⟩, + ⟨5, 8, 5, 6, 6, 6, 16405899197225727947007241466904259319310581760000000⟩, + ⟨5, 8, 6, 6, 7, 6, 16861359946455577895599072613788539874411806720000000⟩, + ⟨5, 8, 7, 6, 8, 6, 3699554306547304204688294204243797759978635264000000⟩, + ⟨5, 8, 2, 7, 2, 6, -120211524792312738571332733068759199268443521024000000⟩, + ⟨5, 8, 3, 7, 3, 6, -335724061431655555441886206635211812054711140352000000⟩, + ⟨5, 8, 4, 7, 4, 6, -215478687664680575847858971854152078423547183104000000⟩, + ⟨5, 8, 5, 7, 5, 6, -18553437207707796023172070938846075382042460160000000⟩, + ⟨5, 8, 6, 7, 6, 6, -18249384514764178064849363277493003300424908800000000⟩, + ⟨5, 8, 7, 7, 7, 6, -1307543247574618668009134501069818663431831552000000⟩, + ⟨5, 8, 8, 7, 8, 6, -5847426679575389462254320102159768434088345600000000⟩, + ⟨6, 1, 8, 7, 8, 0, -1115935551326969559851315781037644170089463808000000000⟩, + ⟨6, 2, 7, 6, 8, 1, 409845155225268212442764774371601549457050566656000000⟩, + ⟨6, 2, 7, 7, 7, 1, -144852655444894130104866679302956307409438507008000000⟩, + ⟨6, 2, 8, 7, 8, 1, -3886748451159637426109193301901971371069957734400000000⟩, + ⟨6, 3, 6, 5, 8, 2, 24854585059654717537286345893922875747482992640000000⟩, + ⟨6, 3, 6, 6, 7, 2, 23472589233023438774218212595689740504200642560000000⟩, + ⟨6, 3, 7, 6, 8, 2, 25750627131681025971984115297799845363171983360000000⟩, + ⟨6, 3, 6, 7, 6, 2, -25404849183627316359364083074121869916792422400000000⟩ +] + +def collectedFourData_15_154 : List CollectedFourTerm := [ + ⟨6, 3, 7, 7, 7, 2, -9101112144036795600625206100451033786854932480000000⟩, + ⟨6, 3, 8, 7, 8, 2, -122102468266873808763266947108148921952632832000000000⟩, + ⟨6, 4, 5, 4, 8, 3, 133736428739031438785194648805942548853352824832000000⟩, + ⟨6, 4, 5, 5, 7, 3, -4549504527227079121079799538941389392972873728000000⟩, + ⟨6, 4, 6, 5, 8, 3, 188375394401237869554235945038760297431086137344000000⟩, + ⟨6, 4, 5, 6, 6, 3, 43273906675308136764957606750531179038220746752000000⟩, + ⟨6, 4, 6, 6, 7, 3, 177901109343664332341178340255526698207282200576000000⟩, + ⟨6, 4, 7, 6, 8, 3, 97583293592852632391941458843048711467594416128000000⟩, + ⟨6, 4, 5, 7, 5, 3, -48938476372468837259032911501617562180944658432000000⟩, + ⟨6, 4, 6, 7, 6, 3, -192545901417524785431682956513867305915032535040000000⟩, + ⟨6, 4, 7, 7, 7, 3, -34489121132136171465326713343420348159339003904000000⟩, + ⟨6, 4, 8, 7, 8, 3, -308475620117722171489208482519911006766261862400000000⟩, + ⟨6, 5, 4, 3, 8, 4, 7471838890323291788910968975429470434507305779200000⟩, + ⟨6, 5, 4, 4, 7, 4, 17026718965366274960000784172227318301469127475200000⟩, + ⟨6, 5, 5, 4, 8, 4, -73980955289189724648512141989731059897374605312000000⟩, + ⟨6, 5, 4, 5, 6, 4, -15618248203432163430780199633592264606994766233600000⟩, + ⟨6, 5, 5, 5, 7, 4, 2516716605866130075690109403664012678317211648000000⟩, + ⟨6, 5, 6, 5, 8, 4, -52103199413138409656153961631037995109163466752000000⟩, + ⟨6, 5, 4, 6, 5, 4, 25341914183080060263309212491407942460761754828800000⟩, + ⟨6, 5, 5, 6, 6, 4, -23938466019469736759835808565078768286833836032000000⟩, + ⟨6, 5, 6, 6, 7, 4, -49206091938993560851105351352923225181921476608000000⟩, + ⟨6, 5, 7, 6, 8, 4, -17993863871730873016739898122017466003295830016000000⟩, + ⟨6, 5, 4, 7, 4, 4, 104804358899006200236327406289011865783608383897600000⟩, + ⟨6, 5, 5, 7, 5, 4, 27072019692537407465659053267049935612162342912000000⟩ +] + +def collectedFourData_15_155 : List CollectedFourTerm := [ + ⟨6, 5, 6, 7, 6, 4, 53256729891013083371868529317172594780479160320000000⟩, + ⟨6, 5, 7, 7, 7, 4, 6359618822629587636312551373613664221148479488000000⟩, + ⟨6, 5, 8, 7, 8, 4, 42661003577916308070597674947210036934973849600000000⟩, + ⟨6, 6, 3, 2, 8, 5, -4865958004567388920883723211449273809392107520000000⟩, + ⟨6, 6, 3, 3, 7, 5, -12149759089995062572259090713714599994878590976000000⟩, + ⟨6, 6, 4, 3, 8, 5, -7058044632570742254560763570672131762540249088000000⟩, + ⟨6, 6, 3, 4, 6, 5, -27908149118667589620036944855372055524507910144000000⟩, + ⟨6, 6, 4, 4, 7, 5, -16083770564088561056652739655969887547742486528000000⟩, + ⟨6, 6, 5, 4, 8, 5, 34941926081112860111454086781904404657041571840000000⟩, + ⟨6, 6, 3, 5, 5, 5, -9172068364854333614179393517156856736511950848000000⟩, + ⟨6, 6, 4, 5, 6, 5, 14753301633036469017521050926703559055406792704000000⟩, + ⟨6, 6, 5, 5, 7, 5, -1188669776776097031446042388950161454121615360000000⟩, + ⟨6, 6, 6, 5, 8, 5, 16405899197225727947007241466904259319310581760000000⟩, + ⟨6, 6, 3, 6, 4, 5, 43273906675308136764957606750531179038220746752000000⟩, + ⟨6, 6, 4, 6, 5, 5, -23938466019469736759835808565078768286833836032000000⟩, + ⟨6, 6, 5, 6, 6, 5, 11306370766339219302185034676088283347539722240000000⟩, + ⟨6, 6, 6, 6, 7, 5, 15493677803535948255140038577801269143970775040000000⟩, + ⟨6, 6, 7, 6, 8, 5, 4249338622770531195792084323182323222246850560000000⟩, + ⟨6, 6, 3, 7, 3, 5, -77123085789560050966602398374853397876169506816000000⟩, + ⟨6, 6, 4, 7, 4, 5, -99000239921546602449787307578548500715918065664000000⟩, + ⟨6, 6, 5, 7, 5, 5, -12786378700645111359552779140526038608343203840000000⟩, + ⟨6, 6, 6, 7, 6, 5, -16769114987313417686883443220773853736835481600000000⟩, + ⟨6, 6, 7, 7, 7, 5, -1501854970213178499282519229475427551627182080000000⟩, + ⟨6, 6, 8, 7, 8, 5, -8059683077833742812015671716352310985411788800000000⟩ +] + +def collectedFourData_15_156 : List CollectedFourTerm := [ + ⟨6, 7, 2, 1, 8, 6, -39122134916962763653253356703248003957688107008000000⟩, + ⟨6, 7, 2, 2, 7, 6, -47554643966087854435471275104052861276002451456000000⟩, + ⟨6, 7, 3, 2, 8, 6, -20004187131229416267884672959003650617518325760000000⟩, + ⟨6, 7, 2, 3, 6, 6, -18891219609349668226819423810183199723869962240000000⟩, + ⟨6, 7, 3, 3, 7, 6, -49948243327929217793096724178398896130084569088000000⟩, + ⟨6, 7, 4, 3, 8, 6, -14507980286511650846960107679700859274680860672000000⟩, + ⟨6, 7, 2, 4, 5, 6, -8773445685731450920323513973800894522955137024000000⟩, + ⟨6, 7, 3, 4, 6, 6, -114731741813648470686544364375245338014983913472000000⟩, + ⟨6, 7, 4, 4, 7, 6, -33060576749510153861033086694757022865956012032000000⟩, + ⟨6, 7, 5, 4, 8, 6, 47882645609632703330243151693100103236205936640000000⟩, + ⟨6, 7, 2, 5, 4, 6, 46518855980081905425063983915411973232266313728000000⟩, + ⟨6, 7, 3, 5, 5, 6, -37706813700149859849079059105627023225571508224000000⟩, + ⟨6, 7, 4, 5, 6, 6, 30325765901978082319821372592126934212858085376000000⟩, + ⟨6, 7, 5, 5, 7, 6, -1628892853133708482253427416314384621303234560000000⟩, + ⟨6, 7, 6, 5, 8, 6, 16861359946455577895599072613788539874411806720000000⟩, + ⟨6, 7, 2, 6, 3, 6, 23472589233023438774218212595689740504200642560000000⟩, + ⟨6, 7, 3, 6, 4, 6, 177901109343664332341178340255526698207282200576000000⟩, + ⟨6, 7, 4, 6, 5, 6, -49206091938993560851105351352923225181921476608000000⟩, + ⟨6, 7, 5, 6, 6, 6, 15493677803535948255140038577801269143970775040000000⟩, + ⟨6, 7, 6, 6, 7, 6, 15923813452663774921155619523716064253711482880000000⟩, + ⟨6, 7, 7, 6, 8, 6, 3493847045702967419023426110364386866554208256000000⟩, + ⟨6, 7, 2, 7, 2, 6, -113527372746433980104978759152433576842201399296000000⟩, + ⟨6, 7, 3, 7, 3, 6, -317056710893126929493082454608047110993905451008000000⟩, + ⟨6, 7, 4, 7, 4, 6, -203497371285194403839015862890312701076482031616000000⟩ +] + +def collectedFourData_15_157 : List CollectedFourTerm := [ + ⟨6, 7, 5, 7, 5, 6, -17521805710775701825229305254550489814154608640000000⟩, + ⟨6, 7, 6, 7, 6, 6, -17234659337197928839706785975438810320941875200000000⟩, + ⟨6, 7, 7, 7, 7, 6, -1234839587185563063890965041276124368425975808000000⟩, + ⟨6, 7, 8, 7, 8, 6, -5522290723842888180493397222833690700572262400000000⟩, + ⟨6, 8, 1, 0, 8, 7, 7442768640399707599928351082701006527159861248000000⟩, + ⟨6, 8, 1, 1, 7, 7, 78050042510100718858904074259512328445386293248000000⟩, + ⟨6, 8, 2, 1, 8, 7, -42918976634443667026919737792300128247058792448000000⟩, + ⟨6, 8, 1, 2, 6, 7, 92552839795868450747365230960285950136142528512000000⟩, + ⟨6, 8, 2, 2, 7, 7, -52169868990326163997449733096467558889250881536000000⟩, + ⟨6, 8, 3, 2, 8, 7, -10972806595276268485902572660232609223441121280000000⟩, + ⟨6, 8, 1, 3, 5, 7, 76462923830647113914390985735966761374074273792000000⟩, + ⟨6, 8, 2, 3, 6, 7, -20724631074728884774639098304183757163661885440000000⟩, + ⟨6, 8, 3, 3, 7, 7, -27397884763612596190354095100499604490854334464000000⟩, + ⟨6, 8, 4, 3, 8, 7, -5305331353136215094552015757239081991137132544000000⟩, + ⟨6, 8, 1, 4, 4, 7, -86121293123058101939645395912107205339952185344000000⟩, + ⟨6, 8, 2, 4, 5, 7, -9624917228793757410139654583741524264662073344000000⟩, + ⟨6, 8, 3, 4, 6, 7, -62933285166832208101888068411077037287031177216000000⟩, + ⟨6, 8, 4, 4, 7, 7, -12089712759329612759156469283656542823345291264000000⟩, + ⟨6, 8, 5, 4, 8, 7, 13132425879090532998035048276523621003779112960000000⟩, + ⟨6, 8, 1, 5, 3, 7, -164469722602081230766977787854218069452850724864000000⟩, + ⟨6, 8, 2, 5, 4, 7, 51033556760331992750285918450807519296270368768000000⟩, + ⟨6, 8, 3, 5, 5, 7, -20683148549932093125300082631827628540949430272000000⟩, + ⟨6, 8, 4, 5, 6, 7, 11089637114906639989456993803715941123439460352000000⟩, + ⟨6, 8, 5, 5, 7, 7, -446744627127607368786624482182802289029283840000000⟩ +] + +def collectedFourData_15_158 : List CollectedFourTerm := [ + ⟨6, 8, 6, 5, 8, 7, 3699554306547304204688294204243797759978635264000000⟩, + ⟨6, 8, 1, 6, 2, 7, 409845155225268212442764774371601549457050566656000000⟩, + ⟨6, 8, 2, 6, 3, 7, 25750627131681025971984115297799845363171983360000000⟩, + ⟨6, 8, 3, 6, 4, 7, 97583293592852632391941458843048711467594416128000000⟩, + ⟨6, 8, 4, 6, 5, 7, -17993863871730873016739898122017466003295830016000000⟩, + ⟨6, 8, 5, 6, 6, 7, 4249338622770531195792084323182323222246850560000000⟩, + ⟨6, 8, 6, 6, 7, 7, 3493847045702967419023426110364386866554208256000000⟩, + ⟨6, 8, 7, 6, 8, 7, 638821390316596431999719551463440747704877056000000⟩, + ⟨6, 8, 1, 7, 1, 7, -1172802464787644297254628681861169930550332358656000000⟩, + ⟨6, 8, 2, 7, 2, 7, -124545316062527661045441254474900110438695960576000000⟩, + ⟨6, 8, 3, 7, 3, 7, -173913688446429363700599520554075921220815028224000000⟩, + ⟨6, 8, 4, 7, 4, 7, -74415663851148711963547186142640802703534456832000000⟩, + ⟨6, 8, 5, 7, 5, 7, -4805578552207157177055022025914124115860520960000000⟩, + ⟨6, 8, 6, 7, 6, 7, -3781459999388091797635616569372130981173002240000000⟩, + ⟨6, 8, 7, 7, 7, 7, -225780330845919208052059962967781320276574208000000⟩, + ⟨6, 8, 8, 7, 8, 7, -865462068060436049002710589064313526498099200000000⟩, + ⟨7, 0, 8, 7, 8, 0, 10884042434552915293747245526142109512785880678400000000⟩, + ⟨7, 1, 7, 6, 8, 1, -1172802464787644297254628681861169930550332358656000000⟩, + ⟨7, 1, 7, 7, 7, 1, 414506672022100744261492386525487394108901163008000000⟩, + ⟨7, 1, 8, 7, 8, 1, 11122220442069393172958894007393570611322578534400000000⟩, + ⟨7, 2, 6, 5, 8, 2, -120211524792312738571332733068759199268443521024000000⟩, + ⟨7, 2, 6, 6, 7, 2, -113527372746433980104978759152433576842201399296000000⟩, + ⟨7, 2, 7, 6, 8, 2, -124545316062527661045441254474900110438695960576000000⟩, + ⟨7, 2, 6, 7, 6, 2, 122872928683083275125787515031282258223657123840000000⟩ +] + +def collectedFourData_15_159 : List CollectedFourTerm := [ + ⟨7, 2, 7, 7, 7, 2, 44018379929280403474211360244859689035070701568000000⟩, + ⟨7, 2, 8, 7, 8, 2, 590560005569845159952401127891203512211813171200000000⟩, + ⟨7, 3, 5, 4, 8, 3, -238346081027967710568059882461850266876778643456000000⟩, + ⟨7, 3, 5, 5, 7, 3, 8108161589984929204797110684865290146387329024000000⟩, + ⟨7, 3, 6, 5, 8, 3, -335724061431655555441886206635211812054711140352000000⟩, + ⟨7, 3, 5, 6, 6, 3, -77123085789560050966602398374853397876169506816000000⟩, + ⟨7, 3, 6, 6, 7, 3, -317056710893126929493082454608047110993905451008000000⟩, + ⟨7, 3, 7, 6, 8, 3, -173913688446429363700599520554075921220815028224000000⟩, + ⟨7, 3, 5, 7, 5, 3, 87218525011005294462766675352764546397824352256000000⟩, + ⟨7, 3, 6, 7, 6, 3, 343156770773485914670223749805400888696970936320000000⟩, + ⟨7, 3, 7, 7, 7, 3, 61466774142626591257283040044549265710049656832000000⟩, + ⟨7, 3, 8, 7, 8, 3, 549767597661840171060260892746230420596798259200000000⟩, + ⟨7, 4, 4, 3, 8, 4, 30900636749051553870795216840885919621252015718400000⟩, + ⟨7, 4, 4, 4, 7, 4, 70415926453977017793101296834864191822344119910400000⟩, + ⟨7, 4, 5, 4, 8, 4, -305956627183132781277901671735540592019949748224000000⟩, + ⟨7, 4, 4, 5, 6, 4, -64591035951780615391079993838936740020624765747200000⟩, + ⟨7, 4, 5, 5, 7, 4, 10408166822078033270176351860993037068398493696000000⟩, + ⟨7, 4, 6, 5, 8, 4, -215478687664680575847858971854152078423547183104000000⟩, + ⟨7, 4, 4, 6, 5, 4, 104804358899006200236327406289011865783608383897600000⟩, + ⟨7, 4, 5, 6, 6, 4, -99000239921546602449787307578548500715918065664000000⟩, + ⟨7, 4, 6, 6, 7, 4, -203497371285194403839015862890312701076482031616000000⟩, + ⟨7, 4, 7, 6, 8, 4, -74415663851148711963547186142640802703534456832000000⟩, + ⟨7, 4, 4, 7, 4, 4, 433430306995724687214459964134977961699243668275200000⟩, + ⟨7, 4, 5, 7, 5, 4, 111959406360550314920964965648844480307657703424000000⟩ +] + +def collectedFourData_15_160 : List CollectedFourTerm := [ + ⟨7, 4, 6, 7, 6, 4, 220249243721761573936083926903740605995302256640000000⟩, + ⟨7, 4, 7, 7, 7, 4, 26300924576279901364437255501274463089119461376000000⟩, + ⟨7, 4, 8, 7, 8, 4, 176429416407577587935952131019001216252457779200000000⟩, + ⟨7, 5, 3, 2, 8, 5, 5502913629284687715250390881972982676528824320000000⟩, + ⟨7, 5, 3, 3, 7, 5, 13740166854317827787716356173337004797975330816000000⟩, + ⟨7, 5, 4, 3, 8, 5, 7981945172608667298685339604868308558841643008000000⟩, + ⟨7, 5, 3, 4, 6, 5, 31561335714174357727898429855788431514590511104000000⟩, + ⟨7, 5, 4, 4, 7, 5, 18189141822501124682062700662355996199824130048000000⟩, + ⟨7, 5, 5, 4, 8, 5, -39515836570050514276422162482330822424070717440000000⟩, + ⟨7, 5, 3, 5, 5, 5, 10372695359539005138809443286407199229286023168000000⟩, + ⟨7, 5, 4, 5, 6, 5, -16684514037560488845028894847802609233049944064000000⟩, + ⟨7, 5, 5, 5, 7, 5, 1344267071191362767833221315483423133673717760000000⟩, + ⟨7, 5, 6, 5, 8, 5, -18553437207707796023172070938846075382042460160000000⟩, + ⟨7, 5, 3, 6, 4, 5, -48938476372468837259032911501617562180944658432000000⟩, + ⟨7, 5, 4, 6, 5, 5, 27072019692537407465659053267049935612162342912000000⟩, + ⟨7, 5, 5, 6, 6, 5, -12786378700645111359552779140526038608343203840000000⟩, + ⟨7, 5, 6, 6, 7, 5, -17521805710775701825229305254550489814154608640000000⟩, + ⟨7, 5, 7, 6, 8, 5, -4805578552207157177055022025914124115860520960000000⟩, + ⟨7, 5, 3, 7, 3, 5, 87218525011005294462766675352764546397824352256000000⟩, + ⟨7, 5, 4, 7, 4, 5, 111959406360550314920964965648844480307657703424000000⟩, + ⟨7, 5, 5, 7, 5, 5, 14460120197282924872677001541906370166983229440000000⟩, + ⟨7, 5, 6, 7, 6, 5, 18964198073249350105986604590628856141552025600000000⟩, + ⟨7, 5, 7, 7, 7, 5, 1698448317276387225742022770410719966165729280000000⟩, + ⟨7, 5, 8, 7, 8, 5, 9114698444806981725568745340957564622130380800000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1508.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1508.lean new file mode 100644 index 0000000000000000000000000000000000000000..95a2775cfba301d81342c6de442370157f1da7a7 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1508.lean @@ -0,0 +1,144 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1501 +import OAI.Analysis.LaughlinFock.Sparse1502 +import OAI.Analysis.LaughlinFock.Sparse1503 +import OAI.Analysis.LaughlinFock.Sparse1504 +import OAI.Analysis.LaughlinFock.Sparse1505 +import OAI.Analysis.LaughlinFock.Sparse1506 +import OAI.Analysis.LaughlinFock.Sparse1507 + +namespace OAI + +/-! Sparse1508. -/ +namespace LaughlinFock +def collectedFourData_15_161 : List CollectedFourTerm := [ + ⟨7, 6, 2, 1, 8, 6, 42342663071386213022002791675738030585749176320000000⟩, + ⟨7, 6, 2, 2, 7, 6, 51469334973913328757277096054155612858341130240000000⟩, + ⟨7, 6, 3, 2, 8, 6, 21650928752033609630683387946077696526018150400000000⟩, + ⟨7, 6, 2, 3, 6, 6, 20446341914214676784013206297724201257769369600000000⟩, + ⟨7, 6, 3, 3, 7, 6, 54059975068618116619176247319740599747760619520000000⟩, + ⟨7, 6, 4, 3, 8, 6, 15702275001656979332355873445118873063789690880000000⟩, + ⟨7, 6, 2, 4, 5, 6, 9495674390841102003837908220578910004272168960000000⟩, + ⟨7, 6, 3, 4, 6, 6, 124176441227449858121033246873714828201825402880000000⟩, + ⟨7, 6, 4, 4, 7, 6, 35782118363976338562899081307060454072548065280000000⟩, + ⟨7, 6, 5, 4, 8, 6, -51824337662518101975617881838666202612341145600000000⟩, + ⟨7, 6, 2, 5, 4, 6, -50348281079540518737016516752746020529630085120000000⟩, + ⟨7, 6, 3, 5, 5, 6, 40810832828775678305319214756432442278501416960000000⟩, + ⟨7, 6, 4, 5, 6, 6, -32822178306338688704666980944137447181165527040000000⟩, + ⟨7, 6, 5, 5, 7, 6, 1762983063322664923899340100393827851200102400000000⟩, + ⟨7, 6, 6, 5, 8, 6, -18249384514764178064849363277493003300424908800000000⟩, + ⟨7, 6, 2, 6, 3, 6, -25404849183627316359364083074121869916792422400000000⟩, + ⟨7, 6, 3, 6, 4, 6, -192545901417524785431682956513867305915032535040000000⟩, + ⟨7, 6, 4, 6, 5, 6, 53256729891013083371868529317172594780479160320000000⟩, + ⟨7, 6, 5, 6, 6, 6, -16769114987313417686883443220773853736835481600000000⟩, + ⟨7, 6, 6, 6, 7, 6, -17234659337197928839706785975438810320941875200000000⟩, + ⟨7, 6, 7, 6, 8, 6, -3781459999388091797635616569372130981173002240000000⟩, + ⟨7, 6, 2, 7, 2, 6, 122872928683083275125787515031282258223657123840000000⟩, + ⟨7, 6, 3, 7, 3, 6, 343156770773485914670223749805400888696970936320000000⟩, + ⟨7, 6, 4, 7, 4, 6, 220249243721761573936083926903740605995302256640000000⟩ +] + +def collectedFourData_15_162 : List CollectedFourTerm := [ + ⟨7, 6, 5, 7, 5, 6, 18964198073249350105986604590628856141552025600000000⟩, + ⟨7, 6, 6, 7, 6, 6, 18653413854177954829090981583235814583697408000000000⟩, + ⟨7, 6, 7, 7, 7, 6, 1336491392874813421198809826395785720569528320000000⟩, + ⟨7, 6, 8, 7, 8, 6, 5976884850436329742688237080273659988279296000000000⟩, + ⟨7, 7, 1, 0, 8, 7, -2630517373887974936047075211833472619657560064000000⟩, + ⟨7, 7, 1, 1, 7, 7, -27585432622622653950713205322953356882491736064000000⟩, + ⟨7, 7, 2, 1, 8, 7, 15168967243395726505622802466629023058219761664000000⟩, + ⟨7, 7, 1, 2, 6, 7, -32711194563294583646035080129138780705040367616000000⟩, + ⟨7, 7, 2, 2, 7, 7, 18438534556562872955057771239932403027015630848000000⟩, + ⟨7, 7, 3, 2, 8, 7, 3878148009668167783912885076435487215887319040000000⟩, + ⟨7, 7, 1, 3, 5, 7, -27024493076811293655312950138425034243787718656000000⟩, + ⟨7, 7, 2, 3, 6, 7, 7324761086025802213306605111383288711133265920000000⟩, + ⟨7, 7, 3, 3, 7, 7, 9683306758624849070586476589211994112657457152000000⟩, + ⟨7, 7, 4, 3, 8, 7, 1875077269351735549270116796310550365803118592000000⟩, + ⟨7, 7, 1, 4, 4, 7, 30438076039635834155613583437427102473353428992000000⟩, + ⟨7, 7, 2, 4, 5, 7, 3401759911647068297450053149578399377357012992000000⟩, + ⟨7, 7, 3, 4, 6, 7, 22242677157610523220102195043441641247985369088000000⟩, + ⟨7, 7, 4, 4, 7, 7, 4272899104522449036493509853604043692338839552000000⟩, + ⟨7, 7, 5, 4, 8, 7, -4641427955818937761960124626679779829250785280000000⟩, + ⟨7, 7, 1, 5, 3, 7, 58128968356602825218397717824212204095748964352000000⟩, + ⟨7, 7, 2, 5, 4, 7, -18036924724579632719323340866766963693190119424000000⟩, + ⟨7, 7, 3, 5, 5, 7, 7310099807748470332384535636238437342873911296000000⟩, + ⟨7, 7, 4, 5, 6, 7, -3919439728722805459419202680134918563468148736000000⟩, + ⟨7, 7, 5, 5, 7, 7, 157894133235769212111450053520025413872517120000000⟩ +] + +def collectedFourData_15_163 : List CollectedFourTerm := [ + ⟨7, 7, 6, 5, 8, 7, -1307543247574618668009134501069818663431831552000000⟩, + ⟨7, 7, 1, 6, 2, 7, -144852655444894130104866679302956307409438507008000000⟩, + ⟨7, 7, 2, 6, 3, 7, -9101112144036795600625206100451033786854932480000000⟩, + ⟨7, 7, 3, 6, 4, 7, -34489121132136171465326713343420348159339003904000000⟩, + ⟨7, 7, 4, 6, 5, 7, 6359618822629587636312551373613664221148479488000000⟩, + ⟨7, 7, 5, 6, 6, 7, -1501854970213178499282519229475427551627182080000000⟩, + ⟨7, 7, 6, 6, 7, 7, -1234839587185563063890965041276124368425975808000000⟩, + ⟨7, 7, 7, 6, 8, 7, -225780330845919208052059962967781320276574208000000⟩, + ⟨7, 7, 1, 7, 1, 7, 414506672022100744261492386525487394108901163008000000⟩, + ⟨7, 7, 2, 7, 2, 7, 44018379929280403474211360244859689035070701568000000⟩, + ⟨7, 7, 3, 7, 3, 7, 61466774142626591257283040044549265710049656832000000⟩, + ⟨7, 7, 4, 7, 4, 7, 26300924576279901364437255501274463089119461376000000⟩, + ⟨7, 7, 5, 7, 5, 7, 1698448317276387225742022770410719966165729280000000⟩, + ⟨7, 7, 6, 7, 6, 7, 1336491392874813421198809826395785720569528320000000⟩, + ⟨7, 7, 7, 7, 7, 7, 79798138524492629580188424693348534105145344000000⟩, + ⟨7, 7, 8, 7, 8, 7, 305882544046368541673961341642803045308825600000000⟩, + ⟨7, 8, 0, 0, 7, 8, -613411297185544067839541072561022856919305420800000000⟩, + ⟨7, 8, 1, 0, 8, 8, -70583168097992862347664064273381881791329075200000000⟩, + ⟨7, 8, 0, 1, 6, 8, -77174221849086147838732575477849501974554214400000000⟩, + ⟨7, 8, 1, 1, 7, 8, -740184135328714259727834388039430964285485875200000000⟩, + ⟨7, 8, 2, 1, 8, 8, 203510110870521176766309347056059427122157977600000000⟩, + ⟨7, 8, 0, 2, 5, 8, 373249151096289242839151249324390504928274022400000000⟩, + ⟨7, 8, 1, 2, 6, 8, -877720773664617712899135281212684632052255948800000000⟩, + ⟨7, 8, 2, 2, 7, 8, 247375325668910031004471569491453288312419123200000000⟩ +] + +def collectedFourData_15_164 : List CollectedFourTerm := [ + ⟨7, 8, 3, 2, 8, 8, 34686709110601256374580378015209342447386624000000000⟩, + ⟨7, 8, 0, 3, 4, 8, -237034730871339545452367968891449662816177356800000000⟩, + ⟨7, 8, 1, 3, 5, 8, -725132765340499484141893490258273055602953420800000000⟩, + ⟨7, 8, 2, 3, 6, 8, 98270562313080066895743313915855834844233728000000000⟩, + ⟨7, 8, 3, 3, 7, 8, 86608877208345353714746301552326461107680051200000000⟩, + ⟨7, 8, 4, 3, 8, 8, 12578218966841852652331195650069639679338086400000000⟩, + ⟨7, 8, 0, 4, 3, 8, -909679473825968213505920120113324255922985369600000000⟩, + ⟨7, 8, 1, 4, 4, 8, 816727484490888933846585943515736875514567065600000000⟩, + ⟨7, 8, 2, 4, 5, 8, 45638738990329081631161471450087272347389132800000000⟩, + ⟨7, 8, 3, 4, 6, 8, 198941677956501369040767225494931474882546892800000000⟩, + ⟨7, 8, 4, 4, 7, 8, 28663064417866407179561369327795899820566118400000000⟩, + ⟨7, 8, 5, 4, 8, 8, -24908156309652502711265635728812944843918540800000000⟩, + ⟨7, 8, 0, 5, 2, 8, 1535273508271255093092444632186669371636265779200000000⟩, + ⟨7, 8, 1, 5, 3, 8, 1559741359477420901379906098823611727996361113600000000⟩, + ⟨7, 8, 2, 5, 4, 8, -241987242213908506176400705907045551247563161600000000⟩, + ⟨7, 8, 3, 5, 5, 8, 65382575644019683391236385698735340218063257600000000⟩, + ⟨7, 8, 4, 5, 6, 8, -26292021102820397335663333573025897016144691200000000⟩, + ⟨7, 8, 5, 5, 7, 8, 847336593059262922891621431940833432777523200000000⟩, + ⟨7, 8, 6, 5, 8, 8, -5847426679575389462254320102159768434088345600000000⟩, + ⟨7, 8, 0, 6, 1, 8, -1115935551326969559851315781037644170089463808000000000⟩, + ⟨7, 8, 1, 6, 2, 8, -3886748451159637426109193301901971371069957734400000000⟩, + ⟨7, 8, 2, 6, 3, 8, -122102468266873808763266947108148921952632832000000000⟩, + ⟨7, 8, 3, 6, 4, 8, -308475620117722171489208482519911006766261862400000000⟩, + ⟨7, 8, 4, 6, 5, 8, 42661003577916308070597674947210036934973849600000000⟩ +] + +def collectedFourData_15_165 : List CollectedFourTerm := [ + ⟨7, 8, 5, 6, 6, 8, -8059683077833742812015671716352310985411788800000000⟩, + ⟨7, 8, 6, 6, 7, 8, -5522290723842888180493397222833690700572262400000000⟩, + ⟨7, 8, 7, 6, 8, 8, -865462068060436049002710589064313526498099200000000⟩, + ⟨7, 8, 0, 7, 0, 8, 10884042434552915293747245526142109512785880678400000000⟩, + ⟨7, 8, 1, 7, 1, 8, 11122220442069393172958894007393570611322578534400000000⟩, + ⟨7, 8, 2, 7, 2, 8, 590560005569845159952401127891203512211813171200000000⟩, + ⟨7, 8, 3, 7, 3, 8, 549767597661840171060260892746230420596798259200000000⟩, + ⟨7, 8, 4, 7, 4, 8, 176429416407577587935952131019001216252457779200000000⟩, + ⟨7, 8, 5, 7, 5, 8, 9114698444806981725568745340957564622130380800000000⟩, + ⟨7, 8, 6, 7, 6, 8, 5976884850436329742688237080273659988279296000000000⟩, + ⟨7, 8, 7, 7, 7, 8, 305882544046368541673961341642803045308825600000000⟩, + ⟨7, 8, 8, 7, 8, 8, 1025946418325480631532733697426500364533760000000000⟩ +] + +def collectedFourData_15 : List CollectedFourTerm := (((((((collectedFourData_15_0 ++ collectedFourData_15_1) ++ (collectedFourData_15_2 ++ (collectedFourData_15_3 ++ collectedFourData_15_4))) ++ ((collectedFourData_15_5 ++ collectedFourData_15_6) ++ (collectedFourData_15_7 ++ (collectedFourData_15_8 ++ collectedFourData_15_9)))) ++ (((collectedFourData_15_10 ++ collectedFourData_15_11) ++ (collectedFourData_15_12 ++ (collectedFourData_15_13 ++ collectedFourData_15_14))) ++ ((collectedFourData_15_15 ++ collectedFourData_15_16) ++ (collectedFourData_15_17 ++ (collectedFourData_15_18 ++ collectedFourData_15_19))))) ++ ((((collectedFourData_15_20 ++ collectedFourData_15_21) ++ (collectedFourData_15_22 ++ (collectedFourData_15_23 ++ collectedFourData_15_24))) ++ ((collectedFourData_15_25 ++ collectedFourData_15_26) ++ (collectedFourData_15_27 ++ (collectedFourData_15_28 ++ collectedFourData_15_29)))) ++ (((collectedFourData_15_30 ++ collectedFourData_15_31) ++ (collectedFourData_15_32 ++ (collectedFourData_15_33 ++ collectedFourData_15_34))) ++ ((collectedFourData_15_35 ++ (collectedFourData_15_36 ++ collectedFourData_15_37)) ++ (collectedFourData_15_38 ++ (collectedFourData_15_39 ++ collectedFourData_15_40)))))) ++ (((((collectedFourData_15_41 ++ collectedFourData_15_42) ++ (collectedFourData_15_43 ++ (collectedFourData_15_44 ++ collectedFourData_15_45))) ++ ((collectedFourData_15_46 ++ collectedFourData_15_47) ++ (collectedFourData_15_48 ++ (collectedFourData_15_49 ++ collectedFourData_15_50)))) ++ (((collectedFourData_15_51 ++ collectedFourData_15_52) ++ (collectedFourData_15_53 ++ (collectedFourData_15_54 ++ collectedFourData_15_55))) ++ ((collectedFourData_15_56 ++ (collectedFourData_15_57 ++ collectedFourData_15_58)) ++ (collectedFourData_15_59 ++ (collectedFourData_15_60 ++ collectedFourData_15_61))))) ++ ((((collectedFourData_15_62 ++ collectedFourData_15_63) ++ (collectedFourData_15_64 ++ (collectedFourData_15_65 ++ collectedFourData_15_66))) ++ ((collectedFourData_15_67 ++ collectedFourData_15_68) ++ (collectedFourData_15_69 ++ (collectedFourData_15_70 ++ collectedFourData_15_71)))) ++ (((collectedFourData_15_72 ++ collectedFourData_15_73) ++ (collectedFourData_15_74 ++ (collectedFourData_15_75 ++ collectedFourData_15_76))) ++ ((collectedFourData_15_77 ++ (collectedFourData_15_78 ++ collectedFourData_15_79)) ++ (collectedFourData_15_80 ++ (collectedFourData_15_81 ++ collectedFourData_15_82))))))) ++ ((((((collectedFourData_15_83 ++ collectedFourData_15_84) ++ (collectedFourData_15_85 ++ (collectedFourData_15_86 ++ collectedFourData_15_87))) ++ ((collectedFourData_15_88 ++ collectedFourData_15_89) ++ (collectedFourData_15_90 ++ (collectedFourData_15_91 ++ collectedFourData_15_92)))) ++ (((collectedFourData_15_93 ++ collectedFourData_15_94) ++ (collectedFourData_15_95 ++ (collectedFourData_15_96 ++ collectedFourData_15_97))) ++ ((collectedFourData_15_98 ++ collectedFourData_15_99) ++ (collectedFourData_15_100 ++ (collectedFourData_15_101 ++ collectedFourData_15_102))))) ++ ((((collectedFourData_15_103 ++ collectedFourData_15_104) ++ (collectedFourData_15_105 ++ (collectedFourData_15_106 ++ collectedFourData_15_107))) ++ ((collectedFourData_15_108 ++ collectedFourData_15_109) ++ (collectedFourData_15_110 ++ (collectedFourData_15_111 ++ collectedFourData_15_112)))) ++ (((collectedFourData_15_113 ++ collectedFourData_15_114) ++ (collectedFourData_15_115 ++ (collectedFourData_15_116 ++ collectedFourData_15_117))) ++ ((collectedFourData_15_118 ++ (collectedFourData_15_119 ++ collectedFourData_15_120)) ++ (collectedFourData_15_121 ++ (collectedFourData_15_122 ++ collectedFourData_15_123)))))) ++ (((((collectedFourData_15_124 ++ collectedFourData_15_125) ++ (collectedFourData_15_126 ++ (collectedFourData_15_127 ++ collectedFourData_15_128))) ++ ((collectedFourData_15_129 ++ collectedFourData_15_130) ++ (collectedFourData_15_131 ++ (collectedFourData_15_132 ++ collectedFourData_15_133)))) ++ (((collectedFourData_15_134 ++ collectedFourData_15_135) ++ (collectedFourData_15_136 ++ (collectedFourData_15_137 ++ collectedFourData_15_138))) ++ ((collectedFourData_15_139 ++ (collectedFourData_15_140 ++ collectedFourData_15_141)) ++ (collectedFourData_15_142 ++ (collectedFourData_15_143 ++ collectedFourData_15_144))))) ++ ((((collectedFourData_15_145 ++ collectedFourData_15_146) ++ (collectedFourData_15_147 ++ (collectedFourData_15_148 ++ collectedFourData_15_149))) ++ ((collectedFourData_15_150 ++ collectedFourData_15_151) ++ (collectedFourData_15_152 ++ (collectedFourData_15_153 ++ collectedFourData_15_154)))) ++ (((collectedFourData_15_155 ++ collectedFourData_15_156) ++ (collectedFourData_15_157 ++ (collectedFourData_15_158 ++ collectedFourData_15_159))) ++ ((collectedFourData_15_160 ++ (collectedFourData_15_161 ++ collectedFourData_15_162)) ++ (collectedFourData_15_163 ++ (collectedFourData_15_164 ++ collectedFourData_15_165)))))))) + +theorem collectedFourChecked_15 : collectedFourTerms 15 = collectedFourData_15 := by + decide +kernel + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1601.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1601.lean new file mode 100644 index 0000000000000000000000000000000000000000..5cc887ac7e0ec2e82c1275b30415df61ff9ca10a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1601.lean @@ -0,0 +1,631 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1601. -/ +namespace LaughlinFock + +def collectedFourData_16_0 : List CollectedFourTerm := [ + ⟨0, 8, 8, 0, 8, 8, 1776811014008272299282632747754600397148736454656000000⟩, + ⟨0, 8, 8, 1, 7, 8, 1484729531752665465069660046362856938890455941120000000⟩, + ⟨0, 8, 8, 2, 6, 8, 80793815339962223371593031887229049751837081600000000⟩, + ⟨0, 8, 8, 3, 5, 8, 1285491685801945514514871639638059077614667038720000000⟩, + ⟨0, 8, 8, 4, 4, 8, -1839145587511602003168419557511311429272537661440000000⟩, + ⟨0, 8, 8, 5, 3, 8, 2572659703459888843319973125061704402401964851200000000⟩, + ⟨0, 8, 8, 6, 2, 8, -9174481563939897177696063025903836319022007189504000000⟩, + ⟨0, 8, 8, 7, 1, 8, 17154266332556660186363142701371221100703168593920000000⟩, + ⟨1, 7, 8, 0, 8, 8, 1484729531752665465069660046362856938890455941120000000⟩, + ⟨1, 7, 8, 1, 7, 8, 1240661930322898212671621764990128982015239782400000000⟩, + ⟨1, 7, 8, 2, 6, 8, 67512505647747492187589997066916357767954432000000000⟩, + ⟨1, 7, 8, 3, 5, 8, 1074175842948585648589117018433585791688402534400000000⟩, + ⟨1, 7, 8, 4, 4, 8, -1536817222227309232659434957153002384563948748800000000⟩, + ⟨1, 7, 8, 5, 3, 8, 2149752453560133411096574640679091831648026624000000000⟩, + ⟨1, 7, 8, 6, 2, 8, -7666332327473138505945665970694741641014626222080000000⟩, + ⟨1, 7, 8, 7, 1, 8, 14334358363775195426686067046041937369847195238400000000⟩, + ⟨2, 6, 8, 0, 8, 8, 80793815339962223371593031887229049751837081600000000⟩, + ⟨2, 6, 8, 1, 7, 8, 67512505647747492187589997066916357767954432000000000⟩, + ⟨2, 6, 8, 2, 6, 8, 3673795662973937611179892237479343565045760000000000⟩, + ⟨2, 6, 8, 3, 5, 8, 58452912023234218981784996008672479298977792000000000⟩, + ⟨2, 6, 8, 4, 4, 8, -83628246228344748290059323524344473383337984000000000⟩, + ⟨2, 6, 8, 5, 3, 8, 116982048949035004898322239321457383775928320000000000⟩, + ⟨2, 6, 8, 6, 2, 8, -417175132005005050529970499425410967262357094400000000⟩, + ⟨2, 6, 8, 7, 1, 8, 780025909023693836170503905642795478665920512000000000⟩ +] + +def collectedFourData_16_1 : List CollectedFourTerm := [ + ⟨3, 5, 8, 0, 8, 8, 1285491685801945514514871639638059077614667038720000000⟩, + ⟨3, 5, 8, 1, 7, 8, 1074175842948585648589117018433585791688402534400000000⟩, + ⟨3, 5, 8, 2, 6, 8, 58452912023234218981784996008672479298977792000000000⟩, + ⟨3, 5, 8, 3, 5, 8, 930030746791754361799241628950883382713542246400000000⟩, + ⟨3, 5, 8, 4, 4, 8, -1330589659275092570235043944191387293778234572800000000⟩, + ⟨3, 5, 8, 5, 3, 8, 1861274290356232973406148787302875469807878144000000000⟩, + ⟨3, 5, 8, 6, 2, 8, -6637576916738461852599415666560992498097303060480000000⟩, + ⟨3, 5, 8, 7, 1, 8, 12410811601616485957475452205740206243122144870400000000⟩, + ⟨4, 4, 8, 0, 8, 8, -1839145587511602003168419557511311429272537661440000000⟩, + ⟨4, 4, 8, 1, 7, 8, -1536817222227309232659434957153002384563948748800000000⟩, + ⟨4, 4, 8, 2, 6, 8, -83628246228344748290059323524344473383337984000000000⟩, + ⟨4, 4, 8, 3, 5, 8, -1330589659275092570235043944191387293778234572800000000⟩, + ⟨4, 4, 8, 4, 4, 8, 1903666999695696392706455813910967730606545305600000000⟩, + ⟨4, 4, 8, 5, 3, 8, -2662914459942183040793849042138190759579353088000000000⟩, + ⟨4, 4, 8, 6, 2, 8, 9496343253727741007942338716754773413299444776960000000⟩, + ⟨4, 4, 8, 7, 1, 8, -17756077030020891937442213115120805320338492620800000000⟩, + ⟨5, 3, 8, 0, 8, 8, 2572659703459888843319973125061704402401964851200000000⟩, + ⟨5, 3, 8, 1, 7, 8, 2149752453560133411096574640679091831648026624000000000⟩, + ⟨5, 3, 8, 2, 6, 8, 116982048949035004898322239321457383775928320000000000⟩, + ⟨5, 3, 8, 3, 5, 8, 1861274290356232973406148787302875469807878144000000000⟩, + ⟨5, 3, 8, 4, 4, 8, -2662914459942183040793849042138190759579353088000000000⟩, + ⟨5, 3, 8, 5, 3, 8, 3724975755792736821180116965324345621862154240000000000⟩, + ⟨5, 3, 8, 6, 2, 8, -13283809495551644216542518095083251737371135180800000000⟩, + ⟨5, 3, 8, 7, 1, 8, 24837807391023807865218596983534755250578653184000000000⟩ +] + +def collectedFourData_16_2 : List CollectedFourTerm := [ + ⟨6, 2, 8, 0, 8, 8, -9174481563939897177696063025903836319022007189504000000⟩, + ⟨6, 2, 8, 1, 7, 8, -7666332327473138505945665970694741641014626222080000000⟩, + ⟨6, 2, 8, 2, 6, 8, -417175132005005050529970499425410967262357094400000000⟩, + ⟨6, 2, 8, 3, 5, 8, -6637576916738461852599415666560992498097303060480000000⟩, + ⟨6, 2, 8, 4, 4, 8, 9496343253727741007942338716754773413299444776960000000⟩, + ⟨6, 2, 8, 5, 3, 8, -13283809495551644216542518095083251737371135180800000000⟩, + ⟨6, 2, 8, 6, 2, 8, 47372011600261943315532723123726947113126053543936000000⟩, + ⟨6, 2, 8, 7, 1, 8, -88575261505117634852669594449526079592649226977280000000⟩, + ⟨7, 1, 8, 0, 8, 8, 17154266332556660186363142701371221100703168593920000000⟩, + ⟨7, 1, 8, 1, 7, 8, 14334358363775195426686067046041937369847195238400000000⟩, + ⟨7, 1, 8, 2, 6, 8, 780025909023693836170503905642795478665920512000000000⟩, + ⟨7, 1, 8, 3, 5, 8, 12410811601616485957475452205740206243122144870400000000⟩, + ⟨7, 1, 8, 4, 4, 8, -17756077030020891937442213115120805320338492620800000000⟩, + ⟨7, 1, 8, 5, 3, 8, 24837807391023807865218596983534755250578653184000000000⟩, + ⟨7, 1, 8, 6, 2, 8, -88575261505117634852669594449526079592649226977280000000⟩, + ⟨7, 1, 8, 7, 1, 8, 165616292947470946321788401739560716679883679334400000000⟩, + ⟨0, 8, 8, 1, 8, 7, -10380549642594335736608257601697443174044265349120000000⟩, + ⟨0, 8, 8, 2, 7, 7, -4457172808093478578038411445494514555441266032640000000⟩, + ⟨0, 8, 8, 3, 6, 7, 239345408281516373596235098950289515273309388800000000⟩, + ⟨0, 8, 8, 4, 5, 7, 3257762182726281314704166547560247946427246837760000000⟩, + ⟨0, 8, 8, 5, 4, 7, 1630843240415858540399972774367928659014351585280000000⟩, + ⟨0, 8, 8, 6, 3, 7, -8658800370380342883235953611926208198342564904960000000⟩, + ⟨0, 8, 8, 7, 2, 7, 3405736736962183451216768926145319109367420682240000000⟩, + ⟨1, 7, 8, 1, 8, 7, 821201406105016989499950778248359042130483609600000000⟩ +] + +def collectedFourData_16_3 : List CollectedFourTerm := [ + ⟨1, 7, 8, 2, 7, 7, 352605276529907831343395643793054873714635571200000000⟩, + ⟨1, 7, 8, 3, 6, 7, -18934525877036132250419287783935581884514304000000000⟩, + ⟨1, 7, 8, 4, 5, 7, -257720349819738292021188589519211466117139660800000000⟩, + ⟨1, 7, 8, 5, 4, 7, -129015399788758781301257281845740528376112742400000000⟩, + ⟨1, 7, 8, 6, 3, 7, 684994464085224861031418449789185147825605836800000000⟩, + ⟨1, 7, 8, 7, 2, 7, -269426561551308614626523091058625434929541939200000000⟩, + ⟨1, 8, 7, 0, 8, 8, -10380549642594335736608257601697443174044265349120000000⟩, + ⟨1, 8, 7, 1, 7, 8, 821201406105016989499950778248359042130483609600000000⟩, + ⟨1, 8, 8, 1, 8, 8, 11867527930342804817428404267441580135256810323968000000⟩, + ⟨1, 8, 7, 2, 6, 8, 515055195894114668687938692769988221547097096192000000⟩, + ⟨1, 8, 8, 2, 7, 8, 5095647592047352006809786253082789733745972740096000000⟩, + ⟨1, 8, 7, 3, 5, 8, 1235352879973257584089368241380071765728913522688000000⟩, + ⟨1, 8, 8, 3, 6, 8, -273630820676881557562151123080042572622929592320000000⟩, + ⟨1, 8, 7, 4, 4, 8, -638683472742802404097887581852299685324094701568000000⟩, + ⟨1, 8, 8, 4, 5, 8, -3724425490465288451654148019170267016445206462464000000⟩, + ⟨1, 8, 7, 5, 3, 8, -728536084923409888644265978515005316407048011776000000⟩, + ⟨1, 8, 8, 5, 4, 8, -1864455965436618462328951035370103374832512008192000000⟩, + ⟨1, 8, 7, 6, 2, 8, -5156211626801796564198915070783310513874483019776000000⟩, + ⟨1, 8, 8, 6, 3, 8, 9899143954488101599882005075967436777013897068544000000⟩, + ⟨1, 8, 7, 7, 1, 8, 26675845814208688145902924355656984935260013723648000000⟩, + ⟨1, 8, 8, 7, 2, 8, -3893596894276975959305045602486049884229427265536000000⟩, + ⟨2, 6, 8, 1, 8, 7, 515055195894114668687938692769988221547097096192000000⟩, + ⟨2, 6, 8, 2, 7, 7, 221153030701441986941388256378650834531646439424000000⟩, + ⟨2, 6, 8, 3, 6, 7, -11875680998909395660274387448851810127792046080000000⟩ +] + +def collectedFourData_16_4 : List CollectedFourTerm := [ + ⟨2, 6, 8, 4, 5, 7, -161641473425984325606015861846134779038155145216000000⟩, + ⟨2, 6, 8, 5, 4, 7, -80918093317364461249575278412193761055733710848000000⟩, + ⟨2, 6, 8, 6, 3, 7, 429626587659156412697272909550761877278593908736000000⟩, + ⟨2, 6, 8, 7, 2, 7, -168983576266722630738355048891157070965882486784000000⟩, + ⟨2, 7, 7, 0, 8, 8, -4457172808093478578038411445494514555441266032640000000⟩, + ⟨2, 7, 7, 1, 7, 8, 352605276529907831343395643793054873714635571200000000⟩, + ⟨2, 7, 8, 1, 8, 8, 5095647592047352006809786253082789733745972740096000000⟩, + ⟨2, 7, 7, 2, 6, 8, 221153030701441986941388256378650834531646439424000000⟩, + ⟨2, 7, 8, 2, 7, 8, 2187955615924801536784501897375965847238278643712000000⟩, + ⟨2, 7, 7, 3, 5, 8, 530432535327739198530337759412324464037971623936000000⟩, + ⟨2, 7, 8, 3, 6, 8, -117490874314868020675122349014195091574662103040000000⟩, + ⟨2, 7, 7, 4, 4, 8, -274236211539996110672275559812890367145118007296000000⟩, + ⟨2, 7, 8, 4, 5, 8, -1599183915440847597758868823339479046841966788608000000⟩, + ⟨2, 7, 7, 5, 3, 8, -312816887278422745049449314627195843679377948672000000⟩, + ⟨2, 7, 8, 5, 4, 8, -800555145647842740507119674230594942001609703424000000⟩, + ⟨2, 7, 7, 6, 2, 8, -2213960440153788455184909239206050658320144924672000000⟩, + ⟨2, 7, 8, 6, 3, 8, 4250468113586341135863738564611024755448629690368000000⟩, + ⟨2, 7, 7, 7, 1, 8, 11454003756035183673032105617444150047361839661056000000⟩, + ⟨2, 7, 8, 7, 2, 8, -1671822283055070258613798790333706302485684027392000000⟩, + ⟨3, 5, 8, 1, 8, 7, 1235352879973257584089368241380071765728913522688000000⟩, + ⟨3, 5, 8, 2, 7, 7, 530432535327739198530337759412324464037971623936000000⟩, + ⟨3, 5, 8, 3, 6, 7, -28483659306025943072095673957032177676970885120000000⟩, + ⟨3, 5, 8, 4, 5, 7, -387694874863395650967053313970425418586756481024000000⟩, + ⟨3, 5, 8, 5, 4, 7, -194080945922738193613933241366222582310210895872000000⟩ +] + +def collectedFourData_16_5 : List CollectedFourTerm := [ + ⟨3, 5, 8, 6, 3, 7, 1030453525386688833326223014812591638470725730304000000⟩, + ⟨3, 5, 8, 7, 2, 7, -405304808636844146913715685137325004840266366976000000⟩, + ⟨3, 6, 7, 0, 8, 8, 239345408281516373596235098950289515273309388800000000⟩, + ⟨3, 6, 7, 1, 7, 8, -18934525877036132250419287783935581884514304000000000⟩, + ⟨3, 6, 8, 1, 8, 8, -273630820676881557562151123080042572622929592320000000⟩, + ⟨3, 6, 7, 2, 6, 8, -11875680998909395660274387448851810127792046080000000⟩, + ⟨3, 6, 8, 2, 7, 8, -117490874314868020675122349014195091574662103040000000⟩, + ⟨3, 6, 7, 3, 5, 8, -28483659306025943072095673957032177676970885120000000⟩, + ⟨3, 6, 8, 3, 6, 8, 6309134173838081723123612544616061150743756800000000⟩, + ⟨3, 6, 7, 4, 4, 8, 14726190983089224171664065168714283375468216320000000⟩, + ⟨3, 6, 8, 4, 5, 8, 85874464293464343042763320246876022137799311360000000⟩, + ⟨3, 6, 7, 5, 3, 8, 16797931968680566899439366249793872145405706240000000⟩, + ⟨3, 6, 8, 5, 4, 8, 42988954307318205328397677125276477989930926080000000⟩, + ⟨3, 6, 7, 6, 2, 8, 118887305537160761275358853024471451296847626240000000⟩, + ⟨3, 6, 8, 6, 3, 8, -228245587468941917419507070142528527918495170560000000⟩, + ⟨3, 6, 7, 7, 1, 8, -615067739906387637059671332489143454617063915520000000⟩, + ⟨3, 6, 8, 7, 2, 8, 89775066873189220610765698626353596014935408640000000⟩, + ⟨4, 4, 8, 1, 8, 7, -638683472742802404097887581852299685324094701568000000⟩, + ⟨4, 4, 8, 2, 7, 7, -274236211539996110672275559812890367145118007296000000⟩, + ⟨4, 4, 8, 3, 6, 7, 14726190983089224171664065168714283375468216320000000⟩, + ⟨4, 4, 8, 4, 5, 7, 200440143910701854572876873689571771650894987264000000⟩, + ⟨4, 4, 8, 5, 4, 7, 100340796985737242779693850698628987476972142592000000⟩, + ⟨4, 4, 8, 6, 3, 7, -532749505637839231391720297932044183404065849344000000⟩, + ⟨4, 4, 8, 7, 2, 7, 209544565683240501328596921654068767756948340736000000⟩ +] + +def collectedFourData_16_6 : List CollectedFourTerm := [ + ⟨4, 5, 7, 0, 8, 8, 3257762182726281314704166547560247946427246837760000000⟩, + ⟨4, 5, 7, 1, 7, 8, -257720349819738292021188589519211466117139660800000000⟩, + ⟨4, 5, 8, 1, 8, 8, -3724425490465288451654148019170267016445206462464000000⟩, + ⟨4, 5, 7, 2, 6, 8, -161641473425984325606015861846134779038155145216000000⟩, + ⟨4, 5, 8, 2, 7, 8, -1599183915440847597758868823339479046841966788608000000⟩, + ⟨4, 5, 7, 3, 5, 8, -387694874863395650967053313970425418586756481024000000⟩, + ⟨4, 5, 8, 3, 6, 8, 85874464293464343042763320246876022137799311360000000⟩, + ⟨4, 5, 7, 4, 4, 8, 200440143910701854572876873689571771650894987264000000⟩, + ⟨4, 5, 8, 4, 5, 8, 1168848753965133280760582217059929769683841974272000000⟩, + ⟨4, 5, 7, 5, 3, 8, 228638885986944831428356762123615361509776949248000000⟩, + ⟨4, 5, 8, 5, 4, 8, 585128374188846403191225302937977928909078921216000000⟩, + ⟨4, 5, 7, 6, 2, 8, 1618190926519216574584700721757550942912929333248000000⟩, + ⟨4, 5, 8, 6, 3, 8, -3106681045478344843043661688609708172195357786112000000⟩, + ⟨4, 5, 7, 7, 1, 8, -8371768805880596114044024733612460454707518767104000000⟩, + ⟨4, 5, 8, 7, 2, 8, 1221940374419895130282203602124852582261328969728000000⟩, + ⟨5, 3, 8, 1, 8, 7, -728536084923409888644265978515005316407048011776000000⟩, + ⟨5, 3, 8, 2, 7, 7, -312816887278422745049449314627195843679377948672000000⟩, + ⟨5, 3, 8, 3, 6, 7, 16797931968680566899439366249793872145405706240000000⟩, + ⟨5, 3, 8, 4, 5, 7, 228638885986944831428356762123615361509776949248000000⟩, + ⟨5, 3, 8, 5, 4, 7, 114457152116603780096474845675876827338945593344000000⟩, + ⟨5, 3, 8, 6, 3, 7, -607698892560152674773950239528279063006499831808000000⟩, + ⟨5, 3, 8, 7, 2, 7, 239024155180105594194014156485948357946483146752000000⟩, + ⟨5, 4, 7, 0, 8, 8, 1630843240415858540399972774367928659014351585280000000⟩, + ⟨5, 4, 7, 1, 7, 8, -129015399788758781301257281845740528376112742400000000⟩ +] + +def collectedFourData_16_7 : List CollectedFourTerm := [ + ⟨5, 4, 8, 1, 8, 8, -1864455965436618462328951035370103374832512008192000000⟩, + ⟨5, 4, 7, 2, 6, 8, -80918093317364461249575278412193761055733710848000000⟩, + ⟨5, 4, 8, 2, 7, 8, -800555145647842740507119674230594942001609703424000000⟩, + ⟨5, 4, 7, 3, 5, 8, -194080945922738193613933241366222582310210895872000000⟩, + ⟨5, 4, 8, 3, 6, 8, 42988954307318205328397677125276477989930926080000000⟩, + ⟨5, 4, 7, 4, 4, 8, 100340796985737242779693850698628987476972142592000000⟩, + ⟨5, 4, 8, 4, 5, 8, 585128374188846403191225302937977928909078921216000000⟩, + ⟨5, 4, 7, 5, 3, 8, 114457152116603780096474845675876827338945593344000000⟩, + ⟨5, 4, 8, 5, 4, 8, 292916609714840569438817719523742537657612238848000000⟩, + ⟨5, 4, 7, 6, 2, 8, 810070099103323933474552006862849610214847545344000000⟩, + ⟨5, 4, 8, 6, 3, 8, -1555211675674400077579213992393893161094124404736000000⟩, + ⟨5, 4, 7, 7, 1, 8, -4190926716439770559806259715537345321757271130112000000⟩, + ⟨5, 4, 8, 7, 2, 8, 611706161481138613118857888542625601041710710784000000⟩, + ⟨6, 2, 8, 1, 8, 7, -5156211626801796564198915070783310513874483019776000000⟩, + ⟨6, 2, 8, 2, 7, 7, -2213960440153788455184909239206050658320144924672000000⟩, + ⟨6, 2, 8, 3, 6, 7, 118887305537160761275358853024471451296847626240000000⟩, + ⟨6, 2, 8, 4, 5, 7, 1618190926519216574584700721757550942912929333248000000⟩, + ⟨6, 2, 8, 5, 4, 7, 810070099103323933474552006862849610214847545344000000⟩, + ⟨6, 2, 8, 6, 3, 7, -4300986814870876394842074847857524798853960695808000000⟩, + ⟨6, 2, 8, 7, 2, 7, 1691692633393312648674141669486613363020898762752000000⟩, + ⟨6, 3, 7, 0, 8, 8, -8658800370380342883235953611926208198342564904960000000⟩, + ⟨6, 3, 7, 1, 7, 8, 684994464085224861031418449789185147825605836800000000⟩, + ⟨6, 3, 8, 1, 8, 8, 9899143954488101599882005075967436777013897068544000000⟩, + ⟨6, 3, 7, 2, 6, 8, 429626587659156412697272909550761877278593908736000000⟩ +] + +def collectedFourData_16_8 : List CollectedFourTerm := [ + ⟨6, 3, 8, 2, 7, 8, 4250468113586341135863738564611024755448629690368000000⟩, + ⟨6, 3, 7, 3, 5, 8, 1030453525386688833326223014812591638470725730304000000⟩, + ⟨6, 3, 8, 3, 6, 8, -228245587468941917419507070142528527918495170560000000⟩, + ⟨6, 3, 7, 4, 4, 8, -532749505637839231391720297932044183404065849344000000⟩, + ⟨6, 3, 8, 4, 5, 8, -3106681045478344843043661688609708172195357786112000000⟩, + ⟨6, 3, 7, 5, 3, 8, -607698892560152674773950239528279063006499831808000000⟩, + ⟨6, 3, 8, 5, 4, 8, -1555211675674400077579213992393893161094124404736000000⟩, + ⟨6, 3, 7, 6, 2, 8, -4300986814870876394842074847857524798853960695808000000⟩, + ⟨6, 3, 8, 6, 3, 8, 8257242081658004385652428753040131591130948042752000000⟩, + ⟨6, 3, 7, 7, 1, 8, 22251309571171391332787791405337801441433285033984000000⟩, + ⟨6, 3, 8, 7, 2, 8, -3247793170020558400965648664287870219712764837888000000⟩, + ⟨7, 1, 8, 1, 8, 7, 26675845814208688145902924355656984935260013723648000000⟩, + ⟨7, 1, 8, 2, 7, 7, 11454003756035183673032105617444150047361839661056000000⟩, + ⟨7, 1, 8, 3, 6, 7, -615067739906387637059671332489143454617063915520000000⟩, + ⟨7, 1, 8, 4, 5, 7, -8371768805880596114044024733612460454707518767104000000⟩, + ⟨7, 1, 8, 5, 4, 7, -4190926716439770559806259715537345321757271130112000000⟩, + ⟨7, 1, 8, 6, 3, 7, 22251309571171391332787791405337801441433285033984000000⟩, + ⟨7, 1, 8, 7, 2, 7, -8752032523037354950314315792868194916664812240896000000⟩, + ⟨7, 2, 7, 0, 8, 8, 3405736736962183451216768926145319109367420682240000000⟩, + ⟨7, 2, 7, 1, 7, 8, -269426561551308614626523091058625434929541939200000000⟩, + ⟨7, 2, 8, 1, 8, 8, -3893596894276975959305045602486049884229427265536000000⟩, + ⟨7, 2, 7, 2, 6, 8, -168983576266722630738355048891157070965882486784000000⟩, + ⟨7, 2, 8, 2, 7, 8, -1671822283055070258613798790333706302485684027392000000⟩, + ⟨7, 2, 7, 3, 5, 8, -405304808636844146913715685137325004840266366976000000⟩ +] + +def collectedFourData_16_9 : List CollectedFourTerm := [ + ⟨7, 2, 8, 3, 6, 8, 89775066873189220610765698626353596014935408640000000⟩, + ⟨7, 2, 7, 4, 4, 8, 209544565683240501328596921654068767756948340736000000⟩, + ⟨7, 2, 8, 4, 5, 8, 1221940374419895130282203602124852582261328969728000000⟩, + ⟨7, 2, 7, 5, 3, 8, 239024155180105594194014156485948357946483146752000000⟩, + ⟨7, 2, 8, 5, 4, 8, 611706161481138613118857888542625601041710710784000000⟩, + ⟨7, 2, 7, 6, 2, 8, 1691692633393312648674141669486613363020898762752000000⟩, + ⟨7, 2, 8, 6, 3, 8, -3247793170020558400965648664287870219712764837888000000⟩, + ⟨7, 2, 7, 7, 1, 8, -8752032523037354950314315792868194916664812240896000000⟩, + ⟨7, 2, 8, 7, 2, 8, 1277443530287558287602613205631592788660188086272000000⟩, + ⟨0, 8, 8, 2, 8, 6, 235010670796799244738552150605187514329345294336000000⟩, + ⟨0, 8, 8, 3, 7, 6, 143957375369949326707265233192521399456057262080000000⟩, + ⟨0, 8, 8, 4, 6, 6, -183623143573471257006373998348735404904642772992000000⟩, + ⟨0, 8, 8, 5, 5, 6, -61379667787329858385365528485329324059534557184000000⟩, + ⟨0, 8, 8, 6, 4, 6, 91434417825816534571652083709603293960825995264000000⟩, + ⟨0, 8, 8, 7, 3, 6, 437920438144294229059229201743671060085516271616000000⟩, + ⟨1, 7, 8, 2, 8, 6, -785975961051887532305760491888397881544057815040000000⟩, + ⟨1, 7, 8, 3, 7, 6, -481454889147290008138619688372625888658010931200000000⟩, + ⟨1, 7, 8, 4, 6, 6, 614114143209761972224134245925538924644406394880000000⟩, + ⟨1, 7, 8, 5, 5, 6, 205279799485807939585425256847897595651827957760000000⟩, + ⟨1, 7, 8, 6, 4, 6, -305795707829811295952455389978059852162751528960000000⟩, + ⟨1, 7, 8, 7, 3, 6, -1464592803670313711369454409831034925210654474240000000⟩, + ⟨1, 8, 7, 1, 8, 7, 1548089070848500863925724374806908217462538371072000000⟩, + ⟨1, 8, 7, 2, 7, 7, -91400951945139937288025677117314389419008983040000000⟩, + ⟨1, 8, 8, 2, 8, 7, -1477576210278400141444183402078654274314161881088000000⟩ +] + +def collectedFourData_16_10 : List CollectedFourTerm := [ + ⟨1, 8, 7, 3, 6, 7, -71367791300744805111113291216919475698869993472000000⟩, + ⟨1, 8, 8, 3, 7, 7, -905099297915164408156034913856215978712120688640000000⟩, + ⟨1, 8, 7, 4, 5, 7, -245712884019501723288555037315086747421837885440000000⟩, + ⟨1, 8, 8, 4, 6, 7, 1154488805469132177521030250379107831375238004736000000⟩, + ⟨1, 8, 7, 5, 4, 7, 155698848452354586096385614727340779039264604160000000⟩, + ⟨1, 8, 8, 5, 5, 7, 385910718904195613787663225698713181237198979072000000⟩, + ⟨1, 8, 7, 6, 3, 7, 466865868628850322066614833237673341024664027136000000⟩, + ⟨1, 8, 8, 6, 4, 7, -574873132875300138788443355606571593179135475712000000⟩, + ⟨1, 8, 7, 7, 2, 7, -829065898075349607646132635026880697791166808064000000⟩, + ⟨1, 8, 8, 7, 3, 7, -2753325281796164008060286281024538957770892771328000000⟩, + ⟨2, 6, 8, 2, 8, 6, 54255620378492746468709955219054599809492058112000000⟩, + ⟨2, 6, 8, 3, 7, 6, 33234647100384041109903899614689518970847887360000000⟩, + ⟨2, 6, 8, 4, 6, 6, -42392064737527710387071620212999508521243377664000000⟩, + ⟨2, 6, 8, 5, 5, 6, -14170386149430643586751665857137528650468425728000000⟩, + ⟨2, 6, 8, 6, 4, 6, 21108960909163775008428225396737557529087705088000000⟩, + ⟨2, 6, 8, 7, 3, 6, 101100281818623018402150150270384035522383183872000000⟩, + ⟨2, 7, 7, 1, 8, 7, -91400951945139937288025677117314389419008983040000000⟩, + ⟨2, 7, 7, 2, 7, 7, 5396416894732623936436235182709260537351372800000000⟩, + ⟨2, 7, 8, 2, 8, 7, 87237791890693145079251119153077296757378908160000000⟩, + ⟨2, 7, 7, 3, 6, 7, 4213636144033287491239352677157510822536151040000000⟩, + ⟨2, 7, 8, 3, 7, 7, 53438099261938180667786218105606599873449164800000000⟩, + ⟨2, 7, 7, 4, 5, 7, 14507170115385462589528228871733647277608140800000000⟩, + ⟨2, 7, 8, 4, 6, 7, -68162341442053042703908526960959913251590635520000000⟩, + ⟨2, 7, 7, 5, 4, 7, -9192638352202386931713675526328429304820531200000000⟩ +] + +def collectedFourData_16_11 : List CollectedFourTerm := [ + ⟨2, 7, 8, 5, 5, 7, -22784610871481721426691415173711251085763543040000000⟩, + ⟨2, 7, 7, 6, 3, 7, -27564295638353182487548573182290362493325803520000000⟩, + ⟨2, 7, 8, 6, 4, 7, 33941168232450761558664653168759111459631267840000000⟩, + ⟨2, 7, 7, 7, 2, 7, 48949000245706822097857248717840737731325460480000000⟩, + ⟨2, 7, 8, 7, 3, 7, 162559478333412821559309927285868613654764584960000000⟩, + ⟨2, 8, 6, 0, 8, 8, 235010670796799244738552150605187514329345294336000000⟩, + ⟨2, 8, 6, 1, 7, 8, -785975961051887532305760491888397881544057815040000000⟩, + ⟨2, 8, 7, 1, 8, 8, -1477576210278400141444183402078654274314161881088000000⟩, + ⟨2, 8, 6, 2, 6, 8, 54255620378492746468709955219054599809492058112000000⟩, + ⟨2, 8, 7, 2, 7, 8, 87237791890693145079251119153077296757378908160000000⟩, + ⟨2, 8, 8, 2, 8, 8, 705137546118085866228389937363501249290909515776000000⟩, + ⟨2, 8, 6, 3, 5, 8, -132174202217908763113739225762196108104372846592000000⟩, + ⟨2, 8, 7, 3, 6, 8, 68117108112065449454238585450756498869282930688000000⟩, + ⟨2, 8, 8, 3, 7, 8, 431936771508286617099674119925486857915497185280000000⟩, + ⟨2, 8, 6, 4, 4, 8, 61082893872745544846009839963540436565318696960000000⟩, + ⟨2, 8, 7, 4, 5, 8, 234521074286197298654289967898929088729721077760000000⟩, + ⟨2, 8, 8, 4, 6, 8, -550951888401017886848512498146754556525304348672000000⟩, + ⟨2, 8, 6, 5, 3, 8, 22626693694860763740225214479293157166710521856000000⟩, + ⟨2, 8, 7, 5, 4, 8, -148607027058751758700462743973693826408267120640000000⟩, + ⟨2, 8, 8, 5, 5, 8, -184166566472736392787157713236872367221499756544000000⟩, + ⟨2, 8, 6, 6, 2, 8, 1621269862721787851666884431014980512063135154176000000⟩, + ⟨2, 8, 7, 6, 3, 8, -445600911386098295443043877317586863209467346944000000⟩, + ⟨2, 8, 8, 6, 4, 8, 274344312953257389150273550237580892797166157824000000⟩, + ⟨2, 8, 6, 7, 1, 8, -3214093067376433135872989379497783131934816206848000000⟩ +] + +def collectedFourData_16_12 : List CollectedFourTerm := [ + ⟨2, 8, 7, 7, 2, 8, 791303337008775513092558235166947390163418873856000000⟩, + ⟨2, 8, 8, 7, 3, 8, 1313957966678976428560285008923520364948022624256000000⟩, + ⟨3, 5, 8, 2, 8, 6, -132174202217908763113739225762196108104372846592000000⟩, + ⟨3, 5, 8, 3, 7, 6, -80964201235607158817699895927466936195885301760000000⟩, + ⟨3, 5, 8, 4, 6, 6, 103272938323524989745317851378158155775527092224000000⟩, + ⟨3, 5, 8, 5, 5, 6, 34521022363300664961498689049836056739051470848000000⟩, + ⟨3, 5, 8, 6, 4, 6, -51424351032280161092987903006605564844187844608000000⟩, + ⟨3, 5, 8, 7, 3, 6, -246294282512330411670713794778760288219275722752000000⟩, + ⟨3, 6, 7, 1, 8, 7, -71367791300744805111113291216919475698869993472000000⟩, + ⟨3, 6, 7, 2, 7, 7, 4213636144033287491239352677157510822536151040000000⟩, + ⟨3, 6, 8, 2, 8, 7, 68117108112065449454238585450756498869282930688000000⟩, + ⟨3, 6, 7, 3, 6, 7, 3290095984176812640687519467393782690319695872000000⟩, + ⟨3, 6, 8, 3, 7, 7, 41725595133008656699221665585680190473387376640000000⟩, + ⟨3, 6, 7, 4, 5, 7, 11327504441974075189610746758136000817859133440000000⟩, + ⟨3, 6, 8, 4, 6, 7, -53222594022066040420000379690197325347276455936000000⟩, + ⟨3, 6, 7, 5, 4, 7, -7177805935948866853315288585077583882915676160000000⟩, + ⟨3, 6, 8, 5, 5, 7, -17790704789602058976633516039765883647764201472000000⟩, + ⟨3, 6, 7, 6, 3, 7, -21522783478784350989256862923935938172300558336000000⟩, + ⟨3, 6, 8, 6, 4, 7, 26501980114724797233040044374219802569040986112000000⟩, + ⟨3, 6, 7, 7, 2, 7, 38220411927574724399558040544511309285230116864000000⟩, + ⟨3, 6, 8, 7, 3, 7, 126929869730682168491631933725196238686863228928000000⟩, + ⟨3, 7, 6, 0, 8, 8, 143957375369949326707265233192521399456057262080000000⟩, + ⟨3, 7, 6, 1, 7, 8, -481454889147290008138619688372625888658010931200000000⟩, + ⟨3, 7, 7, 1, 8, 8, -905099297915164408156034913856215978712120688640000000⟩ +] + +def collectedFourData_16_13 : List CollectedFourTerm := [ + ⟨3, 7, 6, 2, 6, 8, 33234647100384041109903899614689518970847887360000000⟩, + ⟨3, 7, 7, 2, 7, 8, 53438099261938180667786218105606599873449164800000000⟩, + ⟨3, 7, 8, 2, 8, 8, 431936771508286617099674119925486857915497185280000000⟩, + ⟨3, 7, 6, 3, 5, 8, -80964201235607158817699895927466936195885301760000000⟩, + ⟨3, 7, 7, 3, 6, 8, 41725595133008656699221665585680190473387376640000000⟩, + ⟨3, 7, 8, 3, 7, 8, 264585789833630500423277061769906697680610918400000000⟩, + ⟨3, 7, 6, 4, 4, 8, 37416739640408574872252860732665056690228428800000000⟩, + ⟨3, 7, 7, 4, 5, 8, 143657469717080130896120439577608990692789452800000000⟩, + ⟨3, 7, 8, 4, 6, 8, -337489304381016145533642274197202228899647324160000000⟩, + ⟨3, 7, 6, 5, 3, 8, 13860134208239107473134625990658648148992327680000000⟩, + ⟨3, 7, 7, 5, 4, 8, -91030239198824962804931844606722023525397299200000000⟩, + ⟨3, 7, 8, 5, 5, 8, -112812475494927707621704895011650672032816824320000000⟩, + ⟨3, 7, 6, 6, 2, 8, 993119816272637787112527031681113352266087137280000000⟩, + ⟨3, 7, 7, 6, 3, 8, -272955851102884236046129415767699868763889336320000000⟩, + ⟨3, 7, 8, 6, 4, 8, 168051463818726383174357107908638994227496222720000000⟩, + ⟨3, 7, 6, 7, 1, 8, -1968814439810376093487290942429424062807083581440000000⟩, + ⟨3, 7, 7, 7, 2, 8, 484718209309571810028035134666714458915266887680000000⟩, + ⟨3, 7, 8, 7, 3, 8, 804873836529285731497180435718647211563344199680000000⟩, + ⟨4, 4, 8, 2, 8, 6, 61082893872745544846009839963540436565318696960000000⟩, + ⟨4, 4, 8, 3, 7, 6, 37416739640408574872252860732665056690228428800000000⟩, + ⟨4, 4, 8, 4, 6, 6, -47726483880284399873524091892843607873416069120000000⟩, + ⟨4, 4, 8, 5, 5, 6, -15953521262188199405357728303510078422767370240000000⟩, + ⟨4, 4, 8, 6, 4, 6, 23765213815332386409663612679921693245875159040000000⟩, + ⟨4, 4, 8, 7, 3, 6, 113822268398199353448393591316256957405079797760000000⟩ +] + +def collectedFourData_16_14 : List CollectedFourTerm := [ + ⟨4, 5, 7, 1, 8, 7, -245712884019501723288555037315086747421837885440000000⟩, + ⟨4, 5, 7, 2, 7, 7, 14507170115385462589528228871733647277608140800000000⟩, + ⟨4, 5, 8, 2, 8, 7, 234521074286197298654289967898929088729721077760000000⟩, + ⟨4, 5, 7, 3, 6, 7, 11327504441974075189610746758136000817859133440000000⟩, + ⟨4, 5, 8, 3, 7, 7, 143657469717080130896120439577608990692789452800000000⟩, + ⟨4, 5, 7, 4, 5, 7, 38999578583737387425480376614253794194934988800000000⟩, + ⟨4, 5, 8, 4, 6, 7, -183240602431596621291568094871491655607485726720000000⟩, + ⟨4, 5, 7, 5, 4, 7, -24712540003124475426199834543013979816670003200000000⟩, + ⟨4, 5, 8, 5, 5, 7, -61251795844031730246251816875060887968746045440000000⟩, + ⟨4, 5, 7, 6, 3, 7, -74101006971252538324111799597406521918194974720000000⟩, + ⟨4, 5, 8, 6, 4, 7, 91243932977768307782865630693288210333947658240000000⟩, + ⟨4, 5, 7, 7, 2, 7, 131589439325127889562820723358881780652604129280000000⟩, + ⟨4, 5, 8, 7, 3, 7, 437008120768620230818974932624494932326413762560000000⟩, + ⟨4, 6, 6, 0, 8, 8, -183623143573471257006373998348735404904642772992000000⟩, + ⟨4, 6, 6, 1, 7, 8, 614114143209761972224134245925538924644406394880000000⟩, + ⟨4, 6, 7, 1, 8, 8, 1154488805469132177521030250379107831375238004736000000⟩, + ⟨4, 6, 6, 2, 6, 8, -42392064737527710387071620212999508521243377664000000⟩, + ⟨4, 6, 7, 2, 7, 8, -68162341442053042703908526960959913251590635520000000⟩, + ⟨4, 6, 8, 2, 8, 8, -550951888401017886848512498146754556525304348672000000⟩, + ⟨4, 6, 6, 3, 5, 8, 103272938323524989745317851378158155775527092224000000⟩, + ⟨4, 6, 7, 3, 6, 8, -53222594022066040420000379690197325347276455936000000⟩, + ⟨4, 6, 8, 3, 7, 8, -337489304381016145533642274197202228899647324160000000⟩, + ⟨4, 6, 6, 4, 4, 8, -47726483880284399873524091892843607873416069120000000⟩, + ⟨4, 6, 7, 4, 5, 8, -183240602431596621291568094871491655607485726720000000⟩ +] + +def collectedFourData_16_15 : List CollectedFourTerm := [ + ⟨4, 6, 8, 4, 6, 8, 430480528236988818421834977040970496714404265984000000⟩, + ⟨4, 6, 6, 5, 3, 8, -17679131806388433297462492671796498405557010432000000⟩, + ⟨4, 6, 7, 5, 4, 8, 116112555115550736381394226805363383512156078080000000⟩, + ⟨4, 6, 8, 5, 5, 8, 143896631426138163798944978855512759755098554368000000⟩, + ⟨4, 6, 6, 6, 2, 8, -1266762346426864810554108724733079914032473833472000000⟩, + ⟨4, 6, 7, 6, 3, 8, 348165637970825124292851561776668465239234183168000000⟩, + ⟨4, 6, 8, 6, 4, 8, -214356075812143136196183851037198815333374230528000000⟩, + ⟨4, 6, 6, 7, 1, 8, 2511298192411267560726457972711832845184931987456000000⟩, + ⟨4, 6, 7, 7, 2, 8, -618276633010266910098926221331281737574023954432000000⟩, + ⟨4, 6, 8, 7, 3, 8, -1026647392422515044721256427994086547483611103232000000⟩, + ⟨5, 3, 8, 2, 8, 6, 22626693694860763740225214479293157166710521856000000⟩, + ⟨5, 3, 8, 3, 7, 6, 13860134208239107473134625990658648148992327680000000⟩, + ⟨5, 3, 8, 4, 6, 6, -17679131806388433297462492671796498405557010432000000⟩, + ⟨5, 3, 8, 5, 5, 6, -5909599497790719100956115399077336991414616064000000⟩, + ⟨5, 3, 8, 6, 4, 6, 8803253734386790514086720378358596669217439744000000⟩, + ⟨5, 3, 8, 7, 3, 6, 42162730666717955306613704630860749857133428736000000⟩, + ⟨5, 4, 7, 1, 8, 7, 155698848452354586096385614727340779039264604160000000⟩, + ⟨5, 4, 7, 2, 7, 7, -9192638352202386931713675526328429304820531200000000⟩, + ⟨5, 4, 8, 2, 8, 7, -148607027058751758700462743973693826408267120640000000⟩, + ⟨5, 4, 7, 3, 6, 7, -7177805935948866853315288585077583882915676160000000⟩, + ⟨5, 4, 8, 3, 7, 7, -91030239198824962804931844606722023525397299200000000⟩, + ⟨5, 4, 7, 4, 5, 7, -24712540003124475426199834543013979816670003200000000⟩, + ⟨5, 4, 8, 4, 6, 7, 116112555115550736381394226805363383512156078080000000⟩, + ⟨5, 4, 7, 5, 4, 7, 15659390577637935042327151097821740007214284800000000⟩ +] + +def collectedFourData_16_16 : List CollectedFourTerm := [ + ⟨5, 4, 8, 5, 5, 7, 38812918242404985323808897859799920853290844160000000⟩, + ⟨5, 4, 7, 6, 3, 7, 46954971452242678538837820239176988323039150080000000⟩, + ⟨5, 4, 8, 6, 4, 7, -57817787413112615524789993831757060842570383360000000⟩, + ⟨5, 4, 7, 7, 2, 7, -83383190316496713756804239469198777874561105920000000⟩, + ⟨5, 4, 8, 7, 3, 7, -276915316994941731230744662712842709200892067840000000⟩, + ⟨5, 5, 6, 0, 8, 8, -61379667787329858385365528485329324059534557184000000⟩, + ⟨5, 5, 6, 1, 7, 8, 205279799485807939585425256847897595651827957760000000⟩, + ⟨5, 5, 7, 1, 8, 8, 385910718904195613787663225698713181237198979072000000⟩, + ⟨5, 5, 6, 2, 6, 8, -14170386149430643586751665857137528650468425728000000⟩, + ⟨5, 5, 7, 2, 7, 8, -22784610871481721426691415173711251085763543040000000⟩, + ⟨5, 5, 8, 2, 8, 8, -184166566472736392787157713236872367221499756544000000⟩, + ⟨5, 5, 6, 3, 5, 8, 34521022363300664961498689049836056739051470848000000⟩, + ⟨5, 5, 7, 3, 6, 8, -17790704789602058976633516039765883647764201472000000⟩, + ⟨5, 5, 8, 3, 7, 8, -112812475494927707621704895011650672032816824320000000⟩, + ⟨5, 5, 6, 4, 4, 8, -15953521262188199405357728303510078422767370240000000⟩, + ⟨5, 5, 7, 4, 5, 8, -61251795844031730246251816875060887968746045440000000⟩, + ⟨5, 5, 8, 4, 6, 8, 143896631426138163798944978855512759755098554368000000⟩, + ⟨5, 5, 6, 5, 3, 8, -5909599497790719100956115399077336991414616064000000⟩, + ⟨5, 5, 7, 5, 4, 8, 38812918242404985323808897859799920853290844160000000⟩, + ⟨5, 5, 8, 5, 5, 8, 48100295315542405326660219186377842829385793536000000⟩, + ⟨5, 5, 6, 6, 2, 8, -423440370729023732464855175240694504327840006144000000⟩, + ⟨5, 5, 7, 6, 3, 8, 116381251174160012497601925279759173775456731136000000⟩, + ⟨5, 5, 8, 6, 4, 8, -71652758282512579087203509926955316366966521856000000⟩, + ⟨5, 5, 6, 7, 1, 8, 839451094047140376097856690757902216720403136512000000⟩ +] + +def collectedFourData_16_17 : List CollectedFourTerm := [ + ⟨5, 5, 7, 7, 2, 8, -206671194035269590192837581219415311993026904064000000⟩, + ⟨5, 5, 8, 7, 3, 8, -343177197902664065487858751591660083229872881664000000⟩, + ⟨6, 2, 8, 2, 8, 6, 1621269862721787851666884431014980512063135154176000000⟩, + ⟨6, 2, 8, 3, 7, 6, 993119816272637787112527031681113352266087137280000000⟩, + ⟨6, 2, 8, 4, 6, 6, -1266762346426864810554108724733079914032473833472000000⟩, + ⟨6, 2, 8, 5, 5, 6, -423440370729023732464855175240694504327840006144000000⟩, + ⟨6, 2, 8, 6, 4, 6, 630779298377829808787151562127507656381430759424000000⟩, + ⟨6, 2, 8, 7, 3, 6, 3021084984039519820567183303587917490835377094656000000⟩, + ⟨6, 3, 7, 1, 8, 7, 466865868628850322066614833237673341024664027136000000⟩, + ⟨6, 3, 7, 2, 7, 7, -27564295638353182487548573182290362493325803520000000⟩, + ⟨6, 3, 8, 2, 8, 7, -445600911386098295443043877317586863209467346944000000⟩, + ⟨6, 3, 7, 3, 6, 7, -21522783478784350989256862923935938172300558336000000⟩, + ⟨6, 3, 8, 3, 7, 7, -272955851102884236046129415767699868763889336320000000⟩, + ⟨6, 3, 7, 4, 5, 7, -74101006971252538324111799597406521918194974720000000⟩, + ⟨6, 3, 8, 4, 6, 7, 348165637970825124292851561776668465239234183168000000⟩, + ⟨6, 3, 7, 5, 4, 7, 46954971452242678538837820239176988323039150080000000⟩, + ⟨6, 3, 8, 5, 5, 7, 116381251174160012497601925279759173775456731136000000⟩, + ⟨6, 3, 7, 6, 3, 7, 140795347887254286333675832613704689525737914368000000⟩, + ⟨6, 3, 8, 6, 4, 7, -173367701888181953886622044796935530596276371456000000⟩, + ⟨6, 3, 7, 7, 2, 7, -250026033995161967746135276057553515104260063232000000⟩, + ⟨6, 3, 8, 7, 3, 7, -830335685141811415743610982021196939594578264064000000⟩, + ⟨6, 4, 6, 0, 8, 8, 91434417825816534571652083709603293960825995264000000⟩, + ⟨6, 4, 6, 1, 7, 8, -305795707829811295952455389978059852162751528960000000⟩, + ⟨6, 4, 7, 1, 8, 8, -574873132875300138788443355606571593179135475712000000⟩ +] + +def collectedFourData_16_18 : List CollectedFourTerm := [ + ⟨6, 4, 6, 2, 6, 8, 21108960909163775008428225396737557529087705088000000⟩, + ⟨6, 4, 7, 2, 7, 8, 33941168232450761558664653168759111459631267840000000⟩, + ⟨6, 4, 8, 2, 8, 8, 274344312953257389150273550237580892797166157824000000⟩, + ⟨6, 4, 6, 3, 5, 8, -51424351032280161092987903006605564844187844608000000⟩, + ⟨6, 4, 7, 3, 6, 8, 26501980114724797233040044374219802569040986112000000⟩, + ⟨6, 4, 8, 3, 7, 8, 168051463818726383174357107908638994227496222720000000⟩, + ⟨6, 4, 6, 4, 4, 8, 23765213815332386409663612679921693245875159040000000⟩, + ⟨6, 4, 7, 4, 5, 8, 91243932977768307782865630693288210333947658240000000⟩, + ⟨6, 4, 8, 4, 6, 8, -214356075812143136196183851037198815333374230528000000⟩, + ⟨6, 4, 6, 5, 3, 8, 8803253734386790514086720378358596669217439744000000⟩, + ⟨6, 4, 7, 5, 4, 8, -57817787413112615524789993831757060842570383360000000⟩, + ⟨6, 4, 8, 5, 5, 8, -71652758282512579087203509926955316366966521856000000⟩, + ⟨6, 4, 6, 6, 2, 8, 630779298377829808787151562127507656381430759424000000⟩, + ⟨6, 4, 7, 6, 3, 8, -173367701888181953886622044796935530596276371456000000⟩, + ⟨6, 4, 8, 6, 4, 8, 106737759837270967343630545995722812229551128576000000⟩, + ⟨6, 4, 6, 7, 1, 8, -1250490998800891885516081790377887516168082685952000000⟩, + ⟨6, 4, 7, 7, 2, 8, 307868403156818289879553785572295099844336287744000000⟩, + ⟨6, 4, 8, 7, 3, 8, 511215007061382017217667724635323964747985977344000000⟩, + ⟨7, 1, 8, 2, 8, 6, -3214093067376433135872989379497783131934816206848000000⟩, + ⟨7, 1, 8, 3, 7, 6, -1968814439810376093487290942429424062807083581440000000⟩, + ⟨7, 1, 8, 4, 6, 6, 2511298192411267560726457972711832845184931987456000000⟩, + ⟨7, 1, 8, 5, 5, 6, 839451094047140376097856690757902216720403136512000000⟩, + ⟨7, 1, 8, 6, 4, 6, -1250490998800891885516081790377887516168082685952000000⟩, + ⟨7, 1, 8, 7, 3, 6, -5989162277312201236828607324710609960757926821888000000⟩ +] + +def collectedFourData_16_19 : List CollectedFourTerm := [ + ⟨7, 2, 7, 1, 8, 7, -829065898075349607646132635026880697791166808064000000⟩, + ⟨7, 2, 7, 2, 7, 7, 48949000245706822097857248717840737731325460480000000⟩, + ⟨7, 2, 8, 2, 8, 7, 791303337008775513092558235166947390163418873856000000⟩, + ⟨7, 2, 7, 3, 6, 7, 38220411927574724399558040544511309285230116864000000⟩, + ⟨7, 2, 8, 3, 7, 7, 484718209309571810028035134666714458915266887680000000⟩, + ⟨7, 2, 7, 4, 5, 7, 131589439325127889562820723358881780652604129280000000⟩, + ⟨7, 2, 8, 4, 6, 7, -618276633010266910098926221331281737574023954432000000⟩, + ⟨7, 2, 7, 5, 4, 7, -83383190316496713756804239469198777874561105920000000⟩, + ⟨7, 2, 8, 5, 5, 7, -206671194035269590192837581219415311993026904064000000⟩, + ⟨7, 2, 7, 6, 3, 7, -250026033995161967746135276057553515104260063232000000⟩, + ⟨7, 2, 8, 6, 4, 7, 307868403156818289879553785572295099844336287744000000⟩, + ⟨7, 2, 7, 7, 2, 7, 443999170522373305361115970536553844009670279168000000⟩, + ⟨7, 2, 8, 7, 3, 7, 1474519871259584799835770063022398546409722740736000000⟩, + ⟨7, 3, 6, 0, 8, 8, 437920438144294229059229201743671060085516271616000000⟩, + ⟨7, 3, 6, 1, 7, 8, -1464592803670313711369454409831034925210654474240000000⟩, + ⟨7, 3, 7, 1, 8, 8, -2753325281796164008060286281024538957770892771328000000⟩, + ⟨7, 3, 6, 2, 6, 8, 101100281818623018402150150270384035522383183872000000⟩, + ⟨7, 3, 7, 2, 7, 8, 162559478333412821559309927285868613654764584960000000⟩, + ⟨7, 3, 8, 2, 8, 8, 1313957966678976428560285008923520364948022624256000000⟩, + ⟨7, 3, 6, 3, 5, 8, -246294282512330411670713794778760288219275722752000000⟩, + ⟨7, 3, 7, 3, 6, 8, 126929869730682168491631933725196238686863228928000000⟩, + ⟨7, 3, 8, 3, 7, 8, 804873836529285731497180435718647211563344199680000000⟩, + ⟨7, 3, 6, 4, 4, 8, 113822268398199353448393591316256957405079797760000000⟩, + ⟨7, 3, 7, 4, 5, 8, 437008120768620230818974932624494932326413762560000000⟩ +] + +def collectedFourData_16_20 : List CollectedFourTerm := [ + ⟨7, 3, 8, 4, 6, 8, -1026647392422515044721256427994086547483611103232000000⟩, + ⟨7, 3, 6, 5, 3, 8, 42162730666717955306613704630860749857133428736000000⟩, + ⟨7, 3, 7, 5, 4, 8, -276915316994941731230744662712842709200892067840000000⟩, + ⟨7, 3, 8, 5, 5, 8, -343177197902664065487858751591660083229872881664000000⟩, + ⟨7, 3, 6, 6, 2, 8, 3021084984039519820567183303587917490835377094656000000⟩, + ⟨7, 3, 7, 6, 3, 8, -830335685141811415743610982021196939594578264064000000⟩, + ⟨7, 3, 8, 6, 4, 8, 511215007061382017217667724635323964747985977344000000⟩, + ⟨7, 3, 6, 7, 1, 8, -5989162277312201236828607324710609960757926821888000000⟩, + ⟨7, 3, 7, 7, 2, 8, 1474519871259584799835770063022398546409722740736000000⟩, + ⟨7, 3, 8, 7, 3, 8, 2448437964626583949576889587814389070474181083136000000⟩, + ⟨0, 8, 8, 3, 8, 5, 12559522586091285333032966468340452809506816000000000⟩, + ⟨0, 8, 8, 4, 7, 5, 4461474770920932910421579257664338063735652352000000⟩, + ⟨0, 8, 8, 5, 6, 5, 9289961417424420077001186310248314801831804928000000⟩, + ⟨0, 8, 8, 6, 5, 5, -9749400062742297993438579466805605577602891776000000⟩, + ⟨0, 8, 8, 7, 4, 5, 19276725808986418895333803093714901398915645440000000⟩, + ⟨1, 7, 8, 3, 8, 5, -99616311860216297821611463140409170003492864000000000⟩, + ⟨1, 7, 8, 4, 7, 5, -35386350005749849505921513760419324760170692608000000⟩, + ⟨1, 7, 8, 5, 6, 5, -73683668099962110184467741258288903848315584512000000⟩, + ⟨1, 7, 8, 6, 5, 5, 77327722486496288133922144248924995932026568704000000⟩, + ⟨1, 7, 8, 7, 4, 5, -152894054425160331035013817547299221713725685760000000⟩, + ⟨1, 8, 7, 2, 8, 6, 21564864443245261585939619595593955217955094528000000⟩, + ⟨1, 8, 7, 3, 7, 6, -12041369940444996845414841330751575660190236672000000⟩, + ⟨1, 8, 8, 3, 8, 6, -54488970223593328377345688006022667360534528000000000⟩, + ⟨1, 8, 7, 4, 6, 6, 3954691027147208313722771737462966911038914560000000⟩ +] + +def collectedFourData_16_21 : List CollectedFourTerm := [ + ⟨1, 8, 8, 4, 7, 6, -19355924102978213892742643440632425644415778816000000⟩, + ⟨1, 8, 7, 5, 5, 6, 10473769431341700736108538446217692893841195008000000⟩, + ⟨1, 8, 8, 5, 6, 6, -40304114076194943847057576348785278838242279424000000⟩, + ⟨1, 8, 7, 6, 4, 6, -3749458425737695344230137516174666606068105216000000⟩, + ⟨1, 8, 8, 6, 5, 6, 42297369671118394955967453235118169528056414208000000⟩, + ⟨1, 8, 7, 7, 3, 6, -157100672038941013710253200725493440847884058624000000⟩, + ⟨1, 8, 8, 7, 4, 6, -83631279088381718546994770119642498391888363520000000⟩, + ⟨2, 6, 8, 3, 8, 5, -69626622345331658563283358643552568173658112000000000⟩, + ⟨2, 6, 8, 4, 7, 5, -24733218707066473347795279214823268225084555264000000⟩, + ⟨2, 6, 8, 5, 6, 5, -51501052749411473830911413017840968148709277696000000⟩, + ⟨2, 6, 8, 6, 5, 5, 54048057289522275839380712406896198541568376832000000⟩, + ⟨2, 6, 8, 7, 4, 5, -106864994171288007289507526471994844924430254080000000⟩, + ⟨2, 7, 7, 2, 8, 6, 28856255176680032962195429007943744119994580992000000⟩, + ⟨2, 7, 7, 3, 7, 6, -16112730251226900636356775445882597636527095808000000⟩, + ⟨2, 7, 8, 3, 8, 6, -72912474512634084634400090279383069718740992000000000⟩, + ⟨2, 7, 7, 4, 6, 6, 5291828924991533011506952413518058936430755840000000⟩, + ⟨2, 7, 8, 4, 7, 6, -25900440346655719758632794755581415532605210624000000⟩, + ⟨2, 7, 7, 5, 5, 6, 14015101470632029927892941441553137426300403712000000⟩, + ⟨2, 7, 8, 5, 6, 6, -53931514548286261354327564454759509054231412736000000⟩, + ⟨2, 7, 7, 6, 4, 6, -5017204230158276759294509385298751404820660224000000⟩, + ⟨2, 7, 8, 6, 5, 6, 56598718519395504288320501168731006196370112512000000⟩, + ⟨2, 7, 7, 7, 3, 6, -210218668089220280190519808585664145276624961536000000⟩, + ⟨2, 7, 8, 7, 4, 6, -111908217020227933131835530300623316684405473280000000⟩, + ⟨2, 8, 6, 1, 8, 7, 21564864443245261585939619595593955217955094528000000⟩ +] + +def collectedFourData_16_22 : List CollectedFourTerm := [ + ⟨2, 8, 6, 2, 7, 7, 28856255176680032962195429007943744119994580992000000⟩, + ⟨2, 8, 7, 2, 8, 7, 135330260810708228147578424940771780424145829888000000⟩, + ⟨2, 8, 6, 3, 6, 7, -76460638981010387558765799586877641736677490688000000⟩, + ⟨2, 8, 7, 3, 7, 7, -75565591374216564134881727716335245008476045312000000⟩, + ⟨2, 8, 8, 3, 8, 7, -170972708200249123448568568001810179182034944000000000⟩, + ⟨2, 8, 6, 4, 5, 7, 60832180436507694827947560266942714232503795712000000⟩, + ⟨2, 8, 7, 4, 6, 7, 24817655104585463004927424980282828033632501760000000⟩, + ⟨2, 8, 8, 4, 7, 7, -60734030208773242901342618172163606419622330368000000⟩, + ⟨2, 8, 6, 5, 4, 7, 68611466852377482779774228600393413936942153728000000⟩, + ⟨2, 8, 7, 5, 5, 7, 65728117723395743803952558849464222804730707968000000⟩, + ⟨2, 8, 8, 5, 6, 7, -126464190953550452958020067953804030293837873152000000⟩, + ⟨2, 8, 6, 6, 3, 7, -254053804496338162028140480511162082674929041408000000⟩, + ⟨2, 8, 7, 6, 4, 7, -23529718352248993246244474119962051544545755136000000⟩, + ⟨2, 8, 8, 6, 5, 7, 132718526570482346827724686112490822338120515584000000⟩, + ⟨2, 8, 6, 7, 2, 7, 250719989999900068063753063184076231242428710912000000⟩, + ⟨2, 8, 7, 7, 3, 7, -985884932248058707517407740428525745977639829504000000⟩, + ⟨2, 8, 8, 7, 4, 7, -262413956757073478981556103508502122595310632960000000⟩, + ⟨3, 5, 8, 3, 8, 5, 26309098822361223032676447926832211584614400000000000⟩, + ⟨3, 5, 8, 4, 7, 5, 9345688089419635451580374507343196577385676800000000⟩, + ⟨3, 5, 8, 5, 6, 5, 19460175441509857718922702305774874850964275200000000⟩, + ⟨3, 5, 8, 6, 5, 5, -20422585966243155376962250213384260260619878400000000⟩, + ⟨3, 5, 8, 7, 4, 5, 40379981070444383188287785385297267545604096000000000⟩, + ⟨3, 6, 7, 2, 8, 6, -76460638981010387558765799586877641736677490688000000⟩, + ⟨3, 6, 7, 3, 7, 6, 42694023988708281382689997208682003918080704512000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1602.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1602.lean new file mode 100644 index 0000000000000000000000000000000000000000..e1374c38511a7402d2421bf59a8221f06a1141b8 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1602.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1602. -/ +namespace LaughlinFock +def collectedFourData_16_23 : List CollectedFourTerm := [ + ⟨3, 6, 8, 3, 8, 6, 193196738689363186296166285158507223279730688000000000⟩, + ⟨3, 6, 7, 4, 6, 6, -14021799381301347883878212815332309284432117760000000⟩, + ⟨3, 6, 8, 4, 7, 6, 68628593927712944185315922281060825759362318336000000⟩, + ⟨3, 6, 7, 5, 5, 6, -37135921042666404320385903579668046110961696768000000⟩, + ⟨3, 6, 8, 5, 6, 6, 142902744598270417017784839307545969967396552704000000⟩, + ⟨3, 6, 7, 6, 4, 6, 13294124237096041737627806895442669434606452736000000⟩, + ⟨3, 6, 8, 6, 5, 6, -149970055261939295838517351366474855050765139968000000⟩, + ⟨3, 6, 7, 7, 3, 6, 557018004915217207889330548805648078108469755904000000⟩, + ⟨3, 6, 8, 7, 4, 6, 296524054427794955108315840432957886744672337920000000⟩, + ⟨3, 7, 6, 1, 8, 7, -12041369940444996845414841330751575660190236672000000⟩, + ⟨3, 7, 6, 2, 7, 7, -16112730251226900636356775445882597636527095808000000⟩, + ⟨3, 7, 7, 2, 8, 7, -75565591374216564134881727716335245008476045312000000⟩, + ⟨3, 7, 6, 3, 6, 7, 42694023988708281382689997208682003918080704512000000⟩, + ⟨3, 7, 7, 3, 7, 7, 42194248097416266610629775298088362416420159488000000⟩, + ⟨3, 7, 8, 3, 8, 7, 95467589632997308564016741523833201576902656000000000⟩, + ⟨3, 7, 6, 4, 5, 7, -33967419125109826241674436102614592981028569088000000⟩, + ⟨3, 7, 7, 4, 6, 7, -13857660313848696557496935721920822136526602240000000⟩, + ⟨3, 7, 8, 4, 7, 7, 33912614087730625188343274553781867304642936832000000⟩, + ⟨3, 7, 6, 5, 4, 7, -38311210195658741002825629599861770011354857472000000⟩, + ⟨3, 7, 7, 5, 5, 7, -36701208258437933769276384599873074636869599232000000⟩, + ⟨3, 7, 8, 5, 6, 7, 70614963126641128995982960394176052368295067648000000⟩, + ⟨3, 7, 6, 6, 3, 7, 141858338723576456137564111153897626744014241792000000⟩, + ⟨3, 7, 7, 6, 4, 7, 13138503328856081089326118283926307602918539264000000⟩, + ⟨3, 7, 8, 6, 5, 7, -74107253518420880227020283488093681369288278016000000⟩ +] + +def collectedFourData_16_24 : List CollectedFourTerm := [ + ⟨3, 7, 6, 7, 2, 7, -139996806332771022486114731407172665023437733888000000⟩, + ⟨3, 7, 7, 7, 3, 7, 550497556761962091644595816197976389539747332096000000⟩, + ⟨3, 7, 8, 7, 4, 7, 146526473150987315943885598434987142317908951040000000⟩, + ⟨3, 8, 5, 0, 8, 8, 12559522586091285333032966468340452809506816000000000⟩, + ⟨3, 8, 5, 1, 7, 8, -99616311860216297821611463140409170003492864000000000⟩, + ⟨3, 8, 6, 1, 8, 8, -54488970223593328377345688006022667360534528000000000⟩, + ⟨3, 8, 5, 2, 6, 8, -69626622345331658563283358643552568173658112000000000⟩, + ⟨3, 8, 6, 2, 7, 8, -72912474512634084634400090279383069718740992000000000⟩, + ⟨3, 8, 7, 2, 8, 8, -170972708200249123448568568001810179182034944000000000⟩, + ⟨3, 8, 5, 3, 5, 8, 26309098822361223032676447926832211584614400000000000⟩, + ⟨3, 8, 6, 3, 6, 8, 193196738689363186296166285158507223279730688000000000⟩, + ⟨3, 8, 7, 3, 7, 8, 95467589632997308564016741523833201576902656000000000⟩, + ⟨3, 8, 8, 3, 8, 8, 144001628678427505210712557778601297051648000000000000⟩, + ⟨3, 8, 5, 4, 4, 8, -94781365223433891365058961399457788131803136000000000⟩, + ⟨3, 8, 6, 4, 5, 8, -153707568028760727906864640996770604973555712000000000⟩, + ⟨3, 8, 7, 4, 6, 8, -31353975666578837948689173942858263958650880000000000⟩, + ⟨3, 8, 8, 4, 7, 8, 51153189057663999719573596550539287730323456000000000⟩, + ⟨3, 8, 5, 5, 3, 8, 247195249326119477200132561623430195002212352000000000⟩, + ⟨3, 8, 6, 5, 4, 8, -173363861579351817426217859252360499563593728000000000⟩, + ⟨3, 8, 7, 5, 5, 8, -83039182993908489661190584658189521973673984000000000⟩, + ⟨3, 8, 8, 5, 6, 8, 106514365120084048286952831605626111612944384000000000⟩, + ⟨3, 8, 5, 6, 2, 8, 3658471052160713159795542889250988813713408000000000⟩, + ⟨3, 8, 6, 6, 3, 8, 641929849585845143997634405561322289556881408000000000⟩, + ⟨3, 8, 7, 6, 4, 8, 29726830095304095223090487588449075297517568000000000⟩ +] + +def collectedFourData_16_25 : List CollectedFourTerm := [ + ⟨3, 8, 8, 6, 5, 8, -111782074362221315209030133696489535232278528000000000⟩, + ⟨3, 8, 5, 7, 1, 8, -170545332237791480074963631146383105469710336000000000⟩, + ⟨3, 8, 6, 7, 2, 8, -633506141692596641263397443965852162994470912000000000⟩, + ⟨3, 8, 7, 7, 3, 8, 1245541210299154163929328838017708800188874752000000000⟩, + ⟨3, 8, 8, 7, 4, 8, 221017948178667071910458336862301428457144320000000000⟩, + ⟨4, 4, 8, 3, 8, 5, -94781365223433891365058961399457788131803136000000000⟩, + ⟨4, 4, 8, 4, 7, 5, -33668849018678736386291832612861434273980219392000000⟩, + ⟨4, 4, 8, 5, 6, 5, -70107380275076466493445056513945831550629183488000000⟩, + ⟨4, 4, 8, 6, 5, 5, 73574567960049270825774166540739101090482487296000000⟩, + ⟨4, 4, 8, 7, 4, 5, -145473235681496495449199011653474408827442954240000000⟩, + ⟨4, 5, 7, 2, 8, 6, 60832180436507694827947560266942714232503795712000000⟩, + ⟨4, 5, 7, 3, 7, 6, -33967419125109826241674436102614592981028569088000000⟩, + ⟨4, 5, 8, 3, 8, 6, -153707568028760727906864640996770604973555712000000000⟩, + ⟨4, 5, 7, 4, 6, 6, 11155761204397979668270427543139622324524810240000000⟩, + ⟨4, 5, 8, 4, 7, 6, -54600995552120639328173437585127573777194942464000000⟩, + ⟨4, 5, 7, 5, 5, 6, 29545385438178735285162534832517116612294213632000000⟩, + ⟨4, 5, 8, 5, 6, 6, -113693603141783300903211878193304157704993898496000000⟩, + ⟨4, 5, 7, 6, 4, 6, -10576821945435564086324073128455420907895128064000000⟩, + ⟨4, 5, 8, 6, 5, 6, 119316364384988896400656371910426367598035730432000000⟩, + ⟨4, 5, 7, 7, 3, 6, -443164224533900901669731982971314109511993655296000000⟩, + ⟨4, 5, 8, 7, 4, 6, -235914910248087043665360225088739656547256238080000000⟩, + ⟨4, 6, 6, 1, 8, 7, 3954691027147208313722771737462966911038914560000000⟩, + ⟨4, 6, 6, 2, 7, 7, 5291828924991533011506952413518058936430755840000000⟩, + ⟨4, 6, 7, 2, 8, 7, 24817655104585463004927424980282828033632501760000000⟩ +] + +def collectedFourData_16_26 : List CollectedFourTerm := [ + ⟨4, 6, 6, 3, 6, 7, -14021799381301347883878212815332309284432117760000000⟩, + ⟨4, 6, 7, 3, 7, 7, -13857660313848696557496935721920822136526602240000000⟩, + ⟨4, 6, 8, 3, 8, 7, -31353975666578837948689173942858263958650880000000000⟩, + ⟨4, 6, 6, 4, 5, 7, 11155761204397979668270427543139622324524810240000000⟩, + ⟨4, 6, 7, 4, 6, 7, 4551206812138364901385253419439234508600115200000000⟩, + ⟨4, 6, 8, 4, 7, 7, -11137761841315710301552282143005047457694351360000000⟩, + ⟨4, 6, 6, 5, 4, 7, 12582372267380330155420310156065337032373698560000000⟩, + ⟨4, 6, 7, 5, 5, 7, 12053606832358619460936531520439029482242703360000000⟩, + ⟨4, 6, 8, 5, 6, 7, -23191743334889883344231446134233498765009879040000000⟩, + ⟨4, 6, 6, 6, 3, 7, -46589873249538650470394345115657098095660892160000000⟩, + ⟨4, 6, 7, 6, 4, 7, -4315017434208212843271520224286681194005790720000000⟩, + ⟨4, 6, 8, 6, 5, 7, 24338699997202460615378968761090106015277383680000000⟩, + ⟨4, 6, 6, 7, 2, 7, 45978498839561003099432990675767251809064714240000000⟩, + ⟨4, 6, 7, 7, 3, 7, -180797347723753949077992396086845721213487022080000000⟩, + ⟨4, 6, 8, 7, 4, 7, -48123006890055010080061462567557155991532339200000000⟩, + ⟨4, 7, 5, 0, 8, 8, 4461474770920932910421579257664338063735652352000000⟩, + ⟨4, 7, 5, 1, 7, 8, -35386350005749849505921513760419324760170692608000000⟩, + ⟨4, 7, 6, 1, 8, 8, -19355924102978213892742643440632425644415778816000000⟩, + ⟨4, 7, 5, 2, 6, 8, -24733218707066473347795279214823268225084555264000000⟩, + ⟨4, 7, 6, 2, 7, 8, -25900440346655719758632794755581415532605210624000000⟩, + ⟨4, 7, 7, 2, 8, 8, -60734030208773242901342618172163606419622330368000000⟩, + ⟨4, 7, 5, 3, 5, 8, 9345688089419635451580374507343196577385676800000000⟩, + ⟨4, 7, 6, 3, 6, 8, 68628593927712944185315922281060825759362318336000000⟩, + ⟨4, 7, 7, 3, 7, 8, 33912614087730625188343274553781867304642936832000000⟩ +] + +def collectedFourData_16_27 : List CollectedFourTerm := [ + ⟨4, 7, 8, 3, 8, 8, 51153189057663999719573596550539287730323456000000000⟩, + ⟨4, 7, 5, 4, 4, 8, -33668849018678736386291832612861434273980219392000000⟩, + ⟨4, 7, 6, 4, 5, 8, -54600995552120639328173437585127573777194942464000000⟩, + ⟨4, 7, 7, 4, 6, 8, -11137761841315710301552282143005047457694351360000000⟩, + ⟨4, 7, 8, 4, 7, 8, 18170966361862468523491934120545633970455314432000000⟩, + ⟨4, 7, 5, 5, 3, 8, 87810293806973213402395215885699275837663084544000000⟩, + ⟨4, 7, 6, 5, 4, 8, -61583431163398945137567186061502334510317961216000000⟩, + ⟨4, 7, 7, 5, 5, 8, -29497715170756937084801366671783558899195445248000000⟩, + ⟨4, 7, 8, 5, 6, 8, 37836721058981632241853347576995088477661954048000000⟩, + ⟨4, 7, 5, 6, 2, 8, 1299585727680059209651720399634650195008946176000000⟩, + ⟨4, 7, 6, 6, 3, 8, 228030469231364583527378441352133806425873842176000000⟩, + ⟨4, 7, 7, 6, 4, 8, 10559756677098934878873576388290589353308061696000000⟩, + ⟨4, 7, 8, 6, 5, 8, -39707950775178714784796061471103043134675746816000000⟩, + ⟨4, 7, 5, 7, 1, 8, -60582214957744960767227679713385276916516257792000000⟩, + ⟨4, 7, 6, 7, 2, 8, -225038145280695065393246602786431675555448356864000000⟩, + ⟨4, 7, 7, 7, 3, 8, 442449197236676813301448074424058675664041017344000000⟩, + ⟨4, 7, 8, 7, 4, 8, 78511423739292947863881289709659886562878423040000000⟩, + ⟨5, 3, 8, 3, 8, 5, 247195249326119477200132561623430195002212352000000000⟩, + ⟨5, 3, 8, 4, 7, 5, 87810293806973213402395215885699275837663084544000000⟩, + ⟨5, 3, 8, 5, 6, 5, 182844078114353321941706111524296019998582767616000000⟩, + ⟨5, 3, 8, 6, 5, 5, -191886702919628858034054226453467428922926825472000000⟩, + ⟨5, 3, 8, 7, 4, 5, 379402561672259897332652075367168939822604615680000000⟩, + ⟨5, 4, 7, 2, 8, 6, 68611466852377482779774228600393413936942153728000000⟩, + ⟨5, 4, 7, 3, 7, 6, -38311210195658741002825629599861770011354857472000000⟩ +] + +def collectedFourData_16_28 : List CollectedFourTerm := [ + ⟨5, 4, 8, 3, 8, 6, -173363861579351817426217859252360499563593728000000000⟩, + ⟨5, 4, 7, 4, 6, 6, 12582372267380330155420310156065337032373698560000000⟩, + ⟨5, 4, 8, 4, 7, 6, -61583431163398945137567186061502334510317961216000000⟩, + ⟨5, 4, 7, 5, 5, 6, 33323681957251459197326391101316097840364126208000000⟩, + ⟨5, 4, 8, 5, 6, 6, -128232866672132945937694101571722279337039233024000000⟩, + ⟨5, 4, 7, 6, 4, 6, -11929397616614710698274939113134721901963247616000000⟩, + ⟨5, 4, 8, 6, 5, 6, 134574672832766780415004856710784994143694225408000000⟩, + ⟨5, 4, 7, 7, 3, 6, -499836554987587348014897157573080888347379892224000000⟩, + ⟨5, 4, 8, 7, 4, 6, -266083969509567681902504596514334655703962091520000000⟩, + ⟨5, 5, 6, 1, 8, 7, 10473769431341700736108538446217692893841195008000000⟩, + ⟨5, 5, 6, 2, 7, 7, 14015101470632029927892941441553137426300403712000000⟩, + ⟨5, 5, 7, 2, 8, 7, 65728117723395743803952558849464222804730707968000000⟩, + ⟨5, 5, 6, 3, 6, 7, -37135921042666404320385903579668046110961696768000000⟩, + ⟨5, 5, 7, 3, 7, 7, -36701208258437933769276384599873074636869599232000000⟩, + ⟨5, 5, 8, 3, 8, 7, -83039182993908489661190584658189521973673984000000000⟩, + ⟨5, 5, 6, 4, 5, 7, 29545385438178735285162534832517116612294213632000000⟩, + ⟨5, 5, 7, 4, 6, 7, 12053606832358619460936531520439029482242703360000000⟩, + ⟨5, 5, 8, 4, 7, 7, -29497715170756937084801366671783558899195445248000000⟩, + ⟨5, 5, 6, 5, 4, 7, 33323681957251459197326391101316097840364126208000000⟩, + ⟨5, 5, 7, 5, 5, 7, 31923277422064407619496251989175482572863438848000000⟩, + ⟨5, 5, 8, 5, 6, 7, -61421984861284199857721090513592747021117161472000000⟩, + ⟨5, 5, 6, 6, 3, 7, -123390572588703584709731764151581167429183602688000000⟩, + ⟨5, 5, 7, 6, 4, 7, -11428072986707735194988966317790786177671888896000000⟩, + ⟨5, 5, 8, 6, 5, 7, 64459632947149697858549779651976109601559937024000000⟩ +] + +def collectedFourData_16_29 : List CollectedFourTerm := [ + ⟨5, 5, 6, 7, 2, 7, 121771382982645368283183463899551679671363960832000000⟩, + ⟨5, 5, 7, 7, 3, 7, -478831271737230001091591620639424561737466118144000000⟩, + ⟨5, 5, 8, 7, 4, 7, -127450987965776767202877971385277497186252226560000000⟩, + ⟨5, 6, 5, 0, 8, 8, 9289961417424420077001186310248314801831804928000000⟩, + ⟨5, 6, 5, 1, 7, 8, -73683668099962110184467741258288903848315584512000000⟩, + ⟨5, 6, 6, 1, 8, 8, -40304114076194943847057576348785278838242279424000000⟩, + ⟨5, 6, 5, 2, 6, 8, -51501052749411473830911413017840968148709277696000000⟩, + ⟨5, 6, 6, 2, 7, 8, -53931514548286261354327564454759509054231412736000000⟩, + ⟨5, 6, 7, 2, 8, 8, -126464190953550452958020067953804030293837873152000000⟩, + ⟨5, 6, 5, 3, 5, 8, 19460175441509857718922702305774874850964275200000000⟩, + ⟨5, 6, 6, 3, 6, 8, 142902744598270417017784839307545969967396552704000000⟩, + ⟨5, 6, 7, 3, 7, 8, 70614963126641128995982960394176052368295067648000000⟩, + ⟨5, 6, 8, 3, 8, 8, 106514365120084048286952831605626111612944384000000000⟩, + ⟨5, 6, 5, 4, 4, 8, -70107380275076466493445056513945831550629183488000000⟩, + ⟨5, 6, 6, 4, 5, 8, -113693603141783300903211878193304157704993898496000000⟩, + ⟨5, 6, 7, 4, 6, 8, -23191743334889883344231446134233498765009879040000000⟩, + ⟨5, 6, 8, 4, 7, 8, 37836721058981632241853347576995088477661954048000000⟩, + ⟨5, 6, 5, 5, 3, 8, 182844078114353321941706111524296019998582767616000000⟩, + ⟨5, 6, 6, 5, 4, 8, -128232866672132945937694101571722279337039233024000000⟩, + ⟨5, 6, 7, 5, 5, 8, -61421984861284199857721090513592747021117161472000000⟩, + ⟨5, 6, 8, 5, 6, 8, 78785983749322604280722020202701936365165084672000000⟩, + ⟨5, 6, 5, 6, 2, 8, 2706078570134124604525898716702329645211582464000000⟩, + ⟨5, 6, 6, 6, 3, 8, 474819285085699729374720833099510126317576126464000000⟩, + ⟨5, 6, 7, 6, 4, 8, 21988184881607962597675347866973194698037919744000000⟩ +] + +def collectedFourData_16_30 : List CollectedFourTerm := [ + ⟨5, 6, 8, 6, 5, 8, -82682375135397982488636297430833978692729831424000000⟩, + ⟨5, 6, 5, 7, 1, 8, -126148071755965431207560305226469025085116121088000000⟩, + ⟨5, 6, 6, 7, 2, 8, -468588481264653648495854763030518726789060100096000000⟩, + ⟨5, 6, 7, 7, 3, 8, 921295352444788951466919161752302787000654626816000000⟩, + ⟨5, 6, 8, 7, 4, 8, 163481390081812742080517003422068437848487362560000000⟩, + ⟨6, 2, 8, 3, 8, 5, 3658471052160713159795542889250988813713408000000000⟩, + ⟨6, 2, 8, 4, 7, 5, 1299585727680059209651720399634650195008946176000000⟩, + ⟨6, 2, 8, 5, 6, 5, 2706078570134124604525898716702329645211582464000000⟩, + ⟨6, 2, 8, 6, 5, 5, -2839908735462287246246049480650214674308005888000000⟩, + ⟨6, 2, 8, 7, 4, 5, 5615129306803058728637278891994666918184222720000000⟩, + ⟨6, 3, 7, 2, 8, 6, -254053804496338162028140480511162082674929041408000000⟩, + ⟨6, 3, 7, 3, 7, 6, 141858338723576456137564111153897626744014241792000000⟩, + ⟨6, 3, 8, 3, 8, 6, 641929849585845143997634405561322289556881408000000000⟩, + ⟨6, 3, 7, 4, 6, 6, -46589873249538650470394345115657098095660892160000000⟩, + ⟨6, 3, 8, 4, 7, 6, 228030469231364583527378441352133806425873842176000000⟩, + ⟨6, 3, 7, 5, 5, 6, -123390572588703584709731764151581167429183602688000000⟩, + ⟨6, 3, 8, 5, 6, 6, 474819285085699729374720833099510126317576126464000000⟩, + ⟨6, 3, 7, 6, 4, 6, 44172045707334966624067747249835503017919512576000000⟩, + ⟨6, 3, 8, 6, 5, 6, -498301657003995368887212655935753799298489253888000000⟩, + ⟨6, 3, 7, 7, 3, 6, 1850789441568971142556981490356310284035805937664000000⟩, + ⟨6, 3, 8, 7, 4, 6, 985252872013927663425077032299019070098605342720000000⟩, + ⟨6, 4, 6, 1, 8, 7, -3749458425737695344230137516174666606068105216000000⟩, + ⟨6, 4, 6, 2, 7, 7, -5017204230158276759294509385298751404820660224000000⟩, + ⟨6, 4, 7, 2, 8, 7, -23529718352248993246244474119962051544545755136000000⟩ +] + +def collectedFourData_16_31 : List CollectedFourTerm := [ + ⟨6, 4, 6, 3, 6, 7, 13294124237096041737627806895442669434606452736000000⟩, + ⟨6, 4, 7, 3, 7, 7, 13138503328856081089326118283926307602918539264000000⟩, + ⟨6, 4, 8, 3, 8, 7, 29726830095304095223090487588449075297517568000000000⟩, + ⟨6, 4, 6, 4, 5, 7, -10576821945435564086324073128455420907895128064000000⟩, + ⟨6, 4, 7, 4, 6, 7, -4315017434208212843271520224286681194005790720000000⟩, + ⟨6, 4, 8, 4, 7, 7, 10559756677098934878873576388290589353308061696000000⟩, + ⟨6, 4, 6, 5, 4, 7, -11929397616614710698274939113134721901963247616000000⟩, + ⟨6, 4, 7, 5, 5, 7, -11428072986707735194988966317790786177671888896000000⟩, + ⟨6, 4, 8, 5, 6, 7, 21988184881607962597675347866973194698037919744000000⟩, + ⟨6, 4, 6, 6, 3, 7, 44172045707334966624067747249835503017919512576000000⟩, + ⟨6, 4, 7, 6, 4, 7, 4091085337599192764204014997646220076035080192000000⟩, + ⟨6, 4, 8, 6, 5, 7, -23075619093773483073854883637611061196145819648000000⟩, + ⟨6, 4, 6, 7, 2, 7, -43592399176914431380505305918262704418234302464000000⟩, + ⟨6, 4, 7, 7, 3, 7, 171414690584024609089716674184986096377830309888000000⟩, + ⟨6, 4, 8, 7, 4, 7, 45625615861553235424920740960466996154198917120000000⟩, + ⟨6, 5, 5, 0, 8, 8, -9749400062742297993438579466805605577602891776000000⟩, + ⟨6, 5, 5, 1, 7, 8, 77327722486496288133922144248924995932026568704000000⟩, + ⟨6, 5, 6, 1, 8, 8, 42297369671118394955967453235118169528056414208000000⟩, + ⟨6, 5, 5, 2, 6, 8, 54048057289522275839380712406896198541568376832000000⟩, + ⟨6, 5, 6, 2, 7, 8, 56598718519395504288320501168731006196370112512000000⟩, + ⟨6, 5, 7, 2, 8, 8, 132718526570482346827724686112490822338120515584000000⟩, + ⟨6, 5, 5, 3, 5, 8, -20422585966243155376962250213384260260619878400000000⟩, + ⟨6, 5, 6, 3, 6, 8, -149970055261939295838517351366474855050765139968000000⟩, + ⟨6, 5, 7, 3, 7, 8, -74107253518420880227020283488093681369288278016000000⟩ +] + +def collectedFourData_16_32 : List CollectedFourTerm := [ + ⟨6, 5, 8, 3, 8, 8, -111782074362221315209030133696489535232278528000000000⟩, + ⟨6, 5, 5, 4, 4, 8, 73574567960049270825774166540739101090482487296000000⟩, + ⟨6, 5, 6, 4, 5, 8, 119316364384988896400656371910426367598035730432000000⟩, + ⟨6, 5, 7, 4, 6, 8, 24338699997202460615378968761090106015277383680000000⟩, + ⟨6, 5, 8, 4, 7, 8, -39707950775178714784796061471103043134675746816000000⟩, + ⟨6, 5, 5, 5, 3, 8, -191886702919628858034054226453467428922926825472000000⟩, + ⟨6, 5, 6, 5, 4, 8, 134574672832766780415004856710784994143694225408000000⟩, + ⟨6, 5, 7, 5, 5, 8, 64459632947149697858549779651976109601559937024000000⟩, + ⟨6, 5, 8, 5, 6, 8, -82682375135397982488636297430833978692729831424000000⟩, + ⟨6, 5, 5, 6, 2, 8, -2839908735462287246246049480650214674308005888000000⟩, + ⟨6, 5, 6, 6, 3, 8, -498301657003995368887212655935753799298489253888000000⟩, + ⟨6, 5, 7, 6, 4, 8, -23075619093773483073854883637611061196145819648000000⟩, + ⟨6, 5, 8, 6, 5, 8, 86771464068816138395759155766193871089416798208000000⟩, + ⟨6, 5, 5, 7, 1, 8, 132386773575363459422928395302959176926674026496000000⟩, + ⟨6, 5, 6, 7, 2, 8, 491762706363155872162244313490159656252978757632000000⟩, + ⟨6, 5, 7, 7, 3, 8, -966858371454855186728537210521675768559799631872000000⟩, + ⟨6, 5, 8, 7, 4, 8, -171566425639979275809894728841739827821433323520000000⟩, + ⟨7, 1, 8, 3, 8, 5, -170545332237791480074963631146383105469710336000000000⟩, + ⟨7, 1, 8, 4, 7, 5, -60582214957744960767227679713385276916516257792000000⟩, + ⟨7, 1, 8, 5, 6, 5, -126148071755965431207560305226469025085116121088000000⟩, + ⟨7, 1, 8, 6, 5, 5, 132386773575363459422928395302959176926674026496000000⟩, + ⟨7, 1, 8, 7, 4, 5, -261758007521011665962324869234833624970549002240000000⟩, + ⟨7, 2, 7, 2, 8, 6, 250719989999900068063753063184076231242428710912000000⟩, + ⟨7, 2, 7, 3, 7, 6, -139996806332771022486114731407172665023437733888000000⟩ +] + +def collectedFourData_16_33 : List CollectedFourTerm := [ + ⟨7, 2, 8, 3, 8, 6, -633506141692596641263397443965852162994470912000000000⟩, + ⟨7, 2, 7, 4, 6, 6, 45978498839561003099432990675767251809064714240000000⟩, + ⟨7, 2, 8, 4, 7, 6, -225038145280695065393246602786431675555448356864000000⟩, + ⟨7, 2, 7, 5, 5, 6, 121771382982645368283183463899551679671363960832000000⟩, + ⟨7, 2, 8, 5, 6, 6, -468588481264653648495854763030518726789060100096000000⟩, + ⟨7, 2, 7, 6, 4, 6, -43592399176914431380505305918262704418234302464000000⟩, + ⟨7, 2, 8, 6, 5, 6, 491762706363155872162244313490159656252978757632000000⟩, + ⟨7, 2, 7, 7, 3, 6, -1826502504861254429384823747177625102952637136896000000⟩, + ⟨7, 2, 8, 7, 4, 6, -972323916614542405115888640728508693081049006080000000⟩, + ⟨7, 3, 6, 1, 8, 7, -157100672038941013710253200725493440847884058624000000⟩, + ⟨7, 3, 6, 2, 7, 7, -210218668089220280190519808585664145276624961536000000⟩, + ⟨7, 3, 7, 2, 8, 7, -985884932248058707517407740428525745977639829504000000⟩, + ⟨7, 3, 6, 3, 6, 7, 557018004915217207889330548805648078108469755904000000⟩, + ⟨7, 3, 7, 3, 7, 7, 550497556761962091644595816197976389539747332096000000⟩, + ⟨7, 3, 8, 3, 8, 7, 1245541210299154163929328838017708800188874752000000000⟩, + ⟨7, 3, 6, 4, 5, 7, -443164224533900901669731982971314109511993655296000000⟩, + ⟨7, 3, 7, 4, 6, 7, -180797347723753949077992396086845721213487022080000000⟩, + ⟨7, 3, 8, 4, 7, 7, 442449197236676813301448074424058675664041017344000000⟩, + ⟨7, 3, 6, 5, 4, 7, -499836554987587348014897157573080888347379892224000000⟩, + ⟨7, 3, 7, 5, 5, 7, -478831271737230001091591620639424561737466118144000000⟩, + ⟨7, 3, 8, 5, 6, 7, 921295352444788951466919161752302787000654626816000000⟩, + ⟨7, 3, 6, 6, 3, 7, 1850789441568971142556981490356310284035805937664000000⟩, + ⟨7, 3, 7, 6, 4, 7, 171414690584024609089716674184986096377830309888000000⟩, + ⟨7, 3, 8, 6, 5, 7, -966858371454855186728537210521675768559799631872000000⟩ +] + +def collectedFourData_16_34 : List CollectedFourTerm := [ + ⟨7, 3, 6, 7, 2, 7, -1826502504861254429384823747177625102952637136896000000⟩, + ⟨7, 3, 7, 7, 3, 7, 7182200742177618443621612620303085531839680479232000000⟩, + ⟨7, 3, 8, 7, 4, 7, 1911693396795120528219081956517290715775689031680000000⟩, + ⟨7, 4, 5, 0, 8, 8, 19276725808986418895333803093714901398915645440000000⟩, + ⟨7, 4, 5, 1, 7, 8, -152894054425160331035013817547299221713725685760000000⟩, + ⟨7, 4, 6, 1, 8, 8, -83631279088381718546994770119642498391888363520000000⟩, + ⟨7, 4, 5, 2, 6, 8, -106864994171288007289507526471994844924430254080000000⟩, + ⟨7, 4, 6, 2, 7, 8, -111908217020227933131835530300623316684405473280000000⟩, + ⟨7, 4, 7, 2, 8, 8, -262413956757073478981556103508502122595310632960000000⟩, + ⟨7, 4, 5, 3, 5, 8, 40379981070444383188287785385297267545604096000000000⟩, + ⟨7, 4, 6, 3, 6, 8, 296524054427794955108315840432957886744672337920000000⟩, + ⟨7, 4, 7, 3, 7, 8, 146526473150987315943885598434987142317908951040000000⟩, + ⟨7, 4, 8, 3, 8, 8, 221017948178667071910458336862301428457144320000000000⟩, + ⟨7, 4, 5, 4, 4, 8, -145473235681496495449199011653474408827442954240000000⟩, + ⟨7, 4, 6, 4, 5, 8, -235914910248087043665360225088739656547256238080000000⟩, + ⟨7, 4, 7, 4, 6, 8, -48123006890055010080061462567557155991532339200000000⟩, + ⟨7, 4, 8, 4, 7, 8, 78511423739292947863881289709659886562878423040000000⟩, + ⟨7, 4, 5, 5, 3, 8, 379402561672259897332652075367168939822604615680000000⟩, + ⟨7, 4, 6, 5, 4, 8, -266083969509567681902504596514334655703962091520000000⟩, + ⟨7, 4, 7, 5, 5, 8, -127450987965776767202877971385277497186252226560000000⟩, + ⟨7, 4, 8, 5, 6, 8, 163481390081812742080517003422068437848487362560000000⟩, + ⟨7, 4, 5, 6, 2, 8, 5615129306803058728637278891994666918184222720000000⟩, + ⟨7, 4, 6, 6, 3, 8, 985252872013927663425077032299019070098605342720000000⟩, + ⟨7, 4, 7, 6, 4, 8, 45625615861553235424920740960466996154198917120000000⟩ +] + +def collectedFourData_16_35 : List CollectedFourTerm := [ + ⟨7, 4, 8, 6, 5, 8, -171566425639979275809894728841739827821433323520000000⟩, + ⟨7, 4, 5, 7, 1, 8, -261758007521011665962324869234833624970549002240000000⟩, + ⟨7, 4, 6, 7, 2, 8, -972323916614542405115888640728508693081049006080000000⟩, + ⟨7, 4, 7, 7, 3, 8, 1911693396795120528219081956517290715775689031680000000⟩, + ⟨7, 4, 8, 7, 4, 8, 339224867561695084754476774831176676979559628800000000⟩, + ⟨0, 8, 8, 4, 8, 4, 49754584273977267339042701741948626727237320704000000⟩, + ⟨0, 8, 8, 5, 7, 4, -81572752253373066983684594777292556341378180710400000⟩, + ⟨0, 8, 8, 6, 6, 4, 121848198352724807713208151828480297679928583782400000⟩, + ⟨0, 8, 8, 7, 5, 4, 314746793385003482524825402744866776870692061184000000⟩, + ⟨1, 7, 8, 4, 8, 4, -58026170813963195717905705714621940420233396224000000⟩, + ⟨1, 7, 8, 5, 7, 4, 95134036895068066621455208167687705331113551462400000⟩, + ⟨1, 7, 8, 6, 6, 4, -142105184359601690040912086634060228656013665894400000⟩, + ⟨1, 7, 8, 7, 5, 4, -367072732344336537731301464460309759065906479104000000⟩, + ⟨1, 8, 7, 3, 8, 5, 100531386605410735253868222683957199434447585280000000⟩, + ⟨1, 8, 7, 4, 7, 5, 265913846030004048793900108278919946422305423360000000⟩, + ⟨1, 8, 8, 4, 8, 5, -284831982742727614793043539913183596984559206400000000⟩, + ⟨1, 8, 7, 5, 6, 5, -84240990947418177534066953815561489435380940800000000⟩, + ⟨1, 8, 8, 5, 7, 5, 466982673077256879551940452964781848271666544640000000⟩, + ⟨1, 8, 7, 6, 5, 5, -526311829988821179956612442294199370489392005120000000⟩, + ⟨1, 8, 8, 6, 6, 5, -697549068831992969680696796867619787135348899840000000⟩, + ⟨1, 8, 7, 7, 4, 5, -409254570201283335897119038774873112762017382400000000⟩, + ⟨1, 8, 8, 7, 5, 5, -1801843076973613601433144014642942923866793574400000000⟩, + ⟨2, 6, 8, 4, 8, 4, 38256260402981068408031577836067289919819612160000000⟩, + ⟨2, 6, 8, 5, 7, 4, -62721224536993638229779325248152958664301346816000000⟩ +] + +def collectedFourData_16_36 : List CollectedFourTerm := [ + ⟨2, 6, 8, 6, 6, 4, 93688983112536475737689412192117912542637981696000000⟩, + ⟨2, 6, 8, 7, 5, 4, 242008559903447860998338997862939849286599311360000000⟩, + ⟨2, 7, 7, 3, 8, 5, 51531224289734421315812131017854363611466563584000000⟩, + ⟨2, 7, 7, 4, 7, 5, 136304357317802447054632604067525865598519083008000000⟩, + ⟨2, 7, 8, 4, 8, 5, -146001575062481878786448121299741444918917201920000000⟩, + ⟨2, 7, 7, 5, 6, 5, -43180956171823580214558796849504887509341962240000000⟩, + ⟨2, 7, 8, 5, 7, 5, 239369909023702662316729542872157224824725307392000000⟩, + ⟨2, 7, 7, 6, 5, 5, -269781347629744119786261586438458528951001153536000000⟩, + ⟨2, 7, 8, 6, 6, 5, -357555572770167932227224348486608895864263933952000000⟩, + ⟨2, 7, 7, 7, 4, 5, -209779152170831922888494348956784029367764254720000000⟩, + ⟨2, 7, 8, 7, 5, 5, -923603889985887349390184060472087160205680312320000000⟩, + ⟨2, 8, 6, 2, 8, 6, 269174295611026380419602639027815538832657350656000000⟩, + ⟨2, 8, 6, 3, 7, 6, 570721514702620592827153218693415678727159808000000⟩, + ⟨2, 8, 7, 3, 8, 6, -91343720754644685708311622536035714204201648128000000⟩, + ⟨2, 8, 6, 4, 6, 6, 115336429794899487270715045460285086442830430208000000⟩, + ⟨2, 8, 7, 4, 7, 6, -241611708708402269313186125532044726838321217536000000⟩, + ⟨2, 8, 8, 4, 8, 6, 129400448815868527162718787712296855997324984320000000⟩, + ⟨2, 8, 6, 5, 5, 6, 96349895828635950607320885034153785729151401984000000⟩, + ⟨2, 8, 7, 5, 6, 6, 76542120953709870710200010677908239772895150080000000⟩, + ⟨2, 8, 8, 5, 7, 6, -212152325393921718757442752488023239137932869632000000⟩, + ⟨2, 8, 6, 6, 4, 6, -64242089223552704419966225421729556853627551744000000⟩, + ⟨2, 8, 7, 6, 5, 6, 478211655600276320616666139117881326848979238912000000⟩, + ⟨2, 8, 8, 6, 6, 6, 316899674358130608930390646030827366627925819392000000⟩, + ⟨2, 8, 6, 7, 3, 6, -324306307767510644472602621853347665202431131648000000⟩ +] + +def collectedFourData_16_37 : List CollectedFourTerm := [ + ⟨2, 8, 7, 7, 4, 6, 371852378051415043428163389683035741983332106240000000⟩, + ⟨2, 8, 8, 7, 5, 6, 818585401158234959325891969172878776869815582720000000⟩, + ⟨3, 5, 8, 4, 8, 4, 104963507271882842356922880312064191669567750144000000⟩, + ⟨3, 5, 8, 5, 7, 4, -172087905049839175900295289552231391368392894054400000⟩, + ⟨3, 5, 8, 6, 6, 4, 257053986893651938481870754949700262547335571046400000⟩, + ⟨3, 5, 8, 7, 5, 4, 663997656062170195490285606579960010215390183424000000⟩, + ⟨3, 6, 7, 3, 8, 5, -35258435404304960280503229898749514234258784256000000⟩, + ⟨3, 6, 7, 4, 7, 5, -93261482607010809592906006239853307021148291072000000⟩, + ⟨3, 6, 8, 4, 8, 5, 99896464216022794592893975992975368599665377280000000⟩, + ⟨3, 6, 7, 5, 6, 5, 29545056902202543065602244830146704030469980160000000⟩, + ⟨3, 6, 8, 5, 7, 5, -163780476621198318947874049219533459208198422528000000⟩, + ⟨3, 6, 7, 6, 5, 5, 184588438365214258847133937009586435773194829824000000⟩, + ⟨3, 6, 8, 6, 6, 5, 244644877736344581017829403122013301632892141568000000⟩, + ⟨3, 6, 7, 7, 4, 5, 143534037623449167542435686638406690130079252480000000⟩, + ⟨3, 6, 8, 7, 5, 5, 631943613664918513715688978855789784753640570880000000⟩, + ⟨3, 7, 6, 2, 8, 6, 570721514702620592827153218693415678727159808000000⟩, + ⟨3, 7, 6, 3, 7, 6, 1210082287408095091028713943973888780140544000000⟩, + ⟨3, 7, 7, 3, 8, 6, -193673123762893589039657587562166913339490304000000⟩, + ⟨3, 7, 6, 4, 6, 6, 244544085324026234456984882029280837442207744000000⟩, + ⟨3, 7, 7, 4, 7, 6, -512281457079436969250009519014573057819803648000000⟩, + ⟨3, 7, 8, 4, 8, 6, 274363567976459398720441130435299755436277760000000⟩, + ⟨3, 7, 6, 5, 5, 6, 204287554143807566907998067759259925675507712000000⟩, + ⟨3, 7, 7, 5, 6, 6, 162289772543433835065409626680938980641341440000000⟩, + ⟨3, 7, 8, 5, 7, 6, -449819683642713912288571592475855668039909376000000⟩ +] + +def collectedFourData_16_38 : List CollectedFourTerm := [ + ⟨3, 7, 6, 6, 4, 6, -136210414839569811022223412845618813460283392000000⟩, + ⟨3, 7, 7, 6, 5, 6, 1013936638389247395802085522301212823876796416000000⟩, + ⟨3, 7, 8, 6, 6, 6, 671912084873793417837736590878492149527085056000000⟩, + ⟨3, 7, 6, 7, 3, 6, -687616129082965855911353439451594447770353664000000⟩, + ⟨3, 7, 7, 7, 4, 6, 788426517344554392233080670938287768411832320000000⟩, + ⟨3, 7, 8, 7, 5, 6, 1735620033859364402989586949119310998494248960000000⟩, + ⟨3, 8, 5, 1, 8, 7, 100531386605410735253868222683957199434447585280000000⟩, + ⟨3, 8, 5, 2, 7, 7, 51531224289734421315812131017854363611466563584000000⟩, + ⟨3, 8, 6, 2, 8, 7, -91343720754644685708311622536035714204201648128000000⟩, + ⟨3, 8, 5, 3, 6, 7, -35258435404304960280503229898749514234258784256000000⟩, + ⟨3, 8, 6, 3, 7, 7, -193673123762893589039657587562166913339490304000000⟩, + ⟨3, 8, 7, 3, 8, 7, 15498648008648709793965340979925907732778975232000000⟩, + ⟨3, 8, 5, 4, 5, 7, -21379017074481193860489793992326140302641332224000000⟩, + ⟨3, 8, 6, 4, 6, 7, -39139170447564149301438423164908046488650645504000000⟩, + ⟨3, 8, 7, 4, 7, 7, 40995207958498681031834709646954467520659062784000000⟩, + ⟨3, 8, 8, 4, 8, 7, -14637255060989559932464906301930739522569502720000000⟩, + ⟨3, 8, 5, 5, 4, 7, -14181485244732000423207788433811980472641650688000000⟩, + ⟨3, 8, 6, 5, 5, 7, -32696130807482299336259882444119704352893960192000000⟩, + ⟨3, 8, 7, 5, 6, 7, -12987202411903531945545492909850296587932139520000000⟩, + ⟨3, 8, 8, 5, 7, 7, 23997812426382207984903691603667862571525865472000000⟩, + ⟨3, 8, 5, 6, 3, 7, 129229541146288349824727824198458177558033727488000000⟩, + ⟨3, 8, 6, 6, 4, 7, 21800415397802148815772257099732503788961923072000000⟩, + ⟨3, 8, 7, 6, 5, 7, -81140050597347220410551989408248126866643222528000000⟩, + ⟨3, 8, 8, 6, 6, 7, -35846408608094881811412650934835974013747986432000000⟩ +] + +def collectedFourData_16_39 : List CollectedFourTerm := [ + ⟨3, 8, 5, 7, 2, 7, -7159280297861486833075231359493337466236043264000000⟩, + ⟨3, 8, 6, 7, 3, 7, 110052651009786339747149844314161098572351668224000000⟩, + ⟨3, 8, 7, 7, 4, 7, -63093654068222316974366997073510649068844482560000000⟩, + ⟨3, 8, 8, 7, 5, 7, -92595067602935520019291794812334444333099909120000000⟩, + ⟨4, 4, 8, 4, 8, 4, -78666557494580586106287178946155451894212853760000000⟩, + ⟨4, 4, 8, 5, 7, 4, 128973997045080452641472015601754924654553726976000000⟩, + ⟨4, 4, 8, 6, 6, 4, -192653168370236940063349507703799793944316870656000000⟩, + ⟨4, 4, 8, 7, 5, 4, -497643525302376958459831222887596941024123944960000000⟩, + ⟨4, 5, 7, 3, 8, 5, -21379017074481193860489793992326140302641332224000000⟩, + ⟨4, 5, 7, 4, 7, 5, -56549271293055522719875546601656284565563506688000000⟩, + ⟨4, 5, 8, 4, 8, 5, 60572404579639660341540370300285369483127685120000000⟩, + ⟨4, 5, 7, 5, 6, 5, 17914699524686922055082593896923119122791792640000000⟩, + ⟨4, 5, 8, 5, 7, 5, -99308592851620049572761773328923374950612467712000000⟩, + ⟨4, 5, 7, 6, 5, 5, 111925538677757099580153222900009044947129860096000000⟩, + ⟨4, 5, 8, 6, 6, 5, 148340871009581818353262879652450196793036111872000000⟩, + ⟨4, 5, 7, 7, 4, 5, 87032127374156709797255822138270388334803025920000000⟩, + ⟨4, 5, 8, 7, 5, 5, 383180170978377123060865059259318472483033579520000000⟩, + ⟨4, 6, 6, 2, 8, 6, 115336429794899487270715045460285086442830430208000000⟩, + ⟨4, 6, 6, 3, 7, 6, 244544085324026234456984882029280837442207744000000⟩, + ⟨4, 6, 7, 3, 8, 6, -39139170447564149301438423164908046488650645504000000⟩, + ⟨4, 6, 6, 4, 6, 6, 49419622358951790740797433316314148388359634944000000⟩, + ⟨4, 6, 7, 4, 7, 6, -103526348293454297087249752830665218436049666048000000⟩, + ⟨4, 6, 8, 4, 8, 6, 55445806020968884530121112992250904050411765760000000⟩, + ⟨4, 6, 6, 5, 5, 6, 41284228015753127035979079658062999309948813312000000⟩ +] + +def collectedFourData_16_40 : List CollectedFourTerm := [ + ⟨4, 6, 7, 5, 6, 6, 32796946453191096907579206847578334891018813440000000⟩, + ⟨4, 6, 8, 5, 7, 6, -90903523042853231485864891906014267602607538176000000⟩, + ⟨4, 6, 6, 6, 4, 6, -27526600178484637746616695847501348960041172992000000⟩, + ⟨4, 6, 7, 6, 5, 6, 204905245198251236338321784651907483199095177216000000⟩, + ⟨4, 6, 8, 6, 6, 6, 135785911357784985688313887416957139715522297856000000⟩, + ⟨4, 6, 6, 7, 3, 6, -138959522910471905971523034249954039764682276864000000⟩, + ⟨4, 6, 7, 7, 4, 6, 159332173964966798249253645249594353049214648320000000⟩, + ⟨4, 6, 8, 7, 5, 6, 350749381316292757150057072077272787048160296960000000⟩, + ⟨4, 7, 5, 1, 8, 7, 265913846030004048793900108278919946422305423360000000⟩, + ⟨4, 7, 5, 2, 7, 7, 136304357317802447054632604067525865598519083008000000⟩, + ⟨4, 7, 6, 2, 8, 7, -241611708708402269313186125532044726838321217536000000⟩, + ⟨4, 7, 5, 3, 6, 7, -93261482607010809592906006239853307021148291072000000⟩, + ⟨4, 7, 6, 3, 7, 7, -512281457079436969250009519014573057819803648000000⟩, + ⟨4, 7, 7, 3, 8, 7, 40995207958498681031834709646954467520659062784000000⟩, + ⟨4, 7, 5, 4, 5, 7, -56549271293055522719875546601656284565563506688000000⟩, + ⟨4, 7, 6, 4, 6, 7, -103526348293454297087249752830665218436049666048000000⟩, + ⟨4, 7, 7, 4, 7, 7, 108435721272121575403990259716558832428445073408000000⟩, + ⟨4, 7, 8, 4, 8, 7, -38716752250390121111007016414346062064139632640000000⟩, + ⟨4, 7, 5, 5, 4, 7, -37511203328428738262300817105465389196830048256000000⟩, + ⟨4, 7, 6, 5, 5, 7, -86483974675922536284542716006235063530819682304000000⟩, + ⟨4, 7, 7, 5, 6, 7, -34352226295996818705157164823982534994155274240000000⟩, + ⟨4, 7, 8, 5, 7, 7, 63476201951266664440360034631210315836936945664000000⟩, + ⟨4, 7, 5, 6, 3, 7, 341822842270959786819457237770114420498398969856000000⟩, + ⟨4, 7, 6, 6, 4, 7, 57663904768715146156966527853605838313817636864000000⟩ +] + +def collectedFourData_16_41 : List CollectedFourTerm := [ + ⟨4, 7, 7, 6, 5, 7, -214622155825795236263597688003794451383332110336000000⟩, + ⟨4, 7, 8, 6, 6, 7, -94816720441300726835927584963474222737663197184000000⟩, + ⟨4, 7, 5, 7, 2, 7, -18936889493860004501963205187476652213999239168000000⟩, + ⟨4, 7, 6, 7, 3, 7, 291098379162662798572636553675152086363367538688000000⟩, + ⟨4, 7, 7, 7, 4, 7, -166887941964033561772270409819295338113762590720000000⟩, + ⟨4, 7, 8, 7, 5, 7, -244921624789164162141293056625195354225576509440000000⟩, + ⟨4, 8, 4, 0, 8, 8, 49754584273977267339042701741948626727237320704000000⟩, + ⟨4, 8, 4, 1, 7, 8, -58026170813963195717905705714621940420233396224000000⟩, + ⟨4, 8, 5, 1, 8, 8, -284831982742727614793043539913183596984559206400000000⟩, + ⟨4, 8, 4, 2, 6, 8, 38256260402981068408031577836067289919819612160000000⟩, + ⟨4, 8, 5, 2, 7, 8, -146001575062481878786448121299741444918917201920000000⟩, + ⟨4, 8, 6, 2, 8, 8, 129400448815868527162718787712296855997324984320000000⟩, + ⟨4, 8, 4, 3, 5, 8, 104963507271882842356922880312064191669567750144000000⟩, + ⟨4, 8, 5, 3, 6, 8, 99896464216022794592893975992975368599665377280000000⟩, + ⟨4, 8, 6, 3, 7, 8, 274363567976459398720441130435299755436277760000000⟩, + ⟨4, 8, 7, 3, 8, 8, -14637255060989559932464906301930739522569502720000000⟩, + ⟨4, 8, 4, 4, 4, 8, -78666557494580586106287178946155451894212853760000000⟩, + ⟨4, 8, 5, 4, 5, 8, 60572404579639660341540370300285369483127685120000000⟩, + ⟨4, 8, 6, 4, 6, 8, 55445806020968884530121112992250904050411765760000000⟩, + ⟨4, 8, 7, 4, 7, 8, -38716752250390121111007016414346062064139632640000000⟩, + ⟨4, 8, 8, 4, 8, 8, 10367802836781650016009598492668466590803558400000000⟩, + ⟨4, 8, 4, 5, 3, 8, -74960096071961665946894878378445614150569689088000000⟩, + ⟨4, 8, 5, 5, 4, 8, 40179895024708121104367027080575818864724541440000000⟩, + ⟨4, 8, 6, 5, 5, 8, 46318389113960206312842612459458866321010196480000000⟩ +] + +def collectedFourData_16_42 : List CollectedFourTerm := [ + ⟨4, 8, 7, 5, 6, 8, 12265392060368812550882003125170136520274739200000000⟩, + ⟨4, 8, 8, 5, 7, 8, -16998035951009711538454677580792508628955299840000000⟩, + ⟨4, 8, 4, 6, 2, 8, 94944273328979178080821227577931882709141946368000000⟩, + ⟨4, 8, 5, 6, 3, 8, -366141437779085771559182939372869092719921725440000000⟩, + ⟨4, 8, 6, 6, 4, 8, -30883168690109729978582739705827395358089543680000000⟩, + ⟨4, 8, 7, 6, 5, 8, 76630401283532309748838560396147901596570746880000000⟩, + ⟨4, 8, 8, 6, 6, 8, 25390586917210880834976263669743293062751191040000000⟩, + ⟨4, 8, 4, 7, 1, 8, 91205111950179960517687574787136715516257763328000000⟩, + ⟨4, 8, 5, 7, 2, 8, 20284132857479962010701045204110843352260280320000000⟩, + ⟨4, 8, 6, 7, 3, 8, -155904120353214026456186434583564318912607682560000000⟩, + ⟨4, 8, 7, 7, 4, 8, 59586997963374675876106100955564235017525657600000000⟩, + ⟨4, 8, 8, 7, 5, 8, 65586573477445551682177697457326104286488166400000000⟩, + ⟨5, 3, 8, 4, 8, 4, -74960096071961665946894878378445614150569689088000000⟩, + ⟨5, 3, 8, 5, 7, 4, 122897245248721628467370477289754517796058614988800000⟩, + ⟨5, 3, 8, 6, 6, 4, -183576102343052731084061953483251491595210247372800000⟩, + ⟨5, 3, 8, 7, 5, 4, -474196502990813219193431552274654387587040411648000000⟩, + ⟨5, 4, 7, 3, 8, 5, -14181485244732000423207788433811980472641650688000000⟩, + ⟨5, 4, 7, 4, 7, 5, -37511203328428738262300817105465389196830048256000000⟩, + ⟨5, 4, 8, 4, 8, 5, 40179895024708121104367027080575818864724541440000000⟩, + ⟨5, 4, 7, 5, 6, 5, 11883476498852096409767840973856744297652551680000000⟩, + ⟨5, 4, 8, 5, 7, 5, -65875027803846024823443210740641848339720044544000000⟩, + ⟨5, 4, 7, 6, 5, 5, 74244310191506384974582049959033417549744177152000000⟩, + ⟨5, 4, 8, 6, 6, 5, 98399934201096942149125494540279759142297534464000000⟩, + ⟨5, 4, 7, 7, 4, 5, 57731598504941598618936154491801619936617431040000000⟩ +] + +def collectedFourData_16_43 : List CollectedFourTerm := [ + ⟨5, 4, 8, 7, 5, 5, 254177445196488720245282464940107100131153674240000000⟩, + ⟨5, 5, 6, 2, 8, 6, 96349895828635950607320885034153785729151401984000000⟩, + ⟨5, 5, 6, 3, 7, 6, 204287554143807566907998067759259925675507712000000⟩, + ⟨5, 5, 7, 3, 8, 6, -32696130807482299336259882444119704352893960192000000⟩, + ⟨5, 5, 6, 4, 6, 6, 41284228015753127035979079658062999309948813312000000⟩, + ⟨5, 5, 7, 4, 7, 6, -86483974675922536284542716006235063530819682304000000⟩, + ⟨5, 5, 8, 4, 8, 6, 46318389113960206312842612459458866321010196480000000⟩, + ⟨5, 5, 6, 5, 5, 6, 34488071771919668973856135606195539880471166976000000⟩, + ⟨5, 5, 7, 5, 6, 6, 27397955527855754072974593734154671096982405120000000⟩, + ⟨5, 5, 8, 5, 7, 6, -75939102599326730188949413236344580771516776448000000⟩, + ⟨5, 5, 6, 6, 4, 6, -22995206843404424133675989298537334407866351616000000⟩, + ⟨5, 5, 7, 6, 5, 6, 171174008634570104007675226193116861148449210368000000⟩, + ⟨5, 5, 8, 6, 6, 6, 113433010173664531559802129814289278179987161088000000⟩, + ⟨5, 5, 6, 7, 3, 6, -116084185895383140873785510734774347374864105472000000⟩, + ⟨5, 5, 7, 7, 4, 6, 133103117470986138245813244902371486269293199360000000⟩, + ⟨5, 5, 8, 7, 5, 6, 293009471611698999307684061800245938102552494080000000⟩, + ⟨5, 6, 5, 1, 8, 7, -84240990947418177534066953815561489435380940800000000⟩, + ⟨5, 6, 5, 2, 7, 7, -43180956171823580214558796849504887509341962240000000⟩, + ⟨5, 6, 6, 2, 8, 7, 76542120953709870710200010677908239772895150080000000⟩, + ⟨5, 6, 5, 3, 6, 7, 29545056902202543065602244830146704030469980160000000⟩, + ⟨5, 6, 6, 3, 7, 7, 162289772543433835065409626680938980641341440000000⟩, + ⟨5, 6, 7, 3, 8, 7, -12987202411903531945545492909850296587932139520000000⟩, + ⟨5, 6, 5, 4, 5, 7, 17914699524686922055082593896923119122791792640000000⟩, + ⟨5, 6, 6, 4, 6, 7, 32796946453191096907579206847578334891018813440000000⟩ +] + +def collectedFourData_16_44 : List CollectedFourTerm := [ + ⟨5, 6, 7, 4, 7, 7, -34352226295996818705157164823982534994155274240000000⟩, + ⟨5, 6, 8, 4, 8, 7, 12265392060368812550882003125170136520274739200000000⟩, + ⟨5, 6, 5, 5, 4, 7, 11883476498852096409767840973856744297652551680000000⟩, + ⟨5, 6, 6, 5, 5, 7, 27397955527855754072974593734154671096982405120000000⟩, + ⟨5, 6, 7, 5, 6, 7, 10882718698665292717849195293918676277998387200000000⟩, + ⟨5, 6, 8, 5, 7, 7, -20109137729329775427613893201140372505278545920000000⟩, + ⟨5, 6, 5, 6, 3, 7, -108288813806707801527708150074646064365494599680000000⟩, + ⟨5, 6, 6, 6, 4, 7, -18267813249055140008200801926702610113280081920000000⟩, + ⟨5, 6, 7, 6, 5, 7, 67991882919839225665296210289146127081097134080000000⟩, + ⟨5, 6, 8, 6, 6, 7, 30037753233271803315432234326361790991585771520000000⟩, + ⟨5, 6, 5, 7, 2, 7, 5999169882430716478040617714313233924400087040000000⟩, + ⟨5, 6, 6, 7, 3, 7, -92219402223542077659547044656091402982800752640000000⟩, + ⟨5, 6, 7, 7, 4, 7, 52869776501367642627486186714414596994210201600000000⟩, + ⟨5, 6, 8, 7, 5, 7, 77590695951811755828783302123141093710312243200000000⟩, + ⟨5, 7, 4, 0, 8, 8, -81572752253373066983684594777292556341378180710400000⟩, + ⟨5, 7, 4, 1, 7, 8, 95134036895068066621455208167687705331113551462400000⟩, + ⟨5, 7, 5, 1, 8, 8, 466982673077256879551940452964781848271666544640000000⟩, + ⟨5, 7, 4, 2, 6, 8, -62721224536993638229779325248152958664301346816000000⟩, + ⟨5, 7, 5, 2, 7, 8, 239369909023702662316729542872157224824725307392000000⟩, + ⟨5, 7, 6, 2, 8, 8, -212152325393921718757442752488023239137932869632000000⟩, + ⟨5, 7, 4, 3, 5, 8, -172087905049839175900295289552231391368392894054400000⟩, + ⟨5, 7, 5, 3, 6, 8, -163780476621198318947874049219533459208198422528000000⟩, + ⟨5, 7, 6, 3, 7, 8, -449819683642713912288571592475855668039909376000000⟩, + ⟨5, 7, 7, 3, 8, 8, 23997812426382207984903691603667862571525865472000000⟩ +] + +def collectedFourData_16_45 : List CollectedFourTerm := [ + ⟨5, 7, 4, 4, 4, 8, 128973997045080452641472015601754924654553726976000000⟩, + ⟨5, 7, 5, 4, 5, 8, -99308592851620049572761773328923374950612467712000000⟩, + ⟨5, 7, 6, 4, 6, 8, -90903523042853231485864891906014267602607538176000000⟩, + ⟨5, 7, 7, 4, 7, 8, 63476201951266664440360034631210315836936945664000000⟩, + ⟨5, 7, 8, 4, 8, 8, -16998035951009711538454677580792508628955299840000000⟩, + ⟨5, 7, 4, 5, 3, 8, 122897245248721628467370477289754517796058614988800000⟩, + ⟨5, 7, 5, 5, 4, 8, -65875027803846024823443210740641848339720044544000000⟩, + ⟨5, 7, 6, 5, 5, 8, -75939102599326730188949413236344580771516776448000000⟩, + ⟨5, 7, 7, 5, 6, 8, -20109137729329775427613893201140372505278545920000000⟩, + ⟨5, 7, 8, 5, 7, 8, 27868317978306446004899753699405554119170064384000000⟩, + ⟨5, 7, 4, 6, 2, 8, -155661348580337516605511545900398144283168525516800000⟩, + ⟨5, 7, 5, 6, 3, 8, 600289706556112298236264906795090606144245202944000000⟩, + ⟨5, 7, 6, 6, 4, 8, 50633024174921278106975621531719953492285063168000000⟩, + ⟨5, 7, 7, 6, 5, 8, -125635714380745558606280668175315086329394495488000000⟩, + ⟨5, 7, 8, 6, 6, 8, -41627924067464290582382844024070150027953045504000000⟩, + ⟨5, 7, 4, 7, 1, 8, -149530985132648170165156084153769447937595460812800000⟩, + ⟨5, 7, 5, 7, 2, 8, -33255881209786856673615144023237869483937759232000000⟩, + ⟨5, 7, 6, 7, 3, 8, 255605154186854092688832520193327248181985017856000000⟩, + ⟨5, 7, 7, 7, 4, 8, -97693016499202209108880536329961931894696181760000000⟩, + ⟨5, 7, 8, 7, 5, 8, -107529333979814237281691543420975367903133040640000000⟩, + ⟨6, 2, 8, 4, 8, 4, 94944273328979178080821227577931882709141946368000000⟩, + ⟨6, 2, 8, 5, 7, 4, -155661348580337516605511545900398144283168525516800000⟩, + ⟨6, 2, 8, 6, 6, 4, 232517039743320764644821727107607149181225716940800000⟩, + ⟨6, 2, 8, 7, 5, 4, 600616124456197677059963830131641082272733462528000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1603.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1603.lean new file mode 100644 index 0000000000000000000000000000000000000000..63281b507ac844a46eb2696e41902ee79d7413fa --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1603.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1603. -/ +namespace LaughlinFock +def collectedFourData_16_46 : List CollectedFourTerm := [ + ⟨6, 3, 7, 3, 8, 5, 129229541146288349824727824198458177558033727488000000⟩, + ⟨6, 3, 7, 4, 7, 5, 341822842270959786819457237770114420498398969856000000⟩, + ⟨6, 3, 8, 4, 8, 5, -366141437779085771559182939372869092719921725440000000⟩, + ⟨6, 3, 7, 5, 6, 5, -108288813806707801527708150074646064365494599680000000⟩, + ⟨6, 3, 8, 5, 7, 5, 600289706556112298236264906795090606144245202944000000⟩, + ⟨6, 3, 7, 6, 5, 5, -676555238975068747698513594703997361671060324352000000⟩, + ⟨6, 3, 8, 6, 6, 5, -896674651927336399017079135975575120873850404864000000⟩, + ⟨6, 3, 7, 7, 4, 5, -526082272462029355356191563945798601494537175040000000⟩, + ⟨6, 3, 8, 7, 5, 5, -2316205534584599375822799296760391367424988938240000000⟩, + ⟨6, 4, 6, 2, 8, 6, -64242089223552704419966225421729556853627551744000000⟩, + ⟨6, 4, 6, 3, 7, 6, -136210414839569811022223412845618813460283392000000⟩, + ⟨6, 4, 7, 3, 8, 6, 21800415397802148815772257099732503788961923072000000⟩, + ⟨6, 4, 6, 4, 6, 6, -27526600178484637746616695847501348960041172992000000⟩, + ⟨6, 4, 7, 4, 7, 6, 57663904768715146156966527853605838313817636864000000⟩, + ⟨6, 4, 8, 4, 8, 6, -30883168690109729978582739705827395358089543680000000⟩, + ⟨6, 4, 6, 5, 5, 6, -22995206843404424133675989298537334407866351616000000⟩, + ⟨6, 4, 7, 5, 6, 6, -18267813249055140008200801926702610113280081920000000⟩, + ⟨6, 4, 8, 5, 7, 6, 50633024174921278106975621531719953492285063168000000⟩, + ⟨6, 4, 6, 6, 4, 6, 15332244181928667634696521042421583593504505856000000⟩, + ⟨6, 4, 7, 6, 5, 6, -114131684740098747134476288498861319563549605888000000⟩, + ⟨6, 4, 8, 6, 6, 6, -75632396878076467064684443276544256711126417408000000⟩, + ⟨6, 4, 6, 7, 3, 6, 77400090198315055806164503233882789866794647552000000⟩, + ⟨6, 4, 7, 7, 4, 6, -88747603460955027821578990606513403118495989760000000⟩, + ⟨6, 4, 8, 7, 5, 6, -195366486457895009967013404332853815703534305280000000⟩ +] + +def collectedFourData_16_47 : List CollectedFourTerm := [ + ⟨6, 5, 5, 1, 8, 7, -526311829988821179956612442294199370489392005120000000⟩, + ⟨6, 5, 5, 2, 7, 7, -269781347629744119786261586438458528951001153536000000⟩, + ⟨6, 5, 6, 2, 8, 7, 478211655600276320616666139117881326848979238912000000⟩, + ⟨6, 5, 5, 3, 6, 7, 184588438365214258847133937009586435773194829824000000⟩, + ⟨6, 5, 6, 3, 7, 7, 1013936638389247395802085522301212823876796416000000⟩, + ⟨6, 5, 7, 3, 8, 7, -81140050597347220410551989408248126866643222528000000⟩, + ⟨6, 5, 5, 4, 5, 7, 111925538677757099580153222900009044947129860096000000⟩, + ⟨6, 5, 6, 4, 6, 7, 204905245198251236338321784651907483199095177216000000⟩, + ⟨6, 5, 7, 4, 7, 7, -214622155825795236263597688003794451383332110336000000⟩, + ⟨6, 5, 8, 4, 8, 7, 76630401283532309748838560396147901596570746880000000⟩, + ⟨6, 5, 5, 5, 4, 7, 74244310191506384974582049959033417549744177152000000⟩, + ⟨6, 5, 6, 5, 5, 7, 171174008634570104007675226193116861148449210368000000⟩, + ⟨6, 5, 7, 5, 6, 7, 67991882919839225665296210289146127081097134080000000⟩, + ⟨6, 5, 8, 5, 7, 7, -125635714380745558606280668175315086329394495488000000⟩, + ⟨6, 5, 5, 6, 3, 7, -676555238975068747698513594703997361671060324352000000⟩, + ⟨6, 5, 6, 6, 4, 7, -114131684740098747134476288498861319563549605888000000⟩, + ⟨6, 5, 7, 6, 5, 7, 424792395263519816080249030269637563898776256512000000⟩, + ⟨6, 5, 8, 6, 6, 7, 187666653670108981962239630574741240455865827328000000⟩, + ⟨6, 5, 5, 7, 2, 7, 37480970293983713025081468762860327441327456256000000⟩, + ⟨6, 5, 6, 7, 3, 7, -576158492426128503569276498003621275218368004096000000⟩, + ⟨6, 5, 7, 7, 4, 7, 330314120341999516727304598317279552681006858240000000⟩, + ⟨6, 5, 8, 7, 5, 7, 484762830033587540127382635544629828309724692480000000⟩, + ⟨6, 6, 4, 0, 8, 8, 121848198352724807713208151828480297679928583782400000⟩, + ⟨6, 6, 4, 1, 7, 8, -142105184359601690040912086634060228656013665894400000⟩ +] + +def collectedFourData_16_48 : List CollectedFourTerm := [ + ⟨6, 6, 5, 1, 8, 8, -697549068831992969680696796867619787135348899840000000⟩, + ⟨6, 6, 4, 2, 6, 8, 93688983112536475737689412192117912542637981696000000⟩, + ⟨6, 6, 5, 2, 7, 8, -357555572770167932227224348486608895864263933952000000⟩, + ⟨6, 6, 6, 2, 8, 8, 316899674358130608930390646030827366627925819392000000⟩, + ⟨6, 6, 4, 3, 5, 8, 257053986893651938481870754949700262547335571046400000⟩, + ⟨6, 6, 5, 3, 6, 8, 244644877736344581017829403122013301632892141568000000⟩, + ⟨6, 6, 6, 3, 7, 8, 671912084873793417837736590878492149527085056000000⟩, + ⟨6, 6, 7, 3, 8, 8, -35846408608094881811412650934835974013747986432000000⟩, + ⟨6, 6, 4, 4, 4, 8, -192653168370236940063349507703799793944316870656000000⟩, + ⟨6, 6, 5, 4, 5, 8, 148340871009581818353262879652450196793036111872000000⟩, + ⟨6, 6, 6, 4, 6, 8, 135785911357784985688313887416957139715522297856000000⟩, + ⟨6, 6, 7, 4, 7, 8, -94816720441300726835927584963474222737663197184000000⟩, + ⟨6, 6, 8, 4, 8, 8, 25390586917210880834976263669743293062751191040000000⟩, + ⟨6, 6, 4, 5, 3, 8, -183576102343052731084061953483251491595210247372800000⟩, + ⟨6, 6, 5, 5, 4, 8, 98399934201096942149125494540279759142297534464000000⟩, + ⟨6, 6, 6, 5, 5, 8, 113433010173664531559802129814289278179987161088000000⟩, + ⟨6, 6, 7, 5, 6, 8, 30037753233271803315432234326361790991585771520000000⟩, + ⟨6, 6, 8, 5, 7, 8, -41627924067464290582382844024070150027953045504000000⟩, + ⟨6, 6, 4, 6, 2, 8, 232517039743320764644821727107607149181225716940800000⟩, + ⟨6, 6, 5, 6, 3, 8, -896674651927336399017079135975575120873850404864000000⟩, + ⟨6, 6, 6, 6, 4, 8, -75632396878076467064684443276544256711126417408000000⟩, + ⟨6, 6, 7, 6, 5, 8, 187666653670108981962239630574741240455865827328000000⟩, + ⟨6, 6, 8, 6, 6, 8, 62181150061352926396186477614012230603819188224000000⟩, + ⟨6, 6, 4, 7, 1, 8, 223359892035123169494364024672531992781213453516800000⟩ +] + +def collectedFourData_16_49 : List CollectedFourTerm := [ + ⟨6, 6, 5, 7, 2, 8, 49675523972249004078584522970491768149735636992000000⟩, + ⟨6, 6, 6, 7, 3, 8, -381806751237215311652992809608103515503969959936000000⟩, + ⟨6, 6, 7, 7, 4, 8, 145927625625486780374458117935798778725987778560000000⟩, + ⟨6, 6, 8, 7, 5, 8, 160620492181162284615674483962710873968832675840000000⟩, + ⟨7, 1, 8, 4, 8, 4, 91205111950179960517687574787136715516257763328000000⟩, + ⟨7, 1, 8, 5, 7, 4, -149530985132648170165156084153769447937595460812800000⟩, + ⟨7, 1, 8, 6, 6, 4, 223359892035123169494364024672531992781213453516800000⟩, + ⟨7, 1, 8, 7, 5, 4, 576962242686319424591938444819467786628720754688000000⟩, + ⟨7, 2, 7, 3, 8, 5, -7159280297861486833075231359493337466236043264000000⟩, + ⟨7, 2, 7, 4, 7, 5, -18936889493860004501963205187476652213999239168000000⟩, + ⟨7, 2, 8, 4, 8, 5, 20284132857479962010701045204110843352260280320000000⟩, + ⟨7, 2, 7, 5, 6, 5, 5999169882430716478040617714313233924400087040000000⟩, + ⟨7, 2, 8, 5, 7, 5, -33255881209786856673615144023237869483937759232000000⟩, + ⟨7, 2, 7, 6, 5, 5, 37480970293983713025081468762860327441327456256000000⟩, + ⟨7, 2, 8, 6, 6, 5, 49675523972249004078584522970491768149735636992000000⟩, + ⟨7, 2, 7, 7, 4, 5, 29144810194969733784789206890826198978521989120000000⟩, + ⟨7, 2, 8, 7, 5, 5, 128317136333231678299346325453347313024730398720000000⟩, + ⟨7, 3, 6, 2, 8, 6, -324306307767510644472602621853347665202431131648000000⟩, + ⟨7, 3, 6, 3, 7, 6, -687616129082965855911353439451594447770353664000000⟩, + ⟨7, 3, 7, 3, 8, 6, 110052651009786339747149844314161098572351668224000000⟩, + ⟨7, 3, 6, 4, 6, 6, -138959522910471905971523034249954039764682276864000000⟩, + ⟨7, 3, 7, 4, 7, 6, 291098379162662798572636553675152086363367538688000000⟩, + ⟨7, 3, 8, 4, 8, 6, -155904120353214026456186434583564318912607682560000000⟩, + ⟨7, 3, 6, 5, 5, 6, -116084185895383140873785510734774347374864105472000000⟩ +] + +def collectedFourData_16_50 : List CollectedFourTerm := [ + ⟨7, 3, 7, 5, 6, 6, -92219402223542077659547044656091402982800752640000000⟩, + ⟨7, 3, 8, 5, 7, 6, 255605154186854092688832520193327248181985017856000000⟩, + ⟨7, 3, 6, 6, 4, 6, 77400090198315055806164503233882789866794647552000000⟩, + ⟨7, 3, 7, 6, 5, 6, -576158492426128503569276498003621275218368004096000000⟩, + ⟨7, 3, 8, 6, 6, 6, -381806751237215311652992809608103515503969959936000000⟩, + ⟨7, 3, 6, 7, 3, 6, 390730403952757638043147203504209578302199824384000000⟩, + ⟨7, 3, 7, 7, 4, 6, -448014813177736965986988504050511066580301905920000000⟩, + ⟨7, 3, 8, 7, 5, 6, -986247250835710828997129122540071941295581429760000000⟩, + ⟨7, 4, 5, 1, 8, 7, -409254570201283335897119038774873112762017382400000000⟩, + ⟨7, 4, 5, 2, 7, 7, -209779152170831922888494348956784029367764254720000000⟩, + ⟨7, 4, 6, 2, 8, 7, 371852378051415043428163389683035741983332106240000000⟩, + ⟨7, 4, 5, 3, 6, 7, 143534037623449167542435686638406690130079252480000000⟩, + ⟨7, 4, 6, 3, 7, 7, 788426517344554392233080670938287768411832320000000⟩, + ⟨7, 4, 7, 3, 8, 7, -63093654068222316974366997073510649068844482560000000⟩, + ⟨7, 4, 5, 4, 5, 7, 87032127374156709797255822138270388334803025920000000⟩, + ⟨7, 4, 6, 4, 6, 7, 159332173964966798249253645249594353049214648320000000⟩, + ⟨7, 4, 7, 4, 7, 7, -166887941964033561772270409819295338113762590720000000⟩, + ⟨7, 4, 8, 4, 8, 7, 59586997963374675876106100955564235017525657600000000⟩, + ⟨7, 4, 5, 5, 4, 7, 57731598504941598618936154491801619936617431040000000⟩, + ⟨7, 4, 6, 5, 5, 7, 133103117470986138245813244902371486269293199360000000⟩, + ⟨7, 4, 7, 5, 6, 7, 52869776501367642627486186714414596994210201600000000⟩, + ⟨7, 4, 8, 5, 7, 7, -97693016499202209108880536329961931894696181760000000⟩, + ⟨7, 4, 5, 6, 3, 7, -526082272462029355356191563945798601494537175040000000⟩, + ⟨7, 4, 6, 6, 4, 7, -88747603460955027821578990606513403118495989760000000⟩ +] + +def collectedFourData_16_51 : List CollectedFourTerm := [ + ⟨7, 4, 7, 6, 5, 7, 330314120341999516727304598317279552681006858240000000⟩, + ⟨7, 4, 8, 6, 6, 7, 145927625625486780374458117935798778725987778560000000⟩, + ⟨7, 4, 5, 7, 2, 7, 29144810194969733784789206890826198978521989120000000⟩, + ⟨7, 4, 6, 7, 3, 7, -448014813177736965986988504050511066580301905920000000⟩, + ⟨7, 4, 7, 7, 4, 7, 256848802647759712598441520021578599434603724800000000⟩, + ⟨7, 4, 8, 7, 5, 7, 376946502720958126592328812376509767115970969600000000⟩, + ⟨7, 5, 4, 0, 8, 8, 314746793385003482524825402744866776870692061184000000⟩, + ⟨7, 5, 4, 1, 7, 8, -367072732344336537731301464460309759065906479104000000⟩, + ⟨7, 5, 5, 1, 8, 8, -1801843076973613601433144014642942923866793574400000000⟩, + ⟨7, 5, 4, 2, 6, 8, 242008559903447860998338997862939849286599311360000000⟩, + ⟨7, 5, 5, 2, 7, 8, -923603889985887349390184060472087160205680312320000000⟩, + ⟨7, 5, 6, 2, 8, 8, 818585401158234959325891969172878776869815582720000000⟩, + ⟨7, 5, 4, 3, 5, 8, 663997656062170195490285606579960010215390183424000000⟩, + ⟨7, 5, 5, 3, 6, 8, 631943613664918513715688978855789784753640570880000000⟩, + ⟨7, 5, 6, 3, 7, 8, 1735620033859364402989586949119310998494248960000000⟩, + ⟨7, 5, 7, 3, 8, 8, -92595067602935520019291794812334444333099909120000000⟩, + ⟨7, 5, 4, 4, 4, 8, -497643525302376958459831222887596941024123944960000000⟩, + ⟨7, 5, 5, 4, 5, 8, 383180170978377123060865059259318472483033579520000000⟩, + ⟨7, 5, 6, 4, 6, 8, 350749381316292757150057072077272787048160296960000000⟩, + ⟨7, 5, 7, 4, 7, 8, -244921624789164162141293056625195354225576509440000000⟩, + ⟨7, 5, 8, 4, 8, 8, 65586573477445551682177697457326104286488166400000000⟩, + ⟨7, 5, 4, 5, 3, 8, -474196502990813219193431552274654387587040411648000000⟩, + ⟨7, 5, 5, 5, 4, 8, 254177445196488720245282464940107100131153674240000000⟩, + ⟨7, 5, 6, 5, 5, 8, 293009471611698999307684061800245938102552494080000000⟩ +] + +def collectedFourData_16_52 : List CollectedFourTerm := [ + ⟨7, 5, 7, 5, 6, 8, 77590695951811755828783302123141093710312243200000000⟩, + ⟨7, 5, 8, 5, 7, 8, -107529333979814237281691543420975367903133040640000000⟩, + ⟨7, 5, 4, 6, 2, 8, 600616124456197677059963830131641082272733462528000000⟩, + ⟨7, 5, 5, 6, 3, 8, -2316205534584599375822799296760391367424988938240000000⟩, + ⟨7, 5, 6, 6, 4, 8, -195366486457895009967013404332853815703534305280000000⟩, + ⟨7, 5, 7, 6, 5, 8, 484762830033587540127382635544629828309724692480000000⟩, + ⟨7, 5, 8, 6, 6, 8, 160620492181162284615674483962710873968832675840000000⟩, + ⟨7, 5, 4, 7, 1, 8, 576962242686319424591938444819467786628720754688000000⟩, + ⟨7, 5, 5, 7, 2, 8, 128317136333231678299346325453347313024730398720000000⟩, + ⟨7, 5, 6, 7, 3, 8, -986247250835710828997129122540071941295581429760000000⟩, + ⟨7, 5, 7, 7, 4, 8, 376946502720958126592328812376509767115970969600000000⟩, + ⟨7, 5, 8, 7, 5, 8, 414899732202821946438911005723899467141637734400000000⟩, + ⟨0, 8, 8, 5, 8, 3, 56872417834912242101103430630756182741026340864000000⟩, + ⟨0, 8, 8, 6, 7, 3, 15330389042752552044117543232367012379881373696000000⟩, + ⟨0, 8, 8, 7, 6, 3, 22919974352719316698490926673231882423617191936000000⟩, + ⟨1, 7, 8, 5, 8, 3, -759742816879129001925199788972219790314902126592000000⟩, + ⟨1, 7, 8, 6, 7, 3, -204794404714826913180910932444743886907625177088000000⟩, + ⟨1, 7, 8, 7, 6, 3, -306181564639632398244393504202210037536609271808000000⟩, + ⟨1, 8, 7, 4, 8, 4, 429511133899328987583574921034393602200793251840000000⟩, + ⟨1, 8, 7, 5, 7, 4, 195915466323518743116859984096487272566994501632000000⟩, + ⟨1, 8, 8, 5, 8, 4, 1182669837190237277079191878037254165544445149184000000⟩, + ⟨1, 8, 7, 6, 6, 4, 59230445655578548023752905969460842176618430464000000⟩, + ⟨1, 8, 8, 6, 7, 4, 318797571889500717065668018079604063379365298176000000⟩, + ⟨1, 8, 7, 7, 5, 4, -212787548639911756922203187198741746408344256512000000⟩ +] + +def collectedFourData_16_53 : List CollectedFourTerm := [ + ⟨1, 8, 8, 7, 6, 4, 476624053769258846979074179234291578453796847616000000⟩, + ⟨2, 6, 8, 5, 8, 3, 247312142247348910958184120214583909541186895872000000⟩, + ⟨2, 6, 8, 6, 7, 3, 66664852664677793607425800570427863031252779008000000⟩, + ⟨2, 6, 8, 7, 6, 3, 99668489106254561438498295881635949687265558528000000⟩, + ⟨2, 7, 7, 4, 8, 4, -58238057539159186983595735667702719923722649600000000⟩, + ⟨2, 7, 7, 5, 7, 4, -26564471325752781918289156908462742347794350080000000⟩, + ⟨2, 7, 8, 5, 8, 4, -160359973448922670194963388892585059463158824960000000⟩, + ⟨2, 7, 7, 6, 6, 4, -8031144782775592141616632229109181077163868160000000⟩, + ⟨2, 7, 8, 6, 7, 4, -43226239949804443190525069075019424989645373440000000⟩, + ⟨2, 7, 7, 7, 5, 4, 28852182221223614413139591864781938833521377280000000⟩, + ⟨2, 7, 8, 7, 6, 4, -64626168863104211760024750262969232994116567040000000⟩, + ⟨2, 8, 6, 3, 8, 5, 283685201722203913853076389853561614316884459520000000⟩, + ⟨2, 8, 6, 4, 7, 5, -123787864558950700686058520565887180557296599040000000⟩, + ⟨2, 8, 7, 4, 8, 5, 726492550039405164599082289191614844301108838400000000⟩, + ⟨2, 8, 6, 5, 6, 5, -209657433343510624296035944721680713830797148160000000⟩, + ⟨2, 8, 7, 5, 7, 5, 331379364789394805316052638324977106009005752320000000⟩, + ⟨2, 8, 8, 5, 8, 5, 1000207861988052084253513388805894527095060561920000000⟩, + ⟨2, 8, 6, 6, 5, 5, 19942116514195523528194814796647047441950965760000000⟩, + ⟨2, 8, 7, 6, 6, 5, 100184777781284173991552979985477938119851376640000000⟩, + ⟨2, 8, 8, 6, 7, 5, 269613570719052078418237240018059386912904314880000000⟩, + ⟨2, 8, 6, 7, 4, 5, 692064048950431174129152472146545820120907776000000000⟩, + ⟨2, 8, 7, 7, 5, 5, -359917489040637327106591453816666351664753541120000000⟩, + ⟨2, 8, 8, 7, 6, 5, 403090626649630115995230344624994282410952622080000000⟩, + ⟨3, 5, 8, 5, 8, 3, 493998026158263409228930620230840979579016839168000000⟩ +] + +def collectedFourData_16_54 : List CollectedFourTerm := [ + ⟨3, 5, 8, 6, 7, 3, 133160892672811329424013925822234169053441687552000000⟩, + ⟨3, 5, 8, 7, 6, 3, 199084591808770858934666308723711231142167314432000000⟩, + ⟨3, 6, 7, 4, 8, 4, -47430667545657134080586389449518987533992591360000000⟩, + ⟨3, 6, 7, 5, 7, 4, -21634832293826413635336110712858107101449289728000000⟩, + ⟨3, 6, 8, 5, 8, 4, -130601550080409287212232559262168439339284955136000000⟩, + ⟨3, 6, 7, 6, 6, 4, -6540784055971236785933649691715736240711008256000000⟩, + ⟨3, 6, 8, 6, 7, 4, -35204632553710993525508724325181244533379170304000000⟩, + ⟨3, 6, 7, 7, 5, 4, 23498006642502006779917724657503403241004597248000000⟩, + ⟨3, 6, 8, 7, 6, 4, -52633320196751351392251328470902742621370712064000000⟩, + ⟨3, 7, 6, 3, 8, 5, -22348377644443556524531241439409496907495505920000000⟩, + ⟨3, 7, 6, 4, 7, 5, 9751858497263769146096851915357455923376291840000000⟩, + ⟨3, 7, 7, 4, 8, 5, -57232205859135073952149050098222889169217126400000000⟩, + ⟨3, 7, 6, 5, 6, 5, 16516559439409051374667269732568762728956559360000000⟩, + ⟨3, 7, 7, 5, 7, 5, -26105666220620379829007260921784508372190494720000000⟩, + ⟨3, 7, 8, 5, 8, 5, -78795167625766600584403454025501098044104376320000000⟩, + ⟨3, 7, 6, 6, 5, 5, -1571015859068877196771439829004447831252008960000000⟩, + ⟨3, 7, 7, 6, 6, 5, -7892435821426048683517043075217798257379901440000000⟩, + ⟨3, 7, 8, 6, 7, 5, -21239831545378272520237122074811509779181076480000000⟩, + ⟨3, 7, 6, 7, 4, 5, -54519970115439230965915352349717218350596096000000000⟩, + ⟨3, 7, 7, 7, 5, 5, 28353865189614757473286250698414273924190699520000000⟩, + ⟨3, 7, 8, 7, 6, 5, -31754992839290751968737935404657146678927687680000000⟩, + ⟨3, 8, 5, 2, 8, 6, 283685201722203913853076389853561614316884459520000000⟩, + ⟨3, 8, 5, 3, 7, 6, -22348377644443556524531241439409496907495505920000000⟩, + ⟨3, 8, 6, 3, 8, 6, 289609818337143688263017992247522508123836252160000000⟩ +] + +def collectedFourData_16_55 : List CollectedFourTerm := [ + ⟨3, 8, 5, 4, 6, 6, -54730979604246291791489426135677901429381529600000000⟩, + ⟨3, 8, 6, 4, 7, 6, -126373109170377575909011435405271249610677944320000000⟩, + ⟨3, 8, 7, 4, 8, 6, 370832482912224700923974138752573818214652313600000000⟩, + ⟨3, 8, 5, 5, 5, 6, -15062037862647904945786954647452383405984972800000000⟩, + ⟨3, 8, 6, 5, 6, 6, -214036018851290988607816650463691749213895393280000000⟩, + ⟨3, 8, 7, 5, 7, 6, 169150024489668531788366733102083449753467617280000000⟩, + ⟨3, 8, 8, 5, 8, 6, 340365559490127265282588331632239804775787397120000000⟩, + ⟨3, 8, 5, 6, 4, 6, 125603020254286015176781680817332024431156920320000000⟩, + ⟨3, 8, 6, 6, 5, 6, 20358597155835633993044750209303007281104814080000000⟩, + ⟨3, 8, 7, 6, 6, 6, 51138542153843105020615707511702024691971522560000000⟩, + ⟨3, 8, 8, 6, 7, 6, 91748102900852176388808716807478602400194887680000000⟩, + ⟨3, 8, 5, 7, 3, 6, 175115299401085970573073193406608290896664330240000000⟩, + ⟨3, 8, 6, 7, 4, 6, 706517443551638868888309718569656975263531008000000000⟩, + ⟨3, 8, 7, 7, 5, 6, -183717088492144290479632861273306877632425492480000000⟩, + ⟨3, 8, 8, 7, 6, 6, 137169654307782525256158731464826566298440826880000000⟩, + ⟨4, 4, 8, 5, 8, 3, -202027835026340647337930676780337879090307530752000000⟩, + ⟨4, 4, 8, 6, 7, 3, -54458126211711323003584367437469119101511139328000000⟩, + ⟨4, 4, 8, 7, 6, 3, -81418602788795641893720522314885101957203099648000000⟩, + ⟨4, 5, 7, 4, 8, 4, 122650554531747025417859556730676081066067886080000000⟩, + ⟨4, 5, 7, 5, 7, 4, 55945326417446156760076373052329972910243446784000000⟩, + ⟨4, 5, 8, 5, 8, 4, 337721423057108296001523925544119373359227076608000000⟩, + ⟨4, 5, 7, 6, 6, 4, 16913757133294571245110657456213085351437139968000000⟩, + ⟨4, 5, 8, 6, 7, 4, 91035355988667739046896351322500961211317747712000000⟩, + ⟨4, 5, 7, 7, 5, 4, -60763292912107306973956973752569241511965753344000000⟩ +] + +def collectedFourData_16_56 : List CollectedFourTerm := [ + ⟨4, 5, 8, 7, 6, 4, 136104049194847044435896265365516970422270164992000000⟩, + ⟨4, 6, 6, 3, 8, 5, -54730979604246291791489426135677901429381529600000000⟩, + ⟨4, 6, 6, 4, 7, 5, 23882215389802105904776459731792818936689459200000000⟩, + ⟨4, 6, 7, 4, 8, 5, -140161167017022573629807145369811467613765632000000000⟩, + ⟨4, 6, 6, 5, 6, 5, 40448908291800341497329419107490293074414796800000000⟩, + ⟨4, 6, 7, 5, 7, 5, -63932546165438230947412214151196983011416473600000000⟩, + ⟨4, 6, 8, 5, 8, 5, -192968670068595293860947863926656342332905881600000000⟩, + ⟨4, 6, 6, 6, 5, 5, -3847403973058602189034549046266149349412044800000000⟩, + ⟨4, 6, 7, 6, 6, 5, -19328505667957944502465596978402241562227507200000000⟩, + ⟨4, 6, 8, 6, 7, 5, -52016159991673940713847395951781889758881382400000000⟩, + ⟨4, 6, 6, 7, 4, 5, -133518925618930207209718558590562273308180480000000000⟩, + ⟨4, 6, 7, 7, 5, 5, 69438365597879744152908990432174560329177497600000000⟩, + ⟨4, 6, 8, 7, 6, 5, -77767697193550915476644349454004083919054438400000000⟩, + ⟨4, 7, 5, 2, 8, 6, -123787864558950700686058520565887180557296599040000000⟩, + ⟨4, 7, 5, 3, 7, 6, 9751858497263769146096851915357455923376291840000000⟩, + ⟨4, 7, 6, 3, 8, 6, -126373109170377575909011435405271249610677944320000000⟩, + ⟨4, 7, 5, 4, 6, 6, 23882215389802105904776459731792818936689459200000000⟩, + ⟨4, 7, 6, 4, 7, 6, 55143719964620853560371272319431029220326768640000000⟩, + ⟨4, 7, 7, 4, 8, 6, -161815141890092259633384548195794837870687027200000000⟩, + ⟨4, 7, 5, 5, 5, 6, 6572417213179268803548182273272621695605145600000000⟩, + ⟨4, 7, 6, 5, 6, 6, 93395995108146916080712317402426843389818306560000000⟩, + ⟨4, 7, 7, 5, 7, 6, -73809702425628562681147220546056056369378754560000000⟩, + ⟨4, 7, 8, 5, 8, 6, -148520703663470685416298703258958669562500874240000000⟩, + ⟨4, 7, 5, 6, 4, 6, -54807686707105926876032656679038618941668720640000000⟩ +] + +def collectedFourData_16_57 : List CollectedFourTerm := [ + ⟨4, 7, 6, 6, 5, 6, -8883604967892019631253435182367044928704348160000000⟩, + ⟨4, 7, 7, 6, 6, 6, -22314632174860635883884901318771085600222085120000000⟩, + ⟨4, 7, 8, 6, 7, 6, -40034875511599272014447128955645555044106895360000000⟩, + ⟨4, 7, 5, 7, 3, 6, -76412688546542081137128755878726380766604820480000000⟩, + ⟨4, 7, 6, 7, 4, 6, -308293436104393909604627733556751600782934016000000000⟩, + ⟨4, 7, 7, 7, 5, 6, 80166134607543456829514051598618037870091304960000000⟩, + ⟨4, 7, 8, 7, 6, 6, -59854861959550918540379269221612993990371573760000000⟩, + ⟨4, 8, 4, 1, 8, 7, 429511133899328987583574921034393602200793251840000000⟩, + ⟨4, 8, 4, 2, 7, 7, -58238057539159186983595735667702719923722649600000000⟩, + ⟨4, 8, 5, 2, 8, 7, 726492550039405164599082289191614844301108838400000000⟩, + ⟨4, 8, 4, 3, 6, 7, -47430667545657134080586389449518987533992591360000000⟩, + ⟨4, 8, 5, 3, 7, 7, -57232205859135073952149050098222889169217126400000000⟩, + ⟨4, 8, 6, 3, 8, 7, 370832482912224700923974138752573818214652313600000000⟩, + ⟨4, 8, 4, 4, 5, 7, 122650554531747025417859556730676081066067886080000000⟩, + ⟨4, 8, 5, 4, 6, 7, -140161167017022573629807145369811467613765632000000000⟩, + ⟨4, 8, 6, 4, 7, 7, -161815141890092259633384548195794837870687027200000000⟩, + ⟨4, 8, 7, 4, 8, 7, 316556326652245317495987923528001380683874304000000000⟩, + ⟨4, 8, 4, 5, 4, 7, 17127989055383924453254199575227515042109849600000000⟩, + ⟨4, 8, 5, 5, 5, 7, -38572538254358605766158138995740746161586176000000000⟩, + ⟨4, 8, 6, 5, 6, 7, -274063596182616840212280255470603367621643468800000000⟩, + ⟨4, 8, 7, 5, 7, 7, 144392718742119796664219451806316901380076339200000000⟩, + ⟨4, 8, 8, 5, 8, 7, 217911475253572829543484778117964168206850457600000000⟩, + ⟨4, 8, 4, 6, 3, 7, -428135770546195163670296263354479428012448153600000000⟩, + ⟨4, 8, 5, 6, 4, 7, 321658154613728070706051520952785484376335974400000000⟩ +] + +def collectedFourData_16_58 : List CollectedFourTerm := [ + ⟨4, 8, 6, 6, 5, 7, 26068277571720751857259695469026657516178636800000000⟩, + ⟨4, 8, 7, 6, 6, 7, 43653751492970738116972449136195973906064998400000000⟩, + ⟨4, 8, 8, 6, 7, 7, 58739681196860999861248635443506207225439846400000000⟩, + ⟨4, 8, 4, 7, 2, 7, 439977076589651175195384559982358130267992883200000000⟩, + ⟨4, 8, 5, 7, 3, 7, 448454694289580270794085364320054652877720780800000000⟩, + ⟨4, 8, 6, 7, 4, 7, 904664141973425759670791675064656460439879680000000000⟩, + ⟨4, 8, 7, 7, 5, 7, -156827703494583794987425406032217348953551667200000000⟩, + ⟨4, 8, 8, 7, 6, 7, 87819818712000187554802047788238079244265062400000000⟩, + ⟨5, 3, 8, 5, 8, 3, -508643101812610092725715106167774640503043129344000000⟩, + ⟨5, 3, 8, 6, 7, 3, -137108583238621173175623982020926747660481724416000000⟩, + ⟨5, 3, 8, 7, 6, 3, -204986657716459518808477781020393735259953299456000000⟩, + ⟨5, 4, 7, 4, 8, 4, 17127989055383924453254199575227515042109849600000000⟩, + ⟨5, 4, 7, 5, 7, 4, 7812691448776688562701447756847126648276910080000000⟩, + ⟨5, 4, 8, 5, 8, 4, 47162353729053631012820928738062149104917544960000000⟩, + ⟨5, 4, 7, 6, 6, 4, 2361983997304351619038532188852450771504988160000000⟩, + ⟨5, 4, 8, 6, 7, 4, 12712968049592319763175173518217986656635453440000000⟩, + ⟨5, 4, 7, 7, 5, 4, -8485514149862826029419734329938894034074337280000000⟩, + ⟨5, 4, 8, 7, 6, 4, 19006751937671570618897882617799054436901847040000000⟩, + ⟨5, 5, 6, 3, 8, 5, -15062037862647904945786954647452383405984972800000000⟩, + ⟨5, 5, 6, 4, 7, 5, 6572417213179268803548182273272621695605145600000000⟩, + ⟨5, 5, 7, 4, 8, 5, -38572538254358605766158138995740746161586176000000000⟩, + ⟨5, 5, 6, 5, 6, 5, 11131592977126277192127458813305169937589862400000000⟩, + ⟨5, 5, 7, 5, 7, 5, -17594321131511505812916180173049757596175564800000000⟩, + ⟨5, 5, 8, 5, 8, 5, -53105232829643953508888683427933331808636108800000000⟩ +] + +def collectedFourData_16_59 : List CollectedFourTerm := [ + ⟨5, 5, 6, 6, 5, 5, -1058810654114705945977818396175807174567526400000000⟩, + ⟨5, 5, 7, 6, 6, 5, -5319230284279439260093107525833274047437209600000000⟩, + ⟨5, 5, 8, 6, 7, 5, -14314915920184968096979231012464601389544243200000000⟩, + ⟨5, 5, 6, 7, 4, 5, -36744584650123234940443950139282012388720640000000000⟩, + ⟨5, 5, 7, 7, 5, 5, 19109529910086019981557161923524202370747596800000000⟩, + ⟨5, 5, 8, 7, 6, 5, -21401772964599430153544045066869338130297651200000000⟩, + ⟨5, 6, 5, 2, 8, 6, -209657433343510624296035944721680713830797148160000000⟩, + ⟨5, 6, 5, 3, 7, 6, 16516559439409051374667269732568762728956559360000000⟩, + ⟨5, 6, 6, 3, 8, 6, -214036018851290988607816650463691749213895393280000000⟩, + ⟨5, 6, 5, 4, 6, 6, 40448908291800341497329419107490293074414796800000000⟩, + ⟨5, 6, 6, 4, 7, 6, 93395995108146916080712317402426843389818306560000000⟩, + ⟨5, 6, 7, 4, 8, 6, -274063596182616840212280255470603367621643468800000000⟩, + ⟨5, 6, 5, 5, 5, 6, 11131592977126277192127458813305169937589862400000000⟩, + ⟨5, 6, 6, 5, 6, 6, 158183232974441884632949989604922859083519754240000000⟩, + ⟨5, 6, 7, 5, 7, 6, -125010257035625108286336523983855108948743946240000000⟩, + ⟨5, 6, 8, 5, 8, 6, -251547028777013321928306056259702306821332008960000000⟩, + ⟨5, 6, 5, 6, 4, 6, -92826861206858170287463279598079445421323714560000000⟩, + ⟨5, 6, 6, 6, 5, 6, -15046012975843265622670684401043721696198000640000000⟩, + ⟨5, 6, 7, 6, 6, 6, -37793918850242571908912339333944178828094996480000000⟩, + ⟨5, 6, 8, 6, 7, 6, -67806398259593818967773506698457107242879549440000000⟩, + ⟨5, 6, 5, 7, 3, 6, -129418891040936810050337973115555118990669905920000000⟩, + ⟨5, 6, 6, 7, 4, 6, -522151430276249939929435894553095750878756864000000000⟩, + ⟨5, 6, 7, 7, 5, 6, 135776039782024431479961781047222769486229667840000000⟩, + ⟨5, 6, 8, 7, 6, 6, -101375177415662087554791274072507180242740183040000000⟩ +] + +def collectedFourData_16_60 : List CollectedFourTerm := [ + ⟨5, 7, 4, 1, 8, 7, 195915466323518743116859984096487272566994501632000000⟩, + ⟨5, 7, 4, 2, 7, 7, -26564471325752781918289156908462742347794350080000000⟩, + ⟨5, 7, 5, 2, 8, 7, 331379364789394805316052638324977106009005752320000000⟩, + ⟨5, 7, 4, 3, 6, 7, -21634832293826413635336110712858107101449289728000000⟩, + ⟨5, 7, 5, 3, 7, 7, -26105666220620379829007260921784508372190494720000000⟩, + ⟨5, 7, 6, 3, 8, 7, 169150024489668531788366733102083449753467617280000000⟩, + ⟨5, 7, 4, 4, 5, 7, 55945326417446156760076373052329972910243446784000000⟩, + ⟨5, 7, 5, 4, 6, 7, -63932546165438230947412214151196983011416473600000000⟩, + ⟨5, 7, 6, 4, 7, 7, -73809702425628562681147220546056056369378754560000000⟩, + ⟨5, 7, 7, 4, 8, 7, 144392718742119796664219451806316901380076339200000000⟩, + ⟨5, 7, 4, 5, 4, 7, 7812691448776688562701447756847126648276910080000000⟩, + ⟨5, 7, 5, 5, 5, 7, -17594321131511505812916180173049757596175564800000000⟩, + ⟨5, 7, 6, 5, 6, 7, -125010257035625108286336523983855108948743946240000000⟩, + ⟨5, 7, 7, 5, 7, 7, 65862709004217688731476886012097064043974492160000000⟩, + ⟨5, 7, 8, 5, 8, 7, 99397256373698703885711647726386165026631188480000000⟩, + ⟨5, 7, 4, 6, 3, 7, -195288113662722183363018295913741744470260449280000000⟩, + ⟨5, 7, 5, 6, 4, 7, 146719845853126271430241908612909661129141125120000000⟩, + ⟨5, 7, 6, 6, 5, 7, 11890678386725226426190059621510299437907312640000000⟩, + ⟨5, 7, 7, 6, 6, 7, 19912045126450506496191501613827445517262520320000000⟩, + ⟨5, 7, 8, 6, 7, 7, 26793279906162234600060442391585548168561950720000000⟩, + ⟨5, 7, 4, 7, 2, 7, 200689358967638851785484464098517412029514383360000000⟩, + ⟨5, 7, 5, 7, 3, 7, 204556305116195304661556583217636276600402083840000000⟩, + ⟨5, 7, 6, 7, 4, 7, 412649831988829304332365907094021738871128064000000000⟩, + ⟨5, 7, 7, 7, 5, 7, -71534752507229277435547051031467960381797826560000000⟩ +] + +def collectedFourData_16_61 : List CollectedFourTerm := [ + ⟨5, 7, 8, 7, 6, 7, 40057775869998868898533082247043598750601707520000000⟩, + ⟨5, 8, 3, 0, 8, 8, 56872417834912242101103430630756182741026340864000000⟩, + ⟨5, 8, 3, 1, 7, 8, -759742816879129001925199788972219790314902126592000000⟩, + ⟨5, 8, 4, 1, 8, 8, 1182669837190237277079191878037254165544445149184000000⟩, + ⟨5, 8, 3, 2, 6, 8, 247312142247348910958184120214583909541186895872000000⟩, + ⟨5, 8, 4, 2, 7, 8, -160359973448922670194963388892585059463158824960000000⟩, + ⟨5, 8, 5, 2, 8, 8, 1000207861988052084253513388805894527095060561920000000⟩, + ⟨5, 8, 3, 3, 5, 8, 493998026158263409228930620230840979579016839168000000⟩, + ⟨5, 8, 4, 3, 6, 8, -130601550080409287212232559262168439339284955136000000⟩, + ⟨5, 8, 5, 3, 7, 8, -78795167625766600584403454025501098044104376320000000⟩, + ⟨5, 8, 6, 3, 8, 8, 340365559490127265282588331632239804775787397120000000⟩, + ⟨5, 8, 3, 4, 4, 8, -202027835026340647337930676780337879090307530752000000⟩, + ⟨5, 8, 4, 4, 5, 8, 337721423057108296001523925544119373359227076608000000⟩, + ⟨5, 8, 5, 4, 6, 8, -192968670068595293860947863926656342332905881600000000⟩, + ⟨5, 8, 6, 4, 7, 8, -148520703663470685416298703258958669562500874240000000⟩, + ⟨5, 8, 7, 4, 8, 8, 217911475253572829543484778117964168206850457600000000⟩, + ⟨5, 8, 3, 5, 3, 8, -508643101812610092725715106167774640503043129344000000⟩, + ⟨5, 8, 4, 5, 4, 8, 47162353729053631012820928738062149104917544960000000⟩, + ⟨5, 8, 5, 5, 5, 8, -53105232829643953508888683427933331808636108800000000⟩, + ⟨5, 8, 6, 5, 6, 8, -251547028777013321928306056259702306821332008960000000⟩, + ⟨5, 8, 7, 5, 7, 8, 99397256373698703885711647726386165026631188480000000⟩, + ⟨5, 8, 8, 5, 8, 8, 120004958484001721365504295679725491614124081152000000⟩, + ⟨5, 8, 3, 6, 2, 8, -568805961907426284693393312527642808186870693888000000⟩, + ⟨5, 8, 4, 6, 3, 8, -1178882739197779998113707497556812578751365775360000000⟩ +] + +def collectedFourData_16_62 : List CollectedFourTerm := [ + ⟨5, 8, 5, 6, 4, 8, 442846957067582850896872384289151035055506718720000000⟩, + ⟨5, 8, 6, 6, 5, 8, 23926555222355832391179012803847123645298114560000000⟩, + ⟨5, 8, 7, 6, 6, 8, 30050428904036052717408953094211536843398184960000000⟩, + ⟨5, 8, 8, 6, 7, 8, 32348241391097764501077722060435342121844604928000000⟩, + ⟨5, 8, 3, 7, 1, 8, 5228968830872445689362030147954054481429051473920000000⟩, + ⟨5, 8, 4, 7, 2, 8, 1211488076720453639035904304634813318917594808320000000⟩, + ⟨5, 8, 5, 7, 3, 8, 617415706395829145237977372048835597787243479040000000⟩, + ⟨5, 8, 6, 7, 4, 8, 830338578797921003129471933287591264603078656000000000⟩, + ⟨5, 8, 7, 7, 5, 8, -107957268112595011564029584860846370707923271680000000⟩, + ⟨5, 8, 8, 7, 6, 8, 48362821124232409665180449432001190693592629248000000⟩, + ⟨6, 2, 8, 5, 8, 3, -568805961907426284693393312527642808186870693888000000⟩, + ⟨6, 2, 8, 6, 7, 3, -153325935802310504750820381572734111582500421632000000⟩, + ⟨6, 2, 8, 7, 6, 3, -229232702861966657065477272233238589942857203712000000⟩, + ⟨6, 3, 7, 4, 8, 4, -428135770546195163670296263354479428012448153600000000⟩, + ⟨6, 3, 7, 5, 7, 4, -195288113662722183363018295913741744470260449280000000⟩, + ⟨6, 3, 8, 5, 8, 4, -1178882739197779998113707497556812578751365775360000000⟩, + ⟨6, 3, 7, 6, 6, 4, -59040780294392448831924690756016795166504386560000000⟩, + ⟨6, 3, 8, 6, 7, 4, -317776731071093355199611223999912968109204439040000000⟩, + ⟨6, 3, 7, 7, 5, 4, 212106168872766742988573321002096997997981204480000000⟩, + ⟨6, 3, 8, 7, 6, 4, -475097827310761567150938573585336826340195696640000000⟩, + ⟨6, 4, 6, 3, 8, 5, 125603020254286015176781680817332024431156920320000000⟩, + ⟨6, 4, 6, 4, 7, 5, -54807686707105926876032656679038618941668720640000000⟩, + ⟨6, 4, 7, 4, 8, 5, 321658154613728070706051520952785484376335974400000000⟩, + ⟨6, 4, 6, 5, 6, 5, -92826861206858170287463279598079445421323714560000000⟩ +] + +def collectedFourData_16_63 : List CollectedFourTerm := [ + ⟨6, 4, 7, 5, 7, 5, 146719845853126271430241908612909661129141125120000000⟩, + ⟨6, 4, 8, 5, 8, 5, 442846957067582850896872384289151035055506718720000000⟩, + ⟨6, 4, 6, 6, 5, 5, 8829470304547729851492360809896520255180636160000000⟩, + ⟨6, 4, 7, 6, 6, 5, 44357303787583763495494264366220375274805002240000000⟩, + ⟨6, 4, 8, 6, 7, 5, 119372736322766501107279604584970474481600430080000000⟩, + ⟨6, 4, 6, 7, 4, 5, 306414766191100154082037936680289777081122816000000000⟩, + ⟨6, 4, 7, 7, 5, 5, -159355240919867217199547849567974984150595665920000000⟩, + ⟨6, 4, 8, 7, 6, 5, 178470360230367959845241790284790860138969825280000000⟩, + ⟨6, 5, 5, 2, 8, 6, 19942116514195523528194814796647047441950965760000000⟩, + ⟨6, 5, 5, 3, 7, 6, -1571015859068877196771439829004447831252008960000000⟩, + ⟨6, 5, 6, 3, 8, 6, 20358597155835633993044750209303007281104814080000000⟩, + ⟨6, 5, 5, 4, 6, 6, -3847403973058602189034549046266149349412044800000000⟩, + ⟨6, 5, 6, 4, 7, 6, -8883604967892019631253435182367044928704348160000000⟩, + ⟨6, 5, 7, 4, 8, 6, 26068277571720751857259695469026657516178636800000000⟩, + ⟨6, 5, 5, 5, 5, 6, -1058810654114705945977818396175807174567526400000000⟩, + ⟨6, 5, 6, 5, 6, 6, -15046012975843265622670684401043721696198000640000000⟩, + ⟨6, 5, 7, 5, 7, 6, 11890678386725226426190059621510299437907312640000000⟩, + ⟨6, 5, 8, 5, 8, 6, 23926555222355832391179012803847123645298114560000000⟩, + ⟨6, 5, 5, 6, 4, 6, 8829470304547729851492360809896520255180636160000000⟩, + ⟨6, 5, 6, 6, 5, 6, 1431140976274149029461216808302315289224151040000000⟩, + ⟨6, 5, 7, 6, 6, 6, 3594867690690044086526019443477648604691169280000000⟩, + ⟨6, 5, 8, 6, 7, 6, 6449583365285523142568012445756499626389667840000000⟩, + ⟨6, 5, 5, 7, 3, 6, 12310017169998048028975720683080345183185797120000000⟩, + ⟨6, 5, 6, 7, 4, 6, 49665802421429463953272211914768717556219904000000000⟩ +] + +def collectedFourData_16_64 : List CollectedFourTerm := [ + ⟨6, 5, 7, 7, 5, 6, -12914694041555126609337104303666069558777610240000000⟩, + ⟨6, 5, 8, 7, 6, 6, 9642565815246112394302736894111740224539197440000000⟩, + ⟨6, 6, 4, 1, 8, 7, 59230445655578548023752905969460842176618430464000000⟩, + ⟨6, 6, 4, 2, 7, 7, -8031144782775592141616632229109181077163868160000000⟩, + ⟨6, 6, 5, 2, 8, 7, 100184777781284173991552979985477938119851376640000000⟩, + ⟨6, 6, 4, 3, 6, 7, -6540784055971236785933649691715736240711008256000000⟩, + ⟨6, 6, 5, 3, 7, 7, -7892435821426048683517043075217798257379901440000000⟩, + ⟨6, 6, 6, 3, 8, 7, 51138542153843105020615707511702024691971522560000000⟩, + ⟨6, 6, 4, 4, 5, 7, 16913757133294571245110657456213085351437139968000000⟩, + ⟨6, 6, 5, 4, 6, 7, -19328505667957944502465596978402241562227507200000000⟩, + ⟨6, 6, 6, 4, 7, 7, -22314632174860635883884901318771085600222085120000000⟩, + ⟨6, 6, 7, 4, 8, 7, 43653751492970738116972449136195973906064998400000000⟩, + ⟨6, 6, 4, 5, 4, 7, 2361983997304351619038532188852450771504988160000000⟩, + ⟨6, 6, 5, 5, 5, 7, -5319230284279439260093107525833274047437209600000000⟩, + ⟨6, 6, 6, 5, 6, 7, -37793918850242571908912339333944178828094996480000000⟩, + ⟨6, 6, 7, 5, 7, 7, 19912045126450506496191501613827445517262520320000000⟩, + ⟨6, 6, 8, 5, 8, 7, 30050428904036052717408953094211536843398184960000000⟩, + ⟨6, 6, 4, 6, 3, 7, -59040780294392448831924690756016795166504386560000000⟩, + ⟨6, 6, 5, 6, 4, 7, 44357303787583763495494264366220375274805002240000000⟩, + ⟨6, 6, 6, 6, 5, 7, 3594867690690044086526019443477648604691169280000000⟩, + ⟨6, 6, 7, 6, 6, 7, 6019939767318273153915635975544641499577712640000000⟩, + ⟨6, 6, 8, 6, 7, 7, 8100319689901570559570320845530494838180413440000000⟩, + ⟨6, 6, 4, 7, 2, 7, 60673720115371303429493581849980940843713822720000000⟩, + ⟨6, 6, 5, 7, 3, 7, 61842800576466203979366775600819293730300231680000000⟩ +] + +def collectedFourData_16_65 : List CollectedFourTerm := [ + ⟨6, 6, 6, 7, 4, 7, 124754997178412614639730882613416781863190528000000000⟩, + ⟨6, 6, 7, 7, 5, 7, -21626854430512454991854057890223403801111429120000000⟩, + ⟨6, 6, 8, 7, 6, 7, 12110528899404657559070674134537289428149207040000000⟩, + ⟨6, 7, 3, 0, 8, 8, 15330389042752552044117543232367012379881373696000000⟩, + ⟨6, 7, 3, 1, 7, 8, -204794404714826913180910932444743886907625177088000000⟩, + ⟨6, 7, 4, 1, 8, 8, 318797571889500717065668018079604063379365298176000000⟩, + ⟨6, 7, 3, 2, 6, 8, 66664852664677793607425800570427863031252779008000000⟩, + ⟨6, 7, 4, 2, 7, 8, -43226239949804443190525069075019424989645373440000000⟩, + ⟨6, 7, 5, 2, 8, 8, 269613570719052078418237240018059386912904314880000000⟩, + ⟨6, 7, 3, 3, 5, 8, 133160892672811329424013925822234169053441687552000000⟩, + ⟨6, 7, 4, 3, 6, 8, -35204632553710993525508724325181244533379170304000000⟩, + ⟨6, 7, 5, 3, 7, 8, -21239831545378272520237122074811509779181076480000000⟩, + ⟨6, 7, 6, 3, 8, 8, 91748102900852176388808716807478602400194887680000000⟩, + ⟨6, 7, 3, 4, 4, 8, -54458126211711323003584367437469119101511139328000000⟩, + ⟨6, 7, 4, 4, 5, 8, 91035355988667739046896351322500961211317747712000000⟩, + ⟨6, 7, 5, 4, 6, 8, -52016159991673940713847395951781889758881382400000000⟩, + ⟨6, 7, 6, 4, 7, 8, -40034875511599272014447128955645555044106895360000000⟩, + ⟨6, 7, 7, 4, 8, 8, 58739681196860999861248635443506207225439846400000000⟩, + ⟨6, 7, 3, 5, 3, 8, -137108583238621173175623982020926747660481724416000000⟩, + ⟨6, 7, 4, 5, 4, 8, 12712968049592319763175173518217986656635453440000000⟩, + ⟨6, 7, 5, 5, 5, 8, -14314915920184968096979231012464601389544243200000000⟩, + ⟨6, 7, 6, 5, 6, 8, -67806398259593818967773506698457107242879549440000000⟩, + ⟨6, 7, 7, 5, 7, 8, 26793279906162234600060442391585548168561950720000000⟩, + ⟨6, 7, 8, 5, 8, 8, 32348241391097764501077722060435342121844604928000000⟩ +] + +def collectedFourData_16_66 : List CollectedFourTerm := [ + ⟨6, 7, 3, 6, 2, 8, -153325935802310504750820381572734111582500421632000000⟩, + ⟨6, 7, 4, 6, 3, 8, -317776731071093355199611223999912968109204439040000000⟩, + ⟨6, 7, 5, 6, 4, 8, 119372736322766501107279604584970474481600430080000000⟩, + ⟨6, 7, 6, 6, 5, 8, 6449583365285523142568012445756499626389667840000000⟩, + ⟨6, 7, 7, 6, 6, 8, 8100319689901570559570320845530494838180413440000000⟩, + ⟨6, 7, 8, 6, 7, 8, 8719712371186987430761737073978807057951752192000000⟩, + ⟨6, 7, 3, 7, 1, 8, 1409507974540383971993643048978995826851189882880000000⟩, + ⟨6, 7, 4, 7, 2, 8, 326565745643039343755276513456090454172347924480000000⟩, + ⟨6, 7, 5, 7, 3, 8, 166429058944343567121129795865147282586924482560000000⟩, + ⟨6, 7, 6, 7, 4, 8, 223824024628757318941682535641587651480387584000000000⟩, + ⟨6, 7, 7, 7, 5, 8, -29100695612467095072711536330804253280457195520000000⟩, + ⟨6, 7, 8, 7, 6, 8, 13036563087430380830652703243882320665795100672000000⟩, + ⟨7, 1, 8, 5, 8, 3, 5228968830872445689362030147954054481429051473920000000⟩, + ⟨7, 1, 8, 6, 7, 3, 1409507974540383971993643048978995826851189882880000000⟩, + ⟨7, 1, 8, 7, 6, 3, 2107310293060799649107584810710776821238024110080000000⟩, + ⟨7, 2, 7, 4, 8, 4, 439977076589651175195384559982358130267992883200000000⟩, + ⟨7, 2, 7, 5, 7, 4, 200689358967638851785484464098517412029514383360000000⟩, + ⟨7, 2, 8, 5, 8, 4, 1211488076720453639035904304634813318917594808320000000⟩, + ⟨7, 2, 7, 6, 6, 4, 60673720115371303429493581849980940843713822720000000⟩, + ⟨7, 2, 8, 6, 7, 4, 326565745643039343755276513456090454172347924480000000⟩, + ⟨7, 2, 7, 7, 5, 4, -217972565077230567523431513005546456569620725760000000⟩, + ⟨7, 2, 8, 7, 6, 4, 488238001902084879513441176163493896991203655680000000⟩, + ⟨7, 3, 6, 3, 8, 5, 175115299401085970573073193406608290896664330240000000⟩, + ⟨7, 3, 6, 4, 7, 5, -76412688546542081137128755878726380766604820480000000⟩ +] + +def collectedFourData_16_67 : List CollectedFourTerm := [ + ⟨7, 3, 7, 4, 8, 5, 448454694289580270794085364320054652877720780800000000⟩, + ⟨7, 3, 6, 5, 6, 5, -129418891040936810050337973115555118990669905920000000⟩, + ⟨7, 3, 7, 5, 7, 5, 204556305116195304661556583217636276600402083840000000⟩, + ⟨7, 3, 8, 5, 8, 5, 617415706395829145237977372048835597787243479040000000⟩, + ⟨7, 3, 6, 6, 5, 5, 12310017169998048028975720683080345183185797120000000⟩, + ⟨7, 3, 7, 6, 6, 5, 61842800576466203979366775600819293730300231680000000⟩, + ⟨7, 3, 8, 6, 7, 5, 166429058944343567121129795865147282586924482560000000⟩, + ⟨7, 3, 6, 7, 4, 5, 427202414510707297140413890833568197469274112000000000⟩, + ⟨7, 3, 7, 7, 5, 5, -222172529516562317036127594113201449616214589440000000⟩, + ⟨7, 3, 8, 7, 6, 5, 248822763200187406961958689022199943236901928960000000⟩, + ⟨7, 4, 5, 2, 8, 6, 692064048950431174129152472146545820120907776000000000⟩, + ⟨7, 4, 5, 3, 7, 6, -54519970115439230965915352349717218350596096000000000⟩, + ⟨7, 4, 6, 3, 8, 6, 706517443551638868888309718569656975263531008000000000⟩, + ⟨7, 4, 5, 4, 6, 6, -133518925618930207209718558590562273308180480000000000⟩, + ⟨7, 4, 6, 4, 7, 6, -308293436104393909604627733556751600782934016000000000⟩, + ⟨7, 4, 7, 4, 8, 6, 904664141973425759670791675064656460439879680000000000⟩, + ⟨7, 4, 5, 5, 5, 6, -36744584650123234940443950139282012388720640000000000⟩, + ⟨7, 4, 6, 5, 6, 6, -522151430276249939929435894553095750878756864000000000⟩, + ⟨7, 4, 7, 5, 7, 6, 412649831988829304332365907094021738871128064000000000⟩, + ⟨7, 4, 8, 5, 8, 6, 830338578797921003129471933287591264603078656000000000⟩, + ⟨7, 4, 5, 6, 4, 6, 306414766191100154082037936680289777081122816000000000⟩, + ⟨7, 4, 6, 6, 5, 6, 49665802421429463953272211914768717556219904000000000⟩, + ⟨7, 4, 7, 6, 6, 6, 124754997178412614639730882613416781863190528000000000⟩, + ⟨7, 4, 8, 6, 7, 6, 223824024628757318941682535641587651480387584000000000⟩ +] + +def collectedFourData_16_68 : List CollectedFourTerm := [ + ⟨7, 4, 5, 7, 3, 6, 427202414510707297140413890833568197469274112000000000⟩, + ⟨7, 4, 6, 7, 4, 6, 1723584168895985742388491616755997517178470400000000000⟩, + ⟨7, 4, 7, 7, 5, 6, -448186903481002190737929662200400292373069824000000000⟩, + ⟨7, 4, 8, 7, 6, 6, 334632140756973382532405749052974487562092544000000000⟩, + ⟨7, 5, 4, 1, 8, 7, -212787548639911756922203187198741746408344256512000000⟩, + ⟨7, 5, 4, 2, 7, 7, 28852182221223614413139591864781938833521377280000000⟩, + ⟨7, 5, 5, 2, 8, 7, -359917489040637327106591453816666351664753541120000000⟩, + ⟨7, 5, 4, 3, 6, 7, 23498006642502006779917724657503403241004597248000000⟩, + ⟨7, 5, 5, 3, 7, 7, 28353865189614757473286250698414273924190699520000000⟩, + ⟨7, 5, 6, 3, 8, 7, -183717088492144290479632861273306877632425492480000000⟩, + ⟨7, 5, 4, 4, 5, 7, -60763292912107306973956973752569241511965753344000000⟩, + ⟨7, 5, 5, 4, 6, 7, 69438365597879744152908990432174560329177497600000000⟩, + ⟨7, 5, 6, 4, 7, 7, 80166134607543456829514051598618037870091304960000000⟩, + ⟨7, 5, 7, 4, 8, 7, -156827703494583794987425406032217348953551667200000000⟩, + ⟨7, 5, 4, 5, 4, 7, -8485514149862826029419734329938894034074337280000000⟩, + ⟨7, 5, 5, 5, 5, 7, 19109529910086019981557161923524202370747596800000000⟩, + ⟨7, 5, 6, 5, 6, 7, 135776039782024431479961781047222769486229667840000000⟩, + ⟨7, 5, 7, 5, 7, 7, -71534752507229277435547051031467960381797826560000000⟩, + ⟨7, 5, 8, 5, 8, 7, -107957268112595011564029584860846370707923271680000000⟩, + ⟨7, 5, 4, 6, 3, 7, 212106168872766742988573321002096997997981204480000000⟩, + ⟨7, 5, 5, 6, 4, 7, -159355240919867217199547849567974984150595665920000000⟩, + ⟨7, 5, 6, 6, 5, 7, -12914694041555126609337104303666069558777610240000000⟩, + ⟨7, 5, 7, 6, 6, 7, -21626854430512454991854057890223403801111429120000000⟩, + ⟨7, 5, 8, 6, 7, 7, -29100695612467095072711536330804253280457195520000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1604.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1604.lean new file mode 100644 index 0000000000000000000000000000000000000000..2d9a1babca77eb3cdc34ab513225b0b849465bfa --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1604.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1604. -/ +namespace LaughlinFock +def collectedFourData_16_69 : List CollectedFourTerm := [ + ⟨7, 5, 4, 7, 2, 7, -217972565077230567523431513005546456569620725760000000⟩, + ⟨7, 5, 5, 7, 3, 7, -222172529516562317036127594113201449616214589440000000⟩, + ⟨7, 5, 6, 7, 4, 7, -448186903481002190737929662200400292373069824000000000⟩, + ⟨7, 5, 7, 7, 5, 7, 77695267832710175019320085402475500588194856960000000⟩, + ⟨7, 5, 8, 7, 6, 7, -43507519295432091371838933875135463786094264320000000⟩, + ⟨7, 6, 3, 0, 8, 8, 22919974352719316698490926673231882423617191936000000⟩, + ⟨7, 6, 3, 1, 7, 8, -306181564639632398244393504202210037536609271808000000⟩, + ⟨7, 6, 4, 1, 8, 8, 476624053769258846979074179234291578453796847616000000⟩, + ⟨7, 6, 3, 2, 6, 8, 99668489106254561438498295881635949687265558528000000⟩, + ⟨7, 6, 4, 2, 7, 8, -64626168863104211760024750262969232994116567040000000⟩, + ⟨7, 6, 5, 2, 8, 8, 403090626649630115995230344624994282410952622080000000⟩, + ⟨7, 6, 3, 3, 5, 8, 199084591808770858934666308723711231142167314432000000⟩, + ⟨7, 6, 4, 3, 6, 8, -52633320196751351392251328470902742621370712064000000⟩, + ⟨7, 6, 5, 3, 7, 8, -31754992839290751968737935404657146678927687680000000⟩, + ⟨7, 6, 6, 3, 8, 8, 137169654307782525256158731464826566298440826880000000⟩, + ⟨7, 6, 3, 4, 4, 8, -81418602788795641893720522314885101957203099648000000⟩, + ⟨7, 6, 4, 4, 5, 8, 136104049194847044435896265365516970422270164992000000⟩, + ⟨7, 6, 5, 4, 6, 8, -77767697193550915476644349454004083919054438400000000⟩, + ⟨7, 6, 6, 4, 7, 8, -59854861959550918540379269221612993990371573760000000⟩, + ⟨7, 6, 7, 4, 8, 8, 87819818712000187554802047788238079244265062400000000⟩, + ⟨7, 6, 3, 5, 3, 8, -204986657716459518808477781020393735259953299456000000⟩, + ⟨7, 6, 4, 5, 4, 8, 19006751937671570618897882617799054436901847040000000⟩, + ⟨7, 6, 5, 5, 5, 8, -21401772964599430153544045066869338130297651200000000⟩, + ⟨7, 6, 6, 5, 6, 8, -101375177415662087554791274072507180242740183040000000⟩ +] + +def collectedFourData_16_70 : List CollectedFourTerm := [ + ⟨7, 6, 7, 5, 7, 8, 40057775869998868898533082247043598750601707520000000⟩, + ⟨7, 6, 8, 5, 8, 8, 48362821124232409665180449432001190693592629248000000⟩, + ⟨7, 6, 3, 6, 2, 8, -229232702861966657065477272233238589942857203712000000⟩, + ⟨7, 6, 4, 6, 3, 8, -475097827310761567150938573585336826340195696640000000⟩, + ⟨7, 6, 5, 6, 4, 8, 178470360230367959845241790284790860138969825280000000⟩, + ⟨7, 6, 6, 6, 5, 8, 9642565815246112394302736894111740224539197440000000⟩, + ⟨7, 6, 7, 6, 6, 8, 12110528899404657559070674134537289428149207040000000⟩, + ⟨7, 6, 8, 6, 7, 8, 13036563087430380830652703243882320665795100672000000⟩, + ⟨7, 6, 3, 7, 1, 8, 2107310293060799649107584810710776821238024110080000000⟩, + ⟨7, 6, 4, 7, 2, 8, 488238001902084879513441176163493896991203655680000000⟩, + ⟨7, 6, 5, 7, 3, 8, 248822763200187406961958689022199943236901928960000000⟩, + ⟨7, 6, 6, 7, 4, 8, 334632140756973382532405749052974487562092544000000000⟩, + ⟨7, 6, 7, 7, 5, 8, -43507519295432091371838933875135463786094264320000000⟩, + ⟨7, 6, 8, 7, 6, 8, 19490548529345275542234380433561490997328740352000000⟩, + ⟨0, 8, 8, 6, 8, 2, -703091459775340125707347128672488066142431084544000000⟩, + ⟨0, 8, 8, 7, 7, 2, -532379138334486998207207942498775528384371884032000000⟩, + ⟨1, 7, 8, 6, 8, 2, -322305805715318026173573369135824279249407180800000000⟩, + ⟨1, 7, 8, 7, 7, 2, -244049169907072461755075082227874897060062822400000000⟩, + ⟨1, 8, 7, 5, 8, 3, -311771051863419284703480903456544027966439424000000⟩, + ⟨1, 8, 7, 6, 7, 3, 1030210410161292835863364728371004832600817664000000⟩, + ⟨1, 8, 8, 6, 8, 3, -12229313726662083848527116411375114110103453696000000⟩, + ⟨1, 8, 7, 7, 6, 3, -2580040326661678603661321536702865138931204096000000⟩, + ⟨1, 8, 8, 7, 7, 3, -9260006523621871550927425446229021939558514688000000⟩, + ⟨2, 6, 8, 6, 8, 2, -678963705148282447702070084599012525560538595328000000⟩ +] + +def collectedFourData_16_71 : List CollectedFourTerm := [ + ⟨2, 6, 8, 7, 7, 2, -514109661384214672745515879494186738707840630784000000⟩, + ⟨2, 7, 7, 5, 8, 3, 11201932244686514354860449100896789055345262592000000⟩, + ⟨2, 7, 7, 6, 7, 3, -37015454588943372968026966354113045746272960512000000⟩, + ⟨2, 7, 8, 6, 8, 3, 439399177525618552121523239158962984806271418368000000⟩, + ⟨2, 7, 7, 7, 6, 3, 92700835292701041220313966933259450734050541568000000⟩, + ⟨2, 7, 8, 7, 7, 3, 332711985423230887232461671588398884178733563904000000⟩, + ⟨2, 8, 6, 4, 8, 4, 7568950579993138362987624684833294719144427520000000⟩, + ⟨2, 8, 6, 5, 7, 4, -9174470698179123599734805304614155803194032128000000⟩, + ⟨2, 8, 7, 5, 8, 4, -3746692905735855550400687867863508912550445056000000⟩, + ⟨2, 8, 6, 6, 6, 4, 5974000664387524808116468424747412500514865152000000⟩, + ⟨2, 8, 7, 6, 7, 4, 12380501692175961221061385084148519098820591616000000⟩, + ⟨2, 8, 8, 6, 8, 4, -73482580739688998049872087135724460144551002112000000⟩, + ⟨2, 8, 6, 7, 5, 4, -6173771896973308663820233450384729978762690560000000⟩, + ⟨2, 8, 7, 7, 6, 4, -31005504618339243866881139150797713567670861824000000⟩, + ⟨2, 8, 8, 7, 7, 4, -55640830894589817797430300473116893427097665536000000⟩, + ⟨3, 5, 8, 6, 8, 2, 168262764210290867857903585751962060493357580288000000⟩, + ⟨3, 5, 8, 7, 7, 2, 127408154627105142014659589535395515259015921664000000⟩, + ⟨3, 6, 7, 5, 8, 3, -12300327779663809202076447759472326993361502208000000⟩, + ⟨3, 6, 7, 6, 7, 3, 40644972171942110463529555644157005589578252288000000⟩, + ⟨3, 6, 8, 6, 8, 3, -482484074320612658691582385408060558311614840832000000⟩, + ⟨3, 6, 7, 7, 6, 3, -101790533511726284489675791835293414644233797632000000⟩, + ⟨3, 6, 8, 7, 7, 3, -365335764182083280351826619345282632086187933696000000⟩, + ⟨3, 7, 6, 4, 8, 4, 45630475375735382073831669187401812953823969280000000⟩, + ⟨3, 7, 6, 5, 7, 4, -55309577576743513668146405429199285949292347392000000⟩ +] + +def collectedFourData_16_72 : List CollectedFourTerm := [ + ⟨3, 7, 7, 5, 8, 4, -22587461309038880090914768767539276124713385984000000⟩, + ⟨3, 7, 6, 6, 6, 4, 36015097116832923717542667906282101840730390528000000⟩, + ⟨3, 7, 7, 6, 7, 4, 74637583061692756312925438520186523981210189824000000⟩, + ⟨3, 7, 8, 6, 8, 4, -442999997892826192619953724648354899888038739968000000⟩, + ⟨3, 7, 6, 7, 5, 4, -37219445885258120621148197950094868314157219840000000⟩, + ⟨3, 7, 7, 7, 6, 4, -186921013692318376465897499983264685411675406336000000⟩, + ⟨3, 7, 8, 7, 7, 4, -335438517822022670505218788319571837034854088704000000⟩, + ⟨3, 8, 5, 3, 8, 5, 16639235660296549358347784440212722847873761280000000⟩, + ⟨3, 8, 5, 4, 7, 5, 9942481982789190395395681601840713734448742400000000⟩, + ⟨3, 8, 6, 4, 8, 5, -37736816288592705581582671048848527196369715200000000⟩, + ⟨3, 8, 5, 5, 6, 5, -22084463343281779450633187431734455771018035200000000⟩, + ⟨3, 8, 6, 5, 7, 5, 45741521446501016143175121047794274492775137280000000⟩, + ⟨3, 8, 7, 5, 8, 5, 9340017508322517266148169205346798000175841280000000⟩, + ⟨3, 8, 5, 6, 5, 5, 44764667950396682511686184467377307648293601280000000⟩, + ⟨3, 8, 6, 6, 6, 5, -29784811407782657741366432780461040637333995520000000⟩, + ⟨3, 8, 7, 6, 7, 5, -30862978492236298174893155743896994576418734080000000⟩, + ⟨3, 8, 8, 6, 8, 5, 122121669773488302571896683956790911069889495040000000⟩, + ⟨3, 8, 5, 7, 4, 5, 135369670503623781296021693102674525584265052160000000⟩, + ⟨3, 8, 6, 7, 5, 5, 30780818743827687689040384920917198457379225600000000⟩, + ⟨3, 8, 7, 7, 6, 5, 77292685382974283194092451324982784288746373120000000⟩, + ⟨3, 8, 8, 7, 7, 5, 92470230468668782960042396276798418001718149120000000⟩, + ⟨4, 4, 8, 6, 8, 2, 21256383960005962945281605091235938581285437440000000⟩, + ⟨4, 4, 8, 7, 7, 2, 16095282085137187046963859453560830686469816320000000⟩, + ⟨4, 5, 7, 5, 8, 3, -23010447794236268928602107245690485829644845056000000⟩ +] + +def collectedFourData_16_73 : List CollectedFourTerm := [ + ⟨4, 5, 7, 6, 7, 3, 76035291661652144510041346252779854217258991616000000⟩, + ⟨4, 5, 8, 6, 8, 3, -902591768494181757738068714296052784335079604224000000⟩, + ⟨4, 5, 7, 7, 6, 3, -190421409841734560839349413501754504087888461824000000⟩, + ⟨4, 5, 8, 7, 7, 3, -683440285467661436351070859356160300300288131072000000⟩, + ⟨4, 6, 6, 4, 8, 4, -54105600046191521352312483037176189352327249920000000⟩, + ⟨4, 6, 6, 5, 7, 4, 65582439333569165922868366848616646160823615488000000⟩, + ⟨4, 6, 7, 5, 8, 4, 26782717856486668289456714169480600122636107776000000⟩, + ⟨4, 6, 6, 6, 6, 4, -42704320395143452376884637606824270311186235392000000⟩, + ⟨4, 6, 7, 6, 7, 4, -88500310029594241677774486385386557622542401536000000⟩, + ⟨4, 6, 8, 6, 8, 4, 525280100833634129968024426787729819523247767552000000⟩, + ⟨4, 6, 6, 7, 5, 4, 44132357518227815653452424216109608416848117760000000⟩, + ⟨4, 6, 7, 7, 6, 4, 221638576494937033271131820237579508743304904704000000⟩, + ⟨4, 6, 8, 7, 7, 4, 397740811068049360578472057625855521876246265856000000⟩, + ⟨4, 7, 5, 3, 8, 5, 9942481982789190395395681601840713734448742400000000⟩, + ⟨4, 7, 5, 4, 7, 5, 5940954860923334296103171840084457755246592000000000⟩, + ⟨4, 7, 6, 4, 8, 5, -22548969417653631449142911784277964872482816000000000⟩, + ⟨4, 7, 5, 5, 6, 5, -13196181806240137117423522849800576005308416000000000⟩, + ⟨4, 7, 6, 5, 7, 5, 27332039892455997612340450903489484939486822400000000⟩, + ⟨4, 7, 7, 5, 8, 5, 5580962833347910172381412822475865128855142400000000⟩, + ⟨4, 7, 5, 6, 5, 5, 26748338304046084353829628753665945619555942400000000⟩, + ⟨4, 7, 6, 6, 6, 5, -17797389064527211098466463908891264005282201600000000⟩, + ⟨4, 7, 7, 6, 7, 5, -18441628801884571331418006778099173253604966400000000⟩, + ⟨4, 7, 8, 6, 8, 5, 72971651235655317481828082707199337727996723200000000⟩, + ⟨4, 7, 5, 7, 4, 5, 80887760560415161614422494452224833243368652800000000⟩ +] + +def collectedFourData_16_74 : List CollectedFourTerm := [ + ⟨4, 7, 6, 7, 5, 5, 18392535692384820182184136733868449593294848000000000⟩, + ⟨4, 7, 7, 7, 6, 5, 46184881776469720851891145224188668558285209600000000⟩, + ⟨4, 7, 8, 7, 7, 5, 55253956320414172351411563602294348940155289600000000⟩, + ⟨4, 8, 4, 2, 8, 6, 7568950579993138362987624684833294719144427520000000⟩, + ⟨4, 8, 4, 3, 7, 6, 45630475375735382073831669187401812953823969280000000⟩, + ⟨4, 8, 5, 3, 8, 6, -37736816288592705581582671048848527196369715200000000⟩, + ⟨4, 8, 4, 4, 6, 6, -54105600046191521352312483037176189352327249920000000⟩, + ⟨4, 8, 5, 4, 7, 6, -22548969417653631449142911784277964872482816000000000⟩, + ⟨4, 8, 6, 4, 8, 6, 42792449505268188363065461664033054008541184000000000⟩, + ⟨4, 8, 4, 5, 5, 6, -28070259438967205992098475931723631810859499520000000⟩, + ⟨4, 8, 5, 5, 6, 6, 50086275177061307518635809266291457988231168000000000⟩, + ⟨4, 8, 6, 5, 7, 6, -51869551787950587781708796638020405934266777600000000⟩, + ⟨4, 8, 7, 5, 8, 6, -7060871705880680152875468978651740355585638400000000⟩, + ⟨4, 8, 4, 6, 4, 6, 54479446538016199552119609476541883432241725440000000⟩, + ⟨4, 8, 5, 6, 5, 6, -101523656804429597094701205797031323867755315200000000⟩, + ⟨4, 8, 6, 6, 6, 6, 33775107800409699212512643640006634549700198400000000⟩, + ⟨4, 8, 7, 6, 7, 6, 23331811894448361069100083417925334432376422400000000⟩, + ⟨4, 8, 8, 6, 8, 6, -69241206615258959268920524918980801733224038400000000⟩, + ⟨4, 8, 4, 7, 3, 6, -198286012621819921868522029237992463900040232960000000⟩, + ⟨4, 8, 5, 7, 4, 6, -307010519661786775830101040497322262910101094400000000⟩, + ⟨4, 8, 6, 7, 5, 6, -34904551082233860941380513378006989539377152000000000⟩, + ⟨4, 8, 7, 7, 6, 6, -58431767906846099767025982279584556173072793600000000⟩, + ⟨4, 8, 8, 7, 7, 6, -52429272753292295089685650280980953133429555200000000⟩, + ⟨5, 3, 8, 6, 8, 2, 354458713219938417064232216581863479840757252096000000⟩ +] + +def collectedFourData_16_75 : List CollectedFourTerm := [ + ⟨5, 3, 8, 7, 7, 2, 268395273040977482737730108464558785807293349888000000⟩, + ⟨5, 4, 7, 5, 8, 3, 23555776227887914834458387495045836180620836864000000⟩, + ⟨5, 4, 7, 6, 7, 3, -77837264699068691642784811350364806324110229504000000⟩, + ⟨5, 4, 8, 6, 8, 3, 923982441102608405676427748775546413927110803456000000⟩, + ⟨5, 4, 7, 7, 6, 3, 194934238539868021291281193157349486113750777856000000⟩, + ⟨5, 4, 8, 7, 7, 3, 699637250589820792950773606640373494609994579968000000⟩, + ⟨5, 5, 6, 4, 8, 4, -28070259438967205992098475931723631810859499520000000⟩, + ⟨5, 5, 6, 5, 7, 4, 34024501810569895470844285338579823005876092928000000⟩, + ⟨5, 5, 7, 5, 8, 4, 13895009723030680686598303199947397237525446656000000⟩, + ⟨5, 5, 6, 6, 6, 4, -22155217789527739132931184581613475640327012352000000⟩, + ⟨5, 5, 7, 6, 7, 4, -45914409244863478769596374122098981634851209216000000⟩, + ⟨5, 5, 8, 6, 8, 4, 272517977731305893999246009846723001560504205312000000⟩, + ⟨5, 5, 6, 7, 5, 4, 22896090684371015537872281590427312670176706560000000⟩, + ⟨5, 5, 7, 7, 6, 4, 114987216454208564595406673526044816842344628224000000⟩, + ⟨5, 5, 8, 7, 7, 4, 206349948001940033760177539998068963492690395136000000⟩, + ⟨5, 6, 5, 3, 8, 5, -22084463343281779450633187431734455771018035200000000⟩, + ⟨5, 6, 5, 4, 7, 5, -13196181806240137117423522849800576005308416000000000⟩, + ⟨5, 6, 6, 4, 8, 5, 50086275177061307518635809266291457988231168000000000⟩, + ⟨5, 6, 5, 5, 6, 5, 29311654159964237162109431326033611973459968000000000⟩, + ⟨5, 6, 6, 5, 7, 5, -60710538288823380739114085300708852142125875200000000⟩, + ⟨5, 6, 7, 5, 8, 5, -12396559463385980028456789179292506804925235200000000⟩, + ⟨5, 6, 5, 6, 5, 5, -59414007266190558602216655370348880771363635200000000⟩, + ⟨5, 6, 6, 6, 6, 5, 39531958627840835606670101690321105287171276800000000⟩, + ⟨5, 6, 7, 6, 7, 5, 40962958340848389141084279223043563766100787200000000⟩ +] + +def collectedFourData_16_76 : List CollectedFourTerm := [ + ⟨5, 6, 8, 6, 8, 5, -162086263731954279617482453370459667608213913600000000⟩, + ⟨5, 6, 5, 7, 4, 5, -179669702807498502788790120035969534687340134400000000⟩, + ⟨5, 6, 6, 7, 5, 5, -40853911628062612414099386020127659947720704000000000⟩, + ⟨5, 6, 7, 7, 6, 5, -102586892324456980906964509868890922471443660800000000⟩, + ⟨5, 6, 8, 7, 7, 5, -122731323530863301853650962951541356642487500800000000⟩, + ⟨5, 7, 4, 2, 8, 6, -9174470698179123599734805304614155803194032128000000⟩, + ⟨5, 7, 4, 3, 7, 6, -55309577576743513668146405429199285949292347392000000⟩, + ⟨5, 7, 5, 3, 8, 6, 45741521446501016143175121047794274492775137280000000⟩, + ⟨5, 7, 4, 4, 6, 6, 65582439333569165922868366848616646160823615488000000⟩, + ⟨5, 7, 5, 4, 7, 6, 27332039892455997612340450903489484939486822400000000⟩, + ⟨5, 7, 6, 4, 8, 6, -51869551787950587781708796638020405934266777600000000⟩, + ⟨5, 7, 4, 5, 5, 6, 34024501810569895470844285338579823005876092928000000⟩, + ⟨5, 7, 5, 5, 6, 6, -60710538288823380739114085300708852142125875200000000⟩, + ⟨5, 7, 6, 5, 7, 6, 62872082196455382763814675666612488680127856640000000⟩, + ⟨5, 7, 7, 5, 8, 6, 8558618514492014193817470071020821952604405760000000⟩, + ⟨5, 7, 4, 6, 4, 6, -66035585862749659099476000330322674091416354816000000⟩, + ⟨5, 7, 5, 6, 5, 6, 123058778714482942585821128924970951168522977280000000⟩, + ⟨5, 7, 6, 6, 6, 6, -40939458326200466275649677354772850957625589760000000⟩, + ⟨5, 7, 7, 6, 7, 6, -28280938328076345977493254892828847569748623360000000⟩, + ⟨5, 7, 8, 6, 8, 6, 83928599412104458906074185789215253225810165760000000⟩, + ⟨5, 7, 4, 7, 3, 6, 240346292848870986021431414834368952615980498944000000⟩, + ⟨5, 7, 5, 7, 4, 6, 372133360748189997913433131002836416936972124160000000⟩, + ⟨5, 7, 6, 7, 5, 6, 42308478269564983716343813529773499076103372800000000⟩, + ⟨5, 7, 7, 7, 6, 6, 70826270674982902144252000024478674731443159040000000⟩ +] + +def collectedFourData_16_77 : List CollectedFourTerm := [ + ⟨5, 7, 8, 7, 7, 6, 63550530753017193708577357595934821436390113280000000⟩, + ⟨5, 8, 3, 1, 8, 7, -311771051863419284703480903456544027966439424000000⟩, + ⟨5, 8, 3, 2, 7, 7, 11201932244686514354860449100896789055345262592000000⟩, + ⟨5, 8, 4, 2, 8, 7, -3746692905735855550400687867863508912550445056000000⟩, + ⟨5, 8, 3, 3, 6, 7, -12300327779663809202076447759472326993361502208000000⟩, + ⟨5, 8, 4, 3, 7, 7, -22587461309038880090914768767539276124713385984000000⟩, + ⟨5, 8, 5, 3, 8, 7, 9340017508322517266148169205346798000175841280000000⟩, + ⟨5, 8, 3, 4, 5, 7, -23010447794236268928602107245690485829644845056000000⟩, + ⟨5, 8, 4, 4, 6, 7, 26782717856486668289456714169480600122636107776000000⟩, + ⟨5, 8, 5, 4, 7, 7, 5580962833347910172381412822475865128855142400000000⟩, + ⟨5, 8, 6, 4, 8, 7, -7060871705880680152875468978651740355585638400000000⟩, + ⟨5, 8, 3, 5, 4, 7, 23555776227887914834458387495045836180620836864000000⟩, + ⟨5, 8, 4, 5, 5, 7, 13895009723030680686598303199947397237525446656000000⟩, + ⟨5, 8, 5, 5, 6, 7, -12396559463385980028456789179292506804925235200000000⟩, + ⟨5, 8, 6, 5, 7, 7, 8558618514492014193817470071020821952604405760000000⟩, + ⟨5, 8, 7, 5, 8, 7, 873797419111902678840105855080011913892986880000000⟩, + ⟨5, 8, 3, 6, 3, 7, 31334775381087957650040307227460551589962448896000000⟩, + ⟨5, 8, 4, 6, 4, 7, -26967774950459004560905582716884602661457887232000000⟩, + ⟨5, 8, 5, 6, 5, 7, 25127523339824932656093220042401483802835681280000000⟩, + ⟨5, 8, 6, 6, 6, 7, -5572985556753958709949951986015195411345571840000000⟩, + ⟨5, 8, 7, 6, 7, 7, -2887359785845383820996242880619674578116935680000000⟩, + ⟨5, 8, 8, 6, 8, 7, 6854993565309195506008027073836396049023893504000000⟩, + ⟨5, 8, 3, 7, 2, 7, 115342519589369063966314709373111941901060145152000000⟩, + ⟨5, 8, 4, 7, 3, 7, 98153210137289138451026105808774821720031756288000000⟩ +] + +def collectedFourData_16_78 : List CollectedFourTerm := [ + ⟨5, 8, 5, 7, 4, 7, 75986368509499350523384703353287141270654812160000000⟩, + ⟨5, 8, 6, 7, 5, 7, 5759346800483356731048661849979276949140275200000000⟩, + ⟨5, 8, 7, 7, 6, 7, 7231051648852977154216818631944871379227115520000000⟩, + ⟨5, 8, 8, 7, 7, 7, 5190584406691383319696012945078459801547046912000000⟩, + ⟨6, 2, 8, 6, 8, 2, -237209709391259993248581586079947104611689562112000000⟩, + ⟨6, 2, 8, 7, 7, 2, -179614613340126844996195418715597197776609345536000000⟩, + ⟨6, 3, 7, 5, 8, 3, 31334775381087957650040307227460551589962448896000000⟩, + ⟨6, 3, 7, 6, 7, 3, -103542043447332153969085516455762784009486073856000000⟩, + ⟨6, 3, 8, 6, 8, 3, 1229116033703108642189073863538648991763565379584000000⟩, + ⟨6, 3, 7, 7, 6, 3, 259308821735986839681582316240005781675975901184000000⟩, + ⟨6, 3, 8, 7, 7, 3, 930683662613467861008636430368928584543504433152000000⟩, + ⟨6, 4, 6, 4, 8, 4, 54479446538016199552119609476541883432241725440000000⟩, + ⟨6, 4, 6, 5, 7, 4, -66035585862749659099476000330322674091416354816000000⟩, + ⟨6, 4, 7, 5, 8, 4, -26967774950459004560905582716884602661457887232000000⟩, + ⟨6, 4, 6, 6, 6, 4, 42999388934293776381305986688966554750071865344000000⟩, + ⟨6, 4, 7, 6, 7, 4, 89111809216401413431128947043694018259218071552000000⟩, + ⟨6, 4, 8, 6, 8, 4, -528909561051325405049966330743985476007010238464000000⟩, + ⟨6, 4, 6, 7, 5, 4, -44437293181450411620841873147813613806100152320000000⟩, + ⟨6, 4, 7, 7, 6, 4, -223170004003455723110386201931213443009376944128000000⟩, + ⟨6, 4, 8, 7, 7, 4, -400489029491767940572566301178491816694400417792000000⟩, + ⟨6, 5, 5, 3, 8, 5, 44764667950396682511686184467377307648293601280000000⟩, + ⟨6, 5, 5, 4, 7, 5, 26748338304046084353829628753665945619555942400000000⟩, + ⟨6, 5, 6, 4, 8, 5, -101523656804429597094701205797031323867755315200000000⟩, + ⟨6, 5, 5, 5, 6, 5, -59414007266190558602216655370348880771363635200000000⟩ +] + +def collectedFourData_16_79 : List CollectedFourTerm := [ + ⟨6, 5, 6, 5, 7, 5, 123058778714482942585821128924970951168522977280000000⟩, + ⟨6, 5, 7, 5, 8, 5, 25127523339824932656093220042401483802835681280000000⟩, + ⟨6, 5, 5, 6, 5, 5, 120430741989596790473740001859145514316233441280000000⟩, + ⟨6, 5, 6, 6, 6, 5, -80130314868730889763813574771216202304344555520000000⟩, + ⟨6, 5, 7, 6, 7, 5, -83030916345623148629495221490798372835116974080000000⟩, + ⟨6, 5, 8, 6, 8, 5, 328544898850285850786168514555158307953222615040000000⟩, + ⟨6, 5, 5, 7, 4, 5, 364186100513545311967464906827769673165213532160000000⟩, + ⟨6, 5, 6, 7, 5, 5, 82809881321449806711645690924423358977776025600000000⟩, + ⟨6, 5, 7, 7, 6, 5, 207941125830635553346463715058702887398009733120000000⟩, + ⟨6, 5, 8, 7, 7, 5, 248773396010237088021060744841679109677509509120000000⟩, + ⟨6, 6, 4, 2, 8, 6, 5974000664387524808116468424747412500514865152000000⟩, + ⟨6, 6, 4, 3, 7, 6, 36015097116832923717542667906282101840730390528000000⟩, + ⟨6, 6, 5, 3, 8, 6, -29784811407782657741366432780461040637333995520000000⟩, + ⟨6, 6, 4, 4, 6, 6, -42704320395143452376884637606824270311186235392000000⟩, + ⟨6, 6, 5, 4, 7, 6, -17797389064527211098466463908891264005282201600000000⟩, + ⟨6, 6, 6, 4, 8, 6, 33775107800409699212512643640006634549700198400000000⟩, + ⟨6, 6, 4, 5, 5, 6, -22155217789527739132931184581613475640327012352000000⟩, + ⟨6, 6, 5, 5, 6, 6, 39531958627840835606670101690321105287171276800000000⟩, + ⟨6, 6, 6, 5, 7, 6, -40939458326200466275649677354772850957625589760000000⟩, + ⟨6, 6, 7, 5, 8, 6, -5572985556753958709949951986015195411345571840000000⟩, + ⟨6, 6, 4, 6, 4, 6, 42999388934293776381305986688966554750071865344000000⟩, + ⟨6, 6, 5, 6, 5, 6, -80130314868730889763813574771216202304344555520000000⟩, + ⟨6, 6, 6, 6, 6, 6, 26657924940446728579578347189555633323864227840000000⟩, + ⟨6, 6, 7, 6, 7, 6, 18415268838883820768476864861133167575422730240000000⟩ +] + +def collectedFourData_16_80 : List CollectedFourTerm := [ + ⟨6, 6, 8, 6, 8, 6, -54650510655458116688941288570427324376117411840000000⟩, + ⟨6, 6, 4, 7, 3, 6, -156502643084053431281982188527544365204421738496000000⟩, + ⟨6, 6, 5, 7, 4, 6, -242316425381540294626975672775664390152587837440000000⟩, + ⟨6, 6, 6, 7, 5, 6, -27549368852610795761941895669682077292507955200000000⟩, + ⟨6, 6, 7, 7, 6, 6, -46118866361676350213456683110960312037524111360000000⟩, + ⟨6, 6, 8, 7, 7, 6, -41381233362711012167519121952945396405260779520000000⟩, + ⟨6, 7, 3, 1, 8, 7, 1030210410161292835863364728371004832600817664000000⟩, + ⟨6, 7, 3, 2, 7, 7, -37015454588943372968026966354113045746272960512000000⟩, + ⟨6, 7, 4, 2, 8, 7, 12380501692175961221061385084148519098820591616000000⟩, + ⟨6, 7, 3, 3, 6, 7, 40644972171942110463529555644157005589578252288000000⟩, + ⟨6, 7, 4, 3, 7, 7, 74637583061692756312925438520186523981210189824000000⟩, + ⟨6, 7, 5, 3, 8, 7, -30862978492236298174893155743896994576418734080000000⟩, + ⟨6, 7, 3, 4, 5, 7, 76035291661652144510041346252779854217258991616000000⟩, + ⟨6, 7, 4, 4, 6, 7, -88500310029594241677774486385386557622542401536000000⟩, + ⟨6, 7, 5, 4, 7, 7, -18441628801884571331418006778099173253604966400000000⟩, + ⟨6, 7, 6, 4, 8, 7, 23331811894448361069100083417925334432376422400000000⟩, + ⟨6, 7, 3, 5, 4, 7, -77837264699068691642784811350364806324110229504000000⟩, + ⟨6, 7, 4, 5, 5, 7, -45914409244863478769596374122098981634851209216000000⟩, + ⟨6, 7, 5, 5, 6, 7, 40962958340848389141084279223043563766100787200000000⟩, + ⟨6, 7, 6, 5, 7, 7, -28280938328076345977493254892828847569748623360000000⟩, + ⟨6, 7, 7, 5, 8, 7, -2887359785845383820996242880619674578116935680000000⟩, + ⟨6, 7, 3, 6, 3, 7, -103542043447332153969085516455762784009486073856000000⟩, + ⟨6, 7, 4, 6, 4, 7, 89111809216401413431128947043694018259218071552000000⟩, + ⟨6, 7, 5, 6, 5, 7, -83030916345623148629495221490798372835116974080000000⟩ +] + +def collectedFourData_16_81 : List CollectedFourTerm := [ + ⟨6, 7, 6, 6, 6, 7, 18415268838883820768476864861133167575422730240000000⟩, + ⟨6, 7, 7, 6, 7, 7, 9540937465105334970086285527656007106801172480000000⟩, + ⟨6, 7, 8, 6, 8, 7, -22651512032181772754487866638628083914762092544000000⟩, + ⟨6, 7, 3, 7, 2, 7, -381135656132874830373554110375108696569305628672000000⟩, + ⟨6, 7, 4, 7, 3, 7, -324335624715030312833651762964861814478280327168000000⟩, + ⟨6, 7, 5, 7, 4, 7, -251087929430767807991557442979807774639925493760000000⟩, + ⟨6, 7, 6, 7, 5, 7, -19031077433662335921403964449762498825106227200000000⟩, + ⟨6, 7, 7, 7, 6, 7, -23894151302814985936622565351821954689762590720000000⟩, + ⟨6, 7, 8, 7, 7, 7, -17151669658339312857244331034119393282497708032000000⟩, + ⟨6, 8, 2, 0, 8, 8, -703091459775340125707347128672488066142431084544000000⟩, + ⟨6, 8, 2, 1, 7, 8, -322305805715318026173573369135824279249407180800000000⟩, + ⟨6, 8, 3, 1, 8, 8, -12229313726662083848527116411375114110103453696000000⟩, + ⟨6, 8, 2, 2, 6, 8, -678963705148282447702070084599012525560538595328000000⟩, + ⟨6, 8, 3, 2, 7, 8, 439399177525618552121523239158962984806271418368000000⟩, + ⟨6, 8, 4, 2, 8, 8, -73482580739688998049872087135724460144551002112000000⟩, + ⟨6, 8, 2, 3, 5, 8, 168262764210290867857903585751962060493357580288000000⟩, + ⟨6, 8, 3, 3, 6, 8, -482484074320612658691582385408060558311614840832000000⟩, + ⟨6, 8, 4, 3, 7, 8, -442999997892826192619953724648354899888038739968000000⟩, + ⟨6, 8, 5, 3, 8, 8, 122121669773488302571896683956790911069889495040000000⟩, + ⟨6, 8, 2, 4, 4, 8, 21256383960005962945281605091235938581285437440000000⟩, + ⟨6, 8, 3, 4, 5, 8, -902591768494181757738068714296052784335079604224000000⟩, + ⟨6, 8, 4, 4, 6, 8, 525280100833634129968024426787729819523247767552000000⟩, + ⟨6, 8, 5, 4, 7, 8, 72971651235655317481828082707199337727996723200000000⟩, + ⟨6, 8, 6, 4, 8, 8, -69241206615258959268920524918980801733224038400000000⟩ +] + +def collectedFourData_16_82 : List CollectedFourTerm := [ + ⟨6, 8, 2, 5, 3, 8, 354458713219938417064232216581863479840757252096000000⟩, + ⟨6, 8, 3, 5, 4, 8, 923982441102608405676427748775546413927110803456000000⟩, + ⟨6, 8, 4, 5, 5, 8, 272517977731305893999246009846723001560504205312000000⟩, + ⟨6, 8, 5, 5, 6, 8, -162086263731954279617482453370459667608213913600000000⟩, + ⟨6, 8, 6, 5, 7, 8, 83928599412104458906074185789215253225810165760000000⟩, + ⟨6, 8, 7, 5, 8, 8, 6854993565309195506008027073836396049023893504000000⟩, + ⟨6, 8, 2, 6, 2, 8, -237209709391259993248581586079947104611689562112000000⟩, + ⟨6, 8, 3, 6, 3, 8, 1229116033703108642189073863538648991763565379584000000⟩, + ⟨6, 8, 4, 6, 4, 8, -528909561051325405049966330743985476007010238464000000⟩, + ⟨6, 8, 5, 6, 5, 8, 328544898850285850786168514555158307953222615040000000⟩, + ⟨6, 8, 6, 6, 6, 8, -54650510655458116688941288570427324376117411840000000⟩, + ⟨6, 8, 7, 6, 7, 8, -22651512032181772754487866638628083914762092544000000⟩, + ⟨6, 8, 8, 6, 8, 8, 44814865696779037412412446451432202664291598336000000⟩, + ⟨6, 8, 2, 7, 1, 8, 3498692240778517513087615107561387149920831537152000000⟩, + ⟨6, 8, 3, 7, 2, 8, 4524345187442225068608329711870548524059861188608000000⟩, + ⟨6, 8, 4, 7, 3, 8, 1925044664784570850713369194794544554730456088576000000⟩, + ⟨6, 8, 5, 7, 4, 8, 993529422630632593897964090244193962968355962880000000⟩, + ⟨6, 8, 6, 7, 5, 8, 56478029681387567670909074745337300265415475200000000⟩, + ⟨6, 8, 7, 7, 6, 8, 56728037230512336138349235799918364371154108416000000⟩, + ⟨6, 8, 8, 7, 7, 8, 33933706991478072515706367676638656367435972608000000⟩, + ⟨7, 1, 8, 6, 8, 2, 3498692240778517513087615107561387149920831537152000000⟩, + ⟨7, 1, 8, 7, 7, 2, 2649201230574457387437394655686196276871252934656000000⟩, + ⟨7, 2, 7, 5, 8, 3, 115342519589369063966314709373111941901060145152000000⟩, + ⟨7, 2, 7, 6, 7, 3, -381135656132874830373554110375108696569305628672000000⟩ +] + +def collectedFourData_16_83 : List CollectedFourTerm := [ + ⟨7, 2, 8, 6, 8, 3, 4524345187442225068608329711870548524059861188608000000⟩, + ⟨7, 2, 7, 7, 6, 3, 954509246899883376386610866248400192336516087808000000⟩, + ⟨7, 2, 8, 7, 7, 3, 3425823139976582624690778131050994189528280858624000000⟩, + ⟨7, 3, 6, 4, 8, 4, -198286012621819921868522029237992463900040232960000000⟩, + ⟨7, 3, 6, 5, 7, 4, 240346292848870986021431414834368952615980498944000000⟩, + ⟨7, 3, 7, 5, 8, 4, 98153210137289138451026105808774821720031756288000000⟩, + ⟨7, 3, 6, 6, 6, 4, -156502643084053431281982188527544365204421738496000000⟩, + ⟨7, 3, 7, 6, 7, 4, -324335624715030312833651762964861814478280327168000000⟩, + ⟨7, 3, 8, 6, 8, 4, 1925044664784570850713369194794544554730456088576000000⟩, + ⟨7, 3, 6, 7, 5, 4, 161736108506682359454954930619237751206057082880000000⟩, + ⟨7, 3, 7, 7, 6, 4, 812260275070191384958974233533172431048987901952000000⟩, + ⟨7, 3, 8, 7, 7, 4, 1457639124532794380723799875733536335871059427328000000⟩, + ⟨7, 4, 5, 3, 8, 5, 135369670503623781296021693102674525584265052160000000⟩, + ⟨7, 4, 5, 4, 7, 5, 80887760560415161614422494452224833243368652800000000⟩, + ⟨7, 4, 6, 4, 8, 5, -307010519661786775830101040497322262910101094400000000⟩, + ⟨7, 4, 5, 5, 6, 5, -179669702807498502788790120035969534687340134400000000⟩, + ⟨7, 4, 6, 5, 7, 5, 372133360748189997913433131002836416936972124160000000⟩, + ⟨7, 4, 7, 5, 8, 5, 75986368509499350523384703353287141270654812160000000⟩, + ⟨7, 4, 5, 6, 5, 5, 364186100513545311967464906827769673165213532160000000⟩, + ⟨7, 4, 6, 6, 6, 5, -242316425381540294626975672775664390152587837440000000⟩, + ⟨7, 4, 7, 6, 7, 5, -251087929430767807991557442979807774639925493760000000⟩, + ⟨7, 4, 8, 6, 8, 5, 993529422630632593897964090244193962968355962880000000⟩, + ⟨7, 4, 5, 7, 4, 5, 1101309463149527734700455315285359440902509035520000000⟩, + ⟨7, 4, 6, 7, 5, 5, 250419513026445062115110590310905454110389043200000000⟩ +] + +def collectedFourData_16_84 : List CollectedFourTerm := [ + ⟨7, 4, 7, 7, 6, 5, 628820071200735107861156891808010545436179824640000000⟩, + ⟨7, 4, 8, 7, 7, 5, 752298055361201135181499127414266549773155696640000000⟩, + ⟨7, 5, 4, 2, 8, 6, -6173771896973308663820233450384729978762690560000000⟩, + ⟨7, 5, 4, 3, 7, 6, -37219445885258120621148197950094868314157219840000000⟩, + ⟨7, 5, 5, 3, 8, 6, 30780818743827687689040384920917198457379225600000000⟩, + ⟨7, 5, 4, 4, 6, 6, 44132357518227815653452424216109608416848117760000000⟩, + ⟨7, 5, 5, 4, 7, 6, 18392535692384820182184136733868449593294848000000000⟩, + ⟨7, 5, 6, 4, 8, 6, -34904551082233860941380513378006989539377152000000000⟩, + ⟨7, 5, 4, 5, 5, 6, 22896090684371015537872281590427312670176706560000000⟩, + ⟨7, 5, 5, 5, 6, 6, -40853911628062612414099386020127659947720704000000000⟩, + ⟨7, 5, 6, 5, 7, 6, 42308478269564983716343813529773499076103372800000000⟩, + ⟨7, 5, 7, 5, 8, 6, 5759346800483356731048661849979276949140275200000000⟩, + ⟨7, 5, 4, 6, 4, 6, -44437293181450411620841873147813613806100152320000000⟩, + ⟨7, 5, 5, 6, 5, 6, 82809881321449806711645690924423358977776025600000000⟩, + ⟨7, 5, 6, 6, 6, 6, -27549368852610795761941895669682077292507955200000000⟩, + ⟨7, 5, 7, 6, 7, 6, -19031077433662335921403964449762498825106227200000000⟩, + ⟨7, 5, 8, 6, 8, 6, 56478029681387567670909074745337300265415475200000000⟩, + ⟨7, 5, 4, 7, 3, 6, 161736108506682359454954930619237751206057082880000000⟩, + ⟨7, 5, 5, 7, 4, 6, 250419513026445062115110590310905454110389043200000000⟩, + ⟨7, 5, 6, 7, 5, 6, 28470622746246026174128125410941953172832256000000000⟩, + ⟨7, 5, 7, 7, 6, 6, 47661086273611311617068129658213147041647820800000000⟩, + ⟨7, 5, 8, 7, 7, 6, 42765026311390953274527392596334384225294745600000000⟩, + ⟨7, 6, 3, 1, 8, 7, -2580040326661678603661321536702865138931204096000000⟩, + ⟨7, 6, 3, 2, 7, 7, 92700835292701041220313966933259450734050541568000000⟩ +] + +def collectedFourData_16_85 : List CollectedFourTerm := [ + ⟨7, 6, 4, 2, 8, 7, -31005504618339243866881139150797713567670861824000000⟩, + ⟨7, 6, 3, 3, 6, 7, -101790533511726284489675791835293414644233797632000000⟩, + ⟨7, 6, 4, 3, 7, 7, -186921013692318376465897499983264685411675406336000000⟩, + ⟨7, 6, 5, 3, 8, 7, 77292685382974283194092451324982784288746373120000000⟩, + ⟨7, 6, 3, 4, 5, 7, -190421409841734560839349413501754504087888461824000000⟩, + ⟨7, 6, 4, 4, 6, 7, 221638576494937033271131820237579508743304904704000000⟩, + ⟨7, 6, 5, 4, 7, 7, 46184881776469720851891145224188668558285209600000000⟩, + ⟨7, 6, 6, 4, 8, 7, -58431767906846099767025982279584556173072793600000000⟩, + ⟨7, 6, 3, 5, 4, 7, 194934238539868021291281193157349486113750777856000000⟩, + ⟨7, 6, 4, 5, 5, 7, 114987216454208564595406673526044816842344628224000000⟩, + ⟨7, 6, 5, 5, 6, 7, -102586892324456980906964509868890922471443660800000000⟩, + ⟨7, 6, 6, 5, 7, 7, 70826270674982902144252000024478674731443159040000000⟩, + ⟨7, 6, 7, 5, 8, 7, 7231051648852977154216818631944871379227115520000000⟩, + ⟨7, 6, 3, 6, 3, 7, 259308821735986839681582316240005781675975901184000000⟩, + ⟨7, 6, 4, 6, 4, 7, -223170004003455723110386201931213443009376944128000000⟩, + ⟨7, 6, 5, 6, 5, 7, 207941125830635553346463715058702887398009733120000000⟩, + ⟨7, 6, 6, 6, 6, 7, -46118866361676350213456683110960312037524111360000000⟩, + ⟨7, 6, 7, 6, 7, 7, -23894151302814985936622565351821954689762590720000000⟩, + ⟨7, 6, 8, 6, 8, 7, 56728037230512336138349235799918364371154108416000000⟩, + ⟨7, 6, 3, 7, 2, 7, 954509246899883376386610866248400192336516087808000000⟩, + ⟨7, 6, 4, 7, 3, 7, 812260275070191384958974233533172431048987901952000000⟩, + ⟨7, 6, 5, 7, 4, 7, 628820071200735107861156891808010545436179824640000000⟩, + ⟨7, 6, 6, 7, 5, 7, 47661086273611311617068129658213147041647820800000000⟩, + ⟨7, 6, 7, 7, 6, 7, 59840080554967963692315140241029906770773934080000000⟩ +] + +def collectedFourData_16_86 : List CollectedFourTerm := [ + ⟨7, 6, 8, 7, 7, 7, 42954331417760315842494236007740866674554830848000000⟩, + ⟨7, 7, 2, 0, 8, 8, -532379138334486998207207942498775528384371884032000000⟩, + ⟨7, 7, 2, 1, 7, 8, -244049169907072461755075082227874897060062822400000000⟩, + ⟨7, 7, 3, 1, 8, 8, -9260006523621871550927425446229021939558514688000000⟩, + ⟨7, 7, 2, 2, 6, 8, -514109661384214672745515879494186738707840630784000000⟩, + ⟨7, 7, 3, 2, 7, 8, 332711985423230887232461671588398884178733563904000000⟩, + ⟨7, 7, 4, 2, 8, 8, -55640830894589817797430300473116893427097665536000000⟩, + ⟨7, 7, 2, 3, 5, 8, 127408154627105142014659589535395515259015921664000000⟩, + ⟨7, 7, 3, 3, 6, 8, -365335764182083280351826619345282632086187933696000000⟩, + ⟨7, 7, 4, 3, 7, 8, -335438517822022670505218788319571837034854088704000000⟩, + ⟨7, 7, 5, 3, 8, 8, 92470230468668782960042396276798418001718149120000000⟩, + ⟨7, 7, 2, 4, 4, 8, 16095282085137187046963859453560830686469816320000000⟩, + ⟨7, 7, 3, 4, 5, 8, -683440285467661436351070859356160300300288131072000000⟩, + ⟨7, 7, 4, 4, 6, 8, 397740811068049360578472057625855521876246265856000000⟩, + ⟨7, 7, 5, 4, 7, 8, 55253956320414172351411563602294348940155289600000000⟩, + ⟨7, 7, 6, 4, 8, 8, -52429272753292295089685650280980953133429555200000000⟩, + ⟨7, 7, 2, 5, 3, 8, 268395273040977482737730108464558785807293349888000000⟩, + ⟨7, 7, 3, 5, 4, 8, 699637250589820792950773606640373494609994579968000000⟩, + ⟨7, 7, 4, 5, 5, 8, 206349948001940033760177539998068963492690395136000000⟩, + ⟨7, 7, 5, 5, 6, 8, -122731323530863301853650962951541356642487500800000000⟩, + ⟨7, 7, 6, 5, 7, 8, 63550530753017193708577357595934821436390113280000000⟩, + ⟨7, 7, 7, 5, 8, 8, 5190584406691383319696012945078459801547046912000000⟩, + ⟨7, 7, 2, 6, 2, 8, -179614613340126844996195418715597197776609345536000000⟩, + ⟨7, 7, 3, 6, 3, 8, 930683662613467861008636430368928584543504433152000000⟩ +] + +def collectedFourData_16_87 : List CollectedFourTerm := [ + ⟨7, 7, 4, 6, 4, 8, -400489029491767940572566301178491816694400417792000000⟩, + ⟨7, 7, 5, 6, 5, 8, 248773396010237088021060744841679109677509509120000000⟩, + ⟨7, 7, 6, 6, 6, 8, -41381233362711012167519121952945396405260779520000000⟩, + ⟨7, 7, 7, 6, 7, 8, -17151669658339312857244331034119393282497708032000000⟩, + ⟨7, 7, 8, 6, 8, 8, 33933706991478072515706367676638656367435972608000000⟩, + ⟨7, 7, 2, 7, 1, 8, 2649201230574457387437394655686196276871252934656000000⟩, + ⟨7, 7, 3, 7, 2, 8, 3425823139976582624690778131050994189528280858624000000⟩, + ⟨7, 7, 4, 7, 3, 8, 1457639124532794380723799875733536335871059427328000000⟩, + ⟨7, 7, 5, 7, 4, 8, 752298055361201135181499127414266549773155696640000000⟩, + ⟨7, 7, 6, 7, 5, 8, 42765026311390953274527392596334384225294745600000000⟩, + ⟨7, 7, 7, 7, 6, 8, 42954331417760315842494236007740866674554830848000000⟩, + ⟨7, 7, 8, 7, 7, 8, 25694520161559893005871204095241067859619610624000000⟩, + ⟨0, 8, 8, 7, 8, 1, -70583168097992862347664064273381881791329075200000000⟩, + ⟨1, 7, 8, 7, 8, 1, -740184135328714259727834388039430964285485875200000000⟩, + ⟨1, 8, 7, 6, 8, 2, -42918976634443667026919737792300128247058792448000000⟩, + ⟨1, 8, 7, 7, 7, 2, 15168967243395726505622802466629023058219761664000000⟩, + ⟨1, 8, 8, 7, 8, 2, 407020221741042353532618694112118854244315955200000000⟩, + ⟨2, 6, 8, 7, 8, 1, -877720773664617712899135281212684632052255948800000000⟩, + ⟨2, 7, 7, 6, 8, 2, -52169868990326163997449733096467558889250881536000000⟩, + ⟨2, 7, 7, 7, 7, 2, 18438534556562872955057771239932403027015630848000000⟩, + ⟨2, 7, 8, 7, 8, 2, 494750651337820062008943138982906576624838246400000000⟩, + ⟨2, 8, 6, 5, 8, 3, -21181973819185239201139122875154479401339453440000000⟩, + ⟨2, 8, 6, 6, 7, 3, -20004187131229416267884672959003650617518325760000000⟩, + ⟨2, 8, 7, 6, 8, 3, -21945613190552536971805145320465218446882242560000000⟩ +] + +def collectedFourData_16_88 : List CollectedFourTerm := [ + ⟨2, 8, 6, 7, 6, 3, 21650928752033609630683387946077696526018150400000000⟩, + ⟨2, 8, 7, 7, 7, 3, 7756296019336335567825770152870974431774638080000000⟩, + ⟨2, 8, 8, 7, 8, 3, 104060127331803769123741134045628027342159872000000000⟩, + ⟨3, 5, 8, 7, 8, 1, -725132765340499484141893490258273055602953420800000000⟩, + ⟨3, 6, 7, 6, 8, 2, -20724631074728884774639098304183757163661885440000000⟩, + ⟨3, 6, 7, 7, 7, 2, 7324761086025802213306605111383288711133265920000000⟩, + ⟨3, 6, 8, 7, 8, 2, 196541124626160133791486627831711669688467456000000000⟩, + ⟨3, 7, 6, 5, 8, 3, -52889046455419148109403403825045848869801295872000000⟩, + ⟨3, 7, 6, 6, 7, 3, -49948243327929217793096724178398896130084569088000000⟩, + ⟨3, 7, 7, 6, 8, 3, -54795769527225192380708190200999208981708668928000000⟩, + ⟨3, 7, 6, 7, 6, 3, 54059975068618116619176247319740599747760619520000000⟩, + ⟨3, 7, 7, 7, 7, 3, 19366613517249698141172953178423988225314914304000000⟩, + ⟨3, 7, 8, 7, 8, 3, 259826631625036061144238904656979383323040153600000000⟩, + ⟨3, 8, 5, 4, 8, 4, -21812629262319291934748544302943866350215364608000000⟩, + ⟨3, 8, 5, 5, 7, 4, 742031595394957044082944638831809430953132032000000⟩, + ⟨3, 8, 6, 5, 8, 4, -30724333518995516018561662380189753410517467136000000⟩, + ⟨3, 8, 5, 6, 6, 4, -7058044632570742254560763570672131762540249088000000⟩, + ⟨3, 8, 6, 6, 7, 4, -29015960573023301693920215359401718549361721344000000⟩, + ⟨3, 8, 7, 6, 8, 4, -15915994059408645283656047271717245973411397632000000⟩, + ⟨3, 8, 5, 7, 5, 4, 7981945172608667298685339604868308558841643008000000⟩, + ⟨3, 8, 6, 7, 6, 4, 31404550003313958664711746890237746127579381760000000⟩, + ⟨3, 8, 7, 7, 7, 4, 5625231808055206647810350388931651097409355776000000⟩, + ⟨3, 8, 8, 7, 8, 4, 50312875867367410609324782600278558717352345600000000⟩, + ⟨4, 4, 8, 7, 8, 1, 816727484490888933846585943515736875514567065600000000⟩ +] + +def collectedFourData_16_89 : List CollectedFourTerm := [ + ⟨4, 5, 7, 6, 8, 2, -9624917228793757410139654583741524264662073344000000⟩, + ⟨4, 5, 7, 7, 7, 2, 3401759911647068297450053149578399377357012992000000⟩, + ⟨4, 5, 8, 7, 8, 2, 91277477980658163262322942900174544694778265600000000⟩, + ⟨4, 6, 6, 5, 8, 3, -121486803506864837380972033428038459505946656768000000⟩, + ⟨4, 6, 6, 6, 7, 3, -114731741813648470686544364375245338014983913472000000⟩, + ⟨4, 6, 7, 6, 8, 3, -125866570333664416203776136822154074574062354432000000⟩, + ⟨4, 6, 6, 7, 6, 3, 124176441227449858121033246873714828201825402880000000⟩, + ⟨4, 6, 7, 7, 7, 3, 44485354315221046440204390086883282495970738176000000⟩, + ⟨4, 6, 8, 7, 8, 3, 596825033869504107122301676484794424647640678400000000⟩, + ⟨4, 7, 5, 4, 8, 4, -49706305743051912522901800819784159517000859648000000⟩, + ⟨4, 7, 5, 5, 7, 4, 1690930923922216058040610356029913755855880192000000⟩, + ⟨4, 7, 6, 5, 8, 4, -70014169189813016480530147840697993086491426816000000⟩, + ⟨4, 7, 5, 6, 6, 4, -16083770564088561056652739655969887547742486528000000⟩, + ⟨4, 7, 6, 6, 7, 4, -66121153499020307722066173389514045731912024064000000⟩, + ⟨4, 7, 7, 6, 8, 4, -36269138277988838277469407850969628470035873792000000⟩, + ⟨4, 7, 5, 7, 5, 4, 18189141822501124682062700662355996199824130048000000⟩, + ⟨4, 7, 6, 7, 6, 4, 71564236727952677125798162614120908145096130560000000⟩, + ⟨4, 7, 7, 7, 7, 4, 12818697313567347109480529560812131077016518656000000⟩, + ⟨4, 7, 8, 7, 8, 4, 114652257671465628718245477311183599282264473600000000⟩, + ⟨4, 8, 4, 3, 8, 5, -21812629262319291934748544302943866350215364608000000⟩, + ⟨4, 8, 4, 4, 7, 5, -49706305743051912522901800819784159517000859648000000⟩, + ⟨4, 8, 5, 4, 8, 5, 215973493792167743772278739480648169621951610880000000⟩, + ⟨4, 8, 4, 5, 6, 5, 45594540084309791259435189856483298779399716864000000⟩, + ⟨4, 8, 5, 5, 7, 5, -7347081098493169740493603927917102844367339520000000⟩ +] + +def collectedFourData_16_90 : List CollectedFourTerm := [ + ⟨4, 8, 6, 5, 8, 5, 152105497570532570015894296512777691186310676480000000⟩, + ⟨4, 8, 4, 6, 5, 5, -73980955289189724648512141989731059897374605312000000⟩, + ⟨4, 8, 5, 6, 6, 5, 69883852162225720222908173563808809314083143680000000⟩, + ⟨4, 8, 6, 6, 7, 5, 143647936828898109990729455079300309708617809920000000⟩, + ⟨4, 8, 7, 6, 8, 5, 52529703516362131992140193106094484015116451840000000⟩, + ⟨4, 8, 4, 7, 4, 5, -305956627183132781277901671735540592019949748224000000⟩, + ⟨4, 8, 5, 7, 5, 5, -79031673140101028552844324964661644848141434880000000⟩, + ⟨4, 8, 6, 7, 6, 5, -155473012987554305926853645515998607837023436800000000⟩, + ⟨4, 8, 7, 7, 7, 5, -18565711823275751047840498506719119317003141120000000⟩, + ⟨4, 8, 8, 7, 8, 5, -124540781548262513556328178644064724219592704000000000⟩, + ⟨5, 3, 8, 7, 8, 1, 1559741359477420901379906098823611727996361113600000000⟩, + ⟨5, 4, 7, 6, 8, 2, 51033556760331992750285918450807519296270368768000000⟩, + ⟨5, 4, 7, 7, 7, 2, -18036924724579632719323340866766963693190119424000000⟩, + ⟨5, 4, 8, 7, 8, 2, -483974484427817012352801411814091102495126323200000000⟩, + ⟨5, 5, 6, 5, 8, 3, -39926878076169190200648713804638989304102649856000000⟩, + ⟨5, 5, 6, 6, 7, 3, -37706813700149859849079059105627023225571508224000000⟩, + ⟨5, 5, 7, 6, 8, 3, -41366297099864186250600165263655257081898860544000000⟩, + ⟨5, 5, 6, 7, 6, 3, 40810832828775678305319214756432442278501416960000000⟩, + ⟨5, 5, 7, 7, 7, 3, 14620199615496940664769071272476874685747822592000000⟩, + ⟨5, 5, 8, 7, 8, 3, 196147726932059050173709157096206020654189772800000000⟩, + ⟨5, 6, 5, 4, 8, 4, 45594540084309791259435189856483298779399716864000000⟩, + ⟨5, 6, 5, 5, 7, 4, -1551055075167144895314198588585610272892256256000000⟩, + ⟨5, 6, 6, 5, 8, 4, 64222512533850914823263379412087764269125337088000000⟩, + ⟨5, 6, 5, 6, 6, 4, 14753301633036469017521050926703559055406792704000000⟩ +] + +def collectedFourData_16_91 : List CollectedFourTerm := [ + ⟨5, 6, 6, 6, 7, 4, 60651531803956164639642745184253868425716170752000000⟩, + ⟨5, 6, 7, 6, 8, 4, 33268911344719919968370981411147823370318381056000000⟩, + ⟨5, 6, 5, 7, 5, 4, -16684514037560488845028894847802609233049944064000000⟩, + ⟨5, 6, 6, 7, 6, 4, -65644356612677377409333961888274894362331054080000000⟩, + ⟨5, 6, 7, 7, 7, 4, -11758319186168416378257608040404755690404446208000000⟩, + ⟨5, 6, 8, 7, 8, 4, -105168084411281589342653334292103588064578764800000000⟩, + ⟨5, 7, 4, 3, 8, 5, 742031595394957044082944638831809430953132032000000⟩, + ⟨5, 7, 4, 4, 7, 5, 1690930923922216058040610356029913755855880192000000⟩, + ⟨5, 7, 5, 4, 8, 5, -7347081098493169740493603927917102844367339520000000⟩, + ⟨5, 7, 4, 5, 6, 5, -1551055075167144895314198588585610272892256256000000⟩, + ⟨5, 7, 5, 5, 7, 5, 249936229303121855362178739579603707316142080000000⟩, + ⟨5, 7, 6, 5, 8, 5, -5174391572573086542069925803018183935703121920000000⟩, + ⟨5, 7, 4, 6, 5, 5, 2516716605866130075690109403664012678317211648000000⟩, + ⟨5, 7, 5, 6, 6, 5, -2377339553552194062892084777900322908243230720000000⟩, + ⟨5, 7, 6, 6, 7, 5, -4886678559401125446760282248943153863909703680000000⟩, + ⟨5, 7, 7, 6, 8, 5, -1786978508510429475146497928731209156117135360000000⟩, + ⟨5, 7, 4, 7, 4, 5, 10408166822078033270176351860993037068398493696000000⟩, + ⟨5, 7, 5, 7, 5, 5, 2688534142382725535666442630966846267347435520000000⟩, + ⟨5, 7, 6, 7, 6, 5, 5288949189967994771698020301181483553600307200000000⟩, + ⟨5, 7, 7, 7, 7, 5, 631576532943076848445800214080101655490068480000000⟩, + ⟨5, 7, 8, 7, 8, 5, 4236682965296314614458107159704167163887616000000000⟩, + ⟨5, 8, 3, 2, 8, 6, -21181973819185239201139122875154479401339453440000000⟩, + ⟨5, 8, 3, 3, 7, 6, -52889046455419148109403403825045848869801295872000000⟩, + ⟨5, 8, 4, 3, 8, 6, -30724333518995516018561662380189753410517467136000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1605.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1605.lean new file mode 100644 index 0000000000000000000000000000000000000000..95b0bf9dcc33e09510a7c7bfd27baf7c74c2daa2 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1605.lean @@ -0,0 +1,270 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1601 +import OAI.Analysis.LaughlinFock.Sparse1602 +import OAI.Analysis.LaughlinFock.Sparse1603 +import OAI.Analysis.LaughlinFock.Sparse1604 + +namespace OAI + +/-! Sparse1605. -/ +namespace LaughlinFock +def collectedFourData_16_92 : List CollectedFourTerm := [ + ⟨5, 8, 3, 4, 6, 6, -121486803506864837380972033428038459505946656768000000⟩, + ⟨5, 8, 4, 4, 7, 6, -70014169189813016480530147840697993086491426816000000⟩, + ⟨5, 8, 5, 4, 8, 6, 152105497570532570015894296512777691186310676480000000⟩, + ⟨5, 8, 3, 5, 5, 6, -39926878076169190200648713804638989304102649856000000⟩, + ⟨5, 8, 4, 5, 6, 6, 64222512533850914823263379412087764269125337088000000⟩, + ⟨5, 8, 5, 5, 7, 6, -5174391572573086542069925803018183935703121920000000⟩, + ⟨5, 8, 6, 5, 8, 6, 71416425491062790083882553023296942342112542720000000⟩, + ⟨5, 8, 3, 6, 4, 6, 188375394401237869554235945038760297431086137344000000⟩, + ⟨5, 8, 4, 6, 5, 6, -104206398826276819312307923262075990218326933504000000⟩, + ⟨5, 8, 5, 6, 6, 6, 49217697591677183841021724400712777957931745280000000⟩, + ⟨5, 8, 6, 6, 7, 6, 67445439785822311582396290455154159497647226880000000⟩, + ⟨5, 8, 7, 6, 8, 6, 18497771532736521023441471021218988799893176320000000⟩, + ⟨5, 8, 3, 7, 3, 6, -335724061431655555441886206635211812054711140352000000⟩, + ⟨5, 8, 4, 7, 4, 6, -430957375329361151695717943708304156847094366208000000⟩, + ⟨5, 8, 5, 7, 5, 6, -55660311623123388069516212816538226146127380480000000⟩, + ⟨5, 8, 6, 7, 6, 6, -72997538059056712259397453109972013201699635200000000⟩, + ⟨5, 8, 7, 7, 7, 6, -6537716237873093340045672505349093317159157760000000⟩, + ⟨5, 8, 8, 7, 8, 6, -35084560077452336773525920612958610604530073600000000⟩, + ⟨6, 2, 8, 7, 8, 1, -3886748451159637426109193301901971371069957734400000000⟩, + ⟨6, 3, 7, 6, 8, 2, 25750627131681025971984115297799845363171983360000000⟩, + ⟨6, 3, 7, 7, 7, 2, -9101112144036795600625206100451033786854932480000000⟩, + ⟨6, 3, 8, 7, 8, 2, -244204936533747617526533894216297843905265664000000000⟩, + ⟨6, 4, 6, 5, 8, 3, 188375394401237869554235945038760297431086137344000000⟩, + ⟨6, 4, 6, 6, 7, 3, 177901109343664332341178340255526698207282200576000000⟩ +] + +def collectedFourData_16_93 : List CollectedFourTerm := [ + ⟨6, 4, 7, 6, 8, 3, 195166587185705264783882917686097422935188832256000000⟩, + ⟨6, 4, 6, 7, 6, 3, -192545901417524785431682956513867305915032535040000000⟩, + ⟨6, 4, 7, 7, 7, 3, -68978242264272342930653426686840696318678007808000000⟩, + ⟨6, 4, 8, 7, 8, 3, -925426860353166514467625447559733020298785587200000000⟩, + ⟨6, 5, 5, 4, 8, 4, -73980955289189724648512141989731059897374605312000000⟩, + ⟨6, 5, 5, 5, 7, 4, 2516716605866130075690109403664012678317211648000000⟩, + ⟨6, 5, 6, 5, 8, 4, -104206398826276819312307923262075990218326933504000000⟩, + ⟨6, 5, 5, 6, 6, 4, -23938466019469736759835808565078768286833836032000000⟩, + ⟨6, 5, 6, 6, 7, 4, -98412183877987121702210702705846450363842953216000000⟩, + ⟨6, 5, 7, 6, 8, 4, -53981591615192619050219694366052398009887490048000000⟩, + ⟨6, 5, 5, 7, 5, 4, 27072019692537407465659053267049935612162342912000000⟩, + ⟨6, 5, 6, 7, 6, 4, 106513459782026166743737058634345189560958320640000000⟩, + ⟨6, 5, 7, 7, 7, 4, 19078856467888762908937654120840992663445438464000000⟩, + ⟨6, 5, 8, 7, 8, 4, 170644014311665232282390699788840147739895398400000000⟩, + ⟨6, 6, 4, 3, 8, 5, -7058044632570742254560763570672131762540249088000000⟩, + ⟨6, 6, 4, 4, 7, 5, -16083770564088561056652739655969887547742486528000000⟩, + ⟨6, 6, 5, 4, 8, 5, 69883852162225720222908173563808809314083143680000000⟩, + ⟨6, 6, 4, 5, 6, 5, 14753301633036469017521050926703559055406792704000000⟩, + ⟨6, 6, 5, 5, 7, 5, -2377339553552194062892084777900322908243230720000000⟩, + ⟨6, 6, 6, 5, 8, 5, 49217697591677183841021724400712777957931745280000000⟩, + ⟨6, 6, 4, 6, 5, 5, -23938466019469736759835808565078768286833836032000000⟩, + ⟨6, 6, 5, 6, 6, 5, 22612741532678438604370069352176566695079444480000000⟩, + ⟨6, 6, 6, 6, 7, 5, 46481033410607844765420115733403807431912325120000000⟩, + ⟨6, 6, 7, 6, 8, 5, 16997354491082124783168337292729292888987402240000000⟩ +] + +def collectedFourData_16_94 : List CollectedFourTerm := [ + ⟨6, 6, 4, 7, 4, 5, -99000239921546602449787307578548500715918065664000000⟩, + ⟨6, 6, 5, 7, 5, 5, -25572757401290222719105558281052077216686407680000000⟩, + ⟨6, 6, 6, 7, 6, 5, -50307344961940253060650329662321561210506444800000000⟩, + ⟨6, 6, 7, 7, 7, 5, -6007419880852713997130076917901710206508728320000000⟩, + ⟨6, 6, 8, 7, 8, 5, -40298415389168714060078358581761554927058944000000000⟩, + ⟨6, 7, 3, 2, 8, 6, -20004187131229416267884672959003650617518325760000000⟩, + ⟨6, 7, 3, 3, 7, 6, -49948243327929217793096724178398896130084569088000000⟩, + ⟨6, 7, 4, 3, 8, 6, -29015960573023301693920215359401718549361721344000000⟩, + ⟨6, 7, 3, 4, 6, 6, -114731741813648470686544364375245338014983913472000000⟩, + ⟨6, 7, 4, 4, 7, 6, -66121153499020307722066173389514045731912024064000000⟩, + ⟨6, 7, 5, 4, 8, 6, 143647936828898109990729455079300309708617809920000000⟩, + ⟨6, 7, 3, 5, 5, 6, -37706813700149859849079059105627023225571508224000000⟩, + ⟨6, 7, 4, 5, 6, 6, 60651531803956164639642745184253868425716170752000000⟩, + ⟨6, 7, 5, 5, 7, 6, -4886678559401125446760282248943153863909703680000000⟩, + ⟨6, 7, 6, 5, 8, 6, 67445439785822311582396290455154159497647226880000000⟩, + ⟨6, 7, 3, 6, 4, 6, 177901109343664332341178340255526698207282200576000000⟩, + ⟨6, 7, 4, 6, 5, 6, -98412183877987121702210702705846450363842953216000000⟩, + ⟨6, 7, 5, 6, 6, 6, 46481033410607844765420115733403807431912325120000000⟩, + ⟨6, 7, 6, 6, 7, 6, 63695253810655099684622478094864257014845931520000000⟩, + ⟨6, 7, 7, 6, 8, 6, 17469235228514837095117130551821934332771041280000000⟩, + ⟨6, 7, 3, 7, 3, 6, -317056710893126929493082454608047110993905451008000000⟩, + ⟨6, 7, 4, 7, 4, 6, -406994742570388807678031725780625402152964063232000000⟩, + ⟨6, 7, 5, 7, 5, 6, -52565417132327105475687915763651469442463825920000000⟩, + ⟨6, 7, 6, 7, 6, 6, -68938637348791715358827143901755241283767500800000000⟩ +] + +def collectedFourData_16_95 : List CollectedFourTerm := [ + ⟨6, 7, 7, 7, 7, 6, -6174197935927815319454825206380621842129879040000000⟩, + ⟨6, 7, 8, 7, 8, 6, -33133744343057329082960383337002144203433574400000000⟩, + ⟨6, 8, 2, 1, 8, 7, -42918976634443667026919737792300128247058792448000000⟩, + ⟨6, 8, 2, 2, 7, 7, -52169868990326163997449733096467558889250881536000000⟩, + ⟨6, 8, 3, 2, 8, 7, -21945613190552536971805145320465218446882242560000000⟩, + ⟨6, 8, 2, 3, 6, 7, -20724631074728884774639098304183757163661885440000000⟩, + ⟨6, 8, 3, 3, 7, 7, -54795769527225192380708190200999208981708668928000000⟩, + ⟨6, 8, 4, 3, 8, 7, -15915994059408645283656047271717245973411397632000000⟩, + ⟨6, 8, 2, 4, 5, 7, -9624917228793757410139654583741524264662073344000000⟩, + ⟨6, 8, 3, 4, 6, 7, -125866570333664416203776136822154074574062354432000000⟩, + ⟨6, 8, 4, 4, 7, 7, -36269138277988838277469407850969628470035873792000000⟩, + ⟨6, 8, 5, 4, 8, 7, 52529703516362131992140193106094484015116451840000000⟩, + ⟨6, 8, 2, 5, 4, 7, 51033556760331992750285918450807519296270368768000000⟩, + ⟨6, 8, 3, 5, 5, 7, -41366297099864186250600165263655257081898860544000000⟩, + ⟨6, 8, 4, 5, 6, 7, 33268911344719919968370981411147823370318381056000000⟩, + ⟨6, 8, 5, 5, 7, 7, -1786978508510429475146497928731209156117135360000000⟩, + ⟨6, 8, 6, 5, 8, 7, 18497771532736521023441471021218988799893176320000000⟩, + ⟨6, 8, 2, 6, 3, 7, 25750627131681025971984115297799845363171983360000000⟩, + ⟨6, 8, 3, 6, 4, 7, 195166587185705264783882917686097422935188832256000000⟩, + ⟨6, 8, 4, 6, 5, 7, -53981591615192619050219694366052398009887490048000000⟩, + ⟨6, 8, 5, 6, 6, 7, 16997354491082124783168337292729292888987402240000000⟩, + ⟨6, 8, 6, 6, 7, 7, 17469235228514837095117130551821934332771041280000000⟩, + ⟨6, 8, 7, 6, 8, 7, 3832928341899578591998317308780644486229262336000000⟩, + ⟨6, 8, 2, 7, 2, 7, -124545316062527661045441254474900110438695960576000000⟩ +] + +def collectedFourData_16_96 : List CollectedFourTerm := [ + ⟨6, 8, 3, 7, 3, 7, -347827376892858727401199041108151842441630056448000000⟩, + ⟨6, 8, 4, 7, 4, 7, -223246991553446135890641558427922408110603370496000000⟩, + ⟨6, 8, 5, 7, 5, 7, -19222314208828628708220088103656496463442083840000000⟩, + ⟨6, 8, 6, 7, 6, 7, -18907299996940458988178082846860654905865011200000000⟩, + ⟨6, 8, 7, 7, 7, 7, -1354681985075515248312359777806687921659445248000000⟩, + ⟨6, 8, 8, 7, 8, 7, -6058234476423052343018974123450194685486694400000000⟩, + ⟨7, 1, 8, 7, 8, 1, 11122220442069393172958894007393570611322578534400000000⟩, + ⟨7, 2, 7, 6, 8, 2, -124545316062527661045441254474900110438695960576000000⟩, + ⟨7, 2, 7, 7, 7, 2, 44018379929280403474211360244859689035070701568000000⟩, + ⟨7, 2, 8, 7, 8, 2, 1181120011139690319904802255782407024423626342400000000⟩, + ⟨7, 3, 6, 5, 8, 3, -335724061431655555441886206635211812054711140352000000⟩, + ⟨7, 3, 6, 6, 7, 3, -317056710893126929493082454608047110993905451008000000⟩, + ⟨7, 3, 7, 6, 8, 3, -347827376892858727401199041108151842441630056448000000⟩, + ⟨7, 3, 6, 7, 6, 3, 343156770773485914670223749805400888696970936320000000⟩, + ⟨7, 3, 7, 7, 7, 3, 122933548285253182514566080089098531420099313664000000⟩, + ⟨7, 3, 8, 7, 8, 3, 1649302792985520513180782678238691261790394777600000000⟩, + ⟨7, 4, 5, 4, 8, 4, -305956627183132781277901671735540592019949748224000000⟩, + ⟨7, 4, 5, 5, 7, 4, 10408166822078033270176351860993037068398493696000000⟩, + ⟨7, 4, 6, 5, 8, 4, -430957375329361151695717943708304156847094366208000000⟩, + ⟨7, 4, 5, 6, 6, 4, -99000239921546602449787307578548500715918065664000000⟩, + ⟨7, 4, 6, 6, 7, 4, -406994742570388807678031725780625402152964063232000000⟩, + ⟨7, 4, 7, 6, 8, 4, -223246991553446135890641558427922408110603370496000000⟩, + ⟨7, 4, 5, 7, 5, 4, 111959406360550314920964965648844480307657703424000000⟩, + ⟨7, 4, 6, 7, 6, 4, 440498487443523147872167853807481211990604513280000000⟩ +] + +def collectedFourData_16_97 : List CollectedFourTerm := [ + ⟨7, 4, 7, 7, 7, 4, 78902773728839704093311766503823389267358384128000000⟩, + ⟨7, 4, 8, 7, 8, 4, 705717665630310351743808524076004865009831116800000000⟩, + ⟨7, 5, 4, 3, 8, 5, 7981945172608667298685339604868308558841643008000000⟩, + ⟨7, 5, 4, 4, 7, 5, 18189141822501124682062700662355996199824130048000000⟩, + ⟨7, 5, 5, 4, 8, 5, -79031673140101028552844324964661644848141434880000000⟩, + ⟨7, 5, 4, 5, 6, 5, -16684514037560488845028894847802609233049944064000000⟩, + ⟨7, 5, 5, 5, 7, 5, 2688534142382725535666442630966846267347435520000000⟩, + ⟨7, 5, 6, 5, 8, 5, -55660311623123388069516212816538226146127380480000000⟩, + ⟨7, 5, 4, 6, 5, 5, 27072019692537407465659053267049935612162342912000000⟩, + ⟨7, 5, 5, 6, 6, 5, -25572757401290222719105558281052077216686407680000000⟩, + ⟨7, 5, 6, 6, 7, 5, -52565417132327105475687915763651469442463825920000000⟩, + ⟨7, 5, 7, 6, 8, 5, -19222314208828628708220088103656496463442083840000000⟩, + ⟨7, 5, 4, 7, 4, 5, 111959406360550314920964965648844480307657703424000000⟩, + ⟨7, 5, 5, 7, 5, 5, 28920240394565849745354003083812740333966458880000000⟩, + ⟨7, 5, 6, 7, 6, 5, 56892594219748050317959813771886568424656076800000000⟩, + ⟨7, 5, 7, 7, 7, 5, 6793793269105548902968091081642879864662917120000000⟩, + ⟨7, 5, 8, 7, 8, 5, 45573492224034908627843726704787823110651904000000000⟩, + ⟨7, 6, 3, 2, 8, 6, 21650928752033609630683387946077696526018150400000000⟩, + ⟨7, 6, 3, 3, 7, 6, 54059975068618116619176247319740599747760619520000000⟩, + ⟨7, 6, 4, 3, 8, 6, 31404550003313958664711746890237746127579381760000000⟩, + ⟨7, 6, 3, 4, 6, 6, 124176441227449858121033246873714828201825402880000000⟩, + ⟨7, 6, 4, 4, 7, 6, 71564236727952677125798162614120908145096130560000000⟩, + ⟨7, 6, 5, 4, 8, 6, -155473012987554305926853645515998607837023436800000000⟩, + ⟨7, 6, 3, 5, 5, 6, 40810832828775678305319214756432442278501416960000000⟩ +] + +def collectedFourData_16_98 : List CollectedFourTerm := [ + ⟨7, 6, 4, 5, 6, 6, -65644356612677377409333961888274894362331054080000000⟩, + ⟨7, 6, 5, 5, 7, 6, 5288949189967994771698020301181483553600307200000000⟩, + ⟨7, 6, 6, 5, 8, 6, -72997538059056712259397453109972013201699635200000000⟩, + ⟨7, 6, 3, 6, 4, 6, -192545901417524785431682956513867305915032535040000000⟩, + ⟨7, 6, 4, 6, 5, 6, 106513459782026166743737058634345189560958320640000000⟩, + ⟨7, 6, 5, 6, 6, 6, -50307344961940253060650329662321561210506444800000000⟩, + ⟨7, 6, 6, 6, 7, 6, -68938637348791715358827143901755241283767500800000000⟩, + ⟨7, 6, 7, 6, 8, 6, -18907299996940458988178082846860654905865011200000000⟩, + ⟨7, 6, 3, 7, 3, 6, 343156770773485914670223749805400888696970936320000000⟩, + ⟨7, 6, 4, 7, 4, 6, 440498487443523147872167853807481211990604513280000000⟩, + ⟨7, 6, 5, 7, 5, 6, 56892594219748050317959813771886568424656076800000000⟩, + ⟨7, 6, 6, 7, 6, 6, 74613655416711819316363926332943258334789632000000000⟩, + ⟨7, 6, 7, 7, 7, 6, 6682456964374067105994049131978928602847641600000000⟩, + ⟨7, 6, 8, 7, 8, 6, 35861309102617978456129422481641959929675776000000000⟩, + ⟨7, 7, 2, 1, 8, 7, 15168967243395726505622802466629023058219761664000000⟩, + ⟨7, 7, 2, 2, 7, 7, 18438534556562872955057771239932403027015630848000000⟩, + ⟨7, 7, 3, 2, 8, 7, 7756296019336335567825770152870974431774638080000000⟩, + ⟨7, 7, 2, 3, 6, 7, 7324761086025802213306605111383288711133265920000000⟩, + ⟨7, 7, 3, 3, 7, 7, 19366613517249698141172953178423988225314914304000000⟩, + ⟨7, 7, 4, 3, 8, 7, 5625231808055206647810350388931651097409355776000000⟩, + ⟨7, 7, 2, 4, 5, 7, 3401759911647068297450053149578399377357012992000000⟩, + ⟨7, 7, 3, 4, 6, 7, 44485354315221046440204390086883282495970738176000000⟩, + ⟨7, 7, 4, 4, 7, 7, 12818697313567347109480529560812131077016518656000000⟩, + ⟨7, 7, 5, 4, 8, 7, -18565711823275751047840498506719119317003141120000000⟩ +] + +def collectedFourData_16_99 : List CollectedFourTerm := [ + ⟨7, 7, 2, 5, 4, 7, -18036924724579632719323340866766963693190119424000000⟩, + ⟨7, 7, 3, 5, 5, 7, 14620199615496940664769071272476874685747822592000000⟩, + ⟨7, 7, 4, 5, 6, 7, -11758319186168416378257608040404755690404446208000000⟩, + ⟨7, 7, 5, 5, 7, 7, 631576532943076848445800214080101655490068480000000⟩, + ⟨7, 7, 6, 5, 8, 7, -6537716237873093340045672505349093317159157760000000⟩, + ⟨7, 7, 2, 6, 3, 7, -9101112144036795600625206100451033786854932480000000⟩, + ⟨7, 7, 3, 6, 4, 7, -68978242264272342930653426686840696318678007808000000⟩, + ⟨7, 7, 4, 6, 5, 7, 19078856467888762908937654120840992663445438464000000⟩, + ⟨7, 7, 5, 6, 6, 7, -6007419880852713997130076917901710206508728320000000⟩, + ⟨7, 7, 6, 6, 7, 7, -6174197935927815319454825206380621842129879040000000⟩, + ⟨7, 7, 7, 6, 8, 7, -1354681985075515248312359777806687921659445248000000⟩, + ⟨7, 7, 2, 7, 2, 7, 44018379929280403474211360244859689035070701568000000⟩, + ⟨7, 7, 3, 7, 3, 7, 122933548285253182514566080089098531420099313664000000⟩, + ⟨7, 7, 4, 7, 4, 7, 78902773728839704093311766503823389267358384128000000⟩, + ⟨7, 7, 5, 7, 5, 7, 6793793269105548902968091081642879864662917120000000⟩, + ⟨7, 7, 6, 7, 6, 7, 6682456964374067105994049131978928602847641600000000⟩, + ⟨7, 7, 7, 7, 7, 7, 478788831146955777481130548160091204630872064000000⟩, + ⟨7, 7, 8, 7, 8, 7, 2141177808324579791717729391499621317161779200000000⟩, + ⟨7, 8, 1, 0, 8, 8, -70583168097992862347664064273381881791329075200000000⟩, + ⟨7, 8, 1, 1, 7, 8, -740184135328714259727834388039430964285485875200000000⟩, + ⟨7, 8, 2, 1, 8, 8, 407020221741042353532618694112118854244315955200000000⟩, + ⟨7, 8, 1, 2, 6, 8, -877720773664617712899135281212684632052255948800000000⟩, + ⟨7, 8, 2, 2, 7, 8, 494750651337820062008943138982906576624838246400000000⟩, + ⟨7, 8, 3, 2, 8, 8, 104060127331803769123741134045628027342159872000000000⟩ +] + +def collectedFourData_16_100 : List CollectedFourTerm := [ + ⟨7, 8, 1, 3, 5, 8, -725132765340499484141893490258273055602953420800000000⟩, + ⟨7, 8, 2, 3, 6, 8, 196541124626160133791486627831711669688467456000000000⟩, + ⟨7, 8, 3, 3, 7, 8, 259826631625036061144238904656979383323040153600000000⟩, + ⟨7, 8, 4, 3, 8, 8, 50312875867367410609324782600278558717352345600000000⟩, + ⟨7, 8, 1, 4, 4, 8, 816727484490888933846585943515736875514567065600000000⟩, + ⟨7, 8, 2, 4, 5, 8, 91277477980658163262322942900174544694778265600000000⟩, + ⟨7, 8, 3, 4, 6, 8, 596825033869504107122301676484794424647640678400000000⟩, + ⟨7, 8, 4, 4, 7, 8, 114652257671465628718245477311183599282264473600000000⟩, + ⟨7, 8, 5, 4, 8, 8, -124540781548262513556328178644064724219592704000000000⟩, + ⟨7, 8, 1, 5, 3, 8, 1559741359477420901379906098823611727996361113600000000⟩, + ⟨7, 8, 2, 5, 4, 8, -483974484427817012352801411814091102495126323200000000⟩, + ⟨7, 8, 3, 5, 5, 8, 196147726932059050173709157096206020654189772800000000⟩, + ⟨7, 8, 4, 5, 6, 8, -105168084411281589342653334292103588064578764800000000⟩, + ⟨7, 8, 5, 5, 7, 8, 4236682965296314614458107159704167163887616000000000⟩, + ⟨7, 8, 6, 5, 8, 8, -35084560077452336773525920612958610604530073600000000⟩, + ⟨7, 8, 1, 6, 2, 8, -3886748451159637426109193301901971371069957734400000000⟩, + ⟨7, 8, 2, 6, 3, 8, -244204936533747617526533894216297843905265664000000000⟩, + ⟨7, 8, 3, 6, 4, 8, -925426860353166514467625447559733020298785587200000000⟩, + ⟨7, 8, 4, 6, 5, 8, 170644014311665232282390699788840147739895398400000000⟩, + ⟨7, 8, 5, 6, 6, 8, -40298415389168714060078358581761554927058944000000000⟩, + ⟨7, 8, 6, 6, 7, 8, -33133744343057329082960383337002144203433574400000000⟩, + ⟨7, 8, 7, 6, 8, 8, -6058234476423052343018974123450194685486694400000000⟩, + ⟨7, 8, 1, 7, 1, 8, 11122220442069393172958894007393570611322578534400000000⟩, + ⟨7, 8, 2, 7, 2, 8, 1181120011139690319904802255782407024423626342400000000⟩ +] + +def collectedFourData_16_101 : List CollectedFourTerm := [ + ⟨7, 8, 3, 7, 3, 8, 1649302792985520513180782678238691261790394777600000000⟩, + ⟨7, 8, 4, 7, 4, 8, 705717665630310351743808524076004865009831116800000000⟩, + ⟨7, 8, 5, 7, 5, 8, 45573492224034908627843726704787823110651904000000000⟩, + ⟨7, 8, 6, 7, 6, 8, 35861309102617978456129422481641959929675776000000000⟩, + ⟨7, 8, 7, 7, 7, 8, 2141177808324579791717729391499621317161779200000000⟩, + ⟨7, 8, 8, 7, 8, 8, 8207571346603845052261869579412002916270080000000000⟩ +] + +def collectedFourData_16 : List CollectedFourTerm := ((((((collectedFourData_16_0 ++ (collectedFourData_16_1 ++ collectedFourData_16_2)) ++ (collectedFourData_16_3 ++ (collectedFourData_16_4 ++ collectedFourData_16_5))) ++ ((collectedFourData_16_6 ++ (collectedFourData_16_7 ++ collectedFourData_16_8)) ++ (collectedFourData_16_9 ++ (collectedFourData_16_10 ++ collectedFourData_16_11)))) ++ (((collectedFourData_16_12 ++ (collectedFourData_16_13 ++ collectedFourData_16_14)) ++ (collectedFourData_16_15 ++ (collectedFourData_16_16 ++ collectedFourData_16_17))) ++ ((collectedFourData_16_18 ++ (collectedFourData_16_19 ++ collectedFourData_16_20)) ++ ((collectedFourData_16_21 ++ collectedFourData_16_22) ++ (collectedFourData_16_23 ++ collectedFourData_16_24))))) ++ ((((collectedFourData_16_25 ++ (collectedFourData_16_26 ++ collectedFourData_16_27)) ++ (collectedFourData_16_28 ++ (collectedFourData_16_29 ++ collectedFourData_16_30))) ++ ((collectedFourData_16_31 ++ (collectedFourData_16_32 ++ collectedFourData_16_33)) ++ ((collectedFourData_16_34 ++ collectedFourData_16_35) ++ (collectedFourData_16_36 ++ collectedFourData_16_37)))) ++ (((collectedFourData_16_38 ++ (collectedFourData_16_39 ++ collectedFourData_16_40)) ++ (collectedFourData_16_41 ++ (collectedFourData_16_42 ++ collectedFourData_16_43))) ++ ((collectedFourData_16_44 ++ (collectedFourData_16_45 ++ collectedFourData_16_46)) ++ ((collectedFourData_16_47 ++ collectedFourData_16_48) ++ (collectedFourData_16_49 ++ collectedFourData_16_50)))))) ++ (((((collectedFourData_16_51 ++ (collectedFourData_16_52 ++ collectedFourData_16_53)) ++ (collectedFourData_16_54 ++ (collectedFourData_16_55 ++ collectedFourData_16_56))) ++ ((collectedFourData_16_57 ++ (collectedFourData_16_58 ++ collectedFourData_16_59)) ++ (collectedFourData_16_60 ++ (collectedFourData_16_61 ++ collectedFourData_16_62)))) ++ (((collectedFourData_16_63 ++ (collectedFourData_16_64 ++ collectedFourData_16_65)) ++ (collectedFourData_16_66 ++ (collectedFourData_16_67 ++ collectedFourData_16_68))) ++ ((collectedFourData_16_69 ++ (collectedFourData_16_70 ++ collectedFourData_16_71)) ++ ((collectedFourData_16_72 ++ collectedFourData_16_73) ++ (collectedFourData_16_74 ++ collectedFourData_16_75))))) ++ ((((collectedFourData_16_76 ++ (collectedFourData_16_77 ++ collectedFourData_16_78)) ++ (collectedFourData_16_79 ++ (collectedFourData_16_80 ++ collectedFourData_16_81))) ++ ((collectedFourData_16_82 ++ (collectedFourData_16_83 ++ collectedFourData_16_84)) ++ ((collectedFourData_16_85 ++ collectedFourData_16_86) ++ (collectedFourData_16_87 ++ collectedFourData_16_88)))) ++ (((collectedFourData_16_89 ++ (collectedFourData_16_90 ++ collectedFourData_16_91)) ++ (collectedFourData_16_92 ++ (collectedFourData_16_93 ++ collectedFourData_16_94))) ++ ((collectedFourData_16_95 ++ (collectedFourData_16_96 ++ collectedFourData_16_97)) ++ ((collectedFourData_16_98 ++ collectedFourData_16_99) ++ (collectedFourData_16_100 ++ collectedFourData_16_101))))))) + +theorem collectedFourChecked_16 : collectedFourTerms 16 = collectedFourData_16 := by + decide +kernel + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1701.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1701.lean new file mode 100644 index 0000000000000000000000000000000000000000..76889009001a8cb5822f159011c4d74810c45f06 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1701.lean @@ -0,0 +1,631 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1701. -/ +namespace LaughlinFock + +def collectedFourData_17_0 : List CollectedFourTerm := [ + ⟨1, 8, 8, 1, 8, 8, 11867527930342804817428404267441580135256810323968000000⟩, + ⟨1, 8, 8, 2, 7, 8, 5095647592047352006809786253082789733745972740096000000⟩, + ⟨1, 8, 8, 3, 6, 8, -273630820676881557562151123080042572622929592320000000⟩, + ⟨1, 8, 8, 4, 5, 8, -3724425490465288451654148019170267016445206462464000000⟩, + ⟨1, 8, 8, 5, 4, 8, -1864455965436618462328951035370103374832512008192000000⟩, + ⟨1, 8, 8, 6, 3, 8, 9899143954488101599882005075967436777013897068544000000⟩, + ⟨1, 8, 8, 7, 2, 8, -3893596894276975959305045602486049884229427265536000000⟩, + ⟨2, 7, 8, 1, 8, 8, 5095647592047352006809786253082789733745972740096000000⟩, + ⟨2, 7, 8, 2, 7, 8, 2187955615924801536784501897375965847238278643712000000⟩, + ⟨2, 7, 8, 3, 6, 8, -117490874314868020675122349014195091574662103040000000⟩, + ⟨2, 7, 8, 4, 5, 8, -1599183915440847597758868823339479046841966788608000000⟩, + ⟨2, 7, 8, 5, 4, 8, -800555145647842740507119674230594942001609703424000000⟩, + ⟨2, 7, 8, 6, 3, 8, 4250468113586341135863738564611024755448629690368000000⟩, + ⟨2, 7, 8, 7, 2, 8, -1671822283055070258613798790333706302485684027392000000⟩, + ⟨3, 6, 8, 1, 8, 8, -273630820676881557562151123080042572622929592320000000⟩, + ⟨3, 6, 8, 2, 7, 8, -117490874314868020675122349014195091574662103040000000⟩, + ⟨3, 6, 8, 3, 6, 8, 6309134173838081723123612544616061150743756800000000⟩, + ⟨3, 6, 8, 4, 5, 8, 85874464293464343042763320246876022137799311360000000⟩, + ⟨3, 6, 8, 5, 4, 8, 42988954307318205328397677125276477989930926080000000⟩, + ⟨3, 6, 8, 6, 3, 8, -228245587468941917419507070142528527918495170560000000⟩, + ⟨3, 6, 8, 7, 2, 8, 89775066873189220610765698626353596014935408640000000⟩, + ⟨4, 5, 8, 1, 8, 8, -3724425490465288451654148019170267016445206462464000000⟩, + ⟨4, 5, 8, 2, 7, 8, -1599183915440847597758868823339479046841966788608000000⟩, + ⟨4, 5, 8, 3, 6, 8, 85874464293464343042763320246876022137799311360000000⟩ +] + +def collectedFourData_17_1 : List CollectedFourTerm := [ + ⟨4, 5, 8, 4, 5, 8, 1168848753965133280760582217059929769683841974272000000⟩, + ⟨4, 5, 8, 5, 4, 8, 585128374188846403191225302937977928909078921216000000⟩, + ⟨4, 5, 8, 6, 3, 8, -3106681045478344843043661688609708172195357786112000000⟩, + ⟨4, 5, 8, 7, 2, 8, 1221940374419895130282203602124852582261328969728000000⟩, + ⟨5, 4, 8, 1, 8, 8, -1864455965436618462328951035370103374832512008192000000⟩, + ⟨5, 4, 8, 2, 7, 8, -800555145647842740507119674230594942001609703424000000⟩, + ⟨5, 4, 8, 3, 6, 8, 42988954307318205328397677125276477989930926080000000⟩, + ⟨5, 4, 8, 4, 5, 8, 585128374188846403191225302937977928909078921216000000⟩, + ⟨5, 4, 8, 5, 4, 8, 292916609714840569438817719523742537657612238848000000⟩, + ⟨5, 4, 8, 6, 3, 8, -1555211675674400077579213992393893161094124404736000000⟩, + ⟨5, 4, 8, 7, 2, 8, 611706161481138613118857888542625601041710710784000000⟩, + ⟨6, 3, 8, 1, 8, 8, 9899143954488101599882005075967436777013897068544000000⟩, + ⟨6, 3, 8, 2, 7, 8, 4250468113586341135863738564611024755448629690368000000⟩, + ⟨6, 3, 8, 3, 6, 8, -228245587468941917419507070142528527918495170560000000⟩, + ⟨6, 3, 8, 4, 5, 8, -3106681045478344843043661688609708172195357786112000000⟩, + ⟨6, 3, 8, 5, 4, 8, -1555211675674400077579213992393893161094124404736000000⟩, + ⟨6, 3, 8, 6, 3, 8, 8257242081658004385652428753040131591130948042752000000⟩, + ⟨6, 3, 8, 7, 2, 8, -3247793170020558400965648664287870219712764837888000000⟩, + ⟨7, 2, 8, 1, 8, 8, -3893596894276975959305045602486049884229427265536000000⟩, + ⟨7, 2, 8, 2, 7, 8, -1671822283055070258613798790333706302485684027392000000⟩, + ⟨7, 2, 8, 3, 6, 8, 89775066873189220610765698626353596014935408640000000⟩, + ⟨7, 2, 8, 4, 5, 8, 1221940374419895130282203602124852582261328969728000000⟩, + ⟨7, 2, 8, 5, 4, 8, 611706161481138613118857888542625601041710710784000000⟩, + ⟨7, 2, 8, 6, 3, 8, -3247793170020558400965648664287870219712764837888000000⟩ +] + +def collectedFourData_17_2 : List CollectedFourTerm := [ + ⟨7, 2, 8, 7, 2, 8, 1277443530287558287602613205631592788660188086272000000⟩, + ⟨1, 8, 8, 2, 8, 7, -1477576210278400141444183402078654274314161881088000000⟩, + ⟨1, 8, 8, 3, 7, 7, -905099297915164408156034913856215978712120688640000000⟩, + ⟨1, 8, 8, 4, 6, 7, 1154488805469132177521030250379107831375238004736000000⟩, + ⟨1, 8, 8, 5, 5, 7, 385910718904195613787663225698713181237198979072000000⟩, + ⟨1, 8, 8, 6, 4, 7, -574873132875300138788443355606571593179135475712000000⟩, + ⟨1, 8, 8, 7, 3, 7, -2753325281796164008060286281024538957770892771328000000⟩, + ⟨2, 7, 8, 2, 8, 7, 87237791890693145079251119153077296757378908160000000⟩, + ⟨2, 7, 8, 3, 7, 7, 53438099261938180667786218105606599873449164800000000⟩, + ⟨2, 7, 8, 4, 6, 7, -68162341442053042703908526960959913251590635520000000⟩, + ⟨2, 7, 8, 5, 5, 7, -22784610871481721426691415173711251085763543040000000⟩, + ⟨2, 7, 8, 6, 4, 7, 33941168232450761558664653168759111459631267840000000⟩, + ⟨2, 7, 8, 7, 3, 7, 162559478333412821559309927285868613654764584960000000⟩, + ⟨2, 8, 7, 1, 8, 8, -1477576210278400141444183402078654274314161881088000000⟩, + ⟨2, 8, 7, 2, 7, 8, 87237791890693145079251119153077296757378908160000000⟩, + ⟨2, 8, 8, 2, 8, 8, 1410275092236171732456779874727002498581819031552000000⟩, + ⟨2, 8, 7, 3, 6, 8, 68117108112065449454238585450756498869282930688000000⟩, + ⟨2, 8, 8, 3, 7, 8, 863873543016573234199348239850973715830994370560000000⟩, + ⟨2, 8, 7, 4, 5, 8, 234521074286197298654289967898929088729721077760000000⟩, + ⟨2, 8, 8, 4, 6, 8, -1101903776802035773697024996293509113050608697344000000⟩, + ⟨2, 8, 7, 5, 4, 8, -148607027058751758700462743973693826408267120640000000⟩, + ⟨2, 8, 8, 5, 5, 8, -368333132945472785574315426473744734442999513088000000⟩, + ⟨2, 8, 7, 6, 3, 8, -445600911386098295443043877317586863209467346944000000⟩, + ⟨2, 8, 8, 6, 4, 8, 548688625906514778300547100475161785594332315648000000⟩ +] + +def collectedFourData_17_3 : List CollectedFourTerm := [ + ⟨2, 8, 7, 7, 2, 8, 791303337008775513092558235166947390163418873856000000⟩, + ⟨2, 8, 8, 7, 3, 8, 2627915933357952857120570017847040729896045248512000000⟩, + ⟨3, 6, 8, 2, 8, 7, 68117108112065449454238585450756498869282930688000000⟩, + ⟨3, 6, 8, 3, 7, 7, 41725595133008656699221665585680190473387376640000000⟩, + ⟨3, 6, 8, 4, 6, 7, -53222594022066040420000379690197325347276455936000000⟩, + ⟨3, 6, 8, 5, 5, 7, -17790704789602058976633516039765883647764201472000000⟩, + ⟨3, 6, 8, 6, 4, 7, 26501980114724797233040044374219802569040986112000000⟩, + ⟨3, 6, 8, 7, 3, 7, 126929869730682168491631933725196238686863228928000000⟩, + ⟨3, 7, 7, 1, 8, 8, -905099297915164408156034913856215978712120688640000000⟩, + ⟨3, 7, 7, 2, 7, 8, 53438099261938180667786218105606599873449164800000000⟩, + ⟨3, 7, 8, 2, 8, 8, 863873543016573234199348239850973715830994370560000000⟩, + ⟨3, 7, 7, 3, 6, 8, 41725595133008656699221665585680190473387376640000000⟩, + ⟨3, 7, 8, 3, 7, 8, 529171579667261000846554123539813395361221836800000000⟩, + ⟨3, 7, 7, 4, 5, 8, 143657469717080130896120439577608990692789452800000000⟩, + ⟨3, 7, 8, 4, 6, 8, -674978608762032291067284548394404457799294648320000000⟩, + ⟨3, 7, 7, 5, 4, 8, -91030239198824962804931844606722023525397299200000000⟩, + ⟨3, 7, 8, 5, 5, 8, -225624950989855415243409790023301344065633648640000000⟩, + ⟨3, 7, 7, 6, 3, 8, -272955851102884236046129415767699868763889336320000000⟩, + ⟨3, 7, 8, 6, 4, 8, 336102927637452766348714215817277988454992445440000000⟩, + ⟨3, 7, 7, 7, 2, 8, 484718209309571810028035134666714458915266887680000000⟩, + ⟨3, 7, 8, 7, 3, 8, 1609747673058571462994360871437294423126688399360000000⟩, + ⟨4, 5, 8, 2, 8, 7, 234521074286197298654289967898929088729721077760000000⟩, + ⟨4, 5, 8, 3, 7, 7, 143657469717080130896120439577608990692789452800000000⟩, + ⟨4, 5, 8, 4, 6, 7, -183240602431596621291568094871491655607485726720000000⟩ +] + +def collectedFourData_17_4 : List CollectedFourTerm := [ + ⟨4, 5, 8, 5, 5, 7, -61251795844031730246251816875060887968746045440000000⟩, + ⟨4, 5, 8, 6, 4, 7, 91243932977768307782865630693288210333947658240000000⟩, + ⟨4, 5, 8, 7, 3, 7, 437008120768620230818974932624494932326413762560000000⟩, + ⟨4, 6, 7, 1, 8, 8, 1154488805469132177521030250379107831375238004736000000⟩, + ⟨4, 6, 7, 2, 7, 8, -68162341442053042703908526960959913251590635520000000⟩, + ⟨4, 6, 8, 2, 8, 8, -1101903776802035773697024996293509113050608697344000000⟩, + ⟨4, 6, 7, 3, 6, 8, -53222594022066040420000379690197325347276455936000000⟩, + ⟨4, 6, 8, 3, 7, 8, -674978608762032291067284548394404457799294648320000000⟩, + ⟨4, 6, 7, 4, 5, 8, -183240602431596621291568094871491655607485726720000000⟩, + ⟨4, 6, 8, 4, 6, 8, 860961056473977636843669954081940993428808531968000000⟩, + ⟨4, 6, 7, 5, 4, 8, 116112555115550736381394226805363383512156078080000000⟩, + ⟨4, 6, 8, 5, 5, 8, 287793262852276327597889957711025519510197108736000000⟩, + ⟨4, 6, 7, 6, 3, 8, 348165637970825124292851561776668465239234183168000000⟩, + ⟨4, 6, 8, 6, 4, 8, -428712151624286272392367702074397630666748461056000000⟩, + ⟨4, 6, 7, 7, 2, 8, -618276633010266910098926221331281737574023954432000000⟩, + ⟨4, 6, 8, 7, 3, 8, -2053294784845030089442512855988173094967222206464000000⟩, + ⟨5, 4, 8, 2, 8, 7, -148607027058751758700462743973693826408267120640000000⟩, + ⟨5, 4, 8, 3, 7, 7, -91030239198824962804931844606722023525397299200000000⟩, + ⟨5, 4, 8, 4, 6, 7, 116112555115550736381394226805363383512156078080000000⟩, + ⟨5, 4, 8, 5, 5, 7, 38812918242404985323808897859799920853290844160000000⟩, + ⟨5, 4, 8, 6, 4, 7, -57817787413112615524789993831757060842570383360000000⟩, + ⟨5, 4, 8, 7, 3, 7, -276915316994941731230744662712842709200892067840000000⟩, + ⟨5, 5, 7, 1, 8, 8, 385910718904195613787663225698713181237198979072000000⟩, + ⟨5, 5, 7, 2, 7, 8, -22784610871481721426691415173711251085763543040000000⟩ +] + +def collectedFourData_17_5 : List CollectedFourTerm := [ + ⟨5, 5, 8, 2, 8, 8, -368333132945472785574315426473744734442999513088000000⟩, + ⟨5, 5, 7, 3, 6, 8, -17790704789602058976633516039765883647764201472000000⟩, + ⟨5, 5, 8, 3, 7, 8, -225624950989855415243409790023301344065633648640000000⟩, + ⟨5, 5, 7, 4, 5, 8, -61251795844031730246251816875060887968746045440000000⟩, + ⟨5, 5, 8, 4, 6, 8, 287793262852276327597889957711025519510197108736000000⟩, + ⟨5, 5, 7, 5, 4, 8, 38812918242404985323808897859799920853290844160000000⟩, + ⟨5, 5, 8, 5, 5, 8, 96200590631084810653320438372755685658771587072000000⟩, + ⟨5, 5, 7, 6, 3, 8, 116381251174160012497601925279759173775456731136000000⟩, + ⟨5, 5, 8, 6, 4, 8, -143305516565025158174407019853910632733933043712000000⟩, + ⟨5, 5, 7, 7, 2, 8, -206671194035269590192837581219415311993026904064000000⟩, + ⟨5, 5, 8, 7, 3, 8, -686354395805328130975717503183320166459745763328000000⟩, + ⟨6, 3, 8, 2, 8, 7, -445600911386098295443043877317586863209467346944000000⟩, + ⟨6, 3, 8, 3, 7, 7, -272955851102884236046129415767699868763889336320000000⟩, + ⟨6, 3, 8, 4, 6, 7, 348165637970825124292851561776668465239234183168000000⟩, + ⟨6, 3, 8, 5, 5, 7, 116381251174160012497601925279759173775456731136000000⟩, + ⟨6, 3, 8, 6, 4, 7, -173367701888181953886622044796935530596276371456000000⟩, + ⟨6, 3, 8, 7, 3, 7, -830335685141811415743610982021196939594578264064000000⟩, + ⟨6, 4, 7, 1, 8, 8, -574873132875300138788443355606571593179135475712000000⟩, + ⟨6, 4, 7, 2, 7, 8, 33941168232450761558664653168759111459631267840000000⟩, + ⟨6, 4, 8, 2, 8, 8, 548688625906514778300547100475161785594332315648000000⟩, + ⟨6, 4, 7, 3, 6, 8, 26501980114724797233040044374219802569040986112000000⟩, + ⟨6, 4, 8, 3, 7, 8, 336102927637452766348714215817277988454992445440000000⟩, + ⟨6, 4, 7, 4, 5, 8, 91243932977768307782865630693288210333947658240000000⟩, + ⟨6, 4, 8, 4, 6, 8, -428712151624286272392367702074397630666748461056000000⟩ +] + +def collectedFourData_17_6 : List CollectedFourTerm := [ + ⟨6, 4, 7, 5, 4, 8, -57817787413112615524789993831757060842570383360000000⟩, + ⟨6, 4, 8, 5, 5, 8, -143305516565025158174407019853910632733933043712000000⟩, + ⟨6, 4, 7, 6, 3, 8, -173367701888181953886622044796935530596276371456000000⟩, + ⟨6, 4, 8, 6, 4, 8, 213475519674541934687261091991445624459102257152000000⟩, + ⟨6, 4, 7, 7, 2, 8, 307868403156818289879553785572295099844336287744000000⟩, + ⟨6, 4, 8, 7, 3, 8, 1022430014122764034435335449270647929495971954688000000⟩, + ⟨7, 2, 8, 2, 8, 7, 791303337008775513092558235166947390163418873856000000⟩, + ⟨7, 2, 8, 3, 7, 7, 484718209309571810028035134666714458915266887680000000⟩, + ⟨7, 2, 8, 4, 6, 7, -618276633010266910098926221331281737574023954432000000⟩, + ⟨7, 2, 8, 5, 5, 7, -206671194035269590192837581219415311993026904064000000⟩, + ⟨7, 2, 8, 6, 4, 7, 307868403156818289879553785572295099844336287744000000⟩, + ⟨7, 2, 8, 7, 3, 7, 1474519871259584799835770063022398546409722740736000000⟩, + ⟨7, 3, 7, 1, 8, 8, -2753325281796164008060286281024538957770892771328000000⟩, + ⟨7, 3, 7, 2, 7, 8, 162559478333412821559309927285868613654764584960000000⟩, + ⟨7, 3, 8, 2, 8, 8, 2627915933357952857120570017847040729896045248512000000⟩, + ⟨7, 3, 7, 3, 6, 8, 126929869730682168491631933725196238686863228928000000⟩, + ⟨7, 3, 8, 3, 7, 8, 1609747673058571462994360871437294423126688399360000000⟩, + ⟨7, 3, 7, 4, 5, 8, 437008120768620230818974932624494932326413762560000000⟩, + ⟨7, 3, 8, 4, 6, 8, -2053294784845030089442512855988173094967222206464000000⟩, + ⟨7, 3, 7, 5, 4, 8, -276915316994941731230744662712842709200892067840000000⟩, + ⟨7, 3, 8, 5, 5, 8, -686354395805328130975717503183320166459745763328000000⟩, + ⟨7, 3, 7, 6, 3, 8, -830335685141811415743610982021196939594578264064000000⟩, + ⟨7, 3, 8, 6, 4, 8, 1022430014122764034435335449270647929495971954688000000⟩, + ⟨7, 3, 7, 7, 2, 8, 1474519871259584799835770063022398546409722740736000000⟩ +] + +def collectedFourData_17_7 : List CollectedFourTerm := [ + ⟨7, 3, 8, 7, 3, 8, 4896875929253167899153779175628778140948362166272000000⟩, + ⟨1, 8, 8, 3, 8, 6, -54488970223593328377345688006022667360534528000000000⟩, + ⟨1, 8, 8, 4, 7, 6, -19355924102978213892742643440632425644415778816000000⟩, + ⟨1, 8, 8, 5, 6, 6, -40304114076194943847057576348785278838242279424000000⟩, + ⟨1, 8, 8, 6, 5, 6, 42297369671118394955967453235118169528056414208000000⟩, + ⟨1, 8, 8, 7, 4, 6, -83631279088381718546994770119642498391888363520000000⟩, + ⟨2, 7, 8, 3, 8, 6, -72912474512634084634400090279383069718740992000000000⟩, + ⟨2, 7, 8, 4, 7, 6, -25900440346655719758632794755581415532605210624000000⟩, + ⟨2, 7, 8, 5, 6, 6, -53931514548286261354327564454759509054231412736000000⟩, + ⟨2, 7, 8, 6, 5, 6, 56598718519395504288320501168731006196370112512000000⟩, + ⟨2, 7, 8, 7, 4, 6, -111908217020227933131835530300623316684405473280000000⟩, + ⟨2, 8, 7, 2, 8, 7, 135330260810708228147578424940771780424145829888000000⟩, + ⟨2, 8, 7, 3, 7, 7, -75565591374216564134881727716335245008476045312000000⟩, + ⟨2, 8, 8, 3, 8, 7, -341945416400498246897137136003620358364069888000000000⟩, + ⟨2, 8, 7, 4, 6, 7, 24817655104585463004927424980282828033632501760000000⟩, + ⟨2, 8, 8, 4, 7, 7, -121468060417546485802685236344327212839244660736000000⟩, + ⟨2, 8, 7, 5, 5, 7, 65728117723395743803952558849464222804730707968000000⟩, + ⟨2, 8, 8, 5, 6, 7, -252928381907100905916040135907608060587675746304000000⟩, + ⟨2, 8, 7, 6, 4, 7, -23529718352248993246244474119962051544545755136000000⟩, + ⟨2, 8, 8, 6, 5, 7, 265437053140964693655449372224981644676241031168000000⟩, + ⟨2, 8, 7, 7, 3, 7, -985884932248058707517407740428525745977639829504000000⟩, + ⟨2, 8, 8, 7, 4, 7, -524827913514146957963112207017004245190621265920000000⟩, + ⟨3, 6, 8, 3, 8, 6, 193196738689363186296166285158507223279730688000000000⟩, + ⟨3, 6, 8, 4, 7, 6, 68628593927712944185315922281060825759362318336000000⟩ +] + +def collectedFourData_17_8 : List CollectedFourTerm := [ + ⟨3, 6, 8, 5, 6, 6, 142902744598270417017784839307545969967396552704000000⟩, + ⟨3, 6, 8, 6, 5, 6, -149970055261939295838517351366474855050765139968000000⟩, + ⟨3, 6, 8, 7, 4, 6, 296524054427794955108315840432957886744672337920000000⟩, + ⟨3, 7, 7, 2, 8, 7, -75565591374216564134881727716335245008476045312000000⟩, + ⟨3, 7, 7, 3, 7, 7, 42194248097416266610629775298088362416420159488000000⟩, + ⟨3, 7, 8, 3, 8, 7, 190935179265994617128033483047666403153805312000000000⟩, + ⟨3, 7, 7, 4, 6, 7, -13857660313848696557496935721920822136526602240000000⟩, + ⟨3, 7, 8, 4, 7, 7, 67825228175461250376686549107563734609285873664000000⟩, + ⟨3, 7, 7, 5, 5, 7, -36701208258437933769276384599873074636869599232000000⟩, + ⟨3, 7, 8, 5, 6, 7, 141229926253282257991965920788352104736590135296000000⟩, + ⟨3, 7, 7, 6, 4, 7, 13138503328856081089326118283926307602918539264000000⟩, + ⟨3, 7, 8, 6, 5, 7, -148214507036841760454040566976187362738576556032000000⟩, + ⟨3, 7, 7, 7, 3, 7, 550497556761962091644595816197976389539747332096000000⟩, + ⟨3, 7, 8, 7, 4, 7, 293052946301974631887771196869974284635817902080000000⟩, + ⟨3, 8, 6, 1, 8, 8, -54488970223593328377345688006022667360534528000000000⟩, + ⟨3, 8, 6, 2, 7, 8, -72912474512634084634400090279383069718740992000000000⟩, + ⟨3, 8, 7, 2, 8, 8, -341945416400498246897137136003620358364069888000000000⟩, + ⟨3, 8, 6, 3, 6, 8, 193196738689363186296166285158507223279730688000000000⟩, + ⟨3, 8, 7, 3, 7, 8, 190935179265994617128033483047666403153805312000000000⟩, + ⟨3, 8, 8, 3, 8, 8, 432004886035282515632137673335803891154944000000000000⟩, + ⟨3, 8, 6, 4, 5, 8, -153707568028760727906864640996770604973555712000000000⟩, + ⟨3, 8, 7, 4, 6, 8, -62707951333157675897378347885716527917301760000000000⟩, + ⟨3, 8, 8, 4, 7, 8, 153459567172991999158720789651617863190970368000000000⟩, + ⟨3, 8, 6, 5, 4, 8, -173363861579351817426217859252360499563593728000000000⟩ +] + +def collectedFourData_17_9 : List CollectedFourTerm := [ + ⟨3, 8, 7, 5, 5, 8, -166078365987816979322381169316379043947347968000000000⟩, + ⟨3, 8, 8, 5, 6, 8, 319543095360252144860858494816878334838833152000000000⟩, + ⟨3, 8, 6, 6, 3, 8, 641929849585845143997634405561322289556881408000000000⟩, + ⟨3, 8, 7, 6, 4, 8, 59453660190608190446180975176898150595035136000000000⟩, + ⟨3, 8, 8, 6, 5, 8, -335346223086663945627090401089468605696835584000000000⟩, + ⟨3, 8, 6, 7, 2, 8, -633506141692596641263397443965852162994470912000000000⟩, + ⟨3, 8, 7, 7, 3, 8, 2491082420598308327858657676035417600377749504000000000⟩, + ⟨3, 8, 8, 7, 4, 8, 663053844536001215731375010586904285371432960000000000⟩, + ⟨4, 5, 8, 3, 8, 6, -153707568028760727906864640996770604973555712000000000⟩, + ⟨4, 5, 8, 4, 7, 6, -54600995552120639328173437585127573777194942464000000⟩, + ⟨4, 5, 8, 5, 6, 6, -113693603141783300903211878193304157704993898496000000⟩, + ⟨4, 5, 8, 6, 5, 6, 119316364384988896400656371910426367598035730432000000⟩, + ⟨4, 5, 8, 7, 4, 6, -235914910248087043665360225088739656547256238080000000⟩, + ⟨4, 6, 7, 2, 8, 7, 24817655104585463004927424980282828033632501760000000⟩, + ⟨4, 6, 7, 3, 7, 7, -13857660313848696557496935721920822136526602240000000⟩, + ⟨4, 6, 8, 3, 8, 7, -62707951333157675897378347885716527917301760000000000⟩, + ⟨4, 6, 7, 4, 6, 7, 4551206812138364901385253419439234508600115200000000⟩, + ⟨4, 6, 8, 4, 7, 7, -22275523682631420603104564286010094915388702720000000⟩, + ⟨4, 6, 7, 5, 5, 7, 12053606832358619460936531520439029482242703360000000⟩, + ⟨4, 6, 8, 5, 6, 7, -46383486669779766688462892268466997530019758080000000⟩, + ⟨4, 6, 7, 6, 4, 7, -4315017434208212843271520224286681194005790720000000⟩, + ⟨4, 6, 8, 6, 5, 7, 48677399994404921230757937522180212030554767360000000⟩, + ⟨4, 6, 7, 7, 3, 7, -180797347723753949077992396086845721213487022080000000⟩, + ⟨4, 6, 8, 7, 4, 7, -96246013780110020160122925135114311983064678400000000⟩ +] + +def collectedFourData_17_10 : List CollectedFourTerm := [ + ⟨4, 7, 6, 1, 8, 8, -19355924102978213892742643440632425644415778816000000⟩, + ⟨4, 7, 6, 2, 7, 8, -25900440346655719758632794755581415532605210624000000⟩, + ⟨4, 7, 7, 2, 8, 8, -121468060417546485802685236344327212839244660736000000⟩, + ⟨4, 7, 6, 3, 6, 8, 68628593927712944185315922281060825759362318336000000⟩, + ⟨4, 7, 7, 3, 7, 8, 67825228175461250376686549107563734609285873664000000⟩, + ⟨4, 7, 8, 3, 8, 8, 153459567172991999158720789651617863190970368000000000⟩, + ⟨4, 7, 6, 4, 5, 8, -54600995552120639328173437585127573777194942464000000⟩, + ⟨4, 7, 7, 4, 6, 8, -22275523682631420603104564286010094915388702720000000⟩, + ⟨4, 7, 8, 4, 7, 8, 54512899085587405570475802361636901911365943296000000⟩, + ⟨4, 7, 6, 5, 4, 8, -61583431163398945137567186061502334510317961216000000⟩, + ⟨4, 7, 7, 5, 5, 8, -58995430341513874169602733343567117798390890496000000⟩, + ⟨4, 7, 8, 5, 6, 8, 113510163176944896725560042730985265432985862144000000⟩, + ⟨4, 7, 6, 6, 3, 8, 228030469231364583527378441352133806425873842176000000⟩, + ⟨4, 7, 7, 6, 4, 8, 21119513354197869757747152776581178706616123392000000⟩, + ⟨4, 7, 8, 6, 5, 8, -119123852325536144354388184413309129404027240448000000⟩, + ⟨4, 7, 6, 7, 2, 8, -225038145280695065393246602786431675555448356864000000⟩, + ⟨4, 7, 7, 7, 3, 8, 884898394473353626602896148848117351328082034688000000⟩, + ⟨4, 7, 8, 7, 4, 8, 235534271217878843591643869128979659688635269120000000⟩, + ⟨5, 4, 8, 3, 8, 6, -173363861579351817426217859252360499563593728000000000⟩, + ⟨5, 4, 8, 4, 7, 6, -61583431163398945137567186061502334510317961216000000⟩, + ⟨5, 4, 8, 5, 6, 6, -128232866672132945937694101571722279337039233024000000⟩, + ⟨5, 4, 8, 6, 5, 6, 134574672832766780415004856710784994143694225408000000⟩, + ⟨5, 4, 8, 7, 4, 6, -266083969509567681902504596514334655703962091520000000⟩, + ⟨5, 5, 7, 2, 8, 7, 65728117723395743803952558849464222804730707968000000⟩ +] + +def collectedFourData_17_11 : List CollectedFourTerm := [ + ⟨5, 5, 7, 3, 7, 7, -36701208258437933769276384599873074636869599232000000⟩, + ⟨5, 5, 8, 3, 8, 7, -166078365987816979322381169316379043947347968000000000⟩, + ⟨5, 5, 7, 4, 6, 7, 12053606832358619460936531520439029482242703360000000⟩, + ⟨5, 5, 8, 4, 7, 7, -58995430341513874169602733343567117798390890496000000⟩, + ⟨5, 5, 7, 5, 5, 7, 31923277422064407619496251989175482572863438848000000⟩, + ⟨5, 5, 8, 5, 6, 7, -122843969722568399715442181027185494042234322944000000⟩, + ⟨5, 5, 7, 6, 4, 7, -11428072986707735194988966317790786177671888896000000⟩, + ⟨5, 5, 8, 6, 5, 7, 128919265894299395717099559303952219203119874048000000⟩, + ⟨5, 5, 7, 7, 3, 7, -478831271737230001091591620639424561737466118144000000⟩, + ⟨5, 5, 8, 7, 4, 7, -254901975931553534405755942770554994372504453120000000⟩, + ⟨5, 6, 6, 1, 8, 8, -40304114076194943847057576348785278838242279424000000⟩, + ⟨5, 6, 6, 2, 7, 8, -53931514548286261354327564454759509054231412736000000⟩, + ⟨5, 6, 7, 2, 8, 8, -252928381907100905916040135907608060587675746304000000⟩, + ⟨5, 6, 6, 3, 6, 8, 142902744598270417017784839307545969967396552704000000⟩, + ⟨5, 6, 7, 3, 7, 8, 141229926253282257991965920788352104736590135296000000⟩, + ⟨5, 6, 8, 3, 8, 8, 319543095360252144860858494816878334838833152000000000⟩, + ⟨5, 6, 6, 4, 5, 8, -113693603141783300903211878193304157704993898496000000⟩, + ⟨5, 6, 7, 4, 6, 8, -46383486669779766688462892268466997530019758080000000⟩, + ⟨5, 6, 8, 4, 7, 8, 113510163176944896725560042730985265432985862144000000⟩, + ⟨5, 6, 6, 5, 4, 8, -128232866672132945937694101571722279337039233024000000⟩, + ⟨5, 6, 7, 5, 5, 8, -122843969722568399715442181027185494042234322944000000⟩, + ⟨5, 6, 8, 5, 6, 8, 236357951247967812842166060608105809095495254016000000⟩, + ⟨5, 6, 6, 6, 3, 8, 474819285085699729374720833099510126317576126464000000⟩, + ⟨5, 6, 7, 6, 4, 8, 43976369763215925195350695733946389396075839488000000⟩ +] + +def collectedFourData_17_12 : List CollectedFourTerm := [ + ⟨5, 6, 8, 6, 5, 8, -248047125406193947465908892292501936078189494272000000⟩, + ⟨5, 6, 6, 7, 2, 8, -468588481264653648495854763030518726789060100096000000⟩, + ⟨5, 6, 7, 7, 3, 8, 1842590704889577902933838323504605574001309253632000000⟩, + ⟨5, 6, 8, 7, 4, 8, 490444170245438226241551010266205313545462087680000000⟩, + ⟨6, 3, 8, 3, 8, 6, 641929849585845143997634405561322289556881408000000000⟩, + ⟨6, 3, 8, 4, 7, 6, 228030469231364583527378441352133806425873842176000000⟩, + ⟨6, 3, 8, 5, 6, 6, 474819285085699729374720833099510126317576126464000000⟩, + ⟨6, 3, 8, 6, 5, 6, -498301657003995368887212655935753799298489253888000000⟩, + ⟨6, 3, 8, 7, 4, 6, 985252872013927663425077032299019070098605342720000000⟩, + ⟨6, 4, 7, 2, 8, 7, -23529718352248993246244474119962051544545755136000000⟩, + ⟨6, 4, 7, 3, 7, 7, 13138503328856081089326118283926307602918539264000000⟩, + ⟨6, 4, 8, 3, 8, 7, 59453660190608190446180975176898150595035136000000000⟩, + ⟨6, 4, 7, 4, 6, 7, -4315017434208212843271520224286681194005790720000000⟩, + ⟨6, 4, 8, 4, 7, 7, 21119513354197869757747152776581178706616123392000000⟩, + ⟨6, 4, 7, 5, 5, 7, -11428072986707735194988966317790786177671888896000000⟩, + ⟨6, 4, 8, 5, 6, 7, 43976369763215925195350695733946389396075839488000000⟩, + ⟨6, 4, 7, 6, 4, 7, 4091085337599192764204014997646220076035080192000000⟩, + ⟨6, 4, 8, 6, 5, 7, -46151238187546966147709767275222122392291639296000000⟩, + ⟨6, 4, 7, 7, 3, 7, 171414690584024609089716674184986096377830309888000000⟩, + ⟨6, 4, 8, 7, 4, 7, 91251231723106470849841481920933992308397834240000000⟩, + ⟨6, 5, 6, 1, 8, 8, 42297369671118394955967453235118169528056414208000000⟩, + ⟨6, 5, 6, 2, 7, 8, 56598718519395504288320501168731006196370112512000000⟩, + ⟨6, 5, 7, 2, 8, 8, 265437053140964693655449372224981644676241031168000000⟩, + ⟨6, 5, 6, 3, 6, 8, -149970055261939295838517351366474855050765139968000000⟩ +] + +def collectedFourData_17_13 : List CollectedFourTerm := [ + ⟨6, 5, 7, 3, 7, 8, -148214507036841760454040566976187362738576556032000000⟩, + ⟨6, 5, 8, 3, 8, 8, -335346223086663945627090401089468605696835584000000000⟩, + ⟨6, 5, 6, 4, 5, 8, 119316364384988896400656371910426367598035730432000000⟩, + ⟨6, 5, 7, 4, 6, 8, 48677399994404921230757937522180212030554767360000000⟩, + ⟨6, 5, 8, 4, 7, 8, -119123852325536144354388184413309129404027240448000000⟩, + ⟨6, 5, 6, 5, 4, 8, 134574672832766780415004856710784994143694225408000000⟩, + ⟨6, 5, 7, 5, 5, 8, 128919265894299395717099559303952219203119874048000000⟩, + ⟨6, 5, 8, 5, 6, 8, -248047125406193947465908892292501936078189494272000000⟩, + ⟨6, 5, 6, 6, 3, 8, -498301657003995368887212655935753799298489253888000000⟩, + ⟨6, 5, 7, 6, 4, 8, -46151238187546966147709767275222122392291639296000000⟩, + ⟨6, 5, 8, 6, 5, 8, 260314392206448415187277467298581613268250394624000000⟩, + ⟨6, 5, 6, 7, 2, 8, 491762706363155872162244313490159656252978757632000000⟩, + ⟨6, 5, 7, 7, 3, 8, -1933716742909710373457074421043351537119599263744000000⟩, + ⟨6, 5, 8, 7, 4, 8, -514699276919937827429684186525219483464299970560000000⟩, + ⟨7, 2, 8, 3, 8, 6, -633506141692596641263397443965852162994470912000000000⟩, + ⟨7, 2, 8, 4, 7, 6, -225038145280695065393246602786431675555448356864000000⟩, + ⟨7, 2, 8, 5, 6, 6, -468588481264653648495854763030518726789060100096000000⟩, + ⟨7, 2, 8, 6, 5, 6, 491762706363155872162244313490159656252978757632000000⟩, + ⟨7, 2, 8, 7, 4, 6, -972323916614542405115888640728508693081049006080000000⟩, + ⟨7, 3, 7, 2, 8, 7, -985884932248058707517407740428525745977639829504000000⟩, + ⟨7, 3, 7, 3, 7, 7, 550497556761962091644595816197976389539747332096000000⟩, + ⟨7, 3, 8, 3, 8, 7, 2491082420598308327858657676035417600377749504000000000⟩, + ⟨7, 3, 7, 4, 6, 7, -180797347723753949077992396086845721213487022080000000⟩, + ⟨7, 3, 8, 4, 7, 7, 884898394473353626602896148848117351328082034688000000⟩ +] + +def collectedFourData_17_14 : List CollectedFourTerm := [ + ⟨7, 3, 7, 5, 5, 7, -478831271737230001091591620639424561737466118144000000⟩, + ⟨7, 3, 8, 5, 6, 7, 1842590704889577902933838323504605574001309253632000000⟩, + ⟨7, 3, 7, 6, 4, 7, 171414690584024609089716674184986096377830309888000000⟩, + ⟨7, 3, 8, 6, 5, 7, -1933716742909710373457074421043351537119599263744000000⟩, + ⟨7, 3, 7, 7, 3, 7, 7182200742177618443621612620303085531839680479232000000⟩, + ⟨7, 3, 8, 7, 4, 7, 3823386793590241056438163913034581431551378063360000000⟩, + ⟨7, 4, 6, 1, 8, 8, -83631279088381718546994770119642498391888363520000000⟩, + ⟨7, 4, 6, 2, 7, 8, -111908217020227933131835530300623316684405473280000000⟩, + ⟨7, 4, 7, 2, 8, 8, -524827913514146957963112207017004245190621265920000000⟩, + ⟨7, 4, 6, 3, 6, 8, 296524054427794955108315840432957886744672337920000000⟩, + ⟨7, 4, 7, 3, 7, 8, 293052946301974631887771196869974284635817902080000000⟩, + ⟨7, 4, 8, 3, 8, 8, 663053844536001215731375010586904285371432960000000000⟩, + ⟨7, 4, 6, 4, 5, 8, -235914910248087043665360225088739656547256238080000000⟩, + ⟨7, 4, 7, 4, 6, 8, -96246013780110020160122925135114311983064678400000000⟩, + ⟨7, 4, 8, 4, 7, 8, 235534271217878843591643869128979659688635269120000000⟩, + ⟨7, 4, 6, 5, 4, 8, -266083969509567681902504596514334655703962091520000000⟩, + ⟨7, 4, 7, 5, 5, 8, -254901975931553534405755942770554994372504453120000000⟩, + ⟨7, 4, 8, 5, 6, 8, 490444170245438226241551010266205313545462087680000000⟩, + ⟨7, 4, 6, 6, 3, 8, 985252872013927663425077032299019070098605342720000000⟩, + ⟨7, 4, 7, 6, 4, 8, 91251231723106470849841481920933992308397834240000000⟩, + ⟨7, 4, 8, 6, 5, 8, -514699276919937827429684186525219483464299970560000000⟩, + ⟨7, 4, 6, 7, 2, 8, -972323916614542405115888640728508693081049006080000000⟩, + ⟨7, 4, 7, 7, 3, 8, 3823386793590241056438163913034581431551378063360000000⟩, + ⟨7, 4, 8, 7, 4, 8, 1017674602685085254263430324493530030938678886400000000⟩ +] + +def collectedFourData_17_15 : List CollectedFourTerm := [ + ⟨1, 8, 8, 4, 8, 5, -284831982742727614793043539913183596984559206400000000⟩, + ⟨1, 8, 8, 5, 7, 5, 466982673077256879551940452964781848271666544640000000⟩, + ⟨1, 8, 8, 6, 6, 5, -697549068831992969680696796867619787135348899840000000⟩, + ⟨1, 8, 8, 7, 5, 5, -1801843076973613601433144014642942923866793574400000000⟩, + ⟨2, 7, 8, 4, 8, 5, -146001575062481878786448121299741444918917201920000000⟩, + ⟨2, 7, 8, 5, 7, 5, 239369909023702662316729542872157224824725307392000000⟩, + ⟨2, 7, 8, 6, 6, 5, -357555572770167932227224348486608895864263933952000000⟩, + ⟨2, 7, 8, 7, 5, 5, -923603889985887349390184060472087160205680312320000000⟩, + ⟨2, 8, 7, 3, 8, 6, -91343720754644685708311622536035714204201648128000000⟩, + ⟨2, 8, 7, 4, 7, 6, -241611708708402269313186125532044726838321217536000000⟩, + ⟨2, 8, 8, 4, 8, 6, 258800897631737054325437575424593711994649968640000000⟩, + ⟨2, 8, 7, 5, 6, 6, 76542120953709870710200010677908239772895150080000000⟩, + ⟨2, 8, 8, 5, 7, 6, -424304650787843437514885504976046478275865739264000000⟩, + ⟨2, 8, 7, 6, 5, 6, 478211655600276320616666139117881326848979238912000000⟩, + ⟨2, 8, 8, 6, 6, 6, 633799348716261217860781292061654733255851638784000000⟩, + ⟨2, 8, 7, 7, 4, 6, 371852378051415043428163389683035741983332106240000000⟩, + ⟨2, 8, 8, 7, 5, 6, 1637170802316469918651783938345757553739631165440000000⟩, + ⟨3, 6, 8, 4, 8, 5, 99896464216022794592893975992975368599665377280000000⟩, + ⟨3, 6, 8, 5, 7, 5, -163780476621198318947874049219533459208198422528000000⟩, + ⟨3, 6, 8, 6, 6, 5, 244644877736344581017829403122013301632892141568000000⟩, + ⟨3, 6, 8, 7, 5, 5, 631943613664918513715688978855789784753640570880000000⟩, + ⟨3, 7, 7, 3, 8, 6, -193673123762893589039657587562166913339490304000000⟩, + ⟨3, 7, 7, 4, 7, 6, -512281457079436969250009519014573057819803648000000⟩, + ⟨3, 7, 8, 4, 8, 6, 548727135952918797440882260870599510872555520000000⟩ +] + +def collectedFourData_17_16 : List CollectedFourTerm := [ + ⟨3, 7, 7, 5, 6, 6, 162289772543433835065409626680938980641341440000000⟩, + ⟨3, 7, 8, 5, 7, 6, -899639367285427824577143184951711336079818752000000⟩, + ⟨3, 7, 7, 6, 5, 6, 1013936638389247395802085522301212823876796416000000⟩, + ⟨3, 7, 8, 6, 6, 6, 1343824169747586835675473181756984299054170112000000⟩, + ⟨3, 7, 7, 7, 4, 6, 788426517344554392233080670938287768411832320000000⟩, + ⟨3, 7, 8, 7, 5, 6, 3471240067718728805979173898238621996988497920000000⟩, + ⟨3, 8, 6, 2, 8, 7, -91343720754644685708311622536035714204201648128000000⟩, + ⟨3, 8, 6, 3, 7, 7, -193673123762893589039657587562166913339490304000000⟩, + ⟨3, 8, 7, 3, 8, 7, 30997296017297419587930681959851815465557950464000000⟩, + ⟨3, 8, 6, 4, 6, 7, -39139170447564149301438423164908046488650645504000000⟩, + ⟨3, 8, 7, 4, 7, 7, 81990415916997362063669419293908935041318125568000000⟩, + ⟨3, 8, 8, 4, 8, 7, -43911765182968679797394718905792218567708508160000000⟩, + ⟨3, 8, 6, 5, 5, 7, -32696130807482299336259882444119704352893960192000000⟩, + ⟨3, 8, 7, 5, 6, 7, -25974404823807063891090985819700593175864279040000000⟩, + ⟨3, 8, 8, 5, 7, 7, 71993437279146623954711074811003587714577596416000000⟩, + ⟨3, 8, 6, 6, 4, 7, 21800415397802148815772257099732503788961923072000000⟩, + ⟨3, 8, 7, 6, 5, 7, -162280101194694440821103978816496253733286445056000000⟩, + ⟨3, 8, 8, 6, 6, 7, -107539225824284645434237952804507922041243959296000000⟩, + ⟨3, 8, 6, 7, 3, 7, 110052651009786339747149844314161098572351668224000000⟩, + ⟨3, 8, 7, 7, 4, 7, -126187308136444633948733994147021298137688965120000000⟩, + ⟨3, 8, 8, 7, 5, 7, -277785202808806560057875384437003332999299727360000000⟩, + ⟨4, 5, 8, 4, 8, 5, 60572404579639660341540370300285369483127685120000000⟩, + ⟨4, 5, 8, 5, 7, 5, -99308592851620049572761773328923374950612467712000000⟩, + ⟨4, 5, 8, 6, 6, 5, 148340871009581818353262879652450196793036111872000000⟩ +] + +def collectedFourData_17_17 : List CollectedFourTerm := [ + ⟨4, 5, 8, 7, 5, 5, 383180170978377123060865059259318472483033579520000000⟩, + ⟨4, 6, 7, 3, 8, 6, -39139170447564149301438423164908046488650645504000000⟩, + ⟨4, 6, 7, 4, 7, 6, -103526348293454297087249752830665218436049666048000000⟩, + ⟨4, 6, 8, 4, 8, 6, 110891612041937769060242225984501808100823531520000000⟩, + ⟨4, 6, 7, 5, 6, 6, 32796946453191096907579206847578334891018813440000000⟩, + ⟨4, 6, 8, 5, 7, 6, -181807046085706462971729783812028535205215076352000000⟩, + ⟨4, 6, 7, 6, 5, 6, 204905245198251236338321784651907483199095177216000000⟩, + ⟨4, 6, 8, 6, 6, 6, 271571822715569971376627774833914279431044595712000000⟩, + ⟨4, 6, 7, 7, 4, 6, 159332173964966798249253645249594353049214648320000000⟩, + ⟨4, 6, 8, 7, 5, 6, 701498762632585514300114144154545574096320593920000000⟩, + ⟨4, 7, 6, 2, 8, 7, -241611708708402269313186125532044726838321217536000000⟩, + ⟨4, 7, 6, 3, 7, 7, -512281457079436969250009519014573057819803648000000⟩, + ⟨4, 7, 7, 3, 8, 7, 81990415916997362063669419293908935041318125568000000⟩, + ⟨4, 7, 6, 4, 6, 7, -103526348293454297087249752830665218436049666048000000⟩, + ⟨4, 7, 7, 4, 7, 7, 216871442544243150807980519433117664856890146816000000⟩, + ⟨4, 7, 8, 4, 8, 7, -116150256751170363333021049243038186192418897920000000⟩, + ⟨4, 7, 6, 5, 5, 7, -86483974675922536284542716006235063530819682304000000⟩, + ⟨4, 7, 7, 5, 6, 7, -68704452591993637410314329647965069988310548480000000⟩, + ⟨4, 7, 8, 5, 7, 7, 190428605853799993321080103893630947510810836992000000⟩, + ⟨4, 7, 6, 6, 4, 7, 57663904768715146156966527853605838313817636864000000⟩, + ⟨4, 7, 7, 6, 5, 7, -429244311651590472527195376007588902766664220672000000⟩, + ⟨4, 7, 8, 6, 6, 7, -284450161323902180507782754890422668212989591552000000⟩, + ⟨4, 7, 6, 7, 3, 7, 291098379162662798572636553675152086363367538688000000⟩, + ⟨4, 7, 7, 7, 4, 7, -333775883928067123544540819638590676227525181440000000⟩ +] + +def collectedFourData_17_18 : List CollectedFourTerm := [ + ⟨4, 7, 8, 7, 5, 7, -734764874367492486423879169875586062676729528320000000⟩, + ⟨4, 8, 5, 1, 8, 8, -284831982742727614793043539913183596984559206400000000⟩, + ⟨4, 8, 5, 2, 7, 8, -146001575062481878786448121299741444918917201920000000⟩, + ⟨4, 8, 6, 2, 8, 8, 258800897631737054325437575424593711994649968640000000⟩, + ⟨4, 8, 5, 3, 6, 8, 99896464216022794592893975992975368599665377280000000⟩, + ⟨4, 8, 6, 3, 7, 8, 548727135952918797440882260870599510872555520000000⟩, + ⟨4, 8, 7, 3, 8, 8, -43911765182968679797394718905792218567708508160000000⟩, + ⟨4, 8, 5, 4, 5, 8, 60572404579639660341540370300285369483127685120000000⟩, + ⟨4, 8, 6, 4, 6, 8, 110891612041937769060242225984501808100823531520000000⟩, + ⟨4, 8, 7, 4, 7, 8, -116150256751170363333021049243038186192418897920000000⟩, + ⟨4, 8, 8, 4, 8, 8, 41471211347126600064038393970673866363214233600000000⟩, + ⟨4, 8, 5, 5, 4, 8, 40179895024708121104367027080575818864724541440000000⟩, + ⟨4, 8, 6, 5, 5, 8, 92636778227920412625685224918917732642020392960000000⟩, + ⟨4, 8, 7, 5, 6, 8, 36796176181106437652646009375510409560824217600000000⟩, + ⟨4, 8, 8, 5, 7, 8, -67992143804038846153818710323170034515821199360000000⟩, + ⟨4, 8, 5, 6, 3, 8, -366141437779085771559182939372869092719921725440000000⟩, + ⟨4, 8, 6, 6, 4, 8, -61766337380219459957165479411654790716179087360000000⟩, + ⟨4, 8, 7, 6, 5, 8, 229891203850596929246515681188443704789712240640000000⟩, + ⟨4, 8, 8, 6, 6, 8, 101562347668843523339905054678973172251004764160000000⟩, + ⟨4, 8, 5, 7, 2, 8, 20284132857479962010701045204110843352260280320000000⟩, + ⟨4, 8, 6, 7, 3, 8, -311808240706428052912372869167128637825215365120000000⟩, + ⟨4, 8, 7, 7, 4, 8, 178760993890124027628318302866692705052576972800000000⟩, + ⟨4, 8, 8, 7, 5, 8, 262346293909782206728710789829304417145952665600000000⟩, + ⟨5, 4, 8, 4, 8, 5, 40179895024708121104367027080575818864724541440000000⟩ +] + +def collectedFourData_17_19 : List CollectedFourTerm := [ + ⟨5, 4, 8, 5, 7, 5, -65875027803846024823443210740641848339720044544000000⟩, + ⟨5, 4, 8, 6, 6, 5, 98399934201096942149125494540279759142297534464000000⟩, + ⟨5, 4, 8, 7, 5, 5, 254177445196488720245282464940107100131153674240000000⟩, + ⟨5, 5, 7, 3, 8, 6, -32696130807482299336259882444119704352893960192000000⟩, + ⟨5, 5, 7, 4, 7, 6, -86483974675922536284542716006235063530819682304000000⟩, + ⟨5, 5, 8, 4, 8, 6, 92636778227920412625685224918917732642020392960000000⟩, + ⟨5, 5, 7, 5, 6, 6, 27397955527855754072974593734154671096982405120000000⟩, + ⟨5, 5, 8, 5, 7, 6, -151878205198653460377898826472689161543033552896000000⟩, + ⟨5, 5, 7, 6, 5, 6, 171174008634570104007675226193116861148449210368000000⟩, + ⟨5, 5, 8, 6, 6, 6, 226866020347329063119604259628578556359974322176000000⟩, + ⟨5, 5, 7, 7, 4, 6, 133103117470986138245813244902371486269293199360000000⟩, + ⟨5, 5, 8, 7, 5, 6, 586018943223397998615368123600491876205104988160000000⟩, + ⟨5, 6, 6, 2, 8, 7, 76542120953709870710200010677908239772895150080000000⟩, + ⟨5, 6, 6, 3, 7, 7, 162289772543433835065409626680938980641341440000000⟩, + ⟨5, 6, 7, 3, 8, 7, -25974404823807063891090985819700593175864279040000000⟩, + ⟨5, 6, 6, 4, 6, 7, 32796946453191096907579206847578334891018813440000000⟩, + ⟨5, 6, 7, 4, 7, 7, -68704452591993637410314329647965069988310548480000000⟩, + ⟨5, 6, 8, 4, 8, 7, 36796176181106437652646009375510409560824217600000000⟩, + ⟨5, 6, 6, 5, 5, 7, 27397955527855754072974593734154671096982405120000000⟩, + ⟨5, 6, 7, 5, 6, 7, 21765437397330585435698390587837352555996774400000000⟩, + ⟨5, 6, 8, 5, 7, 7, -60327413187989326282841679603421117515835637760000000⟩, + ⟨5, 6, 6, 6, 4, 7, -18267813249055140008200801926702610113280081920000000⟩, + ⟨5, 6, 7, 6, 5, 7, 135983765839678451330592420578292254162194268160000000⟩, + ⟨5, 6, 8, 6, 6, 7, 90113259699815409946296702979085372974757314560000000⟩ +] + +def collectedFourData_17_20 : List CollectedFourTerm := [ + ⟨5, 6, 6, 7, 3, 7, -92219402223542077659547044656091402982800752640000000⟩, + ⟨5, 6, 7, 7, 4, 7, 105739553002735285254972373428829193988420403200000000⟩, + ⟨5, 6, 8, 7, 5, 7, 232772087855435267486349906369423281130936729600000000⟩, + ⟨5, 7, 5, 1, 8, 8, 466982673077256879551940452964781848271666544640000000⟩, + ⟨5, 7, 5, 2, 7, 8, 239369909023702662316729542872157224824725307392000000⟩, + ⟨5, 7, 6, 2, 8, 8, -424304650787843437514885504976046478275865739264000000⟩, + ⟨5, 7, 5, 3, 6, 8, -163780476621198318947874049219533459208198422528000000⟩, + ⟨5, 7, 6, 3, 7, 8, -899639367285427824577143184951711336079818752000000⟩, + ⟨5, 7, 7, 3, 8, 8, 71993437279146623954711074811003587714577596416000000⟩, + ⟨5, 7, 5, 4, 5, 8, -99308592851620049572761773328923374950612467712000000⟩, + ⟨5, 7, 6, 4, 6, 8, -181807046085706462971729783812028535205215076352000000⟩, + ⟨5, 7, 7, 4, 7, 8, 190428605853799993321080103893630947510810836992000000⟩, + ⟨5, 7, 8, 4, 8, 8, -67992143804038846153818710323170034515821199360000000⟩, + ⟨5, 7, 5, 5, 4, 8, -65875027803846024823443210740641848339720044544000000⟩, + ⟨5, 7, 6, 5, 5, 8, -151878205198653460377898826472689161543033552896000000⟩, + ⟨5, 7, 7, 5, 6, 8, -60327413187989326282841679603421117515835637760000000⟩, + ⟨5, 7, 8, 5, 7, 8, 111473271913225784019599014797622216476680257536000000⟩, + ⟨5, 7, 5, 6, 3, 8, 600289706556112298236264906795090606144245202944000000⟩, + ⟨5, 7, 6, 6, 4, 8, 101266048349842556213951243063439906984570126336000000⟩, + ⟨5, 7, 7, 6, 5, 8, -376907143142236675818842004525945258988183486464000000⟩, + ⟨5, 7, 8, 6, 6, 8, -166511696269857162329531376096280600111812182016000000⟩, + ⟨5, 7, 5, 7, 2, 8, -33255881209786856673615144023237869483937759232000000⟩, + ⟨5, 7, 6, 7, 3, 8, 511210308373708185377665040386654496363970035712000000⟩, + ⟨5, 7, 7, 7, 4, 8, -293079049497606627326641608989885795684088545280000000⟩ +] + +def collectedFourData_17_21 : List CollectedFourTerm := [ + ⟨5, 7, 8, 7, 5, 8, -430117335919256949126766173683901471612532162560000000⟩, + ⟨6, 3, 8, 4, 8, 5, -366141437779085771559182939372869092719921725440000000⟩, + ⟨6, 3, 8, 5, 7, 5, 600289706556112298236264906795090606144245202944000000⟩, + ⟨6, 3, 8, 6, 6, 5, -896674651927336399017079135975575120873850404864000000⟩, + ⟨6, 3, 8, 7, 5, 5, -2316205534584599375822799296760391367424988938240000000⟩, + ⟨6, 4, 7, 3, 8, 6, 21800415397802148815772257099732503788961923072000000⟩, + ⟨6, 4, 7, 4, 7, 6, 57663904768715146156966527853605838313817636864000000⟩, + ⟨6, 4, 8, 4, 8, 6, -61766337380219459957165479411654790716179087360000000⟩, + ⟨6, 4, 7, 5, 6, 6, -18267813249055140008200801926702610113280081920000000⟩, + ⟨6, 4, 8, 5, 7, 6, 101266048349842556213951243063439906984570126336000000⟩, + ⟨6, 4, 7, 6, 5, 6, -114131684740098747134476288498861319563549605888000000⟩, + ⟨6, 4, 8, 6, 6, 6, -151264793756152934129368886553088513422252834816000000⟩, + ⟨6, 4, 7, 7, 4, 6, -88747603460955027821578990606513403118495989760000000⟩, + ⟨6, 4, 8, 7, 5, 6, -390732972915790019934026808665707631407068610560000000⟩, + ⟨6, 5, 6, 2, 8, 7, 478211655600276320616666139117881326848979238912000000⟩, + ⟨6, 5, 6, 3, 7, 7, 1013936638389247395802085522301212823876796416000000⟩, + ⟨6, 5, 7, 3, 8, 7, -162280101194694440821103978816496253733286445056000000⟩, + ⟨6, 5, 6, 4, 6, 7, 204905245198251236338321784651907483199095177216000000⟩, + ⟨6, 5, 7, 4, 7, 7, -429244311651590472527195376007588902766664220672000000⟩, + ⟨6, 5, 8, 4, 8, 7, 229891203850596929246515681188443704789712240640000000⟩, + ⟨6, 5, 6, 5, 5, 7, 171174008634570104007675226193116861148449210368000000⟩, + ⟨6, 5, 7, 5, 6, 7, 135983765839678451330592420578292254162194268160000000⟩, + ⟨6, 5, 8, 5, 7, 7, -376907143142236675818842004525945258988183486464000000⟩, + ⟨6, 5, 6, 6, 4, 7, -114131684740098747134476288498861319563549605888000000⟩ +] + +def collectedFourData_17_22 : List CollectedFourTerm := [ + ⟨6, 5, 7, 6, 5, 7, 849584790527039632160498060539275127797552513024000000⟩, + ⟨6, 5, 8, 6, 6, 7, 562999961010326945886718891724223721367597481984000000⟩, + ⟨6, 5, 6, 7, 3, 7, -576158492426128503569276498003621275218368004096000000⟩, + ⟨6, 5, 7, 7, 4, 7, 660628240683999033454609196634559105362013716480000000⟩, + ⟨6, 5, 8, 7, 5, 7, 1454288490100762620382147906633889484929174077440000000⟩, + ⟨6, 6, 5, 1, 8, 8, -697549068831992969680696796867619787135348899840000000⟩, + ⟨6, 6, 5, 2, 7, 8, -357555572770167932227224348486608895864263933952000000⟩, + ⟨6, 6, 6, 2, 8, 8, 633799348716261217860781292061654733255851638784000000⟩, + ⟨6, 6, 5, 3, 6, 8, 244644877736344581017829403122013301632892141568000000⟩, + ⟨6, 6, 6, 3, 7, 8, 1343824169747586835675473181756984299054170112000000⟩, + ⟨6, 6, 7, 3, 8, 8, -107539225824284645434237952804507922041243959296000000⟩, + ⟨6, 6, 5, 4, 5, 8, 148340871009581818353262879652450196793036111872000000⟩, + ⟨6, 6, 6, 4, 6, 8, 271571822715569971376627774833914279431044595712000000⟩, + ⟨6, 6, 7, 4, 7, 8, -284450161323902180507782754890422668212989591552000000⟩, + ⟨6, 6, 8, 4, 8, 8, 101562347668843523339905054678973172251004764160000000⟩, + ⟨6, 6, 5, 5, 4, 8, 98399934201096942149125494540279759142297534464000000⟩, + ⟨6, 6, 6, 5, 5, 8, 226866020347329063119604259628578556359974322176000000⟩, + ⟨6, 6, 7, 5, 6, 8, 90113259699815409946296702979085372974757314560000000⟩, + ⟨6, 6, 8, 5, 7, 8, -166511696269857162329531376096280600111812182016000000⟩, + ⟨6, 6, 5, 6, 3, 8, -896674651927336399017079135975575120873850404864000000⟩, + ⟨6, 6, 6, 6, 4, 8, -151264793756152934129368886553088513422252834816000000⟩, + ⟨6, 6, 7, 6, 5, 8, 562999961010326945886718891724223721367597481984000000⟩, + ⟨6, 6, 8, 6, 6, 8, 248724600245411705584745910456048922415276752896000000⟩, + ⟨6, 6, 5, 7, 2, 8, 49675523972249004078584522970491768149735636992000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1702.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1702.lean new file mode 100644 index 0000000000000000000000000000000000000000..8e6a7a234ef437ece0f343c9dcf3b4ea248493bc --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1702.lean @@ -0,0 +1,630 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1702. -/ +namespace LaughlinFock +def collectedFourData_17_23 : List CollectedFourTerm := [ + ⟨6, 6, 6, 7, 3, 8, -763613502474430623305985619216207031007939919872000000⟩, + ⟨6, 6, 7, 7, 4, 8, 437782876876460341123374353807396336177963335680000000⟩, + ⟨6, 6, 8, 7, 5, 8, 642481968724649138462697935850843495875330703360000000⟩, + ⟨7, 2, 8, 4, 8, 5, 20284132857479962010701045204110843352260280320000000⟩, + ⟨7, 2, 8, 5, 7, 5, -33255881209786856673615144023237869483937759232000000⟩, + ⟨7, 2, 8, 6, 6, 5, 49675523972249004078584522970491768149735636992000000⟩, + ⟨7, 2, 8, 7, 5, 5, 128317136333231678299346325453347313024730398720000000⟩, + ⟨7, 3, 7, 3, 8, 6, 110052651009786339747149844314161098572351668224000000⟩, + ⟨7, 3, 7, 4, 7, 6, 291098379162662798572636553675152086363367538688000000⟩, + ⟨7, 3, 8, 4, 8, 6, -311808240706428052912372869167128637825215365120000000⟩, + ⟨7, 3, 7, 5, 6, 6, -92219402223542077659547044656091402982800752640000000⟩, + ⟨7, 3, 8, 5, 7, 6, 511210308373708185377665040386654496363970035712000000⟩, + ⟨7, 3, 7, 6, 5, 6, -576158492426128503569276498003621275218368004096000000⟩, + ⟨7, 3, 8, 6, 6, 6, -763613502474430623305985619216207031007939919872000000⟩, + ⟨7, 3, 7, 7, 4, 6, -448014813177736965986988504050511066580301905920000000⟩, + ⟨7, 3, 8, 7, 5, 6, -1972494501671421657994258245080143882591162859520000000⟩, + ⟨7, 4, 6, 2, 8, 7, 371852378051415043428163389683035741983332106240000000⟩, + ⟨7, 4, 6, 3, 7, 7, 788426517344554392233080670938287768411832320000000⟩, + ⟨7, 4, 7, 3, 8, 7, -126187308136444633948733994147021298137688965120000000⟩, + ⟨7, 4, 6, 4, 6, 7, 159332173964966798249253645249594353049214648320000000⟩, + ⟨7, 4, 7, 4, 7, 7, -333775883928067123544540819638590676227525181440000000⟩, + ⟨7, 4, 8, 4, 8, 7, 178760993890124027628318302866692705052576972800000000⟩, + ⟨7, 4, 6, 5, 5, 7, 133103117470986138245813244902371486269293199360000000⟩, + ⟨7, 4, 7, 5, 6, 7, 105739553002735285254972373428829193988420403200000000⟩ +] + +def collectedFourData_17_24 : List CollectedFourTerm := [ + ⟨7, 4, 8, 5, 7, 7, -293079049497606627326641608989885795684088545280000000⟩, + ⟨7, 4, 6, 6, 4, 7, -88747603460955027821578990606513403118495989760000000⟩, + ⟨7, 4, 7, 6, 5, 7, 660628240683999033454609196634559105362013716480000000⟩, + ⟨7, 4, 8, 6, 6, 7, 437782876876460341123374353807396336177963335680000000⟩, + ⟨7, 4, 6, 7, 3, 7, -448014813177736965986988504050511066580301905920000000⟩, + ⟨7, 4, 7, 7, 4, 7, 513697605295519425196883040043157198869207449600000000⟩, + ⟨7, 4, 8, 7, 5, 7, 1130839508162874379776986437129529301347912908800000000⟩, + ⟨7, 5, 5, 1, 8, 8, -1801843076973613601433144014642942923866793574400000000⟩, + ⟨7, 5, 5, 2, 7, 8, -923603889985887349390184060472087160205680312320000000⟩, + ⟨7, 5, 6, 2, 8, 8, 1637170802316469918651783938345757553739631165440000000⟩, + ⟨7, 5, 5, 3, 6, 8, 631943613664918513715688978855789784753640570880000000⟩, + ⟨7, 5, 6, 3, 7, 8, 3471240067718728805979173898238621996988497920000000⟩, + ⟨7, 5, 7, 3, 8, 8, -277785202808806560057875384437003332999299727360000000⟩, + ⟨7, 5, 5, 4, 5, 8, 383180170978377123060865059259318472483033579520000000⟩, + ⟨7, 5, 6, 4, 6, 8, 701498762632585514300114144154545574096320593920000000⟩, + ⟨7, 5, 7, 4, 7, 8, -734764874367492486423879169875586062676729528320000000⟩, + ⟨7, 5, 8, 4, 8, 8, 262346293909782206728710789829304417145952665600000000⟩, + ⟨7, 5, 5, 5, 4, 8, 254177445196488720245282464940107100131153674240000000⟩, + ⟨7, 5, 6, 5, 5, 8, 586018943223397998615368123600491876205104988160000000⟩, + ⟨7, 5, 7, 5, 6, 8, 232772087855435267486349906369423281130936729600000000⟩, + ⟨7, 5, 8, 5, 7, 8, -430117335919256949126766173683901471612532162560000000⟩, + ⟨7, 5, 5, 6, 3, 8, -2316205534584599375822799296760391367424988938240000000⟩, + ⟨7, 5, 6, 6, 4, 8, -390732972915790019934026808665707631407068610560000000⟩, + ⟨7, 5, 7, 6, 5, 8, 1454288490100762620382147906633889484929174077440000000⟩ +] + +def collectedFourData_17_25 : List CollectedFourTerm := [ + ⟨7, 5, 8, 6, 6, 8, 642481968724649138462697935850843495875330703360000000⟩, + ⟨7, 5, 5, 7, 2, 8, 128317136333231678299346325453347313024730398720000000⟩, + ⟨7, 5, 6, 7, 3, 8, -1972494501671421657994258245080143882591162859520000000⟩, + ⟨7, 5, 7, 7, 4, 8, 1130839508162874379776986437129529301347912908800000000⟩, + ⟨7, 5, 8, 7, 5, 8, 1659598928811287785755644022895597868566550937600000000⟩, + ⟨1, 8, 8, 5, 8, 4, 1182669837190237277079191878037254165544445149184000000⟩, + ⟨1, 8, 8, 6, 7, 4, 318797571889500717065668018079604063379365298176000000⟩, + ⟨1, 8, 8, 7, 6, 4, 476624053769258846979074179234291578453796847616000000⟩, + ⟨2, 7, 8, 5, 8, 4, -160359973448922670194963388892585059463158824960000000⟩, + ⟨2, 7, 8, 6, 7, 4, -43226239949804443190525069075019424989645373440000000⟩, + ⟨2, 7, 8, 7, 6, 4, -64626168863104211760024750262969232994116567040000000⟩, + ⟨2, 8, 7, 4, 8, 5, 726492550039405164599082289191614844301108838400000000⟩, + ⟨2, 8, 7, 5, 7, 5, 331379364789394805316052638324977106009005752320000000⟩, + ⟨2, 8, 8, 5, 8, 5, 2000415723976104168507026777611789054190121123840000000⟩, + ⟨2, 8, 7, 6, 6, 5, 100184777781284173991552979985477938119851376640000000⟩, + ⟨2, 8, 8, 6, 7, 5, 539227141438104156836474480036118773825808629760000000⟩, + ⟨2, 8, 7, 7, 5, 5, -359917489040637327106591453816666351664753541120000000⟩, + ⟨2, 8, 8, 7, 6, 5, 806181253299260231990460689249988564821905244160000000⟩, + ⟨3, 6, 8, 5, 8, 4, -130601550080409287212232559262168439339284955136000000⟩, + ⟨3, 6, 8, 6, 7, 4, -35204632553710993525508724325181244533379170304000000⟩, + ⟨3, 6, 8, 7, 6, 4, -52633320196751351392251328470902742621370712064000000⟩, + ⟨3, 7, 7, 4, 8, 5, -57232205859135073952149050098222889169217126400000000⟩, + ⟨3, 7, 7, 5, 7, 5, -26105666220620379829007260921784508372190494720000000⟩, + ⟨3, 7, 8, 5, 8, 5, -157590335251533201168806908051002196088208752640000000⟩ +] + +def collectedFourData_17_26 : List CollectedFourTerm := [ + ⟨3, 7, 7, 6, 6, 5, -7892435821426048683517043075217798257379901440000000⟩, + ⟨3, 7, 8, 6, 7, 5, -42479663090756545040474244149623019558362152960000000⟩, + ⟨3, 7, 7, 7, 5, 5, 28353865189614757473286250698414273924190699520000000⟩, + ⟨3, 7, 8, 7, 6, 5, -63509985678581503937475870809314293357855375360000000⟩, + ⟨3, 8, 6, 3, 8, 6, 289609818337143688263017992247522508123836252160000000⟩, + ⟨3, 8, 6, 4, 7, 6, -126373109170377575909011435405271249610677944320000000⟩, + ⟨3, 8, 7, 4, 8, 6, 741664965824449401847948277505147636429304627200000000⟩, + ⟨3, 8, 6, 5, 6, 6, -214036018851290988607816650463691749213895393280000000⟩, + ⟨3, 8, 7, 5, 7, 6, 338300048979337063576733466204166899506935234560000000⟩, + ⟨3, 8, 8, 5, 8, 6, 1021096678470381795847764994896719414327362191360000000⟩, + ⟨3, 8, 6, 6, 5, 6, 20358597155835633993044750209303007281104814080000000⟩, + ⟨3, 8, 7, 6, 6, 6, 102277084307686210041231415023404049383943045120000000⟩, + ⟨3, 8, 8, 6, 7, 6, 275244308702556529166426150422435807200584663040000000⟩, + ⟨3, 8, 6, 7, 4, 6, 706517443551638868888309718569656975263531008000000000⟩, + ⟨3, 8, 7, 7, 5, 6, -367434176984288580959265722546613755264850984960000000⟩, + ⟨3, 8, 8, 7, 6, 6, 411508962923347575768476194394479698895322480640000000⟩, + ⟨4, 5, 8, 5, 8, 4, 337721423057108296001523925544119373359227076608000000⟩, + ⟨4, 5, 8, 6, 7, 4, 91035355988667739046896351322500961211317747712000000⟩, + ⟨4, 5, 8, 7, 6, 4, 136104049194847044435896265365516970422270164992000000⟩, + ⟨4, 6, 7, 4, 8, 5, -140161167017022573629807145369811467613765632000000000⟩, + ⟨4, 6, 7, 5, 7, 5, -63932546165438230947412214151196983011416473600000000⟩, + ⟨4, 6, 8, 5, 8, 5, -385937340137190587721895727853312684665811763200000000⟩, + ⟨4, 6, 7, 6, 6, 5, -19328505667957944502465596978402241562227507200000000⟩, + ⟨4, 6, 8, 6, 7, 5, -104032319983347881427694791903563779517762764800000000⟩ +] + +def collectedFourData_17_27 : List CollectedFourTerm := [ + ⟨4, 6, 7, 7, 5, 5, 69438365597879744152908990432174560329177497600000000⟩, + ⟨4, 6, 8, 7, 6, 5, -155535394387101830953288698908008167838108876800000000⟩, + ⟨4, 7, 6, 3, 8, 6, -126373109170377575909011435405271249610677944320000000⟩, + ⟨4, 7, 6, 4, 7, 6, 55143719964620853560371272319431029220326768640000000⟩, + ⟨4, 7, 7, 4, 8, 6, -323630283780184519266769096391589675741374054400000000⟩, + ⟨4, 7, 6, 5, 6, 6, 93395995108146916080712317402426843389818306560000000⟩, + ⟨4, 7, 7, 5, 7, 6, -147619404851257125362294441092112112738757509120000000⟩, + ⟨4, 7, 8, 5, 8, 6, -445562110990412056248896109776876008687502622720000000⟩, + ⟨4, 7, 6, 6, 5, 6, -8883604967892019631253435182367044928704348160000000⟩, + ⟨4, 7, 7, 6, 6, 6, -44629264349721271767769802637542171200444170240000000⟩, + ⟨4, 7, 8, 6, 7, 6, -120104626534797816043341386866936665132320686080000000⟩, + ⟨4, 7, 6, 7, 4, 6, -308293436104393909604627733556751600782934016000000000⟩, + ⟨4, 7, 7, 7, 5, 6, 160332269215086913659028103197236075740182609920000000⟩, + ⟨4, 7, 8, 7, 6, 6, -179564585878652755621137807664838981971114721280000000⟩, + ⟨4, 8, 5, 2, 8, 7, 726492550039405164599082289191614844301108838400000000⟩, + ⟨4, 8, 5, 3, 7, 7, -57232205859135073952149050098222889169217126400000000⟩, + ⟨4, 8, 6, 3, 8, 7, 741664965824449401847948277505147636429304627200000000⟩, + ⟨4, 8, 5, 4, 6, 7, -140161167017022573629807145369811467613765632000000000⟩, + ⟨4, 8, 6, 4, 7, 7, -323630283780184519266769096391589675741374054400000000⟩, + ⟨4, 8, 7, 4, 8, 7, 949668979956735952487963770584004142051622912000000000⟩, + ⟨4, 8, 5, 5, 5, 7, -38572538254358605766158138995740746161586176000000000⟩, + ⟨4, 8, 6, 5, 6, 7, -548127192365233680424560510941206735243286937600000000⟩, + ⟨4, 8, 7, 5, 7, 7, 433178156226359389992658355418950704140229017600000000⟩, + ⟨4, 8, 8, 5, 8, 7, 871645901014291318173939112471856672827401830400000000⟩ +] + +def collectedFourData_17_28 : List CollectedFourTerm := [ + ⟨4, 8, 5, 6, 4, 7, 321658154613728070706051520952785484376335974400000000⟩, + ⟨4, 8, 6, 6, 5, 7, 52136555143441503714519390938053315032357273600000000⟩, + ⟨4, 8, 7, 6, 6, 7, 130961254478912214350917347408587921718194995200000000⟩, + ⟨4, 8, 8, 6, 7, 7, 234958724787443999444994541774024828901759385600000000⟩, + ⟨4, 8, 5, 7, 3, 7, 448454694289580270794085364320054652877720780800000000⟩, + ⟨4, 8, 6, 7, 4, 7, 1809328283946851519341583350129312920879759360000000000⟩, + ⟨4, 8, 7, 7, 5, 7, -470483110483751384962276218096652046860655001600000000⟩, + ⟨4, 8, 8, 7, 6, 7, 351279274848000750219208191152952316977060249600000000⟩, + ⟨5, 4, 8, 5, 8, 4, 47162353729053631012820928738062149104917544960000000⟩, + ⟨5, 4, 8, 6, 7, 4, 12712968049592319763175173518217986656635453440000000⟩, + ⟨5, 4, 8, 7, 6, 4, 19006751937671570618897882617799054436901847040000000⟩, + ⟨5, 5, 7, 4, 8, 5, -38572538254358605766158138995740746161586176000000000⟩, + ⟨5, 5, 7, 5, 7, 5, -17594321131511505812916180173049757596175564800000000⟩, + ⟨5, 5, 8, 5, 8, 5, -106210465659287907017777366855866663617272217600000000⟩, + ⟨5, 5, 7, 6, 6, 5, -5319230284279439260093107525833274047437209600000000⟩, + ⟨5, 5, 8, 6, 7, 5, -28629831840369936193958462024929202779088486400000000⟩, + ⟨5, 5, 7, 7, 5, 5, 19109529910086019981557161923524202370747596800000000⟩, + ⟨5, 5, 8, 7, 6, 5, -42803545929198860307088090133738676260595302400000000⟩, + ⟨5, 6, 6, 3, 8, 6, -214036018851290988607816650463691749213895393280000000⟩, + ⟨5, 6, 6, 4, 7, 6, 93395995108146916080712317402426843389818306560000000⟩, + ⟨5, 6, 7, 4, 8, 6, -548127192365233680424560510941206735243286937600000000⟩, + ⟨5, 6, 6, 5, 6, 6, 158183232974441884632949989604922859083519754240000000⟩, + ⟨5, 6, 7, 5, 7, 6, -250020514071250216572673047967710217897487892480000000⟩, + ⟨5, 6, 8, 5, 8, 6, -754641086331039965784918168779106920463996026880000000⟩ +] + +def collectedFourData_17_29 : List CollectedFourTerm := [ + ⟨5, 6, 6, 6, 5, 6, -15046012975843265622670684401043721696198000640000000⟩, + ⟨5, 6, 7, 6, 6, 6, -75587837700485143817824678667888357656189992960000000⟩, + ⟨5, 6, 8, 6, 7, 6, -203419194778781456903320520095371321728638648320000000⟩, + ⟨5, 6, 6, 7, 4, 6, -522151430276249939929435894553095750878756864000000000⟩, + ⟨5, 6, 7, 7, 5, 6, 271552079564048862959923562094445538972459335680000000⟩, + ⟨5, 6, 8, 7, 6, 6, -304125532246986262664373822217521540728220549120000000⟩, + ⟨5, 7, 5, 2, 8, 7, 331379364789394805316052638324977106009005752320000000⟩, + ⟨5, 7, 5, 3, 7, 7, -26105666220620379829007260921784508372190494720000000⟩, + ⟨5, 7, 6, 3, 8, 7, 338300048979337063576733466204166899506935234560000000⟩, + ⟨5, 7, 5, 4, 6, 7, -63932546165438230947412214151196983011416473600000000⟩, + ⟨5, 7, 6, 4, 7, 7, -147619404851257125362294441092112112738757509120000000⟩, + ⟨5, 7, 7, 4, 8, 7, 433178156226359389992658355418950704140229017600000000⟩, + ⟨5, 7, 5, 5, 5, 7, -17594321131511505812916180173049757596175564800000000⟩, + ⟨5, 7, 6, 5, 6, 7, -250020514071250216572673047967710217897487892480000000⟩, + ⟨5, 7, 7, 5, 7, 7, 197588127012653066194430658036291192131923476480000000⟩, + ⟨5, 7, 8, 5, 8, 7, 397589025494794815542846590905544660106524753920000000⟩, + ⟨5, 7, 5, 6, 4, 7, 146719845853126271430241908612909661129141125120000000⟩, + ⟨5, 7, 6, 6, 5, 7, 23781356773450452852380119243020598875814625280000000⟩, + ⟨5, 7, 7, 6, 6, 7, 59736135379351519488574504841482336551787560960000000⟩, + ⟨5, 7, 8, 6, 7, 7, 107173119624648938400241769566342192674247802880000000⟩, + ⟨5, 7, 5, 7, 3, 7, 204556305116195304661556583217636276600402083840000000⟩, + ⟨5, 7, 6, 7, 4, 7, 825299663977658608664731814188043477742256128000000000⟩, + ⟨5, 7, 7, 7, 5, 7, -214604257521687832306641153094403881145393479680000000⟩, + ⟨5, 7, 8, 7, 6, 7, 160231103479995475594132328988174395002406830080000000⟩ +] + +def collectedFourData_17_30 : List CollectedFourTerm := [ + ⟨5, 8, 4, 1, 8, 8, 1182669837190237277079191878037254165544445149184000000⟩, + ⟨5, 8, 4, 2, 7, 8, -160359973448922670194963388892585059463158824960000000⟩, + ⟨5, 8, 5, 2, 8, 8, 2000415723976104168507026777611789054190121123840000000⟩, + ⟨5, 8, 4, 3, 6, 8, -130601550080409287212232559262168439339284955136000000⟩, + ⟨5, 8, 5, 3, 7, 8, -157590335251533201168806908051002196088208752640000000⟩, + ⟨5, 8, 6, 3, 8, 8, 1021096678470381795847764994896719414327362191360000000⟩, + ⟨5, 8, 4, 4, 5, 8, 337721423057108296001523925544119373359227076608000000⟩, + ⟨5, 8, 5, 4, 6, 8, -385937340137190587721895727853312684665811763200000000⟩, + ⟨5, 8, 6, 4, 7, 8, -445562110990412056248896109776876008687502622720000000⟩, + ⟨5, 8, 7, 4, 8, 8, 871645901014291318173939112471856672827401830400000000⟩, + ⟨5, 8, 4, 5, 4, 8, 47162353729053631012820928738062149104917544960000000⟩, + ⟨5, 8, 5, 5, 5, 8, -106210465659287907017777366855866663617272217600000000⟩, + ⟨5, 8, 6, 5, 6, 8, -754641086331039965784918168779106920463996026880000000⟩, + ⟨5, 8, 7, 5, 7, 8, 397589025494794815542846590905544660106524753920000000⟩, + ⟨5, 8, 8, 5, 8, 8, 600024792420008606827521478398627458070620405760000000⟩, + ⟨5, 8, 4, 6, 3, 8, -1178882739197779998113707497556812578751365775360000000⟩, + ⟨5, 8, 5, 6, 4, 8, 885693914135165701793744768578302070111013437440000000⟩, + ⟨5, 8, 6, 6, 5, 8, 71779665667067497173537038411541370935894343680000000⟩, + ⟨5, 8, 7, 6, 6, 8, 120201715616144210869635812376846147373592739840000000⟩, + ⟨5, 8, 8, 6, 7, 8, 161741206955488822505388610302176710609223024640000000⟩, + ⟨5, 8, 4, 7, 2, 8, 1211488076720453639035904304634813318917594808320000000⟩, + ⟨5, 8, 5, 7, 3, 8, 1234831412791658290475954744097671195574486958080000000⟩, + ⟨5, 8, 6, 7, 4, 8, 2491015736393763009388415799862773793809235968000000000⟩, + ⟨5, 8, 7, 7, 5, 8, -431829072450380046256118339443385482831693086720000000⟩ +] + +def collectedFourData_17_31 : List CollectedFourTerm := [ + ⟨5, 8, 8, 7, 6, 8, 241814105621162048325902247160005953467963146240000000⟩, + ⟨6, 3, 8, 5, 8, 4, -1178882739197779998113707497556812578751365775360000000⟩, + ⟨6, 3, 8, 6, 7, 4, -317776731071093355199611223999912968109204439040000000⟩, + ⟨6, 3, 8, 7, 6, 4, -475097827310761567150938573585336826340195696640000000⟩, + ⟨6, 4, 7, 4, 8, 5, 321658154613728070706051520952785484376335974400000000⟩, + ⟨6, 4, 7, 5, 7, 5, 146719845853126271430241908612909661129141125120000000⟩, + ⟨6, 4, 8, 5, 8, 5, 885693914135165701793744768578302070111013437440000000⟩, + ⟨6, 4, 7, 6, 6, 5, 44357303787583763495494264366220375274805002240000000⟩, + ⟨6, 4, 8, 6, 7, 5, 238745472645533002214559209169940948963200860160000000⟩, + ⟨6, 4, 7, 7, 5, 5, -159355240919867217199547849567974984150595665920000000⟩, + ⟨6, 4, 8, 7, 6, 5, 356940720460735919690483580569581720277939650560000000⟩, + ⟨6, 5, 6, 3, 8, 6, 20358597155835633993044750209303007281104814080000000⟩, + ⟨6, 5, 6, 4, 7, 6, -8883604967892019631253435182367044928704348160000000⟩, + ⟨6, 5, 7, 4, 8, 6, 52136555143441503714519390938053315032357273600000000⟩, + ⟨6, 5, 6, 5, 6, 6, -15046012975843265622670684401043721696198000640000000⟩, + ⟨6, 5, 7, 5, 7, 6, 23781356773450452852380119243020598875814625280000000⟩, + ⟨6, 5, 8, 5, 8, 6, 71779665667067497173537038411541370935894343680000000⟩, + ⟨6, 5, 6, 6, 5, 6, 1431140976274149029461216808302315289224151040000000⟩, + ⟨6, 5, 7, 6, 6, 6, 7189735381380088173052038886955297209382338560000000⟩, + ⟨6, 5, 8, 6, 7, 6, 19348750095856569427704037337269498879169003520000000⟩, + ⟨6, 5, 6, 7, 4, 6, 49665802421429463953272211914768717556219904000000000⟩, + ⟨6, 5, 7, 7, 5, 6, -25829388083110253218674208607332139117555220480000000⟩, + ⟨6, 5, 8, 7, 6, 6, 28927697445738337182908210682335220673617592320000000⟩, + ⟨6, 6, 5, 2, 8, 7, 100184777781284173991552979985477938119851376640000000⟩ +] + +def collectedFourData_17_32 : List CollectedFourTerm := [ + ⟨6, 6, 5, 3, 7, 7, -7892435821426048683517043075217798257379901440000000⟩, + ⟨6, 6, 6, 3, 8, 7, 102277084307686210041231415023404049383943045120000000⟩, + ⟨6, 6, 5, 4, 6, 7, -19328505667957944502465596978402241562227507200000000⟩, + ⟨6, 6, 6, 4, 7, 7, -44629264349721271767769802637542171200444170240000000⟩, + ⟨6, 6, 7, 4, 8, 7, 130961254478912214350917347408587921718194995200000000⟩, + ⟨6, 6, 5, 5, 5, 7, -5319230284279439260093107525833274047437209600000000⟩, + ⟨6, 6, 6, 5, 6, 7, -75587837700485143817824678667888357656189992960000000⟩, + ⟨6, 6, 7, 5, 7, 7, 59736135379351519488574504841482336551787560960000000⟩, + ⟨6, 6, 8, 5, 8, 7, 120201715616144210869635812376846147373592739840000000⟩, + ⟨6, 6, 5, 6, 4, 7, 44357303787583763495494264366220375274805002240000000⟩, + ⟨6, 6, 6, 6, 5, 7, 7189735381380088173052038886955297209382338560000000⟩, + ⟨6, 6, 7, 6, 6, 7, 18059819301954819461746907926633924498733137920000000⟩, + ⟨6, 6, 8, 6, 7, 7, 32401278759606282238281283382121979352721653760000000⟩, + ⟨6, 6, 5, 7, 3, 7, 61842800576466203979366775600819293730300231680000000⟩, + ⟨6, 6, 6, 7, 4, 7, 249509994356825229279461765226833563726381056000000000⟩, + ⟨6, 6, 7, 7, 5, 7, -64880563291537364975562173670670211403334287360000000⟩, + ⟨6, 6, 8, 7, 6, 7, 48442115597618630236282696538149157712596828160000000⟩, + ⟨6, 7, 4, 1, 8, 8, 318797571889500717065668018079604063379365298176000000⟩, + ⟨6, 7, 4, 2, 7, 8, -43226239949804443190525069075019424989645373440000000⟩, + ⟨6, 7, 5, 2, 8, 8, 539227141438104156836474480036118773825808629760000000⟩, + ⟨6, 7, 4, 3, 6, 8, -35204632553710993525508724325181244533379170304000000⟩, + ⟨6, 7, 5, 3, 7, 8, -42479663090756545040474244149623019558362152960000000⟩, + ⟨6, 7, 6, 3, 8, 8, 275244308702556529166426150422435807200584663040000000⟩, + ⟨6, 7, 4, 4, 5, 8, 91035355988667739046896351322500961211317747712000000⟩ +] + +def collectedFourData_17_33 : List CollectedFourTerm := [ + ⟨6, 7, 5, 4, 6, 8, -104032319983347881427694791903563779517762764800000000⟩, + ⟨6, 7, 6, 4, 7, 8, -120104626534797816043341386866936665132320686080000000⟩, + ⟨6, 7, 7, 4, 8, 8, 234958724787443999444994541774024828901759385600000000⟩, + ⟨6, 7, 4, 5, 4, 8, 12712968049592319763175173518217986656635453440000000⟩, + ⟨6, 7, 5, 5, 5, 8, -28629831840369936193958462024929202779088486400000000⟩, + ⟨6, 7, 6, 5, 6, 8, -203419194778781456903320520095371321728638648320000000⟩, + ⟨6, 7, 7, 5, 7, 8, 107173119624648938400241769566342192674247802880000000⟩, + ⟨6, 7, 8, 5, 8, 8, 161741206955488822505388610302176710609223024640000000⟩, + ⟨6, 7, 4, 6, 3, 8, -317776731071093355199611223999912968109204439040000000⟩, + ⟨6, 7, 5, 6, 4, 8, 238745472645533002214559209169940948963200860160000000⟩, + ⟨6, 7, 6, 6, 5, 8, 19348750095856569427704037337269498879169003520000000⟩, + ⟨6, 7, 7, 6, 6, 8, 32401278759606282238281283382121979352721653760000000⟩, + ⟨6, 7, 8, 6, 7, 8, 43598561855934937153808685369894035289758760960000000⟩, + ⟨6, 7, 4, 7, 2, 8, 326565745643039343755276513456090454172347924480000000⟩, + ⟨6, 7, 5, 7, 3, 8, 332858117888687134242259591730294565173848965120000000⟩, + ⟨6, 7, 6, 7, 4, 8, 671472073886271956825047606924762954441162752000000000⟩, + ⟨6, 7, 7, 7, 5, 8, -116402782449868380290846145323217013121828782080000000⟩, + ⟨6, 7, 8, 7, 6, 8, 65182815437151904153263516219411603328975503360000000⟩, + ⟨7, 2, 8, 5, 8, 4, 1211488076720453639035904304634813318917594808320000000⟩, + ⟨7, 2, 8, 6, 7, 4, 326565745643039343755276513456090454172347924480000000⟩, + ⟨7, 2, 8, 7, 6, 4, 488238001902084879513441176163493896991203655680000000⟩, + ⟨7, 3, 7, 4, 8, 5, 448454694289580270794085364320054652877720780800000000⟩, + ⟨7, 3, 7, 5, 7, 5, 204556305116195304661556583217636276600402083840000000⟩, + ⟨7, 3, 8, 5, 8, 5, 1234831412791658290475954744097671195574486958080000000⟩ +] + +def collectedFourData_17_34 : List CollectedFourTerm := [ + ⟨7, 3, 7, 6, 6, 5, 61842800576466203979366775600819293730300231680000000⟩, + ⟨7, 3, 8, 6, 7, 5, 332858117888687134242259591730294565173848965120000000⟩, + ⟨7, 3, 7, 7, 5, 5, -222172529516562317036127594113201449616214589440000000⟩, + ⟨7, 3, 8, 7, 6, 5, 497645526400374813923917378044399886473803857920000000⟩, + ⟨7, 4, 6, 3, 8, 6, 706517443551638868888309718569656975263531008000000000⟩, + ⟨7, 4, 6, 4, 7, 6, -308293436104393909604627733556751600782934016000000000⟩, + ⟨7, 4, 7, 4, 8, 6, 1809328283946851519341583350129312920879759360000000000⟩, + ⟨7, 4, 6, 5, 6, 6, -522151430276249939929435894553095750878756864000000000⟩, + ⟨7, 4, 7, 5, 7, 6, 825299663977658608664731814188043477742256128000000000⟩, + ⟨7, 4, 8, 5, 8, 6, 2491015736393763009388415799862773793809235968000000000⟩, + ⟨7, 4, 6, 6, 5, 6, 49665802421429463953272211914768717556219904000000000⟩, + ⟨7, 4, 7, 6, 6, 6, 249509994356825229279461765226833563726381056000000000⟩, + ⟨7, 4, 8, 6, 7, 6, 671472073886271956825047606924762954441162752000000000⟩, + ⟨7, 4, 6, 7, 4, 6, 1723584168895985742388491616755997517178470400000000000⟩, + ⟨7, 4, 7, 7, 5, 6, -896373806962004381475859324400800584746139648000000000⟩, + ⟨7, 4, 8, 7, 6, 6, 1003896422270920147597217247158923462686277632000000000⟩, + ⟨7, 5, 5, 2, 8, 7, -359917489040637327106591453816666351664753541120000000⟩, + ⟨7, 5, 5, 3, 7, 7, 28353865189614757473286250698414273924190699520000000⟩, + ⟨7, 5, 6, 3, 8, 7, -367434176984288580959265722546613755264850984960000000⟩, + ⟨7, 5, 5, 4, 6, 7, 69438365597879744152908990432174560329177497600000000⟩, + ⟨7, 5, 6, 4, 7, 7, 160332269215086913659028103197236075740182609920000000⟩, + ⟨7, 5, 7, 4, 8, 7, -470483110483751384962276218096652046860655001600000000⟩, + ⟨7, 5, 5, 5, 5, 7, 19109529910086019981557161923524202370747596800000000⟩, + ⟨7, 5, 6, 5, 6, 7, 271552079564048862959923562094445538972459335680000000⟩ +] + +def collectedFourData_17_35 : List CollectedFourTerm := [ + ⟨7, 5, 7, 5, 7, 7, -214604257521687832306641153094403881145393479680000000⟩, + ⟨7, 5, 8, 5, 8, 7, -431829072450380046256118339443385482831693086720000000⟩, + ⟨7, 5, 5, 6, 4, 7, -159355240919867217199547849567974984150595665920000000⟩, + ⟨7, 5, 6, 6, 5, 7, -25829388083110253218674208607332139117555220480000000⟩, + ⟨7, 5, 7, 6, 6, 7, -64880563291537364975562173670670211403334287360000000⟩, + ⟨7, 5, 8, 6, 7, 7, -116402782449868380290846145323217013121828782080000000⟩, + ⟨7, 5, 5, 7, 3, 7, -222172529516562317036127594113201449616214589440000000⟩, + ⟨7, 5, 6, 7, 4, 7, -896373806962004381475859324400800584746139648000000000⟩, + ⟨7, 5, 7, 7, 5, 7, 233085803498130525057960256207426501764584570880000000⟩, + ⟨7, 5, 8, 7, 6, 7, -174030077181728365487355735500541855144377057280000000⟩, + ⟨7, 6, 4, 1, 8, 8, 476624053769258846979074179234291578453796847616000000⟩, + ⟨7, 6, 4, 2, 7, 8, -64626168863104211760024750262969232994116567040000000⟩, + ⟨7, 6, 5, 2, 8, 8, 806181253299260231990460689249988564821905244160000000⟩, + ⟨7, 6, 4, 3, 6, 8, -52633320196751351392251328470902742621370712064000000⟩, + ⟨7, 6, 5, 3, 7, 8, -63509985678581503937475870809314293357855375360000000⟩, + ⟨7, 6, 6, 3, 8, 8, 411508962923347575768476194394479698895322480640000000⟩, + ⟨7, 6, 4, 4, 5, 8, 136104049194847044435896265365516970422270164992000000⟩, + ⟨7, 6, 5, 4, 6, 8, -155535394387101830953288698908008167838108876800000000⟩, + ⟨7, 6, 6, 4, 7, 8, -179564585878652755621137807664838981971114721280000000⟩, + ⟨7, 6, 7, 4, 8, 8, 351279274848000750219208191152952316977060249600000000⟩, + ⟨7, 6, 4, 5, 4, 8, 19006751937671570618897882617799054436901847040000000⟩, + ⟨7, 6, 5, 5, 5, 8, -42803545929198860307088090133738676260595302400000000⟩, + ⟨7, 6, 6, 5, 6, 8, -304125532246986262664373822217521540728220549120000000⟩, + ⟨7, 6, 7, 5, 7, 8, 160231103479995475594132328988174395002406830080000000⟩ +] + +def collectedFourData_17_36 : List CollectedFourTerm := [ + ⟨7, 6, 8, 5, 8, 8, 241814105621162048325902247160005953467963146240000000⟩, + ⟨7, 6, 4, 6, 3, 8, -475097827310761567150938573585336826340195696640000000⟩, + ⟨7, 6, 5, 6, 4, 8, 356940720460735919690483580569581720277939650560000000⟩, + ⟨7, 6, 6, 6, 5, 8, 28927697445738337182908210682335220673617592320000000⟩, + ⟨7, 6, 7, 6, 6, 8, 48442115597618630236282696538149157712596828160000000⟩, + ⟨7, 6, 8, 6, 7, 8, 65182815437151904153263516219411603328975503360000000⟩, + ⟨7, 6, 4, 7, 2, 8, 488238001902084879513441176163493896991203655680000000⟩, + ⟨7, 6, 5, 7, 3, 8, 497645526400374813923917378044399886473803857920000000⟩, + ⟨7, 6, 6, 7, 4, 8, 1003896422270920147597217247158923462686277632000000000⟩, + ⟨7, 6, 7, 7, 5, 8, -174030077181728365487355735500541855144377057280000000⟩, + ⟨7, 6, 8, 7, 6, 8, 97452742646726377711171902167807454986643701760000000⟩, + ⟨1, 8, 8, 6, 8, 3, -12229313726662083848527116411375114110103453696000000⟩, + ⟨1, 8, 8, 7, 7, 3, -9260006523621871550927425446229021939558514688000000⟩, + ⟨2, 7, 8, 6, 8, 3, 439399177525618552121523239158962984806271418368000000⟩, + ⟨2, 7, 8, 7, 7, 3, 332711985423230887232461671588398884178733563904000000⟩, + ⟨2, 8, 7, 5, 8, 4, -3746692905735855550400687867863508912550445056000000⟩, + ⟨2, 8, 7, 6, 7, 4, 12380501692175961221061385084148519098820591616000000⟩, + ⟨2, 8, 8, 6, 8, 4, -146965161479377996099744174271448920289102004224000000⟩, + ⟨2, 8, 7, 7, 6, 4, -31005504618339243866881139150797713567670861824000000⟩, + ⟨2, 8, 8, 7, 7, 4, -111281661789179635594860600946233786854195331072000000⟩, + ⟨3, 6, 8, 6, 8, 3, -482484074320612658691582385408060558311614840832000000⟩, + ⟨3, 6, 8, 7, 7, 3, -365335764182083280351826619345282632086187933696000000⟩, + ⟨3, 7, 7, 5, 8, 4, -22587461309038880090914768767539276124713385984000000⟩, + ⟨3, 7, 7, 6, 7, 4, 74637583061692756312925438520186523981210189824000000⟩ +] + +def collectedFourData_17_37 : List CollectedFourTerm := [ + ⟨3, 7, 8, 6, 8, 4, -885999995785652385239907449296709799776077479936000000⟩, + ⟨3, 7, 7, 7, 6, 4, -186921013692318376465897499983264685411675406336000000⟩, + ⟨3, 7, 8, 7, 7, 4, -670877035644045341010437576639143674069708177408000000⟩, + ⟨3, 8, 6, 4, 8, 5, -37736816288592705581582671048848527196369715200000000⟩, + ⟨3, 8, 6, 5, 7, 5, 45741521446501016143175121047794274492775137280000000⟩, + ⟨3, 8, 7, 5, 8, 5, 18680035016645034532296338410693596000351682560000000⟩, + ⟨3, 8, 6, 6, 6, 5, -29784811407782657741366432780461040637333995520000000⟩, + ⟨3, 8, 7, 6, 7, 5, -61725956984472596349786311487793989152837468160000000⟩, + ⟨3, 8, 8, 6, 8, 5, 366365009320464907715690051870372733209668485120000000⟩, + ⟨3, 8, 6, 7, 5, 5, 30780818743827687689040384920917198457379225600000000⟩, + ⟨3, 8, 7, 7, 6, 5, 154585370765948566388184902649965568577492746240000000⟩, + ⟨3, 8, 8, 7, 7, 5, 277410691406006348880127188830395254005154447360000000⟩, + ⟨4, 5, 8, 6, 8, 3, -902591768494181757738068714296052784335079604224000000⟩, + ⟨4, 5, 8, 7, 7, 3, -683440285467661436351070859356160300300288131072000000⟩, + ⟨4, 6, 7, 5, 8, 4, 26782717856486668289456714169480600122636107776000000⟩, + ⟨4, 6, 7, 6, 7, 4, -88500310029594241677774486385386557622542401536000000⟩, + ⟨4, 6, 8, 6, 8, 4, 1050560201667268259936048853575459639046495535104000000⟩, + ⟨4, 6, 7, 7, 6, 4, 221638576494937033271131820237579508743304904704000000⟩, + ⟨4, 6, 8, 7, 7, 4, 795481622136098721156944115251711043752492531712000000⟩, + ⟨4, 7, 6, 4, 8, 5, -22548969417653631449142911784277964872482816000000000⟩, + ⟨4, 7, 6, 5, 7, 5, 27332039892455997612340450903489484939486822400000000⟩, + ⟨4, 7, 7, 5, 8, 5, 11161925666695820344762825644951730257710284800000000⟩, + ⟨4, 7, 6, 6, 6, 5, -17797389064527211098466463908891264005282201600000000⟩, + ⟨4, 7, 7, 6, 7, 5, -36883257603769142662836013556198346507209932800000000⟩ +] + +def collectedFourData_17_38 : List CollectedFourTerm := [ + ⟨4, 7, 8, 6, 8, 5, 218914953706965952445484248121598013183990169600000000⟩, + ⟨4, 7, 6, 7, 5, 5, 18392535692384820182184136733868449593294848000000000⟩, + ⟨4, 7, 7, 7, 6, 5, 92369763552939441703782290448377337116570419200000000⟩, + ⟨4, 7, 8, 7, 7, 5, 165761868961242517054234690806883046820465868800000000⟩, + ⟨4, 8, 5, 3, 8, 6, -37736816288592705581582671048848527196369715200000000⟩, + ⟨4, 8, 5, 4, 7, 6, -22548969417653631449142911784277964872482816000000000⟩, + ⟨4, 8, 6, 4, 8, 6, 85584899010536376726130923328066108017082368000000000⟩, + ⟨4, 8, 5, 5, 6, 6, 50086275177061307518635809266291457988231168000000000⟩, + ⟨4, 8, 6, 5, 7, 6, -103739103575901175563417593276040811868533555200000000⟩, + ⟨4, 8, 7, 5, 8, 6, -21182615117642040458626406935955221066756915200000000⟩, + ⟨4, 8, 5, 6, 5, 6, -101523656804429597094701205797031323867755315200000000⟩, + ⟨4, 8, 6, 6, 6, 6, 67550215600819398425025287280013269099400396800000000⟩, + ⟨4, 8, 7, 6, 7, 6, 69995435683345083207300250253776003297129267200000000⟩, + ⟨4, 8, 8, 6, 8, 6, -276964826461035837075682099675923206932896153600000000⟩, + ⟨4, 8, 5, 7, 4, 6, -307010519661786775830101040497322262910101094400000000⟩, + ⟨4, 8, 6, 7, 5, 6, -69809102164467721882761026756013979078754304000000000⟩, + ⟨4, 8, 7, 7, 6, 6, -175295303720538299301077946838753668519218380800000000⟩, + ⟨4, 8, 8, 7, 7, 6, -209717091013169180358742601123923812533718220800000000⟩, + ⟨5, 4, 8, 6, 8, 3, 923982441102608405676427748775546413927110803456000000⟩, + ⟨5, 4, 8, 7, 7, 3, 699637250589820792950773606640373494609994579968000000⟩, + ⟨5, 5, 7, 5, 8, 4, 13895009723030680686598303199947397237525446656000000⟩, + ⟨5, 5, 7, 6, 7, 4, -45914409244863478769596374122098981634851209216000000⟩, + ⟨5, 5, 8, 6, 8, 4, 545035955462611787998492019693446003121008410624000000⟩, + ⟨5, 5, 7, 7, 6, 4, 114987216454208564595406673526044816842344628224000000⟩ +] + +def collectedFourData_17_39 : List CollectedFourTerm := [ + ⟨5, 5, 8, 7, 7, 4, 412699896003880067520355079996137926985380790272000000⟩, + ⟨5, 6, 6, 4, 8, 5, 50086275177061307518635809266291457988231168000000000⟩, + ⟨5, 6, 6, 5, 7, 5, -60710538288823380739114085300708852142125875200000000⟩, + ⟨5, 6, 7, 5, 8, 5, -24793118926771960056913578358585013609850470400000000⟩, + ⟨5, 6, 6, 6, 6, 5, 39531958627840835606670101690321105287171276800000000⟩, + ⟨5, 6, 7, 6, 7, 5, 81925916681696778282168558446087127532201574400000000⟩, + ⟨5, 6, 8, 6, 8, 5, -486258791195862838852447360111379002824641740800000000⟩, + ⟨5, 6, 6, 7, 5, 5, -40853911628062612414099386020127659947720704000000000⟩, + ⟨5, 6, 7, 7, 6, 5, -205173784648913961813929019737781844942887321600000000⟩, + ⟨5, 6, 8, 7, 7, 5, -368193970592589905560952888854624069927462502400000000⟩, + ⟨5, 7, 5, 3, 8, 6, 45741521446501016143175121047794274492775137280000000⟩, + ⟨5, 7, 5, 4, 7, 6, 27332039892455997612340450903489484939486822400000000⟩, + ⟨5, 7, 6, 4, 8, 6, -103739103575901175563417593276040811868533555200000000⟩, + ⟨5, 7, 5, 5, 6, 6, -60710538288823380739114085300708852142125875200000000⟩, + ⟨5, 7, 6, 5, 7, 6, 125744164392910765527629351333224977360255713280000000⟩, + ⟨5, 7, 7, 5, 8, 6, 25675855543476042581452410213062465857813217280000000⟩, + ⟨5, 7, 5, 6, 5, 6, 123058778714482942585821128924970951168522977280000000⟩, + ⟨5, 7, 6, 6, 6, 6, -81878916652400932551299354709545701915251179520000000⟩, + ⟨5, 7, 7, 6, 7, 6, -84842814984229037932479764678486542709245870080000000⟩, + ⟨5, 7, 8, 6, 8, 6, 335714397648417835624296743156861012903240663040000000⟩, + ⟨5, 7, 5, 7, 4, 6, 372133360748189997913433131002836416936972124160000000⟩, + ⟨5, 7, 6, 7, 5, 6, 84616956539129967432687627059546998152206745600000000⟩, + ⟨5, 7, 7, 7, 6, 6, 212478812024948706432756000073436024194329477120000000⟩, + ⟨5, 7, 8, 7, 7, 6, 254202123012068774834309430383739285745560453120000000⟩ +] + +def collectedFourData_17_40 : List CollectedFourTerm := [ + ⟨5, 8, 4, 2, 8, 7, -3746692905735855550400687867863508912550445056000000⟩, + ⟨5, 8, 4, 3, 7, 7, -22587461309038880090914768767539276124713385984000000⟩, + ⟨5, 8, 5, 3, 8, 7, 18680035016645034532296338410693596000351682560000000⟩, + ⟨5, 8, 4, 4, 6, 7, 26782717856486668289456714169480600122636107776000000⟩, + ⟨5, 8, 5, 4, 7, 7, 11161925666695820344762825644951730257710284800000000⟩, + ⟨5, 8, 6, 4, 8, 7, -21182615117642040458626406935955221066756915200000000⟩, + ⟨5, 8, 4, 5, 5, 7, 13895009723030680686598303199947397237525446656000000⟩, + ⟨5, 8, 5, 5, 6, 7, -24793118926771960056913578358585013609850470400000000⟩, + ⟨5, 8, 6, 5, 7, 7, 25675855543476042581452410213062465857813217280000000⟩, + ⟨5, 8, 7, 5, 8, 7, 3495189676447610715360423420320047655571947520000000⟩, + ⟨5, 8, 4, 6, 4, 7, -26967774950459004560905582716884602661457887232000000⟩, + ⟨5, 8, 5, 6, 5, 7, 50255046679649865312186440084802967605671362560000000⟩, + ⟨5, 8, 6, 6, 6, 7, -16718956670261876129849855958045586234036715520000000⟩, + ⟨5, 8, 7, 6, 7, 7, -11549439143381535283984971522478698312467742720000000⟩, + ⟨5, 8, 8, 6, 8, 7, 34274967826545977530040135369181980245119467520000000⟩, + ⟨5, 8, 4, 7, 3, 7, 98153210137289138451026105808774821720031756288000000⟩, + ⟨5, 8, 5, 7, 4, 7, 151972737018998701046769406706574282541309624320000000⟩, + ⟨5, 8, 6, 7, 5, 7, 17278040401450070193145985549937830847420825600000000⟩, + ⟨5, 8, 7, 7, 6, 7, 28924206595411908616867274527779485516908462080000000⟩, + ⟨5, 8, 8, 7, 7, 7, 25952922033456916598480064725392299007735234560000000⟩, + ⟨6, 3, 8, 6, 8, 3, 1229116033703108642189073863538648991763565379584000000⟩, + ⟨6, 3, 8, 7, 7, 3, 930683662613467861008636430368928584543504433152000000⟩, + ⟨6, 4, 7, 5, 8, 4, -26967774950459004560905582716884602661457887232000000⟩, + ⟨6, 4, 7, 6, 7, 4, 89111809216401413431128947043694018259218071552000000⟩ +] + +def collectedFourData_17_41 : List CollectedFourTerm := [ + ⟨6, 4, 8, 6, 8, 4, -1057819122102650810099932661487970952014020476928000000⟩, + ⟨6, 4, 7, 7, 6, 4, -223170004003455723110386201931213443009376944128000000⟩, + ⟨6, 4, 8, 7, 7, 4, -800978058983535881145132602356983633388800835584000000⟩, + ⟨6, 5, 6, 4, 8, 5, -101523656804429597094701205797031323867755315200000000⟩, + ⟨6, 5, 6, 5, 7, 5, 123058778714482942585821128924970951168522977280000000⟩, + ⟨6, 5, 7, 5, 8, 5, 50255046679649865312186440084802967605671362560000000⟩, + ⟨6, 5, 6, 6, 6, 5, -80130314868730889763813574771216202304344555520000000⟩, + ⟨6, 5, 7, 6, 7, 5, -166061832691246297258990442981596745670233948160000000⟩, + ⟨6, 5, 8, 6, 8, 5, 985634696550857552358505543665474923859667845120000000⟩, + ⟨6, 5, 6, 7, 5, 5, 82809881321449806711645690924423358977776025600000000⟩, + ⟨6, 5, 7, 7, 6, 5, 415882251661271106692927430117405774796019466240000000⟩, + ⟨6, 5, 8, 7, 7, 5, 746320188030711264063182234525037329032528527360000000⟩, + ⟨6, 6, 5, 3, 8, 6, -29784811407782657741366432780461040637333995520000000⟩, + ⟨6, 6, 5, 4, 7, 6, -17797389064527211098466463908891264005282201600000000⟩, + ⟨6, 6, 6, 4, 8, 6, 67550215600819398425025287280013269099400396800000000⟩, + ⟨6, 6, 5, 5, 6, 6, 39531958627840835606670101690321105287171276800000000⟩, + ⟨6, 6, 6, 5, 7, 6, -81878916652400932551299354709545701915251179520000000⟩, + ⟨6, 6, 7, 5, 8, 6, -16718956670261876129849855958045586234036715520000000⟩, + ⟨6, 6, 5, 6, 5, 6, -80130314868730889763813574771216202304344555520000000⟩, + ⟨6, 6, 6, 6, 6, 6, 53315849880893457159156694379111266647728455680000000⟩, + ⟨6, 6, 7, 6, 7, 6, 55245806516651462305430594583399502726268190720000000⟩, + ⟨6, 6, 8, 6, 8, 6, -218602042621832466755765154281709297504469647360000000⟩, + ⟨6, 6, 5, 7, 4, 6, -242316425381540294626975672775664390152587837440000000⟩, + ⟨6, 6, 6, 7, 5, 6, -55098737705221591523883791339364154585015910400000000⟩ +] + +def collectedFourData_17_42 : List CollectedFourTerm := [ + ⟨6, 6, 7, 7, 6, 6, -138356599085029050640370049332880936112572334080000000⟩, + ⟨6, 6, 8, 7, 7, 6, -165524933450844048670076487811781585621043118080000000⟩, + ⟨6, 7, 4, 2, 8, 7, 12380501692175961221061385084148519098820591616000000⟩, + ⟨6, 7, 4, 3, 7, 7, 74637583061692756312925438520186523981210189824000000⟩, + ⟨6, 7, 5, 3, 8, 7, -61725956984472596349786311487793989152837468160000000⟩, + ⟨6, 7, 4, 4, 6, 7, -88500310029594241677774486385386557622542401536000000⟩, + ⟨6, 7, 5, 4, 7, 7, -36883257603769142662836013556198346507209932800000000⟩, + ⟨6, 7, 6, 4, 8, 7, 69995435683345083207300250253776003297129267200000000⟩, + ⟨6, 7, 4, 5, 5, 7, -45914409244863478769596374122098981634851209216000000⟩, + ⟨6, 7, 5, 5, 6, 7, 81925916681696778282168558446087127532201574400000000⟩, + ⟨6, 7, 6, 5, 7, 7, -84842814984229037932479764678486542709245870080000000⟩, + ⟨6, 7, 7, 5, 8, 7, -11549439143381535283984971522478698312467742720000000⟩, + ⟨6, 7, 4, 6, 4, 7, 89111809216401413431128947043694018259218071552000000⟩, + ⟨6, 7, 5, 6, 5, 7, -166061832691246297258990442981596745670233948160000000⟩, + ⟨6, 7, 6, 6, 6, 7, 55245806516651462305430594583399502726268190720000000⟩, + ⟨6, 7, 7, 6, 7, 7, 38163749860421339880345142110624028427204689920000000⟩, + ⟨6, 7, 8, 6, 8, 7, -113257560160908863772439333193140419573810462720000000⟩, + ⟨6, 7, 4, 7, 3, 7, -324335624715030312833651762964861814478280327168000000⟩, + ⟨6, 7, 5, 7, 4, 7, -502175858861535615983114885959615549279850987520000000⟩, + ⟨6, 7, 6, 7, 5, 7, -57093232300987007764211893349287496475318681600000000⟩, + ⟨6, 7, 7, 7, 6, 7, -95576605211259943746490261407287818759050362880000000⟩, + ⟨6, 7, 8, 7, 7, 7, -85758348291696564286221655170596966412488540160000000⟩, + ⟨6, 8, 3, 1, 8, 8, -12229313726662083848527116411375114110103453696000000⟩, + ⟨6, 8, 3, 2, 7, 8, 439399177525618552121523239158962984806271418368000000⟩ +] + +def collectedFourData_17_43 : List CollectedFourTerm := [ + ⟨6, 8, 4, 2, 8, 8, -146965161479377996099744174271448920289102004224000000⟩, + ⟨6, 8, 3, 3, 6, 8, -482484074320612658691582385408060558311614840832000000⟩, + ⟨6, 8, 4, 3, 7, 8, -885999995785652385239907449296709799776077479936000000⟩, + ⟨6, 8, 5, 3, 8, 8, 366365009320464907715690051870372733209668485120000000⟩, + ⟨6, 8, 3, 4, 5, 8, -902591768494181757738068714296052784335079604224000000⟩, + ⟨6, 8, 4, 4, 6, 8, 1050560201667268259936048853575459639046495535104000000⟩, + ⟨6, 8, 5, 4, 7, 8, 218914953706965952445484248121598013183990169600000000⟩, + ⟨6, 8, 6, 4, 8, 8, -276964826461035837075682099675923206932896153600000000⟩, + ⟨6, 8, 3, 5, 4, 8, 923982441102608405676427748775546413927110803456000000⟩, + ⟨6, 8, 4, 5, 5, 8, 545035955462611787998492019693446003121008410624000000⟩, + ⟨6, 8, 5, 5, 6, 8, -486258791195862838852447360111379002824641740800000000⟩, + ⟨6, 8, 6, 5, 7, 8, 335714397648417835624296743156861012903240663040000000⟩, + ⟨6, 8, 7, 5, 8, 8, 34274967826545977530040135369181980245119467520000000⟩, + ⟨6, 8, 3, 6, 3, 8, 1229116033703108642189073863538648991763565379584000000⟩, + ⟨6, 8, 4, 6, 4, 8, -1057819122102650810099932661487970952014020476928000000⟩, + ⟨6, 8, 5, 6, 5, 8, 985634696550857552358505543665474923859667845120000000⟩, + ⟨6, 8, 6, 6, 6, 8, -218602042621832466755765154281709297504469647360000000⟩, + ⟨6, 8, 7, 6, 7, 8, -113257560160908863772439333193140419573810462720000000⟩, + ⟨6, 8, 8, 6, 8, 8, 268889194180674224474474678708593215985749590016000000⟩, + ⟨6, 8, 3, 7, 2, 8, 4524345187442225068608329711870548524059861188608000000⟩, + ⟨6, 8, 4, 7, 3, 8, 3850089329569141701426738389589089109460912177152000000⟩, + ⟨6, 8, 5, 7, 4, 8, 2980588267891897781693892270732581888905067888640000000⟩, + ⟨6, 8, 6, 7, 5, 8, 225912118725550270683636298981349201061661900800000000⟩, + ⟨6, 8, 7, 7, 6, 8, 283640186152561680691746178999591821855770542080000000⟩ +] + +def collectedFourData_17_44 : List CollectedFourTerm := [ + ⟨6, 8, 8, 7, 7, 8, 203602241948868435094238206059831938204615835648000000⟩, + ⟨7, 2, 8, 6, 8, 3, 4524345187442225068608329711870548524059861188608000000⟩, + ⟨7, 2, 8, 7, 7, 3, 3425823139976582624690778131050994189528280858624000000⟩, + ⟨7, 3, 7, 5, 8, 4, 98153210137289138451026105808774821720031756288000000⟩, + ⟨7, 3, 7, 6, 7, 4, -324335624715030312833651762964861814478280327168000000⟩, + ⟨7, 3, 8, 6, 8, 4, 3850089329569141701426738389589089109460912177152000000⟩, + ⟨7, 3, 7, 7, 6, 4, 812260275070191384958974233533172431048987901952000000⟩, + ⟨7, 3, 8, 7, 7, 4, 2915278249065588761447599751467072671742118854656000000⟩, + ⟨7, 4, 6, 4, 8, 5, -307010519661786775830101040497322262910101094400000000⟩, + ⟨7, 4, 6, 5, 7, 5, 372133360748189997913433131002836416936972124160000000⟩, + ⟨7, 4, 7, 5, 8, 5, 151972737018998701046769406706574282541309624320000000⟩, + ⟨7, 4, 6, 6, 6, 5, -242316425381540294626975672775664390152587837440000000⟩, + ⟨7, 4, 7, 6, 7, 5, -502175858861535615983114885959615549279850987520000000⟩, + ⟨7, 4, 8, 6, 8, 5, 2980588267891897781693892270732581888905067888640000000⟩, + ⟨7, 4, 6, 7, 5, 5, 250419513026445062115110590310905454110389043200000000⟩, + ⟨7, 4, 7, 7, 6, 5, 1257640142401470215722313783616021090872359649280000000⟩, + ⟨7, 4, 8, 7, 7, 5, 2256894166083603405544497382242799649319467089920000000⟩, + ⟨7, 5, 5, 3, 8, 6, 30780818743827687689040384920917198457379225600000000⟩, + ⟨7, 5, 5, 4, 7, 6, 18392535692384820182184136733868449593294848000000000⟩, + ⟨7, 5, 6, 4, 8, 6, -69809102164467721882761026756013979078754304000000000⟩, + ⟨7, 5, 5, 5, 6, 6, -40853911628062612414099386020127659947720704000000000⟩, + ⟨7, 5, 6, 5, 7, 6, 84616956539129967432687627059546998152206745600000000⟩, + ⟨7, 5, 7, 5, 8, 6, 17278040401450070193145985549937830847420825600000000⟩, + ⟨7, 5, 5, 6, 5, 6, 82809881321449806711645690924423358977776025600000000⟩ +] + +def collectedFourData_17_45 : List CollectedFourTerm := [ + ⟨7, 5, 6, 6, 6, 6, -55098737705221591523883791339364154585015910400000000⟩, + ⟨7, 5, 7, 6, 7, 6, -57093232300987007764211893349287496475318681600000000⟩, + ⟨7, 5, 8, 6, 8, 6, 225912118725550270683636298981349201061661900800000000⟩, + ⟨7, 5, 5, 7, 4, 6, 250419513026445062115110590310905454110389043200000000⟩, + ⟨7, 5, 6, 7, 5, 6, 56941245492492052348256250821883906345664512000000000⟩, + ⟨7, 5, 7, 7, 6, 6, 142983258820833934851204388974639441124943462400000000⟩, + ⟨7, 5, 8, 7, 7, 6, 171060105245563813098109570385337536901178982400000000⟩, + ⟨7, 6, 4, 2, 8, 7, -31005504618339243866881139150797713567670861824000000⟩, + ⟨7, 6, 4, 3, 7, 7, -186921013692318376465897499983264685411675406336000000⟩, + ⟨7, 6, 5, 3, 8, 7, 154585370765948566388184902649965568577492746240000000⟩, + ⟨7, 6, 4, 4, 6, 7, 221638576494937033271131820237579508743304904704000000⟩, + ⟨7, 6, 5, 4, 7, 7, 92369763552939441703782290448377337116570419200000000⟩, + ⟨7, 6, 6, 4, 8, 7, -175295303720538299301077946838753668519218380800000000⟩, + ⟨7, 6, 4, 5, 5, 7, 114987216454208564595406673526044816842344628224000000⟩, + ⟨7, 6, 5, 5, 6, 7, -205173784648913961813929019737781844942887321600000000⟩, + ⟨7, 6, 6, 5, 7, 7, 212478812024948706432756000073436024194329477120000000⟩, + ⟨7, 6, 7, 5, 8, 7, 28924206595411908616867274527779485516908462080000000⟩, + ⟨7, 6, 4, 6, 4, 7, -223170004003455723110386201931213443009376944128000000⟩, + ⟨7, 6, 5, 6, 5, 7, 415882251661271106692927430117405774796019466240000000⟩, + ⟨7, 6, 6, 6, 6, 7, -138356599085029050640370049332880936112572334080000000⟩, + ⟨7, 6, 7, 6, 7, 7, -95576605211259943746490261407287818759050362880000000⟩, + ⟨7, 6, 8, 6, 8, 7, 283640186152561680691746178999591821855770542080000000⟩, + ⟨7, 6, 4, 7, 3, 7, 812260275070191384958974233533172431048987901952000000⟩, + ⟨7, 6, 5, 7, 4, 7, 1257640142401470215722313783616021090872359649280000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1703.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1703.lean new file mode 100644 index 0000000000000000000000000000000000000000..fa755c3ede029f6e8ac29e83bd0bf9eff2198e31 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1703.lean @@ -0,0 +1,286 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1701 +import OAI.Analysis.LaughlinFock.Sparse1702 + +namespace OAI + +/-! Sparse1703. -/ +namespace LaughlinFock +def collectedFourData_17_46 : List CollectedFourTerm := [ + ⟨7, 6, 6, 7, 5, 7, 142983258820833934851204388974639441124943462400000000⟩, + ⟨7, 6, 7, 7, 6, 7, 239360322219871854769260560964119627083095736320000000⟩, + ⟨7, 6, 8, 7, 7, 7, 214771657088801579212471180038704333372774154240000000⟩, + ⟨7, 7, 3, 1, 8, 8, -9260006523621871550927425446229021939558514688000000⟩, + ⟨7, 7, 3, 2, 7, 8, 332711985423230887232461671588398884178733563904000000⟩, + ⟨7, 7, 4, 2, 8, 8, -111281661789179635594860600946233786854195331072000000⟩, + ⟨7, 7, 3, 3, 6, 8, -365335764182083280351826619345282632086187933696000000⟩, + ⟨7, 7, 4, 3, 7, 8, -670877035644045341010437576639143674069708177408000000⟩, + ⟨7, 7, 5, 3, 8, 8, 277410691406006348880127188830395254005154447360000000⟩, + ⟨7, 7, 3, 4, 5, 8, -683440285467661436351070859356160300300288131072000000⟩, + ⟨7, 7, 4, 4, 6, 8, 795481622136098721156944115251711043752492531712000000⟩, + ⟨7, 7, 5, 4, 7, 8, 165761868961242517054234690806883046820465868800000000⟩, + ⟨7, 7, 6, 4, 8, 8, -209717091013169180358742601123923812533718220800000000⟩, + ⟨7, 7, 3, 5, 4, 8, 699637250589820792950773606640373494609994579968000000⟩, + ⟨7, 7, 4, 5, 5, 8, 412699896003880067520355079996137926985380790272000000⟩, + ⟨7, 7, 5, 5, 6, 8, -368193970592589905560952888854624069927462502400000000⟩, + ⟨7, 7, 6, 5, 7, 8, 254202123012068774834309430383739285745560453120000000⟩, + ⟨7, 7, 7, 5, 8, 8, 25952922033456916598480064725392299007735234560000000⟩, + ⟨7, 7, 3, 6, 3, 8, 930683662613467861008636430368928584543504433152000000⟩, + ⟨7, 7, 4, 6, 4, 8, -800978058983535881145132602356983633388800835584000000⟩, + ⟨7, 7, 5, 6, 5, 8, 746320188030711264063182234525037329032528527360000000⟩, + ⟨7, 7, 6, 6, 6, 8, -165524933450844048670076487811781585621043118080000000⟩, + ⟨7, 7, 7, 6, 7, 8, -85758348291696564286221655170596966412488540160000000⟩, + ⟨7, 7, 8, 6, 8, 8, 203602241948868435094238206059831938204615835648000000⟩ +] + +def collectedFourData_17_47 : List CollectedFourTerm := [ + ⟨7, 7, 3, 7, 2, 8, 3425823139976582624690778131050994189528280858624000000⟩, + ⟨7, 7, 4, 7, 3, 8, 2915278249065588761447599751467072671742118854656000000⟩, + ⟨7, 7, 5, 7, 4, 8, 2256894166083603405544497382242799649319467089920000000⟩, + ⟨7, 7, 6, 7, 5, 8, 171060105245563813098109570385337536901178982400000000⟩, + ⟨7, 7, 7, 7, 6, 8, 214771657088801579212471180038704333372774154240000000⟩, + ⟨7, 7, 8, 7, 7, 8, 154167120969359358035227224571446407157717663744000000⟩, + ⟨1, 8, 8, 7, 8, 2, 407020221741042353532618694112118854244315955200000000⟩, + ⟨2, 7, 8, 7, 8, 2, 494750651337820062008943138982906576624838246400000000⟩, + ⟨2, 8, 7, 6, 8, 3, -21945613190552536971805145320465218446882242560000000⟩, + ⟨2, 8, 7, 7, 7, 3, 7756296019336335567825770152870974431774638080000000⟩, + ⟨2, 8, 8, 7, 8, 3, 208120254663607538247482268091256054684319744000000000⟩, + ⟨3, 6, 8, 7, 8, 2, 196541124626160133791486627831711669688467456000000000⟩, + ⟨3, 7, 7, 6, 8, 3, -54795769527225192380708190200999208981708668928000000⟩, + ⟨3, 7, 7, 7, 7, 3, 19366613517249698141172953178423988225314914304000000⟩, + ⟨3, 7, 8, 7, 8, 3, 519653263250072122288477809313958766646080307200000000⟩, + ⟨3, 8, 6, 5, 8, 4, -30724333518995516018561662380189753410517467136000000⟩, + ⟨3, 8, 6, 6, 7, 4, -29015960573023301693920215359401718549361721344000000⟩, + ⟨3, 8, 7, 6, 8, 4, -31831988118817290567312094543434491946822795264000000⟩, + ⟨3, 8, 6, 7, 6, 4, 31404550003313958664711746890237746127579381760000000⟩, + ⟨3, 8, 7, 7, 7, 4, 11250463616110413295620700777863302194818711552000000⟩, + ⟨3, 8, 8, 7, 8, 4, 150938627602102231827974347800835676152057036800000000⟩, + ⟨4, 5, 8, 7, 8, 2, 91277477980658163262322942900174544694778265600000000⟩, + ⟨4, 6, 7, 6, 8, 3, -125866570333664416203776136822154074574062354432000000⟩, + ⟨4, 6, 7, 7, 7, 3, 44485354315221046440204390086883282495970738176000000⟩ +] + +def collectedFourData_17_48 : List CollectedFourTerm := [ + ⟨4, 6, 8, 7, 8, 3, 1193650067739008214244603352969588849295281356800000000⟩, + ⟨4, 7, 6, 5, 8, 4, -70014169189813016480530147840697993086491426816000000⟩, + ⟨4, 7, 6, 6, 7, 4, -66121153499020307722066173389514045731912024064000000⟩, + ⟨4, 7, 7, 6, 8, 4, -72538276555977676554938815701939256940071747584000000⟩, + ⟨4, 7, 6, 7, 6, 4, 71564236727952677125798162614120908145096130560000000⟩, + ⟨4, 7, 7, 7, 7, 4, 25637394627134694218961059121624262154033037312000000⟩, + ⟨4, 7, 8, 7, 8, 4, 343956773014396886154736431933550797846793420800000000⟩, + ⟨4, 8, 5, 4, 8, 5, 215973493792167743772278739480648169621951610880000000⟩, + ⟨4, 8, 5, 5, 7, 5, -7347081098493169740493603927917102844367339520000000⟩, + ⟨4, 8, 6, 5, 8, 5, 304210995141065140031788593025555382372621352960000000⟩, + ⟨4, 8, 5, 6, 6, 5, 69883852162225720222908173563808809314083143680000000⟩, + ⟨4, 8, 6, 6, 7, 5, 287295873657796219981458910158600619417235619840000000⟩, + ⟨4, 8, 7, 6, 8, 5, 157589110549086395976420579318283452045349355520000000⟩, + ⟨4, 8, 5, 7, 5, 5, -79031673140101028552844324964661644848141434880000000⟩, + ⟨4, 8, 6, 7, 6, 5, -310946025975108611853707291031997215674046873600000000⟩, + ⟨4, 8, 7, 7, 7, 5, -55697135469827253143521495520157357951009423360000000⟩, + ⟨4, 8, 8, 7, 8, 5, -498163126193050054225312714576258896878370816000000000⟩, + ⟨5, 4, 8, 7, 8, 2, -483974484427817012352801411814091102495126323200000000⟩, + ⟨5, 5, 7, 6, 8, 3, -41366297099864186250600165263655257081898860544000000⟩, + ⟨5, 5, 7, 7, 7, 3, 14620199615496940664769071272476874685747822592000000⟩, + ⟨5, 5, 8, 7, 8, 3, 392295453864118100347418314192412041308379545600000000⟩, + ⟨5, 6, 6, 5, 8, 4, 64222512533850914823263379412087764269125337088000000⟩, + ⟨5, 6, 6, 6, 7, 4, 60651531803956164639642745184253868425716170752000000⟩, + ⟨5, 6, 7, 6, 8, 4, 66537822689439839936741962822295646740636762112000000⟩ +] + +def collectedFourData_17_49 : List CollectedFourTerm := [ + ⟨5, 6, 6, 7, 6, 4, -65644356612677377409333961888274894362331054080000000⟩, + ⟨5, 6, 7, 7, 7, 4, -23516638372336832756515216080809511380808892416000000⟩, + ⟨5, 6, 8, 7, 8, 4, -315504253233844768027960002876310764193736294400000000⟩, + ⟨5, 7, 5, 4, 8, 5, -7347081098493169740493603927917102844367339520000000⟩, + ⟨5, 7, 5, 5, 7, 5, 249936229303121855362178739579603707316142080000000⟩, + ⟨5, 7, 6, 5, 8, 5, -10348783145146173084139851606036367871406243840000000⟩, + ⟨5, 7, 5, 6, 6, 5, -2377339553552194062892084777900322908243230720000000⟩, + ⟨5, 7, 6, 6, 7, 5, -9773357118802250893520564497886307727819407360000000⟩, + ⟨5, 7, 7, 6, 8, 5, -5360935525531288425439493786193627468351406080000000⟩, + ⟨5, 7, 5, 7, 5, 5, 2688534142382725535666442630966846267347435520000000⟩, + ⟨5, 7, 6, 7, 6, 5, 10577898379935989543396040602362967107200614400000000⟩, + ⟨5, 7, 7, 7, 7, 5, 1894729598829230545337400642240304966470205440000000⟩, + ⟨5, 7, 8, 7, 8, 5, 16946731861185258457832428638816668655550464000000000⟩, + ⟨5, 8, 4, 3, 8, 6, -30724333518995516018561662380189753410517467136000000⟩, + ⟨5, 8, 4, 4, 7, 6, -70014169189813016480530147840697993086491426816000000⟩, + ⟨5, 8, 5, 4, 8, 6, 304210995141065140031788593025555382372621352960000000⟩, + ⟨5, 8, 4, 5, 6, 6, 64222512533850914823263379412087764269125337088000000⟩, + ⟨5, 8, 5, 5, 7, 6, -10348783145146173084139851606036367871406243840000000⟩, + ⟨5, 8, 6, 5, 8, 6, 214249276473188370251647659069890827026337628160000000⟩, + ⟨5, 8, 4, 6, 5, 6, -104206398826276819312307923262075990218326933504000000⟩, + ⟨5, 8, 5, 6, 6, 6, 98435395183354367682043448801425555915863490560000000⟩, + ⟨5, 8, 6, 6, 7, 6, 202336319357466934747188871365462478492941680640000000⟩, + ⟨5, 8, 7, 6, 8, 6, 73991086130946084093765884084875955199572705280000000⟩, + ⟨5, 8, 4, 7, 4, 6, -430957375329361151695717943708304156847094366208000000⟩ +] + +def collectedFourData_17_50 : List CollectedFourTerm := [ + ⟨5, 8, 5, 7, 5, 6, -111320623246246776139032425633076452292254760960000000⟩, + ⟨5, 8, 6, 7, 6, 6, -218992614177170136778192359329916039605098905600000000⟩, + ⟨5, 8, 7, 7, 7, 6, -26150864951492373360182690021396373268636631040000000⟩, + ⟨5, 8, 8, 7, 8, 6, -175422800387261683867629603064793053022650368000000000⟩, + ⟨6, 3, 8, 7, 8, 2, -244204936533747617526533894216297843905265664000000000⟩, + ⟨6, 4, 7, 6, 8, 3, 195166587185705264783882917686097422935188832256000000⟩, + ⟨6, 4, 7, 7, 7, 3, -68978242264272342930653426686840696318678007808000000⟩, + ⟨6, 4, 8, 7, 8, 3, -1850853720706333028935250895119466040597571174400000000⟩, + ⟨6, 5, 6, 5, 8, 4, -104206398826276819312307923262075990218326933504000000⟩, + ⟨6, 5, 6, 6, 7, 4, -98412183877987121702210702705846450363842953216000000⟩, + ⟨6, 5, 7, 6, 8, 4, -107963183230385238100439388732104796019774980096000000⟩, + ⟨6, 5, 6, 7, 6, 4, 106513459782026166743737058634345189560958320640000000⟩, + ⟨6, 5, 7, 7, 7, 4, 38157712935777525817875308241681985326890876928000000⟩, + ⟨6, 5, 8, 7, 8, 4, 511932042934995696847172099366520443219686195200000000⟩, + ⟨6, 6, 5, 4, 8, 5, 69883852162225720222908173563808809314083143680000000⟩, + ⟨6, 6, 5, 5, 7, 5, -2377339553552194062892084777900322908243230720000000⟩, + ⟨6, 6, 6, 5, 8, 5, 98435395183354367682043448801425555915863490560000000⟩, + ⟨6, 6, 5, 6, 6, 5, 22612741532678438604370069352176566695079444480000000⟩, + ⟨6, 6, 6, 6, 7, 5, 92962066821215689530840231466807614863824650240000000⟩, + ⟨6, 6, 7, 6, 8, 5, 50992063473246374349505011878187878666962206720000000⟩, + ⟨6, 6, 5, 7, 5, 5, -25572757401290222719105558281052077216686407680000000⟩, + ⟨6, 6, 6, 7, 6, 5, -100614689923880506121300659324643122421012889600000000⟩, + ⟨6, 6, 7, 7, 7, 5, -18022259642558141991390230753705130619526184960000000⟩, + ⟨6, 6, 8, 7, 8, 5, -161193661556674856240313434327046219708235776000000000⟩ +] + +def collectedFourData_17_51 : List CollectedFourTerm := [ + ⟨6, 7, 4, 3, 8, 6, -29015960573023301693920215359401718549361721344000000⟩, + ⟨6, 7, 4, 4, 7, 6, -66121153499020307722066173389514045731912024064000000⟩, + ⟨6, 7, 5, 4, 8, 6, 287295873657796219981458910158600619417235619840000000⟩, + ⟨6, 7, 4, 5, 6, 6, 60651531803956164639642745184253868425716170752000000⟩, + ⟨6, 7, 5, 5, 7, 6, -9773357118802250893520564497886307727819407360000000⟩, + ⟨6, 7, 6, 5, 8, 6, 202336319357466934747188871365462478492941680640000000⟩, + ⟨6, 7, 4, 6, 5, 6, -98412183877987121702210702705846450363842953216000000⟩, + ⟨6, 7, 5, 6, 6, 6, 92962066821215689530840231466807614863824650240000000⟩, + ⟨6, 7, 6, 6, 7, 6, 191085761431965299053867434284592771044537794560000000⟩, + ⟨6, 7, 7, 6, 8, 6, 69876940914059348380468522207287737331084165120000000⟩, + ⟨6, 7, 4, 7, 4, 6, -406994742570388807678031725780625402152964063232000000⟩, + ⟨6, 7, 5, 7, 5, 6, -105130834264654210951375831527302938884927651840000000⟩, + ⟨6, 7, 6, 7, 6, 6, -206815912046375146076481431705265723851302502400000000⟩, + ⟨6, 7, 7, 7, 7, 6, -24696791743711261277819300825522487368519516160000000⟩, + ⟨6, 7, 8, 7, 8, 6, -165668721715286645414801916685010721017167872000000000⟩, + ⟨6, 8, 3, 2, 8, 7, -21945613190552536971805145320465218446882242560000000⟩, + ⟨6, 8, 3, 3, 7, 7, -54795769527225192380708190200999208981708668928000000⟩, + ⟨6, 8, 4, 3, 8, 7, -31831988118817290567312094543434491946822795264000000⟩, + ⟨6, 8, 3, 4, 6, 7, -125866570333664416203776136822154074574062354432000000⟩, + ⟨6, 8, 4, 4, 7, 7, -72538276555977676554938815701939256940071747584000000⟩, + ⟨6, 8, 5, 4, 8, 7, 157589110549086395976420579318283452045349355520000000⟩, + ⟨6, 8, 3, 5, 5, 7, -41366297099864186250600165263655257081898860544000000⟩, + ⟨6, 8, 4, 5, 6, 7, 66537822689439839936741962822295646740636762112000000⟩, + ⟨6, 8, 5, 5, 7, 7, -5360935525531288425439493786193627468351406080000000⟩ +] + +def collectedFourData_17_52 : List CollectedFourTerm := [ + ⟨6, 8, 6, 5, 8, 7, 73991086130946084093765884084875955199572705280000000⟩, + ⟨6, 8, 3, 6, 4, 7, 195166587185705264783882917686097422935188832256000000⟩, + ⟨6, 8, 4, 6, 5, 7, -107963183230385238100439388732104796019774980096000000⟩, + ⟨6, 8, 5, 6, 6, 7, 50992063473246374349505011878187878666962206720000000⟩, + ⟨6, 8, 6, 6, 7, 7, 69876940914059348380468522207287737331084165120000000⟩, + ⟨6, 8, 7, 6, 8, 7, 19164641709497892959991586543903222431146311680000000⟩, + ⟨6, 8, 3, 7, 3, 7, -347827376892858727401199041108151842441630056448000000⟩, + ⟨6, 8, 4, 7, 4, 7, -446493983106892271781283116855844816221206740992000000⟩, + ⟨6, 8, 5, 7, 5, 7, -57666942626485886124660264310969489390326251520000000⟩, + ⟨6, 8, 6, 7, 6, 7, -75629199987761835952712331387442619623460044800000000⟩, + ⟨6, 8, 7, 7, 7, 7, -6773409925377576241561798889033439608297226240000000⟩, + ⟨6, 8, 8, 7, 8, 7, -36349406858538314058113844740701168112920166400000000⟩, + ⟨7, 2, 8, 7, 8, 2, 1181120011139690319904802255782407024423626342400000000⟩, + ⟨7, 3, 7, 6, 8, 3, -347827376892858727401199041108151842441630056448000000⟩, + ⟨7, 3, 7, 7, 7, 3, 122933548285253182514566080089098531420099313664000000⟩, + ⟨7, 3, 8, 7, 8, 3, 3298605585971041026361565356477382523580789555200000000⟩, + ⟨7, 4, 6, 5, 8, 4, -430957375329361151695717943708304156847094366208000000⟩, + ⟨7, 4, 6, 6, 7, 4, -406994742570388807678031725780625402152964063232000000⟩, + ⟨7, 4, 7, 6, 8, 4, -446493983106892271781283116855844816221206740992000000⟩, + ⟨7, 4, 6, 7, 6, 4, 440498487443523147872167853807481211990604513280000000⟩, + ⟨7, 4, 7, 7, 7, 4, 157805547457679408186623533007646778534716768256000000⟩, + ⟨7, 4, 8, 7, 8, 4, 2117152996890931055231425572228014595029493350400000000⟩, + ⟨7, 5, 5, 4, 8, 5, -79031673140101028552844324964661644848141434880000000⟩, + ⟨7, 5, 5, 5, 7, 5, 2688534142382725535666442630966846267347435520000000⟩ +] + +def collectedFourData_17_53 : List CollectedFourTerm := [ + ⟨7, 5, 6, 5, 8, 5, -111320623246246776139032425633076452292254760960000000⟩, + ⟨7, 5, 5, 6, 6, 5, -25572757401290222719105558281052077216686407680000000⟩, + ⟨7, 5, 6, 6, 7, 5, -105130834264654210951375831527302938884927651840000000⟩, + ⟨7, 5, 7, 6, 8, 5, -57666942626485886124660264310969489390326251520000000⟩, + ⟨7, 5, 5, 7, 5, 5, 28920240394565849745354003083812740333966458880000000⟩, + ⟨7, 5, 6, 7, 6, 5, 113785188439496100635919627543773136849312153600000000⟩, + ⟨7, 5, 7, 7, 7, 5, 20381379807316646708904273244928639593988751360000000⟩, + ⟨7, 5, 8, 7, 8, 5, 182293968896139634511374906819151292442607616000000000⟩, + ⟨7, 6, 4, 3, 8, 6, 31404550003313958664711746890237746127579381760000000⟩, + ⟨7, 6, 4, 4, 7, 6, 71564236727952677125798162614120908145096130560000000⟩, + ⟨7, 6, 5, 4, 8, 6, -310946025975108611853707291031997215674046873600000000⟩, + ⟨7, 6, 4, 5, 6, 6, -65644356612677377409333961888274894362331054080000000⟩, + ⟨7, 6, 5, 5, 7, 6, 10577898379935989543396040602362967107200614400000000⟩, + ⟨7, 6, 6, 5, 8, 6, -218992614177170136778192359329916039605098905600000000⟩, + ⟨7, 6, 4, 6, 5, 6, 106513459782026166743737058634345189560958320640000000⟩, + ⟨7, 6, 5, 6, 6, 6, -100614689923880506121300659324643122421012889600000000⟩, + ⟨7, 6, 6, 6, 7, 6, -206815912046375146076481431705265723851302502400000000⟩, + ⟨7, 6, 7, 6, 8, 6, -75629199987761835952712331387442619623460044800000000⟩, + ⟨7, 6, 4, 7, 4, 6, 440498487443523147872167853807481211990604513280000000⟩, + ⟨7, 6, 5, 7, 5, 6, 113785188439496100635919627543773136849312153600000000⟩, + ⟨7, 6, 6, 7, 6, 6, 223840966250135457949091778998829775004368896000000000⟩, + ⟨7, 6, 7, 7, 7, 6, 26729827857496268423976196527915714411390566400000000⟩, + ⟨7, 6, 8, 7, 8, 6, 179306545513089892280647112408209799648378880000000000⟩, + ⟨7, 7, 3, 2, 8, 7, 7756296019336335567825770152870974431774638080000000⟩ +] + +def collectedFourData_17_54 : List CollectedFourTerm := [ + ⟨7, 7, 3, 3, 7, 7, 19366613517249698141172953178423988225314914304000000⟩, + ⟨7, 7, 4, 3, 8, 7, 11250463616110413295620700777863302194818711552000000⟩, + ⟨7, 7, 3, 4, 6, 7, 44485354315221046440204390086883282495970738176000000⟩, + ⟨7, 7, 4, 4, 7, 7, 25637394627134694218961059121624262154033037312000000⟩, + ⟨7, 7, 5, 4, 8, 7, -55697135469827253143521495520157357951009423360000000⟩, + ⟨7, 7, 3, 5, 5, 7, 14620199615496940664769071272476874685747822592000000⟩, + ⟨7, 7, 4, 5, 6, 7, -23516638372336832756515216080809511380808892416000000⟩, + ⟨7, 7, 5, 5, 7, 7, 1894729598829230545337400642240304966470205440000000⟩, + ⟨7, 7, 6, 5, 8, 7, -26150864951492373360182690021396373268636631040000000⟩, + ⟨7, 7, 3, 6, 4, 7, -68978242264272342930653426686840696318678007808000000⟩, + ⟨7, 7, 4, 6, 5, 7, 38157712935777525817875308241681985326890876928000000⟩, + ⟨7, 7, 5, 6, 6, 7, -18022259642558141991390230753705130619526184960000000⟩, + ⟨7, 7, 6, 6, 7, 7, -24696791743711261277819300825522487368519516160000000⟩, + ⟨7, 7, 7, 6, 8, 7, -6773409925377576241561798889033439608297226240000000⟩, + ⟨7, 7, 3, 7, 3, 7, 122933548285253182514566080089098531420099313664000000⟩, + ⟨7, 7, 4, 7, 4, 7, 157805547457679408186623533007646778534716768256000000⟩, + ⟨7, 7, 5, 7, 5, 7, 20381379807316646708904273244928639593988751360000000⟩, + ⟨7, 7, 6, 7, 6, 7, 26729827857496268423976196527915714411390566400000000⟩, + ⟨7, 7, 7, 7, 7, 7, 2393944155734778887405652740800456023154360320000000⟩, + ⟨7, 7, 8, 7, 8, 7, 12847066849947478750306376348997727902970675200000000⟩, + ⟨7, 8, 2, 1, 8, 8, 407020221741042353532618694112118854244315955200000000⟩, + ⟨7, 8, 2, 2, 7, 8, 494750651337820062008943138982906576624838246400000000⟩, + ⟨7, 8, 3, 2, 8, 8, 208120254663607538247482268091256054684319744000000000⟩, + ⟨7, 8, 2, 3, 6, 8, 196541124626160133791486627831711669688467456000000000⟩ +] + +def collectedFourData_17_55 : List CollectedFourTerm := [ + ⟨7, 8, 3, 3, 7, 8, 519653263250072122288477809313958766646080307200000000⟩, + ⟨7, 8, 4, 3, 8, 8, 150938627602102231827974347800835676152057036800000000⟩, + ⟨7, 8, 2, 4, 5, 8, 91277477980658163262322942900174544694778265600000000⟩, + ⟨7, 8, 3, 4, 6, 8, 1193650067739008214244603352969588849295281356800000000⟩, + ⟨7, 8, 4, 4, 7, 8, 343956773014396886154736431933550797846793420800000000⟩, + ⟨7, 8, 5, 4, 8, 8, -498163126193050054225312714576258896878370816000000000⟩, + ⟨7, 8, 2, 5, 4, 8, -483974484427817012352801411814091102495126323200000000⟩, + ⟨7, 8, 3, 5, 5, 8, 392295453864118100347418314192412041308379545600000000⟩, + ⟨7, 8, 4, 5, 6, 8, -315504253233844768027960002876310764193736294400000000⟩, + ⟨7, 8, 5, 5, 7, 8, 16946731861185258457832428638816668655550464000000000⟩, + ⟨7, 8, 6, 5, 8, 8, -175422800387261683867629603064793053022650368000000000⟩, + ⟨7, 8, 2, 6, 3, 8, -244204936533747617526533894216297843905265664000000000⟩, + ⟨7, 8, 3, 6, 4, 8, -1850853720706333028935250895119466040597571174400000000⟩, + ⟨7, 8, 4, 6, 5, 8, 511932042934995696847172099366520443219686195200000000⟩, + ⟨7, 8, 5, 6, 6, 8, -161193661556674856240313434327046219708235776000000000⟩, + ⟨7, 8, 6, 6, 7, 8, -165668721715286645414801916685010721017167872000000000⟩, + ⟨7, 8, 7, 6, 8, 8, -36349406858538314058113844740701168112920166400000000⟩, + ⟨7, 8, 2, 7, 2, 8, 1181120011139690319904802255782407024423626342400000000⟩, + ⟨7, 8, 3, 7, 3, 8, 3298605585971041026361565356477382523580789555200000000⟩, + ⟨7, 8, 4, 7, 4, 8, 2117152996890931055231425572228014595029493350400000000⟩, + ⟨7, 8, 5, 7, 5, 8, 182293968896139634511374906819151292442607616000000000⟩, + ⟨7, 8, 6, 7, 6, 8, 179306545513089892280647112408209799648378880000000000⟩, + ⟨7, 8, 7, 7, 7, 8, 12847066849947478750306376348997727902970675200000000⟩, + ⟨7, 8, 8, 7, 8, 8, 57452999426226915365833087055884020413890560000000000⟩ +] + +def collectedFourData_17 : List CollectedFourTerm := (((((collectedFourData_17_0 ++ (collectedFourData_17_1 ++ collectedFourData_17_2)) ++ ((collectedFourData_17_3 ++ collectedFourData_17_4) ++ (collectedFourData_17_5 ++ collectedFourData_17_6))) ++ ((collectedFourData_17_7 ++ (collectedFourData_17_8 ++ collectedFourData_17_9)) ++ ((collectedFourData_17_10 ++ collectedFourData_17_11) ++ (collectedFourData_17_12 ++ collectedFourData_17_13)))) ++ (((collectedFourData_17_14 ++ (collectedFourData_17_15 ++ collectedFourData_17_16)) ++ ((collectedFourData_17_17 ++ collectedFourData_17_18) ++ (collectedFourData_17_19 ++ collectedFourData_17_20))) ++ ((collectedFourData_17_21 ++ (collectedFourData_17_22 ++ collectedFourData_17_23)) ++ ((collectedFourData_17_24 ++ collectedFourData_17_25) ++ (collectedFourData_17_26 ++ collectedFourData_17_27))))) ++ ((((collectedFourData_17_28 ++ (collectedFourData_17_29 ++ collectedFourData_17_30)) ++ ((collectedFourData_17_31 ++ collectedFourData_17_32) ++ (collectedFourData_17_33 ++ collectedFourData_17_34))) ++ ((collectedFourData_17_35 ++ (collectedFourData_17_36 ++ collectedFourData_17_37)) ++ ((collectedFourData_17_38 ++ collectedFourData_17_39) ++ (collectedFourData_17_40 ++ collectedFourData_17_41)))) ++ (((collectedFourData_17_42 ++ (collectedFourData_17_43 ++ collectedFourData_17_44)) ++ ((collectedFourData_17_45 ++ collectedFourData_17_46) ++ (collectedFourData_17_47 ++ collectedFourData_17_48))) ++ ((collectedFourData_17_49 ++ (collectedFourData_17_50 ++ collectedFourData_17_51)) ++ ((collectedFourData_17_52 ++ collectedFourData_17_53) ++ (collectedFourData_17_54 ++ collectedFourData_17_55)))))) + +theorem collectedFourChecked_17 : collectedFourTerms 17 = collectedFourData_17 := by + decide +kernel + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1801.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1801.lean new file mode 100644 index 0000000000000000000000000000000000000000..4ce969ef7f2007a08719276581dd369f388085dc --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1801.lean @@ -0,0 +1,631 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse1801. -/ +namespace LaughlinFock + +def collectedFourData_18_0 : List CollectedFourTerm := [ + ⟨2, 8, 8, 2, 8, 8, 1410275092236171732456779874727002498581819031552000000⟩, + ⟨2, 8, 8, 3, 7, 8, 863873543016573234199348239850973715830994370560000000⟩, + ⟨2, 8, 8, 4, 6, 8, -1101903776802035773697024996293509113050608697344000000⟩, + ⟨2, 8, 8, 5, 5, 8, -368333132945472785574315426473744734442999513088000000⟩, + ⟨2, 8, 8, 6, 4, 8, 548688625906514778300547100475161785594332315648000000⟩, + ⟨2, 8, 8, 7, 3, 8, 2627915933357952857120570017847040729896045248512000000⟩, + ⟨3, 7, 8, 2, 8, 8, 863873543016573234199348239850973715830994370560000000⟩, + ⟨3, 7, 8, 3, 7, 8, 529171579667261000846554123539813395361221836800000000⟩, + ⟨3, 7, 8, 4, 6, 8, -674978608762032291067284548394404457799294648320000000⟩, + ⟨3, 7, 8, 5, 5, 8, -225624950989855415243409790023301344065633648640000000⟩, + ⟨3, 7, 8, 6, 4, 8, 336102927637452766348714215817277988454992445440000000⟩, + ⟨3, 7, 8, 7, 3, 8, 1609747673058571462994360871437294423126688399360000000⟩, + ⟨4, 6, 8, 2, 8, 8, -1101903776802035773697024996293509113050608697344000000⟩, + ⟨4, 6, 8, 3, 7, 8, -674978608762032291067284548394404457799294648320000000⟩, + ⟨4, 6, 8, 4, 6, 8, 860961056473977636843669954081940993428808531968000000⟩, + ⟨4, 6, 8, 5, 5, 8, 287793262852276327597889957711025519510197108736000000⟩, + ⟨4, 6, 8, 6, 4, 8, -428712151624286272392367702074397630666748461056000000⟩, + ⟨4, 6, 8, 7, 3, 8, -2053294784845030089442512855988173094967222206464000000⟩, + ⟨5, 5, 8, 2, 8, 8, -368333132945472785574315426473744734442999513088000000⟩, + ⟨5, 5, 8, 3, 7, 8, -225624950989855415243409790023301344065633648640000000⟩, + ⟨5, 5, 8, 4, 6, 8, 287793262852276327597889957711025519510197108736000000⟩, + ⟨5, 5, 8, 5, 5, 8, 96200590631084810653320438372755685658771587072000000⟩, + ⟨5, 5, 8, 6, 4, 8, -143305516565025158174407019853910632733933043712000000⟩, + ⟨5, 5, 8, 7, 3, 8, -686354395805328130975717503183320166459745763328000000⟩ +] + +def collectedFourData_18_1 : List CollectedFourTerm := [ + ⟨6, 4, 8, 2, 8, 8, 548688625906514778300547100475161785594332315648000000⟩, + ⟨6, 4, 8, 3, 7, 8, 336102927637452766348714215817277988454992445440000000⟩, + ⟨6, 4, 8, 4, 6, 8, -428712151624286272392367702074397630666748461056000000⟩, + ⟨6, 4, 8, 5, 5, 8, -143305516565025158174407019853910632733933043712000000⟩, + ⟨6, 4, 8, 6, 4, 8, 213475519674541934687261091991445624459102257152000000⟩, + ⟨6, 4, 8, 7, 3, 8, 1022430014122764034435335449270647929495971954688000000⟩, + ⟨7, 3, 8, 2, 8, 8, 2627915933357952857120570017847040729896045248512000000⟩, + ⟨7, 3, 8, 3, 7, 8, 1609747673058571462994360871437294423126688399360000000⟩, + ⟨7, 3, 8, 4, 6, 8, -2053294784845030089442512855988173094967222206464000000⟩, + ⟨7, 3, 8, 5, 5, 8, -686354395805328130975717503183320166459745763328000000⟩, + ⟨7, 3, 8, 6, 4, 8, 1022430014122764034435335449270647929495971954688000000⟩, + ⟨7, 3, 8, 7, 3, 8, 4896875929253167899153779175628778140948362166272000000⟩, + ⟨2, 8, 8, 3, 8, 7, -341945416400498246897137136003620358364069888000000000⟩, + ⟨2, 8, 8, 4, 7, 7, -121468060417546485802685236344327212839244660736000000⟩, + ⟨2, 8, 8, 5, 6, 7, -252928381907100905916040135907608060587675746304000000⟩, + ⟨2, 8, 8, 6, 5, 7, 265437053140964693655449372224981644676241031168000000⟩, + ⟨2, 8, 8, 7, 4, 7, -524827913514146957963112207017004245190621265920000000⟩, + ⟨3, 7, 8, 3, 8, 7, 190935179265994617128033483047666403153805312000000000⟩, + ⟨3, 7, 8, 4, 7, 7, 67825228175461250376686549107563734609285873664000000⟩, + ⟨3, 7, 8, 5, 6, 7, 141229926253282257991965920788352104736590135296000000⟩, + ⟨3, 7, 8, 6, 5, 7, -148214507036841760454040566976187362738576556032000000⟩, + ⟨3, 7, 8, 7, 4, 7, 293052946301974631887771196869974284635817902080000000⟩, + ⟨3, 8, 7, 2, 8, 8, -341945416400498246897137136003620358364069888000000000⟩, + ⟨3, 8, 7, 3, 7, 8, 190935179265994617128033483047666403153805312000000000⟩ +] + +def collectedFourData_18_2 : List CollectedFourTerm := [ + ⟨3, 8, 8, 3, 8, 8, 864009772070565031264275346671607782309888000000000000⟩, + ⟨3, 8, 7, 4, 6, 8, -62707951333157675897378347885716527917301760000000000⟩, + ⟨3, 8, 8, 4, 7, 8, 306919134345983998317441579303235726381940736000000000⟩, + ⟨3, 8, 7, 5, 5, 8, -166078365987816979322381169316379043947347968000000000⟩, + ⟨3, 8, 8, 5, 6, 8, 639086190720504289721716989633756669677666304000000000⟩, + ⟨3, 8, 7, 6, 4, 8, 59453660190608190446180975176898150595035136000000000⟩, + ⟨3, 8, 8, 6, 5, 8, -670692446173327891254180802178937211393671168000000000⟩, + ⟨3, 8, 7, 7, 3, 8, 2491082420598308327858657676035417600377749504000000000⟩, + ⟨3, 8, 8, 7, 4, 8, 1326107689072002431462750021173808570742865920000000000⟩, + ⟨4, 6, 8, 3, 8, 7, -62707951333157675897378347885716527917301760000000000⟩, + ⟨4, 6, 8, 4, 7, 7, -22275523682631420603104564286010094915388702720000000⟩, + ⟨4, 6, 8, 5, 6, 7, -46383486669779766688462892268466997530019758080000000⟩, + ⟨4, 6, 8, 6, 5, 7, 48677399994404921230757937522180212030554767360000000⟩, + ⟨4, 6, 8, 7, 4, 7, -96246013780110020160122925135114311983064678400000000⟩, + ⟨4, 7, 7, 2, 8, 8, -121468060417546485802685236344327212839244660736000000⟩, + ⟨4, 7, 7, 3, 7, 8, 67825228175461250376686549107563734609285873664000000⟩, + ⟨4, 7, 8, 3, 8, 8, 306919134345983998317441579303235726381940736000000000⟩, + ⟨4, 7, 7, 4, 6, 8, -22275523682631420603104564286010094915388702720000000⟩, + ⟨4, 7, 8, 4, 7, 8, 109025798171174811140951604723273803822731886592000000⟩, + ⟨4, 7, 7, 5, 5, 8, -58995430341513874169602733343567117798390890496000000⟩, + ⟨4, 7, 8, 5, 6, 8, 227020326353889793451120085461970530865971724288000000⟩, + ⟨4, 7, 7, 6, 4, 8, 21119513354197869757747152776581178706616123392000000⟩, + ⟨4, 7, 8, 6, 5, 8, -238247704651072288708776368826618258808054480896000000⟩, + ⟨4, 7, 7, 7, 3, 8, 884898394473353626602896148848117351328082034688000000⟩ +] + +def collectedFourData_18_3 : List CollectedFourTerm := [ + ⟨4, 7, 8, 7, 4, 8, 471068542435757687183287738257959319377270538240000000⟩, + ⟨5, 5, 8, 3, 8, 7, -166078365987816979322381169316379043947347968000000000⟩, + ⟨5, 5, 8, 4, 7, 7, -58995430341513874169602733343567117798390890496000000⟩, + ⟨5, 5, 8, 5, 6, 7, -122843969722568399715442181027185494042234322944000000⟩, + ⟨5, 5, 8, 6, 5, 7, 128919265894299395717099559303952219203119874048000000⟩, + ⟨5, 5, 8, 7, 4, 7, -254901975931553534405755942770554994372504453120000000⟩, + ⟨5, 6, 7, 2, 8, 8, -252928381907100905916040135907608060587675746304000000⟩, + ⟨5, 6, 7, 3, 7, 8, 141229926253282257991965920788352104736590135296000000⟩, + ⟨5, 6, 8, 3, 8, 8, 639086190720504289721716989633756669677666304000000000⟩, + ⟨5, 6, 7, 4, 6, 8, -46383486669779766688462892268466997530019758080000000⟩, + ⟨5, 6, 8, 4, 7, 8, 227020326353889793451120085461970530865971724288000000⟩, + ⟨5, 6, 7, 5, 5, 8, -122843969722568399715442181027185494042234322944000000⟩, + ⟨5, 6, 8, 5, 6, 8, 472715902495935625684332121216211618190990508032000000⟩, + ⟨5, 6, 7, 6, 4, 8, 43976369763215925195350695733946389396075839488000000⟩, + ⟨5, 6, 8, 6, 5, 8, -496094250812387894931817784585003872156378988544000000⟩, + ⟨5, 6, 7, 7, 3, 8, 1842590704889577902933838323504605574001309253632000000⟩, + ⟨5, 6, 8, 7, 4, 8, 980888340490876452483102020532410627090924175360000000⟩, + ⟨6, 4, 8, 3, 8, 7, 59453660190608190446180975176898150595035136000000000⟩, + ⟨6, 4, 8, 4, 7, 7, 21119513354197869757747152776581178706616123392000000⟩, + ⟨6, 4, 8, 5, 6, 7, 43976369763215925195350695733946389396075839488000000⟩, + ⟨6, 4, 8, 6, 5, 7, -46151238187546966147709767275222122392291639296000000⟩, + ⟨6, 4, 8, 7, 4, 7, 91251231723106470849841481920933992308397834240000000⟩, + ⟨6, 5, 7, 2, 8, 8, 265437053140964693655449372224981644676241031168000000⟩, + ⟨6, 5, 7, 3, 7, 8, -148214507036841760454040566976187362738576556032000000⟩ +] + +def collectedFourData_18_4 : List CollectedFourTerm := [ + ⟨6, 5, 8, 3, 8, 8, -670692446173327891254180802178937211393671168000000000⟩, + ⟨6, 5, 7, 4, 6, 8, 48677399994404921230757937522180212030554767360000000⟩, + ⟨6, 5, 8, 4, 7, 8, -238247704651072288708776368826618258808054480896000000⟩, + ⟨6, 5, 7, 5, 5, 8, 128919265894299395717099559303952219203119874048000000⟩, + ⟨6, 5, 8, 5, 6, 8, -496094250812387894931817784585003872156378988544000000⟩, + ⟨6, 5, 7, 6, 4, 8, -46151238187546966147709767275222122392291639296000000⟩, + ⟨6, 5, 8, 6, 5, 8, 520628784412896830374554934597163226536500789248000000⟩, + ⟨6, 5, 7, 7, 3, 8, -1933716742909710373457074421043351537119599263744000000⟩, + ⟨6, 5, 8, 7, 4, 8, -1029398553839875654859368373050438966928599941120000000⟩, + ⟨7, 3, 8, 3, 8, 7, 2491082420598308327858657676035417600377749504000000000⟩, + ⟨7, 3, 8, 4, 7, 7, 884898394473353626602896148848117351328082034688000000⟩, + ⟨7, 3, 8, 5, 6, 7, 1842590704889577902933838323504605574001309253632000000⟩, + ⟨7, 3, 8, 6, 5, 7, -1933716742909710373457074421043351537119599263744000000⟩, + ⟨7, 3, 8, 7, 4, 7, 3823386793590241056438163913034581431551378063360000000⟩, + ⟨7, 4, 7, 2, 8, 8, -524827913514146957963112207017004245190621265920000000⟩, + ⟨7, 4, 7, 3, 7, 8, 293052946301974631887771196869974284635817902080000000⟩, + ⟨7, 4, 8, 3, 8, 8, 1326107689072002431462750021173808570742865920000000000⟩, + ⟨7, 4, 7, 4, 6, 8, -96246013780110020160122925135114311983064678400000000⟩, + ⟨7, 4, 8, 4, 7, 8, 471068542435757687183287738257959319377270538240000000⟩, + ⟨7, 4, 7, 5, 5, 8, -254901975931553534405755942770554994372504453120000000⟩, + ⟨7, 4, 8, 5, 6, 8, 980888340490876452483102020532410627090924175360000000⟩, + ⟨7, 4, 7, 6, 4, 8, 91251231723106470849841481920933992308397834240000000⟩, + ⟨7, 4, 8, 6, 5, 8, -1029398553839875654859368373050438966928599941120000000⟩, + ⟨7, 4, 7, 7, 3, 8, 3823386793590241056438163913034581431551378063360000000⟩ +] + +def collectedFourData_18_5 : List CollectedFourTerm := [ + ⟨7, 4, 8, 7, 4, 8, 2035349205370170508526860648987060061877357772800000000⟩, + ⟨2, 8, 8, 4, 8, 6, 258800897631737054325437575424593711994649968640000000⟩, + ⟨2, 8, 8, 5, 7, 6, -424304650787843437514885504976046478275865739264000000⟩, + ⟨2, 8, 8, 6, 6, 6, 633799348716261217860781292061654733255851638784000000⟩, + ⟨2, 8, 8, 7, 5, 6, 1637170802316469918651783938345757553739631165440000000⟩, + ⟨3, 7, 8, 4, 8, 6, 548727135952918797440882260870599510872555520000000⟩, + ⟨3, 7, 8, 5, 7, 6, -899639367285427824577143184951711336079818752000000⟩, + ⟨3, 7, 8, 6, 6, 6, 1343824169747586835675473181756984299054170112000000⟩, + ⟨3, 7, 8, 7, 5, 6, 3471240067718728805979173898238621996988497920000000⟩, + ⟨3, 8, 7, 3, 8, 7, 30997296017297419587930681959851815465557950464000000⟩, + ⟨3, 8, 7, 4, 7, 7, 81990415916997362063669419293908935041318125568000000⟩, + ⟨3, 8, 8, 4, 8, 7, -87823530365937359594789437811584437135417016320000000⟩, + ⟨3, 8, 7, 5, 6, 7, -25974404823807063891090985819700593175864279040000000⟩, + ⟨3, 8, 8, 5, 7, 7, 143986874558293247909422149622007175429155192832000000⟩, + ⟨3, 8, 7, 6, 5, 7, -162280101194694440821103978816496253733286445056000000⟩, + ⟨3, 8, 8, 6, 6, 7, -215078451648569290868475905609015844082487918592000000⟩, + ⟨3, 8, 7, 7, 4, 7, -126187308136444633948733994147021298137688965120000000⟩, + ⟨3, 8, 8, 7, 5, 7, -555570405617613120115750768874006665998599454720000000⟩, + ⟨4, 6, 8, 4, 8, 6, 110891612041937769060242225984501808100823531520000000⟩, + ⟨4, 6, 8, 5, 7, 6, -181807046085706462971729783812028535205215076352000000⟩, + ⟨4, 6, 8, 6, 6, 6, 271571822715569971376627774833914279431044595712000000⟩, + ⟨4, 6, 8, 7, 5, 6, 701498762632585514300114144154545574096320593920000000⟩, + ⟨4, 7, 7, 3, 8, 7, 81990415916997362063669419293908935041318125568000000⟩, + ⟨4, 7, 7, 4, 7, 7, 216871442544243150807980519433117664856890146816000000⟩ +] + +def collectedFourData_18_6 : List CollectedFourTerm := [ + ⟨4, 7, 8, 4, 8, 7, -232300513502340726666042098486076372384837795840000000⟩, + ⟨4, 7, 7, 5, 6, 7, -68704452591993637410314329647965069988310548480000000⟩, + ⟨4, 7, 8, 5, 7, 7, 380857211707599986642160207787261895021621673984000000⟩, + ⟨4, 7, 7, 6, 5, 7, -429244311651590472527195376007588902766664220672000000⟩, + ⟨4, 7, 8, 6, 6, 7, -568900322647804361015565509780845336425979183104000000⟩, + ⟨4, 7, 7, 7, 4, 7, -333775883928067123544540819638590676227525181440000000⟩, + ⟨4, 7, 8, 7, 5, 7, -1469529748734984972847758339751172125353459056640000000⟩, + ⟨4, 8, 6, 2, 8, 8, 258800897631737054325437575424593711994649968640000000⟩, + ⟨4, 8, 6, 3, 7, 8, 548727135952918797440882260870599510872555520000000⟩, + ⟨4, 8, 7, 3, 8, 8, -87823530365937359594789437811584437135417016320000000⟩, + ⟨4, 8, 6, 4, 6, 8, 110891612041937769060242225984501808100823531520000000⟩, + ⟨4, 8, 7, 4, 7, 8, -232300513502340726666042098486076372384837795840000000⟩, + ⟨4, 8, 8, 4, 8, 8, 124413634041379800192115181912021599089642700800000000⟩, + ⟨4, 8, 6, 5, 5, 8, 92636778227920412625685224918917732642020392960000000⟩, + ⟨4, 8, 7, 5, 6, 8, 73592352362212875305292018751020819121648435200000000⟩, + ⟨4, 8, 8, 5, 7, 8, -203976431412116538461456130969510103547463598080000000⟩, + ⟨4, 8, 6, 6, 4, 8, -61766337380219459957165479411654790716179087360000000⟩, + ⟨4, 8, 7, 6, 5, 8, 459782407701193858493031362376887409579424481280000000⟩, + ⟨4, 8, 8, 6, 6, 8, 304687043006530570019715164036919516753014292480000000⟩, + ⟨4, 8, 6, 7, 3, 8, -311808240706428052912372869167128637825215365120000000⟩, + ⟨4, 8, 7, 7, 4, 8, 357521987780248055256636605733385410105153945600000000⟩, + ⟨4, 8, 8, 7, 5, 8, 787038881729346620186132369487913251437857996800000000⟩, + ⟨5, 5, 8, 4, 8, 6, 92636778227920412625685224918917732642020392960000000⟩, + ⟨5, 5, 8, 5, 7, 6, -151878205198653460377898826472689161543033552896000000⟩ +] + +def collectedFourData_18_7 : List CollectedFourTerm := [ + ⟨5, 5, 8, 6, 6, 6, 226866020347329063119604259628578556359974322176000000⟩, + ⟨5, 5, 8, 7, 5, 6, 586018943223397998615368123600491876205104988160000000⟩, + ⟨5, 6, 7, 3, 8, 7, -25974404823807063891090985819700593175864279040000000⟩, + ⟨5, 6, 7, 4, 7, 7, -68704452591993637410314329647965069988310548480000000⟩, + ⟨5, 6, 8, 4, 8, 7, 73592352362212875305292018751020819121648435200000000⟩, + ⟨5, 6, 7, 5, 6, 7, 21765437397330585435698390587837352555996774400000000⟩, + ⟨5, 6, 8, 5, 7, 7, -120654826375978652565683359206842235031671275520000000⟩, + ⟨5, 6, 7, 6, 5, 7, 135983765839678451330592420578292254162194268160000000⟩, + ⟨5, 6, 8, 6, 6, 7, 180226519399630819892593405958170745949514629120000000⟩, + ⟨5, 6, 7, 7, 4, 7, 105739553002735285254972373428829193988420403200000000⟩, + ⟨5, 6, 8, 7, 5, 7, 465544175710870534972699812738846562261873459200000000⟩, + ⟨5, 7, 6, 2, 8, 8, -424304650787843437514885504976046478275865739264000000⟩, + ⟨5, 7, 6, 3, 7, 8, -899639367285427824577143184951711336079818752000000⟩, + ⟨5, 7, 7, 3, 8, 8, 143986874558293247909422149622007175429155192832000000⟩, + ⟨5, 7, 6, 4, 6, 8, -181807046085706462971729783812028535205215076352000000⟩, + ⟨5, 7, 7, 4, 7, 8, 380857211707599986642160207787261895021621673984000000⟩, + ⟨5, 7, 8, 4, 8, 8, -203976431412116538461456130969510103547463598080000000⟩, + ⟨5, 7, 6, 5, 5, 8, -151878205198653460377898826472689161543033552896000000⟩, + ⟨5, 7, 7, 5, 6, 8, -120654826375978652565683359206842235031671275520000000⟩, + ⟨5, 7, 8, 5, 7, 8, 334419815739677352058797044392866649430040772608000000⟩, + ⟨5, 7, 6, 6, 4, 8, 101266048349842556213951243063439906984570126336000000⟩, + ⟨5, 7, 7, 6, 5, 8, -753814286284473351637684009051890517976366972928000000⟩, + ⟨5, 7, 8, 6, 6, 8, -499535088809571486988594128288841800335436546048000000⟩, + ⟨5, 7, 6, 7, 3, 8, 511210308373708185377665040386654496363970035712000000⟩ +] + +def collectedFourData_18_8 : List CollectedFourTerm := [ + ⟨5, 7, 7, 7, 4, 8, -586158098995213254653283217979771591368177090560000000⟩, + ⟨5, 7, 8, 7, 5, 8, -1290352007757770847380298521051704414837596487680000000⟩, + ⟨6, 4, 8, 4, 8, 6, -61766337380219459957165479411654790716179087360000000⟩, + ⟨6, 4, 8, 5, 7, 6, 101266048349842556213951243063439906984570126336000000⟩, + ⟨6, 4, 8, 6, 6, 6, -151264793756152934129368886553088513422252834816000000⟩, + ⟨6, 4, 8, 7, 5, 6, -390732972915790019934026808665707631407068610560000000⟩, + ⟨6, 5, 7, 3, 8, 7, -162280101194694440821103978816496253733286445056000000⟩, + ⟨6, 5, 7, 4, 7, 7, -429244311651590472527195376007588902766664220672000000⟩, + ⟨6, 5, 8, 4, 8, 7, 459782407701193858493031362376887409579424481280000000⟩, + ⟨6, 5, 7, 5, 6, 7, 135983765839678451330592420578292254162194268160000000⟩, + ⟨6, 5, 8, 5, 7, 7, -753814286284473351637684009051890517976366972928000000⟩, + ⟨6, 5, 7, 6, 5, 7, 849584790527039632160498060539275127797552513024000000⟩, + ⟨6, 5, 8, 6, 6, 7, 1125999922020653891773437783448447442735194963968000000⟩, + ⟨6, 5, 7, 7, 4, 7, 660628240683999033454609196634559105362013716480000000⟩, + ⟨6, 5, 8, 7, 5, 7, 2908576980201525240764295813267778969858348154880000000⟩, + ⟨6, 6, 6, 2, 8, 8, 633799348716261217860781292061654733255851638784000000⟩, + ⟨6, 6, 6, 3, 7, 8, 1343824169747586835675473181756984299054170112000000⟩, + ⟨6, 6, 7, 3, 8, 8, -215078451648569290868475905609015844082487918592000000⟩, + ⟨6, 6, 6, 4, 6, 8, 271571822715569971376627774833914279431044595712000000⟩, + ⟨6, 6, 7, 4, 7, 8, -568900322647804361015565509780845336425979183104000000⟩, + ⟨6, 6, 8, 4, 8, 8, 304687043006530570019715164036919516753014292480000000⟩, + ⟨6, 6, 6, 5, 5, 8, 226866020347329063119604259628578556359974322176000000⟩, + ⟨6, 6, 7, 5, 6, 8, 180226519399630819892593405958170745949514629120000000⟩, + ⟨6, 6, 8, 5, 7, 8, -499535088809571486988594128288841800335436546048000000⟩ +] + +def collectedFourData_18_9 : List CollectedFourTerm := [ + ⟨6, 6, 6, 6, 4, 8, -151264793756152934129368886553088513422252834816000000⟩, + ⟨6, 6, 7, 6, 5, 8, 1125999922020653891773437783448447442735194963968000000⟩, + ⟨6, 6, 8, 6, 6, 8, 746173800736235116754237731368146767245830258688000000⟩, + ⟨6, 6, 6, 7, 3, 8, -763613502474430623305985619216207031007939919872000000⟩, + ⟨6, 6, 7, 7, 4, 8, 875565753752920682246748707614792672355926671360000000⟩, + ⟨6, 6, 8, 7, 5, 8, 1927445906173947415388093807552530487625992110080000000⟩, + ⟨7, 3, 8, 4, 8, 6, -311808240706428052912372869167128637825215365120000000⟩, + ⟨7, 3, 8, 5, 7, 6, 511210308373708185377665040386654496363970035712000000⟩, + ⟨7, 3, 8, 6, 6, 6, -763613502474430623305985619216207031007939919872000000⟩, + ⟨7, 3, 8, 7, 5, 6, -1972494501671421657994258245080143882591162859520000000⟩, + ⟨7, 4, 7, 3, 8, 7, -126187308136444633948733994147021298137688965120000000⟩, + ⟨7, 4, 7, 4, 7, 7, -333775883928067123544540819638590676227525181440000000⟩, + ⟨7, 4, 8, 4, 8, 7, 357521987780248055256636605733385410105153945600000000⟩, + ⟨7, 4, 7, 5, 6, 7, 105739553002735285254972373428829193988420403200000000⟩, + ⟨7, 4, 8, 5, 7, 7, -586158098995213254653283217979771591368177090560000000⟩, + ⟨7, 4, 7, 6, 5, 7, 660628240683999033454609196634559105362013716480000000⟩, + ⟨7, 4, 8, 6, 6, 7, 875565753752920682246748707614792672355926671360000000⟩, + ⟨7, 4, 7, 7, 4, 7, 513697605295519425196883040043157198869207449600000000⟩, + ⟨7, 4, 8, 7, 5, 7, 2261679016325748759553972874259058602695825817600000000⟩, + ⟨7, 5, 6, 2, 8, 8, 1637170802316469918651783938345757553739631165440000000⟩, + ⟨7, 5, 6, 3, 7, 8, 3471240067718728805979173898238621996988497920000000⟩, + ⟨7, 5, 7, 3, 8, 8, -555570405617613120115750768874006665998599454720000000⟩, + ⟨7, 5, 6, 4, 6, 8, 701498762632585514300114144154545574096320593920000000⟩, + ⟨7, 5, 7, 4, 7, 8, -1469529748734984972847758339751172125353459056640000000⟩ +] + +def collectedFourData_18_10 : List CollectedFourTerm := [ + ⟨7, 5, 8, 4, 8, 8, 787038881729346620186132369487913251437857996800000000⟩, + ⟨7, 5, 6, 5, 5, 8, 586018943223397998615368123600491876205104988160000000⟩, + ⟨7, 5, 7, 5, 6, 8, 465544175710870534972699812738846562261873459200000000⟩, + ⟨7, 5, 8, 5, 7, 8, -1290352007757770847380298521051704414837596487680000000⟩, + ⟨7, 5, 6, 6, 4, 8, -390732972915790019934026808665707631407068610560000000⟩, + ⟨7, 5, 7, 6, 5, 8, 2908576980201525240764295813267778969858348154880000000⟩, + ⟨7, 5, 8, 6, 6, 8, 1927445906173947415388093807552530487625992110080000000⟩, + ⟨7, 5, 6, 7, 3, 8, -1972494501671421657994258245080143882591162859520000000⟩, + ⟨7, 5, 7, 7, 4, 8, 2261679016325748759553972874259058602695825817600000000⟩, + ⟨7, 5, 8, 7, 5, 8, 4978796786433863357266932068686793605699652812800000000⟩, + ⟨2, 8, 8, 5, 8, 5, 2000415723976104168507026777611789054190121123840000000⟩, + ⟨2, 8, 8, 6, 7, 5, 539227141438104156836474480036118773825808629760000000⟩, + ⟨2, 8, 8, 7, 6, 5, 806181253299260231990460689249988564821905244160000000⟩, + ⟨3, 7, 8, 5, 8, 5, -157590335251533201168806908051002196088208752640000000⟩, + ⟨3, 7, 8, 6, 7, 5, -42479663090756545040474244149623019558362152960000000⟩, + ⟨3, 7, 8, 7, 6, 5, -63509985678581503937475870809314293357855375360000000⟩, + ⟨3, 8, 7, 4, 8, 6, 741664965824449401847948277505147636429304627200000000⟩, + ⟨3, 8, 7, 5, 7, 6, 338300048979337063576733466204166899506935234560000000⟩, + ⟨3, 8, 8, 5, 8, 6, 2042193356940763591695529989793438828654724382720000000⟩, + ⟨3, 8, 7, 6, 6, 6, 102277084307686210041231415023404049383943045120000000⟩, + ⟨3, 8, 8, 6, 7, 6, 550488617405113058332852300844871614401169326080000000⟩, + ⟨3, 8, 7, 7, 5, 6, -367434176984288580959265722546613755264850984960000000⟩, + ⟨3, 8, 8, 7, 6, 6, 823017925846695151536952388788959397790644961280000000⟩, + ⟨4, 6, 8, 5, 8, 5, -385937340137190587721895727853312684665811763200000000⟩ +] + +def collectedFourData_18_11 : List CollectedFourTerm := [ + ⟨4, 6, 8, 6, 7, 5, -104032319983347881427694791903563779517762764800000000⟩, + ⟨4, 6, 8, 7, 6, 5, -155535394387101830953288698908008167838108876800000000⟩, + ⟨4, 7, 7, 4, 8, 6, -323630283780184519266769096391589675741374054400000000⟩, + ⟨4, 7, 7, 5, 7, 6, -147619404851257125362294441092112112738757509120000000⟩, + ⟨4, 7, 8, 5, 8, 6, -891124221980824112497792219553752017375005245440000000⟩, + ⟨4, 7, 7, 6, 6, 6, -44629264349721271767769802637542171200444170240000000⟩, + ⟨4, 7, 8, 6, 7, 6, -240209253069595632086682773733873330264641372160000000⟩, + ⟨4, 7, 7, 7, 5, 6, 160332269215086913659028103197236075740182609920000000⟩, + ⟨4, 7, 8, 7, 6, 6, -359129171757305511242275615329677963942229442560000000⟩, + ⟨4, 8, 6, 3, 8, 7, 741664965824449401847948277505147636429304627200000000⟩, + ⟨4, 8, 6, 4, 7, 7, -323630283780184519266769096391589675741374054400000000⟩, + ⟨4, 8, 7, 4, 8, 7, 1899337959913471904975927541168008284103245824000000000⟩, + ⟨4, 8, 6, 5, 6, 7, -548127192365233680424560510941206735243286937600000000⟩, + ⟨4, 8, 7, 5, 7, 7, 866356312452718779985316710837901408280458035200000000⟩, + ⟨4, 8, 8, 5, 8, 7, 2614937703042873954521817337415570018482205491200000000⟩, + ⟨4, 8, 6, 6, 5, 7, 52136555143441503714519390938053315032357273600000000⟩, + ⟨4, 8, 7, 6, 6, 7, 261922508957824428701834694817175843436389990400000000⟩, + ⟨4, 8, 8, 6, 7, 7, 704876174362331998334983625322074486705278156800000000⟩, + ⟨4, 8, 6, 7, 4, 7, 1809328283946851519341583350129312920879759360000000000⟩, + ⟨4, 8, 7, 7, 5, 7, -940966220967502769924552436193304093721310003200000000⟩, + ⟨4, 8, 8, 7, 6, 7, 1053837824544002250657624573458856950931180748800000000⟩, + ⟨5, 5, 8, 5, 8, 5, -106210465659287907017777366855866663617272217600000000⟩, + ⟨5, 5, 8, 6, 7, 5, -28629831840369936193958462024929202779088486400000000⟩, + ⟨5, 5, 8, 7, 6, 5, -42803545929198860307088090133738676260595302400000000⟩ +] + +def collectedFourData_18_12 : List CollectedFourTerm := [ + ⟨5, 6, 7, 4, 8, 6, -548127192365233680424560510941206735243286937600000000⟩, + ⟨5, 6, 7, 5, 7, 6, -250020514071250216572673047967710217897487892480000000⟩, + ⟨5, 6, 8, 5, 8, 6, -1509282172662079931569836337558213840927992053760000000⟩, + ⟨5, 6, 7, 6, 6, 6, -75587837700485143817824678667888357656189992960000000⟩, + ⟨5, 6, 8, 6, 7, 6, -406838389557562913806641040190742643457277296640000000⟩, + ⟨5, 6, 7, 7, 5, 6, 271552079564048862959923562094445538972459335680000000⟩, + ⟨5, 6, 8, 7, 6, 6, -608251064493972525328747644435043081456441098240000000⟩, + ⟨5, 7, 6, 3, 8, 7, 338300048979337063576733466204166899506935234560000000⟩, + ⟨5, 7, 6, 4, 7, 7, -147619404851257125362294441092112112738757509120000000⟩, + ⟨5, 7, 7, 4, 8, 7, 866356312452718779985316710837901408280458035200000000⟩, + ⟨5, 7, 6, 5, 6, 7, -250020514071250216572673047967710217897487892480000000⟩, + ⟨5, 7, 7, 5, 7, 7, 395176254025306132388861316072582384263846952960000000⟩, + ⟨5, 7, 8, 5, 8, 7, 1192767076484384446628539772716633980319574261760000000⟩, + ⟨5, 7, 6, 6, 5, 7, 23781356773450452852380119243020598875814625280000000⟩, + ⟨5, 7, 7, 6, 6, 7, 119472270758703038977149009682964673103575121920000000⟩, + ⟨5, 7, 8, 6, 7, 7, 321519358873946815200725308699026578022743408640000000⟩, + ⟨5, 7, 6, 7, 4, 7, 825299663977658608664731814188043477742256128000000000⟩, + ⟨5, 7, 7, 7, 5, 7, -429208515043375664613282306188807762290786959360000000⟩, + ⟨5, 7, 8, 7, 6, 7, 480693310439986426782396986964523185007220490240000000⟩, + ⟨5, 8, 5, 2, 8, 8, 2000415723976104168507026777611789054190121123840000000⟩, + ⟨5, 8, 5, 3, 7, 8, -157590335251533201168806908051002196088208752640000000⟩, + ⟨5, 8, 6, 3, 8, 8, 2042193356940763591695529989793438828654724382720000000⟩, + ⟨5, 8, 5, 4, 6, 8, -385937340137190587721895727853312684665811763200000000⟩, + ⟨5, 8, 6, 4, 7, 8, -891124221980824112497792219553752017375005245440000000⟩ +] + +def collectedFourData_18_13 : List CollectedFourTerm := [ + ⟨5, 8, 7, 4, 8, 8, 2614937703042873954521817337415570018482205491200000000⟩, + ⟨5, 8, 5, 5, 5, 8, -106210465659287907017777366855866663617272217600000000⟩, + ⟨5, 8, 6, 5, 6, 8, -1509282172662079931569836337558213840927992053760000000⟩, + ⟨5, 8, 7, 5, 7, 8, 1192767076484384446628539772716633980319574261760000000⟩, + ⟨5, 8, 8, 5, 8, 8, 2400099169680034427310085913594509832282481623040000000⟩, + ⟨5, 8, 5, 6, 4, 8, 885693914135165701793744768578302070111013437440000000⟩, + ⟨5, 8, 6, 6, 5, 8, 143559331334134994347074076823082741871788687360000000⟩, + ⟨5, 8, 7, 6, 6, 8, 360605146848432632608907437130538442120778219520000000⟩, + ⟨5, 8, 8, 6, 7, 8, 646964827821955290021554441208706842436892098560000000⟩, + ⟨5, 8, 5, 7, 3, 8, 1234831412791658290475954744097671195574486958080000000⟩, + ⟨5, 8, 6, 7, 4, 8, 4982031472787526018776831599725547587618471936000000000⟩, + ⟨5, 8, 7, 7, 5, 8, -1295487217351140138768355018330156448495079260160000000⟩, + ⟨5, 8, 8, 7, 6, 8, 967256422484648193303608988640023813871852584960000000⟩, + ⟨6, 4, 8, 5, 8, 5, 885693914135165701793744768578302070111013437440000000⟩, + ⟨6, 4, 8, 6, 7, 5, 238745472645533002214559209169940948963200860160000000⟩, + ⟨6, 4, 8, 7, 6, 5, 356940720460735919690483580569581720277939650560000000⟩, + ⟨6, 5, 7, 4, 8, 6, 52136555143441503714519390938053315032357273600000000⟩, + ⟨6, 5, 7, 5, 7, 6, 23781356773450452852380119243020598875814625280000000⟩, + ⟨6, 5, 8, 5, 8, 6, 143559331334134994347074076823082741871788687360000000⟩, + ⟨6, 5, 7, 6, 6, 6, 7189735381380088173052038886955297209382338560000000⟩, + ⟨6, 5, 8, 6, 7, 6, 38697500191713138855408074674538997758338007040000000⟩, + ⟨6, 5, 7, 7, 5, 6, -25829388083110253218674208607332139117555220480000000⟩, + ⟨6, 5, 8, 7, 6, 6, 57855394891476674365816421364670441347235184640000000⟩, + ⟨6, 6, 6, 3, 8, 7, 102277084307686210041231415023404049383943045120000000⟩ +] + +def collectedFourData_18_14 : List CollectedFourTerm := [ + ⟨6, 6, 6, 4, 7, 7, -44629264349721271767769802637542171200444170240000000⟩, + ⟨6, 6, 7, 4, 8, 7, 261922508957824428701834694817175843436389990400000000⟩, + ⟨6, 6, 6, 5, 6, 7, -75587837700485143817824678667888357656189992960000000⟩, + ⟨6, 6, 7, 5, 7, 7, 119472270758703038977149009682964673103575121920000000⟩, + ⟨6, 6, 8, 5, 8, 7, 360605146848432632608907437130538442120778219520000000⟩, + ⟨6, 6, 6, 6, 5, 7, 7189735381380088173052038886955297209382338560000000⟩, + ⟨6, 6, 7, 6, 6, 7, 36119638603909638923493815853267848997466275840000000⟩, + ⟨6, 6, 8, 6, 7, 7, 97203836278818846714843850146365938058164961280000000⟩, + ⟨6, 6, 6, 7, 4, 7, 249509994356825229279461765226833563726381056000000000⟩, + ⟨6, 6, 7, 7, 5, 7, -129761126583074729951124347341340422806668574720000000⟩, + ⟨6, 6, 8, 7, 6, 7, 145326346792855890708848089614447473137790484480000000⟩, + ⟨6, 7, 5, 2, 8, 8, 539227141438104156836474480036118773825808629760000000⟩, + ⟨6, 7, 5, 3, 7, 8, -42479663090756545040474244149623019558362152960000000⟩, + ⟨6, 7, 6, 3, 8, 8, 550488617405113058332852300844871614401169326080000000⟩, + ⟨6, 7, 5, 4, 6, 8, -104032319983347881427694791903563779517762764800000000⟩, + ⟨6, 7, 6, 4, 7, 8, -240209253069595632086682773733873330264641372160000000⟩, + ⟨6, 7, 7, 4, 8, 8, 704876174362331998334983625322074486705278156800000000⟩, + ⟨6, 7, 5, 5, 5, 8, -28629831840369936193958462024929202779088486400000000⟩, + ⟨6, 7, 6, 5, 6, 8, -406838389557562913806641040190742643457277296640000000⟩, + ⟨6, 7, 7, 5, 7, 8, 321519358873946815200725308699026578022743408640000000⟩, + ⟨6, 7, 8, 5, 8, 8, 646964827821955290021554441208706842436892098560000000⟩, + ⟨6, 7, 5, 6, 4, 8, 238745472645533002214559209169940948963200860160000000⟩, + ⟨6, 7, 6, 6, 5, 8, 38697500191713138855408074674538997758338007040000000⟩, + ⟨6, 7, 7, 6, 6, 8, 97203836278818846714843850146365938058164961280000000⟩ +] + +def collectedFourData_18_15 : List CollectedFourTerm := [ + ⟨6, 7, 8, 6, 7, 8, 174394247423739748615234741479576141159035043840000000⟩, + ⟨6, 7, 5, 7, 3, 8, 332858117888687134242259591730294565173848965120000000⟩, + ⟨6, 7, 6, 7, 4, 8, 1342944147772543913650095213849525908882325504000000000⟩, + ⟨6, 7, 7, 7, 5, 8, -349208347349605140872538435969651039365486346240000000⟩, + ⟨6, 7, 8, 7, 6, 8, 260731261748607616613054064877646413315902013440000000⟩, + ⟨7, 3, 8, 5, 8, 5, 1234831412791658290475954744097671195574486958080000000⟩, + ⟨7, 3, 8, 6, 7, 5, 332858117888687134242259591730294565173848965120000000⟩, + ⟨7, 3, 8, 7, 6, 5, 497645526400374813923917378044399886473803857920000000⟩, + ⟨7, 4, 7, 4, 8, 6, 1809328283946851519341583350129312920879759360000000000⟩, + ⟨7, 4, 7, 5, 7, 6, 825299663977658608664731814188043477742256128000000000⟩, + ⟨7, 4, 8, 5, 8, 6, 4982031472787526018776831599725547587618471936000000000⟩, + ⟨7, 4, 7, 6, 6, 6, 249509994356825229279461765226833563726381056000000000⟩, + ⟨7, 4, 8, 6, 7, 6, 1342944147772543913650095213849525908882325504000000000⟩, + ⟨7, 4, 7, 7, 5, 6, -896373806962004381475859324400800584746139648000000000⟩, + ⟨7, 4, 8, 7, 6, 6, 2007792844541840295194434494317846925372555264000000000⟩, + ⟨7, 5, 6, 3, 8, 7, -367434176984288580959265722546613755264850984960000000⟩, + ⟨7, 5, 6, 4, 7, 7, 160332269215086913659028103197236075740182609920000000⟩, + ⟨7, 5, 7, 4, 8, 7, -940966220967502769924552436193304093721310003200000000⟩, + ⟨7, 5, 6, 5, 6, 7, 271552079564048862959923562094445538972459335680000000⟩, + ⟨7, 5, 7, 5, 7, 7, -429208515043375664613282306188807762290786959360000000⟩, + ⟨7, 5, 8, 5, 8, 7, -1295487217351140138768355018330156448495079260160000000⟩, + ⟨7, 5, 6, 6, 5, 7, -25829388083110253218674208607332139117555220480000000⟩, + ⟨7, 5, 7, 6, 6, 7, -129761126583074729951124347341340422806668574720000000⟩, + ⟨7, 5, 8, 6, 7, 7, -349208347349605140872538435969651039365486346240000000⟩ +] + +def collectedFourData_18_16 : List CollectedFourTerm := [ + ⟨7, 5, 6, 7, 4, 7, -896373806962004381475859324400800584746139648000000000⟩, + ⟨7, 5, 7, 7, 5, 7, 466171606996261050115920512414853003529169141760000000⟩, + ⟨7, 5, 8, 7, 6, 7, -522090231545185096462067206501625565433131171840000000⟩, + ⟨7, 6, 5, 2, 8, 8, 806181253299260231990460689249988564821905244160000000⟩, + ⟨7, 6, 5, 3, 7, 8, -63509985678581503937475870809314293357855375360000000⟩, + ⟨7, 6, 6, 3, 8, 8, 823017925846695151536952388788959397790644961280000000⟩, + ⟨7, 6, 5, 4, 6, 8, -155535394387101830953288698908008167838108876800000000⟩, + ⟨7, 6, 6, 4, 7, 8, -359129171757305511242275615329677963942229442560000000⟩, + ⟨7, 6, 7, 4, 8, 8, 1053837824544002250657624573458856950931180748800000000⟩, + ⟨7, 6, 5, 5, 5, 8, -42803545929198860307088090133738676260595302400000000⟩, + ⟨7, 6, 6, 5, 6, 8, -608251064493972525328747644435043081456441098240000000⟩, + ⟨7, 6, 7, 5, 7, 8, 480693310439986426782396986964523185007220490240000000⟩, + ⟨7, 6, 8, 5, 8, 8, 967256422484648193303608988640023813871852584960000000⟩, + ⟨7, 6, 5, 6, 4, 8, 356940720460735919690483580569581720277939650560000000⟩, + ⟨7, 6, 6, 6, 5, 8, 57855394891476674365816421364670441347235184640000000⟩, + ⟨7, 6, 7, 6, 6, 8, 145326346792855890708848089614447473137790484480000000⟩, + ⟨7, 6, 8, 6, 7, 8, 260731261748607616613054064877646413315902013440000000⟩, + ⟨7, 6, 5, 7, 3, 8, 497645526400374813923917378044399886473803857920000000⟩, + ⟨7, 6, 6, 7, 4, 8, 2007792844541840295194434494317846925372555264000000000⟩, + ⟨7, 6, 7, 7, 5, 8, -522090231545185096462067206501625565433131171840000000⟩, + ⟨7, 6, 8, 7, 6, 8, 389810970586905510844687608671229819946574807040000000⟩, + ⟨2, 8, 8, 6, 8, 4, -146965161479377996099744174271448920289102004224000000⟩, + ⟨2, 8, 8, 7, 7, 4, -111281661789179635594860600946233786854195331072000000⟩, + ⟨3, 7, 8, 6, 8, 4, -885999995785652385239907449296709799776077479936000000⟩ +] + +def collectedFourData_18_17 : List CollectedFourTerm := [ + ⟨3, 7, 8, 7, 7, 4, -670877035644045341010437576639143674069708177408000000⟩, + ⟨3, 8, 7, 5, 8, 5, 18680035016645034532296338410693596000351682560000000⟩, + ⟨3, 8, 7, 6, 7, 5, -61725956984472596349786311487793989152837468160000000⟩, + ⟨3, 8, 8, 6, 8, 5, 732730018640929815431380103740745466419336970240000000⟩, + ⟨3, 8, 7, 7, 6, 5, 154585370765948566388184902649965568577492746240000000⟩, + ⟨3, 8, 8, 7, 7, 5, 554821382812012697760254377660790508010308894720000000⟩, + ⟨4, 6, 8, 6, 8, 4, 1050560201667268259936048853575459639046495535104000000⟩, + ⟨4, 6, 8, 7, 7, 4, 795481622136098721156944115251711043752492531712000000⟩, + ⟨4, 7, 7, 5, 8, 5, 11161925666695820344762825644951730257710284800000000⟩, + ⟨4, 7, 7, 6, 7, 5, -36883257603769142662836013556198346507209932800000000⟩, + ⟨4, 7, 8, 6, 8, 5, 437829907413931904890968496243196026367980339200000000⟩, + ⟨4, 7, 7, 7, 6, 5, 92369763552939441703782290448377337116570419200000000⟩, + ⟨4, 7, 8, 7, 7, 5, 331523737922485034108469381613766093640931737600000000⟩, + ⟨4, 8, 6, 4, 8, 6, 85584899010536376726130923328066108017082368000000000⟩, + ⟨4, 8, 6, 5, 7, 6, -103739103575901175563417593276040811868533555200000000⟩, + ⟨4, 8, 7, 5, 8, 6, -42365230235284080917252813871910442133513830400000000⟩, + ⟨4, 8, 6, 6, 6, 6, 67550215600819398425025287280013269099400396800000000⟩, + ⟨4, 8, 7, 6, 7, 6, 139990871366690166414600500507552006594258534400000000⟩, + ⟨4, 8, 8, 6, 8, 6, -830894479383107511227046299027769620798688460800000000⟩, + ⟨4, 8, 6, 7, 5, 6, -69809102164467721882761026756013979078754304000000000⟩, + ⟨4, 8, 7, 7, 6, 6, -350590607441076598602155893677507337038436761600000000⟩, + ⟨4, 8, 8, 7, 7, 6, -629151273039507541076227803371771437601154662400000000⟩, + ⟨5, 5, 8, 6, 8, 4, 545035955462611787998492019693446003121008410624000000⟩, + ⟨5, 5, 8, 7, 7, 4, 412699896003880067520355079996137926985380790272000000⟩ +] + +def collectedFourData_18_18 : List CollectedFourTerm := [ + ⟨5, 6, 7, 5, 8, 5, -24793118926771960056913578358585013609850470400000000⟩, + ⟨5, 6, 7, 6, 7, 5, 81925916681696778282168558446087127532201574400000000⟩, + ⟨5, 6, 8, 6, 8, 5, -972517582391725677704894720222758005649283481600000000⟩, + ⟨5, 6, 7, 7, 6, 5, -205173784648913961813929019737781844942887321600000000⟩, + ⟨5, 6, 8, 7, 7, 5, -736387941185179811121905777709248139854925004800000000⟩, + ⟨5, 7, 6, 4, 8, 6, -103739103575901175563417593276040811868533555200000000⟩, + ⟨5, 7, 6, 5, 7, 6, 125744164392910765527629351333224977360255713280000000⟩, + ⟨5, 7, 7, 5, 8, 6, 51351711086952085162904820426124931715626434560000000⟩, + ⟨5, 7, 6, 6, 6, 6, -81878916652400932551299354709545701915251179520000000⟩, + ⟨5, 7, 7, 6, 7, 6, -169685629968458075864959529356973085418491740160000000⟩, + ⟨5, 7, 8, 6, 8, 6, 1007143192945253506872890229470583038709721989120000000⟩, + ⟨5, 7, 6, 7, 5, 6, 84616956539129967432687627059546998152206745600000000⟩, + ⟨5, 7, 7, 7, 6, 6, 424957624049897412865512000146872048388658954240000000⟩, + ⟨5, 7, 8, 7, 7, 6, 762606369036206324502928291151217857236681359360000000⟩, + ⟨5, 8, 5, 3, 8, 7, 18680035016645034532296338410693596000351682560000000⟩, + ⟨5, 8, 5, 4, 7, 7, 11161925666695820344762825644951730257710284800000000⟩, + ⟨5, 8, 6, 4, 8, 7, -42365230235284080917252813871910442133513830400000000⟩, + ⟨5, 8, 5, 5, 6, 7, -24793118926771960056913578358585013609850470400000000⟩, + ⟨5, 8, 6, 5, 7, 7, 51351711086952085162904820426124931715626434560000000⟩, + ⟨5, 8, 7, 5, 8, 7, 10485569029342832146081270260960142966715842560000000⟩, + ⟨5, 8, 5, 6, 5, 7, 50255046679649865312186440084802967605671362560000000⟩, + ⟨5, 8, 6, 6, 6, 7, -33437913340523752259699711916091172468073431040000000⟩, + ⟨5, 8, 7, 6, 7, 7, -34648317430144605851954914567436094937403228160000000⟩, + ⟨5, 8, 8, 6, 8, 7, 137099871306183910120160541476727920980477870080000000⟩ +] + +def collectedFourData_18_19 : List CollectedFourTerm := [ + ⟨5, 8, 5, 7, 4, 7, 151972737018998701046769406706574282541309624320000000⟩, + ⟨5, 8, 6, 7, 5, 7, 34556080802900140386291971099875661694841651200000000⟩, + ⟨5, 8, 7, 7, 6, 7, 86772619786235725850601823583338456550725386240000000⟩, + ⟨5, 8, 8, 7, 7, 7, 103811688133827666393920258901569196030940938240000000⟩, + ⟨6, 4, 8, 6, 8, 4, -1057819122102650810099932661487970952014020476928000000⟩, + ⟨6, 4, 8, 7, 7, 4, -800978058983535881145132602356983633388800835584000000⟩, + ⟨6, 5, 7, 5, 8, 5, 50255046679649865312186440084802967605671362560000000⟩, + ⟨6, 5, 7, 6, 7, 5, -166061832691246297258990442981596745670233948160000000⟩, + ⟨6, 5, 8, 6, 8, 5, 1971269393101715104717011087330949847719335690240000000⟩, + ⟨6, 5, 7, 7, 6, 5, 415882251661271106692927430117405774796019466240000000⟩, + ⟨6, 5, 8, 7, 7, 5, 1492640376061422528126364469050074658065057054720000000⟩, + ⟨6, 6, 6, 4, 8, 6, 67550215600819398425025287280013269099400396800000000⟩, + ⟨6, 6, 6, 5, 7, 6, -81878916652400932551299354709545701915251179520000000⟩, + ⟨6, 6, 7, 5, 8, 6, -33437913340523752259699711916091172468073431040000000⟩, + ⟨6, 6, 6, 6, 6, 6, 53315849880893457159156694379111266647728455680000000⟩, + ⟨6, 6, 7, 6, 7, 6, 110491613033302924610861189166799005452536381440000000⟩, + ⟨6, 6, 8, 6, 8, 6, -655806127865497400267295462845127892513408942080000000⟩, + ⟨6, 6, 6, 7, 5, 6, -55098737705221591523883791339364154585015910400000000⟩, + ⟨6, 6, 7, 7, 6, 6, -276713198170058101280740098665761872225144668160000000⟩, + ⟨6, 6, 8, 7, 7, 6, -496574800352532146010229463435344756863129354240000000⟩, + ⟨6, 7, 5, 3, 8, 7, -61725956984472596349786311487793989152837468160000000⟩, + ⟨6, 7, 5, 4, 7, 7, -36883257603769142662836013556198346507209932800000000⟩, + ⟨6, 7, 6, 4, 8, 7, 139990871366690166414600500507552006594258534400000000⟩, + ⟨6, 7, 5, 5, 6, 7, 81925916681696778282168558446087127532201574400000000⟩ +] + +def collectedFourData_18_20 : List CollectedFourTerm := [ + ⟨6, 7, 6, 5, 7, 7, -169685629968458075864959529356973085418491740160000000⟩, + ⟨6, 7, 7, 5, 8, 7, -34648317430144605851954914567436094937403228160000000⟩, + ⟨6, 7, 5, 6, 5, 7, -166061832691246297258990442981596745670233948160000000⟩, + ⟨6, 7, 6, 6, 6, 7, 110491613033302924610861189166799005452536381440000000⟩, + ⟨6, 7, 7, 6, 7, 7, 114491249581264019641035426331872085281614069760000000⟩, + ⟨6, 7, 8, 6, 8, 7, -453030240643635455089757332772561678295241850880000000⟩, + ⟨6, 7, 5, 7, 4, 7, -502175858861535615983114885959615549279850987520000000⟩, + ⟨6, 7, 6, 7, 5, 7, -114186464601974015528423786698574992950637363200000000⟩, + ⟨6, 7, 7, 7, 6, 7, -286729815633779831239470784221863456277151088640000000⟩, + ⟨6, 7, 8, 7, 7, 7, -343033393166786257144886620682387865649954160640000000⟩, + ⟨6, 8, 4, 2, 8, 8, -146965161479377996099744174271448920289102004224000000⟩, + ⟨6, 8, 4, 3, 7, 8, -885999995785652385239907449296709799776077479936000000⟩, + ⟨6, 8, 5, 3, 8, 8, 732730018640929815431380103740745466419336970240000000⟩, + ⟨6, 8, 4, 4, 6, 8, 1050560201667268259936048853575459639046495535104000000⟩, + ⟨6, 8, 5, 4, 7, 8, 437829907413931904890968496243196026367980339200000000⟩, + ⟨6, 8, 6, 4, 8, 8, -830894479383107511227046299027769620798688460800000000⟩, + ⟨6, 8, 4, 5, 5, 8, 545035955462611787998492019693446003121008410624000000⟩, + ⟨6, 8, 5, 5, 6, 8, -972517582391725677704894720222758005649283481600000000⟩, + ⟨6, 8, 6, 5, 7, 8, 1007143192945253506872890229470583038709721989120000000⟩, + ⟨6, 8, 7, 5, 8, 8, 137099871306183910120160541476727920980477870080000000⟩, + ⟨6, 8, 4, 6, 4, 8, -1057819122102650810099932661487970952014020476928000000⟩, + ⟨6, 8, 5, 6, 5, 8, 1971269393101715104717011087330949847719335690240000000⟩, + ⟨6, 8, 6, 6, 6, 8, -655806127865497400267295462845127892513408942080000000⟩, + ⟨6, 8, 7, 6, 7, 8, -453030240643635455089757332772561678295241850880000000⟩ +] + +def collectedFourData_18_21 : List CollectedFourTerm := [ + ⟨6, 8, 8, 6, 8, 8, 1344445970903371122372373393542966079928747950080000000⟩, + ⟨6, 8, 4, 7, 3, 8, 3850089329569141701426738389589089109460912177152000000⟩, + ⟨6, 8, 5, 7, 4, 8, 5961176535783795563387784541465163777810135777280000000⟩, + ⟨6, 8, 6, 7, 5, 8, 677736356176650812050908896944047603184985702400000000⟩, + ⟨6, 8, 7, 7, 6, 8, 1134560744610246722766984715998367287423082168320000000⟩, + ⟨6, 8, 8, 7, 7, 8, 1018011209744342175471191030299159691023079178240000000⟩, + ⟨7, 3, 8, 6, 8, 4, 3850089329569141701426738389589089109460912177152000000⟩, + ⟨7, 3, 8, 7, 7, 4, 2915278249065588761447599751467072671742118854656000000⟩, + ⟨7, 4, 7, 5, 8, 5, 151972737018998701046769406706574282541309624320000000⟩, + ⟨7, 4, 7, 6, 7, 5, -502175858861535615983114885959615549279850987520000000⟩, + ⟨7, 4, 8, 6, 8, 5, 5961176535783795563387784541465163777810135777280000000⟩, + ⟨7, 4, 7, 7, 6, 5, 1257640142401470215722313783616021090872359649280000000⟩, + ⟨7, 4, 8, 7, 7, 5, 4513788332167206811088994764485599298638934179840000000⟩, + ⟨7, 5, 6, 4, 8, 6, -69809102164467721882761026756013979078754304000000000⟩, + ⟨7, 5, 6, 5, 7, 6, 84616956539129967432687627059546998152206745600000000⟩, + ⟨7, 5, 7, 5, 8, 6, 34556080802900140386291971099875661694841651200000000⟩, + ⟨7, 5, 6, 6, 6, 6, -55098737705221591523883791339364154585015910400000000⟩, + ⟨7, 5, 7, 6, 7, 6, -114186464601974015528423786698574992950637363200000000⟩, + ⟨7, 5, 8, 6, 8, 6, 677736356176650812050908896944047603184985702400000000⟩, + ⟨7, 5, 6, 7, 5, 6, 56941245492492052348256250821883906345664512000000000⟩, + ⟨7, 5, 7, 7, 6, 6, 285966517641667869702408777949278882249886924800000000⟩, + ⟨7, 5, 8, 7, 7, 6, 513180315736691439294328711156012610703536947200000000⟩, + ⟨7, 6, 5, 3, 8, 7, 154585370765948566388184902649965568577492746240000000⟩, + ⟨7, 6, 5, 4, 7, 7, 92369763552939441703782290448377337116570419200000000⟩ +] + +def collectedFourData_18_22 : List CollectedFourTerm := [ + ⟨7, 6, 6, 4, 8, 7, -350590607441076598602155893677507337038436761600000000⟩, + ⟨7, 6, 5, 5, 6, 7, -205173784648913961813929019737781844942887321600000000⟩, + ⟨7, 6, 6, 5, 7, 7, 424957624049897412865512000146872048388658954240000000⟩, + ⟨7, 6, 7, 5, 8, 7, 86772619786235725850601823583338456550725386240000000⟩, + ⟨7, 6, 5, 6, 5, 7, 415882251661271106692927430117405774796019466240000000⟩, + ⟨7, 6, 6, 6, 6, 7, -276713198170058101280740098665761872225144668160000000⟩, + ⟨7, 6, 7, 6, 7, 7, -286729815633779831239470784221863456277151088640000000⟩, + ⟨7, 6, 8, 6, 8, 7, 1134560744610246722766984715998367287423082168320000000⟩, + ⟨7, 6, 5, 7, 4, 7, 1257640142401470215722313783616021090872359649280000000⟩, + ⟨7, 6, 6, 7, 5, 7, 285966517641667869702408777949278882249886924800000000⟩, + ⟨7, 6, 7, 7, 6, 7, 718080966659615564307781682892358881249287208960000000⟩, + ⟨7, 6, 8, 7, 7, 7, 859086628355206316849884720154817333491096616960000000⟩, + ⟨7, 7, 4, 2, 8, 8, -111281661789179635594860600946233786854195331072000000⟩, + ⟨7, 7, 4, 3, 7, 8, -670877035644045341010437576639143674069708177408000000⟩, + ⟨7, 7, 5, 3, 8, 8, 554821382812012697760254377660790508010308894720000000⟩, + ⟨7, 7, 4, 4, 6, 8, 795481622136098721156944115251711043752492531712000000⟩, + ⟨7, 7, 5, 4, 7, 8, 331523737922485034108469381613766093640931737600000000⟩, + ⟨7, 7, 6, 4, 8, 8, -629151273039507541076227803371771437601154662400000000⟩, + ⟨7, 7, 4, 5, 5, 8, 412699896003880067520355079996137926985380790272000000⟩, + ⟨7, 7, 5, 5, 6, 8, -736387941185179811121905777709248139854925004800000000⟩, + ⟨7, 7, 6, 5, 7, 8, 762606369036206324502928291151217857236681359360000000⟩, + ⟨7, 7, 7, 5, 8, 8, 103811688133827666393920258901569196030940938240000000⟩, + ⟨7, 7, 4, 6, 4, 8, -800978058983535881145132602356983633388800835584000000⟩, + ⟨7, 7, 5, 6, 5, 8, 1492640376061422528126364469050074658065057054720000000⟩ +] +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse1802.lean b/lean/OAI/Analysis/LaughlinFock/Sparse1802.lean new file mode 100644 index 0000000000000000000000000000000000000000..7ac4236239c822cbd85e3e3197f6ffa6dedf244e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse1802.lean @@ -0,0 +1,167 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Sparse1801 + +namespace OAI + +/-! Sparse1802. -/ +namespace LaughlinFock +def collectedFourData_18_23 : List CollectedFourTerm := [ + ⟨7, 7, 6, 6, 6, 8, -496574800352532146010229463435344756863129354240000000⟩, + ⟨7, 7, 7, 6, 7, 8, -343033393166786257144886620682387865649954160640000000⟩, + ⟨7, 7, 8, 6, 8, 8, 1018011209744342175471191030299159691023079178240000000⟩, + ⟨7, 7, 4, 7, 3, 8, 2915278249065588761447599751467072671742118854656000000⟩, + ⟨7, 7, 5, 7, 4, 8, 4513788332167206811088994764485599298638934179840000000⟩, + ⟨7, 7, 6, 7, 5, 8, 513180315736691439294328711156012610703536947200000000⟩, + ⟨7, 7, 7, 7, 6, 8, 859086628355206316849884720154817333491096616960000000⟩, + ⟨7, 7, 8, 7, 7, 8, 770835604846796790176136122857232035788588318720000000⟩, + ⟨2, 8, 8, 7, 8, 3, 208120254663607538247482268091256054684319744000000000⟩, + ⟨3, 7, 8, 7, 8, 3, 519653263250072122288477809313958766646080307200000000⟩, + ⟨3, 8, 7, 6, 8, 4, -31831988118817290567312094543434491946822795264000000⟩, + ⟨3, 8, 7, 7, 7, 4, 11250463616110413295620700777863302194818711552000000⟩, + ⟨3, 8, 8, 7, 8, 4, 301877255204204463655948695601671352304114073600000000⟩, + ⟨4, 6, 8, 7, 8, 3, 1193650067739008214244603352969588849295281356800000000⟩, + ⟨4, 7, 7, 6, 8, 4, -72538276555977676554938815701939256940071747584000000⟩, + ⟨4, 7, 7, 7, 7, 4, 25637394627134694218961059121624262154033037312000000⟩, + ⟨4, 7, 8, 7, 8, 4, 687913546028793772309472863867101595693586841600000000⟩, + ⟨4, 8, 6, 5, 8, 5, 304210995141065140031788593025555382372621352960000000⟩, + ⟨4, 8, 6, 6, 7, 5, 287295873657796219981458910158600619417235619840000000⟩, + ⟨4, 8, 7, 6, 8, 5, 315178221098172791952841158636566904090698711040000000⟩, + ⟨4, 8, 6, 7, 6, 5, -310946025975108611853707291031997215674046873600000000⟩, + ⟨4, 8, 7, 7, 7, 5, -111394270939654506287042991040314715902018846720000000⟩, + ⟨4, 8, 8, 7, 8, 5, -1494489378579150162675938143728776690635112448000000000⟩, + ⟨5, 5, 8, 7, 8, 3, 392295453864118100347418314192412041308379545600000000⟩ +] + +def collectedFourData_18_24 : List CollectedFourTerm := [ + ⟨5, 6, 7, 6, 8, 4, 66537822689439839936741962822295646740636762112000000⟩, + ⟨5, 6, 7, 7, 7, 4, -23516638372336832756515216080809511380808892416000000⟩, + ⟨5, 6, 8, 7, 8, 4, -631008506467689536055920005752621528387472588800000000⟩, + ⟨5, 7, 6, 5, 8, 5, -10348783145146173084139851606036367871406243840000000⟩, + ⟨5, 7, 6, 6, 7, 5, -9773357118802250893520564497886307727819407360000000⟩, + ⟨5, 7, 7, 6, 8, 5, -10721871051062576850878987572387254936702812160000000⟩, + ⟨5, 7, 6, 7, 6, 5, 10577898379935989543396040602362967107200614400000000⟩, + ⟨5, 7, 7, 7, 7, 5, 3789459197658461090674801284480609932940410880000000⟩, + ⟨5, 7, 8, 7, 8, 5, 50840195583555775373497285916450005966651392000000000⟩, + ⟨5, 8, 5, 4, 8, 6, 304210995141065140031788593025555382372621352960000000⟩, + ⟨5, 8, 5, 5, 7, 6, -10348783145146173084139851606036367871406243840000000⟩, + ⟨5, 8, 6, 5, 8, 6, 428498552946376740503295318139781654052675256320000000⟩, + ⟨5, 8, 5, 6, 6, 6, 98435395183354367682043448801425555915863490560000000⟩, + ⟨5, 8, 6, 6, 7, 6, 404672638714933869494377742730924956985883361280000000⟩, + ⟨5, 8, 7, 6, 8, 6, 221973258392838252281297652254627865598718115840000000⟩, + ⟨5, 8, 5, 7, 5, 6, -111320623246246776139032425633076452292254760960000000⟩, + ⟨5, 8, 6, 7, 6, 6, -437985228354340273556384718659832079210197811200000000⟩, + ⟨5, 8, 7, 7, 7, 6, -78452594854477120080548070064189119805909893120000000⟩, + ⟨5, 8, 8, 7, 8, 6, -701691201549046735470518412259172212090601472000000000⟩, + ⟨6, 4, 8, 7, 8, 3, -1850853720706333028935250895119466040597571174400000000⟩, + ⟨6, 5, 7, 6, 8, 4, -107963183230385238100439388732104796019774980096000000⟩, + ⟨6, 5, 7, 7, 7, 4, 38157712935777525817875308241681985326890876928000000⟩, + ⟨6, 5, 8, 7, 8, 4, 1023864085869991393694344198733040886439372390400000000⟩, + ⟨6, 6, 6, 5, 8, 5, 98435395183354367682043448801425555915863490560000000⟩ +] + +def collectedFourData_18_25 : List CollectedFourTerm := [ + ⟨6, 6, 6, 6, 7, 5, 92962066821215689530840231466807614863824650240000000⟩, + ⟨6, 6, 7, 6, 8, 5, 101984126946492748699010023756375757333924413440000000⟩, + ⟨6, 6, 6, 7, 6, 5, -100614689923880506121300659324643122421012889600000000⟩, + ⟨6, 6, 7, 7, 7, 5, -36044519285116283982780461507410261239052369920000000⟩, + ⟨6, 6, 8, 7, 8, 5, -483580984670024568720940302981138659124707328000000000⟩, + ⟨6, 7, 5, 4, 8, 6, 287295873657796219981458910158600619417235619840000000⟩, + ⟨6, 7, 5, 5, 7, 6, -9773357118802250893520564497886307727819407360000000⟩, + ⟨6, 7, 6, 5, 8, 6, 404672638714933869494377742730924956985883361280000000⟩, + ⟨6, 7, 5, 6, 6, 6, 92962066821215689530840231466807614863824650240000000⟩, + ⟨6, 7, 6, 6, 7, 6, 382171522863930598107734868569185542089075589120000000⟩, + ⟨6, 7, 7, 6, 8, 6, 209630822742178045141405566621863211993252495360000000⟩, + ⟨6, 7, 5, 7, 5, 6, -105130834264654210951375831527302938884927651840000000⟩, + ⟨6, 7, 6, 7, 6, 6, -413631824092750292152962863410531447702605004800000000⟩, + ⟨6, 7, 7, 7, 7, 6, -74090375231133783833457902476567462105558548480000000⟩, + ⟨6, 7, 8, 7, 8, 6, -662674886861146581659207666740042884068671488000000000⟩, + ⟨6, 8, 4, 3, 8, 7, -31831988118817290567312094543434491946822795264000000⟩, + ⟨6, 8, 4, 4, 7, 7, -72538276555977676554938815701939256940071747584000000⟩, + ⟨6, 8, 5, 4, 8, 7, 315178221098172791952841158636566904090698711040000000⟩, + ⟨6, 8, 4, 5, 6, 7, 66537822689439839936741962822295646740636762112000000⟩, + ⟨6, 8, 5, 5, 7, 7, -10721871051062576850878987572387254936702812160000000⟩, + ⟨6, 8, 6, 5, 8, 7, 221973258392838252281297652254627865598718115840000000⟩, + ⟨6, 8, 4, 6, 5, 7, -107963183230385238100439388732104796019774980096000000⟩, + ⟨6, 8, 5, 6, 6, 7, 101984126946492748699010023756375757333924413440000000⟩, + ⟨6, 8, 6, 6, 7, 7, 209630822742178045141405566621863211993252495360000000⟩ +] + +def collectedFourData_18_26 : List CollectedFourTerm := [ + ⟨6, 8, 7, 6, 8, 7, 76658566837991571839966346175612889724585246720000000⟩, + ⟨6, 8, 4, 7, 4, 7, -446493983106892271781283116855844816221206740992000000⟩, + ⟨6, 8, 5, 7, 5, 7, -115333885252971772249320528621938978780652503040000000⟩, + ⟨6, 8, 6, 7, 6, 7, -226887599963285507858136994162327858870380134400000000⟩, + ⟨6, 8, 7, 7, 7, 7, -27093639701510304966247195556133758433188904960000000⟩, + ⟨6, 8, 8, 7, 8, 7, -181747034292691570290569223703505840564600832000000000⟩, + ⟨7, 3, 8, 7, 8, 3, 3298605585971041026361565356477382523580789555200000000⟩, + ⟨7, 4, 7, 6, 8, 4, -446493983106892271781283116855844816221206740992000000⟩, + ⟨7, 4, 7, 7, 7, 4, 157805547457679408186623533007646778534716768256000000⟩, + ⟨7, 4, 8, 7, 8, 4, 4234305993781862110462851144456029190058986700800000000⟩, + ⟨7, 5, 6, 5, 8, 5, -111320623246246776139032425633076452292254760960000000⟩, + ⟨7, 5, 6, 6, 7, 5, -105130834264654210951375831527302938884927651840000000⟩, + ⟨7, 5, 7, 6, 8, 5, -115333885252971772249320528621938978780652503040000000⟩, + ⟨7, 5, 6, 7, 6, 5, 113785188439496100635919627543773136849312153600000000⟩, + ⟨7, 5, 7, 7, 7, 5, 40762759614633293417808546489857279187977502720000000⟩, + ⟨7, 5, 8, 7, 8, 5, 546881906688418903534124720457453877327822848000000000⟩, + ⟨7, 6, 5, 4, 8, 6, -310946025975108611853707291031997215674046873600000000⟩, + ⟨7, 6, 5, 5, 7, 6, 10577898379935989543396040602362967107200614400000000⟩, + ⟨7, 6, 6, 5, 8, 6, -437985228354340273556384718659832079210197811200000000⟩, + ⟨7, 6, 5, 6, 6, 6, -100614689923880506121300659324643122421012889600000000⟩, + ⟨7, 6, 6, 6, 7, 6, -413631824092750292152962863410531447702605004800000000⟩, + ⟨7, 6, 7, 6, 8, 6, -226887599963285507858136994162327858870380134400000000⟩, + ⟨7, 6, 5, 7, 5, 6, 113785188439496100635919627543773136849312153600000000⟩, + ⟨7, 6, 6, 7, 6, 6, 447681932500270915898183557997659550008737792000000000⟩ +] + +def collectedFourData_18_27 : List CollectedFourTerm := [ + ⟨7, 6, 7, 7, 7, 6, 80189483572488805271928589583747143234171699200000000⟩, + ⟨7, 6, 8, 7, 8, 6, 717226182052359569122588449632839198593515520000000000⟩, + ⟨7, 7, 4, 3, 8, 7, 11250463616110413295620700777863302194818711552000000⟩, + ⟨7, 7, 4, 4, 7, 7, 25637394627134694218961059121624262154033037312000000⟩, + ⟨7, 7, 5, 4, 8, 7, -111394270939654506287042991040314715902018846720000000⟩, + ⟨7, 7, 4, 5, 6, 7, -23516638372336832756515216080809511380808892416000000⟩, + ⟨7, 7, 5, 5, 7, 7, 3789459197658461090674801284480609932940410880000000⟩, + ⟨7, 7, 6, 5, 8, 7, -78452594854477120080548070064189119805909893120000000⟩, + ⟨7, 7, 4, 6, 5, 7, 38157712935777525817875308241681985326890876928000000⟩, + ⟨7, 7, 5, 6, 6, 7, -36044519285116283982780461507410261239052369920000000⟩, + ⟨7, 7, 6, 6, 7, 7, -74090375231133783833457902476567462105558548480000000⟩, + ⟨7, 7, 7, 6, 8, 7, -27093639701510304966247195556133758433188904960000000⟩, + ⟨7, 7, 4, 7, 4, 7, 157805547457679408186623533007646778534716768256000000⟩, + ⟨7, 7, 5, 7, 5, 7, 40762759614633293417808546489857279187977502720000000⟩, + ⟨7, 7, 6, 7, 6, 7, 80189483572488805271928589583747143234171699200000000⟩, + ⟨7, 7, 7, 7, 7, 7, 9575776622939115549622610963201824092617441280000000⟩, + ⟨7, 7, 8, 7, 8, 7, 64235334249737393751531881744988639514853376000000000⟩, + ⟨7, 8, 3, 2, 8, 8, 208120254663607538247482268091256054684319744000000000⟩, + ⟨7, 8, 3, 3, 7, 8, 519653263250072122288477809313958766646080307200000000⟩, + ⟨7, 8, 4, 3, 8, 8, 301877255204204463655948695601671352304114073600000000⟩, + ⟨7, 8, 3, 4, 6, 8, 1193650067739008214244603352969588849295281356800000000⟩, + ⟨7, 8, 4, 4, 7, 8, 687913546028793772309472863867101595693586841600000000⟩, + ⟨7, 8, 5, 4, 8, 8, -1494489378579150162675938143728776690635112448000000000⟩, + ⟨7, 8, 3, 5, 5, 8, 392295453864118100347418314192412041308379545600000000⟩ +] + +def collectedFourData_18_28 : List CollectedFourTerm := [ + ⟨7, 8, 4, 5, 6, 8, -631008506467689536055920005752621528387472588800000000⟩, + ⟨7, 8, 5, 5, 7, 8, 50840195583555775373497285916450005966651392000000000⟩, + ⟨7, 8, 6, 5, 8, 8, -701691201549046735470518412259172212090601472000000000⟩, + ⟨7, 8, 3, 6, 4, 8, -1850853720706333028935250895119466040597571174400000000⟩, + ⟨7, 8, 4, 6, 5, 8, 1023864085869991393694344198733040886439372390400000000⟩, + ⟨7, 8, 5, 6, 6, 8, -483580984670024568720940302981138659124707328000000000⟩, + ⟨7, 8, 6, 6, 7, 8, -662674886861146581659207666740042884068671488000000000⟩, + ⟨7, 8, 7, 6, 8, 8, -181747034292691570290569223703505840564600832000000000⟩, + ⟨7, 8, 3, 7, 3, 8, 3298605585971041026361565356477382523580789555200000000⟩, + ⟨7, 8, 4, 7, 4, 8, 4234305993781862110462851144456029190058986700800000000⟩, + ⟨7, 8, 5, 7, 5, 8, 546881906688418903534124720457453877327822848000000000⟩, + ⟨7, 8, 6, 7, 6, 8, 717226182052359569122588449632839198593515520000000000⟩, + ⟨7, 8, 7, 7, 7, 8, 64235334249737393751531881744988639514853376000000000⟩, + ⟨7, 8, 8, 7, 8, 8, 344717996557361492194998522335304122483343360000000000⟩ +] + +def collectedFourData_18 : List CollectedFourTerm := ((((collectedFourData_18_0 ++ (collectedFourData_18_1 ++ collectedFourData_18_2)) ++ ((collectedFourData_18_3 ++ collectedFourData_18_4) ++ (collectedFourData_18_5 ++ collectedFourData_18_6))) ++ ((collectedFourData_18_7 ++ (collectedFourData_18_8 ++ collectedFourData_18_9)) ++ ((collectedFourData_18_10 ++ collectedFourData_18_11) ++ (collectedFourData_18_12 ++ collectedFourData_18_13)))) ++ (((collectedFourData_18_14 ++ (collectedFourData_18_15 ++ collectedFourData_18_16)) ++ ((collectedFourData_18_17 ++ collectedFourData_18_18) ++ (collectedFourData_18_19 ++ collectedFourData_18_20))) ++ (((collectedFourData_18_21 ++ collectedFourData_18_22) ++ (collectedFourData_18_23 ++ collectedFourData_18_24)) ++ ((collectedFourData_18_25 ++ collectedFourData_18_26) ++ (collectedFourData_18_27 ++ collectedFourData_18_28))))) + +theorem collectedFourChecked_18 : collectedFourTerms 18 = collectedFourData_18 := by + decide +kernel + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse19.lean b/lean/OAI/Analysis/LaughlinFock/Sparse19.lean new file mode 100644 index 0000000000000000000000000000000000000000..37ee38f5c739099de51503225e73f5db3eae0d7a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse19.lean @@ -0,0 +1,373 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse19. -/ +namespace LaughlinFock + +def collectedFourData_19_0 : List CollectedFourTerm := [ + ⟨3, 8, 8, 3, 8, 8, 864009772070565031264275346671607782309888000000000000⟩, + ⟨3, 8, 8, 4, 7, 8, 306919134345983998317441579303235726381940736000000000⟩, + ⟨3, 8, 8, 5, 6, 8, 639086190720504289721716989633756669677666304000000000⟩, + ⟨3, 8, 8, 6, 5, 8, -670692446173327891254180802178937211393671168000000000⟩, + ⟨3, 8, 8, 7, 4, 8, 1326107689072002431462750021173808570742865920000000000⟩, + ⟨4, 7, 8, 3, 8, 8, 306919134345983998317441579303235726381940736000000000⟩, + ⟨4, 7, 8, 4, 7, 8, 109025798171174811140951604723273803822731886592000000⟩, + ⟨4, 7, 8, 5, 6, 8, 227020326353889793451120085461970530865971724288000000⟩, + ⟨4, 7, 8, 6, 5, 8, -238247704651072288708776368826618258808054480896000000⟩, + ⟨4, 7, 8, 7, 4, 8, 471068542435757687183287738257959319377270538240000000⟩, + ⟨5, 6, 8, 3, 8, 8, 639086190720504289721716989633756669677666304000000000⟩, + ⟨5, 6, 8, 4, 7, 8, 227020326353889793451120085461970530865971724288000000⟩, + ⟨5, 6, 8, 5, 6, 8, 472715902495935625684332121216211618190990508032000000⟩, + ⟨5, 6, 8, 6, 5, 8, -496094250812387894931817784585003872156378988544000000⟩, + ⟨5, 6, 8, 7, 4, 8, 980888340490876452483102020532410627090924175360000000⟩, + ⟨6, 5, 8, 3, 8, 8, -670692446173327891254180802178937211393671168000000000⟩, + ⟨6, 5, 8, 4, 7, 8, -238247704651072288708776368826618258808054480896000000⟩, + ⟨6, 5, 8, 5, 6, 8, -496094250812387894931817784585003872156378988544000000⟩, + ⟨6, 5, 8, 6, 5, 8, 520628784412896830374554934597163226536500789248000000⟩, + ⟨6, 5, 8, 7, 4, 8, -1029398553839875654859368373050438966928599941120000000⟩, + ⟨7, 4, 8, 3, 8, 8, 1326107689072002431462750021173808570742865920000000000⟩, + ⟨7, 4, 8, 4, 7, 8, 471068542435757687183287738257959319377270538240000000⟩, + ⟨7, 4, 8, 5, 6, 8, 980888340490876452483102020532410627090924175360000000⟩, + ⟨7, 4, 8, 6, 5, 8, -1029398553839875654859368373050438966928599941120000000⟩ +] + +def collectedFourData_19_1 : List CollectedFourTerm := [ + ⟨7, 4, 8, 7, 4, 8, 2035349205370170508526860648987060061877357772800000000⟩, + ⟨3, 8, 8, 4, 8, 7, -87823530365937359594789437811584437135417016320000000⟩, + ⟨3, 8, 8, 5, 7, 7, 143986874558293247909422149622007175429155192832000000⟩, + ⟨3, 8, 8, 6, 6, 7, -215078451648569290868475905609015844082487918592000000⟩, + ⟨3, 8, 8, 7, 5, 7, -555570405617613120115750768874006665998599454720000000⟩, + ⟨4, 7, 8, 4, 8, 7, -232300513502340726666042098486076372384837795840000000⟩, + ⟨4, 7, 8, 5, 7, 7, 380857211707599986642160207787261895021621673984000000⟩, + ⟨4, 7, 8, 6, 6, 7, -568900322647804361015565509780845336425979183104000000⟩, + ⟨4, 7, 8, 7, 5, 7, -1469529748734984972847758339751172125353459056640000000⟩, + ⟨4, 8, 7, 3, 8, 8, -87823530365937359594789437811584437135417016320000000⟩, + ⟨4, 8, 7, 4, 7, 8, -232300513502340726666042098486076372384837795840000000⟩, + ⟨4, 8, 8, 4, 8, 8, 248827268082759600384230363824043198179285401600000000⟩, + ⟨4, 8, 7, 5, 6, 8, 73592352362212875305292018751020819121648435200000000⟩, + ⟨4, 8, 8, 5, 7, 8, -407952862824233076922912261939020207094927196160000000⟩, + ⟨4, 8, 7, 6, 5, 8, 459782407701193858493031362376887409579424481280000000⟩, + ⟨4, 8, 8, 6, 6, 8, 609374086013061140039430328073839033506028584960000000⟩, + ⟨4, 8, 7, 7, 4, 8, 357521987780248055256636605733385410105153945600000000⟩, + ⟨4, 8, 8, 7, 5, 8, 1574077763458693240372264738975826502875715993600000000⟩, + ⟨5, 6, 8, 4, 8, 7, 73592352362212875305292018751020819121648435200000000⟩, + ⟨5, 6, 8, 5, 7, 7, -120654826375978652565683359206842235031671275520000000⟩, + ⟨5, 6, 8, 6, 6, 7, 180226519399630819892593405958170745949514629120000000⟩, + ⟨5, 6, 8, 7, 5, 7, 465544175710870534972699812738846562261873459200000000⟩, + ⟨5, 7, 7, 3, 8, 8, 143986874558293247909422149622007175429155192832000000⟩, + ⟨5, 7, 7, 4, 7, 8, 380857211707599986642160207787261895021621673984000000⟩ +] + +def collectedFourData_19_2 : List CollectedFourTerm := [ + ⟨5, 7, 8, 4, 8, 8, -407952862824233076922912261939020207094927196160000000⟩, + ⟨5, 7, 7, 5, 6, 8, -120654826375978652565683359206842235031671275520000000⟩, + ⟨5, 7, 8, 5, 7, 8, 668839631479354704117594088785733298860081545216000000⟩, + ⟨5, 7, 7, 6, 5, 8, -753814286284473351637684009051890517976366972928000000⟩, + ⟨5, 7, 8, 6, 6, 8, -999070177619142973977188256577683600670873092096000000⟩, + ⟨5, 7, 7, 7, 4, 8, -586158098995213254653283217979771591368177090560000000⟩, + ⟨5, 7, 8, 7, 5, 8, -2580704015515541694760597042103408829675192975360000000⟩, + ⟨6, 5, 8, 4, 8, 7, 459782407701193858493031362376887409579424481280000000⟩, + ⟨6, 5, 8, 5, 7, 7, -753814286284473351637684009051890517976366972928000000⟩, + ⟨6, 5, 8, 6, 6, 7, 1125999922020653891773437783448447442735194963968000000⟩, + ⟨6, 5, 8, 7, 5, 7, 2908576980201525240764295813267778969858348154880000000⟩, + ⟨6, 6, 7, 3, 8, 8, -215078451648569290868475905609015844082487918592000000⟩, + ⟨6, 6, 7, 4, 7, 8, -568900322647804361015565509780845336425979183104000000⟩, + ⟨6, 6, 8, 4, 8, 8, 609374086013061140039430328073839033506028584960000000⟩, + ⟨6, 6, 7, 5, 6, 8, 180226519399630819892593405958170745949514629120000000⟩, + ⟨6, 6, 8, 5, 7, 8, -999070177619142973977188256577683600670873092096000000⟩, + ⟨6, 6, 7, 6, 5, 8, 1125999922020653891773437783448447442735194963968000000⟩, + ⟨6, 6, 8, 6, 6, 8, 1492347601472470233508475462736293534491660517376000000⟩, + ⟨6, 6, 7, 7, 4, 8, 875565753752920682246748707614792672355926671360000000⟩, + ⟨6, 6, 8, 7, 5, 8, 3854891812347894830776187615105060975251984220160000000⟩, + ⟨7, 4, 8, 4, 8, 7, 357521987780248055256636605733385410105153945600000000⟩, + ⟨7, 4, 8, 5, 7, 7, -586158098995213254653283217979771591368177090560000000⟩, + ⟨7, 4, 8, 6, 6, 7, 875565753752920682246748707614792672355926671360000000⟩, + ⟨7, 4, 8, 7, 5, 7, 2261679016325748759553972874259058602695825817600000000⟩ +] + +def collectedFourData_19_3 : List CollectedFourTerm := [ + ⟨7, 5, 7, 3, 8, 8, -555570405617613120115750768874006665998599454720000000⟩, + ⟨7, 5, 7, 4, 7, 8, -1469529748734984972847758339751172125353459056640000000⟩, + ⟨7, 5, 8, 4, 8, 8, 1574077763458693240372264738975826502875715993600000000⟩, + ⟨7, 5, 7, 5, 6, 8, 465544175710870534972699812738846562261873459200000000⟩, + ⟨7, 5, 8, 5, 7, 8, -2580704015515541694760597042103408829675192975360000000⟩, + ⟨7, 5, 7, 6, 5, 8, 2908576980201525240764295813267778969858348154880000000⟩, + ⟨7, 5, 8, 6, 6, 8, 3854891812347894830776187615105060975251984220160000000⟩, + ⟨7, 5, 7, 7, 4, 8, 2261679016325748759553972874259058602695825817600000000⟩, + ⟨7, 5, 8, 7, 5, 8, 9957593572867726714533864137373587211399305625600000000⟩, + ⟨3, 8, 8, 5, 8, 6, 2042193356940763591695529989793438828654724382720000000⟩, + ⟨3, 8, 8, 6, 7, 6, 550488617405113058332852300844871614401169326080000000⟩, + ⟨3, 8, 8, 7, 6, 6, 823017925846695151536952388788959397790644961280000000⟩, + ⟨4, 7, 8, 5, 8, 6, -891124221980824112497792219553752017375005245440000000⟩, + ⟨4, 7, 8, 6, 7, 6, -240209253069595632086682773733873330264641372160000000⟩, + ⟨4, 7, 8, 7, 6, 6, -359129171757305511242275615329677963942229442560000000⟩, + ⟨4, 8, 7, 4, 8, 7, 1899337959913471904975927541168008284103245824000000000⟩, + ⟨4, 8, 7, 5, 7, 7, 866356312452718779985316710837901408280458035200000000⟩, + ⟨4, 8, 8, 5, 8, 7, 5229875406085747909043634674831140036964410982400000000⟩, + ⟨4, 8, 7, 6, 6, 7, 261922508957824428701834694817175843436389990400000000⟩, + ⟨4, 8, 8, 6, 7, 7, 1409752348724663996669967250644148973410556313600000000⟩, + ⟨4, 8, 7, 7, 5, 7, -940966220967502769924552436193304093721310003200000000⟩, + ⟨4, 8, 8, 7, 6, 7, 2107675649088004501315249146917713901862361497600000000⟩, + ⟨5, 6, 8, 5, 8, 6, -1509282172662079931569836337558213840927992053760000000⟩, + ⟨5, 6, 8, 6, 7, 6, -406838389557562913806641040190742643457277296640000000⟩ +] + +def collectedFourData_19_4 : List CollectedFourTerm := [ + ⟨5, 6, 8, 7, 6, 6, -608251064493972525328747644435043081456441098240000000⟩, + ⟨5, 7, 7, 4, 8, 7, 866356312452718779985316710837901408280458035200000000⟩, + ⟨5, 7, 7, 5, 7, 7, 395176254025306132388861316072582384263846952960000000⟩, + ⟨5, 7, 8, 5, 8, 7, 2385534152968768893257079545433267960639148523520000000⟩, + ⟨5, 7, 7, 6, 6, 7, 119472270758703038977149009682964673103575121920000000⟩, + ⟨5, 7, 8, 6, 7, 7, 643038717747893630401450617398053156045486817280000000⟩, + ⟨5, 7, 7, 7, 5, 7, -429208515043375664613282306188807762290786959360000000⟩, + ⟨5, 7, 8, 7, 6, 7, 961386620879972853564793973929046370014440980480000000⟩, + ⟨5, 8, 6, 3, 8, 8, 2042193356940763591695529989793438828654724382720000000⟩, + ⟨5, 8, 6, 4, 7, 8, -891124221980824112497792219553752017375005245440000000⟩, + ⟨5, 8, 7, 4, 8, 8, 5229875406085747909043634674831140036964410982400000000⟩, + ⟨5, 8, 6, 5, 6, 8, -1509282172662079931569836337558213840927992053760000000⟩, + ⟨5, 8, 7, 5, 7, 8, 2385534152968768893257079545433267960639148523520000000⟩, + ⟨5, 8, 8, 5, 8, 8, 7200297509040103281930257740783529496847444869120000000⟩, + ⟨5, 8, 6, 6, 5, 8, 143559331334134994347074076823082741871788687360000000⟩, + ⟨5, 8, 7, 6, 6, 8, 721210293696865265217814874261076884241556439040000000⟩, + ⟨5, 8, 8, 6, 7, 8, 1940894483465865870064663323626120527310676295680000000⟩, + ⟨5, 8, 6, 7, 4, 8, 4982031472787526018776831599725547587618471936000000000⟩, + ⟨5, 8, 7, 7, 5, 8, -2590974434702280277536710036660312896990158520320000000⟩, + ⟨5, 8, 8, 7, 6, 8, 2901769267453944579910826965920071441615557754880000000⟩, + ⟨6, 5, 8, 5, 8, 6, 143559331334134994347074076823082741871788687360000000⟩, + ⟨6, 5, 8, 6, 7, 6, 38697500191713138855408074674538997758338007040000000⟩, + ⟨6, 5, 8, 7, 6, 6, 57855394891476674365816421364670441347235184640000000⟩, + ⟨6, 6, 7, 4, 8, 7, 261922508957824428701834694817175843436389990400000000⟩ +] + +def collectedFourData_19_5 : List CollectedFourTerm := [ + ⟨6, 6, 7, 5, 7, 7, 119472270758703038977149009682964673103575121920000000⟩, + ⟨6, 6, 8, 5, 8, 7, 721210293696865265217814874261076884241556439040000000⟩, + ⟨6, 6, 7, 6, 6, 7, 36119638603909638923493815853267848997466275840000000⟩, + ⟨6, 6, 8, 6, 7, 7, 194407672557637693429687700292731876116329922560000000⟩, + ⟨6, 6, 7, 7, 5, 7, -129761126583074729951124347341340422806668574720000000⟩, + ⟨6, 6, 8, 7, 6, 7, 290652693585711781417696179228894946275580968960000000⟩, + ⟨6, 7, 6, 3, 8, 8, 550488617405113058332852300844871614401169326080000000⟩, + ⟨6, 7, 6, 4, 7, 8, -240209253069595632086682773733873330264641372160000000⟩, + ⟨6, 7, 7, 4, 8, 8, 1409752348724663996669967250644148973410556313600000000⟩, + ⟨6, 7, 6, 5, 6, 8, -406838389557562913806641040190742643457277296640000000⟩, + ⟨6, 7, 7, 5, 7, 8, 643038717747893630401450617398053156045486817280000000⟩, + ⟨6, 7, 8, 5, 8, 8, 1940894483465865870064663323626120527310676295680000000⟩, + ⟨6, 7, 6, 6, 5, 8, 38697500191713138855408074674538997758338007040000000⟩, + ⟨6, 7, 7, 6, 6, 8, 194407672557637693429687700292731876116329922560000000⟩, + ⟨6, 7, 8, 6, 7, 8, 523182742271219245845704224438728423477105131520000000⟩, + ⟨6, 7, 6, 7, 4, 8, 1342944147772543913650095213849525908882325504000000000⟩, + ⟨6, 7, 7, 7, 5, 8, -698416694699210281745076871939302078730972692480000000⟩, + ⟨6, 7, 8, 7, 6, 8, 782193785245822849839162194632939239947706040320000000⟩, + ⟨7, 4, 8, 5, 8, 6, 4982031472787526018776831599725547587618471936000000000⟩, + ⟨7, 4, 8, 6, 7, 6, 1342944147772543913650095213849525908882325504000000000⟩, + ⟨7, 4, 8, 7, 6, 6, 2007792844541840295194434494317846925372555264000000000⟩, + ⟨7, 5, 7, 4, 8, 7, -940966220967502769924552436193304093721310003200000000⟩, + ⟨7, 5, 7, 5, 7, 7, -429208515043375664613282306188807762290786959360000000⟩, + ⟨7, 5, 8, 5, 8, 7, -2590974434702280277536710036660312896990158520320000000⟩ +] + +def collectedFourData_19_6 : List CollectedFourTerm := [ + ⟨7, 5, 7, 6, 6, 7, -129761126583074729951124347341340422806668574720000000⟩, + ⟨7, 5, 8, 6, 7, 7, -698416694699210281745076871939302078730972692480000000⟩, + ⟨7, 5, 7, 7, 5, 7, 466171606996261050115920512414853003529169141760000000⟩, + ⟨7, 5, 8, 7, 6, 7, -1044180463090370192924134413003251130866262343680000000⟩, + ⟨7, 6, 6, 3, 8, 8, 823017925846695151536952388788959397790644961280000000⟩, + ⟨7, 6, 6, 4, 7, 8, -359129171757305511242275615329677963942229442560000000⟩, + ⟨7, 6, 7, 4, 8, 8, 2107675649088004501315249146917713901862361497600000000⟩, + ⟨7, 6, 6, 5, 6, 8, -608251064493972525328747644435043081456441098240000000⟩, + ⟨7, 6, 7, 5, 7, 8, 961386620879972853564793973929046370014440980480000000⟩, + ⟨7, 6, 8, 5, 8, 8, 2901769267453944579910826965920071441615557754880000000⟩, + ⟨7, 6, 6, 6, 5, 8, 57855394891476674365816421364670441347235184640000000⟩, + ⟨7, 6, 7, 6, 6, 8, 290652693585711781417696179228894946275580968960000000⟩, + ⟨7, 6, 8, 6, 7, 8, 782193785245822849839162194632939239947706040320000000⟩, + ⟨7, 6, 6, 7, 4, 8, 2007792844541840295194434494317846925372555264000000000⟩, + ⟨7, 6, 7, 7, 5, 8, -1044180463090370192924134413003251130866262343680000000⟩, + ⟨7, 6, 8, 7, 6, 8, 1169432911760716532534062826013689459839724421120000000⟩, + ⟨3, 8, 8, 6, 8, 5, 732730018640929815431380103740745466419336970240000000⟩, + ⟨3, 8, 8, 7, 7, 5, 554821382812012697760254377660790508010308894720000000⟩, + ⟨4, 7, 8, 6, 8, 5, 437829907413931904890968496243196026367980339200000000⟩, + ⟨4, 7, 8, 7, 7, 5, 331523737922485034108469381613766093640931737600000000⟩, + ⟨4, 8, 7, 5, 8, 6, -42365230235284080917252813871910442133513830400000000⟩, + ⟨4, 8, 7, 6, 7, 6, 139990871366690166414600500507552006594258534400000000⟩, + ⟨4, 8, 8, 6, 8, 6, -1661788958766215022454092598055539241597376921600000000⟩, + ⟨4, 8, 7, 7, 6, 6, -350590607441076598602155893677507337038436761600000000⟩ +] + +def collectedFourData_19_7 : List CollectedFourTerm := [ + ⟨4, 8, 8, 7, 7, 6, -1258302546079015082152455606743542875202309324800000000⟩, + ⟨5, 6, 8, 6, 8, 5, -972517582391725677704894720222758005649283481600000000⟩, + ⟨5, 6, 8, 7, 7, 5, -736387941185179811121905777709248139854925004800000000⟩, + ⟨5, 7, 7, 5, 8, 6, 51351711086952085162904820426124931715626434560000000⟩, + ⟨5, 7, 7, 6, 7, 6, -169685629968458075864959529356973085418491740160000000⟩, + ⟨5, 7, 8, 6, 8, 6, 2014286385890507013745780458941166077419443978240000000⟩, + ⟨5, 7, 7, 7, 6, 6, 424957624049897412865512000146872048388658954240000000⟩, + ⟨5, 7, 8, 7, 7, 6, 1525212738072412649005856582302435714473362718720000000⟩, + ⟨5, 8, 6, 4, 8, 7, -42365230235284080917252813871910442133513830400000000⟩, + ⟨5, 8, 6, 5, 7, 7, 51351711086952085162904820426124931715626434560000000⟩, + ⟨5, 8, 7, 5, 8, 7, 20971138058685664292162540521920285933431685120000000⟩, + ⟨5, 8, 6, 6, 6, 7, -33437913340523752259699711916091172468073431040000000⟩, + ⟨5, 8, 7, 6, 7, 7, -69296634860289211703909829134872189874806456320000000⟩, + ⟨5, 8, 8, 6, 8, 7, 411299613918551730360481624430183762941433610240000000⟩, + ⟨5, 8, 6, 7, 5, 7, 34556080802900140386291971099875661694841651200000000⟩, + ⟨5, 8, 7, 7, 6, 7, 173545239572471451701203647166676913101450772480000000⟩, + ⟨5, 8, 8, 7, 7, 7, 311435064401482999181760776704707588092822814720000000⟩, + ⟨6, 5, 8, 6, 8, 5, 1971269393101715104717011087330949847719335690240000000⟩, + ⟨6, 5, 8, 7, 7, 5, 1492640376061422528126364469050074658065057054720000000⟩, + ⟨6, 6, 7, 5, 8, 6, -33437913340523752259699711916091172468073431040000000⟩, + ⟨6, 6, 7, 6, 7, 6, 110491613033302924610861189166799005452536381440000000⟩, + ⟨6, 6, 8, 6, 8, 6, -1311612255730994800534590925690255785026817884160000000⟩, + ⟨6, 6, 7, 7, 6, 6, -276713198170058101280740098665761872225144668160000000⟩, + ⟨6, 6, 8, 7, 7, 6, -993149600705064292020458926870689513726258708480000000⟩ +] + +def collectedFourData_19_8 : List CollectedFourTerm := [ + ⟨6, 7, 6, 4, 8, 7, 139990871366690166414600500507552006594258534400000000⟩, + ⟨6, 7, 6, 5, 7, 7, -169685629968458075864959529356973085418491740160000000⟩, + ⟨6, 7, 7, 5, 8, 7, -69296634860289211703909829134872189874806456320000000⟩, + ⟨6, 7, 6, 6, 6, 7, 110491613033302924610861189166799005452536381440000000⟩, + ⟨6, 7, 7, 6, 7, 7, 228982499162528039282070852663744170563228139520000000⟩, + ⟨6, 7, 8, 6, 8, 7, -1359090721930906365269271998317685034885725552640000000⟩, + ⟨6, 7, 6, 7, 5, 7, -114186464601974015528423786698574992950637363200000000⟩, + ⟨6, 7, 7, 7, 6, 7, -573459631267559662478941568443726912554302177280000000⟩, + ⟨6, 7, 8, 7, 7, 7, -1029100179500358771434659862047163596949862481920000000⟩, + ⟨6, 8, 5, 3, 8, 8, 732730018640929815431380103740745466419336970240000000⟩, + ⟨6, 8, 5, 4, 7, 8, 437829907413931904890968496243196026367980339200000000⟩, + ⟨6, 8, 6, 4, 8, 8, -1661788958766215022454092598055539241597376921600000000⟩, + ⟨6, 8, 5, 5, 6, 8, -972517582391725677704894720222758005649283481600000000⟩, + ⟨6, 8, 6, 5, 7, 8, 2014286385890507013745780458941166077419443978240000000⟩, + ⟨6, 8, 7, 5, 8, 8, 411299613918551730360481624430183762941433610240000000⟩, + ⟨6, 8, 5, 6, 5, 8, 1971269393101715104717011087330949847719335690240000000⟩, + ⟨6, 8, 6, 6, 6, 8, -1311612255730994800534590925690255785026817884160000000⟩, + ⟨6, 8, 7, 6, 7, 8, -1359090721930906365269271998317685034885725552640000000⟩, + ⟨6, 8, 8, 6, 8, 8, 5377783883613484489489493574171864319714991800320000000⟩, + ⟨6, 8, 5, 7, 4, 8, 5961176535783795563387784541465163777810135777280000000⟩, + ⟨6, 8, 6, 7, 5, 8, 1355472712353301624101817793888095206369971404800000000⟩, + ⟨6, 8, 7, 7, 6, 8, 3403682233830740168300954147995101862269246504960000000⟩, + ⟨6, 8, 8, 7, 7, 8, 4072044838977368701884764121196638764092316712960000000⟩, + ⟨7, 4, 8, 6, 8, 5, 5961176535783795563387784541465163777810135777280000000⟩ +] + +def collectedFourData_19_9 : List CollectedFourTerm := [ + ⟨7, 4, 8, 7, 7, 5, 4513788332167206811088994764485599298638934179840000000⟩, + ⟨7, 5, 7, 5, 8, 6, 34556080802900140386291971099875661694841651200000000⟩, + ⟨7, 5, 7, 6, 7, 6, -114186464601974015528423786698574992950637363200000000⟩, + ⟨7, 5, 8, 6, 8, 6, 1355472712353301624101817793888095206369971404800000000⟩, + ⟨7, 5, 7, 7, 6, 6, 285966517641667869702408777949278882249886924800000000⟩, + ⟨7, 5, 8, 7, 7, 6, 1026360631473382878588657422312025221407073894400000000⟩, + ⟨7, 6, 6, 4, 8, 7, -350590607441076598602155893677507337038436761600000000⟩, + ⟨7, 6, 6, 5, 7, 7, 424957624049897412865512000146872048388658954240000000⟩, + ⟨7, 6, 7, 5, 8, 7, 173545239572471451701203647166676913101450772480000000⟩, + ⟨7, 6, 6, 6, 6, 7, -276713198170058101280740098665761872225144668160000000⟩, + ⟨7, 6, 7, 6, 7, 7, -573459631267559662478941568443726912554302177280000000⟩, + ⟨7, 6, 8, 6, 8, 7, 3403682233830740168300954147995101862269246504960000000⟩, + ⟨7, 6, 6, 7, 5, 7, 285966517641667869702408777949278882249886924800000000⟩, + ⟨7, 6, 7, 7, 6, 7, 1436161933319231128615563365784717762498574417920000000⟩, + ⟨7, 6, 8, 7, 7, 7, 2577259885065618950549654160464452000473289850880000000⟩, + ⟨7, 7, 5, 3, 8, 8, 554821382812012697760254377660790508010308894720000000⟩, + ⟨7, 7, 5, 4, 7, 8, 331523737922485034108469381613766093640931737600000000⟩, + ⟨7, 7, 6, 4, 8, 8, -1258302546079015082152455606743542875202309324800000000⟩, + ⟨7, 7, 5, 5, 6, 8, -736387941185179811121905777709248139854925004800000000⟩, + ⟨7, 7, 6, 5, 7, 8, 1525212738072412649005856582302435714473362718720000000⟩, + ⟨7, 7, 7, 5, 8, 8, 311435064401482999181760776704707588092822814720000000⟩, + ⟨7, 7, 5, 6, 5, 8, 1492640376061422528126364469050074658065057054720000000⟩, + ⟨7, 7, 6, 6, 6, 8, -993149600705064292020458926870689513726258708480000000⟩, + ⟨7, 7, 7, 6, 7, 8, -1029100179500358771434659862047163596949862481920000000⟩ +] + +def collectedFourData_19_10 : List CollectedFourTerm := [ + ⟨7, 7, 8, 6, 8, 8, 4072044838977368701884764121196638764092316712960000000⟩, + ⟨7, 7, 5, 7, 4, 8, 4513788332167206811088994764485599298638934179840000000⟩, + ⟨7, 7, 6, 7, 5, 8, 1026360631473382878588657422312025221407073894400000000⟩, + ⟨7, 7, 7, 7, 6, 8, 2577259885065618950549654160464452000473289850880000000⟩, + ⟨7, 7, 8, 7, 7, 8, 3083342419387187160704544491428928143154353274880000000⟩, + ⟨3, 8, 8, 7, 8, 4, 301877255204204463655948695601671352304114073600000000⟩, + ⟨4, 7, 8, 7, 8, 4, 687913546028793772309472863867101595693586841600000000⟩, + ⟨4, 8, 7, 6, 8, 5, 315178221098172791952841158636566904090698711040000000⟩, + ⟨4, 8, 7, 7, 7, 5, -111394270939654506287042991040314715902018846720000000⟩, + ⟨4, 8, 8, 7, 8, 5, -2988978757158300325351876287457553381270224896000000000⟩, + ⟨5, 6, 8, 7, 8, 4, -631008506467689536055920005752621528387472588800000000⟩, + ⟨5, 7, 7, 6, 8, 5, -10721871051062576850878987572387254936702812160000000⟩, + ⟨5, 7, 7, 7, 7, 5, 3789459197658461090674801284480609932940410880000000⟩, + ⟨5, 7, 8, 7, 8, 5, 101680391167111550746994571832900011933302784000000000⟩, + ⟨5, 8, 6, 5, 8, 6, 428498552946376740503295318139781654052675256320000000⟩, + ⟨5, 8, 6, 6, 7, 6, 404672638714933869494377742730924956985883361280000000⟩, + ⟨5, 8, 7, 6, 8, 6, 443946516785676504562595304509255731197436231680000000⟩, + ⟨5, 8, 6, 7, 6, 6, -437985228354340273556384718659832079210197811200000000⟩, + ⟨5, 8, 7, 7, 7, 6, -156905189708954240161096140128378239611819786240000000⟩, + ⟨5, 8, 8, 7, 8, 6, -2105073604647140206411555236777516636271804416000000000⟩, + ⟨6, 5, 8, 7, 8, 4, 1023864085869991393694344198733040886439372390400000000⟩, + ⟨6, 6, 7, 6, 8, 5, 101984126946492748699010023756375757333924413440000000⟩, + ⟨6, 6, 7, 7, 7, 5, -36044519285116283982780461507410261239052369920000000⟩, + ⟨6, 6, 8, 7, 8, 5, -967161969340049137441880605962277318249414656000000000⟩ +] + +def collectedFourData_19_11 : List CollectedFourTerm := [ + ⟨6, 7, 6, 5, 8, 6, 404672638714933869494377742730924956985883361280000000⟩, + ⟨6, 7, 6, 6, 7, 6, 382171522863930598107734868569185542089075589120000000⟩, + ⟨6, 7, 7, 6, 8, 6, 419261645484356090282811133243726423986504990720000000⟩, + ⟨6, 7, 6, 7, 6, 6, -413631824092750292152962863410531447702605004800000000⟩, + ⟨6, 7, 7, 7, 7, 6, -148180750462267567666915804953134924211117096960000000⟩, + ⟨6, 7, 8, 7, 8, 6, -1988024660583439744977623000220128652206014464000000000⟩, + ⟨6, 8, 5, 4, 8, 7, 315178221098172791952841158636566904090698711040000000⟩, + ⟨6, 8, 5, 5, 7, 7, -10721871051062576850878987572387254936702812160000000⟩, + ⟨6, 8, 6, 5, 8, 7, 443946516785676504562595304509255731197436231680000000⟩, + ⟨6, 8, 5, 6, 6, 7, 101984126946492748699010023756375757333924413440000000⟩, + ⟨6, 8, 6, 6, 7, 7, 419261645484356090282811133243726423986504990720000000⟩, + ⟨6, 8, 7, 6, 8, 7, 229975700513974715519899038526838669173755740160000000⟩, + ⟨6, 8, 5, 7, 5, 7, -115333885252971772249320528621938978780652503040000000⟩, + ⟨6, 8, 6, 7, 6, 7, -453775199926571015716273988324655717740760268800000000⟩, + ⟨6, 8, 7, 7, 7, 7, -81280919104530914898741586668401275299566714880000000⟩, + ⟨6, 8, 8, 7, 8, 7, -726988137170766281162276894814023362258403328000000000⟩, + ⟨7, 4, 8, 7, 8, 4, 4234305993781862110462851144456029190058986700800000000⟩, + ⟨7, 5, 7, 6, 8, 5, -115333885252971772249320528621938978780652503040000000⟩, + ⟨7, 5, 7, 7, 7, 5, 40762759614633293417808546489857279187977502720000000⟩, + ⟨7, 5, 8, 7, 8, 5, 1093763813376837807068249440914907754655645696000000000⟩, + ⟨7, 6, 6, 5, 8, 6, -437985228354340273556384718659832079210197811200000000⟩, + ⟨7, 6, 6, 6, 7, 6, -413631824092750292152962863410531447702605004800000000⟩, + ⟨7, 6, 7, 6, 8, 6, -453775199926571015716273988324655717740760268800000000⟩, + ⟨7, 6, 6, 7, 6, 6, 447681932500270915898183557997659550008737792000000000⟩ +] + +def collectedFourData_19_12 : List CollectedFourTerm := [ + ⟨7, 6, 7, 7, 7, 6, 160378967144977610543857179167494286468343398400000000⟩, + ⟨7, 6, 8, 7, 8, 6, 2151678546157078707367765348898517595780546560000000000⟩, + ⟨7, 7, 5, 4, 8, 7, -111394270939654506287042991040314715902018846720000000⟩, + ⟨7, 7, 5, 5, 7, 7, 3789459197658461090674801284480609932940410880000000⟩, + ⟨7, 7, 6, 5, 8, 7, -156905189708954240161096140128378239611819786240000000⟩, + ⟨7, 7, 5, 6, 6, 7, -36044519285116283982780461507410261239052369920000000⟩, + ⟨7, 7, 6, 6, 7, 7, -148180750462267567666915804953134924211117096960000000⟩, + ⟨7, 7, 7, 6, 8, 7, -81280919104530914898741586668401275299566714880000000⟩, + ⟨7, 7, 5, 7, 5, 7, 40762759614633293417808546489857279187977502720000000⟩, + ⟨7, 7, 6, 7, 6, 7, 160378967144977610543857179167494286468343398400000000⟩, + ⟨7, 7, 7, 7, 7, 7, 28727329868817346648867832889605472277852323840000000⟩, + ⟨7, 7, 8, 7, 8, 7, 256941336998949575006127526979954558059413504000000000⟩, + ⟨7, 8, 4, 3, 8, 8, 301877255204204463655948695601671352304114073600000000⟩, + ⟨7, 8, 4, 4, 7, 8, 687913546028793772309472863867101595693586841600000000⟩, + ⟨7, 8, 5, 4, 8, 8, -2988978757158300325351876287457553381270224896000000000⟩, + ⟨7, 8, 4, 5, 6, 8, -631008506467689536055920005752621528387472588800000000⟩, + ⟨7, 8, 5, 5, 7, 8, 101680391167111550746994571832900011933302784000000000⟩, + ⟨7, 8, 6, 5, 8, 8, -2105073604647140206411555236777516636271804416000000000⟩, + ⟨7, 8, 4, 6, 5, 8, 1023864085869991393694344198733040886439372390400000000⟩, + ⟨7, 8, 5, 6, 6, 8, -967161969340049137441880605962277318249414656000000000⟩, + ⟨7, 8, 6, 6, 7, 8, -1988024660583439744977623000220128652206014464000000000⟩, + ⟨7, 8, 7, 6, 8, 8, -726988137170766281162276894814023362258403328000000000⟩, + ⟨7, 8, 4, 7, 4, 8, 4234305993781862110462851144456029190058986700800000000⟩, + ⟨7, 8, 5, 7, 5, 8, 1093763813376837807068249440914907754655645696000000000⟩ +] + +def collectedFourData_19_13 : List CollectedFourTerm := [ + ⟨7, 8, 6, 7, 6, 8, 2151678546157078707367765348898517595780546560000000000⟩, + ⟨7, 8, 7, 7, 7, 8, 256941336998949575006127526979954558059413504000000000⟩, + ⟨7, 8, 8, 7, 8, 8, 1723589982786807460974992611676520612416716800000000000⟩ +] + +def collectedFourData_19 : List CollectedFourTerm := (((collectedFourData_19_0 ++ (collectedFourData_19_1 ++ collectedFourData_19_2)) ++ ((collectedFourData_19_3 ++ collectedFourData_19_4) ++ (collectedFourData_19_5 ++ collectedFourData_19_6))) ++ ((collectedFourData_19_7 ++ (collectedFourData_19_8 ++ collectedFourData_19_9)) ++ ((collectedFourData_19_10 ++ collectedFourData_19_11) ++ (collectedFourData_19_12 ++ collectedFourData_19_13)))) + +theorem collectedFourChecked_19 : collectedFourTerms 19 = collectedFourData_19 := by + decide +kernel + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse20.lean b/lean/OAI/Analysis/LaughlinFock/Sparse20.lean new file mode 100644 index 0000000000000000000000000000000000000000..48fd62c09aac600af35f58e5e267675c6be591a6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse20.lean @@ -0,0 +1,159 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse20. -/ +namespace LaughlinFock + +def collectedFourData_20_0 : List CollectedFourTerm := [ + ⟨4, 8, 8, 4, 8, 8, 248827268082759600384230363824043198179285401600000000⟩, + ⟨4, 8, 8, 5, 7, 8, -407952862824233076922912261939020207094927196160000000⟩, + ⟨4, 8, 8, 6, 6, 8, 609374086013061140039430328073839033506028584960000000⟩, + ⟨4, 8, 8, 7, 5, 8, 1574077763458693240372264738975826502875715993600000000⟩, + ⟨5, 7, 8, 4, 8, 8, -407952862824233076922912261939020207094927196160000000⟩, + ⟨5, 7, 8, 5, 7, 8, 668839631479354704117594088785733298860081545216000000⟩, + ⟨5, 7, 8, 6, 6, 8, -999070177619142973977188256577683600670873092096000000⟩, + ⟨5, 7, 8, 7, 5, 8, -2580704015515541694760597042103408829675192975360000000⟩, + ⟨6, 6, 8, 4, 8, 8, 609374086013061140039430328073839033506028584960000000⟩, + ⟨6, 6, 8, 5, 7, 8, -999070177619142973977188256577683600670873092096000000⟩, + ⟨6, 6, 8, 6, 6, 8, 1492347601472470233508475462736293534491660517376000000⟩, + ⟨6, 6, 8, 7, 5, 8, 3854891812347894830776187615105060975251984220160000000⟩, + ⟨7, 5, 8, 4, 8, 8, 1574077763458693240372264738975826502875715993600000000⟩, + ⟨7, 5, 8, 5, 7, 8, -2580704015515541694760597042103408829675192975360000000⟩, + ⟨7, 5, 8, 6, 6, 8, 3854891812347894830776187615105060975251984220160000000⟩, + ⟨7, 5, 8, 7, 5, 8, 9957593572867726714533864137373587211399305625600000000⟩, + ⟨4, 8, 8, 5, 8, 7, 5229875406085747909043634674831140036964410982400000000⟩, + ⟨4, 8, 8, 6, 7, 7, 1409752348724663996669967250644148973410556313600000000⟩, + ⟨4, 8, 8, 7, 6, 7, 2107675649088004501315249146917713901862361497600000000⟩, + ⟨5, 7, 8, 5, 8, 7, 2385534152968768893257079545433267960639148523520000000⟩, + ⟨5, 7, 8, 6, 7, 7, 643038717747893630401450617398053156045486817280000000⟩, + ⟨5, 7, 8, 7, 6, 7, 961386620879972853564793973929046370014440980480000000⟩, + ⟨5, 8, 7, 4, 8, 8, 5229875406085747909043634674831140036964410982400000000⟩, + ⟨5, 8, 7, 5, 7, 8, 2385534152968768893257079545433267960639148523520000000⟩ +] + +def collectedFourData_20_1 : List CollectedFourTerm := [ + ⟨5, 8, 8, 5, 8, 8, 14400595018080206563860515481567058993694889738240000000⟩, + ⟨5, 8, 7, 6, 6, 8, 721210293696865265217814874261076884241556439040000000⟩, + ⟨5, 8, 8, 6, 7, 8, 3881788966931731740129326647252241054621352591360000000⟩, + ⟨5, 8, 7, 7, 5, 8, -2590974434702280277536710036660312896990158520320000000⟩, + ⟨5, 8, 8, 7, 6, 8, 5803538534907889159821653931840142883231115509760000000⟩, + ⟨6, 6, 8, 5, 8, 7, 721210293696865265217814874261076884241556439040000000⟩, + ⟨6, 6, 8, 6, 7, 7, 194407672557637693429687700292731876116329922560000000⟩, + ⟨6, 6, 8, 7, 6, 7, 290652693585711781417696179228894946275580968960000000⟩, + ⟨6, 7, 7, 4, 8, 8, 1409752348724663996669967250644148973410556313600000000⟩, + ⟨6, 7, 7, 5, 7, 8, 643038717747893630401450617398053156045486817280000000⟩, + ⟨6, 7, 8, 5, 8, 8, 3881788966931731740129326647252241054621352591360000000⟩, + ⟨6, 7, 7, 6, 6, 8, 194407672557637693429687700292731876116329922560000000⟩, + ⟨6, 7, 8, 6, 7, 8, 1046365484542438491691408448877456846954210263040000000⟩, + ⟨6, 7, 7, 7, 5, 8, -698416694699210281745076871939302078730972692480000000⟩, + ⟨6, 7, 8, 7, 6, 8, 1564387570491645699678324389265878479895412080640000000⟩, + ⟨7, 5, 8, 5, 8, 7, -2590974434702280277536710036660312896990158520320000000⟩, + ⟨7, 5, 8, 6, 7, 7, -698416694699210281745076871939302078730972692480000000⟩, + ⟨7, 5, 8, 7, 6, 7, -1044180463090370192924134413003251130866262343680000000⟩, + ⟨7, 6, 7, 4, 8, 8, 2107675649088004501315249146917713901862361497600000000⟩, + ⟨7, 6, 7, 5, 7, 8, 961386620879972853564793973929046370014440980480000000⟩, + ⟨7, 6, 8, 5, 8, 8, 5803538534907889159821653931840142883231115509760000000⟩, + ⟨7, 6, 7, 6, 6, 8, 290652693585711781417696179228894946275580968960000000⟩, + ⟨7, 6, 8, 6, 7, 8, 1564387570491645699678324389265878479895412080640000000⟩, + ⟨7, 6, 7, 7, 5, 8, -1044180463090370192924134413003251130866262343680000000⟩ +] + +def collectedFourData_20_2 : List CollectedFourTerm := [ + ⟨7, 6, 8, 7, 6, 8, 2338865823521433065068125652027378919679448842240000000⟩, + ⟨4, 8, 8, 6, 8, 6, -1661788958766215022454092598055539241597376921600000000⟩, + ⟨4, 8, 8, 7, 7, 6, -1258302546079015082152455606743542875202309324800000000⟩, + ⟨5, 7, 8, 6, 8, 6, 2014286385890507013745780458941166077419443978240000000⟩, + ⟨5, 7, 8, 7, 7, 6, 1525212738072412649005856582302435714473362718720000000⟩, + ⟨5, 8, 7, 5, 8, 7, 20971138058685664292162540521920285933431685120000000⟩, + ⟨5, 8, 7, 6, 7, 7, -69296634860289211703909829134872189874806456320000000⟩, + ⟨5, 8, 8, 6, 8, 7, 822599227837103460720963248860367525882867220480000000⟩, + ⟨5, 8, 7, 7, 6, 7, 173545239572471451701203647166676913101450772480000000⟩, + ⟨5, 8, 8, 7, 7, 7, 622870128802965998363521553409415176185645629440000000⟩, + ⟨6, 6, 8, 6, 8, 6, -1311612255730994800534590925690255785026817884160000000⟩, + ⟨6, 6, 8, 7, 7, 6, -993149600705064292020458926870689513726258708480000000⟩, + ⟨6, 7, 7, 5, 8, 7, -69296634860289211703909829134872189874806456320000000⟩, + ⟨6, 7, 7, 6, 7, 7, 228982499162528039282070852663744170563228139520000000⟩, + ⟨6, 7, 8, 6, 8, 7, -2718181443861812730538543996635370069771451105280000000⟩, + ⟨6, 7, 7, 7, 6, 7, -573459631267559662478941568443726912554302177280000000⟩, + ⟨6, 7, 8, 7, 7, 7, -2058200359000717542869319724094327193899724963840000000⟩, + ⟨6, 8, 6, 4, 8, 8, -1661788958766215022454092598055539241597376921600000000⟩, + ⟨6, 8, 6, 5, 7, 8, 2014286385890507013745780458941166077419443978240000000⟩, + ⟨6, 8, 7, 5, 8, 8, 822599227837103460720963248860367525882867220480000000⟩, + ⟨6, 8, 6, 6, 6, 8, -1311612255730994800534590925690255785026817884160000000⟩, + ⟨6, 8, 7, 6, 7, 8, -2718181443861812730538543996635370069771451105280000000⟩, + ⟨6, 8, 8, 6, 8, 8, 16133351650840453468468480722515592959144975400960000000⟩, + ⟨6, 8, 6, 7, 5, 8, 1355472712353301624101817793888095206369971404800000000⟩ +] + +def collectedFourData_20_3 : List CollectedFourTerm := [ + ⟨6, 8, 7, 7, 6, 8, 6807364467661480336601908295990203724538493009920000000⟩, + ⟨6, 8, 8, 7, 7, 8, 12216134516932106105654292363589916292276950138880000000⟩, + ⟨7, 5, 8, 6, 8, 6, 1355472712353301624101817793888095206369971404800000000⟩, + ⟨7, 5, 8, 7, 7, 6, 1026360631473382878588657422312025221407073894400000000⟩, + ⟨7, 6, 7, 5, 8, 7, 173545239572471451701203647166676913101450772480000000⟩, + ⟨7, 6, 7, 6, 7, 7, -573459631267559662478941568443726912554302177280000000⟩, + ⟨7, 6, 8, 6, 8, 7, 6807364467661480336601908295990203724538493009920000000⟩, + ⟨7, 6, 7, 7, 6, 7, 1436161933319231128615563365784717762498574417920000000⟩, + ⟨7, 6, 8, 7, 7, 7, 5154519770131237901099308320928904000946579701760000000⟩, + ⟨7, 7, 6, 4, 8, 8, -1258302546079015082152455606743542875202309324800000000⟩, + ⟨7, 7, 6, 5, 7, 8, 1525212738072412649005856582302435714473362718720000000⟩, + ⟨7, 7, 7, 5, 8, 8, 622870128802965998363521553409415176185645629440000000⟩, + ⟨7, 7, 6, 6, 6, 8, -993149600705064292020458926870689513726258708480000000⟩, + ⟨7, 7, 7, 6, 7, 8, -2058200359000717542869319724094327193899724963840000000⟩, + ⟨7, 7, 8, 6, 8, 8, 12216134516932106105654292363589916292276950138880000000⟩, + ⟨7, 7, 6, 7, 5, 8, 1026360631473382878588657422312025221407073894400000000⟩, + ⟨7, 7, 7, 7, 6, 8, 5154519770131237901099308320928904000946579701760000000⟩, + ⟨7, 7, 8, 7, 7, 8, 9250027258161561482113633474286784429463059824640000000⟩, + ⟨4, 8, 8, 7, 8, 5, -2988978757158300325351876287457553381270224896000000000⟩, + ⟨5, 7, 8, 7, 8, 5, 101680391167111550746994571832900011933302784000000000⟩, + ⟨5, 8, 7, 6, 8, 6, 443946516785676504562595304509255731197436231680000000⟩, + ⟨5, 8, 7, 7, 7, 6, -156905189708954240161096140128378239611819786240000000⟩, + ⟨5, 8, 8, 7, 8, 6, -4210147209294280412823110473555033272543608832000000000⟩, + ⟨6, 6, 8, 7, 8, 5, -967161969340049137441880605962277318249414656000000000⟩ +] + +def collectedFourData_20_4 : List CollectedFourTerm := [ + ⟨6, 7, 7, 6, 8, 6, 419261645484356090282811133243726423986504990720000000⟩, + ⟨6, 7, 7, 7, 7, 6, -148180750462267567666915804953134924211117096960000000⟩, + ⟨6, 7, 8, 7, 8, 6, -3976049321166879489955246000440257304412028928000000000⟩, + ⟨6, 8, 6, 5, 8, 7, 443946516785676504562595304509255731197436231680000000⟩, + ⟨6, 8, 6, 6, 7, 7, 419261645484356090282811133243726423986504990720000000⟩, + ⟨6, 8, 7, 6, 8, 7, 459951401027949431039798077053677338347511480320000000⟩, + ⟨6, 8, 6, 7, 6, 7, -453775199926571015716273988324655717740760268800000000⟩, + ⟨6, 8, 7, 7, 7, 7, -162561838209061829797483173336802550599133429760000000⟩, + ⟨6, 8, 8, 7, 8, 7, -2180964411512298843486830684442070086775209984000000000⟩, + ⟨7, 5, 8, 7, 8, 5, 1093763813376837807068249440914907754655645696000000000⟩, + ⟨7, 6, 7, 6, 8, 6, -453775199926571015716273988324655717740760268800000000⟩, + ⟨7, 6, 7, 7, 7, 6, 160378967144977610543857179167494286468343398400000000⟩, + ⟨7, 6, 8, 7, 8, 6, 4303357092314157414735530697797035191561093120000000000⟩, + ⟨7, 7, 6, 5, 8, 7, -156905189708954240161096140128378239611819786240000000⟩, + ⟨7, 7, 6, 6, 7, 7, -148180750462267567666915804953134924211117096960000000⟩, + ⟨7, 7, 7, 6, 8, 7, -162561838209061829797483173336802550599133429760000000⟩, + ⟨7, 7, 6, 7, 6, 7, 160378967144977610543857179167494286468343398400000000⟩, + ⟨7, 7, 7, 7, 7, 7, 57454659737634693297735665779210944555704647680000000⟩, + ⟨7, 7, 8, 7, 8, 7, 770824010996848725018382580939863674178240512000000000⟩, + ⟨7, 8, 5, 4, 8, 8, -2988978757158300325351876287457553381270224896000000000⟩, + ⟨7, 8, 5, 5, 7, 8, 101680391167111550746994571832900011933302784000000000⟩, + ⟨7, 8, 6, 5, 8, 8, -4210147209294280412823110473555033272543608832000000000⟩, + ⟨7, 8, 5, 6, 6, 8, -967161969340049137441880605962277318249414656000000000⟩, + ⟨7, 8, 6, 6, 7, 8, -3976049321166879489955246000440257304412028928000000000⟩ +] + +def collectedFourData_20_5 : List CollectedFourTerm := [ + ⟨7, 8, 7, 6, 8, 8, -2180964411512298843486830684442070086775209984000000000⟩, + ⟨7, 8, 5, 7, 5, 8, 1093763813376837807068249440914907754655645696000000000⟩, + ⟨7, 8, 6, 7, 6, 8, 4303357092314157414735530697797035191561093120000000000⟩, + ⟨7, 8, 7, 7, 7, 8, 770824010996848725018382580939863674178240512000000000⟩, + ⟨7, 8, 8, 7, 8, 8, 6894359931147229843899970446706082449666867200000000000⟩ +] + +def collectedFourData_20 : List CollectedFourTerm := ((collectedFourData_20_0 ++ (collectedFourData_20_1 ++ collectedFourData_20_2)) ++ (collectedFourData_20_3 ++ (collectedFourData_20_4 ++ collectedFourData_20_5))) + +theorem collectedFourChecked_20 : collectedFourTerms 20 = collectedFourData_20 := by + decide +kernel + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse21.lean b/lean/OAI/Analysis/LaughlinFock/Sparse21.lean new file mode 100644 index 0000000000000000000000000000000000000000..fc60ce8a47cf25da8cef7377827308328de6214f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse21.lean @@ -0,0 +1,62 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse21. -/ +namespace LaughlinFock + +def collectedFourData_21_0 : List CollectedFourTerm := [ + ⟨5, 8, 8, 5, 8, 8, 14400595018080206563860515481567058993694889738240000000⟩, + ⟨5, 8, 8, 6, 7, 8, 3881788966931731740129326647252241054621352591360000000⟩, + ⟨5, 8, 8, 7, 6, 8, 5803538534907889159821653931840142883231115509760000000⟩, + ⟨6, 7, 8, 5, 8, 8, 3881788966931731740129326647252241054621352591360000000⟩, + ⟨6, 7, 8, 6, 7, 8, 1046365484542438491691408448877456846954210263040000000⟩, + ⟨6, 7, 8, 7, 6, 8, 1564387570491645699678324389265878479895412080640000000⟩, + ⟨7, 6, 8, 5, 8, 8, 5803538534907889159821653931840142883231115509760000000⟩, + ⟨7, 6, 8, 6, 7, 8, 1564387570491645699678324389265878479895412080640000000⟩, + ⟨7, 6, 8, 7, 6, 8, 2338865823521433065068125652027378919679448842240000000⟩, + ⟨5, 8, 8, 6, 8, 7, 822599227837103460720963248860367525882867220480000000⟩, + ⟨5, 8, 8, 7, 7, 7, 622870128802965998363521553409415176185645629440000000⟩, + ⟨6, 7, 8, 6, 8, 7, -2718181443861812730538543996635370069771451105280000000⟩, + ⟨6, 7, 8, 7, 7, 7, -2058200359000717542869319724094327193899724963840000000⟩, + ⟨6, 8, 7, 5, 8, 8, 822599227837103460720963248860367525882867220480000000⟩, + ⟨6, 8, 7, 6, 7, 8, -2718181443861812730538543996635370069771451105280000000⟩, + ⟨6, 8, 8, 6, 8, 8, 32266703301680906936936961445031185918289950801920000000⟩, + ⟨6, 8, 7, 7, 6, 8, 6807364467661480336601908295990203724538493009920000000⟩, + ⟨6, 8, 8, 7, 7, 8, 24432269033864212211308584727179832584553900277760000000⟩, + ⟨7, 6, 8, 6, 8, 7, 6807364467661480336601908295990203724538493009920000000⟩, + ⟨7, 6, 8, 7, 7, 7, 5154519770131237901099308320928904000946579701760000000⟩, + ⟨7, 7, 7, 5, 8, 8, 622870128802965998363521553409415176185645629440000000⟩, + ⟨7, 7, 7, 6, 7, 8, -2058200359000717542869319724094327193899724963840000000⟩, + ⟨7, 7, 8, 6, 8, 8, 24432269033864212211308584727179832584553900277760000000⟩, + ⟨7, 7, 7, 7, 6, 8, 5154519770131237901099308320928904000946579701760000000⟩ +] + +def collectedFourData_21_1 : List CollectedFourTerm := [ + ⟨7, 7, 8, 7, 7, 8, 18500054516323122964227266948573568858926119649280000000⟩, + ⟨5, 8, 8, 7, 8, 6, -4210147209294280412823110473555033272543608832000000000⟩, + ⟨6, 7, 8, 7, 8, 6, -3976049321166879489955246000440257304412028928000000000⟩, + ⟨6, 8, 7, 6, 8, 7, 459951401027949431039798077053677338347511480320000000⟩, + ⟨6, 8, 7, 7, 7, 7, -162561838209061829797483173336802550599133429760000000⟩, + ⟨6, 8, 8, 7, 8, 7, -4361928823024597686973661368884140173550419968000000000⟩, + ⟨7, 6, 8, 7, 8, 6, 4303357092314157414735530697797035191561093120000000000⟩, + ⟨7, 7, 7, 6, 8, 7, -162561838209061829797483173336802550599133429760000000⟩, + ⟨7, 7, 7, 7, 7, 7, 57454659737634693297735665779210944555704647680000000⟩, + ⟨7, 7, 8, 7, 8, 7, 1541648021993697450036765161879727348356481024000000000⟩, + ⟨7, 8, 6, 5, 8, 8, -4210147209294280412823110473555033272543608832000000000⟩, + ⟨7, 8, 6, 6, 7, 8, -3976049321166879489955246000440257304412028928000000000⟩, + ⟨7, 8, 7, 6, 8, 8, -4361928823024597686973661368884140173550419968000000000⟩, + ⟨7, 8, 6, 7, 6, 8, 4303357092314157414735530697797035191561093120000000000⟩, + ⟨7, 8, 7, 7, 7, 8, 1541648021993697450036765161879727348356481024000000000⟩, + ⟨7, 8, 8, 7, 8, 8, 20683079793441689531699911340118247349000601600000000000⟩ +] + +def collectedFourData_21 : List CollectedFourTerm := (collectedFourData_21_0 ++ collectedFourData_21_1) + +theorem collectedFourChecked_21 : collectedFourTerms 21 = collectedFourData_21 := by + decide +kernel + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse22.lean b/lean/OAI/Analysis/LaughlinFock/Sparse22.lean new file mode 100644 index 0000000000000000000000000000000000000000..4469c0e7312f1421fe78f72d995d8ab0e5399bb5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse22.lean @@ -0,0 +1,28 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse22. -/ +namespace LaughlinFock + +def collectedFourData_22_0 : List CollectedFourTerm := [ + ⟨6, 8, 8, 6, 8, 8, 32266703301680906936936961445031185918289950801920000000⟩, + ⟨6, 8, 8, 7, 7, 8, 24432269033864212211308584727179832584553900277760000000⟩, + ⟨7, 7, 8, 6, 8, 8, 24432269033864212211308584727179832584553900277760000000⟩, + ⟨7, 7, 8, 7, 7, 8, 18500054516323122964227266948573568858926119649280000000⟩, + ⟨6, 8, 8, 7, 8, 7, -4361928823024597686973661368884140173550419968000000000⟩, + ⟨7, 7, 8, 7, 8, 7, 1541648021993697450036765161879727348356481024000000000⟩, + ⟨7, 8, 7, 6, 8, 8, -4361928823024597686973661368884140173550419968000000000⟩, + ⟨7, 8, 7, 7, 7, 8, 1541648021993697450036765161879727348356481024000000000⟩, + ⟨7, 8, 8, 7, 8, 8, 41366159586883379063399822680236494698001203200000000000⟩ +] + +def collectedFourData_22 : List CollectedFourTerm := collectedFourData_22_0 + +theorem collectedFourChecked_22 : collectedFourTerms 22 = collectedFourData_22 := by + decide +kernel + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/Sparse23.lean b/lean/OAI/Analysis/LaughlinFock/Sparse23.lean new file mode 100644 index 0000000000000000000000000000000000000000..b8b868c4a9543ccceef2d9310c701ca7c7a11da8 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/Sparse23.lean @@ -0,0 +1,20 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SparseTrace + +namespace OAI + +/-! Sparse23. -/ +namespace LaughlinFock + +def collectedFourData_23_0 : List CollectedFourTerm := [ + ⟨7, 8, 8, 7, 8, 8, 41366159586883379063399822680236494698001203200000000000⟩ +] + +def collectedFourData_23 : List CollectedFourTerm := collectedFourData_23_0 + +theorem collectedFourChecked_23 : collectedFourTerms 23 = collectedFourData_23 := by + decide +kernel + +end LaughlinFock + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/SparseTrace.lean b/lean/OAI/Analysis/LaughlinFock/SparseTrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..1ab53cea5d929924e08b7d6cc632b42c677dc605 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/SparseTrace.lean @@ -0,0 +1,93 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FasterTrace + +namespace OAI + +/-! Sparse Trace. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + +structure CollectedFourTerm where + p : ℕ + j : ℕ + k : ℕ + q : ℕ + l : ℕ + i : ℕ + a : ℤ + deriving DecidableEq + +def collectFourTerm (D t : ℕ) (b c : NumericRowEntry) : CollectedFourTerm := + ⟨b.p,b.j,c.i,c.p,c.j,b.i,b.a*c.a*(numericRowFactor D t b c : ℤ)⟩ + +def collectedTermValue (D r s : ℕ) (a : CollectedFourTerm) : ℤ := + let x := memoIntegerCopyPolynomial D (a.p+a.j+a.k) r a.p a.j a.k + if x=0 then 0 else + let y := memoIntegerCopyPolynomial D (a.p+a.j+a.k) s a.q a.l a.i + if y=0 then 0 else a.a*x*y + +theorem collectedTermValue_spec (D t r s : ℕ) (b c : NumericRowEntry) : + collectedTermValue D r s (collectFourTerm D t b c) = + b.a*c.a*(numericRowFactor D t b c : ℤ)* + memoIntegerCopyPolynomial D (b.p+b.j+c.i) r b.p b.j c.i * + memoIntegerCopyPolynomial D (b.p+b.j+c.i) s c.p c.j b.i := by + unfold collectedTermValue collectFourTerm + dsimp only + split_ifs <;> simp_all + +def collectNumericRow (D : ℕ) (t : Fin 8) : List CollectedFourTerm := + (numericRowData t).flatMap fun b => (numericRowData t).flatMap fun c => + if D ≤ b.p+b.j+c.i then [collectFourTerm D t.val b c] else [] + +theorem list_flatMap_sum_int {α : Type*} (xs : List α) (f : α → List ℤ) : + (xs.flatMap f).sum = (xs.map (fun a => (f a).sum)).sum := by + induction xs with + | nil => rfl + | cons a xs ih => simp only [List.flatMap_cons, List.sum_append, List.map_cons, List.sum_cons, ih] + +theorem collectNumericRow_sum (D : ℕ) (t : Fin 8) (r s : ℕ) : + numericFourTrace D t r s = + -(((collectNumericRow D t).map (collectedTermValue D r s)).sum) := by + unfold numericFourTrace collectNumericRow + simp only [List.map_flatMap, list_flatMap_sum_int] + congr 1 + apply congrArg List.sum + apply List.map_congr_left + intro b hb + apply congrArg List.sum + apply List.map_congr_left + intro c hc + unfold numericRowTerm + split_ifs + · simp only [List.map_cons, List.map_nil, List.sum_cons, List.sum_nil, add_zero, + collectedTermValue_spec] + · rfl + +def collectedFourTerms (D : ℕ) : List CollectedFourTerm := + collectNumericRow D 0 ++ collectNumericRow D 1 ++ collectNumericRow D 2 ++ + collectNumericRow D 3 ++ collectNumericRow D 4 ++ collectNumericRow D 5 ++ + collectNumericRow D 6 ++ collectNumericRow D 7 + +def collectedFourTrace (D r s : ℕ) (ls : List CollectedFourTerm) : ℤ := + -(directIntegerSum (collectedTermValue D r s) ls) + +theorem numericRowsFourTrace_collected (D r s : ℕ) : + numericRowsFourTrace D r s = collectedFourTrace D r s (collectedFourTerms D) := by + simp only [numericRowsFourTrace, collectNumericRow_sum, Fin.sum_univ_succ, + collectedFourTrace, collectedFourTerms, ← directIntegerSum_spec, + List.map_append, List.sum_append] + simp only [Fin.isValue, Fin.succ_zero_eq_one] + abel + +theorem integerRowsFourTrace_collected {D : ℕ} (hD : D ≤ 23) (ls : List CollectedFourTerm) + (hls : collectedFourTerms D = ls) (r s : CopyLabel D) : + integerRowsFourTrace D r s = + (collectedFourTrace D r.val.val s.val.val ls : ℚ) / fourCommonDenominator := by + rw [integerRowsFourTrace_numeric hD, numericRowsFourTrace_collected, hls] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/SphereScaling.lean b/lean/OAI/Analysis/LaughlinFock/SphereScaling.lean new file mode 100644 index 0000000000000000000000000000000000000000..c53253fa2267e362c0206870c2419d6dcc63203c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/SphereScaling.lean @@ -0,0 +1,282 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Model + +namespace OAI + +/-! Sphere Scaling. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open scoped BigOperators Polynomial +open Polynomial +open Filter Topology +def occupationDiagonal (Q : ℕ) (d : Orbital Q → ℂ) : FockMatrix Q := + Matrix.diagonal (fun A => ∏ j ∈ A, d j) + + +def occupationDiagonalInv (Q : ℕ) (d : Orbital Q → ℂ) : FockMatrix Q := + Matrix.diagonal (fun A => (∏ j ∈ A, d j)⁻¹) + +theorem occupationDiagonal_inv_mul (Q : ℕ) (d : Orbital Q → ℂ) + (hd : ∀ j, d j ≠ 0) : + occupationDiagonalInv Q d * occupationDiagonal Q d = 1 := by + simp only [occupationDiagonalInv, occupationDiagonal, Matrix.diagonal_mul_diagonal] + convert Matrix.diagonal_one using 1 + congr 1 + funext A + exact inv_mul_cancel₀ (Finset.prod_ne_zero_iff.mpr (fun j _ => hd j)) + +theorem occupationDiagonal_mul_inv (Q : ℕ) (d : Orbital Q → ℂ) + (hd : ∀ j, d j ≠ 0) : + occupationDiagonal Q d * occupationDiagonalInv Q d = 1 := by + simp only [occupationDiagonalInv, occupationDiagonal, Matrix.diagonal_mul_diagonal] + convert Matrix.diagonal_one using 1 + congr 1 + funext A + exact mul_inv_cancel₀ (Finset.prod_ne_zero_iff.mpr (fun j _ => hd j)) + + +theorem annihilator_mul_occupationDiagonal (Q : ℕ) (d : Orbital Q → ℂ) + (j : Orbital Q) : + annihilator Q j * occupationDiagonal Q d = + d j • (occupationDiagonal Q d * annihilator Q j) := by + ext A B + simp only [occupationDiagonal, Matrix.mul_diagonal, Matrix.smul_apply, + Matrix.diagonal_mul, smul_eq_mul] + by_cases h : j ∈ B ∧ A = B.erase j + · obtain ⟨hj, rfl⟩ := h + simp only [annihilator, hj, and_self, ite_true] + rw [← Finset.mul_prod_erase B d hj] + ring + · simp [annihilator, h] + + +def diagonalConjugate (Q : ℕ) (d : Orbital Q → ℂ) (A : FockMatrix Q) : FockMatrix Q := + occupationDiagonalInv Q d * A * occupationDiagonal Q d + +theorem diagonalConjugate_annihilator (Q : ℕ) (d : Orbital Q → ℂ) + (hd : ∀ j, d j ≠ 0) (j : Orbital Q) : + diagonalConjugate Q d (annihilator Q j) = d j • annihilator Q j := by + rw [diagonalConjugate, Matrix.mul_assoc, annihilator_mul_occupationDiagonal, + Matrix.mul_smul, ← Matrix.mul_assoc, occupationDiagonal_inv_mul Q d hd, + Matrix.one_mul] + +theorem diagonalConjugate_mul (Q : ℕ) (d : Orbital Q → ℂ) + (hd : ∀ j, d j ≠ 0) (A B : FockMatrix Q) : + diagonalConjugate Q d (A * B) = + diagonalConjugate Q d A * diagonalConjugate Q d B := by + symm + unfold diagonalConjugate + calc + _ = occupationDiagonalInv Q d * A * + (occupationDiagonal Q d * occupationDiagonalInv Q d) * B * + occupationDiagonal Q d := by simp only [Matrix.mul_assoc] + _ = _ := by rw [occupationDiagonal_mul_inv Q d hd]; simp only [Matrix.mul_one, + Matrix.mul_assoc] + +theorem diagonalConjugate_sum (Q : ℕ) (d : Orbital Q → ℂ) {ι : Type*} + (s : Finset ι) (A : ι → FockMatrix Q) : + diagonalConjugate Q d (∑ i ∈ s, A i) = ∑ i ∈ s, diagonalConjugate Q d (A i) := by + simp only [diagonalConjugate, Matrix.mul_sum, Matrix.sum_mul] + +theorem diagonalConjugate_smul (Q : ℕ) (d : Orbital Q → ℂ) (a : ℂ) (A : FockMatrix Q) : + diagonalConjugate Q d (a • A) = a • diagonalConjugate Q d A := by + simp only [diagonalConjugate, Matrix.mul_smul, Matrix.smul_mul] + +@[simp] theorem diagonalConjugate_zero (Q : ℕ) (d : Orbital Q → ℂ) : + diagonalConjugate Q d 0 = 0 := by simp [diagonalConjugate] + + +def coefficientPairAnnihilator (Q : ℕ) (a : Orbital Q → Orbital Q → ℂ) : FockMatrix Q := + ∑ i : Orbital Q, ∑ j : Orbital Q, + if i < j then a i j • (annihilator Q j * annihilator Q i) else 0 + +theorem pairAnnihilator_eq_coefficientPairAnnihilator (Q p : ℕ) : + pairAnnihilator Q p = + coefficientPairAnnihilator Q (fun i j => (pairCoefficient Q p i j : ℂ)) := rfl + + +theorem diagonalConjugate_pair (Q : ℕ) (d : Orbital Q → ℂ) + (hd : ∀ j, d j ≠ 0) (a : Orbital Q → Orbital Q → ℂ) : + diagonalConjugate Q d (coefficientPairAnnihilator Q a) = + coefficientPairAnnihilator Q (fun i j => a i j * d i * d j) := by + unfold coefficientPairAnnihilator + rw [diagonalConjugate_sum] + apply Finset.sum_congr rfl + intro i _ + rw [diagonalConjugate_sum] + apply Finset.sum_congr rfl + intro j _ + split_ifs + · rw [diagonalConjugate_smul, diagonalConjugate_mul Q d hd, + diagonalConjugate_annihilator Q d hd, diagonalConjugate_annihilator Q d hd, + Matrix.smul_mul, Matrix.mul_smul, smul_smul, smul_smul] + congr 1 + ring + · exact diagonalConjugate_zero Q d + +open Filter Topology + + +def scaledDescFactorial (Q s p : ℕ) : ℝ := + ((Q-s).descFactorial p : ℝ) / (Q : ℝ)^p + +theorem scaledDescFactorial_nonneg (Q s p : ℕ) : + 0 ≤ scaledDescFactorial Q s p := by unfold scaledDescFactorial; positivity + +theorem scaledDescFactorial_pos {Q s p : ℕ} (hQ : 0 < Q) (hp : p ≤ Q-s) : + 0 < scaledDescFactorial Q s p := by + unfold scaledDescFactorial + exact div_pos (by exact_mod_cast Nat.descFactorial_pos.mpr hp) + (pow_pos (by exact_mod_cast hQ) _) + +theorem scaledDescFactorial_le_one {Q : ℕ} (hQ : 0 < Q) (s p : ℕ) : + scaledDescFactorial Q s p ≤ 1 := by + unfold scaledDescFactorial + rw [div_le_one (pow_pos (by exact_mod_cast hQ) _)] + exact_mod_cast (Nat.descFactorial_le_pow (Q-s) p).trans + (Nat.pow_le_pow_left (Nat.sub_le Q s) p) + +theorem scaledDescFactorial_succ {Q s p : ℕ} (hQ : 0 < Q) (hs : s ≤ Q) + (hp : p ≤ Q-s) : + scaledDescFactorial Q s (p+1) = + (1 - ((s : ℝ)+p)/Q) * scaledDescFactorial Q s p := by + unfold scaledDescFactorial + rw [Nat.descFactorial_succ, Nat.cast_mul, Nat.cast_sub hp, Nat.cast_sub hs, + pow_succ', mul_div_mul_comm] + congr 1 + have hn : (Q : ℝ) ≠ 0 := by exact_mod_cast (ne_of_gt hQ) + field_simp + ring + +theorem scaledDescFactorial_tendsto (s p : ℕ) : + Tendsto (fun Q : ℕ => scaledDescFactorial Q s p) atTop (𝓝 1) := by + induction p with + | zero => simpa only [scaledDescFactorial, Nat.descFactorial_zero, + Nat.cast_one, pow_zero, div_one] using (tendsto_const_nhds : Tendsto (fun _ : ℕ => (1:ℝ)) atTop (𝓝 1)) + | succ p ih => + have hf : Tendsto (fun Q : ℕ => 1 - ((s:ℝ)+p)/Q) atTop (𝓝 1) := by + convert (tendsto_const_nhds (x := (1:ℝ))).sub + (tendsto_const_div_atTop_nhds_zero_nat ((s:ℝ)+p)) using 1 + norm_num + have ht := hf.mul ih + simp only [mul_one] at ht + apply ht.congr' + filter_upwards [eventually_ge_atTop (s+p+1)] with Q hQ + exact (scaledDescFactorial_succ (by omega) (by omega) (by omega)).symm + + +def modeScale (Q x : ℕ) : ℝ := Real.sqrt (scaledDescFactorial Q 0 x) + + +def pairScale (Q p : ℕ) : ℝ := Real.sqrt ((scaledDescFactorial (2*Q) 2 p)⁻¹) + +theorem modeScale_nonneg (Q x : ℕ) : 0 ≤ modeScale Q x := Real.sqrt_nonneg _ + +theorem modeScale_pos {Q x : ℕ} (hQ : 0 < Q) (hx : x ≤ Q) : + 0 < modeScale Q x := by + apply Real.sqrt_pos.mpr + exact scaledDescFactorial_pos hQ (by simpa using hx) + +theorem modeScale_le_one {Q : ℕ} (hQ : 0 < Q) (x : ℕ) : modeScale Q x ≤ 1 := by + apply Real.sqrt_le_one.mpr + exact scaledDescFactorial_le_one hQ 0 x + +theorem modeScale_tendsto (x : ℕ) : + Tendsto (fun Q : ℕ => modeScale Q x) atTop (𝓝 1) := by + simpa only [modeScale, Real.sqrt_one] using (scaledDescFactorial_tendsto 0 x).sqrt + +theorem pairScale_tendsto (p : ℕ) : + Tendsto (fun Q : ℕ => pairScale Q p) atTop (𝓝 1) := by + have hd : Tendsto (fun Q : ℕ => 2*Q) atTop atTop := + tendsto_atTop_mono (fun Q => by change Q ≤ 2*Q; omega) tendsto_id + have h := ((scaledDescFactorial_tendsto 2 p).comp hd).inv₀ (by norm_num : (1:ℝ) ≠ 0) + simpa only [pairScale, inv_one, Real.sqrt_one, Function.comp_apply] using h.sqrt + +theorem pairScale_one_le {Q p : ℕ} (hQ : 0 < Q) (hp : p ≤ 2*Q-2) : + 1 ≤ pairScale Q p := by + apply Real.one_le_sqrt.mpr + have hpos := scaledDescFactorial_pos (by omega : 0 < 2*Q) hp + rw [one_le_inv₀ hpos] + exact scaledDescFactorial_le_one (by omega) 2 p + + +def limitPairCoefficient (p i j : ℕ) : ℝ := + if i+j=p+1 then + ((i:ℝ)-(j:ℝ)) * Real.sqrt ((p.factorial:ℝ) / (2^p * i.factorial * j.factorial)) + else 0 + + +def sphericalPairCoefficient (Q p i j : ℕ) : ℝ := + if i+j=p+1 then + ((i:ℝ)-(j:ℝ)) * Real.sqrt + (((Q.descFactorial i:ℝ)*(Q.descFactorial j:ℝ)*(p.factorial:ℝ)) / + ((Q:ℝ)*((2*Q-2).descFactorial p:ℝ)*(i.factorial:ℝ)*(j.factorial:ℝ))) + else 0 + +theorem pairCoefficient_eq_sphericalPairCoefficient (Q p : ℕ) (i j : Orbital Q) : + pairCoefficient Q p i j = sphericalPairCoefficient Q p i.val j.val := + pairCoefficient_eq Q p i j + +private theorem radicand_factorization {Q p i j : ℕ} (hQ : 0 < Q) + (hp : p ≤ 2*Q-2) (hw : i+j=p+1) : + ((Q.descFactorial i:ℝ)*(Q.descFactorial j:ℝ)*(p.factorial:ℝ)) / + ((Q:ℝ)*((2*Q-2).descFactorial p:ℝ)*(i.factorial:ℝ)*(j.factorial:ℝ)) = + (scaledDescFactorial (2*Q) 2 p)⁻¹ * scaledDescFactorial Q 0 i * + scaledDescFactorial Q 0 j * + ((p.factorial:ℝ) / (2^p * i.factorial * j.factorial)) := by + have hQR : (Q:ℝ) ≠ 0 := by exact_mod_cast (ne_of_gt hQ) + have hd : ((2*Q-2).descFactorial p:ℝ) ≠ 0 := by + exact_mod_cast (ne_of_gt (Nat.descFactorial_pos.mpr hp)) + have hi : (i.factorial:ℝ) ≠ 0 := by exact_mod_cast Nat.factorial_ne_zero i + have hj : (j.factorial:ℝ) ≠ 0 := by exact_mod_cast Nat.factorial_ne_zero j + have hpow : (Q:ℝ)^i * (Q:ℝ)^j = (Q:ℝ) * (Q:ℝ)^p := by + rw [← pow_add, hw, pow_succ'] + unfold scaledDescFactorial + simp only [Nat.sub_zero, inv_div, Nat.cast_mul, Nat.cast_ofNat] + symm + calc + _ = ((2*(Q:ℝ))^p * (Q.descFactorial i:ℝ) * (Q.descFactorial j:ℝ) * p.factorial) / + (((2*Q-2).descFactorial p:ℝ) * ((Q:ℝ)^i * (Q:ℝ)^j) * + (2^p * i.factorial * j.factorial)) := by + field_simp + _ = _ := by + rw [hpow, mul_pow] + field_simp + + + +theorem sphericalPairCoefficient_factorization {Q p : ℕ} (hQ : 0 < Q) + (hp : p ≤ 2*Q-2) (i j : ℕ) : + sphericalPairCoefficient Q p i j = pairScale Q p * modeScale Q i * + modeScale Q j * limitPairCoefficient p i j := by + unfold sphericalPairCoefficient limitPairCoefficient + split_ifs with hw + · have h1 := scaledDescFactorial_nonneg (2*Q) 2 p + have h2 := scaledDescFactorial_nonneg Q 0 i + have h3 := scaledDescFactorial_nonneg Q 0 j + rw [radicand_factorization hQ hp hw] + rw [Real.sqrt_mul (by positivity : 0 ≤ + (scaledDescFactorial (2*Q) 2 p)⁻¹ * scaledDescFactorial Q 0 i * + scaledDescFactorial Q 0 j)] + rw [Real.sqrt_mul (by positivity : 0 ≤ + (scaledDescFactorial (2*Q) 2 p)⁻¹ * scaledDescFactorial Q 0 i)] + rw [Real.sqrt_mul (by positivity : 0 ≤ (scaledDescFactorial (2*Q) 2 p)⁻¹)] + unfold pairScale modeScale + ring + · simp + + +theorem sphericalPairCoefficient_tendsto (p i j : ℕ) : + Tendsto (fun Q : ℕ => sphericalPairCoefficient Q p i j) atTop + (𝓝 (limitPairCoefficient p i j)) := by + have ht := (((pairScale_tendsto p).mul (modeScale_tendsto i)).mul + (modeScale_tendsto j)).mul_const (limitPairCoefficient p i j) + simp only [one_mul] at ht + apply ht.congr' + filter_upwards [eventually_ge_atTop (p+2)] with Q hQ + exact (sphericalPairCoefficient_factorization (by omega) (by omega) i j).symm +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/SpinSchur.lean b/lean/OAI/Analysis/LaughlinFock/SpinSchur.lean new file mode 100644 index 0000000000000000000000000000000000000000..3598cfcd082405d0bc851a8ba8572620fd928c4a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/SpinSchur.lean @@ -0,0 +1,226 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.Averaging +import OAI.Analysis.LaughlinFock.LadderCalculus + +namespace OAI + +/-! Spin Schur. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder +open NormedSpace MeasureTheory + +section Derivative +open scoped Matrix.Norms.Operator + + +theorem matrix_commutes_generator_of_flow {ι : Type*} [Fintype ι] [DecidableEq ι] + (A X : Matrix ι ι ℂ) + (h : ∀ t : ℝ, A * exp ((t : ℂ) • X) = exp ((t : ℂ) • X) * A) : + A * X = X * A := by + have hc (t : ℝ) : (t : ℂ) • X = t • X := by + exact (RCLike.real_smul_eq_coe_smul (K:=ℂ) t X).symm + simp_rw [hc] at h + have he : (fun t : ℝ => A * exp (t • X)) = (fun t => exp (t • X) * A) := funext h + have hd := hasDerivAt_exp_smul_const X (0 : ℝ) + have h₁ : HasDerivAt (fun t : ℝ => A * exp (t • X)) + (A * (exp ((0 : ℝ) • X) * X)) 0 := hd.const_mul A + have h₂ := hd.mul_const A + rw [he] at h₁ + simpa only [zero_smul, exp_zero, Matrix.one_mul] using! h₁.unique h₂ + + + +theorem rotationAverage_commutes_generator {J σ : Type*} {I : J → Type*} + [∀ j, Fintype (I j)] [∀ j, DecidableEq (I j)] + (X : σ → ∀ j, Matrix (I j) (I j) ℂ) + (hX : ∀ s j, (X s j)ᴴ = -X s j) + (j : J) (M : Matrix (I j) (I j) ℂ) (s : σ) : + rotationAverage X hX j M * X s j = X s j * rotationAverage X hX j M := by + apply matrix_commutes_generator_of_flow + intro t + exact rotationAverage_commutes X hX j M + ⟨rotationFlow X hX s t, rotationFlow_mem_group X hX s t⟩ + +end Derivative + + +def spinLowerMatrix (n : ℕ) : Matrix (Fin (n+1)) (Fin (n+1)) ℂ := fun i j => + if i.val = j.val+1 then (spinStep n i.val : ℂ) else 0 + + +def spinWeightMatrix (n : ℕ) : Matrix (Fin (n+1)) (Fin (n+1)) ℂ := + Matrix.diagonal (fun i => (n : ℂ) - 2 * (i.val : ℂ)) + + +def spinGenerator (n : ℕ) (s : Fin 3) : Matrix (Fin (n+1)) (Fin (n+1)) ℂ := + if s = 0 then spinLowerMatrix n - (spinLowerMatrix n)ᴴ + else if s = 1 then Complex.I • (spinLowerMatrix n + (spinLowerMatrix n)ᴴ) + else Complex.I • spinWeightMatrix n + +theorem spinWeightMatrix_adjoint (n : ℕ) : (spinWeightMatrix n)ᴴ = spinWeightMatrix n := by + simp [spinWeightMatrix, Matrix.diagonal_conjTranspose] + +theorem spinGenerator_skew (n : ℕ) (s : Fin 3) : + (spinGenerator n s)ᴴ = -spinGenerator n s := by + fin_cases s <;> simp [spinGenerator, Matrix.conjTranspose_add, + Matrix.conjTranspose_smul, spinWeightMatrix_adjoint, sub_eq_add_neg, add_comm] + + + +theorem spinGenerator_intertwiner {n m : ℕ} + (A : Matrix (Fin (n+1)) (Fin (m+1)) ℂ) + (hA : ∀ s, spinGenerator n s * A = A * spinGenerator m s) : + spinLowerMatrix n * A = A * spinLowerMatrix m ∧ + (spinLowerMatrix n)ᴴ * A = A * (spinLowerMatrix m)ᴴ ∧ + spinWeightMatrix n * A = A * spinWeightMatrix m := by + have h₀ : (spinLowerMatrix n - (spinLowerMatrix n)ᴴ) * A = + A * (spinLowerMatrix m - (spinLowerMatrix m)ᴴ) := by + simpa [spinGenerator] using hA 0 + have h₁ : (Complex.I • (spinLowerMatrix n + (spinLowerMatrix n)ᴴ)) * A = + A * (Complex.I • (spinLowerMatrix m + (spinLowerMatrix m)ᴴ)) := by + simpa [spinGenerator] using hA 1 + have h₂ : (Complex.I • spinWeightMatrix n) * A = + A * (Complex.I • spinWeightMatrix m) := by + simpa [spinGenerator] using hA 2 + simp only [Matrix.smul_mul, Matrix.mul_smul] at h₁ h₂ + have hi : (Complex.I : ℂ) ≠ 0 := Complex.I_ne_zero + have he₁ := smul_right_injective _ hi h₁ + have he₂ := smul_right_injective _ hi h₂ + refine ⟨?_, ?_, he₂⟩ + · ext i j + have he := congrArg (fun M => M i j) h₀ + have hf := congrArg (fun M => M i j) he₁ + simp only [Matrix.sub_mul, Matrix.mul_sub, Matrix.add_mul, Matrix.mul_add, + Matrix.sub_apply, Matrix.add_apply] at he hf + linear_combination (he + hf) / 2 + · ext i j + have he := congrArg (fun M => M i j) h₀ + have hf := congrArg (fun M => M i j) he₁ + simp only [Matrix.sub_mul, Matrix.mul_sub, Matrix.add_mul, Matrix.mul_add, + Matrix.sub_apply, Matrix.add_apply] at he hf + linear_combination (hf - he) / 2 + + + +theorem mul_spinLower_succ {κ : Type*} {n : ℕ} + (A : Matrix κ (Fin (n+1)) ℂ) (i : κ) (j : ℕ) (hj : j < n) : + (A * spinLowerMatrix n) i ⟨j, by omega⟩ = + A i ⟨j+1, by omega⟩ * (spinStep n (j+1) : ℂ) := by + classical + simp only [Matrix.mul_apply] + rw [Finset.sum_eq_single (⟨j+1, by omega⟩ : Fin (n+1))] + · simp [spinLowerMatrix] + · intro b _ hb + have hne : b.val ≠ j+1 := fun he => hb (Fin.ext he) + simp [spinLowerMatrix, hne] + · simp + + +theorem mul_spinRaise_zero {κ : Type*} {n : ℕ} + (A : Matrix κ (Fin (n+1)) ℂ) (i : κ) : + (A * (spinLowerMatrix n)ᴴ) i 0 = 0 := by + simp [Matrix.mul_apply, Matrix.conjTranspose_apply, spinLowerMatrix] + + +theorem spinRaise_mul_pred {κ : Type*} {n : ℕ} + (A : Matrix (Fin (n+1)) κ ℂ) (i : Fin (n+1)) (hi : 0 < i.val) (j : κ) : + ((spinLowerMatrix n)ᴴ * A) ⟨i.val-1, by omega⟩ j = + (spinStep n i.val : ℂ) * A i j := by + classical + simp only [Matrix.mul_apply] + rw [Finset.sum_eq_single i] + · simp [Matrix.conjTranspose_apply, spinLowerMatrix, Nat.sub_add_cancel hi] + · intro b _ hb + have hne : b.val ≠ i.val := fun he => hb (Fin.ext he) + simp [Matrix.conjTranspose_apply, spinLowerMatrix, Nat.sub_add_cancel hi, hne] + · simp + + + +theorem spin_intertwiner_zero_of_first_column {n m : ℕ} + (A : Matrix (Fin (n+1)) (Fin (m+1)) ℂ) + (hL : spinLowerMatrix n * A = A * spinLowerMatrix m) + (h₀ : ∀ i, A i 0 = 0) : A = 0 := by + have hc (k : ℕ) (hk : k ≤ m) : ∀ i, A i ⟨k, by omega⟩ = 0 := by + induction k with + | zero => exact h₀ + | succ k ih => + have ih' := ih (by omega) + intro i + have he := congrArg (fun R => R i (⟨k, by omega⟩ : Fin (m+1))) hL + rw [mul_spinLower_succ A i k (by omega)] at he + have hz : (spinLowerMatrix n * A) i ⟨k, by omega⟩ = 0 := by + simp only [Matrix.mul_apply, ih', mul_zero, Finset.sum_const_zero] + rw [hz] at he + have hs : (spinStep m (k+1) : ℂ) ≠ 0 := by + exact_mod_cast (spinStep_pos (by omega) hk).ne' + exact (mul_eq_zero.mp he.symm).resolve_right hs + ext i j + exact hc j.val (by omega) i + +theorem spin_intertwiner_first_column {n m : ℕ} + (A : Matrix (Fin (n+1)) (Fin (m+1)) ℂ) + (hR : (spinLowerMatrix n)ᴴ * A = A * (spinLowerMatrix m)ᴴ) + (i : Fin (n+1)) (hi : 0 < i.val) : A i 0 = 0 := by + have he := congrArg (fun R => R (⟨i.val-1, by omega⟩ : Fin (n+1)) 0) hR + rw [spinRaise_mul_pred A i hi, mul_spinRaise_zero] at he + have hs : (spinStep n i.val : ℂ) ≠ 0 := by + exact_mod_cast (spinStep_pos hi (by omega)).ne' + exact (mul_eq_zero.mp he).resolve_left hs + + + +theorem spin_intertwiner_scalar {n : ℕ} (A : Matrix (Fin (n+1)) (Fin (n+1)) ℂ) + (hA : ∀ s, spinGenerator n s * A = A * spinGenerator n s) : + A = A 0 0 • 1 := by + obtain ⟨hL,hR,_⟩ := spinGenerator_intertwiner A hA + have he : A - A 0 0 • 1 = 0 := by + apply spin_intertwiner_zero_of_first_column + · simp [Matrix.mul_sub, Matrix.sub_mul, hL] + · intro i + by_cases hi : i = 0 + · subst i; simp + · have hip : 0 < i.val := by + have : i.val ≠ 0 := fun h => hi (Fin.ext h) + omega + simp [Matrix.sub_apply, Matrix.smul_apply, hi, + spin_intertwiner_first_column A hR i hip] + exact sub_eq_zero.mp he + + + +theorem spin_intertwiner_zero_of_ne {n m : ℕ} (hnm : n ≠ m) + (A : Matrix (Fin (n+1)) (Fin (m+1)) ℂ) + (hA : ∀ s, spinGenerator n s * A = A * spinGenerator m s) : A = 0 := by + obtain ⟨hL,hR,hW⟩ := spinGenerator_intertwiner A hA + apply spin_intertwiner_zero_of_first_column A hL + intro i + by_cases hi : i = 0 + · subst i + have he := congrArg (fun R => R 0 0) hW + simp [spinWeightMatrix, Matrix.diagonal_mul, Matrix.mul_diagonal] at he + have hz : ((n : ℂ)-(m : ℂ)) * A 0 0 = 0 := by linear_combination he + have hn : (n : ℂ)-(m : ℂ) ≠ 0 := sub_ne_zero.mpr (by exact_mod_cast hnm) + exact (mul_eq_zero.mp hz).resolve_left hn + · have hip : 0 < i.val := by + have : i.val ≠ 0 := fun h => hi (Fin.ext h) + omega + exact spin_intertwiner_first_column A hR i hip + +theorem spin_intertwiner_trace_scalar {n : ℕ} + (A : Matrix (Fin (n+1)) (Fin (n+1)) ℂ) + (hA : ∀ s, spinGenerator n s * A = A * spinGenerator n s) : + A = (A.trace / (n+1 : ℂ)) • 1 := by + have he := spin_intertwiner_scalar A hA + have ht := congrArg Matrix.trace he + have hn : (n+1 : ℂ) ≠ 0 := by exact_mod_cast Nat.succ_ne_zero n + have hz : A 0 0 = A.trace / (n+1 : ℂ) := by + apply (eq_div_iff hn).mpr + simpa [Matrix.trace_smul, Matrix.trace_one] using ht.symm + rwa [hz] at he + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/SpinTails.lean b/lean/OAI/Analysis/LaughlinFock/SpinTails.lean new file mode 100644 index 0000000000000000000000000000000000000000..8529d4967834aadc5934a96189c43c787ea57fbe --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/SpinTails.lean @@ -0,0 +1,307 @@ +import Mathlib + +namespace OAI + +/-! Spin Tails. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open scoped BigOperators Polynomial +open Polynomial +open Filter Topology + + +def fallingRatio (Q z : ℕ) : ℝ := + (Q.descFactorial z : ℝ) / ((2 * Q - 2).descFactorial z : ℝ) + + + +def gramShift (Q z : ℕ) : ℝ := + (-1 : ℝ)^z * fallingRatio Q z * (3 * z - 1 - z * (z + 1) / Q) + +theorem fallingRatio_nonneg (Q z : ℕ) : 0 ≤ fallingRatio Q z := by + unfold fallingRatio + positivity + +theorem fallingRatio_succ {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + fallingRatio Q (z + 1) = + ((Q : ℝ) - z) / (2 * Q - 2 - z) * fallingRatio Q z := by + unfold fallingRatio + rw [Nat.descFactorial_succ, Nat.descFactorial_succ, + Nat.cast_mul, Nat.cast_mul, mul_div_mul_comm, + Nat.cast_sub hz, Nat.cast_sub (show z ≤ 2*Q-2 by omega), + Nat.cast_sub (show 2 ≤ 2*Q by omega)] + push_cast + rfl + + +theorem fallingRatio_le_geometric {Q z : ℕ} (hQ : 4 ≤ Q) (hz : z ≤ Q) : + fallingRatio Q z ≤ (2 / 3 : ℝ)^z := by + induction z with + | zero => simp [fallingRatio] + | succ z ih => + rw [fallingRatio_succ (by omega) (by omega), pow_succ'] + have hQR : (4 : ℝ) ≤ Q := by exact_mod_cast hQ + have hzR : (z : ℝ) + 1 ≤ Q := by exact_mod_cast hz + have hd : 0 < 2 * (Q : ℝ) - 2 - z := by linarith + have hf : ((Q : ℝ)-z) / (2*Q-2-z) ≤ 2/3 := by + rw [div_le_iff₀ hd] + have : (0 : ℝ) ≤ z := Nat.cast_nonneg z + linarith + exact mul_le_mul hf (ih (by omega)) (fallingRatio_nonneg Q z) (by norm_num) + +private theorem affineRatio_tendsto (z : ℕ) : + Tendsto (fun Q : ℕ => ((Q : ℝ)-z)/(2*Q-2-z)) atTop (𝓝 (1/2)) := by + have h1 := tendsto_const_div_atTop_nhds_zero_nat (z : ℝ) + have h2 := tendsto_const_div_atTop_nhds_zero_nat (2 + (z : ℝ)) + have hh : Tendsto (fun Q : ℕ => (1 - (z : ℝ)/Q)/(2 - (2+z)/Q)) + atTop (𝓝 (1/2)) := by + convert ((tendsto_const_nhds (x := (1:ℝ))).sub h1).div + ((tendsto_const_nhds (x := (2:ℝ))).sub h2) + (show (2:ℝ)-0 ≠ 0 by norm_num) using 1 + first | rfl | norm_num + apply hh.congr' + filter_upwards [eventually_ge_atTop (z+2)] with Q hQ + have hn : (Q : ℝ) ≠ 0 := by exact_mod_cast (by omega : Q ≠ 0) + have hzr : (z : ℝ) + 2 ≤ Q := by exact_mod_cast hQ + have hd : 2 * (Q:ℝ) - 2 - z ≠ 0 := by have := Nat.cast_nonneg (α:=ℝ) z; linarith + have hd' : 2 - (2 + (z:ℝ)) / Q ≠ 0 := by + rw [ne_eq, sub_eq_zero, eq_div_iff hn] + linarith + field_simp [hn, hd, hd'] + ring + +theorem fallingRatio_tendsto (z : ℕ) : + Tendsto (fun Q : ℕ => fallingRatio Q z) atTop (𝓝 ((1/2 : ℝ)^z)) := by + induction z with + | zero => simp [fallingRatio] + | succ z ih => + have h := (affineRatio_tendsto z).mul ih + simp only [← pow_succ'] at h + apply h.congr' + filter_upwards [eventually_ge_atTop (z+2)] with Q hQ + exact (fallingRatio_succ (by omega) (by omega)).symm + + +theorem gramShift_tendsto (z : ℕ) : + Tendsto (fun Q : ℕ => gramShift Q z) atTop + (𝓝 ((3 * (z : ℝ) - 1) * (-1/2)^z)) := by + have h := ((fallingRatio_tendsto z).const_mul ((-1:ℝ)^z)).mul + ((tendsto_const_nhds (x := (3*(z:ℝ)-1))).sub + (tendsto_const_div_atTop_nhds_zero_nat ((z:ℝ)*(z+1)))) + convert h using 1 + · simp [gramShift] + · simp only [sub_zero] + rw [mul_assoc, mul_comm ((3*(z:ℝ)-1)), ← mul_assoc, ← mul_pow] + congr 1 + norm_num + + +def spinRatio (Q z : ℕ) : ℝ := + (3 * Q - 1 - 2 * (z : ℝ)) / (2 * Q - 1) + +theorem spinRatio_bounds {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + 0 ≤ spinRatio Q z ∧ spinRatio Q z ≤ 2 := by + have hQR : (2 : ℝ) ≤ Q := by exact_mod_cast hQ + have hzR : (z : ℝ) ≤ Q := by exact_mod_cast hz + have hz0 : (0 : ℝ) ≤ z := Nat.cast_nonneg z + have hd : 0 < 2 * (Q : ℝ) - 1 := by linarith + constructor + · exact div_nonneg (by linarith) hd.le + · rw [spinRatio, div_le_iff₀ hd] + linarith + +private theorem gramBracket_bounds {Q z : ℕ} (hQ : 1 ≤ Q) + (hz1 : 1 ≤ z) (hzQ : z ≤ Q) : + 0 ≤ 3 * (z : ℝ) - 1 - z * (z + 1) / Q ∧ + 3 * (z : ℝ) - 1 - z * (z + 1) / Q ≤ 3 * z := by + have hQR : (0 : ℝ) < Q := by exact_mod_cast (by omega : 0 < Q) + have hzR : (1 : ℝ) ≤ z := by exact_mod_cast hz1 + have hzQR : (z : ℝ) ≤ Q := by exact_mod_cast hzQ + have hd : (z : ℝ) * (z + 1) / Q ≤ z + 1 := by + rw [div_le_iff₀ hQR] + nlinarith + have hn : (0 : ℝ) ≤ (z : ℝ) * (z + 1) / Q := by positivity + constructor <;> linarith + + +theorem gramShift_abs_le {Q z : ℕ} (hQ : 4 ≤ Q) (hz1 : 1 ≤ z) (hzQ : z ≤ Q) : + |gramShift Q z| ≤ 3 * (z : ℝ) * (2/3)^z := by + obtain ⟨hb0, hb⟩ := gramBracket_bounds (by omega : 1 ≤ Q) hz1 hzQ + rw [gramShift, abs_mul, abs_mul, abs_pow, abs_neg, abs_one, one_pow, one_mul, + abs_of_nonneg (fallingRatio_nonneg Q z), abs_of_nonneg hb0] + calc + _ ≤ (2/3 : ℝ)^z * (3*z) := + mul_le_mul (fallingRatio_le_geometric hQ hzQ) hb hb0 (by positivity) + _ = _ := mul_comm _ _ + +theorem spinRatio_tendsto (z : ℕ) : + Tendsto (fun Q : ℕ => spinRatio Q z) atTop (𝓝 (3/2)) := by + have h1 := tendsto_const_div_atTop_nhds_zero_nat (1+2*(z:ℝ)) + have h2 := tendsto_const_div_atTop_nhds_zero_nat (1:ℝ) + have hh : Tendsto (fun Q : ℕ => (3 - (1+2*(z:ℝ))/Q)/(2 - 1/(Q:ℝ))) + atTop (𝓝 (3/2)) := by + convert ((tendsto_const_nhds (x := (3:ℝ))).sub h1).div + ((tendsto_const_nhds (x := (2:ℝ))).sub h2) (show (2:ℝ)-0 ≠ 0 by norm_num) + using 1 + first | rfl | norm_num + apply hh.congr' + filter_upwards [eventually_ge_atTop 1] with Q hQ + have hn : (Q : ℝ) ≠ 0 := by exact_mod_cast (by omega : Q ≠ 0) + have hqr : (1 : ℝ) ≤ Q := by exact_mod_cast hQ + have hd : 2*(Q:ℝ)-1 ≠ 0 := by linarith + have hd' : 2 - 1/(Q:ℝ) ≠ 0 := by + rw [ne_eq, sub_eq_zero, eq_div_iff hn] + linarith + unfold spinRatio + field_simp [hn, hd, hd'] + ring + + + +def tailTerm (Q m : ℕ) : ℝ := + let z := 17 + 2*m + if z ≤ Q then spinRatio Q z * |gramShift Q z| * (z+1) else 0 + + +def tailCoefficient (Q : ℕ) : ℝ := + ∑ m ∈ Finset.range (Q+1), tailTerm Q m + + + +theorem tailTerm_bound {Q : ℕ} (hQ : 4 ≤ Q) (m : ℕ) : + ‖tailTerm Q m‖ ≤ + 6 * ((17+2*m : ℕ) : ℝ) * ((17+2*m : ℕ)+1) * (2/3 : ℝ)^(17+2*m) := by + dsimp [tailTerm] + split_ifs with hm + · rw [abs_of_nonneg (by + exact mul_nonneg (mul_nonneg (spinRatio_bounds (by omega) hm).1 (abs_nonneg _)) + (by positivity))] + calc + _ ≤ 2 * (3 * ((17+2*m : ℕ):ℝ) * (2/3)^(17+2*m)) * ((17+2*m : ℕ)+1) := + mul_le_mul_of_nonneg_right + (mul_le_mul (spinRatio_bounds (by omega) hm).2 + (gramShift_abs_le hQ (by omega) hm) (abs_nonneg _) (by norm_num)) (by positivity) + _ = _ := by ring + · simp only [abs_zero] + positivity + +private theorem tailBound_summable : + Summable (fun m : ℕ => + 6 * ((17+2*m : ℕ) : ℝ) * ((17+2*m : ℕ)+1) * (2/3 : ℝ)^(17+2*m)) := by + have h1 := summable_pow_mul_geometric_of_norm_lt_one 1 + (show ‖(2/3 : ℝ)‖ < 1 by norm_num) + have h2 := summable_pow_mul_geometric_of_norm_lt_one 2 + (show ‖(2/3 : ℝ)‖ < 1 by norm_num) + have h : Summable (fun z : ℕ => 6*(z:ℝ)*(z+1)*(2/3)^z) := by + apply ((h2.mul_left 6).add (h1.mul_left 6)).congr + intro z + ring + exact h.comp_injective (fun i j hij => by omega) + + +theorem tailTerm_tendsto (m : ℕ) : + Tendsto (fun Q : ℕ => tailTerm Q m) atTop + (𝓝 ((3/2 : ℝ)*(3*((17+2*m : ℕ):ℝ)-1)* + (1/2 : ℝ)^(17+2*m)*((17+2*m : ℕ)+1))) := by + let z := 17+2*m + have hb : 0 ≤ 3*(z:ℝ)-1 := by dsimp [z]; push_cast; have := Nat.cast_nonneg (α:=ℝ) m; linarith + have h := ((spinRatio_tendsto z).mul (gramShift_tendsto z).abs).mul_const ((z:ℝ)+1) + have ha : |(-1/2 : ℝ)| = 1/2 := by norm_num + rw [abs_mul, abs_pow, abs_of_nonneg hb, ha] at h + have hh : (3/2 : ℝ)*((3*(z:ℝ)-1)*(1/2)^z)*((z:ℝ)+1) = + (3/2 : ℝ)*(3*(z:ℝ)-1)*(1/2)^z*((z:ℝ)+1) := by ring + rw [hh] at h + apply h.congr' + filter_upwards [eventually_ge_atTop z] with Q hQ + simp [tailTerm, z, hQ] + + +theorem limit_tail_hasSum : + HasSum (fun m : ℕ => (3/2 : ℝ)*(3*((17+2*m : ℕ):ℝ)-1)* + (1/2 : ℝ)^(17+2*m)*((17+2*m : ℕ)+1)) (61/4096) := by + have hr : ‖(1/4 : ℝ)‖ < 1 := by norm_num + have h0 : HasSum (fun m : ℕ => (1/4 : ℝ)^m) (4/3) := by + convert hasSum_geometric_of_lt_one (r := (1/4 : ℝ)) (by norm_num) (by norm_num) using 1 + norm_num + have h1 : HasSum (fun m : ℕ => (m:ℝ)*(1/4 : ℝ)^m) (4/9) := by + convert hasSum_coe_mul_geometric_of_norm_lt_one hr using 1 + first | rfl | norm_num + have h2 : HasSum (fun m : ℕ => ((m+2).choose 2 : ℝ)*(1/4 : ℝ)^m) (64/27) := by + convert hasSum_choose_mul_geometric_of_norm_lt_one 2 hr using 1 + first | rfl | norm_num + have h := (((h2.mul_left 24).add (h1.mul_left 172)).add (h0.mul_left 876)).mul_left + ((3/2 : ℝ)*(1/2)^17) + norm_num only [show (3/2 : ℝ)*(1/2)^17 * (24*(64/27)+172*(4/9)+876*(4/3)) = + 61/4096 by norm_num] at h + apply h.congr_fun + intro m + rw [Nat.cast_choose_two] + push_cast + rw [pow_add, pow_mul] + norm_num + ring + + +theorem tailCoefficient_eq_tsum (Q : ℕ) : tailCoefficient Q = ∑' m, tailTerm Q m := by + symm + apply tsum_eq_sum + intro m hm + have hm' : Q+1 ≤ m := by simpa only [Finset.mem_range, not_lt] using hm + have h : ¬ 17+2*m ≤ Q := by omega + simp [tailTerm, h] + + + +theorem tailCoefficient_tendsto : + Tendsto tailCoefficient atTop (𝓝 (61/4096 : ℝ)) := by + have h := tendsto_tsum_of_dominated_convergence tailBound_summable tailTerm_tendsto + (show ∀ᶠ Q in atTop, ∀ m, ‖tailTerm Q m‖ ≤ + 6 * ((17+2*m : ℕ) : ℝ) * ((17+2*m : ℕ)+1) * (2/3 : ℝ)^(17+2*m) from + (eventually_ge_atTop 4).mono (fun _ hQ m => tailTerm_bound hQ m)) + rw [limit_tail_hasSum.tsum_eq] at h + exact h.congr' (Filter.Eventually.of_forall (fun Q => (tailCoefficient_eq_tsum Q).symm)) + + +theorem tailCoefficient_eq_odd_sum (Q : ℕ) : + tailCoefficient Q = + ∑ z ∈ (Finset.range (Q+1)).filter (fun z => 17 ≤ z ∧ Odd z), + spinRatio Q z * |gramShift Q z| * (z+1) := by + classical + unfold tailCoefficient + simp only [tailTerm] + rw [← Finset.sum_filter] + apply Finset.sum_bij (fun m _ => 17+2*m) + · intro m hm + simp only [Finset.mem_filter, Finset.mem_range] at hm ⊢ + exact ⟨by omega, by omega, Nat.odd_iff.mpr (by omega)⟩ + · intro m hm n hn hmn + omega + · intro z hz + simp only [Finset.mem_filter, Finset.mem_range, Nat.odd_iff] at hz + refine ⟨(z-17)/2, ?_, ?_⟩ + · simp only [Finset.mem_filter, Finset.mem_range] + omega + · omega + · intro m hm + rfl + +theorem tailTerm_nonneg (Q m : ℕ) : 0 ≤ tailTerm Q m := by + dsimp only [tailTerm] + split_ifs with h + · exact mul_nonneg (mul_nonneg (spinRatio_bounds (by omega) h).1 (abs_nonneg _)) + (by positivity) + · exact le_rfl + +theorem tailCoefficient_nonneg (Q : ℕ) : 0 ≤ tailCoefficient Q := + Finset.sum_nonneg (fun m _ => tailTerm_nonneg Q m) + + + +theorem allowance_count : + (∑ D ∈ Finset.Icc 1 23, (D+1)^2 / 4) = (1222 : ℕ) := by + decide +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/SquareSplitting.lean b/lean/OAI/Analysis/LaughlinFock/SquareSplitting.lean new file mode 100644 index 0000000000000000000000000000000000000000..8d7512a885db52cfb126456cc474060d5df3432b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/SquareSplitting.lean @@ -0,0 +1,133 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.FiniteComparison + +namespace OAI + +/-! Square Splitting. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open Filter Topology + + + +def tailThreeTarget (Q : ℕ) : FockMatrix Q := + exteriorLift Q 3 (threeWedgeMatrix Q * + (∑ z ∈ Finset.Ico 16 (Q+1), (gramShift Q z : ℂ) • threeSpinProjection Q z) * + (threeWedgeMatrix Q)ᴴ) + + +theorem fullThreeTarget_split {Q : ℕ} (hQ : 16 ≤ Q+1) : + fullThreeTarget Q = finiteThreeTarget Q + tailThreeTarget Q := by + unfold fullThreeTarget finiteThreeTarget tailThreeTarget + rw [← Finset.sum_range_add_sum_Ico _ hQ, Matrix.mul_add, Matrix.add_mul, exteriorLift_add] + + + +theorem normal_ordered_square_split {Q : ℕ} (hQ : 16 ≤ Q) : + hamiltonian Q * hamiltonian Q = hamiltonian Q + + finiteThreeTarget Q + tailThreeTarget Q + + exteriorLift Q 4 (fourWedgeMatrix Q * (fourWedgeMatrix Q)ᴴ) := by + have h := normal_ordered_square_spectral Q (by omega) + change _ = hamiltonian Q + fullThreeTarget Q + _ at h + rw [fullThreeTarget_split (by omega), ← add_assoc] at h + exact h + + + +theorem threeSpinProjection_lift_posSemidef (Q z : ℕ) : + (exteriorLift Q 3 (threeWedgeMatrix Q * threeSpinProjection Q z * + (threeWedgeMatrix Q)ᴴ)).PosSemidef := + exteriorLift_posSemidef Q 3 _ + ((threeSpinProjection_posSemidef Q z).mul_mul_conjTranspose_same _) + + + +theorem threeSpinProjection_lift (Q z : ℕ) : + exteriorLift Q 3 (threeWedgeMatrix Q * threeSpinProjection Q z * + (threeWedgeMatrix Q)ᴴ) = + ∑ c : CoupledIndex (2*Q-2) Q, if c.1.val=z then + (wedgeAnnihilator Q 3 (threeWedgeMatrix Q *ᵥ + threeCoupledColumn Q c.1.val c.2.val))ᴴ * + wedgeAnnihilator Q 3 (threeWedgeMatrix Q *ᵥ + threeCoupledColumn Q c.1.val c.2.val) else 0 := by + classical + unfold threeSpinProjection + have he : threeWedgeMatrix Q * + (threeCouplingMatrix Q * Matrix.diagonal + (fun c : CoupledIndex (2*Q-2) Q => if c.1.val=z then (1:ℂ) else 0) * + (threeCouplingMatrix Q)ᴴ) * (threeWedgeMatrix Q)ᴴ = + (threeWedgeMatrix Q * threeCouplingMatrix Q) * Matrix.diagonal + (fun c : CoupledIndex (2*Q-2) Q => if c.1.val=z then (1:ℂ) else 0) * + (threeWedgeMatrix Q * threeCouplingMatrix Q)ᴴ := by + rw [Matrix.conjTranspose_mul] + simp only [Matrix.mul_assoc] + rw [he, exteriorLift_congruence] + apply Finset.sum_congr rfl + intro c _ + simp only [Matrix.diagonal_apply, ite_smul, zero_smul] + rw [Finset.sum_ite_eq, ite_eq_left (Finset.mem_univ c)] + split_ifs <;> simp only [one_smul] + rfl + + + +theorem FockInequality.mono {Q : ℕ} {a b : ℝ} (h : FockInequality Q b) + (hab : a ≤ b) : FockInequality Q a := by + have h' := h.add ((hamiltonian_posSemidef Q).smul (sub_nonneg.mpr hab)) + unfold FockInequality at * + convert h' using 1 + simp only [sub_smul] + abel + + + +theorem fockInequality_of_finite_comparisons {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) {Q : ℕ} (hQ : 16 ≤ Q) + (A4 : FockMatrix Q) (δ e : ℝ) + (hK : (rowsEta rows • hamiltonian Q + threeTraceForm rows Q + A4).PosSemidef) + (h3 : (finiteThreeTarget Q - threeTraceForm rows Q).PosSemidef) + (h4 : (exteriorLift Q 4 (fourWedgeMatrix Q * (fourWedgeMatrix Q)ᴴ) + + e • hamiltonian Q - A4).PosSemidef) + (htail : (tailThreeTarget Q + δ • hamiltonian Q).PosSemidef) : + FockInequality Q (1-rowsEta rows-δ-e) := by + have h := ((hK.add h3).add h4).add htail + unfold FockInequality + rw [normal_ordered_square_split hQ] + convert h using 1 + simp only [sub_smul, one_smul] + abel + + + +theorem uniform_integer_threshold_of_eventual_bound (a : ℕ → ℝ) + (ha : Tendsto a atTop (𝓝 gammaStar)) + (hbound : ∀ᶠ Q in atTop, FockInequality Q (a Q)) + (γ : ℝ) (hγ : γ < gammaStar) : + ∃ Qγ : ℤ, 1 ≤ Qγ ∧ ∀ Q : ℤ, Qγ ≤ Q → FockInequality Q.toNat γ := by + have he : ∀ᶠ Q in atTop, γ < a Q := ha.eventually (eventually_gt_nhds hγ) + obtain ⟨q, hq⟩ := eventually_atTop.mp (hbound.and he) + refine ⟨(max 1 q : ℕ), ?_, ?_⟩ + · exact_mod_cast (le_max_left 1 q) + · intro Q hQ + have hQ0 : 0 ≤ Q := le_trans (by positivity) hQ + have hqn : max 1 q ≤ Q.toNat := by exact_mod_cast (show (max 1 q : ℤ) ≤ (Q.toNat : ℤ) by simpa [Int.toNat_of_nonneg hQ0] using hQ) + exact (hq Q.toNat (le_trans (le_max_right 1 q) hqn)).1.mono + (hq Q.toNat (le_trans (le_max_right 1 q) hqn)).2.le + + + +theorem final_coefficient_tendsto {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) + (hEta : rowsEta rows = 93527408868499 / 10^14) + (e : ℕ → ℝ) (he : Tendsto e atTop (𝓝 0)) : + Tendsto (fun Q => 1-rowsEta rows-tailCoefficient Q-1222*(3/10^6)-e Q) + atTop (𝓝 gammaStar) := by + have h := (((tendsto_const_nhds (x := 1-rowsEta rows)).sub + tailCoefficient_tendsto).sub_const (1222*(3/10^6))).sub he + simpa only [hEta, sub_zero, final_margin_arithmetic] using h + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/SwapCompression.lean b/lean/OAI/Analysis/LaughlinFock/SwapCompression.lean new file mode 100644 index 0000000000000000000000000000000000000000..62f3d21db3be7329ad77ac5c924040fcc248c57c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/SwapCompression.lean @@ -0,0 +1,225 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.ScalarAction + +namespace OAI + +/-! Swap Compression. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators + +abbrev CubeVector := ℕ → ℕ → ℕ → ℝ + +def CubeLayer (T : ℕ) (f : CubeVector) : Prop := + ∀ i j k, i+j+k ≠ T → f i j k = 0 + +def cubeLower (Q : ℕ) (f : CubeVector) : CubeVector := fun i j k => + spinStep Q i * f (i-1) j k + spinStep Q j * f i (j-1) k + + spinStep Q k * f i j (k-1) + +def cubeRaise (Q : ℕ) (f : CubeVector) : CubeVector := fun i j k => + spinStep Q (i+1) * f (i+1) j k + spinStep Q (j+1) * f i (j+1) k + + spinStep Q (k+1) * f i j (k+1) + + + +def pairTensorEmbed (Q : ℕ) : GridVector →ₗ[ℝ] CubeVector where + toFun f i j k := ∑ p ∈ Finset.range (2*Q-2+1), coupledVector Q Q 1 p i j * f p k + map_add' f g := by + funext i j k + simp only [Pi.add_apply, mul_add, Finset.sum_add_distrib] + map_smul' a f := by + funext i j k + simp only [Pi.smul_apply, smul_eq_mul, RingHom.id_apply, Finset.mul_sum] + apply Finset.sum_congr rfl + intro p _ + ring + + + +def pairTensorProject (Q : ℕ) : CubeVector →ₗ[ℝ] GridVector where + toFun f p k := gridInner Q Q (coupledVector Q Q 1 p) (fun i j => f i j k) + map_add' f g := by + funext p k + simp only [gridInner, Pi.add_apply, mul_add, Finset.sum_add_distrib] + map_smul' a f := by + funext p k + simp only [gridInner, Pi.smul_apply, smul_eq_mul, RingHom.id_apply, Finset.mul_sum] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + ring + + +def swap23 : CubeVector →ₗ[ℝ] CubeVector where + toFun f i j k := f i k j + map_add' _ _ := rfl + map_smul' _ _ := rfl + + +def pairSwapCompression (Q : ℕ) : GridVector →ₗ[ℝ] GridVector := + (pairTensorProject Q).comp (swap23.comp (pairTensorEmbed Q)) + +theorem pairCoupled_lower {Q : ℕ} (hQ : 1 ≤ Q) (p : ℕ) : + gridLower Q Q (coupledVector Q Q 1 p) = + spinStep (2*Q-2) (p+1) • coupledVector Q Q 1 (p+1) := by + simpa only [two_mul, mul_one] using coupledVector_lower_all hQ hQ p + +theorem pairCoupled_raise {Q : ℕ} (hQ : 1 ≤ Q) (p : ℕ) : + gridRaise Q Q (coupledVector Q Q 1 p) = + spinStep (2*Q-2) p • coupledVector Q Q 1 (p-1) := by + simpa only [two_mul, mul_one] using coupledVector_raise_all hQ hQ p + +theorem gridInner_add_right (n m : ℕ) (f g h : GridVector) : + gridInner n m f (g+h) = gridInner n m f g + gridInner n m f h := by + simp only [gridInner, Pi.add_apply, mul_add, Finset.sum_add_distrib] + +theorem grid_raise_adjoint (n m : ℕ) (f g : GridVector) : + gridInner n m (gridRaise n m f) g = gridInner n m f (gridLower n m g) := by + rw [gridInner_comm, ← grid_adjoint, gridInner_comm] + +theorem pairTensorProject_lower {Q : ℕ} (hQ : 1 ≤ Q) (f : CubeVector) : + pairTensorProject Q (cubeLower Q f) = gridLower (2*Q-2) Q (pairTensorProject Q f) := by + funext p k + change gridInner Q Q (coupledVector Q Q 1 p) + (gridLower Q Q (fun i j => f i j k) + spinStep Q k • (fun i j => f i j (k-1))) = _ + rw [gridInner_add_right, gridInner_smul_right, ← grid_raise_adjoint, + pairCoupled_raise hQ, gridInner_smul_left] + rfl + +theorem pairTensorProject_raise {Q : ℕ} (hQ : 1 ≤ Q) (f : CubeVector) : + pairTensorProject Q (cubeRaise Q f) = gridRaise (2*Q-2) Q (pairTensorProject Q f) := by + funext p k + change gridInner Q Q (coupledVector Q Q 1 p) + (gridRaise Q Q (fun i j => f i j k) + spinStep Q (k+1) • (fun i j => f i j (k+1))) = _ + rw [gridInner_add_right, gridInner_smul_right, ← grid_adjoint, + pairCoupled_lower hQ, gridInner_smul_left] + rfl + +theorem pairTensorEmbed_lower {Q : ℕ} (hQ : 1 ≤ Q) (f : GridVector) : + pairTensorEmbed Q (gridLower (2*Q-2) Q f) = cubeLower Q (pairTensorEmbed Q f) := by + funext i j k + have hp (p : ℕ) : gridLower Q Q (coupledVector Q Q 1 p) i j = + spinStep (2*Q-2) (p+1) * coupledVector Q Q 1 (p+1) i j := + congrArg (fun g : GridVector => g i j) (pairCoupled_lower hQ p) + calc + _ = (∑ p ∈ Finset.range (2*Q-2+1), + (spinStep (2*Q-2) p * f (p-1) k) * coupledVector Q Q 1 p i j) + + spinStep Q k * (∑ p ∈ Finset.range (2*Q-2+1), coupledVector Q Q 1 p i j * f p (k-1)) := by + simp only [pairTensorEmbed, LinearMap.coe_mk, AddHom.coe_mk, gridLower, + mul_add, Finset.sum_add_distrib, Finset.mul_sum] + apply congrArg₂ (·+·) <;> apply Finset.sum_congr rfl <;> intro p _ <;> ring + _ = (∑ p ∈ Finset.range (2*Q-2+1), f p k * + (spinStep (2*Q-2) (p+1) * coupledVector Q Q 1 (p+1) i j)) + + spinStep Q k * (∑ p ∈ Finset.range (2*Q-2+1), coupledVector Q Q 1 p i j * f p (k-1)) := by + rw [spinStep_sum_adjoint (2*Q-2) (fun p => f p k) (fun p => coupledVector Q Q 1 p i j)] + _ = (∑ p ∈ Finset.range (2*Q-2+1), f p k * gridLower Q Q (coupledVector Q Q 1 p) i j) + + spinStep Q k * (∑ p ∈ Finset.range (2*Q-2+1), coupledVector Q Q 1 p i j * f p (k-1)) := by + simp only [hp] + _ = _ := by + simp only [cubeLower, pairTensorEmbed, LinearMap.coe_mk, AddHom.coe_mk, + gridLower, mul_add, Finset.sum_add_distrib, Finset.mul_sum] + congr 1 + apply congrArg₂ (·+·) <;> apply Finset.sum_congr rfl <;> intro p _ <;> ring + +theorem pairTensorEmbed_raise {Q : ℕ} (hQ : 1 ≤ Q) (f : GridVector) : + pairTensorEmbed Q (gridRaise (2*Q-2) Q f) = cubeRaise Q (pairTensorEmbed Q f) := by + funext i j k + have hp (p : ℕ) : gridRaise Q Q (coupledVector Q Q 1 p) i j = + spinStep (2*Q-2) p * coupledVector Q Q 1 (p-1) i j := + congrArg (fun g : GridVector => g i j) (pairCoupled_raise hQ p) + calc + _ = (∑ p ∈ Finset.range (2*Q-2+1), coupledVector Q Q 1 p i j * + (spinStep (2*Q-2) (p+1) * f (p+1) k)) + + spinStep Q (k+1) * (∑ p ∈ Finset.range (2*Q-2+1), coupledVector Q Q 1 p i j * f p (k+1)) := by + simp only [pairTensorEmbed, LinearMap.coe_mk, AddHom.coe_mk, gridRaise, + mul_add, Finset.sum_add_distrib, Finset.mul_sum] + congr 1 + apply Finset.sum_congr rfl + intro p _ + ring + _ = (∑ p ∈ Finset.range (2*Q-2+1), + (spinStep (2*Q-2) p * coupledVector Q Q 1 (p-1) i j) * f p k) + + spinStep Q (k+1) * (∑ p ∈ Finset.range (2*Q-2+1), coupledVector Q Q 1 p i j * f p (k+1)) := by + rw [spinStep_sum_adjoint (2*Q-2) (fun p => coupledVector Q Q 1 p i j) (fun p => f p k)] + _ = (∑ p ∈ Finset.range (2*Q-2+1), gridRaise Q Q (coupledVector Q Q 1 p) i j * f p k) + + spinStep Q (k+1) * (∑ p ∈ Finset.range (2*Q-2+1), coupledVector Q Q 1 p i j * f p (k+1)) := by + simp only [hp] + _ = _ := by + simp only [cubeRaise, pairTensorEmbed, LinearMap.coe_mk, AddHom.coe_mk, + gridRaise, add_mul, Finset.sum_add_distrib, Finset.mul_sum] + congr 1 + apply congrArg₂ (·+·) <;> apply Finset.sum_congr rfl <;> intro p _ <;> ring + +theorem swap23_lower (Q : ℕ) (f : CubeVector) : + swap23 (cubeLower Q f) = cubeLower Q (swap23 f) := by + funext i j k + simp only [swap23, cubeLower, LinearMap.coe_mk, AddHom.coe_mk] + ring + +theorem swap23_raise (Q : ℕ) (f : CubeVector) : + swap23 (cubeRaise Q f) = cubeRaise Q (swap23 f) := by + funext i j k + simp only [swap23, cubeRaise, LinearMap.coe_mk, AddHom.coe_mk] + ring + + + +theorem pairSwapCompression_lower {Q : ℕ} (hQ : 1 ≤ Q) (f : GridVector) : + pairSwapCompression Q (gridLower (2*Q-2) Q f) = + gridLower (2*Q-2) Q (pairSwapCompression Q f) := by + simp only [pairSwapCompression, LinearMap.comp_apply, pairTensorEmbed_lower hQ, + swap23_lower, pairTensorProject_lower hQ] + +theorem pairSwapCompression_raise {Q : ℕ} (hQ : 1 ≤ Q) (f : GridVector) : + pairSwapCompression Q (gridRaise (2*Q-2) Q f) = + gridRaise (2*Q-2) Q (pairSwapCompression Q f) := by + simp only [pairSwapCompression, LinearMap.comp_apply, pairTensorEmbed_raise hQ, + swap23_raise, pairTensorProject_raise hQ] + +theorem pairTensorEmbed_layer {Q T : ℕ} {f : GridVector} (hf : GridLayer T f) : + CubeLayer (T+1) (pairTensorEmbed Q f) := by + intro i j k hijk + simp only [pairTensorEmbed, LinearMap.coe_mk, AddHom.coe_mk] + apply Finset.sum_eq_zero + intro p _ + by_cases hij : i+j=1+p + · rw [hf p k (by omega), mul_zero] + · rw [coupledVector_layer Q Q 1 p i j hij, zero_mul] + +theorem swap23_layer {T : ℕ} {f : CubeVector} (hf : CubeLayer T f) : + CubeLayer T (swap23 f) := by + intro i j k h + exact hf i k j (by omega) + +theorem pairTensorProject_layer {Q T : ℕ} {f : CubeVector} (hf : CubeLayer (T+1) f) : + GridLayer T (pairTensorProject Q f) := by + intro p k hpk + simp only [pairTensorProject, LinearMap.coe_mk, AddHom.coe_mk, gridInner] + apply Finset.sum_eq_zero + intro i _ + apply Finset.sum_eq_zero + intro j _ + by_cases hij : i+j=1+p + · rw [hf i j k (by omega), mul_zero] + · rw [coupledVector_layer Q Q 1 p i j hij, zero_mul] + +theorem pairSwapCompression_layer (Q T : ℕ) (f : GridVector) (hf : GridLayer T f) : + GridLayer T (pairSwapCompression Q f) := + pairTensorProject_layer (swap23_layer (pairTensorEmbed_layer hf)) + + + +theorem pairSwapCompression_coupled {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) (k : ℕ) : + pairSwapCompression Q (coupledVector (2*Q-2) Q z k) = + (pairSwapCompression Q (coupledVector (2*Q-2) Q z 0) 0 z / + highestCoefficient (2*Q-2) Q z 0) • coupledVector (2*Q-2) Q z k := by + exact coupledVector_intertwiner (by omega) hz _ + (pairSwapCompression_lower (by omega)) (pairSwapCompression_raise (by omega)) + (pairSwapCompression_layer Q) k + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/TableTrace.lean b/lean/OAI/Analysis/LaughlinFock/TableTrace.lean new file mode 100644 index 0000000000000000000000000000000000000000..3a52647071ee93f7dbecdbc81532d33dcba82429 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/TableTrace.lean @@ -0,0 +1,61 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.CouplingTables +import OAI.Analysis.LaughlinFock.FastTrace + +namespace OAI + +/-! Table Trace. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +def memoIntegerCopyPolynomial (D T r p j k : ℕ) : ℤ := + if r ≤ j+k then + memoUnitCoupling r (j+k-r) j * memoUnitCoupling (D-r) (T-D) p + else 0 + +theorem memoIntegerCopyPolynomial_spec {D T : ℕ} (hD : D ≤ 23) (hT : T ≤ 23) + (r : CopyLabel D) (p j k : ℕ) (hp : p ≤ 8) (hj : j ≤ 8) (hk : k ≤ 8) : + fastIntegerCopyPolynomial D T r.val.val p j k = + memoIntegerCopyPolynomial D T r.val.val p j k := by + have hr := r.val.isLt + unfold fastIntegerCopyPolynomial memoIntegerCopyPolynomial + split_ifs with hh + · rw [memoUnitCoupling_spec _ _ _ (by omega) (by omega) (by omega), + memoUnitCoupling_spec _ _ _ (by omega) (by omega) (by omega)] + · rfl + +def memoScaledFourTrace (D : ℕ) (t : Fin 8) (r s : CopyLabel D) : ℤ := + -(∑ b : RowEntry t.val, ∑ c : RowEntry t.val, if D ≤ rowFourLevel b c then + certificateAlphaData t b.val.1 b.val.2 * certificateAlphaData t c.val.1 c.val.2 * + (scaledFourFactor D t b c : ℤ) * + memoIntegerCopyPolynomial D (rowFourLevel b c) r.val.val (rowP b) (rowJ b) (rowI c) * + memoIntegerCopyPolynomial D (rowFourLevel b c) s.val.val (rowP c) (rowJ c) (rowI b) + else 0) + +theorem memoScaledFourTrace_spec {D : ℕ} (hD : D ≤ 23) (t : Fin 8) (r s : CopyLabel D) : + scaledFourTrace D t r s = memoScaledFourTrace D t r s := by + unfold scaledFourTrace memoScaledFourTrace + congr 1 + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro c _ + have hb := rowEntry_bounds b + have hc := rowEntry_bounds c + rw [memoIntegerCopyPolynomial_spec hD (rowFourLevel_le b c) r _ _ _ (by omega) hb.2.1 hc.2.2.1, + memoIntegerCopyPolynomial_spec hD (rowFourLevel_le b c) s _ _ _ (by omega) hc.2.1 hb.2.2.1] + +def memoScaledRowsFourTrace (D : ℕ) (r s : CopyLabel D) : ℤ := + ∑ t : Fin 8, memoScaledFourTrace D t r s + +theorem integerRowsFourTrace_memo {D : ℕ} (hD : D ≤ 23) (r s : CopyLabel D) : + integerRowsFourTrace D r s = (memoScaledRowsFourTrace D r s : ℚ) / fourCommonDenominator := by + rw [integerRowsFourTrace_scaled] + unfold scaledRowsFourTrace memoScaledRowsFourTrace + simp only [memoScaledFourTrace_spec hD] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/TailOrbit.lean b/lean/OAI/Analysis/LaughlinFock/TailOrbit.lean new file mode 100644 index 0000000000000000000000000000000000000000..82d07553cd60c33ab1f13a11e929992b8b8fd877 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/TailOrbit.lean @@ -0,0 +1,115 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.SquareSplitting +import OAI.Analysis.LaughlinFock.ThreeOrbit + +namespace OAI + +/-! Tail Orbit. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +theorem threeSpinProjection_relative_bound {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + (((spinRatio Q z * (z+1) : ℝ) : ℂ) • hamiltonian Q - + exteriorLift Q 3 (threeWedgeMatrix Q * threeSpinProjection Q z * + (threeWedgeMatrix Q)ᴴ)).PosSemidef := by + have ha := fockAverage_posSemidef Q _ (highestThreeAnnihilator_pair_posSemidef hQ hz) + rw [map_sub, fockAverage_highestThree hQ hz, + fockAverage_pair_family (by omega : 1 ≤ Q) (fun p : Fin (z+1) => p.val) + (by intro p; have := p.isLt; omega), Fintype.card_fin] at ha + have hn : ((3*Q-1-2*z : ℕ) : ℂ) ≠ 0 := by + exact_mod_cast (show 3*Q-1-2*z ≠ 0 by omega) + have hc : ((3*Q-1-2*z : ℕ) : ℂ) * + ((z+1 : ℕ) / ((2*Q-1 : ℕ) : ℂ)) = ((spinRatio Q z * (z+1) : ℝ) : ℂ) := by + push_cast [spinRatio, Nat.cast_sub (show 2*z ≤ 3*Q-1 by omega), + Nat.cast_sub (show 1 ≤ 3*Q by omega), Nat.cast_sub (show 1 ≤ 2*Q by omega)] + ring + have hh := ha.smul (show (0:ℂ) ≤ ((3*Q-1-2*z : ℕ) : ℂ) by exact_mod_cast (Nat.zero_le _)) + simpa only [smul_sub, smul_smul, hc, one_div, mul_inv_cancel₀ hn, one_smul] using hh + + + +theorem gramShift_even_nonneg {Q z : ℕ} (hQ : 1 ≤ Q) (hz₁ : 1 ≤ z) + (hz : z ≤ Q) (he : Even z) : 0 ≤ gramShift Q z := by + have hQr : 0 < (Q:ℝ) := by exact_mod_cast (show 0 < Q by omega) + have hzr : (1:ℝ) ≤ z := by exact_mod_cast hz₁ + have hzQ : (z:ℝ) ≤ Q := by exact_mod_cast hz + have hdiv : (z:ℝ)*(z+1)/Q ≤ z+1 := by + rw [div_le_iff₀ hQr] + nlinarith + have hb : 0 ≤ 3*(z:ℝ)-1-z*(z+1)/Q := by linarith + rw [gramShift, he.neg_pow, one_pow, one_mul] + exact mul_nonneg (fallingRatio_nonneg Q z) hb + + + +theorem threeSpinProjection_negative_bound {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + ((gramShift Q z : ℂ) • + exteriorLift Q 3 (threeWedgeMatrix Q * threeSpinProjection Q z * (threeWedgeMatrix Q)ᴴ) + + ((spinRatio Q z * |gramShift Q z| * (z+1) : ℝ) : ℂ) • hamiltonian Q).PosSemidef := by + let X := exteriorLift Q 3 (threeWedgeMatrix Q * threeSpinProjection Q z * (threeWedgeMatrix Q)ᴴ) + have h₁ := (threeSpinProjection_relative_bound hQ hz).smul + (show (0:ℂ) ≤ (|gramShift Q z| : ℝ) by exact_mod_cast abs_nonneg (gramShift Q z)) + have h₂ := (threeSpinProjection_lift_posSemidef Q z).smul + (show (0:ℂ) ≤ ((gramShift Q z + |gramShift Q z| : ℝ) : ℂ) by + exact_mod_cast (show 0 ≤ gramShift Q z + |gramShift Q z| by linarith [neg_le_abs (gramShift Q z)])) + have he : ((|gramShift Q z| : ℝ) : ℂ) • (((spinRatio Q z * (z+1) : ℝ) : ℂ) • hamiltonian Q-X) + + ((gramShift Q z+|gramShift Q z| : ℝ) : ℂ) • X = + (gramShift Q z : ℂ) • X + ((spinRatio Q z * |gramShift Q z| * (z+1) : ℝ) : ℂ) • hamiltonian Q := by + push_cast + simp only [smul_sub, smul_smul, add_smul] + rw [show ((|gramShift Q z| : ℝ) : ℂ) * ((spinRatio Q z : ℂ)*((z:ℂ)+1)) = + (spinRatio Q z : ℂ)*((|gramShift Q z| : ℝ) : ℂ)*((z:ℂ)+1) by ring] + abel + exact he ▸ h₁.add h₂ + + + +theorem tailCoefficient_eq_Ico (Q : ℕ) : + tailCoefficient Q = ∑ z ∈ Finset.Ico 16 (Q+1), + if Odd z then spinRatio Q z * |gramShift Q z| * (z+1) else 0 := by + classical + rw [tailCoefficient_eq_odd_sum, ← Finset.sum_filter] + congr 1 + ext z + simp only [Finset.mem_filter, Finset.mem_range, Finset.mem_Ico] + constructor + · rintro ⟨hz, hz₁, ho⟩; exact ⟨⟨by omega,hz⟩,ho⟩ + · rintro ⟨⟨hz₁,hz⟩,ho⟩ + have hp := Nat.odd_iff.mp ho + exact ⟨hz,by omega,ho⟩ + + + +theorem tailThreeTarget_relative_bound {Q : ℕ} (hQ : 2 ≤ Q) : + (tailThreeTarget Q + (tailCoefficient Q : ℂ) • hamiltonian Q).PosSemidef := by + classical + have hm (c : ℂ) (M : Matrix (SectorOccupation Q 3) (SectorOccupation Q 3) ℂ) : + exteriorLift Q 3 (c • M) = c • exteriorLift Q 3 M := + (exteriorLiftLinear Q 3).map_smul c M + have hs : tailThreeTarget Q + (tailCoefficient Q : ℂ) • hamiltonian Q = + ∑ z ∈ Finset.Ico 16 (Q+1), + ((gramShift Q z : ℂ) • exteriorLift Q 3 + (threeWedgeMatrix Q * threeSpinProjection Q z * (threeWedgeMatrix Q)ᴴ) + + ((if Odd z then spinRatio Q z * |gramShift Q z| * (z+1) else 0 : ℝ) : ℂ) • hamiltonian Q) := by + simp only [tailThreeTarget, Matrix.mul_sum, Matrix.sum_mul, Matrix.mul_smul, + Matrix.smul_mul, exteriorLift_sum, hm, + tailCoefficient_eq_Ico, Complex.ofReal_sum, ← Finset.sum_smul, Finset.sum_add_distrib] + rw [hs] + apply Matrix.posSemidef_sum + intro z hm + have hz : z ≤ Q := by have := (Finset.mem_Ico.mp hm).2; omega + have hz₁ : 1 ≤ z := by have := (Finset.mem_Ico.mp hm).1; omega + by_cases ho : Odd z + · rw [ite_eq_left ho] + exact threeSpinProjection_negative_bound hQ hz + · rw [ite_eq_right ho, Complex.ofReal_zero, zero_smul, add_zero] + exact (threeSpinProjection_lift_posSemidef Q z).smul + (by exact_mod_cast gramShift_even_nonneg (by omega : 1 ≤ Q) hz₁ hz (Nat.not_odd_iff_even.mp ho)) + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/TensorBasis.lean b/lean/OAI/Analysis/LaughlinFock/TensorBasis.lean new file mode 100644 index 0000000000000000000000000000000000000000..f60da9a2dc9cb1c488d25b13f78f155885901311 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/TensorBasis.lean @@ -0,0 +1,179 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.LadderCalculus + +namespace OAI + +/-! Tensor Basis. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators + + +theorem highestWeight_swap {n z p : ℕ} (hn : z ≤ n) (hp : p ≤ z) : + highestWeight n n z (z-p) = highestWeight n n z p := by + unfold highestWeight + rw [Nat.choose_symm hp, Nat.sub_sub_self hp, + show n-(z-p) = n-z+p by omega, show n-z+(z-p) = n-p by omega] + ring + + +theorem highestCoefficient_swap {n z p : ℕ} (hn : z ≤ n) (hp : p ≤ z) : + highestCoefficient n n z (z-p) = (-1 : ℝ)^z * highestCoefficient n n z p := by + have hs : (-1 : ℝ)^z * (-1 : ℝ)^(z-p) = (-1 : ℝ)^p := by + calc + _ = ((-1 : ℝ)^(z-p) * (-1 : ℝ)^(z-p)) * (-1 : ℝ)^p := by + conv_lhs => lhs; rw [← Nat.sub_add_cancel hp, pow_add] + ring + _ = _ := by rw [← mul_pow]; norm_num + unfold highestCoefficient + rw [highestWeight_swap hn hp, Nat.sub_sub_self hp, ← mul_assoc, hs] + + + +theorem coupledVector_swap {n z : ℕ} (hn : z ≤ n) (k p q : ℕ) : + coupledVector n n z k q p = (-1 : ℝ)^z * coupledVector n n z k p q := by + induction k generalizing p q with + | zero => + by_cases h : p+q = z + · have hp : p ≤ z := by omega + have hq : q = z-p := by omega + simp only [coupledVector, Nat.add_zero, coupledCoefficient, + ite_eq_left h, ite_eq_left (by omega : q+p = z)] + rw [hq, highestCoefficient_swap hn hp] + · simp [coupledVector, h, show q+p ≠ z by omega] + | succ k ih => + rw [coupledVector_succ (by omega : 2*z ≤ n+n)] + simp only [Pi.smul_apply, smul_eq_mul, gridLower] + rw [ih p (q-1), ih (p-1) q] + ring + +theorem coupledCoefficient_swap {n z : ℕ} (hn : z ≤ n) (k p : ℕ) (hp : p ≤ z+k) : + coupledCoefficient n n z k (z+k-p) = (-1 : ℝ)^z * coupledCoefficient n n z k p := by + simpa only [coupledVector, ite_eq_left (by omega : z+k-p+p = z+k), + ite_eq_left (by omega : p+(z+k-p) = z+k)] using coupledVector_swap hn k p (z+k-p) + + + +theorem coupledVector_antisymm {n z : ℕ} (hn : z ≤ n) (hz : Odd z) (k p q : ℕ) : + coupledVector n n z k q p = -coupledVector n n z k p q := by + rw [coupledVector_swap hn, hz.neg_one_pow, neg_one_mul] + +theorem coupledVector_odd_diagonal {n z : ℕ} (hn : z ≤ n) (hz : Odd z) (k p : ℕ) : + coupledVector n n z k p p = 0 := by + have h := coupledVector_antisymm hn hz k p p + linarith + + + +abbrev CoupledIndex (n m : ℕ) := + (z : Fin (min n m + 1)) × Fin (n+m-2*z.val+1) + +theorem sum_affine_integer (N : ℕ) (a : ℤ) : + (∑ z ∈ Finset.range N, (a-2*z)) = (N : ℤ)*a - (N : ℤ)*((N : ℤ)-1) := by + induction N with + | zero => simp + | succ N ih => + rw [Finset.sum_range_succ, ih] + push_cast + ring + + +theorem coupledIndex_card (n m : ℕ) : + Fintype.card (CoupledIndex n m) = (n+1)*(m+1) := by + have hc : (Fintype.card (CoupledIndex n m) : ℤ) = ((n : ℤ)+1)*((m : ℤ)+1) := by + simp only [CoupledIndex, Fintype.card_sigma, Fintype.card_fin, Nat.cast_sum] + calc + _ = ∑ z : Fin (min n m+1), ((n : ℤ)+m+1-2*z.val) := by + apply Finset.sum_congr rfl + intro z _ + have hz : 2*z.val ≤ n+m := by + have h := z.isLt + have h₁ := min_le_left n m + have h₂ := min_le_right n m + omega + rw [Nat.cast_add, Nat.cast_sub hz] + push_cast + ring + _ = ((min n m+1 : ℕ) : ℤ)*((n : ℤ)+m+1) - + ((min n m+1 : ℕ) : ℤ)*(((min n m+1 : ℕ) : ℤ)-1) := by + rw [Fin.sum_univ_eq_sum_range (fun z : ℕ => (n : ℤ)+m+1-2*z) (min n m+1), sum_affine_integer] + _ = _ := by + rcases le_total n m with h | h + · rw [min_eq_left h] + push_cast + ring + · rw [min_eq_right h] + push_cast + ring + exact_mod_cast hc + +def gridEuclidean (n m : ℕ) (f : GridVector) : EuclideanSpace ℝ (Fin (n+1) × Fin (m+1)) := + WithLp.toLp 2 (fun pq => f pq.1 pq.2) + +theorem gridEuclidean_inner (n m : ℕ) (f g : GridVector) : + inner ℝ (gridEuclidean n m f) (gridEuclidean n m g) = gridInner n m f g := by + rw [PiLp.inner_apply, Fintype.sum_prod_type] + simp only [gridEuclidean, WithLp.ofLp_toLp, RCLike.inner_apply, conj_trivial] + calc + _ = ∑ p : Fin (n+1), ∑ q ∈ Finset.range (m+1), g p.val q * f p.val q := by + apply Finset.sum_congr rfl + intro p _ + exact Fin.sum_univ_eq_sum_range (fun q => g p.val q * f p.val q) (m+1) + _ = ∑ p ∈ Finset.range (n+1), ∑ q ∈ Finset.range (m+1), g p q * f p q := + Fin.sum_univ_eq_sum_range (fun p => ∑ q ∈ Finset.range (m+1), g p q * f p q) (n+1) + _ = _ := by simp only [gridInner, mul_comm] + + + +def coupledEuclidean (n m : ℕ) (i : CoupledIndex n m) : + EuclideanSpace ℝ (Fin (n+1) × Fin (m+1)) := + gridEuclidean n m (coupledVector n m i.1.val i.2.val) + +theorem coupledIndex_bounds {n m : ℕ} (i : CoupledIndex n m) : + i.1.val ≤ n ∧ i.1.val ≤ m ∧ i.2.val ≤ n+m-2*i.1.val := by + have hz := i.1.isLt + have hk := i.2.isLt + have h₁ := min_le_left n m + have h₂ := min_le_right n m + omega + + + +theorem coupledEuclidean_orthonormal (n m : ℕ) : Orthonormal ℝ (coupledEuclidean n m) := by + classical + rw [orthonormal_iff_ite] + intro i j + have hi := coupledIndex_bounds i + have hj := coupledIndex_bounds j + rw [coupledEuclidean, coupledEuclidean, gridEuclidean_inner, + coupledVector_gram hi.1 hi.2.1 hj.1 hj.2.1 hi.2.2 hj.2.2] + have he : (i.1.val = j.1.val ∧ i.2.val = j.2.val) ↔ i = j := by + constructor + · intro ⟨hz, hk⟩ + rcases i with ⟨z, k⟩ + rcases j with ⟨r, l⟩ + have hr : z = r := Fin.ext hz + subst r + have hl : k = l := Fin.ext hk + subst l + rfl + · rintro rfl + exact ⟨rfl, rfl⟩ + simp only [he] + + + +def coupledBasis (n m : ℕ) : + OrthonormalBasis (CoupledIndex n m) ℝ (EuclideanSpace ℝ (Fin (n+1) × Fin (m+1))) := + OrthonormalBasis.mk (coupledEuclidean_orthonormal n m) + (((coupledEuclidean_orthonormal n m).linearIndependent.span_eq_top_of_card_eq_finrank' + (by rw [finrank_euclideanSpace, Fintype.card_prod, Fintype.card_fin, Fintype.card_fin]; exact coupledIndex_card n m)).ge) + +@[simp] theorem coupledBasis_apply (n m : ℕ) (i : CoupledIndex n m) : + coupledBasis n m i = coupledEuclidean n m i := by + simp only [coupledBasis, OrthonormalBasis.coe_mk] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/TensorIntegrals.lean b/lean/OAI/Analysis/LaughlinFock/TensorIntegrals.lean new file mode 100644 index 0000000000000000000000000000000000000000..612b1690153b634619c170f4875105a1ce4a2e65 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/TensorIntegrals.lean @@ -0,0 +1,135 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.AveragedOperators + +namespace OAI + +/-! Tensor Integrals. -/ +noncomputable section +namespace LaughlinFock +open scoped Matrix Matrix.Norms.Elementwise ComplexOrder BigOperators Kronecker +open MeasureTheory +local instance tensorIntegralsContinuousENorm {ι κ : Type*} [Fintype ι] [Fintype κ] : + ContinuousENorm (Matrix ι κ ℂ) := + inferInstanceAs (ContinuousENorm (ι → κ → ℂ)) + + + +def copyBlock {ι κ : Type*} (M : Matrix (ι × κ) (ι × κ) ℂ) (r s : κ) : + Matrix ι ι ℂ := M.submatrix (fun i => (i,r)) (fun j => (j,s)) + + + +def copyPartialTrace {ι κ : Type*} [Fintype ι] + (M : Matrix (ι × κ) (ι × κ) ℂ) : Matrix κ κ ℂ := + fun r s => (copyBlock M r s).trace + +def copyBlockLinear {ι κ : Type*} (r s : κ) : + Matrix (ι × κ) (ι × κ) ℂ →ₗ[ℂ] Matrix ι ι ℂ where + toFun M := copyBlock M r s + map_add' _ _ := rfl + map_smul' _ _ := rfl + + +theorem copyBlock_integral {G ι κ : Type*} [MeasurableSpace G] + [Fintype ι] [Fintype κ] (μ : Measure G) + {M : G → Matrix (ι × κ) (ι × κ) ℂ} (hM : Integrable M μ) (r s : κ) : + copyBlock (∫ g, M g ∂μ) r s = ∫ g, copyBlock (M g) r s ∂μ := + ((copyBlockLinear r s).toContinuousLinearMap.integral_comp_comm hM).symm + + + +theorem copyBlock_conjugation {ι κ : Type*} [Fintype ι] [Fintype κ] + [DecidableEq κ] (A : Matrix ι ι ℂ) (M : Matrix (ι × κ) (ι × κ) ℂ) (r s : κ) : + copyBlock ((A ⊗ₖ (1 : Matrix κ κ ℂ)) * M * (A ⊗ₖ (1 : Matrix κ κ ℂ))ᴴ) r s = + A * copyBlock M r s * Aᴴ := by + classical + ext i j + simp [copyBlock, Matrix.mul_apply, Matrix.conjTranspose_apply, + Fintype.sum_prod_type, Matrix.one_apply, apply_ite, Finset.sum_mul] + + + +theorem schur_multiplicity_average {G ι κ : Type*} + [Group G] [MeasurableSpace G] [MeasurableMul G] + [Fintype ι] [DecidableEq ι] [Nonempty ι] [Fintype κ] [DecidableEq κ] + (μ : Measure G) [μ.IsMulLeftInvariant] [IsProbabilityMeasure μ] + (U : G →* Matrix ι ι ℂ) [Representation.IsIrreducible (matrixRepresentation U)] + (hU : ∀ g, (U g)ᴴ * U g = 1) (M : Matrix (ι × κ) (ι × κ) ℂ) + (hI : Integrable (fun g => (U g ⊗ₖ (1 : Matrix κ κ ℂ)) * M * + (U g ⊗ₖ (1 : Matrix κ κ ℂ))ᴴ) μ) : + matrixConjugationAverage μ (fun g => U g ⊗ₖ (1 : Matrix κ κ ℂ)) M = + ((Fintype.card ι : ℂ)⁻¹) • ((1 : Matrix ι ι ℂ) ⊗ₖ copyPartialTrace M) := by + have hblock (r s : κ) : + copyBlock (matrixConjugationAverage μ (fun g => U g ⊗ₖ (1 : Matrix κ κ ℂ)) M) r s = + ((copyBlock M r s).trace / (Fintype.card ι : ℂ)) • 1 := by + have hi := (copyBlockLinear (ι := ι) r s).toContinuousLinearMap.integrable_comp hI + have hib : Integrable (fun g => U g * copyBlock M r s * (U g)ᴴ) μ := by + change Integrable (fun g => copyBlock ((U g ⊗ₖ (1 : Matrix κ κ ℂ)) * M * + (U g ⊗ₖ (1 : Matrix κ κ ℂ))ᴴ) r s) μ at hi + simpa only [copyBlock_conjugation] using hi + unfold matrixConjugationAverage + rw [copyBlock_integral μ hI] + simp_rw [copyBlock_conjugation] + exact schur_matrix_average μ U hU (copyBlock M r s) hib + ext ⟨i,r⟩ ⟨j,s⟩ + have he := congrArg (fun X : Matrix ι ι ℂ => X i j) (hblock r s) + change _ = _ at he + rw [show matrixConjugationAverage μ (fun g => U g ⊗ₖ 1) M (i,r) (j,s) = + (copyBlock M r s).trace / (Fintype.card ι : ℂ) * (1 : Matrix ι ι ℂ) i j from he] + simp only [Matrix.smul_apply, Matrix.kronecker_apply, smul_eq_mul, copyPartialTrace, div_eq_mul_inv] + ring + + + +theorem matrix_intertwiner_eq_zero_of_card_ne {G ι κ : Type*} [Monoid G] + [Fintype ι] [Fintype κ] [DecidableEq ι] [DecidableEq κ] + (U : G →* Matrix ι ι ℂ) (V : G →* Matrix κ κ ℂ) + [Representation.IsIrreducible (matrixRepresentation U)] + [Representation.IsIrreducible (matrixRepresentation V)] + (hcard : Fintype.card ι ≠ Fintype.card κ) (A : Matrix ι κ ℂ) + (hA : ∀ g, A * V g = U g * A) : A = 0 := by + let f : Representation.IntertwiningMap (matrixRepresentation V) (matrixRepresentation U) := + { toLinearMap := Matrix.toLin' A + isIntertwining' g := by + change Matrix.toLin' A ∘ₗ Matrix.toLin' (V g) = Matrix.toLin' (U g) ∘ₗ Matrix.toLin' A + simp only [← Matrix.toLin'_mul, hA] } + rcases Representation.IsIrreducible.bijective_or_eq_zero f with hf | hf + · have he := (LinearEquiv.ofBijective f.toLinearMap hf).finrank_eq + have hc : Fintype.card κ = Fintype.card ι := by simpa using he + exact False.elim (hcard hc.symm) + · apply Matrix.toLin'.injective + have he := congrArg Representation.IntertwiningMap.toLinearMap hf + change Matrix.toLin' A = 0 at he + simpa only [map_zero] using he + + + +theorem schur_cross_average {G ι κ : Type*} + [Group G] [MeasurableSpace G] [MeasurableMul G] + [Fintype ι] [Fintype κ] [DecidableEq ι] [DecidableEq κ] + (μ : Measure G) [μ.IsMulLeftInvariant] + (U : G →* Matrix ι ι ℂ) (V : G →* Matrix κ κ ℂ) + [Representation.IsIrreducible (matrixRepresentation U)] + [Representation.IsIrreducible (matrixRepresentation V)] + (hcard : Fintype.card ι ≠ Fintype.card κ) + (hV : ∀ g, (V g)ᴴ * V g = 1) (M : Matrix ι κ ℂ) + (hI : Integrable (fun g => U g * M * (V g)ᴴ) μ) : + (∫ g, U g * M * (V g)ᴴ ∂μ) = 0 := by + apply matrix_intertwiner_eq_zero_of_card_ne U V hcard + intro h + have hinv : U h * (∫ g, U g * M * (V g)ᴴ ∂μ) * (V h)ᴴ = + ∫ g, U g * M * (V g)ᴴ ∂μ := by + rw [matrixIntegral_mul_left_right μ hI] + calc + _ = ∫ g, U (h*g) * M * (V (h*g))ᴴ ∂μ := by + apply integral_congr_ae + exact Filter.Eventually.of_forall fun g => by + simp only [map_mul, Matrix.conjTranspose_mul, Matrix.mul_assoc] + _ = _ := integral_mul_left_eq_self (μ := μ) (fun g => U g * M * (V g)ᴴ) h + have he := congrArg (fun A => A * V h) hinv + simpa only [Matrix.mul_assoc, hV, Matrix.mul_one] using he.symm + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/ThreeCertificate.lean b/lean/OAI/Analysis/LaughlinFock/ThreeCertificate.lean new file mode 100644 index 0000000000000000000000000000000000000000..e25cacc410f5400275db0771ce5bfd9e5702623e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/ThreeCertificate.lean @@ -0,0 +1,118 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.CertificateRows +import OAI.Analysis.LaughlinFock.IntegerCoupling + +namespace OAI + +/-! Three Certificate. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators + +def integerThreeTrace (z t : ℕ) (ell : ℚ) (a : RowEntry t → ℚ) : ℚ := + ∑ T ∈ Finset.range 16, if z ≤ T ∧ t ≤ T then + let X := ∑ b : RowEntry t, if rowP b+rowJ b=T then + a b*(integerCoupling 2 z (T-z) (rowP b) : ℚ) else 0 + rationalCouplingWeight 2 z (T-z) t * X * + (X+2*ell*(integerCoupling 2 z (T-z) t : ℚ)) + else 0 + +theorem rationalThreeTrace_integer (z t : ℕ) (ell : ℚ) (a : RowEntry t → ℚ) : + rationalThreeTrace z t ell a = integerThreeTrace z t ell a := by + simp only [rationalThreeTrace, integerThreeTrace, ← rationalCoupling_integer, Int.cast_ofNat] + +def integerRowsThreeTrace (z : ℕ) : ℚ := + ∑ t : Fin 8, integerThreeTrace z t.val (certificateEll t) (certificateAlpha t) + +theorem planarRowsThreeTrace_integer (z : ℕ) : + planarRowsThreeTrace certificateRows z = (integerRowsThreeTrace z : ℝ) := by + unfold planarRowsThreeTrace integerRowsThreeTrace + rw [Rat.cast_sum] + apply Finset.sum_congr rfl + intro t _ + exact (planarRowThreeTrace_rational z t (certificateEll t) (certificateAlpha t)).trans + (congrArg (fun q:ℚ => (q:ℝ)) (rationalThreeTrace_integer z t.val _ _)) + +theorem certificate_three_2 : integerRowsThreeTrace 2 < + (3/2 : ℚ)*(3*(2:ℚ)-1)*(-1/2)^(2:ℕ) := by + decide +kernel + +theorem certificate_three_4 : integerRowsThreeTrace 4 < + (3/2 : ℚ)*(3*(4:ℚ)-1)*(-1/2)^(4:ℕ) := by + decide +kernel + +theorem certificate_three_5 : integerRowsThreeTrace 5 < + (3/2 : ℚ)*(3*(5:ℚ)-1)*(-1/2)^(5:ℕ) := by + decide +kernel + +theorem certificate_three_6 : integerRowsThreeTrace 6 < + (3/2 : ℚ)*(3*(6:ℚ)-1)*(-1/2)^(6:ℕ) := by + decide +kernel + +theorem certificate_three_7 : integerRowsThreeTrace 7 < + (3/2 : ℚ)*(3*(7:ℚ)-1)*(-1/2)^(7:ℕ) := by + decide +kernel + +theorem certificate_three_8 : integerRowsThreeTrace 8 < + (3/2 : ℚ)*(3*(8:ℚ)-1)*(-1/2)^(8:ℕ) := by + decide +kernel + +theorem certificate_three_9 : integerRowsThreeTrace 9 < + (3/2 : ℚ)*(3*(9:ℚ)-1)*(-1/2)^(9:ℕ) := by + decide +kernel + +theorem certificate_three_10 : integerRowsThreeTrace 10 < + (3/2 : ℚ)*(3*(10:ℚ)-1)*(-1/2)^(10:ℕ) := by + decide +kernel + +theorem certificate_three_11 : integerRowsThreeTrace 11 < + (3/2 : ℚ)*(3*(11:ℚ)-1)*(-1/2)^(11:ℕ) := by + decide +kernel + +theorem certificate_three_12 : integerRowsThreeTrace 12 < + (3/2 : ℚ)*(3*(12:ℚ)-1)*(-1/2)^(12:ℕ) := by + decide +kernel + +theorem certificate_three_13 : integerRowsThreeTrace 13 < + (3/2 : ℚ)*(3*(13:ℚ)-1)*(-1/2)^(13:ℕ) := by + decide +kernel + +theorem certificate_three_14 : integerRowsThreeTrace 14 < + (3/2 : ℚ)*(3*(14:ℚ)-1)*(-1/2)^(14:ℕ) := by + decide +kernel + +theorem certificate_three_15 : integerRowsThreeTrace 15 < + (3/2 : ℚ)*(3*(15:ℚ)-1)*(-1/2)^(15:ℕ) := by + decide +kernel + +theorem certificate_three (z : ComparedThreeBlock) : + planarRowsThreeTrace certificateRows z.val.val < + (3/2 : ℝ)*(3*(z.val.val:ℝ)-1)*(-1/2)^z.val.val := by + rw [planarRowsThreeTrace_integer] + have h (n : ℕ) (hn : n=2 ∨ 4≤n) (hn' : n<16) : integerRowsThreeTrace n < + (3/2 : ℚ)*(3*(n:ℚ)-1)*(-1/2)^n := by + interval_cases n + · omega + · omega + · exact certificate_three_2 + · omega + · exact certificate_three_4 + · exact certificate_three_5 + · exact certificate_three_6 + · exact certificate_three_7 + · exact certificate_three_8 + · exact certificate_three_9 + · exact certificate_three_10 + · exact certificate_three_11 + · exact certificate_three_12 + · exact certificate_three_13 + · exact certificate_three_14 + · exact certificate_three_15 + have hl := (Rat.cast_lt (K:=ℝ)).mpr (h z.val.val z.property z.val.isLt) + simpa only [Rat.cast_mul, Rat.cast_div, Rat.cast_ofNat, Rat.cast_natCast, + Rat.cast_sub, Rat.cast_pow, Rat.cast_neg, Rat.cast_one] using hl + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/ThreeGram.lean b/lean/OAI/Analysis/LaughlinFock/ThreeGram.lean new file mode 100644 index 0000000000000000000000000000000000000000..df89270844a8fcf91bedc571157f04d22e87e148 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/ThreeGram.lean @@ -0,0 +1,215 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.NormalOrdering + +namespace OAI + +/-! Three Gram. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder + + +theorem pair_creator_commutator (Q : ℕ) (i j k : Orbital Q) : + (annihilator Q j * annihilator Q i) * creator Q k = + creator Q k * (annihilator Q j * annihilator Q i) + + (if i=k then annihilator Q j else 0) - + (if j=k then annihilator Q i else 0) := by + have hi := eq_sub_of_add_eq (annihilator_creator_anticommute Q i k) + have hj := eq_sub_of_add_eq (annihilator_creator_anticommute Q j k) + rw [Matrix.mul_assoc, hi, Matrix.mul_sub, ← Matrix.mul_assoc _ (creator Q k), hj] + split_ifs <;> simp only [Matrix.mul_one, Matrix.one_mul, Matrix.mul_zero, + Matrix.zero_mul, Matrix.sub_mul] <;> noncomm_ring + + +def pairPartialAnnihilator (Q : ℕ) (a : Orbital Q → Orbital Q → ℂ) (k : Orbital Q) : + FockMatrix Q := ∑ i, a k i • annihilator Q i + + +theorem coefficientPair_creator_commutator (Q : ℕ) (a : Orbital Q → Orbital Q → ℂ) + (ha : ∀ i j, a j i = -a i j) (k : Orbital Q) : + coefficientPairAnnihilator Q a * creator Q k = + creator Q k * coefficientPairAnnihilator Q a + pairPartialAnnihilator Q a k := by + classical + have hdiag : a k k = 0 := by have h := ha k k; linear_combination (1 / 2 : ℂ) * h + have hsum : (∑ i : Orbital Q, ∑ j : Orbital Q, + if i simp only [smul_sub, smul_zero, smul_neg, zero_sub, sub_zero] + simp only [ht, Finset.sum_sub_distrib] + rw [Finset.sum_comm (f := fun i j : Orbital Q => + if i=k then (if i S.card=d), M ∅ S * star (N ∅ S) := + (Finset.sum_subtype _ (by intro S; simp) _).symm + _ = _ := by + apply Finset.sum_subset (Finset.filter_subset _ _) + intro S _ hS + rw [annihilationSpace_entry_eq_zero Q d M hM ∅ S (by simpa only [Finset.mem_filter, Finset.mem_univ, true_and, + Finset.card_empty, zero_add, eq_comm] using hS), zero_mul] + + +theorem creator_mul_vacuum_zero (Q : ℕ) (k : Orbital Q) (M : FockMatrix Q) + (A : Occupation Q) : (creator Q k * M) ∅ A = 0 := by + classical + have hz (B : Occupation Q) : creator Q k ∅ B = 0 := by + apply ite_eq_right + rintro ⟨_, h⟩ + have := congrArg (fun S : Occupation Q => k ∈ S) h + simp at this + simp only [Matrix.mul_apply, hz, zero_mul, Finset.sum_const_zero] + + +theorem mul_annihilator_vacuum_zero (Q : ℕ) (k : Orbital Q) (M : FockMatrix Q) + (A : Occupation Q) : (M * annihilator Q k) A ∅ = 0 := by + rw [mul_annihilator_apply] + simp + + +theorem annihilator_creator_vacuum (Q : ℕ) (i j : Orbital Q) : + (annihilator Q i * creator Q j) ∅ ∅ = if i=j then 1 else 0 := by + rw [annihilator_mul_vacuum] + simp [creator, fermionSign] + + +theorem pairPartial_vacuum_gram (Q : ℕ) (a b : Orbital Q → Orbital Q → ℂ) + (j k : Orbital Q) : + (pairPartialAnnihilator Q a k * (pairPartialAnnihilator Q b j)ᴴ) ∅ ∅ = + ∑ i, a k i * star (b j i) := by + classical + simp only [pairPartialAnnihilator, Matrix.conjTranspose_sum, Matrix.conjTranspose_smul, + Matrix.sum_mul, Matrix.mul_sum, Matrix.smul_mul, Matrix.mul_smul, + Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, ← creator_eq_adjoint, + annihilator_creator_vacuum, mul_ite, mul_one, mul_zero, + Finset.sum_ite_eq', Finset.mem_univ, ite_true, mul_comm] + + + +theorem coefficientTriple_vacuum_gram (Q : ℕ) (a b : Orbital Q → Orbital Q → ℂ) + (ha : ∀ i j, a j i = -a i j) (hb : ∀ i j, b j i = -b i j) + (j k : Orbital Q) : + ((annihilator Q j * coefficientPairAnnihilator Q a) * + (annihilator Q k * coefficientPairAnnihilator Q b)ᴴ) ∅ ∅ = + (if j=k then (coefficientPairAnnihilator Q a * (coefficientPairAnnihilator Q b)ᴴ) ∅ ∅ else 0) - + ∑ i, a k i * star (b j i) := by + classical + let M := coefficientPairAnnihilator Q a + let N := coefficientPairAnnihilator Q b + have hb' : annihilator Q j * Nᴴ = Nᴴ * annihilator Q j + (pairPartialAnnihilator Q b j)ᴴ := by + have h := congrArg Matrix.conjTranspose (coefficientPair_creator_commutator Q b hb j) + simpa only [creator_eq_adjoint, Matrix.conjTranspose_mul, Matrix.conjTranspose_add, + Matrix.conjTranspose_conjTranspose] using h + have hex : (M * creator Q k * annihilator Q j * Nᴴ) ∅ ∅ = + (pairPartialAnnihilator Q a k * (pairPartialAnnihilator Q b j)ᴴ) ∅ ∅ := by + rw [show M * creator Q k = creator Q k * M + pairPartialAnnihilator Q a k from + coefficientPair_creator_commutator Q a ha k] + simp only [Matrix.add_mul, Matrix.add_apply] + rw [Matrix.mul_assoc (creator Q k), Matrix.mul_assoc (creator Q k), creator_mul_vacuum_zero] + rw [zero_add, Matrix.mul_assoc, hb', Matrix.mul_add, Matrix.add_apply, + ← Matrix.mul_assoc _ Nᴴ, mul_annihilator_vacuum_zero, zero_add] + have hJn : (annihilator Q k * N)ᴴ = creator Q k * Nᴴ := by + rw [annihilator_commutes_coefficientPair, Matrix.conjTranspose_mul, ← creator_eq_adjoint] + change ((annihilator Q j * M) * (annihilator Q k * N)ᴴ) ∅ ∅ = _ + rw [hJn, annihilator_commutes_coefficientPair, Matrix.mul_assoc M, + ← Matrix.mul_assoc (annihilator Q j), + eq_sub_of_add_eq (annihilator_creator_anticommute Q j k)] + rw [Matrix.sub_mul, Matrix.mul_sub, Matrix.sub_apply] + rw [← Matrix.mul_assoc M (creator Q k * annihilator Q j), + ← Matrix.mul_assoc M (creator Q k), hex, pairPartial_vacuum_gram] + congr 1 + split_ifs <;> simp [M, N] + + +theorem threeWedgeMatrix_gram_apply (Q : ℕ) (hQ : 1 ≤ Q) + (pj rk : PairLabel Q × Orbital Q) : + ((threeWedgeMatrix Q)ᴴ * threeWedgeMatrix Q) pj rk = + (if pj=rk then 1 else 0) - + ∑ i : Orbital Q, (pairCoefficient Q pj.1.val rk.2 i : ℂ) * + (pairCoefficient Q rk.1.val pj.2 i : ℂ) := by + classical + rw [Matrix.mul_apply] + simp only [Matrix.conjTranspose_apply, threeWedgeMatrix] + rw [annihilatorVector_gram Q 3 _ _ + (annihilationSpace_mul Q 2 1 (pairAnnihilator_mem Q _) + (annihilator_mem Q _))] + have ha (p : ℕ) (i j : Orbital Q) : + (pairCoefficient Q p j i : ℂ) = -(pairCoefficient Q p i j : ℂ) := by + rw [pairCoefficient_antisymm, Complex.ofReal_neg] + rw [pairAnnihilator_eq_coefficientPairAnnihilator, + pairAnnihilator_eq_coefficientPairAnnihilator, coefficientTriple_vacuum_gram Q _ _ (ha _) (ha _)] + simp only [Complex.star_def, Complex.conj_ofReal] + simp only [← pairAnnihilator_eq_coefficientPairAnnihilator] + rw [← annihilatorVector_gram Q 2 (pairAnnihilator Q pj.1.val) (pairAnnihilator Q rk.1.val) + (pairAnnihilator_mem Q _)] + change (if pj.2=rk.2 then + (∑ S, star (pairVector Q pj.1.val S) * pairVector Q rk.1.val S) else 0) - _ = _ + rw [pairVector_orthonormal Q _ _ hQ (by have := pj.1.isLt; omega)] + congr 1 + simp only [Prod.ext_iff, Fin.val_inj, ← ite_and, and_comm] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/ThreeOrbit.lean b/lean/OAI/Analysis/LaughlinFock/ThreeOrbit.lean new file mode 100644 index 0000000000000000000000000000000000000000..548117ddad0432774038fa8d36249cc3c74e23d4 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/ThreeOrbit.lean @@ -0,0 +1,106 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.PairOrbit + +namespace OAI + +/-! Three Orbit. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + +def threeSpinColumns (Q z : ℕ) : + Matrix (PairLabel Q × Orbital Q) (Fin (2*Q-2+Q-2*z+1)) ℂ := + fun pj k => threeCoupledColumn Q z k.val pj + + + +theorem threeSpinProjection_columns {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + threeSpinProjection Q z = threeSpinColumns Q z * (threeSpinColumns Q z)ᴴ := by + classical + let r : Fin (min (2*Q-2) Q+1) := ⟨z, by omega⟩ + ext i j + unfold threeSpinProjection + rw [Matrix.mul_apply, Matrix.mul_apply] + simp only [Matrix.mul_diagonal, Matrix.conjTranspose_apply, threeCouplingMatrix, + mul_ite, mul_one, mul_zero, ite_mul, zero_mul, Fintype.sum_sigma] + rw [Finset.sum_eq_single r] + · simp only [r, ite_true] + rfl + · intro a _ ha + have han : a.val ≠ z := by + intro h; apply ha; exact Fin.ext h + simp only [ite_eq_right han, Finset.sum_const_zero] + · simp + + +def threeSpinWedge (Q z : ℕ) : + Matrix (SectorOccupation Q 3) (Fin (2*Q-2+Q-2*z+1)) ℂ := + threeWedgeMatrix Q * threeSpinColumns Q z + + + +theorem threeSpinWedge_eq_tensor {Q : ℕ} (hQ : 1 ≤ Q) (z : ℕ) : + threeSpinWedge Q z = + wedgeProductMatrix Q 2 1 (pairSpinMatrix Q) (oneParticleMatrix Q) * + coupledSpinMatrix (2*Q-2) Q z := by + classical + let e : (Fin (2*Q-2+1) × Orbital Q) ≃ (PairLabel Q × Orbital Q) := + Equiv.prodCongr (finCongr (by omega)) (Equiv.refl _) + ext S k + change (∑ pj, threeWedgeMatrix Q S pj * threeCoupledColumn Q z k.val pj) = _ + rw [← e.sum_comp (fun pj => threeWedgeMatrix Q S pj * threeCoupledColumn Q z k.val pj)] + rw [Matrix.mul_apply] + apply Finset.sum_congr rfl + intro pj _ + have hv : (fun T => wedgeProductMatrix Q 2 1 (pairSpinMatrix Q) (oneParticleMatrix Q) T pj) = + (fun T => threeWedgeMatrix Q T (e pj)) := by + apply wedgeAnnihilator_injective Q 3 + rw [wedgeProductMatrix_contraction Q 2 1, oneParticleMatrix_contraction, + threeWedgeMatrix_annihilator_column] + simp only [pairSpinMatrix, pairVector, + wedgeAnnihilator_annihilatorVector Q 2 _ (pairAnnihilator_mem Q _)] + rfl + rw [congrFun hv S] + rfl + + +theorem threeSpinWedge_intertwines {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) (s : Fin 3) : + sectorOneBody Q 3 (spinGenerator Q s) * threeSpinWedge Q z = + threeSpinWedge Q z * spinGenerator (2*Q-2+Q-2*z) s := by + rw [threeSpinWedge_eq_tensor (by omega)] + rw [← Matrix.mul_assoc, + wedgeProductMatrix_intertwines Q 2 1 _ (spinGenerator_skew Q s) _ _ _ _ + (pairSpinMatrix_intertwines (by omega) s) + (oneParticleMatrix_intertwines Q _ (spinGenerator_skew Q s)), + Matrix.mul_assoc, coupledSpinMatrix_intertwines (by omega : z ≤ 2*Q-2) hz, + Matrix.mul_assoc] + + +theorem threeSpinWedge_gram {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + threeSpinWedge Q z * (threeSpinWedge Q z)ᴴ = + threeWedgeMatrix Q * threeSpinProjection Q z * (threeWedgeMatrix Q)ᴴ := by + rw [threeSpinProjection_columns hQ hz, threeSpinWedge, Matrix.conjTranspose_mul] + simp only [Matrix.mul_assoc] + + + +theorem fockAverage_highestThree {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + fockAverage Q ((highestThreeAnnihilator Q z hz)ᴴ * highestThreeAnnihilator Q z hz) = + (1 / ((3*Q-1-2*z : ℕ) : ℂ)) • + exteriorLift Q 3 (threeWedgeMatrix Q * threeSpinProjection Q z * (threeWedgeMatrix Q)ᴴ) := by + have h := fockAverage_spin_column (threeSpinWedge Q z) (threeSpinWedge_intertwines hQ hz) + (⟨0,by omega⟩ : Fin (2*Q-2+Q-2*z+1)) + have hc : (fun A => threeSpinWedge Q z A (⟨0,by omega⟩ : Fin (2*Q-2+Q-2*z+1))) = + threeWedgeMatrix Q *ᵥ threeCoupledColumn Q z 0 := rfl + rw [hc, ← highestThreeAnnihilator_eq_wedge hQ hz, threeSpinWedge_gram hQ hz] at h + have hd : ((2*Q-2+Q-2*z : ℕ) : ℂ)+1 = ((3*Q-1-2*z : ℕ) : ℂ) := by + rw [← Nat.cast_add_one] + congr 1 + omega + simpa only [hd] using h + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/ThreeRows.lean b/lean/OAI/Analysis/LaughlinFock/ThreeRows.lean new file mode 100644 index 0000000000000000000000000000000000000000..cd8a8549c99883e857b51d047e0651e24692960a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/ThreeRows.lean @@ -0,0 +1,212 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.CrossOrbit +import OAI.Analysis.LaughlinFock.FiniteComparison +import OAI.Analysis.LaughlinFock.ThreeOrbit +import OAI.Analysis.LaughlinFock.ThreeTraces + +namespace OAI + +/-! Three Rows. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + + + +theorem matrix_complete_column_sandwich {ι κ ν : Type*} + [Fintype ι] [Fintype κ] [DecidableEq κ] + (n : ι → ℕ) (C : ∀ i, Matrix κ (Fin (n i+1)) ℂ) + (hC : ∑ i, C i * (C i)ᴴ = 1) + (W : Matrix ν κ ℂ) (M : Matrix κ κ ℂ) : + W*M*Wᴴ = ∑ i, ∑ j, (W*C i)*((C i)ᴴ*M*C j)*(W*C j)ᴴ := by + calc + _ = W * (∑ i, C i * (C i)ᴴ) * M * (∑ j, C j * (C j)ᴴ) * Wᴴ := by + rw [hC, Matrix.mul_one, Matrix.mul_one] + _ = _ := by + simp only [Matrix.mul_sum, Matrix.sum_mul, Matrix.conjTranspose_mul, Matrix.mul_assoc] + rw [Finset.sum_comm] + + + +theorem sectorAverage_of_complete_spin {ι κ : Type*} [Fintype ι] + [Fintype κ] [DecidableEq κ] {Q k : ℕ} + (n : ι → ℕ) (hn : Function.Injective n) (C : ∀ i, Matrix κ (Fin (n i+1)) ℂ) + (hC : ∑ i, C i * (C i)ᴴ = 1) + (W : Matrix (SectorOccupation Q k) κ ℂ) + (hW : ∀ i s, sectorOneBody Q k (spinGenerator Q s)*(W*C i) = + (W*C i)*spinGenerator (n i) s) + (M : Matrix κ κ ℂ) : + sectorAverage Q k (W*M*Wᴴ) = + ∑ i, (((C i)ᴴ*M*C i).trace / (n i+1:ℂ)) • ((W*C i)*(W*C i)ᴴ) := by + classical + rw [matrix_complete_column_sandwich n C hC W M, map_sum] + apply Finset.sum_congr rfl + intro i _ + rw [map_sum, Finset.sum_eq_single i] + · exact sectorAverage_spin_mixed_sandwich (W*C i) (W*C i) (hW i) (hW i) _ + · intro j _ hji + exact sectorAverage_spin_cross_sandwich (fun hij => hji (hn hij).symm) + (W*C i) (W*C j) (hW i) (hW j) _ + · simp + + +theorem threeSpinColumns_complete {Q : ℕ} (hQ : 2 ≤ Q) : + (∑ z : Fin (Q+1), threeSpinColumns Q z.val * (threeSpinColumns Q z.val)ᴴ) = 1 := by + have h := threeSpinProjection_sum Q hQ + rw [← Fin.sum_univ_eq_sum_range] at h + simpa only [threeSpinProjection_columns hQ (Nat.le_of_lt_succ (Fin.isLt _))] using h + + + +theorem sectorAverage_three_kernel {Q : ℕ} (hQ : 2 ≤ Q) + (M : Matrix (PairLabel Q × Orbital Q) (PairLabel Q × Orbital Q) ℂ) : + sectorAverage Q 3 (threeWedgeMatrix Q*M*(threeWedgeMatrix Q)ᴴ) = + threeWedgeMatrix Q * (∑ z ∈ Finset.range (Q+1), + ((threeSpinProjection Q z*M).trace / ((3*Q-1-2*z : ℕ) : ℂ)) • + threeSpinProjection Q z) * (threeWedgeMatrix Q)ᴴ := by + have hn : Function.Injective (fun z : Fin (Q+1) => 2*Q-2+Q-2*z.val) := by + intro z w h + have hz := z.isLt + have hw := w.isLt + apply Fin.ext + dsimp only at h + omega + have h := sectorAverage_of_complete_spin _ hn (fun z : Fin (Q+1) => threeSpinColumns Q z.val) + (threeSpinColumns_complete hQ) (threeWedgeMatrix Q) + (fun z => threeSpinWedge_intertwines hQ (by have := z.isLt; omega)) M + rw [h, ← Fin.sum_univ_eq_sum_range, Matrix.mul_sum, Matrix.sum_mul] + apply Finset.sum_congr rfl + intro z _ + rw [Matrix.mul_smul, Matrix.smul_mul] + have hz : z.val ≤ Q := Nat.le_of_lt_succ z.isLt + have hd : ((2*Q-2+Q-2*z.val : ℕ) : ℂ)+1 = ((3*Q-1-2*z.val : ℕ) : ℂ) := by + rw [← Nat.cast_add_one] + congr 1 + omega + have ht : ((threeSpinColumns Q z.val)ᴴ * M * threeSpinColumns Q z.val).trace = + (threeSpinProjection Q z.val*M).trace := by + rw [threeSpinProjection_columns hQ hz, Matrix.trace_mul_comm, + ← Matrix.mul_assoc, Matrix.trace_mul_comm] + rw [hd, ht] + exact congrArg (_ • ·) (threeSpinWedge_gram hQ hz) + + + +theorem fockAverage_rowThreeBody {Q t : ℕ} (hQ : 16 ≤ Q) (ht : t ≤ 7) + (ℓ : ℝ) (a : RowEntry t → ℝ) : + fockAverage Q (rowThreeBody Q t ℓ rowP (sourceRowI (by omega : 8 ≤ Q)) + (sourceRowJ (by omega : 8 ≤ Q)) a) = + exteriorLift Q 3 (threeWedgeMatrix Q * (∑ z ∈ Finset.range 16, + ((rowThreeTrace Q z t ℓ a : ℂ) / ((3*Q-1-2*z : ℕ) : ℂ)) • + threeSpinProjection Q z) * (threeWedgeMatrix Q)ᴴ) := by + rw [← sourceRowThreeKernel_lift (by omega : 8 ≤ Q) ht ℓ a, + fockAverage_exteriorLift, sectorAverage_three_kernel (by omega)] + congr 2 + congr 1 + calc + _ = ∑ z ∈ Finset.range (Q+1), + ((rowThreeTrace Q z t ℓ a : ℂ) / ((3*Q-1-2*z : ℕ) : ℂ)) • threeSpinProjection Q z := by + apply Finset.sum_congr rfl + intro z hz + rw [sourceRowThreeKernel_projectionTrace hQ ht (by have := Finset.mem_range.mp hz; omega)] + _ = _ := by + symm + apply Finset.sum_subset (Finset.range_mono (by omega)) + intro z hz hnz + rw [rowThreeTrace_above_support (by simp only [Finset.mem_range] at hnz; omega) ℓ a] + simp + +theorem spinRatio_eq_dimensions {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + spinRatio Q z = ((3*Q-1-2*z : ℕ) : ℝ) / ((2*Q-1 : ℕ) : ℝ) := by + have h1 : 1 ≤ 3*Q := by omega + have h2 : 2*z ≤ 3*Q-1 := by omega + have h3 : 1 ≤ 2*Q := by omega + simp only [spinRatio, Nat.cast_sub h1, Nat.cast_sub h2, Nat.cast_sub h3, + Nat.cast_mul, Nat.cast_ofNat, Nat.cast_one] + + +theorem fockAverage_rowThreeBody_scaled {Q t : ℕ} (hQ : 16 ≤ Q) (ht : t ≤ 7) + (ℓ : ℝ) (a : RowEntry t → ℝ) : + ((2*Q-1 : ℕ) : ℂ) • fockAverage Q + (rowThreeBody Q t ℓ rowP (sourceRowI (by omega : 8 ≤ Q)) + (sourceRowJ (by omega : 8 ≤ Q)) a) = + exteriorLift Q 3 (threeWedgeMatrix Q * (∑ z ∈ Finset.range 16, + ((rowThreeTrace Q z t ℓ a / spinRatio Q z : ℝ) : ℂ) • + threeSpinProjection Q z) * (threeWedgeMatrix Q)ᴴ) := by + rw [fockAverage_rowThreeBody hQ ht] + change ((2*Q-1 : ℕ) : ℂ) • (exteriorLiftLinear Q 3) _ = (exteriorLiftLinear Q 3) _ + rw [← map_smul] + congr 1 + rw [← Matrix.smul_mul, ← Matrix.mul_smul, Finset.smul_sum] + congr 2 + apply Finset.sum_congr rfl + intro z hz + rw [smul_smul, Complex.ofReal_div, spinRatio_eq_dimensions (by omega) + (by have := Finset.mem_range.mp hz; omega), Complex.ofReal_div, + Complex.ofReal_natCast, Complex.ofReal_natCast] + congr 1 + have hn : ((2*Q-1 : ℕ) : ℂ) ≠ 0 := by exact_mod_cast (show 2*Q-1 ≠ 0 by omega) + rw [div_div_eq_mul_div] + ring + + +def averagedRowsFour {ι : Type*} [Fintype ι] {Q : ℕ} (hQ : 8 ≤ Q) + (rows : ι → ComparisonRow) : FockMatrix Q := + ((2*Q-1 : ℕ) : ℂ) • fockAverage Q (∑ i, + rowFourBody Q rowP (sourceRowI hQ) (sourceRowJ hQ) (rows i).alpha) + + + +theorem fockAverage_rowsThreeBody {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) {Q : ℕ} (hQ : 16 ≤ Q) : + ((2*Q-1 : ℕ) : ℂ) • fockAverage Q + (∑ i, rowThreeBody Q (rows i).t.val (rows i).ell rowP + (sourceRowI (by omega : 8 ≤ Q)) (sourceRowJ (by omega : 8 ≤ Q)) (rows i).alpha) = + threeTraceForm rows Q := by + rw [map_sum, Finset.smul_sum] + have hi (i : ι) := fockAverage_rowThreeBody_scaled hQ + (Nat.le_of_lt_succ (rows i).t.isLt) (rows i).ell (rows i).alpha + simp_rw [hi] + unfold threeTraceForm rowsThreeTrace + simp only [Matrix.mul_sum, Matrix.sum_mul, Matrix.mul_smul, Matrix.smul_mul, + exteriorLift_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro z hz + simp only [Finset.sum_div, Complex.ofReal_sum, Finset.sum_smul, exteriorLift_sum, + Complex.ofReal_div] + + + +theorem averagedRows_positive {ι : Type*} [Fintype ι] + (rows : ι → ComparisonRow) {Q : ℕ} (hQ : 16 ≤ Q) : + (rowsEta rows • hamiltonian Q + threeTraceForm rows Q + + averagedRowsFour (by omega : 8 ≤ Q) rows).PosSemidef := by + classical + let F (i : ι) := auxiliaryRow Q (rows i).t.val (rows i).ell rowP + (sourceRowI (by omega : 8 ≤ Q)) (sourceRowJ (by omega : 8 ≤ Q)) (rows i).alpha + have hp := fockAverage_posSemidef Q _ + (Matrix.posSemidef_sum Finset.univ (fun i _ => Matrix.posSemidef_conjTranspose_mul_self (F i))) + have h := hp.smul (show (0:ℂ) ≤ ((2*Q-1 : ℕ) : ℂ) by exact_mod_cast Nat.zero_le _) + dsimp [F] at h + simp_rw [auxiliaryRow_square] at h + rw [Finset.sum_add_distrib, Finset.sum_add_distrib, map_add, map_add, + smul_add, smul_add, fockAverage_rowsThreeBody rows hQ] at h + have he : ((2*Q-1 : ℕ) : ℂ) • fockAverage Q (∑ i, rowTwoBody Q (rows i).t.val (rows i).ell) = + rowsEta rows • hamiltonian Q := by + rw [map_sum, Finset.smul_sum] + unfold rowTwoBody rowsEta + have hh (i : ι) : ((2*Q-1 : ℕ) : ℂ) • fockAverage Q + ((rows i).ell^2 • ((pairAnnihilator Q (rows i).t.val)ᴴ * pairAnnihilator Q (rows i).t.val)) = + (rows i).ell^2 • hamiltonian Q := by + rw [(fockAverage Q).map_smul_of_tower, smul_comm _ ((rows i).ell^2), + fockAverage_pair_energy_scaled (by omega) (by have := (rows i).t.isLt; omega)] + simp_rw [hh] + exact Finset.sum_smul.symm + rw [he] at h + exact h + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/ThreeSpectrum.lean b/lean/OAI/Analysis/LaughlinFock/ThreeSpectrum.lean new file mode 100644 index 0000000000000000000000000000000000000000..d3be73fea8849300d873265df01ff91f5c3c1ae9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/ThreeSpectrum.lean @@ -0,0 +1,292 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.CopyNormalization +import OAI.Analysis.LaughlinFock.ExchangeSpectrum +import OAI.Analysis.LaughlinFock.ThreeGram + +namespace OAI + +/-! Three Spectrum. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder + + + +theorem pairSwapCompression_apply (Q : ℕ) (f : GridVector) (p j : ℕ) : + pairSwapCompression Q f p j = + ∑ r ∈ Finset.range (2*Q-2+1), ∑ k ∈ Finset.range (Q+1), + (∑ i ∈ Finset.range (Q+1), + coupledVector Q Q 1 p i k * coupledVector Q Q 1 r i j) * f r k := by + simp only [pairSwapCompression, LinearMap.comp_apply, pairTensorProject, + pairTensorEmbed, swap23, LinearMap.coe_mk, AddHom.coe_mk, gridInner, + Finset.mul_sum] + rw [Finset.sum_comm] + simp_rw [Finset.sum_comm (s := Finset.range (Q+1)) (t := Finset.range (2*Q-2+1))] + rw [Finset.sum_comm] + conv_lhs => rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro r _ + apply Finset.sum_congr rfl + intro k _ + rw [Finset.sum_mul] + apply Finset.sum_congr rfl + intro i _ + ring + + +theorem pairSwapCompression_apply_fin (Q : ℕ) (hQ : 1 ≤ Q) + (f : GridVector) (p j : ℕ) : + pairSwapCompression Q f p j = + ∑ r : PairLabel Q, ∑ k : Orbital Q, + (∑ i : Orbital Q, + coupledVector Q Q 1 p i.val k.val * coupledVector Q Q 1 r.val i.val j) * f r.val k.val := by + rw [pairSwapCompression_apply] + symm + calc + _ = ∑ r : PairLabel Q, ∑ k ∈ Finset.range (Q+1), + (∑ i ∈ Finset.range (Q+1), + coupledVector Q Q 1 p i k * coupledVector Q Q 1 r.val i j) * f r.val k := by + apply Finset.sum_congr rfl + intro r _ + calc + _ = ∑ k : Orbital Q, (∑ i ∈ Finset.range (Q+1), + coupledVector Q Q 1 p i k.val * coupledVector Q Q 1 r.val i j) * f r.val k.val := by + apply Finset.sum_congr rfl + intro k _ + congr 1 + exact Fin.sum_univ_eq_sum_range + (fun i => coupledVector Q Q 1 p i k.val * coupledVector Q Q 1 r.val i j) (Q+1) + _ = _ := Fin.sum_univ_eq_sum_range + (fun k => (∑ i ∈ Finset.range (Q+1), + coupledVector Q Q 1 p i k * coupledVector Q Q 1 r.val i j) * f r.val k) (Q+1) + _ = _ := by + rw [show 2*Q-2+1 = 2*Q-1 by omega] + exact Fin.sum_univ_eq_sum_range + (fun r => ∑ k ∈ Finset.range (Q+1), (∑ i ∈ Finset.range (Q+1), + coupledVector Q Q 1 p i k * coupledVector Q Q 1 r i j) * f r k) (2*Q-1) + + + +theorem threeWedgeMatrix_gram_mulVec_grid (Q : ℕ) (hQ : 1 ≤ Q) + (f : GridVector) (pj : PairLabel Q × Orbital Q) : + (((threeWedgeMatrix Q)ᴴ * threeWedgeMatrix Q) *ᵥ + (fun rk => (f rk.1.val rk.2.val : ℂ))) pj = + (f pj.1.val pj.2.val : ℂ) - 2 * + (pairSwapCompression Q f pj.1.val pj.2.val : ℂ) := by + classical + have hc (p : PairLabel Q) (j i : Orbital Q) : + (pairCoefficient Q p.val j i : ℂ) = + -(Real.sqrt 2 : ℂ) * (coupledVector Q Q 1 p.val i.val j.val : ℂ) := by + rw [pairCoefficient_antisymm, pairCoefficient_eq_coupled hQ (by have := p.isLt; omega)] + push_cast + ring + have htwo : (Real.sqrt 2 : ℂ) * (Real.sqrt 2 : ℂ) = 2 := by + norm_cast + exact Real.mul_self_sqrt (by norm_num) + have hex (rk : PairLabel Q × Orbital Q) : + (∑ i : Orbital Q, (pairCoefficient Q pj.1.val rk.2 i : ℂ) * + (pairCoefficient Q rk.1.val pj.2 i : ℂ)) = + 2 * (∑ i : Orbital Q, (coupledVector Q Q 1 pj.1.val i.val rk.2.val : ℂ) * + (coupledVector Q Q 1 rk.1.val i.val pj.2.val : ℂ)) := by + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro i _ + rw [hc, hc] + calc + _ = ((Real.sqrt 2 : ℂ)*(Real.sqrt 2 : ℂ)) * + ((coupledVector Q Q 1 pj.1.val i.val rk.2.val : ℂ) * + (coupledVector Q Q 1 rk.1.val i.val pj.2.val : ℂ)) := by ring + _ = _ := by rw [htwo] + simp only [Matrix.mulVec, dotProduct, threeWedgeMatrix_gram_apply Q hQ, hex, + sub_mul, Finset.sum_sub_distrib] + rw [show (∑ rk : PairLabel Q × Orbital Q, + (if pj=rk then (1:ℂ) else 0) * (f rk.1.val rk.2.val : ℂ)) = f pj.1.val pj.2.val by simp] + congr 1 + rw [pairSwapCompression_apply_fin Q hQ, Fintype.sum_prod_type] + push_cast + simp only [Finset.mul_sum, Finset.sum_mul] + apply Finset.sum_congr rfl + intro r _ + apply Finset.sum_congr rfl + intro k _ + apply Finset.sum_congr rfl + intro i _ + ring + + +def threeCoupledColumn (Q z k : ℕ) : PairLabel Q × Orbital Q → ℂ := + fun pj => coupledVector (2*Q-2) Q z k pj.1.val pj.2.val + + + +theorem threeWedgeMatrix_gram_eigenvector {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) (k : ℕ) : + ((threeWedgeMatrix Q)ᴴ * threeWedgeMatrix Q) *ᵥ threeCoupledColumn Q z k = + (1 + gramShift Q z : ℂ) • threeCoupledColumn Q z k := by + funext pj + unfold threeCoupledColumn + rw [threeWedgeMatrix_gram_mulVec_grid Q (by omega), + pairSwapCompression_eigenvector hQ hz] + simp only [Pi.smul_apply, smul_eq_mul] + push_cast + ring + + + +theorem coupledVector_resolution (n m : ℕ) + (pq rs : Fin (n+1) × Fin (m+1)) : + (∑ c : CoupledIndex n m, + coupledVector n m c.1.val c.2.val pq.1.val pq.2.val * + coupledVector n m c.1.val c.2.val rs.1.val rs.2.val) = + if pq=rs then 1 else 0 := by + classical + simpa only [EuclideanSpace.inner_single_left, EuclideanSpace.inner_single_right, + conj_trivial, one_mul, coupledBasis_apply, coupledEuclidean, gridEuclidean, + PiLp.single_apply, eq_comm] using + (coupledBasis n m).sum_inner_mul_inner + (EuclideanSpace.single pq 1) (EuclideanSpace.single rs 1) + + + +def threeCouplingMatrix (Q : ℕ) : + Matrix (PairLabel Q × Orbital Q) (CoupledIndex (2*Q-2) Q) ℂ := + fun pj c => threeCoupledColumn Q c.1.val c.2.val pj + + +theorem threeCouplingMatrix_gram (Q : ℕ) (hQ : 1 ≤ Q) : + (threeCouplingMatrix Q)ᴴ * threeCouplingMatrix Q = 1 := by + classical + ext c d + have hc := coupledIndex_bounds c + have hd := coupledIndex_bounds d + have h := coupledVector_gram hc.1 hc.2.1 hd.1 hd.2.1 hc.2.2 hd.2.2 + rw [gridInner_eq_fin_sum] at h + rw [show 2*Q-2+1 = 2*Q-1 by omega] at h + have he : (c.1.val=d.1.val ∧ c.2.val=d.2.val) ↔ c=d := by + constructor + · intro ⟨hz, hk⟩ + rcases c with ⟨z, k⟩ + rcases d with ⟨r, l⟩ + have hr : z=r := Fin.ext hz + subst r + have hl : k=l := Fin.ext hk + subst l + rfl + · rintro rfl + exact ⟨rfl, rfl⟩ + simp only [he] at h + have h' := congrArg (fun t : ℝ => (t : ℂ)) h + simpa only [Matrix.mul_apply, Matrix.conjTranspose_apply, + threeCouplingMatrix, threeCoupledColumn, Complex.star_def, Complex.conj_ofReal, + Fintype.sum_prod_type, Matrix.one_apply, Complex.ofReal_sum, + Complex.ofReal_mul, apply_ite, Complex.ofReal_one, Complex.ofReal_zero] using h' + + + +theorem threeCouplingMatrix_complete (Q : ℕ) (hQ : 1 ≤ Q) : + threeCouplingMatrix Q * (threeCouplingMatrix Q)ᴴ = 1 := by + classical + ext pj rk + have hdim : 2*Q-1 = 2*Q-2+1 := by omega + let pq : Fin (2*Q-2+1) × Fin (Q+1) := (Fin.cast hdim pj.1, pj.2) + let rs : Fin (2*Q-2+1) × Fin (Q+1) := (Fin.cast hdim rk.1, rk.2) + have h := congrArg (fun t : ℝ => (t : ℂ)) (coupledVector_resolution (2*Q-2) Q pq rs) + simpa only [Matrix.mul_apply, Matrix.conjTranspose_apply, + threeCouplingMatrix, threeCoupledColumn, Complex.star_def, Complex.conj_ofReal, + Matrix.one_apply, Complex.ofReal_sum, Complex.ofReal_mul, + pq, rs, Fin.val_cast, Prod.mk.injEq, Fin.cast_inj, ← Prod.ext_iff, + apply_ite, Complex.ofReal_one, Complex.ofReal_zero] using h + + +theorem threeWedgeMatrix_gram_diagonal (Q : ℕ) (hQ : 2 ≤ Q) : + (threeWedgeMatrix Q)ᴴ * threeWedgeMatrix Q - 1 = + threeCouplingMatrix Q * + Matrix.diagonal (fun c : CoupledIndex (2*Q-2) Q => (gramShift Q c.1.val : ℂ)) * + (threeCouplingMatrix Q)ᴴ := by + classical + have he : ((threeWedgeMatrix Q)ᴴ * threeWedgeMatrix Q) * threeCouplingMatrix Q = + threeCouplingMatrix Q * Matrix.diagonal + (fun c : CoupledIndex (2*Q-2) Q => (1+gramShift Q c.1.val : ℂ)) := by + ext pj c + rw [Matrix.mul_diagonal] + change (((threeWedgeMatrix Q)ᴴ * threeWedgeMatrix Q) *ᵥ + threeCoupledColumn Q c.1.val c.2.val) pj = + threeCoupledColumn Q c.1.val c.2.val pj * (1+gramShift Q c.1.val : ℂ) + simpa only [Pi.smul_apply, smul_eq_mul, mul_comm] using + congrArg (fun v => v pj) + (threeWedgeMatrix_gram_eigenvector hQ (coupledIndex_bounds c).2.1 c.2.val) + have he' := congrArg (fun M => M * (threeCouplingMatrix Q)ᴴ) he + rw [Matrix.mul_assoc, threeCouplingMatrix_complete Q (by omega), Matrix.mul_one] at he' + rw [he'] + have hsum : Matrix.diagonal (fun c : CoupledIndex (2*Q-2) Q => (1+gramShift Q c.1.val : ℂ)) = + 1 + Matrix.diagonal (fun c : CoupledIndex (2*Q-2) Q => (gramShift Q c.1.val : ℂ)) := by + rw [← Matrix.diagonal_one, ← Matrix.diagonal_add] + rw [hsum, Matrix.mul_add, Matrix.add_mul, Matrix.mul_one, + threeCouplingMatrix_complete Q (by omega)] + abel + + + +def threeSpinProjection (Q z : ℕ) : Matrix (PairLabel Q × Orbital Q) (PairLabel Q × Orbital Q) ℂ := + threeCouplingMatrix Q * Matrix.diagonal + (fun c : CoupledIndex (2*Q-2) Q => if c.1.val=z then (1:ℂ) else 0) * (threeCouplingMatrix Q)ᴴ + + +theorem threeSpinProjection_posSemidef (Q z : ℕ) : (threeSpinProjection Q z).PosSemidef := by + classical + apply Matrix.PosSemidef.mul_mul_conjTranspose_same + apply Matrix.posSemidef_diagonal_iff.mpr + intro c + split_ifs <;> norm_num + + +theorem threeSpinProjection_mul (Q z w : ℕ) (hQ : 1 ≤ Q) : + threeSpinProjection Q z * threeSpinProjection Q w = + if z=w then threeSpinProjection Q z else 0 := by + classical + unfold threeSpinProjection + have hd : Matrix.diagonal (fun c : CoupledIndex (2*Q-2) Q => if c.1.val=z then (1:ℂ) else 0) * + Matrix.diagonal (fun c : CoupledIndex (2*Q-2) Q => if c.1.val=w then (1:ℂ) else 0) = + if z=w then Matrix.diagonal (fun c : CoupledIndex (2*Q-2) Q => if c.1.val=z then (1:ℂ) else 0) else 0 := by + rw [Matrix.diagonal_mul_diagonal] + split_ifs with hzw + · subst w + congr 1 + funext c + split_ifs <;> norm_num + · ext c d + rw [Matrix.diagonal_apply] + split_ifs <;> simp_all + calc + _ = threeCouplingMatrix Q * + (Matrix.diagonal (fun c : CoupledIndex (2*Q-2) Q => if c.1.val=z then (1:ℂ) else 0) * + ((threeCouplingMatrix Q)ᴴ * threeCouplingMatrix Q) * + Matrix.diagonal (fun c : CoupledIndex (2*Q-2) Q => if c.1.val=w then (1:ℂ) else 0)) * + (threeCouplingMatrix Q)ᴴ := by simp only [Matrix.mul_assoc] + _ = _ := by + rw [threeCouplingMatrix_gram Q hQ, Matrix.mul_one, hd] + split_ifs <;> simp + + + +theorem threeWedgeMatrix_gram_spectral (Q : ℕ) (hQ : 2 ≤ Q) : + (threeWedgeMatrix Q)ᴴ * threeWedgeMatrix Q - 1 = + ∑ z ∈ Finset.range (Q+1), (gramShift Q z : ℂ) • threeSpinProjection Q z := by + classical + rw [threeWedgeMatrix_gram_diagonal Q hQ] + have hd : Matrix.diagonal (fun c : CoupledIndex (2*Q-2) Q => (gramShift Q c.1.val : ℂ)) = + ∑ z ∈ Finset.range (Q+1), (gramShift Q z : ℂ) • + Matrix.diagonal (fun c : CoupledIndex (2*Q-2) Q => if c.1.val=z then (1:ℂ) else 0) := by + ext c d + simp only [Matrix.diagonal_apply, Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul] + by_cases h : c=d + · subst d + simp only [ite_true, mul_ite, mul_one, mul_zero] + rw [Finset.sum_ite_eq, ite_eq_left (Finset.mem_range.mpr (by have := coupledIndex_bounds c; omega))] + · simp [h] + rw [hd] + simp only [threeSpinProjection, Matrix.mul_sum, Matrix.sum_mul, Matrix.mul_smul, Matrix.smul_mul] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/ThreeTraces.lean b/lean/OAI/Analysis/LaughlinFock/ThreeTraces.lean new file mode 100644 index 0000000000000000000000000000000000000000..7f731d8c9e3ef6c2c3114dbc1090884ea6c41cfc --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/ThreeTraces.lean @@ -0,0 +1,206 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.RowTraces + +namespace OAI + +/-! Three Traces. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexConjugate ComplexOrder +open Filter Topology + + +def sourceRowP {Q t : ℕ} (hQ : 8 ≤ Q) (b : RowEntry t) : PairLabel Q := + ⟨rowP b, by have := (rowEntry_bounds b).1; omega⟩ + +def sourceRowI {Q t : ℕ} (hQ : 8 ≤ Q) (b : RowEntry t) : Orbital Q := + ⟨rowI b, by have := (rowEntry_bounds b).2.2.1; omega⟩ + +def sourceRowJ {Q t : ℕ} (hQ : 8 ≤ Q) (b : RowEntry t) : Orbital Q := + ⟨rowJ b, by have := (rowEntry_bounds b).2.1; omega⟩ + +def sourceRowT {Q t : ℕ} (hQ : 8 ≤ Q) (ht : t ≤ 7) : PairLabel Q := + ⟨t, by omega⟩ + + +def sourceRowThreeKernel {Q t : ℕ} (hQ : 8 ≤ Q) (ht : t ≤ 7) + (ℓ : ℝ) (a : RowEntry t → ℝ) : + Matrix (PairLabel Q × Orbital Q) (PairLabel Q × Orbital Q) ℂ := + rowThreePrewedge Q (sourceRowT hQ ht) ℓ (sourceRowP hQ) (sourceRowI hQ) (sourceRowJ hQ) a + +theorem sourceRowThreeKernel_lift {Q t : ℕ} (hQ : 8 ≤ Q) (ht : t ≤ 7) + (ℓ : ℝ) (a : RowEntry t → ℝ) : + exteriorLift Q 3 (threeWedgeMatrix Q * sourceRowThreeKernel hQ ht ℓ a * + (threeWedgeMatrix Q)ᴴ) = + rowThreeBody Q t ℓ rowP (sourceRowI hQ) (sourceRowJ hQ) a := + rowThreePrewedge_lift Q (sourceRowT hQ ht) ℓ (sourceRowP hQ) (sourceRowI hQ) (sourceRowJ hQ) a + + +def sphericalRowAmplitude (Q z t T : ℕ) (a : RowEntry t → ℝ) : ℝ := + ∑ b : RowEntry t, if rowP b+rowJ b=T then + a b*sphericalThreeCoefficient Q z T (rowP b) else 0 + + +theorem coupledVector_eq_sphericalThree (Q z k p j : ℕ) : + coupledVector (2*Q-2) Q z k p j = + if p+j=z+k then sphericalThreeCoefficient Q z (z+k) p else 0 := by + simp [coupledVector, sphericalThreeCoefficient] + + + +theorem sourceRowThreeKernel_diagonal {Q t : ℕ} (hQ : 8 ≤ Q) (ht : t ≤ 7) + (ℓ : ℝ) (a : RowEntry t → ℝ) (z k : ℕ) : + star (threeCoupledColumn Q z k) ⬝ᵥ + (sourceRowThreeKernel hQ ht ℓ a *ᵥ threeCoupledColumn Q z k) = + ((2*ℓ*sphericalThreeCoefficient Q z (z+k) t * sphericalRowAmplitude Q z t (z+k) a + + (sphericalRowAmplitude Q z t (z+k) a)^2 : ℝ) : ℂ) := by + classical + rw [sourceRowThreeKernel] + unfold threeCoupledColumn + rw [rowThreePrewedge_bilinear] + have hi (b : RowEntry t) : t+rowI b=rowP b+rowJ b := (rowEntry_bounds b).2.2.2 + have hh (b c : RowEntry t) : sourceRowI hQ b=sourceRowI hQ c ↔ rowI b=rowI c := by + exact Fin.ext_iff + simp only [sourceRowT, sourceRowP, sourceRowJ, sourceRowI, coupledVector_eq_sphericalThree, hi] + apply congrArg (fun x : ℝ => (x : ℂ)) + apply congrArg₂ (· + ·) + · unfold sphericalRowAmplitude + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro b _ + split_ifs <;> ring + · unfold sphericalRowAmplitude + rw [pow_two, Finset.sum_mul_sum] + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro c _ + have he : (⟨rowI b, by have := (rowEntry_bounds b).2.2.1; omega⟩ : Orbital Q) = + (⟨rowI c, by have := (rowEntry_bounds c).2.2.1; omega⟩ : Orbital Q) ↔ + rowP b+rowJ b=rowP c+rowJ c := by + rw [Fin.mk.injEq, rowI_eq_iff] + simp only [he] + split_ifs <;> ring_nf + omega + + +theorem sphericalRowAmplitude_zero {Q z t T : ℕ} (a : RowEntry t → ℝ) + (h : T < t ∨ 15 < T) : sphericalRowAmplitude Q z t T a = 0 := by + apply Finset.sum_eq_zero + intro b _ + rw [ite_eq_right] + have hb := rowEntry_bounds b + omega + + +def rowThreeLevelTrace (Q z t : ℕ) (ℓ : ℝ) (a : RowEntry t → ℝ) (T : ℕ) : ℝ := + if z ≤ T ∧ t ≤ T then + 2*ℓ*sphericalThreeCoefficient Q z T t*sphericalRowAmplitude Q z t T a + + (sphericalRowAmplitude Q z t T a)^2 + else 0 + +theorem rowThreeLevelTrace_lower_zero (Q z t : ℕ) (ℓ : ℝ) (a : RowEntry t → ℝ) + (T : ℕ) (hT : T < z) : rowThreeLevelTrace Q z t ℓ a T = 0 := by + simp [rowThreeLevelTrace, Nat.not_le.mpr hT] + +theorem rowThreeLevelTrace_upper_zero (Q z t : ℕ) (ℓ : ℝ) (a : RowEntry t → ℝ) + (T : ℕ) (hT : 15 < T) : rowThreeLevelTrace Q z t ℓ a T = 0 := by + simp [rowThreeLevelTrace, sphericalRowAmplitude_zero a (Or.inr hT)] + +theorem sourceRowThreeKernel_diagonal_level {Q t : ℕ} (hQ : 8 ≤ Q) (ht : t ≤ 7) + (ℓ : ℝ) (a : RowEntry t → ℝ) (z k : ℕ) : + star (threeCoupledColumn Q z k) ⬝ᵥ + (sourceRowThreeKernel hQ ht ℓ a *ᵥ threeCoupledColumn Q z k) = + (rowThreeLevelTrace Q z t ℓ a (z+k) : ℂ) := by + rw [sourceRowThreeKernel_diagonal] + unfold rowThreeLevelTrace + split_ifs with h + · rfl + · have ht' : z+k < t := by omega + rw [sphericalRowAmplitude_zero a (Or.inl ht')] + simp + + + +theorem sum_shifted_of_support {K L z : ℕ} (hKL : L ≤ z+K) (f : ℕ → ℝ) + (hlo : ∀ T, T < z → f T=0) (hhi : ∀ T, L ≤ T → f T=0) : + (∑ k ∈ Finset.range K, f (z+k)) = ∑ T ∈ Finset.range L, f T := by + have hl : ∑ T ∈ Finset.range z, f T = 0 := by + exact Finset.sum_eq_zero fun T hT => hlo T (Finset.mem_range.mp hT) + have hu : (∑ T ∈ Finset.range L, f T) = ∑ T ∈ Finset.range (z+K), f T := by + apply Finset.sum_subset (Finset.range_mono hKL) + intro T _ hT + exact hhi T (by simpa using hT) + rw [hu, Finset.sum_range_add, hl, zero_add] + + + +theorem sourceRowThreeKernel_spinTrace {Q t z : ℕ} (hQ : 16 ≤ Q) (ht : t ≤ 7) + (hz : z ≤ Q) (ℓ : ℝ) (a : RowEntry t → ℝ) : + (∑ k : Fin (2*Q-2+Q-2*z+1), star (threeCoupledColumn Q z k.val) ⬝ᵥ + (sourceRowThreeKernel (by omega : 8 ≤ Q) ht ℓ a *ᵥ threeCoupledColumn Q z k.val)) = + (rowThreeTrace Q z t ℓ a : ℂ) := by + simp only [sourceRowThreeKernel_diagonal_level] + rw [← Complex.ofReal_sum] + apply congrArg (fun x : ℝ => (x : ℂ)) + rw [Fin.sum_univ_eq_sum_range + (fun k => rowThreeLevelTrace Q z t ℓ a (z+k)) (2*Q-2+Q-2*z+1)] + exact sum_shifted_of_support (by omega : 16 ≤ z+(2*Q-2+Q-2*z+1)) + (rowThreeLevelTrace Q z t ℓ a) + (rowThreeLevelTrace_lower_zero Q z t ℓ a) + (fun T hT => rowThreeLevelTrace_upper_zero Q z t ℓ a T (by omega)) + + + +theorem threeSpinProjection_kernel_trace {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) + (M : Matrix (PairLabel Q × Orbital Q) (PairLabel Q × Orbital Q) ℂ) : + (threeSpinProjection Q z * M).trace = + ∑ k : Fin (2*Q-2+Q-2*z+1), star (threeCoupledColumn Q z k.val) ⬝ᵥ + (M *ᵥ threeCoupledColumn Q z k.val) := by + classical + have hz' : z < min (2*Q-2) Q+1 := by omega + let r : Fin (min (2*Q-2) Q+1) := ⟨z,hz'⟩ + unfold threeSpinProjection + rw [Matrix.mul_assoc, Matrix.trace_mul_comm, ← Matrix.mul_assoc, Matrix.trace_mul_comm] + simp only [Matrix.trace, Matrix.diag_apply, Matrix.diagonal_mul, ite_mul, one_mul, zero_mul] + rw [Fintype.sum_sigma, Finset.sum_eq_single r] + · simp only [r, ite_true] + apply Finset.sum_congr rfl + intro k _ + simp only [Matrix.mul_apply, Matrix.conjTranspose_apply, threeCouplingMatrix, + dotProduct, Matrix.mulVec, Pi.star_apply, Finset.sum_mul, Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro a _ + apply Finset.sum_congr rfl + intro b _ + ring + · intro a _ ha + have han : a.val ≠ z := by + intro h + exact ha (Fin.ext h) + simp [han] + · simp + + + +theorem sourceRowThreeKernel_projectionTrace {Q t z : ℕ} (hQ : 16 ≤ Q) + (ht : t ≤ 7) (hz : z ≤ Q) (ℓ : ℝ) (a : RowEntry t → ℝ) : + (threeSpinProjection Q z * sourceRowThreeKernel (by omega : 8 ≤ Q) ht ℓ a).trace = + (rowThreeTrace Q z t ℓ a : ℂ) := by + rw [threeSpinProjection_kernel_trace (by omega) hz, + sourceRowThreeKernel_spinTrace hQ ht hz] + + + +theorem rowThreeTrace_above_support {Q z t : ℕ} (hz : 15 < z) + (ℓ : ℝ) (a : RowEntry t → ℝ) : rowThreeTrace Q z t ℓ a = 0 := by + apply Finset.sum_eq_zero + intro T hT + have hT' := Finset.mem_range.mp hT + simp only [show ¬ (z ≤ T ∧ t ≤ T) by omega, ite_false] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/TraceSymmetry.lean b/lean/OAI/Analysis/LaughlinFock/TraceSymmetry.lean new file mode 100644 index 0000000000000000000000000000000000000000..1c5096e18267ceb50986c7271c47e5f3ab1ecf85 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/TraceSymmetry.lean @@ -0,0 +1,38 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.IntegerFour + +namespace OAI + +/-! Trace Symmetry. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem rationalFourFactor_symm {t : ℕ} (D : ℕ) (b c : RowEntry t) : + rationalFourFactor D b c = rationalFourFactor D c b := by + unfold rationalFourFactor + rw [rowFourLevel_symm b c] + ring + +theorem integerFourTrace_symm (D t : ℕ) (a : RowEntry t → ℚ) (r s : CopyLabel D) : + integerFourTrace D t a r s = integerFourTrace D t a s r := by + unfold integerFourTrace + congr 1 + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro b _ + apply Finset.sum_congr rfl + intro c _ + rw [rowFourLevel_symm c b, rationalFourFactor_symm D c b] + split_ifs <;> ring + +theorem integerRowsFourTrace_symm (D : ℕ) (r s : CopyLabel D) : + integerRowsFourTrace D r s = integerRowsFourTrace D s r := by + unfold integerRowsFourTrace + simp only [Matrix.sum_apply] + exact Finset.sum_congr rfl (fun t _ => integerFourTrace_symm D t.val (certificateAlpha t) r s) + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinFock/WedgeLie.lean b/lean/OAI/Analysis/LaughlinFock/WedgeLie.lean new file mode 100644 index 0000000000000000000000000000000000000000..6c8c833b15640de45b3b1010c7b23d315d084249 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinFock/WedgeLie.lean @@ -0,0 +1,145 @@ +import Mathlib +import OAI.Analysis.LaughlinFock.CopyVectors +import OAI.Analysis.LaughlinFock.FockRotations + +namespace OAI + +/-! Wedge Lie. -/ +noncomputable section +namespace LaughlinFock +open scoped BigOperators Matrix ComplexOrder + +theorem wedgeAnnihilator_neg (Q k : ℕ) (v : SectorOccupation Q k → ℂ) : + wedgeAnnihilator Q k (-v) = -wedgeAnnihilator Q k v := by + simp only [wedgeAnnihilator, Pi.neg_apply, star_neg, neg_smul, Finset.sum_neg_distrib] + + + +theorem oneBody_wedgeAnnihilator_commutator_skew (Q k : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (hA : Aᴴ = -A) + (v : SectorOccupation Q k → ℂ) : + oneBodyLift Q A * wedgeAnnihilator Q k v - + wedgeAnnihilator Q k v * oneBodyLift Q A = + wedgeAnnihilator Q k (sectorOneBody Q k A *ᵥ v) := by + rw [oneBody_wedgeAnnihilator_commutator, sectorOneBody_adjoint, hA] + have hn := (sectorOneBodyLinear Q k).map_neg A + change sectorOneBody Q k (-A) = -sectorOneBody Q k A at hn + rw [hn, Matrix.neg_mulVec, wedgeAnnihilator_neg, neg_neg] + + + +theorem sector_intertwiner_of_commutators {ι : Type*} [Fintype ι] (Q k : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (hA : Aᴴ = -A) + (X : Matrix ι ι ℂ) (C : Matrix (SectorOccupation Q k) ι ℂ) + (B : ι → FockMatrix Q) + (hB : ∀ i, wedgeAnnihilator Q k (fun T => C T i) = B i) + (hcomm : ∀ j, oneBodyLift Q A * B j - B j * oneBodyLift Q A = + ∑ i, star (X i j) • B i) : + sectorOneBody Q k A * C = C*X := by + ext T j + have he : wedgeAnnihilator Q k (sectorOneBody Q k A *ᵥ (fun T => C T j)) = + wedgeAnnihilator Q k (C *ᵥ (fun i => X i j)) := by + rw [← oneBody_wedgeAnnihilator_commutator_skew Q k A hA, hB, + wedgeAnnihilator_mulVec] + simp only [hB] + exact hcomm j + exact congrFun (wedgeAnnihilator_injective Q k he) T + + +theorem wedge_intertwiner_commutator {ι : Type*} [Fintype ι] (Q k : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (hA : Aᴴ = -A) + (X : Matrix ι ι ℂ) (C : Matrix (SectorOccupation Q k) ι ℂ) + (hC : sectorOneBody Q k A * C = C*X) (j : ι) : + oneBodyLift Q A * wedgeAnnihilator Q k (fun T => C T j) - + wedgeAnnihilator Q k (fun T => C T j) * oneBodyLift Q A = + ∑ i, star (X i j) • wedgeAnnihilator Q k (fun T => C T i) := by + rw [oneBody_wedgeAnnihilator_commutator_skew Q k A hA] + have hh : sectorOneBody Q k A *ᵥ (fun T => C T j) = C *ᵥ (fun i => X i j) := by + exact congrArg (fun M => fun T => M T j) hC + rw [hh, wedgeAnnihilator_mulVec] + + +def tensorSum {ι κ : Type*} [DecidableEq ι] [DecidableEq κ] + (X : Matrix ι ι ℂ) (Y : Matrix κ κ ℂ) : Matrix (ι × κ) (ι × κ) ℂ := + Matrix.kronecker X 1 + Matrix.kronecker 1 Y + +theorem tensorSum_apply {ι κ : Type*} [DecidableEq ι] [DecidableEq κ] + (X : Matrix ι ι ℂ) (Y : Matrix κ κ ℂ) (i j : ι × κ) : + tensorSum X Y i j = (if i.2=j.2 then X i.1 j.1 else 0) + + (if i.1=j.1 then Y i.2 j.2 else 0) := by + rcases i with ⟨i₁,i₂⟩ + rcases j with ⟨j₁,j₂⟩ + simp only [tensorSum, Matrix.add_apply, Matrix.kronecker, Matrix.kronecker_apply, Matrix.one_apply, + mul_ite, ite_mul, mul_one, one_mul, mul_zero, zero_mul] + + + +def wedgeProductMatrix {ι κ : Type*} (Q k l : ℕ) + (V : Matrix (SectorOccupation Q k) ι ℂ) (W : Matrix (SectorOccupation Q l) κ ℂ) : + Matrix (SectorOccupation Q (k+l)) (ι × κ) ℂ := fun S ij => + annihilatorVector Q (k+l) + (wedgeAnnihilator Q l (fun T => W T ij.2) * + wedgeAnnihilator Q k (fun T => V T ij.1)) S + +theorem wedgeProductMatrix_contraction {ι κ : Type*} (Q k l : ℕ) + (V : Matrix (SectorOccupation Q k) ι ℂ) (W : Matrix (SectorOccupation Q l) κ ℂ) + (ij : ι × κ) : + wedgeAnnihilator Q (k+l) (fun T => wedgeProductMatrix Q k l V W T ij) = + wedgeAnnihilator Q l (fun T => W T ij.2) * + wedgeAnnihilator Q k (fun T => V T ij.1) := by + apply wedgeAnnihilator_annihilatorVector + exact annihilationSpace_mul Q k l (wedgeAnnihilator_mem Q k _) (wedgeAnnihilator_mem Q l _) + + + +theorem wedgeProductMatrix_intertwines {ι κ : Type*} + [Fintype ι] [Fintype κ] [DecidableEq ι] [DecidableEq κ] (Q k l : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (hA : Aᴴ = -A) + (X : Matrix ι ι ℂ) (Y : Matrix κ κ ℂ) + (V : Matrix (SectorOccupation Q k) ι ℂ) (W : Matrix (SectorOccupation Q l) κ ℂ) + (hV : sectorOneBody Q k A * V = V*X) (hW : sectorOneBody Q l A * W = W*Y) : + sectorOneBody Q (k+l) A * wedgeProductMatrix Q k l V W = + wedgeProductMatrix Q k l V W * tensorSum X Y := by + apply sector_intertwiner_of_commutators Q (k+l) A hA (tensorSum X Y) + (wedgeProductMatrix Q k l V W) + (fun ij => wedgeAnnihilator Q l (fun T => W T ij.2) * + wedgeAnnihilator Q k (fun T => V T ij.1)) + (wedgeProductMatrix_contraction Q k l V W) + intro ij + rw [matrix_commutator_mul, wedge_intertwiner_commutator Q l A hA Y W hW, + wedge_intertwiner_commutator Q k A hA X V hV] + simp only [Matrix.sum_mul, Matrix.mul_sum, Matrix.smul_mul, Matrix.mul_smul, + tensorSum_apply, star_add, apply_ite star, star_zero, add_smul, Finset.sum_add_distrib, + Fintype.sum_prod_type, ite_smul, zero_smul] + simp only [Finset.sum_ite_eq', Finset.mem_univ, ite_true] + rw [Finset.sum_comm] + simp only [Finset.sum_ite_eq', Finset.mem_univ, ite_true] + exact add_comm _ _ + + +def oneParticleMatrix (Q : ℕ) : Matrix (SectorOccupation Q 1) (Orbital Q) ℂ := fun S i => + if S.val={i} then 1 else 0 + +theorem oneParticleMatrix_contraction (Q : ℕ) (i : Orbital Q) : + wedgeAnnihilator Q 1 (fun S => oneParticleMatrix Q S i) = annihilator Q i := by + have he : (fun S => oneParticleMatrix Q S i) = annihilatorVector Q 1 (annihilator Q i) := by + funext S + simp [oneParticleMatrix, annihilatorVector, annihilator_vacuum, eq_comm] + rw [he, wedgeAnnihilator_annihilatorVector Q 1 _ (annihilator_mem Q i)] + + +theorem oneParticleMatrix_intertwines (Q : ℕ) + (A : Matrix (Orbital Q) (Orbital Q) ℂ) (hA : Aᴴ = -A) : + sectorOneBody Q 1 A * oneParticleMatrix Q = oneParticleMatrix Q * A := by + apply sector_intertwiner_of_commutators Q 1 A hA A (oneParticleMatrix Q) + (annihilator Q) (oneParticleMatrix_contraction Q) + intro j + rw [← neg_sub, annihilator_oneBody_commutator] + have hh (i : Orbital Q) : star (A i j) = -A j i := by + exact congrArg (fun M => M j i) hA + simp only [hh, neg_smul, Finset.sum_neg_distrib] + +end LaughlinFock +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/AuxiliaryComparison.lean b/lean/OAI/Analysis/LaughlinGap/AuxiliaryComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..192e06d97a1bd3ffb69cb129c67a493f76998ddc --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/AuxiliaryComparison.lean @@ -0,0 +1,197 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.PhysicalAveraging +import OAI.Analysis.LaughlinGap.ThreeAveraging + +namespace OAI + +/-! Auxiliary Comparison. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin + +abbrev RowEntry (t : Fin 8) := + {a : Fin 8 × Fin 9 // t.val ≤ a.1.val+a.2.val ∧ a.1.val+a.2.val ≤ t.val+8} + +def RowEntry.output {t : Fin 8} (a : RowEntry t) : Fin 9 := + ⟨a.val.1.val+a.val.2.val-t.val,by have := a.property; omega⟩ + +lemma RowEntry.balance {t : Fin 8} (a : RowEntry t) : + t.val+a.output.val = a.val.1.val+a.val.2.val := by + dsimp [RowEntry.output]; have := a.property; omega + +structure RowData where + t : Fin 8 + lam : ℝ + alpha : RowEntry t → ℝ + +noncomputable def rowTriple {Q : ℕ} (hQ : 8 ≤ Q) (a : Fin 8 × Fin 9) : + FockMatrix (Q+1) := + annihilation ⟨a.2.val,by omega⟩ * physicalPair Q a.1.val + +noncomputable def rowAnnihilator {Q : ℕ} (hQ : 8 ≤ Q) (r : RowData) : FockMatrix (Q+1) := + r.lam • physicalPair Q r.t.val + ∑ a : RowEntry r.t, + r.alpha a • (creation ⟨a.output.val,by have := a.output.isLt; omega⟩ * rowTriple hQ a.val) + +noncomputable def rowThree {Q : ℕ} (hQ : 8 ≤ Q) (r : RowData) : FockMatrix (Q+1) := + (∑ a : RowEntry r.t, (r.lam*r.alpha a) • + ((rowTriple hQ (r.t,a.output)).transpose * rowTriple hQ a.val + + (rowTriple hQ a.val).transpose * rowTriple hQ (r.t,a.output))) + + ∑ a : RowEntry r.t, ∑ b : RowEntry r.t, (r.alpha a*r.alpha b) • + (if a.output=b.output then (rowTriple hQ a.val).transpose * rowTriple hQ b.val else 0) + +noncomputable def rowFour {Q : ℕ} (hQ : 8 ≤ Q) (r : RowData) : FockMatrix (Q+1) := + -(∑ a : RowEntry r.t, ∑ b : RowEntry r.t, (r.alpha a*r.alpha b) • + ((annihilation ⟨b.output.val,by have := b.output.isLt; omega⟩ * rowTriple hQ a.val).transpose * + (annihilation ⟨a.output.val,by have := a.output.isLt; omega⟩ * rowTriple hQ b.val))) + +lemma rowSquare_split {Q : ℕ} (hQ : 8 ≤ Q) (r : RowData) : + (rowAnnihilator hQ r).transpose * rowAnnihilator hQ r = + (r.lam^2) • ((physicalPair Q r.t.val).transpose * physicalPair Q r.t.val) + + rowThree hQ r + rowFour hQ r := by + classical + apply complexify_injective + let i : RowEntry r.t → Fin (Q+1) := fun a => ⟨a.output.val,by have := a.output.isLt; omega⟩ + have hi (a b : RowEntry r.t) : i a=i b ↔ a.output=b.output := by + simp only [i,Fin.ext_iff] + have h := Occupation.auxiliaryRow_square r.lam + (complexify (physicalPair Q r.t.val)) r.alpha i + (fun a => complexify (rowTriple hQ a.val)) + have ha : complexify (rowAnnihilator hQ r) = + Occupation.auxiliaryRow r.lam (complexify (physicalPair Q r.t.val)) r.alpha i + (fun a => complexify (rowTriple hQ a.val)) := by + simp only [rowAnnihilator, map_add, map_sum, map_smul, map_mul, complexify_creation, + Occupation.auxiliaryRow, i] + rfl + simp only [map_add, map_smul, map_mul, complexify_transpose, ha] + rw [h] + simp only [rowThree,rowFour,map_add,map_sum,map_smul,map_neg,map_mul, + complexify_transpose, apply_ite, map_zero, hi, rowTriple, complexify_annihilation] + simp only [i,sub_eq_add_neg,add_assoc] + rfl + +lemma rowSquare_average {Q : ℕ} (hQ : 8 ≤ Q) (r : RowData) : + ((2*Q-1:ℕ):ℝ) • average (rotationCommutant (fockLowering Q)) + ((rowAnnihilator hQ r).transpose * rowAnnihilator hQ r) = + r.lam^2 • physicalHamiltonian Q + + ((2*Q-1:ℕ):ℝ) • average (rotationCommutant (fockLowering Q)) (rowThree hQ r) + + ((2*Q-1:ℕ):ℝ) • average (rotationCommutant (fockLowering Q)) (rowFour hQ r) := by + rw [rowSquare_split, map_add, map_add, map_smul, + physicalPair_single_val (by omega) (by have := r.t.isLt; omega)] + have hn : ((2*Q-1:ℕ):ℝ) ≠ 0 := Nat.cast_ne_zero.mpr (by omega) + simp only [smul_add, smul_smul] + congr 2 + field_simp + +noncomputable def threeWeightCoefficient (Q z T p : ℕ) : ℝ := + if z ≤ T then coupledCoefficient (2*Q-2) Q z (T-z) p else 0 + +noncomputable def threeHighestAverage (Q z : ℕ) : FockMatrix (Q+1) := + average (rotationCommutant (fockLowering Q)) + ((combination (physicalTriple Q) (highestTensor (2*Q-2) Q z)).transpose * + combination (physicalTriple Q) (highestTensor (2*Q-2) Q z)) + +lemma sum_fin_extend {M : Type*} [AddCommMonoid M] {T K : ℕ} (h : T ≤ K) (f : ℕ → M) : + (∑ z : Fin (T+1), f z.val) = ∑ z : Fin (K+1), if z.val ≤ T then f z.val else 0 := by + rw [Fin.sum_univ_eq_sum_range f, + Fin.sum_univ_eq_sum_range (fun z => if z ≤ T then f z else 0)] + rw [← Finset.sum_filter] + congr 1 + ext z + simp only [Finset.mem_range,Finset.mem_filter] + omega + +lemma rowTriple_cross_average {Q T : ℕ} (hQ : 15 ≤ Q) + (a b : Fin 8 × Fin 9) (ha : a.1.val+a.2.val=T) (hb : b.1.val+b.2.val=T) : + average (rotationCommutant (fockLowering Q)) + ((rowTriple (by omega) a).transpose * rowTriple (by omega) b) = + ∑ z : Fin 16, + (threeWeightCoefficient Q z.val T a.1.val * threeWeightCoefficient Q z.val T b.1.val) • + threeHighestAverage Q z.val := by + have ht : T ≤ 15 := by have := a.1.isLt; have := a.2.isLt; omega + let a' : Fin (2*Q-2+1) × Fin (Q+1) := (⟨a.1.val,by omega⟩,⟨a.2.val,by omega⟩) + let b' : Fin (2*Q-2+1) × Fin (Q+1) := (⟨b.1.val,by omega⟩,⟨b.2.val,by omega⟩) + change average _ ((physicalTriple Q a').transpose * physicalTriple Q b') = _ + rw [(physicalTriple_covariant (by omega : 2 ≤ Q)).rawTensor_cross_average (by omega) a' b' ha hb] + change (∑ z : Fin (T+1), + (coupledCoefficient (2*Q-2) Q z.val (T-z.val) a.1.val * coupledCoefficient (2*Q-2) Q z.val (T-z.val) b.1.val) • + threeHighestAverage Q z.val) = _ + rw [sum_fin_extend ht (fun z => + (coupledCoefficient (2*Q-2) Q z (T-z) a.1.val * + coupledCoefficient (2*Q-2) Q z (T-z) b.1.val) • threeHighestAverage Q z)] + apply Finset.sum_congr rfl + intro z hz + dsimp [a',b'] + by_cases hzt : z.val ≤ T <;> simp [threeWeightCoefficient,hzt,threeHighestAverage] + +noncomputable def rowTrace (s : ℕ → ℕ → ℕ → ℝ) (z : ℕ) (r : RowData) : ℝ := + (∑ a : RowEntry r.t, 2*r.lam*r.alpha a * + s z (r.t.val+a.output.val) r.t.val * + s z (r.t.val+a.output.val) a.val.1.val) + + ∑ a : RowEntry r.t, ∑ b : RowEntry r.t, + if a.output=b.output then r.alpha a*r.alpha b * + s z (r.t.val+a.output.val) a.val.1.val * + s z (r.t.val+a.output.val) b.val.1.val else 0 + +noncomputable def rowThreeTrace (Q z : ℕ) (r : RowData) : ℝ := + rowTrace (threeWeightCoefficient Q) z r + +lemma rowThree_average {Q : ℕ} (hQ : 15 ≤ Q) (r : RowData) : + average (rotationCommutant (fockLowering Q)) (rowThree (by omega) r) = + ∑ z : Fin 16, rowThreeTrace Q z.val r • threeHighestAverage Q z.val := by + classical + have ha (a : RowEntry r.t) := rowTriple_cross_average hQ (r.t,a.output) a.val rfl a.balance.symm + have hb (a : RowEntry r.t) := rowTriple_cross_average hQ a.val (r.t,a.output) a.balance.symm rfl + have hc (a b : RowEntry r.t) : + average (rotationCommutant (fockLowering Q)) + (if a.output=b.output then (rowTriple (by omega) a.val).transpose * rowTriple (by omega) b.val else 0) = + ∑ z : Fin 16, (if a.output=b.output then + threeWeightCoefficient Q z.val (r.t.val+a.output.val) a.val.1.val * + threeWeightCoefficient Q z.val (r.t.val+a.output.val) b.val.1.val else 0) • + threeHighestAverage Q z.val := by + by_cases hab : a.output=b.output + · rw [ite_eq_left hab,rowTriple_cross_average hQ a.val b.val a.balance.symm (by rw [hab];exact b.balance.symm)] + simp only [hab,ite_true] + · simp [hab] + have hd (a : RowEntry r.t) : + average (rotationCommutant (fockLowering Q)) + ((rowTriple (by omega) (r.t,a.output)).transpose * rowTriple (by omega) a.val + + (rowTriple (by omega) a.val).transpose * rowTriple (by omega) (r.t,a.output)) = + ∑ z : Fin 16, (2 * threeWeightCoefficient Q z.val (r.t.val+a.output.val) r.t.val * + threeWeightCoefficient Q z.val (r.t.val+a.output.val) a.val.1.val) • + threeHighestAverage Q z.val := by + rw [map_add,ha,hb,← Finset.sum_add_distrib] + apply Finset.sum_congr rfl + intro z hz + rw [← add_smul] + congr 1 + ring + rw [rowThree,map_add] + simp only [map_sum,map_smul,hd,hc,Finset.smul_sum,smul_smul] + rw [Finset.sum_comm (f := fun (a : RowEntry r.t) (z : Fin 16) => _)] + conv_lhs => + arg 2; arg 2; ext a + rw [Finset.sum_comm] + rw [Finset.sum_comm (f := fun (a : RowEntry r.t) (z : Fin 16) => _), ← Finset.sum_add_distrib] + apply Finset.sum_congr rfl + intro z hz + simp only [← Finset.sum_smul, ← add_smul, rowThreeTrace, rowTrace] + congr 1 + congr 1 + · apply Finset.sum_congr rfl + intro a ha + ring + · apply Finset.sum_congr rfl + intro a ha + apply Finset.sum_congr rfl + intro b hb + split_ifs <;> ring + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Averaging.lean b/lean/OAI/Analysis/LaughlinGap/Averaging.lean new file mode 100644 index 0000000000000000000000000000000000000000..4c28b871acaa094b4245bb111b10cbfe367d3e27 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Averaging.lean @@ -0,0 +1,285 @@ +import Mathlib + +namespace OAI + +/-! Averaging. -/ + +noncomputable section + + +namespace LaughlinGap.Averaging +open scoped BigOperators InnerProduct + +variable {ι : Type*} [Fintype ι] [DecidableEq ι] + +noncomputable def coordinates : Matrix ι ι ℝ ≃ₗ[ℝ] EuclideanSpace ℝ (ι × ι) where + toFun A := WithLp.toLp 2 (fun ij => A ij.1 ij.2) + invFun x := Matrix.of (fun i j => x (i,j)) + left_inv _ := rfl + right_inv _ := rfl + map_add' _ _ := rfl + map_smul' _ _ := rfl + +omit [DecidableEq ι] in +lemma coordinates_inner (A B : Matrix ι ι ℝ) : + inner ℝ (coordinates A) (coordinates B) = (A.transpose * B).trace := by + change inner ℝ (WithLp.toLp 2 (fun ij : ι × ι => A ij.1 ij.2)) + (WithLp.toLp 2 (fun ij : ι × ι => B ij.1 ij.2)) = _ + simp only [EuclideanSpace.inner_toLp_toLp, star_trivial, dotProduct, + Fintype.sum_prod_type, Matrix.trace, Matrix.diag, Matrix.mul_apply, + Matrix.transpose_apply] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + ring + +noncomputable def invariantSpace (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) : + Submodule ℝ (EuclideanSpace ℝ (ι × ι)) := + S.toSubalgebra.toSubmodule.map coordinates.toLinearMap + +noncomputable def average (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) : + Matrix ι ι ℝ →ₗ[ℝ] Matrix ι ι ℝ := + coordinates.symm.toLinearMap.comp + ((invariantSpace S).starProjection.toLinearMap.comp coordinates.toLinearMap) + +lemma average_mem (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) (A : Matrix ι ι ℝ) : + average S A ∈ S := by + have hm := (invariantSpace S).starProjection_apply_mem (coordinates A) + obtain ⟨B, hB, he⟩ := hm + have hab : average S A = B := by + change coordinates.symm ((invariantSpace S).starProjection (coordinates A)) = B + rw [← he] + exact coordinates.symm_apply_apply B + exact hab ▸ hB + +lemma average_orthogonal (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) + (A : Matrix ι ι ℝ) {B : Matrix ι ι ℝ} (hB : B ∈ S) : + ((A - average S A).transpose * B).trace = 0 := by + rw [← coordinates_inner, map_sub] + have hB' : coordinates B ∈ invariantSpace S := ⟨B, hB, rfl⟩ + have he := (invariantSpace S).starProjection_inner_eq_zero (coordinates A) (coordinates B) hB' + simpa [average] using he + +lemma average_unique (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) + (A B : Matrix ι ι ℝ) (hB : B ∈ S) + (h : ∀ C ∈ S, ((A-B).transpose * C).trace = 0) : + average S A = B := by + apply coordinates.injective + change (invariantSpace S).starProjection (coordinates A) = coordinates B + apply (invariantSpace S).eq_starProjection_of_mem_of_inner_eq_zero + · exact ⟨B, hB, rfl⟩ + · rintro _ ⟨C,hC,rfl⟩ + rw [← map_sub] + change inner ℝ (coordinates (A-B)) (coordinates C) = 0 + rw [coordinates_inner] + exact h C hC + +lemma average_eq_self (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) + {A : Matrix ι ι ℝ} (hA : A ∈ S) : average S A = A := by + apply average_unique S A A hA + simp + +lemma average_transpose (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) (A : Matrix ι ι ℝ) : + average S A.transpose = (average S A).transpose := by + apply average_unique S A.transpose (average S A).transpose + · simpa only [Matrix.star_eq_conjTranspose, Matrix.conjTranspose_eq_transpose_of_trivial] + using (star_mem (average_mem S A) : star (average S A) ∈ S) + · intro C hC + have ht : C.transpose ∈ S := by + simpa only [Matrix.star_eq_conjTranspose, Matrix.conjTranspose_eq_transpose_of_trivial] + using (star_mem hC : star C ∈ S) + have h := average_orthogonal S A ht + rw [← Matrix.transpose_sub, Matrix.transpose_transpose] + rw [← Matrix.trace_transpose, Matrix.transpose_mul] at h + rw [Matrix.transpose_transpose, Matrix.trace_mul_comm] at h + exact h + +lemma average_isHermitian (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) + {A : Matrix ι ι ℝ} (hA : A.IsHermitian) : (average S A).IsHermitian := by + change (average S A).conjTranspose = average S A + rw [Matrix.conjTranspose_eq_transpose_of_trivial, ← average_transpose] + rw [show A.transpose = A from by simpa [Matrix.IsHermitian] using hA] + +lemma trace_mul_average (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) + (A : Matrix ι ι ℝ) {B : Matrix ι ι ℝ} (hB : B ∈ S) : + (A * B).trace = (average S A * B).trace := by + have h := average_orthogonal S A.transpose hB + rw [average_transpose, ← Matrix.transpose_sub, Matrix.transpose_transpose, + Matrix.sub_mul, Matrix.trace_sub] at h + exact sub_eq_zero.mp h + +lemma trace_mul_posSemidef {A B : Matrix ι ι ℝ} (hA : A.PosSemidef) + (hB : B.PosSemidef) : 0 ≤ (A * B).trace := by + let U : Matrix ι ι ℝ := hB.1.eigenvectorUnitary + have hAU := hA.conjTranspose_mul_mul_same U + have hdiag : ∀ i, 0 ≤ (U.conjTranspose * A * U) i i := fun i => hAU.diag_nonneg + have he : (A * B).trace = ((U.conjTranspose * A * U) * + Matrix.diagonal hB.1.eigenvalues).trace := by + conv_lhs => arg 1; rhs; rw [hB.1.spectral_theorem] + change (A * (U * Matrix.diagonal hB.1.eigenvalues * U.conjTranspose)).trace = _ + rw [← Matrix.mul_assoc, Matrix.trace_mul_cycle] + simp only [Matrix.mul_assoc] + rw [he] + simp only [Matrix.trace, Matrix.diag, Matrix.mul_diagonal] + exact Finset.sum_nonneg (fun i _ => mul_nonneg (hdiag i) (hB.eigenvalues_nonneg i)) + +lemma cfc_mem (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) + {A : Matrix ι ι ℝ} (hA : A ∈ S) (f : ℝ → ℝ) : cfc f A ∈ S := by + let : IsClosed (S : Set (Matrix ι ι ℝ)) := + S.toSubalgebra.toSubmodule.closed_of_finiteDimensional + exact _root_.cfc_mem (𝕜' := ℝ) f hA + +lemma trace_mul_cfc {A : Matrix ι ι ℝ} (hA : A.IsHermitian) (f : ℝ → ℝ) : + (A * cfc f A).trace = ∑ i, hA.eigenvalues i * f (hA.eigenvalues i) := by + have ht (M : Matrix ι ι ℝ) : + (Unitary.conjStarAlgAut ℝ _ hA.eigenvectorUnitary M).trace = M.trace := by + rw [Unitary.conjStarAlgAut_apply, Matrix.trace_mul_cycle, + Unitary.star_mul_self_of_mem (SetLike.coe_mem _), one_mul] + rw [hA.cfc_eq, Matrix.IsHermitian.cfc] + conv_lhs => arg 1; lhs; rw [hA.spectral_theorem] + rw [← map_mul, ht, Matrix.diagonal_mul_diagonal, Matrix.trace_diagonal] + rfl + +lemma cfc_nonnegative {A : Matrix ι ι ℝ} (hA : A.IsHermitian) (f : ℝ → ℝ) + (hf : ∀ x, 0 ≤ f x) : (cfc f A).PosSemidef := by + rw [hA.cfc_eq, Matrix.IsHermitian.cfc, Unitary.conjStarAlgAut_apply] + apply Matrix.PosSemidef.mul_mul_conjTranspose_same + exact Matrix.posSemidef_diagonal_iff.mpr (fun i => hf _) + +theorem average_positive (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) + {A : Matrix ι ι ℝ} (hA : A.PosSemidef) : (average S A).PosSemidef := by + classical + have hY := average_isHermitian S hA.isHermitian + rw [hY.posSemidef_iff_eigenvalues_nonneg] + intro i + by_contra hn + have hn : hY.eigenvalues i < 0 := lt_of_not_ge hn + let f : ℝ → ℝ := fun x => if x = hY.eigenvalues i then 1 else 0 + have hf : ∀ x, 0 ≤ f x := by intro x; dsimp [f]; split_ifs <;> norm_num + have hpos := trace_mul_posSemidef hA (cfc_nonnegative hY f hf) + rw [trace_mul_average S A (cfc_mem S (average_mem S A) f), trace_mul_cfc hY] at hpos + have hle : ∀ j : ι, hY.eigenvalues j * f (hY.eigenvalues j) ≤ 0 := by + intro j + dsimp [f] + split_ifs with he + · rw [he, mul_one]; exact hn.le + · simp + have hstrict : (∑ j, hY.eigenvalues j * f (hY.eigenvalues j)) < 0 := by + apply Finset.sum_neg' (fun j _ => hle j) + refine ⟨i, Finset.mem_univ i, ?_⟩ + simpa [f] using hn + exact (not_lt_of_ge hpos) hstrict + +lemma average_trace (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) (A : Matrix ι ι ℝ) : + (average S A).trace = A.trace := by + have h := trace_mul_average S A (one_mem S) + simpa using h.symm + +variable {κ : Type*} [Fintype κ] [DecidableEq κ] + +noncomputable def adjointMap (F : Matrix ι ι ℝ →ₗ[ℝ] Matrix κ κ ℝ) : + Matrix κ κ ℝ →ₗ[ℝ] Matrix ι ι ℝ := + coordinates.symm.toLinearMap.comp + ((coordinates.toLinearMap.comp (F.comp coordinates.symm.toLinearMap)).adjoint.comp + coordinates.toLinearMap) + +omit [DecidableEq ι] [DecidableEq κ] in +lemma adjointMap_inner (F : Matrix ι ι ℝ →ₗ[ℝ] Matrix κ κ ℝ) + (A : Matrix ι ι ℝ) (B : Matrix κ κ ℝ) : + inner ℝ (coordinates (F A)) (coordinates B) = + inner ℝ (coordinates A) (coordinates (adjointMap F B)) := by + let F' := coordinates.toLinearMap.comp (F.comp coordinates.symm.toLinearMap) + exact (LinearMap.adjoint_inner_right F' (coordinates A) (coordinates B)).symm + +theorem average_natural (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) + (T : StarSubalgebra ℝ (Matrix κ κ ℝ)) (F : Matrix ι ι ℝ →ₗ[ℝ] Matrix κ κ ℝ) + (hF : ∀ A ∈ S, F A ∈ T) (hF' : ∀ B ∈ T, adjointMap F B ∈ S) + (A : Matrix ι ι ℝ) : average T (F A) = F (average S A) := by + apply average_unique T (F A) (F (average S A)) (hF _ (average_mem S A)) + intro B hB + rw [← map_sub, ← coordinates_inner, adjointMap_inner, coordinates_inner] + exact average_orthogonal S A (hF' B hB) + +noncomputable def commutator (L : Matrix ι ι ℝ) : + Matrix ι ι ℝ →ₗ[ℝ] Matrix ι ι ℝ where + toFun X := L*X-X*L + map_add' A B := by simp [mul_add, add_mul]; abel + map_smul' r A := by simp [smul_sub] + +lemma commutator_adjoint (L A B : Matrix ι ι ℝ) : + inner ℝ (coordinates (commutator L A)) (coordinates B) = + inner ℝ (coordinates A) (coordinates (commutator L.transpose B)) := by + simp only [coordinates_inner, commutator, LinearMap.coe_mk, AddHom.coe_mk, + Matrix.transpose_sub, Matrix.transpose_mul, sub_mul, mul_sub, Matrix.trace_sub] + rw [Matrix.trace_mul_cycle' A.transpose B L.transpose] + simp only [Matrix.mul_assoc] + +noncomputable def rotationCommutant (L : Matrix ι ι ℝ) : + StarSubalgebra ℝ (Matrix ι ι ℝ) := StarSubalgebra.centralizer ℝ {L} + +lemma rotationCommutant_mem (L A : Matrix ι ι ℝ) : + A ∈ rotationCommutant L ↔ commutator L A = 0 ∧ commutator L.transpose A = 0 := by + simp only [rotationCommutant, StarSubalgebra.mem_centralizer_iff, + Set.mem_singleton_iff, forall_eq, Matrix.star_eq_conjTranspose, + Matrix.conjTranspose_eq_transpose_of_trivial, commutator, + LinearMap.coe_mk, AddHom.coe_mk, sub_eq_zero] + +omit [DecidableEq ι] in +lemma coordinates_eq_zero_of_inner {B : Matrix ι ι ℝ} + (h : ∀ A, inner ℝ (coordinates A) (coordinates B) = 0) : B = 0 := by + have he := inner_self_eq_zero.mp (h B) + apply coordinates.injective + simpa using he + +lemma commutator_intertwines_adjoint {L : Matrix ι ι ℝ} {M : Matrix κ κ ℝ} + (F : Matrix ι ι ℝ →ₗ[ℝ] Matrix κ κ ℝ) + (hF : ∀ A, F (commutator L.transpose A) = commutator M.transpose (F A)) + (B : Matrix κ κ ℝ) : + commutator L (adjointMap F B) = adjointMap F (commutator M B) := by + apply sub_eq_zero.mp + apply coordinates_eq_zero_of_inner + intro A + rw [map_sub, inner_sub_right] + apply sub_eq_zero.mpr + rw [← adjointMap_inner] + have hM := commutator_adjoint M.transpose (F A) B + simp only [Matrix.transpose_transpose] at hM + rw [← hM, ← hF, adjointMap_inner] + have he := commutator_adjoint L.transpose A (adjointMap F B) + simpa only [Matrix.transpose_transpose] using he.symm + +lemma map_rotationCommutant {L : Matrix ι ι ℝ} {M : Matrix κ κ ℝ} + (F : Matrix ι ι ℝ →ₗ[ℝ] Matrix κ κ ℝ) + (hF : ∀ A, F (commutator L A) = commutator M (F A)) + (hF' : ∀ A, F (commutator L.transpose A) = commutator M.transpose (F A)) + {A : Matrix ι ι ℝ} (hA : A ∈ rotationCommutant L) : + F A ∈ rotationCommutant M := by + rw [rotationCommutant_mem] at hA ⊢ + constructor + · rw [← hF, hA.1, map_zero] + · rw [← hF', hA.2, map_zero] + +theorem rotation_average_natural {L : Matrix ι ι ℝ} {M : Matrix κ κ ℝ} + (F : Matrix ι ι ℝ →ₗ[ℝ] Matrix κ κ ℝ) + (hF : ∀ A, F (commutator L A) = commutator M (F A)) + (hF' : ∀ A, F (commutator L.transpose A) = commutator M.transpose (F A)) + (A : Matrix ι ι ℝ) : + average (rotationCommutant M) (F A) = F (average (rotationCommutant L) A) := by + apply average_natural + · intro B hB + exact map_rotationCommutant F hF hF' hB + · intro B hB + rw [rotationCommutant_mem] at hB ⊢ + constructor + · rw [commutator_intertwines_adjoint F hF', hB.1, map_zero] + · have hh : ∀ A, F (commutator L.transpose.transpose A) = + commutator M.transpose.transpose (F A) := by simpa using hF + rw [commutator_intertwines_adjoint F hh, hB.2, map_zero] + +end LaughlinGap.Averaging + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Basic.lean b/lean/OAI/Analysis/LaughlinGap/Basic.lean new file mode 100644 index 0000000000000000000000000000000000000000..5d956a6dd464ae24fa6e81c8943666caeab25bbd --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Basic.lean @@ -0,0 +1,1668 @@ +import Mathlib +import OAI.Analysis.Laughlin.EnergyNonnegative + +namespace OAI + +/-! Basic. -/ + +noncomputable section + + +namespace LaughlinGap +export _root_.OAI.Laughlin (Configuration State Antisymmetric pairCoefficient pairAmplitude energy SpinorVariables bracket laughlinPolynomial monomialExponent laughlinVector distanceToLaughlinSq energy_nonneg) +open scoped BigOperators + +def MainTarget : Prop := + ∃ N₀ : ℕ, 2 ≤ N₀ ∧ ∀ N : ℕ, N₀ ≤ N → + ∀ ψ : State N (3*(N-1)), Antisymmetric ψ → + (1/25 : ℝ) * distanceToLaughlinSq ψ ≤ energy ψ + +theorem distanceToLaughlinSq_le {N Q : ℕ} (ψ : State N Q) (c : ℂ) : + distanceToLaughlinSq ψ ≤ ∑ a, ‖ψ a - c * laughlinVector N Q a‖ ^ 2 := by + apply csInf_le + · refine ⟨0, ?_⟩ + rintro t ⟨d, rfl⟩ + exact Finset.sum_nonneg (fun a ha => sq_nonneg _) + · exact ⟨c, rfl⟩ + +theorem distanceToLaughlinSq_nonneg {N Q : ℕ} (ψ : State N Q) : + 0 ≤ distanceToLaughlinSq ψ := by + apply le_csInf (Set.range_nonempty _) + rintro t ⟨c, rfl⟩ + exact Finset.sum_nonneg (fun a ha => sq_nonneg _) + +theorem distanceToLaughlinSq_le_normSq {N Q : ℕ} (ψ : State N Q) : + distanceToLaughlinSq ψ ≤ ∑ a, ‖ψ a‖ ^ 2 := by + simpa using distanceToLaughlinSq_le ψ 0 + +theorem distanceToLaughlinSq_scalar {N Q : ℕ} (c : ℂ) : + distanceToLaughlinSq (fun a => c * laughlinVector N Q a) = 0 := by + apply le_antisymm _ (distanceToLaughlinSq_nonneg _) + simpa using distanceToLaughlinSq_le (fun a => c * laughlinVector N Q a) c + +theorem bracket_ne_zero {N : ℕ} {i j : Fin N} (hij : i ≠ j) : + bracket i j ≠ 0 := by + classical + intro h + let f : SpinorVariables N → ℂ := fun x => + if x = (i, false) ∨ x = (j, true) then 1 else 0 + have heval := congrArg (MvPolynomial.eval f) h + have hji : j ≠ i := Ne.symm hij + simp [bracket, f, hij, hji] at heval + +theorem laughlinPolynomial_ne_zero (N : ℕ) : laughlinPolynomial N ≠ 0 := by + classical + unfold laughlinPolynomial + apply Finset.prod_ne_zero_iff.mpr + intro i hi + apply Finset.prod_ne_zero_iff.mpr + intro j hj + split_ifs with h + · exact pow_ne_zero _ (bracket_ne_zero (ne_of_lt h)) + · exact one_ne_zero + +def spinorPermutation {N : ℕ} (σ : Equiv.Perm (Fin N)) : Equiv.Perm (SpinorVariables N) := + Equiv.prodCongr σ (Equiv.refl Bool) + +@[simp] +theorem rename_bracket {N : ℕ} (σ : Equiv.Perm (Fin N)) (i j : Fin N) : + MvPolynomial.rename (spinorPermutation σ) (bracket i j) = bracket (σ i) (σ j) := by + simp [bracket, spinorPermutation] + +theorem laughlinPolynomial_rename_swap {N : ℕ} (i j : Fin N) (hij : i ≠ j) : + MvPolynomial.rename (spinorPermutation (Equiv.swap i j)) (laughlinPolynomial N) = + -laughlinPolynomial N := by + classical + unfold laughlinPolynomial + simp only [map_prod, apply_ite, map_pow, rename_bracket, map_one] + simp_rw [← Finset.prod_filter, Finset.filter_lt_eq_Ioi] + have ha (i j : Fin N) : bracket i j ^ 3 = -(bracket j i ^ 3) := by + unfold bracket + ring + rw [(Equiv.swap i j).prod_Ioi_comp_eq_sign_mul_prod ha, Equiv.Perm.sign_swap hij] + simp + +theorem monomialExponent_swap {N Q : ℕ} (i j : Fin N) (a : Configuration N Q) : + monomialExponent (a ∘ Equiv.swap i j) = + Finsupp.mapDomain (spinorPermutation (Equiv.swap i j)) (monomialExponent a) := by + ext k + rw [Finsupp.mapDomain_equiv_apply] + simp [monomialExponent, spinorPermutation] + +theorem laughlinVector_antisymmetric (N Q : ℕ) : Antisymmetric (laughlinVector N Q) := by + classical + intro i j hij a + have hc := MvPolynomial.coeff_rename_mapDomain + (spinorPermutation (Equiv.swap i j)) (spinorPermutation (Equiv.swap i j)).injective + (laughlinPolynomial N) (monomialExponent a) + rw [← monomialExponent_swap, laughlinPolynomial_rename_swap i j hij, + MvPolynomial.coeff_neg] at hc + have hden : + (∏ k : Fin N, Real.sqrt (Nat.choose Q ((a ∘ Equiv.swap i j) k).val : ℝ)) = + ∏ k : Fin N, Real.sqrt (Nat.choose Q (a k).val : ℝ) := + Equiv.prod_comp (Equiv.swap i j) (fun k => Real.sqrt (Nat.choose Q (a k).val : ℝ)) + simp only [laughlinVector, hden] + rw [← neg_div] + congr 1 + exact (neg_eq_iff_eq_neg.mp hc) + +def particleWeight {N : ℕ} (k : Fin N) : SpinorVariables N → ℕ := + fun ib => if ib.1 = k then 1 else 0 + +theorem particleWeight_eq {N : ℕ} (k : Fin N) (d : SpinorVariables N →₀ ℕ) : + Finsupp.weight (particleWeight k) d = d (k, false) + d (k, true) := by + classical + rw [Finsupp.weight_apply, Finsupp.sum_fintype _ _ (by intro; simp)] + simp [particleWeight, Fintype.sum_prod_type, mul_ite, Finset.sum_add_distrib, add_comm] + +private theorem particle_pair_count {N : ℕ} (k : Fin N) : + (∑ i : Fin N, ∑ j : Fin N, + if i < j then (if i = k then 1 else 0) + (if j = k then 1 else 0) else 0) = N - 1 := by + classical + have hterm (i j : Fin N) : + (if i < j then (if i = k then 1 else 0) + (if j = k then 1 else 0) else 0 : ℕ) = + (if i = k then if i < j then 1 else 0 else 0) + + (if j = k then if i < j then 1 else 0 else 0) := by + split_ifs <;> simp + simp_rw [hterm, Finset.sum_add_distrib] + simp only [Finset.sum_ite_irrel, Finset.sum_const_zero, + Finset.sum_ite_eq', Finset.mem_univ, ↓reduceIte] + rw [← Finset.sum_add_distrib] + have hlt (i : Fin N) : + (if k < i then 1 else 0) + (if i < k then 1 else 0) = (if i = k then 0 else 1 : ℕ) := by + rcases lt_trichotomy i k with hi | rfl | hi + · simp [hi, not_lt.mpr (le_of_lt hi), ne_of_lt hi] + · simp + · simp [hi, not_lt.mpr (le_of_lt hi), ne_of_gt hi] + simp_rw [hlt] + simp [Finset.sum_ite, Finset.filter_ne'] + +theorem bracket_isWeightedHomogeneous {N : ℕ} (k i j : Fin N) : + MvPolynomial.IsWeightedHomogeneous (particleWeight k) (bracket i j) + ((if i = k then 1 else 0) + (if j = k then 1 else 0)) := by + have h1 := (MvPolynomial.isWeightedHomogeneous_X (R := ℂ) (particleWeight k) (i, false)).mul + (MvPolynomial.isWeightedHomogeneous_X (R := ℂ) (particleWeight k) (j, true)) + have h2 := (MvPolynomial.isWeightedHomogeneous_X (R := ℂ) (particleWeight k) (j, false)).mul + (MvPolynomial.isWeightedHomogeneous_X (R := ℂ) (particleWeight k) (i, true)) + simp only [particleWeight] at h1 h2 + exact h1.sub (by simpa only [add_comm] using h2) + +theorem laughlinPolynomial_isWeightedHomogeneous (N : ℕ) (k : Fin N) : + MvPolynomial.IsWeightedHomogeneous (particleWeight k) (laughlinPolynomial N) (3 * (N - 1)) := by + classical + have hcount : (∑ i : Fin N, ∑ j : Fin N, + if i < j then 3 * ((if i = k then 1 else 0) + (if j = k then 1 else 0)) else 0) = + 3 * (N - 1) := by + have hterm (i j : Fin N) : + (if i < j then 3 * ((if i = k then 1 else 0) + (if j = k then 1 else 0)) else 0) = + 3 * (if i < j then ((if i = k then 1 else 0) + (if j = k then 1 else 0)) else 0 : ℕ) := by + split_ifs <;> simp + simp_rw [hterm, ← Finset.mul_sum] + rw [particle_pair_count] + rw [← hcount] + unfold laughlinPolynomial + apply MvPolynomial.IsWeightedHomogeneous.prod + intro i hi + apply MvPolynomial.IsWeightedHomogeneous.prod + intro j hj + by_cases hij : i < j + · simp only [ite_eq_left hij] + simpa only [nsmul_eq_mul, Nat.cast_ofNat] using (bracket_isWeightedHomogeneous k i j).pow 3 + · simp only [ite_eq_right hij] + exact MvPolynomial.isWeightedHomogeneous_one ℂ (particleWeight k) + +theorem laughlinPolynomial_support_exponents (N : ℕ) (d : SpinorVariables N →₀ ℕ) + (hd : (laughlinPolynomial N).coeff d ≠ 0) : + ∃ a : Configuration N (3 * (N - 1)), monomialExponent a = d := by + have hdeg (k : Fin N) : d (k, false) + d (k, true) = 3 * (N - 1) := by + simpa only [particleWeight_eq] using (laughlinPolynomial_isWeightedHomogeneous N k) hd + let a : Configuration N (3 * (N - 1)) := fun k => + ⟨d (k, true), by have h := hdeg k; omega⟩ + refine ⟨a, ?_⟩ + ext ⟨k, b⟩ + cases b + · simp only [monomialExponent, Finsupp.onFinset_apply, Bool.false_eq_true, ↓reduceIte] + have h := hdeg k + change 3 * (N - 1) - d (k, true) = d (k, false) + omega + · rfl + +theorem laughlinVector_ne_zero (N : ℕ) : laughlinVector N (3 * (N - 1)) ≠ 0 := by + classical + have hex : ∃ d, (laughlinPolynomial N).coeff d ≠ 0 := by + by_contra! h + apply laughlinPolynomial_ne_zero N + apply MvPolynomial.ext + intro d + simpa using h d + obtain ⟨d, hd⟩ := hex + obtain ⟨a, ha⟩ := laughlinPolynomial_support_exponents N d hd + have hden : (∏ k : Fin N, Real.sqrt ((3 * (N - 1)).choose (a k).val : ℝ)) ≠ 0 := by + apply Finset.prod_ne_zero_iff.mpr + intro k hk + apply ne_of_gt + apply Real.sqrt_pos.mpr + exact_mod_cast Nat.choose_pos (Nat.le_of_lt_succ (a k).isLt) + intro hzero + have hz := congrFun hzero a + have hc : laughlinVector N (3 * (N - 1)) a ≠ 0 := by + unfold laughlinVector + rw [ha] + exact div_ne_zero hd (Complex.ofReal_ne_zero.mpr hden) + exact hc hz + +abbrev TensorHilbert (N Q : ℕ) := EuclideanSpace ℂ (Configuration N Q) + +noncomputable def toTensorHilbert {N Q : ℕ} (ψ : State N Q) : TensorHilbert N Q := + WithLp.toLp 2 ψ + +noncomputable def laughlinLine (N Q : ℕ) : Submodule ℂ (TensorHilbert N Q) := + Submodule.span ℂ {toTensorHilbert (laughlinVector N Q)} + +noncomputable def laughlinProjection (N Q : ℕ) : TensorHilbert N Q →L[ℂ] TensorHilbert N Q := + (laughlinLine N Q).starProjection + +@[simp] +theorem toTensorHilbert_apply {N Q : ℕ} (ψ : State N Q) (a : Configuration N Q) : + toTensorHilbert ψ a = ψ a := rfl + +@[simp] +theorem toTensorHilbert_norm_sq {N Q : ℕ} (ψ : State N Q) : + ‖toTensorHilbert ψ‖ ^ 2 = ∑ a, ‖ψ a‖ ^ 2 := + EuclideanSpace.norm_sq_eq _ + +theorem distanceToLaughlinSq_eq_projection {N Q : ℕ} (ψ : State N Q) : + distanceToLaughlinSq ψ = + ‖toTensorHilbert ψ - laughlinProjection N Q (toTensorHilbert ψ)‖ ^ 2 := by + classical + let x := toTensorHilbert ψ + let L := toTensorHilbert (laughlinVector N Q) + let K := laughlinLine N Q + have hmem : K.starProjection x ∈ Submodule.span ℂ {L} := + K.starProjection_apply_mem x + obtain ⟨c, hc⟩ := Submodule.mem_span_singleton.mp hmem + have hnorm (c : ℂ) : ‖x - c • L‖ ^ 2 = + ∑ a, ‖ψ a - c * laughlinVector N Q a‖ ^ 2 := by + rw [EuclideanSpace.norm_sq_eq] + rfl + change distanceToLaughlinSq ψ = ‖x - K.starProjection x‖ ^ 2 + apply le_antisymm + · rw [← hc, hnorm] + exact distanceToLaughlinSq_le ψ c + · apply le_csInf (Set.range_nonempty _) + rintro _ ⟨d, rfl⟩ + change ‖x - K.starProjection x‖ ^ 2 ≤ ∑ a, ‖ψ a - d * laughlinVector N Q a‖ ^ 2 + rw [← hnorm d] + have hd : d • L ∈ K := + Submodule.mem_span_singleton.mpr ⟨d, rfl⟩ + have hmin : ‖x - K.starProjection x‖ ≤ ‖x - d • L‖ := by + rw [Submodule.starProjection_minimal] + exact ciInf_le ⟨0, fun t ht => by obtain ⟨y, rfl⟩ := ht; positivity⟩ + (⟨d • L, hd⟩ : K) + exact pow_le_pow_left₀ (norm_nonneg _) hmin 2 + +theorem distanceToLaughlinSq_eq_quadraticForm {N Q : ℕ} (ψ : State N Q) : + distanceToLaughlinSq ψ = + (inner ℂ (toTensorHilbert ψ) + (toTensorHilbert ψ - laughlinProjection N Q (toTensorHilbert ψ))).re := by + rw [distanceToLaughlinSq_eq_projection] + let K := laughlinLine N Q + let x := toTensorHilbert ψ + change ‖x - K.starProjection x‖ ^ 2 = + (inner ℂ x (x - K.starProjection x)).re + have h := Kᗮ.re_inner_starProjection_eq_normSq x + change (inner ℂ (Kᗮ.starProjection x) x).re = ‖Kᗮ.starProjection x‖ ^ 2 at h + rw [Submodule.starProjection_orthogonal_val] at h + exact h.symm.trans (inner_re_symm (𝕜 := ℂ) _ _) + +section PairNormalization +open Polynomial + +private noncomputable def euler (P : ℝ[X]) : ℝ[X] := P.derivative * X + +private theorem coeff_euler (P : ℝ[X]) (n : ℕ) : + (euler P).coeff n = (n : ℝ) * P.coeff n := by + cases n with + | zero => simp [euler] + | succ n => simp [euler, coeff_derivative, mul_comm] + +private theorem weighted_binomial_polynomial_identity (n : ℕ) : + let F : ℝ[X] := (X + 1) ^ (n + 2) + euler (euler F) * F + F * euler (euler F) - 2 * (euler F * euler F) = + C (2 * (n + 2 : ℝ)) * X * (X + 1) ^ (2 * n + 2) := by + dsimp only + have hd : ((X + 1) ^ (n + 2) : ℝ[X]).derivative = + C ((n : ℝ) + 2) * (X + 1) ^ (n + 1) := by + rw [show n + 2 = (n + 1) + 1 by omega, derivative_pow_succ] + simp only [Nat.cast_add, Nat.cast_one, derivative_add, derivative_X, derivative_one, + add_zero, mul_one] + congr 2 + ring + have hd' : ((X + 1) ^ (n + 1) : ℝ[X]).derivative = + C ((n : ℝ) + 1) * (X + 1) ^ n := by + simp [derivative_pow_succ, derivative_add] + simp only [euler, derivative_mul, hd, derivative_X] + simp only [derivative_C, hd', zero_mul, zero_add, mul_one] + simp only [show 2 * n + 2 = n + n + 2 by omega, pow_add, pow_two, map_mul, + map_add, map_ofNat, map_one] + ring + +theorem weighted_binomial_antidiagonal (Q : ℕ) (hQ : 2 ≤ Q) (p : ℕ) : + (∑ ij ∈ Finset.HasAntidiagonal.antidiagonal (p + 1), + ((ij.1 : ℝ) - ij.2) ^ 2 * (Q.choose ij.1 : ℝ) * Q.choose ij.2) = + 2 * Q * ((2 * Q - 2).choose p : ℝ) := by + obtain ⟨n, rfl⟩ : ∃ n, Q = n + 2 := ⟨Q - 2, by omega⟩ + have heq : (∑ ij ∈ Finset.HasAntidiagonal.antidiagonal (p + 1), + ((ij.1 : ℝ) - ij.2) ^ 2 * ((n + 2).choose ij.1 : ℝ) * (n + 2).choose ij.2) = + ((euler (euler ((X + 1) ^ (n + 2) : ℝ[X]))) * (X + 1) ^ (n + 2) + + (X + 1) ^ (n + 2) * (euler (euler ((X + 1) ^ (n + 2) : ℝ[X]))) - + 2 * (euler ((X + 1) ^ (n + 2)) * euler ((X + 1) ^ (n + 2)))).coeff (p + 1) := by + simp only [coeff_add, coeff_sub, coeff_ofNat_mul, coeff_mul, coeff_euler, + coeff_X_add_one_pow] + rw [← Finset.sum_add_distrib, Finset.mul_sum, ← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro ij hij + ring + rw [heq, weighted_binomial_polynomial_identity] + rw [mul_assoc, coeff_C_mul, coeff_X_mul, coeff_X_add_one_pow] + congr 2 + norm_cast + +theorem pairCoefficient_sq (Q p : ℕ) (hQ : 2 ≤ Q) (hp : p < 2 * Q - 1) + (x y : Fin (Q + 1)) : + pairCoefficient Q p x y ^ 2 = + if x.val + y.val = p + 1 then + ((x.val : ℝ) - y.val) ^ 2 * (Q.choose x.val : ℝ) * Q.choose y.val / + (2 * Q * ((2 * Q - 2).choose p : ℝ)) + else 0 := by + have hQr : (Q : ℝ) ≠ 0 := by positivity + have hch : ((2 * Q - 2).choose p : ℝ) ≠ 0 := by + exact_mod_cast (Nat.choose_pos (show p ≤ 2 * Q - 2 by omega)).ne' + have hx : (x.val.factorial : ℝ) ≠ 0 := by positivity + have hy : (y.val.factorial : ℝ) ≠ 0 := by positivity + have hpf : (p.factorial : ℝ) ≠ 0 := by positivity + have hrad : + (((Q.descFactorial x.val : ℝ) * (Q.descFactorial y.val : ℝ) * (p.factorial : ℝ)) / + ((Q : ℝ) * ((2*Q-2).descFactorial p : ℝ) * + (x.val.factorial : ℝ) * (y.val.factorial : ℝ))) = + ((Q.choose x.val : ℝ) * Q.choose y.val) / + ((Q : ℝ) * ((2 * Q - 2).choose p : ℝ)) := by + simp only [Nat.descFactorial_eq_factorial_mul_choose, Nat.cast_mul] + field_simp + unfold pairCoefficient + split_ifs with hs + · rw [hrad, div_pow, mul_pow, Real.sq_sqrt (by positivity), Real.sq_sqrt (by norm_num)] + ring + · simp + +theorem pairCoefficient_swap (Q p : ℕ) (x y : Fin (Q + 1)) : + pairCoefficient Q p y x = -pairCoefficient Q p x y := by + unfold pairCoefficient + by_cases hs : x.val + y.val = p + 1 + · simp only [hs, Nat.add_comm y.val x.val, ↓reduceIte] + simp only [mul_comm, mul_left_comm, mul_assoc] + ring + · simp [hs, Nat.add_comm] + +private theorem sum_fin_pair_on_antidiagonal (Q n : ℕ) (f : ℕ → ℕ → ℝ) + (hf : ∀ x y, (Q < x ∨ Q < y) → f x y = 0) : + (∑ x : Fin (Q + 1), ∑ y : Fin (Q + 1), + if x.val + y.val = n then f x.val y.val else 0) = + ∑ ij ∈ Finset.HasAntidiagonal.antidiagonal n, f ij.1 ij.2 := by + classical + rw [Fin.sum_univ_eq_sum_range (fun x => ∑ y : Fin (Q + 1), + if x + y.val = n then f x y.val else 0)] + have hs (x : ℕ) := Fin.sum_univ_eq_sum_range + (fun y => if x + y = n then f x y else 0) (Q + 1) + simp_rw [hs] + rw [← Finset.sum_product'] + rw [← Finset.sum_filter] + apply Finset.sum_subset + · intro ij hij + simpa using (Finset.mem_filter.mp hij).2 + · intro ij hij hnot + simp only [Finset.mem_filter, Finset.mem_product, Finset.mem_range] at hnot + have heq : ij.1 + ij.2 = n := by simpa using hij + apply hf + omega + +theorem pairCoefficient_sum_sq (Q p : ℕ) (hQ : 2 ≤ Q) (hp : p < 2 * Q - 1) : + (∑ x : Fin (Q + 1), ∑ y : Fin (Q + 1), pairCoefficient Q p x y ^ 2) = 1 := by + simp_rw [pairCoefficient_sq Q p hQ hp] + have hch : ((2 * Q - 2).choose p : ℝ) ≠ 0 := by + exact_mod_cast (Nat.choose_pos (show p ≤ 2 * Q - 2 by omega)).ne' + have hQr : (Q : ℝ) ≠ 0 := by positivity + rw [sum_fin_pair_on_antidiagonal Q (p + 1) + (fun x y => ((x : ℝ) - y) ^ 2 * (Q.choose x : ℝ) * Q.choose y / + (2 * Q * ((2 * Q - 2).choose p : ℝ)))] + · rw [← Finset.sum_div, weighted_binomial_antidiagonal Q hQ p] + field_simp + · intro x y hxy + rcases hxy with hx | hy + · simp [Nat.choose_eq_zero_of_lt hx] + · simp [Nat.choose_eq_zero_of_lt hy] + +theorem pairCoefficient_sum_mul_of_ne (Q p r : ℕ) (hpr : p ≠ r) : + (∑ x : Fin (Q + 1), ∑ y : Fin (Q + 1), + pairCoefficient Q p x y * pairCoefficient Q r x y) = 0 := by + apply Finset.sum_eq_zero + intro x hx + apply Finset.sum_eq_zero + intro y hy + unfold pairCoefficient + split_ifs <;> simp_all + +abbrev PairHilbert (Q : ℕ) := EuclideanSpace ℂ (Fin (Q + 1) × Fin (Q + 1)) + +noncomputable def pairVector (Q p : ℕ) : PairHilbert Q := + WithLp.toLp 2 (fun xy => (pairCoefficient Q p xy.1 xy.2 : ℂ)) + +theorem pairVector_inner (Q p r : ℕ) : + inner ℂ (pairVector Q p) (pairVector Q r) = + ((∑ x : Fin (Q + 1), ∑ y : Fin (Q + 1), + pairCoefficient Q p x y * pairCoefficient Q r x y : ℝ) : ℂ) := by + simp [pairVector, PiLp.inner_apply, Fintype.sum_prod_type, mul_comm] + +theorem pairVector_orthonormal (Q : ℕ) (hQ : 2 ≤ Q) : + Orthonormal ℂ (fun p : Fin (2 * Q - 1) => pairVector Q p.val) := by + rw [orthonormal_iff_ite] + intro p r + rw [pairVector_inner] + split_ifs with hpr + · subst r + rw [show (∑ x : Fin (Q + 1), ∑ y : Fin (Q + 1), + pairCoefficient Q p.val x y * pairCoefficient Q p.val x y) = 1 by + simpa only [pow_two] using pairCoefficient_sum_sq Q p.val hQ p.isLt] + rfl + · rw [pairCoefficient_sum_mul_of_ne Q p.val r.val (fun h => hpr (Fin.ext h))] + rfl + +noncomputable def pairChannel (Q : ℕ) : Submodule ℂ (PairHilbert Q) := + Submodule.span ℂ (Set.range (fun p : Fin (2 * Q - 1) => pairVector Q p.val)) + +private theorem projection_span_orthonormal_eq_sum + {E ι : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] + [FiniteDimensional ℂ E] [Fintype ι] (v : ι → E) (hv : Orthonormal ℂ v) (x : E) : + (Submodule.span ℂ (Set.range v)).starProjection x = + ∑ p, inner ℂ (v p) x • v p := by + classical + apply Submodule.eq_starProjection_of_mem_of_inner_eq_zero + · apply Submodule.sum_mem + intro p hp + exact Submodule.smul_mem _ _ (Submodule.subset_span ⟨p, rfl⟩) + · intro w hw + induction hw using Submodule.span_induction with + | mem w hw => + obtain ⟨p, rfl⟩ := hw + rw [inner_sub_left, hv.inner_left_fintype, inner_conj_symm] + simp + | zero => simp + | add u v hu hv ihu ihv => simp [inner_add_right, ihu, ihv] + | smul a w hw ih => simp [inner_smul_right, ih] + +theorem pairChannel_projection_eq (Q : ℕ) (hQ : 2 ≤ Q) (x : PairHilbert Q) : + (pairChannel Q).starProjection x = + ∑ p : Fin (2 * Q - 1), inner ℂ (pairVector Q p.val) x • pairVector Q p.val := + projection_span_orthonormal_eq_sum _ (pairVector_orthonormal Q hQ) x + +theorem pairChannel_projection_norm_sq (Q : ℕ) (hQ : 2 ≤ Q) (x : PairHilbert Q) : + ‖(pairChannel Q).starProjection x‖ ^ 2 = + ∑ p : Fin (2 * Q - 1), ‖inner ℂ (pairVector Q p.val) x‖ ^ 2 := by + rw [pairChannel_projection_eq Q hQ] + rw [@norm_sq_eq_re_inner ℂ] + rw [(pairVector_orthonormal Q hQ).inner_sum] + change (∑ p : Fin (2 * Q - 1), + (starRingEnd ℂ) (inner ℂ (pairVector Q p.val) x) * inner ℂ (pairVector Q p.val) x).re = _ + rw [Complex.re_sum] + apply Finset.sum_congr rfl + intro p hp + rw [mul_comm, Complex.mul_conj, Complex.ofReal_re, Complex.normSq_eq_norm_sq] + +end PairNormalization + +noncomputable def pairSlice {N Q : ℕ} (ψ : State N Q) + (i j : Fin N) (a : Configuration N Q) : PairHilbert Q := + WithLp.toLp 2 (fun xy => ψ (Function.update (Function.update a i xy.1) j xy.2)) + +theorem pairAmplitude_eq_inner {N Q : ℕ} (ψ : State N Q) + (i j : Fin N) (p : ℕ) (a : Configuration N Q) : + pairAmplitude ψ i j p a = inner ℂ (pairVector Q p) (pairSlice ψ i j a) := by + simp [pairAmplitude, pairSlice, pairVector, PiLp.inner_apply, Fintype.sum_prod_type, + mul_comm] + +theorem energy_eq_sum_pair_projections {N Q : ℕ} (hQ : 2 ≤ Q) (ψ : State N Q) : + energy ψ = ∑ i : Fin N, ∑ j : Fin N, if i < j then + ∑ a : Configuration N Q, if a i = 0 ∧ a j = 0 then + ‖(pairChannel Q).starProjection (pairSlice ψ i j a)‖ ^ 2 else 0 + else 0 := by + classical + unfold energy + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + split_ifs with hij + · rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro a ha + by_cases hanchor : a i = 0 ∧ a j = 0 + · simp only [hanchor, and_self, ↓reduceIte] + rw [pairChannel_projection_norm_sq Q hQ] + rw [Fin.sum_univ_eq_sum_range + (fun p : ℕ => ‖inner ℂ (pairVector Q p) (pairSlice ψ i j a)‖ ^ 2)] + simp_rw [pairAmplitude_eq_inner] + · simp [hanchor] + · rfl + +theorem kernel_distance_of_square_lower_bound + {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] + [FiniteDimensional ℂ E] (T : E →ₗ[ℂ] E) (hT : T.IsPositive) + (γ : ℝ) (hsq : ∀ x : E, γ * (inner ℂ x (T x)).re ≤ ‖T x‖ ^ 2) + (x : E) : + ∃ y : E, T y = 0 ∧ γ * ‖x - y‖ ^ 2 ≤ (inner ℂ x (T x)).re := by + classical + let b := hT.isSymmetric.eigenvectorBasis rfl + let lam := hT.isSymmetric.eigenvalues rfl + have hdiag (v : E) (i : Fin (Module.finrank ℂ E)) : + b.repr (T v) i = (lam i : ℂ) * b.repr v i := + hT.isSymmetric.eigenvectorBasis_apply_self_apply rfl v i + have hlambda (i : Fin (Module.finrank ℂ E)) : lam i = 0 ∨ γ ≤ lam i := by + by_cases hi : lam i = 0 + · exact Or.inl hi + right + have hnonneg : 0 ≤ lam i := hT.nonneg_eigenvalues rfl i + have h := hsq (b i) + have heig : T (b i) = (lam i : ℂ) • b i := + hT.isSymmetric.apply_eigenvectorBasis rfl i + rw [heig, inner_smul_right, b.inner_eq_one, mul_one] at h + simp only [Complex.ofReal_re, norm_smul, Complex.norm_real, Real.norm_eq_abs, + b.norm_eq_one, mul_one, sq_abs] at h + exact le_of_mul_le_mul_right (by simpa only [pow_two] using h) (lt_of_le_of_ne hnonneg (Ne.symm hi)) + let c : EuclideanSpace ℂ (Fin (Module.finrank ℂ E)) := + WithLp.toLp 2 (fun i => if lam i = 0 then b.repr x i else 0) + let y := b.repr.symm c + have hyrepr : b.repr y = c := b.repr.apply_symm_apply c + have hTy : T y = 0 := by + apply b.repr.injective + ext i + rw [hdiag, hyrepr, map_zero] + change (lam i : ℂ) * (if lam i = 0 then b.repr x i else 0) = 0 + split_ifs with hi <;> simp [hi] + have henergy : (inner ℂ x (T x)).re = ∑ i, lam i * ‖b.repr x i‖ ^ 2 := by + rw [← b.repr.inner_map_map, PiLp.inner_apply, Complex.re_sum] + apply Finset.sum_congr rfl + intro i hi + rw [hdiag, RCLike.inner_apply, mul_assoc, Complex.mul_conj, Complex.normSq_eq_norm_sq] + norm_cast + refine ⟨y, hTy, ?_⟩ + rw [henergy, ← b.repr.norm_map (x - y), EuclideanSpace.norm_sq_eq, Finset.mul_sum] + apply Finset.sum_le_sum + intro i hi + simp only [map_sub, hyrepr, PiLp.sub_apply] + change γ * ‖b.repr x i - (if lam i = 0 then b.repr x i else 0)‖ ^ 2 ≤ _ + obtain hzero | hge := hlambda i + · simp [hzero] + · by_cases hzero : lam i = 0 + · simp [hzero] + · simp only [hzero, ↓reduceIte, sub_zero] + exact mul_le_mul_of_nonneg_right hge (sq_nonneg _) + +theorem kernel_projection_bound_of_square_lower_bound + {E : Type*} [NormedAddCommGroup E] [InnerProductSpace ℂ E] + [FiniteDimensional ℂ E] (T : E →ₗ[ℂ] E) (hT : T.IsPositive) + (γ : ℝ) (hγ : 0 ≤ γ) + (hsq : ∀ x : E, γ * (inner ℂ x (T x)).re ≤ ‖T x‖ ^ 2) + (x : E) : + γ * ‖x - (LinearMap.ker T).starProjection x‖ ^ 2 ≤ + (inner ℂ x (T x)).re := by + obtain ⟨y, hy, hbound⟩ := kernel_distance_of_square_lower_bound T hT γ hsq x + have hmin : ‖x - (LinearMap.ker T).starProjection x‖ ≤ ‖x - y‖ := by + rw [Submodule.starProjection_minimal] + exact ciInf_le ⟨0, fun t ht => by obtain ⟨z, rfl⟩ := ht; positivity⟩ + (⟨y, hy⟩ : LinearMap.ker T) + exact (mul_le_mul_of_nonneg_left (pow_le_pow_left₀ (norm_nonneg _) hmin 2) hγ).trans + hbound + +theorem orthonormal_rows_coordinate_sq_le + {ι κ τ : Type*} [Fintype ι] [Fintype κ] [Fintype τ] + (S : ι → EuclideanSpace ℂ κ) (hS : Orthonormal ℂ S) (A : κ → τ → ℂ) : + (∑ r, ∑ a, ‖∑ b, star (S r b) * A b a‖ ^ 2) ≤ + ∑ b, ∑ a, ‖A b a‖ ^ 2 := by + classical + rw [Finset.sum_comm] + calc + (∑ a, ∑ r, ‖∑ b, star (S r b) * A b a‖ ^ 2) ≤ + ∑ a, ∑ b, ‖A b a‖ ^ 2 := by + apply Finset.sum_le_sum + intro a ha + let v : EuclideanSpace ℂ κ := WithLp.toLp 2 (fun b => A b a) + have h := hS.sum_inner_products_le (s := Finset.univ) v + simpa [PiLp.inner_apply, RCLike.inner_apply', EuclideanSpace.norm_sq_eq, v, mul_comm] using h + _ = ∑ b, ∑ a, ‖A b a‖ ^ 2 := Finset.sum_comm + +theorem orthonormal_rows_sq_le + {ι κ τ : Type*} [Fintype ι] [Fintype κ] [Fintype τ] + (S : ι → EuclideanSpace ℂ κ) (hS : Orthonormal ℂ S) + (A : κ → EuclideanSpace ℂ τ) : + (∑ r, ‖∑ b, star (S r b) • A b‖ ^ 2) ≤ ∑ b, ‖A b‖ ^ 2 := by + simpa [EuclideanSpace.norm_sq_eq, WithLp.ofLp_sum, Finset.sum_apply] + using orthonormal_rows_coordinate_sq_le S hS (fun b a => A b a) + +def OrbitalTriple (D : ℕ) := + {t : ℕ × ℕ × ℕ // t.1 + t.2.1 + t.2.2 = D ∧ t.2.1 < t.2.2} + +def orbitalTripleEquiv (D : ℕ) : + (Σ n : Fin (D + 1), Fin ((n.val + 1) / 2)) ≃ OrbitalTriple D where + toFun a := ⟨(D - a.1.val, a.2.val, a.1.val - a.2.val), by + have hn := a.1.isLt + have hj := a.2.isLt + constructor <;> dsimp only <;> omega⟩ + invFun t := ⟨⟨t.val.2.1 + t.val.2.2, by have h := t.property; omega⟩, + ⟨t.val.2.1, by have h := t.property; dsimp only; omega⟩⟩ + left_inv a := by + have hn := a.1.isLt + have hj := a.2.isLt + have he : a.2.val + (a.1.val - a.2.val) = a.1.val := by omega + apply Sigma.ext + · exact Fin.ext he + · exact (Fin.heq_ext_iff (congrArg (fun n => (n + 1) / 2) he)).mpr rfl + right_inv t := by + have h := t.property + apply Subtype.ext + apply Prod.ext + · simp only + omega + · apply Prod.ext + · rfl + · simp only + omega + +noncomputable instance (D : ℕ) : Fintype (OrbitalTriple D) := + Fintype.ofEquiv _ (orbitalTripleEquiv D) + +theorem orbitalTriple_card (D : ℕ) : + Fintype.card (OrbitalTriple D) = + ∑ n ∈ Finset.range (D + 1), (n + 1) / 2 := by + rw [← Fintype.card_congr (orbitalTripleEquiv D), Fintype.card_sigma] + simp only [Fintype.card_fin] + exact Fin.sum_univ_eq_sum_range (fun n : ℕ => (n + 1) / 2) (D + 1) + +theorem retained_orbitalTriple_count : + (∑ D ∈ Finset.Icc 1 23, Fintype.card (OrbitalTriple D)) = 1222 := by + simp_rw [orbitalTriple_card] + norm_num [Finset.sum_Icc_succ_top, Finset.sum_range_succ] + +noncomputable def gammaStar : ℝ := 4616733319001 / 10 ^ 14 + +theorem final_margin_arithmetic : + (1 : ℝ) - 93527408868499 / 10 ^ 14 - 61 / 4096 - + 1222 * (3 / 10 ^ 6) = gammaStar := by + norm_num [gammaStar] + +theorem one_div_twenty_five_lt_gammaStar : (1 / 25 : ℝ) < gammaStar := by + norm_num [gammaStar] + +theorem bracket_irreducible {N : ℕ} {i j : Fin N} (hij : i ≠ j) : + Irreducible (bracket i j) := by + classical + let d₁ : SpinorVariables N →₀ ℕ := Finsupp.single (i, false) 1 + Finsupp.single (j, true) 1 + let d₂ : SpinorVariables N →₀ ℕ := Finsupp.single (j, false) 1 + Finsupp.single (i, true) 1 + have h₁ : d₁ (i, false) = 1 := by simp [d₁] + have h₂ : d₂ (i, false) = 0 := by simp [d₂, hij] + have hne : d₁ ≠ d₂ := by intro he; have := congrFun (congrArg DFunLike.coe he) (i, false); omega + have heq : bracket i j = MvPolynomial.monomial d₁ (1 : ℂ) + MvPolynomial.monomial d₂ (-1 : ℂ) := by + simp [bracket, d₁, d₂, MvPolynomial.X, sub_eq_add_neg] + have hcoeff (d) : (bracket i j).coeff d = (if d₁ = d then 1 else 0) + + (if d₂ = d then -1 else 0) := by + by_cases h : d₂ = d <;> simp [heq, MvPolynomial.coeff_monomial, h] + have hsupp : (bracket i j).support = {d₁, d₂} := by + ext d + simp only [MvPolynomial.mem_support_iff, hcoeff, Finset.mem_insert, Finset.mem_singleton] + rcases eq_or_ne d d₁ with rfl | h₁ + · simp [hne.symm] + rcases eq_or_ne d d₂ with rfl | h₂ + · simp [hne] + simp [h₁, h₂, h₁.symm, h₂.symm] + apply MvPolynomial.irreducible_of_disjoint_support + · exact ⟨d₁, by simp [hsupp], d₂, by simp [hsupp], hne⟩ + · rw [hsupp]; exact Finset.mem_insert_self .. + · exact h₁ + · rw [hsupp] + intro a ha b hb hab + simp only [Finset.mem_coe, Finset.mem_insert, Finset.mem_singleton] at ha hb + have hd : Disjoint d₁.support d₂.support := by + simp [d₁, d₂, Finsupp.support_add_eq, hij, Ne.symm hij] + rcases ha with rfl | rfl <;> rcases hb with rfl | rfl + · exact (hab rfl).elim + · exact hd + · exact hd.symm + · exact (hab rfl).elim + · intro r hr + apply isUnit_of_dvd_one + simpa [hcoeff, hne, Ne.symm hne] using hr d₁ + +theorem bracket_not_dvd {N : ℕ} {i j k l : Fin N} (hij : i < j) (hkl : k < l) + (hne : (i, j) ≠ (k, l)) : ¬bracket k l ∣ bracket i j := by + classical + have hex : (i ≠ k ∧ i ≠ l) ∨ (j ≠ k ∧ j ≠ l) := by + by_contra! h + have hi : i = k ∨ i = l := by tauto + have hj : j = k ∨ j = l := by tauto + rcases hi with rfl | rfl <;> rcases hj with rfl | rfl + · exact (lt_irrefl _ hij) + · exact hne rfl + · exact (not_lt_of_ge (le_of_lt hkl) hij) + · exact (lt_irrefl _ hij) + let f (m : Fin N) : SpinorVariables N → ℂ := fun ib => + if ib.2 then (if ib.1 = m then 0 else 1) else (if ib.1 = m then 1 else 0) + intro hdiv + obtain ⟨g, hg⟩ := hdiv + rcases hex with hi | hj + · have h := congrArg (MvPolynomial.eval (f i)) hg + simp [bracket, f, Ne.symm hi.1, Ne.symm hi.2, (ne_of_lt hij).symm] at h + · have h := congrArg (MvPolynomial.eval (f j)) hg + simp [bracket, f, Ne.symm hj.1, Ne.symm hj.2, ne_of_lt hij] at h + +theorem laughlinPolynomial_dvd_of_bracket_cubes_dvd {N : ℕ} + (F : MvPolynomial (SpinorVariables N) ℂ) + (h : ∀ i j : Fin N, i < j → bracket i j ^ 3 ∣ F) : + laughlinPolynomial N ∣ F := by + classical + have heq : laughlinPolynomial N = + ∏ ij ∈ (Finset.univ : Finset (Fin N × Fin N)).filter (fun ij => ij.1 < ij.2), + bracket ij.1 ij.2 ^ 3 := by + simp only [Finset.prod_filter, Fintype.prod_prod_type, laughlinPolynomial] + rw [heq] + apply Finset.prod_dvd_of_isRelPrime + · intro ij hij kl hkl hne + have hij' := (Finset.mem_filter.mp hij).2 + have hkl' := (Finset.mem_filter.mp hkl).2 + exact ((bracket_irreducible (ne_of_lt hij')).isRelPrime_iff_not_dvd.mpr + (bracket_not_dvd hkl' hij' hne.symm)).pow + · intro ij hij + exact h ij.1 ij.2 (Finset.mem_filter.mp hij).2 + +theorem isHomogeneous_of_particle_homogeneous {N Q : ℕ} + (F : MvPolynomial (SpinorVariables N) ℂ) + (h : ∀ k : Fin N, MvPolynomial.IsWeightedHomogeneous (particleWeight k) F Q) : + F.IsHomogeneous (N * Q) := by + classical + intro d hd + have hdeg (k : Fin N) : d (k, false) + d (k, true) = Q := by + simpa only [particleWeight_eq] using h k hd + rw [Finsupp.weight_apply, Finsupp.sum_fintype _ _ (by intro; simp)] + simp only [Pi.one_apply, smul_eq_mul, mul_one, Fintype.sum_prod_type] + simp_rw [Fintype.sum_bool, add_comm (d (_, true)), hdeg] + simp + +theorem laughlinPolynomial_totalDegree (N : ℕ) : + (laughlinPolynomial N).totalDegree = N * (3 * (N - 1)) := + (isHomogeneous_of_particle_homogeneous _ + (laughlinPolynomial_isWeightedHomogeneous N)).totalDegree (laughlinPolynomial_ne_zero N) + +theorem eq_scalar_laughlin_of_bracket_cubes_dvd {N : ℕ} + (F : MvPolynomial (SpinorVariables N) ℂ) + (hdeg : ∀ k : Fin N, + MvPolynomial.IsWeightedHomogeneous (particleWeight k) F (3 * (N - 1))) + (hdiv : ∀ i j : Fin N, i < j → bracket i j ^ 3 ∣ F) : + ∃ c : ℂ, F = c • laughlinPolynomial N := by + obtain ⟨G, hG⟩ := laughlinPolynomial_dvd_of_bracket_cubes_dvd F hdiv + by_cases hG0 : G = 0 + · refine ⟨0, ?_⟩ + simp [hG, hG0] + have htd := (isHomogeneous_of_particle_homogeneous F hdeg).totalDegree_le + rw [hG, MvPolynomial.totalDegree_mul_of_isDomain (laughlinPolynomial_ne_zero N) hG0, + laughlinPolynomial_totalDegree] at htd + have hzero : G.totalDegree = 0 := by omega + refine ⟨G.coeff 0, ?_⟩ + rw [hG, (MvPolynomial.totalDegree_eq_zero_iff_eq_C).mp hzero, mul_comm, + MvPolynomial.C_mul'] + simp + +noncomputable def tensorMonomialScale {N Q : ℕ} (a : Configuration N Q) : ℝ := + ∏ i : Fin N, Real.sqrt (Nat.choose Q (a i).val : ℝ) + +theorem tensorMonomialScale_pos {N Q : ℕ} (a : Configuration N Q) : + 0 < tensorMonomialScale a := by + unfold tensorMonomialScale + exact Finset.prod_pos (fun i _ => Real.sqrt_pos.mpr (by + exact_mod_cast Nat.choose_pos (Nat.le_of_lt_succ (a i).isLt))) + +noncomputable def statePolynomial {N Q : ℕ} (ψ : State N Q) : + MvPolynomial (SpinorVariables N) ℂ := + ∑ a : Configuration N Q, MvPolynomial.monomial (monomialExponent a) + ((tensorMonomialScale a : ℂ) * ψ a) + +theorem monomialExponent_injective (N Q : ℕ) : + Function.Injective (monomialExponent (N := N) (Q := Q)) := by + intro a b he + funext k + apply Fin.ext + have h := congrArg (fun d : SpinorVariables N →₀ ℕ => d (k, true)) he + simpa only [monomialExponent, Finsupp.onFinset_apply, ↓reduceIte] using h + +@[simp] +theorem coeff_statePolynomial {N Q : ℕ} (ψ : State N Q) (a : Configuration N Q) : + (statePolynomial ψ).coeff (monomialExponent a) = (tensorMonomialScale a : ℂ) * ψ a := by + classical + simp [statePolynomial, MvPolynomial.coeff_monomial, (monomialExponent_injective N Q).eq_iff] + +theorem coeff_statePolynomial_of_not_grid {N Q : ℕ} (ψ : State N Q) + (d : SpinorVariables N →₀ ℕ) (h : ∀ a : Configuration N Q, monomialExponent a ≠ d) : + (statePolynomial ψ).coeff d = 0 := by + classical + simp [statePolynomial, MvPolynomial.coeff_monomial, h] + +theorem statePolynomial_injective (N Q : ℕ) : + Function.Injective (statePolynomial (N := N) (Q := Q)) := by + intro ψ φ h + funext a + have ha := congrArg (fun F : MvPolynomial (SpinorVariables N) ℂ => + F.coeff (monomialExponent a)) h + simp only [coeff_statePolynomial] at ha + exact mul_left_cancel₀ (Complex.ofReal_ne_zero.mpr (ne_of_gt (tensorMonomialScale_pos a))) ha + +theorem statePolynomial_isWeightedHomogeneous {N Q : ℕ} (ψ : State N Q) (k : Fin N) : + MvPolynomial.IsWeightedHomogeneous (particleWeight k) (statePolynomial ψ) Q := by + classical + apply MvPolynomial.IsWeightedHomogeneous.sum + intro a ha + apply MvPolynomial.isWeightedHomogeneous_monomial + rw [particleWeight_eq] + simp only [monomialExponent, Finsupp.onFinset_apply, Bool.false_eq_true, ↓reduceIte] + exact Nat.sub_add_cancel (Nat.le_of_lt_succ (a k).isLt) + +@[simp] +theorem statePolynomial_smul {N Q : ℕ} (c : ℂ) (ψ : State N Q) : + statePolynomial (c • ψ) = c • statePolynomial ψ := by + classical + unfold statePolynomial + simp only [Finset.smul_sum, Pi.smul_apply, smul_eq_mul] + apply Finset.sum_congr rfl + intro a ha + rw [← MvPolynomial.C_mul'] + simp only [MvPolynomial.C_mul_monomial] + congr 1 + ring + +@[simp] +theorem statePolynomial_laughlinVector (N : ℕ) : + statePolynomial (laughlinVector N (3 * (N - 1))) = laughlinPolynomial N := by + classical + apply MvPolynomial.ext + intro d + by_cases hd : ∃ a : Configuration N (3 * (N - 1)), monomialExponent a = d + · obtain ⟨a, rfl⟩ := hd + rw [coeff_statePolynomial] + change (tensorMonomialScale a : ℂ) * + ((laughlinPolynomial N).coeff (monomialExponent a) / (tensorMonomialScale a : ℂ)) = _ + exact mul_div_cancel₀ _ (Complex.ofReal_ne_zero.mpr (ne_of_gt (tensorMonomialScale_pos a))) + · push Not at hd + rw [coeff_statePolynomial_of_not_grid _ _ hd] + by_contra hc + obtain ⟨a, ha⟩ := laughlinPolynomial_support_exponents N d (Ne.symm hc) + exact hd a ha + +theorem state_eq_scalar_laughlin_of_bracket_cubes_dvd {N : ℕ} + (ψ : State N (3 * (N - 1))) + (h : ∀ i j : Fin N, i < j → bracket i j ^ 3 ∣ statePolynomial ψ) : + ∃ c : ℂ, ψ = c • laughlinVector N (3 * (N - 1)) := by + obtain ⟨c, hc⟩ := eq_scalar_laughlin_of_bracket_cubes_dvd (statePolynomial ψ) + (statePolynomial_isWeightedHomogeneous ψ) h + refine ⟨c, (statePolynomial_injective _ _).eq_iff.mp ?_⟩ + simpa only [statePolynomial_smul, statePolynomial_laughlinVector] using hc + +theorem pairAmplitude_eq_of_spectators_eq {N Q : ℕ} (ψ : State N Q) + (i j : Fin N) (p : ℕ) (a b : Configuration N Q) + (h : ∀ k, k ≠ i → k ≠ j → a k = b k) : + pairAmplitude ψ i j p a = pairAmplitude ψ i j p b := by + classical + unfold pairAmplitude + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + congr 2 + funext k + by_cases hkj : k = j + · simp [hkj] + by_cases hki : k = i + · simp [Function.update_apply, hki] + simp [hki, hkj, h k hki hkj] + +theorem pairAmplitude_anchor {N Q : ℕ} (ψ : State N Q) (i j : Fin N) + (p : ℕ) (a : Configuration N Q) : + pairAmplitude ψ i j p (Function.update (Function.update a i 0) j 0) = + pairAmplitude ψ i j p a := by + apply pairAmplitude_eq_of_spectators_eq + intro k hki hkj + simp [hki, hkj] + +theorem energy_eq_zero_iff {N Q : ℕ} (ψ : State N Q) : + energy ψ = 0 ↔ ∀ i j : Fin N, i < j → ∀ p : ℕ, p < 2 * Q - 1 → + ∀ a : Configuration N Q, pairAmplitude ψ i j p a = 0 := by + classical + constructor + · intro h i j hij p hp a + unfold energy at h + have hi := (Finset.sum_eq_zero_iff_of_nonneg (by intro _ _; positivity)).mp h i + (Finset.mem_univ i) + have hj := (Finset.sum_eq_zero_iff_of_nonneg (by intro _ _; positivity)).mp hi j + (Finset.mem_univ j) + rw [ite_eq_left hij] at hj + have hpp := (Finset.sum_eq_zero_iff_of_nonneg (by intro _ _; positivity)).mp hj p + (Finset.mem_range.mpr hp) + let b := Function.update (Function.update a i 0) j 0 + have hb : b i = 0 ∧ b j = 0 := by + simp [b, ne_of_lt hij] + have ha := (Finset.sum_eq_zero_iff_of_nonneg (by intro _ _; positivity)).mp hpp b + (Finset.mem_univ b) + rw [ite_eq_left hb] at ha + rw [pairAmplitude_anchor] at ha + exact norm_eq_zero.mp ((pow_eq_zero_iff (by norm_num : (2 : ℕ) ≠ 0)).mp ha) + · intro h + unfold energy + apply Finset.sum_eq_zero + intro i hi + apply Finset.sum_eq_zero + intro j hj + split_ifs with hij + · apply Finset.sum_eq_zero + intro p hp + apply Finset.sum_eq_zero + intro a ha + simp [h i j hij p (Finset.mem_range.mp hp) a] + · rfl + +def antisymmetricSubmodule (N Q : ℕ) : Submodule ℂ (TensorHilbert N Q) where + carrier := {ψ | Antisymmetric (WithLp.ofLp ψ)} + zero_mem' := by intros i j hij a; simp + add_mem' := by + intro ψ φ hψ hφ i j hij a + change ψ (a ∘ Equiv.swap i j) + φ (a ∘ Equiv.swap i j) = -(ψ a + φ a) + rw [hψ i j hij a, hφ i j hij a, neg_add] + smul_mem' := by + intro c ψ hψ i j hij a + change c * ψ (a ∘ Equiv.swap i j) = -(c * ψ a) + rw [hψ i j hij a, mul_neg] + +abbrev SectorHilbert (N Q : ℕ) := ↥(antisymmetricSubmodule N Q) + +abbrev ContractionIndex (N Q : ℕ) := + Fin N × Fin N × Fin (2 * Q - 1) × Configuration N Q + +noncomputable def pairContractions (N Q : ℕ) : + TensorHilbert N Q →ₗ[ℂ] EuclideanSpace ℂ (ContractionIndex N Q) where + toFun ψ := WithLp.toLp 2 (fun t => + if t.1 < t.2.1 ∧ t.2.2.2 t.1 = 0 ∧ t.2.2.2 t.2.1 = 0 then + pairAmplitude (WithLp.ofLp ψ) t.1 t.2.1 t.2.2.1.val t.2.2.2 else 0) + map_add' := by + intro ψ φ + ext t + change (if _ then pairAmplitude _ _ _ _ _ else _) = + (if _ then pairAmplitude _ _ _ _ _ else _) + (if _ then pairAmplitude _ _ _ _ _ else _) + split_ifs + · simp [pairAmplitude, mul_add, Finset.sum_add_distrib] + · simp + map_smul' := by + intro c ψ + ext t + change (if _ then pairAmplitude _ _ _ _ _ else _) = + c * (if _ then pairAmplitude _ _ _ _ _ else _) + split_ifs + · simp [pairAmplitude, Finset.mul_sum, mul_left_comm] + · simp + +theorem pairContractions_norm_sq {N Q : ℕ} (ψ : TensorHilbert N Q) : + ‖pairContractions N Q ψ‖ ^ 2 = energy (WithLp.ofLp ψ) := by + classical + rw [EuclideanSpace.norm_sq_eq] + simp only [pairContractions, LinearMap.coe_mk, AddHom.coe_mk, WithLp.ofLp_toLp, + Fintype.sum_prod_type] + unfold energy + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + by_cases hij : i < j + · simp only [hij, true_and, ↓reduceIte] + rw [Fin.sum_univ_eq_sum_range (fun p : ℕ => + ∑ a : Configuration N Q, + ‖if a i = 0 ∧ a j = 0 then pairAmplitude (WithLp.ofLp ψ) i j p a else 0‖ ^ 2)] + apply Finset.sum_congr rfl + intro p hp + apply Finset.sum_congr rfl + intro a ha + split_ifs <;> simp + · simp [hij] + +noncomputable def sectorContractions (N Q : ℕ) : + SectorHilbert N Q →ₗ[ℂ] EuclideanSpace ℂ (ContractionIndex N Q) := + (pairContractions N Q).comp (antisymmetricSubmodule N Q).subtype + +noncomputable def sectorHamiltonian (N Q : ℕ) : + SectorHilbert N Q →ₗ[ℂ] SectorHilbert N Q := + (LinearMap.adjoint (𝕜 := ℂ) (E := SectorHilbert N Q) + (F := EuclideanSpace ℂ (ContractionIndex N Q)) (sectorContractions N Q)).comp (sectorContractions N Q) + +theorem sectorHamiltonian_positive (N Q : ℕ) : LinearMap.IsPositive (𝕜 := ℂ) (E := SectorHilbert N Q) (sectorHamiltonian N Q) := + LinearMap.isPositive_adjoint_comp_self (𝕜 := ℂ) + (E := SectorHilbert N Q) (F := EuclideanSpace ℂ (ContractionIndex N Q)) _ + +theorem sectorHamiltonian_inner {N Q : ℕ} (ψ : SectorHilbert N Q) : + (inner ℂ ψ (sectorHamiltonian N Q ψ)).re = energy (WithLp.ofLp ψ.val) := by + change (inner ℂ ψ ((LinearMap.adjoint (𝕜 := ℂ) (E := SectorHilbert N Q) + (F := EuclideanSpace ℂ (ContractionIndex N Q)) (sectorContractions N Q)) (sectorContractions N Q ψ))).re = _ + rw [LinearMap.adjoint_inner_right] + exact (norm_sq_eq_re_inner (𝕜 := ℂ) (sectorContractions N Q ψ)).symm.trans + (pairContractions_norm_sq ψ.val) + +theorem sectorHamiltonian_eq_zero_iff {N Q : ℕ} (ψ : SectorHilbert N Q) : + sectorHamiltonian N Q ψ = 0 ↔ energy (WithLp.ofLp ψ.val) = 0 := by + constructor + · intro h + rw [← sectorHamiltonian_inner ψ, h] + simp + · intro h + have ha : sectorContractions N Q ψ = 0 := by + apply norm_eq_zero.mp + have hnorm : ‖sectorContractions N Q ψ‖ ^ 2 = 0 := + (pairContractions_norm_sq ψ.val).trans h + exact (pow_eq_zero_iff (by norm_num : (2 : ℕ) ≠ 0)).mp hnorm + change (LinearMap.adjoint (𝕜 := ℂ) (E := SectorHilbert N Q) + (F := EuclideanSpace ℂ (ContractionIndex N Q)) (sectorContractions N Q)) (sectorContractions N Q ψ) = 0 + rw [ha, map_zero] + +namespace Chart +open MvPolynomial +open scoped BigOperators + +noncomputable def difference {σ : Type*} (i j : σ) : MvPolynomial σ ℂ := X j - X i + +noncomputable def diagonal {σ : Type*} [DecidableEq σ] (i j : σ) : + MvPolynomial σ ℂ →ₐ[ℂ] MvPolynomial σ ℂ := rename (Function.update id j i) + +theorem difference_dvd_sub_diagonal {σ : Type*} [DecidableEq σ] (i j : σ) + (F : MvPolynomial σ ℂ) : difference i j ∣ F - diagonal i j F := by + induction F using MvPolynomial.induction_on with + | C a => simp [diagonal] + | add a b ha hb => simpa only [map_add, add_sub_add_comm] using dvd_add ha hb + | mul_X p k hp => + have hx : difference i j ∣ X k - diagonal i j (X k) := by + by_cases hk : k = j + · simp [hk, diagonal, difference] + · simp [diagonal, hk] + have hd := dvd_add (dvd_mul_of_dvd_left hp (X k)) + (dvd_mul_of_dvd_right hx (diagonal i j p)) + convert hd using 1 + simp only [map_mul] + ring + +theorem difference_dvd_of_diagonal_eq_zero {σ : Type*} [DecidableEq σ] (i j : σ) + (F : MvPolynomial σ ℂ) (h : diagonal i j F = 0) : difference i j ∣ F := by + simpa only [h, sub_zero] using difference_dvd_sub_diagonal i j F + +lemma difference_ne_zero {σ : Type*} {i j : σ} (h : i ≠ j) : difference i j ≠ 0 := by + classical + intro he + have hh := congrArg (MvPolynomial.eval (fun k : σ => if k = j then (1 : ℂ) else 0)) he + simp [difference, h] at hh + +@[simp] +lemma diagonal_difference {σ : Type*} [DecidableEq σ] (i j : σ) : + diagonal i j (difference i j) = 0 := by + by_cases h : i = j + · simp [difference, h] + · simp [diagonal, difference, h] + +lemma diagonal_rename_swap {σ : Type*} [DecidableEq σ] (i j : σ) + (F : MvPolynomial σ ℂ) : + diagonal i j (rename (Equiv.swap i j) F) = diagonal i j F := by + unfold diagonal + rw [rename_rename] + have he : Function.update id j i ∘ Equiv.swap i j = Function.update id j i := by + funext k + by_cases hki : k = i + · subst k; by_cases hij : i = j <;> simp [hij] + by_cases hkj : k = j + · subst k; simp [Ne.symm hki] + simp [Equiv.swap_apply_of_ne_of_ne hki hkj, hkj] + rw [he] + +theorem diagonal_eq_zero_of_antisymmetric {σ : Type*} [DecidableEq σ] (i j : σ) + (F : MvPolynomial σ ℂ) (h : rename (Equiv.swap i j) F = -F) : + diagonal i j F = 0 := by + have hd := congrArg (diagonal i j) h + rw [diagonal_rename_swap, map_neg] at hd + have hs : (2 : ℂ) • diagonal i j F = 0 := by + rw [two_smul] + calc + diagonal i j F + diagonal i j F = -diagonal i j F + diagonal i j F := + congrArg (fun x => x + diagonal i j F) hd + _ = 0 := neg_add_cancel _ + exact (smul_eq_zero.mp hs).resolve_left (by norm_num) + +lemma rename_difference_swap {σ : Type*} [DecidableEq σ] (i j : σ) : + rename (Equiv.swap i j) (difference i j) = -difference i j := by + simp [difference, sub_eq_add_neg] + +theorem difference_cube_dvd {σ : Type*} [DecidableEq σ] (i j : σ) (hij : i ≠ j) + (F : MvPolynomial σ ℂ) (hanti : rename (Equiv.swap i j) F = -F) + (hderiv : diagonal i j (pderiv j F) = 0) : difference i j ^ 3 ∣ F := by + obtain ⟨G, hG⟩ := difference_dvd_of_diagonal_eq_zero i j F + (diagonal_eq_zero_of_antisymmetric i j F hanti) + have hGsym : rename (Equiv.swap i j) G = G := by + rw [hG, map_mul, rename_difference_swap, neg_mul] at hanti + exact mul_left_cancel₀ (difference_ne_zero hij) (neg_inj.mp hanti) + have hdiagG : diagonal i j G = 0 := by + rw [hG, pderiv_mul] at hderiv + simpa [difference, diagonal, hij, Ne.symm hij] using hderiv + obtain ⟨H, hH⟩ := difference_dvd_of_diagonal_eq_zero i j G hdiagG + have hHanti : rename (Equiv.swap i j) H = -H := by + rw [hH, map_mul, rename_difference_swap, neg_mul] at hGsym + apply mul_left_cancel₀ (difference_ne_zero hij) + simpa only [mul_neg] using neg_eq_iff_eq_neg.mp hGsym + obtain ⟨K, hK⟩ := difference_dvd_of_diagonal_eq_zero i j H + (diagonal_eq_zero_of_antisymmetric i j H hHanti) + refine ⟨K, ?_⟩ + rw [hG, hH, hK] + ring + +end Chart + +section LocalKernel +open MvPolynomial + +noncomputable def pairWeightScale (Q p : ℕ) : ℝ := + Real.sqrt (1 / ((Q : ℝ) * (2 * Q - 2).choose p)) / Real.sqrt 2 + +theorem pairWeightScale_pos {Q p : ℕ} (hQ : 2 ≤ Q) (hp : p < 2 * Q - 1) : + 0 < pairWeightScale Q p := by + unfold pairWeightScale + have hc : (0 : ℝ) < ((2 * Q - 2).choose p : ℝ) := by + exact_mod_cast Nat.choose_pos (show p ≤ 2 * Q - 2 by omega) + positivity + +theorem pairCoefficient_binomial (Q p : ℕ) (x y : Fin (Q + 1)) : + pairCoefficient Q p x y = + if x.val + y.val = p + 1 then + pairWeightScale Q p * ((x.val : ℝ) - y.val) * + (Real.sqrt (Q.choose x.val : ℝ) * Real.sqrt (Q.choose y.val : ℝ)) + else 0 := by + have hx : (x.val.factorial : ℝ) ≠ 0 := by positivity + have hy : (y.val.factorial : ℝ) ≠ 0 := by positivity + have hpf : (p.factorial : ℝ) ≠ 0 := by positivity + have hrad : + (((Q.descFactorial x.val : ℝ) * (Q.descFactorial y.val : ℝ) * (p.factorial : ℝ)) / + ((Q : ℝ) * ((2*Q-2).descFactorial p : ℝ) * + (x.val.factorial : ℝ) * (y.val.factorial : ℝ))) = + ((Q.choose x.val : ℝ) * Q.choose y.val) * + (1 / ((Q : ℝ) * ((2 * Q - 2).choose p : ℝ))) := by + simp only [Nat.descFactorial_eq_factorial_mul_choose, Nat.cast_mul] + field_simp + unfold pairCoefficient + split_ifs + · rw [hrad, Real.sqrt_mul (by positivity), Real.sqrt_mul (by positivity)] + unfold pairWeightScale + ring + · rfl + +noncomputable def pairMoment {Q : ℕ} (φ : Fin (Q + 1) → Fin (Q + 1) → ℂ) (n : ℕ) : ℂ := + ∑ x, ∑ y, if x.val + y.val = n then + ((x.val : ℂ) - y.val) * + ((Real.sqrt (Q.choose x.val : ℝ) * Real.sqrt (Q.choose y.val : ℝ) : ℝ) : ℂ) * φ x y + else 0 + +theorem pair_contraction_eq_moment {Q p : ℕ} + (φ : Fin (Q + 1) → Fin (Q + 1) → ℂ) : + (∑ x, ∑ y, (pairCoefficient Q p x y : ℂ) * φ x y) = + (pairWeightScale Q p : ℂ) * pairMoment φ (p + 1) := by + simp only [pairMoment, Finset.mul_sum] + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + rw [pairCoefficient_binomial] + split_ifs + · push_cast + ring + · simp + +noncomputable def localPairPolynomial {Q : ℕ} + (φ : Fin (Q + 1) → Fin (Q + 1) → ℂ) : MvPolynomial Bool ℂ := + ∑ x, ∑ y, C (((Real.sqrt (Q.choose x.val : ℝ) * Real.sqrt (Q.choose y.val : ℝ) : ℝ) : ℂ) * φ x y) * + X false ^ x.val * X true ^ y.val + +theorem localPairPolynomial_antisymmetric {Q : ℕ} + (φ : Fin (Q + 1) → Fin (Q + 1) → ℂ) (hφ : ∀ x y, φ y x = -φ x y) : + rename (Equiv.swap false true) (localPairPolynomial φ) = - localPairPolynomial φ := by + classical + simp only [localPairPolynomial, map_sum, map_mul, map_pow, rename_C, rename_X, + Equiv.swap_apply_left, Equiv.swap_apply_right] + rw [Finset.sum_comm] + simp only [← Finset.sum_neg_distrib] + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + rw [hφ x y] + simp only [mul_neg, map_neg, neg_mul] + push_cast + ring_nf + +private theorem diagonal_difference_derivative_monomial (x y : ℕ) (c : ℂ) : + Chart.diagonal false true + (pderiv false (C c * X false ^ x * X true ^ y) - + pderiv true (C c * X false ^ x * X true ^ y)) = + C (((x : ℂ) - y) * c) * X false ^ (x + y - 1) := by + simp only [pderiv_mul, pderiv_pow, pderiv_C, pderiv_X_self, + pderiv_X_of_ne (by decide : true ≠ false), pderiv_X_of_ne (by decide : false ≠ true)] + cases x <;> cases y <;> simp [Chart.diagonal, pow_add, pow_succ] <;> ring_nf + +theorem pairMoment_eq_zero_of_contractions {Q : ℕ} (hQ : 2 ≤ Q) + (φ : Fin (Q + 1) → Fin (Q + 1) → ℂ) + (h : ∀ p < 2 * Q - 1, ∑ x, ∑ y, (pairCoefficient Q p x y : ℂ) * φ x y = 0) + (n : ℕ) : pairMoment φ n = 0 := by + by_cases hn : 0 < n ∧ n < 2 * Q + · have hp : n - 1 < 2 * Q - 1 := by omega + have he := h (n - 1) hp + rw [pair_contraction_eq_moment, Nat.sub_add_cancel hn.1] at he + exact (mul_eq_zero.mp he).resolve_left + (Complex.ofReal_ne_zero.mpr (pairWeightScale_pos hQ hp).ne') + · unfold pairMoment + apply Finset.sum_eq_zero + intro x hx + apply Finset.sum_eq_zero + intro y hy + split_ifs with hxy + · have he : x.val = y.val := by have := x.isLt; have := y.isLt; omega + simp [he] + · rfl + +theorem localPairPolynomial_diagonal_difference_derivative {Q : ℕ} + (φ : Fin (Q + 1) → Fin (Q + 1) → ℂ) : + Chart.diagonal false true + (pderiv false (localPairPolynomial φ) - pderiv true (localPairPolynomial φ)) = + ∑ n ∈ Finset.range (2 * Q + 1), C (pairMoment φ n) * X false ^ (n - 1) := by + classical + simp only [localPairPolynomial, map_sum, ← Finset.sum_sub_distrib, + diagonal_difference_derivative_monomial] + simp only [pairMoment, map_sum, Finset.sum_mul, apply_ite C, map_zero, ite_mul, zero_mul] + conv_rhs => rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro x hx + conv_rhs => rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro y hy + symm + rw [Finset.sum_eq_single (x.val + y.val)] + · simp [mul_assoc] + · intro b hb hne + simp [Ne.symm hne] + · intro hnot + exact (hnot (Finset.mem_range.mpr (by have := x.isLt; have := y.isLt; omega))).elim + +theorem localPairPolynomial_cubic_divisibility {Q : ℕ} (hQ : 2 ≤ Q) + (φ : Fin (Q + 1) → Fin (Q + 1) → ℂ) + (hanti : ∀ x y, φ y x = -φ x y) + (hker : ∀ p < 2 * Q - 1, ∑ x, ∑ y, (pairCoefficient Q p x y : ℂ) * φ x y = 0) : + Chart.difference false true ^ 3 ∣ localPairPolynomial φ := by + have ha := localPairPolynomial_antisymmetric φ hanti + apply Chart.difference_cube_dvd false true (by decide) _ ha + have hd : Chart.diagonal false true + (pderiv false (localPairPolynomial φ) - pderiv true (localPairPolynomial φ)) = 0 := by + rw [localPairPolynomial_diagonal_difference_derivative] + simp [pairMoment_eq_zero_of_contractions hQ φ hker] + have hs := pderiv_rename (Equiv.swap false true).injective false (localPairPolynomial φ) + simp only [Equiv.swap_apply_left, ha, map_neg] at hs + have hds := congrArg (Chart.diagonal false true) hs + rw [map_neg, Chart.diagonal_rename_swap] at hds + rw [map_sub] at hd + have hz : (2 : MvPolynomial Bool ℂ) * + Chart.diagonal false true (pderiv true (localPairPolynomial φ)) = 0 := by + linear_combination -hd - hds + exact (mul_eq_zero.mp hz).resolve_left (by norm_num) + +end LocalKernel + +namespace Chart +open MvPolynomial + +noncomputable def spinorChart (N : ℕ) : + MvPolynomial (SpinorVariables N) ℂ →ₐ[ℂ] MvPolynomial (Fin N) ℂ := + aeval (fun ib => if ib.2 then X ib.1 else 1) + +noncomputable def exponent {N Q : ℕ} (a : Configuration N Q) : Fin N →₀ ℕ := + Finsupp.onFinset Finset.univ (fun i => (a i).val) (by intro; simp) + +noncomputable def statePolynomial {N Q : ℕ} (ψ : State N Q) : MvPolynomial (Fin N) ℂ := + ∑ a : Configuration N Q, monomial (exponent a) ((tensorMonomialScale a : ℂ) * ψ a) + +noncomputable def laughlinPolynomial (N : ℕ) : MvPolynomial (Fin N) ℂ := + ∏ i : Fin N, ∏ j : Fin N, if i < j then difference i j ^ 3 else 1 + +lemma monomial_as_prod {N Q : ℕ} (a : Configuration N Q) (c : ℂ) : + monomial (exponent a) c = C c * ∏ i : Fin N, X i ^ (a i).val := by + rw [monomial_eq, Finsupp.prod_pow] + rfl + +lemma exponent_injective (N Q : ℕ) : Function.Injective (exponent (N := N) (Q := Q)) := by + intro a b h + funext k + apply Fin.ext + exact congrArg (fun d : Fin N →₀ ℕ => d k) h + +@[simp] theorem coeff_statePolynomial {N Q : ℕ} (ψ : State N Q) (a : Configuration N Q) : + (statePolynomial ψ).coeff (exponent a) = (tensorMonomialScale a : ℂ) * ψ a := by + classical + simp [statePolynomial, coeff_monomial, (exponent_injective N Q).eq_iff] + +theorem statePolynomial_injective (N Q : ℕ) : + Function.Injective (statePolynomial (N := N) (Q := Q)) := by + intro ψ φ h + funext a + have ha := congrArg (fun F : MvPolynomial (Fin N) ℂ => F.coeff (exponent a)) h + simp only [coeff_statePolynomial] at ha + exact mul_left_cancel₀ (Complex.ofReal_ne_zero.mpr (tensorMonomialScale_pos a).ne') ha + +@[simp] theorem statePolynomial_smul {N Q : ℕ} (c : ℂ) (ψ : State N Q) : + statePolynomial (c • ψ) = c • statePolynomial ψ := by + classical + unfold statePolynomial + simp only [Finset.smul_sum, Pi.smul_apply, smul_eq_mul] + apply Finset.sum_congr rfl + intro a ha + rw [← C_mul'] + simp only [C_mul_monomial] + congr 1 + ring + +theorem spinorChart_statePolynomial {N Q : ℕ} (ψ : State N Q) : + spinorChart N (LaughlinGap.statePolynomial ψ) = statePolynomial ψ := by + classical + simp only [LaughlinGap.statePolynomial, map_sum, statePolynomial] + apply Finset.sum_congr rfl + intro a ha + simp only [spinorChart, aeval_monomial] + simp [Fintype.prod_prod_type, LaughlinGap.monomialExponent, monomial_as_prod] + +@[simp] theorem spinorChart_bracket {N : ℕ} (i j : Fin N) : + spinorChart N (bracket i j) = difference i j := by + simp [spinorChart, bracket, difference] + +@[simp] theorem spinorChart_laughlinPolynomial (N : ℕ) : + spinorChart N (LaughlinGap.laughlinPolynomial N) = laughlinPolynomial N := by + classical + simp [LaughlinGap.laughlinPolynomial, laughlinPolynomial, apply_ite] + +@[simp] theorem statePolynomial_laughlinVector (N : ℕ) : + statePolynomial (laughlinVector N (3 * (N - 1))) = laughlinPolynomial N := by + rw [← spinorChart_statePolynomial, LaughlinGap.statePolynomial_laughlinVector, + spinorChart_laughlinPolynomial] + +theorem statePolynomial_degreeOf_le {N Q : ℕ} (ψ : State N Q) (k : Fin N) : + (statePolynomial ψ).degreeOf k ≤ Q := by + classical + apply degreeOf_le_iff.mpr + intro d hd + have hex : ∃ a : Configuration N Q, exponent a = d := by + by_contra! h + have hz : (statePolynomial ψ).coeff d = 0 := by + simp [statePolynomial, coeff_monomial, h] + exact (mem_support_iff.mp hd) hz + obtain ⟨a, rfl⟩ := hex + exact Nat.le_of_lt_succ (a k).isLt + +abbrev PairSpectators {N Q : ℕ} (i j : Fin N) := + {a : Configuration N Q // a i = 0 ∧ a j = 0} + +def pairConfigurationEquiv {N Q : ℕ} (i j : Fin N) (hij : i ≠ j) : + Configuration N Q ≃ PairSpectators (Q := Q) i j × Fin (Q + 1) × Fin (Q + 1) where + toFun a := (⟨Function.update (Function.update a i 0) j 0, by simp [hij]⟩, a i, a j) + invFun t := Function.update (Function.update t.1.val i t.2.1) j t.2.2 + left_inv a := by + funext k + by_cases hkj : k = j + · simp [hkj] + by_cases hki : k = i + · simp [hki, hij] + simp [Function.update_of_ne hkj, Function.update_of_ne hki] + right_inv t := by + rcases t with ⟨⟨a, ha⟩, x, y⟩ + apply Prod.ext + · apply Subtype.ext + funext k + by_cases hkj : k = j + · simp [hkj, ha.2] + by_cases hki : k = i + · simp [hki, hij, ha.1] + simp [Function.update_of_ne hkj, Function.update_of_ne hki] + · simp [hij] + +private lemma prod_update_pair {N Q : ℕ} {M : Type*} [CommMonoid M] + (i j : Fin N) (hij : i ≠ j) (a : Configuration N Q) (x y : Fin (Q + 1)) + (f : Fin N → Fin (Q + 1) → M) : + (∏ k : Fin N, f k (Function.update (Function.update a i x) j y k)) = + f i x * f j y * ∏ k ∈ (Finset.univ.erase i).erase j, f k (a k) := by + rw [← Finset.mul_prod_erase _ _ (Finset.mem_univ i)] + rw [← Finset.mul_prod_erase (Finset.univ.erase i) _ (by simp [Ne.symm hij] : j ∈ Finset.univ.erase i)] + simp only [Function.update_of_ne hij, Function.update_self, mul_assoc] + congr 2 + apply Finset.prod_congr rfl + intro k hk + have hi := (Finset.mem_erase.mp (Finset.mem_erase.mp hk).2).1 + have hj := (Finset.mem_erase.mp hk).1 + simp [Function.update_of_ne hi, Function.update_of_ne hj] + +private lemma monomial_as_normalized_prod {N Q : ℕ} (a : Configuration N Q) (c : ℂ) : + monomial (exponent a) ((tensorMonomialScale a : ℂ) * c) = + C c * ∏ k : Fin N, C (Real.sqrt (Q.choose (a k).val : ℝ) : ℂ) * X k ^ (a k).val := by + rw [monomial_as_prod] + simp only [tensorMonomialScale, Complex.ofReal_prod, map_mul, map_prod, Finset.prod_mul_distrib] + ring + +noncomputable def spectatorMonomial {N Q : ℕ} (i j : Fin N) + (a : PairSpectators (Q := Q) i j) : MvPolynomial (Fin N) ℂ := + ∏ k ∈ (Finset.univ.erase i).erase j, + C (Real.sqrt (Q.choose (a.val k).val : ℝ) : ℂ) * X k ^ (a.val k).val + +theorem statePolynomial_pair_decomposition {N Q : ℕ} (ψ : State N Q) + (i j : Fin N) (hij : i ≠ j) : + statePolynomial ψ = + ∑ a : PairSpectators (Q := Q) i j, spectatorMonomial i j a * + rename (fun b : Bool => if b then j else i) + (localPairPolynomial (fun x y => ψ (Function.update (Function.update a.val i x) j y))) := by + classical + unfold statePolynomial + rw [← (pairConfigurationEquiv (Q := Q) i j hij).symm.sum_comp] + simp only [Fintype.sum_prod_type] + apply Finset.sum_congr rfl + intro a ha + simp only [localPairPolynomial, map_sum, Finset.mul_sum] + apply Finset.sum_congr rfl + intro x hx + apply Finset.sum_congr rfl + intro y hy + change monomial (exponent (Function.update (Function.update a.val i x) j y)) + ((tensorMonomialScale (Function.update (Function.update a.val i x) j y) : ℂ) * + ψ (Function.update (Function.update a.val i x) j y)) = _ + rw [monomial_as_normalized_prod, prod_update_pair i j hij a.val x y + (fun k x => C (Real.sqrt (Q.choose x.val : ℝ) : ℂ) * X k ^ x.val)] + simp only [map_mul, map_pow, rename_C, rename_X, Bool.false_eq_true, ↓reduceIte, + Complex.ofReal_mul] + unfold spectatorMonomial + ring + +private lemma update_pair_swap {N Q : ℕ} (a : Configuration N Q) + (i j : Fin N) (hij : i ≠ j) (x y : Fin (Q + 1)) : + (Function.update (Function.update a i x) j y) ∘ Equiv.swap i j = + Function.update (Function.update a i y) j x := by + funext k + by_cases hki : k = i + · simp [hki, hij] + by_cases hkj : k = j + · simp [hkj, hij] + simp [Function.comp_apply, Equiv.swap_apply_of_ne_of_ne hki hkj, + Function.update_of_ne hki, Function.update_of_ne hkj] + +theorem difference_cube_dvd_statePolynomial_of_energy_zero {N Q : ℕ} (hQ : 2 ≤ Q) + (ψ : State N Q) (hψ : Antisymmetric ψ) (hE : energy ψ = 0) + (i j : Fin N) (hij : i < j) : difference i j ^ 3 ∣ statePolynomial ψ := by + classical + rw [statePolynomial_pair_decomposition ψ i j (ne_of_lt hij)] + apply Finset.dvd_sum + intro a ha + apply dvd_mul_of_dvd_right + have hlocal := localPairPolynomial_cubic_divisibility hQ + (fun x y => ψ (Function.update (Function.update a.val i x) j y)) + (by + intro x y + have h := hψ i j (ne_of_lt hij) (Function.update (Function.update a.val i x) j y) + rwa [update_pair_swap a.val i j (ne_of_lt hij)] at h) + (fun p hp => (LaughlinGap.energy_eq_zero_iff ψ).mp hE i j hij p hp a.val) + have hd := map_dvd (rename (fun b : Bool => if b then j else i)).toRingHom hlocal + simpa [difference] using hd + +theorem difference_irreducible {N : ℕ} {i j : Fin N} (hij : i ≠ j) : + Irreducible (difference i j) := by + have ht : (difference i j).totalDegree = 1 := + ((isHomogeneous_X ℂ j).sub (isHomogeneous_X ℂ i)).totalDegree (difference_ne_zero hij) + apply irreducible_of_totalDegree_eq_one ht + intro r hr + apply isUnit_of_dvd_one + have hs : Finsupp.single i 1 ≠ (Finsupp.single j 1 : Fin N →₀ ℕ) := by + intro h + have hc := congrArg (fun d : Fin N →₀ ℕ => d i) h + simp [hij] at hc + simpa [difference, coeff_X, hs] using hr (Finsupp.single j 1) + +theorem difference_not_dvd {N : ℕ} {i j k l : Fin N} (hij : i < j) (hkl : k < l) + (hne : (i, j) ≠ (k, l)) : ¬ difference k l ∣ difference i j := by + have hex : (i ≠ k ∧ i ≠ l) ∨ (j ≠ k ∧ j ≠ l) := by + by_contra! h + have hi : i = k ∨ i = l := by tauto + have hj : j = k ∨ j = l := by tauto + rcases hi with rfl | rfl <;> rcases hj with rfl | rfl + · exact (lt_irrefl _ hij) + · exact hne rfl + · exact (not_lt_of_ge (le_of_lt hkl) hij) + · exact (lt_irrefl _ hij) + intro hdiv + obtain ⟨g, hg⟩ := hdiv + rcases hex with hi | hj + · have h := congrArg (eval (fun m : Fin N => if m = i then (1 : ℂ) else 0)) hg + simp [difference, Ne.symm hi.1, Ne.symm hi.2, (ne_of_lt hij).symm] at h + · have h := congrArg (eval (fun m : Fin N => if m = j then (1 : ℂ) else 0)) hg + simp [difference, Ne.symm hj.1, Ne.symm hj.2, ne_of_lt hij] at h + +theorem laughlinPolynomial_ne_zero (N : ℕ) : laughlinPolynomial N ≠ 0 := by + classical + apply Finset.prod_ne_zero_iff.mpr + intro i hi + apply Finset.prod_ne_zero_iff.mpr + intro j hj + split_ifs with hij + · exact pow_ne_zero _ (difference_ne_zero (ne_of_lt hij)) + · exact one_ne_zero + +theorem laughlinPolynomial_dvd_of_difference_cubes_dvd {N : ℕ} + (F : MvPolynomial (Fin N) ℂ) (h : ∀ i j : Fin N, i < j → difference i j ^ 3 ∣ F) : + laughlinPolynomial N ∣ F := by + classical + have heq : laughlinPolynomial N = + ∏ ij ∈ (Finset.univ : Finset (Fin N × Fin N)).filter (fun ij => ij.1 < ij.2), + difference ij.1 ij.2 ^ 3 := by + simp only [Finset.prod_filter, Fintype.prod_prod_type, laughlinPolynomial] + rw [heq] + apply Finset.prod_dvd_of_isRelPrime + · intro ij hij kl hkl hne + have hij' := (Finset.mem_filter.mp hij).2 + have hkl' := (Finset.mem_filter.mp hkl).2 + exact ((difference_irreducible (ne_of_lt hij')).isRelPrime_iff_not_dvd.mpr + (difference_not_dvd hkl' hij' hne.symm)).pow + · intro ij hij + exact h ij.1 ij.2 (Finset.mem_filter.mp hij).2 + +lemma difference_degreeOf {N : ℕ} (i j k : Fin N) (hij : i ≠ j) : + (difference i j).degreeOf k = (if i = k then 1 else 0) + (if j = k then 1 else 0) := by + by_cases hki : k = i + · subst k + have hd := degreeOf_add_eq_of_degreeOf_lt + (p := -(X i : MvPolynomial (Fin N) ℂ)) (q := X j) (i := i) + (by simp [degreeOf_X, hij]) + simpa [difference, sub_eq_add_neg, add_comm, Ne.symm hij] using hd + by_cases hkj : k = j + · subst k + have hd := degreeOf_add_eq_of_degreeOf_lt + (p := (X j : MvPolynomial (Fin N) ℂ)) (q := -X i) (i := j) + (by simp [degreeOf_X, Ne.symm hij]) + simpa [difference, sub_eq_add_neg, hij] using hd + have hd := degreeOf_sub_le k (X j : MvPolynomial (Fin N) ℂ) (X i) + have hz : (difference i j).degreeOf k = 0 := by + simpa [difference, degreeOf_X, hkj, hki] using hd + simpa [Ne.symm hki, Ne.symm hkj] using hz + +theorem laughlinPolynomial_degreeOf (N : ℕ) (k : Fin N) : + (laughlinPolynomial N).degreeOf k = 3 * (N - 1) := by + classical + have hf (i j : Fin N) : (if i < j then difference i j ^ 3 else 1) ≠ 0 := by + split_ifs with hij + · exact pow_ne_zero _ (difference_ne_zero (ne_of_lt hij)) + · exact one_ne_zero + have hterm (i j : Fin N) : + degreeOf k (if i < j then difference i j ^ 3 else 1) = + 3 * (if i < j then (if i = k then 1 else 0) + (if j = k then 1 else 0) else 0) := by + by_cases hij : i < j + · simp only [ite_eq_left hij] + rw [degreeOf_pow_eq _ _ _ (difference_ne_zero (ne_of_lt hij)), difference_degreeOf _ _ _ (ne_of_lt hij)] + · simp [hij] + unfold laughlinPolynomial + rw [degreeOf_prod_eq _ _ (fun i _ => Finset.prod_ne_zero_iff.mpr (fun j _ => hf i j))] + simp_rw [degreeOf_prod_eq _ _ (fun j _ => hf _ j), hterm, ← Finset.mul_sum] + rw [LaughlinGap.particle_pair_count] + +private lemma eq_constant_of_degreeOf_eq_zero {N : ℕ} (G : MvPolynomial (Fin N) ℂ) + (h : ∀ k, G.degreeOf k = 0) : G = C (G.coeff 0) := by + classical + apply MvPolynomial.ext + intro d + by_cases hd : d = 0 + · simp [hd] + have hz : G.coeff d = 0 := by + by_contra hc + have hde : d = 0 := by + apply Finsupp.ext + intro k + have hk := monomial_le_degreeOf k (mem_support_iff.mpr hc) + rw [h k] at hk + exact Nat.eq_zero_of_le_zero hk + exact hd hde + simp [hz, coeff_C, Ne.symm hd] + +theorem eq_scalar_laughlin_of_difference_cubes_dvd {N : ℕ} + (F : MvPolynomial (Fin N) ℂ) (hdeg : ∀ k : Fin N, F.degreeOf k ≤ 3 * (N - 1)) + (hdiv : ∀ i j : Fin N, i < j → difference i j ^ 3 ∣ F) : + ∃ c : ℂ, F = c • laughlinPolynomial N := by + obtain ⟨G, hG⟩ := laughlinPolynomial_dvd_of_difference_cubes_dvd F hdiv + by_cases hG0 : G = 0 + · refine ⟨0, ?_⟩ + simp [hG, hG0] + have hz : ∀ k : Fin N, G.degreeOf k = 0 := by + intro k + have hd := hdeg k + rw [hG, degreeOf_mul_eq (laughlinPolynomial_ne_zero N) hG0, laughlinPolynomial_degreeOf] at hd + omega + refine ⟨G.coeff 0, ?_⟩ + rw [hG, eq_constant_of_degreeOf_eq_zero G hz, mul_comm, C_mul'] + simp + +end Chart + +theorem energy_zero_imp_laughlin {N : ℕ} (hN : 2 ≤ N) + (ψ : State N (3 * (N - 1))) (hψ : Antisymmetric ψ) (hE : energy ψ = 0) : + ∃ c : ℂ, ψ = c • laughlinVector N (3 * (N - 1)) := by + obtain ⟨c, hc⟩ := Chart.eq_scalar_laughlin_of_difference_cubes_dvd + (Chart.statePolynomial ψ) (Chart.statePolynomial_degreeOf_le ψ) + (Chart.difference_cube_dvd_statePolynomial_of_energy_zero (by omega) ψ hψ hE) + refine ⟨c, (Chart.statePolynomial_injective _ _).eq_iff.mp ?_⟩ + simpa only [Chart.statePolynomial_smul, Chart.statePolynomial_laughlinVector] using hc + +theorem laughlin_gap_of_sector_square_estimate {N : ℕ} (hN : 2 ≤ N) + (γ : ℝ) (hγ : 0 ≤ γ) + (hsq : ∀ x : SectorHilbert N (3 * (N - 1)), + γ * energy (WithLp.ofLp x.val) ≤ ‖sectorHamiltonian N (3 * (N - 1)) x‖ ^ 2) + (ψ : State N (3 * (N - 1))) (hψ : Antisymmetric ψ) : + γ * distanceToLaughlinSq ψ ≤ energy ψ := by + let x : SectorHilbert N (3 * (N - 1)) := ⟨toTensorHilbert ψ, hψ⟩ + obtain ⟨y, hy, hb⟩ := kernel_distance_of_square_lower_bound + (sectorHamiltonian N (3 * (N - 1))) (sectorHamiltonian_positive _ _) γ + (fun z => by rw [sectorHamiltonian_inner]; exact hsq z) x + have hyE : energy (WithLp.ofLp y.val) = 0 := (sectorHamiltonian_eq_zero_iff y).mp hy + obtain ⟨c, hc⟩ := energy_zero_imp_laughlin hN (WithLp.ofLp y.val) y.property hyE + have hycoord (a) : y.val a = c * laughlinVector N (3 * (N - 1)) a := + congrFun hc a + have hn : ‖x - y‖ ^ 2 = ∑ a, ‖ψ a - c * laughlinVector N (3 * (N - 1)) a‖ ^ 2 := by + change ‖toTensorHilbert ψ - y.val‖ ^ 2 = _ + rw [EuclideanSpace.norm_sq_eq] + apply Finset.sum_congr rfl + intro a ha + change ‖ψ a - y.val a‖ ^ 2 = _ + rw [hycoord a] + rw [sectorHamiltonian_inner, hn] at hb + exact (mul_le_mul_of_nonneg_left (distanceToLaughlinSq_le ψ c) hγ).trans hb + +theorem mainTarget_of_uniform_sector_square_estimate + (h : ∃ Q₀ : ℕ, ∀ Q : ℕ, Q₀ ≤ Q → ∀ N : ℕ, N ≤ Q + 1 → + ∀ x : SectorHilbert N Q, (1 / 25 : ℝ) * energy (WithLp.ofLp x.val) ≤ ‖sectorHamiltonian N Q x‖ ^ 2) : + MainTarget := by + obtain ⟨Q₀, hQ₀⟩ := h + refine ⟨Q₀ + 2, by omega, ?_⟩ + intro N hN ψ hψ + exact laughlin_gap_of_sector_square_estimate (by omega) (1 / 25) (by norm_num) + (hQ₀ _ (by omega) N (by omega)) ψ hψ + +end LaughlinGap + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/CachedIntegerRows.lean b/lean/OAI/Analysis/LaughlinGap/CachedIntegerRows.lean new file mode 100644 index 0000000000000000000000000000000000000000..ba7c989eb5a0491e6b7b2d75e06e59718d6aed3c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/CachedIntegerRows.lean @@ -0,0 +1,29 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.IntegerFourRows + +namespace OAI + +/-! Cached Integer Rows. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators + +def integerTableEval (D : ℕ) (S : Fin ((D+1)/2) → Fin 8 → Fin 9 → Fin 9 → ℤ) + (u v : Fin ((D+1)/2)) : ℚ := + ((-(∑ a : Fin 8, ∑ i : Fin 9, ∑ k : Fin 9, fourRowWeight D a i k * + S u a i k * S v a k i):ℤ):ℚ) / fourMatrixDenominator D + +lemma exactFourEval_table (D : ℕ) (S : Fin ((D+1)/2) → Fin 8 → Fin 9 → Fin 9 → ℤ) + (hS : ∀ u a i k, fourSumInteger a D (2*u.val+1) i k = S u a i k) + (u v : Fin ((D+1)/2)) : + exactFourEval D (2*u.val+1) (2*v.val+1) = integerTableEval D S u v := by + simp only [exactFourEval,exactFourInteger,integerTableEval,hS] + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate10.lean b/lean/OAI/Analysis/LaughlinGap/Certificate10.lean new file mode 100644 index 0000000000000000000000000000000000000000..5ab4fe13001cdef37109e6352236b97ac7232ded --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate10.lean @@ -0,0 +1,265 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Certificate9 +import OAI.Analysis.LaughlinGap.SumTable10 + +namespace OAI + +/-! Certificate10. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate10 + +def keys : Fin 6 → Finset (Fin 25) := ![{0,1,2,8}, {0,1,3,7}, {0,1,4,6}, {0,2,3,6}, {0,2,4,5}, {1,2,3,5}] +def fibers : Fin 6 → Finset (FourTerm 10) := ![{⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩}] +def columns : Matrix (Fin 5) (Fin 6) ℚ := ![![0, 0, 0, 0, 0, 0], ![-15120, 15120, -7560, -7560, 7560, 0], ![0, 0, 0, 0, 0, 0], ![11340, -11340, 5670, 5670, -5670, 0], ![-45360, 45360, -22680, -22680, 22680, 0]] +def Y : Matrix (Fin 5) (Fin 5) ℚ := ![![(200175459945085632193532343/6710886400000000000000), (-19934932341438578630554461/1677721600000000000000), (10688091490272052643120847/1342177280000000000000), (-25539656102181318071634093/3355443200000000000000), (20785777850578541715752031/838860800000000000000)], ![(-19934932341438578630554461/1677721600000000000000), (-23824125720222220870749/671088640000000000000), (-423999878564625416871237/335544320000000000000), (3981191132086811594405091/838860800000000000000), (-581783066891519285684403/41943040000000000000)], ![(10688091490272052643120847/1342177280000000000000), (-423999878564625416871237/335544320000000000000), (13103624809638522434317689/9395240960000000000000), (-2284683579713664648267057/671088640000000000000), (1918711872693053907602859/167772160000000000000)], ![(-25539656102181318071634093/3355443200000000000000), (3981191132086811594405091/838860800000000000000), (-2284683579713664648267057/671088640000000000000), (3925235702466226344344823/1677721600000000000000), (-1818861828136206279263793/419430400000000000000)], ![(20785777850578541715752031/838860800000000000000), (-581783066891519285684403/41943040000000000000), (1918711872693053907602859/167772160000000000000), (-1818861828136206279263793/419430400000000000000), (-7907022897840128737456029/104857600000000000000)]] +def Z : Matrix (Fin 5) (Fin 5) ℚ := ![![0, 0, 0, 0, 0], ![0, 30240, 0, -22680, 90720], ![0, 0, 0, 0, 0], ![0, -22680, 0, 17010, -68040], ![0, 90720, 0, -68040, 272160]] +def W : Matrix (Fin 5) (Fin 5) ℚ := ![![0, 0, 0, 0, 0], ![(-2093488721107348396109/36077725286400000000000000), (438867827883403177801057/1879048192000000000000000), (-1237433244599578471138079/4294967296000000000000000), (-474042061158101800190781/7516192768000000000000000), (1831244066560386205163291/22548578304000000000000000)], ![0, 0, 0, 0, 0], ![(2093488721107348396109/48103633715200000000000000), (-1316603483650209533403171/7516192768000000000000000), (3712299733798735413414237/17179869184000000000000000), (1422126183474305400572343/30064771072000000000000000), (-1831244066560386205163291/30064771072000000000000000)], ![(-2093488721107348396109/12025908428800000000000000), (1316603483650209533403171/1879048192000000000000000), (-3712299733798735413414237/4294967296000000000000000), (-1422126183474305400572343/7516192768000000000000000), (1831244066560386205163291/7516192768000000000000000)]] +def M : Matrix (Fin 5) (Fin 5) ℚ := ![![0, 0, 0, 0, 0], ![0, (425762667787958128783145313/26843545600000000000000), 0, (-1277288003363874386349435939/107374182400000000000000), (1277288003363874386349435939/26843545600000000000000)], ![0, 0, 0, 0, 0], ![0, (-1277288003363874386349435939/107374182400000000000000), 0, (3831864010091623159048307817/429496729600000000000000), (-3831864010091623159048307817/107374182400000000000000)], ![0, (1277288003363874386349435939/26843545600000000000000), 0, (-3831864010091623159048307817/107374182400000000000000), (3831864010091623159048307817/26843545600000000000000)]] +def L : Matrix (Fin 5) (Fin 5) ℚ := ![![1, 0, 0, 0, 0], ![0, 1, 0, 0, 0], ![0, 0, 1, 0, 0], ![0, (-3/4), 0, 1, 0], ![0, 3, 0, 0, 1]] +def diag : Fin 5 → ℚ := ![0, (425762667787958128783145313/26843545600000000000000), 0, 0, 0] + +def keyIndexTable : Fin 11 → Fin 13 → Fin 13 → Fin 6 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 3, 4, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 11) (j : Fin ((n.val+1)/2)) (x : Fin ((10-n.val+2)/2)) : Fin 6 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 6 → FourTerm 10 := ![⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 6, + (fourTermLabels (by omega : 10 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 10 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 5, + (fourTermLabels (by omega : 10 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 10 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 5, + (fourTermLabels (by omega : 10 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 10 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 4, + (fourTermLabels (by omega : 10 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 10 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 4, + (fourTermLabels (by omega : 10 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 10 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 3, + (fourTermLabels (by omega : 10 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 10 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 3, + (fourTermLabels (by omega : 10 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 10 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 2, + (fourTermLabels (by omega : 10 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 10 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 2, + (fourTermLabels (by omega : 10 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 10 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 1, + (fourTermLabels (by omega : 10 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 10 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 1, + (fourTermLabels (by omega : 10 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 10 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 10, (fourTermLabels (by omega : 10 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 10 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x +lemma representatives_checked : ∀ a : Fin 6, + (fourTermLabels (by omega : 10 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 10 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 10 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 10 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 6, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 10, + (fourTermLabels (by omega : 10 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 6, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 10 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 6, ∀ b : FourTerm 10, + (fourTermLabels (by omega : 10 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 10 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 6, (∑ b ∈ fibers v, fourTermEval 10 (2*(0 : Fin 5).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 10 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 6, (∑ b ∈ fibers v, fourTermEval 10 (2*(1 : Fin 5).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 10 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 6, (∑ b ∈ fibers v, fourTermEval 10 (2*(2 : Fin 5).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 10 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 6, (∑ b ∈ fibers v, fourTermEval 10 (2*(3 : Fin 5).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 10 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 6, (∑ b ∈ fibers v, fourTermEval 10 (2*(4 : Fin 5).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 10 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 5, ∀ v : Fin 6, (∑ b ∈ fibers v, fourTermEval 10 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 10 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 +lemma gram_checked_0 : ∀ v : Fin 5, (∑ a : Fin 6, columns (0 : Fin 5) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 5, (∑ a : Fin 6, columns (1 : Fin 5) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 5, (∑ a : Fin 6, columns (2 : Fin 5) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 5, (∑ a : Fin 6, columns (3 : Fin 5) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 5, (∑ a : Fin 6, columns (4 : Fin 5) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 5, ∀ v : Fin 5, (∑ a : Fin 6, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 +lemma rows_table_checked_0 : ∀ v : Fin 5, integerTableEval 10 SumTable10.sums (0 : Fin 5) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 5, integerTableEval 10 SumTable10.sums (1 : Fin 5) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 5, integerTableEval 10 SumTable10.sums (2 : Fin 5) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 5, integerTableEval 10 SumTable10.sums (3 : Fin 5) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 5, integerTableEval 10 SumTable10.sums (4 : Fin 5) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 5, ∀ v : Fin 5, integerTableEval 10 SumTable10.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 +lemma rows_checked (u v : Fin 5) : exactFourEval 10 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 10 SumTable10.sums SumTable10.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 5, (Z * tableComparison 10 (1/200000) Y) (0 : Fin 5) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 5, (Z * tableComparison 10 (1/200000) Y) (1 : Fin 5) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 5, (Z * tableComparison 10 (1/200000) Y) (2 : Fin 5) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 5, (Z * tableComparison 10 (1/200000) Y) (3 : Fin 5) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 5, (Z * tableComparison 10 (1/200000) Y) (4 : Fin 5) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 5, ∀ v : Fin 5, (Z * tableComparison 10 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 +lemma compression_checked_0 : ∀ v : Fin 5, (W * Z) (0 : Fin 5) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 5, (W * Z) (1 : Fin 5) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 5, (W * Z) (2 : Fin 5) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 5, (W * Z) (3 : Fin 5) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 5, (W * Z) (4 : Fin 5) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 5, ∀ v : Fin 5, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 +lemma ldl_checked_0 : ∀ v : Fin 5, (∑ k : Fin 5, L (0 : Fin 5) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 5, (∑ k : Fin 5, L (1 : Fin 5) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 5, (∑ k : Fin 5, L (2 : Fin 5) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 5, (∑ k : Fin 5, L (3 : Fin 5) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 5, (∑ k : Fin 5, L (4 : Fin 5) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 5, ∀ v : Fin 5, (∑ k : Fin 5, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 +lemma diag_checked : ∀ u : Fin 5, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 10 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 10 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 10 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 10 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 10 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate10 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate11.lean b/lean/OAI/Analysis/LaughlinGap/Certificate11.lean new file mode 100644 index 0000000000000000000000000000000000000000..89442e0648fb97e1399bdef0288b8460494380a5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate11.lean @@ -0,0 +1,295 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CachedIntegerRows +import OAI.Analysis.LaughlinGap.FastFourKeys +import OAI.Analysis.LaughlinGap.FourTables +import OAI.Analysis.LaughlinGap.SumTable11 + +namespace OAI + +/-! Certificate11. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate11 + +def keys : Fin 9 → Finset (Fin 25) := ![{0,1,2,9}, {0,1,3,8}, {0,1,4,7}, {0,1,5,6}, {0,2,3,7}, {0,2,4,6}, {0,3,4,5}, {1,2,3,6}, {1,2,4,5}] +def fibers : Fin 9 → Finset (FourTerm 11) := ![{⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}] +def columns : Matrix (Fin 6) (Fin 9) ℚ := ![![226800, -226800, 340200, -340200, -113400, 0, 113400, 113400, -113400], ![90720, -90720, 75600, -75600, 15120, 0, -15120, -15120, 15120], ![28350, -28350, 4725, 16875, 23625, -21600, 19575, -2025, 2025], ![-62370, 62370, -25515, -4725, -36855, 30240, -23625, 6615, -6615], ![45360, -45360, -11340, 56700, 56700, -45360, 34020, -11340, 11340], ![1247400, -1247400, 1247400, -1247400, 0, 0, 0, 0, 0]] +def Y : Matrix (Fin 6) (Fin 6) ℚ := ![![(32839215004495137244466187/167772160000000000000), (-19588648001353140318042429/167772160000000000000), (769969819896078911998041/20971520000000000000), (-3060745927175333645962119/167772160000000000000), (1516286817957572396027451/20971520000000000000), (-19272986732194004208033657/20971520000000000000)], ![(-19588648001353140318042429/167772160000000000000), (24152328740360168247036519/838860800000000000000), (-2148675818210730931634253/167772160000000000000), (1994515423197492856394763/209715200000000000000), (8693018793801331618221/4194304000000000000), (-1927558817628006250840779/10485760000000000000)], ![(769969819896078911998041/20971520000000000000), (-2148675818210730931634253/167772160000000000000), (149319433910496770223741/46976204800000000000), (-342271579617331143233409/167772160000000000000), (65139956566813006253523/10485760000000000000), (2877018097116172834790361/20971520000000000000)], ![(-3060745927175333645962119/167772160000000000000), (1994515423197492856394763/209715200000000000000), (-342271579617331143233409/167772160000000000000), (-652126880335913571881601/104857600000000000000), (966055836873933781002981/104857600000000000000), (-511525534633041298988871/5242880000000000000)], ![(1516286817957572396027451/20971520000000000000), (8693018793801331618221/4194304000000000000), (65139956566813006253523/10485760000000000000), (966055836873933781002981/104857600000000000000), (-1172769771227963717819691/13107200000000000000), (521725615312896324070587/2621440000000000000)], ![(-19272986732194004208033657/20971520000000000000), (-1927558817628006250840779/10485760000000000000), (2877018097116172834790361/20971520000000000000), (-511525534633041298988871/5242880000000000000), (521725615312896324070587/2621440000000000000), (-1369918693771740518109957/131072000000000000)]] +def Z : Matrix (Fin 6) (Fin 6) ℚ := ![![7257600, 0, 0, 0, -453600, 9979200], ![0, 241920, 0, -60480, 0, 2494800], ![0, 0, 54000, -75600, 113400, 0], ![0, -60480, -75600, 120960, -158760, -623700], ![-453600, 0, 113400, -158760, 266490, -623700], ![9979200, 2494800, 0, -623700, -623700, 39449025]] +def W : Matrix (Fin 6) (Fin 6) ℚ := ![![(5964695117267475742980919/1503238553600000000000000), (1744624323817160701107537/1503238553600000000000000), (-161316238397235909250131/134217728000000000000000), (414064887714404869068081/751619276800000000000000), (-64800521002176063679207/187904819200000000000000), (15384382826163865762517/134217728000000000000000)], ![(512866081553008807390337/11274289152000000000000000), (-194897946662990208889687/3758096384000000000000000), (1871635346680482439661/50331648000000000000000), (-303975974406062929067597/5637144576000000000000000), (-19233547957227911298713/1409286144000000000000000), (9276944501934800833223/469762048000000000000000)], ![(-453817708231818879037087/36077725286400000000000000), (2031865538239284389204363/36077725286400000000000000), (-18408098023015419984551/375809638400000000000000), (-24170116272712712981741/721554505728000000000000), (98529294091720413115079/4509715660800000000000000), (-20089466216411214407027/4509715660800000000000000)], ![(1125259631410696923698261/180388626432000000000000000), (-11884283407719108217754297/180388626432000000000000000), (47737752682324330195009/805306368000000000000000), (5445674245348976488075063/90194313216000000000000000), (-204256955604377082203567/7516192768000000000000000), (29302929491660890850513/22548578304000000000000000)], ![(-8250049885990027717041051/30064771072000000000000000), (687492143573648402361607/15032385536000000000000000), (-59580937878949130564481/2147483648000000000000000), (-157502369657418727928627/1503238553600000000000000), (253426915913230802550397/3758096384000000000000000), (-4434231130321885021193/268435456000000000000000)], ![(8906646648378166256760477/1503238553600000000000000), (3189808830527522704705809/3006477107200000000000000), (-1362718846099888865026021/1073741824000000000000000), (302744511597940335001331/1503238553600000000000000), (-1444335560239755819933/2348810240000000000000), (678823330108464950298901/1879048192000000000000000)]] +def M : Matrix (Fin 6) (Fin 6) ℚ := ![![(5049552047366104719126260283/167772160000000000000), (8949117860231088857789367/16777216000000000000), (-39099590117542931979883869/268435456000000000000), (94714773618178746703399743/1342177280000000000000), (-1467660859958626572675955383/671088640000000000000), (7866011844464725027258136361/167772160000000000000)], ![(8949117860231088857789367/16777216000000000000), (1677004120298631639678687/41943040000000000000), (3044749629574206508033791/671088640000000000000), (-54853329812992078349810277/3355443200000000000000), (-39947051071179721194006141/1677721600000000000000), (38445358108099205386269927/33554432000000000000)], ![(-39099590117542931979883869/268435456000000000000), (3044749629574206508033791/671088640000000000000), (35550514566479531937111777/15032385536000000000000), (-47729513084776357969246941/10737418240000000000000), (75537373571788313927688669/5368709120000000000000), (-10300586047406982406675233/67108864000000000000)], ![(94714773618178746703399743/1342177280000000000000), (-54853329812992078349810277/3355443200000000000000), (-47729513084776357969246941/10737418240000000000000), (110703982169080563836793939/10737418240000000000000), (-368973410717799312717796119/26843545600000000000000), (-48018585876798273237896373/671088640000000000000)], ![(-1467660859958626572675955383/671088640000000000000), (-39947051071179721194006141/1677721600000000000000), (75537373571788313927688669/5368709120000000000000), (-368973410717799312717796119/26843545600000000000000), (2231147286200171863965309741/13421772800000000000000), (-8731261072446911549418855933/2684354560000000000000)], ![(7866011844464725027258136361/167772160000000000000), (38445358108099205386269927/33554432000000000000), (-10300586047406982406675233/67108864000000000000), (-48018585876798273237896373/671088640000000000000), (-8731261072446911549418855933/2684354560000000000000), (204769681017405795043351689717/2684354560000000000000)]] +def L : Matrix (Fin 6) (Fin 6) ℚ := ![![1, 0, 0, 0, 0, 0], ![(1104829365460628254048070/62340148732914873075632843), 1, 0, 0, 0, 0], ![(-2413554945527341480239745/498721189863318984605062744), (4136195598756701681574722903125928982590421004929/17739236837277564358431182008444017483217516030648), 1, 0, 0, 0], ![(1169318192817021564239503/498721189863318984605062744), (-51127415237893867219062037832436524732154842072813/88696184186387821792155910042220087416087580153240), (-7/5), 1, 0, 0], ![(-18119269876032426823159943/249360594931659492302531372), (86860107573890735313069180965644508634398841103509/177392368372775643584311820084440174832175160306480), (21/10), 0, 1, 0], ![(97111257339070679348865881/62340148732914873075632843), (165/16), 0, 0, 0, 1]] +def diag : Fin 6 → ℚ := ![(5049552047366104719126260283/167772160000000000000), (19956641441937259903235079759499519668619705534479/653683837977649459501547839815680000000000000), (2458274422641393096494813566379712462387217062728478526502330063469129/10416525283295689221835547659184268682830082450037544058880000000000000), 0, 0, 0] + +def keyIndexTable : Fin 12 → Fin 13 → Fin 13 → Fin 9 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 4, 5, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 4, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 7, 8, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 5, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 12) (j : Fin ((n.val+1)/2)) (x : Fin ((11-n.val+2)/2)) : Fin 9 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 9 → FourTerm 11 := ![⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 6, + (fourTermLabels (by omega : 11 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 6, + (fourTermLabels (by omega : 11 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 5, + (fourTermLabels (by omega : 11 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 5, + (fourTermLabels (by omega : 11 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 4, + (fourTermLabels (by omega : 11 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 4, + (fourTermLabels (by omega : 11 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 3, + (fourTermLabels (by omega : 11 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 3, + (fourTermLabels (by omega : 11 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 2, + (fourTermLabels (by omega : 11 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 2, + (fourTermLabels (by omega : 11 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 1, + (fourTermLabels (by omega : 11 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 1, + (fourTermLabels (by omega : 11 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 11, (fourTermLabels (by omega : 11 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 11 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x +lemma representatives_checked : ∀ a : Fin 9, + (fourTermLabels (by omega : 11 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 11 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 11 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 11 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 9, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 11, + (fourTermLabels (by omega : 11 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 9, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 11 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 9, ∀ b : FourTerm 11, + (fourTermLabels (by omega : 11 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 11 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 9, (∑ b ∈ fibers v, fourTermEval 11 (2*(0 : Fin 6).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 11 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 9, (∑ b ∈ fibers v, fourTermEval 11 (2*(1 : Fin 6).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 11 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 9, (∑ b ∈ fibers v, fourTermEval 11 (2*(2 : Fin 6).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 11 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 9, (∑ b ∈ fibers v, fourTermEval 11 (2*(3 : Fin 6).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 11 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 9, (∑ b ∈ fibers v, fourTermEval 11 (2*(4 : Fin 6).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 11 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 9, (∑ b ∈ fibers v, fourTermEval 11 (2*(5 : Fin 6).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 11 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 6, ∀ v : Fin 9, (∑ b ∈ fibers v, fourTermEval 11 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 11 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 +lemma gram_checked_0 : ∀ v : Fin 6, (∑ a : Fin 9, columns (0 : Fin 6) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 6, (∑ a : Fin 9, columns (1 : Fin 6) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 6, (∑ a : Fin 9, columns (2 : Fin 6) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 6, (∑ a : Fin 9, columns (3 : Fin 6) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 6, (∑ a : Fin 9, columns (4 : Fin 6) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 6, (∑ a : Fin 9, columns (5 : Fin 6) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 6, ∀ v : Fin 6, (∑ a : Fin 9, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 +lemma rows_table_checked_0 : ∀ v : Fin 6, integerTableEval 11 SumTable11.sums (0 : Fin 6) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 6, integerTableEval 11 SumTable11.sums (1 : Fin 6) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 6, integerTableEval 11 SumTable11.sums (2 : Fin 6) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 6, integerTableEval 11 SumTable11.sums (3 : Fin 6) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 6, integerTableEval 11 SumTable11.sums (4 : Fin 6) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 6, integerTableEval 11 SumTable11.sums (5 : Fin 6) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 6, ∀ v : Fin 6, integerTableEval 11 SumTable11.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 +lemma rows_checked (u v : Fin 6) : exactFourEval 11 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 11 SumTable11.sums SumTable11.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 6, (Z * tableComparison 11 (1/200000) Y) (0 : Fin 6) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 6, (Z * tableComparison 11 (1/200000) Y) (1 : Fin 6) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 6, (Z * tableComparison 11 (1/200000) Y) (2 : Fin 6) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 6, (Z * tableComparison 11 (1/200000) Y) (3 : Fin 6) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 6, (Z * tableComparison 11 (1/200000) Y) (4 : Fin 6) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 6, (Z * tableComparison 11 (1/200000) Y) (5 : Fin 6) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 6, ∀ v : Fin 6, (Z * tableComparison 11 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 +lemma compression_checked_0 : ∀ v : Fin 6, (W * Z) (0 : Fin 6) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 6, (W * Z) (1 : Fin 6) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 6, (W * Z) (2 : Fin 6) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 6, (W * Z) (3 : Fin 6) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 6, (W * Z) (4 : Fin 6) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 6, (W * Z) (5 : Fin 6) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 6, ∀ v : Fin 6, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 +lemma ldl_checked_0 : ∀ v : Fin 6, (∑ k : Fin 6, L (0 : Fin 6) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 6, (∑ k : Fin 6, L (1 : Fin 6) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 6, (∑ k : Fin 6, L (2 : Fin 6) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 6, (∑ k : Fin 6, L (3 : Fin 6) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 6, (∑ k : Fin 6, L (4 : Fin 6) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 6, (∑ k : Fin 6, L (5 : Fin 6) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 6, ∀ v : Fin 6, (∑ k : Fin 6, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 +lemma diag_checked : ∀ u : Fin 6, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 11 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 11 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 11 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 11 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 11 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate11 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate12.lean b/lean/OAI/Analysis/LaughlinGap/Certificate12.lean new file mode 100644 index 0000000000000000000000000000000000000000..c2203be4215cdb3795ecea5f3598fd2fb8204c46 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate12.lean @@ -0,0 +1,297 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Certificate11 +import OAI.Analysis.LaughlinGap.SumTable12 + +namespace OAI + +/-! Certificate12. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate12 + +def keys : Fin 11 → Finset (Fin 25) := ![{0,1,2,10}, {0,1,3,9}, {0,1,4,8}, {0,1,5,7}, {0,2,3,8}, {0,2,4,7}, {0,2,5,6}, {0,3,4,6}, {1,2,3,7}, {1,2,4,6}, {1,3,4,5}] +def fibers : Fin 11 → Finset (FourTerm 12) := ![{⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}] +def columns : Matrix (Fin 6) (Fin 11) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![-680400, 680400, -544320, 340200, -136080, 204120, -340200, 68040, -68040, 68040, -68040], ![-340200, 340200, -151200, 18900, -189000, 132300, -18900, -56700, 56700, -56700, 56700], ![255150, -255150, 113400, -14175, 141750, -99225, 14175, 42525, -42525, 42525, -42525], ![340200, -340200, 272160, -170100, 68040, -102060, 170100, -34020, 34020, -34020, 34020], ![-3742200, 3742200, -2494800, 1247400, -1247400, 1247400, -1247400, 0, 0, 0, 0]] +def Y : Matrix (Fin 6) (Fin 6) ℚ := ![![(-25480875896934727535824239/671088640000000000000), (89493563396161211226564537/335544320000000000000), (166617976074040701955346877/671088640000000000000), (-68908946150186095152447963/335544320000000000000), (-25261277378610897429618879/83886080000000000000), (24314236929984946889366037/41943040000000000000)], ![(89493563396161211226564537/335544320000000000000), (-84840177041796958213951827/838860800000000000000), (1570462128759565556774181/335544320000000000000), (2675787208095664591891893/167772160000000000000), (5394085570915940511708381/209715200000000000000), (-4711060210477871245903083/20971520000000000000)], ![(166617976074040701955346877/671088640000000000000), (1570462128759565556774181/335544320000000000000), (-4242903069423142887860187/671088640000000000000), (2505282131696810822676621/335544320000000000000), (-2309313931847977215171231/83886080000000000000), (7605543623364889538589/1677721600000000000)], ![(-68908946150186095152447963/335544320000000000000), (2675787208095664591891893/167772160000000000000), (2505282131696810822676621/335544320000000000000), (-4977035602351515226990971/167772160000000000000), (-611262446479920805714839/41943040000000000000), (6855650584852976870654493/20971520000000000000)], ![(-25261277378610897429618879/83886080000000000000), (5394085570915940511708381/209715200000000000000), (-2309313931847977215171231/83886080000000000000), (-611262446479920805714839/41943040000000000000), (1163227959375792088481937/52428800000000000000), (-776247942028571351610579/1048576000000000000)], ![(24314236929984946889366037/41943040000000000000), (-4711060210477871245903083/20971520000000000000), (7605543623364889538589/1677721600000000000), (6855650584852976870654493/20971520000000000000), (-776247942028571351610579/1048576000000000000), (-5553844753995143389657467/2621440000000000000)]] +def Z : Matrix (Fin 6) (Fin 6) ℚ := ![![0, 0, 0, 0, 0, 0], ![0, 2177280, 0, 0, -1088640, 7484400], ![0, 0, 604800, -453600, 0, 2494800], ![0, 0, -453600, 340200, 0, -1871100], ![0, -1088640, 0, 0, 544320, -3742200], ![0, 7484400, 2494800, -1871100, -3742200, 36018675]] +def W : Matrix (Fin 6) (Fin 6) ℚ := ![![0, 0, 0, 0, 0, 0], ![(-396155945114164818001911/30064771072000000000000000), (1077945941863588424540261/15032385536000000000000000), (-479577620617163210726943/15032385536000000000000000), (-1050502813209997889578023/7516192768000000000000000), (30617903177108088595711/536870912000000000000000), (11852149758487795318257/1879048192000000000000000)], ![(-283112681317272526766123/25769803776000000000000000), (58882953858944877176681/6012954214400000000000000), (1736159344095910418535643/90194313216000000000000000), (-3739388252132182340848349/45097156608000000000000000), (26042765295165198837787/901943132160000000000000), (105371752445598966041579/11274289152000000000000000)], ![(283112681317272526766123/34359738368000000000000000), (-176648861576834631530043/24051816857600000000000000), (-1736159344095910418535643/120259084288000000000000000), (3739388252132182340848349/60129542144000000000000000), (-26042765295165198837787/1202590842880000000000000), (-105371752445598966041579/15032385536000000000000000)], ![(396155945114164818001911/60129542144000000000000000), (-1077945941863588424540261/30064771072000000000000000), (479577620617163210726943/30064771072000000000000000), (1050502813209997889578023/15032385536000000000000000), (-30617903177108088595711/1073741824000000000000000), (-11852149758487795318257/3758096384000000000000000)], ![(-170266615010582224808971/1879048192000000000000000), (431266963682645425524167/1503238553600000000000000), (-113734630451390031032653/3758096384000000000000000), (-441566631696445936054121/536870912000000000000000), (29608833092745380921469/93952409600000000000000), (56592422300575542780047/939524096000000000000000)]] +def M : Matrix (Fin 6) (Fin 6) ℚ := ![![0, 0, 0, 0, 0, 0], ![0, (473961496050849923949854007/3355443200000000000000), (16062813445261653386739783/268435456000000000000), (-48188440335784960160219349/1073741824000000000000), (-473961496050849923949854007/6710886400000000000000), (245748146094610061633139321/335544320000000000000)], ![0, (16062813445261653386739783/268435456000000000000), (194805171953981096565244923/2684354560000000000000), (-584415515861943289695734769/10737418240000000000000), (-16062813445261653386739783/536870912000000000000), (338932636622760339625203837/671088640000000000000)], ![0, (-48188440335784960160219349/1073741824000000000000), (-584415515861943289695734769/10737418240000000000000), (1753246547585829869087204307/42949672960000000000000), (48188440335784960160219349/2147483648000000000000), (-1016797909868281018875611511/2684354560000000000000)], ![0, (-473961496050849923949854007/6710886400000000000000), (-16062813445261653386739783/536870912000000000000), (48188440335784960160219349/2147483648000000000000), (473961496050849923949854007/13421772800000000000000), (-245748146094610061633139321/671088640000000000000)], ![0, (245748146094610061633139321/335544320000000000000), (338932636622760339625203837/671088640000000000000), (-1016797909868281018875611511/2684354560000000000000), (-245748146094610061633139321/671088640000000000000), (6175231260938661149363597319/1342177280000000000000)]] +def L : Matrix (Fin 6) (Fin 6) ℚ := ![![1, 0, 0, 0, 0, 0], ![0, 1, 0, 0, 0, 0], ![0, (4957658470759769563808575/11702752988909874665428494), 1, 0, 0, 0], ![0, (-4957658470759769563808575/15603670651879832887237992), (-3/4), 1, 0, 0], ![0, (-1/2), 0, 0, 1, 0], ![0, (10113092431876957268853470/1950458831484979110904749), (33/8), 0, 0, 1]] +def diag : Fin 6 → ℚ := ![0, (473961496050849923949854007/3355443200000000000000), (643844347625087164297573368870578086732258837953/13634695464554623041307053916160000000000000), 0, 0, 0] + +def keyIndexTable : Fin 13 → Fin 13 → Fin 13 → Fin 11 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 4, 5, 6, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 4, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 8, 9, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 5, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 8, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 9, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 6, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 13) (j : Fin ((n.val+1)/2)) (x : Fin ((12-n.val+2)/2)) : Fin 11 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 11 → FourTerm 12 := ![⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 7, + (fourTermLabels (by omega : 12 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 6, + (fourTermLabels (by omega : 12 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 6, + (fourTermLabels (by omega : 12 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 5, + (fourTermLabels (by omega : 12 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 5, + (fourTermLabels (by omega : 12 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 4, + (fourTermLabels (by omega : 12 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 4, + (fourTermLabels (by omega : 12 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 3, + (fourTermLabels (by omega : 12 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 3, + (fourTermLabels (by omega : 12 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 2, + (fourTermLabels (by omega : 12 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 2, + (fourTermLabels (by omega : 12 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 1, + (fourTermLabels (by omega : 12 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover_12 : ∀ j : Fin 6, ∀ x : Fin 1, + (fourTermLabels (by omega : 12 ≤ 23) ⟨12,j,x⟩).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) ⟨12,j,x⟩).toFinset=keys (keyIndex 12 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 12, (fourTermLabels (by omega : 12 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 12 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x + · exact cover_12 j x +lemma representatives_checked : ∀ a : Fin 11, + (fourTermLabels (by omega : 12 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 12 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 12 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 12 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 11, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 12, + (fourTermLabels (by omega : 12 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 11, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 12 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 11, ∀ b : FourTerm 12, + (fourTermLabels (by omega : 12 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 12 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 11, (∑ b ∈ fibers v, fourTermEval 12 (2*(0 : Fin 6).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 12 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 11, (∑ b ∈ fibers v, fourTermEval 12 (2*(1 : Fin 6).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 12 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 11, (∑ b ∈ fibers v, fourTermEval 12 (2*(2 : Fin 6).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 12 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 11, (∑ b ∈ fibers v, fourTermEval 12 (2*(3 : Fin 6).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 12 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 11, (∑ b ∈ fibers v, fourTermEval 12 (2*(4 : Fin 6).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 12 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 11, (∑ b ∈ fibers v, fourTermEval 12 (2*(5 : Fin 6).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 12 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 6, ∀ v : Fin 11, (∑ b ∈ fibers v, fourTermEval 12 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 12 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 +lemma gram_checked_0 : ∀ v : Fin 6, (∑ a : Fin 11, columns (0 : Fin 6) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 6, (∑ a : Fin 11, columns (1 : Fin 6) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 6, (∑ a : Fin 11, columns (2 : Fin 6) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 6, (∑ a : Fin 11, columns (3 : Fin 6) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 6, (∑ a : Fin 11, columns (4 : Fin 6) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 6, (∑ a : Fin 11, columns (5 : Fin 6) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 6, ∀ v : Fin 6, (∑ a : Fin 11, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 +lemma rows_table_checked_0 : ∀ v : Fin 6, integerTableEval 12 SumTable12.sums (0 : Fin 6) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 6, integerTableEval 12 SumTable12.sums (1 : Fin 6) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 6, integerTableEval 12 SumTable12.sums (2 : Fin 6) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 6, integerTableEval 12 SumTable12.sums (3 : Fin 6) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 6, integerTableEval 12 SumTable12.sums (4 : Fin 6) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 6, integerTableEval 12 SumTable12.sums (5 : Fin 6) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 6, ∀ v : Fin 6, integerTableEval 12 SumTable12.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 +lemma rows_checked (u v : Fin 6) : exactFourEval 12 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 12 SumTable12.sums SumTable12.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 6, (Z * tableComparison 12 (1/200000) Y) (0 : Fin 6) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 6, (Z * tableComparison 12 (1/200000) Y) (1 : Fin 6) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 6, (Z * tableComparison 12 (1/200000) Y) (2 : Fin 6) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 6, (Z * tableComparison 12 (1/200000) Y) (3 : Fin 6) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 6, (Z * tableComparison 12 (1/200000) Y) (4 : Fin 6) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 6, (Z * tableComparison 12 (1/200000) Y) (5 : Fin 6) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 6, ∀ v : Fin 6, (Z * tableComparison 12 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 +lemma compression_checked_0 : ∀ v : Fin 6, (W * Z) (0 : Fin 6) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 6, (W * Z) (1 : Fin 6) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 6, (W * Z) (2 : Fin 6) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 6, (W * Z) (3 : Fin 6) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 6, (W * Z) (4 : Fin 6) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 6, (W * Z) (5 : Fin 6) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 6, ∀ v : Fin 6, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 +lemma ldl_checked_0 : ∀ v : Fin 6, (∑ k : Fin 6, L (0 : Fin 6) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 6, (∑ k : Fin 6, L (1 : Fin 6) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 6, (∑ k : Fin 6, L (2 : Fin 6) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 6, (∑ k : Fin 6, L (3 : Fin 6) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 6, (∑ k : Fin 6, L (4 : Fin 6) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 6, (∑ k : Fin 6, L (5 : Fin 6) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 6, ∀ v : Fin 6, (∑ k : Fin 6, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 +lemma diag_checked : ∀ u : Fin 6, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 12 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 12 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 12 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 12 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 12 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate12 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate13.lean b/lean/OAI/Analysis/LaughlinGap/Certificate13.lean new file mode 100644 index 0000000000000000000000000000000000000000..dff0ffbd5441586056a1eb53eee0b4760abec845 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate13.lean @@ -0,0 +1,327 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CachedIntegerRows +import OAI.Analysis.LaughlinGap.FastFourKeys +import OAI.Analysis.LaughlinGap.FourTables +import OAI.Analysis.LaughlinGap.SumTable13 + +namespace OAI + +/-! Certificate13. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate13 + +def keys : Fin 15 → Finset (Fin 25) := ![{0,1,2,11}, {0,1,3,10}, {0,1,4,9}, {0,1,5,8}, {0,1,6,7}, {0,2,3,9}, {0,2,4,8}, {0,2,5,7}, {0,3,4,7}, {0,3,5,6}, {1,2,3,8}, {1,2,4,7}, {1,2,5,6}, {1,3,4,6}, {2,3,4,5}] +def fibers : Fin 15 → Finset (FourTerm 13) := ![{⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩}] +def columns : Matrix (Fin 7) (Fin 15) ℚ := ![![9355500, -9355500, 14968800, -14968800, 16839900, -5613300, 0, -1871100, 7484400, -5613300, 5613300, -5613300, 7484400, -1871100, 1871100], ![4677750, -4677750, 4762800, -4762800, 4337550, -85050, 0, 425250, -340200, -85050, 85050, -85050, -340200, 425250, -425250], ![3274425, -3274425, 1701000, -491400, 42525, 1573425, -1209600, 448875, 396900, -240975, -363825, 363825, -207900, -155925, 155925], ![-467775, 467775, -340200, 340200, -411075, -127575, 0, 70875, 56700, -127575, 127575, -127575, 56700, 70875, -70875], ![-3742200, 3742200, -1973160, 340200, 510300, -1769040, 1632960, -850500, -646380, 680400, 136080, -136080, 170100, -34020, 34020], ![9355500, -9355500, 3742200, 1247400, -3742200, 5613300, -4989600, 2494800, 1871100, -1871100, -623700, 623700, -623700, 0, 0], ![97297200, -97297200, 97297200, -97297200, 97297200, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Y : Matrix (Fin 7) (Fin 7) ℚ := ![![(-251839151268331040358014961/41943040000000000000), (-46874153992556821049553357/41943040000000000000), (-25859766171309160725669177/8388608000000000000), (50582089306178241712160139/20971520000000000000), (-13552253472962587859513433/5242880000000000000), (19383207361412165471625381/1310720000000000000), (-610255650447424138062274083/2621440000000000000)], ![(-46874153992556821049553357/41943040000000000000), (44870346217788652708105509/83886080000000000000), (13655425844208758783924331/41943040000000000000), (-3161342093808007008219357/20971520000000000000), (-744703562398457224684467/5242880000000000000), (-3596861348652718123622667/5242880000000000000), (21361606258273238908704897/2621440000000000000)], ![(-25859766171309160725669177/8388608000000000000), (13655425844208758783924331/41943040000000000000), (-10382017631950642371404427/41943040000000000000), (195751427625490755693087/10485760000000000000), (1996722594805280378163651/5242880000000000000), (-2146289399351278589700567/2621440000000000000), (16056239782467396663247239/2621440000000000000)], ![(50582089306178241712160139/20971520000000000000), (-3161342093808007008219357/20971520000000000000), (195751427625490755693087/10485760000000000000), (-196134629690386723946157/20971520000000000000), (-139848552795666216461211/524288000000000000), (1701017595534794460591789/2621440000000000000), (-92309060511862267120047/65536000000000000)], ![(-13552253472962587859513433/5242880000000000000), (-744703562398457224684467/5242880000000000000), (1996722594805280378163651/5242880000000000000), (-139848552795666216461211/524288000000000000), (-471610220949050484117933/655360000000000000), (155671217561575490113647/163840000000000000), (-36284315401494109563471/65536000000000000)], ![(19383207361412165471625381/1310720000000000000), (-3596861348652718123622667/5242880000000000000), (-2146289399351278589700567/2621440000000000000), (1701017595534794460591789/2621440000000000000), (155671217561575490113647/163840000000000000), (-808423367051529180056853/81920000000000000), (3299431615695312593637141/163840000000000000)], ![(-610255650447424138062274083/2621440000000000000), (21361606258273238908704897/2621440000000000000), (16056239782467396663247239/2621440000000000000), (-92309060511862267120047/65536000000000000), (-36284315401494109563471/65536000000000000), (3299431615695312593637141/163840000000000000), (-29496262650250696000860159/32768000000000000)]] +def Z : Matrix (Fin 7) (Fin 7) ℚ := ![![958003200, 0, 0, 0, 0, -29937600, 972972000], ![0, 21772800, 0, 0, -2721600, 0, 291891600], ![0, 0, 4838400, -907200, -4082400, 12474000, 48648600], ![0, 0, -907200, 453600, 0, 0, -24324300], ![0, -2721600, -4082400, 0, 5851440, -16839900, -36486450], ![-29937600, 0, 12474000, 0, -16839900, 52390800, -30405375], ![972972000, 291891600, 48648600, -24324300, -36486450, -30405375, (12411474075/2)]] +def W : Matrix (Fin 7) (Fin 7) ℚ := ![![(8831729987737786013738573/2147483648000000000000000), (34748628211019859443241/1073741824000000000000000), (2175442601701750730797569/2147483648000000000000000), (-1128958923458752922056081/939524096000000000000000), (48438050204416062501949/75161927680000000000000), (-8573098207642290777219/18790481920000000000000), (92608358609211905476251/939524096000000000000000)], ![(704355043989103561462739/30064771072000000000000000), (-94799695758939067836079/2147483648000000000000000), (-3067525806525348938659353/30064771072000000000000000), (69083236828150945907529/1879048192000000000000000), (-4910735017771293411479/751619276800000000000000), (458868912964094577561/939524096000000000000000), (10221836670894438945003/1879048192000000000000000)], ![(248813601151941368981393/60129542144000000000000000), (-76203924028572529522213/4294967296000000000000000), (6348203556056114499720509/60129542144000000000000000), (-734561681117907727253339/11274289152000000000000000), (-481053601353272974503703/4509715660800000000000000), (66163226149991696581643/1879048192000000000000000), (-1720323125791409334903/3758096384000000000000000)], ![(-224556771463107840590339/60129542144000000000000000), (462797852877355205514539/90194313216000000000000000), (-308497566527027712898347/60129542144000000000000000), (-1290010974934108149769/5637144576000000000000000), (53121711501985771085789/4509715660800000000000000), (-3670859581048323286559/1879048192000000000000000), (-3968443850398932428773/11274289152000000000000000)], ![(1886323207959888622067/1202590842880000000000000), (234754241029267043867483/15032385536000000000000000), (-871281239927680314391539/7516192768000000000000000), (631207934101804270913409/7516192768000000000000000), (84946132005814233951163/751619276800000000000000), (-79523751661899341155899/1879048192000000000000000), (834644129363458012941/939524096000000000000000)], ![(-611000071363531735703093/4294967296000000000000000), (-479049630298473675900877/15032385536000000000000000), (2717215308549307723810983/7516192768000000000000000), (-1751995012933833209080121/7516192768000000000000000), (-54563777660804950852039/150323855360000000000000), (10777185928957969598559/75161927680000000000000), (-7396399577159528967533/939524096000000000000000)], ![(35259962251620035869883411/7516192768000000000000000), (-783658293849616354379353/939524096000000000000000), (-120022021767360028330443/1879048192000000000000000), (-1343991723371246071176483/1879048192000000000000000), (-2433044524619679829573/37580963840000000000000), (-165388004737776008739681/469762048000000000000000), (1287911404311002548883/6710886400000000000000)]] +def M : Matrix (Fin 7) (Fin 7) ℚ := ![![(679383827619707163253971626307/167772160000000000000), (9302050916298637474435869411/335544320000000000000), (330800053606043496481081053/134217728000000000000), (-518308919087766906124880811/134217728000000000000), (304844664596175032853703311/83886080000000000000), (-12435058782401141646184436253/83886080000000000000), (6149178943024853651772080367/1310720000000000000)], ![(9302050916298637474435869411/335544320000000000000), (86502352716019080426588039/134217728000000000000), (-308176606888633430456770863/1342177280000000000000), (-30981537341857890960211431/1342177280000000000000), (2447253932672797413599853/8388608000000000000), (-168098909438954386585025487/83886080000000000000), (1595240264012864128510203639/41943040000000000000)], ![(330800053606043496481081053/134217728000000000000), (-308176606888633430456770863/1342177280000000000000), (3818086724212768479176683371/2684354560000000000000), (-306545151431943830292769053/2684354560000000000000), (-265606313568676921717740837/167772160000000000000), (81336626278502226196173741/16777216000000000000), (465464830069039455237485331/83886080000000000000)], ![(-518308919087766906124880811/134217728000000000000), (-30981537341857890960211431/1342177280000000000000), (-306545151431943830292769053/2684354560000000000000), (35198751633344272173271779/2684354560000000000000), (81636177339639777191864319/671088640000000000000), (-32508298712591186910006483/134217728000000000000), (-827898465330432286082750601/167772160000000000000)], ![(304844664596175032853703311/83886080000000000000), (2447253932672797413599853/8388608000000000000), (-265606313568676921717740837/167772160000000000000), (81636177339639777191864319/671088640000000000000), (2378767750254200009443536657/1342177280000000000000), (-7570433753960369609446538013/1342177280000000000000), (361901366398657158054228819/335544320000000000000)], ![(-12435058782401141646184436253/83886080000000000000), (-168098909438954386585025487/83886080000000000000), (81336626278502226196173741/16777216000000000000), (-32508298712591186910006483/134217728000000000000), (-7570433753960369609446538013/1342177280000000000000), (30376681419317532547754017809/1342177280000000000000), (-55173586526011810923123519891/335544320000000000000)], ![(6149178943024853651772080367/1310720000000000000), (1595240264012864128510203639/41943040000000000000), (465464830069039455237485331/83886080000000000000), (-827898465330432286082750601/167772160000000000000), (361901366398657158054228819/335544320000000000000), (-55173586526011810923123519891/335544320000000000000), (92933407695426524496291761883/16777216000000000000)]] +def L : Matrix (Fin 7) (Fin 7) ℚ := ![![1, 0, 0, 0, 0, 0, 0], ![(3480004083912696398965907/508330585574042022636716518), 1, 0, 0, 0, 0, 0], ![(618780496831357082830305/1016661171148084045273433036), (-32439708799189059971384216868547739288924048209841/59844370252069954335025159500493333113384925260918), 1, 0, 0, 0, 0], ![(-35043130034465600186935/36746789318605447419521676), (882835082009016384226944621005887338723325380011/119688740504139908670050319000986666226769850521836), (-106549992448321565050494614978843827137059325811169374408783674627429082/1246542322781118734185307686555808314832555582764943797608745762542928169), 1, 0, 0, 0], ![(228091780468518543100414/254165292787021011318358259), (1734381888231324175347366547981226345362857291983/2955277543312096510371612814839176943870860506712), (-5580588624576168262055319665629851567015559428170067263472363431755578027/4986169291124474936741230746223233259330222331059775190434983050171712676), (-27/10), 1, 0, 0], ![(-489694558938355943299838/13377120673001105858860961), (-6428252053499638508494999902277043915781628724595/2955277543312096510371612814839176943870860506712), (34103597150187694934782509067737981798428418727705966610108887638506310165/9972338582248949873482461492446466518660444662119550380869966100343425352), (33/4), 0, 1, 0], ![(294461243811141514188861312/254165292787021011318358259), (259539191018482024500615363967589464260599164175879/19948123417356651445008386500164444371128308420306), (22854973380164975703331094912962000920899225386495830810684098207583538089/4986169291124474936741230746223233259330222331059775190434983050171712676), (-429/8), 0, 0, 1]] +def diag : Fin 7 → ℚ := ![(679383827619707163253971626307/167772160000000000000), (2423696995208833150568518959769979991092089473067179/5330232520988866879283176595783680000000000000), (1246542322781118734185307686555808314832555582764943797608745762542928169/968385345392507784518570087166501500967603570839388160000000000000), (2513845326467649635666674520447585664534112472365505536452626526778469811923314148719593/8169339766578339736356832454612145372086636267208335672008676229401334048358400000000000), 0, 0, 0] + +def keyIndexTable : Fin 14 → Fin 13 → Fin 13 → Fin 15 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 4, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 5, 6, 7, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 5, 0, 8, 9, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 10, 11, 12, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 6, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 10, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 7, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 11, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 10, 0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 11, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 7, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 12, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 12, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 13, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 14) (j : Fin ((n.val+1)/2)) (x : Fin ((13-n.val+2)/2)) : Fin 15 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 15 → FourTerm 13 := ![⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 7, + (fourTermLabels (by omega : 13 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 7, + (fourTermLabels (by omega : 13 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 6, + (fourTermLabels (by omega : 13 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 6, + (fourTermLabels (by omega : 13 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 5, + (fourTermLabels (by omega : 13 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 5, + (fourTermLabels (by omega : 13 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 4, + (fourTermLabels (by omega : 13 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 4, + (fourTermLabels (by omega : 13 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 3, + (fourTermLabels (by omega : 13 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 3, + (fourTermLabels (by omega : 13 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 2, + (fourTermLabels (by omega : 13 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 2, + (fourTermLabels (by omega : 13 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover_12 : ∀ j : Fin 6, ∀ x : Fin 1, + (fourTermLabels (by omega : 13 ≤ 23) ⟨12,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨12,j,x⟩).toFinset=keys (keyIndex 12 j x) := by decide +kernel +lemma cover_13 : ∀ j : Fin 7, ∀ x : Fin 1, + (fourTermLabels (by omega : 13 ≤ 23) ⟨13,j,x⟩).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) ⟨13,j,x⟩).toFinset=keys (keyIndex 13 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 13, (fourTermLabels (by omega : 13 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 13 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x + · exact cover_12 j x + · exact cover_13 j x +lemma representatives_checked : ∀ a : Fin 15, + (fourTermLabels (by omega : 13 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 13 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 13 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 13 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 15, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 13, + (fourTermLabels (by omega : 13 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 15, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 13 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 15, ∀ b : FourTerm 13, + (fourTermLabels (by omega : 13 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 13 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 15, (∑ b ∈ fibers v, fourTermEval 13 (2*(0 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 13 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 15, (∑ b ∈ fibers v, fourTermEval 13 (2*(1 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 13 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 15, (∑ b ∈ fibers v, fourTermEval 13 (2*(2 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 13 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 15, (∑ b ∈ fibers v, fourTermEval 13 (2*(3 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 13 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 15, (∑ b ∈ fibers v, fourTermEval 13 (2*(4 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 13 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 15, (∑ b ∈ fibers v, fourTermEval 13 (2*(5 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 13 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_6 : ∀ v : Fin 15, (∑ b ∈ fibers v, fourTermEval 13 (2*(6 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 13 ≤ 23) b)) = columns 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 7, ∀ v : Fin 15, (∑ b ∈ fibers v, fourTermEval 13 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 13 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 + · exact columns_checked_6 +lemma gram_checked_0 : ∀ v : Fin 7, (∑ a : Fin 15, columns (0 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 7, (∑ a : Fin 15, columns (1 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 7, (∑ a : Fin 15, columns (2 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 7, (∑ a : Fin 15, columns (3 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 7, (∑ a : Fin 15, columns (4 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 7, (∑ a : Fin 15, columns (5 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_6 : ∀ v : Fin 7, (∑ a : Fin 15, columns (6 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 7, ∀ v : Fin 7, (∑ a : Fin 15, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 + · exact gram_checked_6 +lemma rows_table_checked_0 : ∀ v : Fin 7, integerTableEval 13 SumTable13.sums (0 : Fin 7) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 7, integerTableEval 13 SumTable13.sums (1 : Fin 7) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 7, integerTableEval 13 SumTable13.sums (2 : Fin 7) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 7, integerTableEval 13 SumTable13.sums (3 : Fin 7) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 7, integerTableEval 13 SumTable13.sums (4 : Fin 7) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 7, integerTableEval 13 SumTable13.sums (5 : Fin 7) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_6 : ∀ v : Fin 7, integerTableEval 13 SumTable13.sums (6 : Fin 7) v = Y 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 7, ∀ v : Fin 7, integerTableEval 13 SumTable13.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 + · exact rows_table_checked_6 +lemma rows_checked (u v : Fin 7) : exactFourEval 13 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 13 SumTable13.sums SumTable13.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 7, (Z * tableComparison 13 (1/200000) Y) (0 : Fin 7) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 7, (Z * tableComparison 13 (1/200000) Y) (1 : Fin 7) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 7, (Z * tableComparison 13 (1/200000) Y) (2 : Fin 7) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 7, (Z * tableComparison 13 (1/200000) Y) (3 : Fin 7) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 7, (Z * tableComparison 13 (1/200000) Y) (4 : Fin 7) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 7, (Z * tableComparison 13 (1/200000) Y) (5 : Fin 7) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_6 : ∀ v : Fin 7, (Z * tableComparison 13 (1/200000) Y) (6 : Fin 7) v = W 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 7, ∀ v : Fin 7, (Z * tableComparison 13 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 + · exact product_checked_6 +lemma compression_checked_0 : ∀ v : Fin 7, (W * Z) (0 : Fin 7) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 7, (W * Z) (1 : Fin 7) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 7, (W * Z) (2 : Fin 7) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 7, (W * Z) (3 : Fin 7) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 7, (W * Z) (4 : Fin 7) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 7, (W * Z) (5 : Fin 7) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_6 : ∀ v : Fin 7, (W * Z) (6 : Fin 7) v = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 7, ∀ v : Fin 7, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 + · exact compression_checked_6 +lemma ldl_checked_0 : ∀ v : Fin 7, (∑ k : Fin 7, L (0 : Fin 7) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 7, (∑ k : Fin 7, L (1 : Fin 7) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 7, (∑ k : Fin 7, L (2 : Fin 7) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 7, (∑ k : Fin 7, L (3 : Fin 7) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 7, (∑ k : Fin 7, L (4 : Fin 7) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 7, (∑ k : Fin 7, L (5 : Fin 7) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_6 : ∀ v : Fin 7, (∑ k : Fin 7, L (6 : Fin 7) k * diag k * L v k) = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 7, ∀ v : Fin 7, (∑ k : Fin 7, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 + · exact ldl_checked_6 +lemma diag_checked : ∀ u : Fin 7, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 13 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 13 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 13 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 13 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 13 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate13 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate14.lean b/lean/OAI/Analysis/LaughlinGap/Certificate14.lean new file mode 100644 index 0000000000000000000000000000000000000000..8750f09ebf50a7a867cbc0e94c2b973149f7663a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate14.lean @@ -0,0 +1,329 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Certificate13 +import OAI.Analysis.LaughlinGap.SumTable14 + +namespace OAI + +/-! Certificate14. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate14 + +def keys : Fin 18 → Finset (Fin 25) := ![{0,1,2,12}, {0,1,3,11}, {0,1,4,10}, {0,1,5,9}, {0,1,6,8}, {0,2,3,10}, {0,2,4,9}, {0,2,5,8}, {0,2,6,7}, {0,3,4,8}, {0,3,5,7}, {0,4,5,6}, {1,2,3,9}, {1,2,4,8}, {1,2,5,7}, {1,3,4,7}, {1,3,5,6}, {2,3,4,6}] +def fibers : Fin 18 → Finset (FourTerm 14) := ![{⟨⟨14,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩}] +def columns : Matrix (Fin 7) (Fin 18) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![-37422000, 37422000, -37422000, 29937600, -14968800, 0, 7484400, -14968800, 14968800, 0, 3742200, -7484400, -7484400, 7484400, -3742200, -3742200, 3742200, 0], ![-29937600, 29937600, -19051200, 10886400, -5443200, -10886400, 8164800, -5443200, 5443200, 0, -1360800, 2721600, 2721600, -2721600, 1360800, 1360800, -1360800, 0], ![-6548850, 6548850, -1786050, -2381400, 2778300, -4762800, 4167450, -396900, -2778300, -3175200, 2877525, -2579850, 595350, -595350, 297675, 297675, -297675, 0], ![26195400, -26195400, 12587400, -1360800, -2041200, 13608000, -11226600, 3402000, 2041200, 5443200, -4252500, 3061800, -2381400, 2381400, -1190700, -1190700, 1190700, 0], ![-3742200, 3742200, 7484400, -14968800, 11226600, -11226600, 7484400, 3742200, -11226600, -7484400, 5613300, -3742200, 3742200, -3742200, 1871100, 1871100, -1871100, 0], ![-389188800, 389188800, -291891600, 194594400, -97297200, -97297200, 97297200, -97297200, 97297200, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Y : Matrix (Fin 7) (Fin 7) ℚ := ![![(15219600345752738461520645079/83886080000000000000), (-100699762768020161113872933/4194304000000000000), (-623729805467846140120843071/83886080000000000000), (-584089516007342278316570187/41943040000000000000), (190555190136371424746095857/10485760000000000000), (1571730082844728778022051/5242880000000000000), (-1139960040141741640450909137/5242880000000000000)], ![(-100699762768020161113872933/4194304000000000000), (142741640769102658893312549/41943040000000000000), (-1420959356539230918345309/5242880000000000000), (10401301871960478637221063/10485760000000000000), (-317763072506796368043537/262144000000000000), (6764197770693769340624481/2621440000000000000), (-3847922209486781646037389/327680000000000000)], ![(-623729805467846140120843071/83886080000000000000), (-1420959356539230918345309/5242880000000000000), (-80601890371374760912183311/83886080000000000000), (19362242855862308868505137/41943040000000000000), (-739855777506079978431279/2097152000000000000), (2827689580002698468430219/5242880000000000000), (11349999406573499998071603/1048576000000000000)], ![(-584089516007342278316570187/41943040000000000000), (10401301871960478637221063/10485760000000000000), (19362242855862308868505137/41943040000000000000), (-12463140124899425974493061/20971520000000000000), (810008762072598110220849/5242880000000000000), (4281511287086331709548753/2621440000000000000), (24114645682193842356171591/2621440000000000000)], ![(190555190136371424746095857/10485760000000000000), (-317763072506796368043537/262144000000000000), (-739855777506079978431279/2097152000000000000), (810008762072598110220849/5242880000000000000), (-457283495233465719845067/262144000000000000), (-2055131064044619675411429/655360000000000000), (17042174237599294094951211/655360000000000000)], ![(1571730082844728778022051/5242880000000000000), (6764197770693769340624481/2621440000000000000), (2827689580002698468430219/5242880000000000000), (4281511287086331709548753/2621440000000000000), (-2055131064044619675411429/655360000000000000), (-3397198876302593138403627/327680000000000000), (-23457664774180455687416691/327680000000000000)], ![(-1139960040141741640450909137/5242880000000000000), (-3847922209486781646037389/327680000000000000), (11349999406573499998071603/1048576000000000000), (24114645682193842356171591/2621440000000000000), (17042174237599294094951211/655360000000000000), (-23457664774180455687416691/327680000000000000), (-36053847999379672913103939/65536000000000000)]] +def Z : Matrix (Fin 7) (Fin 7) ℚ := ![![0, 0, 0, 0, 0, 0, 0], ![0, 239500800, 0, 0, 0, -74844000, 778377600], ![0, 0, 43545600, 0, -21772800, 0, 389188800], ![0, 0, 0, 11113200, -19051200, 26195400, 0], ![0, 0, -21772800, -19051200, 43545600, -44906400, -194594400], ![0, -74844000, 0, 26195400, -44906400, 85135050, -243243000], ![0, 778377600, 389188800, 0, -194594400, -243243000, 6008102100]] +def W : Matrix (Fin 7) (Fin 7) ℚ := ![![0, 0, 0, 0, 0, 0, 0], ![(123795619616625230857561/15032385536000000000000000), (-221210576158217105563/46976204800000000000000), (-315334141815200876317037/15032385536000000000000000), (-17240348303552013281301/268435456000000000000000), (-18606396763756514900187/268435456000000000000000), (1227009175825425140409/93952409600000000000000), (8772549315849100608091/939524096000000000000000)], ![(18172541700157367690841/3758096384000000000000000), (12224389970059675949/7340032000000000000000), (9334405490547223614403/3758096384000000000000000), (-17741117058979611456699/469762048000000000000000), (-3305365487436044767739/67108864000000000000000), (165804218614708974899/16777216000000000000000), (1379163013793970768619/234881024000000000000000)], ![(115960184441607400478711/51539607552000000000000000), (-2095680593639597551879/402653184000000000000000), (-98307993990097050306151/10307921510400000000000000), (37792678041424947070259/6442450944000000000000000), (-24059909713700877186417/2147483648000000000000000), (-1280999549817774216473/322122547200000000000000), (1570739546172222142769/644245094400000000000000)], ![(-7546014049689474849683/1202590842880000000000000), (380018070823728547339/46976204800000000000000), (454202347988296357073143/30064771072000000000000000), (4738827170641928393791/536870912000000000000000), (164729962789311885055943/3758096384000000000000000), (1762479627877019785193/939524096000000000000000), (-13370349786036993788321/1879048192000000000000000)], ![(20518247836704851593063/7516192768000000000000000), (-40574708656115718502263/3758096384000000000000000), (-2992397625296354207229/187904819200000000000000), (63695728067499680163649/1879048192000000000000000), (-4461035431895341426413/939524096000000000000000), (-180589651135023590029/13421772800000000000000), (132899776438208483787/46976204800000000000000)], ![(150286304219236842176377/2147483648000000000000000), (-393985324535842575939/939524096000000000000000), (-98732994944619943402209/2147483648000000000000000), (-1026462858764329411726587/1879048192000000000000000), (-178637605658047273872277/268435456000000000000000), (61431404815494079500121/469762048000000000000000), (3112634520785761278177/37580963840000000000000)]] +def M : Matrix (Fin 7) (Fin 7) ℚ := ![![0, 0, 0, 0, 0, 0, 0], ![0, (433072404967000467346093053/83886080000000000000), (88702260823986477866596629/20971520000000000000), (636782555035305004693648743/671088640000000000000), (-627715852596790913477950263/167772160000000000000), (52288304842143292837295997/83886080000000000000), (4578591140600268102605631909/83886080000000000000)], ![0, (88702260823986477866596629/20971520000000000000), (18170625719261128544184429/5242880000000000000), (130446532111511337136927407/167772160000000000000), (-128588159496263658663992319/41943040000000000000), (10715682418217387501676093/20971520000000000000), (937882217141541398521032381/20971520000000000000)], ![0, (636782555035305004693648743/671088640000000000000), (130446532111511337136927407/167772160000000000000), (187330355546167953656478081/1073741824000000000000), (-923208318902119534954448373/1342177280000000000000), (15396641498003637837573531/134217728000000000000), (1346601365370254313579902643/134217728000000000000)], ![0, (-627715852596790913477950263/167772160000000000000), (-128588159496263658663992319/41943040000000000000), (-923208318902119534954448373/1342177280000000000000), (910013346085963006779304293/335544320000000000000), (-75855532882877345372933367/167772160000000000000), (-6637103222930996266041063759/167772160000000000000)], ![0, (52288304842143292837295997/83886080000000000000), (10715682418217387501676093/20971520000000000000), (15396641498003637837573531/134217728000000000000), (-75855532882877345372933367/167772160000000000000), (1268491388742116060525487/16777216000000000000), (110604527437647460981226463/16777216000000000000)], ![0, (4578591140600268102605631909/83886080000000000000), (937882217141541398521032381/20971520000000000000), (1346601365370254313579902643/134217728000000000000), (-6637103222930996266041063759/167772160000000000000), (110604527437647460981226463/16777216000000000000), (1936388418790439053223808453/3355443200000000000)]] +def L : Matrix (Fin 7) (Fin 7) ℚ := ![![1, 0, 0, 0, 0, 0, 0], ![0, 1, 0, 0, 0, 0, 0], ![0, (132738138157854811622292/162017360631126250410061), 1, 0, 0, 0, 0], ![0, (238227667428097644853591/1296138885049010003280488), (9557801666835981004170464449335712364327/38681444879414949802360013223276559109056), 1, 0, 0, 0], ![0, (-234835709912753802273831/324034721262252500820122), (-8931381324285146298510914988339160901915/9670361219853737450590003305819139777264), (-12/7), 1, 0, 0], ![0, (1778332307660554801799/14728850966466022764551), (45058207857941053305375046689725501146113/77362889758829899604720026446553118218112), (33/14), 0, 1, 0], ![0, (155718502894271608427903/14728850966466022764551), (143/16), 0, 0, 0, 1]] +def diag : Fin 7 → ℚ := ![0, (433072404967000467346093053/83886080000000000000), (146868611026528637530835675207128185367197/301646867793224146218004480000000000000), (335384473774632721168007398488458696062030883255156572440519/10140108686469352600989863306402610311084376064000000000000), 0, 0, 0] + +def keyIndexTable : Fin 15 → Fin 13 → Fin 13 → Fin 18 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 4, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 5, 6, 7, 8, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 5, 0, 9, 10, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 12, 13, 14, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 6, 9, 0, 11, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 12, 0, 15, 16, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 7, 10, 11, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 13, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 12, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 8, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 14, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 13, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 8, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 15, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 7, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 14, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 16, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 15) (j : Fin ((n.val+1)/2)) (x : Fin ((14-n.val+2)/2)) : Fin 18 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 18 → FourTerm 14 := ![⟨⟨14,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 8, + (fourTermLabels (by omega : 14 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 7, + (fourTermLabels (by omega : 14 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 7, + (fourTermLabels (by omega : 14 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 6, + (fourTermLabels (by omega : 14 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 6, + (fourTermLabels (by omega : 14 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 5, + (fourTermLabels (by omega : 14 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 5, + (fourTermLabels (by omega : 14 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 4, + (fourTermLabels (by omega : 14 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 4, + (fourTermLabels (by omega : 14 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 3, + (fourTermLabels (by omega : 14 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 3, + (fourTermLabels (by omega : 14 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 2, + (fourTermLabels (by omega : 14 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover_12 : ∀ j : Fin 6, ∀ x : Fin 2, + (fourTermLabels (by omega : 14 ≤ 23) ⟨12,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨12,j,x⟩).toFinset=keys (keyIndex 12 j x) := by decide +kernel +lemma cover_13 : ∀ j : Fin 7, ∀ x : Fin 1, + (fourTermLabels (by omega : 14 ≤ 23) ⟨13,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨13,j,x⟩).toFinset=keys (keyIndex 13 j x) := by decide +kernel +lemma cover_14 : ∀ j : Fin 7, ∀ x : Fin 1, + (fourTermLabels (by omega : 14 ≤ 23) ⟨14,j,x⟩).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) ⟨14,j,x⟩).toFinset=keys (keyIndex 14 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 14, (fourTermLabels (by omega : 14 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 14 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x + · exact cover_12 j x + · exact cover_13 j x + · exact cover_14 j x +lemma representatives_checked : ∀ a : Fin 18, + (fourTermLabels (by omega : 14 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 14 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 14 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 14 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 18, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 14, + (fourTermLabels (by omega : 14 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 18, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 14 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 18, ∀ b : FourTerm 14, + (fourTermLabels (by omega : 14 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 14 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 18, (∑ b ∈ fibers v, fourTermEval 14 (2*(0 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 14 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 18, (∑ b ∈ fibers v, fourTermEval 14 (2*(1 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 14 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 18, (∑ b ∈ fibers v, fourTermEval 14 (2*(2 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 14 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 18, (∑ b ∈ fibers v, fourTermEval 14 (2*(3 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 14 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 18, (∑ b ∈ fibers v, fourTermEval 14 (2*(4 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 14 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 18, (∑ b ∈ fibers v, fourTermEval 14 (2*(5 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 14 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_6 : ∀ v : Fin 18, (∑ b ∈ fibers v, fourTermEval 14 (2*(6 : Fin 7).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 14 ≤ 23) b)) = columns 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 7, ∀ v : Fin 18, (∑ b ∈ fibers v, fourTermEval 14 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 14 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 + · exact columns_checked_6 +lemma gram_checked_0 : ∀ v : Fin 7, (∑ a : Fin 18, columns (0 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 7, (∑ a : Fin 18, columns (1 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 7, (∑ a : Fin 18, columns (2 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 7, (∑ a : Fin 18, columns (3 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 7, (∑ a : Fin 18, columns (4 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 7, (∑ a : Fin 18, columns (5 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_6 : ∀ v : Fin 7, (∑ a : Fin 18, columns (6 : Fin 7) a * columns v a / setFactorial (keys a)) = Z 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 7, ∀ v : Fin 7, (∑ a : Fin 18, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 + · exact gram_checked_6 +lemma rows_table_checked_0 : ∀ v : Fin 7, integerTableEval 14 SumTable14.sums (0 : Fin 7) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 7, integerTableEval 14 SumTable14.sums (1 : Fin 7) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 7, integerTableEval 14 SumTable14.sums (2 : Fin 7) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 7, integerTableEval 14 SumTable14.sums (3 : Fin 7) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 7, integerTableEval 14 SumTable14.sums (4 : Fin 7) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 7, integerTableEval 14 SumTable14.sums (5 : Fin 7) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_6 : ∀ v : Fin 7, integerTableEval 14 SumTable14.sums (6 : Fin 7) v = Y 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 7, ∀ v : Fin 7, integerTableEval 14 SumTable14.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 + · exact rows_table_checked_6 +lemma rows_checked (u v : Fin 7) : exactFourEval 14 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 14 SumTable14.sums SumTable14.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 7, (Z * tableComparison 14 (1/200000) Y) (0 : Fin 7) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 7, (Z * tableComparison 14 (1/200000) Y) (1 : Fin 7) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 7, (Z * tableComparison 14 (1/200000) Y) (2 : Fin 7) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 7, (Z * tableComparison 14 (1/200000) Y) (3 : Fin 7) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 7, (Z * tableComparison 14 (1/200000) Y) (4 : Fin 7) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 7, (Z * tableComparison 14 (1/200000) Y) (5 : Fin 7) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_6 : ∀ v : Fin 7, (Z * tableComparison 14 (1/200000) Y) (6 : Fin 7) v = W 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 7, ∀ v : Fin 7, (Z * tableComparison 14 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 + · exact product_checked_6 +lemma compression_checked_0 : ∀ v : Fin 7, (W * Z) (0 : Fin 7) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 7, (W * Z) (1 : Fin 7) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 7, (W * Z) (2 : Fin 7) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 7, (W * Z) (3 : Fin 7) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 7, (W * Z) (4 : Fin 7) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 7, (W * Z) (5 : Fin 7) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_6 : ∀ v : Fin 7, (W * Z) (6 : Fin 7) v = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 7, ∀ v : Fin 7, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 + · exact compression_checked_6 +lemma ldl_checked_0 : ∀ v : Fin 7, (∑ k : Fin 7, L (0 : Fin 7) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 7, (∑ k : Fin 7, L (1 : Fin 7) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 7, (∑ k : Fin 7, L (2 : Fin 7) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 7, (∑ k : Fin 7, L (3 : Fin 7) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 7, (∑ k : Fin 7, L (4 : Fin 7) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 7, (∑ k : Fin 7, L (5 : Fin 7) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_6 : ∀ v : Fin 7, (∑ k : Fin 7, L (6 : Fin 7) k * diag k * L v k) = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 7, ∀ v : Fin 7, (∑ k : Fin 7, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 + · exact ldl_checked_6 +lemma diag_checked : ∀ u : Fin 7, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 14 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 14 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 14 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 14 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 14 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate14 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate15.lean b/lean/OAI/Analysis/LaughlinGap/Certificate15.lean new file mode 100644 index 0000000000000000000000000000000000000000..7cf3270fecb8d365fd276bdef146b238d5f522e9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate15.lean @@ -0,0 +1,359 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CachedIntegerRows +import OAI.Analysis.LaughlinGap.FastFourKeys +import OAI.Analysis.LaughlinGap.FourTables +import OAI.Analysis.LaughlinGap.SumTable15 + +namespace OAI + +/-! Certificate15. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate15 + +def keys : Fin 23 → Finset (Fin 25) := ![{0,1,2,13}, {0,1,3,12}, {0,1,4,11}, {0,1,5,10}, {0,1,6,9}, {0,1,7,8}, {0,2,3,11}, {0,2,4,10}, {0,2,5,9}, {0,2,6,8}, {0,3,4,9}, {0,3,5,8}, {0,3,6,7}, {0,4,5,7}, {1,2,3,10}, {1,2,4,9}, {1,2,5,8}, {1,2,6,7}, {1,3,4,8}, {1,3,5,7}, {1,4,5,6}, {2,3,4,7}, {2,3,5,6}] +def fibers : Fin 23 → Finset (FourTerm 15) := ![{⟨⟨15,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩}] +def columns : Matrix (Fin 8) (Fin 23) ℚ := ![![510810300, -510810300, 851350500, -851350500, 1021620600, -1021620600, -340540200, 0, -170270100, 0, 510810300, -340540200, 510810300, -170270100, 340540200, -340540200, 510810300, -510810300, -170270100, 0, 170270100, 170270100, -170270100], ![291891600, -291891600, 336798000, -336798000, 314344800, -314344800, -44906400, 0, 22453200, 0, 22453200, -44906400, 22453200, 22453200, 44906400, -44906400, 22453200, -22453200, 22453200, 0, -22453200, -22453200, 22453200], ![273648375, -273648375, 194126625, -126086625, 67614750, -26790750, 79521750, -68040000, 58471875, -40824000, -1913625, -2126250, 18498375, -9568125, -11481750, 11481750, -15521625, 22325625, 4039875, -6804000, 9568125, 2764125, -2764125], ![127702575, -127702575, 55665225, 1488375, -16074450, 9724050, 72037350, -57153600, 14586075, 6350400, 27683775, -16868250, -893025, 8235675, -14883750, 14883750, -4068225, -5457375, -10815525, 9525600, -8235675, 1289925, -1289925], ![-145945800, 145945800, -72972900, 17860500, -4592700, 10716300, -72972900, 55112400, -13267800, -6123600, -23984100, 12757500, 3572100, -7144200, 17860500, -17860500, 6633900, 2551500, 11226600, -9185400, 7144200, -2041200, 2041200], ![-218918700, 218918700, -149688000, 74844000, -5613300, -39293100, -69230700, 74844000, -69230700, 44906400, -11226600, 20582100, -33679800, 5613300, -5613300, 5613300, 3742200, -11226600, -9355500, 7484400, -5613300, 1871100, -1871100], ![1459458000, -1459458000, 827026200, -243243000, -145945800, 340540200, 632431800, -583783200, 389188800, -194594400, 145945800, -145945800, 145945800, 0, -48648600, 48648600, -48648600, 48648600, 0, 0, 0, 0, 0], ![10216206000, -10216206000, 10216206000, -10216206000, 10216206000, -10216206000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Y : Matrix (Fin 8) (Fin 8) ℚ := ![![(1540544771597130957914763507/10485760000000000000), (8037635297992966358373681/83886080000000000), (-196504875626302099010931777/2097152000000000000), (2586884560636137142908333807/10485760000000000000), (-22235504722232215044800169/163840000000000000), (-230270366230043944857743691/1310720000000000000), (1153907198163353400803203167/655360000000000000), (-972657324021112936414194987/26214400000000000)], ![(8037635297992966358373681/83886080000000000), (-692533335533526947926985409/20971520000000000000), (841046210790525654919389/209715200000000000), (-4329863123205807097951887/655360000000000000), (3101070896965312486516323/655360000000000000), (19013396125152405689781849/1310720000000000000), (-28953209885495466093722199/327680000000000000), (-9620158906079410510144323/6553600000000000)], ![(-196504875626302099010931777/2097152000000000000), (841046210790525654919389/209715200000000000), (-20304386448442998398379/8388608000000000), (-3659266956100511606383323/2097152000000000000), (711492727963558706463429/262144000000000000), (464682305848495391795853/262144000000000000), (-582797522297044821016107/16384000000000000), (941965010282641430784699/1048576000000000)], ![(2586884560636137142908333807/10485760000000000000), (-4329863123205807097951887/655360000000000000), (-3659266956100511606383323/2097152000000000000), (-5204548429380491383217907/2621440000000000000), (966497010040918415248119/262144000000000000), (-321734504500567930961343/40960000000000000), (29763751211006210816084667/655360000000000000), (657002094147162782275257/1310720000000000)], ![(-22235504722232215044800169/163840000000000000), (3101070896965312486516323/655360000000000000), (711492727963558706463429/262144000000000000), (966497010040918415248119/262144000000000000), (-303285231875676331713717/40960000000000000), (961191960314626089289647/163840000000000000), (4804381152608431737275361/81920000000000000), (1378835830614431386197/655360000000000)], ![(-230270366230043944857743691/1310720000000000000), (19013396125152405689781849/1310720000000000000), (464682305848495391795853/262144000000000000), (-321734504500567930961343/40960000000000000), (961191960314626089289647/163840000000000000), (-3373881146994944091014091/81920000000000000), (-13835556976759815400186941/81920000000000000), (106314579289080444909627/204800000000000)], ![(1153907198163353400803203167/655360000000000000), (-28953209885495466093722199/327680000000000000), (-582797522297044821016107/16384000000000000), (29763751211006210816084667/655360000000000000), (4804381152608431737275361/81920000000000000), (-13835556976759815400186941/81920000000000000), (-23901136870490290058007789/20480000000000000), (-9810277788593695164462711/1638400000000000)], ![(-972657324021112936414194987/26214400000000000), (-9620158906079410510144323/6553600000000000), (941965010282641430784699/1048576000000000), (657002094147162782275257/1310720000000000), (1378835830614431386197/655360000000000), (106314579289080444909627/204800000000000), (-9810277788593695164462711/1638400000000000), (-20965450326471445613397579/81920000000000)]] +def Z : Matrix (Fin 8) (Fin 8) ℚ := ![![174356582400, 0, 0, 0, 0, 0, -2724321600, 122594472000], ![0, 2874009600, 0, 0, 0, -179625600, 0, 40864824000], ![0, 0, 435456000, 0, -40824000, -299376000, 1459458000, 10216206000], ![0, 0, 0, 177811200, -171460800, 0, 681080400, 0], ![0, 0, -40824000, -171460800, 175543200, 0, -656756100, -2554051500], ![0, -179625600, -299376000, 0, 0, 340540200, -1605403800, -2554051500], ![-2724321600, 0, 1459458000, 681080400, -656756100, -1605403800, 10477692225, -1915538625], ![122594472000, 40864824000, 10216206000, 0, -2554051500, -2554051500, -1915538625, 1306397342250]] +def W : Matrix (Fin 8) (Fin 8) ℚ := ![![(2169473049901776379541983/536870912000000000000000), (-13700629893018336374821/536870912000000000000000), (235241600470654526468291/1073741824000000000000000), (-19620273589573631868313277/7516192768000000000000000), (7296195921450220378451/6710886400000000000000), (37232380467957914474807/134217728000000000000000), (-17326261100256896546623/67108864000000000000000), (6961374028657009087359/93952409600000000000000)], ![(11108342880031208496333/939524096000000000000000), (3812130957426910587379/134217728000000000000000), (-137008748542793421575193/1879048192000000000000000), (-97368580054254887731683/1879048192000000000000000), (-25969495310742925887/1835008000000000000000), (-9427447178878691908857/234881024000000000000000), (2299081364402895027813/117440512000000000000000), (34354129413272784397/4697620480000000000000)], ![(3487776606418334857737/3006477107200000000000000), (24148684914564772856769/3006477107200000000000000), (7608190436756519647041/6012954214400000000000000), (-277309301366127564083393/6012954214400000000000000), (-6420266893591314109993/187904819200000000000000), (315169599711858355697/150323855360000000000000), (1059204223167617638431/75161927680000000000000), (16137908375546271229/10737418240000000000000)], ![(-29649954893665821005303/6442450944000000000000000), (30751417977154432396721/6442450944000000000000000), (155439549410595338435713/12884901888000000000000000), (106137603232761625260479/12884901888000000000000000), (-17404316851674872196137/402653184000000000000000), (33555794481106336393589/1610612736000000000000000), (1348739820810516553673/268435456000000000000000), (-4506329088512485511/53687091200000000000000)], ![(53615841848714771692473/15032385536000000000000000), (-20796707626368209617449/3758096384000000000000000), (-125801226158914270665759/15032385536000000000000000), (-34869157524995015148231/7516192768000000000000000), (82259462702673831224999/1879048192000000000000000), (-17942564560694018581011/939524096000000000000000), (-5858640463815064273587/939524096000000000000000), (-22264644776823291503/93952409600000000000000)], ![(976204824914806510419/536870912000000000000000), (-48959833740921508142159/7516192768000000000000000), (-84159261956453926284603/7516192768000000000000000), (296376159500882166680117/7516192768000000000000000), (490614475899907272859/16777216000000000000000), (-3913236476983854035887/939524096000000000000000), (-4982183524503039030297/469762048000000000000000), (-66846099380996153543/93952409600000000000000)], ![(-140154606133518867137633/1503238553600000000000000), (4486458812862890302153/107374182400000000000000), (898836507487063493667033/7516192768000000000000000), (-195611959641346915939701/1879048192000000000000000), (-301398021092215316382971/939524096000000000000000), (25367666438648441918153/234881024000000000000000), (32421970688297378791177/469762048000000000000000), (-5612174499743950707/23488102400000000000000)], ![(2165895624099203666469/671088640000000000000), (2658177556547604813917/4294967296000000000000), (-36497742058347312641613/21474836480000000000000), (-510957244853728295242191/150323855360000000000000), (25831604842619401397/671088640000000000000), (-1675167248210860645761/2684354560000000000000), (597075250760304432849/1342177280000000000000), (442778154259987146117/1879048192000000000000)]] +def M : Matrix (Fin 8) (Fin 8) ℚ := ![![(936318957267810739300317130491/1310720000000000000), (7614482354374949368225577667/2621440000000000000), (1460169407541786715381869261/4194304000000000000), (-17331199714987632693600588207/20971520000000000000), (51154712612315503969490059347/83886080000000000000), (5425447712804599871981789199/20971520000000000000), (-690947564556501211314128064291/41943040000000000000), (247632081209759714100949945629/419430400000000000)], ![(7614482354374949368225577667/2621440000000000000), (254074665617979642442331721/655360000000000000), (176425559180653660060860369/2097152000000000000), (13727835351821479482935649/2097152000000000000), (-92937269281984344881798409/4194304000000000000), (-493331500401959793822416091/10485760000000000000), (953384483402549915775392763/10485760000000000000), (2415962116052585313636209787/209715200000000000)], ![(1460169407541786715381869261/4194304000000000000), (176425559180653660060860369/2097152000000000000), (12495614451611520295921131/335544320000000000), (60867648384347450372277159/8388608000000000000), (-754025341822340736944495673/67108864000000000000), (-462549171857276857397613327/16777216000000000000), (175993519027665943110159081/1342177280000000000), (839451909235502661762082419/335544320000000000)], ![(-17331199714987632693600588207/20971520000000000000), (13727835351821479482935649/2097152000000000000), (60867648384347450372277159/8388608000000000000), (515814862702619852233659063/41943040000000000000), (-4220484883803645473793799701/335544320000000000000), (-87677579528547961259537307/16777216000000000000), (14009086554668944228857380013/167772160000000000000), (-516747108218811734497542309/1677721600000000000)], ![(51154712612315503969490059347/83886080000000000000), (-92937269281984344881798409/4194304000000000000), (-754025341822340736944495673/67108864000000000000), (-4220484883803645473793799701/335544320000000000000), (2268698490513961434030331647/167772160000000000000), (255419344547683095409049277/33554432000000000000), (-3693685133402349191350524423/41943040000000000000), (-788713505654903367261695973/3355443200000000000)], ![(5425447712804599871981789199/20971520000000000000), (-493331500401959793822416091/10485760000000000000), (-462549171857276857397613327/16777216000000000000), (-87677579528547961259537307/16777216000000000000), (255419344547683095409049277/33554432000000000000), (3682181256494226339637447191/167772160000000000000), (-4895546988801590817022694367/41943040000000000000), (-3794625374447623058617080807/3355443200000000000)], ![(-690947564556501211314128064291/41943040000000000000), (953384483402549915775392763/10485760000000000000), (175993519027665943110159081/1342177280000000000), (14009086554668944228857380013/167772160000000000000), (-3693685133402349191350524423/41943040000000000000), (-4895546988801590817022694367/41943040000000000000), (11728715278712816765481536007/10485760000000000000), (-7047919680144388073331774471/838860800000000000)], ![(247632081209759714100949945629/419430400000000000), (2415962116052585313636209787/209715200000000000), (839451909235502661762082419/335544320000000000), (-516747108218811734497542309/1677721600000000000), (-788713505654903367261695973/3355443200000000000), (-3794625374447623058617080807/3355443200000000000), (-7047919680144388073331774471/838860800000000000), (238933246610110513168919694483/335544320000000000)]] +def L : Matrix (Fin 8) (Fin 8) ℚ := ![![1, 0, 0, 0, 0, 0, 0, 0], ![(10434671438814887949123/2566210078721856303642358), 1, 0, 0, 0, 0, 0, 0], ![(10004874463957076636545/20529680629774850429138864), (185030076113887424887461134931455619610089682465/840863365866873905541450683392233980047368017464), 1, 0, 0, 0, 0, 0], ![(-213751676903191039745447/184767125667973653862249776), (199450231595646459065956152537209865377463874297/7567770292801865149873056150530105820426312157176), (795189003562671759317218662408787907888371489866166156917875199224467/2738722769378210545618025750170352644897404763258791921243523808994799), 1, 0, 0, 0, 0], ![(70100972569701223289043/82118722519099401716555456), (-661393410782244716564630172060366032852412542059/10090360390402486866497408200706807760568416209568), (-3548081417706071352905732125942249026824519476256722122445104123274695/10954891077512842182472103000681410579589619053035167684974095235979196), (-8412216617831318776146276415722245156635962108849201309830596878277864799772875503916231223/8449015472959538704699207111371861277033965332331274294260952376294267187418062229157872772), 1, 0, 0, 0], ![(7434880226501344844431/20529680629774850429138864), (-322807993672098163304117117731784446582651138507/2522590097600621716624352050176701940142104052392), (-24835788305266890050865793114424855319208357084201531873155321424302101/27387227693782105456180257501703526448974047632587919212435238089947990), (291446867225225670562102228446459674874245092225591207258289224107803584524575618379682155/2112253868239884676174801777842965319258491333082818573565238094073566796854515557289468193), (-22/5), 1, 0, 0], ![(-2840565050408444277180137/123178083778649102574833184), (2119485010402175441619172542537417229924206336811/5045180195201243433248704100353403880284208104784), (151533046785353426921817777698300635081507827316963296570718661628052773/27387227693782105456180257501703526448974047632587919212435238089947990), (8209087032636673735737166439152364170115988588322597460400672813128564820880976774086542837/2599697068602934986061294495806726546779681640717315167464908423475159134590172993587037776), (429/20), 0, 1, 0], ![(499041185575015064216325/603814136169848542033496), (30601612604174106531104666416632406047712425634375/1261295048800310858312176025088350970071052026196), (30087797273018860095928537656741322718396354584981957044227067699518913/2738722769378210545618025750170352644897404763258791921243523808994799), (1457234336126128352810511142232298374371225461127956036291446120539017922622878091898410775/185692647757352499004378178271909039055691545765522511961779173105368509613583785256216984), (-1001/4), 0, 0, 1]] +def diag : Fin 8 → ℚ := ![(936318957267810739300317130491/1310720000000000000), (2528581249082423193201334886295871607249941549516431/6727165748764622988620222955520000000000000), (665509632958905162585180257291395692710069357471886436862176285585736157/35268365789088926895081287671547805514485958651213250560000000000), (133071993699112734599012512004106815113284953984217570134609999926634708201834480109236496159/14022260579216437993564291840872205541874712387885014636766841902053370880000000000000), (72314903978527499225808160071092279240609479097629030356475437810590032454486907719489163261345328374207/6179851317364691166865705772889132819773414643076589198088010880946663999940068373326901227520000000000), 0, 0, 0] + +def keyIndexTable : Fin 16 → Fin 13 → Fin 13 → Fin 23 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 4, 5, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 6, 7, 8, 9, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 6, 0, 10, 11, 12, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 14, 15, 16, 17, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 7, 10, 0, 13, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 14, 0, 18, 19, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 8, 11, 13, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 15, 18, 0, 20, 0, 0, 0, 0, 0, 0, 0], ![6, 14, 0, 0, 21, 22, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 9, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 16, 19, 20, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 15, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 0, 12, 13, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 17, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 16, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 18, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 9, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 17, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 17, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 19, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 8, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 16, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 17, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 19, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 20, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 16) (j : Fin ((n.val+1)/2)) (x : Fin ((15-n.val+2)/2)) : Fin 23 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 23 → FourTerm 15 := ![⟨⟨15,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 8, + (fourTermLabels (by omega : 15 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 8, + (fourTermLabels (by omega : 15 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 7, + (fourTermLabels (by omega : 15 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 7, + (fourTermLabels (by omega : 15 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 6, + (fourTermLabels (by omega : 15 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 6, + (fourTermLabels (by omega : 15 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 5, + (fourTermLabels (by omega : 15 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 5, + (fourTermLabels (by omega : 15 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 4, + (fourTermLabels (by omega : 15 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 4, + (fourTermLabels (by omega : 15 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 3, + (fourTermLabels (by omega : 15 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 3, + (fourTermLabels (by omega : 15 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover_12 : ∀ j : Fin 6, ∀ x : Fin 2, + (fourTermLabels (by omega : 15 ≤ 23) ⟨12,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨12,j,x⟩).toFinset=keys (keyIndex 12 j x) := by decide +kernel +lemma cover_13 : ∀ j : Fin 7, ∀ x : Fin 2, + (fourTermLabels (by omega : 15 ≤ 23) ⟨13,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨13,j,x⟩).toFinset=keys (keyIndex 13 j x) := by decide +kernel +lemma cover_14 : ∀ j : Fin 7, ∀ x : Fin 1, + (fourTermLabels (by omega : 15 ≤ 23) ⟨14,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨14,j,x⟩).toFinset=keys (keyIndex 14 j x) := by decide +kernel +lemma cover_15 : ∀ j : Fin 8, ∀ x : Fin 1, + (fourTermLabels (by omega : 15 ≤ 23) ⟨15,j,x⟩).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) ⟨15,j,x⟩).toFinset=keys (keyIndex 15 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 15, (fourTermLabels (by omega : 15 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 15 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x + · exact cover_12 j x + · exact cover_13 j x + · exact cover_14 j x + · exact cover_15 j x +lemma representatives_checked : ∀ a : Fin 23, + (fourTermLabels (by omega : 15 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 15 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 15 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 15 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 23, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 15, + (fourTermLabels (by omega : 15 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 23, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 15 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 23, ∀ b : FourTerm 15, + (fourTermLabels (by omega : 15 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 15 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 23, (∑ b ∈ fibers v, fourTermEval 15 (2*(0 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 15 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 23, (∑ b ∈ fibers v, fourTermEval 15 (2*(1 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 15 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 23, (∑ b ∈ fibers v, fourTermEval 15 (2*(2 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 15 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 23, (∑ b ∈ fibers v, fourTermEval 15 (2*(3 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 15 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 23, (∑ b ∈ fibers v, fourTermEval 15 (2*(4 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 15 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 23, (∑ b ∈ fibers v, fourTermEval 15 (2*(5 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 15 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_6 : ∀ v : Fin 23, (∑ b ∈ fibers v, fourTermEval 15 (2*(6 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 15 ≤ 23) b)) = columns 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_7 : ∀ v : Fin 23, (∑ b ∈ fibers v, fourTermEval 15 (2*(7 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 15 ≤ 23) b)) = columns 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 8, ∀ v : Fin 23, (∑ b ∈ fibers v, fourTermEval 15 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 15 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 + · exact columns_checked_6 + · exact columns_checked_7 +lemma gram_checked_0 : ∀ v : Fin 8, (∑ a : Fin 23, columns (0 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 8, (∑ a : Fin 23, columns (1 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 8, (∑ a : Fin 23, columns (2 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 8, (∑ a : Fin 23, columns (3 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 8, (∑ a : Fin 23, columns (4 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 8, (∑ a : Fin 23, columns (5 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_6 : ∀ v : Fin 8, (∑ a : Fin 23, columns (6 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_7 : ∀ v : Fin 8, (∑ a : Fin 23, columns (7 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 8, ∀ v : Fin 8, (∑ a : Fin 23, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 + · exact gram_checked_6 + · exact gram_checked_7 +lemma rows_table_checked_0 : ∀ v : Fin 8, integerTableEval 15 SumTable15.sums (0 : Fin 8) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 8, integerTableEval 15 SumTable15.sums (1 : Fin 8) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 8, integerTableEval 15 SumTable15.sums (2 : Fin 8) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 8, integerTableEval 15 SumTable15.sums (3 : Fin 8) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 8, integerTableEval 15 SumTable15.sums (4 : Fin 8) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 8, integerTableEval 15 SumTable15.sums (5 : Fin 8) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_6 : ∀ v : Fin 8, integerTableEval 15 SumTable15.sums (6 : Fin 8) v = Y 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_7 : ∀ v : Fin 8, integerTableEval 15 SumTable15.sums (7 : Fin 8) v = Y 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 8, ∀ v : Fin 8, integerTableEval 15 SumTable15.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 + · exact rows_table_checked_6 + · exact rows_table_checked_7 +lemma rows_checked (u v : Fin 8) : exactFourEval 15 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 15 SumTable15.sums SumTable15.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 8, (Z * tableComparison 15 (1/200000) Y) (0 : Fin 8) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 8, (Z * tableComparison 15 (1/200000) Y) (1 : Fin 8) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 8, (Z * tableComparison 15 (1/200000) Y) (2 : Fin 8) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 8, (Z * tableComparison 15 (1/200000) Y) (3 : Fin 8) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 8, (Z * tableComparison 15 (1/200000) Y) (4 : Fin 8) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 8, (Z * tableComparison 15 (1/200000) Y) (5 : Fin 8) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_6 : ∀ v : Fin 8, (Z * tableComparison 15 (1/200000) Y) (6 : Fin 8) v = W 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_7 : ∀ v : Fin 8, (Z * tableComparison 15 (1/200000) Y) (7 : Fin 8) v = W 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 8, ∀ v : Fin 8, (Z * tableComparison 15 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 + · exact product_checked_6 + · exact product_checked_7 +lemma compression_checked_0 : ∀ v : Fin 8, (W * Z) (0 : Fin 8) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 8, (W * Z) (1 : Fin 8) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 8, (W * Z) (2 : Fin 8) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 8, (W * Z) (3 : Fin 8) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 8, (W * Z) (4 : Fin 8) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 8, (W * Z) (5 : Fin 8) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_6 : ∀ v : Fin 8, (W * Z) (6 : Fin 8) v = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_7 : ∀ v : Fin 8, (W * Z) (7 : Fin 8) v = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 8, ∀ v : Fin 8, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 + · exact compression_checked_6 + · exact compression_checked_7 +lemma ldl_checked_0 : ∀ v : Fin 8, (∑ k : Fin 8, L (0 : Fin 8) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 8, (∑ k : Fin 8, L (1 : Fin 8) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 8, (∑ k : Fin 8, L (2 : Fin 8) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 8, (∑ k : Fin 8, L (3 : Fin 8) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 8, (∑ k : Fin 8, L (4 : Fin 8) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 8, (∑ k : Fin 8, L (5 : Fin 8) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_6 : ∀ v : Fin 8, (∑ k : Fin 8, L (6 : Fin 8) k * diag k * L v k) = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_7 : ∀ v : Fin 8, (∑ k : Fin 8, L (7 : Fin 8) k * diag k * L v k) = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 8, ∀ v : Fin 8, (∑ k : Fin 8, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 + · exact ldl_checked_6 + · exact ldl_checked_7 +lemma diag_checked : ∀ u : Fin 8, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 15 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 15 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 15 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 15 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 15 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate15 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate16.lean b/lean/OAI/Analysis/LaughlinGap/Certificate16.lean new file mode 100644 index 0000000000000000000000000000000000000000..0ee0fc5b79689928f0163ff3720df00323e64ec2 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate16.lean @@ -0,0 +1,361 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Certificate15 +import OAI.Analysis.LaughlinGap.SumTable16 + +namespace OAI + +/-! Certificate16. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate16 + +def keys : Fin 27 → Finset (Fin 25) := ![{0,1,2,14}, {0,1,3,13}, {0,1,4,12}, {0,1,5,11}, {0,1,6,10}, {0,1,7,9}, {0,2,3,12}, {0,2,4,11}, {0,2,5,10}, {0,2,6,9}, {0,2,7,8}, {0,3,4,10}, {0,3,5,9}, {0,3,6,8}, {0,4,5,8}, {0,4,6,7}, {1,2,3,11}, {1,2,4,10}, {1,2,5,9}, {1,2,6,8}, {1,3,4,9}, {1,3,5,8}, {1,3,6,7}, {1,4,5,7}, {2,3,4,8}, {2,3,5,7}, {2,4,5,6}] +def fibers : Fin 27 → Finset (FourTerm 16) := ![{⟨⟨16,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩}] +def columns : Matrix (Fin 8) (Fin 27) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![-2554051500, 2554051500, -2918916000, 2554051500, -1824322500, 1021620600, 364864500, 364864500, -729729000, 802701900, -1021620600, -364864500, 510810300, -145945800, -583783200, 510810300, -729729000, 729729000, -583783200, 364864500, -145945800, 218918700, -364864500, 72972900, -72972900, 72972900, -72972900], ![-2554051500, 2554051500, -2020788000, 1506235500, -926194500, 392931000, -533263500, 514552500, -580041000, 533263500, -392931000, 84199500, -28066500, -56133000, 74844000, -28066500, 18711000, -18711000, 74844000, -84199500, -56133000, 9355500, 84199500, -46777500, 46777500, -46777500, 46777500], ![-1660133475, 1660133475, -864448200, 245581875, -22325625, -1786050, -795685275, 618866325, -223256250, 24111675, 1786050, -218791125, 120558375, -16074450, -35721000, 6251175, 176818950, -176818950, 78586200, -9823275, 98232750, -68762925, 9823275, 29469825, -29469825, 29469825, -29469825], ![510810300, -510810300, 314344800, -196465500, 160744500, -107163000, 196465500, -117879300, 35721000, -53581500, 107163000, 3572100, 46437300, -50009400, -28576800, 46437300, -78586200, 78586200, -28576800, -3572100, -50009400, 32148900, 3572100, -17860500, 17860500, -17860500, 17860500], ![2554051500, -2554051500, 1403325000, -374220000, -140332500, 196465500, 1150726500, -1029105000, 514552500, -56133000, -196465500, 392931000, -364864500, 196465500, 130977000, -140332500, -121621500, 121621500, -93555000, 56133000, -28066500, 37422000, -56133000, 9355500, -9355500, 9355500, -9355500], ![-4086482400, 4086482400, -1459458000, -729729000, 1459458000, -1021620600, -2627024400, 2189187000, -729729000, -437837400, 1021620600, -1021620600, 875674800, -437837400, -291891600, 291891600, 437837400, -437837400, 291891600, -145945800, 145945800, -145945800, 145945800, 0, 0, 0, 0], ![-51081030000, 51081030000, -40864824000, 30648618000, -20432412000, 10216206000, -10216206000, 10216206000, -10216206000, 10216206000, -10216206000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Y : Matrix (Fin 8) (Fin 8) ℚ := ![![(-42369009382151265659712407541/1677721600000000000), (381420438271222851919266849/838860800000000000), (466753179463362065428447293/335544320000000000), (-4079359638185221230689787939/4194304000000000000), (99425450050547924401167069/1048576000000000000), (67736924451848019977385777/104857600000000000), (-450390389962818731193861093/524288000000000000), (40207728205285880932003311/52428800000000000)], ![(381420438271222851919266849/838860800000000000), (-354766265760092424302967903/2097152000000000000), (-43619415521470651609778889/838860800000000000), (217958118446659121411960079/2097152000000000000), (-33031992523282206264751941/524288000000000000), (-4153526303709674461787217/52428800000000000), (139264441883965944468849069/262144000000000000), (-112012682016638363061688587/26214400000000000)], ![(466753179463362065428447293/335544320000000000), (-43619415521470651609778889/838860800000000000), (-15478465509682054465477419/335544320000000000), (27233210623906780387468497/838860800000000000), (-227525218116088089603483/209715200000000000), (-101012324487327688239387/4194304000000000), (5686272971061909615645399/104857600000000000), (-13365170893566327762035109/10485760000000000)], ![(-4079359638185221230689787939/4194304000000000000), (217958118446659121411960079/2097152000000000000), (27233210623906780387468497/838860800000000000), (-98647784043058788030538227/2097152000000000000), (11785198376323237130842689/524288000000000000), (7683658157867632887812481/262144000000000000), (-61190574759718212554999253/262144000000000000), (51338828723013384719877711/26214400000000000)], ![(99425450050547924401167069/1048576000000000000), (-33031992523282206264751941/524288000000000000), (-227525218116088089603483/209715200000000000), (11785198376323237130842689/524288000000000000), (-665040209935289453471367/26214400000000000), (556795056592685773303749/65536000000000000), (16202547607257078387463143/65536000000000000), (-1025905880324342049589557/6553600000000000)], ![(67736924451848019977385777/104857600000000000), (-4153526303709674461787217/52428800000000000), (-101012324487327688239387/4194304000000000), (7683658157867632887812481/262144000000000000), (556795056592685773303749/65536000000000000), (-88781369602105273629987/1310720000000000), (-1936027477613263272276753/32768000000000000), (-2126072065565577231771669/3276800000000000)], ![(-450390389962818731193861093/524288000000000000), (139264441883965944468849069/262144000000000000), (5686272971061909615645399/104857600000000000), (-61190574759718212554999253/262144000000000000), (16202547607257078387463143/65536000000000000), (-1936027477613263272276753/32768000000000000), (-108605937589037758421556147/32768000000000000), (-3465243237880150409930247/3276800000000000)], ![(40207728205285880932003311/52428800000000000), (-112012682016638363061688587/26214400000000000), (-13365170893566327762035109/10485760000000000), (51338828723013384719877711/26214400000000000), (-1025905880324342049589557/6553600000000000), (-2126072065565577231771669/3276800000000000), (-3465243237880150409930247/3276800000000000), (-38739085547977162163658843/327680000000000)]] +def Z : Matrix (Fin 8) (Fin 8) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0], ![0, 37362124800, 0, 0, 0, 0, -7005398400, 102162060000], ![0, 0, 4790016000, 0, 0, -1496880000, 0, 61297236000], ![0, 0, 0, 1828915200, -685843200, -1571724000, 4086482400, 15324309000], ![0, 0, 0, -685843200, 457228800, 0, 0, -10216206000], ![0, 0, -1496880000, -1571724000, 0, 3555090000, -8027019000, -19155386250], ![0, -7005398400, 0, 4086482400, 0, -8027019000, 22183761600, -19155386250], ![0, 102162060000, 61297236000, 15324309000, -10216206000, -19155386250, -19155386250, (2584061605125/2)]] +def W : Matrix (Fin 8) (Fin 8) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0], ![(-2219208248215338737071/4294967296000000000000000), (48505336804465316340683/3006477107200000000000000), (8121579831670965330099/240518168576000000000000), (-494306611879341638051103/3006477107200000000000000), (49968822799290583308549/751619276800000000000000), (46616596650824294948139/1879048192000000000000000), (-10763849708732625017089/375809638400000000000000), (1912751130461876784229/187904819200000000000000)], ![(-5633304603121156069317/6012954214400000000000000), (3661895441171061496127/601295421440000000000000), (4939610931710572316131/240518168576000000000000), (-7568708254012088934311/120259084288000000000000), (26014715099748460987/4294967296000000000000), (2614363766747090320159/375809638400000000000000), (-46513292312583523229/75161927680000000000000), (190073139180417087921/37580963840000000000000)], ![(120021362291295738684703/120259084288000000000000000), (-7429950290601440132651/1717986918400000000000000), (-4557588307630383102879/687194767360000000000000), (444996160140222206131449/12025908428800000000000000), (-12778434295848912984293/429496729600000000000000), (-7687102935230577770763/1073741824000000000000000), (3918091043705288328673/214748364800000000000000), (-418931139497683526691/751619276800000000000000)], ![(-8792609224748925753683/30064771072000000000000000), (49068474110668919427/85899345920000000000000), (89220133337701924371/171798691840000000000000), (-13089195397044678967173/3006477107200000000000000), (795572113150294718561/107374182400000000000000), (212876214340054682223/268435456000000000000000), (-226466483671754868461/53687091200000000000000), (-21571300439391593497/187904819200000000000000)], ![(-60575570899730308411/75161927680000000000000), (737927805222496727619/150323855360000000000000), (21815723130684180293/4294967296000000000000), (-6041399376976294402027/150323855360000000000000), (163090708288989474081/4697620480000000000000), (179489010335491546409/18790481920000000000000), (-218122242944214317819/9395240960000000000000), (-1385293544286236859/9395240960000000000000)], ![(44398302255840924685723/15032385536000000000000000), (-31171723376082256989041/1503238553600000000000000), (-21781498470701906642277/601295421440000000000000), (280287321869882211259089/1503238553600000000000000), (-40456928113166044942319/375809638400000000000000), (-33014303680833705897381/939524096000000000000000), (12445947668302763403499/187904819200000000000000), (-529388850289581000027/93952409600000000000000)], ![(-2064606447258431285781/300647710720000000000000), (2346877080707360242069/21474836480000000000000), (2951003971356751343241/8589934592000000000000), (-174027663407819075520237/150323855360000000000000), (503284171753666307719/5368709120000000000000), (373500739579902658659/2684354560000000000000), (21516056976119121393/2684354560000000000000), (893693681564817492951/9395240960000000000000)]] +def M : Matrix (Fin 8) (Fin 8) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0], ![0, (61853486868958255188173683227/33554432000000000000), (5023606727849962487210912079/6710886400000000000), (-46484923775195918863219862493/134217728000000000000), (1314158647407502745259660249/33554432000000000000), (555297891347123301910488813/1677721600000000000), (-30440710734935278575711157101/16777216000000000000), (23059986630328564154170129197/1677721600000000000)], ![0, (5023606727849962487210912079/6710886400000000000), (534165056850553396613121843/1342177280000000000), (-1482222186682037607788286921/26843545600000000000), (-7699177007845296728401647/1342177280000000000), (333472045361590903090257/335544320000000000), (-1564656175643021933526773433/3355443200000000000), (2438739219361604270313058857/335544320000000000)], ![0, (-46484923775195918863219862493/134217728000000000000), (-1482222186682037607788286921/26843545600000000000), (88771483612414143812782850283/536870912000000000000), (-893558281997028840811831107/26843545600000000000), (-1405656942284965955803832691/6710886400000000000), (43915805920031621135146469883/67108864000000000000), (-6105952967846463744649936299/6710886400000000000)], ![0, (1314158647407502745259660249/33554432000000000000), (-7699177007845296728401647/1342177280000000000), (-893558281997028840811831107/26843545600000000000), (50643756145577435209705287/6710886400000000000), (3016126960550799960081987/67108864000000000), (-2005490131066544561523555471/16777216000000000000), (-45275897246905958100464997/335544320000000000)], ![0, (555297891347123301910488813/1677721600000000000), (333472045361590903090257/335544320000000000), (-1405656942284965955803832691/6710886400000000000), (3016126960550799960081987/67108864000000000), (187034738547109819608905751/671088640000000000), (-1321198885368080909609908203/1677721600000000000), (-29011999463090018720127783/335544320000000000)], ![0, (-30440710734935278575711157101/16777216000000000000), (-1564656175643021933526773433/3355443200000000000), (43915805920031621135146469883/67108864000000000000), (-2005490131066544561523555471/16777216000000000000), (-1321198885368080909609908203/1677721600000000000), (23207609997960122493877986153/8388608000000000000), (-3463492394705738220923009913/419430400000000000)], ![0, (23059986630328564154170129197/1677721600000000000), (2438739219361604270313058857/335544320000000000), (-6105952967846463744649936299/6710886400000000000), (-45275897246905958100464997/335544320000000000), (-29011999463090018720127783/335544320000000000), (-3463492394705738220923009913/419430400000000000), (22415402232669759084890739621/167772160000000000)]] +def L : Matrix (Fin 8) (Fin 8) ℚ := ![![1, 0, 0, 0, 0, 0, 0, 0], ![0, 1, 0, 0, 0, 0, 0, 0], ![0, (240947304375663687550285/593335893301085452705341), 1, 0, 0, 0, 0, 0], ![0, (-5791056901098143515447/30822643807848594945732), (66279490036488354386467309028088067921211311/72926800131785480079171901018250991054699780), 1, 0, 0, 0, 0], ![0, (1800885873259117761881/84762270471583636100763), (-41975302339135251310428432780671771221870027/182317000329463700197929752545627477636749450), (-439788212572825599532612837790323569324885025093904103854495768/1590119230265167036323217878589678523296954009211792718738410081), 1, 0, 0, 0], ![0, (35511678439803115159860/197778631100361817568447), (-24355432571164026459700149989011524849357431/17159247089831877665687506121941409659929360), (-7310575732475153576619489172104374901718493705200215851802379085/6360476921060668145292871514358714093187816036847170874953640324), (-165/56), 1, 0, 0], ![0, (-53091932420876778796706/53939626663735041155031), (123455591061345170479623228118381423149091789/42898117724579694164218765304853524149823400), (19007496904435399299210671847471374744468083633520561214686185621/6360476921060668145292871514358714093187816036847170874953640324), (429/56), 0, 1, 0], ![0, (632015080401863271273860/84762270471583636100763), (2616778820184927247950214077640369212897149227/145853600263570960158343802036501982109399560), (39306071498696287958227272377510169008411599117767679281995559265/6360476921060668145292871514358714093187816036847170874953640324), (-715/32), 0, 0, 1]] +def diag : Fin 8 → ℚ := ![0, (61853486868958255188173683227/33554432000000000000), (886060621601193582961938597371749541314602327/9426632994758772419029630976000000000), (300532534520116569865088179053449240903124307741028823841559505309/13275918815101925617968360292033602638224457728000000000000), (711885449373387948293915628446002427571558860462014844246948082438507839600794839/2035352614739413806493718884594788509820101131791094679985164903680000000000000), 0, 0, 0] + +def keyIndexTable : Fin 17 → Fin 13 → Fin 13 → Fin 27 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 4, 5, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 6, 7, 8, 9, 10, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 6, 0, 11, 12, 13, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 16, 17, 18, 19, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 7, 11, 0, 14, 15, 0, 0, 0, 0, 0, 0], ![1, 0, 16, 0, 20, 21, 22, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 8, 12, 14, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 17, 20, 0, 23, 0, 0, 0, 0, 0, 0, 0], ![6, 16, 0, 0, 24, 25, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 9, 13, 15, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 18, 21, 23, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 17, 0, 24, 0, 26, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 10, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 19, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 18, 0, 25, 26, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 20, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 10, 13, 14, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 22, 23, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 19, 0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 21, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 9, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 19, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 0, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 23, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 8, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 18, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 19, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 22, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 21, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 23, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 17) (j : Fin ((n.val+1)/2)) (x : Fin ((16-n.val+2)/2)) : Fin 27 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 27 → FourTerm 16 := ![⟨⟨16,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 9, + (fourTermLabels (by omega : 16 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 8, + (fourTermLabels (by omega : 16 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 8, + (fourTermLabels (by omega : 16 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 7, + (fourTermLabels (by omega : 16 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 7, + (fourTermLabels (by omega : 16 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 6, + (fourTermLabels (by omega : 16 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 6, + (fourTermLabels (by omega : 16 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 5, + (fourTermLabels (by omega : 16 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 5, + (fourTermLabels (by omega : 16 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 4, + (fourTermLabels (by omega : 16 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 4, + (fourTermLabels (by omega : 16 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 3, + (fourTermLabels (by omega : 16 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover_12 : ∀ j : Fin 6, ∀ x : Fin 3, + (fourTermLabels (by omega : 16 ≤ 23) ⟨12,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨12,j,x⟩).toFinset=keys (keyIndex 12 j x) := by decide +kernel +lemma cover_13 : ∀ j : Fin 7, ∀ x : Fin 2, + (fourTermLabels (by omega : 16 ≤ 23) ⟨13,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨13,j,x⟩).toFinset=keys (keyIndex 13 j x) := by decide +kernel +lemma cover_14 : ∀ j : Fin 7, ∀ x : Fin 2, + (fourTermLabels (by omega : 16 ≤ 23) ⟨14,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨14,j,x⟩).toFinset=keys (keyIndex 14 j x) := by decide +kernel +lemma cover_15 : ∀ j : Fin 8, ∀ x : Fin 1, + (fourTermLabels (by omega : 16 ≤ 23) ⟨15,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨15,j,x⟩).toFinset=keys (keyIndex 15 j x) := by decide +kernel +lemma cover_16 : ∀ j : Fin 8, ∀ x : Fin 1, + (fourTermLabels (by omega : 16 ≤ 23) ⟨16,j,x⟩).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) ⟨16,j,x⟩).toFinset=keys (keyIndex 16 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 16, (fourTermLabels (by omega : 16 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 16 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x + · exact cover_12 j x + · exact cover_13 j x + · exact cover_14 j x + · exact cover_15 j x + · exact cover_16 j x +lemma representatives_checked : ∀ a : Fin 27, + (fourTermLabels (by omega : 16 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 16 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 16 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 16 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 27, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 16, + (fourTermLabels (by omega : 16 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 27, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 16 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 27, ∀ b : FourTerm 16, + (fourTermLabels (by omega : 16 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 16 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 27, (∑ b ∈ fibers v, fourTermEval 16 (2*(0 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 16 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 27, (∑ b ∈ fibers v, fourTermEval 16 (2*(1 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 16 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 27, (∑ b ∈ fibers v, fourTermEval 16 (2*(2 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 16 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 27, (∑ b ∈ fibers v, fourTermEval 16 (2*(3 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 16 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 27, (∑ b ∈ fibers v, fourTermEval 16 (2*(4 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 16 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 27, (∑ b ∈ fibers v, fourTermEval 16 (2*(5 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 16 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_6 : ∀ v : Fin 27, (∑ b ∈ fibers v, fourTermEval 16 (2*(6 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 16 ≤ 23) b)) = columns 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_7 : ∀ v : Fin 27, (∑ b ∈ fibers v, fourTermEval 16 (2*(7 : Fin 8).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 16 ≤ 23) b)) = columns 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 8, ∀ v : Fin 27, (∑ b ∈ fibers v, fourTermEval 16 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 16 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 + · exact columns_checked_6 + · exact columns_checked_7 +lemma gram_checked_0 : ∀ v : Fin 8, (∑ a : Fin 27, columns (0 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 8, (∑ a : Fin 27, columns (1 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 8, (∑ a : Fin 27, columns (2 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 8, (∑ a : Fin 27, columns (3 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 8, (∑ a : Fin 27, columns (4 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 8, (∑ a : Fin 27, columns (5 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_6 : ∀ v : Fin 8, (∑ a : Fin 27, columns (6 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_7 : ∀ v : Fin 8, (∑ a : Fin 27, columns (7 : Fin 8) a * columns v a / setFactorial (keys a)) = Z 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 8, ∀ v : Fin 8, (∑ a : Fin 27, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 + · exact gram_checked_6 + · exact gram_checked_7 +lemma rows_table_checked_0 : ∀ v : Fin 8, integerTableEval 16 SumTable16.sums (0 : Fin 8) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 8, integerTableEval 16 SumTable16.sums (1 : Fin 8) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 8, integerTableEval 16 SumTable16.sums (2 : Fin 8) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 8, integerTableEval 16 SumTable16.sums (3 : Fin 8) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 8, integerTableEval 16 SumTable16.sums (4 : Fin 8) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 8, integerTableEval 16 SumTable16.sums (5 : Fin 8) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_6 : ∀ v : Fin 8, integerTableEval 16 SumTable16.sums (6 : Fin 8) v = Y 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_7 : ∀ v : Fin 8, integerTableEval 16 SumTable16.sums (7 : Fin 8) v = Y 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 8, ∀ v : Fin 8, integerTableEval 16 SumTable16.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 + · exact rows_table_checked_6 + · exact rows_table_checked_7 +lemma rows_checked (u v : Fin 8) : exactFourEval 16 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 16 SumTable16.sums SumTable16.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 8, (Z * tableComparison 16 (1/200000) Y) (0 : Fin 8) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 8, (Z * tableComparison 16 (1/200000) Y) (1 : Fin 8) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 8, (Z * tableComparison 16 (1/200000) Y) (2 : Fin 8) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 8, (Z * tableComparison 16 (1/200000) Y) (3 : Fin 8) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 8, (Z * tableComparison 16 (1/200000) Y) (4 : Fin 8) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 8, (Z * tableComparison 16 (1/200000) Y) (5 : Fin 8) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_6 : ∀ v : Fin 8, (Z * tableComparison 16 (1/200000) Y) (6 : Fin 8) v = W 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_7 : ∀ v : Fin 8, (Z * tableComparison 16 (1/200000) Y) (7 : Fin 8) v = W 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 8, ∀ v : Fin 8, (Z * tableComparison 16 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 + · exact product_checked_6 + · exact product_checked_7 +lemma compression_checked_0 : ∀ v : Fin 8, (W * Z) (0 : Fin 8) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 8, (W * Z) (1 : Fin 8) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 8, (W * Z) (2 : Fin 8) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 8, (W * Z) (3 : Fin 8) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 8, (W * Z) (4 : Fin 8) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 8, (W * Z) (5 : Fin 8) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_6 : ∀ v : Fin 8, (W * Z) (6 : Fin 8) v = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_7 : ∀ v : Fin 8, (W * Z) (7 : Fin 8) v = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 8, ∀ v : Fin 8, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 + · exact compression_checked_6 + · exact compression_checked_7 +lemma ldl_checked_0 : ∀ v : Fin 8, (∑ k : Fin 8, L (0 : Fin 8) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 8, (∑ k : Fin 8, L (1 : Fin 8) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 8, (∑ k : Fin 8, L (2 : Fin 8) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 8, (∑ k : Fin 8, L (3 : Fin 8) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 8, (∑ k : Fin 8, L (4 : Fin 8) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 8, (∑ k : Fin 8, L (5 : Fin 8) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_6 : ∀ v : Fin 8, (∑ k : Fin 8, L (6 : Fin 8) k * diag k * L v k) = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_7 : ∀ v : Fin 8, (∑ k : Fin 8, L (7 : Fin 8) k * diag k * L v k) = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 8, ∀ v : Fin 8, (∑ k : Fin 8, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 + · exact ldl_checked_6 + · exact ldl_checked_7 +lemma diag_checked : ∀ u : Fin 8, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 16 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 16 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 16 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 16 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 16 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate16 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate17.lean b/lean/OAI/Analysis/LaughlinGap/Certificate17.lean new file mode 100644 index 0000000000000000000000000000000000000000..f3b40ef897bced865c0a214a9de08f3643921fe4 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate17.lean @@ -0,0 +1,391 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CachedIntegerRows +import OAI.Analysis.LaughlinGap.FastFourKeys +import OAI.Analysis.LaughlinGap.FourTables +import OAI.Analysis.LaughlinGap.SumTable17 + +namespace OAI + +/-! Certificate17. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate17 + +def keys : Fin 34 → Finset (Fin 25) := ![{0,1,2,15}, {0,1,3,14}, {0,1,4,13}, {0,1,5,12}, {0,1,6,11}, {0,1,7,10}, {0,1,8,9}, {0,2,3,13}, {0,2,4,12}, {0,2,5,11}, {0,2,6,10}, {0,2,7,9}, {0,3,4,11}, {0,3,5,10}, {0,3,6,9}, {0,3,7,8}, {0,4,5,9}, {0,4,6,8}, {0,5,6,7}, {1,2,3,12}, {1,2,4,11}, {1,2,5,10}, {1,2,6,9}, {1,2,7,8}, {1,3,4,10}, {1,3,5,9}, {1,3,6,8}, {1,4,5,8}, {1,4,6,7}, {2,3,4,9}, {2,3,5,8}, {2,3,6,7}, {2,4,5,7}, {3,4,5,6}] +def fibers : Fin 34 → Finset (FourTerm 17) := ![{⟨⟨17,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨5,by decide⟩)⟩}] +def columns : Matrix (Fin 9) (Fin 34) ℚ := ![![35756721000, -35756721000, 61297236000, -61297236000, 76621545000, -76621545000, 81729648000, -25540515000, 0, -15324309000, 0, -5108103000, 40864824000, -25540515000, 45972927000, -40864824000, -20432412000, 0, 15324309000, 25540515000, -25540515000, 40864824000, -40864824000, 45972927000, -15324309000, 0, -5108103000, 20432412000, -15324309000, 15324309000, -15324309000, 20432412000, -5108103000, 5108103000], ![22347950625, -22347950625, 28094566500, -28094566500, 27456053625, -27456053625, 26562135600, -5746615875, 0, 638512875, 0, 893918025, 5108103000, -5746615875, 4214184975, -5108103000, 1532430900, 0, -638512875, 5746615875, -5746615875, 5108103000, -5108103000, 4214184975, 638512875, 0, 893918025, -1532430900, 638512875, -638512875, 638512875, -1532430900, 893918025, -893918025], ![(49165491375/2), (-49165491375/2), 20979708750, -16489068750, (21604188375/2), (-12622908375/2), 4322241000, (7206073875/2), -4490640000, (11373949125/2), -4490640000, (3978426375/2), -308731500, (-1775206125/2), (2589134625/2), -589396500, 491163750, -898128000, (2097970875/2), (1775206125/2), (-1775206125/2), -308731500, 1206859500, (-2799633375/2), (2392669125/2), -898128000, (385914375/2), 406964250, (-301714875/2), (-596413125/2), (596413125/2), -42099750, (-512213625/2), (512213625/2)], ![(38949285375/2), (-38949285375/2), 11493231750, -5206335750, (3978426375/2), (-549210375/2), -678699000, (15962821875/2), -6286896000, (6434245125/2), -1714608000, (1906608375/2), 1375258500, (-1183258125/2), (843908625/2), -803722500, -401861250, 571536000, (-1290421125/2), (-3389029875/2), (3389029875/2), -910885500, 339349500, (-299163375/2), (-1567258875/2), 571536000, (-379535625/2), -169674750, (147349125/2), (424186875/2), (-424186875/2), 116093250, (192000375/2), (-192000375/2)], ![2554051500, -2554051500, 510810300, 1375258500, -1768189500, 910885500, 14288400, 2043241200, -1886068800, 392931000, 857304000, -925173900, 1335965400, -1214514000, 203609700, 664410600, 839443500, -742996800, 607257000, -157172400, 157172400, -35721000, -135739800, 260763300, -121451400, 171460800, -125023500, -96446700, 135739800, -50009400, 50009400, -10716300, -39293100, 39293100], ![-21709437750, 21709437750, -11310799500, 2666317500, 631496250, -294698250, -785862000, -10398638250, 8644482000, -3297813750, -336798000, 1080560250, -3592512000, 2736483750, -631496250, -785862000, -1319125500, 1010394000, -687629250, 1754156250, -1754156250, 898128000, -112266000, -294698250, 856028250, -785862000, 406964250, 308731500, -322764750, -70166250, 70166250, -84199500, 14033250, -14033250], ![-5108103000, 5108103000, -8318910600, 9486477000, -5837832000, 0, 4086482400, 3210807600, -1167566400, -3648645000, 5837832000, -4086482400, 2772970200, -1459458000, -1313512200, 3064861800, 1605403800, -1167566400, 729729000, -2043241200, 2043241200, -729729000, -437837400, 1021620600, -1313512200, 1167566400, -583783200, -437837400, 437837400, 145945800, -145945800, 145945800, 0, 0], ![250297047000, -250297047000, 163459296000, -81729648000, 20432412000, 20432412000, -40864824000, 86837751000, -81729648000, 61297236000, -40864824000, 20432412000, 15324309000, -15324309000, 15324309000, -15324309000, 0, 0, 0, -5108103000, 5108103000, -5108103000, 5108103000, -5108103000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1389404016000, -1389404016000, 1389404016000, -1389404016000, 1389404016000, -1389404016000, 1389404016000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Y : Matrix (Fin 9) (Fin 9) ℚ := ![![(-24864061565705232283989897321/1048576000000000000), (-2519234598769524491312339883/1048576000000000000), (509073619399032506392615041/209715200000000000), (-16740485476669118133178209/13107200000000000), (9786130044776366891937327/131072000000000000), (101007096490676615861751129/65536000000000000), (-293305745697097847260419873/65536000000000000), (10209034765047983111610363/409600000000000), 0], ![(-2519234598769524491312339883/1048576000000000000), (-499082307733958104305862713/2097152000000000000), (48575304574566310215972297/209715200000000000), (-1165324508656833797140869/10485760000000000), (-896064738199582387242807/131072000000000000), (17257398290044449572084049/131072000000000000), (-18065984876610864884111421/65536000000000000), (511459595450373852303021/163840000000000), 0], ![(509073619399032506392615041/209715200000000000), (48575304574566310215972297/209715200000000000), (-1887030774879449019523461/8388608000000000), (59809592331554330521179/524288000000000), (-303488355540628109924919/26214400000000000), (-1637345679067668836338479/13107200000000000), (6598818029966491766057049/13107200000000000), (-333300113264581923701241/163840000000000), 0], ![(-16740485476669118133178209/13107200000000000), (-1165324508656833797140869/10485760000000000), (59809592331554330521179/524288000000000), (-345973185847142954399313/5242880000000000), (7443429829808789750913/327680000000000), (109592490624795112569327/1638400000000000), (-76187622211039311073101/163840000000000), (107571412324085165773317/327680000000000), 0], ![(9786130044776366891937327/131072000000000000), (-896064738199582387242807/131072000000000000), (-303488355540628109924919/26214400000000000), (7443429829808789750913/327680000000000), (-430793455153499792827641/16384000000000000), (-196956449691076254474603/8192000000000000), (2681153678415821204819223/8192000000000000), (39545435018054146552371/51200000000000), 0], ![(101007096490676615861751129/65536000000000000), (17257398290044449572084049/131072000000000000), (-1637345679067668836338479/13107200000000000), (109592490624795112569327/1638400000000000), (-196956449691076254474603/8192000000000000), (-486332934964923009366117/8192000000000000), (2128240984594905228109347/4096000000000000), (-30491027862300413749341/204800000000000), 0], ![(-293305745697097847260419873/65536000000000000), (-18065984876610864884111421/65536000000000000), (6598818029966491766057049/13107200000000000), (-76187622211039311073101/163840000000000), (2681153678415821204819223/8192000000000000), (2128240984594905228109347/4096000000000000), (-18855963662914661935394457/4096000000000000), (-270633002397931399633407/51200000000000), 0], ![(10209034765047983111610363/409600000000000), (511459595450373852303021/163840000000000), (-333300113264581923701241/163840000000000), (107571412324085165773317/327680000000000), (39545435018054146552371/51200000000000), (-30491027862300413749341/204800000000000), (-270633002397931399633407/51200000000000), (-1068956360811806345980101/20480000000000), 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Z : Matrix (Fin 9) (Fin 9) ℚ := ![![41845579776000, 0, 0, 0, 0, 0, 0, -326918592000, 19451656224000], ![0, 523069747200, 0, 0, 0, 0, -16345929600, 0, 6947020080000], ![0, 0, 57480192000, 0, 0, -2694384000, -29189160000, 204324120000, 2084106024000], ![0, 0, 0, 18289152000, -1143072000, -12573792000, 0, 143026884000, 347351004000], ![0, 0, 0, -1143072000, 5372438400, -9430344000, 12259447200, 0, -173675502000], ![0, 0, -2694384000, -12573792000, -9430344000, 28740096000, -24081057000, -112378266000, -260513253000], ![0, -16345929600, -29189160000, 0, 12259447200, -24081057000, 55532376900, -166013347500, -217094377500], ![-326918592000, 0, 204324120000, 143026884000, 0, -112378266000, -166013347500, 2442950259750, -151966064250], ![19451656224000, 6947020080000, 2084106024000, 347351004000, -173675502000, -260513253000, -217094377500, -151966064250, 355589735626125]] +def W : Matrix (Fin 9) (Fin 9) ℚ := ![![(60166003902823838585312969/15032385536000000000000000), (3732643812908181026427/375809638400000000000000), (-9544076184422693607837/107374182400000000000000), (6666437000775751929301/46976204800000000000000), (-96829888353845173527/26843545600000000000000), (-1810288369549509631353/16777216000000000000000), (372268479812729568497/6710886400000000000000), (-63286863921817272133/2936012800000000000000), (7/25600000)], ![(10995586272710023905349/120259084288000000000000000), (1209589161176875111751/3006477107200000000000000), (-527709162483743247293/171798691840000000000000), (61925451026803705627/18790481920000000000000), (4380234117520885358163/1503238553600000000000000), (-349475525767811493193/134217728000000000000000), (-16375731558100195007/10737418240000000000000), (-16613870252919915261/11744051200000000000000), (1/10240000)], ![(-58676520851682473939573/240518168576000000000000000), (-5943241665000503943959/6012954214400000000000000), (98497409525671323978183/12025908428800000000000000), (-1152121379925736745899/93952409600000000000000), (2651813199459358216733/3006477107200000000000000), (15198029252307889867807/1879048192000000000000000), (-4732827195695153209043/751619276800000000000000), (45503619425988838823/23488102400000000000000), (3/102400000)], ![(6831467328167397544771/240518168576000000000000000), (-28915435600521663047/6012954214400000000000000), (-1744988364033644661423/1717986918400000000000000), (3253469828506614768829/751619276800000000000000), (-15931684131570429268331/3006477107200000000000000), (-809433291788895723227/268435456000000000000000), (723476983849567686123/107374182400000000000000), (45300583457059142263/46976204800000000000000), (1/204800000)], ![(440054794814851534963/12025908428800000000000000), (88198752757906705527/751619276800000000000000), (-264911489262053132699/214748364800000000000000), (3914265085601460871301/1503238553600000000000000), (-1214177214309412613017/751619276800000000000000), (-45897986341811508133/26843545600000000000000), (4478572724726368397/1677721600000000000000), (4370496730598273721/93952409600000000000000), (-1/409600000)], ![(-5482176078921498832667/60129542144000000000000000), (-321587114115925540861/1503238553600000000000000), (1170569552663988528619/375809638400000000000000), (-12588251839463901248439/1503238553600000000000000), (5550462265607475758377/751619276800000000000000), (5278555727452072429031/939524096000000000000000), (-141337253367407858783/13421772800000000000000), (-83270680260599757563/93952409600000000000000), (-3/819200000)], ![(4046114965590393441031/15032385536000000000000000), (108127262056045779717/107374182400000000000000), (-968219129720421319481/107374182400000000000000), (2929138616377733527911/187904819200000000000000), (-985448940560412692507/187904819200000000000000), (-2382803408250679268283/234881024000000000000000), (560609579628263137023/46976204800000000000000), (-13728559831408080451/11744051200000000000000), (-1/327680000)], ![(-194008752615040224617813/6012954214400000000000000), (-775691813047433865297/150323855360000000000000), (179092935552027861559/5368709120000000000000), (-3865880557063422832649/150323855360000000000000), (-17237777525767609239/429496729600000000000), (200151687538023888667/13421772800000000000000), (32613722737462742863/1342177280000000000000), (170156589783629298571/9395240960000000000000), (-7/3276800000)], ![(47600119/25600000), (17/256000), (4641/25600000), (2431/25600000), (-2431/40960000), (-4641/102400000), (-119/16384000), (-119/409600000), (32759/6553600000)]] +def M : Matrix (Fin 9) (Fin 9) ℚ := ![![(43906726546695367195188901233681/262144000000000000), (8997671708456527981905961941/2097152000000000000), (-45471993521069187654688183077/4194304000000000000), (3663232213214281929970727979/4194304000000000000), (158960753954368680036431709/104857600000000000), (-924188102768942644807451277/262144000000000000), (3052733148772468886724388389/262144000000000000), (-35548664596180693092054162243/26214400000000000), (15934856548169598039/204800)], ![(8997671708456527981905961941/2097152000000000000), (3960315771180462995770990521/16777216000000000000), (-13887312732529739314003289097/33554432000000000000), (-3778858479484353336802451721/33554432000000000000), (18589381738083829141870401/1048576000000000000), (252515655315986927659105311/4194304000000000000), (139102570903896480060567387/419430400000000000), (-259738020314595012677069583/83886080000000000), (5699943137889/81920)], ![(-45471993521069187654688183077/4194304000000000000), (-13887312732529739314003289097/33554432000000000000), (69034475116561659579995461209/67108864000000000000), (-3347836938528750828500051943/67108864000000000000), (-28252619912541800095309143/209715200000000000), (2434158878144081277713357493/8388608000000000000), (-4522201744625437809816605583/4194304000000000000), (4084000192135307962891059687/838860800000000000), (17295735379923/819200)], ![(3663232213214281929970727979/4194304000000000000), (-3778858479484353336802451721/33554432000000000000), (-3347836938528750828500051943/67108864000000000000), (17519810144309559589917219561/67108864000000000000), (26045297282594678777211033/335544320000000000), (-752892010534544096309463909/2097152000000000000), (1054677470631984082989876771/4194304000000000000), (414895971241822085975478519/209715200000000000), (266678733321/65536)], ![(158960753954368680036431709/104857600000000000), (18589381738083829141870401/1048576000000000000), (-28252619912541800095309143/209715200000000000), (26045297282594678777211033/335544320000000000), (624035521860954911315891073/16777216000000000000), (-445715949234613041027207549/3355443200000000000), (821991034617908142918139209/4194304000000000000), (-48588557140361613541225059/1677721600000000000), (-3136492728369/3276800)], ![(-924188102768942644807451277/262144000000000000), (252515655315986927659105311/4194304000000000000), (2434158878144081277713357493/8388608000000000000), (-752892010534544096309463909/2097152000000000000), (-445715949234613041027207549/3355443200000000000), (9091905185633031798111246501/16777216000000000000), (-2390022411404985221357839203/4194304000000000000), (-2650587134374087446921183801/1677721600000000000), (-23068709066403/6553600)], ![(3052733148772468886724388389/262144000000000000), (139102570903896480060567387/419430400000000000), (-4522201744625437809816605583/4194304000000000000), (1054677470631984082989876771/4194304000000000000), (821991034617908142918139209/4194304000000000000), (-2390022411404985221357839203/4194304000000000000), (672940655667104792490108729/524288000000000000), (-1425128559723823474403536653/419430400000000000), (-97696203898293/13107200)], ![(-35548664596180693092054162243/26214400000000000), (-259738020314595012677069583/83886080000000000), (4084000192135307962891059687/838860800000000000), (414895971241822085975478519/209715200000000000), (-48588557140361613541225059/1677721600000000000), (-2650587134374087446921183801/1677721600000000000), (-1425128559723823474403536653/419430400000000000), (8761082729414007231498560301/167772160000000000), (-15933382939323208359/26214400)], ![(15934856548169598039/204800), (5699943137889/81920), (17295735379923/819200), (266678733321/65536), (-3136492728369/3276800), (-23068709066403/6553600), (-97696203898293/13107200), (-15933382939323208359/26214400), (379277143371728621019/10485760)]] +def L : Matrix (Fin 9) (Fin 9) ℚ := ![![1, 0, 0, 0, 0, 0, 0, 0, 0], ![(12330155041743617126229/481348298304662330209586312), 1, 0, 0, 0, 0, 0, 0, 0], ![(-62313534916481581045413/962696596609324660419172624), (-14303573950882974955267658543848561832459654745/8159723145978646318406943581441036927855280538), 1, 0, 0, 0, 0, 0, 0], ![(5019989904765031854251/962696596609324660419172624), (-1947756937424586687159016380164211042330577879/4079861572989323159203471790720518463927640269), (-329808269456763417252265574891223212982459757668755859956291133835/404089366714043883860858835080347348790107595543274047086380439179), 1, 0, 0, 0, 0, 0], ![(1089176625530633153105/120337074576165582552396578), (6117591022656574591533735446718235207304609119/81597231459786463184069435814410369278552805380), (-460633102581204214554017545544244188452855762459540414508249063931/1346964555713479612869529450267824495967025318477580156954601463930), (1080380729554704515637238303668946829764816664754142165243448077450612047159688011/3951290642451697441054843254905538446229355062623839318848456057605149223517626930), 1, 0, 0, 0, 0], ![(-1266481259164625011213/60168537288082791276198289), (4170394321150556676619257657763000095526958781/16319446291957292636813887162882073855710561076), (4221385334300103950973915951557307823872893182911257679531575571209/3232714933712351070886870680642778790320860764346192376691043513432), (-29562261619532140474712833321495231975489582758181282524040039506557220942515376613/22127227597729505669907122227471015298884388350693500185551353922588835651698710808), (-1630342947923160261820666845551722566371460872836196271388007980590601221910751141175659687430205/822278136057168163341136997145523547417275184602589941913775654988437869474606158819617949964468), 1, 0, 0, 0], ![(4183379239104474245541/60168537288082791276198289), (28647861362554416637588800029748544362612855223/20399307864946615796017358953602592319638201345), (-4415392074830326896829153280682281988651547129566652676666927955391/2693929111426959225739058900535648991934050636955160313909202927860), (1906594551902337140331304234017236221535738451999956047831778408235127388594688303/2431563472277967656033749695326485197679603115460824196214434496987784137549308880), (628070098057806866691797803130548699165971184284153040870179746334655017530809655832238055331219/234936610302048046668896284898721013547792909886454269118221615710982248421316045377033699989848), (-13/2), 1, 0, 0], ![(-487148853837255927776670/60168537288082791276198289), (-105879912556801055418001024676162577991886428029/8159723145978646318406943581441036927855280538), (-3126578969158749602269726875419683354100194497235222642638253043279/1616357466856175535443435340321389395160430382173096188345521756716), (4054024939053945123098425920843644606184853398545397547304397662227832305588139623/486312694455593531206749939065297039535920623092164839242886899397556827509861776), (-24624847156942404079507941168650347124375003221087653200380855438597179023080409963898625000000/29367076287756005833612035612340126693474113735806783639777701963872781052664505672129212498731), (91/2), 0, 1, 0], ![(27950946696180480000000000/60168537288082791276198289), (-33260804618873541012764099522489927552000000000/4079861572989323159203471790720518463927640269), (749369107500604040559009017443170539515625108847804062256000000000/134696455571347961286952945026782449596702531847758015695460146393), (310669440620604690940770513274475664959151993487127309893210501208946330298828125/30394543403474595700421871191581064970995038943260302452680431212347301719366361), (418622401668020869351634999867055901114375054758490104406474542456152043392366969386276625000000/29367076287756005833612035612340126693474113735806783639777701963872781052664505672129212498731), (-1547/2), 0, 0, 1]] +def diag : Fin 9 → ℚ := ![(43906726546695367195188901233681/262144000000000000), (2977193305795925799642390266370693218163453005857101/12618256831077740189046179417292800000000000), (3240392631679917904680226998509305389947872808661514583585684741776401/10695112321897131302462349091066395922078473306767360000000000), (4704801767967236143064001863616024627925293073066205476952856627790451180442438385551/862057315656626952236498848171407677418896203825651300450944936915200000000000), (1648462093260607875458144395027488331684782426332042186051641744338070818829216696893629085191267223/115603474796301090846861699800664896255395988117908898928594828656790651568058570752000000000000), (38730273917706481197065821448570844185152862316419889597236757452789024962567046438935812607907843035521/76984028463775103932463934635612901719340780711593334904658859036174663162696841749146402812673392640), 0, 0, 0] + +def keyIndexTable : Fin 18 → Fin 13 → Fin 13 → Fin 34 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 4, 5, 6, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 7, 8, 9, 10, 11, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 7, 0, 12, 13, 14, 15, 0, 0, 0, 0, 0], ![0, 0, 0, 19, 20, 21, 22, 23, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 8, 12, 0, 16, 17, 0, 0, 0, 0, 0, 0], ![1, 0, 19, 0, 24, 25, 26, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 9, 13, 16, 0, 18, 0, 0, 0, 0, 0, 0], ![2, 0, 20, 24, 0, 27, 28, 0, 0, 0, 0, 0, 0], ![7, 19, 0, 0, 29, 30, 31, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 10, 14, 17, 18, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 21, 25, 27, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 20, 0, 29, 0, 32, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 11, 15, 0, 18, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 22, 26, 28, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 21, 0, 30, 32, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 24, 29, 0, 0, 33, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 0, 15, 17, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 23, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 22, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 25, 30, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 11, 14, 16, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 23, 26, 27, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 23, 0, 31, 32, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 26, 31, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 27, 32, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 10, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 22, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 23, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 28, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 9, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 21, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 22, 0, 29, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 26, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 28, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 0, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 25, 29, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 0, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 0, 29, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 27, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 28, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 20, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 18) (j : Fin ((n.val+1)/2)) (x : Fin ((17-n.val+2)/2)) : Fin 34 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 34 → FourTerm 17 := ![⟨⟨17,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 9, + (fourTermLabels (by omega : 17 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 9, + (fourTermLabels (by omega : 17 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 8, + (fourTermLabels (by omega : 17 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 8, + (fourTermLabels (by omega : 17 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 7, + (fourTermLabels (by omega : 17 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 7, + (fourTermLabels (by omega : 17 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 6, + (fourTermLabels (by omega : 17 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 6, + (fourTermLabels (by omega : 17 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 5, + (fourTermLabels (by omega : 17 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 5, + (fourTermLabels (by omega : 17 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 4, + (fourTermLabels (by omega : 17 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 4, + (fourTermLabels (by omega : 17 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover_12 : ∀ j : Fin 6, ∀ x : Fin 3, + (fourTermLabels (by omega : 17 ≤ 23) ⟨12,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨12,j,x⟩).toFinset=keys (keyIndex 12 j x) := by decide +kernel +lemma cover_13 : ∀ j : Fin 7, ∀ x : Fin 3, + (fourTermLabels (by omega : 17 ≤ 23) ⟨13,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨13,j,x⟩).toFinset=keys (keyIndex 13 j x) := by decide +kernel +lemma cover_14 : ∀ j : Fin 7, ∀ x : Fin 2, + (fourTermLabels (by omega : 17 ≤ 23) ⟨14,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨14,j,x⟩).toFinset=keys (keyIndex 14 j x) := by decide +kernel +lemma cover_15 : ∀ j : Fin 8, ∀ x : Fin 2, + (fourTermLabels (by omega : 17 ≤ 23) ⟨15,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨15,j,x⟩).toFinset=keys (keyIndex 15 j x) := by decide +kernel +lemma cover_16 : ∀ j : Fin 8, ∀ x : Fin 1, + (fourTermLabels (by omega : 17 ≤ 23) ⟨16,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨16,j,x⟩).toFinset=keys (keyIndex 16 j x) := by decide +kernel +lemma cover_17 : ∀ j : Fin 9, ∀ x : Fin 1, + (fourTermLabels (by omega : 17 ≤ 23) ⟨17,j,x⟩).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) ⟨17,j,x⟩).toFinset=keys (keyIndex 17 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 17, (fourTermLabels (by omega : 17 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 17 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x + · exact cover_12 j x + · exact cover_13 j x + · exact cover_14 j x + · exact cover_15 j x + · exact cover_16 j x + · exact cover_17 j x +lemma representatives_checked : ∀ a : Fin 34, + (fourTermLabels (by omega : 17 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 17 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 17 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 17 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 34, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 17, + (fourTermLabels (by omega : 17 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 34, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 17 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 34, ∀ b : FourTerm 17, + (fourTermLabels (by omega : 17 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 17 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 34, (∑ b ∈ fibers v, fourTermEval 17 (2*(0 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 17 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 34, (∑ b ∈ fibers v, fourTermEval 17 (2*(1 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 17 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 34, (∑ b ∈ fibers v, fourTermEval 17 (2*(2 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 17 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 34, (∑ b ∈ fibers v, fourTermEval 17 (2*(3 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 17 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 34, (∑ b ∈ fibers v, fourTermEval 17 (2*(4 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 17 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 34, (∑ b ∈ fibers v, fourTermEval 17 (2*(5 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 17 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_6 : ∀ v : Fin 34, (∑ b ∈ fibers v, fourTermEval 17 (2*(6 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 17 ≤ 23) b)) = columns 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_7 : ∀ v : Fin 34, (∑ b ∈ fibers v, fourTermEval 17 (2*(7 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 17 ≤ 23) b)) = columns 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_8 : ∀ v : Fin 34, (∑ b ∈ fibers v, fourTermEval 17 (2*(8 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 17 ≤ 23) b)) = columns 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 9, ∀ v : Fin 34, (∑ b ∈ fibers v, fourTermEval 17 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 17 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 + · exact columns_checked_6 + · exact columns_checked_7 + · exact columns_checked_8 +lemma gram_checked_0 : ∀ v : Fin 9, (∑ a : Fin 34, columns (0 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 9, (∑ a : Fin 34, columns (1 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 9, (∑ a : Fin 34, columns (2 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 9, (∑ a : Fin 34, columns (3 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 9, (∑ a : Fin 34, columns (4 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 9, (∑ a : Fin 34, columns (5 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_6 : ∀ v : Fin 9, (∑ a : Fin 34, columns (6 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_7 : ∀ v : Fin 9, (∑ a : Fin 34, columns (7 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_8 : ∀ v : Fin 9, (∑ a : Fin 34, columns (8 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 9, ∀ v : Fin 9, (∑ a : Fin 34, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 + · exact gram_checked_6 + · exact gram_checked_7 + · exact gram_checked_8 +lemma rows_table_checked_0 : ∀ v : Fin 9, integerTableEval 17 SumTable17.sums (0 : Fin 9) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 9, integerTableEval 17 SumTable17.sums (1 : Fin 9) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 9, integerTableEval 17 SumTable17.sums (2 : Fin 9) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 9, integerTableEval 17 SumTable17.sums (3 : Fin 9) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 9, integerTableEval 17 SumTable17.sums (4 : Fin 9) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 9, integerTableEval 17 SumTable17.sums (5 : Fin 9) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_6 : ∀ v : Fin 9, integerTableEval 17 SumTable17.sums (6 : Fin 9) v = Y 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_7 : ∀ v : Fin 9, integerTableEval 17 SumTable17.sums (7 : Fin 9) v = Y 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_8 : ∀ v : Fin 9, integerTableEval 17 SumTable17.sums (8 : Fin 9) v = Y 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 9, ∀ v : Fin 9, integerTableEval 17 SumTable17.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 + · exact rows_table_checked_6 + · exact rows_table_checked_7 + · exact rows_table_checked_8 +lemma rows_checked (u v : Fin 9) : exactFourEval 17 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 17 SumTable17.sums SumTable17.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 9, (Z * tableComparison 17 (1/200000) Y) (0 : Fin 9) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 9, (Z * tableComparison 17 (1/200000) Y) (1 : Fin 9) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 9, (Z * tableComparison 17 (1/200000) Y) (2 : Fin 9) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 9, (Z * tableComparison 17 (1/200000) Y) (3 : Fin 9) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 9, (Z * tableComparison 17 (1/200000) Y) (4 : Fin 9) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 9, (Z * tableComparison 17 (1/200000) Y) (5 : Fin 9) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_6 : ∀ v : Fin 9, (Z * tableComparison 17 (1/200000) Y) (6 : Fin 9) v = W 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_7 : ∀ v : Fin 9, (Z * tableComparison 17 (1/200000) Y) (7 : Fin 9) v = W 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_8 : ∀ v : Fin 9, (Z * tableComparison 17 (1/200000) Y) (8 : Fin 9) v = W 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 9, ∀ v : Fin 9, (Z * tableComparison 17 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 + · exact product_checked_6 + · exact product_checked_7 + · exact product_checked_8 +lemma compression_checked_0 : ∀ v : Fin 9, (W * Z) (0 : Fin 9) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 9, (W * Z) (1 : Fin 9) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 9, (W * Z) (2 : Fin 9) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 9, (W * Z) (3 : Fin 9) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 9, (W * Z) (4 : Fin 9) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 9, (W * Z) (5 : Fin 9) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_6 : ∀ v : Fin 9, (W * Z) (6 : Fin 9) v = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_7 : ∀ v : Fin 9, (W * Z) (7 : Fin 9) v = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_8 : ∀ v : Fin 9, (W * Z) (8 : Fin 9) v = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 9, ∀ v : Fin 9, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 + · exact compression_checked_6 + · exact compression_checked_7 + · exact compression_checked_8 +lemma ldl_checked_0 : ∀ v : Fin 9, (∑ k : Fin 9, L (0 : Fin 9) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 9, (∑ k : Fin 9, L (1 : Fin 9) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 9, (∑ k : Fin 9, L (2 : Fin 9) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 9, (∑ k : Fin 9, L (3 : Fin 9) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 9, (∑ k : Fin 9, L (4 : Fin 9) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 9, (∑ k : Fin 9, L (5 : Fin 9) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_6 : ∀ v : Fin 9, (∑ k : Fin 9, L (6 : Fin 9) k * diag k * L v k) = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_7 : ∀ v : Fin 9, (∑ k : Fin 9, L (7 : Fin 9) k * diag k * L v k) = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_8 : ∀ v : Fin 9, (∑ k : Fin 9, L (8 : Fin 9) k * diag k * L v k) = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 9, ∀ v : Fin 9, (∑ k : Fin 9, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 + · exact ldl_checked_6 + · exact ldl_checked_7 + · exact ldl_checked_8 +lemma diag_checked : ∀ u : Fin 9, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 17 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 17 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 17 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 17 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 17 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate17 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate18.lean b/lean/OAI/Analysis/LaughlinGap/Certificate18.lean new file mode 100644 index 0000000000000000000000000000000000000000..aa064ec720c41a543a3b5d608bf0a74370e5f4ec --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate18.lean @@ -0,0 +1,393 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Certificate17 +import OAI.Analysis.LaughlinGap.SumTable18 + +namespace OAI + +/-! Certificate18. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate18 + +def keys : Fin 39 → Finset (Fin 25) := ![{0,1,2,16}, {0,1,3,15}, {0,1,4,14}, {0,1,5,13}, {0,1,6,12}, {0,1,7,11}, {0,1,8,10}, {0,2,3,14}, {0,2,4,13}, {0,2,5,12}, {0,2,6,11}, {0,2,7,10}, {0,2,8,9}, {0,3,4,12}, {0,3,5,11}, {0,3,6,10}, {0,3,7,9}, {0,4,5,10}, {0,4,6,9}, {0,4,7,8}, {0,5,6,8}, {1,2,3,13}, {1,2,4,12}, {1,2,5,11}, {1,2,6,10}, {1,2,7,9}, {1,3,4,11}, {1,3,5,10}, {1,3,6,9}, {1,3,7,8}, {1,4,5,9}, {1,4,6,8}, {1,5,6,7}, {2,3,4,10}, {2,3,5,9}, {2,3,6,8}, {2,4,5,8}, {2,4,6,7}, {3,4,5,7}] +def fibers : Fin 39 → Finset (FourTerm 18) := ![{⟨⟨18,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨18,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨18,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨18,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨18,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨5,by decide⟩)⟩}] +def columns : Matrix (Fin 9) (Fin 39) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![-214540326000, 214540326000, -268175407500, 245188944000, -206878171500, 153243090000, -76621545000, 53635081500, 22986463500, -38310772500, 53635081500, -76621545000, 76621545000, -61297236000, 61297236000, -38310772500, 30648618000, -38310772500, 38310772500, -61297236000, 15324309000, -76621545000, 76621545000, -76621545000, 61297236000, -30648618000, 0, 15324309000, -30648618000, 30648618000, 0, 7662154500, -15324309000, -15324309000, 15324309000, -7662154500, -7662154500, 7662154500, 0], ![-245188944000, 245188944000, -224756532000, 186810624000, -131351220000, 81729648000, -40864824000, -20432412000, 37945908000, -55459404000, 49621572000, -40864824000, 40864824000, 0, 11675664000, -8756748000, 0, -8756748000, 8756748000, 0, -5837832000, -17513496000, 17513496000, -5837832000, 0, 0, -11675664000, 5837832000, 0, 0, 0, -2918916000, 5837832000, 5837832000, -5837832000, 2918916000, 2918916000, -2918916000, 0], ![-222202480500, 222202480500, -144942422625, 81729648000, -40815707625, 14341981500, -1669956750, -77260057875, 63212774625, -40913940375, 26473726125, -12672024750, 1669956750, -8251551000, 4322241000, -6336012375, 6483361500, 4666055625, -3094331625, -1964655000, 2848749750, 14047283250, -14047283250, 10117973250, -7465689000, 4518706500, 3929310000, -2652284250, 2946982500, -4518706500, -1571724000, 2210236875, -2848749750, -1277025750, 1277025750, -638512875, -638512875, 638512875, 0], ![-91945854000, 91945854000, -41375634300, 0, 12377326500, -7072758000, 964467000, -50570219700, 41375634300, -12377326500, -5304568500, 6108291000, -964467000, -19803722400, 14145516000, -2089678500, -2957698800, -7233502500, 4147208100, 771573600, -2250423000, 9194585400, -9194585400, 3536379000, 1285956000, -2186125200, 5658206400, -4822335000, 900169200, 2186125200, 3086294400, -2668358700, 2250423000, -835871400, 835871400, -417935700, -417935700, 417935700, 0], ![153243090000, -153243090000, 81729648000, -25540515000, 5893965000, -5893965000, 5893965000, 71513442000, -56189133000, 19646550000, 0, 0, -5893965000, 21218274000, -12770257500, 0, 4125775500, 5893965000, -2357586000, -2357586000, 1964655000, -15324309000, 15324309000, -6876292500, 0, 1768189500, -8448016500, 6876292500, -1768189500, -1768189500, -3536379000, 2750517000, -1964655000, 1571724000, -1571724000, 785862000, 785862000, -785862000, 0], ![245188944000, -245188944000, 158351193000, -72972900000, 10945935000, 20432412000, -20432412000, 86837751000, -85378293000, 62026965000, -31378347000, 0, 20432412000, 21891870000, -25540515000, 24081057000, -15324309000, 3648645000, -6567561000, 10216206000, -1459458000, -1459458000, 1459458000, -5108103000, 7297290000, -5108103000, 3648645000, -2189187000, -2189187000, 5108103000, 2918916000, -2189187000, 1459458000, -1459458000, 1459458000, -729729000, -729729000, 729729000, 0], ![-1103350248000, 1103350248000, -582323742000, 122594472000, 122594472000, -183891708000, 122594472000, -521026506000, 459729270000, -245188944000, 61297236000, 61297236000, -122594472000, -153243090000, 137918781000, -91945854000, 45972927000, -30648618000, 30648618000, -30648618000, 0, 61297236000, -61297236000, 45972927000, -30648618000, 15324309000, 15324309000, -15324309000, 15324309000, -15324309000, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![-8336424096000, 8336424096000, -6947020080000, 5557616064000, -4168212048000, 2778808032000, -1389404016000, -1389404016000, 1389404016000, -1389404016000, 1389404016000, -1389404016000, 1389404016000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Y : Matrix (Fin 9) (Fin 9) ℚ := ![![(-69912637365968552879910957771/2097152000000000000), (9214410830777558333938819809/524288000000000000), (-3174411782048976735918610959/419430400000000000), (142429803155004148453266597/41943040000000000), (-99298862583805837635549867/52428800000000000), (444400754169792692329196139/131072000000000000), (-1250792888783890658692114629/131072000000000000), (-424665049549385783959541721/13107200000000000), 0], ![(9214410830777558333938819809/524288000000000000), (-392830529556391576254495891/209715200000000000), (30426554308602923525016963/104857600000000000), (-8381792718047555249804361/52428800000000000), (22751405344240922381008977/65536000000000000), (-49034422333383487341388047/65536000000000000), (6391380643369945332830721/6553600000000000), (10751545438948904258932263/3276800000000000), 0], ![(-3174411782048976735918610959/419430400000000000), (30426554308602923525016963/104857600000000000), (9452746950541565879331981/83886080000000000), (-805750220703755238218307/41943040000000000), (-6210678240724319186932107/52428800000000000), (5527754682661439867349711/26214400000000000), (506507815228225116839247/26214400000000000), (231485456683659732516963/2621440000000000), 0], ![(142429803155004148453266597/41943040000000000), (-8381792718047555249804361/52428800000000000), (-805750220703755238218307/41943040000000000), (-86531215874556520621323/4194304000000000), (1989886145535198031275693/26214400000000000), (-245930582666763986421969/2621440000000000), (-772186883283939592918449/13107200000000000), (-443944709714681777218617/1310720000000000), 0], ![(-99298862583805837635549867/52428800000000000), (22751405344240922381008977/65536000000000000), (-6210678240724319186932107/52428800000000000), (1989886145535198031275693/26214400000000000), (-122991101936708768097867/1310720000000000), (567893268322184935822923/3276800000000000), (-4851536712934014040394457/16384000000000000), (-859271948102941900764237/1638400000000000), 0], ![(444400754169792692329196139/131072000000000000), (-49034422333383487341388047/65536000000000000), (5527754682661439867349711/26214400000000000), (-245930582666763986421969/2621440000000000), (567893268322184935822923/3276800000000000), (-4613713245838144663577901/8192000000000000), (10958765207225665927438341/8192000000000000), (2586782960232936911434989/819200000000000), 0], ![(-1250792888783890658692114629/131072000000000000), (6391380643369945332830721/6553600000000000), (506507815228225116839247/26214400000000000), (-772186883283939592918449/13107200000000000), (-4851536712934014040394457/16384000000000000), (10958765207225665927438341/8192000000000000), (-1017822230260041755192787/327680000000000), (-6154051560168210764047983/819200000000000), 0], ![(-424665049549385783959541721/13107200000000000), (10751545438948904258932263/3276800000000000), (231485456683659732516963/2621440000000000), (-443944709714681777218617/1310720000000000), (-859271948102941900764237/1638400000000000), (2586782960232936911434989/819200000000000), (-6154051560168210764047983/819200000000000), (-1776128349089499360186231/81920000000000), 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Z : Matrix (Fin 9) (Fin 9) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 7846046208000, 0, 0, 0, 0, 0, -858161304000, 16672848192000], ![0, 0, 747242496000, 0, 0, 0, -140107968000, 0, 11115232128000], ![0, 0, 0, 201180672000, 0, -47151720000, -163459296000, 643620978000, 4168212048000], ![0, 0, 0, 0, 98761420800, -113164128000, 0, 367783416000, 0], ![0, 0, 0, -47151720000, -113164128000, 149313780000, 0, -421418497500, -1736755020000], ![0, 0, -140107968000, -163459296000, 0, 0, 329837508000, -1195296102000, -2084106024000], ![0, -858161304000, 0, 643620978000, 367783416000, -421418497500, -1195296102000, 6169949911125, -1823592771000], ![0, 16672848192000, 11115232128000, 4168212048000, 0, -1736755020000, -2084106024000, -1823592771000, 354298024080000]] +def W : Matrix (Fin 9) (Fin 9) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![(-7140327064241251293699/120259084288000000000000000), (54394453669059988259/187904819200000000000000), (-322462782053194127631/858993459200000000000000), (917753850753862786521/1503238553600000000000000), (-4617888408507639200793/1503238553600000000000000), (729581257120682107713/134217728000000000000000), (-129101907787873358481/53687091200000000000000), (-67737172132011381247/93952409600000000000000), (3/12800000)], ![(244242166368554621839/15032385536000000000000000), (-1606248743610797/117440512000000000000), (-105943408951940492403/751619276800000000000000), (7625596590539243459/187904819200000000000000), (12829973237668749019/26843545600000000000000), (23326395384042356749/117440512000000000000000), (-37872086248790246829/46976204800000000000000), (-2240510057377799493/11744051200000000000000), (1/6400000)], ![(-2746569118783363795009/481036337152000000000000000), (-273244723794532391/30064771072000000000000), (301713244246493761979/3435973836800000000000000), (434744028156055516211/6012954214400000000000000), (-2604706921981222280563/6012954214400000000000000), (-12860171735831672917/536870912000000000000000), (88630371560210863717/214748364800000000000000), (58303169765380410603/375809638400000000000000), (3/51200000)], ![(1638571311148740348609/120259084288000000000000000), (-99991440511429130829/939524096000000000000000), (233724357023419450053/858993459200000000000000), (-701070948296205591987/1503238553600000000000000), (88101292129244544747/60129542144000000000000), (-397195704624384214443/134217728000000000000000), (476597459725176492423/268435456000000000000000), (38171014173605365653/93952409600000000000000), 0], ![(-10752403582585959899/751619276800000000000000), (23767227800967390443/187904819200000000000000), (-1854106947544628183/5368709120000000000000), (20846886768302400023/37580963840000000000000), (-3142305048678622959/1879048192000000000000), (11930236761752004317/3355443200000000000000), (-3737446458550338963/1677721600000000000000), (-1209518848595567257/2348810240000000000000), (-1/40960000)], ![(104205799991268082679/60129542144000000000000000), (-292700446735961693/375809638400000000000000), (39201594091172281157/3006477107200000000000000), (-174758224354277699941/751619276800000000000000), (515264188426888324853/751619276800000000000000), (-341191536639688159711/469762048000000000000000), (46277064492073281499/187904819200000000000000), (-1506727128153094653/46976204800000000000000), (-3/102400000)], ![(230988429575957641731/6012954214400000000000000), (-155897099336119824817/375809638400000000000000), (47546854588901856903/42949672960000000000000), (-68997799533234827229/75161927680000000000000), (205953768991363797833/75161927680000000000000), (-59738968579169598147/6710886400000000000000), (87244803185236679853/13421772800000000000000), (8732725409305723747/4697620480000000000000), (-21/819200000)], ![0, (17/1600000), (119/1600000), (663/6400000), 0, (-221/5120000), (-357/25600000), (-119/102400000), (51/10240000)]] +def M : Matrix (Fin 9) (Fin 9) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, (4855129574232866382282007179/1677721600000000000), (12375779569434410117725737/209715200000000000), (-1365446796209146227792141927/6710886400000000000), (-9929520853923149484851466621/8388608000000000000), (300713462414935997709711429/209715200000000000), (17553592070225551602311049/838860800000000000), (-2034445792202890918564944231/419430400000000000), (85708860237/512)], ![0, (12375779569434410117725737/209715200000000000), (245495883926280518003187/26214400000000000), (7081447586047032581786403/838860800000000000), (-47645939107916422644850479/1048576000000000000), (704938704034275503315523/13107200000000000), (-526133540974095866775249/20971520000000000), (-4393337794268760944375769/52428800000000000), (1128890763/10)], ![0, (-1365446796209146227792141927/6710886400000000000), (7081447586047032581786403/838860800000000000), (1296765876097529320629400947/26843545600000000000), (569988504493455877325338689/33554432000000000000), (-19667722398367391030790261/838860800000000000), (-49359979906659612224931897/671088640000000000), (618898210149382284783721059/1677721600000000000), (2312576146881/51200)], ![0, (-9929520853923149484851466621/8388608000000000000), (-47645939107916422644850479/1048576000000000000), (569988504493455877325338689/33554432000000000000), (5276589830618783854020996159/8388608000000000000), (-158733616145540491991965491/209715200000000000), (579234730431600147227564241/4194304000000000000), (822788867020993332155749053/419430400000000000), (57052402407/12800)], ![0, (300713462414935997709711429/209715200000000000), (704938704034275503315523/13107200000000000), (-19667722398367391030790261/838860800000000000), (-158733616145540491991965491/209715200000000000), (152844084595101451519834713/167772160000000000), (-67736039141688510080098611/419430400000000000), (-199591867583263724494586661/83886080000000000), (-798299444943/40960)], ![0, (17553592070225551602311049/838860800000000000), (-526133540974095866775249/20971520000000000), (-49359979906659612224931897/671088640000000000), (579234730431600147227564241/4194304000000000000), (-67736039141688510080098611/419430400000000000), (65351586017127193427279493/419430400000000000), (-8702135327037179965844907/104857600000000000), (-2096350146891/51200)], ![0, (-2034445792202890918564944231/419430400000000000), (-4393337794268760944375769/52428800000000000), (618898210149382284783721059/1677721600000000000), (822788867020993332155749053/419430400000000000), (-199591867583263724494586661/83886080000000000), (-8702135327037179965844907/104857600000000000), (344955574918714660890032043/41943040000000000), (62393184606753/819200)], ![0, (85708860237/512), (1128890763/10), (2312576146881/51200), (57052402407/12800), (-798299444943/40960), (-2096350146891/51200), (62393184606753/819200), (338571620536149/102400)]] +def L : Matrix (Fin 9) (Fin 9) ℚ := ![![1, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 1, 0, 0, 0, 0, 0, 0, 0], ![0, (45225116244283965208/2217777455389999293017), 1, 0, 0, 0, 0, 0, 0], ![0, (-623723234337288787021/8871109821559997172068), (1755456397153066342028700123103935848033/1137906194081320844453817726735235379384), 1, 0, 0, 0, 0, 0], ![0, (-4535711592441919984383/11088887276949996465085), (-3712271301559652913012236390837005666167/1422382742601651055567272158419044224230), (-17595974907558603788931181369293549529176393482596181108/7685685753055827130592673856305843309029223597431331985), 1, 0, 0, 0, 0], ![0, (1098904615877715326136/2217777455389999293017), (13686908675895172110642563311520300999249/4551624776325283377815270906940941517536), (149973822666041533714125816607212392386579369495418494141/55336937422001955340267251765402071825010409901505590292), (-349741368857313987644335133403526730410406075624350723439714732769698795/282968060942672263546399381004349848603664584320175569431944110053555312), 1, 0, 0, 0], ![0, (16036631014367938054/2217777455389999293017), (-7114675282885104344451648691031756629039/2275812388162641688907635453470470758768), (-10349518005487341143253734126655880087814380649480627069/4611411451833496278355604313783505985417534158458799191), (16579636034326312348322464401760977108826263959030540919314536000000000/41266175554139705100516576396467686254701085213358937208825182716143483), (-156/35), 1, 0, 0], ![0, (-3717262695608718521652/2217777455389999293017), (4214894473202299440191617988401220309391/2275812388162641688907635453470470758768), (1435220712530150410668469751692253116515619619654126921/4611411451833496278355604313783505985417534158458799191), (808148127583771286263693763606814141801839065453550055681343639335361445/377290747923563018061865841339133131471552779093567425909258813404740416), (351/20), 0, 1, 0], ![0, (128289996800000000000/2217777455389999293017), (1907923837840860620892680629760000000000/142238274260165105556727215841904422423), (-106235355898895459265302903862947453836318124134400000000/13834234355500488835066812941350517956252602475376397573), (140926906291773654960740947414968305425023243651759597814173556000000000/17685503808917016471649961312771865537729036520010973089496506878347207), (-442/5), 0, 0, 1]] +def diag : Fin 9 → ℚ := ![0, (4855129574232866382282007179/1677721600000000000), (14827913376799431758972142069871010324330481/1816803291455487420839526400000000000), (5435899539541162578451637875857800371068291343252123274756463/372869101676567214310626992696601929116549120000000000), (631743881558324745383808268053523808873218913531311969729904722201440581247/49188388819557293635793112680357397177787031023560524704000000000000), (630419662018338629831660524520176257617401370750426680850307159401234527006947/32195477156144044207945885127606027218905837149317753677590085410537848832), 0, 0, 0] + +def keyIndexTable : Fin 19 → Fin 13 → Fin 13 → Fin 39 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 4, 5, 6, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 7, 8, 9, 10, 11, 12, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 7, 0, 13, 14, 15, 16, 0, 0, 0, 0, 0], ![0, 0, 0, 21, 22, 23, 24, 25, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 8, 13, 0, 17, 18, 19, 0, 0, 0, 0, 0], ![1, 0, 21, 0, 26, 27, 28, 29, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 9, 14, 17, 0, 20, 0, 0, 0, 0, 0, 0], ![2, 0, 22, 26, 0, 30, 31, 0, 0, 0, 0, 0, 0], ![7, 21, 0, 0, 33, 34, 35, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 10, 15, 18, 20, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 23, 27, 30, 0, 32, 0, 0, 0, 0, 0, 0], ![8, 22, 0, 33, 0, 36, 37, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 11, 16, 19, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 24, 28, 31, 32, 0, 0, 0, 0, 0, 0, 0], ![9, 23, 0, 34, 36, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 26, 33, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 12, 0, 19, 20, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 25, 29, 0, 32, 0, 0, 0, 0, 0, 0, 0], ![10, 24, 0, 35, 37, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 27, 34, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 12, 16, 18, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 29, 31, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 25, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 28, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 30, 36, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 11, 15, 17, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 25, 28, 30, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 0, 0, 35, 36, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 29, 0, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 31, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 10, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 24, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 25, 0, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 29, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 0, 37, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 9, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 23, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 24, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 28, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 31, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 32, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 27, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 32, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 30, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 31, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 29, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 21, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 22, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 23, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 19) (j : Fin ((n.val+1)/2)) (x : Fin ((18-n.val+2)/2)) : Fin 39 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 39 → FourTerm 18 := ![⟨⟨18,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 10, + (fourTermLabels (by omega : 18 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 9, + (fourTermLabels (by omega : 18 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 9, + (fourTermLabels (by omega : 18 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 8, + (fourTermLabels (by omega : 18 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 8, + (fourTermLabels (by omega : 18 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 7, + (fourTermLabels (by omega : 18 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 7, + (fourTermLabels (by omega : 18 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 6, + (fourTermLabels (by omega : 18 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 6, + (fourTermLabels (by omega : 18 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 5, + (fourTermLabels (by omega : 18 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 5, + (fourTermLabels (by omega : 18 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 4, + (fourTermLabels (by omega : 18 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover_12 : ∀ j : Fin 6, ∀ x : Fin 4, + (fourTermLabels (by omega : 18 ≤ 23) ⟨12,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨12,j,x⟩).toFinset=keys (keyIndex 12 j x) := by decide +kernel +lemma cover_13 : ∀ j : Fin 7, ∀ x : Fin 3, + (fourTermLabels (by omega : 18 ≤ 23) ⟨13,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨13,j,x⟩).toFinset=keys (keyIndex 13 j x) := by decide +kernel +lemma cover_14 : ∀ j : Fin 7, ∀ x : Fin 3, + (fourTermLabels (by omega : 18 ≤ 23) ⟨14,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨14,j,x⟩).toFinset=keys (keyIndex 14 j x) := by decide +kernel +lemma cover_15 : ∀ j : Fin 8, ∀ x : Fin 2, + (fourTermLabels (by omega : 18 ≤ 23) ⟨15,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨15,j,x⟩).toFinset=keys (keyIndex 15 j x) := by decide +kernel +lemma cover_16 : ∀ j : Fin 8, ∀ x : Fin 2, + (fourTermLabels (by omega : 18 ≤ 23) ⟨16,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨16,j,x⟩).toFinset=keys (keyIndex 16 j x) := by decide +kernel +lemma cover_17 : ∀ j : Fin 9, ∀ x : Fin 1, + (fourTermLabels (by omega : 18 ≤ 23) ⟨17,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨17,j,x⟩).toFinset=keys (keyIndex 17 j x) := by decide +kernel +lemma cover_18 : ∀ j : Fin 9, ∀ x : Fin 1, + (fourTermLabels (by omega : 18 ≤ 23) ⟨18,j,x⟩).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) ⟨18,j,x⟩).toFinset=keys (keyIndex 18 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 18, (fourTermLabels (by omega : 18 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 18 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x + · exact cover_12 j x + · exact cover_13 j x + · exact cover_14 j x + · exact cover_15 j x + · exact cover_16 j x + · exact cover_17 j x + · exact cover_18 j x +lemma representatives_checked : ∀ a : Fin 39, + (fourTermLabels (by omega : 18 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 18 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 18 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 18 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 39, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 18, + (fourTermLabels (by omega : 18 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 39, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 18 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 39, ∀ b : FourTerm 18, + (fourTermLabels (by omega : 18 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 18 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 39, (∑ b ∈ fibers v, fourTermEval 18 (2*(0 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 18 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 39, (∑ b ∈ fibers v, fourTermEval 18 (2*(1 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 18 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 39, (∑ b ∈ fibers v, fourTermEval 18 (2*(2 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 18 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 39, (∑ b ∈ fibers v, fourTermEval 18 (2*(3 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 18 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 39, (∑ b ∈ fibers v, fourTermEval 18 (2*(4 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 18 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 39, (∑ b ∈ fibers v, fourTermEval 18 (2*(5 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 18 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_6 : ∀ v : Fin 39, (∑ b ∈ fibers v, fourTermEval 18 (2*(6 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 18 ≤ 23) b)) = columns 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_7 : ∀ v : Fin 39, (∑ b ∈ fibers v, fourTermEval 18 (2*(7 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 18 ≤ 23) b)) = columns 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_8 : ∀ v : Fin 39, (∑ b ∈ fibers v, fourTermEval 18 (2*(8 : Fin 9).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 18 ≤ 23) b)) = columns 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 9, ∀ v : Fin 39, (∑ b ∈ fibers v, fourTermEval 18 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 18 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 + · exact columns_checked_6 + · exact columns_checked_7 + · exact columns_checked_8 +lemma gram_checked_0 : ∀ v : Fin 9, (∑ a : Fin 39, columns (0 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 9, (∑ a : Fin 39, columns (1 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 9, (∑ a : Fin 39, columns (2 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 9, (∑ a : Fin 39, columns (3 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 9, (∑ a : Fin 39, columns (4 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 9, (∑ a : Fin 39, columns (5 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_6 : ∀ v : Fin 9, (∑ a : Fin 39, columns (6 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_7 : ∀ v : Fin 9, (∑ a : Fin 39, columns (7 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_8 : ∀ v : Fin 9, (∑ a : Fin 39, columns (8 : Fin 9) a * columns v a / setFactorial (keys a)) = Z 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 9, ∀ v : Fin 9, (∑ a : Fin 39, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 + · exact gram_checked_6 + · exact gram_checked_7 + · exact gram_checked_8 +lemma rows_table_checked_0 : ∀ v : Fin 9, integerTableEval 18 SumTable18.sums (0 : Fin 9) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 9, integerTableEval 18 SumTable18.sums (1 : Fin 9) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 9, integerTableEval 18 SumTable18.sums (2 : Fin 9) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 9, integerTableEval 18 SumTable18.sums (3 : Fin 9) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 9, integerTableEval 18 SumTable18.sums (4 : Fin 9) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 9, integerTableEval 18 SumTable18.sums (5 : Fin 9) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_6 : ∀ v : Fin 9, integerTableEval 18 SumTable18.sums (6 : Fin 9) v = Y 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_7 : ∀ v : Fin 9, integerTableEval 18 SumTable18.sums (7 : Fin 9) v = Y 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_8 : ∀ v : Fin 9, integerTableEval 18 SumTable18.sums (8 : Fin 9) v = Y 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 9, ∀ v : Fin 9, integerTableEval 18 SumTable18.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 + · exact rows_table_checked_6 + · exact rows_table_checked_7 + · exact rows_table_checked_8 +lemma rows_checked (u v : Fin 9) : exactFourEval 18 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 18 SumTable18.sums SumTable18.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 9, (Z * tableComparison 18 (1/200000) Y) (0 : Fin 9) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 9, (Z * tableComparison 18 (1/200000) Y) (1 : Fin 9) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 9, (Z * tableComparison 18 (1/200000) Y) (2 : Fin 9) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 9, (Z * tableComparison 18 (1/200000) Y) (3 : Fin 9) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 9, (Z * tableComparison 18 (1/200000) Y) (4 : Fin 9) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 9, (Z * tableComparison 18 (1/200000) Y) (5 : Fin 9) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_6 : ∀ v : Fin 9, (Z * tableComparison 18 (1/200000) Y) (6 : Fin 9) v = W 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_7 : ∀ v : Fin 9, (Z * tableComparison 18 (1/200000) Y) (7 : Fin 9) v = W 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_8 : ∀ v : Fin 9, (Z * tableComparison 18 (1/200000) Y) (8 : Fin 9) v = W 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 9, ∀ v : Fin 9, (Z * tableComparison 18 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 + · exact product_checked_6 + · exact product_checked_7 + · exact product_checked_8 +lemma compression_checked_0 : ∀ v : Fin 9, (W * Z) (0 : Fin 9) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 9, (W * Z) (1 : Fin 9) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 9, (W * Z) (2 : Fin 9) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 9, (W * Z) (3 : Fin 9) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 9, (W * Z) (4 : Fin 9) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 9, (W * Z) (5 : Fin 9) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_6 : ∀ v : Fin 9, (W * Z) (6 : Fin 9) v = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_7 : ∀ v : Fin 9, (W * Z) (7 : Fin 9) v = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_8 : ∀ v : Fin 9, (W * Z) (8 : Fin 9) v = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 9, ∀ v : Fin 9, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 + · exact compression_checked_6 + · exact compression_checked_7 + · exact compression_checked_8 +lemma ldl_checked_0 : ∀ v : Fin 9, (∑ k : Fin 9, L (0 : Fin 9) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 9, (∑ k : Fin 9, L (1 : Fin 9) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 9, (∑ k : Fin 9, L (2 : Fin 9) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 9, (∑ k : Fin 9, L (3 : Fin 9) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 9, (∑ k : Fin 9, L (4 : Fin 9) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 9, (∑ k : Fin 9, L (5 : Fin 9) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_6 : ∀ v : Fin 9, (∑ k : Fin 9, L (6 : Fin 9) k * diag k * L v k) = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_7 : ∀ v : Fin 9, (∑ k : Fin 9, L (7 : Fin 9) k * diag k * L v k) = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_8 : ∀ v : Fin 9, (∑ k : Fin 9, L (8 : Fin 9) k * diag k * L v k) = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 9, ∀ v : Fin 9, (∑ k : Fin 9, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 + · exact ldl_checked_6 + · exact ldl_checked_7 + · exact ldl_checked_8 +lemma diag_checked : ∀ u : Fin 9, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 18 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 18 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 18 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 18 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 18 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate18 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate19.lean b/lean/OAI/Analysis/LaughlinGap/Certificate19.lean new file mode 100644 index 0000000000000000000000000000000000000000..2ab4d2a6b890e126e609a6293e3e1b932ee23e59 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate19.lean @@ -0,0 +1,423 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CachedIntegerRows +import OAI.Analysis.LaughlinGap.FastFourKeys +import OAI.Analysis.LaughlinGap.FourTables +import OAI.Analysis.LaughlinGap.SumTable19 + +namespace OAI + +/-! Certificate19. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate19 + +def keys : Fin 47 → Finset (Fin 25) := ![{0,1,2,17}, {0,1,3,16}, {0,1,4,15}, {0,1,5,14}, {0,1,6,13}, {0,1,7,12}, {0,1,8,11}, {0,1,9,10}, {0,2,3,15}, {0,2,4,14}, {0,2,5,13}, {0,2,6,12}, {0,2,7,11}, {0,2,8,10}, {0,3,4,13}, {0,3,5,12}, {0,3,6,11}, {0,3,7,10}, {0,3,8,9}, {0,4,5,11}, {0,4,6,10}, {0,4,7,9}, {0,5,6,9}, {0,5,7,8}, {1,2,3,14}, {1,2,4,13}, {1,2,5,12}, {1,2,6,11}, {1,2,7,10}, {1,2,8,9}, {1,3,4,12}, {1,3,5,11}, {1,3,6,10}, {1,3,7,9}, {1,4,5,10}, {1,4,6,9}, {1,4,7,8}, {1,5,6,8}, {2,3,4,11}, {2,3,5,10}, {2,3,6,9}, {2,3,7,8}, {2,4,5,9}, {2,4,6,8}, {2,5,6,7}, {3,4,5,8}, {3,4,6,7}] +def fibers : Fin 47 → Finset (FourTerm 19) := ![{⟨⟨19,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by 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decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨6,by decide⟩)⟩}] +def columns : Matrix (Fin 10) (Fin 47) ℚ := ![![3126159036000, -3126159036000, 5470778313000, -5470778313000, 7033857831000, -7033857831000, 7815397590000, -7815397590000, -2344619277000, 0, -1563079518000, 0, -781539759000, 0, 3907698795000, -2344619277000, 4689238554000, -3907698795000, 4689238554000, -2344619277000, 0, -781539759000, 2344619277000, -1563079518000, 2344619277000, -2344619277000, 3907698795000, -3907698795000, 4689238554000, -4689238554000, -1563079518000, 0, -781539759000, 0, 2344619277000, -1563079518000, 2344619277000, -781539759000, 1563079518000, -1563079518000, 2344619277000, -2344619277000, -781539759000, 0, 781539759000, 781539759000, -781539759000], ![2084106024000, -2084106024000, 2789024238000, -2789024238000, 2850321474000, -2850321474000, 2758375620000, -2758375620000, -704918214000, 0, -61297236000, 0, 91945854000, 0, 766215450000, -704918214000, 674269596000, -766215450000, 674269596000, 30648618000, 0, 91945854000, -30648618000, -61297236000, 704918214000, -704918214000, 766215450000, -766215450000, 674269596000, -674269596000, -61297236000, 0, 91945854000, 0, -30648618000, -61297236000, -30648618000, 91945854000, 61297236000, -61297236000, -30648618000, 30648618000, 91945854000, 0, -91945854000, -91945854000, 91945854000], ![2540004216750, -2540004216750, (4921018727625/2), (-4205884307625/2), (3108919188375/2), (-2189460648375/2), 761745859875, -557421739875, (158989705875/2), -357567210000, 548482559625, -459729270000, (665968928625/2), -204324120000, (174314014875/2), (-453982654125/2), 162820783125, (-174314014875/2), 101523547125, (332665207875/2), -153243090000, (93861392625/2), (178145092125/2), -64489800375, (556144714125/2), (-556144714125/2), (276476074875/2), (-72151954875/2), -41503336875, 102800572875, 139834319625, -102162060000, (155158628625/2), -61297236000, (-26179027875/2), 17239847625, (35118208125/2), (-49165491375/2), -37672259625, 37672259625, (-67043851875/2), (87476263875/2), (-8300667375/2), -10216206000, (49165491375/2), (28733079375/2), (-28733079375/2)], ![2540004216750, -2540004216750, (3603128153625/2), (-2315886197625/2), (1300650726375/2), (-550938378375/2), 71759023875, -5746615875, (1476880279875/2), -643620978000, 507617735625, -374856174000, (407420330625/2), -66012408000, (82368160875/2), (-79126480125/2), 82662859125, (-157810912875/2), 40226311125, (-95629582125/2), 25933446000, (11345882625/2), (-41110405875/2), 7809503625, (-189638323875/2), (189638323875/2), (-186396643125/2), (176966299125/2), -58792300875, 25786096875, -1620840375, 4715172000, (-59381697375/2), 33006204000, (43762690125/2), -11051184375, (-26964889875/2), (25491398625/2), -3094331625, 3094331625, (15471658125/2), (-39047518125/2), (-21660321375/2), 11787930000, (-25491398625/2), (-1915538625/2), (1915538625/2)], ![1563079518000, -1563079518000, 816019454250, -218371403250, -11493231750, 36247884750, -28291032000, 34720812000, 747060063750, -597648051000, 229864635000, -24754653000, -7956852750, -6429780000, 218371403250, -137034686250, 28291032000, 2813028750, 10930626000, 45088832250, -15109983000, -6670896750, 4098984750, 4822335000, -149412012750, 149412012750, -68075295750, 4420473750, 11573604000, -4500846000, -81336717000, 63654822000, -15994077750, -7072758000, -29978849250, 17681895000, 1848561750, -8921319750, 17681895000, -17681895000, 5384940750, 5224196250, 12296954250, -10609137000, 8921319750, -1687817250, 1687817250], ![-781539759000, 781539759000, -467391424500, 242634892500, -153243090000, 101376198000, -33595600500, -22986463500, -314148334500, 224756532000, -89391802500, 51866892000, -67780597500, 56582064000, -45972927000, -2946982500, 21807670500, 8251551000, -44204737500, 15717240000, -33006204000, 26522842500, 14145516000, -20235946500, 89391802500, -89391802500, 40471893000, -5893965000, 2946982500, -12377326500, 48919909500, -34577928000, 2946982500, 9430344000, 17288964000, -7662154500, -6286896000, 6090430500, -14341981500, 14341981500, -4715172000, -3143448000, -9626809500, 7858620000, -6090430500, 1768189500, -1768189500], ![-3126159036000, 3126159036000, -1769957689500, 574661587500, 27364837500, -145580935500, 30648618000, 91945854000, -1356201346500, 1195296102000, -602026425000, 118216098000, 114932317500, -122594472000, -432364432500, 377634757500, -183891708000, 7662154500, 91945854000, -136824187500, 126972846000, -68959390500, -42689146500, 45972927000, 160905244500, -160905244500, 106175569500, -49256707500, 0, 30648618000, 54729675000, -56918862000, 49256707500, -30648618000, 9851341500, -15324309000, 22986463500, -3283780500, 2189187000, -2189187000, -3283780500, 7662154500, 5472967500, -4378374000, 3283780500, -1094593500, 1094593500], ![3126159036000, -3126159036000, 965431467000, 750891141000, -1164647484000, 674269596000, 61297236000, -551675124000, 2160727569000, -1716322608000, 413756343000, 490377888000, -735566832000, 490377888000, 858161304000, -658945287000, 183891708000, 183891708000, -367783416000, 291161871000, -245188944000, 122594472000, 76621545000, -76621545000, -444404961000, 444404961000, -245188944000, 61297236000, 61297236000, -122594472000, -199216017000, 183891708000, -122594472000, 61297236000, -45972927000, 45972927000, -45972927000, 0, 15324309000, -15324309000, 15324309000, -15324309000, 0, 0, 0, 0, 0], ![50018544576000, -50018544576000, 35429802408000, -21535762248000, 10420530120000, -2084106024000, -3473510040000, 6252318072000, 14588742168000, -13894040160000, 11115232128000, -8336424096000, 5557616064000, -2778808032000, 2084106024000, -2084106024000, 2084106024000, -2084106024000, 2084106024000, 0, 0, 0, 0, 0, -694702008000, 694702008000, -694702008000, 694702008000, -694702008000, 694702008000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![237588086736000, -237588086736000, 237588086736000, -237588086736000, 237588086736000, -237588086736000, 237588086736000, -237588086736000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Y : Matrix (Fin 10) (Fin 10) ℚ := ![![(7134258282424991785116902853/262144000000000000), (-952292014865249127204065931/262144000000000000), (13099081619669139353195937/26214400000000000), (12445185998604296615556879/52428800000000000), (-3863236878262606027976793/6553600000000000), (31293997972671021148982421/32768000000000000), (-5832994723812297550307799/4096000000000000), (1011728883016569015130833/655360000000000), 0, 0], ![(-952292014865249127204065931/262144000000000000), (-4231783306973256793285527/6553600000000000), (4260281397273942382805463/10485760000000000), (-405635818636975780286433/13107200000000000), (-2677063064824149766675911/6553600000000000), (2233782741787599437397963/2048000000000000), (-6512414109643931745959703/3276800000000000), (554725239796014113785959/819200000000000), 0, 0], ![(13099081619669139353195937/26214400000000000), (4260281397273942382805463/10485760000000000), (-2120982099963565366024497/10485760000000000), (291693987723563592508341/10485760000000000), (51643945900630514209779/327680000000000), (-2922191244412318089488277/6553600000000000), (569061858954403871303247/655360000000000), (-399218783730676496059473/655360000000000), 0, 0], ![(12445185998604296615556879/52428800000000000), (-405635818636975780286433/13107200000000000), (291693987723563592508341/10485760000000000), (-25908133030678389751029/655360000000000), (14953374016904686340439/262144000000000), (-119672423160377156262963/1638400000000000), (54560080949987851200963/3276800000000000), (7971588122134182999453/16384000000000), 0, 0], ![(-3863236878262606027976793/6553600000000000), (-2677063064824149766675911/6553600000000000), (51643945900630514209779/327680000000000), (14953374016904686340439/262144000000000), (-47346247587015754423767/163840000000000), (510532174408649808251529/819200000000000), (-193544804639186339842503/204800000000000), (-30335953777217483041647/81920000000000), 0, 0], ![(31293997972671021148982421/32768000000000000), (2233782741787599437397963/2048000000000000), (-2922191244412318089488277/6553600000000000), (-119672423160377156262963/1638400000000000), (510532174408649808251529/819200000000000), (-732673210646503091776041/512000000000000), (4777244880619944661181253/2048000000000000), (1717714702679304982653/20480000000000), 0, 0], ![(-5832994723812297550307799/4096000000000000), (-6512414109643931745959703/3276800000000000), (569061858954403871303247/655360000000000), (54560080949987851200963/3276800000000000), (-193544804639186339842503/204800000000000), (4777244880619944661181253/2048000000000000), (-166547698406078604083469/40960000000000), (212644772360684817113961/204800000000000), 0, 0], ![(1011728883016569015130833/655360000000000), (554725239796014113785959/819200000000000), (-399218783730676496059473/655360000000000), (7971588122134182999453/16384000000000), (-30335953777217483041647/81920000000000), (1717714702679304982653/20480000000000), (212644772360684817113961/204800000000000), (-127943886395992389723/25600000000), 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Z : Matrix (Fin 10) (Fin 10) ℚ := ![![12804747411456000, 0, 0, 0, 0, 0, 0, 0, -50018544576000, 3801409387776000], ![0, 125536739328000, 0, 0, 0, 0, 0, -1961511552000, 0, 1425528520416000], ![0, 0, 10461394944000, 0, 0, 0, -245188944000, -3677834160000, 34735100400000, 475176173472000], ![0, 0, 0, 2414168064000, 0, -75442752000, -1225944720000, 0, 29177484336000, 118794043368000], ![0, 0, 0, 0, 1265380704000, -678984768000, -1103350248000, 2574483912000, 9378477108000, 0], ![0, 0, 0, -75442752000, -678984768000, 572107536000, 0, 0, -7641722088000, -29698510842000], ![0, 0, -245188944000, -1225944720000, -1103350248000, 0, 3544293753000, -6574128561000, -16933361445000, -29698510842000], ![0, -1961511552000, -3677834160000, 0, 2574483912000, 0, -6574128561000, 17439063642000, -19538493975000, -22273883131500], ![-50018544576000, 0, 34735100400000, 29177484336000, 9378477108000, -7641722088000, -16933361445000, -19538493975000, 693290894546250, -14849255421000], ![3801409387776000, 1425528520416000, 475176173472000, 118794043368000, 0, -29698510842000, -29698510842000, -22273883131500, -14849255421000, 121635819624193875]] +def W : Matrix (Fin 10) (Fin 10) ℚ := ![![(30064782334673161107452531/7516192768000000000000000), (434998022035234599513/7516192768000000000000000), (-17950611281268990753/187904819200000000000000), (-10557566933807968503/53687091200000000000000), (84116900260470007359/93952409600000000000000), (-557497336195660683537/469762048000000000000000), (2664457044470069277/4194304000000000000000), (-462148223526162459/4697620480000000000000), (-9/25600000), (1/6400000)], ![(2188979056977395397/3758096384000000000000000), (7877567152711182599/751619276800000000000000), (-798155921753935173/18790481920000000000000), (4775653209007683717/187904819200000000000000), (13746724671424556097/46976204800000000000000), (-22630406100774474717/33554432000000000000000), (23999558975848599/52428800000000000000), (-373950404376140957/11744051200000000000000), 0, (3/51200000)], ![(-7450630998497204661/120259084288000000000000000), (-83462326548944594823/24051816857600000000000000), (378826251591815987/17179869184000000000000), (74994064240939199499/6012954214400000000000000), (-288454615854307972641/1503238553600000000000000), (2723975842995230856747/7516192768000000000000000), (-290451542310531281/1342177280000000000000), (740885684600377581/375809638400000000000000), (1/4096000), (1/51200000)], ![(-10932025982211307061/120259084288000000000000000), (-441967345229058622083/120259084288000000000000000), (54233483988467759613/3006477107200000000000000), (131340544057345627691/6012954214400000000000000), (-326762353406450054049/1503238553600000000000000), (3004794276948335095947/7516192768000000000000000), (-7673130472245955841/33554432000000000000000), (-475876302995583831/75161927680000000000000), (21/102400000), (1/204800000)], ![(4623200384325994647/60129542144000000000000000), (10538705436238377801/4294967296000000000000000), (-21812884047179840133/3006477107200000000000000), (-75619698987032071317/1503238553600000000000000), (196772777258970145641/751619276800000000000000), (-745801946910473595147/1879048192000000000000000), (23975204486319800739/134217728000000000000000), (3201977636889835953/93952409600000000000000), (27/409600000), 0], ![(-1493320123278171969/15032385536000000000000000), (-143528225638085712369/30064771072000000000000000), (34577724261147230823/1503238553600000000000000), (33477554042311438393/1503238553600000000000000), (-1896572570821952727/6710886400000000000000), (969731903643466478201/1879048192000000000000000), (-19697255929238542479/67108864000000000000000), (-123068818626578253/18790481920000000000000), (-11/204800000), (-1/819200000)], ![(5106655275763800473/30064771072000000000000000), (16339230887814068949/1503238553600000000000000), (-19364685764001413193/300647710720000000000000), (8639458520447239511/187904819200000000000000), (18531064515143638029/53687091200000000000000), (-394563295233273794199/469762048000000000000000), (8042516161949140907/13421772800000000000000), (-185049506181420309/2936012800000000000000), (-39/327680000), (-1/819200000)], ![(-393174483374313927/1503238553600000000000000), (-56732573666145700517/3006477107200000000000000), (17536838382422228187/150323855360000000000000), (-4335907284118188207/30064771072000000000000), (-563733066068164421/1342177280000000000000), (235327018956391403613/187904819200000000000000), (-6661016244104449227/6710886400000000000000), (293805165061292119/1879048192000000000000), (-9/65536000), (-3/3276800000)], ![(-400001/25600000), 0, (17/1024000), (1547/25600000), (7293/204800000), (-2431/102400000), (-1547/81920000), (-51/16384000), (6387/1310720000), (-1/1638400000)], ![(7600019/6400000), (2907/51200000), (2907/12800000), (12597/51200000), 0, (-37791/409600000), (-6783/204800000), (-2907/819200000), (-171/1638400000), (65531/13107200000)]] +def M : Matrix (Fin 10) (Fin 10) ℚ := ![![(3356689002968562208669654883097147/65536000000000000), (251695015259695758145584189/32768000000000000), (-766803933858865618990230957/1048576000000000000), (-1211837479120090378218419757/1048576000000000000), (514444918267288473407381439/524288000000000000), (-166983101984896664373259353/131072000000000000), (570494718089042760370358001/262144000000000000), (-43852939386889485328274799/13107200000000000), (-819506890935181449/4096), (778531562291974932441/51200)], ![(251695015259695758145584189/32768000000000000), (4789730217481703648397243/3276800000000000), (-43164661985167436375548887/104857600000000000), (-231726799786939372049032899/524288000000000000), (63224869740023476289531727/262144000000000000), (-77096736876740903063799057/131072000000000000), (38964878723257986016244727/26214400000000000), (-35086624828143587107660251/13107200000000000), (268068137337/51200), (5841593137833453/409600)], ![(-766803933858865618990230957/1048576000000000000), (-43164661985167436375548887/104857600000000000), (197467850512766501938841571/671088640000000000), (4655848800844080473421774987/16777216000000000000), (-2036355255829439196825454281/8388608000000000000), (350479070867737958984666829/1048576000000000000), (-497987619565316704100580303/838860800000000000), (92644981306699568760560547/104857600000000000), (146933556066297/409600), (1953434399887971/409600)], ![(-1211837479120090378218419757/1048576000000000000), (-231726799786939372049032899/524288000000000000), (4655848800844080473421774987/16777216000000000000), (5192238021603734824792644267/16777216000000000000), (-2588441158756143353032921089/8388608000000000000), (195531804308825200423031517/524288000000000000), (-2364987062223555704255812491/4194304000000000000), (40373723883761502249456441/52428800000000000), (128178512280819/409600), (2019186902892159/1638400)], ![(514444918267288473407381439/524288000000000000), (63224869740023476289531727/262144000000000000), (-2036355255829439196825454281/8388608000000000000), (-2588441158756143353032921089/8388608000000000000), (2063743584722300230167937491/4194304000000000000), (-1684170847462301003481126759/4194304000000000000), (191407410811514887337407059/1048576000000000000), (48060655602365319946935903/419430400000000000), (196120368663219/1638400), (36484620569397/409600)], ![(-166983101984896664373259353/131072000000000000), (-77096736876740903063799057/131072000000000000), (350479070867737958984666829/1048576000000000000), (195531804308825200423031517/524288000000000000), (-1684170847462301003481126759/4194304000000000000), (2038039141169449150562726127/4194304000000000000), (-752261230191991506868444563/1048576000000000000), (425148172202540098459928781/419430400000000000), (-32579179555923/409600), (-1435432973781807/6553600)], ![(570494718089042760370358001/262144000000000000), (38964878723257986016244727/26214400000000000), (-497987619565316704100580303/838860800000000000), (-2364987062223555704255812491/4194304000000000000), (191407410811514887337407059/1048576000000000000), (-752261230191991506868444563/1048576000000000000), (55542507775704709295567031/26214400000000000), (-412289663780452218518656899/104857600000000000), (-64594521594603/262144), (-3919594611671739/6553600)], ![(-43852939386889485328274799/13107200000000000), (-35086624828143587107660251/13107200000000000), (92644981306699568760560547/104857600000000000), (40373723883761502249456441/52428800000000000), (48060655602365319946935903/419430400000000000), (425148172202540098459928781/419430400000000000), (-412289663780452218518656899/104857600000000000), (326373963677452580650367607/41943040000000000), (34658943692373/6553600), (-943833523814181/1048576)], ![(-819506890935181449/4096), (268068137337/51200), (146933556066297/409600), (128178512280819/409600), (196120368663219/1638400), (-32579179555923/409600), (-64594521594603/262144), (34658943692373/6553600), (20661033476386646343/26214400), (-155663503730012254977/2621440)], ![(778531562291974932441/51200), (5841593137833453/409600), (1953434399887971/409600), (2019186902892159/1638400), (36484620569397/409600), (-1435432973781807/6553600), (-3919594611671739/6553600), (-943833523814181/1048576), (-155663503730012254977/2621440), (473433631893892579650741/104857600)]] +def L : Matrix (Fin 10) (Fin 10) ℚ := ![![1, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![(500966937106087866/3340531410405177900828059), 1, 0, 0, 0, 0, 0, 0, 0, 0], ![(-6868015958497204661/481036523098345617719240496), (-41166215690640044636802164030562923173237179/146175101805157503866517473411574637875103216), 1, 0, 0, 0, 0, 0, 0, 0], ![(-3618012714070435687/160345507699448539239746832), (-44199647504740787665783830057126936168404685/146175101805157503866517473411574637875103216), (2296052701740691535743831482300296414216880188353506916516209/2675369428096150741745913630097016703018032987984424545369485), 1, 0, 0, 0, 0, 0, 0], ![(511968611591777183/26724251283241423206624472), (48238120915521782654097727331961410456820819/292350203610315007733034946823149275750206432), (-5246007042086202504429981358552242802856910525173487379928421/5350738856192301483491827260194033406036065975968849090738970), (-397860564178602264609243020569979763170317868443186954354230050956760269923/206827082115462272759339304108326483933009847491716671616676255924019820442), 1, 0, 0, 0, 0, 0], ![(-115047221790628613/4625351183637938631915774), (-117643667500073328261867948420567589930998795/292350203610315007733034946823149275750206432), (2529419642596344084009091356613433124078384222133024197042934/2675369428096150741745913630097016703018032987984424545369485), (117135123812643487789295834132099754913716637724684965942347977724842410221/103413541057731136379669652054163241966504923745858335808338127962009910221), (-278254791127514844159834426074973766218588388160240845678065678629359601076623843365/765340991235405030596100693322995780378338673121991677062411240182744031442978916952), 1, 0, 0, 0, 0], ![(567748612862644497/13362125641620711603312236), (74321753176962813113289681353871882877753359/73087550902578751933258736705787318937551608), (-18383731484354004059239586067969769765035142093073570632866201/18727585996673055192221395410679116921126230915890971817586395), (9323246947033175806534475317711509758683126163335689701839017555605515947053/11582316598465887274523001030066283100248551459536133610533870331745109944752), (-10171953294371337412169029844459026854499913925835132020595854694472919815691388131901/7143182584863780285563606471014627283531160949138588985915838241705610960134469891552), (-811626993359040652797648919154619402513423782586445890237600258597900577888878581668824318747/258685057980712740411670673508923565387277139080128996122148884168300114345496636119911726372), 1, 0, 0, 0], ![(-654627765623856545/10021594231215533702484177), (-267697438260512011923309464359556971091983125/146175101805157503866517473411574637875103216), (1945264693797759854455430404377077558972188337918647854736032/2675369428096150741745913630097016703018032987984424545369485), (-2800613993813540443361256897868224046734339063424256494177898725398468351903/827308328461849091037357216433305935732039389966866686466705023696079281768), (2593187592931401049211629091796144868893944602969289043262159795065579047583540863669/765340991235405030596100693322995780378338673121991677062411240182744031442978916952), (67856177816022055311454315847249749594165391390189925520941540724764513693726875574483888261/9238752070739740728988238339604413049545612110004607004362460148867861226624879861425418799), -9, 1, 0, 0], ![(-13048994448000000000000/3340531410405177900828059), (220257593216739938846323925790720000000000/9135943862822343991657342088223414867193951), (1097610626631294140457340505312177222130890206289155072000000/535073885619230148349182726019403340603606597596884909073897), (11962300707526752595587698511201985171349121814238052628188014952892500000/103413541057731136379669652054163241966504923745858335808338127962009910221), (12813414473528293635192898875891504664859736248817498779940126550457314182788081980535/3061363964941620122384402773291983121513354692487966708249644960730976125771915667808), (-521691398749572721770762370065748589607778953985045705049243401146862075123361294549929335281/36955008282958962915952953358417652198182448440018428017449840595471444906499519445701675196), 85, 0, 1, 0], ![(991723598306560000000000/3340531410405177900828059), (74885684896381023965490712609789170000000000/9135943862822343991657342088223414867193951), (25086685338642469563880000984369673295400720862927053056000000/535073885619230148349182726019403340603606597596884909073897), (-4594009905222382226855924916949561601807409002146604094875738677485974062500/103413541057731136379669652054163241966504923745858335808338127962009910221), (38914473591256902870496888104212097964502537394944280745349633345985017405769857553795/2040909309961080081589601848861322081008903128325311138833096640487317417181277111872), (513015815958813320133796402198777449089505151772477263454716993239221051266552708601577566613/73910016565917925831905906716835304396364896880036856034899681190942889812999038891403350392), -1938, 0, 0, 1]] +def diag : Fin 10 → ℚ := ![(3356689002968562208669654883097147/65536000000000000), (139862164595947264168282250028612258201872195859/95684032566570690082459648000000000000), (2733212520353246378472905330327892262347304672004440594695100487391/15327570355044483477433742620001528748452422982041600000000), (17414736900580865635199989736269035783917462653878797891788332410674506871306179/391368327767208337078259365317049300555780825670864390636907520000000000), (30756088741409890985163726974464573804756465210414497783389690899388774490571481128997691/264738665107791709131954309258657899434252604789397339669345607582745370165760000), (3630192089907837064382077479019101623971006911996220234831145828754797579638940668829751234109869/208989113340014600354775229323399381095311680340511860616509095985901303519362776255692800), (189539417072846287320117229635753144851652620702544075922863209367725984214473406214807124995965945777/3784192848174997802593582423901967585093882720257887028986863676976275958425550791239851540070400), 0, 0, 0] + +def keyIndexTable : Fin 20 → Fin 13 → Fin 13 → Fin 47 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 8, 9, 10, 11, 12, 13, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 8, 0, 14, 15, 16, 17, 18, 0, 0, 0, 0], ![0, 0, 0, 24, 25, 26, 27, 28, 29, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 9, 14, 0, 19, 20, 21, 0, 0, 0, 0, 0], ![1, 0, 24, 0, 30, 31, 32, 33, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 10, 15, 19, 0, 22, 23, 0, 0, 0, 0, 0], ![2, 0, 25, 30, 0, 34, 35, 36, 0, 0, 0, 0, 0], ![8, 24, 0, 0, 38, 39, 40, 41, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 11, 16, 20, 22, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 26, 31, 34, 0, 37, 0, 0, 0, 0, 0, 0], ![9, 25, 0, 38, 0, 42, 43, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 12, 17, 21, 23, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 27, 32, 35, 37, 0, 0, 0, 0, 0, 0, 0], ![10, 26, 0, 39, 42, 0, 44, 0, 0, 0, 0, 0, 0], ![14, 30, 38, 0, 0, 45, 46, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 13, 18, 0, 23, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 28, 33, 36, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 27, 0, 40, 43, 44, 0, 0, 0, 0, 0, 0, 0], ![15, 31, 39, 0, 45, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 7, 0, 18, 21, 22, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 29, 0, 36, 37, 0, 0, 0, 0, 0, 0, 0], ![12, 28, 0, 41, 0, 44, 0, 0, 0, 0, 0, 0, 0], ![16, 32, 40, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 34, 42, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 7, 13, 17, 20, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 29, 33, 35, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 29, 0, 41, 43, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 33, 41, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 35, 43, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 12, 16, 19, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 28, 32, 34, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 29, 0, 40, 42, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 0, 41, 0, 45, 0, 0, 0, 0, 0, 0, 0, 0], ![21, 36, 0, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![22, 37, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 11, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 27, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 28, 0, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 33, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 36, 43, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 10, 14, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 26, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 27, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 32, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![21, 35, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 37, 0, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 44, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 31, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![22, 0, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 37, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 34, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![22, 35, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 36, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![21, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 24, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 25, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 26, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 29, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 20) (j : Fin ((n.val+1)/2)) (x : Fin ((19-n.val+2)/2)) : Fin 47 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 47 → FourTerm 19 := ![⟨⟨19,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 10, + (fourTermLabels (by omega : 19 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 10, + (fourTermLabels (by omega : 19 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 9, + (fourTermLabels (by omega : 19 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 9, + (fourTermLabels (by omega : 19 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 8, + (fourTermLabels (by omega : 19 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 8, + (fourTermLabels (by omega : 19 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 7, + (fourTermLabels (by omega : 19 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 7, + (fourTermLabels (by omega : 19 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 6, + (fourTermLabels (by omega : 19 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 6, + (fourTermLabels (by omega : 19 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 5, + (fourTermLabels (by omega : 19 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 5, + (fourTermLabels (by omega : 19 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover_12 : ∀ j : Fin 6, ∀ x : Fin 4, + (fourTermLabels (by omega : 19 ≤ 23) ⟨12,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨12,j,x⟩).toFinset=keys (keyIndex 12 j x) := by decide +kernel +lemma cover_13 : ∀ j : Fin 7, ∀ x : Fin 4, + (fourTermLabels (by omega : 19 ≤ 23) ⟨13,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨13,j,x⟩).toFinset=keys (keyIndex 13 j x) := by decide +kernel +lemma cover_14 : ∀ j : Fin 7, ∀ x : Fin 3, + (fourTermLabels (by omega : 19 ≤ 23) ⟨14,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨14,j,x⟩).toFinset=keys (keyIndex 14 j x) := by decide +kernel +lemma cover_15 : ∀ j : Fin 8, ∀ x : Fin 3, + (fourTermLabels (by omega : 19 ≤ 23) ⟨15,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨15,j,x⟩).toFinset=keys (keyIndex 15 j x) := by decide +kernel +lemma cover_16 : ∀ j : Fin 8, ∀ x : Fin 2, + (fourTermLabels (by omega : 19 ≤ 23) ⟨16,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨16,j,x⟩).toFinset=keys (keyIndex 16 j x) := by decide +kernel +lemma cover_17 : ∀ j : Fin 9, ∀ x : Fin 2, + (fourTermLabels (by omega : 19 ≤ 23) ⟨17,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨17,j,x⟩).toFinset=keys (keyIndex 17 j x) := by decide +kernel +lemma cover_18 : ∀ j : Fin 9, ∀ x : Fin 1, + (fourTermLabels (by omega : 19 ≤ 23) ⟨18,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨18,j,x⟩).toFinset=keys (keyIndex 18 j x) := by decide +kernel +lemma cover_19 : ∀ j : Fin 10, ∀ x : Fin 1, + (fourTermLabels (by omega : 19 ≤ 23) ⟨19,j,x⟩).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) ⟨19,j,x⟩).toFinset=keys (keyIndex 19 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 19, (fourTermLabels (by omega : 19 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 19 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x + · exact cover_12 j x + · exact cover_13 j x + · exact cover_14 j x + · exact cover_15 j x + · exact cover_16 j x + · exact cover_17 j x + · exact cover_18 j x + · exact cover_19 j x +lemma representatives_checked : ∀ a : Fin 47, + (fourTermLabels (by omega : 19 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 19 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 19 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 19 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 47, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 19, + (fourTermLabels (by omega : 19 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 47, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 19 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 47, ∀ b : FourTerm 19, + (fourTermLabels (by omega : 19 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 19 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 47, (∑ b ∈ fibers v, fourTermEval 19 (2*(0 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 19 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 47, (∑ b ∈ fibers v, fourTermEval 19 (2*(1 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 19 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 47, (∑ b ∈ fibers v, fourTermEval 19 (2*(2 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 19 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 47, (∑ b ∈ fibers v, fourTermEval 19 (2*(3 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 19 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 47, (∑ b ∈ fibers v, fourTermEval 19 (2*(4 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 19 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 47, (∑ b ∈ fibers v, fourTermEval 19 (2*(5 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 19 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_6 : ∀ v : Fin 47, (∑ b ∈ fibers v, fourTermEval 19 (2*(6 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 19 ≤ 23) b)) = columns 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_7 : ∀ v : Fin 47, (∑ b ∈ fibers v, fourTermEval 19 (2*(7 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 19 ≤ 23) b)) = columns 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_8 : ∀ v : Fin 47, (∑ b ∈ fibers v, fourTermEval 19 (2*(8 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 19 ≤ 23) b)) = columns 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_9 : ∀ v : Fin 47, (∑ b ∈ fibers v, fourTermEval 19 (2*(9 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 19 ≤ 23) b)) = columns 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 10, ∀ v : Fin 47, (∑ b ∈ fibers v, fourTermEval 19 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 19 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 + · exact columns_checked_6 + · exact columns_checked_7 + · exact columns_checked_8 + · exact columns_checked_9 +lemma gram_checked_0 : ∀ v : Fin 10, (∑ a : Fin 47, columns (0 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 10, (∑ a : Fin 47, columns (1 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 10, (∑ a : Fin 47, columns (2 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 10, (∑ a : Fin 47, columns (3 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 10, (∑ a : Fin 47, columns (4 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 10, (∑ a : Fin 47, columns (5 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_6 : ∀ v : Fin 10, (∑ a : Fin 47, columns (6 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_7 : ∀ v : Fin 10, (∑ a : Fin 47, columns (7 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_8 : ∀ v : Fin 10, (∑ a : Fin 47, columns (8 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_9 : ∀ v : Fin 10, (∑ a : Fin 47, columns (9 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 10, ∀ v : Fin 10, (∑ a : Fin 47, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 + · exact gram_checked_6 + · exact gram_checked_7 + · exact gram_checked_8 + · exact gram_checked_9 +lemma rows_table_checked_0 : ∀ v : Fin 10, integerTableEval 19 SumTable19.sums (0 : Fin 10) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 10, integerTableEval 19 SumTable19.sums (1 : Fin 10) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 10, integerTableEval 19 SumTable19.sums (2 : Fin 10) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 10, integerTableEval 19 SumTable19.sums (3 : Fin 10) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 10, integerTableEval 19 SumTable19.sums (4 : Fin 10) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 10, integerTableEval 19 SumTable19.sums (5 : Fin 10) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_6 : ∀ v : Fin 10, integerTableEval 19 SumTable19.sums (6 : Fin 10) v = Y 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_7 : ∀ v : Fin 10, integerTableEval 19 SumTable19.sums (7 : Fin 10) v = Y 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_8 : ∀ v : Fin 10, integerTableEval 19 SumTable19.sums (8 : Fin 10) v = Y 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_9 : ∀ v : Fin 10, integerTableEval 19 SumTable19.sums (9 : Fin 10) v = Y 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 10, ∀ v : Fin 10, integerTableEval 19 SumTable19.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 + · exact rows_table_checked_6 + · exact rows_table_checked_7 + · exact rows_table_checked_8 + · exact rows_table_checked_9 +lemma rows_checked (u v : Fin 10) : exactFourEval 19 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 19 SumTable19.sums SumTable19.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 10, (Z * tableComparison 19 (1/200000) Y) (0 : Fin 10) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 10, (Z * tableComparison 19 (1/200000) Y) (1 : Fin 10) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 10, (Z * tableComparison 19 (1/200000) Y) (2 : Fin 10) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 10, (Z * tableComparison 19 (1/200000) Y) (3 : Fin 10) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 10, (Z * tableComparison 19 (1/200000) Y) (4 : Fin 10) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 10, (Z * tableComparison 19 (1/200000) Y) (5 : Fin 10) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_6 : ∀ v : Fin 10, (Z * tableComparison 19 (1/200000) Y) (6 : Fin 10) v = W 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_7 : ∀ v : Fin 10, (Z * tableComparison 19 (1/200000) Y) (7 : Fin 10) v = W 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_8 : ∀ v : Fin 10, (Z * tableComparison 19 (1/200000) Y) (8 : Fin 10) v = W 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_9 : ∀ v : Fin 10, (Z * tableComparison 19 (1/200000) Y) (9 : Fin 10) v = W 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 10, ∀ v : Fin 10, (Z * tableComparison 19 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 + · exact product_checked_6 + · exact product_checked_7 + · exact product_checked_8 + · exact product_checked_9 +lemma compression_checked_0 : ∀ v : Fin 10, (W * Z) (0 : Fin 10) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 10, (W * Z) (1 : Fin 10) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 10, (W * Z) (2 : Fin 10) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 10, (W * Z) (3 : Fin 10) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 10, (W * Z) (4 : Fin 10) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 10, (W * Z) (5 : Fin 10) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_6 : ∀ v : Fin 10, (W * Z) (6 : Fin 10) v = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_7 : ∀ v : Fin 10, (W * Z) (7 : Fin 10) v = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_8 : ∀ v : Fin 10, (W * Z) (8 : Fin 10) v = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_9 : ∀ v : Fin 10, (W * Z) (9 : Fin 10) v = M 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 10, ∀ v : Fin 10, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 + · exact compression_checked_6 + · exact compression_checked_7 + · exact compression_checked_8 + · exact compression_checked_9 +lemma ldl_checked_0 : ∀ v : Fin 10, (∑ k : Fin 10, L (0 : Fin 10) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 10, (∑ k : Fin 10, L (1 : Fin 10) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 10, (∑ k : Fin 10, L (2 : Fin 10) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 10, (∑ k : Fin 10, L (3 : Fin 10) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 10, (∑ k : Fin 10, L (4 : Fin 10) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 10, (∑ k : Fin 10, L (5 : Fin 10) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_6 : ∀ v : Fin 10, (∑ k : Fin 10, L (6 : Fin 10) k * diag k * L v k) = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_7 : ∀ v : Fin 10, (∑ k : Fin 10, L (7 : Fin 10) k * diag k * L v k) = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_8 : ∀ v : Fin 10, (∑ k : Fin 10, L (8 : Fin 10) k * diag k * L v k) = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_9 : ∀ v : Fin 10, (∑ k : Fin 10, L (9 : Fin 10) k * diag k * L v k) = M 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 10, ∀ v : Fin 10, (∑ k : Fin 10, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 + · exact ldl_checked_6 + · exact ldl_checked_7 + · exact ldl_checked_8 + · exact ldl_checked_9 +lemma diag_checked : ∀ u : Fin 10, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 19 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 19 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 19 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 19 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 19 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate19 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate20.lean b/lean/OAI/Analysis/LaughlinGap/Certificate20.lean new file mode 100644 index 0000000000000000000000000000000000000000..00a9150d98b809e177d4768b28105bfdcdf10746 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate20.lean @@ -0,0 +1,425 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Certificate19 +import OAI.Analysis.LaughlinGap.SumTable20 + +namespace OAI + +/-! Certificate20. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate20 + +def keys : Fin 54 → Finset (Fin 25) := ![{0,1,2,18}, {0,1,3,17}, {0,1,4,16}, {0,1,5,15}, {0,1,6,14}, {0,1,7,13}, {0,1,8,12}, {0,1,9,11}, {0,2,3,16}, {0,2,4,15}, {0,2,5,14}, {0,2,6,13}, {0,2,7,12}, {0,2,8,11}, {0,2,9,10}, {0,3,4,14}, {0,3,5,13}, {0,3,6,12}, {0,3,7,11}, {0,3,8,10}, {0,4,5,12}, {0,4,6,11}, {0,4,7,10}, {0,4,8,9}, {0,5,6,10}, {0,5,7,9}, {0,6,7,8}, {1,2,3,15}, {1,2,4,14}, {1,2,5,13}, {1,2,6,12}, {1,2,7,11}, {1,2,8,10}, {1,3,4,13}, {1,3,5,12}, {1,3,6,11}, {1,3,7,10}, {1,3,8,9}, {1,4,5,11}, {1,4,6,10}, {1,4,7,9}, {1,5,6,9}, {1,5,7,8}, {2,3,4,12}, {2,3,5,11}, {2,3,6,10}, {2,3,7,9}, {2,4,5,10}, {2,4,6,9}, {2,4,7,8}, {2,5,6,8}, {3,4,5,9}, {3,4,6,8}, {3,5,6,7}] +def fibers : Fin 54 → Finset (FourTerm 20) := ![{⟨⟨20,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨9,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨5,by 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decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨6,by decide⟩)⟩}] +def columns : Matrix (Fin 10) (Fin 54) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![-21883113252000, 21883113252000, -29177484336000, 27353891565000, -25530298794000, 21101573493000, -14588742168000, 7815397590000, 7294371084000, 1823592771000, -1823592771000, 4428725301000, -6512831325000, 6773344578000, -7815397590000, -9117963855000, 7815397590000, -7033857831000, 6252318072000, -2605132530000, -2084106024000, 3386672289000, -6512831325000, 6252318072000, 1302566265000, 781539759000, -2605132530000, -9117963855000, 9117963855000, -10420530120000, 9117963855000, -6512831325000, 3647185542000, 1302566265000, 1302566265000, -2605132530000, 2865645783000, -3647185542000, -1302566265000, 1823592771000, -521026506000, -2084106024000, 1823592771000, -2605132530000, 2605132530000, -2084106024000, 1302566265000, -521026506000, 781539759000, -1302566265000, 260513253000, -260513253000, 260513253000, -260513253000], ![-27353891565000, 27353891565000, -27890242380000, 24538049786250, -19040453932500, 13964276576250, -9041342310000, 4252495747500, 536350815000, 3352192593750, -5497595853750, 5076177356250, -4922934266250, 4788846562500, -4252495747500, -1743140148750, 3026551027500, -1896383238750, 1072701630000, -804526222500, -1992160170000, 1628207831250, -938613926250, 1072701630000, -363952338750, -95776931250, 421418497500, -3888543408750, 3888543408750, -2605132530000, 1743140148750, -938613926250, 268175407500, -1283410878750, 861992381250, -804526222500, 670438518750, -268175407500, 363952338750, -325641566250, -38310772500, 459729270000, -325641566250, 421418497500, -421418497500, 459729270000, -363952338750, -38310772500, -95776931250, 363952338750, -134087703750, 134087703750, -134087703750, 134087703750], ![-29503125902250, 29503125902250, -22480761303000, (31539343460625/2), -9625581590625, (9763500371625/2), -2168389723500, 856245765375, -7022364599250, (13422179145375/2), (-12288180279375/2), (9487662809625/2), (-5426720924625/2), 1312143958125, -856245765375, (-511448812875/2), 672354057375, (-2120501257875/2), 666607441500, -132172165125, 145580935500, (316063873125/2), (-247104482625/2), -191553862500, (-373530031875/2), (572746048875/2), -316063873125, (622550053125/2), (-622550053125/2), 727904677500, (-1940440627125/2), (1469218125375/2), -323726027625, (-833259301875/2), (484631272125/2), 235611250875, (-821766070125/2), 323726027625, (-607225744125/2), (304570641375/2), 28733079375, -99608008500, (59381697375/2), 174314014875, -174314014875, 22986463500, (116847856125/2), 151327551375, (-162820783125/2), (-116847856125/2), (139834319625/2), (-139834319625/2), (139834319625/2), (-139834319625/2)], ![-22664653011000, 22664653011000, -13056311268000, 5344352763750, -1678011835500, 287330793750, 261692046000, -320042299500, -9608341743000, 7711958504250, -3666340928250, 1390681041750, -549022839750, 58350253500, 320042299500, -2149234337250, 1264255492500, -501281723250, 389001690000, -327115057500, -91945854000, -126425549250, -11493231750, 275837562000, 234285108750, -255503382750, 238705582500, 1896383238750, -1896383238750, 1011404394000, -340376478750, 101670896250, -51277495500, 884978844750, -671027915250, 238705582500, -50393400750, 51277495500, 218371403250, -96366327750, -8840947500, 21218274000, 16797800250, -213950929500, 213950929500, -91945854000, 7956852750, -122005075500, 83989001250, -7956852750, -38016074250, 38016074250, -38016074250, 38016074250], ![-781539759000, 781539759000, 459729270000, -1723984762500, 1953849397500, -1195296102000, 258155667000, 150296107500, -1241269029000, 1264255492500, -229864635000, -758553295500, 937140435000, -408451774500, -150296107500, -1057377321000, 1034390857500, -302360404500, -343028763000, 415524532500, -654230115000, 583502535000, -114932317500, -272301183000, -353637900000, 300592215000, -228096445500, -22986463500, 22986463500, -45972927000, 123773265000, -185659897500, 143223349500, 22986463500, -77800338000, 61886632500, 42436548000, -143223349500, 70727580000, -114932317500, 86641285500, 53045685000, -72495769500, 54813874500, -54813874500, 10609137000, 14145516000, 44204737500, -24754653000, -14145516000, 19450084500, -19450084500, 19450084500, -19450084500], ![31261590360000, -31261590360000, 17101928844000, -5248575832500, 153243090000, 344796952500, 459729270000, -643620978000, 14159661516000, -11853353011500, 5095332742500, -498040042500, -804526222500, 183891708000, 643620978000, 4451711764500, -3371347980000, 1034390857500, 429080652000, -612972360000, 1379187810000, -1003742239500, 160905244500, 398432034000, 498040042500, -375445570500, 245188944000, -2306308504500, 2306308504500, -1225944720000, 268175407500, 191553862500, -214540326000, -1080363784500, 957769312500, -459729270000, 22986463500, 214540326000, -375445570500, 344796952500, -183891708000, -122594472000, 130256626500, 122594472000, -122594472000, 91945854000, -53635081500, 30648618000, -38310772500, 53635081500, -7662154500, 7662154500, -7662154500, 7662154500], ![15630795180000, -15630795180000, 14711336640000, -12029582565000, 6359588235000, -306486180000, -3064861800000, 2758375620000, 919458540000, -2681754075000, 5669994330000, -6053102055000, 3371347980000, 306486180000, -2758375620000, -1225944720000, -76621545000, 2068781715000, -2758375620000, 1838917080000, -919458540000, 383107725000, 612972360000, -1225944720000, -536350815000, 383107725000, -229864635000, 1762295535000, -1762295535000, 459729270000, 612972360000, -919458540000, 612972360000, 1302566265000, -1072701630000, 306486180000, 306486180000, -612972360000, 536350815000, -459729270000, 229864635000, 153243090000, -153243090000, -229864635000, 229864635000, -153243090000, 76621545000, -76621545000, 76621545000, -76621545000, 0, 0, 0, 0], ![-287606631312000, 287606631312000, -175064906016000, 72943710840000, -8336424096000, -22925166264000, 29177484336000, -18756954216000, -112541725296000, 102121195176000, -64607286744000, 31261590360000, -6252318072000, -10420530120000, 18756954216000, -27093378312000, 25009272288000, -18756954216000, 12504636144000, -6252318072000, -4168212048000, 4168212048000, -4168212048000, 4168212048000, 0, 0, 0, 10420530120000, -10420530120000, 8336424096000, -6252318072000, 4168212048000, -2084106024000, 2084106024000, -2084106024000, 2084106024000, -2084106024000, 2084106024000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![-1663116607152000, 1663116607152000, -1425528520416000, 1187940433680000, -950352346944000, 712764260208000, -475176173472000, 237588086736000, -237588086736000, 237588086736000, -237588086736000, 237588086736000, -237588086736000, 237588086736000, -237588086736000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Y : Matrix (Fin 10) (Fin 10) ℚ := ![![(-2575378098051295967192330108541/1048576000000000000), (304560484952628826937344536207/524288000000000000), (-1939199525243506958203164393/8388608000000000), (2667680548706604422400836427/20971520000000000), (-2180894479334694535020990381/26214400000000000), (3112903415386975802967714339/65536000000000000), (1523977354474445030408597349/65536000000000000), (-246018212942377731018902739/1310720000000000), 0, 0], ![(304560484952628826937344536207/524288000000000000), (-35684955666676559351531331909/262144000000000000), (1128064325531575378304348991/20971520000000000), (-308620770457624942690221849/10485760000000000), (251101146559099718303188767/13107200000000000), (-356615001431456188681413153/32768000000000000), (-175879380110528140204221063/32768000000000000), (28138995565098927397665777/655360000000000), 0, 0], ![(-1939199525243506958203164393/8388608000000000), (1128064325531575378304348991/20971520000000000), (-177325353696949684010401617/8388608000000000), (48298505108325694172493543/4194304000000000), (-1565856307352147926492377/209715200000000), (2214497891800951482644919/524288000000000), (5501367213876638925537717/2621440000000000), (-4365428948288665784750223/262144000000000), 0, 0], ![(2667680548706604422400836427/20971520000000000), (-308620770457624942690221849/10485760000000000), (48298505108325694172493543/4194304000000000), (-13107186318534533962770033/2097152000000000), (2117819265086190595372443/524288000000000), (-2983564518432997321635813/1310720000000000), (-1495684547709622049983203/1310720000000000), (1176945201090242185298697/131072000000000), 0, 0], ![(-2180894479334694535020990381/26214400000000000), (251101146559099718303188767/13107200000000000), (-1565856307352147926492377/209715200000000), (2117819265086190595372443/524288000000000), (-1705739301331431466478301/655360000000000), (2392701578504065053046899/1638400000000000), (1217141085026707524152469/1638400000000000), (-189378851128424803264419/32768000000000), 0, 0], ![(3112903415386975802967714339/65536000000000000), (-356615001431456188681413153/32768000000000000), (2214497891800951482644919/524288000000000), (-2983564518432997321635813/1310720000000000), (2392701578504065053046899/1638400000000000), (-3327093583199410306463181/4096000000000000), (-1769892401190414420090171/4096000000000000), (267391692111935410240221/81920000000000), 0, 0], ![(1523977354474445030408597349/65536000000000000), (-175879380110528140204221063/32768000000000000), (5501367213876638925537717/2621440000000000), (-1495684547709622049983203/1310720000000000), (1217141085026707524152469/1638400000000000), (-1769892401190414420090171/4096000000000000), (-674877628307291743675341/4096000000000000), (126282531094226812764459/81920000000000), 0, 0], ![(-246018212942377731018902739/1310720000000000), (28138995565098927397665777/655360000000000), (-4365428948288665784750223/262144000000000), (1176945201090242185298697/131072000000000), (-189378851128424803264419/32768000000000), (267391692111935410240221/81920000000000), (126282531094226812764459/81920000000000), (-102414748220651390741217/8192000000000), 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Z : Matrix (Fin 10) (Fin 10) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 2134124568576000, 0, 0, 0, 0, 0, 0, -133382785536000, 3326233214304000], ![0, 0, 156920924160000, 0, 0, 0, 0, -17163226080000, 0, 2375880867360000], ![0, 0, 0, 31384184832000, 0, 0, -4413400992000, -21454032600000, 116709937344000, 1069146390312000], ![0, 0, 0, 0, 14485008384000, -2263282560000, -11769069312000, 0, 100037089152000, 237588086736000], ![0, 0, 0, 0, -2263282560000, 5148967824000, -8091235152000, 10114043940000, 0, -148492554210000], ![0, 0, 0, -4413400992000, -11769069312000, -8091235152000, 31384184832000, -21913761870000, -108373513248000, -267286597578000], ![0, 0, -17163226080000, -21454032600000, 0, 10114043940000, -21913761870000, 62791356127500, -182359277100000, -259861969867500], ![0, -133382785536000, 0, 116709937344000, 100037089152000, 0, -108373513248000, -182359277100000, 1921545754128000, -207889575894000], ![0, 3326233214304000, 2375880867360000, 1069146390312000, 237588086736000, -148492554210000, -267286597578000, -259861969867500, -207889575894000, 121494751697694375]] +def W : Matrix (Fin 10) (Fin 10) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![(-143571063613964741469/30064771072000000000000000), (147716843492797251553/2147483648000000000000000), (-515289157815926815893/1503238553600000000000000), (140975060813728997427/150323855360000000000000), (-497036099895881642811/375809638400000000000000), (705892951524763980549/939524096000000000000000), (80340044094235960749/469762048000000000000000), (-12853628111759720571/46976204800000000000000), (-1/3200000), (7/51200000)], ![(8329648243368914319/4810363371520000000000000), (-55329583461737387517/2405181685760000000000000), (154055448873777525779/1202590842880000000000000), (-40361281977747763461/120259084288000000000000), (28370934735603152121/60129542144000000000000), (-40129369480076023719/150323855360000000000000), (-4622152748985669183/75161927680000000000000), (3640146909175697021/37580963840000000000000), 0, (1/10240000)], ![(-591568108631483678981/481036337152000000000000000), (3893578125269712186879/240518168576000000000000000), (-2068715858794517117757/24051816857600000000000000), (572790244145566956203/2405181685760000000000000), (-1961463867048630941139/6012954214400000000000000), (2762358990155751029901/15032385536000000000000000), (312926109366307012501/7516192768000000000000000), (-50671742820744032179/751619276800000000000000), (7/25600000), (9/204800000)], ![(98204696760722954721/120259084288000000000000000), (-644389615957393049139/60129542144000000000000000), (48793154510418879231/858993459200000000000000), (-92404887463508461743/601295421440000000000000), (330218712813359202199/1503238553600000000000000), (-456799165215012814441/3758096384000000000000000), (-55743185763522483441/1879048192000000000000000), (8223444102292030359/187904819200000000000000), (3/12800000), (1/102400000)], ![(-36426302783360193/375809638400000000000000), (3818797692408020421/3006477107200000000000000), (-721014037506946953/107374182400000000000000), (543509871921907539/30064771072000000000000), (-483992375534844041/18790481920000000000000), (2865466959865803563/187904819200000000000000), (130796173471393617/46976204800000000000000), (-242340452936398443/46976204800000000000000), 0, (-1/163840000)], ![(-35906309864805835169/60129542144000000000000000), (235415741851246250151/30064771072000000000000000), (-124764778468736161041/3006477107200000000000000), (33572774247116580187/300647710720000000000000), (-17343972907187735393/107374182400000000000000), (163477460216262026549/1879048192000000000000000), (22114272655097515769/939524096000000000000000), (-2997635324092583603/93952409600000000000000), (-13/51200000), (-9/819200000)], ![(1184839991603713731/1202590842880000000000000), (-1109550534080133717/85899345920000000000000), (20411287668439143283/300647710720000000000000), (-5671783558782331343/30064771072000000000000), (779643737133757353/3006477107200000000000), (-5407261487217242081/37580963840000000000000), (-652769923006786871/18790481920000000000000), (504761796709830847/9395240960000000000000), (-7/16384000), (-7/655360000)], ![0, (-1/3200000), 0, (119/6400000), (221/6400000), 0, (-221/12800000), (-119/20480000), (461/102400000), (-7/819200000)], ![0, (399/51200000), (969/12800000), (8721/51200000), (4199/51200000), (-4199/81920000), (-8721/204800000), (-6783/819200000), (-399/819200000), (13091/2621440000)]] +def M : Matrix (Fin 10) (Fin 10) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, (38612334337392258551531331909/262144000000000000), (-2045531430861669080825037543/41943040000000000), (145364217717507017625370315341/4194304000000000000), (-23980438818470450490112819881/1048576000000000000), (141056663856866549023591359/52428800000000000), (8759871201249933098698393029/524288000000000000), (-288827602241903765290651401/10485760000000000), (-33172976097261/25600), (13642441583679909/409600)], ![0, (-2045531430861669080825037543/41943040000000000), (626514922291838732214919857/33554432000000000), (-8211034707144484699925247807/671088640000000000), (1373316798350137192080355827/167772160000000000), (-41090693134423011929871021/41943040000000000), (-502519783994923300621022007/83886080000000000), (81420246564122478295402119/8388608000000000), (406661187933/5120), (391352126620455/16384)], ![0, (145364217717507017625370315341/4194304000000000000), (-8211034707144484699925247807/671088640000000000), (591605372872441117200819717909/67108864000000000000), (-93838284428266220688224748369/16777216000000000000), (552998226300698225007691731/838860800000000000), (33922382252375903124955137021/8388608000000000000), (-1171264771210799796256294569/167772160000000000), (26638261659009/20480), (18011894388330843/1638400)], ![0, (-23980438818470450490112819881/1048576000000000000), (1373316798350137192080355827/167772160000000000), (-93838284428266220688224748369/16777216000000000000), (16072367243417045033433035229/4194304000000000000), (-92658012858142890084294291/209715200000000000), (-5959419654870181138286809161/2097152000000000000), (186457453288081507380557709/41943040000000000), (58967956356309/51200), (2410791466854771/819200)], ![0, (141056663856866549023591359/52428800000000000), (-41090693134423011929871021/41943040000000000), (552998226300698225007691731/838860800000000000), (-92658012858142890084294291/209715200000000000), (26431332591424231014174477/419430400000000000), (12668040635092950190530447/41943040000000000), (-4208699413227311439850413/8388608000000000), (1657645828839/409600), (-6096673647455391/6553600)], ![0, (8759871201249933098698393029/524288000000000000), (-502519783994923300621022007/83886080000000000), (33922382252375903124955137021/8388608000000000000), (-5959419654870181138286809161/2097152000000000000), (12668040635092950190530447/41943040000000000), (2278143844664573671779112119/1048576000000000000), (-34326345943861097756713083/10485760000000000), (-568773635523093/409600), (-24505176798825723/6553600)], ![0, (-288827602241903765290651401/10485760000000000), (81420246564122478295402119/8388608000000000), (-1171264771210799796256294569/167772160000000000), (186457453288081507380557709/41943040000000000), (-4208699413227311439850413/8388608000000000), (-34326345943861097756713083/10485760000000000), (23665613075608579744868199/4194304000000000), (-394579364798619/327680), (-32860704331668213/5242880)], ![0, (-33172976097261/25600), (406661187933/5120), (26638261659009/20480), (58967956356309/51200), (1657645828839/409600), (-568773635523093/409600), (-394579364798619/327680), (7065351017641917/409600), (204439188055121019/6553600)], ![0, (13642441583679909/409600), (391352126620455/16384), (18011894388330843/1638400), (2410791466854771/819200), (-6096673647455391/6553600), (-24505176798825723/6553600), (-32860704331668213/5242880), (204439188055121019/6553600), (4342559154816151269/4194304)]] +def L : Matrix (Fin 10) (Fin 10) ℚ := ![![1, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 1, 0, 0, 0, 0, 0, 0, 0, 0], ![0, (-1374087484143434687925/4150058966278323043484), 1, 0, 0, 0, 0, 0, 0, 0], ![0, (355085590151792016989/1509112351373935652176), (-377811106278238091966693436495569929495/1254327522290478703626245381788415824388), 1, 0, 0, 0, 0, 0, 0], ![0, (-644355209557393049139/4150058966278323043484), (76218070155939889910766668771922916938/313581880572619675906561345447103956097), (-9166344201269779762994634628758205392877125702867036/144798467338926733973729828839798622090847931671439289), 1, 0, 0, 0, 0, 0], ![0, (18950986862040102105/1037514741569580760871), (-441643472682582102482949154275508216737/12543275222904787036262453817884158243880), (-1975073046153649009405964690830783780098839873982489/1447984673389267339737298288397986220908479316714392890), (-35433574342151478407795065143516080222561934678905601091839/1820949125212779981835926954425799919927530133356448680597320), 1, 0, 0, 0, 0], ![0, (235378038171246250151/2075029483139161521742), (-1139078931221170511253511728237649353737/6271637611452393518131226908942079121940), (-171298571399561809669856789843728871006409268717290101/2895969346778534679474596576795972441816958633428785780), (-2886604268700287712200059109711430820953492920342125085417107/2731423687819169972753890431638699879891295200034673020895980), (-9067604287855341858770638752516966722824603769033539902342352058/4405649391697254060747779019658244617660965328459895416724527827), 1, 0, 0, 0], ![0, (-27717169752003342925/148216391652797251553), (291194140185114308828991870747169960609/1254327522290478703626245381788415824388), (-217026700650558738813313287377472753436135429904988293/289596934677853467947459657679597244181695863342878578), (32815389198523475961574963571079599416529139671750903808739/728379650085111992734370781770319967971012053342579472238928), (8944658389042300959215552823600058659659982498144090708457315570/4405649391697254060747779019658244617660965328459895416724527827), (-25/4), 1, 0, 0], ![0, (-186275840000000000/21173770236113893079), (-43435866011268755324742808307200000000/313581880572619675906561345447103956097), (502995931961494171380778426482420059917532546080000000/144798467338926733973729828839798622090847931671439289), (4739868771878019383336068172296926438596639352255683035784513/546284737563833994550778086327739975978259040006934604179196), (5416986467094253092294890065304606086107083683135090784133415539/1468549797232418020249259673219414872553655109486631805574842609), 34, 0, 1, 0], ![0, (4787890560000000000/21173770236113893079), (4337629871518529765642561977116000000000/313581880572619675906561345447103956097), (4584113048907919898558240364076878241516260801870000000/144798467338926733973729828839798622090847931671439289), (581006373044570632971360078608691680406325282283012888731167/153343084228444630049341217214804203783370958598437783629248), (-308768228624372426260808733722362546908103769938700174695604685723/11748398377859344161994077385755318980429240875893054444598740872), (-969/4), 0, 0, 1]] +def diag : Fin 10 → ℚ := ![0, (38612334337392258551531331909/262144000000000000), (8915446446560150005699445612406612575793807/3532185252130080246464512000000000), (2218936456228120999774233779658185582694379776944022139376301/5137725531301800770053101083805351216693248000000000), (482967468485313424453871514537401692127504931410170847148155242821/3706840763876524389727483618298844725525707050788845798400), (15580045990160943618093170021760003442759266907293676493900868992318433/1456759300170223985468741563540639935942024106685158944477856000), (1316319188586113376948543568605232977341506374873703278416794028116064940621/751897496182998026367620952688340414747471416057155484454319415808000), 0, 0, 0] + +def keyIndexTable : Fin 21 → Fin 13 → Fin 13 → Fin 54 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 8, 9, 10, 11, 12, 13, 14, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 8, 0, 15, 16, 17, 18, 19, 0, 0, 0, 0], ![0, 0, 0, 27, 28, 29, 30, 31, 32, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 9, 15, 0, 20, 21, 22, 23, 0, 0, 0, 0], ![1, 0, 27, 0, 33, 34, 35, 36, 37, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 10, 16, 20, 0, 24, 25, 0, 0, 0, 0, 0], ![2, 0, 28, 33, 0, 38, 39, 40, 0, 0, 0, 0, 0], ![8, 27, 0, 0, 43, 44, 45, 46, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 11, 17, 21, 24, 0, 26, 0, 0, 0, 0, 0], ![3, 0, 29, 34, 38, 0, 41, 42, 0, 0, 0, 0, 0], ![9, 28, 0, 43, 0, 47, 48, 49, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 12, 18, 22, 25, 26, 0, 0, 0, 0, 0, 0], ![4, 0, 30, 35, 39, 41, 0, 0, 0, 0, 0, 0, 0], ![10, 29, 0, 44, 47, 0, 50, 0, 0, 0, 0, 0, 0], ![15, 33, 43, 0, 0, 51, 52, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 13, 19, 23, 0, 26, 0, 0, 0, 0, 0, 0], ![5, 0, 31, 36, 40, 42, 0, 0, 0, 0, 0, 0, 0], ![11, 30, 0, 45, 48, 50, 0, 0, 0, 0, 0, 0, 0], ![16, 34, 44, 0, 51, 0, 53, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 7, 14, 0, 23, 25, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 32, 37, 0, 42, 0, 0, 0, 0, 0, 0, 0], ![12, 31, 0, 46, 49, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 35, 45, 0, 52, 53, 0, 0, 0, 0, 0, 0, 0], ![20, 38, 47, 51, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 14, 19, 22, 24, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 37, 40, 41, 0, 0, 0, 0, 0, 0, 0], ![13, 32, 0, 0, 49, 50, 0, 0, 0, 0, 0, 0, 0], ![18, 36, 46, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0], ![21, 39, 48, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 7, 13, 18, 21, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 32, 36, 39, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 0, 0, 46, 48, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 37, 0, 0, 52, 0, 0, 0, 0, 0, 0, 0, 0], ![22, 40, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![24, 41, 50, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 12, 17, 20, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 31, 35, 38, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 32, 0, 45, 47, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 37, 46, 0, 51, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 0, 49, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![25, 42, 0, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 11, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 30, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 31, 0, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 36, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 40, 48, 51, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 42, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![26, 0, 0, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 10, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 29, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 30, 0, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 35, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![22, 39, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![25, 41, 0, 51, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![26, 0, 50, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 29, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 34, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![21, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![24, 0, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 41, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![26, 42, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 0, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 38, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![24, 39, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![25, 40, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![21, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![22, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 27, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 28, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 29, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 21) (j : Fin ((n.val+1)/2)) (x : Fin ((20-n.val+2)/2)) : Fin 54 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 54 → FourTerm 20 := ![⟨⟨20,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 11, + (fourTermLabels (by omega : 20 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 10, + (fourTermLabels (by omega : 20 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 10, + (fourTermLabels (by omega : 20 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 9, + (fourTermLabels (by omega : 20 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 9, + (fourTermLabels (by omega : 20 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 8, + (fourTermLabels (by omega : 20 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 8, + (fourTermLabels (by omega : 20 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 7, + (fourTermLabels (by omega : 20 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 7, + (fourTermLabels (by omega : 20 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 6, + (fourTermLabels (by omega : 20 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 6, + (fourTermLabels (by omega : 20 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 5, + (fourTermLabels (by omega : 20 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover_12 : ∀ j : Fin 6, ∀ x : Fin 5, + (fourTermLabels (by omega : 20 ≤ 23) ⟨12,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨12,j,x⟩).toFinset=keys (keyIndex 12 j x) := by decide +kernel +lemma cover_13 : ∀ j : Fin 7, ∀ x : Fin 4, + (fourTermLabels (by omega : 20 ≤ 23) ⟨13,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨13,j,x⟩).toFinset=keys (keyIndex 13 j x) := by decide +kernel +lemma cover_14 : ∀ j : Fin 7, ∀ x : Fin 4, + (fourTermLabels (by omega : 20 ≤ 23) ⟨14,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨14,j,x⟩).toFinset=keys (keyIndex 14 j x) := by decide +kernel +lemma cover_15 : ∀ j : Fin 8, ∀ x : Fin 3, + (fourTermLabels (by omega : 20 ≤ 23) ⟨15,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨15,j,x⟩).toFinset=keys (keyIndex 15 j x) := by decide +kernel +lemma cover_16 : ∀ j : Fin 8, ∀ x : Fin 3, + (fourTermLabels (by omega : 20 ≤ 23) ⟨16,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨16,j,x⟩).toFinset=keys (keyIndex 16 j x) := by decide +kernel +lemma cover_17 : ∀ j : Fin 9, ∀ x : Fin 2, + (fourTermLabels (by omega : 20 ≤ 23) ⟨17,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨17,j,x⟩).toFinset=keys (keyIndex 17 j x) := by decide +kernel +lemma cover_18 : ∀ j : Fin 9, ∀ x : Fin 2, + (fourTermLabels (by omega : 20 ≤ 23) ⟨18,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨18,j,x⟩).toFinset=keys (keyIndex 18 j x) := by decide +kernel +lemma cover_19 : ∀ j : Fin 10, ∀ x : Fin 1, + (fourTermLabels (by omega : 20 ≤ 23) ⟨19,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨19,j,x⟩).toFinset=keys (keyIndex 19 j x) := by decide +kernel +lemma cover_20 : ∀ j : Fin 10, ∀ x : Fin 1, + (fourTermLabels (by omega : 20 ≤ 23) ⟨20,j,x⟩).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) ⟨20,j,x⟩).toFinset=keys (keyIndex 20 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 20, (fourTermLabels (by omega : 20 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 20 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x + · exact cover_12 j x + · exact cover_13 j x + · exact cover_14 j x + · exact cover_15 j x + · exact cover_16 j x + · exact cover_17 j x + · exact cover_18 j x + · exact cover_19 j x + · exact cover_20 j x +lemma representatives_checked : ∀ a : Fin 54, + (fourTermLabels (by omega : 20 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 20 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 20 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 20 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 54, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 20, + (fourTermLabels (by omega : 20 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 54, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 20 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 54, ∀ b : FourTerm 20, + (fourTermLabels (by omega : 20 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 20 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 54, (∑ b ∈ fibers v, fourTermEval 20 (2*(0 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 20 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 54, (∑ b ∈ fibers v, fourTermEval 20 (2*(1 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 20 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 54, (∑ b ∈ fibers v, fourTermEval 20 (2*(2 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 20 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 54, (∑ b ∈ fibers v, fourTermEval 20 (2*(3 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 20 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 54, (∑ b ∈ fibers v, fourTermEval 20 (2*(4 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 20 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 54, (∑ b ∈ fibers v, fourTermEval 20 (2*(5 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 20 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_6 : ∀ v : Fin 54, (∑ b ∈ fibers v, fourTermEval 20 (2*(6 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 20 ≤ 23) b)) = columns 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_7 : ∀ v : Fin 54, (∑ b ∈ fibers v, fourTermEval 20 (2*(7 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 20 ≤ 23) b)) = columns 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_8 : ∀ v : Fin 54, (∑ b ∈ fibers v, fourTermEval 20 (2*(8 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 20 ≤ 23) b)) = columns 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_9 : ∀ v : Fin 54, (∑ b ∈ fibers v, fourTermEval 20 (2*(9 : Fin 10).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 20 ≤ 23) b)) = columns 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 10, ∀ v : Fin 54, (∑ b ∈ fibers v, fourTermEval 20 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 20 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 + · exact columns_checked_6 + · exact columns_checked_7 + · exact columns_checked_8 + · exact columns_checked_9 +lemma gram_checked_0 : ∀ v : Fin 10, (∑ a : Fin 54, columns (0 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 10, (∑ a : Fin 54, columns (1 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 10, (∑ a : Fin 54, columns (2 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 10, (∑ a : Fin 54, columns (3 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 10, (∑ a : Fin 54, columns (4 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 10, (∑ a : Fin 54, columns (5 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_6 : ∀ v : Fin 10, (∑ a : Fin 54, columns (6 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_7 : ∀ v : Fin 10, (∑ a : Fin 54, columns (7 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_8 : ∀ v : Fin 10, (∑ a : Fin 54, columns (8 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_9 : ∀ v : Fin 10, (∑ a : Fin 54, columns (9 : Fin 10) a * columns v a / setFactorial (keys a)) = Z 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 10, ∀ v : Fin 10, (∑ a : Fin 54, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 + · exact gram_checked_6 + · exact gram_checked_7 + · exact gram_checked_8 + · exact gram_checked_9 +lemma rows_table_checked_0 : ∀ v : Fin 10, integerTableEval 20 SumTable20.sums (0 : Fin 10) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 10, integerTableEval 20 SumTable20.sums (1 : Fin 10) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 10, integerTableEval 20 SumTable20.sums (2 : Fin 10) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 10, integerTableEval 20 SumTable20.sums (3 : Fin 10) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 10, integerTableEval 20 SumTable20.sums (4 : Fin 10) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 10, integerTableEval 20 SumTable20.sums (5 : Fin 10) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_6 : ∀ v : Fin 10, integerTableEval 20 SumTable20.sums (6 : Fin 10) v = Y 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_7 : ∀ v : Fin 10, integerTableEval 20 SumTable20.sums (7 : Fin 10) v = Y 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_8 : ∀ v : Fin 10, integerTableEval 20 SumTable20.sums (8 : Fin 10) v = Y 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_9 : ∀ v : Fin 10, integerTableEval 20 SumTable20.sums (9 : Fin 10) v = Y 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 10, ∀ v : Fin 10, integerTableEval 20 SumTable20.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 + · exact rows_table_checked_6 + · exact rows_table_checked_7 + · exact rows_table_checked_8 + · exact rows_table_checked_9 +lemma rows_checked (u v : Fin 10) : exactFourEval 20 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 20 SumTable20.sums SumTable20.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 10, (Z * tableComparison 20 (1/200000) Y) (0 : Fin 10) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 10, (Z * tableComparison 20 (1/200000) Y) (1 : Fin 10) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 10, (Z * tableComparison 20 (1/200000) Y) (2 : Fin 10) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 10, (Z * tableComparison 20 (1/200000) Y) (3 : Fin 10) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 10, (Z * tableComparison 20 (1/200000) Y) (4 : Fin 10) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 10, (Z * tableComparison 20 (1/200000) Y) (5 : Fin 10) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_6 : ∀ v : Fin 10, (Z * tableComparison 20 (1/200000) Y) (6 : Fin 10) v = W 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_7 : ∀ v : Fin 10, (Z * tableComparison 20 (1/200000) Y) (7 : Fin 10) v = W 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_8 : ∀ v : Fin 10, (Z * tableComparison 20 (1/200000) Y) (8 : Fin 10) v = W 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_9 : ∀ v : Fin 10, (Z * tableComparison 20 (1/200000) Y) (9 : Fin 10) v = W 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 10, ∀ v : Fin 10, (Z * tableComparison 20 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 + · exact product_checked_6 + · exact product_checked_7 + · exact product_checked_8 + · exact product_checked_9 +lemma compression_checked_0 : ∀ v : Fin 10, (W * Z) (0 : Fin 10) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 10, (W * Z) (1 : Fin 10) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 10, (W * Z) (2 : Fin 10) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 10, (W * Z) (3 : Fin 10) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 10, (W * Z) (4 : Fin 10) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 10, (W * Z) (5 : Fin 10) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_6 : ∀ v : Fin 10, (W * Z) (6 : Fin 10) v = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_7 : ∀ v : Fin 10, (W * Z) (7 : Fin 10) v = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_8 : ∀ v : Fin 10, (W * Z) (8 : Fin 10) v = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_9 : ∀ v : Fin 10, (W * Z) (9 : Fin 10) v = M 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 10, ∀ v : Fin 10, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 + · exact compression_checked_6 + · exact compression_checked_7 + · exact compression_checked_8 + · exact compression_checked_9 +lemma ldl_checked_0 : ∀ v : Fin 10, (∑ k : Fin 10, L (0 : Fin 10) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 10, (∑ k : Fin 10, L (1 : Fin 10) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 10, (∑ k : Fin 10, L (2 : Fin 10) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 10, (∑ k : Fin 10, L (3 : Fin 10) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 10, (∑ k : Fin 10, L (4 : Fin 10) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 10, (∑ k : Fin 10, L (5 : Fin 10) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_6 : ∀ v : Fin 10, (∑ k : Fin 10, L (6 : Fin 10) k * diag k * L v k) = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_7 : ∀ v : Fin 10, (∑ k : Fin 10, L (7 : Fin 10) k * diag k * L v k) = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_8 : ∀ v : Fin 10, (∑ k : Fin 10, L (8 : Fin 10) k * diag k * L v k) = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_9 : ∀ v : Fin 10, (∑ k : Fin 10, L (9 : Fin 10) k * diag k * L v k) = M 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 10, ∀ v : Fin 10, (∑ k : Fin 10, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 + · exact ldl_checked_6 + · exact ldl_checked_7 + · exact ldl_checked_8 + · exact ldl_checked_9 +lemma diag_checked : ∀ u : Fin 10, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 20 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 20 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 20 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 20 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 20 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate20 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate21.lean b/lean/OAI/Analysis/LaughlinGap/Certificate21.lean new file mode 100644 index 0000000000000000000000000000000000000000..0350fca51fd968520faa019827825729a431a41c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate21.lean @@ -0,0 +1,455 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CachedIntegerRows +import OAI.Analysis.LaughlinGap.FastFourKeys +import OAI.Analysis.LaughlinGap.FourTables +import OAI.Analysis.LaughlinGap.SumTable21 + +namespace OAI + +/-! Certificate21. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate21 + +def keys : Fin 64 → Finset (Fin 25) := ![{0,1,2,19}, {0,1,3,18}, {0,1,4,17}, {0,1,5,16}, {0,1,6,15}, {0,1,7,14}, {0,1,8,13}, {0,1,9,12}, {0,1,10,11}, {0,2,3,17}, {0,2,4,16}, {0,2,5,15}, {0,2,6,14}, {0,2,7,13}, {0,2,8,12}, {0,2,9,11}, {0,3,4,15}, {0,3,5,14}, {0,3,6,13}, {0,3,7,12}, {0,3,8,11}, {0,3,9,10}, {0,4,5,13}, {0,4,6,12}, {0,4,7,11}, {0,4,8,10}, {0,5,6,11}, {0,5,7,10}, {0,5,8,9}, {0,6,7,9}, {1,2,3,16}, {1,2,4,15}, {1,2,5,14}, {1,2,6,13}, {1,2,7,12}, {1,2,8,11}, {1,2,9,10}, {1,3,4,14}, {1,3,5,13}, {1,3,6,12}, {1,3,7,11}, {1,3,8,10}, {1,4,5,12}, {1,4,6,11}, {1,4,7,10}, {1,4,8,9}, {1,5,6,10}, {1,5,7,9}, {1,6,7,8}, {2,3,4,13}, {2,3,5,12}, {2,3,6,11}, {2,3,7,10}, {2,3,8,9}, {2,4,5,11}, {2,4,6,10}, {2,4,7,9}, {2,5,6,9}, {2,5,7,8}, {3,4,5,10}, {3,4,6,9}, {3,4,7,8}, {3,5,6,8}, {4,5,6,7}] +def fibers : Fin 64 → Finset (FourTerm 21) := ![{⟨⟨21,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨20,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨9,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨10,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨10,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by 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decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨5,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨5,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨5,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨6,by decide⟩)⟩}] +def columns : Matrix (Fin 11) (Fin 64) ℚ := ![![334108246972500, -334108246972500, 593970216840000, -593970216840000, 779585909602500, -779585909602500, 890955325260000, -890955325260000, 928078463812500, -259861969867500, 0, -185615692762500, 0, -111369415657500, 0, -37123138552500, 445477662630000, -259861969867500, 556847078287500, -445477662630000, 593970216840000, -556847078287500, -296985108420000, 0, -148492554210000, 0, 334108246972500, -185615692762500, 296985108420000, -111369415657500, 259861969867500, -259861969867500, 445477662630000, -445477662630000, 556847078287500, -556847078287500, 593970216840000, -185615692762500, 0, -111369415657500, 0, -37123138552500, 296985108420000, -185615692762500, 334108246972500, -296985108420000, -148492554210000, 0, 111369415657500, 185615692762500, -185615692762500, 296985108420000, -296985108420000, 334108246972500, -111369415657500, 0, -37123138552500, 148492554210000, -111369415657500, 111369415657500, -111369415657500, 148492554210000, -37123138552500, 37123138552500], ![233875772880750, -233875772880750, 328246698780000, -328246698780000, 348762117453750, -348762117453750, 342314414442000, -342314414442000, 337039021068750, -94370925899250, 0, -20515418673750, 0, 6447703011750, 0, 5275393373250, 114886344573000, -94370925899250, 108438641561250, -114886344573000, 103163248188000, -108438641561250, -14067715662000, 0, 11723096385000, 0, 8792322288750, -20515418673750, 14067715662000, 6447703011750, 94370925899250, -94370925899250, 114886344573000, -114886344573000, 108438641561250, -108438641561250, 103163248188000, -20515418673750, 0, 6447703011750, 0, 5275393373250, 14067715662000, -20515418673750, 8792322288750, -14067715662000, 11723096385000, 0, -6447703011750, 20515418673750, -20515418673750, 14067715662000, -14067715662000, 8792322288750, 6447703011750, 0, 5275393373250, -11723096385000, 6447703011750, -6447703011750, 6447703011750, -11723096385000, 5275393373250, -5275393373250], ![306265893058125, -306265893058125, 325641566250000, -291315114090000, 235122788525625, -183633110285625, 135390270015000, -98611928415000, 81458280028125, -19375673191875, -34326452160000, 56192325564375, -51489678240000, 48242840270625, -36778341600000, 17153648386875, 31836251947500, -45120512311875, 31405255756875, -24480583627500, 20381330970000, -13016084956875, 25974703755000, -22067004960000, 16358699857500, -12259447200000, 4683491938125, -5104910435625, 10803637845000, -3246837969375, 53702125351875, -53702125351875, 40417864987500, -28158417787500, 13016084956875, -756637756875, -4137563430000, 13284260364375, -12259447200000, 15142332830625, -12259447200000, 4894201186875, -3907698795000, 1024813164375, 1005657778125, 1455809355000, 421418497500, -2451889440000, 3246837969375, -1024813164375, 1024813164375, -3907698795000, 6359588235000, -6350010541875, 2882885630625, -2451889440000, -9577693125, 2030470942500, -794948529375, -430996190625, 430996190625, 804526222500, -1235522413125, 1235522413125], ![350813659321125, -350813659321125, 284480472276000, -212394922740000, 137775115603125, -77703824323125, 39689960310000, -17377766406000, 5832815113125, 66333187045125, -72085549536000, 74619807136875, -60071291280000, 38013864013125, -22312193904000, 11544951292875, 3218104890000, -11759491618875, 14119435204875, -8367072714000, 5148967824000, -6395983468875, 2789024238000, -5148967824000, 1501782282000, 1716322608000, 3687411853125, -2614710223125, -1072701630000, 1971089245125, 5752362490875, -5752362490875, -2789024238000, 7937992062000, -7334597395125, 5618274787125, -5148967824000, 8541386728875, -5148967824000, -603394666875, 1716322608000, -469306963125, 2359943586000, -40226311125, -603394666875, -643620978000, -1072701630000, 1716322608000, -1971089245125, -3392418904875, 3392418904875, -1072701630000, -643620978000, 1112927941125, -2319717274875, 1716322608000, -469306963125, -643620978000, 254766637125, 603394666875, -603394666875, 214540326000, 388854340875, -388854340875], ![311834363841000, -311834363841000, 194603399991000, -98611928415000, 43961611443750, -14722829871750, 620634514500, 2901598969500, -1803553290000, 117230963850000, -95991471576000, 54650316971250, -29238781572000, 14102195357250, -3522233484000, -1098045679500, 20101662330750, -12136852728000, 7930329907500, -6903895902750, 3617715717000, 281142130500, -1861903543500, 2503756332000, 612677661750, -2079390852000, -2917512675000, 1816814711250, 631243651500, -1217398470750, -21239492274000, 21239492274000, -13274682671250, 7206256307250, -3676065970500, 1002563446500, 816903549000, -7964809602750, 6068426364000, -3530190336750, 2673502524000, -1819466995500, -641852788500, -198921318750, -350101521000, 1448147200500, 1100697963750, -1230659892000, 1217398470750, 1896383238750, -1896383238750, 1055609131500, -503934007500, 371319795000, 840774107250, -551675124000, 132614212500, 129961928250, 13261421250, -289098983250, 289098983250, -145875633750, -143223349500, 143223349500], ![111369415657500, -111369415657500, 50800084335000, -229864635000, -16722652196250, 11665630226250, -3333037207500, 610025377500, -1564847707500, 60569331322500, -50570219700000, 16952516831250, 5057021970000, -8332593018750, 2723011830000, 954822330000, 23618591246250, -17814509212500, 4137563430000, 3222525363750, -2457783405000, -689593905000, 8619923812500, -5835025350000, 402263111250, 1662098130000, 3067808782500, -1613472918750, -592343482500, 968083751250, -9999111622500, 9999111622500, -4195029588750, -861992381250, 2387055825000, -1220050755000, -265228425000, -5804082033750, 5057021970000, -1525063443750, -1167005070000, 1485279180000, -2784898462500, 2364953456250, -450888322500, -1069754647500, -1454335863750, 1237732650000, -968083751250, 747060063750, -747060063750, 327115057500, 132614212500, -415524532500, 419945006250, -459729270000, 282910320000, 216603213750, -269648898750, 39784263750, -39784263750, -13261421250, 53045685000, -53045685000], ![-267286597578000, 267286597578000, -148492554210000, 52868866050000, -13562013465000, 7187100921000, -6727371651000, 2068781715000, 3218104890000, -118794043368000, 95623688160000, -39306852585000, 6374912544000, -459729270000, 4658589936000, -5286886605000, -33146480367000, 21454032600000, -3999644649000, -2896294401000, 306486180000, 3999644649000, -7892019135000, 3677834160000, 1609052445000, -2697078384000, -2145403260000, 536350815000, 1517106591000, -827512686000, 23170355208000, -23170355208000, 11477907441000, -1915538625000, -1302566265000, 321810489000, 1287241956000, 11692447767000, -9562368816000, 3218104890000, 980755776000, -1609052445000, 4214184975000, -3141483345000, 551675124000, 1179971793000, 1609052445000, -1225944720000, 827512686000, -2130078951000, 2130078951000, -1057377321000, 76621545000, 429080652000, -1072701630000, 980755776000, -505702197000, -383107725000, 398432034000, 91945854000, -91945854000, 107270163000, -15324309000, 15324309000], ![-445477662630000, 445477662630000, -281354313240000, 126885278520000, -26549365342500, -18504103117500, 21147546420000, -2758375620000, -13791878100000, -164123349390000, 154469034720000, -100335913177500, 45053468460000, -2643443302500, -18389170800000, 16550253720000, -44478806872500, 45053468460000, -33100507440000, 15975592132500, 1379187810000, -12412690290000, -11033502480000, 12872419560000, -11838028702500, 7355668320000, -1838917080000, 3103172572500, -4597292700000, 574661587500, 9654314670000, -9654314670000, 10228976257500, -9309517717500, 5057021970000, 459729270000, -4137563430000, -574661587500, -919458540000, 4252495747500, -5516751240000, 3677834160000, -1838917080000, 804526222500, 1379187810000, -2758375620000, -1264255492500, 919458540000, -574661587500, 1494120127500, -1494120127500, 459729270000, 459729270000, -919458540000, 1034390857500, -919458540000, 459729270000, 344796952500, -344796952500, -114932317500, 114932317500, -114932317500, 0, 0], ![1425528520416000, -1425528520416000, 725268896352000, -125046361440000, -156307951800000, 189653648184000, -97952983128000, -18756954216000, 93784771080000, 700259624064000, -600222534912000, 281354313240000, -33345696384000, -91700665056000, 116709937344000, -75027816864000, 218831132520000, -183401330112000, 93784771080000, -18756954216000, -31261590360000, 56270862648000, 56270862648000, -50018544576000, 33345696384000, -16672848192000, 10420530120000, -10420530120000, 10420530120000, 0, -100037089152000, 100037089152000, -64607286744000, 31261590360000, -6252318072000, -10420530120000, 18756954216000, -35429802408000, 33345696384000, -25009272288000, 16672848192000, -8336424096000, -6252318072000, 6252318072000, -6252318072000, 6252318072000, 0, 0, 0, 2084106024000, -2084106024000, 2084106024000, -2084106024000, 2084106024000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11760610293432000, -11760610293432000, 8790759209232000, -5939702168400000, 3563821301040000, -1663116607152000, 237588086736000, 712764260208000, -1187940433680000, 2969851084200000, -2851057040832000, 2375880867360000, -1900704693888000, 1425528520416000, -950352346944000, 475176173472000, 356382130104000, -356382130104000, 356382130104000, -356382130104000, 356382130104000, -356382130104000, 0, 0, 0, 0, 0, 0, 0, 0, -118794043368000, 118794043368000, -118794043368000, 118794043368000, -118794043368000, 118794043368000, -118794043368000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![49893498214560000, -49893498214560000, 49893498214560000, -49893498214560000, 49893498214560000, -49893498214560000, 49893498214560000, -49893498214560000, 49893498214560000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Y : Matrix (Fin 11) (Fin 11) ℚ := ![![(-1461811305218600588339055969/262144000000000), (599127581039968177728978447/1310720000000000), (8184921909258845821897827/65536000000000), (-65607368042422177522469919/262144000000000), (443538138316115794788837/1310720000000), (-15688266120401398555900869/32768000000000), (29305002686410969905227841/40960000000000), (-15406789942389489384161421/16384000000000), 0, 0, 0], ![(599127581039968177728978447/1310720000000000), (-204198780631062080088954729/6553600000000000), (-995278748784101690181273/65536000000000), (32565598676971748984116521/1310720000000000), (-5293148434760008837857843/163840000000000), (7365523373995339204759107/163840000000000), (-13632519785777633825731647/204800000000000), (1425081450305314278107631/16384000000000), 0, 0, 0], ![(8184921909258845821897827/65536000000000), (-995278748784101690181273/65536000000000), (17770487280230710912887/16384000000000), (144749204505613278199629/65536000000000), (-32732592461383339964439/8192000000000), (51149329532101630436607/8192000000000), (-4019372737051817652507/409600000000), (54465545131237940378679/4096000000000), 0, 0, 0], ![(-65607368042422177522469919/262144000000000), (32565598676971748984116521/1310720000000000), (144749204505613278199629/65536000000000), (-2165425638926863552440201/262144000000000), (394922287978743572546499/32768000000000), (-575681600679006134412099/32768000000000), (1092636874881165894623343/40960000000000), (-580171568525424112183947/16384000000000), 0, 0, 0], ![(443538138316115794788837/1310720000000), (-5293148434760008837857843/163840000000000), (-32732592461383339964439/8192000000000), (394922287978743572546499/32768000000000), (-70562821339871804028393/4096000000000), (20413478883621925670877/819200000000), (-192937286383612987204989/5120000000000), (102190239403314695289657/2048000000000), 0, 0, 0], ![(-15688266120401398555900869/32768000000000), (7365523373995339204759107/163840000000000), (51149329532101630436607/8192000000000), (-575681600679006134412099/32768000000000), (20413478883621925670877/819200000000), (-147199245911921946711969/4096000000000), (277811585141616160656021/5120000000000), (-147000873128290742121561/2048000000000), 0, 0, 0], ![(29305002686410969905227841/40960000000000), (-13632519785777633825731647/204800000000000), (-4019372737051817652507/409600000000), (1092636874881165894623343/40960000000000), (-192937286383612987204989/5120000000000), (277811585141616160656021/5120000000000), (-523879610077227927043521/6400000000000), (55412213090943739031001/512000000000), 0, 0, 0], ![(-15406789942389489384161421/16384000000000), (1425081450305314278107631/16384000000000), (54465545131237940378679/4096000000000), (-580171568525424112183947/16384000000000), (102190239403314695289657/2048000000000), (-147000873128290742121561/2048000000000), (55412213090943739031001/512000000000), (-146480372738912231676657/1024000000000), 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Z : Matrix (Fin 11) (Fin 11) ℚ := ![![4865804016353280000, 0, 0, 0, 0, 0, 0, 0, 0, -9503523469440000, 898082967862080000], ![0, 38414242234368000, 0, 0, 0, 0, 0, 0, -300111267456000, 0, 349254487501920000], ![0, 0, 2510734786560000, 0, 0, 0, 0, -29422673280000, -583549686720000, 7127642602080000, 124733745536400000], ![0, 0, 0, 439378587648000, 0, 0, -6865290432000, -154469034720000, 0, 6652466428608000, 37420123660920000], ![0, 0, 0, 0, 173820100608000, -3394923840000, -66201014880000, -154469034720000, 525194718048000, 3207439170936000, 6236687276820000], ![0, 0, 0, 0, -3394923840000, 95057867520000, -121368527280000, 0, 343877493960000, 0, -3118343638410000], ![0, 0, 0, -6865290432000, -66201014880000, -121368527280000, 198480450168000, 0, -447040742148000, -1930403204730000, -4677515457615000], ![0, 0, -29422673280000, -154469034720000, -154469034720000, 0, 0, 481336545690000, -1422402361380000, -2672865975780000, -3897929548012500], ![0, -300111267456000, -583549686720000, 0, 525194718048000, 343877493960000, -447040742148000, -1422402361380000, 6322135623804000, -2650592092648500, -2728550683608750], ![-9503523469440000, 0, 7127642602080000, 6652466428608000, 3207439170936000, 0, -1930403204730000, -2672865975780000, -2650592092648500, 241033113993672000, -1754068296605625], ![898082967862080000, 349254487501920000, 124733745536400000, 37420123660920000, 6236687276820000, -3118343638410000, -4677515457615000, -3897929548012500, -2728550683608750, -1754068296605625, (102179740482167473125/2)]] +def W : Matrix (Fin 11) (Fin 11) ℚ := ![![(85899659111772484353589/21474836480000000000000), (-255532992890243211/10737418240000000000000), (-534113604029966103/5368709120000000000000), (611608728910220613/536870912000000000000), (-41807183592418101/10737418240000000000), (4436251352132053311/671088640000000000000), (-1912321311610916349/335544320000000000000), (335127453215878323/167772160000000000000), 0, (-1/5120000), (9/102400000)], ![(-40347314666880507/214748364800000000000000), (623963423195395277/107374182400000000000000), (64947708166423797/10737418240000000000000), (-303584871750141267/5368709120000000000000), (498923563222909539/2684354560000000000000), (-2082786764087033433/6710886400000000000000), (889600946168446083/3355443200000000000000), (-30998275361177553/335544320000000000000), (-9/51200000), 0, (7/204800000)], ![(-5447152932804297/85899345920000000000000), (800753583548919/1717986918400000000000), (101651356456552387/21474836480000000000000), (-16203622293091233/2147483648000000000000), (34314853233998337/1073741824000000000000), (-157278252524716323/2684354560000000000000), (14107463023162509/268435456000000000000), (-12768935608102807/671088640000000000000), (-7/20480000), (3/20480000), (1/81920000)], ![(40800591080049801/858993459200000000000000), (-138590480455438011/429496729600000000000000), (-5053905989683551/42949672960000000000000), (262811016154383181/21474836480000000000000), (-302450490859293777/10737418240000000000000), (1348392443892613119/26843545600000000000000), (-598312813069114969/13421772800000000000000), (20141608404972159/1342177280000000000000), 0, (7/51200000), (3/819200000)], ![(-44521994825077671/343597383680000000000000), (134522616594392829/171798691840000000000000), (127826191760274117/85899345920000000000000), (-219740077767908907/8589934592000000000000), (16733850457162391/171798691840000000000), (-1723266607590631929/10737418240000000000000), (744056231311361511/5368709120000000000000), (-134811361956073197/2684354560000000000000), (63/204800000), (27/409600000), (1/1638400000)], ![(94150617033009339/343597383680000000000000), (-278669244238773993/171798691840000000000000), (-305147492260552161/85899345920000000000000), (482100905745808767/8589934592000000000000), (-862905411138100147/4294967296000000000000), (3763845320791174581/10737418240000000000000), (-1636232258722682907/5368709120000000000000), (286234457959282041/2684354560000000000000), (33/163840000), 0, (-1/3276800000)], ![(-148603673413094757/429496729600000000000000), (438132239666173767/214748364800000000000000), (98376740735589459/21474836480000000000000), (-766893569584805297/10737418240000000000000), (1357924567010294829/5368709120000000000000), (-5966954859707353083/13421772800000000000000), (2598860827461273893/6710886400000000000000), (-18139592032495791/134217728000000000000), (-429/1638400000), (-13/327680000), (-3/6553600000)], ![(49072703952177477/171798691840000000000000), (-28899875654469963/17179869184000000000000), (-166047095761628127/42949672960000000000000), (245969973313435233/4294967296000000000000), (-462071311506327757/2147483648000000000000), (1954616457897660843/5368709120000000000000), (-170109673738422561/536870912000000000000), (153367655040715047/1342177280000000000000), (-273/327680000), (-9/163840000), (-1/2621440000)], ![0, (-1/25600000), (-119/102400000), 0, (1547/102400000), (2431/204800000), (-7293/819200000), (-1547/204800000), (6067/1638400000), (-357/6553600000), (-7/26214400000)], ![(-400001/51200000), 0, (2907/204800000), (969/12800000), (37791/409600000), 0, (-12597/327680000), (-2907/204800000), (-20349/13107200000), (2029/409600000), (-9/52428800000)], ![(75600189/102400000), (931/20480000), (20349/81920000), (8721/20480000), (29393/163840000), (-88179/819200000), (-61047/655360000), (-6783/327680000), (-8379/5242880000), (-189/5242880000), (524277/104857600000)]] +def M : Matrix (Fin 11) (Fin 11) ℚ := ![![(1275545984022142603500581939055969/65536000000000), (-579010522559857585728978447/655360000000000), (-78377235020528095959344037/262144000000000), (611073931955462424449221221/2621440000000000), (-661200583452794514442804491/1048576000000000), (1397779173818192997489376719/1048576000000000), (-2206698569570217260768927697/1310720000000000), (728787200067346981096352817/524288000000000), (22763908560393/81920), (-6228252449823281999121/163840), (1177139721974977902258117/327680)], ![(-579010522559857585728978447/655360000000000), (1541535403547372096088954729/6553600000000000), (2335264019943706199911563/104857600000000), (-291413481284327380069138047/26214400000000000), (316671509875399731383964633/10485760000000000), (-655124731306123910834063061/10485760000000000), (1026187749941392530939906459/13107200000000000), (-67636730154124472867276751/1048576000000000), (-2216042700468597/819200), (665142698072853/1638400), (2289164527085318883/655360)], ![(-78377235020528095959344037/262144000000000), (2335264019943706199911563/104857600000000), (15949461771719697779310753/1048576000000000), (291208644676133143066107/419430400000000), (23405507256001335841218843/4194304000000000), (-51221073506080768849557999/4194304000000000), (16033932561040877672121933/1048576000000000), (-27308529452929764973446513/2097152000000000), (-1729482618867003/327680), (47348439780188547/655360), (327315380833886445/262144)], ![(611073931955462424449221221/2621440000000000), (-291413481284327380069138047/26214400000000000), (291208644676133143066107/419430400000000), (462598471642402634832664371/104857600000000000), (-166610074101558728231559969/41943040000000000), (430731946168722549900521973/41943040000000000), (-704887980518067515465483187/52428800000000000), (39039222175487602398993663/4194304000000000), (2803483934161911/3276800), (450010561189069881/6553600), (198073134065073267/524288)], ![(-661200583452794514442804491/1048576000000000), (316671509875399731383964633/10485760000000000), (23405507256001335841218843/4194304000000000), (-166610074101558728231559969/41943040000000000), (275735607076142030380107699/16777216000000000), (-541961414382434242566853791/16777216000000000), (848215554758572380229482633/20971520000000000), (-301382274258447514734114513/8388608000000000), (40044205143403461/6553600), (469850146482383667/13107200), (372982899749673213/5242880)], ![(1397779173818192997489376719/1048576000000000), (-655124731306123910834063061/10485760000000000), (-51221073506080768849557999/4194304000000000), (430731946168722549900521973/41943040000000000), (-541961414382434242566853791/16777216000000000), (1192242144102930222317691291/16777216000000000), (-1891812978425370136604569101/20971520000000000), (616642656986130467052308949/8388608000000000), (1799233479278235/524288), (20023641814257081/5242880), (-164380678389508581/10485760)], ![(-2206698569570217260768927697/1310720000000000), (1026187749941392530939906459/13107200000000000), (16033932561040877672121933/1048576000000000), (-704887980518067515465483187/52428800000000000), (848215554758572380229482633/20971520000000000), (-1891812978425370136604569101/20971520000000000), (3008428878337623032102549739/26214400000000000), (-194500701194562020732472999/2097152000000000), (-150910076297259279/26214400), (-242487999492055317/10485760), (-898155001600127271/20971520)], ![(728787200067346981096352817/524288000000000), (-67636730154124472867276751/1048576000000000), (-27308529452929764973446513/2097152000000000), (39039222175487602398993663/4194304000000000), (-301382274258447514734114513/8388608000000000), (616642656986130467052308949/8388608000000000), (-194500701194562020732472999/2097152000000000), (339063106326056838526123323/4194304000000000), (-115928795909763837/10485760), (-927504673733777139/20971520), (-1072746696233609397/8388608)], ![(22763908560393/81920), (-2216042700468597/819200), (-1729482618867003/327680), (2803483934161911/3276800), (40044205143403461/6553600), (1799233479278235/524288), (-150910076297259279/26214400), (-115928795909763837/10485760), (5346302636320747101/104857600), (11451286151672153787/209715200), (-4526221843807170507/83886080)], ![(-6228252449823281999121/163840), (665142698072853/1638400), (47348439780188547/655360), (450010561189069881/6553600), (469850146482383667/13107200), (20023641814257081/5242880), (-242487999492055317/10485760), (-927504673733777139/20971520), (11451286151672153787/209715200), (6413713766637780155553/83886080), (-1176232167936397119745197/167772160)], ![(1177139721974977902258117/327680), (2289164527085318883/655360), (327315380833886445/262144), (198073134065073267/524288), (372982899749673213/5242880), (-164380678389508581/10485760), (-898155001600127271/20971520), (-1072746696233609397/8388608), (-4526221843807170507/83886080), (-1176232167936397119745197/167772160), (222586575557047769527789329/335544320)]] +def L : Matrix (Fin 11) (Fin 11) ℚ := ![![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![(-12997520888960169/286332198227764281178630), 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![(-159945240388009/10412079935555064770132), (445608642725699131206117881131723360335/4706426644791988689924012155339531967598), 1, 0, 0, 0, 0, 0, 0, 0, 0], ![(41151823080049801/3435986378733171374143560), (-889707169980810394870206521365926060039/18825706579167954759696048621358127870392), (686703169094283460155211943679742299851722137/5150589187740445131178089056470478445058681676), 1, 0, 0, 0, 0, 0, 0, 0], ![(-14842508141692557/458131517164422849885808), (4834109128533174739654136711995519404875/37651413158335909519392097242716255740784), (2139275756021335841020781867145166975385385369/10301178375480890262356178112940956890117363352), (-7148433203298873948077615999831963851701231978554739/8981459648826981998081544513078630167662575723791522), 1, 0, 0, 0, 0, 0, 0], ![(31377087811003113/458131517164422849885808), (-10000724029683038876766185919793968776395/37651413158335909519392097242716255740784), (-4950592062736924845133220375439356189669648631/10301178375480890262356178112940956890117363352), (40102123020939936572972438196336556984101914108958525/17962919297653963996163089026157260335325151447583044), (-102061822017204900577595657834207477441586015756075274735205/59928947832031623802734919218267593374561305190591247818492), 1, 0, 0, 0, 0, 0], ![(-148606681413094757/1717993189366585687071780), (3133027932310805972170290210412802096253/9412853289583977379848024310679063935196), (12388464214355932382166896596091941612884865785/20602356750961780524712356225881913780234726704), (-15164581743575890737143579516188866702538979387057579/5132262656472561141760882578902074381521471842166584), (249741499458035261862109798900248340547358476808764454991923/119857895664063247605469838436535186749122610381182495636984), (-15981498582966364774792742684306606361455601845147056979149969163/11486093924406066922525284830347669840561187276770950391786732106), 1, 0, 0, 0, 0], ![(1487243634914469/20824159871110129540264), (-5162499854212699897927101159955330157245/18825706579167954759696048621358127870392), (-2718184978176725728478413020781980953303176413/5150589187740445131178089056470478445058681676), (141230405524405055821804420975266517284711838248852045/71851677190615855984652356104629041341300605790332176), (-507614801587691851528439764355130225531243553978388651347765/239715791328126495210939676873070373498245220762364991273968), (725200974801401397221268842868201723278970830561942695514265715/1767091372985548757311582281591949206240182657964761598736420324), (-264475508500188064109814644617414480716467077480637717996569067487465/59108778169735044542392210936763588819709226558995175035885133837348), 1, 0, 0, 0], ![(408800000000/28633219822776428117863), (-27063002554722261265393230122000000000/2353213322395994344962006077669765983799), (-31586611680206108432219839201749580721036801895/82409427003847122098849424903527655120938906816), (54959316589216461232330778330559448782666878980542495/143703354381231711969304712209258082682601211580664352), (426639411312318663884786839482909008400225063831859675874153/479431582656252990421879353746140746996490441524729982547936), (316309411536548680033867283379379893450524551578953851991324920589/137833127092872803070303417964172038086734247321251404701440785272), (1772695572319745018320584405232050096344160612276046798073131067644545/118217556339470089084784421873527177639418453117990350071770267674696), (-119/10), 1, 0, 0], ![(-55924262626800000000/28633219822776428117863), (-13201858578521966874947940015000000000/2353213322395994344962006077669765983799), (14110685134862852904199579133292677203121918697/2575294593870222565589044528235239222529340838), (4679784570620594880725207855775880202735959333406241465/287406708762463423938609424418516165365202423161328704), (6660025200417851188840483634377340366102158119087361087670841/958863165312505980843758707492281493992980883049459965095872), (396015956143527218132462366645732934409364454557615259923054702019/91888751395248535380202278642781358724489498214167603134293856848), (-10575045525826195069501103386254985172808357508076957718773519116236621/236435112678940178169568843747054355278836906235980700143540535349392), (2907/20), 0, 1, 0], ![(5284842858451800000000/28633219822776428117863), (36576370528821089502135593194883500000000/2353213322395994344962006077669765983799), (24093508380610236861852433890384610274856574839801/329637708015388488395397699614110620483755627264), (8538380288241609440669524914697786199904673268114655165/82116202503560978268174121262433190104343549474665344), (-35350503667144638030125757031572398917325528689619290231083625/1917726330625011961687517414984562987985961766098919930191744), (629993465762894779884577019428889035016586910118856603948528365997/183777502790497070760404557285562717448978996428335206268587713696), (-51347081535659966164179580441904903192991951611617920185559489584082915/472870225357880356339137687494108710557673812471961400287081070698784), (-33915/8), 0, 0, 1]] +def diag : Fin 11 → ℚ := ![(1275545984022142603500581939055969/65536000000000), (501580847143896742616446116572335687790364099393/2132393970801677264923033600000000000), (19732305061248398246929642682718015267479690283915471/1506056526333436380775683889708650229631360), (481721320253796558866136483604850144950940913445479771479043/131855083206155395358159079845644248193502250905600), (158948604453969121313918933167633450192753300416448414776833190351/16423240500712195653634824252486638020868709894933068800), (792074036252795449479554362739671215300331652562479547123349252016541393/153418106450000956935001393198765039038876941287913594415339520), (156773281376332085312835318390255812599990871182104598573671325285940162169/2827346196776878011698531650547118729984292252743618557978272518400), (91234705086689778255128612076721886263624381415513776892660761548288562383417/11004979790147033747529022545317439082069499635711101679408432190808064), 0, 0, 0] + +def keyIndexTable : Fin 22 → Fin 13 → Fin 13 → Fin 64 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 9, 10, 11, 12, 13, 14, 15, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 9, 0, 16, 17, 18, 19, 20, 21, 0, 0, 0], ![0, 0, 0, 30, 31, 32, 33, 34, 35, 36, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 10, 16, 0, 22, 23, 24, 25, 0, 0, 0, 0], ![1, 0, 30, 0, 37, 38, 39, 40, 41, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 11, 17, 22, 0, 26, 27, 28, 0, 0, 0, 0], ![2, 0, 31, 37, 0, 42, 43, 44, 45, 0, 0, 0, 0], ![9, 30, 0, 0, 49, 50, 51, 52, 53, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 12, 18, 23, 26, 0, 29, 0, 0, 0, 0, 0], ![3, 0, 32, 38, 42, 0, 46, 47, 0, 0, 0, 0, 0], ![10, 31, 0, 49, 0, 54, 55, 56, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 13, 19, 24, 27, 29, 0, 0, 0, 0, 0, 0], ![4, 0, 33, 39, 43, 46, 0, 48, 0, 0, 0, 0, 0], ![11, 32, 0, 50, 54, 0, 57, 58, 0, 0, 0, 0, 0], ![16, 37, 49, 0, 0, 59, 60, 61, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 14, 20, 25, 28, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 34, 40, 44, 47, 48, 0, 0, 0, 0, 0, 0], ![12, 33, 0, 51, 55, 57, 0, 0, 0, 0, 0, 0, 0], ![17, 38, 50, 0, 59, 0, 62, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 7, 15, 21, 0, 28, 29, 0, 0, 0, 0, 0, 0], ![6, 0, 35, 41, 45, 0, 48, 0, 0, 0, 0, 0, 0], ![13, 34, 0, 52, 56, 58, 0, 0, 0, 0, 0, 0, 0], ![18, 39, 51, 0, 60, 62, 0, 0, 0, 0, 0, 0, 0], ![22, 42, 54, 59, 0, 0, 63, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 8, 0, 21, 25, 27, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 36, 0, 45, 47, 0, 0, 0, 0, 0, 0, 0], ![14, 35, 0, 53, 0, 58, 0, 0, 0, 0, 0, 0, 0], ![19, 40, 52, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 43, 55, 60, 0, 63, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 8, 15, 20, 24, 26, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 36, 41, 44, 46, 0, 0, 0, 0, 0, 0, 0], ![15, 36, 0, 53, 56, 57, 0, 0, 0, 0, 0, 0, 0], ![20, 41, 53, 0, 61, 62, 0, 0, 0, 0, 0, 0, 0], ![24, 44, 56, 61, 0, 63, 0, 0, 0, 0, 0, 0, 0], ![26, 46, 57, 62, 63, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 7, 14, 19, 23, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 35, 40, 43, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 36, 0, 52, 55, 0, 0, 0, 0, 0, 0, 0, 0], ![21, 0, 53, 0, 60, 0, 0, 0, 0, 0, 0, 0, 0], ![25, 45, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![27, 47, 58, 0, 63, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 13, 18, 22, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 34, 39, 42, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 35, 0, 51, 54, 0, 0, 0, 0, 0, 0, 0, 0], ![21, 41, 52, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 45, 56, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![28, 0, 58, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![29, 48, 0, 0, 63, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 12, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 33, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 34, 0, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 40, 51, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![25, 44, 55, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![28, 47, 57, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 48, 0, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 11, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 32, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 33, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 39, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![24, 43, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![27, 46, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![29, 0, 57, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 48, 58, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 38, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![26, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 46, 55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![29, 47, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![22, 0, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 42, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![26, 43, 51, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![27, 44, 52, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![28, 45, 53, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![22, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![24, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![25, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 31, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 32, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![21, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 22) (j : Fin ((n.val+1)/2)) (x : Fin ((21-n.val+2)/2)) : Fin 64 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 64 → FourTerm 21 := ![⟨⟨21,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨10,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨9,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨13,by decide⟩,(⟨6,by decide⟩,⟨4,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 11, + (fourTermLabels (by omega : 21 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 11, + (fourTermLabels (by omega : 21 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 10, + (fourTermLabels (by omega : 21 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 10, + (fourTermLabels (by omega : 21 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 9, + (fourTermLabels (by omega : 21 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 9, + (fourTermLabels (by omega : 21 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 8, + (fourTermLabels (by omega : 21 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 8, + (fourTermLabels (by omega : 21 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 7, + (fourTermLabels (by omega : 21 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 7, + (fourTermLabels (by omega : 21 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 6, + (fourTermLabels (by omega : 21 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 6, + (fourTermLabels (by omega : 21 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover_12 : ∀ j : Fin 6, ∀ x : Fin 5, + (fourTermLabels (by omega : 21 ≤ 23) ⟨12,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨12,j,x⟩).toFinset=keys (keyIndex 12 j x) := by decide +kernel +lemma cover_13 : ∀ j : Fin 7, ∀ x : Fin 5, + (fourTermLabels (by omega : 21 ≤ 23) ⟨13,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨13,j,x⟩).toFinset=keys (keyIndex 13 j x) := by decide +kernel +lemma cover_14 : ∀ j : Fin 7, ∀ x : Fin 4, + (fourTermLabels (by omega : 21 ≤ 23) ⟨14,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨14,j,x⟩).toFinset=keys (keyIndex 14 j x) := by decide +kernel +lemma cover_15 : ∀ j : Fin 8, ∀ x : Fin 4, + (fourTermLabels (by omega : 21 ≤ 23) ⟨15,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨15,j,x⟩).toFinset=keys (keyIndex 15 j x) := by decide +kernel +lemma cover_16 : ∀ j : Fin 8, ∀ x : Fin 3, + (fourTermLabels (by omega : 21 ≤ 23) ⟨16,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨16,j,x⟩).toFinset=keys (keyIndex 16 j x) := by decide +kernel +lemma cover_17 : ∀ j : Fin 9, ∀ x : Fin 3, + (fourTermLabels (by omega : 21 ≤ 23) ⟨17,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨17,j,x⟩).toFinset=keys (keyIndex 17 j x) := by decide +kernel +lemma cover_18 : ∀ j : Fin 9, ∀ x : Fin 2, + (fourTermLabels (by omega : 21 ≤ 23) ⟨18,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨18,j,x⟩).toFinset=keys (keyIndex 18 j x) := by decide +kernel +lemma cover_19 : ∀ j : Fin 10, ∀ x : Fin 2, + (fourTermLabels (by omega : 21 ≤ 23) ⟨19,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨19,j,x⟩).toFinset=keys (keyIndex 19 j x) := by decide +kernel +lemma cover_20 : ∀ j : Fin 10, ∀ x : Fin 1, + (fourTermLabels (by omega : 21 ≤ 23) ⟨20,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨20,j,x⟩).toFinset=keys (keyIndex 20 j x) := by decide +kernel +lemma cover_21 : ∀ j : Fin 11, ∀ x : Fin 1, + (fourTermLabels (by omega : 21 ≤ 23) ⟨21,j,x⟩).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) ⟨21,j,x⟩).toFinset=keys (keyIndex 21 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 21, (fourTermLabels (by omega : 21 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 21 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x + · exact cover_12 j x + · exact cover_13 j x + · exact cover_14 j x + · exact cover_15 j x + · exact cover_16 j x + · exact cover_17 j x + · exact cover_18 j x + · exact cover_19 j x + · exact cover_20 j x + · exact cover_21 j x +lemma representatives_checked : ∀ a : Fin 64, + (fourTermLabels (by omega : 21 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 21 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 21 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 21 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 64, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 21, + (fourTermLabels (by omega : 21 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 64, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 21 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 64, ∀ b : FourTerm 21, + (fourTermLabels (by omega : 21 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 21 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 64, (∑ b ∈ fibers v, fourTermEval 21 (2*(0 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 21 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 64, (∑ b ∈ fibers v, fourTermEval 21 (2*(1 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 21 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 64, (∑ b ∈ fibers v, fourTermEval 21 (2*(2 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 21 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 64, (∑ b ∈ fibers v, fourTermEval 21 (2*(3 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 21 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 64, (∑ b ∈ fibers v, fourTermEval 21 (2*(4 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 21 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 64, (∑ b ∈ fibers v, fourTermEval 21 (2*(5 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 21 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_6 : ∀ v : Fin 64, (∑ b ∈ fibers v, fourTermEval 21 (2*(6 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 21 ≤ 23) b)) = columns 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_7 : ∀ v : Fin 64, (∑ b ∈ fibers v, fourTermEval 21 (2*(7 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 21 ≤ 23) b)) = columns 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_8 : ∀ v : Fin 64, (∑ b ∈ fibers v, fourTermEval 21 (2*(8 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 21 ≤ 23) b)) = columns 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_9 : ∀ v : Fin 64, (∑ b ∈ fibers v, fourTermEval 21 (2*(9 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 21 ≤ 23) b)) = columns 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_10 : ∀ v : Fin 64, (∑ b ∈ fibers v, fourTermEval 21 (2*(10 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 21 ≤ 23) b)) = columns 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 11, ∀ v : Fin 64, (∑ b ∈ fibers v, fourTermEval 21 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 21 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 + · exact columns_checked_6 + · exact columns_checked_7 + · exact columns_checked_8 + · exact columns_checked_9 + · exact columns_checked_10 +lemma gram_checked_0 : ∀ v : Fin 11, (∑ a : Fin 64, columns (0 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 11, (∑ a : Fin 64, columns (1 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 11, (∑ a : Fin 64, columns (2 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 11, (∑ a : Fin 64, columns (3 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 11, (∑ a : Fin 64, columns (4 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 11, (∑ a : Fin 64, columns (5 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_6 : ∀ v : Fin 11, (∑ a : Fin 64, columns (6 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_7 : ∀ v : Fin 11, (∑ a : Fin 64, columns (7 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_8 : ∀ v : Fin 11, (∑ a : Fin 64, columns (8 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_9 : ∀ v : Fin 11, (∑ a : Fin 64, columns (9 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_10 : ∀ v : Fin 11, (∑ a : Fin 64, columns (10 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 11, ∀ v : Fin 11, (∑ a : Fin 64, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 + · exact gram_checked_6 + · exact gram_checked_7 + · exact gram_checked_8 + · exact gram_checked_9 + · exact gram_checked_10 +lemma rows_table_checked_0 : ∀ v : Fin 11, integerTableEval 21 SumTable21.sums (0 : Fin 11) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 11, integerTableEval 21 SumTable21.sums (1 : Fin 11) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 11, integerTableEval 21 SumTable21.sums (2 : Fin 11) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 11, integerTableEval 21 SumTable21.sums (3 : Fin 11) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 11, integerTableEval 21 SumTable21.sums (4 : Fin 11) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 11, integerTableEval 21 SumTable21.sums (5 : Fin 11) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_6 : ∀ v : Fin 11, integerTableEval 21 SumTable21.sums (6 : Fin 11) v = Y 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_7 : ∀ v : Fin 11, integerTableEval 21 SumTable21.sums (7 : Fin 11) v = Y 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_8 : ∀ v : Fin 11, integerTableEval 21 SumTable21.sums (8 : Fin 11) v = Y 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_9 : ∀ v : Fin 11, integerTableEval 21 SumTable21.sums (9 : Fin 11) v = Y 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_10 : ∀ v : Fin 11, integerTableEval 21 SumTable21.sums (10 : Fin 11) v = Y 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 11, ∀ v : Fin 11, integerTableEval 21 SumTable21.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 + · exact rows_table_checked_6 + · exact rows_table_checked_7 + · exact rows_table_checked_8 + · exact rows_table_checked_9 + · exact rows_table_checked_10 +lemma rows_checked (u v : Fin 11) : exactFourEval 21 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 21 SumTable21.sums SumTable21.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 11, (Z * tableComparison 21 (1/200000) Y) (0 : Fin 11) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 11, (Z * tableComparison 21 (1/200000) Y) (1 : Fin 11) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 11, (Z * tableComparison 21 (1/200000) Y) (2 : Fin 11) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 11, (Z * tableComparison 21 (1/200000) Y) (3 : Fin 11) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 11, (Z * tableComparison 21 (1/200000) Y) (4 : Fin 11) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 11, (Z * tableComparison 21 (1/200000) Y) (5 : Fin 11) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_6 : ∀ v : Fin 11, (Z * tableComparison 21 (1/200000) Y) (6 : Fin 11) v = W 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_7 : ∀ v : Fin 11, (Z * tableComparison 21 (1/200000) Y) (7 : Fin 11) v = W 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_8 : ∀ v : Fin 11, (Z * tableComparison 21 (1/200000) Y) (8 : Fin 11) v = W 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_9 : ∀ v : Fin 11, (Z * tableComparison 21 (1/200000) Y) (9 : Fin 11) v = W 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_10 : ∀ v : Fin 11, (Z * tableComparison 21 (1/200000) Y) (10 : Fin 11) v = W 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 11, ∀ v : Fin 11, (Z * tableComparison 21 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 + · exact product_checked_6 + · exact product_checked_7 + · exact product_checked_8 + · exact product_checked_9 + · exact product_checked_10 +lemma compression_checked_0 : ∀ v : Fin 11, (W * Z) (0 : Fin 11) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 11, (W * Z) (1 : Fin 11) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 11, (W * Z) (2 : Fin 11) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 11, (W * Z) (3 : Fin 11) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 11, (W * Z) (4 : Fin 11) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 11, (W * Z) (5 : Fin 11) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_6 : ∀ v : Fin 11, (W * Z) (6 : Fin 11) v = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_7 : ∀ v : Fin 11, (W * Z) (7 : Fin 11) v = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_8 : ∀ v : Fin 11, (W * Z) (8 : Fin 11) v = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_9 : ∀ v : Fin 11, (W * Z) (9 : Fin 11) v = M 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_10 : ∀ v : Fin 11, (W * Z) (10 : Fin 11) v = M 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 11, ∀ v : Fin 11, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 + · exact compression_checked_6 + · exact compression_checked_7 + · exact compression_checked_8 + · exact compression_checked_9 + · exact compression_checked_10 +lemma ldl_checked_0 : ∀ v : Fin 11, (∑ k : Fin 11, L (0 : Fin 11) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 11, (∑ k : Fin 11, L (1 : Fin 11) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 11, (∑ k : Fin 11, L (2 : Fin 11) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 11, (∑ k : Fin 11, L (3 : Fin 11) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 11, (∑ k : Fin 11, L (4 : Fin 11) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 11, (∑ k : Fin 11, L (5 : Fin 11) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_6 : ∀ v : Fin 11, (∑ k : Fin 11, L (6 : Fin 11) k * diag k * L v k) = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_7 : ∀ v : Fin 11, (∑ k : Fin 11, L (7 : Fin 11) k * diag k * L v k) = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_8 : ∀ v : Fin 11, (∑ k : Fin 11, L (8 : Fin 11) k * diag k * L v k) = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_9 : ∀ v : Fin 11, (∑ k : Fin 11, L (9 : Fin 11) k * diag k * L v k) = M 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_10 : ∀ v : Fin 11, (∑ k : Fin 11, L (10 : Fin 11) k * diag k * L v k) = M 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 11, ∀ v : Fin 11, (∑ k : Fin 11, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 + · exact ldl_checked_6 + · exact ldl_checked_7 + · exact ldl_checked_8 + · exact ldl_checked_9 + · exact ldl_checked_10 +lemma diag_checked : ∀ u : Fin 11, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 21 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 21 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 21 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 21 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 21 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate21 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate22.lean b/lean/OAI/Analysis/LaughlinGap/Certificate22.lean new file mode 100644 index 0000000000000000000000000000000000000000..7646546e67c320b5494a360d5145ab479b537807 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate22.lean @@ -0,0 +1,457 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Certificate21 +import OAI.Analysis.LaughlinGap.SumTable22 + +namespace OAI + +/-! Certificate22. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate22 + +def keys : Fin 72 → Finset (Fin 25) := ![{0,1,2,20}, {0,1,3,19}, {0,1,4,18}, {0,1,5,17}, {0,1,6,16}, {0,1,7,15}, {0,1,8,14}, {0,1,9,13}, {0,1,10,12}, {0,2,3,18}, {0,2,4,17}, {0,2,5,16}, {0,2,6,15}, {0,2,7,14}, {0,2,8,13}, {0,2,9,12}, {0,2,10,11}, {0,3,4,16}, {0,3,5,15}, {0,3,6,14}, {0,3,7,13}, {0,3,8,12}, {0,3,9,11}, {0,4,5,14}, {0,4,6,13}, {0,4,7,12}, {0,4,8,11}, {0,4,9,10}, {0,5,6,12}, {0,5,7,11}, {0,5,8,10}, {0,6,7,10}, {0,6,8,9}, {1,2,3,17}, {1,2,4,16}, {1,2,5,15}, {1,2,6,14}, {1,2,7,13}, {1,2,8,12}, {1,2,9,11}, {1,3,4,15}, {1,3,5,14}, {1,3,6,13}, {1,3,7,12}, {1,3,8,11}, {1,3,9,10}, {1,4,5,13}, {1,4,6,12}, {1,4,7,11}, {1,4,8,10}, {1,5,6,11}, {1,5,7,10}, {1,5,8,9}, {1,6,7,9}, {2,3,4,14}, {2,3,5,13}, {2,3,6,12}, {2,3,7,11}, {2,3,8,10}, {2,4,5,12}, {2,4,6,11}, {2,4,7,10}, {2,4,8,9}, {2,5,6,10}, {2,5,7,9}, {2,6,7,8}, {3,4,5,11}, {3,4,6,10}, {3,4,7,9}, {3,5,6,9}, {3,5,7,8}, {4,5,6,8}] +def fibers : Fin 72 → Finset (FourTerm 22) := ![{⟨⟨22,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨21,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨20,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨20,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨9,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨10,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨10,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨20,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨9,by decide⟩)⟩}, {⟨⟨21,by decide⟩,(⟨10,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨10,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨9,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨19,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨4,by 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(-271326468538125/2), (175185584949375/2), (-45254600015625/2), (-1005657778125/2), 19107497784375, -41634232014375, -16895050672500, -4022631112500, (-6637341335625/2), 13274682671250, (38416127124375/2), (-31979917344375/2), -4022631112500, 12269024893125, 48070441794375, -48070441794375, 27152760009375, -15285998227500, 9252051558750, 20917681785000, -11866761781875, 6033946668750, -9252051558750, -3218104890000, (15487129783125/2), -12269024893125, -9050920003125, 9050920003125, (-9050920003125/2), (-9050920003125/2), (9050920003125/2), 0], ![-4232037794985000, 4232037794985000, -2829955467339000, 1641233493900000, -852338066580000, 354796064122500, -94612283766000, 8550964422000, 689593905000, -1402082327646000, 1188721973439000, -788895427320000, 497542002457500, -260183780356500, 86061319344000, -9240558327000, -689593905000, -186466191912000, 132229631283750, -122609796309000, 103542524835750, -49099086036000, 6551142097500, 34755532812000, -25101218142000, -11585177604000, 18205279092000, -3172131963000, 27583756200000, -13274682671250, -2758375620000, 7240736002500, -827512686000, 213360354207000, -213360354207000, 159123793578750, -114748425792000, 70579936176750, -27721674981000, 3379010134500, 54236560628250, -44375367786750, 44168489615250, -42858261195750, 24342664846500, -3379010134500, -9654314670000, 9102639546000, 6654581183250, -12274771509000, -14309073528750, 8792322288750, 3585888306000, -6413223316500, -9861192841500, 9861192841500, -10412867965500, 11861015166000, -8688883203000, 551675124000, -1448147200500, -3172131963000, 8688883203000, 5516751240000, -5964987278250, 6413223316500, 896472076500, -896472076500, 448236038250, 448236038250, -448236038250, 0], ![-2450127144465000, 2450127144465000, -1289540602350000, 343877493960000, 37927664775000, -79648096027500, 44248942237500, -30342131820000, 22464847597500, -1160586542115000, 945663108390000, -381805158735000, 41720431252500, 35399153790000, -13906810417500, 7877284222500, -22464847597500, -348934515930000, 237047904843750, -64477030117500, -5689149716250, -1750507605000, 13128807037500, -82176607012500, 41720431252500, -583502535000, -2139509295000, -11670050700000, -13420558305000, -437626901250, 7293781687500, 583502535000, -4959771547500, 214923433725000, -214923433725000, 103036822638750, -12642554925000, -15803193656250, 7780033800000, 1458756337500, 111886611086250, -90394267713750, 28445748581250, 8023159856250, -9238790137500, -1458756337500, 40456175760000, -27716370412500, 3160638731250, 6515778307500, 13858185206250, -7439657321250, -2334010140000, 4376269012500, -21492343372500, 21492343372500, -8752538025000, -1945008450000, 4181768167500, -12739805347500, 10697546475000, -2236759717500, -4181768167500, -6418527885000, 5397398448750, -4376269012500, 2042258872500, -2042258872500, 1021129436250, 1021129436250, -1021129436250, 0], ![1781910650520000, -1781910650520000, 1064457151758000, -515816240940000, 271699998570000, -164123349390000, 72407360025000, 4689238554000, -28273350105000, 717453498762000, -548640910818000, 244116242370000, -107576649180000, 91715989365000, -77096598579000, 23584111551000, 28273350105000, 135712080504000, -51719542875000, -6206345145000, -8413045641000, 41375634300000, -39720608928000, -4827157335000, 30480050601000, -27032081076000, -1655025372000, 27583756200000, -16550253720000, 24135786675000, -17239847625000, -8964720765000, 11998933947000, -168812587944000, 168812587944000, -84820050315000, 22067004960000, -6206345145000, 12136852728000, -12136852728000, -83992537629000, 62753045355000, -15860659815000, -5930507583000, 0, 12136852728000, -25652893266000, 13102284195000, 4551319773000, -8688883203000, -7585532955000, 2068781715000, 5240913678000, -3034213182000, 21239492274000, -21239492274000, 8688883203000, 1379187810000, -3447969525000, 12550609071000, -10068071013000, 2068781715000, 3447969525000, 5516751240000, -4275482211000, 3034213182000, -2482538058000, 2482538058000, -1241269029000, -1241269029000, 1241269029000, 0], ![6236687276820000, -6236687276820000, 3610713686580000, -1312986795120000, 135160405380000, 168950506725000, -67580202690000, -77234517360000, 96543146700000, 2625973590240000, -2297726891460000, 1177826389740000, -304110912105000, -101370304035000, 144814720050000, -19308629340000, -96543146700000, 791653802940000, -668561290897500, 318592384110000, -37812732457500, -93325041810000, 86888832030000, 231703552080000, -199522503180000, 93325041810000, 3218104890000, -57925888020000, 70798307580000, -65166624022500, 35399153790000, 20917681785000, -22526734230000, -328246698780000, 328246698780000, -205154186737500, 86888832030000, -5631683557500, -32181048900000, 28962944010000, -123092512042500, 118265354707500, -81257148472500, 37812732457500, 3218104890000, -28962944010000, -32181048900000, 35399153790000, -31376522677500, 19308629340000, -5631683557500, 8849788447500, -12872419560000, 1609052445000, 4827157335000, -4827157335000, 8045262225000, -9654314670000, 6436209780000, -3218104890000, 1609052445000, 3218104890000, -6436209780000, -3218104890000, 2413578667500, -1609052445000, 1609052445000, -1609052445000, 804526222500, 804526222500, -804526222500, 0], ![-3563821301040000, 3563821301040000, -750278168640000, -1375509975840000, 1688125879440000, -875324530080000, -72943710840000, 562708626480000, -468923855400000, -2813543132400000, 2125788144480000, -312615903600000, -812801349360000, 948268240920000, -489764915640000, -93784771080000, 468923855400000, -1125417252960000, 781539759000000, -93784771080000, -343877493960000, 437662265040000, -281354313240000, -385559614440000, 281354313240000, -62523180720000, -104205301200000, 187569542160000, -125046361440000, 104205301200000, -52102650600000, -31261590360000, 31261590360000, 687754987920000, -687754987920000, 343877493960000, -41682120480000, -114625831320000, 145887421680000, -93784771080000, 343877493960000, -302195373480000, 156307951800000, -31261590360000, -52102650600000, 93784771080000, 104205301200000, -93784771080000, 62523180720000, -31261590360000, 20841060240000, -20841060240000, 20841060240000, 0, -41682120480000, 41682120480000, -31261590360000, 20841060240000, -10420530120000, -10420530120000, 10420530120000, -10420530120000, 10420530120000, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![-81967889923920000, 81967889923920000, -54170083775808000, 28510570408320000, -10691463903120000, 0, 4989349821456000, -5702114081664000, 3563821301040000, -27797806148112000, 25659513367488000, -17819106505200000, 10691463903120000, -4989349821456000, 712764260208000, 2138292780624000, -3563821301040000, -5702114081664000, 5345731951560000, -4276585561248000, 3207439170936000, -2138292780624000, 1069146390312000, -712764260208000, 712764260208000, -712764260208000, 712764260208000, -712764260208000, 0, 0, 0, 0, 0, 2138292780624000, -2138292780624000, 1781910650520000, -1425528520416000, 1069146390312000, -712764260208000, 356382130104000, 356382130104000, -356382130104000, 356382130104000, -356382130104000, 356382130104000, -356382130104000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![-399147985716480000, 399147985716480000, -349254487501920000, 299360989287360000, -249467491072800000, 199573992858240000, -149680494643680000, 99786996429120000, -49893498214560000, -49893498214560000, 49893498214560000, -49893498214560000, 49893498214560000, -49893498214560000, 49893498214560000, -49893498214560000, 49893498214560000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Y : Matrix (Fin 11) (Fin 11) ℚ := ![![(-60063449024758068838097137989/131072000000000), (60063449024758068838097137989/655360000000000), (-1053744719732597698913984877/32768000000000), (433894884595775523082229067/26214400000000), (-185954950541046652749526743/16384000000000), (157346496611654860018830321/16384000000000), (-185954950541046652749526743/20480000000000), (61984983513682217583175581/8192000000000), 0, 0, 0], ![(60063449024758068838097137989/655360000000000), (-60063449024758068838097137989/3276800000000000), (1053744719732597698913984877/163840000000000), (-433894884595775523082229067/131072000000000), (185954950541046652749526743/81920000000000), (-157346496611654860018830321/81920000000000), (185954950541046652749526743/102400000000000), (-61984983513682217583175581/40960000000000), 0, 0, 0], ![(-1053744719732597698913984877/32768000000000), (1053744719732597698913984877/163840000000000), (-18486749468992942086210261/8192000000000), (7612190957820623211968931/6553600000000), (-3262367553351695662272399/4096000000000), (2760464852836050175768953/4096000000000), (-3262367553351695662272399/5120000000000), (1087455851117231887424133/2048000000000), 0, 0, 0], ![(433894884595775523082229067/26214400000000), (-433894884595775523082229067/131072000000000), (7612190957820623211968931/6553600000000), (-3134431570867315440222501/5242880000000), (1343327816085992331523929/3276800000000), (-1136661998226608895904863/3276800000000), (1343327816085992331523929/4096000000000), (-447775938695330777174643/1638400000000), 0, 0, 0], ![(-185954950541046652749526743/16384000000000), (185954950541046652749526743/81920000000000), (-3262367553351695662272399/4096000000000), (1343327816085992331523929/3276800000000), (-575711921179710999224541/2048000000000), (487140856382832383959227/2048000000000), (-575711921179710999224541/2560000000000), (191903973726570333074847/1024000000000), 0, 0, 0], ![(157346496611654860018830321/16384000000000), (-157346496611654860018830321/81920000000000), (2760464852836050175768953/4096000000000), (-1136661998226608895904863/3276800000000), (487140856382832383959227/2048000000000), (-412196109247012017196269/2048000000000), (487140856382832383959227/2560000000000), (-162380285460944127986409/1024000000000), 0, 0, 0], ![(-185954950541046652749526743/20480000000000), (185954950541046652749526743/102400000000000), (-3262367553351695662272399/5120000000000), (1343327816085992331523929/4096000000000), (-575711921179710999224541/2560000000000), (487140856382832383959227/2560000000000), (-575711921179710999224541/3200000000000), (191903973726570333074847/1280000000000), 0, 0, 0], ![(61984983513682217583175581/8192000000000), (-61984983513682217583175581/40960000000000), (1087455851117231887424133/2048000000000), (-447775938695330777174643/1638400000000), (191903973726570333074847/1024000000000), (-162380285460944127986409/1024000000000), (191903973726570333074847/1280000000000), (-63967991242190111024949/512000000000), 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Z : Matrix (Fin 11) (Fin 11) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 729870602452992000, 0, 0, 0, 0, 0, 0, 0, -25659513367488000, 798295971432960000], ![0, 0, 42682491371520000, 0, 0, 0, 0, 0, -2667655710720000, 0, 598721978574720000], ![0, 0, 0, 6590678814720000, 0, 0, 0, -540641621520000, -3501298120320000, 24946749107280000, 299360989287360000], ![0, 0, 0, 0, 2259661307904000, 0, -211843247616000, -1544690347200000, 0, 25659513367488000, 99786996429120000], ![0, 0, 0, 0, 0, 1437750246240000, -970948218240000, -1274369536440000, 2751019951680000, 9800508577860000, 0], ![0, 0, 0, 0, -211843247616000, -970948218240000, 997428624192000, 0, 0, -9265935382704000, -37420123660920000], ![0, 0, 0, -540641621520000, -1544690347200000, -1274369536440000, 0, 5440206316545000, -8534414168280000, -23387577288075000, -43656810937740000], ![0, 0, -2667655710720000, -3501298120320000, 0, 2751019951680000, 0, -8534414168280000, 22841802023040000, -30292481058840000, -37420123660920000], ![0, -25659513367488000, 0, 24946749107280000, 25659513367488000, 9800508577860000, -9265935382704000, -23387577288075000, -30292481058840000, 698765124659852250, -28065092745690000], ![0, 798295971432960000, 598721978574720000, 299360989287360000, 99786996429120000, 0, -37420123660920000, -43656810937740000, -37420123660920000, -28065092745690000, 51071452523969377500]] +def W : Matrix (Fin 11) (Fin 11) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![(-1348293170754218403/751619276800000000000000), (1616728626754218403/53687091200000000000000), (-4044879512262655209/26843545600000000000000), (1348293170754218403/2684354560000000000000), (-1348293170754218403/1342177280000000000000), (4044879512262655209/3355443200000000000000), (-1348293170754218403/1677721600000000000000), (1348293170754218403/5872025600000000000000), 0, (-9/51200000), (1/12800000)], ![(23654266153582779/37580963840000000000000), (-23654266153582779/2684354560000000000000), (77673684860748337/1342177280000000000000), (-23654266153582779/134217728000000000000), (23654266153582779/67108864000000000000), (-70962798460748337/167772160000000000000), (23654266153582779/83886080000000000000), (-23654266153582779/293601280000000000000), (-1/3200000), 0, (3/51200000)], ![(-107139911401521999/343597383680000000000000), (749979379810653993/171798691840000000000000), (-2249938139431961979/85899345920000000000000), (792929052770653993/8589934592000000000000), (-749979379810653993/4294967296000000000000), (2249938139431961979/10737418240000000000000), (-749979379810653993/5368709120000000000000), (106038906601521999/2684354560000000000000), (-21/51200000), (7/40960000), (3/102400000)], ![(722150831394674253/3006477107200000000000000), (-722150831394674253/214748364800000000000000), (2166452494184022759/107374182400000000000000), (-722150831394674253/10737418240000000000000), (748994376994674253/5368709120000000000000), (-2166452494184022759/13421772800000000000000), (719005103394674253/6710886400000000000000), (-749675951394674253/23488102400000000000000), 0, (9/51200000), (1/102400000)], ![(-130687144676581779/601295421440000000000000), (130687144676581779/42949672960000000000000), (-392061434029745337/21474836480000000000000), (130687144676581779/2147483648000000000000), (-130687144676581779/1073741824000000000000), (404172486829745337/2684354560000000000000), (-133570728676581779/1342177280000000000000), (126145499876581779/4697620480000000000000), (33/102400000), (11/163840000), 0], ![(129402750134305791/751619276800000000000000), (-129402750134305791/53687091200000000000000), (388208250402917373/26843545600000000000000), (-129402750134305791/2684354560000000000000), (128773604534305791/1342177280000000000000), (-398431866402917373/3355443200000000000000), (133105534134305791/1677721600000000000000), (-129402750134305791/5872025600000000000000), 0, (-13/204800000), (-3/819200000)], ![(-4174282262396961/42949672960000000000000), (29219975836778727/21474836480000000000000), (-87659927510336181/10737418240000000000000), (28779573916778727/1073741824000000000000), (-31054983836778727/536870912000000000000), (82292529110336181/1342177280000000000000), (-29219975836778727/671088640000000000000), (5559139862396961/335544320000000000000), (-819/819200000), (-21/131072000), (-7/1638400000)], ![0, 0, (-1/3200000), (-17/6400000), 0, (221/25600000), 0, (-663/102400000), (137/51200000), (-17/81920000), (-3/819200000)], ![0, (-9/51200000), 0, (969/51200000), (2907/51200000), (12597/409600000), (-4199/204800000), (-2907/163840000), (-2907/819200000), (62743/13107200000), (-9/3276800000)], ![0, (7/1280000), (3591/51200000), (2907/12800000), (2261/10240000), 0, (-6783/81920000), (-6783/204800000), (-3591/819200000), (-63/327680000), (65511/13107200000)]] +def M : Matrix (Fin 11) (Fin 11) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, (72240792623734400614097137989/3276800000000000), (-1046081078406841282913984877/163840000000000), (33609160788344382093331638159/10485760000000000), (-32127144078056344397668126539/13107200000000000), (5817304300278551932696721877/2621440000000000), (-5768845839649204251235329033/3276800000000000), (1302602694154474473246687201/1310720000000000), (3073795872147/1280), (-51879927659993433/204800), (5111277057717831/640)], ![0, (-1046081078406841282913984877/163840000000000), (20529240063905710086210261/8192000000000), (-576368681477247059321607687/524288000000000), (568221407392721557573125027/655360000000000), (-102249881332154669303451261/131072000000000), (100774160966757733530444369/163840000000000), (-22829430225296416835906793/65536000000000), (-29016226632393/1280), (40048441870437/5120), (122834362426244469/20480)], ![0, (33609160788344382093331638159/10485760000000000), (-576368681477247059321607687/524288000000000), (20182743107487417757079208429/33554432000000000), (-17561350568070296168230258209/41943040000000000), (3247319419560137486832954687/8388608000000000), (-3234623515191703887347618523/10485760000000000), (695909879615185860291397731/4194304000000000), (-151797685850811/5120), (8694877566978603/32768), (123760510486852239/40960)], ![0, (-32127144078056344397668126539/13107200000000000), (568221407392721557573125027/655360000000000), (-17561350568070296168230258209/41943040000000000), (18210519794838614335791287589/52428800000000000), (-3079692466749730569723012027/10485760000000000), (3041392981793644488841213383/13107200000000000), (-794894114743824388060919151/5242880000000000), (11036122936839/2560), (57877304336448597/204800), (43476882509803743/40960)], ![0, (5817304300278551932696721877/2621440000000000), (-102249881332154669303451261/131072000000000), (3247319419560137486832954687/8388608000000000), (-3079692466749730569723012027/10485760000000000), (588097796275554305941692261/2097152000000000), (-577482483676682120401233369/2621440000000000), (110095094218314003445439793/1048576000000000), (106455875192667/4096), (81190843236994491/655360), (1780262383168269/16384)], ![0, (-5768845839649204251235329033/3276800000000000), (100774160966757733530444369/163840000000000), (-3234623515191703887347618523/10485760000000000), (3041392981793644488841213383/13107200000000000), (-577482483676682120401233369/2621440000000000), (572868254346638622254783901/3276800000000000), (-116735707843081830831725397/1310720000000000), (-129476910333771/20480), (-87319724919458031/819200), (-103091505182743077/327680)], ![0, (1302602694154474473246687201/1310720000000000), (-22829430225296416835906793/65536000000000), (695909879615185860291397731/4194304000000000), (-794894114743824388060919151/5242880000000000), (110095094218314003445439793/1048576000000000), (-116735707843081830831725397/1310720000000000), (52073605274298676562002509/524288000000000), (-5129133678131463/81920), (-826284041090781273/2621440), (-537609615452252343/655360)], ![0, (3073795872147/1280), (-29016226632393/1280), (-151797685850811/5120), (11036122936839/2560), (106455875192667/4096), (-129476910333771/20480), (-5129133678131463/81920), (3208867565102199/20480), (-18413685541512261/327680), (-321437926744211277/327680)], ![0, (-51879927659993433/204800), (40048441870437/5120), (8694877566978603/32768), (57877304336448597/204800), (81190843236994491/655360), (-87319724919458031/819200), (-826284041090781273/2621440), (-18413685541512261/327680), (13196070159215374431/2097152), (8251604083275529977/655360)], ![0, (5111277057717831/640), (122834362426244469/20480), (123760510486852239/40960), (43476882509803743/40960), (1780262383168269/16384), (-103091505182743077/327680), (-537609615452252343/655360), (-321437926744211277/327680), (8251604083275529977/655360), (2078028103002300129681/5242880)]] +def L : Matrix (Fin 11) (Fin 11) ℚ := ![![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, (-469644683071655580/1621647922754218403), 1, 0, 0, 0, 0, 0, 0, 0, 0], ![0, (3772261059053269965/25946366764067494448), (-136307780588366520384153/523418589198268358692312), 1, 0, 0, 0, 0, 0, 0, 0], ![0, (-721184175394674253/6486591691016873612), (78270007053774031133463/327136618248917724182695), (-178257885759749956411310758308/757352056566793019987774016065), 1, 0, 0, 0, 0, 0, 0], ![0, (59357167580264445/589690153728806692), (-547484554040993421438531/2617092945991341793461560), (34132374349470653976636205311/108193150938113288569682002295), (-41906938351374320553804762514455/183588909157826296848236241173264), 1, 0, 0, 0, 0, 0], ![0, (-129497982134305791/1621647922754218403), (838333669045543978880601/5234185891982683586923120), (-209208263009073278647235428488/757352056566793019987774016065), (20467237508389681008172566641907/126217375046005579083162415806619), (-165500190961687915725420187240032154944/243332290324112049106858155557462232995), 1, 0, 0, 0, 0], ![0, (146202919183893635/3243295845508436806), (-482316859963523439620451/5234185891982683586923120), (26968650035602561091375458287/432772603752453154278728009180), (-12704536092134320940750585312180195/16155824005888714122644789223247232), (-338175814806536444523604831584615152655/389331664518579278570973048891939572792), (-201913743014102900451765883466723744695815/62863500432755182696024214796990588261689), 1, 0, 0, 0], ![0, (176640000000000/1621647922754218403), (-175079429668725135756123/5234185891982683586923120), (-297456297486867864795929848842/757352056566793019987774016065), (89619351819892375823779664339355/2019478000736089265330598652905904), (272000804523270658038708331082266156315/145999374194467229464114893334477339797), (1227010360445209829230395966167813539370465/188590501298265548088072644390971764785067), (-408/49), 1, 0, 0], ![0, (-18633456000000000/1621647922754218403), (-835556465179471882150989/8374697427172293739076992), (37988121594158704791848790711213/12117632905068688319804384257040), (84654209545681023143011473786531609/8077912002944357061322394611623616), (6794966720784158726219511997317342567309/973329161296448196427432622229848931980), (-376035776084882843070212747220062154939161/62863500432755182696024214796990588261689), (2907/49), 0, 1, 0], ![0, (587453440000000000/1621647922754218403), (1059483832382931539295691539/83746974271722937390769920), (19151734438512993131020520004447/432772603752453154278728009180), (7125005837681272641710583481494665/252434750092011158166324831613238), (-52685038329470926775980237500487345341/48666458064822409821371631111492446599), (-19300786878481903742661031426233932451102255/502908003462041461568193718375924706093512), (-3876/7), 0, 0, 1]] +def diag : Fin 11 → ℚ := ![0, (72240792623734400614097137989/3276800000000000), (1549516810826267637385284377397/2358760614915226768), (48744767133783064584810466026274301157/535980635339026799300927488), (17407746507364908386348858013064024211439/540965754690566442848410011475), (516309120914455826465077162375285640433975063/29374225465252207495717798587722240), (26010172047235701806603859753849313204575167643327/17696893841753603571407865858724526036000), (69196804609505941208263422409310211063441861407376141/257488897772565228322915183808473449519878144), 0, 0, 0] + +def keyIndexTable : Fin 23 → Fin 13 → Fin 13 → Fin 72 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 9, 10, 11, 12, 13, 14, 15, 16, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 9, 0, 17, 18, 19, 20, 21, 22, 0, 0, 0], ![0, 0, 0, 33, 34, 35, 36, 37, 38, 39, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 10, 17, 0, 23, 24, 25, 26, 27, 0, 0, 0], ![1, 0, 33, 0, 40, 41, 42, 43, 44, 45, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 11, 18, 23, 0, 28, 29, 30, 0, 0, 0, 0], ![2, 0, 34, 40, 0, 46, 47, 48, 49, 0, 0, 0, 0], ![9, 33, 0, 0, 54, 55, 56, 57, 58, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 12, 19, 24, 28, 0, 31, 32, 0, 0, 0, 0], ![3, 0, 35, 41, 46, 0, 50, 51, 52, 0, 0, 0, 0], ![10, 34, 0, 54, 0, 59, 60, 61, 62, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 13, 20, 25, 29, 31, 0, 0, 0, 0, 0, 0], ![4, 0, 36, 42, 47, 50, 0, 53, 0, 0, 0, 0, 0], ![11, 35, 0, 55, 59, 0, 63, 64, 0, 0, 0, 0, 0], ![17, 40, 54, 0, 0, 66, 67, 68, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 14, 21, 26, 30, 32, 0, 0, 0, 0, 0, 0], ![5, 0, 37, 43, 48, 51, 53, 0, 0, 0, 0, 0, 0], ![12, 36, 0, 56, 60, 63, 0, 65, 0, 0, 0, 0, 0], ![18, 41, 55, 0, 66, 0, 69, 70, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 7, 15, 22, 27, 0, 32, 0, 0, 0, 0, 0, 0], ![6, 0, 38, 44, 49, 52, 0, 0, 0, 0, 0, 0, 0], ![13, 37, 0, 57, 61, 64, 65, 0, 0, 0, 0, 0, 0], ![19, 42, 56, 0, 67, 69, 0, 0, 0, 0, 0, 0, 0], ![23, 46, 59, 66, 0, 0, 71, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 8, 16, 0, 27, 30, 31, 0, 0, 0, 0, 0, 0], ![7, 0, 39, 45, 0, 52, 53, 0, 0, 0, 0, 0, 0], ![14, 38, 0, 58, 62, 0, 65, 0, 0, 0, 0, 0, 0], ![20, 43, 57, 0, 68, 70, 0, 0, 0, 0, 0, 0, 0], ![24, 47, 60, 67, 0, 71, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 16, 22, 26, 29, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 45, 49, 51, 0, 0, 0, 0, 0, 0, 0], ![15, 39, 0, 0, 62, 64, 0, 0, 0, 0, 0, 0, 0], ![21, 44, 58, 0, 0, 70, 0, 0, 0, 0, 0, 0, 0], ![25, 48, 61, 68, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![28, 50, 63, 69, 71, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 8, 15, 21, 25, 28, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 39, 44, 48, 50, 0, 0, 0, 0, 0, 0, 0], ![16, 0, 0, 58, 61, 63, 0, 0, 0, 0, 0, 0, 0], ![22, 45, 0, 0, 68, 69, 0, 0, 0, 0, 0, 0, 0], ![26, 49, 62, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0], ![29, 51, 64, 70, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 7, 14, 20, 24, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 38, 43, 47, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 39, 0, 57, 60, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 45, 58, 0, 67, 0, 0, 0, 0, 0, 0, 0, 0], ![27, 0, 62, 68, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![30, 52, 0, 70, 71, 0, 0, 0, 0, 0, 0, 0, 0], ![31, 53, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 13, 19, 23, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 37, 42, 46, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 38, 0, 56, 59, 0, 0, 0, 0, 0, 0, 0, 0], ![22, 44, 57, 0, 66, 0, 0, 0, 0, 0, 0, 0, 0], ![27, 49, 61, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 52, 64, 69, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![32, 0, 65, 0, 71, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 12, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 36, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 37, 0, 55, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![21, 43, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![26, 48, 60, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![30, 51, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![32, 53, 0, 69, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 65, 70, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 11, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 35, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 36, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 42, 55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![25, 47, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![29, 50, 0, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![31, 0, 63, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 53, 64, 68, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 41, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![24, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![28, 0, 59, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 50, 60, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![31, 51, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![32, 52, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 0, 54, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 46, 55, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![28, 47, 56, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![29, 48, 57, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![30, 49, 58, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![24, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![25, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![26, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![27, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 33, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 34, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 35, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![21, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![22, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 23) (j : Fin ((n.val+1)/2)) (x : Fin ((22-n.val+2)/2)) : Fin 72 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 72 → FourTerm 22 := ![⟨⟨22,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨10,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨10,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨9,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨9,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨14,by decide⟩,(⟨6,by decide⟩,⟨4,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 12, + (fourTermLabels (by omega : 22 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 11, + (fourTermLabels (by omega : 22 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 11, + (fourTermLabels (by omega : 22 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 10, + (fourTermLabels (by omega : 22 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 10, + (fourTermLabels (by omega : 22 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 9, + (fourTermLabels (by omega : 22 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 9, + (fourTermLabels (by omega : 22 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 8, + (fourTermLabels (by omega : 22 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 8, + (fourTermLabels (by omega : 22 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 7, + (fourTermLabels (by omega : 22 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 7, + (fourTermLabels (by omega : 22 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 6, + (fourTermLabels (by omega : 22 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover_12 : ∀ j : Fin 6, ∀ x : Fin 6, + (fourTermLabels (by omega : 22 ≤ 23) ⟨12,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨12,j,x⟩).toFinset=keys (keyIndex 12 j x) := by decide +kernel +lemma cover_13 : ∀ j : Fin 7, ∀ x : Fin 5, + (fourTermLabels (by omega : 22 ≤ 23) ⟨13,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨13,j,x⟩).toFinset=keys (keyIndex 13 j x) := by decide +kernel +lemma cover_14 : ∀ j : Fin 7, ∀ x : Fin 5, + (fourTermLabels (by omega : 22 ≤ 23) ⟨14,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨14,j,x⟩).toFinset=keys (keyIndex 14 j x) := by decide +kernel +lemma cover_15 : ∀ j : Fin 8, ∀ x : Fin 4, + (fourTermLabels (by omega : 22 ≤ 23) ⟨15,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨15,j,x⟩).toFinset=keys (keyIndex 15 j x) := by decide +kernel +lemma cover_16 : ∀ j : Fin 8, ∀ x : Fin 4, + (fourTermLabels (by omega : 22 ≤ 23) ⟨16,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨16,j,x⟩).toFinset=keys (keyIndex 16 j x) := by decide +kernel +lemma cover_17 : ∀ j : Fin 9, ∀ x : Fin 3, + (fourTermLabels (by omega : 22 ≤ 23) ⟨17,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨17,j,x⟩).toFinset=keys (keyIndex 17 j x) := by decide +kernel +lemma cover_18 : ∀ j : Fin 9, ∀ x : Fin 3, + (fourTermLabels (by omega : 22 ≤ 23) ⟨18,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨18,j,x⟩).toFinset=keys (keyIndex 18 j x) := by decide +kernel +lemma cover_19 : ∀ j : Fin 10, ∀ x : Fin 2, + (fourTermLabels (by omega : 22 ≤ 23) ⟨19,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨19,j,x⟩).toFinset=keys (keyIndex 19 j x) := by decide +kernel +lemma cover_20 : ∀ j : Fin 10, ∀ x : Fin 2, + (fourTermLabels (by omega : 22 ≤ 23) ⟨20,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨20,j,x⟩).toFinset=keys (keyIndex 20 j x) := by decide +kernel +lemma cover_21 : ∀ j : Fin 11, ∀ x : Fin 1, + (fourTermLabels (by omega : 22 ≤ 23) ⟨21,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨21,j,x⟩).toFinset=keys (keyIndex 21 j x) := by decide +kernel +lemma cover_22 : ∀ j : Fin 11, ∀ x : Fin 1, + (fourTermLabels (by omega : 22 ≤ 23) ⟨22,j,x⟩).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) ⟨22,j,x⟩).toFinset=keys (keyIndex 22 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 22, (fourTermLabels (by omega : 22 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 22 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x + · exact cover_12 j x + · exact cover_13 j x + · exact cover_14 j x + · exact cover_15 j x + · exact cover_16 j x + · exact cover_17 j x + · exact cover_18 j x + · exact cover_19 j x + · exact cover_20 j x + · exact cover_21 j x + · exact cover_22 j x +lemma representatives_checked : ∀ a : Fin 72, + (fourTermLabels (by omega : 22 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 22 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 22 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 22 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 72, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 22, + (fourTermLabels (by omega : 22 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 72, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 22 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 72, ∀ b : FourTerm 22, + (fourTermLabels (by omega : 22 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 22 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 72, (∑ b ∈ fibers v, fourTermEval 22 (2*(0 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 22 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 72, (∑ b ∈ fibers v, fourTermEval 22 (2*(1 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 22 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 72, (∑ b ∈ fibers v, fourTermEval 22 (2*(2 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 22 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 72, (∑ b ∈ fibers v, fourTermEval 22 (2*(3 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 22 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 72, (∑ b ∈ fibers v, fourTermEval 22 (2*(4 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 22 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 72, (∑ b ∈ fibers v, fourTermEval 22 (2*(5 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 22 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_6 : ∀ v : Fin 72, (∑ b ∈ fibers v, fourTermEval 22 (2*(6 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 22 ≤ 23) b)) = columns 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_7 : ∀ v : Fin 72, (∑ b ∈ fibers v, fourTermEval 22 (2*(7 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 22 ≤ 23) b)) = columns 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_8 : ∀ v : Fin 72, (∑ b ∈ fibers v, fourTermEval 22 (2*(8 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 22 ≤ 23) b)) = columns 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_9 : ∀ v : Fin 72, (∑ b ∈ fibers v, fourTermEval 22 (2*(9 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 22 ≤ 23) b)) = columns 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_10 : ∀ v : Fin 72, (∑ b ∈ fibers v, fourTermEval 22 (2*(10 : Fin 11).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 22 ≤ 23) b)) = columns 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 11, ∀ v : Fin 72, (∑ b ∈ fibers v, fourTermEval 22 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 22 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 + · exact columns_checked_6 + · exact columns_checked_7 + · exact columns_checked_8 + · exact columns_checked_9 + · exact columns_checked_10 +lemma gram_checked_0 : ∀ v : Fin 11, (∑ a : Fin 72, columns (0 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 11, (∑ a : Fin 72, columns (1 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 11, (∑ a : Fin 72, columns (2 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 11, (∑ a : Fin 72, columns (3 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 11, (∑ a : Fin 72, columns (4 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 11, (∑ a : Fin 72, columns (5 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_6 : ∀ v : Fin 11, (∑ a : Fin 72, columns (6 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_7 : ∀ v : Fin 11, (∑ a : Fin 72, columns (7 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_8 : ∀ v : Fin 11, (∑ a : Fin 72, columns (8 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_9 : ∀ v : Fin 11, (∑ a : Fin 72, columns (9 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_10 : ∀ v : Fin 11, (∑ a : Fin 72, columns (10 : Fin 11) a * columns v a / setFactorial (keys a)) = Z 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 11, ∀ v : Fin 11, (∑ a : Fin 72, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 + · exact gram_checked_6 + · exact gram_checked_7 + · exact gram_checked_8 + · exact gram_checked_9 + · exact gram_checked_10 +lemma rows_table_checked_0 : ∀ v : Fin 11, integerTableEval 22 SumTable22.sums (0 : Fin 11) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 11, integerTableEval 22 SumTable22.sums (1 : Fin 11) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 11, integerTableEval 22 SumTable22.sums (2 : Fin 11) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 11, integerTableEval 22 SumTable22.sums (3 : Fin 11) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 11, integerTableEval 22 SumTable22.sums (4 : Fin 11) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 11, integerTableEval 22 SumTable22.sums (5 : Fin 11) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_6 : ∀ v : Fin 11, integerTableEval 22 SumTable22.sums (6 : Fin 11) v = Y 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_7 : ∀ v : Fin 11, integerTableEval 22 SumTable22.sums (7 : Fin 11) v = Y 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_8 : ∀ v : Fin 11, integerTableEval 22 SumTable22.sums (8 : Fin 11) v = Y 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_9 : ∀ v : Fin 11, integerTableEval 22 SumTable22.sums (9 : Fin 11) v = Y 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_10 : ∀ v : Fin 11, integerTableEval 22 SumTable22.sums (10 : Fin 11) v = Y 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 11, ∀ v : Fin 11, integerTableEval 22 SumTable22.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 + · exact rows_table_checked_6 + · exact rows_table_checked_7 + · exact rows_table_checked_8 + · exact rows_table_checked_9 + · exact rows_table_checked_10 +lemma rows_checked (u v : Fin 11) : exactFourEval 22 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 22 SumTable22.sums SumTable22.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 11, (Z * tableComparison 22 (1/200000) Y) (0 : Fin 11) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 11, (Z * tableComparison 22 (1/200000) Y) (1 : Fin 11) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 11, (Z * tableComparison 22 (1/200000) Y) (2 : Fin 11) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 11, (Z * tableComparison 22 (1/200000) Y) (3 : Fin 11) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 11, (Z * tableComparison 22 (1/200000) Y) (4 : Fin 11) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 11, (Z * tableComparison 22 (1/200000) Y) (5 : Fin 11) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_6 : ∀ v : Fin 11, (Z * tableComparison 22 (1/200000) Y) (6 : Fin 11) v = W 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_7 : ∀ v : Fin 11, (Z * tableComparison 22 (1/200000) Y) (7 : Fin 11) v = W 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_8 : ∀ v : Fin 11, (Z * tableComparison 22 (1/200000) Y) (8 : Fin 11) v = W 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_9 : ∀ v : Fin 11, (Z * tableComparison 22 (1/200000) Y) (9 : Fin 11) v = W 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_10 : ∀ v : Fin 11, (Z * tableComparison 22 (1/200000) Y) (10 : Fin 11) v = W 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 11, ∀ v : Fin 11, (Z * tableComparison 22 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 + · exact product_checked_6 + · exact product_checked_7 + · exact product_checked_8 + · exact product_checked_9 + · exact product_checked_10 +lemma compression_checked_0 : ∀ v : Fin 11, (W * Z) (0 : Fin 11) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 11, (W * Z) (1 : Fin 11) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 11, (W * Z) (2 : Fin 11) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 11, (W * Z) (3 : Fin 11) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 11, (W * Z) (4 : Fin 11) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 11, (W * Z) (5 : Fin 11) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_6 : ∀ v : Fin 11, (W * Z) (6 : Fin 11) v = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_7 : ∀ v : Fin 11, (W * Z) (7 : Fin 11) v = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_8 : ∀ v : Fin 11, (W * Z) (8 : Fin 11) v = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_9 : ∀ v : Fin 11, (W * Z) (9 : Fin 11) v = M 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_10 : ∀ v : Fin 11, (W * Z) (10 : Fin 11) v = M 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 11, ∀ v : Fin 11, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 + · exact compression_checked_6 + · exact compression_checked_7 + · exact compression_checked_8 + · exact compression_checked_9 + · exact compression_checked_10 +lemma ldl_checked_0 : ∀ v : Fin 11, (∑ k : Fin 11, L (0 : Fin 11) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 11, (∑ k : Fin 11, L (1 : Fin 11) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 11, (∑ k : Fin 11, L (2 : Fin 11) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 11, (∑ k : Fin 11, L (3 : Fin 11) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 11, (∑ k : Fin 11, L (4 : Fin 11) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 11, (∑ k : Fin 11, L (5 : Fin 11) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_6 : ∀ v : Fin 11, (∑ k : Fin 11, L (6 : Fin 11) k * diag k * L v k) = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_7 : ∀ v : Fin 11, (∑ k : Fin 11, L (7 : Fin 11) k * diag k * L v k) = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_8 : ∀ v : Fin 11, (∑ k : Fin 11, L (8 : Fin 11) k * diag k * L v k) = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_9 : ∀ v : Fin 11, (∑ k : Fin 11, L (9 : Fin 11) k * diag k * L v k) = M 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_10 : ∀ v : Fin 11, (∑ k : Fin 11, L (10 : Fin 11) k * diag k * L v k) = M 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 11, ∀ v : Fin 11, (∑ k : Fin 11, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 + · exact ldl_checked_6 + · exact ldl_checked_7 + · exact ldl_checked_8 + · exact ldl_checked_9 + · exact ldl_checked_10 +lemma diag_checked : ∀ u : Fin 11, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 22 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 22 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 22 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 22 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 22 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate22 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate23.lean b/lean/OAI/Analysis/LaughlinGap/Certificate23.lean new file mode 100644 index 0000000000000000000000000000000000000000..30cdfa0b2a5eafa3205cb74a3d26a66b749e2d84 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate23.lean @@ -0,0 +1,487 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CachedIntegerRows +import OAI.Analysis.LaughlinGap.FastFourKeys +import OAI.Analysis.LaughlinGap.FourTables +import OAI.Analysis.LaughlinGap.SumTable23 + +namespace OAI + +/-! Certificate23. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate23 + +def keys : Fin 84 → Finset (Fin 25) := ![{0,1,2,21}, {0,1,3,20}, {0,1,4,19}, {0,1,5,18}, {0,1,6,17}, {0,1,7,16}, {0,1,8,15}, {0,1,9,14}, {0,1,10,13}, {0,1,11,12}, {0,2,3,19}, {0,2,4,18}, {0,2,5,17}, {0,2,6,16}, {0,2,7,15}, {0,2,8,14}, {0,2,9,13}, {0,2,10,12}, {0,3,4,17}, {0,3,5,16}, {0,3,6,15}, {0,3,7,14}, {0,3,8,13}, {0,3,9,12}, {0,3,10,11}, {0,4,5,15}, {0,4,6,14}, {0,4,7,13}, {0,4,8,12}, {0,4,9,11}, {0,5,6,13}, {0,5,7,12}, {0,5,8,11}, {0,5,9,10}, {0,6,7,11}, {0,6,8,10}, {0,7,8,9}, {1,2,3,18}, {1,2,4,17}, {1,2,5,16}, {1,2,6,15}, {1,2,7,14}, {1,2,8,13}, {1,2,9,12}, {1,2,10,11}, {1,3,4,16}, {1,3,5,15}, {1,3,6,14}, {1,3,7,13}, {1,3,8,12}, {1,3,9,11}, {1,4,5,14}, {1,4,6,13}, {1,4,7,12}, {1,4,8,11}, {1,4,9,10}, {1,5,6,12}, {1,5,7,11}, {1,5,8,10}, {1,6,7,10}, {1,6,8,9}, {2,3,4,15}, {2,3,5,14}, {2,3,6,13}, {2,3,7,12}, {2,3,8,11}, {2,3,9,10}, {2,4,5,13}, {2,4,6,12}, {2,4,7,11}, {2,4,8,10}, {2,5,6,11}, {2,5,7,10}, {2,5,8,9}, {2,6,7,9}, {3,4,5,12}, {3,4,6,11}, {3,4,7,10}, {3,4,8,9}, {3,5,6,10}, {3,5,7,9}, {3,6,7,8}, {4,5,6,9}, {4,5,7,8}] +def fibers : Fin 84 → Finset (FourTerm 23) := ![{⟨⟨23,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨22,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨21,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨23,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨21,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨20,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨23,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨20,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨23,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨23,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨23,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨23,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨23,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨9,by decide⟩)⟩}, {⟨⟨23,by decide⟩,(⟨10,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨10,by decide⟩)⟩}, {⟨⟨23,by decide⟩,(⟨11,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨12,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨11,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨21,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨20,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨7,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨10,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨14,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨8,by decide⟩)⟩}, {⟨⟨22,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨11,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨13,by decide⟩,(⟨0,by decide⟩,⟨2,by 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decide⟩)⟩,⟨⟨11,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨10,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨19,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨18,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨16,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨5,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨17,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨15,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨6,by decide⟩)⟩}, {⟨⟨20,by decide⟩,(⟨7,by decide⟩,⟨1,by 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-275147968095000, -276757020540000, 205958712960000, -130333248045000, 4923700481700000, -4923700481700000, 2703208107600000, -765908963820000, -162514296945000, 284802282765000, -38617258680000, -193086293400000, 2220492374100000, -1937299143780000, 928423260765000, -122287985820000, -246185024085000, 231703552080000, 725682652695000, -624312348660000, 289629440100000, 8045262225000, -173777664060000, 231703552080000, -212394922740000, 114242723595000, 70798307580000, -75625464915000, -283193230320000, 283193230320000, -181822926285000, 78843569805000, 6436209780000, -57925888020000, -101370304035000, 102979356480000, -85279779585000, 51489678240000, -19308629340000, 27353891565000, -38617258680000, 4827157335000, -1609052445000, 1609052445000, 6436209780000, -12872419560000, -8045262225000, 6436209780000, -4827157335000, 1609052445000, -1609052445000], ![-49893498214560000, 49893498214560000, -39202034311440000, 26447305444560000, -12567159324720000, 1312986795120000, 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437662265040000, -437662265040000, 234461927700000, -46892385540000, -78153975900000, 140677156620000, 203200337340000, -187569542160000, 125046361440000, -62523180720000, 46892385540000, -46892385540000, 46892385540000, 0, -15630795180000, 15630795180000, -15630795180000, 15630795180000, 0, 0, 0, 0, 0], ![536355105806520000, -536355105806520000, 314329038751728000, -117606102934320000, 5345731951560000, 37420123660920000, -37420123660920000, 17462724375096000, 5345731951560000, -19601017155720000, 222026067054792000, -196722935817408000, 112260370982760000, -42765855612480000, 0, 19957399285824000, -22808456326656000, 14255285204160000, 59159433597264000, -51675408865080000, 32074391709360000, -14968049464368000, 2138292780624000, 6414878341872000, -10691463903120000, 12473374553640000, -11404228163328000, 8553171122496000, -5702114081664000, 2851057040832000, 1781910650520000, -1781910650520000, 1781910650520000, -1781910650520000, 0, 0, 0, -25303131237384000, 25303131237384000, -17819106505200000, 10691463903120000, -4989349821456000, 712764260208000, 2138292780624000, -3563821301040000, -7484024732184000, 7127642602080000, -5702114081664000, 4276585561248000, -2851057040832000, 1425528520416000, -1069146390312000, 1069146390312000, -1069146390312000, 1069146390312000, -1069146390312000, 0, 0, 0, 0, 0, 356382130104000, -356382130104000, 356382130104000, -356382130104000, 356382130104000, -356382130104000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3243077383946400000, -3243077383946400000, 2519621659835280000, -1821112684831440000, 1222390706256720000, -723455724111120000, 324307738394640000, -24946749107280000, -174627243750960000, 274414240180080000, 723455724111120000, -698508975003840000, 598721978574720000, -498934982145600000, 399147985716480000, -299360989287360000, 199573992858240000, -99786996429120000, 74840247321840000, -74840247321840000, 74840247321840000, -74840247321840000, 74840247321840000, -74840247321840000, 74840247321840000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -24946749107280000, 24946749107280000, -24946749107280000, 24946749107280000, -24946749107280000, 24946749107280000, -24946749107280000, 24946749107280000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12623055048283680000, -12623055048283680000, 12623055048283680000, -12623055048283680000, 12623055048283680000, -12623055048283680000, 12623055048283680000, -12623055048283680000, 12623055048283680000, -12623055048283680000, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Y : Matrix (Fin 12) (Fin 12) ℚ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]] +def Z : Matrix (Fin 12) (Fin 12) ℚ := ![![2248001455555215360000, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2195313921440640000, 252461100965673600000], ![0, 14597412049059840000, 0, 0, 0, 0, 0, 0, 0, -57021140816640000, 0, 100984440386269440000], ![0, 0, 768284844687360000, 0, 0, 0, 0, 0, -4501669011840000, -114042281633280000, 1746272437509600000, 37869165144851040000], ![0, 0, 0, 105450861035520000, 0, 0, 0, -823834851840000, -24509086842240000, 0, 1746272437509600000, 12623055048283680000], ![0, 0, 0, 0, 31635258310656000, 0, -308938069440000, -8341327874880000, -26259735902400000, 119744395714944000, 1010343338844840000, 3155763762070920000], ![0, 0, 0, 0, 0, 18896146093440000, -4854741091200000, -16991593819200000, 0, 117606102934320000, 274414240180080000, 0], ![0, 0, 0, 0, -308938069440000, -4854741091200000, 8396495387280000, -11044535982480000, 13411222264440000, 0, -202692336496650000, -788940940517730000], ![0, 0, 0, -823834851840000, -8341327874880000, -16991593819200000, -11044535982480000, 52725430517760000, -31292851950360000, -162153869197320000, -420976391185350000, -788940940517730000], ![0, 0, -4501669011840000, -24509086842240000, -26259735902400000, 0, 13411222264440000, -31292851950360000, 111009907368360000, -302924810588400000, -463853616213487500, -591705705388297500], ![0, -57021140816640000, -114042281633280000, 0, 119744395714944000, 117606102934320000, 0, -162153869197320000, -302924810588400000, 2530981340232345000, -414739703908530000, -394470470258865000], ![-2195313921440640000, 0, 1746272437509600000, 1746272437509600000, 1010343338844840000, 274414240180080000, -202692336496650000, -420976391185350000, -463853616213487500, -414739703908530000, 101850365435360416875, -246544043911790625], ![252461100965673600000, 100984440386269440000, 37869165144851040000, 12623055048283680000, 3155763762070920000, 0, -788940940517730000, -788940940517730000, -591705705388297500, -394470470258865000, -246544043911790625, 25851868812458629565625]] +def W : Matrix (Fin 12) (Fin 12) ℚ := ![![(400001/100000), 0, 0, 0, 0, 0, 0, 0, 0, 0, (-11/102400000), (1/20480000)], ![0, (1/200000), 0, 0, 0, 0, 0, 0, 0, (-1/10240000), 0, (1/51200000)], ![0, 0, (1/200000), 0, 0, 0, 0, 0, (-9/102400000), (-1/5120000), (7/81920000), (3/409600000)], ![0, 0, 0, (1/200000), 0, 0, 0, (-1/12800000), (-49/102400000), 0, (7/81920000), (1/409600000)], ![0, 0, 0, 0, (1/200000), 0, (-7/102400000), (-81/102400000), (-21/40960000), (21/102400000), (81/1638400000), (1/1638400000)], ![0, 0, 0, 0, 0, (253/51200000), (-11/10240000), (-33/20480000), 0, (33/163840000), (11/819200000), 0], ![0, 0, 0, 0, (-1/20480000), (-13/10240000), (761/409600000), (-429/409600000), (429/1638400000), 0, (-13/1310720000), (-1/6553600000)], ![0, 0, 0, (-1/25600000), (-27/20480000), (-91/20480000), (-1001/409600000), (1/200000), (-1001/1638400000), (-91/327680000), (-27/1310720000), (-1/6553600000)], ![0, 0, (-3/102400000), (-119/102400000), (-17/4096000), 0, (2431/819200000), (-2431/819200000), (3551/1638400000), (-17/32768000), (-119/5242880000), (-3/26214400000)], ![0, (-1/51200000), (-19/25600000), 0, (969/51200000), (12597/409600000), 0, (-12597/819200000), (-969/163840000), (11363/2621440000), (-133/6553600000), (-1/13107200000)], ![(-400001/102400000), 0, (931/81920000), (6783/81920000), (26163/163840000), (29393/409600000), (-29393/655360000), (-26163/655360000), (-47481/5242880000), (-931/1310720000), (522587/104857600000), (-1/20971520000)], ![(9200023/20480000), (1771/51200000), (100947/409600000), (245157/409600000), (81719/163840000), 0, (-572033/3276800000), (-245157/3276800000), (-302841/26214400000), (-1771/2621440000), (-253/20971520000), (104857/20971520000)]] +def M : Matrix (Fin 12) (Fin 12) ℚ := ![![(719362265183875514031831/80), (78894094051773/16), (106335518069781/64), (3430178002251/8), (58313026038267/1280), (-37731958024761/1280), (-17150890011255/1024), (3430178002251/512), (85754450056275/4096), (517956878339901/20480), (-719363161448225366191119/81920), (4136338189510533687437757/4096)], ![(78894094051773/16), (374824905336882/5), (240246103456359/320), (78894094051773/320), (12785208917481/256), (-1470076286679/128), (-78894094051773/5120), (2182840546887/5120), (369167339021481/20480), (-2764678922048043/5120), (584689432201875/16384), (82729372645911840849/81920)], ![(106335518069781/64), (240246103456359/320), (5492061985256847/1280), (39012120150003/160), (452438837263413/5120), (490025428893/1024), (-497192930022789/20480), (-75053607676047/10240), (-1398356727614847/81920), (-88166221573987557/81920), (1150442722659505275/65536), (31031177331101718771/81920)], ![(3430178002251/8), (78894094051773/320), (39012120150003/160), (920425304681883/1280), (68643142735167/640), (25370573521293/1024), (-63489669564321/2560), (-638207160143553/20480), (-2194444067688873/10240), (1986073063303329/16384), (144905375030182767/8192), (41469181550527493763/327680)], ![(58313026038267/1280), (12785208917481/256), (452438837263413/5120), (68643142735167/640), (26080429212328491/102400), (210770101581039/4096), (-881497820690487/81920), (-4962826522763109/40960), (-81852236888843421/327680), (2261975688902022093/1638400), (13875949703845690461/1310720), (10631847008510981253/327680)], ![(-37731958024761/1280), (-1470076286679/128), (490025428893/1024), (25370573521293/1024), (210770101581039/4096), (78510149383743/512), (-293834721651471/16384), (-3200929542391581/16384), (-2046423563493309/65536), (220632479282786571/163840), (4634894248599575961/1310720), (533718546260244345/262144)], ![(-17150890011255/1024), (-78894094051773/5120), (-497192930022789/20480), (-63489669564321/2560), (-881497820690487/81920), (-293834721651471/16384), (12775666454942391/327680), (-1889462336400639/32768), (24309099414849249/262144), (-79248649723460217/1310720), (-1536133808238790761/1048576), (-6410381823988711569/1310720)], ![(3430178002251/512), (2182840546887/5120), (-75053607676047/10240), (-638207160143553/20480), (-4962826522763109/40960), (-3200929542391581/16384), (-1889462336400639/32768), (147485437848820071/327680), (-83698843400613441/655360), (-2621966009882260041/1310720), (-3108243635199553851/524288), (-10631215855758567069/1048576)], ![(85754450056275/4096), (369167339021481/20480), (-1398356727614847/81920), (-2194444067688873/10240), (-81852236888843421/327680), (-2046423563493309/65536), (24309099414849249/262144), (-83698843400613441/655360), (3557893010133621159/5242880), (-2068428028768308207/1048576), (-36607721238369964683/4194304), (-34505673233141801691/1048576)], ![(517956878339901/20480), (-2764678922048043/5120), (-88166221573987557/81920), (1986073063303329/16384), (2261975688902022093/1638400), (220632479282786571/163840), (-79248649723460217/1310720), (-2621966009882260041/1310720), (-2068428028768308207/1048576), (69577338265481805759/3276800), (663057165751036947891/20971520), (872434639146815417673/20971520)], ![(-719363161448225366191119/81920), (584689432201875/16384), (1150442722659505275/65536), (144905375030182767/8192), (13875949703845690461/1310720), (4634894248599575961/1310720), (-1536133808238790761/1048576), (-3108243635199553851/524288), (-36607721238369964683/4194304), (663057165751036947891/20971520), (793472230046333663913087/83886080), (-4127736559884387492195153/4194304)], ![(4136338189510533687437757/4096), (82729372645911840849/81920), (31031177331101718771/81920), (41469181550527493763/327680), (10631847008510981253/327680), (533718546260244345/262144), (-6410381823988711569/1310720), (-10631215855758567069/1048576), (-34505673233141801691/1048576), (872434639146815417673/20971520), (-4127736559884387492195153/4194304), (1905253556423838329417099391/16777216)]] +def L : Matrix (Fin 12) (Fin 12) ℚ := ![![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![(115/209715724581), 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![(155/838862898324), (25704475029382/2566615427724929), 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![(10/209715724581), (4823461660763/1466637387271388), (42273449148319317047/750191596060481726171), 1, 0, 0, 0, 0, 0, 0, 0, 0], ![(1/197379505488), (244271156350/366659346817847), (30779617648760626891/1500383192120963452342), (30477199392796926300916086/210265651248130218677263415), 1, 0, 0, 0, 0, 0, 0, 0], ![(-1/305041053936), (-6291471728575/41065846843598864), (103961918291566170/750191596060481726171), (1344390397902047182604553/38230118408750948850411530), (3335650689270226358315406623215/16590794336554066450644608161726), 1, 0, 0, 0, 0, 0, 0], ![(-25/13421806373184), (-9884142751/48086471713816), (-67601131021086359207/12003065536967707618736), (-13959002725254002801868729/420531302496260437354526830), (-956895589116657171521172971595/33181588673108132901289216323452), (-34077466479713603480659996756084849/309447980022555881300966047939372551), 1, 0, 0, 0, 0, 0], ![(5/6710903186592), (133455459947/23466198196342208), (-20551947050717837657/12003065536967707618736), (-146809989156775311435372987/3364250419970083498836214640), (-4641851609721589716495861958185/9480453906602323686082633235272), (-4441488196267679852006070698900689583/3713375760270670575611592575272470612), (-5280432445724671717665493840992066646685/2359065529261681880350961572828935619119), 1, 0, 0, 0, 0], ![(125/53687225492736), (617157034267/2566615427724929), (-48342083157145507629/12003065536967707618736), (-23153683272129950497860009/76460236817501897700823060), (-60918755999324663108684057350715/66363177346216265802578432646904), (131395803727585505079910898628691529/928343940067667643902898143818117653), (5318293573619528711290060370797803607667/2359065529261681880350961572828935619119), (-13027197312078228082098695632569243402590420/2165384596732381358615964581579253982085263), 1, 0, 0, 0], ![(151/53687225492736), (-4732788212202079/657053549497581824), (-1500455164382774234879/6001532768483853809368), (4376479710843642526484299167/16821252099850417494181073200), (767391364143321956604257826343773/132726354692432531605156865293808), (92158418805367722954035822815113831197/12377919200902235252038641917574902040), (10475252818259790164102980806742481468056/3931775882102803133918269288048226031865), (290647770973386155406544308225163462383331971/10826922983661906793079822907896269910426315), (-76/5), 1, 0, 0], ![(-69905328623/71582967323648), (25356541364445/46932396392684416), (787161044680496502221975/192049048591483321899776), (15945561689262782529370349169/672850083994016699767242928), (1243477381072346524209861164239165/37921815626409294744330532941088), (23864947565445718263864628801716377803/2475583840180447050407728383514980408), (-75720259252818328140805876227765084142127/6290841411364485014269230860877161650984), (-234403275407970870776645169080095257098760459/2165384596732381358615964581579253982085263), (931/4), 0, 1, 0], ![(182707109395/1626885620992), (5055171113380675419/375459171141475328), (16523048659928326437893279/192049048591483321899776), (711243624735671388174656954937/4893455156320121452852675840), (2983098331522191665972814029830865/75843631252818589488661065882176), (-21057369184542869807596952885046033797/900212305520162563784628503096356512), (121110569964989727799501535376726321606191/6290841411364485014269230860877161650984), (-8060994593626767754612029529730338302597950325/17323076773859050868927716652634031856682104), (-33649/4), 0, 0, 1]] +def diag : Fin 12 → ℚ := ![(719362265183875514031831/80), (2241901650221566802946477/29905985680), (251273382509543244726680285481/58665495490855520), (67665692048064246008207072762959935/96024524295741660949888), (728057950683394731739150325146150246911/3058409472700075908032922400), (108338208476274428350963672152933245890750071/758436312528185894886610658821760), (108453147364963664982597490767469840705457591313/3000707685067208545948761676987855040), (6271591283527639024356191326842301046070501531512463/1006534625818317602283076937740345864157440), (43644256453302925372827507467823711516761413624303125/34646153547718101737855433305268063713364208), 0, 0, 0] + +def keyIndexTable : Fin 24 → Fin 13 → Fin 13 → Fin 84 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 10, 11, 12, 13, 14, 15, 16, 17, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 10, 0, 18, 19, 20, 21, 22, 23, 24, 0, 0], ![0, 0, 0, 37, 38, 39, 40, 41, 42, 43, 44, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 11, 18, 0, 25, 26, 27, 28, 29, 0, 0, 0], ![1, 0, 37, 0, 45, 46, 47, 48, 49, 50, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 12, 19, 25, 0, 30, 31, 32, 33, 0, 0, 0], ![2, 0, 38, 45, 0, 51, 52, 53, 54, 55, 0, 0, 0], ![10, 37, 0, 0, 61, 62, 63, 64, 65, 66, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 13, 20, 26, 30, 0, 34, 35, 0, 0, 0, 0], ![3, 0, 39, 46, 51, 0, 56, 57, 58, 0, 0, 0, 0], ![11, 38, 0, 61, 0, 67, 68, 69, 70, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 14, 21, 27, 31, 34, 0, 36, 0, 0, 0, 0], ![4, 0, 40, 47, 52, 56, 0, 59, 60, 0, 0, 0, 0], ![12, 39, 0, 62, 67, 0, 71, 72, 73, 0, 0, 0, 0], ![18, 45, 61, 0, 0, 75, 76, 77, 78, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 15, 22, 28, 32, 35, 36, 0, 0, 0, 0, 0], ![5, 0, 41, 48, 53, 57, 59, 0, 0, 0, 0, 0, 0], ![13, 40, 0, 63, 68, 71, 0, 74, 0, 0, 0, 0, 0], ![19, 46, 62, 0, 75, 0, 79, 80, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 7, 16, 23, 29, 33, 0, 36, 0, 0, 0, 0, 0], ![6, 0, 42, 49, 54, 58, 60, 0, 0, 0, 0, 0, 0], ![14, 41, 0, 64, 69, 72, 74, 0, 0, 0, 0, 0, 0], ![20, 47, 63, 0, 76, 79, 0, 81, 0, 0, 0, 0, 0], ![25, 51, 67, 75, 0, 0, 82, 83, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 8, 17, 24, 0, 33, 35, 0, 0, 0, 0, 0, 0], ![7, 0, 43, 50, 55, 0, 60, 0, 0, 0, 0, 0, 0], ![15, 42, 0, 65, 70, 73, 0, 0, 0, 0, 0, 0, 0], ![21, 48, 64, 0, 77, 80, 81, 0, 0, 0, 0, 0, 0], ![26, 52, 68, 76, 0, 82, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 9, 0, 24, 29, 32, 34, 0, 0, 0, 0, 0, 0], ![8, 0, 44, 0, 55, 58, 59, 0, 0, 0, 0, 0, 0], ![16, 43, 0, 66, 0, 73, 74, 0, 0, 0, 0, 0, 0], ![22, 49, 65, 0, 78, 0, 81, 0, 0, 0, 0, 0, 0], ![27, 53, 69, 77, 0, 83, 0, 0, 0, 0, 0, 0, 0], ![30, 56, 71, 79, 82, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 9, 17, 23, 28, 31, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 44, 50, 54, 57, 0, 0, 0, 0, 0, 0, 0], ![17, 44, 0, 66, 70, 72, 0, 0, 0, 0, 0, 0, 0], ![23, 50, 66, 0, 78, 80, 0, 0, 0, 0, 0, 0, 0], ![28, 54, 70, 78, 0, 83, 0, 0, 0, 0, 0, 0, 0], ![31, 57, 72, 80, 83, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 8, 16, 22, 27, 30, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 43, 49, 53, 56, 0, 0, 0, 0, 0, 0, 0], ![0, 44, 0, 65, 69, 71, 0, 0, 0, 0, 0, 0, 0], ![24, 0, 66, 0, 77, 79, 0, 0, 0, 0, 0, 0, 0], ![29, 55, 0, 78, 0, 82, 0, 0, 0, 0, 0, 0, 0], ![32, 58, 73, 0, 83, 0, 0, 0, 0, 0, 0, 0, 0], ![34, 59, 74, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 7, 15, 21, 26, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 42, 48, 52, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 43, 0, 64, 68, 0, 0, 0, 0, 0, 0, 0, 0], ![24, 50, 65, 0, 76, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 55, 70, 77, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![33, 0, 73, 80, 82, 0, 0, 0, 0, 0, 0, 0, 0], ![35, 60, 0, 81, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 6, 14, 20, 25, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 41, 47, 51, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 42, 0, 63, 67, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 49, 64, 0, 75, 0, 0, 0, 0, 0, 0, 0, 0], ![29, 54, 69, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![33, 58, 72, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 60, 74, 0, 82, 0, 0, 0, 0, 0, 0, 0, 0], ![36, 0, 0, 81, 83, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 5, 13, 19, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 40, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 41, 0, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![22, 48, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![28, 53, 68, 75, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![32, 57, 71, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![35, 59, 0, 79, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![36, 0, 74, 80, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 4, 12, 18, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 39, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 40, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![21, 47, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![27, 52, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![31, 56, 0, 75, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![34, 0, 71, 76, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 59, 72, 77, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![36, 60, 73, 78, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 3, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 46, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![26, 51, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![30, 0, 67, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 56, 68, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![34, 57, 69, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![35, 58, 70, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![25, 0, 61, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 51, 62, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![30, 52, 63, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![31, 53, 64, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![32, 54, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![33, 55, 66, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 45, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![25, 46, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![26, 47, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![27, 48, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![28, 49, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![29, 50, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![18, 38, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![19, 39, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![20, 40, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![21, 41, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![22, 42, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![23, 43, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![24, 44, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![14, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 24) (j : Fin ((n.val+1)/2)) (x : Fin ((23-n.val+2)/2)) : Fin 84 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 84 → FourTerm 23 := ![⟨⟨23,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨23,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨23,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨23,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨23,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨23,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨23,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨23,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨23,by decide⟩,(⟨10,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨23,by decide⟩,(⟨11,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨22,by decide⟩,(⟨10,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨10,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨5,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨6,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨9,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨9,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨21,by decide⟩,(⟨10,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨4,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨20,by decide⟩,(⟨9,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨5,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨9,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨6,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨1,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨4,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨8,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨19,by decide⟩,(⟨9,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨5,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨18,by decide⟩,(⟨8,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨2,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨5,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨7,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨17,by decide⟩,(⟨8,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨6,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨16,by decide⟩,(⟨7,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨3,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨6,by decide⟩,⟨4,by decide⟩)⟩, ⟨⟨15,by decide⟩,(⟨7,by decide⟩,⟨4,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 12, + (fourTermLabels (by omega : 23 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 12, + (fourTermLabels (by omega : 23 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 11, + (fourTermLabels (by omega : 23 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 11, + (fourTermLabels (by omega : 23 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 10, + (fourTermLabels (by omega : 23 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 10, + (fourTermLabels (by omega : 23 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 9, + (fourTermLabels (by omega : 23 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 9, + (fourTermLabels (by omega : 23 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 8, + (fourTermLabels (by omega : 23 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 8, + (fourTermLabels (by omega : 23 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover_10 : ∀ j : Fin 5, ∀ x : Fin 7, + (fourTermLabels (by omega : 23 ≤ 23) ⟨10,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨10,j,x⟩).toFinset=keys (keyIndex 10 j x) := by decide +kernel +lemma cover_11 : ∀ j : Fin 6, ∀ x : Fin 7, + (fourTermLabels (by omega : 23 ≤ 23) ⟨11,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨11,j,x⟩).toFinset=keys (keyIndex 11 j x) := by decide +kernel +lemma cover_12 : ∀ j : Fin 6, ∀ x : Fin 6, + (fourTermLabels (by omega : 23 ≤ 23) ⟨12,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨12,j,x⟩).toFinset=keys (keyIndex 12 j x) := by decide +kernel +lemma cover_13 : ∀ j : Fin 7, ∀ x : Fin 6, + (fourTermLabels (by omega : 23 ≤ 23) ⟨13,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨13,j,x⟩).toFinset=keys (keyIndex 13 j x) := by decide +kernel +lemma cover_14 : ∀ j : Fin 7, ∀ x : Fin 5, + (fourTermLabels (by omega : 23 ≤ 23) ⟨14,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨14,j,x⟩).toFinset=keys (keyIndex 14 j x) := by decide +kernel +lemma cover_15 : ∀ j : Fin 8, ∀ x : Fin 5, + (fourTermLabels (by omega : 23 ≤ 23) ⟨15,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨15,j,x⟩).toFinset=keys (keyIndex 15 j x) := by decide +kernel +lemma cover_16 : ∀ j : Fin 8, ∀ x : Fin 4, + (fourTermLabels (by omega : 23 ≤ 23) ⟨16,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨16,j,x⟩).toFinset=keys (keyIndex 16 j x) := by decide +kernel +lemma cover_17 : ∀ j : Fin 9, ∀ x : Fin 4, + (fourTermLabels (by omega : 23 ≤ 23) ⟨17,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨17,j,x⟩).toFinset=keys (keyIndex 17 j x) := by decide +kernel +lemma cover_18 : ∀ j : Fin 9, ∀ x : Fin 3, + (fourTermLabels (by omega : 23 ≤ 23) ⟨18,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨18,j,x⟩).toFinset=keys (keyIndex 18 j x) := by decide +kernel +lemma cover_19 : ∀ j : Fin 10, ∀ x : Fin 3, + (fourTermLabels (by omega : 23 ≤ 23) ⟨19,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨19,j,x⟩).toFinset=keys (keyIndex 19 j x) := by decide +kernel +lemma cover_20 : ∀ j : Fin 10, ∀ x : Fin 2, + (fourTermLabels (by omega : 23 ≤ 23) ⟨20,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨20,j,x⟩).toFinset=keys (keyIndex 20 j x) := by decide +kernel +lemma cover_21 : ∀ j : Fin 11, ∀ x : Fin 2, + (fourTermLabels (by omega : 23 ≤ 23) ⟨21,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨21,j,x⟩).toFinset=keys (keyIndex 21 j x) := by decide +kernel +lemma cover_22 : ∀ j : Fin 11, ∀ x : Fin 1, + (fourTermLabels (by omega : 23 ≤ 23) ⟨22,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨22,j,x⟩).toFinset=keys (keyIndex 22 j x) := by decide +kernel +lemma cover_23 : ∀ j : Fin 12, ∀ x : Fin 1, + (fourTermLabels (by omega : 23 ≤ 23) ⟨23,j,x⟩).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) ⟨23,j,x⟩).toFinset=keys (keyIndex 23 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 23, (fourTermLabels (by omega : 23 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 23 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x + · exact cover_10 j x + · exact cover_11 j x + · exact cover_12 j x + · exact cover_13 j x + · exact cover_14 j x + · exact cover_15 j x + · exact cover_16 j x + · exact cover_17 j x + · exact cover_18 j x + · exact cover_19 j x + · exact cover_20 j x + · exact cover_21 j x + · exact cover_22 j x + · exact cover_23 j x +lemma representatives_checked : ∀ a : Fin 84, + (fourTermLabels (by omega : 23 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 23 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 23 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 23 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 84, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 23, + (fourTermLabels (by omega : 23 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 84, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 23 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 84, ∀ b : FourTerm 23, + (fourTermLabels (by omega : 23 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 23 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*(0 : Fin 12).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*(1 : Fin 12).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*(2 : Fin 12).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*(3 : Fin 12).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*(4 : Fin 12).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_5 : ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*(5 : Fin 12).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_6 : ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*(6 : Fin 12).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_7 : ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*(7 : Fin 12).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_8 : ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*(8 : Fin 12).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_9 : ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*(9 : Fin 12).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_10 : ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*(10 : Fin 12).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_11 : ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*(11 : Fin 12).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns 11 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 12, ∀ v : Fin 84, (∑ b ∈ fibers v, fourTermEval 23 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 23 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 + · exact columns_checked_5 + · exact columns_checked_6 + · exact columns_checked_7 + · exact columns_checked_8 + · exact columns_checked_9 + · exact columns_checked_10 + · exact columns_checked_11 +lemma gram_checked_0 : ∀ v : Fin 12, (∑ a : Fin 84, columns (0 : Fin 12) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 12, (∑ a : Fin 84, columns (1 : Fin 12) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 12, (∑ a : Fin 84, columns (2 : Fin 12) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 12, (∑ a : Fin 84, columns (3 : Fin 12) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 12, (∑ a : Fin 84, columns (4 : Fin 12) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_5 : ∀ v : Fin 12, (∑ a : Fin 84, columns (5 : Fin 12) a * columns v a / setFactorial (keys a)) = Z 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_6 : ∀ v : Fin 12, (∑ a : Fin 84, columns (6 : Fin 12) a * columns v a / setFactorial (keys a)) = Z 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_7 : ∀ v : Fin 12, (∑ a : Fin 84, columns (7 : Fin 12) a * columns v a / setFactorial (keys a)) = Z 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_8 : ∀ v : Fin 12, (∑ a : Fin 84, columns (8 : Fin 12) a * columns v a / setFactorial (keys a)) = Z 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_9 : ∀ v : Fin 12, (∑ a : Fin 84, columns (9 : Fin 12) a * columns v a / setFactorial (keys a)) = Z 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_10 : ∀ v : Fin 12, (∑ a : Fin 84, columns (10 : Fin 12) a * columns v a / setFactorial (keys a)) = Z 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_11 : ∀ v : Fin 12, (∑ a : Fin 84, columns (11 : Fin 12) a * columns v a / setFactorial (keys a)) = Z 11 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 12, ∀ v : Fin 12, (∑ a : Fin 84, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 + · exact gram_checked_5 + · exact gram_checked_6 + · exact gram_checked_7 + · exact gram_checked_8 + · exact gram_checked_9 + · exact gram_checked_10 + · exact gram_checked_11 +lemma rows_table_checked_0 : ∀ v : Fin 12, integerTableEval 23 SumTable23.sums (0 : Fin 12) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 12, integerTableEval 23 SumTable23.sums (1 : Fin 12) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 12, integerTableEval 23 SumTable23.sums (2 : Fin 12) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 12, integerTableEval 23 SumTable23.sums (3 : Fin 12) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 12, integerTableEval 23 SumTable23.sums (4 : Fin 12) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_5 : ∀ v : Fin 12, integerTableEval 23 SumTable23.sums (5 : Fin 12) v = Y 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_6 : ∀ v : Fin 12, integerTableEval 23 SumTable23.sums (6 : Fin 12) v = Y 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_7 : ∀ v : Fin 12, integerTableEval 23 SumTable23.sums (7 : Fin 12) v = Y 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_8 : ∀ v : Fin 12, integerTableEval 23 SumTable23.sums (8 : Fin 12) v = Y 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_9 : ∀ v : Fin 12, integerTableEval 23 SumTable23.sums (9 : Fin 12) v = Y 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_10 : ∀ v : Fin 12, integerTableEval 23 SumTable23.sums (10 : Fin 12) v = Y 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_11 : ∀ v : Fin 12, integerTableEval 23 SumTable23.sums (11 : Fin 12) v = Y 11 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 12, ∀ v : Fin 12, integerTableEval 23 SumTable23.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 + · exact rows_table_checked_5 + · exact rows_table_checked_6 + · exact rows_table_checked_7 + · exact rows_table_checked_8 + · exact rows_table_checked_9 + · exact rows_table_checked_10 + · exact rows_table_checked_11 +lemma rows_checked (u v : Fin 12) : exactFourEval 23 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 23 SumTable23.sums SumTable23.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) (0 : Fin 12) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) (1 : Fin 12) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) (2 : Fin 12) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) (3 : Fin 12) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) (4 : Fin 12) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_5 : ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) (5 : Fin 12) v = W 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_6 : ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) (6 : Fin 12) v = W 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_7 : ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) (7 : Fin 12) v = W 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_8 : ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) (8 : Fin 12) v = W 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_9 : ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) (9 : Fin 12) v = W 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_10 : ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) (10 : Fin 12) v = W 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_11 : ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) (11 : Fin 12) v = W 11 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 12, ∀ v : Fin 12, (Z * tableComparison 23 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 + · exact product_checked_5 + · exact product_checked_6 + · exact product_checked_7 + · exact product_checked_8 + · exact product_checked_9 + · exact product_checked_10 + · exact product_checked_11 +lemma compression_checked_0 : ∀ v : Fin 12, (W * Z) (0 : Fin 12) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 12, (W * Z) (1 : Fin 12) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 12, (W * Z) (2 : Fin 12) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 12, (W * Z) (3 : Fin 12) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 12, (W * Z) (4 : Fin 12) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_5 : ∀ v : Fin 12, (W * Z) (5 : Fin 12) v = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_6 : ∀ v : Fin 12, (W * Z) (6 : Fin 12) v = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_7 : ∀ v : Fin 12, (W * Z) (7 : Fin 12) v = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_8 : ∀ v : Fin 12, (W * Z) (8 : Fin 12) v = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_9 : ∀ v : Fin 12, (W * Z) (9 : Fin 12) v = M 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_10 : ∀ v : Fin 12, (W * Z) (10 : Fin 12) v = M 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_11 : ∀ v : Fin 12, (W * Z) (11 : Fin 12) v = M 11 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 12, ∀ v : Fin 12, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 + · exact compression_checked_5 + · exact compression_checked_6 + · exact compression_checked_7 + · exact compression_checked_8 + · exact compression_checked_9 + · exact compression_checked_10 + · exact compression_checked_11 +lemma ldl_checked_0 : ∀ v : Fin 12, (∑ k : Fin 12, L (0 : Fin 12) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 12, (∑ k : Fin 12, L (1 : Fin 12) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 12, (∑ k : Fin 12, L (2 : Fin 12) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 12, (∑ k : Fin 12, L (3 : Fin 12) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 12, (∑ k : Fin 12, L (4 : Fin 12) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_5 : ∀ v : Fin 12, (∑ k : Fin 12, L (5 : Fin 12) k * diag k * L v k) = M 5 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_6 : ∀ v : Fin 12, (∑ k : Fin 12, L (6 : Fin 12) k * diag k * L v k) = M 6 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_7 : ∀ v : Fin 12, (∑ k : Fin 12, L (7 : Fin 12) k * diag k * L v k) = M 7 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_8 : ∀ v : Fin 12, (∑ k : Fin 12, L (8 : Fin 12) k * diag k * L v k) = M 8 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_9 : ∀ v : Fin 12, (∑ k : Fin 12, L (9 : Fin 12) k * diag k * L v k) = M 9 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_10 : ∀ v : Fin 12, (∑ k : Fin 12, L (10 : Fin 12) k * diag k * L v k) = M 10 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_11 : ∀ v : Fin 12, (∑ k : Fin 12, L (11 : Fin 12) k * diag k * L v k) = M 11 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 12, ∀ v : Fin 12, (∑ k : Fin 12, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 + · exact ldl_checked_5 + · exact ldl_checked_6 + · exact ldl_checked_7 + · exact ldl_checked_8 + · exact ldl_checked_9 + · exact ldl_checked_10 + · exact ldl_checked_11 +lemma diag_checked : ∀ u : Fin 12, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 23 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 23 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 23 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 23 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 23 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate23 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate5.lean b/lean/OAI/Analysis/LaughlinGap/Certificate5.lean new file mode 100644 index 0000000000000000000000000000000000000000..f376feb80cf5a579ff3e2313b199bad4dd2bfe6f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate5.lean @@ -0,0 +1,154 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CachedIntegerRows +import OAI.Analysis.LaughlinGap.FourTables +import OAI.Analysis.LaughlinGap.SumTable5 + +namespace OAI + +/-! Certificate5. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate5 + +def keys : Fin 1 → Finset (Fin 25) := ![{0,1,2,3}] +def fibers : Fin 1 → Finset (FourTerm 5) := ![{⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}] +def columns : Matrix (Fin 3) (Fin 1) ℚ := ![![24], ![-12], ![30]] +def Y : Matrix (Fin 3) (Fin 3) ℚ := ![![(-691918059642960348268939/469762048000000000000000), (143591010688663997337363/469762048000000000000000), (52406720056687264286281/187904819200000000000000)], ![(143591010688663997337363/469762048000000000000000), (-235485533349233444433063/1879048192000000000000000), (-32668914245365634602367/187904819200000000000000)], ![(52406720056687264286281/187904819200000000000000), (-32668914245365634602367/187904819200000000000000), (-382288393294507346704323/26843545600000000000000)]] +def Z : Matrix (Fin 3) (Fin 3) ℚ := ![![48, -24, 60], ![-24, 12, -30], ![60, -30, 75]] +def W : Matrix (Fin 3) (Fin 3) ℚ := ![![(62270372121978546147806337/15032385536000000000000000), (-41616573336114019844377/644245094400000000000000), (778609652914953277125223/15032385536000000000000000)], ![(-62270372121978546147806337/30064771072000000000000000), (41616573336114019844377/1288490188800000000000000), (-778609652914953277125223/30064771072000000000000000)], ![(62270372121978546147806337/12025908428800000000000000), (-41616573336114019844377/515396075520000000000000), (778609652914953277125223/12025908428800000000000000)]] +def M : Matrix (Fin 3) (Fin 3) ℚ := ![![(109249990074931830815538167/536870912000000000000000), (-109249990074931830815538167/1073741824000000000000000), (109249990074931830815538167/429496729600000000000000)], ![(-109249990074931830815538167/1073741824000000000000000), (109249990074931830815538167/2147483648000000000000000), (-109249990074931830815538167/858993459200000000000000)], ![(109249990074931830815538167/429496729600000000000000), (-109249990074931830815538167/858993459200000000000000), (109249990074931830815538167/343597383680000000000000)]] +def L : Matrix (Fin 3) (Fin 3) ℚ := ![![1, 0, 0], ![(-1/2), 1, 0], ![(5/4), 0, 1]] +def diag : Fin 3 → ℚ := ![(109249990074931830815538167/536870912000000000000000), 0, 0] + +lemma keys_checked : fourKeys (by omega : 5 ≤ 23) = Finset.univ.image keys := by decide +kernel +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma fibers_checked_0 : ∀ b : FourTerm 5, + (fourTermLabels (by omega : 5 ≤ 23) b).toFinset=keys 0 ↔ b ∈ fibers 0 := by decide +kernel +lemma fibers_checked : ∀ a : Fin 1, ∀ b : FourTerm 5, + (fourTermLabels (by omega : 5 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := by + intro a + fin_cases a + · exact fibers_checked_0 +lemma columns_checked_0 : ∀ v : Fin 1, (∑ b ∈ fibers v, fourTermEval 5 (2*(0 : Fin 3).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 5 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 1, (∑ b ∈ fibers v, fourTermEval 5 (2*(1 : Fin 3).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 5 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 1, (∑ b ∈ fibers v, fourTermEval 5 (2*(2 : Fin 3).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 5 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 3, ∀ v : Fin 1, (∑ b ∈ fibers v, fourTermEval 5 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 5 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 +lemma gram_checked_0 : ∀ v : Fin 3, (∑ a : Fin 1, columns (0 : Fin 3) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 3, (∑ a : Fin 1, columns (1 : Fin 3) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 3, (∑ a : Fin 1, columns (2 : Fin 3) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 3, ∀ v : Fin 3, (∑ a : Fin 1, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 +lemma rows_table_checked_0 : ∀ v : Fin 3, integerTableEval 5 SumTable5.sums (0 : Fin 3) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 3, integerTableEval 5 SumTable5.sums (1 : Fin 3) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 3, integerTableEval 5 SumTable5.sums (2 : Fin 3) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 3, ∀ v : Fin 3, integerTableEval 5 SumTable5.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 +lemma rows_checked (u v : Fin 3) : exactFourEval 5 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 5 SumTable5.sums SumTable5.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 3, (Z * tableComparison 5 (1/200000) Y) (0 : Fin 3) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 3, (Z * tableComparison 5 (1/200000) Y) (1 : Fin 3) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 3, (Z * tableComparison 5 (1/200000) Y) (2 : Fin 3) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 3, ∀ v : Fin 3, (Z * tableComparison 5 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 +lemma compression_checked_0 : ∀ v : Fin 3, (W * Z) (0 : Fin 3) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 3, (W * Z) (1 : Fin 3) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 3, (W * Z) (2 : Fin 3) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 3, ∀ v : Fin 3, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 +lemma ldl_checked_0 : ∀ v : Fin 3, (∑ k : Fin 3, L (0 : Fin 3) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 3, (∑ k : Fin 3, L (1 : Fin 3) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 3, (∑ k : Fin 3, L (2 : Fin 3) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 3, ∀ v : Fin 3, (∑ k : Fin 3, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 +lemma diag_checked : ∀ u : Fin 3, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 5 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 5 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 5 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 5 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 5 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate5 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate6.lean b/lean/OAI/Analysis/LaughlinGap/Certificate6.lean new file mode 100644 index 0000000000000000000000000000000000000000..abc5573457414897a91000d518107f2561e1ce87 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate6.lean @@ -0,0 +1,84 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Certificate5 + +namespace OAI + +/-! Certificate6. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate6 + +def keys : Fin 1 → Finset (Fin 25) := ![{0,1,2,4}] +def fibers : Fin 1 → Finset (FourTerm 6) := ![{⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}] +def columns : Matrix (Fin 3) (Fin 1) ℚ := ![![0], ![0], ![0]] +def Y : Matrix (Fin 3) (Fin 3) ℚ := ![![(-796881811066228176743533/53687091200000000000000), (1382924902976753673/335544320000000000), (2719883565749028608244643/375809638400000000000000)], ![(1382924902976753673/335544320000000000), (-253735112474554296132261/134217728000000000000000), (-79579850485959191284893/46976204800000000000000)], ![(2719883565749028608244643/375809638400000000000000), (-79579850485959191284893/46976204800000000000000), (-692584773830283706404217/75161927680000000000000)]] +def Z : Matrix (Fin 3) (Fin 3) ℚ := ![![0, 0, 0], ![0, 0, 0], ![0, 0, 0]] +def W : Matrix (Fin 3) (Fin 3) ℚ := ![![0, 0, 0], ![0, 0, 0], ![0, 0, 0]] +def M : Matrix (Fin 3) (Fin 3) ℚ := ![![0, 0, 0], ![0, 0, 0], ![0, 0, 0]] +def L : Matrix (Fin 3) (Fin 3) ℚ := ![![1, 0, 0], ![0, 1, 0], ![0, 0, 1]] +def diag : Fin 3 → ℚ := ![0, 0, 0] + +lemma keys_checked : fourKeys (by omega : 6 ≤ 23) = Finset.univ.image keys := by decide +kernel +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma fibers_checked_0 : ∀ b : FourTerm 6, + (fourTermLabels (by omega : 6 ≤ 23) b).toFinset=keys 0 ↔ b ∈ fibers 0 := by decide +kernel +lemma fibers_checked : ∀ a : Fin 1, ∀ b : FourTerm 6, + (fourTermLabels (by omega : 6 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := by + intro a + fin_cases a + · exact fibers_checked_0 +lemma columns_checked_0 : ∀ v : Fin 1, (∑ b ∈ fibers v, fourTermEval 6 (2*(0 : Fin 3).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 6 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 1, (∑ b ∈ fibers v, fourTermEval 6 (2*(1 : Fin 3).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 6 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 1, (∑ b ∈ fibers v, fourTermEval 6 (2*(2 : Fin 3).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 6 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 3, ∀ v : Fin 1, (∑ b ∈ fibers v, fourTermEval 6 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 6 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 +lemma gram_checked_0 : ∀ v : Fin 3, (∑ a : Fin 1, columns (0 : Fin 3) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 3, (∑ a : Fin 1, columns (1 : Fin 3) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 3, (∑ a : Fin 1, columns (2 : Fin 3) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 3, ∀ v : Fin 3, (∑ a : Fin 1, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 6 (by omega) := by + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 6 (by omega) by simpa using this + apply fourCertificate_of_rational exactRows (1/200000) (by omega : 6 ≤ 23) + have hg : rationalCreatedGram (by omega : 6 ≤ 23) = 0 := by + ext u v + obtain ⟨u,rfl⟩ := (fourCopyEquiv 6).symm.surjective u + obtain ⟨v,rfl⟩ := (fourCopyEquiv 6).symm.surjective v + rw [rationalCreatedGram_of_columns (by omega : 6 ≤ 23) keys columns keys_checked keys_injective] + · have hz : Z=0 := by ext i j; fin_cases i <;> fin_cases j <;> rfl + simpa only [hz,Matrix.zero_apply] using gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 6 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + simpa [rationalFourCompression,hg] using (Matrix.PosSemidef.zero : (0 : Matrix (FourCopy 6) (FourCopy 6) ℂ).PosSemidef) +end Certificate6 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate7.lean b/lean/OAI/Analysis/LaughlinGap/Certificate7.lean new file mode 100644 index 0000000000000000000000000000000000000000..a6b51810b56c7425268cf4d8ffcd206a031fa4a7 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate7.lean @@ -0,0 +1,230 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Certificate5 +import OAI.Analysis.LaughlinGap.FastFourKeys +import OAI.Analysis.LaughlinGap.SumTable7 + +namespace OAI + +/-! Certificate7. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate7 + +def keys : Fin 2 → Finset (Fin 25) := ![{0,1,2,5}, {0,1,3,4}] +def fibers : Fin 2 → Finset (FourTerm 7) := ![{⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}] +def columns : Matrix (Fin 4) (Fin 2) ℚ := ![![360, -360], ![0, 0], ![-90, 90], ![630, -630]] +def Y : Matrix (Fin 4) (Fin 4) ℚ := ![![(-4632089907509278349061891/46976204800000000000000), (327691045601249463001419/46976204800000000000000), (85691451729534780245181/6710886400000000000000), (-1280593247714135855042781/6710886400000000000000)], ![(327691045601249463001419/46976204800000000000000), (-3603080105019277846386081/469762048000000000000000), (109645300320687128044413/11744051200000000000000), (40370480375433730078707/838860800000000000000)], ![(85691451729534780245181/6710886400000000000000), (109645300320687128044413/11744051200000000000000), (-295378677873477919377801/11744051200000000000000), (-223612408700275743444459/6710886400000000000000)], ![(-1280593247714135855042781/6710886400000000000000), (40370480375433730078707/838860800000000000000), (-223612408700275743444459/6710886400000000000000), (-899527074001425723560433/1677721600000000000000)]] +def Z : Matrix (Fin 4) (Fin 4) ℚ := ![![1440, 0, -360, 2520], ![0, 0, 0, 0], ![-360, 0, 90, -630], ![2520, 0, -630, 4410]] +def W : Matrix (Fin 4) (Fin 4) ℚ := ![![(12494818706487725615278993/2818572288000000000000000), (-93990311649210049995013/563714457600000000000000), (-1459595678781352891762489/7516192768000000000000000), (894423686122077676008831/7516192768000000000000000)], ![0, 0, 0, 0], ![(-12494818706487725615278993/11274289152000000000000000), (93990311649210049995013/2254857830400000000000000), (1459595678781352891762489/30064771072000000000000000), (-894423686122077676008831/30064771072000000000000000)], ![(12494818706487725615278993/1610612736000000000000000), (-93990311649210049995013/322122547200000000000000), (-1459595678781352891762489/4294967296000000000000000), (894423686122077676008831/4294967296000000000000000)]] +def M : Matrix (Fin 4) (Fin 4) ℚ := ![![(634493824578772364340601041/93952409600000000000000), 0, (-634493824578772364340601041/375809638400000000000000), (634493824578772364340601041/53687091200000000000000)], ![0, 0, 0, 0], ![(-634493824578772364340601041/375809638400000000000000), 0, (634493824578772364340601041/1503238553600000000000000), (-634493824578772364340601041/214748364800000000000000)], ![(634493824578772364340601041/53687091200000000000000), 0, (-634493824578772364340601041/214748364800000000000000), (4441456772051406550384207287/214748364800000000000000)]] +def L : Matrix (Fin 4) (Fin 4) ℚ := ![![1, 0, 0, 0], ![0, 1, 0, 0], ![(-1/4), 0, 1, 0], ![(7/4), 0, 0, 1]] +def diag : Fin 4 → ℚ := ![(634493824578772364340601041/93952409600000000000000), 0, 0, 0] + +def keyIndexTable : Fin 8 → Fin 13 → Fin 13 → Fin 2 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 8) (j : Fin ((n.val+1)/2)) (x : Fin ((7-n.val+2)/2)) : Fin 2 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 2 → FourTerm 7 := ![⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 4, + (fourTermLabels (by omega : 7 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 7 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 4, + (fourTermLabels (by omega : 7 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 7 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 3, + (fourTermLabels (by omega : 7 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 7 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 3, + (fourTermLabels (by omega : 7 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 7 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 2, + (fourTermLabels (by omega : 7 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 7 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 2, + (fourTermLabels (by omega : 7 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 7 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 1, + (fourTermLabels (by omega : 7 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 7 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 1, + (fourTermLabels (by omega : 7 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 7 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 7, (fourTermLabels (by omega : 7 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 7 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x +lemma representatives_checked : ∀ a : Fin 2, + (fourTermLabels (by omega : 7 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 7 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 7 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 7 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 2, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 7, + (fourTermLabels (by omega : 7 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 2, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 7 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 2, ∀ b : FourTerm 7, + (fourTermLabels (by omega : 7 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 7 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 2, (∑ b ∈ fibers v, fourTermEval 7 (2*(0 : Fin 4).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 7 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 2, (∑ b ∈ fibers v, fourTermEval 7 (2*(1 : Fin 4).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 7 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 2, (∑ b ∈ fibers v, fourTermEval 7 (2*(2 : Fin 4).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 7 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 2, (∑ b ∈ fibers v, fourTermEval 7 (2*(3 : Fin 4).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 7 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 4, ∀ v : Fin 2, (∑ b ∈ fibers v, fourTermEval 7 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 7 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 +lemma gram_checked_0 : ∀ v : Fin 4, (∑ a : Fin 2, columns (0 : Fin 4) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 4, (∑ a : Fin 2, columns (1 : Fin 4) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 4, (∑ a : Fin 2, columns (2 : Fin 4) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 4, (∑ a : Fin 2, columns (3 : Fin 4) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 4, ∀ v : Fin 4, (∑ a : Fin 2, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 +lemma rows_table_checked_0 : ∀ v : Fin 4, integerTableEval 7 SumTable7.sums (0 : Fin 4) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 4, integerTableEval 7 SumTable7.sums (1 : Fin 4) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 4, integerTableEval 7 SumTable7.sums (2 : Fin 4) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 4, integerTableEval 7 SumTable7.sums (3 : Fin 4) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 4, ∀ v : Fin 4, integerTableEval 7 SumTable7.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 +lemma rows_checked (u v : Fin 4) : exactFourEval 7 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 7 SumTable7.sums SumTable7.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 4, (Z * tableComparison 7 (1/200000) Y) (0 : Fin 4) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 4, (Z * tableComparison 7 (1/200000) Y) (1 : Fin 4) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 4, (Z * tableComparison 7 (1/200000) Y) (2 : Fin 4) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 4, (Z * tableComparison 7 (1/200000) Y) (3 : Fin 4) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 4, ∀ v : Fin 4, (Z * tableComparison 7 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 +lemma compression_checked_0 : ∀ v : Fin 4, (W * Z) (0 : Fin 4) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 4, (W * Z) (1 : Fin 4) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 4, (W * Z) (2 : Fin 4) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 4, (W * Z) (3 : Fin 4) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 4, ∀ v : Fin 4, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 +lemma ldl_checked_0 : ∀ v : Fin 4, (∑ k : Fin 4, L (0 : Fin 4) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 4, (∑ k : Fin 4, L (1 : Fin 4) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 4, (∑ k : Fin 4, L (2 : Fin 4) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 4, (∑ k : Fin 4, L (3 : Fin 4) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 4, ∀ v : Fin 4, (∑ k : Fin 4, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 +lemma diag_checked : ∀ u : Fin 4, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 7 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 7 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 7 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 7 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 7 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate7 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate8.lean b/lean/OAI/Analysis/LaughlinGap/Certificate8.lean new file mode 100644 index 0000000000000000000000000000000000000000..1a7e9c4efaedc378d5bfb6ebb7b7cbd5a7766111 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate8.lean @@ -0,0 +1,233 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Certificate7 +import OAI.Analysis.LaughlinGap.SumTable8 + +namespace OAI + +/-! Certificate8. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate8 + +def keys : Fin 3 → Finset (Fin 25) := ![{0,1,2,6}, {0,1,3,5}, {0,2,3,4}] +def fibers : Fin 3 → Finset (FourTerm 8) := ![{⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}] +def columns : Matrix (Fin 4) (Fin 3) ℚ := ![![0, 0, 0], ![-360, 360, -360], ![360, -360, 360], ![-630, 630, -630]] +def Y : Matrix (Fin 4) (Fin 4) ℚ := ![![(-1827294336107386054342149/5368709120000000000000), (-789463800364931469995103/13421772800000000000000), (3526618533545862210398961/26843545600000000000000), (492113156078622412304121/13421772800000000000000)], ![(-789463800364931469995103/13421772800000000000000), (-1254450751674697246750761/46976204800000000000000), (3487489846557600630411933/93952409600000000000000), (3450831678396568633599/6710886400000000000000)], ![(3526618533545862210398961/26843545600000000000000), (3487489846557600630411933/93952409600000000000000), (-18773913360925793266587393/187904819200000000000000), (377817184867522132286589/2684354560000000000000)], ![(492113156078622412304121/13421772800000000000000), (3450831678396568633599/6710886400000000000000), (377817184867522132286589/2684354560000000000000), (-7761563551634662760452407/6710886400000000000000)]] +def Z : Matrix (Fin 4) (Fin 4) ℚ := ![![0, 0, 0, 0], ![0, 720, -720, 1260], ![0, -720, 720, -1260], ![0, 1260, -1260, 2205]] +def W : Matrix (Fin 4) (Fin 4) ℚ := ![![0, 0, 0, 0], ![(3239659704157609296158071/90194313216000000000000000), (3989767778471444755797239/45097156608000000000000000), (-21574246831047834561617711/90194313216000000000000000), (3842033729311192602927967/45097156608000000000000000)], ![(-3239659704157609296158071/90194313216000000000000000), (-3989767778471444755797239/45097156608000000000000000), (21574246831047834561617711/90194313216000000000000000), (-3842033729311192602927967/45097156608000000000000000)], ![(3239659704157609296158071/51539607552000000000000000), (3989767778471444755797239/25769803776000000000000000), (-21574246831047834561617711/51539607552000000000000000), (3842033729311192602927967/25769803776000000000000000)]] +def M : Matrix (Fin 4) (Fin 4) ℚ := ![![0, 0, 0, 0], ![0, (258005402643479389100760441/751619276800000000000000), (-258005402643479389100760441/751619276800000000000000), (258005402643479389100760441/429496729600000000000000)], ![0, (-258005402643479389100760441/751619276800000000000000), (258005402643479389100760441/751619276800000000000000), (-258005402643479389100760441/429496729600000000000000)], ![0, (258005402643479389100760441/429496729600000000000000), (-258005402643479389100760441/429496729600000000000000), (1806037818504355723705323087/1717986918400000000000000)]] +def L : Matrix (Fin 4) (Fin 4) ℚ := ![![1, 0, 0, 0], ![0, 1, 0, 0], ![0, -1, 1, 0], ![0, (7/4), 0, 1]] +def diag : Fin 4 → ℚ := ![0, (258005402643479389100760441/751619276800000000000000), 0, 0] + +def keyIndexTable : Fin 9 → Fin 13 → Fin 13 → Fin 3 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 9) (j : Fin ((n.val+1)/2)) (x : Fin ((8-n.val+2)/2)) : Fin 3 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 3 → FourTerm 8 := ![⟨⟨8,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 5, + (fourTermLabels (by omega : 8 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 8 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 4, + (fourTermLabels (by omega : 8 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 8 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 4, + (fourTermLabels (by omega : 8 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 8 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 3, + (fourTermLabels (by omega : 8 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 8 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 3, + (fourTermLabels (by omega : 8 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 8 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 2, + (fourTermLabels (by omega : 8 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 8 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 2, + (fourTermLabels (by omega : 8 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 8 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 1, + (fourTermLabels (by omega : 8 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 8 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 1, + (fourTermLabels (by omega : 8 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 8 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 8, (fourTermLabels (by omega : 8 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 8 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x +lemma representatives_checked : ∀ a : Fin 3, + (fourTermLabels (by omega : 8 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 8 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 8 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 8 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 3, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 8, + (fourTermLabels (by omega : 8 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 3, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 8 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 3, ∀ b : FourTerm 8, + (fourTermLabels (by omega : 8 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 8 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 3, (∑ b ∈ fibers v, fourTermEval 8 (2*(0 : Fin 4).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 8 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 3, (∑ b ∈ fibers v, fourTermEval 8 (2*(1 : Fin 4).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 8 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 3, (∑ b ∈ fibers v, fourTermEval 8 (2*(2 : Fin 4).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 8 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 3, (∑ b ∈ fibers v, fourTermEval 8 (2*(3 : Fin 4).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 8 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 4, ∀ v : Fin 3, (∑ b ∈ fibers v, fourTermEval 8 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 8 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 +lemma gram_checked_0 : ∀ v : Fin 4, (∑ a : Fin 3, columns (0 : Fin 4) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 4, (∑ a : Fin 3, columns (1 : Fin 4) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 4, (∑ a : Fin 3, columns (2 : Fin 4) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 4, (∑ a : Fin 3, columns (3 : Fin 4) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 4, ∀ v : Fin 4, (∑ a : Fin 3, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 +lemma rows_table_checked_0 : ∀ v : Fin 4, integerTableEval 8 SumTable8.sums (0 : Fin 4) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 4, integerTableEval 8 SumTable8.sums (1 : Fin 4) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 4, integerTableEval 8 SumTable8.sums (2 : Fin 4) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 4, integerTableEval 8 SumTable8.sums (3 : Fin 4) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 4, ∀ v : Fin 4, integerTableEval 8 SumTable8.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 +lemma rows_checked (u v : Fin 4) : exactFourEval 8 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 8 SumTable8.sums SumTable8.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 4, (Z * tableComparison 8 (1/200000) Y) (0 : Fin 4) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 4, (Z * tableComparison 8 (1/200000) Y) (1 : Fin 4) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 4, (Z * tableComparison 8 (1/200000) Y) (2 : Fin 4) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 4, (Z * tableComparison 8 (1/200000) Y) (3 : Fin 4) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 4, ∀ v : Fin 4, (Z * tableComparison 8 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 +lemma compression_checked_0 : ∀ v : Fin 4, (W * Z) (0 : Fin 4) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 4, (W * Z) (1 : Fin 4) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 4, (W * Z) (2 : Fin 4) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 4, (W * Z) (3 : Fin 4) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 4, ∀ v : Fin 4, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 +lemma ldl_checked_0 : ∀ v : Fin 4, (∑ k : Fin 4, L (0 : Fin 4) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 4, (∑ k : Fin 4, L (1 : Fin 4) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 4, (∑ k : Fin 4, L (2 : Fin 4) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 4, (∑ k : Fin 4, L (3 : Fin 4) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 4, ∀ v : Fin 4, (∑ k : Fin 4, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 +lemma diag_checked : ∀ u : Fin 4, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 8 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 8 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 8 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 8 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 8 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate8 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Certificate9.lean b/lean/OAI/Analysis/LaughlinGap/Certificate9.lean new file mode 100644 index 0000000000000000000000000000000000000000..3403eb5ffbcf66c9a7a643c8ad5cff8f9fd8a81b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Certificate9.lean @@ -0,0 +1,263 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CachedIntegerRows +import OAI.Analysis.LaughlinGap.FastFourKeys +import OAI.Analysis.LaughlinGap.FourTables +import OAI.Analysis.LaughlinGap.SumTable9 + +namespace OAI + +/-! Certificate9. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin +namespace Certificate9 + +def keys : Fin 5 → Finset (Fin 25) := ![{0,1,2,7}, {0,1,3,6}, {0,1,4,5}, {0,2,3,5}, {1,2,3,4}] +def fibers : Fin 5 → Finset (FourTerm 9) := ![{⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨8,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩}, {⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨0,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨1,by decide⟩,(⟨0,by decide⟩,⟨4,by decide⟩)⟩}, {⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨7,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨0,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨2,by decide⟩,(⟨0,by decide⟩,⟨3,by decide⟩)⟩}, {⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨6,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨2,by decide⟩,⟨1,by decide⟩)⟩,⟨⟨5,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨4,by decide⟩,(⟨1,by decide⟩,⟨2,by decide⟩)⟩,⟨⟨3,by decide⟩,(⟨1,by decide⟩,⟨3,by decide⟩)⟩}] +def columns : Matrix (Fin 5) (Fin 5) ℚ := ![![7560, -7560, 10080, -2520, 2520], ![1890, -1890, 1080, 810, -810], ![-945, 945, -540, -405, 405], ![-945, 945, -1260, 315, -315], ![22680, -22680, 22680, 0, 0]] +def Y : Matrix (Fin 5) (Fin 5) ℚ := ![![(-1993356271308944354745267/3355443200000000000000), (-3284709033344580598207581/3355443200000000000000), (220435709772188372765463/3355443200000000000000), (18025848804266699467101/20971520000000000000), (-5110372706225052814324011/419430400000000000000)], ![(-3284709033344580598207581/3355443200000000000000), (-6303681221439531121448661/46976204800000000000000), (3680632002651070355996409/23488102400000000000000), (-4180244998969476023589/33554432000000000000), (-101619883073527424950473/83886080000000000000)], ![(220435709772188372765463/3355443200000000000000), (3680632002651070355996409/23488102400000000000000), (-7301855792057631625658517/23488102400000000000000), (221714838839488589341929/419430400000000000000), (72921350514083330593971/83886080000000000000)], ![(18025848804266699467101/20971520000000000000), (-4180244998969476023589/33554432000000000000), (221714838839488589341929/419430400000000000000), (-351953897925137600168457/209715200000000000000), (-3864463501759889910633/2621440000000000000)], ![(-5110372706225052814324011/419430400000000000000), (-101619883073527424950473/83886080000000000000), (72921350514083330593971/83886080000000000000), (-3864463501759889910633/2621440000000000000), (-4006946887530397561029987/52428800000000000000)]] +def Z : Matrix (Fin 5) (Fin 5) ℚ := ![![80640, 0, 0, -10080, 136080], ![0, 4320, -2160, 0, 22680], ![0, -2160, 1080, 0, -11340], ![-10080, 0, 0, 1260, -17010], ![136080, 22680, -11340, -17010, 348705]] +def W : Matrix (Fin 5) (Fin 5) ℚ := ![![(187789732893557986355732909/45097156608000000000000000), (852854645877236107590373/1610612736000000000000000), (26558559273364667810549/1073741824000000000000000), (-66283059844861654687943/234881024000000000000000), (114410356059279766804427/805306368000000000000000)], ![(76256789444904740126269/1717986918400000000000000), (3418297737558505895268851/45097156608000000000000000), (-662438168393439514960939/4294967296000000000000000), (114303922948592796181173/1879048192000000000000000), (137534591949037451604679/7516192768000000000000000)], ![(-76256789444904740126269/3435973836800000000000000), (-3418297737558505895268851/90194313216000000000000000), (662438168393439514960939/8589934592000000000000000), (-114303922948592796181173/3758096384000000000000000), (-137534591949037451604679/15032385536000000000000000)], ![(-187789732893557986355732909/360777252864000000000000000), (-852854645877236107590373/12884901888000000000000000), (-26558559273364667810549/8589934592000000000000000), (66283059844861654687943/1879048192000000000000000), (-114410356059279766804427/6442450944000000000000000)], ![(218269542035503357649300487/30064771072000000000000000), (10833974170364873890217/8388608000000000000000), (-824632527242586486455931/1073741824000000000000000), (-1178902849702080633344289/7516192768000000000000000), (36057424509515756401347/107374182400000000000000)]] +def M : Matrix (Fin 5) (Fin 5) ℚ := ![![(240230765972923924837514271/671088640000000000000), (73232800741607405694442011/13421772800000000000000), (-73232800741607405694442011/26843545600000000000000), (-240230765972923924837514271/5368709120000000000000), (2123065138869905335790481801/3355443200000000000000)], ![(73232800741607405694442011/13421772800000000000000), (404223759648674750677002093/375809638400000000000000), (-404223759648674750677002093/751619276800000000000000), (-73232800741607405694442011/107374182400000000000000), (99686153092794506430654393/6710886400000000000000)], ![(-73232800741607405694442011/26843545600000000000000), (-404223759648674750677002093/751619276800000000000000), (404223759648674750677002093/1503238553600000000000000), (73232800741607405694442011/214748364800000000000000), (-99686153092794506430654393/13421772800000000000000)], ![(-240230765972923924837514271/5368709120000000000000), (-73232800741607405694442011/107374182400000000000000), (73232800741607405694442011/214748364800000000000000), (240230765972923924837514271/42949672960000000000000), (-2123065138869905335790481801/26843545600000000000000)], ![(2123065138869905335790481801/3355443200000000000000), (99686153092794506430654393/6710886400000000000000), (-99686153092794506430654393/13421772800000000000000), (-2123065138869905335790481801/26843545600000000000000), (61509577179384813336430493133/53687091200000000000000)]] +def L : Matrix (Fin 5) (Fin 5) ℚ := ![![1, 0, 0, 0, 0], ![(24410933580535801898147337/1601538439819492832250095140), 1, 0, 0, 0], ![(-24410933580535801898147337/3203076879638985664500190280), (-1/2), 1, 0, 0], ![(-1/8), 0, 0, 1, 0], ![(707688379623301778596827267/400384609954873208062523785), (21/4), 0, 0, 1]] +def diag : Fin 5 → ℚ := ![(240230765972923924837514271/671088640000000000000), (9333200318605444737087413951811823601046190946453691/9404274718004121289989064264515584000000000000000), 0, 0, 0] + +def keyIndexTable : Fin 10 → Fin 13 → Fin 13 → Fin 5 := ![![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 2, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], ![![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]]] +def keyIndex (n : Fin 10) (j : Fin ((n.val+1)/2)) (x : Fin ((9-n.val+2)/2)) : Fin 5 := + keyIndexTable n ⟨j.val,by have := j.isLt; have := n.isLt; omega⟩ ⟨x.val,by have := x.isLt; omega⟩ +def representatives : Fin 5 → FourTerm 9 := ![⟨⟨9,by decide⟩,(⟨2,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨9,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨9,by decide⟩,(⟨4,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨8,by decide⟩,(⟨3,by decide⟩,⟨0,by decide⟩)⟩, ⟨⟨7,by decide⟩,(⟨3,by decide⟩,⟨1,by decide⟩)⟩] +lemma cover_0 : ∀ j : Fin 0, ∀ x : Fin 5, + (fourTermLabels (by omega : 9 ≤ 23) ⟨0,j,x⟩).Nodup → + (fourTermLabels (by omega : 9 ≤ 23) ⟨0,j,x⟩).toFinset=keys (keyIndex 0 j x) := by decide +kernel +lemma cover_1 : ∀ j : Fin 1, ∀ x : Fin 5, + (fourTermLabels (by omega : 9 ≤ 23) ⟨1,j,x⟩).Nodup → + (fourTermLabels (by omega : 9 ≤ 23) ⟨1,j,x⟩).toFinset=keys (keyIndex 1 j x) := by decide +kernel +lemma cover_2 : ∀ j : Fin 1, ∀ x : Fin 4, + (fourTermLabels (by omega : 9 ≤ 23) ⟨2,j,x⟩).Nodup → + (fourTermLabels (by omega : 9 ≤ 23) ⟨2,j,x⟩).toFinset=keys (keyIndex 2 j x) := by decide +kernel +lemma cover_3 : ∀ j : Fin 2, ∀ x : Fin 4, + (fourTermLabels (by omega : 9 ≤ 23) ⟨3,j,x⟩).Nodup → + (fourTermLabels (by omega : 9 ≤ 23) ⟨3,j,x⟩).toFinset=keys (keyIndex 3 j x) := by decide +kernel +lemma cover_4 : ∀ j : Fin 2, ∀ x : Fin 3, + (fourTermLabels (by omega : 9 ≤ 23) ⟨4,j,x⟩).Nodup → + (fourTermLabels (by omega : 9 ≤ 23) ⟨4,j,x⟩).toFinset=keys (keyIndex 4 j x) := by decide +kernel +lemma cover_5 : ∀ j : Fin 3, ∀ x : Fin 3, + (fourTermLabels (by omega : 9 ≤ 23) ⟨5,j,x⟩).Nodup → + (fourTermLabels (by omega : 9 ≤ 23) ⟨5,j,x⟩).toFinset=keys (keyIndex 5 j x) := by decide +kernel +lemma cover_6 : ∀ j : Fin 3, ∀ x : Fin 2, + (fourTermLabels (by omega : 9 ≤ 23) ⟨6,j,x⟩).Nodup → + (fourTermLabels (by omega : 9 ≤ 23) ⟨6,j,x⟩).toFinset=keys (keyIndex 6 j x) := by decide +kernel +lemma cover_7 : ∀ j : Fin 4, ∀ x : Fin 2, + (fourTermLabels (by omega : 9 ≤ 23) ⟨7,j,x⟩).Nodup → + (fourTermLabels (by omega : 9 ≤ 23) ⟨7,j,x⟩).toFinset=keys (keyIndex 7 j x) := by decide +kernel +lemma cover_8 : ∀ j : Fin 4, ∀ x : Fin 1, + (fourTermLabels (by omega : 9 ≤ 23) ⟨8,j,x⟩).Nodup → + (fourTermLabels (by omega : 9 ≤ 23) ⟨8,j,x⟩).toFinset=keys (keyIndex 8 j x) := by decide +kernel +lemma cover_9 : ∀ j : Fin 5, ∀ x : Fin 1, + (fourTermLabels (by omega : 9 ≤ 23) ⟨9,j,x⟩).Nodup → + (fourTermLabels (by omega : 9 ≤ 23) ⟨9,j,x⟩).toFinset=keys (keyIndex 9 j x) := by decide +kernel +lemma cover : ∀ b : FourTerm 9, (fourTermLabels (by omega : 9 ≤ 23) b).Nodup → + (fourTermLabels (by omega : 9 ≤ 23) b).toFinset=keys (keyIndex b.1 b.2.1 b.2.2) := by + rintro ⟨n,j,x⟩ + fin_cases n + · exact cover_0 j x + · exact cover_1 j x + · exact cover_2 j x + · exact cover_3 j x + · exact cover_4 j x + · exact cover_5 j x + · exact cover_6 j x + · exact cover_7 j x + · exact cover_8 j x + · exact cover_9 j x +lemma representatives_checked : ∀ a : Fin 5, + (fourTermLabels (by omega : 9 ≤ 23) (representatives a)).Nodup ∧ + (fourTermLabels (by omega : 9 ≤ 23) (representatives a)).toFinset=keys a := by decide +kernel +lemma keys_checked : fourKeys (by omega : 9 ≤ 23) = Finset.univ.image keys := + fourKeys_of_index (by omega : 9 ≤ 23) keys (fun b => keyIndex b.1 b.2.1 b.2.2) + representatives cover representatives_checked +lemma keys_injective : Function.Injective keys := by decide +kernel +lemma keys_card : ∀ a : Fin 5, (keys a).card=4 := by decide +kernel +lemma fibers_cover : ∀ b : FourTerm 9, + (fourTermLabels (by omega : 9 ≤ 23) b).Nodup → + b ∈ fibers (keyIndex b.1 b.2.1 b.2.2) := by + apply checkFourTerms_sound + decide +kernel +lemma fibers_sound : ∀ a : Fin 5, ∀ b ∈ fibers a, + (fourTermLabels (by omega : 9 ≤ 23) b).toFinset=keys a := by + apply checkFourFibersSound_sound + decide +kernel +lemma fibers_checked : ∀ a : Fin 5, ∀ b : FourTerm 9, + (fourTermLabels (by omega : 9 ≤ 23) b).toFinset=keys a ↔ b ∈ fibers a := + fourFibers_of_index (by omega : 9 ≤ 23) keys + (fun b => keyIndex b.1 b.2.1 b.2.2) fibers keys_injective keys_card cover fibers_cover fibers_sound +lemma columns_checked_0 : ∀ v : Fin 5, (∑ b ∈ fibers v, fourTermEval 9 (2*(0 : Fin 5).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 9 ≤ 23) b)) = columns 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_1 : ∀ v : Fin 5, (∑ b ∈ fibers v, fourTermEval 9 (2*(1 : Fin 5).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 9 ≤ 23) b)) = columns 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_2 : ∀ v : Fin 5, (∑ b ∈ fibers v, fourTermEval 9 (2*(2 : Fin 5).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 9 ≤ 23) b)) = columns 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_3 : ∀ v : Fin 5, (∑ b ∈ fibers v, fourTermEval 9 (2*(3 : Fin 5).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 9 ≤ 23) b)) = columns 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked_4 : ∀ v : Fin 5, (∑ b ∈ fibers v, fourTermEval 9 (2*(4 : Fin 5).val+1) b * Occupation.wordSign (fourTermLabels (by omega : 9 ≤ 23) b)) = columns 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma columns_checked : ∀ u : Fin 5, ∀ v : Fin 5, (∑ b ∈ fibers v, fourTermEval 9 (2*u.val+1) b * Occupation.wordSign (fourTermLabels (by omega : 9 ≤ 23) b)) = columns u v := by + intro u + fin_cases u + · exact columns_checked_0 + · exact columns_checked_1 + · exact columns_checked_2 + · exact columns_checked_3 + · exact columns_checked_4 +lemma gram_checked_0 : ∀ v : Fin 5, (∑ a : Fin 5, columns (0 : Fin 5) a * columns v a / setFactorial (keys a)) = Z 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_1 : ∀ v : Fin 5, (∑ a : Fin 5, columns (1 : Fin 5) a * columns v a / setFactorial (keys a)) = Z 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_2 : ∀ v : Fin 5, (∑ a : Fin 5, columns (2 : Fin 5) a * columns v a / setFactorial (keys a)) = Z 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_3 : ∀ v : Fin 5, (∑ a : Fin 5, columns (3 : Fin 5) a * columns v a / setFactorial (keys a)) = Z 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked_4 : ∀ v : Fin 5, (∑ a : Fin 5, columns (4 : Fin 5) a * columns v a / setFactorial (keys a)) = Z 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma gram_checked : ∀ u : Fin 5, ∀ v : Fin 5, (∑ a : Fin 5, columns u a * columns v a / setFactorial (keys a)) = Z u v := by + intro u + fin_cases u + · exact gram_checked_0 + · exact gram_checked_1 + · exact gram_checked_2 + · exact gram_checked_3 + · exact gram_checked_4 +lemma rows_table_checked_0 : ∀ v : Fin 5, integerTableEval 9 SumTable9.sums (0 : Fin 5) v = Y 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_1 : ∀ v : Fin 5, integerTableEval 9 SumTable9.sums (1 : Fin 5) v = Y 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_2 : ∀ v : Fin 5, integerTableEval 9 SumTable9.sums (2 : Fin 5) v = Y 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_3 : ∀ v : Fin 5, integerTableEval 9 SumTable9.sums (3 : Fin 5) v = Y 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked_4 : ∀ v : Fin 5, integerTableEval 9 SumTable9.sums (4 : Fin 5) v = Y 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma rows_table_checked : ∀ u : Fin 5, ∀ v : Fin 5, integerTableEval 9 SumTable9.sums u v = Y u v := by + intro u + fin_cases u + · exact rows_table_checked_0 + · exact rows_table_checked_1 + · exact rows_table_checked_2 + · exact rows_table_checked_3 + · exact rows_table_checked_4 +lemma rows_checked (u v : Fin 5) : exactFourEval 9 (2*u.val+1) (2*v.val+1) = Y u v := by + rw [exactFourEval_table 9 SumTable9.sums SumTable9.sums_checked] + exact rows_table_checked u v +lemma product_checked_0 : ∀ v : Fin 5, (Z * tableComparison 9 (1/200000) Y) (0 : Fin 5) v = W 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_1 : ∀ v : Fin 5, (Z * tableComparison 9 (1/200000) Y) (1 : Fin 5) v = W 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_2 : ∀ v : Fin 5, (Z * tableComparison 9 (1/200000) Y) (2 : Fin 5) v = W 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_3 : ∀ v : Fin 5, (Z * tableComparison 9 (1/200000) Y) (3 : Fin 5) v = W 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked_4 : ∀ v : Fin 5, (Z * tableComparison 9 (1/200000) Y) (4 : Fin 5) v = W 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma product_checked : ∀ u : Fin 5, ∀ v : Fin 5, (Z * tableComparison 9 (1/200000) Y) u v = W u v := by + intro u + fin_cases u + · exact product_checked_0 + · exact product_checked_1 + · exact product_checked_2 + · exact product_checked_3 + · exact product_checked_4 +lemma compression_checked_0 : ∀ v : Fin 5, (W * Z) (0 : Fin 5) v = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_1 : ∀ v : Fin 5, (W * Z) (1 : Fin 5) v = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_2 : ∀ v : Fin 5, (W * Z) (2 : Fin 5) v = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_3 : ∀ v : Fin 5, (W * Z) (3 : Fin 5) v = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked_4 : ∀ v : Fin 5, (W * Z) (4 : Fin 5) v = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma compression_checked : ∀ u : Fin 5, ∀ v : Fin 5, (W * Z) u v = M u v := by + intro u + fin_cases u + · exact compression_checked_0 + · exact compression_checked_1 + · exact compression_checked_2 + · exact compression_checked_3 + · exact compression_checked_4 +lemma ldl_checked_0 : ∀ v : Fin 5, (∑ k : Fin 5, L (0 : Fin 5) k * diag k * L v k) = M 0 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_1 : ∀ v : Fin 5, (∑ k : Fin 5, L (1 : Fin 5) k * diag k * L v k) = M 1 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_2 : ∀ v : Fin 5, (∑ k : Fin 5, L (2 : Fin 5) k * diag k * L v k) = M 2 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_3 : ∀ v : Fin 5, (∑ k : Fin 5, L (3 : Fin 5) k * diag k * L v k) = M 3 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked_4 : ∀ v : Fin 5, (∑ k : Fin 5, L (4 : Fin 5) k * diag k * L v k) = M 4 v := by + apply Arithmetic.checkVector_sound + decide +kernel +lemma ldl_checked : ∀ u : Fin 5, ∀ v : Fin 5, (∑ k : Fin 5, L u k * diag k * L v k) = M u v := by + intro u + fin_cases u + · exact ldl_checked_0 + · exact ldl_checked_1 + · exact ldl_checked_2 + · exact ldl_checked_3 + · exact ldl_checked_4 +lemma diag_checked : ∀ u : Fin 5, 0 ≤ diag u := by decide +kernel +lemma certificate : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 9 (by omega) := by + have hh := fourCertificate_of_tables exactRows (1/200000) (by omega : 9 ≤ 23) Y Z + suffices FourCertificate (fun a : Fin 8 => (exactRows a).toReal) ((1/200000:ℚ):ℝ) 9 (by omega) by simpa using this + apply hh + · intro u v + rw [exactFourEval_eq (by omega)] + exact rows_checked u v + · intro u v + rw [rationalCreatedGram_of_columns (by omega : 9 ≤ 23) keys columns keys_checked keys_injective] + · exact gram_checked u v + · intro i a + rw [fourColumn_eq_fiber (by omega : 9 ≤ 23) (2*i.val+1) (keys a) (fibers a) (fibers_checked a)] + exact columns_checked i a + · rw [Matrix.ext product_checked, Matrix.ext compression_checked] + apply rational_ldl_positive M L diag diag_checked + ext u v + rw [Matrix.mul_apply] + simpa only [Matrix.mul_diagonal,Matrix.transpose_apply] using (ldl_checked u v).symm +end Certificate9 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/CheckedTables.lean b/lean/OAI/Analysis/LaughlinGap/CheckedTables.lean new file mode 100644 index 0000000000000000000000000000000000000000..88e3b3c62f0a57fc0add8972db1fa3fe2fc58e71 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/CheckedTables.lean @@ -0,0 +1,40 @@ +import Mathlib + +namespace OAI + +/-! Checked Tables. -/ + +noncomputable section + + +namespace LaughlinGap.Arithmetic + +def checkMatrix {n m : ℕ} {α : Type*} [DecidableEq α] + (A B : Fin n → Fin m → α) : Bool := + (List.finRange n).all fun i => (List.finRange m).all fun j => decide (A i j = B i j) + +lemma checkMatrix_sound {n m : ℕ} {α : Type*} [DecidableEq α] + (A B : Fin n → Fin m → α) (h : checkMatrix A B = true) : ∀ i j, A i j = B i j := by + intro i j + unfold checkMatrix at h + have hh := List.all_eq_true.mp h i (List.mem_finRange i) + exact of_decide_eq_true (List.all_eq_true.mp hh j (List.mem_finRange j)) + +end LaughlinGap.Arithmetic + +namespace LaughlinGap.Arithmetic + +def checkVector {n : ℕ} {α : Type*} [DecidableEq α] + (A B : Fin n → α) : Bool := + (List.finRange n).all fun i => decide (A i = B i) + +lemma checkVector_sound {n : ℕ} {α : Type*} [DecidableEq α] + (A B : Fin n → α) (h : checkVector A B = true) : ∀ i, A i = B i := by + intro i + exact of_decide_eq_true (List.all_eq_true.mp h i (List.mem_finRange i)) + +end LaughlinGap.Arithmetic + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Contraction.lean b/lean/OAI/Analysis/LaughlinGap/Contraction.lean new file mode 100644 index 0000000000000000000000000000000000000000..7708907bbc43a9c57eb839893d50d85422ae1753 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Contraction.lean @@ -0,0 +1,622 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.PairEnergy + +namespace OAI + +/-! Contraction. -/ + +noncomputable section + + +namespace LaughlinGap +open scoped BigOperators InnerProduct Topology + +section BlockOperator +variable {ι E : Type*} [Fintype ι] [DecidableEq ι] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] [FiniteDimensional ℂ E] + +abbrev ColumnSpace (ι E : Type*) [Fintype ι] [NormedAddCommGroup E] := PiLp 2 (fun _ : ι => E) + +noncomputable def columnProjection (b : ι) : ColumnSpace ι E →L[ℂ] E := + (PiLp.projₗ 2 (fun _ : ι => E) b).toContinuousLinearMap + +noncomputable def columnInclusion (b : ι) : E →L[ℂ] ColumnSpace ι E := + (((WithLp.linearEquiv 2 ℂ (ι → E)).symm.toLinearMap).comp + (LinearMap.single ℂ (fun _ : ι => E) b)).toContinuousLinearMap + +omit [DecidableEq ι] in +@[simp] lemma columnProjection_apply (b : ι) (x : ColumnSpace ι E) : + columnProjection b x = x b := rfl + +@[simp] lemma columnInclusion_apply (b c : ι) (x : E) : + columnInclusion b x c = if c = b then x else 0 := by + change (Pi.single b x : ι → E) c = _ + rw [Pi.single_apply] + +noncomputable def blockOperator (M : Matrix ι ι ℂ) (T : E →L[ℂ] E) : + ColumnSpace ι E →L[ℂ] ColumnSpace ι E := + ∑ b, ∑ c, M b c • (columnInclusion b).comp (T.comp (columnProjection c)) + +@[simp] lemma blockOperator_apply (M : Matrix ι ι ℂ) (T : E →L[ℂ] E) + (x : ColumnSpace ι E) (b : ι) : blockOperator M T x b = ∑ c, M b c • T (x c) := by + classical + simp [blockOperator, columnInclusion_apply, smul_ite] + +lemma blockOperator_inner (M : Matrix ι ι ℂ) (T : E →L[ℂ] E) + (x y : ColumnSpace ι E) : + inner ℂ x (blockOperator M T y) = ∑ b, ∑ c, M b c * inner ℂ (x b) (T (y c)) := by + simp only [PiLp.inner_apply, blockOperator_apply, inner_sum, inner_smul_right] + +theorem blockOperator_tendsto {M : ℕ → Matrix ι ι ℂ} {M₀ : Matrix ι ι ℂ} + {T : ℕ → E →L[ℂ] E} {T₀ : E →L[ℂ] E} + (hM : ∀ b c, Filter.Tendsto (fun Q => M Q b c) Filter.atTop (𝓝 (M₀ b c))) + (hT : Filter.Tendsto T Filter.atTop (𝓝 T₀)) : + Filter.Tendsto (fun Q => blockOperator (M Q) (T Q)) Filter.atTop (𝓝 (blockOperator M₀ T₀)) := by + apply tendsto_finsetSum + intro b _ + apply tendsto_finsetSum + intro c _ + apply (hM b c).smul + have hf : Continuous (fun T : E →L[ℂ] E => + (columnInclusion b).comp (T.comp (columnProjection c))) := by fun_prop + exact hf.continuousAt.tendsto.comp hT + +theorem matrixLift_inner_eq_block (A : ι → Module.End ℂ E) (M : Matrix ι ι ℂ) (x : E) : + inner ℂ x (matrixLift A M x) = + inner ℂ (WithLp.toLp 2 (fun b => A b x)) + (blockOperator M (1 : E →L[ℂ] E) (WithLp.toLp 2 (fun b => A b x))) := by + rw [blockOperator_inner] + simp only [matrixLift, LinearMap.coe_mk, AddHom.coe_mk, LinearMap.sum_apply, + LinearMap.smul_apply, Module.End.mul_apply, inner_sum, inner_smul_right, + LinearMap.adjoint_inner_right, one_apply_eq_self] + +theorem conjugated_matrix_transfer + (A : ι → Module.End ℂ E) (Δ : ℕ → E → E) + (eStar : E → ℝ) (eQ : ℕ → E → ℝ) {C₀ : ℝ} (hC₀ : 0 ≤ C₀) + (hA : ∀ x, (∑ b, ‖A b x‖ ^ 2) ≤ C₀ * eStar x) + (hΔ : ∀ᶠ Q in Filter.atTop, ∀ x, eStar (Δ Q x) ≤ eQ Q x) + (U : ℕ → E →L[ℂ] E) (M : ℕ → Matrix ι ι ℂ) (M₀ : Matrix ι ι ℂ) + (hU : Filter.Tendsto U Filter.atTop (𝓝 1)) + (hM : ∀ b c, Filter.Tendsto (fun Q => M Q b c) Filter.atTop (𝓝 (M₀ b c))) + (h₀ : (matrixLift A M₀).IsPositive) : + ∃ ρ : ℕ → ℝ, (∀ Q, 0 ≤ ρ Q) ∧ Filter.Tendsto ρ Filter.atTop (𝓝 0) ∧ + ∀ᶠ Q in Filter.atTop, ∀ x, + -(ρ Q) * eQ Q x ≤ + (∑ b, ∑ c, M Q b c * inner ℂ (U Q (A b (Δ Q x))) + (U Q (A c (Δ Q x)))).re := by + let S := blockOperator M₀ (1 : E →L[ℂ] E) + let T := fun Q => blockOperator (M Q) ((U Q).adjoint * U Q) + have hAdj : Filter.Tendsto (fun Q => (U Q).adjoint) Filter.atTop (𝓝 1) := by + simpa only [Function.comp_def, ContinuousLinearMap.adjoint_one] using + ContinuousLinearMap.adjoint.continuous.continuousAt.tendsto.comp hU + have hT : Filter.Tendsto T Filter.atTop (𝓝 S) := by + exact blockOperator_tendsto hM (by simpa using hAdj.mul hU) + refine ⟨fun Q => C₀ * ‖T Q - S‖, fun Q => mul_nonneg hC₀ (norm_nonneg _), + relative_column_error_tendsto hT, ?_⟩ + filter_upwards [hΔ] with Q hΔQ + intro x + have hp := relative_column_perturbation_bound (fun b x => A b x) (Δ Q) eStar (eQ Q) + hC₀ hA hΔQ (T Q) S (fun x => ?_) x + · simpa only [T, blockOperator_inner, PiLp.toLp_apply, mul_apply_eq_comp, + ContinuousLinearMap.adjoint_inner_right, RCLike.re_eq_complex_re] using hp + · rw [← matrixLift_inner_eq_block] + exact h₀.re_inner_nonneg_right x + +omit [DecidableEq ι] in + +theorem matrixLift_conjugated_inner (A : ι → Module.End ℂ E) (M : Matrix ι ι ℂ) + (U D : Module.End ℂ E) (x : E) : + inner ℂ x (matrixLift (fun b => U * A b * D) M x) = + ∑ b, ∑ c, M b c * inner ℂ (U (A b (D x))) (U (A c (D x))) := by + simp only [matrixLift, LinearMap.coe_mk, AddHom.coe_mk, LinearMap.sum_apply, + LinearMap.smul_apply, Module.End.mul_apply, inner_sum, inner_smul_right, + LinearMap.adjoint_inner_right] + +omit [Fintype ι] [DecidableEq ι] in + +theorem matrix_compression_tendsto {κ : Type*} [Fintype κ] + {W : ℕ → Matrix ι κ ℂ} {W₀ : Matrix ι κ ℂ} + {C : ℕ → Matrix κ κ ℂ} {C₀ : Matrix κ κ ℂ} + (hW : ∀ b r, Filter.Tendsto (fun Q => W Q b r) Filter.atTop (𝓝 (W₀ b r))) + (hC : ∀ r s, Filter.Tendsto (fun Q => C Q r s) Filter.atTop (𝓝 (C₀ r s))) + (b c : ι) : + Filter.Tendsto (fun Q => (W Q * C Q * (W Q).conjTranspose) b c) + Filter.atTop (𝓝 ((W₀ * C₀ * W₀.conjTranspose) b c)) := by + simp only [Matrix.mul_apply, Matrix.conjTranspose_apply] + apply tendsto_finsetSum + intro r _ + apply Filter.Tendsto.mul + · apply tendsto_finsetSum + intro s _ + exact (hW b s).mul (hC s r) + · exact (hW c r).star + +end BlockOperator +end LaughlinGap + +namespace LaughlinGap.Occupation +open scoped BigOperators Topology InnerProduct + +theorem extendLocal_relative_energy_bound {n m : ℕ} {ι : Type*} [Fintype ι] + (S : Module.End ℂ (Hilbert n)) (B : ι → Module.End ℂ (Hilbert n)) (c : ℝ) + (h : ∀ x, c * (∑ b, ‖B b x‖ ^ 2) ≤ (inner ℂ x (S x)).re) (x : Hilbert (n+m)) : + c * (∑ b, ‖extendLocal (B b) x‖ ^ 2) ≤ (inner ℂ x (extendLocal S x)).re := by + rw [inner_eq_sum_slice] + simp_rw [norm_sq_eq_sum_slice, slice_extendLocal] + rw [Complex.re_sum, Finset.sum_comm, Finset.mul_sum] + exact Finset.sum_le_sum (fun R _ => h (slice R x)) + +theorem local_relative_matrix_transfer {n L : ℕ} {ι : Type*} [Fintype ι] [DecidableEq ι] + (p : ι → Fin L) (j k : ι → Fin n) + (M : ℕ → Matrix ι ι ℂ) (M₀ : Matrix ι ι ℂ) + (hM : ∀ b c, Filter.Tendsto (fun Q => M Q b c) Filter.atTop (𝓝 (M₀ b c))) + (h₀ : (matrixLift (fun b => annihilation (k b) * annihilation (j b) * + localPairStar n (p b).val) M₀).IsPositive) : + ∃ ρ : ℕ → ℝ, (∀ Q, 0 ≤ ρ Q) ∧ Filter.Tendsto ρ Filter.atTop (𝓝 0) ∧ + ∀ᶠ Q in Filter.atTop, ∀ m (x : Hilbert (n+m)), + -(ρ Q) * (∑ a : Fin L, ‖extendLocal (localPair n Q a.val) x‖ ^ 2) ≤ + (inner ℂ x (extendLocal (matrixLift + (fun b => (localDeltaInv n Q).toLinearMap * + (annihilation (k b) * annihilation (j b) * localPairStar n (p b).val) * + (localDelta n Q).toLinearMap) (M Q)) x)).re := by + let A : ι → Module.End ℂ (Hilbert n) := + fun b => annihilation (k b) * annihilation (j b) * localPairStar n (p b).val + have hA (x : Hilbert n) : + ∑ b, ‖A b x‖ ^ 2 ≤ (Fintype.card ι : ℝ) * localPairEnergyStar n L x := by + apply annihilator_collection_bound p (fun a : Fin L => localPairStar n a.val) + (fun b y => annihilation (k b) (annihilation (j b) y)) + · intro a + simpa only [Finset.card_univ] using Finset.card_le_card + (Finset.filter_subset (fun b => p b = a) Finset.univ) + · intro b y + exact double_annihilation_norm_le (j b) (k b) y + have hΔ : ∀ᶠ Q in Filter.atTop, ∀ x, + localPairEnergyStar n L (localDelta n Q x) ≤ localPairEnergy n L Q x := by + filter_upwards [Filter.eventually_ge_atTop (L+2)] with Q hQ + intro x + exact localPairEnergy_transfer (by omega) (by omega) x + obtain ⟨ρ, hρ, ht, hq⟩ := conjugated_matrix_transfer A (fun Q x => localDelta n Q x) + (localPairEnergyStar n L) (fun Q => localPairEnergy n L Q) + (C₀ := (Fintype.card ι : ℝ)) (Nat.cast_nonneg _) hA hΔ + (localDeltaInv n) M M₀ (localDeltaInv_tendsto n) hM h₀ + refine ⟨ρ, hρ, ht, ?_⟩ + filter_upwards [hq] with Q hqQ + intro m x + apply extendLocal_relative_energy_bound _ (fun a : Fin L => localPair n Q a.val) (-ρ Q) ?_ x + intro y + rw [matrixLift_conjugated_inner] + exact hqQ y + +theorem localFour_factor_tendsto (p j k : ℕ) : + Filter.Tendsto (fun Q => pairRescalingFactor Q p / + (orbitalDiagonalFactor Q j * orbitalDiagonalFactor Q k)) Filter.atTop (𝓝 1) := by + simpa only [Pi.div_def, Pi.mul_def, one_mul, div_one] using (pairRescalingFactor_tendsto p).div + ((orbitalDiagonalFactor_tendsto j).mul (orbitalDiagonalFactor_tendsto k)) (by norm_num) + +theorem local_four_family_transfer {n L : ℕ} {ι κ : Type*} + [Fintype ι] [DecidableEq ι] [Fintype κ] + (p : ι → Fin L) (j k : ι → Fin n) + (s : ℕ → κ → ι → ℝ) (s₀ : κ → ι → ℝ) + (C : ℕ → Matrix κ κ ℂ) (C₀ : Matrix κ κ ℂ) + (hs : ∀ r b, Filter.Tendsto (fun Q => s Q r b) Filter.atTop (𝓝 (s₀ r b))) + (hC : ∀ r t, Filter.Tendsto (fun Q => C Q r t) Filter.atTop (𝓝 (C₀ r t))) + (h₀ : (matrixLift (fun r => ∑ b, (s₀ r b : ℂ) • + (annihilation (k b) * annihilation (j b) * localPairStar n (p b).val)) C₀).IsPositive) : + ∃ ρ : ℕ → ℝ, (∀ Q, 0 ≤ ρ Q) ∧ Filter.Tendsto ρ Filter.atTop (𝓝 0) ∧ + ∀ᶠ Q in Filter.atTop, ∀ m (x : Hilbert (n+m)), + -(ρ Q) * (∑ a : Fin L, ‖extendLocal (localPair n Q a.val) x‖ ^ 2) ≤ + (inner ℂ x (extendLocal (matrixLift + (fun r => ∑ b, (s Q r b : ℂ) • + (annihilation (k b) * annihilation (j b) * localPair n Q (p b).val)) (C Q)) x)).re := by + let A : ι → Module.End ℂ (Hilbert n) := + fun b => annihilation (k b) * annihilation (j b) * localPairStar n (p b).val + let w : ℕ → Matrix ι κ ℂ := fun Q b r => + ((s Q r b * (pairRescalingFactor Q (p b).val / + (orbitalDiagonalFactor Q (j b).val * orbitalDiagonalFactor Q (k b).val)) : ℝ) : ℂ) + let w₀ : Matrix ι κ ℂ := fun b r => (s₀ r b : ℂ) + have hw : ∀ b r, Filter.Tendsto (fun Q => w Q b r) Filter.atTop (𝓝 (w₀ b r)) := by + intro b r + have h := (hs r b).mul (localFour_factor_tendsto (p b).val (j b).val (k b).val) + simpa only [Function.comp_def, mul_one, w, w₀] using + Complex.continuous_ofReal.continuousAt.tendsto.comp h + have hM₀ : (matrixLift A (w₀ * C₀ * w₀.conjTranspose)).IsPositive := by + rw [matrixLift_columns] + simpa only [contractCombination, w₀, Complex.star_def, Complex.conj_ofReal] using h₀ + obtain ⟨ρ, hρ, ht, hq⟩ := local_relative_matrix_transfer p j k + (fun Q => w Q * C Q * (w Q).conjTranspose) (w₀ * C₀ * w₀.conjTranspose) + (matrix_compression_tendsto hw hC) hM₀ + refine ⟨ρ, hρ, ht, ?_⟩ + filter_upwards [hq, Filter.eventually_ge_atTop (n+L+2)] with Q hqQ hQ + intro m x + have hf (r : κ) : + contractCombination (fun b => (localDeltaInv n Q).toLinearMap * A b * + (localDelta n Q).toLinearMap) (fun b => w Q b r) = + ∑ b, (s Q r b : ℂ) • (annihilation (k b) * annihilation (j b) * localPair n Q (p b).val) := by + unfold contractCombination + apply Finset.sum_congr rfl + intro b _ + have hqb : (p b).val ≤ 2*Q-2 := by have := (p b).is_lt; omega + rw [localFour_conjugation (by omega : 0 < Q) (by omega : n ≤ Q+1) hqb] + simp [w, A, smul_smul] + have heq : matrixLift + (fun r => ∑ b, (s Q r b : ℂ) • + (annihilation (k b) * annihilation (j b) * localPair n Q (p b).val)) (C Q) = + matrixLift (fun b => (localDeltaInv n Q).toLinearMap * A b * + (localDelta n Q).toLinearMap) (w Q * C Q * (w Q).conjTranspose) := by + rw [matrixLift_columns] + simp only [hf] + rw [heq] + exact hqQ m x + +end LaughlinGap.Occupation + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct Topology ComplexOrder + +@[simp] lemma word_nil {n : ℕ} : word ([] : List (Fin n)) = 1 := rfl +@[simp] lemma word_cons {n : ℕ} (j : Fin n) (js : List (Fin n)) : + word (j :: js) = word js * annihilation j := rfl + +lemma annihilation_anticommute {n : ℕ} (i j : Fin n) : + annihilation i * annihilation j = -(annihilation j * annihilation i) := by + by_cases h : i = j + · subst j + have hz : annihilation i * annihilation i = 0 := transition_square i false + simp only [hz, neg_zero] + · exact transition_anticommute_of_ne h false false + +lemma word_perm_scalar {n : ℕ} {js ks : List (Fin n)} (h : js.Perm ks) : + ∃ c : ℂ, word js = c • word ks := by + induction h with + | nil => exact ⟨1, by simp⟩ + | cons j h ih => + obtain ⟨c,hc⟩ := ih + exact ⟨c, by simp only [word_cons, hc, smul_mul_assoc]⟩ + | swap i j js => + refine ⟨-1, ?_⟩ + rw [word_cons, word_cons, word_cons, word_cons] + rw [mul_assoc, annihilation_anticommute i j, mul_neg, ← mul_assoc] + simp only [neg_smul, one_smul] + | trans h h' ih ih' => + obtain ⟨c,hc⟩ := ih + obtain ⟨d,hd⟩ := ih' + exact ⟨c*d, by rw [hc, hd, smul_smul]⟩ + +lemma word_eq_zero_of_not_nodup {n : ℕ} (js : List (Fin n)) (h : ¬ js.Nodup) : + word js = 0 := by + induction js with + | nil => simp at h + | cons j js ih => + by_cases hj : js.Nodup + · have hm : j ∈ js := by simpa only [List.nodup_cons, hj, and_true, not_not] using h + obtain ⟨c,hc⟩ := word_perm_scalar (List.perm_cons_erase hm) + rw [word_cons, hc, word_cons, smul_mul_assoc, mul_assoc] + have hz : annihilation j * annihilation j = 0 := transition_square j false + rw [hz, mul_zero, smul_zero] + · rw [word_cons, ih hj, zero_mul] + +theorem word_normal_form {n : ℕ} (js : List (Fin n)) : + ∃ c : ℂ, word js = c • word (js.toFinset.sort (· ≤ ·)) := by + by_cases hn : js.Nodup + · apply word_perm_scalar + exact ((js.toFinset.sort_perm_toList (· ≤ ·)).trans (List.toFinset_toList hn)).symm + · exact ⟨0, by rw [word_eq_zero_of_not_nodup js hn, zero_smul]⟩ + +@[simp] lemma inner_vacuum_left {n : ℕ} (x : Hilbert n) : + inner ℂ (vacuum n) x = x ∅ := by + simp [vacuum, EuclideanSpace.inner_single_left] + +theorem basisContraction_adjoint_vacuum {n k : ℕ} (A : BasisLabel n k) : + (basisContraction A).adjoint (vacuum n) = EuclideanSpace.single A.val 1 := by + apply ext_inner_right ℂ + intro x + rw [LinearMap.adjoint_inner_left, inner_vacuum_left, basisContraction_apply_empty] + simp [EuclideanSpace.inner_single_left] + +noncomputable def allBasisContraction {n : ℕ} (A : Finset (Fin n)) : Module.End ℂ (Hilbert n) := + word (A.sort (· ≤ ·)) + +noncomputable def fullContraction {n : ℕ} (v : Hilbert n) : Module.End ℂ (Hilbert n) := + contractCombination allBasisContraction v + +@[simp] theorem fullContraction_single {n : ℕ} (A : Finset (Fin n)) (c : ℂ) : + fullContraction (EuclideanSpace.single A c) = star c • allBasisContraction A := by + classical + simp [fullContraction, contractCombination, PiLp.single_apply, apply_ite, ite_smul] + +@[simp] theorem fullContraction_add {n : ℕ} (v w : Hilbert n) : + fullContraction (v+w) = fullContraction v + fullContraction w := by + simp [fullContraction, contractCombination, add_smul, Finset.sum_add_distrib] + +@[simp] theorem fullContraction_smul {n : ℕ} (c : ℂ) (v : Hilbert n) : + fullContraction (c • v) = star c • fullContraction v := by + simp [fullContraction, contractCombination, smul_smul, Finset.smul_sum] + +@[simp] theorem fullContraction_zero {n : ℕ} : fullContraction (0 : Hilbert n) = 0 := by + simp [fullContraction, contractCombination] + +noncomputable def reconstruct {n : ℕ} : + Module.End ℂ (Hilbert n) →ₗ[ℂ] Module.End ℂ (Hilbert n) where + toFun B := fullContraction (B.adjoint (vacuum n)) + map_add' B B' := by simp + map_smul' c B := by + simp only [map_smulₛₗ, LinearMap.smul_apply, fullContraction_smul, + Complex.star_def, Complex.conj_conj, RingHom.id_apply] + +@[simp] lemma reconstruct_allBasisContraction {n : ℕ} (A : Finset (Fin n)) : + reconstruct (allBasisContraction A) = allBasisContraction A := by + change fullContraction ((basisContraction (⟨A,rfl⟩ : BasisLabel n A.card)).adjoint (vacuum n)) = _ + rw [basisContraction_adjoint_vacuum, fullContraction_single] + simp + +theorem reconstruct_word {n : ℕ} (js : List (Fin n)) : reconstruct (word js) = word js := by + obtain ⟨c,hc⟩ := word_normal_form js + rw [hc] + change reconstruct (c • allBasisContraction js.toFinset) = c • allBasisContraction js.toFinset + rw [map_smul, reconstruct_allBasisContraction] + +theorem reconstruct_four_pair {n : ℕ} (v : Fin n → Fin n → ℂ) (j k : Fin n) : + reconstruct (annihilation k * annihilation j * pairAnnihilator v) = + annihilation k * annihilation j * pairAnnihilator v := by + simp only [pairAnnihilator, Finset.mul_sum, mul_ite, mul_zero, mul_smul_comm, + map_sum] + apply Finset.sum_congr rfl + intro x _ + apply Finset.sum_congr rfl + intro y _ + by_cases h : x < y + · rw [ite_eq_left h, map_smul] + congr 1 + have he : annihilation k * annihilation j * (annihilation y * annihilation x) = + word [x,y,j,k] := by simp only [word_cons, word_nil, one_mul, mul_assoc] + rw [he, reconstruct_word] + · rw [ite_eq_right h, map_zero] + +noncomputable def createdGram {n : ℕ} {ι : Type*} (B : ι → Module.End ℂ (Hilbert n)) : + Matrix ι ι ℂ := fun r s => inner ℂ ((B r).adjoint (vacuum n)) ((B s).adjoint (vacuum n)) + +theorem annihilator_gram_positive {n : ℕ} {ι : Type*} [Fintype ι] [DecidableEq ι] + (B : ι → Module.End ℂ (Hilbert n)) (hB : ∀ r, reconstruct (B r) = B r) + (C : Matrix ι ι ℂ) (hC : C.IsHermitian) + (hG : (createdGram B * C * createdGram B).PosSemidef) : + (matrixLift B C).IsPositive := by + let W : Matrix (Finset (Fin n)) ι ℂ := fun A r => (B r).adjoint (vacuum n) A + have heq : W.conjTranspose * W = createdGram B := by + ext r s + change (∑ A : Finset (Fin n), star (W A r) * W A s) = _ + simp only [W, createdGram, PiLp.inner_apply, RCLike.inner_apply] + exact Finset.sum_congr rfl (fun A _ => mul_comm _ _) + have hp := matrixLift_gram_positive allBasisContraction W C hC (by rwa [heq]) + have hf (r : ι) : contractCombination allBasisContraction (fun A => W A r) = B r := hB r + simpa only [hf] using hp + +theorem local_four_family_transfer_of_gram {n L : ℕ} {ι κ : Type*} + [Fintype ι] [DecidableEq ι] [Fintype κ] [DecidableEq κ] + (p : ι → Fin L) (j k : ι → Fin n) + (s : ℕ → κ → ι → ℝ) (s₀ : κ → ι → ℝ) + (C : ℕ → Matrix κ κ ℂ) (C₀ : Matrix κ κ ℂ) + (hs : ∀ r b, Filter.Tendsto (fun Q => s Q r b) Filter.atTop (𝓝 (s₀ r b))) + (hC : ∀ r t, Filter.Tendsto (fun Q => C Q r t) Filter.atTop (𝓝 (C₀ r t))) + (hC₀ : C₀.IsHermitian) + (hG : let B := fun r => ∑ b, (s₀ r b : ℂ) • + (annihilation (k b) * annihilation (j b) * localPairStar n (p b).val) + (createdGram B * C₀ * createdGram B).PosSemidef) : + ∃ ρ : ℕ → ℝ, (∀ Q, 0 ≤ ρ Q) ∧ Filter.Tendsto ρ Filter.atTop (𝓝 0) ∧ + ∀ᶠ Q in Filter.atTop, ∀ m (x : Hilbert (n+m)), + -(ρ Q) * (∑ a : Fin L, ‖extendLocal (localPair n Q a.val) x‖ ^ 2) ≤ + (inner ℂ x (extendLocal (matrixLift + (fun r => ∑ b, (s Q r b : ℂ) • + (annihilation (k b) * annihilation (j b) * localPair n Q (p b).val)) (C Q)) x)).re := by + apply local_four_family_transfer p j k s s₀ C C₀ hs hC + apply annihilator_gram_positive _ _ C₀ hC₀ hG + intro r + simp only [map_sum, map_smul, localPairStar, reconstruct_four_pair] + +end LaughlinGap.Occupation + +namespace LaughlinGap +open scoped BigOperators + +theorem monic_eval_pos_of_nonnegative_coefficients (P : Polynomial ℝ) (hP : P.Monic) + (hc : ∀ k, 0 ≤ P.coeff k) {x : ℝ} (hx : 0 < x) : 0 < P.eval x := by + rw [Polynomial.eval_eq_sum, Polynomial.sum_def] + apply Finset.sum_pos' + · intro k _ + exact mul_nonneg (hc k) (pow_nonneg hx.le k) + · refine ⟨P.natDegree, Polynomial.natDegree_mem_support_of_nonzero hP.ne_zero, ?_⟩ + rw [hP.coeff_natDegree, one_mul] + exact pow_pos hx _ + +theorem symmetric_posSemidef_of_charpoly_coefficients {ι : Type*} + [Fintype ι] [DecidableEq ι] (M : Matrix ι ι ℝ) (hM : M.IsHermitian) + (hc : ∀ k, 0 ≤ (-M).charpoly.coeff k) : M.PosSemidef := by + rw [hM.posSemidef_iff_eigenvalues_nonneg] + intro i + by_contra hn + have hneg : hM.eigenvalues i < 0 := lt_of_not_ge hn + have hm : -hM.eigenvalues i ∈ spectrum ℝ (-M) := by + rw [← spectrum.neg_eq] + simpa only [Set.mem_neg, neg_neg] using hM.eigenvalues_mem_spectrum_real i + have hz := (Matrix.mem_spectrum_iff_isRoot_charpoly).mp hm + have hp := monic_eval_pos_of_nonnegative_coefficients (-M).charpoly + (-M).charpoly_monic hc (neg_pos.mpr hneg) + exact (ne_of_gt hp) hz + +theorem rational_charpoly_certificate_sound {ι : Type*} + [Fintype ι] [DecidableEq ι] (M : Matrix ι ι ℚ) (hM : M.IsHermitian) + (hc : ∀ k ≤ Fintype.card ι, 0 ≤ (-M).charpoly.coeff k) : + (M.map (algebraMap ℚ ℝ)).PosSemidef := by + apply symmetric_posSemidef_of_charpoly_coefficients + · exact hM.map _ (fun x => by simp) + · intro k + have heq : -(M.map (algebraMap ℚ ℝ)) = (-M).map (algebraMap ℚ ℝ) := by + ext i j + simp + rw [heq, Matrix.charpoly_map, Polynomial.coeff_map] + have hh : 0 ≤ (-M).charpoly.coeff k := by + by_cases hk : k ≤ Fintype.card ι + · exact hc k hk + · rw [Polynomial.coeff_eq_zero_of_natDegree_lt (by simpa using lt_of_not_ge hk)] + change (0 : ℝ) ≤ ((-M).charpoly.coeff k : ℝ) + exact_mod_cast hh + +end LaughlinGap + +namespace LaughlinGap +open scoped Topology + +theorem comparison_coefficient_tendsto {ρ : ℕ → ℝ} + (hρ : Filter.Tendsto ρ Filter.atTop (𝓝 0)) : + Filter.Tendsto (fun Q => 1 - (93527408868499 / 10^14 : ℝ) - + threeBodyTail Q - 1222*(3/10^6) - ρ Q) Filter.atTop (𝓝 gammaStar) := by + have h := ((threeBodyTail_tendsto.const_sub + (1 - (93527408868499 / 10^14 : ℝ))).sub_const (1222*(3/10^6))).sub hρ + simpa only [sub_zero, final_margin_arithmetic] using h + +theorem comparison_coefficient_eventually_lt {ρ : ℕ → ℝ} + (hρ : Filter.Tendsto ρ Filter.atTop (𝓝 0)) {γ : ℝ} (hγ : γ < gammaStar) : + ∃ Q₀ : ℕ, ∀ Q ≥ Q₀, γ < 1 - (93527408868499 / 10^14 : ℝ) - + threeBodyTail Q - 1222*(3/10^6) - ρ Q := by + exact Filter.eventually_atTop.mp ((comparison_coefficient_tendsto hρ).eventually + (Ioi_mem_nhds hγ)) + +theorem comparison_coefficient_eventually_one_div_twenty_five {ρ : ℕ → ℝ} + (hρ : Filter.Tendsto ρ Filter.atTop (𝓝 0)) : + ∃ Q₀ : ℕ, ∀ Q ≥ Q₀, (1/25 : ℝ) < 1 - (93527408868499 / 10^14 : ℝ) - + threeBodyTail Q - 1222*(3/10^6) - ρ Q := + comparison_coefficient_eventually_lt hρ one_div_twenty_five_lt_gammaStar + +end LaughlinGap + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct ComplexOrder + +abbrev PairLabel (n : ℕ) := {a : Fin n × Fin n // a.1 < a.2} + +noncomputable def basicPair {n : ℕ} (a : PairLabel n) : Module.End ℂ (Hilbert n) := + annihilation a.val.2 * annihilation a.val.1 + +noncomputable def pairContraction {n : ℕ} (v : PairLabel n → ℂ) : Module.End ℂ (Hilbert n) := + ∑ a, star (v a) • basicPair a + +noncomputable def oneContraction {n : ℕ} (a b : PairLabel n) : Module.End ℂ (Hilbert n) := + -(if a.val.1 = b.val.1 then creation b.val.2 * annihilation a.val.2 else 0) + + (if a.val.2 = b.val.1 then creation b.val.2 * annihilation a.val.1 else 0) + + (if a.val.1 = b.val.2 then creation b.val.1 * annihilation a.val.2 else 0) - + (if a.val.2 = b.val.2 then creation b.val.1 * annihilation a.val.1 else 0) + +lemma basicPair_middle {n : ℕ} (a b : PairLabel n) : + basicPair a * (basicPair b).adjoint = + (if a = b then 1 else 0) + oneContraction a b + (basicPair b).adjoint * basicPair a := by + have hcross : ¬(a.val.2 = b.val.1 ∧ a.val.1 = b.val.2) := by + rintro ⟨ha,hb⟩ + have h := a.property + rw [ha,hb] at h + exact lt_asymm h b.property + have hdiag : (a.val.1 = b.val.1 ∧ a.val.2 = b.val.2) ↔ a = b := by + constructor + · rintro ⟨h₁,h₂⟩ + apply Subtype.ext + exact Prod.ext h₁ h₂ + · rintro rfl; exact ⟨rfl,rfl⟩ + simp only [basicPair, adjoint_mul, annihilation_adjoint] + rw [← mul_assoc, pair_normal_order, ite_eq_right hcross] + simp only [hdiag] + unfold oneContraction + noncomm_ring + +lemma annihilation_commute_basicPair {n : ℕ} (i : Fin n) (a : PairLabel n) : + annihilation i * basicPair a = basicPair a * annihilation i := by + unfold basicPair + rw [← mul_assoc, annihilation_anticommute i a.val.2, neg_mul, mul_assoc, + annihilation_anticommute i a.val.1, mul_neg, neg_neg, ← mul_assoc] + +lemma basicPair_commute {n : ℕ} (a b : PairLabel n) : + basicPair a * basicPair b = basicPair b * basicPair a := by + change annihilation a.val.2 * annihilation a.val.1 * basicPair b = _ + rw [mul_assoc, annihilation_commute_basicPair, ← mul_assoc, + annihilation_commute_basicPair, mul_assoc] + rfl + +lemma pairContraction_commute {n : ℕ} (v w : PairLabel n → ℂ) : + pairContraction v * pairContraction w = pairContraction w * pairContraction v := by + simp only [pairContraction, Finset.sum_mul] + simp only [Finset.mul_sum] + simp only [smul_mul_assoc, mul_smul_comm, smul_smul] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro a _ + apply Finset.sum_congr rfl + intro b _ + rw [basicPair_commute, mul_comm] + +noncomputable def pairOneContraction {n : ℕ} (v w : PairLabel n → ℂ) : + Module.End ℂ (Hilbert n) := + ∑ a, ∑ b, (star (v a) * w b) • oneContraction a b + +theorem pairContraction_middle {n : ℕ} (v w : PairLabel n → ℂ) : + pairContraction v * (pairContraction w).adjoint = + (∑ a, star (v a) * w a) • 1 + pairOneContraction v w + + (pairContraction w).adjoint * pairContraction v := by + classical + simp only [pairContraction, map_sum, map_smulₛₗ, Complex.star_def, Complex.conj_conj, Finset.sum_mul] + simp only [Finset.mul_sum] + simp only [smul_mul_assoc, mul_smul_comm, smul_smul] + simp only [basicPair_middle, smul_add, Finset.sum_add_distrib] + have hdiag : (∑ a : PairLabel n, ∑ b : PairLabel n, + (star (v a) * w b) • (if a = b then (1 : Module.End ℂ (Hilbert n)) else 0)) = + (∑ a, star (v a) * w a) • 1 := by + simp [smul_ite, ← Finset.sum_smul] + simp only [mul_comm (w _) ((starRingEnd ℂ) (v _))] + simp only [Complex.star_def] at hdiag + rw [hdiag] + congr 1 + rw [Finset.sum_comm] + +noncomputable def pairHamiltonian {n : ℕ} {ι : Type*} [Fintype ι] + (v : ι → PairLabel n → ℂ) : Module.End ℂ (Hilbert n) := + ∑ p, (pairContraction (v p)).adjoint * pairContraction (v p) + +noncomputable def pairThreeTerm {n : ℕ} {ι : Type*} [Fintype ι] + (v : ι → PairLabel n → ℂ) : Module.End ℂ (Hilbert n) := + ∑ p, ∑ r, (pairContraction (v p)).adjoint * pairOneContraction (v p) (v r) * + pairContraction (v r) + +noncomputable def pairFourTerm {n : ℕ} {ι : Type*} [Fintype ι] + (v : ι → PairLabel n → ℂ) : Module.End ℂ (Hilbert n) := + ∑ p, ∑ r, (pairContraction (v r) * pairContraction (v p)).adjoint * + (pairContraction (v r) * pairContraction (v p)) + +theorem pairHamiltonian_square {n : ℕ} {ι : Type*} [Fintype ι] [DecidableEq ι] + (v : ι → PairLabel n → ℂ) + (hv : ∀ p r, (∑ a, star (v p a) * v r a) = if p = r then 1 else 0) : + pairHamiltonian v * pairHamiltonian v = + pairHamiltonian v + pairThreeTerm v + pairFourTerm v := by + classical + have hp (p r : ι) : + ((pairContraction (v p)).adjoint * pairContraction (v p)) * + ((pairContraction (v r)).adjoint * pairContraction (v r)) = + (if p = r then (pairContraction (v p)).adjoint * pairContraction (v r) else 0) + + (pairContraction (v p)).adjoint * pairOneContraction (v p) (v r) * pairContraction (v r) + + (pairContraction (v r) * pairContraction (v p)).adjoint * + (pairContraction (v r) * pairContraction (v p)) := by + rw [mul_assoc, ← mul_assoc (pairContraction (v p)), pairContraction_middle, hv] + simp only [add_mul, mul_add, smul_mul_assoc, mul_smul_comm, one_mul, adjoint_mul] + have he : (pairContraction (v p)).adjoint * + ((pairContraction (v r)).adjoint * pairContraction (v p) * pairContraction (v r)) = + (pairContraction (v p)).adjoint * (pairContraction (v r)).adjoint * + (pairContraction (v r) * pairContraction (v p)) := by + rw [mul_assoc, pairContraction_commute (v p) (v r), ← mul_assoc] + rw [he] + by_cases h : p = r <;> simp [h, mul_assoc] + unfold pairHamiltonian + rw [Finset.sum_mul] + simp only [Finset.mul_sum, hp, Finset.sum_add_distrib] + simp only [Finset.sum_ite_eq, Finset.mem_univ, ite_true] + rfl + +end LaughlinGap.Occupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/CovariantFamily.lean b/lean/OAI/Analysis/LaughlinGap/CovariantFamily.lean new file mode 100644 index 0000000000000000000000000000000000000000..7a8c1bb4b1d08830eeaa11451f237650e842ce4d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/CovariantFamily.lean @@ -0,0 +1,138 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CovariantLift +import OAI.Analysis.LaughlinGap.SpinAveraging + +namespace OAI + +/-! Covariant Family. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Averaging Spin + +variable {ι κ σ : Type*} [Fintype ι] [DecidableEq ι] + [Fintype κ] [DecidableEq κ] [Fintype σ] [DecidableEq σ] + +omit [DecidableEq ι] in +lemma Covariant.combination_lower [DecidableEq ι] {L : Matrix σ σ ℝ} {D : Matrix ι ι ℝ} + {B : ι → Matrix σ σ ℝ} (h : Covariant L D B) (x : ι → ℝ) : + commutator L (combination B x) = -combination B (D.transpose.mulVec x) := by + simp only [combination, LinearMap.coe_mk, AddHom.coe_mk, map_sum, map_smul, + h.lower, smul_neg, Finset.smul_sum, smul_smul, Finset.sum_neg_distrib, + Matrix.mulVec, dotProduct, Matrix.transpose_apply, Finset.sum_smul] + congr 1 + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro j hj + apply Finset.sum_congr rfl + intro i hi + rw [mul_comm] + +lemma Covariant.combination_raise {L : Matrix σ σ ℝ} {D : Matrix ι ι ℝ} + {B : ι → Matrix σ σ ℝ} (h : Covariant L D B) (x : ι → ℝ) : + commutator L.transpose (combination B x) = -combination B (D.mulVec x) := by + simpa using h.transpose.combination_lower x + +noncomputable def embeddingFamily {S : LadderSystem ι} {T : LadderSystem κ} + (A : LadderMap S T) (B : κ → Matrix σ σ ℝ) : ι → Matrix σ σ ℝ := + fun i => combination B (A.toLinearMap (Pi.single i 1)) + +omit [DecidableEq κ] [Fintype σ] [DecidableEq σ] in +lemma combination_embeddingFamily [DecidableEq κ] [Fintype σ] [DecidableEq σ] + {S : LadderSystem ι} {T : LadderSystem κ} + (A : LadderMap S T) (B : κ → Matrix σ σ ℝ) (x : ι → ℝ) : + combination (embeddingFamily A B) x = combination B (A.toLinearMap x) := by + rw [A.toLinearMap.pi_apply_eq_sum_univ x, map_sum] + simp only [combination, LinearMap.coe_mk, AddHom.coe_mk, embeddingFamily, map_smul] + apply Finset.sum_congr rfl + intro i hi + have hs : (Pi.single i 1 : ι → ℝ) = (fun j => if i=j then 1 else 0) := by + funext j; simp [Pi.single_apply, eq_comm] + rw [hs] + +lemma Covariant.embedding {L : Matrix σ σ ℝ} {S : LadderSystem ι} + {T : LadderSystem κ} {B : κ → Matrix σ σ ℝ} + (h : Covariant L (loweringMatrix T) B) (A : LadderMap S T) : + Covariant L (loweringMatrix S) (embeddingFamily A B) where + lower i := by + change commutator L (combination B _) = _ + rw [h.combination_lower, loweringMatrix_transpose, LinearMap.toMatrix'_mulVec] + change -combination B (T.raise (A.toLinearMap (Pi.single i 1))) = _ + rw [A.raise, ← combination_embeddingFamily] + congr 1 + simp only [combination, LinearMap.coe_mk, AddHom.coe_mk] + apply Finset.sum_congr rfl + intro j hj + congr 1 + have he := congrArg (fun M : Matrix ι ι ℝ => M j i) (loweringMatrix_transpose S) + simpa only [Matrix.transpose_apply, loweringMatrix, LinearMap.toMatrix'_apply] using he.symm + raise i := by + change commutator L.transpose (combination B _) = _ + rw [h.combination_raise, loweringMatrix, LinearMap.toMatrix'_mulVec] + change -combination B (T.lower (A.toLinearMap (Pi.single i 1))) = _ + rw [A.lower, ← combination_embeddingFamily] + rfl + +noncomputable def productFamily (B : ι → Matrix σ σ ℝ) (C : κ → Matrix σ σ ℝ) : + (ι × κ) → Matrix σ σ ℝ := fun ij => C ij.2 * B ij.1 + +lemma loweringMatrix_tensor (S : LadderSystem ι) (T : LadderSystem κ) + (i j : ι × κ) : + loweringMatrix (S.tensor T) i j = + (if i.2=j.2 then loweringMatrix S i.1 j.1 else 0) + + (if i.1=j.1 then loweringMatrix T i.2 j.2 else 0) := by + rcases i with ⟨i₁,i₂⟩ + rcases j with ⟨j₁,j₂⟩ + simp only [loweringMatrix, LinearMap.toMatrix'_apply, LadderSystem.tensor, + LinearMap.add_apply, onFirstEnd_apply, onSecondEnd_apply, Pi.add_apply] + have hf : (fun a : ι => (Pi.single (j₁,j₂) (1 : ℝ) : (ι × κ) → ℝ) (a,i₂)) = + if i₂=j₂ then Pi.single j₁ 1 else 0 := by + funext a + by_cases he : i₂=j₂ <;> simp [he, Pi.single_apply, Prod.mk.injEq, eq_comm] + have hs : (fun a : κ => (Pi.single (j₁,j₂) (1 : ℝ) : (ι × κ) → ℝ) (i₁,a)) = + if i₁=j₁ then Pi.single j₂ 1 else 0 := by + funext a + by_cases he : i₁=j₁ <;> simp [he, Pi.single_apply, Prod.mk.injEq, eq_comm] + change S.lower (fun a => (Pi.single (j₁,j₂) (1 : ℝ) : (ι × κ) → ℝ) (a,i₂)) i₁ + + T.lower (fun a => (Pi.single (j₁,j₂) (1 : ℝ) : (ι × κ) → ℝ) (i₁,a)) i₂ = _ + rw [hf, hs] + split_ifs <;> simp_all + +lemma product_commutator {L : Matrix σ σ ℝ} {D : Matrix ι ι ℝ} {E : Matrix κ κ ℝ} + {B : ι → Matrix σ σ ℝ} {C : κ → Matrix σ σ ℝ} + (hB : ∀ i, commutator L (B i) = -∑ j, D i j • B j) + (hC : ∀ i, commutator L (C i) = -∑ j, E i j • C j) (i : ι × κ) : + commutator L (productFamily B C i) = + -∑ j : ι × κ, ((if i.2=j.2 then D i.1 j.1 else 0) + + (if i.1=j.1 then E i.2 j.2 else 0)) • productFamily B C j := by + simp only [productFamily, commutator_mul, hB, hC, neg_mul, Matrix.mul_neg, + Matrix.sum_mul, Matrix.mul_sum, smul_mul_assoc, mul_smul_comm, + Fintype.sum_prod_type, add_smul, Finset.sum_add_distrib, ite_smul, zero_smul] + simp only [Finset.sum_ite_irrel, Finset.sum_ite_eq] + simp only [Finset.mem_univ, ite_true, Finset.sum_const_zero, Finset.sum_ite_eq] + abel + +lemma Covariant.product {L : Matrix σ σ ℝ} {S : LadderSystem ι} {T : LadderSystem κ} + {B : ι → Matrix σ σ ℝ} {C : κ → Matrix σ σ ℝ} + (hB : Covariant L (loweringMatrix S) B) (hC : Covariant L (loweringMatrix T) C) : + Covariant L (loweringMatrix (S.tensor T)) (productFamily B C) where + lower i := by simpa only [loweringMatrix_tensor] using product_commutator hB.lower hC.lower i + raise i := by + simpa only [Matrix.transpose_apply, loweringMatrix_tensor, eq_comm] using + product_commutator hB.transpose.lower hC.transpose.lower i + +omit [DecidableEq ι] in +lemma Covariant.smul [DecidableEq ι] {L : Matrix σ σ ℝ} {D : Matrix ι ι ℝ} + {B : ι → Matrix σ σ ℝ} (h : Covariant L D B) (r : ℝ) : + Covariant L D (fun i => r • B i) where + lower i := by simp only [map_smul, h.lower, smul_neg, Finset.smul_sum, smul_comm r] + raise i := by simp only [map_smul, h.raise, smul_neg, Finset.smul_sum, smul_comm r] + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/CovariantLift.lean b/lean/OAI/Analysis/LaughlinGap/CovariantLift.lean new file mode 100644 index 0000000000000000000000000000000000000000..f8e5e32009729277404b4f4441755609174b9211 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/CovariantLift.lean @@ -0,0 +1,141 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.RealOccupation + +namespace OAI + +/-! Covariant Lift. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging + +variable {ι κ : Type*} [Fintype ι] [DecidableEq ι] [Fintype κ] [DecidableEq κ] + +noncomputable def lift (B : ι → Matrix κ κ ℝ) : + Matrix ι ι ℝ →ₗ[ℝ] Matrix κ κ ℝ where + toFun A := ∑ i, ∑ j, A i j • ((B i).transpose * B j) + map_add' A C := by simp [add_smul, Finset.sum_add_distrib] + map_smul' r A := by simp [Finset.smul_sum, smul_smul] + +noncomputable def combination (B : ι → Matrix κ κ ℝ) : + (ι → ℝ) →ₗ[ℝ] Matrix κ κ ℝ where + toFun a := ∑ i, a i • B i + map_add' a b := by simp [add_smul, Finset.sum_add_distrib] + map_smul' r a := by simp [Finset.smul_sum, smul_smul] + +omit [DecidableEq ι] in +lemma lift_rankOne [DecidableEq ι] (B : ι → Matrix κ κ ℝ) (x y : ι → ℝ) : + lift B (Matrix.vecMulVec x y) = (combination B x).transpose * combination B y := by + simp only [lift, combination, LinearMap.coe_mk, AddHom.coe_mk, Matrix.vecMulVec_apply, + Matrix.transpose_sum, Matrix.transpose_smul, Matrix.sum_mul, Matrix.mul_sum, + smul_mul_assoc, mul_smul_comm, Finset.smul_sum, smul_smul] + rw [Finset.sum_comm] + simp only [mul_comm] + +omit [DecidableEq ι] [DecidableEq κ] in +lemma lift_transpose [DecidableEq ι] [DecidableEq κ] + (B : ι → Matrix κ κ ℝ) (A : Matrix ι ι ℝ) : + (lift B A).transpose = lift B A.transpose := by + simp only [lift, LinearMap.coe_mk, AddHom.coe_mk, Matrix.transpose_sum, + Matrix.transpose_smul, Matrix.transpose_mul, Matrix.transpose_transpose, + Matrix.transpose_apply] + rw [Finset.sum_comm] + +lemma lift_positive (B : ι → Matrix κ κ ℝ) {A : Matrix ι ι ℝ} + (hA : A.PosSemidef) : (lift B A).PosSemidef := by + obtain ⟨C, rfl⟩ := CStarAlgebra.nonneg_iff_eq_star_mul_self.mp hA.nonneg + have he : star C * C = ∑ k, Matrix.vecMulVec (fun i => C k i) (fun i => C k i) := by + ext i j + simp [Matrix.star_eq_conjTranspose, Matrix.mul_apply, + Matrix.sum_apply, Matrix.vecMulVec_apply] + rw [he, map_sum] + apply Matrix.posSemidef_sum + intro k hk + rw [lift_rankOne] + simpa only [Matrix.conjTranspose_eq_transpose_of_trivial] using + Matrix.posSemidef_conjTranspose_mul_self (combination B (fun i => C k i)) + +omit [DecidableEq ι] in +lemma complexify_combination [DecidableEq ι] (B : ι → Matrix κ κ ℝ) (a : ι → ℝ) : + complexify (combination B a) = ∑ i, (a i : ℂ) • complexify (B i) := by + simp only [combination, LinearMap.coe_mk, AddHom.coe_mk, map_sum, map_smul] + apply Finset.sum_congr rfl + intro i hi + exact_mod_cast (rfl : a i • complexify (B i) = a i • complexify (B i)) + +omit [DecidableEq ι] in +lemma complexify_lift [DecidableEq ι] (B : ι → Matrix κ κ ℝ) (A : Matrix ι ι ℝ) : + complexify (lift B A) = matrixLift (fun i => complexify (B i)) (A.map (algebraMap ℝ ℂ)) := by + simp only [lift, matrixLift, LinearMap.coe_mk, AddHom.coe_mk, map_sum, map_smul, + map_mul, complexify_transpose, Matrix.map_apply] + rfl + +structure Covariant (L : Matrix κ κ ℝ) (D : Matrix ι ι ℝ) + (B : ι → Matrix κ κ ℝ) : Prop where + lower : ∀ i, commutator L (B i) = -∑ j, D i j • B j + raise : ∀ i, commutator L.transpose (B i) = -∑ j, D j i • B j + +lemma commutator_transpose (L A : Matrix κ κ ℝ) : + commutator L A.transpose = -(commutator L.transpose A).transpose := by + simp only [Averaging.commutator, LinearMap.coe_mk, AddHom.coe_mk, Matrix.transpose_sub, + Matrix.transpose_mul, Matrix.transpose_transpose] + abel + +omit [DecidableEq ι] in +lemma Covariant.transpose [DecidableEq ι] {L : Matrix κ κ ℝ} {D : Matrix ι ι ℝ} + {B : ι → Matrix κ κ ℝ} (h : Covariant L D B) : + Covariant L.transpose D.transpose B where + lower i := h.raise i + raise i := by simpa using h.lower i + +lemma Covariant.commutator_lift {L : Matrix κ κ ℝ} {D : Matrix ι ι ℝ} + {B : ι → Matrix κ κ ℝ} (h : Covariant L D B) (A : Matrix ι ι ℝ) : + commutator L (lift B A) = lift B (commutator D A) := by + have ht (i : ι) : commutator L (B i).transpose = ∑ k, D k i • (B k).transpose := by + rw [commutator_transpose, h.raise, Matrix.transpose_neg, neg_neg] + simp only [Matrix.transpose_sum, Matrix.transpose_smul] + simp only [lift, LinearMap.coe_mk, AddHom.coe_mk] + simp only [map_sum, map_smul, commutator_mul, ht, h.lower, Matrix.sum_mul, + Matrix.mul_neg, Matrix.mul_sum, smul_mul_assoc, mul_smul_comm, + ← sub_eq_add_neg, smul_sub, Finset.sum_sub_distrib, Finset.smul_sum, smul_smul] + simp only [Averaging.commutator, LinearMap.coe_mk, AddHom.coe_mk, Matrix.sub_apply, + Matrix.mul_apply, sub_smul, Finset.sum_sub_distrib, Finset.sum_smul] + congr 1 + · conv_lhs => + rw [Finset.sum_comm] + arg 2 + ext j + rw [Finset.sum_comm] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro k hk + apply Finset.sum_congr rfl + intro j hj + apply Finset.sum_congr rfl + intro i hi + congr 1 + ring + · apply Finset.sum_congr rfl + intro i hi + exact Finset.sum_comm + +theorem Covariant.average_lift {L : Matrix κ κ ℝ} {D : Matrix ι ι ℝ} + {B : ι → Matrix κ κ ℝ} (h : Covariant L D B) (A : Matrix ι ι ℝ) : + average (rotationCommutant L) (lift B A) = lift B (average (rotationCommutant D) A) := by + apply rotation_average_natural + · exact fun A => (h.commutator_lift A).symm + · exact fun A => (h.transpose.commutator_lift A).symm + +theorem annihilation_covariant {n : ℕ} (L : Matrix (Fin n) (Fin n) ℝ) : + Covariant (secondQuantization L) L annihilation where + lower i := commutator_annihilation L i + raise i := by rw [secondQuantization_transpose]; exact commutator_annihilation L.transpose i + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Creation.lean b/lean/OAI/Analysis/LaughlinGap/Creation.lean new file mode 100644 index 0000000000000000000000000000000000000000..24f9a7af0fe4e08e6a967e26328efe71fe695f81 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Creation.lean @@ -0,0 +1,536 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.NormalOrder + +namespace OAI + +/-! Creation. -/ + +noncomputable section + + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct + +lemma creation_anticommute {n : ℕ} (i j : Fin n) : + creation i * creation j = -(creation j * creation i) := by + have h := congrArg (fun T : Module.End ℂ (Hilbert n) => T.adjoint) + (annihilation_anticommute j i) + simpa only [adjoint_mul, annihilation_adjoint, map_neg] using h + +noncomputable def creationCombination (n : ℕ) : (Fin n → ℂ) →ₗ[ℂ] Module.End ℂ (Hilbert n) where + toFun v := ∑ i, (v i) • creation i + map_add' _ _ := by simp [add_smul, Finset.sum_add_distrib] + map_smul' _ _ := by simp [smul_smul, Finset.smul_sum] + +lemma creationCombination_square (n : ℕ) (v : Fin n → ℂ) : + creationCombination n v * creationCombination n v = 0 := by + have h : creationCombination n v * creationCombination n v = + -(creationCombination n v * creationCombination n v) := by + simp only [creationCombination, LinearMap.coe_mk, AddHom.coe_mk, Finset.sum_mul] + simp only [Finset.mul_sum, smul_mul_assoc, mul_smul_comm, smul_smul] + simp only [← Finset.sum_neg_distrib] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + rw [creation_anticommute j i, mul_comm (v j) (v i), smul_neg] + apply LinearMap.ext + intro x + ext A + have he := congrArg (fun T : Module.End ℂ (Hilbert n) => T x A) h + change (creationCombination n v * creationCombination n v) x A = + -((creationCombination n v * creationCombination n v) x A) at he + change (creationCombination n v * creationCombination n v) x A = 0 + linear_combination (1/2 : ℂ) * he + +noncomputable def creationExteriorHom (n : ℕ) : + ExteriorAlgebra ℂ (Fin n → ℂ) →ₐ[ℂ] Module.End ℂ (Hilbert n) := + ExteriorAlgebra.lift ℂ ⟨creationCombination n, creationCombination_square n⟩ + +@[simp] lemma creationCombination_single {n : ℕ} (j : Fin n) : + creationCombination n (Pi.single j 1) = creation j := by + classical + simp [creationCombination, Pi.single_apply, ite_smul] + +lemma creationExteriorHom_multi {n N : ℕ} (a : Fin N → Fin n) : + creationExteriorHom n (ExteriorAlgebra.ιMulti ℂ N (fun i => Pi.single (a i) 1)) = + (word (List.ofFn a)).adjoint := by + induction N with + | zero => simp [ExteriorAlgebra.ιMulti_zero_apply, word_nil] + | succ N ih => + rw [ExteriorAlgebra.ιMulti_succ_apply, map_mul] + simp only [creationExteriorHom, ExteriorAlgebra.lift_ι_apply, creationCombination_single] + change creation (a 0) * creationExteriorHom n + (ExteriorAlgebra.ιMulti ℂ N (fun i => Pi.single (a i.succ) 1)) = _ + rw [ih] + simp only [List.ofFn_succ, word_cons, adjoint_mul, annihilation_adjoint] + +lemma word_ofFn_swap {n N : ℕ} (a : Fin N → Fin n) (i j : Fin N) (hij : i ≠ j) : + word (List.ofFn (a ∘ Equiv.swap i j)) = -word (List.ofFn a) := by + have hh := (ExteriorAlgebra.ιMulti ℂ N (M := Fin n → ℂ)).map_swap + (fun k => Pi.single (a k) 1) hij + have he := congrArg (creationExteriorHom n) hh + simp only [map_neg] at he + change creationExteriorHom n (ExteriorAlgebra.ιMulti ℂ N + (fun k => Pi.single ((a ∘ Equiv.swap i j) k) 1)) = _ at he + rw [creationExteriorHom_multi, creationExteriorHom_multi] at he + have hf := congrArg (fun T : Module.End ℂ (Hilbert n) => T.adjoint) he + simpa only [LinearMap.adjoint_adjoint, map_neg] using hf + +theorem normalizedReadout_antisymmetric {Q N : ℕ} (x : Hilbert (Q+1)) : + Antisymmetric (WithLp.ofLp (normalizedReadout (Q+1) N x)) := by + intro i j hij a + simp only [normalizedReadout_apply, word_ofFn_swap a i j hij, + LinearMap.neg_apply, PiLp.neg_apply, mul_neg] + +end LaughlinGap.Occupation + +namespace LaughlinGap +open scoped BigOperators InnerProduct + +lemma Antisymmetric.perm {N Q : ℕ} {ψ : State N Q} (hψ : Antisymmetric ψ) + (a : Configuration N Q) (σ : Equiv.Perm (Fin N)) : + ψ (a ∘ σ) = Equiv.Perm.sign σ • ψ a := by + induction σ using Equiv.Perm.swap_induction_on' with + | one => simp + | mul_swap s i j hij ih => simp_all [← Function.comp_assoc, hψ i j hij] + +lemma Antisymmetric.eq_zero_of_not_injective {N Q : ℕ} {ψ : State N Q} + (hψ : Antisymmetric ψ) {a : Configuration N Q} (ha : ¬ Function.Injective a) : + ψ a = 0 := by + classical + obtain ⟨i,j,hij,hne⟩ := Function.not_injective_iff.mp ha + have he : a ∘ Equiv.swap i j = a := by + ext k + by_cases hki : k = i + · subst k; simp [hij] + by_cases hkj : k = j + · subst k; simp [hij] + simp [Equiv.swap_apply_of_ne_of_ne hki hkj] + have hh := hψ i j hne a + rw [he] at hh + linear_combination (1/2 : ℂ) * hh + +lemma Antisymmetric.ext_increasing {N Q : ℕ} {ψ φ : State N Q} + (hψ : Antisymmetric ψ) (hφ : Antisymmetric φ) + (he : ∀ a, StrictMono a → ψ a = φ a) : ψ = φ := by + funext a + by_cases hi : Function.Injective a + · have hs : StrictMono (a ∘ Tuple.sort a) := + (Tuple.monotone_sort a).strictMono_of_injective (hi.comp (Tuple.sort a).injective) + have he' := he (a ∘ Tuple.sort a) hs + rw [Antisymmetric.perm hψ, Antisymmetric.perm hφ] at he' + exact (smul_left_cancel _ he') + · rw [Antisymmetric.eq_zero_of_not_injective hψ hi, + Antisymmetric.eq_zero_of_not_injective hφ hi] + +end LaughlinGap + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct + +noncomputable def increasingConfiguration {n N : ℕ} (A : BasisLabel n N) : Fin N → Fin n := + A.val.orderEmbOfFin A.property + +lemma increasingConfiguration_strictMono {n N : ℕ} (A : BasisLabel n N) : + StrictMono (increasingConfiguration A) := (A.val.orderEmbOfFin A.property).strictMono + +lemma ofFn_increasingConfiguration {n N : ℕ} (A : BasisLabel n N) : + List.ofFn (increasingConfiguration A) = A.val.sort (· ≤ ·) := by + rw [List.ofFn_eq_map] + exact A.val.listMap_orderEmbOfFin_finRange A.property + +@[simp] lemma normalizedReadout_increasing {n N : ℕ} (x : Hilbert n) (A : BasisLabel n N) : + normalizedReadout n N x (increasingConfiguration A) = + ((Real.sqrt (N.factorial : ℝ))⁻¹ : ℂ) * x A.val := by + rw [normalizedReadout_apply, ofFn_increasingConfiguration] + rw [show word (A.val.sort (· ≤ ·)) = basisContraction A from rfl, + basisContraction_apply_empty] + +noncomputable def coordinatesFromTensor (Q N : ℕ) : TensorHilbert N Q →ₗ[ℂ] + ExteriorCoordinates (Q+1) N where + toFun ψ := WithLp.toLp 2 (fun A => (Real.sqrt (N.factorial : ℝ) : ℂ) * + ψ (increasingConfiguration A)) + map_add' ψ φ := by ext A; exact mul_add _ _ _ + map_smul' c ψ := by ext A; exact mul_left_comm _ _ _ + +@[simp] lemma coordinatesFromTensor_apply {Q N : ℕ} (ψ : TensorHilbert N Q) + (A : BasisLabel (Q+1) N) : + coordinatesFromTensor Q N ψ A = (Real.sqrt (N.factorial : ℝ) : ℂ) * + ψ (increasingConfiguration A) := rfl + +lemma coordinatesFromTensor_readout {Q N : ℕ} (x : ExteriorCoordinates (Q+1) N) : + coordinatesFromTensor Q N (normalizedReadout (Q+1) N (sectorInclusion (Q+1) N x)) = x := by + have hs : (Real.sqrt (N.factorial : ℝ) : ℂ) ≠ 0 := by + exact_mod_cast ne_of_gt (Real.sqrt_pos.mpr (by exact_mod_cast Nat.factorial_pos N)) + ext A + simp only [coordinatesFromTensor_apply, normalizedReadout_increasing, + sectorInclusion_apply_label] + field_simp + +theorem readout_coordinatesFromTensor {Q N : ℕ} {ψ : TensorHilbert N Q} + (hψ : Antisymmetric (WithLp.ofLp ψ)) : + normalizedReadout (Q+1) N (sectorInclusion (Q+1) N (coordinatesFromTensor Q N ψ)) = ψ := by + classical + apply (WithLp.equiv 2 _).injective + apply Antisymmetric.ext_increasing (normalizedReadout_antisymmetric _) hψ + intro a ha + let A : BasisLabel (Q+1) N := ⟨Finset.univ.image a, by + rw [Finset.card_image_of_injective _ ha.injective, Finset.card_fin]⟩ + have he : increasingConfiguration A = a := by + symm + exact Finset.orderEmbOfFin_unique A.property (by intro i; exact Finset.mem_image.mpr ⟨i, by simp, rfl⟩) ha + rw [← he] + change normalizedReadout (Q+1) N _ (increasingConfiguration A) = ψ (increasingConfiguration A) + rw [normalizedReadout_increasing, sectorInclusion_apply_label, + coordinatesFromTensor_apply, ← mul_assoc, inv_mul_cancel₀, one_mul] + exact_mod_cast ne_of_gt (Real.sqrt_pos.mpr (by exact_mod_cast Nat.factorial_pos N)) + +@[simp] lemma sectorReadout_inclusion {n k : ℕ} (x : ExteriorCoordinates n k) : + sectorReadout n k (sectorInclusion n k x) = x := by + ext A + rw [sectorReadout_apply, sectorInclusion_apply_label] + +lemma sectorInclusion_norm_sq {n k : ℕ} (x : ExteriorCoordinates n k) : + ‖sectorInclusion n k x‖ ^ 2 = ‖x‖ ^ 2 := by + rw [norm_sq_eq_re_inner (𝕜 := ℂ), norm_sq_eq_re_inner (𝕜 := ℂ), + ← LinearMap.adjoint_inner_right, sectorInclusion_adjoint, sectorReadout_inclusion] + +noncomputable def exteriorTensorIsometry (Q N : ℕ) : + ExteriorCoordinates (Q+1) N ≃ₗᵢ[ℂ] SectorHilbert N Q where + toFun x := ⟨normalizedReadout (Q+1) N (sectorInclusion (Q+1) N x), normalizedReadout_antisymmetric _⟩ + invFun ψ := coordinatesFromTensor Q N ψ.val + left_inv x := coordinatesFromTensor_readout x + right_inv ψ := Subtype.ext (readout_coordinatesFromTensor ψ.property) + map_add' x y := by apply Subtype.ext; simp + map_smul' c x := by apply Subtype.ext; simp + norm_map' x := by + change ‖normalizedReadout (Q+1) N (sectorInclusion (Q+1) N x)‖ = ‖x‖ + have he := normalizedReadout_norm_sq (sectorInclusion_homogeneous x) + rw [sectorInclusion_norm_sq] at he + nlinarith [norm_nonneg (normalizedReadout (Q+1) N (sectorInclusion (Q+1) N x)), norm_nonneg x] + +end LaughlinGap.Occupation + +namespace LaughlinGap +open scoped InnerProduct + +lemma unitary_conj_eq_of_quadraticForm {E F : Type*} + [NormedAddCommGroup E] [InnerProductSpace ℂ E] + [NormedAddCommGroup F] [InnerProductSpace ℂ F] + (U : E ≃ₗᵢ[ℂ] F) (A : Module.End ℂ E) (B : Module.End ℂ F) + (hA : A.IsSymmetric) (hB : B.IsSymmetric) + (h : ∀ x, (inner ℂ (U x) (B (U x))).re = (inner ℂ x (A x)).re) : + U.symm.toLinearMap ∘ₗ B ∘ₗ U.toLinearMap = A := by + apply (ext_inner_map _ _).mp + intro x + change inner ℂ (U.symm (B (U x))) x = inner ℂ (A x) x + have hi := U.inner_map_map (U.symm (B (U x))) x + simp only [LinearIsometryEquiv.apply_symm_apply] at hi + rw [← hi, ← hB.coe_re_inner_apply_self, ← hA.coe_re_inner_apply_self] + congr 1 + rw [inner_re_symm, inner_re_symm (𝕜 := ℂ) (A x) x] + exact h x + +end LaughlinGap + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct + +lemma sum_symmetric_triangle {n : ℕ} {A : Type*} [AddCommMonoid A] + (f : Fin n → Fin n → A) (hs : ∀ i j, f i j = f j i) (hd : ∀ i, f i i = 0) : + (∑ i, ∑ j, f i j) = (∑ i, ∑ j, if i < j then f i j else 0) + + (∑ i, ∑ j, if i < j then f i j else 0) := by + classical + have he (i j : Fin n) : f i j = + (if i < j then f i j else 0) + (if j < i then f j i else 0) := by + rcases lt_trichotomy i j with h | h | h + · simp [h, not_lt_of_gt h] + · subst j; simp [hd] + · simp [h, not_lt_of_gt h, hs i j] + conv_lhs => arg 2; intro i; arg 2; intro j; rw [he i j] + simp only [Finset.sum_add_distrib] + rw [Finset.sum_comm (f := fun i j : Fin n => if j < i then f j i else 0)] + +lemma orderedPair_contraction (Q p : ℕ) : + (∑ i : Fin (Q+1), ∑ j : Fin (Q+1), (pairCoefficient Q p i j : ℂ) • + (annihilation j * annihilation i)) = + (Real.sqrt 2 : ℂ) • localPair (Q+1) Q p := by + have hs : (Real.sqrt 2 : ℂ) * (Real.sqrt 2 : ℂ) = 2 := by + rw [← Complex.ofReal_mul, ← pow_two, Real.sq_sqrt (by norm_num)] + norm_num + let T : Module.End ℂ (Hilbert (Q+1)) := ∑ i, ∑ j, if i < j then + (pairCoefficient Q p i j : ℂ) • (annihilation j * annihilation i) else 0 + have he : localPair (Q+1) Q p = (Real.sqrt 2 : ℂ) • T := by + simp only [localPair, pairAnnihilator, sphericalExteriorPairCoefficient_eq_tensor, + Complex.star_def, map_mul, Complex.conj_ofReal, Complex.ofReal_mul, mul_smul, T, + Finset.smul_sum, smul_ite, smul_zero] + rw [sum_symmetric_triangle, he, smul_smul, hs] + · change T + T = (2:ℂ) • T + module + · intro i j + rw [pairCoefficient_swap Q p i j, annihilation_anticommute i j] + simp + · intro i + simp [pairCoefficient] + +lemma update_cons_cons {N Q : ℕ} (a : Configuration N Q) (u v x y : Fin (Q+1)) : + Function.update (Function.update (Fin.cons u (Fin.cons v a) : Configuration (N+2) Q) (0 : Fin (N+2)) x) + (1 : Fin (N+2)) y = (Fin.cons x (Fin.cons y a) : Configuration (N+2) Q) := by + funext k + refine Fin.cases ?_ (fun k => Fin.cases ?_ (fun k => ?_) k) k + · simp + · simp + · have hk : k.succ.succ ≠ (1 : Fin (N+2)) := by + intro h + have hv := congrArg Fin.val h + simp only [Fin.val_succ, Fin.val_one] at hv + omega + simp [Function.update_of_ne hk] + +lemma readout_pairAmplitude_head {N Q : ℕ} (x : Hilbert (Q+1)) (p : ℕ) + (a : Configuration N Q) : + pairAmplitude (WithLp.ofLp (normalizedReadout (Q+1) (N+2) x)) + 0 1 p (Fin.cons 0 (Fin.cons 0 a)) = + (((Real.sqrt ((N+2).factorial : ℝ))⁻¹ : ℂ) * (Real.sqrt 2 : ℂ)) * + rawReadout (Q+1) N (localPair (Q+1) Q p x) a := by + have he := congrArg (fun T : Module.End ℂ (Hilbert (Q+1)) => + rawReadout (Q+1) N (T x) a) (orderedPair_contraction Q p) + simp only [LinearMap.sum_apply, LinearMap.smul_apply, map_sum, map_smul, + WithLp.ofLp_sum, Finset.sum_apply, PiLp.smul_apply, smul_eq_mul] at he + simp only [pairAmplitude, update_cons_cons, normalizedReadout_apply, + List.ofFn_cons, word_cons, Module.End.mul_apply] + simp only [rawReadout_apply, Module.End.mul_apply] at he + change (∑ i : Fin (Q+1), ∑ j : Fin (Q+1), (pairCoefficient Q p i j : ℂ) * + (((Real.sqrt ((N+2).factorial : ℝ))⁻¹ : ℂ) * + word (List.ofFn a) (annihilation j (annihilation i x)) ∅)) = _ + calc + _ = (((Real.sqrt ((N+2).factorial : ℝ))⁻¹ : ℂ)) * + (∑ i : Fin (Q+1), ∑ j : Fin (Q+1), (pairCoefficient Q p i j : ℂ) * + word (List.ofFn a) (annihilation j (annihilation i x)) ∅) := by + simp only [Finset.mul_sum] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + ring + _ = _ := by rw [he]; exact (mul_assoc _ _ _).symm + +end LaughlinGap.Occupation + +namespace LaughlinGap +open scoped BigOperators InnerProduct + +noncomputable def pairEnergyAt {N Q : ℕ} (ψ : State N Q) (i j : Fin N) (p : ℕ) : ℝ := + ∑ a, if a i = 0 ∧ a j = 0 then ‖pairAmplitude ψ i j p a‖ ^ 2 else 0 + +lemma sum_head_anchored {N Q : ℕ} (f : Configuration (N+2) Q → ℝ) : + (∑ a, if a 0 = 0 ∧ a 1 = 0 then f a else 0) = + ∑ a : Configuration N Q, f (Fin.cons 0 (Fin.cons 0 a)) := by + rw [← (Fin.consEquiv (fun _ : Fin (N+2) => Fin (Q+1))).sum_comp] + simp only [Fintype.sum_prod_type] + change (∑ x : Fin (Q+1), ∑ a : Configuration (N+1) Q, + if x = 0 ∧ a 0 = 0 then f (Fin.cons x a) else 0) = _ + simp only [ite_and] + simp_rw [Finset.sum_ite_irrel] + simp only [Finset.sum_const_zero, Finset.sum_ite_eq', Finset.mem_univ, ite_true] + rw [← (Fin.consEquiv (fun _ : Fin (N+1) => Fin (Q+1))).sum_comp] + simp only [Fintype.sum_prod_type] + change (∑ y : Fin (Q+1), ∑ a : Configuration N Q, + if y = 0 then f (Fin.cons 0 (Fin.cons y a)) else 0) = _ + simp_rw [Finset.sum_ite_irrel] + simp + +lemma pairAmplitude_perm {N Q : ℕ} {ψ : State N Q} (hψ : Antisymmetric ψ) + (σ : Equiv.Perm (Fin N)) (i j : Fin N) (p : ℕ) (a : Configuration N Q) : + pairAmplitude ψ i j p (a ∘ σ) = + Equiv.Perm.sign σ • pairAmplitude ψ (σ i) (σ j) p a := by + have hu (x y : Fin (Q+1)) : Function.update (Function.update (a ∘ σ) i x) j y = + Function.update (Function.update a (σ i) x) (σ j) y ∘ σ := by + simp only [Function.update_comp_equiv, Equiv.symm_apply_apply] + simp only [pairAmplitude, hu, Antisymmetric.perm hψ, Finset.smul_sum, mul_smul_comm] + +lemma pairEnergyAt_perm {N Q : ℕ} {ψ : State N Q} (hψ : Antisymmetric ψ) + (σ : Equiv.Perm (Fin N)) (i j : Fin N) (p : ℕ) : + pairEnergyAt ψ i j p = pairEnergyAt ψ (σ i) (σ j) p := by + let e : Configuration N Q ≃ Configuration N Q := + ⟨fun a => a ∘ σ, fun a => a ∘ σ.symm, + by intro a; ext k; simp, by intro a; ext k; simp⟩ + unfold pairEnergyAt + rw [← e.sum_comp] + change (∑ a, if a (σ i) = 0 ∧ a (σ j) = 0 then + ‖pairAmplitude ψ i j p (a ∘ σ)‖ ^ 2 else 0) = _ + simp only [pairAmplitude_perm hψ, norm_units_zsmul] + +lemma exists_perm_head_pair {N : ℕ} (i j : Fin (N+2)) (hij : i ≠ j) : + ∃ σ : Equiv.Perm (Fin (N+2)), σ 0 = i ∧ σ 1 = j := by + let τ : Equiv.Perm (Fin (N+2)) := Equiv.swap 0 i + have hτ : τ 0 = i := Equiv.swap_apply_left _ _ + have h10 : (1 : Fin (N+2)) ≠ 0 := by + intro h + have hv := congrArg Fin.val h + simp only [Fin.val_one, Fin.val_zero] at hv + omega + have hi : i ≠ τ 1 := by rw [← hτ]; exact fun h => h10 (τ.injective h).symm + refine ⟨Equiv.swap (τ 1) j * τ, ?_, ?_⟩ + · simp only [Equiv.Perm.mul_apply, hτ] + exact Equiv.swap_apply_of_ne_of_ne hi hij + · simp + +lemma pairEnergyAt_eq_head {N Q : ℕ} {ψ : State (N+2) Q} (hψ : Antisymmetric ψ) + (i j : Fin (N+2)) (hij : i ≠ j) (p : ℕ) : + pairEnergyAt ψ i j p = pairEnergyAt ψ 0 1 p := by + obtain ⟨σ,h0,h1⟩ := exists_perm_head_pair i j hij + simpa only [h0,h1] using (pairEnergyAt_perm hψ σ 0 1 p).symm + +end LaughlinGap + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct + +theorem readout_pairEnergyAt_head {N Q : ℕ} {x : Hilbert (Q+1)} + (hx : Homogeneous (N+2) x) (p : Fin (2*Q-1)) : + pairEnergyAt (WithLp.ofLp (normalizedReadout (Q+1) (N+2) x)) 0 1 p.val = + (2 * (N.factorial : ℝ) / ((N+2).factorial : ℝ)) * + ‖localPair (Q+1) Q p.val x‖ ^ 2 := by + have hs : 0 < Real.sqrt ((N+2).factorial : ℝ) := + Real.sqrt_pos.mpr (by exact_mod_cast Nat.factorial_pos (N+2)) + have hh : Homogeneous N (localPair (Q+1) Q p.val x) := by + rw [← physicalPair_contraction] + exact pairContraction_homogeneous _ hx + rw [pairEnergyAt, sum_head_anchored] + simp only [readout_pairAmplitude_head, norm_mul, norm_inv, Complex.norm_real, + Real.norm_eq_abs, abs_of_pos hs, abs_of_nonneg (Real.sqrt_nonneg 2), + mul_pow, inv_pow, Real.sq_sqrt (by positivity : 0 ≤ ((N+2).factorial : ℝ)), + Real.sq_sqrt (by norm_num : (0:ℝ) ≤ 2), ← Finset.mul_sum, + ← EuclideanSpace.norm_sq_eq, rawReadout_norm_sq hh] + ring + +end LaughlinGap.Occupation + +namespace LaughlinGap +open scoped BigOperators InnerProduct + +lemma sum_increasing_positions (N : ℕ) (c : ℝ) : + (∑ i : Fin N, ∑ j : Fin N, if i < j then c else 0) = + (N.choose 2 : ℝ) * c := by + rw [← Fintype.sum_prod_type (f := fun ij : Fin N × Fin N => if ij.1 < ij.2 then c else 0), + ← Finset.sum_filter, Finset.sum_const, + Fintype.card_product_filter_lt, Fintype.card_fin, nsmul_eq_mul] + +lemma energy_eq_pairEnergyAt_head {N Q : ℕ} {ψ : State (N+2) Q} + (hψ : Antisymmetric ψ) : + energy ψ = ((N+2).choose 2 : ℝ) * + ∑ p : Fin (2*Q-1), pairEnergyAt ψ 0 1 p.val := by + change (∑ i, ∑ j, if i < j then + ∑ p ∈ Finset.range (2*Q-1), pairEnergyAt ψ i j p else 0) = _ + have he (i j : Fin (N+2)) : + (if i < j then ∑ p ∈ Finset.range (2*Q-1), pairEnergyAt ψ i j p else 0) = + if i < j then ∑ p ∈ Finset.range (2*Q-1), pairEnergyAt ψ 0 1 p else 0 := by + split_ifs with hij + · simp_rw [pairEnergyAt_eq_head hψ i j (ne_of_lt hij)] + · rfl + simp_rw [he] + rw [sum_increasing_positions, Fin.sum_univ_eq_sum_range] + +end LaughlinGap + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct + +theorem readout_energy {N Q : ℕ} {x : Hilbert (Q+1)} (hx : Homogeneous (N+2) x) : + energy (WithLp.ofLp (normalizedReadout (Q+1) (N+2) x)) = + localPairEnergy (Q+1) (2*Q-1) Q x := by + rw [energy_eq_pairEnergyAt_head (normalizedReadout_antisymmetric x)] + simp_rw [readout_pairEnergyAt_head hx] + rw [← Finset.mul_sum, ← mul_assoc] + have he : ((N+2).choose 2 : ℝ) * 2 * (N.factorial : ℝ) = ((N+2).factorial : ℝ) := by + have hn := Nat.choose_mul_factorial_mul_factorial (n := N+2) (k := 2) (by omega) + norm_num only [Nat.add_sub_cancel, Nat.factorial_two] at hn + exact_mod_cast hn + have hpos : ((N+2).factorial : ℝ) ≠ 0 := by exact_mod_cast Nat.factorial_ne_zero (N+2) + rw [← mul_div_assoc, ← mul_assoc, he, div_self hpos, one_mul] + rfl + +noncomputable def exteriorHamiltonian (N Q : ℕ) : + Module.End ℂ (ExteriorCoordinates (Q+1) N) := + sectorReadout (Q+1) N ∘ₗ physicalOccupationHamiltonian Q ∘ₗ sectorInclusion (Q+1) N + +lemma exteriorHamiltonian_positive (N Q : ℕ) : (exteriorHamiltonian N Q).IsPositive := by + rw [exteriorHamiltonian, ← sectorInclusion_adjoint] + exact (physicalOccupationHamiltonian_positive Q).adjoint_conj _ + +lemma exteriorHamiltonian_inner (N Q : ℕ) (x : ExteriorCoordinates (Q+1) N) : + (inner ℂ x (exteriorHamiltonian N Q x)).re = + localPairEnergy (Q+1) (2*Q-1) Q (sectorInclusion (Q+1) N x) := by + change (inner ℂ x (sectorReadout (Q+1) N + (physicalOccupationHamiltonian Q (sectorInclusion (Q+1) N x)))).re = _ + rw [← sectorInclusion_adjoint, LinearMap.adjoint_inner_right, + physicalOccupationHamiltonian_inner] + +lemma exteriorHamiltonian_inclusion (N Q : ℕ) (x : ExteriorCoordinates (Q+1) N) : + sectorInclusion (Q+1) N (exteriorHamiltonian N Q x) = + physicalOccupationHamiltonian Q (sectorInclusion (Q+1) N x) := by + apply sectorInclusion_readout + exact pairHamiltonian_preserves_degree _ (sectorInclusion_homogeneous x) + +theorem tensor_exteriorHamiltonian (N Q : ℕ) : + (exteriorTensorIsometry Q (N+2)).symm.toLinearMap ∘ₗ sectorHamiltonian (N+2) Q ∘ₗ + (exteriorTensorIsometry Q (N+2)).toLinearMap = exteriorHamiltonian (N+2) Q := by + apply unitary_conj_eq_of_quadraticForm _ _ _ + (exteriorHamiltonian_positive (N+2) Q).isSymmetric + (sectorHamiltonian_positive (N+2) Q).isSymmetric + intro x + rw [sectorHamiltonian_inner, exteriorHamiltonian_inner] + exact readout_energy (sectorInclusion_homogeneous x) + +lemma exteriorTensorIsometry_intertwines (N Q : ℕ) (x : ExteriorCoordinates (Q+1) (N+2)) : + sectorHamiltonian (N+2) Q (exteriorTensorIsometry Q (N+2) x) = + exteriorTensorIsometry Q (N+2) (exteriorHamiltonian (N+2) Q x) := by + have he := congrArg (fun T : Module.End ℂ (ExteriorCoordinates (Q+1) (N+2)) => + exteriorTensorIsometry Q (N+2) (T x)) (tensor_exteriorHamiltonian N Q) + simpa using he + +lemma exteriorTensorIsometry_hamiltonian_norm_sq (N Q : ℕ) + (x : ExteriorCoordinates (Q+1) (N+2)) : + ‖sectorHamiltonian (N+2) Q (exteriorTensorIsometry Q (N+2) x)‖ ^ 2 = + ‖physicalOccupationHamiltonian Q (sectorInclusion (Q+1) (N+2) x)‖ ^ 2 := by + rw [exteriorTensorIsometry_intertwines, LinearIsometryEquiv.norm_map, + ← exteriorHamiltonian_inclusion, sectorInclusion_norm_sq] + +end LaughlinGap.Occupation + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct + +theorem sector_square_of_occupation_square {Q : ℕ} (γ : ℝ) + (h : ∀ x : Hilbert (Q+1), γ * localPairEnergy (Q+1) (2*Q-1) Q x ≤ + ‖physicalOccupationHamiltonian Q x‖ ^ 2) (N : ℕ) (x : SectorHilbert (N+2) Q) : + γ * energy (WithLp.ofLp x.val) ≤ ‖sectorHamiltonian (N+2) Q x‖ ^ 2 := by + let y := (exteriorTensorIsometry Q (N+2)).symm x + have hy : exteriorTensorIsometry Q (N+2) y = x := + (exteriorTensorIsometry Q (N+2)).apply_symm_apply x + rw [← hy, exteriorTensorIsometry_hamiltonian_norm_sq] + change γ * energy (WithLp.ofLp (normalizedReadout (Q+1) (N+2) + (sectorInclusion (Q+1) (N+2) y))) ≤ _ + rw [readout_energy (sectorInclusion_homogeneous y)] + exact h _ + +theorem mainTarget_of_uniform_occupation_square_estimate + (h : ∃ Q₀ : ℕ, ∀ Q ≥ Q₀, ∀ x : Hilbert (Q+1), + (1/25 : ℝ) * localPairEnergy (Q+1) (2*Q-1) Q x ≤ + ‖physicalOccupationHamiltonian Q x‖ ^ 2) : MainTarget := by + obtain ⟨Q₀,hQ₀⟩ := h + refine ⟨Q₀+2, by omega, ?_⟩ + intro N hN ψ hψ + have hN2 : 2 ≤ N := by omega + obtain ⟨n,rfl⟩ : ∃ n, N = n+2 := ⟨N-2, by omega⟩ + exact laughlin_gap_of_sector_square_estimate hN2 (1/25) (by norm_num) + (sector_square_of_occupation_square _ (hQ₀ _ (by omega)) n) ψ hψ + +end LaughlinGap.Occupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/ExactRows.lean b/lean/OAI/Analysis/LaughlinGap/ExactRows.lean new file mode 100644 index 0000000000000000000000000000000000000000..2aa7ba77a32cc45d5cf8cf2987e49a6ebf7ed19c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/ExactRows.lean @@ -0,0 +1,115 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.GlobalBoundCore +import OAI.Analysis.LaughlinGap.RationalRowComputable + +namespace OAI + +/-! Exact Rows. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Spin + +def rowLambdaInteger : Fin 8 → ℤ := ![6971289, 4543418, 2122516, 3473755, 1187195, 1558861, -522862, 1523334] + +def rowAlphaInteger : Fin 8 → Fin 8 → Fin 9 → ℤ := ![ + ![![0, 0, 2967, -8940, 597844, -3700599, -1482135, -1339330, -1774974], ![0, -1484, 0, -400546, -727512, 452505, 336757, -687973, 0], ![742, 2235, 200273, -333763, -26754, 152623, 53954, 0, 0], ![-2235, -74731, 515641, -77419, 104592, -28049, 0, 0, 0], ![11959, 64406, 79631, -160154, 59858, 0, 0, 0, 0], ![-689922, -67178, 66061, -77891, 0, 0, 0, 0, 0], ![59862, -44385, 84784, 0, 0, 0, 0, 0, 0], ![153877, -34627, 0, 0, 0, 0, 0, 0, 0]], + ![![0, 0, -25023, -53790, 766486, 9140658, 6404627, 13809118, 23999206], ![0, 12512, 0, -81797, -655373, -2080938, -2714428, 2099732, -5178959], ![-6256, 13448, 40899, 710335, 786050, -693550, 623937, -1143911, 0], ![-13448, -95811, -546491, -138110, 34419, -267131, -144692, 0, 0], ![123267, -216124, -122255, 80152, -24553, 132133, 0, 0, 0], ![937778, 118499, 304496, 31238, 59346, 0, 0, 0, 0], ![1417, -356711, 56605, -65505, 0, 0, 0, 0, 0], ![-131919, -496957, 74692, 0, 0, 0, 0, 0, 0]], + ![![0, 0, 40292, 23298, -1528688, 1746358, -12625070, -2802951, -6221618], ![0, -20146, 0, 520862, 3752616, 3182905, 4997631, 2764684, 861720], ![10073, -5824, -260431, -498930, 791582, 797383, 224990, -770365, 257970], ![5824, 191086, -439224, -64123, 275842, 867800, 34013, 364701, 0], ![-156414, -358613, -895366, -226478, -106557, 44603, 621822, 0, 0], ![1390987, 809119, -671849, -312442, 38220, 292352, 0, 0, 0], ![-51065, 534431, -193959, -39966, 151939, 0, 0, 0, 0], ![996138, 485619, -35844, 2051, 0, 0, 0, 0, 0]], + ![![0, 0, 0, 260793, 1619513, -9479213, -9905866, -2635931, -19784496], ![0, 0, 0, -921422, -5959267, -3855561, -5424538, -3111939, 8971929], ![0, -65198, 460711, 981829, 1266048, 467412, 2221895, 5826028, -4062050], ![65198, -202439, 507988, -1218507, -969129, -1457246, 510645, -2757862, -105174], ![73303, 1083365, 1360170, 496901, 546989, 591478, -1611153, 541242, 0], ![-3047173, -422296, 565219, 51950, -138923, -157439, 384768, 0, 0], ![-1096705, -516126, -272886, -590124, 310843, 424224, 0, 0, 0], ![-907772, 513824, -898660, 386231, 250109, 0, 0, 0, 0]], + ![![0, 0, 0, 0, 105594, -4061461, 6356394, 10585121, -6662244], ![0, 0, 0, 110095, -1847081, -3073897, -2667170, -8745701, 5964734], ![0, 0, -55047, -433408, -2935870, -4255122, -2157050, -4954706, -4844675], ![0, -13199, 895178, 1245604, -560549, -1093209, -872791, 718839, 1986698], ![47323, 37137, 717733, 1000936, -51292, -45155, -380146, 602091, 78888], ![-1084895, -476551, 1133209, 876644, -325993, -113185, 946782, -228390, 0], ![-1146443, -1427889, 250513, 803576, -775332, 795845, 94822, 0, 0], ![-1103184, -439205, 578684, -576406, 521912, 2369, 0, 0, 0]], + ![![0, 0, 0, 0, 0, 1307234, 1613443, -12951363, 31680953], ![0, 0, 0, 0, 281037, 661119, -2279616, 5048517, -23313511], ![0, 0, 0, 58302, -216885, -757322, -7019672, -5556231, -4399124], ![0, 0, -128561, -217031, 206708, -4699975, -3183010, -1044281, 2334083], ![0, -52551, 405571, 290575, 700566, -1549534, 387879, 5277042, -3807459], ![251228, -457263, -370075, 2178628, 928006, -250704, 3565738, -1838288, -1006797], ![447635, 843581, 712865, 1465846, 157586, 2126100, -1099955, 74867, 0], ![-1885572, -2909636, 386414, 199797, 509416, -417784, -153850, 0, 0]], + ![![0, 0, 0, 0, 0, 0, 962082, -4231547, 6336802], ![0, 0, 0, 0, 0, 554480, 519996, -3314368, -8609585], ![0, 0, 0, 0, 8439, 936902, -1855598, -3611338, -2870966], ![0, 0, 0, -22438, 326366, -903827, -684137, -5872845, 530800], ![0, 0, -41983, -291963, 67578, 107968, -4215760, 473171, -2108792], ![0, -52838, -406574, 473590, 277799, -2954710, 85152, -1038229, 12413], ![245134, 588941, 460312, 152807, -910473, 428359, -647302, 35163, -1436712], ![-2025, -885233, -317059, -405381, -399637, -622199, -249650, -812670, 0]], + ![![0, 0, 0, 0, 0, 0, 0, 4582620, -21402093], ![0, 0, 0, 0, 0, 0, 2744534, -4053241, 2091862], ![0, 0, 0, 0, 0, 1254615, 119326, -1351192, 846998], ![0, 0, 0, 0, 251416, 819674, -831726, 1116146, -3026818], ![0, 0, 0, -366503, -138643, -262993, -69789, -2014575, 2467955], ![0, 0, -442958, -386858, 237177, 21361, -945799, 490916, 623063], ![0, 312317, 378534, 414641, -381651, -1214503, 525474, 331451, -671780], ![1126574, 51881, -475448, -1232794, -905053, 27808, -429230, -574069, -776706]] + ] + +def exactRows (a : Fin 8) : RationalRow where + t := a + lam := (rowLambdaInteger a : ℚ)/10000000 + alpha p j := (rowAlphaInteger a p j : ℚ)/10000000 + +def etaRational : ℚ := ∑ a : Fin 8, (exactRows a).lam^2 + +lemma etaRational_value : etaRational = (11530872018309/12500000000000:ℚ) := by decide +kernel + +lemma small_margin : (1/25:ℚ) < 1-etaRational-61/4096-1222*(1/200000) := by + rw [etaRational_value] + norm_num + +lemma test_sum : (exactRows 0).threeSumFast 2 0 = (0:ℚ) := by decide +kernel +lemma test_trace : (∑ i : Fin 9, threeRowFactor 0 2 i.val * (exactRows 0).threeSumFast 2 i * + ((exactRows 0).threeSumFast 2 i + 2*(exactRows 0).lam*uCoefficient 2 2 (0+i.val) 0)) = (3805540785952177/16402500000000000:ℚ) := by decide +kernel + +end LaughlinGap.RealOccupation + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Spin + +def traceRational (z : ℕ) : ℚ := + ∑ a : Fin 8, ∑ i : Fin 9, threeRowFactor a.val z i.val * + (exactRows a).threeSumFast z i * + ((exactRows a).threeSumFast z i + 2*(exactRows a).lam*uCoefficient 2 z (a.val+i.val) a.val) + +lemma traceRational_eq (z : ℕ) : + (traceRational z : ℝ) = ∑ a : Fin 8, rowTrace threeWeightCoefficientStar z (exactRows a).toReal := by + simp only [RationalRow.threeTrace_eq,RationalRow.threeTrace,RationalRow.threeSum_eq_fast, + traceRational, exactRows, Rat.cast_sum,Rat.cast_mul,Rat.cast_add,Rat.cast_ofNat] + +lemma trace_bound_2 : traceRational 2 < (3/2:ℚ)*(3*2-1)*(-1/2:ℚ)^2 := by decide +kernel +lemma trace_bound_4 : traceRational 4 < (3/2:ℚ)*(3*4-1)*(-1/2:ℚ)^4 := by decide +kernel +lemma trace_bound_5 : traceRational 5 < (3/2:ℚ)*(3*5-1)*(-1/2:ℚ)^5 := by decide +kernel +lemma trace_bound_6 : traceRational 6 < (3/2:ℚ)*(3*6-1)*(-1/2:ℚ)^6 := by decide +kernel +lemma trace_bound_7 : traceRational 7 < (3/2:ℚ)*(3*7-1)*(-1/2:ℚ)^7 := by decide +kernel +lemma trace_bound_8 : traceRational 8 < (3/2:ℚ)*(3*8-1)*(-1/2:ℚ)^8 := by decide +kernel +lemma trace_bound_9 : traceRational 9 < (3/2:ℚ)*(3*9-1)*(-1/2:ℚ)^9 := by decide +kernel +lemma trace_bound_10 : traceRational 10 < (3/2:ℚ)*(3*10-1)*(-1/2:ℚ)^10 := by decide +kernel +lemma trace_bound_11 : traceRational 11 < (3/2:ℚ)*(3*11-1)*(-1/2:ℚ)^11 := by decide +kernel +lemma trace_bound_12 : traceRational 12 < (3/2:ℚ)*(3*12-1)*(-1/2:ℚ)^12 := by decide +kernel +lemma trace_bound_13 : traceRational 13 < (3/2:ℚ)*(3*13-1)*(-1/2:ℚ)^13 := by decide +kernel +lemma trace_bound_14 : traceRational 14 < (3/2:ℚ)*(3*14-1)*(-1/2:ℚ)^14 := by decide +kernel +lemma trace_bound_15 : traceRational 15 < (3/2:ℚ)*(3*15-1)*(-1/2:ℚ)^15 := by decide +kernel + +lemma exact_three (z : Fin 16) (h0 : z.val ≠ 0) (h1 : z.val ≠ 1) (h3 : z.val ≠ 3) : + (∑ a : Fin 8, rowTrace threeWeightCoefficientStar z.val (exactRows a).toReal) < + (3/2:ℝ)*((3*(z.val:ℝ)-1)*(-1/2:ℝ)^z.val) := by + rw [← traceRational_eq] + have h : traceRational z.val < (3/2:ℚ)*(3*(z.val:ℚ)-1)*(-1/2:ℚ)^z.val := by + fin_cases z + · exact False.elim (h0 rfl) + · exact False.elim (h1 rfl) + · exact trace_bound_2 + · exact False.elim (h3 rfl) + · exact trace_bound_4 + · exact trace_bound_5 + · exact trace_bound_6 + · exact trace_bound_7 + · exact trace_bound_8 + · exact trace_bound_9 + · exact trace_bound_10 + · exact trace_bound_11 + · exact trace_bound_12 + · exact trace_bound_13 + · exact trace_bound_14 + · exact trace_bound_15 + have hh := (Rat.cast_lt (K := ℝ)).mpr h + push_cast at hh + nlinarith only [hh] + +lemma exact_margin : (1/25:ℝ) < + 1-rowEta (fun a : Fin 8 => (exactRows a).toReal) -61/4096-1222*(1/200000) := by + have he : rowEta (fun a : Fin 8 => (exactRows a).toReal) = (etaRational:ℝ) := by + simp [rowEta,etaRational,RationalRow.toReal] + rw [he] + have h := (Rat.cast_lt (K := ℝ)).mpr small_margin + push_cast at h + exact h + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/ExtendedPair.lean b/lean/OAI/Analysis/LaughlinGap/ExtendedPair.lean new file mode 100644 index 0000000000000000000000000000000000000000..e8bccf0a0c4961407547b83cc630b8b144472578 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/ExtendedPair.lean @@ -0,0 +1,108 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Contraction + +namespace OAI + +/-! Extended Pair. -/ + +noncomputable section + + +namespace LaughlinGap.Occupation +open scoped BigOperators ComplexOrder + +noncomputable def endCongr {n m : ℕ} (h : n=m) : + Module.End ℂ (Hilbert n) ≃ₐ[ℂ] Module.End ℂ (Hilbert m) := h ▸ AlgEquiv.refl + +lemma endCongr_transition {n m : ℕ} (h : n=m) (j : Fin n) (ε : Bool) : + endCongr h (transition j ε) = transition (Fin.cast h j) ε := by subst m; rfl + +lemma endCongr_adjoint {n m : ℕ} (h : n=m) (T : Module.End ℂ (Hilbert n)) : + endCongr h T.adjoint = (endCongr h T).adjoint := by subst m; rfl + +noncomputable def extendTo {n m : ℕ} (h : n ≤ m) : + Module.End ℂ (Hilbert n) →ₐ[ℂ] Module.End ℂ (Hilbert m) := + (endCongr (Nat.add_sub_of_le h)).toAlgHom.comp (extendLocalHom n (m-n)).toAlgHom + +lemma endCongr_extendLocal {n m k : ℕ} (h : m=k) (T : Module.End ℂ (Hilbert n)) : + endCongr (congrArg (n+·) h) (extendLocal (m := m) T) = extendLocal (m := k) T := by + subst k + rfl + +@[simp] lemma extendTo_add_dim (n m : ℕ) (T : Module.End ℂ (Hilbert n)) : + extendTo (Nat.le_add_right n m) T = extendLocal (m := m) T := by + exact endCongr_extendLocal (Nat.add_sub_cancel_left n m) T + +@[simp] lemma extendTo_annihilation {n m : ℕ} (h : n ≤ m) (j : Fin n) : + extendTo h (annihilation j) = annihilation (Fin.castLE h j) := by + simp only [extendTo,AlgHom.comp_apply,AlgEquiv.coe_toAlgHom,annihilation] + change endCongr _ (extendLocal (transition j false)) = _ + rw [extendLocal_transition,endCongr_transition] + rfl + +@[simp] lemma extendTo_adjoint {n m : ℕ} (h : n ≤ m) (T : Module.End ℂ (Hilbert n)) : + extendTo h T.adjoint = (extendTo h T).adjoint := by + simp only [extendTo,AlgHom.comp_apply,AlgEquiv.coe_toAlgHom] + change endCongr _ (extendLocal T.adjoint) = (endCongr _ (extendLocal T)).adjoint + rw [← extendLocal_adjoint,endCongr_adjoint] + +lemma extendTo_matrixLift {n m : ℕ} (h : n ≤ m) {ι : Type*} [Fintype ι] + (B : ι → Module.End ℂ (Hilbert n)) (C : Matrix ι ι ℂ) : + extendTo h (matrixLift B C) = matrixLift (fun r => extendTo h (B r)) C := by + simp only [matrixLift,LinearMap.coe_mk,AddHom.coe_mk,map_sum,map_smul,map_mul,extendTo_adjoint] + +lemma localPair_support {n Q p : ℕ} (i j : Fin n) (h : i.val+j.val ≠ p+1) : + (sphericalExteriorPairCoefficient Q p i.val j.val : ℂ) = 0 := by + simp [sphericalExteriorPairCoefficient,h] + +lemma extendTo_localPair {n m Q p : ℕ} (h : n ≤ m) (hp : p+1 < n) : + extendTo h (localPair n Q p) = localPair m Q p := by + classical + simp only [localPair,pairAnnihilator,map_sum,apply_ite,map_smul,map_mul, + extendTo_annihilation,map_zero] + rw [← Fintype.sum_prod_type', ← Fintype.sum_prod_type'] + apply Finset.sum_bij_ne_zero (fun a _ _ => (Fin.castLE h a.1,Fin.castLE h a.2)) + · simp + · intro a ha ha0 b hb hb0 he + apply Prod.ext + · exact Fin.ext (congrArg (fun x : Fin m × Fin m => x.1.val) he) + · exact Fin.ext (congrArg (fun x : Fin m × Fin m => x.2.val) he) + · intro b hb hb0 + have hw : b.1.val+b.2.val=p+1 := by + by_contra hn + exact hb0 (by simp [localPair_support b.1 b.2 hn]) + let a : Fin n × Fin n := (⟨b.1.val,by omega⟩,⟨b.2.val,by omega⟩) + have he : (Fin.castLE h a.1,Fin.castLE h a.2)=b := by apply Prod.ext <;> rfl + exact ⟨a,Finset.mem_univ _,by simpa [a] using hb0,he⟩ + · intro a ha ha0 + rfl + +theorem local_four_family_transfer_to {n L : ℕ} {ι κ : Type*} + [Fintype ι] [DecidableEq ι] [Fintype κ] [DecidableEq κ] + (p : ι → Fin L) (j k : ι → Fin n) + (s : ℕ → κ → ι → ℝ) (s₀ : κ → ι → ℝ) + (C : ℕ → Matrix κ κ ℂ) (C₀ : Matrix κ κ ℂ) + (hs : ∀ r b, Filter.Tendsto (fun Q => s Q r b) Filter.atTop (nhds (s₀ r b))) + (hC : ∀ r t, Filter.Tendsto (fun Q => C Q r t) Filter.atTop (nhds (C₀ r t))) + (hC₀ : C₀.IsHermitian) + (hG : let B := fun r => ∑ b, (s₀ r b : ℂ) • + (annihilation (k b) * annihilation (j b) * localPairStar n (p b).val) + (createdGram B * C₀ * createdGram B).PosSemidef) : + ∃ ρ : ℕ → ℝ, (∀ Q, 0 ≤ ρ Q) ∧ Filter.Tendsto ρ Filter.atTop (nhds 0) ∧ + ∀ᶠ Q in Filter.atTop, ∀ m (h : n ≤ m) (x : Hilbert m), + -(ρ Q) * (∑ a : Fin L, ‖extendTo h (localPair n Q a.val) x‖ ^ 2) ≤ + (inner ℂ x (extendTo h (matrixLift + (fun r => ∑ b, (s Q r b : ℂ) • + (annihilation (k b) * annihilation (j b) * localPair n Q (p b).val)) (C Q)) x)).re := by + obtain ⟨ρ,hpos,hlim,hbound⟩ := local_four_family_transfer_of_gram p j k s s₀ C C₀ hs hC hC₀ hG + refine ⟨ρ,hpos,hlim,?_⟩ + filter_upwards [hbound] with Q hQ + intro m hm x + obtain ⟨d,rfl⟩ := Nat.exists_eq_add_of_le hm + simpa only [extendTo_add_dim] using hQ d x + +end LaughlinGap.Occupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/ExteriorTermExpansion.lean b/lean/OAI/Analysis/LaughlinGap/ExteriorTermExpansion.lean new file mode 100644 index 0000000000000000000000000000000000000000..f832eefb97fcb470276b475511fa77b4f1c641bb --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/ExteriorTermExpansion.lean @@ -0,0 +1,85 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.FourTransfer +import OAI.Analysis.LaughlinGap.RationalExterior + +namespace OAI + +/-! Exterior Term Expansion. -/ + +noncomputable section + + +namespace LaughlinGap.Occupation +open scoped BigOperators + +def pairLeft {n p : ℕ} (hp : p+1 < n) (i : Fin ((p+2)/2)) : Fin n := + ⟨i.val,by have := i.isLt; omega⟩ +def pairRight {n p : ℕ} (hp : p+1 < n) (i : Fin ((p+2)/2)) : Fin n := + ⟨p+1-i.val,by omega⟩ + +lemma localPairStar_sum {n p : ℕ} (hp : p+1 < n) : + localPairStar n p = ∑ i : Fin ((p+2)/2), + (limitingExteriorPairCoefficient p i.val (p+1-i.val):ℂ) • + (annihilation (pairRight hp i) * annihilation (pairLeft hp i)) := by + classical + symm + unfold localPairStar pairAnnihilator + simp only [Complex.star_def, Complex.conj_ofReal] + rw [← Fintype.sum_prod_type'] + apply Finset.sum_bij_ne_zero (fun i _ _ => (pairLeft hp i,pairRight hp i)) + · simp + · intro i hi h0 j hj h0' e + exact Fin.ext (congrArg (fun a : Fin n × Fin n => a.1.val) e) + · intro a ha h0 + have hlt : a.1 < a.2 := by + by_contra h + exact h0 (by simp [h]) + have he : a.1.val+a.2.val=p+1 := by + by_contra h + exact h0 (by simp [limitingExteriorPairCoefficient,h]) + let i : Fin ((p+2)/2) := ⟨a.1.val,by have := a.1.isLt; have := a.2.isLt; omega⟩ + have e₁ : pairLeft hp i=a.1 := rfl + have e₂ : pairRight hp i=a.2 := Fin.ext (by dsimp [pairRight,i]; omega) + refine ⟨i,Finset.mem_univ _,?_,by rw [e₁,e₂]⟩ + have ey : p+1-i.val=a.2.val := by dsimp [i]; omega + simpa only [e₁,e₂,ey,ite_eq_left hlt] using h0 + · intro i hi h0 + have ht : pairLeft hp i < pairRight hp i := by have := i.isLt; change i.val < p+1-i.val; omega + change _ = if pairLeft hp i < pairRight hp i then _ else _ + rw [ite_eq_left ht] + rfl + +end LaughlinGap.Occupation + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Spin + +lemma fourLocalHighestStar_terms {D : ℕ} (hD : D ≤ 23) (r : FourCopy D) : + fourLocalHighestStar hD r = ∑ a : FourTerm D, + (fourBodyCoefficientStar D D r.val.val (fourTermP a) (fourTermJ a) (fourTermK a) * + limitingExteriorPairCoefficient (fourTermP a) (fourTermX a) (fourTermY a):ℂ) • + Occupation.word (fourTermLabels hD a) := by + classical + rw [fourLocalHighestStar,← (orbitalTripleEquiv D).sum_comp] + simp only [fourHighestRowsStar] + conv_rhs => rw [Fintype.sum_sigma]; simp only [Fintype.sum_prod_type] + rw [Fintype.sum_sigma] + apply Finset.sum_congr rfl + intro n hn + apply Finset.sum_congr rfl + intro j hj + rw [Occupation.localPairStar_sum (by change D-n.val+1 < 25; omega)] + simp only [Finset.mul_sum, mul_smul_comm,Finset.smul_sum,smul_smul] + apply Finset.sum_congr rfl + intro x hx + simp only [fourTermP,fourTermJ,fourTermK,fourTermX,fourTermY,fourTermLabels, + localTripleP,localTripleJ,localTripleK,orbitalTripleEquiv,Occupation.pairLeft,Occupation.pairRight, + Occupation.word_cons,Occupation.word_nil,one_mul,mul_assoc] + rfl + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/FastCoupling.lean b/lean/OAI/Analysis/LaughlinGap/FastCoupling.lean new file mode 100644 index 0000000000000000000000000000000000000000..82fb4914c2563d7625b7dbfc49239462903aa393 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/FastCoupling.lean @@ -0,0 +1,72 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.RationalCreatedGram +import OAI.Analysis.LaughlinGap.RationalFourComputable + +namespace OAI + +/-! Fast Coupling. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators + +def chooseFast (n k : ℕ) : ℕ := n.descFactorial k / k.factorial +lemma chooseFast_eq (n k : ℕ) : chooseFast n k = n.choose k := + (Nat.choose_eq_descFactorial_div_factorial n k).symm + +def uFast (c z T p : ℕ) : ℚ := + if z ≤ T then ∑ h ∈ Finset.range (p+1), + (-1:ℚ)^(z-h) * (chooseFast z h) * (chooseFast (T-z) (p-h)) * (c:ℚ)^(p-h) else 0 + +lemma uCoefficient_eq_fast (c z T p : ℕ) : uCoefficient c z T p = uFast c z T p := by + simp only [uCoefficient,uFast,chooseFast_eq] + +end LaughlinGap.Spin + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Spin + +def vFast (D T r p j k : ℕ) : ℚ := + if D ≤ T ∧ r ≤ j+k ∧ p+j+k=T then + uFast 1 r (j+k) j * uFast 1 (D-r) (T-r) p else 0 + +lemma vCoefficient_eq_fast (D T r p j k : ℕ) : vCoefficient D T r p j k = vFast D T r p j k := by + simp only [vCoefficient,vFast,uCoefficient_eq_fast] + +def RationalRow.fourSumEval (r : RationalRow) (D s : ℕ) (i k : Fin 9) : ℚ := + ∑ p : Fin 8, if h : p.val ≤ r.t.val+i.val ∧ r.t.val+i.val-p.val < 9 then + r.alpha p ⟨r.t.val+i.val-p.val,h.2⟩ * + vFast D (r.t.val+i.val+k.val) s p.val (r.t.val+i.val-p.val) k.val * + (2:ℚ)^((s+1)/2+p.val) else 0 + +def RationalRow.fourMatrixEval (r : RationalRow) (D u v : ℕ) : ℚ := + -(∑ i : Fin 9, ∑ k : Fin 9, fourRowFactor r.t.val D i.val k.val * + r.fourSumEval D u i k * r.fourSumEval D v k i) + +lemma RationalRow.fourMatrix_eq_eval (r : RationalRow) (D : ℕ) (u v : FourCopy D) : + r.fourMatrix D u v = r.fourMatrixEval D u.val.val v.val.val := by + simp only [RationalRow.fourMatrix_eq_fast,RationalRow.fourMatrixFast,RationalRow.fourMatrixEval, + RationalRow.fourSumFast,RationalRow.fourSumEval,vCoefficient_eq_fast] + +def fourTermEval (D r : ℕ) (a : FourTerm D) : ℚ := + vFast D D r (fourTermP a) (fourTermJ a) (fourTermK a) * (2:ℚ)^((r+1)/2) * + ((fourTermX a:ℚ)-(fourTermY a:ℚ)) * (fourTermP a).factorial * + (fourTermJ a).factorial * (fourTermK a).factorial / (2:ℚ)^D + +lemma fourTermCoefficient_eq_eval (D r : ℕ) (a : FourTerm D) : + fourTermCoefficient D r a = fourTermEval D r a := by + simp only [fourTermCoefficient,fourTermEval,vCoefficient_eq_fast] + +lemma fourColumn_eq_fiber {D : ℕ} (hD : D ≤ 23) (r : ℕ) (A : Finset (Fin 25)) + (s : Finset (FourTerm D)) (hs : ∀ a, (fourTermLabels hD a).toFinset=A ↔ a ∈ s) : + fourColumn hD r A = ∑ a ∈ s, fourTermEval D r a * Occupation.wordSign (fourTermLabels hD a) := by + simp only [fourColumn,hs,fourTermCoefficient_eq_eval,Finset.sum_ite_mem,Finset.univ_inter] + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/FastFourKeys.lean b/lean/OAI/Analysis/LaughlinGap/FastFourKeys.lean new file mode 100644 index 0000000000000000000000000000000000000000..c229c53dade885644223c6006de645a591d4bb3d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/FastFourKeys.lean @@ -0,0 +1,111 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.RationalCreatedGram + +namespace OAI + +/-! Fast Four Keys. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation + +lemma fourKeys_of_index {D K : ℕ} (hD : D ≤ 23) + (keys : Fin K → Finset (Fin 25)) (index : FourTerm D → Fin K) + (rep : Fin K → FourTerm D) + (cover : ∀ b, (fourTermLabels hD b).Nodup → (fourTermLabels hD b).toFinset=keys (index b)) + (hrep : ∀ a, (fourTermLabels hD (rep a)).Nodup ∧ (fourTermLabels hD (rep a)).toFinset=keys a) : + fourKeys hD = Finset.univ.image keys := by + ext A + constructor + · intro h + obtain ⟨b,hb,rfl⟩ := Finset.mem_image.mp h + exact Finset.mem_image.mpr ⟨index b,Finset.mem_univ _,(cover b (Finset.mem_filter.mp hb).2).symm⟩ + · intro h + obtain ⟨a,ha,rfl⟩ := Finset.mem_image.mp h + exact Finset.mem_image.mpr ⟨rep a,Finset.mem_filter.mpr ⟨Finset.mem_univ _,(hrep a).1⟩,(hrep a).2⟩ + +end LaughlinGap.RealOccupation + +namespace LaughlinGap.RealOccupation + +def checkFourTerms (D : ℕ) (P : FourTerm D → Bool) : Bool := + (List.finRange (D+1)).all fun n => + (List.finRange ((n.val+1)/2)).all fun j => + (List.finRange ((D-n.val+2)/2)).all fun x => P ⟨n,j,x⟩ + +lemma checkFourTerms_sound {D : ℕ} (P : FourTerm D → Prop) [DecidablePred P] + (h : checkFourTerms D (fun b => decide (P b)) = true) : ∀ b, P b := by + rintro ⟨n,j,x⟩ + have hn := List.all_eq_true.mp h n (List.mem_finRange n) + have hj := List.all_eq_true.mp hn j (List.mem_finRange j) + exact of_decide_eq_true (List.all_eq_true.mp hj x (List.mem_finRange x)) + +end LaughlinGap.RealOccupation + +namespace LaughlinGap.RealOccupation + +def fourTermCode {D : ℕ} (b : FourTerm D) : ℕ × ℕ × ℕ := + (b.1.val,b.2.1.val,b.2.2.val) + +lemma fourTermCode_injective (D : ℕ) : Function.Injective (@fourTermCode D) := by + rintro ⟨⟨n,hn⟩,⟨j,hj⟩,⟨x,hx⟩⟩ ⟨⟨n',hn'⟩,⟨j',hj'⟩,⟨x',hx'⟩⟩ h + simp only [fourTermCode, Prod.mk.injEq] at h + obtain ⟨rfl,rfl,rfl⟩ := h + rfl + +lemma checkFourFiber_sound {D : ℕ} (hD : D ≤ 23) (A : Finset (Fin 25)) + (s : Finset (FourTerm D)) + (h : checkFourTerms D (fun b => decide + ((fourTermLabels hD b).toFinset=A ↔ fourTermCode b ∈ s.image fourTermCode))=true) : + ∀ b, (fourTermLabels hD b).toFinset=A ↔ b ∈ s := by + intro b + have hb := checkFourTerms_sound _ h b + simpa only [Finset.mem_image, fourTermCode_injective D |>.eq_iff, exists_eq_right] using hb + +end LaughlinGap.RealOccupation + +namespace LaughlinGap.RealOccupation + +lemma fourFibers_of_index {D K : ℕ} (hD : D ≤ 23) + (keys : Fin K → Finset (Fin 25)) (index : FourTerm D → Fin K) + (fibers : Fin K → Finset (FourTerm D)) + (hi : Function.Injective keys) (hcard : ∀ a, (keys a).card=4) + (cover : ∀ b, (fourTermLabels hD b).Nodup → (fourTermLabels hD b).toFinset=keys (index b)) + (fiberCover : ∀ b, (fourTermLabels hD b).Nodup → b ∈ fibers (index b)) + (fiberSound : ∀ a, ∀ b ∈ fibers a, (fourTermLabels hD b).toFinset=keys a) : + ∀ a b, (fourTermLabels hD b).toFinset=keys a ↔ b ∈ fibers a := by + intro a b + constructor + · intro h + have hn : (fourTermLabels hD b).Nodup := by + apply (Multiset.toFinset_card_eq_card_iff_nodup (m := (↑(fourTermLabels hD b) : Multiset (Fin 25)))).mp + change (fourTermLabels hD b).toFinset.card=(fourTermLabels hD b).length + rw [h,hcard] + rfl + have hind : index b=a := hi ((cover b hn).symm.trans h) + simpa only [hind] using fiberCover b hn + · exact fiberSound a b + +end LaughlinGap.RealOccupation + +namespace LaughlinGap.RealOccupation + +def checkFourFibersSound {D K : ℕ} (hD : D ≤ 23) + (keys : Fin K → Finset (Fin 25)) (fibers : Fin K → Finset (FourTerm D)) : Bool := + (List.finRange K).all fun a => @decide (∀ b ∈ fibers a, + (fourTermLabels hD b).toFinset=keys a) (Finset.decidableDforallFinset (s := fibers a)) + +lemma checkFourFibersSound_sound {D K : ℕ} (hD : D ≤ 23) + (keys : Fin K → Finset (Fin 25)) (fibers : Fin K → Finset (FourTerm D)) + (h : checkFourFibersSound hD keys fibers=true) : + ∀ a b, b ∈ fibers a → (fourTermLabels hD b).toFinset=keys a := by + intro a b hb + have ha := List.all_eq_true.mp h a (List.mem_finRange a) + exact @of_decide_eq_true _ (Finset.decidableDforallFinset (s := fibers a)) ha b hb + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Four.lean b/lean/OAI/Analysis/LaughlinGap/Four.lean new file mode 100644 index 0000000000000000000000000000000000000000..79e24bf93cc9187437c1a7a652b04144f82cae9a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Four.lean @@ -0,0 +1,139 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.FourAveraging +import OAI.Analysis.LaughlinGap.RealSpinSquare + +namespace OAI + +/-! Four. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators + +lemma tensorProjection_positive {n m z : ℕ} (hz : z ≤ min n m) : + (tensorProjection hz).PosSemidef := by + rw [tensorProjection_eq] + apply Matrix.posSemidef_sum + intro l hl + simpa only [star_trivial] using Matrix.posSemidef_vecMulVec_self_star + (coupledTensor n m z l.val) + +lemma sum_tensorProjection (n m : ℕ) : + (∑ z : Fin (min n m+1), tensorProjection (Nat.le_of_lt_succ z.isLt)) = 1 := by + classical + ext a b + have h := congrFun (coupledTensor_expansion n m (Pi.single b 1)) a + simpa only [tensorProjection_eq, Matrix.sum_apply, Matrix.vecMulVec_apply, + Fintype.sum_sigma, Finset.sum_apply, Pi.smul_apply, smul_eq_mul, + dotProduct_single_one, Pi.single_apply, Matrix.one_apply, eq_comm, mul_comm] using h.symm + +end LaughlinGap.Spin + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin + +variable {ι : Type*} [Fintype ι] [DecidableEq ι] + +lemma Covariant.average_highest {n m z : ℕ} (hz : z ≤ min n m) + {L : Matrix ι ι ℝ} {B : (Fin (n+1) × Fin (m+1)) → Matrix ι ι ℝ} + (h : Covariant L (loweringMatrix (tensorSpin n m)) B) : + average (rotationCommutant L) + ((combination B (highestTensor n m z)).transpose * combination B (highestTensor n m z)) = + (1/(n+m-2*z+1 : ℕ) : ℝ) • lift B (tensorProjection hz) := by + have he : (coupledEmbedding hz).toLinearMap (Pi.single (0 : Fin (n+m-2*z+1)) 1) = + highestTensor n m z := by + rw [coupledEmbedding_apply] + simp [Pi.single_apply, ite_smul] + rw [← lift_rankOne, h.average_lift, ← he, equal_copy_average] + simp only [ite_true, map_smul] + simp only [tensorProjection, LadderMap.comp, LadderMap.transpose, + LinearMap.toMatrix'_comp, toMatrix_transposeMap, LadderMap.matrix] + +noncomputable def physicalPairPair (Q : ℕ) : + (Fin (2*Q-2+1) × Fin (2*Q-2+1)) → FockMatrix (Q+1) := + productFamily (fun p => physicalPair Q p.val) (fun p => physicalPair Q p.val) + +lemma physicalPairPair_covariant {Q : ℕ} (hQ : 2 ≤ Q) : + Covariant (fockLowering Q) (loweringMatrix (tensorSpin (2*Q-2) (2*Q-2))) + (physicalPairPair Q) := (physicalPair_covariant hQ).product (physicalPair_covariant hQ) + +lemma fourAnnihilator_first {Q D T : ℕ} (hQ : 2 ≤ Q) : + fourAnnihilator Q D T 1 = + combination (physicalPairPair Q) (coupledTensor (2*Q-2) (2*Q-2) (D-1) (T-D)) := by + classical + unfold fourAnnihilator + unfold nestedTensor + rw [show Q+Q-2*1=2*Q-2 by omega] + simp only [combination, LinearMap.coe_mk, AddHom.coe_mk, Fintype.sum_prod_type, + physicalFour, productFamily, smul_smul, Finset.sum_mul, Finset.sum_smul] + apply Finset.sum_congr rfl + intro p hp + rw [Finset.sum_comm] + conv_lhs => arg 2; ext k; rw [Finset.sum_comm] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro r hr + rw [← physicalPairTensor_eq_coupled hQ (Nat.le_of_lt_succ r.isLt)] + simp only [physicalPairPair, productFamily, physicalPair, combination, + LinearMap.coe_mk, AddHom.coe_mk, Fintype.sum_prod_type, Matrix.smul_mul, + Finset.sum_mul, Finset.smul_sum, smul_smul, Matrix.mul_assoc] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro j hj + apply Finset.sum_congr rfl + intro k hk + congr 1 + ring + +lemma lift_physicalPairPair_one {Q : ℕ} (hQ : 2 ≤ Q) : + lift (physicalPairPair Q) 1 = fourTarget Q := by + rw [lift_identity] + simp only [physicalPairPair, productFamily, Fintype.sum_prod_type, fourTarget] + let e : Fin (2*Q-2+1) ≃ Fin (2*Q-1) := finCongr (by omega) + have he := e.sum_comp (fun p : Fin (2*Q-1) => ∑ q : Fin (2*Q-1), + (physicalPair Q q.val * physicalPair Q p.val).transpose * + (physicalPair Q q.val * physicalPair Q p.val)) + rw [← he] + apply Finset.sum_congr rfl + intro p hp + exact e.sum_comp (fun q : Fin (2*Q-1) => + (physicalPair Q q.val * physicalPair Q p.val).transpose * + (physicalPair Q q.val * physicalPair Q p.val)) + +theorem fourTarget_retained {Q K : ℕ} (hQ : 2 ≤ Q) (hK : K ≤ Q) : + (∑ d : Fin K, ((4*Q-1-2*(d.val+1) : ℕ) : ℝ) • + average (rotationCommutant (fockLowering Q)) + ((fourAnnihilator Q (d.val+1) (d.val+1) 1).transpose * + fourAnnihilator Q (d.val+1) (d.val+1) 1)) ≤ fourTarget Q := by + classical + have hz (d : Fin K) : d.val ≤ min (2*Q-2) (2*Q-2) := by omega + have he (d : Fin K) : + ((4*Q-1-2*(d.val+1) : ℕ) : ℝ) • average (rotationCommutant (fockLowering Q)) + ((fourAnnihilator Q (d.val+1) (d.val+1) 1).transpose * + fourAnnihilator Q (d.val+1) (d.val+1) 1) = + lift (physicalPairPair Q) (tensorProjection (hz d)) := by + rw [fourAnnihilator_first hQ] + simp only [Nat.add_sub_cancel, Nat.sub_self, coupledTensor_zero] + rw [(physicalPairPair_covariant hQ).average_highest (hz d), smul_smul] + have hn : 4*Q-1-2*(d.val+1) = (2*Q-2)+(2*Q-2)-2*d.val+1 := by omega + rw [hn, mul_one_div_cancel (by positivity), one_smul] + simp only [he] + rw [← lift_physicalPairPair_one hQ, ← sum_tensorProjection (2*Q-2) (2*Q-2), map_sum] + let e : Fin K ↪ Fin (min (2*Q-2) (2*Q-2)+1) := + ⟨fun d => ⟨d.val,Nat.lt_succ_of_le (hz d)⟩, + fun a b he => Fin.ext (congrArg (fun z : Fin (min (2*Q-2) (2*Q-2)+1) => z.val) he)⟩ + have hh := Finset.sum_le_sum_of_subset_of_nonneg + (s := Finset.univ.map e) (t := Finset.univ) + (f := fun z : Fin (min (2*Q-2) (2*Q-2)+1) => + lift (physicalPairPair Q) (tensorProjection (Nat.le_of_lt_succ z.isLt))) + (Finset.subset_univ _) (fun z _ _ => (lift_positive _ (tensorProjection_positive _)).nonneg) + simpa only [Finset.sum_map, e, Function.Embedding.coeFn_mk] using hh + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/FourAllowance.lean b/lean/OAI/Analysis/LaughlinGap/FourAllowance.lean new file mode 100644 index 0000000000000000000000000000000000000000..9136715ba1c877f2fbf88ae9f771f11b385ab861 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/FourAllowance.lean @@ -0,0 +1,142 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.FourHighest +import OAI.Analysis.LaughlinGap.ThreeBounds + +namespace OAI + +/-! Four Allowance. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators InnerProduct + +abbrev FourCoordinates (Q : ℕ) := Fin (2*Q-2+1) × Occupation.PairLabel (Q+1) + +noncomputable instance (D : ℕ) : DecidableEq (OrbitalTriple D) := Classical.decEq _ + +def orbitalTripleFinite {Q D : ℕ} (hQ : 2 ≤ Q) (hD : D ≤ Q) + (b : OrbitalTriple D) : FourCoordinates Q := + (⟨b.val.1,by have := b.property; omega⟩, + ⟨(⟨b.val.2.1,by have := b.property; omega⟩, + ⟨b.val.2.2,by have := b.property; omega⟩),b.property.2⟩) + +lemma orbitalTripleFinite_injective {Q D : ℕ} (hQ : 2 ≤ Q) (hD : D ≤ Q) : + Function.Injective (orbitalTripleFinite hQ hD) := by + intro a b he + apply Subtype.ext + apply Prod.ext + · exact congrArg (fun x : FourCoordinates Q => x.1.val) he + · apply Prod.ext + · exact congrArg (fun x : FourCoordinates Q => x.2.val.1.val) he + · exact congrArg (fun x : FourCoordinates Q => x.2.val.2.val) he + +lemma sum_orbitalTriple {Q D : ℕ} {M : Type*} [AddCommMonoid M] + (hQ : 2 ≤ Q) (hD : D ≤ Q) (f : FourCoordinates Q → M) + (hf : ∀ a, a.1.val+a.2.val.1.val+a.2.val.2.val ≠ D → f a = 0) : + ∑ b : OrbitalTriple D, f (orbitalTripleFinite hQ hD b) = ∑ a, f a := by + classical + apply Finset.sum_bij_ne_zero (fun b _ _ => orbitalTripleFinite hQ hD b) + · simp + · intros a _ _ b _ _ he + exact orbitalTripleFinite_injective hQ hD he + · intro a ha hfa + have hw : a.1.val+a.2.val.1.val+a.2.val.2.val=D := by + by_contra hn; exact hfa (hf a hn) + let b : OrbitalTriple D := ⟨(a.1.val,a.2.val.1.val,a.2.val.2.val), hw,a.2.property⟩ + have hb : orbitalTripleFinite hQ hD b = a := by + apply Prod.ext + · rfl + · apply Subtype.ext; rfl + exact ⟨b,Finset.mem_univ _,by rwa [hb],hb⟩ + · simp + +noncomputable def fourHighestRows (Q D : ℕ) : Matrix (FourCopy D) (OrbitalTriple D) ℝ := + fun r b => fourBodyCoefficient Q D D r.val.val b.val.1 b.val.2.1 b.val.2.2 + +lemma fourHighestRows_orthonormal {Q D : ℕ} (hQ : 2 ≤ Q) (hD : D ≤ Q) : + fourHighestRows Q D * (fourHighestRows Q D).transpose = 1 := by + classical + ext r s + simp only [Matrix.mul_apply, Matrix.transpose_apply, Matrix.one_apply] + let f := fun a : FourCoordinates Q => fourBodyCoupled Q D D r.val.val a * + fourBodyCoupled Q D D s.val.val a + have he (b : OrbitalTriple D) : f (orbitalTripleFinite hQ hD b) = + fourHighestRows Q D r b * fourHighestRows Q D s b := by + simp only [f, fourBodyCoupled_coefficient (Nat.le_of_lt_succ r.val.isLt) le_rfl hD, + fourBodyCoupled_coefficient (Nat.le_of_lt_succ s.val.isLt) le_rfl hD] + rfl + rw [← show (∑ b, f (orbitalTripleFinite hQ hD b)) = + ∑ b, fourHighestRows Q D r b * fourHighestRows Q D s b by simp only [he], + sum_orbitalTriple hQ hD f] + · have ho := (orthonormal_iff_ite.mp (fourBodyHighestFamily_orthonormal hQ hD)) s r + simpa only [fourBodyHighestFamily, EuclideanSpace.inner_toLp_toLp, star_trivial, + dotProduct, eq_comm] using ho + · intro a ha + dsimp [f] + rw [fourBodyCoupled_coefficient (Nat.le_of_lt_succ r.val.isLt) le_rfl hD] + simp [fourBodyCoefficient,ha] + +end LaughlinGap.Spin + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin + +noncomputable def localFourCoordinates {Q D : ℕ} (hQ : 2 ≤ Q) (hD : D ≤ Q) + (b : OrbitalTriple D) : FockMatrix (Q+1) := + let a := orbitalTripleFinite hQ hD b + annihilation a.2.val.2 * annihilation a.2.val.1 * physicalPair Q a.1.val + +lemma fourAnnihilator_high_local {Q D : ℕ} (hQ : 2 ≤ Q) (hD : D ≤ Q) (r : FourCopy D) : + fourAnnihilator Q D D r.val.val = + combination (localFourCoordinates hQ hD) (fourHighestRows Q D r) := by + classical + rw [fourAnnihilator_exterior hQ hD le_rfl (Nat.le_of_lt_succ r.val.isLt) r.property] + simp only [combination, LinearMap.coe_mk, AddHom.coe_mk] + let f := fun a : FourCoordinates Q => + fourBodyCoefficient Q D D r.val.val a.1.val a.2.val.1.val a.2.val.2.val • + (annihilation a.2.val.2 * annihilation a.2.val.1 * physicalPair Q a.1.val) + change _ = ∑ b, f (orbitalTripleFinite hQ hD b) + rw [sum_orbitalTriple hQ hD f] + · exact (Fintype.sum_prod_type f).symm + · intro a ha + simp [f, fourBodyCoefficient, ha] + +lemma fourHighest_bessel {Q D : ℕ} (hQ : 2 ≤ Q) (hD : D ≤ Q) : + (∑ r : FourCopy D, (fourAnnihilator Q D D r.val.val).transpose * + fourAnnihilator Q D D r.val.val) ≤ + ∑ b : OrbitalTriple D, (physicalPair Q b.val.1).transpose * physicalPair Q b.val.1 := by + simp only [fourAnnihilator_high_local hQ hD] + apply (sub_nonneg.mp (combination_bessel (fourHighestRows Q D) + (fourHighestRows_orthonormal hQ hD) (localFourCoordinates hQ hD)).nonneg).trans + apply Finset.sum_le_sum + intro b hb + simpa only [localFourCoordinates, orbitalTripleFinite, Matrix.mul_assoc] using + sub_nonneg.mp (double_annihilation_square_le + (orbitalTripleFinite hQ hD b).2.val.1 (orbitalTripleFinite hQ hD b).2.val.2 + (physicalPair Q b.val.1)).nonneg + +theorem fourHighest_average_bessel {Q D : ℕ} (hQ : 2 ≤ Q) (hD : D ≤ Q) : + ((2*Q-1 : ℕ):ℝ) • + (∑ r : FourCopy D, average (rotationCommutant (fockLowering Q)) + ((fourAnnihilator Q D D r.val.val).transpose * fourAnnihilator Q D D r.val.val)) ≤ + (Fintype.card (OrbitalTriple D):ℝ) • physicalHamiltonian Q := by + have h := average_mono (rotationCommutant (fockLowering Q)) (fourHighest_bessel hQ hD) + simp only [map_sum] at h + have he (b : OrbitalTriple D) := physicalPair_single_val hQ + (show b.val.1 < 2*Q-1 by have := b.property; omega) + simp only [he, ← Finset.sum_smul, Finset.sum_const, Finset.card_univ, nsmul_eq_mul] at h + have h' := smul_le_smul_of_nonneg_left h (Nat.cast_nonneg (α := ℝ) (2*Q-1)) + have hn : ((2*Q-1 : ℕ):ℝ) ≠ 0 := by exact_mod_cast (show 2*Q-1 ≠ 0 by omega) + convert h' using 1 + rw [smul_smul] + congr 1 + field_simp + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/FourAveraging.lean b/lean/OAI/Analysis/LaughlinGap/FourAveraging.lean new file mode 100644 index 0000000000000000000000000000000000000000..88881eb5988cdeebda7829d896b6aad90135160f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/FourAveraging.lean @@ -0,0 +1,143 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.LowNested + +namespace OAI + +/-! Four Averaging. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin + +@[simp] lemma combination_single {ι κ : Type*} [Fintype ι] [DecidableEq ι] + [Fintype κ] [DecidableEq κ] (B : ι → Matrix κ κ ℝ) + (i : ι) : combination B (Pi.single i 1) = B i := by + simp [combination, Pi.single_apply, ite_smul] + +noncomputable def fourAnnihilator (Q D T r : ℕ) : FockMatrix (Q+1) := + combination (physicalFour Q) (nestedTensor (2*Q-2) Q Q r (D-r) (T-D)) + +lemma fourAnnihilator_even {Q D T r : ℕ} (hQ : 2 ≤ Q) (hT : T ≤ Q) + (hD : D ≤ T) (hr : r ≤ D) (he : Even r) : fourAnnihilator Q D T r = 0 := by + exact physicalFour_even_null (by omega) he (by omega) + +lemma fourAnnihilator_eq_embedding {Q D T r : ℕ} (hQ : 2 ≤ Q) (hT : T ≤ Q) + (hD : D ≤ T) (hr : r ≤ D) : + fourAnnihilator Q D T r = combination (physicalFour Q) + ((nestedAtDeficit (show r ≤ min Q Q by omega) hr + (show D-r ≤ min (2*Q-2) (Q+Q-2*r) by omega)).toLinearMap + (Pi.single (⟨T-D, by omega⟩ : Fin ((2*Q-2)+Q+Q-2*D+1)) 1)) := by + rw [nestedAtDeficit_single] + rfl + +lemma fourAnnihilator_average {Q T U D E r s : ℕ} (hQ : 2 ≤ Q) + (hT : T ≤ Q) (hU : U ≤ Q) (hD : D ≤ T) (hE : E ≤ U) + (hr : r ≤ D) (hs : s ≤ E) : + average (rotationCommutant (fockLowering Q)) + ((fourAnnihilator Q D T r).transpose * fourAnnihilator Q E U s) = + if D=E ∧ T=U then average (rotationCommutant (fockLowering Q)) + ((fourAnnihilator Q D D r).transpose * fourAnnihilator Q E E s) else 0 := by + classical + by_cases hDE : D=E + · subst E + rw [fourAnnihilator_eq_embedding hQ hT hD hr, + fourAnnihilator_eq_embedding hQ hU hE hs, + (physicalFour_covariant hQ).equal_descendant_average, + fourAnnihilator_eq_embedding hQ (by omega : D ≤ Q) le_rfl hr, + fourAnnihilator_eq_embedding hQ (by omega : D ≤ Q) le_rfl hs] + simp only [true_and, Nat.sub_self] + congr 1 + apply propext + simp only [Fin.mk.injEq] + omega + · rw [ite_eq_right (by tauto), fourAnnihilator_eq_embedding hQ hT hD hr, + fourAnnihilator_eq_embedding hQ hU hE hs] + exact (physicalFour_covariant hQ).distinct_descendant_average (by omega) _ _ _ _ + +lemma rawFour_expansion {Q T : ℕ} (hQ : 2 ≤ Q) (hT : T ≤ Q) + (a : Fin (2*Q-2+1) × (Fin (Q+1) × Fin (Q+1))) + (ha : a.1.val+a.2.1.val+a.2.2.val=T) : + annihilation a.2.2 * annihilation a.2.1 * physicalPair Q a.1.val = + ∑ D : Fin (T+1), ∑ r : FourCopy D.val, + fourBodyCoefficient Q D.val T r.val.val a.1.val a.2.1.val a.2.2.val • + fourAnnihilator Q D.val T r.val.val := by + classical + have h := congrArg (combination (physicalFour Q)) (nestedTensor_low_expansion hQ hT a ha) + simp only [map_sum, map_smul, combination_single] at h + have h' := congrArg (fun M => Real.sqrt 2 • M) h + have hn : Real.sqrt 2 ≠ 0 := Real.sqrt_ne_zero'.mpr (by norm_num) + have hc (D : Fin (T+1)) (r : Fin (D.val+1)) := lowNested_coefficient + (Nat.le_of_lt_succ r.isLt) (Nat.le_of_lt_succ D.isLt) hT a + simp only [Fintype.sum_sigma, Finset.smul_sum, smul_smul, hc, + physicalFour, productFamily] at h' + rw [mul_one_div_cancel hn, one_smul] at h' + change (∑ D : Fin (T+1), ∑ r : Fin (D.val+1), + fourBodyCoefficient Q D.val T r.val a.1.val a.2.1.val a.2.2.val • + fourAnnihilator Q D.val T r.val) = _ at h' + rw [← h'] + apply Finset.sum_congr rfl + intro D hD + rw [← Finset.sum_subtype (Finset.univ.filter (fun r : Fin (D.val+1) => Odd r.val)) + (by simp) (fun r => fourBodyCoefficient Q D.val T r.val a.1.val a.2.1.val a.2.2.val • + fourAnnihilator Q D.val T r.val)] + rw [Finset.sum_filter] + apply Finset.sum_congr rfl + intro r hr + by_cases ho : Odd r.val + · simp [ho] + · have he : Even r.val := Nat.not_odd_iff_even.mp ho + rw [ite_eq_right ho, fourAnnihilator_even hQ hT (Nat.le_of_lt_succ D.isLt) + (Nat.le_of_lt_succ r.isLt) he, smul_zero] + +lemma rawFour_cross_average {Q T : ℕ} (hQ : 2 ≤ Q) (hT : T ≤ Q) + (a b : Fin (2*Q-2+1) × (Fin (Q+1) × Fin (Q+1))) + (ha : a.1.val+a.2.1.val+a.2.2.val=T) + (hb : b.1.val+b.2.1.val+b.2.2.val=T) : + average (rotationCommutant (fockLowering Q)) + ((annihilation a.2.2 * annihilation a.2.1 * physicalPair Q a.1.val).transpose * + (annihilation b.2.2 * annihilation b.2.1 * physicalPair Q b.1.val)) = + ∑ D : Fin (T+1), ∑ r : FourCopy D.val, ∑ s : FourCopy D.val, + (fourBodyCoefficient Q D.val T r.val.val a.1.val a.2.1.val a.2.2.val * + fourBodyCoefficient Q D.val T s.val.val b.1.val b.2.1.val b.2.2.val) • + average (rotationCommutant (fockLowering Q)) + ((fourAnnihilator Q D.val D.val r.val.val).transpose * + fourAnnihilator Q D.val D.val s.val.val) := by + classical + rw [rawFour_expansion hQ hT a ha, rawFour_expansion hQ hT b hb] + simp only [Matrix.transpose_sum, Matrix.transpose_smul, Finset.sum_mul, Finset.mul_sum, + Matrix.smul_mul, Matrix.mul_smul, smul_smul, map_sum, map_smul] + conv_lhs => + arg 2; ext E + rw [Finset.sum_comm] + rw [Finset.sum_comm] + conv_lhs => + arg 2; ext D + arg 2; ext E + rw [Finset.sum_comm] + conv_lhs => + arg 2; ext D + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro D hD + apply Finset.sum_congr rfl + intro r hr + have hblock (E : Fin (T+1)) (s : FourCopy E.val) := + fourAnnihilator_average hQ hT hT (Nat.le_of_lt_succ D.isLt) + (Nat.le_of_lt_succ E.isLt) (Nat.le_of_lt_succ r.val.isLt) (Nat.le_of_lt_succ s.val.isLt) + simp only [hblock, and_true, Fin.val_inj] + rw [Finset.sum_eq_single D] + · simp only [ite_true, mul_comm] + · intro E hE hED + apply Finset.sum_eq_zero + intro s hs + rw [ite_eq_right (Ne.symm hED), smul_zero] + · simp + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/FourBound.lean b/lean/OAI/Analysis/LaughlinGap/FourBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..ff22e815e3c7fc0e4d5045f7f4ee42a0c2c37d61 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/FourBound.lean @@ -0,0 +1,76 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.FourBoundCore + +namespace OAI + +/-! Four Bound. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin Filter Topology +variable {ι : Type*} [Fintype ι] + +lemma four_comparison_summed {Q : ℕ} (hQ : 24 ≤ Q) + (rows : ι → RowData) (ε : ℝ) (ρ : Fin 23 → ℝ) + (hQb : ∀ d : Fin 23, + -(ρ d) • (∑ p : Fin 24, (physicalPair Q p.val).transpose * physicalPair Q p.val) ≤ + lift (fun r : FourCopy (d.val+1) => fourAnnihilator Q (d.val+1) (d.val+1) r.val.val) + (fourComparison rows ε Q (d.val+1))) : + -(24*∑ d, ρ d) • physicalHamiltonian Q ≤ + retainedFourTarget Q - ((2*Q-1:ℕ):ℝ) • average (rotationCommutant (fockLowering Q)) + (∑ r, rowFour (by omega) (rows r)) + + ε • (((2*Q-1:ℕ):ℝ) • (∑ d : Fin 23, fourAverage Q (d.val+1) 1)) := by + have hb := Finset.sum_le_sum (fun d (_ : d ∈ (Finset.univ : Finset (Fin 23))) => + fourAverage_lower hQ (fourComparison rows ε Q (d.val+1)) (ρ d) (hQb d)) + simpa only [← Finset.smul_sum,← Finset.sum_smul,Finset.sum_neg_distrib, + ← Finset.mul_sum,fourComparison_difference hQ] using hb + +lemma rearrange_comparison {A : Type*} [AddCommGroup A] [PartialOrder A] [IsOrderedAddMonoid A] + {x y e r : A} (h : -r ≤ y-x+e) : x ≤ y+e+r := by + calc + x = -r+(x+r) := by abel + _ ≤ (y-x+e)+(x+r) := add_le_add h (le_refl _) + _ = y+e+r := by abel + +lemma four_comparison_pointwise {Q : ℕ} (hQ : 24 ≤ Q) + (rows : ι → RowData) (ε : ℝ) (hε : 0 ≤ ε) (ρ : Fin 23 → ℝ) + (hQb : ∀ d : Fin 23, + -(ρ d) • (∑ p : Fin 24, (physicalPair Q p.val).transpose * physicalPair Q p.val) ≤ + lift (fun r : FourCopy (d.val+1) => fourAnnihilator Q (d.val+1) (d.val+1) r.val.val) + (fourComparison rows ε Q (d.val+1))) : + ((2*Q-1:ℕ):ℝ) • average (rotationCommutant (fockLowering Q)) + (∑ r, rowFour (by omega) (rows r)) ≤ + fourTarget Q + (1222*ε+24*∑ d, ρ d) • physicalHamiltonian Q := by + have hb := four_comparison_summed hQ rows ε ρ hQb + rw [neg_smul] at hb + have hh := rearrange_comparison hb + have he := smul_le_smul_of_nonneg_left (fourAllowance_le hQ) hε + have ht := add_le_add (retainedFourTarget_le hQ) he + have h := add_le_add ht (le_refl ((24*∑ d, ρ d) • physicalHamiltonian Q)) + apply hh.trans + convert h using 1 + rw [smul_smul,add_assoc,← add_smul,mul_comm ε] + +theorem four_comparison_of_certificates (rows : ι → RowData) (ε : ℝ) (hε : 0 ≤ ε) + (hc : ∀ d : Fin 23, FourCertificate rows ε (d.val+1) (by omega)) : + ∃ R : ℕ → ℝ, (∀ Q, 0 ≤ R Q) ∧ Tendsto R atTop (𝓝 0) ∧ + ∀ᶠ Q in atTop, ∀ hQ : 24 ≤ Q, + ((2*Q-1:ℕ):ℝ) • average (rotationCommutant (fockLowering Q)) + (∑ r, rowFour (by omega) (rows r)) ≤ + fourTarget Q + (1222*ε+R Q) • physicalHamiltonian Q := by + classical + choose ρ hpos hlim hbound using (fun d : Fin 23 => four_local_transfer rows ε (by omega) (hc d)) + refine ⟨fun Q => 24*∑ d, ρ d Q,fun Q => mul_nonneg (by norm_num) (Finset.sum_nonneg (fun d _ => hpos d Q)),?_,?_⟩ + · simpa using (tendsto_finsetSum Finset.univ (fun d _ => hlim d)).const_mul 24 + · filter_upwards [eventually_all.mpr hbound] with Q hQb + intro hQ + exact four_comparison_pointwise hQ rows ε hε (fun d => ρ d Q) (fun d => hQb d hQ) + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/FourBoundCore.lean b/lean/OAI/Analysis/LaughlinGap/FourBoundCore.lean new file mode 100644 index 0000000000000000000000000000000000000000..e9571a19fa9e65c4b35e7e6c151becb69c68d10f --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/FourBoundCore.lean @@ -0,0 +1,89 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Four +import OAI.Analysis.LaughlinGap.FourTransfer + +namespace OAI + +/-! Four Bound Core. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin Filter Topology + +lemma localPair_average {Q L : ℕ} (hQ : 2 ≤ Q) (hL : L ≤ 2*Q-1) : + ((2*Q-1:ℕ):ℝ) • average (rotationCommutant (fockLowering Q)) + (∑ p : Fin L, (physicalPair Q p.val).transpose * physicalPair Q p.val) = + (L:ℝ) • physicalHamiltonian Q := by + have he (p : Fin L) := physicalPair_single_val hQ (show p.val < 2*Q-1 by omega) + simp only [map_sum,he,← Finset.sum_smul,Finset.sum_const,Finset.card_univ,Fintype.card_fin,nsmul_eq_mul, + smul_smul] + congr 1 + have hn : ((2*Q-1:ℕ):ℝ) ≠ 0 := by exact_mod_cast (show 2*Q-1 ≠ 0 by omega) + field_simp + +lemma fourAverage_identity (Q D : ℕ) : + fourAverage Q D 1 = ∑ r : FourCopy D, fourHighestAverage Q D r.val.val r.val.val := by + simp only [fourAverage,LinearMap.comp_apply,lift_identity,map_sum,fourHighestAverage] + +lemma fourAverage_lower {Q D : ℕ} (hQ : 24 ≤ Q) (C : Matrix (FourCopy D) (FourCopy D) ℝ) + (ρ : ℝ) (h : -ρ • (∑ p : Fin 24, (physicalPair Q p.val).transpose * physicalPair Q p.val) ≤ + lift (fun r : FourCopy D => fourAnnihilator Q D D r.val.val) C) : + -(24*ρ) • physicalHamiltonian Q ≤ ((2*Q-1:ℕ):ℝ) • fourAverage Q D C := by + have hh := smul_le_smul_of_nonneg_left + (average_mono (rotationCommutant (fockLowering Q)) h) + (Nat.cast_nonneg (α := ℝ) (2*Q-1)) + simp only [map_smul] at hh + rw [smul_comm ((2*Q-1:ℕ):ℝ) (-ρ),localPair_average (by omega : 2 ≤ Q) (by omega)] at hh + convert hh using 1 <;> simp [smul_smul,mul_comm,fourAverage] + +lemma retained_orbitalTriple_count_fin : + (∑ d : Fin 23, Fintype.card (OrbitalTriple (d.val+1))) = 1222 := by + simp_rw [orbitalTriple_card] + norm_num [Fin.sum_univ_succ] + +lemma fourAllowance_le {Q : ℕ} (hQ : 24 ≤ Q) : + ((2*Q-1:ℕ):ℝ) • (∑ d : Fin 23, fourAverage Q (d.val+1) 1) ≤ + (1222:ℝ) • physicalHamiltonian Q := by + have hh := Finset.sum_le_sum (s := Finset.univ) (fun d (_ : d ∈ (Finset.univ : Finset (Fin 23))) => + fourHighest_average_bessel (by omega : 2 ≤ Q) (show d.val+1 ≤ Q by omega)) + simpa only [fourAverage_identity,← Finset.smul_sum,← Finset.sum_smul, + ← Nat.cast_sum,retained_orbitalTriple_count_fin,fourHighestAverage,Nat.cast_ofNat] using hh + +noncomputable def retainedFourTarget (Q : ℕ) : FockMatrix (Q+1) := + ∑ d : Fin 23, ((4*Q-1-2*(d.val+1):ℕ):ℝ) • fourHighestAverage Q (d.val+1) 1 1 + +lemma retainedFourTarget_le {Q : ℕ} (hQ : 24 ≤ Q) : + retainedFourTarget Q ≤ fourTarget Q := fourTarget_retained (by omega) (by omega) + +variable {ι : Type*} [Fintype ι] + +lemma fourComparison_difference {Q : ℕ} (hQ : 24 ≤ Q) (rows : ι → RowData) (ε : ℝ) : + ((2*Q-1:ℕ):ℝ) • (∑ d : Fin 23, fourAverage Q (d.val+1) (fourComparison rows ε Q (d.val+1))) = + retainedFourTarget Q - ((2*Q-1:ℕ):ℝ) • average (rotationCommutant (fockLowering Q)) + (∑ r, rowFour (by omega) (rows r)) + + ε • (((2*Q-1:ℕ):ℝ) • (∑ d : Fin 23, fourAverage Q (d.val+1) 1)) := by + simp only [fourComparison,map_add,map_sub,map_smul,map_sum,Finset.smul_sum, + Finset.sum_add_distrib,Finset.sum_sub_distrib,smul_add,smul_sub, + rowFour_average_retained (by omega : 23 ≤ Q)] + rw [Finset.sum_comm (f := fun r (d : Fin 23) => _)] + congr 2 + · unfold retainedFourTarget + apply Finset.sum_congr rfl + intro d hd + rw [smul_smul,fourAverage_copyTarget Q (by omega), + fourDimensionRatio_eq (by omega : 2 ≤ Q) (by omega)] + have hn : ((2*Q-1:ℕ):ℝ) ≠ 0 := by exact_mod_cast (show 2*Q-1 ≠ 0 by omega) + congr 1 + field_simp + · simp only [smul_smul] + funext d + rw [mul_comm] + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/FourComparison.lean b/lean/OAI/Analysis/LaughlinGap/FourComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..0b7c28fe8cbb81ba0426f6d4ab7933985b4194cc --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/FourComparison.lean @@ -0,0 +1,188 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.AuxiliaryComparison +import OAI.Analysis.LaughlinGap.FourAveraging + +namespace OAI + +/-! Four Comparison. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin Filter Topology + +noncomputable def fourHighestAverage (Q D r s : ℕ) : FockMatrix (Q+1) := + average (rotationCommutant (fockLowering Q)) + ((fourAnnihilator Q D D r).transpose * fourAnnihilator Q D D s) + +noncomputable def fourWeightCoefficient (Q D T r p j k : ℕ) : ℝ := + if D ≤ T then fourBodyCoefficient Q D T r p j k else 0 + +noncomputable def fourWeightCoefficientStar (D T r p j k : ℕ) : ℝ := + if D ≤ T then fourBodyCoefficientStar D T r p j k else 0 + +lemma fourWeightCoefficient_tendsto {D r : ℕ} (hr : r ≤ D) (T p j k : ℕ) : + Tendsto (fun Q => fourWeightCoefficient Q D T r p j k) atTop + (𝓝 (fourWeightCoefficientStar D T r p j k)) := by + by_cases h : D ≤ T + · simp only [fourWeightCoefficient,fourWeightCoefficientStar,ite_eq_left h] + exact fourBodyCoefficient_tendsto hr h p j k + · simp only [fourWeightCoefficient,fourWeightCoefficientStar,ite_eq_right h] + exact tendsto_const_nhds + +lemma rowFour_cross_average {Q : ℕ} (hQ : 23 ≤ Q) (r : RowData) (a b : RowEntry r.t) : + average (rotationCommutant (fockLowering Q)) + ((annihilation ⟨b.output.val,by have := b.output.isLt; omega⟩ * rowTriple (by omega) a.val).transpose * + (annihilation ⟨a.output.val,by have := a.output.isLt; omega⟩ * rowTriple (by omega) b.val)) = + ∑ D : Fin 24, ∑ s : FourCopy D.val, ∑ t : FourCopy D.val, + (fourWeightCoefficient Q D.val (a.val.1.val+a.val.2.val+b.output.val) s.val.val + a.val.1.val a.val.2.val b.output.val * + fourWeightCoefficient Q D.val (a.val.1.val+a.val.2.val+b.output.val) t.val.val + b.val.1.val b.val.2.val a.output.val) • + fourHighestAverage Q D.val s.val.val t.val.val := by + let T := a.val.1.val+a.val.2.val+b.output.val + have ht : T ≤ 23 := by have := a.val.1.isLt; have := a.val.2.isLt; have := b.output.isLt; omega + let a' : Fin (2*Q-2+1) × (Fin (Q+1) × Fin (Q+1)) := + (⟨a.val.1.val,by have := a.val.1.isLt; omega⟩, + (⟨a.val.2.val,by have := a.val.2.isLt; omega⟩,⟨b.output.val,by have := b.output.isLt; omega⟩)) + let b' : Fin (2*Q-2+1) × (Fin (Q+1) × Fin (Q+1)) := + (⟨b.val.1.val,by have := b.val.1.isLt; omega⟩, + (⟨b.val.2.val,by have := b.val.2.isLt; omega⟩,⟨a.output.val,by have := a.output.isLt; omega⟩)) + have he : b'.1.val+b'.2.1.val+b'.2.2.val=T := by + dsimp [b',T]; have := a.balance; have := b.balance; omega + change average _ ((annihilation a'.2.2 * (annihilation a'.2.1 * physicalPair Q a'.1.val)).transpose * + (annihilation b'.2.2 * (annihilation b'.2.1 * physicalPair Q b'.1.val))) = _ + rw [← Matrix.mul_assoc (annihilation a'.2.2), ← Matrix.mul_assoc (annihilation b'.2.2), + rawFour_cross_average (by omega : 2 ≤ Q) (show T ≤ Q by omega) a' b' rfl he] + change (∑ D : Fin (T+1), ∑ s : FourCopy D.val, ∑ t : FourCopy D.val, + (fourBodyCoefficient Q D.val T s.val.val a.val.1.val a.val.2.val b.output.val * + fourBodyCoefficient Q D.val T t.val.val b.val.1.val b.val.2.val a.output.val) • + fourHighestAverage Q D.val s.val.val t.val.val) = _ + rw [sum_fin_extend ht (fun D => ∑ s : FourCopy D, ∑ t : FourCopy D, + (fourBodyCoefficient Q D T s.val.val a.val.1.val a.val.2.val b.output.val * + fourBodyCoefficient Q D T t.val.val b.val.1.val b.val.2.val a.output.val) • + fourHighestAverage Q D s.val.val t.val.val)] + apply Finset.sum_congr rfl + intro D hD + by_cases h : D.val ≤ T <;> simp [fourWeightCoefficient,h,T] + +noncomputable def rowFourMatrix + (s : ℕ → ℕ → ℕ → ℕ → ℕ → ℕ → ℝ) (D : ℕ) (r : RowData) : + Matrix (FourCopy D) (FourCopy D) ℝ := fun u v => + -(∑ a : RowEntry r.t, ∑ b : RowEntry r.t, r.alpha a*r.alpha b * + s D (a.val.1.val+a.val.2.val+b.output.val) u.val.val a.val.1.val a.val.2.val b.output.val * + s D (a.val.1.val+a.val.2.val+b.output.val) v.val.val b.val.1.val b.val.2.val a.output.val) + +lemma rowFourMatrix_symmetric (s : ℕ → ℕ → ℕ → ℕ → ℕ → ℕ → ℝ) + (D : ℕ) (r : RowData) : (rowFourMatrix s D r).IsHermitian := by + rw [Matrix.IsHermitian, Matrix.conjTranspose_eq_transpose_of_trivial] + ext u v + simp only [rowFourMatrix,Matrix.transpose_apply] + congr 1 + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro a ha + apply Finset.sum_congr rfl + intro b hb + have he : b.val.1.val+b.val.2.val+a.output.val = a.val.1.val+a.val.2.val+b.output.val := by + have := a.balance; have := b.balance; omega + rw [he] + ring + +lemma rowFourMatrix_tendsto (D : ℕ) (r : RowData) (u v : FourCopy D) : + Tendsto (fun Q => rowFourMatrix (fourWeightCoefficient Q) D r u v) atTop + (𝓝 (rowFourMatrix fourWeightCoefficientStar D r u v)) := by + unfold rowFourMatrix + apply Tendsto.neg + apply tendsto_finsetSum + intro a ha + apply tendsto_finsetSum + intro b hb + exact ((fourWeightCoefficient_tendsto (Nat.le_of_lt_succ u.val.isLt) _ _ _ _).const_mul _).mul + (fourWeightCoefficient_tendsto (Nat.le_of_lt_succ v.val.isLt) _ _ _ _) + +lemma rowFour_average {Q : ℕ} (hQ : 23 ≤ Q) (r : RowData) : + average (rotationCommutant (fockLowering Q)) (rowFour (by omega) r) = + ∑ D : Fin 24, ∑ u : FourCopy D.val, ∑ v : FourCopy D.val, + rowFourMatrix (fourWeightCoefficient Q) D.val r u v • + fourHighestAverage Q D.val u.val.val v.val.val := by + simp only [rowFour, map_neg, map_sum, map_smul, rowFour_cross_average hQ, + Finset.smul_sum, smul_smul] + conv_lhs => + arg 1; arg 2; ext a + rw [Finset.sum_comm] + conv_lhs => arg 1; rw [Finset.sum_comm] + rw [← Finset.sum_neg_distrib] + apply Finset.sum_congr rfl + intro D hD + conv_lhs => + arg 1; arg 2; ext a + rw [Finset.sum_comm] + conv_lhs => arg 1; rw [Finset.sum_comm] + rw [← Finset.sum_neg_distrib] + apply Finset.sum_congr rfl + intro u hu + conv_lhs => + arg 1; arg 2; ext a + rw [Finset.sum_comm] + conv_lhs => arg 1; rw [Finset.sum_comm] + rw [← Finset.sum_neg_distrib] + apply Finset.sum_congr rfl + intro v hv + simp only [← Finset.sum_smul, rowFourMatrix, neg_smul] + congr 2 + apply Finset.sum_congr rfl + intro a ha + apply Finset.sum_congr rfl + intro b hb + ring + +noncomputable def fourAverage (Q D : ℕ) : + Matrix (FourCopy D) (FourCopy D) ℝ →ₗ[ℝ] FockMatrix (Q+1) := + (average (rotationCommutant (fockLowering Q))).comp + (lift (fun r : FourCopy D => fourAnnihilator Q D D r.val.val)) + +lemma fourAverage_eq (Q D : ℕ) (C : Matrix (FourCopy D) (FourCopy D) ℝ) : + fourAverage Q D C = ∑ u, ∑ v, C u v • fourHighestAverage Q D u.val.val v.val.val := by + simp only [fourAverage,LinearMap.comp_apply,lift,LinearMap.coe_mk,AddHom.coe_mk,map_sum,map_smul, + fourHighestAverage] + +lemma rowFour_average_retained {Q : ℕ} (hQ : 23 ≤ Q) (r : RowData) : + average (rotationCommutant (fockLowering Q)) (rowFour (by omega) r) = + ∑ d : Fin 23, fourAverage Q (d.val+1) + (rowFourMatrix (fourWeightCoefficient Q) (d.val+1) r) := by + rw [rowFour_average hQ, Fin.sum_univ_succ] + have hzero (u : FourCopy 0) : False := by have := u.property.pos; have := u.val.isLt; omega + have hz : (∑ u : FourCopy 0, ∑ v : FourCopy 0, + rowFourMatrix (fourWeightCoefficient Q) 0 r u v • fourHighestAverage Q 0 u.val.val v.val.val) = 0 := + Finset.sum_eq_zero (fun u _ => (hzero u).elim) + simp only [Fin.val_zero,Fin.val_succ] + rw [hz,zero_add] + apply Finset.sum_congr rfl + intro d hd + exact (fourAverage_eq _ _ _).symm + +noncomputable def fourCopyTarget (D : ℕ) : Matrix (FourCopy D) (FourCopy D) ℝ := + fun r s => if r.val.val=1 ∧ s.val.val=1 then 1 else 0 + +lemma fourCopyTarget_symmetric (D : ℕ) : (fourCopyTarget D).IsHermitian := by + ext r s + simp [fourCopyTarget,and_comm] + +lemma fourAverage_copyTarget (Q : ℕ) {D : ℕ} (hD : 1 ≤ D) : + fourAverage Q D (fourCopyTarget D) = fourHighestAverage Q D 1 1 := by + classical + let r : FourCopy D := ⟨⟨1,by omega⟩,show Odd 1 by decide⟩ + have he (s : FourCopy D) : s.val.val=1 ↔ s=r := by + constructor + · intro hs; exact Subtype.ext (Fin.ext hs) + · rintro rfl; rfl + simp [fourAverage_eq,fourCopyTarget,he,ite_and,r] + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/FourHighest.lean b/lean/OAI/Analysis/LaughlinGap/FourHighest.lean new file mode 100644 index 0000000000000000000000000000000000000000..eb51acea8c5921aab36bed7e35558fb1e51e10d5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/FourHighest.lean @@ -0,0 +1,93 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.FourAveraging + +namespace OAI + +/-! Four Highest. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin + +lemma sum_increasing_matrices {n : ℕ} {κ : Type*} (f : Fin n → Fin n → Matrix κ κ ℝ) + (hs : ∀ i j, f i j = f j i) (hd : ∀ i, f i i = 0) : + (2:ℝ) • (∑ a : Occupation.PairLabel n, f a.val.1 a.val.2) = + ∑ i, ∑ j, f i j := by + ext x y + simp only [Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul] + exact Occupation.sum_increasing_pairs (fun i j => f i j x y) + (fun i j => congrFun (congrFun (hs i j) x) y) + (fun i => congrFun (congrFun (hd i) x) y) + +lemma annihilation_square_zero {n : ℕ} (i : Fin n) : annihilation i * annihilation i = 0 := by + apply complexify_injective + rw [map_mul, map_zero, complexify_annihilation] + exact Occupation.transition_square i false + +lemma fourAnnihilator_exterior {Q D T r : ℕ} (hQ : 2 ≤ Q) + (hT : T ≤ Q) (hD : D ≤ T) (hr : r ≤ D) (ho : Odd r) : + fourAnnihilator Q D T r = + ∑ p : Fin (2*Q-2+1), ∑ a : Occupation.PairLabel (Q+1), + fourBodyCoefficient Q D T r p.val a.val.1.val a.val.2.val • + (annihilation a.val.2 * annihilation a.val.1 * physicalPair Q p.val) := by + classical + simp only [fourAnnihilator, combination, LinearMap.coe_mk, AddHom.coe_mk, + Fintype.sum_prod_type] + apply Finset.sum_congr rfl + intro p hp + have hf (j k : Fin (Q+1)) : + nestedTensor (2*Q-2) Q Q r (D-r) (T-D) (p,(k,j)) = + -nestedTensor (2*Q-2) Q Q r (D-r) (T-D) (p,(j,k)) := by + rw [nestedTensor_flip _ _ _ _ _ (by omega) (by omega), ho.neg_one_pow, neg_one_mul] + let f := fun j k : Fin (Q+1) => + nestedTensor (2*Q-2) Q Q r (D-r) (T-D) (p,(j,k)) • physicalFour Q (p,(j,k)) + have hs (j k : Fin (Q+1)) : f j k = f k j := by + dsimp [f] + rw [hf, physicalFour_flip, neg_smul, smul_neg, neg_neg] + have hd (j : Fin (Q+1)) : f j j = 0 := by + simp [f, physicalFour, productFamily, annihilation_square_zero] + rw [← sum_increasing_matrices f hs hd, Finset.smul_sum] + apply Finset.sum_congr rfl + intro a ha + dsimp [f] + rw [physicalFour, productFamily, productFamily, smul_smul, smul_smul, + ← lowNested_coefficient hr hD hT (p,(a.val.1,a.val.2))] + congr 1 + have hn := Real.sq_sqrt (by norm_num : (0:ℝ) ≤ 2) + field_simp + rw [hn] + ring + +lemma fourAnnihilator_weight_local {Q D T r : ℕ} (hQ : 2 ≤ Q) + (hT : T ≤ Q) (hD : D ≤ T) (hr : r ≤ D) (ho : Odd r) : + fourAnnihilator Q D T r = + ∑ a : {a : Fin (2*Q-2+1) × Occupation.PairLabel (Q+1) // + a.1.val+a.2.val.1.val+a.2.val.2.val=T}, + fourBodyCoefficient Q D T r a.val.1.val a.val.2.val.1.val a.val.2.val.2.val • + (annihilation a.val.2.val.2 * annihilation a.val.2.val.1 * physicalPair Q a.val.1.val) := by + classical + rw [fourAnnihilator_exterior hQ hT hD hr ho] + rw [← Finset.sum_subtype (Finset.univ.filter (fun a : Fin (2*Q-2+1) × + Occupation.PairLabel (Q+1) => a.1.val+a.2.val.1.val+a.2.val.2.val=T)) (by simp) + (fun a => fourBodyCoefficient Q D T r a.1.val a.2.val.1.val a.2.val.2.val • + (annihilation a.2.val.2 * annihilation a.2.val.1 * physicalPair Q a.1.val))] + rw [Finset.sum_filter, Fintype.sum_prod_type] + apply Finset.sum_congr rfl + intro p hp + apply Finset.sum_congr rfl + intro b hb + let a := (p,b) + change _ = if a.1.val+a.2.val.1.val+a.2.val.2.val=T then _ else _ + by_cases h : a.1.val+a.2.val.1.val+a.2.val.2.val=T + · simp [h] + · dsimp [a] at h + simp [fourBodyCoefficient, h, a] + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/FourSpin.lean b/lean/OAI/Analysis/LaughlinGap/FourSpin.lean new file mode 100644 index 0000000000000000000000000000000000000000..9b23fb2c1248885bcf4f94fe33a085ff76d90a1c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/FourSpin.lean @@ -0,0 +1,222 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.PairDecomposition + +namespace OAI + +/-! Four Spin. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators InnerProduct +open Occupation Filter Topology + +lemma orbitalPair_orthonormal_twice {Q r s : ℕ} (hr : r ≤ Q) (hs : s ≤ Q) + (hro : Odd r) (hso : Odd s) + (l : Fin (2*Q-2*r+1)) (k : Fin (2*Q-2*s+1)) : + (∑ a : PairLabel (Q+1), orbitalPairCoefficient Q r l.val a * + orbitalPairCoefficient Q s k.val a) = if r=s ∧ l.val=k.val then 1 else 0 := by + exact orbitalPair_orthonormal hr hs hro hso + ⟨l.val, by omega⟩ ⟨k.val, by omega⟩ + +noncomputable def pairFactorInclusion (Q n r : ℕ) + (x : (Fin (n+1) × Fin (2*Q-2*r+1)) → ℝ) : + (Fin (n+1) × PairLabel (Q+1)) → ℝ := fun pa => + ∑ k : Fin (2*Q-2*r+1), x (pa.1,k) * orbitalPairCoefficient Q r k.val pa.2 + +lemma pairFactorInclusion_isometry {Q n r : ℕ} (hr : r ≤ Q) (ho : Odd r) + (x y : (Fin (n+1) × Fin (2*Q-2*r+1)) → ℝ) : + dotProduct (pairFactorInclusion Q n r x) (pairFactorInclusion Q n r y) = + dotProduct x y := by + classical + simp only [dotProduct, Fintype.sum_prod_type, pairFactorInclusion] + apply Finset.sum_congr rfl + intro p hp + simp only [Finset.sum_mul, Finset.mul_sum] + rw [Finset.sum_comm] + apply Eq.trans _ (by simp : (∑ k : Fin (2*Q-2*r+1), + ∑ l : Fin (2*Q-2*r+1), x (p,l) * y (p,k) * if k=l then (1:ℝ) else 0) = _) + apply Finset.sum_congr rfl + intro k hk + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro l hl + have he := orbitalPair_orthonormal_twice hr hr ho ho k l + simp only [true_and, Fin.val_inj] at he + rw [← he, Finset.mul_sum] + apply Finset.sum_congr rfl + intro a ha + ring + +lemma pairFactorInclusion_orthogonal {Q n r s : ℕ} (hr : r ≤ Q) (hs : s ≤ Q) + (hro : Odd r) (hso : Odd s) (hrs : r ≠ s) + (x : (Fin (n+1) × Fin (2*Q-2*r+1)) → ℝ) + (y : (Fin (n+1) × Fin (2*Q-2*s+1)) → ℝ) : + dotProduct (pairFactorInclusion Q n r x) (pairFactorInclusion Q n s y) = 0 := by + simp only [dotProduct, Fintype.sum_prod_type, pairFactorInclusion, + Finset.sum_mul, Finset.mul_sum] + apply Finset.sum_eq_zero + intro p hp + rw [Finset.sum_comm] + apply Finset.sum_eq_zero + intro k hk + rw [Finset.sum_comm] + apply Finset.sum_eq_zero + intro l hl + have he := orbitalPair_orthonormal_twice hr hs hro hso l k + simp only [hrs, false_and, ite_false] at he + calc + _ = (x (p,l) * y (p,k)) * ∑ a : PairLabel (Q+1), + orbitalPairCoefficient Q r l.val a * orbitalPairCoefficient Q s k.val a := by + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro a ha + ring + _ = 0 := by rw [he, mul_zero] + +noncomputable def fourBodyCoupled (Q D T r : ℕ) : + (Fin (2*Q-2+1) × PairLabel (Q+1)) → ℝ := + pairFactorInclusion Q (2*Q-2) r + (coupledTensor (2*Q-2) (2*Q-2*r) (D-r) (T-D)) + +noncomputable def fourBodyCoefficient (Q D T r p j k : ℕ) : ℝ := + if r ≤ j+k ∧ p+j+k=T then + Real.sqrt 2 * coupledCoefficient Q Q r (j+k-r) j * + coupledCoefficient (2*Q-2) (2*Q-2*r) (D-r) (T-D) p + else 0 + +theorem fourBodyCoupled_coefficient {Q D T r : ℕ} (hrD : r ≤ D) + (hDT : D ≤ T) (hT : T ≤ Q) (p : Fin (2*Q-2+1)) (a : PairLabel (Q+1)) : + fourBodyCoupled Q D T r (p,a) = + fourBodyCoefficient Q D T r p.val a.val.1.val a.val.2.val := by + classical + unfold fourBodyCoupled pairFactorInclusion fourBodyCoefficient + by_cases hw : r ≤ a.val.1.val+a.val.2.val ∧ p.val+a.val.1.val+a.val.2.val=T + · rw [ite_eq_left hw] + let l : Fin (2*Q-2*r+1) := ⟨a.val.1.val+a.val.2.val-r, by omega⟩ + rw [Finset.sum_eq_single l] + · simp only [orbitalPairCoefficient, coupledTensor] + rw [ite_eq_left (by dsimp [l]; omega), ite_eq_left (by dsimp [l]; omega)] + dsimp [l] + ring + · intro k hk hkl + have he : a.val.1.val+a.val.2.val ≠ r+k.val := by + intro he + apply hkl + apply Fin.ext + dsimp [l] + omega + simp only [orbitalPairCoefficient, coupledTensor, ite_eq_right he, mul_zero] + · simp + · rw [ite_eq_right hw] + apply Finset.sum_eq_zero + intro k hk + simp only [coupledTensor, orbitalPairCoefficient] + split_ifs with h₁ h₂ h₂ <;> try simp + exfalso + exact hw ⟨by omega, by omega⟩ + +lemma fourBodyCoupled_norm_sq {Q D T r : ℕ} (hr : r ≤ Q) (hro : Odd r) + (hz : D-r ≤ min (2*Q-2) (2*Q-2*r)) + (hl : T-D ≤ (2*Q-2)+(2*Q-2*r)-2*(D-r)) : + dotProduct (fourBodyCoupled Q D T r) (fourBodyCoupled Q D T r) = 1 := by + rw [fourBodyCoupled, pairFactorInclusion_isometry hr hro] + exact coupledTensor_norm_sq hz hl + +lemma fourBodyCoupled_orthogonal {Q D T r s : ℕ} (hr : r ≤ Q) (hs : s ≤ Q) + (hro : Odd r) (hso : Odd s) (h : r ≠ s) : + dotProduct (fourBodyCoupled Q D T r) (fourBodyCoupled Q D T s) = 0 := by + exact pairFactorInclusion_orthogonal hr hs hro hso h _ _ + +abbrev FourCopy (D : ℕ) := {r : Fin (D+1) // Odd r.val} + +noncomputable def fourBodyHighestFamily (Q D : ℕ) (r : FourCopy D) : + EuclideanSpace ℝ (Fin (2*Q-2+1) × PairLabel (Q+1)) := + WithLp.toLp 2 (fourBodyCoupled Q D D r.val.val) + +theorem fourBodyHighestFamily_orthonormal {Q D : ℕ} (hQ : 2 ≤ Q) (hD : D ≤ Q) : + Orthonormal ℝ (fourBodyHighestFamily Q D) := by + rw [orthonormal_iff_ite] + intro r s + simp only [fourBodyHighestFamily, EuclideanSpace.inner_toLp_toLp] + by_cases he : r=s + · subst s + rw [ite_eq_left rfl] + apply fourBodyCoupled_norm_sq (by omega) r.property + · have : 1 ≤ r.val.val := r.property.pos + omega + · omega + · rw [ite_eq_right he] + exact fourBodyCoupled_orthogonal (by omega) (by omega) s.property r.property + (by intro h; apply he; exact Subtype.ext (Fin.ext h.symm)) + +noncomputable def balancedCouplingCoefficient (z T p : ℕ) : ℝ := + if z ≤ T then monomialWeight T p * + (couplingPolynomial (1/Real.sqrt 2) (1/Real.sqrt 2) z (T-z)).coeff p else 0 + +noncomputable def fourBodyCoefficientStar (D T r p j k : ℕ) : ℝ := + if r ≤ j+k ∧ p+j+k=T then + Real.sqrt 2 * balancedCouplingCoefficient r (j+k) j * + balancedCouplingCoefficient (D-r) (T-r) p + else 0 + +lemma affine_twice_spin_tendsto (r : ℕ) : + Tendsto (fun Q : ℕ => ((2*Q-2*r : ℕ) : ℝ)) atTop atTop := by + apply tendsto_natCast_atTop_atTop.comp + apply tendsto_atTop_mono (fun Q => show Q-r ≤ 2*Q-2*r by omega) + exact tendsto_sub_atTop_nat r + +lemma affine_twice_spin_ratio_tendsto (r : ℕ) : + Tendsto (fun Q : ℕ => ((2*Q-2*r : ℕ) : ℝ) / (2*Q-2 : ℕ)) atTop (𝓝 (1:ℝ)) := by + have h := ((tendsto_const_nhds (x := (1:ℝ))).sub + ((tendsto_const_nhds (x := ((2*r:ℕ):ℝ)-2)).div_atTop (affine_twice_spin_tendsto 1))) + simp only [sub_zero, mul_one] at h + apply h.congr' + filter_upwards [eventually_ge_atTop (max r 1+1)] with Q hQ + have hr : 2*r ≤ 2*Q := by omega + have h2 : 2 ≤ 2*Q := by omega + have hd : ((2*Q-2 : ℕ):ℝ) ≠ 0 := by exact_mod_cast (show 2*Q-2 ≠ 0 by omega) + simp only [Nat.cast_sub hr, Nat.cast_mul, Nat.cast_ofNat, Nat.cast_sub h2] + simp only [Nat.cast_sub h2, Nat.cast_mul, Nat.cast_ofNat] at hd + calc + _ = ((2*(Q:ℝ)-2) - (2*(r:ℝ)-2)) / (2*(Q:ℝ)-2) := by + conv_rhs => rw [sub_div, div_self hd] + _ = _ := by congr 1; ring + +lemma equal_spin_ratio_tendsto : + Tendsto (fun Q : ℕ => (Q:ℝ)/Q) atTop (𝓝 (1:ℝ)) := by + apply tendsto_const_nhds.congr' + filter_upwards [eventually_ge_atTop 1] with Q hQ + exact (div_self (Nat.cast_ne_zero.mpr (by omega))).symm + +lemma balanced_coupling_limit {n m : ℕ → ℕ} + (hn : Tendsto (fun Q => (n Q : ℝ)) atTop atTop) + (hr : Tendsto (fun Q => (m Q : ℝ)/(n Q:ℝ)) atTop (𝓝 (1:ℝ))) + {z T : ℕ} (hzT : z ≤ T) (p : ℕ) : + Tendsto (fun Q => coupledCoefficient (n Q) (m Q) z (T-z) p) atTop + (𝓝 (balancedCouplingCoefficient z T p)) := by + have h := coupledCoefficient_tendsto_polynomial (by norm_num : (0:ℝ) ≤ 1) hn hr z (T-z) p + simpa [balancedCouplingCoefficient, hzT, Nat.add_sub_of_le hzT, + show (1:ℝ)+1=2 by norm_num] using h + +theorem fourBodyCoefficient_tendsto {D T r : ℕ} (hrD : r ≤ D) (hDT : D ≤ T) + (p j k : ℕ) : + Tendsto (fun Q => fourBodyCoefficient Q D T r p j k) atTop + (𝓝 (fourBodyCoefficientStar D T r p j k)) := by + by_cases h : r ≤ j+k ∧ p+j+k=T + · simp only [fourBodyCoefficient, fourBodyCoefficientStar, ite_eq_left h] + have h₁ := balanced_coupling_limit tendsto_natCast_atTop_atTop + equal_spin_ratio_tendsto h.1 j + have h₂ := balanced_coupling_limit (affine_twice_spin_tendsto 1) + (affine_twice_spin_ratio_tendsto r) (show D-r ≤ T-r by omega) p + have he : T-r-(D-r)=T-D := by omega + simpa only [he, mul_one] using (h₁.const_mul (Real.sqrt 2)).mul h₂ + · simp only [fourBodyCoefficient, fourBodyCoefficientStar, ite_eq_right h] + exact tendsto_const_nhds + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/FourTables.lean b/lean/OAI/Analysis/LaughlinGap/FourTables.lean new file mode 100644 index 0000000000000000000000000000000000000000..1ab34c4650e470f8f89e063e39509d32dc8f203a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/FourTables.lean @@ -0,0 +1,64 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.FastCoupling +import OAI.Analysis.LaughlinGap.RationalFourCertificate + +namespace OAI + +/-! Four Tables. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin + +variable {ι : Type*} [Fintype ι] + +def tableComparison (D : ℕ) (ε : ℚ) + (Y : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ) : + Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ := fun u v => + (if u=v then ((if 2*u.val+1=1 then 2 else 0)+ε)*copyNormalizationSq D (2*u.val+1) else 0) - + copyNormalizationSq D (2*u.val+1) * Y u v * copyNormalizationSq D (2*v.val+1) + +lemma fourCertificate_of_tables (rows : ι → RationalRow) (ε : ℚ) {D : ℕ} (hD : D ≤ 23) + (Y Z : Matrix (Fin ((D+1)/2)) (Fin ((D+1)/2)) ℚ) + (hY : ∀ u v : Fin ((D+1)/2), + (∑ a, (rows a).fourMatrixEval D (2*u.val+1) (2*v.val+1))=Y u v) + (hZ : ∀ u v : Fin ((D+1)/2), rationalCreatedGram hD + ((fourCopyEquiv D).symm u) ((fourCopyEquiv D).symm v)=Z u v) + (hp : ((Z * tableComparison D ε Y * Z).map (algebraMap ℚ ℂ)).PosSemidef) : + FourCertificate (fun a => (rows a).toReal) (ε:ℝ) D hD := by + apply fourCertificate_of_rational rows ε hD + rw [← Matrix.posSemidef_submatrix_equiv (fourCopyEquiv D).symm] + have hB : (rationalFourComparison rows ε D).submatrix (fourCopyEquiv D).symm + (fourCopyEquiv D).symm = tableComparison D ε Y := by + ext u v + simp only [rationalFourComparison,Matrix.submatrix_apply,fourCopyEquiv_symm_val, + Equiv.apply_eq_iff_eq,RationalRow.fourMatrix_eq_eval,hY,tableComparison] + rfl + have hG : (rationalCreatedGram hD).submatrix (fourCopyEquiv D).symm + (fourCopyEquiv D).symm=Z := Matrix.ext hZ + have he : (rationalFourCompression rows ε hD).submatrix (fourCopyEquiv D).symm + (fourCopyEquiv D).symm = Z * tableComparison D ε Y * Z := by + unfold rationalFourCompression + rw [Matrix.submatrix_mul _ _ _ _ _ (fourCopyEquiv D).symm.bijective, + Matrix.submatrix_mul _ _ _ _ _ (fourCopyEquiv D).symm.bijective,hG,hB] + simpa only [Matrix.submatrix_map,he] using hp + +lemma rationalCreatedGram_of_columns {D : ℕ} (hD : D ≤ 23) {K : ℕ} + (keys : Fin K → Finset (Fin 25)) (cols : Matrix (Fin ((D+1)/2)) (Fin K) ℚ) + (hk : fourKeys hD=Finset.univ.image keys) (hi : Function.Injective keys) + (hc : ∀ u a, fourColumn hD (2*u.val+1) (keys a)=cols u a) + (u v : Fin ((D+1)/2)) : + rationalCreatedGram hD ((fourCopyEquiv D).symm u) ((fourCopyEquiv D).symm v) = + ∑ a : Fin K, cols u a * cols v a / setFactorial (keys a) := by + unfold rationalCreatedGram + rw [hk,Finset.sum_image (fun _ _ _ _ h => hi h)] + simp only [fourCopyEquiv_symm_val,hc] + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/FourTransfer.lean b/lean/OAI/Analysis/LaughlinGap/FourTransfer.lean new file mode 100644 index 0000000000000000000000000000000000000000..7753d06be8ace208e43b30fed0c258679c816c5a --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/FourTransfer.lean @@ -0,0 +1,202 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.ExtendedPair +import OAI.Analysis.LaughlinGap.FourAllowance +import OAI.Analysis.LaughlinGap.FourComparison + +namespace OAI + +/-! Four Transfer. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators InnerProduct ComplexOrder MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin Filter Topology + +noncomputable def fourDimensionRatio (Q D : ℕ) : ℝ := + (4*(Q:ℝ)-1-2*(D:ℝ))/(2*(Q:ℝ)-1) + +lemma fourDimensionRatio_tendsto (D : ℕ) : + Tendsto (fun Q => fourDimensionRatio Q D) atTop (𝓝 2) := by + have ht : Tendsto (fun Q : ℕ => (4-(1+2*(D:ℝ))/Q)/(2-(1:ℝ)/Q)) + atTop (𝓝 (2:ℝ)) := by + convert ((tendsto_const_nhds (x := (4:ℝ))).sub + (tendsto_const_div_atTop_nhds_zero_nat (1+2*(D:ℝ)))).div + ((tendsto_const_nhds (x := (2:ℝ))).sub + (tendsto_const_div_atTop_nhds_zero_nat (1:ℝ))) (by norm_num : (2:ℝ)-0 ≠ 0) using 1 + norm_num [Pi.div_def] + apply ht.congr' + filter_upwards [eventually_ge_atTop 1] with Q hQ + have hn : (Q:ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + unfold fourDimensionRatio + field_simp [hn] + ring + +lemma fourDimensionRatio_eq {Q D : ℕ} (hQ : 2 ≤ Q) (hD : D ≤ Q) : + fourDimensionRatio Q D = ((4*Q-1-2*D:ℕ):ℝ)/((2*Q-1:ℕ):ℝ) := by + rw [fourDimensionRatio,Nat.cast_sub (by omega : 2*D ≤ 4*Q-1), + Nat.cast_sub (by omega : 1 ≤ 4*Q),Nat.cast_sub (by omega : 1 ≤ 2*Q)] + norm_cast + +variable {ι : Type*} [Fintype ι] + +noncomputable def fourComparison (rows : ι → RowData) (ε : ℝ) (Q D : ℕ) : + Matrix (FourCopy D) (FourCopy D) ℝ := + fourDimensionRatio Q D • fourCopyTarget D - + ∑ a, rowFourMatrix (fourWeightCoefficient Q) D (rows a) + ε • 1 + +noncomputable def fourComparisonStar (rows : ι → RowData) (ε : ℝ) (D : ℕ) : + Matrix (FourCopy D) (FourCopy D) ℝ := + (2:ℝ) • fourCopyTarget D - + ∑ a, rowFourMatrix fourWeightCoefficientStar D (rows a) + ε • 1 + +lemma fourComparison_symmetric (rows : ι → RowData) (ε : ℝ) (Q D : ℕ) : + (fourComparison rows ε Q D).IsHermitian := by + unfold fourComparison + apply Matrix.IsHermitian.add + · apply Matrix.IsHermitian.sub + · exact (fourCopyTarget_symmetric D).smul (by rfl) + · apply Matrix.IsHermitian.ext + intro u v + simp only [Matrix.sum_apply,star_trivial] + exact Finset.sum_congr rfl (fun a _ => (rowFourMatrix_symmetric _ _ _).apply u v) + · exact Matrix.isHermitian_one.smul (by rfl) + +lemma fourComparisonStar_symmetric (rows : ι → RowData) (ε : ℝ) (D : ℕ) : + (fourComparisonStar rows ε D).IsHermitian := by + unfold fourComparisonStar + apply Matrix.IsHermitian.add + · apply Matrix.IsHermitian.sub + · exact (fourCopyTarget_symmetric D).smul (by rfl) + · apply Matrix.IsHermitian.ext + intro u v + simp only [Matrix.sum_apply,star_trivial] + exact Finset.sum_congr rfl (fun a _ => (rowFourMatrix_symmetric _ _ _).apply u v) + · exact Matrix.isHermitian_one.smul (by rfl) + +lemma fourComparison_tendsto (rows : ι → RowData) (ε : ℝ) (D : ℕ) + (u v : FourCopy D) : Tendsto (fun Q => fourComparison rows ε Q D u v) atTop + (𝓝 (fourComparisonStar rows ε D u v)) := by + simp only [fourComparison,fourComparisonStar,Matrix.add_apply,Matrix.sub_apply, + Matrix.smul_apply,Matrix.sum_apply,smul_eq_mul] + exact (((fourDimensionRatio_tendsto D).mul_const _).sub + (tendsto_finsetSum Finset.univ (fun a _ => rowFourMatrix_tendsto D (rows a) u v))).add_const _ + +def localTripleP {D : ℕ} (hD : D ≤ 23) (b : OrbitalTriple D) : Fin 24 := + ⟨b.val.1,by have := b.property; omega⟩ +def localTripleJ {D : ℕ} (hD : D ≤ 23) (b : OrbitalTriple D) : Fin 25 := + ⟨b.val.2.1,by have := b.property; omega⟩ +def localTripleK {D : ℕ} (hD : D ≤ 23) (b : OrbitalTriple D) : Fin 25 := + ⟨b.val.2.2,by have := b.property; omega⟩ + +noncomputable def fourHighestRowsStar (D : ℕ) : + Matrix (FourCopy D) (OrbitalTriple D) ℝ := fun r b => + fourBodyCoefficientStar D D r.val.val b.val.1 b.val.2.1 b.val.2.2 + +noncomputable def fourLocalHighestStar {D : ℕ} (hD : D ≤ 23) + (r : FourCopy D) : Module.End ℂ (Occupation.Hilbert 25) := + ∑ b : OrbitalTriple D, (fourHighestRowsStar D r b : ℂ) • + (Occupation.annihilation (localTripleK hD b) * Occupation.annihilation (localTripleJ hD b) * + Occupation.localPairStar 25 (localTripleP hD b).val) + +lemma fourHighestRows_tendsto (D : ℕ) (r : FourCopy D) (b : OrbitalTriple D) : + Tendsto (fun Q => fourHighestRows Q D r b) atTop (𝓝 (fourHighestRowsStar D r b)) := + fourBodyCoefficient_tendsto (Nat.le_of_lt_succ r.val.isLt) le_rfl _ _ _ + +def FourCertificate (rows : ι → RowData) (ε : ℝ) (D : ℕ) (hD : D ≤ 23) : Prop := + (Occupation.createdGram (fourLocalHighestStar hD) * + (fourComparisonStar rows ε D).map (algebraMap ℝ ℂ) * + Occupation.createdGram (fourLocalHighestStar hD)).PosSemidef + +lemma complexify_four_highest {Q D : ℕ} (hQ : 24 ≤ Q) (hD : D ≤ 23) + (r : FourCopy D) : + complexify (fourAnnihilator Q D D r.val.val) = + Occupation.extendTo (show 25 ≤ Q+1 by omega) + (∑ b : OrbitalTriple D, (fourHighestRows Q D r b : ℂ) • + (Occupation.annihilation (localTripleK hD b) * Occupation.annihilation (localTripleJ hD b) * + Occupation.localPair 25 Q (localTripleP hD b).val)) := by + rw [fourAnnihilator_high_local (by omega) (by omega),complexify_combination] + simp only [map_sum,map_smul,map_mul,Occupation.extendTo_annihilation] + apply Finset.sum_congr rfl + intro b hb + rw [Occupation.extendTo_localPair _ (by have := (localTripleP hD b).isLt; omega)] + simp only [localFourCoordinates,orbitalTripleFinite,map_mul,complexify_annihilation, + complexify_physicalPair,localTripleP,localTripleJ,localTripleK] + rfl + +lemma lift_symmetric {α β : Type*} [Fintype α] [Fintype β] + (B : α → Matrix β β ℝ) {C : Matrix α α ℝ} (hC : C.IsHermitian) : + (lift B C).IsHermitian := by + classical + rw [Matrix.IsHermitian,Matrix.conjTranspose_eq_transpose_of_trivial] + rw [lift_transpose,(Matrix.conjTranspose_eq_transpose_of_trivial C).symm,hC.eq] + +lemma posSemidef_of_complex_re {α : Type*} [Fintype α] [DecidableEq α] + (A : Matrix α α ℝ) (hA : A.IsHermitian) + (h : ∀ x : EuclideanSpace ℂ α, 0 ≤ (inner ℂ x (complexify A x)).re) : A.PosSemidef := by + rw [Matrix.posSemidef_iff_dotProduct_mulVec] + refine ⟨hA,fun x => ?_⟩ + simpa [complexify,Matrix.toLpLin_apply,EuclideanSpace.inner_toLp_toLp, + Matrix.mulVec,dotProduct,Complex.mul_re,Complex.add_re,mul_comm] using + h (WithLp.toLp 2 (fun i => (x i : ℂ))) + +lemma complexify_square_sum_inner {α β : Type*} [Fintype α] [DecidableEq α] [Fintype β] + (B : β → Matrix α α ℝ) (c : ℝ) (x : EuclideanSpace ℂ α) : + (inner ℂ x (complexify (c • ∑ p, (B p).transpose * B p) x)).re = + c * ∑ p, ‖complexify (B p) x‖^2 := by + simp only [map_smul,map_sum,map_mul,complexify_transpose,LinearMap.smul_apply, + LinearMap.sum_apply,Module.End.mul_apply,inner_smul_right_eq_smul,inner_sum, + LinearMap.adjoint_inner_right,inner_self_eq_norm_sq_to_K] + simp [← Complex.ofReal_pow] + +lemma complexify_four_local_lift {Q D : ℕ} (hQ : 24 ≤ Q) (hD : D ≤ 23) + (C : Matrix (FourCopy D) (FourCopy D) ℝ) : + complexify (lift (fun r : FourCopy D => fourAnnihilator Q D D r.val.val) C) = + Occupation.extendTo (show 25 ≤ Q+1 by omega) + (matrixLift (fun r => ∑ b : OrbitalTriple D, (fourHighestRows Q D r b : ℂ) • + (Occupation.annihilation (localTripleK hD b) * Occupation.annihilation (localTripleJ hD b) * + Occupation.localPair 25 Q (localTripleP hD b).val)) (C.map (algebraMap ℝ ℂ))) := by + rw [complexify_lift,Occupation.extendTo_matrixLift] + simp only [complexify_four_highest hQ hD] + +theorem four_local_transfer (rows : ι → RowData) (ε : ℝ) {D : ℕ} (hD : D ≤ 23) + (hc : FourCertificate rows ε D hD) : + ∃ ρ : ℕ → ℝ, (∀ Q, 0 ≤ ρ Q) ∧ Tendsto ρ atTop (𝓝 0) ∧ + ∀ᶠ Q in atTop, ∀ _hQ : 24 ≤ Q, + -(ρ Q) • (∑ p : Fin 24, (physicalPair Q p.val).transpose * physicalPair Q p.val) ≤ + lift (fun r : FourCopy D => fourAnnihilator Q D D r.val.val) (fourComparison rows ε Q D) := by + classical + have hc₀ := (fourComparisonStar_symmetric rows ε D).map (algebraMap ℝ ℂ) (fun x => by simp) + obtain ⟨ρ,hpos,hlim,hbound⟩ := Occupation.local_four_family_transfer_to + (localTripleP hD) (localTripleJ hD) (localTripleK hD) + (fun Q => fourHighestRows Q D) (fourHighestRowsStar D) + (fun Q => (fourComparison rows ε Q D).map (algebraMap ℝ ℂ)) + ((fourComparisonStar rows ε D).map (algebraMap ℝ ℂ)) + (fourHighestRows_tendsto D) + (fun r s => Complex.continuous_ofReal.continuousAt.tendsto.comp (fourComparison_tendsto rows ε D r s)) + hc₀ hc + refine ⟨ρ,hpos,hlim,?_⟩ + filter_upwards [hbound] with Q bound + intro hQ + apply sub_nonneg.mp + apply Matrix.PosSemidef.nonneg + apply posSemidef_of_complex_re + · exact (lift_symmetric _ (fourComparison_symmetric rows ε Q D)).sub + ((Matrix.posSemidef_sum Finset.univ (fun p _ => + transpose_square_positive (physicalPair Q (p : Fin 24).val))).isHermitian.smul (by rfl)) + · intro x + have hb := bound (Q+1) (by omega) x + simp only [map_sub,LinearMap.sub_apply,inner_sub_right,Complex.sub_re] + rw [complexify_four_local_lift hQ hD,complexify_square_sum_inner] + simp only [complexify_physicalPair] + apply sub_nonneg.mpr + have hpair (p : Fin 24) := Occupation.extendTo_localPair (show 25 ≤ Q+1 by omega) + (show p.val+1 < 25 by omega) (Q := Q) + simpa only [hpair] using hb + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/GlobalBound.lean b/lean/OAI/Analysis/LaughlinGap/GlobalBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..34694dfacc8846ae8583bcd427ca890f26a7a85d --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/GlobalBound.lean @@ -0,0 +1,71 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.FourBound +import OAI.Analysis.LaughlinGap.GlobalBoundCore +import OAI.Analysis.LaughlinGap.ThreeComparison + +namespace OAI + +/-! Global Bound. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators InnerProduct MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin Filter Topology +variable {ι : Type*} [Fintype ι] + +theorem physical_square_eventually_of_certificates + (rows : ι → RowData) (ε γ : ℝ) (hε : 0 ≤ ε) + (hmargin : γ < 1-rowEta rows-(61/4096:ℝ)-1222*ε) + (hthree : ∀ z : Fin 16, z.val ≠ 0 → z.val ≠ 1 → z.val ≠ 3 → + (∑ r, rowTrace threeWeightCoefficientStar z.val (rows r)) < + (3/2:ℝ) * ((3*(z.val:ℝ)-1)*(-1/2:ℝ)^z.val)) + (hfour : ∀ d : Fin 23, FourCertificate rows ε (d.val+1) (by omega)) : + ∀ᶠ Q in atTop, γ • physicalHamiltonian Q ≤ physicalHamiltonian Q * physicalHamiltonian Q := by + obtain ⟨R,hpos,hlimR,hR⟩ := four_comparison_of_certificates rows ε hε hfour + have hlim : Tendsto (fun Q => 1-rowEta rows-threeBodyTail Q-(1222*ε+R Q)) atTop + (𝓝 (1-rowEta rows-(61/4096:ℝ)-1222*ε)) := by + simpa only [add_zero] using (threeBodyTail_tendsto.const_sub (1-rowEta rows)).sub + (hlimR.const_add (1222*ε)) + filter_upwards [eventually_ge_atTop 24,three_comparison_of_strict_traces rows hthree,hR, + hlim.eventually (Ioi_mem_nhds hmargin)] with Q hQ h₃ h₄ hγ + apply le_trans _ (physical_square_of_comparisons hQ rows (1222*ε+R Q) (h₃ (by omega)) (h₄ hQ)) + exact smul_le_smul_of_nonneg_right (le_of_lt hγ) (physicalHamiltonian_positive Q).nonneg + +lemma occupation_square_of_real_square {Q : ℕ} (γ : ℝ) + (h : γ • physicalHamiltonian Q ≤ physicalHamiltonian Q * physicalHamiltonian Q) : + ∀ x : Occupation.Hilbert (Q+1), γ * Occupation.localPairEnergy (Q+1) (2*Q-1) Q x ≤ + ‖Occupation.physicalOccupationHamiltonian Q x‖^2 := by + have hp := complexify_positive (Matrix.nonneg_iff_posSemidef.mp (sub_nonneg.mpr h)) + intro x + have hx := hp.re_inner_nonneg_right x + simp only [map_sub,map_mul,map_smul,complexify_physicalHamiltonian, + LinearMap.sub_apply,LinearMap.smul_apply,Module.End.mul_apply,inner_sub_right, + inner_smul_right_eq_smul] at hx + rw [← (Occupation.physicalOccupationHamiltonian_positive Q).isSymmetric x + (Occupation.physicalOccupationHamiltonian Q x),inner_self_eq_norm_sq_to_K] at hx + change 0 ≤ ((‖Occupation.physicalOccupationHamiltonian Q x‖:ℂ)^2).re - + (γ • inner ℂ x (Occupation.physicalOccupationHamiltonian Q x)).re at hx + rw [← Complex.ofReal_pow,Complex.ofReal_re,Complex.real_smul,Complex.mul_re, + Complex.ofReal_re,Complex.ofReal_im,zero_mul,sub_zero, + Occupation.physicalOccupationHamiltonian_inner] at hx + exact sub_nonneg.mp hx + +theorem mainTarget_of_finite_certificates + (rows : ι → RowData) (ε : ℝ) (hε : 0 ≤ ε) + (hmargin : (1/25:ℝ) < 1-rowEta rows-(61/4096:ℝ)-1222*ε) + (hthree : ∀ z : Fin 16, z.val ≠ 0 → z.val ≠ 1 → z.val ≠ 3 → + (∑ r, rowTrace threeWeightCoefficientStar z.val (rows r)) < + (3/2:ℝ) * ((3*(z.val:ℝ)-1)*(-1/2:ℝ)^z.val)) + (hfour : ∀ d : Fin 23, FourCertificate rows ε (d.val+1) (by omega)) : MainTarget := by + apply Occupation.mainTarget_of_uniform_occupation_square_estimate + obtain ⟨Q₀, hQ₀⟩ := eventually_atTop.mp + (physical_square_eventually_of_certificates rows ε (1/25) hε hmargin hthree hfour) + exact ⟨Q₀,fun Q hQ => occupation_square_of_real_square _ (hQ₀ Q hQ)⟩ + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/GlobalBoundCore.lean b/lean/OAI/Analysis/LaughlinGap/GlobalBoundCore.lean new file mode 100644 index 0000000000000000000000000000000000000000..d541da1053704fbbe04fed752d9f9877a4a443bb --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/GlobalBoundCore.lean @@ -0,0 +1,91 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.AuxiliaryComparison +import OAI.Analysis.LaughlinGap.RealSpinSquare + +namespace OAI + +/-! Global Bound Core. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin Filter Topology +variable {ι : Type*} [Fintype ι] + +noncomputable def rowEta (rows : ι → RowData) : ℝ := ∑ r, (rows r).lam^2 + +noncomputable def auxiliaryThree {Q : ℕ} (hQ : 8 ≤ Q) (rows : ι → RowData) : FockMatrix (Q+1) := + ((2*Q-1:ℕ):ℝ) • average (rotationCommutant (fockLowering Q)) (∑ r, rowThree hQ (rows r)) +noncomputable def auxiliaryFour {Q : ℕ} (hQ : 8 ≤ Q) (rows : ι → RowData) : FockMatrix (Q+1) := + ((2*Q-1:ℕ):ℝ) • average (rotationCommutant (fockLowering Q)) (∑ r, rowFour hQ (rows r)) + +lemma auxiliary_positive {Q : ℕ} (hQ : 8 ≤ Q) (rows : ι → RowData) : + 0 ≤ rowEta rows • physicalHamiltonian Q + auxiliaryThree hQ rows + auxiliaryFour hQ rows := by + have hh (r : ι) := smul_nonneg (show (0:ℝ) ≤ ((2*Q-1:ℕ):ℝ) by positivity) + (average_positive (rotationCommutant (fockLowering Q)) + (transpose_square_positive (rowAnnihilator hQ (rows r)))).nonneg + simp only [rowSquare_average] at hh + have h := Finset.sum_nonneg (fun r (_ : r ∈ (Finset.univ : Finset ι)) => hh r) + simpa only [Finset.sum_add_distrib,← Finset.sum_smul,← Finset.smul_sum,← map_sum, + rowEta,auxiliaryThree,auxiliaryFour] using h + +noncomputable def threeRetained {Q : ℕ} (hQ : 15 ≤ Q) : FockMatrix (Q+1) := + ∑ z : Fin 16, threeBodyGramCoefficient Q z.val • + threeSpinLift (by omega : 2 ≤ Q) (show z.val ≤ Q by omega) + +lemma spin_sum_split {Q : ℕ} (hQ : 15 ≤ Q) : + (∑ z : Fin (Q+1), threeBodyGramCoefficient Q z.val • + threeSpinLift (by omega : 2 ≤ Q) (Nat.le_of_lt_succ z.isLt)) = + threeRetained hQ + threeTailLift (by omega : 2 ≤ Q) := by + classical + let f : ℕ → FockMatrix (Q+1) := fun z => if hz : z ≤ Q then + threeBodyGramCoefficient Q z • threeSpinLift (by omega) hz else 0 + have hret : threeRetained hQ = ∑ z : Fin (Q+1), if z.val ≤ 15 then f z.val else 0 := by + rw [← sum_fin_extend hQ] + apply Finset.sum_congr rfl + intro z hz + dsimp [f,threeRetained] + rw [dite_eq_left (by omega)] + have htail : threeTailLift (by omega : 2 ≤ Q) = + ∑ z : Fin (Q+1), if 16 ≤ z.val then f z.val else 0 := by + unfold threeTailLift + apply Finset.sum_congr rfl + intro z hz + simp only [f,dite_eq_left (Nat.le_of_lt_succ z.isLt)] + rw [hret,htail,← Finset.sum_add_distrib] + apply Finset.sum_congr rfl + intro z hz + by_cases h : z.val ≤ 15 <;> simp [h,show (16 ≤ z.val) ↔ ¬ z.val ≤ 15 by omega,f,Nat.le_of_lt_succ z.isLt] + +lemma physical_spin_square_split {Q : ℕ} (hQ : 15 ≤ Q) : + physicalHamiltonian Q * physicalHamiltonian Q = physicalHamiltonian Q + + (threeRetained hQ + threeTailLift (by omega : 2 ≤ Q)) + fourTarget Q := by + rw [physical_spin_square_real (by omega : 2 ≤ Q),spin_sum_split hQ] + +lemma comparison_additive_step {A : Type*} [AddCommGroup A] [PartialOrder A] [IsOrderedAddMonoid A] + {h s a b c t η e f τ : A} (hid : s = h+(c+t)+f) (haux : 0 ≤ η+a+b) + (ha : a ≤ c) (hb : b ≤ f+e) (ht : -τ ≤ t) : + h-η-τ-e ≤ s := by + have hr := haux.trans (add_le_add (add_le_add (le_refl η) ha) hb) + have hh := add_le_add (le_refl (h-η-e)) (add_le_add hr ht) + convert hh using 1 <;> (try rw [hid]) <;> abel + +lemma physical_square_of_comparisons {Q : ℕ} (hQ : 24 ≤ Q) + (rows : ι → RowData) (δ : ℝ) + (hthree : auxiliaryThree (by omega) rows ≤ threeRetained (by omega : 15 ≤ Q)) + (hfour : auxiliaryFour (by omega) rows ≤ fourTarget Q + δ • physicalHamiltonian Q) : + (1-rowEta rows-threeBodyTail Q-δ) • physicalHamiltonian Q ≤ + physicalHamiltonian Q * physicalHamiltonian Q := by + have ht := threeTailLift_le (by omega : 4 ≤ Q) + rw [neg_smul] at ht + have hh := comparison_additive_step (physical_spin_square_split (by omega : 15 ≤ Q)) + (auxiliary_positive (by omega : 8 ≤ Q) rows) hthree hfour ht + simpa only [sub_smul,one_smul] using hh + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/HighestRatios.lean b/lean/OAI/Analysis/LaughlinGap/HighestRatios.lean new file mode 100644 index 0000000000000000000000000000000000000000..355bdb6391b9e46c7a398ad5bc1843bab7b518d6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/HighestRatios.lean @@ -0,0 +1,74 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SpinWork + +namespace OAI + +/-! Highest Ratios. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators + +lemma highest_numerator_product {m z : ℕ} (hz : z ≤ m) (p : ℕ) : + (∏ k ∈ Finset.range p, ((m : ℝ)-z+k+1)) = + ((m-z+p).descFactorial p : ℝ) := by + induction p with + | zero => simp + | succ p ih => + rw [Finset.prod_range_succ, ih] + rw [show m-z+(p+1) = (m-z+p)+1 by omega, Nat.succ_descFactorial_succ] + push_cast + rw [Nat.cast_sub hz] + ring + +lemma highest_denominator_product {n p : ℕ} (hp : p ≤ n) : + (∏ k ∈ Finset.range p, ((n : ℝ)-k)) = (n.descFactorial p : ℝ) := by + rw [Nat.descFactorial_eq_prod_range, Nat.cast_prod] + apply Finset.prod_congr rfl + intro k hk + rw [Nat.cast_sub ((Finset.mem_range.mp hk).le.trans hp)] + +theorem highestWeight_factorial {n m z p : ℕ} (hz : z ≤ min n m) (hp : p ≤ z) : + highestWeight n m z p = (z.choose p : ℝ) * + ((m-z+p).descFactorial p : ℝ) / (n.descFactorial p : ℝ) := by + simp only [highestWeight, highestFactor, Finset.prod_div_distrib, + highest_numerator_product (le_min_iff.mp hz).2 p, + highest_denominator_product (hp.trans (le_min_iff.mp hz).1), mul_div_assoc] + +lemma highestCoefficient_zero_ne {n m z : ℕ} (hz : z ≤ min n m) : + highestCoefficient n m z 0 ≠ 0 := by + simp only [highestCoefficient, highestWeight_zero, Real.sqrt_one, mul_one, Nat.sub_zero] + exact div_ne_zero (pow_ne_zero _ (by norm_num)) (Real.sqrt_pos.mpr (highestNormalization_pos hz)).ne' + +theorem highestCoefficient_ratio {n m z p : ℕ} (_hz : z ≤ min n m) (hp : p ≤ z) : + highestCoefficient n m z p = highestCoefficient n m z 0 * + ((-1 : ℝ)^p * Real.sqrt (highestWeight n m z p)) := by + have he : (-1 : ℝ)^(z-p) = (-1 : ℝ)^z * (-1 : ℝ)^p := by + have hzz : z=(z-p)+p := by omega + conv_rhs => rw [hzz, pow_add, mul_assoc, ← pow_add, ← two_mul, pow_mul] + norm_num + simp only [highestCoefficient, highestWeight_zero, Real.sqrt_one, mul_one, Nat.sub_zero] + rw [he] + ring + +lemma highestCoefficient_last {n m z : ℕ} (hz : z ≤ min n m) : + highestCoefficient n m z z = highestCoefficient n m z 0 * + ((-1 : ℝ)^z * Real.sqrt ((m.descFactorial z : ℝ)/(n.descFactorial z : ℝ))) := by + rw [highestCoefficient_ratio hz (le_refl z), highestWeight_factorial hz (le_refl z), + Nat.sub_add_cancel (le_min_iff.mp hz).2, Nat.choose_self, Nat.cast_one, one_mul] + +lemma highestCoefficient_penultimate {n m z : ℕ} (hz : z ≤ min n m) (hpos : 0 ∑ k, A (fun j => if i=j then 1 else 0) k * x k + map_add' := by intro x y; funext i; simp [mul_add, Finset.sum_add_distrib] + map_smul' := by intro r x; funext i; simp [Finset.mul_sum, mul_left_comm] } + +lemma transposeMap_adjoint {ι κ : Type*} [Fintype ι] [Fintype κ] + (A : (ι → ℝ) →ₗ[ℝ] (κ → ℝ)) (x : ι → ℝ) (y : κ → ℝ) : + dotProduct (A x) y = dotProduct x (transposeMap A y) := by + classical + rw [A.pi_apply_eq_sum_univ x] + simp only [dotProduct, transposeMap, LinearMap.coe_mk, AddHom.coe_mk, + Finset.sum_apply, Pi.smul_apply, smul_eq_mul, + Finset.sum_mul, Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro k hk + ring + +lemma eq_of_dotProduct_eq {ι : Type*} [Fintype ι] {x y : ι → ℝ} + (h : ∀ a, dotProduct a x = dotProduct a y) : x = y := by + classical + funext i + simpa [dotProduct] using h (fun j => if j=i then 1 else 0) + +structure LadderMap {ι κ : Type*} [Fintype ι] [Fintype κ] + (S : LadderSystem ι) (T : LadderSystem κ) extends (ι → ℝ) →ₗ[ℝ] (κ → ℝ) where + lower : ∀ x, T.lower (toLinearMap x) = toLinearMap (S.lower x) + raise : ∀ x, T.raise (toLinearMap x) = toLinearMap (S.raise x) + +namespace LadderMap +variable {ι κ σ : Type*} [Fintype ι] [Fintype κ] [Fintype σ] +variable {S : LadderSystem ι} {T : LadderSystem κ} {U : LadderSystem σ} + +lemma weight (A : LadderMap S T) (x : ι → ℝ) : + T.weight (A.toLinearMap x) = A.toLinearMap (S.weight x) := by + rw [T.weight_eq, A.raise, A.lower, S.weight_eq, map_sub, A.lower, A.raise] + +lemma casimir (A : LadderMap S T) (x : ι → ℝ) : + T.casimir (A.toLinearMap x) = A.toLinearMap (S.casimir x) := by + simp only [LadderSystem.casimir_apply, A.weight, A.lower, A.raise, map_add, map_smul] + +noncomputable def comp (B : LadderMap T U) (A : LadderMap S T) : LadderMap S U where + toLinearMap := B.toLinearMap.comp A.toLinearMap + lower x := by simp only [LinearMap.comp_apply, B.lower, A.lower] + raise x := by simp only [LinearMap.comp_apply, B.raise, A.raise] + +noncomputable def transpose (A : LadderMap S T) : LadderMap T S where + toLinearMap := transposeMap A.toLinearMap + lower x := by + apply eq_of_dotProduct_eq + intro a + rw [← S.raise_adjoint, ← transposeMap_adjoint, ← A.raise, + T.raise_adjoint, transposeMap_adjoint] + raise x := by + apply eq_of_dotProduct_eq + intro a + rw [← S.adjoint, ← transposeMap_adjoint, ← A.lower, + T.adjoint, transposeMap_adjoint] + +lemma raw (A : LadderMap S T) (x : ι → ℝ) (l : ℕ) : + T.raw (A.toLinearMap x) l = A.toLinearMap (S.raw x l) := by + induction l with + | zero => rfl + | succ l ih => rw [LadderSystem.raw_succ, LadderSystem.raw_succ, ih, A.lower] + +lemma normalized (A : LadderMap S T) (x : ι → ℝ) (d l : ℕ) : + T.normalized (A.toLinearMap x) d l = A.toLinearMap (S.normalized x d l) := by + simp only [LadderSystem.normalized, map_smul, A.raw] + +end LadderMap + +noncomputable def LadderSystem.embeddingMap {ι : Type*} [Fintype ι] + (S : LadderSystem ι) {x : ι → ℝ} {d : ℕ} + (hw : S.weight x = (d : ℝ) • x) (he : S.raise x = 0) : + LadderMap (standardLadderSystem d) S where + toLinearMap := S.embedding x d + lower a := S.embedding_lower hw he a + raise a := S.embedding_raise hw he a + +noncomputable def coupledEmbedding {n m z : ℕ} (hz : z ≤ min n m) : + LadderMap (standardLadderSystem (n+m-2*z)) (tensorSpin n m) := + (tensorSpin n m).embeddingMap (highestTensor_weight hz) (highestTensor_raise hz) + +lemma coupledEmbedding_apply {n m z : ℕ} (hz : z ≤ min n m) + (a : Fin (n+m-2*z+1) → ℝ) : + (coupledEmbedding hz).toLinearMap a = + ∑ l : Fin (n+m-2*z+1), a l • coupledTensor n m z l.val := by + simp only [coupledEmbedding, LadderSystem.embeddingMap, LadderSystem.embedding_apply, + coupledTensor_eq_normalized hz (Nat.le_of_lt_succ (Fin.isLt _))] + +theorem coupledTensor_expansion (n m : ℕ) + (y : (Fin (n+1) × Fin (m+1)) → ℝ) : + (∑ i : CoupledIndex n m, + dotProduct (coupledTensor n m i.1.val i.2.val) y • + coupledTensor n m i.1.val i.2.val) = y := by + funext pq + have h := congrArg (fun x : EuclideanSpace ℝ (Fin (n+1) × Fin (m+1)) => x pq) + ((coupledBasis n m).sum_repr (WithLp.toLp 2 y)) + simpa only [OrthonormalBasis.repr_apply_apply, coupledBasis_apply, coupledFamily, + PiLp.inner_apply, RCLike.inner_apply, conj_trivial, Finset.sum_apply, + WithLp.ofLp_sum, WithLp.ofLp_smul, PiLp.smul_apply, WithLp.toLp_ofLp, Pi.smul_apply, + smul_eq_mul, dotProduct, mul_comm] using h + +lemma spinCasimir_injective : + Function.Injective (fun d : ℕ => (d : ℝ)*(d+2)) := by + intro d e h + have hd : (0 : ℝ) ≤ d := by positivity + have he : (0 : ℝ) ≤ e := by positivity + have hs : 0 < (d : ℝ)+e+2 := by positivity + have hh : ((d : ℝ)-e)*((d : ℝ)+e+2) = 0 := by nlinarith + have heq := sub_eq_zero.mp ((mul_eq_zero.mp hh).resolve_right hs.ne') + exact_mod_cast heq + +theorem coupledHighest_eigenline {n m z : ℕ} (hz : z ≤ min n m) + {y : (Fin (n+1) × Fin (m+1)) → ℝ} + (hyH : (tensorSpin n m).weight y = ((n+m-2*z : ℕ) : ℝ) • y) + (hyC : (tensorSpin n m).casimir y = + (((n+m-2*z : ℕ) : ℝ)*((n+m-2*z : ℕ)+2)) • y) : + y = dotProduct (highestTensor n m z) y • highestTensor n m z := by + classical + let iz : CoupledIndex n m := ⟨⟨z,by omega⟩,0⟩ + calc + y = ∑ i : CoupledIndex n m, + dotProduct (coupledTensor n m i.1.val i.2.val) y • + coupledTensor n m i.1.val i.2.val := (coupledTensor_expansion n m y).symm + _ = dotProduct (highestTensor n m z) y • highestTensor n m z := by + apply Finset.sum_eq_single iz + · intro i _ hne + obtain ⟨w,k⟩ := i + have hw : w.val ≤ min n m := Nat.le_of_lt_succ w.isLt + have hk : k.val ≤ n+m-2*w.val := Nat.le_of_lt_succ k.isLt + have horth : dotProduct (coupledTensor n m w.val k.val) y = 0 := by + by_cases hwz : w.val=z + · have hk0 : k.val ≠ 0 := by + intro hk0 + apply hne + apply Sigma.ext + · exact Fin.ext hwz + · apply (Fin.heq_ext_iff (by dsimp [iz]; omega)).mpr + exact hk0 + apply dot_eq_zero_of_distinct_eigenvalues _ (tensorSpin n m).weight_adjoint + (coupledTensor_weight hw hk) hyH + simp only [hwz] + intro hh + apply hk0 + have : (k.val : ℝ) = 0 := by linarith + exact_mod_cast this + · apply dot_eq_zero_of_distinct_eigenvalues _ (tensorSpin n m).casimir_adjoint + (coupledTensor_casimir hw hk) hyC + intro hh + have HD := spinCasimir_injective hh + have := le_min_iff.mp hw + have := le_min_iff.mp hz + omega + rw [horth, zero_smul] + · simp + +lemma LadderSystem.raw_smul {ι : Type*} [Fintype ι] (S : LadderSystem ι) + (c : ℝ) (x : ι → ℝ) (l : ℕ) : S.raw (c • x) l = c • S.raw x l := by + induction l with + | zero => rfl + | succ l ih => rw [S.raw_succ, ih, map_smul, S.raw_succ] + +lemma LadderSystem.normalized_smul {ι : Type*} [Fintype ι] (S : LadderSystem ι) + (c : ℝ) (x : ι → ℝ) (d l : ℕ) : + S.normalized (c • x) d l = c • S.normalized x d l := by + simp only [LadderSystem.normalized, S.raw_smul, smul_comm c] + +theorem tensorSpin_schur {n m z l : ℕ} (hz : z ≤ min n m) (hl : l ≤ n+m-2*z) + (A : LadderMap (tensorSpin n m) (tensorSpin n m)) : + A.toLinearMap (coupledTensor n m z l) = + dotProduct (highestTensor n m z) (A.toLinearMap (highestTensor n m z)) • + coupledTensor n m z l := by + have hh : A.toLinearMap (highestTensor n m z) = + dotProduct (highestTensor n m z) (A.toLinearMap (highestTensor n m z)) • + highestTensor n m z := by + apply coupledHighest_eigenline hz + · rw [A.weight, highestTensor_weight hz, map_smul] + · rw [A.casimir] + have hc := coupledTensor_casimir hz (by omega : 0 ≤ n+m-2*z) + rw [coupledTensor_zero] at hc + rw [hc, map_smul] + rw [coupledTensor_eq_normalized hz hl, ← A.normalized] + conv_lhs => rw [hh, LadderSystem.normalized_smul] + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/IrrepAveraging.lean b/lean/OAI/Analysis/LaughlinGap/IrrepAveraging.lean new file mode 100644 index 0000000000000000000000000000000000000000..b544d69cf809869f76a0a94e49ffd7813d858295 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/IrrepAveraging.lean @@ -0,0 +1,130 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SpinAveraging + +namespace OAI + +/-! Irrep Averaging. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators +open Averaging + +lemma standardLadderSystem_casimir (n : ℕ) (x : Fin (n+1) → ℝ) : + (standardLadderSystem n).casimir x = ((n : ℝ)*(n+2)) • x := by + funext p + simp only [LadderSystem.casimir_apply, standardLadderSystem, Pi.add_apply, + Pi.smul_apply, smul_eq_mul, weight_apply, lowering_raising_apply] + ring + +theorem standardLadderMap_eq_zero {n m : ℕ} (hnm : n ≠ m) + (A : LadderMap (standardLadderSystem n) (standardLadderSystem m)) : + A.toLinearMap = 0 := by + apply LinearMap.ext + intro x + have h := A.casimir x + rw [standardLadderSystem_casimir, standardLadderSystem_casimir, map_smul] at h + have hne : (m : ℝ)*(m+2) ≠ (n : ℝ)*(n+2) := by + intro he + exact hnm (spinCasimir_injective he).symm + funext j + have he := congrFun h j + change (m : ℝ)*(m+2)*A.toLinearMap x j = (n : ℝ)*(n+2)*A.toLinearMap x j at he + exact (mul_left_cancel₀ (sub_ne_zero.mpr hne) (by nlinarith : + ((m : ℝ)*(m+2)-(n : ℝ)*(n+2)) * A.toLinearMap x j = + ((m : ℝ)*(m+2)-(n : ℝ)*(n+2))*0)) + +lemma ladderStep_pos (n : ℕ) (p : Fin n) : 0 < ladderStep n p := by + apply Real.sqrt_pos.mpr + have hp : (p.val : ℝ) < n := by exact_mod_cast p.isLt + exact mul_pos (by positivity) (by linarith) + +lemma weight_single (n : ℕ) (i : Fin (n+1)) : + weight n (Pi.single i 1) = ((n : ℝ)-2*i.val) • Pi.single i 1 := by + funext j + by_cases h : i=j + · subst j; simp + · simp [h, eq_comm] + +lemma lowering_single (n : ℕ) (p : Fin n) : + lowering n (Pi.single p.castSucc 1) = ladderStep n p • Pi.single p.succ 1 := by + funext j + cases j using Fin.cases with + | zero => simp + | succ j => + by_cases h : j=p + · subst j; simp + · have hn : p.val ≠ j.val := by intro hp; apply h; exact (Fin.ext hp).symm + simp [Fin.ext_iff, hn, eq_comm] + +theorem standardLadderMap_schur {n : ℕ} + (A : LadderMap (standardLadderSystem n) (standardLadderSystem n)) (x : Fin (n+1) → ℝ) : + A.toLinearMap x = A.toLinearMap (Pi.single 0 1) 0 • x := by + let c : Fin (n+1) → ℝ := fun i => A.toLinearMap (Pi.single i 1) i + have hd (i : Fin (n+1)) : A.toLinearMap (Pi.single i 1) = c i • Pi.single i 1 := by + have hw := A.weight (Pi.single i 1) + change weight n (A.toLinearMap (Pi.single i 1)) = A.toLinearMap (weight n _) at hw + rw [weight_single, map_smul] at hw + funext j + by_cases h : i=j + · subst j; simp [c] + · have hv : i.val ≠ j.val := by exact fun he => h (Fin.ext he) + have he := congrFun hw j + simp only [weight_apply, Pi.smul_apply, smul_eq_mul] at he + have hne : ((n : ℝ)-2*j.val)-((n : ℝ)-2*i.val) ≠ 0 := by + intro he + apply hv + exact_mod_cast (by linarith : (i.val : ℝ)=j.val) + have hz : A.toLinearMap (Pi.single i 1) j = 0 := by + apply (mul_eq_zero.mp (show (((n : ℝ)-2*j.val)-((n : ℝ)-2*i.val)) * + A.toLinearMap (Pi.single i 1) j = 0 by nlinarith)).resolve_left hne + simp [hz, h, eq_comm] + have hc : ∀ i, c i = c 0 := by + intro i + induction i using Fin.induction with + | zero => rfl + | succ i ih => + have he := A.lower (Pi.single i.castSucc 1) + change lowering n (A.toLinearMap (Pi.single i.castSucc 1)) = A.toLinearMap (lowering n _) at he + rw [hd, map_smul, lowering_single, map_smul, hd] at he + have hh := congrFun he i.succ + simp only [Pi.smul_apply, smul_eq_mul, Pi.single_eq_same, mul_one] at hh + have hci : c i.succ = c i.castSucc := by + nlinarith [ladderStep_pos n i] + exact hci.trans ih + rw [A.toLinearMap.pi_apply_eq_sum_univ x] + have hs (i : Fin (n+1)) : (fun j => if i=j then (1:ℝ) else 0) = Pi.single i 1 := by + funext j; simp [Pi.single_apply, eq_comm] + simp only [hs, hd, hc, smul_smul] + funext j + simp [Finset.sum_apply, Pi.single_apply, smul_eq_mul, Pi.smul_apply, c, mul_comm] + +theorem standardSpin_average (n : ℕ) (A : Matrix (Fin (n+1)) (Fin (n+1)) ℝ) : + average (rotationCommutant (loweringMatrix (standardLadderSystem n))) A = + (A.trace / (n+1 : ℕ)) • 1 := by + let S := rotationCommutant (loweringMatrix (standardLadderSystem n)) + let Y := average S A + let L := commutantLadderMap (standardLadderSystem n) (average_mem S A) + let c := L.toLinearMap (Pi.single 0 1) 0 + have he : Y = c • 1 := by + apply Matrix.mulVec_injective + funext x + rw [Matrix.smul_mulVec, Matrix.one_mulVec] + have hv := standardLadderMap_schur L x + change Matrix.toLin' Y x = c • x at hv + rwa [Matrix.toLin'_apply] at hv + have hc : c = A.trace / (n+1 : ℕ) := by + have ht := average_trace S A + change Y.trace = A.trace at ht + rw [he, Matrix.trace_smul, Matrix.trace_one] at ht + apply (eq_div_iff (by positivity : ((n+1 : ℕ) : ℝ) ≠ 0)).mpr + simpa using ht + exact he.trans (congrArg (fun t : ℝ => t • (1 : Matrix (Fin (n+1)) (Fin (n+1)) ℝ)) hc) + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/LowNested.lean b/lean/OAI/Analysis/LaughlinGap/LowNested.lean new file mode 100644 index 0000000000000000000000000000000000000000..be08c387f60f58f3001443217adc9fd7c64a19f2 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/LowNested.lean @@ -0,0 +1,132 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.FourSpin +import OAI.Analysis.LaughlinGap.NestedAveraging + +namespace OAI + +/-! Low Nested. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators + +abbrev LowNestedIndex (T : ℕ) := (D : Fin (T+1)) × Fin (D.val+1) + +lemma lowNested_valid {Q T D r : ℕ} (hQ : 2 ≤ Q) (hT : T ≤ Q) + (hD : D ≤ T) (hr : r ≤ D) : + r ≤ Q ∧ D-r ≤ min (2*Q-2) (Q+Q-2*r) ∧ + T-D ≤ (2*Q-2)+(Q+Q-2*r)-2*(D-r) := by omega + +noncomputable def lowNestedInclusion {Q T : ℕ} (hQ : 2 ≤ Q) (hT : T ≤ Q) + (a : LowNestedIndex T) : NestedIndex (2*Q-2) Q Q := + ⟨⟨a.2.val, by have := a.1.isLt; have := a.2.isLt; omega⟩, + ⟨⟨a.1.val-a.2.val, (lowNested_valid hQ hT (by have := a.1.isLt; omega) + (by have := a.2.isLt; exact Nat.le_of_lt_succ this)).2.1 |> Nat.lt_succ_of_le⟩, + ⟨T-a.1.val, (lowNested_valid hQ hT (by have := a.1.isLt; omega) + (by have := a.2.isLt; exact Nat.le_of_lt_succ this)).2.2 |> Nat.lt_succ_of_le⟩⟩⟩ + +lemma lowNestedInclusion_injective {Q T : ℕ} (hQ : 2 ≤ Q) (hT : T ≤ Q) : + Function.Injective (lowNestedInclusion hQ hT) := by + intro a b h + have hr := congrArg (fun x : NestedIndex (2*Q-2) Q Q => x.1.val) h + have hz := congrArg (fun x : NestedIndex (2*Q-2) Q Q => x.2.1.val) h + dsimp [lowNestedInclusion] at hr hz + have hD : a.1=b.1 := Fin.ext (by have := a.2.isLt; have := b.2.isLt; omega) + rcases a with ⟨D,r⟩ + rcases b with ⟨D',r'⟩ + dsimp at hD + subst D' + have : r=r' := Fin.ext hr + subst r' + rfl + +lemma lowNested_coefficient {Q D T r : ℕ} (hrD : r ≤ D) + (hDT : D ≤ T) (hT : T ≤ Q) + (a : Fin (2*Q-2+1) × (Fin (Q+1) × Fin (Q+1))) : + Real.sqrt 2 * nestedTensor (2*Q-2) Q Q r (D-r) (T-D) a = + fourBodyCoefficient Q D T r a.1.val a.2.1.val a.2.2.val := by + classical + unfold nestedTensor fourBodyCoefficient + by_cases hw : r ≤ a.2.1.val+a.2.2.val ∧ a.1.val+a.2.1.val+a.2.2.val=T + · rw [ite_eq_left hw] + let l : Fin (Q+Q-2*r+1) := ⟨a.2.1.val+a.2.2.val-r, by omega⟩ + rw [Finset.sum_eq_single l] + · simp only [coupledTensor] + rw [ite_eq_left (by dsimp [l]; omega), ite_eq_left (by dsimp [l]; omega)] + dsimp [l] + rw [show Q+Q=2*Q by omega] + ring + · intro k hk hkl + have he : a.2.1.val+a.2.2.val ≠ r+k.val := by + intro he + apply hkl + apply Fin.ext + dsimp [l] + omega + simp only [coupledTensor, ite_eq_right he, mul_zero] + · simp + · rw [ite_eq_right hw] + have he : (∑ k : Fin (Q+Q-2*r+1), + coupledTensor (2*Q-2) (Q+Q-2*r) (D-r) (T-D) (a.1,k) * + coupledTensor Q Q r k.val a.2) = 0 := by + apply Finset.sum_eq_zero + intro k hk + simp only [coupledTensor] + split_ifs with h₁ h₂ h₂ <;> try simp + exfalso + exact hw ⟨by omega, by omega⟩ + rw [he, mul_zero] + +lemma nestedTensor_low_expansion {Q T : ℕ} (hQ : 2 ≤ Q) (hT : T ≤ Q) + (a : Fin (2*Q-2+1) × (Fin (Q+1) × Fin (Q+1))) + (ha : a.1.val+a.2.1.val+a.2.2.val=T) : + ∑ b : LowNestedIndex T, + nestedTensor (2*Q-2) Q Q b.2.val (b.1.val-b.2.val) (T-b.1.val) a • + nestedTensor (2*Q-2) Q Q b.2.val (b.1.val-b.2.val) (T-b.1.val) = + Pi.single a 1 := by + classical + have hex := nestedTensor_expansion (2*Q-2) Q Q (Pi.single a 1) + simp only [dotProduct, Pi.single_apply, mul_ite, mul_one, mul_zero, + Finset.sum_ite_eq', Finset.mem_univ, ite_true] at hex + rw [← hex] + apply Finset.sum_bij_ne_zero (fun b _ _ => lowNestedInclusion hQ hT b) + · simp + · intro b hb hb0 c hc hc0 he + exact lowNestedInclusion_injective hQ hT he + · intro b hb hb0 + have hw : b.1.val+b.2.1.val+b.2.2.val=T := by + by_contra he + have hz := nestedTensor_weight_support (2*Q-2) Q Q b.1.val b.2.1.val b.2.2.val a + (by omega) + exact hb0 (by rw [hz, zero_smul]) + let c : LowNestedIndex T := ⟨⟨b.1.val+b.2.1.val, by omega⟩,⟨b.1.val, by dsimp; omega⟩⟩ + have hc : lowNestedInclusion hQ hT c=b := by + rcases b with ⟨r,⟨z,l⟩⟩ + dsimp at hw + have hr : (lowNestedInclusion hQ hT c).1=r := Fin.ext rfl + apply Sigma.ext hr + apply heq_of_eq + apply Sigma.ext (Fin.ext (by dsimp [lowNestedInclusion,c]; omega)) + apply (Fin.heq_ext_iff (by dsimp [lowNestedInclusion,c]; omega)).mpr + dsimp [lowNestedInclusion,c] + omega + refine ⟨c, Finset.mem_univ _, ?_, hc⟩ + have hc0 : nestedTensor (2*Q-2) Q Q c.2.val (c.1.val-c.2.val) (T-c.1.val) a • + nestedTensor (2*Q-2) Q Q c.2.val (c.1.val-c.2.val) (T-c.1.val) ≠ 0 := by + change nestedTensor (2*Q-2) Q Q (lowNestedInclusion hQ hT c).1.val + (lowNestedInclusion hQ hT c).2.1.val (lowNestedInclusion hQ hT c).2.2.val a • + nestedTensor (2*Q-2) Q Q (lowNestedInclusion hQ hT c).1.val + (lowNestedInclusion hQ hT c).2.1.val (lowNestedInclusion hQ hT c).2.2.val ≠ 0 + rw [hc] + exact hb0 + exact hc0 + · intros + rfl + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Main.lean b/lean/OAI/Analysis/LaughlinGap/Main.lean new file mode 100644 index 0000000000000000000000000000000000000000..dc4098415bdd516e6491ec63ef82b953f42d0548 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Main.lean @@ -0,0 +1,67 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Certificate10 +import OAI.Analysis.LaughlinGap.Certificate12 +import OAI.Analysis.LaughlinGap.Certificate14 +import OAI.Analysis.LaughlinGap.Certificate16 +import OAI.Analysis.LaughlinGap.Certificate18 +import OAI.Analysis.LaughlinGap.Certificate20 +import OAI.Analysis.LaughlinGap.Certificate22 +import OAI.Analysis.LaughlinGap.Certificate23 +import OAI.Analysis.LaughlinGap.Certificate6 +import OAI.Analysis.LaughlinGap.Certificate8 +import OAI.Analysis.LaughlinGap.GlobalBound +import OAI.Analysis.LaughlinGap.ZeroCertificates + +namespace OAI + +/-! Main. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators + +lemma exact_four (d : Fin 23) : + FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) + (d.val+1) (by omega) := by + fin_cases d + · exact certificate_1 + · exact certificate_2 + · exact certificate_3 + · exact certificate_4 + · exact Certificate5.certificate + · exact Certificate6.certificate + · exact Certificate7.certificate + · exact Certificate8.certificate + · exact Certificate9.certificate + · exact Certificate10.certificate + · exact Certificate11.certificate + · exact Certificate12.certificate + · exact Certificate13.certificate + · exact Certificate14.certificate + · exact Certificate15.certificate + · exact Certificate16.certificate + · exact Certificate17.certificate + · exact Certificate18.certificate + · exact Certificate19.certificate + · exact Certificate20.certificate + · exact Certificate21.certificate + · exact Certificate22.certificate + · exact Certificate23.certificate + +end LaughlinGap.RealOccupation + +namespace LaughlinGap + +theorem thm_main : MainTarget := by + exact RealOccupation.mainTarget_of_finite_certificates + (fun a : Fin 8 => (RealOccupation.exactRows a).toReal) (1/200000) + (by norm_num) RealOccupation.exact_margin RealOccupation.exact_three + RealOccupation.exact_four + +end LaughlinGap + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/NestedAveraging.lean b/lean/OAI/Analysis/LaughlinGap/NestedAveraging.lean new file mode 100644 index 0000000000000000000000000000000000000000..2c539a1af6b91230c04c543602a0fac2f1fc7bfa --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/NestedAveraging.lean @@ -0,0 +1,146 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.IntertwinerAveraging +import OAI.Analysis.LaughlinGap.NestedSpin +import OAI.Analysis.LaughlinGap.PairDecomposition +import OAI.Analysis.LaughlinGap.PhysicalAveraging + +namespace OAI + +/-! Nested Averaging. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators + +variable {ι : Type*} [Fintype ι] + +noncomputable def LadderMap.changeSource {n d : ℕ} {S : LadderSystem ι} (h : n=d) + (A : LadderMap (standardLadderSystem n) S) : LadderMap (standardLadderSystem d) S := + h ▸ A + +lemma LadderMap.changeSource_single {n d : ℕ} {S : LadderSystem ι} (h : n=d) + (A : LadderMap (standardLadderSystem n) S) (i : Fin (d+1)) : + (A.changeSource h).toLinearMap (Pi.single i 1) = + A.toLinearMap (Pi.single (⟨i.val,by omega⟩ : Fin (n+1)) 1) := by + subst d + rfl + +lemma nestedTensor_weight_support (n m k r z l : ℕ) + (a : Fin (n+1) × (Fin (m+1) × Fin (k+1))) + (ha : a.1.val+a.2.1.val+a.2.2.val ≠ r+z+l) : nestedTensor n m k r z l a = 0 := by + unfold nestedTensor + apply Finset.sum_eq_zero + intro q hq + simp only [coupledTensor] + split_ifs with h₁ h₂ h₂ <;> try simp + exfalso + apply ha + omega + +lemma nestedTensor_flip (n Q r z l : ℕ) (hr : r ≤ Q) (_hl : l ≤ n+(2*Q-2*r)-2*z) + (a : Fin (n+1)) (j k : Fin (Q+1)) : + nestedTensor n Q Q r z l (a,(k,j)) = (-1:ℝ)^r * nestedTensor n Q Q r z l (a,(j,k)) := by + unfold nestedTensor + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro q hq + rw [coupledTensor_swap hr (Nat.le_of_lt_succ q.isLt)] + ring + +noncomputable def nestedAtDeficit {n m k D r : ℕ} (hr : r ≤ min m k) (hrD : r ≤ D) + (hz : D-r ≤ min n (m+k-2*r)) : + LadderMap (standardLadderSystem (n+m+k-2*D)) (nestedSpin n m k) := + (nestedEmbedding hr hz).changeSource (by omega) + +lemma nestedAtDeficit_single {n m k D r : ℕ} (hr : r ≤ min m k) (hrD : r ≤ D) + (hz : D-r ≤ min n (m+k-2*r)) (l : Fin (n+m+k-2*D+1)) : + (nestedAtDeficit hr hrD hz).toLinearMap (Pi.single l 1) = + nestedTensor n m k r (D-r) l.val := by + rw [nestedAtDeficit, LadderMap.changeSource_single, nestedEmbedding_apply] + simp [Pi.single_apply, ite_smul] + +end LaughlinGap.Spin + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Averaging Spin +variable {ι κ : Type*} [Fintype ι] [DecidableEq ι] [Fintype κ] [DecidableEq κ] + +lemma Covariant.equal_descendant_average {L : Matrix κ κ ℝ} {S : LadderSystem ι} + {B : ι → Matrix κ κ ℝ} (h : Covariant L (loweringMatrix S) B) {n : ℕ} + (A C : LadderMap (standardLadderSystem n) S) (i j : Fin (n+1)) : + average (rotationCommutant L) + ((combination B (A.toLinearMap (Pi.single i 1))).transpose * + combination B (C.toLinearMap (Pi.single j 1))) = + if i=j then average (rotationCommutant L) + ((combination B (A.toLinearMap (Pi.single (0 : Fin (n+1)) 1))).transpose * + combination B (C.toLinearMap (Pi.single (0 : Fin (n+1)) 1))) else 0 := by + simp only [← lift_rankOne, h.average_lift, equal_copy_average, map_smul] + split_ifs <;> simp + +lemma Covariant.distinct_descendant_average {L : Matrix κ κ ℝ} {S : LadderSystem ι} + {B : ι → Matrix κ κ ℝ} (h : Covariant L (loweringMatrix S) B) {n m : ℕ} + (hnm : n ≠ m) (A : LadderMap (standardLadderSystem n) S) + (C : LadderMap (standardLadderSystem m) S) (x : Fin (n+1) → ℝ) (y : Fin (m+1) → ℝ) : + average (rotationCommutant L) + ((combination B (A.toLinearMap x)).transpose * combination B (C.toLinearMap y)) = 0 := by + rw [← lift_rankOne, h.average_lift, distinct_copy_average hnm, map_zero] + +noncomputable def physicalFour (Q : ℕ) : + (Fin (2*Q-2+1) × (Fin (Q+1) × Fin (Q+1))) → FockMatrix (Q+1) := + fun a => (1/Real.sqrt 2) • + productFamily (fun p => physicalPair Q p.val) (productFamily annihilation annihilation) a + +lemma physicalFour_covariant {Q : ℕ} (hQ : 2 ≤ Q) : + Covariant (fockLowering Q) (loweringMatrix (nestedSpin (2*Q-2) Q Q)) (physicalFour Q) := + ((physicalPair_covariant hQ).product ((annihilation_covariant _).product + (annihilation_covariant _))).smul (1/Real.sqrt 2) + +lemma annihilation_anticommute' {n : ℕ} (j k : Fin n) : + annihilation k * annihilation j = -(annihilation j * annihilation k) := by + apply complexify_injective + simpa only [map_mul, map_neg, complexify_annihilation] using + Occupation.annihilation_anticommute k j + +lemma physicalFour_flip (Q : ℕ) (a : Fin (2*Q-2+1)) (j k : Fin (Q+1)) : + physicalFour Q (a,(k,j)) = -physicalFour Q (a,(j,k)) := by + simp only [physicalFour, productFamily] + rw [annihilation_anticommute' k j, neg_mul, smul_neg] + +lemma four_combination_flip (Q : ℕ) + (x : (Fin (2*Q-2+1) × (Fin (Q+1) × Fin (Q+1))) → ℝ) : + combination (physicalFour Q) (fun a => x (a.1,(a.2.2,a.2.1))) = + -combination (physicalFour Q) x := by + simp only [combination, LinearMap.coe_mk, AddHom.coe_mk, Fintype.sum_prod_type, + ← Finset.sum_neg_distrib] + apply Finset.sum_congr rfl + intro p hp + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro j hj + apply Finset.sum_congr rfl + intro k hk + rw [physicalFour_flip, smul_neg] + +lemma physicalFour_even_null {Q r z l : ℕ} (hr : r ≤ Q) (he : Even r) + (hl : l ≤ (2*Q-2)+(2*Q-2*r)-2*z) : + combination (physicalFour Q) (nestedTensor (2*Q-2) Q Q r z l) = 0 := by + have hf : (fun a : Fin (2*Q-2+1) × (Fin (Q+1) × Fin (Q+1)) => + nestedTensor (2*Q-2) Q Q r z l (a.1,(a.2.2,a.2.1))) = + nestedTensor (2*Q-2) Q Q r z l := by + funext a + rw [nestedTensor_flip _ _ _ _ _ hr hl, he.neg_one_pow, one_mul] + have hh := four_combination_flip Q (nestedTensor (2*Q-2) Q Q r z l) + rw [hf] at hh + have h2 : (2:ℝ) • combination (physicalFour Q) (nestedTensor (2*Q-2) Q Q r z l) = 0 := by + rw [two_smul ℝ] + exact eq_neg_iff_add_eq_zero.mp hh + exact (smul_eq_zero.mp h2).resolve_left (by norm_num) + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/NestedSpin.lean b/lean/OAI/Analysis/LaughlinGap/NestedSpin.lean new file mode 100644 index 0000000000000000000000000000000000000000..c02cc6a8b2c070b0462e01e2b560e9232c0d835c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/NestedSpin.lean @@ -0,0 +1,214 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SpinAveraging + +namespace OAI + +/-! Nested Spin. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators InnerProduct + +noncomputable def onSecondMap {ι κ σ : Type*} (A : (ι → ℝ) →ₗ[ℝ] (κ → ℝ)) : + ((σ × ι) → ℝ) →ₗ[ℝ] ((σ × κ) → ℝ) where + toFun x pq := A (fun i => x (pq.1,i)) pq.2 + map_add' x y := by + funext ⟨p,q⟩ + exact congrFun (A.map_add (fun i => x (p,i)) (fun i => y (p,i))) q + map_smul' r x := by + funext ⟨p,q⟩ + exact congrFun (A.map_smul r (fun i => x (p,i))) q + +@[simp] lemma onSecondMap_apply {ι κ σ : Type*} (A : (ι → ℝ) →ₗ[ℝ] (κ → ℝ)) + (x : (σ × ι) → ℝ) (p : σ) (q : κ) : + onSecondMap A x (p,q) = A (fun i => x (p,i)) q := rfl + +lemma onSecondMap_onFirst {ι κ σ : Type*} [Fintype ι] + (A : (ι → ℝ) →ₗ[ℝ] (κ → ℝ)) (B : Module.End ℝ (σ → ℝ)) (x : (σ × ι) → ℝ) : + onSecondMap A (onFirstEnd B x) = onFirstEnd B (onSecondMap A x) := by + classical + funext ⟨p,q⟩ + simp only [onSecondMap_apply, onFirstEnd_apply] + have hfun : (fun j => A (fun i => x (j,i)) q) = + ∑ i : ι, (A (fun k => if i = k then 1 else 0) q) • (fun j => x (j,i)) := by + funext j + rw [A.pi_apply_eq_sum_univ (fun i => x (j,i))] + simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul] + apply Finset.sum_congr rfl + intro i hi + ring + rw [hfun, map_sum, A.pi_apply_eq_sum_univ (fun i => B (fun j => x (j,i)) p)] + simp only [Finset.sum_apply, map_smul, Pi.smul_apply, smul_eq_mul] + apply Finset.sum_congr rfl + intro i hi + ring + +noncomputable def LadderMap.tensorLeft {ι κ σ : Type*} + [Fintype ι] [Fintype κ] [Fintype σ] + {S : LadderSystem ι} {T : LadderSystem κ} + (A : LadderMap S T) (U : LadderSystem σ) : LadderMap (U.tensor S) (U.tensor T) where + toLinearMap := onSecondMap A.toLinearMap + lower x := by + change onFirstEnd U.lower (onSecondMap A.toLinearMap x) + + onSecondEnd T.lower (onSecondMap A.toLinearMap x) = + onSecondMap A.toLinearMap (onFirstEnd U.lower x + onSecondEnd S.lower x) + rw [map_add, ← onSecondMap_onFirst] + congr 1 + funext ⟨p,q⟩ + exact congrFun (A.lower (fun i => x (p,i))) q + raise x := by + change onFirstEnd U.raise (onSecondMap A.toLinearMap x) + + onSecondEnd T.raise (onSecondMap A.toLinearMap x) = + onSecondMap A.toLinearMap (onFirstEnd U.raise x + onSecondEnd S.raise x) + rw [map_add, ← onSecondMap_onFirst] + congr 1 + funext ⟨p,q⟩ + exact congrFun (A.raise (fun i => x (p,i))) q + +noncomputable def nestedSpin (n m k : ℕ) := + (standardLadderSystem n).tensor (tensorSpin m k) + +noncomputable def nestedEmbedding {n m k r z : ℕ} (hr : r ≤ min m k) + (hz : z ≤ min n (m+k-2*r)) : + LadderMap (standardLadderSystem (n+(m+k-2*r)-2*z)) (nestedSpin n m k) := + ((coupledEmbedding hr).tensorLeft (standardLadderSystem n)).comp (coupledEmbedding hz) + +noncomputable def nestedTensor (n m k r z l : ℕ) : + (Fin (n+1) × (Fin (m+1) × Fin (k+1))) → ℝ := + fun a => ∑ q : Fin (m+k-2*r+1), + coupledTensor n (m+k-2*r) z l (a.1,q) * coupledTensor m k r q.val a.2 + +lemma nestedEmbedding_apply {n m k r z : ℕ} (hr : r ≤ min m k) + (hz : z ≤ min n (m+k-2*r)) (x : Fin (n+(m+k-2*r)-2*z+1) → ℝ) : + (nestedEmbedding hr hz).toLinearMap x = + ∑ l : Fin (n+(m+k-2*r)-2*z+1), x l • nestedTensor n m k r z l.val := by + funext ⟨a,b⟩ + simp only [nestedEmbedding, LadderMap.comp, LinearMap.coe_comp, Function.comp_apply, + LadderMap.tensorLeft, onSecondMap_apply, coupledEmbedding_apply, nestedTensor, + Finset.sum_apply, Pi.smul_apply, smul_eq_mul, Finset.sum_mul] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro l hl + rw [Finset.mul_sum] + apply Finset.sum_congr rfl + intro q hq + ring + +abbrev NestedIndex (n m k : ℕ) := + (r : Fin (min m k+1)) × CoupledIndex n (m+k-2*r.val) + +noncomputable def nestedFamily (n m k : ℕ) (a : NestedIndex n m k) : + EuclideanSpace ℝ (Fin (n+1) × (Fin (m+1) × Fin (k+1))) := + WithLp.toLp 2 (nestedTensor n m k a.1.val a.2.1.val a.2.2.val) + +lemma coupled_tensor_second_dot {n m k r s : ℕ} (hr : r ≤ min m k) (hs : s ≤ min m k) + (x : (Fin (n+1) × Fin (m+k-2*r+1)) → ℝ) + (y : (Fin (n+1) × Fin (m+k-2*s+1)) → ℝ) : + dotProduct (onSecondMap (coupledEmbedding hr).toLinearMap x) + (onSecondMap (coupledEmbedding hs).toLinearMap y) = + ∑ p : Fin (n+1), ∑ l : Fin (m+k-2*r+1), ∑ t : Fin (m+k-2*s+1), + x (p,l) * y (p,t) * if r=s ∧ l.val=t.val then (1:ℝ) else 0 := by + rw [dotProduct, Fintype.sum_prod_type] + simp only [onSecondMap_apply, coupledEmbedding_apply, Finset.sum_apply, + Pi.smul_apply, smul_eq_mul, Finset.sum_mul, Finset.mul_sum] + apply Finset.sum_congr rfl + intro p hp + rw [Finset.sum_comm] + conv_rhs => rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro t ht + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro l hl + have hd := coupledTensor_dot (⟨⟨r,by omega⟩,l⟩ : CoupledIndex m k) ⟨⟨s,by omega⟩,t⟩ + have he : ((⟨⟨r,by omega⟩,l⟩ : CoupledIndex m k) = ⟨⟨s,by omega⟩,t⟩) ↔ + r=s ∧ l.val=t.val := by + constructor + · intro h + exact ⟨congrArg (fun a : CoupledIndex m k => a.1.val) h, + congrArg (fun a : CoupledIndex m k => a.2.val) h⟩ + · rintro ⟨rfl,hl⟩ + have : l=t := Fin.ext hl + subst t + rfl + rw [if_congr he rfl rfl] at hd + rw [← hd, dotProduct, Finset.mul_sum] + apply Finset.sum_congr rfl + intro a ha + ring + +lemma nestedTensor_as_map {n m k r z l : ℕ} (hr : r ≤ min m k) : + nestedTensor n m k r z l = onSecondMap (coupledEmbedding hr).toLinearMap + (coupledTensor n (m+k-2*r) z l) := by + funext a + simp [nestedTensor, onSecondMap, coupledEmbedding_apply] + +lemma nestedTensor_dot (n m k : ℕ) (a b : NestedIndex n m k) : + dotProduct (nestedTensor n m k a.1.val a.2.1.val a.2.2.val) + (nestedTensor n m k b.1.val b.2.1.val b.2.2.val) = if a=b then 1 else 0 := by + rcases a with ⟨r,a⟩ + rcases b with ⟨s,b⟩ + rw [nestedTensor_as_map (Nat.le_of_lt_succ r.isLt), + nestedTensor_as_map (Nat.le_of_lt_succ s.isLt), coupled_tensor_second_dot] + by_cases he : r=s + · subst s + simp only [true_and, Fin.val_inj, mul_ite, mul_one, mul_zero, + Finset.sum_ite_eq, Finset.mem_univ, ite_true, Sigma.mk.inj_iff, heq_eq_eq, true_and] + convert coupledTensor_dot a b using 1 + simp only [dotProduct, Fintype.sum_prod_type] + · have hv : r.val ≠ s.val := by exact fun hv => he (Fin.ext hv) + have hab : (⟨r,a⟩ : NestedIndex n m k) ≠ ⟨s,b⟩ := by + intro h; exact he (congrArg Sigma.fst h) + simp [hv,hab] + +lemma nestedFamily_orthonormal (n m k : ℕ) : Orthonormal ℝ (nestedFamily n m k) := by + rw [orthonormal_iff_ite] + intro a b + simpa only [nestedFamily, EuclideanSpace.inner_toLp_toLp, star_trivial, eq_comm] using + nestedTensor_dot n m k b a + +lemma nestedIndex_card (n m k : ℕ) : + Fintype.card (NestedIndex n m k) = (n+1)*((m+1)*(k+1)) := by + change Fintype.card ((r : Fin (min m k+1)) × CoupledIndex n (m+k-2*r.val)) = _ + rw [Fintype.card_sigma] + simp only [coupledIndex_card] + rw [← Finset.mul_sum] + have hh := coupledIndex_card m k + change Fintype.card ((z : Fin (min m k+1)) × Fin (m+k-2*z.val+1)) = _ at hh + rw [Fintype.card_sigma] at hh + simp only [Fintype.card_fin] at hh + rw [hh] + +noncomputable def nestedBasis (n m k : ℕ) : OrthonormalBasis (NestedIndex n m k) ℝ + (EuclideanSpace ℝ (Fin (n+1) × (Fin (m+1) × Fin (k+1)))) := by + letI : Nonempty (NestedIndex n m k) := ⟨⟨0,0,0⟩⟩ + have hc : Fintype.card (NestedIndex n m k) = + Module.finrank ℝ (EuclideanSpace ℝ (Fin (n+1) × (Fin (m+1) × Fin (k+1)))) := by + rw [finrank_euclideanSpace, Fintype.card_prod, Fintype.card_prod, + Fintype.card_fin, Fintype.card_fin, Fintype.card_fin, nestedIndex_card] + let b := basisOfOrthonormalOfCardEqFinrank (nestedFamily_orthonormal n m k) hc + exact b.toOrthonormalBasis (by simpa [b] using nestedFamily_orthonormal n m k) + +@[simp] lemma nestedBasis_apply (n m k : ℕ) (a : NestedIndex n m k) : + nestedBasis n m k a = nestedFamily n m k a := by simp [nestedBasis] + +lemma nestedTensor_expansion (n m k : ℕ) + (x : (Fin (n+1) × (Fin (m+1) × Fin (k+1))) → ℝ) : + ∑ a : NestedIndex n m k, + dotProduct (nestedTensor n m k a.1.val a.2.1.val a.2.2.val) x • + nestedTensor n m k a.1.val a.2.1.val a.2.2.val = x := by + funext p + have h := congrArg (fun y : EuclideanSpace ℝ (Fin (n+1) × (Fin (m+1) × Fin (k+1))) => y p) + ((nestedBasis n m k).sum_repr (WithLp.toLp 2 x)) + simpa only [OrthonormalBasis.repr_apply_apply, nestedBasis_apply, nestedFamily, + PiLp.inner_apply, RCLike.inner_apply, conj_trivial, Finset.sum_apply, + WithLp.ofLp_sum, WithLp.ofLp_smul, PiLp.smul_apply, WithLp.toLp_ofLp, Pi.smul_apply, + smul_eq_mul, dotProduct, mul_comm] using h + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/NormalOrder.lean b/lean/OAI/Analysis/LaughlinGap/NormalOrder.lean new file mode 100644 index 0000000000000000000000000000000000000000..d248544c6fbe688bdbc74258a1e87324681b0c55 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/NormalOrder.lean @@ -0,0 +1,635 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Contraction + +namespace OAI + +/-! Normal Order. -/ + +noncomputable section + + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct ComplexOrder + +noncomputable def bodySpace (n k : ℕ) : Submodule ℂ (Module.End ℂ (Hilbert n)) := + (exteriorLift (n := n) (k := k)).range + +@[simp] lemma exteriorLift_single {n k : ℕ} (A B : BasisLabel n k) (c : ℂ) : + exteriorLift (Matrix.single A B c) = c • ((basisContraction A).adjoint * basisContraction B) := by + classical + simp [exteriorLift, matrixLift, Matrix.single_apply, ite_smul, ite_and] + +lemma word_rankOne_mem_bodySpace {n k : ℕ} (js ks : List (Fin n)) + (hj : js.length = k) (hk : ks.length = k) : + (word js).adjoint * word ks ∈ bodySpace n k := by + classical + by_cases hn : js.Nodup + · by_cases hm : ks.Nodup + · obtain ⟨c,hc⟩ := word_normal_form js + obtain ⟨d,hd⟩ := word_normal_form ks + let A : BasisLabel n k := ⟨js.toFinset, (List.toFinset_card_of_nodup hn).trans hj⟩ + let B : BasisLabel n k := ⟨ks.toFinset, (List.toFinset_card_of_nodup hm).trans hk⟩ + have hA : word js = c • basisContraction A := hc + have hB : word ks = d • basisContraction B := hd + rw [hA,hB,map_smulₛₗ,smul_mul_assoc,mul_smul_comm,smul_smul] + exact ⟨Matrix.single A B ((starRingEnd ℂ) c * d), exteriorLift_single _ _ _⟩ + · rw [word_eq_zero_of_not_nodup ks hm, mul_zero] + exact (bodySpace n k).zero_mem + · rw [word_eq_zero_of_not_nodup js hn, map_zero, zero_mul] + exact (bodySpace n k).zero_mem + +lemma triple_basic_eq_word {n : ℕ} (i : Fin n) (a : PairLabel n) : + annihilation i * basicPair a = word [a.val.1,a.val.2,i] := by + simp only [basicPair, word_cons, word_nil, one_mul, mul_assoc] + +lemma triple_rankOne_mem_bodySpace {n : ℕ} (v w : PairLabel n → ℂ) (i j : Fin n) : + (annihilation i * pairContraction v).adjoint * + (annihilation j * pairContraction w) ∈ bodySpace n 3 := by + classical + simp only [pairContraction, Finset.mul_sum, mul_smul_comm, map_sum, + map_smulₛₗ] + simp only [Finset.sum_mul] + simp only [smul_mul_assoc, Finset.smul_sum, smul_smul] + apply Submodule.sum_mem + intro a _ + apply Submodule.sum_mem + intro b _ + apply Submodule.smul_mem + rw [triple_basic_eq_word, triple_basic_eq_word] + exact word_rankOne_mem_bodySpace _ _ rfl rfl + +lemma middle_rankOne_mem_bodySpace {n : ℕ} (v w : PairLabel n → ℂ) (i j : Fin n) : + (pairContraction v).adjoint * (creation i * annihilation j) * pairContraction w ∈ + bodySpace n 3 := by + convert triple_rankOne_mem_bodySpace v w i j using 1 + rw [adjoint_mul, annihilation_adjoint] + simp only [mul_assoc] + +theorem pairThreeTerm_mem_bodySpace {n : ℕ} {ι : Type*} [Fintype ι] + (v : ι → PairLabel n → ℂ) : pairThreeTerm v ∈ bodySpace n 3 := by + classical + unfold pairThreeTerm + apply Submodule.sum_mem + intro p _ + apply Submodule.sum_mem + intro r _ + simp only [pairOneContraction, Finset.mul_sum, Finset.sum_mul, + mul_smul_comm, smul_mul_assoc] + apply Submodule.sum_mem + intro a _ + apply Submodule.sum_mem + intro b _ + apply Submodule.smul_mem + simp only [oneContraction, mul_add, add_mul, mul_sub, sub_mul, mul_neg, neg_mul, + mul_ite, ite_mul, mul_zero, zero_mul] + have h (i j : Fin n) := middle_rankOne_mem_bodySpace (v p) (v r) i j + have hc (P : Prop) [Decidable P] (i j : Fin n) : + (if P then (pairContraction (v p)).adjoint * (creation i * annihilation j) * + pairContraction (v r) else 0) ∈ bodySpace n 3 := by + split_ifs + · exact h i j + · exact (bodySpace n 3).zero_mem + exact Submodule.sub_mem _ + (Submodule.add_mem _ (Submodule.add_mem _ (Submodule.neg_mem _ (hc _ _ _)) + (hc _ _ _)) (hc _ _ _)) (hc _ _ _) + +end LaughlinGap.Occupation + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct ComplexOrder + +lemma homogeneous_smul {n k : ℕ} {x : Hilbert n} (hx : Homogeneous k x) (c : ℂ) : + Homogeneous k (c • x) := by + intro A hA + simp [hx A hA] + +lemma homogeneous_sum {n k : ℕ} {ι : Type*} (s : Finset ι) (x : ι → Hilbert n) + (hx : ∀ i ∈ s, Homogeneous k (x i)) : Homogeneous k (∑ i ∈ s, x i) := by + intro A hA + simp only [WithLp.ofLp_sum, Finset.sum_apply] + exact Finset.sum_eq_zero (fun i hi => hx i hi A hA) + +lemma vacuum_homogeneous (n : ℕ) : Homogeneous 0 (vacuum n) := by + intro A hA + have hh : A ≠ ∅ := by intro h; apply hA; simp [h] + simp [vacuum_apply, hh] + +lemma creation_homogeneous {n k : ℕ} {x : Hilbert n} (hx : Homogeneous k x) + (i : Fin n) : Homogeneous (k+1) (creation i x) := by + intro A hA + by_cases hi : i ∈ A + · have hc : (A.erase i).card ≠ k := by + have hh := Finset.card_erase_add_one hi + omega + simp [transition_apply, hi, hx _ hc] + · simp [transition_apply, hi] + +lemma pairContraction_adjoint_homogeneous {n k : ℕ} (v : PairLabel n → ℂ) + {x : Hilbert n} (hx : Homogeneous k x) : + Homogeneous (k+2) ((pairContraction v).adjoint x) := by + simp only [pairContraction, map_sum, map_smulₛₗ, LinearMap.sum_apply, LinearMap.smul_apply] + apply homogeneous_sum + intro a _ + apply homogeneous_smul + simpa only [basicPair, adjoint_mul, annihilation_adjoint, Module.End.mul_apply] using + creation_homogeneous (creation_homogeneous hx a.val.2) a.val.1 + +noncomputable def sectorReadout (n k : ℕ) : Hilbert n →ₗ[ℂ] ExteriorCoordinates n k where + toFun x := WithLp.toLp 2 (fun A => x A.val) + map_add' _ _ := rfl + map_smul' _ _ := rfl + +@[simp] lemma sectorReadout_apply {n k : ℕ} (x : Hilbert n) (A : BasisLabel n k) : + sectorReadout n k x A = x A.val := rfl + +lemma fullContraction_eq_exteriorContraction {n k : ℕ} {x : Hilbert n} + (hx : Homogeneous k x) : + fullContraction x = exteriorContraction (sectorReadout n k x) := by + classical + change (∑ A, star (x A) • allBasisContraction A) = + ∑ A : BasisLabel n k, star (x A.val) • basisContraction A + calc + (∑ A, star (x A) • allBasisContraction A) = + ∑ A ∈ Finset.univ.filter (fun A : Finset (Fin n) => A.card = k), + star (x A) • allBasisContraction A := by + symm + apply Finset.sum_subset (Finset.filter_subset _ _) + intro A _ hA + have hh : A.card ≠ k := by simpa using hA + simp [hx A hh] + _ = _ := Finset.sum_subtype _ (by simp) _ + +lemma reconstruct_pair_product {n : ℕ} (v w : PairLabel n → ℂ) : + reconstruct (pairContraction v * pairContraction w) = pairContraction v * pairContraction w := by + simp only [pairContraction, Finset.sum_mul] + simp only [Finset.mul_sum] + simp only [smul_mul_assoc, mul_smul_comm, smul_smul, map_sum, map_smul] + apply Finset.sum_congr rfl + intro a _ + apply Finset.sum_congr rfl + intro b _ + congr 1 + have he : basicPair a * basicPair b = word [b.val.1,b.val.2,a.val.1,a.val.2] := by + simp only [basicPair, word_cons, word_nil, one_mul, mul_assoc] + rw [he,reconstruct_word] + +noncomputable def pairWedgeColumn {n : ℕ} (v w : PairLabel n → ℂ) : ExteriorCoordinates n 4 := + sectorReadout n 4 ((pairContraction w * pairContraction v).adjoint (vacuum n)) + +lemma pairWedgeColumn_contraction {n : ℕ} (v w : PairLabel n → ℂ) : + exteriorContraction (pairWedgeColumn v w) = pairContraction w * pairContraction v := by + have hh : Homogeneous 4 ((pairContraction w * pairContraction v).adjoint (vacuum n)) := by + rw [adjoint_mul, Module.End.mul_apply] + exact pairContraction_adjoint_homogeneous v + (pairContraction_adjoint_homogeneous w (vacuum_homogeneous n)) + rw [pairWedgeColumn, ← fullContraction_eq_exteriorContraction hh] + exact reconstruct_pair_product w v + +noncomputable def pairWedgeMatrix {n : ℕ} {ι : Type*} (v : ι → PairLabel n → ℂ) : + Matrix (BasisLabel n 4) (ι × ι) ℂ := fun A pr => pairWedgeColumn (v pr.1) (v pr.2) A + +theorem pairFourTerm_eq_lift {n : ℕ} {ι : Type*} [Fintype ι] + (v : ι → PairLabel n → ℂ) : + pairFourTerm v = exteriorLift (pairWedgeMatrix v * (pairWedgeMatrix v).conjTranspose) := by + classical + have hw := matrixLift_columns basisContraction (pairWedgeMatrix v) (1 : Matrix (ι × ι) (ι × ι) ℂ) + simp only [Matrix.mul_one] at hw + rw [exteriorLift, hw] + have he (pr : ι × ι) : + contractCombination basisContraction (fun A => pairWedgeMatrix v A pr) = + pairContraction (v pr.2) * pairContraction (v pr.1) := + pairWedgeColumn_contraction (v pr.1) (v pr.2) + simp only [matrixLift, LinearMap.coe_mk, AddHom.coe_mk, he, + Matrix.one_apply, ite_smul, one_smul, zero_smul] + simp only [Finset.sum_ite_eq, Finset.mem_univ, ite_true, Fintype.sum_prod_type] + rfl + +theorem pairFourTerm_positive {n : ℕ} {ι : Type*} [Fintype ι] + (v : ι → PairLabel n → ℂ) : (pairFourTerm v).IsPositive := by + rw [pairFourTerm_eq_lift] + exact exteriorLift_positive (Matrix.posSemidef_self_mul_conjTranspose _) + +end LaughlinGap.Occupation + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct ComplexOrder + +lemma pairContraction_eq_pairAnnihilator {n : ℕ} (v : Fin n → Fin n → ℂ) : + pairContraction (fun a => v a.val.1 a.val.2) = pairAnnihilator v := by + classical + simp only [pairContraction, basicPair] + rw [← Finset.sum_subtype (Finset.univ.filter (fun a : Fin n × Fin n => a.1 < a.2)) + (by simp) (fun a => star (v a.1 a.2) • (annihilation a.2 * annihilation a.1))] + simp only [Finset.sum_filter, Fintype.sum_prod_type, pairAnnihilator] + +lemma sectorInclusion_readout {n k : ℕ} {x : Hilbert n} (hx : Homogeneous k x) : + sectorInclusion n k (sectorReadout n k x) = x := by + ext A + by_cases hA : A.card = k + · simp [sectorInclusion_apply, hA] + · simp [sectorInclusion_apply, hA, hx A hA] + +lemma sectorInclusion_adjoint (n k : ℕ) : (sectorInclusion n k).adjoint = sectorReadout n k := by + classical + symm + rw [LinearMap.eq_adjoint_iff] + intro x y + rw [PiLp.inner_apply, PiLp.inner_apply] + let f : Finset (Fin n) → ℂ := fun A => inner ℂ (x A) (sectorInclusion n k y A) + calc + (∑ A : BasisLabel n k, inner ℂ (sectorReadout n k x A) (y A)) = + ∑ A ∈ Finset.univ.filter (fun A : Finset (Fin n) => A.card = k), f A := by + have h := Finset.sum_subtype (p := fun A : Finset (Fin n) => A.card = k) (F := inferInstance) (Finset.univ.filter (fun A : Finset (Fin n) => A.card = k)) + (by simp) f + simpa only [f, sectorInclusion_apply_label, sectorReadout_apply] using h.symm + _ = ∑ A, inner ℂ (x A) (sectorInclusion n k y A) := by + apply Finset.sum_subset (Finset.filter_subset _ _) + intro A _ hA + have hh : A.card ≠ k := by simpa using hA + simp [f, sectorInclusion_apply, hh] + +noncomputable def sectorExtract (n k : ℕ) : + Module.End ℂ (Hilbert n) →ₗ[ℂ] Matrix (BasisLabel n k) (BasisLabel n k) ℂ where + toFun T := Matrix.toEuclideanLin.symm (sectorReadout n k ∘ₗ T ∘ₗ sectorInclusion n k) + map_add' _ _ := by simp only [LinearMap.comp_add, LinearMap.add_comp, map_add] + map_smul' _ _ := by simp only [LinearMap.comp_smul, LinearMap.smul_comp, map_smul, RingHom.id_apply] + +@[simp] lemma sectorExtract_toEuclideanLin (n k : ℕ) (T : Module.End ℂ (Hilbert n)) : + (sectorExtract n k T).toEuclideanLin = sectorReadout n k ∘ₗ T ∘ₗ sectorInclusion n k := + Matrix.toEuclideanLin.apply_symm_apply _ + +@[simp] theorem sectorExtract_exteriorLift {n k : ℕ} + (M : Matrix (BasisLabel n k) (BasisLabel n k) ℂ) : + sectorExtract n k (exteriorLift M) = M := by + apply Matrix.toEuclideanLin.injective + rw [sectorExtract_toEuclideanLin] + apply LinearMap.ext + intro y + apply ext_inner_left ℂ + intro x + change inner ℂ x (sectorReadout n k (exteriorLift M (sectorInclusion n k y))) = _ + rw [← sectorInclusion_adjoint, LinearMap.adjoint_inner_right] + exact exteriorLift_inner_sector M x y + +lemma exteriorLift_sectorExtract {n k : ℕ} {T : Module.End ℂ (Hilbert n)} + (hT : T ∈ bodySpace n k) : exteriorLift (sectorExtract n k T) = T := by + obtain ⟨M,rfl⟩ := hT + rw [sectorExtract_exteriorLift] + +lemma sectorExtract_mul {n k : ℕ} (T S : Module.End ℂ (Hilbert n)) + (hS : ∀ x, Homogeneous k x → Homogeneous k (S x)) : + sectorExtract n k (T * S) = sectorExtract n k T * sectorExtract n k S := by + apply Matrix.toEuclideanLin.injective + simp only [Matrix.toEuclideanLin, Matrix.toLpLin_mul_same, sectorExtract_toEuclideanLin] + apply LinearMap.ext + intro x + change sectorReadout n k (T (S (sectorInclusion n k x))) = + sectorReadout n k (T (sectorInclusion n k (sectorReadout n k (S (sectorInclusion n k x))))) + rw [sectorInclusion_readout (hS _ (sectorInclusion_homogeneous x))] + +lemma sectorExtract_eq_zero {n k : ℕ} (T : Module.End ℂ (Hilbert n)) + (hT : ∀ x, Homogeneous k x → T x = 0) : sectorExtract n k T = 0 := by + apply Matrix.toEuclideanLin.injective + rw [map_zero, sectorExtract_toEuclideanLin] + apply LinearMap.ext + intro x + change sectorReadout n k (T (sectorInclusion n k x)) = 0 + rw [hT _ (sectorInclusion_homogeneous x), map_zero] + +lemma pairContraction_homogeneous {n k : ℕ} (v : PairLabel n → ℂ) + {x : Hilbert n} (hx : Homogeneous (k+2) x) : Homogeneous k (pairContraction v x) := by + simp only [pairContraction, LinearMap.sum_apply, LinearMap.smul_apply] + apply homogeneous_sum + intro a _ + apply homogeneous_smul + exact annihilation_homogeneous (annihilation_homogeneous hx a.val.1) a.val.2 + +lemma pairHamiltonian_homogeneous {n k : ℕ} {ι : Type*} [Fintype ι] + (v : ι → PairLabel n → ℂ) {x : Hilbert n} (hx : Homogeneous (k+2) x) : + Homogeneous (k+2) (pairHamiltonian v x) := by + simp only [pairHamiltonian, LinearMap.sum_apply, Module.End.mul_apply] + exact homogeneous_sum _ _ (fun p _ => pairContraction_adjoint_homogeneous _ + (pairContraction_homogeneous _ hx)) + +lemma numberOperator_apply {n : ℕ} (x : Hilbert n) (A : Finset (Fin n)) : + (∑ i : Fin n, creation i (annihilation i x)) A = (A.card : ℂ) * x A := by + simp only [WithLp.ofLp_sum, Finset.sum_apply] + have ht (i : Fin n) : creation i (annihilation i x) A = if i ∈ A then x A else 0 := by + by_cases hi : i ∈ A <;> + simp [transition_apply, hi, ← mul_assoc] + simp only [ht] + rw [← Finset.sum_filter] + simp + +lemma numberOperator_one {n : ℕ} {x : Hilbert n} (hx : Homogeneous 1 x) : + (∑ i : Fin n, creation i (annihilation i x)) = x := by + ext A + rw [numberOperator_apply] + by_cases hA : A.card = 1 + · simp [hA] + · simp [hx A hA] + +noncomputable def pairTripleOperator {n : ℕ} {ι : Type*} [Fintype ι] + (v : ι → PairLabel n → ℂ) : Module.End ℂ (Hilbert n) := + ∑ p, ∑ i : Fin n, (annihilation i * pairContraction (v p)).adjoint * + (annihilation i * pairContraction (v p)) + +lemma pairTripleOperator_three {n : ℕ} {ι : Type*} [Fintype ι] + (v : ι → PairLabel n → ℂ) {x : Hilbert n} (hx : Homogeneous 3 x) : + pairTripleOperator v x = pairHamiltonian v x := by + simp only [pairTripleOperator, pairHamiltonian, LinearMap.sum_apply, + adjoint_mul, annihilation_adjoint, Module.End.mul_apply] + apply Finset.sum_congr rfl + intro p _ + rw [← map_sum, numberOperator_one (pairContraction_homogeneous (v p) hx)] + +lemma reconstruct_triple_pair {n : ℕ} (v : PairLabel n → ℂ) (i : Fin n) : + reconstruct (annihilation i * pairContraction v) = annihilation i * pairContraction v := by + simp only [pairContraction, Finset.mul_sum, mul_smul_comm, map_sum, map_smul, + triple_basic_eq_word, reconstruct_word] + +noncomputable def tripleWedgeColumn {n : ℕ} (v : PairLabel n → ℂ) (i : Fin n) : + ExteriorCoordinates n 3 := + sectorReadout n 3 ((annihilation i * pairContraction v).adjoint (vacuum n)) + +lemma tripleWedgeColumn_contraction {n : ℕ} (v : PairLabel n → ℂ) (i : Fin n) : + exteriorContraction (tripleWedgeColumn v i) = annihilation i * pairContraction v := by + have hh : Homogeneous 3 ((annihilation i * pairContraction v).adjoint (vacuum n)) := by + rw [adjoint_mul, annihilation_adjoint, Module.End.mul_apply] + exact pairContraction_adjoint_homogeneous v (creation_homogeneous (vacuum_homogeneous n) i) + rw [tripleWedgeColumn, ← fullContraction_eq_exteriorContraction hh] + exact reconstruct_triple_pair v i + +noncomputable def tripleWedgeMatrix {n : ℕ} {ι : Type*} (v : ι → PairLabel n → ℂ) : + Matrix (BasisLabel n 3) (ι × Fin n) ℂ := fun A pi => tripleWedgeColumn (v pi.1) pi.2 A + +lemma pairTripleOperator_eq_lift {n : ℕ} {ι : Type*} [Fintype ι] + (v : ι → PairLabel n → ℂ) : + pairTripleOperator v = exteriorLift (tripleWedgeMatrix v * (tripleWedgeMatrix v).conjTranspose) := by + classical + have hw := matrixLift_columns basisContraction (tripleWedgeMatrix v) + (1 : Matrix (ι × Fin n) (ι × Fin n) ℂ) + simp only [Matrix.mul_one] at hw + rw [exteriorLift, hw] + have he (pi : ι × Fin n) : + contractCombination basisContraction (fun A => tripleWedgeMatrix v A pi) = + annihilation pi.2 * pairContraction (v pi.1) := tripleWedgeColumn_contraction _ _ + simp only [matrixLift, LinearMap.coe_mk, AddHom.coe_mk, he, + Matrix.one_apply, ite_smul, one_smul, zero_smul] + simp only [Finset.sum_ite_eq, Finset.mem_univ, ite_true, Fintype.sum_prod_type] + rfl + +end LaughlinGap.Occupation + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct ComplexOrder + +lemma pairHamiltonian_sector_three {n : ℕ} {ι : Type*} [Fintype ι] + (v : ι → PairLabel n → ℂ) : + sectorExtract n 3 (pairHamiltonian v) = tripleWedgeMatrix v * (tripleWedgeMatrix v).conjTranspose := by + rw [← sectorExtract_exteriorLift (tripleWedgeMatrix v * (tripleWedgeMatrix v).conjTranspose), + ← pairTripleOperator_eq_lift] + apply Matrix.toEuclideanLin.injective + rw [sectorExtract_toEuclideanLin, sectorExtract_toEuclideanLin] + apply LinearMap.ext + intro x + change sectorReadout n 3 (pairHamiltonian v (sectorInclusion n 3 x)) = + sectorReadout n 3 (pairTripleOperator v (sectorInclusion n 3 x)) + rw [pairTripleOperator_three v (sectorInclusion_homogeneous x)] + +theorem pairThreeTerm_eq_lift {n : ℕ} {ι : Type*} [Fintype ι] [DecidableEq ι] + (v : ι → PairLabel n → ℂ) + (hv : ∀ p r, (∑ a, star (v p a) * v r a) = if p = r then 1 else 0) : + pairThreeTerm v = exteriorLift (tripleWedgeMatrix v * + ((tripleWedgeMatrix v).conjTranspose * tripleWedgeMatrix v - 1) * + (tripleWedgeMatrix v).conjTranspose) := by + have h4 : sectorExtract n 3 (pairFourTerm v) = 0 := by + apply sectorExtract_eq_zero + intro x hx + rw [pairFourTerm_eq_lift] + exact exteriorLift_eq_zero_of_degree_lt hx (by omega) _ + have he := congrArg (sectorExtract n 3) (pairHamiltonian_square v hv) + rw [sectorExtract_mul _ _ (fun x hx => pairHamiltonian_homogeneous v hx), + pairHamiltonian_sector_three v, map_add, map_add, pairHamiltonian_sector_three v, + h4, add_zero] at he + have h3 : sectorExtract n 3 (pairThreeTerm v) = + tripleWedgeMatrix v * ((tripleWedgeMatrix v).conjTranspose * tripleWedgeMatrix v - 1) * + (tripleWedgeMatrix v).conjTranspose := by + rw [Matrix.mul_sub, Matrix.sub_mul, Matrix.mul_one] + simp only [Matrix.mul_assoc] at he ⊢ + exact eq_sub_of_add_eq' he.symm + rw [← exteriorLift_sectorExtract (pairThreeTerm_mem_bodySpace v), h3] + +theorem normal_ordered_square {n : ℕ} {ι : Type*} [Fintype ι] [DecidableEq ι] + (v : ι → PairLabel n → ℂ) + (hv : ∀ p r, (∑ a, star (v p a) * v r a) = if p = r then 1 else 0) : + pairHamiltonian v * pairHamiltonian v = pairHamiltonian v + + exteriorLift (tripleWedgeMatrix v * + ((tripleWedgeMatrix v).conjTranspose * tripleWedgeMatrix v - 1) * + (tripleWedgeMatrix v).conjTranspose) + + exteriorLift (pairWedgeMatrix v * (pairWedgeMatrix v).conjTranspose) := by + rw [pairHamiltonian_square v hv, pairThreeTerm_eq_lift v hv, pairFourTerm_eq_lift] + +end LaughlinGap.Occupation + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct ComplexOrder + +lemma sum_increasing_pairs {n : ℕ} (f : Fin n → Fin n → ℝ) + (hs : ∀ i j, f i j = f j i) (hd : ∀ i, f i i = 0) : + 2 * (∑ a : PairLabel n, f a.val.1 a.val.2) = ∑ i, ∑ j, f i j := by + classical + have htri : (∑ a : PairLabel n, f a.val.1 a.val.2) = + ∑ i, ∑ j, if i < j then f i j else 0 := by + rw [← Finset.sum_subtype (Finset.univ.filter (fun a : Fin n × Fin n => a.1 < a.2)) + (by simp) (fun a => f a.1 a.2)] + simp only [Finset.sum_filter, Fintype.sum_prod_type] + have he (i j : Fin n) : f i j = + (if i < j then f i j else 0) + (if j < i then f j i else 0) := by + rcases lt_trichotomy i j with h | h | h + · simp [h, not_lt_of_gt h] + · subst j; simp [hd] + · simp [h, not_lt_of_gt h, hs i j] + rw [htri] + conv_rhs => arg 2; intro i; arg 2; intro j; rw [he i j] + simp only [Finset.sum_add_distrib] + rw [Finset.sum_comm (f := fun i j : Fin n => if j < i then f j i else 0)] + ring + +lemma sphericalExteriorPairCoefficient_eq_tensor (Q p : ℕ) (i j : Fin (Q+1)) : + sphericalExteriorPairCoefficient Q p i.val j.val = Real.sqrt 2 * pairCoefficient Q p i j := by + unfold sphericalExteriorPairCoefficient pairCoefficient + split_ifs + · have h : Real.sqrt 2 ≠ 0 := Real.sqrt_ne_zero'.mpr (by norm_num) + field_simp + · simp + +noncomputable def physicalPairForms (Q : ℕ) : Fin (2*Q-1) → PairLabel (Q+1) → ℂ := fun p a => + (sphericalExteriorPairCoefficient Q p.val a.val.1.val a.val.2.val : ℂ) + +lemma physicalPair_contraction (Q : ℕ) (p : Fin (2*Q-1)) : + pairContraction (physicalPairForms Q p) = localPair (Q+1) Q p.val := by + exact pairContraction_eq_pairAnnihilator (fun x y : Fin (Q+1) => + (sphericalExteriorPairCoefficient Q p.val x.val y.val : ℂ)) + +theorem physicalPairForms_orthonormal {Q : ℕ} (hQ : 2 ≤ Q) : + ∀ p r, (∑ a, star (physicalPairForms Q p a) * physicalPairForms Q r a) = + if p = r then 1 else 0 := by + intro p r + have hs : (Real.sqrt 2) ^ 2 = 2 := Real.sq_sqrt (by norm_num) + have hprod (a : PairLabel (Q+1)) : + star (physicalPairForms Q p a) * physicalPairForms Q r a = + ((2 * (pairCoefficient Q p.val a.val.1 a.val.2 * + pairCoefficient Q r.val a.val.1 a.val.2) : ℝ) : ℂ) := by + simp only [physicalPairForms, sphericalExteriorPairCoefficient_eq_tensor, + Complex.star_def, Complex.conj_ofReal, ← Complex.ofReal_mul] + congr 1 + linear_combination (pairCoefficient Q p.val a.val.1 a.val.2 * + pairCoefficient Q r.val a.val.1 a.val.2) * hs + simp_rw [hprod] + rw [← Complex.ofReal_sum, ← Finset.mul_sum] + have hsum := sum_increasing_pairs + (fun i j : Fin (Q+1) => pairCoefficient Q p.val i j * pairCoefficient Q r.val i j) + (by intro i j; rw [pairCoefficient_swap Q p.val j i, pairCoefficient_swap Q r.val j i]; ring) + (by intro i; simp [pairCoefficient]) + rw [hsum, ← pairVector_inner] + exact (orthonormal_iff_ite.mp (pairVector_orthonormal Q hQ)) p r + +noncomputable def physicalOccupationHamiltonian (Q : ℕ) : Module.End ℂ (Hilbert (Q+1)) := + pairHamiltonian (physicalPairForms Q) + +theorem physical_normal_ordered_square {Q : ℕ} (hQ : 2 ≤ Q) : + physicalOccupationHamiltonian Q * physicalOccupationHamiltonian Q = + physicalOccupationHamiltonian Q + + exteriorLift (tripleWedgeMatrix (physicalPairForms Q) * + ((tripleWedgeMatrix (physicalPairForms Q)).conjTranspose * + tripleWedgeMatrix (physicalPairForms Q) - 1) * + (tripleWedgeMatrix (physicalPairForms Q)).conjTranspose) + + exteriorLift (pairWedgeMatrix (physicalPairForms Q) * + (pairWedgeMatrix (physicalPairForms Q)).conjTranspose) := + normal_ordered_square _ (physicalPairForms_orthonormal hQ) + +end LaughlinGap.Occupation + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct ComplexOrder + +lemma pairContraction_eq_zero_of_degree_lt {n k : ℕ} (v : PairLabel n → ℂ) + {x : Hilbert n} (hx : Homogeneous k x) (hk : k < 2) : pairContraction v x = 0 := by + simp only [pairContraction, LinearMap.sum_apply, LinearMap.smul_apply] + apply Finset.sum_eq_zero + intro a _ + have he : basicPair a = word [a.val.1,a.val.2] := by + simp only [basicPair, word_cons, word_nil, one_mul] + rw [he, word_eq_zero_of_degree_lt _ hx (by simpa using hk), smul_zero] + +lemma pairHamiltonian_preserves_degree {n k : ℕ} {ι : Type*} [Fintype ι] + (v : ι → PairLabel n → ℂ) {x : Hilbert n} (hx : Homogeneous k x) : + Homogeneous k (pairHamiltonian v x) := by + by_cases hk : 2 ≤ k + · obtain ⟨l, rfl⟩ : ∃ l, k = l+2 := ⟨k-2, by omega⟩ + exact pairHamiltonian_homogeneous v hx + · have he : pairHamiltonian v x = 0 := by + simp only [pairHamiltonian, LinearMap.sum_apply, Module.End.mul_apply, + pairContraction_eq_zero_of_degree_lt _ hx (by omega), map_zero, Finset.sum_const_zero] + rw [he] + exact fun _ _ => rfl + +theorem physicalOccupationHamiltonian_positive (Q : ℕ) : + (physicalOccupationHamiltonian Q).IsPositive := by + apply LinearMap.isPositive_sum + intro p _ + exact LinearMap.isPositive_adjoint_comp_self _ + +theorem physicalOccupationHamiltonian_inner (Q : ℕ) (x : Hilbert (Q+1)) : + (inner ℂ x (physicalOccupationHamiltonian Q x)).re = + localPairEnergy (Q+1) (2*Q-1) Q x := by + simp only [physicalOccupationHamiltonian, pairHamiltonian, LinearMap.sum_apply, + inner_sum, Complex.re_sum, localPairEnergy] + apply Finset.sum_congr rfl + intro p _ + change (inner ℂ x ((pairContraction (physicalPairForms Q p)).adjoint + (pairContraction (physicalPairForms Q p) x))).re = _ + rw [LinearMap.adjoint_inner_right, physicalPair_contraction] + exact (norm_sq_eq_re_inner (𝕜 := ℂ) _).symm + +end LaughlinGap.Occupation + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct + +lemma numberOperator_homogeneous {n k : ℕ} {x : Hilbert n} (hx : Homogeneous k x) : + (∑ i : Fin n, creation i (annihilation i x)) = (k : ℂ) • x := by + ext A + rw [numberOperator_apply] + change (A.card : ℂ) * x A = (k : ℂ) * x A + by_cases hA : A.card = k + · rw [hA] + · rw [hx A hA, mul_zero, mul_zero] + +lemma sum_annihilation_norm_sq {n k : ℕ} {x : Hilbert n} (hx : Homogeneous k x) : + ∑ i : Fin n, ‖annihilation i x‖ ^ 2 = (k : ℝ) * ‖x‖ ^ 2 := by + have h := congrArg (fun y : Hilbert n => (inner ℂ x y).re) (numberOperator_homogeneous hx) + simp only [inner_sum, Complex.re_sum, ← annihilation_adjoint, + LinearMap.adjoint_inner_right, inner_smul_right, + Complex.mul_re, Complex.natCast_re, Complex.natCast_im, + zero_mul, sub_zero] at h + have hr (y : Hilbert n) : (inner ℂ y y).re = ‖y‖ ^ 2 := + (norm_sq_eq_re_inner (𝕜 := ℂ) y).symm + simpa only [hr] using h + +noncomputable def rawReadout (n N : ℕ) : Hilbert n →ₗ[ℂ] EuclideanSpace ℂ (Fin N → Fin n) where + toFun x := WithLp.toLp 2 (fun a => word (List.ofFn a) x ∅) + map_add' x y := by ext a; simp only [map_add, PiLp.add_apply] + map_smul' c x := by ext a; simp only [map_smul, RingHom.id_apply, PiLp.smul_apply] + +@[simp] lemma rawReadout_apply {n N : ℕ} (x : Hilbert n) (a : Fin N → Fin n) : + rawReadout n N x a = word (List.ofFn a) x ∅ := rfl + +lemma rawReadout_succ {n N : ℕ} (x : Hilbert n) (a : Fin (N+1) → Fin n) : + rawReadout n (N+1) x a = rawReadout n N (annihilation (a 0) x) (fun i => a i.succ) := by + simp only [rawReadout_apply, List.ofFn_succ, word_cons, Module.End.mul_apply] + +theorem rawReadout_norm_sq {n N : ℕ} {x : Hilbert n} (hx : Homogeneous N x) : + ‖rawReadout n N x‖ ^ 2 = (N.factorial : ℝ) * ‖x‖ ^ 2 := by + induction N generalizing x with + | zero => + rw [EuclideanSpace.norm_sq_eq] + simp only [Fintype.sum_unique, rawReadout_apply, List.ofFn_zero, word_nil, + Module.End.one_apply, Nat.factorial_zero, Nat.cast_one, one_mul] + rw [degree_zero_eq_vacuum hx, norm_smul, vacuum_norm, mul_one] + simp + | succ N ih => + rw [EuclideanSpace.norm_sq_eq] + rw [← (Fin.consEquiv (fun _ : Fin (N+1) => Fin n)).sum_comp] + simp only [Fintype.sum_prod_type] + change (∑ i : Fin n, ∑ a : Fin N → Fin n, + ‖rawReadout n (N+1) x (Fin.cons i a)‖ ^ 2) = _ + simp only [rawReadout_succ, Fin.cons_zero, Fin.cons_succ] + simp_rw [← EuclideanSpace.norm_sq_eq, ih (annihilation_homogeneous hx _)] + rw [← Finset.mul_sum, sum_annihilation_norm_sq hx, Nat.factorial_succ, Nat.cast_mul, + Nat.cast_add, Nat.cast_one] + ring + +noncomputable def normalizedReadout (n N : ℕ) : + Hilbert n →ₗ[ℂ] EuclideanSpace ℂ (Fin N → Fin n) := + ((Real.sqrt (N.factorial : ℝ))⁻¹ : ℂ) • rawReadout n N + +@[simp] lemma normalizedReadout_apply {n N : ℕ} (x : Hilbert n) (a : Fin N → Fin n) : + normalizedReadout n N x a = + ((Real.sqrt (N.factorial : ℝ))⁻¹ : ℂ) * word (List.ofFn a) x ∅ := rfl + +lemma normalizedReadout_norm_sq {n N : ℕ} {x : Hilbert n} (hx : Homogeneous N x) : + ‖normalizedReadout n N x‖ ^ 2 = ‖x‖ ^ 2 := by + have hf : 0 < (N.factorial : ℝ) := by exact_mod_cast Nat.factorial_pos N + have hs : 0 < Real.sqrt (N.factorial : ℝ) := Real.sqrt_pos.mpr hf + simp only [normalizedReadout, LinearMap.smul_apply, norm_smul, norm_inv, + Complex.norm_real, Real.norm_eq_abs, abs_of_pos hs, mul_pow, + inv_pow, Real.sq_sqrt hf.le, rawReadout_norm_sq hx] + field_simp + +end LaughlinGap.Occupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/Occupation.lean b/lean/OAI/Analysis/LaughlinGap/Occupation.lean new file mode 100644 index 0000000000000000000000000000000000000000..e769f12c86e76a87abd26070a5875b56c728427b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/Occupation.lean @@ -0,0 +1,607 @@ +import Mathlib + +namespace OAI + +/-! Occupation. -/ + +noncomputable section + + +namespace LaughlinGap +namespace Occupation +open scoped BigOperators InnerProduct + +abbrev Hilbert (n : ℕ) := EuclideanSpace ℂ (Finset (Fin n)) + +def flip {n : ℕ} (j : Fin n) : Equiv.Perm (Finset (Fin n)) := + let f : Finset (Fin n) → Finset (Fin n) := fun A => if j ∈ A then A.erase j else insert j A + have h : Function.Involutive f := by + intro A + by_cases hj : j ∈ A <;> simp [f, hj] + ⟨f, f, h, h⟩ + +@[simp] lemma flip_of_mem {n : ℕ} {j : Fin n} {A : Finset (Fin n)} (h : j ∈ A) : + flip j A = A.erase j := ite_eq_left h + +@[simp] lemma flip_of_not_mem {n : ℕ} {j : Fin n} {A : Finset (Fin n)} (h : j ∉ A) : + flip j A = insert j A := ite_eq_right h + +@[simp] lemma flip_flip {n : ℕ} (j : Fin n) (A : Finset (Fin n)) : flip j (flip j A) = A := + (flip j).left_inv A + +@[simp] lemma mem_flip_self {n : ℕ} (j : Fin n) (A : Finset (Fin n)) : + j ∈ flip j A ↔ j ∉ A := by + by_cases hj : j ∈ A <;> simp [hj] + +@[simp] lemma mem_flip_other {n : ℕ} {i j : Fin n} (hij : i ≠ j) (A : Finset (Fin n)) : + i ∈ flip j A ↔ i ∈ A := by + by_cases hj : j ∈ A <;> simp [hj, hij] + +lemma flip_comm {n : ℕ} (i j : Fin n) (A : Finset (Fin n)) : + flip i (flip j A) = flip j (flip i A) := by + by_cases hij : i = j + · subst j; rfl + ext k + by_cases hki : k = i + · subst k + simp [hij] + by_cases hkj : k = j + · subst k + simp [Ne.symm hij] + simp [hki, hkj] + +def sign {n : ℕ} (j : Fin n) (A : Finset (Fin n)) : ℂ := + (-1 : ℂ) ^ (A.filter (fun k => k < j)).card + +@[simp] lemma sign_norm {n : ℕ} (j : Fin n) (A : Finset (Fin n)) : ‖sign j A‖ = 1 := by + simp [sign, norm_pow] + +@[simp] lemma sign_star {n : ℕ} (j : Fin n) (A : Finset (Fin n)) : star (sign j A) = sign j A := by + simp [sign] + +@[simp] lemma sign_sq {n : ℕ} (j : Fin n) (A : Finset (Fin n)) : sign j A * sign j A = 1 := by + unfold sign + rw [← mul_pow] + norm_num + +lemma sign_insert {n : ℕ} (j : Fin n) {i : Fin n} {A : Finset (Fin n)} (hi : i ∉ A) : + sign j (insert i A) = if i < j then -sign j A else sign j A := by + by_cases hij : i < j + · simp [sign, Finset.filter_insert, hij, Finset.card_insert_of_notMem, hi, pow_succ] + · simp [sign, Finset.filter_insert, hij] + +lemma sign_flip {n : ℕ} (i j : Fin n) (A : Finset (Fin n)) : + sign j (flip i A) = if i < j then -sign j A else sign j A := by + by_cases hi : i ∈ A + · have h := sign_insert j (Finset.notMem_erase i A) + rw [Finset.insert_erase hi] at h + rw [flip_of_mem hi] + split_ifs with hij + · simp only [ite_eq_left hij] at h + rw [h, neg_neg] + · simpa [hij] using h.symm + · rw [flip_of_not_mem hi, sign_insert j hi] + +@[simp] lemma sign_flip_self {n : ℕ} (j : Fin n) (A : Finset (Fin n)) : + sign j (flip j A) = sign j A := by simp [sign_flip] + +@[simp] lemma sign_conj {n : ℕ} (j : Fin n) (A : Finset (Fin n)) : + starRingEnd ℂ (sign j A) = sign j A := by + simp only [sign, map_pow, map_neg, map_one] + +@[simp] lemma sign_erase_self {n : ℕ} (j : Fin n) (A : Finset (Fin n)) : + sign j (A.erase j) = sign j A := by + simp [sign, Finset.filter_erase] + +@[simp] lemma sign_insert_self {n : ℕ} (j : Fin n) (A : Finset (Fin n)) : + sign j (insert j A) = sign j A := by + simp [sign, Finset.filter_insert] + +noncomputable def transition {n : ℕ} (j : Fin n) (ε : Bool) : Hilbert n →ₗ[ℂ] Hilbert n where + toFun x := WithLp.toLp 2 (fun A => + if (decide (j ∈ A)) = ε then sign j A * x (flip j A) else 0) + map_add' x y := by + ext A + by_cases h : (decide (j ∈ A)) = ε <;> simp [h, mul_add] + map_smul' c x := by + ext A + by_cases h : (decide (j ∈ A)) = ε <;> simp [h, mul_left_comm] + +@[simp] lemma transition_apply {n : ℕ} (j : Fin n) (ε : Bool) (x : Hilbert n) + (A : Finset (Fin n)) : + transition j ε x A = if (decide (j ∈ A)) = ε then sign j A * x (flip j A) else 0 := rfl + +noncomputable abbrev annihilation {n : ℕ} (j : Fin n) := transition j false + +noncomputable abbrev creation {n : ℕ} (j : Fin n) := transition j true + +theorem transition_norm_le {n : ℕ} (j : Fin n) (ε : Bool) (x : Hilbert n) : + ‖transition j ε x‖ ≤ ‖x‖ := by + apply (sq_le_sq₀ (norm_nonneg _) (norm_nonneg _)).mp + rw [EuclideanSpace.norm_sq_eq, EuclideanSpace.norm_sq_eq] + calc + (∑ A, ‖transition j ε x A‖ ^ 2) ≤ ∑ A, ‖x (flip j A)‖ ^ 2 := by + apply Finset.sum_le_sum + intro A _ + rw [transition_apply] + split_ifs + · simp + · simp + _ = _ := Equiv.sum_comp (flip j) (fun A => ‖x A‖ ^ 2) + +theorem transition_adjoint {n : ℕ} (j : Fin n) (ε : Bool) : + (transition j ε).adjoint = transition j (!ε) := by + symm + rw [LinearMap.eq_adjoint_iff] + intro x y + rw [PiLp.inner_apply, PiLp.inner_apply] + rw [← Equiv.sum_comp (flip j) (fun A => inner ℂ (x A) (transition j ε y A))] + apply Finset.sum_congr rfl + intro A _ + cases ε <;> by_cases hj : j ∈ A <;> + simp [transition_apply, hj] <;> ring + +theorem transition_anticommute_of_ne {n : ℕ} {i j : Fin n} (hij : i ≠ j) + (ε η : Bool) : + (transition i ε ∘ₗ transition j η) = -(transition j η ∘ₗ transition i ε) := by + ext x A + change transition i ε (transition j η x) A = -transition j η (transition i ε x) A + simp only [transition_apply, mem_flip_other hij, mem_flip_other (Ne.symm hij), sign_flip] + rw [flip_comm j i A] + by_cases hi : (decide (i ∈ A)) = ε <;> by_cases hj : (decide (j ∈ A)) = η + · rcases lt_or_gt_of_ne hij with hlt | hgt + · simp [hi, hj, hlt, not_lt_of_ge (le_of_lt hlt)] + ring + · simp [hi, hj, hgt, not_lt_of_ge (le_of_lt hgt)] + ring + all_goals simp [hi, hj] + +theorem transition_square {n : ℕ} (j : Fin n) (ε : Bool) : + transition j ε ∘ₗ transition j ε = 0 := by + ext x A + change transition j ε (transition j ε x) A = 0 + cases ε <;> by_cases hj : j ∈ A <;> simp [transition_apply, hj] + +theorem transition_complement {n : ℕ} (j : Fin n) (ε : Bool) : + transition j ε ∘ₗ transition j (!ε) + transition j (!ε) ∘ₗ transition j ε = + LinearMap.id := by + ext x A + change transition j ε (transition j (!ε) x) A + + transition j (!ε) (transition j ε x) A = x A + cases ε <;> by_cases hj : j ∈ A <;> simp [transition_apply, hj, ← mul_assoc] + +theorem annihilation_creation_CAR {n : ℕ} (i j : Fin n) : + annihilation i ∘ₗ creation j + creation j ∘ₗ annihilation i = + if i = j then LinearMap.id else 0 := by + by_cases hij : i = j + · subst j + simpa using transition_complement i false + · rw [ite_eq_right hij, transition_anticommute_of_ne hij false true] + exact neg_add_cancel _ + +@[simp] lemma annihilation_adjoint {n : ℕ} (i : Fin n) : + (annihilation i).adjoint = creation i := transition_adjoint i false + +@[simp] lemma creation_adjoint {n : ℕ} (i : Fin n) : + (creation i).adjoint = annihilation i := transition_adjoint i true + +lemma adjoint_mul {n : ℕ} (A B : Module.End ℂ (Hilbert n)) : + (A * B).adjoint = B.adjoint * A.adjoint := LinearMap.adjoint_comp A B + +theorem annihilation_creation {n : ℕ} (i j : Fin n) : + annihilation i * creation j = (if i = j then 1 else 0) - creation j * annihilation i := by + exact eq_sub_of_add_eq (annihilation_creation_CAR i j) + +theorem annihilation_creation_mul {n : ℕ} (i j : Fin n) + (X : Module.End ℂ (Hilbert n)) : + annihilation i * (creation j * X) = + (if i = j then X else 0) - creation j * (annihilation i * X) := by + rw [← mul_assoc, annihilation_creation, sub_mul] + by_cases hij : i = j <;> simp [hij, mul_assoc] + +theorem pair_normal_order {n : ℕ} (i j k l : Fin n) : + annihilation j * annihilation i * creation k * creation l = + (if i = k ∧ j = l then 1 else 0) - + (if j = k ∧ i = l then 1 else 0) - + (if i = k then creation l * annihilation j else 0) + + (if j = k then creation l * annihilation i else 0) + + (if i = l then creation k * annihilation j else 0) - + (if j = l then creation k * annihilation i else 0) + + creation k * creation l * annihilation j * annihilation i := by + rw [mul_assoc, mul_assoc, annihilation_creation_mul] + simp only [mul_sub] + rw [annihilation_creation_mul] + rw [annihilation_creation] + simp only [mul_sub, mul_ite, mul_one, mul_zero, annihilation_creation_mul] + rw [annihilation_creation] + simp only [ite_and] + split_ifs <;> noncomm_ring + +theorem auxiliary_normal_order {n : ℕ} (i k : Fin n) + (A B : Module.End ℂ (Hilbert n)) : + (creation i * A).adjoint * (creation k * B) = + (if i = k then A.adjoint * B else 0) - + (annihilation k * A).adjoint * (annihilation i * B) := by + rw [adjoint_mul, creation_adjoint, mul_assoc, annihilation_creation_mul, + mul_sub, adjoint_mul, annihilation_adjoint, mul_assoc] + by_cases hik : i = k <;> simp [hik] + +noncomputable def auxiliaryRow {n : ℕ} {ι : Type*} [Fintype ι] (lam : ℝ) + (Bt : Module.End ℂ (Hilbert n)) (α : ι → ℝ) (i : ι → Fin n) + (A : ι → Module.End ℂ (Hilbert n)) : Module.End ℂ (Hilbert n) := + (lam : ℂ) • Bt + ∑ b, (α b : ℂ) • (creation (i b) * A b) + +theorem auxiliaryRow_square {n : ℕ} {ι : Type*} [Fintype ι] (lam : ℝ) + (Bt : Module.End ℂ (Hilbert n)) (α : ι → ℝ) (i : ι → Fin n) + (A : ι → Module.End ℂ (Hilbert n)) : + (auxiliaryRow lam Bt α i A).adjoint * auxiliaryRow lam Bt α i A = + ((lam ^ 2 : ℝ) : ℂ) • (Bt.adjoint * Bt) + + (∑ b, ((lam * α b : ℝ) : ℂ) • + ((annihilation (i b) * Bt).adjoint * A b + (A b).adjoint * (annihilation (i b) * Bt))) + + (∑ b, ∑ c, ((α b * α c : ℝ) : ℂ) • + (if i b = i c then (A b).adjoint * A c else 0)) - + (∑ b, ∑ c, ((α b * α c : ℝ) : ℂ) • + ((annihilation (i c) * A b).adjoint * (annihilation (i b) * A c))) := by + classical + have hcross (b : ι) : + Bt.adjoint * (creation (i b) * A b) = (annihilation (i b) * Bt).adjoint * A b := by + rw [adjoint_mul, annihilation_adjoint, mul_assoc] + rw [auxiliaryRow, map_add, map_sum] + simp only [map_smulₛₗ, Complex.conj_ofReal, add_mul, mul_add, + Finset.sum_mul, Finset.mul_sum, smul_mul_assoc, mul_smul_comm] + simp only [smul_add, Finset.smul_sum, smul_smul, Finset.sum_add_distrib] + rw [Finset.sum_comm (f := fun c b => ((α c : ℂ) * (α b : ℂ)) • (LinearMap.adjoint (creation (i b) * A b) * (creation (i c) * A c)))] + simp only [auxiliary_normal_order, smul_sub, Finset.sum_sub_distrib, hcross] + simp only [adjoint_mul, creation_adjoint, annihilation_adjoint, mul_assoc, + Complex.ofReal_mul, pow_two] + simp only [mul_comm] + abel + +theorem double_annihilation_norm_le {n : ℕ} (j k : Fin n) (x : Hilbert n) : + ‖annihilation k (annihilation j x)‖ ≤ ‖x‖ := + (transition_norm_le k false _).trans (transition_norm_le j false x) + +noncomputable def weight {n : ℕ} (d : Fin n → ℝ) (A : Finset (Fin n)) : ℝ := + ∏ j ∈ A, d j + +noncomputable def diagonal {n : ℕ} (d : Fin n → ℝ) : Hilbert n →ₗ[ℂ] Hilbert n where + toFun x := WithLp.toLp 2 (fun A => (weight d A : ℂ) * x A) + map_add' x y := by ext A; simp [mul_add] + map_smul' c x := by ext A; simp [mul_left_comm] + +@[simp] lemma diagonal_apply {n : ℕ} (d : Fin n → ℝ) (x : Hilbert n) (A : Finset (Fin n)) : + diagonal d x A = (weight d A : ℂ) * x A := rfl + +lemma weight_nonneg {n : ℕ} {d : Fin n → ℝ} (hd : ∀ j, 0 ≤ d j) (A : Finset (Fin n)) : + 0 ≤ weight d A := Finset.prod_nonneg (fun j _ => hd j) + +lemma weight_le_one {n : ℕ} {d : Fin n → ℝ} (hd₀ : ∀ j, 0 ≤ d j) (hd₁ : ∀ j, d j ≤ 1) + (A : Finset (Fin n)) : weight d A ≤ 1 := + Finset.prod_le_one₀ (fun index _ => hd₀ index) (fun index _ => hd₁ index) + +theorem diagonal_norm_le {n : ℕ} {d : Fin n → ℝ} (hd₀ : ∀ j, 0 ≤ d j) + (hd₁ : ∀ j, d j ≤ 1) (x : Hilbert n) : ‖diagonal d x‖ ≤ ‖x‖ := by + apply (sq_le_sq₀ (norm_nonneg _) (norm_nonneg _)).mp + simp only [EuclideanSpace.norm_sq_eq, diagonal_apply, norm_mul, Complex.norm_real, + Real.norm_of_nonneg (weight_nonneg hd₀ _)] + apply Finset.sum_le_sum + intro A _ + exact pow_le_pow_left₀ (mul_nonneg (weight_nonneg hd₀ A) (norm_nonneg _)) + (mul_le_of_le_one_left (norm_nonneg _) (weight_le_one hd₀ hd₁ A)) 2 + +@[simp] theorem diagonal_one {n : ℕ} : diagonal (fun _ : Fin n => (1 : ℝ)) = LinearMap.id := by + ext x A + simp [diagonal_apply, weight] + +theorem diagonal_comp {n : ℕ} (d e : Fin n → ℝ) : + diagonal d ∘ₗ diagonal e = diagonal (fun j => d j * e j) := by + ext x A + simp [diagonal_apply, weight, Finset.prod_mul_distrib, mul_assoc] + +theorem diagonal_comp_inv {n : ℕ} (d : Fin n → ℝ) (hd : ∀ j, d j ≠ 0) : + diagonal d ∘ₗ diagonal (fun j => (d j)⁻¹) = LinearMap.id := by + rw [diagonal_comp] + have h : (fun j => d j * (d j)⁻¹) = (fun _ : Fin n => (1 : ℝ)) := by + funext j + exact mul_inv_cancel₀ (hd j) + rw [h, diagonal_one] + +theorem annihilation_diagonal {n : ℕ} (d : Fin n → ℝ) (j : Fin n) : + annihilation j ∘ₗ diagonal d = (d j : ℂ) • (diagonal d ∘ₗ annihilation j) := by + ext x A + change annihilation j (diagonal d x) A = (d j : ℂ) * diagonal d (annihilation j x) A + by_cases hj : j ∈ A + · simp [transition_apply, hj] + · simp [transition_apply, hj, weight, Finset.prod_insert, mul_assoc, mul_comm, mul_left_comm] + +noncomputable def word {n : ℕ} : List (Fin n) → Hilbert n →ₗ[ℂ] Hilbert n + | [] => LinearMap.id + | j :: js => word js ∘ₗ annihilation j + +theorem word_diagonal {n : ℕ} (d : Fin n → ℝ) (js : List (Fin n)) : + word js ∘ₗ diagonal d = ((js.map (fun j => (d j : ℂ))).prod) • (diagonal d ∘ₗ word js) := by + induction js with + | nil => simp [word] + | cons j js ih => + rw [word, LinearMap.comp_assoc, annihilation_diagonal, + LinearMap.comp_smul, ← LinearMap.comp_assoc, ih] + simp only [List.map_cons, List.prod_cons, LinearMap.smul_comp, smul_smul, + LinearMap.comp_assoc] + +noncomputable def pairAnnihilator {n : ℕ} (v : Fin n → Fin n → ℂ) : + Module.End ℂ (Hilbert n) := + ∑ x, ∑ y, if x < y then star (v x y) • (annihilation y * annihilation x) else 0 + +lemma pairAnnihilator_smul_real {n : ℕ} (v : Fin n → Fin n → ℂ) (r : ℝ) : + pairAnnihilator (fun x y => (r : ℂ) * v x y) = (r : ℂ) • pairAnnihilator v := by + simp only [pairAnnihilator, Finset.smul_sum, smul_ite, smul_zero, star_mul, + Complex.star_def, Complex.conj_ofReal, smul_smul, mul_comm] + +theorem pairAnnihilator_diagonal {n : ℕ} (d : Fin n → ℝ) (v : Fin n → Fin n → ℂ) : + pairAnnihilator v * diagonal d = + diagonal d * pairAnnihilator (fun x y => (d x * d y : ℝ) * v x y) := by + simp only [pairAnnihilator, Finset.sum_mul, Finset.mul_sum] + apply Finset.sum_congr rfl + intro x _ + apply Finset.sum_congr rfl + intro y _ + by_cases hxy : x < y + · simp only [ite_eq_left hxy, smul_mul_assoc, mul_smul_comm, star_mul, Complex.ofReal_mul, + Complex.star_def, Complex.conj_ofReal] + have hw := word_diagonal d [x,y] + simp only [word, List.map_cons, List.prod_cons, List.map_nil, List.prod_nil, + mul_one, LinearMap.id_comp] at hw + change starRingEnd ℂ (v x y) • ((annihilation y ∘ₗ annihilation x) ∘ₗ diagonal d) = _ + rw [hw, smul_smul] + simp only [mul_comm] + rfl + · simp [hxy] + +theorem pairAnnihilator_conjugation {n : ℕ} (d : Fin n → ℝ) (hd : ∀ j, d j ≠ 0) + (v : Fin n → Fin n → ℂ) (r : ℝ) : + pairAnnihilator (fun x y => (r : ℂ) * ((d x * d y : ℝ) * v x y)) = + (r : ℂ) • (diagonal (fun j => (d j)⁻¹) * pairAnnihilator v * diagonal d) := by + rw [pairAnnihilator_smul_real] + congr 1 + rw [mul_assoc, pairAnnihilator_diagonal, ← mul_assoc] + have hd' : ∀ j, (d j)⁻¹ ≠ 0 := fun j => inv_ne_zero (hd j) + have hinv := diagonal_comp_inv (fun j => (d j)⁻¹) hd' + simp only [inv_inv] at hinv + change _ = (diagonal (fun j => (d j)⁻¹) ∘ₗ diagonal d) * _ + rw [hinv] + exact (one_mul _).symm + +theorem fourAnnihilator_conjugation {n : ℕ} (d : Fin n → ℝ) (hd : ∀ j, d j ≠ 0) + (v : Fin n → Fin n → ℂ) (r : ℝ) (j k : Fin n) : + annihilation k * annihilation j * + pairAnnihilator (fun x y => (r : ℂ) * ((d x * d y : ℝ) * v x y)) = + ((r / (d j * d k) : ℝ) : ℂ) • + (diagonal (fun s => (d s)⁻¹) * (annihilation k * annihilation j * pairAnnihilator v) * diagonal d) := by + rw [pairAnnihilator_conjugation d hd v r, mul_smul_comm, ← mul_assoc, ← mul_assoc] + have hw := word_diagonal (fun s => (d s)⁻¹) [j,k] + simp only [word, List.map_cons, List.prod_cons, List.map_nil, List.prod_nil, + mul_one, LinearMap.id_comp] at hw + change (r : ℂ) • ((((annihilation k ∘ₗ annihilation j) ∘ₗ diagonal (fun s => (d s)⁻¹)) * + pairAnnihilator v) * diagonal d) = _ + rw [hw] + simp only [← Module.End.mul_eq_comp, smul_mul_assoc, smul_smul, mul_assoc, + Complex.ofReal_inv, Complex.ofReal_mul, mul_inv_rev, div_eq_mul_inv, mul_comm] + +theorem pairAnnihilator_energy_transfer {n : ℕ} (d : Fin n → ℝ) + (hd₀ : ∀ j, 0 ≤ d j) (hd₁ : ∀ j, d j ≤ 1) + (v : Fin n → Fin n → ℂ) {r : ℝ} (hr : 1 ≤ r) (x : Hilbert n) : + ‖pairAnnihilator v (diagonal d x)‖ ^ 2 ≤ + ‖pairAnnihilator (fun i j => (r : ℂ) * ((d i * d j : ℝ) * v i j)) x‖ ^ 2 := by + have hc := LinearMap.congr_fun (pairAnnihilator_diagonal d v) x + change pairAnnihilator v (diagonal d x) = + diagonal d (pairAnnihilator (fun i j => (d i * d j : ℝ) * v i j) x) at hc + rw [hc, pairAnnihilator_smul_real, LinearMap.smul_apply, norm_smul, Complex.norm_real, + Real.norm_of_nonneg (by linarith : 0 ≤ r)] + apply pow_le_pow_left₀ (norm_nonneg _) + exact (diagonal_norm_le hd₀ hd₁ _).trans (le_mul_of_one_le_left (norm_nonneg _) hr) + +end Occupation +end LaughlinGap +namespace LaughlinGap +open scoped BigOperators Topology +open Filter + +noncomputable def orbitalDiagonalFactor (Q x : ℕ) : ℝ := + Real.sqrt ((Q.descFactorial x : ℝ) / (Q : ℝ)^x) + +noncomputable def pairRescalingFactor (Q p : ℕ) : ℝ := + Real.sqrt ((2 * (Q : ℝ))^p / ((2*Q-2).descFactorial p : ℝ)) + +noncomputable def sphericalExteriorPairCoefficient (Q p x y : ℕ) : ℝ := + if x + y = p + 1 then + ((x : ℝ) - (y : ℝ)) * Real.sqrt + ((Q.descFactorial x : ℝ) * (Q.descFactorial y : ℝ) * (p.factorial : ℝ) / + ((Q : ℝ) * ((2*Q-2).descFactorial p : ℝ) * (x.factorial : ℝ) * (y.factorial : ℝ))) + else 0 + +noncomputable def limitingExteriorPairCoefficient (p x y : ℕ) : ℝ := + if x + y = p + 1 then + ((x : ℝ) - (y : ℝ)) * Real.sqrt + ((p.factorial : ℝ) / ((2 : ℝ)^p * (x.factorial : ℝ) * (y.factorial : ℝ))) + else 0 + +lemma orbitalDiagonalFactor_nonneg (Q x : ℕ) : 0 ≤ orbitalDiagonalFactor Q x := + Real.sqrt_nonneg _ + +lemma orbitalDiagonalFactor_pos {Q x : ℕ} (hQ : 0 < Q) (hx : x ≤ Q) : + 0 < orbitalDiagonalFactor Q x := by + apply Real.sqrt_pos_of_pos + have : (0 : ℝ) < (Q.descFactorial x : ℝ) := by + exact_mod_cast Nat.descFactorial_pos.mpr hx + positivity + +lemma orbitalDiagonalFactor_le_one (Q x : ℕ) : orbitalDiagonalFactor Q x ≤ 1 := by + rw [orbitalDiagonalFactor, Real.sqrt_le_one] + by_cases hQ : (Q : ℝ)^x = 0 + · simp [hQ] + · rw [div_le_one (lt_of_le_of_ne (by positivity) (Ne.symm hQ))] + exact_mod_cast Nat.descFactorial_le_pow Q x + +lemma pairRescalingFactor_nonneg (Q p : ℕ) : 0 ≤ pairRescalingFactor Q p := + Real.sqrt_nonneg _ + +lemma one_le_pairRescalingFactor {Q p : ℕ} (hp : p ≤ 2*Q-2) : + 1 ≤ pairRescalingFactor Q p := by + rw [pairRescalingFactor, Real.one_le_sqrt] + have hd : (0 : ℝ) < ((2*Q-2).descFactorial p : ℝ) := by + exact_mod_cast Nat.descFactorial_pos.mpr hp + rw [le_div_iff₀ hd, one_mul] + exact_mod_cast (Nat.descFactorial_le_pow (2*Q-2) p).trans + (Nat.pow_le_pow_left (by omega : 2*Q-2 ≤ 2*Q) p) + +theorem sphericalExteriorPairCoefficient_factor {Q p : ℕ} (hQ : 0 < Q) + (hp : p ≤ 2*Q-2) (x y : ℕ) : + sphericalExteriorPairCoefficient Q p x y = + pairRescalingFactor Q p * orbitalDiagonalFactor Q x * orbitalDiagonalFactor Q y * + limitingExteriorPairCoefficient p x y := by + by_cases hxy : x + y = p + 1 + · have hQ0 : (Q : ℝ) ≠ 0 := by exact_mod_cast (Nat.ne_of_gt hQ) + have hD0 : ((2*Q-2).descFactorial p : ℝ) ≠ 0 := by + exact_mod_cast (Nat.ne_of_gt (Nat.descFactorial_pos.mpr hp)) + have hx0 : (x.factorial : ℝ) ≠ 0 := by exact_mod_cast x.factorial_ne_zero + have hy0 : (y.factorial : ℝ) ≠ 0 := by exact_mod_cast y.factorial_ne_zero + have hpow : (Q : ℝ)^x * (Q : ℝ)^y = (Q : ℝ)^p * Q := by + rw [← pow_add, hxy, pow_succ] + have hr : Real.sqrt + ((Q.descFactorial x : ℝ) * (Q.descFactorial y : ℝ) * (p.factorial : ℝ) / + ((Q : ℝ) * ((2*Q-2).descFactorial p : ℝ) * (x.factorial : ℝ) * (y.factorial : ℝ))) = + pairRescalingFactor Q p * orbitalDiagonalFactor Q x * orbitalDiagonalFactor Q y * + Real.sqrt ((p.factorial : ℝ) / ((2 : ℝ)^p * (x.factorial : ℝ) * (y.factorial : ℝ))) := by + apply (sq_eq_sq₀ (Real.sqrt_nonneg _) (by + unfold pairRescalingFactor orbitalDiagonalFactor; positivity)).mp + simp only [pairRescalingFactor, orbitalDiagonalFactor, mul_pow, + Real.sq_sqrt (show (0 : ℝ) ≤ (Q.descFactorial x : ℝ) * (Q.descFactorial y : ℝ) * (p.factorial : ℝ) / + ((Q : ℝ) * ((2*Q-2).descFactorial p : ℝ) * (x.factorial : ℝ) * (y.factorial : ℝ)) from by positivity), + Real.sq_sqrt (show (0 : ℝ) ≤ (2:ℝ)^p * (Q : ℝ)^p / ((2*Q-2).descFactorial p : ℝ) from by positivity), + Real.sq_sqrt (show (0 : ℝ) ≤ (Q.descFactorial x : ℝ) / (Q : ℝ)^x from by positivity), + Real.sq_sqrt (show (0 : ℝ) ≤ (Q.descFactorial y : ℝ) / (Q : ℝ)^y from by positivity), + Real.sq_sqrt (show (0 : ℝ) ≤ (p.factorial : ℝ) / ((2 : ℝ)^p * (x.factorial : ℝ) * (y.factorial : ℝ)) from by positivity)] + field_simp + calc + _ = (Q.descFactorial x : ℝ) * (Q.descFactorial y : ℝ) * ((Q:ℝ)^x * (Q:ℝ)^y) := by ring + _ = _ := by rw [hpow]; ring + simp only [sphericalExteriorPairCoefficient, limitingExteriorPairCoefficient, ite_eq_left hxy] + rw [hr] + ring + · simp [sphericalExteriorPairCoefficient, limitingExteriorPairCoefficient, hxy] + +lemma normalizedFallingFactorial_eq_prod (Q x : ℕ) : + (Q.descFactorial x : ℝ) / (Q : ℝ)^x = + ∏ k ∈ Finset.range x, ((Q - k : ℕ) : ℝ) / (Q : ℝ) := by + simp [Nat.descFactorial_eq_prod_range, Nat.cast_prod, Finset.prod_div_distrib] + +lemma normalizedFallingFactor_tendsto (k : ℕ) : + Tendsto (fun Q : ℕ => ((Q - k : ℕ) : ℝ) / (Q : ℝ)) atTop (𝓝 1) := by + have ht := (tendsto_const_nhds (x := (1 : ℝ))).sub + (tendsto_const_div_atTop_nhds_zero_nat (k : ℝ)) + simp only [sub_zero] at ht + apply ht.congr' + filter_upwards [eventually_ge_atTop (k+1)] with Q hQ + have hQ0 : (Q : ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + rw [Nat.cast_sub (by omega : k ≤ Q)] + field_simp + +theorem orbitalDiagonalFactor_tendsto (x : ℕ) : + Tendsto (fun Q : ℕ => orbitalDiagonalFactor Q x) atTop (𝓝 1) := by + have h := tendsto_finsetProd (Finset.range x) (fun k _ => normalizedFallingFactor_tendsto k) + simp only [Finset.prod_const_one, ← normalizedFallingFactorial_eq_prod] at h + simpa only [Real.sqrt_one, orbitalDiagonalFactor, Function.comp_def] using Real.continuous_sqrt.tendsto 1 |>.comp h + +lemma pairRescalingFactor_sq_eq_prod (Q p : ℕ) : + (2 * (Q : ℝ))^p / ((2*Q-2).descFactorial p : ℝ) = + ∏ k ∈ Finset.range p, (2*(Q : ℝ)) / ((2*Q-2-k : ℕ) : ℝ) := by + simp [Nat.descFactorial_eq_prod_range, Nat.cast_prod, Finset.prod_div_distrib] + +lemma rescalingFactor_tendsto (k : ℕ) : + Tendsto (fun Q : ℕ => (2*(Q : ℝ)) / ((2*Q-2-k : ℕ) : ℝ)) atTop (𝓝 1) := by + have ht : Tendsto (fun Q : ℕ => (2 : ℝ) / (2 - ((k : ℝ)+2)/Q)) atTop (𝓝 1) := by + have h := (tendsto_const_nhds (x := (2 : ℝ))).div + ((tendsto_const_nhds (x := (2 : ℝ))).sub + (tendsto_const_div_atTop_nhds_zero_nat ((k : ℝ)+2))) (by norm_num : (2 : ℝ)-0 ≠ 0) + simpa only [Pi.div_def, sub_zero, div_self (by norm_num : (2:ℝ) ≠ 0)] using h + apply ht.congr' + filter_upwards [eventually_ge_atTop (k+3)] with Q hQ + have hQ0 : (Q : ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + rw [Nat.cast_sub (by omega : k ≤ 2*Q-2), Nat.cast_sub (by omega : 2 ≤ 2*Q)] + push_cast + field_simp + ring + +theorem pairRescalingFactor_tendsto (p : ℕ) : + Tendsto (fun Q : ℕ => pairRescalingFactor Q p) atTop (𝓝 1) := by + have h := tendsto_finsetProd (Finset.range p) (fun k _ => rescalingFactor_tendsto k) + simp only [Finset.prod_const_one, ← pairRescalingFactor_sq_eq_prod] at h + simpa only [Real.sqrt_one, pairRescalingFactor, Function.comp_def] using Real.continuous_sqrt.tendsto 1 |>.comp h + +theorem sphericalExteriorPairCoefficient_tendsto (p x y : ℕ) : + Tendsto (fun Q : ℕ => sphericalExteriorPairCoefficient Q p x y) atTop + (𝓝 (limitingExteriorPairCoefficient p x y)) := by + have h := (((pairRescalingFactor_tendsto p).mul (orbitalDiagonalFactor_tendsto x)).mul + (orbitalDiagonalFactor_tendsto y)).mul_const (limitingExteriorPairCoefficient p x y) + simp only [one_mul] at h + apply h.congr' + filter_upwards [eventually_ge_atTop (p+2)] with Q hQ + exact (sphericalExteriorPairCoefficient_factor (by omega) (by omega) x y).symm + +end LaughlinGap + +namespace LaughlinGap.Occupation +open scoped BigOperators Topology +open Filter + +noncomputable def diagonalCLM {n : ℕ} (d : Fin n → ℝ) : Hilbert n →L[ℂ] Hilbert n := + LinearMap.toContinuousLinearMap (diagonal d) + +@[simp] lemma diagonalCLM_apply {n : ℕ} (d : Fin n → ℝ) (x : Hilbert n) : + diagonalCLM d x = diagonal d x := rfl + +lemma diagonalCLM_eq_matrix {n : ℕ} (d : Fin n → ℝ) : + diagonalCLM d = Matrix.toEuclideanCLM (𝕜 := ℂ) (n := Finset (Fin n)) (Matrix.diagonal (fun A => (weight d A : ℂ))) := by + ext x A + change (diagonalCLM d x).ofLp A = _ + rw [Matrix.ofLp_toEuclideanCLM, Matrix.mulVec_diagonal] + rfl + +theorem diagonalCLM_tendsto {n : ℕ} {ι : Type*} {l : Filter ι} + {d : ι → Fin n → ℝ} {e : Fin n → ℝ} + (hd : ∀ j, Tendsto (fun q => d q j) l (𝓝 (e j))) : + Tendsto (fun q => diagonalCLM (d q)) l (𝓝 (diagonalCLM e)) := by + have hw (A : Finset (Fin n)) : Tendsto (fun q => weight (d q) A) l (𝓝 (weight e A)) := + tendsto_finsetProd A (fun j _ => hd j) + have hM : Tendsto (fun q => Matrix.diagonal (fun A => (weight (d q) A : ℂ))) l + (𝓝 (Matrix.diagonal (fun A => (weight e A : ℂ)))) := by + apply tendsto_pi_nhds.mpr + intro A + apply tendsto_pi_nhds.mpr + intro B + by_cases hAB : A = B + · subst B + simpa only [Matrix.diagonal_apply_eq, Function.comp_def] using + Complex.continuous_ofReal.continuousAt.tendsto.comp (hw A) + · simpa [Matrix.diagonal, hAB] using (tendsto_const_nhds (x := (0 : ℂ))) + have hc : Continuous (Matrix.toEuclideanCLM (𝕜 := ℂ) (n := Finset (Fin n))) := + (Matrix.toEuclideanCLM (𝕜 := ℂ) (n := Finset (Fin n))).toAlgEquiv.toLinearMap.continuous_of_finiteDimensional + simp_rw [diagonalCLM_eq_matrix] + exact hc.continuousAt.tendsto.comp hM + +@[simp] lemma diagonalCLM_one {n : ℕ} : diagonalCLM (fun _ : Fin n => (1 : ℝ)) = 1 := by + ext x A + simp [diagonalCLM_apply, diagonal_one] + +theorem diagonalCLM_inv_tendsto_one {n : ℕ} {ι : Type*} {l : Filter ι} + {d : ι → Fin n → ℝ} (hd : ∀ j, Tendsto (fun q => d q j) l (𝓝 1)) : + Tendsto (fun q => diagonalCLM (fun j => (d q j)⁻¹)) l (𝓝 1) := by + have hi (j : Fin n) : Tendsto (fun q => (d q j)⁻¹) l (𝓝 1) := by + simpa using (hd j).inv₀ (by norm_num : (1 : ℝ) ≠ 0) + simpa using diagonalCLM_tendsto hi + +end LaughlinGap.Occupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/PairDecomposition.lean b/lean/OAI/Analysis/LaughlinGap/PairDecomposition.lean new file mode 100644 index 0000000000000000000000000000000000000000..26e3796fd73e7be30e20810fc26949a84fa2a547 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/PairDecomposition.lean @@ -0,0 +1,126 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.HighestRatios +import OAI.Analysis.LaughlinGap.IntertwiningSpin +import OAI.Analysis.LaughlinGap.NormalOrder +import OAI.Analysis.LaughlinGap.PairSpin + +namespace OAI + +/-! Pair Decomposition. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators InnerProduct ComplexOrder +open Occupation + +noncomputable def tensorSwap (Q : ℕ) : LadderMap (tensorSpin Q Q) (tensorSpin Q Q) where + toLinearMap := { + toFun := fun x ij => x (ij.2,ij.1) + map_add' := by intros; rfl + map_smul' := by intros; rfl } + lower x := by + funext ⟨i,j⟩ + change lowering Q (fun i => x (j,i)) i + lowering Q (fun j => x (j,i)) j = + lowering Q (fun j => x (j,i)) j + lowering Q (fun i => x (j,i)) i + ring + raise x := by + funext ⟨i,j⟩ + change raising Q (fun i => x (j,i)) i + raising Q (fun j => x (j,i)) j = + raising Q (fun j => x (j,i)) j + raising Q (fun i => x (j,i)) i + ring + +lemma highestCoefficient_last_equal_spin {Q r : ℕ} (hr : r ≤ Q) : + highestCoefficient Q Q r r = (-1 : ℝ)^r * highestCoefficient Q Q r 0 := by + have hf : (Q.descFactorial r : ℝ) ≠ 0 := by + exact_mod_cast (Nat.descFactorial_pos.mpr hr).ne' + rw [highestCoefficient_last (by simpa using hr), div_self hf, Real.sqrt_one, mul_one, + mul_comm] + +theorem coupledTensor_swap {Q r l : ℕ} (hr : r ≤ Q) (hl : l ≤ Q+Q-2*r) + (i j : Fin (Q+1)) : + coupledTensor Q Q r l (j,i) = (-1 : ℝ)^r * coupledTensor Q Q r l (i,j) := by + have h0 := tensorSpin_schur (by simpa using hr : r ≤ min Q Q) + (Nat.zero_le _) (tensorSwap Q) + let r' : Fin (Q+1) := ⟨r, by omega⟩ + have hc := congrFun h0 (0,r') + simp only [coupledTensor_zero, tensorSwap, highestTensor, LinearMap.coe_mk, + AddHom.coe_mk, Fin.val_zero, r', zero_add, add_zero, ite_true, Pi.smul_apply, + smul_eq_mul] at hc + have hb : dotProduct (highestTensor Q Q r) + ((tensorSwap Q).toLinearMap (highestTensor Q Q r)) = (-1 : ℝ)^r := by + apply mul_right_cancel₀ (highestCoefficient_zero_ne (by simpa using hr : r ≤ min Q Q)) + exact hc.symm.trans (highestCoefficient_last_equal_spin hr) + have h := congrFun (tensorSpin_schur (by simpa using hr : r ≤ min Q Q) hl + (tensorSwap Q)) (i,j) + rw [hb] at h + exact h + +noncomputable def orbitalPairCoefficient (Q r l : ℕ) (a : PairLabel (Q+1)) : ℝ := + Real.sqrt 2 * coupledTensor Q Q r l (a.val.1,a.val.2) + +lemma coupledTensor_antisymmetric {Q r l : ℕ} (hr : r ≤ Q) (hl : l ≤ Q+Q-2*r) + (hodd : Odd r) (i j : Fin (Q+1)) : + coupledTensor Q Q r l (j,i) = -coupledTensor Q Q r l (i,j) := by + rw [coupledTensor_swap hr hl, hodd.neg_one_pow, neg_one_mul] + +lemma coupledTensor_diag_zero {Q r l : ℕ} (hr : r ≤ Q) (hl : l ≤ Q+Q-2*r) + (hodd : Odd r) (i : Fin (Q+1)) : coupledTensor Q Q r l (i,i) = 0 := by + have h := coupledTensor_antisymmetric hr hl hodd i i + linarith + +lemma orbitalPair_inner {Q r s l k : ℕ} (hr : r ≤ Q) (hs : s ≤ Q) + (hl : l ≤ Q+Q-2*r) (hk : k ≤ Q+Q-2*s) (hro : Odd r) (hso : Odd s) : + (∑ a : PairLabel (Q+1), orbitalPairCoefficient Q r l a * orbitalPairCoefficient Q s k a) = + dotProduct (coupledTensor Q Q r l) (coupledTensor Q Q s k) := by + have hsum := sum_increasing_pairs + (fun i j : Fin (Q+1) => coupledTensor Q Q r l (i,j) * coupledTensor Q Q s k (i,j)) + (by intro i j; rw [coupledTensor_antisymmetric hr hl hro j i, + coupledTensor_antisymmetric hs hk hso j i]; ring) + (by intro i; rw [coupledTensor_diag_zero hr hl hro i, zero_mul]) + have he (a : PairLabel (Q+1)) : + orbitalPairCoefficient Q r l a * orbitalPairCoefficient Q s k a = + 2 * (coupledTensor Q Q r l (a.val.1,a.val.2) * + coupledTensor Q Q s k (a.val.1,a.val.2)) := by + unfold orbitalPairCoefficient + linear_combination (coupledTensor Q Q r l (a.val.1,a.val.2) * + coupledTensor Q Q s k (a.val.1,a.val.2)) * + Real.sq_sqrt (by norm_num : (0:ℝ) ≤ 2) + simp only [he, ← Finset.mul_sum] + rw [hsum] + simp only [dotProduct, Fintype.sum_prod_type] + +theorem orbitalPair_orthonormal {Q r s : ℕ} (hr : r ≤ Q) (hs : s ≤ Q) + (hro : Odd r) (hso : Odd s) + (l : Fin (Q+Q-2*r+1)) (k : Fin (Q+Q-2*s+1)) : + (∑ a : PairLabel (Q+1), orbitalPairCoefficient Q r l.val a * + orbitalPairCoefficient Q s k.val a) = if r=s ∧ l.val=k.val then 1 else 0 := by + rw [orbitalPair_inner hr hs (Nat.le_of_lt_succ l.isLt) (Nat.le_of_lt_succ k.isLt) hro hso] + by_cases hrs : r=s + · subst s + by_cases hlk : l.val=k.val + · have : l=k := Fin.ext hlk + subst k + simp only [and_self, ite_true] + exact coupledTensor_norm_sq (by simpa using hr) (Nat.le_of_lt_succ l.isLt) + · rw [ite_eq_right (by simpa using hlk)] + exact coupledTensor_orthogonal_same_spin (by simpa using hr) + (Nat.le_of_lt_succ l.isLt) (Nat.le_of_lt_succ k.isLt) hlk + · rw [ite_eq_right (by simp [hrs])] + exact coupledTensor_orthogonal_distinct_spin (by simpa using hr) (by simpa using hs) + (Nat.le_of_lt_succ l.isLt) (Nat.le_of_lt_succ k.isLt) hrs + +theorem orbitalPairCoefficient_one {Q : ℕ} (hQ : 2 ≤ Q) (l : Fin (2*Q-2+1)) + (a : PairLabel (Q+1)) : + orbitalPairCoefficient Q 1 l.val a = + sphericalExteriorPairCoefficient Q l.val a.val.1 a.val.2 := by + unfold orbitalPairCoefficient + rw [← physicalPairTensor_eq_coupled hQ (Nat.le_of_lt_succ l.isLt)] + exact (sphericalExteriorPairCoefficient_eq_tensor Q l.val a.val.1 a.val.2).symm + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/PairEndpoints.lean b/lean/OAI/Analysis/LaughlinGap/PairEndpoints.lean new file mode 100644 index 0000000000000000000000000000000000000000..e1d87ea6b83eb46f2c0500bb41fbe479ae71c38b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/PairEndpoints.lean @@ -0,0 +1,82 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SpectralBound + +namespace OAI + +/-! Pair Endpoints. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators + +lemma pairCoefficient_one {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + pairCoefficient Q z ⟨1,by omega⟩ ⟨z,by omega⟩ = + (1-(z : ℝ))*Real.sqrt (fallingRatio Q z)/Real.sqrt 2 := by + have hn : 0 < ((2*Q-2).descFactorial z : ℝ) := by + exact_mod_cast Nat.descFactorial_pos.mpr (by omega : z ≤ 2*Q-2) + have hf : (0 : ℝ) < z.factorial := by exact_mod_cast z.factorial_pos + have hq : (0 : ℝ) < Q := by exact_mod_cast (by omega : 0 < Q) + unfold pairCoefficient + rw [ite_eq_left (by simp [Nat.add_comm] : 1+z=z+1)] + simp only [Nat.descFactorial_one, Nat.factorial_one, Nat.cast_one, mul_one] + congr 2 + congr 1 + unfold fallingRatio + field_simp + +lemma pairCoefficient_zero_succ {Q a : ℕ} (hQ : 2 ≤ Q) (hz : a+1 ≤ Q) : + pairCoefficient Q a 0 ⟨a+1,by omega⟩ = + -Real.sqrt (((a : ℝ)+1)*((Q-1).descFactorial a : ℝ)/ + ((2*Q-2).descFactorial a : ℝ))/Real.sqrt 2 := by + have hn : 0 < ((2*Q-2).descFactorial a : ℝ) := by + exact_mod_cast Nat.descFactorial_pos.mpr (by omega : a ≤ 2*Q-2) + have hf : (0 : ℝ) < a.factorial := by exact_mod_cast a.factorial_pos + have hq : (0 : ℝ) < Q := by exact_mod_cast (by omega : 0 < Q) + have ha : (0 : ℝ) < (a : ℝ)+1 := by positivity + have hdesc : Q.descFactorial (a+1) = Q*(Q-1).descFactorial a := by + have h := Nat.succ_descFactorial_succ (Q-1) a + simpa only [Nat.sub_add_cancel (by omega : 1 ≤ Q)] using h + simp only [pairCoefficient, Fin.val_zero, Nat.zero_add, ite_true, + Nat.cast_zero, Nat.cast_add, Nat.cast_one, zero_sub, Nat.descFactorial_zero, + Nat.factorial_zero, hdesc, Nat.factorial_succ, Nat.cast_mul, one_mul, mul_one] + congr 1 + rw [neg_mul, neg_inj] + rw [show Real.sqrt (((a : ℝ)+1)*((Q-1).descFactorial a : ℝ)/ + ((2*Q-2).descFactorial a : ℝ)) = + ((a : ℝ)+1)*Real.sqrt (((Q : ℝ)*((Q-1).descFactorial a : ℝ)*(a.factorial : ℝ))/ + ((Q : ℝ)*((2*Q-2).descFactorial a : ℝ)*(((a : ℝ)+1)*(a.factorial : ℝ)))) by + rw [← Real.sqrt_sq ha.le, ← Real.sqrt_mul (sq_nonneg _)] + congr 1 + rw [Real.sqrt_sq ha.le] + field_simp] + +lemma pairCoefficient_zero_formula {Q : ℕ} (hQ : 2 ≤ Q) (i j : Fin (Q+1)) : + pairCoefficient Q 0 i j = + if i=⟨1,by omega⟩ ∧ j=0 then 1/Real.sqrt 2 + else if i=0 ∧ j=⟨1,by omega⟩ then -1/Real.sqrt 2 else 0 := by + have h0 : fallingRatio Q 0 = 1 := by simp [fallingRatio] + by_cases hi1 : i=⟨1,by omega⟩ ∧ j=0 + · rcases hi1 with ⟨rfl,rfl⟩ + rw [ite_eq_left ⟨rfl,rfl⟩] + simpa only [Fin.mk_zero, h0, Nat.cast_zero, sub_zero, Real.sqrt_one, mul_one] using + pairCoefficient_one hQ (Nat.zero_le Q) + · rw [ite_eq_right hi1] + by_cases hi0 : i=0 ∧ j=⟨1,by omega⟩ + · rcases hi0 with ⟨rfl,rfl⟩ + rw [ite_eq_left ⟨rfl,rfl⟩] + simpa only [Nat.cast_zero, zero_add, Nat.descFactorial_zero, Nat.cast_one, + mul_one, div_one, Real.sqrt_one] using + pairCoefficient_zero_succ hQ (by omega : 0+1 ≤ Q) + · rw [ite_eq_right hi0, pairCoefficient, ite_eq_right] + intro h + rcases (show i.val=1 ∧ j.val=0 ∨ i.val=0 ∧ j.val=1 by omega) with hh | hh + · exact hi1 ⟨Fin.ext hh.1,Fin.ext hh.2⟩ + · exact hi0 ⟨Fin.ext hh.1,Fin.ext hh.2⟩ + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/PairEnergy.lean b/lean/OAI/Analysis/LaughlinGap/PairEnergy.lean new file mode 100644 index 0000000000000000000000000000000000000000..9551000898b77ab838175559d0b852311e24d0d1 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/PairEnergy.lean @@ -0,0 +1,578 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Occupation +import OAI.Analysis.LaughlinGap.SpectralBound + +namespace OAI + +/-! Pair Energy. -/ + +noncomputable section + + +namespace LaughlinGap.Occupation +open scoped BigOperators Topology +open Filter + +noncomputable def localPair (n Q p : ℕ) : Module.End ℂ (Hilbert n) := + pairAnnihilator (fun x y => (sphericalExteriorPairCoefficient Q p x.val y.val : ℂ)) + +noncomputable def localPairStar (n p : ℕ) : Module.End ℂ (Hilbert n) := + pairAnnihilator (fun x y => (limitingExteriorPairCoefficient p x.val y.val : ℂ)) + +noncomputable def localDelta (n Q : ℕ) : Hilbert n →L[ℂ] Hilbert n := + diagonalCLM (fun x => orbitalDiagonalFactor Q x.val) + +noncomputable def localDeltaInv (n Q : ℕ) : Hilbert n →L[ℂ] Hilbert n := + diagonalCLM (fun x => (orbitalDiagonalFactor Q x.val)⁻¹) + +lemma localPair_eq_factored {n Q p : ℕ} (hQ : 0 < Q) (hp : p ≤ 2*Q-2) : + localPair n Q p = pairAnnihilator (fun x y : Fin n => + (pairRescalingFactor Q p : ℂ) * + ((orbitalDiagonalFactor Q x.val * orbitalDiagonalFactor Q y.val : ℝ) * + (limitingExteriorPairCoefficient p x.val y.val : ℂ))) := by + unfold localPair + congr 1 + funext x y + rw [sphericalExteriorPairCoefficient_factor hQ hp] + push_cast + ring + +theorem localPair_conjugation {n Q p : ℕ} (hQ : 0 < Q) (hn : n ≤ Q+1) + (hp : p ≤ 2*Q-2) : + localPair n Q p = (pairRescalingFactor Q p : ℂ) • + ((localDeltaInv n Q).toLinearMap * localPairStar n p * (localDelta n Q).toLinearMap) := by + rw [localPair_eq_factored hQ hp] + apply pairAnnihilator_conjugation + intro j + exact ne_of_gt (orbitalDiagonalFactor_pos hQ (by have := j.is_lt; omega)) + +theorem localFour_conjugation {n Q p : ℕ} (hQ : 0 < Q) (hn : n ≤ Q+1) + (hp : p ≤ 2*Q-2) (j k : Fin n) : + annihilation k * annihilation j * localPair n Q p = + ((pairRescalingFactor Q p / (orbitalDiagonalFactor Q j.val * + orbitalDiagonalFactor Q k.val) : ℝ) : ℂ) • + ((localDeltaInv n Q).toLinearMap * + (annihilation k * annihilation j * localPairStar n p) * (localDelta n Q).toLinearMap) := by + rw [localPair_eq_factored hQ hp] + apply fourAnnihilator_conjugation + intro j + exact ne_of_gt (orbitalDiagonalFactor_pos hQ (by have := j.is_lt; omega)) + +theorem localDelta_norm_le (n Q : ℕ) (x : Hilbert n) : ‖localDelta n Q x‖ ≤ ‖x‖ := + diagonal_norm_le (fun j => orbitalDiagonalFactor_nonneg Q j.val) + (fun j => orbitalDiagonalFactor_le_one Q j.val) x + +theorem localDelta_tendsto (n : ℕ) : + Tendsto (localDelta n) atTop (𝓝 1) := by + change Tendsto (fun Q => diagonalCLM (fun j : Fin n => orbitalDiagonalFactor Q j.val)) atTop (𝓝 1) + simpa only [diagonalCLM_one] using + diagonalCLM_tendsto (fun j : Fin n => orbitalDiagonalFactor_tendsto j.val) + +theorem localDeltaInv_tendsto (n : ℕ) : + Tendsto (localDeltaInv n) atTop (𝓝 1) := + diagonalCLM_inv_tendsto_one (fun j => orbitalDiagonalFactor_tendsto j.val) + +theorem localDelta_mul_inv {n Q : ℕ} (hQ : 0 < Q) (hn : n ≤ Q+1) : + localDelta n Q * localDeltaInv n Q = 1 := by + have h := diagonal_comp_inv (fun j : Fin n => orbitalDiagonalFactor Q j.val) + (fun j => ne_of_gt (orbitalDiagonalFactor_pos hQ (by have := j.is_lt; omega))) + ext x A + exact congrArg (fun z : Hilbert n => z A) (LinearMap.congr_fun h x) + +noncomputable def localPairEnergyStar (n L : ℕ) (x : Hilbert n) : ℝ := + ∑ p : Fin L, ‖localPairStar n p.val x‖ ^ 2 + +noncomputable def localPairEnergy (n L Q : ℕ) (x : Hilbert n) : ℝ := + ∑ p : Fin L, ‖localPair n Q p.val x‖ ^ 2 + +theorem localPairEnergy_transfer {n L Q : ℕ} (hQ : 0 < Q) (hL : L ≤ 2*Q-1) + (x : Hilbert n) : + localPairEnergyStar n L (localDelta n Q x) ≤ localPairEnergy n L Q x := by + apply Finset.sum_le_sum + intro p _ + have hp : p.val ≤ 2*Q-2 := by have := p.is_lt; omega + rw [localPair_eq_factored hQ hp] + exact pairAnnihilator_energy_transfer _ + (fun j => orbitalDiagonalFactor_nonneg Q j.val) + (fun j => orbitalDiagonalFactor_le_one Q j.val) _ (one_le_pairRescalingFactor hp) x + +end LaughlinGap.Occupation + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct + +def joinEquiv (n m : ℕ) : (Finset (Fin n) × Finset (Fin m)) ≃ Finset (Fin (n+m)) := + Finset.sumEquiv.toEquiv.symm.trans finSumFinEquiv.finsetCongr + +def join {n m : ℕ} (A : Finset (Fin n)) (R : Finset (Fin m)) : Finset (Fin (n+m)) := + joinEquiv n m (A,R) + +lemma join_eq_map {n m : ℕ} (A : Finset (Fin n)) (R : Finset (Fin m)) : + join A R = Finset.map finSumFinEquiv.toEmbedding (A.disjSum R) := rfl + +@[simp] lemma mem_join_left {n m : ℕ} (j : Fin n) (A : Finset (Fin n)) (R : Finset (Fin m)) : + Fin.castAdd m j ∈ join A R ↔ j ∈ A := by + rw [join_eq_map, ← finSumFinEquiv_apply_left] + simp + +@[simp] lemma mem_join_right {n m : ℕ} (j : Fin m) (A : Finset (Fin n)) (R : Finset (Fin m)) : + Fin.natAdd n j ∈ join A R ↔ j ∈ R := by + rw [join_eq_map, ← finSumFinEquiv_apply_right] + simp + +@[simp] lemma join_card {n m : ℕ} (A : Finset (Fin n)) (R : Finset (Fin m)) : + (join A R).card = A.card + R.card := by simp [join_eq_map] + +lemma prefix_ne_suffix {n m : ℕ} (i : Fin n) (j : Fin m) : + Fin.castAdd m i ≠ Fin.natAdd n j := by + intro h + have hv := congrArg Fin.val h + have := i.is_lt + simp only [Fin.val_castAdd, Fin.val_natAdd] at hv + omega + +lemma join_erase_left {n m : ℕ} (j : Fin n) (A : Finset (Fin n)) (R : Finset (Fin m)) : + join (A.erase j) R = (join A R).erase (Fin.castAdd m j) := by + ext x + obtain ⟨x, rfl⟩ := finSumFinEquiv.surjective x + cases x with + | inl i => simp + | inr i => simp [Ne.symm (prefix_ne_suffix j i)] + +lemma join_insert_left {n m : ℕ} (j : Fin n) (A : Finset (Fin n)) (R : Finset (Fin m)) : + join (insert j A) R = insert (Fin.castAdd m j) (join A R) := by + ext x + obtain ⟨x, rfl⟩ := finSumFinEquiv.surjective x + cases x with + | inl i => simp + | inr i => simp [Ne.symm (prefix_ne_suffix j i)] + +lemma join_flip_left {n m : ℕ} (j : Fin n) (A : Finset (Fin n)) (R : Finset (Fin m)) : + join (flip j A) R = flip (Fin.castAdd m j) (join A R) := by + by_cases hi : j ∈ A + · simp [hi, join_erase_left] + · simp [hi, join_insert_left] + +lemma join_filter_prefix {n m : ℕ} (j : Fin n) (A : Finset (Fin n)) (R : Finset (Fin m)) : + (join A R).filter (fun k => k < Fin.castAdd m j) = + join (A.filter (fun k => k < j)) (∅ : Finset (Fin m)) := by + ext x + obtain ⟨x, rfl⟩ := finSumFinEquiv.surjective x + cases x with + | inl i => + simp only [finSumFinEquiv_apply_left, Finset.mem_filter, mem_join_left] + rfl + | inr i => + have h : ¬ Fin.natAdd n i < Fin.castAdd m j := by + simp only [Fin.lt_def, Fin.val_natAdd, Fin.val_castAdd] + have := j.is_lt + omega + simp [h] + +theorem sign_join_left {n m : ℕ} (j : Fin n) (A : Finset (Fin n)) (R : Finset (Fin m)) : + sign (Fin.castAdd m j) (join A R) = sign j A := by + simp [sign, join_filter_prefix] + +noncomputable def slice {n m : ℕ} (R : Finset (Fin m)) : Hilbert (n+m) →ₗ[ℂ] Hilbert n where + toFun x := WithLp.toLp 2 (fun A => x (join A R)) + map_add' _ _ := rfl + map_smul' _ _ := rfl + +@[simp] lemma slice_apply {n m : ℕ} (R : Finset (Fin m)) (x : Hilbert (n+m)) + (A : Finset (Fin n)) : slice R x A = x (join A R) := rfl + +theorem norm_sq_eq_sum_slice {n m : ℕ} (x : Hilbert (n+m)) : + ‖x‖ ^ 2 = ∑ R : Finset (Fin m), ‖slice R x‖ ^ 2 := by + simp only [EuclideanSpace.norm_sq_eq, slice_apply] + rw [← Equiv.sum_comp (joinEquiv n m) (fun A => ‖x A‖ ^ 2), Fintype.sum_prod_type, + Finset.sum_comm] + rfl + +lemma inner_eq_sum_slice {n m : ℕ} (x y : Hilbert (n+m)) : + inner ℂ x y = ∑ R : Finset (Fin m), inner ℂ (slice R x) (slice R y) := by + simp only [PiLp.inner_apply, slice_apply] + rw [← Equiv.sum_comp (joinEquiv n m) (fun A => inner ℂ (x A) (y A)), Fintype.sum_prod_type, + Finset.sum_comm] + rfl + +theorem slice_transition {n m : ℕ} (R : Finset (Fin m)) (j : Fin n) (ε : Bool) + (x : Hilbert (n+m)) : + slice R (transition (Fin.castAdd m j) ε x) = transition j ε (slice R x) := by + ext A + simp [transition_apply, slice_apply, sign_join_left, ← join_flip_left] + +noncomputable def extendLocal {n m : ℕ} (T : Module.End ℂ (Hilbert n)) : + Module.End ℂ (Hilbert (n+m)) where + toFun x := WithLp.toLp 2 (fun S => + T (slice ((joinEquiv n m).symm S).2 x) ((joinEquiv n m).symm S).1) + map_add' x y := by ext S; simp + map_smul' c x := by ext S; simp + +@[simp] lemma slice_extendLocal {n m : ℕ} (R : Finset (Fin m)) (T : Module.End ℂ (Hilbert n)) + (x : Hilbert (n+m)) : slice R (extendLocal T x) = T (slice R x) := by + ext A + simp [slice_apply, extendLocal, join] + +lemma eq_of_slice_eq {n m : ℕ} {x y : Hilbert (n+m)} + (h : ∀ R : Finset (Fin m), slice R x = slice R y) : x = y := by + ext S + obtain ⟨⟨A,R⟩, rfl⟩ := (joinEquiv n m).surjective S + exact congrArg (fun z : Hilbert n => z A) (h R) + +@[simp] theorem extendLocal_transition {n m : ℕ} (j : Fin n) (ε : Bool) : + extendLocal (m := m) (transition j ε) = transition (Fin.castAdd m j) ε := by + apply LinearMap.ext + intro x + apply eq_of_slice_eq + intro R + rw [slice_extendLocal, slice_transition] + +@[simp] theorem extendLocal_one {n m : ℕ} : + extendLocal (m := m) (1 : Module.End ℂ (Hilbert n)) = 1 := by + apply LinearMap.ext + intro x + apply eq_of_slice_eq + intro R + simp + +@[simp] theorem extendLocal_add {n m : ℕ} (T S : Module.End ℂ (Hilbert n)) : + extendLocal (m := m) (T + S) = extendLocal T + extendLocal S := by + apply LinearMap.ext + intro x + apply eq_of_slice_eq + intro R + simp + +@[simp] theorem extendLocal_mul {n m : ℕ} (T S : Module.End ℂ (Hilbert n)) : + extendLocal (m := m) (T * S) = extendLocal T * extendLocal S := by + apply LinearMap.ext + intro x + apply eq_of_slice_eq + intro R + simp only [Module.End.mul_apply, slice_extendLocal] + +theorem extendLocal_quadraticForm_le {n m : ℕ} (T S : Module.End ℂ (Hilbert n)) + (h : ∀ x, (inner ℂ x (T x)).re ≤ (inner ℂ x (S x)).re) (x : Hilbert (n+m)) : + (inner ℂ x (extendLocal T x)).re ≤ (inner ℂ x (extendLocal S x)).re := by + rw [inner_eq_sum_slice, inner_eq_sum_slice] + simp only [Complex.re_sum, slice_extendLocal] + exact Finset.sum_le_sum (fun R _ => h (slice R x)) + +theorem extendLocal_energy_le {n m : ℕ} {ι κ : Type*} [Fintype ι] [Fintype κ] + (A : ι → Module.End ℂ (Hilbert n)) (B : κ → Module.End ℂ (Hilbert n)) (c : ℝ) + (h : ∀ x, (∑ a, ‖A a x‖ ^ 2) ≤ c * (∑ b, ‖B b x‖ ^ 2)) (x : Hilbert (n+m)) : + (∑ a, ‖extendLocal (A a) x‖ ^ 2) ≤ c * (∑ b, ‖extendLocal (B b) x‖ ^ 2) := by + simp_rw [norm_sq_eq_sum_slice, slice_extendLocal] + rw [Finset.sum_comm, Finset.sum_comm (f := fun (b : κ) (R : Finset (Fin m)) => ‖B b (slice R x)‖ ^ 2), Finset.mul_sum] + exact Finset.sum_le_sum (fun R _ => h (slice R x)) + +@[simp] theorem extendLocal_zero {n m : ℕ} : + extendLocal (m := m) (0 : Module.End ℂ (Hilbert n)) = 0 := by + apply LinearMap.ext + intro x + apply eq_of_slice_eq + intro R + simp + +@[simp] theorem extendLocal_smul {n m : ℕ} (c : ℂ) (T : Module.End ℂ (Hilbert n)) : + extendLocal (m := m) (c • T) = c • extendLocal T := by + apply LinearMap.ext + intro x + apply eq_of_slice_eq + intro R + simp + +@[simp] theorem extendLocal_adjoint {n m : ℕ} (T : Module.End ℂ (Hilbert n)) : + (extendLocal (m := m) T).adjoint = extendLocal T.adjoint := by + symm + rw [LinearMap.eq_adjoint_iff] + intro x y + rw [inner_eq_sum_slice, inner_eq_sum_slice] + simp only [slice_extendLocal, LinearMap.adjoint_inner_left] + +noncomputable def extendLocalHom (n m : ℕ) : + Module.End ℂ (Hilbert n) →⋆ₐ[ℂ] Module.End ℂ (Hilbert (n+m)) where + toFun := extendLocal + map_one' := extendLocal_one + map_mul' := extendLocal_mul + map_zero' := extendLocal_zero + map_add' := extendLocal_add + commutes' c := by + change extendLocal (m := m) (c • (1 : Module.End ℂ (Hilbert n))) = c • 1 + rw [extendLocal_smul, extendLocal_one] + map_star' T := (extendLocal_adjoint T).symm + +theorem extendLocal_positive {n m : ℕ} {T : Module.End ℂ (Hilbert n)} + (hT : T.IsPositive) : (extendLocal (m := m) T).IsPositive := by + refine ⟨?_, fun x => ?_⟩ + · intro x y + rw [inner_eq_sum_slice, inner_eq_sum_slice] + simp only [slice_extendLocal] + exact Finset.sum_congr rfl (fun R _ => hT.isSymmetric _ _) + · rw [inner_eq_sum_slice] + simp only [slice_extendLocal, map_sum] + exact Finset.sum_nonneg (fun R _ => hT.re_inner_nonneg_left (slice R x)) + +end LaughlinGap.Occupation + +namespace LaughlinGap +open scoped BigOperators InnerProduct ComplexOrder + +section PositiveLifting +variable {ι E : Type*} [Fintype ι] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] [FiniteDimensional ℂ E] + +noncomputable def matrixLift (B : ι → Module.End ℂ E) : + Matrix ι ι ℂ →ₗ[ℂ] Module.End ℂ E where + toFun M := ∑ i, ∑ j, M i j • ((B i).adjoint * B j) + map_add' M N := by simp [add_smul, Finset.sum_add_distrib] + map_smul' c M := by simp [Finset.smul_sum, smul_smul] + +noncomputable def contractCombination (B : ι → Module.End ℂ E) (v : ι → ℂ) : + Module.End ℂ E := ∑ i, star (v i) • B i + +theorem matrixLift_rankOne (B : ι → Module.End ℂ E) (v w : ι → ℂ) : + matrixLift B (Matrix.vecMulVec v (star w)) = + (contractCombination B v).adjoint * contractCombination B w := by + simp only [matrixLift, LinearMap.coe_mk, AddHom.coe_mk, Matrix.vecMulVec_apply, + Pi.star_apply, contractCombination, map_sum, map_smulₛₗ, + Finset.sum_mul, Finset.mul_sum, smul_mul_assoc, mul_smul_comm, + Complex.star_def, Complex.conj_conj, Finset.smul_sum, smul_smul] + rw [Finset.sum_comm] + simp only [mul_comm] + +theorem matrixLift_positive (B : ι → Module.End ℂ E) {M : Matrix ι ι ℂ} + (hM : M.PosSemidef) : (matrixLift B M).IsPositive := by + classical + obtain ⟨m, v, rfl⟩ := Matrix.posSemidef_iff_eq_sum_vecMulVec.mp hM + rw [map_sum] + apply LinearMap.isPositive_sum + intro i _ + rw [matrixLift_rankOne] + exact LinearMap.isPositive_adjoint_comp_self _ + +theorem matrixLift_columns {κ : Type*} [Fintype κ] + (B : ι → Module.End ℂ E) (W : Matrix ι κ ℂ) (C : Matrix κ κ ℂ) : + matrixLift B (W * C * W.conjTranspose) = + matrixLift (fun r => contractCombination B (fun i => W i r)) C := by + classical + have hm : W * C * W.conjTranspose = + ∑ r, ∑ s, C r s • Matrix.vecMulVec (fun i => W i r) (star (fun i => W i s)) := by + ext i j + simp only [Matrix.mul_apply, Matrix.conjTranspose_apply, Matrix.sum_apply, + Matrix.smul_apply, Matrix.vecMulVec_apply, Pi.star_apply, smul_eq_mul, + Finset.sum_mul] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro r _ + apply Finset.sum_congr rfl + intro s _ + ring + rw [hm] + simp only [map_sum, map_smul, matrixLift_rankOne] + rfl + +theorem matrixLift_gram_positive {κ : Type*} [Fintype κ] [DecidableEq κ] + [DecidableEq ι] (B : ι → Module.End ℂ E) (W : Matrix ι κ ℂ) + (C : Matrix κ κ ℂ) (hC : C.IsHermitian) + (hG : ((W.conjTranspose * W) * C * (W.conjTranspose * W)).PosSemidef) : + (matrixLift (fun r => contractCombination B (fun i => W i r)) C).IsPositive := by + rw [← matrixLift_columns] + apply matrixLift_positive + rw [← Matrix.isPositive_toEuclideanLin_iff] + rw [← Matrix.isPositive_toEuclideanLin_iff] at hG + simp only [Matrix.toEuclideanLin, Matrix.toLpLin_mul_same, + Matrix.toEuclideanLin_conjTranspose_eq_adjoint] at hG ⊢ + exact (gram_compression_positive_iff W.toEuclideanLin C.toEuclideanLin + (Matrix.isSymmetric_toEuclideanLin_iff.mpr hC)).mp hG + +end PositiveLifting + +namespace Occupation + +abbrev BasisLabel (n k : ℕ) := {A : Finset (Fin n) // A.card = k} + +abbrev ExteriorCoordinates (n k : ℕ) := EuclideanSpace ℂ (BasisLabel n k) + +noncomputable def basisContraction {n k : ℕ} (A : BasisLabel n k) : + Module.End ℂ (Hilbert n) := word (A.val.sort (· ≤ ·)) + +noncomputable def exteriorContraction {n k : ℕ} (v : ExteriorCoordinates n k) : + Module.End ℂ (Hilbert n) := contractCombination basisContraction v + +noncomputable def exteriorLift {n k : ℕ} : + Matrix (BasisLabel n k) (BasisLabel n k) ℂ →ₗ[ℂ] Module.End ℂ (Hilbert n) := + matrixLift basisContraction + +theorem exteriorLift_rankOne {n k : ℕ} (v w : ExteriorCoordinates n k) : + exteriorLift (Matrix.vecMulVec (WithLp.ofLp v) (star (WithLp.ofLp w))) = + (exteriorContraction v).adjoint * exteriorContraction w := + matrixLift_rankOne basisContraction v w + +theorem exteriorLift_positive {n k : ℕ} + {M : Matrix (BasisLabel n k) (BasisLabel n k) ℂ} (hM : M.PosSemidef) : + (exteriorLift M).IsPositive := matrixLift_positive basisContraction hM + +end Occupation +end LaughlinGap + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct + +def Homogeneous {n : ℕ} (k : ℕ) (x : Hilbert n) : Prop := + ∀ A, A.card ≠ k → x A = 0 + +lemma annihilation_homogeneous {n k : ℕ} {x : Hilbert n} (hx : Homogeneous (k+1) x) + (j : Fin n) : Homogeneous k (annihilation j x) := by + intro A hA + by_cases hj : j ∈ A + · simp [transition_apply, hj] + · rw [transition_apply] + simp only [hj, decide_false, ite_true, flip_of_not_mem hj] + rw [hx (insert j A) (by rw [Finset.card_insert_of_notMem hj]; omega), mul_zero] + +lemma annihilation_eq_zero_of_degree_zero {n : ℕ} {x : Hilbert n} + (hx : Homogeneous 0 x) (j : Fin n) : annihilation j x = 0 := by + ext A + by_cases hj : j ∈ A + · simp [transition_apply, hj] + · simp only [transition_apply, hj, decide_false, ite_true, + flip_of_not_mem hj] + rw [hx (insert j A) (by simp), mul_zero] + rfl + +lemma word_homogeneous {n k : ℕ} (js : List (Fin n)) {x : Hilbert n} + (hx : Homogeneous (k + js.length) x) : Homogeneous k (word js x) := by + induction js generalizing x with + | nil => simpa only [word, List.length_nil, Nat.add_zero, LinearMap.id_apply] using hx + | cons j js ih => + exact ih (annihilation_homogeneous (by simpa only [List.length_cons, Nat.add_assoc] using hx) j) + +lemma word_eq_zero_of_degree_lt {n k : ℕ} (js : List (Fin n)) {x : Hilbert n} + (hx : Homogeneous k x) (hk : k < js.length) : word js x = 0 := by + induction js generalizing k x with + | nil => simp at hk + | cons j js ih => + cases k with + | zero => simp only [word, LinearMap.comp_apply, annihilation_eq_zero_of_degree_zero hx, map_zero] + | succ k => + exact ih (annihilation_homogeneous hx j) (by simpa only [List.length_cons, Nat.succ_lt_succ_iff] using hk) + +lemma word_apply_empty_sorted {n : ℕ} (js : List (Fin n)) + (hs : js.Pairwise (· < ·)) (x : Hilbert n) : word js x ∅ = x js.toFinset := by + induction js generalizing x with + | nil => rfl + | cons j js ih => + obtain ⟨hj, hs⟩ := List.pairwise_cons.mp hs + change word js (annihilation j x) ∅ = _ + rw [ih hs] + have hj' : j ∉ js.toFinset := by + intro h + exact lt_irrefl j (hj j (List.mem_toFinset.mp h)) + have he : (js.toFinset.filter (fun k => k < j)) = ∅ := by + apply Finset.filter_eq_empty_iff.mpr + intro i hi hij + exact not_lt_of_gt (hj i (List.mem_toFinset.mp hi)) hij + simp [transition_apply, hj', sign, he] + +@[simp] lemma basisContraction_apply_empty {n k : ℕ} (A : BasisLabel n k) (x : Hilbert n) : + basisContraction A x ∅ = x A.val := by + simpa only [basisContraction, Finset.sort_toFinset] using + word_apply_empty_sorted (A.val.sort (· ≤ ·)) A.val.sortedLT_sort.pairwise x + +noncomputable def vacuum (n : ℕ) : Hilbert n := EuclideanSpace.single ∅ 1 + +@[simp] lemma vacuum_apply (n : ℕ) (A : Finset (Fin n)) : + vacuum n A = if A = ∅ then 1 else 0 := by + simp only [vacuum, PiLp.single_apply] + +@[simp] lemma vacuum_norm (n : ℕ) : ‖vacuum n‖ = 1 := by + simp [vacuum] + +lemma degree_zero_eq_vacuum {n : ℕ} {x : Hilbert n} (hx : Homogeneous 0 x) : + x = x ∅ • vacuum n := by + ext A + by_cases h : A = ∅ + · simp [h] + · have hc : A.card ≠ 0 := by simpa using h + simp [vacuum_apply, h, hx A hc] + +lemma basisContraction_degree {n k : ℕ} {x : Hilbert n} (hx : Homogeneous k x) + (A : BasisLabel n k) : basisContraction A x = x A.val • vacuum n := by + have hd : Homogeneous 0 (basisContraction A x) := + word_homogeneous (A.val.sort (· ≤ ·)) (by simpa only [Finset.length_sort, A.property, Nat.zero_add] using hx) + rw [degree_zero_eq_vacuum hd, basisContraction_apply_empty] + +lemma basisContraction_eq_zero_of_degree_lt {n j k : ℕ} {x : Hilbert n} + (hx : Homogeneous j x) (hjk : j < k) (A : BasisLabel n k) : basisContraction A x = 0 := + word_eq_zero_of_degree_lt (A.val.sort (· ≤ ·)) hx (by simpa only [Finset.length_sort, A.property] using hjk) + +noncomputable def sectorInclusion (n k : ℕ) : ExteriorCoordinates n k →ₗ[ℂ] Hilbert n where + toFun x := WithLp.toLp 2 (fun A => if h : A.card = k then x ⟨A,h⟩ else 0) + map_add' x y := by + ext A + by_cases h : A.card = k <;> simp [h] + map_smul' c x := by + ext A + by_cases h : A.card = k <;> simp [h] + +@[simp] lemma sectorInclusion_apply {n k : ℕ} (x : ExteriorCoordinates n k) + (A : Finset (Fin n)) : + sectorInclusion n k x A = if h : A.card = k then x ⟨A,h⟩ else 0 := rfl + +@[simp] lemma sectorInclusion_apply_label {n k : ℕ} (x : ExteriorCoordinates n k) + (A : BasisLabel n k) : sectorInclusion n k x A.val = x A := by + simp only [sectorInclusion_apply, A.property, ↓reduceDIte] + +lemma sectorInclusion_homogeneous {n k : ℕ} (x : ExteriorCoordinates n k) : + Homogeneous k (sectorInclusion n k x) := fun A h => by simp [h] + +@[simp] lemma basisContraction_sectorInclusion {n k : ℕ} (x : ExteriorCoordinates n k) + (A : BasisLabel n k) : basisContraction A (sectorInclusion n k x) = x A • vacuum n := by + rw [basisContraction_degree (sectorInclusion_homogeneous x), sectorInclusion_apply_label] + +theorem exteriorContraction_sectorInclusion {n k : ℕ} (v x : ExteriorCoordinates n k) : + exteriorContraction v (sectorInclusion n k x) = inner ℂ v x • vacuum n := by + simp only [exteriorContraction, contractCombination, LinearMap.sum_apply, + LinearMap.smul_apply, basisContraction_sectorInclusion, smul_smul, + PiLp.inner_apply, RCLike.inner_apply, ← Finset.sum_smul] + simp only [Complex.star_def, mul_comm] + +theorem exteriorContraction_eq_zero_of_degree_lt {n j k : ℕ} {x : Hilbert n} + (hx : Homogeneous j x) (hjk : j < k) (v : ExteriorCoordinates n k) : + exteriorContraction v x = 0 := by + simp only [exteriorContraction, contractCombination, LinearMap.sum_apply, + LinearMap.smul_apply, basisContraction_eq_zero_of_degree_lt hx hjk, + smul_zero, Finset.sum_const_zero] + +theorem exteriorLift_eq_zero_of_degree_lt {n j k : ℕ} {x : Hilbert n} + (hx : Homogeneous j x) (hjk : j < k) (M : Matrix (BasisLabel n k) (BasisLabel n k) ℂ) : + exteriorLift M x = 0 := by + simp only [exteriorLift, matrixLift, LinearMap.coe_mk, AddHom.coe_mk, LinearMap.sum_apply, + LinearMap.smul_apply, Module.End.mul_apply, basisContraction_eq_zero_of_degree_lt hx hjk, + map_zero, smul_zero, Finset.sum_const_zero] + +theorem exteriorLift_inner_sector {n k : ℕ} + (M : Matrix (BasisLabel n k) (BasisLabel n k) ℂ) (x y : ExteriorCoordinates n k) : + inner ℂ (sectorInclusion n k x) (exteriorLift M (sectorInclusion n k y)) = + inner ℂ x (M.toEuclideanLin y) := by + classical + simp only [exteriorLift, matrixLift, LinearMap.coe_mk, AddHom.coe_mk, LinearMap.sum_apply, + LinearMap.smul_apply, Module.End.mul_apply, inner_sum, inner_smul_right, + LinearMap.adjoint_inner_right, basisContraction_sectorInclusion, + inner_smul_left] + simp only [inner_self_eq_norm_sq_to_K, vacuum_norm, RCLike.ofReal_one, + one_pow, mul_one] + simp only [PiLp.inner_apply, RCLike.inner_apply, Matrix.toLpLin_apply, + Matrix.mulVec, dotProduct, Finset.sum_mul] + apply Finset.sum_congr rfl + intro A _ + apply Finset.sum_congr rfl + intro B _ + ring + +end LaughlinGap.Occupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/PairSpin.lean b/lean/OAI/Analysis/LaughlinGap/PairSpin.lean new file mode 100644 index 0000000000000000000000000000000000000000..d591c18107099befa14fec2e926964ac16189261 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/PairSpin.lean @@ -0,0 +1,197 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Basic +import OAI.Analysis.LaughlinGap.TensorSpin + +namespace OAI + +/-! Pair Spin. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators + +theorem pairCoefficient_binomial {Q p : ℕ} (hQ : 2 ≤ Q) (hp : p < 2*Q-1) + (i j : Fin (Q+1)) : + pairCoefficient Q p i j = if i.val+j.val=p+1 then + ((i.val : ℝ)-j.val)*Real.sqrt (Q.choose i.val : ℝ)*Real.sqrt (Q.choose j.val : ℝ) / + Real.sqrt (2*Q*((2*Q-2).choose p : ℝ)) else 0 := by + have hch : ((2*Q-2).choose p : ℝ) ≠ 0 := by + exact_mod_cast (Nat.choose_pos (show p ≤ 2*Q-2 by omega)).ne' + have hQr : (Q : ℝ) ≠ 0 := by positivity + have hrad : + (((Q.descFactorial i.val : ℝ)*(Q.descFactorial j.val : ℝ)*(p.factorial : ℝ)) / + ((Q : ℝ)*((2*Q-2).descFactorial p : ℝ)* + (i.val.factorial : ℝ)*(j.val.factorial : ℝ))) = + ((Q.choose i.val : ℝ)*Q.choose j.val) / ((Q : ℝ)*((2*Q-2).choose p : ℝ)) := by + simp only [Nat.descFactorial_eq_factorial_mul_choose, Nat.cast_mul] + field_simp + unfold pairCoefficient + split_ifs + · rw [hrad, Real.sqrt_div (by positivity), Real.sqrt_mul (by positivity : + 0 ≤ (Q.choose i.val : ℝ)), + show (2 : ℝ)*Q*((2*Q-2).choose p : ℝ) = + 2*(Q*((2*Q-2).choose p : ℝ)) by ring, + Real.sqrt_mul (by norm_num : (0 : ℝ) ≤ 2)] + ring + · rfl + +lemma sqrt_choose_lowering {Q k : ℕ} (hk : k < Q) : + Real.sqrt (((k : ℝ)+1)*((Q : ℝ)-k))*Real.sqrt (Q.choose k : ℝ) = + ((k : ℝ)+1)*Real.sqrt (Q.choose (k+1) : ℝ) := by + have hq : (k : ℝ) ≤ Q := by exact_mod_cast hk.le + have hc : (Q.choose (k+1) : ℝ)*((k : ℝ)+1) = + (Q.choose k : ℝ)*((Q : ℝ)-k) := by + have H := congrArg (fun a : ℕ => (a : ℝ)) (Nat.choose_succ_right_eq Q k) + simpa only [Nat.cast_mul, Nat.cast_add, Nat.cast_one, Nat.cast_sub hk.le] using H + rw [← Real.sqrt_mul (by positivity : 0 ≤ ((k : ℝ)+1)*((Q : ℝ)-k))] + rw [show (((k : ℝ)+1)*((Q : ℝ)-k))*(Q.choose k : ℝ) = + (((k : ℝ)+1)^2)*(Q.choose (k+1) : ℝ) by nlinarith [hc]] + rw [Real.sqrt_mul (sq_nonneg _), Real.sqrt_sq (by positivity)] + +noncomputable def binomialPairTensor (Q p : ℕ) : (Fin (Q+1) × Fin (Q+1)) → ℝ := + fun ij => if ij.1.val + ij.2.val = p+1 then + ((ij.1.val : ℝ)-ij.2.val)*Real.sqrt (Q.choose ij.1.val : ℝ)* + Real.sqrt (Q.choose ij.2.val : ℝ) else 0 + +lemma binomialPairTensor_swap (Q p : ℕ) (i j : Fin (Q+1)) : + binomialPairTensor Q p (j,i) = -binomialPairTensor Q p (i,j) := by + unfold binomialPairTensor + by_cases h : i.val+j.val=p+1 + · simp only [h, Nat.add_comm j.val i.val, ite_true] + ring + · simp [h, Nat.add_comm j.val i.val] + +lemma binomialPairTensor_lower_first (Q p : ℕ) (i j : Fin (Q+1)) : + lowering Q (fun a => binomialPairTensor Q p (a,j)) i = + if i.val+j.val=p+2 then + (i.val : ℝ)*((i.val : ℝ)-1-j.val)*Real.sqrt (Q.choose i.val : ℝ)* + Real.sqrt (Q.choose j.val : ℝ) else 0 := by + cases i using Fin.cases with + | zero => simp + | succ i => + rw [lowering_succ] + simp only [binomialPairTensor, Fin.val_castSucc, Fin.val_succ] + by_cases h : i.val+j.val=p+1 + · rw [ite_eq_left h, ite_eq_left (by omega : i.val+1+j.val=p+2)] + simp only [Nat.cast_add, Nat.cast_one, ladderStep] + have hc := sqrt_choose_lowering i.isLt + calc + _ = (((i.val : ℝ)-j.val)*Real.sqrt (Q.choose j.val : ℝ)) * + (Real.sqrt (((i.val : ℝ)+1)*((Q : ℝ)-i.val))*Real.sqrt (Q.choose i.val : ℝ)) := by ring + _ = _ := by rw [hc]; ring + · rw [ite_eq_right h, ite_eq_right (by omega : ¬i.val+1+j.val=p+2), mul_zero] + +theorem binomialPairTensor_lower (Q p : ℕ) : + (tensorSpin Q Q).lower (binomialPairTensor Q p) = + ((p : ℝ)+1) • binomialPairTensor Q (p+1) := by + funext ⟨i,j⟩ + rw [tensorSpin_lower, binomialPairTensor_lower_first] + have hswap : (fun a => binomialPairTensor Q p (i,a)) = + -(fun a => binomialPairTensor Q p (a,i)) := by + funext a + exact binomialPairTensor_swap Q p a i + rw [hswap, map_neg] + simp only [Pi.neg_apply] + rw [binomialPairTensor_lower_first] + simp only [binomialPairTensor, Pi.smul_apply, smul_eq_mul] + by_cases h : i.val+j.val=p+2 + · simp only [ite_eq_left h, ite_eq_left (by omega : j.val+i.val=p+2)] + have hc : (i.val : ℝ)+j.val=(p : ℝ)+2 := by exact_mod_cast h + rw [show (p : ℝ)+1=(i.val : ℝ)+j.val-1 by linarith] + ring + · simp only [ite_eq_right h, ite_eq_right (by omega : ¬j.val+i.val=p+2), neg_zero, zero_add, mul_zero] + +noncomputable def physicalPairTensor (Q p : ℕ) : (Fin (Q+1) × Fin (Q+1)) → ℝ := + fun ij => pairCoefficient Q p ij.1 ij.2 + +lemma physicalPairTensor_binomial {Q p : ℕ} (hQ : 2 ≤ Q) (hp : p < 2*Q-1) : + physicalPairTensor Q p = + (1/Real.sqrt (2*Q*((2*Q-2).choose p : ℝ))) • binomialPairTensor Q p := by + funext ⟨i,j⟩ + simp only [physicalPairTensor, pairCoefficient_binomial hQ hp, binomialPairTensor, + Pi.smul_apply, smul_eq_mul] + split_ifs <;> ring + +lemma pairNormalization_step {Q p : ℕ} (hQ : 2 ≤ Q) (hp : p < 2*Q-2) : + (1/Real.sqrt (2*Q*((2*Q-2).choose p : ℝ)))*((p : ℝ)+1) = + Real.sqrt (((p : ℝ)+1)*(((2*Q-2 : ℕ) : ℝ)-p))* + (1/Real.sqrt (2*Q*((2*Q-2).choose (p+1) : ℝ))) := by + have hc := sqrt_choose_lowering hp + have hs0 : Real.sqrt (((2*Q-2).choose p : ℝ)) ≠ 0 := by + apply (Real.sqrt_pos.mpr _).ne' + exact_mod_cast Nat.choose_pos hp.le + have hs1 : Real.sqrt (((2*Q-2).choose (p+1) : ℝ)) ≠ 0 := by + apply (Real.sqrt_pos.mpr _).ne' + exact_mod_cast Nat.choose_pos hp + simp only [Real.sqrt_mul (by positivity : (0 : ℝ) ≤ 2*Q)] + field_simp + nlinarith [congrArg (fun a => a*Real.sqrt (2*(Q : ℝ))) hc] + +theorem physicalPairTensor_lower {Q p : ℕ} (hQ : 2 ≤ Q) (hp : p < 2*Q-2) : + (tensorSpin Q Q).lower (physicalPairTensor Q p) = + Real.sqrt (((p : ℝ)+1)*(((2*Q-2 : ℕ) : ℝ)-p)) • physicalPairTensor Q (p+1) := by + rw [physicalPairTensor_binomial hQ (by omega), map_smul, binomialPairTensor_lower, + physicalPairTensor_binomial hQ (by omega), smul_smul, smul_smul, + pairNormalization_step hQ hp] + +lemma highestWeight_first_one {Q : ℕ} (hQ : 0 < Q) : + highestWeight Q Q 1 1 = 1 := by + have hQr : (Q : ℝ) ≠ 0 := by positivity + simp only [highestWeight, Nat.choose_self, Nat.cast_one, Finset.prod_range_one, + one_mul, highestFactor, Nat.cast_zero, sub_zero] + rw [show (Q : ℝ)-1+0+1 = Q by ring, div_self hQr] + +lemma highestNormalization_first {Q : ℕ} (hQ : 0 < Q) : + highestNormalization Q Q 1 = 2 := by + norm_num [highestNormalization, Finset.sum_range_succ, highestWeight_first_one hQ] + +lemma sqrt_Q_over_sqrt_twoQ {Q : ℕ} (hQ : 0 < Q) : + Real.sqrt (Q : ℝ)/Real.sqrt (2*Q : ℝ) = 1/Real.sqrt 2 := by + have hQr : Real.sqrt (Q : ℝ) ≠ 0 := by positivity + rw [Real.sqrt_mul (by norm_num : (0 : ℝ) ≤ 2)] + field_simp + +theorem physicalPairTensor_zero {Q : ℕ} (hQ : 2 ≤ Q) : + physicalPairTensor Q 0 = highestTensor Q Q 1 := by + have hQ0 : 0 < Q := by omega + funext ⟨i,j⟩ + simp only [physicalPairTensor, pairCoefficient_binomial hQ (by omega : 0 < 2*Q-1), + highestTensor] + by_cases h : i.val+j.val=1 + · rw [ite_eq_left h, ite_eq_left h] + rcases (show i.val=0 ∧ j.val=1 ∨ i.val=1 ∧ j.val=0 by omega) with hij | hij + · simp only [hij.1, hij.2, Nat.cast_zero, Nat.cast_one, zero_sub, + Nat.choose_zero_right, Nat.choose_one_right, mul_one, highestCoefficient, + highestWeight_zero, highestNormalization_first hQ0] + simp only [Nat.sub_zero, pow_one, Real.sqrt_one, one_mul, neg_mul, neg_div] + exact congrArg Neg.neg (sqrt_Q_over_sqrt_twoQ hQ0) + · simp only [hij.1, hij.2, Nat.cast_zero, Nat.cast_one, sub_zero, + Nat.choose_zero_right, Nat.choose_one_right, mul_one, one_mul, highestCoefficient, + highestWeight_first_one hQ0, highestNormalization_first hQ0, + Nat.sub_self, pow_zero, Real.sqrt_one] + exact sqrt_Q_over_sqrt_twoQ hQ0 + · simp only [ite_eq_right h] + +theorem physicalPairTensor_eq_coupled {Q p : ℕ} (hQ : 2 ≤ Q) (hp : p ≤ 2*Q-2) : + physicalPairTensor Q p = coupledTensor Q Q 1 p := by + have hz : 1 ≤ min Q Q := by omega + have hd : Q+Q-2*1=2*Q-2 := by omega + rw [coupledTensor_eq_normalized hz (by omega), hd] + induction p with + | zero => rw [LadderSystem.normalized_zero, physicalPairTensor_zero hQ] + | succ p ih => + have hl : p < 2*Q-2 := by omega + have ha : Real.sqrt (((p : ℝ)+1)*(((2*Q-2 : ℕ) : ℝ)-p)) ≠ 0 := by + apply (Real.sqrt_pos.mpr _).ne' + have hpr : (p : ℝ) < (2*Q-2 : ℕ) := by exact_mod_cast hl + exact mul_pos (by positivity) (by linarith) + rw [LadderSystem.normalized_succ _ _ hl, ← ih (by omega), physicalPairTensor_lower hQ hl, + smul_smul, one_div_mul_cancel ha, one_smul] + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/PhysicalAveraging.lean b/lean/OAI/Analysis/LaughlinGap/PhysicalAveraging.lean new file mode 100644 index 0000000000000000000000000000000000000000..f87b284efe5396aabba47261f1d5c594711161f4 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/PhysicalAveraging.lean @@ -0,0 +1,112 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CovariantFamily +import OAI.Analysis.LaughlinGap.IrrepAveraging +import OAI.Analysis.LaughlinGap.ThreeSpin + +namespace OAI + +/-! Physical Averaging. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Averaging Spin + +noncomputable def fockLowering (Q : ℕ) : FockMatrix (Q+1) := + secondQuantization (loweringMatrix (standardLadderSystem Q)) + +noncomputable def physicalPair (Q p : ℕ) : FockMatrix (Q+1) := + (1/Real.sqrt 2) • combination (productFamily annihilation annihilation) (physicalPairTensor Q p) + +@[simp] lemma complexify_physicalPair (Q p : ℕ) : + complexify (physicalPair Q p) = Occupation.localPair (Q+1) Q p := by + rw [physicalPair, map_smul, complexify_combination] + simp only [productFamily, map_mul, complexify_annihilation, Fintype.sum_prod_type, + physicalPairTensor, Occupation.orderedPair_contraction] + have he : (1/Real.sqrt 2 : ℝ) • ((Real.sqrt 2 : ℂ) • Occupation.localPair (Q+1) Q p) = + ((1/Real.sqrt 2)*Real.sqrt 2 : ℝ) • Occupation.localPair (Q+1) Q p := by + rw [mul_smul]; rfl + rw [he, one_div_mul_cancel (by positivity : Real.sqrt 2 ≠ 0), one_smul] + +lemma physicalPair_embedding {Q : ℕ} (hQ : 2 ≤ Q) (p : Fin (2*Q-2+1)) : + physicalPair Q p.val = (1/Real.sqrt 2) • + embeddingFamily (pairInclusion hQ) (productFamily annihilation annihilation) p := by + simp only [embeddingFamily, pairInclusion_apply, Pi.single_apply, + ite_smul, one_smul, zero_smul] + simp only [Finset.sum_ite_eq', Finset.mem_univ, ite_true] + rfl + +theorem physicalPair_covariant {Q : ℕ} (hQ : 2 ≤ Q) : + Covariant (fockLowering Q) (loweringMatrix (standardLadderSystem (2*Q-2))) + (fun p : Fin (2*Q-2+1) => physicalPair Q p.val) := by + have ha := annihilation_covariant (loweringMatrix (standardLadderSystem Q)) + have hp := (ha.product ha).embedding (pairInclusion hQ) + have he : (fun p : Fin (2*Q-2+1) => physicalPair Q p.val) = + (fun p => (1/Real.sqrt 2) • embeddingFamily (pairInclusion hQ) + (productFamily annihilation annihilation) p) := funext (physicalPair_embedding hQ) + rw [he] + exact hp.smul (1/Real.sqrt 2) + +noncomputable def physicalHamiltonian (Q : ℕ) : FockMatrix (Q+1) := + ∑ p : Fin (2*Q-1), (physicalPair Q p.val).transpose * physicalPair Q p.val + +@[simp] lemma complexify_physicalHamiltonian (Q : ℕ) : + complexify (physicalHamiltonian Q) = Occupation.physicalOccupationHamiltonian Q := by + simp only [physicalHamiltonian, map_sum, map_mul, complexify_transpose, + complexify_physicalPair, Occupation.physicalOccupationHamiltonian, Occupation.pairHamiltonian, + Occupation.physicalPair_contraction] + +lemma lift_identity {ι κ : Type*} (B : ι → Matrix κ κ ℝ) [Fintype ι] [DecidableEq ι] + [Fintype κ] : lift B 1 = ∑ i, (B i).transpose * B i := by + simp [lift, Matrix.one_apply, ite_smul] + +lemma physicalPair_sum {Q : ℕ} (hQ : 2 ≤ Q) : + (∑ p : Fin (2*Q-2+1), (physicalPair Q p.val).transpose * physicalPair Q p.val) = + physicalHamiltonian Q := by + let e : Fin (2*Q-2+1) ≃ Fin (2*Q-1) := finCongr (by omega) + exact e.sum_comp (fun p => (physicalPair Q p.val).transpose * physicalPair Q p.val) + +lemma physicalPair_single {Q : ℕ} (hQ : 2 ≤ Q) (p : Fin (2*Q-2+1)) : + average (rotationCommutant (fockLowering Q)) + ((physicalPair Q p.val).transpose * physicalPair Q p.val) = + (1/(2*Q-1 : ℕ) : ℝ) • physicalHamiltonian Q := by + let B := fun p : Fin (2*Q-2+1) => physicalPair Q p.val + have hc : combination B (Pi.single p 1) = physicalPair Q p.val := by + simp [combination, B, Pi.single_apply, ite_smul] + rw [← hc, ← lift_rankOne B, (physicalPair_covariant hQ).average_lift, + standardSpin_average, Matrix.trace_vecMulVec] + simp only [dotProduct_single_one, Pi.single_eq_same, map_smul] + rw [lift_identity, physicalPair_sum hQ] + rw [show 2*Q-2+1=2*Q-1 by omega] + +lemma physicalPair_single_val {Q p : ℕ} (hQ : 2 ≤ Q) (hp : p < 2*Q-1) : + average (rotationCommutant (fockLowering Q)) + ((physicalPair Q p).transpose * physicalPair Q p) = + (1/(2*Q-1 : ℕ) : ℝ) • physicalHamiltonian Q := + physicalPair_single hQ ⟨p,by omega⟩ + +lemma physicalHamiltonian_mem {Q : ℕ} (hQ : 2 ≤ Q) : + physicalHamiltonian Q ∈ rotationCommutant (fockLowering Q) := by + have h := average_mem (rotationCommutant (fockLowering Q)) + ((physicalPair Q 0).transpose * physicalPair Q 0) + rw [physicalPair_single_val hQ (by omega)] at h + have hd : ((2*Q-1 : ℕ) : ℝ) ≠ 0 := by exact_mod_cast (show 2*Q-1 ≠ 0 by omega) + have he : ((2*Q-1 : ℕ) : ℝ) • ((1/(2*Q-1 : ℕ) : ℝ) • physicalHamiltonian Q) = + physicalHamiltonian Q := by rw [smul_smul, mul_one_div_cancel hd, one_smul] + exact he ▸ (rotationCommutant (fockLowering Q)).smul_mem h ((2*Q-1 : ℕ) : ℝ) + +noncomputable def physicalTriple (Q : ℕ) : + (Fin (2*Q-2+1) × Fin (Q+1)) → FockMatrix (Q+1) := + productFamily (fun p => physicalPair Q p.val) annihilation + +theorem physicalTriple_covariant {Q : ℕ} (hQ : 2 ≤ Q) : + Covariant (fockLowering Q) (loweringMatrix (tensorSpin (2*Q-2) Q)) (physicalTriple Q) := + (physicalPair_covariant hQ).product (annihilation_covariant _) + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/PhysicalSpinSpectrum.lean b/lean/OAI/Analysis/LaughlinGap/PhysicalSpinSpectrum.lean new file mode 100644 index 0000000000000000000000000000000000000000..a4c69a586a52e794ac5f8564c280d6fc9510a434 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/PhysicalSpinSpectrum.lean @@ -0,0 +1,196 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.WedgeIdentification + +namespace OAI + +/-! Physical Spin Spectrum. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators InnerProduct ComplexOrder +open Occupation + +noncomputable def physicalThreeFamily {Q : ℕ} (hQ : 2 ≤ Q) + (i : CoupledIndex (2*Q-2) Q) : + EuclideanSpace ℂ (Fin (2*Q-1) × Fin (Q+1)) := + WithLp.toLp 2 (physicalThreeVector hQ i.1.val i.2.val) + +theorem physicalThreeFamily_orthonormal {Q : ℕ} (hQ : 2 ≤ Q) : + Orthonormal ℂ (physicalThreeFamily hQ) := by + classical + rw [orthonormal_iff_ite] + intro i j + have h := (orthonormal_iff_ite.mp (coupledFamily_orthonormal (2*Q-2) Q)) i j + simp only [coupledFamily, EuclideanSpace.inner_toLp_toLp, star_trivial] at h + simp only [physicalThreeFamily, EuclideanSpace.inner_toLp_toLp, + physicalThreeVector, dotProduct, Pi.star_apply, Complex.star_def, Complex.conj_ofReal, + ← Complex.ofReal_mul, ← Complex.ofReal_sum] + rw [(physicalThreeIndexEquiv hQ).sum_comp (fun a => + coupledTensor (2*Q-2) Q j.1.val j.2.val a * + coupledTensor (2*Q-2) Q i.1.val i.2.val a)] + rw [show (∑ a, coupledTensor (2*Q-2) Q j.1.val j.2.val a * + coupledTensor (2*Q-2) Q i.1.val i.2.val a) = + if i=j then 1 else 0 from h] + split_ifs <;> rfl + +noncomputable def physicalThreeBasis {Q : ℕ} (hQ : 2 ≤ Q) : + OrthonormalBasis (CoupledIndex (2*Q-2) Q) ℂ + (EuclideanSpace ℂ (Fin (2*Q-1) × Fin (Q+1))) := by + letI : Nonempty (CoupledIndex (2*Q-2) Q) := ⟨⟨0,0⟩⟩ + have hc : Fintype.card (CoupledIndex (2*Q-2) Q) = + Module.finrank ℂ (EuclideanSpace ℂ (Fin (2*Q-1) × Fin (Q+1))) := by + rw [finrank_euclideanSpace, Fintype.card_prod, Fintype.card_fin, + Fintype.card_fin, coupledIndex_card] + congr 1 + omega + let b := basisOfOrthonormalOfCardEqFinrank (physicalThreeFamily_orthonormal hQ) hc + exact b.toOrthonormalBasis (by simpa [b] using physicalThreeFamily_orthonormal hQ) + +@[simp] lemma physicalThreeBasis_apply {Q : ℕ} (hQ : 2 ≤ Q) + (i : CoupledIndex (2*Q-2) Q) : + physicalThreeBasis hQ i = physicalThreeFamily hQ i := by + simp [physicalThreeBasis] + +noncomputable def physicalThreeRankOne {Q : ℕ} (hQ : 2 ≤ Q) (z l : ℕ) : + Matrix (Fin (2*Q-1) × Fin (Q+1)) (Fin (2*Q-1) × Fin (Q+1)) ℂ := + Matrix.vecMulVec (physicalThreeVector hQ z l) (star (physicalThreeVector hQ z l)) + +theorem physicalThreeRankOne_positive {Q : ℕ} (hQ : 2 ≤ Q) (z l : ℕ) : + (physicalThreeRankOne hQ z l).PosSemidef := + Matrix.posSemidef_vecMulVec_self_star _ + +noncomputable def physicalThreeProjection {Q : ℕ} (hQ : 2 ≤ Q) (z : ℕ) : + Matrix (Fin (2*Q-1) × Fin (Q+1)) (Fin (2*Q-1) × Fin (Q+1)) ℂ := + ∑ l : Fin ((2*Q-2)+Q-2*z+1), physicalThreeRankOne hQ z l.val + +lemma physicalThreeProjection_positive {Q : ℕ} (hQ : 2 ≤ Q) (z : ℕ) : + (physicalThreeProjection hQ z).PosSemidef := by + apply Matrix.posSemidef_sum + exact fun l _ => physicalThreeRankOne_positive hQ z l.val + +theorem physicalTripleGram_spectral {Q : ℕ} (hQ : 2 ≤ Q) : + (tripleWedgeMatrix (physicalPairForms Q)).conjTranspose * + tripleWedgeMatrix (physicalPairForms Q) - 1 = + ∑ i : CoupledIndex (2*Q-2) Q, + (threeBodyGramCoefficient Q i.1.val : ℂ) • + physicalThreeRankOne hQ i.1.val i.2.val := by + classical + ext a b + have he := congrFun (orderedThreeGram_defect_expansion hQ + (Pi.single (physicalThreeIndexEquiv hQ b) 1)) (physicalThreeIndexEquiv hQ a) + have hid : (Pi.single (physicalThreeIndexEquiv hQ b) (1 : ℝ) : + (Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) (physicalThreeIndexEquiv hQ a) = if a=b then 1 else 0 := by + simp [Pi.single_apply] + simp only [Pi.sub_apply, hid, Finset.sum_apply, Pi.smul_apply, smul_eq_mul, + dotProduct_single_one] at he + rw [Matrix.sub_apply, physicalTripleGram_entry hQ, Matrix.one_apply] + simp only [Matrix.sum_apply, Matrix.smul_apply, smul_eq_mul, physicalThreeRankOne, + Matrix.vecMulVec_apply, Pi.star_apply, physicalThreeVector, + Complex.star_def, Complex.conj_ofReal, ← Complex.ofReal_mul, + ← Complex.ofReal_sum] + have hcast : (if a=b then (1 : ℂ) else 0) = ↑(if a=b then (1:ℝ) else 0) := by + split_ifs <;> rfl + rw [hcast, ← Complex.ofReal_sub, he] + congr 1 + apply Finset.sum_congr rfl + intro i hi + ring + +theorem physicalTripleGram_spin_blocks {Q : ℕ} (hQ : 2 ≤ Q) : + (tripleWedgeMatrix (physicalPairForms Q)).conjTranspose * + tripleWedgeMatrix (physicalPairForms Q) - 1 = + ∑ z : Fin (min (2*Q-2) Q+1), + (threeBodyGramCoefficient Q z.val : ℂ) • physicalThreeProjection hQ z.val := by + rw [physicalTripleGram_spectral hQ, Fintype.sum_sigma] + simp only [physicalThreeProjection, Finset.smul_sum] + +lemma physicalThreeVector_inner {Q : ℕ} (hQ : 2 ≤ Q) + (i j : CoupledIndex (2*Q-2) Q) : + dotProduct (star (physicalThreeVector hQ i.1.val i.2.val)) + (physicalThreeVector hQ j.1.val j.2.val) = if i=j then 1 else 0 := by + have h := (orthonormal_iff_ite.mp (physicalThreeFamily_orthonormal hQ)) i j + simpa only [physicalThreeFamily, EuclideanSpace.inner_toLp_toLp, dotProduct_comm] using h + +lemma physicalThreeRankOne_mul {Q : ℕ} (hQ : 2 ≤ Q) + (i j : CoupledIndex (2*Q-2) Q) : + physicalThreeRankOne hQ i.1.val i.2.val * physicalThreeRankOne hQ j.1.val j.2.val = + if i=j then physicalThreeRankOne hQ i.1.val i.2.val else 0 := by + classical + simp only [physicalThreeRankOne, Matrix.vecMulVec_mul_vecMulVec, + physicalThreeVector_inner hQ] + split_ifs with h + · subst j + simp + · simp + +theorem physicalThreeProjection_idempotent {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + physicalThreeProjection hQ z * physicalThreeProjection hQ z = + physicalThreeProjection hQ z := by + classical + let z' : Fin (min (2*Q-2) Q+1) := ⟨z, by omega⟩ + have hr (l k : Fin ((2*Q-2)+Q-2*z+1)) : + physicalThreeRankOne hQ z l.val * physicalThreeRankOne hQ z k.val = + if l=k then physicalThreeRankOne hQ z l.val else 0 := by + simpa using physicalThreeRankOne_mul hQ ⟨z',l⟩ ⟨z',k⟩ + simp only [physicalThreeProjection, Matrix.sum_mul, Matrix.mul_sum, hr] + simp + +theorem physicalThreeProjection_orthogonal {Q z w : ℕ} (hQ : 2 ≤ Q) + (hz : z ≤ Q) (hw : w ≤ Q) (hne : z ≠ w) : + physicalThreeProjection hQ z * physicalThreeProjection hQ w = 0 := by + classical + let z' : Fin (min (2*Q-2) Q+1) := ⟨z, by omega⟩ + let w' : Fin (min (2*Q-2) Q+1) := ⟨w, by omega⟩ + have hr (l : Fin ((2*Q-2)+Q-2*z+1)) (k : Fin ((2*Q-2)+Q-2*w+1)) : + physicalThreeRankOne hQ z l.val * physicalThreeRankOne hQ w k.val = 0 := by + have hh : (Sigma.mk z' l : CoupledIndex (2*Q-2) Q) ≠ ⟨w',k⟩ := by + intro he + exact hne (congrArg (fun i : CoupledIndex (2*Q-2) Q => i.1.val) he) + exact (physicalThreeRankOne_mul hQ ⟨z',l⟩ ⟨w',k⟩).trans (ite_eq_right hh) + simp only [physicalThreeProjection, Matrix.sum_mul, Matrix.mul_sum, hr, + Finset.sum_const_zero] + +theorem physicalThreeProjection_wedge_null {Q z : ℕ} (hQ : 2 ≤ Q) + (hz : z ≤ Q) (hn : z=0 ∨ z=1 ∨ z=3) : + tripleWedgeMatrix (physicalPairForms Q) * physicalThreeProjection hQ z = 0 := by + simp only [physicalThreeProjection, physicalThreeRankOne, Matrix.mul_sum, + Matrix.mul_vecMulVec] + apply Finset.sum_eq_zero + intro l hl + rw [physicalTripleWedge_null hQ hz (by omega : l.val ≤ (2*Q-2)+Q-2*z) hn] + simp + +end LaughlinGap.Spin + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct ComplexOrder +open Spin + +noncomputable def physicalSpinThreeLift {Q : ℕ} (hQ : 2 ≤ Q) (z : ℕ) : + Module.End ℂ (Hilbert (Q+1)) := + exteriorLift (tripleWedgeMatrix (physicalPairForms Q) * physicalThreeProjection hQ z * + (tripleWedgeMatrix (physicalPairForms Q)).conjTranspose) + +theorem physicalSpinThreeLift_positive {Q : ℕ} (hQ : 2 ≤ Q) (z : ℕ) : + (physicalSpinThreeLift hQ z).IsPositive := by + apply exteriorLift_positive + exact (physicalThreeProjection_positive hQ z).mul_mul_conjTranspose_same _ + +theorem physical_spin_square {Q : ℕ} (hQ : 2 ≤ Q) : + physicalOccupationHamiltonian Q * physicalOccupationHamiltonian Q = + physicalOccupationHamiltonian Q + + (∑ z : Fin (min (2*Q-2) Q+1), + (threeBodyGramCoefficient Q z.val : ℂ) • physicalSpinThreeLift hQ z.val) + + exteriorLift (pairWedgeMatrix (physicalPairForms Q) * + (pairWedgeMatrix (physicalPairForms Q)).conjTranspose) := by + rw [physical_normal_ordered_square hQ, physicalTripleGram_spin_blocks hQ] + simp only [Matrix.mul_sum, Matrix.sum_mul, Matrix.mul_smul, Matrix.smul_mul, + map_sum, map_smul, physicalSpinThreeLift] + +end LaughlinGap.Occupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/RationalCoupling.lean b/lean/OAI/Analysis/LaughlinGap/RationalCoupling.lean new file mode 100644 index 0000000000000000000000000000000000000000..ee96668ff0fd6f05fb05178f7092949d38db42d6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/RationalCoupling.lean @@ -0,0 +1,119 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.ThreeComparison + +namespace OAI + +/-! Rational Coupling. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators Polynomial +open Polynomial + +noncomputable def rootFactorial (n : ℕ) : ℝ := Real.sqrt (n.factorial : ℝ) +lemma rootFactorial_pos (n : ℕ) : 0 < rootFactorial n := + Real.sqrt_pos.mpr (by exact_mod_cast n.factorial_pos) +lemma rootFactorial_ne_zero (n : ℕ) : rootFactorial n ≠ 0 := (rootFactorial_pos n).ne' +@[simp] lemma rootFactorial_sq (n : ℕ) : rootFactorial n ^ 2 = (n.factorial : ℝ) := + Real.sq_sqrt (by positivity) +@[simp] lemma rootFactorial_zero : rootFactorial 0 = 1 := by simp [rootFactorial] + +lemma monomialWeight_roots (T p : ℕ) : monomialWeight T p = rootFactorial p * rootFactorial (T-p) := + Real.sqrt_mul (by positivity) _ + +noncomputable def integerCoupling (c z l : ℕ) : ℚ[X] := (X-1)^z * (C (c:ℚ)*X+1)^l + +def uCoefficient (c z T p : ℕ) : ℚ := + if z ≤ T then ∑ h ∈ Finset.range (p+1), + (-1:ℚ)^(z-h) * (z.choose h) * ((T-z).choose (p-h)) * (c:ℚ)^(p-h) else 0 + +lemma integerCoupling_coeff (c z l p : ℕ) : + (integerCoupling c z l).coeff p = + ∑ h ∈ Finset.range (p+1), (-1:ℚ)^(z-h) * (z.choose h) * + (l.choose (p-h)) * (c:ℚ)^(p-h) := by + have h₁ (h : ℕ) : ((X-1:ℚ[X])^z).coeff h = (-1:ℚ)^(z-h) * (z.choose h) := by + simpa [sub_eq_add_neg] using coeff_X_add_C_pow (-1:ℚ) z h + have h₂ (h : ℕ) : ((C (c:ℚ)*X+1 : ℚ[X])^l).coeff h = (l.choose h : ℚ) * (c:ℚ)^h := by + have he : ((X+1:ℚ[X])^l).comp (C (c:ℚ)*X) = (C (c:ℚ)*X+1)^l := by simp + rw [← he,comp_C_mul_X_coeff,coeff_X_add_one_pow] + simp only [integerCoupling,coeff_mul,Finset.Nat.sum_antidiagonal_eq_sum_range_succ_mk,h₁,h₂] + apply Finset.sum_congr rfl + intro h hh + ring + +lemma uCoefficient_eq_coeff {z T : ℕ} (hz : z ≤ T) (c p : ℕ) : + uCoefficient c z T p = (integerCoupling c z (T-z)).coeff p := by + rw [uCoefficient,ite_eq_left hz,integerCoupling_coeff] + +lemma couplingPolynomial_equal (a : ℝ) (z l : ℕ) : + couplingPolynomial a a z l = + C (a^(z+l)/(rootFactorial z * rootFactorial l)) * + (integerCoupling 1 z l).map (algebraMap ℚ ℝ) := by + have ha : C a * X - C a = C a * (X-1) := by ring + have hb : C a * X + C a = C a * (X+1) := by ring + have he : (integerCoupling 1 z l).map (algebraMap ℚ ℝ) = (X-1)^z*(X+1)^l := by + simp [integerCoupling] + rw [he] + have hc : a^(z+l)/(rootFactorial z*rootFactorial l) = + (1/(rootFactorial z*rootFactorial l))* a^z * a^l := by rw [pow_add]; ring + rw [hc] + simp only [couplingPolynomial,ha,hb,mul_pow,C_mul,C_pow,rootFactorial] + ring + +lemma balancedCouplingCoefficient_rational {z T : ℕ} (hz : z ≤ T) (p : ℕ) : + balancedCouplingCoefficient z T p = (uCoefficient 1 z T p : ℝ) * + (rootFactorial p * rootFactorial (T-p)) / + ((Real.sqrt 2)^T * rootFactorial z * rootFactorial (T-z)) := by + rw [balancedCouplingCoefficient,ite_eq_left hz,couplingPolynomial_equal, + coeff_C_mul,coeff_map,monomialWeight_roots,uCoefficient_eq_coeff hz, + Nat.add_sub_of_le hz] + change _ = (algebraMap ℚ ℝ _) * _ / _ + simp only [one_div,inv_pow] + ring + +lemma couplingPolynomial_scaled (a b : ℝ) (hb : b ≠ 0) (z l : ℕ) : + couplingPolynomial a (b*a) z l = + C (b^z*a^(z+l)/(rootFactorial z*rootFactorial l)) * + (((X-1)^z*(C (b^2)*X+1)^l).comp (C b⁻¹*X)) := by + have h₁ : C a * X - C (b*a) = C (b*a) * (C b⁻¹*X-1) := by + rw [C_mul] + have hi : (C b : ℝ[X]) * C b⁻¹ = 1 := by rw [← C_mul,mul_inv_cancel₀ hb,C_1] + linear_combination -(C a * X) * hi + have h₂ : C (b*a) * X + C a = C a * (C (b^2)*(C b⁻¹*X)+1) := by + rw [pow_two,C_mul,C_mul] + have hi : (C b : ℝ[X]) * C b⁻¹ = 1 := by rw [← C_mul,mul_inv_cancel₀ hb,C_1] + linear_combination -(C a * C b * X) * hi + have hc : b^z*a^(z+l)/(rootFactorial z*rootFactorial l) = + (1/(rootFactorial z*rootFactorial l)) * (b*a)^z * a^l := by + rw [pow_add,mul_pow]; ring + rw [hc] + rw [couplingPolynomial,h₁,h₂] + simp only [mul_comp,pow_comp,sub_comp,add_comp, + X_comp,C_comp,one_comp,mul_pow,C_mul,C_pow,rootFactorial] + ring + +lemma threeWeightCoefficientStar_rational {z T : ℕ} (hz : z ≤ T) (p : ℕ) : + RealOccupation.threeWeightCoefficientStar z T p = (uCoefficient 2 z T p : ℝ) * + (Real.sqrt 2)^z * rootFactorial p * rootFactorial (T-p) / + ((Real.sqrt 3)^T * (Real.sqrt 2)^p * rootFactorial z * rootFactorial (T-z)) := by + have hb : Real.sqrt 2 ≠ 0 := Real.sqrt_ne_zero'.mpr (by norm_num) + rw [RealOccupation.threeWeightCoefficientStar,ite_eq_left hz] + rw [show Real.sqrt 2 / Real.sqrt 3 = Real.sqrt 2 * (1/Real.sqrt 3) by ring, + couplingPolynomial_scaled _ _ hb,coeff_C_mul, + Real.sq_sqrt (by norm_num : (0:ℝ) ≤ 2)] + have he : ((X-1)^z*(C (2:ℝ)*X+1)^(T-z)) = + (integerCoupling 2 z (T-z)).map (algebraMap ℚ ℝ) := by + simp [integerCoupling] + rw [he,comp_C_mul_X_coeff,coeff_map,monomialWeight_roots, + uCoefficient_eq_coeff hz,Nat.add_sub_of_le hz] + change _ = (algebraMap ℚ ℝ _) * _ * _ * _ / _ + simp only [one_div,inv_pow] + ring + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/RationalCreatedGram.lean b/lean/OAI/Analysis/LaughlinGap/RationalCreatedGram.lean new file mode 100644 index 0000000000000000000000000000000000000000..01e6a05dedaa176122c2b4a72e5a10f0e140b475 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/RationalCreatedGram.lean @@ -0,0 +1,135 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.ExteriorTermExpansion + +namespace OAI + +/-! Rational Created Gram. -/ + +noncomputable section + + +namespace LaughlinGap.Occupation +open scoped BigOperators + +lemma wordSign_ne_zero_nodup {n : ℕ} (js : List (Fin n)) (h : wordSign js ≠ 0) : js.Nodup := by + induction js with + | nil => simp + | cons j js ih => + by_cases hj : j ∈ js + · exact False.elim (h (by simp [wordSign,hj])) + · exact List.nodup_cons.mpr ⟨hj,ih (by intro he; apply h; simp [wordSign,hj,he])⟩ + +end LaughlinGap.Occupation + +namespace LaughlinGap.RealOccupation +open scoped BigOperators InnerProduct +open Spin + +noncomputable def rootSetWeight {n : ℕ} (A : Finset (Fin n)) : ℝ := + ∏ a ∈ A, rootFactorial a.val + +def setFactorial {n : ℕ} (A : Finset (Fin n)) : ℚ := ∏ a ∈ A, (a.val.factorial : ℚ) + +lemma rootSetWeight_sq {n : ℕ} (A : Finset (Fin n)) : + rootSetWeight A^2 = (setFactorial A:ℝ) := by + simp [rootSetWeight,setFactorial,← Finset.prod_pow] + +lemma rootSetWeight_ne_zero {n : ℕ} (A : Finset (Fin n)) : rootSetWeight A ≠ 0 := by + exact Finset.prod_ne_zero_iff.mpr fun a _ => rootFactorial_ne_zero a.val + +def fourColumn {D : ℕ} (hD : D ≤ 23) (r : ℕ) (A : Finset (Fin 25)) : ℚ := + ∑ a : FourTerm D, if (fourTermLabels hD a).toFinset=A then + fourTermCoefficient D r a * Occupation.wordSign (fourTermLabels hD a) else 0 + +def fourKeys {D : ℕ} (hD : D ≤ 23) : Finset (Finset (Fin 25)) := + (Finset.univ.filter (fun a : FourTerm D => (fourTermLabels hD a).Nodup)).image + (fun a => (fourTermLabels hD a).toFinset) + +lemma fourColumn_support {D : ℕ} (hD : D ≤ 23) (r : ℕ) (A : Finset (Fin 25)) + (h : A ∉ fourKeys hD) : fourColumn hD r A = 0 := by + apply Finset.sum_eq_zero + intro a ha + by_cases he : (fourTermLabels hD a).toFinset=A + · have hz : Occupation.wordSign (fourTermLabels hD a)=0 := by + by_contra hz + apply h + exact Finset.mem_image.mpr ⟨a,Finset.mem_filter.mpr ⟨ha,Occupation.wordSign_ne_zero_nodup _ hz⟩,he⟩ + simp [he,hz] + · simp [he] + +lemma four_term_denominator {D : ℕ} (hD : D ≤ 23) (r : ℕ) (a : FourTerm D) : + copyNormalization D r * (fourTermCoefficient D r a : ℝ) * + (Occupation.wordSign (fourTermLabels hD a):ℝ) / + (rootFactorial (fourTermX a)*rootFactorial (fourTermY a)* + rootFactorial (fourTermJ a)*rootFactorial (fourTermK a)) = + copyNormalization D r * + (fourTermCoefficient D r a * Occupation.wordSign (fourTermLabels hD a):ℚ) / + rootSetWeight (fourTermLabels hD a).toFinset := by + by_cases hs : Occupation.wordSign (fourTermLabels hD a)=0 + · simp [hs] + · have hn := Occupation.wordSign_ne_zero_nodup _ hs + rw [rootSetWeight,List.prod_toFinset _ hn] + simp only [fourTermLabels,List.map_cons,List.prod_cons,List.map_nil,List.prod_nil,mul_one, + Rat.cast_mul] + ring + +lemma four_created_column {D : ℕ} (hD : D ≤ 23) (r : FourCopy D) (A : Finset (Fin 25)) : + ((fourLocalHighestStar hD r).adjoint (Occupation.vacuum 25)) A = + ((copyNormalization D r.val.val * (fourColumn hD r.val.val A:ℝ) / rootSetWeight A : ℝ):ℂ) := by + rw [fourLocalHighestStar_terms] + simp only [fourColumn,Rat.cast_sum] + rw [Finset.mul_sum,Finset.sum_div] + simp only [map_sum,map_smulₛₗ,LinearMap.sum_apply,LinearMap.smul_apply, + Occupation.word_adjoint_vacuum,smul_smul,WithLp.ofLp_sum,Finset.sum_apply,WithLp.ofLp_smul,Pi.smul_apply,PiLp.single_apply, + smul_eq_mul,map_mul,Complex.conj_ofReal,Complex.ofReal_sum] + apply Finset.sum_congr rfl + intro a ha + by_cases he : (fourTermLabels hD a).toFinset=A + · simp only [he,← Complex.ofReal_ratCast,← Complex.ofReal_mul] + rw [four_pair_normalization] + have hd := four_term_denominator hD r.val.val a + rw [he] at hd + push_cast + norm_cast + convert hd using 1 + ring + · have hne : A ≠ (fourTermLabels hD a).toFinset := Ne.symm he + simp only [ite_eq_right he,ite_eq_right hne,Rat.cast_zero,mul_zero,zero_div,Complex.ofReal_zero] + +def rationalCreatedGram {D : ℕ} (hD : D ≤ 23) : Matrix (FourCopy D) (FourCopy D) ℚ := + fun u v => ∑ A ∈ fourKeys hD, fourColumn hD u.val.val A * fourColumn hD v.val.val A / setFactorial A + +lemma createdGram_rational {D : ℕ} (hD : D ≤ 23) (u v : FourCopy D) : + Occupation.createdGram (fourLocalHighestStar hD) u v = + ((copyNormalization D u.val.val * (rationalCreatedGram hD u v:ℝ) * + copyNormalization D v.val.val : ℝ):ℂ) := by + unfold Occupation.createdGram + simp only [PiLp.inner_apply,RCLike.inner_apply, + four_created_column,Complex.conj_ofReal] + have he : (∑ A : Finset (Fin 25), + (copyNormalization D u.val.val * (fourColumn hD u.val.val A:ℝ) / rootSetWeight A)* + (copyNormalization D v.val.val * (fourColumn hD v.val.val A:ℝ) / rootSetWeight A)) = + ∑ A ∈ fourKeys hD, + (copyNormalization D u.val.val * (fourColumn hD u.val.val A:ℝ) / rootSetWeight A)* + (copyNormalization D v.val.val * (fourColumn hD v.val.val A:ℝ) / rootSetWeight A) := by + symm + apply Finset.sum_subset (Finset.subset_univ _) + intro A ha hnot + simp [fourColumn_support hD u.val.val A hnot] + simp only [← Complex.ofReal_mul,← Complex.ofReal_sum] + simp only [mul_comm (copyNormalization D v.val.val * _ / _) + (copyNormalization D u.val.val * _ / _)] + rw [he] + congr 1 + simp only [rationalCreatedGram,Rat.cast_sum,Rat.cast_div,Rat.cast_mul, + Finset.mul_sum,Finset.sum_mul] + apply Finset.sum_congr rfl + intro A ha + rw [← rootSetWeight_sq] + ring + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/RationalExterior.lean b/lean/OAI/Analysis/LaughlinGap/RationalExterior.lean new file mode 100644 index 0000000000000000000000000000000000000000..7a33cfdeeea57c5136532fa2bfbdb27be03307ca --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/RationalExterior.lean @@ -0,0 +1,113 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.RationalFourCoefficients +import OAI.Analysis.LaughlinGap.RationalRows + +namespace OAI + +/-! Rational Exterior. -/ + +noncomputable section + + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct + +def wordSign {n : ℕ} : List (Fin n) → ℚ + | [] => 1 + | j :: js => if j ∈ js then 0 else + (-1:ℚ)^(js.toFinset.filter (fun k => k < j)).card * wordSign js + +lemma word_empty (n : ℕ) (js : List (Fin n)) (x : Hilbert n) : + word js x ∅ = (wordSign js : ℂ) * x js.toFinset := by + induction js generalizing x with + | nil => simp [wordSign,word] + | cons j js ih => + rw [word_cons,Module.End.mul_apply,ih] + by_cases h : j ∈ js + · simp [wordSign,h,transition_apply,List.mem_toFinset] + · simp only [wordSign,Rat.cast_mul,Rat.cast_pow,Rat.cast_neg,Rat.cast_one, + transition_apply,List.mem_toFinset,h,decide_false,ite_true,flip_of_not_mem + (show j ∉ js.toFinset by simpa using h),List.toFinset_cons,sign,ite_false] + ring + +lemma word_adjoint_vacuum {n : ℕ} (js : List (Fin n)) : + (word js).adjoint (vacuum n) = (wordSign js : ℂ) • EuclideanSpace.single js.toFinset 1 := by + apply ext_inner_right ℂ + intro x + simp only [LinearMap.adjoint_inner_left,inner_vacuum_left,word_empty,inner_smul_left, + EuclideanSpace.inner_single_left,map_ratCast] + simp + +end LaughlinGap.Occupation + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Spin + +lemma limitingPair_roots {p x y : ℕ} (h : x+y=p+1) : + limitingExteriorPairCoefficient p x y = ((x:ℝ)-(y:ℝ))*rootFactorial p / + (Real.sqrt 2^p*rootFactorial x*rootFactorial y) := by + have he : Real.sqrt ((2:ℝ)^p) = Real.sqrt 2^p := + (Real.sqrt_eq_iff_eq_sq (by positivity) (by positivity)).mpr (sqrt_natpow_sq (by norm_num) p).symm + unfold limitingExteriorPairCoefficient + rw [ite_eq_left h,Real.sqrt_div (by positivity),Real.sqrt_mul (by positivity : (0:ℝ) ≤ 2^p * x.factorial), + Real.sqrt_mul (by positivity : (0:ℝ) ≤ 2^p),he] + dsimp [rootFactorial] + ring + +abbrev FourTerm (D : ℕ) := + (Σ n : Fin (D+1), Fin ((n.val+1)/2) × Fin ((D-n.val+2)/2)) + +def fourTermP {D : ℕ} (a : FourTerm D) : ℕ := D-a.1.val + +def fourTermJ {D : ℕ} (a : FourTerm D) : ℕ := a.2.1.val + +def fourTermK {D : ℕ} (a : FourTerm D) : ℕ := a.1.val-a.2.1.val + +def fourTermX {D : ℕ} (a : FourTerm D) : ℕ := a.2.2.val + +def fourTermY {D : ℕ} (a : FourTerm D) : ℕ := D-a.1.val+1-a.2.2.val + +lemma fourTerm_balance {D : ℕ} (a : FourTerm D) : + fourTermX a+fourTermY a=fourTermP a+1 ∧ + fourTermP a+fourTermJ a+fourTermK a=D ∧ + fourTermX a + (if u=v then ((if u.val.val=1 then 2 else 0)+ε)*copyNormalizationSq D u.val.val else 0) - + copyNormalizationSq D u.val.val * (∑ a, (rows a).fourMatrix D u v) * + copyNormalizationSq D v.val.val + +def rationalFourCompression (rows : ι → RationalRow) (ε : ℚ) {D : ℕ} (hD : D ≤ 23) : + Matrix (FourCopy D) (FourCopy D) ℚ := + rationalCreatedGram hD * rationalFourComparison rows ε D * rationalCreatedGram hD + +noncomputable def copyDiagonal (D : ℕ) : Matrix (FourCopy D) (FourCopy D) ℂ := + Matrix.diagonal (fun r => (copyNormalization D r.val.val:ℂ)) + +lemma createdGram_eq_diagonal {D : ℕ} (hD : D ≤ 23) : + Occupation.createdGram (fourLocalHighestStar hD) = + copyDiagonal D * (rationalCreatedGram hD).map (algebraMap ℚ ℂ) * copyDiagonal D := by + ext u v + simp only [copyDiagonal,Matrix.diagonal_mul,Matrix.mul_diagonal,Matrix.map_apply] + rw [createdGram_rational] + push_cast + rfl + +lemma rationalFourComparison_real (rows : ι → RationalRow) (ε : ℚ) (D : ℕ) : + (rationalFourComparison rows ε D).map (algebraMap ℚ ℝ) = + Matrix.diagonal (fun u : FourCopy D => copyNormalization D u.val.val) * + fourComparisonStar (fun a => (rows a).toReal) (ε:ℝ) D * + Matrix.diagonal (fun u : FourCopy D => copyNormalization D u.val.val) := by + ext u v + simp only [Matrix.diagonal_mul,Matrix.mul_diagonal,Matrix.map_apply, + rationalFourComparison,fourComparisonStar,Matrix.add_apply,Matrix.sub_apply, + Matrix.sum_apply,Matrix.smul_apply,smul_eq_mul,RationalRow.fourMatrix_eq] + change (((if u=v then ((if u.val.val=1 then 2 else 0)+ε)*copyNormalizationSq D u.val.val else 0) - + copyNormalizationSq D u.val.val * (∑ a, (rows a).fourMatrix D u v) * + copyNormalizationSq D v.val.val : ℚ) : ℝ) = _ + by_cases h : u=v + · subst v + simp only [ite_true,Matrix.one_apply_eq,mul_one,fourCopyTarget,and_self] + by_cases hu : u.val.val=1 + all_goals simp only [hu,ite_true,ite_false]; push_cast + all_goals simp only [← Finset.mul_sum,← Finset.sum_mul,← copyNormalization_sq]; ring + · have ht : ¬ (u.val.val=1 ∧ v.val.val=1) := by + rintro ⟨hu,hv⟩ + exact h (Subtype.ext (Fin.ext (hu.trans hv.symm))) + simp only [ite_eq_right h,Matrix.one_apply_ne h,mul_zero,add_zero,fourCopyTarget,ite_eq_right ht, + zero_sub] + push_cast + simp only [← Finset.mul_sum,← Finset.sum_mul,← copyNormalization_sq] + ring + +lemma rationalFourComparison_eq (rows : ι → RationalRow) (ε : ℚ) (D : ℕ) : + (rationalFourComparison rows ε D).map (algebraMap ℚ ℂ) = + copyDiagonal D * (fourComparisonStar (fun a => (rows a).toReal) (ε:ℝ) D).map + (algebraMap ℝ ℂ) * copyDiagonal D := by + have h := congrArg (fun A : Matrix (FourCopy D) (FourCopy D) ℝ => + A.map (algebraMap ℝ ℂ)) (rationalFourComparison_real rows ε D) + convert h using 1 + · ext u v + simp [Matrix.map_apply] + · simp only [Matrix.map_mul,Matrix.diagonal_map (map_zero _)] + rfl + +lemma fourCertificate_of_rational (rows : ι → RationalRow) (ε : ℚ) {D : ℕ} (hD : D ≤ 23) + (h : ((rationalFourCompression rows ε hD).map (algebraMap ℚ ℂ)).PosSemidef) : + FourCertificate (fun a => (rows a).toReal) (ε:ℝ) D hD := by + have he : (copyDiagonal D).conjTranspose=copyDiagonal D := by + simp [copyDiagonal] + have hp := h.mul_mul_conjTranspose_same (copyDiagonal D) + rw [he] at hp + unfold FourCertificate + rw [createdGram_eq_diagonal] + convert hp using 1 + rw [rationalFourCompression,Matrix.map_mul,Matrix.map_mul,rationalFourComparison_eq] + simp only [Matrix.mul_assoc] + +lemma rational_ldl_positive {κ : Type*} [Fintype κ] [DecidableEq κ] + (M L : Matrix κ κ ℚ) (d : κ → ℚ) (hd : ∀ i, 0 ≤ d i) + (he : M = L * Matrix.diagonal d * L.transpose) : + (M.map (algebraMap ℚ ℂ)).PosSemidef := by + have hp : (Matrix.diagonal (fun i => (d i:ℂ))).PosSemidef := by + apply Matrix.posSemidef_diagonal_iff.mpr + intro i + simpa only [← Complex.ofReal_ratCast,Complex.nonneg_iff,Complex.ofReal_re,Complex.ofReal_im, + and_true] using (Rat.cast_nonneg (K := ℝ)).mpr (hd i) + have hh := hp.mul_mul_conjTranspose_same (L.map (algebraMap ℚ ℂ)) + convert hh using 1 + rw [he,Matrix.map_mul,Matrix.map_mul] + congr 1 + · congr 1 + ext i j + by_cases h : i=j <;> simp [h] + · ext i j + simp [Matrix.conjTranspose_apply] + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/RationalFourCoefficients.lean b/lean/OAI/Analysis/LaughlinGap/RationalFourCoefficients.lean new file mode 100644 index 0000000000000000000000000000000000000000..6abd5e507446f9915d80f12a20b6517c2872a96b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/RationalFourCoefficients.lean @@ -0,0 +1,74 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.FourComparison +import OAI.Analysis.LaughlinGap.RationalCoupling + +namespace OAI + +/-! Rational Four Coefficients. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Spin + +def vCoefficient (D T r p j k : ℕ) : ℚ := + if D ≤ T ∧ r ≤ j+k ∧ p+j+k=T then + uCoefficient 1 r (j+k) j * uCoefficient 1 (D-r) (T-r) p else 0 + +noncomputable def copyNormalization (D r : ℕ) : ℝ := + 1/(rootFactorial r*rootFactorial (D-r)) + +lemma two_pow_odd_sqrt {r : ℕ} (hr : Odd r) : + (2:ℝ)^((r+1)/2) = Real.sqrt 2 ^ (r+1) := by + have he : 2*((r+1)/2) = r+1 := by obtain ⟨k,hk⟩ := hr; omega + calc + (2:ℝ)^((r+1)/2) = (Real.sqrt 2 ^ 2)^((r+1)/2) := by + rw [Real.sq_sqrt (by norm_num : (0:ℝ) ≤ 2)] + _ = Real.sqrt 2^(r+1) := by rw [← pow_mul,he] + +lemma coupling_exponent_identity {p j k T r : ℕ} (ht : p+j+k=T) (hr : r ≤ j+k) + (ho : Odd r) : + Real.sqrt 2 * (2:ℝ)^T = (2:ℝ)^((r+1)/2) * Real.sqrt 2 ^ p * + Real.sqrt 2 ^ (j+k) * Real.sqrt 2 ^ (T-r) := by + rw [two_pow_odd_sqrt ho] + have hpow : (2:ℝ)^T = Real.sqrt 2^(2*T) := by + rw [pow_mul,Real.sq_sqrt (by norm_num : (0:ℝ) ≤ 2)] + rw [hpow,← pow_add,← pow_add,← pow_add,← pow_succ'] + congr 1 + omega + +lemma fourWeightCoefficientStar_rational {D r : ℕ} (hD : r ≤ D) (ho : Odd r) + (T p j k : ℕ) : + fourWeightCoefficientStar D T r p j k = + (vCoefficient D T r p j k : ℝ) * (2:ℝ)^((r+1)/2) * Real.sqrt 2 ^ p * + rootFactorial p * rootFactorial j * rootFactorial k * copyNormalization D r / + ((2:ℝ)^T * rootFactorial (T-D)) := by + by_cases hT : D ≤ T + · by_cases ht : r ≤ j+k ∧ p+j+k=T + · have hr : D-r ≤ T-r := Nat.sub_le_sub_right hT r + have he₁ : j+k-j=k := by omega + have he₂ : T-r-p=j+k-r := by omega + have he₃ : T-r-(D-r)=T-D := by omega + rw [fourWeightCoefficientStar,ite_eq_left hT,fourBodyCoefficientStar,ite_eq_left ht, + balancedCouplingCoefficient_rational ht.1,balancedCouplingCoefficient_rational hr, + he₁,he₂,he₃,vCoefficient,ite_eq_left ⟨hT,ht.1,ht.2⟩] + push_cast + unfold copyNormalization + have he := coupling_exponent_identity ht.2 ht.1 ho + field_simp [rootFactorial_ne_zero, + Real.sqrt_ne_zero'.mpr (by norm_num : (0:ℝ) < 2)] + linear_combination + (uCoefficient 1 r (j+k) j : ℝ) * (uCoefficient 1 (D-r) (T-r) p : ℝ) * he + · simp only [fourWeightCoefficientStar,ite_eq_left hT,fourBodyCoefficientStar,ite_eq_right ht] + have hn : ¬ (D ≤ T ∧ r ≤ j+k ∧ p+j+k=T) := by tauto + simp only [vCoefficient,ite_eq_right hn,Rat.cast_zero,zero_mul,zero_div] + · have hn : ¬ (D ≤ T ∧ r ≤ j+k ∧ p+j+k=T) := by tauto + simp [fourWeightCoefficientStar,hT,vCoefficient] + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/RationalFourComputable.lean b/lean/OAI/Analysis/LaughlinGap/RationalFourComputable.lean new file mode 100644 index 0000000000000000000000000000000000000000..bf3b7a6c819f04a877d3bc1fd5cb3b3b598ba376 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/RationalFourComputable.lean @@ -0,0 +1,55 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.RationalFourRows +import OAI.Analysis.LaughlinGap.RationalRowComputable + +namespace OAI + +/-! Rational Four Computable. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Spin + +def RationalRow.fourSumFast (r : RationalRow) (D s : ℕ) (i k : Fin 9) : ℚ := + ∑ p : Fin 8, if h : p.val ≤ r.t.val+i.val ∧ r.t.val+i.val-p.val < 9 then + r.alpha p ⟨r.t.val+i.val-p.val,h.2⟩ * + vCoefficient D (r.t.val+i.val+k.val) s p.val (r.t.val+i.val-p.val) k.val * + (2:ℚ)^((s+1)/2+p.val) else 0 + +lemma RationalRow.fourSum_eq_fast (r : RationalRow) (D s : ℕ) (i k : Fin 9) : + r.fourSum D s i k = r.fourSumFast D s i k := by + rw [RationalRow.fourSum,sum_row_fiber r.t i (fun p j => + r.alpha p j * vCoefficient D (r.t.val+i.val+k.val) s p.val j.val k.val * + (2:ℚ)^((s+1)/2+p.val))] + simp only [sum_fixed_pair,RationalRow.fourSumFast] + +def RationalRow.fourMatrixFast (r : RationalRow) (D u v : ℕ) : ℚ := + -(∑ i : Fin 9, ∑ k : Fin 9, fourRowFactor r.t.val D i.val k.val * + r.fourSumFast D u i k * r.fourSumFast D v k i) + +lemma RationalRow.fourMatrix_eq_fast (r : RationalRow) (D : ℕ) (u v : FourCopy D) : + r.fourMatrix D u v = r.fourMatrixFast D u.val.val v.val.val := by + simp only [RationalRow.fourMatrix,RationalRow.fourMatrixFast,RationalRow.fourSum_eq_fast] + +def fourCopyEquiv (D : ℕ) : FourCopy D ≃ Fin ((D+1)/2) where + toFun r := ⟨r.val.val/2, by have := r.val.isLt; obtain ⟨k,hk⟩ := r.property; omega⟩ + invFun i := ⟨⟨2*i.val+1,by have := i.isLt; omega⟩,⟨i.val,by rfl⟩⟩ + left_inv r := by + apply Subtype.ext; apply Fin.ext + have := r.property + obtain ⟨k,hk⟩ := this + dsimp + omega + right_inv i := by apply Fin.ext; dsimp; omega + +@[simp] lemma fourCopyEquiv_symm_val (D : ℕ) (i : Fin ((D+1)/2)) : + ((fourCopyEquiv D).symm i).val.val = 2*i.val+1 := rfl + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/RationalFourRows.lean b/lean/OAI/Analysis/LaughlinGap/RationalFourRows.lean new file mode 100644 index 0000000000000000000000000000000000000000..765e404ec6e0116d07a893f91d2949b2e4d860d1 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/RationalFourRows.lean @@ -0,0 +1,158 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.RationalFourCoefficients +import OAI.Analysis.LaughlinGap.RationalRows + +namespace OAI + +/-! Rational Four Rows. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Spin + +noncomputable def fourRowScale (t D i k : ℕ) : ℝ := + if D ≤ t+i+k then rootFactorial t * rootFactorial i * rootFactorial k / + ((2:ℝ)^(t+i+k)*Real.sqrt 2^t*rootFactorial (t+i+k-D)) else 0 + +def fourRowFactor (t D i k : ℕ) : ℚ := + if D ≤ t+i+k then (t.factorial * i.factorial * k.factorial : ℚ) / + ((2:ℚ)^(2*(t+i+k)+t)*(t+i+k-D).factorial) else 0 + +lemma fourRowScale_swap (t D i k : ℕ) : fourRowScale t D i k = fourRowScale t D k i := by + have he : t+i+k=t+k+i := by omega + simp only [fourRowScale,he] + split_ifs <;> ring + +lemma fourRowScale_sq (t D i k : ℕ) : (fourRowScale t D i k)^2 = (fourRowFactor t D i k : ℝ) := by + by_cases h : D ≤ t+i+k + · simp only [fourRowScale,fourRowFactor,ite_eq_left h,div_pow,mul_pow,rootFactorial_sq, + sqrt_natpow_sq (by norm_num : (0:ℝ) ≤ 2)] + push_cast + rw [← pow_mul,← pow_add] + simp only [Nat.mul_comm] + · simp [fourRowScale,fourRowFactor,h] + +lemma rowNormalization_four {t : Fin 8} (a : RowEntry t) {D r : ℕ} + (hr : r ≤ D) (ho : Odd r) (k : ℕ) : + rowNormalization t.val a.val.1.val a.val.2.val * + fourWeightCoefficientStar D (t.val+a.output.val+k) r a.val.1.val a.val.2.val k = + ((vCoefficient D (t.val+a.output.val+k) r a.val.1.val a.val.2.val k * + (2:ℚ)^((r+1)/2+a.val.1.val) : ℚ) : ℝ) * copyNormalization D r * + fourRowScale t.val D a.output.val k := by + by_cases hD : D ≤ t.val+a.output.val+k + · rw [fourWeightCoefficientStar_rational hr ho,fourRowScale,ite_eq_left hD] + dsimp [rowNormalization,RowEntry.output] + push_cast + have ht : (Real.sqrt 2 ^ a.val.1.val)^2 = (2:ℝ)^a.val.1.val := sqrt_natpow_sq (by norm_num) _ + field_simp [rootFactorial_ne_zero,Real.sqrt_ne_zero'.mpr (by norm_num : (0:ℝ) < 2)] + linear_combination (vCoefficient D (t.val+(a.val.1.val+a.val.2.val-t.val)+k) + r a.val.1.val a.val.2.val k : ℝ) * (2:ℝ)^((r+1)/2) * copyNormalization D r * ht + · simp [fourWeightCoefficientStar,vCoefficient,fourRowScale,hD] + +lemma sum_fibers_cross {α β S : Type*} [Fintype α] [Fintype β] [DecidableEq β] + [CommSemiring S] (o : α → β) (f g : α → β → S) : + (∑ i, ∑ k, (∑ a, if o a=i then f a k else 0) * + (∑ b, if o b=k then g b i else 0)) = ∑ a, ∑ b, f a (o b)*g b (o a) := by + calc + _ = ∑ i, ∑ b, g b i*(∑ a, if o a=i then f a (o b) else 0) := by + apply Finset.sum_congr rfl + intro i hi + simpa only [mul_comm] using sum_fibers_multiply o (fun b => g b i) + (fun k => ∑ a, if o a=i then f a k else 0) + _ = ∑ b, ∑ i, (∑ a, if o a=i then f a (o b) else 0)*g b i := by + rw [Finset.sum_comm] + simp only [mul_comm] + _ = ∑ b, ∑ a, f a (o b)*g b (o a) := by + simp only [sum_fibers_multiply] + _ = _ := Finset.sum_comm + +lemma rowFourMatrix_regroup (s : ℕ → ℕ → ℕ → ℕ → ℕ → ℕ → ℝ) + (D : ℕ) (r : RowData) (u v : FourCopy D) : + rowFourMatrix s D r u v = -(∑ i : Fin 9, ∑ k : Fin 9, + (∑ a : RowEntry r.t, if a.output=i then r.alpha a * + s D (r.t.val+i.val+k.val) u.val.val a.val.1.val a.val.2.val k.val else 0) * + (∑ b : RowEntry r.t, if b.output=k then r.alpha b * + s D (r.t.val+i.val+k.val) v.val.val b.val.1.val b.val.2.val i.val else 0)) := by + classical + have hf (i k : Fin 9) (w : FourCopy D) : + (∑ a : RowEntry r.t, if a.output=i then r.alpha a * + s D (r.t.val+i.val+k.val) w.val.val a.val.1.val a.val.2.val k.val else 0) = + ∑ a : RowEntry r.t, if a.output=i then r.alpha a * + s D (r.t.val+a.output.val+k.val) w.val.val a.val.1.val a.val.2.val k.val else 0 := by + apply Finset.sum_congr rfl + intro a ha + split_ifs with h + · rw [h] + · rfl + have hk (i k : Fin 9) : r.t.val+i.val+k.val=r.t.val+k.val+i.val := by omega + conv_rhs => arg 1; arg 2; ext i; arg 2; ext k; arg 2; rw [hk i k] + simp_rw [hf] + rw [sum_fibers_cross] + unfold rowFourMatrix + congr 1 + apply Finset.sum_congr rfl + intro a ha + apply Finset.sum_congr rfl + intro b hb + rw [a.balance] + have he : r.t.val+b.output.val+a.output.val=a.val.1.val+a.val.2.val+b.output.val := by + have := a.balance; omega + rw [he] + ring + +def RationalRow.fourSum (r : RationalRow) (D s : ℕ) (i k : Fin 9) : ℚ := + ∑ a : RowEntry r.t, if a.output=i then r.alpha a.val.1 a.val.2 * + vCoefficient D (r.t.val+i.val+k.val) s a.val.1.val a.val.2.val k.val * + (2:ℚ)^((s+1)/2+a.val.1.val) else 0 + +def RationalRow.fourMatrix (r : RationalRow) (D : ℕ) : Matrix (FourCopy D) (FourCopy D) ℚ := + fun u v => -(∑ i : Fin 9, ∑ k : Fin 9, fourRowFactor r.t.val D i.val k.val * + r.fourSum D u.val.val i k * r.fourSum D v.val.val k i) + +lemma RationalRow.fourSum_normalized (r : RationalRow) (D : ℕ) (s : FourCopy D) (i k : Fin 9) : + (∑ a : RowEntry r.t, if a.output=i then r.toReal.alpha a * + fourWeightCoefficientStar D (r.t.val+i.val+k.val) s.val.val a.val.1.val a.val.2.val k.val else 0) = + (r.fourSum D s.val.val i k : ℝ) * copyNormalization D s.val.val * + fourRowScale r.t.val D i.val k.val := by + unfold RationalRow.fourSum + push_cast + rw [Finset.sum_mul,Finset.sum_mul] + apply Finset.sum_congr rfl + intro a ha + by_cases h : a.output=i + · simp only [ite_eq_left h,RationalRow.toReal] + rw [mul_assoc,← h,rowNormalization_four a (Nat.le_of_lt_succ s.val.isLt) s.property] + push_cast + ring + · simp [h] + +lemma RationalRow.fourMatrix_eq (r : RationalRow) (D : ℕ) (u v : FourCopy D) : + rowFourMatrix fourWeightCoefficientStar D r.toReal u v = + copyNormalization D u.val.val * (r.fourMatrix D u v : ℝ) * copyNormalization D v.val.val := by + rw [rowFourMatrix_regroup] + change -(∑ i : Fin 9, ∑ k : Fin 9, + (∑ a : RowEntry r.t, if a.output=i then r.toReal.alpha a * + fourWeightCoefficientStar D (r.t.val+i.val+k.val) u.val.val a.val.1.val a.val.2.val k.val else 0) * + (∑ b : RowEntry r.t, if b.output=k then r.toReal.alpha b * + fourWeightCoefficientStar D (r.t.val+i.val+k.val) v.val.val b.val.1.val b.val.2.val i.val else 0)) = _ + have he (i k : Fin 9) : r.t.val+i.val+k.val=r.t.val+k.val+i.val := by omega + conv_lhs => arg 1; arg 2; ext i; arg 2; ext k; arg 2; rw [he i k] + simp only [RationalRow.fourSum_normalized] + simp only [RationalRow.fourMatrix,Rat.cast_neg,Rat.cast_sum,Rat.cast_mul] + simp only [mul_neg,neg_mul,Finset.mul_sum,Finset.sum_mul] + congr 1 + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro k hk + rw [fourRowScale_swap r.t.val D k.val i.val,← fourRowScale_sq] + ring + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/RationalRowComputable.lean b/lean/OAI/Analysis/LaughlinGap/RationalRowComputable.lean new file mode 100644 index 0000000000000000000000000000000000000000..126de60a61bcbbf0af1423c55c914e0570a6f971 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/RationalRowComputable.lean @@ -0,0 +1,75 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.RationalRows + +namespace OAI + +/-! Rational Row Computable. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Spin + +lemma sum_row_fiber {S : Type*} [AddCommMonoid S] (t : Fin 8) (i : Fin 9) + (f : Fin 8 → Fin 9 → S) : + (∑ a : RowEntry t, if a.output=i then f a.val.1 a.val.2 else 0) = + ∑ p : Fin 8, ∑ j : Fin 9, if p.val+j.val=t.val+i.val then f p j else 0 := by + classical + rw [← Fintype.sum_prod_type (fun a : Fin 8 × Fin 9 => + if a.1.val+a.2.val=t.val+i.val then f a.1 a.2 else 0)] + symm + apply Finset.sum_congr_set (s := {a : Fin 8 × Fin 9 | t.val ≤ a.1.val+a.2.val ∧ + a.1.val+a.2.val ≤ t.val+8}) + · intro a ha + change t.val ≤ a.1.val+a.2.val ∧ a.1.val+a.2.val ≤ t.val+8 at ha + have he : a.1.val+a.2.val=t.val+i.val ↔ RowEntry.output (⟨a,ha⟩ : RowEntry t)=i := by + simp only [RowEntry.output,Fin.ext_iff] + omega + simp only [he] + · intro a ha + change ¬ (t.val ≤ a.1.val+a.2.val ∧ a.1.val+a.2.val ≤ t.val+8) at ha + have hi := i.isLt + have hn : a.1.val+a.2.val ≠ t.val+i.val := by omega + simp only [ite_eq_right hn] + +lemma sum_fixed_pair {S : Type*} [AddCommMonoid S] (T : ℕ) (p : Fin 8) + (f : Fin 9 → S) : + (∑ j : Fin 9, if p.val+j.val=T then f j else 0) = + if h : p.val ≤ T ∧ T-p.val < 9 then f ⟨T-p.val,h.2⟩ else 0 := by + classical + by_cases h : p.val ≤ T ∧ T-p.val < 9 + · rw [dite_eq_left h] + rw [Finset.sum_eq_single (⟨T-p.val,h.2⟩ : Fin 9)] + · simp only [Nat.add_sub_of_le h.1,ite_true] + · intro j hj hn + have he : p.val+j.val ≠ T := by + intro he + apply hn + apply Fin.ext + dsimp + omega + simp only [ite_eq_right he] + · simp + · rw [dite_eq_right h] + apply Finset.sum_eq_zero + intro j hj + have he : p.val+j.val ≠ T := by have := j.isLt; omega + simp only [ite_eq_right he] + +def RationalRow.threeSumFast (r : RationalRow) (z : ℕ) (i : Fin 9) : ℚ := + ∑ p : Fin 8, if h : p.val ≤ r.t.val+i.val ∧ r.t.val+i.val-p.val < 9 then + r.alpha p ⟨r.t.val+i.val-p.val,h.2⟩ * uCoefficient 2 z (r.t.val+i.val) p.val else 0 + +lemma RationalRow.threeSum_eq_fast (r : RationalRow) (z : ℕ) (i : Fin 9) : + r.threeSum z i = r.threeSumFast z i := by + rw [RationalRow.threeSum,sum_row_fiber r.t i (fun p j => + r.alpha p j * uCoefficient 2 z (r.t.val+i.val) p.val)] + simp only [sum_fixed_pair,RationalRow.threeSumFast] + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/RationalRows.lean b/lean/OAI/Analysis/LaughlinGap/RationalRows.lean new file mode 100644 index 0000000000000000000000000000000000000000..b77346c41b7b482dd1aba0f6234ec1e8ae2f49e0 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/RationalRows.lean @@ -0,0 +1,164 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.RationalCoupling + +namespace OAI + +/-! Rational Rows. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +open Spin + +structure RationalRow where + t : Fin 8 + lam : ℚ + alpha : Fin 8 → Fin 9 → ℚ + +noncomputable def rowNormalization (t p j : ℕ) : ℝ := + (Real.sqrt 2)^p * rootFactorial t * rootFactorial (p+j-t) / + ((Real.sqrt 2)^t * rootFactorial p * rootFactorial j) + +noncomputable def RationalRow.toReal (r : RationalRow) : RowData where + t := r.t + lam := r.lam + alpha a := (r.alpha a.val.1 a.val.2 : ℝ) * rowNormalization r.t.val a.val.1.val a.val.2.val + +noncomputable def threeRowScale (t z i : ℕ) : ℝ := + if z ≤ t+i then (Real.sqrt 2)^z * rootFactorial t * rootFactorial i / + ((Real.sqrt 3)^(t+i)*(Real.sqrt 2)^t*rootFactorial z*rootFactorial (t+i-z)) else 0 + +def threeRowFactor (t z i : ℕ) : ℚ := + if z ≤ t+i then (2:ℚ)^z * t.factorial * i.factorial / + ((3:ℚ)^(t+i)*(2:ℚ)^t*z.factorial*(t+i-z).factorial) else 0 + +lemma sqrt_natpow_sq {x : ℝ} (h : 0 ≤ x) (n : ℕ) : (Real.sqrt x ^ n)^2 = x^n := by + rw [← pow_mul,mul_comm n 2,pow_mul,Real.sq_sqrt h] + +lemma threeRowScale_sq (t z i : ℕ) : (threeRowScale t z i)^2 = (threeRowFactor t z i : ℝ) := by + by_cases h : z ≤ t+i + · simp only [threeRowScale,threeRowFactor,ite_eq_left h,div_pow,mul_pow,rootFactorial_sq, + sqrt_natpow_sq (by norm_num : (0:ℝ) ≤ 2),sqrt_natpow_sq (by norm_num : (0:ℝ) ≤ 3)] + push_cast + rfl + · simp [threeRowScale,threeRowFactor,h] + +lemma rowNormalization_three {t : Fin 8} (a : RowEntry t) (z : ℕ) : + rowNormalization t.val a.val.1.val a.val.2.val * + threeWeightCoefficientStar z (t.val+a.output.val) a.val.1.val = + (uCoefficient 2 z (t.val+a.output.val) a.val.1.val : ℝ) * + threeRowScale t.val z a.output.val := by + by_cases hz : z ≤ t.val+a.output.val + · have he : t.val+a.output.val-a.val.1.val = a.val.2.val := by have := a.balance; omega + rw [threeWeightCoefficientStar_rational hz,he,threeRowScale,ite_eq_left hz] + dsimp [rowNormalization,RowEntry.output] + field_simp [rootFactorial_ne_zero,Real.sqrt_ne_zero'.mpr (by norm_num : (0:ℝ) < 2)] + + · simp [threeWeightCoefficientStar,hz,threeRowScale] + +lemma threeWeight_row_t (t z i : ℕ) : + threeWeightCoefficientStar z (t+i) t = (uCoefficient 2 z (t+i) t : ℝ) * + threeRowScale t z i := by + by_cases hz : z ≤ t+i + · rw [threeWeightCoefficientStar_rational hz,threeRowScale,ite_eq_left hz,Nat.add_sub_cancel_left] + ring + · simp [threeWeightCoefficientStar,threeRowScale,hz] + +lemma sum_fibers_multiply {α β S : Type*} [Fintype α] [Fintype β] [DecidableEq β] + [CommSemiring S] (o : α → β) (f : α → S) (g : β → S) : + (∑ i, (∑ a, if o a=i then f a else 0)*g i) = ∑ a, f a*g (o a) := by + simp only [Finset.sum_mul] + rw [Finset.sum_comm] + simp [ite_mul] + +lemma sum_fibers_trace {α β S : Type*} [Fintype α] [Fintype β] [DecidableEq β] + [CommSemiring S] (o : α → β) (f : α → S) (g : β → S) : + (∑ a, f a*g (o a)) + (∑ a, ∑ b, if o a=o b then f a*f b else 0) = + ∑ i, (∑ a, if o a=i then f a else 0)*((∑ a, if o a=i then f a else 0)+g i) := by + rw [sum_fibers_multiply] + simp only [mul_add,Finset.sum_add_distrib,Finset.mul_sum,mul_ite,mul_zero] + rw [add_comm] + congr 1 + apply Finset.sum_congr rfl + intro a ha + apply Finset.sum_congr rfl + intro b hb + simp only [eq_comm] + +lemma rowTrace_regroup (s : ℕ → ℕ → ℕ → ℝ) (z : ℕ) (r : RowData) : + rowTrace s z r = ∑ i : Fin 9, + (∑ a : RowEntry r.t, if a.output=i then r.alpha a*s z (r.t.val+i.val) a.val.1.val else 0)* + ((∑ a : RowEntry r.t, if a.output=i then r.alpha a*s z (r.t.val+i.val) a.val.1.val else 0) + + 2*r.lam*s z (r.t.val+i.val) r.t.val) := by + classical + have hf (i : Fin 9) : (∑ a : RowEntry r.t, if a.output=i then + r.alpha a*s z (r.t.val+i.val) a.val.1.val else 0) = ∑ a : RowEntry r.t, + if a.output=i then r.alpha a*s z (r.t.val+a.output.val) a.val.1.val else 0 := by + apply Finset.sum_congr rfl + intro a ha + split_ifs with h + · rw [h] + · rfl + simp_rw [hf] + rw [← sum_fibers_trace] + unfold rowTrace + congr 1 + · apply Finset.sum_congr rfl + intro a ha + ring + · apply Finset.sum_congr rfl + intro a ha + apply Finset.sum_congr rfl + intro b hb + split_ifs with h + · rw [h] + ring + · rfl + +def RationalRow.threeSum (r : RationalRow) (z : ℕ) (i : Fin 9) : ℚ := + ∑ a : RowEntry r.t, if a.output=i then + r.alpha a.val.1 a.val.2 * uCoefficient 2 z (r.t.val+i.val) a.val.1.val else 0 + +def RationalRow.threeTrace (r : RationalRow) (z : ℕ) : ℚ := + ∑ i : Fin 9, threeRowFactor r.t.val z i.val * r.threeSum z i * + (r.threeSum z i + 2*r.lam*uCoefficient 2 z (r.t.val+i.val) r.t.val) + +lemma RationalRow.threeSum_normalized (r : RationalRow) (z : ℕ) (i : Fin 9) : + (∑ a : RowEntry r.t, if a.output=i then r.toReal.alpha a * + threeWeightCoefficientStar z (r.t.val+i.val) a.val.1.val else 0) = + (r.threeSum z i : ℝ) * threeRowScale r.t.val z i.val := by + unfold RationalRow.threeSum + push_cast + rw [Finset.sum_mul] + apply Finset.sum_congr rfl + intro a ha + by_cases h : a.output=i + · simp only [ite_eq_left h,RationalRow.toReal] + rw [mul_assoc,← h,rowNormalization_three] + push_cast + ring + · simp [h] + +lemma RationalRow.threeTrace_eq (r : RationalRow) (z : ℕ) : + rowTrace threeWeightCoefficientStar z r.toReal = (r.threeTrace z : ℝ) := by + rw [rowTrace_regroup] + simp only [RationalRow.toReal] + change (∑ i : Fin 9, (∑ a : RowEntry r.t, if a.output=i then r.toReal.alpha a * + threeWeightCoefficientStar z (r.t.val+i.val) a.val.1.val else 0) * + ((∑ a : RowEntry r.t, if a.output=i then r.toReal.alpha a * + threeWeightCoefficientStar z (r.t.val+i.val) a.val.1.val else 0) + + 2*(r.lam:ℝ)*threeWeightCoefficientStar z (r.t.val+i.val) r.t.val)) = _ + simp_rw [r.threeSum_normalized,threeWeight_row_t] + simp only [RationalRow.threeTrace,Rat.cast_sum,Rat.cast_mul,Rat.cast_add,Rat.cast_ofNat] + apply Finset.sum_congr rfl + intro i hi + rw [← threeRowScale_sq] + ring + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/RealOccupation.lean b/lean/OAI/Analysis/LaughlinGap/RealOccupation.lean new file mode 100644 index 0000000000000000000000000000000000000000..6675933111e0f41c097577fdc0892ea331c917d3 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/RealOccupation.lean @@ -0,0 +1,156 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Averaging +import OAI.Analysis.LaughlinGap.Creation + +namespace OAI + +/-! Real Occupation. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators InnerProduct ComplexOrder MatrixOrder Matrix.Norms.L2Operator + +variable {ι : Type*} [Fintype ι] [DecidableEq ι] + +noncomputable def complexify : Matrix ι ι ℝ →ₐ[ℝ] + Module.End ℂ (EuclideanSpace ℂ ι) where + toFun A := (A.map (algebraMap ℝ ℂ)).toEuclideanLin + map_one' := by simp [Module.End.one_eq_id] + map_mul' A B := by + rw [Matrix.map_mul, Matrix.toEuclideanLin, Matrix.toLpLin_mul_same] + rfl + map_zero' := by simp + map_add' A B := by + rw [Matrix.map_add _ (map_add (algebraMap ℝ ℂ)), map_add] + commutes' r := by + apply LinearMap.ext + intro x + ext i + simp [Algebra.algebraMap_eq_smul_one, Matrix.toLpLin_apply, + Matrix.mulVec, dotProduct, Matrix.one_apply, apply_ite] + +lemma complexify_injective : Function.Injective (complexify (ι := ι)) := by + intro A B h + apply_fun Matrix.toEuclideanLin.symm at h + simp only [complexify, AlgHom.coe_mk, RingHom.coe_mk, MonoidHom.coe_mk, + OneHom.coe_mk, LinearEquiv.symm_apply_apply] at h + ext i j + exact Complex.ofReal_injective (congrFun (congrFun h i) j) + +@[simp] lemma complexify_transpose (A : Matrix ι ι ℝ) : + complexify A.transpose = (complexify A).adjoint := by + rw [complexify, AlgHom.coe_mk, RingHom.coe_mk, MonoidHom.coe_mk, OneHom.coe_mk, + ← Matrix.toEuclideanLin_conjTranspose_eq_adjoint] + congr 1 + ext i j + simp [Matrix.conjTranspose_apply] + +lemma complexify_positive {A : Matrix ι ι ℝ} (hA : A.PosSemidef) : + (complexify A).IsPositive := by + rw [complexify, AlgHom.coe_mk, RingHom.coe_mk, MonoidHom.coe_mk, OneHom.coe_mk, + Matrix.isPositive_toEuclideanLin_iff] + obtain ⟨B, rfl⟩ := CStarAlgebra.nonneg_iff_eq_star_mul_self.mp hA.nonneg + rw [Matrix.map_mul] + have he : (star B).map (algebraMap ℝ ℂ) = + (B.map (algebraMap ℝ ℂ)).conjTranspose := by + ext i j + simp [Matrix.star_eq_conjTranspose, Matrix.conjTranspose_apply] + rw [he] + exact Matrix.posSemidef_conjTranspose_mul_self _ + +abbrev FockMatrix (n : ℕ) := Matrix (Finset (Fin n)) (Finset (Fin n)) ℝ + +noncomputable def annihilation {n : ℕ} (j : Fin n) : FockMatrix n := fun A B => + if j ∉ A ∧ B = Occupation.flip j A then + (-1 : ℝ) ^ (A.filter (fun k => k < j)).card else 0 + +noncomputable def creation {n : ℕ} (j : Fin n) : FockMatrix n := + (annihilation j).transpose + +@[simp] theorem complexify_annihilation {n : ℕ} (j : Fin n) : + complexify (annihilation j) = Occupation.annihilation j := by + apply LinearMap.ext + intro x + ext A + change (∑ B, (annihilation j A B : ℂ) * x B) = _ + by_cases hj : j ∈ A + · simp [annihilation, Occupation.annihilation, Occupation.transition, hj] + · simp [annihilation, Occupation.annihilation, Occupation.transition, hj, + Occupation.sign, apply_ite] + +@[simp] theorem complexify_creation {n : ℕ} (j : Fin n) : + complexify (creation j) = Occupation.creation j := by + rw [creation, complexify_transpose, complexify_annihilation] + exact Occupation.annihilation_adjoint j + +lemma creation_transpose {n : ℕ} (j : Fin n) : (creation j).transpose = annihilation j := + Matrix.transpose_transpose _ + +lemma annihilation_creation {n : ℕ} (i j : Fin n) : + annihilation i * creation j + creation j * annihilation i = if i=j then 1 else 0 := by + apply complexify_injective + simp only [map_add, map_mul, complexify_annihilation, complexify_creation, apply_ite, + map_one, map_zero] + by_cases h : i=j <;> simpa [h, Module.End.one_eq_id, Module.End.mul_eq_comp] using + Occupation.annihilation_creation_CAR i j + +lemma annihilation_anticommute {n : ℕ} (i j : Fin n) : + annihilation i * annihilation j = -(annihilation j * annihilation i) := by + apply complexify_injective + simp only [map_mul, map_neg, complexify_annihilation] + exact Occupation.annihilation_anticommute i j + +lemma creation_anticommute {n : ℕ} (i j : Fin n) : + creation i * creation j = -(creation j * creation i) := by + have h := congrArg Matrix.transpose (annihilation_anticommute j i) + simpa [Matrix.transpose_mul, Matrix.transpose_neg, creation] using h + +noncomputable def secondQuantization {n : ℕ} (L : Matrix (Fin n) (Fin n) ℝ) : FockMatrix n := + ∑ i, ∑ j, L i j • (creation i * annihilation j) + +lemma secondQuantization_transpose {n : ℕ} (L : Matrix (Fin n) (Fin n) ℝ) : + (secondQuantization L).transpose = secondQuantization L.transpose := by + simp only [secondQuantization, Matrix.transpose_sum, Matrix.transpose_smul, + Matrix.transpose_mul, creation, Matrix.transpose_apply, Matrix.transpose_transpose] + rw [Finset.sum_comm] + +lemma elementary_commutator_annihilation {n : ℕ} (i j k : Fin n) : + (creation i * annihilation j) * annihilation k - + annihilation k * (creation i * annihilation j) = + -(if k=i then annihilation j else 0) := by + have h := annihilation_creation k i + have h' := annihilation_anticommute j k + have hm := congrArg (fun B : FockMatrix n => B * annihilation j) h + simp only [add_mul] at hm + rw [← mul_assoc] + rw [mul_assoc (creation i), h', mul_neg, ← mul_assoc] + rw [sub_eq_add_neg, ← neg_add, add_comm, hm] + split_ifs <;> simp + +lemma commutator_annihilation {n : ℕ} (L : Matrix (Fin n) (Fin n) ℝ) (k : Fin n) : + Averaging.commutator (secondQuantization L) (annihilation k) = + -∑ j, L k j • annihilation j := by + simp only [Averaging.commutator, LinearMap.coe_mk, AddHom.coe_mk, + secondQuantization, Finset.sum_mul, Finset.mul_sum, smul_mul_assoc, + mul_smul_comm, ← Finset.sum_sub_distrib, ← smul_sub, + elementary_commutator_annihilation, smul_neg, Finset.sum_neg_distrib] + congr 1 + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro j hj + simp only [smul_ite, smul_zero] + simp + +lemma commutator_mul {ι : Type*} [Fintype ι] [DecidableEq ι] + (L A B : Matrix ι ι ℝ) : + Averaging.commutator L (A*B) = Averaging.commutator L A * B + A * Averaging.commutator L B := by + simp only [Averaging.commutator, LinearMap.coe_mk, AddHom.coe_mk] + noncomm_ring + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/RealPositivity.lean b/lean/OAI/Analysis/LaughlinGap/RealPositivity.lean new file mode 100644 index 0000000000000000000000000000000000000000..de1071ba039ff8d2f3dc5469a660b368c7c5a26e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/RealPositivity.lean @@ -0,0 +1,90 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.PhysicalAveraging + +namespace OAI + +/-! Real Positivity. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators InnerProduct ComplexOrder MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin + +variable {ι κ : Type*} [Fintype ι] [DecidableEq ι] [Fintype κ] [DecidableEq κ] + +lemma complexify_isPositive_iff (A : Matrix ι ι ℝ) : + (complexify A).IsPositive ↔ A.PosSemidef := by + refine ⟨fun h => ?_, complexify_positive⟩ + rw [Matrix.posSemidef_iff_dotProduct_mulVec] + refine ⟨?_, fun x => ?_⟩ + · have ha : (complexify A).adjoint = complexify A := h.isSymmetric.adjoint_eq + rw [← complexify_transpose] at ha + exact (Matrix.isHermitian_iff_isSymm).mpr (complexify_injective ha) + · have hx := h.re_inner_nonneg_right (WithLp.toLp 2 (fun i => (x i : ℂ))) + simpa [complexify, Matrix.toLpLin_apply, EuclideanSpace.inner_toLp_toLp, + Matrix.mulVec, dotProduct, Complex.mul_re, Complex.add_re, mul_comm] using hx + +omit [DecidableEq ι] in +lemma transpose_square_positive [DecidableEq ι] (B : Matrix ι ι ℝ) : + (B.transpose * B).PosSemidef := by + simpa only [Matrix.conjTranspose_eq_transpose_of_trivial] using + Matrix.posSemidef_conjTranspose_mul_self B + +lemma square_diff_positive {A B : Matrix ι ι ℝ} + (h : ∀ x, ‖complexify B x‖ ≤ ‖complexify A x‖) : + (A.transpose * A - B.transpose * B).PosSemidef := by + rw [← complexify_isPositive_iff, map_sub, map_mul, map_mul, + complexify_transpose, complexify_transpose] + apply (LinearMap.isPositive_iff_complex _).mpr + intro x + rw [LinearMap.sub_apply] + simp only [Module.End.mul_apply, inner_sub_left, LinearMap.adjoint_inner_left, + inner_self_eq_norm_sq_to_K] + change (Complex.ofReal ((Complex.ofReal ‖complexify A x‖ ^ 2 - + Complex.ofReal ‖complexify B x‖ ^ 2).re) = + Complex.ofReal ‖complexify A x‖ ^ 2 - Complex.ofReal ‖complexify B x‖ ^ 2 ∧ + (0 : ℝ) ≤ (Complex.ofReal ‖complexify A x‖ ^ 2 - Complex.ofReal ‖complexify B x‖ ^ 2).re) + simp only [← Complex.ofReal_pow, ← Complex.ofReal_sub, Complex.ofReal_re] + exact ⟨trivial, sub_nonneg.mpr ((sq_le_sq₀ (norm_nonneg _) (norm_nonneg _)).mpr (h x))⟩ + +lemma annihilation_square_le {n : ℕ} (j : Fin n) (B : FockMatrix n) : + (B.transpose * B - (annihilation j * B).transpose * (annihilation j * B)).PosSemidef := by + apply square_diff_positive + intro x + simpa only [map_mul, complexify_annihilation, Module.End.mul_apply] using + Occupation.transition_norm_le j false (complexify B x) + +lemma double_annihilation_square_le {n : ℕ} (j k : Fin n) (B : FockMatrix n) : + (B.transpose * B - (annihilation k * (annihilation j * B)).transpose * + (annihilation k * (annihilation j * B))).PosSemidef := by + apply square_diff_positive + intro x + simpa only [map_mul, complexify_annihilation, Module.End.mul_apply] using + Occupation.double_annihilation_norm_le j k (complexify B x) + +lemma combination_bessel {σ : Type*} [Fintype σ] [DecidableEq σ] + (S : Matrix σ ι ℝ) (hS : S * S.transpose = 1) (B : ι → Matrix κ κ ℝ) : + ((∑ i, (B i).transpose * B i) - + ∑ r, (combination B (S r)).transpose * combination B (S r)).PosSemidef := by + have h : (1 - S.transpose * S).PosSemidef := by + have he : 1 - S.transpose * S = + (1 - S.transpose * S).transpose * (1 - S.transpose * S) := by + simp only [Matrix.transpose_sub, Matrix.transpose_one, Matrix.transpose_mul, + Matrix.transpose_transpose, sub_mul, mul_sub, one_mul, mul_one] + rw [Matrix.mul_assoc S.transpose S (S.transpose*S), ← Matrix.mul_assoc S S.transpose S, hS, Matrix.one_mul] + abel + rw [he] + exact transpose_square_positive _ + have he : S.transpose * S = ∑ r, Matrix.vecMulVec (S r) (S r) := by + ext i j; simp [Matrix.mul_apply, Matrix.vecMulVec_apply, Matrix.sum_apply] + have hh := lift_positive B h + rw [map_sub, lift_identity, he, map_sum] at hh + simpa only [lift_rankOne] using hh + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/RealSpinSquare.lean b/lean/OAI/Analysis/LaughlinGap/RealSpinSquare.lean new file mode 100644 index 0000000000000000000000000000000000000000..81f3106985acc346ca049e59df9c3a1c369c9e5b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/RealSpinSquare.lean @@ -0,0 +1,104 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.PhysicalSpinSpectrum +import OAI.Analysis.LaughlinGap.ThreeBounds + +namespace OAI + +/-! Real Spin Square. -/ + +noncomputable section + + +namespace LaughlinGap +open scoped BigOperators +lemma matrixLift_reindex {ι κ E : Type*} [Fintype ι] [Fintype κ] + [NormedAddCommGroup E] [InnerProductSpace ℂ E] [FiniteDimensional ℂ E] + (e : ι ≃ κ) (B : κ → Module.End ℂ E) (A : Matrix κ κ ℂ) : + matrixLift (fun i => B (e i)) (fun i j => A (e i) (e j)) = matrixLift B A := by + simp only [matrixLift, LinearMap.coe_mk, AddHom.coe_mk] + have hh (i : κ) : (∑ j : ι, A i (e j) • ((B i).adjoint * B (e j))) = + ∑ j : κ, A i j • ((B i).adjoint * B j) := e.sum_comp (fun j : κ => A i j • ((B i).adjoint * B j)) + simp only [hh] + exact e.sum_comp (fun i : κ => ∑ j : κ, A i j • ((B i).adjoint * B j)) +end LaughlinGap + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin Occupation + +@[simp] lemma complexify_physicalTriple (Q : ℕ) (a : Fin (2*Q-2+1) × Fin (Q+1)) : + complexify (physicalTriple Q a) = Occupation.annihilation a.2 * Occupation.localPair (Q+1) Q a.1.val := by + simp [physicalTriple, productFamily] + +lemma complexify_three_lift {Q : ℕ} (hQ : 2 ≤ Q) + (A : Matrix (Fin (2*Q-2+1) × Fin (Q+1)) (Fin (2*Q-2+1) × Fin (Q+1)) ℝ) : + complexify (lift (physicalTriple Q) A) = + exteriorLift (tripleWedgeMatrix (physicalPairForms Q) * + (Matrix.of (fun i j => (A (physicalThreeIndexEquiv hQ i) (physicalThreeIndexEquiv hQ j) : ℂ)) : + Matrix (Fin (2*Q-1) × Fin (Q+1)) (Fin (2*Q-1) × Fin (Q+1)) ℂ) * + (tripleWedgeMatrix (physicalPairForms Q)).conjTranspose) := by + rw [complexify_lift, exteriorLift, matrixLift_columns] + have he (i : Fin (2*Q-1) × Fin (Q+1)) : + contractCombination basisContraction (fun a => tripleWedgeMatrix (physicalPairForms Q) a i) = + complexify (physicalTriple Q (physicalThreeIndexEquiv hQ i)) := by + rw [show (fun a => tripleWedgeMatrix (physicalPairForms Q) a i) = + (tripleWedgeColumn (physicalPairForms Q i.1) i.2 : BasisLabel (Q+1) 3 → ℂ) from rfl] + change exteriorContraction (tripleWedgeColumn (physicalPairForms Q i.1) i.2) = _ + rw [tripleWedgeColumn_contraction, physicalPair_contraction, complexify_physicalTriple] + rfl + simp only [he] + exact (matrixLift_reindex (physicalThreeIndexEquiv hQ) + (fun a => complexify (physicalTriple Q a)) (A.map (algebraMap ℝ ℂ))).symm + +lemma physicalThreeProjection_real {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + (Matrix.of (fun i j => ((tensorProjection (show z ≤ min (2*Q-2) Q by omega)) + (physicalThreeIndexEquiv hQ i) (physicalThreeIndexEquiv hQ j) : ℂ))) = + physicalThreeProjection hQ z := by + ext i j + simp [tensorProjection_eq, physicalThreeProjection, physicalThreeRankOne, + physicalThreeVector, Matrix.vecMulVec_apply, Matrix.sum_apply] + +@[simp] lemma complexify_threeSpinLift {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + complexify (threeSpinLift hQ hz) = physicalSpinThreeLift hQ z := by + rw [threeSpinLift, complexify_three_lift hQ, physicalThreeProjection_real hQ hz] + rfl + +lemma threeSpinLift_null {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) (hn : z=0 ∨ z=1 ∨ z=3) : + threeSpinLift hQ hz = 0 := by + apply complexify_injective + rw [map_zero, complexify_threeSpinLift, physicalSpinThreeLift, + physicalThreeProjection_wedge_null hQ hz hn, Matrix.zero_mul, map_zero] + +noncomputable def fourTarget (Q : ℕ) : FockMatrix (Q+1) := + ∑ p : Fin (2*Q-1), ∑ q : Fin (2*Q-1), + (physicalPair Q q.val * physicalPair Q p.val).transpose * + (physicalPair Q q.val * physicalPair Q p.val) + +lemma fourTarget_positive (Q : ℕ) : (fourTarget Q).PosSemidef := + Matrix.posSemidef_sum _ fun _ _ => Matrix.posSemidef_sum _ fun _ _ => transpose_square_positive _ + +@[simp] lemma complexify_fourTarget (Q : ℕ) : + complexify (fourTarget Q) = exteriorLift (pairWedgeMatrix (physicalPairForms Q) * + (pairWedgeMatrix (physicalPairForms Q)).conjTranspose) := by + rw [← pairFourTerm_eq_lift] + simp [fourTarget, pairFourTerm, physicalPair_contraction, adjoint_mul] + +theorem physical_spin_square_real {Q : ℕ} (hQ : 2 ≤ Q) : + physicalHamiltonian Q * physicalHamiltonian Q = physicalHamiltonian Q + + (∑ z : Fin (Q+1), (threeBodyGramCoefficient Q z.val) • + threeSpinLift hQ (Nat.le_of_lt_succ z.isLt)) + fourTarget Q := by + apply complexify_injective + simp only [map_mul, map_add, map_sum, map_smul, complexify_physicalHamiltonian, + complexify_threeSpinLift, complexify_fourTarget] + rw [physical_spin_square hQ] + congr 2 + let e : Fin (min (2*Q-2) Q+1) ≃ Fin (Q+1) := finCongr (by omega) + have he := e.sum_comp (fun z : Fin (Q+1) => + (threeBodyGramCoefficient Q z.val : ℂ) • physicalSpinThreeLift hQ z.val) + exact he + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SpectralBound.lean b/lean/OAI/Analysis/LaughlinGap/SpectralBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..56c8428fdb3d351a50ce842cfec4aa851fd741c7 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SpectralBound.lean @@ -0,0 +1,603 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Basic + +namespace OAI + +/-! Spectral Bound. -/ + +noncomputable section + + +namespace LaughlinGap +open scoped BigOperators +namespace Chart +open MvPolynomial + +noncomputable def splitPair {N : ℕ} (i j : Fin N) : + MvPolynomial (Fin N) ℂ →ₐ[ℂ] MvPolynomial (Fin N) (MvPolynomial Bool ℂ) := + aeval (fun k => if k = i then C (X false) else if k = j then C (X true) else X k) + +@[simp] theorem splitPair_C {N : ℕ} (i j : Fin N) (c : ℂ) : + splitPair i j (C c) = C (C c) := by + simp [splitPair, algebraMap_eq] + +@[simp] theorem splitPair_X {N : ℕ} (i j k : Fin N) : + splitPair i j (X k) = + if k = i then C (X false) else if k = j then C (X true) else X k := by + simp [splitPair] + +@[simp] theorem splitPair_difference {N : ℕ} (i j : Fin N) (hij : i ≠ j) : + splitPair i j (difference i j) = C (difference false true) := by + simp [difference, Ne.symm hij] + +@[simp] theorem splitPair_rename {N : ℕ} (i j : Fin N) (hij : i ≠ j) + (F : MvPolynomial Bool ℂ) : + splitPair i j (rename (fun b : Bool => if b then j else i) F) = C F := by + induction F using MvPolynomial.induction_on with + | C c => simp + | add a b ha hb => simp [ha, hb] + | mul_X p k hp => cases k <;> simp [hp, Ne.symm hij] + +lemma spectatorMonomial_eq {N Q : ℕ} (i j : Fin N) (hij : i ≠ j) + (a : PairSpectators (Q := Q) i j) : + spectatorMonomial i j a = monomial (exponent a.val) (tensorMonomialScale a.val : ℂ) := by + have hnorm : monomial (exponent a.val) (tensorMonomialScale a.val : ℂ) = + ∏ k : Fin N, C (Real.sqrt (Q.choose (a.val k).val : ℝ) : ℂ) * X k ^ (a.val k).val := by + rw [monomial_as_prod] + simp only [tensorMonomialScale, Complex.ofReal_prod, map_prod, Finset.prod_mul_distrib] + rw [hnorm] + rw [← Finset.mul_prod_erase _ _ (Finset.mem_univ i)] + rw [← Finset.mul_prod_erase (Finset.univ.erase i) _ + (by simp [Ne.symm hij] : j ∈ Finset.univ.erase i)] + simp [a.property.1, a.property.2, spectatorMonomial] + +lemma splitPair_spectatorMonomial {N Q : ℕ} (i j : Fin N) (hij : i ≠ j) + (a : PairSpectators (Q := Q) i j) : + splitPair i j (spectatorMonomial i j a) = + monomial (exponent a.val) (C (tensorMonomialScale a.val : ℂ)) := by + rw [spectatorMonomial_eq i j hij a, monomial_as_prod] + simp only [map_mul, map_prod, map_pow, splitPair_C] + rw [monomial_eq] + rw [Finsupp.prod_fintype _ _ (by intro; simp)] + congr 1 + apply Finset.prod_congr rfl + intro k hk + by_cases hki : k = i + · subst k; simp [exponent, a.property.1] + by_cases hkj : k = j + · subst k; simp [exponent, a.property.2] + simp [exponent, hki, hkj] + +theorem coeff_splitPair_statePolynomial {N Q : ℕ} (ψ : State N Q) + (i j : Fin N) (hij : i ≠ j) (a : PairSpectators (Q := Q) i j) : + (splitPair i j (statePolynomial ψ)).coeff (exponent a.val) = + C (tensorMonomialScale a.val : ℂ) * + localPairPolynomial (fun x y => ψ (Function.update (Function.update a.val i x) j y)) := by + classical + rw [statePolynomial_pair_decomposition ψ i j hij] + simp only [map_sum, map_mul, splitPair_spectatorMonomial i j hij, + splitPair_rename i j hij, coeff_sum] + rw [Finset.sum_eq_single a] + · rw [mul_comm, coeff_C_mul, coeff_monomial] + simp [mul_comm] + · intro b hb hba + have hab : exponent b.val ≠ exponent a.val := by + intro h + exact hba (Subtype.ext ((exponent_injective N Q) h)) + rw [mul_comm, coeff_C_mul, coeff_monomial, ite_eq_right hab, mul_zero] + · simp + +theorem localPairPolynomial_cube_dvd_of_statePolynomial_cube_dvd {N Q : ℕ} + (ψ : State N Q) (i j : Fin N) (hij : i ≠ j) + (hdiv : difference i j ^ 3 ∣ statePolynomial ψ) + (a : PairSpectators (Q := Q) i j) : + difference false true ^ 3 ∣ + localPairPolynomial (fun x y => ψ (Function.update (Function.update a.val i x) j y)) := by + obtain ⟨G, hG⟩ := hdiv + have h := congrArg (fun F => (splitPair i j F).coeff (exponent a.val)) hG + rw [coeff_splitPair_statePolynomial ψ i j hij a, map_mul, map_pow, + splitPair_difference i j hij, ← map_pow, coeff_C_mul] at h + have hd : difference false true ^ 3 ∣ C (tensorMonomialScale a.val : ℂ) * + localPairPolynomial (fun x y => ψ (Function.update (Function.update a.val i x) j y)) := + ⟨_, h⟩ + exact (IsUnit.dvd_mul_left ((isUnit_iff_ne_zero.mpr + (Complex.ofReal_ne_zero.mpr (tensorMonomialScale_pos a.val).ne')).map C)).mp hd + +theorem diagonal_derivative_eq_zero_of_cube_dvd {σ : Type*} [DecidableEq σ] + (i j k : σ) (F : MvPolynomial σ ℂ) (hdiv : difference i j ^ 3 ∣ F) : + diagonal i j (pderiv k F) = 0 := by + obtain ⟨G, rfl⟩ := hdiv + simp + +end Chart + +section LocalKernelConverse +open MvPolynomial + +@[simp] theorem pairMoment_zero {Q : ℕ} (φ : Fin (Q + 1) → Fin (Q + 1) → ℂ) : + pairMoment φ 0 = 0 := by + unfold pairMoment + apply Finset.sum_eq_zero + intro x hx + apply Finset.sum_eq_zero + intro y hy + split_ifs with hxy + · have hx0 : x.val = 0 := by omega + have hy0 : y.val = 0 := by omega + simp [hx0, hy0] + · rfl + +theorem coeff_localPairPolynomial_diagonal_difference_derivative {Q p : ℕ} + (φ : Fin (Q + 1) → Fin (Q + 1) → ℂ) (hp : p < 2 * Q) : + (Chart.diagonal false true + (pderiv false (localPairPolynomial φ) - pderiv true (localPairPolynomial φ))).coeff + (Finsupp.single false p) = + pairMoment φ (p + 1) := by + classical + rw [localPairPolynomial_diagonal_difference_derivative, Finset.sum_range_succ'] + simp only [pairMoment_zero, map_zero, zero_mul, add_zero, Nat.add_sub_cancel, + C_mul_X_pow_eq_monomial, coeff_sum, coeff_monomial, + (Finsupp.single_injective false).eq_iff] + simp [hp] + +theorem pair_contraction_eq_zero_of_cubic_divisibility {Q : ℕ} + (φ : Fin (Q + 1) → Fin (Q + 1) → ℂ) + (hdiv : Chart.difference false true ^ 3 ∣ localPairPolynomial φ) + (p : ℕ) (hp : p < 2 * Q - 1) : + ∑ x, ∑ y, (pairCoefficient Q p x y : ℂ) * φ x y = 0 := by + have hf := Chart.diagonal_derivative_eq_zero_of_cube_dvd false true false _ hdiv + have ht := Chart.diagonal_derivative_eq_zero_of_cube_dvd false true true _ hdiv + have he := coeff_localPairPolynomial_diagonal_difference_derivative φ (by omega : p < 2 * Q) + rw [map_sub, hf, ht, sub_self, AddMonoidAlgebra.coeff_zero, Finsupp.zero_apply] at he + rw [pair_contraction_eq_moment, ← he, mul_zero] + +end LocalKernelConverse + +theorem energy_zero_of_difference_cubes_dvd {N Q : ℕ} (ψ : State N Q) + (hdiv : ∀ i j : Fin N, i < j → Chart.difference i j ^ 3 ∣ Chart.statePolynomial ψ) : + energy ψ = 0 := by + apply (energy_eq_zero_iff ψ).mpr + intro i j hij p hp a + let a' : Chart.PairSpectators (Q := Q) i j := + ⟨Function.update (Function.update a i 0) j 0, by simp [ne_of_lt hij]⟩ + have hd := Chart.localPairPolynomial_cube_dvd_of_statePolynomial_cube_dvd + ψ i j (ne_of_lt hij) (hdiv i j hij) a' + have hc := pair_contraction_eq_zero_of_cubic_divisibility _ hd p hp + exact (pairAmplitude_anchor ψ i j p a).symm.trans hc + +namespace Chart + +theorem difference_cube_dvd_laughlinPolynomial {N : ℕ} (i j : Fin N) (hij : i < j) : + difference i j ^ 3 ∣ laughlinPolynomial N := by + classical + have hj := Finset.dvd_prod_of_mem (fun k : Fin N => if i < k then difference i k ^ 3 else 1) + (Finset.mem_univ j) + rw [ite_eq_left hij] at hj + exact hj.trans (Finset.dvd_prod_of_mem + (fun k : Fin N => ∏ l : Fin N, if k < l then difference k l ^ 3 else 1) + (Finset.mem_univ i)) + +end Chart + +theorem energy_scalar_laughlin (N : ℕ) (c : ℂ) : + energy (c • laughlinVector N (3 * (N - 1))) = 0 := by + apply energy_zero_of_difference_cubes_dvd + intro i j hij + rw [Chart.statePolynomial_smul, Chart.statePolynomial_laughlinVector, + MvPolynomial.smul_eq_C_mul] + exact dvd_mul_of_dvd_right (Chart.difference_cube_dvd_laughlinPolynomial i j hij) _ + +@[simp] theorem energy_laughlin (N : ℕ) : + energy (laughlinVector N (3 * (N - 1))) = 0 := by + simpa only [one_smul] using energy_scalar_laughlin N 1 + +theorem energy_zero_iff_laughlin {N : ℕ} (hN : 2 ≤ N) + (ψ : State N (3 * (N - 1))) (hψ : Antisymmetric ψ) : + energy ψ = 0 ↔ ∃ c : ℂ, ψ = c • laughlinVector N (3 * (N - 1)) := by + constructor + · exact energy_zero_imp_laughlin hN ψ hψ + · rintro ⟨c, rfl⟩ + exact energy_scalar_laughlin N c + +theorem sectorHamiltonian_ker_eq_laughlin {N : ℕ} (hN : 2 ≤ N) : + (sectorHamiltonian N (3 * (N - 1))).ker = + Submodule.span ℂ {( + ⟨toTensorHilbert (laughlinVector N (3 * (N - 1))), + laughlinVector_antisymmetric N (3 * (N - 1))⟩ : SectorHilbert N (3 * (N - 1)))} := by + ext ψ + rw [LinearMap.mem_ker, sectorHamiltonian_eq_zero_iff, energy_zero_iff_laughlin hN _ ψ.property, + Submodule.mem_span_singleton] + constructor + · rintro ⟨c, hc⟩ + refine ⟨c, Subtype.ext ?_⟩ + exact congrArg (WithLp.toLp 2) hc.symm + · rintro ⟨c, hc⟩ + exact ⟨c, congrArg (fun x : SectorHilbert N (3 * (N - 1)) => WithLp.ofLp x.val) hc.symm⟩ + +end LaughlinGap +namespace LaughlinGap +open scoped BigOperators Topology +open Filter + +noncomputable def fallingRatio (Q z : ℕ) : ℝ := + (Q.descFactorial z : ℝ) / ((2 * Q - 2).descFactorial z : ℝ) + +noncomputable def threeBodyGramCoefficient (Q z : ℕ) : ℝ := + (-1 : ℝ) ^ z * fallingRatio Q z * + (3 * (z : ℝ) - 1 - (z : ℝ) * ((z : ℝ) + 1) / (Q : ℝ)) + +noncomputable def threeBodyDimensionRatio (Q z : ℕ) : ℝ := + (3 * (Q : ℝ) - 1 - 2 * (z : ℝ)) / (2 * (Q : ℝ) - 1) + +noncomputable def threeBodyTailTerm (Q z : ℕ) : ℝ := + if 17 ≤ z ∧ Odd z ∧ z ≤ Q then + threeBodyDimensionRatio Q z * |threeBodyGramCoefficient Q z| * ((z : ℝ) + 1) + else 0 + +noncomputable def threeBodyTail (Q : ℕ) : ℝ := + ∑ z ∈ Finset.range (Q + 1), threeBodyTailTerm Q z + +noncomputable def threeBodyTailStar (z : ℕ) : ℝ := + if 17 ≤ z ∧ Odd z then + (3 / 2 : ℝ) * (3 * (z : ℝ) - 1) * ((z : ℝ) + 1) * (1 / 2 : ℝ) ^ z + else 0 + +lemma fallingRatio_eq_prod (Q z : ℕ) : + fallingRatio Q z = ∏ k ∈ Finset.range z, + ((Q - k : ℕ) : ℝ) / ((2 * Q - 2 - k : ℕ) : ℝ) := by + simp [fallingRatio, Nat.descFactorial_eq_prod_range, Nat.cast_prod, Finset.prod_div_distrib] + +lemma fallingRatio_nonneg (Q z : ℕ) : 0 ≤ fallingRatio Q z := by + unfold fallingRatio + positivity + +theorem fallingRatio_le_two_thirds_pow {Q z : ℕ} (hQ : 4 ≤ Q) (hz : z ≤ Q) : + fallingRatio Q z ≤ (2 / 3 : ℝ) ^ z := by + rw [fallingRatio_eq_prod] + calc + (∏ k ∈ Finset.range z, ((Q - k : ℕ) : ℝ) / ((2 * Q - 2 - k : ℕ) : ℝ)) ≤ + ∏ _k ∈ Finset.range z, (2 / 3 : ℝ) := by + apply Finset.prod_le_prod₀ + · intro k hk + positivity + · intro k hk + have hkz := Finset.mem_range.mp hk + have hkQ : k ≤ Q := by omega + have hkden : k ≤ 2 * Q - 2 := by omega + have hden : 0 < ((2 * Q - 2 - k : ℕ) : ℝ) := by + exact_mod_cast (show 0 < 2 * Q - 2 - k by omega) + rw [div_le_iff₀ hden] + rw [Nat.cast_sub hkQ, Nat.cast_sub hkden, Nat.cast_sub (by omega : 2 ≤ 2 * Q)] + push_cast + have hQR : (4 : ℝ) ≤ Q := by exact_mod_cast hQ + have hkR : (0 : ℝ) ≤ k := by positivity + linarith + _ = (2 / 3 : ℝ) ^ z := by rw [Finset.prod_const, Finset.card_range] + +lemma fallingFactor_tendsto (k : ℕ) : + Tendsto (fun Q : ℕ => ((Q - k : ℕ) : ℝ) / ((2 * Q - 2 - k : ℕ) : ℝ)) + atTop (𝓝 (1 / 2 : ℝ)) := by + have ht : Tendsto (fun Q : ℕ => (1 - (k : ℝ) / Q) / (2 - ((k : ℝ) + 2) / Q)) + atTop (𝓝 (1 / 2 : ℝ)) := by + simpa only [Pi.div_def, sub_zero] using ((tendsto_const_nhds (x := (1 : ℝ))).sub + (tendsto_const_div_atTop_nhds_zero_nat (k : ℝ))).div + ((tendsto_const_nhds (x := (2 : ℝ))).sub + (tendsto_const_div_atTop_nhds_zero_nat ((k : ℝ) + 2))) + (by norm_num : (2 : ℝ) - 0 ≠ 0) + apply ht.congr' + filter_upwards [eventually_ge_atTop (k + 3)] with Q hQ + have hQ0 : (Q : ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + rw [Nat.cast_sub (by omega : k ≤ Q), Nat.cast_sub (by omega : k ≤ 2 * Q - 2), + Nat.cast_sub (by omega : 2 ≤ 2 * Q)] + push_cast + field_simp [hQ0] + ring_nf + +theorem fallingRatio_tendsto (z : ℕ) : + Tendsto (fun Q : ℕ => fallingRatio Q z) atTop (𝓝 ((1 / 2 : ℝ) ^ z)) := by + simpa only [fallingRatio_eq_prod, Finset.prod_const, Finset.card_range] using + (tendsto_finsetProd (Finset.range z) (fun k _ => fallingFactor_tendsto k)) + +theorem threeBodyGramCoefficient_tendsto (z : ℕ) : + Tendsto (fun Q : ℕ => threeBodyGramCoefficient Q z) + atTop (𝓝 ((3 * (z : ℝ) - 1) * (-1 / 2 : ℝ) ^ z)) := by + have h := ((tendsto_const_nhds (x := (-1 : ℝ) ^ z)).mul (fallingRatio_tendsto z)).mul + ((tendsto_const_nhds (x := 3 * (z : ℝ) - 1)).sub + (tendsto_const_div_atTop_nhds_zero_nat ((z : ℝ) * ((z : ℝ) + 1)))) + convert h using 1 + · rfl + · + rw [sub_zero, div_pow, div_pow] + ring_nf + +theorem threeBodyDimensionRatio_tendsto (z : ℕ) : + Tendsto (fun Q : ℕ => threeBodyDimensionRatio Q z) atTop (𝓝 (3 / 2 : ℝ)) := by + have ht : Tendsto (fun Q : ℕ => (3 - (1 + 2 * (z : ℝ)) / Q) / (2 - (1 : ℝ) / Q)) + atTop (𝓝 (3 / 2 : ℝ)) := by + simpa only [Pi.div_def, sub_zero] using ((tendsto_const_nhds (x := (3 : ℝ))).sub + (tendsto_const_div_atTop_nhds_zero_nat (1 + 2 * (z : ℝ)))).div + ((tendsto_const_nhds (x := (2 : ℝ))).sub + (tendsto_const_div_atTop_nhds_zero_nat (1 : ℝ))) + (by norm_num : (2 : ℝ) - 0 ≠ 0) + apply ht.congr' + filter_upwards [eventually_ge_atTop 1] with Q hQ + have hQ0 : (Q : ℝ) ≠ 0 := by exact_mod_cast (show Q ≠ 0 by omega) + unfold threeBodyDimensionRatio + field_simp [hQ0] + ring_nf + +theorem threeBodyBracket_nonneg {Q z : ℕ} (hQ : 4 ≤ Q) (hz : z ≤ Q) (hz16 : 16 ≤ z) : + 0 ≤ 3 * (z : ℝ) - 1 - (z : ℝ) * ((z : ℝ) + 1) / Q := by + have hQpos : (0 : ℝ) < Q := by exact_mod_cast (show 0 < Q by omega) + have hzQ : (z : ℝ) ≤ Q := by exact_mod_cast hz + have hzR : (16 : ℝ) ≤ z := by exact_mod_cast hz16 + have hdiv : (z : ℝ) * ((z : ℝ) + 1) / Q ≤ (z : ℝ) + 1 := by + rw [div_le_iff₀ hQpos] + exact mul_le_mul_of_nonneg_right hzQ (by positivity) |>.trans_eq (mul_comm _ _) + linarith + +theorem threeBodyGramCoefficient_abs_le {Q z : ℕ} (hQ : 4 ≤ Q) (hz : z ≤ Q) + (hz16 : 16 ≤ z) : + |threeBodyGramCoefficient Q z| ≤ (2 / 3 : ℝ) ^ z * (3 * (z : ℝ)) := by + rw [threeBodyGramCoefficient, abs_mul, abs_mul, abs_pow] + simp only [abs_neg, abs_one, one_pow, one_mul, + abs_of_nonneg (fallingRatio_nonneg Q z), + abs_of_nonneg (threeBodyBracket_nonneg hQ hz hz16)] + apply mul_le_mul (fallingRatio_le_two_thirds_pow hQ hz) + · have hn : (0 : ℝ) ≤ (z : ℝ) * ((z : ℝ) + 1) / Q := by positivity + linarith + · exact threeBodyBracket_nonneg hQ hz hz16 + · positivity + +lemma threeBodyDimensionRatio_nonneg {Q z : ℕ} (hQ : 4 ≤ Q) (hz : z ≤ Q) : + 0 ≤ threeBodyDimensionRatio Q z := by + have hQR : (4 : ℝ) ≤ Q := by exact_mod_cast hQ + have hzR : (z : ℝ) ≤ Q := by exact_mod_cast hz + exact div_nonneg (by linarith) (by linarith) + +lemma threeBodyDimensionRatio_le_two {Q z : ℕ} (hQ : 4 ≤ Q) : + threeBodyDimensionRatio Q z ≤ 2 := by + have hQR : (4 : ℝ) ≤ Q := by exact_mod_cast hQ + unfold threeBodyDimensionRatio + rw [div_le_iff₀ (by linarith : (0 : ℝ) < 2 * Q - 1)] + have hzR : (0 : ℝ) ≤ z := by positivity + linarith + +lemma threeBodyTailTerm_nonneg {Q : ℕ} (hQ : 4 ≤ Q) (z : ℕ) : + 0 ≤ threeBodyTailTerm Q z := by + unfold threeBodyTailTerm + split_ifs with hz + · exact mul_nonneg (mul_nonneg (threeBodyDimensionRatio_nonneg hQ hz.2.2) + (abs_nonneg _)) (by positivity) + · rfl + +theorem threeBodyTailTerm_norm_le {Q : ℕ} (hQ : 4 ≤ Q) (z : ℕ) : + ‖threeBodyTailTerm Q z‖ ≤ 6 * (z : ℝ) * ((z : ℝ) + 1) * (2 / 3 : ℝ) ^ z := by + rw [Real.norm_of_nonneg (threeBodyTailTerm_nonneg hQ z)] + unfold threeBodyTailTerm + split_ifs with hz + · calc + _ ≤ 2 * ((2 / 3 : ℝ) ^ z * (3 * (z : ℝ))) * ((z : ℝ) + 1) := by + apply mul_le_mul_of_nonneg_right _ (by positivity) + exact mul_le_mul (threeBodyDimensionRatio_le_two hQ) + (threeBodyGramCoefficient_abs_le hQ hz.2.2 (by omega)) (abs_nonneg _) + (by norm_num) + _ = _ := by ring + · positivity + +lemma summable_threeBodyTail_majorant : + Summable (fun z : ℕ => 6 * (z : ℝ) * ((z : ℝ) + 1) * (2 / 3 : ℝ) ^ z) := by + have hs2 := summable_pow_mul_geometric_of_norm_lt_one 2 (by norm_num : ‖(2 / 3 : ℝ)‖ < 1) + have hs1 := summable_pow_mul_geometric_of_norm_lt_one 1 (by norm_num : ‖(2 / 3 : ℝ)‖ < 1) + exact ((hs2.add hs1).mul_left (6 : ℝ)).congr (fun z => by ring) + +theorem threeBodyTailTerm_tendsto (z : ℕ) : + Tendsto (fun Q : ℕ => threeBodyTailTerm Q z) atTop (𝓝 (threeBodyTailStar z)) := by + by_cases hz : 17 ≤ z ∧ Odd z + · have ha := (threeBodyGramCoefficient_tendsto z).abs + have hzR : (17 : ℝ) ≤ z := by exact_mod_cast hz.1 + have he : |(3 * (z : ℝ) - 1) * (-1 / 2 : ℝ) ^ z| = + (3 * (z : ℝ) - 1) * (1 / 2 : ℝ) ^ z := by + rw [abs_mul, abs_of_nonneg (by linarith : (0 : ℝ) ≤ 3 * (z : ℝ) - 1), abs_pow] + norm_num + rw [he] at ha + have hh := ((threeBodyDimensionRatio_tendsto z).mul ha).mul_const ((z : ℝ) + 1) + have hlim : (3 / 2 : ℝ) * ((3 * (z : ℝ) - 1) * (1 / 2 : ℝ) ^ z) * ((z : ℝ) + 1) = + threeBodyTailStar z := by + simp only [threeBodyTailStar, ite_eq_left hz] + ring + rw [hlim] at hh + apply hh.congr' + filter_upwards [eventually_ge_atTop z] with Q hQ + simp [threeBodyTailTerm, hz.1, hz.2, hQ] + · have he : ∀ Q, threeBodyTailTerm Q z = 0 := by + intro Q + simp only [threeBodyTailTerm] + rw [ite_eq_right (by tauto)] + simpa only [he, threeBodyTailStar, ite_eq_right hz] using + (tendsto_const_nhds : Tendsto (fun _ : ℕ => (0 : ℝ)) atTop (𝓝 0)) + +private lemma hasSum_square_quarter : + HasSum (fun n : ℕ => (n : ℝ) ^ 2 * (1 / 4 : ℝ) ^ n) (20 / 27 : ℝ) := by + have h0 := hasSum_geometric_of_norm_lt_one (by norm_num : ‖(1 / 4 : ℝ)‖ < 1) + have h1 := hasSum_coe_mul_geometric_of_norm_lt_one (by norm_num : ‖(1 / 4 : ℝ)‖ < 1) + have h2 := hasSum_choose_mul_geometric_of_norm_lt_one 2 (by norm_num : ‖(1 / 4 : ℝ)‖ < 1) + convert ((h2.mul_left (2 : ℝ)).sub (h1.mul_left (3 : ℝ))).sub (h0.mul_left (2 : ℝ)) using 1 <;> try rfl + · ext n + rw [Nat.cast_choose_two] + push_cast + ring + · norm_num + +theorem hasSum_threeBodyTailStar_progression : + HasSum (fun m : ℕ => threeBodyTailStar (17 + 2 * m)) (61 / 4096 : ℝ) := by + have h0 := hasSum_geometric_of_norm_lt_one (by norm_num : ‖(1 / 4 : ℝ)‖ < 1) + have h1 := hasSum_coe_mul_geometric_of_norm_lt_one (by norm_num : ‖(1 / 4 : ℝ)‖ < 1) + have h2 := hasSum_square_quarter + convert (((h0.mul_left (900 : ℝ)).add (h1.mul_left (208 : ℝ))).add + (h2.mul_left (12 : ℝ))).mul_left (3 / 262144 : ℝ) using 1 <;> try rfl + · ext m + have hm : 17 ≤ 17 + 2 * m ∧ Odd (17 + 2 * m) := by + constructor + · omega + · rw [Nat.odd_iff]; omega + simp only [threeBodyTailStar, ite_eq_left hm, pow_add, pow_mul] + push_cast + norm_num + ring + · norm_num + +theorem hasSum_threeBodyTailStar : HasSum threeBodyTailStar (61 / 4096 : ℝ) := by + have hinj : Function.Injective (fun m : ℕ => 17 + 2 * m) := by + intro a b hab + dsimp at hab + omega + have hout : ∀ z, z ∉ Set.range (fun m : ℕ => 17 + 2 * m) → threeBodyTailStar z = 0 := by + intro z hz + have hbad : ¬ (17 ≤ z ∧ Odd z) := by + rintro ⟨hz17, hzodd⟩ + have hp := Nat.odd_iff.mp hzodd + apply hz + exact ⟨(z - 17) / 2, by dsimp; omega⟩ + exact ite_eq_right hbad + exact (hinj.hasSum_iff hout).mp hasSum_threeBodyTailStar_progression + +theorem threeBodyTail_tendsto : + Tendsto threeBodyTail atTop (𝓝 (61 / 4096 : ℝ)) := by + have ht := tendsto_tsum_of_dominated_convergence summable_threeBodyTail_majorant + threeBodyTailTerm_tendsto + (show ∀ᶠ Q in atTop, ∀ z, ‖threeBodyTailTerm Q z‖ ≤ + 6 * (z : ℝ) * ((z : ℝ) + 1) * (2 / 3 : ℝ) ^ z by + filter_upwards [eventually_ge_atTop 4] with Q hQ z + exact threeBodyTailTerm_norm_le hQ z) + rw [hasSum_threeBodyTailStar.tsum_eq] at ht + have he : threeBodyTail = (fun Q => ∑' z, threeBodyTailTerm Q z) := by + funext Q + unfold threeBodyTail + symm + apply tsum_eq_sum + intro z hz + have hzQ : ¬ z ≤ Q := by + simp only [Finset.mem_range] at hz + omega + simp [threeBodyTailTerm, hzQ] + rw [he] + exact ht + +end LaughlinGap +namespace LaughlinGap +open scoped BigOperators InnerProduct ComplexConjugate + +section Compression +variable {𝕜 E F : Type*} [RCLike 𝕜] + [NormedAddCommGroup E] [InnerProductSpace 𝕜 E] [FiniteDimensional 𝕜 E] + [NormedAddCommGroup F] [InnerProductSpace 𝕜 F] [FiniteDimensional 𝕜 F] + +theorem compression_positive_iff (W : E →ₗ[𝕜] F) (C : E →ₗ[𝕜] E) + (hC : C.IsSymmetric) : + (W ∘ₗ C ∘ₗ W.adjoint).IsPositive ↔ + ∀ x ∈ W.adjoint.range, 0 ≤ RCLike.re (inner 𝕜 (C x) x) := by + constructor + · intro h x hx + obtain ⟨y, rfl⟩ := hx + simpa only [LinearMap.comp_apply, ← LinearMap.adjoint_inner_right] using + h.re_inner_nonneg_left y + · intro h + refine ⟨hC.conj_adjoint W, fun y => ?_⟩ + simpa only [LinearMap.comp_apply, ← LinearMap.adjoint_inner_right] using + h (W.adjoint y) (LinearMap.mem_range_self W.adjoint y) + +theorem gram_compression_positive_iff (W : E →ₗ[𝕜] F) (C : E →ₗ[𝕜] E) + (hC : C.IsSymmetric) : + ((W.adjoint ∘ₗ W) ∘ₗ C ∘ₗ (W.adjoint ∘ₗ W)).IsPositive ↔ + (W ∘ₗ C ∘ₗ W.adjoint).IsPositive := by + have hG : (W.adjoint ∘ₗ W).IsSymmetric := LinearMap.isSymmetric_adjoint_comp_self W + have h := compression_positive_iff (W.adjoint ∘ₗ W) C hC + rw [hG.adjoint_eq, LinearMap.range_adjoint_comp_self] at h + exact h.trans (compression_positive_iff W C hC).symm + +end Compression + +section AnnihilatorBound +variable {ι κ E F : Type*} [Fintype ι] [Fintype κ] [DecidableEq κ] + [NormedAddCommGroup F] + +theorem annihilator_collection_bound (p : ι → κ) (B : κ → E → F) + (A : ι → F → F) {M : ℕ} + (hM : ∀ k, (Finset.univ.filter (fun b => p b = k)).card ≤ M) + (hA : ∀ b y, ‖A b y‖ ≤ ‖y‖) (x : E) : + ∑ b, ‖A b (B (p b) x)‖ ^ 2 ≤ (M : ℝ) * ∑ k, ‖B k x‖ ^ 2 := by + classical + calc + (∑ b, ‖A b (B (p b) x)‖ ^ 2) ≤ ∑ b, ‖B (p b) x‖ ^ 2 := by + apply Finset.sum_le_sum + intro b _ + exact pow_le_pow_left₀ (norm_nonneg _) (hA b _) 2 + _ = ∑ k, ((Finset.univ.filter (fun b => p b = k)).card : ℝ) * ‖B k x‖ ^ 2 := by + rw [← Finset.sum_fiberwise' Finset.univ p (fun k => ‖B k x‖ ^ 2)] + simp + _ ≤ ∑ k, (M : ℝ) * ‖B k x‖ ^ 2 := by + apply Finset.sum_le_sum + intro k _ + exact mul_le_mul_of_nonneg_right (by exact_mod_cast hM k) (sq_nonneg _) + _ = _ := by rw [Finset.mul_sum] + +end AnnihilatorBound + +section Perturbation +variable {𝕜 E F : Type*} [RCLike 𝕜] + [NormedAddCommGroup E] [InnerProductSpace 𝕜 E] + [NormedAddCommGroup F] [InnerProductSpace 𝕜 F] + +theorem quadratic_perturbation_abs_le (T S : E →L[𝕜] E) (x : E) : + |RCLike.re (inner 𝕜 x (T x)) - RCLike.re (inner 𝕜 x (S x))| ≤ + ‖T - S‖ * ‖x‖ ^ 2 := by + have h₁ := RCLike.norm_re_le_norm (inner 𝕜 x ((T - S) x)) + have h₂ := norm_inner_le_norm (𝕜 := 𝕜) x ((T - S) x) + have h₃ := mul_le_mul_of_nonneg_left ((T - S).le_opNorm x) (norm_nonneg x) + have h := (h₁.trans h₂).trans h₃ + simpa only [sub_apply, inner_sub_right, map_sub, Real.norm_eq_abs, + mul_left_comm ‖x‖ ‖T - S‖ ‖x‖, ← pow_two, mul_assoc] using h + +theorem quadratic_perturbation_lower_bound (T S : E →L[𝕜] E) (x : E) + (hS : 0 ≤ RCLike.re (inner 𝕜 x (S x))) : + -‖T - S‖ * ‖x‖ ^ 2 ≤ RCLike.re (inner 𝕜 x (T x)) := by + have h := (abs_le.mp (quadratic_perturbation_abs_le T S x)).1 + nlinarith + +omit [NormedAddCommGroup E] [InnerProductSpace 𝕜 E] in + +theorem relative_column_perturbation_bound {ι : Type*} [Fintype ι] + (A : ι → E → F) (Δ : E → E) (eStar eQ : E → ℝ) {C₀ : ℝ} (hC₀ : 0 ≤ C₀) + (hA : ∀ x, (∑ b, ‖A b x‖ ^ 2) ≤ C₀ * eStar x) + (hΔ : ∀ x, eStar (Δ x) ≤ eQ x) + (T S : (PiLp 2 (fun _ : ι => F)) →L[𝕜] (PiLp 2 (fun _ : ι => F))) + (hS : ∀ x, 0 ≤ RCLike.re (inner 𝕜 (WithLp.toLp 2 (fun b => A b x)) + (S (WithLp.toLp 2 (fun b => A b x))))) (x : E) : + -(C₀ * ‖T - S‖) * eQ x ≤ + RCLike.re (inner 𝕜 (WithLp.toLp 2 (fun b => A b (Δ x))) + (T (WithLp.toLp 2 (fun b => A b (Δ x))))) := by + let v : PiLp 2 (fun _ : ι => F) := WithLp.toLp 2 (fun b => A b (Δ x)) + have hv : ‖v‖ ^ 2 ≤ C₀ * eQ x := by + rw [PiLp.norm_sq_eq_of_L2] + exact (hA (Δ x)).trans (mul_le_mul_of_nonneg_left (hΔ x) hC₀) + have hp := quadratic_perturbation_lower_bound T S v (hS (Δ x)) + calc + -(C₀ * ‖T - S‖) * eQ x = -‖T - S‖ * (C₀ * eQ x) := by ring + _ ≤ -‖T - S‖ * ‖v‖ ^ 2 := by + exact mul_le_mul_of_nonpos_left hv (neg_nonpos.mpr (norm_nonneg _)) + _ ≤ _ := hp + +theorem relative_column_error_tendsto {G : Type*} [NormedAddCommGroup G] [NormedSpace 𝕜 G] + {T : ℕ → G →L[𝕜] G} {S : G →L[𝕜] G} {C₀ : ℝ} + (hT : Filter.Tendsto T Filter.atTop (nhds S)) : + Filter.Tendsto (fun Q => C₀ * ‖T Q - S‖) Filter.atTop (nhds 0) := by + simpa using (((hT.sub (tendsto_const_nhds (x := S))).norm).const_mul C₀) + +end Perturbation + +end LaughlinGap + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SpinAveraging.lean b/lean/OAI/Analysis/LaughlinGap/SpinAveraging.lean new file mode 100644 index 0000000000000000000000000000000000000000..097e8c475a43f794966fcf8b3ea6573610dac10c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SpinAveraging.lean @@ -0,0 +1,192 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Averaging +import OAI.Analysis.LaughlinGap.IntertwiningSpin + +namespace OAI + +/-! Spin Averaging. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators +open Averaging + +noncomputable def loweringMatrix {ι : Type*} [Fintype ι] [DecidableEq ι] + (S : LadderSystem ι) : Matrix ι ι ℝ := LinearMap.toMatrix' S.lower + +lemma loweringMatrix_transpose {ι : Type*} [Fintype ι] [DecidableEq ι] + (S : LadderSystem ι) : (loweringMatrix S).transpose = LinearMap.toMatrix' S.raise := by + ext i j + have he := S.adjoint (Pi.single i 1) (Pi.single j 1) + simpa [loweringMatrix, LinearMap.toMatrix'_apply, dotProduct_single, single_dotProduct] using he + +noncomputable def commutantLadderMap {ι : Type*} [Fintype ι] [DecidableEq ι] + (S : LadderSystem ι) {A : Matrix ι ι ℝ} + (hA : A ∈ rotationCommutant (loweringMatrix S)) : LadderMap S S where + toLinearMap := Matrix.toLin' A + lower x := by + have he := (rotationCommutant_mem _ _).mp hA |>.1 + have hh : loweringMatrix S * A = A * loweringMatrix S := sub_eq_zero.mp he + have hr := congrArg (fun M : Matrix ι ι ℝ => Matrix.toLin' M x) hh + simpa [loweringMatrix, Matrix.toLin'_mul] using hr + raise x := by + have he := (rotationCommutant_mem _ _).mp hA |>.2 + have hh : (loweringMatrix S).transpose * A = A * (loweringMatrix S).transpose := + sub_eq_zero.mp he + rw [loweringMatrix_transpose] at hh + have hr := congrArg (fun M : Matrix ι ι ℝ => Matrix.toLin' M x) hh + simpa [Matrix.toLin'_mul] using hr + +lemma ladderMap_matrix_mem {ι : Type*} [Fintype ι] [DecidableEq ι] + (S : LadderSystem ι) (A : LadderMap S S) : + LinearMap.toMatrix' A.toLinearMap ∈ rotationCommutant (loweringMatrix S) := by + rw [rotationCommutant_mem] + constructor + · apply sub_eq_zero.mpr + apply Matrix.toLin'.injective + simp only [Matrix.toLin'_mul, loweringMatrix, Matrix.toLin'_toMatrix'] + apply LinearMap.ext + intro x + exact A.lower x + · apply sub_eq_zero.mpr + rw [loweringMatrix_transpose] + apply Matrix.toLin'.injective + simp only [Matrix.toLin'_mul, Matrix.toLin'_toMatrix'] + apply LinearMap.ext + intro x + exact A.raise x + +lemma toMatrix_transposeMap {ι κ : Type*} [Fintype ι] [DecidableEq ι] + [Fintype κ] [DecidableEq κ] (A : (ι → ℝ) →ₗ[ℝ] (κ → ℝ)) : + LinearMap.toMatrix' (transposeMap A) = (LinearMap.toMatrix' A).transpose := by + ext i j + simp only [LinearMap.toMatrix'_apply, transposeMap, Matrix.transpose_apply, + LinearMap.coe_mk, AddHom.coe_mk] + change dotProduct (A _) (Pi.single j 1) = _ + rw [dotProduct_single_one] + apply congrArg (fun x : ι → ℝ => A x j) + funext k + by_cases hk : i=k <;> simp [hk, eq_comm] + +noncomputable def tensorProjection {n m z : ℕ} (hz : z ≤ min n m) : + Matrix (Fin (n+1) × Fin (m+1)) (Fin (n+1) × Fin (m+1)) ℝ := + LinearMap.toMatrix' ((coupledEmbedding hz).comp (coupledEmbedding hz).transpose).toLinearMap + +lemma tensorProjection_mem {n m z : ℕ} (hz : z ≤ min n m) : + tensorProjection hz ∈ rotationCommutant (loweringMatrix (tensorSpin n m)) := + ladderMap_matrix_mem _ _ + +lemma coupledEmbedding_entry {n m z : ℕ} (hz : z ≤ min n m) + (a : Fin (n+1) × Fin (m+1)) (l : Fin (n+m-2*z+1)) : + LinearMap.toMatrix' (coupledEmbedding hz).toLinearMap a l = coupledTensor n m z l.val a := by + rw [LinearMap.toMatrix'_apply, coupledEmbedding_apply] + simp [Pi.single_apply, ite_apply] + +lemma tensorProjection_eq {n m z : ℕ} (hz : z ≤ min n m) : + tensorProjection hz = ∑ l : Fin (n+m-2*z+1), + Matrix.vecMulVec (coupledTensor n m z l.val) (coupledTensor n m z l.val) := by + simp only [tensorProjection, LadderMap.comp, LadderMap.transpose, + LinearMap.toMatrix'_comp, toMatrix_transposeMap] + ext a b + simp only [Matrix.mul_apply, Matrix.transpose_apply, coupledEmbedding_entry, + Matrix.sum_apply, Matrix.vecMulVec_apply] + +lemma coupledTensor_dot {n m : ℕ} (i j : CoupledIndex n m) : + dotProduct (coupledTensor n m i.1.val i.2.val) (coupledTensor n m j.1.val j.2.val) = + if i=j then 1 else 0 := by + have hh := (orthonormal_iff_ite.mp (coupledFamily_orthonormal n m)) j i + simpa only [coupledFamily, EuclideanSpace.inner_toLp_toLp, star_trivial, eq_comm] using hh + +lemma tensorProjection_mulVec {n m z : ℕ} (hz : z ≤ min n m) + (i : CoupledIndex n m) : + (tensorProjection hz).mulVec (coupledTensor n m i.1.val i.2.val) = + if i.1.val=z then coupledTensor n m i.1.val i.2.val else 0 := by + rw [tensorProjection_eq] + simp only [Matrix.sum_mulVec, Matrix.vecMulVec_mulVec] + let z' : Fin (min n m+1) := ⟨z, by omega⟩ + have he (l : Fin (n+m-2*z+1)) : + dotProduct (coupledTensor n m z l.val) (coupledTensor n m i.1.val i.2.val) = + if (⟨z',l⟩ : CoupledIndex n m)=i then 1 else 0 := coupledTensor_dot ⟨z',l⟩ i + simp only [he] + split_ifs with hi + · obtain ⟨w,k⟩ := i + have hw : w=z' := Fin.ext hi + subst w + simp + rfl + · have hne (l : Fin (n+m-2*z+1)) : (⟨z',l⟩ : CoupledIndex n m) ≠ i := by + intro he + apply hi + exact (congrArg (fun j : CoupledIndex n m => j.1.val) he).symm + simp only [hne, ite_false, MulOpposite.op_zero, zero_smul, Finset.sum_const_zero] + +lemma trace_mul_rankOne {ι : Type*} [Fintype ι] (A : Matrix ι ι ℝ) (x y : ι → ℝ) : + (A * Matrix.vecMulVec x y).trace = dotProduct y (A.mulVec x) := by + rw [Matrix.mul_vecMulVec, Matrix.trace_vecMulVec, dotProduct_comm] + +theorem tensorSpin_average {n m : ℕ} + (A : Matrix (Fin (n+1) × Fin (m+1)) (Fin (n+1) × Fin (m+1)) ℝ) : + average (rotationCommutant (loweringMatrix (tensorSpin n m))) A = + ∑ z : Fin (min n m+1), + ((A * tensorProjection (Nat.le_of_lt_succ z.isLt)).trace / + (n+m-2*z.val+1 : ℕ)) • tensorProjection (Nat.le_of_lt_succ z.isLt) := by + classical + let S := rotationCommutant (loweringMatrix (tensorSpin n m)) + let Y := average S A + have hm : Y ∈ S := average_mem S A + let L := commutantLadderMap (tensorSpin n m) hm + let c : ℕ → ℝ := fun z => dotProduct (highestTensor n m z) (Y.mulVec (highestTensor n m z)) + have he (i : CoupledIndex n m) : Y.mulVec (coupledTensor n m i.1.val i.2.val) = + c i.1.val • coupledTensor n m i.1.val i.2.val := + tensorSpin_schur (Nat.le_of_lt_succ i.1.isLt) (Nat.le_of_lt_succ i.2.isLt) L + have ht (z : Fin (min n m+1)) : + (A * tensorProjection (Nat.le_of_lt_succ z.isLt)).trace = + (n+m-2*z.val+1 : ℕ) * c z.val := by + rw [trace_mul_average S A (tensorProjection_mem (Nat.le_of_lt_succ z.isLt)), + tensorProjection_eq, Matrix.mul_sum, Matrix.trace_sum] + have hrow (l : Fin (n+m-2*z.val+1)) : + (Y * Matrix.vecMulVec (coupledTensor n m z.val l.val) + (coupledTensor n m z.val l.val)).trace = c z.val := by + rw [trace_mul_rankOne, he ⟨z,l⟩, dotProduct_smul] + rw [coupledTensor_dot (⟨z,l⟩ : CoupledIndex n m) ⟨z,l⟩] + simp + change (∑ l : Fin (n+m-2*z.val+1), + (Y * Matrix.vecMulVec (coupledTensor n m z.val l.val) + (coupledTensor n m z.val l.val)).trace) = _ + simp only [hrow, Finset.sum_const, Finset.card_univ, Fintype.card_fin, nsmul_eq_mul] + have hcoef (z : Fin (min n m+1)) : + (A * tensorProjection (Nat.le_of_lt_succ z.isLt)).trace / + (n+m-2*z.val+1 : ℕ) = c z.val := by + rw [ht] + have hd : ((n+m-2*z.val+1 : ℕ) : ℝ) ≠ 0 := by positivity + exact mul_div_cancel_left₀ _ hd + simp only [hcoef] + apply Matrix.mulVec_injective + funext x + change Y.mulVec x = _ + nth_rw 1 [← coupledTensor_expansion n m x] + rw [Matrix.mulVec_sum] + simp only [Matrix.mulVec_smul, he, smul_smul] + rw [Matrix.sum_mulVec] + have hx (z : Fin (min n m+1)) : + (tensorProjection (Nat.le_of_lt_succ z.isLt)).mulVec x = + ∑ l : Fin (n+m-2*z.val+1), + dotProduct (coupledTensor n m z.val l.val) x • coupledTensor n m z.val l.val := by + rw [tensorProjection_eq] + simp [Matrix.sum_mulVec, Matrix.vecMulVec_mulVec] + simp only [Matrix.smul_mulVec, hx, Finset.smul_sum, smul_smul] + rw [Fintype.sum_sigma] + apply Finset.sum_congr rfl + intro z hz + apply Finset.sum_congr rfl + intro l hl + congr 1 + exact mul_comm _ _ + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SpinWork.lean b/lean/OAI/Analysis/LaughlinGap/SpinWork.lean new file mode 100644 index 0000000000000000000000000000000000000000..b101acedc9ec2f808817f486bce27f7900247896 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SpinWork.lean @@ -0,0 +1,560 @@ +import Mathlib + +namespace OAI + +/-! Spin Work. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators Topology +open Filter + +noncomputable def highestFactor (n m z k : ℕ) : ℝ := + ((m : ℝ) - z + k + 1) / ((n : ℝ) - k) + +noncomputable def highestWeight (n m z p : ℕ) : ℝ := + (z.choose p : ℝ) * ∏ k ∈ Finset.range p, highestFactor n m z k + +noncomputable def highestNormalization (n m z : ℕ) : ℝ := + ∑ p ∈ Finset.range (z+1), highestWeight n m z p + +noncomputable def highestCoefficient (n m z p : ℕ) : ℝ := + (-1 : ℝ) ^ (z-p) * Real.sqrt (highestWeight n m z p) / + Real.sqrt (highestNormalization n m z) + +lemma highestFactor_pos {n m z k : ℕ} (hz : z ≤ min n m) (hk : k < z) : + 0 < highestFactor n m z k := by + have hzN : (z : ℝ) ≤ n := by exact_mod_cast (le_min_iff.mp hz).1 + have hzM : (z : ℝ) ≤ m := by exact_mod_cast (le_min_iff.mp hz).2 + have hkZ : (k : ℝ) < z := by exact_mod_cast hk + have hk0 : (0 : ℝ) ≤ k := by positivity + exact div_pos (by linarith) (by linarith) + +lemma highestWeight_nonneg {n m z p : ℕ} (hz : z ≤ min n m) : + 0 ≤ highestWeight n m z p := by + by_cases hp : p ≤ z + · apply mul_nonneg (by positivity) + exact Finset.prod_nonneg fun k hk => + (highestFactor_pos hz ((Finset.mem_range.mp hk).trans_le hp)).le + · simp [highestWeight, Nat.choose_eq_zero_of_lt (by omega : z < p)] + +@[simp] lemma highestWeight_zero (n m z : ℕ) : highestWeight n m z 0 = 1 := by + simp [highestWeight] + +lemma highestNormalization_pos {n m z : ℕ} (hz : z ≤ min n m) : + 0 < highestNormalization n m z := by + apply Finset.sum_pos' (fun p _ => highestWeight_nonneg hz) + exact ⟨0, by simp, by simp⟩ + +lemma highestCoefficient_sq {n m z p : ℕ} (hz : z ≤ min n m) : + highestCoefficient n m z p ^ 2 = + highestWeight n m z p / highestNormalization n m z := by + simp only [highestCoefficient, div_pow, mul_pow, ← pow_mul (-1 : ℝ), + mul_comm (z-p) 2, pow_mul (-1 : ℝ) 2, neg_one_sq, one_pow, one_mul, + Real.sq_sqrt (highestWeight_nonneg hz), Real.sq_sqrt (highestNormalization_pos hz).le] + +theorem highestCoefficient_sum_sq {n m z : ℕ} (hz : z ≤ min n m) : + ∑ p ∈ Finset.range (z+1), highestCoefficient n m z p ^ 2 = 1 := by + simp_rw [highestCoefficient_sq hz] + rw [← Finset.sum_div] + exact div_self (highestNormalization_pos hz).ne' + +lemma highestCoefficient_eq_zero {n m z p : ℕ} (hp : z < p) : + highestCoefficient n m z p = 0 := by + simp [highestCoefficient, highestWeight, Nat.choose_eq_zero_of_lt hp] + +lemma highestWeight_step {n m z p : ℕ} (hz : z ≤ min n m) (hp : p < z) : + highestWeight n m z (p+1) * ((p : ℝ)+1) * ((n : ℝ)-p) = + highestWeight n m z p * ((z : ℝ)-p) * ((m : ℝ)-z+p+1) := by + have hnp : (n : ℝ) - p ≠ 0 := by + have hn : p < n := hp.trans_le (le_min_iff.mp hz).1 + exact sub_ne_zero.mpr (Ne.symm (by exact_mod_cast hn.ne)) + have hc : (z.choose (p+1) : ℝ) * ((p : ℝ)+1) = (z.choose p : ℝ) * ((z : ℝ)-p) := by + have H := congrArg (fun a : ℕ => (a : ℝ)) (Nat.choose_succ_right_eq z p) + simpa only [Nat.cast_mul, Nat.cast_add, Nat.cast_one, Nat.cast_sub hp.le] using H + simp only [highestWeight, Finset.prod_range_succ, highestFactor] + rw [mul_assoc (z.choose (p+1) : ℝ), mul_comm _ ((p : ℝ)+1), + ← mul_assoc (z.choose (p+1) : ℝ), hc] + field_simp + +theorem highestCoefficient_raising {n m z p : ℕ} (hz : z ≤ min n m) (hp : p < z) : + highestCoefficient n m z (p+1) * Real.sqrt (((p : ℝ)+1)*((n : ℝ)-p)) + + highestCoefficient n m z p * Real.sqrt (((z : ℝ)-p)*((m : ℝ)-z+p+1)) = 0 := by + have he : Real.sqrt (highestWeight n m z (p+1)) * + Real.sqrt (((p : ℝ)+1)*((n : ℝ)-p)) = + Real.sqrt (highestWeight n m z p) * + Real.sqrt (((z : ℝ)-p)*((m : ℝ)-z+p+1)) := by + rw [← Real.sqrt_mul (highestWeight_nonneg hz), + ← Real.sqrt_mul (highestWeight_nonneg hz)] + congr 1 + simpa only [mul_assoc] using highestWeight_step hz hp + have hpz : z-p = (z-(p+1))+1 := by omega + simp only [highestCoefficient, hpz, pow_succ, mul_neg_one] + linear_combination + ((-1 : ℝ) ^ (z-(p+1)) / Real.sqrt (highestNormalization n m z)) * he + +theorem highestFactor_tendsto {n m : ℕ → ℕ} {r : ℝ} + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (z k : ℕ) : + Tendsto (fun q => highestFactor (n q) (m q) z k) atTop (𝓝 r) := by + have hquot : Tendsto + (fun q => ((m q : ℝ) / n q + (-(z : ℝ) + k + 1) / n q) / + (1 - (k : ℝ) / n q)) atTop (𝓝 r) := by + simpa only [add_zero, sub_zero, div_one, Pi.div_def] using + (hmn.add (hn.const_div_atTop (-(z : ℝ) + k + 1))).div + ((tendsto_const_nhds (x := (1 : ℝ))).sub (hn.const_div_atTop (k : ℝ))) + (by norm_num : (1 : ℝ) - 0 ≠ 0) + apply hquot.congr' + filter_upwards [hn.eventually (eventually_gt_atTop (k : ℝ))] with q hq + have hN : (n q : ℝ) ≠ 0 := by + have hk : (0 : ℝ) ≤ k := by positivity + linarith + have hNk : (n q : ℝ) - k ≠ 0 := by linarith + dsimp [highestFactor] + field_simp + ring + +theorem highestWeight_tendsto {n m : ℕ → ℕ} {r : ℝ} + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (z p : ℕ) : + Tendsto (fun q => highestWeight (n q) (m q) z p) atTop + (𝓝 ((z.choose p : ℝ) * r ^ p)) := by + have h := (tendsto_const_nhds (x := (z.choose p : ℝ))).mul + (tendsto_finsetProd (Finset.range p) (fun k _ => highestFactor_tendsto hn hmn z k)) + simpa only [Finset.prod_const, Finset.card_range, highestWeight] using h + +theorem highestNormalization_tendsto {n m : ℕ → ℕ} {r : ℝ} + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (z : ℕ) : + Tendsto (fun q => highestNormalization (n q) (m q) z) atTop (𝓝 ((r+1)^z)) := by + have hsum : (∑ p ∈ Finset.range (z+1), (z.choose p : ℝ) * r^p) = (r+1)^z := by + rw [add_pow] + apply Finset.sum_congr rfl + intro p hp + simp [mul_comm] + simpa only [highestNormalization, hsum] using + tendsto_finsetSum (Finset.range (z+1)) (fun p _ => highestWeight_tendsto hn hmn z p) + +theorem highestCoefficient_tendsto_ratio {n m : ℕ → ℕ} {r : ℝ} (hr : 0 ≤ r) + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (z p : ℕ) : + Tendsto (fun q => highestCoefficient (n q) (m q) z p) atTop + (𝓝 ((-1 : ℝ)^(z-p) * Real.sqrt ((z.choose p : ℝ) * r^p) / + Real.sqrt ((r+1)^z))) := by + have hpos : 0 < (r+1)^z := pow_pos (by linarith) z + exact ((tendsto_const_nhds.mul (highestWeight_tendsto hn hmn z p).sqrt).div + (highestNormalization_tendsto hn hmn z).sqrt (Real.sqrt_pos.mpr hpos).ne') + +lemma sqrt_nat_pow {x : ℝ} (hx : 0 ≤ x) (k : ℕ) : + Real.sqrt (x ^ k) = Real.sqrt x ^ k := by + induction k with + | zero => simp + | succ k hk => rw [pow_succ, Real.sqrt_mul (pow_nonneg hx k), hk, pow_succ] + +noncomputable def limitingHighestCoefficient (u v : ℝ) (z p : ℕ) : ℝ := + (-1 : ℝ)^(z-p) * Real.sqrt (z.choose p : ℝ) * u^p * v^(z-p) + +lemma highest_ratio_eq {r : ℝ} (hr : 0 ≤ r) (z p : ℕ) : + (-1 : ℝ)^(z-p) * Real.sqrt ((z.choose p : ℝ) * r^p) / + Real.sqrt ((r+1)^z) = + limitingHighestCoefficient (Real.sqrt r / Real.sqrt (r+1)) + (1 / Real.sqrt (r+1)) z p := by + by_cases hp : p ≤ z + · have he : z = p + (z-p) := (Nat.add_sub_of_le hp).symm + have hpos : Real.sqrt (r+1) ≠ 0 := (Real.sqrt_pos.mpr (by linarith)).ne' + rw [Real.sqrt_mul (by positivity), sqrt_nat_pow hr, + sqrt_nat_pow (by linarith : 0 ≤ r+1)] + unfold limitingHighestCoefficient + rw [div_pow, div_pow, one_pow] + rw [show Real.sqrt (r+1)^z = Real.sqrt (r+1)^p * Real.sqrt (r+1)^(z-p) by + rw [← pow_add, Nat.add_sub_of_le hp]] + ring + · simp [Nat.choose_eq_zero_of_lt (by omega : z < p), limitingHighestCoefficient] + +theorem highestCoefficient_tendsto {n m : ℕ → ℕ} {r : ℝ} (hr : 0 ≤ r) + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (z p : ℕ) : + Tendsto (fun q => highestCoefficient (n q) (m q) z p) atTop + (𝓝 (limitingHighestCoefficient (Real.sqrt r / Real.sqrt (r+1)) + (1 / Real.sqrt (r+1)) z p)) := by + simpa only [highest_ratio_eq hr] using highestCoefficient_tendsto_ratio hr hn hmn z p + +lemma firstAffineRatio_tendsto {n m : ℕ → ℕ} {r : ℝ} (hr : 0 ≤ r) + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (a b : ℝ) : + Tendsto (fun q => ((n q : ℝ) + a) / ((n q : ℝ) + m q + b)) atTop + (𝓝 (1 / (1+r))) := by + have h : Tendsto (fun q => (1 + a / (n q : ℝ)) / + (1 + (m q : ℝ) / n q + b / n q)) atTop (𝓝 (1 / (1+r))) := by + simpa only [add_zero, Pi.div_def] using + ((tendsto_const_nhds (x := (1 : ℝ))).add (hn.const_div_atTop a)).div + (((tendsto_const_nhds (x := (1 : ℝ))).add hmn).add (hn.const_div_atTop b)) + (by linarith : 1 + r + 0 ≠ 0) + apply h.congr' + filter_upwards [hn.eventually (eventually_gt_atTop (0 : ℝ))] with q hq + simpa only [add_div, div_self hq.ne'] using + div_div_div_cancel_right₀ hq.ne' ((n q : ℝ) + a) ((n q : ℝ) + m q + b) + +lemma secondAffineRatio_tendsto {n m : ℕ → ℕ} {r : ℝ} (hr : 0 ≤ r) + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (a b : ℝ) : + Tendsto (fun q => ((m q : ℝ) + a) / ((n q : ℝ) + m q + b)) atTop + (𝓝 (r / (1+r))) := by + have h : Tendsto (fun q => ((m q : ℝ) / n q + a / n q) / + (1 + (m q : ℝ) / n q + b / n q)) atTop (𝓝 (r / (1+r))) := by + simpa only [add_zero, Pi.div_def] using + (hmn.add (hn.const_div_atTop a)).div + (((tendsto_const_nhds (x := (1 : ℝ))).add hmn).add (hn.const_div_atTop b)) + (by linarith : 1 + r + 0 ≠ 0) + apply h.congr' + filter_upwards [hn.eventually (eventually_gt_atTop (0 : ℝ))] with q hq + simpa only [add_div, div_self hq.ne'] using + div_div_div_cancel_right₀ hq.ne' ((m q : ℝ) + a) ((n q : ℝ) + m q + b) + +lemma firstSqrtRatio_tendsto {n m : ℕ → ℕ} {r : ℝ} (hr : 0 ≤ r) + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (a b : ℝ) : + Tendsto (fun q => Real.sqrt ((n q : ℝ) + a) / + Real.sqrt ((n q : ℝ) + m q + b)) atTop (𝓝 (1 / Real.sqrt (1+r))) := by + have h := (firstAffineRatio_tendsto hr hn hmn a b).sqrt + rw [Real.sqrt_div (by norm_num : (0 : ℝ) ≤ 1), Real.sqrt_one] at h + apply h.congr' + filter_upwards [hn.eventually (eventually_gt_atTop (-b))] with q hq + have hm : (0 : ℝ) ≤ m q := by positivity + rw [Real.sqrt_div' _ (by linarith)] + +lemma secondSqrtRatio_tendsto {n m : ℕ → ℕ} {r : ℝ} (hr : 0 ≤ r) + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (a b : ℝ) : + Tendsto (fun q => Real.sqrt ((m q : ℝ) + a) / + Real.sqrt ((n q : ℝ) + m q + b)) atTop + (𝓝 (Real.sqrt r / Real.sqrt (1+r))) := by + have h := (secondAffineRatio_tendsto hr hn hmn a b).sqrt + rw [Real.sqrt_div hr] at h + apply h.congr' + filter_upwards [hn.eventually (eventually_gt_atTop (-b))] with q hq + have hm : (0 : ℝ) ≤ m q := by positivity + rw [Real.sqrt_div' _ (by linarith)] + +noncomputable def firstLoweringCoefficient (n m z l p : ℕ) : ℝ := + Real.sqrt ((p : ℝ) * ((n : ℝ)-p+1)) / + Real.sqrt (((l : ℝ)+1) * ((n : ℝ)+m-2*z-l)) + +noncomputable def secondLoweringCoefficient (n m z l p : ℕ) : ℝ := + Real.sqrt (((z : ℝ)+l-p+1) * ((m : ℝ)-z-l+p)) / + Real.sqrt (((l : ℝ)+1) * ((n : ℝ)+m-2*z-l)) + +lemma firstLoweringCoefficient_tendsto {n m : ℕ → ℕ} {r : ℝ} (hr : 0 ≤ r) + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (z l p : ℕ) : + Tendsto (fun q => firstLoweringCoefficient (n q) (m q) z l p) atTop + (𝓝 (Real.sqrt (p : ℝ) / Real.sqrt ((l : ℝ)+1) / Real.sqrt (1+r))) := by + have h := (firstSqrtRatio_tendsto hr hn hmn (1-(p : ℝ)) (-2*(z : ℝ)-l)).const_mul + (Real.sqrt (p : ℝ) / Real.sqrt ((l : ℝ)+1)) + have hf (q : ℕ) : firstLoweringCoefficient (n q) (m q) z l p = + Real.sqrt (p : ℝ) / Real.sqrt ((l : ℝ)+1) * + (Real.sqrt ((n q : ℝ)+(1-(p : ℝ))) / + Real.sqrt ((n q : ℝ)+m q+(-2*(z : ℝ)-l))) := by + simp only [firstLoweringCoefficient, Real.sqrt_mul (Nat.cast_nonneg p), + Real.sqrt_mul (by positivity : (0 : ℝ) ≤ (l : ℝ)+1)] + ring_nf + simpa only [hf, mul_one_div] using h + +lemma secondLoweringCoefficient_tendsto {n m : ℕ → ℕ} {r : ℝ} (hr : 0 ≤ r) + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (z l p : ℕ) + (hp : p ≤ z+l+1) : + Tendsto (fun q => secondLoweringCoefficient (n q) (m q) z l p) atTop + (𝓝 (Real.sqrt ((z : ℝ)+l-p+1) / Real.sqrt ((l : ℝ)+1) * + (Real.sqrt r / Real.sqrt (1+r)))) := by + have hp' : (0 : ℝ) ≤ (z : ℝ)+l-p+1 := by + have h : (p : ℝ) ≤ (z : ℝ)+l+1 := by exact_mod_cast hp + linarith + have h := (secondSqrtRatio_tendsto hr hn hmn (-(z : ℝ)-l+p) (-2*(z : ℝ)-l)).const_mul + (Real.sqrt ((z : ℝ)+l-p+1) / Real.sqrt ((l : ℝ)+1)) + have hf (q : ℕ) : secondLoweringCoefficient (n q) (m q) z l p = + Real.sqrt ((z : ℝ)+l-p+1) / Real.sqrt ((l : ℝ)+1) * + (Real.sqrt ((m q : ℝ)+(-(z : ℝ)-l+p)) / + Real.sqrt ((n q : ℝ)+m q+(-2*(z : ℝ)-l))) := by + simp only [secondLoweringCoefficient, Real.sqrt_mul hp', + Real.sqrt_mul (by positivity : (0 : ℝ) ≤ (l : ℝ)+1)] + ring_nf + simpa only [hf] using h + +noncomputable def coupledCoefficient (n m z : ℕ) : ℕ → ℕ → ℝ + | 0, p => highestCoefficient n m z p + | l+1, p => + (if p = 0 then 0 else firstLoweringCoefficient n m z l p * + coupledCoefficient n m z l (p-1)) + + secondLoweringCoefficient n m z l p * coupledCoefficient n m z l p + +noncomputable def limitingCoupledCoefficient (u v : ℝ) (z : ℕ) : ℕ → ℕ → ℝ + | 0, p => limitingHighestCoefficient u v z p + | l+1, p => + ((if p = 0 then 0 else Real.sqrt (p : ℝ) * v * + limitingCoupledCoefficient u v z l (p-1)) + + Real.sqrt ((z : ℝ)+l-p+1) * u * limitingCoupledCoefficient u v z l p) / + Real.sqrt ((l : ℝ)+1) + +lemma coupledCoefficient_eq_zero {n m z l p : ℕ} (hp : z+l < p) : + coupledCoefficient n m z l p = 0 := by + induction l generalizing p with + | zero => exact highestCoefficient_eq_zero (by omega) + | succ l ih => + simp [coupledCoefficient, ih (show z+l < p-1 by omega), ih (show z+l < p by omega)] + +lemma limitingCoupledCoefficient_eq_zero {u v : ℝ} {z l p : ℕ} (hp : z+l < p) : + limitingCoupledCoefficient u v z l p = 0 := by + induction l generalizing p with + | zero => simp [limitingCoupledCoefficient, limitingHighestCoefficient, + Nat.choose_eq_zero_of_lt (show z < p by omega)] + | succ l ih => + simp [limitingCoupledCoefficient, ih (show z+l < p-1 by omega), ih (show z+l < p by omega)] + +theorem coupledCoefficient_tendsto {n m : ℕ → ℕ} {r : ℝ} (hr : 0 ≤ r) + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (z l p : ℕ) : + Tendsto (fun q => coupledCoefficient (n q) (m q) z l p) atTop + (𝓝 (limitingCoupledCoefficient (Real.sqrt r / Real.sqrt (1+r)) + (1 / Real.sqrt (1+r)) z l p)) := by + induction l generalizing p with + | zero => simpa only [coupledCoefficient, limitingCoupledCoefficient, add_comm 1 r] using + highestCoefficient_tendsto hr hn hmn z p + | succ l ih => + by_cases hp : p ≤ z+l+1 + · have h₁ : Tendsto (fun q => if p = 0 then (0 : ℝ) else + firstLoweringCoefficient (n q) (m q) z l p * coupledCoefficient (n q) (m q) z l (p-1)) + atTop (𝓝 (if p = 0 then 0 else + Real.sqrt (p : ℝ) / Real.sqrt ((l : ℝ)+1) / Real.sqrt (1+r) * + limitingCoupledCoefficient (Real.sqrt r / Real.sqrt (1+r)) + (1 / Real.sqrt (1+r)) z l (p-1))) := by + split_ifs with hp0 + · exact tendsto_const_nhds + · exact (firstLoweringCoefficient_tendsto hr hn hmn z l p).mul (ih (p-1)) + have h₂ := (secondLoweringCoefficient_tendsto hr hn hmn z l p hp).mul (ih p) + convert h₁.add h₂ using 1 + · rfl + · congr 1 + simp only [limitingCoupledCoefficient] + split_ifs <;> ring + · simpa only [coupledCoefficient_eq_zero (show z+(l+1) < p by omega), + limitingCoupledCoefficient_eq_zero (show z+(l+1) < p by omega)] using + (tendsto_const_nhds : Tendsto (fun _ : ℕ => (0 : ℝ)) atTop (𝓝 0)) + +open Polynomial + +noncomputable def couplingPolynomial (u v : ℝ) (z l : ℕ) : ℝ[X] := + C (1 / (Real.sqrt (z.factorial : ℝ) * Real.sqrt (l.factorial : ℝ))) * + (C u * X - C v)^z * (C v * X + C u)^l + +noncomputable def monomialWeight (T p : ℕ) : ℝ := + Real.sqrt ((p.factorial : ℝ) * ((T-p).factorial : ℝ)) + +lemma monomialWeight_pos (T p : ℕ) : 0 < monomialWeight T p := by + apply Real.sqrt_pos.mpr + exact mul_pos (by exact_mod_cast p.factorial_pos) + (by exact_mod_cast (T-p).factorial_pos) + +lemma binomial_linear_coeff (u v : ℝ) (z p : ℕ) : + ((C u * X - C v)^z).coeff p = (z.choose p : ℝ) * u^p * (-v)^(z-p) := by + have h := comp_C_mul_X_coeff (p := (X + C (-v))^z) (r := u) (n := p) + simp only [pow_comp, add_comp, X_comp, C_comp, coeff_X_add_C_pow] at h + rw [map_neg] at h + rw [sub_eq_add_neg] + rw [h] + ring + +lemma monomialWeight_choose {z p : ℕ} (hp : p ≤ z) : + monomialWeight z p * (z.choose p : ℝ) / Real.sqrt (z.factorial : ℝ) = + Real.sqrt (z.choose p : ℝ) := by + have hc : (z.choose p : ℝ) * (p.factorial : ℝ) * ((z-p).factorial : ℝ) = + (z.factorial : ℝ) := by exact_mod_cast (Nat.choose_mul_factorial_mul_factorial hp) + have hs : Real.sqrt (z.choose p : ℝ) * monomialWeight z p = + Real.sqrt (z.factorial : ℝ) := by + rw [monomialWeight, ← Real.sqrt_mul (by positivity)] + congr 1 + simpa only [mul_assoc] using hc + apply (div_eq_iff (Real.sqrt_pos.mpr (by exact_mod_cast z.factorial_pos)).ne').mpr + rw [← hs] + have he : Real.sqrt (z.choose p : ℝ) ^ 2 = (z.choose p : ℝ) := + Real.sq_sqrt (by positivity) + calc + _ = monomialWeight z p * Real.sqrt (z.choose p : ℝ) ^ 2 := by rw [he] + _ = _ := by ring + +lemma highestCoefficient_eq_polynomial (u v : ℝ) (z p : ℕ) : + limitingHighestCoefficient u v z p = + monomialWeight z p * (couplingPolynomial u v z 0).coeff p := by + simp only [couplingPolynomial, Nat.factorial_zero, Nat.cast_one, Real.sqrt_one, + mul_one, pow_zero, coeff_C_mul, binomial_linear_coeff] + by_cases hp : p ≤ z + · rw [show (-v)^(z-p) = (-1 : ℝ)^(z-p)*v^(z-p) by rw [← mul_pow]; congr 1; ring] + calc + limitingHighestCoefficient u v z p = + (monomialWeight z p * (z.choose p : ℝ) / Real.sqrt (z.factorial : ℝ)) * + (-1 : ℝ)^(z-p)*u^p*v^(z-p) := by + rw [monomialWeight_choose hp] + unfold limitingHighestCoefficient + ring + _ = _ := by ring + · simp [limitingHighestCoefficient, Nat.choose_eq_zero_of_lt (show z < p by omega)] + +lemma couplingPolynomial_step (u v : ℝ) (z l : ℕ) : + couplingPolynomial u v z (l+1) = + C (1 / Real.sqrt ((l : ℝ)+1)) * + ((C v * X + C u) * couplingPolynomial u v z l) := by + have hf : Real.sqrt ((l+1).factorial : ℝ) = + Real.sqrt ((l : ℝ)+1) * Real.sqrt (l.factorial : ℝ) := by + rw [Nat.factorial_succ, Nat.cast_mul, Nat.cast_add, Nat.cast_one, + Real.sqrt_mul (by positivity)] + have hn : 1 / (Real.sqrt (z.factorial : ℝ) * Real.sqrt ((l+1).factorial : ℝ)) = + (1 / Real.sqrt ((l : ℝ)+1)) * + (1 / (Real.sqrt (z.factorial : ℝ) * Real.sqrt (l.factorial : ℝ))) := by + rw [hf] + ring + unfold couplingPolynomial + rw [hn, map_mul, pow_succ] + ring + +lemma couplingPolynomial_natDegree_le (u v : ℝ) (z l : ℕ) : + (couplingPolynomial u v z l).natDegree ≤ z+l := by + have ha : (C u * X - C v : ℝ[X]).natDegree ≤ 1 := by + exact (natDegree_sub_le _ _).trans + (max_le ((natDegree_C_mul_le _ _).trans natDegree_X_le) (by simp)) + have hb : (C v * X + C u : ℝ[X]).natDegree ≤ 1 := by + exact (natDegree_add_le _ _).trans + (max_le ((natDegree_C_mul_le _ _).trans natDegree_X_le) (by simp)) + unfold couplingPolynomial + apply natDegree_mul_le.trans + apply add_le_add + · exact (natDegree_C_mul_le _ _).trans (natDegree_pow_le.trans (by nlinarith)) + · exact natDegree_pow_le.trans (by nlinarith) + +lemma couplingPolynomial_coeff_eq_zero {u v : ℝ} {z l p : ℕ} (hp : z+l < p) : + (couplingPolynomial u v z l).coeff p = 0 := + coeff_eq_zero_of_natDegree_lt ((couplingPolynomial_natDegree_le u v z l).trans_lt hp) + +lemma monomialWeight_first {T p : ℕ} (hp : 0 < p) (hpT : p ≤ T+1) : + monomialWeight (T+1) p = Real.sqrt (p : ℝ) * monomialWeight T (p-1) := by + have hpp : (p-1)+1 = p := by omega + have hfac : p.factorial = p * (p-1).factorial := by + simpa only [hpp] using Nat.factorial_succ (p-1) + have hTp : (T+1)-p = T-(p-1) := by omega + simp only [monomialWeight, hfac, Nat.cast_mul, hTp] + rw [← Real.sqrt_mul (Nat.cast_nonneg p)] + congr 1 + ring + +lemma monomialWeight_second {T p : ℕ} (hp : p ≤ T) : + monomialWeight (T+1) p = + Real.sqrt ((T : ℝ)-p+1) * monomialWeight T p := by + have hTp : (T+1)-p = (T-p)+1 := by omega + simp only [monomialWeight, hTp, Nat.factorial_succ, Nat.cast_mul, + Nat.cast_add, Nat.cast_one, Nat.cast_sub hp] + rw [← Real.sqrt_mul (by + have h : (p : ℝ) ≤ T := by exact_mod_cast hp + linarith : (0 : ℝ) ≤ (T : ℝ)-p+1)] + congr 1 + ring + +lemma couplingPolynomial_step_coeff (u v : ℝ) (z l p : ℕ) : + (couplingPolynomial u v z (l+1)).coeff p = + ((if p = 0 then 0 else v * (couplingPolynomial u v z l).coeff (p-1)) + + u * (couplingPolynomial u v z l).coeff p) / Real.sqrt ((l : ℝ)+1) := by + rw [couplingPolynomial_step, coeff_C_mul, add_mul, mul_assoc (C v), coeff_add] + simp only [coeff_C_mul] + cases p with + | zero => simp [div_eq_mul_inv, mul_comm] + | succ p => simp [coeff_X_mul, mul_add, mul_comm, div_eq_mul_inv, mul_left_comm] + +theorem limitingCoupledCoefficient_eq_polynomial (u v : ℝ) (z l p : ℕ) : + limitingCoupledCoefficient u v z l p = + monomialWeight (z+l) p * (couplingPolynomial u v z l).coeff p := by + induction l generalizing p with + | zero => simpa only [Nat.add_zero, limitingCoupledCoefficient] using + highestCoefficient_eq_polynomial u v z p + | succ l ih => + by_cases hp : p ≤ z+l+1 + · have hfirst : monomialWeight (z+l+1) p * + (if p = 0 then 0 else v * (couplingPolynomial u v z l).coeff (p-1)) = + (if p = 0 then 0 else Real.sqrt (p : ℝ) * v * + (monomialWeight (z+l) (p-1) * (couplingPolynomial u v z l).coeff (p-1))) := by + split_ifs with hp0 + · simp + · rw [monomialWeight_first (by omega : 0 < p) hp] + ring + have hsecond : monomialWeight (z+l+1) p * + (u * (couplingPolynomial u v z l).coeff p) = + Real.sqrt ((z : ℝ)+l-p+1) * u * + (monomialWeight (z+l) p * (couplingPolynomial u v z l).coeff p) := by + by_cases hpT : p ≤ z+l + · rw [monomialWeight_second hpT, Nat.cast_add] + ring + · rw [couplingPolynomial_coeff_eq_zero (by omega : z+l < p)] + ring + simp only [limitingCoupledCoefficient, ih, couplingPolynomial_step_coeff, + ← Nat.add_assoc] + rw [← mul_div_assoc, mul_add, hfirst, hsecond] + · rw [limitingCoupledCoefficient_eq_zero (by omega : z+(l+1) < p), + couplingPolynomial_coeff_eq_zero (by omega : z+(l+1) < p), mul_zero] + +theorem coupledCoefficient_tendsto_polynomial {n m : ℕ → ℕ} {r : ℝ} (hr : 0 ≤ r) + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hmn : Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 r)) (z l p : ℕ) : + Tendsto (fun q => coupledCoefficient (n q) (m q) z l p) atTop + (𝓝 (monomialWeight (z+l) p * + (couplingPolynomial (Real.sqrt r / Real.sqrt (1+r)) + (1 / Real.sqrt (1+r)) z l).coeff p)) := by + simpa only [limitingCoupledCoefficient_eq_polynomial] using + coupledCoefficient_tendsto hr hn hmn z l p + +lemma ratio_to_total_ratio {n m : ℕ → ℕ} {s : ℝ} (hs : s < 1) + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hm : Tendsto (fun q => (m q : ℝ) / ((n q : ℝ)+m q)) atTop (𝓝 s)) : + Tendsto (fun q => (m q : ℝ) / n q) atTop (𝓝 (s / (1-s))) := by + have h := hm.div ((tendsto_const_nhds (x := (1 : ℝ))).sub hm) (by linarith) + apply h.congr' + filter_upwards [hn.eventually (eventually_gt_atTop (0 : ℝ))] with q hq + have hm0 : 0 ≤ (m q : ℝ) := by positivity + have hsum : (n q : ℝ)+m q ≠ 0 := by linarith + have hden : 1 - (m q : ℝ) / ((n q : ℝ)+m q) ≠ 0 := by + apply sub_ne_zero.mpr + intro he + have he' := (eq_div_iff hsum).mp he + linarith + dsimp + field_simp [hq.ne'] + ring + +theorem fixed_deficit_coupling_limit {n m : ℕ → ℕ} {u : ℝ} + (hu : 0 < u) (hu1 : u < 1) + (hn : Tendsto (fun q => (n q : ℝ)) atTop atTop) + (hm : Tendsto (fun q => (m q : ℝ) / ((n q : ℝ)+m q)) atTop (𝓝 (u^2))) + (z l p : ℕ) : + Tendsto (fun q => coupledCoefficient (n q) (m q) z l p) atTop + (𝓝 (monomialWeight (z+l) p * + (couplingPolynomial u (Real.sqrt (1-u^2)) z l).coeff p)) := by + have huu : u^2 < 1 := by nlinarith + have hd : 0 < 1-u^2 := by linarith + have hv : Real.sqrt (1-u^2) ≠ 0 := (Real.sqrt_pos.mpr hd).ne' + have hr : 0 ≤ u^2 / (1-u^2) := div_nonneg (sq_nonneg u) hd.le + have hrr : 1 + u^2 / (1-u^2) = 1 / (1-u^2) := by field_simp; ring + have hs₁ : Real.sqrt (u^2 / (1-u^2)) = u / Real.sqrt (1-u^2) := by + rw [Real.sqrt_div (sq_nonneg u), Real.sqrt_sq_eq_abs, abs_of_pos hu] + have hs₂ : Real.sqrt (1 + u^2 / (1-u^2)) = 1 / Real.sqrt (1-u^2) := by + rw [hrr, Real.sqrt_div (by norm_num : (0 : ℝ) ≤ 1), Real.sqrt_one] + have hU : Real.sqrt (u^2 / (1-u^2)) / Real.sqrt (1 + u^2 / (1-u^2)) = u := by + rw [hs₁, hs₂] + field_simp + have hV : 1 / Real.sqrt (1 + u^2 / (1-u^2)) = Real.sqrt (1-u^2) := by + rw [hs₂, one_div_one_div] + simpa only [hU, hV] using + coupledCoefficient_tendsto_polynomial hr hn (ratio_to_total_ratio huu hn hm) z l p + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable10.lean b/lean/OAI/Analysis/LaughlinGap/SumTable10.lean new file mode 100644 index 0000000000000000000000000000000000000000..b8ea7ffbfd1e4d6326ff10aac950ec97317f26a0 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable10.lean @@ -0,0 +1,264 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SumTable9 + +namespace OAI + +/-! Sum Table10. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable10 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 747882], ![0, 0, 0, 0, 0, 0, 0, 6007680, 3754800], ![0, 0, 0, 0, 0, 0, 1811881008, 1948463280, 2033826696], ![0, 0, 0, 0, 0, -613988928, -6463036524, -6972576312, -4144923486], ![0, 0, 0, 0, 4746984900, 1517402796, -1413324024, -4241750808, -7090723146], ![0, 0, 0, -2882508240, 1762595832, 3477060360, 5415566160, 6833741232, 4550304180], ![0, 0, -3100156092, -3583213548, -5109745548, -3302711172, 2994135804, 11909381388, 18886325004]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 10 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -6305994], ![0, 0, 0, 0, 0, 0, 0, 36148416, 22592940], ![0, 0, 0, 0, 0, 0, 1452603432, 1047459288, 794243784], ![0, 0, 0, 0, 0, -1243155816, 10368260616, 15689419464, 17079166620], ![0, 0, 0, 0, -5974835244, 1837570980, 10678295376, 19037538648, 25971676470], ![0, 0, 0, -12399988800, 634098504, 7619322960, 2610291408, -5441686272, 1725140316], ![0, 0, 47670012, -19677292068, -11259892908, 9505137492, 11169117924, -23014158588, -79456160952], ![0, 1100888700, -3391243968, -4104084492, -12663279240, -32485411788, -51469640208, -39714708516, 45853892688]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 10 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 10153584], ![0, 0, 0, 0, 0, 0, 0, -15654720, -9784020], ![0, 0, 0, 0, 0, 0, -3618255648, -3291014496, -3086488848], ![0, 0, 0, 0, 0, -15590780352, -5601693384, -5532066576, -11662103700], ![0, 0, 0, 0, -35078239728, -6412121352, 15469461000, 20178485424, 1222438464], ![0, 0, 0, 17092882416, 6909369468, -20287302048, -21788317704, 3774673680, 31932233106], ![0, 0, 4549948812, 27885726156, 14918062452, -15144074172, -17307375468, 37583594004, 136134528768], ![0, 2511263136, 3468978336, 7246292640, 12305287680, 10474046304, -2911054368, -17890847904, -3856098864], ![-1348543104, -488085456, 68779440, 4315808448, 14489280864, 15194294640, -20003838288, -84387516960, -74047920768]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 10 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -175252128, -109532490], ![0, 0, 0, 0, 0, 0, 4578366996, 4728446196, 4822245786], ![0, 0, 0, 0, 0, 42862496040, 14969428572, 6825748128, 11025433854], ![0, 0, 0, 0, 32922696912, 40110511560, 20644394904, -6932007408, -31028918160], ![0, 0, 0, -25460635776, -7721012868, 20917955784, 18459702168, -18199615008, -67855892574], ![0, 0, -42682612176, -19032551040, -11951580792, -30947600448, -62796139728, -94481351424, -125110458612], ![0, -12867122340, -25425770400, -18165166764, 34443034488, 48296110932, -47379645360, -209460168324, -286078789728], ![2907205632, -218197488, 4784763792, -8887977024, -7439586912, 86769080016, 240060026256, 159026696736, -639313000320], ![-1600914048, 3174870240, 8375737536, 3323117376, 20535016320, 96028573536, 134413156416, -163929178368, -1087207038720]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 10 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, -44551752, -263478936, -400308336], ![0, 0, 0, 0, 0, -2297106504, -9855330660, -8554302096, -1716241122], ![0, 0, 0, 0, 3218023872, -7959766248, -29017167816, -34853238096, -9779889192], ![0, 0, 0, -29129692416, 23576849388, 50440669224, 3307343544, -88833486624, -148777140054], ![0, 0, 8756900424, -24285140520, -8188024656, 30036527784, 27818522712, -55698569496, -198150399828], ![0, -14905419960, 26359855296, 46501945176, 38044021776, 73901814360, 194453302752, 329931101448, 328721705856], ![6005622816, 14853339192, 7359278424, 30440200032, 40675486224, -85010240424, -353954699496, -452837852496, 250839552384], ![-1418218176, 7350452832, 5630944320, -39582382272, -64249644480, 30563303904, 106394385216, -412666861824, -2243848666752], ![1135183104, 3721708800, -1312992000, -25727880960, -63182092800, -84396264960, -82921165824, -173564531712, -678251109888]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 10 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -1224940248, 1113849576, 1662037464, 1091099340], ![0, 0, 0, 0, 25707512460, 4041428916, -9762517464, -16538473416, -16807783278], ![0, 0, 0, 44874444960, -33264935940, -31004547432, -1501476072, 27690511488, 45019721538], ![0, 0, 21205287882, -88956518118, 21683798430, 194539133214, 142458020934, -283484414346, -925375641084], ![0, 1817179740, 4140260352, -53816354028, -85142753544, -11890773804, 71934380976, -108948587460, -819271789872], ![-3575206656, -3135782304, 21766221792, 47539954176, 57811711680, 68353275360, 104108364768, 167746559040, 253623229440], ![-129558912, 7017662352, 1661377824, 35858266464, 210413443200, 334276173648, -312971127840, -2326018988928, -4181412305664], ![-1061355840, -13016208096, -37914994080, -109163802720, -258049011360, -228435743424, 777137563776, 3442803230592, 5924924020224], ![901778688, -5099925312, -43419582720, -150346113600, -318666391680, -372369236736, 106256037888, 1431841796352, 2641266321408]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 10 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 3416986776, -1639708728, -2302230000, -1400191536, -702103260], ![0, 0, 0, 18586450272, -12857953572, -21525321288, -1576538280, 33886262592, 59922670482], ![0, 0, 8254541844, -31695565740, -12936107220, 40309717788, 55230698700, -17705904948, -158187872736], ![0, -1755395964, 1143457632, -2585573172, 12104583240, 14734101324, -48329450640, -182237574684, -274164866688], ![-7841688192, 887272944, 9237123696, 4969725120, -14499705120, 24202403376, 237920053104, 538104832608, 270576193920], ![6985310016, 11702050944, -12526929792, -32715571200, -26494173120, -92410925184, -412012000512, -970220132352, -1134052748928], ![-138326400, -21338240256, -50726421504, -55552838400, -79285384320, -136511370240, 190365579264, 1960874302464, 5933339115264], ![-2329373952, -12526107840, -3621784320, 77449780800, 199073078400, 190194144000, 49905580032, 696369307392, 4513468557312], ![-869197824, 57928227840, 311371084800, 505932134400, -650688675840, -4587915644928, -8933775814656, -3786851008512, 19278144737280]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 10 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 2435052000, 5413218912, -13881427536, -12293225760, 13799129184, 43307970384], ![0, 0, 3748695534, 3212697822, -15192805110, -13322953782, 34364461506, 121149645138, 197358992748], ![0, -6046021464, 6341183616, 1071168504, 37567713168, 94673485944, 76623853728, -114894540312, -478055846400], ![-5548108800, 28473399888, -3151572528, -6761341248, 31134069792, -72287741424, -482536657968, -993112297824, -851018640768], ![4975115712, -18674516064, -48624176448, -1516391232, 64706616000, -26127177696, -179771726400, 371329716480, 2882706786432], ![1936500288, 9164883168, 24588856224, 57952180320, 74263197600, -114642093888, -815775649920, -1965469435776, -2116177367040], ![-5391320832, -31455065664, -16650097920, 204178948800, 652852986240, 903664597248, 470416472064, 602535935232, 7045848336384], ![-2195057664, 27086169600, 190307289600, 403503959040, -53840855040, -2145224632320, -4728168732672, -1770661601280, 13618055632896], ![0, 62633571840, 375801431040, 835114291200, 0, -4960578889728, -14330561236992, -18425007304704, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 10 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 534228], ![0, 0, 0, 0, 0, 0, 0, 4291200, 2682000], ![0, 0, 0, 0, 0, 0, -237020448, -139460960, -78486784], ![0, 0, 0, 0, 0, 4015486272, -457877112, -1117306768, 606972660], ![0, 0, 0, 0, -1103591160, -469689864, 323661744, 1136064944, 1879772156], ![0, 0, 0, 197967904, -180546064, -2227859472, -2607623808, -768526176, 2100097224], ![0, 0, 919602120, 1221243432, 787314440, -208292424, -1479210184, -2981224168, -4358111736]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 10 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -4504308], ![0, 0, 0, 0, 0, 0, 0, 25820096, 16137560], ![0, 0, 0, 0, 0, 0, 276374000, -13014160, -193881904], ![0, 0, 0, 0, 0, -6009197712, -1034365584, -552573648, -2878932264], ![0, 0, 0, 0, 1736422856, -1074110296, -2580657632, -3861647856, -5591097684], ![0, 0, 0, 3127076128, -1213511088, 2842859552, 2167638432, -5727224000, -16679461480], ![0, 0, -67402248, 4968878712, -341226168, 3307580424, 7389373192, 4653513544, -4375571712], ![0, -772430840, 172457872, 85000888, 3659852480, 9134782808, 10844354640, 359020392, -26806274544]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 10 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 7252560], ![0, 0, 0, 0, 0, 0, 0, -11182144, -6988840], ![0, 0, 0, 0, 0, 0, -70421344, 163322496, 309412144], ![0, 0, 0, 0, 0, -2948043840, 5417148464, 6697014048, 3548548920], ![0, 0, 0, 0, 6108349632, -1760235792, 209357232, 4597112992, 6765520912], ![0, 0, 0, -7685221696, 6054011896, -4888165056, -5716258896, 8836322272, 25580607716], ![0, 0, -980419368, -7489476584, 967109032, -3088973688, -11298865368, -7645613528, 11490966048], ![0, 509631680, 585559040, -1289146816, -1686651296, 909134272, 2314024960, -2481654336, -14108909136], ![-556476480, -378531776, 341517056, -2014751520, -3792384288, 5820969600, 18650457792, -2996391328, -87216743264]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 10 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -125180192, -78237620], ![0, 0, 0, 0, 0, 0, -422157176, -314957848, -247958268], ![0, 0, 0, 0, 0, 5915959728, -10238605832, -12286465280, -5517634308], ![0, 0, 0, 0, -15594212928, -1601053104, -2747201968, -5787196640, -2442623504], ![0, 0, 0, 11897611456, -3635559176, 6009123760, 8209908304, -1874423424, -11722268572], ![0, 0, 10812590496, 3585026240, 6408756496, 5967057312, 9255245408, 21808308544, 42576049368], ![0, -2197121976, 4317578640, -7116991624, -7646815968, 5073486744, -16858969008, -61116412248, -11920181952], ![1102549664, 1517595200, 436616960, 8267935264, -12807239968, -46340382720, 5952603456, 184267409312, 289682012032], ![15461760, -744045056, 1568690688, 4063681728, -10888444800, -8276121984, 79402111488, 200539774400, 85018768128]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 10 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 201187280, 44810512, -52924608], ![0, 0, 0, 0, 0, 6177127152, -1379181832, -2607452448, 119300556], ![0, 0, 0, 0, -2584543808, 11758802608, 3971894864, -8016020064, -12999165120], ![0, 0, 0, 6613250688, -17593722088, 6825414640, 12968503760, -10963707904, -42331160620], ![0, 0, -3428547696, 6792369200, -3400560896, 3977362896, 19452278640, 14305522256, -21798728568], ![0, 6221538768, -5871628704, -3035771504, -14800209536, -36584207984, -21365239072, 22013747504, -15114211168], ![4074471312, 3137052768, 6655012224, -5302022864, 16232376528, 61526085440, 39613375328, -80722703376, -153525414560], ![442402176, -2755437824, 617886720, 9997690048, -12528875520, -12676409472, 128962367744, 326791134656, 127431255168], ![489661952, -127791104, 792395776, 4949199360, 5040680960, -5214866944, -11009987072, 22288573440, 101202941952]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 10 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -1130374224, 346184496, 543741584, -58077240], ![0, 0, 0, 0, -4013405480, -1805856920, 666252496, 2807107184, 4244320676], ![0, 0, 0, -5661980320, -1405218440, 10686546000, 10732621456, -2859594624, -20252652700], ![0, 0, -779176524, 21735889012, -37230577444, -6447992676, 52296051212, 30613016620, -103443105864], ![0, -1582273784, -6023392496, 15457880184, 185359552, -2340278888, 82018046288, 193257186472, 135264554320], ![-1414328416, 2683300096, -1990337280, -4280429248, -7417487744, -4830678912, 22780674944, 61073701696, 23712630816], ![710883136, 980088832, 14807547648, -12807074656, -70479197120, 83462083008, 522022384128, 489817020448, -1392858028800], ![-1828514432, -6292211072, -16120967552, 5887554880, 32136073280, -184406813248, -789306367808, -1018699065216, 953083837440], ![-898492928, -5476560128, -10883048960, -6004693120, -14757783040, -156046242688, -545501166336, -952659477504, -596091589632]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 10 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 371556976, -896339024, 125466880, 1415822848, 1711507576], ![0, 0, 0, -3871632608, 4827668408, -276097392, -2382368496, 1779951744, 7026046020], ![0, 0, -1737758328, 9242096680, -5896147368, -417911112, 10960780376, -260034920, -40797799296], ![0, 502114616, -228666640, -3660428984, -4946276320, 14349344936, 37924093232, 25809376664, -42338628640], ![-2687887360, -2560305600, -3906546944, 7712543584, 13929904608, -50059435648, -124783941696, 56336165088, 674474596320], ![2848129536, 2332243200, 9108801024, 3788264960, 4865388160, 45038158080, 76627258624, -39392421376, -377292795264], ![-2577498368, -3348502528, -12803375104, -20339043840, -2634394880, -97358073344, -537152057344, -1073361816576, -489743944704], ![-1148590592, 581608704, -5017500160, -22010769280, -6931330560, 53392081792, 2069625600, -377721437184, -783496885248], ![7645698048, 16643481600, -22067896320, 64364697600, 667956387840, 1372937416704, 238710398976, -3058610429952, 1153393274880]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 10 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -3475853536, 7206667936, -5080466784, -7206475424, 5720596480, 20943437776], ![0, 0, -1189335588, 1533526012, 3761511412, -5459149068, -17857876412, -23527228444, -16331577432], ![0, 1906730416, -650628512, -3007949104, -15101808192, -8467938672, 19215444320, 40183225328, 25862043200], ![1231965984, -5775564992, 10013699840, -1114117472, 19784473184, 84873114624, 73872856640, -81245887968, -172367210624], ![-1233598592, 1791850496, 387551232, -20037091776, -6436879360, -25206569088, -249820453120, -589912388800, -467948960640], ![1445467776, 4750564224, 6865960320, -4396708160, 7275648960, 143051227200, 382857651008, 322595231616, -645916981248], ![-2946046464, 2292340480, -4005506560, -54720159360, -65335621120, 106284368512, 288843948288, -222426215424, -1924006081536], ![4171199488, 11756933120, -10318540800, 30095744000, 388837980160, 892369336320, 412107558912, -1430149754880, 814755465216], ![7953469440, 23860408320, 0, 69592857600, 751602862080, 2104488013824, 2204701728768, -1102350864384, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 10 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 40], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, -88002240, -88000960, -88000800], ![0, 0, 0, 0, 0, -609888768, -626869168, -643850848, -660832568], ![0, 0, 0, 0, 752345360, 286434864, -182576992, -654694368, -1129917544], ![0, 0, 0, -19695680, 913252320, 1289963936, 1172677568, 623636416, -294916400], ![0, 0, -225214960, -348078000, 350912080, 1037549296, 2058077424, 2968896560, 2536568560]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 10 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -40], ![0, 0, 0, 0, 0, 0, 0, 0, -80], ![0, 0, 0, 0, 0, 0, -43747680, -43747360, -43747040], ![0, 0, 0, 0, 0, 2341382752, 2150632352, 1959882912, 1769134192], ![0, 0, 0, 0, -1308805680, -165616368, 1010302784, 2218948576, 3460321368], ![0, 0, 0, -206369920, -1786802400, -1505317056, 127639872, 2601612544, 5406149360], ![0, 0, 674948720, 192261360, -1788543280, 784452816, -2693686896, -9791320560, -5040228640], ![0, 222319920, 370491840, 1246663440, -575658720, -4065653104, -627670400, 12616126000, 22037903360]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 10 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -80], ![0, 0, 0, 0, 0, 0, 144485120, 144485760, 144485760], ![0, 0, 0, 0, 0, -1916141312, -1845447072, -1774748992, -1704050512], ![0, 0, 0, 0, 913494720, -945047584, -1959666528, -2130359872, -1457128896], ![0, 0, 0, 2670894400, 1310238320, 115031168, -668221216, -793016512, -12848440], ![0, 0, -893047120, 259229360, 1234430160, 1860375568, -314407088, -3816395440, -3247074560], ![0, -562014080, -1140550400, 336890240, -1057436800, -1722470016, -1075745920, -186023040, 1479382400], ![-172265728, -344113088, -1358886848, 1833837952, -2807806208, -11595007680, 3812395840, 39382073600, 22152401280]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 10 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -40], ![0, 0, 0, 0, 0, 0, -212207920, -212207920, -212207960], ![0, 0, 0, 0, 0, 2427109408, 2643720048, 2860332928, 3076946168], ![0, 0, 0, 0, 6653027520, 3428603936, 428271072, -2347969472, -4900116736], ![0, 0, 0, -7181456640, -3726989840, -1994916192, -2136075296, -4301273472, -8641314680], ![0, 0, -923556800, 934148480, 1853073440, -1580181632, -1153867328, 1425108480, -5468826320], ![0, 3722470320, -1073962560, 8488843920, -9020423520, 22046998800, 38299947520, -34951622480, -134380062080], ![525657856, 1002857536, -590288704, -1742617984, 23293122816, -5174538560, -82662698560, -60141920000, 187873178240], ![169595136, 303926912, -4379462912, 2320024064, 6104263680, -39913944960, -61179232000, 80668440320, 273770046720]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 10 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 13391840, 13390880, 13391040], ![0, 0, 0, 0, 0, -335796000, -459795600, -583794240, -707792840], ![0, 0, 0, 0, -4283154560, -1247364128, 922135904, 2225351616, 2662282528], ![0, 0, 0, 2621568000, 474757680, 1718799648, 4485522784, 6906762368, 7114349480], ![0, 0, 2860311840, -332738720, -2589123520, -9869970272, -2555802528, 13774936480, 8345888880], ![0, -1670757600, 674767360, -6830754080, 11174896320, -12563509536, -32890279680, 15492761760, 103864828160], ![2224671040, 1475976480, 654729760, 4476882880, -14869206400, 9305367840, 30127961760, -44361340800, -134865956480], ![-176693888, 1355420544, -5253378304, 7450587648, 16741593600, -55823838080, -57377440000, 257393237760, 610652453760], ![-151200256, 1012314112, 1308063744, 2446837760, 10342338560, 22124928000, 31020723200, 52327480320, 142103462400]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 10 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 129537312, 118387872, 107238112, 96088432], ![0, 0, 0, 0, 1595291440, 1046909648, 190980256, -972492576, -2443507128], ![0, 0, 0, 2333438720, -360872720, -2898322976, -4239339808, -3344342016, 826252040], ![0, 0, -4513384920, 4351770600, 215120120, -3110253576, 8846805016, 34624527320, 56828226000], ![0, -734182480, 5666374720, 950253200, 16398619680, -40382917360, -67634500480, 37073392560, 162207781760], ![426957056, -2878891264, -1765544064, -1709608704, -1339636224, -27402389120, -61027201920, -46046192640, 19349470720], ![814554368, 1708354496, -13866054016, 40588197632, -2232345600, -239001023040, -104652944000, 881621573760, 1468660158720], ![-1645655424, -1154327552, 2890457856, -46894816000, -10558434560, 249160035200, 211208208000, -923547576960, -2149756853760], ![-1308019200, -650723840, -1533276160, -19188697600, -5734476800, 114246278400, 197467315200, -130189858560, -665989125120]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 10 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 59007200, 48919840, -9962560, -117636160, -274101680], ![0, 0, 0, 452747520, 132206960, -837890720, -1731693600, -1823353600, -387023800], ![0, 0, 544178640, -699493040, -1118621520, -1217555856, 4716799536, 13948853040, 15294325120], ![0, -388131120, -127048640, 6958859760, -3526016160, -16674030224, -13303778560, 7466276560, 16876753280], ![-898231040, -2136776640, -495497920, -21650276480, 10041291520, 70447594560, -70677115840, -373060796160, -202673833600], ![434953600, 4176779520, 4411192320, 14650839040, 7102599680, 14507028480, 91076108800, 201874892800, 214569970560], ![-1258289408, -3896126464, 3480993792, -26753013760, -31294837760, 140055321600, 199586457600, -529062958080, -1698133121280], ![494342656, -3230793216, -720138240, -10066777600, -51446092800, -60315782400, -19063065600, -230220437760, -1211955655680], ![386310144, 7355965440, 70066790400, 0, -92875161600, 827546112000, 2900576563200, 2184721735680, -6590818713600]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 10 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 407893760, -110142080, -484842816, -583716608, -274276736, 575965440], ![0, 0, 495214520, -3314204040, 966519720, 5290605992, 10731120648, 13300656200, 3951326320], ![0, -412046560, -793858560, 4724843360, -81862720, -9721455008, -16181972480, -16318333920, -15085457280], ![493427456, 1334035776, -8033745984, 1879876736, -26830033664, 16005609920, 83824335040, 6172775680, -185353960320], ![-942655360, -491587200, 7605397760, -6073643520, -11522972160, 107177486720, 123969056000, -306478933760, -696990729600], ![926513024, 333965312, 4194516224, 26556619520, 250430720, -89757078400, 2544777600, 512231414400, 824640030720], ![1496681984, -7589026304, -6788116480, -9606054400, -103856716800, -255477548800, -296286336000, -402756053760, -1671663375360], ![975581184, 3439513600, 40711434240, 0, -83174195200, 386945280000, 1535119718400, 1021535539200, -4655745515520], ![0, 7953469440, 79534694400, 79534694400, 0, 894765312000, 3936967372800, 6299147796480, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 10 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -427440], ![0, 0, 0, 0, 0, 0, 0, -3432960, -2145600], ![0, 0, 0, 0, 0, 0, 337457792, 259411840, 210632064], ![0, 0, 0, 0, 0, -1466664192, 2140556320, 2696627904, 1345732176], ![0, 0, 0, 0, -1287002080, -482624800, 199410624, 871416768, 1603593072], ![0, 0, 0, 113112704, -1865289792, -1090606400, -336486656, -148542336, 320132384], ![0, 0, -663588576, -676702048, -1318931168, -3037810464, -3940548896, -2662837152, 872606112]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 10 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3603504], ![0, 0, 0, 0, 0, 0, 0, -20655872, -12909728], ![0, 0, 0, 0, 0, 0, -147603008, 83906752, 228600640], ![0, 0, 0, 0, 0, -1321233984, -4980639552, -5045614656, -2864069280], ![0, 0, 0, 0, 3612684320, 2586865568, 462879872, -1896536768, -3952171088], ![0, 0, 0, -3786026624, 4475964736, 1950418048, -2249088, 1465941760, 3882723680], ![0, 0, -1934558496, -3886200096, -3838792672, 3129426720, 5675416608, 415608096, -8522945664], ![0, 1297758880, 234563008, -3584274080, 390780288, -2743027488, -15507946816, -21692269792, 2946175424]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 10 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -5802048], ![0, 0, 0, 0, 0, 0, 0, 8945920, 5591392], ![0, 0, 0, 0, 0, 0, -186399360, -373393408, -490265024], ![0, 0, 0, 0, 0, 7565273856, 754346432, -388314496, 2011688160], ![0, 0, 0, 0, -7393111040, 2215288768, 2535347136, -496913280, -3171484992], ![0, 0, 0, 1266371072, -6776203552, 3910916864, 5077222592, -7904701056, -24897813872], ![0, 0, 4149788256, 6575468896, -2925037408, 3218633760, 13838715552, 11499450016, -10466348928], ![0, -1331561728, 283333376, -1010573568, -65349504, 3335716608, 4314059776, 1638486784, 729453376], ![-2848512, -554124288, 266911488, -4900661120, 12526963328, -10335892224, -37468131328, 33505403008, 174084038016]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 10 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 100144256, 62590256], ![0, 0, 0, 0, 0, 0, 694234912, 608475552, 554876048], ![0, 0, 0, 0, 0, -12013882944, 545859552, 1820239360, -3958733328], ![0, 0, 0, 0, -2495951360, -5164058816, 3902807104, 14108274816, 18829612608], ![0, 0, 0, 5935500544, 9059569632, -2798074432, -3286685632, 11720102912, 32458395536], ![0, 0, -11329844352, -8235032576, -6093209536, -10733817984, -15508064384, -18341067520, -21079010976], ![0, 1947520416, 3072244416, 13733328992, -21502056960, 12366302688, 62690048704, 22660157472, -126282664704], ![426907264, -1348889856, 8169862400, -19719662720, 9430898816, 63395436288, 27602188288, -118897824896, -182590939904], ![165482496, -682283520, 5797122048, -27779134208, 28307584512, 1536620544, -177539246080, -131730733824, 471358978560]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 10 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, -183445696, -58346688, 19841536], ![0, 0, 0, 0, 0, -3723714624, 2529650144, 3720586112, 1747502256], ![0, 0, 0, 0, 11135455744, -6898945088, -5773788608, 167540864, 1960419968], ![0, 0, 0, -10281403904, 12374342496, -9180479296, -18285637568, -2363190784, 23613346128], ![0, 0, -3537306048, -6763728704, 17868987136, -636328128, -24541502528, -11189689024, 48767949216], ![0, -7788872896, 4030558592, 2705926464, 34022478592, 20223445312, 6881303168, 59451444672, 154751458944], ![1022188992, 1785358336, -3187059328, 17555945280, -54145135168, -12562697600, 79067314176, -68664811200, -412253870976], ![-354459392, 74518528, 13414603776, -44127320832, 71166588416, -8292716544, -393804500992, -278047648512, 948843498240], ![-137131008, -376754176, 4085952512, 5477064704, 7271120896, 14790135808, 15697260544, -22577817600, -138119961600]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 10 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 566569920, -595945280, -735260352, -235074144], ![0, 0, 0, 0, -1499431584, -1041099360, -277740736, 1267296704, 3891920528], ![0, 0, 0, -1303958912, 3402757088, -926384064, -133329088, 5309517312, 5785708432], ![0, 0, 8591920848, -26112788784, 31271764080, 3610372464, -63759341008, -78706315088, -3395412384], ![0, 7641684128, -1398581056, -36079333792, 42276109184, 11696937440, -100068519744, -112162449376, 90106917824], ![710963840, -2299094784, -3636303872, -14938832128, 11283649536, 31425327616, 14095929344, 10873928448, 136429474432], ![753397504, -1686442240, 13297508352, -89557687936, 223277677824, -44606985216, -1005476484096, -288408135296, 3764742013440], ![33506048, -6736165120, -2375740672, 69135171584, -189276248576, -16076372480, 1277594748416, 1537148056320, -3032523878400], ![76663808, -5986590208, -770354176, 29115200512, -28849737728, 32670561280, 649504880640, 1363494597120, 265640094720]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 10 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, -630236992, 521624768, -76308736, -807105280, -660189856], ![0, 0, 0, 1597910912, -3488133408, 2661130048, 5385826624, 849652224, -8018965744], ![0, 0, -291240672, -6657048416, 8702062944, -4116468000, -23447892128, -17659291040, 24050675712], ![0, 585326176, 1379342656, -11319784800, 10797736192, 23265782560, -3806593216, -34728586016, 14066049664], ![-200498688, -1466048000, -5734622464, 26567872128, -127148737920, 98578067712, 351772360704, -296297421184, -1546428772736], ![-14753024, 1101029888, 6304269312, 21839962112, 17982398464, -19026683904, -47246997504, -14465353728, 22080602880], ![8277504, -3457900544, -18422841344, 61194895360, -109569931264, -16547442688, 956998762496, 1427628718080, -1319191626240], ![36006912, 3458272768, -15006438400, -2723902464, -54239137792, -148727936000, -8007874560, 354110123520, 124763950080], ![-3135541248, 5260247040, 35308634112, 333082017792, -116710440960, -1198330675200, 655372615680, 5097684049920, -5766966374400]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 10 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 1659486080, -5303037824, 5412043392, 7077531776, -4442727936, -19165474112], ![0, 0, -203053200, 5871461872, -1718226224, -12106556208, -13364886768, -1119998576, 23504006688], ![0, -1815440448, 1968693120, -5840063936, 13589605888, 31956136768, 25208404096, 4718028992, 7150453760], ![-19756928, 1839462144, -1480822528, 15467231616, -90416180608, -78520880384, 19993425920, -128067331712, -624807577344], ![259134208, -3578970624, -13739123712, 81877583616, -87122134528, 67702745088, 704238940160, 525101686528, -1431158572800], ![-380447488, 5710349568, -2989382400, -13659373568, 88268020224, -27212527104, -574401848832, -638052238080, 1201458677760], ![339405824, 8902130176, -35786406912, -42776517632, -69944971264, -242709519360, -401950402560, -70487815680, 1176041180160], ![-1863596032, 7229292544, 16509665280, 181181390848, -107038326784, -846499184640, 20258242560, 2383582924800, -4073777326080], ![-3181387776, 0, 38176653312, 384947920896, 286324899840, -858974699520, 0, 5511754321920, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 10 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1708704], ![0, 0, 0, 0, 0, 0, 0, 13731840, 8582400], ![0, 0, 0, 0, 0, 0, -1349832960, -1037644032, -842527104], ![0, 0, 0, 0, 0, 5866656768, -8562224832, -10786512768, -5382929376], ![0, 0, 0, 0, 5640989760, 2423477952, -304655232, -2992684416, -5921400480], ![0, 0, 0, -3867616512, 2204352384, -2736014208, -7594141440, -10187562240, -13903887552], ![0, 0, -51512256, -1772895936, -2412451008, -180187200, -2647033920, -16846466880, -43087857984]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 10 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -14412960], ![0, 0, 0, 0, 0, 0, 0, 82621440, 51638976], ![0, 0, 0, 0, 0, 0, 590416512, -335627904, -914404224], ![0, 0, 0, 0, 0, 5284927872, 19922566272, 20182460544, 11456270784], ![0, 0, 0, 0, -25388502720, -21285233088, -12789283584, -3351619200, 4870911840], ![0, 0, 0, 35803570176, -8534223744, -9721940736, -13201072896, -30363641856, -51320675904], ![0, 0, -15897531456, 9418895808, 16279318848, -15003373248, -39056888256, -18592214976, 29882286720], ![0, 2983080384, -5271141888, 3179125056, -12485774976, 8723009856, 50332009728, 15803020224, -181613106432]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 10 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 23208192], ![0, 0, 0, 0, 0, 0, 0, -35785728, -22365504], ![0, 0, 0, 0, 0, 0, 745597440, 1493574144, 1961059584], ![0, 0, 0, 0, 0, -30261095424, -3017390208, 1553262336, -8046745920], ![0, 0, 0, 0, 42635040000, 4201459584, 2921202816, 15050244864, 25748553216], ![0, 0, 0, -31172596992, 12322026432, -19102192128, -12443072640, 50808965376, 130105685280], ![0, 0, 11745309888, -6600019776, 24887463744, -4073632704, -48812342976, -34622203584, 65165635584], ![0, -496350720, -3549841920, 5159858688, 6586948608, 1410749952, -10424013312, -27197323776, -42122375424], ![0, -297181440, 4252628736, -35706212352, 78498132480, 26164839168, -207980110080, -143126570496, 519266141184]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 10 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -400578048, -250360992], ![0, 0, 0, 0, 0, 0, -2776939200, -2433902784, -2219504736], ![0, 0, 0, 0, 0, 48055529088, -2183436864, -7280954880, 15834933216], ![0, 0, 0, 0, -17777760000, -7105338240, -43372796544, -84194664192, -103080017664], ![0, 0, 0, 25113526272, 7032321984, 48877975680, 45247460736, -20364618240, -108902661600], ![0, 0, 9923897088, -37184996352, -53348808576, -15249604608, 50517191424, 118417010688, 195834845376], ![0, -5167831104, 26846337024, -34717753536, 80145325440, -40290856128, -378805032192, -325402694208, 739381418496], ![0, 4679481600, -39454900992, 137069684736, -143856849408, -230046177024, 397800006912, 917908919808, -243240668160], ![0, 242320896, 8522247168, -71870063616, 167349086208, 70945132032, -752058768384, -917479962624, 1523021211648]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 10 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 733789056, 233382528, -79368960], ![0, 0, 0, 0, 0, 14894861184, -10118606400, -14882343168, -6990002208], ![0, 0, 0, 0, -33330898944, 38806717824, 34306070400, 10540757760, 3369264000], ![0, 0, 0, 30597451776, -66594264384, 13056362112, 42908241792, -27350297088, -137825107296], ![0, 0, -14393916288, 18715573632, -55973378304, 45527865984, 172266642816, 112992755328, -169689151296], ![0, -3435686784, -22831285248, 57226813824, -1067416320, 58647933312, 244619770368, 169668244608, -566638159872], ![0, 5581065600, -10118376576, -1316868096, -74822227200, 187104902016, 396968827776, -364249181952, -2068187606016], ![0, -4577352192, 38561854464, -147190342656, 358994893824, 129718052352, -1817503693824, -2515859208192, 2737058798592], ![0, -363515904, -5147725824, 24349863936, 49179992064, -3684237312, -151468154880, -386729385984, -816906055680]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 10 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -2266282368, 2383785600, 2941041024, 940291776], ![0, 0, 0, 0, 3162796224, 1329453888, -1723972992, -7904115840, -18402612960], ![0, 0, 0, -7638077952, -14700750912, 14380004736, 22971970944, 12964780032, 22824217632], ![0, 0, -15740560224, 96765113760, -160029176352, -77582594592, 162754292832, 179184461664, -179632529856], ![0, 13428582336, -25603112448, 71251571520, -248982478464, -96690521280, 655718795520, 1046675093952, 23992502016], ![0, 5067790848, -24827466240, 8982349824, -34522696704, 26378952192, 374179923456, 746932657152, 408321091584], ![0, -5377727232, 129532801536, -720872332800, 1081001527296, 1576733333760, -3462556672512, -6731843601408, 6164772489216], ![0, 17544771072, -225669588480, 755338581504, -323863758336, -2273325293568, 1716845233152, 10047524539392, 2085975797760], ![0, 9278641152, -105823899648, 210987082752, 218020669440, -504689203200, 231831355392, 3990264145920, 3743207424000]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 10 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 3178288512, -1429142400, 962567424, 3885756672, 3298119744], ![0, 0, 0, -9295154688, 14297898432, -7050268800, -14700177024, 6693393408, 45416743200], ![0, 0, -13111300800, 24209720640, -34927258944, 9088016832, 69596538048, 8333724864, -217905772032], ![0, 4959120960, -16641045504, 25328460480, -37501176192, -2394966336, 149276303616, 219723782208, 8364364800], ![0, 3307352832, -64046198016, 325642444800, -654998349312, -201796014336, 1815236303616, 1121591333376, -4980011387904], ![0, -1222963200, 16059267072, -47917547520, 117918145536, 276703635456, -188945498112, -1295888498688, -1995172881408], ![0, 9717313536, -125729095680, 428849442816, -396336445440, -1315322437632, 2285148880896, 8448910516224, 2560484874240], ![0, -114398208, 3965276160, 66209897472, -268540618752, -784764266496, 108884901888, 3289091512320, 6074044416000], ![0, 26481475584, -517055201280, 1823726075904, 2623887507456, -6864209215488, -16346085949440, 0, 19772456140800]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 10 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -7715710464, 21114293760, -20766160128, -26448188928, 20612771328, 80483623680], ![0, 0, 9152741088, -15665199648, 7033048224, 33785274528, 16876905504, -72529203936, -229936659264], ![0, -1204912512, -6226292736, 28998622080, -27622165248, -39649113216, 65839707648, 242815632000, 413848476672], ![0, -975741696, 13213626624, -24428918784, 679503360, 86101855488, -363628201728, -1599245406720, -2376949005312], ![0, 6973788672, -78975378432, 262428779520, -445163891712, -49792366080, 2884887333888, 3526802405376, -5813661551616], ![0, -11372336640, 120448157184, -319593616896, 42616714752, 886148186112, -638381097984, -4212182780928, -1176123801600], ![0, -5742148608, 93343002624, -135817325568, -741238192128, -712193685504, 1026363211776, 4490477291520, 10443268915200], ![0, 12382248960, -270383652864, 1081686147072, 1322275307520, -4583250542592, -10218764943360, 0, 13967236546560], ![0, 28632489984, -515384819712, 1336182865920, 4123078557696, -2576924098560, -18897443389440, -18897443389440, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 10 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 5 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7]] +lemma sums_checked : ∀ u : Fin 5, ∀ a i k, fourSumInteger a 10 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k +end SumTable10 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable11.lean b/lean/OAI/Analysis/LaughlinGap/SumTable11.lean new file mode 100644 index 0000000000000000000000000000000000000000..ee70ded1bcfe2c081a320d6ea22403bdee71f15e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable11.lean @@ -0,0 +1,313 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CheckedTables +import OAI.Analysis.LaughlinGap.IntegerFourRows + +namespace OAI + +/-! Sum Table11. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable11 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -8582400], ![0, 0, 0, 0, 0, 0, 0, -3259891440, -3455008920], ![0, 0, 0, 0, 0, 0, 3022287660, 12513531960, 14376907950], ![0, 0, 0, 0, 0, -12829642476, -5394239928, 1542591480, 8261644818], ![0, 0, 0, 0, 18977030040, 4450161768, -3841124592, -10833928080, -15895272156], ![0, 0, 0, -2321766420, 6374570460, 15177060324, 15434719908, 4213495668, -15979643700]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 11 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -51640620], ![0, 0, 0, 0, 0, 0, 0, -2521587480, -1942810080], ![0, 0, 0, 0, 0, 0, -1332446808, -20943858648, -31569188148], ![0, 0, 0, 0, 0, 7864400796, -10501256304, -30433588824, -49775740614], ![0, 0, 0, 0, 50124461880, 7831400496, -21099126864, -28710472320, -28326992412], ![0, 0, 0, -21362941980, 49232955180, 39562469388, -13282162020, -49676009028, -30827772360], ![0, 0, 930631080, 4558861620, 2597519040, 21305456772, 66511846248, 112264800060, 97460983680]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 11 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 22363860], ![0, 0, 0, 0, 0, 0, 0, 6402734880, 5935247520], ![0, 0, 0, 0, 0, 0, 33863809224, 17797486224, 15901820724], ![0, 0, 0, 0, 0, 100948542408, 40050206280, -6877883088, -24995694456], ![0, 0, 0, 0, -63945139980, -22242644880, 48137928936, 78313067088, 58457059926], ![0, 0, 0, 9383351220, -65922691380, -41892754692, 34165619436, 76333963116, 19543187040], ![0, 0, -9924598560, -10886778720, -19531968480, -29837929632, -24768904416, 6045529440, 47848733760], ![0, 10608083376, 7207102416, 5583239136, -5519028384, -29592284112, -35665658544, 28918311936, 167968848576]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 11 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 250360170], ![0, 0, 0, 0, 0, 0, 0, -8202455220, -8416854090], ![0, 0, 0, 0, 0, 0, -91003303692, -44720930832, -26651967942], ![0, 0, 0, 0, 0, -119993253576, -128073766632, -91869338928, -37870892664], ![0, 0, 0, 0, 53611544100, -5320328424, -78408904152, -97605440544, -50422232370], ![0, 0, 0, 129193250880, 12012534120, -36768826944, -596669904, 100586257728, 243113145660], ![0, 0, 33781854600, 104045706900, 75428657760, -73440178524, -154299074424, 22108183260, 476316768960], ![0, -21107484912, -16231270032, -23782411872, 22129338528, 39612348048, -141535348752, -508090271232, -595719806592], ![1353334656, 13229862624, -2123179008, -14470562880, -2075542272, -48210696864, -259906056576, -517155401088, -288680029440]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 11 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 118650840, 431403960], ![0, 0, 0, 0, 0, 0, 6924214164, 18839033664, 18097777914], ![0, 0, 0, 0, 0, 5477195304, 30223275768, 68129208432, 83336503776], ![0, 0, 0, 0, 123946033140, -20821103304, -100497359544, -42868419360, 114074226918], ![0, 0, 0, -18740942040, 68010268320, 22611902520, -88447488696, -145409532264, -57062800980], ![0, 0, 48102173040, -77475315240, -93442810560, -17330248392, -16467575184, -219668151480, -586410183360], ![0, -53069109000, -72187058520, -65954838480, -149778222000, -211848693192, 24340449960, 646756853760, 1168966163520], ![-9678931776, -48174240, -32776923264, -25000177728, 88566934848, 134227717344, -164184316800, -665947223424, -331566119808], ![385928448, -8925810432, -26435001600, -25480832256, 19489551360, 87089599488, 105908963328, 57552675840, 196502321664]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 11 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 2136449448, -1720210632, -3018867972], ![0, 0, 0, 0, 0, -70665477204, -23833813752, 9107274120, 29349424902], ![0, 0, 0, 0, -167875705020, 44415420264, 89284797096, 57083773056, 1587524574], ![0, 0, 0, -142916616090, 240062368530, 49760408130, -346201475046, -398264281974, 243939035940], ![0, 0, -19013301720, 2464302420, 149291738880, 192439373988, -42649514904, -419240583780, -458814702720], ![0, 30582682848, 18480413088, -50587029312, -101448309312, -100196081184, -99866013792, -208765204992, -538925134272], ![14972368896, 13148649360, -10758016896, 73697568, -100981476288, -541210544304, -966440880960, 15595026624, 3886722816768], ![-9736549056, -8077725024, 39614543136, 143151654624, 397218890400, 904341742464, 1247001133056, 15437321856, -4222398445056], ![-5788359168, -23396353344, -21234826368, 84357366720, 404857985280, 968149335552, 1512567952896, 1431841796352, 493331604480]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 11 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -8023606248, 2285666544, 5253488016, 4922164668], ![0, 0, 0, 0, -67443866460, 18226939656, 52567082472, 28531937088, -33864196626], ![0, 0, 0, -63959919060, 86117699220, 68785607844, -53108008908, -142783961676, -92198457600], ![0, 0, -5970581640, 12926229900, 24664518240, -22732097412, -72624534024, -20969586300, 169994568000], ![0, 60871121520, 26538235920, 837775200, 6364512480, 35768483568, -55863776880, -483857479680, -1146695198400], ![24578380224, -34261109376, -66972706176, -26692909056, -18117830976, -96800520576, -28550232576, 683942575104, 2347611007104], ![-14138130816, -22005547776, 55193541120, 174103318272, 269840004480, 493880377344, 1053123907584, 1469618304000, -38161651968], ![-3407639040, 10882029888, 67667236992, 94510217280, -32478685440, -222053690880, -35720627712, 696369307392, 231704478720], ![14109935616, 55117863936, -135503815680, -1082437632000, -2422423019520, -1546410184704, 4320202715136, 9467127521280, -10710080409600]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 11 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, -11445207840, -13894974096, 23930915712, 32028486624, -3128584080], ![0, 0, 0, -38078946270, -4907831610, 57100071702, 70156253790, -17512465362, -203579143380], ![0, 0, -2371668240, 12255052920, 35752761600, -61328909736, -238056891792, -304248090840, -34674654720], ![0, 30520008528, -70263225552, -576548832, -55633282272, -264429822768, -214334497872, 584955806208, 2083456449408], ![2684780352, -33115637088, 54205141632, 141488158272, 38943659712, -61341459168, 367159078272, 1463202436992, 2087843548032], ![3603876288, -9541770912, -49926247200, -130019748576, -279768999840, -437613501312, -257361764352, 820952119680, 2731433785344], ![-6924089856, 28200291264, 174584644992, 267829997760, -84793056000, -894079474176, -1114787283456, 602535935232, 2184076477440], ![8386182144, 47235737088, -18643161600, -553824829440, -1508294000640, -1457606363136, 1469146871808, 4426654003200, -7565586462720], ![14316244992, 62633571840, -107371837440, -1252671436800, -3674502881280, -4960578889728, 0, 10236115169280, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 11 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -7187760], ![0, 0, 0, 0, 0, 0, 0, -63722400, -227134240], ![0, 0, 0, 0, 0, 0, -7833546504, 629899920, 2705007148], ![0, 0, 0, 0, 0, 1484643720, 772490096, -263150960, -1387112492], ![0, 0, 0, 0, -3251572304, -2186950032, 2355157440, 4354006560, 2453789352], ![0, 0, 0, -117060392, -3644908520, -3807000184, -2429494264, -701047064, 1162584680]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 11 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -43248728], ![0, 0, 0, 0, 0, 0, 0, -786291952, -301566592], ![0, 0, 0, 0, 0, 0, 13293783664, 2648927920, -470085128], ![0, 0, 0, 0, 0, 1585937752, 5721657760, 7553618928, 8888188980], ![0, 0, 0, 0, -10350951248, -882942880, -4342182944, 1401674304, 20656135976], ![0, 0, 0, 699249288, -10374516552, -4041245640, -11338607240, -16217001928, -395704832], ![0, 0, 915172544, 941452440, -1499128784, -11409140840, -22320786336, -23022014520, -1968831408]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 11 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 18730024], ![0, 0, 0, 0, 0, 0, 0, 984381056, 592860208], ![0, 0, 0, 0, 0, 0, 8098646864, -7499022368, -11228768504], ![0, 0, 0, 0, 0, -8143458288, -1909947536, -9547248736, -18626835520], ![0, 0, 0, 0, 21895730792, -12191018016, 4540149136, 6930168672, -20719112404], ![0, 0, 0, 4737511016, 15199307736, 1629595640, 10089775064, 23807680472, 11191848736], ![0, 0, 751823488, 1277879616, 5873833184, 5964209984, 391898368, -2245513536, 7508270832], ![0, 753088896, 786953600, 282749664, 6980830368, 10394085696, -7103012928, -29420083488, 4743387040]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 11 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 209676788], ![0, 0, 0, 0, 0, 0, 0, -439653608, -619212516], ![0, 0, 0, 0, 0, 0, -20188697816, 12009436448, 20578838452], ![0, 0, 0, 0, 0, 43201119024, 12761910672, 12621329696, 20593226432], ![0, 0, 0, 0, -18778772792, 16342316176, 135709872, -5838039680, 13449231548], ![0, 0, 0, -40302075584, -8076445872, -5751305632, -6116588064, -19059742144, -57924636680], ![0, 0, -2369305536, -29579680680, 7365400592, 14158663512, -11784553888, 8347859464, 68128092864], ![0, -1857301504, -1391632768, -6244561888, -21126468320, 25649417280, 92584760896, 10710810912, -289463412224], ![1871610112, -618998528, 4957352448, -6174528, 1316620800, 41807842176, 56884259072, -73135612480, -287124880896]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 11 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -306388624, -44457648], ![0, 0, 0, 0, 0, 0, -11277010584, 2458811264, 5595169124], ![0, 0, 0, 0, 0, -3776275888, -25748798320, -10451457504, 12084258864], ![0, 0, 0, 0, -17553203544, 22167960400, -20594228048, -28754758912, 22474014092], ![0, 0, 0, -489183792, -11440341472, 9281226352, -1977240624, -24510903888, -7180054040], ![0, 0, -22196647680, 21944746960, 11281275552, 31183687952, 71305018048, 56480400496, -2475612896], ![0, -9954954432, -8229128256, -2116681680, 25321422640, -25140474208, -124665655072, -103210848976, 120449807968], ![-4082463104, -7909042688, 6657862656, -7857872704, -26841069696, 25345630848, 47369796096, -186624391744, -611965976832], ![-994016768, -2188992512, -932853760, -6821072384, -22339456000, -32736111104, -32003030528, -62932617216, -219893087232]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 11 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 2527343728, -364771952, -1114559992], ![0, 0, 0, 0, 0, 3902404184, 4820562320, 3423920912, 710472460], ![0, 0, 0, 0, 11319772040, 17847380400, -10516614672, -29602171520, -25871796004], ![0, 0, 0, 1215358604, -24432522492, 56599771300, -26044806476, -144056580396, -84885576616], ![0, 0, 12835496000, -3864554152, -45036231248, -775610920, 23734152672, -94168425976, -262567801072], ![0, 75138944, -4273566720, 12302221632, 20568720128, 31080195072, 41800413056, 36156436544, 50685477024], ![7052578304, 4355826816, 1767745280, -22050554208, 61790615936, 185957946688, -90197198720, -881772611552, -984036017664], ![-3099326080, 999840128, 9849427328, 17036527680, -57798497600, -135671054528, 223904161600, 1243156061952, 1663530817536], ![-3246514176, -3142927616, 1832541184, -6571912320, -58164586240, -107748043648, 38638559232, 516030423552, 820287046656]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 11 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -2111311216, 1540502656, 522271296, -1780575352], ![0, 0, 0, 0, 7352119240, -4472122896, 3448844144, 3221935488, -10384081092], ![0, 0, 0, 8051436120, -17730886232, 2950904776, -10521095384, -29890551960, 206511104], ![0, 0, 1533151936, -6636804248, 5748989616, 11384141800, -17382087008, -46032001736, -3788472608], ![0, 1508482688, 9406427008, 14488328544, -8279168864, -6435358912, 119521515712, 257524356960, -6866472480], ![5265633408, 3666007296, -1323047424, -19031546368, -11379638144, -30269256960, -152250680576, -315735379456, -302935820544], ![-5481441024, 546337792, -7477950464, 1850722816, -6684770560, -78600584704, 24022799360, 708186544128, 1674212617728], ![941030400, 3130838272, -2083265536, 19209659520, 73856817920, 76076436352, 18147483648, 253282401792, 1392324240384], ![4004739072, -24237662208, -22067896320, 123952896000, -27182346240, -1297592303616, -2877905092608, -1019536809984, 5766966374400]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 11 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 10136130656, -15747575136, 7278228448, 16570794112, -3212589584], ![0, 0, 0, 13603269124, -8498662228, -13601797556, 4959285372, 26856574492, 32366491784], ![0, 0, -691956736, -11515427312, 5883436384, 40115470608, 36461375424, -5127698896, -28493633600], ![0, -10537930752, 17863941248, -3658116960, 33563064736, -4317077184, -144622113984, -188925541984, -6280881152], ![-1820211328, 12098839296, -15075544064, -11178622400, 21835552384, -35757244288, -80891162112, 193587786560, 739498523904], ![-390834560, -4998275968, -13251551616, -12002112576, 16509117760, -12276429120, -273894789952, -709029990144, -621832071168], ![2803263488, 10560274176, -5430301696, 31555296640, 197001657600, 320110037632, 171060535296, 221975050752, 2201554510848], ![4058653696, -9743183872, -10318540800, 89756072960, 63803944960, -606730199040, -1545982599168, -476716584960, 4073777326080], ![3181387776, -23860408320, -47720816640, 69592857600, 0, -1402992009216, -4409403457536, -5511754321920, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 11 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2145600], ![0, 0, 0, 0, 0, 0, 0, 505046720, 456265440], ![0, 0, 0, 0, 0, 0, -1770321232, 857206368, 1577768568], ![0, 0, 0, 0, 0, -406896432, -73056096, 182704480, 430589576], ![0, 0, 0, 0, 1940322400, -753145312, -1004522560, -981705024, -1460076144], ![0, 0, 0, 530549680, 2493870320, 1926634640, 840771984, -621467184, -1793617040]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 11 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -12910000], ![0, 0, 0, 0, 0, 0, 0, 25810720, 170504320], ![0, 0, 0, 0, 0, 0, -1129684192, -3171296992, -2966390992], ![0, 0, 0, 0, 0, -3306192400, -3126176192, -3828755424, -4874712216], ![0, 0, 0, 0, 2369046240, 7841116352, 1311103680, -7575076096, -14491747056], ![0, 0, 0, 1764030480, -589724880, 10556546736, 8458749552, 4725660912, 1360566560], ![0, 0, -1197470240, -2474948720, 1008331200, 7630711376, 12630920928, 5850916400, -12871919040]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 11 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 5591120], ![0, 0, 0, 0, 0, 0, 0, -566597760, -683470400], ![0, 0, 0, 0, 0, 0, 5616106912, 539072832, -995302448], ![0, 0, 0, 0, 0, -7008205536, 6792463008, 11426835392, 10604917216], ![0, 0, 0, 0, -4342966960, -9731314496, 2652933280, 11891313728, 11829818328], ![0, 0, 0, -6013735600, 124209200, -10952999696, -13663928656, -3259362128, 11287411840], ![0, 0, 1567281920, 937212800, -1842128640, 474522496, 874591360, -2469696640, -6750638400], ![0, -1364638912, -358965312, 3236608, -5602639872, 3672950592, 15656181440, -10548272000, -67919925120]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 11 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 62590120], ![0, 0, 0, 0, 0, 0, 0, 1132506160, 1078906520], ![0, 0, 0, 0, 0, 0, -6588395568, 1733015232, 3001070312], ![0, 0, 0, 0, 0, -13252248096, -15757848352, -10553601728, -4262241824], ![0, 0, 0, 0, 4592178320, 8877677792, -1726676704, -7946425728, -4397415880], ![0, 0, 0, 22897338240, 9434515360, -1107518848, 5610716608, 17966278400, 33496765680], ![0, 0, -6391065120, 8265755920, -11010688320, 5070760656, -42193947296, -65235296080, 52160286720], ![0, 2406835264, -129511616, 13064542464, -295640576, -43509984064, 7661144640, 128794710400, 83027015040], ![800006400, 1063113344, -2135644672, 8330959872, -8097306624, -12202354560, 64224230400, 110370622720, -82661146880]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 11 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -171208480, -93019040], ![0, 0, 0, 0, 0, 0, -4360282800, 478403840, 2153070120], ![0, 0, 0, 0, 0, 20666916640, 443048288, -3496551744, -116513856], ![0, 0, 0, 0, -13408794800, 19735025760, 2729193632, -18350175104, -24978422888], ![0, 0, 0, 2745769120, -6524373760, 8003885280, 18639075872, -1384009632, -34885359120], ![0, 0, 16673000640, -6004702240, -6515463040, -34379405984, -2785378240, 17804697760, -81784311040], ![0, 7644754080, 11170932960, -3587868800, 7643089920, 51110105120, 20497284960, -22938398400, 75458888320], ![-2433743232, 339526016, -10458144256, 8655711232, -17568171520, -24996778880, 104614822400, 162833634560, -200598599040], ![-817017344, 24946688, -1877080064, 403855360, 1642332160, -5923148800, -10239257600, 10885125120, 50722675200]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 11 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 465585568, -331333792, -488751952], ![0, 0, 0, 0, 0, 888444592, -1658062816, -3064060384, -3031645672], ![0, 0, 0, 0, -4500893680, -4590628832, -3442529248, 5937580032, 21399819128], ![0, 0, 0, 24426364440, -44834737720, 29095293832, 55228066152, -489913304, -89720983600], ![0, 0, -11268087200, 7432808720, -2996240960, -15792926000, 77041472480, 116409533360, -48679519040], ![0, -4739708416, 4945742464, 902854144, -6015141376, -9931200128, 18456990080, 39250684160, -39881146880], ![2755884032, 2018193344, 10649610496, 24367886848, -76992232960, 31183527360, 420351052800, 225572044160, -1265482113280], ![589432192, -1195583232, -16904252672, -20166787328, 53341482240, -70122640000, -555707139200, -595945023360, 978192944640], ![-247462912, -2159750656, -13250378752, -19188697600, -7666380800, -80476793600, -351782233600, -594121916160, -252184043520]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 11 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 160073824, 706624064, 149705664, -500109776], ![0, 0, 0, 0, 3048603280, -6679495264, -1429134048, 6150797568, 10176147384], ![0, 0, 0, 1417122480, -4799964080, 14304786576, 17290248144, -4817530160, -35859258880], ![0, 0, -94048480, 3464192880, -12506142400, 5633531312, 21768566432, 1938314960, -44208142720], ![0, -5196569280, -8083922240, -4054872320, 29538677760, -38520726976, -122567640640, 93457895040, 541305859200], ![317590656, 6619481856, 10630665216, 8645328896, 2586134016, 38733383680, 62033728000, -9829632000, -108388397440], ![-22491392, -6790045696, -9173942272, -30534420480, 7996349440, -34938291200, -389361971200, -652167060480, 122528229120], ![1107291136, -268988928, 4136901632, -10066777600, -3600691200, 45118585600, 2489587200, -224500527360, -281927393280], ![-5884772352, 14785978368, -3492864000, -73559654400, 239994470400, 757688832000, -78589440000, -2118518046720, 1647704678400]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 11 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 2261191040, -5718223424, 2233336448, 6627537536, 2095466240], ![0, 0, 0, -8478973560, 10723863960, 747288536, -8351056264, -13113689672, -11936689680], ![0, 0, 1265659840, 10512113760, -16491452800, -14773065504, -1946762688, -2853092320, -20280254080], ![0, 3961027904, -7569802176, -3961623296, 6053784064, 72157034432, 32546501440, -43719227520, 129963690880], ![837264768, -4812514432, 11544882688, -16287982592, 8687072768, 4031246720, -201724787200, -309144290560, 168220656000], ![-1765158784, -619319552, 8188452096, 360177920, -21968282880, 64653302400, 256628739200, 177623369600, -491196948480], ![3074954240, -1758221824, 15245128704, -9606054400, -33940582400, 79839187200, 198360281600, -115648623360, -884322754560], ![-2751610880, 10093449216, 6316298240, -34395136000, 151964467200, 513271244800, 142116710400, -990579916800, 1163936378880], ![-6362775552, 7953469440, 0, -79534694400, 159069388800, 894765312000, 715812249600, -1574786949120, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 11 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4720320], ![0, 0, 0, 0, 0, 0, 0, -741492608, -634180096], ![0, 0, 0, 0, 0, 0, 4286297568, -1422947008, -2936861136], ![0, 0, 0, 0, 0, 315011872, -40683328, -211580608, -352108080], ![0, 0, 0, 0, -1523436864, 2267732672, 1670449664, 1192688256, 2278869664], ![0, 0, 0, -345293984, -1930235040, -1327349728, 1765535264, 4047594400, 3593989664]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 11 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 28401824], ![0, 0, 0, 0, 0, 0, 0, 126955840, -191370752], ![0, 0, 0, 0, 0, 0, -1082605888, 4210092992, 4560447968], ![0, 0, 0, 0, 0, 4438383712, 3315596928, 3997049536, 5296480208], ![0, 0, 0, 0, -1743243584, -12079486592, -1742431360, 10190762752, 16347531168], ![0, 0, 0, 378934560, 3528469472, -4090168864, -20108703264, -15005560608, 18996683904], ![0, 0, 222124928, 4654829536, 381022784, -9650104608, -3015436288, 15183618464, 17211473344]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 11 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -12300640], ![0, 0, 0, 0, 0, 0, 0, 639678464, 896794944], ![0, 0, 0, 0, 0, 0, -10124495808, 748066176, 3826759712], ![0, 0, 0, 0, 0, 12356681792, -9586402112, -14908106624, -11770460544], ![0, 0, 0, 0, 2908864160, 18261190016, -3641101248, -17812728960, -11750177872], ![0, 0, 0, 3249099936, -8017609376, 14265538016, 12954333536, -5005520544, -16482092928], ![0, 0, -2701481216, -1904161024, -2087900032, -1434781440, -2985125888, -2897422592, 2264809280], ![0, -489245952, -2696493312, 57868928, -1339999360, -21093845504, 9906634240, 46161084544, -30581686912]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 11 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -137698352], ![0, 0, 0, 0, 0, 0, 0, -1600240032, -1482320912], ![0, 0, 0, 0, 0, 0, 14138310816, -5078556032, -8778050864], ![0, 0, 0, 0, 0, 10447172288, 20561670976, 12773323904, 1652139648], ![0, 0, 0, 0, -7528296672, -21340353728, -2118631488, 8366615552, -1096362256], ![0, 0, 0, -15642006528, -1203158720, 5918791808, 10588835200, -4197662464, -42557725728], ![0, 0, 13971819648, 5340567264, -23324312896, 74030233056, 42548406272, -77899754848, -79518782208], ![0, 2214170112, 8422404352, -21834178176, 51876268928, 1222981120, -89232592384, -8697578624, 235520028928], ![192407040, 1249657344, 2336467968, -8965001984, 19338614784, -62667293696, -54517405696, 153170834688, 134679687680]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 11 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 320411328, 148400192], ![0, 0, 0, 0, 0, 0, 8883387296, -1240924672, -4404397040], ![0, 0, 0, 0, 0, -29994091456, 4879344960, 7565818496, -2212518080], ![0, 0, 0, 0, 26048182176, -31927249856, 2417911232, 35562544640, 34598688304], ![0, 0, 0, 406497088, 17922451840, -29299044928, -11000063680, 22511055552, 9766337056], ![0, 0, -11497902080, -6016090048, 31083172224, -40868827840, -26339107840, 59117226176, 84584684160], ![0, 12191271040, 2482191744, 32520294464, -36668699584, 34031745792, 3545401088, -135435050688, -49493236608], ![-863054080, -3161804800, 5359269888, -13910358784, 40088065024, -103814638592, -31857774592, 423340295424, 343542152960], ![-177521664, -1981935616, 1730732032, 1332891648, 10524712960, 24739966976, 36575465472, 67167221760, 161797800960]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 11 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, -1226494528, 573555520, 966705056], ![0, 0, 0, 0, 0, -2152056480, 1444666944, 3823967296, 4330442800], ![0, 0, 0, 0, 3833174048, 2676257728, 7046073024, -2810758656, -26530740880], ![0, 0, 0, -39560325840, 73907398416, -56504041584, -63737771824, 48014963536, 153584239584], ![0, 0, 6369167488, -14360970016, 75124937280, -73003653152, -61769081856, 101565346464, 96978627520], ![0, 4543207680, -10693995520, -10422366464, 11389017600, -34270197760, -69928477696, -28272530688, 19364494976], ![155872256, 8549378304, -12620996096, 36246143360, 73285859328, -355964134912, -26271640576, 1198244979072, 580046891520], ![1982925056, -8283511552, 11617398016, -64330827264, -106348591616, 286668024320, 130720188928, -1347609811200, -1584762531840], ![1107623936, -5066624512, -2453241856, -36474926080, -67138267136, 60317824000, 101402685440, -389237276160, -721566397440]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 11 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 216397888, -1370871040, -325564416, 1129036960], ![0, 0, 0, 0, -6314712288, 10733335232, 1246906560, -9995020800, -13095874832], ![0, 0, 0, -2574940832, 13649148576, -24355974368, -15893847392, 21658355104, 45248362496], ![0, 0, -2303619712, 1576425504, 12135767616, -8850575584, -16168306688, 9313867360, 22056350336], ![0, -4974483200, 428772096, -31761383296, -30980780160, 131841357312, -160727792128, -489859029376, 208830805632], ![-150637824, 1195763200, 7836947456, 39936196608, 20203074560, 31712081920, 118127646720, 190648743936, 157100885760], ![1087979008, -4438272000, -9580711936, -35630149632, -105536530432, 162332545024, 142509989888, -896282224640, -1355831677440], ![23296000, 3890355712, -1152221184, -732761088, -57314473984, -54364369920, -21943398400, -366121935360, -1254407132160], ![-193155072, -29423861760, 70913458176, 74152034304, -162900049920, 884196802560, 3052033966080, 1390277468160, -5766966374400]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 11 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, -5550403712, 11826614912, -4899981184, -13412333568, -2455271872], ![0, 0, 0, 7501414928, -14130873424, -2041832400, 18477405168, 22500291184, 4759976608], ![0, 0, -406175232, -10670539456, 18691724928, 9690395456, -12573504512, -15105513536, -3127046144], ![0, 1927626240, 3591159040, 17960050560, -90541674112, 26638609920, 41822525952, -158672475776, -188232639232], ![1033999616, -2019090944, -13081040896, 22300256000, -51078136832, 183117423616, 84923297792, -566245888256, -276921189120], ![-1644040448, 2408572672, -6683436288, 41698567680, 43227355648, -94344043008, 57515677184, 686358841600, 629566064640], ![-298610688, 12975000064, -10860986368, 10193558528, -83387435008, -235866659840, -279389573120, -532437788160, -1894500357120], ![-487790592, -13758054400, 45877018624, 60110512128, -90478149632, 477030072320, 1713256611840, 650068070400, -4073777326080], ![0, -31813877760, 38176653312, 104985796608, -63627755520, 858974699520, 4008548597760, 5511754321920, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 11 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -3432960], ![0, 0, 0, 0, 0, 0, 0, 1652882688, 1574834304], ![0, 0, 0, 0, 0, 0, -2526119232, 1840947072, 3156865248], ![0, 0, 0, 0, 0, -1560500928, -592314240, 280755072, 1171032864], ![0, 0, 0, 0, 908249472, -5821830528, -6789808896, -6061838592, -5476060608], ![0, 0, 0, -3614236992, 74590656, -4952865216, -12731276736, -17433176256, -15843303744]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 11 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -20654784], ![0, 0, 0, 0, 0, 0, 0, 461263488, 692777472], ![0, 0, 0, 0, 0, 0, -8170807680, -9606211968, -7447169856], ![0, 0, 0, 0, 0, -4069595712, -4337673984, -6332098944, -9190121568], ![0, 0, 0, 0, 755839872, 22094267136, 11898231552, -9498574848, -30274713024], ![0, 0, 0, -9935283648, -31899879744, 1787163840, 36867209664, 26559314880, -50153978496], ![0, 0, 12627340416, -10877253312, 6767116800, 3013601856, -38091935616, -69203608128, -25096508928]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 11 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 8947008], ![0, 0, 0, 0, 0, 0, 0, -2293618176, -2480612352], ![0, 0, 0, 0, 0, 0, 12462463104, 3660505344, 526807872], ![0, 0, 0, 0, 0, -29734728576, 11432292480, 29831596800, 31399163520], ![0, 0, 0, 0, -13468904640, -25560191232, -4395903360, 14187871488, 17978286432], ![0, 0, 0, 18748053312, 33219327168, 2663286720, -8511736128, 7981457088, 35538040320], ![0, 0, -6527946240, -4306386432, 1694148096, 1933321728, -690470400, 6856975872, 26125816320], ![0, -297181440, 2469540096, -25356473856, 53995534848, -66320734464, -66394869504, 172747994112, 239706679296]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 11 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 100144800], ![0, 0, 0, 0, 0, 0, 0, 3849206976, 3763448160], ![0, 0, 0, 0, 0, 0, -8740331712, 2494437120, 2443846560], ![0, 0, 0, 0, 0, -33732306048, -29760248448, -15603745536, -1859156352], ![0, 0, 0, 0, 37206835776, 42804790656, 23359739520, 11158574592, 16263752928], ![0, 0, 0, -29714386944, -43051014528, -64875104256, -74290119936, -48425217024, 24820937664], ![0, 0, -4160649600, 36872478528, 47106207744, -41581351872, -52019494272, 113183217600, 227936130048], ![0, 4679481600, -11378011392, 47454887424, -91508685312, 60779126016, 163131777792, -94749705216, -274230555648], ![0, 242320896, 9976172544, -47528598528, 141321203712, -161201410560, -412982519808, 247750656000, 1001776674816]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 11 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -402493056, -277387392], ![0, 0, 0, 0, 0, 0, -9131306688, -199019520, 3670829472], ![0, 0, 0, 0, 0, 55892704896, 2739596160, -16042324224, -14796478464], ![0, 0, 0, 0, -56320244928, 37444480896, 9491243136, -48523651584, -89026355616], ![0, 0, 0, -26063957376, -21268419072, 24582824832, 23256300672, 8031984000, 40042398912], ![0, 0, -43445405952, -3656613504, -10523467776, 109927675776, 222498540288, 156806484096, -9840804864], ![0, 5581065600, 23368017024, -9695653632, -54056361216, 187329316224, -54409250688, -689792871936, -533864583168], ![0, -4577352192, 11097741312, -74874412032, 343582460928, -307012962816, -835488331776, 591242477568, 2082907026432], ![0, -363515904, -7328821248, 6987436032, 32547225600, 62667153408, 89164701696, 69633810432, -74463473664]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 11 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 380795520, -787241088, -932069952], ![0, 0, 0, 0, 0, 5666388672, -4055920512, -9001035648, -8692285344], ![0, 0, 0, 0, 2527788096, -15459935616, -10565646720, 18421364736, 58081342944], ![0, 0, 0, 85204001376, -139298349792, 39404714016, 128515987872, -528357216, -284420064192], ![0, 0, 54968381568, 2976604992, -108497908224, -13509956544, 30345164928, -109888707648, -111454874112], ![0, 5067790848, 5579278848, -40331590656, -57620659200, -5441536512, 61641994752, 98042652672, 230253327360], ![0, -5377727232, 97266438144, -411303043584, 936090172416, -622773126912, -2162276809728, 1940418379776, 7302154991616], ![0, 17544771072, -120400962048, 329000722944, -751334963712, 68059388928, 2751844795392, 585607283712, -7907774017536], ![0, 9278641152, -50152052736, 52505232384, -220892049408, -81836009472, 1221732642816, 1812398008320, -781587947520]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 11 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 1156934016, 1053303552, -347450112, -1428437568], ![0, 0, 0, 0, 13127313984, -16799753088, -7357916544, 14246482944, 31630657248], ![0, 0, 0, -4670418240, -25925863104, 17416796736, 21335915328, -20333970624, -74568081408], ![0, 0, 13113680256, -19047660864, 1418216448, 7191913920, -28235885184, -2437849536, 192477462528], ![0, 3307352832, -44202081024, 165877092864, -509769702912, 545405350656, 476628829440, -1642441817088, -2020018065408], ![0, -1222963200, 8721487872, -13245923328, 133990757376, 160191019008, 15944355840, -34625224704, 19456496640], ![0, 9717313536, -67425214464, 190744989696, -627530225664, 27552915456, 2072342888448, 746047807488, -4652492138496], ![0, -114398208, 3278886912, 75258657792, -172146708480, -345183885312, -52310716416, -244897966080, -1936531169280], ![0, 26481475584, -358166347776, 886270132224, 159777423360, -587923881984, 6280108277760, 11122219745280, -19772456140800]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 11 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 4599952896, -10207803648, 3006237696, 11788801536, 6277751040], ![0, 0, 0, -11803899360, 42732871776, 1497341280, -52826010144, -65565029664, -15842368320], ![0, 0, -13455767808, 12395174784, -19041635328, 941408640, 63550520064, 149357801088, 236111434752], ![0, -975741696, 7359176448, 7554946560, 10538589696, 57863672064, -373147750656, -978466427904, -868075127808], ![0, 6973788672, -37132646400, 98319694848, -484628155392, 646949485056, 1551461308416, -666063740928, -2984262054912], ![0, -11372336640, 52214137344, -112121897472, 317517974016, -5315189760, -1087694275584, -286477157376, 2990212595712], ![0, -5742148608, 58890110976, 36535366656, -242750877696, -671120443392, -1146021875712, -1585606440960, -1231644303360], ![0, 12382248960, -196090159104, 567033888768, 112866557952, -503847862272, 3108171792384, 5200544563200, -13967236546560], ![0, 28632489984, -343589879808, 534473146368, 687179759616, 171794939904, 6871797596160, 18897443389440, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 11 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -94406400], ![0, 0, 0, 0, 0, 0, 0, -12626465280, -14772764160], ![0, 0, 0, 0, 0, 0, -109419311232, -532553472, 24447622848], ![0, 0, 0, 0, 0, 43823767680, 26759335680, 5030150400, -18275040960], ![0, 0, 0, 0, -28286649600, -8599802112, 29365687296, 14869983744, -61555959168], ![0, 0, 0, 18743725440, -47803704960, 13117991040, 39483388032, -5624353152, -102065673600]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 11 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -568022400], ![0, 0, 0, 0, 0, 0, 0, -16188184320, -9821644800], ![0, 0, 0, 0, 0, 0, 270270975744, 104903234304, 38382436224], ![0, 0, 0, 0, 0, -189372011136, -123058349568, -82618272000, -44326425792], ![0, 0, 0, 0, 291648572160, 43860985344, -198686974464, -213713685504, -13028078976], ![0, 0, 0, -253431615360, 342124295040, -94062097536, -321678420096, -89472670848, 367602385920], ![0, 0, 0, 109379614080, -315396829440, 84563377536, 556951853568, 279542567040, -813123843840]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 11 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 246026880], ![0, 0, 0, 0, 0, 0, 0, 32285890560, 27143550720], ![0, 0, 0, 0, 0, 0, 51636313344, -143757267456, -183273611136], ![0, 0, 0, 0, 0, 373298069760, 188224270080, -65972712960, -226052597760], ![0, 0, 0, 0, -59198325120, -271860576768, 117987412224, 287549154816, 63664421568], ![0, 0, 0, 65700286080, 51079966080, -133174276224, 104556752256, 355642666368, 70007308800], ![0, 0, 0, -18199526400, -28681382400, 80970667008, 133615325184, -27297346560, -385491744000], ![0, 0, 0, -10896652800, 94309839360, -379692352512, -35242994688, 1431513380352, 1722375148032]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 11 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 2753974080], ![0, 0, 0, 0, 0, 0, 0, -34204114560, -36562489920], ![0, 0, 0, 0, 0, 0, -280281369984, 171639046656, 313211992896], ![0, 0, 0, 0, 0, 292896645888, -228002455296, -320927608320, -277278971904], ![0, 0, 0, 0, -55670862720, 343053824256, 77550097152, -63830587392, 96092044224], ![0, 0, 0, 208924277760, -340372581120, -199414178304, -61610267136, -2936355840, 167619534720], ![0, 0, 0, -189487140480, 871157126400, -597717141120, -1356186822144, 270287107200, 2315525667840], ![0, 0, 0, 171580992000, -980711339520, 1301869341696, 2744394402816, -2397944845824, -11334349154304], ![0, 0, 0, 8885099520, 147356098560, -747621439488, -187976650752, 3300364176384, 3899424460800]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 11 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -2230145280, 1210133760], ![0, 0, 0, 0, 0, 0, -120089278848, 43709478912, 68291353152], ![0, 0, 0, 0, 0, -187945857792, -181777972992, 197847986688, 556488607488], ![0, 0, 0, 0, 223557755520, 68302662912, -592684891392, -471850401792, 506096302272], ![0, 0, 0, 70353296640, -439771706880, 536582686464, 226922040576, -673335379200, -576534752640], ![0, 0, 0, -125975182080, -166623198720, 784326859008, 680873825280, -777991061760, -1541447339520], ![0, 0, 0, 204639072000, -492462178560, -260052435456, 634921351680, 1935410906880, 2975984647680], ![0, 0, 0, -167836247040, 874803578880, -967067092992, -1728767631360, 3451494976512, 6366797420544], ![0, 0, 0, -13328916480, -87710515200, 231002382336, 1025641537536, 896171950080, -2627819200512]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 11 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 38652294912, -827490048, -12169204608], ![0, 0, 0, 0, 0, -47706282624, 39095933184, 54293344512, 10993963200], ![0, 0, 0, 0, -273532786560, 244220486400, 19843127040, -227248834560, -179977089600], ![0, 0, 0, -334550863680, 547800221760, 726541333056, -1568380634304, -3131290759872, -520720041600], ![0, 0, 0, 492381352320, -1454153099520, 1020761579904, 1575186252288, -2348482055040, -5444510565120], ![0, 0, 0, 185818997760, -733898711040, -124176949248, 1583470749696, 1839151666176, -596024968704], ![0, 0, 0, -197183331840, 2571951360000, -6545885119488, -9042178590720, 22771568675328, 64378168774656], ![0, 0, 0, 643308272640, -4458929925120, 3133309774848, 22364348869632, 6752785324032, -80363410440192], ![0, 0, 0, 340216842240, -1940104826880, -1129983461376, 10297888161792, 19731261394944, -8597467422720]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 11 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -28446840576, 32789729280, 26151730176, -3895571328], ![0, 0, 0, 0, -89370272640, 4997625600, 146557382400, 66194135040, -207558880320], ![0, 0, 0, -66916629120, -73082275200, 344847735936, -85946146176, -683549116800, -424624865280], ![0, 0, 0, 181834435200, -668754704640, 418830842496, 1219687011840, -31642427520, -2581133744640], ![0, 0, 0, 121269603840, -1356084702720, 3436543368192, 1901045498880, -11018030031360, -17424181209600], ![0, 0, 0, -44841984000, 339261880320, -310672699392, -686861463552, 2243305709568, 7024836876288], ![0, 0, 0, 356301496320, -2483184168960, 1840042795008, 11021576552448, -217212272640, -42516696600576], ![0, 0, 0, -4194600960, 72696729600, 829387130880, -673264779264, -10035582898176, -21301842862080], ![0, 0, 0, 970987438080, -8993851637760, 1592676974592, 80573696704512, 122344417198080, -217497017548800]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 11 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 96784934400, -201014736384, 109671851520, 223823542272, -42326347008], ![0, 0, 0, 226006102080, -397215001920, 77652974784, 534943307712, 428234879424, -378664936320], ![0, 0, 0, -44180125440, -25788449280, 360226310400, 43505746944, -1032688968960, -1424183946240], ![0, 0, 0, -35777195520, 295915614720, -225785472000, -948788020224, 87024554496, 1841394948096], ![0, 0, 0, 255705584640, -1703587522560, 1745011513344, 4854790938624, -2149386894336, -10651505965056], ![0, 0, 0, -416985676800, 2416709053440, -539698351104, -11438411787264, -9317784115200, 30169551126528], ![0, 0, 0, -210545448960, 1711288381440, 1254355458048, -12092102787072, -32626466205696, -13548087336960], ![0, 0, 0, 454015795200, -4730025738240, 2423640096768, 45229974552576, 57205990195200, -153639602012160], ![0, 0, 0, 1049857966080, -8398863728640, -7558977355776, 75589773557760, 207871877283840, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 11 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 6 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7]] +lemma sums_checked : ∀ u : Fin 6, ∀ a i k, fourSumInteger a 11 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k +end SumTable11 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable12.lean b/lean/OAI/Analysis/LaughlinGap/SumTable12.lean new file mode 100644 index 0000000000000000000000000000000000000000..c43b363737f14338809d8bb6ad5266317969df3b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable12.lean @@ -0,0 +1,312 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SumTable11 + +namespace OAI + +/-! Sum Table12. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable12 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 5405649480], ![0, 0, 0, 0, 0, 0, 0, -7890552120, -22502273310], ![0, 0, 0, 0, 0, 0, 29636411112, 14726432424, 600487206], ![0, 0, 0, 0, 0, -67645136856, -31412001456, -7100924688, 12668421348], ![0, 0, 0, 0, 41187812820, 5580746556, -26589473988, -39597722868, -27113869860]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 12 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4081037400], ![0, 0, 0, 0, 0, 0, 0, 7443574248, 38566817388], ![0, 0, 0, 0, 0, 0, -6928407024, 30331165656, 69879185046], ![0, 0, 0, 0, 0, -152347693872, -45064788912, 36063840384, 80835863196], ![0, 0, 0, 0, 117059205780, -85075450284, -96088693404, 8811023364, 123199174824], ![0, 0, 0, -27007587420, -5784972600, 19245657156, -5570790720, -91181763156, -188966487600]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 12 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -10500233040], ![0, 0, 0, 0, 0, 0, 0, -65596118544, -41035151124], ![0, 0, 0, 0, 0, 0, -241524443160, -125207601552, -33982171344], ![0, 0, 0, 0, 0, 187347762624, 71778161400, -89364271920, -190542186846], ![0, 0, 0, 0, -93316295820, 109683516228, 81564021396, -79303136748, -219014078976], ![0, 0, 0, 26740565280, 23253500160, 38063882208, 54729205344, 39567803616, -29646658800], ![0, 0, -42519046416, -33353576256, -31179319776, -8437643280, 40410065520, 56540477664, -61138689216]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 12 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 13563530970], ![0, 0, 0, 0, 0, 0, 0, 173751464832, 101264893422], ![0, 0, 0, 0, 0, 0, 319258707768, 325829377104, 262972395840], ![0, 0, 0, 0, 0, -95857297272, 55180951320, 222165790176, 300456435906], ![0, 0, 0, 0, -319305601560, 66214215936, 261689729136, 239995210752, 29718567516], ![0, 0, 0, -11836357500, -283166604600, -228426769692, 137139126432, 426570695628, 213417299040], ![0, 0, 72286024272, 93826172352, 109206775392, -24066896304, -128825969712, 148742982432, 884211115392], ![0, -16312624416, -58904159424, -18718320192, -7492383360, -73572057504, -23757999936, 425648336256, 1206112942848]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 12 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -238777440], ![0, 0, 0, 0, 0, 0, 0, -15745584624, -33664826514], ![0, 0, 0, 0, 0, 0, -31882470312, -80380701456, -145662146520], ![0, 0, 0, 0, 0, -385149237528, -47593723848, 153073771488, 112852925130], ![0, 0, 0, 0, 22803594000, -177170506392, -72773069160, 197776870632, 419614875900], ![0, 0, 0, -79483236360, 232927926000, 179232638904, -148877631936, -399463321752, -256380020160], ![0, 0, 253450944120, 231441107040, 219804961200, 468285730968, 724744631160, 403661763120, -808702678080], ![0, 82558961760, 54622628544, 150563041728, 104144158272, -205699364640, -344102552640, 414857672064, 2154936862848], ![-12993353472, -14812545792, 27607531776, 97469044992, 125654217216, 69444131328, 11327213568, 160719922176, 647580375552]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 12 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -3506378568, 2505385212], ![0, 0, 0, 0, 0, 0, 164845870728, 74405147256, 6720022914], ![0, 0, 0, 0, 0, 491843654808, -46074600, -176323990656, -181040593470], ![0, 0, 0, 0, 591659582910, -487558016418, -274353266682, 491240654454, 821398270836], ![0, 0, 0, 106115917380, -33305811000, -392728479132, -451046433024, 165116641932, 1295319909840], ![0, 0, -139773145248, -59079280128, 110682720192, 168508664544, 38232778848, -153198141888, -116071779648], ![0, -137870628720, -110683973664, -54963345888, -101906758272, 117349493712, 1106177619360, 2273436407616, 1063046468352], ![15604814016, 104015570208, 125451793632, 6156873888, -262411384224, -891007744704, -2141581001472, -3397096864128, -2302439158272], ![-3306521856, 48468699840, 172071871488, 267995099328, 122596045440, -505475030016, -1654242670080, -2828684888832, -3035931604992]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 12 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 16890938064, -2265907248, -9865175100], ![0, 0, 0, 0, 0, 194527535928, -4302605736, -101461947840, -89047461294], ![0, 0, 0, 0, 276112921260, -164503007460, -206551743156, 15885562572, 260858229984], ![0, 0, 0, 75966524700, -54538763400, -117093185220, -12955940448, 160678472724, 215419089600], ![0, 0, -238289486160, -146545945920, -98805564000, -127175577936, -189361496016, -4092638880, 826890905280], ![0, -210191811456, 52850523264, 165878744064, 115684160064, 227772707712, 688146902784, 1044513321984, 161742201984], ![-22714032000, 109416595200, 180177321984, -4674540288, -277349821056, -474212259840, -1003960320000, -2675101879296, -5451808167168], ![8541037824, 45562034496, 7024140288, -179371017408, -326457943680, -173742683136, -30820145664, -1155162531072, -4698832140288], ![3187058688, -127442101248, -466544212992, -188169062400, 2210483404800, 6125773344768, 6053640671232, -3786851008512, -10710080409600]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 12 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 36966128496, 35028659424, -35155884192, -65846620752], ![0, 0, 0, 0, 175071162090, 32066245002, -151152044670, -230008736430, -106715811972], ![0, 0, 0, 128235960600, -65760385680, -201674365992, -22741825920, 403356356040, 730876882560], ![0, 0, -30574109808, 84775280832, -135700427808, 91798110096, 868904450832, 1367972133792, 420468039552], ![0, -10212283488, 109960944192, -147967562688, -311266790208, 50289618720, 421781735232, -591154405248, -4011852713088], ![-40271411136, -70090818336, -22172983008, 118888327008, 383534592672, 845318848704, 1408403952384, 1476010580352, 79564075008], ![19768176384, 96912513984, -10742510592, -512478643776, -983372269440, -573592267776, 487565320704, -730517475072, -8793109518336], ![8048544768, -59589573120, -316522483200, -350317777920, 836831170560, 3231565252608, 3748737484800, -1770661601280, -7565586462720], ![0, -137793858048, -590545105920, -656161228800, 1837251440640, 8267631482880, 14330561236992, 10236115169280, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 12 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 836376192], ![0, 0, 0, 0, 0, 0, 0, 13084289136, -1460365452], ![0, 0, 0, 0, 0, 0, 93481584, -84691920, 324014172], ![0, 0, 0, 0, 0, 9263470896, 8836079232, 1490056224, -2841513048], ![0, 0, 0, 0, -8090997048, 3233513016, 5808732600, 5282980632, 5035414824]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 12 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1725091056], ![0, 0, 0, 0, 0, 0, 0, -24237720720, -4194847368], ![0, 0, 0, 0, 0, 0, -11315162208, -14899697904, -14756975508], ![0, 0, 0, 0, 0, 18565957152, 5792976288, 10138459968, -2585318760], ![0, 0, 0, 0, -2694538296, 7205430024, 972558600, 20810421576, 35404820928], ![0, 0, 0, 5979912216, -4299812256, 285183096, 18825178608, 34329615624, 27143631504]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 12 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2899656144], ![0, 0, 0, 0, 0, 0, 0, -20225811168, 6254215992], ![0, 0, 0, 0, 0, 0, -4260960144, 1389335328, 24146041968], ![0, 0, 0, 0, 0, -40902103296, 24310577328, -3701296032, -13915004796], ![0, 0, 0, 0, -10886334552, -11114730360, 10312481064, -12454348248, -44440489440], ![0, 0, 0, -5603994816, -7469096352, -15271789632, -12127622400, 1153918656, 7856961840], ![0, 0, 5164094592, 4546485216, 2793967200, -12536159616, -17363295936, 16065244512, 57630455712]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 12 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 2513072772], ![0, 0, 0, 0, 0, 0, 0, 54018576576, -3634155684], ![0, 0, 0, 0, 0, 0, -79008167280, -22670529888, -20751535344], ![0, 0, 0, 0, 0, 9495799344, -51492008880, -20542250880, -3223180764], ![0, 0, 0, 0, 73801184976, -2001813984, -18854087712, -26612252352, -12907772424], ![0, 0, 0, 14847052248, 85646888640, 1996008120, -12222066960, 45138251592, 34588729152], ![0, 0, -5532840576, -19558205664, 7454626656, 38910629376, -50991246144, -170253749088, -29818797696], ![0, -7981744896, 4271625216, -9823742784, 4428038016, -4418340480, -97443316224, -161033283648, 10533341952]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 12 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 421158240], ![0, 0, 0, 0, 0, 0, 0, 17752350240, -5057613972], ![0, 0, 0, 0, 0, 0, 18818942352, 47537466144, 18734921952], ![0, 0, 0, 0, 0, 21906014832, -18078125616, 63295103232, 78282683028], ![0, 0, 0, 0, 31529513664, 14333155920, -29232482832, -8323140528, 31499369640], ![0, 0, 0, 28710580944, -56101414848, -10034292912, -21320666208, -67566955536, -20189563488], ![0, 0, -21052640448, -2463142224, -46687480944, -114806794176, -20895405408, 161753775984, 118843502688], ![0, 11960027136, 21963456000, -14337340224, 34756694784, 72811511424, -54009268992, -170765748288, 125143853184], ![-6315013632, 383373312, -1926340608, -9362953728, 2230769664, 30297862656, 38780775936, 16175416320, 49261814784]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 12 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -4911082416, 198914472], ![0, 0, 0, 0, 0, 0, 8207965584, -4127691024, -9910454652], ![0, 0, 0, 0, 0, 6556616784, -54498189168, -16291799424, 35963277156], ![0, 0, 0, 0, 20411233308, -34407714276, -125390660724, 103817483820, 384616975896], ![0, 0, 0, -54391331112, 49728687456, 112458137016, -10727948304, -106137162936, 31145825232], ![0, 0, 28788332544, 6587873088, -32682634368, -38093399424, -40667147136, -53031897792, -65479278816], ![0, -18167421312, -20265804288, -3162517344, 25387565760, -191690168256, -455595199488, 18444059424, 1416781304064], ![17008278144, 18876633216, 15416942208, 11333365056, 48492788544, 283697698752, 537495000768, 59384191104, -1458722248704], ![4585987584, 18320189184, 19589488128, 22406749056, 88564101120, 284257130112, 526181886720, 516030423552, 159384056832]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 12 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 6808991616, -1852621056, -2008925640], ![0, 0, 0, 0, 0, -1377881712, 638760720, -17947867008, -14727807036], ![0, 0, 0, 0, -17550370728, 11768447160, -12137810856, 30996702360, 85066998912], ![0, 0, 0, -18735078936, 25313265024, 1107710088, -11046290544, 30882512376, 59068891872], ![0, 0, 36137471616, 4676746848, -5647957152, 35959600512, 10409735232, -230652516384, -489060076320], ![0, 5388509952, -40835658240, -30892202496, -13411965312, -63737789184, -62894082816, 147763689984, 486788545152], ![2711951616, 10045507584, 5756067840, 48756920832, 64655647488, 152836655616, 427362637824, 532210258944, -163172233728], ![6513470976, 1322873088, 9031500288, 39476386944, 8053724160, -76329387648, -11143367424, 253282401792, 74858370048], ![-12951005184, -29958266880, 39722213376, -82754611200, -660190003200, -724141264896, 1200242147328, 3058610429952, -3460179824640]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 12 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -22515966432, 30688366176, -8861718528, -33569117424], ![0, 0, 0, 0, -50330001996, 19113050484, 31599615684, -333541404, -30832016184], ![0, 0, 0, -30821067504, 45615908736, 9138011472, -58469971680, -52856095824, 16661800512], ![0, 0, 17201948544, -1075894368, 2876692704, -126975131136, -111977372736, 96980820768, 153247402368], ![0, 9510895872, -41500316160, 45691008576, 20801039616, -41760275328, 130641728256, 405591015744, 276900559488], ![-22771331712, -14251692672, -8200430208, -6301346112, -46508970816, -149559468480, -144104133312, 250837243776, 869740591104], ![14112517632, -1602643200, 7209911808, 91318601088, 40936826880, -258036939648, -374374215936, 221975050752, 705624708096], ![-5459438592, -21162479616, 18573373440, -38694528000, -407067678720, -589004236800, 360883740672, 1430149754880, -2444266395648], ![-14316244992, -42948734976, 0, -89476531200, -751602862080, -1402992009216, 0, 3307052593152, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 12 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -987130400], ![0, 0, 0, 0, 0, 0, 0, 7974803872, 194106312], ![0, 0, 0, 0, 0, 0, -1575313376, -1173368032, -518564008], ![0, 0, 0, 0, 0, -4995605984, -521660480, -1964992320, -3195356784], ![0, 0, 0, 0, 1996668880, -2639333904, -3502060048, -3615550416, -3536906192]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 12 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 185052000], ![0, 0, 0, 0, 0, 0, 0, -5805059808, 1464276912], ![0, 0, 0, 0, 0, 0, 11862007360, 7682087392, 5953580504], ![0, 0, 0, 0, 0, 54199616, -16288808128, -2492465408, 15568174576], ![0, 0, 0, 0, -8761101360, 8915619024, -16605540464, -19502308848, -8456746912], ![0, 0, 0, -1117583920, 5984618080, -3836794160, -15741321792, -19215968912, -4631792640]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 12 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 832881280], ![0, 0, 0, 0, 0, 0, 0, -12123733312, 2683193008], ![0, 0, 0, 0, 0, 0, 23218053152, -10018632512, -20819972096], ![0, 0, 0, 0, 0, -8819014144, 23977693408, -2442343872, -26802771704], ![0, 0, 0, 0, 20905674960, -11718465520, 16028182352, 26985110864, 7755642624], ![0, 0, 0, 17660800, 4500871040, 6783225728, 1428395392, 1166213504, 8822518400], ![0, 0, 2040523072, -263390848, 4442102272, 13223165760, -4300016064, -20491616000, 23972362880]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 12 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2124270680], ![0, 0, 0, 0, 0, 0, 0, 16383929088, -9879973192], ![0, 0, 0, 0, 0, 0, 815389792, 22377832768, 19466183744], ![0, 0, 0, 0, 0, 26018182560, -9528463904, 10405898880, 28902845192], ![0, 0, 0, 0, -40866266720, -21526672256, 5713767104, 2906894848, -16671464336], ![0, 0, 0, -10879801520, -23675491360, -7510982832, -27589784768, 44548614640, 86191515520], ![0, 0, -5835668544, 5427189376, -36106891264, 3502274752, 70397198016, -27898412800, -227210546560], ![0, 3680696960, -1413314304, 4728430592, -8276723712, 33174642816, 47323436800, -63391527680, -124583719680]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 12 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 433276160], ![0, 0, 0, 0, 0, 0, 0, 14939339840, 1167274360], ![0, 0, 0, 0, 0, 0, -45672447520, 5399828672, 12817028704], ![0, 0, 0, 0, 0, 45265834016, -61340176544, -24727153536, 28085573160], ![0, 0, 0, 0, -31049775680, 22053864352, -8901894816, -26397079136, 12382899120], ![0, 0, 0, -24635108000, 6216956480, 25546829920, 60021936768, -1249639904, -48231575040], ![0, 0, -18741944160, -36206040640, 25432487680, -7559878624, -82782586336, -21181052800, 89163656320], ![0, -5588123776, -12442393344, 7804448768, -28524177920, 27454663808, 41963910400, -163144477440, -283709632640], ![-1918659072, -3617931264, -3961628672, -3309131776, -14766739456, -24649344000, -23871104000, -43526497280, -133839193600]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 12 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -2137255328, 320400432], ![0, 0, 0, 0, 0, 0, -9657652704, -1913828896, 4253735432], ![0, 0, 0, 0, 0, -3621679648, 6035420896, 20521897984, 12617772296], ![0, 0, 0, 0, -72292683400, 148051707128, -56156061928, -153675541544, -54837466736], ![0, 0, 0, 47175192400, -55483622560, -1388781744, 19652444608, -114129367824, -147785088640], ![0, 0, -4074707584, 1184983296, 9789124096, 25159163264, 33559944832, 5297986560, 11007537920], ![0, 12417287616, 14693143424, -30252740608, -2849968640, 186550665664, -30439331200, -645278515840, -314181799680], ![10689207936, 209124352, 4338649344, 45117823232, 13741079296, -127321347200, 102221776000, 854774112640, 816619543040], ![5090261504, 172657152, 4667265024, 21822819840, 5734476800, -49811270400, 26832332800, 353844010240, 472109460480]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 12 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 39293632, -2251239488, -938604848], ![0, 0, 0, 0, 0, -17230124192, 17516597216, 9810178304, -6757812408], ![0, 0, 0, 0, -12657081680, 29322181232, -23761335248, -44011906256, -8907736448], ![0, 0, 0, 6503241520, -9300329440, 9842017584, -20610034752, -32052015216, 28180836480], ![0, 0, 1481089600, 24475767680, 8270906880, -27750503872, 109226924864, 232063811840, -93945033600], ![0, 9864384768, 13579711488, -17589870592, -11302487552, -13754544128, -103189286400, -185285478400, -134670067840], ![5548667648, -8813605888, -1086328832, 6871894016, 24027462656, -72573977600, -24962713600, 487072517120, 828306277120], ![1741409792, 6179886592, 5098459136, 5912957440, 51446092800, 59521350400, 12602419200, 175946167040, 793928862720], ![-6657392640, 3016433664, -71463936000, 0, 92875161600, -643646976000, -1741086412800, -463425822720, 3145618022400]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 12 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -14139618880, 19447627008, -846273920, -17351263104], ![0, 0, 0, 0, 23978704680, -16343738200, -566918392, 8808495176, 2723911856], ![0, 0, 0, 9689449440, -29861327040, 20096951264, 17430532480, 31478688, 22235413120], ![0, 0, -13449852224, -12240443264, 47701118976, 29467495360, -72915125824, 1798042880, 156985214080], ![0, -8793917056, 25878328064, -23511996416, 23880815104, -44933185152, -72395936000, 188316138240, 300414352000], ![-10272097408, -7097497600, -14847301888, -35812448512, -11619713792, 10782518400, -169833884800, -486853718400, -329895802880], ![2779972096, 12781814272, 16535867392, -616532480, 103856716800, 215601516800, 118792038400, 156940663040, 1277611453440], ![-4702773248, 4590227456, -38184914944, 0, 83174195200, -300957440000, -953216051200, -216689356800, 2222060359680], ![-6362775552, -4772081664, -79534694400, -79534694400, 0, -695928576000, -2505342873600, -3006411448320, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 12 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 674341760], ![0, 0, 0, 0, 0, 0, 0, -6644648256, -821856176], ![0, 0, 0, 0, 0, 0, 2439548608, 1632826816, 634149104], ![0, 0, 0, 0, 0, 2851039168, 463612672, 1921938048, 2674994336], ![0, 0, 0, 0, 392711200, 3059682016, 4800874720, 3729312864, 3396612640]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 12 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -171600960], ![0, 0, 0, 0, 0, 0, 0, 6858504384, 1263435744], ![0, 0, 0, 0, 0, 0, -13470418304, -9091573440, -6526730576], ![0, 0, 0, 0, 0, 6405760128, 13699626624, 320968448, -14706726560], ![0, 0, 0, 0, 7001568800, 626853664, 6671666208, 31512892704, 28409376384], ![0, 0, 0, -1953800480, -10226365440, 4727332192, 21364771136, 11358302624, -10507227200]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 12 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -516299200], ![0, 0, 0, 0, 0, 0, 0, 7028771456, -4023415584], ![0, 0, 0, 0, 0, 0, -13107943744, 9946805888, 16807981120], ![0, 0, 0, 0, 0, 4133657088, -19901673280, 695873408, 20153922832], ![0, 0, 0, 0, -21290393440, 3656905760, -19857243488, -23671361888, -9320251264], ![0, 0, 0, 5575279360, -3159267200, 1612209920, -369790976, -3018619136, -5839072960], ![0, 0, -4760445696, 2028768384, -11773712256, 632497408, 22709391872, -25391418240, -78239908480]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 12 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1434047120], ![0, 0, 0, 0, 0, 0, 0, -9622471424, 10237905776], ![0, 0, 0, 0, 0, 0, 2880490816, -16747112832, -17851085120], ![0, 0, 0, 0, 0, -21041025088, 9568864320, -3322996736, -17141030256], ![0, 0, 0, 0, 51523192640, 27353047424, 13384471936, -1383394048, 12366830048], ![0, 0, 0, -949882400, -14821321600, 62146939488, -92519312064, -75565796704, 109010325760], ![0, 0, 6737706752, -1356288128, 48395088512, -65622145280, 19209305600, 147084187520, -8250766080], ![0, 3450843648, 3632762880, 6599955712, -3980883456, -29413385216, 88528343040, 80570123520, -213370816000]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 12 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -314910080], ![0, 0, 0, 0, 0, 0, 0, -11588947840, -1352901840], ![0, 0, 0, 0, 0, 0, 30573682496, -4586121600, -7654356736], ![0, 0, 0, 0, 0, -30804374848, 44706445376, 16165060096, -22565183408], ![0, 0, 0, 0, 24901450240, -20314848960, 26414509504, 892689728, -35832451552], ![0, 0, 0, 40898643520, 23913735680, -84536403904, 18486791552, 9228392640, -144273555840], ![0, 0, 22257938560, 41595914560, -29382617920, 75626887808, 1440700672, 26087437120, 228405425280], ![0, -11484075008, -3866870784, -11003892480, -25529652736, -66822167552, 144919398400, 85669090560, -473187923200], ![-217912320, -3991023616, -4608774144, -5477064704, -1561952256, -10564382720, -15639531520, 5474867200, 35805824000]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 12 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 1741414464, -110188256], ![0, 0, 0, 0, 0, 0, 9053197888, 2600004544, -2901669360], ![0, 0, 0, 0, 0, 3438053440, -5315635392, -17348143616, -11464837232], ![0, 0, 0, 0, 52987252080, -102009833616, 51660455984, 101607422128, 21033040864], ![0, 0, 0, -56981393440, 54714959360, -75070340512, 128516422464, 100703031968, -167840575040], ![0, 0, -11893480448, 2648849152, 6565384192, -23569303040, 26977047552, 39092867840, -91970456960], ![0, 12809946368, -2480275456, 92529335680, -101358599424, -31742674432, 574982246400, 80607287680, -1618700377600], ![3932344064, 9663332096, 7188540160, -69135171584, 78285617664, 11483123200, -649176046080, -512822816000, 1355314278400], ![2138584064, 6162942464, -1682887680, -31568442368, -4599828480, -48542899200, -360836044800, -577078976000, -120745497600]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 12 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 224715008, 1923561728, 883423328], ![0, 0, 0, 0, 0, 12933053248, -12987176640, -7650272768, 4294490384], ![0, 0, 0, 0, 10732003680, -20573788448, 26327881568, 30339351136, 1721416704], ![0, 0, 0, 293809440, -8902087040, 10700835488, 22296643776, -7334046112, -61805137280], ![0, 0, -10848300800, -41980292480, 46035054720, -35343394560, -213700408832, 192062270080, 611042545280], ![0, -68351488, 11615224832, 48177283072, 6581420032, 60783708160, 85635901440, 18011043840, 30129120000], ![2167680512, 5378371584, -11270717440, -61194895360, 1092286464, 11819601920, -473659310080, -604179302400, 546833600000], ![10585088, 4195329536, 13854217216, 1571681280, -2160414720, 65331584000, 4448819200, -198952256000, -56710886400], ![2749231104, -34684108800, 35604824064, -161831239680, 26301235200, 665739264000, -364095897600, -2317129113600, 2621348352000]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 12 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 11154475136, -14616040320, 201656832, 12454409152], ![0, 0, 0, 0, -14948613680, 6241890000, 2992045328, -9835594352, -4534109536], ![0, 0, 0, 1636733760, 18318071040, -7878799808, -18290301056, -26121136192, -51739581440], ![0, 0, 11283391232, 11309401472, -83254209408, 97153803008, -17126468096, -29361818240, 326878603520], ![0, 7289442816, -19627971584, 13320404736, 17477674496, 59341935616, -277257390080, -195292586240, 614582176000], ![-2907633408, -13529133824, -9915880192, 13659373568, -54945995264, 19437519360, 279371676160, 133344697600, -579504896000], ![-936627200, 10667704832, 24925420544, 31915531264, -20364349440, 103038899200, 223305779200, -72492992000, -534564172800], ![888014848, -20987346944, 29367353344, -75669299200, 36146462720, 470277324800, -11254579200, -1083446784000, 1851716966400], ![3181387776, -31813877760, 0, -174976327680, -159069388800, 477208166400, 0, -2505342873600, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 12 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -227288448], ![0, 0, 0, 0, 0, 0, 0, -3701411712, 3844950048], ![0, 0, 0, 0, 0, 0, -5745307008, -3357671808, -1265725344], ![0, 0, 0, 0, 0, 884797056, -3095848704, -1003096320, 1891722816], ![0, 0, 0, 0, -2515951296, -6520546368, -5044978752, -4992503616, -6142045248]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 12 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -788757120], ![0, 0, 0, 0, 0, 0, 0, 1718614656, -8183050560], ![0, 0, 0, 0, 0, 0, 26488180992, 22614688128, 16741453152], ![0, 0, 0, 0, 0, -38907470592, -11720780544, -654692352, 13121758656], ![0, 0, 0, 0, -363010752, 4347756864, -33306479040, -47131254720, -25334810496], ![0, 0, 0, 2908451904, 29534103168, -18070965696, -18558217728, 7675220160, 2447979264]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 12 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1161015552], ![0, 0, 0, 0, 0, 0, 0, 19578984192, 5747670720], ![0, 0, 0, 0, 0, 0, -14279212416, -11131633920, -18773287680], ![0, 0, 0, 0, 0, 34632336384, -579659904, 10622354688, 10363901472], ![0, 0, 0, 0, 15802724160, 21405695040, 4823720256, 21131106624, 51278635008], ![0, 0, 0, -18405238272, -832091136, -12266045952, -14647527936, -303653376, 11549221632], ![0, 0, 686451456, -17780428800, 23686036992, -78430991616, 39897889536, 64707832320, -170618572800]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 12 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -804200544], ![0, 0, 0, 0, 0, 0, 0, -40563818496, -11310668064], ![0, 0, 0, 0, 0, 0, 25307291520, 11230242048, 24719777280], ![0, 0, 0, 0, 0, -9446656896, 3567160704, -21880441344, -30952389600], ![0, 0, 0, 0, -96348500352, -43929234432, 6214131456, 12852486144, -29289259584], ![0, 0, 0, 60229620288, -3830467968, 65803996224, 17176227840, 69810787008, 170163353088], ![0, 0, 16698878208, 1515251712, 33937562112, 9687843072, -60604290816, 62615127552, 330677609472], ![0, 242320896, 11430097920, -20925471744, 114458241024, -209380041216, -20343026688, 325629186048, -286393300992]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 12 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -248467968], ![0, 0, 0, 0, 0, 0, 0, -7068024576, 4992855264], ![0, 0, 0, 0, 0, 0, 4223662464, -22354135296, -17231648640], ![0, 0, 0, 0, 0, -15621049728, 18800150400, -19291249152, -28656765792], ![0, 0, 0, 0, 3845221632, -35072514432, 40237597056, 21415575168, -64827630144], ![0, 0, 0, -96606450816, -4758662400, 18602534784, 66833891328, 4128610944, -25632181248], ![0, 0, 56854410624, 34015506432, 29265745152, 207853653888, -210074701440, -288442869504, 323026569216], ![0, -4577352192, -16366371840, -45280435200, 210915081216, -411075463680, 94660242432, 861915598848, -450598597632], ![0, -363515904, -9509916672, -13767806976, 8440799232, 34203795456, 61421690880, 126115209216, 271603372032]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 12 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 1939883904, -671635008], ![0, 0, 0, 0, 0, 0, -13496219520, -3329480832, 4169439264], ![0, 0, 0, 0, 0, -10130426496, 31862068608, 18097981440, -9856560096], ![0, 0, 0, 0, -16832671776, -31055461920, 67404785760, -7595153568, -147955038912], ![0, 0, 0, 60035073600, 49055403648, -115922406336, 75399544320, 139478195904, -81482430720], ![0, 0, 35986023936, -42346149888, -13489069056, -80890974720, -82047939072, -31439078400, -40953388032], ![0, -5377727232, 65000074752, -151925875200, 597269071872, -998639472384, 351817345536, 2257818089472, -1604225488896], ![0, 17544771072, -15132335616, 66414061056, -502016644608, 595827351552, -119743239168, -2856336786432, -572115750912], ![0, 9278641152, 5519794176, -19375967232, -218109855744, 11513493504, -77277118464, -1148599203840, -1020874752000]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 12 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, -4817729280, -121458432, 298273344], ![0, 0, 0, 0, 0, -1459271808, -663828096, 11328070656, 10941558048], ![0, 0, 0, 0, 10066389696, -21457198656, 5992320192, -18033890112, -62674868736], ![0, 0, 0, -17138653248, 51431639424, -59372268096, -16670211072, 106334223168, 99791173632], ![0, 0, -24357964032, 36980367360, -288770062848, 496990787328, -654372976896, -823634615808, 1363408533504], ![0, -1222963200, 1383708672, 10011377664, 114897927168, 172768831488, 247881056256, 320409206784, 311484386304], ![0, 9717313536, -9121333248, 43335462912, -483385202688, 340996300800, -61879762944, -2082327699456, -670001006592], ![0, -114398208, 2592497664, 83239701504, -82972243968, -21426370560, -36294967296, -801864714240, -1656557568000], ![0, 26481475584, -199277494272, 195974627328, -635555414016, 1329405198336, 4490030776320, 0, -5392488038400]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 12 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 8743069440, -15635289600, 6678093312, 19841571072], ![0, 0, 0, 0, 10692840096, -3569394528, 2849259552, 2538630432, -7712963136], ![0, 0, 0, -15454122624, -6310243584, -23963762304, 35686437888, 108925419648, 103205544960], ![0, 0, 1504726272, 30431889408, 1831174656, 105913730304, -343080530688, -460892742144, 76794983424], ![0, 6973788672, 4710085632, -700695552, -331966393344, 679601576448, -106750884864, -1204490170368, 1137154212864], ![0, -11372336640, -16019882496, -10791986688, 170950362624, -198981107712, 232587334656, 1371257275392, 383840354304], ![0, -5742148608, 24437219328, 155294671872, -36178176000, -229950646272, -342121070592, -990485452800, -2848164249600], ![0, 12382248960, -121796665344, 167949287424, -297173975040, 850550833152, 2729055633408, 0, -3809246330880], ![0, 28632489984, -171794939904, 0, -687179759616, 629914779648, 5153848197120, 5153848197120, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 12 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2146298880], ![0, 0, 0, 0, 0, 0, 0, 61992767232, -21913814208], ![0, 0, 0, 0, 0, 0, 26759335680, 14781254400, 5891920320], ![0, 0, 0, 0, 0, -31229121792, 6736367616, -18204274176, -44780258688], ![0, 0, 0, 0, -10316254080, -2632502400, -29505049728, -35264777856, -32294756736]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 12 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 6366539520], ![0, 0, 0, 0, 0, 0, 0, -49537323264, 49309620096], ![0, 0, 0, 0, 0, 0, -123058349568, -120511792896, -94239883584], ![0, 0, 0, 0, 0, 277179843072, 34631883264, 16611099648, -10973060736], ![0, 0, 0, 0, -164738935680, -124480599936, 124347805824, 124248355968, -79421270016], ![0, 0, 0, 109379614080, -96637601280, 94756987776, -68745000192, -202968974208, -1856490240]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 12 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -5142339840], ![0, 0, 0, 0, 0, 0, 0, -173263732224, -17386495104], ![0, 0, 0, 0, 0, 0, 188224270080, 39783744000, 54583499520], ![0, 0, 0, 0, 0, -319219236864, 70628752128, -104101071360, -193772449728], ![0, 0, 0, 0, 182480538240, -13469960064, 212564812416, 113886360192, -197400006144], ![0, 0, 0, -18199526400, -65080435200, 14346697728, 42940575744, 29612706816, 11412698880], ![0, 0, 0, -10896652800, 72516533760, -343472431104, 240396524544, 563702312448, -465725517312]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 12 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2358375360], ![0, 0, 0, 0, 0, 0, 0, 331799829504, 21452359104], ![0, 0, 0, 0, 0, 0, -228002455296, -23270979072, -109939661568], ![0, 0, 0, 0, 0, 298517134080, 33013406976, 271191816192, 401881178688], ![0, 0, 0, 0, 77475974400, -221003109888, -522636685824, -507166116864, -204779524224], ![0, 0, 0, -189487140480, 492182845440, -355560577152, 507205712640, 743836131456, -1049260354560], ![0, 0, 0, 171580992000, -637549355520, 1134991841280, 17912497152, -2194030603776, -550285418496], ![0, 0, 0, 8885099520, 165126297600, -587088082944, 436988141568, 1380190006272, -1739010392064]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 12 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 3440279040], ![0, 0, 0, 0, 0, 0, 0, 112331923968, -26884959552], ![0, 0, 0, 0, 0, 0, -181777972992, 194323481088, 175981521408], ![0, 0, 0, 0, 0, 247148867328, -413838686976, -4014219264, 264357935424], ![0, 0, 0, 0, -299065113600, 269189276928, -448571371776, -172646259456, 800989267584], ![0, 0, 0, -125975182080, -418573562880, 348687863040, 129807929856, 310790489856, 1619216755200], ![0, 0, 0, 204639072000, -83184034560, 82678480896, -449823846912, 54773748480, 1534859927040], ![0, 0, 0, -167836247040, 539131084800, -1072838215680, 1099101696000, 3547591584768, -3051299733504], ![0, 0, 0, -13328916480, -114368348160, 80860471296, 524657565696, 733116628992, 415519678464]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 12 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -22914515712, 5223554688], ![0, 0, 0, 0, 0, 0, 39095933184, 4692078336, -16603764672], ![0, 0, 0, 0, 0, 25394257152, -198983102208, -22000416768, 154004592192], ![0, 0, 0, 0, -121301505600, 763320474048, -825720624960, -671290965312, 703809346944], ![0, 0, 0, 492381352320, -469390394880, 1039154345856, -1323923563776, -2572053340032, 702205067520], ![0, 0, 0, 185818997760, -362260715520, -42347526144, -319039531008, -779415960576, 351309894144], ![0, 0, 0, -197183331840, 2177584696320, -5434804024320, 456893521920, 13637554985472, 1966713053184], ![0, 0, 0, 643308272640, -3172313379840, 3426015470592, 4821334864896, -11036617506816, -15448203116544], ![0, 0, 0, 340216842240, -1259671142400, -232506058752, 2291122606080, -469474013184, -4714059423744]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 12 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 32789729280, -8840595456, -6005653632], ![0, 0, 0, 0, 0, -66498592512, 75061164288, -32268859392, -90840564672], ![0, 0, 0, 0, -206915533440, 206081960832, -229644438144, -104854468224, 376379283456], ![0, 0, 0, 181834435200, -305085834240, 320229723264, -167122957056, -563741633664, 167164208640], ![0, 0, 0, 121269603840, -1113545495040, 2788246179840, -2147378500608, -5177377835520, 3677474465280], ![0, 0, 0, -44841984000, 249577912320, -254504718336, 490818121728, 2580074078208, 2672188366848], ![0, 0, 0, 356301496320, -1770581176320, 1991304437760, 1240101519360, -8936559869952, -6932525715456], ![0, 0, 0, -4194600960, 64307527680, 857343387648, -301397741568, -5434385240064, -9119604105216], ![0, 0, 0, 970987438080, -7051876761600, 2553890144256, 33888105529344, 24468883439616, -59317368422400]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 12 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -123586788864, 187099799040, -46454943744, -202996544256], ![0, 0, 0, 0, 54797202240, 31088295744, -10198254528, 22040276544, 59889498240], ![0, 0, 0, -44180125440, -114148700160, 233563249920, -71402681856, -299836931328, 175301913600], ![0, 0, 0, -35777195520, 224361223680, -117850884096, -87723322368, 599134001664, -707911581696], ![0, 0, 0, 255705584640, -1192176353280, 1609528301568, -936736813056, -3904823172096, 6953642471424], ![0, 0, 0, -416985676800, 1582737699840, -1108245169152, -2340122391552, 4157947183104, 7209419390976], ![0, 0, 0, -210545448960, 1290197483520, 1107458930688, -4277469622272, -11051487473664, -11064232599552], ![0, 0, 0, 454015795200, -3821994147840, 2453352185856, 20042786734080, 11441198039040, -41901709639680], ![0, 0, 0, 1049857966080, -6299147796480, -4199431864320, 30235909423104, 56692330168320, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 12 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 6 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7]] +lemma sums_checked : ∀ u : Fin 6, ∀ a i k, fourSumInteger a 12 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k +end SumTable12 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable13.lean b/lean/OAI/Analysis/LaughlinGap/SumTable13.lean new file mode 100644 index 0000000000000000000000000000000000000000..5179df64c037156dcba7b3c55c5e70af58c8a2f0 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable13.lean @@ -0,0 +1,361 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CheckedTables +import OAI.Analysis.LaughlinGap.IntegerFourRows + +namespace OAI + +/-! Sum Table13. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable13 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 16547692590], ![0, 0, 0, 0, 0, 0, 0, -61288818888, -34085188830], ![0, 0, 0, 0, 0, 0, 187081615248, 108509594160, 51005591604], ![0, 0, 0, 0, 0, -182377843164, -78213460380, 13833827700, 66980246652]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 13 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -19189955268], ![0, 0, 0, 0, 0, 0, 0, -962149848, -69450390438], ![0, 0, 0, 0, 0, 0, 388843143216, 153937090560, -34003536732], ![0, 0, 0, 0, 0, -420888770676, 77027906076, 171936942012, 2031994008], ![0, 0, 0, 0, 151808582640, 25993709940, -90459100776, -96117357204, 30484175040]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 13 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 116966519604], ![0, 0, 0, 0, 0, 0, 0, 510816957552, 305412510744], ![0, 0, 0, 0, 0, 0, -468032434584, -202858786416, 131435029638], ![0, 0, 0, 0, 0, 385988101884, -94664558868, -95106959508, 201056603616], ![0, 0, 0, 0, -51272807520, -28184505888, -44480750688, -62714269728, -19680750144], ![0, 0, 0, 106774537056, 89192506656, 93439325232, 58804754448, -24322032768, -50363622144]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 13 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -306746607222], ![0, 0, 0, 0, 0, 0, 0, -717479629680, -718144714056], ![0, 0, 0, 0, 0, 0, 147538395048, -185092572192, -532193938386], ![0, 0, 0, 0, 0, 679991431680, -346492684560, -936365732544, -1047271056084], ![0, 0, 0, 0, -300582255600, 538061505300, 507500904504, -272833203060, -1062494877312], ![0, 0, 0, -113923526112, -296802778272, -368095659888, -47740347600, 312792830592, 19375602048], ![0, 0, 106431405696, 185880070464, 68189755392, 90146887776, 372364937472, 511792275456, -157194107136]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 13 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 30915391914], ![0, 0, 0, 0, 0, 0, 0, 92097284400, 179261931024], ![0, 0, 0, 0, 0, 0, 995234404296, 292883643360, -152231565882], ![0, 0, 0, 0, 0, 14232966264, 432424042248, 222382800024, -357956667684], ![0, 0, 0, 0, -52224485280, -722986641960, -411606969840, 622637874408, 1692826962816], ![0, 0, 0, -860087154960, -517730687760, -392479057608, -975519760248, -1751404024128, -1556190113280], ![0, 0, -351898043904, -340284043968, -605975950272, -417949763616, 451488280320, 1014216124416, -462946796928], ![0, 132359555328, 128718585600, -15487862016, -215975147520, -303382852608, -222568338432, -239295851520, -949662168576]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 13 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 5483219148], ![0, 0, 0, 0, 0, 0, 0, -343094342712, -182161093290], ![0, 0, 0, 0, 0, 0, -1228721517144, -209443124352, 257636806878], ![0, 0, 0, 0, 0, -1896716331774, 735046533210, 737387171466, -536130150732], ![0, 0, 0, 0, -427549185360, 99922923540, 955859529240, 1073420095308, -299448329664], ![0, 0, 0, 445366139328, 94327915968, -308267216928, -289156368864, 326592744192, 1288431331968], ![0, 0, 666271197504, 488899786848, 383236953792, 604012399056, 300873978240, -1614182270976, -4280269162752], ![0, -174739423584, -593056260192, -726275042592, -512874889824, -40508079744, 1041025451136, 3259012234368, 5749690096128], ![91080591360, 115555602624, -138918603648, -673623610176, -1206141150720, -1275907733760, -516688313856, 849565085952, 1464845251584]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 13 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -32694739440, 475367772], ![0, 0, 0, 0, 0, 0, -481357131288, -68904893376, 159528652206], ![0, 0, 0, 0, 0, -903206556252, 198915638196, 460666544052, 136147467456], ![0, 0, 0, 0, -390122750160, 111583676556, 372984140232, 218893093716, -194091279360], ![0, 0, 0, 567151215840, 394351716000, 375793371888, 540488131920, 756468332928, 490736125440], ![0, 0, 900128642688, 90258736128, -106933307712, 62655120000, -334869579264, -1912572321792, -3986186447232], ![0, 203751508224, -448699384320, -748146778368, -395888254080, -24773692416, -177210249216, -22009912320, 2625451521792], ![54146644992, -40267803840, -251537582208, -211660726464, 216295749120, 511256815872, 77096701440, -248482046208, 2869956350976], ![-51736430592, -117137433600, 516580568064, 2092510126080, 2324421918720, -2381201805312, -10276053258240, -8204843851776, 19278144737280]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 13 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, -97505599488, -83163583008, 40984182096], ![0, 0, 0, 0, 0, -589020532650, -162953768802, 310357508142, 580547017116], ![0, 0, 0, 0, -743327412960, 91318689528, 654602983056, 473035236168, -355157784960], ![0, 0, 0, -426847309152, -10328078112, 893050218192, 447028808688, -1682478703488, -3999512787072], ![0, 0, -54648101376, -228424739136, 512075872704, 710593991712, -625935999744, -2342209115136, -1185392393856], ![0, 412537343328, 532514394720, 399083022624, 35188195680, -595320435072, -1631812947072, -2927385521280, -3495246391296], ![94646796288, -121823794752, -569818389888, -389329140288, 859660792320, 1986287770368, 1060186372608, -1021972562688, 3386786337792], ![-30749334528, -133471320576, 143168509440, 1188285812736, 1873856962560, -169005754368, -4621259360256, -3836433469440, 13618055632896], ![-52492898304, -137793858048, 472436084736, 2624644915200, 4724360847360, 1653526296576, -9553707491328, -18425007304704, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 13 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -19473461460], ![0, 0, 0, 0, 0, 0, 0, -7114081776, -3930814860], ![0, 0, 0, 0, 0, 0, -13532707392, -18743455584, -10910244792], ![0, 0, 0, 0, 0, 31497700104, 7811412360, 1941091560, 847056456]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 13 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 38943768024], ![0, 0, 0, 0, 0, 0, 0, 31177568496, 29556716916], ![0, 0, 0, 0, 0, 0, -10783885344, -6661975488, -21696891864], ![0, 0, 0, 0, 0, -5186233800, 23273528184, 37593072696, -9906230592], ![0, 0, 0, 0, -35832724080, 7344852600, 6138117312, -18631409112, -28752415920]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 13 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 44805376008], ![0, 0, 0, 0, 0, 0, 0, 58466880288, 21273355872], ![0, 0, 0, 0, 0, 0, 45075095952, -56288816928, -117692916], ![0, 0, 0, 0, 0, 27856549368, -32889938472, -75631791144, -19909469664], ![0, 0, 0, 0, 12456699360, 16972544832, 25997466624, 11386828224, -20331488016], ![0, 0, 0, -24507463968, -25074383328, -17614088640, 11625818688, 13322285280, -54895303008]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 13 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -122101027884], ![0, 0, 0, 0, 0, 0, 0, 98880007584, 5224531872], ![0, 0, 0, 0, 0, 0, 46128271536, 128281997952, 60049168380], ![0, 0, 0, 0, 0, -36329449248, 72798038112, 97110032448, 121064930136], ![0, 0, 0, 0, -22683615120, -141277961160, 22944686016, 26298169704, -123048899136], ![0, 0, 0, 22530156576, 94040681376, 17875692864, -43494147648, 121344597792, 322667006976], ![0, 0, 3715001856, -16861946688, 6573028608, -42891714432, -38062340352, 130576752576, 262916485632]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 13 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -24773348412], ![0, 0, 0, 0, 0, 0, 0, -44111474016, -75292069488], ![0, 0, 0, 0, 0, 0, 29217974448, 16979556864, -152141707572], ![0, 0, 0, 0, 0, -135161292816, -10286143152, 84302661552, 38041091784], ![0, 0, 0, 0, 71024125920, 136289340240, -26450575872, -67334030928, -41332872672], ![0, 0, 0, 183537034800, 58527897840, 180244418592, 321977634336, 150841830960, -162566059680], ![0, 0, 6036977664, 16007660736, 77188825728, -73854186624, -163418314752, 113425573824, 457551726336], ![0, 23012290560, 3074746368, 26810257920, 56422480896, 43221247488, 15677637120, 66798286848, 235780392960]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 13 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 8673714216], ![0, 0, 0, 0, 0, 0, 0, -52003761264, -12604874580], ![0, 0, 0, 0, 0, 0, -122964987408, 98144190336, 91300081116], ![0, 0, 0, 0, 0, -172864016604, 240001045812, 363796888788, -179085882888], ![0, 0, 0, 0, 156677133840, -171766152264, -238686061248, 67900433256, 321781357584], ![0, 0, 0, -131883935424, -368615424, 71087569920, 30488538240, -37061567424, -85834979424], ![0, 0, -45857597184, 4935455904, -63177811968, -89060113728, 387427271040, 888059617056, 40018834944], ![0, -94058692224, -31691863680, -18991366080, -26479393344, -170383285440, -718052531904, -1285272956160, -608042695680], ![45952637952, 7538274048, -10995247104, 23427743616, 41434691328, -102592994688, -503451090432, -952659477504, -926543084544]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 13 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -17222482368, 771692616], ![0, 0, 0, 0, 0, 0, -44440965264, -387765888, 52440809148], ![0, 0, 0, 0, 0, -4405931064, 35242690344, 79565654376, -29069699328], ![0, 0, 0, 0, 76206173520, -51884312568, -16992461760, -4899124008, -81871481376], ![0, 0, 0, -141801474720, -78065318880, -81021598656, -169186472640, -107444942496, 317278706400], ![0, 0, -143368321536, 71108212224, 56295233664, 76819283712, 283493456640, 433556181504, 232851204864], ![0, -52847219712, 35653281792, 41543551488, -59237409024, -87167153664, -271733363712, -878387816448, -1408436370432], ![16828465152, -12460214016, 12499593216, -34720384896, -135820567296, -101491049088, -15077270016, -377721437184, -1442229820416], ![-22000306176, 52740808704, 39722213376, -190013368320, 233559797760, 1782545301504, 2277784018944, -1019536809984, -3460179824640]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 13 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 40066746336, -57180481920, 7484262192], ![0, 0, 0, 0, 0, 117257929164, -34644672516, -52001362404, 6464694888], ![0, 0, 0, 0, 156923344800, -91342909872, -44344860672, 51666202224, 169550784], ![0, 0, 0, 104429321376, -117978738144, -102368885184, 227288177856, 300783630240, 38893118976], ![0, 0, 2909233152, 62597385792, -137405194368, 5400114048, 206903393280, -120589979328, -817076452608], ![0, 96087454848, 50101877376, 50322199488, 90397329984, 251270564544, 540586093248, 632927575296, 99869349888], ![24093176832, -36955200768, 32581810176, -63977219712, -353751268608, -331980455808, 88738601472, -222426215424, -2671970982912], ![-19230120960, 15121231872, 18573373440, -146083120128, 10833223680, 905030737920, 1365540728832, -476716584960, -2444266395648], ![-19088326656, 42948734976, 85897469952, -89476531200, 214743674880, 2104488013824, 4409403457536, 3307052593152, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 13 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -19774676872], ![0, 0, 0, 0, 0, 0, 0, 5557191264, 3910779080], ![0, 0, 0, 0, 0, 0, 5364251072, -256693824, 5998743504], ![0, 0, 0, 0, 0, -8109000304, -4114988912, -2166052400, 469562416]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 13 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 22235363568], ![0, 0, 0, 0, 0, 0, 0, -21194486240, -10060576792], ![0, 0, 0, 0, 0, 0, -18368020288, 20708483328, 2274619920], ![0, 0, 0, 0, 0, 24494737584, -33014527888, 6792312048, 16845047456], ![0, 0, 0, 0, 13109105280, -5988441584, 7867752352, 18154405616, 8335974720]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 13 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 24416107472], ![0, 0, 0, 0, 0, 0, 0, -51481236288, 5643974176], ![0, 0, 0, 0, 0, 0, 60818550432, -39424459456, -2708063592], ![0, 0, 0, 0, 0, -40584678160, 48904595120, 469882032, -24248235392], ![0, 0, 0, 0, -4878547200, -16408514176, -12631028096, 1052335488, 2464345280], ![0, 0, 0, 6874432768, 11509827328, -5559297216, -16249639488, 17997409920, 42410794880]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 13 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -40599961048], ![0, 0, 0, 0, 0, 0, 0, 56949838912, -5411738464], ![0, 0, 0, 0, 0, 0, -102992250080, 5991884416, -17758785096], ![0, 0, 0, 0, 0, -13944644736, 2581212352, -31323046144, -34664826192], ![0, 0, 0, 0, 65446491520, 10932849808, 28074716192, 83704018800, -9163994880], ![0, 0, 0, -3722240256, -35385157376, 47219810496, -40430345408, -132827236480, 63240442240], ![0, 0, -14413552640, -6305214976, -94666752, 16272676992, -67517488640, -93093710080, 80845848320]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 13 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -33573404440], ![0, 0, 0, 0, 0, 0, 0, 73241823680, -24373519232], ![0, 0, 0, 0, 0, 0, -119083411808, 118225388672, 60329094424], ![0, 0, 0, 0, 0, 90692761056, -48214222560, 3447861344, 32864277680], ![0, 0, 0, 0, -53255729920, -201978912, -30873831744, -58893093088, 72536040960], ![0, 0, 0, -37760365440, 21393272960, -112610301408, -36542503712, 76018920000, -77368369280], ![0, 0, 31200538624, 16362266112, 17762214400, 86462286976, -28880025600, -68584874240, 240041964160], ![0, -11255711744, 5334616064, -2128340992, -2819612672, 18657029120, 26476774400, 7003755520, 19089728000]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 13 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 5614170608], ![0, 0, 0, 0, 0, 0, 0, 24606617376, 12321304408], ![0, 0, 0, 0, 0, 0, 33152509984, 17415554048, -34140563592], ![0, 0, 0, 0, 0, 165373483656, -327121341848, 61467423784, 266535099408], ![0, 0, 0, 0, -93331376000, 149414222992, -4102864224, -51050124688, 140459226560], ![0, 0, 0, 66469978624, -14263241216, -25410363008, -35332994176, -28649347840, 25554494720], ![0, 0, -35451487744, -58682615552, 63612945920, -81877549632, -412057296640, 10771013760, 990499198720], ![0, 15024357632, 20374403328, 17957996288, -34648965888, 124732497280, 430517846400, 88552282240, -957387880960], ![16767074304, 15207491072, 35709512704, 31905533440, 33645926400, 144911801600, 344115852800, 353844010240, 96596398080]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 13 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -2314018368, 4328936112], ![0, 0, 0, 0, 0, 0, 50059097376, -27652365056, -21332285768], ![0, 0, 0, 0, 0, 52637590672, -82078311984, 10981225168, 59881661184], ![0, 0, 0, 0, -20463566720, 3804872176, -1254793760, 60068245008, 66702491520], ![0, 0, 0, 50658720000, -1519197440, 46743395904, 68104273088, -182237769600, -352269174400], ![0, 0, 17505051648, -71791849472, -22157240832, -73368877056, -96395763200, 26419046400, 114159980160], ![0, -3422377984, 2476748800, 30246991872, 30184451072, 64446929920, 321052876800, 367243781120, -215662388480], ![2371276800, 16302201344, -3526953984, 22274019840, 25365186560, -45913017600, -6090278400, 175946167040, 45368709120], ![3953221632, -23613136896, -21739560960, 102983516160, -239994470400, -573789696000, 576042700800, 1853703290880, -2097078681600]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 13 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 46999601280, -43783175552, -7799269248], ![0, 0, 0, 0, 0, -25784190760, 16427785080, -14491911752, -18838571088], ![0, 0, 0, 0, -46970732800, 32054739808, -22314116416, 17323723936, 69953573760], ![0, 0, 0, -35489920256, 108155890944, -78378273856, -68817293248, 54990570880, -150292744320], ![0, 0, 10503696384, -28890000896, 28288310784, -66985320064, 83036682240, 190981495040, -114805904000], ![0, -29725706496, -13514750208, 5679667456, 16752847616, -79032718720, -139609430400, 132062742400, 517588664320], ![-664297472, 33642196480, -19859719168, 27513484800, 76299171840, -119715219200, -232300864000, 156940663040, 427651338240], ![-2126295040, -14220865536, -27653910528, 48153190400, -151964467200, -427283404800, 130230732800, 866757427200, -1481373573120], ![6362775552, -17497632768, -31813877760, 79534694400, -159069388800, -695928576000, 0, 2004274298880, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 13 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 5015259696], ![0, 0, 0, 0, 0, 0, 0, -5220884672, -3319490480], ![0, 0, 0, 0, 0, 0, 1254261248, -2747921280, -6504639200], ![0, 0, 0, 0, 0, 1803742752, 3552039968, 263539616, -2375278176]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 13 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -11402315424], ![0, 0, 0, 0, 0, 0, 0, 13309486784, 7612736720], ![0, 0, 0, 0, 0, 0, -4434947200, 1388452608, 9142534048], ![0, 0, 0, 0, 0, -9963238944, -6953858592, 9456509152, -11682328704], ![0, 0, 0, 0, -3076202560, 4763486816, -11812714112, -21224649952, 3143646656]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 13 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3304840224], ![0, 0, 0, 0, 0, 0, 0, -371851648, -2497749760], ![0, 0, 0, 0, 0, 0, -23336485824, -3875704448, -4747515088], ![0, 0, 0, 0, 0, 20965604832, -476038816, 2764595552, -2569591680], ![0, 0, 0, 0, 998838400, 18119479552, 3191170048, 4136502016, 10574706496], ![0, 0, 0, 2383067776, -5426740864, 26038522368, -2616971264, -26225000320, 48749147520]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 13 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -3022981296], ![0, 0, 0, 0, 0, 0, 0, -38904746368, -18640222720], ![0, 0, 0, 0, 0, 0, 62468446144, 28431104000, 19614939120], ![0, 0, 0, 0, 0, -4023831936, -7818293376, -18033227520, 735632736], ![0, 0, 0, 0, -76817357760, 30979623264, -117882311296, 63668482080, 36890694912], ![0, 0, 0, -4325983872, -13319012992, -40376024576, 98902112256, -71253509248, -265139060480], ![0, 0, 10009101312, 7678670080, -27314537472, 34790529024, 67759470592, -93192026880, -57578688000]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 13 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 6084040080], ![0, 0, 0, 0, 0, 0, 0, 10346157184, 14067862720], ![0, 0, 0, 0, 0, 0, -1984057920, -23732514304, -14084602064], ![0, 0, 0, 0, 0, -48840995904, -1880752320, -18703795520, 35666889120], ![0, 0, 0, 0, 22759829120, -39945462208, 110729697536, -43100545600, -54892936576], ![0, 0, 0, -42961552320, -52019529920, 19264421120, -98775238656, 43482669376, 80889265280], ![0, 0, -20366954496, -516248320, -58449004544, 28699754496, 65163886592, -240309021440, -163562553600], ![0, -6404018176, -15417253888, -5691731968, -15690489856, -31389159424, -29776261120, -49441638400, -130815155200]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 13 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -1256692704], ![0, 0, 0, 0, 0, 0, 0, -12205695424, -8272482640], ![0, 0, 0, 0, 0, 0, -23311783232, -7658561024, 11808893296], ![0, 0, 0, 0, 0, 34761814416, 37357175504, -28609864880, -27673459104], ![0, 0, 0, 0, 76144651200, -82287626400, 50463508864, -209090447328, -112148882496], ![0, 0, 0, -41498034432, 20766140928, 27609950208, 50242375680, -19035100416, -6325733760], ![0, 0, 36549367296, 45415054720, -137125300736, 279614475264, 40116898816, -790243272320, 56096524800], ![0, 47104365824, 7730713856, 29184723456, 121509599744, -165109634560, 33120606720, 962264057600, 551002419200], ![3169544192, 27702110720, 13912229888, 38928167936, 65298335744, -17877376000, 30665523200, 396660953600, 427702553600]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 13 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -219648000, -1097770080], ![0, 0, 0, 0, 0, 0, -11015305024, 1786000896, 4384193776], ![0, 0, 0, 0, 0, -15942483168, 13037169312, -2674287200, 2463418368], ![0, 0, 0, 0, 4219281600, 35413979040, -52348273024, -61390859040, 21253548672], ![0, 0, 0, -4486350720, 55190015360, -85648223744, 142931705856, 342558697088, -237654081920], ![0, 0, 16008483840, 50768650240, -18378542080, 10044942336, -103254370304, -157444802560, -67997702400], ![0, 25992030208, -10536439808, -28985520128, 71296657408, -92822614016, -95763783680, 548556544000, 567189184000], ![-2125824, 4373194240, 29860345856, 1884982272, 56450308096, 79734348800, 14402764800, 201176665600, 709495270400], ![5691617280, -10520494080, -35308634112, -138884530176, 173420544000, -441357926400, -1695574425600, -257458790400, 2621348352000]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 13 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, -10427211648, 5379829760, 2470807360], ![0, 0, 0, 0, 0, -10987138512, 22032087536, 14503563888, 2768747040], ![0, 0, 0, 0, 4964855680, 19161299008, -22012527360, -33471506240, -1434570752], ![0, 0, 0, 682694528, -84269978752, 102318238208, -67548153856, 159247395200, 275291352320], ![0, 0, -24081530880, 19756670720, 58069882880, -56072742912, -113309261824, 302167842560, 102336441600], ![0, -42102769920, -27849829632, -58265201152, -70170892800, 26303473152, -162885859840, -546927302400, -261786777600], ![-1574643712, 1980244480, 63916615680, 667427840, 75241695232, 238801228800, 135762329600, 184145881600, 1171292236800], ![2263820288, -14458585088, -16509665280, -90378231808, 104936734720, -206370816000, -951809228800, -120382976000, 1851716966400], ![6362775552, 0, -38176653312, -174976327680, 0, -477208166400, -2226971443200, -2505342873600, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 13 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 15264631008], ![0, 0, 0, 0, 0, 0, 0, 8091963264, 4582214688], ![0, 0, 0, 0, 0, 0, -8855526144, 10614958848, 11492717376], ![0, 0, 0, 0, 0, 3707947584, -35840448, -51185856, 10063899072]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 13 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2751571008], ![0, 0, 0, 0, 0, 0, 0, -13892149632, -12848377440], ![0, 0, 0, 0, 0, 0, 43206722304, -29399021568, -25966868928], ![0, 0, 0, 0, 0, 9270316224, 26892898752, 40112708544, 451988352], ![0, 0, 0, 0, -15778745088, -12361557696, 31779083136, 5941174464, -18739966464]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 13 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -48283929792], ![0, 0, 0, 0, 0, 0, 0, 67180502784, -1213653120], ![0, 0, 0, 0, 0, 0, -26826338688, 69507141888, 16502830176], ![0, 0, 0, 0, 0, -13139671104, -80479013184, 5428895424, 28765711872], ![0, 0, 0, 0, 10920648192, -12788617728, -4042421760, 2621246976, -12106962432], ![0, 0, 0, -12978077184, -5298006528, -39432059136, 57120816384, -82180273152, -119633298432]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 13 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 78792403104], ![0, 0, 0, 0, 0, 0, 0, 16534059264, 55768664448], ![0, 0, 0, 0, 0, 0, -38423015808, -102250990080, -37307182368], ![0, 0, 0, 0, 0, 59363785728, 64112551680, 48800830464, 62689878720], ![0, 0, 0, 0, 51363244800, 67094491968, -179275317888, 120421151424, 219398713344], ![0, 0, 0, -749222400, 120174334464, -142552523520, 133255100160, 256491709440, -97292424192], ![0, 0, 12884023296, 7939316736, 80944496640, -149523005952, 205817241600, 20263925760, -474620774400]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 13 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 31867729056], ![0, 0, 0, 0, 0, 0, 0, -123633272064, 4009028352], ![0, 0, 0, 0, 0, 0, 168387438720, -96513907200, -25424421792], ![0, 0, 0, 0, 0, 12412798848, 146461481088, -83723126400, -115924908096], ![0, 0, 0, 0, 98683482624, -32677207680, 97703576832, -148867077504, -251148767232], ![0, 0, 0, 129816612096, 41198517504, 240327878016, -176024648064, 191771536896, 461745748992], ![0, 0, -43830484992, -58408412160, 70849207296, -344489015808, 340408061952, -117561870336, -1042369293312], ![0, -363515904, -11691012096, -37915865088, -14414905344, -30443741184, -37980561408, -7552327680, 25519804416]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 13 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -5175326016], ![0, 0, 0, 0, 0, 0, 0, 6426803328, 7592133984], ![0, 0, 0, 0, 0, 0, 30895355520, -15923288064, 2322957792], ![0, 0, 0, 0, 0, -309024472032, 344385265056, -82344294240, -253609990848], ![0, 0, 0, 0, -98608518912, -199102971072, 458563539840, 22647209664, -337346465280], ![0, 0, 0, 2938672128, -23754906624, -82434286080, 97095621120, 50713835520, -191476389888], ![0, 0, 32733711360, 57259172352, 193603679232, -415040843520, 1315113099264, -319303965696, -2743951804416], ![0, 17544771072, 90136290816, -32421404160, 3016693248, 273186290688, -1220431893504, -506090806272, 2512715157504], ![0, 9278641152, 61191641088, -4656516096, 3679862784, 28117469184, -545678880768, -785621514240, 33668259840]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 13 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 5917359360, -2838253632], ![0, 0, 0, 0, 0, 0, -33615848832, 32476111872, 10703913696], ![0, 0, 0, 0, 0, -31843546560, 96565711680, -46808196288, -70292321280], ![0, 0, 0, 0, -6479810304, -68959148352, 118736851584, 64350747456, -112478020608], ![0, 0, 0, -61047731712, -71375897088, 112412234496, -711782883072, 577127955456, 816408677376], ![0, 0, -5954070528, 21854355456, 89990771712, 225097758720, 199711838208, 122320601088, 268892845056], ![0, 9717313536, 49182547968, -13379137536, -197116901376, 164409434112, -949311602688, -735700377600, 1367336761344], ![0, -114398208, 1906108416, 90153028608, 1728331776, 162107553792, 12048887808, -212866467840, 277386485760], ![0, 26481475584, -40388640768, -247160438784, -397666418688, 905701588992, -1134704885760, -3707406581760, 5392488038400]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 13 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, -40139344896, 51530774016, 2809470720], ![0, 0, 0, 0, 0, 43983982944, -62649396768, -49938576672, 26774170560], ![0, 0, 0, 0, 39489910272, -64554284160, 80254303488, 56488603776, -95191753728], ![0, 0, 0, 44201909760, -2024941056, 140154884352, -438008966400, 6962181120, 568473590784], ![0, 0, 46552817664, -34632391680, -154549533696, 456805698048, -640662638592, 79470200832, 1461325040640], ![0, -11372336640, -84253902336, -15603884544, -124150040064, -112562666496, 468888327168, 69042723840, -988536619008], ![0, -5742148608, -10015672320, 220460590080, 16291479552, 232069195776, 393403355136, 22195169280, -222377287680], ![0, 12382248960, -47503171584, -115567656960, -205020266496, 652434849792, -358857916416, -1733514854400, 3809246330880], ![0, 28632489984, 0, -267236573184, -687179759616, 171794939904, -1145299599360, -5153848197120, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 13 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -37012590912], ![0, 0, 0, 0, 0, 0, 0, -25551947520, -15149872320], ![0, 0, 0, 0, 0, 0, 29365687296, -28519147008, -32966896512], ![0, 0, 0, 0, 0, -33377976192, -7012579200, -12627407232, -48835180416]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 13 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -16983474816], ![0, 0, 0, 0, 0, 0, 0, 58019841792, 53325053760], ![0, 0, 0, 0, 0, 0, -198686974464, 63483982848, 89318832768], ![0, 0, 0, 0, 0, 47846189952, -179770132608, -185930177664, 659214336], ![0, 0, 0, 0, 122121626880, 17446906752, -14799544320, 62937249408, -21586388736]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 13 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 133747388544], ![0, 0, 0, 0, 0, 0, 0, -281086164480, -38528540160], ![0, 0, 0, 0, 0, 0, 117987412224, -157991404032, -42552637248], ![0, 0, 0, 0, 0, 53674127232, 291405155712, 60222188928, -34622049792], ![0, 0, 0, 0, -101479488000, -37717650432, -30963204096, -35318891520, -38706074880], ![0, 0, 0, -10896652800, 50723228160, -298535187456, 338988334080, -124818811392, -732664339968]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 13 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -190226883264], ![0, 0, 0, 0, 0, 0, 0, -60353373696, -128511060480], ![0, 0, 0, 0, 0, 0, 77550097152, 239602243584, 75152527296], ![0, 0, 0, 0, 0, -409731463680, -271927552512, -209648507904, -276165479040], ![0, 0, 0, 0, 113208564480, 38185699200, 673567420416, -8876529024, -536141607936], ![0, 0, 0, 171580992000, -294387371520, 830849547264, -727636884480, -390455391744, 1418074454016], ![0, 0, 0, 8885099520, 182896496640, -433662806016, 854615494656, 89324792832, -2442374787072]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 13 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -87750049728], ![0, 0, 0, 0, 0, 0, 0, 405594241536, 8507448576], ![0, 0, 0, 0, 0, 0, -592684891392, 283563945984, 164290931904], ![0, 0, 0, 0, 0, -54486769920, -364147415808, 205326637824, 266471145600], ![0, 0, 0, 0, -670523927040, 13829012736, -356221138944, 256603902720, 1064414224896], ![0, 0, 0, 204639072000, 326094109440, 261698139648, -255495787008, 915404928768, 811040017920], ![0, 0, 0, -167836247040, 203458590720, -1044340340736, 1990209306624, 639415299072, -4630346704896], ![0, 0, 0, -13328916480, -141026181120, -58618306560, 110694752256, 295290716160, 643168002048]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 13 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 11572801152], ![0, 0, 0, 0, 0, 0, 0, 9612278016, -14480659776], ![0, 0, 0, 0, 0, 0, 19843127040, 29182433280, -45759996480], ![0, 0, 0, 0, 0, 1067740305984, -1227181661376, 36951731520, 878800728960], ![0, 0, 0, 0, 515372309760, 663642029952, -1108578256896, -110961079680, 1097310694656], ![0, 0, 0, 185818997760, 9377280000, -109173301248, -601346279424, -512474704896, 35550890496], ![0, 0, 0, -197183331840, 1783218032640, -4165976263680, 5209856796672, 3626930723328, -12145288556544], ![0, 0, 0, 643308272640, -1885696834560, 3204074548224, -3014158169088, -8045782001664, 6121568403456], ![0, 0, 0, 340216842240, -579237457920, 392797870080, -978434383872, -4188739670016, -1423212797952]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 13 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -11322246144, 6898776192], ![0, 0, 0, 0, 0, 0, 146557382400, -95588444160, -60311254080], ![0, 0, 0, 0, 0, 120849489024, -309944393088, 62422800000, 170132312064], ![0, 0, 0, 0, 58583036160, 76161055872, -192990302208, 28420233600, 149409756672], ![0, 0, 0, 121269603840, -871006287360, 2042933308416, -3735019926528, 130213264896, 5123046213120], ![0, 0, 0, -44841984000, 159893944320, -162463150080, 982184349696, 1932713435136, 1380382857216], ![0, 0, 0, 356301496320, -1057978183680, 1857524883456, -3143072858112, -6228965867520, 4292664397824], ![0, 0, 0, -4194600960, 55918325760, 888655325184, -65979555840, -2124425588736, -1819367497728], ![0, 0, 0, 970987438080, -5109901885440, 2738313363456, 7030206627840, -8156294479872, 3954491228160]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 13 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 109671851520, -131246843904, -11690891520], ![0, 0, 0, 0, 0, -196281264960, 261009067968, 174389375424, -137014576512], ![0, 0, 0, 0, -202508951040, 142244289792, -215737792512, -109927276800, 313928930304], ![0, 0, 0, -35777195520, 152806832640, 18705460224, 214011122688, 558318875136, -1141483014144], ![0, 0, 0, 255705584640, -680765184000, 1269480622080, -3184266657792, -546059492352, 8359362029568], ![0, 0, 0, -416985676800, 748766346240, -1343203445760, 1223489811456, 3758630430720, -1453618839552], ![0, 0, 0, -210545448960, 869106585600, 1128998762496, -211516022784, -1944580509696, -4666537598976], ![0, 0, 0, 454015795200, -2913962557440, 2119851638784, 4966128549888, -3813732679680, 2793447309312], ![0, 0, 0, 1049857966080, -4199431864320, -1679772745728, 5039318237184, -3779488677888, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 13 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -609621876864], ![0, 0, 0, 0, 0, 0, 0, 325547988480, 230474724480], ![0, 0, 0, 0, 0, 0, -294181155840, -147936003072, 100147297536], ![0, 0, 0, 0, 0, 292402116864, -399691159296, -144870925056, 154149735168]] +lemma s_6_0_checked : ∀ i k : Fin 9, fourSumInteger 0 13 13 i k = s_6_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1505795436288], ![0, 0, 0, 0, 0, 0, 0, -1406763511296, -1037301682560], ![0, 0, 0, 0, 0, 0, 3033145150464, 1192437362688, -619078217472], ![0, 0, 0, 0, 0, -3953533199616, 2240248268544, 769658343168, -1454991183360], ![0, 0, 0, 0, 0, 1706321979648, -2142579039744, -1452071512320, 2110070037504]] +lemma s_6_1_checked : ∀ i k : Fin 9, fourSumInteger 1 13 13 i k = s_6_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 287688031488], ![0, 0, 0, 0, 0, 0, 0, 2773071375360, 1741945920000], ![0, 0, 0, 0, 0, 0, -615662581248, -2195439307776, -418373265024], ![0, 0, 0, 0, 0, 1024924462848, 872873134848, -539315901696, 84521428992], ![0, 0, 0, 0, 0, -283912611840, -487561451520, 224145512448, 1073051206656], ![0, 0, 0, 0, 0, -169987783680, 810834545664, -1845335771136, -2792607307776]] +lemma s_6_2_checked : ∀ i k : Fin 9, fourSumInteger 2 13 13 i k = s_6_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1561567632768], ![0, 0, 0, 0, 0, 0, 0, 2175803655168, -726348480000], ![0, 0, 0, 0, 0, 0, -578976972288, 2382977845248, 1644231498624], ![0, 0, 0, 0, 0, 3259218733056, -2453468599296, -3038545416192, -2359294629120], ![0, 0, 0, 0, 0, -2955999391488, 7089367853568, 2058702167808, -7016346095616], ![0, 0, 0, 0, 0, 2676663475200, -7522734455808, 308857595904, 18362960259072], ![0, 0, 0, 0, 0, 138607552512, 1717313495040, -3166457868288, -6716974657536]] +lemma s_6_3_checked : ∀ i k : Fin 9, fourSumInteger 3 13 13 i k = s_6_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -669068839296], ![0, 0, 0, 0, 0, 0, 0, -1396169229312, -1361805299712], ![0, 0, 0, 0, 0, 0, 2325000657408, 1171677112320, -2799298719360], ![0, 0, 0, 0, 0, 1097511427584, -4207788609024, 1529329731072, 2862111732480], ![0, 0, 0, 0, 0, -1965212840448, -3043023160320, 3498867220992, 7944383496192], ![0, 0, 0, 0, 0, 3192369523200, -1929237133824, -5048766108672, -2084525414400], ![0, 0, 0, 0, 0, -2618245453824, 5606963281920, 2072804118528, -9526229526528], ![0, 0, 0, 0, 0, -207931097088, -1258741186560, -293302124544, 6145065738240]] +lemma s_6_4_checked : ∀ i k : Fin 9, fourSumInteger 4 13 13 i k = s_6_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 215348500224], ![0, 0, 0, 0, 0, 0, 0, -354389528064, 129222817152], ![0, 0, 0, 0, 0, 0, -2844740980224, 1001426190336, 712865552256], ![0, 0, 0, 0, 0, -5218993473408, 3957457815168, 7907092152960, -3231814899456], ![0, 0, 0, 0, 0, 7681149096192, -10002426170880, -2088014852352, 8831399875584], ![0, 0, 0, 0, 0, 2898776365056, -4733770229760, -7160702275584, 1561948557312], ![0, 0, 0, 0, 0, -3076059976704, 22646880841728, -14809097791488, -84723756429312], ![0, 0, 0, 0, 0, 10035609053184, -29646856132608, -34715458652160, 86084461731840], ![0, 0, 0, 0, 0, 5307382738944, -9562324721664, -32826195038208, 1283882975232]] +lemma s_6_5_checked : ∀ i k : Fin 9, fourSumInteger 5 13 13 i k = s_6_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -211319387136, 129855787776], ![0, 0, 0, 0, 0, 0, -929450835456, -228432162816, 735512578944], ![0, 0, 0, 0, 0, -1043899414272, -1108022133504, 1978280029440, 1123583864832], ![0, 0, 0, 0, 0, 2836617189120, -5063970802176, -1634462598912, 6246073067520], ![0, 0, 0, 0, 0, 1891805819904, -12211475088384, 11032120399872, 28742930810880], ![0, 0, 0, 0, 0, -699534950400, 2595610288128, 1733272240128, -2617396733952], ![0, 0, 0, 0, 0, 5558303342592, -16561276452864, -18692086972416, 41115731644416], ![0, 0, 0, 0, 0, -65435774976, 625174437888, 7476946194432, 10577671323648], ![0, 0, 0, 0, 0, 15147404034048, -58192114286592, -141375770984448, 205633543864320]] +lemma s_6_6_checked : ∀ i k : Fin 9, fourSumInteger 6 13 13 i k = s_6_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 1006563317760, -1205662808064, -27751206912], ![0, 0, 0, 0, 0, 3525695192448, -2955804289152, -1280070599808, 2337038795520], ![0, 0, 0, 0, 0, -689209956864, -727673177088, 2150705576448, 2549024704512], ![0, 0, 0, 0, 0, -558124250112, 2519398142976, 1361512728576, -4483998824448], ![0, 0, 0, 0, 0, 3989007120384, -12398634074112, -6648918921216, 23716867958784], ![0, 0, 0, 0, 0, -6504976558080, 14292146558976, 25138046748672, -30455822352384], ![0, 0, 0, 0, 0, -3284509003776, 11228381159424, 35059340439552, -8479987236864], ![0, 0, 0, 0, 0, 7082646405120, -32666092732416, -66104699781120, 145259260084224], ![0, 0, 0, 0, 0, 16377784270848, -43674091388928, -196533411250176, 0]] +lemma s_6_7_checked : ∀ i k : Fin 9, fourSumInteger 7 13 13 i k = s_6_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 7 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7], ![s_6_0, s_6_1, s_6_2, s_6_3, s_6_4, s_6_5, s_6_6, s_6_7]] +lemma sums_checked : ∀ u : Fin 7, ∀ a i k, fourSumInteger a 13 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k + · exact s_6_0_checked i k + · exact s_6_1_checked i k + · exact s_6_2_checked i k + · exact s_6_3_checked i k + · exact s_6_4_checked i k + · exact s_6_5_checked i k + · exact s_6_6_checked i k + · exact s_6_7_checked i k +end SumTable13 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable14.lean b/lean/OAI/Analysis/LaughlinGap/SumTable14.lean new file mode 100644 index 0000000000000000000000000000000000000000..d300be4a4dc1853e3829b9b6fa06f0610d8511a4 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable14.lean @@ -0,0 +1,360 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SumTable13 + +namespace OAI + +/-! Sum Table14. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable14 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 116630087574], ![0, 0, 0, 0, 0, 0, 0, -443621205456, -289197299820], ![0, 0, 0, 0, 0, 0, 576127360380, 321485899020, 96650925228]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 14 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 22427549430], ![0, 0, 0, 0, 0, 0, 0, -878411668992, -413826518820], ![0, 0, 0, 0, 0, 0, 1215143469540, 116524535556, -204729216120], ![0, 0, 0, 0, 0, -578745447852, -143905263216, 242017492860, 398834978256]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 14 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -987337020384], ![0, 0, 0, 0, 0, 0, 0, 1042543067280, 502672599858], ![0, 0, 0, 0, 0, 0, -1187370369900, -156088360428, -41657341440], ![0, 0, 0, 0, 0, 58042189920, -23874378528, -27467435424, -28636491312], ![0, 0, 0, 0, -141286887456, -121350996624, -159652473552, -133056786720, -23161003008]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 14 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1442445253392], ![0, 0, 0, 0, 0, 0, 0, -191958363168, 468342873570], ![0, 0, 0, 0, 0, 0, -1286240409168, 1094484129024, 2585631828780], ![0, 0, 0, 0, 0, 1655351317620, -567854361360, -773704144356, 692117176608], ![0, 0, 0, 0, -199215395808, 583743560400, 915191211792, 284164067616, -658313335680], ![0, 0, 0, -498277281216, -461003647104, -44270836896, -126452863680, -1018450008576, -1960624064256]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 14 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -210500721288], ![0, 0, 0, 0, 0, 0, 0, -2266030619424, -923723863062], ![0, 0, 0, 0, 0, 0, -180254875944, -990775071000, -607432372404], ![0, 0, 0, 0, 0, 891536567064, 2173634535072, 1167601094088, -1539340847616], ![0, 0, 0, 0, 2295704233680, 687127333464, -34605133992, 1027299839280, 2896167276288], ![0, 0, 0, 903250041408, 1190931373632, 1954364796384, 1410207070272, -894578201088, -2911401347712], ![0, 0, -707192648448, -628338577152, -210919408128, 237807837696, 313988133888, -34982458368, -94536279552]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 14 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 655843116786], ![0, 0, 0, 0, 0, 0, 0, 2736974917248, 794584386882], ![0, 0, 0, 0, 0, 0, 5142474273222, -624122427786, -1445416292892], ![0, 0, 0, 0, 0, 1395551608308, -165167876016, -2128752000804, -2479620487344], ![0, 0, 0, 0, -1077829017408, 118157596128, 1074403181280, 779661140544, -1155504814464], ![0, 0, 0, -2189714031648, -1390226378112, -1186188315312, -1999198879392, -2003639489280, 1072505271552], ![0, 0, 1054437013344, 2381169936288, 2725434432864, 2342623483200, 1795432129920, 766777275264, -1537630228992], ![0, -1017089755968, -1077356197632, -152188086336, 1549044182400, 3248512979712, 4046314601472, 3673693740288, 3562151983104]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 14 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 59204575716], ![0, 0, 0, 0, 0, 0, 0, 1065367068480, 278781261330], ![0, 0, 0, 0, 0, 0, 2478107886540, 21084613836, -815026294368], ![0, 0, 0, 0, 0, 1436099408172, -59334276144, -914591886780, -835384053504], ![0, 0, 0, 0, -588719582880, -405761797584, -662365930512, -1347035193504, -2132351020800], ![0, 0, 0, -2336127805440, -491523764160, -662734520448, -1715519520000, -1218306625536, 2611305840000], ![0, 0, -877075110912, 1342102983936, 2064567043968, 1252157457408, 1020875581440, 3205017074688, 6635249677056], ![0, -587535089856, -26348205312, 807105938496, 873319624320, 86768098560, -18182900736, 2164776776448, 4945983584256], ![-41431762944, 552249105408, 1074978837504, -1088615024640, -6311418347520, -8552181141504, 118077493248, 13885120364544, -714005360640]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 14 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 224860892256, 183646573968], ![0, 0, 0, 0, 0, 0, 1642052265282, 590679691602, -502214583156], ![0, 0, 0, 0, 0, 2865062054712, 257043277920, -1558794710616, -1758880231680], ![0, 0, 0, 0, 3171970936992, 106345688592, -3322711659696, -3206066099808, 1383676145280], ![0, 0, 0, 739136249280, 306432434880, -1931319547872, -2121862087488, 2024501546496, 8272585326720], ![0, 0, -2221815394656, -2486311919520, -2114237844576, -1345075617600, -240411270528, 1375672831104, 3237128294400], ![0, -1020367233600, 251832691968, 2038793794752, 1898746861440, -682695526656, -2172171555840, 2334207752448, 11122791094272], ![-104631081984, 258221483520, 928932026880, 173050555392, -2951102668800, -5362975647744, -1649956239360, 6492425871360, -504372430848], ![0, 597106718208, 1535417275392, 0, -6824076779520, -15354172753920, -14330561236992, 682407677952, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 14 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 25730759868], ![0, 0, 0, 0, 0, 0, 0, -1057287264, 21876032904], ![0, 0, 0, 0, 0, 0, -69349452744, -34739712744, -31201308600]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 14 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -64996760532], ![0, 0, 0, 0, 0, 0, 0, -58260827328, -21517101672], ![0, 0, 0, 0, 0, 0, 75719846664, -97406366904, -159002887296], ![0, 0, 0, 0, 0, 108569916312, -3566495856, -14052760920, 10141368336]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 14 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -204169415472], ![0, 0, 0, 0, 0, 0, 0, 18987901152, 144877410084], ![0, 0, 0, 0, 0, 0, -99550639320, 149965019688, 257904566304], ![0, 0, 0, 0, 0, -7943166528, -19057387008, -23564312640, 19244524464], ![0, 0, 0, 0, 44934471648, 56325050496, 39647357376, -7858512288, 8044258464]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 14 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -48312826320], ![0, 0, 0, 0, 0, 0, 0, -197232317568, -270992245788], ![0, 0, 0, 0, 0, 0, -265118604960, -299410524864, -256979685864], ![0, 0, 0, 0, 0, 11047304664, 77761741200, -246700566552, -185240468160], ![0, 0, 0, 0, -912131616, -225494843904, -61537882560, 35468012448, -280835077248], ![0, 0, 0, 86463393984, 44722516608, 3913658496, 147466344960, 187722177984, -65549696256]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 14 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 77508816000], ![0, 0, 0, 0, 0, 0, 0, -259243454976, -74714206380], ![0, 0, 0, 0, 0, 0, 389104627824, -15457505712, -219712916280], ![0, 0, 0, 0, 0, -518104291056, -321468294048, 144374771376, 306696332448], ![0, 0, 0, 0, -563020209840, -128428149696, -364029955872, -587886892560, -222383687328], ![0, 0, 0, -98420410176, -272893598208, -343693620864, 65715648768, 282692025792, -270672057216], ![0, 0, 16230432768, 35996944896, -57624821760, -129756261888, -100848185856, -77864573952, -283261169664]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 14 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 162211669092], ![0, 0, 0, 0, 0, 0, 0, 509816055936, -83710041756], ![0, 0, 0, 0, 0, 0, 795657371916, -666692989908, -986118925704], ![0, 0, 0, 0, 0, -326557517352, 440192438928, 430558241256, -267859609776], ![0, 0, 0, 0, 321695451264, -86453110656, -176167415424, 25151480640, 300806146080], ![0, 0, 0, 393617179296, 160677219648, 362436271296, 384012946944, -533337884640, -1353008726784], ![0, 0, 192819200640, -121969205952, -181726902720, -186283082304, 88607699136, 1028191824000, 1822063592448], ![0, -222317677824, -71828123136, -124685185152, -347938601472, -523561281408, -388238171904, 79356524544, 277323475968]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 14 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 37606508280], ![0, 0, 0, 0, 0, 0, 0, 198859638912, 31145619780], ![0, 0, 0, 0, 0, 0, 190951608408, -136335990120, -286521518976], ![0, 0, 0, 0, 0, -186684314520, 69268091376, 11165040216, 13319757792], ![0, 0, 0, 0, 210358468320, 157999492992, 255079442112, 469961639136, 383885735904], ![0, 0, 0, 532194719232, 39337660032, 156424055040, 86186200320, -444208596480, -950456884608], ![0, 0, 295877885952, -223313063424, -242973510912, -97803763200, -235376418816, -199730285568, 546954541056], ![0, -48296295168, -33115501056, -144222427008, -15830622720, 181302523776, 26736221952, -204984907776, 633780145152], ![32614078464, 109846978560, -145648115712, 182060144640, 1015473659904, 118399463424, -2982121021440, -3058610429952, 5766966374400]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 14 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -56391920640, 106114274640], ![0, 0, 0, 0, 0, 0, -175373934780, 79301032932, 67236406248], ![0, 0, 0, 0, 0, -444005269488, 108436879584, 45229894512, -62062976448], ![0, 0, 0, 0, -762619905696, 385713326592, 445472596800, -189685967328, -348982862976], ![0, 0, 0, -216125367744, 43365797376, 458521193856, -73021006080, -729671304384, -314206257024], ![0, 0, -46167225984, 75228145344, 42855096768, -96836921280, -478471105728, -1045089581184, -1192760211456], ![0, -40389085440, -26436343296, -308516689536, 4684432896, 657871429248, 470052506880, -474436233216, 512756665344], ![-17541934080, 77595758592, -68102369280, 85127961600, 691241785344, 448861501440, -1236984680448, -1430149754880, 4073777326080], ![52492898304, 157478694912, 0, 196848368640, 1181090211840, 1102350864384, -2204701728768, -5511754321920, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 14 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -10411504872], ![0, 0, 0, 0, 0, 0, 0, 3592460736, 10182091344], ![0, 0, 0, 0, 0, 0, 8746999536, 17209365552, 19172301168]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 14 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 24354183000], ![0, 0, 0, 0, 0, 0, 0, 64821002496, -11212249872], ![0, 0, 0, 0, 0, 0, -56050287216, 70956273168, 23018270688], ![0, 0, 0, 0, 0, -31209652464, -4668595968, -19696943952, -13847754240]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 14 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 82937456064], ![0, 0, 0, 0, 0, 0, 0, -180226632384, 49733430600], ![0, 0, 0, 0, 0, 0, 57065301840, -117340394160, -43568414976], ![0, 0, 0, 0, 0, 6291201408, 27634595712, 7734013824, -22207109760], ![0, 0, 0, 0, -25964437248, -35592986304, 1556233536, 6448262400, -62145544320]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 14 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -185619901056], ![0, 0, 0, 0, 0, 0, 0, 229278234240, -13795957368], ![0, 0, 0, 0, 0, 0, 238314554304, 90472570368, 88047778224], ![0, 0, 0, 0, 0, -166745979504, 121904383104, 29555749680, -125413833600], ![0, 0, 0, 0, 33321290496, 78710773440, -37273149504, 152535962880, 280469473920], ![0, 0, 0, -10898680320, 24022434816, -27370606464, -55395336960, 84944874240, 96468952320]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 14 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -92630283360], ![0, 0, 0, 0, 0, 0, 0, 249478786176, -175961244504], ![0, 0, 0, 0, 0, 0, -155519469984, 94257621408, 4495480560], ![0, 0, 0, 0, 0, 337828178400, -8460690432, 4943956896, 14952625920], ![0, 0, 0, 0, 212197841280, 99294486816, 292264688544, 89129416320, -100015056000], ![0, 0, 0, -40412232192, 100830374400, -6557066112, -139337729280, 87393473280, 174375308160], ![0, 0, 44072859648, 9578072064, 45162614784, 48912768000, 22828354560, 52327480320, 159957619200]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 14 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -37085074488], ![0, 0, 0, 0, 0, 0, 0, -72796320768, -93415017720], ![0, 0, 0, 0, 0, 0, -295403033064, 541070470104, -84872757936], ![0, 0, 0, 0, 0, 57379598736, -285649350912, 82142750256, 170188548480], ![0, 0, 0, 0, -178705549824, 48598235520, 36356982912, 2996904960, -57957442560], ![0, 0, 0, -57414667008, 26475663360, -205128484416, 190402346880, 693062006400, -174431911680], ![0, 0, -179865141504, -73748712192, -38101050624, 9868786560, -397277746560, -923547576960, -288955215360], ![0, 55929583104, -21563830272, -50344389120, -10322058240, -26322727680, -266464742400, -594121916160, -520407659520]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 14 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 10019586384], ![0, 0, 0, 0, 0, 0, 0, -100498305792, 31118587464], ![0, 0, 0, 0, 0, 0, -150936270288, 151434283824, 25515760512], ![0, 0, 0, 0, 0, 12787012848, 36641391744, 10999896144, -113431063680], ![0, 0, 0, 0, -116392538880, -74254326720, -211177392576, -203608523520, 206242300800], ![0, 0, 0, -187479527424, 37984006656, 1215025152, 183085171200, 293869209600, 175331928960], ![0, 0, -114711601152, 71131293696, -12726457344, 9166740480, -75043584000, -529062958080, -623163674880], ![0, 30233479680, -27566174208, 6802721280, -92602967040, -105708453120, -13343155200, -224500527360, -816613217280], ![31831842816, -48993656832, 134503096320, 0, -167175290880, 827546112000, 1576502784000, -463425822720, -2097078681600]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 14 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -118060548480, 81020192256], ![0, 0, 0, 0, 0, 0, -47302988280, -20587640760, 57863141616], ![0, 0, 0, 0, 0, 72570485088, 32331899136, 74125232928, -72540720000], ![0, 0, 0, 0, 297743582976, -260290895424, 60897959616, -5875050240, -217368593280], ![0, 0, 0, 105910798848, -94888407552, -64316522112, 176956842240, -70485707520, -261166550400], ![0, 0, 181900230912, 103336889088, 68666473728, 122745674880, 379374652800, 512231414400, 114149099520], ![0, 55881973248, -70705115136, 44044623360, -186942090240, -316305872640, -9178905600, -115648623360, -1491437122560], ![7729434624, -41987321856, 58121465856, 0, -149713551360, 386945280000, 916007270400, -216689356800, -1481373573120], ![38176653312, -4772081664, 143162449920, 143162449920, 0, 894765312000, 2505342873600, 2004274298880, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 14 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4943916656], ![0, 0, 0, 0, 0, 0, 0, -15350773632, 154533920], ![0, 0, 0, 0, 0, 0, 832144096, -14603426720, -14870353248]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 14 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4604222896], ![0, 0, 0, 0, 0, 0, 0, 2572533504, -37603327648], ![0, 0, 0, 0, 0, 0, -11085722592, 24623672608, -37230125696], ![0, 0, 0, 0, 0, 8022495712, 21197643712, 26131081248, 5975175616]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 14 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 45308777920], ![0, 0, 0, 0, 0, 0, 0, 24901286272, 58066477968], ![0, 0, 0, 0, 0, 0, 39422696096, -7889596768, 28506392704], ![0, 0, 0, 0, 0, -14430658816, -29597467648, 1425890048, 1815010112], ![0, 0, 0, 0, 22604484224, 20538160384, -24715285504, 32967745664, 58058589568]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 14 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 67146022720], ![0, 0, 0, 0, 0, 0, 0, -51859502080, -68571540080], ![0, 0, 0, 0, 0, 0, -177169075328, -106730818304, -20856644000], ![0, 0, 0, 0, 0, 171388188384, -96546017344, 115918304544, -74543825664], ![0, 0, 0, 0, -49290709888, 40191164160, -56992617472, -220145964160, 106851310848], ![0, 0, 0, -19335287552, -47473574400, 57185013760, -70340114432, -90096175872, 164875532800]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 14 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -109544708224], ![0, 0, 0, 0, 0, 0, 0, 125304158720, -53178173616], ![0, 0, 0, 0, 0, 0, -7839078464, 49664013632, 23739515552], ![0, 0, 0, 0, 0, -253082126528, 3394871424, -98468183104, 160426165888], ![0, 0, 0, 0, -58730960960, -147327578496, -75458234880, 82436563264, -201518130048], ![0, 0, 0, 97200579840, -46916993536, 171567671296, -11969814528, -33029061376, 419240569600], ![0, 0, -31179395072, 13504339968, -8952315904, 14790135808, 28093427712, 1593497600, 5121664000]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 14 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 83589520], ![0, 0, 0, 0, 0, 0, 0, 35942153728, 29599932304], ![0, 0, 0, 0, 0, 0, -357712566736, 232782577840, 74933154144], ![0, 0, 0, 0, 0, 104591710944, 30447449536, -71074673376, 280279032768], ![0, 0, 0, 0, 158347348992, -24440532480, -53673654272, -41501656320, 83660774016], ![0, 0, 0, -86391312000, -47974450944, 96418373632, -604473805824, -20945804928, 1145877414400], ![0, 0, 36636947200, 33542569984, -51461132800, -16076372480, 540098180608, 171674489600, -1025893068800], ![0, 59550880256, 56703632384, 79383929856, 41729257472, 103249556480, 360836044800, 396660953600, 93913164800]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 14 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 274788192], ![0, 0, 0, 0, 0, 0, 0, -25362691584, 23795277584], ![0, 0, 0, 0, 0, 0, -13265506464, 44039506528, -21695805440], ![0, 0, 0, 0, 0, 14882626080, -89280744896, 85562800096, 94273157760], ![0, 0, 0, 0, 64038907520, 58899912960, 245063347200, -190029224320, -374973118848], ![0, 0, 0, 63873589248, -72672223232, -117038860288, -192533526528, -54989441024, -72525241600], ![0, 0, 5578539008, -47501934592, 60275812352, -16547442688, 369247305728, 415231539200, -360782963200], ![0, 4423949824, 46713633792, -978740224, 60288299008, -34200499200, -4448819200, 201176665600, 44108467200], ![8634003456, 43066982400, -106518282240, 120045453312, 43066982400, -665739264000, 364095897600, 1802211532800, -2038826496000]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 14 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -18579289600, 23467143360], ![0, 0, 0, 0, 0, 0, 113705088784, -54168752752, -48604877024], ![0, 0, 0, 0, 0, 23356950848, -143864129920, 21551646400, 113507013632], ![0, 0, 0, 0, -136030265728, 106862115584, 13034585088, 195102218624, -250449839872], ![0, 0, 0, -61760461056, 121722499584, -158105522176, 72081752064, 130198712064, -434076256000], ![0, 0, -75648400128, -23367221248, 58960581120, -27212527104, -207838844416, 87784070400, 491532748800], ![0, -13087380992, 98456400896, -49127271424, 126965149696, -45799398400, -223305779200, 184145881600, 415772134400], ![3639625728, 5828231168, -75244371968, 30692646912, 5828231168, -470277324800, 11254579200, 842680832000, -1440224307200], ![9544163328, 63627755520, -38176653312, 104985796608, 159069388800, -477208166400, 0, 1948600012800, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 14 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1789933728], ![0, 0, 0, 0, 0, 0, 0, 22004411136, -7051132608], ![0, 0, 0, 0, 0, 0, -2617598016, 13781520576, 21182312640]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 14 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -26733096096], ![0, 0, 0, 0, 0, 0, 0, -21233915904, 78569388480], ![0, 0, 0, 0, 0, 0, 18399010368, -30875496384, -27580250496], ![0, 0, 0, 0, 0, 14581674816, -48572383488, -54921941568, 35176686336]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 14 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -112582050816], ![0, 0, 0, 0, 0, 0, 0, 36004290816, -133641982176], ![0, 0, 0, 0, 0, 0, -90829586112, 88234989888, -40951455744], ![0, 0, 0, 0, 0, 36705953280, 22580141568, 22208656896, 13075418880], ![0, 0, 0, 0, -25824241152, 26164839168, 9048426240, -66232309248, 119500999680]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 14 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -22298916096], ![0, 0, 0, 0, 0, 0, 0, -12752226816, 141096093216], ![0, 0, 0, 0, 0, 0, 212604015360, 97989439488, 35495901888], ![0, 0, 0, 0, 0, -169795263168, -219890191104, 352231290816, -202874826240], ![0, 0, 0, 0, 54894073344, -230046177024, 370351422720, -171483314688, -405237009408], ![0, 0, 0, 39065766912, 34964269056, -61439685120, 166303233024, -229953570816, 46509189120]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 14 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 231651179904], ![0, 0, 0, 0, 0, 0, 0, -338729888256, 174274188960], ![0, 0, 0, 0, 0, 0, 96275481984, -231717691776, 91216777920], ![0, 0, 0, 0, 0, 193709718912, 269884786176, -308838956928, 1547821056], ![0, 0, 0, 0, -152203618560, 187104902016, -398744338560, 214930675968, 13660916736], ![0, 0, 0, -114258342912, 33241291776, -196035549696, 179161371648, -586970351616, -7968384000], ![0, 0, -13872107520, -65456738304, -27295506432, -66828632064, -59791515648, -88086159360, -193503375360]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 14 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 20066225952], ![0, 0, 0, 0, 0, 0, 0, -27524597760, -6508098528], ![0, 0, 0, 0, 0, 0, 780601377888, -677486925984, -31928943552], ![0, 0, 0, 0, 0, -273084068544, 437868958464, -688869751872, -42674426112], ![0, 0, 0, 0, -210045152256, 26378952192, 193649407488, -77662405632, -14524600320], ![0, 0, 0, 216252099072, -145840551936, 349891254528, 379697124864, -1573328772096, 823947724800], ![0, 0, 195404917248, 32494327296, 342690544128, -217372434432, -167745629184, 1688213376000, 320647311360], ![0, 9278641152, 116863488000, 96663585792, 221789718528, 72275822592, 55197941760, 690793113600, 567152640000]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 14 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -5098243008], ![0, 0, 0, 0, 0, 0, 0, 93059429376, -56491628256], ![0, 0, 0, 0, 0, 0, 97875268800, -177889440576, 66117886464], ![0, 0, 0, 0, 0, 32213701824, 46492100352, -112467747264, -42873639936], ![0, 0, 0, 0, 63036326400, -201796014336, 39810884352, 802239128064, -751928767488], ![0, 0, 0, 22283010048, 88620407808, 247405897728, -100498145280, -130335817728, 30063467520], ![0, 0, 107486429184, 20601188352, -1940846592, -118282985472, -366272790528, 963108495360, 347505039360], ![0, -114398208, 1219719168, 95998639104, 84700575744, 182847535104, 25924976640, 362403993600, 920309760000], ![0, 26481475584, 118500212736, -443135066112, 237888995328, -264814755840, -2522404454400, 0, 2995826688000]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 14 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 91422469632, -80725661952], ![0, 0, 0, 0, 0, 0, -152188543968, 79589551392, 91954755264], ![0, 0, 0, 0, 0, -51741214848, 195640275456, -46732542336, -143405601792], ![0, 0, 0, 0, 22388043264, 86101855488, -579873722112, 499166486016, 380348138496], ![0, 0, 0, -3475393536, -119748504576, 275623021056, -311115875328, 795813218304, -240300887040], ![0, 0, -152487922176, -126557591040, -294847154688, 18184421376, -213451871232, -956038302720, -268313886720], ![0, -5742148608, -44468563968, 232033121280, 52469655552, 427566950400, 244372193280, 345817958400, 1582313472000], ![0, 12382248960, 26790322176, -283516944384, 92153708544, -123822489600, -1465611632640, 0, 2116247961600], ![0, 28632489984, 171794939904, -267236573184, 0, -286324899840, -2863248998400, -2863248998400, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 14 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -6273960000], ![0, 0, 0, 0, 0, 0, 0, -16074634752, 7633008768], ![0, 0, 0, 0, 0, 0, 16990917504, -27682123392, -23138324352]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 14 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 73730652864], ![0, 0, 0, 0, 0, 0, 0, -73095035904, -136931118720], ![0, 0, 0, 0, 0, 0, -17560481664, 196463481984, 55614501888], ![0, 0, 0, 0, 0, -147366865536, 193766073600, 27216942720, -117849625344]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 14 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 134550831360], ![0, 0, 0, 0, 0, 0, 0, 125878156800, 152759999040], ![0, 0, 0, 0, 0, 0, 25716408960, -120711220608, -47821204992], ![0, 0, 0, 0, 0, -75222377472, -738287616, -47376688128, -81061339392], ![0, 0, 0, 0, 28929922560, -244880621568, 312836367360, -477138190848, -174294793728]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 14 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 169115367168], ![0, 0, 0, 0, 0, 0, 0, -158599305216, -200565875136], ![0, 0, 0, 0, 0, 0, -312319400448, -113220062208, 133919871360], ![0, 0, 0, 0, 0, 583521687936, 52436575488, -168774325632, 104096830464], ![0, 0, 0, 0, 48774612480, 389442459648, -315842503680, 542014505472, 350684725248], ![0, 0, 0, 8885099520, 200666695680, -287345608704, 1022256930816, -742825374720, -1029526536192]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 14 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -268126510080], ![0, 0, 0, 0, 0, 0, 0, 390884093952, -60256295616], ![0, 0, 0, 0, 0, 0, 142498084608, 122887488768, 30465452160], ![0, 0, 0, 0, 0, -220249691904, -172532507136, 268810924800, 161794963968], ![0, 0, 0, 0, 735372253440, 277006540800, 235637985792, 1570501810944, -53141991936], ![0, 0, 0, -167836247040, -132213903360, -881573468160, 1750169186304, -2050577937408, -2347542134784], ![0, 0, 0, -13328916480, -167684014080, -187433951232, -152268103680, -97411792896, -29766426624]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 14 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -64418920896], ![0, 0, 0, 0, 0, 0, 0, -73700284416, 108306183744], ![0, 0, 0, 0, 0, 0, -1166919597888, 599281476288, 403909723008], ![0, 0, 0, 0, 0, -105775367808, -142208318208, 307933743744, 411140446464], ![0, 0, 0, 0, 381015275520, -324654274560, -155380684800, -35818134528, -164034461184], ![0, 0, 0, -197183331840, 1388851368960, -2739401837568, 6163191226368, -3474384139776, -5140136534016], ![0, 0, 0, 643308272640, -599080289280, 2467487007744, -4230009940992, 285893296128, 5804588630016], ![0, 0, 0, 340216842240, 101196226560, 745928325120, -1143823650816, -1224780632064, 573164494848]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 14 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -13948294272], ![0, 0, 0, 0, 0, 0, 0, -123764619264, 45802591296], ![0, 0, 0, 0, 0, 0, -5646191232, 139482507648, 4855166976], ![0, 0, 0, 0, 0, -313375159680, 269279687424, -767403648, -160358803968], ![0, 0, 0, 0, -628467079680, 1200604753920, -3443972877312, 3158460974592, -142602324480], ![0, 0, 0, -44841984000, 70209976320, -34547994624, 1002478743552, 1162189873152, 1092575109120], ![0, 0, 0, 356301496320, -345375191040, 1438704132096, -3838193762304, -645666177024, 3362886438912], ![0, 0, 0, -4194600960, 47529123840, 923322943488, 53123862528, 15100563456, 1420122857472], ![0, 0, 0, 970987438080, -3167927009280, 2145946632192, -4660739702784, -8156294479872, 14499801169920]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 14 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -30552158208, 21076889856], ![0, 0, 0, 0, 0, 0, 263735985216, -199547113920, -171768026496], ![0, 0, 0, 0, 0, 86269430016, -177434982912, -38830801152, 150835964928], ![0, 0, 0, 0, 81252441600, 183883560960, 128145853440, 479770790400, -1213126582272], ![0, 0, 0, 255705584640, -169354014720, 724868474880, -3115185401856, 3017356919808, 3268936028160], ![0, 0, 0, -416985676800, -85205007360, -1244573180928, 1253956070400, -508078129152, -2301859676160], ![0, 0, 0, -210545448960, 448015687680, 1318974953472, 1116376166400, 757963616256, 903205822464], ![0, 0, 0, 454015795200, -2005930967040, 1423138455552, -2179275816960, -3813732679680, 10242640134144], ![0, 0, 0, 1049857966080, -2099715932160, 0, -5039318237184, -13858125152256, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 14 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 67700730240], ![0, 0, 0, 0, 0, 0, 0, -147936003072, 27024721152], ![0, 0, 0, 0, 0, 0, -204756414720, 50063819520, -124372275456]] +lemma s_6_0_checked : ∀ i k : Fin 9, fourSumInteger 0 14 13 i k = s_6_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -333919926912], ![0, 0, 0, 0, 0, 0, 0, 1192437362688, 301275676416], ![0, 0, 0, 0, 0, 0, -395440531200, -1866030456576, -258494286336], ![0, 0, 0, 0, 0, 1706321979648, -1005031053312, 823024460544, 475398223872]] +lemma s_6_1_checked : ∀ i k : Fin 9, fourSumInteger 1 14 13 i k = s_6_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 355410232320], ![0, 0, 0, 0, 0, 0, 0, -2195439307776, 371515098240], ![0, 0, 0, 0, 0, 0, 1556156110080, 143967073536, 1397873258496], ![0, 0, 0, 0, 0, -283912611840, -676836526080, -154404636672, 87679967232], ![0, 0, 0, 0, 0, -169987783680, 697509356544, -2185311338496, -418258114560]] +lemma s_6_2_checked : ∀ i k : Fin 9, fourSumInteger 2 14 13 i k = s_6_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1814250307584], ![0, 0, 0, 0, 0, 0, 0, 2382977845248, 163254089856], ![0, 0, 0, 0, 0, 0, -280656110592, -865732927488, -2750287398144], ![0, 0, 0, 0, 0, -2955999391488, 5118701592576, -1882630354176, 1110354905088], ![0, 0, 0, 0, 0, 2676663475200, -5738292139008, 5662184546304, 5839726024704], ![0, 0, 0, 0, 0, 138607552512, 1809718530048, -2796837728256, -609449398272]] +lemma s_6_3_checked : ∀ i k : Fin 9, fourSumInteger 3 14 13 i k = s_6_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -663720685056], ![0, 0, 0, 0, 0, 0, 0, 1171677112320, -2222636946816], ![0, 0, 0, 0, 0, 0, -3476114323968, 2261004016128, -1927423170816], ![0, 0, 0, 0, 0, -1965212840448, -4353165053952, 878583433728, 647808724992], ![0, 0, 0, 0, 0, 3192369523200, 199009214976, 1335972937728, -226247104512], ![0, 0, 0, 0, 0, -2618245453824, 3861466312704, -4909183758336, -908965804032], ![0, 0, 0, 0, 0, -207931097088, -1397361917952, -986405781504, 1995665498112]] +lemma s_6_4_checked : ∀ i k : Fin 9, fourSumInteger 4 14 13 i k = s_6_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 306417581184], ![0, 0, 0, 0, 0, 0, 0, 1001426190336, -1210218033024], ![0, 0, 0, 0, 0, 0, 478128832896, 4427763170688, -4097735406336], ![0, 0, 0, 0, 0, 7681149096192, -4881660106752, 8153517275904, -1287657406464], ![0, 0, 0, 0, 0, 2898776365056, -2801252653056, -1363149545472, -1426464399360], ![0, 0, 0, 0, 0, -3076059976704, 20596174190592, -23011924396032, -25828772057088], ![0, 0, 0, 0, 0, 10035609053184, -22956450097152, -1263428474880, 39590645293056], ![0, 0, 0, 0, 0, 5307382738944, -6024069562368, -11596664082432, 2804683554816]] +lemma s_6_5_checked : ∀ i k : Fin 9, fourSumInteger 5 14 13 i k = s_6_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 235515481344], ![0, 0, 0, 0, 0, 0, 0, -228432162816, 385003242624], ![0, 0, 0, 0, 0, 0, -1803955076352, 1282347086592, -1147561519104], ![0, 0, 0, 0, 0, 2836617189120, -3172892676096, 2147693653248, 885656758272], ![0, 0, 0, 0, 0, 1891805819904, -10950271208448, 14815732039680, 695726254080], ![0, 0, 0, 0, 0, -699534950400, 2129253654528, -132154294272, 1839101282304], ![0, 0, 0, 0, 0, 5558303342592, -12855740891136, -164409163776, 14673704128512], ![0, 0, 0, 0, 0, -65435774976, 581550587904, 7215203094528, 8798283546624], ![0, 0, 0, 0, 0, 15147404034048, -48093844930560, -70687885492224, 114240857702400]] +lemma s_6_6_checked : ∀ i k : Fin 9, fourSumInteger 6 14 13 i k = s_6_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -1205662808064, 1078361856000], ![0, 0, 0, 0, 0, 0, -605340827520, 1070392861824, 608885671680], ![0, 0, 0, 0, 0, -689209956864, -1187146481664, 1231758967296, 37557172224], ![0, 0, 0, 0, 0, -558124250112, 2147315309568, 245264228352, -684083152896], ![0, 0, 0, 0, 0, 3989007120384, -9739295993856, 3988433399808, 2693087434752], ![0, 0, 0, 0, 0, -6504976558080, 9955495520256, 3454791555072, -16410847444992], ![0, 0, 0, 0, 0, -3284509003776, 9038708490240, 21921304424448, 1793895088128], ![0, 0, 0, 0, 0, 7082646405120, -27944328462336, -33052349890560, 80699588935680], ![0, 0, 0, 0, 0, 16377784270848, -32755568541696, -109185228472320, 0]] +lemma s_6_7_checked : ∀ i k : Fin 9, fourSumInteger 7 14 13 i k = s_6_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 7 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7], ![s_6_0, s_6_1, s_6_2, s_6_3, s_6_4, s_6_5, s_6_6, s_6_7]] +lemma sums_checked : ∀ u : Fin 7, ∀ a i k, fourSumInteger a 14 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k + · exact s_6_0_checked i k + · exact s_6_1_checked i k + · exact s_6_2_checked i k + · exact s_6_3_checked i k + · exact s_6_4_checked i k + · exact s_6_5_checked i k + · exact s_6_6_checked i k + · exact s_6_7_checked i k +end SumTable14 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable15.lean b/lean/OAI/Analysis/LaughlinGap/SumTable15.lean new file mode 100644 index 0000000000000000000000000000000000000000..580c9599fbc79bbb5497d83650961be3946514b0 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable15.lean @@ -0,0 +1,409 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CheckedTables +import OAI.Analysis.LaughlinGap.IntegerFourRows + +namespace OAI + +/-! Sum Table15. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable15 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 944658969540], ![0, 0, 0, 0, 0, 0, 0, -1514205454476, -961494583764]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 15 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1810700626020], ![0, 0, 0, 0, 0, 0, 0, -3036722538564, -809785469064], ![0, 0, 0, 0, 0, 0, 1779840021960, 585677065116, -467701593216]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 15 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2127795323082], ![0, 0, 0, 0, 0, 0, 0, 3076866371436, 1029500485728], ![0, 0, 0, 0, 0, 0, 40191479328, 267808446048, 349292898240], ![0, 0, 0, 0, 0, -180441717456, -166811556912, -14823604224, 41859554880]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 15 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 192354487182], ![0, 0, 0, 0, 0, 0, 0, 2198332099392, -2798130406500], ![0, 0, 0, 0, 0, 0, -5901440464920, -642740712900, 380127578688], ![0, 0, 0, 0, 0, 2152310304144, -392030695056, -1613867414016, -635028561024], ![0, 0, 0, 0, 1873731315456, 942016115040, -564532096128, -591825117312, 1630629302016]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 15 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4696595354022], ![0, 0, 0, 0, 0, 0, 0, 659343316632, 2137043002380], ![0, 0, 0, 0, 0, 0, -3843675435600, -6065431295352, -3470688167232], ![0, 0, 0, 0, 0, -5029150598472, 400579034856, 3223718564352, 1897851823296], ![0, 0, 0, 0, -985629957312, -2702332817184, -4956889601664, -3783698016384, 1762593545856], ![0, 0, 0, 2585558207232, 2088801082368, 975225259008, 167370018816, 605504959488, 2327862231552]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 15 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -5586067279650], ![0, 0, 0, 0, 0, 0, 0, -12350792988534, -720933846204], ![0, 0, 0, 0, 0, 0, -3918775780920, 38389684476, 4338071776896], ![0, 0, 0, 0, 0, 1983010629600, -1468628345184, -3737889931776, -2823515433024], ![0, 0, 0, 0, 5222885059392, 2359834036560, 1840515733056, 4247497590336, 5889601386240], ![0, 0, 0, -4540982942496, -7483641381216, -7518868925568, -6211726160640, -5710064899968, -6497580350976], ![0, 0, 5950922769792, 5771000883648, 2923766926080, -1406642485248, -5104402727424, -6450122435328, -5980429458432]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 15 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2164374062994], ![0, 0, 0, 0, 0, 0, 0, -5998536469068, -980852146560], ![0, 0, 0, 0, 0, 0, -4335052553832, -527378999004, 1820672677824], ![0, 0, 0, 0, 0, -1864246400016, -1669732432368, -385349133312, 1854375906240], ![0, 0, 0, 0, 2700943557312, -259022924160, 2471233949184, 7420307321856, 8812117471872], ![0, 0, 0, 2005571952384, -3633169507968, -4102644209664, -1036901978112, -649909877760, -8531502710016], ![0, 0, 3298146563712, 924307255872, -1583097035520, -1751640963072, -159001210368, -1246517445888, -9666428648448], ![0, 418288425984, -3185228547072, -5712042885120, 334901698560, 14168924909568, 19747007115264, -631141834752, -30702230507520]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 15 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -470119924560], ![0, 0, 0, 0, 0, 0, 0, -4015786752978, -1720699727604], ![0, 0, 0, 0, 0, 0, -8860769950032, -2045494620312, 2879073829632], ![0, 0, 0, 0, 0, -13878726733872, -2099358909648, 9024014697984, 11777262566784], ![0, 0, 0, 0, -4345124207424, -340615443168, 6540836125824, 7200658937472, -3496136392320], ![0, 0, 0, 8223310935840, 8255134663776, 7028179686528, 5520831283968, 4255968782208, 3235744512000], ![0, 0, 5672282808192, 364691431104, -5034780791040, -4678297688064, 835473999360, 1227082551552, -16738799041536], ![0, 1218684200448, -1063062274560, -4034979446784, -2401156792320, 5260993959936, 10256436123648, -295110266880, -21688014526464], ![682407677952, 597106718208, -3070834550784, -8530095974400, -6824076779520, 9212503652352, 30025937829888, 29343530151936, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 15 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 75159303912], ![0, 0, 0, 0, 0, 0, 0, 86668825320, 60992508456]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 15 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 283525170984], ![0, 0, 0, 0, 0, 0, 0, -363565245384, 195426101376], ![0, 0, 0, 0, 0, 0, -215892246240, -3072609144, 11422906704]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 15 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -263504808468], ![0, 0, 0, 0, 0, 0, 0, 364049637336, -344306188512], ![0, 0, 0, 0, 0, 0, -43545934080, -13036034880, -21416102928], ![0, 0, 0, 0, 0, 10128520512, -39972161856, -12830341920, 54407989152]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 15 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 514581397308], ![0, 0, 0, 0, 0, 0, 0, 1217439609408, 843125409720], ![0, 0, 0, 0, 0, 0, -64614214368, 318988165320, 1023222644928], ![0, 0, 0, 0, 0, -212674917312, 297857921856, -27740400864, -145950976512], ![0, 0, 0, 0, -453213978624, -69380707968, 38216428800, -295662514752, -444707974656]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 15 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 922123940364], ![0, 0, 0, 0, 0, 0, 0, -905213813328, 103736393640], ![0, 0, 0, 0, 0, 0, 1739021216064, 668075079408, -462592634592], ![0, 0, 0, 0, 0, 975100284576, -76285166496, 332683474992, 585320950368], ![0, 0, 0, 0, 172217662848, 950850857088, 978542906880, 1114305984, -462046337280], ![0, 0, 0, -371394743808, -274321800192, -5566573056, 95374287360, -62749919232, -179656823808]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 15 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1502899594020], ![0, 0, 0, 0, 0, 0, 0, -2726600174892, 1251218163096], ![0, 0, 0, 0, 0, 0, 445831006368, -1000069342008, -662879939568], ![0, 0, 0, 0, 0, -406484508672, 507027041664, 502790730816, -113014601568], ![0, 0, 0, 0, -1190998309248, -514543499712, -1025013492096, -1047895089120, 581323792896], ![0, 0, 0, 177258776640, 961637265600, 1020724964160, 1048744648512, 701258469120, -477051125760], ![0, 0, 181421577216, -128428831872, 284161971456, 1041964361856, 1591693526016, 1570777376256, 1343064019968]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 15 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -594973169604], ![0, 0, 0, 0, 0, 0, 0, -898903032984, 225671339520], ![0, 0, 0, 0, 0, 0, 255380994528, -76255318920, 98607952608], ![0, 0, 0, 0, 0, 266459814720, 126336830400, -272474481312, -785202013728], ![0, 0, 0, 0, -715988135808, -251741318400, -973323318528, -1049184677376, -100234176768], ![0, 0, 0, -796881237504, 692308049664, 540780556800, 312686871552, 1053176813568, 1902150683136], ![0, 0, -206243288064, 127832403072, 506045734656, 227849516928, 9641769984, 796659595776, 1925589169152], ![0, -360454938624, -145648115712, 575342254080, -950775902208, -3357237362688, -1471142559744, 4223795355648, 1153393274880]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 15 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 53838659952], ![0, 0, 0, 0, 0, 0, 0, 64465561116, -250203188664], ![0, 0, 0, 0, 0, 0, 788227395648, -87124285776, 130342331328], ![0, 0, 0, 0, 0, 2715233640768, -732896134080, -1057726030944, -12920371200], ![0, 0, 0, 0, 1210102540416, -533662842240, -1391735026176, 105770947392, 1846004928768], ![0, 0, 0, -919511512128, -1022065336512, -843534736704, -532594725696, 91662024960, 790850598912], ![0, 0, -537599867904, 260901320064, 1167637760256, 378401721984, -678645107712, 729217691136, 4107414795264], ![0, -11142033408, -68102369280, 478886132736, -228140199936, -1884582273024, -1317479251968, 1974968709120, 814755465216], ![314957389824, -157478694912, -314957389824, 196848368640, -944872169472, -4409403457536, -5669233016832, -1102350864384, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 15 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -27268489200], ![0, 0, 0, 0, 0, 0, 0, 22382811600, -22110827280]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 15 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -140235248880], ![0, 0, 0, 0, 0, 0, 0, 102715684080, -102046710240], ![0, 0, 0, 0, 0, 0, 16927893600, 23141119920, 48613408320]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 15 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 385018979160], ![0, 0, 0, 0, 0, 0, 0, -49546505040, 199255340160], ![0, 0, 0, 0, 0, 0, 10273902720, -21699346560, 28056849600], ![0, 0, 0, 0, 0, 23907873600, 41340960960, -20722070400, -4556160]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 15 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -374723561160], ![0, 0, 0, 0, 0, 0, 0, -685616820480, -264623068560], ![0, 0, 0, 0, 0, 0, 329235636960, -491611734480, -273110115840], ![0, 0, 0, 0, 0, -71474767680, -32436926400, 82164689280, -322266430080], ![0, 0, 0, 0, 174978385920, -42347491200, 92416419840, 128715966720, -101263069440]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 15 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -411442929000], ![0, 0, 0, 0, 0, 0, 0, 121274671200, -190728155280], ![0, 0, 0, 0, 0, 0, -871627903680, 66239602080, 76571516160], ![0, 0, 0, 0, 0, -311795651040, -279590900640, -472425466560, 54667313280], ![0, 0, 0, 0, -11819619840, -490076453760, -120000483840, 100280275200, -361855958400], ![0, 0, 0, 28431882240, 10019880960, -93123548160, -84156042240, -40444554240, -141907392000]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 15 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 40877848440], ![0, 0, 0, 0, 0, 0, 0, 325004518440, -679766082480], ![0, 0, 0, 0, 0, 0, 297631644000, 444742086960, -361546939200], ![0, 0, 0, 0, 0, 151939424640, -188186440320, -50210154240, 92529561600], ![0, 0, 0, 0, 400100835840, 270665695680, 597756986880, -272718057600, -922491797760], ![0, 0, 0, 346677630720, -16140430080, -161467044480, -198695975040, 543375573120, 1144828362240], ![0, 0, -394761415680, -110840670720, -169676759040, -376824257280, -420036226560, -130189858560, 31392276480]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 15 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 139050097080], ![0, 0, 0, 0, 0, 0, 0, 314255524560, -196842716160], ![0, 0, 0, 0, 0, 0, 120375555360, -121774549680, -76634559360], ![0, 0, 0, 0, 0, -45997033920, 55057552320, 388969518720, 338287155840], ![0, 0, 0, 0, 328215344640, 257150330880, 337679823360, -38280407040, -226346060160], ![0, 0, 0, 463764879360, -214691374080, -77985530880, -260592537600, -264784665600, 240665829120], ![0, 0, -72472949760, -91363653120, -137068216320, 84073409280, 15155781120, -230220437760, 178227486720], ![0, -45246504960, 145107394560, -308950548480, 431990046720, 701803008000, -1402663219200, -2118518046720, 3145618022400]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 15 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 248235402240], ![0, 0, 0, 0, 0, 0, 0, 302077450680, 58946548080], ![0, 0, 0, 0, 0, 0, 108241707840, -182575254240, -253185198720], ![0, 0, 0, 0, 0, -822411048000, 310222367040, -134998638720, 218396269440], ![0, 0, 0, 0, -598634273280, 501210495360, 193847953920, -354234896640, 47572341120], ![0, 0, 0, -126199576320, -8250297600, 13113498240, -186784513920, -658679898240, -749259694080], ![0, 0, -47062809600, -124735480320, -315244584960, 287264252160, 364391631360, -402756053760, -93166018560], ![0, -68853411840, 139395010560, -144459571200, 273536040960, 614332016640, -476995737600, -990579916800, 2222060359680], ![95441633280, 71581224960, 190883266560, -143162449920, 286324899840, 894765312000, -715812249600, -3006411448320, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 15 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 37493662624], ![0, 0, 0, 0, 0, 0, 0, -20525034592, 14588826912]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 15 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -28262150240], ![0, 0, 0, 0, 0, 0, 0, 87612588256, -73079480704], ![0, 0, 0, 0, 0, 0, 21054417664, -57708219232, -46140933696]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 15 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 64761738928], ![0, 0, 0, 0, 0, 0, 0, -199232515744, 51067623552], ![0, 0, 0, 0, 0, 0, 22957326336, 11736862464, -36853804224], ![0, 0, 0, 0, 0, -50134321664, -17066710528, 18938521728, -92845042304]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 15 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -113237817104], ![0, 0, 0, 0, 0, 0, 0, 382433706240, 270140439264], ![0, 0, 0, 0, 0, 0, -130392591616, 229271858592, -7718568704], ![0, 0, 0, 0, 0, 154209617408, -156277893632, 212520031104, 408027566336], ![0, 0, 0, 0, -70262857728, 60359885824, -107485665280, 111536276736, 65336865280]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 15 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -427249377232], ![0, 0, 0, 0, 0, 0, 0, 264424743616, -105902159584], ![0, 0, 0, 0, 0, 0, 483284612608, 86766031552, 67958698624], ![0, 0, 0, 0, 0, 149637886720, 568433945856, 127013668160, -151233516416], ![0, 0, 0, 0, -75352761344, 267920751616, -165082222592, 178321708288, 157590880000], ![0, 0, 0, 68480978944, 47940100096, 88756154368, 46798065664, 65614673920, 171742643200]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 15 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1156240752], ![0, 0, 0, 0, 0, 0, 0, 1102026605392, -820301283104], ![0, 0, 0, 0, 0, 0, -682375764224, 183831068064, 219216181184], ![0, 0, 0, 0, 0, -111343110144, 33811764224, 41050348288, -39079471488], ![0, 0, 0, 0, -73158880256, -318487497216, -81652673536, 930782648704, -358858790400], ![0, 0, 0, -424696792576, -191125254656, 101619571200, -223457887744, -1073810888960, -221581209600], ![0, 0, 139062841344, -96556622848, -101016946688, -10261171200, -187266150400, -577078976000, -454534886400]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 15 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 136829334256], ![0, 0, 0, 0, 0, 0, 0, 156852983200, -188810549248], ![0, 0, 0, 0, 0, 0, -104860982016, 140170670944, -97846715776], ![0, 0, 0, 0, 0, 20403901952, -223386164736, -436205097344, 246117858944], ![0, 0, 0, 0, -207665253376, -243094104064, 58634541056, 231172831232, 67209578240], ![0, 0, 0, -320257781760, 103824193536, 54396260352, 125628604416, -488517888000, -381138547200], ![0, 0, 64261550080, -7086808064, -53349373952, -168891806720, -18384343040, -198952256000, -722097689600], ![0, 126078320640, -142715486208, 333082017792, -322677473280, 351605391360, 1695574425600, -257458790400, -2038826496000]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 15 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 118085192768], ![0, 0, 0, 0, 0, 0, 0, -296816209296, 69230211488], ![0, 0, 0, 0, 0, 0, -203070984704, 318270982592, 29618012160], ![0, 0, 0, 0, 0, 284327640576, 197401218560, -142294163072, -542580474624], ![0, 0, 0, 0, 432948196352, -442397770752, 198467153920, -171342913792, -154025583360], ![0, 0, 0, 380257428992, 218095686144, 97386558976, 398564730368, 668134590720, 173814630400], ![0, 0, 120888578048, -26899633152, -25283815424, -432776780800, -100744949760, -72492992000, -1290084275200], ![0, 39873101824, -130327101440, 181181390848, -203344707584, 100808212480, 951809228800, -120382976000, -1440224307200], ![12725551104, 159069388800, 38176653312, 384947920896, 63627755520, 477208166400, 2226971443200, 1948600012800, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 15 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -25037341632], ![0, 0, 0, 0, 0, 0, 0, 8023037760, -10074417984]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 15 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2699734464], ![0, 0, 0, 0, 0, 0, 0, -72322491456, -112993920], ![0, 0, 0, 0, 0, 0, -28150376832, 104551809984, 67447392768]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 15 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -99643289760], ![0, 0, 0, 0, 0, 0, 0, 236975414976, -50682456576], ![0, 0, 0, 0, 0, 0, -79538130432, 20312077824, -267646464], ![0, 0, 0, 0, 0, 98603382528, -50541930240, 83303937024, 135728676864]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 15 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 200345245920], ![0, 0, 0, 0, 0, 0, 0, -420662725632, -261042030144], ![0, 0, 0, 0, 0, 0, -80496035712, 363734027712, -644929311744], ![0, 0, 0, 0, 0, -161769026304, 244021377792, -655807890432, 160240020480], ![0, 0, 0, 0, -29298143232, -28816593408, -78461343744, -174805807104, 393462724608]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 15 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 412785412704], ![0, 0, 0, 0, 0, 0, 0, -341364811392, 199568067264], ![0, 0, 0, 0, 0, 0, -376855740672, -628602076032, 510473745408], ![0, 0, 0, 0, 0, -138759410304, -772236649344, 250194989568, -468040329216], ![0, 0, 0, 0, 207947787264, 18740639232, 65890277376, -76901363712, 928204526592], ![0, 0, 0, -96390426624, -21476622336, -4687798272, 39610736640, -13141499904, -18727464960]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 15 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -35208772128], ![0, 0, 0, 0, 0, 0, 0, -998258661216, 845506649664], ![0, 0, 0, 0, 0, 0, 1010270981760, -679920264768, 729025783296], ![0, 0, 0, 0, 0, 200914509312, 53627920896, -142275237888, 205709405184], ![0, 0, 0, 0, -291998168064, 604068952320, -1246080893952, -250231523328, 2100866512896], ![0, 0, 0, 261161255424, 95930402304, -474073801728, 932943025152, 479585313792, -1706789744640], ![0, 0, 172535334912, 284584338432, 213532323840, 99830200320, 567758057472, 690793113600, 137994854400]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 15 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -149905723680], ![0, 0, 0, 0, 0, 0, 0, -199700726976, 219674769408], ![0, 0, 0, 0, 0, 0, -37695041664, 89409050688, 36458711040], ![0, 0, 0, 0, 0, -92017310976, 734422093056, -133453200384, -607693031424], ![0, 0, 0, 0, 140137952256, 189488756736, -485139935232, -184903630848, -344082336768], ![0, 0, 0, 145276440576, -131072563200, -278633275392, 521159049216, 732251234304, -845602007040], ![0, 0, 533329920, 100776532992, 168690044928, 20053592064, -1678897152, 362403993600, 64812441600], ![0, 26481475584, 277389066240, -391949254656, 635555414016, -1011627491328, 125743104000, 2648147558400, -2995826688000]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 15 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -142443313920], ![0, 0, 0, 0, 0, 0, 0, 191807326944, -13828209984], ![0, 0, 0, 0, 0, 0, 87823826688, -213267926400, -55422901248], ![0, 0, 0, 0, 0, -115118767872, -604092373248, 954251258880, -280160658432], ![0, 0, 0, 0, -394934234112, 321534097920, 26925139968, 228195864576, -1186118931456], ![0, 0, 0, -343653106176, -68204901888, 139461829632, -449752863744, 3435420672, 700239790080], ![0, 0, -78921455616, 190012265472, 210167918592, 161044862976, -295654477824, 345817958400, 610930483200], ![0, 12382248960, 101083815936, -335898574848, 297173975040, -701963845632, -227386736640, 1238224896000, -2116247961600], ![0, 28632489984, 343589879808, 0, 687179759616, -286324899840, 0, 2863248998400, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 15 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -25007579520], ![0, 0, 0, 0, 0, 0, 0, 9540955776, 33856530048]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 15 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 285411510912], ![0, 0, 0, 0, 0, 0, 0, 54957581184, -41059881984], ![0, 0, 0, 0, 0, 0, 31929705984, -310129894272, -42772224]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 15 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -256550361408], ![0, 0, 0, 0, 0, 0, 0, -113552495232, -282614644224], ![0, 0, 0, 0, 0, 0, 220973051904, -6560683008, 26747542272], ![0, 0, 0, 0, 0, -182508733440, 214244557824, -440951892480, 409305076224]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 15 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -8966134848], ![0, 0, 0, 0, 0, 0, 0, 784955753472, 574982871936], ![0, 0, 0, 0, 0, 0, -446648547840, 264142741632, -516852458496], ![0, 0, 0, 0, 0, -189229421568, 429706877952, -220209673728, -209148487680], ![0, 0, 0, 0, 218436894720, -148136491008, 897263972352, -1201557451776, 558579732480]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 15 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 397641892032], ![0, 0, 0, 0, 0, 0, 0, -82267882752, 530318388864], ![0, 0, 0, 0, 0, 0, 1285554699264, 347411556096, 269855764992], ![0, 0, 0, 0, 0, 128603684352, 41309925888, 1037796849408, -1332368835072], ![0, 0, 0, 0, -467886397440, -584537597952, 1184595320832, -2911160153088, 796516571136], ![0, 0, 0, -13328916480, -194341847040, -305586462720, -200252203008, -253054500864, -429080272896]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 15 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 190822796736], ![0, 0, 0, 0, 0, 0, 0, -590145876672, 702388866432], ![0, 0, 0, 0, 0, 0, -788244238848, -1315368869760, 1060954557696], ![0, 0, 0, 0, 0, -688790446080, 126926063616, -241377438720, 284901112320], ![0, 0, 0, 0, 994484705280, -1155080745984, 4263376803840, -5773429618176, 4359315197952], ![0, 0, 0, 643308272640, 687536256000, 1216252849152, -1914100159488, 4694769260544, -903923023872], ![0, 0, 0, 340216842240, 781629911040, 826885306368, 161913962496, 1890239729664, 1058906382336]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 15 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -39702797376], ![0, 0, 0, 0, 0, 0, 0, -194875165056, 256774053888], ![0, 0, 0, 0, 0, 0, 346881722880, -651304545408, 247484818944], ![0, 0, 0, 0, 0, 261260516352, -1856331451392, 3325271195136, -3937531783680], ![0, 0, 0, 0, -19473991680, 129240748032, 766942826496, 698986438656, 519410817024], ![0, 0, 0, 356301496320, 367227801600, 734842183680, -2555508375552, 2682597654528, -885894991872], ![0, 0, 0, -4194600960, 39139921920, 961346242560, 76046598144, 1064729554944, 1648262651904], ![0, 0, 0, 970987438080, -1225952133120, 776789950464, -5845473165312, 1165184925696, 3954491228160]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 15 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, -150639236352], ![0, 0, 0, 0, 0, 0, 0, -14939901504, -68564436864], ![0, 0, 0, 0, 0, 0, 255570349056, -86547504384, 297248117760], ![0, 0, 0, 0, 0, 377683418112, -173588591616, 535220285952, -1771446183936], ![0, 0, 0, 0, 342057154560, -24308140032, -1956879851520, 4330652451840, -1882025097216], ![0, 0, 0, -416985676800, -919176360960, -812354374656, -247192366080, -2637584750592, -225052016640], ![0, 0, 0, -210545448960, 26924789760, 1677387503616, 716825100288, 1098617524224, 3053681123328], ![0, 0, 0, 454015795200, -1097899376640, 363212636160, -3572702183424, 544818954240, 2793447309312], ![0, 0, 0, 1049857966080, 0, 839886372864, -5039318237184, -3779488677888, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 15 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 248083300608], ![0, 0, 0, 0, 0, 0, 0, -144870925056, -100670499072]] +lemma s_6_0_checked : ∀ i k : Fin 9, fourSumInteger 0 15 13 i k = s_6_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1811515580160], ![0, 0, 0, 0, 0, 0, 0, 769658343168, 15598742016], ![0, 0, 0, 0, 0, 0, 132516933120, 823024460544, -154242536448]] +lemma s_6_1_checked : ∀ i k : Fin 9, fourSumInteger 1 15 13 i k = s_6_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1777066042752], ![0, 0, 0, 0, 0, 0, 0, -539315901696, 1496710465536], ![0, 0, 0, 0, 0, 0, -866111600640, -154404636672, -220854746112], ![0, 0, 0, 0, 0, -169987783680, 584184167424, -2298636527616, 1315244316672]] +lemma s_6_2_checked : ∀ i k : Fin 9, fourSumInteger 2 15 13 i k = s_6_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -738746346624], ![0, 0, 0, 0, 0, 0, 0, -3038545416192, -1774217812224], ![0, 0, 0, 0, 0, 0, 3148035331584, -1882630354176, 4118354313216], ![0, 0, 0, 0, 0, 2676663475200, -3953849822208, 7446626863104, -1837437229056], ![0, 0, 0, 0, 0, 138607552512, 1902123565056, -2612027658240, 3595952295936]] +lemma s_6_3_checked : ∀ i k : Fin 9, fourSumInteger 3 15 13 i k = s_6_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -3970975831680], ![0, 0, 0, 0, 0, 0, 0, 1529329731072, -2875006607616], ![0, 0, 0, 0, 0, 0, -5663306947584, 878583433728, -2295600992256], ![0, 0, 0, 0, 0, 3192369523200, 2327255563776, 3464219286528, 368898816000], ![0, 0, 0, 0, 0, -2618245453824, 2115969343488, -8400177696768, 5592328574976], ![0, 0, 0, 0, 0, -207931097088, -1535982649344, -1402267975680, -548441726976]] +lemma s_6_4_checked : ∀ i k : Fin 9, fourSumInteger 4 15 13 i k = s_6_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -288560638080], ![0, 0, 0, 0, 0, 0, 0, 7907092152960, -7181449237248], ![0, 0, 0, 0, 0, 0, 239105957376, 8153517275904, -6525054581760], ![0, 0, 0, 0, 0, 2898776365056, -868735076352, 569368031232, -2579883491328], ![0, 0, 0, 0, 0, -3076059976704, 18545467539456, -27113337698304, 14520744775680], ![0, 0, 0, 0, 0, 10035609053184, -16266044061696, 18807789631488, 6017669898240], ![0, 0, 0, 0, 0, 5307382738944, -2485814403072, 2556356554752, 3273043378176]] +lemma s_6_5_checked : ∀ i k : Fin 9, fourSumInteger 5 15 13 i k = s_6_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 963944741760], ![0, 0, 0, 0, 0, 0, 0, 1978280029440, -1962718298112], ![0, 0, 0, 0, 0, 0, -1281814550016, 2147693653248, -1301866874880], ![0, 0, 0, 0, 0, 1891805819904, -9689067328512, 16076935919616, -17031809034240], ![0, 0, 0, 0, 0, -699534950400, 1662897020928, -1064867561472, 4632702277632], ![0, 0, 0, 0, 0, 5558303342592, -9150205329408, 10952197521408, -4470885838848], ![0, 0, 0, 0, 0, -65435774976, 537926737920, 7040707694592, 6524592881664], ![0, 0, 0, 0, 0, 15147404034048, -37995575574528, -20196538712064, 45696343080960]] +lemma s_6_6_checked : ∀ i k : Fin 9, fourSumInteger 6 15 13 i k = s_6_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 1177911601152], ![0, 0, 0, 0, 0, 0, 0, -1280070599808, 661305106176], ![0, 0, 0, 0, 0, 0, -1646619786240, 1231758967296, -1286763878400], ![0, 0, 0, 0, 0, -558124250112, 1775232476160, -126818605056, 1154558625792], ![0, 0, 0, 0, 0, 3989007120384, -7079957913600, 9307109560320, -11250735175680], ![0, 0, 0, 0, 0, -6504976558080, 5618844481536, -9555161561088, -5816391499776], ![0, 0, 0, 0, 0, -3284509003776, 6849035821056, 13162613747712, 7408414261248], ![0, 0, 0, 0, 0, 7082646405120, -23222564192256, -9443528540160, 32279835574272], ![0, 0, 0, 0, 0, 16377784270848, -21837045694464, -43674091388928, 0]] +lemma s_6_7_checked : ∀ i k : Fin 9, fourSumInteger 7 15 13 i k = s_6_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2206358668800], ![0, 0, 0, 0, 0, 0, 0, 2924021168640, -2266678402560]] +lemma s_7_0_checked : ∀ i k : Fin 9, fourSumInteger 0 15 15 i k = s_7_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 22748588628480], ![0, 0, 0, 0, 0, 0, 0, -39535331996160, 6918029015040], ![0, 0, 0, 0, 0, 0, 0, 17063219796480, -7537732899840]] +lemma s_7_1_checked : ∀ i k : Fin 9, fourSumInteger 1 15 15 i k = s_7_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -4617469359360], ![0, 0, 0, 0, 0, 0, 0, 10249244628480, 9108859668480], ![0, 0, 0, 0, 0, 0, 0, -2839126118400, -5076273945600], ![0, 0, 0, 0, 0, 0, 0, -1699877836800, 4806350714880]] +lemma s_7_2_checked : ∀ i k : Fin 9, fourSumInteger 2 15 15 i k = s_7_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -4342327292160], ![0, 0, 0, 0, 0, 0, 0, 32592187330560, -10252967662080], ![0, 0, 0, 0, 0, 0, 0, -29559993914880, 38390261944320], ![0, 0, 0, 0, 0, 0, 0, 26766634752000, -36345532354560], ![0, 0, 0, 0, 0, 0, 0, 1386075525120, 14265926737920]] +lemma s_7_3_checked : ∀ i k : Fin 9, fourSumInteger 3 15 15 i k = s_7_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 17437504930560], ![0, 0, 0, 0, 0, 0, 0, 10975114275840, -28814635998720], ![0, 0, 0, 0, 0, 0, 0, -19652128404480, -32648737904640], ![0, 0, 0, 0, 0, 0, 0, 31923695232000, 9473492920320], ![0, 0, 0, 0, 0, 0, 0, -26182454538240, 15869770076160], ![0, 0, 0, 0, 0, 0, 0, -2079310970880, -12039697612800]] +lemma s_7_4_checked : ∀ i k : Fin 9, fourSumInteger 4 15 15 i k = s_7_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -21335557351680], ![0, 0, 0, 0, 0, 0, 0, -52189934734080, 16633449930240], ![0, 0, 0, 0, 0, 0, 0, 76811490961920, -36612450800640], ![0, 0, 0, 0, 0, 0, 0, 28987763650560, -13762453985280], ![0, 0, 0, 0, 0, 0, 0, -30760599767040, 139091006545920], ![0, 0, 0, 0, 0, 0, 0, 100356090531840, -96906307829760], ![0, 0, 0, 0, 0, 0, 0, 53073827389440, 7893305671680]] +lemma s_7_5_checked : ∀ i k : Fin 9, fourSumInteger 5 15 15 i k = s_7_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -6970881265920], ![0, 0, 0, 0, 0, 0, 0, -10438994142720, -10919914536960], ![0, 0, 0, 0, 0, 0, 0, 28366171891200, -23796695070720], ![0, 0, 0, 0, 0, 0, 0, 18918058199040, -77397519513600], ![0, 0, 0, 0, 0, 0, 0, -6995349504000, 12471727656960], ![0, 0, 0, 0, 0, 0, 0, 55583033425920, -54730781614080], ![0, 0, 0, 0, 0, 0, 0, -654357749760, 3707271659520], ![0, 0, 0, 0, 0, 0, 0, 151474040340480, -171361286553600]] +lemma s_7_6_checked : ∀ i k : Fin 9, fourSumInteger 6 15 15 i k = s_7_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 7549224883200], ![0, 0, 0, 0, 0, 0, 0, 35256951924480, -13354294187520], ![0, 0, 0, 0, 0, 0, 0, -6892099568640, -8903598612480], ![0, 0, 0, 0, 0, 0, 0, -5581242501120, 14709554196480], ![0, 0, 0, 0, 0, 0, 0, 39890071203840, -53099684352000], ![0, 0, 0, 0, 0, 0, 0, -65049765580800, 25878892216320], ![0, 0, 0, 0, 0, 0, 0, -32845090037760, 34945223639040], ![0, 0, 0, 0, 0, 0, 0, 70826464051200, -121049383403520], ![0, 0, 0, 0, 0, 0, 0, 163777842708480, 0]] +lemma s_7_7_checked : ∀ i k : Fin 9, fourSumInteger 7 15 15 i k = s_7_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 8 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7], ![s_6_0, s_6_1, s_6_2, s_6_3, s_6_4, s_6_5, s_6_6, s_6_7], ![s_7_0, s_7_1, s_7_2, s_7_3, s_7_4, s_7_5, s_7_6, s_7_7]] +lemma sums_checked : ∀ u : Fin 8, ∀ a i k, fourSumInteger a 15 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k + · exact s_6_0_checked i k + · exact s_6_1_checked i k + · exact s_6_2_checked i k + · exact s_6_3_checked i k + · exact s_6_4_checked i k + · exact s_6_5_checked i k + · exact s_6_6_checked i k + · exact s_6_7_checked i k + · exact s_7_0_checked i k + · exact s_7_1_checked i k + · exact s_7_2_checked i k + · exact s_7_3_checked i k + · exact s_7_4_checked i k + · exact s_7_5_checked i k + · exact s_7_6_checked i k + · exact s_7_7_checked i k +end SumTable15 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable16.lean b/lean/OAI/Analysis/LaughlinGap/SumTable16.lean new file mode 100644 index 0000000000000000000000000000000000000000..25ad40566fa70d939bf1ab204cb5f154596a88c9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable16.lean @@ -0,0 +1,408 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SumTable15 + +namespace OAI + +/-! Sum Table16. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable16 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3517792852860]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 16 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 6830921508840], ![0, 0, 0, 0, 0, 0, 0, -4734158569140, -1886698173360]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 16 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -7085610005760], ![0, 0, 0, 0, 0, 0, 0, -462460146720, -1008836640240], ![0, 0, 0, 0, 0, 0, 1891216799472, 1733122371552, 1274576352192]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 16 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -3420343838340], ![0, 0, 0, 0, 0, 0, 0, 17015131118700, 5632028344800], ![0, 0, 0, 0, 0, 0, -9367043750064, -2377519963104, 1345780166016], ![0, 0, 0, 0, 0, -6010476439968, -1612815876672, 3351118852224, 4472399543040]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 16 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1796581652580], ![0, 0, 0, 0, 0, 0, 0, 12015211888680, 15538928982720], ![0, 0, 0, 0, 0, 0, 9075823356600, -6151561999440, -14929901088960], ![0, 0, 0, 0, 0, -3570345690912, 2999399282880, 9495472052352, 7734401161344], ![0, 0, 0, 0, -7015815206400, -4863240205824, -1996527396864, -833131453440, -3494753213952]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 16 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 27031195182420], ![0, 0, 0, 0, 0, 0, 0, 9816995305260, 830322876240], ![0, 0, 0, 0, 0, 0, -2370250026144, 6442555369536, 11720474415936], ![0, 0, 0, 0, 0, -8345313024048, 373528515360, 2025049211328, -3994382456064], ![0, 0, 0, 0, 15604724335200, 19329979276608, 15395358730752, 9231300304512, 7301325977088], ![0, 0, 0, -23911086239040, -21507009363840, -13446122866176, -4183517065728, 675055290624, -2320295577600]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 16 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 13201607184480], ![0, 0, 0, 0, 0, 0, 0, 11398299618420, 2727400104000], ![0, 0, 0, 0, 0, 0, 13442269080240, 11693848863840, 7506775848000], ![0, 0, 0, 0, 0, 8323680613248, 10211284731648, -2208708682752, -20171926000512], ![0, 0, 0, 0, 307024798080, 10838103564288, 5999846780928, -7013876812800, -11912612464896], ![0, 0, 0, -12417737492160, -4434713162880, 1490894845440, 273513816576, -4870477936896, -1869050726400], ![0, 0, -1923991280640, 13332348057600, 21755062517760, 5823225188352, -26262814076928, -31557091737600, 32130241228800]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 16 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 8901504328860], ![0, 0, 0, 0, 0, 0, 0, 23649418083720, 7872206010240], ![0, 0, 0, 0, 0, 0, 47189837110416, 12034958391456, -19297071640704], ![0, 0, 0, 0, 0, 18309814627104, 1316197506624, -18981933649536, -22910901526656], ![0, 0, 0, 0, -22793062612320, -20206791468864, -15782620998144, -12516218732160, -12362216435712], ![0, 0, 0, -21009974905920, -3466538275200, 9223191065088, 4912416757248, -10554696911616, -9165845145600], ![0, 0, -7293999398400, 2823625559040, 12730016133120, 8861434103808, -8528639268864, -14755513344000, 22696759388160], ![0, -8956600773120, -7677086376960, 8530095974400, 30708345507840, 33779180058624, 3412038389760, -30708345507840, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 16 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 34969941864]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 16 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1231041075264], ![0, 0, 0, 0, 0, 0, 0, 233269954632, -52833821040]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 16 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1160278191072], ![0, 0, 0, 0, 0, 0, 0, 207828713664, 122079033648], ![0, 0, 0, 0, 0, 0, -334064263104, -184587909792, -220438938720]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 16 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -3493756990152], ![0, 0, 0, 0, 0, 0, 0, 671920326792, -1237035983040], ![0, 0, 0, 0, 0, 0, 846648234432, 8250322080, 708165744000], ![0, 0, 0, 0, 0, 1383331847040, -47983643136, -348324085824, 320135092992]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 16 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1819384528104], ![0, 0, 0, 0, 0, 0, 0, -4280109559440, -1072571042400], ![0, 0, 0, 0, 0, 0, -379447781856, 1451905698672, 594115098720], ![0, 0, 0, 0, 0, 414097377408, -1937646686976, -1749323374656, 374083661952], ![0, 0, 0, 0, 1495877560320, 884231901696, 253674769920, 276428325888, 951347764224]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 16 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 7746935233752], ![0, 0, 0, 0, 0, 0, 0, -44286785400, 2184503150544], ![0, 0, 0, 0, 0, 0, -342515082624, -1877867150016, -1368978605280], ![0, 0, 0, 0, 0, 1809148790592, 408927467520, 1632559197984, 1660417304832], ![0, 0, 0, 0, -2604394643136, -3431773460544, -2835372581184, -2578541606784, -2164483436544], ![0, 0, 0, 2173759775616, 2171156782080, 589223826048, -1192466905344, -1990268527104, -1523390229504]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 16 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 2920521352320], ![0, 0, 0, 0, 0, 0, 0, 155155019448, 199512689376], ![0, 0, 0, 0, 0, 0, -2484011065536, -1716804419616, -619346695968], ![0, 0, 0, 0, 0, -1829657187072, -540695071488, 2311322737152, 3237872077440], ![0, 0, 0, 0, 456240415488, -1906347615744, -355407157248, 531629429760, -1359881842176], ![0, 0, 0, 1868075324544, 60419893248, -828346696320, -80412583680, 24538415616, -2585745017856], ![0, 0, 1893425504256, -788927293440, -2506960355328, 2342957101056, 7573702017024, 1893425504256, -10710080409600]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 16 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 630896944392], ![0, 0, 0, 0, 0, 0, 0, -459950167248, 287135644224], ![0, 0, 0, 0, 0, 0, -6531600558912, 1134607956768, 1604669599104], ![0, 0, 0, 0, 0, -4163273592192, 1870607481600, 3520861481280, -93288843648], ![0, 0, 0, 0, 4355183371968, 3782881447488, 3046771041600, 2458123544448, 1799605057536], ![0, 0, 0, 3668580609408, -430862834688, -2475214794624, -257785152768, 1231690876416, -4088601234432], ![0, 0, 885330800640, -368887833600, -2110050269184, 72423217152, 3541323202560, 885330800640, -7565586462720], ![0, -2047223033856, 0, -853009597440, -3070834550784, 0, 8188892135424, 10236115169280, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 16 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -128269661520]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 16 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -118283748000], ![0, 0, 0, 0, 0, 0, 0, 131937534960, -17380492800]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 16 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -46947267840], ![0, 0, 0, 0, 0, 0, 0, -56331285120, -18268103040], ![0, 0, 0, 0, 0, 0, 67453362240, 48729457920, 136686211200]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 16 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1227957949680], ![0, 0, 0, 0, 0, 0, 0, -587503670160, 1150487986560], ![0, 0, 0, 0, 0, 0, 138679907520, -316775965440, -385520403840], ![0, 0, 0, 0, 0, -537035368320, 76127589120, -190328835840, -181807338240]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 16 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 249911204400], ![0, 0, 0, 0, 0, 0, 0, 1361181238560, -397289840640], ![0, 0, 0, 0, 0, 0, -385501644000, 222879888000, 370586578560], ![0, 0, 0, 0, 0, 77432784000, 1080520700160, 167330085120, -86833549440], ![0, 0, 0, 0, -506275123200, -196007961600, 16799185920, -91128407040, -232626746880]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 16 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 254820226320], ![0, 0, 0, 0, 0, 0, 0, -1396700799120, -579769111680], ![0, 0, 0, 0, 0, 0, 527069727360, 612004377600, 80146049280], ![0, 0, 0, 0, 0, -657428650560, -801017627520, -1139109840000, 586255253760], ![0, 0, 0, 0, 384767496960, 767949790080, 952089874560, 873849778560, -293030622720], ![0, 0, 0, 387423505920, 37847546880, 521787720960, 1096547696640, 1205003162880, 893680634880]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 16 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -431326727040], ![0, 0, 0, 0, 0, 0, 0, -589607554800, 212271565440], ![0, 0, 0, 0, 0, 0, 875906391360, 398078588160, -261637411200], ![0, 0, 0, 0, 0, 651379322880, -571891330560, -1003903887360, -486472947840], ![0, 0, 0, 0, -512924206080, 411765488640, 2470533120, 522595814400, 820002712320], ![0, 0, 0, -344787463680, 339544212480, 382354410240, 23063040000, 495159540480, 1318896184320], ![0, 0, -600758231040, 0, 612976066560, -1820601446400, -2011824967680, 2184721735680, 1647704678400]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 16 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -863063501520], ![0, 0, 0, 0, 0, 0, 0, -953115942240, 320272318080], ![0, 0, 0, 0, 0, 0, 906954164160, -97581285120, 732384259200], ![0, 0, 0, 0, 0, 1619230673280, -1331281501440, -316862388480, 707848479360], ![0, 0, 0, 0, -1127211866880, -971299570560, -827205793920, -376334893440, 231809402880], ![0, 0, 0, -948636142080, 685454330880, 896606388480, -295624581120, 317590606080, 2679698672640], ![0, 0, -18570055680, 0, 548949688320, -851279616000, -1334192302080, 1021535539200, 1163936378880], ![0, 262464491520, -524928983040, -524928983040, 0, -1968483686400, -3936967372800, -1574786949120, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 16 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 58231927584]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 16 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -266950682496], ![0, 0, 0, 0, 0, 0, 0, -130312085856, 69775955904]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 16 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 483184789632], ![0, 0, 0, 0, 0, 0, 0, -21712449792, 55048868160], ![0, 0, 0, 0, 0, 0, 23451778560, -77294050176, -58956573312]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 16 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -275215196448], ![0, 0, 0, 0, 0, 0, 0, -292005046368, -323787679488], ![0, 0, 0, 0, 0, 0, -251031535104, 484746389376, -309929325312], ![0, 0, 0, 0, 0, 276778865664, 50221645824, 190874227968, -209484449280]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 16 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -818156062944], ![0, 0, 0, 0, 0, 0, 0, -133220430144, -90243066240], ![0, 0, 0, 0, 0, 0, 286194601728, -864636343488, 172516424832], ![0, 0, 0, 0, 0, -248383521792, -536842586112, 51973956864, -657527788800], ![0, 0, 0, 0, 187421982720, -44370407424, -102874533888, -15591352320, -82888473600]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 16 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2462748254496], ![0, 0, 0, 0, 0, 0, 0, 1690139658144, -678040802880], ![0, 0, 0, 0, 0, 0, -546379846656, -151677013248, -3407631744], ![0, 0, 0, 0, 0, 333239090688, 1211917400064, 38084825472, -1211498012160], ![0, 0, 0, 0, 432257892864, 48229117440, -514049690112, 305052906240, 1253649346560], ![0, 0, 0, -765973447680, -231056265216, -415617162240, -649504880640, -389237276160, -120745497600]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 16 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -562267966464], ![0, 0, 0, 0, 0, 0, 0, 269703477600, -111911839104], ![0, 0, 0, 0, 0, 0, -540804192768, 179170679424, 314908317312], ![0, 0, 0, 0, 0, -269764024320, 795530373120, 311361878016, 206858453760], ![0, 0, 0, 0, 604707575808, 49642328064, -226114732032, -407310796800, 314518187520], ![0, 0, 0, -15387982848, -352656052224, -69189657600, 8007874560, -366121935360, -56710886400], ![0, 0, -108591611904, -40581513216, -368867082240, 1198330675200, -655372615680, -2317129113600, 2621348352000]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 16 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 450689731488], ![0, 0, 0, 0, 0, 0, 0, 627283015104, -391095757824], ![0, 0, 0, 0, 0, 0, 307171748352, -1001759062656, 9800886528], ![0, 0, 0, 0, 0, -891450491904, 731990525952, -286406881536, 456426604800], ![0, 0, 0, 0, 16033586688, 81637581312, 73672026624, -556043109120, -726409082880], ![0, 0, 0, 214064729088, -676260630528, -157966986240, 401950402560, -532437788160, -534564172800], ![0, 0, -165248188416, 133655175168, -186784530432, 846499184640, -20258242560, -1083446784000, 1851716966400], ![0, 286324899840, 229059919872, 104985796608, -286324899840, 858974699520, 0, -2505342873600, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 16 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -9937318464]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 16 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 84258958464], ![0, 0, 0, 0, 0, 0, 0, 69224778432, -81759552768]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 16 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -245212139520], ![0, 0, 0, 0, 0, 0, 0, 72893763072, -130250108160], ![0, 0, 0, 0, 0, 0, -85419097344, 153797908992, -161443129344]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 16 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 121129136064], ![0, 0, 0, 0, 0, 0, 0, 918403980480, -510401106432], ![0, 0, 0, 0, 0, 0, 64013951232, -155831609856, 765156467712], ![0, 0, 0, 0, 0, -139217379840, -269662675968, 247750656000, 156167571456]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 16 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 505024178112], ![0, 0, 0, 0, 0, 0, 0, -307708385664, 735228681216], ![0, 0, 0, 0, 0, 0, 254948410752, 878834536704, -288624795648], ![0, 0, 0, 0, 0, 357532890624, -99247604736, 591242477568, 472910072832], ![0, 0, 0, 0, 11766128640, 232058093568, 140056928256, 120526036992, 270206078976]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 16 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 241669309248], ![0, 0, 0, 0, 0, 0, 0, -1388857743168, 845105495808], ![0, 0, 0, 0, 0, 0, 585329966592, 16777731072, -19975173120], ![0, 0, 0, 0, 0, -258551983872, -1658044620288, 1940418379776, -702828140544], ![0, 0, 0, 0, -1158338237952, -375859126272, 295576845312, -1870660666368, -325696720896], ![0, 0, 0, 559105741824, -243779708928, -81836009472, -77277118464, -785621514240, -567152640000]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 16 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 241958518272], ![0, 0, 0, 0, 0, 0, 0, 94202528064, -406787100672], ![0, 0, 0, 0, 0, 0, 433842958080, -971822919168, 699653025792], ![0, 0, 0, 0, 0, 20709255168, -842734878720, -34625224704, -395662095360], ![0, 0, 0, 0, -817727576064, -243670769664, 711918993408, -614376087552, -303013103616], ![0, 0, 0, 104486710272, 256442296320, -345183885312, -36294967296, -212866467840, -920309760000], ![0, 0, 436277919744, -93603004416, 159777423360, -587923881984, 2572701696000, 0, -2995826688000]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 16 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 70863099840], ![0, 0, 0, 0, 0, 0, 0, -43825464192, -132448078848], ![0, 0, 0, 0, 0, 0, -415678077696, 1331329199616, -823052848128], ![0, 0, 0, 0, 0, 668438862336, 40179987456, -666063740928, -464311729152], ![0, 0, 0, 0, 828712797696, 379428618240, 504432854016, 1305649972224, 367438528512], ![0, 0, 0, 94398022656, 627197835264, -671120443392, -342121070592, 22195169280, -1582313472000], ![0, 0, 175377309696, -272712548352, 112866557952, -503847862272, 1374656937984, 0, -2116247961600], ![0, 28632489984, 515384819712, 534473146368, 687179759616, 171794939904, 2863248998400, 2863248998400, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 16 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -28277800320]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 16 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 9856450560], ![0, 0, 0, 0, 0, 0, 0, 100941033600, 158577112320]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 16 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -224074329600], ![0, 0, 0, 0, 0, 0, 0, -87586329600, 114735118080], ![0, 0, 0, 0, 0, 0, 95516838912, -68563849728, 513832653312]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 16 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -34421988480], ![0, 0, 0, 0, 0, 0, 0, -529201875840, -1424819235840], ![0, 0, 0, 0, 0, 0, 685422498816, -1853539167744, 1045232787456], ![0, 0, 0, 0, 0, -16035452928, 436988141568, -1286871438336, 1258892574720]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 16 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 430167788160], ![0, 0, 0, 0, 0, 0, 0, -716955951360, 737940318720], ![0, 0, 0, 0, 0, 0, -1820747512320, 299557589760, -2718339064320], ![0, 0, 0, 0, 0, -153232730112, 1099101696000, -1942331347968, 2777833242624], ![0, 0, 0, 0, -220999680000, -413075841024, 30721253376, -107658608640, -121474670592]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 16 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4221087615360], ![0, 0, 0, 0, 0, 0, 0, -254007937920, 3210939367680], ![0, 0, 0, 0, 0, 0, -646357223424, -237221428224, 1067784638976], ![0, 0, 0, 0, 0, 586987011072, 456893521920, -3270205711872, 6289659273216], ![0, 0, 0, 0, 1974152801280, -549627927552, 845691466752, 2092966182912, -4472212242432], ![0, 0, 0, 340216842240, 1462063595520, 635668813824, 1305737613312, 1890239729664, 303588679680]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 16 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 630120437760], ![0, 0, 0, 0, 0, 0, 0, -177580613760, 918154913280], ![0, 0, 0, 0, 0, 0, 445810252800, 1212738024960, -2842727078400], ![0, 0, 0, 0, 0, 328903077888, 490818121728, 543103131648, -860973391872], ![0, 0, 0, 0, 1079830794240, -254060961792, -1005263880192, 2045578444800, -2985763393536], ![0, 0, 0, -4194600960, 30750720000, 1002725222400, 22922735616, 1064729554944, 142587371520], ![0, 0, 0, 970987438080, 716022743040, -1369156681728, -1184733462528, 5825924628480, -6590818713600]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 16 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -673400112000], ![0, 0, 0, 0, 0, 0, 0, -677206590720, 816476728320], ![0, 0, 0, 0, 0, 0, -519461673984, 552936823296, -2759842381824], ![0, 0, 0, 0, 0, -978049222656, -936736813056, 3393827103744, -3925583794176], ![0, 0, 0, 0, -1753147714560, -46547026944, -1278424249344, -628358184960, 1479602454528], ![0, 0, 0, -210545448960, -394166108160, 2204236412928, -399551066112, 1098617524224, 1344047063040], ![0, 0, 0, 454015795200, -189867786240, -1059925819392, -1393426366464, 2724094771200, -4655745515520], ![0, 0, 0, 1049857966080, 2099715932160, 839886372864, 0, 6299147796480, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 16 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 225255064320]] +lemma s_6_0_checked : ∀ i k : Fin 9, fourSumInteger 0 16 13 i k = s_6_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -632712098304], ![0, 0, 0, 0, 0, 0, 0, -1452071512320, 221147756544]] +lemma s_6_1_checked : ∀ i k : Fin 9, fourSumInteger 1 16 13 i k = s_6_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 381033050112], ![0, 0, 0, 0, 0, 0, 0, 224145512448, 147447066624], ![0, 0, 0, 0, 0, 0, 470858978304, -2185311338496, 2407899985920]] +lemma s_6_2_checked : ∀ i k : Fin 9, fourSumInteger 2 16 13 i k = s_6_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 568914128640], ![0, 0, 0, 0, 0, 0, 0, 2058702167808, 2007652128768], ![0, 0, 0, 0, 0, 0, -2169407505408, 5662184546304, -4668529502208], ![0, 0, 0, 0, 0, 138607552512, 1994528600064, -2612027658240, 5899230425088]] +lemma s_6_3_checked : ∀ i k : Fin 9, fourSumInteger 3 16 13 i k = s_6_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 19361422080], ![0, 0, 0, 0, 0, 0, 0, 3498867220992, -885845655552], ![0, 0, 0, 0, 0, 0, 4455501912576, 1335972937728, -299087652864], ![0, 0, 0, 0, 0, -2618245453824, 370472374272, -8400177696768, 9977653610496], ![0, 0, 0, 0, 0, -207931097088, -1674603380736, -1540888707072, -1487255937024]] +lemma s_6_4_checked : ∀ i k : Fin 9, fourSumInteger 4 16 13 i k = s_6_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -12482956392192], ![0, 0, 0, 0, 0, 0, 0, -2088014852352, -6880791650304], ![0, 0, 0, 0, 0, 0, 1063782500352, -1363149545472, -1898308718592], ![0, 0, 0, 0, 0, -3076059976704, 16494760888320, -27113337698304, 36324794068992], ![0, 0, 0, 0, 0, 10035609053184, -9575638026240, 25498195666944, -14634464452608], ![0, 0, 0, 0, 0, 5307382738944, 1052440756224, 9632866873344, 2688962445312]] +lemma s_6_5_checked : ∀ i k : Fin 9, fourSumInteger 5 16 13 i k = s_6_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1321886472192], ![0, 0, 0, 0, 0, 0, 0, -1634462598912, -316497831936], ![0, 0, 0, 0, 0, 0, -8427863448576, 14815732039680, -24439675054080], ![0, 0, 0, 0, 0, -699534950400, 1196540387328, -1064867561472, 5763406252032], ![0, 0, 0, 0, 0, 5558303342592, -5444669767680, 14657733083136, -16318038257664], ![0, 0, 0, 0, 0, -65435774976, 494302887936, 6953459994624, 3756599328768], ![0, 0, 0, 0, 0, 15147404034048, -27897306218496, 10098269356032, 0]] +lemma s_6_6_checked : ∀ i k : Fin 9, fourSumInteger 6 16 13 i k = s_6_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 2494297099008], ![0, 0, 0, 0, 0, 0, 0, 2150705576448, -1423938447360], ![0, 0, 0, 0, 0, 0, 1403149642752, 245264228352, 1031926511616], ![0, 0, 0, 0, 0, 3989007120384, -4420619833344, 9307109560320, -18114599872512], ![0, 0, 0, 0, 0, -6504976558080, 1282193442816, -13891812599808, 1327545483264], ![0, 0, 0, 0, 0, -3284509003776, 4659363151872, 8783268409344, 8363570282496], ![0, 0, 0, 0, 0, 7082646405120, -18500799922176, 4721764270080, 0], ![0, 0, 0, 0, 0, 16377784270848, -10918522847232, 0, 0]] +lemma s_6_7_checked : ∀ i k : Fin 9, fourSumInteger 7 16 13 i k = s_6_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2266678402560]] +lemma s_7_0_checked : ∀ i k : Fin 9, fourSumInteger 0 16 15 i k = s_7_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 6918029015040], ![0, 0, 0, 0, 0, 0, 0, 17063219796480, -7537732899840]] +lemma s_7_1_checked : ∀ i k : Fin 9, fourSumInteger 1 16 15 i k = s_7_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 9108859668480], ![0, 0, 0, 0, 0, 0, 0, -2839126118400, -5076273945600], ![0, 0, 0, 0, 0, 0, 0, -1699877836800, 4806350714880]] +lemma s_7_2_checked : ∀ i k : Fin 9, fourSumInteger 2 16 15 i k = s_7_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -10252967662080], ![0, 0, 0, 0, 0, 0, 0, -29559993914880, 38390261944320], ![0, 0, 0, 0, 0, 0, 0, 26766634752000, -36345532354560], ![0, 0, 0, 0, 0, 0, 0, 1386075525120, 14265926737920]] +lemma s_7_3_checked : ∀ i k : Fin 9, fourSumInteger 3 16 15 i k = s_7_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -28814635998720], ![0, 0, 0, 0, 0, 0, 0, -19652128404480, -32648737904640], ![0, 0, 0, 0, 0, 0, 0, 31923695232000, 9473492920320], ![0, 0, 0, 0, 0, 0, 0, -26182454538240, 15869770076160], ![0, 0, 0, 0, 0, 0, 0, -2079310970880, -12039697612800]] +lemma s_7_4_checked : ∀ i k : Fin 9, fourSumInteger 4 16 15 i k = s_7_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 16633449930240], ![0, 0, 0, 0, 0, 0, 0, 76811490961920, -36612450800640], ![0, 0, 0, 0, 0, 0, 0, 28987763650560, -13762453985280], ![0, 0, 0, 0, 0, 0, 0, -30760599767040, 139091006545920], ![0, 0, 0, 0, 0, 0, 0, 100356090531840, -96906307829760], ![0, 0, 0, 0, 0, 0, 0, 53073827389440, 7893305671680]] +lemma s_7_5_checked : ∀ i k : Fin 9, fourSumInteger 5 16 15 i k = s_7_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -10919914536960], ![0, 0, 0, 0, 0, 0, 0, 28366171891200, -23796695070720], ![0, 0, 0, 0, 0, 0, 0, 18918058199040, -77397519513600], ![0, 0, 0, 0, 0, 0, 0, -6995349504000, 12471727656960], ![0, 0, 0, 0, 0, 0, 0, 55583033425920, -54730781614080], ![0, 0, 0, 0, 0, 0, 0, -654357749760, 3707271659520], ![0, 0, 0, 0, 0, 0, 0, 151474040340480, -171361286553600]] +lemma s_7_6_checked : ∀ i k : Fin 9, fourSumInteger 6 16 15 i k = s_7_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -13354294187520], ![0, 0, 0, 0, 0, 0, 0, -6892099568640, -8903598612480], ![0, 0, 0, 0, 0, 0, 0, -5581242501120, 14709554196480], ![0, 0, 0, 0, 0, 0, 0, 39890071203840, -53099684352000], ![0, 0, 0, 0, 0, 0, 0, -65049765580800, 25878892216320], ![0, 0, 0, 0, 0, 0, 0, -32845090037760, 34945223639040], ![0, 0, 0, 0, 0, 0, 0, 70826464051200, -121049383403520], ![0, 0, 0, 0, 0, 0, 0, 163777842708480, 0]] +lemma s_7_7_checked : ∀ i k : Fin 9, fourSumInteger 7 16 15 i k = s_7_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 8 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7], ![s_6_0, s_6_1, s_6_2, s_6_3, s_6_4, s_6_5, s_6_6, s_6_7], ![s_7_0, s_7_1, s_7_2, s_7_3, s_7_4, s_7_5, s_7_6, s_7_7]] +lemma sums_checked : ∀ u : Fin 8, ∀ a i k, fourSumInteger a 16 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k + · exact s_6_0_checked i k + · exact s_6_1_checked i k + · exact s_6_2_checked i k + · exact s_6_3_checked i k + · exact s_6_4_checked i k + · exact s_6_5_checked i k + · exact s_6_6_checked i k + · exact s_6_7_checked i k + · exact s_7_0_checked i k + · exact s_7_1_checked i k + · exact s_7_2_checked i k + · exact s_7_3_checked i k + · exact s_7_4_checked i k + · exact s_7_5_checked i k + · exact s_7_6_checked i k + · exact s_7_7_checked i k +end SumTable16 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable17.lean b/lean/OAI/Analysis/LaughlinGap/SumTable17.lean new file mode 100644 index 0000000000000000000000000000000000000000..d3173ab47be2709359495e7a9ba46ccce426d8ad --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable17.lean @@ -0,0 +1,457 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CheckedTables +import OAI.Analysis.LaughlinGap.IntegerFourRows + +namespace OAI + +/-! Sum Table17. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable17 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 17 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 11308748468160]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 17 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1677591389760], ![0, 0, 0, 0, 0, 0, 0, -7614466983552, -7040504245632]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 17 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -42768636768000], ![0, 0, 0, 0, 0, 0, 0, 30521855405184, 13468078825344], ![0, 0, 0, 0, 0, 0, 17066023822848, 2286519535872, -12294511367424]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 17 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -31587952830720], ![0, 0, 0, 0, 0, 0, 0, -12751474781760, 24887796785280], ![0, 0, 0, 0, 0, 0, 26926883343360, 6703494091008, -10920118095744], ![0, 0, 0, 0, 0, 13874518834176, 6368175830016, -878118878208, -2148286373376]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 17 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -22473227874240], ![0, 0, 0, 0, 0, 0, 0, -496060621056, -20954543740416], ![0, 0, 0, 0, 0, 0, 2725255653120, -20772014110848, -26044569298176], ![0, 0, 0, 0, 0, -45378440435328, -41705199279744, -19629275293056, 5834983604736], ![0, 0, 0, 0, 72270234516480, 59043205148928, 36985021032960, 19695314386176, 21383418541056]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 17 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -27014401814400], ![0, 0, 0, 0, 0, 0, 0, -50797536366720, -44637486791040], ![0, 0, 0, 0, 0, 0, -66000511729152, -57715464947712, -16586699555712], ![0, 0, 0, 0, 0, -26031822136320, -37087643873280, -7422313147392, 41191765764864], ![0, 0, 0, 0, 33378968663040, 10773684649728, 209807549952, 10807524938496, 31551086121984], ![0, 0, 0, 3791036620800, -46189338624000, -65354946269184, -20237293080576, 52384772284416, 39270294835200]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 17 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -56622943977600], ![0, 0, 0, 0, 0, 0, 0, -136417959739776, -46281449824896], ![0, 0, 0, 0, 0, 0, -62891351018496, -8089151406336, 47601349471104], ![0, 0, 0, 0, 0, 47195869488768, 33147833566848, 17890993321344, 9214939109376], ![0, 0, 0, 0, 54634143083520, 6047245171968, -15918167096832, 10849911511296, 64127513269248], ![0, 0, 0, 29055292231680, -6250777927680, -31922899666944, -17988420003840, 24494152151040, 27740483696640], ![0, 0, 61416691015680, 51180575846400, -6824076779520, -76770863769600, -94172259557376, -37532422287360, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 17 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 17 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 266599249488]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 17 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -577263752208], ![0, 0, 0, 0, 0, 0, 0, 1240812020448, 883392750240]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 17 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -3406319332416], ![0, 0, 0, 0, 0, 0, 0, -1850055828192, -1120110790656], ![0, 0, 0, 0, 0, 0, -2956557956352, 839222155200, 1451178533376]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 17 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 8504919769632], ![0, 0, 0, 0, 0, 0, 0, -4144543610064, -5973764583072], ![0, 0, 0, 0, 0, 0, -3371493565440, 2170918985664, 1148400025344], ![0, 0, 0, 0, 0, -3445887244800, -1379152879104, -156963096576, -831044358144]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 17 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2133684689136], ![0, 0, 0, 0, 0, 0, 0, 3698067667008, 5363250441120], ![0, 0, 0, 0, 0, 0, 871849410432, 2723415950112, -248769151488], ![0, 0, 0, 0, 0, 10246965368640, 8172440308032, 4376417760000, 2439027182592], ![0, 0, 0, 0, -12016956247296, -9290693892480, -4643959896576, -1622056550400, -2312720796672]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 17 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2301970633248], ![0, 0, 0, 0, 0, 0, 0, 8248743236448, 6060601239264], ![0, 0, 0, 0, 0, 0, 13962438986496, 5949149606400, -2461557466368], ![0, 0, 0, 0, 0, 5900016105984, 5635515325440, -1696393340928, -5508339572736], ![0, 0, 0, 0, -6650357505792, -991879464576, 57256303104, -2632085913600, -2956472183808], ![0, 0, 0, -5901594716160, 6013454413824, 8568064327680, -4685914202112, -13253978529792, 6426048245760]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 17 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2850649868352], ![0, 0, 0, 0, 0, 0, 0, 10395039296928, -2706118491648], ![0, 0, 0, 0, 0, 0, 10349271668736, -5085790607040, -7440173275392], ![0, 0, 0, 0, 0, -11087485561152, -7781853887808, -5398671852288, -4334541539328], ![0, 0, 0, 0, -11854183461120, 651784189056, 2873945378304, -4525416529920, -7583123598336], ![0, 0, 0, -5487744058368, 1873938333696, 6052469170176, -144846434304, -6197315604480, 4539351877632], ![0, 0, 4094446067712, -853009597440, 6141669101568, 14330561236992, 8188892135424, -6141669101568, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 17 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 17 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -589922815680]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 17 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 113672560320], ![0, 0, 0, 0, 0, 0, 0, -296761491840, -317468257920]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 17 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 940302570240], ![0, 0, 0, 0, 0, 0, 0, -453386524800, 1185629639040], ![0, 0, 0, 0, 0, 0, 773951270400, -279742045440, 278185332480]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 17 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -786834216960], ![0, 0, 0, 0, 0, 0, 0, 3230316048960, 578270647680], ![0, 0, 0, 0, 0, 0, -28101258240, -1222611498240, 795685714560], ![0, 0, 0, 0, 0, 1499680680960, 469055431680, 202384512000, 663008924160]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 17 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3806992812480], ![0, 0, 0, 0, 0, 0, 0, -2671748217600, -1472318664960], ![0, 0, 0, 0, 0, 0, -718726821120, 824617073280, 1027569227520], ![0, 0, 0, 0, 0, -3780438794880, -2670930514560, -2253289484160, -1583771650560], ![0, 0, 0, 0, 2622573127680, 1806959996160, 128667348480, -836297890560, -472073564160]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 17 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1667495280000], ![0, 0, 0, 0, 0, 0, 0, -2604774268800, -1509578801280], ![0, 0, 0, 0, 0, 0, -5004315655680, -144757831680, 1136675210880], ![0, 0, 0, 0, 0, -2192574489600, -920540037120, 800630645760, -27907165440], ![0, 0, 0, 0, 2178449602560, -313512418560, -62557355520, 520327146240, -941047050240], ![0, 0, 0, 3398456033280, -1583963504640, -1359543398400, 4542340239360, 2912962314240, -6590818713600]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 17 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3167226226560], ![0, 0, 0, 0, 0, 0, 0, 2061100103040, -58022152320], ![0, 0, 0, 0, 0, 0, -2229461836800, 2769195982080, -177313403520], ![0, 0, 0, 0, 0, 4404511140480, 3125146696320, 2457556717440, 1633637744640], ![0, 0, 0, 0, 4417508198400, -1316484069120, -717928696320, 1580863299840, -1068521287680], ![0, 0, 0, 1589055283200, -1002965483520, -1685030983680, 1730414315520, 1362047385600, -4655745515520], ![0, 0, -3149573898240, 524928983040, -1049857966080, -1968483686400, 3149573898240, 6299147796480, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 17 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 17 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 317334598080]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 17 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 32796275520], ![0, 0, 0, 0, 0, 0, 0, 88241354880, 313111182720]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 17 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1433425593600], ![0, 0, 0, 0, 0, 0, 0, 243834241920, -1038056021760], ![0, 0, 0, 0, 0, 0, -221868165120, -289119456000, -266579381760]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 17 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1751098193280], ![0, 0, 0, 0, 0, 0, 0, -1761942778560, 490376615040], ![0, 0, 0, 0, 0, 0, 1020908421120, 152977409280, -388056203520], ![0, 0, 0, 0, 0, -938438430720, -155728097280, -169069086720, -382806236160]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 17 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2682226344000], ![0, 0, 0, 0, 0, 0, 0, 2103556504320, 373326003840], ![0, 0, 0, 0, 0, 0, 228962012160, -2014713544320, 782772226560], ![0, 0, 0, 0, 0, 1638150044160, 1201640778240, 1582600308480, -194112000000], ![0, 0, 0, 0, 23566018560, 136652006400, 994801704960, 1363494597120, 866460994560]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 17 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -325168782720], ![0, 0, 0, 0, 0, 0, 0, 1409438121600, 152888284800], ![0, 0, 0, 0, 0, 0, 2441212139520, -668697200640, -219417811200], ![0, 0, 0, 0, 0, 970142208000, -351563735040, 173695211520, 351158238720], ![0, 0, 0, 0, -912332359680, 678466575360, 49814446080, 354110123520, 1322460195840], ![0, 0, 0, -1800681799680, 1207698554880, -255929057280, -3052033966080, 1390277468160, 2621348352000]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 17 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1079480893440], ![0, 0, 0, 0, 0, 0, 0, -3131729178240, 1979251150080], ![0, 0, 0, 0, 0, 0, -3518914560, -566490927360, 927554653440], ![0, 0, 0, 0, 0, -2305330997760, -1707267770880, -1181003831040, -154516469760], ![0, 0, 0, 0, -2306427648000, 1593695523840, 34267914240, -70487815680, 2535977364480], ![0, 0, 0, -460389703680, 779333959680, 261908152320, -1713256611840, 650068070400, 1851716966400], ![0, 0, 572649799680, -1574786949120, -381766533120, -858974699520, -4008548597760, -2505342873600, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 17 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 17 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -56159248896]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 17 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -7216270848], ![0, 0, 0, 0, 0, 0, 0, -108116628480, -352374328320]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 17 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2091607160832], ![0, 0, 0, 0, 0, 0, 0, 598093120512, -166402618368], ![0, 0, 0, 0, 0, 0, 88674496512, 834042513408, -433670326272]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 17 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 2235004372992], ![0, 0, 0, 0, 0, 0, 0, 115317505536, 577926644736], ![0, 0, 0, 0, 0, 0, -1703283499008, 770000160768, -1283753659392], ![0, 0, 0, 0, 0, 725304631296, -100575928320, 75222982656, 26917097472]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 17 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 12763968000], ![0, 0, 0, 0, 0, 0, 0, -1987530885120, -329884434432], ![0, 0, 0, 0, 0, 0, 883372578816, 2046330043392, -2800557950976], ![0, 0, 0, 0, 0, -82386060288, -739422716928, -400068836352, 2266296127488], ![0, 0, 0, 0, -1372833767424, -813797677056, -1376286879744, -1148599203840, -420053852160]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 17 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -420352539648], ![0, 0, 0, 0, 0, 0, 0, -798995063808, 559008543744], ![0, 0, 0, 0, 0, 0, -1313608740864, 472706433024, 506869945344], ![0, 0, 0, 0, 0, -95901818880, 924724985856, -721903804416, 1000348858368], ![0, 0, 0, 0, 350702886912, -929944135680, -20279218176, -801864714240, -458861322240], ![0, 0, 0, 451903684608, -1825000390656, 1329405198336, 782624194560, -3707406581760, 2995826688000]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 17 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -522355430400], ![0, 0, 0, 0, 0, 0, 0, 2078450635776, -1150115398656], ![0, 0, 0, 0, 0, 0, 1032858279936, -1487598716928, 1057819290624], ![0, 0, 0, 0, 0, 1048201233408, 953746031616, -220869854208, -972134793216], ![0, 0, 0, 0, 1441370972160, -2080677967872, 461779734528, -990485452800, -1488228065280], ![0, 0, 0, -93958864896, -757942517760, 850550833152, 995540779008, -1733514854400, 2116247961600], ![0, 0, 687179759616, 1336182865920, -687179759616, 629914779648, 1145299599360, -2863248998400, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 17 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 17 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -279107516160]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 17 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -299470152960], ![0, 0, 0, 0, 0, 0, 0, 483114137088, -69239250432]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 17 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 716844395520], ![0, 0, 0, 0, 0, 0, 0, -1887207691776, 3183838377984], ![0, 0, 0, 0, 0, 0, -401219039232, -913470379008, 886263730176]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 17 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1093760785920], ![0, 0, 0, 0, 0, 0, 0, 2302586668800, -3319767052800], ![0, 0, 0, 0, 0, 0, 2299302297600, -755319493632, 2549012944896], ![0, 0, 0, 0, 0, -509902086144, 604631064576, 274797084672, 585444777984]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 17 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4772207320320], ![0, 0, 0, 0, 0, 0, 0, 2652443464704, 1023122901504], ![0, 0, 0, 0, 0, 0, -4309778626560, 2142327593472, -853065117696], ![0, 0, 0, 0, 0, -2830155322368, 961485229056, -4431636228096, -1331989807104], ![0, 0, 0, 0, 2142497280000, 172278847488, 654606458880, -1224780632064, -937470910464]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 17 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -67546237440], ![0, 0, 0, 0, 0, 0, 0, -1432856240640, 1797902599680], ![0, 0, 0, 0, 0, 0, 389346152448, 264056905728, -2802949957632], ![0, 0, 0, 0, 0, -1528005304320, -897707458560, -846476623872, -836850364416], ![0, 0, 0, 0, 22361518080, 1047459883008, -86113640448, 15100563456, -1591227703296], ![0, 0, 0, 970987438080, 2657997619200, -4291893264384, 4660739702784, 1165184925696, -6590818713600]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 17 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1223919375360], ![0, 0, 0, 0, 0, 0, 0, 17728786944, -3216512403456], ![0, 0, 0, 0, 0, 0, -1282143092736, 2661654488064, -2961475393536], ![0, 0, 0, 0, 0, 1052848862208, 161791669248, 3518070319104, 1107449266176], ![0, 0, 0, 0, -815257006080, 2899521681408, -1222134177792, 757963616256, -2516062298112], ![0, 0, 0, 454015795200, 718163804160, -2846276911104, 2179275816960, 544818954240, -4655745515520], ![0, 0, 0, 1049857966080, 4199431864320, 0, 5039318237184, 6299147796480, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 17 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_0_checked : ∀ i k : Fin 9, fourSumInteger 0 17 13 i k = s_6_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1601569102848]] +lemma s_6_1_checked : ∀ i k : Fin 9, fourSumInteger 1 17 13 i k = s_6_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1192585405440], ![0, 0, 0, 0, 0, 0, 0, -1845335771136, 2859708893184]] +lemma s_6_2_checked : ∀ i k : Fin 9, fourSumInteger 2 17 13 i k = s_6_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -5221751648256], ![0, 0, 0, 0, 0, 0, 0, 308857595904, -2653550794752], ![0, 0, 0, 0, 0, 0, 2086933635072, -2796837728256, 6300384989184]] +lemma s_6_3_checked : ∀ i k : Fin 9, fourSumInteger 3 17 13 i k = s_6_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4877074735104], ![0, 0, 0, 0, 0, 0, 0, -5048766108672, -2230206511104], ![0, 0, 0, 0, 0, 0, -1375024594944, -4909183758336, 12247009302528], ![0, 0, 0, 0, 0, -207931097088, -1813224112128, -1402267975680, -820777132032]] +lemma s_6_4_checked : ∀ i k : Fin 9, fourSumInteger 4 17 13 i k = s_6_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2354868612096], ![0, 0, 0, 0, 0, 0, 0, -7160702275584, 618259918848], ![0, 0, 0, 0, 0, 0, 14444054237184, -23011924396032, 39583375822848], ![0, 0, 0, 0, 0, 10035609053184, -2885231990784, 18807789631488, -22365757759488], ![0, 0, 0, 0, 0, 5307382738944, 4590695915520, 9632866873344, 1052440756224]] +lemma s_6_5_checked : ∀ i k : Fin 9, fourSumInteger 5 17 13 i k = s_6_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3841763887104], ![0, 0, 0, 0, 0, 0, 0, 11032120399872, -21527871805440], ![0, 0, 0, 0, 0, 0, 730183753728, -132154294272, 5231213205504], ![0, 0, 0, 0, 0, 5558303342592, -1739134205952, 10952197521408, -20867753127936], ![0, 0, 0, 0, 0, -65435774976, 450679037952, 6953459994624, 494302887936], ![0, 0, 0, 0, 0, 15147404034048, -17799036862464, 20196538712064, -22848171540480]] +lemma s_6_6_checked : ∀ i k : Fin 9, fourSumInteger 6 17 13 i k = s_6_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -373966534656], ![0, 0, 0, 0, 0, 0, 0, 1361512728576, -1051979495424], ![0, 0, 0, 0, 0, 0, -1761281753088, 3988433399808, -17898506655744], ![0, 0, 0, 0, 0, -6504976558080, -3054457595904, -9555161561088, 5020963504128], ![0, 0, 0, 0, 0, -3284509003776, 2469690482688, 8783268409344, 4659363151872], ![0, 0, 0, 0, 0, 7082646405120, -13779035652096, 9443528540160, -16139917787136], ![0, 0, 0, 0, 0, 16377784270848, 0, 21837045694464, 0]] +lemma s_6_7_checked : ∀ i k : Fin 9, fourSumInteger 7 17 13 i k = s_6_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_0_checked : ∀ i k : Fin 9, fourSumInteger 0 17 15 i k = s_7_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -7537732899840]] +lemma s_7_1_checked : ∀ i k : Fin 9, fourSumInteger 1 17 15 i k = s_7_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -5076273945600], ![0, 0, 0, 0, 0, 0, 0, -1699877836800, 4806350714880]] +lemma s_7_2_checked : ∀ i k : Fin 9, fourSumInteger 2 17 15 i k = s_7_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 38390261944320], ![0, 0, 0, 0, 0, 0, 0, 26766634752000, -36345532354560], ![0, 0, 0, 0, 0, 0, 0, 1386075525120, 14265926737920]] +lemma s_7_3_checked : ∀ i k : Fin 9, fourSumInteger 3 17 15 i k = s_7_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -32648737904640], ![0, 0, 0, 0, 0, 0, 0, 31923695232000, 9473492920320], ![0, 0, 0, 0, 0, 0, 0, -26182454538240, 15869770076160], ![0, 0, 0, 0, 0, 0, 0, -2079310970880, -12039697612800]] +lemma s_7_4_checked : ∀ i k : Fin 9, fourSumInteger 4 17 15 i k = s_7_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -36612450800640], ![0, 0, 0, 0, 0, 0, 0, 28987763650560, -13762453985280], ![0, 0, 0, 0, 0, 0, 0, -30760599767040, 139091006545920], ![0, 0, 0, 0, 0, 0, 0, 100356090531840, -96906307829760], ![0, 0, 0, 0, 0, 0, 0, 53073827389440, 7893305671680]] +lemma s_7_5_checked : ∀ i k : Fin 9, fourSumInteger 5 17 15 i k = s_7_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -23796695070720], ![0, 0, 0, 0, 0, 0, 0, 18918058199040, -77397519513600], ![0, 0, 0, 0, 0, 0, 0, -6995349504000, 12471727656960], ![0, 0, 0, 0, 0, 0, 0, 55583033425920, -54730781614080], ![0, 0, 0, 0, 0, 0, 0, -654357749760, 3707271659520], ![0, 0, 0, 0, 0, 0, 0, 151474040340480, -171361286553600]] +lemma s_7_6_checked : ∀ i k : Fin 9, fourSumInteger 6 17 15 i k = s_7_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -8903598612480], ![0, 0, 0, 0, 0, 0, 0, -5581242501120, 14709554196480], ![0, 0, 0, 0, 0, 0, 0, 39890071203840, -53099684352000], ![0, 0, 0, 0, 0, 0, 0, -65049765580800, 25878892216320], ![0, 0, 0, 0, 0, 0, 0, -32845090037760, 34945223639040], ![0, 0, 0, 0, 0, 0, 0, 70826464051200, -121049383403520], ![0, 0, 0, 0, 0, 0, 0, 163777842708480, 0]] +lemma s_7_7_checked : ∀ i k : Fin 9, fourSumInteger 7 17 15 i k = s_7_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_0_checked : ∀ i k : Fin 9, fourSumInteger 0 17 17 i k = s_8_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_1_checked : ∀ i k : Fin 9, fourSumInteger 1 17 17 i k = s_8_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_2_checked : ∀ i k : Fin 9, fourSumInteger 2 17 17 i k = s_8_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_3_checked : ∀ i k : Fin 9, fourSumInteger 3 17 17 i k = s_8_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_4_checked : ∀ i k : Fin 9, fourSumInteger 4 17 17 i k = s_8_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_5_checked : ∀ i k : Fin 9, fourSumInteger 5 17 17 i k = s_8_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_6_checked : ∀ i k : Fin 9, fourSumInteger 6 17 17 i k = s_8_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_7_checked : ∀ i k : Fin 9, fourSumInteger 7 17 17 i k = s_8_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 9 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7], ![s_6_0, s_6_1, s_6_2, s_6_3, s_6_4, s_6_5, s_6_6, s_6_7], ![s_7_0, s_7_1, s_7_2, s_7_3, s_7_4, s_7_5, s_7_6, s_7_7], ![s_8_0, s_8_1, s_8_2, s_8_3, s_8_4, s_8_5, s_8_6, s_8_7]] +lemma sums_checked : ∀ u : Fin 9, ∀ a i k, fourSumInteger a 17 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k + · exact s_6_0_checked i k + · exact s_6_1_checked i k + · exact s_6_2_checked i k + · exact s_6_3_checked i k + · exact s_6_4_checked i k + · exact s_6_5_checked i k + · exact s_6_6_checked i k + · exact s_6_7_checked i k + · exact s_7_0_checked i k + · exact s_7_1_checked i k + · exact s_7_2_checked i k + · exact s_7_3_checked i k + · exact s_7_4_checked i k + · exact s_7_5_checked i k + · exact s_7_6_checked i k + · exact s_7_7_checked i k + · exact s_8_0_checked i k + · exact s_8_1_checked i k + · exact s_8_2_checked i k + · exact s_8_3_checked i k + · exact s_8_4_checked i k + · exact s_8_5_checked i k + · exact s_8_6_checked i k + · exact s_8_7_checked i k +end SumTable17 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable18.lean b/lean/OAI/Analysis/LaughlinGap/SumTable18.lean new file mode 100644 index 0000000000000000000000000000000000000000..14196c08533d7e9dd9e7933e62cad0279784102c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable18.lean @@ -0,0 +1,456 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SumTable17 + +namespace OAI + +/-! Sum Table18. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable18 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 18 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 18 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 23175574511232]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 18 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -84220815828864], ![0, 0, 0, 0, 0, 0, 0, -43967125433088, -2514297806592]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 18 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 10111197233280], ![0, 0, 0, 0, 0, 0, 0, -107665480336128, -53626265886336], ![0, 0, 0, 0, 0, 0, -15012215522304, 7506679065600, 25451699040768]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 18 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 13620900623616], ![0, 0, 0, 0, 0, 0, 0, 40808880697728, 98323618288896], ![0, 0, 0, 0, 0, 0, 115661661827712, 73694744213376, -9278465923584], ![0, 0, 0, 0, 0, -166246821861120, -113090619113472, -53674812761856, -24158829606912]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 18 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 150598508311680], ![0, 0, 0, 0, 0, 0, 0, 266668172998656, 222288361316736], ![0, 0, 0, 0, 0, 0, 144729967269888, 130228400839680, 17312994825984], ![0, 0, 0, 0, 0, -58095757015296, -2378568192000, 8176007034624, -40491475335168], ![0, 0, 0, 0, 11386657751040, 143766994415616, 163488513576960, 21458822381568, -157795184701440]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 18 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 350568548643456], ![0, 0, 0, 0, 0, 0, 0, 186894429266688, 36525506928768], ![0, 0, 0, 0, 0, 0, -60786159417984, -9302026631040, 38392584941568], ![0, 0, 0, 0, 0, -85776514247424, 30488748466176, 48883185272064, -65570500909056], ![0, 0, 0, 0, -81639330938880, 20842246723584, 70646641747968, 10033749073920, -111466307217408], ![0, 0, 0, -290023263129600, -232018610503680, -52204187363328, 127610235777024, 150812096827392, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 18 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 18 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 18 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2995043347296]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 18 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1755554815872], ![0, 0, 0, 0, 0, 0, 0, 4037024452032, -3887362043136]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 18 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 18909787010400], ![0, 0, 0, 0, 0, 0, 0, 11358672481728, 801468150912], ![0, 0, 0, 0, 0, 0, 3951967219200, -1232216054784, -3025409587200]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 18 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -13091232911328], ![0, 0, 0, 0, 0, 0, 0, -15166616575968, -14990837951232], ![0, 0, 0, 0, 0, 0, -26762174607168, -12670100277120, 897013877760], ![0, 0, 0, 0, 0, 34930608096384, 22279148027136, 10909976343552, 7989918723072]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 18 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -18737259409440], ![0, 0, 0, 0, 0, 0, 0, -48312543831552, -22691829992832], ![0, 0, 0, 0, 0, 0, -32570953519104, -16615558941696, 7873454324736], ![0, 0, 0, 0, 0, 12836711631744, 391119176448, 2517573307392, 12168772881408], ![0, 0, 0, 0, 9203022766080, -24968764035072, -21822042857472, 13253978529792, 23562176901120]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 18 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -4375787315328], ![0, 0, 0, 0, 0, 0, 0, -18306277868736, 13306662255744], ![0, 0, 0, 0, 0, 0, 15833919157056, 5267370506112, -831874627584], ![0, 0, 0, 0, 0, 19999019424384, -6817340065536, -1222474226688, 23422081453056], ![0, 0, 0, 0, 18370792028160, -6559431690240, -12249784774656, 6197315604480, 16644290217984], ![0, 0, 0, 12795143961600, 15354172753920, -14330561236992, -36850014609408, -22519453372416, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 18 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 18 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 18 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 537951722880]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 18 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1691932344960], ![0, 0, 0, 0, 0, 0, 0, 437485551360, 1131523810560]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 18 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -9695663852160], ![0, 0, 0, 0, 0, 0, 0, 211147073280, -380828173440], ![0, 0, 0, 0, 0, 0, -1871482229760, 221613849600, 89845916160]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 18 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 6970262407680], ![0, 0, 0, 0, 0, 0, 0, 6834433457280, 1218405576960], ![0, 0, 0, 0, 0, 0, 10908584269440, 4576325170560, 2064094855680], ![0, 0, 0, 0, 0, -12311764058880, -6963116160000, -3010270897920, -2520902292480]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 18 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4251197808000], ![0, 0, 0, 0, 0, 0, 0, 14425518581760, 2960325413760], ![0, 0, 0, 0, 0, 0, 12776682547200, 2367337589760, -2990222526720], ![0, 0, 0, 0, 0, -4902445067520, -72674933760, -2172956248320, -3521811870720], ![0, 0, 0, 0, -7968688865280, 7889272934400, 2406489845760, -9467127521280, 0]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 18 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -13890519477120], ![0, 0, 0, 0, 0, 0, 0, -1698449575680, -5414888519040], ![0, 0, 0, 0, 0, 0, -7417802071680, -3790029260160, -2234606499840], ![0, 0, 0, 0, 0, -8234519504640, 2649585269760, -2744771377920, -7840847139840], ![0, 0, 0, 0, -7136345948160, 3688878336000, 2830397306880, -4426654003200, 0], ![0, 0, 0, 6824076779520, 0, 8530095974400, 10236115169280, 0, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 18 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 18 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 18 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -187549676160]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 18 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 30573354240], ![0, 0, 0, 0, 0, 0, 0, -1101667818240, 448040778240]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 18 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3704922207360], ![0, 0, 0, 0, 0, 0, 0, -2403175484160, 2054882691840], ![0, 0, 0, 0, 0, 0, 1336156631040, 103819499520, 574045824000]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 18 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -3920929668480], ![0, 0, 0, 0, 0, 0, 0, -2907221243520, 1321527820800], ![0, 0, 0, 0, 0, 0, -6514146777600, -3370106277120, -2422534287360], ![0, 0, 0, 0, 0, 5736342205440, 2381517895680, 236444398080, 265640094720]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 18 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1499801297280], ![0, 0, 0, 0, 0, 0, 0, -5663097538560, -1038295399680], ![0, 0, 0, 0, 0, 0, -7210636984320, 246417684480, 74700848640], ![0, 0, 0, 0, 0, 2650788940800, -29362206720, 1357128199680, 124763950080], ![0, 0, 0, 0, 6693865390080, -4393879142400, 2403032924160, 5097684049920, -5766966374400]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 18 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 9369313409280], ![0, 0, 0, 0, 0, 0, 0, 5584272080640, -482225145600], ![0, 0, 0, 0, 0, 0, 5237897280000, 3498274602240, 2082883799040], ![0, 0, 0, 0, 0, 4986653844480, -1473818142720, 2689180961280, 1176041180160], ![0, 0, 0, 0, 3916928040960, -3103830343680, 74280222720, 2383582924800, -4073777326080], ![0, 0, 0, -5774218813440, 1049857966080, -3149573898240, 0, 5511754321920, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 18 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 18 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 18 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 413391541248]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 18 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2073522834432], ![0, 0, 0, 0, 0, 0, 0, 959594342400, -1132344023040]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 18 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 148673774592], ![0, 0, 0, 0, 0, 0, 0, 2915357681664, -2803993224192], ![0, 0, 0, 0, 0, 0, -1304527085568, -353194352640, -808522297344]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 18 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 2314400643072], ![0, 0, 0, 0, 0, 0, 0, -685763490816, 756388399104], ![0, 0, 0, 0, 0, 0, 5102007837696, 4133467819008, 607461617664], ![0, 0, 0, 0, 0, -2585587931136, 231831355392, 1812398008320, 1020874752000]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 18 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -150698548224], ![0, 0, 0, 0, 0, 0, 0, 2417444241408, 2247706008576], ![0, 0, 0, 0, 0, 0, 5152848003072, -358799155200, 358557456384], ![0, 0, 0, 0, 0, -1749476026368, 108884901888, -244897966080, 1656557568000], ![0, 0, 0, 0, -5954333442048, 4639765266432, -4842111467520, 0, 5392488038400]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 18 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -3352200477696], ![0, 0, 0, 0, 0, 0, 0, -6858218170368, 3795134100480], ![0, 0, 0, 0, 0, 0, -5056553198592, -3818538961920, -1077712846848], ![0, 0, 0, 0, 0, -3987502331904, 1026363211776, -1585606440960, 2848164249600], ![0, 0, 0, 0, -2612427227136, 3543141629952, -2092372770816, 0, 3809246330880], ![0, 0, 0, 2405129158656, -4123078557696, 171794939904, -5153848197120, -5153848197120, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 18 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 18 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 18 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1252662394368]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 18 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3040029966336], ![0, 0, 0, 0, 0, 0, 0, 89239636992, 133448122368]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 18 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1662382993920], ![0, 0, 0, 0, 0, 0, 0, -2572580533248, 39261978624], ![0, 0, 0, 0, 0, 0, 1585456029696, 702376181760, 643168002048]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 18 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1857497562624], ![0, 0, 0, 0, 0, 0, 0, 6678250326528, -10013372227584], ![0, 0, 0, 0, 0, 0, -4654598581248, -5615398846464, 6121568403456], ![0, 0, 0, 0, 0, -563284592640, -3424520343552, -4188739670016, -1423212797952]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 18 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3877523781120], ![0, 0, 0, 0, 0, 0, 0, -999118331904, -4293400387584], ![0, 0, 0, 0, 0, 0, -3943086292992, -862826004480, 4292664397824], ![0, 0, 0, 0, 0, 1095550224384, -230928445440, -2124425588736, -1819367497728], ![0, 0, 0, 0, 4599972495360, -7991419797504, 7030206627840, -8156294479872, 3954491228160]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 18 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1274450141184], ![0, 0, 0, 0, 0, 0, 0, 7043681829888, -2357108109312], ![0, 0, 0, 0, 0, 0, 6074986638336, 3797107015680, -1453618839552], ![0, 0, 0, 0, 0, 3763243309056, -740306079744, -1944580509696, -4666537598976], ![0, 0, 0, 0, 1626195394560, -4995840638976, 4966128549888, -3813732679680, 2793447309312], ![0, 0, 0, 1049857966080, 6299147796480, -1679772745728, 5039318237184, -3779488677888, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 18 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_0_checked : ∀ i k : Fin 9, fourSumInteger 0 18 13 i k = s_6_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_1_checked : ∀ i k : Fin 9, fourSumInteger 1 18 13 i k = s_6_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 2670671038464]] +lemma s_6_2_checked : ∀ i k : Fin 9, fourSumInteger 2 18 13 i k = s_6_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4207498893312], ![0, 0, 0, 0, 0, 0, 0, -3166457868288, 4799415988224]] +lemma s_6_3_checked : ∀ i k : Fin 9, fourSumInteger 3 18 13 i k = s_6_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -5424457758720], ![0, 0, 0, 0, 0, 0, 0, 2072804118528, 12400395651072], ![0, 0, 0, 0, 0, 0, -1951844843520, -986405781504, 1450994688000]] +lemma s_6_4_checked : ∀ i k : Fin 9, fourSumInteger 4 18 13 i k = s_6_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4969822420992], ![0, 0, 0, 0, 0, 0, 0, -14809097791488, 24296490037248], ![0, 0, 0, 0, 0, 0, 3805174044672, -1263428474880, -17176210022400], ![0, 0, 0, 0, 0, 5307382738944, 8128951074816, 2556356554752, -1636521689088]] +lemma s_6_5_checked : ∀ i k : Fin 9, fourSumInteger 5 18 13 i k = s_6_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -8296399288320], ![0, 0, 0, 0, 0, 0, 0, 1733272240128, 3036123138048], ![0, 0, 0, 0, 0, 0, 1966401355776, -164409163776, -18120030449664], ![0, 0, 0, 0, 0, -65435774976, 407055187968, 7040707694592, -3262296440832], ![0, 0, 0, 0, 0, 15147404034048, -7700767506432, 10098269356032, -22848171540480]] +lemma s_6_6_checked : ∀ i k : Fin 9, fourSumInteger 6 18 13 i k = s_6_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -5097159395328], ![0, 0, 0, 0, 0, 0, 0, -6648918921216, -10602455525376], ![0, 0, 0, 0, 0, 0, -7391108634624, 3454791555072, 5263862562816], ![0, 0, 0, 0, 0, -3284509003776, 280017813504, 13162613747712, -3704207130624], ![0, 0, 0, 0, 0, 7082646405120, -9057271382016, 4721764270080, -16139917787136], ![0, 0, 0, 0, 0, 16377784270848, 10918522847232, 21837045694464, 0]] +lemma s_6_7_checked : ∀ i k : Fin 9, fourSumInteger 7 18 13 i k = s_6_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_0_checked : ∀ i k : Fin 9, fourSumInteger 0 18 15 i k = s_7_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_1_checked : ∀ i k : Fin 9, fourSumInteger 1 18 15 i k = s_7_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4806350714880]] +lemma s_7_2_checked : ∀ i k : Fin 9, fourSumInteger 2 18 15 i k = s_7_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -36345532354560], ![0, 0, 0, 0, 0, 0, 0, 1386075525120, 14265926737920]] +lemma s_7_3_checked : ∀ i k : Fin 9, fourSumInteger 3 18 15 i k = s_7_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 9473492920320], ![0, 0, 0, 0, 0, 0, 0, -26182454538240, 15869770076160], ![0, 0, 0, 0, 0, 0, 0, -2079310970880, -12039697612800]] +lemma s_7_4_checked : ∀ i k : Fin 9, fourSumInteger 4 18 15 i k = s_7_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -13762453985280], ![0, 0, 0, 0, 0, 0, 0, -30760599767040, 139091006545920], ![0, 0, 0, 0, 0, 0, 0, 100356090531840, -96906307829760], ![0, 0, 0, 0, 0, 0, 0, 53073827389440, 7893305671680]] +lemma s_7_5_checked : ∀ i k : Fin 9, fourSumInteger 5 18 15 i k = s_7_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -77397519513600], ![0, 0, 0, 0, 0, 0, 0, -6995349504000, 12471727656960], ![0, 0, 0, 0, 0, 0, 0, 55583033425920, -54730781614080], ![0, 0, 0, 0, 0, 0, 0, -654357749760, 3707271659520], ![0, 0, 0, 0, 0, 0, 0, 151474040340480, -171361286553600]] +lemma s_7_6_checked : ∀ i k : Fin 9, fourSumInteger 6 18 15 i k = s_7_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 14709554196480], ![0, 0, 0, 0, 0, 0, 0, 39890071203840, -53099684352000], ![0, 0, 0, 0, 0, 0, 0, -65049765580800, 25878892216320], ![0, 0, 0, 0, 0, 0, 0, -32845090037760, 34945223639040], ![0, 0, 0, 0, 0, 0, 0, 70826464051200, -121049383403520], ![0, 0, 0, 0, 0, 0, 0, 163777842708480, 0]] +lemma s_7_7_checked : ∀ i k : Fin 9, fourSumInteger 7 18 15 i k = s_7_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_0_checked : ∀ i k : Fin 9, fourSumInteger 0 18 17 i k = s_8_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_1_checked : ∀ i k : Fin 9, fourSumInteger 1 18 17 i k = s_8_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_2_checked : ∀ i k : Fin 9, fourSumInteger 2 18 17 i k = s_8_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_3_checked : ∀ i k : Fin 9, fourSumInteger 3 18 17 i k = s_8_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_4_checked : ∀ i k : Fin 9, fourSumInteger 4 18 17 i k = s_8_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_5_checked : ∀ i k : Fin 9, fourSumInteger 5 18 17 i k = s_8_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_6_checked : ∀ i k : Fin 9, fourSumInteger 6 18 17 i k = s_8_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_7_checked : ∀ i k : Fin 9, fourSumInteger 7 18 17 i k = s_8_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 9 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7], ![s_6_0, s_6_1, s_6_2, s_6_3, s_6_4, s_6_5, s_6_6, s_6_7], ![s_7_0, s_7_1, s_7_2, s_7_3, s_7_4, s_7_5, s_7_6, s_7_7], ![s_8_0, s_8_1, s_8_2, s_8_3, s_8_4, s_8_5, s_8_6, s_8_7]] +lemma sums_checked : ∀ u : Fin 9, ∀ a i k, fourSumInteger a 18 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k + · exact s_6_0_checked i k + · exact s_6_1_checked i k + · exact s_6_2_checked i k + · exact s_6_3_checked i k + · exact s_6_4_checked i k + · exact s_6_5_checked i k + · exact s_6_6_checked i k + · exact s_6_7_checked i k + · exact s_7_0_checked i k + · exact s_7_1_checked i k + · exact s_7_2_checked i k + · exact s_7_3_checked i k + · exact s_7_4_checked i k + · exact s_7_5_checked i k + · exact s_7_6_checked i k + · exact s_7_7_checked i k + · exact s_8_0_checked i k + · exact s_8_1_checked i k + · exact s_8_2_checked i k + · exact s_8_3_checked i k + · exact s_8_4_checked i k + · exact s_8_5_checked i k + · exact s_8_6_checked i k + · exact s_8_7_checked i k +end SumTable18 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable19.lean b/lean/OAI/Analysis/LaughlinGap/SumTable19.lean new file mode 100644 index 0000000000000000000000000000000000000000..317e1ff27f8fbb6cbcd7be00046d249f421c033e --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable19.lean @@ -0,0 +1,505 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CheckedTables +import OAI.Analysis.LaughlinGap.IntegerFourRows + +namespace OAI + +/-! Sum Table19. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable19 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 19 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 19 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 19 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 104598434274048]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 19 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 337358477529216], ![0, 0, 0, 0, 0, 0, 0, -23880100248576, -84198323049984]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 19 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -198531538672896], ![0, 0, 0, 0, 0, 0, 0, -264217051942272, -95437561849344], ![0, 0, 0, 0, 0, 0, 260324539098624, 83318138931456, -73600524721152]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 19 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -839361125116800], ![0, 0, 0, 0, 0, 0, 0, -554665127537664, -428995909824768], ![0, 0, 0, 0, 0, 0, 8109061728768, -113740840122624, -98156668566528], ![0, 0, 0, 0, 0, -139986796105728, -424468988596224, -354070569295872, 109242820177920]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 19 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -497368620777600], ![0, 0, 0, 0, 0, 0, 0, -31241086411392, -186157201950720], ![0, 0, 0, 0, 0, 0, -42609173967360, -286554554567424, -235548622273536], ![0, 0, 0, 0, 0, 143257211615232, -111510338734080, -165556859719680, 77168981919744], ![0, 0, 0, 0, 1044083747266560, 783062810449920, 278422332604416, -104408374726656, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 19 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 19 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 19 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 19 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 179869966848]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 19 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -25215385358592], ![0, 0, 0, 0, 0, 0, 0, 5588796635136, 15859594662912]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 19 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 57513952184832], ![0, 0, 0, 0, 0, 0, 0, 50822013116160, 4131660589056], ![0, 0, 0, 0, 0, 0, -61252832729088, -22775379973632, 449936188416]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 19 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 119268184299264], ![0, 0, 0, 0, 0, 0, 0, 107743746299904, 42686638106112], ![0, 0, 0, 0, 0, 0, -1908014524416, 16193309603328, -1658927102976], ![0, 0, 0, 0, 0, 14194412863488, 81131399331840, 39761935589376, -53550402048000]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 19 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 15394371962112], ![0, 0, 0, 0, 0, 0, 0, 4457964056832, 29546872363008], ![0, 0, 0, 0, 0, 0, 10025687992320, 47270116827648, 4647704675328], ![0, 0, 0, 0, 0, -34286964940800, 25658341023744, 18591946813440, -37827932313600], ![0, 0, 0, 0, -122833382031360, -85983367421952, 8188892135424, 51180575846400, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 19 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 19 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 19 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 19 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -6158368170240]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 19 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -3055895356800], ![0, 0, 0, 0, 0, 0, 0, -2294484741120, -4794550126080]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 19 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -20961905352960], ![0, 0, 0, 0, 0, 0, 0, -17493420996480, -418219676160], ![0, 0, 0, 0, 0, 0, 25522013637120, 10258185949440, 4055141376000]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 19 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -24252118450560], ![0, 0, 0, 0, 0, 0, 0, -35986511109120, -3876844857600], ![0, 0, 0, 0, 0, 0, 795006051840, -2336545685760, 6580214784000], ![0, 0, 0, 0, 0, 1895518310400, -25994892718080, 0, 21420160819200]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 19 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 20582661390720], ![0, 0, 0, 0, 0, 0, 0, 25483286400, -6152621629440], ![0, 0, 0, 0, 0, 0, -4177369996800, -10956043887360, 11313541324800], ![0, 0, 0, 0, 0, 14527646115840, -10449564702720, 0, 15131172925440], ![0, 0, 0, 0, 13648153559040, 8530095974400, -20472230338560, -20472230338560, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 19 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 19 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 19 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 19 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4988905320960]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 19 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 4760947572480], ![0, 0, 0, 0, 0, 0, 0, 1367630837760, 1673744286720]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 19 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 7103877327360], ![0, 0, 0, 0, 0, 0, 0, 9624868366080, 2885923983360], ![0, 0, 0, 0, 0, 0, -15705854545920, -6190239137280, -3354117043200]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 19 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3728533374720], ![0, 0, 0, 0, 0, 0, 0, 17288016599040, -59646005760], ![0, 0, 0, 0, 0, 0, -489234493440, -1283722682880, -4932196684800], ![0, 0, 0, 0, 0, -5972538654720, 11190791208960, -8496140083200, -5766966374400]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 19 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -20088714412800], ![0, 0, 0, 0, 0, 0, 0, -1904156686080, -14055782400], ![0, 0, 0, 0, 0, 0, 2570689228800, 995364395520, -10082611123200], ![0, 0, 0, 0, 0, -9088650362880, 6281940910080, -3972638208000, -4073777326080], ![0, 0, 0, 0, 6299147796480, 3149573898240, 14698011525120, 5511754321920, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 19 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 19 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 19 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 19 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -3112016578560]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 19 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1925781212160], ![0, 0, 0, 0, 0, 0, 0, -1044507156480, -82847232000]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 19 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 883462256640], ![0, 0, 0, 0, 0, 0, 0, -8784109255680, -6429259837440], ![0, 0, 0, 0, 0, 0, 12850244628480, 3990264145920, 1940744724480]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 19 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 2344948945920], ![0, 0, 0, 0, 0, 0, 0, -11190717112320, -2450564720640], ![0, 0, 0, 0, 0, 0, 400282767360, 3289091512320, 2480955678720], ![0, 0, 0, 0, 0, 8818858229760, -5223866204160, 11122219745280, -5392488038400]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 19 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 15476545981440], ![0, 0, 0, 0, 0, 0, 0, 4297157360640, 2891801640960], ![0, 0, 0, 0, 0, 0, -2103291187200, 4490477291520, 6363460362240], ![0, 0, 0, 0, 0, 7557717934080, -5018220380160, 5200544563200, -3809246330880], ![0, 0, 0, 0, -10307696394240, -2576924098560, -6871797596160, 5153848197120, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 19 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 19 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 19 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 19 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 571103858688]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 19 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -3845612120064], ![0, 0, 0, 0, 0, 0, 0, 855184687104, -1737719537664]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 19 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -5576329752576], ![0, 0, 0, 0, 0, 0, 0, 13981076871168, 9529821413376], ![0, 0, 0, 0, 0, 0, -12564683636736, -469474013184, 573164494848]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 19 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -3551715256320], ![0, 0, 0, 0, 0, 0, 0, 10547766214656, 7766553096192], ![0, 0, 0, 0, 0, 0, -391387594752, -5434385240064, 1420122857472], ![0, 0, 0, 0, 0, -12467736281088, 1262927609856, -8156294479872, 14499801169920]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 19 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -8747563038720], ![0, 0, 0, 0, 0, 0, 0, -9798904338432, -4723161907200], ![0, 0, 0, 0, 0, 0, 2056551383040, -11051487473664, 903205822464], ![0, 0, 0, 0, 0, -7508617003008, 4787856015360, -3813732679680, 10242640134144], ![0, 0, 0, 0, 8398863728640, -4199431864320, -5039318237184, -13858125152256, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 19 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_0_checked : ∀ i k : Fin 9, fourSumInteger 0 19 13 i k = s_6_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_1_checked : ∀ i k : Fin 9, fourSumInteger 1 19 13 i k = s_6_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_2_checked : ∀ i k : Fin 9, fourSumInteger 2 19 13 i k = s_6_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1396323422208]] +lemma s_6_3_checked : ∀ i k : Fin 9, fourSumInteger 3 19 13 i k = s_6_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 10437812656128], ![0, 0, 0, 0, 0, 0, 0, -293302124544, 5328059523072]] +lemma s_6_4_checked : ∀ i k : Fin 9, fourSumInteger 4 19 13 i k = s_6_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -9535863287808], ![0, 0, 0, 0, 0, 0, 0, -34715458652160, 934178758656], ![0, 0, 0, 0, 0, 0, 11667206234112, -11596664082432, -5377924890624]] +lemma s_6_5_checked : ∀ i k : Fin 9, fourSumInteger 5 19 13 i k = s_6_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -821863950336], ![0, 0, 0, 0, 0, 0, 0, -18692086972416, -8074870222848], ![0, 0, 0, 0, 0, 0, 363431337984, 7215203094528, -7513198657536], ![0, 0, 0, 0, 0, 15147404034048, 2397501849600, -20196538712064, 0]] +lemma s_6_6_checked : ∀ i k : Fin 9, fourSumInteger 6 19 13 i k = s_6_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3773553518592], ![0, 0, 0, 0, 0, 0, 0, 25138046748672, 2056242659328], ![0, 0, 0, 0, 0, 0, -1909654855680, 21921304424448, -16727140564992], ![0, 0, 0, 0, 0, 7082646405120, -4335507111936, -9443528540160, 0], ![0, 0, 0, 0, 0, 16377784270848, 21837045694464, 0, 0]] +lemma s_6_7_checked : ∀ i k : Fin 9, fourSumInteger 7 19 13 i k = s_6_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_0_checked : ∀ i k : Fin 9, fourSumInteger 0 19 15 i k = s_7_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_1_checked : ∀ i k : Fin 9, fourSumInteger 1 19 15 i k = s_7_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_2_checked : ∀ i k : Fin 9, fourSumInteger 2 19 15 i k = s_7_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 14265926737920]] +lemma s_7_3_checked : ∀ i k : Fin 9, fourSumInteger 3 19 15 i k = s_7_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 15869770076160], ![0, 0, 0, 0, 0, 0, 0, -2079310970880, -12039697612800]] +lemma s_7_4_checked : ∀ i k : Fin 9, fourSumInteger 4 19 15 i k = s_7_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 139091006545920], ![0, 0, 0, 0, 0, 0, 0, 100356090531840, -96906307829760], ![0, 0, 0, 0, 0, 0, 0, 53073827389440, 7893305671680]] +lemma s_7_5_checked : ∀ i k : Fin 9, fourSumInteger 5 19 15 i k = s_7_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 12471727656960], ![0, 0, 0, 0, 0, 0, 0, 55583033425920, -54730781614080], ![0, 0, 0, 0, 0, 0, 0, -654357749760, 3707271659520], ![0, 0, 0, 0, 0, 0, 0, 151474040340480, -171361286553600]] +lemma s_7_6_checked : ∀ i k : Fin 9, fourSumInteger 6 19 15 i k = s_7_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -53099684352000], ![0, 0, 0, 0, 0, 0, 0, -65049765580800, 25878892216320], ![0, 0, 0, 0, 0, 0, 0, -32845090037760, 34945223639040], ![0, 0, 0, 0, 0, 0, 0, 70826464051200, -121049383403520], ![0, 0, 0, 0, 0, 0, 0, 163777842708480, 0]] +lemma s_7_7_checked : ∀ i k : Fin 9, fourSumInteger 7 19 15 i k = s_7_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_0_checked : ∀ i k : Fin 9, fourSumInteger 0 19 17 i k = s_8_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_1_checked : ∀ i k : Fin 9, fourSumInteger 1 19 17 i k = s_8_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_2_checked : ∀ i k : Fin 9, fourSumInteger 2 19 17 i k = s_8_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_3_checked : ∀ i k : Fin 9, fourSumInteger 3 19 17 i k = s_8_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_4_checked : ∀ i k : Fin 9, fourSumInteger 4 19 17 i k = s_8_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_5_checked : ∀ i k : Fin 9, fourSumInteger 5 19 17 i k = s_8_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_6_checked : ∀ i k : Fin 9, fourSumInteger 6 19 17 i k = s_8_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_7_checked : ∀ i k : Fin 9, fourSumInteger 7 19 17 i k = s_8_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_0_checked : ∀ i k : Fin 9, fourSumInteger 0 19 19 i k = s_9_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_1_checked : ∀ i k : Fin 9, fourSumInteger 1 19 19 i k = s_9_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_2_checked : ∀ i k : Fin 9, fourSumInteger 2 19 19 i k = s_9_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_3_checked : ∀ i k : Fin 9, fourSumInteger 3 19 19 i k = s_9_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_4_checked : ∀ i k : Fin 9, fourSumInteger 4 19 19 i k = s_9_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_5_checked : ∀ i k : Fin 9, fourSumInteger 5 19 19 i k = s_9_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_6_checked : ∀ i k : Fin 9, fourSumInteger 6 19 19 i k = s_9_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_7_checked : ∀ i k : Fin 9, fourSumInteger 7 19 19 i k = s_9_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 10 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7], ![s_6_0, s_6_1, s_6_2, s_6_3, s_6_4, s_6_5, s_6_6, s_6_7], ![s_7_0, s_7_1, s_7_2, s_7_3, s_7_4, s_7_5, s_7_6, s_7_7], ![s_8_0, s_8_1, s_8_2, s_8_3, s_8_4, s_8_5, s_8_6, s_8_7], ![s_9_0, s_9_1, s_9_2, s_9_3, s_9_4, s_9_5, s_9_6, s_9_7]] +lemma sums_checked : ∀ u : Fin 10, ∀ a i k, fourSumInteger a 19 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k + · exact s_6_0_checked i k + · exact s_6_1_checked i k + · exact s_6_2_checked i k + · exact s_6_3_checked i k + · exact s_6_4_checked i k + · exact s_6_5_checked i k + · exact s_6_6_checked i k + · exact s_6_7_checked i k + · exact s_7_0_checked i k + · exact s_7_1_checked i k + · exact s_7_2_checked i k + · exact s_7_3_checked i k + · exact s_7_4_checked i k + · exact s_7_5_checked i k + · exact s_7_6_checked i k + · exact s_7_7_checked i k + · exact s_8_0_checked i k + · exact s_8_1_checked i k + · exact s_8_2_checked i k + · exact s_8_3_checked i k + · exact s_8_4_checked i k + · exact s_8_5_checked i k + · exact s_8_6_checked i k + · exact s_8_7_checked i k + · exact s_9_0_checked i k + · exact s_9_1_checked i k + · exact s_9_2_checked i k + · exact s_9_3_checked i k + · exact s_9_4_checked i k + · exact s_9_5_checked i k + · exact s_9_6_checked i k + · exact s_9_7_checked i k +end SumTable19 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable20.lean b/lean/OAI/Analysis/LaughlinGap/SumTable20.lean new file mode 100644 index 0000000000000000000000000000000000000000..fb4431a112f1975b4f0470d3d369e03fdc8efda6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable20.lean @@ -0,0 +1,504 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SumTable19 + +namespace OAI + +/-! Sum Table20. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable20 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 20 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 20 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 20 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 20 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 205112220977664]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 20 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 548668704849408], ![0, 0, 0, 0, 0, 0, 0, -59466234237696, 456681642633216]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 20 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1750772769977088], ![0, 0, 0, 0, 0, 0, 0, 429044829168384, 667559031220224], ![0, 0, 0, 0, 0, 0, 756775143641088, 1223152875749376, 691871194460160]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 20 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 519624919756800], ![0, 0, 0, 0, 0, 0, 0, 929772846123264, 1378464835258368], ![0, 0, 0, 0, 0, 0, 23392699140096, 571923697213440, 488736885491712], ![0, 0, 0, 0, 0, -2975638679709696, -1983759119806464, -661253039935488, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 20 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 20 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 20 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 20 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 20 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -46164558375936]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 20 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -61221208688640], ![0, 0, 0, 0, 0, 0, 0, 23797395528192, -66891214900224]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 20 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -268695583123968], ![0, 0, 0, 0, 0, 0, 0, -90464278215168, -95005487655936], ![0, 0, 0, 0, 0, 0, -159321082871808, -225317635006464, -36414273392640]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 20 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -108879560165376], ![0, 0, 0, 0, 0, 0, 0, -202721233448448, -205845182180352], ![0, 0, 0, 0, 0, 0, -4924778766336, -105354365276160, -25722993973248], ![0, 0, 0, 0, 0, 487239082057728, 278422332604416, 34802791575552, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 20 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 20 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 20 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 20 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 20 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 18445209868800]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 20 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 5577298721280], ![0, 0, 0, 0, 0, 0, 0, -14553992344320, 13591174671360]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 20 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 63771890307840], ![0, 0, 0, 0, 0, 0, 0, 33330496193280, 18072468311040], ![0, 0, 0, 0, 0, 0, 58573927526400, 66269892648960, -21420160819200]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 20 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 39031137699840], ![0, 0, 0, 0, 0, 0, 0, 78122296961280, 43572388654080], ![0, 0, 0, 0, 0, 0, 1810580428800, 30986578022400, -15131172925440], ![0, 0, 0, 0, 0, -127951439616000, -51180575846400, 20472230338560, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 20 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 20 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 20 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 20 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 20 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -10974174182400]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 20 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3228605952000], ![0, 0, 0, 0, 0, 0, 0, 12406089146880, -1151107077120]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 20 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -16934255669760], ![0, 0, 0, 0, 0, 0, 0, -17833520939520, -540643783680], ![0, 0, 0, 0, 0, 0, -31239428014080, -22089964216320, 24990187622400]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 20 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -19529479157760], ![0, 0, 0, 0, 0, 0, 0, -44539170424320, -5096178447360], ![0, 0, 0, 0, 0, 0, -965642895360, -10328859340800, 17653035079680], ![0, 0, 0, 0, 0, 40944460677120, 0, -23884268728320, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 20 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 20 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 20 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 20 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 20 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 8870689935360]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 20 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2616163799040], ![0, 0, 0, 0, 0, 0, 0, -13947246213120, -3743207424000]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 20 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 2111168378880], ![0, 0, 0, 0, 0, 0, 0, 12412348692480, -6074044416000], ![0, 0, 0, 0, 0, 0, 21627296317440, 0, -19772456140800]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 20 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 11584211189760], ![0, 0, 0, 0, 0, 0, 0, 34150901114880, -10443268915200], ![0, 0, 0, 0, 0, 0, 668522004480, 0, -13967236546560], ![0, 0, 0, 0, 0, -9448721694720, 18897443389440, 18897443389440, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 20 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 20 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 20 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 20 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 20 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -9087536848896]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 20 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -5429336850432], ![0, 0, 0, 0, 0, 0, 0, 19731261394944, 7264204333056]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 20 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 1580539834368], ![0, 0, 0, 0, 0, 0, 0, -10035582898176, 10317338025984], ![0, 0, 0, 0, 0, 0, -17301837053952, 24468883439616, 3954491228160]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 20 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -5628192768000], ![0, 0, 0, 0, 0, 0, 0, -32626466205696, 22354227929088], ![0, 0, 0, 0, 0, 0, -534817603584, 11441198039040, 2793447309312], ![0, 0, 0, 0, 0, -7558977355776, -30235909423104, -3779488677888, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 20 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_0_checked : ∀ i k : Fin 9, fourSumInteger 0 20 13 i k = s_6_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_1_checked : ∀ i k : Fin 9, fourSumInteger 1 20 13 i k = s_6_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_2_checked : ∀ i k : Fin 9, fourSumInteger 2 20 13 i k = s_6_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_3_checked : ∀ i k : Fin 9, fourSumInteger 3 20 13 i k = s_6_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 10810417373184]] +lemma s_6_4_checked : ∀ i k : Fin 9, fourSumInteger 4 20 13 i k = s_6_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 31965408583680], ![0, 0, 0, 0, 0, 0, 0, -32826195038208, -10171768848384]] +lemma s_6_5_checked : ∀ i k : Fin 9, fourSumInteger 5 20 13 i k = s_6_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 9267727552512], ![0, 0, 0, 0, 0, 0, 0, 7476946194432, -12258403762176], ![0, 0, 0, 0, 0, 0, 12495771205632, -70687885492224, 45696343080960]] +lemma s_6_6_checked : ∀ i k : Fin 9, fourSumInteger 6 20 13 i k = s_6_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -4601896206336], ![0, 0, 0, 0, 0, 0, 0, 35059340439552, -34409437151232], ![0, 0, 0, 0, 0, 0, 386257158144, -33052349890560, 32279835574272], ![0, 0, 0, 0, 0, 16377784270848, 32755568541696, -43674091388928, 0]] +lemma s_6_7_checked : ∀ i k : Fin 9, fourSumInteger 7 20 13 i k = s_6_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_0_checked : ∀ i k : Fin 9, fourSumInteger 0 20 15 i k = s_7_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_1_checked : ∀ i k : Fin 9, fourSumInteger 1 20 15 i k = s_7_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_2_checked : ∀ i k : Fin 9, fourSumInteger 2 20 15 i k = s_7_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_3_checked : ∀ i k : Fin 9, fourSumInteger 3 20 15 i k = s_7_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -12039697612800]] +lemma s_7_4_checked : ∀ i k : Fin 9, fourSumInteger 4 20 15 i k = s_7_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -96906307829760], ![0, 0, 0, 0, 0, 0, 0, 53073827389440, 7893305671680]] +lemma s_7_5_checked : ∀ i k : Fin 9, fourSumInteger 5 20 15 i k = s_7_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -54730781614080], ![0, 0, 0, 0, 0, 0, 0, -654357749760, 3707271659520], ![0, 0, 0, 0, 0, 0, 0, 151474040340480, -171361286553600]] +lemma s_7_6_checked : ∀ i k : Fin 9, fourSumInteger 6 20 15 i k = s_7_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 25878892216320], ![0, 0, 0, 0, 0, 0, 0, -32845090037760, 34945223639040], ![0, 0, 0, 0, 0, 0, 0, 70826464051200, -121049383403520], ![0, 0, 0, 0, 0, 0, 0, 163777842708480, 0]] +lemma s_7_7_checked : ∀ i k : Fin 9, fourSumInteger 7 20 15 i k = s_7_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_0_checked : ∀ i k : Fin 9, fourSumInteger 0 20 17 i k = s_8_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_1_checked : ∀ i k : Fin 9, fourSumInteger 1 20 17 i k = s_8_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_2_checked : ∀ i k : Fin 9, fourSumInteger 2 20 17 i k = s_8_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_3_checked : ∀ i k : Fin 9, fourSumInteger 3 20 17 i k = s_8_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_4_checked : ∀ i k : Fin 9, fourSumInteger 4 20 17 i k = s_8_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_5_checked : ∀ i k : Fin 9, fourSumInteger 5 20 17 i k = s_8_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_6_checked : ∀ i k : Fin 9, fourSumInteger 6 20 17 i k = s_8_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_7_checked : ∀ i k : Fin 9, fourSumInteger 7 20 17 i k = s_8_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_0_checked : ∀ i k : Fin 9, fourSumInteger 0 20 19 i k = s_9_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_1_checked : ∀ i k : Fin 9, fourSumInteger 1 20 19 i k = s_9_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_2_checked : ∀ i k : Fin 9, fourSumInteger 2 20 19 i k = s_9_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_3_checked : ∀ i k : Fin 9, fourSumInteger 3 20 19 i k = s_9_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_4_checked : ∀ i k : Fin 9, fourSumInteger 4 20 19 i k = s_9_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_5_checked : ∀ i k : Fin 9, fourSumInteger 5 20 19 i k = s_9_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_6_checked : ∀ i k : Fin 9, fourSumInteger 6 20 19 i k = s_9_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_7_checked : ∀ i k : Fin 9, fourSumInteger 7 20 19 i k = s_9_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 10 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7], ![s_6_0, s_6_1, s_6_2, s_6_3, s_6_4, s_6_5, s_6_6, s_6_7], ![s_7_0, s_7_1, s_7_2, s_7_3, s_7_4, s_7_5, s_7_6, s_7_7], ![s_8_0, s_8_1, s_8_2, s_8_3, s_8_4, s_8_5, s_8_6, s_8_7], ![s_9_0, s_9_1, s_9_2, s_9_3, s_9_4, s_9_5, s_9_6, s_9_7]] +lemma sums_checked : ∀ u : Fin 10, ∀ a i k, fourSumInteger a 20 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k + · exact s_6_0_checked i k + · exact s_6_1_checked i k + · exact s_6_2_checked i k + · exact s_6_3_checked i k + · exact s_6_4_checked i k + · exact s_6_5_checked i k + · exact s_6_6_checked i k + · exact s_6_7_checked i k + · exact s_7_0_checked i k + · exact s_7_1_checked i k + · exact s_7_2_checked i k + · exact s_7_3_checked i k + · exact s_7_4_checked i k + · exact s_7_5_checked i k + · exact s_7_6_checked i k + · exact s_7_7_checked i k + · exact s_8_0_checked i k + · exact s_8_1_checked i k + · exact s_8_2_checked i k + · exact s_8_3_checked i k + · exact s_8_4_checked i k + · exact s_8_5_checked i k + · exact s_8_6_checked i k + · exact s_8_7_checked i k + · exact s_9_0_checked i k + · exact s_9_1_checked i k + · exact s_9_2_checked i k + · exact s_9_3_checked i k + · exact s_9_4_checked i k + · exact s_9_5_checked i k + · exact s_9_6_checked i k + · exact s_9_7_checked i k +end SumTable20 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable21.lean b/lean/OAI/Analysis/LaughlinGap/SumTable21.lean new file mode 100644 index 0000000000000000000000000000000000000000..7c9b837236095c784f828aa40c961dd7ee7e5d1c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable21.lean @@ -0,0 +1,553 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CheckedTables +import OAI.Analysis.LaughlinGap.IntegerFourRows + +namespace OAI + +/-! Sum Table21. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable21 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 21 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 21 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 21 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 21 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 21 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1469156772695040]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 21 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2200249921858560], ![0, 0, 0, 0, 0, 0, 0, -3057882189373440, -3459355972300800]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 21 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -4359730550123520], ![0, 0, 0, 0, 0, 0, 0, -1429809243033600, -2443684427458560], ![0, 0, 0, 0, 0, 0, 6612530399354880, 3306265199677440, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 21 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 21 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 21 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 21 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 21 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 21 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 283398528771072]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 21 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 419252844561408], ![0, 0, 0, 0, 0, 0, 0, 675952905019392, 546214100889600]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 21 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 848331789566976], ![0, 0, 0, 0, 0, 0, 0, 316063095828480, 385844909598720], ![0, 0, 0, 0, 0, 0, -1252900496719872, -522041873633280, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 21 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 21 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 21 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 21 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 21 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 21 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -94916112445440]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 21 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -138092021084160], ![0, 0, 0, 0, 0, 0, 0, -265079570595840, -128520964915200]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 21 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -287424967864320], ![0, 0, 0, 0, 0, 0, 0, -123946312089600, -90787037552640], ![0, 0, 0, 0, 0, 0, 409444606771200, 122833382031360, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 21 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 21 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 21 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 21 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 21 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 21 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 45905735715840]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 21 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 65199844469760], ![0, 0, 0, 0, 0, 0, 0, 154629749514240, 24990187622400]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 21 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 141266301496320], ![0, 0, 0, 0, 0, 0, 0, 72302015385600, 17653035079680], ![0, 0, 0, 0, 0, 0, -191074149826560, -23884268728320, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 21 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 21 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 21 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 21 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 21 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 21 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -28834606817280]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 21 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -39438601297920], ![0, 0, 0, 0, 0, 0, 0, -122344417198080, 19772456140800]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 21 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -90884601815040], ![0, 0, 0, 0, 0, 0, 0, -57205990195200, 13967236546560], ![0, 0, 0, 0, 0, 0, 113384660336640, -18897443389440, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 21 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 21 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 21 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 21 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 21 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 21 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 21348191969280]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 21 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 27290512465920], ![0, 0, 0, 0, 0, 0, 0, 122344417198080, -59317368422400]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 21 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 69998063984640], ![0, 0, 0, 0, 0, 0, 0, 57205990195200, -41901709639680], ![0, 0, 0, 0, 0, 0, -75589773557760, 56692330168320, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 21 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_0_checked : ∀ i k : Fin 9, fourSumInteger 0 21 13 i k = s_6_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_1_checked : ∀ i k : Fin 9, fourSumInteger 1 21 13 i k = s_6_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_2_checked : ∀ i k : Fin 9, fourSumInteger 2 21 13 i k = s_6_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_3_checked : ∀ i k : Fin 9, fourSumInteger 3 21 13 i k = s_6_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_4_checked : ∀ i k : Fin 9, fourSumInteger 4 21 13 i k = s_6_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -16018053562368]] +lemma s_6_5_checked : ∀ i k : Fin 9, fourSumInteger 5 21 13 i k = s_6_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -17497911754752], ![0, 0, 0, 0, 0, 0, 0, -141375770984448, 114240857702400]] +lemma s_6_6_checked : ∀ i k : Fin 9, fourSumInteger 6 21 13 i k = s_6_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -56751096889344], ![0, 0, 0, 0, 0, 0, 0, -66104699781120, 80699588935680], ![0, 0, 0, 0, 0, 0, 43674091388928, -109185228472320, 0]] +lemma s_6_7_checked : ∀ i k : Fin 9, fourSumInteger 7 21 13 i k = s_6_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_0_checked : ∀ i k : Fin 9, fourSumInteger 0 21 15 i k = s_7_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_1_checked : ∀ i k : Fin 9, fourSumInteger 1 21 15 i k = s_7_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_2_checked : ∀ i k : Fin 9, fourSumInteger 2 21 15 i k = s_7_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_3_checked : ∀ i k : Fin 9, fourSumInteger 3 21 15 i k = s_7_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_4_checked : ∀ i k : Fin 9, fourSumInteger 4 21 15 i k = s_7_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 7893305671680]] +lemma s_7_5_checked : ∀ i k : Fin 9, fourSumInteger 5 21 15 i k = s_7_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 3707271659520], ![0, 0, 0, 0, 0, 0, 0, 151474040340480, -171361286553600]] +lemma s_7_6_checked : ∀ i k : Fin 9, fourSumInteger 6 21 15 i k = s_7_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 34945223639040], ![0, 0, 0, 0, 0, 0, 0, 70826464051200, -121049383403520], ![0, 0, 0, 0, 0, 0, 0, 163777842708480, 0]] +lemma s_7_7_checked : ∀ i k : Fin 9, fourSumInteger 7 21 15 i k = s_7_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_0_checked : ∀ i k : Fin 9, fourSumInteger 0 21 17 i k = s_8_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_1_checked : ∀ i k : Fin 9, fourSumInteger 1 21 17 i k = s_8_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_2_checked : ∀ i k : Fin 9, fourSumInteger 2 21 17 i k = s_8_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_3_checked : ∀ i k : Fin 9, fourSumInteger 3 21 17 i k = s_8_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_4_checked : ∀ i k : Fin 9, fourSumInteger 4 21 17 i k = s_8_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_5_checked : ∀ i k : Fin 9, fourSumInteger 5 21 17 i k = s_8_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_6_checked : ∀ i k : Fin 9, fourSumInteger 6 21 17 i k = s_8_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_7_checked : ∀ i k : Fin 9, fourSumInteger 7 21 17 i k = s_8_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_0_checked : ∀ i k : Fin 9, fourSumInteger 0 21 19 i k = s_9_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_1_checked : ∀ i k : Fin 9, fourSumInteger 1 21 19 i k = s_9_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_2_checked : ∀ i k : Fin 9, fourSumInteger 2 21 19 i k = s_9_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_3_checked : ∀ i k : Fin 9, fourSumInteger 3 21 19 i k = s_9_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_4_checked : ∀ i k : Fin 9, fourSumInteger 4 21 19 i k = s_9_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_5_checked : ∀ i k : Fin 9, fourSumInteger 5 21 19 i k = s_9_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_6_checked : ∀ i k : Fin 9, fourSumInteger 6 21 19 i k = s_9_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_7_checked : ∀ i k : Fin 9, fourSumInteger 7 21 19 i k = s_9_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_0_checked : ∀ i k : Fin 9, fourSumInteger 0 21 21 i k = s_10_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_1_checked : ∀ i k : Fin 9, fourSumInteger 1 21 21 i k = s_10_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_2_checked : ∀ i k : Fin 9, fourSumInteger 2 21 21 i k = s_10_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_3_checked : ∀ i k : Fin 9, fourSumInteger 3 21 21 i k = s_10_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_4_checked : ∀ i k : Fin 9, fourSumInteger 4 21 21 i k = s_10_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_5_checked : ∀ i k : Fin 9, fourSumInteger 5 21 21 i k = s_10_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_6_checked : ∀ i k : Fin 9, fourSumInteger 6 21 21 i k = s_10_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_7_checked : ∀ i k : Fin 9, fourSumInteger 7 21 21 i k = s_10_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 11 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7], ![s_6_0, s_6_1, s_6_2, s_6_3, s_6_4, s_6_5, s_6_6, s_6_7], ![s_7_0, s_7_1, s_7_2, s_7_3, s_7_4, s_7_5, s_7_6, s_7_7], ![s_8_0, s_8_1, s_8_2, s_8_3, s_8_4, s_8_5, s_8_6, s_8_7], ![s_9_0, s_9_1, s_9_2, s_9_3, s_9_4, s_9_5, s_9_6, s_9_7], ![s_10_0, s_10_1, s_10_2, s_10_3, s_10_4, s_10_5, s_10_6, s_10_7]] +lemma sums_checked : ∀ u : Fin 11, ∀ a i k, fourSumInteger a 21 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k + · exact s_6_0_checked i k + · exact s_6_1_checked i k + · exact s_6_2_checked i k + · exact s_6_3_checked i k + · exact s_6_4_checked i k + · exact s_6_5_checked i k + · exact s_6_6_checked i k + · exact s_6_7_checked i k + · exact s_7_0_checked i k + · exact s_7_1_checked i k + · exact s_7_2_checked i k + · exact s_7_3_checked i k + · exact s_7_4_checked i k + · exact s_7_5_checked i k + · exact s_7_6_checked i k + · exact s_7_7_checked i k + · exact s_8_0_checked i k + · exact s_8_1_checked i k + · exact s_8_2_checked i k + · exact s_8_3_checked i k + · exact s_8_4_checked i k + · exact s_8_5_checked i k + · exact s_8_6_checked i k + · exact s_8_7_checked i k + · exact s_9_0_checked i k + · exact s_9_1_checked i k + · exact s_9_2_checked i k + · exact s_9_3_checked i k + · exact s_9_4_checked i k + · exact s_9_5_checked i k + · exact s_9_6_checked i k + · exact s_9_7_checked i k + · exact s_10_0_checked i k + · exact s_10_1_checked i k + · exact s_10_2_checked i k + · exact s_10_3_checked i k + · exact s_10_4_checked i k + · exact s_10_5_checked i k + · exact s_10_6_checked i k + · exact s_10_7_checked i k +end SumTable21 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable22.lean b/lean/OAI/Analysis/LaughlinGap/SumTable22.lean new file mode 100644 index 0000000000000000000000000000000000000000..5b7f9a668d8bc0cff0f867a219c428f7bd4b8d5b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable22.lean @@ -0,0 +1,552 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SumTable21 + +namespace OAI + +/-! Sum Table22. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable22 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 22 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 22 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 22 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 22 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 22 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 22 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 10378067916902400]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 22 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 7331053282375680], ![0, 0, 0, 0, 0, 0, 0, -9918795599032320, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 22 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 22 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 22 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 22 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 22 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 22 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 22 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -2075613583380480]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 22 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -1466210656475136], ![0, 0, 0, 0, 0, 0, 0, 1983759119806464, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 22 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 22 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 22 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 22 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 22 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 22 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 22 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 728285467852800]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 22 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 514459879464960], ![0, 0, 0, 0, 0, 0, 0, -696055831511040, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 22 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 22 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 22 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 22 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 22 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 22 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 22 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -374852814336000]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 22 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -264795526195200], ![0, 0, 0, 0, 0, 0, 0, 358264030924800, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 22 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 22 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 22 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 22 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 22 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 22 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 22 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 257041929830400]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 22 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 181574075105280], ![0, 0, 0, 0, 0, 0, 0, -245666764062720, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 22 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 22 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 22 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 22 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 22 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 22 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 22 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -217497017548800]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 22 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -153639602012160], ![0, 0, 0, 0, 0, 0, 0, 207871877283840, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 22 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_0_checked : ∀ i k : Fin 9, fourSumInteger 0 22 13 i k = s_6_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_1_checked : ∀ i k : Fin 9, fourSumInteger 1 22 13 i k = s_6_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_2_checked : ∀ i k : Fin 9, fourSumInteger 2 22 13 i k = s_6_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_3_checked : ∀ i k : Fin 9, fourSumInteger 3 22 13 i k = s_6_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_4_checked : ∀ i k : Fin 9, fourSumInteger 4 22 13 i k = s_6_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_5_checked : ∀ i k : Fin 9, fourSumInteger 5 22 13 i k = s_6_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 205633543864320]] +lemma s_6_6_checked : ∀ i k : Fin 9, fourSumInteger 6 22 13 i k = s_6_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 145259260084224], ![0, 0, 0, 0, 0, 0, 0, -196533411250176, 0]] +lemma s_6_7_checked : ∀ i k : Fin 9, fourSumInteger 7 22 13 i k = s_6_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_0_checked : ∀ i k : Fin 9, fourSumInteger 0 22 15 i k = s_7_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_1_checked : ∀ i k : Fin 9, fourSumInteger 1 22 15 i k = s_7_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_2_checked : ∀ i k : Fin 9, fourSumInteger 2 22 15 i k = s_7_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_3_checked : ∀ i k : Fin 9, fourSumInteger 3 22 15 i k = s_7_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_4_checked : ∀ i k : Fin 9, fourSumInteger 4 22 15 i k = s_7_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_5_checked : ∀ i k : Fin 9, fourSumInteger 5 22 15 i k = s_7_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -171361286553600]] +lemma s_7_6_checked : ∀ i k : Fin 9, fourSumInteger 6 22 15 i k = s_7_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, -121049383403520], ![0, 0, 0, 0, 0, 0, 0, 163777842708480, 0]] +lemma s_7_7_checked : ∀ i k : Fin 9, fourSumInteger 7 22 15 i k = s_7_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_0_checked : ∀ i k : Fin 9, fourSumInteger 0 22 17 i k = s_8_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_1_checked : ∀ i k : Fin 9, fourSumInteger 1 22 17 i k = s_8_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_2_checked : ∀ i k : Fin 9, fourSumInteger 2 22 17 i k = s_8_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_3_checked : ∀ i k : Fin 9, fourSumInteger 3 22 17 i k = s_8_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_4_checked : ∀ i k : Fin 9, fourSumInteger 4 22 17 i k = s_8_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_5_checked : ∀ i k : Fin 9, fourSumInteger 5 22 17 i k = s_8_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_6_checked : ∀ i k : Fin 9, fourSumInteger 6 22 17 i k = s_8_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_7_checked : ∀ i k : Fin 9, fourSumInteger 7 22 17 i k = s_8_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_0_checked : ∀ i k : Fin 9, fourSumInteger 0 22 19 i k = s_9_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_1_checked : ∀ i k : Fin 9, fourSumInteger 1 22 19 i k = s_9_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_2_checked : ∀ i k : Fin 9, fourSumInteger 2 22 19 i k = s_9_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_3_checked : ∀ i k : Fin 9, fourSumInteger 3 22 19 i k = s_9_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_4_checked : ∀ i k : Fin 9, fourSumInteger 4 22 19 i k = s_9_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_5_checked : ∀ i k : Fin 9, fourSumInteger 5 22 19 i k = s_9_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_6_checked : ∀ i k : Fin 9, fourSumInteger 6 22 19 i k = s_9_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_7_checked : ∀ i k : Fin 9, fourSumInteger 7 22 19 i k = s_9_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_0_checked : ∀ i k : Fin 9, fourSumInteger 0 22 21 i k = s_10_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_1_checked : ∀ i k : Fin 9, fourSumInteger 1 22 21 i k = s_10_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_2_checked : ∀ i k : Fin 9, fourSumInteger 2 22 21 i k = s_10_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_3_checked : ∀ i k : Fin 9, fourSumInteger 3 22 21 i k = s_10_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_4_checked : ∀ i k : Fin 9, fourSumInteger 4 22 21 i k = s_10_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_5_checked : ∀ i k : Fin 9, fourSumInteger 5 22 21 i k = s_10_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_6_checked : ∀ i k : Fin 9, fourSumInteger 6 22 21 i k = s_10_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_7_checked : ∀ i k : Fin 9, fourSumInteger 7 22 21 i k = s_10_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 11 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7], ![s_6_0, s_6_1, s_6_2, s_6_3, s_6_4, s_6_5, s_6_6, s_6_7], ![s_7_0, s_7_1, s_7_2, s_7_3, s_7_4, s_7_5, s_7_6, s_7_7], ![s_8_0, s_8_1, s_8_2, s_8_3, s_8_4, s_8_5, s_8_6, s_8_7], ![s_9_0, s_9_1, s_9_2, s_9_3, s_9_4, s_9_5, s_9_6, s_9_7], ![s_10_0, s_10_1, s_10_2, s_10_3, s_10_4, s_10_5, s_10_6, s_10_7]] +lemma sums_checked : ∀ u : Fin 11, ∀ a i k, fourSumInteger a 22 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k + · exact s_6_0_checked i k + · exact s_6_1_checked i k + · exact s_6_2_checked i k + · exact s_6_3_checked i k + · exact s_6_4_checked i k + · exact s_6_5_checked i k + · exact s_6_6_checked i k + · exact s_6_7_checked i k + · exact s_7_0_checked i k + · exact s_7_1_checked i k + · exact s_7_2_checked i k + · exact s_7_3_checked i k + · exact s_7_4_checked i k + · exact s_7_5_checked i k + · exact s_7_6_checked i k + · exact s_7_7_checked i k + · exact s_8_0_checked i k + · exact s_8_1_checked i k + · exact s_8_2_checked i k + · exact s_8_3_checked i k + · exact s_8_4_checked i k + · exact s_8_5_checked i k + · exact s_8_6_checked i k + · exact s_8_7_checked i k + · exact s_9_0_checked i k + · exact s_9_1_checked i k + · exact s_9_2_checked i k + · exact s_9_3_checked i k + · exact s_9_4_checked i k + · exact s_9_5_checked i k + · exact s_9_6_checked i k + · exact s_9_7_checked i k + · exact s_10_0_checked i k + · exact s_10_1_checked i k + · exact s_10_2_checked i k + · exact s_10_3_checked i k + · exact s_10_4_checked i k + · exact s_10_5_checked i k + · exact s_10_6_checked i k + · exact s_10_7_checked i k +end SumTable22 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable23.lean b/lean/OAI/Analysis/LaughlinGap/SumTable23.lean new file mode 100644 index 0000000000000000000000000000000000000000..362686a0ddf3ca45e5655b66d7861ff8fcd161c5 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable23.lean @@ -0,0 +1,601 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CheckedTables +import OAI.Analysis.LaughlinGap.IntegerFourRows + +namespace OAI + +/-! Sum Table23. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable23 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 23 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 23 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 23 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 23 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 23 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 23 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 23 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 23 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 23 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 23 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 23 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 23 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 23 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 23 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 23 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 23 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 23 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 23 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 23 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 23 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 23 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 23 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 23 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 23 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 23 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 23 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 23 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 23 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 23 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 23 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 23 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 23 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 23 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 23 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 23 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 23 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 23 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 23 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 23 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 23 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_0_checked : ∀ i k : Fin 9, fourSumInteger 0 23 11 i k = s_5_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_1_checked : ∀ i k : Fin 9, fourSumInteger 1 23 11 i k = s_5_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_2_checked : ∀ i k : Fin 9, fourSumInteger 2 23 11 i k = s_5_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_3_checked : ∀ i k : Fin 9, fourSumInteger 3 23 11 i k = s_5_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_4_checked : ∀ i k : Fin 9, fourSumInteger 4 23 11 i k = s_5_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_5_checked : ∀ i k : Fin 9, fourSumInteger 5 23 11 i k = s_5_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_6_checked : ∀ i k : Fin 9, fourSumInteger 6 23 11 i k = s_5_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_5_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_5_7_checked : ∀ i k : Fin 9, fourSumInteger 7 23 11 i k = s_5_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_0_checked : ∀ i k : Fin 9, fourSumInteger 0 23 13 i k = s_6_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_1_checked : ∀ i k : Fin 9, fourSumInteger 1 23 13 i k = s_6_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_2_checked : ∀ i k : Fin 9, fourSumInteger 2 23 13 i k = s_6_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_3_checked : ∀ i k : Fin 9, fourSumInteger 3 23 13 i k = s_6_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_4_checked : ∀ i k : Fin 9, fourSumInteger 4 23 13 i k = s_6_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_5_checked : ∀ i k : Fin 9, fourSumInteger 5 23 13 i k = s_6_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_6_checked : ∀ i k : Fin 9, fourSumInteger 6 23 13 i k = s_6_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_6_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_6_7_checked : ∀ i k : Fin 9, fourSumInteger 7 23 13 i k = s_6_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_0_checked : ∀ i k : Fin 9, fourSumInteger 0 23 15 i k = s_7_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_1_checked : ∀ i k : Fin 9, fourSumInteger 1 23 15 i k = s_7_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_2_checked : ∀ i k : Fin 9, fourSumInteger 2 23 15 i k = s_7_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_3_checked : ∀ i k : Fin 9, fourSumInteger 3 23 15 i k = s_7_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_4_checked : ∀ i k : Fin 9, fourSumInteger 4 23 15 i k = s_7_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_5_checked : ∀ i k : Fin 9, fourSumInteger 5 23 15 i k = s_7_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_6_checked : ∀ i k : Fin 9, fourSumInteger 6 23 15 i k = s_7_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_7_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_7_7_checked : ∀ i k : Fin 9, fourSumInteger 7 23 15 i k = s_7_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_0_checked : ∀ i k : Fin 9, fourSumInteger 0 23 17 i k = s_8_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_1_checked : ∀ i k : Fin 9, fourSumInteger 1 23 17 i k = s_8_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_2_checked : ∀ i k : Fin 9, fourSumInteger 2 23 17 i k = s_8_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_3_checked : ∀ i k : Fin 9, fourSumInteger 3 23 17 i k = s_8_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_4_checked : ∀ i k : Fin 9, fourSumInteger 4 23 17 i k = s_8_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_5_checked : ∀ i k : Fin 9, fourSumInteger 5 23 17 i k = s_8_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_6_checked : ∀ i k : Fin 9, fourSumInteger 6 23 17 i k = s_8_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_8_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_8_7_checked : ∀ i k : Fin 9, fourSumInteger 7 23 17 i k = s_8_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_0_checked : ∀ i k : Fin 9, fourSumInteger 0 23 19 i k = s_9_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_1_checked : ∀ i k : Fin 9, fourSumInteger 1 23 19 i k = s_9_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_2_checked : ∀ i k : Fin 9, fourSumInteger 2 23 19 i k = s_9_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_3_checked : ∀ i k : Fin 9, fourSumInteger 3 23 19 i k = s_9_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_4_checked : ∀ i k : Fin 9, fourSumInteger 4 23 19 i k = s_9_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_5_checked : ∀ i k : Fin 9, fourSumInteger 5 23 19 i k = s_9_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_6_checked : ∀ i k : Fin 9, fourSumInteger 6 23 19 i k = s_9_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_9_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_9_7_checked : ∀ i k : Fin 9, fourSumInteger 7 23 19 i k = s_9_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_0_checked : ∀ i k : Fin 9, fourSumInteger 0 23 21 i k = s_10_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_1_checked : ∀ i k : Fin 9, fourSumInteger 1 23 21 i k = s_10_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_2_checked : ∀ i k : Fin 9, fourSumInteger 2 23 21 i k = s_10_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_3_checked : ∀ i k : Fin 9, fourSumInteger 3 23 21 i k = s_10_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_4_checked : ∀ i k : Fin 9, fourSumInteger 4 23 21 i k = s_10_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_5_checked : ∀ i k : Fin 9, fourSumInteger 5 23 21 i k = s_10_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_6_checked : ∀ i k : Fin 9, fourSumInteger 6 23 21 i k = s_10_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_10_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_10_7_checked : ∀ i k : Fin 9, fourSumInteger 7 23 21 i k = s_10_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_11_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_11_0_checked : ∀ i k : Fin 9, fourSumInteger 0 23 23 i k = s_11_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_11_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_11_1_checked : ∀ i k : Fin 9, fourSumInteger 1 23 23 i k = s_11_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_11_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_11_2_checked : ∀ i k : Fin 9, fourSumInteger 2 23 23 i k = s_11_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_11_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_11_3_checked : ∀ i k : Fin 9, fourSumInteger 3 23 23 i k = s_11_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_11_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_11_4_checked : ∀ i k : Fin 9, fourSumInteger 4 23 23 i k = s_11_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_11_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_11_5_checked : ∀ i k : Fin 9, fourSumInteger 5 23 23 i k = s_11_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_11_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_11_6_checked : ∀ i k : Fin 9, fourSumInteger 6 23 23 i k = s_11_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_11_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0]] +lemma s_11_7_checked : ∀ i k : Fin 9, fourSumInteger 7 23 23 i k = s_11_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 12 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7], ![s_5_0, s_5_1, s_5_2, s_5_3, s_5_4, s_5_5, s_5_6, s_5_7], ![s_6_0, s_6_1, s_6_2, s_6_3, s_6_4, s_6_5, s_6_6, s_6_7], ![s_7_0, s_7_1, s_7_2, s_7_3, s_7_4, s_7_5, s_7_6, s_7_7], ![s_8_0, s_8_1, s_8_2, s_8_3, s_8_4, s_8_5, s_8_6, s_8_7], ![s_9_0, s_9_1, s_9_2, s_9_3, s_9_4, s_9_5, s_9_6, s_9_7], ![s_10_0, s_10_1, s_10_2, s_10_3, s_10_4, s_10_5, s_10_6, s_10_7], ![s_11_0, s_11_1, s_11_2, s_11_3, s_11_4, s_11_5, s_11_6, s_11_7]] +lemma sums_checked : ∀ u : Fin 12, ∀ a i k, fourSumInteger a 23 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k + · exact s_5_0_checked i k + · exact s_5_1_checked i k + · exact s_5_2_checked i k + · exact s_5_3_checked i k + · exact s_5_4_checked i k + · exact s_5_5_checked i k + · exact s_5_6_checked i k + · exact s_5_7_checked i k + · exact s_6_0_checked i k + · exact s_6_1_checked i k + · exact s_6_2_checked i k + · exact s_6_3_checked i k + · exact s_6_4_checked i k + · exact s_6_5_checked i k + · exact s_6_6_checked i k + · exact s_6_7_checked i k + · exact s_7_0_checked i k + · exact s_7_1_checked i k + · exact s_7_2_checked i k + · exact s_7_3_checked i k + · exact s_7_4_checked i k + · exact s_7_5_checked i k + · exact s_7_6_checked i k + · exact s_7_7_checked i k + · exact s_8_0_checked i k + · exact s_8_1_checked i k + · exact s_8_2_checked i k + · exact s_8_3_checked i k + · exact s_8_4_checked i k + · exact s_8_5_checked i k + · exact s_8_6_checked i k + · exact s_8_7_checked i k + · exact s_9_0_checked i k + · exact s_9_1_checked i k + · exact s_9_2_checked i k + · exact s_9_3_checked i k + · exact s_9_4_checked i k + · exact s_9_5_checked i k + · exact s_9_6_checked i k + · exact s_9_7_checked i k + · exact s_10_0_checked i k + · exact s_10_1_checked i k + · exact s_10_2_checked i k + · exact s_10_3_checked i k + · exact s_10_4_checked i k + · exact s_10_5_checked i k + · exact s_10_6_checked i k + · exact s_10_7_checked i k + · exact s_11_0_checked i k + · exact s_11_1_checked i k + · exact s_11_2_checked i k + · exact s_11_3_checked i k + · exact s_11_4_checked i k + · exact s_11_5_checked i k + · exact s_11_6_checked i k + · exact s_11_7_checked i k +end SumTable23 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable5.lean b/lean/OAI/Analysis/LaughlinGap/SumTable5.lean new file mode 100644 index 0000000000000000000000000000000000000000..805dd2fe3515f7a74445df272c9be04aa9ba08f4 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable5.lean @@ -0,0 +1,169 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CheckedTables +import OAI.Analysis.LaughlinGap.IntegerFourRows + +namespace OAI + +/-! Sum Table5. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable5 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, -94972, -94966, -94958, -94948, -94936, -94922], ![0, 0, -286080, 0, 286080, 572160, 858240, 1144320, 1430400], ![0, 25634952, 19131000, 19131064, 25635040, 38642864, 58154512, 84170000, 116689384], ![-42721662, 46560744, -118419118, -283399044, -194116708, 403690304, 1764284460, 4141928248, 7790884142], ![-23243770, -48779574, -67247544, -78647880, -92340500, -127044844, -210839832, -381163976, -684815646], ![-8911972, -105223452, -181752880, -131318480, -32407560, -334846008, -2045467760, -6913784016, -17617651980], ![-2454728, -42413476, -196716260, -682508052, -1848042244, -3908003548, -6324839580, -6786849420, 216963516]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 5 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 800764, 800758, 800750, 800740, 800728, 800714], ![0, 0, -1721336, 0, 1721324, 3442632, 5163920, 6885184, 8606420], ![0, 5235028, 24527572, 24527596, 5235092, -33349960, -91227592, -168397848, -264860784], ![90922820, 41943908, 292501020, 543058204, 494079448, -153971368, -1700630520, -4445434488, -8687920004], ![65258206, 97823790, 169591948, 280562536, 358840396, 260635548, -229736752, -1399856088, -3609197094], ![-30114484, 282232328, 600249456, 587145664, 615496888, 2476613552, 10089906736, 30212252160, 73147350948], ![-131018508, 193034676, 829815300, 2393216484, 7698911596, 20943759244, 43134396444, 63022681020, 43547979288], ![95513248, 281358748, -39831112, -3368608700, -14750208720, -38529334860, -66557844264, -52036780884, 137698925760]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 5 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -1289344, -1289344, -1289344, -1289344, -1289344, -1289344], ![0, 0, 745480, 0, -745492, -1491000, -2236528, -2982080, -3727660], ![0, -33335152, -48918064, -48918032, -33335120, -2169376, 44579168, 106910496, 184824608], ![-63863060, -240167408, 55883404, 351934408, 175630312, -945384384, -3483465272, -7910967920, -14700247756], ![84907128, -220121340, -420417660, -515981776, -1001481568, -2866252856, -7594299160, -17164291216, -34049566248], ![127339010, -339915648, -155103224, 1928437040, 5188772884, 4966785680, -9302423960, -56058132336, -163582591290], ![211657276, -85170876, -560417292, 476409268, 4094214092, 6000761596, -11264637204, -89361299604, -308400205344], ![53678048, 317068064, 646948960, 844972064, 1634871200, 5868554208, 19282466208, 50368343520, 109582342848], ![120164096, 881947312, 701672720, -7704787104, -29896742880, -36812785104, 88482198288, 563991821184, 1516635833856]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 5 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 8345348, 0, -8345354, -16690716, -25036088, -33381472, -41726870], ![0, 58971014, 51824394, 51824394, 58971008, 73264228, 94704044, 123290444, 159023414], ![125674086, 381393124, -303334882, -988062768, -732343564, 1404269544, 6362223252, 15081964176, 28503938890], ![-149883720, -65181956, -628925556, -1841114416, -2818717568, -1795673288, 3877110776, 17731757456, 44183419896], ![-181952102, 111706036, -313498424, -2652036672, -6246344348, -6734789544, 5800358312, 48684959712, 148505037486], ![58610372, -177702848, -382190352, -625010368, -2465656824, -8444837120, -18898605072, -25556147904, -1921219476], ![229274368, 787940860, -2268549096, -1651868636, 43230135632, 198263696724, 465865417080, 561667478988, -489593884032], ![-617961344, 457966096, 15244919856, 49524862496, 53810139744, -113123089776, -566054436816, -841715039616, 1541898593664], ![-60018304, 3118159584, 13659411584, 9840027456, -78457752576, -270185791392, -135581217024, 1963308492288, 9575072542464]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 5 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, -7046068, 3379036, 3378996, -7046092, -27896184, -59171288, -100871464, -152996824], ![-55476218, 118213148, -129966706, -378146520, -204457100, 812970744, 3096006260, 7066518816, 13146377962], ![-56916672, 515604084, 522279212, -36891024, 33376400, 3123647016, 12819768920, 33902873136, 72349374288], ![-319177054, 765156196, 1302160232, -659004352, -3395650508, 2161961848, 36104153544, 133215355872, 346647643206], ![-296788340, 94049736, 710905880, -2892777432, -16421280064, -35034835080, -19934391288, 137936555160, 667073059356], ![-261550080, -428047992, 4364291408, 12010627000, -4331597856, -92564809896, -258894728304, -307248746904, 450214469760], ![979782560, 1557990008, -6551010360, -21353305872, -6431024784, 73486634040, 67729128456, -734302536000, -4041085112064], ![-353774400, 4400009056, 20951896064, 9461640000, -146808328128, -424417349664, 118408426752, 4699206200832, 19667816158848], ![-53501696, 716597504, 6968086272, 29064469248, 78617966592, 159682440192, 287996746752, 638807110656, 2045351852544]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 5 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![7462644, -17986340, 41831452, 101649236, 76200248, -119782296, -571565240, -1364415528, -2583600244], ![-83321342, -97871658, -3929872, 198504264, 469709892, 730244780, 860945064, 702925000, 57576726], ![157671658, 602196060, 243548488, -2008295328, -6024153788, -9236434584, -5419930200, 16527386496, 73803566814], ![-1201114610, 1605219998, 7332913878, 7771673446, 291334514, 15324404226, 159456363354, 674538505866, 2012823318132], ![-870224288, -585112196, 6756751032, 6346984164, -62304437776, -271428647340, -532567563432, -199637804916, 2631125479488], ![-99467776, 197676768, 2359978272, -536133184, -42106356288, -185666341920, -456454191072, -613813204224, 356828444544], ![2278452480, 19912259472, 29841008192, -159944924832, -878714793792, -1799609891376, 105894585984, 12940156120320, 47735681081088], ![-2245477056, -14282096992, 10963797408, 356723779296, 1596573476256, 3686657606016, 3049883261568, -11583051782016, -56965049636352], ![-562241536, -960079680, 31584440448, 257875476672, 1054346810880, 2722292601600, 4183517065728, 675055290624, -15923882118144]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 5 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![-4663852, -41230836, 25042544, 194156432, 331367272, 167187736, -702613072, -2817009136, -6849716772], ![137537882, -81600660, -249665656, 41092640, 296459556, -1781707896, -11197444632, -36562640832, -90999005010], ![-342899644, 188856092, 951063532, -1295546324, -8963094508, -14958860892, 11981195700, 148314357684, 543068509632], ![58055488, 1242370276, 2306920296, -3010129284, -22726651920, -50744544180, -29529224568, 220553976852, 1121072570112], ![-595029248, -4472047760, 1885216848, 77398399200, 268651116960, 344211585264, -632052239280, -4357552662144, -11520668839680], ![955853760, 4094446976, 2435466880, -19600837632, -46723858752, 55886717568, 596268034560, 1792515698688, 2575305642624], ![-729632640, -11855865600, -28568130048, 95386304256, 756768152448, 2080256369664, 1715663499264, -9396454898688, -49732117324032], ![-378903552, -10581734592, -62806303872, -184123929792, -287589434880, -160383345408, -273513816576, -4870477936896, -28986889890816], ![-14109935616, -124631737344, -357308126208, 334958469120, 6311418347520, 25593010679808, 57679049945088, 52384772284416, -157795184701440]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 5 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![101665968, -357861960, -158855168, 1918414816, 5211088160, 5291128496, -7917265920, -52020252192, -154036934448], ![35685498, -592389238, -2382640654, -6341471966, -14919434394, -32111009962, -62009000034, -105459011538, -154814040612], ![-219552704, 717668968, 3562439248, 6809181144, 9725013152, 24052540536, 98847956496, 363866661576, 1098362229888], ![1354052224, 3800208976, -3384387344, -14893048160, 49990710240, 352951826640, 922600326384, 1026979941504, -1992472530048], ![1074762048, -2722422624, -17612638208, 21258031296, 296085441984, 782112191520, 89491074816, -6511919411712, -28124782967424], ![864949696, 1754418528, -31286547360, -230283291360, -799263274656, -1590662443392, -1053533340288, 4646878963584, 18339320862720], ![627865600, -13127151168, -128764858752, -557280212544, -1531684323840, -3012377102592, -4912416757248, -10554696911616, -39957066918912], ![-8386182144, -79739140608, -265445706240, -53246324736, 2951102668800, 13330952853504, 30721026226176, 24494152151040, -111466307217408], ![-14316244992, -137793858048, -472436084736, 0, 6824076779520, 33779180058624, 94172259557376, 150812096827392, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 5 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 59352, 59348, 59348, 59352, 59360, 59372], ![0, 0, 178800, 0, -178800, -357600, -536400, -715200, -894000], ![0, -24821952, -20757040, -20756976, -24821904, -32951888, -45146912, -61406880, -81731616], ![-8502412, -66002048, 35412308, 136826600, 79326904, -296000640, -1148069896, -2635794800, -4918089428], ![-11597924, -22073820, -37277408, -57208928, -76018600, -82006392, -57622096, 20534288, 181711860], ![-20491112, -6194408, -17874384, -116295200, -246177680, -120156624, 897262016, 3905744544, 10585173960], ![-18674208, -65581096, -12273032, 309187288, 977337688, 1920570632, 2924528520, 3609119976, 3178118856]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 5 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, -500472, -500468, -500468, -500472, -500480, -500492], ![0, 0, 1075824, 0, -1075816, -2151632, -3227456, -4303296, -5379160], ![0, -7646600, -19704440, -19704456, -7646616, 16469088, 52642640, 100874000, 161163104], ![58413960, 69950872, -105722264, -281395448, -269858560, 116098544, 1063685936, 2760113520, 5392590936], ![25269692, 74245068, 101991832, 108509760, 138733176, 282531160, 674707488, 1495000304, 2968081524], ![82559800, -36225584, -196906400, -240034272, -449515088, -1995960736, -7380041760, -20875843008, -48974224344], ![112352152, 284161016, -655092152, -3508878456, -7761244872, -12641403336, -20205286536, -38949401544, -84987642432], ![-56073408, -408047000, -55216160, 3848424632, 14797515792, 33774824184, 54213952320, 54851745960, -10653744816]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 5 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 805840, 805840, 805840, 805840, 805840, 805840], ![0, 0, -465936, 0, 465944, 931888, 1397824, 1863744, 2329640], ![0, 35283024, 45022304, 45022336, 35283056, 15804432, -13413536, -52370816, -101067344], ![-61039304, 56220672, -121741512, -299703504, -182443376, 525260608, 2118630224, 4892887520, 9143255048], ![-90680768, 146740616, 403096664, 678387712, 1281781152, 2831611152, 6255378864, 12789753120, 23980571616], ![-51222652, 322190528, 365727344, -675125312, -2324509528, -1645823712, 7988649360, 38128112352, 106473619596], ![-112320104, 312321800, 1058286120, 1355226728, 1504614360, 5512353272, 24727492056, 82797245400, 222558759456], ![18458128, 143502080, 317626496, 768132160, 2515547616, 6746532672, 12026296320, 9348368832, -23123350800], ![-98047360, -605785728, 2768248064, 11362409184, 5244961824, -51829797312, -131900142528, 42008937696, 1220623156896]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 5 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, -5215848, 0, 5215852, 10431704, 15647552, 20863392, 26079220], ![0, -58077684, -53611052, -53611052, -58077680, -67010936, -80410824, -98277352, -120610532], ![73140684, -65022456, 384593692, 834209920, 696046856, -617674960, -3694735000, -9122912672, -17489987244], ![-68027968, -260262568, -24809560, 638331040, 1177264992, 488203824, -3084535216, -11748529248, -28263249888], ![6300756, -407155432, -508905984, 432513408, 1991046472, 1425592336, -7477518160, -35562043776, -99459349764], ![-40213496, -154560976, 293051232, 1531542592, 2718935952, 2769289952, 2670288480, 8214302784, 30988555224], ![-239518768, 3055262952, 3122856288, -12689125512, -41635610896, -49383933768, 21493475904, 222267141096, 596821680576], ![1308159584, -943068416, -8457409792, -1719495648, 56814122400, 158136098112, 81881460672, -894958621920, -4418371955712], ![416694784, -2683856384, 4165160448, 48236725440, 80035064064, -133258713984, -841733857536, -1466483523648, 1045358645760]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 5 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 5742920, -772712, -772792, 5742856, 18774304, 38321520, 64384368, 96962608], ![6372924, -114582792, 28129724, 170842320, 49886648, -598405712, -2037703128, -4531673792, -8343985596], ![136850000, -206327000, -282479416, -91606784, -380760800, -2644045744, -9122618288, -22804686688, -47425509360], ![242564292, -535803592, -1302646176, -1025504832, -967875288, -6985164080, -31820644176, -97401408000, -237134316084], ![151304136, -969814960, -1483941712, 1252555728, 5769351008, 1803663856, -34178557104, -145800699984, -411010657464], ![411579456, -1670867440, -1883966528, 6625959824, 16298588896, -5266277808, -102841409280, -301540354896, -595847458272], ![-975944848, 2283992000, 1571858560, -9928906704, 28755374064, 283985262624, 891400208160, 1556321329200, 1062212772192], ![759433088, -4913331968, 10455988224, 92045012160, 102745060992, -496287563904, -2255511379968, -3846992525376, 1628809737984], ![348294656, 1085206528, 1970006016, 5057253888, 17098447872, 40739956224, 32747979264, -206916323328, -1275902724096]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 5 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![1665176, 16455816, -22045272, -60546408, -45755792, 75618416, 356868016, 851284688, 1612159912], ![-2310012, -78356180, -252964320, -526134384, -873040568, -1244031400, -1564629808, -1735533168, -1632613332], ![-8974348, -3703320, 801035936, 3190466720, 7187809160, 11292276144, 11717069296, 1627375488, -29621635620], ![1016240460, -964062900, -6005573364, -11054382964, -18915158844, -54546336476, -188673359052, -569549511468, -1464523446408], ![835305088, -4310946712, -7604688288, 10176451704, 47704715408, 44943606840, -140890019904, -754697544216, -2225133925872], ![163809696, -1805275008, -3978706176, 5797318976, 43703860224, 108405974016, 148566937728, 19861419072, -594239858784], ![-2281316992, -17932829696, 43951909120, 303577555104, 388911410688, -974977253184, -4431877253760, -3971364155616, 24589695297024], ![4994452096, 27353536896, -23117536896, -322911944640, -498756118080, 1393441532736, 7827462037824, 13185898083072, -19397631052800], ![2709867520, 15100309248, 10995247104, -84206694528, -145017159936, 786556467840, 4643959896576, 10909976343552, 3694049289216]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 5 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![-1440552, 12179112, -43355888, -168045168, -277673968, -203813488, 306179328, 1589162560, 4066210632], ![-65592684, 184690696, 568591392, 903850592, 1571936968, 4081774320, 11633469296, 29682039168, 66501139644], ![181000840, -592001288, -1714498248, -1575776424, -614433368, -5962798136, -37680255192, -137308778136, -380217285888], ![110922768, -409258216, -680610144, 4896463176, 25176885968, 60436905864, 75486049728, -44090016168, -549755408928], ![957761728, 6243074176, -21220732672, -88532666016, -3846030816, 579771518016, 1425784633152, 5164780896, -10625781003552], ![-794186624, 636398336, 10534479360, 27283551744, 34255206528, 36503596800, 202869553920, 1182264365568, 4644109806336], ![1201456896, 15430388736, -17224439808, -244012463616, -454595944704, 751283563008, 5550290144256, 11423424190464, -4069547209728], ![-1193078784, -189417216, -12499593216, -125210777472, -440693189376, -735664904832, -57256303104, 2517573307392, 3605244724224], ![17944049664, 132629520384, 145648115712, -1182209402880, -5347098611712, -8568064327680, 4685914202112, 39761935589376, -36414273392640]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 5 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![-45273392, 291716112, 261887248, -883841952, -2717935648, -2459621088, 6201730016, 34283218560, 98685032496], ![-232702844, -489954012, 178427556, 2755633924, 7956699116, 17044192204, 33760772604, 66669592092, 130484512488], ![345246752, 303492976, -1001930560, -3068408624, -5261468000, -14785738416, -64916529408, -245607830160, -746165310528], ![-1064263200, 5361890048, 10414070528, -7311157088, -11777997792, 158332843584, 715349764800, 1612753744800, 2163684576768], ![-936189824, 9012087296, -11041128448, -123386575296, -90899227776, 969095081856, 3951414567936, 6722019340608, -1852271486208], ![-2977107584, -12036047744, 8712987264, 106782118848, 70937097792, -943068937536, -3864766551360, -5985037124352, 8863347677184], ![-5179104256, -15857687808, -32581810176, -129310414464, -551616189696, -1601584203648, -2873945378304, -1222474226688, 13698537735168], ![8986518528, 71554510848, 68102369280, -762646004736, -3438046470144, -6052469170176, 144846434304, 18591946813440, -25722993973248], ![19088326656, 157478694912, 314957389824, -853009597440, -6141669101568, -14330561236992, -8188892135424, 34802791575552, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 5 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, -237360, -237400, -237432, -237456, -237472, -237480], ![0, 0, -715200, 0, 715200, 1430400, 2145600, 2860800, 3576000], ![0, -23913760, -40173600, -40173600, -23913920, 8605440, 57384640, 122424000, 203724000], ![-29604792, 176620128, -252810872, -682241872, -476016912, 1001519872, 4386024112, 10313151072, 19418555512], ![-4617000, -18068760, -16955680, -1277920, 5565360, -43223856, -217842912, -611889568, -1342363704], ![4945520, -119140400, -42062080, 566376640, 1572198880, 1913080736, -865822272, -11076047424, -35349994800], ![-43838048, 61595888, 230813040, 99717040, -458845840, -500992624, 2746782864, 13979601360, 38451470640]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 5 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 2001840, 2001880, 2001912, 2001936, 2001952, 2001960], ![0, 0, -4303200, 0, 4303280, 8606624, 12910016, 17213440, 21516880], ![0, -30659440, 17571920, 17571760, -30659760, -127122528, -271816480, -464741600, -705897920], ![73125264, -240071216, 195572784, 631216304, 318019104, -1492858528, -5550255968, -12603012448, -23399967248], ![17942008, -13118984, 86554544, 316962272, 498366640, 271292912, -903471296, -3744877024, -9151615512], ![1417648, 425240864, -80955712, -2869601920, -7519714080, -10063471936, -1212794688, 35414079744, 125066008080], ![335582352, -530890992, -2200766320, -2339101680, -484174800, -2697144144, -21113171856, -59485977360, -72848450400], ![-571212416, 1010005040, 5426708000, 5985886160, -10010253440, -50114202864, -97507087200, -91314381840, 78863780160]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 5 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -3223360, -3223360, -3223360, -3223360, -3223360, -3223360], ![0, 0, 1863840, 0, -1863760, -3727456, -5591104, -7454720, -9318320], ![0, 61147520, 22190400, 22190400, 61147520, 139061824, 255933440, 411762560, 606549440], ![13970864, -356092736, 454731824, 1265556384, 895492384, -1836348672, -8110854752, -19108912832, -36011408432], ![-50074080, -231063280, 693701200, 2724220480, 4623825920, 3919178016, -3099733728, -21379589952, -57103739616], ![163016840, -1069276160, -333718880, 5732845120, 15572085200, 17782704448, -13801038176, -125030807232, -386365674600], ![160070128, -1254131568, -1365269680, 7315672400, 30383301680, 59146052848, 53589608112, -77443214160, -496374384000], ![-78343488, 195685760, 1152943360, 2415518080, 1598846720, -8580925056, -44248344960, -131692513920, -297618235200], ![788767232, -6824329408, -5390591808, 57168332032, 177582281472, 132919698240, -610489366080, -2667759600000, -5918795625600]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 5 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 20863440, 0, -20863400, -41726768, -62590112, -83453440, -104316760], ![0, -64780520, -82647000, -82647000, -64780480, -29047408, 24552240, 96018480, 185351320], ![-75833704, 780076176, -715131144, -2210338624, -1354429104, 4203714848, 16815211088, 38831178048, 72602734888], ![-140935904, 528684912, -198714512, -2323134656, -3636999040, 274846176, 16035132512, 52474169408, 120629844384], ![-179715480, 953943440, 263981920, -5386594560, -14504698480, -16337077792, 13759771424, 118949701248, 365547021240], ![-187610864, 418939584, 1315906880, 514039680, -2806523360, -5140865152, 687820992, 14603923200, -533831760], ![1899235136, -6763212880, -19752476640, 20918055760, 187151821440, 406278026640, 195966062880, -1586864898960, -6713322105600], ![-4136329984, 18461699136, 61473782336, -30806786304, -533167037184, -1488210757440, -1975309744320, 823456360320, 12231635644800], ![1712768256, -18181710208, -12219323392, 208041629184, 663344087040, 377447114880, -3416133219840, -14471306952960, -32695958380800]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 5 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, -4223760, 21838960, 21838800, -4223920, -56349088, -134536800, -238787360, -369101280], ![-32491688, 277733232, -466715208, -1211163488, -900938608, 1518632160, 7102221520, 16904502400, 31980148200], ![1668800, 710644560, -861280400, -4714105280, -7859622720, -4321419488, 14865124064, 61652835776, 150982754688], ![-136832376, 2028053072, -250614176, -13718100480, -35935851440, -46097680032, 4154044064, 199912207488, 672188772120], ![-750133776, 3567481376, 5826046560, -14045921120, -69551893120, -133679787552, -100675285728, 241230434400, 1205827135920], ![-798774912, 4902459680, 10408293440, -27062640800, -155588322560, -305207033376, -80691766080, 1437475126560, 5673297400320], ![-1362507840, 5355115680, -7161410720, -57231807360, 33767291520, 758976921120, 2515104488160, 4148255453760, 247527646080], ![5560717952, -39196062336, -51539953664, 370320188928, 1362334794240, 1094725737600, -5976053698560, -27757774936320, -65069145947520], ![-532138496, 1685829632, 15037384704, 31925114880, -24361328640, -352580490240, -1221697551360, -2627506252800, -3423625920000]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 5 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![10457872, -64314448, 74080432, 212475152, 137702752, -363403488, -1504010208, -3497284128, -6556392208], ![23485448, -88644264, -237086016, -421840608, -742212080, -1396806992, -2683533664, -4999601376, -8841519528], ![-200792920, 760151600, 1197350880, -574677760, -3193404400, 799726624, 28007311392, 107224003584, 282484535160], ![-478910472, 7508085432, 6420941400, -47765251560, -189651680440, -374257746296, -375931724184, 338692551720, 2757056578320], ![-3572051968, 14311407280, 41664066720, -36127755440, -382985861760, -955168782960, -1045503166560, 1221391847280, 9092800812480], ![-1891997184, 3687661056, 24184496256, 23340868096, -104269208064, -463476362880, -915271969920, -638518721280, 2390842671360], ![19685083648, -143106844224, -281847343616, 1039857038592, 5180016207360, 8258661512640, -6023785870080, -67884544590720, -203338174490880], ![-31310102144, 147819036928, 623429304576, -269369944320, -6427258295040, -18689101537920, -20452694021760, 41236447824000, 259260360353280], ![-14620487680, 43050063360, 330363816960, 387423505920, -1914199541760, -9680662168320, -20917585328640, -14553992344320, 67289542594560]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 5 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![16568336, -95413648, 912128, 305546624, 481631520, -144551840, -2583582400, -8182898240, -18626794320], ![12768360, -471382160, 292771040, 4050451200, 10291972240, 13997828000, 3383780640, -42354051840, -155294109000], ![-344377584, 2324638064, 2844899120, -12465660240, -53586956720, -103819238256, -88983338544, 156801454800, 922895466240], ![-1405709504, 3681585360, 15940927200, 12307601200, -54549302400, -232486523664, -517870690080, -772030287600, -600183196800], ![-8131822080, 61179873600, 63689048000, -457645950720, -1509301612800, -1252376410560, 4728483883200, 21358160208000, 46974912716160], ![1938025600, -10896748800, -39140039680, 33594839040, 478847301120, 1450849044480, 2150490186240, -628593039360, -14135131570560], ![-17985969408, 96890259456, 336751030272, -453704878080, -4465986032640, -10612694737920, -4593015398400, 51478939100160, 213059409488640], ![-1363083264, 24184318464, 42227143680, -344787463680, -1845745735680, -3666687847680, 1367569082880, 33330496193280, 125116570275840], ![-91748376576, 354197053440, 2797697802240, 3398456033280, -20591525560320, -112345339392000, -272775535718400, -265079570595840, 728285467852800]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 5 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![164633728, -1030760096, -404369472, 5225615360, 14334531200, 15984773824, -14880669568, -122144689536, -373222527360], ![-301857880, -129314840, 1167329480, 4111219080, 10303620120, 23415243992, 47128151928, 75774147000, 71997528240], ![-372134656, 2664003360, 7158948160, -4449054240, -64962568960, -203687003808, -401342932800, -508762969440, -115613013120], ![946176256, -2016123584, -31569431744, -31815144704, 284989860096, 1338297723840, 2846663730240, 1887860684160, -9962526288000], ![-9816883840, 62129496960, 99078809600, -520889341440, -2051401597440, -1784595246720, 8615058862080, 40983655215360, 96015554743680], ![15607377024, -59699218688, -306529894656, -85195011840, 2401206762240, 8385879173760, 12910249672320, -3883618527360, -82159141109760], ![10167660544, -1138205184, -238038082560, -948636142080, -1281398384640, 3413888375040, 24562083786240, 78122296961280, 165116685127680], ![-50054393856, 213312983040, 1570485227520, 1589055283200, -13038551285760, -66171942819840, -153122309683200, -123946312089600, 514459879464960], ![-95441633280, 262464491520, 3149573898240, 6824076779520, -13648153559040, -127951439616000, -409444606771200, -696055831511040, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 5 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 3 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7]] +lemma sums_checked : ∀ u : Fin 3, ∀ a i k, fourSumInteger a 5 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k +end SumTable5 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable7.lean b/lean/OAI/Analysis/LaughlinGap/SumTable7.lean new file mode 100644 index 0000000000000000000000000000000000000000..5fe536fd71cc0d23560b970432683f008abbdc9b --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable7.lean @@ -0,0 +1,216 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SumTable5 + +namespace OAI + +/-! Sum Table7. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable7 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, -284910, -284900, -284888, -284874], ![0, 0, 0, 0, -1430400, -572160, 286080, 1144320, 2002560], ![0, 0, 0, -95655240, -128174880, -141182544, -134678384, -108662512, -63135000], ![0, 0, -355257390, 469641980, 23229980, -931706688, -1632381140, -1316006344, 780204846], ![0, 12215434, -43188872, -133931688, -213214004, -262316780, -290600440, -335504520, -462547470], ![-133838132, 19013588, 231211824, -33151824, -381639976, -50476376, 1538446608, 4220560112, 6531610756], ![-101230648, -11286596, 39309084, 28991980, 99173020, 388071780, 1039909156, 2635743092, 7242972012]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 7 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 2402286, 2402276, 2402264, 2402250], ![0, 0, 0, 0, -8606740, -3442744, 1721232, 6885184, 12049108], ![0, 0, 0, -122638100, -26175260, 12410008, -6882312, -84052248, -219099840], ![0, 0, 877503276, -375282644, -130388264, 713578488, 1258009576, 604296808, -2146168212], ![0, 576320942, 791625452, 810917032, 993671692, 1483679644, 2209045776, 2882189992, 2999847418], ![-125588084, 412661576, 967921968, 3224148352, 5318462008, 3969250096, -3395733328, -16511266176, -30146558108], ![-69228908, 234405492, 483866628, 3894296548, 10095296940, 14466846732, 9584840092, -14935436356, -77167233288], ![-100115248, 38430700, 1223125768, 3445512340, 4991165280, 1975112868, -8584283896, -16242793764, 33263241600]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 7 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -3868032, -3868032, -3868032, -3868032], ![0, 0, 0, 0, 3727340, 1490888, -745584, -2982080, -5218604], ![0, 0, 0, 244590320, 166675760, 135509984, 151092896, 213424416, 322504480], ![0, 0, 167650572, -1312604088, -431082648, 1395149760, 2749027528, 2213484688, -1628544972], ![0, -529040700, -1129929804, -2254479408, -1429350912, 2334791112, 8543278600, 15217439920, 18894600040], ![99555218, -939477680, -22309080, -3382243152, -7409616716, -4557579472, 10752126184, 36223385040, 55779927926], ![-35426884, -251339708, 342464244, -2514863692, -8425173300, -7901973252, 15647560428, 76753690476, 170907912288], ![-24509344, -210751072, 103058912, 1557812640, 3116144160, 2169865824, -2451415008, -4482874272, 18217763520], ![-29385728, -337280848, 444820560, 5483776480, 11323508960, -3130702032, -66157159728, -147898438656, -20019231936]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 7 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 41726710, 16690660, -8345400, -33381472, -58417558], ![0, 0, 0, -259121910, -294855040, -309148316, -302001748, -273415348, -223389130], ![0, 0, -910004466, 2513635264, 1235039924, -1924449144, -4143490892, -2600744528, 5525130522], ![0, 2299956796, 608726428, 2159722160, 2537790112, -23130824, -4640009128, -7780720816, -3264049624], ![446532026, 1276975700, -49166008, 2440467072, 5458061220, 2011737240, -13038345432, -37423887904, -55912353266], ![547816852, -634017248, -2565251856, -7667057088, -16299883480, -26194390464, -33543871312, -33065195712, -14873884452], ![468810416, -1929618996, -3247342104, -5038193420, -28747296000, -89007154236, -135328454360, -13183657092, 473683878720], ![335094848, 353199632, -6348574480, -11009306720, 31290052640, 156819131280, 240151161456, -222486793728, -2198222387328], ![346499968, -502160160, -4578197760, 1963053760, 44587549440, 82311336288, -123462604416, -1007889404544, -2692718975232]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 7 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -16895180, 35230340, 56080488, 45655400, 3955160, -69020200], ![0, 0, -389899938, 850999032, -17447948, -1729633128, -3019948844, -2622787456, 727458714], ![0, -1004185164, -984159492, 1865093840, 1567159792, -4268527064, -14446683336, -24186177296, -25120029056], ![-383529406, -82360956, -1423180184, 5348210560, 11618374516, 1426821304, -37513413048, -102795185952, -166296667098], ![334127516, 747671080, -144191976, 3503827240, 11131000160, 6507741624, -39537160248, -148051929448, -287481950388], ![-559991072, 996322728, 1163069616, 3646584600, 31386661120, 101845483000, 170826305328, 81928145928, -418190130240], ![-585477504, -1364382600, 7342209000, 22255917360, 8218113680, -54842301512, -45783910296, 432287232000, 2048808146880], ![838314688, -827579040, -12556195200, -16866580800, 21885335360, 15303909600, -485188206720, -2274461751936, -5564316269952], ![56106240, -948657920, -6870283520, -21383271680, -40193111040, -51829988352, -75310743552, -262351186944, -1052599561728]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 7 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 125494284, -173594556, -46349576, 251428872, 463940456, 335384824, -390038436], ![0, 150865046, 432691232, 172055528, -432435996, -1301339988, -2474376248, -4110428152, -6487543066], ![261346026, -18614180, -2708089912, -2356958240, 388875076, 2445093736, 1946587816, 1905069696, 13866689246], ![-225328066, -1559564354, -7260973482, 10885440102, 49046275410, 44686750914, -110724955750, -517582167926, -1170913868028], ![1079749776, 3044240332, -1706806136, -1357896780, 32352878240, 78211201988, -25102039288, -598527868356, -1931487707520], ![49497664, 1770723552, 6276367520, 19032839360, 53428632000, 113474503648, 152336009376, 41931228672, -355730810688], ![-514427904, -6944671600, 1674259200, 111384213920, 331328435520, 200534821200, -1388197076160, -4911080712384, -5778132611328], ![296532800, 1286361760, -25965924320, -172053028640, -433096614240, -213807963264, 2039922770688, 7324926229632, 9576103899648], ![-191659520, -3977072960, -31094718080, -127346971200, -294462101760, -252484463616, 810157370880, 3673693740288, 5914651911168]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 7 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, -77739892, 121080464, -194301360, -350167704, -77031144, 490365040, 813046672, -52191236], ![78414746, -51518292, -28231160, -1890472928, -3167171676, 416672264, 12234093544, 32050269504, 53316628334], ![-241579900, 291902108, -332165076, 5262401068, 16649509780, 17656410276, -20214095052, -121161570892, -273799389312], ![417878160, 195362324, 1440817688, 9202259500, 18282454720, 2544596572, -76903200168, -226443544092, -316718694720], ![259986048, 1340119408, -4411907440, -34670282400, -61599346080, 65681368560, 541774127376, 1114109736960, 42812594880], ![-675968064, -4329160320, -5326949760, 4247306240, -1522591040, -104402971008, -346162561536, -402997410816, 987666413184], ![-774629760, 1199924480, 4606292480, -40434991360, -186473631360, -137628641280, 1311999406080, 6033290486784, 13175464803072], ![-90017280, 5934351680, 35983227520, 88251854400, 84328638720, -54919873536, 60737757696, 2164776776448, 9635534717952], ![7838853120, 56366914560, 63107251200, -682994073600, -3858188083200, -10290184261632, -14398184706048, -631141834752, 32130241228800]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 7 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![47548112, -344738472, 1238578816, -1301142624, -4649603232, -1727326992, 12662573440, 36186631648, 53333261872], ![-448349366, 447245930, 1191533490, -715880414, -4099730810, -3300300138, 10890416606, 50320127022, 130013268300], ![714091616, 69914440, -2143670480, 600782520, 9377241280, 4164234520, -62361084368, -248937550104, -574815624960], ![-242747072, -4715681200, -3433957200, 897975840, -49031106400, -219347049008, -397390251984, -33980057088, 1955916792192], ![-1954453184, -3268996960, 8642229120, 16651348800, -21715474240, 24930211104, 808957034112, 3512894132352, 8578228804992], ![-125858880, 1566261600, 21295903200, 85147597600, 137325794400, -139010898816, -1302002946816, -3198015646848, -2072160110592], ![-848514560, 10084184000, 89591425920, 306000696000, 573537442560, 546446951424, 239059121664, 2334207752448, 16447588844544], ![4658990080, 38280373760, 74223705600, -271658434560, -2000767549440, -5755900372992, -8437492377600, -295110266880, 22696759388160], ![7953469440, 62633571840, 107371837440, -656161228800, -4724360847360, -15354172753920, -30025937829888, -30708345507840, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 7 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, -35628, -35624, -35616, -35604], ![0, 0, 0, 0, -178800, -71520, 35760, 143040, 250320], ![0, 0, 0, 49644048, 45578864, 43952944, 44766048, 48018016, 53708768], ![0, 0, 51014484, 166013672, 122099128, 14618880, -61078792, -9645424, 264267564], ![0, -38468572, 31119104, 98462304, 169411608, 246306696, 327977200, 409743248, 483415700], ![-25119368, -112357256, -76648592, -28550816, 37421104, 173169904, 407390144, 675941664, 752222824], ![-12119936, -101311208, -155527560, -179470120, -29419624, 338178696, 498439432, -634385688, -4626451800]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 7 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 300300, 300296, 300288, 300276], ![0, 0, 0, 0, -1075816, -430288, 215232, 860736, 1506216], ![0, 0, 0, 15293304, 27351048, 32174112, 29762512, 20116240, 3235264], ![0, 0, -350483832, -373557464, -209421312, 29598768, 231176944, 282987312, 72703800], ![0, -61725492, -213343656, -412373312, -613879560, -799889064, -979389280, -1188327952, -1489612876], ![76241464, 87268304, -397063584, -808944608, -1023918416, -1094871968, -986021920, -306899392, 1953664808], ![57185496, 181765880, -300370488, -248170360, -1691726408, -6481981896, -10542514824, -177417160, 46595385216], ![42226976, 94743432, -286371456, -1273794728, -609144976, 4999758296, 13418420128, 7013313288, -57193600176]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 7 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -483504, -483504, -483504, -483504], ![0, 0, 0, 0, 465944, 186416, -93120, -372672, -652248], ![0, 0, 0, -70566016, -80305424, -84201072, -82253088, -74461568, -60826576], ![0, 0, 366235704, 131716144, 192417936, 371208768, 490955600, 374524896, -155217144], ![0, 29002632, 573087288, 460967616, 1810784, -680715760, -1648445200, -3148711776, -5614350720], ![-144389596, 11001824, 473729072, 292075328, -255305240, -397611168, 389884816, 1647615072, 1193495660], ![-48033640, -184558584, 264345384, 759608936, -65160232, -3132639240, -8006239272, -13260685352, -18759153888], ![-19978224, 105809280, -133233024, -438073536, -719057696, -1697183936, -4559383808, -10699695936, -23304106512], ![-8090880, 344834944, -725511040, -2755619616, 3116331936, 20578149696, 16940765376, -87851994912, -353888514144]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 7 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 5215852, 2086360, -1043136, -4172640, -7302156], ![0, 0, 0, 116155348, 111688720, 109902088, 110795448, 114368792, 120622108], ![0, 0, -438844164, -162517664, -473970936, -1020535824, -1449544536, -1408329568, -544223628], ![0, -734254504, -326086840, 330494432, 683594656, 512455984, -72542704, -629885920, -386921728], ![363763220, 144891608, -111785344, 445850752, 1512391112, 2319420816, 2330033328, 1933340544, 3138980412], ![-124986840, 97799920, 909640416, 1462039360, 3461766864, 8750989152, 15131246816, 13662851648, -10405913544], ![-324766800, 299248776, -1889956608, 5785174296, 13788612432, -13594981992, -87337541728, -120919461048, 99267486912], ![-200486688, 479534080, 4916930432, -3999669728, -33639968224, -31615925184, 106432614720, 404289308448, 549807717888], ![-226568448, 1263785728, 1320497664, -10855953216, -11896335360, 67908910464, 217432638720, 101709913536, -1006373998080]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 7 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -11485880, -4970072, -2363936, -3667216, -8879760, -18001520], ![0, 0, -38237604, 203673968, 181917112, 54692976, -19797528, 116646400, 622225572], ![0, 488338984, -332761112, -193806784, 158149216, 424286800, 754017040, 1744981280, 4443050864], ![-144991612, 133775352, -1042843424, -1147854912, 49779112, 1862716496, 4062806192, 8258658560, 19273216268], ![166315368, 487593360, 56008368, -1425126960, 1636168096, 13691418480, 28871621840, 27273008560, -18213514200], ![164181888, -353898800, 1697742208, -5184301488, -16778914784, -7731832688, 33646750784, 56959300080, -61584482016], ![175393072, -9738432, -3259870912, 2932752688, 7959247536, -33597521248, -128880694944, -149497969104, 102656432736], ![-583742336, 1495518208, 756538368, -20530764608, -12791033472, 153270135936, 425645950464, 121332860352, -2071651076352], ![-247059968, -622772224, -748730368, -3195571712, -14331386880, -36762757632, -57862430208, -55064807424, -48370443264]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 7 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, -9991032, -39572360, -15861904, 29165232, 63534064, 55269648, -27603000], ![0, -106154836, -92295040, 69037776, 402668424, 918527064, 1611648784, 2462173200, 3435344076], ![-59422476, 191560168, 496388768, 808624544, 319823752, -2083257936, -7361462800, -15866029696, -26881393444], ![-375512788, 943747084, -2139664884, -6494690676, -5420716668, 6102465444, 29891883444, 69254445780, 141554940696], ![291347808, 1300689032, 4787115776, -5322403304, -8510524688, 54302047768, 204387353376, 317077952328, 73236624912], ![343604128, 1154945408, 2426835456, -1523229376, -7047855872, 12028336128, 83616153984, 168582044736, 65489272992], ![-150742272, 6938251136, -9752508672, -71824237408, 7953321088, 513491508288, 972397390464, -964408911840, -9023662517760], ![-891893888, -7672461952, 8420372864, 67689957440, -49264794432, -814166449344, -1986061480128, -654046195968, 9432456523776], ![-877938688, -4403266816, -1832541184, 11367160704, -64203842304, -508381847424, -1470258054144, -1990268527104, 931392304128]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 7 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 5354792, 13998032, -7478896, 25138192, 145535632, 336870784, 531771456, 612335880], ![-4083948, -23209080, 351222048, 356271456, -207270456, -1313122320, -3047748752, -5948596864, -11342332356], ![35312520, 105074424, -876719304, -2097371048, -967770712, 4188784584, 11814467368, 17361412968, 17569442304], ![69057328, 1159555960, 188569600, -1795311448, 1501633904, 16761007016, 39938601824, 38986841592, -67369909536], ![-75278016, -1999950720, 6139167360, 20229413728, -33878461536, -188733064384, -169964679744, 688214694240, 2819486663136], ![-256941952, -593491712, -6237940224, -11727436288, -2814447488, -507002112, -115556062464, -531059240448, -1331531663616], ![329964800, -4330634240, 1335003136, 49443392000, 20339064576, -450763255296, -1384448744448, -965256652800, 5464690463232], ![1059636224, 1085705472, 2083265536, 34291391616, 125126514432, 188431892352, 47393178624, 24538415616, 2307699643392], ![-2652653568, -37552447488, -39722213376, 289318901760, 797001486336, -720909877248, -7573702017024, -13253978529792, 23562176901120]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 7 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![-4689008, -15939760, 244449936, -78592800, -663522464, -718147168, 314401248, 2049697920, 2456055408], ![45048612, -626689180, -618995292, -126384124, 1600792620, 4717848396, 6009934204, -2994072036, -35599927608], ![-56049312, 1033324336, 1152152704, 379742864, 1369723104, 7808368272, 22217936704, 43429488048, 64114342848], ![-488595872, -580233216, -6380197504, 2949963424, 19765908128, -34052163264, -226561387968, -433828651104, -252919738368], ![470054272, -2964817664, -4025723904, 19818704448, -13810596736, -310971961728, -803996748288, -483428392128, 2520428841216], ![729682048, 2724831360, -6353403264, -21412099136, 65241836352, 423193275072, 866307701952, 181872066816, -3740521973760], ![2884853760, 7044022016, 5430301696, 42444162432, 252947738880, 725073782400, 1216263932928, 1231690876416, 1467709461504], ![-644119552, -19148730368, -18573373440, 192516553728, 589088231424, -22284066816, -3541323202560, -6197315604480, 16644290217984], ![-3181387776, -42948734976, -85897469952, 196848368640, 944872169472, 0, -8188892135424, -22519453372416, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 7 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 142472, 142448, 142432, 142424], ![0, 0, 0, 0, 715200, 286080, -143040, -572160, -1001280], ![0, 0, 0, -40173600, -23913920, -17409792, -20661568, -33669440, -56433440], ![0, 0, -20007032, -449438032, -243213072, 217274112, 550630064, 375461472, -689624968], ![0, 97772520, -28793440, -140794720, -261630160, -400660272, -553205856, -700547232, -809924088], ![-16606928, 23659920, -171906432, -273109824, -413928096, -914007264, -2000157760, -3527851840, -4702721264], ![-6713888, -13750160, -35566224, -365227088, -1058837520, -1926358384, -2634730608, -2726266416, -1552303632]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 7 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, -1201160, -1201136, -1201120, -1201112], ![0, 0, 0, 0, 4303280, 1721248, -860736, -3442688, -6024624], ![0, 0, 0, 17571760, -30659440, -49951968, -40305696, -1720544, 65803520], ![0, 0, 405292144, 840935664, 527739424, -84993056, -547957728, -411850208, 772634032], ![0, -545839112, -283337424, 109898464, 454131632, 677466608, 815850560, 1013073952, 1520770664], ![175141040, -451026912, -294910016, -708938112, -1272118560, -854096704, 1320793792, 4609486592, 5886140176], ![121335568, -56483824, -916039024, -903622640, -338739920, 31426224, -206091664, -4021132048, -23484468192], ![90123328, -262733968, 407757664, 231882000, -4624763840, -15550442800, -25923103392, -15637818192, 52530269760]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 7 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 1934016, 1934016, 1934016, 1934016], ![0, 0, 0, 0, -1863760, -745568, 372672, 1490944, 2609232], ![0, 0, 0, 22190400, 61147520, 76730432, 68939008, 37773184, -16767040], ![0, 0, -746105296, 64719264, -305344736, -1147763456, -1754004064, -1415534272, 576178128], ![0, 583760400, -16617200, 488760000, 863221120, 612099360, -17270368, -35552832, 2288587104], ![-156831544, 298529088, -251229920, 1557047872, 4165039184, 4045823936, -1343224672, -10607545792, -15462495144], ![-45668368, 161167504, -878402736, -51608240, 3859904560, 8198067440, 7729614512, -1389898576, -14989282176], ![55012544, -171091584, -331559168, -5660800, 3395840, -1105311872, -881084288, 9104217984, 42534770880], ![91243520, -553939136, 2484210112, -3589184768, -17183595008, 1708157760, 81018277056, 122974784640, -154613754240]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 7 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, -20863400, -8345392, 4172640, 16690688, 29208744], ![0, 0, 0, -82647000, -64780480, -57633904, -61207248, -75500496, -100513640], ![0, 0, 1191834296, -303373184, 552536656, 2348893600, 3675027152, 3120266688, -726058392], ![0, -458338704, -762229328, -2463140672, -3353495296, -2550262304, -494957088, 1046358848, -1016922016], ![167454952, 151747088, 690468704, -1353374720, -4486696304, -5364370720, -1567285984, 5619600000, 8429202232], ![-272849328, 234806848, 1944538944, 3792410496, 5883855520, 8401263744, 11073015744, 15358336768, 29347964784], ![-297156608, 673253104, -3881113760, 3946292880, 28925957440, 52147543888, 56228890592, 47725953840, 33875781120], ![366445568, -2634016704, 1359564096, 14999152896, 11237984256, -47229255488, -125861168064, 4780272000, 845386270080], ![371849472, -3523358080, 9415584256, 4728430592, -55793498112, -43997560704, 314051481600, 956501356800, 759288794880]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 7 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 21838800, -4223600, -14648864, -9436512, 11413728, 47901920], ![0, 0, 124350712, -620097568, -309873008, 422221152, 943381072, 620802560, -1178318680], ![0, -76273072, 1214405808, 224184768, -58730432, 1560944416, 4485569120, 6324577472, 2894476864], ![33866504, -662666032, 1214802016, -1078995712, -5105513136, -4752673184, 4254842016, 18845295744, 23089599640], ![85693488, -328028768, 2901424736, 971961504, -8350494720, -18004777248, -15537015776, 11444912224, 68265018480], ![311321344, -624399456, 1250118080, -6483963680, -21932240000, -25189359520, -7110569152, 3556795296, -46830216960], ![140413760, 2283692704, -10677247520, -2197051520, 26654552320, -41225463264, -306290714016, -528058157760, 87446705280], ![306562688, -6882569856, 19883337216, 7804448768, -107796559360, -25053301632, 850795107840, 2318785624320, 1726696878720], ![39116288, -988166144, -2547955712, -1895458816, 3775709184, 19134704640, 66782622720, 228001551360, 714669795840]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 7 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, -15851408, 122543312, 47771232, -112267872, -229673824, -176546208, 175015472], ![0, 80602200, -140591232, -398097504, -791219056, -1359676752, -2083609824, -2883575776, -3620550248], ![-54897496, -65283536, 834848224, 960015104, 1672747024, 5554780192, 14578248736, 28276875264, 41917161336], ![96502456, -2049586888, 4138385496, 2752210456, -12692600120, -26552474232, -8237490328, 62379959336, 151329551184], ![157258432, -1954943504, 11468430304, 12850674320, -17447394240, -58284587184, -59830645152, 34541065776, 295921732800], ![400680192, -416476672, 3055666816, 3983504896, -15374216704, -66438082176, -136588495488, -173436184320, -59111162880], ![1641234432, -10907934784, 52095805184, -30252740608, -435620748800, -367239214656, 1636306014720, 4608503856000, 597302787840], ![-151169664, 4964735232, -63891015936, -23111842048, 464208880896, 742088273280, -1460316147840, -6770971701120, -5183992619520], ![554118144, 172657152, -31416339456, -50344389120, 105279160320, 319395267840, -381657914880, -3010270897920, -4055141376000]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 7 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 46533232, -39975552, 81824384, 75072800, -194972576, -660938688, -1053338688, -900572368], ![-20511384, 108150896, -298264864, 505464576, 2009651856, 2802645408, 1923775776, 216301824, 1680356792], ![105258512, -450219152, 1092461104, -1027724624, -8869652400, -17367836528, -16776842288, 484287184, 28587589632], ![244945536, -998068848, 2044721568, 6129665520, -1526758720, -27138083536, -46205732832, 14316673104, 270967386240], ![-360557056, 3664437568, -24353999680, 32252604160, 152014072320, -33681895872, -759852879936, -1063329540480, 1794134052480], ![66466944, 124421888, -4030835712, -17589870592, -31646935552, -13320787968, 67116986880, 154104698880, 13150684800], ![-547547392, 9345585152, -38875881472, -30917658624, 281860709376, 432324787200, -1333660078080, -5927480908800, -7255580217600], ![-963263488, 6179886592, 5543341056, 6802721280, 106822410240, 287296162560, -56265454080, -2172956248320, -6580214784000], ![-6657392640, 3016433664, -174447452160, -308950548480, 1583963504640, 7428214886400, 11873617367040, 0, -21420160819200]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 7 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![-11016448, 138553312, -696063040, 666944256, 2702916480, 2004603840, -3893951872, -13693531520, -19505851904], ![-57724184, 282858856, -53241400, -2267571832, -6483561320, -12682682920, -20945390472, -29578798664, -31131106704], ![52813184, -694739296, 1830303936, 6744629600, 8580126080, 6260745184, 14181785920, 66046087968, 201280982400], ![-200539136, 1505050944, -14345604544, -4224107264, 52370671616, 65668977600, -56894771904, -124499280000, 518667557760], ![-73343616, 9274913664, -37148734976, -23511996416, 148380747264, -2428778112, -1393234214400, -3600101218560, -2144590884480], ![-618213248, 480259840, 29378451712, 8413305088, -176283278592, -228181534080, 736490494080, 2758256856960, 1227972894720], ![-1717330944, 12781814272, 38866445312, 44044623360, 30143692800, 575013120, -402110522880, -2744771377920, -11313541324800], ![-4702773248, 4590227456, -86338105344, -144459571200, 1002965483520, 4522629703680, 7257051310080, 0, -15131172925440], ![-6362775552, -4772081664, -190883266560, -524928983040, 1049857966080, 8530095974400, 20472230338560, 20472230338560, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 7 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, -996912, -997024, -997120, -997200], ![0, 0, 0, 0, -5006400, -2002560, 1001280, 4005120, 7008960], ![0, 0, 0, -334792640, -448611520, -494139072, -471375744, -380321664, -220976640], ![0, 0, -1243401264, 1643747616, 81305056, -3260974080, -5713334816, -4606022336, 2730717744], ![0, 165999120, -27914880, -345515520, -623005600, -794866912, -893858112, -1051013824, -1495644976], ![-21429280, 53142112, 335425344, -1050257024, -2730373952, -2031708992, 3069112832, 11996096128, 19624346016], ![-50414720, 382008160, -543929376, -1352152224, -858140320, 387503136, 820802080, 357462944, 3869148960]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 7 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 8407728, 8407840, 8407936, 8408016], ![0, 0, 0, 0, -30122400, -12048960, 6024704, 24098560, 42172576], ![0, 0, 0, -429232160, -91612640, 43434496, -24090304, -294186688, -766854400], ![0, 0, 3071261088, -1313489632, -456356992, 2497526976, 4403032256, 2115030464, -7511605536], ![0, -717318224, 36246112, 103768448, 743411424, 2458438752, 4997216896, 7353215680, 7765007824], ![220945888, -717643456, -1596691584, 3477632384, 7985266368, 440572288, -28159321216, -76886158592, -127432188000], ![451178720, -3005757344, 3723650592, 8508775712, -339509280, -23402212896, -55485539872, -101015428896, -187615921536], ![-404663680, 3933329824, -5829620096, -18403095840, -2648281280, 56372035552, 127240176896, 130322845344, -24946658880]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 7 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -13538112, -13538112, -13538112, -13538112], ![0, 0, 0, 0, 13046880, 5218752, -2609152, -10436864, -18264416], ![0, 0, 0, 856065280, 583365440, 474285504, 528825472, 746985472, 1128765760], ![0, 0, 586776288, -4594114112, -1508787392, 4883026176, 9621595200, 7747188096, -5699925984], ![0, 1414007840, -689103520, -4625026560, -1737079680, 11437414464, 33167123136, 56526699648, 69396781440], ![-44847216, -850386048, 5190782400, -3737915392, -15002645344, -2189425792, 54225632320, 146206099328, 217485009072], ![-11076000, -664704736, 4762059168, -3529608032, -26317673120, -27142179360, 58586235232, 288393072992, 653943666816], ![5846720, 443359232, -1552069888, -3911829760, 215288960, 18962827520, 54642438144, 90839572224, 72908208960], ![96211968, -2729968896, 18516259584, -7825728896, -129931102336, -153760492032, 347783557632, 1588993472640, 2770851726720]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 7 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 146044080, 58417632, -29208704, -116834944, -204461104], ![0, 0, 0, -906927280, -1031992640, -1082018784, -1057005600, -956952992, -781860880], ![0, 0, -3185015568, 8797722752, 4322640672, -6735570240, -14502218080, -9102610304, 19337946576], ![0, 1109456992, -4809850976, 618635136, 1941876608, -7021344064, -23180421824, -34172927872, -18364608640], ![-42174896, 1468145888, -4569583488, 2747895296, 11913247520, -1545097408, -55616598080, -142362254336, -208468253456], ![-416133984, 1782335296, -1284248448, -1124178944, 8541314880, 24344390784, 36987472256, 41801875712, 47530630368], ![947069248, -11475648096, 28182867840, 37510072800, -96194287680, -260259324192, 9562905856, 1283305224096, 3486843198720], ![-1132919936, 19158474240, -66604288768, -103745738368, 300321402752, 1122128053760, 1152745090560, -2087424228480, -10967701958400], ![84708864, -4862633472, 41489832960, -26886288128, -386699636736, -421553212416, 1612284979200, 6926143530240, 11853844738560]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 7 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -59132640, 123306400, 196281344, 159793088, 13842112, -241571520], ![0, 0, -1364650896, 2978497984, -61066656, -6053716032, -10569822816, -9179760640, 2546096400], ![0, -711916128, -641826528, 9330560512, 8287791232, -12137112512, -47760658624, -81848887680, -85117373376], ![169361936, -418725536, -6753772800, 15303922944, 35607319456, -1705306048, -139638315584, -369766685184, -593663988688], ![-386458336, 4857687104, -15773182272, -1832454336, 62489827200, 93731398080, -63524463296, -537533545792, -1278789096672], ![64641792, 3626769728, -19429318144, -8219190720, 96773777280, 174563785536, -150788259328, -1297407508800, -3122218147200], ![-838166208, 7774724224, -9970046080, -3782185920, -28472364480, -320895036672, -799803019008, -79565419200, 5124893473920], ![1171324672, -20732192768, 91587127296, 23787070720, -693037986816, -1025225413632, 2476233338880, 12657013290240, 23170123595520], ![-15959040, 2015350784, -7907221504, -37380173824, -15505760256, 240273223680, 869644554240, 1521333073920, 689204904960]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 7 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 439230624, -607581856, -162223936, 880001472, 1623792576, 1173848384, -1365131616], ![0, -180705616, 805683200, -106540224, -2222254048, -5263412896, -9369045952, -15095254976, -23415212240], ![-207221808, 1753964832, -4718151168, -548144768, 12003317792, 22141133760, 23337417408, 26133154304, 70939858288], ![668447792, -1328293712, -26104464336, 38157878576, 183848726800, 183386069904, -360512092976, -1817057893552, -4188762298656], ![-1847663488, 20443240352, -57167240320, -58341900320, 259540866880, 697495845088, 303152222464, -2326510442592, -7871739785280], ![-978299776, 10959270144, -14884533248, -62707228928, 1912038912, 279730411520, 542648558592, 24049416960, -2372688869760], ![2545973248, -68245418752, 379111401984, 243408654720, -2768483329024, -6475411579392, 1224790103040, 37326074628480, 100055539837440], ![-5814750976, 114871014656, -388817416960, -1076355843584, 1853308337664, 11125480880640, 16001642764800, -17481224935680, -132069026918400], ![-3016216576, 53111120384, -104717455360, -662937289728, -216758814720, 4319595033600, 12872360202240, 12406089146880, -29790236636160]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 7 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, -107753184, 588116928, -515717440, -1061249728, -105273280, 1880612608, 3009998848, -18335072], ![-67704752, 289749408, 1183474688, -4522150272, -8178377952, 5177289408, 47350479040, 117519324672, 192763841264], ![-4670944, 1597081056, -9658602528, 3594497376, 44998208160, 50248180512, -95795215712, -493596543584, -1120901953536], ![-782139072, 8905848928, -18723569024, -40555864800, 36727818560, 239697133088, 417895713536, 198706559328, -951657747840], ![-1302949632, 31108276480, -172965648640, 9114253440, 1083102993280, 1518296675840, -2270601672192, -12245679047040, -22122781127040], ![392901376, -7336258048, 31486006272, 45734019072, -237978897408, -880268175360, -879518115840, 2442962565120, 12627772819200], ![-3230827008, 64265304064, -237706219520, -511112376320, 1483488835584, 6328400547840, 5259915386880, -23080652728320, -96554265899520], ![74139648, 1399369216, -48130453504, 33005306880, 821594941440, 1985381207040, -841580974080, -17833520939520, -57630831498240], ![-11962699776, 285855744000, -850072928256, -4996230266880, -103046676480, 46754011054080, 145480285716480, 154629749514240, -374852814336000]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 7 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![73321920, -1054707136, 4731880384, -3912173440, -15386813568, -4913869184, 45695762560, 128274941952, 188533116992], ![-472137200, 3215153936, -1616157552, -12550469104, -20511270480, -13134225360, 26919389168, 125872820848, 319295431584], ![47402880, 1297705920, -10723249152, -2773803200, 68599350400, 179217140032, 167965059584, -282693237312, -1578691338240], ![305490304, -4929974784, 12034625792, 44562646912, -107137948288, -601240453632, -748618676736, 1826057343360, 10762154261760], ![-2065462016, 38233314816, -151927302144, -106814322944, 975288452096, 1707834756096, -2977007308800, -17398399729920, -32255379383040], ![3410331392, -60199897344, 162493594368, 592709150208, -453479652864, -4838928837120, -9356601408000, -99955848960, 45105336207360], ![2253455360, -41597470208, 31165231104, 670226156544, 1451124971520, -1285565783040, -15115128483840, -44539170424320, -69919803233280], ![-5991012352, 152739659776, -511951159296, -2717720862720, 738817474560, 28157313761280, 81665231831040, 72302015385600, -264795526195200], ![-12725551104, 286324899840, -572649799680, -5774218813440, -6299147796480, 40944460677120, 191074149826560, 358264030924800, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 7 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 4 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7]] +lemma sums_checked : ∀ u : Fin 4, ∀ a i k, fourSumInteger a 7 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k +end SumTable7 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable8.lean b/lean/OAI/Analysis/LaughlinGap/SumTable8.lean new file mode 100644 index 0000000000000000000000000000000000000000..d3e1b4ec2a4f5b7443cf8d64d57d9613302dfce9 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable8.lean @@ -0,0 +1,216 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SumTable7 + +namespace OAI + +/-! Sum Table8. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable8 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 415492, 415480, 415466], ![0, 0, 0, 0, 0, 2503200, 1251600, 0, -1251600], ![0, 0, 0, 0, 363247920, 420157248, 448611632, 448611248, 420156232], ![0, 0, 0, 495771780, -1278978540, -828933952, 733508244, 2295950536, 2745995234], ![0, 0, 235218704, 22367800, -107747164, -237024340, -406411992, -615909080, -824565690], ![0, 544508276, 445915600, -16349392, 221089880, 597004776, -262136752, -3729867664, -10367418876], ![-297042448, 161948980, 116895300, 331669524, 879026964, 1221076924, 421921980, -2852334836, -10841755588]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 8 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, -3503332, -3503320, -3503306], ![0, 0, 0, 0, 0, 15061816, 7530992, 192, -7530580], ![0, 0, 0, 0, 344828260, 176018248, 91613032, 91612632, 176017080], ![0, 0, 0, -1480112116, 1594168184, 2047507896, 1190376936, 333245352, 786583372], ![0, 0, -1676684156, -1288231336, -528274796, -25897564, -95640944, -737505064, -1636949290], ![0, 241633592, -290166320, -1408507264, -5903752760, -10359306800, -8255092912, 6928965504, 38609464604], ![-352076532, -576923908, -108321156, 255535836, -6706917100, -21992103084, -36645220764, -31760234492, 22248079208], ![-313873880, -55562932, -661414768, -3536785340, -7542222040, -7825128924, 3490478880, 30626826764, 54026858832]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 8 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 5640880, 5640880, 5640880], ![0, 0, 0, 0, 0, -6522824, -3261328, 192, 3261740], ![0, 0, 0, 0, -787890880, -651540400, -583365216, -583365216, -651540304], ![0, 0, 0, -1704380552, 1409956408, 391185088, -2694141128, -5779468304, -6798242068], ![0, 0, -714362796, 2874623808, 6132250992, 4730176248, -3495771608, -18545592080, -38255112880], ![0, 10211272, 1868870648, -890742544, 4935339676, 15325892352, 17647093752, -734878896, -43841253374], ![535551588, 1349093084, 566910604, -1572703028, 4875929972, 22223284036, 35930459796, 14609181204, -79833398016], ![63773264, 320245664, 1004164384, 493117472, -2327265280, -4727436576, 577672032, 21615529440, 58195065360], ![4319232, 261028784, 1433283952, 271409600, -9662109280, -22789361168, -1011500560, 119546441184, 347670142656]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 8 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -73021732, -36510824, 96, 36511030], ![0, 0, 0, 0, 938193200, 1000726188, 1031992724, 1031992820, 1000726490], ![0, 0, 0, 5384312136, -2483971364, -2123343544, 2351739516, 6826822080, 7187448718], ![0, 0, -3537527140, -241185952, -4429376784, -8375580472, -8216538120, -3952250928, 554020000], ![0, -2791056004, -3743223304, -331503552, -5356506948, -15413540088, -18995263464, -4594343968, 31193896578], ![-1403663500, -3303196000, -2087381328, -161414528, 7195106856, 22269436800, 42021388784, 58083330048, 56422887740], ![124510200, -1388226772, 4664147760, 6002306596, 859765800, 27120360900, 133785028608, 300657269548, 362164377312], ![470241088, -897610096, -741750832, 15828118720, 31908869600, -41582906288, -302631889840, -617137969632, -228079573632], ![7952512, -1716494112, -785370560, 7430998720, -6126986880, -104601895328, -262284520512, -115764833664, 1206066580224]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 8 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 13523300, -77696360, -123306120, -123306136, -77696512], ![0, 0, 0, 393815968, -2103652852, -909766312, 2129797628, 5169361104, 6363246286], ![0, 0, 2521877820, 1455746208, -4283319264, -4236592360, 6825289240, 28902324848, 56765151368], ![0, 980645772, 3206060600, 5592833856, -9927046100, -29278230680, -22313691336, 41113600992, 175078996362], ![417392668, -2059703544, -1992150712, 273134552, -8984543664, -32996435480, -48129614824, -3886986008, 153101193820], ![1345814800, 4718166120, 3456984096, 7962659512, 14384508720, -18540879112, -138700214912, -317270839640, -352684610112], ![-939311936, 1217535864, 3206374584, -17473124640, -53194051600, -21218570856, 178344983096, 458445219504, 251965500480], ![-341839040, -5622007200, -6903840320, 12435235520, 13500934720, -106234949408, -297401848128, 87062215296, 2597256638592], ![-363050752, -1890906880, -2118219520, 7918516480, 37017827840, 77676587520, 105908963328, 151753958400, 508260217344]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 8 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -308633724, 365135176, 292819912, -152537336, -597894408, -670209124], ![0, 0, 1076176696, -1368338440, -2088017876, -1430422476, 430665928, 3495245048, 7937092642], ![0, 26897572, -3660938664, 3843783456, 8799658492, 8133331096, 4105469720, -1023258240, -10326210110], ![-614836278, -2623355470, 10222362442, 28306737946, -12560773250, -119982782498, -187940813178, 3204685430, 727192503700], ![551550120, -5610168020, -13201805104, -6250496028, -12022798040, -97269198524, -268681429408, -322595566100, 241730610768], ![1089128768, 2381095776, -279146912, -8768133120, -31892773440, -93997521184, -215051397792, -353875796928, -352545020352], ![-701335040, 1590794640, 23887202400, 20616966560, -185806508160, -655633718320, -631192764384, 2027259820224, 9617961585408], ![234697408, -1297481440, -6121361440, 53917578400, 385156012640, 1076072246592, 1247001133056, -1815908088192, -11162514012672], ![-500988160, -1677158720, 6708083200, 78986649280, 342815491200, 897311976960, 1441730594304, 849565085952, -2115045943296]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 8 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 371225680, -406262976, 26452888, 490367304, 395976784, -256719152, -878217724], ![0, 150354804, -1293379432, -866471328, 4620607836, 10465200184, 8018555480, -11368075200, -52397346350], ![-378120164, -360472508, 1110339924, 4797712212, -6143554644, -36222886628, -61358466484, -28877233460, 124029727072], ![556517992, -1021169996, -872258288, -5203200900, -25526463720, -54171484324, -42815831744, 92025445300, 410551269696], ![112281216, -1216372880, -5703290064, 4151332800, 62903995680, 128340570288, -49567112784, -861266892192, -2223529824960], ![-1442037696, -956321664, 7949427840, 13148359680, -1750705600, 21008176000, 291569096448, 1089245580288, 2314225423488], ![780521600, 7130883840, 12867573760, 25085553920, 159562049920, 600249151488, 1053123907584, -320262835200, -7327049756928], ![1294096640, 7014559040, 3150604800, -56321970880, -187730901120, -255324077568, -68991014400, -248482046208, -4266317113344], ![482887680, -45055288320, -319415147520, -892120320000, -723195002880, 3050057945088, 11813910958080, 13885120364544, -30702230507520]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 8 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, -154250856, 926538224, -3128131808, 790663968, 9319201776, 10857434080, -6194686112, -45200881040], ![-322257810, 1755150406, -296062546, -618017058, 6069463338, 16277452810, 14893005314, -24820837038, -140497156516], ![1276045776, -1270814328, 496248416, 4357615320, -7123340880, -42679537384, -69423292736, 10102881800, 352262243712], ![-2629374912, -4153591600, 3445516048, -5843762240, -32800765600, 39994146192, 419149979024, 1142846325408, 1632070178688], ![-192256064, 10047111584, 25743132480, 22427389760, 45667867840, 244935097120, 600856248384, 314068846464, -2638555598976], ![-70654400, 436617440, -5007514080, -58469473440, -230666626400, -463011796800, -257361764352, 1370765531520, 4584105529344], ![2995178240, 20266358720, 29698009600, -99214749760, -545940151680, -1207690455552, -1428398264832, -1021972562688, -4716166760448], ![1219476480, -21067020800, -184131673600, -584078423040, -713766359040, 1058884012032, 5707599980544, 6492425871360, -21688014526464], ![0, -48715000320, -375801431040, -1252671436800, -1837251440640, 1653526296576, 14330561236992, 29343530151936, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 8 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 154344, 154336, 154324], ![0, 0, 0, 0, 0, 929760, 464880, 0, -464880], ![0, 0, 0, 0, -164283600, -143145488, -132576672, -132576864, -143145856], ![0, 0, 0, 375587480, -341341400, -231918144, 290681480, 813281392, 922705268], ![0, 0, -55247792, -36300800, 2821832, 31699704, 35123440, 13093680, -19179620], ![0, -137150504, 83487952, -36357984, 109901488, 525432496, 911688320, 970121504, 703896808], ![-67151952, -191075960, -81147960, -9466328, 11413320, -86435528, -91195208, 981264152, 5143347944]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 8 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, -1301256, -1301248, -1301236], ![0, 0, 0, 0, 0, 5594320, 2797120, -64, -2797224], ![0, 0, 0, 0, -20661240, -83361888, -114712208, -114712208, -83361872], ![0, 0, 0, -33449912, 459878048, -20285776, -987195600, -1954105616, -2434269896], ![0, 0, 812147592, 593191232, 623498312, 669408936, 614093984, 457554192, 316619500], ![0, -295693328, -317979936, 1606403872, 2705505616, 2512813600, 1714538912, 996893504, -106633576], ![-185463960, -207150552, -1143999368, 703560056, 2721788104, 5878000392, 12244390152, 17574665544, 4872189760], ![-79085680, -536068056, -507962064, 506439000, 2017595680, 693713464, -6757124432, -14611500600, 4271344272]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 8 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 2095184, 2095184, 2095184], ![0, 0, 0, 0, 0, -2422832, -1211456, -64, 1211352], ![0, 0, 0, 0, 198605360, 249249936, 274572064, 274571904, 249249584], ![0, 0, 0, -638038704, 759084976, 621055168, -284552144, -1190160096, -1328191176], ![0, 0, 248750616, -2213639776, -1929765248, -507295760, 1249933040, 3341920800, 6572502960], ![0, 247103504, 426912464, -2343188672, -2320750024, -161250432, 280868016, -4848836768, -16205844412], ![371277096, 96718136, 1426593752, -332137448, -3003895896, -2900262776, 951057704, 5255168552, 4817659936], ![73677264, 70029888, -74560512, 556310848, 1220179040, 1118797760, 836174080, 2056154304, 6021530928], ![58285376, -33286848, -604845184, 1913649120, 6007329120, -2329714560, -30519485888, -37821076128, 84368882592]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 8 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -27122392, -13561216, -32, 13561164], ![0, 0, 0, 0, -373035440, -349808936, -338195704, -338195736, -349809020], ![0, 0, 0, 509407792, -1676615848, -806186128, 1592469816, 3991125312, 4861554076], ![0, 0, 1608806248, 2310827904, 994795520, 530559824, 2353046032, 6462253984, 11423258320], ![0, 215199752, -255052096, 1939096000, 1530354040, -729447120, -1078923184, 4243304064, 15989053092], ![-1035548376, -51764976, -140138464, -3017790528, -6469931696, -11670417632, -21456074528, -34940742336, -42777797960], ![-69650720, 869536232, 342531888, 2544852248, -12514686080, -35201746824, -15287010896, 70318470664, 105560592192], ![-70447584, 1619214912, -1027447168, -9011557600, 8769148000, 64660823040, 73759457216, -141234592608, -671222657664], ![-157619072, 432438016, -3258040320, -3562432320, 18509132160, 29337626496, -86781196800, -377677537344, -494648149248]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 8 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 50553640, 16671904, -268720, -268528, 16672288], ![0, 0, 0, 812187456, -537039544, -515191376, 192194232, 899579808, 921428012], ![0, 0, -1969680952, 1329810784, -51733760, -2229643600, -3261584624, -3147557856, -3829898336], ![0, 193454696, -2587748192, 3221434496, 4558252440, 298918256, -4710875696, -5625437440, -3568554220], ![-199254072, 414488976, -1363618416, 921999408, 5601708864, 2857911632, -12591700752, -28799514544, -14037689240], ![945422240, 1114819216, 1525105184, -318756784, 14718351040, 42965970896, 44601113120, -10388916624, -63604351584], ![126701264, -2318572448, -940490560, 5946072240, -5194780400, -25864734400, 17181801248, 182616035184, 365513908320], ![-596227968, 570706432, -6112089600, -9052352320, 21006316800, 11473454208, -255412765440, -840060403776, -1042114322304], ![-113450496, 91279360, -673341440, -4696757760, -10108958720, -11798982144, -19310768640, -87470963712, -333459624960]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 8 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -83154408, 129193552, 64424432, -138903184, -342230832, -407000088], ![0, 0, -207220688, 485851120, 773928728, 527919720, -316722672, -1759998992, -3737363004], ![0, 274356504, 426040352, -375307168, -3699072136, -7152220080, -6360508272, 3050304128, 23473247588], ![-250944348, 1963761044, -8560261964, 1599034484, 18381463964, 18630262556, -6567330676, -47732319700, -95357225128], ![-897267248, 547730984, -2978423888, -6773075432, 15086453280, 32705505656, -42531109200, -249951793656, -419822545968], ![310772128, 468556288, 365145600, 2535329600, 17796848000, 43780610688, 47081733760, -6822136512, -55403361504], ![680137664, -1167285376, -16328448000, 21182820000, 144779948480, 64374899008, -692215197696, -1659178270944, 170296752384], ![-220473216, 4494436480, 19359253120, -18071423680, -149695154880, -55135545408, 970631683776, 2722322655360, 1307093483520], ![191659520, 3461707520, 10883048960, -438807680, -50615516160, -12896339328, 479314775808, 1570777376256, 1720722871296]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 8 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, -60719696, -109165488, 125997680, 206854064, -85555072, -751230208, -1571212872], ![0, -80516808, 830739744, -996309984, -1909098312, -1186442352, 427149072, 2187167872, 4814798532], ![-111256328, -29901752, -2115089528, 1326397224, 6554367064, 6950840504, 964393048, -4223311720, 3757974656], ![-55164416, 291290520, -1159543216, 2400215208, 7944109760, 2937482440, -22250441008, -56062368456, -48689114400], ![-249967232, 683177280, 4155255168, -13443872160, -39818333600, 35437695872, 268237365568, 313959630816, -734380549920], ![153391616, -1320282368, -3289797120, 2428782080, 1796859520, -41171116800, -116704463616, -79652169216, 338326268544], ![623842560, 2391787520, 16920043520, 13590909440, -63042059520, -38529713664, 663558064128, 2323311547392, 2952084883968], ![90017280, -1145839360, 5017500160, 22090212480, 9769697280, -59362962048, 16039989504, 796659595776, 2678426809344], ![-7838853120, -16643481600, 22067896320, -82754611200, -1057412136960, -3177009893376, -3801512411136, 1893425504256, 6426048245760]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 8 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, -71798768, 599878800, -1309106016, -479260896, 2290493216, 3142029920, -1782776832, -13282847856], ![161530188, -654619332, 965909212, 510618876, -910178764, -2087442316, -930361916, 9078718436, 42355354760], ![75590656, 1663746416, -340836832, 551491728, 4552647680, 4053282768, -10632734304, -45154448336, -100442602944], ![-549816160, -3067455680, -3817282432, 2234960800, -25155322400, -92328615936, -95275205952, 93043561248, 350876624256], ![1403375232, 129569536, 9327383040, 14978228800, -21928336640, 10658563712, 437488429824, 1334481774912, 1623322115712], ![-89536640, -3393260160, -7856031360, 12294164160, 49194808000, -59073831360, -554001308352, -1157852133504, -61476636672], ![848514560, -2893190400, 4005506560, 58707762560, 127069056000, 65124358272, -66838387968, 729217691136, 4962231825408], ![-4658990080, -11756933120, 10318540800, -38694528000, -592801413120, -1879011256320, -2407117160448, 885330800640, 4539351877632], ![-7953469440, -23860408320, 0, -89476531200, -1181090211840, -4409403457536, -8188892135424, -6141669101568, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 8 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, -189936, -189920, -189912], ![0, 0, 0, 0, 0, -1144320, -572160, 0, 572160], ![0, 0, 0, 0, 168348160, 142332864, 129324864, 129324608, 142332384], ![0, 0, 0, -326984368, 548858832, 407652352, -242078640, -891809376, -1033015352], ![0, 0, -38700160, 32381600, 77439120, 133910064, 220514592, 337253664, 465407960], ![0, -44784496, -336347008, -155895360, -226064032, -526808800, -666747968, -254501184, 729973264], ![-25797632, -22839728, -267994608, -599302064, -492880688, -84860944, -189766672, -1906449360, -6205643344]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 8 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 1601520, 1601504, 1601496], ![0, 0, 0, 0, 0, -6885280, -3442624, 0, 3442608], ![0, 0, 0, 0, 8603280, 85773408, 124358560, 124358624, 85773536], ![0, 0, 0, -246286864, -926825184, -409219360, 707458848, 1824137248, 2341743408], ![0, 0, -463105392, -448001760, -727095088, -1012806384, -1161344960, -1172709920, -1190691112], ![0, 334486240, 696181568, -1241584512, -2263502560, -1991737024, -1467181248, -1730723072, -2404516880], ![-168200848, -63446352, 875597424, 956884208, -3574055472, -9469568816, -9370961008, 2252821008, 26057583456], ![-130293088, 165411440, 53137152, -1822609328, -1559318560, 4411009616, 11641974592, 3270944496, -48518392320]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 8 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, -2578688, -2578688, -2578688], ![0, 0, 0, 0, 0, 2981984, 1491008, 0, -1491024], ![0, 0, 0, 0, -188866240, -251197568, -282363392, -282363520, -251197824], ![0, 0, 0, 1097906016, -594440864, -397365504, 744419936, 1886204608, 2083278512], ![0, 0, -470219760, 2161188480, 1737163840, 236379104, -1351831264, -3027468608, -5779868544], ![0, -546580448, -875973536, 2169438016, 1616834288, -1632234752, -2739028768, 3135196224, 16891996808], ![216417936, 285797360, -1297336656, 1035190960, 2805338320, 519030800, -4369823920, -6700196528, -2808810752], ![28930560, 71795328, 74066688, 212572032, -337882240, -1489886336, -2360575616, -3971746432, -12124103040], ![-34922752, 302609984, 259083072, -3554794112, 3948546048, 20893863744, 331660352, -101324378880, -207094688640]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 8 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 33381424, 16690720, 0, -16690728], ![0, 0, 0, 0, 377502080, 348915632, 334622416, 334622416, 348915624], ![0, 0, 0, -1300334176, 1473468144, 485483168, -2383395856, -5252275200, -6240260808], ![0, 0, -1731108304, -2164297600, -27539136, 1147043872, -406610080, -4688500928, -9932567104], ![0, 1228566064, 1519096480, -994402304, 112871152, 3857592224, 5552364000, 509782656, -12253489656], ![-297662768, -1055294784, -907171776, 408785280, 5272416928, 11779135104, 15924766912, 15914308096, 14285835248], ![297448352, -212536592, -5485757184, 9482907088, 10434869600, -23935014192, -49820804928, 17079936880, 224553962880], ![258958336, -2261849536, 7702133184, 1159297664, -25042950656, -15010686784, 86023035072, 210574275840, 84451052160], ![9365760, -826996096, 3510652160, -12520498176, -8815214592, 77238175872, 130216631040, -184055904000, -961932153600]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 8 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, -57069040, -15369184, 5481184, 5481504, -15368576], ![0, 0, 0, -821263232, 791631728, 717050208, -201270032, -1119590592, -1194172680], ![0, 0, 2160559408, -1712291072, -157055232, 2045137888, 2503721184, 1218692800, 580618208], ![0, -901156752, 2149372192, -4346929408, -5031358672, 760685088, 6346744672, 5044358272, -2481881816], ![-229384272, -20469216, 2986303776, -2278942880, -1188072768, 10286894496, 20119331680, 10383710624, -27134239440], ![296808896, 597766560, 6034255744, -4762998688, -9288301760, 5117961568, 6702751616, -53806833888, -178384481280], ![-382387264, 2012010528, -6318897760, 6563108800, 1804047360, -49501071328, -50025451232, 130853934720, 307058555520], ![176269696, -2039734400, 3623487744, -30461662208, -18352284160, 154281817216, 222570789120, -486480326400, -2006452990080], ![196085248, -429727744, -929376256, -3542013952, -14191808512, -35280921600, -61436298240, -91128407040, -154068456960]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 8 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 86980688, -178658912, -103231584, 142729504, 388690784, 464118448], ![0, 0, 22753760, -443826208, -530239056, -77599536, 993534752, 2683163616, 4911844488], ![0, -235915312, -28905312, 378391808, 3317362928, 6242575840, 4170186464, -7883651072, -32464372472], ![361971304, -2924406904, 7573173288, -6423271448, -22584596360, -17087360264, 9977506072, 37922898904, 54192410128], ![-536947424, -2119271184, 10233745280, -8259928624, -8500332320, 56256336592, 141276254016, 123489385072, -94452416640], ![-261704704, 465732352, 5853360512, 2911367424, -57319936, 23413132672, 75944874624, 95416427520, -48225841920], ![-937820928, 4857621952, 9511801216, -80134180352, 9100536320, 512528461248, 539095939200, -1840249065600, -6643349856000], ![1882881664, -5603795968, -5684630272, 86187661568, 15822537472, -667797701760, -1295244167040, 873849778560, 7894496586240], ![1154691584, -933129728, -374091776, 31905533440, 10322058240, -321626315520, -944753356800, -836297890560, 1534239083520]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 8 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 23597312, 129411776, -132598560, -223457504, 126320832, 916734912, 1878297552], ![0, 112749072, -751276128, 1225005312, 1825299312, 441167712, -1731899424, -3498411776, -5466806968], ![-89491600, -243195376, 1987938512, -2945624752, -6437962064, -2749611408, 4148000816, 3505785648, -12425355136], ![-174117280, 36992912, 2127665920, 716993712, 468247200, 13144300976, 39370564160, 47906729488, -30033648000], ![351193856, -2250131904, -1561990080, 32810938240, -35215395840, -187876943296, -4542461632, 885615770880, 1720244419200], ![37622144, 1626534144, -5288471552, -12409372672, -8584791552, -20070895616, -117674012160, -354100930560, -659120330880], ![638585600, -80897024, -3583815680, 68036544512, 63598083072, -373565998080, -867924633600, 522595814400, 5549868276480], ![-566356480, 307121664, -3082072064, 22274019840, 92602967040, 109998385920, 48230645760, 520327146240, 3058402913280], ![5884772352, -23613136896, -124723077120, 0, 167175290880, -1820601446400, -7837749596160, -9467127521280, 21420160819200]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 8 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 79428064, -659036416, 1630488576, 451894400, -3160577088, -4407504640, 1510535808, 15627791232], ![17665016, 596595288, -1618493256, -2482162056, 374468648, 4198206120, 2986106120, -9678464952, -39662089168], ![139737408, -618138976, 2742808960, 4092347104, 2598260800, 5607368928, 20960887424, 46947255456, 71288714880], ![-74257408, 815317824, -14934599488, 1486150784, 4981825024, -68862415936, -140606260288, -13749569280, 308841413760], ![151771264, 3976008064, -5118095616, 43407268864, 8383506944, -293907048064, -455451690240, 541193875200, 2625474867840], ![-1027200128, 2894546944, -2156076288, -38546086144, 10918507776, 303716949120, 523986526080, -376334893440, -2894350694400], ![-2175493632, 3672271360, 2470858752, 27513484800, 186942090240, 531636445440, 967648112640, 1580863299840, 3472694184960], ![2751610880, -14220865536, -75807100928, 0, 149713551360, -851279616000, -4058287073280, -4426654003200, 15131172925440], ![6362775552, -17497632768, -143162449920, -143162449920, 0, -1968483686400, -10236115169280, -20472230338560, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 8 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 332192, 332288, 332368], ![0, 0, 0, 0, 0, 2002560, 1001280, 0, -1001280], ![0, 0, 0, 0, -448611520, -403083968, -380320640, -380320896, -403084416], ![0, 0, 0, -14120736, -1576563296, -1359169280, -251856864, 855455424, 1072848976], ![0, 0, 636081600, 59928960, -476113120, -1037564192, -1657182016, -2334965312, -3038155280], ![0, -204009248, 376559552, -433888128, -1261821248, -2033390144, -3324589312, -5711415680, -9120024160], ![6384448, -166169312, 234266912, 228837536, -1452868064, -4929321248, -8445254432, -8765670304, -2685701856]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 8 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, -2802464, -2802560, -2802640], ![0, 0, 0, 0, 0, 12048960, 6024704, 256, -6024352], ![0, 0, 0, 0, -91612640, -226661120, -294185024, -294184768, -226660672], ![0, 0, 0, 2781525152, 3638657792, 2399035072, 111036352, -2176960832, -3416580384], ![0, 0, -2833026784, -1760752000, -116356576, 1596893088, 3127365248, 4475060544, 5891610800], ![0, 1933707200, -2699698304, -1300343424, -388290240, -1518062464, -3761392000, -6189992192, -10358349472], ![-316795872, 1640412704, -1848493856, -4121530656, 1924786720, 13168793376, 10930379808, -33090292448, -139602086784], ![-73210304, -259727584, 1186131008, 4156171232, -3597297920, -30983019424, -62195413952, -46600256352, 87949957056]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 8 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 4512704, 4512704, 4512704], ![0, 0, 0, 0, 0, -5218752, -2609152, 256, 2609504], ![0, 0, 0, 0, 583365440, 692445376, 746985344, 746985472, 692445760], ![0, 0, 0, -3811745728, -726419008, -947579136, -2821983808, -4696388992, -4917549856], ![0, 0, 4966927840, -1773143680, -1689345280, 1755655104, 6830518464, 13535240832, 23601157440], ![0, -1388552640, 1430460480, -1591449600, 2179551200, 11597118464, 18624835776, 15226301312, 255200272], ![188015776, -598524960, 2125116000, -2475957920, -6215786336, -104586208, 16542708384, 37347282592, 60456671360], ![-49303360, 403219712, 196238080, -1285596416, -4262268800, -5359255808, 1987586048, 23677058816, 61562208576], ![63191808, -1674485760, 10477046016, -14735864704, -29198748544, 47385603328, 128026461696, -80519994240, -755109264000]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 8 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -58417632, -29208704, 128, 29208880], ![0, 0, 0, 0, -1031992640, -981966496, -956953312, -956953184, -981966192], ![0, 0, 0, 4551035328, 75953248, 2183998656, 7583608032, 12983217920, 15091264624], ![0, 0, -372023008, -2835947520, -9405116672, -13898316992, -13224940736, -7384987008, 530937280], ![0, 962047136, 965600896, 4260295936, -661202464, -12341990464, -22843054016, -24225382400, -15032075120], ![216969888, -2578168640, -179947136, 5397132288, 9925632320, 14398940544, 28748093824, 67532965120, 137607857376], ![372865792, -1259224032, 3287327040, -19310280992, -26305390720, 80611131744, 305350860864, 415198137760, -13354645248], ![-612977536, 7123262208, -23104175360, 7671893888, 67822118528, -24604201216, -270687839744, -122742446208, 1426724179200], ![111633408, -3738428928, 25696899072, -42053446400, -122813332992, 137952338944, 693416435712, 440681575680, -2048385123840]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 8 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 123306400, 50330112, 13842752, 13843264, 50331008], ![0, 0, 0, 1158963456, -1880601184, -1967079744, -577016608, 813045376, 726564400], ![0, 0, -3489491040, 6576348800, 5627032320, 2029544384, -32627392, -559486336, -3734522880], ![0, 1613617696, -7073779456, 4968953344, 7594773856, -3628644672, -20276291520, -33923172864, -49001649584], ![-173266528, 433378880, -2312575424, 10027991232, 11257543680, -14822564544, -47094314560, -37278724800, 42434962720], ![-317101184, 3638985280, -4516065152, 5102160960, 16278876160, -38901233088, -180971534464, -275402644800, -56194824576], ![-218047808, -422915072, -1971757440, 48086395200, -10489769280, -294121752960, -488097869056, 41971903296, 1436930870400], ![662729984, -8710675456, 50425396224, -102277763840, -272541556224, 354236517376, 1754165532672, 1522085479680, -3835145360640], ![-56349696, 1621889024, -1217712128, -13504339968, -31011864576, -44370407424, -28497530880, 129436538880, 776561280000]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 8 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -21941024, 423416896, 271905984, -178038336, -627981760, -779490784], ![0, 0, 82860736, 485822400, -314706336, -2596777568, -6499416000, -12022620224, -19027364080], ![0, -732696864, 639933696, 1410283136, -682314784, 635910208, 15905945408, 55668778496, 126198181776], ![-345342704, 5679289296, -21736265008, 2406950608, 43679941488, 48769817456, -4248198096, -109228988240, -288865978144], ![-355598784, 1255407904, -15262008512, 30339370208, 84556253440, -159506080, -229582768576, -266487521888, 462991886784], ![-415211904, 908936448, 1025481728, 17025219328, 32203511808, -30551639552, -233837184000, -465930521856, -320019834240], ![1948448000, -40083840768, 201993404416, -151308821120, -805459097856, 438029243904, 3617933469696, 1642858807680, -16924685606400], ![-3865331968, 54841097984, -179200120064, -33542569984, 828395549184, 48229117440, -4939029096960, -7887788494080, 13293434204160], ![-1985256448, 23102282240, -39530939392, -62211236864, 192417705984, 7856808960, -2381517895680, -6190239137280, -1151107077120]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 8 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 157104192, -18903360, 363391168, 360789184, -498313984, -2213922560, -4314436000], ![0, -522707616, 1800834304, -1759945856, -2556300576, 1746772800, 10327402816, 22363716096, 40190711056], ![-207448608, 1338252064, -3547791072, 3215496352, 5984797024, -10385807648, -43433945248, -76022181280, -99315366912], ![-231125632, 622206944, -218470720, 6650701856, 2118181760, -25884836960, -40149609024, 54591861600, 369330809472], ![-935465984, 16575331840, -88022029056, 127454597760, 222819617920, -501542625024, -1211567010304, 816779860608, 7343642240640], ![257016576, -3164980736, 16498181120, -950353920, -99274506240, -175260309504, -76188801024, 68217354240, -360776613120], ![-2151125504, 30893887488, -119529177088, 47501934592, 699067701248, 49642328064, -3752623472640, -6481693870080, 6064970165760], ![61428736, 2212779520, -38648085504, 9044288512, 334508568576, 617974963200, 29362206720, -1283722682880, -540643783680], ![-9020313600, 162900049920, -389875924992, -1318800900096, 589797457920, 4393879142400, -2403032924160, -22089964216320, 24990187622400]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 8 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, -174844096, 1099627200, -2837054080, -384832896, 6878211200, 10784943232, 3168238080, -17549963840], ![212729776, -1765625488, 4375129968, 4146557424, -10278874160, -36694689072, -61173855984, -60904850032, -11550324320], ![-86476288, 1598782144, -4796393856, -2247896768, 15640487680, 47472769088, 95437408640, 165756271040, 247043601408], ![197074560, -1589338368, 1439921920, 10084476288, -86647449472, -237292573952, -33103289856, 937258239360, 2255947311360], ![-1290596608, 16547232256, -73863869440, 152609324800, 365788720640, -731207242752, -3060952602624, -2655824728320, 6438920505600], ![2146738432, -25593885440, 66436017408, 23367221248, -292214755840, 81637581312, 2273050053120, 3798974741760, -4985964656640], ![1615438848, -18384104960, -22429496320, 125154176000, 505200095232, 1023493739520, 1473818142720, 995364395520, -5096178447360], ![-4615206912, 90478149632, -245894758400, -769277288448, 490414817280, 3103830343680, -74280222720, -10328859340800, 17653035079680], ![-9544163328, 159069388800, -229059919872, -1574786949120, -1049857966080, 3149573898240, 0, -23884268728320, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 8 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 4 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7]] +lemma sums_checked : ∀ u : Fin 4, ∀ a i k, fourSumInteger a 8 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k +end SumTable8 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/SumTable9.lean b/lean/OAI/Analysis/LaughlinGap/SumTable9.lean new file mode 100644 index 0000000000000000000000000000000000000000..757f43c9d1e4faed4f2c2cbfbd00a620074fb8af --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/SumTable9.lean @@ -0,0 +1,265 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.CheckedTables +import OAI.Analysis.LaughlinGap.IntegerFourRows + +namespace OAI + +/-! Sum Table9. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators +namespace SumTable9 + +def s_0_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, -569816, -569802], ![0, 0, 0, 0, 0, 0, -4005120, -2288640, -572160], ![0, 0, 0, 0, 0, -894558672, -985613552, -1037644528, -1050651800], ![0, 0, 0, 0, -325219300, 3044263488, 2854074412, 629786936, -2103025234], ![0, 0, 0, -1368510472, -258553428, 685596436, 1594976040, 2544462520, 3552773890], ![0, 0, -608598512, -1509386960, -1232436552, -1680008824, -2154996848, -474939216, 5913965204], ![0, 1532631580, 695158300, 761628396, -247675844, -2685979740, -5408771868, -6044412556, -1012538596]] +lemma s_0_0_checked : ∀ i k : Fin 9, fourSumInteger 0 9 1 i k = s_0_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 4804568, 4804554], ![0, 0, 0, 0, 0, 0, -24098928, -13770944, -3442988], ![0, 0, 0, 0, 0, -760063752, -489967688, -335626776, -297041040], ![0, 0, 0, 0, 1825433176, -4504463208, -6640854584, -6380956856, -5521986084], ![0, 0, 0, 3563320040, 1004754380, -2193786980, -5025771184, -6916036824, -7720793318], ![0, 0, 1583397616, -603999680, -524616264, 6035636400, 13359711536, 10055627008, -16687333340], ![0, 1403009460, 5140197892, 1698928100, -3735179028, 4380175756, 31706353948, 65428764092, 71365759064], ![-265322624, 1489298748, 1469668440, 4174393572, 11790794384, 19747729812, 15119723320, -20987014900, -101784885312]] +lemma s_0_1_checked : ∀ i k : Fin 9, fourSumInteger 1 9 1 i k = s_0_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -7736064, -7736064], ![0, 0, 0, 0, 0, 0, 10436496, 5963584, 1490644], ![0, 0, 0, 0, 0, 1836397920, 1618237152, 1493573920, 1462408096], ![0, 0, 0, 0, 6035152872, 213987648, 1005795784, 5576446864, 11091809844], ![0, 0, 0, 8747648112, -2804149152, -11829346872, -11402597080, 2433441776, 30668104440], ![0, 0, -2869236280, -3084445904, 6044494420, -281861168, -19302649752, -32508260080, -17451892570], ![0, -2647756220, -8164135436, -3485451340, 5814178764, -2200050436, -38075490580, -84495528084, -92315559456], ![-337511840, -699017696, -1915855008, -3959260384, -3100533856, 2816036064, 8075052192, -3485976864, -54506256576], ![-115635456, -214815312, -1459307888, -5173776544, -4108502880, 14767199536, 43771241360, 17391931776, -192682187904]] +lemma s_0_2_checked : ∀ i k : Fin 9, fourSumInteger 2 9 1 i k = s_0_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 116834760, 66762656, 16690538], ![0, 0, 0, 0, 0, -2276676892, -2376729684, -2433902772, -2448196170], ![0, 0, 0, 0, -17290561036, -1698245080, 727812820, -4369704752, -11348115606], ![0, 0, 0, -2599452016, -7892408384, 1686904632, 13776056504, 21310802192, 22525081944], ![0, 0, 9825551304, 7152969280, -2911095836, 3872700120, 25815216296, 46411042272, 45450707822], ![0, 10357166464, 10214554608, 9600166720, 13560280904, 13863240832, 4293450096, -12763579584, -24136363060], ![2108652640, 3006017180, 3874667448, -13228173884, -14310523728, 19972043828, 38346518744, -58076189396, -314690631168], ![586173696, -1611768560, 2490184368, 948995616, -40408617760, -93711530096, 9517926320, 502612968576, 1334570335104], ![-811942528, -1806347040, 1930701184, -1554289600, -24131658240, -8581234592, 191728954368, 638851956480, 894601999104]] +lemma s_0_3_checked : ∀ i k : Fin 9, fourSumInteger 3 9 1 i k = s_0_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 4031944, 149983400, 233384152, 254234376], ![0, 0, 0, 0, 244269172, 4761652280, 3372866868, -1390871584, -6998347702], ![0, 0, 0, -4077620176, 93453136, 11296077352, 12796290584, -4968170064, -44387869520], ![0, 0, 2893657192, -11786127424, -19448736588, 10411713528, 56871730376, 69619606496, -9003419898], ![0, -2642559608, 7818639640, 3967160872, -6346823680, 7278639608, 59616126344, 122913180824, 121437874300], ![2243378368, -7724911416, -18225743344, -18717506952, -38050318304, -81773356392, -88612056368, 36341984680, 307982337024], ![-1541315872, 2490369016, -3795348600, -6481045264, 47127654960, 146861338040, 119348989256, -322206155328, -1290917693568], ![-1322430784, -302706336, 17288156416, 28220665920, -4934480320, 580810720, 310804419072, 1093352015616, 1695217147008], ![-103595776, 2081011968, 10475267840, 21392812800, 18828615680, -7553688576, -22274595840, 75484603392, 355995898368]] +lemma s_0_4_checked : ∀ i k : Fin 9, fourSumInteger 4 9 1 i k = s_0_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 648894904, -669716824, -794593912, -237337064, 490453036], ![0, 0, 0, -7147682808, 1315188868, 5777479596, 6795287016, 4686383176, -469786058], ![0, 0, -7532869304, 14748552544, 3504146756, -12553933464, -21782414936, -22291668608, -14630475298], ![0, 103202014, 22480541398, -24014907034, -85715590350, -22439196798, 214650709466, 479750949514, 407010088084], ![18700096, -2445620452, 18563211352, 36687416452, 17369073744, 15323811636, 173798085816, 582735209452, 1047836523072], ![171289472, -6732000544, -15005480416, -16190228032, -11544598080, 3256192480, 55620475680, 176569003776, 328194494208], ![-1126330112, 1624159376, -7510478912, -71819676960, -95866290240, 280555748816, 1264201473024, 1697310598272, -2258206334208], ![1415185216, 3857317536, 16599564960, 46993187040, -45251029600, -682062476928, -2149915076736, -3146940230016, 1080001663488], ![1098888192, 8487523520, 29178122880, 46787849920, -48298199040, -514043953920, -1583405311488, -2828684888832, -2319953366016]] +lemma s_0_5_checked : ∀ i k : Fin 9, fourSumInteger 5 9 1 i k = s_0_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -1254297968, 927828328, 677066264, -120174544, -385945072, 149242524], ![0, 0, -3398451320, 5514172960, 6229200420, -5751363448, -22298014744, -28065537472, -5904789202], ![0, 595309340, 7218365292, -1142702036, -18522621164, -8673241692, 47025478324, 120721151924, 131244536128], ![522767584, -2025399228, 799493320, -1716311588, 5204827024, 47231519340, 117903570472, 138590292916, -45735433344], ![-1176816128, -2760633744, 394670032, 11508842720, -5924040160, -115770558480, -254252137776, -9932732544, 1357848324480], ![-76493376, 8502798720, 14902627968, 6590356480, 18375582400, 104952496768, 184922927616, -159614121984, -1695506904960], ![2898595968, 4717121792, -9536924160, -27465519360, -64490975360, -366300705792, -1430806228992, -3240059784192, -3461307911424], ![630951936, -5989961920, -36883400320, -71444873920, -22684354560, 123653370624, 2450241024, -1155162531072, -3271577447424], ![-7838853120, -43493975040, 28154219520, 772376371200, 2747767357440, 4605020614656, 1635647827968, -8204843851776, -714005360640]] +lemma s_0_6_checked : ∀ i k : Fin 9, fourSumInteger 6 9 1 i k = s_0_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_0_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, -97340288, -2200207264, 7019277472, 2688753456, -13707901952, -25626104864, -12756095472], ![0, 872509514, -3192973966, 2217371938, 649873318, -19686097962, -52811886562, -68908312530, -12443363908], ![1396264064, -5084275160, -976132592, -10333697640, -24471270176, -65881672, 97852731984, 235088745224, 255798267264], ![-5320707840, 7170137424, 14393188720, 5373523616, 51815450720, 190694855120, 234830514800, -261211785600, -1700139632256], ![3625028416, 9163585184, -16900227328, -59703955520, -60956200000, -112466624480, -603901229568, -1926937464576, -3567150702720], ![-512544832, -1717375648, -6256496800, 2635070240, 118880698720, 498555340416, 1081509179520, 1031442217344, -1536306309120], ![1747975168, -12875506240, -98076571520, -241765195840, -213825669120, 276442634496, 801176302080, -730517475072, -7172518898688], ![-4658990080, -32261224960, -21614656000, 361148928000, 1535214428160, 2887756118016, 1682965616640, -3836433469440, -504372430848], ![-7953469440, -48715000320, 0, 835114291200, 3674502881280, 8267631482880, 9553707491328, 682407677952, 0]] +lemma s_0_7_checked : ∀ i k : Fin 9, fourSumInteger 7 9 1 i k = s_0_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, -320544, -320532], ![0, 0, 0, 0, 0, 0, -2252880, -1287360, -321840], ![0, 0, 0, 0, 0, 262421424, 211202528, 181934944, 174618336], ![0, 0, 0, 0, -1609556040, 433514112, 474269176, -629156208, -2018627028], ![0, 0, 0, 437764896, 151550424, -200921976, -545942480, -841392368, -1076742860], ![0, 0, 396664752, 256003808, 888776176, 683457456, -509333568, -2003466336, -2903931384], ![0, -184523688, 133435512, 283692760, 571904472, 981320712, 1519051400, 1780625640, 323933832]] +lemma s_1_0_checked : ∀ i k : Fin 9, fourSumInteger 0 9 3 i k = s_1_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 2702592, 2702580], ![0, 0, 0, 0, 0, 0, -13555520, -7745984, -1936472], ![0, 0, 0, 0, 0, -46935840, 104992848, 191809296, 213513504], ![0, 0, 0, 0, 1854062592, -46985616, 410812080, 2216521968, 4359210264], ![0, 0, 0, -1787321024, -536102024, 70394200, 598342944, 1371271920, 2470062324], ![0, 0, -122990496, 987521056, -2486571088, -3733922208, -1529449504, 2159777344, 4568649768], ![0, 264240888, -878795448, 2047569288, -797133768, -4638869448, -7782605960, -12178571208, -15769288128], ![131154944, -35606872, 830915360, 116021752, -2210982704, -3882900296, 505595904, 14858222952, 30516530256]] +lemma s_1_1_checked : ∀ i k : Fin 9, fourSumInteger 1 9 3 i k = s_1_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -4351536, -4351536], ![0, 0, 0, 0, 0, 0, 5870656, 3354688, 838696], ![0, 0, 0, 0, 0, -224049648, -346765216, -416888192, -434418768], ![0, 0, 0, 0, 1166177424, -2723292864, -2892967088, -937042464, 1550282760], ![0, 0, 0, -2198097024, 3227973408, 2733118224, 212845616, -2106839008, -3669434080], ![0, 0, 1280554224, -2293704512, 4169628968, 4576267680, -1665401968, -6288324128, 1189224780], ![0, -514727160, 1640569896, -2540386712, 326929368, 5811207672, 5955217880, -564288552, -4267979232], ![-244783856, -421999616, 17349760, 224571968, -1099238944, -2090749120, -425909760, 3875319744, 8442982896], ![-76829824, -402257024, 217625088, 1139197152, -4021290720, -11464651200, 1771976512, 50737325792, 86501388960]] +lemma s_1_2_checked : ∀ i k : Fin 9, fourSumInteger 2 9 3 i k = s_1_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 65719616, 37554080, 9388532], ![0, 0, 0, 0, 0, 565578888, 509299256, 477139480, 469099548], ![0, 0, 0, 0, -1341117432, 5545033392, 5025163240, 273281760, -5536601964], ![0, 0, 0, 1835961120, -2981753376, -1383422928, -322915888, -3773870944, -12729697312], ![0, 0, -4068454656, 567798144, -4851220920, -5378777328, -652920656, 1354146944, -9413307012], ![0, 358849200, -382147488, -2032686528, 935647248, 4208493024, 6809641824, 11708198976, 20315121048], ![1164221328, 549225000, 1565567136, 1073517240, -4205412432, 16484783736, 52255696128, 28109505192, -109931681856], ![-9606816, 808910592, -3509924352, 4394617376, 20092953760, -12462479040, -115821295424, -159378097888, 138858135552], ![-240673792, -791949312, -2623713792, 3927410880, 1601130240, -45686769024, -94534835456, 34449135552, 475672379904]] +lemma s_1_3_checked : ∀ i k : Fin 9, fourSumInteger 3 9 3 i k = s_1_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -114237024, -32139152, 14773616, 26501616], ![0, 0, 0, 0, -2730868296, 888948528, 1186545064, -414269760, -2489687292], ![0, 0, 0, 3428658560, -4397040736, -730798000, 5014531536, 7460175264, 5261441232], ![0, 0, -1287030432, 9046283200, -4395083224, -8198499888, 2119638192, 14512066560, 12798803532], ![0, 1445319888, -2727103824, 2051893200, -2699674656, -12541931280, -10799609264, 9009726384, 24239259912], ![-504121152, -459236976, -1580875968, 1648119056, 8852519264, -10258990384, -50644820096, -46936312016, 67395213856], ![-124084752, -2069880384, 4210909440, -2097837776, -19311560080, -373233120, 58677388448, 54372480304, -134659606176], ![99780992, 336249600, -3201374208, 9230594240, 11732196480, -54292939392, -100862798848, 195959627712, 1032784015104], ![339305984, 780455936, 600565760, 3505246720, 14544808960, 30409156096, 41779782144, 65051670528, 197372583936]] +lemma s_1_4_checked : ∀ i k : Fin 9, fourSumInteger 4 9 3 i k = s_1_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 399935088, -244781328, -218021840, 192438096, 698823144], ![0, 0, 0, 1661387024, -170651704, -1577391016, -2246028464, -1997818736, -788074388], ![0, 0, 813274272, -1608294752, -3714900088, 1599716784, 11840566768, 19026236288, 13803707868], ![0, 337141452, -8670367476, 22585357452, 5823519300, -28238114268, -26404240332, 26510282964, 88203373752], ![-2325184, 3796679336, -4349627488, 2289182648, 3658927952, -44329174024, -100069123456, -33928707928, 219356691728], ![-978735200, -703209856, -1247939328, -1866830528, -8158159360, -36660037632, -83429403008, -98627686336, -25763165280], ![-119043968, -4998679296, 3221129472, 32459701920, -46137335040, -281287060032, -204851711104, 998150939424, 3011654462976], ![621161600, 3621979520, -6524928640, -26778353600, 71825199040, 372578811712, 392750639424, -977249168640, -3753388311552], ![954602496, 2695069440, 0, 128411520, 62381095680, 249758416512, 415134383616, 79356524544, -902860434432]] +lemma s_1_5_checked : ∀ i k : Fin 9, fourSumInteger 5 9 3 i k = s_1_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 60625040, 383174672, -238278256, -742629376, -523532224, 570600392], ![0, 0, 1014848544, -2794418080, 780563656, 2894788848, 1806222192, -168332928, 302635452], ![0, 257917176, -2209377480, 5367374168, 690922920, -8358578232, -7556951256, 5330820456, 12117435648], ![-86195120, 660710872, 469309792, 1256769544, -8825195504, -22558055480, -17288668928, 20754175384, 66872022496], ![-570696256, -84703616, -4451409408, -10176627872, 23325512480, 67265942592, -48829854144, -426558617760, -643453212960], ![1065806976, -21137664, 4922021376, 10742699520, 3165816960, 12332578560, 117274946304, 345151517184, 531525802752], ![281461504, 2048244736, 2193909760, -16391288320, 13888167680, 208448969216, 347194801152, -419652937728, -2734089836544], ![-1023629312, -1505908480, 0, -19130216320, -71876437760, -92532498048, -26402692608, -204984907776, -1718837480448], ![-482887680, 22067896320, 22067896320, -142342809600, -163662336000, 1183379963904, 4300284764160, 4223795355648, -10710080409600]] +lemma s_1_6_checked : ∀ i k : Fin 9, fourSumInteger 6 9 3 i k = s_1_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_1_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 786416400, -2628613280, 2994846944, 2513439264, -4390809120, -9564223872, -2735219280], ![0, -590906460, 940165284, -1003653884, 2129329260, 7179081420, 9659425020, 5134698012, -14158414680], ![-220867936, 1011450608, -1706332096, 1894918224, -2545706208, -16467354672, -25188040832, -11962241552, 25502130112], ![-152352544, -4165691648, 2340481536, -1228044640, -20245672160, 17784926784, 144686081984, 220942285216, 24001915392], ![1027543680, -51028992, 7756677120, -1702055360, 5238291840, 114040854912, 207967404032, -154051966656, -1179550220544], ![-248547456, -291356544, 7001769600, 9677231040, -45331185600, -148004884800, -50282356032, 612425293056, 1470762399744], ![-2545447936, -6287248640, 0, -27567693440, -178334337280, -410769560448, -479734110720, -474436233216, -2158546553856], ![-1219476480, 10318540800, 10318540800, -98354856960, -174900510720, 481781145600, 2168133783552, 1974968709120, -7565586462720], ![0, 23860408320, 47720816640, -89476531200, -214743674880, 1102350864384, 5669233016832, 10236115169280, 0]] +lemma s_1_7_checked : ∀ i k : Fin 9, fourSumInteger 7 9 3 i k = s_1_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 142432, 142424], ![0, 0, 0, 0, 0, 0, 1001280, 572160, 143040], ![0, 0, 0, 0, 0, -145964800, -123201856, -110193984, -106941728], ![0, 0, 0, 0, 844024048, -69668096, -93441360, 391309920, 1003191928], ![0, 0, 0, -348801760, -132440400, 112331984, 352758816, 570120288, 759735368], ![0, 0, -223607808, -108227392, -291220256, -35603808, 745759168, 1768668096, 2656089424], ![0, -171969552, -385916560, -451393616, -304376208, -526243952, -833873264, -61253168, 3155507888]] +lemma s_2_0_checked : ∀ i k : Fin 9, fourSumInteger 0 9 5 i k = s_2_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, -1201120, -1201112], ![0, 0, 0, 0, 0, 0, 6024640, 3442688, 860752], ![0, 0, 0, 0, 0, 6278304, -61245728, -99831008, -109477440], ![0, 0, 0, 0, -1080997856, -299669920, -566718560, -1432839776, -2448729232], ![0, 0, 0, 1915122656, 1117019824, 616368624, 161538368, -391261664, -1077980440], ![0, 0, -863961920, -502634624, 2024134880, 3518928576, 3267120320, 1972813056, 694787088], ![0, -540443888, -543765360, -1724249072, -2562260432, 4230269104, 14499167344, 15539105008, -2790928992], ![165776640, 80385712, -1405196128, -1213740464, 1402303744, 181320336, -8378206688, -15156843152, 3238226240]] +lemma s_2_1_checked : ∀ i k : Fin 9, fourSumInteger 1 9 5 i k = s_2_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 1934016, 1934016], ![0, 0, 0, 0, 0, 0, -2609216, -1490944, -372656], ![0, 0, 0, 0, 0, 147739712, 202279424, 233445248, 241236928], ![0, 0, 0, 0, -228921056, 1523300096, 1622275488, 776540480, -305371184], ![0, 0, 0, 279749440, -2569073920, -2505066208, -1259566560, 178090688, 1560573344], ![0, 0, 239519136, 1243122240, -2473311536, -3674597824, -2015625568, -1088474304, -5469524200], ![0, 1230881936, 266701648, 2614273360, 882558000, -1438524176, -1568344400, -1399581520, -6317725056], ![-206058304, 146496896, -286324480, 418102656, 782345984, 1239594368, 2182644352, 2536417664, 1096237760], ![-100745728, 270080832, -1226312000, 519482624, 6413178112, -3594504384, -26824944704, -5952065920, 117587352960]] +lemma s_2_2_checked : ∀ i k : Fin 9, fourSumInteger 2 9 5 i k = s_2_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, -29208736, -16690688, -4172632], ![0, 0, 0, 0, 0, -322104432, -297091280, -282798032, -279224680], ![0, 0, 0, 0, -53979824, -3042286048, -2739029168, -554878400, 2099496360], ![0, 0, 0, 637936192, 3168764288, 2922715616, 2990397280, 5137870400, 9806650144], ![0, 0, 1356270432, -846205696, 1878929296, 2838426592, 1821136672, 2319980160, 8753904312], ![0, -3362156608, -1194269376, -684249216, -1973557472, -9880320640, -21564973376, -28715104512, -25631999696], ![489377984, 575164976, -821711200, 12208437712, -10774654976, -22285151984, 21627928224, 62718818800, -44641296640], ![-34599168, -454836160, 4685780032, -10732206336, 3745236736, 50939081920, 37533449536, -119929833600, -315079102080], ![-76002048, 79277696, -2531506176, -8105704960, 16081330176, 16547688576, -101225720320, -227826996480, 51208646400]] +lemma s_2_3_checked : ∀ i k : Fin 9, fourSumInteger 3 9 5 i k = s_2_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 55235424, 18748320, -2102048, -7315040], ![0, 0, 0, 0, 1390717072, -259422752, -433020976, 237119360, 1118194536], ![0, 0, 0, -2353352384, 1364669376, -313598176, -3204668960, -4917976128, -4855875840], ![0, 0, 501595744, -4381636608, 2403505744, 5384244064, 1945137824, -3182195584, -3429370344], ![0, -910310112, 1066176096, -2386376544, 3703110272, 2177979360, -8616975584, -9381060512, 23733444400], ![-1115391872, 1603574304, 5721655104, -4971072928, 14362567680, 32553268960, 15459748288, -2636801504, 66290856960], ![-101047104, 1083995808, -6416181664, 3670999168, -14507064960, -20274733024, 42321673184, 85291035200, -84105037440], ![354247296, 295234944, -3479514112, -12108099072, 30430220800, 8958428288, -251710653440, -499367128320, 82275338880], ![159573504, 522000384, 1478985728, 170973184, -1778917376, -52679680, -3526548480, -47431019520, -184563371520]] +lemma s_2_4_checked : ∀ i k : Fin 9, fourSumInteger 4 9 5 i k = s_2_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, -191413408, 91410464, 75800864, -110342432, -339119248], ![0, 0, 0, -929580000, 270972688, 1179991728, 1658450848, 1626906912, 1065499352], ![0, 0, 84596704, 1226559744, 1236917264, -2696137696, -9117198304, -14132446208, -13238457480], ![0, -825043016, 4231199320, -11686112744, -2922481080, 13553110152, 15056607336, -1402448856, -18575612016], ![1041778560, -2753507024, 2516118304, -15400181296, 14981986048, 24089616656, -59780141792, -161731052304, -66900952640], ![-628337664, -374016512, 227579008, -3237555712, 10249063936, 31096519040, 23637892992, -8111676160, 42578922240], ![-815030784, 5460591040, -20565325824, -11662835968, 130136204800, 24439935424, -656851831040, -874469001600, 1823800907520], ![85107072, -3833995008, 23120911616, 20903051008, -114707184384, -25860055680, 874718156160, 1775470723200, -850575813120], ![-153327616, -37413376, 12637068288, 21822819840, -12180060160, 28875214080, 461434682880, 1205003162880, 775662243840]] +lemma s_2_5_checked : ∀ i k : Fin 9, fourSumInteger 5 9 5 i k = s_2_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -120294016, -216603360, 90381408, 329055040, 229931456, -274359376], ![0, 0, -409606944, 1509634816, -404804464, -1979864160, -2199356128, -1851020032, -2173578056], ![0, -374877840, 314636592, -3804281168, -11472304, 4273845392, 4470422992, 5679407824, 19262304512], ![46595520, 121955920, -1432120224, 1214510256, 6684772864, 5571405168, -9705619616, -28735238256, -12247854720], ![-73019904, -2424261312, 6818911680, -5464989440, -51037945600, 41904564800, 248020716224, 59812073600, -1034340416640], ![251040896, 2654301952, -2330860544, 4123488256, 5100176896, -28290357248, -67608133120, -21951313920, 142850586240], ![-318129408, -2357471232, 14373818368, 30630230016, -52574229504, -20604789760, 629461647360, 1570154849280, 491898274560], ![-72013824, -2942737920, -4424956928, 5912957440, -15283251200, -79783476480, 4287951360, 495159540480, 1083634421760], ![6271082496, -11843592192, 31519580160, 102983516160, -431990046720, -1694858342400, -1283584389120, 2912962314240, 0]] +lemma s_2_6_checked : ∀ i k : Fin 9, fourSumInteger 6 9 5 i k = s_2_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_2_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, -345393728, 1249700352, -1321530240, -1284543296, 1546147968, 3590851200, 328576896], ![0, 511747816, -556655928, 250466696, 371289368, -3019051304, -5649780360, 1973197240, 29136109616], ![-214049280, -114799072, 2137040960, 2880475360, 4763577856, 7386865248, 5085125056, -8047666272, -31341412480], ![229341952, 449612096, -12060232384, 4235793152, -28986150144, -71890217024, -20640992704, 53240677760, -170337790080], ![-654576256, 2095790976, 8676076544, 23773982208, -33925509632, 16954558848, 440534225920, 824943064320, -113216123520], ![330103936, 1333122816, -10454695168, -2373459712, 44758344448, -38816880000, -445119753600, -740689027200, 498161664000], ![-678811648, -4873779712, -17960375296, -616532480, 18734458880, -71933679360, -181112486400, 317590606080, 2412568350720], ![3727192064, -8717643776, 9968275456, 48153190400, -273536040960, -1078666352640, -993680455680, 1362047385600, 0], ![6362775552, -4772081664, 31813877760, 143162449920, -286324899840, -1968483686400, -3149573898240, 0, 0]] +lemma s_2_7_checked : ∀ i k : Fin 9, fourSumInteger 7 9 5 i k = s_2_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 142592, 142512], ![0, 0, 0, 0, 0, 0, 1001280, 572160, 143040], ![0, 0, 0, 0, 0, 223639360, 246402688, 259411072, 262663680], ![0, 0, 0, 0, 81305056, -761065984, -713518624, -157446848, 525755952], ![0, 0, 0, 465373440, 187883360, -48154848, -275498048, -512867520, -764945584], ![0, 0, -268043200, -503256192, -1032903744, -1381419072, -1723082240, -2603509632, -4661148640], ![0, -146355104, -32816160, -848723104, -1409555872, -1799429600, -2649245664, -5118321760, -10791331168]] +lemma s_3_0_checked : ∀ i k : Fin 9, fourSumInteger 0 9 7 i k = s_3_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, -1201280, -1201200], ![0, 0, 0, 0, 0, 0, 6024704, 3442432, 860320], ![0, 0, 0, 0, 0, 190014720, 122491712, 83906880, 74260608], ![0, 0, 0, 0, -456356992, 1126114752, 1660213184, 1595239616, 1380496992], ![0, 0, 0, -3625272448, -2985629472, -2185995168, -1477999488, -1005433152, -804244784], ![0, 0, 3267563392, 991949184, -1850355008, -6312887936, -10966371456, -12962800896, -9099507808], ![0, -1393163168, -662665184, 4443855136, 2237270496, -8569826848, -24196400672, -32901902112, -15748203136], ![258243072, -1138251232, 1881711872, -2188673696, -5007815488, 2021266272, 14055069312, 7188494368, -55347136064]] +lemma s_3_1_checked : ∀ i k : Fin 9, fourSumInteger 1 9 7 i k = s_3_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 1934016, 1934016], ![0, 0, 0, 0, 0, 0, -2609152, -1491200, -373088], ![0, 0, 0, 0, 0, -459099200, -404559232, -373393408, -365601984], ![0, 0, 0, 0, -1508787392, -53496576, -251450304, -1394113152, -2772952032], ![0, 0, 0, 1078739200, 3966686080, 6222988352, 6116300736, 2657288832, -4401377280], ![0, 0, -3764972352, -880094720, -331249248, 4081411200, 11667682368, 17800168832, 16867164208], ![0, 1458572576, 1124658592, -140254048, -3114132128, -1770390048, 7613548896, 22492242272, 32751031424], ![-104453440, -188420608, 1028639488, 247419648, -1048788864, 146628864, 1500224512, -4968396032, -25412924608], ![30171648, -949204224, 4526010624, -11312078208, 10677489024, 33978049024, -33960930304, -149245466496, -60468949632]] +lemma s_3_2_checked : ∀ i k : Fin 9, fourSumInteger 2 9 7 i k = s_3_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, -29208704, -16690816, -4172848], ![0, 0, 0, 0, 0, 569169440, 594182624, 608475744, 612048880], ![0, 0, 0, 0, 4322640672, 424561088, -181953632, 1092426112, 2837029456], ![0, 0, 0, -6290530176, -4967288704, -7362117952, -10384407488, -12268094848, -12571664640], ![0, 0, 5151188608, 4423099904, 5542884640, 2450707776, -4431157312, -10976358400, -12132514320], ![0, -607633856, -6060894592, -8383092736, -1295457216, 15374866048, 39411583872, 64024422656, 78380158560], ![-201337664, 3215165472, -2786066944, -2438090656, -10261671616, -3527798176, 15826641536, 31124018464, 97310336256], ![-93035136, 287474176, -259227904, 5272318336, -11948347008, -8264916480, 88591254528, 201553712000, -3010797312], ![138557952, -2344978944, 13691630592, -40974732032, -4711910400, 134777466880, 14791211008, -538926803712, -682636316160]] +lemma s_3_3_checked : ∀ i k : Fin 9, fourSumInteger 3 9 7 i k = s_3_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -1008896, -37495360, -58345792, -63558976], ![0, 0, 0, 0, -61066656, -1190412608, -843217760, 347716352, 1749586576], ![0, 0, 0, 3822137088, 2779367808, -21285824, -396340672, 4044771456, 13899696576], ![0, 0, -1974204160, 53565696, 327036320, -8780247488, -22037426752, -26866583040, -8853017296], ![0, -1859011264, 913282752, -712978624, 9072160896, 18225086400, 14166401856, -10764612928, -55407461728], ![-698844160, -166228928, 4830865664, 13176835392, 22388270208, -2731963328, -56756797696, -91994762304, -98224268672], ![402070592, -2419370368, -2191235456, 29876805696, -46107642560, -98227458816, 98174917120, 343019849024, -120065063808], ![154135296, -1775105024, 26402267136, -91790119680, -14328631296, 257883437056, -68060561408, -1317134113536, -1503763841280], ![-96740352, 824520704, 2941575168, 1248759808, -11779661824, -42211807232, -94392496128, -178384373760, -323137182720]] +lemma s_3_4_checked : ∀ i k : Fin 9, fourSumInteger 4 9 7 i k = s_3_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, -162223936, 167428800, 198649024, 59335232, -122612960], ![0, 0, 0, 1078185024, -1037528800, -2153103008, -2407557824, -1880333760, -591290960], ![0, 0, -633079296, -3262386816, 2489761824, 9445329856, 14693497536, 17761858048, 18787608944], ![0, 2548967344, -6115641296, -701223632, 11182212112, -6962623088, -70248292656, -146993951920, -151543604896], ![1136465920, -3011777504, -2640714240, -13593112992, 14572658880, 65239820384, 117502893696, 151066520864, 86110922688], ![147875968, -3510518528, 2522540032, 5320568576, 17651528192, 52051712000, 103990949888, 132438465280, 22662205056], ![1350922752, -17897515264, 82445540864, -198423102080, 55397874176, 852935114752, -15264134144, -3619487526528, -4850661864960], ![-1915912960, 14305371392, -58183904000, 185251367424, 84998197760, -952528299520, -923427681792, 3225393841920, 7984975933440], ![-954296320, 3403045376, -9005746176, 79383929856, 113896466432, -286821964800, -737211310080, 236444398080, 2468650060800]] +lemma s_3_5_checked : ∀ i k : Fin 9, fourSumInteger 5 9 7 i k = s_3_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 477910720, -67621568, -4928448, 194380032, 260818944, 127021472], ![0, 0, 251641856, -1164293504, -530831584, 3276529344, 8225413312, 10479515136, 5751548144], ![0, -948353568, 385773536, 509778272, 3065488032, -2292419808, -22785529184, -55667257952, -85778442240], ![319887808, -2151300640, 4278446080, -4697679200, -3182154816, 33089707680, 81589227904, 70084507616, -75892223360], ![-567982336, 5717223680, -33748288256, 101066408064, -106895201920, -298908761600, 347958768640, 1364412001920, 376610604672], ![121131776, -352551424, 8647808000, 1641013248, -16213281792, -49205065728, -162747475968, -425552676864, -758765656320], ![-1071424000, 8319485952, -50753523712, 147752685568, 135854917632, -540965777408, -452852047872, 2620281231360, 6199317020160], ![48717824, 2899080704, -27555903488, -978740224, 59398535168, -8698045440, 71168778240, 1357128199680, 4516316851200], ![-6077927424, 69368217600, -106518282240, 120045453312, 249034014720, -3451477524480, -11190791208960, -8496140083200, 24990187622400]] +lemma s_3_6_checked : ∀ i k : Fin 9, fourSumInteger 6 9 7 i k = s_3_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_3_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, -186324544, 584366720, -1475528320, -147926912, 4196210816, 7420743680, 4448225600], ![0, 102264848, 2106696848, -2524527088, -4714896720, -2757528016, -628625936, -9859812752, -49297198304], ![-220355456, 561066688, -30229760, -1187688896, 8106892672, 31246011968, 54700071680, 59254322880, 50740027392], ![88658816, 667140608, -2631564544, 8204119936, -85213368448, -157596448256, -17321823232, 168626135424, -146835862272], ![-515731200, 2609803776, -30900604928, 159045590784, 19331293184, -446914994176, 234594304, 1802926919424, 1664928288000], ![883145472, -3623803136, 16329396992, -80730024448, -29490926080, 378897430016, 339026548224, -1290349336320, -2889025075200], ![977422336, -1550904832, -42194642944, -49127271424, 82303993856, 412234798080, 1106135654400, 2689180961280, 6162473856000], ![-3239401472, 41974693888, -75244371968, 30692646912, 102134611968, -1995423006720, -6281940910080, -3972638208000, 17653035079680], ![-6362775552, 63627755520, -38176653312, 104985796608, 381766533120, -3149573898240, -14698011525120, -23884268728320, 0]] +lemma s_3_7_checked : ∀ i k : Fin 9, fourSumInteger 7 9 7 i k = s_3_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_0 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, -3417984, -3418272], ![0, 0, 0, 0, 0, 0, -24030720, -13731840, -3432960], ![0, 0, 0, 0, 0, -2410507008, -2956837632, -3269026560, -3347074944], ![0, 0, 0, 0, -14920815168, 5866656768, 5296089792, -7479070848, -23305379616], ![0, 0, 0, 3983978880, 1657010880, -1560500928, -4882329984, -7859206272, -10378810848], ![0, 0, -1542908160, 246805248, 4529060736, -2201019264, -17852111616, -31420771584, -29675521728], ![0, 511192512, -3118667328, 4839575232, 2291544000, -8972770752, -20601387456, -27578960064, -30701505600]] +lemma s_4_0_checked : ∀ i k : Fin 9, fourSumInteger 0 9 9 i k = s_4_0 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_1 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, 0, 0], ![0, 0, 0, 0, 0, 0, 0, 28826496, 28826784], ![0, 0, 0, 0, 0, 0, -144587520, -82621440, -20654784], ![0, 0, 0, 0, 0, -3090471552, -1469897856, -543858048, -312350976], ![0, 0, 0, 0, 36855133056, 5284927872, -1124237184, 6844328064, 18407318976], ![0, 0, 0, -17215637376, -8172865344, -4069595712, 1133352192, 10886934144, 26053885344], ![0, 0, 15908103936, -6618040320, -28429689984, -7091262720, 40246137600, 62381807616, -397402560], ![0, -6911771328, 25573096512, -35736790464, -21707926848, 47972576448, 92796600768, 44577602496, -134263748736], ![0, 2983080384, -23169624192, 45077587008, 43369357056, -90841162944, -237763433088, -191410152768, 182132153856]] +lemma s_4_1_checked : ∀ i k : Fin 9, fourSumInteger 1 9 9 i k = s_4_1 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_2 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 0, -46416384, -46416384], ![0, 0, 0, 0, 0, 0, 62625024, 35785728, 8947008], ![0, 0, 0, 0, 0, 6163670016, 4854710784, 4106734080, 3919739904], ![0, 0, 0, 0, 7041315456, -30261095424, -27885664128, -2837180160, 27879564096], ![0, 0, 0, 33936188160, 8698851840, -29734728576, -39812481408, 2209650432, 102267694464], ![0, 0, -3228999552, -22561931520, 40265623872, 28174337280, -50553164160, -93141759744, 26806752864], ![0, 1791825984, 994353984, -15224383680, 33810957504, 37818984384, -85833828672, -267216167232, -252602601984], ![0, -496350720, -571737600, 9993497088, 1933893120, -34290885120, -69482276352, -39658258944, 130674885120], ![0, -297181440, 6035717376, -48829644288, 90061475328, 233046759168, -205979585280, -1308718322688, -1785484753920]] +lemma s_4_2_checked : ∀ i k : Fin 9, fourSumInteger 2 9 9 i k = s_4_2 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_3 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, 0, 701011584, 400578048, 100144800], ![0, 0, 0, 0, 0, -6529876416, -7130190144, -7473226560, -7558985376], ![0, 0, 0, 0, -38220186816, 48055529088, 55333707072, 17470432512, -31678208352], ![0, 0, 0, 26626967808, -44404727808, -33732306048, -15530352768, -32184352512, -94290685056], ![0, 0, -3036592512, 33211106304, -21117796800, -15519841920, 44937584256, 66289473024, -67653605664], ![0, 5697934848, -24263712000, 8525119488, 9508553856, 2004526080, 38000152320, 147177796608, 324171672768], ![0, -5167831104, 57853323648, -154541075904, -28741061376, 367131477312, 301271435136, -656906289984, -1590493685760], ![0, 4679481600, -67531790592, 270359643648, -10799371776, -1178427273984, -1293001785600, 2463099896832, 10168607296512], ![0, 242320896, 7068321792, -93949867008, 198357590016, 559114698240, -735453229056, -4294973085696, -5409578649600]] +lemma s_4_3_checked : ∀ i k : Fin 9, fourSumInteger 3 9 9 i k = s_4_3 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_4 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 0, -425755008, 449952384, 950354304, 1075453056], ![0, 0, 0, 0, -16375810752, 14894861184, 10728508224, -13687570944, -43166081376], ![0, 0, 0, -17085987072, -16244911872, 55892704896, 98923085184, 55472653056, -88801979136], ![0, 0, 12194059392, -1920039936, -84997656768, 8767069056, 216603621504, 299412186624, -25989328800], ![0, 1918726272, -25906273920, 81403216512, -54220225536, -148787961984, 88118050944, 578701425024, 783290335680], ![0, -3435686784, -2217164544, 86043831168, -58846990848, -262915986048, -2470850304, 856478692992, 1327686998016], ![0, 5581065600, -43604770176, 59151863040, 100913721600, 126233398656, 16598037120, -1230584381952, -4846791527424], ![0, -4577352192, 66025967616, -262228227072, 147295927296, 1134374782464, -576535314432, -6942220425216, -10061519293440], ![0, -363515904, -2966630400, 38319476736, 49614716928, -217664692224, -846497046528, -1128344739840, 796042874880]] +lemma s_4_4_checked : ∀ i k : Fin 9, fourSumInteger 4 9 9 i k = s_4_4 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_5 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, 0, 5270767488, -2266282368, -2640914304, 1077261696, 5818638528], ![0, 0, 0, -4336934784, 7499731008, 5666388672, -6500376960, -27093957504, -55637716128], ![0, 0, -14919970176, 32148509184, -21982643136, -39970366848, 13115160192, 113681909760, 223507387872], ![0, -9124114464, 39004126560, 23167824480, -298003898592, -215970206688, 721192809888, 2019347204256, 2065931903808], ![0, 13428582336, -106174606464, 264859973184, -50112331008, -785146317504, -274384142976, 2627792357568, 6309503144448], ![0, 5067790848, -55234211328, 105595671552, 177431798784, -184049238528, -668674954752, -323925215232, 1526275215360], ![0, -5377727232, 161799164928, -1080633742848, 902937682944, 6550098686208, 2492726175744, -27020284425216, -68407417866240], ![0, 17544771072, -330938214912, 1345427636736, 1201471477248, -7672250729472, -17004403713024, 6001032545280, 91051428188160], ![0, 9278641152, -161495746560, 456069583872, 1321315688448, -1658262509568, -10531931074560, -13947246213120, 16083882270720]] +lemma s_4_5_checked : ∀ i k : Fin 9, fourSumInteger 5 9 9 i k = s_4_5 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_6 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 0, -2586076416, 5764364928, 1156934016, -5089937664, -6508561152, -1482005568], ![0, 0, -4874742144, 3704157696, 18718310976, -11208756096, -61688546688, -65038285824, 57248381664], ![0, -1824998976, -2161306944, 36056535744, -60737773248, -92933977536, 101593285440, 412820806464, 399910892544], ![0, 4959120960, -46395771264, 115989710784, 53692364544, -300607208256, -478613251968, 165199446336, 1883601122304], ![0, 3307352832, -83890315008, 516276423168, -645079534080, -2256982891776, 835712301312, 10125098671104, 15868294751232], ![0, -1222963200, 23397046272, -94003494912, 37328974848, 631213406208, 471256289280, -2888340553728, -10239845575680], ![0, 9717313536, -184032976896, 757648822272, 443411662848, -4382508490752, -7090967052288, 10828557066240, 57232713922560], ![0, -114398208, 4651665408, 56093420544, -374899531776, -1313936418816, 688566251520, 12412348692480, 33449931694080], ![0, 26481475584, -675944054784, 3008342458368, 7392330252288, -19941077975040, -100717120880640, -122344417198080, 257041929830400]] +lemma s_4_6_checked : ∀ i k : Fin 9, fourSumInteger 6 9 9 i k = s_4_6 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def s_4_7 : Fin 9 → Fin 9 → ℤ := ![![0, 0, 5279178240, -21793519104, 34109182464, 19301425920, -61765143552, -114274626048, -20820079872], ![0, 6163802784, -27830075616, 38002326048, 51524636256, -30725355168, -184012781088, -338535429408, -385206129216], ![0, -1204912512, 1003182336, 34356219264, -60969733632, -176267069568, 37712476416, 866150788224, 2126499253248], ![0, -975741696, 19068076800, -65519706624, -51163885056, 296337293568, 248820972288, -1887778581504, -6492433941504], ![0, 6973788672, -120818110464, 491626558464, -46202674176, -1930846385664, -381294133248, 8184985196544, 13420095482880], ![0, -11372336640, 188682177024, -633207144960, -926689494528, 3075079504896, 9272590967808, 3313047813120, -33162968678400], ![0, -5742148608, 127795894272, -361763404800, -1669451685888, 117950515200, 12366923304960, 34150901114880, 34434625167360], ![0, 12382248960, -344677146624, 1711906062336, 3628226248704, -12758262497280, -56537468190720, -57205990195200, 181574075105280], ![0, 28632489984, -687179759616, 2405129158656, 10307696394240, -9448721694720, -113384660336640, -245666764062720, 0]] +lemma s_4_7_checked : ∀ i k : Fin 9, fourSumInteger 7 9 9 i k = s_4_7 i k := by + apply Arithmetic.checkMatrix_sound + decide +kernel + +def sums : Fin 5 → Fin 8 → Fin 9 → Fin 9 → ℤ := ![![s_0_0, s_0_1, s_0_2, s_0_3, s_0_4, s_0_5, s_0_6, s_0_7], ![s_1_0, s_1_1, s_1_2, s_1_3, s_1_4, s_1_5, s_1_6, s_1_7], ![s_2_0, s_2_1, s_2_2, s_2_3, s_2_4, s_2_5, s_2_6, s_2_7], ![s_3_0, s_3_1, s_3_2, s_3_3, s_3_4, s_3_5, s_3_6, s_3_7], ![s_4_0, s_4_1, s_4_2, s_4_3, s_4_4, s_4_5, s_4_6, s_4_7]] +lemma sums_checked : ∀ u : Fin 5, ∀ a i k, fourSumInteger a 9 (2*u.val+1) i k = sums u a i k := by + intro u a i k + fin_cases u <;> fin_cases a + · exact s_0_0_checked i k + · exact s_0_1_checked i k + · exact s_0_2_checked i k + · exact s_0_3_checked i k + · exact s_0_4_checked i k + · exact s_0_5_checked i k + · exact s_0_6_checked i k + · exact s_0_7_checked i k + · exact s_1_0_checked i k + · exact s_1_1_checked i k + · exact s_1_2_checked i k + · exact s_1_3_checked i k + · exact s_1_4_checked i k + · exact s_1_5_checked i k + · exact s_1_6_checked i k + · exact s_1_7_checked i k + · exact s_2_0_checked i k + · exact s_2_1_checked i k + · exact s_2_2_checked i k + · exact s_2_3_checked i k + · exact s_2_4_checked i k + · exact s_2_5_checked i k + · exact s_2_6_checked i k + · exact s_2_7_checked i k + · exact s_3_0_checked i k + · exact s_3_1_checked i k + · exact s_3_2_checked i k + · exact s_3_3_checked i k + · exact s_3_4_checked i k + · exact s_3_5_checked i k + · exact s_3_6_checked i k + · exact s_3_7_checked i k + · exact s_4_0_checked i k + · exact s_4_1_checked i k + · exact s_4_2_checked i k + · exact s_4_3_checked i k + · exact s_4_4_checked i k + · exact s_4_5_checked i k + · exact s_4_6_checked i k + · exact s_4_7_checked i k +end SumTable9 +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/TensorSpin.lean b/lean/OAI/Analysis/LaughlinGap/TensorSpin.lean new file mode 100644 index 0000000000000000000000000000000000000000..6ff97fc31f164c9e7d87d33679d90074ed8f6f28 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/TensorSpin.lean @@ -0,0 +1,835 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.SpinWork + +namespace OAI + +/-! Tensor Spin. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators + +noncomputable def ladderStep (n : ℕ) (p : Fin n) : ℝ := + Real.sqrt (((p.val : ℝ)+1) * ((n : ℝ)-p.val)) + +lemma ladderStep_sq (n : ℕ) (p : Fin n) : + ladderStep n p ^ 2 = ((p.val : ℝ)+1) * ((n : ℝ)-p.val) := by + have h : (p.val : ℝ) ≤ n := by exact_mod_cast p.isLt.le + exact Real.sq_sqrt (mul_nonneg (by positivity) (by linarith)) + +noncomputable def lowering (n : ℕ) : Module.End ℝ (Fin (n+1) → ℝ) where + toFun x := Fin.cases 0 (fun p => ladderStep n p * x p.castSucc) + map_add' x y := by + funext p + cases p using Fin.cases <;> simp [mul_add] + map_smul' r x := by + funext p + cases p using Fin.cases <;> simp [mul_left_comm] + +noncomputable def raising (n : ℕ) : Module.End ℝ (Fin (n+1) → ℝ) where + toFun x := Fin.lastCases 0 (fun p => ladderStep n p * x p.succ) + map_add' x y := by + funext p + cases p using Fin.lastCases <;> simp [mul_add] + map_smul' r x := by + funext p + cases p using Fin.lastCases <;> simp [mul_left_comm] + +noncomputable def weight (n : ℕ) : Module.End ℝ (Fin (n+1) → ℝ) where + toFun x p := ((n : ℝ)-2*p.val) * x p + map_add' x y := by funext p; simp [mul_add] + map_smul' r x := by funext p; simp [mul_left_comm] + +@[simp] lemma lowering_zero (n : ℕ) (x : Fin (n+1) → ℝ) : lowering n x 0 = 0 := rfl +@[simp] lemma lowering_succ (n : ℕ) (x : Fin (n+1) → ℝ) (p : Fin n) : + lowering n x p.succ = ladderStep n p * x p.castSucc := rfl +@[simp] lemma raising_castSucc (n : ℕ) (x : Fin (n+1) → ℝ) (p : Fin n) : + raising n x p.castSucc = ladderStep n p * x p.succ := by simp [raising] +@[simp] lemma raising_last (n : ℕ) (x : Fin (n+1) → ℝ) : + raising n x (Fin.last n) = 0 := by simp [raising] +@[simp] lemma weight_apply (n : ℕ) (x : Fin (n+1) → ℝ) (p : Fin (n+1)) : + weight n x p = ((n : ℝ)-2*p.val) * x p := rfl + +lemma raising_lowering_apply (n : ℕ) (x : Fin (n+1) → ℝ) (p : Fin (n+1)) : + raising n (lowering n x) p = + (((p.val : ℝ)+1) * ((n : ℝ)-p.val)) * x p := by + cases p using Fin.lastCases with + | last => simp + | cast p => + rw [raising_castSucc, lowering_succ, ← mul_assoc, ← pow_two, ladderStep_sq] + rfl + +lemma lowering_raising_apply (n : ℕ) (x : Fin (n+1) → ℝ) (p : Fin (n+1)) : + lowering n (raising n x) p = + ((p.val : ℝ) * ((n : ℝ)-p.val+1)) * x p := by + cases p using Fin.cases with + | zero => simp + | succ p => + rw [lowering_succ, raising_castSucc, ← mul_assoc, ← pow_two, ladderStep_sq] + simp only [Fin.val_succ, Nat.cast_add, Nat.cast_one] + ring + +theorem raising_lowering_commutator (n : ℕ) (x : Fin (n+1) → ℝ) : + raising n (lowering n x) = lowering n (raising n x) + weight n x := by + funext p + simp only [raising_lowering_apply, lowering_raising_apply, Pi.add_apply, weight_apply] + ring + +theorem weight_lowering_commutator (n : ℕ) (x : Fin (n+1) → ℝ) : + weight n (lowering n x) = lowering n (weight n x) - (2 : ℝ) • lowering n x := by + funext p + cases p using Fin.cases with + | zero => simp + | succ p => + simp only [weight_apply, lowering_succ, Pi.sub_apply, Pi.smul_apply, smul_eq_mul, + Fin.val_succ, Fin.val_castSucc, Nat.cast_add, Nat.cast_one] + ring + +theorem lowering_raising_dot (n : ℕ) (x y : Fin (n+1) → ℝ) : + dotProduct (lowering n x) y = dotProduct x (raising n y) := by + unfold dotProduct + rw [Fin.sum_univ_succ, Fin.sum_univ_castSucc] + simp only [lowering_zero, zero_mul, zero_add, lowering_succ, raising_last, mul_zero, + add_zero, raising_castSucc] + apply Finset.sum_congr rfl + intro p hp + ring + +structure LadderSystem (ι : Type*) [Fintype ι] where + lower : Module.End ℝ (ι → ℝ) + raise : Module.End ℝ (ι → ℝ) + weight : Module.End ℝ (ι → ℝ) + adjoint : ∀ x y, dotProduct (lower x) y = dotProduct x (raise y) + raise_lower : ∀ x, raise (lower x) = lower (raise x) + weight x + weight_lower : ∀ x, weight (lower x) = lower (weight x) - (2 : ℝ) • lower x + +noncomputable def standardLadderSystem (n : ℕ) : LadderSystem (Fin (n+1)) where + lower := lowering n + raise := raising n + weight := weight n + adjoint := lowering_raising_dot n + raise_lower := raising_lowering_commutator n + weight_lower := weight_lowering_commutator n + +namespace LadderSystem +variable {ι : Type*} [Fintype ι] + +noncomputable def raw (S : LadderSystem ι) (x : ι → ℝ) (l : ℕ) : ι → ℝ := + (S.lower ^ l) x + +@[simp] lemma raw_zero (S : LadderSystem ι) (x : ι → ℝ) : S.raw x 0 = x := rfl +lemma raw_succ (S : LadderSystem ι) (x : ι → ℝ) (l : ℕ) : + S.raw x (l+1) = S.lower (S.raw x l) := by rw [raw, pow_succ']; rfl + +lemma weight_raw (S : LadderSystem ι) {x : ι → ℝ} {μ : ℝ} + (hx : S.weight x = μ • x) (l : ℕ) : + S.weight (S.raw x l) = (μ - 2*l) • S.raw x l := by + induction l with + | zero => simpa using hx + | succ l ih => + rw [raw_succ, S.weight_lower, ih, map_smul, ← sub_smul, + Nat.cast_add, Nat.cast_one] + congr 1 + ring + +lemma raise_raw (S : LadderSystem ι) {x : ι → ℝ} {μ : ℝ} + (hx : S.weight x = μ • x) (he : S.raise x = 0) (l : ℕ) : + S.raise (S.raw x (l+1)) = (((l : ℝ)+1)*(μ-l)) • S.raw x l := by + induction l with + | zero => simpa [raw_succ, S.raise_lower, he] using hx + | succ l ih => + rw [raw_succ, S.raise_lower, ih, S.weight_raw hx (l+1), map_smul, + ← raw_succ, ← add_smul, Nat.cast_add, Nat.cast_one] + congr 1 + ring + +theorem raw_norm_sq (S : LadderSystem ι) {x : ι → ℝ} {d l : ℕ} + (hw : S.weight x = (d : ℝ) • x) (he : S.raise x = 0) (hl : l ≤ d+1) : + dotProduct (S.raw x l) (S.raw x l) = + (l.factorial : ℝ) * (d.descFactorial l : ℝ) * dotProduct x x := by + induction l with + | zero => simp [dotProduct] + | succ l ih => + have hld : l ≤ d := by omega + rw [raw_succ, S.adjoint, ← raw_succ, S.raise_raw hw he] + simp only [dotProduct, Pi.smul_apply, smul_eq_mul] + have hsum : (∑ i : ι, S.raw x l i * + ((((l : ℝ)+1)*((d : ℝ)-l))*S.raw x l i)) = + (((l : ℝ)+1)*((d : ℝ)-l)) * dotProduct (S.raw x l) (S.raw x l) := by + simp only [dotProduct, Finset.mul_sum] + apply Finset.sum_congr rfl + intro i hi + ring + rw [hsum, ih (by omega), Nat.factorial_succ, Nat.descFactorial_succ, + Nat.cast_mul, Nat.cast_add, Nat.cast_one, Nat.cast_mul, Nat.cast_sub hld] + unfold dotProduct + ring + +noncomputable def normalizationFactor (d l : ℕ) : ℝ := + (l.factorial : ℝ) * (d.descFactorial l : ℝ) + +lemma normalizationFactor_pos {d l : ℕ} (hl : l ≤ d) : + 0 < normalizationFactor d l := + mul_pos (by exact_mod_cast l.factorial_pos) + (by exact_mod_cast Nat.descFactorial_pos.mpr hl) + +lemma normalizationFactor_succ {d l : ℕ} (hl : l ≤ d) : + normalizationFactor d (l+1) = + (((l : ℝ)+1)*((d : ℝ)-l)) * normalizationFactor d l := by + rw [normalizationFactor, Nat.factorial_succ, Nat.descFactorial_succ, + Nat.cast_mul, Nat.cast_mul, Nat.cast_sub hl, Nat.cast_add, Nat.cast_one] + unfold normalizationFactor + ring + +noncomputable def normalized (S : LadderSystem ι) (x : ι → ℝ) (d l : ℕ) : ι → ℝ := + (1 / Real.sqrt (normalizationFactor d l)) • S.raw x l + +@[simp] lemma normalized_zero (S : LadderSystem ι) (x : ι → ℝ) (d : ℕ) : + S.normalized x d 0 = x := by simp [normalized, normalizationFactor] + +lemma normalized_succ (S : LadderSystem ι) (x : ι → ℝ) {d l : ℕ} (hl : l < d) : + S.normalized x d (l+1) = + (1 / Real.sqrt (((l : ℝ)+1)*((d : ℝ)-l))) • S.lower (S.normalized x d l) := by + have hα : 0 ≤ ((l : ℝ)+1)*((d : ℝ)-l) := by + have hld : (l : ℝ) < d := by exact_mod_cast hl + positivity + simp only [normalized, raw_succ, normalizationFactor_succ hl.le, + Real.sqrt_mul hα, map_smul, smul_smul, one_div_mul_one_div] + +lemma normalized_weight (S : LadderSystem ι) {x : ι → ℝ} {d : ℕ} + (hw : S.weight x = (d : ℝ) • x) (l : ℕ) : + S.weight (S.normalized x d l) = ((d : ℝ)-2*l) • S.normalized x d l := by + simp only [normalized, map_smul, S.weight_raw hw] + exact smul_comm _ _ _ + +theorem normalized_norm_sq (S : LadderSystem ι) {x : ι → ℝ} {d l : ℕ} + (hw : S.weight x = (d : ℝ) • x) (he : S.raise x = 0) (hl : l ≤ d) : + dotProduct (S.normalized x d l) (S.normalized x d l) = dotProduct x x := by + have hf : 0 < normalizationFactor d l := normalizationFactor_pos hl + have hs : Real.sqrt (normalizationFactor d l) ≠ 0 := (Real.sqrt_pos.mpr hf).ne' + have heq := Real.sq_sqrt hf.le + simp only [normalized, smul_dotProduct, dotProduct_smul, smul_eq_mul, + S.raw_norm_sq hw he (by omega : l ≤ d+1)] + change (1 / Real.sqrt (normalizationFactor d l)) * + ((1 / Real.sqrt (normalizationFactor d l)) * + (normalizationFactor d l * dotProduct x x)) = dotProduct x x + field_simp + rw [heq] + +end LadderSystem + +noncomputable def onFirstEnd {ι κ : Type*} (A : Module.End ℝ (ι → ℝ)) : + Module.End ℝ ((ι × κ) → ℝ) where + toFun x pq := A (fun p => x (p, pq.2)) pq.1 + map_add' x y := by + funext pq + exact congrFun (A.map_add (fun p => x (p,pq.2)) (fun p => y (p,pq.2))) pq.1 + map_smul' r x := by + funext pq + exact congrFun (A.map_smul r (fun p => x (p,pq.2))) pq.1 + +noncomputable def onSecondEnd {ι κ : Type*} (A : Module.End ℝ (κ → ℝ)) : + Module.End ℝ ((ι × κ) → ℝ) where + toFun x pq := A (fun q => x (pq.1, q)) pq.2 + map_add' x y := by + funext pq + exact congrFun (A.map_add (fun q => x (pq.1,q)) (fun q => y (pq.1,q))) pq.2 + map_smul' r x := by + funext pq + exact congrFun (A.map_smul r (fun q => x (pq.1,q))) pq.2 + +@[simp] lemma onFirstEnd_apply {ι κ : Type*} (A : Module.End ℝ (ι → ℝ)) + (x : (ι × κ) → ℝ) (p : ι) (q : κ) : + onFirstEnd A x (p,q) = A (fun i => x (i,q)) p := rfl + +@[simp] lemma onSecondEnd_apply {ι κ : Type*} (A : Module.End ℝ (κ → ℝ)) + (x : (ι × κ) → ℝ) (p : ι) (q : κ) : + onSecondEnd A x (p,q) = A (fun j => x (p,j)) q := rfl + +lemma tensor_factor_commute {ι κ : Type*} [Fintype ι] + (A : Module.End ℝ (ι → ℝ)) (B : Module.End ℝ (κ → ℝ)) (x : (ι×κ) → ℝ) : + onFirstEnd A (onSecondEnd B x) = onSecondEnd B (onFirstEnd A x) := by + classical + funext ⟨p,q⟩ + simp only [onFirstEnd_apply, onSecondEnd_apply] + have hfun : (fun j => A (fun i => x (i,j)) p) = + ∑ i : ι, (A (fun k => if i = k then 1 else 0) p) • (fun j => x (i,j)) := by + funext j + rw [A.pi_apply_eq_sum_univ (fun i => x (i,j))] + simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul] + apply Finset.sum_congr rfl + intro i hi + ring + rw [hfun, map_sum, A.pi_apply_eq_sum_univ (fun i => B (fun j => x (i,j)) q)] + simp only [Finset.sum_apply, map_smul, Pi.smul_apply, smul_eq_mul] + apply Finset.sum_congr rfl + intro i hi + ring + +namespace LadderSystem +variable {ι κ : Type*} [Fintype ι] [Fintype κ] + +noncomputable def onFirst (S : LadderSystem ι) : LadderSystem (ι × κ) where + lower := onFirstEnd S.lower + raise := onFirstEnd S.raise + weight := onFirstEnd S.weight + adjoint x y := by + simp only [dotProduct, Fintype.sum_prod_type, onFirstEnd_apply] + rw [Finset.sum_comm, Finset.sum_comm (f := fun p q => x (p,q) * S.raise (fun i => y (i,q)) p)] + apply Finset.sum_congr rfl + intro q hq + exact S.adjoint (fun p => x (p,q)) (fun p => y (p,q)) + raise_lower x := by + funext ⟨p,q⟩ + exact congrFun (S.raise_lower (fun i => x (i,q))) p + weight_lower x := by + funext ⟨p,q⟩ + exact congrFun (S.weight_lower (fun i => x (i,q))) p + +noncomputable def onSecond (S : LadderSystem κ) : LadderSystem (ι × κ) where + lower := onSecondEnd S.lower + raise := onSecondEnd S.raise + weight := onSecondEnd S.weight + adjoint x y := by + simp only [dotProduct, Fintype.sum_prod_type, onSecondEnd_apply] + apply Finset.sum_congr rfl + intro p hp + exact S.adjoint (fun q => x (p,q)) (fun q => y (p,q)) + raise_lower x := by + funext ⟨p,q⟩ + exact congrFun (S.raise_lower (fun j => x (p,j))) q + weight_lower x := by + funext ⟨p,q⟩ + exact congrFun (S.weight_lower (fun j => x (p,j))) q + +noncomputable def tensor (S : LadderSystem ι) (T : LadderSystem κ) : + LadderSystem (ι × κ) where + lower := onFirstEnd S.lower + onSecondEnd T.lower + raise := onFirstEnd S.raise + onSecondEnd T.raise + weight := onFirstEnd S.weight + onSecondEnd T.weight + adjoint x y := by + simp only [LinearMap.add_apply, add_dotProduct, dotProduct_add] + exact congrArg₂ (· + ·) (S.onFirst.adjoint x y) (T.onSecond.adjoint x y) + raise_lower x := by + simp only [LinearMap.add_apply, map_add] + rw [show onFirstEnd S.raise (onFirstEnd S.lower x) = + onFirstEnd S.lower (onFirstEnd S.raise x) + onFirstEnd S.weight x from + S.onFirst.raise_lower x, + show onSecondEnd T.raise (onSecondEnd T.lower x) = + onSecondEnd T.lower (onSecondEnd T.raise x) + onSecondEnd T.weight x from + T.onSecond.raise_lower x, + tensor_factor_commute S.raise T.lower x, ← tensor_factor_commute S.lower T.raise x] + abel + weight_lower x := by + simp only [LinearMap.add_apply, map_add, smul_add] + rw [show onFirstEnd S.weight (onFirstEnd S.lower x) = + onFirstEnd S.lower (onFirstEnd S.weight x) - (2 : ℝ) • onFirstEnd S.lower x from + S.onFirst.weight_lower x, + show onSecondEnd T.weight (onSecondEnd T.lower x) = + onSecondEnd T.lower (onSecondEnd T.weight x) - (2 : ℝ) • onSecondEnd T.lower x from + T.onSecond.weight_lower x, + tensor_factor_commute S.weight T.lower x, ← tensor_factor_commute S.lower T.weight x] + abel + +end LadderSystem + +noncomputable def tensorSpin (n m : ℕ) : LadderSystem (Fin (n+1) × Fin (m+1)) := + (standardLadderSystem n).tensor (standardLadderSystem m) + +noncomputable def highestTensor (n m z : ℕ) : (Fin (n+1) × Fin (m+1)) → ℝ := + fun pq => if pq.1.val + pq.2.val = z then highestCoefficient n m z pq.1.val else 0 + +noncomputable def coupledTensor (n m z l : ℕ) : (Fin (n+1) × Fin (m+1)) → ℝ := + fun pq => if pq.1.val + pq.2.val = z+l then coupledCoefficient n m z l pq.1.val else 0 + +@[simp] lemma coupledTensor_zero (n m z : ℕ) : coupledTensor n m z 0 = highestTensor n m z := by + rfl + +lemma tensorSpin_weight (n m : ℕ) (x : (Fin (n+1) × Fin (m+1)) → ℝ) + (p : Fin (n+1)) (q : Fin (m+1)) : + (tensorSpin n m).weight x (p,q) = ((n : ℝ)+m-2*(p.val+q.val)) * x (p,q) := by + simp only [tensorSpin, LadderSystem.tensor, standardLadderSystem, + LinearMap.add_apply, onFirstEnd_apply, onSecondEnd_apply, Pi.add_apply, weight_apply] + ring + +lemma tensorSpin_lower (n m : ℕ) (x : (Fin (n+1) × Fin (m+1)) → ℝ) + (p : Fin (n+1)) (q : Fin (m+1)) : + (tensorSpin n m).lower x (p,q) = + lowering n (fun i => x (i,q)) p + lowering m (fun j => x (p,j)) q := rfl + +lemma tensorSpin_raise (n m : ℕ) (x : (Fin (n+1) × Fin (m+1)) → ℝ) + (p : Fin (n+1)) (q : Fin (m+1)) : + (tensorSpin n m).raise x (p,q) = + raising n (fun i => x (i,q)) p + raising m (fun j => x (p,j)) q := rfl + +lemma raising_apply_of_lt {n : ℕ} (x : Fin (n+1) → ℝ) (p : Fin (n+1)) + (hp : p.val < n) : + raising n x p = + Real.sqrt (((p.val : ℝ)+1)*((n : ℝ)-p.val)) * x ⟨p.val+1,by omega⟩ := by + exact raising_castSucc n x ⟨p.val,hp⟩ + +lemma raising_apply_of_not_lt {n : ℕ} (x : Fin (n+1) → ℝ) (p : Fin (n+1)) + (hp : ¬p.val < n) : raising n x p = 0 := by + have he : p = Fin.last n := by ext; simp only [Fin.val_last]; omega + rw [he, raising_last] + +theorem highestTensor_weight {n m z : ℕ} (hz : z ≤ min n m) : + (tensorSpin n m).weight (highestTensor n m z) = + ((n+m-2*z : ℕ) : ℝ) • highestTensor n m z := by + have hzn : z ≤ n := (le_min_iff.mp hz).1 + have hzm : z ≤ m := (le_min_iff.mp hz).2 + have hzsum : 2*z ≤ n+m := by omega + funext ⟨p,q⟩ + rw [tensorSpin_weight] + simp only [highestTensor, Pi.smul_apply, smul_eq_mul] + split_ifs with h + · have hc : (p.val : ℝ)+q.val = z := by exact_mod_cast h + rw [hc, Nat.cast_sub hzsum, Nat.cast_add, Nat.cast_mul, Nat.cast_ofNat] + · simp + +theorem highestTensor_raise {n m z : ℕ} (hz : z ≤ min n m) : + (tensorSpin n m).raise (highestTensor n m z) = 0 := by + have hzn : z ≤ n := (le_min_iff.mp hz).1 + have hzm : z ≤ m := (le_min_iff.mp hz).2 + funext ⟨p,q⟩ + rw [tensorSpin_raise] + by_cases h : p.val+q.val+1 = z + · have hp : p.val < n := by omega + have hq : q.val < m := by omega + rw [raising_apply_of_lt _ p hp, raising_apply_of_lt _ q hq] + simp only [highestTensor, show p.val+1+q.val = z by omega, + show p.val+(q.val+1) = z by omega, ite_true, Pi.zero_apply] + have hc : (p.val : ℝ)+q.val+1 = z := by exact_mod_cast h + have he : Real.sqrt (((q.val : ℝ)+1)*((m : ℝ)-q.val)) = + Real.sqrt (((z : ℝ)-p.val)*((m : ℝ)-z+p.val+1)) := by + congr 1 + rw [← hc] + ring + rw [he] + simpa only [mul_comm] using highestCoefficient_raising hz (by omega : p.val < z) + · have h₁ : raising n (fun i => highestTensor n m z (i,q)) p = 0 := by + by_cases hp : p.val < n + · rw [raising_apply_of_lt _ p hp] + simp [highestTensor, show ¬ (p.val+1+q.val = z) by omega] + · exact raising_apply_of_not_lt _ p hp + have h₂ : raising m (fun j => highestTensor n m z (p,j)) q = 0 := by + by_cases hq : q.val < m + · rw [raising_apply_of_lt _ q hq] + simp [highestTensor, show ¬ (p.val+(q.val+1) = z) by omega] + · exact raising_apply_of_not_lt _ q hq + simp only [h₁, h₂, zero_add, Pi.zero_apply] + +theorem highestTensor_norm_sq {n m z : ℕ} (hz : z ≤ min n m) : + dotProduct (highestTensor n m z) (highestTensor n m z) = 1 := by + have hzn : z ≤ n := (le_min_iff.mp hz).1 + have hzm : z ≤ m := (le_min_iff.mp hz).2 + have hinner (p : Fin (n+1)) : + (∑ q : Fin (m+1), highestTensor n m z (p,q) * highestTensor n m z (p,q)) = + highestCoefficient n m z p.val ^ 2 := by + by_cases hp : p.val ≤ z + · let q₀ : Fin (m+1) := ⟨z-p.val, by omega⟩ + rw [Finset.sum_eq_single q₀] + · simp only [highestTensor, show p.val+q₀.val = z by dsimp [q₀]; omega, + ite_true, pow_two] + · intro q hq hne + have hne' : p.val+q.val ≠ z := by + intro he + apply hne + ext + dsimp [q₀] + omega + simp [highestTensor, hne'] + · simp + · have hpz : z < p.val := by omega + rw [highestCoefficient_eq_zero hpz, zero_pow (by omega : (2:ℕ) ≠ 0)] + apply Finset.sum_eq_zero + intro q hq + simp [highestTensor, show p.val+q.val ≠ z by omega] + unfold dotProduct + rw [Fintype.sum_prod_type] + simp_rw [hinner] + rw [Fin.sum_univ_eq_sum_range (fun p => highestCoefficient n m z p ^ 2) (n+1)] + calc + _ = ∑ p ∈ Finset.range (z+1), highestCoefficient n m z p ^ 2 := by + symm + apply Finset.sum_subset (Finset.range_mono (by omega : z+1 ≤ n+1)) + intro p hp hpn + simp only [Finset.mem_range, not_lt] at hpn + rw [highestCoefficient_eq_zero (by omega : z < p), zero_pow (by omega : (2:ℕ) ≠ 0)] + _ = 1 := highestCoefficient_sum_sq hz + +lemma firstLoweringCoefficient_succ (n m z l : ℕ) (p : Fin n) : + firstLoweringCoefficient n m z l p.succ.val = + ladderStep n p / Real.sqrt (((l : ℝ)+1)*((n : ℝ)+m-2*z-l)) := by + unfold firstLoweringCoefficient ladderStep + simp only [Fin.val_succ, Nat.cast_add, Nat.cast_one] + congr 2 + ring + +lemma secondLoweringCoefficient_succ {n m z l : ℕ} (p : Fin (n+1)) (q : Fin m) + (h : p.val+q.succ.val = z+(l+1)) : + secondLoweringCoefficient n m z l p.val = + ladderStep m q / Real.sqrt (((l : ℝ)+1)*((n : ℝ)+m-2*z-l)) := by + have hc : (p.val : ℝ)+q.val+1 = (z : ℝ)+l+1 := by + have he : p.val+q.val+1 = z+l+1 := by simpa [Nat.add_assoc] using h + exact_mod_cast he + unfold secondLoweringCoefficient ladderStep + congr 2 + congr 1 <;> linarith + +lemma secondLoweringCoefficient_last {n m z l : ℕ} {p : Fin (n+1)} + (h : p.val = z+(l+1)) : secondLoweringCoefficient n m z l p.val = 0 := by + have hc : (p.val : ℝ) = (z : ℝ)+l+1 := by exact_mod_cast h + unfold secondLoweringCoefficient + rw [show (z : ℝ)+l-p.val+1 = 0 by linarith] + simp + +theorem coupledTensor_succ (n m z l : ℕ) : + coupledTensor n m z (l+1) = + (1 / Real.sqrt (((l : ℝ)+1)*((n : ℝ)+m-2*z-l))) • + (tensorSpin n m).lower (coupledTensor n m z l) := by + funext ⟨p,q⟩ + simp only [Pi.smul_apply, smul_eq_mul, tensorSpin_lower] + by_cases h : p.val+q.val = z+(l+1) + · rw [coupledTensor, ite_eq_left h, coupledCoefficient] + cases p using Fin.cases with + | zero => + simp only [Fin.val_zero, ↓reduceIte, zero_add, lowering_zero] + cases q using Fin.cases with + | zero => simp only [Fin.val_zero] at h; omega + | succ q => + have hs := secondLoweringCoefficient_succ (0 : Fin (n+1)) q h + simp only [Fin.val_zero] at hs + rw [lowering_succ, hs] + simp only [coupledTensor, Fin.val_zero, Fin.val_castSucc, zero_add, + show q.val = z+l by simp only [Fin.val_zero, Fin.val_succ] at h; omega, ite_true] + ring + | succ p => + simp only [Fin.val_succ, Nat.add_eq_zero_iff, one_ne_zero, and_false, + ↓reduceIte, Nat.add_sub_cancel, lowering_succ] + rw [show firstLoweringCoefficient n m z l (p.val+1) = + ladderStep n p / Real.sqrt (((l : ℝ)+1)*((n : ℝ)+m-2*z-l)) from + firstLoweringCoefficient_succ n m z l p] + cases q using Fin.cases with + | zero => + have hs := secondLoweringCoefficient_last (m := m) + (by simpa using h : p.succ.val = z+(l+1)) + simp only [Fin.val_succ] at hs + rw [hs, lowering_zero] + simp only [zero_mul, add_zero, coupledTensor, Fin.val_castSucc, Fin.val_zero, + add_zero, ite_eq_left (by simp only [Fin.val_succ, Fin.val_zero] at h; omega : p.val = z+l)] + ring + | succ q => + have hs := secondLoweringCoefficient_succ p.succ q h + simp only [Fin.val_succ] at hs + rw [lowering_succ, hs] + have h₁ : p.val+(q.val+1) = z+l := by simp only [Fin.val_succ] at h; omega + have h₂ : p.val+1+q.val = z+l := by simp only [Fin.val_succ] at h; omega + simp only [coupledTensor, Fin.val_castSucc, Fin.val_succ, ite_eq_left h₁, ite_eq_left h₂] + ring + · rw [coupledTensor, ite_eq_right h] + have h₁ : lowering n (fun i => coupledTensor n m z l (i,q)) p = 0 := by + cases p using Fin.cases with + | zero => rfl + | succ p => + rw [lowering_succ] + have hn : p.val+q.val ≠ z+l := by simp only [Fin.val_succ] at h; omega + simp only [coupledTensor, Fin.val_castSucc, ite_eq_right hn, mul_zero] + have h₂ : lowering m (fun j => coupledTensor n m z l (p,j)) q = 0 := by + cases q using Fin.cases with + | zero => rfl + | succ q => + rw [lowering_succ] + have hn : p.val+q.val ≠ z+l := by simp only [Fin.val_succ] at h; omega + simp only [coupledTensor, Fin.val_castSucc, ite_eq_right hn, mul_zero] + simp only [h₁, h₂, zero_add, mul_zero] + +theorem coupledTensor_eq_normalized {n m z l : ℕ} (hz : z ≤ min n m) + (hl : l ≤ n+m-2*z) : + coupledTensor n m z l = (tensorSpin n m).normalized (highestTensor n m z) (n+m-2*z) l := by + have hzsum : 2*z ≤ n+m := by have := le_min_iff.mp hz; omega + induction l with + | zero => simp + | succ l ih => + rw [coupledTensor_succ, ih (by omega), LadderSystem.normalized_succ _ _ (by omega)] + simp only [Nat.cast_sub hzsum, Nat.cast_add, Nat.cast_mul, Nat.cast_ofNat] + +theorem coupledTensor_norm_sq {n m z l : ℕ} (hz : z ≤ min n m) + (hl : l ≤ n+m-2*z) : + dotProduct (coupledTensor n m z l) (coupledTensor n m z l) = 1 := by + rw [coupledTensor_eq_normalized hz hl, LadderSystem.normalized_norm_sq _ + (highestTensor_weight hz) (highestTensor_raise hz) hl, highestTensor_norm_sq hz] + +theorem coupledTensor_weight {n m z l : ℕ} (hz : z ≤ min n m) + (hl : l ≤ n+m-2*z) : + (tensorSpin n m).weight (coupledTensor n m z l) = + (((n+m-2*z : ℕ) : ℝ)-2*l) • coupledTensor n m z l := by + rw [coupledTensor_eq_normalized hz hl] + exact LadderSystem.normalized_weight _ (highestTensor_weight hz) l + +namespace LadderSystem +variable {ι : Type*} [Fintype ι] + +lemma raise_adjoint (S : LadderSystem ι) (x y : ι → ℝ) : + dotProduct (S.raise x) y = dotProduct x (S.lower y) := by + rw [dotProduct_comm, ← S.adjoint, dotProduct_comm] + +lemma weight_eq (S : LadderSystem ι) (x : ι → ℝ) : + S.weight x = S.raise (S.lower x) - S.lower (S.raise x) := by + rw [S.raise_lower] + abel + +lemma weight_adjoint (S : LadderSystem ι) (x y : ι → ℝ) : + dotProduct (S.weight x) y = dotProduct x (S.weight y) := by + rw [S.weight_eq x, S.weight_eq y, sub_dotProduct, dotProduct_sub] + simp only [S.raise_adjoint, S.adjoint] + +noncomputable def casimir (S : LadderSystem ι) : Module.End ℝ (ι → ℝ) := + S.weight.comp S.weight + (2 : ℝ) • S.weight + (4 : ℝ) • S.lower.comp S.raise + +lemma casimir_apply (S : LadderSystem ι) (x : ι → ℝ) : + S.casimir x = S.weight (S.weight x) + (2 : ℝ) • S.weight x + + (4 : ℝ) • S.lower (S.raise x) := rfl + +lemma casimir_adjoint (S : LadderSystem ι) (x y : ι → ℝ) : + dotProduct (S.casimir x) y = dotProduct x (S.casimir y) := by + simp only [casimir_apply, add_dotProduct, dotProduct_add, + smul_dotProduct, dotProduct_smul, S.weight_adjoint, S.adjoint, S.raise_adjoint] + +lemma lower_raise_raw (S : LadderSystem ι) {x : ι → ℝ} {μ : ℝ} + (hw : S.weight x = μ • x) (he : S.raise x = 0) (l : ℕ) : + S.lower (S.raise (S.raw x l)) = ((l : ℝ)*(μ-l+1)) • S.raw x l := by + cases l with + | zero => simp [he] + | succ l => + rw [S.raise_raw hw he, map_smul, raw_succ] + simp only [Nat.cast_add, Nat.cast_one] + congr 1 + ring + +lemma casimir_raw (S : LadderSystem ι) {x : ι → ℝ} {μ : ℝ} + (hw : S.weight x = μ • x) (he : S.raise x = 0) (l : ℕ) : + S.casimir (S.raw x l) = (μ*(μ+2)) • S.raw x l := by + simp only [casimir_apply, S.lower_raise_raw hw he, + map_smul, S.weight_raw hw, smul_smul, ← add_smul] + congr 1 + ring + +lemma casimir_normalized (S : LadderSystem ι) {x : ι → ℝ} {d : ℕ} + (hw : S.weight x = (d : ℝ) • x) (he : S.raise x = 0) (l : ℕ) : + S.casimir (S.normalized x d l) = ((d : ℝ)*(d+2)) • S.normalized x d l := by + simp only [normalized, map_smul, S.casimir_raw hw he] + exact smul_comm _ _ _ + +end LadderSystem + +lemma dot_eq_zero_of_distinct_eigenvalues {ι : Type*} [Fintype ι] + (A : Module.End ℝ (ι → ℝ)) (hA : ∀ x y, dotProduct (A x) y = dotProduct x (A y)) + {x y : ι → ℝ} {μ ν : ℝ} (hx : A x = μ • x) (hy : A y = ν • y) (hμν : μ ≠ ν) : + dotProduct x y = 0 := by + have h := hA x y + rw [hx, hy, smul_dotProduct, dotProduct_smul] at h + exact (mul_eq_zero.mp (show (μ-ν)*dotProduct x y = 0 by + simp only [smul_eq_mul] at h; nlinarith)).resolve_left (sub_ne_zero.mpr hμν) + +theorem coupledTensor_casimir {n m z l : ℕ} (hz : z ≤ min n m) + (hl : l ≤ n+m-2*z) : + (tensorSpin n m).casimir (coupledTensor n m z l) = + (((n+m-2*z : ℕ) : ℝ)*((n+m-2*z : ℕ)+2)) • coupledTensor n m z l := by + rw [coupledTensor_eq_normalized hz hl] + exact LadderSystem.casimir_normalized _ (highestTensor_weight hz) (highestTensor_raise hz) l + +theorem coupledTensor_orthogonal_same_spin {n m z l k : ℕ} (hz : z ≤ min n m) + (hl : l ≤ n+m-2*z) (hk : k ≤ n+m-2*z) (hlk : l ≠ k) : + dotProduct (coupledTensor n m z l) (coupledTensor n m z k) = 0 := by + apply dot_eq_zero_of_distinct_eigenvalues _ (tensorSpin n m).weight_adjoint + (coupledTensor_weight hz hl) (coupledTensor_weight hz hk) + intro h + apply hlk + have H : (l : ℝ) = k := by linarith + exact_mod_cast H + +theorem coupledTensor_orthogonal_distinct_spin {n m z w l k : ℕ} + (hz : z ≤ min n m) (hw : w ≤ min n m) + (hl : l ≤ n+m-2*z) (hk : k ≤ n+m-2*w) (hzw : z ≠ w) : + dotProduct (coupledTensor n m z l) (coupledTensor n m w k) = 0 := by + apply dot_eq_zero_of_distinct_eigenvalues _ (tensorSpin n m).casimir_adjoint + (coupledTensor_casimir hz hl) (coupledTensor_casimir hw hk) + have hd : n+m-2*z ≠ n+m-2*w := by + have := le_min_iff.mp hz + have := le_min_iff.mp hw + omega + have hd' : ((n+m-2*z : ℕ) : ℝ) ≠ (n+m-2*w : ℕ) := by exact_mod_cast hd + have hsum : 0 < ((n+m-2*z : ℕ) : ℝ)+(n+m-2*w : ℕ)+2 := by positivity + intro he + have hh : (((n+m-2*z : ℕ) : ℝ)-(n+m-2*w : ℕ)) * + (((n+m-2*z : ℕ) : ℝ)+(n+m-2*w : ℕ)+2) = 0 := by nlinarith + exact hd' (sub_eq_zero.mp ((mul_eq_zero.mp hh).resolve_right hsum.ne')) + +abbrev CoupledIndex (n m : ℕ) := + (z : Fin (min n m + 1)) × Fin (n+m-2*z.val+1) + +noncomputable def coupledFamily (n m : ℕ) (i : CoupledIndex n m) : + EuclideanSpace ℝ (Fin (n+1) × Fin (m+1)) := + WithLp.toLp 2 (coupledTensor n m i.1.val i.2.val) + +theorem coupledFamily_orthonormal (n m : ℕ) : Orthonormal ℝ (coupledFamily n m) := by + classical + rw [orthonormal_iff_ite] + rintro ⟨z,l⟩ ⟨w,k⟩ + simp only [coupledFamily, EuclideanSpace.inner_toLp_toLp, star_trivial] + rw [dotProduct_comm] + have hz : z.val ≤ min n m := by omega + have hw : w.val ≤ min n m := by omega + have hl : l.val ≤ n+m-2*z.val := by omega + have hk : k.val ≤ n+m-2*w.val := by omega + by_cases hzw : z = w + · subst w + by_cases hlk : l = k + · subst k + rw [ite_eq_left rfl] + exact coupledTensor_norm_sq hz hl + · rw [ite_eq_right (by simpa using hlk : (Sigma.mk z l : CoupledIndex n m) ≠ ⟨z,k⟩)] + exact coupledTensor_orthogonal_same_spin hz hl hk (fun h => hlk (Fin.ext h)) + · rw [ite_eq_right (fun h => hzw (congrArg Sigma.fst h))] + exact coupledTensor_orthogonal_distinct_spin hz hw hl hk (fun h => hzw (Fin.ext h)) + +theorem coupledIndex_card (n m : ℕ) : Fintype.card (CoupledIndex n m) = (n+1)*(m+1) := by + let k := min n m + have hz (z : Fin (k+1)) : 2*z.val ≤ n+m := by + have hzn : z.val ≤ n := (Nat.le_of_lt_succ z.isLt).trans (min_le_left n m) + have hzm : z.val ≤ m := (Nat.le_of_lt_succ z.isLt).trans (min_le_right n m) + omega + have hdim (z : Fin (k+1)) : ((n+m-2*z.val+1 : ℕ) : ℝ) = + (n : ℝ)+m-2*z.val+1 := by + rw [Nat.cast_add, Nat.cast_sub (hz z), Nat.cast_add, Nat.cast_mul, + Nat.cast_one, Nat.cast_ofNat] + have hid : (∑ z : Fin (k+1), (z.val : ℝ))*2 = ((k : ℝ)+1)*k := by + rw [Fin.sum_univ_eq_sum_range] + have h := congrArg (fun a : ℕ => (a : ℝ)) (Finset.sum_range_id_mul_two (k+1)) + simpa only [Nat.add_sub_cancel, Nat.cast_mul, Nat.cast_sum, Nat.cast_add, Nat.cast_one, + Nat.cast_ofNat] using h + simp only [CoupledIndex, Fintype.card_sigma, Fintype.card_fin] + apply Nat.cast_injective (R := ℝ) + change ((∑ z : Fin (k+1), (n+m-2*z.val+1) : ℕ) : ℝ) = (((n+1)*(m+1) : ℕ) : ℝ) + rw [Nat.cast_sum] + simp only [hdim, Finset.sum_add_distrib, Finset.sum_sub_distrib, + ← Finset.mul_sum, Finset.sum_const, Finset.card_univ, Fintype.card_fin, + nsmul_eq_mul, Nat.cast_add, Nat.cast_one, Nat.cast_mul] + rcases le_total n m with h | h + · have hk : (k : ℝ) = n := by exact_mod_cast min_eq_left h + nlinarith + · have hk : (k : ℝ) = m := by exact_mod_cast min_eq_right h + nlinarith + +noncomputable def coupledBasis (n m : ℕ) : + OrthonormalBasis (CoupledIndex n m) ℝ (EuclideanSpace ℝ (Fin (n+1) × Fin (m+1))) := by + letI : Nonempty (CoupledIndex n m) := ⟨⟨0,0⟩⟩ + have hc : Fintype.card (CoupledIndex n m) = + Module.finrank ℝ (EuclideanSpace ℝ (Fin (n+1) × Fin (m+1))) := by + rw [finrank_euclideanSpace, Fintype.card_prod, Fintype.card_fin, Fintype.card_fin] + exact coupledIndex_card n m + let b := basisOfOrthonormalOfCardEqFinrank (coupledFamily_orthonormal n m) hc + exact b.toOrthonormalBasis (by simpa [b] using coupledFamily_orthonormal n m) + +@[simp] theorem coupledBasis_apply (n m : ℕ) (i : CoupledIndex n m) : + coupledBasis n m i = coupledFamily n m i := by + simp [coupledBasis] + +namespace LadderSystem +variable {ι : Type*} [Fintype ι] + +lemma raw_top_succ (S : LadderSystem ι) {x : ι → ℝ} {d : ℕ} + (hw : S.weight x = (d : ℝ) • x) (he : S.raise x = 0) : S.raw x (d+1) = 0 := by + apply dotProduct_self_eq_zero.mp + rw [S.raw_norm_sq hw he (by omega)] + simp + +lemma normalized_lower (S : LadderSystem ι) (x : ι → ℝ) {d l : ℕ} (hl : l < d) : + S.lower (S.normalized x d l) = + Real.sqrt (((l : ℝ)+1)*((d : ℝ)-l)) • S.normalized x d (l+1) := by + have hα : 0 < ((l : ℝ)+1)*((d : ℝ)-l) := by + have hld : (l : ℝ) < d := by exact_mod_cast hl + exact mul_pos (by positivity) (by linarith) + rw [normalized_succ _ _ hl, smul_smul, mul_one_div_cancel (Real.sqrt_pos.mpr hα).ne', one_smul] + +lemma normalized_lower_top (S : LadderSystem ι) {x : ι → ℝ} {d : ℕ} + (hw : S.weight x = (d : ℝ) • x) (he : S.raise x = 0) : + S.lower (S.normalized x d d) = 0 := by + rw [normalized, map_smul, ← raw_succ, S.raw_top_succ hw he, smul_zero] + +lemma normalized_raise_zero (S : LadderSystem ι) {x : ι → ℝ} (he : S.raise x = 0) (d : ℕ) : + S.raise (S.normalized x d 0) = 0 := by simp [he] + +lemma normalized_raise_succ (S : LadderSystem ι) {x : ι → ℝ} {d l : ℕ} + (hw : S.weight x = (d : ℝ) • x) (he : S.raise x = 0) (hl : l < d) : + S.raise (S.normalized x d (l+1)) = + Real.sqrt (((l : ℝ)+1)*((d : ℝ)-l)) • S.normalized x d l := by + have hα : 0 < ((l : ℝ)+1)*((d : ℝ)-l) := by + have hld : (l : ℝ) < d := by exact_mod_cast hl + exact mul_pos (by positivity) (by linarith) + have ha : Real.sqrt (((l : ℝ)+1)*((d : ℝ)-l)) ≠ 0 := (Real.sqrt_pos.mpr hα).ne' + have hf : Real.sqrt (normalizationFactor d l) ≠ 0 := + (Real.sqrt_pos.mpr (normalizationFactor_pos hl.le)).ne' + simp only [normalized, map_smul, S.raise_raw hw he, smul_smul, + normalizationFactor_succ hl.le, Real.sqrt_mul hα.le] + congr 1 + field_simp + rw [Real.sq_sqrt hα.le] + +noncomputable def embedding (S : LadderSystem ι) (x : ι → ℝ) (d : ℕ) : + (Fin (d+1) → ℝ) →ₗ[ℝ] (ι → ℝ) where + toFun a := ∑ l : Fin (d+1), a l • S.normalized x d l.val + map_add' a b := by simp [add_smul, Finset.sum_add_distrib] + map_smul' t a := by simp [Finset.smul_sum, smul_smul] + +lemma embedding_apply (S : LadderSystem ι) (x : ι → ℝ) (d : ℕ) (a : Fin (d+1) → ℝ) : + S.embedding x d a = ∑ l : Fin (d+1), a l • S.normalized x d l.val := rfl + +theorem embedding_lower (S : LadderSystem ι) {x : ι → ℝ} {d : ℕ} + (hw : S.weight x = (d : ℝ) • x) (he : S.raise x = 0) (a : Fin (d+1) → ℝ) : + S.lower (S.embedding x d a) = S.embedding x d (lowering d a) := by + rw [embedding_apply, embedding_apply, map_sum, Fin.sum_univ_castSucc, Fin.sum_univ_succ] + simp only [map_smul, Fin.val_last, S.normalized_lower_top hw he, + lowering_zero, zero_smul, smul_zero, add_zero, zero_add] + apply Finset.sum_congr rfl + intro l hl + simp only [Fin.val_castSucc, Fin.val_succ] + rw [S.normalized_lower _ l.isLt, lowering_succ] + simp only [ladderStep, smul_smul] + congr 1 + ring + +theorem embedding_raise (S : LadderSystem ι) {x : ι → ℝ} {d : ℕ} + (hw : S.weight x = (d : ℝ) • x) (he : S.raise x = 0) (a : Fin (d+1) → ℝ) : + S.raise (S.embedding x d a) = S.embedding x d (raising d a) := by + rw [embedding_apply, embedding_apply, map_sum, Fin.sum_univ_succ, Fin.sum_univ_castSucc] + simp only [map_smul, Fin.val_zero, S.normalized_raise_zero he, + raising_last, zero_smul, smul_zero, add_zero, zero_add] + apply Finset.sum_congr rfl + intro l hl + simp only [Fin.val_castSucc, Fin.val_succ] + rw [S.normalized_raise_succ hw he l.isLt, raising_castSucc] + simp only [ladderStep, smul_smul] + congr 1 + ring + +theorem embedding_weight (S : LadderSystem ι) {x : ι → ℝ} {d : ℕ} + (hw : S.weight x = (d : ℝ) • x) (a : Fin (d+1) → ℝ) : + S.weight (S.embedding x d a) = S.embedding x d (LaughlinGap.Spin.weight d a) := by + simp only [embedding_apply, map_sum, map_smul, S.normalized_weight hw, weight_apply, + smul_smul] + apply Finset.sum_congr rfl + intro l hl + congr 1 + ring + +end LadderSystem + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/ThreeAveraging.lean b/lean/OAI/Analysis/LaughlinGap/ThreeAveraging.lean new file mode 100644 index 0000000000000000000000000000000000000000..c1951cce78f63e5453960478edb761646bbf8ca8 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/ThreeAveraging.lean @@ -0,0 +1,148 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.FourAveraging +import OAI.Analysis.LaughlinGap.ThreeBounds + +namespace OAI + +/-! Three Averaging. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators + +noncomputable def lowCoupledInclusion {n m T : ℕ} (hT : T ≤ min n m) + (z : Fin (T+1)) : CoupledIndex n m := + ⟨⟨z.val, by omega⟩, ⟨T-z.val, by dsimp; have := z.isLt; omega⟩⟩ + +lemma coupledTensor_low_expansion {n m T : ℕ} (hT : T ≤ min n m) + (a : Fin (n+1) × Fin (m+1)) (ha : a.1.val+a.2.val=T) : + (∑ z : Fin (T+1), coupledTensor n m z.val (T-z.val) a • + coupledTensor n m z.val (T-z.val)) = Pi.single a 1 := by + classical + have hex := coupledTensor_expansion n m (Pi.single a 1) + simp only [dotProduct_single_one] at hex + rw [← hex] + apply Finset.sum_bij_ne_zero (fun z _ _ => lowCoupledInclusion hT z) + · simp + · intro z hz hz0 w hw hw0 he + exact Fin.ext (congrArg (fun i : CoupledIndex n m => i.1.val) he) + · intro b hb hb0 + have hw : b.1.val+b.2.val=T := by + by_contra hn + exact hb0 (by simp [coupledTensor, show a.1.val+a.2.val ≠ b.1.val+b.2.val by omega]) + let z : Fin (T+1) := ⟨b.1.val,by omega⟩ + have hz : lowCoupledInclusion hT z = b := by + rcases b with ⟨r,l⟩ + have hr : (lowCoupledInclusion hT z).1 = r := Fin.ext rfl + apply Sigma.ext hr + apply (Fin.heq_ext_iff (by rfl)).mpr + dsimp [lowCoupledInclusion,z] + dsimp at hw + omega + refine ⟨z,Finset.mem_univ _,?_,hz⟩ + change coupledTensor n m (lowCoupledInclusion hT z).1.val + (lowCoupledInclusion hT z).2.val a • coupledTensor n m + (lowCoupledInclusion hT z).1.val (lowCoupledInclusion hT z).2.val ≠ 0 + rwa [hz] + · intros + rfl + +lemma coupledEmbedding_single {n m z : ℕ} (hz : z ≤ min n m) + (l : Fin (n+m-2*z+1)) : + (coupledEmbedding hz).toLinearMap (Pi.single l 1) = coupledTensor n m z l.val := by + rw [coupledEmbedding_apply] + simp [Pi.single_apply, ite_smul] + +end LaughlinGap.Spin + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin + +variable {ι : Type*} [Fintype ι] [DecidableEq ι] + +lemma Covariant.coupled_average {n m z w T U : ℕ} + (hT : T ≤ min n m) (hU : U ≤ min n m) (hz : z ≤ T) (hw : w ≤ U) + {L : Matrix ι ι ℝ} {B : (Fin (n+1) × Fin (m+1)) → Matrix ι ι ℝ} + (h : Covariant L (loweringMatrix (tensorSpin n m)) B) : + average (rotationCommutant L) + ((combination B (coupledTensor n m z (T-z))).transpose * + combination B (coupledTensor n m w (U-w))) = + if z=w ∧ T=U then + average (rotationCommutant L) + ((combination B (highestTensor n m z)).transpose * + combination B (highestTensor n m z)) else 0 := by + let hz' : z ≤ min n m := hz.trans hT + let hw' : w ≤ min n m := hw.trans hU + rw [← coupledEmbedding_single hz' (⟨T-z,by omega⟩ : Fin (n+m-2*z+1)), + ← coupledEmbedding_single hw' (⟨U-w,by omega⟩ : Fin (n+m-2*w+1))] + by_cases hzw : z=w + · subst w + rw [h.equal_descendant_average] + simp only [coupledEmbedding_single, Fin.val_zero, coupledTensor_zero, true_and, + Fin.mk.injEq] + congr 1 + apply propext + omega + · rw [ite_eq_right (by tauto)] + exact h.distinct_descendant_average (by omega) _ _ _ _ + +lemma Covariant.rawTensor_cross_average {n m T : ℕ} (hT : T ≤ min n m) + {L : Matrix ι ι ℝ} {B : (Fin (n+1) × Fin (m+1)) → Matrix ι ι ℝ} + (h : Covariant L (loweringMatrix (tensorSpin n m)) B) + (a b : Fin (n+1) × Fin (m+1)) + (ha : a.1.val+a.2.val=T) (hb : b.1.val+b.2.val=T) : + average (rotationCommutant L) ((B a).transpose * B b) = + ∑ z : Fin (T+1), + (coupledCoefficient n m z.val (T-z.val) a.1.val * + coupledCoefficient n m z.val (T-z.val) b.1.val) • + average (rotationCommutant L) + ((combination B (highestTensor n m z.val)).transpose * + combination B (highestTensor n m z.val)) := by + classical + have hex (c : Fin (n+1) × Fin (m+1)) (hc : c.1.val+c.2.val=T) := + congrArg (combination B) (coupledTensor_low_expansion hT c hc) + have hea := hex a ha + have heb := hex b hb + simp only [map_sum, map_smul, combination_single] at hea heb + rw [← hea, ← heb] + simp only [Matrix.transpose_sum, Matrix.transpose_smul, Finset.sum_mul, Finset.mul_sum, + Matrix.smul_mul, Matrix.mul_smul, smul_smul, map_sum, map_smul] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro z hz + have hh (w : Fin (T+1)) := h.coupled_average hT hT + (Nat.le_of_lt_succ z.isLt) (Nat.le_of_lt_succ w.isLt) + simp only [hh, and_true, Fin.val_inj] + rw [Finset.sum_eq_single z] + · simp only [ite_true, coupledTensor, show a.1.val+a.2.val=z.val+(T-z.val) by omega, + show b.1.val+b.2.val=z.val+(T-z.val) by omega] + rw [mul_comm] + · intro w hw hwz + rw [ite_eq_right (Ne.symm hwz), smul_zero] + · simp + +lemma rawTriple_cross_average {Q T : ℕ} (hQ : 2 ≤ Q) (hT : T ≤ Q) + (a b : Fin (2*Q-2+1) × Fin (Q+1)) + (ha : a.1.val+a.2.val=T) (hb : b.1.val+b.2.val=T) : + average (rotationCommutant (fockLowering Q)) + ((physicalTriple Q a).transpose * physicalTriple Q b) = + ∑ z : Fin (T+1), + (coupledCoefficient (2*Q-2) Q z.val (T-z.val) a.1.val * + coupledCoefficient (2*Q-2) Q z.val (T-z.val) b.1.val / + ((2*Q-2)+Q-2*z.val+1 : ℕ)) • + threeSpinLift hQ (show z.val ≤ Q by omega) := by + rw [(physicalTriple_covariant hQ).rawTensor_cross_average (by omega) a b ha hb] + apply Finset.sum_congr rfl + intro z hz + rw [threeSpinLift_average_highest hQ (show z.val ≤ Q by omega), smul_smul] + congr 1 + ring + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/ThreeBounds.lean b/lean/OAI/Analysis/LaughlinGap/ThreeBounds.lean new file mode 100644 index 0000000000000000000000000000000000000000..53207a4422281c0cacd7a7a01b3a643faa5002d6 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/ThreeBounds.lean @@ -0,0 +1,197 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.IntertwinerAveraging +import OAI.Analysis.LaughlinGap.RealPositivity + +namespace OAI + +/-! Three Bounds. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin + +variable {ι : Type*} [Fintype ι] [DecidableEq ι] + +lemma combination_one_bessel {κ : Type*} [Fintype κ] [DecidableEq κ] + (a : ι → ℝ) (ha : dotProduct a a = 1) (B : ι → Matrix κ κ ℝ) : + ((∑ i, (B i).transpose * B i) - (combination B a).transpose * combination B a).PosSemidef := by + let S : Matrix Unit ι ℝ := fun _ => a + have hS : S * S.transpose = 1 := by + ext i j + change (∑ k, a k * a k) = 1 + exact ha + simpa [S] using combination_bessel S hS B + +omit [Fintype ι] [DecidableEq ι] in +lemma highestCombination_range [Fintype ι] [DecidableEq ι] {n m z : ℕ} (hz : z ≤ min n m) + (B : (Fin (n+1) × Fin (m+1)) → Matrix ι ι ℝ) : + combination B (highestTensor n m z) = + ∑ p : Fin (z+1), highestCoefficient n m z p.val • + B (⟨p.val, by omega⟩,⟨z-p.val,by omega⟩) := by + simp only [combination, LinearMap.coe_mk, AddHom.coe_mk] + let f : Fin (z+1) → Fin (n+1) × Fin (m+1) := + fun p => (⟨p.val,by omega⟩, ⟨z-p.val,by omega⟩) + symm + apply Finset.sum_bij_ne_zero (fun p _ _ => f p) + · intro p hp hn; exact Finset.mem_univ _ + · intro p hp hn q hq hnq he + exact Fin.ext (congrArg (fun a : Fin (n+1) × Fin (m+1) => a.1.val) he) + · intro a ha hn + have he : a.1.val+a.2.val=z := by + by_contra he + simp [highestTensor, he] at hn + let p : Fin (z+1) := ⟨a.1.val,by omega⟩ + have hf : f p = a := by + apply Prod.ext + · rfl + · apply Fin.ext + dsimp [f,p] + omega + refine ⟨p,Finset.mem_univ _,?_,hf⟩ + simpa only [← hf, highestTensor, show (f p).1.val+(f p).2.val=z by dsimp [f]; omega, + ite_true] using hn + · intro p hp hn + simp only [highestTensor, show (f p).1.val+(f p).2.val=z by dsimp [f]; omega, ite_true] + rfl + +noncomputable def threeSpinLift {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : FockMatrix (Q+1) := + lift (physicalTriple Q) (tensorProjection (show z ≤ min (2*Q-2) Q by omega)) + +lemma threeSpinLift_positive {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + (threeSpinLift hQ hz).PosSemidef := by + apply lift_positive + rw [tensorProjection_eq] + apply Matrix.posSemidef_sum + intro l hl + simpa only [star_trivial] using Matrix.posSemidef_vecMulVec_self_star + (coupledTensor (2*Q-2) Q z l.val) + +lemma threeSpinLift_average_highest {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + average (rotationCommutant (fockLowering Q)) + ((combination (physicalTriple Q) (highestTensor (2*Q-2) Q z)).transpose * + combination (physicalTriple Q) (highestTensor (2*Q-2) Q z)) = + (1/((2*Q-2)+Q-2*z+1 : ℕ) : ℝ) • threeSpinLift hQ hz := by + let hz' : z ≤ min (2*Q-2) Q := by omega + have he : (coupledEmbedding hz').toLinearMap (Pi.single (0 : Fin ((2*Q-2)+Q-2*z+1)) 1) = + highestTensor (2*Q-2) Q z := by + rw [coupledEmbedding_apply] + simp [Pi.single_apply, ite_smul] + rw [← lift_rankOne, (physicalTriple_covariant hQ).average_lift, ← he, + equal_copy_average] + simp only [ite_true, map_smul] + simp only [threeSpinLift, tensorProjection, LadderMap.comp, LadderMap.transpose, + LinearMap.toMatrix'_comp, toMatrix_transposeMap, LadderMap.matrix] + +lemma average_mono (S : StarSubalgebra ℝ (Matrix ι ι ℝ)) + {A B : Matrix ι ι ℝ} (h : A ≤ B) : average S A ≤ average S B := by + have hh := average_positive S (Matrix.nonneg_iff_posSemidef.mp (sub_nonneg.mpr h)) + rw [map_sub] at hh + exact sub_nonneg.mp hh.nonneg + +lemma threeSpinLift_le {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + threeSpinLift hQ hz ≤ + (threeBodyDimensionRatio Q z * (z+1 : ℕ)) • physicalHamiltonian Q := by + let hz' : z ≤ min (2*Q-2) Q := by omega + let a : Fin (z+1) → ℝ := fun p => highestCoefficient (2*Q-2) Q z p.val + let B : Fin (z+1) → FockMatrix (Q+1) := fun p => + annihilation ⟨z-p.val,by omega⟩ * physicalPair Q p.val + have hn : dotProduct a a = 1 := by + simp only [a, dotProduct, ← sq] + rw [Fin.sum_univ_eq_sum_range (fun p => highestCoefficient (2*Q-2) Q z p ^ 2)] + exact highestCoefficient_sum_sq hz' + have hc : combination B a = combination (physicalTriple Q) (highestTensor (2*Q-2) Q z) := by + rw [highestCombination_range hz'] + rfl + have hb := (combination_one_bessel a hn B).nonneg + have hbs : (combination B a).transpose * combination B a ≤ + ∑ p : Fin (z+1), (physicalPair Q p.val).transpose * physicalPair Q p.val := by + apply (sub_nonneg.mp hb).trans + apply Finset.sum_le_sum + intro p hp + exact sub_nonneg.mp (annihilation_square_le ⟨z-p.val,by omega⟩ (physicalPair Q p.val)).nonneg + have ha := average_mono (rotationCommutant (fockLowering Q)) hbs + rw [hc, threeSpinLift_average_highest hQ hz, map_sum] at ha + have hf (p : Fin (z+1)) : average (rotationCommutant (fockLowering Q)) + ((physicalPair Q p.val).transpose * physicalPair Q p.val) = + (1/(2*Q-1 : ℕ) : ℝ) • physicalHamiltonian Q := + physicalPair_single_val hQ (by omega) + simp only [hf, ← Finset.sum_smul, Finset.sum_const, Finset.card_univ, Fintype.card_fin, + nsmul_eq_mul] at ha + have hd : (0 : ℝ) < ((2*Q-2)+Q-2*z+1 : ℕ) := by positivity + have hb' := smul_le_smul_of_nonneg_left ha hd.le + have hr : ((2*Q-2+Q-2*z+1 : ℕ) : ℝ) / + ((2*Q-1 : ℕ) : ℝ) = threeBodyDimensionRatio Q z := by + rw [threeBodyDimensionRatio, Nat.cast_add, Nat.cast_sub (by omega : 2*z ≤ 2*Q-2+Q), + Nat.cast_add, Nat.cast_sub (by omega : 2 ≤ 2*Q), Nat.cast_sub (by omega : 1 ≤ 2*Q)] + push_cast + ring + simp only [smul_smul, mul_one_div_cancel hd.ne', one_smul] at hb' + convert hb' using 1 + congr 1 + rw [← hr] + push_cast + ring + +lemma physicalHamiltonian_positive (Q : ℕ) : (physicalHamiltonian Q).PosSemidef := + Matrix.posSemidef_sum _ (fun _ _ => transpose_square_positive _) + +lemma threeTailTerm_le {Q z : ℕ} (hQ : 4 ≤ Q) (hz : z ≤ Q) (hz16 : 16 ≤ z) : + -(threeBodyTailTerm Q z) • physicalHamiltonian Q ≤ + (threeBodyGramCoefficient Q z) • threeSpinLift (hQ.trans' (by omega : 2 ≤ 4)) hz := by + let hQ' : 2 ≤ Q := by omega + have heq : (-1 : ℝ)^z * fallingRatio Q z * + (3*(z:ℝ)-1-(z:ℝ)*((z:ℝ)+1)/(Q:ℝ)) = threeBodyGramCoefficient Q z := rfl + rcases Nat.even_or_odd z with he | ho + · have hq : 0 ≤ threeBodyGramCoefficient Q z := by + rw [threeBodyGramCoefficient, he.neg_one_pow, one_mul] + exact mul_nonneg (fallingRatio_nonneg Q z) (threeBodyBracket_nonneg hQ hz hz16) + have ht : threeBodyTailTerm Q z = 0 := by + simp [threeBodyTailTerm, (Nat.not_odd_iff_even.mpr he)] + rw [ht, neg_zero, zero_smul] + exact smul_nonneg hq (threeSpinLift_positive hQ' hz).nonneg + · have h17 : 17 ≤ z := by + have hn : z ≠ 16 := by rintro rfl; norm_num at ho + omega + have hq : threeBodyGramCoefficient Q z ≤ 0 := by + rw [threeBodyGramCoefficient, ho.neg_one_pow, neg_one_mul, neg_mul] + exact neg_nonpos.mpr (mul_nonneg (fallingRatio_nonneg Q z) (threeBodyBracket_nonneg hQ hz hz16)) + have hh := smul_le_smul_of_nonneg_left (threeSpinLift_le hQ' hz) + (abs_nonneg (threeBodyGramCoefficient Q z)) + have hhh := neg_le_neg hh + simp only [smul_smul, ← neg_smul, abs_of_nonpos hq, neg_neg] at hhh + convert hhh using 1 + congr 1 + rw [threeBodyTailTerm, ite_eq_left ⟨h17,ho,hz⟩, abs_of_nonpos hq] + push_cast + ring + +noncomputable def threeTailLift {Q : ℕ} (hQ : 2 ≤ Q) : FockMatrix (Q+1) := + ∑ z : Fin (Q+1), if 16 ≤ z.val then + (threeBodyGramCoefficient Q z.val) • threeSpinLift hQ (Nat.le_of_lt_succ z.isLt) else 0 + +theorem threeTailLift_le {Q : ℕ} (hQ : 4 ≤ Q) : + -(threeBodyTail Q) • physicalHamiltonian Q ≤ threeTailLift (by omega : 2 ≤ Q) := by + have hh : (∑ z : Fin (Q+1), -(threeBodyTailTerm Q z.val) • physicalHamiltonian Q) ≤ + threeTailLift (by omega : 2 ≤ Q) := by + unfold threeTailLift + apply Finset.sum_le_sum + intro z hz + by_cases he : 16 ≤ z.val + · rw [ite_eq_left he] + exact threeTailTerm_le hQ (Nat.le_of_lt_succ z.isLt) he + · have ht : threeBodyTailTerm Q z.val = 0 := by + simp [threeBodyTailTerm, show ¬ 17 ≤ z.val by omega] + simp [he,ht] + convert hh using 1 + rw [← Finset.sum_smul, Finset.sum_neg_distrib, + Fin.sum_univ_eq_sum_range (fun z => threeBodyTailTerm Q z)] + rfl + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/ThreeComparison.lean b/lean/OAI/Analysis/LaughlinGap/ThreeComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..eb0d23623fe1dfb305b1e3ae0987dc311e2d93f4 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/ThreeComparison.lean @@ -0,0 +1,124 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.AuxiliaryComparison +import OAI.Analysis.LaughlinGap.FourSpin +import OAI.Analysis.LaughlinGap.RealSpinSquare + +namespace OAI + +/-! Three Comparison. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators MatrixOrder Matrix.Norms.L2Operator +open Averaging Spin Filter Topology + +noncomputable def threeWeightCoefficientStar (z T p : ℕ) : ℝ := + if z ≤ T then monomialWeight T p * + (couplingPolynomial (1/Real.sqrt 3) (Real.sqrt 2 / Real.sqrt 3) z (T-z)).coeff p else 0 + +lemma threeWeightCoefficient_tendsto (z T p : ℕ) : + Tendsto (fun Q => threeWeightCoefficient Q z T p) atTop + (𝓝 (threeWeightCoefficientStar z T p)) := by + by_cases hz : z ≤ T + · have hr : Tendsto (fun Q : ℕ => (Q:ℝ) / (2*Q-2:ℕ)) atTop (𝓝 (1/2:ℝ)) := by + simpa [Nat.sub_zero] using fallingFactor_tendsto 0 + have hu : Real.sqrt (1/2:ℝ) / Real.sqrt (1+(1/2:ℝ)) = 1/Real.sqrt 3 := by + rw [show (1:ℝ)+1/2=3/2 by norm_num, Real.sqrt_div (by norm_num : (0:ℝ) ≤ 1), + Real.sqrt_div (by norm_num : (0:ℝ) ≤ 3), Real.sqrt_one] + field_simp + have hv : 1 / Real.sqrt (1+(1/2:ℝ)) = Real.sqrt 2 / Real.sqrt 3 := by + rw [show (1:ℝ)+1/2=3/2 by norm_num, Real.sqrt_div (by norm_num : (0:ℝ) ≤ 3)] + field_simp + have h := coupledCoefficient_tendsto_polynomial (by norm_num : (0:ℝ) ≤ 1/2) + (affine_twice_spin_tendsto 1) hr z (T-z) p + simpa only [threeWeightCoefficient,threeWeightCoefficientStar,ite_eq_left hz, + Nat.add_sub_of_le hz,hu,hv,mul_one] using h + · simp only [threeWeightCoefficient,threeWeightCoefficientStar,ite_eq_right hz] + exact tendsto_const_nhds + +lemma rowTrace_tendsto {s : ℕ → ℕ → ℕ → ℕ → ℝ} {s₀ : ℕ → ℕ → ℕ → ℝ} + (hs : ∀ z T p, Tendsto (fun Q => s Q z T p) atTop (𝓝 (s₀ z T p))) + (r : RowData) (z : ℕ) : + Tendsto (fun Q => rowTrace (s Q) z r) atTop (𝓝 (rowTrace s₀ z r)) := by + unfold rowTrace + apply Tendsto.add + · apply tendsto_finsetSum + intro a ha + exact ((hs _ _ _).const_mul _).mul (hs _ _ _) + · apply tendsto_finsetSum + intro a ha + apply tendsto_finsetSum + intro b hb + by_cases he : a.output=b.output + · simp only [ite_eq_left he] + exact ((hs _ _ _).const_mul _).mul (hs _ _ _) + · simp only [ite_eq_right he] + exact tendsto_const_nhds + +lemma rowThreeTrace_tendsto (r : RowData) (z : ℕ) : + Tendsto (fun Q => rowThreeTrace Q z r) atTop + (𝓝 (rowTrace threeWeightCoefficientStar z r)) := + rowTrace_tendsto threeWeightCoefficient_tendsto r z + +lemma threeHighestAverage_eq {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + threeHighestAverage Q z = + (1/((2*Q-2)+Q-2*z+1 : ℕ):ℝ) • threeSpinLift hQ hz := + threeSpinLift_average_highest hQ hz + +lemma three_dimension_identity {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + ((2*Q-2+Q-2*z+1:ℕ):ℝ) / ((2*Q-1:ℕ):ℝ) = threeBodyDimensionRatio Q z := by + rw [threeBodyDimensionRatio, Nat.cast_add, Nat.cast_sub (by omega : 2*z ≤ 2*Q-2+Q), + Nat.cast_add, Nat.cast_sub (by omega : 2 ≤ 2*Q), Nat.cast_sub (by omega : 1 ≤ 2*Q)] + push_cast + ring + +theorem three_comparison_of_strict_traces {ι : Type*} [Fintype ι] + (rows : ι → RowData) + (hc : ∀ z : Fin 16, z.val ≠ 0 → z.val ≠ 1 → z.val ≠ 3 → + (∑ r, rowTrace threeWeightCoefficientStar z.val (rows r)) < + (3/2:ℝ) * ((3*(z.val:ℝ)-1)*(-1/2:ℝ)^z.val)) : + ∀ᶠ Q in atTop, ∀ hQ : 15 ≤ Q, + ((2*Q-1:ℕ):ℝ) • average (rotationCommutant (fockLowering Q)) + (∑ r, rowThree (by omega) (rows r)) ≤ + ∑ z : Fin 16, threeBodyGramCoefficient Q z.val • + threeSpinLift (by omega : 2 ≤ Q) (show z.val ≤ Q by omega) := by + have hseq (z : Fin 16) : ∀ᶠ Q in atTop, + z.val=0 ∨ z.val=1 ∨ z.val=3 ∨ + (∑ r, rowThreeTrace Q z.val (rows r)) ≤ + threeBodyDimensionRatio Q z.val * threeBodyGramCoefficient Q z.val := by + by_cases hn : z.val=0 ∨ z.val=1 ∨ z.val=3 + · exact Eventually.of_forall (fun _ => by tauto) + · have hlim := tendsto_finsetSum Finset.univ (fun r _ => rowThreeTrace_tendsto (rows r) z.val) + have htarget := (threeBodyDimensionRatio_tendsto z.val).mul + (threeBodyGramCoefficient_tendsto z.val) + filter_upwards [hlim.eventually_lt htarget (hc z (by tauto) (by tauto) (by tauto))] with Q hQ + exact Or.inr (Or.inr (Or.inr hQ.le)) + filter_upwards [eventually_all.mpr hseq] with Q hs + intro hQ + simp only [map_sum,rowThree_average hQ,Finset.smul_sum,smul_smul] + rw [Finset.sum_comm] + apply Finset.sum_le_sum + intro z hz + rw [← Finset.sum_smul, threeHighestAverage_eq (by omega) (by omega),smul_smul] + rcases hs z with hn | hn | hn | he + · simp [threeSpinLift_null (by omega : 2 ≤ Q) (by omega : z.val ≤ Q) (Or.inl hn)] + · simp [threeSpinLift_null (by omega : 2 ≤ Q) (by omega : z.val ≤ Q) (Or.inr (Or.inl hn))] + · simp [threeSpinLift_null (by omega : 2 ≤ Q) (by omega : z.val ≤ Q) (Or.inr (Or.inr hn))] + · apply smul_le_smul_of_nonneg_right _ (threeSpinLift_positive (by omega : 2 ≤ Q) (by omega : z.val ≤ Q)).nonneg + have hd : (0:ℝ) < ((2*Q-2)+Q-2*z.val+1:ℕ) := by positivity + have hd₂ : (0:ℝ) < (2*Q-1:ℕ) := by exact_mod_cast (show 0 < 2*Q-1 by omega) + rw [← three_dimension_identity (by omega : 2 ≤ Q) (by omega : z.val ≤ Q)] at he + rw [← Finset.mul_sum] + rw [div_mul_eq_mul_div] at he + have hh := (le_div_iff₀ hd₂).mp he + rw [mul_comm _ ((2*Q-1:ℕ):ℝ)] at hh + rw [mul_comm (↑(2 * Q - 2 + Q - 2 * ↑z + 1) : ℝ)] at hh + simpa only [div_eq_mul_inv, one_div, one_mul] using (div_le_iff₀ hd).mpr hh + +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/ThreeGram.lean b/lean/OAI/Analysis/LaughlinGap/ThreeGram.lean new file mode 100644 index 0000000000000000000000000000000000000000..e39af256ced4a77c4bc205ff8431f102c742450c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/ThreeGram.lean @@ -0,0 +1,274 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.ThreeSpectrum + +namespace OAI + +/-! Three Gram. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators + +abbrev ThreeIndex (ι : Type*) := (ι × ι) × ι + +def cycleIndex (ι : Type*) : ThreeIndex ι ≃ ThreeIndex ι where + toFun t := ((t.1.2,t.2),t.1.1) + invFun t := ((t.2,t.1.1),t.1.2) + left_inv _ := rfl + right_inv _ := rfl + +def cycleMap (ι : Type*) : Module.End ℝ (ThreeIndex ι → ℝ) where + toFun x t := x (cycleIndex ι t) + map_add' _ _ := rfl + map_smul' _ _ := rfl + +@[simp] lemma cycleMap_apply {ι : Type*} (x : ThreeIndex ι → ℝ) (i j k : ι) : + cycleMap ι x ((i,j),k) = x ((j,k),i) := rfl + +@[simp] lemma cycleMap_cube {ι : Type*} (x : ThreeIndex ι → ℝ) : + cycleMap ι (cycleMap ι (cycleMap ι x)) = x := rfl + +lemma cycleMap_dot {ι : Type*} [Fintype ι] (x y : ThreeIndex ι → ℝ) : + dotProduct (cycleMap ι x) (cycleMap ι y) = dotProduct x y := by + exact (cycleIndex ι).sum_comp (fun t => x t * y t) + +lemma cycleMap_adjoint {ι : Type*} [Fintype ι] (x y : ThreeIndex ι → ℝ) : + dotProduct (cycleMap ι x) y = dotProduct x (cycleMap ι (cycleMap ι y)) := by + simpa only [cycleMap_cube] using cycleMap_dot x (cycleMap ι (cycleMap ι y)) + +def cyclicSum (ι : Type*) : Module.End ℝ (ThreeIndex ι → ℝ) := + LinearMap.id + cycleMap ι + (cycleMap ι).comp (cycleMap ι) + +@[simp] lemma cyclicSum_apply {ι : Type*} (x : ThreeIndex ι → ℝ) : + cyclicSum ι x = x + cycleMap ι x + cycleMap ι (cycleMap ι x) := rfl + +lemma cyclicSum_dot {ι : Type*} [Fintype ι] (x y : ThreeIndex ι → ℝ) : + dotProduct (cyclicSum ι x) (cyclicSum ι y) = + 3 * (dotProduct x y + dotProduct x (cycleMap ι y) + + dotProduct x (cycleMap ι (cycleMap ι y))) := by + simp only [cyclicSum_apply, add_dotProduct, dotProduct_add, + cycleMap_adjoint, cycleMap_cube] + ring + +lemma pairSpectatorInclusion_antisymmetric {Q : ℕ} (hQ : 2 ≤ Q) + (a : (Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) (i j k : Fin (Q+1)) : + (pairSpectatorInclusion hQ).toLinearMap a ((j,i),k) = + -(pairSpectatorInclusion hQ).toLinearMap a ((i,j),k) := by + simp only [pairSpectatorInclusion_apply, pairCoefficient_swap Q _ j i, + neg_mul, Finset.sum_neg_distrib, neg_neg] + +lemma pairSpectatorInclusion_isometry {Q : ℕ} (hQ : 2 ≤ Q) + (a b : (Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) : + dotProduct ((pairSpectatorInclusion hQ).toLinearMap a) + ((pairSpectatorInclusion hQ).toLinearMap b) = dotProduct a b := by + have hab (p r : Fin (2*Q-2+1)) : + (∑ i : Fin (Q+1), ∑ j : Fin (Q+1), + pairCoefficient Q p.val i j * pairCoefficient Q r.val i j) = + if p=r then 1 else 0 := by + split_ifs with hh + · subst r + simpa only [← sq] using pairCoefficient_sum_sq Q p.val hQ (by omega) + · exact pairCoefficient_sum_mul_of_ne Q p.val r.val (fun he => hh (Fin.ext he)) + classical + have hfixed (aa bb : Fin (2*Q-2+1) → ℝ) : + (∑ i : Fin (Q+1), ∑ j : Fin (Q+1), + (∑ p, pairCoefficient Q p.val i j * aa p) * + (∑ r, pairCoefficient Q r.val i j * bb r)) = ∑ p, aa p * bb p := by + simp_rw [Finset.sum_mul] + simp_rw [Finset.mul_sum] + let f := fun (i j : Fin (Q+1)) (p r : Fin (2*Q-2+1)) => + pairCoefficient Q p.val i j * aa p * (pairCoefficient Q r.val i j * bb r) + change (∑ i, ∑ j, ∑ p, ∑ r, f i j p r) = _ + calc + _ = ∑ i, ∑ p, ∑ j, ∑ r, f i j p r := by + apply Finset.sum_congr rfl + intro i hi + exact Finset.sum_comm + _ = ∑ p, ∑ i, ∑ j, ∑ r, f i j p r := Finset.sum_comm + _ = ∑ p, ∑ i, ∑ r, ∑ j, f i j p r := by + apply Finset.sum_congr rfl + intro p hp + apply Finset.sum_congr rfl + intro i hi + exact Finset.sum_comm + _ = ∑ p, ∑ r, ∑ i, ∑ j, f i j p r := by + apply Finset.sum_congr rfl + intro p hp + exact Finset.sum_comm + _ = ∑ p, ∑ r, (∑ i, ∑ j, + pairCoefficient Q p.val i j * pairCoefficient Q r.val i j) * (aa p * bb r) := by + simp only [Finset.sum_mul] + apply Finset.sum_congr rfl + intro p hp + apply Finset.sum_congr rfl + intro r hr + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + dsimp [f] + ring + _ = _ := by simp [hab] + simp only [dotProduct, Fintype.sum_prod_type, pairSpectatorInclusion_apply] + let f := fun (i j k : Fin (Q+1)) => + (∑ p : Fin (2*Q-2+1), pairCoefficient Q p.val i j * a (p,k)) * + (∑ r : Fin (2*Q-2+1), pairCoefficient Q r.val i j * b (r,k)) + change (∑ i, ∑ j, ∑ k, f i j k) = _ + calc + _ = ∑ i, ∑ k, ∑ j, f i j k := by + apply Finset.sum_congr rfl + intro i hi + exact Finset.sum_comm + _ = ∑ k, ∑ i, ∑ j, f i j k := Finset.sum_comm + _ = ∑ k, ∑ p, a (p,k)*b (p,k) := by + apply Finset.sum_congr rfl + intro k hk + exact hfixed (fun p => a (p,k)) (fun p => b (p,k)) + _ = _ := Finset.sum_comm + +noncomputable def orderedThreeWedge {Q : ℕ} (hQ : 2 ≤ Q) : + ((Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) →ₗ[ℝ] + (ThreeIndex (Fin (Q+1)) → ℝ) := + (Real.sqrt 3)⁻¹ • ((cyclicSum (Fin (Q+1))).comp (pairSpectatorInclusion hQ).toLinearMap) + +lemma swap23Linear_adjoint (Q : ℕ) + (x y : ThreeIndex (Fin (Q+1)) → ℝ) : + dotProduct (swap23Linear Q x) y = dotProduct x (swap23Linear Q y) := by + let e : ThreeIndex (Fin (Q+1)) ≃ ThreeIndex (Fin (Q+1)) := { + toFun := fun t => ((t.1.1,t.2),t.1.2) + invFun := fun t => ((t.1.1,t.2),t.1.2) + left_inv := fun _ => rfl + right_inv := fun _ => rfl } + exact e.sum_comp (fun t => x t * swap23Linear Q y t) + +lemma cycleSquare_pairSpectatorInclusion {Q : ℕ} (hQ : 2 ≤ Q) + (a : (Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) : + cycleMap (Fin (Q+1)) (cycleMap (Fin (Q+1)) + ((pairSpectatorInclusion hQ).toLinearMap a)) = + -(swap23Linear Q ((pairSpectatorInclusion hQ).toLinearMap a)) := by + funext ⟨⟨i,j⟩,k⟩ + exact pairSpectatorInclusion_antisymmetric hQ a i k j + +lemma cyclicSum_pair_dot {Q : ℕ} (hQ : 2 ≤ Q) + (a b : (Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) : + dotProduct (cyclicSum (Fin (Q+1)) ((pairSpectatorInclusion hQ).toLinearMap a)) + (cyclicSum (Fin (Q+1)) ((pairSpectatorInclusion hQ).toLinearMap b)) = + 3 * (dotProduct a b - 2 * dotProduct a ((compressedSwap hQ).toLinearMap b)) := by + have hab : dotProduct ((pairSpectatorInclusion hQ).toLinearMap a) + (swap23Linear Q ((pairSpectatorInclusion hQ).toLinearMap b)) = + dotProduct a ((compressedSwap hQ).toLinearMap b) := + transposeMap_adjoint (pairSpectatorInclusion hQ).toLinearMap a _ + have hc : dotProduct ((pairSpectatorInclusion hQ).toLinearMap a) + (cycleMap (Fin (Q+1)) ((pairSpectatorInclusion hQ).toLinearMap b)) = + - dotProduct a ((compressedSwap hQ).toLinearMap b) := by + rw [dotProduct_comm, cycleMap_adjoint, + cycleSquare_pairSpectatorInclusion, dotProduct_neg, dotProduct_comm, + swap23Linear_adjoint, hab] + rw [cyclicSum_dot, pairSpectatorInclusion_isometry, hc, + cycleSquare_pairSpectatorInclusion, dotProduct_neg, hab] + ring + +theorem orderedThreeWedge_dot {Q : ℕ} (hQ : 2 ≤ Q) + (a b : (Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) : + dotProduct (orderedThreeWedge hQ a) (orderedThreeWedge hQ b) = + dotProduct a b - 2 * dotProduct a ((compressedSwap hQ).toLinearMap b) := by + simp only [orderedThreeWedge, LinearMap.smul_apply, LinearMap.comp_apply, + smul_dotProduct, dotProduct_smul, smul_eq_mul, cyclicSum_pair_dot] + have hs : (Real.sqrt (3 : ℝ))^2 = 3 := Real.sq_sqrt (by norm_num) + have hn : Real.sqrt (3 : ℝ) ≠ 0 := by positivity + field_simp + rw [hs] + +noncomputable def orderedThreeGram {Q : ℕ} (hQ : 2 ≤ Q) : + Module.End ℝ ((Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) := + (transposeMap (orderedThreeWedge hQ)).comp (orderedThreeWedge hQ) + +theorem orderedThreeGram_apply {Q : ℕ} (hQ : 2 ≤ Q) + (a : (Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) : + orderedThreeGram hQ a = a - (2 : ℝ) • (compressedSwap hQ).toLinearMap a := by + apply eq_of_dotProduct_eq + intro b + change dotProduct b (transposeMap (orderedThreeWedge hQ) (orderedThreeWedge hQ a)) = _ + rw [← transposeMap_adjoint, orderedThreeWedge_dot, + dotProduct_sub, dotProduct_smul, smul_eq_mul] + +theorem orderedThreeGram_eigenvalue {Q z l : ℕ} (hQ : 2 ≤ Q) + (hz : z ≤ Q) (hl : l ≤ (2*Q-2)+Q-2*z) : + orderedThreeGram hQ (coupledTensor (2*Q-2) Q z l) = + (1+threeBodyGramCoefficient Q z) • coupledTensor (2*Q-2) Q z l := by + rw [orderedThreeGram_apply, compressedSwap_eigenvalue hQ hz hl] + funext pq + simp only [Pi.sub_apply, Pi.smul_apply, smul_eq_mul] + ring + +theorem orderedThreeGram_defect_expansion {Q : ℕ} (hQ : 2 ≤ Q) + (a : (Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) : + orderedThreeGram hQ a - a = + ∑ i : CoupledIndex (2*Q-2) Q, + (threeBodyGramCoefficient Q i.1.val * + dotProduct (coupledTensor (2*Q-2) Q i.1.val i.2.val) a) • + coupledTensor (2*Q-2) Q i.1.val i.2.val := by + let D := orderedThreeGram hQ - LinearMap.id + change D a = _ + conv_lhs => rw [← coupledTensor_expansion (2*Q-2) Q a] + rw [map_sum] + apply Finset.sum_congr rfl + intro i hi + rw [map_smul] + dsimp [D] + rw [orderedThreeGram_eigenvalue hQ (by have := i.1.isLt; omega) + (Nat.le_of_lt_succ i.2.isLt)] + funext pq + simp only [Pi.sub_apply, Pi.smul_apply, smul_eq_mul] + ring + +lemma threeBodyGramCoefficient_zero (Q : ℕ) : threeBodyGramCoefficient Q 0 = -1 := by + norm_num [threeBodyGramCoefficient, fallingRatio] + +lemma threeBodyGramCoefficient_one {Q : ℕ} (hQ : 2 ≤ Q) : + threeBodyGramCoefficient Q 1 = -1 := by + have hq : (2 : ℝ) ≤ Q := by exact_mod_cast hQ + have hq0 : (Q : ℝ) ≠ 0 := by linarith + have hd : (Q : ℝ)-1 ≠ 0 := by linarith + simp only [threeBodyGramCoefficient, fallingRatio, Nat.descFactorial_one, + Nat.cast_sub (by omega : 2 ≤ 2*Q)] + push_cast + field_simp + ring + +lemma threeBodyGramCoefficient_three {Q : ℕ} (hQ : 3 ≤ Q) : + threeBodyGramCoefficient Q 3 = -1 := by + have hq : (3 : ℝ) ≤ Q := by exact_mod_cast hQ + have hq0 : (Q : ℝ) ≠ 0 := by linarith + have h1 : (Q : ℝ)-1 ≠ 0 := by linarith + have h2 : (Q : ℝ)-1-1 ≠ 0 := by linarith + have h3 : ((Q : ℝ)-1)*2-1 ≠ 0 := by linarith + rw [threeBodyGramCoefficient, fallingRatio_eq_prod] + norm_num [Finset.prod_range_succ, Nat.cast_sub (by omega : 2 ≤ Q), + Nat.cast_sub (by omega : 1 ≤ Q), Nat.cast_sub (by omega : 2 ≤ 2*Q), + Nat.cast_sub (by omega : 1 ≤ 2*Q-2), Nat.cast_sub (by omega : 2 ≤ 2*Q-2)] + field_simp + ring + +theorem orderedThreeWedge_null {Q z l : ℕ} (hQ : 2 ≤ Q) + (hz : z ≤ Q) (hl : l ≤ (2*Q-2)+Q-2*z) (hn : z=0 ∨ z=1 ∨ z=3) : + orderedThreeWedge hQ (coupledTensor (2*Q-2) Q z l) = 0 := by + have hq : threeBodyGramCoefficient Q z = -1 := by + rcases hn with rfl | rfl | rfl + · exact threeBodyGramCoefficient_zero Q + · exact threeBodyGramCoefficient_one hQ + · exact threeBodyGramCoefficient_three hz + apply dotProduct_self_eq_zero.mp + rw [transposeMap_adjoint] + change dotProduct (coupledTensor (2*Q-2) Q z l) + (orderedThreeGram hQ (coupledTensor (2*Q-2) Q z l)) = 0 + rw [orderedThreeGram_eigenvalue hQ hz hl, hq] + simp + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/ThreeSpectrum.lean b/lean/OAI/Analysis/LaughlinGap/ThreeSpectrum.lean new file mode 100644 index 0000000000000000000000000000000000000000..c252277f5ee4735976a17df3b0f1047b8dff49a2 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/ThreeSpectrum.lean @@ -0,0 +1,202 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.HighestRatios +import OAI.Analysis.LaughlinGap.PairEndpoints +import OAI.Analysis.LaughlinGap.ThreeSpin + +namespace OAI + +/-! Three Spectrum. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators + +lemma pairSpectatorInclusion_transpose_apply {Q : ℕ} (hQ : 2 ≤ Q) + (x : ((Fin (Q+1) × Fin (Q+1)) × Fin (Q+1)) → ℝ) + (p : Fin (2*Q-2+1)) (k : Fin (Q+1)) : + (pairSpectatorInclusion hQ).transpose.toLinearMap x (p,k) = + ∑ i : Fin (Q+1), ∑ j : Fin (Q+1), pairCoefficient Q p.val i j * x ((i,j),k) := by + classical + change transposeMap (pairSpectatorInclusion hQ).toLinearMap x (p,k) = _ + simp only [transposeMap, LinearMap.coe_mk, AddHom.coe_mk, Fintype.sum_prod_type] + simp_rw [pairSpectatorInclusion_apply] + simp only [Prod.mk.injEq, ite_and, mul_ite, mul_one, mul_zero, Finset.sum_ite_eq] + simp + +lemma compressedSwap_apply {Q : ℕ} (hQ : 2 ≤ Q) + (a : (Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) + (p : Fin (2*Q-2+1)) (k : Fin (Q+1)) : + (compressedSwap hQ).toLinearMap a (p,k) = + ∑ i : Fin (Q+1), ∑ j : Fin (Q+1), pairCoefficient Q p.val i j * + (∑ b : Fin (2*Q-2+1), pairCoefficient Q b.val i k * a (b,j)) := by + change (pairSpectatorInclusion hQ).transpose.toLinearMap + ((swap23 Q).toLinearMap ((pairSpectatorInclusion hQ).toLinearMap a)) (p,k) = _ + rw [pairSpectatorInclusion_transpose_apply] + apply Finset.sum_congr rfl + intro i hi + apply Finset.sum_congr rfl + intro j hj + congr 1 + exact pairSpectatorInclusion_apply hQ a i k j + +lemma pairCoefficient_zero_contract {Q : ℕ} (hQ : 2 ≤ Q) + (f : Fin (Q+1) → Fin (Q+1) → ℝ) : + (∑ i : Fin (Q+1), ∑ j : Fin (Q+1), pairCoefficient Q 0 i j * f i j) = + (f ⟨1,by omega⟩ 0 - f 0 ⟨1,by omega⟩)/Real.sqrt 2 := by + have hneq : (⟨1,by omega⟩ : Fin (Q+1)) ≠ 0 := by + intro h; have := congrArg Fin.val h; simp at this + have hc (i j : Fin (Q+1)) : pairCoefficient Q 0 i j = + (if i=⟨1,by omega⟩ ∧ j=0 then 1/Real.sqrt 2 else 0) + + (if i=0 ∧ j=⟨1,by omega⟩ then -1/Real.sqrt 2 else 0) := by + rw [pairCoefficient_zero_formula hQ] + by_cases h1 : i=⟨1,by omega⟩ ∧ j=0 + · obtain ⟨rfl,rfl⟩ := h1 + simp [hneq] + · simp [h1] + simp_rw [hc, add_mul, Finset.sum_add_distrib, ite_and, ite_mul, zero_mul, + Finset.sum_ite_irrel] + simp only [Finset.sum_const_zero, Finset.sum_ite_eq', Finset.mem_univ, ite_true] + ring + +lemma pairSpectatorInclusion_highest {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) + (i j k : Fin (Q+1)) (hk : k.val ≤ z) : + (pairSpectatorInclusion hQ).toLinearMap (highestTensor (2*Q-2) Q z) ((i,j),k) = + pairCoefficient Q (z-k.val) i j * highestCoefficient (2*Q-2) Q z (z-k.val) := by + classical + let p : Fin (2*Q-2+1) := ⟨z-k.val,by omega⟩ + rw [pairSpectatorInclusion_apply] + calc + _ = pairCoefficient Q p.val i j * highestTensor (2*Q-2) Q z (p,k) := by + apply Finset.sum_eq_single p + · intro q hq hqp + have hne : q.val+k.val ≠ z := by + intro hs + apply hqp + apply Fin.ext + dsimp [p] + omega + simp [highestTensor, hne] + · simp + _ = _ := by simp [p, highestTensor, Nat.sub_add_cancel hk] + +theorem swapScalar_coordinate {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + highestCoefficient (2*Q-2) Q z 0 * swapScalar Q z hQ = + (((pairSpectatorInclusion hQ).toLinearMap (highestTensor (2*Q-2) Q z) + ((⟨1,by omega⟩,⟨z,by omega⟩),0)) - + ((pairSpectatorInclusion hQ).toLinearMap (highestTensor (2*Q-2) Q z) + ((0,⟨z,by omega⟩),⟨1,by omega⟩)))/Real.sqrt 2 := by + have h := congrFun (compressedSwap_eigenvector hQ hz (by omega : 0 ≤ (2*Q-2)+Q-2*z)) + ((0 : Fin (2*Q-2+1)), (⟨z,by omega⟩ : Fin (Q+1))) + rw [coupledTensor_zero, compressedSwap_apply] at h + simp only [Pi.smul_apply, smul_eq_mul, highestTensor, Fin.val_zero, + Nat.zero_add, ite_true] at h + rw [mul_comm] + rw [← h, pairCoefficient_zero_contract hQ] + simp only [pairSpectatorInclusion_apply, highestTensor] + +lemma fallingRatio_penultimate {Q a : ℕ} (hQ : 2 ≤ Q) (ha : a+1 ≤ Q) : + (((a : ℝ)+1)*((Q-1).descFactorial a : ℝ) / ((2*Q-2).descFactorial a : ℝ)) = + fallingRatio Q (a+1) * ((a : ℝ)+1) * (2*(Q : ℝ)-2-a)/(Q : ℝ) := by + have hq : (0 : ℝ) < Q := by exact_mod_cast (by omega : 0 < Q) + have hd : 0 < ((2*Q-2).descFactorial a : ℝ) := by + exact_mod_cast Nat.descFactorial_pos.mpr (by omega : a ≤ 2*Q-2) + have hf : 0 < 2*(Q : ℝ)-2-a := by + have hqa : (a : ℝ)+1 ≤ Q := by exact_mod_cast ha + have hQ' : (2 : ℝ) ≤ Q := by exact_mod_cast hQ + linarith + unfold fallingRatio + rw [show Q.descFactorial (a+1) = Q * (Q-1).descFactorial a by + simpa only [Nat.sub_add_cancel (by omega : 1 ≤ Q)] using + Nat.succ_descFactorial_succ (Q-1) a] + rw [Nat.descFactorial_succ, Nat.cast_mul, Nat.cast_mul, + Nat.cast_sub (by omega : a ≤ 2*Q-2), Nat.cast_sub (by omega : 2 ≤ 2*Q)] + push_cast + field_simp + rw [mul_div_cancel_right₀ _ (by linarith : 2*((Q : ℝ)-1)-a ≠ 0)] + +lemma swapScalar_succ {Q a : ℕ} (hQ : 2 ≤ Q) (ha : a+1 ≤ Q) : + swapScalar Q (a+1) hQ = -(threeBodyGramCoefficient Q (a+1))/2 := by + have hz : a+1 ≤ min (2*Q-2) Q := by omega + have hs0 := highestCoefficient_zero_ne hz + have hf : 0 ≤ fallingRatio Q (a+1) := by unfold fallingRatio; positivity + have hg : 0 ≤ ((a : ℝ)+1)*((Q-1).descFactorial a : ℝ) / + ((2*Q-2).descFactorial a : ℝ) := by positivity + have ht : Real.sqrt (2 : ℝ) ≠ 0 := by positivity + have hs := swapScalar_coordinate hQ ha + rw [pairSpectatorInclusion_highest hQ ha _ _ _ (by simp), + pairSpectatorInclusion_highest hQ ha _ _ _ (by simp)] at hs + simp only [Fin.val_zero, Nat.sub_zero, Nat.add_sub_cancel] at hs + rw [pairCoefficient_one hQ ha, pairCoefficient_zero_succ hQ ha, + highestCoefficient_last hz] at hs + have hp := highestCoefficient_penultimate hz (by omega : 0 < a+1) + simp only [Nat.add_sub_cancel, Nat.cast_add, Nat.cast_one] at hp + rw [hp, ← fallingRatio] at hs + simp only [Nat.cast_add, Nat.cast_one] at hs + have hsqf := Real.sq_sqrt hf + have hsqg := Real.sq_sqrt hg + have hsq2 := Real.sq_sqrt (by norm_num : (0 : ℝ) ≤ 2) + have he : highestCoefficient (2*Q-2) Q (a+1) 0 * swapScalar Q (a+1) hQ = + highestCoefficient (2*Q-2) Q (a+1) 0 * + (((-1 : ℝ)^(a+1)* (1-((a : ℝ)+1))*fallingRatio Q (a+1) + + (-1 : ℝ)^a * (((a : ℝ)+1)*((Q-1).descFactorial a : ℝ) / + ((2*Q-2).descFactorial a : ℝ)))/2) := by + rw [hs] + calc + _ = highestCoefficient (2*Q-2) Q (a+1) 0 * + (((-1 : ℝ)^(a+1)* (1-((a : ℝ)+1))*(Real.sqrt (fallingRatio Q (a+1)))^2 + + (-1 : ℝ)^a * (Real.sqrt (((a : ℝ)+1)*((Q-1).descFactorial a : ℝ) / + ((2*Q-2).descFactorial a : ℝ)))^2)/(Real.sqrt 2)^2) := by ring + _ = _ := by rw [hsqf, hsqg, hsq2] + apply (mul_left_cancel₀ hs0) at he + rw [he, fallingRatio_penultimate hQ ha, threeBodyGramCoefficient] + push_cast + rw [pow_succ] + have hq : (Q : ℝ) ≠ 0 := by positivity + field_simp + ring + +lemma pairSpectatorInclusion_highest_eq_zero {Q z : ℕ} (hQ : 2 ≤ Q) + (i j k : Fin (Q+1)) (hk : z < k.val) : + (pairSpectatorInclusion hQ).toLinearMap (highestTensor (2*Q-2) Q z) ((i,j),k) = 0 := by + rw [pairSpectatorInclusion_apply] + apply Finset.sum_eq_zero + intro p hp + simp [highestTensor, show p.val+k.val ≠ z by omega] + +@[simp] lemma highestCoefficient_zero_zero (n m : ℕ) : highestCoefficient n m 0 0 = 1 := by + simp [highestCoefficient, highestNormalization, highestWeight] + +lemma swapScalar_zero {Q : ℕ} (hQ : 2 ≤ Q) : swapScalar Q 0 hQ = 1/2 := by + have h := swapScalar_coordinate hQ (Nat.zero_le Q) + rw [pairSpectatorInclusion_highest hQ (Nat.zero_le Q) _ _ _ (by simp), + pairSpectatorInclusion_highest_eq_zero hQ _ _ _ (by simp)] at h + simp only [Fin.val_zero, Nat.sub_zero, highestCoefficient_zero_zero, mul_one, one_mul, + Fin.mk_zero, sub_zero] at h + have hc := pairCoefficient_one hQ (Nat.zero_le Q) + simp only [Fin.mk_zero] at hc + rw [hc] at h + simp only [fallingRatio, Nat.descFactorial_zero, Nat.cast_one, Nat.cast_zero, + div_one, Real.sqrt_one, sub_zero, mul_one] at h + rw [h, div_div, ← pow_two, Real.sq_sqrt (by norm_num : (0 : ℝ) ≤ 2)] + +theorem swapScalar_eq {Q z : ℕ} (hQ : 2 ≤ Q) (hz : z ≤ Q) : + swapScalar Q z hQ = -(threeBodyGramCoefficient Q z)/2 := by + cases z with + | zero => + rw [swapScalar_zero hQ] + norm_num [threeBodyGramCoefficient, fallingRatio] + | succ a => exact swapScalar_succ hQ hz + +theorem compressedSwap_eigenvalue {Q z l : ℕ} (hQ : 2 ≤ Q) + (hz : z ≤ Q) (hl : l ≤ (2*Q-2)+Q-2*z) : + (compressedSwap hQ).toLinearMap (coupledTensor (2*Q-2) Q z l) = + (-(threeBodyGramCoefficient Q z)/2) • coupledTensor (2*Q-2) Q z l := by + rw [compressedSwap_eigenvector hQ hz hl, swapScalar_eq hQ hz] + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/ThreeSpin.lean b/lean/OAI/Analysis/LaughlinGap/ThreeSpin.lean new file mode 100644 index 0000000000000000000000000000000000000000..01157ea6aab3c50ad17826f41bf7e2a24db961a8 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/ThreeSpin.lean @@ -0,0 +1,146 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.IntertwiningSpin +import OAI.Analysis.LaughlinGap.PairSpin + +namespace OAI + +/-! Three Spin. -/ + +noncomputable section + + +namespace LaughlinGap.Spin +open scoped BigOperators + +noncomputable def onFirstMap {ι κ σ : Type*} (A : (ι → ℝ) →ₗ[ℝ] (κ → ℝ)) : + ((ι × σ) → ℝ) →ₗ[ℝ] ((κ × σ) → ℝ) where + toFun x pq := A (fun i => x (i,pq.2)) pq.1 + map_add' x y := by + funext ⟨p,q⟩ + exact congrFun (A.map_add (fun i => x (i,q)) (fun i => y (i,q))) p + map_smul' r x := by + funext ⟨p,q⟩ + exact congrFun (A.map_smul r (fun i => x (i,q))) p + +@[simp] lemma onFirstMap_apply {ι κ σ : Type*} (A : (ι → ℝ) →ₗ[ℝ] (κ → ℝ)) + (x : (ι × σ) → ℝ) (p : κ) (q : σ) : + onFirstMap A x (p,q) = A (fun i => x (i,q)) p := rfl + +lemma onFirstMap_onSecond {ι κ σ : Type*} [Fintype ι] + (A : (ι → ℝ) →ₗ[ℝ] (κ → ℝ)) (B : Module.End ℝ (σ → ℝ)) (x : (ι × σ) → ℝ) : + onFirstMap A (onSecondEnd B x) = onSecondEnd B (onFirstMap A x) := by + classical + funext ⟨p,q⟩ + simp only [onFirstMap_apply, onSecondEnd_apply] + have hfun : (fun j => A (fun i => x (i,j)) p) = + ∑ i : ι, (A (fun k => if i = k then 1 else 0) p) • (fun j => x (i,j)) := by + funext j + rw [A.pi_apply_eq_sum_univ (fun i => x (i,j))] + simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul] + apply Finset.sum_congr rfl + intro i hi + ring + rw [hfun, map_sum, A.pi_apply_eq_sum_univ (fun i => B (fun j => x (i,j)) q)] + simp only [Finset.sum_apply, map_smul, Pi.smul_apply, smul_eq_mul] + apply Finset.sum_congr rfl + intro i hi + ring + +noncomputable def LadderMap.tensorRight {ι κ σ : Type*} + [Fintype ι] [Fintype κ] [Fintype σ] + {S : LadderSystem ι} {T : LadderSystem κ} + (A : LadderMap S T) (U : LadderSystem σ) : LadderMap (S.tensor U) (T.tensor U) where + toLinearMap := onFirstMap A.toLinearMap + lower x := by + change onFirstEnd T.lower (onFirstMap A.toLinearMap x) + + onSecondEnd U.lower (onFirstMap A.toLinearMap x) = + onFirstMap A.toLinearMap (onFirstEnd S.lower x + onSecondEnd U.lower x) + rw [map_add, ← onFirstMap_onSecond] + congr 1 + funext ⟨p,q⟩ + exact congrFun (A.lower (fun i => x (i,q))) p + raise x := by + change onFirstEnd T.raise (onFirstMap A.toLinearMap x) + + onSecondEnd U.raise (onFirstMap A.toLinearMap x) = + onFirstMap A.toLinearMap (onFirstEnd S.raise x + onSecondEnd U.raise x) + rw [map_add, ← onFirstMap_onSecond] + congr 1 + funext ⟨p,q⟩ + exact congrFun (A.raise (fun i => x (i,q))) p + +noncomputable def tripleSpin (Q : ℕ) := + (tensorSpin Q Q).tensor (standardLadderSystem Q) + +def swap23Linear (Q : ℕ) : Module.End ℝ (((Fin (Q+1) × Fin (Q+1)) × Fin (Q+1)) → ℝ) where + toFun x ijk := x ((ijk.1.1,ijk.2),ijk.1.2) + map_add' _ _ := rfl + map_smul' _ _ := rfl + +noncomputable def swap23 (Q : ℕ) : LadderMap (tripleSpin Q) (tripleSpin Q) where + toLinearMap := swap23Linear Q + lower x := by + funext ⟨⟨i,j⟩,k⟩ + change lowering Q (fun i => x ((i,k),j)) i + + lowering Q (fun j => x ((i,k),j)) j + lowering Q (fun k => x ((i,k),j)) k = + lowering Q (fun i => x ((i,k),j)) i + + lowering Q (fun k => x ((i,k),j)) k + lowering Q (fun j => x ((i,k),j)) j + ring + raise x := by + funext ⟨⟨i,j⟩,k⟩ + change raising Q (fun i => x ((i,k),j)) i + + raising Q (fun j => x ((i,k),j)) j + raising Q (fun k => x ((i,k),j)) k = + raising Q (fun i => x ((i,k),j)) i + + raising Q (fun k => x ((i,k),j)) k + raising Q (fun j => x ((i,k),j)) j + ring + +noncomputable def pairInclusion {Q : ℕ} (hQ : 2 ≤ Q) : + LadderMap (standardLadderSystem (2*Q-2)) (tensorSpin Q Q) := + (tensorSpin Q Q).embeddingMap + (show (tensorSpin Q Q).weight (highestTensor Q Q 1) = + ((2*Q-2 : ℕ) : ℝ) • highestTensor Q Q 1 by + have h := highestTensor_weight (n := Q) (m := Q) (z := 1) (by omega : 1 ≤ min Q Q) + simpa only [mul_one, ← two_mul] using h) + (highestTensor_raise (by omega : 1 ≤ min Q Q)) + +lemma pairInclusion_apply {Q : ℕ} (hQ : 2 ≤ Q) (a : Fin (2*Q-2+1) → ℝ) : + (pairInclusion hQ).toLinearMap a = + ∑ p : Fin (2*Q-2+1), a p • physicalPairTensor Q p.val := by + simp only [pairInclusion, LadderSystem.embeddingMap, LadderSystem.embedding_apply] + apply Finset.sum_congr rfl + intro p hp + rw [physicalPairTensor_eq_coupled hQ (Nat.le_of_lt_succ p.isLt), + coupledTensor_eq_normalized (by omega : 1 ≤ min Q Q) (by omega : p.val ≤ Q+Q-2*1)] + congr 2 + omega + +noncomputable def pairSpectatorInclusion {Q : ℕ} (hQ : 2 ≤ Q) : + LadderMap (tensorSpin (2*Q-2) Q) (tripleSpin Q) := + (pairInclusion hQ).tensorRight (standardLadderSystem Q) + +lemma pairSpectatorInclusion_apply {Q : ℕ} (hQ : 2 ≤ Q) + (a : (Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) (i j k : Fin (Q+1)) : + (pairSpectatorInclusion hQ).toLinearMap a ((i,j),k) = + ∑ p : Fin (2*Q-2+1), pairCoefficient Q p.val i j * a (p,k) := by + change (pairInclusion hQ).toLinearMap (fun p => a (p,k)) (i,j) = _ + rw [pairInclusion_apply] + simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul, physicalPairTensor, mul_comm] + +noncomputable def compressedSwap {Q : ℕ} (hQ : 2 ≤ Q) : + LadderMap (tensorSpin (2*Q-2) Q) (tensorSpin (2*Q-2) Q) := + (pairSpectatorInclusion hQ).transpose.comp ((swap23 Q).comp (pairSpectatorInclusion hQ)) + +noncomputable def swapScalar (Q z : ℕ) (hQ : 2 ≤ Q) : ℝ := + dotProduct (highestTensor (2*Q-2) Q z) + ((compressedSwap hQ).toLinearMap (highestTensor (2*Q-2) Q z)) + +theorem compressedSwap_eigenvector {Q z l : ℕ} (hQ : 2 ≤ Q) + (hz : z ≤ Q) (hl : l ≤ (2*Q-2)+Q-2*z) : + (compressedSwap hQ).toLinearMap (coupledTensor (2*Q-2) Q z l) = + swapScalar Q z hQ • coupledTensor (2*Q-2) Q z l := by + exact tensorSpin_schur (by omega : z ≤ min (2*Q-2) Q) hl (compressedSwap hQ) + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/WedgeIdentification.lean b/lean/OAI/Analysis/LaughlinGap/WedgeIdentification.lean new file mode 100644 index 0000000000000000000000000000000000000000..a64be0f74c1341418a667a46ec707099ecd4860c --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/WedgeIdentification.lean @@ -0,0 +1,412 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.Creation +import OAI.Analysis.LaughlinGap.ThreeGram + +namespace OAI + +/-! Wedge Identification. -/ + +noncomputable section + + +namespace LaughlinGap.Occupation +open scoped BigOperators InnerProduct + +@[simp] lemma annihilation_vacuum {n : ℕ} (i : Fin n) : + annihilation i (vacuum n) = 0 := by + have h := word_eq_zero_of_degree_lt [i] (vacuum_homogeneous n) (by simp) + simpa only [word_cons, word_nil, one_mul] using h + +lemma annihilation_creation_apply {n : ℕ} (i j : Fin n) (x : Hilbert n) : + annihilation i (creation j x) = (if i=j then x else 0) - creation j (annihilation i x) := by + have h := congrArg (fun A : Module.End ℂ (Hilbert n) => A x) + (annihilation_creation_CAR i j) + simp only [LinearMap.add_apply, LinearMap.comp_apply] at h + convert eq_sub_of_add_eq h using 2 + split_ifs <;> simp only [LinearMap.id_apply, LinearMap.zero_apply] + +lemma annihilation_creation_vacuum {n : ℕ} (i j : Fin n) : + annihilation i (creation j (vacuum n)) = if i=j then vacuum n else 0 := by + rw [annihilation_creation_apply, annihilation_vacuum, map_zero, sub_zero] + +lemma double_creation_vacuum {n : ℕ} (i x y : Fin n) : + annihilation i (creation x (creation y (vacuum n))) = + (if i=x then creation y (vacuum n) else 0) - + (if i=y then creation x (vacuum n) else 0) := by + rw [annihilation_creation_apply, annihilation_creation_vacuum] + congr 1 + split_ifs <;> simp + +lemma triple_creation_vacuum {n : ℕ} (i x y z : Fin n) : + annihilation i (creation x (creation y (creation z (vacuum n)))) = + (if i=x then creation y (creation z (vacuum n)) else 0) - + (if i=y then creation x (creation z (vacuum n)) else 0) + + (if i=z then creation x (creation y (vacuum n)) else 0) := by + rw [annihilation_creation_apply, double_creation_vacuum, map_sub] + have h₁ : creation x (if i=y then creation z (vacuum n) else 0) = + if i=y then creation x (creation z (vacuum n)) else 0 := by + split_ifs <;> simp + have h₂ : creation x (if i=z then creation y (vacuum n) else 0) = + if i=z then creation x (creation y (vacuum n)) else 0 := by + split_ifs <;> simp + rw [h₁,h₂] + abel + +def orbitalDelta {n : ℕ} (i j : Fin n) : ℂ := if i=j then 1 else 0 + +lemma orbitalDelta_smul {n : ℕ} (i j : Fin n) (x : Hilbert n) : + orbitalDelta i j • x = if i=j then x else 0 := by + simp [orbitalDelta, ite_smul] + +lemma annihilation_creation_vacuum_delta {n : ℕ} (i j : Fin n) : + annihilation i (creation j (vacuum n)) = orbitalDelta i j • vacuum n := by + rw [orbitalDelta_smul, annihilation_creation_vacuum] + +lemma double_creation_vacuum_delta {n : ℕ} (i x y : Fin n) : + annihilation i (creation x (creation y (vacuum n))) = + orbitalDelta i x • creation y (vacuum n) - + orbitalDelta i y • creation x (vacuum n) := by + simp only [orbitalDelta_smul, double_creation_vacuum] + +lemma triple_creation_vacuum_delta {n : ℕ} (i x y z : Fin n) : + annihilation i (creation x (creation y (creation z (vacuum n)))) = + orbitalDelta i x • creation y (creation z (vacuum n)) - + orbitalDelta i y • creation x (creation z (vacuum n)) + + orbitalDelta i z • creation x (creation y (vacuum n)) := by + simp only [orbitalDelta_smul, triple_creation_vacuum] + +lemma word_three_creation_vacuum {n : ℕ} (i j k x y z : Fin n) : + word [i,j,k] (creation x (creation y (creation z (vacuum n)))) ∅ = + orbitalDelta i x * (orbitalDelta j y * orbitalDelta k z - + orbitalDelta j z * orbitalDelta k y) - + orbitalDelta i y * (orbitalDelta j x * orbitalDelta k z - + orbitalDelta j z * orbitalDelta k x) + + orbitalDelta i z * (orbitalDelta j x * orbitalDelta k y - + orbitalDelta j y * orbitalDelta k x) := by + simp only [word_cons, word_nil, one_mul, Module.End.mul_apply, + triple_creation_vacuum_delta, map_add, map_sub, map_smul, + double_creation_vacuum_delta, annihilation_creation_vacuum_delta, + PiLp.add_apply, PiLp.sub_apply, PiLp.smul_apply, smul_eq_mul, vacuum_apply, + ite_true, mul_one] + +lemma sum_increasing_pairs_add {n : ℕ} {M : Type*} [AddCommGroup M] + (f : Fin n → Fin n → M) (hs : ∀ i j, f i j = f j i) (hd : ∀ i, f i i = 0) : + (∑ a : PairLabel n, f a.val.1 a.val.2) + + (∑ a : PairLabel n, f a.val.1 a.val.2) = ∑ i, ∑ j, f i j := by + classical + have htri : (∑ a : PairLabel n, f a.val.1 a.val.2) = + ∑ i, ∑ j, if i < j then f i j else 0 := by + rw [← Finset.sum_subtype (Finset.univ.filter (fun a : Fin n × Fin n => a.1 < a.2)) + (by simp) (fun a => f a.1 a.2)] + simp only [Finset.sum_filter, Fintype.sum_prod_type] + have he (i j : Fin n) : f i j = + (if i < j then f i j else 0) + (if j < i then f j i else 0) := by + rcases lt_trichotomy i j with h | h | h + · simp [h, not_lt_of_gt h] + · subst j; simp [hd] + · simp [h, not_lt_of_gt h, hs i j] + rw [htri] + conv_rhs => arg 2; intro i; arg 2; intro j; rw [he i j] + simp only [Finset.sum_add_distrib] + rw [Finset.sum_comm (f := fun i j : Fin n => if j < i then f j i else 0)] + +lemma pairContraction_adjoint_apply {n : ℕ} (v : PairLabel n → ℂ) (x : Hilbert n) : + (pairContraction v).adjoint x = + ∑ a : PairLabel n, v a • creation a.val.1 (creation a.val.2 x) := by + simp only [pairContraction, map_sum, map_smulₛₗ, basicPair, + adjoint_mul, annihilation_adjoint, LinearMap.sum_apply, + LinearMap.smul_apply, Module.End.mul_apply, Complex.star_def, Complex.conj_conj] + +lemma pairContraction_ordered_adjoint {n : ℕ} (c : Fin n → Fin n → ℝ) + (hc : ∀ i j, c j i = -c i j) (x : Hilbert n) : + (pairContraction (fun a : PairLabel n => + ((Real.sqrt 2 * c a.val.1 a.val.2 : ℝ) : ℂ))).adjoint x = + ((Real.sqrt 2)⁻¹ : ℂ) • + ∑ i, ∑ j, (c i j : ℂ) • creation i (creation j x) := by + have hsum := sum_increasing_pairs_add + (fun i j : Fin n => (c i j : ℂ) • creation i (creation j x)) (by + intro i j + have he := congrArg (fun A : Module.End ℂ (Hilbert n) => A x) + (creation_anticommute j i) + simp only [Module.End.mul_apply, LinearMap.neg_apply] at he + rw [hc i j, Complex.ofReal_neg, he, neg_smul, smul_neg, neg_neg]) (by + intro i + have h : c i i = 0 := by have hh := hc i i; linarith + simp [h]) + rw [← hsum, ← two_smul ℂ (∑ a : PairLabel n, + (c a.val.1 a.val.2 : ℂ) • creation a.val.1 (creation a.val.2 x)), smul_smul] + have hs : ((Real.sqrt 2)⁻¹ : ℂ) * 2 = (Real.sqrt 2 : ℂ) := by + have hh : (Real.sqrt 2)^2 = 2 := Real.sq_sqrt (by norm_num) + have hz : Real.sqrt 2 ≠ 0 := Real.sqrt_ne_zero'.mpr (by norm_num) + have hr : (Real.sqrt 2)⁻¹ * 2 = Real.sqrt 2 := by + field_simp + nlinarith + exact_mod_cast hr + rw [hs, pairContraction_adjoint_apply, Finset.smul_sum] + apply Finset.sum_congr rfl + intro a ha + rw [smul_smul, Complex.ofReal_mul] + +lemma sum_orbitalDelta_mul {n : ℕ} (i : Fin n) (f : Fin n → ℂ) : + (∑ j, orbitalDelta i j * f j) = f i := by + simp [orbitalDelta, ite_mul] + +lemma sum_mul_orbitalDelta {n : ℕ} (i : Fin n) (f : Fin n → ℂ) : + (∑ j, f j * orbitalDelta i j) = f i := by + simp [orbitalDelta, mul_ite] + +lemma pair_times_three_determinant {n : ℕ} (c : Fin n → Fin n → ℝ) + (hc : ∀ i j, c j i = -c i j) (i j k l : Fin n) : + (∑ x, ∑ y, (c x y : ℂ) * + (orbitalDelta i x * (orbitalDelta j y * orbitalDelta k l - + orbitalDelta j l * orbitalDelta k y) - + orbitalDelta i y * (orbitalDelta j x * orbitalDelta k l - + orbitalDelta j l * orbitalDelta k x) + + orbitalDelta i l * (orbitalDelta j x * orbitalDelta k y - + orbitalDelta j y * orbitalDelta k x))) = + 2 * ((c i j : ℂ) * orbitalDelta k l + + (c j k : ℂ) * orbitalDelta i l + (c k i : ℂ) * orbitalDelta j l) := by + have he (x y : Fin n) : (c x y : ℂ) * + (orbitalDelta i x * (orbitalDelta j y * orbitalDelta k l - + orbitalDelta j l * orbitalDelta k y) - + orbitalDelta i y * (orbitalDelta j x * orbitalDelta k l - + orbitalDelta j l * orbitalDelta k x) + + orbitalDelta i l * (orbitalDelta j x * orbitalDelta k y - + orbitalDelta j y * orbitalDelta k x)) = + orbitalDelta i x * ((c x y : ℂ) * orbitalDelta j y) * orbitalDelta k l - + orbitalDelta i x * ((c x y : ℂ) * orbitalDelta k y) * orbitalDelta j l - + orbitalDelta j x * ((c x y : ℂ) * orbitalDelta i y) * orbitalDelta k l + + orbitalDelta k x * ((c x y : ℂ) * orbitalDelta i y) * orbitalDelta j l + + orbitalDelta j x * ((c x y : ℂ) * orbitalDelta k y) * orbitalDelta i l - + orbitalDelta k x * ((c x y : ℂ) * orbitalDelta j y) * orbitalDelta i l := by ring + simp only [he, Finset.sum_sub_distrib, Finset.sum_add_distrib] + simp_rw [← Finset.sum_mul, ← Finset.mul_sum, sum_mul_orbitalDelta, + sum_orbitalDelta_mul] + rw [hc i j, hc k i, hc j k] + push_cast + ring + +lemma rawReadout_three_pair {n : ℕ} (c : Fin n → Fin n → ℝ) + (hc : ∀ i j, c j i = -c i j) (i j k l : Fin n) : + rawReadout n 3 + ((annihilation l * pairContraction (fun a : PairLabel n => + ((Real.sqrt 2 * c a.val.1 a.val.2 : ℝ) : ℂ))).adjoint (vacuum n)) ![i,j,k] = + (Real.sqrt 2 : ℂ) * ((c i j : ℂ) * orbitalDelta k l + + (c j k : ℂ) * orbitalDelta i l + (c k i : ℂ) * orbitalDelta j l) := by + rw [rawReadout_apply] + simp only [List.ofFn_succ, Matrix.cons_val_zero, Matrix.cons_val_succ, + List.ofFn_zero, adjoint_mul, annihilation_adjoint, Module.End.mul_apply, + pairContraction_ordered_adjoint c hc, map_smul, map_sum, PiLp.smul_apply, + WithLp.ofLp_sum, Finset.sum_apply, smul_eq_mul, word_three_creation_vacuum] + rw [pair_times_three_determinant c hc i j k l] + have hs : ((Real.sqrt 2)⁻¹ : ℂ) * 2 = (Real.sqrt 2 : ℂ) := by + have hr : (Real.sqrt 2)⁻¹ * 2 = Real.sqrt 2 := by + have hs : (Real.sqrt 2)^2 = 2 := Real.sq_sqrt (by norm_num) + have hz : Real.sqrt 2 ≠ 0 := Real.sqrt_ne_zero'.mpr (by norm_num) + field_simp + nlinarith + exact_mod_cast hr + rw [← mul_assoc, hs] + +lemma normalizedReadout_three_pair {n : ℕ} (c : Fin n → Fin n → ℝ) + (hc : ∀ i j, c j i = -c i j) (i j k l : Fin n) : + normalizedReadout n 3 + ((annihilation l * pairContraction (fun a : PairLabel n => + ((Real.sqrt 2 * c a.val.1 a.val.2 : ℝ) : ℂ))).adjoint (vacuum n)) ![i,j,k] = + ((Real.sqrt 3)⁻¹ : ℂ) * ((c i j : ℂ) * orbitalDelta k l + + (c j k : ℂ) * orbitalDelta i l + (c k i : ℂ) * orbitalDelta j l) := by + change ((Real.sqrt ((3:ℕ).factorial : ℝ))⁻¹ : ℂ) * rawReadout n 3 _ ![i,j,k] = _ + rw [rawReadout_three_pair c hc i j k l, ← mul_assoc] + have hs : (Real.sqrt ((3:ℕ).factorial : ℝ))⁻¹ * Real.sqrt 2 = (Real.sqrt 3)⁻¹ := by + norm_num only [Nat.factorial, Nat.cast_mul, Nat.cast_one, Nat.cast_ofNat, mul_one] + rw [show (6:ℝ)=3*2 by norm_num, Real.sqrt_mul (by norm_num : (0 : ℝ) ≤ 3)] + have hz : Real.sqrt 2 ≠ 0 := Real.sqrt_ne_zero'.mpr (by norm_num) + field_simp + have hs' : ((Real.sqrt ((3:ℕ).factorial : ℝ))⁻¹ : ℂ) * (Real.sqrt 2 : ℂ) = + ((Real.sqrt 3)⁻¹ : ℂ) := by exact_mod_cast hs + rw [hs'] + +lemma normalizedReadout_inner_sector {n N : ℕ} (x y : ExteriorCoordinates n N) : + inner ℂ (normalizedReadout n N (sectorInclusion n N x)) + (normalizedReadout n N (sectorInclusion n N y)) = inner ℂ x y := by + let f := (normalizedReadout n N).comp (sectorInclusion n N) + apply (LinearMap.norm_map_iff_inner_map_map f).mp _ x y + intro a + apply (sq_eq_sq₀ (norm_nonneg _) (norm_nonneg _)).mp + exact (normalizedReadout_norm_sq (sectorInclusion_homogeneous a)).trans + (sectorInclusion_norm_sq a) + +end LaughlinGap.Occupation + +namespace LaughlinGap.Spin +open scoped BigOperators InnerProduct +open Occupation + +def tupleThreeEquiv (ι : Type*) : ThreeIndex ι ≃ (Fin 3 → ι) where + toFun t := ![t.1.1,t.1.2,t.2] + invFun a := ((a 0,a 1),a 2) + left_inv _ := rfl + right_inv a := by ext i; fin_cases i <;> rfl + +noncomputable def spinPairForms (Q : ℕ) : Fin (2*Q-2+1) → PairLabel (Q+1) → ℂ := fun p a => + (sphericalExteriorPairCoefficient Q p.val a.val.1.val a.val.2.val : ℂ) + +lemma normalizedReadout_spin_three_column {Q : ℕ} (hQ : 2 ≤ Q) + (p : Fin (2*Q-2+1)) (l i j k : Fin (Q+1)) : + normalizedReadout (Q+1) 3 + (sectorInclusion (Q+1) 3 (tripleWedgeColumn (spinPairForms Q p) l)) ![i,j,k] = + ((orderedThreeWedge hQ (Pi.single (p,l) 1) ((i,j),k) : ℝ) : ℂ) := by + have hh : Homogeneous 3 + ((annihilation l * pairContraction (spinPairForms Q p)).adjoint (vacuum (Q+1))) := by + rw [adjoint_mul, annihilation_adjoint, Module.End.mul_apply] + exact pairContraction_adjoint_homogeneous _ (creation_homogeneous (vacuum_homogeneous _) _) + rw [tripleWedgeColumn, sectorInclusion_readout hh] + have hv : spinPairForms Q p = fun a : PairLabel (Q+1) => + ((Real.sqrt 2 * pairCoefficient Q p.val a.val.1 a.val.2 : ℝ) : ℂ) := by + funext a + exact congrArg Complex.ofReal (sphericalExteriorPairCoefficient_eq_tensor _ _ _ _) + rw [hv, normalizedReadout_three_pair _ (fun i j => pairCoefficient_swap Q p.val i j)] + simp only [orderedThreeWedge, LinearMap.smul_apply, LinearMap.comp_apply, + Pi.smul_apply, smul_eq_mul, cyclicSum_apply, Pi.add_apply, cycleMap_apply, + pairSpectatorInclusion_apply] + simp [Pi.single_apply, mul_ite, Complex.ofReal_add, Complex.ofReal_mul, + Complex.ofReal_inv, orbitalDelta, ite_and] + simp only [apply_ite Complex.ofReal, Complex.ofReal_zero] + +lemma spinTripleGram_entry {Q : ℕ} (hQ : 2 ≤ Q) + (a b : Fin (2*Q-2+1) × Fin (Q+1)) : + ((tripleWedgeMatrix (spinPairForms Q)).conjTranspose * + tripleWedgeMatrix (spinPairForms Q)) a b = + ((orderedThreeGram hQ (Pi.single b 1) a : ℝ) : ℂ) := by + have he : ((tripleWedgeMatrix (spinPairForms Q)).conjTranspose * + tripleWedgeMatrix (spinPairForms Q)) a b = + inner ℂ (tripleWedgeColumn (spinPairForms Q a.1) a.2) + (tripleWedgeColumn (spinPairForms Q b.1) b.2) := by + simp only [Matrix.mul_apply, Matrix.conjTranspose_apply, tripleWedgeMatrix, + PiLp.inner_apply, RCLike.inner_apply] + exact Finset.sum_congr rfl (fun _ _ => mul_comm _ _) + rw [he, ← normalizedReadout_inner_sector, PiLp.inner_apply] + rw [← (tupleThreeEquiv (Fin (Q+1))).sum_comp] + change (∑ t : ThreeIndex (Fin (Q+1)), + inner ℂ + (normalizedReadout (Q+1) 3 (sectorInclusion (Q+1) 3 + (tripleWedgeColumn (spinPairForms Q a.1) a.2)) ![t.1.1,t.1.2,t.2]) + (normalizedReadout (Q+1) 3 (sectorInclusion (Q+1) 3 + (tripleWedgeColumn (spinPairForms Q b.1) b.2)) ![t.1.1,t.1.2,t.2])) = _ + simp only [normalizedReadout_spin_three_column hQ, RCLike.inner_apply, + Complex.conj_ofReal, ← Complex.ofReal_mul, ← Complex.ofReal_sum] + congr 1 + change dotProduct (orderedThreeWedge hQ (Pi.single b 1)) + (orderedThreeWedge hQ (Pi.single a 1)) = _ + rw [dotProduct_comm, transposeMap_adjoint, dotProduct_comm, dotProduct_single_one] + rfl + +lemma linearMap_apply_coordinates {ι κ : Type*} [Fintype ι] [DecidableEq ι] + (A : (ι → ℝ) →ₗ[ℝ] (κ → ℝ)) (x : ι → ℝ) (k : κ) : + (∑ i, A (Pi.single i 1) k * x i) = A x k := by + conv_rhs => rw [A.pi_apply_eq_sum_univ x] + simp only [Finset.sum_apply, Pi.smul_apply, smul_eq_mul] + apply Finset.sum_congr rfl + intro i hi + rw [mul_comm] + have he : Pi.single i (1:ℝ) = (fun j : ι => if i=j then (1:ℝ) else 0) := by + funext j + simp [Pi.single_apply, eq_comm] + rw [he] + +theorem spinTripleGram_mulVec_real {Q : ℕ} (hQ : 2 ≤ Q) + (a : (Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) : + ((tripleWedgeMatrix (spinPairForms Q)).conjTranspose * + tripleWedgeMatrix (spinPairForms Q)).mulVec (fun i => (a i : ℂ)) = + fun i => ((orderedThreeGram hQ a i : ℝ) : ℂ) := by + funext i + simp only [Matrix.mulVec, dotProduct, spinTripleGram_entry hQ, + ← Complex.ofReal_mul, ← Complex.ofReal_sum, linearMap_apply_coordinates] + +theorem spinTripleGram_eigenvalue {Q z l : ℕ} (hQ : 2 ≤ Q) + (hz : z ≤ Q) (hl : l ≤ (2*Q-2)+Q-2*z) : + ((tripleWedgeMatrix (spinPairForms Q)).conjTranspose * + tripleWedgeMatrix (spinPairForms Q)).mulVec + (fun i => (coupledTensor (2*Q-2) Q z l i : ℂ)) = + (1+(threeBodyGramCoefficient Q z : ℂ)) • + (fun i => (coupledTensor (2*Q-2) Q z l i : ℂ)) := by + rw [spinTripleGram_mulVec_real hQ, orderedThreeGram_eigenvalue hQ hz hl] + funext i + simp only [Pi.smul_apply, smul_eq_mul, Complex.ofReal_mul, Complex.ofReal_add, + Complex.ofReal_one] + +end LaughlinGap.Spin + +namespace LaughlinGap.Spin +open scoped BigOperators InnerProduct ComplexOrder +open Occupation + +def physicalPairIndexEquiv {Q : ℕ} (hQ : 2 ≤ Q) : + Fin (2*Q-1) ≃ Fin (2*Q-2+1) := finCongr (by omega) + +def physicalThreeIndexEquiv {Q : ℕ} (hQ : 2 ≤ Q) : + (Fin (2*Q-1) × Fin (Q+1)) ≃ (Fin (2*Q-2+1) × Fin (Q+1)) := + Equiv.prodCongr (physicalPairIndexEquiv hQ) (Equiv.refl _) + +@[simp] lemma spinPairForms_physical_index {Q : ℕ} (hQ : 2 ≤ Q) (p : Fin (2*Q-1)) : + spinPairForms Q (physicalPairIndexEquiv hQ p) = physicalPairForms Q p := rfl + +@[simp] lemma spinTripleWedge_physical_index {Q : ℕ} (hQ : 2 ≤ Q) + (a : BasisLabel (Q+1) 3) (p : Fin (2*Q-1) × Fin (Q+1)) : + tripleWedgeMatrix (spinPairForms Q) a (physicalThreeIndexEquiv hQ p) = + tripleWedgeMatrix (physicalPairForms Q) a p := rfl + +lemma physicalTripleGram_entry {Q : ℕ} (hQ : 2 ≤ Q) + (a b : Fin (2*Q-1) × Fin (Q+1)) : + ((tripleWedgeMatrix (physicalPairForms Q)).conjTranspose * + tripleWedgeMatrix (physicalPairForms Q)) a b = + ((orderedThreeGram hQ (Pi.single (physicalThreeIndexEquiv hQ b) 1) + (physicalThreeIndexEquiv hQ a) : ℝ) : ℂ) := by + exact spinTripleGram_entry hQ (physicalThreeIndexEquiv hQ a) + (physicalThreeIndexEquiv hQ b) + +theorem physicalTripleGram_mulVec_real {Q : ℕ} (hQ : 2 ≤ Q) + (a : (Fin (2*Q-2+1) × Fin (Q+1)) → ℝ) : + ((tripleWedgeMatrix (physicalPairForms Q)).conjTranspose * + tripleWedgeMatrix (physicalPairForms Q)).mulVec + (fun i => (a (physicalThreeIndexEquiv hQ i) : ℂ)) = + fun i => ((orderedThreeGram hQ a (physicalThreeIndexEquiv hQ i) : ℝ) : ℂ) := by + funext i + simp only [Matrix.mulVec, dotProduct, physicalTripleGram_entry hQ, + ← Complex.ofReal_mul, ← Complex.ofReal_sum] + rw [(physicalThreeIndexEquiv hQ).sum_comp (fun j => + orderedThreeGram hQ (Pi.single j 1) (physicalThreeIndexEquiv hQ i) * a j)] + rw [linearMap_apply_coordinates] + +noncomputable def physicalThreeVector {Q : ℕ} (hQ : 2 ≤ Q) (z l : ℕ) : + (Fin (2*Q-1) × Fin (Q+1)) → ℂ := fun i => + (coupledTensor (2*Q-2) Q z l (physicalThreeIndexEquiv hQ i) : ℂ) + +theorem physicalTripleGram_eigenvalue {Q z l : ℕ} (hQ : 2 ≤ Q) + (hz : z ≤ Q) (hl : l ≤ (2*Q-2)+Q-2*z) : + ((tripleWedgeMatrix (physicalPairForms Q)).conjTranspose * + tripleWedgeMatrix (physicalPairForms Q)).mulVec (physicalThreeVector hQ z l) = + (1+(threeBodyGramCoefficient Q z : ℂ)) • physicalThreeVector hQ z l := by + unfold physicalThreeVector + rw [physicalTripleGram_mulVec_real hQ, orderedThreeGram_eigenvalue hQ hz hl] + funext i + simp only [Pi.smul_apply, smul_eq_mul, Complex.ofReal_mul, Complex.ofReal_add, + Complex.ofReal_one] + +theorem physicalTripleWedge_null {Q z l : ℕ} (hQ : 2 ≤ Q) + (hz : z ≤ Q) (hl : l ≤ (2*Q-2)+Q-2*z) (hn : z=0 ∨ z=1 ∨ z=3) : + (tripleWedgeMatrix (physicalPairForms Q)).mulVec (physicalThreeVector hQ z l) = 0 := by + apply (Matrix.conjTranspose_mul_self_mulVec_eq_zero _ _).mp + have hq : threeBodyGramCoefficient Q z = -1 := by + rcases hn with rfl | rfl | rfl + · exact threeBodyGramCoefficient_zero Q + · exact threeBodyGramCoefficient_one hQ + · exact threeBodyGramCoefficient_three hz + rw [physicalTripleGram_eigenvalue hQ hz hl, hq] + simp + +end LaughlinGap.Spin + +end + +end OAI diff --git a/lean/OAI/Analysis/LaughlinGap/ZeroCertificates.lean b/lean/OAI/Analysis/LaughlinGap/ZeroCertificates.lean new file mode 100644 index 0000000000000000000000000000000000000000..ef30335d14dd480570e2bfb78483b1f77a3306a7 --- /dev/null +++ b/lean/OAI/Analysis/LaughlinGap/ZeroCertificates.lean @@ -0,0 +1,48 @@ +import Mathlib +import OAI.Analysis.LaughlinGap.ExactRows +import OAI.Analysis.LaughlinGap.RationalFourCertificate + +namespace OAI + +/-! Zero Certificates. -/ + +noncomputable section + + +namespace LaughlinGap.RealOccupation +open scoped BigOperators ComplexOrder +open Spin + +lemma fourCertificate_of_empty_keys {ι : Type*} [Fintype ι] (rows : ι → RationalRow) (ε : ℚ) + {D : ℕ} (hD : D ≤ 23) (hk : fourKeys hD=∅) : + FourCertificate (fun a => (rows a).toReal) (ε:ℝ) D hD := by + apply fourCertificate_of_rational rows ε hD + have hg : rationalCreatedGram hD=0 := by ext u v; simp [rationalCreatedGram,hk] + simpa [rationalFourCompression,hg] using (Matrix.PosSemidef.zero : (0 : Matrix (FourCopy D) (FourCopy D) ℂ).PosSemidef) + +lemma keys_empty_1 : fourKeys (by omega : 1 ≤ 23)=∅ := by decide +kernel +lemma keys_empty_2 : fourKeys (by omega : 2 ≤ 23)=∅ := by decide +kernel +lemma keys_empty_3 : fourKeys (by omega : 3 ≤ 23)=∅ := by decide +kernel +lemma keys_empty_4 : fourKeys (by omega : 4 ≤ 23)=∅ := by decide +kernel + +lemma certificate_1 : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 1 + (by omega) := by + convert fourCertificate_of_empty_keys exactRows (1/200000) _ keys_empty_1 using 1 + norm_num +lemma certificate_2 : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 2 + (by omega) := by + convert fourCertificate_of_empty_keys exactRows (1/200000) _ keys_empty_2 using 1 + norm_num +lemma certificate_3 : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 3 + (by omega) := by + convert fourCertificate_of_empty_keys exactRows (1/200000) _ keys_empty_3 using 1 + norm_num +lemma certificate_4 : FourCertificate (fun a : Fin 8 => (exactRows a).toReal) (1/200000) 4 + (by omega) := by + convert fourCertificate_of_empty_keys exactRows (1/200000) _ keys_empty_4 using 1 + norm_num +end LaughlinGap.RealOccupation + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/ActionBounds.lean b/lean/OAI/Analysis/LiebThirring/ActionBounds.lean new file mode 100644 index 0000000000000000000000000000000000000000..987dc88f4ef8d5a5d5ad5392595e11dee9e6fd40 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/ActionBounds.lean @@ -0,0 +1,307 @@ +import OAI.Analysis.LiebThirring.BoundaryValues + +namespace OAI + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +noncomputable section +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder CStarAlgebra +noncomputable section +open MeasureTheory Set Filter +open scoped Topology +open scoped NNReal + + +namespace SharpLiebThirring.ActionProof +open Matrix MatrixProof MeasureTheory +open scoped Matrix.Norms.L2Operator +variable {N : ℕ} + +lemma trace_square_real {H : Matrix (Fin N) (Fin N) ℝ} (hH : H.IsHermitian) : + trace (H * H) = ∑ i, ∑ j, H i j ^ 2 := by + simp only [trace, diag, Matrix.mul_apply] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + have he : H j i = H i j := by simpa only [conjTranspose_apply, star_trivial] using congrFun (congrFun hH i) j + rw [he, pow_two] + +lemma quadratic_swap {B : Matrix (Fin N) (Fin N) ℝ} (hB : B.IsHermitian) + (a b : Fin N → ℝ) : + (∑ i, a i * (B *ᵥ b) i) = ∑ i, b i * (B *ᵥ a) i := by + simp only [mulVec, dotProduct, Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + have he : B j i = B i j := by simpa only [conjTranspose_apply, star_trivial] using congrFun (congrFun hB i) j + rw [he] + ring + +lemma trace_rankone_mul (a : Fin N → ℝ) (H : Matrix (Fin N) (Fin N) ℝ) : + trace (vecMulVec a a * H) = ∑ i, a i * (H *ᵥ a) i := by + simp only [trace, diag, mul_apply, vecMulVec_apply, mulVec, dotProduct, Finset.mul_sum] + rw [Finset.sum_comm] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + ring + +lemma quadratic_hasDerivAt {a a' : ℝ → Fin N → ℝ} + {B B' : ℝ → Matrix (Fin N) (Fin N) ℝ} {x : ℝ} + (ha : ∀ i, HasDerivAt (fun t ↦ a t i) (a' x i) x) + (hB : ∀ i j, HasDerivAt (fun t ↦ B t i j) (B' x i j) x) + (hBx : (B x).IsHermitian) : + HasDerivAt (fun t ↦ ∑ i, a t i * (B t *ᵥ a t) i) + (2 * (∑ i, a' x i * (B x *ᵥ a x) i) + + trace (vecMulVec (a x) (a x) * B' x)) x := by + have hh := HasDerivAt.sum (u := Finset.univ) (fun i _ ↦ + (ha i).mul (HasDerivAt.sum (u := Finset.univ) (fun j _ ↦ (hB i j).mul (ha j)))) + simp only [Finset.sum_apply, Pi.mul_apply] at hh + convert! hh using 1 + · funext t + simp only [mulVec, dotProduct, Finset.sum_apply, Pi.mul_apply] + · rw [trace_rankone_mul] + have hs := quadratic_swap hBx (a x) (a' x) + change 2 * (∑ i, a' x i * (∑ j, B x i j * a x j)) + + (∑ i, a x i * (∑ j, B' x i j * a x j)) = + ∑ i, (a' x i * (∑ j, B x i j * a x j) + + a x i * ∑ j, (B' x i j * a x j + B x i j * a' x j)) + simp_rw [Finset.sum_add_distrib, mul_add, Finset.sum_add_distrib] + change (∑ i, a x i * (∑ j, B x i j * a' x j)) = + (∑ i, a' x i * (∑ j, B x i j * a x j)) at hs + linarith + +end SharpLiebThirring.ActionProof +namespace SharpLiebThirring.SpectralProof +open Matrix MeasureTheory +open scoped Matrix.Norms.L2Operator + +def actionYoungConstant (σ : ℝ) : ℝ := σ ^ σ / (1 + σ) ^ (1 + σ) + +lemma sigma_holderConjugate {σ : ℝ} (hσ : 0 < σ) : + (1 + σ).HolderConjugate (1 + 1 / σ) := by + rw [Real.holderConjugate_iff] + constructor + · linarith + · have h1 : 1 + σ ≠ 0 := by positivity + have h2 : 1 + 1 / σ ≠ 0 := by positivity + field_simp + ring + +lemma young_action_bound {σ W m : ℝ} (hσ : 0 < σ) (hW : 0 ≤ W) (hm : 0 ≤ m) : + W * m - m ^ (1 + 1 / σ) ≤ actionYoungConstant σ * W ^ (1 + σ) := by + let q := 1 + 1 / σ + have hq : 0 < q := by dsimp [q]; positivity + have hp : 0 < 1 + σ := by positivity + have hy := Real.young_inequality_of_nonneg (div_nonneg hW hq.le) hm (sigma_holderConjugate hσ) + change W / q * m ≤ (W / q) ^ (1 + σ) / (1 + σ) + m ^ q / q at hy + have hc : q * ((W / q) ^ (1 + σ) / (1 + σ)) = actionYoungConstant σ * W ^ (1 + σ) := by + rw [Real.div_rpow hW hq.le] + have hqe : q = (1 + σ) / σ := by dsimp [q]; field_simp; ring + have hpow : q ^ (1 + σ) = q * ((1 + σ) ^ σ / σ ^ σ) := by + rw [Real.rpow_add hq, Real.rpow_one, hqe, Real.div_rpow hp.le hσ.le] + rw [hpow] + unfold actionYoungConstant + rw [Real.rpow_add hp, Real.rpow_one] + have hsp := Real.rpow_pos_of_pos hσ σ + have hpp := Real.rpow_pos_of_pos hp σ + field_simp + have hy' := mul_le_mul_of_nonneg_left hy hq.le + have hm' : q * (m ^ q / q) = m ^ q := by field_simp + have hw' : q * (W / q * m) = W * m := by field_simp + rw [mul_add, hc, hm', hw'] at hy' + linarith + +lemma triangular_diagonal_energy_nonpos {N : ℕ} (k : Fin N → ℝ) + (hk : ∀ i, 0 ≤ k i) (hkord : Antitone k) (C : Matrix (Fin N) (Fin N) ℝ) + (hC : ∀ i j, i < j → C i j = 0) : + (∑ i, ∑ j, C i j ^ 2 * (k i ^ 2 - k j ^ 2)) ≤ 0 := by + apply Finset.sum_nonpos + intro i _ + apply Finset.sum_nonpos + intro j _ + by_cases hij : i < j + · simp [hC i j hij] + · apply mul_nonpos_of_nonneg_of_nonpos (sq_nonneg _) + have hh := hkord (le_of_not_gt hij) + nlinarith [hk i, hk j] + +end SharpLiebThirring.SpectralProof +namespace SharpLiebThirring.PathProof +open Set Filter +open scoped Topology + +/-- The endpoint barrier used to remove the field cutoff. No strict negativity +or Lipschitz property of the scalar derivative is needed. -/ +lemma upper_barrier {f f' : ℝ → ℝ} {l r κ : ℝ} + (hc : ContinuousOn f (Icc l r)) + (hd : ∀ x ∈ Icc l r, HasDerivAt f (f' x) x) + (hl : f l ≤ κ) + (hb : ∀ x ∈ Icc l r, κ < f x → f' x ≤ 0) : + ∀ x ∈ Icc l r, f x ≤ κ := by + intro x hx + have he (η : ℝ) (hη : 0 < η) : f x ≤ κ + η + η * (x - l) := by + apply image_le_of_deriv_right_lt_deriv_boundary hc + (fun t ht ↦ (hd t ⟨ht.1, ht.2.le⟩).hasDerivWithinAt) + (B := fun t ↦ κ + η + η * (t - l)) (B' := fun _ ↦ η) + · simpa using (hl.trans (le_add_of_nonneg_right hη.le)) + · intro t + convert! ((hasDerivAt_id t).sub_const l).const_mul η |>.const_add (κ + η) using 1 + simp + · intro t ht hft + have hgt : κ < f t := by + rw [hft] + nlinarith [mul_nonneg hη.le (sub_nonneg.2 ht.1)] + exact lt_of_le_of_lt (hb t ⟨ht.1, ht.2.le⟩ hgt) hη + · exact hx + have ht : Tendsto (fun η : ℝ ↦ κ + η + η * (x - l)) (𝓝[>] 0) (𝓝 κ) := by + have hh : Continuous (fun η : ℝ ↦ κ + η + η * (x - l)) := by fun_prop + simpa using (hh.continuousAt (x := (0 : ℝ))).tendsto.mono_left (nhdsWithin_le_nhds (s := Ioi 0)) + exact ge_of_tendsto ht (by filter_upwards [self_mem_nhdsWithin] with η hη using he η hη) + +lemma two_endpoint_barrier {f f' : ℝ → ℝ} {l r κ : ℝ} + (hc : ContinuousOn f (Icc l r)) + (hd : ∀ x ∈ Icc l r, HasDerivAt f (f' x) x) + (hl : f l ≤ κ) (hr : -κ ≤ f r) + (hb : ∀ x ∈ Icc l r, κ < |f x| → f' x ≤ 0) : + ∀ x ∈ Icc l r, |f x| ≤ κ := by + have hup := upper_barrier hc hd hl (fun x hx hh ↦ hb x hx (hh.trans_le (le_abs_self _))) + let g := fun t : ℝ ↦ -f (l + r - t) + have hmap : MapsTo (fun t : ℝ ↦ l + r - t) (Icc l r) (Icc l r) := by + intro t ht + constructor <;> linarith [ht.1, ht.2] + have hgc : ContinuousOn g (Icc l r) := hc.comp (by fun_prop) hmap |>.neg + have hgd (t : ℝ) (ht : t ∈ Icc l r) : HasDerivAt g (f' (l + r - t)) t := by + convert! ((hd (l + r - t) (hmap ht)).comp t ((hasDerivAt_id t).const_sub (l + r))).neg using 1 + ring + have hgl : g l ≤ κ := by simpa [g] using (neg_le_neg hr) + have hgb (t : ℝ) (ht : t ∈ Icc l r) (hh : κ < g t) : f' (l + r - t) ≤ 0 := by + exact hb _ (hmap ht) (hh.trans_le (neg_le_abs _)) + have hlow := upper_barrier hgc hgd hgl hgb + intro x hx + apply abs_le.2 + constructor + · have hh := hlow (l + r - x) (hmap hx) + have he : l + r - (l + r - x) = x := by ring + simpa [g, he] using (neg_le_neg hh) + · exact hup x hx + +end SharpLiebThirring.PathProof + +namespace SharpLiebThirring.ActionProof +open Matrix MatrixProof MeasureTheory +open scoped Matrix.Norms.L2Operator +variable {N : ℕ} + +/-- Real entry evaluation on the actual symmetric-matrix normed space. -/ +def realSelfAdjointEntryCLM (i j : Fin N) : + selfAdjoint (Matrix (Fin N) (Fin N) ℝ) →L[ℝ] ℝ := + { toFun := fun B ↦ (B : Matrix (Fin N) (Fin N) ℝ) i j + map_add' := fun _ _ ↦ rfl + map_smul' := fun _ _ ↦ rfl + cont := by + have hc : Continuous (fun A : Matrix (Fin N) (Fin N) ℝ ↦ A i j) := + (({ toFun := fun A : Matrix (Fin N) (Fin N) ℝ ↦ A i j + map_add' := fun _ _ ↦ rfl + map_smul' := fun _ _ ↦ rfl } : Matrix (Fin N) (Fin N) ℝ →ₗ[ℝ] ℝ).toContinuousLinearMap).continuous + exact hc.comp continuous_subtype_val } + +lemma realSelfAdjoint_entry_derivative + {B : ℝ → selfAdjoint (Matrix (Fin N) (Fin N) ℝ)} + {B' : selfAdjoint (Matrix (Fin N) (Fin N) ℝ)} {x : ℝ} + (hB : HasDerivAt B B' x) (i j : Fin N) : + HasDerivAt (fun t ↦ (B t : Matrix (Fin N) (Fin N) ℝ) i j) + ((B' : Matrix (Fin N) (Fin N) ℝ) i j) x := + (realSelfAdjointEntryCLM i j).hasFDerivAt.comp_hasDerivAt x hB + +lemma real_rankone_isHermitian (a : Fin N → ℝ) : (vecMulVec a a).IsHermitian := by + ext i j + simp [vecMulVec, conjTranspose_apply, mul_comm] + +/-- The exact penalized action identity, pointwise wherever the amplitude is + differentiable. Hence it applies to the a.e. derivative of H¹ amplitudes. -/ +lemma action_ode_identity {σ δ ε : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (hε : 0 < ε) + (k : Fin N → ℝ) {a a' : ℝ → Fin N → ℝ} + {B : ℝ → selfAdjoint (Matrix (Fin N) (Fin N) ℝ)} + {B' : selfAdjoint (Matrix (Fin N) (Fin N) ℝ)} {x : ℝ} + (ha : ∀ i, HasDerivAt (fun t ↦ a t i) (a' x i) x) + (hB : HasDerivAt B B' x) + (hode : ε • (B' : Matrix (Fin N) (Fin N) ℝ) = + matrixField σ δ k (B x) - vecMulVec (a x) (a x)) : + HasDerivAt (fun t ↦ fieldPrimitive σ δ k (B t) + + ∑ i, a t i * ((B t : Matrix (Fin N) (Fin N) ℝ) *ᵥ a t) i) + (2 * (∑ i, a' x i * ((B x : Matrix (Fin N) (Fin N) ℝ) *ᵥ a x) i) - + constraintDefect σ δ k (B x, a x) / ε) x := by + let D := matrixField σ δ k (B x) - vecMulVec (a x) (a x) + have hD : D.IsHermitian := + (matrixField_isHermitian hσ hδ k (B x).prop).sub (real_rankone_isHermitian _) + have hb' : (B' : Matrix (Fin N) (Fin N) ℝ) = ε⁻¹ • D := by + rw [show D = ε • (B' : Matrix (Fin N) (Fin N) ℝ) from hode.symm, + smul_smul, inv_mul_cancel₀ hε.ne', one_smul] + have ht : trace (D * (B' : Matrix (Fin N) (Fin N) ℝ)) = + constraintDefect σ δ k (B x, a x) / ε := by + rw [hb', Matrix.mul_smul, trace_smul, trace_square_real hD] + simp only [smul_eq_mul, constraintDefect, D, Matrix.sub_apply, vecMulVec_apply, + div_eq_mul_inv, mul_comm] + have hq := quadratic_hasDerivAt (B := fun t ↦ (B t : Matrix (Fin N) (Fin N) ℝ)) + (B' := fun _ ↦ (B' : Matrix (Fin N) (Fin N) ℝ)) ha + (fun i j ↦ realSelfAdjoint_entry_derivative hB i j) (B x).prop + have hj := fieldPrimitive_path_derivative hσ hδ k hB + convert! hj.add hq using 1 + dsimp only [D] at ht + rw [Matrix.sub_mul, trace_sub] at ht + linarith + +lemma quadratic_square_real {B : Matrix (Fin N) (Fin N) ℝ} (hB : B.IsHermitian) + (a : Fin N → ℝ) : + (∑ i, a i * (B ^ 2 *ᵥ a) i) = ∑ i, (B *ᵥ a) i ^ 2 := by + rw [pow_two, ← Matrix.mulVec_mulVec, quadratic_swap hB] + simp [pow_two] + +lemma action_pointwise_square_bound {B : Matrix (Fin N) (Fin N) ℝ} (hB : B.IsHermitian) + (a v : Fin N → ℝ) : + 2 * (∑ i, v i * (B *ᵥ a) i) ≤ + (∑ i, v i ^ 2) + ∑ i, a i * (B ^ 2 *ᵥ a) i := by + rw [quadratic_square_real hB] + rw [← Finset.sum_add_distrib, Finset.mul_sum] + apply Finset.sum_le_sum + intro i _ + nlinarith [sq_nonneg (v i - (B *ᵥ a) i)] + +lemma action_penalty_pointwise {σ δ ε : ℝ} (k : Fin N → ℝ) + (B : selfAdjoint (Matrix (Fin N) (Fin N) ℝ)) (a v : Fin N → ℝ) : + 2 * (∑ i, v i * ((B : Matrix (Fin N) (Fin N) ℝ) *ᵥ a) i) - + constraintDefect σ δ k (B, a) / ε ≤ + (∑ i, v i ^ 2) + (∑ i, k i ^ 2 * a i ^ 2) - (∑ i, a i ^ 2) ^ (1 + 1 / σ) + + (actionDefect σ k (B, a) - constraintDefect σ δ k (B, a) / ε) := by + have hh := action_pointwise_square_bound B.prop a v + have hK : (∑ i, a i * ((diagonal (fun i ↦ k i ^ 2) - + (B : Matrix (Fin N) (Fin N) ℝ) ^ 2) *ᵥ a) i) = + (∑ i, k i ^ 2 * a i ^ 2) - ∑ i, a i * ((B : Matrix (Fin N) (Fin N) ℝ) ^ 2 *ᵥ a) i := by + rw [sub_mulVec] + simp only [Pi.sub_apply, mul_sub, Finset.sum_sub_distrib, mulVec_diagonal] + congr 1 + apply Finset.sum_congr rfl + intro i _ + ring + unfold actionDefect + dsimp only + rw [hK] + linarith + +end SharpLiebThirring.ActionProof + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/ActionPenalty.lean b/lean/OAI/Analysis/LiebThirring/ActionPenalty.lean new file mode 100644 index 0000000000000000000000000000000000000000..d08f14b60061ed38bf25cd89744c0cc41d114164 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/ActionPenalty.lean @@ -0,0 +1,234 @@ +import OAI.Analysis.LiebThirring.FieldPrimitive + +namespace OAI + +universe u35 + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +noncomputable section +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder CStarAlgebra +noncomputable section +open MeasureTheory Set Filter +open scoped Topology +open scoped NNReal + + +namespace SharpLiebThirring.ActionProof +open Set Filter + +/-- The compact penalty argument, with no convergence of +minimizers or chosen coefficients required. -/ +lemma compact_penalty_bound {E : Type u35} [TopologicalSpace E] {K : Set E} + (hK : IsCompact K) {f g : E → ℝ} (hf : Continuous f) (hg : Continuous g) + (hg0 : ∀ x ∈ K, 0 ≤ g x) (hzero : ∀ x ∈ K, g x = 0 → f x ≤ 0) + {η : ℝ} (hη : 0 < η) : + ∃ ε₀ : ℝ, 0 < ε₀ ∧ ∀ ε : ℝ, 0 < ε → ε ≤ ε₀ → + ∀ x ∈ K, f x - g x / ε ≤ η := by + let S := K ∩ {x | η ≤ f x} + have hS : IsCompact S := hK.inter_right (isClosed_le continuous_const hf) + obtain ⟨F, hF⟩ := (hK.image hf).bddAbove + by_cases hne : S.Nonempty + · obtain ⟨y, hy, hmin⟩ := hS.exists_isMinOn hne hg.continuousOn + have hgy : 0 < g y := lt_of_le_of_ne (hg0 y hy.1) (by + intro he + have := hzero y hy.1 he.symm + dsimp [S] at hy + have hηy : η ≤ f y := hy.2 + linarith) + have hF1 : 0 < max F 1 := lt_of_lt_of_le (by norm_num) (le_max_right F 1) + refine ⟨g y / max F 1, div_pos hgy hF1, ?_⟩ + intro ε hε hε₀ x hx + by_cases hfx : η ≤ f x + · have hxy : g y ≤ g x := hmin ⟨hx, hfx⟩ + have hprod : ε * max F 1 ≤ g y := (le_div_iff₀ hF1).mp hε₀ + have hr : max F 1 ≤ g x / ε := (le_div_iff₀ hε).mpr (by nlinarith) + have := (hF (Set.mem_image_of_mem f hx)).trans (le_max_left F 1) + linarith + · exact (sub_le_self _ (div_nonneg (hg0 x hx) hε.le)).trans (le_of_not_ge hfx) + · refine ⟨1, by norm_num, ?_⟩ + intro ε hε _ x hx + have hfx : f x < η := lt_of_not_ge (fun hh ↦ hne ⟨x, hx, hh⟩) + exact (sub_le_self _ (div_nonneg (hg0 x hx) hε.le)).trans hfx.le + +end SharpLiebThirring.ActionProof + +namespace SharpLiebThirring.ActionProof +open Matrix MatrixProof Set +open scoped Matrix.Norms.L2Operator +variable {N : ℕ} + +def actionDefect (σ : ℝ) (k : Fin N → ℝ) + (z : selfAdjoint (Matrix (Fin N) (Fin N) ℝ) × (Fin N → ℝ)) : ℝ := + (∑ i, z.2 i ^ 2) ^ (1 + 1 / σ) - + ∑ i, z.2 i * ((diagonal (fun i ↦ k i ^ 2) - (z.1 : Matrix (Fin N) (Fin N) ℝ) ^ 2) *ᵥ z.2) i + +def constraintDefect (σ δ : ℝ) (k : Fin N → ℝ) + (z : selfAdjoint (Matrix (Fin N) (Fin N) ℝ) × (Fin N → ℝ)) : ℝ := + ∑ i, ∑ j, (matrixField σ δ k z.1 i j - z.2 i * z.2 j) ^ 2 + +lemma actionDefect_continuous {σ : ℝ} (hσ : 0 < σ) (k : Fin N → ℝ) : + Continuous (actionDefect σ k) := by + apply Continuous.sub + · exact (by fun_prop : Continuous (fun z : selfAdjoint (Matrix (Fin N) (Fin N) ℝ) × (Fin N → ℝ) ↦ + ∑ i, z.2 i ^ 2)).rpow_const (fun _ ↦ Or.inr (by positivity)) + · unfold mulVec dotProduct + fun_prop + +lemma constraintDefect_continuous {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (k : Fin N → ℝ) : + Continuous (constraintDefect σ δ k) := by + have hc : Continuous (fun z : selfAdjoint (Matrix (Fin N) (Fin N) ℝ) × (Fin N → ℝ) ↦ + matrixField σ δ k z.1) := (matrixField_continuous hσ hδ k).comp continuous_fst + unfold constraintDefect + fun_prop + +lemma constraintDefect_nonneg (σ δ : ℝ) (k : Fin N → ℝ) + (z : selfAdjoint (Matrix (Fin N) (Fin N) ℝ) × (Fin N → ℝ)) : + 0 ≤ constraintDefect σ δ k z := by + unfold constraintDefect + exact Finset.sum_nonneg (fun i _ ↦ Finset.sum_nonneg (fun j _ ↦ sq_nonneg _)) + +lemma constraintDefect_eq_zero_iff (σ δ : ℝ) (k : Fin N → ℝ) + (z : selfAdjoint (Matrix (Fin N) (Fin N) ℝ) × (Fin N → ℝ)) : + constraintDefect σ δ k z = 0 ↔ matrixField σ δ k z.1 = vecMulVec z.2 z.2 := by + constructor + · intro h + ext i j + have hi := (Finset.sum_eq_zero_iff_of_nonneg + (fun i _ ↦ Finset.sum_nonneg (fun j _ ↦ sq_nonneg + (matrixField σ δ k z.1 i j - z.2 i * z.2 j)))).mp h i (Finset.mem_univ i) + have hij := (Finset.sum_eq_zero_iff_of_nonneg (fun j _ ↦ sq_nonneg + (matrixField σ δ k z.1 i j - z.2 i * z.2 j))).mp hi j (Finset.mem_univ j) + exact sub_eq_zero.mp (sq_eq_zero_iff.mp hij) + · intro h + simp [constraintDefect, h, vecMulVec] + +/-- Uniform compact penalty estimate for the matrix field and rank-one +constraint. -/ +lemma matrix_compact_penalty {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) + (k : Fin N → ℝ) + {K : Set (selfAdjoint (Matrix (Fin N) (Fin N) ℝ) × (Fin N → ℝ))} (hK : IsCompact K) + {η : ℝ} (hη : 0 < η) : + ∃ ε₀ : ℝ, 0 < ε₀ ∧ ∀ ε : ℝ, 0 < ε → ε ≤ ε₀ → ∀ z ∈ K, + actionDefect σ k z - constraintDefect σ δ k z / ε ≤ η := by + apply compact_penalty_bound hK (actionDefect_continuous hσ₀ k) + (constraintDefect_continuous hσ₁ hδ k) (fun z _ ↦ constraintDefect_nonneg σ δ k z) _ hη + intro z _ hz + exact sub_nonpos.mpr (source_rankone_comparison hσ₀ hσ₁ hδ k z.1.prop z.2 + ((constraintDefect_eq_zero_iff σ δ k z).mp hz)) + +end SharpLiebThirring.ActionProof +namespace SharpLiebThirring.PathProof +open Matrix +variable {N : ℕ} + +/-- The initial row-sign orbit calculation, without assuming invertibility +of any later matching solution. -/ +lemma lower_gram_diagonal {C : Matrix (Fin N) (Fin N) ℝ} (hC : LowerTriangular C) + {d : Fin N → ℝ} (hd : ∀ i, 0 < d i) (hgram : C * C.transpose = diagonal d) : + (∀ i j, i ≠ j → C i j = 0) ∧ (∀ i, C i i ^ 2 = d i) := by + have hrow : ∀ i : Fin N, (∀ j, i ≠ j → C i j = 0) ∧ C i i ^ 2 = d i := by + intro i + induction i using WellFoundedLT.induction with + | ind i ih => + have hoff : ∀ j, i ≠ j → C i j = 0 := by + intro j hij + rcases lt_or_gt_of_ne hij with hijlt | hjilt + · exact hC i j hijlt + · have hj := ih j hjilt + have hne : C j j ≠ 0 := by + intro he + have := hd j + rw [← hj.2, he] at this + norm_num at this + have hg := congrArg (fun A : Matrix (Fin N) (Fin N) ℝ ↦ A i j) hgram + have hsum : (C * C.transpose) i j = C i j * C j j := by + simp only [mul_apply, transpose_apply] + apply Finset.sum_eq_single j + · intro b _ hbj + rw [hj.1 b hbj.symm, mul_zero] + · simp + rw [hsum, diagonal_apply_ne _ hij] at hg + exact (mul_eq_zero.mp hg).resolve_right hne + refine ⟨hoff, ?_⟩ + have hg := congrArg (fun A : Matrix (Fin N) (Fin N) ℝ ↦ A i i) hgram + have hsum : (C * C.transpose) i i = C i i ^ 2 := by + simp only [mul_apply, transpose_apply] + rw [Finset.sum_eq_single i] + · ring + · intro b _ hbi + rw [hoff b hbi.symm, zero_mul] + · simp + simpa only [hsum, diagonal_apply_eq] using hg + exact ⟨fun i j hij ↦ (hrow i).1 j hij, fun i ↦ (hrow i).2⟩ + +lemma lower_gram_initial_orbit {ε : ℝ} (hε : 0 < ε) (k : Fin N → ℝ) + (hk : ∀ i, 0 < k i) {C : Matrix (Fin N) (Fin N) ℝ} (hC : LowerTriangular C) + (hgram : C * C.transpose = diagonal (fun i ↦ 2 * ε * k i)) : + ∃ s : Fin N → ℝ, (∀ i, s i = 1 ∨ s i = -1) ∧ + C = diagonal (fun i ↦ s i * Real.sqrt (2 * ε * k i)) := by + have hpos (i : Fin N) : 0 < 2 * ε * k i := mul_pos (mul_pos (by norm_num) hε) (hk i) + obtain ⟨hoff, hdiag⟩ := lower_gram_diagonal hC hpos hgram + let s := fun i ↦ C i i / Real.sqrt (2 * ε * k i) + refine ⟨s, ?_, ?_⟩ + · intro i + have hsqrt : 0 < Real.sqrt (2 * ε * k i) := Real.sqrt_pos.2 (hpos i) + have hs : s i ^ 2 = 1 := by + dsimp [s] + rw [div_pow, hdiag i, Real.sq_sqrt (hpos i).le] + exact div_self (ne_of_gt (hpos i)) + rcases (sq_eq_one_iff).mp hs with h | h + · exact Or.inl h + · exact Or.inr h + · ext i j + by_cases hij : i = j + · subst j + rw [diagonal_apply_eq] + dsimp [s] + rw [div_mul_cancel₀ _ (ne_of_gt (Real.sqrt_pos.2 (hpos i)))] + · rw [diagonal_apply_ne _ hij, hoff i j hij] + +/-- Explicit inverse for the initial linearized endpoint map, apart from +its nonzero scalar factor -1/ε. -/ +def triangularLinearInverse (c : Fin N → ℝ) (Z : Matrix (Fin N) (Fin N) ℝ) : + Matrix (Fin N) (Fin N) ℝ := + fun i j ↦ if i < j then 0 else if i = j then Z i j / (2 * c i) else Z i j / c j + +lemma triangularLinearInverse_lower (c : Fin N → ℝ) (Z : Matrix (Fin N) (Fin N) ℝ) : + LowerTriangular (triangularLinearInverse c Z) := by + intro i j hij + simp [triangularLinearInverse, hij] + +lemma triangularLinearInverse_right (c : Fin N → ℝ) (hc : ∀ i, c i ≠ 0) + {Z : Matrix (Fin N) (Fin N) ℝ} (hZ : Z.IsHermitian) : + triangularLinearInverse c Z * (diagonal c).transpose + + diagonal c * (triangularLinearInverse c Z).transpose = Z := by + ext i j + simp only [diagonal_transpose, Matrix.add_apply, mul_diagonal, diagonal_mul, transpose_apply] + rcases lt_trichotomy i j with hij | hij | hij + · have hji : ¬ j < i := not_lt_of_gt hij + have hne : i ≠ j := ne_of_lt hij + have hsym : Z j i = Z i j := by simpa using congrArg (fun A ↦ A i j) hZ + simp [triangularLinearInverse, hij, hji, hne.symm, hsym] + field_simp [hc] + · subst j + simp [triangularLinearInverse] + field_simp [hc] + ring + · have hji : ¬ i < j := not_lt_of_gt hij + have hne : i ≠ j := ne_of_gt hij + simp [triangularLinearInverse, hij, hji, hne] + field_simp [hc] + +end SharpLiebThirring.PathProof + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/BoundState.lean b/lean/OAI/Analysis/LiebThirring/BoundState.lean new file mode 100644 index 0000000000000000000000000000000000000000..8804354db54fa673e53a890f1a4b2795a6de6431 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/BoundState.lean @@ -0,0 +1,651 @@ +import OAI.Analysis.LiebThirring.ActionBounds + +namespace OAI + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +noncomputable section +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder CStarAlgebra +noncomputable section +open MeasureTheory Set Filter +open scoped Topology +open scoped NNReal + + +namespace SharpLiebThirring.ExtremizerProof +open MeasureTheory Set Filter +open scoped Topology ENNReal + +/-- The positive, unnormalized bound state. -/ +def profile (r x : ℝ) : ℝ := (Real.cosh (r * x)) ^ (-1 / r) + +def potential (r x : ℝ) : ℝ := (r + 1) * (Real.cosh (r * x))⁻¹ ^ 2 + +def profileDerivative (r x : ℝ) : ℝ := -Real.tanh (r * x) * profile r x + +lemma profile_pos (r x : ℝ) : 0 < profile r x := + Real.rpow_pos_of_pos (Real.cosh_pos _) _ + +lemma profile_continuous (r : ℝ) : Continuous (profile r) := by + exact (Real.continuous_cosh.comp (continuous_const.mul continuous_id)).rpow_const + (fun _ ↦ Or.inl (ne_of_gt (Real.cosh_pos _))) + +lemma profile_contDiff (r : ℝ) : ContDiff ℝ ⊤ (profile r) := by + exact (Real.contDiff_cosh.comp (contDiff_const.mul contDiff_id)).rpow_const_of_ne + (fun _ ↦ ne_of_gt (Real.cosh_pos _)) + +lemma profile_hasDerivAt {r : ℝ} (hr : 0 < r) (x : ℝ) : + HasDerivAt (profile r) (profileDerivative r x) x := by + have hh := ((Real.hasDerivAt_cosh (r*x)).comp x ((hasDerivAt_id x).const_mul r)).rpow_const (p := -1 / r) + (Or.inl (ne_of_gt (Real.cosh_pos _))) + convert! hh using 1 + unfold profileDerivative profile + simp only [Function.comp_apply] + rw [Real.tanh_eq_sinh_div_cosh, Real.rpow_sub (Real.cosh_pos _), Real.rpow_one] + field_simp + +lemma tanh_hasDerivAt (x : ℝ) : + HasDerivAt Real.tanh ((Real.cosh x)⁻¹ ^ 2) x := by + have hh := (Real.hasDerivAt_sinh x).div (Real.hasDerivAt_cosh x) (ne_of_gt (Real.cosh_pos x)) + convert! hh using 1 + · funext t + exact Real.tanh_eq_sinh_div_cosh t + · have hx := Real.cosh_sq_sub_sinh_sq x + field_simp + nlinarith + +lemma tanh_sq_add_sech_sq (x : ℝ) : + Real.tanh x ^ 2 + (Real.cosh x)⁻¹ ^ 2 = 1 := by + rw [Real.tanh_eq_sinh_div_cosh] + have hx := Real.cosh_sq_sub_sinh_sq x + have hn : Real.cosh x ≠ 0 := ne_of_gt (Real.cosh_pos x) + field_simp + nlinarith + +lemma profileDerivative_hasDerivAt {r : ℝ} (hr : 0 < r) (x : ℝ) : + HasDerivAt (profileDerivative r) ((1 - potential r x) * profile r x) x := by + have ht := (tanh_hasDerivAt (r*x)).comp x ((hasDerivAt_id x).const_mul r) + have hh := ht.neg.mul (profile_hasDerivAt hr x) + convert! hh using 1 + unfold profileDerivative potential + simp only [Function.comp_apply, Pi.neg_apply, mul_one] + have he := congrArg (fun y : ℝ ↦ y * profile r x) (tanh_sq_add_sech_sq (r*x)) + nlinarith + +lemma profileDerivative_continuous (r : ℝ) : Continuous (profileDerivative r) := by + have ht : Continuous Real.tanh := continuous_iff_continuousAt.mpr + (fun x ↦ (tanh_hasDerivAt x).continuousAt) + exact ((ht.comp (continuous_const.mul continuous_id)).neg).mul + (profile_continuous r) + +lemma potential_continuous (r : ℝ) : Continuous (potential r) := by + unfold potential + exact continuous_const.mul (((Real.continuous_cosh.comp (continuous_const.mul continuous_id)).inv₀ + (fun _ ↦ ne_of_gt (Real.cosh_pos _))).pow 2) + +lemma potential_nonneg {r : ℝ} (hr : 0 < r) (x : ℝ) : 0 ≤ potential r x := by + unfold potential + positivity + +lemma cosh_lower_exponential (x : ℝ) : Real.exp |x| / 2 ≤ Real.cosh x := by + rw [← Real.cosh_abs x, Real.cosh_eq] + have hh := Real.exp_pos (-|x|) + linarith + +lemma profile_exponential_bound {r : ℝ} (hr : 0 < r) (x : ℝ) : + profile r x ≤ 2 ^ (1 / r) * Real.exp (-|x|) := by + have he : 0 < Real.exp |r*x| / 2 := by positivity + have hp : -1 / r ≤ 0 := div_nonpos_of_nonpos_of_nonneg (by norm_num) hr.le + have hh := Real.rpow_le_rpow_of_nonpos he (cosh_lower_exponential (r*x)) hp + change (Real.cosh (r*x)) ^ (-1 / r) ≤ _ + apply hh.trans_eq + rw [Real.div_rpow (Real.exp_pos _).le (by norm_num), ← Real.exp_mul, + abs_mul, abs_of_pos hr] + have hmul : r * |x| * (-1 / r) = -|x| := by field_simp + rw [hmul] + have hpow : (2 : ℝ) ^ (-1 / r) = (2 ^ (1 / r))⁻¹ := by + rw [show -1 / r = -(1 / r) by ring, Real.rpow_neg (by norm_num)] + rw [hpow, div_inv_eq_mul, mul_comm] + +lemma profileDerivative_exponential_bound {r : ℝ} (hr : 0 < r) (x : ℝ) : + |profileDerivative r x| ≤ 2 ^ (1 / r) * Real.exp (-|x|) := by + unfold profileDerivative + rw [abs_mul, abs_neg, abs_of_pos (profile_pos r x)] + exact (mul_le_of_le_one_left (profile_pos r x).le (Real.abs_tanh_lt_one _).le).trans + (profile_exponential_bound hr x) + +lemma integrable_exp_neg_abs {c : ℝ} (hc : 0 < c) : + Integrable (fun x : ℝ ↦ Real.exp (-c * |x|)) := by + have hp : IntegrableOn (fun x : ℝ ↦ Real.exp (-c * |x|)) (Ioi 0) := by + apply (integrableOn_exp_mul_Ioi (neg_neg_of_pos hc) 0).congr_fun + · intro x hx + dsimp only + rw [abs_of_pos (show 0 < x from hx)] + · exact measurableSet_Ioi + have hn : IntegrableOn (fun x : ℝ ↦ Real.exp (-c * |x|)) (Iic 0) := by + apply (integrableOn_exp_mul_Iic hc 0).congr_fun + · intro x hx + dsimp only + rw [abs_of_nonpos (show x ≤ 0 from hx)] + congr 1 + ring + · exact measurableSet_Iic + have hh := hn.union hp + simpa using hh + +lemma memLp_exp_neg_abs {p : ℝ≥0∞} (hp : p ≠ 0) (hp' : p ≠ ⊤) : + MemLp (fun x : ℝ ↦ Real.exp (-|x|)) p volume := by + have hc : Continuous (fun x : ℝ ↦ Real.exp (-|x|)) := by fun_prop + apply (integrable_norm_rpow_iff hc.aestronglyMeasurable hp hp').mp + have hh := integrable_exp_neg_abs (ENNReal.toReal_pos hp hp') + convert! hh using 1 + funext x + rw [Real.norm_eq_abs, abs_of_pos (Real.exp_pos _), ← Real.exp_mul] + congr 1 + ring + +lemma profile_memLp (r : ℝ) (hr : 0 < r) {p : ℝ≥0∞} (hp : p ≠ 0) (hp' : p ≠ ⊤) : + MemLp (profile r) p volume := by + apply ((memLp_exp_neg_abs hp hp').const_mul (2 ^ (1 / r))).mono' + (profile_continuous r).aestronglyMeasurable + exact Filter.Eventually.of_forall (fun x ↦ by + rw [Real.norm_eq_abs, abs_of_pos (profile_pos r x)] + exact profile_exponential_bound hr x) + +lemma profileDerivative_memLp (r : ℝ) (hr : 0 < r) {p : ℝ≥0∞} (hp : p ≠ 0) (hp' : p ≠ ⊤) : + MemLp (profileDerivative r) p volume := by + apply ((memLp_exp_neg_abs hp hp').const_mul (2 ^ (1 / r))).mono' + (profileDerivative_continuous r).aestronglyMeasurable + exact Filter.Eventually.of_forall (profileDerivative_exponential_bound hr) + +end SharpLiebThirring.ExtremizerProof + +namespace SharpLiebThirring.SobolevProof +open MeasureTheory Set Filter +open scoped Topology ENNReal ContDiff + +/-- Fixed smooth compact cutoff, equal to one on [-1,1]. -/ +def baseCutoff : ContDiffBump (0 : ℝ) := ⟨1, 2, by norm_num, by norm_num⟩ + +def cutoff (n : ℕ) (x : ℝ) : ℝ := baseCutoff ((n + 1 : ℝ)⁻¹ * x) + +def cutoffDerivative (n : ℕ) (x : ℝ) : ℝ := + deriv (baseCutoff : ℝ → ℝ) ((n + 1 : ℝ)⁻¹ * x) * (n + 1 : ℝ)⁻¹ + +lemma baseCutoff_smooth : ContDiff ℝ ∞ (baseCutoff : ℝ → ℝ) := baseCutoff.contDiff + +lemma scale_pos (n : ℕ) : 0 < (n + 1 : ℝ) := by positivity + +lemma cutoff_contDiff (n : ℕ) : ContDiff ℝ ∞ (cutoff n) := + baseCutoff_smooth.comp (contDiff_const.mul contDiff_id) + +lemma cutoff_compact (n : ℕ) : HasCompactSupport (cutoff n) := by + change HasCompactSupport (fun x : ℝ ↦ baseCutoff ((n + 1 : ℝ)⁻¹ * x)) + simpa only [smul_eq_mul] using baseCutoff.hasCompactSupport.comp_smul + (inv_ne_zero (ne_of_gt (scale_pos n))) + +lemma cutoff_hasDerivAt (n : ℕ) (x : ℝ) : + HasDerivAt (cutoff n) (cutoffDerivative n x) x := by + change HasDerivAt (fun y : ℝ ↦ baseCutoff ((n + 1 : ℝ)⁻¹ * y)) + (deriv (baseCutoff : ℝ → ℝ) ((n + 1 : ℝ)⁻¹ * x) * (n + 1 : ℝ)⁻¹) x + convert! + (((baseCutoff_smooth.differentiable (by norm_num)) _).hasDerivAt.comp x + ((hasDerivAt_id x).const_mul (n + 1 : ℝ)⁻¹)) using 1; simp only [id_eq, mul_one] + +lemma cutoffDerivative_continuous (n : ℕ) : Continuous (cutoffDerivative n) := by + exact (((baseCutoff_smooth.continuous_deriv (by norm_num)).comp + (continuous_const.mul continuous_id)).mul continuous_const) + +lemma cutoff_bound (n : ℕ) (x : ℝ) : |cutoff n x| ≤ 1 := by + unfold cutoff + rw [abs_of_nonneg (baseCutoff.nonneg)] + exact baseCutoff.le_one + +lemma scale_tendsto : Tendsto (fun n : ℕ ↦ (n + 1 : ℝ)⁻¹) atTop (𝓝 0) := by + simpa only [one_div] using (tendsto_one_div_add_atTop_nhds_zero_nat (𝕜 := ℝ)) + +lemma cutoff_tendsto (x : ℝ) : Tendsto (fun n : ℕ ↦ cutoff n x) atTop (𝓝 1) := by + have hh := baseCutoff_smooth.continuous.continuousAt.tendsto.comp + (scale_tendsto.mul_const x) + have hb : (baseCutoff : ℝ → ℝ) 0 = 1 := by + apply baseCutoff.one_of_mem_closedBall + simp [baseCutoff, Metric.mem_closedBall] + change Tendsto (fun n : ℕ ↦ baseCutoff ((n + 1 : ℝ)⁻¹ * x)) atTop (𝓝 1) + convert! hh using 1; simp only [zero_mul, hb] + +lemma cutoffDerivative_uniform_bound : ∃ D : ℝ, 0 ≤ D ∧ + ∀ n x, |cutoffDerivative n x| ≤ D := by + obtain ⟨D, hD⟩ := baseCutoff.hasCompactSupport.deriv.exists_bound_of_continuous + (baseCutoff_smooth.continuous_deriv (by norm_num)) + have hD0 : 0 ≤ D := (norm_nonneg _).trans (hD 0) + refine ⟨D, hD0, fun n x ↦ ?_⟩ + unfold cutoffDerivative + rw [abs_mul, abs_of_pos (inv_pos.mpr (scale_pos n))] + have hi : (n + 1 : ℝ)⁻¹ ≤ 1 := by + apply inv_le_one_of_one_le₀ + norm_num + exact (mul_le_mul_of_nonneg_right (hD _) (inv_pos.mpr (scale_pos n)).le).trans + (mul_le_of_le_one_right hD0 hi) + +lemma cutoffDerivative_tendsto (x : ℝ) : + Tendsto (fun n : ℕ ↦ cutoffDerivative n x) atTop (𝓝 0) := by + have hh := (baseCutoff_smooth.continuous_deriv (by norm_num)).continuousAt.tendsto.comp + (scale_tendsto.mul_const x) + simpa [cutoffDerivative] using hh.mul scale_tendsto + +/-- Dominated convergence for a uniformly bounded multiplier of an L¹ function. -/ +lemma integral_multiplier_tendsto {a : ℕ → ℝ → ℂ} {l : ℂ} {g : ℝ → ℂ} + (hg : Integrable g) (ha : ∀ n, AEStronglyMeasurable (a n) volume) + {D : ℝ} (_hD : 0 ≤ D) (hb : ∀ n x, ‖a n x‖ ≤ D) + (hl : ∀ x, Tendsto (fun n ↦ a n x) atTop (𝓝 l)) : + Tendsto (fun n ↦ ∫ x : ℝ, a n x * g x) atTop (𝓝 (∫ x : ℝ, l * g x)) := by + apply tendsto_integral_of_dominated_convergence (fun x ↦ D * ‖g x‖) + · exact fun n ↦ (ha n).mul hg.aestronglyMeasurable + · exact hg.norm.const_mul D + · intro n + exact Filter.Eventually.of_forall (fun x ↦ by + rw [norm_mul] + exact mul_le_mul_of_nonneg_right (hb n x) (norm_nonneg _)) + · exact Filter.Eventually.of_forall (fun x ↦ (hl x).mul_const (g x)) + +end SharpLiebThirring.SobolevProof + +namespace SharpLiebThirring.SobolevProof +open MeasureTheory Set Filter +open scoped Topology ENNReal ContDiff + +/-- Extend the distributional H¹ identity from compactly supported tests to +smooth L² tests with L² classical derivative. No pointwise representative of +an arbitrary H¹ element is assumed. -/ +lemma weak_derivative_smooth_L2 (v : H1) {f f' : ℝ → ℂ} + (hf : ContDiff ℝ ∞ f) (hd : ∀ x, HasDerivAt f (f' x) x) + (hf2 : MemLp f 2 volume) (hf'2 : MemLp f' 2 volume) : + (∫ x : ℝ, v.val x * f' x) = -(∫ x : ℝ, v.grad x * f x) := by + have hg0 : Integrable (fun x ↦ v.val x * f x) := v.val_memLp.integrable_mul hf2 + have hg1 : Integrable (fun x ↦ v.val x * f' x) := v.val_memLp.integrable_mul hf'2 + have hg2 : Integrable (fun x ↦ v.grad x * f x) := v.grad_memLp.integrable_mul hf2 + obtain ⟨D, hD, hDb⟩ := cutoffDerivative_uniform_bound + have hc (n : ℕ) : ContDiff ℝ ∞ (fun x ↦ (cutoff n x : ℂ)) := + Complex.ofRealCLM.contDiff.comp (cutoff_contDiff n) + have hcm (n : ℕ) : AEStronglyMeasurable (fun x ↦ (cutoff n x : ℂ)) volume := + (hc n).continuous.aestronglyMeasurable + have hdm (n : ℕ) : AEStronglyMeasurable (fun x ↦ (cutoffDerivative n x : ℂ)) volume := + (Complex.continuous_ofReal.comp (cutoffDerivative_continuous n)).aestronglyMeasurable + have hcb (n : ℕ) (x : ℝ) : ‖(cutoff n x : ℂ)‖ ≤ 1 := by + simpa only [Complex.norm_real, Real.norm_eq_abs] using cutoff_bound n x + have hdb (n : ℕ) (x : ℝ) : ‖(cutoffDerivative n x : ℂ)‖ ≤ D := by + simpa only [Complex.norm_real, Real.norm_eq_abs] using hDb n x + have hcl (x : ℝ) : Tendsto (fun n ↦ (cutoff n x : ℂ)) atTop (𝓝 1) := by + exact_mod_cast Complex.continuous_ofReal.continuousAt.tendsto.comp (cutoff_tendsto x) + have hdl (x : ℝ) : Tendsto (fun n ↦ (cutoffDerivative n x : ℂ)) atTop (𝓝 0) := by + exact_mod_cast Complex.continuous_ofReal.continuousAt.tendsto.comp (cutoffDerivative_tendsto x) + have h0 := integral_multiplier_tendsto hg0 hdm hD hdb hdl + have h1 := integral_multiplier_tendsto hg1 hcm (by norm_num : (0 : ℝ) ≤ 1) hcb hcl + have h2 := integral_multiplier_tendsto hg2 hcm (by norm_num : (0 : ℝ) ≤ 1) hcb hcl + simp only [zero_mul, one_mul, integral_zero] at h0 h1 h2 + have heq (n : ℕ) : + (∫ x : ℝ, (cutoffDerivative n x : ℂ) * (v.val x * f x)) + + (∫ x : ℝ, (cutoff n x : ℂ) * (v.val x * f' x)) = + -(∫ x : ℝ, (cutoff n x : ℂ) * (v.grad x * f x)) := by + let φ : ℝ → ℂ := fun x ↦ (cutoff n x : ℂ) * f x + have hφ : ContDiff ℝ ∞ φ := (hc n).mul hf + have hcc : HasCompactSupport (fun x ↦ (cutoff n x : ℂ)) := + (cutoff_compact n).comp_left (g := Complex.ofReal) Complex.ofReal_zero + have hφc : HasCompactSupport φ := hcc.mul_right + have hφd (x : ℝ) : deriv φ x = + (cutoffDerivative n x : ℂ) * f x + (cutoff n x : ℂ) * f' x := by + exact (((cutoff_hasDerivAt n x).ofReal_comp).mul (hd x)).deriv + have hh := v.weak_derivative φ hφ hφc + have hi0 := hg0.bdd_mul (hdm n) (Filter.Eventually.of_forall (hdb n)) + have hi1 := hg1.bdd_mul (hcm n) (Filter.Eventually.of_forall (hcb n)) + rw [← integral_add hi0 hi1] + calc + _ = ∫ x : ℝ, v.val x * deriv φ x := by + apply integral_congr_ae + exact Filter.Eventually.of_forall (fun x ↦ by dsimp only; rw [hφd]; ring) + _ = -(∫ x : ℝ, v.grad x * φ x) := hh + _ = _ := by + congr 1 + apply integral_congr_ae + exact Filter.Eventually.of_forall (fun x ↦ by dsimp [φ]; ring) + have he : Tendsto (fun n ↦ -(∫ x : ℝ, (cutoff n x : ℂ) * (v.grad x * f x))) + atTop (𝓝 (∫ x : ℝ, v.val x * f' x)) := by + simpa only [zero_add] using (h0.add h1).congr (fun n ↦ heq n) + exact tendsto_nhds_unique he h2.neg + +end SharpLiebThirring.SobolevProof + +namespace SharpLiebThirring.SobolevProof +open MeasureTheory +open scoped ContDiff + +/-- Classical smooth L² functions with L² derivative belong to the exact weak H¹ domain. -/ +def smoothH1 (f f' : ℝ → ℂ) (hf : ContDiff ℝ ∞ f) + (hd : ∀ x, HasDerivAt f (f' x) x) (hfc : Continuous f') + (hf2 : MemLp f 2 volume) (hf'2 : MemLp f' 2 volume) : H1 where + val := f + grad := f' + val_memLp := hf2 + grad_memLp := hf'2 + weak_derivative := by + intro φ hφ hφc + apply integral_mul_deriv_eq_deriv_mul_of_integrable + · exact fun x _ ↦ hd x + · exact fun x _ ↦ ((hφ.differentiable (by norm_num)) x).hasDerivAt + · exact (hf.continuous.mul (hφ.continuous_deriv (by norm_num))).integrable_of_hasCompactSupport + hφc.deriv.mul_left + · exact (hfc.mul hφ.continuous).integrable_of_hasCompactSupport hφc.mul_left + · exact (hf.continuous.mul hφ.continuous).integrable_of_hasCompactSupport hφc.mul_left + +end SharpLiebThirring.SobolevProof + +namespace SharpLiebThirring.ExtremizerProof +open MeasureTheory Set Filter +open scoped Topology ENNReal ContDiff + +lemma potential_le {r : ℝ} (hr : 0 < r) (x : ℝ) : potential r x ≤ r + 1 := by + have hi : (Real.cosh (r*x))⁻¹ ≤ 1 := inv_le_one_of_one_le₀ (Real.one_le_cosh _) + have hi0 : 0 ≤ (Real.cosh (r*x))⁻¹ := inv_nonneg.mpr (Real.cosh_pos _).le + have hs : (Real.cosh (r*x))⁻¹ ^ 2 ≤ 1 := by nlinarith + exact mul_le_of_le_one_right (by linarith) hs + +lemma potential_contDiff (r : ℝ) : ContDiff ℝ ∞ (potential r) := by + unfold potential + exact contDiff_const.mul + (((Real.contDiff_cosh.comp (contDiff_const.mul contDiff_id)).inv + (fun _ ↦ ne_of_gt (Real.cosh_pos _))).pow 2) + +lemma profileDerivative_contDiff (r : ℝ) : ContDiff ℝ ∞ (profileDerivative r) := by + have ht : ContDiff ℝ ∞ Real.tanh := by + convert! (Real.contDiff_sinh.div Real.contDiff_cosh + (fun _ ↦ ne_of_gt (Real.cosh_pos _))) using 1 + funext t + exact Real.tanh_eq_sinh_div_cosh t + exact ((ht.comp (contDiff_const.mul contDiff_id)).neg).mul + ((profile_contDiff r).of_le le_top) + +def profileSecond (r x : ℝ) : ℝ := (1 - potential r x) * profile r x + +lemma profileSecond_continuous (r : ℝ) : Continuous (profileSecond r) := + (continuous_const.sub (potential_continuous r)).mul (profile_continuous r) + +lemma profileSecond_memLp (r : ℝ) (hr : 0 < r) : MemLp (profileSecond r) 2 volume := by + apply ((profile_memLp r hr (p := 2) (by norm_num) (by norm_num)).const_mul (r + 2)).mono' + (profileSecond_continuous r).aestronglyMeasurable + exact Filter.Eventually.of_forall (fun x ↦ by + rw [profileSecond, Real.norm_eq_abs, abs_mul, abs_of_pos (profile_pos r x)] + apply mul_le_mul_of_nonneg_right _ (profile_pos r x).le + have hW := potential_nonneg hr x + have hW' := potential_le hr x + apply abs_le.mpr + constructor <;> linarith) + +/-- The exact unnormalized extremizing bound state, as an element of the weak form domain. -/ +def boundState (r : ℝ) (hr : 0 < r) : H1 := + SobolevProof.smoothH1 (fun x ↦ (profile r x : ℂ)) (fun x ↦ (profileDerivative r x : ℂ)) + (Complex.ofRealCLM.contDiff.comp ((profile_contDiff r).of_le le_top)) + (fun x ↦ (profile_hasDerivAt hr x).ofReal_comp) + (Complex.continuous_ofReal.comp (profileDerivative_continuous r)) + (profile_memLp r hr (by norm_num) (by norm_num)).ofReal + (profileDerivative_memLp r hr (by norm_num) (by norm_num)).ofReal + +lemma boundState_weak_ode {r : ℝ} (hr : 0 < r) (v : H1) : + (∫ x : ℝ, star (v.grad x) * (profileDerivative r x : ℂ)) = + -(∫ x : ℝ, star (v.val x) * (profileSecond r x : ℂ)) := by + have hh := SobolevProof.weak_derivative_smooth_L2 v + (f := fun x ↦ (profileDerivative r x : ℂ)) + (f' := fun x ↦ (profileSecond r x : ℂ)) + (Complex.ofRealCLM.contDiff.comp (profileDerivative_contDiff r)) + (fun x ↦ (profileDerivative_hasDerivAt hr x).ofReal_comp) + (profileDerivative_memLp r hr (by norm_num) (by norm_num)).ofReal + (profileSecond_memLp r hr).ofReal + have hc := congrArg (starRingEnd ℂ) hh + simp only [map_neg, ← integral_conj, map_mul, Complex.conj_ofReal] at hc + change (∫ x : ℝ, star (v.val x) * (profileSecond r x : ℂ)) = + -(∫ x : ℝ, star (v.grad x) * (profileDerivative r x : ℂ)) at hc + exact (neg_eq_iff_eq_neg.mpr hc).symm + +lemma boundState_negativeEigenfunction {r : ℝ} (hr : 0 < r) : + IsNegativeEigenfunction (potential r) 1 (boundState r hr) := by + refine ⟨by norm_num, fun v ↦ ?_⟩ + have hψ := (profile_memLp r hr (p := 2) (by norm_num) (by norm_num)).ofReal (K := ℂ) + have hi : Integrable (fun x ↦ star (v.val x) * (profile r x : ℂ)) := + v.val_memLp.star.integrable_mul hψ + have hWm : AEStronglyMeasurable (fun x ↦ (potential r x : ℂ)) volume := + (Complex.continuous_ofReal.comp (potential_continuous r)).aestronglyMeasurable + have hWb : ∀ᵐ x : ℝ, ‖(potential r x : ℂ)‖ ≤ r + 1 := by + exact Filter.Eventually.of_forall (fun x ↦ by + rw [Complex.norm_real, Real.norm_eq_abs, abs_of_nonneg (potential_nonneg hr x)] + exact potential_le hr x) + have hiW := hi.bdd_mul hWm hWb + change (∫ x : ℝ, star (v.grad x) * (profileDerivative r x : ℂ)) - + (∫ x : ℝ, (potential r x : ℂ) * star (v.val x) * (profile r x : ℂ)) = + -(1 ^ 2 : ℝ) * (∫ x : ℝ, star (v.val x) * (profile r x : ℂ)) + rw [boundState_weak_ode hr] + have hs : (∫ x : ℝ, star (v.val x) * (profileSecond r x : ℂ)) = + (∫ x : ℝ, star (v.val x) * (profile r x : ℂ)) - + (∫ x : ℝ, (potential r x : ℂ) * (star (v.val x) * (profile r x : ℂ))) := by + rw [← integral_sub hi hiW] + apply integral_congr_ae + exact Filter.Eventually.of_forall (fun x ↦ by + simp only [profileSecond, Complex.ofReal_mul, Complex.ofReal_sub, Complex.ofReal_one] + ring) + rw [hs] + simp only [mul_assoc, one_pow, Complex.ofReal_one, neg_mul, one_mul] + ring + +end SharpLiebThirring.ExtremizerProof + +namespace SharpLiebThirring +open MeasureTheory + +/-- Scalar multiplication in the weak form domain, without choosing pointwise representatives. -/ +def scaleH1 (c : ℂ) (u : H1) : H1 where + val := fun x ↦ c * u.val x + grad := fun x ↦ c * u.grad x + val_memLp := u.val_memLp.const_mul c + grad_memLp := u.grad_memLp.const_mul c + weak_derivative := by + intro φ hφ hφc + simp only [mul_assoc, integral_const_mul, u.weak_derivative φ hφ hφc, mul_neg] + +lemma l2Pairing_scale_both (c : ℂ) (u : H1) : + l2Pairing (scaleH1 c u) (scaleH1 c u) = star c * c * l2Pairing u u := by + change (∫ x : ℝ, star (c * u.val x) * (c * u.val x)) = _ + simp only [star_mul] + have he (x : ℝ) : star (u.val x) * star c * (c * u.val x) = + (star c * c) * (star (u.val x) * u.val x) := by ring + simp_rw [he] + exact integral_const_mul _ _ + +lemma l2Pairing_scale_right (c : ℂ) (v u : H1) : + l2Pairing v (scaleH1 c u) = c * l2Pairing v u := by + change (∫ x : ℝ, star (v.val x) * (c * u.val x)) = _ + simp_rw [show ∀ a b : ℂ, a * (c * b) = c * (a*b) by intros; ring] + exact integral_const_mul _ _ + +lemma schrodingerForm_scale_right (W : ℝ → ℝ) (c : ℂ) (v u : H1) : + schrodingerForm W v (scaleH1 c u) = c * schrodingerForm W v u := by + change (∫ x : ℝ, star (v.grad x) * (c * u.grad x)) - + (∫ x : ℝ, (W x : ℂ) * star (v.val x) * (c * u.val x)) = _ + simp_rw [show ∀ a b : ℂ, a * (c * b) = c * (a*b) by intros; ring] + rw [integral_const_mul, integral_const_mul] + exact (mul_sub _ _ _).symm + +lemma IsNegativeEigenfunction.scale {W : ℝ → ℝ} {k : ℝ} {u : H1} + (hu : IsNegativeEigenfunction W k u) (c : ℂ) : + IsNegativeEigenfunction W k (scaleH1 c u) := by + refine ⟨hu.1, fun v ↦ ?_⟩ + rw [schrodingerForm_scale_right, l2Pairing_scale_right, hu.2 v] + ring + +lemma oneStateMoment_le_negativeMoment (γ : ℝ) (W : ℝ → ℝ) : + oneStateMoment γ W ≤ negativeMoment γ W := by + unfold oneStateMoment + refine iSup_le (fun u ↦ iSup_le (fun k ↦ iSup_le (fun hnorm ↦ iSup_le (fun hneg ↦ ?_)))) + have hu : IsOrthonormalFamily (fun _ : Fin 1 ↦ u) := by + intro i j + have hij : i = j := Subsingleton.elim _ _ + simp [hij, hnorm] + unfold negativeMoment + apply le_iSup_of_le 1 + apply le_iSup_of_le (fun _ : Fin 1 ↦ u) + apply le_iSup_of_le (fun _ : Fin 1 ↦ k) + apply le_iSup_of_le hu + apply le_iSup_of_le (fun _ : Fin 1 ↦ hneg) + simp + +lemma oneStateConstant_le_optimalConstant (γ : ℝ) : + oneStateConstant γ ≤ optimalConstant γ := by + unfold oneStateConstant + refine iSup_le (fun W ↦ iSup_le (fun hW ↦ iSup_le (fun hpos ↦ ?_))) + unfold optimalConstant + apply le_iSup_of_le W + apply le_iSup_of_le hW + apply le_iSup_of_le hpos + exact ENNReal.div_le_div_right (oneStateMoment_le_negativeMoment γ W) _ + +end SharpLiebThirring + +namespace SharpLiebThirring.ExtremizerProof +open MeasureTheory + +lemma profile_norm_integrable {r : ℝ} (hr : 0 < r) : + Integrable (fun x : ℝ ↦ profile r x ^ 2) := by + convert! + (profile_memLp r hr (p := 2) (by norm_num) (by norm_num)).integrable_mul + (profile_memLp r hr (p := 2) (by norm_num) (by norm_num)) using 1 + funext x + simp only [pow_two, Pi.mul_apply] + +lemma profile_norm_pos {r : ℝ} (hr : 0 < r) : + 0 < ∫ x : ℝ, profile r x ^ 2 := by + apply (integral_pos_iff_support_of_nonneg (fun x ↦ sq_nonneg _) (profile_norm_integrable hr)).mpr + have hs : Function.support (fun x : ℝ ↦ profile r x ^ 2) = Set.univ := by + ext x + simp only [Function.mem_support, Set.mem_univ, iff_true] + exact (sq_pos_of_pos (profile_pos r x)).ne' + rw [hs] + simp + +lemma boundState_l2Pairing {r : ℝ} (hr : 0 < r) : + l2Pairing (boundState r hr) (boundState r hr) = + ((∫ x : ℝ, profile r x ^ 2) : ℝ) := by + change (∫ x : ℝ, star (profile r x : ℂ) * (profile r x : ℂ)) = _ + have ht : (fun x : ℝ ↦ star (profile r x : ℂ) * (profile r x : ℂ)) = + (fun x : ℝ ↦ ((profile r x ^ 2 : ℝ) : ℂ)) := by + funext x + simp only [Complex.star_def, Complex.conj_ofReal, pow_two, Complex.ofReal_mul] + rw [ht] + exact integral_ofReal (𝕜 := ℂ) + +def normalizedBoundState (r : ℝ) (hr : 0 < r) : H1 := + scaleH1 (((Real.sqrt (∫ x : ℝ, profile r x ^ 2))⁻¹ : ℝ) : ℂ) (boundState r hr) + +lemma normalizedBoundState_norm {r : ℝ} (hr : 0 < r) : + l2Pairing (normalizedBoundState r hr) (normalizedBoundState r hr) = 1 := by + rw [normalizedBoundState, l2Pairing_scale_both, boundState_l2Pairing hr] + simp only [Complex.star_def, Complex.conj_ofReal, ← Complex.ofReal_mul] + norm_cast + have hpos := profile_norm_pos hr + have hs := Real.sq_sqrt hpos.le + have hn : Real.sqrt (∫ x : ℝ, profile r x ^ 2) ≠ 0 := ne_of_gt (Real.sqrt_pos.mpr hpos) + field_simp + nlinarith + +lemma normalizedBoundState_eigenfunction {r : ℝ} (hr : 0 < r) : + IsNegativeEigenfunction (potential r) 1 (normalizedBoundState r hr) := + (boundState_negativeEigenfunction hr).scale _ + +lemma one_le_oneStateMoment {r : ℝ} (hr : 0 < r) (γ : ℝ) : + 1 ≤ oneStateMoment γ (potential r) := by + unfold oneStateMoment + apply le_iSup_of_le (normalizedBoundState r hr) + apply le_iSup_of_le 1 + apply le_iSup_of_le (normalizedBoundState_norm hr) + apply le_iSup_of_le (normalizedBoundState_eigenfunction hr) + simp + +lemma one_le_negativeMoment {r : ℝ} (hr : 0 < r) (γ : ℝ) : + 1 ≤ negativeMoment γ (potential r) := + (one_le_oneStateMoment hr γ).trans (oneStateMoment_le_negativeMoment γ (potential r)) + +end SharpLiebThirring.ExtremizerProof + +namespace SharpLiebThirring.ExtremizerProof +open MeasureTheory Set Filter +open scoped ENNReal Topology + +lemma memLp_exp_neg_mul_abs {c : ℝ} (hc : 0 < c) {p : ℝ≥0∞} + (hp : p ≠ 0) (hp' : p ≠ ⊤) : + MemLp (fun x : ℝ ↦ Real.exp (-c * |x|)) p volume := by + have hm : Continuous (fun x : ℝ ↦ Real.exp (-c * |x|)) := by fun_prop + apply (integrable_norm_rpow_iff hm.aestronglyMeasurable hp hp').mp + have hi := integrable_exp_neg_abs (mul_pos hc (ENNReal.toReal_pos hp hp')) + convert! hi using 1 + funext x + rw [Real.norm_eq_abs, abs_of_pos (Real.exp_pos _), ← Real.exp_mul] + congr 1 + ring + +lemma cosh_inv_exponential_bound (x : ℝ) : + (Real.cosh x)⁻¹ ≤ 2 * Real.exp (-|x|) := by + apply (inv_le_iff_one_le_mul₀ (Real.cosh_pos x)).mpr + have hh := mul_le_mul_of_nonneg_right (cosh_lower_exponential x) (Real.exp_pos (-|x|)).le + have he : Real.exp |x| * Real.exp (-|x|) = 1 := by rw [← Real.exp_add]; simp + nlinarith + +lemma potential_exponential_bound {r : ℝ} (hr : 0 < r) (x : ℝ) : + potential r x ≤ 4 * (r + 1) * Real.exp (-(2*r) * |x|) := by + have hi0 : 0 ≤ (Real.cosh (r*x))⁻¹ := inv_nonneg.mpr (Real.cosh_pos _).le + have hh := pow_le_pow_left₀ hi0 (cosh_inv_exponential_bound (r*x)) 2 + have he : (2 * Real.exp (-|r*x|)) ^ 2 = 4 * Real.exp (-(2*r) * |x|) := by + rw [mul_pow, ← Real.exp_nat_mul, abs_mul, abs_of_pos hr] + congr 2 <;> ring + rw [he] at hh + exact (mul_le_mul_of_nonneg_left hh (by linarith : 0 ≤ r + 1)).trans_eq (by ring) + +lemma potential_memLp {r : ℝ} (hr : 0 < r) {p : ℝ≥0∞} + (hp : p ≠ 0) (hp' : p ≠ ⊤) : MemLp (potential r) p volume := by + apply ((memLp_exp_neg_mul_abs (by positivity : 0 < 2*r) hp hp').const_mul + (4 * (r + 1))).mono' (potential_continuous r).aestronglyMeasurable + exact Filter.Eventually.of_forall (fun x ↦ by + rw [Real.norm_eq_abs, abs_of_nonneg (potential_nonneg hr x)] + exact potential_exponential_bound hr x) + +lemma equalityPotential_admissible {γ : ℝ} (hγ : 1 / 2 < γ) : + Admissible γ (equalityPotential γ) := by + have hr : 0 < (γ - 1 / 2)⁻¹ := inv_pos.mpr (by linarith) + constructor + · exact Filter.Eventually.of_forall (fun x ↦ potential_nonneg hr x) + · exact potential_memLp hr (ne_of_gt (ENNReal.ofReal_pos.mpr (by linarith))) ENNReal.ofReal_ne_top + +lemma potential_pos {r : ℝ} (hr : 0 < r) (x : ℝ) : 0 < potential r x := by + unfold potential + positivity + +lemma potential_mass_pos {γ r : ℝ} (hr : 0 < r) : + 0 < potentialMass γ (potential r) := by + unfold potentialMass + have hm : Measurable (fun x : ℝ ↦ (ENNReal.ofReal (potential r x)) ^ (γ + 1/2)) := + ((potential_continuous r).measurable.ennreal_ofReal).pow_const _ + apply (lintegral_pos_iff_support hm).mpr + have hs : Function.support (fun x : ℝ ↦ (ENNReal.ofReal (potential r x)) ^ (γ + 1/2)) = Set.univ := by + apply Function.support_eq_univ + intro x + exact (ENNReal.rpow_pos (ENNReal.ofReal_pos.mpr (potential_pos hr x)) ENNReal.ofReal_ne_top).ne' + rw [hs] + simp + +end SharpLiebThirring.ExtremizerProof + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/BoundaryParity.lean b/lean/OAI/Analysis/LiebThirring/BoundaryParity.lean new file mode 100644 index 0000000000000000000000000000000000000000..956138a5bc7829ddb400310a66759635bcbd2298 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/BoundaryParity.lean @@ -0,0 +1,452 @@ +import OAI.Analysis.LiebThirring.FreeLocus + +namespace OAI + +universe u136 u137 u138 u139 u140 u141 u142 + +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Finset + + +namespace SharpLiebThirring.CubeFlags +open Finset SharpLiebThirring.PLParity + +lemma bottom_hit_unique {d : ℕ} (H : Subgroup (Signs (d + 1))) + (hHt : ∀ s : H, s.val.val (Fin.last d) = false) + (D : SubMulAction H (Flag (d + 1))) + {V : Type u136} [NormedAddCommGroup V] [NormedSpace ℝ V] + (ρ : H →* (V ≃ₗ[ℝ] V)) (L : (Fin d → ℝ) ≃ₗ[ℝ] V) + (p q : Fin d → ℝ) (R h : ℝ) (hR : 0 < R) (hh : 0 < h) (hhr : h ≤ R / 2) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • embedSpatial p) (k • embedSpatial p)) + (a : vertices H D → V) + (haf : ∀ F : D, ∀ k, gridPoint h (F.val.vertex k) (Fin.last d) = 0 → + gridPoint h (F.val.vertex k) ∈ orbitBall (G := H) (embedSpatial p) R → + a (flagVertex H D F k) = affineOrbitModel H ρ L (embedSpatial p) R q (gridPoint h (F.val.vertex k))) + (w₀ : Fin (d + 2) → ℝ) (hw₀ : ∀ k, 0 ≤ w₀ k) + (hwp : ∀ k, k ≠ Fin.last (d + 1) → 0 < w₀ k) (hs₀ : ∑ k, w₀ k = 1) + (he₀ : (bottomSeed h p).combination h w₀ = embedSpatial q) + (F : D) (ht : (F.val.order.symm (Fin.last d)).val = d) + (hb : F.val.base (Fin.last d) = 0) (hc : F.val.corner (Fin.last d) = false) + (w : Fin (d + 2) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) + (hj : w (Fin.last (d + 1)) = 0) (hz : ∑ k, w k • a (flagVertex H D F k) = 0) + (hx : F.val.combination h w ∈ orbitBall (G := H) (embedSpatial p) (R / 2)) : + ∃ s : H, F.val = s • bottomSeed h p := by + obtain ⟨s,hxs⟩ := hx + have hdist (k : Fin (d + 2)) : dist (gridPoint h (F.val.vertex k)) (s • embedSpatial p) < R := by + calc + _ ≤ dist (gridPoint h (F.val.vertex k)) (F.val.combination h w) + + dist (F.val.combination h w) (s • embedSpatial p) := dist_triangle _ _ _ + _ < h + R / 2 := add_lt_add_of_le_of_lt + (by rw [dist_comm]; exact F.val.dist_combination_gridPoint h hh.le w hw hs k) hxs + _ ≤ R := by linarith + have htime (k : Fin (d + 2)) (hk : k ≠ Fin.last (d + 1)) : + gridPoint h (F.val.vertex k) (Fin.last d) = 0 := by + rw [gridPoint_vertex] + change h * F.val.point k (Fin.last d) = 0 + rw [F.val.point_time_boundary (Fin.last d) (by simpa using ht) k hk, hb, hc] + simp + have hlabel (k : Fin (d + 2)) : + ballLabel (G := H) (embedSpatial p) R (gridPoint h (F.val.vertex k)) = s := + ballLabel_eq (embedSpatial p) R hR hsep (hdist k) + have hval (k : Fin (d + 2)) (hk : k ≠ Fin.last (d + 1)) : + a (flagVertex H D F k) = ρ s (L (spatial (s⁻¹ • gridPoint h (F.val.vertex k)) - q)) := by + rw [haf F k (htime k hk) ⟨s,hdist k⟩] + simp only [affineOrbitModel, hlabel] + have hxt : F.val.combination h w (Fin.last d) = 0 := by + rw [F.val.combination_time_boundary h (Fin.last d) (by simpa using ht) w hs hj, hb, hc] + simp + have hxq := mesh_affine_zero_point H ρ L F.val _ h s q w hs hj + (fun k ↦ a (flagVertex H D F k)) hz hval hxt + exact ⟨s, bottom_facet_unique h hh.ne' p q s.val (hHt s) F.val hb hc + w₀ w hw₀ hwp hw hs₀ hs he₀ hxq⟩ + +/-- Finite equivariant parity rules out a bounded approximating cylinder whose +only boundary hits lie in the one initial root orbit. -/ +lemma mesh_parity_contradiction {d : ℕ} (H : Subgroup (Signs (d + 1))) + (hHt : ∀ s : H, s.val.val (Fin.last d) = false) + (D : SubMulAction H (Flag (d + 1))) [Fintype D] + {V : Type u137} [NormedAddCommGroup V] [NormedSpace ℝ V] [FiniteDimensional ℝ V] + (ρ : H →* (V ≃ₗ[ℝ] V)) (L : (Fin d → ℝ) ≃ₗ[ℝ] V) + (p q : Fin d → ℝ) (R h : ℝ) (hR : 0 < R) (hh : 0 < h) (hhr : 2*h < R) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • embedSpatial p) (k • embedSpatial p)) + (a : vertices H D → V) (ha : ∀ s : H, ∀ z, a (s • z) = ρ s (a z)) + (haug : ∀ F : D, ∀ j : Fin (d + 2), LinearIndependent ℝ + (fun k : {k // k ≠ j} ↦ ((1 : ℝ), a (flagVertex H D F k)))) + (hvec : ∀ F : D, ∀ i j : Fin (d + 2), i ≠ j → LinearIndependent ℝ + (fun k : {k // k ≠ i ∧ k ≠ j} ↦ a (flagVertex H D F k))) + (hfree : ∀ z : vertices H D, ∀ s : H, s • gridPoint h z.val = gridPoint h z.val → s = 1) + (haf : ∀ F : D, ∀ k, gridPoint h (F.val.vertex k) (Fin.last d) = 0 → + gridPoint h (F.val.vertex k) ∈ orbitBall (G := H) (embedSpatial p) R → + a (flagVertex H D F k) = affineOrbitModel H ρ L (embedSpatial p) R q (gridPoint h (F.val.vertex k))) + (F₀ : D) (hF₀ : F₀.val = bottomSeed h p) + (hout₀ : F₀.val.neighbor (Fin.last (d + 1)) ∉ D) + (w₀ : Fin (d + 2) → ℝ) (hw₀ : ∀ k, 0 ≤ w₀ k) + (hwp : ∀ k, k ≠ Fin.last (d + 1) → 0 < w₀ k) (hs₀ : ∑ k, w₀ k = 1) + (hj₀ : w₀ (Fin.last (d + 1)) = 0) + (he₀ : (bottomSeed h p).combination h w₀ = embedSpatial q) + (hbdy : ∀ F : D, ∀ j : Fin (d + 2), F.val.neighbor j ∉ D → + ∀ w : Fin (d + 2) → ℝ, (∀ k, 0 ≤ w k) → ∑ k, w k = 1 → w j = 0 → + ∑ k, w k • a (flagVertex H D F k) = 0 → + j = Fin.last (d + 1) ∧ (F.val.order.symm (Fin.last d)).val = d ∧ + F.val.base (Fin.last d) = 0 ∧ F.val.corner (Fin.last d) = false ∧ + F.val.combination h w ∈ orbitBall (G := H) (embedSpatial p) (R / 2)) : False := by + have hseed : cellHit H D a F₀.val (Fin.last (d + 1)) := by + apply model_seed_hit H D ρ L p q R h hR hh hhr hsep F₀ hF₀ a + (fun k hk ↦ haf F₀ k ?_ ?_) w₀ hw₀ hs₀ hj₀ + · rw [hF₀, ← Flag.combination_eq_sum_gridPoint] + exact he₀ + · rw [hF₀, gridPoint_vertex] + change h * (bottomSeed h p).point k (Fin.last d) = 0 + rw [bottomSeed_time h p k hk, mul_zero] + · refine ⟨1,?_⟩ + rw [one_smul, hF₀, gridPoint_vertex] + exact (bottomSeed_dist_point h hh p k).trans_lt hhr + let p₀ : FinitePairing.selected D (cellHit H D a) (cellHit_equivariant H D ρ a ha) := + ⟨⟨F₀, Fin.last (d + 1)⟩, hseed⟩ + have hdim : d + 1 = Module.finrank ℝ V + 1 := by + have he := L.finrank_eq + simpa only [Module.finrank_fintype_fun_eq_card, Fintype.card_fin] using congrArg (· + 1) he + obtain ⟨b,hb,hborb⟩ := another_boundary H D ρ a ha hdim haug hvec h hfree p₀ hout₀ + obtain ⟨w,hw,hs,hj,hz⟩ := cellHit_weights H D a b.val.cell b.val.facet b.prop + obtain ⟨hjl,ht,hbase,hcorner,hx⟩ := hbdy b.val.cell b.val.facet hb w hw hs hj hz + have hj' : w (Fin.last (d + 1)) = 0 := hjl ▸ hj + obtain ⟨s,hF⟩ := bottom_hit_unique H hHt D ρ L p q R h hR hh (by linarith) hsep + a haf w₀ hw₀ hwp hs₀ he₀ b.val.cell ht hbase hcorner w hw hs hj' hz hx + apply hborb + apply MulAction.orbitRel_apply.mpr + apply MulAction.mem_orbit_iff.mpr + refine ⟨s,?_⟩ + apply Subtype.ext + apply FinitePairing.CellFacet.ext + · apply Subtype.ext + change s • F₀.val = b.val.cell.val + rw [hF₀, hF] + · exact hjl.symm + +end SharpLiebThirring.CubeFlags + +namespace SharpLiebThirring.CubeFlags +open Finset SharpLiebThirring.PLParity +attribute [local instance] Classical.propDecidable + +lemma fixed_initial_vectors {d : ℕ} + (H : Subgroup (Signs (d + 1))) (D : SubMulAction H (Flag (d + 1))) + {V : Type u138} [NormedAddCommGroup V] [NormedSpace ℝ V] + (ρ : H →* (V ≃ₗ[ℝ] V)) (L : (Fin d → ℝ) ≃ₗ[ℝ] V) + (p : Fin (d + 1) → ℝ) (R h : ℝ) (hR : 0 < R) (hh : 0 < h) (hhr : h ≤ R) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • p) (k • p)) + (P : vertices H D → Prop) + (hb : ∀ z : vertices H D, P z → gridPoint h z.val ∈ orbitBall (G := H) p R) + (q : Fin d → ℝ) (F : D) (i j : Fin (d + 2)) + (hq : ∀ s : H, LinearIndependent ℝ + (fun k : {k : {k : Fin (d + 2) // k ≠ i ∧ k ≠ j} // P (flagVertex H D F k.val)} ↦ + spatial (s⁻¹ • gridPoint h (F.val.vertex k.val.val)) - q)) : + LinearIndependent ℝ (fun k : {k : {k : Fin (d + 2) // k ≠ i ∧ k ≠ j} // + P (flagVertex H D F k.val)} ↦ + affineOrbitModel H ρ L p R q (gridPoint h (F.val.vertex k.val.val))) := by + obtain ⟨s,hs⟩ := common_flag_label H p R h hR hh hhr hsep F.val + (fun k ↦ P (flagVertex H D F k)) (fun k hk ↦ hb (flagVertex H D F k) hk) + exact affineOrbitModel_independent H ρ L p R q + (fun k : {k : {k : Fin (d + 2) // k ≠ i ∧ k ≠ j} // P (flagVertex H D F k.val)} ↦ + gridPoint h (F.val.vertex k.val.val)) s (fun k ↦ hs k.val.val k.prop) (hq s) + +lemma generic_initial_approximation {d : ℕ} + (H : Subgroup (Signs (d + 1))) (D : SubMulAction H (Flag (d + 1))) + [Fintype D] [IsCancelSMul H (vertices H D)] + {V : Type u139} [NormedAddCommGroup V] [NormedSpace ℝ V] [FiniteDimensional ℝ V] + (ρ : H →* (V ≃ₗ[ℝ] V)) (L : (Fin d → ℝ) ≃ₗ[ℝ] V) + (hρ : ∀ s : H, ∀ v : V, ‖ρ s v‖ = ‖v‖) + (p : Fin d → ℝ) (R h η : ℝ) (hR : 0 < R) (hh : 0 < h) (hhr : h ≤ R) (hη : 0 < η) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • embedSpatial p) (k • embedSpatial p)) + (hbnd : ∀ q, dist (embedSpatial q) (embedSpatial p) ≤ 2*h → dist (L q) (L p) < η) + (f : (Fin (d + 1) → ℝ) → V) (hf : ∀ s : H, ∀ x, f (s • x) = ρ s (f x)) + (hmodel : ∀ x, x (Fin.last d) = 0 → x ∈ orbitBall (G := H) (embedSpatial p) R → + f x = affineOrbitModel H ρ L (embedSpatial p) R p x) : + ∃ (q : Fin d → ℝ) (w : Fin (d + 2) → ℝ) (a : vertices H D → V), + (∀ k, 0 ≤ w k) ∧ (∀ k, k ≠ Fin.last (d + 1) → 0 < w k) ∧ + ∑ k, w k = 1 ∧ w (Fin.last (d + 1)) = 0 ∧ + (bottomSeed h p).combination h w = embedSpatial q ∧ + (∀ s : H, ∀ z, a (s • z) = ρ s (a z)) ∧ + (∀ z, dist (a z) (f (gridPoint h z.val)) < 2*η) ∧ + (∀ z, gridPoint h z.val (Fin.last d) = 0 → + gridPoint h z.val ∈ orbitBall (G := H) (embedSpatial p) R → + a z = affineOrbitModel H ρ L (embedSpatial p) R q (gridPoint h z.val)) ∧ + (∀ F : D, ∀ j : Fin (d + 2), LinearIndependent ℝ + (fun k : {k // k ≠ j} ↦ ((1 : ℝ), a (flagVertex H D F k)))) ∧ + (∀ F : D, ∀ i j : Fin (d + 2), i ≠ j → LinearIndependent ℝ + (fun k : {k // k ≠ i ∧ k ≠ j} ↦ a (flagVertex H D F k))) := by + classical + let P : vertices H D → Prop := fun z ↦ gridPoint h z.val (Fin.last d) = 0 ∧ + gridPoint h z.val ∈ orbitBall (G := H) (embedSpatial p) R + have hP : ∀ s : H, ∀ z, P (s • z) ↔ P z := by + intro s z + suffices hs : ∀ s : H, ∀ z, P z → P (s • z) from + ⟨fun hz ↦ by simpa only [inv_smul_smul] using hs s⁻¹ (s • z) hz, hs s z⟩ + intro s z hz + change gridPoint h (s.val • z.val) (Fin.last d) = 0 ∧ + gridPoint h (s.val • z.val) ∈ orbitBall (G := H) (embedSpatial p) R + rw [gridPoint_smul] + exact ⟨s.val.smul_time_zero _ hz.1, orbitBall_smul (embedSpatial p) R s hz.2⟩ + obtain ⟨U,hU,hUn,hUw⟩ := bottomSeed_open_roots h hh p + obtain ⟨q,hq,hqg⟩ := exists_generic_initial_root H D h hh.ne' P (fun _ hz ↦ hz.1) U hU hUn + obtain ⟨w,hw,hwp,hs,hj,he,hd⟩ := hUw q hq + let b : vertices H D → V := fun z ↦ if P z then + affineOrbitModel H ρ L (embedSpatial p) R q (gridPoint h z.val) else f (gridPoint h z.val) + have hb : ∀ s : H, ∀ z, b (s • z) = ρ s (b z) := by + intro s z + dsimp only [b] + by_cases hz : P z + · rw [ite_eq_left hz, ite_eq_left ((hP s z).mpr hz)] + change affineOrbitModel H ρ L (embedSpatial p) R q (gridPoint h (s.val • z.val)) = _ + rw [gridPoint_smul] + exact affineOrbitModel_smul H ρ L (embedSpatial p) R hR hsep q s hz.2 + · rw [ite_eq_right hz, ite_eq_right (fun hs ↦ hz ((hP s z).mp hs))] + change f (gridPoint h (s.val • z.val)) = _ + rw [gridPoint_smul] + exact hf s _ + have hbfix (z : vertices H D) (hz : P z) : b z = + affineOrbitModel H ρ L (embedSpatial p) R q (gridPoint h z.val) := ite_eq_left hz + have haug : ∀ F : D, ∀ j : Fin (d + 2), LinearIndependent ℝ + (fun k : {k : {k : Fin (d + 2) // k ≠ j} // P (flagVertex H D F k.val)} ↦ + ((1 : ℝ), b (flagVertex H D F k.val.val))) := by + intro F j + convert fixed_initial_augmented H D ρ L (embedSpatial p) R h hR hh hhr hsep P + (fun _ hz ↦ hz.1) (fun _ hz ↦ hz.2) q F j using 1 + funext k + rw [hbfix _ k.prop] + rfl + have hvec : ∀ F : D, ∀ i j : Fin (d + 2), i ≠ j → LinearIndependent ℝ + (fun k : {k : {k : Fin (d + 2) // k ≠ i ∧ k ≠ j} // P (flagVertex H D F k.val)} ↦ + b (flagVertex H D F k.val.val)) := by + intro F i j hij + convert fixed_initial_vectors H D ρ L (embedSpatial p) R h hR hh hhr hsep P + (fun _ hz ↦ hz.2) q F i j (hqg F i j hij) using 1 + funext k + rw [hbfix _ k.prop] + rfl + have hdim : d + 1 = Module.finrank ℝ V + 1 := by + have hdim := L.finrank_eq + simpa only [Module.finrank_fintype_fun_eq_card, Fintype.card_fin] using congrArg (· + 1) hdim + obtain ⟨a,ha,hab,haf,hag,hvg⟩ := generic_on_complex H D ρ hdim P hP b hb haug hvec η hη + refine ⟨q,w,a,hw,hwp,hs,hj,?_,ha,?_,?_,hag,hvg⟩ + · rw [Flag.combination_eq_sum_gridPoint] + exact he + · intro z + have hbf : dist (b z) (f (gridPoint h z.val)) < η := by + by_cases hz : P z + · rw [hbfix z hz, hmodel _ hz.1 hz.2, affineOrbitModel_dist H ρ L _ _ hρ] + exact hbnd q hd + · simp only [b, ite_eq_right hz, dist_self] + exact hη + have ht := dist_triangle (a z) (b z) (f (gridPoint h z.val)) + linarith [hab z] + · intro z ht hz + exact (haf z ⟨ht,hz⟩).trans (hbfix z ⟨ht,hz⟩) + +end SharpLiebThirring.CubeFlags + +namespace SharpLiebThirring.CubeFlags +open Finset SharpLiebThirring.PLParity + +lemma mesh_boundary_bottom {d : ℕ} + (K : Set (Fin (d + 1) → ℝ)) (h r : ℝ) (hh : 0 < h) (hhr : h < r) + (m : ℕ) (hm : h * m = 1) (F : Flag (d + 1)) + (hF : F ∈ nearCylinder K h r (Fin.last d) m) (j : Fin (d + 2)) + (hout : F.neighbor j ∉ nearCylinder K h r (Fin.last d) m) + (w : Fin (d + 2) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) (hj : w j = 0) + (hx : F.combination h w ∈ Metric.thickening (r/2) K) + (htop : F.combination h w (Fin.last d) < 1) : + j = Fin.last (d + 1) ∧ (F.order.symm (Fin.last d)).val = d ∧ + F.base (Fin.last d) = 0 ∧ F.corner (Fin.last d) = false := by + have hn := neighbor_near_centers_of_combination K h r hh.le hhr F j w hw hs hj + (Metric.mem_thickening_iff.mp hx) + have hnt : ¬ (0 ≤ (F.neighbor j).base (Fin.last d) ∧ + (F.neighbor j).base (Fin.last d) < (m : ℤ)) := + fun ht ↦ hout ⟨hn,ht⟩ + obtain ⟨hjl,ht,hbc⟩ := F.neighbor_outside_time j (Fin.last d) m hF.2.1 hF.2.2 hnt + refine ⟨hjl,by simpa using ht,?_⟩ + rcases hbc with hbot | htop' + · exact hbot + · have hj' : w (Fin.last (d + 1)) = 0 := hjl ▸ hj + have he := F.combination_time_boundary h (Fin.last d) ht w hs hj' + simp only [htop'.1, htop'.2, ↓reduceIte, Int.cast_sub, Int.cast_natCast, + Int.cast_one, sub_add_cancel, hm] at he + linarith + +lemma isOpen_orbitBall {G : Type u140} {E : Type u141} [Group G] [MulAction G E] [MetricSpace E] + (p : E) (R : ℝ) : IsOpen (orbitBall (G := G) p R) := by + have he : orbitBall (G := G) p R = ⋃ s : G, Metric.ball (s • p) R := by + ext x + simp only [orbitBall, Set.mem_ofPred_eq, Set.mem_iUnion, Metric.mem_ball] + rw [he] + exact isOpen_iUnion (fun _ ↦ Metric.isOpen_ball) + +lemma dist_spatial_le {d : ℕ} (x y : Fin (d + 1) → ℝ) : + dist (spatial x) (spatial y) ≤ dist x y := by + rw [dist_pi_le_iff dist_nonneg] + intro i + exact dist_le_pi_dist x y i.castSucc + +lemma exists_positive_mesh (δ : ℝ) (hδ : 0 < δ) : + ∃ m : ℕ, ∃ h : ℝ, 0 < m ∧ 0 < h ∧ h < δ ∧ h * m = 1 := by + obtain ⟨n,hn⟩ := exists_nat_one_div_lt hδ + refine ⟨n+1,1 / ((n : ℝ)+1), Nat.succ_pos _, by positivity,hn,?_⟩ + push_cast + exact div_mul_cancel₀ 1 (by positivity) + +lemma bottomSeed_mem_nearCylinder {d : ℕ} (K : Set (Fin (d + 1) → ℝ)) + (p : Fin d → ℝ) (hp : embedSpatial p ∈ K) (h r : ℝ) (hh : 0 < h) (hhr : h < r) + (m : ℕ) (hm : 0 < m) : bottomSeed h p ∈ nearCylinder K h r (Fin.last d) m := by + refine ⟨⟨embedSpatial p,hp,(bottomSeed_dist_center h hh p).trans_lt hhr⟩,?_,?_⟩ + · simp [bottomSeed] + · simpa only [bottomSeed,Fin.snoc_last] using (Int.natCast_pos.mpr hm) + +lemma bottomSeed_neighbor_not_mem {d : ℕ} (K : Set (Fin (d + 1) → ℝ)) + (p : Fin d → ℝ) (h r : ℝ) (m : ℕ) : + (bottomSeed h p).neighbor (Fin.last (d + 1)) ∉ nearCylinder K h r (Fin.last d) m := by + intro hb + have hn : ((bottomSeed h p).neighbor (Fin.last (d + 1))).base (Fin.last d) = -1 := by + simp only [Flag.neighbor, Fin.val_last, Nat.add_eq_zero_iff, Nat.one_ne_zero, + and_false, dite_eq_left, bottomSeed, Flag.cross, Equiv.refl_apply, + Bool.false_eq_true, ↓reduceIte] + change Function.update _ (Fin.last d) _ (Fin.last d) = -1 + simp only [Function.update_self] + have hi : (⟨d + 1 - 1, by omega⟩ : Fin (d + 1)) = Fin.last d := Fin.ext (by simp only [Fin.val_last]; omega) + rw [hi, Fin.snoc_last, zero_add] + have hneg := hb.2.1 + rw [hn] at hneg + exact (by norm_num : ¬ (0 : ℤ) ≤ -1) hneg + +end SharpLiebThirring.CubeFlags + +namespace SharpLiebThirring.CubeFlags +open Finset SharpLiebThirring.PLParity + +/-- The exact continuation principle needed below, first for an affine initial +model in disjoint neighborhoods of its one free zero orbit. The proof uses +finite equivariant PL perturbation and mod-two boundary pairing. -/ +theorem exists_terminal_zero_affine {d : ℕ} + (H : Subgroup (Signs (d + 1))) (hHt : ∀ s : H, s.val.val (Fin.last d) = false) + {V : Type u142} [NormedAddCommGroup V] [NormedSpace ℝ V] [FiniteDimensional ℝ V] + (ρ : H →* (V ≃ₗ[ℝ] V)) (L : (Fin d → ℝ) ≃ₗ[ℝ] V) + (hρ : ∀ s : H, ∀ v : V, ‖ρ s v‖ = ‖v‖) + (p : Fin d → ℝ) (R : ℝ) (hR : 0 < R) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • embedSpatial p) (k • embedSpatial p)) + (f : (Fin (d + 1) → ℝ) → V) + (hf : ContinuousOn f {x | x (Fin.last d) ∈ Set.Icc (0 : ℝ) 1}) + (hfe : ∀ s : H, ∀ x, f (s • x) = ρ s (f x)) + (hmodel : ∀ x, x (Fin.last d) = 0 → x ∈ orbitBall (G := H) (embedSpatial p) R → + f x = affineOrbitModel H ρ L (embedSpatial p) R p x) + (hz0 : ∀ x, x (Fin.last d) = 0 → f x = 0 → ∃ s : H, s • embedSpatial p = x) + (hK : IsCompact {x | x (Fin.last d) ∈ Set.Icc (0 : ℝ) 1 ∧ f x = 0}) + (hfree : ∀ x, x (Fin.last d) ∈ Set.Icc (0 : ℝ) 1 → f x = 0 → + ∀ s : H, s • x = x → s = 1) : + ∃ x : Fin (d + 1) → ℝ, x (Fin.last d) = 1 ∧ f x = 0 := by + classical + by_contra hterm + let K := {x : Fin (d + 1) → ℝ | x (Fin.last d) ∈ Set.Icc (0 : ℝ) 1 ∧ f x = 0} + have hp0 : (embedSpatial p) (Fin.last d) = 0 := by + change Fin.snoc (α := fun _ : Fin (d + 1) ↦ ℝ) p 0 (Fin.last d) = 0 + simp only [Fin.snoc_last] + have fp0 : f (embedSpatial p) = 0 := by + rw [hmodel _ hp0 ⟨1,by simpa using hR⟩] + have hl : ballLabel (G := H) (embedSpatial p) R (embedSpatial p) = 1 := + ballLabel_eq _ _ hR hsep (by simpa using hR) + simp only [affineOrbitModel,hl,inv_one,one_smul,spatial_embed,sub_self,map_zero] + have hpK : embedSpatial p ∈ K := ⟨by rw [hp0]; exact ⟨le_refl _,zero_le_one⟩,fp0⟩ + have hKfree : K ⊆ freeLocus (G := H) := fun x hx ↦ hfree x hx.1 hx.2 + obtain ⟨r₀,hr₀,hrt⟩ := compact_free_tube (G := H) hK hKfree + let r := r₀ / 4 + have hr : 0 < r := by dsimp [r]; positivity + let C := Metric.cthickening r₀ K ∩ {x | x (Fin.last d) ∈ Set.Icc (0 : ℝ) 1} + have hC : IsCompact C := hK.cthickening.inter_right + (isClosed_Icc.preimage (continuous_apply (Fin.last d))) + let U := Metric.thickening (r/2) K ∩ {x | x (Fin.last d) < 1} ∩ + ({x | x (Fin.last d) ≠ 0} ∪ orbitBall (G := H) (embedSpatial p) (R/2)) + have hU : IsOpen U := (Metric.isOpen_thickening.inter + (isOpen_lt (continuous_apply _) continuous_const)).inter + ((isOpen_ne_fun (continuous_apply _) continuous_const).union (isOpen_orbitBall _ _)) + have hCU : ∀ x ∈ C, f x = 0 → x ∈ U := by + intro x hx hfx + have hxK : x ∈ K := ⟨hx.2,hfx⟩ + refine ⟨⟨Metric.mem_thickening_iff.mpr ⟨x,hxK,by simp; positivity⟩,?_⟩,?_⟩ + · exact lt_of_le_of_ne hx.2.2 (fun he ↦ hterm ⟨x,he,hfx⟩) + · by_cases ht : x (Fin.last d) = 0 + · obtain ⟨s,rfl⟩ := hz0 x ht hfx + exact Or.inr ⟨s,by simp; positivity⟩ + · exact Or.inl ht + obtain ⟨ε,hε,hsmall⟩ := small_norm_near_zeros hC hU f (hf.mono Set.inter_subset_right) hCU + obtain ⟨δ,hδ,hδf⟩ := Metric.uniformContinuousOn_iff.mp + (hC.uniformContinuousOn_of_continuous (hf.mono Set.inter_subset_right)) (ε/4) (by positivity) + have hLc : ContinuousAt (fun x : Fin (d + 1) → ℝ ↦ L (spatial x)) (embedSpatial p) := + (L.toContinuousLinearEquiv.continuous.comp spatial.continuous_of_finiteDimensional).continuousAt + obtain ⟨δL,hδL,hδLf⟩ := Metric.continuousAt_iff.mp hLc (ε/8) (by positivity) + obtain ⟨m,h,hm,hh,hbound,hhm⟩ := exists_positive_mesh + (min (r/4) (min (R/4) (min δ (δL/4)))) (by positivity) + have hhr : h < r/4 := (lt_min_iff.mp hbound).1 + have hhR : h < R/4 := (lt_min_iff.mp (lt_min_iff.mp hbound).2).1 + have hhδ : h < δ := (lt_min_iff.mp (lt_min_iff.mp (lt_min_iff.mp hbound).2).2).1 + have hhδL : h < δL/4 := (lt_min_iff.mp (lt_min_iff.mp (lt_min_iff.mp hbound).2).2).2 + have hsize : r + h/2 ≤ r₀ := by dsimp [r] at *; linarith + have hKs : ∀ s : H, ∀ x ∈ K, s • x ∈ K := by + intro s x hx + constructor + · change (if s.val.val (Fin.last d) then -x (Fin.last d) else x (Fin.last d)) ∈ _ + simpa only [hHt s,Bool.false_eq_true,↓reduceIte] using hx.1 + · rw [hfe,hx.2,map_zero] + let D : SubMulAction H (Flag (d + 1)) := + ⟨nearCylinder K h r (Fin.last d) m, + fun s _ hF ↦ nearCylinder_smul K h r (Fin.last d) m s.val (hHt s) (hKs s) hF⟩ + let : Fintype D := (finite_nearCylinder hK.isBounded h r hh (Fin.last d) m).fintype + have hpoint : ∀ F : D, ∀ k, gridPoint h (F.val.vertex k) ∈ C := by + intro F k + rw [gridPoint_vertex] + exact ⟨Metric.cthickening_mono hsize K + (nearCylinder_point_cthickening K h r hh.le (Fin.last d) m F.prop k), + nearCylinder_point_time K h r hh.le (Fin.last d) m hhm F.prop k⟩ + have hvfree : ∀ z : vertices H D, ∀ s : H, s • gridPoint h z.val = gridPoint h z.val → s = 1 := by + intro z s hs + obtain ⟨F,k,hFk⟩ := z.prop + have hmem : gridPoint h z.val ∈ Metric.cthickening r₀ K := by + rw [← hFk] + exact (hpoint F k).1 + exact hrt hmem s hs + let : IsCancelSMul H (vertices H D) := verticesIsCancel H D h hvfree + obtain ⟨q,w₀,a,hw₀,hwp,hs₀,hj₀,he₀,ha,hap,haf,haug,hvec⟩ := + generic_initial_approximation H D ρ L hρ p R h (ε/8) hR hh (by linarith) (by positivity) + hsep (fun q hqp ↦ by + have hdq : dist (embedSpatial q) (embedSpatial p) < δL := by linarith + simpa only [spatial_embed] using hδLf hdq) f hfe hmodel + let F₀ : D := ⟨bottomSeed h p, bottomSeed_mem_nearCylinder K p hpK h r hh (by linarith) m hm⟩ + apply mesh_parity_contradiction H hHt D ρ L p q R h hR hh (by linarith) hsep + a ha haug hvec hvfree (fun F k ht hb ↦ haf (flagVertex H D F k) ht hb) + F₀ rfl (bottomSeed_neighbor_not_mem K p h r m) w₀ hw₀ hwp hs₀ hj₀ he₀ + intro F j hout w hw hs hj hz + have hxC : F.val.combination h w ∈ C := + ⟨Metric.cthickening_mono hsize K + (nearCylinder_combination_cthickening K h r hh.le (Fin.last d) m F.prop w hw hs), + nearCylinder_combination_time K h r hh.le (Fin.last d) m hhm F.prop w hw hs⟩ + have hn := norm_at_mesh_zero H D a f h (ε/4) (ε/4) hh.le C + (fun z ↦ by have hz := hap z; linarith) + (fun x hx y hy hxy ↦ (hδf x hx y hy (hxy.trans_lt hhδ)).le) + F w hw hs hz hxC (hpoint F) + have hxU := hsmall _ hxC (by linarith : ‖f (F.val.combination h w)‖ < ε) + obtain ⟨hjl,ht,hbase,hcorner⟩ := mesh_boundary_bottom K h r hh (by linarith) m hhm + F.val F.prop j hout w hw hs hj hxU.1.1 hxU.1.2 + refine ⟨hjl,ht,hbase,hcorner,?_⟩ + have htime : F.val.combination h w (Fin.last d) = 0 := by + rw [F.val.combination_time_boundary h (Fin.last d) (by simpa using ht) w hs (hjl ▸ hj)] + simp only [hbase,hcorner,Int.cast_zero,Bool.false_eq_true,↓reduceIte,add_zero,mul_zero] + exact hxU.2.resolve_left (fun hne ↦ hne htime) + +end SharpLiebThirring.CubeFlags + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/BoundaryValues.lean b/lean/OAI/Analysis/LiebThirring/BoundaryValues.lean new file mode 100644 index 0000000000000000000000000000000000000000..d9c7281c8faf294ad000054c0b282bc2cdc2ec6a --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/BoundaryValues.lean @@ -0,0 +1,286 @@ +import OAI.Analysis.LiebThirring.ActionPenalty + +namespace OAI + +universe u36 + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +noncomputable section +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder CStarAlgebra +noncomputable section +open MeasureTheory Set Filter +open scoped Topology +open scoped NNReal + +namespace SharpLiebThirring.MatrixProof +open Matrix ScalarProof MeasureTheory Filter +open scoped Matrix.Norms.L2Operator Topology +variable {n : Type u36} [Fintype n] [DecidableEq n] + +omit [Fintype n] in +lemma quadraticMatrix_diagonal (c b : n → ℝ) (s : ℝ) : + quadraticMatrix (diagonal (fun i ↦ (c i : ℂ))) (diagonal (fun i ↦ (b i : ℂ))) s = + diagonal (fun i ↦ (((s - b i) ^ 2 + (c i - b i ^ 2) : ℝ) : ℂ)) := by + ext i j + by_cases hij : i = j + · subst j + simp only [quadraticMatrix, Matrix.add_apply, Matrix.sub_apply, Matrix.smul_apply, + diagonal_apply_eq, one_apply_eq, Complex.real_smul] + push_cast + ring + · simp [quadraticMatrix, hij] + +lemma fieldIntegrand_diagonal {δ : ℝ} (hδ : 0 < δ) (σ : ℝ) (c b : n → ℝ) (s : ℝ) : + fieldIntegrand σ δ (diagonal (fun i ↦ (c i : ℂ))) (diagonal (fun i ↦ (b i : ℂ))) s = + diagonal (fun i ↦ ((regularizedPrimitive σ δ ((s - b i) ^ 2 + (c i - b i ^ 2)) - + regularizedPrimitive σ δ (s ^ 2) : ℝ) : ℂ)) := by + rw [fieldIntegrand, quadraticMatrix_diagonal, + cfc_diagonal_real _ _ (primitive_differentiable σ hδ).continuous] + ext i j + by_cases hij : i = j <;> simp [hij, Complex.real_smul] + +lemma hermitianField_diagonal {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (c b : n → ℝ) : + hermitianField σ δ (diagonal (fun i ↦ (c i : ℂ))) (diagonal (fun i ↦ (b i : ℂ))) = + diagonal (fun i ↦ (scalarMu σ δ (c i - b i ^ 2) : ℂ)) := by + have hC : (diagonal (fun i ↦ (c i : ℂ))).IsHermitian := isHermitian_diagonal_iff.2 (fun i ↦ by simp [IsSelfAdjoint]) + have hB : (diagonal (fun i ↦ (b i : ℂ))).IsHermitian := isHermitian_diagonal_iff.2 (fun i ↦ by simp [IsSelfAdjoint]) + apply tendsto_nhds_unique (hermitianField_cutoff_limit hσ hδ hC hB) + apply tendsto_pi_nhds.2 + intro i + apply tendsto_pi_nhds.2 + intro j + have hc := continuous_fieldIntegrand hδ σ hC hB + have he (R : ℝ) := (entryCLM i j).intervalIntegral_comp_comm (μ := volume) + (hc.intervalIntegrable (-R) R) + simp only [entryCLM_apply] at he + have he' (R : ℝ) : + (fieldNormalization σ • ∫ s in -R..R, fieldIntegrand σ δ + (diagonal (fun i ↦ (c i : ℂ))) (diagonal (fun i ↦ (b i : ℂ))) s) i j = + fieldNormalization σ • ∫ s in -R..R, fieldIntegrand σ δ + (diagonal (fun i ↦ (c i : ℂ))) (diagonal (fun i ↦ (b i : ℂ))) s i j := by + simp only [Matrix.smul_apply] + rw [← he R] + suffices ht : Tendsto (fun R : ℝ ↦ fieldNormalization σ • ∫ s in -R..R, + fieldIntegrand σ δ (diagonal (fun i ↦ (c i : ℂ))) + (diagonal (fun i ↦ (b i : ℂ))) s i j) atTop + (𝓝 ((diagonal (fun i ↦ (scalarMu σ δ (c i - b i ^ 2) : ℂ))) i j)) by + apply ht.congr + intro R + exact (he' R).symm + simp only [fieldIntegrand_diagonal hδ] + by_cases hij : i = j + · subst j + simp only [diagonal_apply_eq] + have hs := Complex.continuous_ofReal.continuousAt.tendsto.comp + (primitive_shift_limit hσ hδ (c i - b i ^ 2) (b i)) + convert! hs using 1 + funext R + rw [intervalIntegral.integral_ofReal] + simp [Complex.real_smul] + · simp only [diagonal_apply_ne _ hij, intervalIntegral.integral_zero, smul_zero] + exact tendsto_const_nhds + +lemma matrixField_diagonal {N : ℕ} {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (k b : Fin N → ℝ) : + matrixField σ δ k (diagonal b) = diagonal (fun i ↦ scalarMu σ δ (k i ^ 2 - b i ^ 2)) := by + rw [matrixField_eq_realPart hσ hδ k (isHermitian_diagonal b), + complexify_diagonal, complexify_diagonal, hermitianField_diagonal hσ hδ] + ext i j + by_cases hij : i = j <;> simp [realPartCLM, hij] + +lemma continuous_scalarMu {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) : + Continuous (scalarMu σ δ) := + continuous_iff_continuousAt.mpr (fun _ ↦ (mu_hasDerivAt_integral hσ hδ _).continuousAt) + +lemma fieldPrimitive_diagonal {N : ℕ} {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (k b : Fin N → ℝ) : + fieldPrimitive σ δ k (diagonal b) = + -(∑ i, ∫ s in (0 : ℝ)..b i, scalarMu σ δ (k i ^ 2 - s ^ 2)) := by + have hc := continuous_scalarMu hσ hδ + have he (t : ℝ) : trace (diagonal b * matrixField σ δ k (t • diagonal b)) = + ∑ i, b i * scalarMu σ δ (k i ^ 2 - (t * b i) ^ 2) := by + rw [← diagonal_smul, matrixField_diagonal hσ hδ] + simp [trace, diag] + unfold fieldPrimitive + simp_rw [he] + congr 1 + rw [intervalIntegral.integral_finsetSum] + · apply Finset.sum_congr rfl + intro i _ + rw [intervalIntegral.integral_const_mul] + exact_mod_cast (by simpa using (intervalIntegral.smul_integral_comp_mul_right + (fun s : ℝ ↦ scalarMu σ δ (k i ^ 2 - s ^ 2)) (a := 0) (b := 1) (b i))) + · intro i _ + exact (by fun_prop : Continuous (fun t : ℝ ↦ b i * scalarMu σ δ (k i ^ 2 - (t * b i) ^ 2))).intervalIntegrable _ _ + +lemma fieldPrimitive_endpoint_jump {N : ℕ} {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (k : Fin N → ℝ) : + fieldPrimitive σ δ k (-diagonal k) - fieldPrimitive σ δ k (diagonal k) = + ∑ i, ∫ s in -(k i)..k i, scalarMu σ δ (k i ^ 2 - s ^ 2) := by + rw [diagonal_neg, fieldPrimitive_diagonal hσ hδ, fieldPrimitive_diagonal hσ hδ] + rw [neg_sub_neg, ← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro i _ + have hc : Continuous (fun s : ℝ ↦ scalarMu σ δ (k i ^ 2 - s ^ 2)) := by + have := continuous_scalarMu hσ hδ + fun_prop + rw [intervalIntegral.integral_interval_sub_left (hc.intervalIntegrable _ _) (hc.intervalIntegrable _ _)] + +end SharpLiebThirring.MatrixProof +namespace SharpLiebThirring.MatrixProof +open Matrix ScalarProof MeasureTheory Filter Set +open scoped Matrix.Norms.L2Operator Topology + +lemma scalar_boundary_regularized {σ δ k : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (hk : 0 ≤ k) : + (∫ s in -k..k, scalarMu σ δ (k ^ 2 - s ^ 2)) = + ∫ s in -k..k, (k ^ 2 - s ^ 2 + δ) ^ σ - δ ^ σ := by + apply intervalIntegral.integral_congr + intro s hs + rw [Set.uIcc_of_le (by linarith : -k ≤ k)] at hs + exact mu_eq_nonneg hσ hδ (by nlinarith [mul_nonneg (sub_nonneg.2 hs.2) (show 0 ≤ k + s by linarith [hs.1])]) + +lemma scalar_boundary_limit {σ k : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hk : 0 ≤ k) : + Tendsto (fun δ : ℝ ↦ ∫ s in -k..k, scalarMu σ δ (k ^ 2 - s ^ 2)) + (𝓝[>] 0) (𝓝 (∫ s in -k..k, (k ^ 2 - s ^ 2) ^ σ)) := by + have hc : Continuous (fun δ : ℝ ↦ ∫ s in -k..k, (k ^ 2 - s ^ 2 + δ) ^ σ - δ ^ σ) := by + simp_rw [intervalIntegral.integral_of_le (by linarith : -k ≤ k), ← integral_Icc_eq_integral_Ioc] + apply continuous_parametric_integral_of_continuous _ isCompact_Icc + exact ((Real.continuous_rpow_const hσ₀.le).comp (by fun_prop)).sub + ((Real.continuous_rpow_const hσ₀.le).comp (by fun_prop)) + have ht := (hc.continuousAt (x := (0 : ℝ))).tendsto.mono_left (nhdsWithin_le_nhds (s := Ioi 0)) + simp only [add_zero, Real.zero_rpow hσ₀.ne', sub_zero] at ht + apply ht.congr' + filter_upwards [self_mem_nhdsWithin] with δ hδ + exact (scalar_boundary_regularized hσ₁ hδ hk).symm + +lemma fieldPrimitive_endpoint_limit {N : ℕ} {σ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (k : Fin N → ℝ) (hk : ∀ i, 0 ≤ k i) : + Tendsto (fun δ : ℝ ↦ fieldPrimitive σ δ k (-diagonal k) - fieldPrimitive σ δ k (diagonal k)) + (𝓝[>] 0) (𝓝 (∑ i, ∫ s in -(k i)..k i, (k i ^ 2 - s ^ 2) ^ σ)) := by + have h := tendsto_finsetSum Finset.univ (fun i _ ↦ scalar_boundary_limit hσ₀ hσ₁ (hk i)) + apply h.congr' + filter_upwards [self_mem_nhdsWithin] with δ hδ + exact (fieldPrimitive_endpoint_jump hσ₁ hδ k).symm + +end SharpLiebThirring.MatrixProof +namespace SharpLiebThirring.MatrixProof +open Matrix ScalarProof MeasureTheory Filter +open scoped Matrix.Norms.L2Operator Topology +variable {N : ℕ} + +local instance : SeminormedAddCommGroup (selfAdjoint (Matrix (Fin N) (Fin N) ℂ)) := + (inferInstance : NormedAddCommGroup (selfAdjoint (Matrix (Fin N) (Fin N) ℂ))).toSeminormedAddCommGroup +local instance : NormedSpace ℝ (selfAdjoint (Matrix (Fin N) (Fin N) ℂ)) := inferInstance + +@[simp] lemma realHermitianComplexify_smul (t : ℝ) + (B : selfAdjoint (Matrix (Fin N) (Fin N) ℝ)) : + realHermitianComplexify (t • B) = t • realHermitianComplexify B := by + apply Subtype.ext + exact map_smul complexify t (B : Matrix (Fin N) (Fin N) ℝ) + +def realHermitianComplexifyCLM : + selfAdjoint (Matrix (Fin N) (Fin N) ℝ) →L[ℝ] selfAdjoint (Matrix (Fin N) (Fin N) ℂ) := + { toFun := realHermitianComplexify + map_add' := by + intro A B + apply Subtype.ext + exact map_add complexify (A : Matrix (Fin N) (Fin N) ℝ) (B : Matrix (Fin N) (Fin N) ℝ) + map_smul' := realHermitianComplexify_smul + cont := realHermitianComplexify_continuous } + +@[simp] lemma realHermitianComplexifyCLM_apply (B : selfAdjoint (Matrix (Fin N) (Fin N) ℝ)) : + realHermitianComplexifyCLM B = realHermitianComplexify B := rfl + +def realK2SelfAdjoint (k : Fin N → ℝ) : selfAdjoint (Matrix (Fin N) (Fin N) ℂ) := + ⟨complexify (diagonal (fun i ↦ k i ^ 2)), complexify_hermitian (isHermitian_diagonal _)⟩ + +lemma fieldPrimitive_eq_hermitianPotential {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (k : Fin N → ℝ) (B : selfAdjoint (Matrix (Fin N) (Fin N) ℝ)) : + fieldPrimitive σ δ k B = + -hermitianPotential σ δ (realK2SelfAdjoint k) (realHermitianComplexify B) := by + rw [hermitianPotential_radial hσ hδ] + unfold fieldPrimitive + congr 1 + apply intervalIntegral.integral_congr + intro t _ + dsimp only + rw [← realHermitianComplexify_smul] + change trace ((B : Matrix (Fin N) (Fin N) ℝ) * matrixField σ δ k (t • B)) = + (trace (complexify B * hermitianField σ δ (complexify (diagonal (fun i ↦ k i ^ 2))) + (complexify (t • (B : Matrix (Fin N) (Fin N) ℝ))))).re + have hf := complexify_matrixField hσ hδ k (t • B).prop + change complexify (matrixField σ δ k (t • (B : Matrix (Fin N) (Fin N) ℝ))) = + hermitianField σ δ (complexify (diagonal (fun i ↦ k i ^ 2))) + (complexify (t • (B : Matrix (Fin N) (Fin N) ℝ))) at hf + rw [← hf, ← map_mul, complexify_trace_real] + +lemma fieldPrimitive_hasFDerivAt {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (k : Fin N → ℝ) (B : selfAdjoint (Matrix (Fin N) (Fin N) ℝ)) : + HasFDerivAt (fun B : selfAdjoint (Matrix (Fin N) (Fin N) ℝ) ↦ fieldPrimitive σ δ k B) + ((-traceGradientMap (complexify (matrixField σ δ k B))).comp realHermitianComplexifyCLM) B := by + have hh := ((hermitianPotential_hasFDerivAt hσ hδ (realK2SelfAdjoint k) + (realHermitianComplexify B)).neg).comp B realHermitianComplexifyCLM.hasFDerivAt + convert! hh using 1 + · funext A + exact fieldPrimitive_eq_hermitianPotential hσ hδ k A + · rw [complexify_matrixField hσ hδ k B.prop] + rfl + +lemma fieldPrimitive_path_derivative {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (k : Fin N → ℝ) {B : ℝ → selfAdjoint (Matrix (Fin N) (Fin N) ℝ)} + {B' : selfAdjoint (Matrix (Fin N) (Fin N) ℝ)} {x : ℝ} (hB : HasDerivAt B B' x) : + HasDerivAt (fun x ↦ fieldPrimitive σ δ k (B x)) + (-trace (matrixField σ δ k (B x) * (B' : Matrix (Fin N) (Fin N) ℝ))) x := by + convert! (fieldPrimitive_hasFDerivAt hσ hδ k (B x)).comp_hasDerivAt x hB using 1 + change -trace (matrixField σ δ k (B x) * (B' : Matrix (Fin N) (Fin N) ℝ)) = + -(trace (complexify (matrixField σ δ k (B x)) * complexify (B' : Matrix (Fin N) (Fin N) ℝ))).re + rw [← map_mul, complexify_trace_real] + +end SharpLiebThirring.MatrixProof +namespace SharpLiebThirring.MatrixProof +open Matrix ScalarProof MeasureTheory Filter +open scoped Matrix.Norms.L2Operator Topology +variable {N : ℕ} + +lemma hermitian_integral {f : ℝ → Matrix (Fin N) (Fin N) ℂ} + (hf : ∀ x, (f x).IsHermitian) : (∫ x, f x).IsHermitian := by + change star (∫ x, f x) = ∫ x, f x + have hh := (starL ℝ : Matrix (Fin N) (Fin N) ℂ ≃L[ℝ] Matrix (Fin N) (Fin N) ℂ).integral_comp_comm (μ := volume) f + change (∫ x, star (f x)) = star (∫ x, f x) at hh + rw [← hh] + apply integral_congr_ae + exact Eventually.of_forall (fun x ↦ hf x) + +lemma hermitianField_isHermitian (σ δ : ℝ) (C B : Matrix (Fin N) (Fin N) ℂ) : + (hermitianField σ δ C B).IsHermitian := by + apply Matrix.IsHermitian.smul _ (IsSelfAdjoint.all _) + apply hermitian_integral + intro s + exact ((cfc_predicate (regularizedPrimitive σ δ) (quadraticMatrix C B s)).add + (cfc_predicate (regularizedPrimitive σ δ) (quadraticMatrix C B (-s)))).sub + (isHermitian_one.smul (IsSelfAdjoint.all _)) + +lemma matrixField_isHermitian {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (k : Fin N → ℝ) {B : Matrix (Fin N) (Fin N) ℝ} (hB : B.IsHermitian) : + (matrixField σ δ k B).IsHermitian := by + have hh := hermitianField_isHermitian σ δ + (complexify (diagonal (fun i ↦ k i ^ 2))) (complexify B) + rw [← complexify_matrixField hσ hδ k hB] at hh + change star (matrixField σ δ k B) = matrixField σ δ k B + ext i j + have he := congrFun (congrFun hh i) j + simpa [complexify, conjTranspose_apply] using congrArg Complex.re he + +end SharpLiebThirring.MatrixProof + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/CoerciveInverse.lean b/lean/OAI/Analysis/LiebThirring/CoerciveInverse.lean new file mode 100644 index 0000000000000000000000000000000000000000..a61b8c1776c07bcb5e7994d53b4690cf10a0d495 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/CoerciveInverse.lean @@ -0,0 +1,127 @@ +import OAI.Analysis.LiebThirring.Multiplication + +namespace OAI + +universe u182 u183 u184 u185 u186 + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set +open scoped Topology + +lemma coercive_bijective {E : Type u182} [NormedAddCommGroup E] [InnerProductSpace ℂ E] + [CompleteSpace E] (B : E →L[ℂ] E) {c : ℝ} (hc : 0 < c) + (hB : ∀ u, c*‖u‖^2 ≤ (inner ℂ u (B u)).re) : Function.Bijective B := by + have hbound : ∀ u, c*‖u‖ ≤ ‖B u‖ := by + intro u + by_cases hu : u = 0 + · simp [hu] + · have hn : 0 < ‖u‖ := norm_pos_iff.mpr hu + have hinner : (inner ℂ u (B u)).re ≤ ‖u‖*‖B u‖ := + (Complex.re_le_norm _).trans (norm_inner_le_norm _ _) + have hs := hB u + have hm : c*‖u‖*‖u‖ ≤ ‖B u‖*‖u‖ := by nlinarith + exact (mul_le_mul_iff_left₀ hn).mp (by nlinarith [hm]) + have hanti := B.antilipschitz_of_bound (K := ⟨c⁻¹,le_of_lt (inv_pos.mpr hc)⟩) + (fun u ↦ by + change ‖u‖ ≤ c⁻¹*‖B u‖ + rw [← div_eq_inv_mul,le_div_iff₀ hc] + simpa only [mul_comm] using hbound u) + refine ⟨hanti.injective,?_⟩ + have hclosed : IsClosed (B.range : Set E) := hanti.isClosed_range B.uniformContinuous + let : CompleteSpace B.range := hclosed.completeSpace_coe + have hr : B.range = ⊤ := by + rw [← B.range.orthogonal_orthogonal] + rw [Submodule.eq_top_iff'] + intro v w hw + have hz : w = 0 := by + have he : inner ℂ (B w) w = 0 := hw _ ⟨w,rfl⟩ + have he' : inner ℂ w (B w) = 0 := by rw [← inner_conj_symm,he]; simp + have hs := hB w + rw [he',Complex.zero_re] at hs + have hnorm : ‖w‖^2 = 0 := (nonpos_of_mul_nonpos_right hs hc).antisymm (sq_nonneg _) + exact norm_eq_zero.mp (sq_eq_zero_iff.mp hnorm) + simp [hz] + exact LinearMap.range_eq_top.mp hr + +end SharpLiebThirring.OperatorProof + +end + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open Set +open scoped Topology + +/-- A densely defined symmetric operator whose real translate is onto is self-adjoint. -/ +lemma selfAdjoint_of_surjective_shift {E : Type u183} [NormedAddCommGroup E] + [InnerProductSpace ℂ E] [CompleteSpace E] (A : E →ₗ.[ℂ] E) + (hd : Dense (A.domain : Set E)) (hs : A.IsFormalAdjoint A) (c : ℝ) + (hr : ∀ f : E, ∃ u : A.domain, A u+(c:ℂ) • (u:E) = f) : IsSelfAdjoint A := by + rw [LinearPMap.isSelfAdjoint_def] + apply le_antisymm + · refine ⟨?_,?_⟩ + · intro x hx + let x' : A.adjoint.domain := ⟨x,hx⟩ + obtain ⟨y,hy⟩ := hr (A.adjoint x'+(c:ℂ) • x) + have he : x = (y:E) := by + apply ext_inner_right ℂ + intro f + obtain ⟨v,hv⟩ := hr f + have ha := (A.adjoint_isFormalAdjoint hd) x' v + have hb := hs y v + have heq : inner ℂ ((A y)+(c:ℂ) • (y:E)) (v:E) = + inner ℂ ((A.adjoint x')+(c:ℂ) • x) (v:E) := congrArg (fun t ↦ inner ℂ t (v:E)) hy + simp only [inner_add_left,inner_smul_left] at heq + rw [ha,hb] at heq + rw [← hv] + simp only [inner_add_right,inner_smul_right] + have hc : (starRingEnd ℂ) (c:ℂ) = (c:ℂ) := by simp + rw [hc] at heq + exact heq.symm + exact he ▸ y.2 + · intro x y hxy + apply hd.eq_of_inner_left ℂ + intro z hz + have h1 := (A.adjoint_isFormalAdjoint hd) x ⟨z,hz⟩ + have h2 := hs y ⟨z,hz⟩ + rw [h1,h2,hxy] + · exact hs.le_adjoint hd + +/-- The inverse of an injective bounded symmetric map, translated by a real scalar. -/ +def inverseShift {E : Type u184} [NormedAddCommGroup E] [InnerProductSpace ℂ E] + (R : E →L[ℂ] E) (hR : Function.Injective R) (c : ℝ) : E →ₗ.[ℂ] E where + domain := R.range + toFun := (LinearEquiv.ofInjective R.toLinearMap hR).symm.toLinearMap - + (c:ℂ) • R.range.subtype + +lemma inverseShift_apply {E : Type u185} [NormedAddCommGroup E] [InnerProductSpace ℂ E] + (R : E →L[ℂ] E) (hR : Function.Injective R) (c : ℝ) (x : E) : + inverseShift R hR c ⟨R x,⟨x,rfl⟩⟩ = x-(c:ℂ) • R x := by + change (LinearEquiv.ofInjective R.toLinearMap hR).symm + ((LinearEquiv.ofInjective R.toLinearMap hR) x)-(c:ℂ) • R x = _ + rw [LinearEquiv.symm_apply_apply] + +lemma inverseShift_selfAdjoint {E : Type u186} [NormedAddCommGroup E] + [InnerProductSpace ℂ E] [CompleteSpace E] + (R : E →L[ℂ] E) (hR : Function.Injective R) (hS : R.IsSymmetric) + (hd : Dense (Set.range R)) (c : ℝ) : IsSelfAdjoint (inverseShift R hR c) := by + refine selfAdjoint_of_surjective_shift _ hd ?_ c ?_ + · intro x y + rcases x with ⟨x,⟨u,rfl⟩⟩ + rcases y with ⟨y,⟨v,rfl⟩⟩ + erw [inverseShift_apply R hR c u,inverseShift_apply R hR c v] + simp only [inner_sub_left,inner_smul_left,inner_sub_right,inner_smul_right] + rw [hS] + simp + · intro f + refine ⟨⟨R f,⟨f,rfl⟩⟩,?_⟩ + rw [inverseShift_apply,sub_add_cancel] + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/CompactAlternative.lean b/lean/OAI/Analysis/LiebThirring/CompactAlternative.lean new file mode 100644 index 0000000000000000000000000000000000000000..eb7d0dc80589d1bb80f81fc2f9e2d0e394d87923 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/CompactAlternative.lean @@ -0,0 +1,47 @@ +import OAI.Analysis.LiebThirring.PotentialCompactness + +namespace OAI + +universe u190 + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open Module + +/-- The Fredholm alternative, transported through an arbitrary bounded isomorphism. -/ +lemma compact_perturbation_alternative {E : Type u190} [NormedAddCommGroup E] + [NormedSpace ℂ E] [CompleteSpace E] (B : E ≃L[ℂ] E) (C : E →L[ℂ] E) + (hC : IsCompactOperator C) : + (∃ u : E, u ≠ 0 ∧ B u-C u = 0) ∨ + Function.Bijective (B.toContinuousLinearMap-C) := by + let K : E →L[ℂ] E := B.symm.toContinuousLinearMap.comp C + have hK : IsCompactOperator K := hC.clm_comp B.symm.toContinuousLinearMap + rcases hK.hasEigenvalue_or_mem_resolventSet (by norm_num : (1:ℂ) ≠ 0) with he | hr + · obtain ⟨u,hu⟩ := he.exists_hasEigenvector + have hk := hu.apply_eq_smul + change K u = (1:ℂ) • u at hk + simp only [one_smul] at hk + have hb : C u = B u := by + have hh := congrArg B hk + simpa only [K,ContinuousLinearMap.comp_apply,ContinuousLinearEquiv.coe_coe, + ContinuousLinearEquiv.apply_symm_apply] using hh + exact Or.inl ⟨u,hu.2,sub_eq_zero.mpr hb.symm⟩ + · have hb : Function.Bijective (1-K : E →L[ℂ] E) := by + rw [spectrum.mem_resolventSet_iff,ContinuousLinearMap.isUnit_iff_bijective] at hr + simpa only [map_one] using hr + have hcomp : (B.toContinuousLinearMap-C : E → E) = + B ∘ ((1-K : E →L[ℂ] E) : E → E) := by + funext u + change B u-C u = B (u-B.symm (C u)) + rw [map_sub,ContinuousLinearEquiv.apply_symm_apply] + right + change Function.Bijective (B.toContinuousLinearMap-C : E → E) + rw [hcomp] + exact B.bijective.comp hb + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/ComplexFamilies.lean b/lean/OAI/Analysis/LiebThirring/ComplexFamilies.lean new file mode 100644 index 0000000000000000000000000000000000000000..7a1effdace4015205478108c49c99570c99dfbf2 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/ComplexFamilies.lean @@ -0,0 +1,184 @@ +import OAI.Analysis.LiebThirring.SpectralTrials + +namespace OAI + +universe u180 + + +noncomputable section +namespace SharpLiebThirring.SpectralProof +open SobolevProof SobolevProof.C1L2 ConstantProof MeasureTheory Set Filter +open scoped Topology + +lemma real_family_bound_sorted {N : ℕ} {σ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) + (hWn : ∀ᵐ x, 0 ≤ W x) (hWp : Integrable (fun x ↦ W x^(1+σ))) + (u : Fin N → C1L2) (k : Fin N → ℝ) + (ho : Orthonormal ℝ u) (he : ∀ i, (u i).IsEigen W (k i)) + (hk : ∀ i, 0 < k i) (horder : Antitone k) : + (∑ i, k i^(1+2*σ))*betaAction σ ≤ actionYoungConstant σ*∫ x, W x^(1+σ) := by + have hc : ContinuousAt (fun t : ℝ ↦ ∑ i, (t*k i)^(1+2*σ)*betaAction σ) 1 := by + apply tendsto_finsetSum + intro i _ + exact (((continuousAt_id.mul_const (k i)).rpow_const + (Or.inl (by simpa using (hk i).ne'))).mul_const _) + have ht : Tendsto (fun t : ℝ ↦ ∑ i, (t*k i)^(1+2*σ)*betaAction σ) (𝓝[<] 1) + (𝓝 ((∑ i, k i^(1+2*σ))*betaAction σ)) := by + simpa only [one_mul,Finset.sum_mul] using hc.tendsto.mono_left nhdsWithin_le_nhds + apply le_of_tendsto ht + filter_upwards [self_mem_nhdsWithin, + (eventually_gt_nhds (by norm_num : (0 : ℝ)<1)).filter_mono nhdsWithin_le_nhds] with t ht ht0 + have hκ (i : Fin N) : 0 < t*k i ∧ t*k i < k i := + ⟨mul_pos ht0 (hk i),by simpa using mul_lt_mul_of_pos_right (show t < 1 from ht) (hk i)⟩ + obtain ⟨q,hqo,hqc,hqe⟩ := exists_compact_negative_flag hW u k (fun i ↦ t*k i) + ho he hk hκ horder + have h := compact_trial_bound hσ₀ hσ₁ hW hWn hWp (fun i ↦ t*k i) + (fun i ↦ (hκ i).1) q hqo hqc hqe + simpa only [boundary_action_scaling hσ₀ (hκ _).1] using h + +lemma real_family_action_bound {N : ℕ} {σ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) + (hWn : ∀ᵐ x, 0 ≤ W x) (hWp : Integrable (fun x ↦ W x^(1+σ))) + (u : Fin N → C1L2) (k : Fin N → ℝ) + (ho : Orthonormal ℝ u) (he : ∀ i, (u i).IsEigen W (k i)) + (hk : ∀ i, 0 < k i) : + (∑ i, k i^(1+2*σ))*betaAction σ ≤ actionYoungConstant σ*∫ x, W x^(1+σ) := by + let e := Tuple.sort (fun i ↦ -k i) + have horder : Antitone (fun i ↦ k (e i)) := by + intro i j hij + have h := Tuple.monotone_sort (fun i ↦ -k i) hij + dsimp at h + linarith + have h := real_family_bound_sorted hσ₀ hσ₁ hW hWn hWp + (fun i ↦ u (e i)) (fun i ↦ k (e i)) (ho.comp e e.injective) + (fun i ↦ he (e i)) (fun i ↦ hk (e i)) horder + simpa only [Equiv.sum_comp e (fun i ↦ k i^(1+2*σ))] using h + +lemma action_constant_eq_sharp {σ : ℝ} (hσ : 0 < σ) : + actionYoungConstant σ / betaAction σ = sharpConstant (σ+1/2) := by + rw [actionYoungConstant,young_over_beta hσ,sharpConstant,semiclassicalConstant] + have h1 : σ+1/2-1/2 = σ := by ring + have h2 : σ+1/2+1/2 = σ+1 := by ring + have h3 : σ+1/2+1 = σ+3/2 := by ring + have h4 : σ+1/2+3/2 = σ+2 := by ring + rw [h1,h2,h3,h4] + ring + +lemma real_family_bound {ι : Type u180} [Fintype ι] {γ : ℝ} + (hγ₀ : 1/2 < γ) (hγ₁ : γ < 3/2) {W : ℝ → ℝ} + (hW : LocallyIntegrable W volume) (hWn : ∀ᵐ x, 0 ≤ W x) + (hWp : Integrable (fun x ↦ W x^(γ+1/2))) + (u : ι → C1L2) (k : ι → ℝ) (ho : Orthonormal ℝ u) + (he : ∀ i, (u i).IsEigen W (k i)) (hk : ∀ i, 0 < k i) : + (∑ i, k i^(2*γ)) ≤ sharpConstant γ*∫ x, W x^(γ+1/2) := by + classical + let e := (Fintype.equivFin ι).symm + have hσ₀ : 0 < γ-1/2 := by linarith + have hσ₁ : γ-1/2 < 1 := by linarith + have he2 : 1+(γ-1/2) = γ+1/2 := by ring + have h := real_family_action_bound hσ₀ hσ₁ hW hWn + (by simpa only [he2] using hWp) + (fun i ↦ u (e i)) (fun i ↦ k (e i)) (ho.comp e e.injective) + (fun i ↦ he (e i)) (fun i ↦ hk (e i)) + rw [Equiv.sum_comp e (fun i ↦ k i^(1+2*(γ-1/2)))] at h + have he1 : 1+2*(γ-1/2) = 2*γ := by ring + rw [he1,he2] at h + have hh := (le_div_iff₀ (betaAction_pos hσ₀)).mpr h + rw [mul_div_right_comm,action_constant_eq_sharp hσ₀,sub_add_cancel] at hh + exact hh + +end SharpLiebThirring.SpectralProof + +end + + +noncomputable section +namespace SharpLiebThirring.SpectralProof +open SobolevProof SobolevProof.C1L2 MeasureTheory Set Module + +/-- Finite realification, retaining all complex multiplicities at each energy. -/ +lemma realify_finite_family {ι : Type} [Fintype ι] [DecidableEq ι] + {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) (k : ι → ℝ) + (hk : ∀ i, 0 < k i) (a b : ι → C1L2) + (ha : ∀ i, (a i).IsEigen W (k i)) (hb : ∀ i, (b i).IsEigen W (k i)) + (hr : ∀ i j, inner ℝ (a i) (a j)+inner ℝ (b i) (b j) = if i=j then 1 else 0) + (hi : ∀ i j, inner ℝ (a i) (b j)-inner ℝ (b i) (a j) = 0) + (p : ℝ) : + ∃ (J : Type) (_ : Fintype J) (v : J → C1L2) (l : J → ℝ), + Orthonormal ℝ v ∧ (∀ j, (v j).IsEigen W (l j)) ∧ (∀ j, 0 < l j) ∧ + (∑ i, k i^p) ≤ ∑ j, l j^p := by + classical + let T := range k + let : Fintype T := (finite_range k).fintype + let I := fun t : T ↦ {i : ι // k i = t.val} + let g := fun (t : T) (z : I t × Bool) ↦ if z.2 then b z.1 else a z.1 + let E := fun t : T ↦ Submodule.span ℝ (range (g t)) + have (t : T) : FiniteDimensional ℝ (E t) := FiniteDimensional.span_of_finite ℝ (finite_range _) + have hE (t : T) : E t ≤ eigenSubmodule hW t.val := by + apply Submodule.span_le.mpr + rintro v ⟨⟨i,c⟩,rfl⟩ + change (if c then b i else a i).IsEigen W t.val + cases c + · simpa only [i.property,Bool.false_eq_true,ite_false] using ha i + · simpa only [i.property,ite_true] using hb i + let ar := fun (t : T) (i : I t) ↦ (⟨a i,Submodule.subset_span (mem_range.mpr ⟨(i,false),rfl⟩)⟩ : E t) + let br := fun (t : T) (i : I t) ↦ (⟨b i,Submodule.subset_span (mem_range.mpr ⟨(i,true),rfl⟩)⟩ : E t) + have hdim (t : T) : Fintype.card (I t) ≤ finrank ℝ (E t) := by + apply complex_family_card_le_real_dimension (ar t) (br t) + · intro i j + change inner ℝ (a i) (a j)+inner ℝ (b i) (b j) = _ + rw [hr] + congr 1 + exact propext Subtype.ext_iff.symm + · intro i j + exact hi i j + let B := fun t : T ↦ stdOrthonormalBasis ℝ (E t) + let J := (t : T) × Fin (finrank ℝ (E t)) + let v : J → C1L2 := fun z ↦ (B z.1 z.2).val + let l : J → ℝ := fun z ↦ z.1.val + have hl (t : T) : 0 < t.val := by obtain ⟨i,he⟩ := t.property; rw [← he]; exact hk i + have hv (j : J) : (v j).IsEigen W (l j) := hE j.1 (B j.1 j.2).property + refine ⟨J,inferInstance,v,l,?_,hv,fun j ↦ hl j.1,?_⟩ + · rw [orthonormal_iff_ite] + rintro ⟨t,i⟩ ⟨s,j⟩ + by_cases hts : t=s + · subst s + have hh := (B t).orthonormal + have heq := orthonormal_iff_ite.mp hh i j + change inner ℝ (B t i) (B t j) = _ + rw [heq] + congr 1 + apply propext + constructor + · intro h; subst j; rfl + · intro h + exact eq_of_heq (Sigma.mk.inj h).2 + · have hneq : t.val^2 ≠ s.val^2 := by + intro he + have hval : t.val = s.val := by nlinarith [hl t,hl s] + exact hts (Subtype.ext hval) + rw [eigen_orthogonal (hv ⟨t,i⟩) (hv ⟨s,j⟩) hW hneq,ite_eq_right] + exact fun h ↦ hts (congrArg Sigma.fst h) + · have heq : (∑ i, k i^p) = ∑ t : T, (Fintype.card (I t) : ℝ)*t.val^p := by + let f : ι ≃ (t : T) × I t := + { toFun := fun i ↦ ⟨⟨k i,mem_range_self i⟩,⟨i,rfl⟩⟩ + invFun := fun z ↦ z.2.val + left_inv := fun _ ↦ rfl + right_inv := by rintro ⟨⟨t,ht⟩,⟨i,hi⟩⟩; dsimp at hi; subst t; rfl } + calc + (∑ i, k i^p) = ∑ z : (t : T) × I t, z.1.val^p := + Equiv.sum_comp f (fun z ↦ z.1.val^p) + _ = _ := by + rw [Fintype.sum_sigma] + simp only [Finset.sum_const,Finset.card_univ,nsmul_eq_mul] + rw [heq,Fintype.sum_sigma] + apply Finset.sum_le_sum + intro t _ + simp only [l,Finset.sum_const,Finset.card_univ,Fintype.card_fin,nsmul_eq_mul] + exact mul_le_mul_of_nonneg_right (by exact_mod_cast hdim t) (Real.rpow_nonneg (hl t).le _) + +end SharpLiebThirring.SpectralProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/ConnectingPath.lean b/lean/OAI/Analysis/LiebThirring/ConnectingPath.lean new file mode 100644 index 0000000000000000000000000000000000000000..1810d51200f01e1c6513e8e6e636fbd01f18efb9 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/ConnectingPath.lean @@ -0,0 +1,182 @@ +import OAI.Analysis.LiebThirring.FieldFlow + +namespace OAI + +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Set Metric MeasureTheory Filter +open scoped Topology NNReal +noncomputable section +open Matrix Set MeasureTheory WithLp +open scoped Matrix.Norms.L2Operator Topology +noncomputable section +open Set Metric +open scoped NNReal +noncomputable section +open Matrix +open scoped Matrix.Norms.L2Operator + +namespace SharpLiebThirring.MatrixFlow +open ODEProof MatrixProof ScalarProof Matrix Set +open scoped Matrix.Norms.L2Operator ComplexOrder MatrixOrder +variable {N : ℕ} + +lemma state_diagonal_le (φ : Matrix (Fin N) (Fin N) ℂ →L[ℝ] ℝ) + (hφ : ∀ A, A.PosSemidef → 0 ≤ φ A) (hφ₁ : φ 1 = 1) + (f : Fin N → ℝ) (b : ℝ) (hf : ∀ i, f i ≤ b) : + φ (complexify (diagonal f)) ≤ b := by + have hp := hφ (diagonal (fun i ↦ ((b-f i : ℝ) : ℂ))) + (diagonal_real_posSemidef _ (fun i ↦ sub_nonneg.mpr (hf i))) + have he : diagonal (fun i ↦ ((b-f i : ℝ) : ℂ)) = b • (1 : Matrix (Fin N) (Fin N) ℂ) - complexify (diagonal f) := by + rw [complexify_diagonal] + ext i j + by_cases hij : i=j + · subst j + simp + · simp [diagonal_apply_ne _ hij,one_apply_ne hij] + rw [he,map_sub,map_smul,hφ₁,smul_eq_mul,mul_one] at hp + linarith + +lemma sourceField_state_nonpos {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) + (k : Fin N → ℝ) (A : Sym N) + (φ : Matrix (Fin N) (Fin N) ℂ →L[ℝ] ℝ) + (hφ : ∀ A, A.PosSemidef → 0 ≤ φ A) (hφ₁ : φ 1 = 1) + (h : ‖k‖ < |φ (complexify A.val)|) : + φ (complexify (sourceField σ δ hσ₁ hδ k A).val) ≤ 0 := by + have hC : φ (complexify (diagonal (fun i ↦ k i^2))) ≤ ‖k‖^2 := + state_diagonal_le φ hφ hφ₁ _ _ (fun i ↦ by + have hh : |k i| ≤ ‖k‖ := norm_le_pi_norm k i + simpa only [sq_abs] using (sq_le_sq₀ (abs_nonneg _) (norm_nonneg _)).mpr hh) + have hj := hermitianField_state_jensen hσ₀ hσ₁ hδ φ hφ hφ₁ + (realK2SelfAdjoint k).prop (complexify_hermitian A.prop) + change φ (hermitianField σ δ (complexify (diagonal (fun i ↦ k i^2))) (complexify A.val)) ≤ _ at hj + rw [← complexify_matrixField hσ₁ hδ k A.prop] at hj + apply hj.trans + have hz : φ (complexify (diagonal (fun i ↦ k i^2))) - (φ (complexify A.val))^2 ≤ 0 := by + nlinarith [sq_abs (φ (complexify A.val)),norm_nonneg k] + exact (mu_strictMono hσ₀ hσ₁ hδ).monotone hz |>.trans_eq (mu_zero σ δ) + +lemma source_path_state_barrier {σ δ ε l r : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) + (hε : 0 < ε) (k : Fin N → ℝ) (a : ℝ → Fin N → ℝ) + (q : Sym N → ℝ) (hq : ∀ A, 0 ≤ q A) (X : ℝ → Sym N) + (hXi : X l = symDiag k) (hXf : X r = -symDiag k) + (hXd : ∀ t ∈ Icc l r, HasDerivWithinAt X + (ε⁻¹ • (q (X t) • sourceField σ δ hσ₁ hδ k (X t) - symOuter (a t))) (Icc l r) t) + (φ : Matrix (Fin N) (Fin N) ℂ →L[ℝ] ℝ) + (hφ : ∀ A, A.PosSemidef → 0 ≤ φ A) (hφ₁ : φ 1 = 1) : + ∀ t ∈ Icc l r, |φ (complexify (X t).val)| ≤ ‖k‖ := by + let ψ := φ.comp (complexifyCLM.comp symInclude.toContinuousLinearMap) + have hψ (A : Sym N) : ψ A = φ (complexify A.val) := rfl + have hK : ψ (symDiag k) ≤ ‖k‖ := state_diagonal_le φ hφ hφ₁ _ _ + (fun i ↦ (le_abs_self _).trans (norm_le_pi_norm k i)) + apply two_sided_barrier (h := fun t ↦ ψ (X t)) + (h' := fun t ↦ ψ (ε⁻¹ • (q (X t) • sourceField σ δ hσ₁ hδ k (X t) - symOuter (a t)))) + · intro t ht + exact ψ.hasFDerivAt.comp_hasDerivWithinAt t (hXd t ht) + · rw [hXi]; exact hK + · rw [hXf,map_neg]; exact neg_le_neg hK + · intro t ht h + have hF := sourceField_state_nonpos hσ₀ hσ₁ hδ k (X t) φ hφ hφ₁ h + have hA : 0 ≤ ψ (symOuter (a t)) := by + change 0 ≤ φ (complexify (vecMulVec (a t) (a t))) + rw [complexify_vecMulVec] + exact hφ _ (posSemidef_vecMulVec_self_star _) + rw [map_smul,map_sub,map_smul,smul_eq_mul,smul_eq_mul] + exact mul_nonpos_of_nonneg_of_nonpos (inv_nonneg.mpr hε.le) + (sub_nonpos.mpr (le_trans (mul_nonpos_of_nonneg_of_nonpos (hq _) hF) hA)) + +lemma sym_norm_le_of_states (A : Sym N) {R : ℝ} (hR : 0 ≤ R) + (h : ∀ (φ : Matrix (Fin N) (Fin N) ℂ →L[ℝ] ℝ), + (∀ B, B.PosSemidef → 0 ≤ φ B) → φ 1 = 1 → |φ (complexify A.val)| ≤ R) : + ‖A‖ ≤ R := by + have hA : A.val.IsHermitian := A.prop + have he (i : Fin N) : |hA.eigenvalues i| ≤ R := by + have hh := h (unitaryState (complexUnitary (star hA.eigenvectorUnitary)) i) + (fun B hB ↦ unitaryState_positive _ _ hB) (unitaryState_one _ _) + rw [unitaryState_apply,← complexify_conj,hA.conjStarAlgAut_star_eigenvectorUnitary] at hh + simpa only [complexify_apply,Function.comp_apply,RCLike.ofReal_real_eq_id,id_eq, + diagonal_apply_eq,Complex.ofReal_re] using hh + have hd := hA.conjStarAlgAut_star_eigenvectorUnitary + have hn := congrArg (fun B : Matrix (Fin N) (Fin N) ℝ ↦ ‖B‖) hd + simp only [Unitary.conjStarAlgAut_apply,CStarRing.norm_mul_coe_unitary, + CStarRing.norm_coe_unitary_mul,← Unitary.coe_star,Matrix.l2_opNorm_diagonal, + RCLike.ofReal_real_eq_id,Function.id_comp] at hn + change ‖A.val‖ ≤ R + rw [hn] + exact (pi_norm_le_iff_of_nonneg hR).mpr he + +end SharpLiebThirring.MatrixFlow +namespace SharpLiebThirring.MatrixFlow +open ODEProof MatrixProof ScalarProof Matrix Set ContinuationGap +open scoped Matrix.Norms.L2Operator +variable {N : ℕ} + +/-- The connecting path, with one coefficient box for all small penalties. +The radial cutoff has been removed by the two endpoint barriers. -/ +lemma source_connecting_path {σ δ l r : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) + (hlr : l ≤ r) (k : Fin N → ℝ) (hk : ∀ i, 0 < k i) + (u : ℝ → Fin N → ℝ) (hu : ContinuousOn u (Icc l r)) + (ho : ∀ i j, (∫ t in l..r, u t i * u t j) = if i=j then 1 else 0) : + ∃ R : ℝ, ∀ ε : ℝ, 0 < ε → ε ≤ 1 → + ∃ (C : LowerSpace N) (X : ℝ → Sym N), + (∀ i j, |C.val i j| ≤ R) ∧ X l = symDiag k ∧ X r = -symDiag k ∧ + (∀ t ∈ Icc l r, ‖X t‖ ≤ ‖k‖) ∧ + (∀ t ∈ Icc l r, HasDerivWithinAt X + (ε⁻¹ • (sourceField σ δ hσ₁ hδ k (X t) - symOuter (C.val *ᵥ u t))) (Icc l r) t) := by + let χ : Sym N → ℝ := radialCutoff ‖k‖ + let M := fun A ↦ χ A • sourceField σ δ hσ₁ hδ k A + obtain ⟨L,B,hL,hB⟩ := bounded_lipschitz_radial_cutoff + (sourceField σ δ hσ₁ hδ k) (sourceField_locallyLipschitz hσ₁ hδ k) ‖k‖ + refine ⟨max (2*‖k‖+(r-l)*B) 0+1,?_⟩ + intro ε hε hε₁ + have hχ (A : Sym N) : |χ A| ≤ (1 : ℝ≥0) := by + rw [abs_of_nonneg (radialCutoff_nonneg _ _)] + exact radialCutoff_le_one _ _ + have hg (i : Fin N) : LocallyLipschitz (fun x ↦ scalarMu σ δ (k i^2-x^2)) := + coordinate_mu_locallyLipschitz hσ₁ hδ k i + have hc (i : Fin N) (A : Sym N) (hi : ∀ j, i ≠ j → A.val i j = 0) : + (M A).val i i = χ A * scalarMu σ δ (k i^2-A.val i i^2) := by + change χ A * (sourceField σ δ hσ₁ hδ k A).val i i = _ + rw [matrixField_isolated_coordinate hσ₁ hδ k A i hi] + have he (s : Fin N → ℝ) (hs : ∀ i, s i = 1 ∨ s i = -1) (A : Sym N) : + M (symConj s A) = symConj s (M A) := by + dsimp only [M] + rw [sourceField_equivariant hσ₁ hδ k s hs,map_smul] + congr 1 + unfold χ radialCutoff + rw [norm_symConj s hs] + obtain ⟨C,X,hXi,hXf,hXd,hC⟩ := terminal_matching hlr hε M L B 1 hL hB χ hχ + (fun i x ↦ scalarMu σ δ (k i^2-x^2)) hg k hk + (fun i ↦ by simp only [sub_self,mu_zero]) hc he u hu ho + have hX (t : ℝ) (ht : t ∈ Icc l r) : ‖X t‖ ≤ ‖k‖ := by + apply sym_norm_le_of_states (X t) (norm_nonneg _) + intro φ hφ hφ₁ + exact source_path_state_barrier hσ₀ hσ₁ hδ hε k (fun t ↦ C.val *ᵥ u t) χ + (radialCutoff_nonneg _) X hXi hXf hXd φ hφ hφ₁ t ht + refine ⟨C,X,?_,hXi,hXf,hX,?_⟩ + · apply gram_entry_bound + apply hC.trans + rw [abs_of_pos hε] + nlinarith [norm_nonneg k] + · intro t ht + have hh := hXd t ht + change HasDerivWithinAt X (ε⁻¹ • (χ (X t) • sourceField σ δ hσ₁ hδ k (X t) - _)) _ t at hh + rw [show χ (X t) = 1 from radialCutoff_eq_one (hX t ht),one_smul] at hh + exact hh + +end SharpLiebThirring.MatrixFlow + +end +end +end +end +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/Continuation.lean b/lean/OAI/Analysis/LiebThirring/Continuation.lean new file mode 100644 index 0000000000000000000000000000000000000000..44799c99af01135c7e29bbdb97a3cef8e3412503 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/Continuation.lean @@ -0,0 +1,375 @@ +import OAI.Analysis.LiebThirring.BoundaryParity + +namespace OAI + +universe u143 u144 u145 u146 u147 + +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Finset + + +namespace SharpLiebThirring.CubeFlags +open Finset SharpLiebThirring.PLParity + +/-- A continuous cutoff equal to one on the inner half ball. -/ +def radialCut (R t : ℝ) : ℝ := max 0 (min 1 (2 - 2*t/R)) + +lemma radialCut_nonneg (R t : ℝ) : 0 ≤ radialCut R t := le_max_left _ _ +lemma radialCut_le_one (R t : ℝ) : radialCut R t ≤ 1 := + max_le zero_le_one (min_le_left _ _) +lemma radialCut_eq_zero (R : ℝ) (hR : 0 < R) {t : ℝ} (ht : R ≤ t) : radialCut R t = 0 := by + classical + apply max_eq_left + apply (min_le_right _ _).trans + have hd : 2 ≤ 2*t/R := (le_div_iff₀ hR).mpr (by linarith) + linarith +lemma radialCut_eq_one (R : ℝ) (hR : 0 < R) {t : ℝ} (ht : t ≤ R/2) : radialCut R t = 1 := by + classical + have hd : 2*t/R ≤ 1 := (div_le_iff₀ hR).mpr (by linarith) + simp only [radialCut, min_eq_left (by linarith : 1 ≤ 2 - 2*t/R), max_eq_right zero_le_one] +lemma continuous_radialCut (R : ℝ) : Continuous (radialCut R) := by + classical + unfold radialCut + fun_prop + +section Flatten +variable {d : ℕ} (H : Subgroup (Signs (d + 1))) +variable {V : Type u143} [NormedAddCommGroup V] [NormedSpace ℝ V] +variable (ρ : H →* (V ≃ₗ[ℝ] V)) (L : (Fin d → ℝ) ≃ₗ[ℝ] V) +variable (p : Fin d → ℝ) (R : ℝ) (f : (Fin (d + 1) → ℝ) → V) + +def localAffine (s : H) (x : Fin (d + 1) → ℝ) : V := + ρ s (L (spatial (s⁻¹ • x) - p)) + +def flattenTerm (s : H) (x : Fin (d + 1) → ℝ) : V := + radialCut R (dist x (s • embedSpatial p)) • (localAffine H ρ L p s x - f x) + +def flattenInitial (x : Fin (d + 1) → ℝ) : V := by + classical + exact f x + ∑ s : H, flattenTerm H ρ L p R f s x + +lemma localAffine_smul (s g : H) (x : Fin (d + 1) → ℝ) : + localAffine H ρ L p (g*s) (g • x) = ρ g (localAffine H ρ L p s x) := by + classical + simp only [localAffine,mul_inv_rev,mul_smul,inv_smul_smul,map_mul,LinearEquiv.mul_apply] + +lemma continuous_localAffine [FiniteDimensional ℝ V] (s : H) : Continuous (localAffine H ρ L p s) := by + classical + unfold localAffine + exact (ρ s).toContinuousLinearEquiv.continuous.comp + (L.toContinuousLinearEquiv.continuous.comp + ((spatial.continuous_of_finiteDimensional.comp (continuous_const_smul s⁻¹)).sub continuous_const)) + +lemma continuous_flattenInitial [FiniteDimensional ℝ V] (hf : Continuous f) : Continuous (flattenInitial H ρ L p R f) := by + classical + apply hf.add + apply continuous_finsetSum + intro s _ + exact ((continuous_radialCut R).comp (continuous_id.dist continuous_const)).smul + ((continuous_localAffine H ρ L p s).sub hf) + +lemma flattenInitial_equivariant (hfe : ∀ s : H, ∀ x, f (s • x) = ρ s (f x)) + (g : H) (x : Fin (d + 1) → ℝ) : + flattenInitial H ρ L p R f (g • x) = ρ g (flattenInitial H ρ L p R f x) := by + classical + have ht (s : H) : flattenTerm H ρ L p R f (g*s) (g • x) = + ρ g (flattenTerm H ρ L p R f s x) := by + simp only [flattenTerm,mul_smul,dist_smul,localAffine_smul,hfe,map_smul,map_sub] + have he := Fintype.sum_equiv (Equiv.mulLeft g) + (fun s : H ↦ ρ g (flattenTerm H ρ L p R f s x)) + (fun s : H ↦ flattenTerm H ρ L p R f s (g • x)) (fun s ↦ (ht s).symm) + simp only [flattenInitial,hfe,map_add,map_sum] + exact congrArg (ρ g (f x) + ·) he.symm + +lemma flattenInitial_eq_self {x : Fin (d + 1) → ℝ} (hR : 0 < R) + (hx : x ∉ orbitBall (G := H) (embedSpatial p) R) : + flattenInitial H ρ L p R f x = f x := by + classical + have ht : ∀ s : H, R ≤ dist x (s • embedSpatial p) := + fun s ↦ le_of_not_gt (fun hs ↦ hx ⟨s,hs⟩) + unfold flattenInitial + have hz : ∀ s : H, flattenTerm H ρ L p R f s x = 0 := by + intro s + unfold flattenTerm + rw [radialCut_eq_zero R hR (ht s),zero_smul] + simp only [hz,Finset.sum_const_zero,add_zero] + +lemma flattenInitial_in_ball (hR : 0 < R) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • embedSpatial p) (k • embedSpatial p)) + {x : Fin (d + 1) → ℝ} (hx : x ∈ orbitBall (G := H) (embedSpatial p) R) : + flattenInitial H ρ L p R f x = f x + + radialCut R (dist x (ballLabel (G := H) (embedSpatial p) R x • embedSpatial p)) • + (affineOrbitModel H ρ L (embedSpatial p) R p x - f x) := by + classical + let s := ballLabel (G := H) (embedSpatial p) R x + have hs := ballLabel_dist (embedSpatial p) R hx + have ht (k : H) (hk : k ≠ s) : flattenTerm H ρ L p R f k x = 0 := by + have hd := hsep s k hk.symm + have he := dist_triangle (s • embedSpatial p) x (k • embedSpatial p) + rw [dist_comm (s • embedSpatial p) x] at he + have hdk : R ≤ dist x (k • embedSpatial p) := by + change dist x (s • embedSpatial p) < R at hs + linarith + simp only [flattenTerm,radialCut_eq_zero R hR hdk,zero_smul] + have hsum : ∑ k : H, flattenTerm H ρ L p R f k x = flattenTerm H ρ L p R f s x := by + apply Finset.sum_eq_single s + · intro k _ hk + exact ht k hk + · simp only [Finset.mem_univ,not_true_eq_false,false_implies] + rw [flattenInitial,hsum] + rfl + +lemma flattenInitial_inner (hR : 0 < R) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • embedSpatial p) (k • embedSpatial p)) + {x : Fin (d + 1) → ℝ} (hx : x ∈ orbitBall (G := H) (embedSpatial p) (R/2)) : + flattenInitial H ρ L p R f x = affineOrbitModel H ρ L (embedSpatial p) (R/2) p x := by + classical + obtain ⟨s,hs⟩ := hx + have hsR : dist x (s • embedSpatial p) < R := by linarith + have hlR := ballLabel_eq (embedSpatial p) R hR hsep hsR + have hsep' : ∀ g k : H, g ≠ k → 8 * (R/2) < dist (g • embedSpatial p) (k • embedSpatial p) := by + intro g k hgk + linarith [hsep g k hgk] + have hlhalf := ballLabel_eq (embedSpatial p) (R/2) (by positivity) hsep' hs + rw [flattenInitial_in_ball H ρ L p R f hR hsep ⟨s,hsR⟩,hlR, + radialCut_eq_one R hR hs.le,one_smul] + simp only [affineOrbitModel,hlR,hlhalf] + abel + +lemma affineOrbitModel_zero_bottom + {x : Fin (d + 1) → ℝ} (ht : x (Fin.last d) = 0) + (hz : affineOrbitModel H ρ L (embedSpatial p) R p x = 0) : + ∃ s : H, s • embedSpatial p = x := by + classical + let s := ballLabel (G := H) (embedSpatial p) R x + have hu : spatial (s⁻¹ • x) - p = 0 := by + apply L.injective + apply (ρ s).injective + simpa only [affineOrbitModel,map_zero,s] using hz + have he := embed_spatial_of_time_zero (s⁻¹ • x) ((s⁻¹).val.smul_time_zero x ht) + rw [sub_eq_zero.mp hu] at he + refine ⟨s,?_⟩ + rw [he,smul_inv_smul] + +lemma flattenInitial_zero_bottom (hR : 0 < R) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • embedSpatial p) (k • embedSpatial p)) + (hz0 : ∀ x, x (Fin.last d) = 0 → f x = 0 → ∃ s : H, s • embedSpatial p = x) + (herr : ∀ x, x (Fin.last d) = 0 → x ∈ orbitBall (G := H) (embedSpatial p) R → + ‖f x - affineOrbitModel H ρ L (embedSpatial p) R p x‖ ≤ + ‖affineOrbitModel H ρ L (embedSpatial p) R p x‖ / 2) + {x : Fin (d + 1) → ℝ} (ht : x (Fin.last d) = 0) + (hz : flattenInitial H ρ L p R f x = 0) : ∃ s : H, s • embedSpatial p = x := by + classical + by_cases hx : x ∈ orbitBall (G := H) (embedSpatial p) R + · let m := affineOrbitModel H ρ L (embedSpatial p) R p x + let a := radialCut R (dist x (ballLabel (G := H) (embedSpatial p) R x • embedSpatial p)) + have hz' : f x + a • (m - f x) = 0 := by + rw [flattenInitial_in_ball H ρ L p R f hR hsep hx] at hz + exact hz + have ha : 0 ≤ a := radialCut_nonneg _ _ + have ha1 : a ≤ 1 := radialCut_le_one _ _ + have he : f x + a • (m - f x) = m + (1-a) • (f x-m) := by + rw [sub_smul,one_smul,smul_sub,smul_sub] + abel + rw [he] at hz' + have hn : ‖m‖ ≤ ‖f x-m‖ := by + have hm : m = -((1-a) • (f x-m)) := eq_neg_of_add_eq_zero_left hz' + have heN := congrArg norm hm + rw [norm_neg,norm_smul,Real.norm_eq_abs,abs_of_nonneg (by linarith : 0 ≤ 1-a)] at heN + nlinarith [norm_nonneg (f x-m)] + have hm0 : m = 0 := norm_eq_zero.mp (by linarith [herr x ht hx,norm_nonneg m]) + exact affineOrbitModel_zero_bottom H ρ L p R ht hm0 + · exact hz0 x ht ((flattenInitial_eq_self H ρ L p R f hR hx).symm.trans hz) + +lemma flattenInitial_final (hR : 0 < R) (hR1 : R ≤ 1) {x : Fin (d + 1) → ℝ} (ht : x (Fin.last d) = 1) : + flattenInitial H ρ L p R f x = f x := by + classical + apply flattenInitial_eq_self H ρ L p R f hR + rintro ⟨s,hs⟩ + have hd := dist_le_pi_dist x (s • embedSpatial p) (Fin.last d) + have hst : (s • embedSpatial p) (Fin.last d) = 0 := + s.val.smul_time_zero _ (by change Fin.snoc (α := fun _ : Fin (d + 1) ↦ ℝ) p 0 (Fin.last d) = 0; simp only [Fin.snoc_last]) + rw [ht,hst] at hd + norm_num at hd + linarith + +end Flatten +end SharpLiebThirring.CubeFlags + +namespace SharpLiebThirring.CubeFlags +open Finset SharpLiebThirring.PLParity +section FlattenCompact +variable {d : ℕ} (H : Subgroup (Signs (d + 1))) +variable {V : Type u144} [NormedAddCommGroup V] [NormedSpace ℝ V] [FiniteDimensional ℝ V] +variable (ρ : H →* (V ≃ₗ[ℝ] V)) (L : (Fin d → ℝ) ≃ₗ[ℝ] V) +variable (p : Fin d → ℝ) (R : ℝ) (f : (Fin (d + 1) → ℝ) → V) + +lemma compact_zeros_flattenInitial (hR : 0 < R) (hf : Continuous f) + (hK : IsCompact {x | x (Fin.last d) ∈ Set.Icc (0 : ℝ) 1 ∧ f x = 0}) : + IsCompact {x | x (Fin.last d) ∈ Set.Icc (0 : ℝ) 1 ∧ flattenInitial H ρ L p R f x = 0} := by + classical + have hc := hK.union (isCompact_iUnion + (fun s : H ↦ isCompact_closedBall (s • embedSpatial p) R)) + apply hc.of_isClosed_subset + · exact (isClosed_Icc.preimage (continuous_apply _)).inter + (isClosed_eq (continuous_flattenInitial H ρ L p R f hf) continuous_const) + · intro x hx + by_cases hb : x ∈ orbitBall (G := H) (embedSpatial p) R + · obtain ⟨s,hs⟩ := hb + exact Or.inr (Set.mem_iUnion.mpr ⟨s,hs.le⟩) + · exact Or.inl ⟨hx.1,(flattenInitial_eq_self H ρ L p R f hR hb).symm.trans hx.2⟩ + +/-- A simple initial zero need only agree with its invertible linearization up +to a relative error of one half. Compactly supported flattening turns this +into the affine continuation theorem, without adding any new final zeros. -/ +theorem exists_terminal_zero_local + (hHt : ∀ s : H, s.val.val (Fin.last d) = false) + (hρ : ∀ s : H, ∀ v : V, ‖ρ s v‖ = ‖v‖) + (hR : 0 < R) (hR1 : R ≤ 1) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • embedSpatial p) (k • embedSpatial p)) + (hball : orbitBall (G := H) (embedSpatial p) R ⊆ freeLocus (G := H)) + (hf : Continuous f) (hfe : ∀ s : H, ∀ x, f (s • x) = ρ s (f x)) + (hz0 : ∀ x, x (Fin.last d) = 0 → f x = 0 → ∃ s : H, s • embedSpatial p = x) + (herr : ∀ x, x (Fin.last d) = 0 → x ∈ orbitBall (G := H) (embedSpatial p) R → + ‖f x - affineOrbitModel H ρ L (embedSpatial p) R p x‖ ≤ + ‖affineOrbitModel H ρ L (embedSpatial p) R p x‖ / 2) + (hK : IsCompact {x | x (Fin.last d) ∈ Set.Icc (0 : ℝ) 1 ∧ f x = 0}) + (hfree : ∀ x, x (Fin.last d) ∈ Set.Icc (0 : ℝ) 1 → f x = 0 → + ∀ s : H, s • x = x → s = 1) : + ∃ x : Fin (d + 1) → ℝ, x (Fin.last d) = 1 ∧ f x = 0 := by + classical + let g := flattenInitial H ρ L p R f + have hsep' : ∀ s t : H, s ≠ t → 8 * (R/2) < dist (s • embedSpatial p) (t • embedSpatial p) := by + intro s t hst + linarith [hsep s t hst] + have hgfree : ∀ x, x (Fin.last d) ∈ Set.Icc (0 : ℝ) 1 → g x = 0 → + ∀ s : H, s • x = x → s = 1 := by + intro x hx hz s hs + by_cases hb : x ∈ orbitBall (G := H) (embedSpatial p) R + · exact hball hb s hs + · apply hfree x hx _ s hs + exact (flattenInitial_eq_self H ρ L p R f hR hb).symm.trans hz + obtain ⟨x,hxt,hxg⟩ := exists_terminal_zero_affine H hHt ρ L hρ p (R/2) (by positivity) + hsep' g (continuous_flattenInitial H ρ L p R f hf).continuousOn + (flattenInitial_equivariant H ρ L p R f hfe) + (fun x _ hx ↦ flattenInitial_inner H ρ L p R f hR hsep hx) + (fun x ht hz ↦ flattenInitial_zero_bottom H ρ L p R f hR hsep hz0 herr ht hz) + (compact_zeros_flattenInitial H ρ L p R f hR hf hK) hgfree + refine ⟨x,hxt,?_⟩ + exact (flattenInitial_final H ρ L p R f hR hR1 hxt).symm.trans hxg + +end FlattenCompact +end SharpLiebThirring.CubeFlags + +namespace SharpLiebThirring.CubeFlags +lemma hasFDerivAt_relative_error {E : Type u145} {V : Type u146} + [NormedAddCommGroup E] [NormedSpace ℝ E] [NormedAddCommGroup V] [NormedSpace ℝ V] + (f : E → V) (p : E) (L : E ≃L[ℝ] V) (hf0 : f p = 0) + (hd : HasFDerivAt f L.toContinuousLinearMap p) : + ∃ δ > 0, ∀ u : E, dist u p < δ → ‖f u - L (u-p)‖ ≤ ‖L (u-p)‖ / 2 := by + let M := ‖L.symm.toContinuousLinearMap‖ + have hM : 0 ≤ M := norm_nonneg _ + let c := 1 / (2*(M+1)) + have hc : 0 < c := by dsimp [c]; positivity + have hcM : c*M ≤ 1/2 := by + dsimp [c] + rw [one_div_mul_eq_div, div_le_iff₀ (by positivity : 0 < 2*(M+1))] + linarith + obtain ⟨δ,hδ,he⟩ := Metric.eventually_nhds_iff.mp (hd.isLittleO.def hc) + refine ⟨δ,hδ,fun u hu ↦ ?_⟩ + have hsmall : ‖f u - L (u-p)‖ ≤ c * ‖u-p‖ := by simpa only [hf0,sub_zero,ContinuousLinearEquiv.coe_coe] using he hu + have hnorm : ‖u-p‖ ≤ M * ‖L (u-p)‖ := by + have h := L.symm.toContinuousLinearMap.le_opNorm (L (u-p)) + simpa only [ContinuousLinearEquiv.coe_coe,L.symm_apply_apply] using h + calc + ‖f u - L (u-p)‖ ≤ c*‖u-p‖ := hsmall + _ ≤ c*(M*‖L (u-p)‖) := mul_le_mul_of_nonneg_left hnorm hc.le + _ = (c*M)*‖L (u-p)‖ := by ring + _ ≤ (1/2)*‖L (u-p)‖ := mul_le_mul_of_nonneg_right hcM (norm_nonneg _) + _ = ‖L (u-p)‖/2 := by ring +end SharpLiebThirring.CubeFlags + + +namespace SharpLiebThirring.CubeFlags +open Finset SharpLiebThirring.PLParity + +/-- A continuous equivariant homotopy with compact free zero set and one simple +initial zero orbit must have a terminal zero. No smoothness is required away +from the distinguished initial point. -/ +theorem exists_terminal_zero_simple {d : ℕ} + (H : Subgroup (Signs (d + 1))) (hHt : ∀ s : H, s.val.val (Fin.last d) = false) + {V : Type u147} [NormedAddCommGroup V] [NormedSpace ℝ V] [FiniteDimensional ℝ V] + (ρ : H →* (V ≃ₗ[ℝ] V)) (L : (Fin d → ℝ) ≃ₗ[ℝ] V) + (hρ : ∀ s : H, ∀ v : V, ‖ρ s v‖ = ‖v‖) + (p : Fin d → ℝ) (f : (Fin (d + 1) → ℝ) → V) + (hf : Continuous f) (hfe : ∀ s : H, ∀ x, f (s • x) = ρ s (f x)) + (hp0 : f (embedSpatial p) = 0) + (hd : HasFDerivAt (fun u : Fin d → ℝ ↦ f (embedSpatial u)) + L.toContinuousLinearEquiv.toContinuousLinearMap p) + (hz0 : ∀ x, x (Fin.last d) = 0 → f x = 0 → ∃ s : H, s • embedSpatial p = x) + (hK : IsCompact {x | x (Fin.last d) ∈ Set.Icc (0 : ℝ) 1 ∧ f x = 0}) + (hfree : ∀ x, x (Fin.last d) ∈ Set.Icc (0 : ℝ) 1 → f x = 0 → + ∀ s : H, s • x = x → s = 1) : + ∃ x : Fin (d + 1) → ℝ, x (Fin.last d) = 1 ∧ f x = 0 := by + classical + have ht0 : (embedSpatial p) (Fin.last d) = 0 := by + change Fin.snoc (α := fun _ : Fin (d + 1) ↦ ℝ) p 0 (Fin.last d) = 0 + simp only [Fin.snoc_last] + have hpFree : embedSpatial p ∈ freeLocus (G := H) := + hfree _ (by rw [ht0]; exact ⟨le_refl _,zero_le_one⟩) hp0 + obtain ⟨R₁,hR₁,hsep⟩ := orbit_separation (G := H) (embedSpatial p) hpFree + obtain ⟨R₂,hR₂,hball⟩ := Metric.isOpen_iff.mp (isOpen_freeLocus (G := H)) _ hpFree + obtain ⟨δ,hδ,herr⟩ := hasFDerivAt_relative_error (fun u : Fin d → ℝ ↦ f (embedSpatial u)) + p L.toContinuousLinearEquiv hp0 hd + let R := min 1 (min R₁ (min R₂ δ)) + have hR : 0 < R := lt_min zero_lt_one (lt_min hR₁ (lt_min hR₂ hδ)) + have hR1 : R ≤ 1 := min_le_left _ _ + have hRR₁ : R ≤ R₁ := (min_le_right _ _).trans (min_le_left _ _) + have hRR₂ : R ≤ R₂ := (min_le_right _ _).trans ((min_le_right _ _).trans (min_le_left _ _)) + have hRδ : R ≤ δ := (min_le_right _ _).trans ((min_le_right _ _).trans (min_le_right _ _)) + have hsep' : ∀ s t : H, s ≠ t → 8*R < dist (s • embedSpatial p) (t • embedSpatial p) := by + intro s t hst + linarith [hsep s t hst] + have hball' : orbitBall (G := H) (embedSpatial p) R ⊆ freeLocus (G := H) := by + rintro x ⟨s,hs⟩ + have hx : dist (s⁻¹ • x) (embedSpatial p) < R₂ := by + have he := dist_smul s⁻¹ x (s • embedSpatial p) + rw [inv_smul_smul] at he + rw [he] + exact hs.trans_le hRR₂ + have hb := freeLocus_smul s (hball hx) + simpa only [smul_inv_smul] using hb + apply exists_terminal_zero_local H ρ L p R f hHt hρ hR hR1 hsep' hball' hf hfe hz0 + · intro x ht hx + let s := ballLabel (G := H) (embedSpatial p) R x + let y := s⁻¹ • x + let u := spatial y + have htY : y (Fin.last d) = 0 := (s⁻¹).val.smul_time_zero x ht + have hY : embedSpatial u = y := embed_spatial_of_time_zero y htY + have hdist : dist u p < δ := by + have hs := ballLabel_dist (embedSpatial p) R hx + have he := dist_smul s⁻¹ x (s • embedSpatial p) + rw [inv_smul_smul] at he + have hdu := dist_spatial_le y (embedSpatial p) + rw [spatial_embed] at hdu + exact hdu.trans_lt ((he ▸ hs).trans_le hRδ) + have her := herr u hdist + have hfx : f x = ρ s (f (embedSpatial u)) := by + rw [hY,← hfe,smul_inv_smul] + change ‖f x - ρ s (L (u-p))‖ ≤ ‖ρ s (L (u-p))‖ / 2 + rw [hfx,← map_sub,hρ,hρ] + exact her + · exact hK + · exact hfree + +end SharpLiebThirring.CubeFlags + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/ContinuousRepresentative.lean b/lean/OAI/Analysis/LiebThirring/ContinuousRepresentative.lean new file mode 100644 index 0000000000000000000000000000000000000000..4a844a511fd17b54df6152a498564182b33cfc0b --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/ContinuousRepresentative.lean @@ -0,0 +1,116 @@ +import OAI.Analysis.LiebThirring.LowestEigenvalue + +namespace OAI + +universe u189 + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set Filter +open scoped Topology + +lemma integral_norm_Icc_le_sqrt_length {E : Type u189} [NormedAddCommGroup E] {f : ℝ → E} + (hf : MemLp f 2 volume) {a b : ℝ} (hab : a ≤ b) : + (∫ x in Icc a b, ‖f x‖) ≤ ‖hf.toLp f‖ * Real.sqrt (b-a) := by + let q : Lp ℝ 2 (volume : Measure ℝ) := + indicatorConstLp (s := Icc a b) 2 measurableSet_Icc (measure_Icc_lt_top.ne) (1 : ℝ) + have hq : ‖q‖ = Real.sqrt (b-a) := by + rw [show q = indicatorConstLp (s := Icc a b) 2 measurableSet_Icc (measure_Icc_lt_top.ne) (1 : ℝ) from rfl, + norm_indicatorConstLp (by norm_num) (by norm_num)] + simp only [norm_one,one_mul,ENNReal.toReal_ofNat,Real.volume_real_Icc, + max_eq_left (sub_nonneg.mpr hab),Real.sqrt_eq_rpow] + have hi : inner ℝ (hf.norm.toLp (fun x ↦ ‖f x‖)) q = ∫ x in Icc a b, ‖f x‖ := by + rw [L2.inner_def,← integral_indicator measurableSet_Icc] + apply integral_congr_ae + filter_upwards [hf.norm.coeFn_toLp,indicatorConstLp_coeFn (p := 2) + (s := Icc a b) (hs := measurableSet_Icc) (hμs := measure_Icc_lt_top.ne) (c := (1:ℝ))] with x hx hy + change q x * (hf.norm.toLp (fun x ↦ ‖f x‖)) x = (Icc a b).indicator (fun x ↦ ‖f x‖) x + rw [hx,show q x = (Icc a b).indicator (fun _ ↦ (1:ℝ)) x from hy] + by_cases h : x ∈ Icc a b <;> simp [h] + rw [← hi] + calc + _ ≤ ‖hf.norm.toLp (fun x ↦ ‖f x‖)‖ * ‖q‖ := real_inner_le_norm _ _ + _ = _ := by simp only [hq,Lp.norm_toLp,eLpNorm_norm f hf.aestronglyMeasurable] + +lemma primitive_holder {g : ℝ → ℝ} (hg : MemLp g 2 volume) (c x y : ℝ) : + |(c + ∫ t in (0:ℝ)..x, g t) - (c + ∫ t in (0:ℝ)..y, g t)| ≤ + ‖hg.toLp g‖ * Real.sqrt |x-y| := by + have hgI := SobolevProof.locallyIntegrable_intervalIntegrable (hg.locallyIntegrable (by norm_num)) + have h (a b : ℝ) (hab : a ≤ b) : + |(c + ∫ t in (0:ℝ)..b, g t) - (c + ∫ t in (0:ℝ)..a, g t)| ≤ + ‖hg.toLp g‖ * Real.sqrt (b-a) := by + have hd : (c + ∫ t in (0:ℝ)..b, g t) - (c + ∫ t in (0:ℝ)..a, g t) = + ∫ t in a..b, g t := by + rw [← intervalIntegral.integral_add_adjacent_intervals (hgI 0 a) (hgI a b)] + ring + rw [hd] + calc + _ ≤ ∫ t in a..b, ‖g t‖ := intervalIntegral.norm_integral_le_integral_norm hab + _ = ∫ t in Icc a b, ‖g t‖ := by + rw [intervalIntegral.integral_of_le hab, integral_Icc_eq_integral_Ioc] + _ ≤ _ := integral_norm_Icc_le_sqrt_length hg hab + rcases le_total y x with hyx | hxy + · simpa [abs_of_nonneg (sub_nonneg.mpr hyx)] using h y x hyx + · rw [abs_sub_comm, abs_sub_comm x y, abs_of_nonneg (sub_nonneg.mpr hxy)] + exact h x y hxy + +lemma h1_exists_continuous_rep (u : H1) : ∃ F : ℝ → ℂ, Continuous F ∧ + u.val =ᵐ[volume] F ∧ + (∀ x, ‖F x‖ ≤ 2*(‖u.val_memLp.toLp u.val‖ + ‖u.grad_memLp.toLp u.grad‖)) ∧ + (∀ x y, ‖F x-F y‖ ≤ 2*‖u.grad_memLp.toLp u.grad‖*Real.sqrt |x-y|) := by + obtain ⟨cr,hr⟩ := SobolevProof.weak_derivative_representation + ((Complex.reCLM.comp_memLp' u.val_memLp).locallyIntegrable (by norm_num)) + ((Complex.reCLM.comp_memLp' u.grad_memLp).locallyIntegrable (by norm_num)) + (SobolevProof.h1_project_weak u Complex.reCLM) + obtain ⟨ci,hi⟩ := SobolevProof.weak_derivative_representation + ((Complex.imCLM.comp_memLp' u.val_memLp).locallyIntegrable (by norm_num)) + ((Complex.imCLM.comp_memLp' u.grad_memLp).locallyIntegrable (by norm_num)) + (SobolevProof.h1_project_weak u Complex.imCLM) + let Fr := fun x ↦ cr+∫ t in (0:ℝ)..x, (u.grad t).re + let Fi := fun x ↦ ci+∫ t in (0:ℝ)..x, (u.grad t).im + have hcr : Continuous Fr := continuous_const.add (intervalIntegral.continuous_primitive + (SobolevProof.locallyIntegrable_intervalIntegrable + ((Complex.reCLM.comp_memLp' u.grad_memLp).locallyIntegrable (by norm_num))) 0) + have hci : Continuous Fi := continuous_const.add (intervalIntegral.continuous_primitive + (SobolevProof.locallyIntegrable_intervalIntegrable + ((Complex.imCLM.comp_memLp' u.grad_memLp).locallyIntegrable (by norm_num))) 0) + let F := fun x ↦ (Fr x : ℂ) + (Fi x : ℂ)*Complex.I + have hFc : Continuous F := (Complex.continuous_ofReal.comp hcr).add + ((Complex.continuous_ofReal.comp hci).mul continuous_const) + have hrep : u.val =ᵐ[volume] F := by + filter_upwards [hr,hi] with x hx hy + apply Complex.ext + · simpa [F,Fr,Fi] using hx + · simpa [F,Fr,Fi] using hy + have hrv := project_L2_norm_le Complex.reCLM (fun z ↦ Complex.abs_re_le_norm z) u.val_memLp + have hrg := project_L2_norm_le Complex.reCLM (fun z ↦ Complex.abs_re_le_norm z) u.grad_memLp + have hiv := project_L2_norm_le Complex.imCLM (fun z ↦ Complex.abs_im_le_norm z) u.val_memLp + have hig := project_L2_norm_le Complex.imCLM (fun z ↦ Complex.abs_im_le_norm z) u.grad_memLp + refine ⟨F,hFc,hrep,?_,?_⟩ + · intro x + have hxr := primitive_pointwise_bound (Complex.reCLM.comp_memLp' u.val_memLp) + (Complex.reCLM.comp_memLp' u.grad_memLp) cr hr x + have hxi := primitive_pointwise_bound (Complex.imCLM.comp_memLp' u.val_memLp) + (Complex.imCLM.comp_memLp' u.grad_memLp) ci hi x + have he : ‖F x‖ ≤ |Fr x|+|Fi x| := by simpa [F] using Complex.norm_le_abs_re_add_abs_im (F x) + change |Fr x| ≤ _ at hxr + change |Fi x| ≤ _ at hxi + dsimp only [Function.comp_def] at hxr hxi + linarith + · intro x y + have hrh := primitive_holder (Complex.reCLM.comp_memLp' u.grad_memLp) cr x y + have hih := primitive_holder (Complex.imCLM.comp_memLp' u.grad_memLp) ci x y + have he : ‖F x-F y‖ ≤ |Fr x-Fr y|+|Fi x-Fi y| := by + simpa [F] using Complex.norm_le_abs_re_add_abs_im (F x-F y) + have hs := Real.sqrt_nonneg |x-y| + change |Fr x-Fr y| ≤ _ at hrh + change |Fi x-Fi y| ≤ _ at hih + dsimp only [Function.comp_def] at hrh hih + nlinarith [mul_le_mul_of_nonneg_right hrg hs, mul_le_mul_of_nonneg_right hig hs] + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/CubeFlags.lean b/lean/OAI/Analysis/LiebThirring/CubeFlags.lean new file mode 100644 index 0000000000000000000000000000000000000000..bd51bef0e436c04dde9d320302b2223c38a590f0 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/CubeFlags.lean @@ -0,0 +1,750 @@ +import OAI.Analysis.LiebThirring.BoundState + +namespace OAI + +universe u37 u38 + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +noncomputable section +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder CStarAlgebra +noncomputable section +open MeasureTheory Set Filter +open scoped Topology +open scoped NNReal + + +end +end +end + +/-! Equivariant cubical barycentric flags. A codimension-one face of a full +flag has one canonical neighboring flag; this avoids any orientation choices. -/ +noncomputable section +open Finset +namespace SharpLiebThirring.CubeFlags + +/-- A maximal flag in the barycentric subdivision of an integer cube. -/ +@[ext] structure Flag (n : ℕ) where + base : Fin n → ℤ + corner : Fin n → Bool + order : Equiv.Perm (Fin n) + +/-- Twice the barycenter of the `k`th cubical face in a maximal flag. -/ +def Flag.vertex {n : ℕ} (F : Flag n) (k : Fin (n + 1)) (i : Fin n) : ℤ := + 2 * F.base i + if (F.order.symm i).val < k.val then 1 else if F.corner i then 2 else 0 + +/-- The real vertex obtained by rescaling the half-integer grid. -/ +def Flag.point {n : ℕ} (F : Flag n) (k : Fin (n + 1)) : Fin n → ℝ := + fun i ↦ (F.vertex k i : ℝ) / 2 + +lemma Flag.vertex_bounds {n : ℕ} (F : Flag n) (k : Fin (n + 1)) (i : Fin n) : + 2 * F.base i ≤ F.vertex k i ∧ F.vertex k i ≤ 2 * F.base i + 2 := by + simp only [vertex] + split_ifs <;> omega + +lemma Flag.point_bounds {n : ℕ} (F : Flag n) (k : Fin (n + 1)) (i : Fin n) : + (F.base i : ℝ) ≤ F.point k i ∧ F.point k i ≤ F.base i + 1 := by + obtain ⟨h₁, h₂⟩ := F.vertex_bounds k i + have h₁r : (2 : ℝ) * F.base i ≤ F.vertex k i := by exact_mod_cast h₁ + have h₂r : (F.vertex k i : ℝ) ≤ 2 * F.base i + 2 := by exact_mod_cast h₂ + dsimp [point] + constructor <;> linarith + +/-- Toggle the endpoint chosen in coordinate `i`. -/ +def Flag.flip {n : ℕ} (F : Flag n) (i : Fin n) : Flag n := + { F with corner := Function.update F.corner i (!(F.corner i)) } + +@[simp] lemma Flag.flip_base {n : ℕ} (F : Flag n) (i : Fin n) : (F.flip i).base = F.base := rfl +@[simp] lemma Flag.flip_order {n : ℕ} (F : Flag n) (i : Fin n) : (F.flip i).order = F.order := rfl + +lemma Flag.flip_flip {n : ℕ} (F : Flag n) (i : Fin n) : (F.flip i).flip i = F := by + ext j <;> simp [flip] + +/-- Across the final facet, pass to the neighboring cube and toggle its endpoint. -/ +def Flag.cross {n : ℕ} (F : Flag n) (i : Fin n) : Flag n := + { F.flip i with base := Function.update F.base i (F.base i + if F.corner i then 1 else -1) } + +@[simp] lemma Flag.cross_order {n : ℕ} (F : Flag n) (i : Fin n) : (F.cross i).order = F.order := rfl + +lemma Flag.cross_cross {n : ℕ} (F : Flag n) (i : Fin n) : (F.cross i).cross i = F := by + ext j <;> simp [cross, flip, Function.update_apply] + split_ifs <;> simp_all + +/-- Swap the order of two successive face expansions. -/ +def Flag.swap {n : ℕ} (F : Flag n) (i j : Fin n) : Flag n := + { F with order := (Equiv.swap i j).trans F.order } + +lemma Flag.swap_swap {n : ℕ} (F : Flag n) (i j : Fin n) : + (F.swap i j).swap i j = F := by + ext k <;> simp [swap] + +lemma Flag.flip_vertex {n : ℕ} (F : Flag n) (i : Fin n) (k : Fin (n + 1)) + (hik : (F.order.symm i).val < k.val) : (F.flip i).vertex k = F.vertex k := by + funext j + by_cases hj : j = i + · subst j; simp [vertex, flip, hik] + · simp [vertex, flip, Function.update_of_ne hj] + +lemma Flag.cross_vertex {n : ℕ} (F : Flag n) (i : Fin n) (k : Fin (n + 1)) + (hik : k.val ≤ (F.order.symm i).val) : (F.cross i).vertex k = F.vertex k := by + funext j + by_cases hj : j = i + · subst j + simp only [vertex, cross, flip, Function.update_self] + have h : ¬ (F.order.symm i).val < k.val := by omega + simp only [h, ↓reduceIte] + cases F.corner i <;> norm_num <;> ring + · simp [vertex, cross, flip, Function.update_of_ne hj] + +lemma Flag.swap_vertex {n : ℕ} (F : Flag n) (i j : Fin n) (k : Fin (n + 1)) + (hik : i.val < k.val ↔ j.val < k.val) : (F.swap i j).vertex k = F.vertex k := by + funext a + simp only [vertex, swap, Equiv.symm_trans, Equiv.symm_swap, Equiv.trans_apply] + congr 1 + have h : ((Equiv.swap i j) (F.order.symm a)).val < k.val ↔ (F.order.symm a).val < k.val := by + by_cases hi : F.order.symm a = i + · simp [hi, hik] + by_cases hj : F.order.symm a = j + · simp [hj, hik] + · simp [Equiv.swap_apply_of_ne_of_ne hi hj] + simp only [h] + split_ifs <;> simp_all + +/-- The other maximal flag sharing the facet obtained by deleting vertex `j`. -/ +def Flag.neighbor {n : ℕ} [NeZero n] (F : Flag n) (j : Fin (n + 1)) : Flag n := + if h₀ : j.val = 0 then F.flip (F.order ⟨0, NeZero.pos n⟩) + else if hₙ : j.val = n then F.cross (F.order ⟨n - 1, by omega⟩) + else F.swap ⟨j.val - 1, by omega⟩ ⟨j.val, by omega⟩ + +lemma Flag.neighbor_neighbor {n : ℕ} [NeZero n] (F : Flag n) (j : Fin (n + 1)) : + (F.neighbor j).neighbor j = F := by + by_cases h₀ : j.val = 0 + · simp only [neighbor, dite_eq_left h₀, flip_order] + exact flip_flip F _ + by_cases hₙ : j.val = n + · simp only [neighbor, dite_eq_right h₀, dite_eq_left hₙ, cross_order] + exact cross_cross F _ + · simp only [neighbor, dite_eq_right h₀, dite_eq_right hₙ] + exact swap_swap F _ _ + +lemma Flag.neighbor_vertex {n : ℕ} [NeZero n] (F : Flag n) (j k : Fin (n + 1)) + (hjk : k ≠ j) : (F.neighbor j).vertex k = F.vertex k := by + have hval : k.val ≠ j.val := fun h ↦ hjk (Fin.ext h) + by_cases h₀ : j.val = 0 + · simp only [neighbor, dite_eq_left h₀] + apply flip_vertex + simp only [Equiv.symm_apply_apply] + omega + by_cases hₙ : j.val = n + · simp only [neighbor, dite_eq_right h₀, dite_eq_left hₙ] + apply cross_vertex + simp only [Equiv.symm_apply_apply] + omega + · simp only [neighbor, dite_eq_right h₀, dite_eq_right hₙ] + apply swap_vertex + simp only + omega + +lemma Flag.flip_ne {n : ℕ} (F : Flag n) (i : Fin n) : F.flip i ≠ F := by + intro he + have h := congrArg (fun G : Flag n ↦ G.corner i) he + simp only [flip, Function.update_self] at h + exact (Bool.not_eq_self (F.corner i)).mp h + +lemma Flag.cross_ne {n : ℕ} (F : Flag n) (i : Fin n) : F.cross i ≠ F := by + intro he + have h := congrArg (fun G : Flag n ↦ G.base i) he + simp only [cross, Function.update_self] at h + split_ifs at h <;> omega + +lemma Flag.swap_ne {n : ℕ} (F : Flag n) (i j : Fin n) (hij : i ≠ j) : F.swap i j ≠ F := by + intro he + have h := congrArg (fun G : Flag n ↦ G.order i) he + simp only [swap, Equiv.trans_apply, Equiv.swap_apply_left] at h + exact hij (F.order.injective h).symm + +lemma Flag.neighbor_ne {n : ℕ} [NeZero n] (F : Flag n) (j : Fin (n + 1)) : + F.neighbor j ≠ F := by + by_cases h₀ : j.val = 0 + · simp only [neighbor, dite_eq_left h₀] + exact flip_ne F _ + by_cases hₙ : j.val = n + · simp only [neighbor, dite_eq_right h₀, dite_eq_left hₙ] + exact cross_ne F _ + · simp only [neighbor, dite_eq_right h₀, dite_eq_right hₙ] + apply swap_ne + intro h + have hf := congrArg Fin.val h + simp only at hf + omega + +section Consecutive +variable {V : Type u37} [AddCommGroup V] [Module ℝ V] + +lemma span_consecutive {n : ℕ} (v : Fin (n + 1) → V) : + Submodule.span ℝ (Set.range (Fin.cons (v 0) (fun i ↦ v i.succ - v i.castSucc))) = + Submodule.span ℝ (Set.range v) := by + apply le_antisymm + · apply Submodule.span_le.mpr + rintro _ ⟨i, rfl⟩ + refine Fin.cases ?_ (fun j ↦ ?_) i + · exact Submodule.subset_span ⟨0, rfl⟩ + · exact Submodule.sub_mem _ (Submodule.subset_span ⟨j.succ, rfl⟩) + (Submodule.subset_span ⟨j.castSucc, rfl⟩) + · apply Submodule.span_le.mpr + rintro _ ⟨i, rfl⟩ + refine Fin.induction ?_ (fun j hj ↦ ?_) i + · exact Submodule.subset_span ⟨0, rfl⟩ + · have hd : v j.succ - v j.castSucc ∈ + Submodule.span ℝ (Set.range (Fin.cons (v 0) (fun i ↦ v i.succ - v i.castSucc))) := + Submodule.subset_span ⟨j.succ, rfl⟩ + have hsum := Submodule.add_mem _ hd hj + rw [sub_add_cancel] at hsum + exact hsum + +lemma linearIndependent_consecutive_iff {n : ℕ} (v : Fin (n + 1) → V) : + LinearIndependent ℝ (Fin.cons (v 0) (fun i ↦ v i.succ - v i.castSucc)) ↔ + LinearIndependent ℝ v := by + rw [linearIndependent_iff_card_eq_finrank_span, linearIndependent_iff_card_eq_finrank_span] + change _ = Module.finrank ℝ (Submodule.span ℝ _) ↔ _ = Module.finrank ℝ (Submodule.span ℝ _) + rw [span_consecutive] +end Consecutive + +def Flag.step {n : ℕ} (F : Flag n) (i : Fin n) : ℝ := + if F.corner (F.order i) then -1 / 2 else 1 / 2 + +lemma Flag.step_ne_zero {n : ℕ} (F : Flag n) (i : Fin n) : F.step i ≠ 0 := by + dsimp [step] + split_ifs <;> norm_num + +lemma Flag.point_succ_sub {n : ℕ} (F : Flag n) (k : Fin n) : + F.point k.succ - F.point k.castSucc = Pi.single (F.order k) (F.step k) := by + ext i + by_cases hi : i = F.order k + · subst i + simp only [Pi.sub_apply, point, vertex, Equiv.symm_apply_apply, + Fin.val_succ, Fin.val_castSucc, Nat.lt_succ_self, ↓reduceIte, lt_self_iff_false, + Pi.single_eq_same, step] + split_ifs <;> push_cast <;> ring + · have hik : F.order.symm i ≠ k := by + intro h + apply hi + simpa using congrArg F.order h + have hval : (F.order.symm i).val ≠ k.val := fun h ↦ hik (Fin.ext h) + have hlt : (F.order.symm i).val < k.val + 1 ↔ (F.order.symm i).val < k.val := by omega + simp [hi, point, vertex, hlt] + +lemma Flag.linearIndependent_steps {n : ℕ} (F : Flag n) : + LinearIndependent ℝ (fun k : Fin n ↦ F.point k.succ - F.point k.castSucc) := by + classical + have hb := (Pi.basisFun ℝ (Fin n)).linearIndependent.comp F.order F.order.injective + have hs := hb.units_smul (fun k ↦ Units.mk0 (F.step k) (F.step_ne_zero k)) + have he : (fun k : Fin n ↦ F.point k.succ - F.point k.castSucc) = + (fun k ↦ Units.mk0 (F.step k) (F.step_ne_zero k)) • + ((Pi.basisFun ℝ (Fin n)) ∘ F.order) := by + funext k + rw [F.point_succ_sub k] + ext i + simp [Pi.basisFun_apply, Pi.single_apply, Units.smul_def] + rw [he] + exact hs + +lemma Flag.augmented_linearIndependent {n : ℕ} (F : Flag n) : + LinearIndependent ℝ (fun k ↦ ((1 : ℝ), F.point k)) := by + apply (linearIndependent_consecutive_iff _).mp + apply linearIndependent_finCons.mpr + constructor + · have h := F.linearIndependent_steps.map' (LinearMap.inr ℝ ℝ (Fin n → ℝ)) + (LinearMap.ker_eq_bot.mpr LinearMap.inr_injective) + simpa only [LinearMap.inr_apply, Function.comp_def, Prod.mk_sub_mk, sub_self] using h + · have hspan : Submodule.span ℝ + (Set.range (fun i : Fin n ↦ ((1 : ℝ), F.point i.succ) - (1, F.point i.castSucc))) ≤ + LinearMap.ker (LinearMap.fst ℝ ℝ (Fin n → ℝ)) := by + apply Submodule.span_le.mpr + rintro _ ⟨i, rfl⟩ + simp + intro hmem + have h := hspan hmem + simp at h + +/-- Coordinate reflections preserve the entire flag subdivision. -/ +def Flag.reflect {n : ℕ} (s : Fin n → Bool) (F : Flag n) : Flag n where + base i := if s i then -F.base i - 1 else F.base i + corner i := xor (s i) (F.corner i) + order := F.order + +lemma Flag.reflect_false {n : ℕ} (F : Flag n) : F.reflect (fun _ ↦ false) = F := by + ext i <;> simp [reflect] + +lemma Flag.reflect_reflect {n : ℕ} (s t : Fin n → Bool) (F : Flag n) : + (F.reflect t).reflect s = F.reflect (fun i ↦ xor (s i) (t i)) := by + ext i <;> simp only [reflect] + · rcases Bool.eq_false_or_eq_true (s i) with hs | hs <;> + rcases Bool.eq_false_or_eq_true (t i) with ht | ht <;> simp [hs, ht] + · exact (Bool.xor_assoc _ _ _).symm + +lemma Flag.reflect_vertex {n : ℕ} (s : Fin n → Bool) (F : Flag n) + (k : Fin (n + 1)) (i : Fin n) : + (F.reflect s).vertex k i = if s i then -F.vertex k i else F.vertex k i := by + simp only [vertex, reflect] + rcases Bool.eq_false_or_eq_true (s i) with hs | hs <;> + rcases Bool.eq_false_or_eq_true (F.corner i) with hc | hc <;> + simp [hs, hc] <;> split_ifs <;> omega + +lemma Flag.reflect_point {n : ℕ} (s : Fin n → Bool) (F : Flag n) + (k : Fin (n + 1)) (i : Fin n) : + (F.reflect s).point k i = if s i then -F.point k i else F.point k i := by + dsimp [point] + rw [reflect_vertex] + rcases Bool.eq_false_or_eq_true (s i) with hs | hs <;> simp [hs] + ring + +lemma Flag.reflect_flip {n : ℕ} (s : Fin n → Bool) (F : Flag n) (i : Fin n) : + (F.flip i).reflect s = (F.reflect s).flip i := by + ext j <;> simp only [reflect, flip] + by_cases hji : j = i + · subst j + simp only [Function.update_self] + cases s i <;> cases F.corner i <;> rfl + · simp [Function.update_of_ne hji] + +lemma Flag.reflect_cross {n : ℕ} (s : Fin n → Bool) (F : Flag n) (i : Fin n) : + (F.cross i).reflect s = (F.reflect s).cross i := by + ext j <;> simp only [reflect, cross, flip] + · by_cases hji : j = i + · subst j + simp only [Function.update_self] + rcases Bool.eq_false_or_eq_true (s i) with hs | hs <;> + rcases Bool.eq_false_or_eq_true (F.corner i) with hc | hc <;> + simp [hs, hc] + omega + · simp [Function.update_of_ne hji] + · by_cases hji : j = i + · subst j + simp only [Function.update_self] + cases s i <;> cases F.corner i <;> rfl + · simp [Function.update_of_ne hji] + +lemma Flag.reflect_swap {n : ℕ} (s : Fin n → Bool) (F : Flag n) (i j : Fin n) : + (F.swap i j).reflect s = (F.reflect s).swap i j := rfl + +lemma Flag.reflect_neighbor {n : ℕ} [NeZero n] (s : Fin n → Bool) + (F : Flag n) (j : Fin (n + 1)) : + (F.neighbor j).reflect s = (F.reflect s).neighbor j := by + by_cases h₀ : j.val = 0 + · simp only [neighbor, dite_eq_left h₀, reflect] + exact reflect_flip s F _ + by_cases hₙ : j.val = n + · simp only [neighbor, dite_eq_right h₀, dite_eq_left hₙ, reflect] + exact reflect_cross s F _ + · simp only [neighbor, dite_eq_right h₀, dite_eq_right hₙ] + exact reflect_swap s F _ _ + +/-- Coordinate reflections form an elementary two-group. -/ +@[ext] structure Signs (n : ℕ) where + val : Fin n → Bool + +def Signs.equiv (n : ℕ) : Signs n ≃ (Fin n → Bool) where + toFun := Signs.val + invFun := Signs.mk + left_inv _ := rfl + right_inv _ := rfl + +instance {n : ℕ} : Fintype (Signs n) := Fintype.ofEquiv _ (Signs.equiv n).symm +instance {n : ℕ} : DecidableEq (Signs n) := Classical.decEq _ + +instance {n : ℕ} : CommGroup (Signs n) where + mul s t := ⟨fun i ↦ xor (s.val i) (t.val i)⟩ + one := ⟨fun _ ↦ false⟩ + inv s := s + mul_assoc s t u := by ext i; exact Bool.xor_assoc _ _ _ + one_mul s := by ext i; exact Bool.false_xor _ + mul_one s := by ext i; exact Bool.xor_false _ + inv_mul_cancel s := by ext i; exact Bool.xor_self _ + mul_comm s t := by ext i; exact Bool.xor_comm _ _ + +@[simp] lemma Signs.mul_val {n : ℕ} (s t : Signs n) (i : Fin n) : + (s * t).val i = xor (s.val i) (t.val i) := rfl +@[simp] lemma Signs.one_val {n : ℕ} (i : Fin n) : (1 : Signs n).val i = false := rfl +@[simp] lemma Signs.inv_eq {n : ℕ} (s : Signs n) : s⁻¹ = s := rfl + +instance {n : ℕ} : MulAction (Signs n) (Flag n) where + smul s F := F.reflect s.val + one_smul := Flag.reflect_false + mul_smul s t F := (F.reflect_reflect s.val t.val).symm + +lemma Flag.smul_def {n : ℕ} (s : Signs n) (F : Flag n) : s • F = F.reflect s.val := rfl + +instance {n : ℕ} : IsCancelSMul (Signs n) (Flag n) where + right_cancel' s t F he := by + ext i + have hb := congrArg (fun G : Flag n ↦ G.base i) he + change (if s.val i then -F.base i - 1 else F.base i) = + (if t.val i then -F.base i - 1 else F.base i) at hb + rcases Bool.eq_false_or_eq_true (s.val i) with hs | hs <;> + rcases Bool.eq_false_or_eq_true (t.val i) with ht | ht <;> + simp_all <;> omega + +lemma Flag.smul_neighbor {n : ℕ} [NeZero n] (s : Signs n) + (F : Flag n) (j : Fin (n + 1)) : + s • F.neighbor j = (s • F).neighbor j := F.reflect_neighbor s.val j + +/-- No two vertices of a flag belong to the same coordinate-reflection orbit. +Parity records the order in which coordinates become barycenters. -/ +lemma Flag.vertex_orbits_distinct {n : ℕ} (F : Flag n) + (j k : Fin (n + 1)) (s : Signs n) + (he : ∀ i, F.vertex j i = if s.val i then -F.vertex k i else F.vertex k i) : j = k := by + apply Fin.ext + by_contra h + have hlt : j.val < k.val ∨ k.val < j.val := lt_or_gt_of_ne h + have hbad (a b : Fin (n + 1)) (hab : a.val < b.val) + (hh : ∀ i, F.vertex a i = if s.val i then -F.vertex b i else F.vertex b i) : False := by + let i : Fin n := F.order ⟨a.val, by omega⟩ + have hi : (F.order.symm i).val = a.val := by simp [i] + have hh' := hh i + simp only [vertex, hi, lt_self_iff_false, ↓reduceIte, hab] at hh' + rcases Bool.eq_false_or_eq_true (s.val i) with hs | hs <;> + rcases Bool.eq_false_or_eq_true (F.corner i) with hc | hc <;> + simp [hs, hc] at hh' <;> omega + rcases hlt with hlt | hlt + · exact hbad j k hlt he + · apply hbad k j hlt + intro i + have hi := he i + rcases Bool.eq_false_or_eq_true (s.val i) with hs | hs <;> + simp_all + +/-- Distance, with the corner sign, from the chosen endpoint of a coordinate. -/ +def Flag.depth {n : ℕ} (F : Flag n) (i : Fin n) (x : Fin n → ℝ) : ℝ := + if F.corner i then (F.base i : ℝ) + 1 - x i else x i - F.base i + +lemma Flag.depth_point {n : ℕ} (F : Flag n) (i : Fin n) (k : Fin (n + 1)) : + F.depth i (F.point k) = if (F.order.symm i).val < k.val then 1 / 2 else 0 := by + simp only [depth, point, vertex] + rcases Bool.eq_false_or_eq_true (F.corner i) with hc | hc <;> + simp only [hc, Bool.false_eq_true, ↓reduceIte, Int.cast_add, Int.cast_mul, + Int.cast_ofNat] <;> split_ifs <;> norm_num <;> ring + +lemma Flag.depth_combination {n : ℕ} (F : Flag n) (i : Fin n) + {ι : Type u38} [Fintype ι] (w : ι → ℝ) (x : ι → Fin n → ℝ) (hw : ∑ k, w k = 1) : + F.depth i (∑ k, w k • x k) = ∑ k, w k * F.depth i (x k) := by + simp only [depth, Finset.sum_apply, Pi.smul_apply, smul_eq_mul] + rcases Bool.eq_false_or_eq_true (F.corner i) with hc | hc <;> + simp only [hc, Bool.false_eq_true, ↓reduceIte, mul_sub, Finset.sum_sub_distrib, + ← Finset.sum_mul, hw, one_mul] + +lemma Flag.depth_nonneg {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) (i : Fin n) : + 0 ≤ F.depth i (∑ k, w k • F.point k) := by + rw [F.depth_combination i w F.point hs] + apply Finset.sum_nonneg + intro k _ + have hk := hw k + rw [F.depth_point] + split_ifs <;> positivity + +lemma Flag.depth_le_half {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) (i : Fin n) : + F.depth i (∑ k, w k • F.point k) ≤ 1 / 2 := by + rw [F.depth_combination i w F.point hs] + calc + _ ≤ ∑ k, w k * (1 / 2) := by + apply Finset.sum_le_sum + intro k _ + apply mul_le_mul_of_nonneg_left _ (hw k) + rw [F.depth_point] + split_ifs <;> norm_num + _ = 1 / 2 := by rw [← Finset.sum_mul, hs, one_mul] + +lemma Flag.depth_pos {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 < w k) (hs : ∑ k, w k = 1) (i : Fin n) : + 0 < F.depth i (∑ k, w k • F.point k) := by + rw [F.depth_combination i w F.point hs] + apply Finset.sum_pos' + · intro k _ + have hk := (hw k).le + rw [F.depth_point] + split_ifs <;> positivity + · refine ⟨Fin.last n, Finset.mem_univ _, ?_⟩ + rw [F.depth_point] + simp only [Fin.val_last, (F.order.symm i).isLt, ↓reduceIte] + exact mul_pos (hw _) (by norm_num) + +lemma Flag.depth_lt_half {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 < w k) (hs : ∑ k, w k = 1) (i : Fin n) : + F.depth i (∑ k, w k • F.point k) < 1 / 2 := by + rw [F.depth_combination i w F.point hs] + calc + _ < ∑ k, w k * (1 / 2) := by + apply Finset.sum_lt_sum + · intro k _ + apply mul_le_mul_of_nonneg_left _ (hw k).le + rw [F.depth_point] + split_ifs <;> norm_num + · refine ⟨0, Finset.mem_univ _, ?_⟩ + rw [F.depth_point] + simp only [Fin.val_zero, Nat.not_lt_zero, ↓reduceIte, mul_zero] + exact mul_pos (hw _) (by norm_num) + _ = 1 / 2 := by rw [← Finset.sum_mul, hs, one_mul] + +lemma Flag.depth_antitone {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) + (i j : Fin n) (hij : F.order.symm i ≤ F.order.symm j) : + F.depth j (∑ k, w k • F.point k) ≤ F.depth i (∑ k, w k • F.point k) := by + rw [F.depth_combination i w F.point hs, F.depth_combination j w F.point hs] + apply Finset.sum_le_sum + intro k _ + apply mul_le_mul_of_nonneg_left _ (hw k) + rw [F.depth_point, F.depth_point] + split_ifs <;> try norm_num + exact False.elim (by omega) + +lemma Flag.depth_strictAnti {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 < w k) (hs : ∑ k, w k = 1) + (i j : Fin n) (hij : F.order.symm i < F.order.symm j) : + F.depth j (∑ k, w k • F.point k) < F.depth i (∑ k, w k • F.point k) := by + rw [F.depth_combination i w F.point hs, F.depth_combination j w F.point hs] + apply Finset.sum_lt_sum + · intro k _ + apply mul_le_mul_of_nonneg_left _ (hw k).le + rw [F.depth_point, F.depth_point] + split_ifs <;> try norm_num + exact False.elim (by omega) + · refine ⟨(F.order.symm i).succ, Finset.mem_univ _, ?_⟩ + rw [F.depth_point, F.depth_point] + simp only [Fin.val_succ] + rw [ite_eq_right (by omega), ite_eq_left (by omega)] + nlinarith [hw (F.order.symm i).succ] + +lemma Flag.combination_bounds {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) (i : Fin n) : + (F.base i : ℝ) ≤ (∑ k, w k • F.point k) i ∧ + (∑ k, w k • F.point k) i ≤ F.base i + 1 := by + have h₀ := F.depth_nonneg w hw hs i + have h₁ := F.depth_le_half w hw hs i + rcases Bool.eq_false_or_eq_true (F.corner i) with hc | hc <;> + simp only [depth, hc, Bool.false_eq_true, ↓reduceIte] at h₀ h₁ <;> + constructor <;> linarith + +lemma Flag.combination_strict_bounds {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 < w k) (hs : ∑ k, w k = 1) (i : Fin n) : + (F.base i : ℝ) < (∑ k, w k • F.point k) i ∧ + (∑ k, w k • F.point k) i < F.base i + 1 := by + have h₀ := F.depth_pos w hw hs i + have h₁ := F.depth_lt_half w hw hs i + rcases Bool.eq_false_or_eq_true (F.corner i) with hc | hc <;> + simp only [depth, hc, Bool.false_eq_true, ↓reduceIte] at h₀ h₁ <;> + constructor <;> linarith + +/-- Relative interiors of the maximal flag simplices are disjoint, even across +neighboring integer cubes. This is the only uniqueness fact needed to count +an initial affine zero. -/ +lemma Flag.eq_of_strict_combination {n : ℕ} (F G : Flag n) + (w z : Fin (n + 1) → ℝ) (hw : ∀ k, 0 < w k) (hz : ∀ k, 0 ≤ z k) + (hsw : ∑ k, w k = 1) (hsz : ∑ k, z k = 1) + (he : ∑ k, w k • F.point k = ∑ k, z k • G.point k) : F = G := by + have hb : F.base = G.base := by + funext i + have hF := F.combination_strict_bounds w hw hsw i + have hG := G.combination_bounds z hz hsz i + rw [← he] at hG + by_contra hne + rcases lt_or_gt_of_ne hne with hlt | hlt + · have hc : (F.base i : ℝ) + 1 ≤ G.base i := by + exact_mod_cast (show F.base i + 1 ≤ G.base i by omega) + linarith + · have hc : (G.base i : ℝ) + 1 ≤ F.base i := by + exact_mod_cast (show G.base i + 1 ≤ F.base i by omega) + linarith + have hc : F.corner = G.corner := by + funext i + have hF := F.depth_lt_half w hw hsw i + have hG := G.depth_le_half z hz hsz i + rw [← he] at hG + cases hf : F.corner i <;> cases hg : G.corner i <;> try rfl + all_goals + simp only [depth, ← hb, hf, hg, Bool.false_eq_true, ↓reduceIte] at hF hG + linarith + have hd (i : Fin n) (x : Fin n → ℝ) : F.depth i x = G.depth i x := by + simp only [depth, hb, hc] + have hm : StrictMono (fun i : Fin n ↦ G.order.symm (F.order i)) := by + intro i j hij + by_contra hnot + have hle : G.order.symm (F.order j) ≤ G.order.symm (F.order i) := le_of_not_gt hnot + have hG := G.depth_antitone z hz hsz (F.order j) (F.order i) hle + have hF := F.depth_strictAnti w hw hsw (F.order i) (F.order j) (by simpa using hij) + rw [← he, ← hd, ← hd] at hG + linarith + have ho : F.order = G.order := by + ext i + have hh := congrFun hm.eq_id i + have ha := congrArg G.order hh + exact congrArg Fin.val (by simpa only [Equiv.apply_symm_apply, id_eq] using ha) + exact Flag.ext hb hc ho + + +/-- The corner vertex controls strict distance from the midplanes. -/ +lemma Flag.depth_lt_half_of_pos_zero {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (h₀ : 0 < w 0) + (hs : ∑ k, w k = 1) (i : Fin n) : + F.depth i (∑ k, w k • F.point k) < 1 / 2 := by + rw [F.depth_combination i w F.point hs] + calc + _ < ∑ k, w k * (1 / 2) := by + apply Finset.sum_lt_sum + · intro k _ + apply mul_le_mul_of_nonneg_left _ (hw k) + rw [F.depth_point] + split_ifs <;> norm_num + · refine ⟨0, Finset.mem_univ _, ?_⟩ + rw [F.depth_point] + simp only [Fin.val_zero, Nat.not_lt_zero, ↓reduceIte, mul_zero] + exact mul_pos h₀ (by norm_num) + _ = 1 / 2 := by rw [← Finset.sum_mul, hs, one_mul] + +lemma Flag.depth_pos_of_weight {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) + (i : Fin n) (k : Fin (n + 1)) (hk : (F.order.symm i).val < k.val) (hkw : 0 < w k) : + 0 < F.depth i (∑ k, w k • F.point k) := by + rw [F.depth_combination i w F.point hs] + apply Finset.sum_pos' + · intro l _ + have hl := hw l + rw [F.depth_point] + split_ifs <;> positivity + · refine ⟨k, Finset.mem_univ _, ?_⟩ + rw [F.depth_point, ite_eq_left hk] + exact mul_pos hkw (by norm_num) + +lemma Flag.depth_strictAnti_of_weight {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) + (i j : Fin n) (hij : F.order.symm i < F.order.symm j) + (hpos : 0 < w (F.order.symm i).succ) : + F.depth j (∑ k, w k • F.point k) < F.depth i (∑ k, w k • F.point k) := by + rw [F.depth_combination i w F.point hs, F.depth_combination j w F.point hs] + apply Finset.sum_lt_sum + · intro k _ + apply mul_le_mul_of_nonneg_left _ (hw k) + rw [F.depth_point, F.depth_point] + split_ifs <;> try norm_num + exact False.elim (by omega) + · refine ⟨(F.order.symm i).succ, Finset.mem_univ _, ?_⟩ + rw [F.depth_point, F.depth_point] + simp only [Fin.val_succ] + rw [ite_eq_right (by omega), ite_eq_left (by omega)] + nlinarith + +/-- Bottom-facet interiors are disjoint among flags on the same side of the +bottom hyperplane. The last coordinate expanded is the time coordinate `t`. -/ +lemma Flag.eq_of_facet_combination {n : ℕ} [NeZero n] (F G : Flag n) + (t : Fin n) (ht : (F.order.symm t).val = n - 1) + (hbt : F.base t = G.base t) (hct : F.corner t = G.corner t) + (w z : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) + (hwp : ∀ k, k ≠ Fin.last n → 0 < w k) (hz : ∀ k, 0 ≤ z k) + (hsw : ∑ k, w k = 1) (hsz : ∑ k, z k = 1) + (he : ∑ k, w k • F.point k = ∑ k, z k • G.point k) : F = G := by + have hn : n ≠ 0 := NeZero.ne n + have hw₀ : 0 < w 0 := hwp 0 (by intro h; have hh := congrArg Fin.val h; simp at hh; omega) + have hdep (i : Fin n) (hi : i ≠ t) : 0 < F.depth i (∑ k, w k • F.point k) := by + have hp : (F.order.symm i).val < n - 1 := by + have hne : F.order.symm i ≠ F.order.symm t := fun h ↦ hi (F.order.symm.injective h) + have hval : (F.order.symm i).val ≠ (F.order.symm t).val := fun h ↦ hne (Fin.ext h) + have := (F.order.symm i).isLt + omega + apply F.depth_pos_of_weight w hw hsw i (F.order.symm i).succ (by simp) + apply hwp + intro hh + have hv := congrArg Fin.val hh + simp only [Fin.val_succ, Fin.val_last] at hv + omega + have hb : F.base = G.base := by + funext i + by_cases hi : i = t + · simpa only [hi] using hbt + have h₀ := hdep i hi + have h₁ := F.depth_lt_half_of_pos_zero w hw hw₀ hsw i + have hF : (F.base i : ℝ) < (∑ k, w k • F.point k) i ∧ + (∑ k, w k • F.point k) i < F.base i + 1 := by + rcases Bool.eq_false_or_eq_true (F.corner i) with hc | hc <;> + simp only [depth, hc, Bool.false_eq_true, ↓reduceIte] at h₀ h₁ <;> + constructor <;> linarith + have hG := G.combination_bounds z hz hsz i + rw [← he] at hG + by_contra hne + rcases lt_or_gt_of_ne hne with hlt | hlt + · have hc : (F.base i : ℝ) + 1 ≤ G.base i := by + exact_mod_cast (show F.base i + 1 ≤ G.base i by omega) + linarith + · have hc : (G.base i : ℝ) + 1 ≤ F.base i := by + exact_mod_cast (show G.base i + 1 ≤ F.base i by omega) + linarith + have hc : F.corner = G.corner := by + funext i + by_cases hi : i = t + · simpa only [hi] using hct + have hF := F.depth_lt_half_of_pos_zero w hw hw₀ hsw i + have hG := G.depth_le_half z hz hsz i + rw [← he] at hG + cases hf : F.corner i <;> cases hg : G.corner i <;> try rfl + all_goals + simp only [depth, ← hb, hf, hg, Bool.false_eq_true, ↓reduceIte] at hF hG + linarith + have hd (i : Fin n) (x : Fin n → ℝ) : F.depth i x = G.depth i x := by + simp only [depth, hb, hc] + have hm : StrictMono (fun i : Fin n ↦ G.order.symm (F.order i)) := by + intro i j hij + by_contra hnot + have hle : G.order.symm (F.order j) ≤ G.order.symm (F.order i) := le_of_not_gt hnot + have hG := G.depth_antitone z hz hsz (F.order j) (F.order i) hle + have hF := F.depth_strictAnti_of_weight w hw hsw (F.order i) (F.order j) + (by simpa using hij) (by + apply hwp + intro h + have hh := congrArg Fin.val h + simp only [Equiv.symm_apply_apply, Fin.val_succ, Fin.val_last] at hh + have := j.isLt + have : i.val < j.val := hij + omega) + rw [← he, ← hd, ← hd] at hG + linarith + have ho : F.order = G.order := by + ext i + have hh := congrFun hm.eq_id i + have ha := congrArg G.order hh + exact congrArg Fin.val (by simpa only [Equiv.apply_symm_apply, id_eq] using ha) + exact Flag.ext hb hc ho + +/-- A shared facet whose vertices have trivial stabilizers cannot identify its +two incident flags under a reflection action. The hypothesis will be supplied +by the positive distance from zero-row strata. -/ +lemma Flag.neighbor_ne_reflect_of_free {n : ℕ} [NeZero n] (F : Flag n) + (j : Fin (n + 1)) (s : Signs n) + (hfree : ∀ k : Fin (n + 1), + (∀ i, (if s.val i then -F.vertex k i else F.vertex k i) = F.vertex k i) → s = 1) : + F.neighbor j ≠ s • F := by + intro he + have hn : n ≠ 0 := NeZero.ne n + obtain ⟨k, hk⟩ : ∃ k : Fin (n + 1), k ≠ j := by + by_cases hj : j.val = 0 + · exact ⟨⟨n, by omega⟩, by intro h; have hh := congrArg Fin.val h; simp at hh; omega⟩ + · exact ⟨0, by intro h; have hh := congrArg Fin.val h; simp at hh; omega⟩ + have hs : s = 1 := by + apply hfree k + intro i + have hv := congrArg (fun G : Flag n ↦ G.vertex k i) he + rw [F.neighbor_vertex j k hk] at hv + simpa only [smul_def, reflect_vertex] using hv.symm + rw [hs, one_smul] at he + exact F.neighbor_ne j he + +end SharpLiebThirring.CubeFlags + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/CutoffEnergy.lean b/lean/OAI/Analysis/LiebThirring/CutoffEnergy.lean new file mode 100644 index 0000000000000000000000000000000000000000..7d6a83fb715b76a0ecfda00cf78347b1640e1a3f --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/CutoffEnergy.lean @@ -0,0 +1,370 @@ +import OAI.Analysis.LiebThirring.QuadraticForms + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.SobolevProof +open MeasureTheory Set +open scoped Topology + +/-- C¹ representatives of real H¹, with the L² inner product (not the H¹ norm). -/ +def c1L2Submodule : Submodule ℝ ((ℝ → ℝ) × (ℝ → ℝ)) where + carrier := {u | MemLp u.1 2 volume ∧ MemLp u.2 2 volume ∧ Continuous u.2 ∧ + ∀ x, HasDerivAt u.1 (u.2 x) x} + zero_mem' := ⟨by simp,by simp,continuous_zero,fun x ↦ hasDerivAt_const x 0⟩ + add_mem' := by + rintro u v ⟨hu,hu',hc,hd⟩ ⟨hv,hv',hvc,hvd⟩ + exact ⟨hu.add hv,hu'.add hv',hc.add hvc,fun x ↦ (hd x).add (hvd x)⟩ + smul_mem' := by + rintro c u ⟨hu,hu',hc,hd⟩ + exact ⟨hu.const_smul c,hu'.const_smul c,continuous_const.smul hc, + fun x ↦ (hd x).const_smul c⟩ + +def C1L2 : Type := ↥c1L2Submodule +instance : AddCommGroup C1L2 := inferInstanceAs (AddCommGroup ↥c1L2Submodule) +instance : Module ℝ C1L2 := inferInstanceAs (Module ℝ ↥c1L2Submodule) +namespace C1L2 + +def val (u : C1L2) : ℝ → ℝ := u.1.1 +def grad (u : C1L2) : ℝ → ℝ := u.1.2 +lemma val_memLp (u : C1L2) : MemLp u.val 2 volume := u.property.1 +lemma grad_memLp (u : C1L2) : MemLp u.grad 2 volume := u.property.2.1 +lemma grad_continuous (u : C1L2) : Continuous u.grad := u.property.2.2.1 +lemma hasDerivAt (u : C1L2) (x : ℝ) : HasDerivAt u.val (u.grad x) x := u.property.2.2.2 x +lemma continuous (u : C1L2) : Continuous u.val := continuous_iff_continuousAt.mpr (fun x ↦ (u.hasDerivAt x).continuousAt) + +def toLp : C1L2 →ₗ[ℝ] Lp ℝ 2 (volume : Measure ℝ) where + toFun u := u.val_memLp.toLp u.val + map_add' u v := u.val_memLp.toLp_add v.val_memLp + map_smul' c u := u.val_memLp.toLp_const_smul c + +lemma toLp_injective : Function.Injective toLp := by + intro u v h + have ha : u.val =ᵐ[volume] v.val := (MemLp.toLp_eq_toLp_iff u.val_memLp v.val_memLp).mp h + have hv : u.val = v.val := MeasureTheory.Measure.eq_of_ae_eq ha u.continuous v.continuous + apply Subtype.ext + apply Prod.ext + · exact hv + · funext x + exact ((hv ▸ u.hasDerivAt x) : HasDerivAt v.val (u.grad x) x).unique (v.hasDerivAt x) + +instance : NormedAddCommGroup C1L2 := NormedAddCommGroup.induced C1L2 (Lp ℝ 2 (volume : Measure ℝ)) toLp toLp_injective +instance : InnerProductSpace ℝ C1L2 := InnerProductSpace.induced toLp + +@[simp] lemma val_zero (x : ℝ) : (0 : C1L2).val x = 0 := rfl +@[simp] lemma grad_zero (x : ℝ) : (0 : C1L2).grad x = 0 := rfl +@[simp] lemma val_add (u v : C1L2) (x : ℝ) : (u+v).val x = u.val x+v.val x := rfl +@[simp] lemma grad_add (u v : C1L2) (x : ℝ) : (u+v).grad x = u.grad x+v.grad x := rfl +@[simp] lemma val_smul (c : ℝ) (u : C1L2) (x : ℝ) : (c • u).val x = c*u.val x := rfl +@[simp] lemma grad_smul (c : ℝ) (u : C1L2) (x : ℝ) : (c • u).grad x = c*u.grad x := rfl + +lemma inner_eq_integral (u v : C1L2) : inner ℝ u v = ∫ x, u.val x*v.val x := by + change inner ℝ (toLp u) (toLp v) = _ + rw [L2.inner_def] + apply integral_congr_ae + filter_upwards [u.val_memLp.coeFn_toLp,v.val_memLp.coeFn_toLp] with x hx hy + change (toLp v) x*(toLp u) x = u.val x*v.val x + rw [show (toLp u) x = u.val x from hx,show (toLp v) x = v.val x from hy,mul_comm] + +end C1L2 +end SharpLiebThirring.SobolevProof +namespace SharpLiebThirring.SobolevProof +open MeasureTheory Set +lemma locallyIntegrable_intervalIntegrable {f : ℝ → ℝ} (hf : LocallyIntegrable f volume) (a b : ℝ) : + IntervalIntegrable f volume a b := + (intervalIntegrable_iff').mpr (hf.integrableOn_isCompact isCompact_uIcc) +end SharpLiebThirring.SobolevProof +namespace SharpLiebThirring.SobolevProof +open MeasureTheory Set Filter Metric +open scoped Topology ContDiff +namespace C1L2 + +lemma contDiff (u : C1L2) : ContDiff ℝ 1 u.val := by + rw [contDiff_one_iff_deriv] + exact ⟨fun x ↦ (u.hasDerivAt x).differentiableAt, + by convert u.grad_continuous using 1; ext x; exact (u.hasDerivAt x).deriv⟩ + +lemma ac (u : C1L2) (a b : ℝ) : AbsolutelyContinuousOnInterval u.val a b := + u.contDiff.contDiffOn.absolutelyContinuousOnInterval + +@[simp] lemma deriv_val (u : C1L2) : deriv u.val = u.grad := funext (fun x ↦ (u.hasDerivAt x).deriv) + +/-- Exact integrated real eigen-equation; no regularity of W beyond local L¹. -/ +def IsEigen (W : ℝ → ℝ) (k : ℝ) (u : C1L2) : Prop := + ∀ a b, u.grad b-u.grad a = ∫ x in a..b, (k^2-W x)*u.val x + +lemma eigen_integrable {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) + (k : ℝ) (u : C1L2) : LocallyIntegrable (fun x ↦ (k^2-W x)*u.val x) volume := + ((locallyIntegrable_const (c := k^2)).sub hW).mul_continuous u.continuous + +def eigenSubmodule {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) (k : ℝ) : Submodule ℝ C1L2 where + carrier := {u | u.IsEigen W k} + zero_mem' := by intro a b; simp + add_mem' := by + intro u v hu hv a b + simp only [val_add,grad_add,mul_add] + rw [intervalIntegral.integral_add + (locallyIntegrable_intervalIntegrable (eigen_integrable hW k u) a b) + (locallyIntegrable_intervalIntegrable (eigen_integrable hW k v) a b),← hu a b,← hv a b] + ring + smul_mem' := by + intro c u hu a b + simp only [val_smul,grad_smul] + simp_rw [mul_left_comm (k^2-_)] + rw [intervalIntegral.integral_const_mul,← hu a b] + ring + +lemma IsEigen.grad_ac {W : ℝ → ℝ} {k : ℝ} {u : C1L2} + (hu : u.IsEigen W k) (hW : LocallyIntegrable W volume) (a b : ℝ) : + AbsolutelyContinuousOnInterval u.grad a b := by + have hh : u.grad = fun x ↦ u.grad a+∫ t in a..x, (k^2-W t)*u.val t := by + funext x; linarith [hu a x] + rw [hh] + exact ((contDiff_const : ContDiff ℝ 1 (fun _ : ℝ ↦ u.grad a)).contDiffOn.absolutelyContinuousOnInterval).add + ((locallyIntegrable_intervalIntegrable (eigen_integrable hW k u) a b).absolutelyContinuousOnInterval_intervalIntegral (by simp)) + +lemma IsEigen.grad_deriv {W : ℝ → ℝ} {k : ℝ} {u : C1L2} + (hu : u.IsEigen W k) (hW : LocallyIntegrable W volume) : + ∀ᵐ x, deriv u.grad x = (k^2-W x)*u.val x := by + have hh : u.grad = fun x ↦ u.grad 0+∫ t in (0 : ℝ)..x, (k^2-W t)*u.val t := by + funext x; linarith [hu 0 x] + have hd := LocallyIntegrable.ae_hasDerivAt_integral (eigen_integrable hW k u) + filter_upwards [hd] with x hx + rw [hh] + exact ((hx 0).const_add (u.grad 0)).deriv + +lemma IsEigen.weak_interval {W : ℝ → ℝ} {k a b : ℝ} {u : C1L2} + (hu : u.IsEigen W k) (hW : LocallyIntegrable W volume) (v : C1L2) + (ha : v.val a = 0) (hb : v.val b = 0) : + (∫ x in a..b, u.grad x*v.grad x) = -(∫ x in a..b, (k^2-W x)*u.val x*v.val x) := by + have h := (hu.grad_ac hW a b).integral_mul_deriv_eq_deriv_mul (v.ac a b) + rw [v.deriv_val,ha,hb,mul_zero,mul_zero,sub_self,zero_sub] at h + rw [h] + congr 1 + apply intervalIntegral.integral_congr_ae + filter_upwards [hu.grad_deriv hW] with x hx _ + rw [hx] + +lemma IsEigen.weak_compact {W : ℝ → ℝ} {k : ℝ} {u : C1L2} + (hu : u.IsEigen W k) (hW : LocallyIntegrable W volume) (v : C1L2) + (hvc : HasCompactSupport v.val) : + (∫ x, u.grad x*v.grad x) = -(∫ x, (k^2-W x)*u.val x*v.val x) := by + obtain ⟨R,hR,hzero⟩ := hvc.exists_pos_le_norm + have hvd : v.grad = deriv v.val := v.deriv_val.symm + have hi1 : Function.support (fun x ↦ u.grad x*v.grad x) ⊆ Ioc (-(R+1)) (R+1) := by + intro x hx + have hxs : x ∈ tsupport v.val := + tsupport_deriv_subset (subset_tsupport (deriv v.val) (by + rw [← hvd]; exact (mul_ne_zero_iff.mp hx).2)) + have hRp : tsupport v.val ⊆ closedBall (0 : ℝ) R := by + apply closure_minimal _ isClosed_closedBall + intro x hx + simp only [mem_closedBall,dist_zero_right,Real.norm_eq_abs] + exact le_of_lt (lt_of_not_ge (fun h ↦ hx (hzero x h))) + have hxR := hRp hxs + simp only [mem_closedBall,dist_zero_right,Real.norm_eq_abs,abs_le] at hxR + constructor <;> linarith [hxR.1,hxR.2] + have hi2 : Function.support (fun x ↦ (k^2-W x)*u.val x*v.val x) ⊆ Ioc (-(R+1)) (R+1) := by + intro x hx + have hxR : |x| < R := lt_of_not_ge (fun hh ↦ (mul_ne_zero_iff.mp hx).2 (hzero x hh)) + rw [abs_lt] at hxR + constructor <;> linarith [hxR.1,hxR.2] + rw [← intervalIntegral.integral_eq_integral_of_support_subset hi1, + ← intervalIntegral.integral_eq_integral_of_support_subset hi2] + exact hu.weak_interval hW v (hzero _ (by rw [Real.norm_eq_abs,abs_neg,abs_of_pos (by linarith)]; linarith)) + (hzero _ (by rw [Real.norm_eq_abs,abs_of_pos (by linarith)]; linarith)) + +end C1L2 +end SharpLiebThirring.SobolevProof +namespace SharpLiebThirring.SobolevProof +open MeasureTheory Set Filter +open scoped Topology ContDiff + +lemma cutoffDerivative_compact (n : ℕ) : HasCompactSupport (cutoffDerivative n) := by + have hh : cutoffDerivative n = deriv (cutoff n) := funext (fun x ↦ (cutoff_hasDerivAt n x).deriv.symm) + rw [hh] + exact (cutoff_compact n).deriv + +namespace C1L2 + +def cut (n : ℕ) (u : C1L2) : C1L2 := + ⟨⟨fun x ↦ cutoff n x*u.val x,fun x ↦ cutoffDerivative n x*u.val x+cutoff n x*u.grad x⟩, + ⟨(((cutoff_contDiff n).continuous).mul u.continuous).memLp_of_hasCompactSupport + ((cutoff_compact n).mul_right), + (((cutoffDerivative_continuous n).mul u.continuous).add + (((cutoff_contDiff n).continuous).mul u.grad_continuous)).memLp_of_hasCompactSupport + (((cutoffDerivative_compact n).mul_right).add ((cutoff_compact n).mul_right)), + ((cutoffDerivative_continuous n).mul u.continuous).add + (((cutoff_contDiff n).continuous).mul u.grad_continuous), + fun x ↦ (cutoff_hasDerivAt n x).mul (u.hasDerivAt x)⟩⟩ + +@[simp] lemma cut_val (n : ℕ) (u : C1L2) (x : ℝ) : (u.cut n).val x = cutoff n x*u.val x := rfl +@[simp] lemma cut_grad (n : ℕ) (u : C1L2) (x : ℝ) : + (u.cut n).grad x = cutoffDerivative n x*u.val x+cutoff n x*u.grad x := rfl +lemma cut_compact (n : ℕ) (u : C1L2) : HasCompactSupport (u.cut n).val := (cutoff_compact n).mul_right + +def cutMap (n : ℕ) : C1L2 →ₗ[ℝ] C1L2 where + toFun := cut n + map_add' u v := by + apply Subtype.ext + apply Prod.ext <;> funext x + · change cutoff n x*(u.val x+v.val x) = cutoff n x*u.val x+cutoff n x*v.val x + ring + · change cutoffDerivative n x*(u.val x+v.val x)+cutoff n x*(u.grad x+v.grad x) = + (cutoffDerivative n x*u.val x+cutoff n x*u.grad x)+ + (cutoffDerivative n x*v.val x+cutoff n x*v.grad x) + ring + map_smul' c u := by + apply Subtype.ext + apply Prod.ext <;> funext x + · change cutoff n x*(c*u.val x) = c*(cutoff n x*u.val x) + ring + · change cutoffDerivative n x*(c*u.val x)+cutoff n x*(c*u.grad x) = + c*(cutoffDerivative n x*u.val x+cutoff n x*u.grad x) + ring + +lemma integrable_val_mul (u v : C1L2) : Integrable (fun x ↦ u.val x*v.val x) := + u.val_memLp.integrable_mul v.val_memLp +lemma integrable_grad_mul (u v : C1L2) : Integrable (fun x ↦ u.grad x*v.grad x) := + u.grad_memLp.integrable_mul v.grad_memLp + +lemma integral_real_multiplier_tendsto {a : ℕ → ℝ → ℝ} {l : ℝ} {g : ℝ → ℝ} + (hg : Integrable g) (ha : ∀ n, AEStronglyMeasurable (a n)) + {D : ℝ} (hD : ∀ n x, |a n x| ≤ D) + (hl : ∀ x, Tendsto (fun n ↦ a n x) atTop (𝓝 l)) : + Tendsto (fun n ↦ ∫ x, a n x*g x) atTop (𝓝 (l*∫ x, g x)) := by + rw [← integral_const_mul] + apply tendsto_integral_of_dominated_convergence (fun x ↦ D*|g x|) + · exact fun n ↦ (ha n).mul hg.aestronglyMeasurable + · exact hg.abs.const_mul D + · intro n; exact ae_of_all _ (fun x ↦ by rw [Real.norm_eq_abs,abs_mul]; exact mul_le_mul_of_nonneg_right (hD n x) (abs_nonneg _)) + · exact ae_of_all _ (fun x ↦ (hl x).mul_const _) + +lemma cutoff_inner_tendsto (u v : C1L2) : + Tendsto (fun n ↦ inner ℝ (u.cut n) (v.cut n)) atTop (𝓝 (inner ℝ u v)) := by + simp_rw [inner_eq_integral,cut_val,show ∀ (n : ℕ) (x : ℝ), + cutoff n x*u.val x*(cutoff n x*v.val x) = cutoff n x^2*(u.val x*v.val x) by intros; ring] + simpa only [one_mul] using integral_real_multiplier_tendsto (l := 1) (a := fun n x ↦ cutoff n x^2) (u.integrable_val_mul v) + (fun n ↦ ((cutoff_contDiff n).continuous.pow 2).aestronglyMeasurable) + (D := 1) (fun n x ↦ by + rw [abs_pow]; have h := cutoff_bound n x; nlinarith [abs_nonneg (cutoff n x)]) + (fun x ↦ by simpa using (cutoff_tendsto x).pow 2) + +end C1L2 +end SharpLiebThirring.SobolevProof +namespace SharpLiebThirring.SobolevProof.C1L2 +open MeasureTheory Set Filter +open scoped Topology ContDiff + +def energy (W : ℝ → ℝ) (u v : C1L2) : ℝ := + (∫ x, u.grad x*v.grad x)-(∫ x, W x*u.val x*v.val x) + +lemma energy_symm (W : ℝ → ℝ) (u v : C1L2) : energy W u v = energy W v u := by + unfold energy + congr 1 <;> apply integral_congr_ae <;> exact ae_of_all _ (fun _ ↦ by ring) + +lemma integrable_potential {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) (u v : C1L2) + (hv : HasCompactSupport v.val) : Integrable (fun x ↦ W x*u.val x*v.val x) := + (hW.mul_continuous u.continuous).integrable_smul_right_of_hasCompactSupport v.continuous hv + +private lemma cut_energy_algebra (c d u v du dv k w : ℝ) : + (d*u+c*du)*(d*v+c*dv)-w*(c*u)*(c*v) = + (du*(d*(c*v)+c*(d*v+c*dv))+(k^2-w)*u*(c*(c*v)))+ + -k^2*((c*u)*(c*v))+d^2*(u*v)+(c*d)*(u*dv-du*v) := by ring + +lemma cut_error_integrable (u v : C1L2) (n : ℕ) : + Integrable (fun x ↦ cutoffDerivative n x^2*(u.val x*v.val x)) := by + obtain ⟨D,hD,hDb⟩ := cutoffDerivative_uniform_bound + apply (u.integrable_val_mul v).bdd_mul + (((cutoffDerivative_continuous n).pow 2).aestronglyMeasurable) (c := D^2) + exact ae_of_all _ (fun x ↦ by + rw [Real.norm_eq_abs,Pi.pow_apply,abs_pow] + nlinarith [hDb n x,abs_nonneg (cutoffDerivative n x)]) + +lemma cut_cross_integrable (u v : C1L2) (n : ℕ) : + Integrable (fun x ↦ (cutoff n x*cutoffDerivative n x)*(u.val x*v.grad x-u.grad x*v.val x)) := + (((cutoff_contDiff n).continuous.mul (cutoffDerivative_continuous n)).mul + ((u.continuous.mul v.grad_continuous).sub (u.grad_continuous.mul v.continuous))).integrable_of_hasCompactSupport + (((cutoff_compact n).mul_right).mul_right) + +lemma cut_weak_integrable {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) (k : ℝ) + (u v : C1L2) (n : ℕ) : + Integrable (fun x ↦ (k^2-W x)*u.val x*((v.cut n).cut n).val x) := + ((locallyIntegrable_const (c := k^2)).sub hW).mul_continuous u.continuous |>.integrable_smul_right_of_hasCompactSupport + ((v.cut n).cut n).continuous ((v.cut n).cut_compact n) + +lemma cut_weak_zero {W : ℝ → ℝ} {k : ℝ} {u : C1L2} + (hu : u.IsEigen W k) (hW : LocallyIntegrable W volume) (v : C1L2) (n : ℕ) : + (∫ x, u.grad x*((v.cut n).cut n).grad x+(k^2-W x)*u.val x*((v.cut n).cut n).val x) = 0 := by + rw [integral_add (u.integrable_grad_mul _) (cut_weak_integrable hW k u v n), + hu.weak_compact hW _ ((v.cut n).cut_compact n)] + ring + +lemma cut_energy_identity {W : ℝ → ℝ} {k : ℝ} {u : C1L2} + (hu : u.IsEigen W k) (hW : LocallyIntegrable W volume) (v : C1L2) (n : ℕ) : + energy W (u.cut n) (v.cut n) = -k^2*inner ℝ (u.cut n) (v.cut n)+ + (∫ x, cutoffDerivative n x^2*(u.val x*v.val x))+ + (∫ x, (cutoff n x*cutoffDerivative n x)*(u.val x*v.grad x-u.grad x*v.val x)) := by + let z := (v.cut n).cut n + have hiw := cut_weak_integrable hW k u v n + have hig := u.integrable_grad_mul z + have hiz : Integrable (fun x ↦ u.grad x*z.grad x+(k^2-W x)*u.val x*z.val x) := hig.add hiw + have hzero := cut_weak_zero hu hW v n + have hpair := (u.cut n).integrable_val_mul (v.cut n) + have hi3 := cut_error_integrable u v n + have hic := cut_cross_integrable u v n + rw [energy,inner_eq_integral,← integral_const_mul, + ← integral_sub ((u.cut n).integrable_grad_mul (v.cut n)) (integrable_potential hW _ _ (v.cut_compact n))] + calc + _ = (∫ x, u.grad x*z.grad x+(k^2-W x)*u.val x*z.val x) + + (∫ x, -k^2*((u.cut n).val x*(v.cut n).val x))+ + (∫ x, cutoffDerivative n x^2*(u.val x*v.val x))+ + (∫ x, (cutoff n x*cutoffDerivative n x)*(u.val x*v.grad x-u.grad x*v.val x)) := by + have h1 := integral_add hiz (hpair.const_mul (-k^2)) + have h2 := integral_add (hiz.add (hpair.const_mul (-k^2))) hi3 + have h3 := integral_add ((hiz.add (hpair.const_mul (-k^2))).add hi3) hic + simp only [Pi.add_apply] at h1 h2 h3 + rw [← h1, ← h2, ← h3] + apply integral_congr_ae + exact ae_of_all _ (fun x ↦ by simp only [z,cut_val,cut_grad]; exact cut_energy_algebra _ _ _ _ _ _ _ _) + _ = _ := by rw [hzero,zero_add] + +lemma cut_energy_tendsto {W : ℝ → ℝ} {k : ℝ} {u : C1L2} + (hu : u.IsEigen W k) (hW : LocallyIntegrable W volume) (v : C1L2) : + Tendsto (fun n ↦ energy W (u.cut n) (v.cut n)) atTop (𝓝 (-k^2*inner ℝ u v)) := by + obtain ⟨D,hD,hDb⟩ := cutoffDerivative_uniform_bound + have hd : Tendsto (fun n ↦ ∫ x, cutoffDerivative n x^2*(u.val x*v.val x)) atTop (𝓝 0) := by + simpa only [zero_mul] using integral_real_multiplier_tendsto (l := 0) (a := fun n x ↦ cutoffDerivative n x^2) (u.integrable_val_mul v) + (fun n ↦ ((cutoffDerivative_continuous n).pow 2).aestronglyMeasurable) + (D := D^2) (fun n x ↦ by + rw [abs_pow]; nlinarith [hDb n x,abs_nonneg (cutoffDerivative n x)]) + (fun x ↦ by simpa using (cutoffDerivative_tendsto x).pow 2) + have hc : Tendsto (fun n ↦ ∫ x, (cutoff n x*cutoffDerivative n x)*(u.val x*v.grad x-u.grad x*v.val x)) atTop (𝓝 0) := by + simpa only [zero_mul,Pi.sub_apply,Pi.mul_apply] using integral_real_multiplier_tendsto (l := 0) (a := fun n x ↦ cutoff n x*cutoffDerivative n x) + ((u.val_memLp.integrable_mul v.grad_memLp).sub (u.grad_memLp.integrable_mul v.val_memLp)) + (fun n ↦ (((cutoff_contDiff n).continuous).mul (cutoffDerivative_continuous n)).aestronglyMeasurable) + (D := D) (fun n x ↦ by + rw [abs_mul] + exact (mul_le_mul_of_nonneg_right (cutoff_bound n x) (abs_nonneg _)).trans (by simpa using hDb n x)) + (fun x ↦ by simpa using (cutoff_tendsto x).mul (cutoffDerivative_tendsto x)) + simp_rw [cut_energy_identity hu hW v] + simpa only [add_zero] using (((u.cutoff_inner_tendsto v).const_mul (-k^2)).add hd).add hc + +lemma eigen_orthogonal {W : ℝ → ℝ} {k l : ℝ} {u v : C1L2} + (hu : u.IsEigen W k) (hv : v.IsEigen W l) (hW : LocallyIntegrable W volume) + (hkl : k^2 ≠ l^2) : inner ℝ u v = 0 := by + have h1 := cut_energy_tendsto hu hW v + have h2 := cut_energy_tendsto hv hW u + have h2' : Tendsto (fun n ↦ energy W (u.cut n) (v.cut n)) atTop (𝓝 (-l^2*inner ℝ u v)) := by + convert h2 using 1 + · ext n; exact energy_symm W _ _ + · rw [real_inner_comm v u] + have hh := tendsto_nhds_unique h1 h2' + exact (mul_eq_zero.mp (show (k^2-l^2)*inner ℝ u v = 0 by linarith)).resolve_left (sub_ne_zero.mpr hkl) + +end SharpLiebThirring.SobolevProof.C1L2 + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/DiscreteSpectrum.lean b/lean/OAI/Analysis/LiebThirring/DiscreteSpectrum.lean new file mode 100644 index 0000000000000000000000000000000000000000..3fa64be161a152c84c3678ea6c96988d8aadf735 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/DiscreteSpectrum.lean @@ -0,0 +1,91 @@ +import OAI.Analysis.LiebThirring.NegativeResolvent + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set +open scoped Topology ENNReal + +/-- Negative eigenvalues at or below a threshold form a finite set whenever +one positive spectral moment is finite. No enumeration is presupposed. -/ +lemma finite_eigenvalues_below {γ : ℝ} (hγ : 0 < γ) {A : L2C →ₗ.[ℂ] L2C} + (hA : IsSelfAdjoint A) (hfin : eigenvalueSum γ A hA ≠ ∞) + {a : ℝ} (ha : 0 < a) : + {e : ℝ | e ≤ -a ∧ ∃ f : L2C, f ≠ 0 ∧ IsOperatorEigenfunction A e f}.Finite := by + classical + let c := (ENNReal.ofReal a)^γ + have hc : c ≠ 0 := ne_of_gt (ENNReal.rpow_pos (ENNReal.ofReal_pos.mpr ha) ENNReal.ofReal_ne_top) + let w := fun i : EigenIndex A hA ↦ (ENNReal.ofReal |i.1.1|)^γ + have hs : {i : EigenIndex A hA | c ≤ w i}.Finite := + ENNReal.finite_const_le_of_tsum_ne_top hfin hc + apply (hs.image (fun i ↦ i.1.1)).subset + rintro e ⟨he,f,hf,haf⟩ + have he₀ : e < 0 := lt_of_le_of_lt he (neg_neg_of_pos ha) + obtain ⟨i⟩ := eigenBasis_nonempty hA hf haf + refine ⟨⟨⟨e,he₀⟩,i⟩,?_,rfl⟩ + change (ENNReal.ofReal a)^γ ≤ (ENNReal.ofReal |e|)^γ + apply ENNReal.rpow_le_rpow _ hγ.le + apply ENNReal.ofReal_le_ofReal + rw [abs_of_neg he₀] + linarith + +/-- Every negative eigenvalue is isolated from all other negative eigenvalues. -/ +lemma negative_eigenvalue_isolated {γ : ℝ} (hγ : 0 < γ) {A : L2C →ₗ.[ℂ] L2C} + (hA : IsSelfAdjoint A) (hfin : eigenvalueSum γ A hA ≠ ∞) {e : ℝ} (he : e < 0) : + ∃ ε : ℝ, 0 < ε ∧ ∀ t : ℝ, |t-e| < ε → + (∃ f : L2C, f ≠ 0 ∧ IsOperatorEigenfunction A t f) → t = e := by + let S := {t : ℝ | t ≤ e/2 ∧ ∃ f : L2C, f ≠ 0 ∧ IsOperatorEigenfunction A t f} + have hs : S.Finite := by + have hh := finite_eigenvalues_below hγ hA hfin (show 0 < -e/2 by linarith) + simpa only [neg_div,neg_neg] using hh + have hc : IsClosed (S \ {e}) := hs.sdiff.isClosed + have hmem : e ∈ (S \ {e})ᶜ := by simp + obtain ⟨δ,hδ,hsub⟩ := Metric.isOpen_iff.mp hc.isOpen_compl e hmem + refine ⟨min δ (-e/2),lt_min hδ (by linarith),fun t ht hex ↦ ?_⟩ + have htδ : dist t e < δ := (Real.dist_eq t e).symm ▸ (lt_of_lt_of_le ht (min_le_left _ _)) + have hte : t ≤ e/2 := by + have hab : t-e ≤ |t-e| := le_abs_self _ + have hε := lt_of_lt_of_le ht (min_le_right δ (-e/2)) + linarith + have hn : t ∉ S \ {e} := hsub (show t ∈ Metric.ball e δ from htδ) + by_contra hne + exact hn ⟨⟨hte,hex⟩,show t ∉ ({e} : Set ℝ) from hne⟩ + +/-- The negative part of the operator has only isolated +finite-multiplicity eigenvalues, with zero as its only possible finite +accumulation point. The first clause excludes continuous/residual spectrum. -/ +theorem schrodinger_negative_spectrum {γ : ℝ} (hγ₀ : 1/2 < γ) (hγ₁ : γ < 3/2) + {W : ℝ → ℝ} (hW : Admissible γ W) : + (∀ e : ℝ, e < 0 → + (¬ HasBoundedResolventAt (schrodingerOperator hγ₀ hW) e ↔ + ∃ f : L2C, f ≠ 0 ∧ IsOperatorEigenfunction (schrodingerOperator hγ₀ hW) e f)) ∧ + (∀ e : NegativeEnergy, FiniteDimensional ℂ (eigenSpace (schrodingerOperator hγ₀ hW) e.1)) ∧ + (∀ a : ℝ, 0 < a → + {e : ℝ | e ≤ -a ∧ ∃ f : L2C, f ≠ 0 ∧ + IsOperatorEigenfunction (schrodingerOperator hγ₀ hW) e f}.Finite) ∧ + (∀ e : ℝ, e < 0 → ∃ ε : ℝ, 0 < ε ∧ ∀ t : ℝ, |t-e| < ε → + (∃ f : L2C, f ≠ 0 ∧ IsOperatorEigenfunction (schrodingerOperator hγ₀ hW) t f) → t = e) := by + let A := schrodingerOperator hγ₀ hW + have hA : IsSelfAdjoint A := schrodingerOperator_selfAdjoint hγ₀ hW + have hb := sharp_bound_for_associated_operator hγ₀ hγ₁ hW hA + (schrodingerOperator_associated hγ₀ hW) + have hfin : eigenvalueSum γ A hA ≠ ∞ := ne_top_of_le_ne_top + (ENNReal.mul_ne_top ENNReal.ofReal_ne_top (hW.mass_ne_top hγ₀)) hb.1 + have hγ : 0 < γ := by linarith + refine ⟨fun e he ↦ ?_,hb.2,fun a ha ↦ finite_eigenvalues_below hγ hA hfin ha, + fun e he ↦ negative_eigenvalue_isolated hγ hA hfin he⟩ + constructor + · intro hr + rcases negative_resolvent_or_eigenvalue hγ₀ hW (potentialData hγ₀ hW) he with hi | hn + · exact (hr hi).elim + · exact hn + · intro hn hr + exact hasBoundedResolventAt_not_eigenvalue hr hn + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/Eigenspace.lean b/lean/OAI/Analysis/LiebThirring/Eigenspace.lean new file mode 100644 index 0000000000000000000000000000000000000000..74dd173106232755f6ed3feea4f57ce04cbb3e19 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/Eigenspace.lean @@ -0,0 +1,91 @@ +import OAI.Analysis.LiebThirring.SpectralMoment + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set Filter +open scoped Topology ENNReal + +/-- The true eigenspace, including the operator-domain condition. -/ +def eigenSpace (A : L2C →ₗ.[ℂ] L2C) (e : ℝ) : Submodule ℂ L2C := + A.graph.comap ((LinearMap.id : L2C →ₗ[ℂ] L2C).prod + ((e:ℂ) • (LinearMap.id : L2C →ₗ[ℂ] L2C))) + +lemma mem_eigenSpace (A : L2C →ₗ.[ℂ] L2C) (e : ℝ) (f : L2C) : + f ∈ eigenSpace A e ↔ IsOperatorEigenfunction A e f := by + change (f,(e:ℂ) • f) ∈ A.graph ↔ _ + simp only [LinearPMap.mem_graph_iff,Subtype.exists,exists_and_left,exists_eq_left, + IsOperatorEigenfunction] + +lemma eigenSpace_closed {A : L2C →ₗ.[ℂ] L2C} (hA : IsSelfAdjoint A) (e : ℝ) : + IsClosed (eigenSpace A e : Set L2C) := by + change IsClosed ((fun f : L2C ↦ (f,(e:ℂ) • f)) ⁻¹' (A.graph : Set (L2C × L2C))) + exact hA.isClosed.preimage (continuous_id.prodMk (continuous_id.const_smul (e:ℂ))) + +lemma eigenSpace_orthogonal {A : L2C →ₗ.[ℂ] L2C} (hA : IsSelfAdjoint A) + {e t : ℝ} (het : e ≠ t) {f g : L2C} + (hf : f ∈ eigenSpace A e) (hg : g ∈ eigenSpace A t) : inner ℂ f g = 0 := by + obtain ⟨hfd,hfe⟩ := (mem_eigenSpace A e f).mp hf + obtain ⟨hgd,hge⟩ := (mem_eigenSpace A t g).mp hg + have hs : A.IsFormalAdjoint A := by + have h := A.adjoint_isFormalAdjoint hA.dense_domain + rwa [LinearPMap.isSelfAdjoint_def.mp hA] at h + have h := hs ⟨f,hfd⟩ ⟨g,hgd⟩ + rw [hfe,hge,inner_smul_left,inner_smul_right] at h + simp only [Complex.conj_ofReal] at h + have hc : (e:ℂ) ≠ (t:ℂ) := by exact_mod_cast het + exact (mul_eq_mul_right_iff.mp h).resolve_left hc + +lemma eigenBasis_exists (A : L2C →ₗ.[ℂ] L2C) (hA : IsSelfAdjoint A) (e : ℝ) : + ∃ I : Set (eigenSpace A e), Nonempty (HilbertBasis I ℂ (eigenSpace A e)) := by + let : CompleteSpace (eigenSpace A e) := (eigenSpace_closed hA e).completeSpace_coe + obtain ⟨I,b,_⟩ := exists_hilbertBasis ℂ (eigenSpace A e) + exact ⟨I,⟨b⟩⟩ + +def eigenBasisSet (A : L2C →ₗ.[ℂ] L2C) (hA : IsSelfAdjoint A) (e : ℝ) : + Set (eigenSpace A e) := Classical.choose (eigenBasis_exists A hA e) + +def eigenBasis (A : L2C →ₗ.[ℂ] L2C) (hA : IsSelfAdjoint A) (e : ℝ) : + HilbertBasis (eigenBasisSet A hA e) ℂ (eigenSpace A e) := + Classical.choice (Classical.choose_spec (eigenBasis_exists A hA e)) + +abbrev NegativeEnergy := {e : ℝ // e < 0} +abbrev EigenIndex (A : L2C →ₗ.[ℂ] L2C) (hA : IsSelfAdjoint A) := + (e : NegativeEnergy) × eigenBasisSet A hA e.1 + +def eigenBasisVector (A : L2C →ₗ.[ℂ] L2C) (hA : IsSelfAdjoint A) + (i : EigenIndex A hA) : L2C := eigenBasis A hA i.1.1 i.2 + +lemma eigenBasisVector_member (A : L2C →ₗ.[ℂ] L2C) (hA : IsSelfAdjoint A) + (i : EigenIndex A hA) : IsOperatorEigenfunction A i.1.1 (eigenBasisVector A hA i) := + (mem_eigenSpace A i.1.1 _).mp (eigenBasis A hA i.1.1 i.2).2 + +lemma eigenBasisVector_orthonormal (A : L2C →ₗ.[ℂ] L2C) (hA : IsSelfAdjoint A) : + Orthonormal ℂ (eigenBasisVector A hA) := by + classical + apply orthonormal_iff_ite.mpr + rintro ⟨e,i⟩ ⟨t,j⟩ + by_cases het : e = t + · subst t + have h := orthonormal_iff_ite.mp (eigenBasis A hA e.1).orthonormal i j + change inner ℂ (eigenBasisVector A hA ⟨e,i⟩) (eigenBasisVector A hA ⟨e,j⟩) = + if i = j then 1 else 0 at h + simpa only [Sigma.mk.inj_iff,heq_eq_eq,true_and] using h + · have hne : e.1 ≠ t.1 := fun h ↦ het (Subtype.ext h) + have hp : (⟨e,i⟩ : EigenIndex A hA) ≠ ⟨t,j⟩ := fun h ↦ het (congrArg Sigma.fst h) + rw [ite_eq_right hp] + exact eigenSpace_orthogonal hA hne (eigenBasis A hA e.1 i).2 (eigenBasis A hA t.1 j).2 + +/-- The extended sum over every negative eigenvalue, repeated once for each +member of a full Hilbert basis of its eigenspace. This is a literal spectral +sum with multiplicities; no enumeration and no finiteness assumption is made. -/ +def eigenvalueSum (γ : ℝ) (A : L2C →ₗ.[ℂ] L2C) (hA : IsSelfAdjoint A) : ℝ≥0∞ := + ∑' i : EigenIndex A hA, (ENNReal.ofReal |i.1.1|)^γ + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/EigenvalueSum.lean b/lean/OAI/Analysis/LiebThirring/EigenvalueSum.lean new file mode 100644 index 0000000000000000000000000000000000000000..739ec4b7a459486ec779ebae5647ba12b5730072 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/EigenvalueSum.lean @@ -0,0 +1,118 @@ +import OAI.Analysis.LiebThirring.Eigenspace + +namespace OAI + +universe u187 u188 + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set +open scoped Topology ENNReal + +lemma finite_family_le_moment {ι : Type u187} [Fintype ι] {γ : ℝ} + {A : L2C →ₗ.[ℂ] L2C} (f : ι → L2C) (e : ι → ℝ) + (hf : Orthonormal ℂ f) + (he : ∀ i, e i < 0 ∧ IsOperatorEigenfunction A (e i) (f i)) : + (∑ i, (ENNReal.ofReal |e i|)^γ) ≤ eigenvalueMoment γ A := by + classical + let q := (Fintype.equivFin ι).symm + have h : (∑ i : Fin (Fintype.card ι), (ENNReal.ofReal |e (q i)|)^γ) ≤ + eigenvalueMoment γ A := + le_iSup_of_le _ (le_iSup_of_le (f ∘ q) (le_iSup_of_le (e ∘ q) + (le_iSup_of_le (hf.comp q q.injective) (le_iSup_of_le (fun i ↦ he (q i)) le_rfl)))) + rw [Equiv.sum_comp q (fun i ↦ (ENNReal.ofReal |e i|)^γ)] at h + exact h + +lemma eigenvalueSum_le_moment (γ : ℝ) (A : L2C →ₗ.[ℂ] L2C) (hA : IsSelfAdjoint A) : + eigenvalueSum γ A hA ≤ eigenvalueMoment γ A := by + classical + unfold eigenvalueSum + rw [ENNReal.tsum_eq_iSup_sum] + refine iSup_le (fun s ↦ ?_) + have h := finite_family_le_moment (γ:=γ) + (fun i : s ↦ eigenBasisVector A hA i.1) (fun i : s ↦ i.1.1.1) + ((eigenBasisVector_orthonormal A hA).comp Subtype.val Subtype.val_injective) + (fun i ↦ ⟨i.1.1.2,eigenBasisVector_member A hA i.1⟩) + rw [← Finset.sum_coe_sort s (fun i : EigenIndex A hA ↦ (ENNReal.ofReal |i.1.1|)^γ)] + exact h + +lemma eigenBasis_finite {γ : ℝ} {A : L2C →ₗ.[ℂ] L2C} (hA : IsSelfAdjoint A) + (hfin : eigenvalueSum γ A hA ≠ ∞) (e : NegativeEnergy) : + Finite (eigenBasisSet A hA e.1) := by + classical + by_contra h + let : Infinite (eigenBasisSet A hA e.1) := not_finite_iff_infinite.mp h + have hp : ENNReal.ofReal |e.1| ≠ 0 := by + exact ne_of_gt (ENNReal.ofReal_pos.mpr (abs_pos.mpr (ne_of_lt e.2))) + have hp' : (ENNReal.ofReal |e.1|)^γ ≠ 0 := + ne_of_gt (ENNReal.rpow_pos (pos_iff_ne_zero.mpr hp) ENNReal.ofReal_ne_top) + have hle := ENNReal.tsum_comp_le_tsum_of_injective + (show Function.Injective (fun i : eigenBasisSet A hA e.1 ↦ (⟨e,i⟩ : EigenIndex A hA)) from + fun i j h ↦ by cases h; rfl) (fun i : EigenIndex A hA ↦ (ENNReal.ofReal |i.1.1|)^γ) + have ht : (∑' _ : eigenBasisSet A hA e.1, (ENNReal.ofReal |e.1|)^γ) = ∞ := + ENNReal.tsum_const_eq_top_of_ne_zero hp' + rw [ht] at hle + exact hfin (top_le_iff.mp hle) + +lemma eigenSpace_finiteDimensional {γ : ℝ} {A : L2C →ₗ.[ℂ] L2C} + (hA : IsSelfAdjoint A) (hfin : eigenvalueSum γ A hA ≠ ∞) (e : NegativeEnergy) : + FiniteDimensional ℂ (eigenSpace A e.1) := by + let := eigenBasis_finite hA hfin e + let := Fintype.ofFinite (eigenBasisSet A hA e.1) + exact Module.Finite.of_basis (eigenBasis A hA e.1).toOrthonormalBasis.toBasis + + +lemma finite_family_le_sum {ι : Type u188} [Fintype ι] {γ : ℝ} + {A : L2C →ₗ.[ℂ] L2C} (hA : IsSelfAdjoint A) + (hfin : eigenvalueSum γ A hA ≠ ∞) + (f : ι → L2C) (e : ι → ℝ) (hf : Orthonormal ℂ f) + (he : ∀ i, e i < 0 ∧ IsOperatorEigenfunction A (e i) (f i)) : + (∑ i, (ENNReal.ofReal |e i|)^γ) ≤ eigenvalueSum γ A hA := by + classical + let E : ι → NegativeEnergy := fun i ↦ ⟨e i,(he i).1⟩ + have hlocal : ∀ t : NegativeEnergy, + (∑' i : E ⁻¹' {t}, (ENNReal.ofReal |e i.1|)^γ) ≤ + ∑' _ : eigenBasisSet A hA t.1, (ENNReal.ofReal |t.1|)^γ := by + intro t + let := eigenBasis_finite hA hfin t + let := Fintype.ofFinite (eigenBasisSet A hA t.1) + let := eigenSpace_finiteDimensional hA hfin t + have heq (i : E ⁻¹' {t}) : e i.1 = t.1 := congrArg Subtype.val i.2 + let v : (E ⁻¹' {t}) → eigenSpace A t.1 := fun i ↦ + ⟨f i.1,(mem_eigenSpace A t.1 _).mpr (by rw [← heq i]; exact (he i.1).2)⟩ + have hv : Orthonormal ℂ v := by + apply orthonormal_iff_ite.mpr + intro i j + change inner ℂ (f i.1) (f j.1) = _ + simpa only [Subtype.val_inj] using orthonormal_iff_ite.mp hf i.1 j.1 + have hc := hv.linearIndependent.fintype_card_le_finrank + rw [Module.finrank_eq_card_basis (eigenBasis A hA t.1).toOrthonormalBasis.toBasis] at hc + calc + _ = (Fintype.card (E ⁻¹' {t}) : ℝ≥0∞) * (ENNReal.ofReal |t.1|)^γ := by + simp only [heq,tsum_fintype,Finset.sum_const,Finset.card_univ,nsmul_eq_mul] + _ ≤ (Fintype.card (eigenBasisSet A hA t.1) : ℝ≥0∞) * (ENNReal.ofReal |t.1|)^γ := + mul_le_mul_left (by exact_mod_cast hc) _ + _ = _ := by simp only [tsum_fintype,Finset.sum_const,Finset.card_univ,nsmul_eq_mul] + calc + _ = ∑' t : NegativeEnergy, ∑' i : E ⁻¹' {t}, (ENNReal.ofReal |e i.1|)^γ := by + rw [ENNReal.tsum_fiberwise (fun i ↦ (ENNReal.ofReal |e i|)^γ) E,tsum_fintype] + _ ≤ ∑' t : NegativeEnergy, ∑' _ : eigenBasisSet A hA t.1, + (ENNReal.ofReal |t.1|)^γ := ENNReal.tsum_le_tsum hlocal + _ = eigenvalueSum γ A hA := (ENNReal.tsum_sigma _).symm + +lemma eigenvalueMoment_eq_sum {γ : ℝ} {A : L2C →ₗ.[ℂ] L2C} (hA : IsSelfAdjoint A) + (hfin : eigenvalueSum γ A hA ≠ ∞) : + eigenvalueMoment γ A = eigenvalueSum γ A hA := by + apply le_antisymm + · unfold eigenvalueMoment + refine iSup_le (fun N ↦ iSup_le (fun f ↦ iSup_le (fun e ↦ + iSup_le (fun hf ↦ iSup_le (fun he ↦ ?_))))) + exact finite_family_le_sum hA hfin f e hf he + · exact eigenvalueSum_le_moment γ A hA + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/EnergyAlgebra.lean b/lean/OAI/Analysis/LiebThirring/EnergyAlgebra.lean new file mode 100644 index 0000000000000000000000000000000000000000..e119d558733e9d875682fb01186469d216755915 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/EnergyAlgebra.lean @@ -0,0 +1,129 @@ +import OAI.Analysis.LiebThirring.SobolevProjection + +namespace OAI + +universe u171 u172 u173 u174 u175 u176 u177 u178 + + +noncomputable section +namespace SharpLiebThirring.SobolevProof.C1L2 +open MeasureTheory Set Filter InnerProductSpace +open scoped Topology + +@[simp] lemma val_sub (u v : C1L2) (x : ℝ) : (u-v).val x = u.val x-v.val x := rfl +@[simp] lemma grad_sub (u v : C1L2) (x : ℝ) : (u-v).grad x = u.grad x-v.grad x := rfl + +lemma cut_tendsto (u : C1L2) : Tendsto (fun n ↦ u.cut n) atTop (𝓝 u) := by + have h : Tendsto (fun n ↦ ∫ x, (cutoff n x-1)^2*(u.val x*u.val x)) atTop (𝓝 0) := by + simpa only [zero_mul] using integral_real_multiplier_tendsto (l := 0) + (a := fun n x ↦ (cutoff n x-1)^2) (u.integrable_val_mul u) + (fun n ↦ (((cutoff_contDiff n).continuous.sub continuous_const).pow 2).aestronglyMeasurable) + (D := 4) (fun n x ↦ by + rw [abs_pow]; have hb := abs_sub (cutoff n x) 1 + have hb' := cutoff_bound n x + have hn := abs_nonneg (cutoff n x-1) + norm_num at hb + nlinarith) + (fun x ↦ by simpa using ((cutoff_tendsto x).sub_const 1).pow 2) + have heq (n : ℕ) : ‖u.cut n-u‖^2 = ∫ x, (cutoff n x-1)^2*(u.val x*u.val x) := by + rw [← real_inner_self_eq_norm_sq,inner_eq_integral] + apply integral_congr_ae + exact ae_of_all _ (fun x ↦ by simp only [val_sub,cut_val]; ring) + have hn : Tendsto (fun n ↦ ‖u.cut n-u‖) atTop (𝓝 0) := by + have hh := h.sqrt + simpa only [← heq,Real.sqrt_sq_eq_abs,abs_norm,Real.sqrt_zero] using hh + exact tendsto_iff_norm_sub_tendsto_zero.mpr hn + +lemma eventually_cut_linearIndependent {ι : Type u171} [Finite ι] {u : ι → C1L2} + (hu : LinearIndependent ℝ u) : ∀ᶠ n in atTop, LinearIndependent ℝ (fun i ↦ (u i).cut n) := + (tendsto_pi_nhds.mpr (fun i ↦ (u i).cut_tendsto)).eventually hu.eventually + +lemma val_sum {ι : Type u172} (s : Finset ι) (u : ι → C1L2) (x : ℝ) : + (∑ i ∈ s, u i).val x = ∑ i ∈ s, (u i).val x := by + classical + induction s using Finset.induction_on with + | empty => simp + | insert a s ha ih => simpa only [Finset.sum_insert ha,val_add] using congrArg ((u a).val x+·) ih + +lemma grad_sum {ι : Type u173} (s : Finset ι) (u : ι → C1L2) (x : ℝ) : + (∑ i ∈ s, u i).grad x = ∑ i ∈ s, (u i).grad x := by + classical + induction s using Finset.induction_on with + | empty => simp + | insert a s ha ih => simpa only [Finset.sum_insert ha,grad_add] using congrArg ((u a).grad x+·) ih + +lemma compact_smul (c : ℝ) {u : C1L2} (hu : HasCompactSupport u.val) : + HasCompactSupport (c • u).val := hu.mul_left + +lemma compact_sum {ι : Type u174} (s : Finset ι) (u : ι → C1L2) + (hu : ∀ i ∈ s, HasCompactSupport (u i).val) : HasCompactSupport (∑ i ∈ s, u i).val := by + classical + convert HasCompactSupport.finset_sum hu using 1; try rfl + funext x + simp only [val_sum, Finset.sum_apply] + +lemma compact_of_mem_span {ι : Type u175} (u : ι → C1L2) + (hu : ∀ i, HasCompactSupport (u i).val) {v : C1L2} + (hv : v ∈ Submodule.span ℝ (range u)) : HasCompactSupport v.val := by + induction hv using Submodule.span_induction with + | mem x hx => obtain ⟨i,rfl⟩ := hx; exact hu i + | zero => + change IsCompact (tsupport (fun _ : ℝ ↦ (0 : ℝ))) + simp + | add x y _ _ hx hy => exact hx.add hy + | smul c x _ hx => exact compact_smul c hx + +lemma energy_add_left {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) + (u v w : C1L2) (hw : HasCompactSupport w.val) : + energy W (u+v) w = energy W u w+energy W v w := by + simp only [energy,grad_add,val_add,add_mul,mul_add] + rw [integral_add (u.integrable_grad_mul w) (v.integrable_grad_mul w), + integral_add (integrable_potential hW u w hw) (integrable_potential hW v w hw)] + ring + +lemma energy_smul_left (W : ℝ → ℝ) (c : ℝ) (u v : C1L2) : + energy W (c • u) v = c*energy W u v := by + simp only [energy,grad_smul,val_smul] + simp_rw [show ∀ x, c*u.grad x*v.grad x = c*(u.grad x*v.grad x) by intros; ring, + show ∀ x, W x*(c*u.val x)*v.val x = c*(W x*u.val x*v.val x) by intros; ring] + rw [integral_const_mul,integral_const_mul]; ring + +lemma energy_sum_left {ι : Type u176} {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) + (s : Finset ι) (u : ι → C1L2) (v : C1L2) (hv : HasCompactSupport v.val) : + energy W (∑ i ∈ s, u i) v = ∑ i ∈ s, energy W (u i) v := by + classical + induction s using Finset.induction_on with + | empty => simp [energy] + | insert a s ha ih => rw [Finset.sum_insert ha,energy_add_left hW _ _ _ hv,ih,Finset.sum_insert ha] + +lemma energy_sum_sum {ι : Type u177} [Fintype ι] {W : ℝ → ℝ} + (hW : LocallyIntegrable W volume) (u : ι → C1L2) + (hu : ∀ i, HasCompactSupport (u i).val) (c : ι → ℝ) : + energy W (∑ i, c i • u i) (∑ i, c i • u i) = + ∑ i, ∑ j, c i*c j*energy W (u i) (u j) := by + classical + rw [energy_sum_left hW _ _ _ (compact_sum _ _ (fun i _ ↦ compact_smul _ (hu i)))] + apply Finset.sum_congr rfl + intro i _ + rw [energy_symm,energy_sum_left hW _ _ _ (compact_smul _ (hu i))] + apply Finset.sum_congr rfl + intro j _ + rw [energy_smul_left,energy_symm,energy_smul_left] + ring + +lemma inner_sum_sum {ι : Type u178} [Fintype ι] (u : ι → C1L2) (c : ι → ℝ) : + inner ℝ (∑ i, c i • u i) (∑ i, c i • u i) = + ∑ i, ∑ j, c i*c j*inner ℝ (u i) (u j) := by + simp only [sum_inner,inner_sum,real_inner_smul_left,real_inner_smul_right, + mul_assoc] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + rw [real_inner_comm (u j) (u i)] + +end SharpLiebThirring.SobolevProof.C1L2 + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/EquivariantFlags.lean b/lean/OAI/Analysis/LiebThirring/EquivariantFlags.lean new file mode 100644 index 0000000000000000000000000000000000000000..6ecc9d84c6efc98cb4bf5253d2fb3aa33554826e --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/EquivariantFlags.lean @@ -0,0 +1,330 @@ +import OAI.Analysis.LiebThirring.GenericPosition + +namespace OAI + +universe u95 u96 u97 u98 u99 u100 u101 u102 u193 u194 + +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Finset +section +open Set Finset Filter + + +namespace SharpLiebThirring.PLParity +section EquivariantAssignment +variable {G : Type u95} {X : Type u96} [Group G] [MulAction G X] [IsCancelSMul G X] + +abbrev Orbit := Quotient (MulAction.orbitRel G X) + +omit [IsCancelSMul G X] in +lemma assignment_orbit_smul (g : G) (x : X) : + (Quotient.mk'' (g • x) : Orbit (G := G) (X := X)) = Quotient.mk'' x := + Quotient.sound' (MulAction.orbitRel_apply.mpr (MulAction.mem_orbit_iff.mpr ⟨g, rfl⟩)) + +def assignmentEquiv : (Orbit (G := G) (X := X) × G) ≃ X := + Equiv.ofBijective (fun z ↦ z.2 • z.1.out) (by + constructor + · rintro ⟨q, g⟩ ⟨r, h⟩ he + have hq : q = r := by + have hh := congrArg (fun x : X ↦ (Quotient.mk'' x : Orbit (G := G) (X := X))) he + simpa only [assignment_orbit_smul, Quotient.out_eq'] using hh + subst r + have hg : g = h := IsCancelSMul.right_cancel g h q.out he + subst h + rfl + · intro x + let q : Orbit (G := G) (X := X) := Quotient.mk'' x + have hr : (MulAction.orbitRel G X) x q.out := + Quotient.exact' (by rw [Quotient.out_eq']) + obtain ⟨g, hg⟩ := MulAction.mem_orbit_iff.mp (MulAction.orbitRel_apply.mp hr) + exact ⟨(q, g), hg⟩) + +def orbitLabel (x : X) : Orbit (G := G) (X := X) := assignmentEquiv.symm x |>.1 +def orbitTransport (x : X) : G := assignmentEquiv.symm x |>.2 + +lemma assignment_reconstruct (x : X) : orbitTransport (G := G) x • (orbitLabel (G := G) x).out = x := + assignmentEquiv.apply_symm_apply x + +lemma assignment_symm_smul (g : G) (x : X) : + assignmentEquiv.symm (g • x) = (orbitLabel (G := G) x, g * orbitTransport x) := by + apply assignmentEquiv.injective + rw [Equiv.apply_symm_apply] + change g • x = (g * orbitTransport x) • (orbitLabel (G := G) x).out + rw [mul_smul, assignment_reconstruct] + +lemma orbitLabel_smul (g : G) (x : X) : orbitLabel (G := G) (g • x) = orbitLabel x := by + simpa only [orbitLabel] using congrArg Prod.fst (assignment_symm_smul g x) + +lemma orbitTransport_smul (g : G) (x : X) : orbitTransport (g • x) = g * orbitTransport x := + congrArg Prod.snd (assignment_symm_smul g x) + +lemma orbitLabel_eq_mk (x : X) : orbitLabel (G := G) x = Quotient.mk'' x := by + have h := assignment_orbit_smul (orbitTransport (G := G) x) (orbitLabel (G := G) x).out + rw [assignment_reconstruct, Quotient.out_eq'] at h + exact h.symm + +variable {V : Type u97} [NormedAddCommGroup V] [NormedSpace ℝ V] [FiniteDimensional ℝ V] +variable (ρ : G →* (V ≃ₗ[ℝ] V)) + +def equivariantAssignment (a : Orbit (G := G) (X := X) → V) (x : X) : V := + ρ (orbitTransport x) (a (orbitLabel x)) + +omit [FiniteDimensional ℝ V] in +lemma equivariantAssignment_smul (a : Orbit (G := G) (X := X) → V) (g : G) (x : X) : + equivariantAssignment ρ a (g • x) = ρ g (equivariantAssignment ρ a x) := by + simp only [equivariantAssignment, orbitLabel_smul, orbitTransport_smul, map_mul, + LinearEquiv.mul_apply] + +omit [FiniteDimensional ℝ V] in +lemma equivariantAssignment_recovers (b : X → V) + (hb : ∀ g : G, ∀ x, b (g • x) = ρ g (b x)) (x : X) : + ρ (orbitTransport x) (b (orbitLabel (G := G) x).out) = b x := by + rw [← hb, assignment_reconstruct] + +/-- Free finite group actions admit arbitrarily close equivariant generic +vertex values, while retaining a prescribed invariant family exactly. -/ +lemma exists_equivariant_generic [Fintype X] + {T₁ : Type u98} {T₂ : Type u99} [Fintype T₁] [Fintype T₂] + (J₁ : T₁ → Type u193) (J₂ : T₂ → Type u194) [∀ t, Fintype (J₁ t)] [∀ t, Fintype (J₂ t)] + (P : X → Prop) (hP : ∀ g : G, ∀ x, P (g • x) ↔ P x) + (b : X → V) (hb : ∀ g : G, ∀ x, b (g • x) = ρ g (b x)) + (v₁ : ∀ t, J₁ t → X) (v₂ : ∀ t, J₂ t → X) + (he₁ : ∀ t, Function.Injective (orbitLabel (G := G) ∘ v₁ t)) + (he₂ : ∀ t, Function.Injective (orbitLabel (G := G) ∘ v₂ t)) + (hf₁ : ∀ t, LinearIndependent ℝ (fun i : {i // P (v₁ t i)} ↦ b (v₁ t i.val))) + (hf₂ : ∀ t, LinearIndependent ℝ (fun i : {i // P (v₂ t i)} ↦ ((1 : ℝ), b (v₂ t i.val)))) + (hc₁ : ∀ t, Fintype.card (J₁ t) ≤ Module.finrank ℝ V) + (hc₂ : ∀ t, Fintype.card (J₂ t) ≤ Module.finrank ℝ V + 1) + (ε : ℝ) (hε : 0 < ε) : + ∃ a : X → V, + (∀ g : G, ∀ x, a (g • x) = ρ g (a x)) ∧ + (∀ x, dist (a x) (b x) < ε) ∧ + (∀ x, P x → a x = b x) ∧ + (∀ t, LinearIndependent ℝ (fun i ↦ a (v₁ t i))) ∧ + (∀ t, LinearIndependent ℝ (fun i ↦ ((1 : ℝ), a (v₂ t i)))) := by + classical + let Q := Orbit (G := G) (X := X) + let P' : Q → Prop := fun q ↦ P q.out + let b' : Q → V := fun q ↦ b q.out + let e : X → Q := orbitLabel (G := G) + let A : X → V ≃ₗ[ℝ] V := fun x ↦ ρ (orbitTransport x) + have hpe (x : X) : P' (e x) ↔ P x := by + change P (orbitLabel (G := G) x).out ↔ P x + have h := hP (orbitTransport (G := G) x) (orbitLabel (G := G) x).out + rw [assignment_reconstruct] at h + exact h.symm + have hbe (x : X) : A x (b' (e x)) = b x := equivariantAssignment_recovers ρ b hb x + have hfix₁ (t : T₁) : LinearIndependent ℝ + (fun i : {i // P' (e (v₁ t i))} ↦ A (v₁ t i.val) (b' (e (v₁ t i.val)))) := by + simp only [hbe] + exact (hf₁ t).comp (fun i : {i // P' (e (v₁ t i))} ↦ ⟨i.val, (hpe _).mp i.prop⟩) + (by + intro i j h + apply Subtype.ext + exact congrArg (fun z : {i // P (v₁ t i)} ↦ z.val) h) + have hfix₂ (t : T₂) : LinearIndependent ℝ + (fun i : {i // P' (e (v₂ t i))} ↦ ((1 : ℝ), A (v₂ t i.val) (b' (e (v₂ t i.val))))) := by + simp only [hbe] + exact (hf₂ t).comp (fun i : {i // P' (e (v₂ t i))} ↦ ⟨i.val, (hpe _).mp i.prop⟩) + (by + intro i j h + apply Subtype.ext + exact congrArg (fun z : {i // P (v₂ t i)} ↦ z.val) h) + obtain ⟨c, hc, h₁, h₂⟩ := exists_mixed_generic J₁ J₂ P' b' e A v₁ v₂ + he₁ he₂ hfix₁ hfix₂ hc₁ hc₂ ε hε + let a' : Q → V := fun q ↦ if h : P' q then b' q else c ⟨q, h⟩ + let a : X → V := equivariantAssignment ρ a' + have ha (x : X) : a x = mixedVertexEvaluation P' b' e A c x := rfl + refine ⟨a, equivariantAssignment_smul ρ a', ?_, ?_, ?_, ?_⟩ + · intro x + rw [ha, ← hbe] + exact hc x + · intro x hx + rw [ha] + simp only [mixedVertexEvaluation, dite_eq_left ((hpe x).mpr hx), hbe] + · simpa only [← ha] using h₁ + · simpa only [← ha] using h₂ + +end EquivariantAssignment +end SharpLiebThirring.PLParity + +namespace SharpLiebThirring.CubeFlags +open SharpLiebThirring.PLParity +open Finset +attribute [local instance] Classical.propDecidable + +lemma card_omit_one_le {n : ℕ} (i : Fin (n + 1)) : Fintype.card {k // k ≠ i} ≤ n := by + have h := Fintype.card_subtype_lt (p := fun k : Fin (n + 1) ↦ k ≠ i) (x := i) (by simp) + simp only [Fintype.card_fin] at h + omega + +lemma card_omit_two_le {n : ℕ} (i j : Fin (n + 1)) (hij : i ≠ j) : + Fintype.card {k // k ≠ i ∧ k ≠ j} + 1 ≤ n := by + let e : {k // k ≠ i ∧ k ≠ j} ≃ {k : {k : Fin (n + 1) // k ≠ i} // k.val ≠ j} := + ⟨fun k ↦ ⟨⟨k.val, k.prop.1⟩, k.prop.2⟩, fun k ↦ ⟨k.val.val, k.val.prop, k.prop⟩, + by intro k; rfl, by intro k; rfl⟩ + have hc := Fintype.card_congr e + have hl := Fintype.card_subtype_lt (p := fun k : {k : Fin (n + 1) // k ≠ i} ↦ k.val ≠ j) + (x := ⟨j, hij.symm⟩) (by simp) + have hu := card_omit_one_le i + omega + +/-- General position on all facets of an invariant finite cubical complex, +retaining an already independent invariant part of its vertex data. -/ +lemma generic_on_complex {n : ℕ} (H : Subgroup (Signs n)) (D : SubMulAction H (Flag n)) + [Fintype D] [IsCancelSMul H (vertices H D)] + {V : Type u100} [NormedAddCommGroup V] [NormedSpace ℝ V] [FiniteDimensional ℝ V] + (ρ : H →* (V ≃ₗ[ℝ] V)) (hc : n = Module.finrank ℝ V + 1) + (P : vertices H D → Prop) (hP : ∀ s : H, ∀ z, P (s • z) ↔ P z) + (b : vertices H D → V) (hb : ∀ s : H, ∀ z, b (s • z) = ρ s (b z)) + (haug : ∀ F : D, ∀ j : Fin (n + 1), LinearIndependent ℝ + (fun k : {k : {k : Fin (n + 1) // k ≠ j} // P (flagVertex H D F k.val)} ↦ + ((1 : ℝ), b (flagVertex H D F k.val.val)))) + (hvec : ∀ F : D, ∀ i j : Fin (n + 1), i ≠ j → LinearIndependent ℝ + (fun k : {k : {k : Fin (n + 1) // k ≠ i ∧ k ≠ j} // P (flagVertex H D F k.val)} ↦ + b (flagVertex H D F k.val.val))) + (ε : ℝ) (hε : 0 < ε) : + ∃ a : vertices H D → V, + (∀ s : H, ∀ z, a (s • z) = ρ s (a z)) ∧ + (∀ z, dist (a z) (b z) < ε) ∧ + (∀ z, P z → a z = b z) ∧ + (∀ F : D, ∀ j : Fin (n + 1), LinearIndependent ℝ + (fun k : {k // k ≠ j} ↦ ((1 : ℝ), a (flagVertex H D F k)))) ∧ + (∀ F : D, ∀ i j : Fin (n + 1), i ≠ j → LinearIndependent ℝ + (fun k : {k // k ≠ i ∧ k ≠ j} ↦ a (flagVertex H D F k))) := by + classical + let T₁ := D × {p : Fin (n + 1) × Fin (n + 1) // p.1 ≠ p.2} + let T₂ := D × Fin (n + 1) + let J₁ (t : T₁) := {k // k ≠ t.2.val.1 ∧ k ≠ t.2.val.2} + let J₂ (t : T₂) := {k // k ≠ t.2} + let v₁ (t : T₁) (k : J₁ t) := flagVertex H D t.1 k.val + let v₂ (t : T₂) (k : J₂ t) := flagVertex H D t.1 k.val + have hi₁ (t : T₁) : Function.Injective (orbitLabel (G := H) ∘ v₁ t) := by + intro k l he + simp only [Function.comp_apply, orbitLabel_eq_mk] at he + exact Subtype.ext (flagVertex_orbits_injective H D t.1 he) + have hi₂ (t : T₂) : Function.Injective (orbitLabel (G := H) ∘ v₂ t) := by + intro k l he + simp only [Function.comp_apply, orbitLabel_eq_mk] at he + exact Subtype.ext (flagVertex_orbits_injective H D t.1 he) + obtain ⟨a, ha, he, hp, hv, hu⟩ := exists_equivariant_generic ρ J₁ J₂ P hP b hb v₁ v₂ + hi₁ hi₂ (fun t ↦ hvec t.1 _ _ t.2.prop) (fun t ↦ haug t.1 t.2) + (fun t ↦ by + change Fintype.card {k // k ≠ t.2.val.1 ∧ k ≠ t.2.val.2} ≤ _ + have hk := card_omit_two_le t.2.val.1 t.2.val.2 t.2.prop + omega) + (fun t ↦ by + change Fintype.card {k // k ≠ t.2} ≤ _ + have hk := card_omit_one_le t.2 + omega) ε hε + refine ⟨a, ha, he, hp, ?_, ?_⟩ + · intro F j + exact hu (F,j) + · intro F i j hij + exact hv (F,⟨(i,j),hij⟩) + +end SharpLiebThirring.CubeFlags + + +namespace SharpLiebThirring.CubeFlags +open Finset + +def spatial {d : ℕ} : (Fin (d + 1) → ℝ) →ₗ[ℝ] (Fin d → ℝ) where + toFun := Fin.init + map_add' _ _ := rfl + map_smul' _ _ := rfl + +def embedSpatial {d : ℕ} : (Fin d → ℝ) →ₗ[ℝ] (Fin (d + 1) → ℝ) where + toFun x := Fin.snoc x 0 + map_add' x y := by ext i; refine Fin.lastCases ?_ (fun j ↦ ?_) i <;> simp + map_smul' a x := by ext i; refine Fin.lastCases ?_ (fun j ↦ ?_) i <;> simp + +@[simp] lemma spatial_embed {d : ℕ} (x : Fin d → ℝ) : spatial (embedSpatial x) = x := by + ext i + change (Fin.snoc (α := fun _ : Fin (d + 1) ↦ ℝ) x 0) i.castSucc = x i + simp only [Fin.snoc_castSucc] + +lemma embed_spatial_of_time_zero {d : ℕ} (x : Fin (d + 1) → ℝ) (hx : x (Fin.last d) = 0) : + embedSpatial (spatial x) = x := by + change Fin.snoc (Fin.init x) 0 = x + rw [← hx, Fin.snoc_init_self] + +lemma augmented_spatial_independent {d : ℕ} {ι : Type u101} (v : ι → Fin (d + 1) → ℝ) + (hv : LinearIndependent ℝ (fun i ↦ ((1 : ℝ), v i))) + (ht : ∀ i, v i (Fin.last d) = 0) : + LinearIndependent ℝ (fun i ↦ ((1 : ℝ), spatial (v i))) := by + let L : (ℝ × (Fin d → ℝ)) →ₗ[ℝ] (ℝ × (Fin (d + 1) → ℝ)) := + (LinearMap.id : ℝ →ₗ[ℝ] ℝ).prodMap embedSpatial + have he : (fun i ↦ L ((1 : ℝ), spatial (v i))) = (fun i ↦ ((1 : ℝ), v i)) := by + funext i + exact Prod.ext rfl (embed_spatial_of_time_zero (v i) (ht i)) + apply LinearIndependent.of_comp L + change LinearIndependent ℝ (fun i ↦ L ((1 : ℝ), spatial (v i))) + rw [he] + exact hv + +lemma augmented_scale_independent {d : ℕ} {ι : Type u102} (v : ι → Fin d → ℝ) + (hv : LinearIndependent ℝ (fun i ↦ ((1 : ℝ), v i))) {h : ℝ} (hh : h ≠ 0) : + LinearIndependent ℝ (fun i ↦ ((1 : ℝ), h • v i)) := by + let L : (ℝ × (Fin d → ℝ)) →ₗ[ℝ] (ℝ × (Fin d → ℝ)) := + (LinearMap.id : ℝ →ₗ[ℝ] ℝ).prodMap (h • LinearMap.id) + have hL : Function.Injective L := by + rintro ⟨a,x⟩ ⟨b,y⟩ he + have hab := congrArg Prod.fst he + have hxy : h • x = h • y := congrArg Prod.snd he + exact Prod.ext hab ((smul_right_injective _ hh) hxy) + exact hv.map' L (LinearMap.ker_eq_bot.mpr hL) + +/-- A bottom flag with its cube chosen within one mesh of any given spatial point. -/ +def bottomSeed {d : ℕ} (h : ℝ) (p : Fin d → ℝ) : Flag (d + 1) where + base := Fin.snoc (fun i ↦ ⌊p i / h⌋) 0 + corner := fun _ ↦ false + order := Equiv.refl _ + +lemma bottomSeed_time {d : ℕ} (h : ℝ) (p : Fin d → ℝ) (k : Fin (d + 2)) + (hk : k ≠ Fin.last (d + 1)) : (bottomSeed h p).point k (Fin.last d) = 0 := by + rw [Flag.point_time_boundary _ _ (by simp [bottomSeed]) k hk] + simp [bottomSeed] + +lemma bottomSeed_dist_center {d : ℕ} (h : ℝ) (hh : 0 < h) (p : Fin d → ℝ) : + dist (h • (bottomSeed h p).center) (embedSpatial p) ≤ h := by + rw [dist_pi_le_iff hh.le] + intro i + refine Fin.lastCases ?_ (fun j ↦ ?_) i + · simp only [Pi.smul_apply, smul_eq_mul, Flag.center_apply, bottomSeed, + Fin.snoc_last, Int.cast_zero, zero_add, embedSpatial, LinearMap.coe_mk, AddHom.coe_mk] + simp only [dist_zero_right, Real.norm_eq_abs, abs_of_nonneg (by positivity : 0 ≤ h * (1/2))] + linarith + · have hl := Int.floor_le (p j / h) + have hu := Int.lt_floor_add_one (p j / h) + have hl' : h * (⌊p j / h⌋ : ℝ) ≤ p j := by + have := (le_div_iff₀ hh).mp hl + nlinarith + have hu' : p j < h * ((⌊p j / h⌋ : ℝ) + 1) := by + have := (div_lt_iff₀ hh).mp hu + nlinarith + simp only [Pi.smul_apply, smul_eq_mul, Flag.center_apply, bottomSeed, + Fin.snoc_castSucc, embedSpatial, LinearMap.coe_mk, AddHom.coe_mk, Real.dist_eq, abs_le] + constructor <;> nlinarith + +lemma bottomSeed_dist_point {d : ℕ} (h : ℝ) (hh : 0 < h) (p : Fin d → ℝ) + (k : Fin (d + 2)) : dist (h • (bottomSeed h p).point k) (embedSpatial p) ≤ 2 * h := by + calc + _ ≤ dist (h • (bottomSeed h p).point k) (h • (bottomSeed h p).center) + + dist (h • (bottomSeed h p).center) (embedSpatial p) := dist_triangle _ _ _ + _ ≤ h / 2 + h := add_le_add ((bottomSeed h p).dist_scaled_point_center h hh.le k) + (bottomSeed_dist_center h hh p) + _ ≤ 2 * h := by linarith + +end SharpLiebThirring.CubeFlags + +end +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/ExtremizerMass.lean b/lean/OAI/Analysis/LiebThirring/ExtremizerMass.lean new file mode 100644 index 0000000000000000000000000000000000000000..1224b31cb161af08480a4dfe87eb82350ca57010 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/ExtremizerMass.lean @@ -0,0 +1,85 @@ +import OAI.Analysis.LiebThirring.MomentBound + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.ExtremizerProof +open ConstantProof SpectralProof MeasureTheory Set + +/-- Exact substitution `z = tanh (r*x)`; no integrability convention is used to + guess the integral, since the Jacobian theorem applies to the full line. -/ +lemma potential_power_integral {r σ : ℝ} (hr : 0 < r) : + (∫ x, (potential r x)^(1+σ)) = (r+1)^(1+σ)/r * betaAction σ := by + let f : ℝ → ℝ := fun x ↦ Real.tanh (r*x) + have hf' (x : ℝ) : HasDerivAt f ((Real.cosh (r*x))⁻¹^2*r) x := by + convert! (tanh_hasDerivAt (r*x)).comp x ((hasDerivAt_id x).const_mul r) using 1 + simp + have hinj : Function.Injective f := by + intro x y h + exact mul_left_cancel₀ hr.ne' (Real.tanh_injective h) + have himg : f '' univ = Ioo (-1 : ℝ) 1 := by + ext z + constructor + · rintro ⟨x,_,rfl⟩ + exact ⟨Real.neg_one_lt_tanh _,Real.tanh_lt_one _⟩ + · intro hz + obtain ⟨x,_,hx⟩ := Real.tanh_surjOn hz + refine ⟨x/r,mem_univ _,?_⟩ + dsimp [f] + rw [mul_div_cancel₀ _ hr.ne',hx] + have hj := integral_image_eq_integral_abs_deriv_smul MeasurableSet.univ + (fun x _ ↦ (hf' x).hasDerivWithinAt) hinj.injOn (fun z : ℝ ↦ (1-z^2)^σ) + rw [himg,setIntegral_univ] at hj + have halg (x : ℝ) : |(Real.cosh (r*x))⁻¹^2*r| * (1-f x^2)^σ = + r*((Real.cosh (r*x))⁻¹^2)^(1+σ) := by + have hs : 0 < (Real.cosh (r*x))⁻¹^2 := by positivity + have ht : 1-f x^2 = (Real.cosh (r*x))⁻¹^2 := by + dsimp [f] + linarith [tanh_sq_add_sech_sq (r*x)] + rw [abs_of_pos (mul_pos hs hr),ht,Real.rpow_add hs,Real.rpow_one] + ring + have hj' : betaAction σ = r*∫ x, ((Real.cosh (r*x))⁻¹^2)^(1+σ) := by + rw [betaAction,intervalIntegral.integral_of_le (by norm_num),integral_Ioc_eq_integral_Ioo,hj] + simp only [smul_eq_mul,halg] + exact integral_const_mul _ _ + have hi : (∫ x, (potential r x)^(1+σ)) = + (r+1)^(1+σ)*∫ x, ((Real.cosh (r*x))⁻¹^2)^(1+σ) := by + rw [← integral_const_mul] + apply integral_congr_ae + exact Filter.Eventually.of_forall (fun x ↦ by + dsimp only [potential] + rw [Real.mul_rpow (by linarith : 0 ≤ r+1) (sq_nonneg _)]) + rw [hi,hj'] + field_simp + +lemma young_times_extremizer_factor {σ : ℝ} (hσ : 0 < σ) : + actionYoungConstant σ * ((σ⁻¹+1)^(1+σ)/σ⁻¹) = 1 := by + have hp : 0 < 1+σ := by linarith + have he : σ⁻¹+1 = (1+σ)/σ := by field_simp + rw [actionYoungConstant,he,Real.div_rpow hp.le hσ.le] + rw [Real.rpow_add hσ,Real.rpow_one] + have hn : (1+σ)^(1+σ) ≠ 0 := (Real.rpow_pos_of_pos hp _).ne' + have hn' : σ^σ ≠ 0 := (Real.rpow_pos_of_pos hσ _).ne' + field_simp + +lemma sharp_times_extremizer_integral {γ : ℝ} (hγ : 1/2 < γ) : + sharpConstant γ * (∫ x, (equalityPotential γ x)^(γ+1/2)) = 1 := by + have hσ : 0 < γ-1/2 := by linarith + have hr : 0 < (γ-1/2)⁻¹ := inv_pos.mpr hσ + have hpow : γ+1/2 = 1+(γ-1/2) := by ring + change sharpConstant γ * (∫ x, (potential ((γ-1/2)⁻¹) x)^(γ+1/2)) = 1 + rw [hpow,potential_power_integral hr] + have hc := action_constant_eq_sharp hσ + rw [sub_add_cancel] at hc + rw [← hc] + calc + _ = actionYoungConstant (γ-1/2)*(((γ-1/2)⁻¹+1)^(1+(γ-1/2))/(γ-1/2)⁻¹) := by + rw [mul_comm _ (betaAction (γ-1/2)),← mul_assoc,div_mul_cancel₀ _ (betaAction_pos hσ).ne'] + _ = 1 := young_times_extremizer_factor hσ + +end SharpLiebThirring.ExtremizerProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/FieldFlow.lean b/lean/OAI/Analysis/LiebThirring/FieldFlow.lean new file mode 100644 index 0000000000000000000000000000000000000000..ef94378c74866880722227de351bc650b5bfec04 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/FieldFlow.lean @@ -0,0 +1,315 @@ +import OAI.Analysis.LiebThirring.FlowContinuation + +namespace OAI + +universe u158 u159 u160 u161 u162 u163 u164 u165 + +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Set Metric MeasureTheory Filter +open scoped Topology NNReal +noncomputable section +open Matrix Set MeasureTheory WithLp +open scoped Matrix.Norms.L2Operator Topology + +noncomputable section +open Set Metric +open scoped NNReal +namespace SharpLiebThirring.ODEProof + +/-- A radial auxiliary cutoff; its lack of smoothness is harmless because only +Lipschitz regularity is needed for the flow and barriers. -/ +def radialCutoff {E : Type u158} [NormedAddCommGroup E] (R : ℝ) (x : E) : ℝ := + max 0 (min 1 (R+1-‖x‖)) + +lemma radialCutoff_nonneg {E : Type u159} [NormedAddCommGroup E] (R : ℝ) (x : E) : + 0 ≤ radialCutoff R x := le_max_left _ _ +lemma radialCutoff_le_one {E : Type u160} [NormedAddCommGroup E] (R : ℝ) (x : E) : + radialCutoff R x ≤ 1 := max_le zero_le_one (min_le_left _ _) +lemma radialCutoff_eq_one {E : Type u161} [NormedAddCommGroup E] {R : ℝ} {x : E} + (hx : ‖x‖ ≤ R) : radialCutoff R x = 1 := by + unfold radialCutoff + rw [min_eq_left (by linarith),max_eq_right zero_le_one] +lemma radialCutoff_eq_zero {E : Type u162} [NormedAddCommGroup E] {R : ℝ} {x : E} + (hx : R+1 ≤ ‖x‖) : radialCutoff R x = 0 := by + unfold radialCutoff + exact max_eq_left ((min_le_right _ _).trans (by linarith)) +lemma radialCutoff_lipschitz {E : Type u163} [NormedAddCommGroup E] (R : ℝ) : + LipschitzWith 1 (radialCutoff R : E → ℝ) := by + have h : LipschitzWith 1 (fun x : E ↦ R+1-‖x‖) := by + apply LipschitzWith.of_dist_le_mul + intro x y + simpa only [Real.dist_eq,sub_sub_sub_cancel_left,Real.norm_eq_abs,abs_sub_comm,NNReal.coe_one,one_mul,dist_eq_norm] + using abs_norm_sub_norm_le x y + exact (h.const_min 1).const_max 0 + +lemma bounded_lipschitz_radial_cutoff {E : Type u164} [NormedAddCommGroup E] [NormedSpace ℝ E] + [ProperSpace E] (M : E → E) (hM : LocallyLipschitz M) (R : ℝ) : + ∃ K B : ℝ≥0, LipschitzWith K (fun x ↦ radialCutoff R x • M x) ∧ + ∀ x, ‖radialCutoff R x • M x‖ ≤ B := by + obtain ⟨L,hL⟩ := hM.locallyLipschitzOn.exists_lipschitzOnWith_of_compact + (isCompact_closedBall (0 : E) (R+2)) + obtain ⟨b,hb⟩ := (isCompact_closedBall (0 : E) (R+2)).bddAbove_image + hM.continuous.norm.continuousOn + let B : ℝ≥0 := ⟨max b 0, le_max_right _ _⟩ + have hB (x : E) (hx : ‖x‖ ≤ R+2) : ‖M x‖ ≤ B := + (hb (mem_image_of_mem _ (by simpa only [mem_closedBall,dist_zero_right] using hx))).trans + (le_max_left b 0) + let F := fun x ↦ radialCutoff R x • M x + have hzero (x : E) (hx : R+1 ≤ ‖x‖) : F x = 0 := by + simp only [F,radialCutoff_eq_zero hx,zero_smul] + have hbound (x : E) : ‖F x‖ ≤ B := by + by_cases hx : ‖x‖ ≤ R+2 + · dsimp only [F] + rw [norm_smul,Real.norm_eq_abs,abs_of_nonneg (radialCutoff_nonneg R x)] + exact (mul_le_mul_of_nonneg_right (radialCutoff_le_one R x) (norm_nonneg _)).trans + (by simpa only [one_mul] using hB x hx) + · rw [hzero x (by linarith [lt_of_not_ge hx]),norm_zero]; exact B.prop + have hlocal : LipschitzOnWith (L+B) F (closedBall (0 : E) (R+2)) := by + apply lipschitzOnWith_iff_norm_sub_le.mpr + intro x hx y hy + have hyd : ‖y‖ ≤ R+2 := by simpa only [mem_closedBall,dist_zero_right] using hy + have hid : F x - F y = radialCutoff R x • (M x-M y) + + (radialCutoff R x-radialCutoff R y) • M y := by dsimp [F]; module + rw [hid] + apply (norm_add_le _ _).trans + simp only [norm_smul,Real.norm_eq_abs,abs_of_nonneg (radialCutoff_nonneg R x)] + have hh := hL.dist_le_mul x hx y hy + rw [dist_eq_norm,dist_eq_norm] at hh + have hχ := (radialCutoff_lipschitz (E := E) R).dist_le_mul x y + simp only [dist_eq_norm,Real.norm_eq_abs,NNReal.coe_one,one_mul] at hχ + calc + _ ≤ 1 * ((L : ℝ)*‖x-y‖) + ‖x-y‖ * (B : ℝ) := by + exact add_le_add + (mul_le_mul (radialCutoff_le_one R x) hh (norm_nonneg _) zero_le_one) + (mul_le_mul hχ (hB y hyd) (norm_nonneg _) (norm_nonneg _)) + _ = _ := by push_cast; ring + have hfar (x y : E) (hx : ‖x‖ < R+1) (hy : R+2 < ‖y‖) : + ‖F x - F y‖ ≤ (L+B : ℝ≥0) * ‖x-y‖ := by + rw [hzero y (by linarith),sub_zero] + have hd : 1 ≤ ‖x-y‖ := by + have hh := norm_le_norm_add_norm_sub x y + linarith + calc + _ ≤ (B : ℝ) := hbound x + _ ≤ (L : ℝ) + B := le_add_of_nonneg_left L.prop + _ ≤ ((L : ℝ) + B) * ‖x-y‖ := le_mul_of_one_le_right (add_nonneg L.prop B.prop) hd + _ = _ := rfl + refine ⟨L+B,B,?_,hbound⟩ + apply lipschitzWith_iff_norm_sub_le.mpr + intro x y + change ‖F x - F y‖ ≤ (L+B : ℝ≥0) * ‖x-y‖ + by_cases hx : ‖x‖ ≤ R+2 + · by_cases hy : ‖y‖ ≤ R+2 + · exact lipschitzOnWith_iff_norm_sub_le.mp hlocal + (by simpa only [mem_closedBall,dist_zero_right] using hx) + (by simpa only [mem_closedBall,dist_zero_right] using hy) + · by_cases hx' : R+1 ≤ ‖x‖ + · rw [hzero x hx',hzero y (by linarith [lt_of_not_ge hy]),sub_self,norm_zero] + positivity + · exact hfar x y (lt_of_not_ge hx') (lt_of_not_ge hy) + · by_cases hy : R+1 ≤ ‖y‖ + · rw [hzero x (by linarith [lt_of_not_ge hx]),hzero y hy,sub_self,norm_zero]; positivity + · simpa only [norm_sub_rev] using hfar y x (lt_of_not_ge hy) (lt_of_not_ge hx) + +end SharpLiebThirring.ODEProof +noncomputable section +open Matrix +open scoped Matrix.Norms.L2Operator +namespace SharpLiebThirring.MatrixFlow +variable {n : Type u165} [Fintype n] [DecidableEq n] + +lemma cfc_isolated_row {A : Matrix n n ℝ} (hA : A.IsHermitian) (i : n) + (hi : ∀ j, i ≠ j → A i j = 0) (f : ℝ → ℝ) (j : n) : + cfc f A i j = f (A i i) * (1 : Matrix n n ℝ) i j := by + let U : Matrix n n ℝ := hA.eigenvectorUnitary + have hU : U * star U = 1 := Unitary.coe_mul_star_self hA.eigenvectorUnitary + have hAU : A * U = U * diagonal hA.eigenvalues := by + conv_lhs => rw [hA.spectral_theorem] + simp only [Unitary.conjStarAlgAut_apply] + change U * diagonal hA.eigenvalues * star U * U = _ + rw [mul_assoc,mul_assoc,Unitary.star_mul_self_of_mem hA.eigenvectorUnitary.prop,mul_one] + have hspec (l : n) : U i l = 0 ∨ hA.eigenvalues l = A i i := by + have he := congrFun (congrFun hAU i) l + rw [mul_diagonal] at he + have hr : (A * U) i l = A i i * U i l := by + rw [mul_apply] + apply Finset.sum_eq_single i + · intro b _ hbi + rw [hi b (Ne.symm hbi),zero_mul] + · simp + rw [hr] at he + by_cases hz : U i l = 0 + · exact Or.inl hz + · exact Or.inr (mul_right_cancel₀ hz (by nlinarith : hA.eigenvalues l * U i l = A i i * U i l)) + rw [hA.cfc_eq,IsHermitian.cfc,Unitary.conjStarAlgAut_apply] + change (U * diagonal (f ∘ hA.eigenvalues) * star U) i j = _ + rw [← hU] + conv_rhs => rw [Matrix.mul_apply,Finset.mul_sum] + rw [Matrix.mul_apply] + apply Finset.sum_congr rfl + intro l _ + rw [mul_diagonal] + rcases hspec l with h|h + · simp only [h,zero_mul,mul_zero] + · simp only [Function.comp_apply,h] + ring + +end SharpLiebThirring.MatrixFlow +namespace SharpLiebThirring.MatrixFlow +open MatrixProof ScalarProof Matrix +open scoped Matrix.Norms.L2Operator Topology +variable {N : ℕ} + +def sourceField (σ δ : ℝ) (hσ : σ < 1) (hδ : 0 < δ) (k : Fin N → ℝ) : Sym N → Sym N := + fun A ↦ ⟨matrixField σ δ k A.val,matrixField_isHermitian hσ hδ k A.prop⟩ + +lemma sourceField_locallyLipschitz {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (k : Fin N → ℝ) : + LocallyLipschitz (sourceField σ δ hσ hδ k) := by + have h := (realPartCLM.lipschitzWith.locallyLipschitz).comp + ((hermitianField_locallyLipschitz hσ hδ (realK2SelfAdjoint k).prop).comp + realHermitianComplexifyCLM.lipschitzWith.locallyLipschitz) + have hh : LocallyLipschitz (fun A : Sym N ↦ matrixField σ δ k A.val) := by + convert! h using 1 + funext A + exact matrixField_eq_realPart hσ hδ k A.prop + intro A + obtain ⟨L,s,hs,hL⟩ := hh A + refine ⟨L,s,hs,?_⟩ + intro x hx y hy + exact hL hx hy + +end SharpLiebThirring.MatrixFlow +namespace SharpLiebThirring.MatrixFlow +open MatrixProof ScalarProof Matrix MeasureTheory Filter +open scoped Matrix.Norms.L2Operator Topology +variable {N : ℕ} + +def complexUnitary (U : unitary (Matrix (Fin N) (Fin N) ℝ)) : + unitary (Matrix (Fin N) (Fin N) ℂ) := + Unitary.map (StarMonoidHom.ofClass (complexify (n := Fin N))) U + +lemma complexify_conj (U : unitary (Matrix (Fin N) (Fin N) ℝ)) + (A : Matrix (Fin N) (Fin N) ℝ) : + complexify (Unitary.conjStarAlgAut ℝ _ U A) = + Unitary.conjStarAlgAut ℂ _ (complexUnitary U) (complexify A) := by + simp only [Unitary.conjStarAlgAut_apply,map_mul,map_star] + rfl + +lemma complexify_symConj (s : Fin N → ℝ) (hs : ∀ i, s i = 1 ∨ s i = -1) (A : Sym N) : + complexify (symConj s A).val = Unitary.conjStarAlgAut ℂ _ + (complexUnitary ⟨diagonal s,sign_diagonal_unitary s hs⟩) (complexify A.val) := by + rw [← complexify_conj] + congr 1 + rw [Unitary.conjStarAlgAut_apply,symConj_val] + congr 1 + exact (isHermitian_diagonal s).symm + +lemma sourceField_equivariant {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (k : Fin N → ℝ) + (s : Fin N → ℝ) (hs : ∀ i, s i = 1 ∨ s i = -1) (A : Sym N) : + sourceField σ δ hσ hδ k (symConj s A) = symConj s (sourceField σ δ hσ hδ k A) := by + let U := complexUnitary ⟨diagonal s,sign_diagonal_unitary s hs⟩ + have hK := complexify_symConj s hs (symDiag (fun i ↦ k i ^ 2)) + rw [symConj_diag s hs] at hK + have hh := hermitianField_conj hσ hδ (realK2SelfAdjoint k).prop (complexify_hermitian A.prop) U + change complexify (diagonal (fun i ↦ k i^2)) = Unitary.conjStarAlgAut ℂ _ U (complexify (diagonal (fun i ↦ k i^2))) at hK + change hermitianField σ δ (Unitary.conjStarAlgAut ℂ _ U (complexify (diagonal (fun i ↦ k i^2)))) _ = Unitary.conjStarAlgAut ℂ _ U (hermitianField σ δ (complexify (diagonal (fun i ↦ k i^2))) (complexify A.val)) at hh + rw [← hK,← complexify_symConj s hs A,← complexify_matrixField hσ hδ k (symConj s A).prop, + ← complexify_matrixField hσ hδ k A.prop] at hh + have hf := complexify_symConj s hs (sourceField σ δ hσ hδ k A) + change complexify (symConj s (sourceField σ δ hσ hδ k A)).val = _ at hf + change complexify (symConj s (sourceField σ δ hσ hδ k A)).val = + Unitary.conjStarAlgAut ℂ _ U (complexify (matrixField σ δ k A.val)) at hf + rw [← hf] at hh + apply Subtype.ext + simpa only [realPartCLM_complexify,sourceField] using congrArg realPartCLM hh + +def matrixEntry (i j : Fin N) : Matrix (Fin N) (Fin N) ℝ →L[ℝ] ℝ := + LinearMap.toContinuousLinearMap + {toFun := fun A ↦ A i j, map_add' := by intros; rfl, map_smul' := by intros; rfl} +@[simp] lemma matrixEntry_apply (i j : Fin N) (A : Matrix (Fin N) (Fin N) ℝ) : matrixEntry i j A = A i j := rfl + +lemma matrixField_tendsto {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (k : Fin N → ℝ) + {A : Matrix (Fin N) (Fin N) ℝ} (hA : A.IsHermitian) : + Tendsto (truncatedField σ δ k A) atTop (𝓝 (matrixField σ δ k A)) := by + have ht : Tendsto (fun R ↦ complexify (truncatedField σ δ k A R)) atTop + (𝓝 (hermitianField σ δ (complexify (diagonal (fun i ↦ k i^2))) (complexify A))) := by + have h := hermitianField_cutoff_limit hσ hδ (realK2SelfAdjoint k).prop (complexify_hermitian hA) + change Tendsto (fun R ↦ fieldNormalization σ • ∫ s in -R..R, fieldIntegrand σ δ (complexify (diagonal (fun i ↦ k i^2))) (complexify A) s) atTop (𝓝 _) at h + simpa only [complexify_truncatedField hδ k hA,realK2SelfAdjoint] using h + have hh := realPartCLM.continuous.continuousAt.tendsto.comp ht + rw [matrixField_eq_realPart hσ hδ k hA] + change Tendsto (fun R ↦ realPartCLM (complexify (truncatedField σ δ k A R))) atTop (𝓝 _) at hh + simpa only [realPartCLM_complexify] using hh + +lemma matrixField_isolated_coordinate {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (k : Fin N → ℝ) + (A : Sym N) (i : Fin N) (hi : ∀ j, i ≠ j → A.val i j = 0) : + (sourceField σ δ hσ hδ k A).val i i = scalarMu σ δ (k i ^ 2 - A.val i i ^ 2) := by + have hx (s : ℝ) : (cfc (regularizedPrimitive σ δ) (matrixX k A.val s)) i i = + regularizedPrimitive σ δ ((s-A.val i i)^2+(k i^2-A.val i i^2)) := by + rw [cfc_isolated_row (matrixX_hermitian k A.prop s) i (fun j hij ↦ ?_) _ i] + · simp only [one_apply_eq,mul_one] + congr 1 + simp only [matrixX,Matrix.add_apply,Matrix.sub_apply,Matrix.smul_apply,smul_eq_mul, + diagonal_apply_eq,one_apply_eq,mul_one] + ring + · simp only [matrixX,Matrix.add_apply,Matrix.sub_apply,Matrix.smul_apply,smul_eq_mul, + diagonal_apply_ne _ hij,one_apply_ne hij,hi j hij,mul_zero,sub_zero,add_zero] + have hc : Continuous (fun s : ℝ ↦ cfc (regularizedPrimitive σ δ) (matrixX k A.val s) - + regularizedPrimitive σ δ (s^2) • (1 : Matrix (Fin N) (Fin N) ℝ)) := by + have hx : Continuous (fun s ↦ cfc (regularizedPrimitive σ δ) (matrixX k A.val s)) := + Continuous.cfc_of_mem_nhdsSet (s := Set.univ) _ Filter.univ_mem + (by unfold matrixX; fun_prop) (matrixX_hermitian k A.prop) + (primitive_differentiable σ hδ).continuous.continuousOn + exact hx.sub (((primitive_differentiable σ hδ).continuous.comp (continuous_pow 2)).smul continuous_const) + have he (R : ℝ) : truncatedField σ δ k A.val R i i = fieldNormalization σ * ∫ s in -R..R, + regularizedPrimitive σ δ ((s-A.val i i)^2+(k i^2-A.val i i^2)) - regularizedPrimitive σ δ (s^2) := by + have h := (matrixEntry i i).intervalIntegral_comp_comm (μ := volume) (hc.intervalIntegrable (-R) R) + simp only [matrixEntry_apply] at h + rw [truncatedField,Matrix.smul_apply,smul_eq_mul,← h] + congr 1 + apply intervalIntegral.integral_congr + intro s _ + simp only [Matrix.sub_apply,Matrix.smul_apply,smul_eq_mul,one_apply_eq,mul_one,hx] + have hl := (matrixEntry i i).continuous.continuousAt.tendsto.comp (matrixField_tendsto hσ hδ k A.prop) + change Tendsto (fun R ↦ truncatedField σ δ k A.val R i i) atTop (𝓝 _) at hl + simp only [he] at hl + exact tendsto_nhds_unique hl (primitive_shift_limit hσ hδ (k i^2-A.val i i^2) (A.val i i)) + +def scalarDiag : ℝ →L[ℝ] Sym N := + LinearMap.toContinuousLinearMap + ({toFun := fun x : ℝ ↦ symDiag (fun _ ↦ x) + map_add' := by + intro x y + apply Subtype.ext + exact (diagonal_add (fun _ : Fin N ↦ x) (fun _ ↦ y)).symm + map_smul' := by + intro r x + apply Subtype.ext + exact diagonal_smul r (fun _ : Fin N ↦ x)} : ℝ →ₗ[ℝ] Sym N) + +lemma coordinate_mu_locallyLipschitz {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (k : Fin N → ℝ) (i : Fin N) : LocallyLipschitz (fun x : ℝ ↦ scalarMu σ δ (k i ^ 2-x^2)) := by + have hh := (symEntry i i).lipschitzWith.locallyLipschitz.comp + ((sourceField_locallyLipschitz hσ hδ k).comp scalarDiag.lipschitzWith.locallyLipschitz) + convert! hh using 1 + funext x + change _ = matrixField σ δ k (diagonal (fun _ ↦ x)) i i + rw [matrixField_diagonal hσ hδ,diagonal_apply_eq] + +end SharpLiebThirring.MatrixFlow + +end +end +end +end +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/FieldLimit.lean b/lean/OAI/Analysis/LiebThirring/FieldLimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..7ed02d58986db11e64c3da1407e19815ec3667b6 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/FieldLimit.lean @@ -0,0 +1,482 @@ +import OAI.Analysis.LiebThirring.MatrixTangent + +namespace OAI + +universe u16 u17 u18 + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +noncomputable section +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder CStarAlgebra + + +noncomputable section +open MeasureTheory Set Filter +open scoped Topology +namespace SharpLiebThirring.ScalarProof + +lemma symmetric_shift_boundary {g : ℝ → ℝ} (hg : Continuous g) (he : Function.Even g) + (R b : ℝ) : + (∫ s in -R..R, g (s - b) - g s) = + ∫ t in 0..b, g (R + t) - g (R - b + t) := by + have hc1 : Continuous (fun s : ℝ ↦ g (s - b)) := by fun_prop + have hc2 : Continuous (fun t : ℝ ↦ g (R + t)) := by fun_prop + have hc3 : Continuous (fun t : ℝ ↦ g (R - b + t)) := by fun_prop + rw [intervalIntegral.integral_sub (hc1.intervalIntegrable _ _) + (hg.intervalIntegrable _ _), intervalIntegral.integral_comp_sub_right] + rw [intervalIntegral.integral_interval_sub_interval_comm + (hg.intervalIntegrable _ _) (hg.intervalIntegrable _ _) (hg.intervalIntegrable _ _)] + have hn : (∫ s in -R - b..-R, g s) = ∫ t in R..R + b, g t := by + have h := intervalIntegral.integral_comp_neg (f := g) (a := R) (b := R + b) + calc + _ = ∫ x in R..R + b, g (-x) := by + simpa only [show -(R + b) = -R - b by ring] using h.symm + _ = _ := intervalIntegral.integral_congr (fun x _ ↦ he x) + rw [hn, intervalIntegral.integral_sub (hc2.intervalIntegrable _ _) + (hc3.intervalIntegrable _ _)] + simp only [intervalIntegral.integral_comp_add_left, add_zero, sub_add_cancel] + +lemma symmetric_shift_norm_le {g g' : ℝ → ℝ} (hg : ∀ x, HasDerivAt g (g' x) x) + (he : Function.Even g) (R b C T : ℝ) (hR : T + 2 * |b| ≤ R) + (hbound : ∀ x, T ≤ x → ‖g' x‖ ≤ C) : + ‖∫ s in -R..R, g (s - b) - g s‖ ≤ C * |b| ^ 2 := by + rw [symmetric_shift_boundary (continuous_iff_continuousAt.2 (fun x ↦ (hg x).continuousAt)) he] + apply le_trans (intervalIntegral.norm_integral_le_of_norm_le_const + (C := C * |b|) (fun t ht ↦ ?_)) (by simp [pow_two, mul_assoc]) + have ht' : -|b| ≤ t := by + have := ht.1 + have hmin : -|b| ≤ min 0 b := le_min (by linarith [abs_nonneg b]) (neg_abs_le b) + linarith + have hx : R - b + t ∈ Ici T := by + have := le_abs_self b + change T ≤ _ + linarith + have hy : R + t ∈ Ici T := by change T ≤ _; linarith [abs_nonneg b] + have hm := (convex_Ici T).norm_image_sub_le_of_norm_hasDerivWithin_le + (fun x _ ↦ (hg x).hasDerivWithinAt) (fun x hx ↦ hbound x hx) hx hy + simpa only [show R + t - (R - b + t) = b by ring, Real.norm_eq_abs] using hm + +lemma symmetric_shift_tendsto_zero {g g' : ℝ → ℝ} (hg : ∀ x, HasDerivAt g (g' x) x) + (he : Function.Even g) (hlim : Tendsto g' atTop (𝓝 0)) (b : ℝ) : + Tendsto (fun R : ℝ ↦ ∫ s in -R..R, g (s - b) - g s) atTop (𝓝 0) := by + apply Metric.tendsto_atTop.2 + intro ε hε + have hc : 0 < ε / (|b| ^ 2 + 1) := div_pos hε (by positivity) + obtain ⟨T, hT⟩ := (Metric.tendsto_atTop.1 hlim) _ hc + refine ⟨T + 2 * |b|, fun R hR ↦ ?_⟩ + rw [Real.dist_eq, sub_zero, ← Real.norm_eq_abs] + refine lt_of_le_of_lt (symmetric_shift_norm_le hg he R b (ε / (|b| ^ 2 + 1)) T hR (fun x hx ↦ ?_)) ?_ + · simpa only [dist_zero_right] using (hT x hx).le + · have hden : 0 < |b| ^ 2 + 1 := by positivity + rw [div_mul_eq_mul_div, div_lt_iff₀ hden] + nlinarith + +end SharpLiebThirring.ScalarProof + +namespace SharpLiebThirring.ScalarProof + +lemma primitive_quadratic_hasDerivAt (σ : ℝ) {δ : ℝ} (hδ : 0 < δ) (z s : ℝ) : + HasDerivAt (fun t : ℝ ↦ regularizedPrimitive σ δ (t ^ 2 + z)) + (2 * s * (max (s ^ 2 + z) 0 + δ) ^ (σ - 3 / 2)) s := by + convert! (primitive_hasDerivAt σ hδ (s ^ 2 + z)).comp s + (((hasDerivAt_id s).pow 2).add_const z) using 1 + simp only [id_eq, Nat.cast_ofNat, mul_one] + ring + +lemma primitive_quadratic_deriv_tendsto {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (z : ℝ) : + Tendsto (fun s : ℝ ↦ 2 * s * (max (s ^ 2 + z) 0 + δ) ^ (σ - 3 / 2)) atTop (𝓝 0) := by + let a := δ / (δ + |z| + 1) + have ha : 0 < a := by dsimp [a]; positivity + have ht : Tendsto (fun s : ℝ ↦ (2 * a ^ (σ - 3 / 2)) * s ^ (2 * σ - 2)) atTop (𝓝 0) := by + have h := (tendsto_rpow_neg_atTop (show 0 < 2 - 2 * σ by linarith)).const_mul + (2 * a ^ (σ - 3 / 2)) + simpa only [show -(2 - 2 * σ) = 2 * σ - 2 by ring, mul_zero] using h + apply squeeze_zero' _ _ ht + · filter_upwards [eventually_ge_atTop (0 : ℝ)] with s hs + positivity + · filter_upwards [eventually_ge_atTop (1 : ℝ)] with s hs + have hs₀ : 0 < s := by linarith + have hb := Real.rpow_le_rpow_of_nonpos (show 0 < a * (1 + s ^ 2) by positivity) + (shifted_base_lower hδ z s) (show σ - 3 / 2 ≤ 0 by linarith) + have hsq := Real.rpow_le_rpow_of_nonpos (sq_pos_of_pos hs₀) + (show s ^ 2 ≤ 1 + s ^ 2 by linarith) (show σ - 3 / 2 ≤ 0 by linarith) + rw [Real.mul_rpow ha.le (by positivity)] at hb + calc + _ ≤ 2 * s * (a ^ (σ - 3 / 2) * (1 + s ^ 2) ^ (σ - 3 / 2)) := + mul_le_mul_of_nonneg_left hb (by positivity) + _ ≤ 2 * s * (a ^ (σ - 3 / 2) * (s ^ 2) ^ (σ - 3 / 2)) := by + gcongr + _ = _ := by + rw [← Real.rpow_natCast, ← Real.rpow_mul hs₀.le] + norm_num only [Nat.cast_ofNat] + conv_lhs => arg 1; arg 2; rw [← Real.rpow_one s] + rw [show 2 * s ^ (1 : ℝ) * (a ^ (σ - 3 / 2) * s ^ ((2 : ℝ) * (σ - 3 / 2))) = + (2 * a ^ (σ - 3 / 2)) * (s ^ (1 : ℝ) * s ^ (2 * (σ - 3 / 2))) by ring, + ← Real.rpow_add hs₀] + congr 2 + ring + +lemma primitive_symmetric_shift_zero {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (z b : ℝ) : + Tendsto (fun R : ℝ ↦ ∫ s in -R..R, + regularizedPrimitive σ δ ((s - b) ^ 2 + z) - regularizedPrimitive σ δ (s ^ 2 + z)) + atTop (𝓝 0) := + symmetric_shift_tendsto_zero (primitive_quadratic_hasDerivAt σ hδ z) + (fun s ↦ by simp) (primitive_quadratic_deriv_tendsto hσ hδ z) b + +/-- The symmetric shift identity, with exactly the cutoff used in the field. -/ +lemma primitive_shift_limit {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (z b : ℝ) : + Tendsto (fun R : ℝ ↦ fieldNormalization σ * ∫ s in -R..R, + regularizedPrimitive σ δ ((s - b) ^ 2 + z) - regularizedPrimitive σ δ (s ^ 2)) + atTop (𝓝 (scalarMu σ δ z)) := by + have hc := (primitive_differentiable σ hδ).continuous + have h₁ := primitive_symmetric_shift_zero hσ hδ z b + have h₂ := intervalIntegral_tendsto_integral (mu_integrand_integrable hσ hδ z) + tendsto_neg_atTop_atBot tendsto_id + have hh := (h₁.add h₂).const_mul (fieldNormalization σ) + simp only [zero_add] at hh + apply hh.congr + intro R + congr 1 + simp only [id_eq] + rw [← intervalIntegral.integral_add + (show IntervalIntegrable (fun s : ℝ ↦ regularizedPrimitive σ δ ((s - b) ^ 2 + z) - + regularizedPrimitive σ δ (s ^ 2 + z)) volume (-R) R from + (by fun_prop : Continuous _).intervalIntegrable _ _) + (show IntervalIntegrable (fun s : ℝ ↦ regularizedPrimitive σ δ (s ^ 2 + z) - + regularizedPrimitive σ δ (s ^ 2)) volume (-R) R from + (by fun_prop : Continuous _).intervalIntegrable _ _)] + apply intervalIntegral.integral_congr + intro s hs + ring + +end SharpLiebThirring.ScalarProof + +namespace SharpLiebThirring.ScalarProof + +lemma derivative_lipschitz_on_positive {σ δ a : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (ha : 0 < a) {x y : ℝ} (hx : a ≤ x) (hy : a ≤ y) : + ‖(x + δ) ^ (σ - 3 / 2) - (y + δ) ^ (σ - 3 / 2)‖ ≤ + (3 / 2 - σ) * (a + δ) ^ (σ - 5 / 2) * ‖x - y‖ := by + have hd : ∀ t ∈ Ici a, HasDerivWithinAt (fun t : ℝ ↦ (t + δ) ^ (σ - 3 / 2)) + ((σ - 3 / 2) * (t + δ) ^ (σ - 5 / 2)) (Ici a) t := by + intro t ht + change a ≤ t at ht + have hp : t + δ ≠ 0 := by linarith + convert! (((hasDerivAt_id t).add_const δ).rpow_const (p := σ - 3 / 2) + (Or.inl hp)).hasDerivWithinAt using 1 + simp only [id_eq] + ring_nf + have hb : ∀ t ∈ Ici a, ‖(σ - 3 / 2) * (t + δ) ^ (σ - 5 / 2)‖ ≤ + (3 / 2 - σ) * (a + δ) ^ (σ - 5 / 2) := by + intro t ht + change a ≤ t at ht + rw [norm_mul, Real.norm_eq_abs, abs_of_neg (show σ - 3 / 2 < 0 by linarith), + Real.norm_eq_abs, abs_of_nonneg (Real.rpow_nonneg (by linarith) _)] + have hr := Real.rpow_le_rpow_of_nonpos (show 0 < a + δ by linarith) + (show a + δ ≤ t + δ by linarith) (show σ - 5 / 2 ≤ 0 by linarith) + nlinarith + exact (convex_Ici a).norm_image_sub_le_of_norm_hasDerivWithin_le hd hb hy hx + +lemma primitive_taylor_bound {σ δ a x r y : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (ha : 0 < a) (hr : 0 ≤ r) (hxr : a ≤ x - r) (hy : |y| ≤ r) : + ‖regularizedPrimitive σ δ (x + y) - regularizedPrimitive σ δ x - + (x + δ) ^ (σ - 3 / 2) * y‖ ≤ + (3 / 2 - σ) * (a + δ) ^ (σ - 5 / 2) * r ^ 2 := by + let L := (3 / 2 - σ) * (a + δ) ^ (σ - 5 / 2) + have hL : 0 ≤ L := mul_nonneg (by linarith) (Real.rpow_nonneg (by linarith) _) + have hx : a ≤ x := by linarith + have hxy : x + y ∈ Icc (x - r) (x + r) := by + constructor <;> linarith [(abs_le.1 hy).1, (abs_le.1 hy).2] + have hxx : x ∈ Icc (x - r) (x + r) := ⟨by linarith, by linarith⟩ + have hd (t : ℝ) (ht : t ∈ Icc (x - r) (x + r)) : + HasDerivWithinAt (fun t : ℝ ↦ regularizedPrimitive σ δ t - + regularizedPrimitive σ δ x - (x + δ) ^ (σ - 3 / 2) * (t - x)) + ((t + δ) ^ (σ - 3 / 2) - (x + δ) ^ (σ - 3 / 2)) (Icc (x - r) (x + r)) t := by + have ht₀ : 0 ≤ t := by have := ht.1; linarith + convert! (((primitive_hasDerivAt σ hδ t).sub_const (regularizedPrimitive σ δ x)).sub + (((hasDerivAt_id t).sub_const x).const_mul ((x + δ) ^ (σ - 3 / 2)))).hasDerivWithinAt + using 1 + simp [max_eq_left ht₀] + have hb (t : ℝ) (ht : t ∈ Icc (x - r) (x + r)) : + ‖(t + δ) ^ (σ - 3 / 2) - (x + δ) ^ (σ - 3 / 2)‖ ≤ L * r := by + refine (derivative_lipschitz_on_positive hσ hδ ha (hxr.trans ht.1) hx).trans ?_ + apply mul_le_mul_of_nonneg_left _ hL + rw [Real.norm_eq_abs, abs_le] + constructor <;> linarith [ht.1, ht.2] + have hm := (convex_Icc (x - r) (x + r)).norm_image_sub_le_of_norm_hasDerivWithin_le + hd hb hxx hxy + simp only [sub_self, mul_zero, sub_zero, add_sub_cancel_left, Real.norm_eq_abs] at hm + refine hm.trans ((mul_le_mul_of_nonneg_left hy (mul_nonneg hL hr)).trans_eq ?_) + dsimp [L] + ring + +end SharpLiebThirring.ScalarProof + +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {n : Type u16} [Fintype n] [DecidableEq n] + +lemma cfc_scalar_add (f : ℝ → ℝ) (hf : Continuous f) (x : ℝ) + {A : Matrix n n ℂ} (hA : A.IsHermitian) : + cfc f (x • 1 + A) = cfc (fun y : ℝ ↦ f (x + y)) A := by + have h := cfc_comp' f (fun y : ℝ ↦ x + y) A hf.continuousOn (by fun_prop) hA + erw [cfc_const_add x id A (by fun_prop) hA, cfc_id ℝ A hA, + Algebra.algebraMap_eq_smul_one] at h + exact h.symm + +lemma spectrum_abs_le_matrix_norm {A : Matrix n n ℂ} {y : ℝ} (hy : y ∈ spectrum ℝ A) : + |y| ≤ ‖A‖ := by + cases isEmpty_or_nonempty n with + | inl h => + have h1 : (1 : Matrix n n ℂ) = 0 := Subsingleton.elim _ _ + have hy0 : y = 0 := by simpa [h1] using spectrum.norm_le_norm_mul_of_mem hy + simp [hy0] + | inr h => simpa using spectrum.norm_le_norm_mul_of_mem hy + +lemma primitive_cfc_taylor_bound {σ δ a x r : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (ha : 0 < a) (hr : 0 ≤ r) (hxr : a ≤ x - r) + {A : Matrix n n ℂ} (hA : A.IsHermitian) (hAr : ‖A‖ ≤ r) : + ‖cfc (regularizedPrimitive σ δ) (x • 1 + A) - + regularizedPrimitive σ δ x • 1 - (x + δ) ^ (σ - 3 / 2) • A‖ ≤ + (3 / 2 - σ) * (a + δ) ^ (σ - 5 / 2) * r ^ 2 := by + have hc := (primitive_differentiable σ hδ).continuous + have he : cfc (fun y : ℝ ↦ regularizedPrimitive σ δ (x + y) - + regularizedPrimitive σ δ x - (x + δ) ^ (σ - 3 / 2) * y) A = + cfc (regularizedPrimitive σ δ) (x • 1 + A) - + regularizedPrimitive σ δ x • 1 - (x + δ) ^ (σ - 3 / 2) • A := by + erw [cfc_sub (fun y : ℝ ↦ regularizedPrimitive σ δ (x + y) - + regularizedPrimitive σ δ x) (fun y : ℝ ↦ (x + δ) ^ (σ - 3 / 2) * y) A + (by fun_prop) (by fun_prop), + cfc_sub (fun y : ℝ ↦ regularizedPrimitive σ δ (x + y)) + (fun _ : ℝ ↦ regularizedPrimitive σ δ x) A (by fun_prop) (by fun_prop), + cfc_const (regularizedPrimitive σ δ x) A hA, + cfc_const_mul_id ((x + δ) ^ (σ - 3 / 2)) A hA, + Algebra.algebraMap_eq_smul_one, ← cfc_scalar_add _ hc x hA] + rw [← he] + have hb : 0 ≤ (3 / 2 - σ) * (a + δ) ^ (σ - 5 / 2) * r ^ 2 := by + have : 0 ≤ 3 / 2 - σ := by linarith + positivity + apply norm_cfc_le hb + intro y hy + exact primitive_taylor_bound hσ hδ ha hr hxr + ((spectrum_abs_le_matrix_norm hy).trans hAr) + +end SharpLiebThirring.MatrixProof + +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {n : Type u17} [Fintype n] [DecidableEq n] + +lemma quadratic_taylor_weight {σ δ s A : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (hs : 1 ≤ s) : + (s ^ 2 / 2 + δ) ^ (σ - 5 / 2) * (A * s) ^ 2 ≤ + (1 / 4 : ℝ) ^ (σ - 5 / 2) * A ^ 2 * (1 + s ^ 2) ^ (σ - 3 / 2) := by + have hs2 : 1 ≤ s ^ 2 := by nlinarith + have hb : 0 < (1 + s ^ 2) / 4 := by positivity + have hle : (1 + s ^ 2) / 4 ≤ s ^ 2 / 2 + δ := by nlinarith + have hr := Real.rpow_le_rpow_of_nonpos hb hle (by linarith : σ - 5 / 2 ≤ 0) + have he : ((1 + s ^ 2) / 4) ^ (σ - 5 / 2) = + (1 / 4 : ℝ) ^ (σ - 5 / 2) * (1 + s ^ 2) ^ (σ - 5 / 2) := by + rw [show (1 + s ^ 2) / 4 = (1 / 4 : ℝ) * (1 + s ^ 2) by ring, + Real.mul_rpow (by positivity) (by positivity)] + have he2 : (1 + s ^ 2) ^ (σ - 5 / 2) * (1 + s ^ 2) = + (1 + s ^ 2) ^ (σ - 3 / 2) := by + rw [← Real.rpow_add_one (by positivity)] + congr 1 + ring + calc + _ ≤ ((1 + s ^ 2) / 4) ^ (σ - 5 / 2) * (A * s) ^ 2 := + mul_le_mul_of_nonneg_right hr (sq_nonneg _) + _ = (1 / 4 : ℝ) ^ (σ - 5 / 2) * A ^ 2 * + ((1 + s ^ 2) ^ (σ - 5 / 2) * s ^ 2) := by rw [he]; ring + _ ≤ (1 / 4 : ℝ) ^ (σ - 5 / 2) * A ^ 2 * + ((1 + s ^ 2) ^ (σ - 5 / 2) * (1 + s ^ 2)) := by gcongr; linarith + _ = _ := by rw [he2] + +lemma quadratic_derivative_weight {σ δ s : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (hs : 1 ≤ s) : + (s ^ 2 + δ) ^ (σ - 3 / 2) ≤ + (1 / 2 : ℝ) ^ (σ - 3 / 2) * (1 + s ^ 2) ^ (σ - 3 / 2) := by + have hs2 : 1 ≤ s ^ 2 := by nlinarith + have hr := Real.rpow_le_rpow_of_nonpos (by positivity : 0 < (1 + s ^ 2) / 2) + (by nlinarith : (1 + s ^ 2) / 2 ≤ s ^ 2 + δ) (by linarith : σ - 3 / 2 ≤ 0) + simpa only [show (1 + s ^ 2) / 2 = (1 / 2 : ℝ) * (1 + s ^ 2) by ring, + Real.mul_rpow (by positivity : 0 ≤ (1 / 2 : ℝ)) (by positivity : 0 ≤ 1 + s ^ 2)] using hr + +def quadraticMatrix (C B : Matrix n n ℂ) (s : ℝ) : Matrix n n ℂ := + s ^ 2 • 1 + (C - (2 * s) • B) + +def pairedFieldIntegrand (σ δ : ℝ) (C B : Matrix n n ℂ) (s : ℝ) : Matrix n n ℂ := + cfc (regularizedPrimitive σ δ) (quadraticMatrix C B s) + + cfc (regularizedPrimitive σ δ) (quadraticMatrix C B (-s)) - + (2 * regularizedPrimitive σ δ (s ^ 2)) • 1 + +lemma pairedFieldIntegrand_even (σ δ : ℝ) (C B : Matrix n n ℂ) : + Function.Even (pairedFieldIntegrand σ δ C B) := by + intro s + simp only [pairedFieldIntegrand, neg_neg, neg_sq, add_comm] + +omit [Fintype n] in +lemma quadraticMatrix_hermitian {C B : Matrix n n ℂ} + (hC : C.IsHermitian) (hB : B.IsHermitian) (s : ℝ) : + (quadraticMatrix C B s).IsHermitian := + ((isHermitian_one (n := n) (α := ℂ)).smul (isSelfAdjoint_iff.2 rfl : IsSelfAdjoint (s ^ 2))).add (hC.sub (hB.smul (isSelfAdjoint_iff.2 rfl : IsSelfAdjoint (2 * s)))) + +lemma perturbed_norm_le {C B : Matrix n n ℂ} {s : ℝ} (hs : 1 ≤ |s|) : + ‖C - (2 * s) • B‖ ≤ (‖C‖ + 2 * ‖B‖) * |s| := by + calc + _ ≤ ‖C‖ + ‖(2 * s) • B‖ := norm_sub_le _ _ + _ = ‖C‖ + 2 * |s| * ‖B‖ := by simp [norm_smul] + _ ≤ _ := by nlinarith [norm_nonneg C, norm_nonneg B] + +lemma pairedFieldIntegrand_bound {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) + {s : ℝ} (hs : max 1 (2 * (‖C‖ + 2 * ‖B‖)) ≤ s) : + ‖pairedFieldIntegrand σ δ C B s‖ ≤ + (2 * (3 / 2 - σ) * (1 / 4 : ℝ) ^ (σ - 5 / 2) * (‖C‖ + 2 * ‖B‖) ^ 2 + + 2 * ‖C‖ * (1 / 2 : ℝ) ^ (σ - 3 / 2)) * (1 + s ^ 2) ^ (σ - 3 / 2) := by + have hs1 : 1 ≤ s := (le_max_left _ _).trans hs + have hsA : 2 * (‖C‖ + 2 * ‖B‖) ≤ s := (le_max_right _ _).trans hs + have hs0 : 0 < s := by linarith + let A := ‖C‖ + 2 * ‖B‖ + have hA : 0 ≤ A := by dsimp [A]; positivity + have hxr : s ^ 2 / 2 ≤ s ^ 2 - A * s := by dsimp [A]; nlinarith + have hn₁ : ‖C - (2 * s) • B‖ ≤ A * s := by + simpa only [abs_of_pos hs0] using (perturbed_norm_le (C := C) (B := B) + (s := s) (by rwa [abs_of_pos hs0])) + have hn₂ : ‖C - (2 * -s) • B‖ ≤ A * s := by + simpa only [abs_neg, abs_of_pos hs0] using (perturbed_norm_le (C := C) (B := B) + (s := -s) (by rwa [abs_neg, abs_of_pos hs0])) + have ht₁ := primitive_cfc_taylor_bound hσ hδ (by positivity : 0 < s ^ 2 / 2) + (mul_nonneg hA hs0.le) hxr (hC.sub (hB.smul (isSelfAdjoint_iff.2 rfl : IsSelfAdjoint (2 * s)))) hn₁ + have ht₂ := primitive_cfc_taylor_bound hσ hδ (by positivity : 0 < s ^ 2 / 2) + (mul_nonneg hA hs0.le) hxr (hC.sub (hB.smul (isSelfAdjoint_iff.2 rfl : IsSelfAdjoint (2 * -s)))) hn₂ + let E₁ := cfc (regularizedPrimitive σ δ) (quadraticMatrix C B s) - + regularizedPrimitive σ δ (s ^ 2) • (1 : Matrix n n ℂ) - + (s ^ 2 + δ) ^ (σ - 3 / 2) • (C - (2 * s) • B) + let E₂ := cfc (regularizedPrimitive σ δ) (quadraticMatrix C B (-s)) - + regularizedPrimitive σ δ (s ^ 2) • (1 : Matrix n n ℂ) - + (s ^ 2 + δ) ^ (σ - 3 / 2) • (C - (2 * -s) • B) + have he : pairedFieldIntegrand σ δ C B s = + E₁ + E₂ + (2 * (s ^ 2 + δ) ^ (σ - 3 / 2)) • C := by + dsimp [pairedFieldIntegrand, E₁, E₂] + module + have ht₂' : ‖E₂‖ ≤ (3 / 2 - σ) * (s ^ 2 / 2 + δ) ^ (σ - 5 / 2) * (A * s) ^ 2 := by + simpa only [E₂, quadraticMatrix, neg_sq] using ht₂ + have hw := quadratic_taylor_weight (A := A) hσ hδ hs1 + have hd := quadratic_derivative_weight hσ hδ hs1 + have hr : 0 ≤ (s ^ 2 + δ) ^ (σ - 3 / 2) := Real.rpow_nonneg (by positivity) _ + have hp : 0 ≤ 3 / 2 - σ := by linarith + rw [he] + calc + _ ≤ ‖E₁‖ + ‖E₂‖ + ‖(2 * (s ^ 2 + δ) ^ (σ - 3 / 2)) • C‖ := + by linarith [norm_add_le E₁ E₂, norm_add_le (E₁ + E₂) ((2 * (s ^ 2 + δ) ^ (σ - 3 / 2)) • C)] + _ ≤ 2 * ((3 / 2 - σ) * (s ^ 2 / 2 + δ) ^ (σ - 5 / 2) * (A * s) ^ 2) + + 2 * (s ^ 2 + δ) ^ (σ - 3 / 2) * ‖C‖ := by + rw [norm_smul, Real.norm_eq_abs, abs_of_nonneg (mul_nonneg (by norm_num) hr)] + have ht₁' : ‖E₁‖ ≤ (3 / 2 - σ) * (s ^ 2 / 2 + δ) ^ (σ - 5 / 2) * (A * s) ^ 2 := ht₁ + linarith + _ ≤ _ := by dsimp [A] at *; nlinarith [mul_le_mul_of_nonneg_left hw (mul_nonneg (by norm_num : (0 : ℝ) ≤ 2) hp), + mul_le_mul_of_nonneg_left hd (mul_nonneg (by norm_num : (0 : ℝ) ≤ 2) (norm_nonneg C))] + +end SharpLiebThirring.MatrixProof + +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {n : Type u18} [Fintype n] [DecidableEq n] + +lemma continuous_quadratic_cfc {δ : ℝ} (hδ : 0 < δ) (σ : ℝ) + {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) : + Continuous (fun s : ℝ ↦ cfc (regularizedPrimitive σ δ) (quadraticMatrix C B s)) := by + exact Continuous.cfc_of_mem_nhdsSet (s := Set.univ) _ (Filter.univ_mem) (by + unfold quadraticMatrix + fun_prop) (fun s ↦ quadraticMatrix_hermitian hC hB s) + (primitive_differentiable σ hδ).continuous.continuousOn + +lemma continuous_pairedFieldIntegrand {δ : ℝ} (hδ : 0 < δ) (σ : ℝ) + {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) : + Continuous (pairedFieldIntegrand σ δ C B) := by + unfold pairedFieldIntegrand + exact ((continuous_quadratic_cfc hδ σ hC hB).add + ((continuous_quadratic_cfc hδ σ hC hB).comp continuous_neg)).sub + (((continuous_const.mul ((primitive_differentiable σ hδ).continuous.comp + (continuous_pow 2)))).smul continuous_const) + +lemma integrable_pairedFieldIntegrand {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) : + Integrable (pairedFieldIntegrand σ δ C B) := by + apply MeasureTheory.LocallyIntegrable.integrable_of_isBigO_atTop_of_norm_isNegInvariant + (continuous_pairedFieldIntegrand hδ σ hC hB).locallyIntegrable + (g := fun s : ℝ ↦ (1 + s ^ 2) ^ (σ - 3 / 2)) + · exact Filter.Eventually.of_forall (fun s ↦ congrArg norm + ((pairedFieldIntegrand_even σ δ C B s).symm)) + · apply Asymptotics.IsBigO.of_bound + (2 * (3 / 2 - σ) * (1 / 4 : ℝ) ^ (σ - 5 / 2) * (‖C‖ + 2 * ‖B‖) ^ 2 + + 2 * ‖C‖ * (1 / 2 : ℝ) ^ (σ - 3 / 2)) + filter_upwards [eventually_ge_atTop (max 1 (2 * (‖C‖ + 2 * ‖B‖)))] with s hs + rw [Real.norm_eq_abs, abs_of_nonneg (Real.rpow_nonneg (by positivity : 0 ≤ 1 + s ^ 2) _)] + exact pairedFieldIntegrand_bound hσ hδ hC hB hs + · exact (normalization_integrable hσ).integrableAtFilter atTop + +def fieldIntegrand (σ δ : ℝ) (C B : Matrix n n ℂ) (s : ℝ) : Matrix n n ℂ := + cfc (regularizedPrimitive σ δ) (quadraticMatrix C B s) - + regularizedPrimitive σ δ (s ^ 2) • 1 + +def hermitianField (σ δ : ℝ) (C B : Matrix n n ℂ) : Matrix n n ℂ := + (fieldNormalization σ / 2) • ∫ s : ℝ, pairedFieldIntegrand σ δ C B s + +lemma continuous_fieldIntegrand {δ : ℝ} (hδ : 0 < δ) (σ : ℝ) + {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) : + Continuous (fieldIntegrand σ δ C B) := + (continuous_quadratic_cfc hδ σ hC hB).sub + (((primitive_differentiable σ hδ).continuous.comp (continuous_pow 2)).smul continuous_const) + +lemma cutoff_paired_identity {δ : ℝ} (hδ : 0 < δ) (σ : ℝ) + {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) (R : ℝ) : + (∫ s in -R..R, pairedFieldIntegrand σ δ C B s) = + (2 : ℝ) • ∫ s in -R..R, fieldIntegrand σ δ C B s := by + have hc := continuous_fieldIntegrand hδ σ hC hB + have he : pairedFieldIntegrand σ δ C B = fun s ↦ + fieldIntegrand σ δ C B s + fieldIntegrand σ δ C B (-s) := by + funext s + simp only [pairedFieldIntegrand, fieldIntegrand, neg_sq] + module + rw [he] + dsimp only + erw [intervalIntegral.integral_add (hc.intervalIntegrable _ _) + ((hc.comp continuous_neg).intervalIntegrable _ _)] + have hn := intervalIntegral.integral_comp_neg (f := fieldIntegrand σ δ C B) (a := -R) (b := R) + simp only [neg_neg] at hn + simp only [Function.comp_apply] + erw [hn] + module + +lemma hermitianField_cutoff_limit {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) : + Tendsto (fun R : ℝ ↦ fieldNormalization σ • ∫ s in -R..R, fieldIntegrand σ δ C B s) + atTop (𝓝 (hermitianField σ δ C B)) := by + have hi := integrable_pairedFieldIntegrand hσ hδ hC hB + have ht := intervalIntegral_tendsto_integral hi tendsto_neg_atTop_atBot tendsto_id + have hh := ht.const_smul (fieldNormalization σ / 2) + simp only [id_eq] at hh + convert! hh using 1 + funext R + rw [cutoff_paired_identity hδ σ hC hB, smul_smul] + congr 1 + ring + +end SharpLiebThirring.MatrixProof + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/FieldPrimitive.lean b/lean/OAI/Analysis/LiebThirring/FieldPrimitive.lean new file mode 100644 index 0000000000000000000000000000000000000000..40e8e98c1a81450aac6ccd81139e578b96e77e43 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/FieldPrimitive.lean @@ -0,0 +1,309 @@ +import OAI.Analysis.LiebThirring.FieldRegularity + +namespace OAI + +universe u32 u33 u34 + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +noncomputable section +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder CStarAlgebra +noncomputable section +open MeasureTheory Set Filter +open scoped Topology +open scoped NNReal + + +namespace SharpLiebThirring.MatrixProof +open Matrix ScalarProof MeasureTheory Filter +open scoped Matrix.Norms.L2Operator Topology +variable {n : Type u32} [Fintype n] [DecidableEq n] + +-- Select the inherited subspace seminorm, avoiding the duplicate subgroup +-- class instance during elaboration of iterated continuous-linear maps. +local instance : SeminormedAddCommGroup (selfAdjoint (Matrix n n ℂ)) := + (inferInstance : NormedAddCommGroup (selfAdjoint (Matrix n n ℂ))).toSeminormedAddCommGroup +local instance : NormedSpace ℝ (selfAdjoint (Matrix n n ℂ)) := inferInstance + +def traceGradientMap : Matrix n n ℂ →L[ℝ] (selfAdjoint (Matrix n n ℂ) →L[ℝ] ℝ) := + LinearMap.toContinuousLinearMap + { toFun := fun M ↦ (tracePairCLM M).comp hermitianInclusion + map_add' := by + intro M N + ext H + simp [tracePairCLM_apply, hermitianInclusion, add_mul, trace_add] + map_smul' := by + intro r M + ext H + simp [tracePairCLM_apply, hermitianInclusion, trace_smul] } + +@[simp] lemma traceGradientMap_apply (M : Matrix n n ℂ) (B : selfAdjoint (Matrix n n ℂ)) : + traceGradientMap M B = (trace (M * (B : Matrix n n ℂ))).re := rfl + +def traceGradientNorm : ℝ := ‖traceGradientMap (n := n)‖ + +lemma traceGradientNorm_nonneg : 0 ≤ traceGradientNorm (n := n) := + (traceGradientMap (n := n)).opNorm_nonneg + +lemma traceGradientMap_bound (M : Matrix n n ℂ) : + ‖traceGradientMap M‖ ≤ traceGradientNorm (n := n) * ‖M‖ := by + have hh := (traceGradientMap (n := n)).le_opNorm M + convert! hh + +def quadraticSelfAdjoint (C : selfAdjoint (Matrix n n ℂ)) (s : ℝ) + (B : selfAdjoint (Matrix n n ℂ)) : selfAdjoint (Matrix n n ℂ) := + C - (2 * s) • B + (s ^ 2) • 1 + +@[simp] lemma quadraticSelfAdjoint_coe (C : selfAdjoint (Matrix n n ℂ)) (s : ℝ) + (B : selfAdjoint (Matrix n n ℂ)) : + (quadraticSelfAdjoint C s B : Matrix n n ℂ) = quadraticMatrix C B s := by + simp [quadraticSelfAdjoint, quadraticMatrix, add_comm] + +lemma quadraticSelfAdjoint_hasFDerivAt (C B : selfAdjoint (Matrix n n ℂ)) (s : ℝ) : + HasFDerivAt (quadraticSelfAdjoint C s) ((-2 * s) • ContinuousLinearMap.id ℝ _) B := by + convert! (((hasFDerivAt_id (𝕜 := ℝ) B).const_smul (2 * s)).const_sub C).add_const ((s ^ 2) • 1) using 1 + ext H : 1 + change (-2 * s) • H = -((2 * s) • H) + module + +/-- Paired trace potential. At s=0 the assigned value is immaterial to its integral. -/ +def pairedTracePotential (σ δ : ℝ) (C : selfAdjoint (Matrix n n ℂ)) + (B : selfAdjoint (Matrix n n ℂ)) (s : ℝ) : ℝ := + -( (trace (cfc (secondPrimitive σ δ) (quadraticMatrix (C : Matrix n n ℂ) (B : Matrix n n ℂ) s))).re - + (trace (cfc (secondPrimitive σ δ) (quadraticMatrix (C : Matrix n n ℂ) (B : Matrix n n ℂ) (-s)))).re) / (2 * s) - + 2 * regularizedPrimitive σ δ (s ^ 2) * (trace (B : Matrix n n ℂ)).re + +lemma pairedTracePotential_zero (σ δ : ℝ) (C : selfAdjoint (Matrix n n ℂ)) (s : ℝ) : + pairedTracePotential σ δ C 0 s = 0 := by + simp [pairedTracePotential, quadraticMatrix] + +lemma pairedTracePotential_hasFDerivAt {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (C B : selfAdjoint (Matrix n n ℂ)) {s : ℝ} (hs : s ≠ 0) : + HasFDerivAt (fun B ↦ pairedTracePotential σ δ C B s) + (traceGradientMap (pairedFieldIntegrand σ δ C B s)) B := by + have h1 := (trace_secondPrimitive_hasFDerivAt hσ hδ (quadraticSelfAdjoint C s B)).comp B + (quadraticSelfAdjoint_hasFDerivAt C B s) + have h2 := (trace_secondPrimitive_hasFDerivAt hσ hδ (quadraticSelfAdjoint C (-s) B)).comp B + (quadraticSelfAdjoint_hasFDerivAt C B (-s)) + have h3 := (traceGradientMap (1 : Matrix n n ℂ)).hasFDerivAt (x := B) + have hh := ((h1.sub h2).neg.const_mul (2 * s)⁻¹).sub (h3.const_mul + (2 * regularizedPrimitive σ δ (s ^ 2))) + convert! hh using 1 + · funext D + simp [pairedTracePotential, Function.comp_def, traceGradientMap_apply, div_eq_mul_inv, mul_comm] + · ext H + simp only [_root_.sub_apply, _root_.smul_apply, + ContinuousLinearMap.comp_apply, ContinuousLinearMap.id_apply, + _root_.neg_apply, traceGradientMap_apply, tracePairCLM_apply, + quadraticSelfAdjoint_coe] + change (trace (pairedFieldIntegrand σ δ C B s * (H : Matrix n n ℂ))).re = _ + simp only [pairedFieldIntegrand, sub_mul, add_mul, smul_mul_assoc, one_mul, + trace_sub, trace_add, trace_smul, Complex.sub_re, Complex.add_re, Complex.real_smul, + hermitianInclusion, ContinuousLinearMap.coe_mk', LinearMap.coe_mk, + AddHom.coe_mk, selfAdjoint.val_smul, mul_smul_comm, Complex.mul_re, Complex.ofReal_re, + Complex.ofReal_im] + simp only [smul_eq_mul] + field_simp [hs] + ring + +end SharpLiebThirring.MatrixProof + +namespace SharpLiebThirring.MatrixProof +open Matrix ScalarProof MeasureTheory Filter +open scoped Matrix.Norms.L2Operator Topology +variable {n : Type u33} [Fintype n] [DecidableEq n] + +-- Select the inherited subspace seminorm, avoiding the duplicate subgroup +-- class instance during elaboration of iterated continuous-linear maps. +local instance : SeminormedAddCommGroup (selfAdjoint (Matrix n n ℂ)) := + (inferInstance : NormedAddCommGroup (selfAdjoint (Matrix n n ℂ))).toSeminormedAddCommGroup +local instance : NormedSpace ℝ (selfAdjoint (Matrix n n ℂ)) := inferInstance + +lemma measurable_pairedTracePotential {δ : ℝ} (hδ : 0 < δ) (σ : ℝ) + (C B : selfAdjoint (Matrix n n ℂ)) : Measurable (pairedTracePotential σ δ C B) := by + have hc : Continuous (fun s : ℝ ↦ cfc (secondPrimitive σ δ) + (quadraticMatrix (C : Matrix n n ℂ) (B : Matrix n n ℂ) s)) := + Continuous.cfc_of_mem_nhdsSet (s := Set.univ) _ (Filter.univ_mem) + (by unfold quadraticMatrix; fun_prop) + (fun s ↦ quadraticMatrix_hermitian C.prop B.prop s) + (continuous_iff_continuousAt.mpr (fun y ↦ (secondPrimitive_hasDerivAt σ hδ y).continuousAt)).continuousOn + have ht : Continuous (fun s : ℝ ↦ (trace (cfc (secondPrimitive σ δ) + (quadraticMatrix (C : Matrix n n ℂ) (B : Matrix n n ℂ) s))).re) := by fun_prop + unfold pairedTracePotential + exact (((ht.measurable.sub (ht.comp continuous_neg).measurable).neg).div + (by fun_prop)).sub (((continuous_const.mul + ((primitive_differentiable σ hδ).continuous.comp (continuous_pow 2))).mul + continuous_const).measurable) + +def fieldGradientEnvelope (σ δ M : ℝ) (C : Matrix n n ℂ) (s : ℝ) : ℝ := + traceGradientNorm (n := n) * + (‖pairedFieldIntegrand σ δ (C : Matrix n n ℂ) 0 s‖ + fieldLipEnvelope σ δ M (C : Matrix n n ℂ) s * M) + +lemma integrable_fieldGradientEnvelope {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (M : ℝ) {C : Matrix n n ℂ} (hC : C.IsHermitian) : + Integrable (fieldGradientEnvelope σ δ M (C : Matrix n n ℂ)) := + ((integrable_pairedFieldIntegrand hσ hδ hC Matrix.isHermitian_zero).norm.add + ((integrable_fieldLipEnvelope hσ M C).mul_const M)).const_mul _ + +lemma fieldGradientEnvelope_bound {σ δ M : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (hM : 0 ≤ M) (C B : selfAdjoint (Matrix n n ℂ)) (hB : ‖B‖ ≤ M) (s : ℝ) : + ‖traceGradientMap (pairedFieldIntegrand σ δ (C : Matrix n n ℂ) (B : Matrix n n ℂ) s)‖ ≤ fieldGradientEnvelope σ δ M (C : Matrix n n ℂ) s := by + have hnorm := pairedFieldIntegrand_norm_on_ball hσ hδ hM C.prop B.prop hB s + have hscaled := mul_le_mul_of_nonneg_left hnorm (traceGradientNorm_nonneg (n := n)) + have hop := traceGradientMap_bound (n := n) + (pairedFieldIntegrand σ δ (C : Matrix n n ℂ) (B : Matrix n n ℂ) s) + have hr := le_trans hop hscaled + convert! hr using 1 + + +lemma pairedTracePotential_bound {σ δ M : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (hM : 0 ≤ M) (C B : selfAdjoint (Matrix n n ℂ)) (hB : ‖B‖ ≤ M) + {s : ℝ} (hs : s ≠ 0) : + ‖pairedTracePotential σ δ C B s‖ ≤ fieldGradientEnvelope σ δ M (C : Matrix n n ℂ) s * ‖B‖ := by + have hh := (convex_closedBall (0 : selfAdjoint (Matrix n n ℂ)) M).norm_image_sub_le_of_norm_hasFDerivWithin_le + (x := 0) (y := B) + (fun A _ ↦ (pairedTracePotential_hasFDerivAt hσ hδ C A hs).hasFDerivWithinAt) + (fun A hA ↦ fieldGradientEnvelope_bound hσ hδ hM C A (by simpa using hA) s) + (by simpa using hM) (by simpa using hB) + simpa only [pairedTracePotential_zero, sub_zero] using hh + +lemma integrable_pairedTracePotential {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (C B : selfAdjoint (Matrix n n ℂ)) : Integrable (pairedTracePotential σ δ C B) := by + apply ((integrable_fieldGradientEnvelope hσ hδ ‖B‖ C.prop).mul_const ‖B‖).mono' + (measurable_pairedTracePotential hδ σ C B).aestronglyMeasurable + filter_upwards [volume.ae_ne (0 : ℝ)] with s hs + exact pairedTracePotential_bound hσ hδ (norm_nonneg _) C B le_rfl hs + +def hermitianPotential (σ δ : ℝ) (C B : selfAdjoint (Matrix n n ℂ)) : ℝ := + (fieldNormalization σ / 2) * ∫ s : ℝ, pairedTracePotential σ δ C B s + +lemma hermitianPotential_hasFDerivAt {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (C B : selfAdjoint (Matrix n n ℂ)) : + HasFDerivAt (hermitianPotential σ δ C) + (traceGradientMap (hermitianField σ δ C B)) B := by + let M : ℝ := ‖B‖ + 1 + have hM : 0 ≤ M := by dsimp [M]; positivity + have hh := hasFDerivAt_integral_of_dominated_of_fderiv_le + (F := fun A s ↦ pairedTracePotential σ δ C A s) + (F' := fun (A : selfAdjoint (Matrix n n ℂ)) (s : ℝ) ↦ + traceGradientMap (pairedFieldIntegrand σ δ (C : Matrix n n ℂ) (A : Matrix n n ℂ) s)) + (bound := fieldGradientEnvelope σ δ M (C : Matrix n n ℂ)) + (Metric.ball_mem_nhds B (by norm_num : (0 : ℝ) < 1)) + (Eventually.of_forall (fun A ↦ (measurable_pairedTracePotential hδ σ C A).aestronglyMeasurable)) + (integrable_pairedTracePotential hσ hδ C B) + ((traceGradientMap.continuous.comp (continuous_pairedFieldIntegrand hδ σ C.prop B.prop)).aestronglyMeasurable) + (Eventually.of_forall (fun s A hA ↦ fieldGradientEnvelope_bound hσ hδ hM C A + (norm_le_norm_add_const_of_dist_le (Metric.mem_ball.mp hA).le) s)) + (integrable_fieldGradientEnvelope hσ hδ M C.prop) + (by filter_upwards [volume.ae_ne (0 : ℝ)] with s hs using fun A _ ↦ + pairedTracePotential_hasFDerivAt hσ hδ C A hs) + have hi := (traceGradientMap (n := n)).integral_comp_comm (𝕜 := ℝ) + (Fₗ := selfAdjoint (Matrix n n ℂ) →L[ℝ] ℝ) + (integrable_pairedFieldIntegrand hσ hδ C.prop B.prop) + have he : (∫ s : ℝ, traceGradientMap (pairedFieldIntegrand σ δ (C : Matrix n n ℂ) (B : Matrix n n ℂ) s)) = + traceGradientMap (∫ s : ℝ, pairedFieldIntegrand σ δ (C : Matrix n n ℂ) (B : Matrix n n ℂ) s) := by + convert! hi + rw [he] at hh + convert! hh.const_smul (fieldNormalization σ / 2) using 1 + simp [hermitianField] + +end SharpLiebThirring.MatrixProof + +namespace SharpLiebThirring.MatrixProof +open Matrix ScalarProof MeasureTheory Filter +open scoped Matrix.Norms.L2Operator Topology +variable {n : Type u34} [Fintype n] [DecidableEq n] + +local instance : SeminormedAddCommGroup (selfAdjoint (Matrix n n ℂ)) := + (inferInstance : NormedAddCommGroup (selfAdjoint (Matrix n n ℂ))).toSeminormedAddCommGroup +local instance : NormedSpace ℝ (selfAdjoint (Matrix n n ℂ)) := inferInstance + +@[simp] lemma hermitianPotential_zero (σ δ : ℝ) (C : selfAdjoint (Matrix n n ℂ)) : + hermitianPotential σ δ C 0 = 0 := by + simp [hermitianPotential, pairedTracePotential_zero] + +lemma hermitianPotential_radial_hasDerivAt {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (C B : selfAdjoint (Matrix n n ℂ)) (t : ℝ) : + HasDerivAt (fun t : ℝ ↦ hermitianPotential σ δ C (t • B)) + (traceGradientMap (hermitianField σ δ C (t • B)) B) t := by + convert! (hermitianPotential_hasFDerivAt hσ hδ C (t • B)).comp_hasDerivAt t + ((hasDerivAt_id t).smul_const B) using 1 + simp + +lemma hermitianPotential_radial {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (C B : selfAdjoint (Matrix n n ℂ)) : + hermitianPotential σ δ C B = + ∫ t in (0 : ℝ)..1, (trace ((B : Matrix n n ℂ) * hermitianField σ δ C (t • B))).re := by + have hc : Continuous (fun t : ℝ ↦ hermitianField σ δ (C : Matrix n n ℂ) (t • B)) := by + have hcf := (hermitianField_locallyLipschitz hσ hδ C.prop).continuous + have hsm : Continuous (fun t : ℝ ↦ t • B) := by fun_prop + have hh := hcf.comp hsm + convert! hh + have ht : Continuous (fun t : ℝ ↦ traceGradientMap (hermitianField σ δ C (t • B)) B) := by + simp only [traceGradientMap_apply] + fun_prop + have hi := intervalIntegral.integral_eq_sub_of_hasDerivAt + (fun t _ ↦ hermitianPotential_radial_hasDerivAt hσ hδ C B t) + (ht.intervalIntegrable 0 1) + simp only [one_smul, zero_smul, hermitianPotential_zero, sub_zero] at hi + rw [← hi] + apply intervalIntegral.integral_congr + intro t _ + change traceGradientMap (hermitianField σ δ C (t • B)) B = _ + rw [traceGradientMap_apply, trace_mul_comm] + +/-- The potential is a genuine trace primitive, not a radial definition +whose derivative has been assumed. -/ +lemma radial_trace_hasFDerivAt {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (C B : selfAdjoint (Matrix n n ℂ)) : + HasFDerivAt (fun B : selfAdjoint (Matrix n n ℂ) ↦ + -(∫ t in (0 : ℝ)..1, (trace ((B : Matrix n n ℂ) * hermitianField σ δ C (t • B))).re)) + (-traceGradientMap (hermitianField σ δ C B)) B := by + convert! (hermitianPotential_hasFDerivAt hσ hδ C B).neg using 1 + funext A + change -_ = -hermitianPotential σ δ C A + rw [hermitianPotential_radial hσ hδ] + +end SharpLiebThirring.MatrixProof + +namespace SharpLiebThirring.MatrixProof +open Matrix ScalarProof MeasureTheory Filter +open scoped Matrix.Norms.L2Operator Topology +variable {N : ℕ} + +def realHermitianComplexify (B : selfAdjoint (Matrix (Fin N) (Fin N) ℝ)) : + selfAdjoint (Matrix (Fin N) (Fin N) ℂ) := ⟨complexify B, complexify_hermitian B.prop⟩ + +@[simp] lemma realHermitianComplexify_coe (B : selfAdjoint (Matrix (Fin N) (Fin N) ℝ)) : + (realHermitianComplexify B : Matrix (Fin N) (Fin N) ℂ) = complexify B := rfl + +lemma realHermitianComplexify_continuous : Continuous (realHermitianComplexify (N := N)) := + (complexifyCLM.continuous.comp continuous_subtype_val).subtype_mk _ + +lemma matrixField_eq_realPart {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (k : Fin N → ℝ) {B : Matrix (Fin N) (Fin N) ℝ} (hB : B.IsHermitian) : + matrixField σ δ k B = realPartCLM (hermitianField σ δ + (complexify (diagonal (fun i ↦ k i ^ 2))) (complexify B)) := by + rw [← complexify_matrixField hσ hδ k hB, realPartCLM_complexify] + +lemma matrixField_continuous {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (k : Fin N → ℝ) : + Continuous (fun B : selfAdjoint (Matrix (Fin N) (Fin N) ℝ) ↦ matrixField σ δ k B) := by + have hc := (hermitianField_locallyLipschitz hσ hδ + (complexify_hermitian (isHermitian_diagonal (fun i ↦ k i ^ 2)))).continuous + have hh := realPartCLM.continuous.comp (hc.comp realHermitianComplexify_continuous) + convert! hh using 1 + funext B + exact matrixField_eq_realPart hσ hδ k B.prop + +end SharpLiebThirring.MatrixProof + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/FieldRegularity.lean b/lean/OAI/Analysis/LiebThirring/FieldRegularity.lean new file mode 100644 index 0000000000000000000000000000000000000000..81eb1a071c1cf953a2d06638fcdbc39ecbb69968 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/FieldRegularity.lean @@ -0,0 +1,571 @@ +import OAI.Analysis.LiebThirring.RankOne + +namespace OAI + +universe u25 u26 u27 u28 u29 u30 u31 + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +noncomputable section +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder CStarAlgebra +noncomputable section +open MeasureTheory Set Filter +open scoped Topology + +namespace SharpLiebThirring.MatrixProof +open Matrix +open scoped Matrix.Norms.L2Operator +variable {n : Type u25} [Fintype n] [DecidableEq n] + +omit [DecidableEq n] in +lemma hsSquared_nonneg (A : Matrix n n ℂ) : 0 ≤ hsSquared A := by + exact Finset.sum_nonneg fun i _ ↦ Finset.sum_nonneg fun j _ ↦ Complex.normSq_nonneg _ + +def flattenCLM : Matrix n n ℂ →L[ℝ] EuclideanSpace ℂ (n × n) := + LinearMap.toContinuousLinearMap + { toFun := fun A ↦ WithLp.toLp 2 (fun ij ↦ A ij.1 ij.2) + map_add' := by intros; rfl + map_smul' := by intros; rfl } + +def unflattenCLM : EuclideanSpace ℂ (n × n) →L[ℝ] Matrix n n ℂ := + LinearMap.toContinuousLinearMap + { toFun := fun v i j ↦ v (i, j) + map_add' := by intros; rfl + map_smul' := by intros; rfl } + +omit [DecidableEq n] in +@[simp] lemma unflatten_flatten (A : Matrix n n ℂ) : unflattenCLM (flattenCLM A) = A := rfl + +omit [DecidableEq n] in +lemma flatten_norm_sq (A : Matrix n n ℂ) : ‖flattenCLM A‖ ^ 2 = hsSquared A := by + rw [EuclideanSpace.norm_sq_eq, hsSquared, Fintype.sum_prod_type] + change (∑ i, ∑ j, ‖A i j‖ ^ 2) = _ + simp only [Complex.sq_norm] + + +lemma cfc_lipschitz_norm {A B : Matrix n n ℂ} (hA : A.IsHermitian) (hB : B.IsHermitian) + {f : ℝ → ℝ} {L : ℝ} (hL : 0 ≤ L) + (hf : ∀ x ∈ spectrum ℝ A, ∀ y ∈ spectrum ℝ B, |f x - f y| ≤ L * |x - y|) : + ‖cfc f A - cfc f B‖ ≤ + (‖(unflattenCLM : EuclideanSpace ℂ (n × n) →L[ℝ] Matrix n n ℂ)‖ * + ‖(flattenCLM : Matrix n n ℂ →L[ℝ] EuclideanSpace ℂ (n × n))‖) * L * ‖A - B‖ := by + have hs := hsSquared_cfc_sub hA hB f L hL + (fun i j ↦ hf _ (hA.eigenvalues_mem_spectrum_real i) _ (hB.eigenvalues_mem_spectrum_real j)) + rw [← hA.cfc_eq, ← hB.cfc_eq, ← flatten_norm_sq, ← flatten_norm_sq] at hs + have h1 : ‖flattenCLM (cfc f A - cfc f B)‖ ≤ L * ‖flattenCLM (A - B)‖ := by + apply (sq_le_sq₀ (norm_nonneg _) (mul_nonneg hL (norm_nonneg _))).1 + simpa only [mul_pow] using hs + calc + _ = ‖unflattenCLM (flattenCLM (cfc f A - cfc f B))‖ := rfl + _ ≤ ‖unflattenCLM (n := n)‖ * ‖flattenCLM (cfc f A - cfc f B)‖ := (unflattenCLM (n := n)).le_opNorm _ + _ ≤ ‖unflattenCLM (n := n)‖ * (L * (‖flattenCLM (n := n)‖ * ‖A - B‖)) := by + exact mul_le_mul_of_nonneg_left (h1.trans + (mul_le_mul_of_nonneg_left ((flattenCLM (n := n)).le_opNorm _) hL)) (norm_nonneg _) + _ = _ := by ring + +end SharpLiebThirring.MatrixProof +namespace SharpLiebThirring.MatrixProof +open Matrix +open scoped Matrix.Norms.L2Operator +variable {n : Type u26} [Fintype n] [DecidableEq n] + +lemma mixed_left_cfc_apply {A : Matrix n n ℂ} (hA : A.IsHermitian) + (V : unitary (Matrix n n ℂ)) (f : ℝ → ℝ) (i j : n) : + (star (hA.eigenvectorUnitary : Matrix n n ℂ) * cfc f A * (V : Matrix n n ℂ)) i j = + (f (hA.eigenvalues i) : ℂ) * + (star (hA.eigenvectorUnitary : Matrix n n ℂ) * (V : Matrix n n ℂ)) i j := by + rw [hA.cfc_eq] + change (star (hA.eigenvectorUnitary : Matrix n n ℂ) * + ((hA.eigenvectorUnitary : Matrix n n ℂ) * diagonal (fun i ↦ (f (hA.eigenvalues i) : ℂ)) * + star (hA.eigenvectorUnitary : Matrix n n ℂ)) * (V : Matrix n n ℂ)) i j = _ + simp only [← mul_assoc, Unitary.coe_star_mul_self, one_mul] + rw [mul_assoc, diagonal_mul] + +lemma mixed_right_cfc_apply {B : Matrix n n ℂ} (hB : B.IsHermitian) + (U : unitary (Matrix n n ℂ)) (g : ℝ → ℝ) (i j : n) : + (star (U : Matrix n n ℂ) * cfc g B * (hB.eigenvectorUnitary : Matrix n n ℂ)) i j = + (g (hB.eigenvalues j) : ℂ) * + (star (U : Matrix n n ℂ) * (hB.eigenvectorUnitary : Matrix n n ℂ)) i j := by + rw [hB.cfc_eq] + change (star (U : Matrix n n ℂ) * + ((hB.eigenvectorUnitary : Matrix n n ℂ) * diagonal (fun j ↦ (g (hB.eigenvalues j) : ℂ)) * + star (hB.eigenvectorUnitary : Matrix n n ℂ)) * (hB.eigenvectorUnitary : Matrix n n ℂ)) i j = _ + simp only [mul_assoc, Unitary.coe_star_mul_self, mul_one] + rw [← mul_assoc, mul_diagonal, mul_comm] + +lemma real_star_mul_real (x y : ℝ) (z : ℂ) : + (star ((x : ℂ) * z) * ((y : ℂ) * z)).re = x * y * Complex.normSq z := by + simp [Complex.mul_re, Complex.mul_im, Complex.normSq_apply] + ring + +lemma trace_cfc_product {A B : Matrix n n ℂ} (hA : A.IsHermitian) (hB : B.IsHermitian) + (f g : ℝ → ℝ) : + (trace (cfc f A * cfc g B)).re = + ∑ i, ∑ j, f (hA.eigenvalues i) * g (hB.eigenvalues j) * + Complex.normSq ((star (hA.eigenvectorUnitary : Matrix n n ℂ) * + (hB.eigenvectorUnitary : Matrix n n ℂ)) i j) := by + have hF : (cfc f A).IsHermitian := (cfc_predicate f A).isHermitian + rw [← hF.star_eq, ← trace_star_mul_change hA.eigenvectorUnitary hB.eigenvectorUnitary, + trace_star_mul_sum] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + rw [mixed_left_cfc_apply, mixed_right_cfc_apply, real_star_mul_real] + +lemma trace_taylor_identity {A B : Matrix n n ℂ} (hA : A.IsHermitian) (hB : B.IsHermitian) + (F f : ℝ → ℝ) : + (trace (cfc F B)).re - (trace (cfc F A)).re - (trace (cfc f A * (B - A))).re = + ∑ i, ∑ j, (F (hB.eigenvalues j) - F (hA.eigenvalues i) - + f (hA.eigenvalues i) * (hB.eigenvalues j - hA.eigenvalues i)) * + Complex.normSq ((star (hA.eigenvectorUnitary : Matrix n n ℂ) * + (hB.eigenvectorUnitary : Matrix n n ℂ)) i j) := by + have h₁ := trace_cfc_product hA hB (fun _ ↦ 1) F + have h₂ := trace_cfc_product hA hB F (fun _ ↦ 1) + have h₃ := trace_cfc_product hA hB f id + have h₄ := trace_cfc_product hA hB (fun x ↦ f x * x) (fun _ ↦ 1) + have hcA : cfc (fun _ : ℝ ↦ 1) A = 1 := by + erw [cfc_const (1 : ℝ) A hA]; simp + have hcB : cfc (fun _ : ℝ ↦ 1) B = 1 := by + erw [cfc_const (1 : ℝ) B hB]; simp + rw [hcA, one_mul] at h₁ + rw [hcB, mul_one] at h₂ h₄ + erw [cfc_id ℝ B hB] at h₃ + have hm : cfc (fun x ↦ f x * x) A = cfc f A * A := by + erw [cfc_mul f id A (A.finite_real_spectrum.continuousOn f) + (by fun_prop), cfc_id ℝ A hA] + rw [hm] at h₄ + rw [mul_sub, trace_sub, Complex.sub_re, h₁, h₂, h₃, h₄] + simp only [id_eq, ← Finset.sum_sub_distrib] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + ring + +lemma trace_taylor_bound {A B : Matrix n n ℂ} (hA : A.IsHermitian) (hB : B.IsHermitian) + {F f : ℝ → ℝ} {L : ℝ} + (hF : ∀ x ∈ spectrum ℝ A, ∀ y ∈ spectrum ℝ B, + |F y - F x - f x * (y - x)| ≤ L * (y - x) ^ 2) : + |(trace (cfc F B)).re - (trace (cfc F A)).re - (trace (cfc f A * (B - A))).re| ≤ + L * hsSquared (B - A) := by + let U := hA.eigenvectorUnitary + let V := hB.eigenvectorUnitary + have hm (i j : n) : + (star (U : Matrix n n ℂ) * (B - A) * (V : Matrix n n ℂ)) i j = + ((hB.eigenvalues j - hA.eigenvalues i : ℝ) : ℂ) * + (star (U : Matrix n n ℂ) * (V : Matrix n n ℂ)) i j := by + have ha : A = conjStarAlgAut ℂ (Matrix n n ℂ) U + (diagonal (fun i ↦ (hA.eigenvalues i : ℂ))) := hA.spectral_theorem + have hb : B = conjStarAlgAut ℂ (Matrix n n ℂ) V + (diagonal (fun i ↦ (hB.eigenvalues i : ℂ))) := hB.spectral_theorem + have hh := mixed_diagonal_sub_apply U V hA.eigenvalues hB.eigenvalues i j + rw [← ha, ← hb] at hh + rw [← neg_sub A B, Matrix.mul_neg, Matrix.neg_mul, Matrix.neg_apply, hh] + simp only [Complex.ofReal_sub] + ring + rw [trace_taylor_identity hA hB, ← hsSquared_change U V (B - A)] + refine (Finset.abs_sum_le_sum_abs _ _).trans ?_ + simp only [hsSquared, Finset.mul_sum] + apply Finset.sum_le_sum + intro i _ + refine (Finset.abs_sum_le_sum_abs _ _).trans ?_ + apply Finset.sum_le_sum + intro j _ + rw [hm, Complex.normSq_mul, Complex.normSq_ofReal, abs_mul, + abs_of_nonneg (Complex.normSq_nonneg _)] + have hh := hF _ (hA.eigenvalues_mem_spectrum_real i) _ (hB.eigenvalues_mem_spectrum_real j) + have hp := mul_le_mul_of_nonneg_right hh + (Complex.normSq_nonneg ((star (U : Matrix n n ℂ) * (V : Matrix n n ℂ)) i j)) + nlinarith [hp] + +end SharpLiebThirring.MatrixProof + +open scoped NNReal +namespace SharpLiebThirring.ScalarProof +open Set +lemma primitive_lipschitz {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) : + LipschitzWith ⟨δ ^ (σ - 3 / 2), Real.rpow_nonneg hδ.le _⟩ + (regularizedPrimitive σ δ) := by + apply lipschitzWith_of_nnnorm_deriv_le (fun x ↦ (primitive_hasDerivAt σ hδ x).differentiableAt) + intro x + rw [(primitive_hasDerivAt σ hδ x).deriv] + change ‖(max x 0 + δ) ^ (σ - 3 / 2)‖ ≤ δ ^ (σ - 3 / 2) + rw [Real.norm_eq_abs, abs_of_nonneg (Real.rpow_nonneg (by positivity) _)] + exact Real.rpow_le_rpow_of_nonpos hδ (by have := le_max_right x 0; linarith) (by linarith) + +lemma scalar_trace_taylor {F f : ℝ → ℝ} {C : ℝ≥0} + (hF : ∀ x, HasDerivAt F (f x) x) (hf : LipschitzWith C f) (x y : ℝ) : + |F y - F x - f x * (y - x)| ≤ (C : ℝ) * (y - x) ^ 2 := by + have hd (t : ℝ) (_ : t ∈ uIcc x y) : + HasDerivWithinAt (fun t ↦ F t - F x - f x * (t - x)) + (f t - f x) (uIcc x y) t := by + convert! ((hF t).sub_const (F x) |>.sub + (((hasDerivAt_id t).sub_const x).const_mul (f x))).hasDerivWithinAt using 1 + simp + have hb (t : ℝ) (ht : t ∈ uIcc x y) : ‖f t - f x‖ ≤ (C : ℝ) * ‖y - x‖ := by + exact (hf.norm_sub_le t x).trans (mul_le_mul_of_nonneg_left + (abs_sub_left_of_mem_uIcc ht) C.coe_nonneg) + have hh := (convex_uIcc x y).norm_image_sub_le_of_norm_hasDerivWithin_le + hd hb (left_mem_uIcc) (right_mem_uIcc) + simpa only [sub_self, mul_zero, sub_zero, Real.norm_eq_abs, mul_assoc, ← sq, sq_abs] using hh + +/-- The second scalar primitive used for the matrix trace potential. -/ +def secondPrimitive (σ δ y : ℝ) : ℝ := ∫ t in 0..y, regularizedPrimitive σ δ t + +lemma secondPrimitive_hasDerivAt (σ : ℝ) {δ : ℝ} (hδ : 0 < δ) (y : ℝ) : + HasDerivAt (secondPrimitive σ δ) (regularizedPrimitive σ δ y) y := by + exact intervalIntegral.integral_hasDerivAt_right + ((primitive_differentiable σ hδ).continuous.intervalIntegrable 0 y) + (primitive_differentiable σ hδ).continuous.stronglyMeasurable.stronglyMeasurableAtFilter + (primitive_differentiable σ hδ).continuous.continuousAt + +end SharpLiebThirring.ScalarProof + +namespace SharpLiebThirring.MatrixProof +open Matrix ScalarProof Asymptotics Filter +open scoped Matrix.Norms.L2Operator Topology +variable {n : Type u27} [Fintype n] [DecidableEq n] + +def hermitianInclusion : selfAdjoint (Matrix n n ℂ) →L[ℝ] Matrix n n ℂ := + { toFun := Subtype.val + map_add' := fun _ _ ↦ rfl + map_smul' := fun _ _ ↦ rfl + cont := continuous_subtype_val } + +lemma trace_primitive_hasFDerivAt {F f : ℝ → ℝ} {C : ℝ≥0} + (hF : ∀ x, HasDerivAt F (f x) x) (hf : LipschitzWith C f) + (A : selfAdjoint (Matrix n n ℂ)) : + HasFDerivAt (fun B : selfAdjoint (Matrix n n ℂ) ↦ (trace (cfc F (B : Matrix n n ℂ))).re) + ((tracePairCLM (cfc f (A : Matrix n n ℂ))).comp hermitianInclusion) A := by + rw [hasFDerivAt_iff_isLittleO] + apply IsBigO.trans_isLittleO (g := fun B : selfAdjoint (Matrix n n ℂ) ↦ ‖B - A‖ ^ 2) + ?_ (isLittleO_pow_sub_sub A (by norm_num : 1 < (2 : ℕ))) + apply IsBigO.of_bound ((C : ℝ) * ‖flattenCLM (n := n)‖ ^ 2) + filter_upwards [] with B + have hh := trace_taylor_bound A.property.isHermitian B.property.isHermitian + (F := F) (f := f) (L := (C : ℝ)) + (fun x _ y _ ↦ scalar_trace_taylor hF hf x y) + change |(trace (cfc F (B : Matrix n n ℂ))).re - (trace (cfc F (A : Matrix n n ℂ))).re - + (trace (cfc f (A : Matrix n n ℂ) * ((B : Matrix n n ℂ) - (A : Matrix n n ℂ)))).re| ≤ _ + have hb := (flattenCLM (n := n)).le_opNorm ((B : Matrix n n ℂ) - (A : Matrix n n ℂ)) + have hb2 := sq_le_sq₀ (norm_nonneg _) (mul_nonneg (norm_nonneg _) (norm_nonneg _)) |>.2 hb + rw [flatten_norm_sq, mul_pow] at hb2 + refine hh.trans ((mul_le_mul_of_nonneg_left hb2 C.coe_nonneg).trans_eq ?_) + change (C : ℝ) * (‖flattenCLM (n := n)‖ ^ 2 * ‖B - A‖ ^ 2) = _ + rw [Real.norm_eq_abs, abs_of_nonneg (sq_nonneg _)] + ring + +lemma trace_secondPrimitive_hasFDerivAt {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (A : selfAdjoint (Matrix n n ℂ)) : + HasFDerivAt (fun B : selfAdjoint (Matrix n n ℂ) ↦ + (trace (cfc (secondPrimitive σ δ) (B : Matrix n n ℂ))).re) + ((tracePairCLM (cfc (regularizedPrimitive σ δ) (A : Matrix n n ℂ))).comp hermitianInclusion) A := + trace_primitive_hasFDerivAt (secondPrimitive_hasDerivAt σ hδ) (primitive_lipschitz hσ hδ) A + +end SharpLiebThirring.MatrixProof + +namespace SharpLiebThirring.ScalarProof +open Set +lemma primitive_remainder_lipschitz {σ δ a x r y z : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (ha : 0 < a) (hr : 0 ≤ r) (hxr : a ≤ x - r) (hy : |y| ≤ r) (hz : |z| ≤ r) : + ‖(regularizedPrimitive σ δ (x + y) - regularizedPrimitive σ δ x - + (x + δ) ^ (σ - 3 / 2) * y) - + (regularizedPrimitive σ δ (x + z) - regularizedPrimitive σ δ x - + (x + δ) ^ (σ - 3 / 2) * z)‖ ≤ + ((3 / 2 - σ) * (a + δ) ^ (σ - 5 / 2) * r) * ‖y - z‖ := by + have hd (t : ℝ) (ht : t ∈ Icc (-r) r) : + HasDerivWithinAt (fun t : ℝ ↦ regularizedPrimitive σ δ (x + t) - + regularizedPrimitive σ δ x - (x + δ) ^ (σ - 3 / 2) * t) + ((x + t + δ) ^ (σ - 3 / 2) - (x + δ) ^ (σ - 3 / 2)) (Icc (-r) r) t := by + have hxt : 0 ≤ x + t := by have := ht.1; linarith + convert! (((primitive_hasDerivAt σ hδ (x + t)).comp t ((hasDerivAt_id t).const_add x)).sub_const + (regularizedPrimitive σ δ x) |>.sub + ((hasDerivAt_id t).const_mul ((x + δ) ^ (σ - 3 / 2)))).hasDerivWithinAt using 1 + simp [max_eq_left hxt] + have hb (t : ℝ) (ht : t ∈ Icc (-r) r) : + ‖(x + t + δ) ^ (σ - 3 / 2) - (x + δ) ^ (σ - 3 / 2)‖ ≤ + (3 / 2 - σ) * (a + δ) ^ (σ - 5 / 2) * r := by + have hh := derivative_lipschitz_on_positive hσ hδ ha + (show a ≤ x + t by have := ht.1; linarith) (show a ≤ x by linarith) + simp only [add_sub_cancel_left] at hh + refine hh.trans (mul_le_mul_of_nonneg_left ?_ (mul_nonneg (by linarith) + (Real.rpow_nonneg (by linarith) _))) + exact abs_le.2 ht + exact (convex_Icc (-r) r).norm_image_sub_le_of_norm_hasDerivWithin_le hd hb + (abs_le.1 hz) (abs_le.1 hy) +end SharpLiebThirring.ScalarProof + +namespace SharpLiebThirring.MatrixProof +open Matrix ScalarProof +open scoped Matrix.Norms.L2Operator +variable {n : Type u28} [Fintype n] [DecidableEq n] + +def matrixNormBridge (n : Type u29) [Fintype n] [DecidableEq n] : ℝ := + ‖(unflattenCLM : EuclideanSpace ℂ (n × n) →L[ℝ] Matrix n n ℂ)‖ * + ‖(flattenCLM : Matrix n n ℂ →L[ℝ] EuclideanSpace ℂ (n × n))‖ + +lemma matrixNormBridge_nonneg : 0 ≤ matrixNormBridge n := mul_nonneg (norm_nonneg _) (norm_nonneg _) + +lemma cfc_remainder_eq (σ : ℝ) {δ : ℝ} (hδ : 0 < δ) (x : ℝ) + {A : Matrix n n ℂ} (hA : A.IsHermitian) : + cfc (fun y : ℝ ↦ regularizedPrimitive σ δ (x + y) - + regularizedPrimitive σ δ x - (x + δ) ^ (σ - 3 / 2) * y) A = + cfc (regularizedPrimitive σ δ) (x • 1 + A) - + regularizedPrimitive σ δ x • 1 - (x + δ) ^ (σ - 3 / 2) • A := by + have hc := (primitive_differentiable σ hδ).continuous + erw [cfc_sub (fun y : ℝ ↦ regularizedPrimitive σ δ (x + y) - + regularizedPrimitive σ δ x) (fun y : ℝ ↦ (x + δ) ^ (σ - 3 / 2) * y) A + (by fun_prop) (by fun_prop), + cfc_sub (fun y : ℝ ↦ regularizedPrimitive σ δ (x + y)) + (fun _ : ℝ ↦ regularizedPrimitive σ δ x) A (by fun_prop) (by fun_prop), + cfc_const (regularizedPrimitive σ δ x) A hA, + cfc_const_mul_id ((x + δ) ^ (σ - 3 / 2)) A hA, + Algebra.algebraMap_eq_smul_one, ← cfc_scalar_add _ hc x hA] + +lemma cfc_remainder_lipschitz {σ δ a x r : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (ha : 0 < a) (hr : 0 ≤ r) (hxr : a ≤ x - r) + {A B : Matrix n n ℂ} (hA : A.IsHermitian) (hB : B.IsHermitian) + (hnA : ‖A‖ ≤ r) (hnB : ‖B‖ ≤ r) : + ‖(cfc (regularizedPrimitive σ δ) (x • 1 + A) - + regularizedPrimitive σ δ x • 1 - (x + δ) ^ (σ - 3 / 2) • A) - + (cfc (regularizedPrimitive σ δ) (x • 1 + B) - + regularizedPrimitive σ δ x • 1 - (x + δ) ^ (σ - 3 / 2) • B)‖ ≤ + matrixNormBridge n * ((3 / 2 - σ) * (a + δ) ^ (σ - 5 / 2) * r) * ‖A - B‖ := by + rw [← cfc_remainder_eq σ hδ x hA, ← cfc_remainder_eq σ hδ x hB] + apply cfc_lipschitz_norm hA hB (mul_nonneg (mul_nonneg (by linarith) + (Real.rpow_nonneg (by linarith) _)) hr) + intro y hy z hz + exact primitive_remainder_lipschitz hσ hδ ha hr hxr + ((spectrum_abs_le_matrix_norm hy).trans hnA) ((spectrum_abs_le_matrix_norm hz).trans hnB) + +omit [Fintype n] in +lemma quadraticMatrix_sub (C B D : Matrix n n ℂ) (s : ℝ) : + quadraticMatrix C B s - quadraticMatrix C D s = (-2 * s) • (B - D) := by + unfold quadraticMatrix + module + +lemma cfc_quadratic_lipschitz {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + {C B D : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) + (hD : D.IsHermitian) (s : ℝ) : + ‖cfc (regularizedPrimitive σ δ) (quadraticMatrix C B s) - + cfc (regularizedPrimitive σ δ) (quadraticMatrix C D s)‖ ≤ + matrixNormBridge n * δ ^ (σ - 3 / 2) * (2 * |s|) * ‖B - D‖ := by + have hh := cfc_lipschitz_norm (quadraticMatrix_hermitian hC hB s) + (quadraticMatrix_hermitian hC hD s) (Real.rpow_nonneg hδ.le (σ - 3 / 2)) + (fun x _ y _ ↦ (primitive_lipschitz hσ hδ).norm_sub_le x y) + rw [quadraticMatrix_sub, norm_smul] at hh + simpa [Real.norm_eq_abs, abs_mul, mul_assoc, matrixNormBridge] using hh + +lemma pairedFieldIntegrand_lipschitz_global {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + {C B D : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) + (hD : D.IsHermitian) (s : ℝ) : + ‖pairedFieldIntegrand σ δ C B s - pairedFieldIntegrand σ δ C D s‖ ≤ + (4 * matrixNormBridge n * δ ^ (σ - 3 / 2) * |s|) * ‖B - D‖ := by + have he : pairedFieldIntegrand σ δ C B s - pairedFieldIntegrand σ δ C D s = + (cfc (regularizedPrimitive σ δ) (quadraticMatrix C B s) - + cfc (regularizedPrimitive σ δ) (quadraticMatrix C D s)) + + (cfc (regularizedPrimitive σ δ) (quadraticMatrix C B (-s)) - + cfc (regularizedPrimitive σ δ) (quadraticMatrix C D (-s))) := by + unfold pairedFieldIntegrand + abel + rw [he] + have h1 := cfc_quadratic_lipschitz hσ hδ hC hB hD s + have h2 := cfc_quadratic_lipschitz hσ hδ hC hB hD (-s) + rw [abs_neg] at h2 + linarith [norm_add_le + (cfc (regularizedPrimitive σ δ) (quadraticMatrix C B s) - + cfc (regularizedPrimitive σ δ) (quadraticMatrix C D s)) + (cfc (regularizedPrimitive σ δ) (quadraticMatrix C B (-s)) - + cfc (regularizedPrimitive σ δ) (quadraticMatrix C D (-s)))] + +end SharpLiebThirring.MatrixProof + +namespace SharpLiebThirring.MatrixProof +open Matrix ScalarProof +open scoped Matrix.Norms.L2Operator +variable {n : Type u30} [Fintype n] [DecidableEq n] + +def quadraticRemainder (σ δ : ℝ) (C B : Matrix n n ℂ) (s : ℝ) : Matrix n n ℂ := + cfc (regularizedPrimitive σ δ) (quadraticMatrix C B s) - + regularizedPrimitive σ δ (s ^ 2) • 1 - + (s ^ 2 + δ) ^ (σ - 3 / 2) • (C - (2 * s) • B) + +lemma quadraticRemainder_lipschitz_tail {σ δ M : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + {C B D : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) (hD : D.IsHermitian) + (hBM : ‖B‖ ≤ M) (hDM : ‖D‖ ≤ M) {s : ℝ} + (hs : max 1 (2 * (‖C‖ + 2 * M)) ≤ |s|) : + ‖quadraticRemainder σ δ C B s - quadraticRemainder σ δ C D s‖ ≤ + (2 * matrixNormBridge n * (3 / 2 - σ) * (‖C‖ + 2 * M) * + (1 / 4 : ℝ) ^ (σ - 5 / 2) * (1 + s ^ 2) ^ (σ - 3 / 2)) * ‖B - D‖ := by + have hs1 : 1 ≤ |s| := (le_max_left _ _).trans hs + have hsA : 2 * (‖C‖ + 2 * M) ≤ |s| := (le_max_right _ _).trans hs + have hM : 0 ≤ M := (norm_nonneg _).trans hBM + let A := ‖C‖ + 2 * M + have hA : 0 ≤ A := by dsimp [A]; positivity + have hs2 : 0 < s ^ 2 := by nlinarith [sq_abs s] + have hxr : s ^ 2 / 2 ≤ s ^ 2 - A * |s| := by + dsimp [A]; nlinarith [sq_abs s] + have hnB : ‖C - (2 * s) • B‖ ≤ A * |s| := + (perturbed_norm_le hs1).trans (mul_le_mul_of_nonneg_right (by dsimp [A]; linarith) (abs_nonneg _)) + have hnD : ‖C - (2 * s) • D‖ ≤ A * |s| := + (perturbed_norm_le hs1).trans (mul_le_mul_of_nonneg_right (by dsimp [A]; linarith) (abs_nonneg _)) + have hh := cfc_remainder_lipschitz hσ hδ (by linarith : 0 < s ^ 2 / 2) + (mul_nonneg hA (abs_nonneg s)) hxr + (hC.sub (hB.smul (isSelfAdjoint_iff.2 rfl : IsSelfAdjoint (2 * s)))) + (hC.sub (hD.smul (isSelfAdjoint_iff.2 rfl : IsSelfAdjoint (2 * s)))) hnB hnD + have he : (C - (2 * s) • B) - (C - (2 * s) • D) = (-2 * s) • (B - D) := by module + rw [he, norm_smul] at hh + simp only [Real.norm_eq_abs, abs_mul, abs_neg, abs_of_pos (by norm_num : (0 : ℝ) < 2)] at hh + have hw := quadratic_taylor_weight (A := 1) hσ hδ hs1 + simp only [one_mul, one_pow, mul_one, sq_abs] at hw + have hp : 0 ≤ 2 * matrixNormBridge n * (3 / 2 - σ) * A * ‖B - D‖ := by + have := matrixNormBridge_nonneg (n := n) + have : 0 ≤ 3 / 2 - σ := by linarith + positivity + calc + _ ≤ matrixNormBridge n * ((3 / 2 - σ) * (s ^ 2 / 2 + δ) ^ (σ - 5 / 2) * (A * |s|)) * + (2 * |s| * ‖B - D‖) := hh + _ = (2 * matrixNormBridge n * (3 / 2 - σ) * A * ‖B - D‖) * + ((s ^ 2 / 2 + δ) ^ (σ - 5 / 2) * s ^ 2) := by rw [← sq_abs s]; ring + _ ≤ (2 * matrixNormBridge n * (3 / 2 - σ) * A * ‖B - D‖) * + ((1 / 4 : ℝ) ^ (σ - 5 / 2) * (1 + s ^ 2) ^ (σ - 3 / 2)) := + mul_le_mul_of_nonneg_left hw hp + _ = _ := by dsimp [A]; ring + +lemma pairedFieldIntegrand_remainder_difference (σ δ : ℝ) (C B D : Matrix n n ℂ) (s : ℝ) : + pairedFieldIntegrand σ δ C B s - pairedFieldIntegrand σ δ C D s = + (quadraticRemainder σ δ C B s - quadraticRemainder σ δ C D s) + + (quadraticRemainder σ δ C B (-s) - quadraticRemainder σ δ C D (-s)) := by + unfold pairedFieldIntegrand quadraticRemainder + simp only [neg_sq] + module + +lemma pairedFieldIntegrand_lipschitz_tail {σ δ M : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + {C B D : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) (hD : D.IsHermitian) + (hBM : ‖B‖ ≤ M) (hDM : ‖D‖ ≤ M) {s : ℝ} + (hs : max 1 (2 * (‖C‖ + 2 * M)) ≤ |s|) : + ‖pairedFieldIntegrand σ δ C B s - pairedFieldIntegrand σ δ C D s‖ ≤ + (4 * matrixNormBridge n * (3 / 2 - σ) * (‖C‖ + 2 * M) * + (1 / 4 : ℝ) ^ (σ - 5 / 2) * (1 + s ^ 2) ^ (σ - 3 / 2)) * ‖B - D‖ := by + have h1 := quadraticRemainder_lipschitz_tail hσ hδ hC hB hD hBM hDM hs + have h2 := quadraticRemainder_lipschitz_tail hσ hδ hC hB hD hBM hDM + (s := -s) (by rwa [abs_neg]) + rw [neg_sq] at h2 + rw [pairedFieldIntegrand_remainder_difference] + linarith [norm_add_le (quadraticRemainder σ δ C B s - quadraticRemainder σ δ C D s) + (quadraticRemainder σ δ C B (-s) - quadraticRemainder σ δ C D (-s))] + +end SharpLiebThirring.MatrixProof + +namespace SharpLiebThirring.MatrixProof +open Matrix ScalarProof MeasureTheory +open scoped Matrix.Norms.L2Operator NNReal +variable {n : Type u31} [Fintype n] [DecidableEq n] + +def fieldLipEnvelope (σ δ M : ℝ) (C : Matrix n n ℂ) (s : ℝ) : ℝ := + (Set.Icc (-max 1 (2 * (‖C‖ + 2 * M))) (max 1 (2 * (‖C‖ + 2 * M)))).indicator + (fun s : ℝ ↦ 4 * matrixNormBridge n * δ ^ (σ - 3 / 2) * |s|) s + + 4 * matrixNormBridge n * (3 / 2 - σ) * (‖C‖ + 2 * M) * + (1 / 4 : ℝ) ^ (σ - 5 / 2) * (1 + s ^ 2) ^ (σ - 3 / 2) + +lemma fieldLipEnvelope_nonneg {σ δ M : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (hM : 0 ≤ M) (C : Matrix n n ℂ) (s : ℝ) : 0 ≤ fieldLipEnvelope σ δ M C s := by + have h1 : 0 ≤ matrixNormBridge n := matrixNormBridge_nonneg + have h2 : 0 ≤ 3 / 2 - σ := by linarith + unfold fieldLipEnvelope + apply add_nonneg + · exact Set.indicator_nonneg (fun _ _ ↦ by positivity) _ + · positivity + +lemma integrable_fieldLipEnvelope {σ δ : ℝ} (hσ : σ < 1) (M : ℝ) + (C : Matrix n n ℂ) : Integrable (fieldLipEnvelope σ δ M C) := by + apply Integrable.add + · apply IntegrableOn.integrable_indicator _ measurableSet_Icc + exact (by fun_prop : Continuous (fun s : ℝ ↦ + 4 * matrixNormBridge n * δ ^ (σ - 3 / 2) * |s|)).integrableOn_Icc + · exact (normalization_integrable hσ).const_mul _ + +lemma pairedFieldIntegrand_lipschitz_envelope {σ δ M : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + {C B D : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) (hD : D.IsHermitian) + (hBM : ‖B‖ ≤ M) (hDM : ‖D‖ ≤ M) (s : ℝ) : + ‖pairedFieldIntegrand σ δ C B s - pairedFieldIntegrand σ δ C D s‖ ≤ + fieldLipEnvelope σ δ M C s * ‖B - D‖ := by + have hM : 0 ≤ M := (norm_nonneg _).trans hBM + have h1 : 0 ≤ matrixNormBridge n := matrixNormBridge_nonneg + have h2 : 0 ≤ 3 / 2 - σ := by linarith + let R := max 1 (2 * (‖C‖ + 2 * M)) + by_cases hs : |s| ≤ R + · have hs' : s ∈ Set.Icc (-R) R := abs_le.mp hs + have hh := pairedFieldIntegrand_lipschitz_global hσ hδ hC hB hD s + apply hh.trans + apply mul_le_mul_of_nonneg_right _ (norm_nonneg _) + unfold fieldLipEnvelope + rw [Set.indicator_of_mem hs'] + exact le_add_of_nonneg_right (by positivity) + · have hh := pairedFieldIntegrand_lipschitz_tail hσ hδ hC hB hD hBM hDM + (le_of_not_ge hs) + apply hh.trans + apply mul_le_mul_of_nonneg_right _ (norm_nonneg _) + exact le_add_of_nonneg_left (Set.indicator_nonneg (fun _ _ ↦ by positivity) _) + +lemma pairedFieldIntegrand_norm_on_ball {σ δ M : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (hM : 0 ≤ M) {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) + (hBM : ‖B‖ ≤ M) (s : ℝ) : + ‖pairedFieldIntegrand σ δ C B s‖ ≤ + ‖pairedFieldIntegrand σ δ C 0 s‖ + fieldLipEnvelope σ δ M C s * M := by + have hh := pairedFieldIntegrand_lipschitz_envelope hσ hδ hC hB Matrix.isHermitian_zero + hBM (by simpa using hM) s + simp only [sub_zero] at hh + have hs := hh.trans (mul_le_mul_of_nonneg_left hBM (fieldLipEnvelope_nonneg hσ hδ hM C s)) + have ht := norm_le_norm_add_norm_sub' (pairedFieldIntegrand σ δ C B s) + (pairedFieldIntegrand σ δ C 0 s) + linarith + +lemma hermitianField_lipschitz_bound {σ δ M : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + {C B D : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) (hD : D.IsHermitian) + (hBM : ‖B‖ ≤ M) (hDM : ‖D‖ ≤ M) : + ‖hermitianField σ δ C B - hermitianField σ δ C D‖ ≤ + (|fieldNormalization σ / 2| * ∫ s : ℝ, fieldLipEnvelope σ δ M C s) * ‖B - D‖ := by + have hiB := integrable_pairedFieldIntegrand hσ hδ hC hB + have hiD := integrable_pairedFieldIntegrand hσ hδ hC hD + unfold hermitianField + rw [← smul_sub, ← integral_sub hiB hiD, norm_smul, Real.norm_eq_abs] + have hh := norm_integral_le_of_norm_le (integrable_fieldLipEnvelope hσ M C |>.mul_const ‖B - D‖) + (Filter.Eventually.of_forall (pairedFieldIntegrand_lipschitz_envelope hσ hδ hC hB hD hBM hDM)) + rw [integral_mul_const] at hh + exact (mul_le_mul_of_nonneg_left hh (abs_nonneg _)).trans_eq (mul_assoc _ _ _).symm + +lemma hermitianField_locallyLipschitz {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + {C : Matrix n n ℂ} (hC : C.IsHermitian) : + LocallyLipschitz (fun B : selfAdjoint (Matrix n n ℂ) ↦ hermitianField σ δ C B) := by + intro B + let M : ℝ := ‖B‖ + 1 + let L : ℝ := |fieldNormalization σ / 2| * ∫ s : ℝ, fieldLipEnvelope σ δ M C s + have hL : 0 ≤ L := mul_nonneg (abs_nonneg _) (integral_nonneg (fun s ↦ + fieldLipEnvelope_nonneg hσ hδ (by dsimp [M]; positivity) C s)) + refine ⟨⟨L, hL⟩, Metric.ball B 1, Metric.ball_mem_nhds B (by norm_num), ?_⟩ + change @LipschitzOnWith _ _ (PseudoMetricSpace.toPseudoEMetricSpace) + (PseudoMetricSpace.toPseudoEMetricSpace) _ _ _ + apply lipschitzOnWith_iff_norm_sub_le.mpr + intro A hA D hD + have hAM : ‖(A : Matrix n n ℂ)‖ ≤ M := by + change ‖A‖ ≤ ‖B‖ + 1 + exact norm_le_norm_add_const_of_dist_le (Metric.mem_ball.mp hA).le + have hDM : ‖(D : Matrix n n ℂ)‖ ≤ M := by + change ‖D‖ ≤ ‖B‖ + 1 + exact norm_le_norm_add_const_of_dist_le (Metric.mem_ball.mp hD).le + exact hermitianField_lipschitz_bound hσ hδ hC A.prop D.prop hAM hDM + +end SharpLiebThirring.MatrixProof + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/FiniteParity.lean b/lean/OAI/Analysis/LiebThirring/FiniteParity.lean new file mode 100644 index 0000000000000000000000000000000000000000..b50f20e9b5bcb0f102781c53dd3ba0929589f122 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/FiniteParity.lean @@ -0,0 +1,761 @@ +import OAI.Analysis.LiebThirring.FlagGeometry + +namespace OAI + +universe u40 u41 u42 u43 u44 u45 u46 u47 u48 u49 u50 u51 u52 u53 u54 u55 u56 u57 u58 u59 u60 u61 u62 u63 u64 u65 u66 u67 + +noncomputable section +open Finset + + +/-! Finite parity for the PL continuation argument. +The argument constructs continuation without assuming a topological degree theorem. -/ +noncomputable section +open Finset +namespace SharpLiebThirring.PLParity + +/-- Endpoints of a line meeting a simplex: in general position either no facet, +or exactly two facets, are met. The roots `r` are the facet crossing parameters. -/ +lemma affine_constraints_endpoints {ι : Type u40} [Fintype ι] [DecidableEq ι] + (b r : ι → ℝ) (hb : ∀ i, b i ≠ 0) (hr : Function.Injective r) + (hpos : ∃ i, 0 < b i) (hneg : ∃ i, b i < 0) : + ∃ i j : ι, i ≠ j ∧ + ({k | ∀ l, 0 ≤ b l * (r k - r l)} : Finset ι) = + if r i < r j then {i, j} else ∅ := by + classical + have hp : (univ.filter (fun i ↦ 0 < b i)).Nonempty := by + obtain ⟨i, hi⟩ := hpos + exact ⟨i, by simp [hi]⟩ + have hn : (univ.filter (fun i ↦ b i < 0)).Nonempty := by + obtain ⟨i, hi⟩ := hneg + exact ⟨i, by simp [hi]⟩ + obtain ⟨i, hi, hmax⟩ := exists_max_image (univ.filter (fun i ↦ 0 < b i)) r hp + obtain ⟨j, hj, hmin⟩ := exists_min_image (univ.filter (fun i ↦ b i < 0)) r hn + simp only [mem_filter, mem_univ, true_and] at hi hj hmax hmin + have hij : i ≠ j := by rintro rfl; linarith + have hrij : r i ≠ r j := fun h ↦ hij (hr h) + refine ⟨i, j, hij, ?_⟩ + ext k + simp only [mem_filter, mem_univ, true_and] + by_cases hlt : r i < r j + · rw [ite_eq_left hlt] + simp only [mem_insert, mem_singleton] + constructor + · intro hk + have hleft : r i ≤ r k := by + have hh := (mul_nonneg_iff_of_pos_left hi).mp (hk i) + linarith + have hright : r k ≤ r j := by + have hh := nonpos_of_mul_nonneg_right (hk j) hj + linarith + rcases lt_or_gt_of_ne (hb k) with hkn | hkp + · right + have hh := hmin k hkn + exact hr (le_antisymm hright hh) + · left + have hh := hmax k hkp + exact hr (le_antisymm hh hleft) + · rintro (rfl | rfl) l + · rcases lt_or_gt_of_ne (hb l) with hln | hlp + · apply mul_nonneg_of_nonpos_of_nonpos hln.le + have hh := hmin l hln + linarith + · exact mul_nonneg hlp.le (sub_nonneg.mpr (hmax l hlp)) + · rcases lt_or_gt_of_ne (hb l) with hln | hlp + · exact mul_nonneg_of_nonpos_of_nonpos hln.le (sub_nonpos.mpr (hmin l hln)) + · apply mul_nonneg hlp.le + have hh := hmax l hlp + linarith + · rw [ite_eq_right hlt] + simp only [Finset.notMem_empty, iff_false] + intro hk + have hleft : r i ≤ r k := by + have hh := (mul_nonneg_iff_of_pos_left hi).mp (hk i) + linarith + have hright : r k ≤ r j := by + have hh := nonpos_of_mul_nonneg_right (hk j) hj + linarith + exact hrij (le_antisymm (hleft.trans hright) (le_of_not_gt hlt)) + +lemma even_affine_constraints_endpoints {ι : Type u41} [Fintype ι] [DecidableEq ι] + (b r : ι → ℝ) (hb : ∀ i, b i ≠ 0) (hr : Function.Injective r) + (hpos : ∃ i, 0 < b i) (hneg : ∃ i, b i < 0) : + Even ({k | ∀ l, 0 ≤ b l * (r k - r l)} : Finset ι).card := by + obtain ⟨i, j, hij, he⟩ := affine_constraints_endpoints b r hb hr hpos hneg + rw [he] + split_ifs <;> simp [hij] + + +section AffineFiber +attribute [local instance] Classical.propDecidable +variable {ι : Type u42} {V : Type u43} [Fintype ι] + [AddCommGroup V] [Module ℝ V] + +/-- Total affine weights and their vector sum. -/ +def augmentedMap (v : ι → V) : (ι → ℝ) →ₗ[ℝ] ℝ × V where + toFun w := (∑ i, w i, ∑ i, w i • v i) + map_add' a b := by simp [add_smul, Finset.sum_add_distrib] + map_smul' c a := by simp [Finset.mul_sum, Finset.smul_sum, smul_smul] + +@[simp] lemma augmentedMap_apply (v : ι → V) (w : ι → ℝ) : + augmentedMap v w = (∑ i, w i, ∑ i, w i • v i) := rfl + +/-- A facet is selected when its affine image contains zero. -/ +def facetHit (v : ι → V) (i : ι) : Prop := + ∃ w : ι → ℝ, augmentedMap v w = (1, 0) ∧ w i = 0 ∧ ∀ j, 0 ≤ w j + +lemma facetHit_congr (v u : ι → V) (i : ι) (he : ∀ j, j ≠ i → v j = u j) : + facetHit v i ↔ facetHit u i := by + have hs (w : ι → ℝ) (hw : w i = 0) : ∑ j, w j • v j = ∑ j, w j • u j := by + apply Finset.sum_congr rfl + intro j _ + by_cases hji : j = i + · simp only [hji, hw, zero_smul] + · rw [he j hji] + constructor <;> rintro ⟨w, hw, hi, hn⟩ <;> refine ⟨w, ?_, hi, hn⟩ + · apply Prod.ext + · simpa only [augmentedMap_apply] using congrArg Prod.fst hw + · change ∑ j, w j • u j = 0 + rw [← hs w hi] + exact congrArg Prod.snd hw + · apply Prod.ext + · simpa only [augmentedMap_apply] using congrArg Prod.fst hw + · change ∑ j, w j • v j = 0 + rw [hs w hi] + exact congrArg Prod.snd hw + +lemma facetHit_linearEquiv (v : ι → V) (A : V ≃ₗ[ℝ] V) (i : ι) : + facetHit (fun j ↦ A (v j)) i ↔ facetHit v i := by + constructor <;> rintro ⟨w, hw, hi, hn⟩ <;> refine ⟨w, ?_, hi, hn⟩ + · apply Prod.ext + · simpa only [augmentedMap_apply] using congrArg Prod.fst hw + · change ∑ j, w j • v j = 0 + apply A.injective + simpa only [augmentedMap_apply, map_sum, map_smul, map_zero] using congrArg Prod.snd hw + · apply Prod.ext + · simpa only [augmentedMap_apply] using congrArg Prod.fst hw + · change ∑ j, w j • A (v j) = 0 + have hh := congrArg A (congrArg Prod.snd hw) + simpa only [augmentedMap_apply, map_sum, map_smul, map_zero] using hh + +lemma kernel_line_parameterization (v : ι → V) + (hdim : Module.finrank ℝ (LinearMap.ker (augmentedMap v)) = 1) + {b : ι → ℝ} (hb : b ∈ LinearMap.ker (augmentedMap v)) (hb0 : b ≠ 0) + {a w : ι → ℝ} (ha : augmentedMap v a = (1, 0)) + (hw : augmentedMap v w = (1, 0)) : + ∃ t : ℝ, w = a + t • b := by + have hwb : w - a ∈ LinearMap.ker (augmentedMap v) := by + rw [LinearMap.mem_ker, map_sub, hw, ha, sub_self] + obtain ⟨t, ht⟩ := exists_smul_eq_of_finrank_eq_one hdim + (x := (⟨b, hb⟩ : LinearMap.ker (augmentedMap v))) + (by simpa using hb0) (⟨w - a, hwb⟩ : LinearMap.ker (augmentedMap v)) + refine ⟨t, ?_⟩ + have h := congrArg Subtype.val ht + change t • b = w - a at h + rw [h, add_sub_cancel] + +/-- Parity of facet hits for a generic affine map from a (d+1)-simplex to +R^d. The algebraic general-position conditions are separated from the +finite counting argument so they can be supplied by generic vertex choices. -/ +lemma even_facetHit_of_kernel_line (v : ι → V) + (hsur : Function.Surjective (augmentedMap v)) + (hdim : Module.finrank ℝ (LinearMap.ker (augmentedMap v)) = 1) + (hcoord : ∀ b : ι → ℝ, augmentedMap v b = 0 → b ≠ 0 → ∀ i, b i ≠ 0) + (hpair : ∀ w : ι → ℝ, augmentedMap v w = (1, 0) → + ∀ i j, w i = 0 → w j = 0 → i = j) : + Even ({i | facetHit v i} : Finset ι).card := by + classical + obtain ⟨a, ha⟩ := hsur (1, 0) + have hkne : LinearMap.ker (augmentedMap v) ≠ ⊥ := by + intro h + rw [h] at hdim + simp at hdim + obtain ⟨b, hb, hb0⟩ := (LinearMap.ker (augmentedMap v)).ne_bot_iff.mp hkne + have hbA : augmentedMap v b = 0 := hb + have hbi := hcoord b hbA hb0 + have hbSum : ∑ i, b i = 0 := congrArg Prod.fst hbA + have hpos : ∃ i, 0 < b i := by + by_contra! h + have hh := (Finset.sum_eq_zero_iff_of_nonpos (by simpa using h)).mp hbSum + apply hb0 + ext i + exact hh i (mem_univ i) + have hneg : ∃ i, b i < 0 := by + by_contra! h + have hh := (Finset.sum_eq_zero_iff_of_nonneg (by simpa using h)).mp hbSum + apply hb0 + ext i + exact hh i (mem_univ i) + let r : ι → ℝ := fun i ↦ -a i / b i + have hroot (i : ι) : a i + r i * b i = 0 := by + dsimp [r] + rw [div_mul_cancel₀ _ (hbi i)] + ring + have hr : Function.Injective r := by + intro i j hij + apply hpair (a + r i • b) + · rw [map_add, map_smul, hbA, smul_zero, add_zero, ha] + · exact hroot i + · change a j + r i * b j = 0 + rw [hij] + exact hroot j + have heq : ({i | facetHit v i} : Finset ι) = + ({i | ∀ j, 0 ≤ b j * (r i - r j)} : Finset ι) := by + ext i + simp only [mem_filter, mem_univ, true_and] + constructor + · rintro ⟨w, hw, hwi, hwj⟩ + obtain ⟨t, rfl⟩ := kernel_line_parameterization v hdim hb hb0 ha hw + have ht : t = r i := by + change a i + t * b i = 0 at hwi + apply (mul_right_cancel₀ (hbi i)) + linarith [hroot i] + subst t + intro j + have hj := hwj j + change 0 ≤ a j + r i * b j at hj + nlinarith [hroot j] + · intro hi + refine ⟨a + r i • b, ?_, hroot i, ?_⟩ + · rw [map_add, map_smul, hbA, smul_zero, add_zero, ha] + · intro j + change 0 ≤ a j + r i * b j + nlinarith [hi j, hroot j] + rw [heq] + exact even_affine_constraints_endpoints b r hbi hr hpos hneg + + +lemma sum_subtype_eq_of_zero {M : Type u44} [AddCommMonoid M] + (P : ι → Prop) [DecidablePred P] (f : ι → M) (h : ∀ i, ¬ P i → f i = 0) : + (∑ i : {i // P i}, f i) = ∑ i, f i := by + have h0 : (∑ i : {i // ¬ P i}, f i) = 0 := + Finset.sum_eq_zero (fun i _ ↦ h i i.prop) + simpa only [h0, add_zero] using Fintype.sum_subtype_add_sum_subtype P f + +lemma augmentedMap_single (v : ι → V) (i : ι) : + augmentedMap v (Pi.single i 1) = (1, v i) := by + classical + simp [augmentedMap, Pi.single_apply, ite_smul] + +lemma augmented_kernel_nonzero_coordinates (v : ι → V) + (hgen : ∀ i : ι, LinearIndependent ℝ (fun j : {j // j ≠ i} ↦ ((1 : ℝ), v j))) + (b : ι → ℝ) (hb : augmentedMap v b = 0) (hb0 : b ≠ 0) : + ∀ i, b i ≠ 0 := by + intro i hi + have hs : (∑ j : {j // j ≠ i}, b j • ((1 : ℝ), v j)) = 0 := by + calc + _ = ∑ j, b j • ((1 : ℝ), v j) := sum_subtype_eq_of_zero (fun j ↦ j ≠ i) (fun j ↦ b j • ((1 : ℝ), v j)) (by + intro j hj + have : j = i := by simpa using hj + simp [this, hi]) + _ = 0 := by + simpa only [augmentedMap_apply, Prod.smul_mk, smul_eq_mul, mul_one, ← prod_mk_sum] using hb + have hz := Fintype.linearIndependent_iff.mp (hgen i) (fun j ↦ b j) hs + apply hb0 + ext j + by_cases hj : j = i + · simpa [hj] using hi + · exact hz ⟨j, hj⟩ + +lemma augmented_nonzero_two_coordinates (v : ι → V) + (hgen : ∀ i j : ι, i ≠ j → + LinearIndependent ℝ (fun k : {k // k ≠ i ∧ k ≠ j} ↦ v k)) + (w : ι → ℝ) (hw : augmentedMap v w = (1, 0)) + (i j : ι) (hi : w i = 0) (hj : w j = 0) : i = j := by + by_contra hij + have hs : (∑ k : {k // k ≠ i ∧ k ≠ j}, w k • v k) = 0 := by + calc + _ = ∑ k, w k • v k := sum_subtype_eq_of_zero (fun k ↦ k ≠ i ∧ k ≠ j) (fun k ↦ w k • v k) (by + intro k hk + by_cases hki : k = i + · simp [hki, hi] + · have hkj : k = j := by aesop + simp [hkj, hj]) + _ = 0 := congrArg Prod.snd hw + have hz := Fintype.linearIndependent_iff.mp (hgen i j hij) (fun k ↦ w k) hs + have hw0 : w = 0 := by + ext k + by_cases hki : k = i + · simpa [hki] using hi + by_cases hkj : k = j + · simpa [hkj] using hj + exact hz ⟨k, hki, hkj⟩ + simpa [hw0] using congrArg Prod.fst hw + +lemma facetHit_positive (v : ι → V) + (hgen : ∀ i j : ι, i ≠ j → + LinearIndependent ℝ (fun k : {k // k ≠ i ∧ k ≠ j} ↦ v k)) + (i : ι) (hi : facetHit v i) : + ∃ w : ι → ℝ, augmentedMap v w = (1, 0) ∧ w i = 0 ∧ + (∀ j, 0 ≤ w j) ∧ ∀ j, j ≠ i → 0 < w j := by + obtain ⟨w, hw, hwi, hn⟩ := hi + refine ⟨w, hw, hwi, hn, ?_⟩ + intro j hji + refine lt_of_le_of_ne (hn j) ?_ + intro h + exact hji ((augmented_nonzero_two_coordinates v hgen w hw i j hwi h.symm).symm) + +lemma augmentedMap_surjective [FiniteDimensional ℝ V] (v : ι → V) + (hcard : Fintype.card ι = Module.finrank ℝ V + 2) + (hgen : ∀ i : ι, LinearIndependent ℝ (fun j : {j // j ≠ i} ↦ ((1 : ℝ), v j))) : + Function.Surjective (augmentedMap v) := by + classical + have hcpos : 0 < Fintype.card ι := by omega + let : Nonempty ι := Fintype.card_pos_iff.mp hcpos + let i : ι := Classical.arbitrary ι + have hc : Fintype.card {j : ι // j ≠ i} = Module.finrank ℝ (ℝ × V) := by + rw [Fintype.card_subtype_compl (fun j ↦ j = i)] + simp [hcard, Module.finrank_prod, Nat.add_comm] + have hspan : Submodule.span ℝ (Set.range (fun j : {j // j ≠ i} ↦ ((1 : ℝ), v j))) + ≤ LinearMap.range (augmentedMap v) := by + apply Submodule.span_le.mpr + rintro _ ⟨j, rfl⟩ + exact ⟨Pi.single j.val 1, augmentedMap_single v j.val⟩ + apply LinearMap.range_eq_top.mp + apply top_unique + have hs := (hgen i).span_eq_top_of_card_eq_finrank' hc + rwa [hs] at hspan + +lemma even_facetHit [FiniteDimensional ℝ V] (v : ι → V) + (hcard : Fintype.card ι = Module.finrank ℝ V + 2) + (haug : ∀ i : ι, LinearIndependent ℝ (fun j : {j // j ≠ i} ↦ ((1 : ℝ), v j))) + (hvec : ∀ i j : ι, i ≠ j → + LinearIndependent ℝ (fun k : {k // k ≠ i ∧ k ≠ j} ↦ v k)) : + Even ({i | facetHit v i} : Finset ι).card := by + have hsur := augmentedMap_surjective v hcard haug + apply even_facetHit_of_kernel_line v hsur + · have hd := LinearMap.finrank_range_add_finrank_ker (augmentedMap v) + rw [LinearMap.range_eq_top.mpr hsur] at hd + simp only [finrank_top, Module.finrank_prod, Module.finrank_self, Module.finrank_pi] at hd + omega + · exact augmented_kernel_nonzero_coordinates v haug + · exact augmented_nonzero_two_coordinates v hvec + +end AffineFiber +end SharpLiebThirring.PLParity + + +/-! Free-action double counting for continuation modulo two. -/ +noncomputable section +open Finset +namespace SharpLiebThirring.PLParity +attribute [local instance] Classical.propDecidable + +section OrbitSum +variable {G : Type u45} {X : Type u46} [Group G] [MulAction G X] [IsCancelSMul G X] + +omit [IsCancelSMul G X] in +lemma orbit_mk_smul (g : G) (x : X) : + (Quotient.mk'' (g • x) : Quotient (MulAction.orbitRel G X)) = Quotient.mk'' x := + Quotient.sound' (MulAction.orbitRel_apply.mpr (MulAction.mem_orbit_iff.mpr ⟨g, rfl⟩)) + +/-- Reconstruct a point in a free orbit from its representative and a group element. -/ +def orbitProductEquiv : (Quotient (MulAction.orbitRel G X) × G) ≃ X := + Equiv.ofBijective (fun z ↦ z.2 • z.1.out) (by + constructor + · rintro ⟨q, g⟩ ⟨r, h⟩ he + have hq : q = r := by + have hh := congrArg (fun x : X ↦ (Quotient.mk'' x : Quotient (MulAction.orbitRel G X))) he + simpa only [orbit_mk_smul, Quotient.out_eq'] using hh + subst r + have hg : g = h := IsCancelSMul.right_cancel g h q.out he + subst h + rfl + · intro x + let q : Quotient (MulAction.orbitRel G X) := Quotient.mk'' x + have hr : (MulAction.orbitRel G X) x q.out := + Quotient.exact' (by rw [Quotient.out_eq']) + obtain ⟨g, hg⟩ := MulAction.mem_orbit_iff.mp (MulAction.orbitRel_apply.mp hr) + exact ⟨(q, g), hg⟩) + +lemma sum_eq_card_mul_orbit_sum [Fintype G] [Fintype X] + (f : X → ℕ) (hf : ∀ g : G, ∀ x, f (g • x) = f x) : + ∑ x, f x = Fintype.card G * ∑ q : Quotient (MulAction.orbitRel G X), f q.out := by + classical + have h := Fintype.sum_equiv (orbitProductEquiv (G := G) (X := X)) + (fun z ↦ f (z.2 • z.1.out)) f (fun _ ↦ rfl) + rw [← h, Fintype.sum_prod_type] + simp only [hf, sum_const, card_univ, smul_eq_mul] + exact (Finset.mul_sum _ _ _).symm +end OrbitSum + +section Incidence +variable {G : Type u47} {T : Type u48} {F : Type u49} [Group G] [Fintype G] [Fintype T] [Fintype F] + [MulAction G T] [MulAction G F] [IsCancelSMul G T] [IsCancelSMul G F] + +def rowDegree (R : T → F → Prop) (t : T) : ℕ := Fintype.card {f // R t f} +def colDegree (R : T → F → Prop) (f : F) : ℕ := Fintype.card {t // R t f} + +omit [Fintype G] [Fintype T] [IsCancelSMul G T] [IsCancelSMul G F] in +lemma rowDegree_invariant {R : T → F → Prop} + (hR : ∀ g : G, ∀ t f, R (g • t) (g • f) ↔ R t f) (g : G) (t : T) : + rowDegree R (g • t) = rowDegree R t := by + symm + exact Fintype.card_congr ((MulAction.toPerm g).subtypeEquiv (fun f ↦ (hR g t f).symm)) + +omit [Fintype G] [Fintype F] [IsCancelSMul G T] [IsCancelSMul G F] in +lemma colDegree_invariant {R : T → F → Prop} + (hR : ∀ g : G, ∀ t f, R (g • t) (g • f) ↔ R t f) (g : G) (f : F) : + colDegree R (g • f) = colDegree R f := by + symm + exact Fintype.card_congr ((MulAction.toPerm g).subtypeEquiv (fun t ↦ (hR g t f).symm)) + +lemma sum_rowDegree_eq_sum_colDegree (R : T → F → Prop) : + ∑ t, rowDegree R t = ∑ f, colDegree R f := by + classical + simp only [rowDegree, colDegree, Fintype.card_subtype, Finset.card_eq_sum_ones, + Finset.sum_filter] + exact Finset.sum_comm + +/-- The number of odd-degree facet orbits is even whenever every top-cell +has even degree. This is the equivariant handshaking lemma: the action must +be free, but neither the base nor the target needs an orientation. -/ +lemma even_odd_degree_orbits (R : T → F → Prop) + (hR : ∀ g : G, ∀ t f, R (g • t) (g • f) ↔ R t f) + (hEven : ∀ t, Even (rowDegree R t)) : + Even ({q : Quotient (MulAction.orbitRel G F) | Odd (colDegree R q.out)} : + Finset (Quotient (MulAction.orbitRel G F))).card := by + classical + have hsum := sum_rowDegree_eq_sum_colDegree R + rw [sum_eq_card_mul_orbit_sum (rowDegree R) (rowDegree_invariant hR), + sum_eq_card_mul_orbit_sum (colDegree R) (colDegree_invariant hR)] at hsum + have heq := Nat.mul_left_cancel (Fintype.card_pos (α := G)) hsum + have heven : Even (∑ q : Quotient (MulAction.orbitRel G F), colDegree R q.out) := by + rw [← heq] + exact Finset.even_sum _ (fun q _ ↦ hEven q.out) + exact (Finset.even_sum_iff_even_card_odd _).mp heven + +end Incidence +section HalfEdges +variable {G : Type u50} {T : Type u51} {H : Type u52} [Group G] [Fintype G] [Fintype T] [Fintype H] + [MulAction G T] [MulAction G H] [IsCancelSMul G T] [IsCancelSMul G H] + +lemma even_orbit_card_of_even_fibers (p : H → T) + (hp : ∀ g : G, ∀ h, p (g • h) = g • p h) + (hEven : ∀ t, Even (Nat.card {h // p h = t})) : + Even (Fintype.card (Quotient (MulAction.orbitRel G H))) := by + classical + have hc (h : H) : colDegree (fun t h ↦ p h = t) h = 1 := by + simp [colDegree, eq_comm] + have he := even_odd_degree_orbits (fun t h ↦ p h = t) + (by intro g t h; rw [hp]; exact smul_left_cancel_iff g) + (fun t ↦ by simpa only [Nat.card_eq_fintype_card, rowDegree] using hEven t) + simpa [hc] using he + +omit [Fintype G] [Fintype T] [Fintype H] [MulAction G T] + [IsCancelSMul G T] [IsCancelSMul G H] in +lemma orbit_map_respects (f : H → H) (hf : ∀ g : G, ∀ h, f (g • h) = g • f h) + {a b : H} (hab : (MulAction.orbitRel G H) a b) : + (MulAction.orbitRel G H) (f a) (f b) := by + obtain ⟨g, hg⟩ := MulAction.mem_orbit_iff.mp (MulAction.orbitRel_apply.mp hab) + apply MulAction.orbitRel_apply.mpr + apply MulAction.mem_orbit_iff.mpr + refine ⟨g, ?_⟩ + rw [← hf, hg] + +/-- An equivariant involution descends to orbit classes. -/ +def orbitMap (f : H → H) (hf : ∀ g : G, ∀ h, f (g • h) = g • f h) : + Quotient (MulAction.orbitRel G H) → Quotient (MulAction.orbitRel G H) := + Quotient.map f (by intro a b hab; exact orbit_map_respects f hf hab) + +omit [Fintype G] [Fintype T] [Fintype H] [MulAction G T] + [IsCancelSMul G T] [IsCancelSMul G H] in +lemma orbitMap_involutive (f : H → H) (hf : ∀ g : G, ∀ h, f (g • h) = g • f h) + (hi : Function.Involutive f) : Function.Involutive (orbitMap f hf) := by + intro q + induction q using Quotient.inductionOn with + | h x => + change Quotient.mk'' (f (f x)) = Quotient.mk'' x + rw [hi] + +lemma even_fixedPoints_of_even_card {X : Type u53} [Fintype X] + (f : X → X) (hi : Function.Involutive f) (he : Even (Fintype.card X)) : + Even (Nat.card (Function.fixedPoints f)) := by + classical + rw [Nat.card_eq_fintype_card] + let F : Function.End X := f + have hf : F ^ (2 : ℕ) ^ (1 : ℕ) = 1 := by + funext x + exact hi x + have hm := Equiv.Perm.card_fixedPoints_modEq hf + rw [Nat.ModEq] at hm + exact Nat.even_iff.mpr (hm.symm.trans (Nat.even_iff.mp he)) + +/-- One initial crossing orbit cannot be the only fixed orbit of an equivariant +half-edge pairing; a second boundary crossing orbit must exist. -/ +lemma exists_other_fixed_orbit (p : H → T) + (hp : ∀ g : G, ∀ h, p (g • h) = g • p h) + (hEven : ∀ t, Even (Nat.card {h // p h = t})) + (f : H → H) (hf : ∀ g : G, ∀ h, f (g • h) = g • f h) + (hi : Function.Involutive f) + (q₀ : Quotient (MulAction.orbitRel G H)) (hq₀ : orbitMap f hf q₀ = q₀) : + ∃ q : Quotient (MulAction.orbitRel G H), orbitMap f hf q = q ∧ q ≠ q₀ := by + classical + have he := even_fixedPoints_of_even_card (orbitMap f hf) (orbitMap_involutive f hf hi) + (even_orbit_card_of_even_fibers p hp hEven) + by_contra! h + have hsingle : Function.fixedPoints (orbitMap f hf) = {q₀} := by + ext q + constructor + · exact fun hq ↦ h q hq + · intro hq + change orbitMap f hf q = q + simpa [Set.mem_singleton_iff.mp hq] using hq₀ + have hcard : Nat.card (Function.fixedPoints (orbitMap f hf)) = 1 := + (Nat.card_congr (Set.equivOfEq hsingle)).trans Nat.card_unique + rw [hcard] at he + norm_num at he + + +end HalfEdges +end SharpLiebThirring.PLParity + +namespace SharpLiebThirring.PLParity +namespace FinitePairing +attribute [local instance] Classical.propDecidable + +@[ext] structure CellFacet (X : Type u54) (J : Type u55) where + cell : X + facet : J + +instance {X : Type u56} {J : Type u57} [Fintype X] [Fintype J] : Fintype (CellFacet X J) := + Fintype.ofEquiv (X × J) ⟨fun p ↦ ⟨p.1, p.2⟩, fun p ↦ (p.cell, p.facet), + fun _ ↦ rfl, fun _ ↦ rfl⟩ + +instance {G : Type u58} {X : Type u59} {J : Type u60} [Group G] [MulAction G X] : MulAction G (CellFacet X J) where + smul g p := ⟨g • p.cell, p.facet⟩ + one_smul p := by + apply CellFacet.ext + · exact one_smul _ _ + · rfl + mul_smul g h p := by + apply CellFacet.ext + · exact mul_smul g h p.cell + · rfl + +instance {G : Type u61} {X : Type u62} {J : Type u63} [Group G] [MulAction G X] [IsCancelSMul G X] : + IsCancelSMul G (CellFacet X J) where + right_cancel' g h p he := IsCancelSMul.right_cancel g h p.cell + (congrArg CellFacet.cell he) + +variable {G : Type u64} {X : Type u65} {J : Type u66} [Group G] [MulAction G X] +variable (D : SubMulAction G X) +variable (hit : X → J → Prop) (hHit : ∀ g : G, ∀ x j, hit (g • x) j ↔ hit x j) +variable (nbr : X → J → X) +variable (hInv : ∀ x j, nbr (nbr x j) j = x) +variable (hNbr : ∀ g : G, ∀ x j, nbr (g • x) j = g • nbr x j) +variable (hAdj : ∀ x j, hit x j → hit (nbr x j) j) + +/-- Selected simplex-facet incidences in a finite invariant domain. -/ +def selected : SubMulAction G (CellFacet D J) where + carrier := {p | hit p.cell.val p.facet} + smul_mem' g p hp := (hHit g p.cell.val p.facet).mpr hp + +instance selectedFintype [Fintype D] [Fintype J] : Fintype (selected D hit hHit) := + Fintype.ofFinite _ + +/-- Pair an interior selected facet with its neighbor, and keep boundary facets fixed. -/ +def pairing (p : selected D hit hHit) : selected D hit hHit := + if hn : nbr p.val.cell.val p.val.facet ∈ D then + ⟨⟨⟨nbr p.val.cell.val p.val.facet, hn⟩, p.val.facet⟩, + hAdj p.val.cell.val p.val.facet p.property⟩ + else p + +lemma pairing_boundary (p : selected D hit hHit) + (hn : nbr p.val.cell.val p.val.facet ∉ D) : + pairing D hit hHit nbr hAdj p = p := by + simp only [pairing, dite_eq_right hn] + +include hInv in +lemma pairing_involutive : Function.Involutive (pairing D hit hHit nbr hAdj) := by + intro p + by_cases hn : nbr p.val.cell.val p.val.facet ∈ D + · have hnn : nbr (nbr p.val.cell.val p.val.facet) p.val.facet ∈ D := by + rw [hInv]; exact p.val.cell.property + simp only [pairing, dite_eq_left hn, hnn, ↓reduceDIte] + apply Subtype.ext + apply CellFacet.ext + · exact Subtype.ext (hInv _ _) + · rfl + · simp only [pairing, dite_eq_right hn] + +include hNbr in +lemma pairing_equivariant (g : G) (p : selected D hit hHit) : + pairing D hit hHit nbr hAdj (g • p) = g • pairing D hit hHit nbr hAdj p := by + have hg : nbr (g • p.val.cell.val) p.val.facet ∈ D ↔ + nbr p.val.cell.val p.val.facet ∈ D := by + rw [hNbr] + exact D.smul_mem_iff' g + by_cases hn : nbr p.val.cell.val p.val.facet ∈ D + · have hn' : nbr (g • p).val.cell.val (g • p).val.facet ∈ D := hg.mpr hn + simp only [pairing, dite_eq_left hn, dite_eq_left hn'] + apply Subtype.ext + apply CellFacet.ext + · exact Subtype.ext (hNbr _ _ _) + · rfl + · have hn' : nbr (g • p).val.cell.val (g • p).val.facet ∉ D := fun h ↦ hn (hg.mp h) + simp only [pairing, dite_eq_right hn, dite_eq_right hn'] + +lemma selected_projection_equivariant (g : G) (p : selected D hit hHit) : + (g • p).val.cell = g • p.val.cell := rfl + +lemma even_projection_fiber [Fintype D] [Fintype J] + (hEven : ∀ x : D, Even (Nat.card {j // hit x.val j})) (x : D) : + Even (Nat.card {p : selected D hit hHit // p.val.cell = x}) := by + let e : {p : selected D hit hHit // p.val.cell = x} ≃ {j // hit x.val j} := + { toFun := fun p ↦ ⟨p.val.val.facet, by + exact (congrArg (fun y : D ↦ hit y.val p.val.val.facet) p.property).mp p.val.property⟩ + invFun := fun j ↦ ⟨⟨⟨x, j.val⟩, j.property⟩, rfl⟩ + left_inv := by + intro p + apply Subtype.ext + apply Subtype.ext + apply CellFacet.ext + · exact p.property.symm + · rfl + right_inv := fun _ ↦ rfl } + simpa only [Nat.card_congr e] using hEven x + +include hInv hNbr hAdj in +/-- In a free finite equivariant complex with even selected facet counts, a +boundary crossing orbit forces another boundary crossing orbit. -/ +lemma exists_other_boundary [Fintype D] [Fintype J] [Fintype G] [IsCancelSMul G X] + (hEven : ∀ x : D, Even (Nat.card {j // hit x.val j})) + (hNoOrbit : ∀ x : D, ∀ j, nbr x.val j ∈ D → ∀ g : G, nbr x.val j ≠ g • x.val) + (p₀ : selected D hit hHit) (hp₀ : nbr p₀.val.cell.val p₀.val.facet ∉ D) : + ∃ p : selected D hit hHit, nbr p.val.cell.val p.val.facet ∉ D ∧ + ¬ (MulAction.orbitRel G (selected D hit hHit)) p p₀ := by + let f := pairing D hit hHit nbr hAdj + have hf := pairing_equivariant D hit hHit nbr hNbr hAdj + have hi := pairing_involutive D hit hHit nbr hInv hAdj + let q₀ : Quotient (MulAction.orbitRel G (selected D hit hHit)) := Quotient.mk'' p₀ + have hq₀ : orbitMap f hf q₀ = q₀ := by + change Quotient.mk'' (f p₀) = Quotient.mk'' p₀ + exact congrArg Quotient.mk'' (pairing_boundary D hit hHit nbr hAdj p₀ hp₀) + obtain ⟨q, hq, hne⟩ := exists_other_fixed_orbit (fun p : selected D hit hHit ↦ p.val.cell) + (selected_projection_equivariant D hit hHit) + (even_projection_fiber D hit hHit hEven) f hf hi q₀ hq₀ + refine ⟨q.out, ?_, ?_⟩ + · intro hin + have hre : (MulAction.orbitRel G (selected D hit hHit)) (f q.out) q.out := by + apply Quotient.exact' + change orbitMap f hf (Quotient.mk'' q.out) = Quotient.mk'' q.out + simpa only [Quotient.out_eq'] using hq + obtain ⟨g, hg⟩ := MulAction.mem_orbit_iff.mp (MulAction.orbitRel_apply.mp hre) + have he := congrArg (fun p : selected D hit hHit ↦ p.val.cell.val) hg + have hp : (f q.out).val.cell.val = nbr q.out.val.cell.val q.out.val.facet := by + simp only [f, pairing, dite_eq_left hin] + rw [hp] at he + exact hNoOrbit q.out.val.cell q.out.val.facet hin g he.symm + · intro hr + apply hne + exact (Quotient.out_eq' q).symm.trans (Quotient.sound' hr) + +end FinitePairing +end SharpLiebThirring.PLParity + +namespace SharpLiebThirring.CubeFlags +open SharpLiebThirring.PLParity +section PLComplex +variable {n : ℕ} [NeZero n] (H : Subgroup (Signs n)) (D : SubMulAction H (Flag n)) +variable {V : Type u67} [NormedAddCommGroup V] [NormedSpace ℝ V] [FiniteDimensional ℝ V] +variable (ρ : H →* (V ≃ₗ[ℝ] V)) +attribute [local instance] Classical.propDecidable + +/-- Extend finite equivariant vertex data by zero outside the invariant complex. -/ +def extendValues (a : vertices H D → V) (z : Fin n → ℤ) : V := + if hz : z ∈ vertices H D then a ⟨z, hz⟩ else 0 + +omit [NeZero n] [NormedSpace ℝ V] [FiniteDimensional ℝ V] in +lemma extendValues_at (a : vertices H D → V) (F : D) (k : Fin (n + 1)) : + extendValues H D a (F.val.vertex k) = a (flagVertex H D F k) := by + simp only [extendValues, dite_eq_left (show F.val.vertex k ∈ vertices H D from ⟨F, k, rfl⟩)] + rfl + +omit [NeZero n] [FiniteDimensional ℝ V] in +lemma extendValues_equivariant (a : vertices H D → V) + (ha : ∀ s : H, ∀ z, a (s • z) = ρ s (a z)) (s : H) (z : Fin n → ℤ) : + extendValues H D a (s • z) = ρ s (extendValues H D a z) := by + by_cases hz : z ∈ vertices H D + · have hsz : s • z ∈ vertices H D := (vertices H D).smul_mem s hz + simp only [extendValues, dite_eq_left hz, dite_eq_left hsz] + exact ha s ⟨z, hz⟩ + · have hsz : s • z ∉ vertices H D := fun h ↦ hz (((vertices H D).smul_mem_iff' s).mp h) + simp only [extendValues, dite_eq_right hz, dite_eq_right hsz, map_zero] + +def cellHit (a : vertices H D → V) (F : Flag n) (j : Fin (n + 1)) : Prop := + facetHit (fun k ↦ extendValues H D a (F.vertex k)) j + +omit [NeZero n] [FiniteDimensional ℝ V] in +lemma cellHit_equivariant (a : vertices H D → V) + (ha : ∀ s : H, ∀ z, a (s • z) = ρ s (a z)) (s : H) (F : Flag n) (j : Fin (n + 1)) : + cellHit H D a (s • F) j ↔ cellHit H D a F j := by + unfold cellHit + have he (k : Fin (n + 1)) : extendValues H D a ((s • F).vertex k) = + ρ s (extendValues H D a (F.vertex k)) := by + rw [show (s • F).vertex k = s • F.vertex k from F.vertex_smul s.val k] + exact extendValues_equivariant H D ρ a ha s _ + simp only [he] + exact facetHit_linearEquiv _ (ρ s) _ + +omit [FiniteDimensional ℝ V] in +lemma cellHit_neighbor (a : vertices H D → V) (F : Flag n) (j : Fin (n + 1)) : + cellHit H D a (F.neighbor j) j ↔ cellHit H D a F j := by + apply facetHit_congr + intro k hk + rw [F.neighbor_vertex j k hk] + +omit [NeZero n] in +lemma cellHit_even (a : vertices H D → V) (F : D) + (hc : n = Module.finrank ℝ V + 1) + (haug : ∀ j : Fin (n + 1), LinearIndependent ℝ + (fun k : {k // k ≠ j} ↦ ((1 : ℝ), a (flagVertex H D F k)))) + (hvec : ∀ i j : Fin (n + 1), i ≠ j → LinearIndependent ℝ + (fun k : {k // k ≠ i ∧ k ≠ j} ↦ a (flagVertex H D F k))) : + Even (Nat.card {j // cellHit H D a F.val j}) := by + have he := even_facetHit (fun k ↦ a (flagVertex H D F k)) (by simpa using hc) + haug hvec + simpa only [cellHit, extendValues_at, Nat.card_eq_fintype_card, Fintype.card_subtype] using he + +lemma neighbor_not_orbit (h : ℝ) (F : D) + (hfree : ∀ z : vertices H D, ∀ s : H, s • gridPoint h z.val = gridPoint h z.val → s = 1) + (j : Fin (n + 1)) (s : H) : F.val.neighbor j ≠ s • F.val := by + apply F.val.neighbor_ne_reflect_of_free j s.val + intro k hk + have hz : s • (flagVertex H D F k) = flagVertex H D F k := by + apply Subtype.ext + exact funext hk + have hp : s • gridPoint h (F.val.vertex k) = gridPoint h (F.val.vertex k) := by + calc + _ = gridPoint h (s • F.val.vertex k) := (gridPoint_smul h s.val _).symm + _ = _ := congrArg (gridPoint h) (congrArg Subtype.val hz) + exact congrArg Subtype.val (hfree (flagVertex H D F k) s hp) + +/-- The geometric complex now satisfies the abstract mod-two boundary lemma. -/ +lemma another_boundary [Fintype D] (a : vertices H D → V) + (ha : ∀ s : H, ∀ z, a (s • z) = ρ s (a z)) (hc : n = Module.finrank ℝ V + 1) + (haug : ∀ F : D, ∀ j : Fin (n + 1), LinearIndependent ℝ + (fun k : {k // k ≠ j} ↦ ((1 : ℝ), a (flagVertex H D F k)))) + (hvec : ∀ F : D, ∀ i j : Fin (n + 1), i ≠ j → LinearIndependent ℝ + (fun k : {k // k ≠ i ∧ k ≠ j} ↦ a (flagVertex H D F k))) + (h : ℝ) (hfree : ∀ z : vertices H D, ∀ s : H, + s • gridPoint h z.val = gridPoint h z.val → s = 1) + (p₀ : FinitePairing.selected D (cellHit H D a) (cellHit_equivariant H D ρ a ha)) + (hp₀ : p₀.val.cell.val.neighbor p₀.val.facet ∉ D) : + ∃ p : FinitePairing.selected D (cellHit H D a) (cellHit_equivariant H D ρ a ha), + p.val.cell.val.neighbor p.val.facet ∉ D ∧ + ¬ (MulAction.orbitRel H _) p p₀ := by + exact FinitePairing.exists_other_boundary D (cellHit H D a) (cellHit_equivariant H D ρ a ha) + Flag.neighbor Flag.neighbor_neighbor (fun s F j ↦ (F.smul_neighbor s.val j).symm) + (fun F j hh ↦ (cellHit_neighbor H D a F j).mpr hh) + (fun F ↦ cellHit_even H D a F hc (haug F) (hvec F)) + (fun F j _ s ↦ neighbor_not_orbit H D h F hfree j s) p₀ hp₀ + +end PLComplex +end SharpLiebThirring.CubeFlags + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/FlagApproximation.lean b/lean/OAI/Analysis/LiebThirring/FlagApproximation.lean new file mode 100644 index 0000000000000000000000000000000000000000..03fc8063b33bcfafc930cad3b00bd50a583d7ab1 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/FlagApproximation.lean @@ -0,0 +1,83 @@ +import OAI.Analysis.LiebThirring.EnergyAlgebra + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.SpectralProof +open SobolevProof SobolevProof.C1L2 MeasureTheory Set Filter InnerProductSpace +open scoped Topology + +lemma eventually_cut_prefix_negative {N : ℕ} {W : ℝ → ℝ} + (hW : LocallyIntegrable W volume) (u : Fin N → C1L2) (k κ : Fin N → ℝ) + (ho : Orthonormal ℝ u) (he : ∀ i, (u i).IsEigen W (k i)) + (hk : ∀ i, 0 < k i) (hκ : ∀ i, 0 < κ i ∧ κ i < k i) + (horder : Antitone k) : + ∀ᶠ n in atTop, ∀ i (v : C1L2), + v ∈ Submodule.span ℝ ((fun j ↦ (u j).cut n) '' Iic i) → + energy W v v+κ i^2*inner ℝ v v ≤ 0 := by + classical + apply eventually_all.mpr + intro i + let d : Iic i → ℝ := fun j ↦ κ i^2-k j^2 + have hd (j : Iic i) : d j < 0 := by + have hj := horder j.property + have hki := hk i + have hkj := hk j + have hκi := hκ i + dsimp [d]; nlinarith + let M := fun n (j l : Iic i) ↦ energy W ((u j).cut n) ((u l).cut n)+ + κ i^2*inner ℝ ((u j).cut n) ((u l).cut n) + have hM (j l : Iic i) : Tendsto (fun n ↦ M n j l) atTop (𝓝 (if j=l then d j else 0)) := by + have hh := (cut_energy_tendsto (he j) hW (u l)).add (((u j).cutoff_inner_tendsto (u l)).const_mul (κ i^2)) + convert hh using 1 + rw [orthonormal_iff_ite.mp ho] + by_cases hjl : j=l + · simp [hjl,d]; ring + · have hn : (j : Fin N) ≠ l := fun h ↦ hjl (Subtype.ext h) + simp [hjl,hn] + filter_upwards [eventually_negative_quadratic M d hd hM] with n hn v hv + have him : ((fun j ↦ (u j).cut n) '' Iic i) = range (fun j : Iic i ↦ (u j).cut n) := by + ext x + simp + rw [him,Submodule.mem_span_range_iff_exists_fun ℝ] at hv + obtain ⟨c,rfl⟩ := hv + rw [energy_sum_sum hW (fun j : Iic i ↦ (u j).cut n) (fun j ↦ (u j).cut_compact n),inner_sum_sum] + convert hn c using 1 + simp only [Finset.mul_sum,← Finset.sum_add_distrib,M] + apply Finset.sum_congr rfl; intro j _ + apply Finset.sum_congr rfl; intro l _ + ring + +/-- A compact orthonormal flag with the exact strict spectral margins. -/ +lemma exists_compact_negative_flag {N : ℕ} {W : ℝ → ℝ} + (hW : LocallyIntegrable W volume) (u : Fin N → C1L2) (k κ : Fin N → ℝ) + (ho : Orthonormal ℝ u) (he : ∀ i, (u i).IsEigen W (k i)) + (hk : ∀ i, 0 < k i) (hκ : ∀ i, 0 < κ i ∧ κ i < k i) + (horder : Antitone k) : + ∃ q : Fin N → C1L2, Orthonormal ℝ q ∧ + (∀ i, HasCompactSupport (q i).val) ∧ + ∀ i (v : C1L2), v ∈ Submodule.span ℝ (q '' Iic i) → + energy W v v+κ i^2*inner ℝ v v ≤ 0 := by + classical + obtain ⟨n,hli,hn⟩ := ((eventually_cut_linearIndependent ho.linearIndependent).and + (eventually_cut_prefix_negative hW u k κ ho he hk hκ horder)).exists + let f := fun j ↦ (u j).cut n + let q := gramSchmidtNormed ℝ f + have hs (i : Fin N) : Submodule.span ℝ (q '' Iic i) = Submodule.span ℝ (f '' Iic i) := by + rw [show q = gramSchmidtNormed ℝ f from rfl,span_gramSchmidtNormed,span_gramSchmidt_Iic] + refine ⟨q,gramSchmidtNormed_orthonormal hli,?_,?_⟩ + · intro i + apply compact_of_mem_span f (fun j ↦ (u j).cut_compact n) + apply Submodule.span_mono (image_subset_range _ _) + rw [← hs i] + exact Submodule.subset_span (mem_image_of_mem q (mem_Iic.mpr le_rfl)) + · intro i v hv + rw [hs i] at hv + exact hn i v hv + +end SharpLiebThirring.SpectralProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/FlagGeometry.lean b/lean/OAI/Analysis/LiebThirring/FlagGeometry.lean new file mode 100644 index 0000000000000000000000000000000000000000..186aa501844518eefb03792c6e32a84a7b70356d --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/FlagGeometry.lean @@ -0,0 +1,397 @@ +import OAI.Analysis.LiebThirring.CubeFlags + +namespace OAI + +universe u39 + +noncomputable section +open Finset + + +namespace SharpLiebThirring.CubeFlags + +/-- Coordinate reflection as an isometric linear equivalence in the sup norm. -/ +def Signs.linearIsometry {n : ℕ} (s : Signs n) : + (Fin n → ℝ) ≃ₗᵢ[ℝ] (Fin n → ℝ) where + toFun x i := if s.val i then -x i else x i + invFun x i := if s.val i then -x i else x i + left_inv x := by + funext i + rcases Bool.eq_false_or_eq_true (s.val i) with hs | hs <;> simp [hs] + right_inv x := by + funext i + rcases Bool.eq_false_or_eq_true (s.val i) with hs | hs <;> simp [hs] + map_add' x y := by + funext i + rcases Bool.eq_false_or_eq_true (s.val i) with hs | hs <;> simp [hs, add_comm] + map_smul' a x := by + funext i + rcases Bool.eq_false_or_eq_true (s.val i) with hs | hs <;> simp [hs] + norm_map' x := by + simp only [Pi.norm_def] + congr 1 + apply Finset.sup_congr rfl + intro i _ + change ‖(if s.val i then -x i else x i)‖₊ = ‖x i‖₊ + rcases Bool.eq_false_or_eq_true (s.val i) with hs | hs <;> simp [hs] + +instance {n : ℕ} : MulAction (Signs n) (Fin n → ℝ) where + smul s x := s.linearIsometry x + one_smul x := by + ext i + change (if (1 : Signs n).val i then -x i else x i) = x i + simp + mul_smul s t x := by + ext i + change (if (s * t).val i then -x i else x i) = + if s.val i then -(if t.val i then -x i else x i) else (if t.val i then -x i else x i) + simp only [Signs.mul_val] + rcases Bool.eq_false_or_eq_true (s.val i) with hs | hs <;> + rcases Bool.eq_false_or_eq_true (t.val i) with ht | ht <;> simp [hs, ht] + +lemma Signs.smul_real {n : ℕ} (s : Signs n) (x : Fin n → ℝ) (i : Fin n) : + (s • x) i = if s.val i then -x i else x i := rfl + +instance {n : ℕ} : IsIsometricSMul (Signs n) (Fin n → ℝ) where + isometry_smul s := s.linearIsometry.isometry + +instance {n : ℕ} : MulAction (Signs n) (Fin n → ℤ) where + smul s x i := if s.val i then -x i else x i + one_smul x := by + ext i + change (if (1 : Signs n).val i then -x i else x i) = x i + simp + mul_smul s t x := by + ext i + change (if (s * t).val i then -x i else x i) = + if s.val i then -(if t.val i then -x i else x i) else (if t.val i then -x i else x i) + simp only [Signs.mul_val] + rcases Bool.eq_false_or_eq_true (s.val i) with hs | hs <;> + rcases Bool.eq_false_or_eq_true (t.val i) with ht | ht <;> simp [hs, ht] + +lemma Signs.smul_int {n : ℕ} (s : Signs n) (x : Fin n → ℤ) (i : Fin n) : + (s • x) i = if s.val i then -x i else x i := rfl + +lemma Flag.point_smul {n : ℕ} (s : Signs n) (F : Flag n) (k : Fin (n + 1)) : + (s • F).point k = s • F.point k := by + ext i + exact F.reflect_point s.val k i + +lemma Flag.vertex_smul {n : ℕ} (s : Signs n) (F : Flag n) (k : Fin (n + 1)) : + (s • F).vertex k = s • F.vertex k := by + ext i + exact F.reflect_vertex s.val k i + +/-- The common final vertex is the cube center. -/ +def Flag.center {n : ℕ} (F : Flag n) : Fin n → ℝ := F.point (Fin.last n) + +@[simp] lemma Flag.center_apply {n : ℕ} (F : Flag n) (i : Fin n) : + F.center i = (F.base i : ℝ) + 1 / 2 := by + simp only [center, point, vertex, Fin.val_last, (F.order.symm i).isLt, ↓reduceIte] + push_cast + ring + +lemma Flag.center_smul {n : ℕ} (s : Signs n) (F : Flag n) : + (s • F).center = s • F.center := F.point_smul s _ + +lemma Flag.dist_point_center {n : ℕ} (F : Flag n) (k : Fin (n + 1)) : + dist (F.point k) F.center ≤ 1 / 2 := by + rw [dist_pi_le_iff (by norm_num : (0 : ℝ) ≤ 1 / 2)] + intro i + rw [Real.dist_eq, abs_le, F.center_apply] + have hb := F.point_bounds k i + constructor <;> linarith + +lemma Flag.dist_combination_center {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) : + dist (∑ k, w k • F.point k) F.center ≤ 1 / 2 := by + rw [dist_pi_le_iff (by norm_num : (0 : ℝ) ≤ 1 / 2)] + intro i + rw [Real.dist_eq, abs_le, F.center_apply] + have hb := F.combination_bounds w hw hs i + constructor <;> linarith + +lemma Flag.neighbor_center_dist {n : ℕ} [NeZero n] (F : Flag n) (j : Fin (n + 1)) : + dist (F.neighbor j).center F.center ≤ 1 := by + have hn : n ≠ 0 := NeZero.ne n + obtain ⟨k, hk⟩ : ∃ k : Fin (n + 1), k ≠ j := by + by_cases hj : j.val = 0 + · exact ⟨⟨n, by omega⟩, by intro h; have hh := congrArg Fin.val h; simp at hh; omega⟩ + · exact ⟨0, by intro h; have hh := congrArg Fin.val h; simp at hh; omega⟩ + have he : (F.neighbor j).point k = F.point k := by + ext i + simp only [point, congrFun (F.neighbor_vertex j k hk) i] + calc + _ ≤ dist (F.neighbor j).center (F.point k) + dist (F.point k) F.center := dist_triangle _ _ _ + _ ≤ 1 / 2 + 1 / 2 := by + apply add_le_add + · rw [dist_comm, ← he] + exact (F.neighbor j).dist_point_center k + · exact F.dist_point_center k + _ = 1 := by norm_num + +lemma Flag.dist_combination_point {n : ℕ} (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) (k : Fin (n + 1)) : + dist (∑ l, w l • F.point l) (F.point k) ≤ 1 := by + calc + _ ≤ dist (∑ l, w l • F.point l) F.center + dist F.center (F.point k) := dist_triangle _ _ _ + _ ≤ 1 / 2 + 1 / 2 := add_le_add (F.dist_combination_center w hw hs) + (by rw [dist_comm]; exact F.dist_point_center k) + _ = 1 := by norm_num + +lemma dist_scale {E : Type u39} [NormedAddCommGroup E] [NormedSpace ℝ E] + (h : ℝ) (hh : 0 ≤ h) (x y : E) : dist (h • x) (h • y) = h * dist x y := by + simp only [dist_eq_norm, ← smul_sub, norm_smul, Real.norm_eq_abs, abs_of_nonneg hh] + +lemma Flag.dist_scaled_point_center {n : ℕ} (F : Flag n) (h : ℝ) (hh : 0 ≤ h) + (k : Fin (n + 1)) : dist (h • F.point k) (h • F.center) ≤ h / 2 := by + rw [dist_scale h hh] + nlinarith [F.dist_point_center k] + +lemma Flag.finite_base_bounds {n : ℕ} (L U : ℤ) : + Set.Finite {F : Flag n | ∀ i, L ≤ F.base i ∧ F.base i ≤ U} := by + let e : {F : Flag n // ∀ i, L ≤ F.base i ∧ F.base i ≤ U} → + ((Fin n → ↥(Finset.Icc L U)) × (Fin n → Bool) × Equiv.Perm (Fin n)) := + fun F ↦ (fun i ↦ ⟨F.val.base i, by simpa only [Finset.mem_Icc] using F.prop i⟩, + F.val.corner, F.val.order) + have he : Function.Injective e := by + intro F G h + apply Subtype.ext + apply Flag.ext + · funext i + exact congrArg Subtype.val (congrFun (congrArg Prod.fst h) i) + · exact congrArg (fun z ↦ z.2.1) h + · exact congrArg (fun z ↦ z.2.2) h + exact Set.finite_def.mpr ⟨Fintype.ofInjective e he⟩ + +/-- Cubes whose centers are close to a compact set form a finite collection. -/ +lemma Flag.finite_near_centers {n : ℕ} {K : Set (Fin n → ℝ)} (hK : Bornology.IsBounded K) + (h r : ℝ) (hh : 0 < h) : + Set.Finite {F : Flag n | ∃ x ∈ K, dist (h • F.center) x < r} := by + obtain ⟨B, hB⟩ := hK.exists_norm_le + obtain ⟨U, hU⟩ := exists_int_gt ((B + r) / h + 1) + apply (Flag.finite_base_bounds (-U) U).subset + rintro F ⟨x, hx, hd⟩ i + have hc : ‖h • F.center‖ < B + r := by + have ht := norm_add_le (h • F.center - x) x + rw [sub_add_cancel, ← dist_eq_norm] at ht + linarith [hB x hx] + rw [norm_smul, Real.norm_eq_abs, abs_of_pos hh] at hc + have hc' : ‖F.center‖ < (B + r) / h := (lt_div_iff₀ hh).mpr (by nlinarith) + have hi : |F.center i| ≤ ‖F.center‖ := by simpa only [Real.norm_eq_abs] using norm_le_pi_norm F.center i + rw [F.center_apply] at hi + have hl : -(U : ℝ) ≤ F.base i := by + have := (abs_le.mp hi).1 + linarith + have hu : (F.base i : ℝ) ≤ U := by + have := (abs_le.mp hi).2 + linarith + constructor + · exact_mod_cast hl + · exact_mod_cast hu + +/-- The spatially truncated cylinder of cubical flags used in continuation. -/ +def nearCylinder {n : ℕ} (K : Set (Fin n → ℝ)) (h r : ℝ) (t : Fin n) (m : ℕ) : Set (Flag n) := + {F | (∃ x ∈ K, dist (h • F.center) x < r) ∧ 0 ≤ F.base t ∧ F.base t < (m : ℤ)} + +lemma finite_nearCylinder {n : ℕ} {K : Set (Fin n → ℝ)} (hK : Bornology.IsBounded K) + (h r : ℝ) (hh : 0 < h) (t : Fin n) (m : ℕ) : (nearCylinder K h r t m).Finite := + (Flag.finite_near_centers hK h r hh).subset (fun _ hF ↦ hF.1) + +lemma nearCylinder_smul {n : ℕ} (K : Set (Fin n → ℝ)) (h r : ℝ) (t : Fin n) (m : ℕ) + (s : Signs n) (ht : s.val t = false) (hK : ∀ x ∈ K, s • x ∈ K) + {F : Flag n} (hF : F ∈ nearCylinder K h r t m) : s • F ∈ nearCylinder K h r t m := by + obtain ⟨⟨x, hx, hd⟩, hlo, hhi⟩ := hF + refine ⟨⟨s • x, hK x hx, ?_⟩, ?_, ?_⟩ + · rw [F.center_smul] + have he : h • (s • F.center) = s • (h • F.center) := by + ext i + simp only [Pi.smul_apply, Signs.smul_real, smul_eq_mul] + rcases Bool.eq_false_or_eq_true (s.val i) with hi | hi <;> simp [hi] + ring + rw [he, dist_smul] + exact hd + · simpa only [Flag.smul_def, Flag.reflect, ht, Bool.false_eq_true, ↓reduceIte] using hlo + · simpa only [Flag.smul_def, Flag.reflect, ht, Bool.false_eq_true, ↓reduceIte] using hhi + +lemma nearCylinder_point_cthickening {n : ℕ} (K : Set (Fin n → ℝ)) (h r : ℝ) + (hh : 0 ≤ h) (t : Fin n) (m : ℕ) {F : Flag n} (hF : F ∈ nearCylinder K h r t m) + (k : Fin (n + 1)) : h • F.point k ∈ Metric.cthickening (r + h / 2) K := by + obtain ⟨x, hx, hd⟩ := hF.1 + apply Metric.mem_cthickening_of_dist_le _ x _ K hx + calc + _ ≤ dist (h • F.point k) (h • F.center) + dist (h • F.center) x := dist_triangle _ _ _ + _ ≤ h / 2 + r := add_le_add (F.dist_scaled_point_center h hh k) hd.le + _ = r + h / 2 := add_comm _ _ + + +lemma Flag.neighbor_base_of_ne_last {n : ℕ} [NeZero n] (F : Flag n) (j : Fin (n + 1)) + (hj : j ≠ Fin.last n) : (F.neighbor j).base = F.base := by + have hn : j.val ≠ n := fun h ↦ hj (Fin.ext h) + by_cases hz : j.val = 0 + · simp only [neighbor, dite_eq_left hz, flip_base] + · simp only [neighbor, dite_eq_right hz, dite_eq_right hn, swap] + +/-- A time-boundary facet is exactly the last facet of a flag expanding time last. -/ +lemma Flag.neighbor_outside_time {n : ℕ} [NeZero n] (F : Flag n) (j : Fin (n + 1)) + (t : Fin n) (m : ℤ) (hlo : 0 ≤ F.base t) (hhi : F.base t < m) + (hout : ¬ (0 ≤ (F.neighbor j).base t ∧ (F.neighbor j).base t < m)) : + j = Fin.last n ∧ (F.order.symm t).val = n - 1 ∧ + ((F.base t = 0 ∧ F.corner t = false) ∨ (F.base t = m - 1 ∧ F.corner t = true)) := by + have hj : j = Fin.last n := by + by_contra hj + rw [F.neighbor_base_of_ne_last j hj] at hout + exact hout ⟨hlo, hhi⟩ + have hp : 0 < n := NeZero.pos n + have hc : F.neighbor j = F.cross (F.order ⟨n - 1, by omega⟩) := by + subst j + simp only [neighbor, Fin.val_last, ne_of_gt hp, ↓reduceDIte] + rw [hc] at hout + have ht : t = F.order ⟨n - 1, by omega⟩ := by + by_contra ht + simp only [cross, Function.update_of_ne ht] at hout + exact hout ⟨hlo, hhi⟩ + refine ⟨hj, ?_, ?_⟩ + · rw [ht, Equiv.symm_apply_apply] + · have hh : (F.cross (F.order ⟨n - 1, by omega⟩)).base t = + F.base t + if F.corner t then 1 else -1 := by + simp only [cross, ← ht, Function.update_self] + simp only [hh] at hout + rcases Bool.eq_false_or_eq_true (F.corner t) with htrue | hfalse + · simp only [htrue, ↓reduceIte] at hout + exact Or.inr ⟨by omega, htrue⟩ + · simp only [hfalse, Bool.false_eq_true, ↓reduceIte] at hout + exact Or.inl ⟨by omega, hfalse⟩ + +lemma Flag.point_time_boundary {n : ℕ} [NeZero n] (F : Flag n) (t : Fin n) + (ht : (F.order.symm t).val = n - 1) (k : Fin (n + 1)) (hk : k ≠ Fin.last n) : + F.point k t = (F.base t : ℝ) + if F.corner t then 1 else 0 := by + have hp : 0 < n := NeZero.pos n + have hk' : k.val < n := by + have hh : k.val ≠ n := fun h ↦ hk (Fin.ext h) + omega + simp only [point, vertex, ht, show ¬ n - 1 < k.val by omega, ↓reduceIte] + rcases Bool.eq_false_or_eq_true (F.corner t) with hc | hc <;> simp [hc] + ring + +lemma nearCylinder_point_time {n : ℕ} (K : Set (Fin n → ℝ)) (h r : ℝ) + (hh : 0 ≤ h) (t : Fin n) (m : ℕ) (hm : h * m = 1) + {F : Flag n} (hF : F ∈ nearCylinder K h r t m) (k : Fin (n + 1)) : + (h • F.point k) t ∈ Set.Icc (0 : ℝ) 1 := by + obtain ⟨hl, hu⟩ := F.point_bounds k t + have hb : (0 : ℝ) ≤ F.base t := by exact_mod_cast hF.2.1 + have hc : (F.base t : ℝ) + 1 ≤ m := by + have hh := hF.2.2 + exact_mod_cast (show F.base t + 1 ≤ (m : ℤ) by omega) + change 0 ≤ h * F.point k t ∧ h * F.point k t ≤ 1 + constructor + · exact mul_nonneg hh (by linarith) + · nlinarith + +lemma nearCylinder_combination_time {n : ℕ} (K : Set (Fin n → ℝ)) (h r : ℝ) + (hh : 0 ≤ h) (t : Fin n) (m : ℕ) (hm : h * m = 1) + {F : Flag n} (hF : F ∈ nearCylinder K h r t m) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) : + (h • (∑ k, w k • F.point k)) t ∈ Set.Icc (0 : ℝ) 1 := by + obtain ⟨hl, hu⟩ := F.combination_bounds w hw hs t + have hb : (0 : ℝ) ≤ F.base t := by exact_mod_cast hF.2.1 + have hc : (F.base t : ℝ) + 1 ≤ m := by + have hh := hF.2.2 + exact_mod_cast (show F.base t + 1 ≤ (m : ℤ) by omega) + change 0 ≤ h * (∑ k, w k • F.point k) t ∧ h * (∑ k, w k • F.point k) t ≤ 1 + constructor + · exact mul_nonneg hh (by linarith) + · nlinarith + +end SharpLiebThirring.CubeFlags + +namespace SharpLiebThirring.CubeFlags + +/-- Embed the twice-barycenter lattice at mesh size `h`. -/ +def gridPoint {n : ℕ} (h : ℝ) (z : Fin n → ℤ) : Fin n → ℝ := + fun i ↦ h * (z i : ℝ) / 2 + +lemma gridPoint_vertex {n : ℕ} (h : ℝ) (F : Flag n) (k : Fin (n + 1)) : + gridPoint h (F.vertex k) = h • F.point k := by + ext i + simp only [gridPoint, Pi.smul_apply, smul_eq_mul, Flag.point] + ring + +lemma gridPoint_smul {n : ℕ} (h : ℝ) (s : Signs n) (z : Fin n → ℤ) : + gridPoint h (s • z) = s • gridPoint h z := by + ext i + simp only [gridPoint, Signs.smul_real, Signs.smul_int] + rcases Bool.eq_false_or_eq_true (s.val i) with hs | hs <;> simp [hs] + ring + +lemma gridPoint_injective {n : ℕ} {h : ℝ} (hh : h ≠ 0) : + Function.Injective (gridPoint (n := n) h) := by + intro z w he + ext i + have hx : h * (z i : ℝ) / 2 = h * (w i : ℝ) / 2 := congrFun he i + have hi : (z i : ℝ) = (w i : ℝ) := mul_left_cancel₀ hh ((div_left_inj' (by norm_num : (2 : ℝ) ≠ 0)).mp hx) + exact_mod_cast hi + +section VertexComplex +variable {n : ℕ} (H : Subgroup (Signs n)) (D : SubMulAction H (Flag n)) + +/-- All vertices of a group-invariant collection of cubical flags. -/ +def vertices : SubMulAction H (Fin n → ℤ) where + carrier := {z | ∃ F : D, ∃ k, F.val.vertex k = z} + smul_mem' s z hz := by + obtain ⟨F, k, rfl⟩ := hz + refine ⟨s • F, k, ?_⟩ + exact F.val.vertex_smul s.val k + +instance verticesFintype [Fintype D] : Fintype (vertices H D) := by + have hfin : Set.Finite (vertices H D : Set (Fin n → ℤ)) := by + have he : (vertices H D : Set (Fin n → ℤ)) = Set.range + (fun p : D × Fin (n + 1) ↦ p.1.val.vertex p.2) := by + ext z + constructor + · rintro ⟨F, k, rfl⟩ + exact ⟨(F, k), rfl⟩ + · rintro ⟨⟨F, k⟩, rfl⟩ + exact ⟨F, k, rfl⟩ + rw [he] + exact Set.finite_range _ + exact hfin.fintype + +def flagVertex (F : D) (k : Fin (n + 1)) : vertices H D := ⟨F.val.vertex k, F, k, rfl⟩ + +lemma flagVertex_smul (s : H) (F : D) (k : Fin (n + 1)) : + flagVertex H D (s • F) k = s • flagVertex H D F k := + Subtype.ext (F.val.vertex_smul s.val k) + +lemma flagVertex_orbits_injective (F : D) : + Function.Injective (fun k ↦ (Quotient.mk'' (flagVertex H D F k) : + Quotient (MulAction.orbitRel H (vertices H D)))) := by + intro j k he + have hr := Quotient.exact' he + obtain ⟨s, hs⟩ := MulAction.mem_orbit_iff.mp (MulAction.orbitRel_apply.mp hr) + have hh : F.val.vertex j = s.val • F.val.vertex k := (congrArg Subtype.val hs).symm + apply F.val.vertex_orbits_distinct j k s.val + intro i + exact congrFun hh i + +/-- Freeness of the real vertex positions induces freeness on the finite +vertex set. It is supplied by the compact free-locus tube, not presumed. -/ +theorem verticesIsCancel (h : ℝ) + (hfree : ∀ z : vertices H D, ∀ s : H, s • gridPoint h z.val = gridPoint h z.val → s = 1) : + IsCancelSMul H (vertices H D) where + right_cancel' s t z he := by + have he' : s • z.val = t • z.val := congrArg Subtype.val he + have he'' : (t⁻¹ * s) • z.val = z.val := by + rw [mul_smul, he', inv_smul_smul] + have hp : (t⁻¹ * s) • gridPoint h z.val = gridPoint h z.val := by + calc + _ = gridPoint h ((t⁻¹ * s) • z.val) := (gridPoint_smul h (t⁻¹ * s).val z.val).symm + _ = _ := congrArg (gridPoint h) he'' + exact (inv_mul_eq_one.mp (hfree z _ hp)).symm + +end VertexComplex +end SharpLiebThirring.CubeFlags + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/FlowContinuation.lean b/lean/OAI/Analysis/LiebThirring/FlowContinuation.lean new file mode 100644 index 0000000000000000000000000000000000000000..129d9b04dbb90491a5eda74235f31a3af85aef43 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/FlowContinuation.lean @@ -0,0 +1,278 @@ +import OAI.Analysis.LiebThirring.MatrixFlow + +namespace OAI + +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Set Metric MeasureTheory Filter +open scoped Topology NNReal +noncomputable section +open Matrix Set MeasureTheory WithLp +open scoped Matrix.Norms.L2Operator Topology + +namespace SharpLiebThirring.ODEProof +open Set Metric Filter + +lemma scalar_stationary_unique {l r k : ℝ} (hlr : l ≤ r) + {b q g : ℝ → ℝ} (hg : LocallyLipschitz g) (hgk : g k = 0) + (A : ℝ≥0) (hq : ∀ t ∈ Icc l r, |q t| ≤ A) + (hb : ∀ t ∈ Icc l r, HasDerivWithinAt b (q t * g (b t)) (Icc l r) t) + (hbl : b l = k) : EqOn b (fun _ ↦ k) (Icc l r) := by + have hc := HasDerivWithinAt.continuousOn hb + obtain ⟨L,hL⟩ := hg.locallyLipschitzOn.exists_lipschitzOnWith_of_compact + (isCompact_Icc.image_of_continuousOn hc) + have hk : k ∈ b '' Icc l r := hbl ▸ mem_image_of_mem b ⟨le_refl _,hlr⟩ + apply ODE_solution_unique_of_mem_Icc_right (K := A*L) + (v := fun t x ↦ q t * g x) (s := fun _ ↦ b '' Icc l r) _ hc + (fun t ht ↦ derivative_right_of_Icc ht (hb t (Ico_subset_Icc_self ht))) + (fun t ht ↦ mem_image_of_mem b (Ico_subset_Icc_self ht)) continuousOn_const + (fun t _ ↦ by simpa only [hgk,mul_zero] using hasDerivWithinAt_const t (Ici t) k) + (fun _ _ ↦ hk) hbl + intro t ht + apply lipschitzOnWith_iff_norm_sub_le.mpr + intro x hx y hy + rw [← mul_sub,norm_mul] + calc + _ ≤ (A : ℝ) * ((L : ℝ)*‖x-y‖) := + mul_le_mul (hq t (Ico_subset_Icc_self ht)) + (lipschitzOnWith_iff_norm_sub_le.mp hL hx hy) (norm_nonneg _) A.prop + _ = _ := by push_cast; ring + +/-- An upper barrier needs the derivative sign only strictly outside the barrier. -/ +lemma upper_barrier {l r κ : ℝ} {h h' : ℝ → ℝ} + (hd : ∀ t ∈ Icc l r, HasDerivWithinAt h (h' t) (Icc l r) t) + (hi : h l ≤ κ) + (hs : ∀ t ∈ Icc l r, κ < h t → h' t ≤ 0) : + ∀ t ∈ Icc l r, h t ≤ κ := by + intro t ht + have hη : ∀ η > (0 : ℝ), h t ≤ κ + η*(1+t-l) := by + intro η hη + apply image_le_of_deriv_right_lt_deriv_boundary + (HasDerivWithinAt.continuousOn hd) + (fun x hx ↦ derivative_right_of_Icc hx (hd x (Ico_subset_Icc_self hx))) + (B := fun x ↦ κ + η*(1+x-l)) (B' := fun _ ↦ η) + · simpa only [add_sub_cancel_right,mul_one] using hi.trans (le_add_of_nonneg_right hη.le) + · intro x + simpa only [mul_one,id_eq] using + (((hasDerivAt_id x).const_add 1).sub_const l |>.const_mul η |>.const_add κ) + · intro x hx he + have hpos : κ < h x := by rw [he]; have := hx.1; nlinarith + exact (hs x (Ico_subset_Icc_self hx) hpos).trans_lt hη + · exact ht + have hc : ContinuousWithinAt (fun η : ℝ ↦ κ + η*(1+t-l)) (Ioi 0) 0 := by fun_prop + have hh := continuousWithinAt_const.closure_le (by simp : (0 : ℝ) ∈ closure (Ioi 0)) hc hη + simpa only [zero_mul,add_zero] using hh + +lemma two_sided_barrier {l r κ : ℝ} {h h' : ℝ → ℝ} + (hd : ∀ t ∈ Icc l r, HasDerivWithinAt h (h' t) (Icc l r) t) + (hi : h l ≤ κ) (hf : -κ ≤ h r) + (hs : ∀ t ∈ Icc l r, κ < |h t| → h' t ≤ 0) : + ∀ t ∈ Icc l r, |h t| ≤ κ := by + have hup := upper_barrier hd hi (fun t ht h ↦ hs t ht (h.trans_le (le_abs_self _))) + have hrev : ∀ t ∈ Icc (-r) (-l), HasDerivWithinAt (fun t ↦ -h (-t)) (h' (-t)) + (Icc (-r) (-l)) t := by + intro t ht + have hm : -t ∈ Icc l r := ⟨by linarith [ht.2],by linarith [ht.1]⟩ + have hh := (hd (-t) hm).comp t (hasDerivWithinAt_id t (Icc (-r) (-l)) |>.neg) + (fun x hx ↦ ⟨by linarith [hx.2],by linarith [hx.1]⟩) + convert! hh.neg using 1 + simp + have hlo := upper_barrier hrev (by simpa only [neg_neg] using neg_le_neg hf) + (fun t ht h ↦ hs (-t) ⟨by linarith [ht.2],by linarith [ht.1]⟩ + (h.trans_le (neg_le_abs _))) + intro t ht + apply abs_le.mpr + constructor + · have hh := hlo (-t) ⟨by linarith [ht.2],by linarith [ht.1]⟩ + simp only [neg_neg] at hh + linarith + · exact hup t ht + +end SharpLiebThirring.ODEProof +namespace SharpLiebThirring.MatrixFlow +open ODEProof Set Matrix +variable {N : ℕ} + +lemma vanishing_row_stationary {l r ε : ℝ} (hlr : l ≤ r) + (M : Sym N → Sym N) (L Q : ℝ≥0) (hL : LipschitzWith L M) + (q : Sym N → ℝ) (hq : ∀ A, |q A| ≤ Q) + (g : Fin N → ℝ → ℝ) (hg : ∀ i, LocallyLipschitz (g i)) + (k : Fin N → ℝ) (hgk : ∀ i, g i (k i) = 0) + (hc : ∀ i A, (∀ j, i ≠ j → A.val i j = 0) → (M A).val i i = q A * g i (A.val i i)) + (he : ∀ s : Fin N → ℝ, (∀ i, s i = 1 ∨ s i = -1) → ∀ A, M (symConj s A) = symConj s (M A)) + (u : ℝ → Fin N → ℝ) (X : (Matrix (Fin N) (Fin N) ℝ × ℝ) → ℝ → Sym N) + (hXi : ∀ p, X p l = symDiag k) + (hXd : ∀ p t, t ∈ Icc l r → HasDerivWithinAt (X p) (flowRhs ε M u p t (X p t)) (Icc l r) t) + (C : Matrix (Fin N) (Fin N) ℝ) (θ : ℝ) (i : Fin N) (hi : ∀ j, C i j = 0) : + ∀ t ∈ Icc l r, (X (C,θ) t).val i i = k i := by + let s : Fin N → ℝ := fun j ↦ if j=i then -1 else 1 + have hs := zero_row_sign i + have hC : (fun j a ↦ s j * C j a) = C := by + ext j a + by_cases hj : j=i + · subst j; simp only [s,ite_true,hi,mul_zero] + · simp only [s,ite_eq_right hj,one_mul] + have hfixed : ∀ t ∈ Icc l r, symConj s (X (C,θ) t) = X (C,θ) t := by + have hh := matrix_flow_equivariant hL k u X hXi hXd s hs (he s hs) C θ + rw [hC] at hh + exact fun t ht ↦ (hh ht).symm + have hoff : ∀ t ∈ Icc l r, ∀ j, i ≠ j → (X (C,θ) t).val i j = 0 := + fun t ht ↦ fixed_reflection_offdiag i _ (hfixed t ht) + have hCu (t : ℝ) : (C *ᵥ u t) i = 0 := by simp [mulVec,dotProduct,hi] + have hd : ∀ t ∈ Icc l r, HasDerivWithinAt (fun x ↦ (X (C,θ) x).val i i) + ((ε⁻¹*θ*q (X (C,θ) t))*g i ((X (C,θ) t).val i i)) (Icc l r) t := by + intro t ht + have hh := (symEntry i i).hasFDerivAt.comp_hasDerivWithinAt t (hXd (C,θ) t ht) + change HasDerivWithinAt (fun x ↦ (X (C,θ) x).val i i) + ((ε⁻¹*θ)*(M (X (C,θ) t)).val i i - ε⁻¹*((C*ᵥu t) i*(C*ᵥu t) i)) (Icc l r) t at hh + simp only [hCu,mul_zero,sub_zero,hc i _ (hoff t ht)] at hh + convert hh using 1 + ring + have hinit : (X (C,θ) l).val i i = k i := by rw [hXi]; exact diagonal_apply_eq _ _ + let A : ℝ≥0 := ⟨|ε⁻¹*θ| * Q,mul_nonneg (abs_nonneg _) Q.prop⟩ + apply scalar_stationary_unique hlr (hg i) (hgk i) A _ hd hinit + intro t _ + exact (abs_mul _ _).le.trans (mul_le_mul_of_nonneg_left (hq _) (abs_nonneg _)) + +lemma matching_nonzero_rows {l r ε : ℝ} (hlr : l ≤ r) + (M : Sym N → Sym N) (L Q : ℝ≥0) (hL : LipschitzWith L M) + (q : Sym N → ℝ) (hq : ∀ A, |q A| ≤ Q) + (g : Fin N → ℝ → ℝ) (hg : ∀ i, LocallyLipschitz (g i)) + (k : Fin N → ℝ) (hk : ∀ i, 0 < k i) (hgk : ∀ i, g i (k i) = 0) + (hc : ∀ i A, (∀ j, i ≠ j → A.val i j = 0) → (M A).val i i = q A * g i (A.val i i)) + (he : ∀ s : Fin N → ℝ, (∀ i, s i = 1 ∨ s i = -1) → ∀ A, M (symConj s A) = symConj s (M A)) + (u : ℝ → Fin N → ℝ) (X : (Matrix (Fin N) (Fin N) ℝ × ℝ) → ℝ → Sym N) + (hXi : ∀ p, X p l = symDiag k) + (hXd : ∀ p t, t ∈ Icc l r → HasDerivWithinAt (X p) (flowRhs ε M u p t (X p t)) (Icc l r) t) + (C : Matrix (Fin N) (Fin N) ℝ) (θ : ℝ) (hXf : X (C,θ) r = -symDiag k) : + ∀ i, ∃ j, C i j ≠ 0 := by + intro i + by_contra hn + push Not at hn + have hh := vanishing_row_stationary hlr M L Q hL q hq g hg k hgk hc he u X hXi hXd C θ i hn r ⟨hlr,le_refl _⟩ + rw [hXf] at hh + change -diagonal k i i = k i at hh + rw [diagonal_apply_eq] at hh + linarith [hk i] + +end SharpLiebThirring.MatrixFlow +namespace SharpLiebThirring.MatrixFlow +open Matrix Set ContinuationGap +variable {N : ℕ} + +lemma isClosed_lower : IsClosed {C : Matrix (Fin N) (Fin N) ℝ | ∀ i j, i < j → C i j = 0} := by + simp only [ofPred_forall] + apply isClosed_iInter + intro i + apply isClosed_iInter + intro j + apply isClosed_iInter + intro _ + exact isClosed_eq (by fun_prop) continuous_const + +lemma compact_lower_box (R : ℝ) : IsCompact {C : LowerSpace N | ∀ i j, |C.val i j| ≤ R} := by + have hh := (isClosed_lower (N := N)).isClosedEmbedding_subtypeVal.isCompact_preimage + (isCompact_Icc : IsCompact (Icc (fun _ _ : Fin N ↦ -R) (fun _ _ : Fin N ↦ R))) + convert! hh using 1 + ext C + change (∀ i j, |C.val i j| ≤ R) ↔ ((∀ i j, -R ≤ C.val i j) ∧ (∀ i j, C.val i j ≤ R)) + constructor + · intro h + exact ⟨fun i j ↦ (abs_le.mp (h i j)).1,fun i j ↦ (abs_le.mp (h i j)).2⟩ + · rintro ⟨hl,hu⟩ i j + exact abs_le.mpr ⟨hl i j,hu i j⟩ + +lemma compact_matching_zeros (Φ : ℝ → LowerSpace N → Matrix (Fin N) (Fin N) ℝ) + (hc : Continuous (fun z : LowerSpace N × ℝ ↦ Φ z.2 z.1)) + (R : ℝ) (hb : ∀ θ ∈ Icc (0 : ℝ) 1, ∀ C, Φ θ C = 0 → ∀ i j, |C.val i j| ≤ R) : + IsCompact {z : LowerSpace N × ℝ | z.2 ∈ Icc (0 : ℝ) 1 ∧ Φ z.2 z.1 = 0} := by + apply ((compact_lower_box R).prod isCompact_Icc).of_isClosed_subset + ((isClosed_Icc.preimage continuous_snd).inter (isClosed_eq hc continuous_const)) + intro z hz + exact ⟨hb z.2 hz.1 z.1 hz.2,hz.1⟩ + +end SharpLiebThirring.MatrixFlow +namespace SharpLiebThirring.MatrixFlow +open ODEProof Set Matrix ContinuationGap +variable {N : ℕ} + +lemma terminal_zero_parameter {l r ε : ℝ} (hlr : l ≤ r) + (M : Sym N → Sym N) (hM : Continuous M) (k : Fin N → ℝ) + (u : ℝ → Fin N → ℝ) (hu : ContinuousOn u (Icc l r)) + (ho : ∀ i j, (∫ t in l..r, u t i * u t j) = if i=j then 1 else 0) + (C : Matrix (Fin N) (Fin N) ℝ) (X : ℝ → Sym N) + (hXi : X l = symDiag k) + (hXd : ∀ t ∈ Icc l r, HasDerivWithinAt X (flowRhs ε M u (C,0) t (X t)) (Icc l r) t) : + (X r + symDiag k).val = 2 • diagonal k - ε⁻¹ • (C*C.transpose) := by + have hh := flow_integral_sub hlr M hM u hu C X hXd + simp only [mul_zero,zero_smul,zero_sub,hXi] at hh + have he := congrArg (fun A : Sym N ↦ A.val) hh + change -(ε⁻¹ • (∫ t in l..r, symOuter (C*ᵥu t)).val) = (X r).val - diagonal k at he + rw [integral_outer_mulVec hlr u hu ho C] at he + have he' := sub_eq_iff_eq_add.mp he.symm + change (X r).val + diagonal k = _ + rw [he'] + simp only [two_smul] + abel + +lemma terminal_matching {l r ε : ℝ} (hlr : l ≤ r) (hε : 0 < ε) + (M : Sym N → Sym N) (L B Q : ℝ≥0) (hL : LipschitzWith L M) (hB : ∀ A, ‖M A‖ ≤ B) + (q : Sym N → ℝ) (hq : ∀ A, |q A| ≤ Q) + (g : Fin N → ℝ → ℝ) (hg : ∀ i, LocallyLipschitz (g i)) + (k : Fin N → ℝ) (hk : ∀ i, 0 < k i) (hgk : ∀ i, g i (k i) = 0) + (hc : ∀ i A, (∀ j, i ≠ j → A.val i j = 0) → (M A).val i i = q A * g i (A.val i i)) + (he : ∀ s : Fin N → ℝ, (∀ i, s i = 1 ∨ s i = -1) → ∀ A, M (symConj s A) = symConj s (M A)) + (u : ℝ → Fin N → ℝ) (hu : ContinuousOn u (Icc l r)) + (ho : ∀ i j, (∫ t in l..r, u t i * u t j) = if i=j then 1 else 0) : + ∃ (C : LowerSpace N) (X : ℝ → Sym N), X l = symDiag k ∧ X r = -symDiag k ∧ + (∀ t ∈ Icc l r, HasDerivWithinAt X (ε⁻¹ • (M (X t) - symOuter (C.val *ᵥ u t))) (Icc l r) t) ∧ + ‖C.val * C.val.transpose‖ ≤ |ε| * (2*‖k‖) + (r-l)*B := by + obtain ⟨Y,hYi,hYd,hYc⟩ := matrix_flow_exists hlr ε k u hu M L B hL hB + let Φ : ℝ → LowerSpace N → Matrix (Fin N) (Fin N) ℝ := fun θ C ↦ (Y (C.val,θ) r + symDiag k).val + have hΦc : Continuous (fun z : LowerSpace N × ℝ ↦ Φ z.2 z.1) := by + have hYr : Continuous (fun p ↦ Y p r) := hYc.comp + (continuous_id.prodMk (continuous_const (y := (⟨r,hlr,le_refl r⟩ : Icc l r)))) + exact ((hYr.comp ((continuous_subtype_val.comp continuous_fst).prodMk continuous_snd)).add continuous_const).subtype_val + have hzero (θ : ℝ) (C : LowerSpace N) (h : Φ θ C = 0) : Y (C.val,θ) r = -symDiag k := by + apply eq_neg_iff_add_eq_zero.mpr + apply Subtype.ext + exact h + have hsym (θ : ℝ) (_ : θ ∈ Icc (0 : ℝ) 1) (C : LowerSpace N) : (Φ θ C).IsHermitian := + (Y (C.val,θ) r + symDiag k).prop + have heq (θ : ℝ) (_ : θ ∈ Icc (0 : ℝ) 1) (C : LowerSpace N) + (s : Fin N → ℝ) (hs : ∀ i, s i = 1 ∨ s i = -1) : + Φ θ (rowSign s C) = signConjugate s (Φ θ C) := by + have hh := matrix_flow_equivariant hL k u Y hYi hYd s hs (he s hs) C.val θ ⟨hlr,le_refl r⟩ + change (Y ((rowSign s C).val,θ) r + symDiag k).val = (symConj s (Y (C.val,θ) r + symDiag k)).val + rw [map_add,symConj_diag s hs] + exact congrArg (fun A : Sym N ↦ (A + symDiag k).val) hh + have hinit (C : LowerSpace N) : Φ 0 C = 2 • diagonal k - ε⁻¹ • (C.val*C.val.transpose) := + terminal_zero_parameter hlr M hL.continuous k u hu ho C.val (Y (C.val,0)) (hYi _) (hYd _) + have hcomp : IsCompact {z : LowerSpace N × ℝ | z.2 ∈ Icc (0 : ℝ) 1 ∧ Φ z.2 z.1 = 0} := by + apply compact_matching_zeros Φ hΦc (max (|ε| * (2*‖k‖) + (r-l)*B) 0 + 1) + intro θ hθ C hC + exact gram_entry_bound C.val (matching_gram_norm hlr (ne_of_gt hε) M hL.continuous B hB k u hu ho C.val + hθ (Y (C.val,θ)) (hYi _) (hzero θ C hC) (hYd _)) + have hn (θ : ℝ) (_ : θ ∈ Icc (0 : ℝ) 1) (C : LowerSpace N) (hC : Φ θ C = 0) : NonzeroRows C := + matching_nonzero_rows hlr M L Q hL q hq g hg k hk hgk hc he u Y hYi hYd C.val θ (hzero θ C hC) + obtain ⟨C,hC⟩ := PathTopology.equivariant_continuation N ε k hε hk Φ hΦc.continuousOn hsym heq hinit hcomp hn + refine ⟨C,Y (C.val,1),hYi _,hzero 1 C hC,?_,?_⟩ + · intro t ht + simpa only [flowRhs,mul_one,smul_sub] using hYd (C.val,1) t ht + · exact matching_gram_norm hlr (ne_of_gt hε) M hL.continuous B hB k u hu ho C.val + ⟨zero_le_one,le_refl _⟩ (Y (C.val,1)) (hYi _) (hzero 1 C hC) (hYd _) + +end SharpLiebThirring.MatrixFlow + +end +end +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/FormCongruence.lean b/lean/OAI/Analysis/LiebThirring/FormCongruence.lean new file mode 100644 index 0000000000000000000000000000000000000000..eac18e14318a99700aac0c8ee61da52ac4c9c788 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/FormCongruence.lean @@ -0,0 +1,95 @@ +import OAI.Analysis.LiebThirring.Resolvent + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set +open scoped Topology + +lemma form_congr_ae {W : ℝ → ℝ} {u u' v v' : H1} + (hu : u.val =ᵐ[volume] u'.val) (hdu : u.grad =ᵐ[volume] u'.grad) + (hv : v.val =ᵐ[volume] v'.val) (hdv : v.grad =ᵐ[volume] v'.grad) : + schrodingerForm W u v = schrodingerForm W u' v' := by + unfold schrodingerForm + congr 1 + · apply integral_congr_ae + filter_upwards [hdu,hdv] with x hx hy + rw [hx,hy] + · apply integral_congr_ae + filter_upwards [hu,hv] with x hx hy + rw [hx,hy] + +lemma toH1_ofH1_val (u : H1) : (toH1 (ofH1 u)).val =ᵐ[volume] u.val := + u.val_memLp.coeFn_toLp + +lemma toH1_ofH1_grad (u : H1) : (toH1 (ofH1 u)).grad =ᵐ[volume] u.grad := + u.grad_memLp.coeFn_toLp + +lemma form_ofH1 (W : ℝ → ℝ) (u v : H1) : + schrodingerForm W (toH1 (ofH1 u)) (toH1 (ofH1 v)) = schrodingerForm W u v := + form_congr_ae (toH1_ofH1_val u) (toH1_ofH1_grad u) + (toH1_ofH1_val v) (toH1_ofH1_grad v) + +lemma ofH1_toH1 (u : H1C) : ofH1 (toH1 u) = u := by + apply valL_injective + rw [valL_ofH1,toLp_toH1] + +lemma form_eq_of_valLp_eq {W : ℝ → ℝ} (v u u' : H1) + (hu : u.val_memLp.toLp u.val = u'.val_memLp.toLp u'.val) : + schrodingerForm W v u = schrodingerForm W v u' := by + have he : ofH1 u = ofH1 u' := valL_injective hu + rw [← form_ofH1 W v u,← form_ofH1 W v u',he] + +/-- The usual graph characterization of the operator associated with a closed +semibounded form. The quantifier is over the entire weak H¹ domain. -/ +def IsAssociated (W : ℝ → ℝ) (A : L2C →ₗ.[ℂ] L2C) : Prop := + ∀ f g : L2C, (∃ hf : f ∈ A.domain, A ⟨f,hf⟩ = g) ↔ + ∃ u : H1, u.val_memLp.toLp u.val = f ∧ + ∀ v : H1, schrodingerForm W v u = inner ℂ (v.val_memLp.toLp v.val) g + +lemma isAssociated_iff_graph (W : ℝ → ℝ) (A : L2C →ₗ.[ℂ] L2C) : + IsAssociated W A ↔ ∀ f g : L2C, (∃ hf : f ∈ A.domain, A ⟨f,hf⟩ = g) ↔ + ∃ u : H1C, valL u = f ∧ + ∀ v : H1C, schrodingerForm W (toH1 v) (toH1 u) = inner ℂ (valL v) g := by + have he (f g : L2C) : + (∃ u : H1, u.val_memLp.toLp u.val = f ∧ + ∀ v : H1, schrodingerForm W v u = inner ℂ (v.val_memLp.toLp v.val) g) ↔ + ∃ u : H1C, valL u = f ∧ + ∀ v : H1C, schrodingerForm W (toH1 v) (toH1 u) = inner ℂ (valL v) g := by + constructor + · rintro ⟨u,hu,hq⟩ + refine ⟨ofH1 u,hu,fun v ↦ ?_⟩ + have h := hq (toH1 v) + rw [toLp_toH1] at h + rw [← form_ofH1 W (toH1 v) u,ofH1_toH1] at h + exact h + · rintro ⟨u,hu,hq⟩ + refine ⟨toH1 u,(toLp_toH1 u).trans hu,fun v ↦ ?_⟩ + have h := hq (ofH1 v) + rw [← ofH1_toH1 u,form_ofH1] at h + exact h + unfold IsAssociated + simp only [he] + +lemma negativeEigenfunction_iff_operator {W : ℝ → ℝ} {A : L2C →ₗ.[ℂ] L2C} + (hA : IsAssociated W A) (k : ℝ) (u : H1) : + IsNegativeEigenfunction W k u ↔ 0 < k ∧ + ∃ hu : u.val_memLp.toLp u.val ∈ A.domain, + A ⟨u.val_memLp.toLp u.val,hu⟩ = (-(k^2 : ℝ) : ℂ) • u.val_memLp.toLp u.val := by + constructor + · rintro ⟨hk,hq⟩ + refine ⟨hk,(hA _ _).mpr ⟨u,rfl,fun v ↦ ?_⟩⟩ + rw [inner_smul_right] + simpa only [l2Pairing_eq_inner] using hq v + · rintro ⟨hk,hu⟩ + obtain ⟨u',he,hq⟩ := (hA _ _).mp hu + refine ⟨hk,fun v ↦ ?_⟩ + rw [form_eq_of_valLp_eq v u u' he.symm,hq,inner_smul_right,l2Pairing_eq_inner] + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/FreeForm.lean b/lean/OAI/Analysis/LiebThirring/FreeForm.lean new file mode 100644 index 0000000000000000000000000000000000000000..1de4b0cca34934281b417273daa51cbe2a19bcdb --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/FreeForm.lean @@ -0,0 +1,55 @@ +import OAI.Analysis.LiebThirring.CompactAlternative + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set +open scoped Topology + +/-- Positive free form `∫|u'|² + a∫|u|²` on the full H¹ graph. -/ +def freeFormMap (a : ℝ) : H1C →L[ℂ] H1C := + gradL.adjoint.comp gradL + (a:ℂ) • (valL.adjoint.comp valL) + +lemma freeFormMap_inner (a : ℝ) (u v : H1C) : + inner ℂ u (freeFormMap a v) = + inner ℂ (gradL u) (gradL v)+(a:ℂ)*inner ℂ (valL u) (valL v) := by + change inner ℂ u (gradL.adjoint (gradL v)+(a:ℂ) • valL.adjoint (valL v)) = _ + rw [inner_add_right,inner_smul_right u (valL.adjoint (valL v)) (a:ℂ), + ContinuousLinearMap.adjoint_inner_right,ContinuousLinearMap.adjoint_inner_right] + +lemma freeFormMap_coercive {a : ℝ} (_ha : 0 < a) (u : H1C) : + min 1 a * ‖u‖^2 ≤ (inner ℂ u (freeFormMap a u)).re := by + rw [freeFormMap_inner,Complex.add_re,Complex.mul_re,Complex.ofReal_re, + Complex.ofReal_im,zero_mul,sub_zero] + have hi (v : L2C) : (inner ℂ v v).re = ‖v‖^2 := (norm_sq_eq_re_inner (𝕜 := ℂ) v).symm + rw [hi,hi,h1_norm_sq] + have h1 := mul_le_mul_of_nonneg_right (min_le_left (1:ℝ) a) (sq_nonneg ‖gradL u‖) + have h2 := mul_le_mul_of_nonneg_right (min_le_right (1:ℝ) a) (sq_nonneg ‖valL u‖) + nlinarith + +lemma freeFormMap_bijective {a : ℝ} (ha : 0 < a) : Function.Bijective (freeFormMap a) := + coercive_bijective _ (lt_min (by norm_num) ha) (freeFormMap_coercive ha) + +def freeFormEquiv {a : ℝ} (ha : 0 < a) : H1C ≃L[ℂ] H1C := + ContinuousLinearEquiv.ofBijective (freeFormMap a) + (LinearMap.ker_eq_bot.mpr (freeFormMap_bijective ha).1) + (LinearMap.range_eq_top.mpr (freeFormMap_bijective ha).2) + +/-- Form of `H+a` on H¹. -/ +def energyFormMap {W : ℝ → ℝ} (d : PotentialData W) (a : ℝ) : H1C →L[ℂ] H1C := + freeFormMap a-(weightedL d).adjoint.comp (weightedL d) + +lemma energyFormMap_inner {W : ℝ → ℝ} (d : PotentialData W) (a : ℝ) (u v : H1C) : + inner ℂ u (energyFormMap d a v) = + schrodingerForm W (toH1 u) (toH1 v)+(a:ℂ)*inner ℂ (valL u) (valL v) := by + change inner ℂ u (freeFormMap a v-(weightedL d).adjoint (weightedL d v)) = _ + rw [inner_sub_right,freeFormMap_inner,ContinuousLinearMap.adjoint_inner_right,form_eq_inner] + ring + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/FreeLocus.lean b/lean/OAI/Analysis/LiebThirring/FreeLocus.lean new file mode 100644 index 0000000000000000000000000000000000000000..bdbfbfa36983729aed45f48f41ff081e0725dc1f --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/FreeLocus.lean @@ -0,0 +1,371 @@ +import OAI.Analysis.LiebThirring.InitialOrbit + +namespace OAI + +universe u116 u117 u118 u119 u120 u121 u122 u123 u124 u125 u126 u127 u128 u129 u130 u131 u132 u133 u134 u135 + +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Finset +section +open Set Finset Filter +open Set Finset + +end + +section + + +/-! Analytic compactness and free-locus facts for the PL continuation proof. -/ + +open Set Finset +namespace SharpLiebThirring.PLParity + +section Compactness +variable {E : Type u116} {V : Type u117} [TopologicalSpace E] [NormedAddCommGroup V] + +/-- On a compact domain, sufficiently small values lie in any open neighborhood +of the zero set. This is not an existence assumption about zeros. -/ +lemma small_norm_near_zeros {C U : Set E} (hC : IsCompact C) (hU : IsOpen U) + (f : E → V) (hf : ContinuousOn f C) (hzero : ∀ x ∈ C, f x = 0 → x ∈ U) : + ∃ ε > 0, ∀ x ∈ C, ‖f x‖ < ε → x ∈ U := by + by_cases hn : (C \ U).Nonempty + · obtain ⟨x, hx, hmin⟩ := (hC.diff hU).exists_isMinOn hn (hf.norm.mono sdiff_subset) + have hp : 0 < ‖f x‖ := norm_pos_iff.mpr (fun h ↦ hx.2 (hzero x hx.1 h)) + refine ⟨‖f x‖, hp, ?_⟩ + intro y hy hfy + by_contra hu + exact (not_lt_of_ge (hmin ⟨hy, hu⟩)) hfy + · refine ⟨1, by norm_num, ?_⟩ + intro x hx _ + by_contra hu + exact hn ⟨x, hx, hu⟩ +end Compactness + +section ConvexError +variable {ι : Type u118} {V : Type u119} [Fintype ι] [NormedAddCommGroup V] [NormedSpace ℝ V] + +lemma norm_of_convex_zero (w : ι → ℝ) (hw : ∀ i, 0 ≤ w i) (hs : ∑ i, w i = 1) + (a : ι → V) (ha : ∑ i, w i • a i = 0) (z : V) (ε : ℝ) + (he : ∀ i, ‖a i - z‖ ≤ ε) : ‖z‖ ≤ ε := by + have hid : ∑ i, w i • (a i - z) = -z := by + simp only [smul_sub, Finset.sum_sub_distrib, ha, ← Finset.sum_smul, hs, one_smul, zero_sub] + calc + ‖z‖ = ‖∑ i, w i • (a i - z)‖ := by rw [hid, norm_neg] + _ ≤ ∑ i, ‖w i • (a i - z)‖ := norm_sum_le _ _ + _ ≤ ∑ i, w i * ε := by + apply Finset.sum_le_sum + intro i _ + rw [norm_smul, Real.norm_eq_abs, abs_of_nonneg (hw i)] + exact mul_le_mul_of_nonneg_left (he i) (hw i) + _ = ε := by rw [← Finset.sum_mul, hs, one_mul] + +lemma norm_of_approximate_convex_zero (w : ι → ℝ) (hw : ∀ i, 0 ≤ w i) + (hs : ∑ i, w i = 1) (a b : ι → V) (ha : ∑ i, w i • a i = 0) + (z : V) (ε δ : ℝ) (he : ∀ i, dist (a i) (b i) ≤ ε) + (hd : ∀ i, dist (b i) z ≤ δ) : ‖z‖ ≤ ε + δ := by + apply norm_of_convex_zero w hw hs a ha z (ε + δ) + intro i + rw [← dist_eq_norm] + exact (dist_triangle _ _ _).trans (add_le_add (he i) (hd i)) +end ConvexError + +section FreeLocus +variable {G : Type u120} {E : Type u121} [Group G] [MulAction G E] + +def freeLocus : Set E := {x | ∀ g : G, g • x = x → g = 1} + +lemma freeLocus_smul (g : G) {x : E} (hx : x ∈ freeLocus (G := G)) : + g • x ∈ freeLocus (G := G) := by + intro s hs + have hfix : (g⁻¹ * s * g) • x = x := by + rw [mul_smul, mul_smul, hs, inv_smul_smul] + have he := hx _ hfix + have hh := congrArg (fun a : G ↦ g * a * g⁻¹) he + simpa only [mul_assoc, mul_inv_cancel, mul_one, mul_inv_cancel_left] using hh + +def freeSubMulAction : SubMulAction G E where + carrier := freeLocus (G := G) + smul_mem' g _ hx := freeLocus_smul g hx + +instance : IsCancelSMul G (freeSubMulAction (G := G) (E := E)) where + right_cancel' g h x he := by + have he' : g • x.val = h • x.val := congrArg Subtype.val he + have hh : (h⁻¹ * g) • x.val = x.val := by + rw [mul_smul, he', inv_smul_smul] + exact (inv_mul_eq_one.mp (x.prop _ hh)).symm + +variable [TopologicalSpace E] [T2Space E] [ContinuousConstSMul G E] [Finite G] + +lemma isOpen_freeLocus : IsOpen (freeLocus (G := G) (E := E)) := by + classical + have hset : freeLocus (G := G) (E := E) = ⋂ g : {g : G // g ≠ 1}, {x | g.val • x ≠ x} := by + ext x + simp only [freeLocus, mem_ofPred_eq, mem_iInter] + constructor + · intro h ⟨g, hg⟩ he + exact hg (h g he) + · intro h g hg + by_contra hn + exact h ⟨g, hn⟩ hg + rw [hset] + apply isOpen_iInter_of_finite + intro g + exact (isClosed_eq (continuous_const_smul g.val) continuous_id).isOpen_compl + +end FreeLocus +section FreeTube +variable {G : Type u122} {E : Type u123} [Group G] [MulAction G E] [MetricSpace E] + [ContinuousConstSMul G E] [Finite G] + +lemma compact_free_tube {K : Set E} + (hK : IsCompact K) (hfree : K ⊆ freeLocus (G := G)) : + ∃ r > 0, Metric.cthickening r K ⊆ freeLocus (G := G) := + hK.exists_cthickening_subset_open isOpen_freeLocus hfree + +end FreeTube +end SharpLiebThirring.PLParity + +namespace SharpLiebThirring.CubeFlags +open Finset SharpLiebThirring.PLParity + +def Flag.combination {n : ℕ} (h : ℝ) (F : Flag n) (w : Fin (n + 1) → ℝ) : Fin n → ℝ := + h • ∑ k, w k • F.point k + +lemma Flag.combination_neighbor {n : ℕ} [NeZero n] (h : ℝ) (F : Flag n) + (w : Fin (n + 1) → ℝ) (j : Fin (n + 1)) (hj : w j = 0) : + (F.neighbor j).combination h w = F.combination h w := by + unfold combination + congr 1 + apply Finset.sum_congr rfl + intro k _ + by_cases hk : k = j + · simp only [hk, hj, zero_smul] + · have he : (F.neighbor j).point k = F.point k := by + ext i + simp only [point, congrFun (F.neighbor_vertex j k hk) i] + rw [he] + +lemma Flag.dist_combination_scaled_center {n : ℕ} (h : ℝ) (hh : 0 ≤ h) (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) : + dist (F.combination h w) (h • F.center) ≤ h / 2 := by + rw [combination, dist_scale h hh] + nlinarith [F.dist_combination_center w hw hs] + +lemma Flag.dist_combination_gridPoint {n : ℕ} (h : ℝ) (hh : 0 ≤ h) (F : Flag n) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) (k : Fin (n + 1)) : + dist (F.combination h w) (gridPoint h (F.vertex k)) ≤ h := by + rw [gridPoint_vertex, combination, dist_scale h hh] + nlinarith [F.dist_combination_point w hw hs k] + +lemma nearCylinder_combination_cthickening {n : ℕ} (K : Set (Fin n → ℝ)) (h r : ℝ) + (hh : 0 ≤ h) (t : Fin n) (m : ℕ) {F : Flag n} (hF : F ∈ nearCylinder K h r t m) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) : + F.combination h w ∈ Metric.cthickening (r + h / 2) K := by + obtain ⟨x, hx, hd⟩ := hF.1 + apply Metric.mem_cthickening_of_dist_le _ x _ K hx + calc + _ ≤ dist (F.combination h w) (h • F.center) + dist (h • F.center) x := dist_triangle _ _ _ + _ ≤ h / 2 + r := add_le_add (F.dist_combination_scaled_center h hh w hw hs) hd.le + _ = r + h / 2 := add_comm _ _ + +lemma cellHit_weights {n : ℕ} (H : Subgroup (Signs n)) (D : SubMulAction H (Flag n)) + {V : Type u124} [NormedAddCommGroup V] [NormedSpace ℝ V] + (a : vertices H D → V) (F : D) (j : Fin (n + 1)) (hj : cellHit H D a F.val j) : + ∃ w : Fin (n + 1) → ℝ, (∀ k, 0 ≤ w k) ∧ ∑ k, w k = 1 ∧ w j = 0 ∧ + ∑ k, w k • a (flagVertex H D F k) = 0 := by + obtain ⟨w,he,hj,hw⟩ := hj + refine ⟨w,hw,?_,hj,?_⟩ + · exact congrArg Prod.fst he + · simpa only [augmentedMap_apply, extendValues_at] using congrArg Prod.snd he + +/-- A PL zero gives a small value of the continuous map at its geometric point. -/ +lemma norm_at_mesh_zero {n : ℕ} (H : Subgroup (Signs n)) (D : SubMulAction H (Flag n)) + {V : Type u125} [NormedAddCommGroup V] [NormedSpace ℝ V] + (a : vertices H D → V) (f : (Fin n → ℝ) → V) (h ε δ : ℝ) (hh : 0 ≤ h) + (C : Set (Fin n → ℝ)) + (ha : ∀ z : vertices H D, dist (a z) (f (gridPoint h z.val)) ≤ ε) + (hf : ∀ x ∈ C, ∀ y ∈ C, dist x y ≤ h → dist (f x) (f y) ≤ δ) + (F : D) (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) + (hz : ∑ k, w k • a (flagVertex H D F k) = 0) + (hC : F.val.combination h w ∈ C) + (hp : ∀ k, gridPoint h (F.val.vertex k) ∈ C) : + ‖f (F.val.combination h w)‖ ≤ ε + δ := by + apply norm_of_approximate_convex_zero w hw hs (fun k ↦ a (flagVertex H D F k)) + (fun k ↦ f (gridPoint h (F.val.vertex k))) hz (f (F.val.combination h w)) ε δ + · intro k + exact ha (flagVertex H D F k) + · intro k + exact hf _ (hp k) _ hC (by + rw [dist_comm] + exact F.val.dist_combination_gridPoint h hh w hw hs k) + +lemma neighbor_near_centers_of_combination {n : ℕ} [NeZero n] + (K : Set (Fin n → ℝ)) (h r : ℝ) (hh : 0 ≤ h) (hhr : h < r) + (F : Flag n) (j : Fin (n + 1)) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) (hj : w j = 0) + (hx : ∃ x ∈ K, dist (F.combination h w) x < r / 2) : + ∃ x ∈ K, dist (h • (F.neighbor j).center) x < r := by + obtain ⟨x,hx,hd⟩ := hx + refine ⟨x,hx,?_⟩ + have hc := (F.neighbor j).dist_combination_scaled_center h hh w hw hs + rw [F.combination_neighbor h w j hj, dist_comm] at hc + have ht := dist_triangle (h • (F.neighbor j).center) (F.combination h w) x + linarith + +lemma Flag.combination_time_boundary {n : ℕ} [NeZero n] (F : Flag n) (h : ℝ) + (t : Fin n) (ht : (F.order.symm t).val = n - 1) + (w : Fin (n + 1) → ℝ) (hs : ∑ k, w k = 1) (hz : w (Fin.last n) = 0) : + F.combination h w t = h * ((F.base t : ℝ) + if F.corner t then 1 else 0) := by + change h * (∑ k, w k • F.point k) t = _ + rw [Finset.sum_apply] + have he : (∑ k, w k * F.point k t) = + ∑ k, w k * ((F.base t : ℝ) + if F.corner t then 1 else 0) := by + apply Finset.sum_congr rfl + intro k _ + by_cases hk : k = Fin.last n + · simp only [hk,hz,zero_mul] + · rw [F.point_time_boundary t ht k hk] + simp only [Pi.smul_apply, smul_eq_mul] + rw [he, ← Finset.sum_mul, hs, one_mul] + +end SharpLiebThirring.CubeFlags +end + +namespace SharpLiebThirring.CubeFlags +open Finset SharpLiebThirring.PLParity + +lemma Flag.combination_eq_sum_gridPoint {n : ℕ} (h : ℝ) (F : Flag n) + (w : Fin (n + 1) → ℝ) : + F.combination h w = ∑ k, w k • gridPoint h (F.vertex k) := by + simp only [combination, gridPoint_vertex, Finset.smul_sum, smul_comm h] + +lemma Signs.smul_sum_real {n : ℕ} {ι : Type u126} [Fintype ι] (s : Signs n) + (w : ι → ℝ) (x : ι → Fin n → ℝ) : + s • (∑ i, w i • x i) = ∑ i, w i • (s • x i) := by + change s.linearIsometry (∑ i, w i • x i) = _ + rw [map_sum] + exact Finset.sum_congr rfl (fun i _ ↦ map_smul s.linearIsometry (w i) (x i)) + +lemma Flag.combination_smul {n : ℕ} (s : Signs n) (h : ℝ) (F : Flag n) + (w : Fin (n + 1) → ℝ) : (s • F).combination h w = s • F.combination h w := by + rw [Flag.combination_eq_sum_gridPoint, Flag.combination_eq_sum_gridPoint, s.smul_sum_real] + apply Finset.sum_congr rfl + intro k _ + rw [F.vertex_smul, gridPoint_smul] + +lemma sum_affine_linear {ι : Type u127} {E : Type u128} {V : Type u129} [Fintype ι] + [AddCommGroup E] [Module ℝ E] [AddCommGroup V] [Module ℝ V] + (L : E →ₗ[ℝ] V) (w : ι → ℝ) (hs : ∑ i, w i = 1) (x : ι → E) (q : E) : + (∑ i, w i • L (x i - q)) = L ((∑ i, w i • x i) - q) := by + simp only [map_sub, map_sum, map_smul, smul_sub, Finset.sum_sub_distrib, + ← Finset.sum_smul, hs, one_smul] + +lemma cellHit_of_weights {n : ℕ} (H : Subgroup (Signs n)) (D : SubMulAction H (Flag n)) + {V : Type u130} [NormedAddCommGroup V] [NormedSpace ℝ V] + (a : vertices H D → V) (F : D) (j : Fin (n + 1)) + (w : Fin (n + 1) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) + (hj : w j = 0) (hz : ∑ k, w k • a (flagVertex H D F k) = 0) : cellHit H D a F.val j := by + refine ⟨w,?_,hj,hw⟩ + apply Prod.ext + · exact hs + · simpa only [augmentedMap_apply, extendValues_at] using hz + +lemma affine_sum_on_facet {ι : Type u131} {E : Type u132} {V : Type u133} [Fintype ι] [DecidableEq ι] + [AddCommGroup E] [Module ℝ E] [AddCommGroup V] [Module ℝ V] + (L : E →ₗ[ℝ] V) (w : ι → ℝ) (hs : ∑ i, w i = 1) + (j : ι) (hj : w j = 0) (x : ι → E) (q : E) (a : ι → V) + (ha : ∀ k, k ≠ j → a k = L (x k - q)) : + ∑ k, w k • a k = L ((∑ k, w k • x k) - q) := by + rw [← sum_affine_linear L w hs x q] + apply Finset.sum_congr rfl + intro k _ + by_cases hk : k = j + · simp only [hk, hj, zero_smul] + · rw [ha k hk] + +lemma mesh_affine_zero_point {d : ℕ} (H : Subgroup (Signs (d + 1))) + {V : Type u134} [NormedAddCommGroup V] [NormedSpace ℝ V] + (ρ : H →* (V ≃ₗ[ℝ] V)) (L : (Fin d → ℝ) ≃ₗ[ℝ] V) + (F : Flag (d + 1)) (j : Fin (d + 2)) (h : ℝ) (s : H) (q : Fin d → ℝ) + (w : Fin (d + 2) → ℝ) (hs : ∑ k, w k = 1) (hj : w j = 0) + (a : Fin (d + 2) → V) (hz : ∑ k, w k • a k = 0) + (ha : ∀ k, k ≠ j → a k = ρ s (L (spatial (s⁻¹ • gridPoint h (F.vertex k)) - q))) + (ht : F.combination h w (Fin.last d) = 0) : + F.combination h w = s • embedSpatial q := by + have he := affine_sum_on_facet (L.trans (ρ s)).toLinearMap w hs j hj + (fun k ↦ spatial (s⁻¹ • gridPoint h (F.vertex k))) q a ha + rw [hz] at he + have hq : (∑ k, w k • spatial (s⁻¹ • gridPoint h (F.vertex k))) = q := by + apply sub_eq_zero.mp + apply (L.trans (ρ s)).injective + change (L.trans (ρ s)) _ = (L.trans (ρ s)) 0 + rw [map_zero] + exact he.symm + have hsum : spatial (s⁻¹ • F.combination h w) = q := by + rw [F.combination_eq_sum_gridPoint] + rw [Subgroup.smul_def, Signs.smul_sum_real, map_sum] + simpa only [map_smul, Subgroup.smul_def] using hq + have ht' : (s⁻¹ • F.combination h w) (Fin.last d) = 0 := + s⁻¹.val.smul_time_zero _ ht + have hx : s⁻¹ • F.combination h w = embedSpatial q := by + rw [← hsum] + exact (embed_spatial_of_time_zero _ ht').symm + simpa only [smul_inv_smul] using congrArg (fun x ↦ s • x) hx + +lemma model_seed_hit {d : ℕ} (H : Subgroup (Signs (d + 1))) + (D : SubMulAction H (Flag (d + 1))) + {V : Type u135} [NormedAddCommGroup V] [NormedSpace ℝ V] + (ρ : H →* (V ≃ₗ[ℝ] V)) (L : (Fin d → ℝ) ≃ₗ[ℝ] V) + (p q : Fin d → ℝ) (R h : ℝ) (hR : 0 < R) (hh : 0 < h) (hhr : 2*h < R) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • embedSpatial p) (k • embedSpatial p)) + (F : D) (hF : F.val = bottomSeed h p) (a : vertices H D → V) + (ha : ∀ k, k ≠ Fin.last (d + 1) → + a (flagVertex H D F k) = affineOrbitModel H ρ L (embedSpatial p) R q (gridPoint h (F.val.vertex k))) + (w : Fin (d + 2) → ℝ) (hw : ∀ k, 0 ≤ w k) (hs : ∑ k, w k = 1) + (hj : w (Fin.last (d + 1)) = 0) + (he : ∑ k, w k • gridPoint h (F.val.vertex k) = embedSpatial q) : + cellHit H D a F.val (Fin.last (d + 1)) := by + apply cellHit_of_weights H D a F _ w hw hs hj + have hv (k : Fin (d + 2)) : ballLabel (G := H) (embedSpatial p) R (gridPoint h (F.val.vertex k)) = 1 := by + apply ballLabel_eq (embedSpatial p) R hR hsep + rw [one_smul, hF, gridPoint_vertex] + exact (bottomSeed_dist_point h hh p k).trans_lt hhr + have haf (k : Fin (d + 2)) (hk : k ≠ Fin.last (d + 1)) : + a (flagVertex H D F k) = L (spatial (gridPoint h (F.val.vertex k)) - q) := by + rw [ha k hk] + simp only [affineOrbitModel, hv, inv_one, one_smul, map_one] + rfl + rw [affine_sum_on_facet L.toLinearMap w hs _ hj + (fun k ↦ spatial (gridPoint h (F.val.vertex k))) q _ haf] + have hsp := congrArg spatial he + simp only [map_sum, map_smul, spatial_embed] at hsp + rw [hsp, sub_self, map_zero] + +lemma bottom_facet_unique {d : ℕ} (h : ℝ) (hh : h ≠ 0) (p q : Fin d → ℝ) + (s : Signs (d + 1)) (hst : s.val (Fin.last d) = false) + (G : Flag (d + 1)) (hGb : G.base (Fin.last d) = 0) (hGc : G.corner (Fin.last d) = false) + (w z : Fin (d + 2) → ℝ) (hw : ∀ k, 0 ≤ w k) + (hwp : ∀ k, k ≠ Fin.last (d + 1) → 0 < w k) (hz : ∀ k, 0 ≤ z k) + (hsw : ∑ k, w k = 1) (hsz : ∑ k, z k = 1) + (he : (bottomSeed h p).combination h w = embedSpatial q) + (hg : G.combination h z = s • embedSpatial q) : G = s • bottomSeed h p := by + have hx : (s • bottomSeed h p).combination h w = G.combination h z := by + rw [Flag.combination_smul, he, hg] + have hx' := (smul_right_injective (Fin (d + 1) → ℝ) hh) hx + apply Eq.symm + apply Flag.eq_of_facet_combination _ _ (Fin.last d) _ _ _ w z hw hwp hz hsw hsz hx' + · simp [Flag.smul_def, Flag.reflect, bottomSeed] + · simp [Flag.smul_def, Flag.reflect, bottomSeed, hst, hGb] + · simp [Flag.smul_def, Flag.reflect, bottomSeed, hst, hGc] + +end SharpLiebThirring.CubeFlags + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/Gamma.lean b/lean/OAI/Analysis/LiebThirring/Gamma.lean new file mode 100644 index 0000000000000000000000000000000000000000..41c3fc323ba72637a90ea55185e704bd74a969f5 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/Gamma.lean @@ -0,0 +1,126 @@ +import OAI.Analysis.LiebThirring.IntervalAction + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.ConstantProof +open MeasureTheory Set Filter +open scoped Topology + +def betaAction (σ : ℝ) : ℝ := ∫ t in (-1 : ℝ)..1, (1-t^2)^σ + +lemma real_beta_symmetric {σ : ℝ} (hσ : 0 < σ) : + (∫ t in (0 : ℝ)..1, t^σ*(1-t)^σ) = + Real.Gamma (σ+1)^2 / Real.Gamma (2*(σ+1)) := by + have h := Complex.betaIntegral_eq_Gamma_mul_div ((σ+1 : ℝ) : ℂ) ((σ+1 : ℝ) : ℂ) + (by simpa using (show 0 < σ+1 by linarith)) (by simpa using (show 0 < σ+1 by linarith)) + have hi : Complex.betaIntegral ((σ+1 : ℝ) : ℂ) ((σ+1 : ℝ) : ℂ) = + ((∫ t in (0 : ℝ)..1, t^σ*(1-t)^σ : ℝ) : ℂ) := by + rw [Complex.betaIntegral,← intervalIntegral.integral_ofReal] + apply intervalIntegral.integral_congr + intro x hx + rw [uIcc_of_le (by norm_num)] at hx + push_cast + rw [add_sub_cancel_right,← Complex.ofReal_cpow hx.1, + show (1 : ℂ)-(x : ℂ) = ((1-x : ℝ) : ℂ) by push_cast; rfl,← Complex.ofReal_cpow (sub_nonneg.mpr hx.2)] + rw [hi,Complex.Gamma_ofReal,← Complex.ofReal_add, + Complex.Gamma_ofReal] at h + have hh : (σ+1)+(σ+1) = 2*(σ+1) := by ring + rw [hh] at h + have hh' : (∫ t in (0 : ℝ)..1, t^σ*(1-t)^σ) = + Real.Gamma (σ+1)*Real.Gamma (σ+1) / Real.Gamma (2*(σ+1)) := by exact_mod_cast h + simpa only [pow_two] using hh' + +lemma betaAction_eq_beta {σ : ℝ} (_hσ : 0 < σ) : + betaAction σ = 2 * (4 : ℝ)^σ * (∫ t in (0 : ℝ)..1, t^σ*(1-t)^σ) := by + have h := intervalIntegral.integral_comp_mul_add + (fun x : ℝ ↦ (1-x^2)^σ) (a := 0) (b := 1) (c := (2 : ℝ)) (by norm_num) (-1) + norm_num at h + have hi : (∫ t in (0 : ℝ)..1, (1-(2*t-1)^2)^σ) = + (4 : ℝ)^σ * (∫ t in (0 : ℝ)..1, t^σ*(1-t)^σ) := by + rw [← intervalIntegral.integral_const_mul] + apply intervalIntegral.integral_congr + intro x hx + rw [uIcc_of_le (by norm_num)] at hx + dsimp only + rw [show 1-(2*x-1)^2 = 4*(x*(1-x)) by ring, + Real.mul_rpow (by norm_num) (mul_nonneg hx.1 (sub_nonneg.mpr hx.2)), + Real.mul_rpow hx.1 (sub_nonneg.mpr hx.2)] + rw [show (fun x : ℝ ↦ (1-(2*x+ -1)^2)^σ) = fun x ↦ (1-(2*x-1)^2)^σ by ext; congr 2] at h + rw [hi] at h + unfold betaAction + linarith + +lemma betaAction_pos {σ : ℝ} (hσ : 0 < σ) : 0 < betaAction σ := by + rw [betaAction_eq_beta hσ,real_beta_symmetric hσ] + have hG := Real.Gamma_pos_of_pos (show 0 < σ+1 by linarith) + have hG' := Real.Gamma_pos_of_pos (show 0 < 2*(σ+1) by linarith) + positivity + +end SharpLiebThirring.ConstantProof +namespace SharpLiebThirring.ConstantProof +open MeasureTheory Set Filter +open scoped Topology + +lemma betaAction_eq_Gamma {σ : ℝ} (hσ : 0 < σ) : + betaAction σ = Real.sqrt Real.pi * Real.Gamma (σ+1) / Real.Gamma (σ+3/2) := by + have h := Real.Gamma_mul_Gamma_add_half (σ+1) + have he : σ+1+1/2 = σ+3/2 := by ring + rw [he] at h + have hp : (2 : ℝ)*4^σ*2^(1-2*(σ+1)) = 1 := by + have hh : (2 : ℝ)*4^σ*2^(1-2*(σ+1)) = 2^(1+2*σ+(1-2*(σ+1))) := by + rw [Real.rpow_add (by norm_num),Real.rpow_add (by norm_num),Real.rpow_one, + Real.rpow_mul (by norm_num),Real.rpow_two] + norm_num + rw [hh,show 1+2*σ+(1-2*(σ+1)) = 0 by ring,Real.rpow_zero] + have hg' : Real.Gamma (σ+3/2) ≠ 0 := (Real.Gamma_pos_of_pos (by linarith : 0 < σ+3/2)).ne' + have hg'' : Real.Gamma (2*(σ+1)) ≠ 0 := (Real.Gamma_pos_of_pos (by positivity : 0 < 2*(σ+1))).ne' + rw [betaAction_eq_beta hσ,real_beta_symmetric hσ] + apply (eq_div_iff hg').mpr + calc + (2*4^σ*(Real.Gamma (σ+1)^2/Real.Gamma (2*(σ+1))))*Real.Gamma (σ+3/2) = + (Real.Gamma (σ+1)/Real.Gamma (2*(σ+1)))*(2*4^σ*(Real.Gamma (σ+1)*Real.Gamma (σ+3/2))) := by ring + _ = (Real.Gamma (σ+1)/Real.Gamma (2*(σ+1)))*(2*4^σ*(Real.Gamma (2*(σ+1))*2^(1-2*(σ+1))*Real.sqrt Real.pi)) := by rw [h] + _ = (Real.Gamma (σ+1)/Real.Gamma (2*(σ+1)))*(Real.Gamma (2*(σ+1))*Real.sqrt Real.pi) := by + congr 1 + calc + _ = Real.Gamma (2*(σ+1))*Real.sqrt Real.pi*(2*4^σ*2^(1-2*(σ+1))) := by ring + _ = _ := by rw [hp,mul_one] + _ = _ := by field_simp + +lemma boundary_action_scaling {σ k : ℝ} (_hσ : 0 < σ) (hk : 0 < k) : + (∫ s in -k..k, (k^2-s^2)^σ) = k^(1+2*σ)*betaAction σ := by + have hi := intervalIntegral.integral_comp_mul_left (fun s : ℝ ↦ (k^2-s^2)^σ) + (a := -1) (b := 1) (c := k) hk.ne' + simp only [mul_neg_one,mul_one] at hi + have hj : (∫ s in (-1 : ℝ)..1, (k^2-(k*s)^2)^σ) = k^(2*σ)*betaAction σ := by + rw [betaAction,← intervalIntegral.integral_const_mul] + apply intervalIntegral.integral_congr + intro s hs + rw [uIcc_of_le (by norm_num)] at hs + dsimp only + have hs' : 0 ≤ 1-s^2 := by nlinarith [hs.1,hs.2] + rw [show k^2-(k*s)^2 = k^2*(1-s^2) by ring,Real.mul_rpow (sq_nonneg _) hs', + ← Real.rpow_two k,← Real.rpow_mul hk.le] + rw [hj] at hi + have he : k^(1+2*σ) = k*k^(2*σ) := by rw [Real.rpow_add hk,Real.rpow_one] + rw [he] + simp only [smul_eq_mul] at hi + field_simp [hk.ne'] at hi + nlinarith [hi] + +lemma young_over_beta {σ : ℝ} (hσ : 0 < σ) : + (σ^σ/(1+σ)^(1+σ))/betaAction σ = + (σ/(σ+1))^σ*Real.Gamma (σ+3/2)/(Real.sqrt Real.pi*Real.Gamma (σ+2)) := by + have hg := Real.Gamma_add_one (show σ+1 ≠ 0 by linarith) + rw [show σ+1+1 = σ+2 by ring] at hg + rw [betaAction_eq_Gamma hσ,Real.div_rpow hσ.le (by linarith : 0 ≤ σ+1), + show 1+σ = σ+1 by ring,Real.rpow_add (by linarith : 0 < σ+1),Real.rpow_one,hg] + field_simp + +end SharpLiebThirring.ConstantProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/GenericPosition.lean b/lean/OAI/Analysis/LiebThirring/GenericPosition.lean new file mode 100644 index 0000000000000000000000000000000000000000..81ed2f990f9a9d27f793acffb20f29e1754876cb --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/GenericPosition.lean @@ -0,0 +1,603 @@ +import OAI.Analysis.LiebThirring.FiniteParity + +namespace OAI + +universe u68 u69 u70 u71 u72 u73 u74 u75 u76 u77 u78 u79 u80 u81 u82 u83 u84 u85 u86 u87 u88 u89 u90 u91 u92 u93 u94 u191 u192 + +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Finset + + +section + + +/-! Generic vertex positions for the piecewise-linear continuation argument. -/ + +open Set Finset Filter +namespace SharpLiebThirring.PLParity + +variable {V : Type u68} [NormedAddCommGroup V] [NormedSpace ℝ V] [FiniteDimensional ℝ V] + +omit [FiniteDimensional ℝ V] in +lemma dense_compl_proper_submodule (S : Submodule ℝ V) (hS : S ≠ ⊤) : + Dense (S : Set V)ᶜ := by + apply interior_eq_empty_iff_dense_compl.mp + by_contra h + exact hS (S.eq_top_of_nonempty_interior' (Set.nonempty_iff_ne_empty.mpr h)) + +omit [FiniteDimensional ℝ V] in +lemma dense_linearIndependent_fin (n : ℕ) (hn : n ≤ Module.finrank ℝ V) : + Dense {v : Fin n → V | LinearIndependent ℝ v} := by + induction n with + | zero => + have : {v : Fin 0 → V | LinearIndependent ℝ v} = Set.univ := by + ext v + simp only [Set.mem_ofPred_eq, Set.mem_univ, iff_true] + exact linearIndependent_empty_type + rw [this] + exact dense_univ + | succ n ih => + rw [Metric.dense_iff] + intro v ε hε + obtain ⟨w, hw, hwε⟩ := (ih (by omega)).exists_dist_lt (Fin.tail v) hε + let S : Submodule ℝ V := Submodule.span ℝ (Set.range w) + have hS : S ≠ ⊤ := by + intro he + have hd := finrank_span_eq_card hw + change Module.finrank ℝ S = Fintype.card (Fin n) at hd + rw [he, finrank_top, Fintype.card_fin] at hd + omega + obtain ⟨x, hx, hxε⟩ := (dense_compl_proper_submodule S hS).exists_dist_lt (v 0) hε + refine ⟨Fin.cons x w, ?_, linearIndependent_finCons.mpr ⟨hw, hx⟩⟩ + apply (dist_pi_lt_iff hε).mpr + intro i + refine Fin.cases ?_ (fun j ↦ ?_) i + · simpa [dist_comm] using hxε + · simpa [Fin.tail, dist_comm] using (dist_pi_lt_iff hε).mp hwε j + +omit [FiniteDimensional ℝ V] in +lemma dense_linearIndependent {ι : Type u69} [Fintype ι] + (hn : Fintype.card ι ≤ Module.finrank ℝ V) : + Dense {v : ι → V | LinearIndependent ℝ v} := by + classical + rw [Metric.dense_iff] + intro v ε hε + let e := Fintype.equivFin ι + obtain ⟨w, hw, hwε⟩ := (dense_linearIndependent_fin (Fintype.card ι) hn).exists_dist_lt + (v ∘ e.symm) hε + refine ⟨w ∘ e, ?_, hw.comp e e.injective⟩ + apply (dist_pi_lt_iff hε).mpr + intro i + simpa [Function.comp_def, dist_comm] using (dist_pi_lt_iff hε).mp hwε (e i) + +/-- Put a new extension vector before the previous extension vectors. -/ +def sumFinSuccEmbedding (ι : Type u70) (n : ℕ) : + ι ⊕ Fin (n + 1) ↪ Option (ι ⊕ Fin n) where + toFun := Sum.elim (fun i ↦ some (Sum.inl i)) + (Fin.cases none (fun j ↦ some (Sum.inr j))) + inj' := by + intro i j + rcases i with i | i <;> rcases j with j | j + · simp + · refine Fin.cases ?_ (fun j ↦ ?_) j <;> simp + · refine Fin.cases ?_ (fun i ↦ ?_) i <;> simp + · refine Fin.cases ?_ (fun i ↦ ?_) i <;> + refine Fin.cases ?_ (fun j ↦ ?_) j <;> simp + +omit [FiniteDimensional ℝ V] in +lemma dense_linearIndependent_extension {ι : Type u71} [Fintype ι] + (v : ι → V) (hv : LinearIndependent ℝ v) (n : ℕ) + (hn : Fintype.card ι + n ≤ Module.finrank ℝ V) : + Dense {w : Fin n → V | LinearIndependent ℝ (Sum.elim v w)} := by + classical + induction n with + | zero => + have he : {w : Fin 0 → V | LinearIndependent ℝ (Sum.elim v w)} = Set.univ := by + ext w + simp only [Set.mem_ofPred_eq, Set.mem_univ, iff_true] + rw [linearIndependent_sum] + refine ⟨hv, linearIndependent_empty_type, ?_⟩ + simp + rw [he] + exact dense_univ + | succ n ih => + rw [Metric.dense_iff] + intro w ε hε + obtain ⟨z, hz, hzε⟩ := (ih (by omega)).exists_dist_lt (Fin.tail w) hε + let S : Submodule ℝ V := Submodule.span ℝ (Set.range (Sum.elim v z)) + have hS : S ≠ ⊤ := by + intro he + have hd := finrank_span_eq_card hz + change Module.finrank ℝ S = Fintype.card (ι ⊕ Fin n) at hd + rw [he, finrank_top, Fintype.card_sum, Fintype.card_fin] at hd + omega + obtain ⟨x, hx, hxε⟩ := (dense_compl_proper_submodule S hS).exists_dist_lt (w 0) hε + refine ⟨Fin.cons x z, ?_, ?_⟩ + · apply (dist_pi_lt_iff hε).mpr + intro i + refine Fin.cases ?_ (fun j ↦ ?_) i + · simpa [dist_comm] using hxε + · simpa [Fin.tail, dist_comm] using (dist_pi_lt_iff hε).mp hzε j + · have hl := (hz.option hx).comp (sumFinSuccEmbedding ι n) + (sumFinSuccEmbedding ι n).injective + change LinearIndependent ℝ (Sum.elim v (Fin.cons x z)) + have heq : Sum.elim v (Fin.cons x z) = + (fun o ↦ o.casesOn' x (Sum.elim v z)) ∘ (sumFinSuccEmbedding ι n) := by + ext i + rcases i with i | i + · rfl + · exact Fin.cases rfl (fun j ↦ rfl) i + rw [heq] + exact hl + +lemma dense_augmented_linearIndependent {ι : Type u72} [Fintype ι] + (hn : Fintype.card ι ≤ Module.finrank ℝ V + 1) : + Dense {v : ι → V | LinearIndependent ℝ (fun i ↦ ((1 : ℝ), v i))} := by + classical + rw [Metric.dense_iff] + intro v ε hε + let a : ι → ℝ × V := fun i ↦ (1, v i) + let normal : (ι → ℝ × V) → (ι → V) := fun u i ↦ (u i).1⁻¹ • (u i).2 + have hnorm : ContinuousAt normal a := by + apply continuousAt_pi.mpr + intro i + exact (((continuous_apply i).fst.continuousAt).inv₀ (by norm_num [a])).smul + (continuous_apply i).snd.continuousAt + have hnval : normal a = v := by ext i; simp [normal, a] + obtain ⟨δ, hδ, hcδ⟩ := Metric.continuousAt_iff.mp hnorm ε hε + obtain ⟨u, hu, huδ⟩ := (dense_linearIndependent (V := ℝ × V) + (ι := ι) (by simpa [Module.finrank_prod, Nat.add_comm] using hn)).exists_dist_lt a + (lt_min hδ (by norm_num : (0 : ℝ) < 1)) + rw [dist_comm] at huδ + have hfst (i : ι) : (u i).1 ≠ 0 := by + intro he + have hdi : dist (u i) (a i) < 1 := + lt_of_lt_of_le ((dist_pi_lt_iff (lt_min hδ (by norm_num))).mp huδ i) (min_le_right _ _) + rw [Prod.dist_eq] at hdi + have hdf := (max_lt_iff.mp hdi).1 + simp [he, a] at hdf + refine ⟨normal u, ?_, ?_⟩ + · have hd := hcδ (lt_of_lt_of_le huδ (min_le_left _ _)) + simpa [hnval, dist_comm] using hd + · change LinearIndependent ℝ (fun i ↦ ((1 : ℝ), normal u i)) + have hul := hu.units_smul (fun i ↦ (Units.mk0 (u i).1 (hfst i))⁻¹) + have heq : (fun i ↦ ((1 : ℝ), normal u i)) = + (fun i ↦ (Units.mk0 (u i).1 (hfst i))⁻¹) • u := by + ext i <;> simp [normal, Units.smul_def, hfst i] + rw [heq] + exact hul + +lemma dense_augmentedIndependent_extension_fin {ι : Type u73} [Fintype ι] + (v : ι → V) (hv : LinearIndependent ℝ (fun i ↦ ((1 : ℝ), v i))) (n : ℕ) + (hn : Fintype.card ι + n ≤ Module.finrank ℝ V + 1) : + Dense {w : Fin n → V | LinearIndependent ℝ + (fun i ↦ ((1 : ℝ), Sum.elim v w i))} := by + classical + rw [Metric.dense_iff] + intro w ε hε + let a : Fin n → ℝ × V := fun i ↦ (1, w i) + let normal : (Fin n → ℝ × V) → (Fin n → V) := fun u i ↦ (u i).1⁻¹ • (u i).2 + have hnorm : ContinuousAt normal a := by + apply continuousAt_pi.mpr + intro i + exact (((continuous_apply i).fst.continuousAt).inv₀ (by norm_num [a])).smul + (continuous_apply i).snd.continuousAt + have hnval : normal a = w := by ext i; simp [normal, a] + obtain ⟨δ, hδ, hcδ⟩ := Metric.continuousAt_iff.mp hnorm ε hε + obtain ⟨u, hu, huδ⟩ := (dense_linearIndependent_extension + (V := ℝ × V) (fun i ↦ ((1 : ℝ), v i)) hv n + (by simpa [Module.finrank_prod, Nat.add_comm] using hn)).exists_dist_lt a + (lt_min hδ (by norm_num : (0 : ℝ) < 1)) + rw [dist_comm] at huδ + have hfst (i : Fin n) : (u i).1 ≠ 0 := by + intro he + have hdi : dist (u i) (a i) < 1 := + lt_of_lt_of_le ((dist_pi_lt_iff (lt_min hδ (by norm_num))).mp huδ i) (min_le_right _ _) + rw [Prod.dist_eq] at hdi + have hdf := (max_lt_iff.mp hdi).1 + simp [he, a] at hdf + refine ⟨normal u, ?_, ?_⟩ + · have hd := hcδ (lt_of_lt_of_le huδ (min_le_left _ _)) + simpa [hnval, dist_comm] using hd + · let c : ι ⊕ Fin n → ℝˣ := Sum.elim (fun _ ↦ 1) + (fun i ↦ (Units.mk0 (u i).1 (hfst i))⁻¹) + have hul := hu.units_smul c + change LinearIndependent ℝ (fun i ↦ ((1 : ℝ), Sum.elim v (normal u) i)) + have heq : (fun i ↦ ((1 : ℝ), Sum.elim v (normal u) i)) = + c • Sum.elim (fun i ↦ ((1 : ℝ), v i)) u := by + funext i + rcases i with i | i <;> ext <;> simp [c, normal, Units.smul_def, hfst] + rw [heq] + exact hul + +omit [FiniteDimensional ℝ V] in +lemma dense_linearIndependent_extension_fintype {ι : Type u74} {κ : Type u75} [Fintype ι] [Fintype κ] + (v : ι → V) (hv : LinearIndependent ℝ v) + (hn : Fintype.card ι + Fintype.card κ ≤ Module.finrank ℝ V) : + Dense {w : κ → V | LinearIndependent ℝ (Sum.elim v w)} := by + classical + rw [Metric.dense_iff] + intro w ε hε + let e := Fintype.equivFin κ + obtain ⟨z, hz, hzε⟩ := (dense_linearIndependent_extension v hv (Fintype.card κ) hn).exists_dist_lt (w ∘ e.symm) hε + refine ⟨z ∘ e, ?_, ?_⟩ + · apply (dist_pi_lt_iff hε).mpr + intro i + simpa [Function.comp_def, dist_comm] using (dist_pi_lt_iff hε).mp hzε (e i) + · have heq : Sum.elim v (z ∘ e) = + (Sum.elim v z) ∘ (Equiv.sumCongr (Equiv.refl ι) e) := by + funext i + cases i <;> rfl + change LinearIndependent ℝ (Sum.elim v (z ∘ e)) + rw [heq] + exact hz.comp _ (Equiv.sumCongr (Equiv.refl ι) e).injective + +lemma dense_augmentedIndependent_extension {ι : Type u76} {κ : Type u77} [Fintype ι] [Fintype κ] + (v : ι → V) (hv : LinearIndependent ℝ (fun i ↦ ((1 : ℝ), v i))) + (hn : Fintype.card ι + Fintype.card κ ≤ Module.finrank ℝ V + 1) : + Dense {w : κ → V | LinearIndependent ℝ (fun i ↦ ((1 : ℝ), Sum.elim v w i))} := by + classical + rw [Metric.dense_iff] + intro w ε hε + let e := Fintype.equivFin κ + obtain ⟨z, hz, hzε⟩ := (dense_augmentedIndependent_extension_fin v hv (Fintype.card κ) hn).exists_dist_lt (w ∘ e.symm) hε + refine ⟨z ∘ e, ?_, ?_⟩ + · apply (dist_pi_lt_iff hε).mpr + intro i + simpa [Function.comp_def, dist_comm] using (dist_pi_lt_iff hε).mp hzε (e i) + · have heq : (fun i ↦ ((1 : ℝ), Sum.elim v (z ∘ e) i)) = + (fun i ↦ ((1 : ℝ), Sum.elim v z i)) ∘ (Equiv.sumCongr (Equiv.refl ι) e) := by + funext i + cases i <;> rfl + change LinearIndependent ℝ (fun i ↦ ((1 : ℝ), Sum.elim v (z ∘ e) i)) + rw [heq] + exact hz.comp _ (Equiv.sumCongr (Equiv.refl ι) e).injective + +omit [FiniteDimensional ℝ V] in +lemma affineIndependent_of_augmented {ι : Type u78} (v : ι → V) + (hv : LinearIndependent ℝ (fun i ↦ ((1 : ℝ), v i))) : AffineIndependent ℝ v := by + rw [affineIndependent_iff] + intro s w hs hsum i hi + apply (linearIndependent_iff'.mp hv) s w _ i hi + apply Prod.ext + · simpa [Prod.fst_sum] using hs + · simpa [Prod.snd_sum] using hsum + +omit [FiniteDimensional ℝ V] in +lemma independent_shift_of_augmented_extra {ι : Type u79} (v : ι → V) (a : V) + (hv : LinearIndependent ℝ + (fun i : ι ⊕ Unit ↦ ((1 : ℝ), Sum.elim v (fun _ ↦ a) i))) : + LinearIndependent ℝ (fun i ↦ v i - a) := by + have hh := (affineIndependent_iff_linearIndependent_vsub ℝ + (Sum.elim v (fun _ : Unit ↦ a)) (Sum.inr ())).mp (affineIndependent_of_augmented _ hv) + let e : ι → {i : ι ⊕ Unit // i ≠ Sum.inr ()} := fun i ↦ ⟨Sum.inl i, by simp⟩ + have he : Function.Injective e := by + intro i j hij + exact Sum.inl.inj (congrArg Subtype.val hij) + exact hh.comp e he + +/-- A generic root avoids the affine hull of every prescribed independent +proper face. This permits an initial zero inside exactly one maximal flag. -/ +lemma dense_independent_shift {ι : Type u80} [Fintype ι] (v : ι → V) + (hv : LinearIndependent ℝ (fun i ↦ ((1 : ℝ), v i))) + (hn : Fintype.card ι ≤ Module.finrank ℝ V) : + Dense {a : V | LinearIndependent ℝ (fun i ↦ v i - a)} := by + classical + rw [Metric.dense_iff] + intro a ε hε + have hc : Fintype.card ι + Fintype.card Unit ≤ Module.finrank ℝ V + 1 := by + simpa using Nat.add_le_add_right hn 1 + obtain ⟨w, hw, hwε⟩ := (dense_augmentedIndependent_extension v hv hc).exists_dist_lt + (fun _ : Unit ↦ a) hε + refine ⟨w (), ?_, independent_shift_of_augmented_extra v (w ()) ?_⟩ + · exact (dist_comm _ _).le.trans_lt ((dist_pi_lt_iff hε).mp hwε ()) + · have he : w = (fun _ : Unit ↦ w ()) := by funext i; cases i; rfl + rw [he] at hw + exact hw + +omit [FiniteDimensional ℝ V] in +lemma isOpen_independent_shift {ι : Type u81} [Fintype ι] (v : ι → V) : + IsOpen {a : V | LinearIndependent ℝ (fun i ↦ v i - a)} := by + apply isOpen_setOfPred_linearIndependent.preimage + exact continuous_pi (fun _ ↦ continuous_const.sub continuous_id) + +/-- Positive barycentric coordinates remain positive on a neighborhood when +an augmented vertex family is a basis. -/ +lemma positive_barycentric_neighborhood {ι : Type u82} [Fintype ι] + (v : ι → V) (hv : LinearIndependent ℝ (fun i ↦ ((1 : ℝ), v i))) + (hn : Fintype.card ι = Module.finrank ℝ V + 1) + (w : ι → ℝ) (hw : ∀ i, 0 < w i) (hs : ∑ i, w i = 1) : + ∃ U : Set V, IsOpen U ∧ (∑ i, w i • v i) ∈ U ∧ + ∀ x ∈ U, ∃ z : ι → ℝ, (∀ i, 0 < z i) ∧ ∑ i, z i = 1 ∧ ∑ i, z i • v i = x := by + classical + let B : Module.Basis ι ℝ (ℝ × V) := basisOfLinearIndependentOfCardEqFinrank' + (fun i ↦ ((1 : ℝ), v i)) hv (by simpa [Module.finrank_prod, Nat.add_comm] using hn) + have hB (i : ι) : B i = ((1 : ℝ), v i) := by + simp [B] + let z : V → ι → ℝ := fun x ↦ B.equivFun (1, x) + have hz : Continuous z := B.equivFun.toContinuousLinearEquiv.continuous.comp + (continuous_const.prodMk continuous_id) + have hrep (x : V) : ∑ i, z x i • ((1 : ℝ), v i) = (1, x) := by + simpa only [z, Module.Basis.equivFun_apply, hB] using B.sum_repr (1, x) + let x₀ : V := ∑ i, w i • v i + have hzw : z x₀ = w := by + apply B.equivFun.symm.injective + change B.equivFun.symm (B.equivFun (1, x₀)) = B.equivFun.symm w + rw [B.equivFun.symm_apply_apply, Module.Basis.equivFun_symm_apply] + apply Prod.ext + · simp only [hB, Prod.fst_sum, Prod.smul_fst, smul_eq_mul, mul_one, hs] + · simp only [hB, Prod.snd_sum, Prod.smul_snd] + rfl + refine ⟨{x | ∀ i, 0 < z x i}, ?_, ?_, ?_⟩ + · have ho : IsOpen (⋂ i, {x | (0 : ℝ) < z x i}) := isOpen_iInter_of_finite + (fun i ↦ isOpen_lt continuous_const ((continuous_apply i).comp hz)) + simpa only [Set.ofPred_forall] using ho + · change ∀ i, 0 < z x₀ i + rwa [hzw] + · intro x hx + refine ⟨z x, hx, ?_, ?_⟩ + · simpa only [Prod.fst_sum, Prod.smul_fst, smul_eq_mul, mul_one] using congrArg Prod.fst (hrep x) + · simpa only [Prod.snd_sum, Prod.smul_snd] using congrArg Prod.snd (hrep x) + +section VertexEvaluation +variable {Q : Type u83} {ι : Type u84} [Fintype Q] [Fintype ι] + +/-- On distinct vertex orbits, equivariant vertex values may be varied independently. -/ +def vertexEvaluation (e : ι → Q) (A : ι → V ≃ₗ[ℝ] V) : + (Q → V) →ₗ[ℝ] (ι → V) where + toFun w i := A i (w (e i)) + map_add' w z := by ext i; simp + map_smul' c w := by ext i; simp + +omit [FiniteDimensional ℝ V] [Fintype Q] [Fintype ι] in +lemma vertexEvaluation_surjective (e : ι → Q) (he : Function.Injective e) + (A : ι → V ≃ₗ[ℝ] V) : Function.Surjective (vertexEvaluation e A) := by + classical + intro v + refine ⟨Function.extend e (fun i ↦ (A i).symm (v i)) 0, ?_⟩ + ext i + simp only [vertexEvaluation, LinearMap.coe_mk, AddHom.coe_mk, + he.extend_apply, LinearEquiv.apply_symm_apply] + +lemma vertexEvaluation_isOpenMap (e : ι → Q) (he : Function.Injective e) + (A : ι → V ≃ₗ[ℝ] V) : IsOpenMap (vertexEvaluation e A) := + (vertexEvaluation e A).toContinuousLinearMap.isOpenMap + (vertexEvaluation_surjective e he A) + +omit [Fintype ι] in +lemma vertexEvaluation_continuous (e : ι → Q) (A : ι → V ≃ₗ[ℝ] V) : + Continuous (vertexEvaluation e A) := + (vertexEvaluation e A).toContinuousLinearMap.continuous + +lemma dense_vertex_linearlyIndependent (e : ι → Q) (he : Function.Injective e) + (A : ι → V ≃ₗ[ℝ] V) (hn : Fintype.card ι ≤ Module.finrank ℝ V) : + Dense {w : Q → V | LinearIndependent ℝ (vertexEvaluation e A w)} := + (dense_linearIndependent hn).preimage (vertexEvaluation_isOpenMap e he A) + +lemma dense_vertex_augmentedIndependent (e : ι → Q) (he : Function.Injective e) + (A : ι → V ≃ₗ[ℝ] V) (hn : Fintype.card ι ≤ Module.finrank ℝ V + 1) : + Dense {w : Q → V | LinearIndependent ℝ (fun i ↦ ((1 : ℝ), vertexEvaluation e A w i))} := + (dense_augmented_linearIndependent hn).preimage (vertexEvaluation_isOpenMap e he A) + +lemma isOpen_vertex_linearlyIndependent (e : ι → Q) (A : ι → V ≃ₗ[ℝ] V) : + IsOpen {w : Q → V | LinearIndependent ℝ (vertexEvaluation e A w)} := + isOpen_setOfPred_linearIndependent.preimage (vertexEvaluation_continuous e A) + +lemma isOpen_vertex_augmentedIndependent (e : ι → Q) (A : ι → V ≃ₗ[ℝ] V) : + IsOpen {w : Q → V | LinearIndependent ℝ (fun i ↦ ((1 : ℝ), vertexEvaluation e A w i))} := by + apply isOpen_setOfPred_linearIndependent.preimage + exact continuous_pi (fun i ↦ continuous_const.prodMk + ((continuous_apply i).comp (vertexEvaluation_continuous e A))) + +/-- Genericity may be imposed while retaining an independent prescribed part. +This is used for the initial boundary of the continuation cylinder. -/ +lemma dense_vertex_independent_extension {κ : Type u85} [Fintype κ] + (v : κ → V) (hv : LinearIndependent ℝ v) + (e : ι → Q) (he : Function.Injective e) (A : ι → V ≃ₗ[ℝ] V) + (hn : Fintype.card κ + Fintype.card ι ≤ Module.finrank ℝ V) : + Dense {w : Q → V | LinearIndependent ℝ (Sum.elim v (vertexEvaluation e A w))} := + (dense_linearIndependent_extension_fintype v hv hn).preimage + (vertexEvaluation_isOpenMap e he A) + +lemma dense_vertex_augmented_extension {κ : Type u86} [Fintype κ] + (v : κ → V) (hv : LinearIndependent ℝ (fun i ↦ ((1 : ℝ), v i))) + (e : ι → Q) (he : Function.Injective e) (A : ι → V ≃ₗ[ℝ] V) + (hn : Fintype.card κ + Fintype.card ι ≤ Module.finrank ℝ V + 1) : + Dense {w : Q → V | LinearIndependent ℝ + (fun i ↦ ((1 : ℝ), Sum.elim v (vertexEvaluation e A w) i))} := + (dense_augmentedIndependent_extension v hv hn).preimage + (vertexEvaluation_isOpenMap e he A) + +lemma isOpen_vertex_independent_extension {κ : Type u87} [Fintype κ] + (v : κ → V) (e : ι → Q) (A : ι → V ≃ₗ[ℝ] V) : + IsOpen {w : Q → V | LinearIndependent ℝ (Sum.elim v (vertexEvaluation e A w))} := by + apply isOpen_setOfPred_linearIndependent.preimage + apply continuous_pi + rintro (i | i) + · exact continuous_const + · exact (continuous_apply i).comp (vertexEvaluation_continuous e A) + +lemma isOpen_vertex_augmented_extension {κ : Type u88} [Fintype κ] + (v : κ → V) (e : ι → Q) (A : ι → V ≃ₗ[ℝ] V) : + IsOpen {w : Q → V | LinearIndependent ℝ + (fun i ↦ ((1 : ℝ), Sum.elim v (vertexEvaluation e A w) i))} := by + apply isOpen_setOfPred_linearIndependent.preimage + apply continuous_pi + rintro (i | i) + · change Continuous (fun _ : Q → V ↦ ((1 : ℝ), v i)) + exact continuous_const + · exact continuous_const.prodMk + ((continuous_apply i).comp (vertexEvaluation_continuous e A)) + +attribute [local instance] Classical.propDecidable + +/-- Extend vertex values on the free orbits while retaining the prescribed orbits. -/ +def mixedVertexEvaluation (P : Q → Prop) (b : Q → V) (e : ι → Q) + (A : ι → V ≃ₗ[ℝ] V) (a : {q // ¬ P q} → V) (i : ι) : V := + A i (if h : P (e i) then b (e i) else a ⟨e i, h⟩) + +omit [Fintype Q] [Fintype ι] in +lemma mixedVertexEvaluation_continuous (P : Q → Prop) (b : Q → V) (e : ι → Q) + (A : ι → V ≃ₗ[ℝ] V) : Continuous (mixedVertexEvaluation P b e A) := by + apply continuous_pi + intro i + by_cases h : P (e i) + · simp only [mixedVertexEvaluation, dite_eq_left h] + exact continuous_const + · simp only [mixedVertexEvaluation, dite_eq_right h] + exact (A i).toContinuousLinearEquiv.continuous.comp (continuous_apply (⟨e i, h⟩ : {q // ¬ P q})) + +omit [Fintype Q] in +lemma isOpen_mixed_independent (P : Q → Prop) (b : Q → V) (e : ι → Q) + (A : ι → V ≃ₗ[ℝ] V) : + IsOpen {a : {q // ¬ P q} → V | LinearIndependent ℝ (mixedVertexEvaluation P b e A a)} := + isOpen_setOfPred_linearIndependent.preimage (mixedVertexEvaluation_continuous P b e A) + +omit [Fintype Q] in +lemma isOpen_mixed_augmented (P : Q → Prop) (b : Q → V) (e : ι → Q) + (A : ι → V ≃ₗ[ℝ] V) : + IsOpen {a : {q // ¬ P q} → V | LinearIndependent ℝ + (fun i ↦ ((1 : ℝ), mixedVertexEvaluation P b e A a i))} := by + apply isOpen_setOfPred_linearIndependent.preimage + exact continuous_pi (fun i ↦ continuous_const.prodMk + ((continuous_apply i).comp (mixedVertexEvaluation_continuous P b e A))) + +lemma dense_mixed_independent (P : Q → Prop) (b : Q → V) (e : ι → Q) + (he : Function.Injective e) (A : ι → V ≃ₗ[ℝ] V) + (hfixed : LinearIndependent ℝ (fun i : {i // P (e i)} ↦ A i.val (b (e i.val)))) + (hn : Fintype.card ι ≤ Module.finrank ℝ V) : + Dense {a : {q // ¬ P q} → V | LinearIndependent ℝ (mixedVertexEvaluation P b e A a)} := by + let e' : {i // ¬ P (e i)} → {q // ¬ P q} := fun i ↦ ⟨e i.val, i.prop⟩ + have he' : Function.Injective e' := by + intro i j h + exact Subtype.ext (he (congrArg Subtype.val h)) + have hc : Fintype.card {i // P (e i)} + Fintype.card {i // ¬ P (e i)} = Fintype.card ι := by + simpa only [Fintype.card_sum] using Fintype.card_congr (Equiv.sumCompl (fun i ↦ P (e i))) + have hh := dense_vertex_independent_extension + (fun i : {i // P (e i)} ↦ A i.val (b (e i.val))) hfixed + e' he' (fun i ↦ A i.val) (by rw [hc]; exact hn) + have heval (a : {q // ¬ P q} → V) : + mixedVertexEvaluation P b e A a ∘ Equiv.sumCompl (fun i ↦ P (e i)) = + Sum.elim (fun i : {i // P (e i)} ↦ A i.val (b (e i.val))) + (vertexEvaluation e' (fun i ↦ A i.val) a) := by + funext i + cases i with + | inl i => simp [mixedVertexEvaluation, i.prop] + | inr i => simp [mixedVertexEvaluation, vertexEvaluation, e', i.prop] + have hset : {a : {q // ¬ P q} → V | LinearIndependent ℝ (mixedVertexEvaluation P b e A a)} = + {a | LinearIndependent ℝ (Sum.elim (fun i : {i // P (e i)} ↦ A i.val (b (e i.val))) + (vertexEvaluation e' (fun i ↦ A i.val) a))} := by + ext a + exact (linearIndependent_equiv' (Equiv.sumCompl (fun i ↦ P (e i))) (heval a)).symm + rwa [hset] + +lemma dense_mixed_augmented (P : Q → Prop) (b : Q → V) (e : ι → Q) + (he : Function.Injective e) (A : ι → V ≃ₗ[ℝ] V) + (hfixed : LinearIndependent ℝ + (fun i : {i // P (e i)} ↦ ((1 : ℝ), A i.val (b (e i.val))))) + (hn : Fintype.card ι ≤ Module.finrank ℝ V + 1) : + Dense {a : {q // ¬ P q} → V | LinearIndependent ℝ + (fun i ↦ ((1 : ℝ), mixedVertexEvaluation P b e A a i))} := by + let e' : {i // ¬ P (e i)} → {q // ¬ P q} := fun i ↦ ⟨e i.val, i.prop⟩ + have he' : Function.Injective e' := by + intro i j h + exact Subtype.ext (he (congrArg Subtype.val h)) + have hc : Fintype.card {i // P (e i)} + Fintype.card {i // ¬ P (e i)} = Fintype.card ι := by + simpa only [Fintype.card_sum] using Fintype.card_congr (Equiv.sumCompl (fun i ↦ P (e i))) + have hh := dense_vertex_augmented_extension + (fun i : {i // P (e i)} ↦ A i.val (b (e i.val))) hfixed + e' he' (fun i ↦ A i.val) (by rw [hc]; exact hn) + have heval (a : {q // ¬ P q} → V) : + (fun i ↦ ((1 : ℝ), mixedVertexEvaluation P b e A a i)) ∘ Equiv.sumCompl (fun i ↦ P (e i)) = + (fun i ↦ ((1 : ℝ), Sum.elim (fun i : {i // P (e i)} ↦ A i.val (b (e i.val))) + (vertexEvaluation e' (fun i ↦ A i.val) a) i)) := by + funext i + cases i with + | inl i => simp [mixedVertexEvaluation, i.prop] + | inr i => simp [mixedVertexEvaluation, vertexEvaluation, e', i.prop] + have hset : {a : {q // ¬ P q} → V | LinearIndependent ℝ + (fun i ↦ ((1 : ℝ), mixedVertexEvaluation P b e A a i))} = + {a | LinearIndependent ℝ (fun i ↦ ((1 : ℝ), + Sum.elim (fun i : {i // P (e i)} ↦ A i.val (b (e i.val))) + (vertexEvaluation e' (fun i ↦ A i.val) a) i))} := by + ext a + exact (linearIndependent_equiv' (Equiv.sumCompl (fun i ↦ P (e i))) (heval a)).symm + rwa [hset] + +end VertexEvaluation + +/-- Finitely many open genericity conditions can be imposed at once. -/ +lemma dense_finite_conditions {X : Type u89} {κ : Type u90} [TopologicalSpace X] [Finite κ] + (P : κ → X → Prop) (ho : ∀ k, IsOpen {x | P k x}) (hd : ∀ k, Dense {x | P k x}) : + Dense {x | ∀ k, P k x} := by + have h := (Set.finite_range (fun k ↦ {x | P k x})).dense_sInter + (by rintro _ ⟨k, rfl⟩; exact ho k) (by rintro _ ⟨k, rfl⟩; exact hd k) + simpa only [sInter_range, mem_iInter, mem_ofPred_eq, ofPred_forall] using h + +/-- Arbitrarily small generic perturbations of finitely many equivariant vertex +values, with an already generic prescribed part retained exactly. The orbit +labels and transports are abstract here; a free finite group action supplies them. -/ +lemma exists_mixed_generic + {Q : Type u91} {W : Type u92} {T₁ : Type u93} {T₂ : Type u94} [Fintype Q] [Fintype W] [Fintype T₁] [Fintype T₂] + (J₁ : T₁ → Type u191) (J₂ : T₂ → Type u192) [∀ t, Fintype (J₁ t)] [∀ t, Fintype (J₂ t)] + (P : Q → Prop) (b : Q → V) (e : W → Q) (A : W → V ≃ₗ[ℝ] V) + (v₁ : ∀ t, J₁ t → W) (v₂ : ∀ t, J₂ t → W) + (he₁ : ∀ t, Function.Injective (e ∘ v₁ t)) + (he₂ : ∀ t, Function.Injective (e ∘ v₂ t)) + (hf₁ : ∀ t, LinearIndependent ℝ + (fun i : {i // P (e (v₁ t i))} ↦ A (v₁ t i.val) (b (e (v₁ t i.val))))) + (hf₂ : ∀ t, LinearIndependent ℝ + (fun i : {i // P (e (v₂ t i))} ↦ ((1 : ℝ), A (v₂ t i.val) (b (e (v₂ t i.val)))))) + (hc₁ : ∀ t, Fintype.card (J₁ t) ≤ Module.finrank ℝ V) + (hc₂ : ∀ t, Fintype.card (J₂ t) ≤ Module.finrank ℝ V + 1) + (ε : ℝ) (hε : 0 < ε) : + ∃ a : {q // ¬ P q} → V, + (∀ w, dist (mixedVertexEvaluation P b e A a w) (A w (b (e w))) < ε) ∧ + (∀ t, LinearIndependent ℝ (fun i ↦ mixedVertexEvaluation P b e A a (v₁ t i))) ∧ + (∀ t, LinearIndependent ℝ (fun i ↦ ((1 : ℝ), mixedVertexEvaluation P b e A a (v₂ t i)))) := by + classical + let C : T₁ ⊕ T₂ → ({q // ¬ P q} → V) → Prop := Sum.elim + (fun t a ↦ LinearIndependent ℝ (fun i ↦ mixedVertexEvaluation P b e A a (v₁ t i))) + (fun t a ↦ LinearIndependent ℝ (fun i ↦ ((1 : ℝ), mixedVertexEvaluation P b e A a (v₂ t i)))) + have hco : ∀ t, IsOpen {a | C t a} := by + rintro (t | t) + · exact isOpen_mixed_independent P b (e ∘ v₁ t) (fun i ↦ A (v₁ t i)) + · exact isOpen_mixed_augmented P b (e ∘ v₂ t) (fun i ↦ A (v₂ t i)) + have hcd : ∀ t, Dense {a | C t a} := by + rintro (t | t) + · exact dense_mixed_independent P b (e ∘ v₁ t) (he₁ t) (fun i ↦ A (v₁ t i)) (hf₁ t) (hc₁ t) + · exact dense_mixed_augmented P b (e ∘ v₂ t) (he₂ t) (fun i ↦ A (v₂ t i)) (hf₂ t) (hc₂ t) + have hd := dense_finite_conditions C hco hcd + let U : Set ({q // ¬ P q} → V) := + {a | dist (mixedVertexEvaluation P b e A a) (fun w ↦ A w (b (e w))) < ε} + have hU : IsOpen U := isOpen_lt + ((mixedVertexEvaluation_continuous P b e A).dist continuous_const) continuous_const + have hUn : U.Nonempty := by + refine ⟨fun q ↦ b q.val, ?_⟩ + have heq : mixedVertexEvaluation P b e A (fun q ↦ b q.val) = (fun w ↦ A w (b (e w))) := by + funext w + simp only [mixedVertexEvaluation] + split_ifs <;> rfl + change dist _ _ < ε + rw [heq, dist_self] + exact hε + obtain ⟨a, hau, ha⟩ := hd.inter_open_nonempty U hU hUn + refine ⟨a, ?_, ?_, ?_⟩ + · exact (dist_pi_lt_iff hε).mp hau + · intro t + exact ha (Sum.inl t) + · intro t + exact ha (Sum.inr t) + +end SharpLiebThirring.PLParity + +end +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/InitialOrbit.lean b/lean/OAI/Analysis/LiebThirring/InitialOrbit.lean new file mode 100644 index 0000000000000000000000000000000000000000..36539e85265e769fdf5d0b7fecb5b588253b23bc --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/InitialOrbit.lean @@ -0,0 +1,390 @@ +import OAI.Analysis.LiebThirring.EquivariantFlags + +namespace OAI + +universe u103 u104 u105 u106 u107 u108 u109 u110 u111 u112 u113 u114 u115 + +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Finset +section +open Set Finset Filter + + +/-! Disjoint equivariant coordinate balls for the unique initial zero orbit. -/ + +open Set Finset +namespace SharpLiebThirring.PLParity +section OrbitBalls +attribute [local instance] Classical.propDecidable +variable {G : Type u103} {E : Type u104} [Group G] [MetricSpace E] [MulAction G E] + [IsIsometricSMul G E] + +omit [IsIsometricSMul G E] in +lemma orbit_separation [Fintype G] (p : E) (hp : ∀ g : G, g • p = p → g = 1) : + ∃ R > 0, ∀ g k : G, g ≠ k → 8 * R < dist (g • p) (k • p) := by + classical + let d : G × G → ℝ := fun q ↦ if q.1 = q.2 then 1 else dist (q.1 • p) (q.2 • p) + have hd (q : G × G) : 0 < d q := by + dsimp [d] + split_ifs with he + · norm_num + · apply dist_pos.mpr + intro hh + have hx : (q.2⁻¹ * q.1) • p = p := by rw [mul_smul, hh, inv_smul_smul] + exact he (inv_mul_eq_one.mp (hp _ hx)).symm + have hn : (Finset.univ : Finset (G × G)).Nonempty := ⟨(1,1), Finset.mem_univ _⟩ + let b := Finset.univ.inf' hn d + have hb : 0 < b := (Finset.lt_inf'_iff _).mpr (fun q _ ↦ hd q) + refine ⟨b / 16, by positivity, ?_⟩ + intro g k hgk + have hle : b ≤ d (g,k) := Finset.inf'_le _ (Finset.mem_univ _) + dsimp [d] at hle + rw [ite_eq_right hgk] at hle + linarith + +variable (p : E) (R : ℝ) + +def orbitBall : Set E := {x | ∃ g : G, dist x (g • p) < R} + +noncomputable def ballLabel (x : E) : G := + if hx : x ∈ orbitBall (G := G) p R then hx.choose else 1 + +omit [IsIsometricSMul G E] in +lemma ballLabel_dist {x : E} (hx : x ∈ orbitBall (G := G) p R) : + dist x (ballLabel (G := G) p R x • p) < R := by + simp only [ballLabel, dite_eq_left hx] + exact hx.choose_spec + +lemma orbitBall_smul (g : G) {x : E} (hx : x ∈ orbitBall (G := G) p R) : + g • x ∈ orbitBall (G := G) p R := by + obtain ⟨k,hk⟩ := hx + refine ⟨g*k, ?_⟩ + rw [mul_smul, dist_smul] + exact hk + +lemma mem_orbitBall_smul_iff (g : G) (x : E) : + g • x ∈ orbitBall (G := G) p R ↔ x ∈ orbitBall (G := G) p R := by + constructor + · intro hx + simpa only [inv_smul_smul] using orbitBall_smul p R g⁻¹ hx + · exact orbitBall_smul p R g + +variable (hR : 0 < R) (hsep : ∀ g k : G, g ≠ k → 8 * R < dist (g • p) (k • p)) + +include hR hsep in +omit [IsIsometricSMul G E] in +lemma ballLabel_eq {x : E} {g : G} (hx : dist x (g • p) < R) : + ballLabel (G := G) p R x = g := by + by_contra hn + have hl := ballLabel_dist p R (show x ∈ orbitBall (G := G) p R from ⟨g,hx⟩) + have hd := dist_triangle (ballLabel (G := G) p R x • p) x (g • p) + rw [dist_comm (ballLabel (G := G) p R x • p) x] at hd + have hs := hsep _ _ hn + linarith + +include hR hsep in +lemma ballLabel_smul (g : G) {x : E} (hx : x ∈ orbitBall (G := G) p R) : + ballLabel (G := G) p R (g • x) = g * ballLabel (G := G) p R x := by + apply ballLabel_eq p R hR hsep + rw [mul_smul, dist_smul] + exact ballLabel_dist p R hx + +include hR hsep in +omit [IsIsometricSMul G E] in +lemma ballLabel_eq_of_dist {x y : E} (hx : x ∈ orbitBall (G := G) p R) + (hy : y ∈ orbitBall (G := G) p R) (hxy : dist x y ≤ R) : + ballLabel (G := G) p R x = ballLabel (G := G) p R y := by + by_contra hn + have hlx := ballLabel_dist p R hx + have hly := ballLabel_dist p R hy + have hd := dist_triangle4 (ballLabel (G := G) p R x • p) x y (ballLabel (G := G) p R y • p) + rw [dist_comm (ballLabel (G := G) p R x • p) x] at hd + have hs := hsep _ _ hn + linarith + +include hR hsep in +omit [IsIsometricSMul G E] in +lemma exists_common_ballLabel {ι : Type u105} (v : ι → E) (P : ι → Prop) + (hv : ∀ i, P i → v i ∈ orbitBall (G := G) p R) + (hd : ∀ i j, dist (v i) (v j) ≤ R) : + ∃ g : G, ∀ i, P i → ballLabel (G := G) p R (v i) = g := by + by_cases hn : ∃ i, P i + · obtain ⟨j,hj⟩ := hn + refine ⟨ballLabel (G := G) p R (v j), ?_⟩ + intro i hi + exact ballLabel_eq_of_dist p R hR hsep (hv i hi) (hv j hj) (hd i j) + · exact ⟨1, fun i hi ↦ False.elim (hn ⟨i,hi⟩)⟩ + +end OrbitBalls +end SharpLiebThirring.PLParity + +namespace SharpLiebThirring.CubeFlags +open Finset SharpLiebThirring.PLParity +section Translate +variable {V : Type u106} {W : Type u107} {ι : Type u108} [AddCommGroup V] [Module ℝ V] [AddCommGroup W] [Module ℝ W] +lemma augmented_translate_independent (v : ι → V) (p : V) + (hv : LinearIndependent ℝ (fun i ↦ ((1 : ℝ), v i))) : + LinearIndependent ℝ (fun i ↦ ((1 : ℝ), v i - p)) := by + let fst : (ℝ × V) →ₗ[ℝ] ℝ := LinearMap.fst ℝ ℝ V + let snd : (ℝ × V) →ₗ[ℝ] V := LinearMap.snd ℝ ℝ V + let T : (ℝ × V) →ₗ[ℝ] (ℝ × V) := fst.prod (snd - fst.smulRight p) + have hT : Function.Injective T := by + rintro ⟨a,x⟩ ⟨b,y⟩ he + have hab : a = b := congrArg Prod.fst he + have hxy : x - a • p = y - b • p := congrArg Prod.snd he + rw [← hab] at hxy + exact Prod.ext hab (sub_left_inj.mp hxy) + have hh := hv.map' T (LinearMap.ker_eq_bot.mpr hT) + change LinearIndependent ℝ (fun i ↦ T ((1 : ℝ), v i)) at hh + have he : (fun i ↦ T ((1 : ℝ), v i)) = (fun i ↦ ((1 : ℝ), v i - p)) := by + funext i + change ((1 : ℝ), v i - (1 : ℝ) • p) = (1, v i - p) + rw [one_smul] + rwa [he] at hh + +lemma augmented_equiv_independent (v : ι → V) (L : V ≃ₗ[ℝ] W) + (hv : LinearIndependent ℝ (fun i ↦ ((1 : ℝ), v i))) : + LinearIndependent ℝ (fun i ↦ ((1 : ℝ), L (v i))) := + hv.map' ((LinearEquiv.refl ℝ ℝ).prodCongr L).toLinearMap + (LinearMap.ker_eq_bot.mpr (LinearEquiv.injective _)) +end Translate + +lemma Signs.smul_time_zero {d : ℕ} (s : Signs (d + 1)) (x : Fin (d + 1) → ℝ) + (hx : x (Fin.last d) = 0) : (s • x) (Fin.last d) = 0 := by + simp only [Signs.smul_real, hx, neg_zero, ite_self] + +lemma Flag.augmented_spatial_scaled {d : ℕ} {ι : Type u109} (F : Flag (d + 1)) + (v : ι → Fin (d + 2)) (hv : Function.Injective v) {h : ℝ} (hh : h ≠ 0) + (s : Signs (d + 1)) (ht : ∀ i, (h • F.point (v i)) (Fin.last d) = 0) : + LinearIndependent ℝ (fun i ↦ ((1 : ℝ), spatial (s • (h • F.point (v i))))) := by + have hu := augmented_scale_independent (fun i ↦ F.point (v i)) + (F.augmented_linearIndependent.comp v hv) hh + have hr := augmented_equiv_independent (fun i ↦ h • F.point (v i)) + s.linearIsometry.toLinearEquiv hu + exact augmented_spatial_independent _ hr (fun i ↦ s.smul_time_zero _ (ht i)) + +instance signsSubgroupIsIsometric {n : ℕ} (H : Subgroup (Signs n)) : + IsIsometricSMul H (Fin n → ℝ) where + isometry_smul s := s.val.linearIsometry.isometry + +section Model +variable {d : ℕ} (H : Subgroup (Signs (d + 1))) +variable {V : Type u110} [NormedAddCommGroup V] [NormedSpace ℝ V] +variable (ρ : H →* (V ≃ₗ[ℝ] V)) (L : (Fin d → ℝ) ≃ₗ[ℝ] V) +variable (p : Fin (d + 1) → ℝ) (R : ℝ) + +def affineOrbitModel (q : Fin d → ℝ) (x : Fin (d + 1) → ℝ) : V := + let s := ballLabel (G := H) p R x + ρ s (L (spatial (s⁻¹ • x) - q)) + +lemma affineOrbitModel_smul (hR : 0 < R) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • p) (k • p)) + (q : Fin d → ℝ) (s : H) {x : Fin (d + 1) → ℝ} (hx : x ∈ orbitBall (G := H) p R) : + affineOrbitModel H ρ L p R q (s • x) = ρ s (affineOrbitModel H ρ L p R q x) := by + simp only [affineOrbitModel, ballLabel_smul p R hR hsep s hx, mul_inv_rev, + mul_smul, inv_smul_smul, map_mul, LinearEquiv.mul_apply] + +lemma affineOrbitModel_dist (hρ : ∀ s : H, ∀ v : V, ‖ρ s v‖ = ‖v‖) + (q q' : Fin d → ℝ) (x : Fin (d + 1) → ℝ) : + dist (affineOrbitModel H ρ L p R q x) (affineOrbitModel H ρ L p R q' x) = dist (L q) (L q') := by + let s := ballLabel (G := H) p R x + simp only [dist_eq_norm, affineOrbitModel, ← map_sub, hρ] + have he : spatial (s⁻¹ • x) - q - (spatial (s⁻¹ • x) - q') = q' - q := by abel + change ‖L (spatial (s⁻¹ • x) - q - (spatial (s⁻¹ • x) - q'))‖ = ‖L (q - q')‖ + rw [he, map_sub, map_sub, norm_sub_rev] + +lemma affineOrbitModel_augmented {ι : Type u111} (q : Fin d → ℝ) + (x : ι → Fin (d + 1) → ℝ) (s : H) + (hs : ∀ i, ballLabel (G := H) p R (x i) = s) + (hi : LinearIndependent ℝ (fun i ↦ ((1 : ℝ), spatial (s⁻¹ • x i)))) : + LinearIndependent ℝ (fun i ↦ ((1 : ℝ), affineOrbitModel H ρ L p R q (x i))) := by + simp only [affineOrbitModel, hs] + exact augmented_equiv_independent _ (L.trans (ρ s)) (augmented_translate_independent _ q hi) + +lemma affineOrbitModel_independent {ι : Type u112} (q : Fin d → ℝ) + (x : ι → Fin (d + 1) → ℝ) (s : H) + (hs : ∀ i, ballLabel (G := H) p R (x i) = s) + (hi : LinearIndependent ℝ (fun i ↦ spatial (s⁻¹ • x i) - q)) : + LinearIndependent ℝ (fun i ↦ affineOrbitModel H ρ L p R q (x i)) := by + simp only [affineOrbitModel, hs] + exact hi.map' (L.trans (ρ s)).toLinearMap (LinearMap.ker_eq_bot.mpr (LinearEquiv.injective _)) + +end Model +end SharpLiebThirring.CubeFlags + +namespace SharpLiebThirring.CubeFlags +open Finset SharpLiebThirring.PLParity +attribute [local instance] Classical.propDecidable + +lemma Flag.dist_gridPoint_gridPoint {n : ℕ} (F : Flag n) (h : ℝ) (hh : 0 ≤ h) + (j k : Fin (n + 1)) : dist (gridPoint h (F.vertex j)) (gridPoint h (F.vertex k)) ≤ h := by + rw [gridPoint_vertex, gridPoint_vertex] + calc + _ ≤ dist (h • F.point j) (h • F.center) + dist (h • F.center) (h • F.point k) := dist_triangle _ _ _ + _ ≤ h / 2 + h / 2 := by + apply add_le_add (F.dist_scaled_point_center h hh j) + rw [dist_comm] + exact F.dist_scaled_point_center h hh k + _ = h := by ring + +lemma exists_generic_initial_root {d : ℕ} + (H : Subgroup (Signs (d + 1))) (D : SubMulAction H (Flag (d + 1))) [Fintype D] + (h : ℝ) (hh : h ≠ 0) (P : vertices H D → Prop) + (hP : ∀ z : vertices H D, P z → gridPoint h z.val (Fin.last d) = 0) + (U : Set (Fin d → ℝ)) (hU : IsOpen U) (hUn : U.Nonempty) : + ∃ q ∈ U, ∀ F : D, ∀ i j : Fin (d + 2), i ≠ j → ∀ s : H, + LinearIndependent ℝ (fun k : {k : {k : Fin (d + 2) // k ≠ i ∧ k ≠ j} // + P (flagVertex H D F k.val)} ↦ + spatial (s⁻¹ • gridPoint h (F.val.vertex k.val.val)) - q) := by + classical + let T := (D × {p : Fin (d + 2) × Fin (d + 2) // p.1 ≠ p.2}) × H + let J (t : T) := {k : {k : Fin (d + 2) // k ≠ t.1.2.val.1 ∧ k ≠ t.1.2.val.2} // + P (flagVertex H D t.1.1 k.val)} + let v (t : T) (k : J t) := spatial (t.2⁻¹ • gridPoint h (t.1.1.val.vertex k.val.val)) + have hv (t : T) : LinearIndependent ℝ (fun k ↦ ((1 : ℝ), v t k)) := by + have hh' := t.1.1.val.augmented_spatial_scaled (fun k : J t ↦ k.val.val) + (fun _ _ he ↦ Subtype.ext (Subtype.ext he)) hh t.2⁻¹.val (fun k ↦ by + rw [← gridPoint_vertex] + exact hP (flagVertex H D t.1.1 k.val.val) k.prop) + simpa only [v, gridPoint_vertex, Subgroup.smul_def] using hh' + have hc (t : T) : Fintype.card (J t) ≤ Module.finrank ℝ (Fin d → ℝ) := by + have h₁ := Fintype.card_subtype_le (fun k : {k : Fin (d + 2) // k ≠ t.1.2.val.1 ∧ k ≠ t.1.2.val.2} ↦ + P (flagVertex H D t.1.1 k.val)) + have h₂ := card_omit_two_le t.1.2.val.1 t.1.2.val.2 t.1.2.prop + change Fintype.card (J t) ≤ _ at h₁ + simp only [Module.finrank_fintype_fun_eq_card, Fintype.card_fin] + exact h₁.trans (Nat.le_of_succ_le_succ h₂) + have hd := dense_finite_conditions (fun t : T ↦ fun q : Fin d → ℝ ↦ + LinearIndependent ℝ (fun k ↦ v t k - q)) + (fun t ↦ isOpen_independent_shift (v t)) (fun t ↦ dense_independent_shift (v t) (hv t) (hc t)) + obtain ⟨q,hqu,hq⟩ := hd.inter_open_nonempty U hU hUn + exact ⟨q,hqu,fun F i j hij s ↦ hq ((F,⟨(i,j),hij⟩),s)⟩ + +lemma common_flag_label {d : ℕ} (H : Subgroup (Signs (d + 1))) + (p : Fin (d + 1) → ℝ) (R h : ℝ) (hR : 0 < R) (hh : 0 < h) (hhr : h ≤ R) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • p) (k • p)) + (F : Flag (d + 1)) (P : Fin (d + 2) → Prop) + (hb : ∀ k, P k → gridPoint h (F.vertex k) ∈ orbitBall (G := H) p R) : + ∃ s : H, ∀ k, P k → ballLabel (G := H) p R (gridPoint h (F.vertex k)) = s := by + have hd : ∀ i j : Fin (d + 2), + dist (gridPoint h (F.vertex i)) (gridPoint h (F.vertex j)) ≤ R := + fun i j ↦ (F.dist_gridPoint_gridPoint h hh.le i j).trans hhr + exact exists_common_ballLabel (G := H) p R hR hsep + (fun k : Fin (d + 2) ↦ gridPoint h (F.vertex k)) P hb hd + +lemma fixed_initial_augmented {d : ℕ} + (H : Subgroup (Signs (d + 1))) (D : SubMulAction H (Flag (d + 1))) + {V : Type u113} [NormedAddCommGroup V] [NormedSpace ℝ V] + (ρ : H →* (V ≃ₗ[ℝ] V)) (L : (Fin d → ℝ) ≃ₗ[ℝ] V) + (p : Fin (d + 1) → ℝ) (R h : ℝ) (hR : 0 < R) (hh : 0 < h) (hhr : h ≤ R) + (hsep : ∀ g k : H, g ≠ k → 8 * R < dist (g • p) (k • p)) + (P : vertices H D → Prop) + (ht : ∀ z : vertices H D, P z → gridPoint h z.val (Fin.last d) = 0) + (hb : ∀ z : vertices H D, P z → gridPoint h z.val ∈ orbitBall (G := H) p R) + (q : Fin d → ℝ) (F : D) (j : Fin (d + 2)) : + LinearIndependent ℝ (fun k : {k : {k : Fin (d + 2) // k ≠ j} // P (flagVertex H D F k.val)} ↦ + ((1 : ℝ), affineOrbitModel H ρ L p R q (gridPoint h (F.val.vertex k.val.val)))) := by + obtain ⟨s,hs⟩ := common_flag_label H p R h hR hh hhr hsep + F.val (fun k ↦ P (flagVertex H D F k)) (fun k hk ↦ hb (flagVertex H D F k) hk) + apply affineOrbitModel_augmented H ρ L p R q + (fun k : {k : {k : Fin (d + 2) // k ≠ j} // P (flagVertex H D F k.val)} ↦ + gridPoint h (F.val.vertex k.val.val)) s (fun k ↦ hs k.val.val k.prop) + have hu := F.val.augmented_spatial_scaled + (fun k : {k : {k : Fin (d + 2) // k ≠ j} // P (flagVertex H D F k.val)} ↦ k.val.val) + (fun _ _ he ↦ Subtype.ext (Subtype.ext he)) hh.ne' s⁻¹.val (fun k ↦ by + rw [← gridPoint_vertex] + exact ht (flagVertex H D F k.val.val) k.prop) + simpa only [gridPoint_vertex, Subgroup.smul_def] using hu + +end SharpLiebThirring.CubeFlags + +namespace SharpLiebThirring.CubeFlags +open Finset SharpLiebThirring.PLParity + +lemma dist_convex_sum_le {ι : Type u114} {E : Type u115} [Fintype ι] [NormedAddCommGroup E] [NormedSpace ℝ E] + (w : ι → ℝ) (hw : ∀ i, 0 ≤ w i) (hs : ∑ i, w i = 1) (x : ι → E) (p : E) (r : ℝ) + (hx : ∀ i, dist (x i) p ≤ r) : dist (∑ i, w i • x i) p ≤ r := by + have he : (∑ i, w i • x i) - p = ∑ i, w i • (x i - p) := by + simp only [smul_sub, Finset.sum_sub_distrib, ← Finset.sum_smul, hs, one_smul] + rw [dist_eq_norm, he] + calc + _ ≤ ∑ i, ‖w i • (x i - p)‖ := norm_sum_le _ _ + _ ≤ ∑ i, w i * r := by + apply Finset.sum_le_sum + intro i _ + rw [norm_smul, Real.norm_eq_abs, abs_of_nonneg (hw i)] + exact mul_le_mul_of_nonneg_left (by simpa only [dist_eq_norm] using hx i) (hw i) + _ = r := by rw [← Finset.sum_mul, hs, one_mul] + +/-- The bottom cube has a nonempty open family of roots with strictly positive +facet barycentric coordinates. A generic root can be chosen in this family. -/ +lemma bottomSeed_open_roots {d : ℕ} (h : ℝ) (hh : 0 < h) (p : Fin d → ℝ) : + ∃ U : Set (Fin d → ℝ), IsOpen U ∧ U.Nonempty ∧ + ∀ q ∈ U, ∃ w : Fin (d + 2) → ℝ, + (∀ k, 0 ≤ w k) ∧ (∀ k, k ≠ Fin.last (d + 1) → 0 < w k) ∧ + ∑ k, w k = 1 ∧ w (Fin.last (d + 1)) = 0 ∧ + ∑ k, w k • gridPoint h ((bottomSeed h p).vertex k) = embedSpatial q ∧ + dist (embedSpatial q) (embedSpatial p) ≤ 2 * h := by + classical + let F := bottomSeed h p + let v : Fin (d + 1) → Fin d → ℝ := fun k ↦ spatial (h • F.point k.castSucc) + have hv : LinearIndependent ℝ (fun k ↦ ((1 : ℝ), v k)) := by + have hi := F.augmented_spatial_scaled Fin.castSucc (Fin.castSucc_injective _) hh.ne' 1 + (fun k ↦ by + change h * F.point k.castSucc (Fin.last d) = 0 + rw [bottomSeed_time h p _ (Fin.castSucc_ne_last k), mul_zero]) + simpa only [one_smul] using hi + let w₀ : Fin (d + 1) → ℝ := fun _ ↦ (d + 1 : ℝ)⁻¹ + have hw₀ : ∀ k, 0 < w₀ k := fun _ ↦ by dsimp [w₀]; positivity + have hs₀ : ∑ k, w₀ k = 1 := by + simp only [w₀, sum_const, card_univ, Fintype.card_fin, nsmul_eq_mul, Nat.cast_add, Nat.cast_one] + exact mul_inv_cancel₀ (by positivity) + obtain ⟨U,hU,hq₀,hpos⟩ := positive_barycentric_neighborhood v hv (by simp) w₀ hw₀ hs₀ + refine ⟨U,hU,⟨_,hq₀⟩,?_⟩ + intro q hq + obtain ⟨z,hz,hzs,he⟩ := hpos q hq + let w : Fin (d + 2) → ℝ := Fin.snoc z 0 + have hw : ∀ k, 0 ≤ w k := by + intro k + refine Fin.lastCases ?_ (fun j ↦ ?_) k + · simp [w] + · simpa only [w,Fin.snoc_castSucc] using (hz j).le + have hp : ∀ k, k ≠ Fin.last (d + 1) → 0 < w k := by + intro k + refine Fin.lastCases ?_ (fun j ↦ ?_) k + · exact fun hk ↦ False.elim (hk rfl) + · intro _ + simpa only [w,Fin.snoc_castSucc] using hz j + have hs : ∑ k, w k = 1 := by + rw [Fin.sum_univ_castSucc] + simpa only [w,Fin.snoc_castSucc,Fin.snoc_last,add_zero] using hzs + have hlast : w (Fin.last (d + 1)) = 0 := Fin.snoc_last _ _ + have hgrid (k : Fin (d + 1)) : gridPoint h (F.vertex k.castSucc) = embedSpatial (v k) := by + rw [gridPoint_vertex] + apply (embed_spatial_of_time_zero _ ?_).symm + change h * F.point k.castSucc (Fin.last d) = 0 + rw [bottomSeed_time h p _ (Fin.castSucc_ne_last k), mul_zero] + have hsum : ∑ k, w k • gridPoint h (F.vertex k) = embedSpatial q := by + rw [Fin.sum_univ_castSucc] + simp only [w, Fin.snoc_castSucc, Fin.snoc_last, zero_smul, add_zero, hgrid] + rw [← he, map_sum] + exact Finset.sum_congr rfl (fun k _ ↦ (map_smul embedSpatial (z k) (v k)).symm) + refine ⟨w,hw,hp,hs,hlast,hsum,?_⟩ + rw [← hsum] + apply dist_convex_sum_le w hw hs _ _ _ + intro k + rw [gridPoint_vertex] + exact bottomSeed_dist_point h hh p k + +end SharpLiebThirring.CubeFlags + +end +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/IntervalAction.lean b/lean/OAI/Analysis/LiebThirring/IntervalAction.lean new file mode 100644 index 0000000000000000000000000000000000000000..648381d9a569d0944b3903445c717079524439b8 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/IntervalAction.lean @@ -0,0 +1,183 @@ +import OAI.Analysis.LiebThirring.ConnectingPath + +namespace OAI + +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Set Metric MeasureTheory Filter +open scoped Topology NNReal +noncomputable section +open Matrix Set MeasureTheory WithLp +open scoped Matrix.Norms.L2Operator Topology +noncomputable section +open Set Metric +open scoped NNReal +noncomputable section +open Matrix +open scoped Matrix.Norms.L2Operator + +namespace SharpLiebThirring.ActionProof +open Matrix MatrixProof MatrixFlow MeasureTheory Set +open scoped Matrix.Norms.L2Operator +variable {N : ℕ} + +def actionDensity (σ : ℝ) (k a v : Fin N → ℝ) : ℝ := + (∑ i, v i^2) + (∑ i, k i^2*a i^2) - (∑ i, a i^2) ^ (1+1/σ) + +lemma actionDensity_continuous {σ : ℝ} (hσ : 0 < σ) (k : Fin N → ℝ) : + Continuous (fun z : (Fin N → ℝ) × (Fin N → ℝ) ↦ actionDensity σ k z.1 z.2) := by + unfold actionDensity + apply Continuous.sub + · fun_prop + · exact (by fun_prop : Continuous (fun z : (Fin N → ℝ) × (Fin N → ℝ) ↦ ∑ i, z.1 i^2)).rpow_const + (fun _ ↦ Or.inr (by positivity)) + +lemma penalized_action_integral {σ δ ε l r η : ℝ} + (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) (hε : 0 < ε) (hlr : l ≤ r) + (k : Fin N → ℝ) (a v : ℝ → Fin N → ℝ) + (ha : ContinuousOn a (Icc l r)) (hv : ContinuousOn v (Icc l r)) + (had : ∀ t ∈ Ioo l r, ∀ i, HasDerivAt (fun t ↦ a t i) (v t i) t) + (hal : a l = 0) (har : a r = 0) (X : ℝ → Sym N) + (hXi : X l = symDiag k) (hXf : X r = -symDiag k) + (hXd : ∀ t ∈ Icc l r, HasDerivWithinAt X + (ε⁻¹ • (sourceField σ δ hσ₁ hδ k (X t) - symOuter (a t))) (Icc l r) t) + (hp : ∀ t ∈ Icc l r, actionDefect σ k (X t,a t) - constraintDefect σ δ k (X t,a t)/ε ≤ η) : + fieldPrimitive σ δ k (-diagonal k) - fieldPrimitive σ δ k (diagonal k) ≤ + (∫ t in l..r, actionDensity σ k (a t) (v t)) + (r-l)*η := by + have hX := HasDerivWithinAt.continuousOn hXd + have hXval := continuous_subtype_val.comp_continuousOn hX + let G := fun t ↦ fieldPrimitive σ δ k (X t) + ∑ i, a t i * ((X t).val *ᵥ a t) i + let G' := fun t ↦ 2*(∑ i, v t i * ((X t).val *ᵥ a t) i) - constraintDefect σ δ k (X t,a t)/ε + have hJ : Continuous (fun A : Sym N ↦ fieldPrimitive σ δ k A) := + continuous_iff_continuousAt.mpr (fun A ↦ (fieldPrimitive_hasFDerivAt hσ₁ hδ k A).continuousAt) + have hMV : ContinuousOn (fun t ↦ (X t).val *ᵥ a t) (Icc l r) := + (show Continuous (fun z : Matrix (Fin N) (Fin N) ℝ × (Fin N → ℝ) ↦ z.1 *ᵥ z.2) + by fun_prop).comp_continuousOn (hXval.prodMk ha) + have hdot : Continuous (fun z : (Fin N → ℝ) × (Fin N → ℝ) ↦ ∑ i, z.1 i * z.2 i) := by + fun_prop + have hG : ContinuousOn G (Icc l r) := + (hJ.comp_continuousOn hX).add (hdot.comp_continuousOn (ha.prodMk hMV)) + have hG' : ContinuousOn G' (Icc l r) := + ((hdot.comp_continuousOn (hv.prodMk hMV)).const_mul 2).sub + (((constraintDefect_continuous hσ₁ hδ k).comp_continuousOn (hX.prodMk ha)).div_const ε) + have hd (t : ℝ) (ht : t ∈ Ioo l r) : HasDerivAt G (G' t) t := by + apply action_ode_identity hσ₁ hδ hε k (had t ht) + ((hXd t (Ioo_subset_Icc_self ht)).hasDerivAt (Icc_mem_nhds ht.1 ht.2)) + change ε • (ε⁻¹ • (matrixField σ δ k (X t).val - vecMulVec (a t) (a t))) = _ + rw [smul_smul,mul_inv_cancel₀ hε.ne',one_smul] + have hi := intervalIntegral.integral_eq_sub_of_hasDerivAt_of_le hlr hG hd + (hG'.intervalIntegrable_of_Icc (μ := volume) hlr) + have hlim : G r - G l = fieldPrimitive σ δ k (-diagonal k) - fieldPrimitive σ δ k (diagonal k) := by + simp only [G,har,hal,hXi,hXf,Pi.zero_apply,zero_mul,Finset.sum_const_zero,add_zero] + rfl + rw [hlim] at hi + have hec := (actionDensity_continuous hσ₀ k).comp_continuousOn (ha.prodMk hv) + have hbound := intervalIntegral.integral_mono_on hlr + (hG'.intervalIntegrable_of_Icc (μ := volume) hlr) + ((hec.add (continuousOn_const (c := η))).intervalIntegrable_of_Icc (μ := volume) hlr) + (fun t ht ↦ (action_penalty_pointwise k (X t) (a t) (v t)).trans + (add_le_add (le_refl (actionDensity σ k (a t) (v t))) (hp t ht))) + change (∫ t in l..r, G' t) ≤ (∫ t in l..r, actionDensity σ k (a t) (v t) + η) at hbound + change ContinuousOn (fun t ↦ actionDensity σ k (a t) (v t)) (Icc l r) at hec + rw [hi,intervalIntegral.integral_add (hec.intervalIntegrable_of_Icc (μ := volume) hlr) + (intervalIntegrable_const),intervalIntegral.integral_const,smul_eq_mul] at hbound + exact hbound + +end SharpLiebThirring.ActionProof +namespace SharpLiebThirring.ActionProof +open Matrix MatrixProof MatrixFlow MeasureTheory Set Filter ContinuationGap +open scoped Matrix.Norms.L2Operator Topology +variable {N : ℕ} + +lemma mulVec_hasDerivAt (C : Matrix (Fin N) (Fin N) ℝ) + {u v : ℝ → Fin N → ℝ} {t : ℝ} (hu : ∀ i, HasDerivAt (fun t ↦ u t i) (v t i) t) (i : Fin N) : + HasDerivAt (fun t ↦ (C *ᵥ u t) i) ((C *ᵥ v t) i) t := by + simpa only [mulVec,dotProduct] using + HasDerivAt.fun_sum (u := Finset.univ) (fun j _ ↦ (hu j).const_mul (C i j)) + +lemma compact_amplitudes {l r R : ℝ} {u : ℝ → Fin N → ℝ} + (hu : ContinuousOn u (Icc l r)) : + IsCompact ((fun z : LowerSpace N × ℝ ↦ z.1.val *ᵥ u z.2) '' + ({C : LowerSpace N | ∀ i j, |C.val i j| ≤ R} ×ˢ Icc l r)) := by + apply ((compact_lower_box R).prod isCompact_Icc).image_of_continuousOn + have hu' : ContinuousOn (fun z : LowerSpace N × ℝ ↦ u z.2) + ({C : LowerSpace N | ∀ i j, |C.val i j| ≤ R} ×ˢ Icc l r) := + hu.comp continuousOn_snd (fun _ hz ↦ hz.2) + have hC : Continuous (fun z : LowerSpace N × ℝ ↦ z.1.val) := continuous_subtype_val.comp continuous_fst + exact (show Continuous (fun z : Matrix (Fin N) (Fin N) ℝ × (Fin N → ℝ) ↦ z.1 *ᵥ z.2) + by fun_prop).comp_continuousOn (hC.continuousOn.prodMk hu') + +/-- An arbitrary finite upper bound on all triangular actions bounds the endpoint +jump. This avoids imposing a finiteness convention on a real-valued supremum. -/ +lemma regularized_action_upper_test {σ δ l r S : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hδ : 0 < δ) (hlr : l ≤ r) (k : Fin N → ℝ) (hk : ∀ i, 0 < k i) + (u v : ℝ → Fin N → ℝ) (hu : ContinuousOn u (Icc l r)) (hv : ContinuousOn v (Icc l r)) + (hud : ∀ t ∈ Ioo l r, ∀ i, HasDerivAt (fun t ↦ u t i) (v t i) t) + (hul : u l = 0) (hur : u r = 0) + (ho : ∀ i j, (∫ t in l..r, u t i*u t j) = if i=j then 1 else 0) + (hS : ∀ C : LowerSpace N, + (∫ t in l..r, actionDensity σ k (C.val *ᵥ u t) (C.val *ᵥ v t)) ≤ S) : + fieldPrimitive σ δ k (-diagonal k) - fieldPrimitive σ δ k (diagonal k) ≤ S := by + obtain ⟨R,hpath⟩ := source_connecting_path hσ₀ hσ₁ hδ hlr k hk u hu ho + let A := (fun z : LowerSpace N × ℝ ↦ z.1.val *ᵥ u z.2) '' + ({C : LowerSpace N | ∀ i j, |C.val i j| ≤ R} ×ˢ Icc l r) + let K : Set (Sym N × (Fin N → ℝ)) := Metric.closedBall 0 ‖k‖ ×ˢ A + have hK : IsCompact K := (isCompact_closedBall (0 : Sym N) ‖k‖).prod (compact_amplitudes hu) + have hη (η : ℝ) (hη : 0 < η) : + fieldPrimitive σ δ k (-diagonal k) - fieldPrimitive σ δ k (diagonal k) ≤ S+(r-l)*η := by + obtain ⟨ε₀,hε₀,hpen⟩ := matrix_compact_penalty hσ₀ hσ₁ hδ k hK hη + let ε := min ε₀ 1 + have hε : 0 < ε := lt_min hε₀ zero_lt_one + obtain ⟨C,X,hC,hXi,hXf,hX,hXd⟩ := hpath ε hε (min_le_right _ _) + have ha : ContinuousOn (fun t ↦ C.val *ᵥ u t) (Icc l r) := + (show Continuous (fun a : Fin N → ℝ ↦ C.val *ᵥ a) by fun_prop).comp_continuousOn hu + have ha' : ContinuousOn (fun t ↦ C.val *ᵥ v t) (Icc l r) := + (show Continuous (fun a : Fin N → ℝ ↦ C.val *ᵥ a) by fun_prop).comp_continuousOn hv + have hh := penalized_action_integral hσ₀ hσ₁ hδ hε hlr k + (fun t ↦ C.val *ᵥ u t) (fun t ↦ C.val *ᵥ v t) ha ha' + (fun t ht ↦ mulVec_hasDerivAt C.val (hud t ht)) + (by rw [hul,mulVec_zero]) (by rw [hur,mulVec_zero]) X hXi hXf hXd + (fun t ht ↦ hpen ε hε (min_le_left _ _) (X t,C.val *ᵥ u t) + ⟨by simpa only [Metric.mem_closedBall,dist_zero_right] using hX t ht, + ⟨(C,t),⟨hC,ht⟩,rfl⟩⟩) + exact hh.trans (add_le_add (hS C) (le_refl _)) + have ht : Tendsto (fun η : ℝ ↦ S+(r-l)*η) (𝓝[>] 0) (𝓝 S) := by + have hc : Continuous (fun η : ℝ ↦ S+(r-l)*η) := by fun_prop + simpa only [mul_zero,add_zero] using (hc.continuousAt (x := (0 : ℝ))).tendsto.mono_left nhdsWithin_le_nhds + exact ge_of_tendsto ht (by filter_upwards [self_mem_nhdsWithin] with η h using hη η h) + +lemma finite_action_upper_test {σ l r S : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hlr : l ≤ r) (k : Fin N → ℝ) (hk : ∀ i, 0 < k i) + (u v : ℝ → Fin N → ℝ) (hu : ContinuousOn u (Icc l r)) (hv : ContinuousOn v (Icc l r)) + (hud : ∀ t ∈ Ioo l r, ∀ i, HasDerivAt (fun t ↦ u t i) (v t i) t) + (hul : u l = 0) (hur : u r = 0) + (ho : ∀ i j, (∫ t in l..r, u t i*u t j) = if i=j then 1 else 0) + (hS : ∀ C : LowerSpace N, + (∫ t in l..r, actionDensity σ k (C.val *ᵥ u t) (C.val *ᵥ v t)) ≤ S) : + (∑ i, ∫ s in -(k i)..k i, (k i^2-s^2)^σ) ≤ S := by + apply le_of_tendsto (fieldPrimitive_endpoint_limit hσ₀ hσ₁ k (fun i ↦ (hk i).le)) + filter_upwards [self_mem_nhdsWithin] with δ hδ + exact regularized_action_upper_test hσ₀ hσ₁ hδ hlr k hk u v hu hv hud hul hur ho hS + +end SharpLiebThirring.ActionProof + +end + +end + +end + +end + +end + +end + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/LocalCompactness.lean b/lean/OAI/Analysis/LiebThirring/LocalCompactness.lean new file mode 100644 index 0000000000000000000000000000000000000000..9a455fc7d45d6fe4935685ca8c1009e755571556 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/LocalCompactness.lean @@ -0,0 +1,73 @@ +import OAI.Analysis.LiebThirring.ContinuousRepresentative + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set Filter +open scoped Topology BoundedContinuousFunction + +def continuousRep (u : H1C) : ℝ → ℂ := (h1_exists_continuous_rep (toH1 u)).choose +lemma continuousRep_continuous (u : H1C) : Continuous (continuousRep u) := + (h1_exists_continuous_rep (toH1 u)).choose_spec.1 +lemma continuousRep_ae (u : H1C) : (fun x ↦ valL u x) =ᵐ[volume] continuousRep u := + (h1_exists_continuous_rep (toH1 u)).choose_spec.2.1 +lemma valL_norm_le (u : H1C) : ‖valL u‖ ≤ ‖u‖ := by + apply (sq_le_sq₀ (norm_nonneg _) (norm_nonneg _)).mp + rw [h1_norm_sq] + exact le_add_of_nonneg_right (sq_nonneg _) +lemma gradL_norm_le (u : H1C) : ‖gradL u‖ ≤ ‖u‖ := by + apply (sq_le_sq₀ (norm_nonneg _) (norm_nonneg _)).mp + rw [h1_norm_sq] + exact le_add_of_nonneg_left (sq_nonneg _) +lemma continuousRep_norm (u : H1C) (x : ℝ) : ‖continuousRep u x‖ ≤ 4*‖u‖ := by + have h := (h1_exists_continuous_rep (toH1 u)).choose_spec.2.2.1 x + simp only [toLp_toH1,grad_toLp_toH1] at h + change ‖continuousRep u x‖ ≤ _ at h + linarith [valL_norm_le u, gradL_norm_le u] +lemma continuousRep_holder (u : H1C) (x y : ℝ) : + ‖continuousRep u x-continuousRep u y‖ ≤ 2*‖u‖*Real.sqrt |x-y| := by + have h := (h1_exists_continuous_rep (toH1 u)).choose_spec.2.2.2 x y + simp only [grad_toLp_toH1] at h + change ‖continuousRep u x-continuousRep u y‖ ≤ _ at h + have hg := mul_le_mul_of_nonneg_right (gradL_norm_le u) (Real.sqrt_nonneg |x-y|) + linarith + +abbrev Interval (R : ℝ) := Icc (-R) R + +def localRep (R : ℝ) (u : H1C) : Interval R →ᵇ ℂ := + BoundedContinuousFunction.mkOfCompact + ⟨fun x ↦ continuousRep u x, (continuousRep_continuous u).comp continuous_subtype_val⟩ + +lemma localRep_compact (R : ℝ) : + IsCompact (closure (localRep R '' Metric.closedBall 0 1)) := by + let A := localRep R '' Metric.closedBall 0 1 + have hin : ∀ (f : Interval R →ᵇ ℂ) (x : Interval R), f ∈ A → + f x ∈ Metric.closedBall 0 4 := by + rintro f x ⟨u,hu,rfl⟩ + rw [Metric.mem_closedBall,dist_zero_right] at hu ⊢ + exact (continuousRep_norm u x).trans (by linarith) + have heq : Equicontinuous ((↑) : A → Interval R → ℂ) := + (Metric.uniformEquicontinuous_of_continuity_modulus (fun t ↦ 2*Real.sqrt t) + (by + have h : Tendsto (fun t : ℝ ↦ 2*Real.sqrt t) (𝓝 0) (𝓝 (2*Real.sqrt 0)) := + tendsto_const_nhds.mul (Real.continuous_sqrt.tendsto (0:ℝ)) + simpa only [Real.sqrt_zero,mul_zero] using h) _ (by + intro x y f + rcases f.2 with ⟨u,hu,huf⟩ + have hn : ‖u‖ ≤ 1 := by simpa only [Metric.mem_closedBall,dist_zero_right] using hu + have h : ‖continuousRep u x-continuousRep u y‖ ≤ 2*Real.sqrt |(x:ℝ)-y| := by + exact (continuousRep_holder u x y).trans (by + nlinarith [Real.sqrt_nonneg |(x:ℝ)-y|]) + rw [← huf] + simpa only [dist_eq_norm,Real.norm_eq_abs,Subtype.dist_eq,localRep, + BoundedContinuousFunction.mkOfCompact_apply,ContinuousMap.coe_mk] using h)).equicontinuous + exact BoundedContinuousFunction.arzela_ascoli (Metric.closedBall 0 4) + (isCompact_closedBall 0 4) A hin heq + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/LocalWeight.lean b/lean/OAI/Analysis/LiebThirring/LocalWeight.lean new file mode 100644 index 0000000000000000000000000000000000000000..b3568f7b5acfb0d5db256f3bfca9e4adee784d9b --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/LocalWeight.lean @@ -0,0 +1,62 @@ +import OAI.Analysis.LiebThirring.WeightedCutoff + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set Filter +open scoped Topology BoundedContinuousFunction + +def localSqrt (W : ℝ → ℝ) (R : ℝ) : ℝ → ℂ := + (Interval R).indicator (fun x ↦ (Real.sqrt ‖W x‖ : ℂ)) + +lemma localSqrt_memLp {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) (R : ℝ) : + MemLp (localSqrt W R) 2 volume := by + have hm : AEStronglyMeasurable (localSqrt W R) volume := + ((Complex.continuous_ofReal.comp Real.continuous_sqrt).comp_aestronglyMeasurable + hW.aestronglyMeasurable.norm).indicator measurableSet_Icc + apply (memLp_two_iff_integrable_sq_norm hm).mpr + have hi : Integrable ((Interval R).indicator (fun x ↦ ‖W x‖)) volume := + IntegrableOn.integrable_indicator + (s := Interval R) (hW.integrableOn_isCompact isCompact_Icc).norm measurableSet_Icc + apply hi.congr + filter_upwards [] with x + symm + by_cases hx : x ∈ Interval R + · simp only [localSqrt,indicator_of_mem hx,Complex.norm_real, + Real.norm_of_nonneg (Real.sqrt_nonneg _),Real.sq_sqrt (norm_nonneg _)] + · simp only [localSqrt,indicator_of_notMem hx,norm_zero,zero_pow (by decide : 2 ≠ 0)] + +def localWeightedL {W : ℝ → ℝ} (d : PotentialData W) (R : ℝ) : H1C →L[ℂ] L2C := + (cutoffL (Interval R) measurableSet_Icc).comp (weightedL d) + +lemma localWeightedL_ae {W : ℝ → ℝ} (d : PotentialData W) (R : ℝ) (u : H1C) : + localWeightedL d R u =ᵐ[volume] (fun x ↦ localSqrt W R x * valL u x) := by + filter_upwards [cutoffL_ae (Interval R) measurableSet_Icc (weightedL d u), + (weightedVal_memLp d u).coeFn_toLp] with x hx hy + change localWeightedL d R u x = (Interval R).indicator (weightedL d u) x at hx + change weightedL d u x = weightedVal d u x at hy + rw [hx] + by_cases hs : x ∈ Interval R + · simp only [indicator_of_mem hs,localSqrt,hy,weightedVal] + · simp only [indicator_of_notMem hs,localSqrt,zero_mul] + +lemma localWeightedL_compact {W : ℝ → ℝ} (d : PotentialData W) + (hW : LocallyIntegrable W volume) {R : ℝ} (hR : 0 ≤ R) : + IsCompactOperator (localWeightedL d R) := by + have he : (fun u : H1C ↦ localWeightedL d R u) = + (fun u : H1C ↦ weightedBCF hR (localSqrt_memLp hW R) (localRep R u)) := by + funext u + apply Lp.ext + exact (localWeightedL_ae d R u).trans + (weightedBCF_localRep_ae hR (localSqrt_memLp hW R) + (fun x hx ↦ by simp only [localSqrt,indicator_of_notMem hx]) u).symm + rw [show (localWeightedL d R : H1C → L2C) = _ from he] + exact weightedBCF_localRep_isCompact hR (localSqrt_memLp hW R) + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/LowestEigenvalue.lean b/lean/OAI/Analysis/LiebThirring/LowestEigenvalue.lean new file mode 100644 index 0000000000000000000000000000000000000000..39a6bc8fb4fa476469862a14447a92a9d853ef56 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/LowestEigenvalue.lean @@ -0,0 +1,83 @@ +import OAI.Analysis.LiebThirring.SpectralMain + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set +open scoped Topology ENNReal + +lemma eigenBasis_nonempty {A : L2C →ₗ.[ℂ] L2C} (hA : IsSelfAdjoint A) {e : ℝ} + {f : L2C} (hf : f ≠ 0) (he : IsOperatorEigenfunction A e f) : + Nonempty (eigenBasisSet A hA e) := by + classical + by_contra h + let : IsEmpty (eigenBasisSet A hA e) := ⟨fun i ↦ h ⟨i⟩⟩ + let u : eigenSpace A e := ⟨f,(mem_eigenSpace A e f).mpr he⟩ + have hz : (eigenBasis A hA e).repr u = 0 := by ext i; exact isEmptyElim i + have hu : u = 0 := (eigenBasis A hA e).repr.injective (by simpa only [map_zero] using hz) + exact hf (congrArg Subtype.val hu) + +lemma oneEigenvalueMoment_eq_iSup (γ : ℝ) {A : L2C →ₗ.[ℂ] L2C} (hA : IsSelfAdjoint A) : + oneEigenvalueMoment γ A = ⨆ i : EigenIndex A hA, (ENNReal.ofReal |i.1.1|)^γ := by + classical + apply le_antisymm + · unfold oneEigenvalueMoment + refine iSup_le (fun f ↦ iSup_le (fun e ↦ iSup_le (fun hf ↦ iSup_le (fun he ↦ ?_)))) + have hn : f ≠ 0 := by intro h; simp only [h,inner_zero_left,zero_ne_one] at hf + obtain ⟨i⟩ := eigenBasis_nonempty hA hn he.2 + exact le_iSup_of_le (⟨⟨e,he.1⟩,i⟩ : EigenIndex A hA) le_rfl + · refine iSup_le (fun i ↦ ?_) + have hf : inner ℂ (eigenBasisVector A hA i) (eigenBasisVector A hA i) = 1 := by + simpa using orthonormal_iff_ite.mp (eigenBasisVector_orthonormal A hA) i i + exact le_iSup_of_le (eigenBasisVector A hA i) (le_iSup_of_le i.1.1 + (le_iSup_of_le hf (le_iSup_of_le ⟨i.1.2,eigenBasisVector_member A hA i⟩ le_rfl))) + +lemma exists_max_weight {γ : ℝ} {A : L2C →ₗ.[ℂ] L2C} (hA : IsSelfAdjoint A) + (hfin : eigenvalueSum γ A hA ≠ ∞) [Nonempty (EigenIndex A hA)] : + ∃ i : EigenIndex A hA, ∀ j : EigenIndex A hA, + (ENNReal.ofReal |j.1.1|)^γ ≤ (ENNReal.ofReal |i.1.1|)^γ := by + classical + let i₀ : EigenIndex A hA := Classical.choice inferInstance + let w := fun i : EigenIndex A hA ↦ (ENNReal.ofReal |i.1.1|)^γ + have hp : w i₀ ≠ 0 := ne_of_gt (ENNReal.rpow_pos + (ENNReal.ofReal_pos.mpr (abs_pos.mpr (ne_of_lt i₀.1.2))) ENNReal.ofReal_ne_top) + have hs : {i : EigenIndex A hA | w i₀ ≤ w i}.Finite := + ENNReal.finite_const_le_of_tsum_ne_top hfin hp + obtain ⟨i,hi,hmax⟩ := Set.exists_max_image _ w hs ⟨i₀,show w i₀ ≤ w i₀ from le_rfl⟩ + refine ⟨i,fun j ↦ ?_⟩ + by_cases hj : w i₀ ≤ w j + · exact hmax j hj + · exact (le_of_lt (not_le.mp hj)).trans hi + +/-- If there is a negative eigenvalue, retaining one state means precisely the +lowest negative eigenvalue, not an assumed minimizer or a finite spectral cutoff. -/ +theorem one_state_is_lowest {γ : ℝ} (hγ : 0 < γ) {A : L2C →ₗ.[ℂ] L2C} + (hA : IsSelfAdjoint A) (hfin : eigenvalueSum γ A hA ≠ ∞) + (hex : ∃ (e : ℝ) (f : L2C), e < 0 ∧ f ≠ 0 ∧ IsOperatorEigenfunction A e f) : + ∃ (e : ℝ) (f : L2C), e < 0 ∧ inner ℂ f f = 1 ∧ + IsOperatorEigenfunction A e f ∧ + oneEigenvalueMoment γ A = (ENNReal.ofReal |e|)^γ ∧ + ∀ (t : ℝ) (g : L2C), t < 0 → g ≠ 0 → IsOperatorEigenfunction A t g → e ≤ t := by + classical + obtain ⟨e₀,f₀,he₀,hf₀,ha₀⟩ := hex + obtain ⟨i₀⟩ := eigenBasis_nonempty hA hf₀ ha₀ + let : Nonempty (EigenIndex A hA) := ⟨⟨⟨e₀,he₀⟩,i₀⟩⟩ + obtain ⟨i,hi⟩ := exists_max_weight hA hfin + refine ⟨i.1.1,eigenBasisVector A hA i,i.1.2,?_,eigenBasisVector_member A hA i,?_,?_⟩ + · simpa using orthonormal_iff_ite.mp (eigenBasisVector_orthonormal A hA) i i + · rw [oneEigenvalueMoment_eq_iSup γ hA] + exact le_antisymm (iSup_le hi) (le_iSup (fun j : EigenIndex A hA ↦ (ENNReal.ofReal |j.1.1|)^γ) i) + · intro t g ht hg ha + obtain ⟨j⟩ := eigenBasis_nonempty hA hg ha + have h := (ENNReal.rpow_le_rpow_iff hγ).mp (hi ⟨⟨t,ht⟩,j⟩) + have hab : |t| ≤ |i.1.1| := (ENNReal.ofReal_le_ofReal_iff (abs_nonneg _)).mp h + rw [abs_of_neg ht,abs_of_neg i.1.2] at hab + linarith + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/Main.lean b/lean/OAI/Analysis/LiebThirring/Main.lean new file mode 100644 index 0000000000000000000000000000000000000000..f39af72d5696c7861255c5c552774be23f73a972 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/Main.lean @@ -0,0 +1,56 @@ +import OAI.Analysis.LiebThirring.ExtremizerMass + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring +open MeasureTheory Set ExtremizerProof + +lemma sharp_times_extremizer_mass {γ : ℝ} (hγ : 1/2 < γ) : + ENNReal.ofReal (sharpConstant γ)*potentialMass γ (equalityPotential γ) = 1 := by + rw [(equalityPotential_admissible hγ).mass_eq_ofReal hγ, + ← ENNReal.ofReal_mul (sharpConstant_pos hγ).le, + sharp_times_extremizer_integral hγ,ENNReal.ofReal_one] + +lemma optimalConstant_le_sharp {γ : ℝ} (hγ₀ : 1/2 < γ) (hγ₁ : γ < 3/2) : + optimalConstant γ ≤ ENNReal.ofReal (sharpConstant γ) := by + unfold optimalConstant + refine iSup_le (fun W ↦ iSup_le (fun hW ↦ iSup_le (fun _ ↦ ?_))) + exact ENNReal.div_le_of_le_mul (negativeMoment_bound hγ₀ hγ₁ hW) + +lemma sharp_le_oneStateConstant {γ : ℝ} (hγ : 1/2 < γ) : + ENNReal.ofReal (sharpConstant γ) ≤ oneStateConstant γ := by + have hr : 0 < (γ-1/2)⁻¹ := inv_pos.mpr (by linarith) + have hW := equalityPotential_admissible hγ + have hpos : 0 < potentialMass γ (equalityPotential γ) := potential_mass_pos hr + have hle : ENNReal.ofReal (sharpConstant γ) ≤ + oneStateMoment γ (equalityPotential γ) / potentialMass γ (equalityPotential γ) := by + apply (ENNReal.le_div_iff_mul_le (Or.inl hpos.ne') (Or.inl (hW.mass_ne_top hγ))).mpr + rw [sharp_times_extremizer_mass hγ] + exact one_le_oneStateMoment hr γ + unfold oneStateConstant + exact hle.trans (le_iSup_of_le (equalityPotential γ) + (le_iSup_of_le hW (le_iSup_of_le hpos le_rfl))) + +/-- Full sharp Lieb–Thirring bound, both optimal constants, and equality at the +explicit potential; no finite spectral cutoff is imposed. -/ +theorem sharp_lieb_thirring : MainClaim := by + intro γ hγ₀ hγ₁ + have hupper := optimalConstant_le_sharp hγ₀ hγ₁ + have hlower := sharp_le_oneStateConstant hγ₀ + have hone := oneStateConstant_le_optimalConstant γ + have hr : 0 < (γ-1/2)⁻¹ := inv_pos.mpr (by linarith) + have hW := equalityPotential_admissible hγ₀ + refine ⟨fun _ hW ↦ negativeMoment_bound hγ₀ hγ₁ hW, + le_antisymm hupper (hlower.trans hone),le_antisymm (hone.trans hupper) hlower, + hW,potential_mass_pos hr,?_⟩ + apply le_antisymm (negativeMoment_bound hγ₀ hγ₁ hW) + rw [sharp_times_extremizer_mass hγ₀] + exact one_le_negativeMoment hr γ + +end SharpLiebThirring + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/MatrixFlow.lean b/lean/OAI/Analysis/LiebThirring/MatrixFlow.lean new file mode 100644 index 0000000000000000000000000000000000000000..d7365a1bbbd855c2718adfcec321d6197e74066b --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/MatrixFlow.lean @@ -0,0 +1,490 @@ +import OAI.Analysis.LiebThirring.RowSigns + +namespace OAI + +universe u148 u149 u150 u151 u152 u153 u154 u155 u156 u157 + +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Finset + +noncomputable section +open Set Metric MeasureTheory Filter +open scoped Topology NNReal +namespace SharpLiebThirring.ODEProof + +/-- Bounded globally Lipschitz fields have solutions on the entire prescribed +compact interval. There is no restriction on the length of the interval. -/ +lemma bounded_ode_exists {E : Type u148} [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E] + {l r : ℝ} (hlr : l ≤ r) (x₀ : E) (f : ℝ → E → E) (K L : ℝ≥0) + (hK : ∀ t ∈ Icc l r, LipschitzWith K (f t)) + (hc : ∀ x, ContinuousOn (fun t ↦ f t x) (Icc l r)) + (hL : ∀ t ∈ Icc l r, ∀ x, ‖f t x‖ ≤ L) : + ∃ x : ℝ → E, x l = x₀ ∧ ∀ t ∈ Icc l r, HasDerivWithinAt x (f t (x t)) (Icc l r) t := by + let a : ℝ≥0 := L * ⟨r-l,sub_nonneg.mpr hlr⟩ + have hp : IsPicardLindelof f ⟨l,⟨le_refl _,hlr⟩⟩ x₀ a 0 L K := + { lipschitzOnWith := fun t ht ↦ (hK t ht).lipschitzOnWith + continuousOn := fun x _ ↦ hc x + norm_le := fun t ht x _ ↦ hL t ht x + mul_max_le := by + change (L : ℝ) * max (r-l) (l-l) ≤ (a : ℝ) - 0 + simp only [sub_self,max_eq_left (sub_nonneg.mpr hlr),sub_zero] + rfl } + exact hp.exists_eq_forall_mem_Icc_hasDerivWithinAt₀ + +lemma derivative_right_of_Icc {E : Type u149} [NormedAddCommGroup E] [NormedSpace ℝ E] + {l r t : ℝ} {f : ℝ → E} {v : E} (ht : t ∈ Ico l r) + (h : HasDerivWithinAt f v (Icc l r) t) : HasDerivWithinAt f v (Ici t) t := + h.mono_of_mem_nhdsWithin (Icc_mem_nhdsGE_of_mem ht) + +/-- Uniform perturbation estimate for solutions, including both endpoint times. -/ +lemma bounded_ode_perturbation {E : Type u150} [NormedAddCommGroup E] [NormedSpace ℝ E] + {l r : ℝ} {f g : ℝ → E → E} {x y : ℝ → E} {K : ℝ≥0} {η : ℝ} + (hK : ∀ t, LipschitzWith K (g t)) + (hx : ∀ t ∈ Icc l r, HasDerivWithinAt x (f t (x t)) (Icc l r) t) + (hy : ∀ t ∈ Icc l r, HasDerivWithinAt y (g t (y t)) (Icc l r) t) + (hxy : x l = y l) + (herr : ∀ t ∈ Icc l r, ∀ z, dist (f t z) (g t z) ≤ η) : + ∀ t ∈ Icc l r, dist (x t) (y t) ≤ gronwallBound 0 K η (t-l) := by + have hh := dist_le_of_approx_trajectories_ODE hK + (HasDerivWithinAt.continuousOn hx) + (fun t ht ↦ derivative_right_of_Icc ht (hx t (mem_Icc_of_Ico ht))) + (fun t ht ↦ herr t (mem_Icc_of_Ico ht) (x t)) + (HasDerivWithinAt.continuousOn hy) + (fun t ht ↦ derivative_right_of_Icc ht (hy t (mem_Icc_of_Ico ht))) + (fun t _ ↦ (dist_self _).le) + (show dist (x l) (y l) ≤ 0 by rw [hxy,dist_self]) + simpa only [add_zero] using hh + +lemma bounded_ode_unique {E : Type u151} [NormedAddCommGroup E] [NormedSpace ℝ E] + {l r : ℝ} {f : ℝ → E → E} {x y : ℝ → E} {K : ℝ≥0} + (hK : ∀ t, LipschitzWith K (f t)) + (hx : ∀ t ∈ Icc l r, HasDerivWithinAt x (f t (x t)) (Icc l r) t) + (hy : ∀ t ∈ Icc l r, HasDerivWithinAt y (f t (y t)) (Icc l r) t) + (hxy : x l = y l) : EqOn x y (Icc l r) := by + intro t ht + apply dist_le_zero.mp + have hh := bounded_ode_perturbation hK hx hy hxy (fun _ _ _ ↦ (dist_self _).le) t ht + simpa only [gronwallBound_ε0_δ0] using hh + +end SharpLiebThirring.ODEProof +namespace SharpLiebThirring.ODEProof +open Set Metric Filter + +/-- Continuous parameter dependence, uniform even when the evaluation time varies. -/ +lemma continuous_solution_family {E : Type u152} {P : Type u153} [NormedAddCommGroup E] [NormedSpace ℝ E] + [TopologicalSpace P] {l r : ℝ} {f : P → ℝ → E → E} {x : P → ℝ → E} + (K : P → ℝ≥0) (η : P → P → ℝ) + (hK : ∀ p t, LipschitzWith (K p) (f p t)) + (hx : ∀ p t, t ∈ Icc l r → HasDerivWithinAt (x p) (f p t (x p t)) (Icc l r) t) + (hinit : ∀ p q, x p l = x q l) + (hη : ∀ p, Continuous (fun q ↦ η q p)) (hη0 : ∀ p, η p p = 0) + (hηpos : ∀ p q, 0 ≤ η p q) + (herr : ∀ p q t, t ∈ Icc l r → ∀ z, dist (f p t z) (f q t z) ≤ η p q) : + Continuous (fun z : P × Icc l r ↦ x z.1 z.2) := by + apply continuous_iff_continuousAt.mpr + intro z + apply tendsto_iff_dist_tendsto_zero.mpr + have hb : ∀ w : P × Icc l r, + dist (x w.1 w.2) (x z.1 z.2) ≤ + gronwallBound 0 (K z.1) (η w.1 z.1) (r-l) + dist (x z.1 w.2) (x z.1 z.2) := by + intro w + apply (dist_triangle _ (x z.1 w.2) _).trans + apply add_le_add _ (le_refl _) + exact (bounded_ode_perturbation (hK z.1) (hx w.1) (hx z.1) (hinit w.1 z.1) + (herr w.1 z.1) w.2 w.2.prop).trans + (gronwallBound_mono (by positivity) (hηpos w.1 z.1) (K z.1).prop + (sub_le_sub_right w.2.prop.2 l)) + apply squeeze_zero' (Eventually.of_forall (fun _ ↦ dist_nonneg)) (Eventually.of_forall hb) + have hfirst : Tendsto (fun w : P × Icc l r ↦ gronwallBound 0 (K z.1) (η w.1 z.1) (r-l)) + (𝓝 z) (𝓝 0) := by + have hh := ((gronwallBound_continuous_ε 0 (K z.1) (r-l)).comp + ((hη z.1).comp continuous_fst)).continuousAt (x := z) + simpa only [ContinuousAt,Function.comp_def,hη0,gronwallBound_ε0_δ0] using hh + have hc : Continuous (fun t : Icc l r ↦ x z.1 t) := + (HasDerivWithinAt.continuousOn (hx z.1)).domRestrict + have hsecond : Tendsto (fun w : P × Icc l r ↦ dist (x z.1 w.2) (x z.1 z.2)) + (𝓝 z) (𝓝 0) := by + have hh := ((hc.comp continuous_snd).dist (continuous_const (y := x z.1 z.2))).continuousAt (x := z) + simpa only [ContinuousAt,Function.comp_def,dist_self] using hh + simpa only [add_zero] using hfirst.add hsecond + +/-- Ready-to-use parameterized affine forcing in a bounded Lipschitz field. -/ +lemma affine_forcing_exists_family {E : Type u154} {P : Type u155} [NormedAddCommGroup E] [NormedSpace ℝ E] + [CompleteSpace E] [TopologicalSpace P] {l r : ℝ} (hlr : l ≤ r) (x₀ : E) + (M : E → E) (K B : ℝ≥0) (hK : LipschitzWith K M) (hB : ∀ x, ‖M x‖ ≤ B) + (a : P → ℝ) (ha : Continuous a) (v : P → C(Icc l r,E)) (hv : Continuous v) : + ∃ x : P → ℝ → E, (∀ p, x p l = x₀) ∧ + (∀ p t (ht : t ∈ Icc l r), HasDerivWithinAt (x p) + (a p • M (x p t) + v p ⟨t,ht⟩) (Icc l r) t) ∧ + Continuous (fun z : P × Icc l r ↦ x z.1 z.2) := by + let V : P → ℝ → E := fun p t ↦ if ht : t ∈ Icc l r then v p ⟨t,ht⟩ else 0 + have hV (p : P) : ContinuousOn (V p) (Icc l r) := by + rw [continuousOn_iff_continuous_domRestrict] + convert (v p).continuous using 1 + funext t + simp only [Set.domRestrict,V,dite_eq_left t.prop] + have hVnorm (p : P) (t : ℝ) (ht : t ∈ Icc l r) : ‖V p t‖ ≤ ‖v p‖ := by + simpa only [V,dite_eq_left ht] using (v p).norm_coe_le_norm ⟨t,ht⟩ + let f := fun p t y ↦ a p • M y + V p t + have hLip (p : P) (t : ℝ) : LipschitzWith (‖a p‖₊ * K) (f p t) := by + apply lipschitzWith_iff_norm_sub_le.mpr + intro y z + simp only [f,add_sub_add_right_eq_sub,← smul_sub,norm_smul,NNReal.coe_mul,coe_nnnorm] + exact (mul_le_mul_of_nonneg_left (lipschitzWith_iff_norm_sub_le.mp hK y z) + (norm_nonneg _)).trans_eq (mul_assoc _ _ _).symm + have hex (p : P) : ∃ x : ℝ → E, x l = x₀ ∧ + ∀ t ∈ Icc l r, HasDerivWithinAt x (f p t (x t)) (Icc l r) t := by + apply bounded_ode_exists hlr x₀ (f p) (‖a p‖₊ * K) (‖a p‖₊ * B + ‖v p‖₊) + (fun t _ ↦ hLip p t) (fun y ↦ continuousOn_const.add (hV p)) + intro t ht y + calc ‖f p t y‖ ≤ ‖a p • M y‖ + ‖V p t‖ := norm_add_le _ _ + _ ≤ ‖a p‖ * B + ‖v p‖ := by rw [norm_smul]; gcongr; exact hB _; exact hVnorm p t ht + _ = _ := by rfl + choose x hxi hxd using hex + refine ⟨x,hxi,?_,?_⟩ + · intro p t ht + simpa only [f,V,dite_eq_left ht] using hxd p t ht + · let η := fun p q ↦ ‖a p - a q‖ * B + ‖v p - v q‖ + apply continuous_solution_family (fun p ↦ ‖a p‖₊ * K) η hLip hxd + (fun p q ↦ (hxi p).trans (hxi q).symm) + (fun p ↦ (ha.sub continuous_const).norm.mul_const _ |>.add (hv.sub continuous_const).norm) + (fun p ↦ by simp [η]) (fun p q ↦ by dsimp [η]; positivity) + intro p q t ht y + have hdiff : f p t y - f q t y = (a p-a q) • M y + (V p t - V q t) := by + dsimp [f]; module + rw [dist_eq_norm,hdiff] + apply (norm_add_le _ _).trans + apply add_le_add + · rw [norm_smul]; exact mul_le_mul_of_nonneg_left (hB _) (norm_nonneg _) + · simpa only [V,dite_eq_left ht,ContinuousMap.sub_apply] using + (v p-v q).norm_coe_le_norm ⟨t,ht⟩ + +end SharpLiebThirring.ODEProof +noncomputable section +open Matrix Set MeasureTheory WithLp +open scoped Matrix.Norms.L2Operator Topology +namespace SharpLiebThirring.MatrixFlow +abbrev Sym (N : ℕ) := selfAdjoint (Matrix (Fin N) (Fin N) ℝ) +def symInclude {N : ℕ} : Sym N →ₗ[ℝ] Matrix (Fin N) (Fin N) ℝ where + toFun := Subtype.val + map_add' := fun _ _ ↦ rfl + map_smul' := fun _ _ ↦ rfl +instance {N : ℕ} : FiniteDimensional ℝ (Sym N) := + FiniteDimensional.of_injective symInclude Subtype.val_injective + +def symDiag {N : ℕ} (k : Fin N → ℝ) : Sym N := ⟨diagonal k,isHermitian_diagonal _⟩ +def symOuter {N : ℕ} (a : Fin N → ℝ) : Sym N := + ⟨vecMulVec a a,by ext i j; simp [vecMulVec,mul_comm]⟩ +@[simp] lemma symOuter_apply {N : ℕ} (a : Fin N → ℝ) (i j : Fin N) : + (symOuter a).val i j = a i * a j := rfl + +def symEntry {N : ℕ} (i j : Fin N) : Sym N →L[ℝ] ℝ := + LinearMap.toContinuousLinearMap + { toFun := fun A ↦ A.val i j + map_add' := fun _ _ ↦ rfl + map_smul' := fun _ _ ↦ rfl } +@[simp] lemma symEntry_apply {N : ℕ} (i j : Fin N) (A : Sym N) : symEntry i j A = A.val i j := rfl +lemma continuous_symOuter {N : ℕ} : Continuous (symOuter : (Fin N → ℝ) → Sym N) := by + apply Continuous.subtype_mk + change Continuous (fun a : Fin N → ℝ ↦ vecMulVec a a) + fun_prop + +def symConj {N : ℕ} (s : Fin N → ℝ) : Sym N →L[ℝ] Sym N := + LinearMap.toContinuousLinearMap + { toFun := fun A ↦ ⟨fun i j ↦ s i * A.val i j * s j,by + ext i j + change s j * A.val j i * s i = s i * A.val i j * s j + have hh : A.val j i = A.val i j := congrFun (congrFun A.prop i) j + rw [hh]; ring⟩ + map_add' := by intro A B; apply Subtype.ext; ext i j; change s i * (_ + _) * s j = _ + _; ring + map_smul' := by intro r A; apply Subtype.ext; ext i j; change s i * (r * _) * s j = r * _; ring } +@[simp] lemma symConj_apply {N : ℕ} (s : Fin N → ℝ) (A : Sym N) (i j : Fin N) : + (symConj s A).val i j = s i * A.val i j * s j := rfl +lemma symConj_val {N : ℕ} (s : Fin N → ℝ) (A : Sym N) : + (symConj s A).val = diagonal s * A.val * diagonal s := by + ext i j; simp [diagonal_mul,mul_diagonal] +lemma sign_sq {N : ℕ} (s : Fin N → ℝ) (hs : ∀ i, s i = 1 ∨ s i = -1) (i : Fin N) : + s i * s i = 1 := by rcases hs i with h|h <;> rw [h] <;> norm_num +lemma sign_diagonal_unitary {N : ℕ} (s : Fin N → ℝ) (hs : ∀ i, s i = 1 ∨ s i = -1) : + diagonal s ∈ unitary (Matrix (Fin N) (Fin N) ℝ) := by + rw [Unitary.mem_iff] + have h : star (diagonal s) = diagonal s := isHermitian_diagonal s + rw [h,diagonal_mul_diagonal] + have hh : diagonal (fun i ↦ s i*s i) = (1 : Matrix (Fin N) (Fin N) ℝ) := by + simp only [sign_sq s hs,diagonal_one] + exact ⟨hh,hh⟩ +lemma norm_symConj {N : ℕ} (s : Fin N → ℝ) (hs : ∀ i, s i = 1 ∨ s i = -1) (A : Sym N) : + ‖symConj s A‖ = ‖A‖ := by + change ‖(symConj s A).val‖ = ‖A.val‖ + rw [symConj_val,CStarRing.norm_mul_mem_unitary _ (sign_diagonal_unitary s hs), + CStarRing.norm_mem_unitary_mul _ (sign_diagonal_unitary s hs)] +lemma symConj_diag {N : ℕ} (s : Fin N → ℝ) (hs : ∀ i, s i = 1 ∨ s i = -1) + (k : Fin N → ℝ) : symConj s (symDiag k) = symDiag k := by + apply Subtype.ext + ext i j + by_cases hij : i=j + · subst j + change s i * diagonal k i i * s i = diagonal k i i + rw [diagonal_apply_eq] + rcases hs i with h|h <;> rw [h] <;> ring + · change s i * diagonal k i j * s j = diagonal k i j + simp only [diagonal_apply_ne _ hij,mul_zero,zero_mul] +lemma symConj_outer {N : ℕ} (s a : Fin N → ℝ) : + symConj s (symOuter a) = symOuter (fun i ↦ s i * a i) := by + apply Subtype.ext; ext i j; dsimp [symOuter,symConj,vecMulVec]; ring + +lemma zero_row_sign {N : ℕ} (i : Fin N) : + ∀ j : Fin N, (if j=i then (-1 : ℝ) else 1) = 1 ∨ (if j=i then (-1 : ℝ) else 1) = -1 := by + intro j; split_ifs <;> simp +lemma fixed_reflection_offdiag {N : ℕ} (i : Fin N) (A : Sym N) + (h : symConj (fun j ↦ if j=i then -1 else 1) A = A) (j : Fin N) (hij : i ≠ j) : + A.val i j = 0 := by + have hh := congrArg (fun B : Sym N ↦ B.val i j) h + simp only [symConj_apply,ite_true,ite_eq_right (Ne.symm hij),neg_mul,one_mul,mul_one] at hh + linarith + +lemma matrix_norm_entry {N : ℕ} (B : Matrix (Fin N) (Fin N) ℝ) (i j : Fin N) : + |B i j| ≤ ‖B‖ := by + let T : EuclideanSpace ℝ (Fin N) →L[ℝ] EuclideanSpace ℝ (Fin N) := + Matrix.toEuclideanCLM (𝕜 := ℝ) (n := Fin N) B + have h := T.le_opNorm (toLp 2 (Pi.single j (1 : ℝ))) + have hh := PiLp.norm_apply_le (T (toLp 2 (Pi.single j (1 : ℝ)))) i + simpa [T, Matrix.toEuclideanCLM_toLp, Matrix.l2_opNorm_toEuclideanCLM] using hh.trans h + +end SharpLiebThirring.MatrixFlow +namespace SharpLiebThirring.MatrixFlow +open ODEProof Set Matrix +open scoped Topology +variable {N : ℕ} + +/-- The outer-product forcing, viewed in the supremum-norm space on the time interval. -/ +def matrixForcing (ε : ℝ) {l r : ℝ} (u : ℝ → Fin N → ℝ) + (hu : ContinuousOn u (Icc l r)) (C : Matrix (Fin N) (Fin N) ℝ) : C(Icc l r, Sym N) := + ⟨fun t ↦ -ε⁻¹ • symOuter (C *ᵥ u t), by + exact (continuous_symOuter.comp (continuous_const.matrix_mulVec hu.domRestrict)).const_smul (-ε⁻¹)⟩ + +lemma continuous_matrixForcing (ε : ℝ) {l r : ℝ} (u : ℝ → Fin N → ℝ) + (hu : ContinuousOn u (Icc l r)) : Continuous (matrixForcing ε u hu) := by + apply ContinuousMap.continuous_of_continuous_uncurry + change Continuous (fun z : Matrix (Fin N) (Fin N) ℝ × Icc l r ↦ + -ε⁻¹ • symOuter (z.1 *ᵥ u z.2)) + have hu' := hu.domRestrict.comp (continuous_snd (X := Matrix (Fin N) (Fin N) ℝ)) + exact (continuous_symOuter.comp (continuous_fst.matrix_mulVec hu')).const_smul (-ε⁻¹) + +def flowRhs (ε : ℝ) (M : Sym N → Sym N) (u : ℝ → Fin N → ℝ) + (p : Matrix (Fin N) (Fin N) ℝ × ℝ) (t : ℝ) (B : Sym N) : Sym N := + (ε⁻¹ * p.2) • M B - ε⁻¹ • symOuter (p.1 *ᵥ u t) + +lemma flowRhs_lipschitz (ε : ℝ) (M : Sym N → Sym N) {L : ℝ≥0} + (hL : LipschitzWith L M) (u : ℝ → Fin N → ℝ) + (p : Matrix (Fin N) (Fin N) ℝ × ℝ) (t : ℝ) : + LipschitzWith (‖ε⁻¹*p.2‖₊ * L) (flowRhs ε M u p t) := by + apply lipschitzWith_iff_norm_sub_le.mpr + intro A B + simp only [flowRhs,sub_sub_sub_cancel_right,← smul_sub,norm_smul, + NNReal.coe_mul,coe_nnnorm] + exact (mul_le_mul_of_nonneg_left (lipschitzWith_iff_norm_sub_le.mp hL A B) + (norm_nonneg _)).trans_eq (mul_assoc _ _ _).symm + +lemma matrix_flow_exists {l r : ℝ} (hlr : l ≤ r) (ε : ℝ) (k : Fin N → ℝ) + (u : ℝ → Fin N → ℝ) (hu : ContinuousOn u (Icc l r)) + (M : Sym N → Sym N) (L B : ℝ≥0) (hL : LipschitzWith L M) (hB : ∀ A, ‖M A‖ ≤ B) : + ∃ X : (Matrix (Fin N) (Fin N) ℝ × ℝ) → ℝ → Sym N, + (∀ p, X p l = symDiag k) ∧ + (∀ p t, t ∈ Icc l r → HasDerivWithinAt (X p) (flowRhs ε M u p t (X p t)) (Icc l r) t) ∧ + Continuous (fun z : (Matrix (Fin N) (Fin N) ℝ × ℝ) × Icc l r ↦ X z.1 z.2) := by + obtain ⟨X,hXi,hXd,hXc⟩ := affine_forcing_exists_family hlr (symDiag k) M L B hL hB + (fun p : Matrix (Fin N) (Fin N) ℝ × ℝ ↦ ε⁻¹*p.2) (by fun_prop) + (fun p ↦ matrixForcing ε u hu p.1) ((continuous_matrixForcing ε u hu).comp continuous_fst) + refine ⟨X,hXi,?_,hXc⟩ + intro p t ht + simpa only [flowRhs,matrixForcing,ContinuousMap.coe_mk,neg_smul,sub_eq_add_neg] using hXd p t ht + +lemma matrix_rowSign_mulVec (s : Fin N → ℝ) (C : Matrix (Fin N) (Fin N) ℝ) + (u : Fin N → ℝ) : (fun i j ↦ s i * C i j) *ᵥ u = fun i ↦ s i * (C *ᵥ u) i := by + ext i + simp only [mulVec,dotProduct,Finset.mul_sum] + apply Finset.sum_congr rfl + intro j _ + ring + +lemma flowRhs_equivariant (ε : ℝ) (M : Sym N → Sym N) (u : ℝ → Fin N → ℝ) + (s : Fin N → ℝ) (hM : ∀ A, M (symConj s A) = symConj s (M A)) + (C : Matrix (Fin N) (Fin N) ℝ) (θ t : ℝ) (A : Sym N) : + flowRhs ε M u (fun i j ↦ s i * C i j,θ) t (symConj s A) = + symConj s (flowRhs ε M u (C,θ) t A) := by + simp only [flowRhs,hM,map_sub,map_smul,matrix_rowSign_mulVec,symConj_outer] + +lemma matrix_flow_equivariant {l r ε : ℝ} {M : Sym N → Sym N} {L : ℝ≥0} + (hL : LipschitzWith L M) (k : Fin N → ℝ) (u : ℝ → Fin N → ℝ) + (X : (Matrix (Fin N) (Fin N) ℝ × ℝ) → ℝ → Sym N) + (hXi : ∀ p, X p l = symDiag k) + (hXd : ∀ p t, t ∈ Icc l r → HasDerivWithinAt (X p) (flowRhs ε M u p t (X p t)) (Icc l r) t) + (s : Fin N → ℝ) (hs : ∀ i, s i = 1 ∨ s i = -1) + (hM : ∀ A, M (symConj s A) = symConj s (M A)) + (C : Matrix (Fin N) (Fin N) ℝ) (θ : ℝ) : + EqOn (X (fun i j ↦ s i*C i j,θ)) (fun t ↦ symConj s (X (C,θ) t)) (Icc l r) := by + apply bounded_ode_unique (fun t ↦ flowRhs_lipschitz ε M hL u (fun i j ↦ s i*C i j,θ) t) + (hXd _) _ (by rw [hXi,hXi,symConj_diag s hs]) + intro t ht + have hh := (symConj s).hasFDerivAt.comp_hasDerivWithinAt t (hXd (C,θ) t ht) + simpa only [Function.comp_def,← flowRhs_equivariant ε M u s hM C θ t (X (C,θ) t)] using hh + +end SharpLiebThirring.MatrixFlow +namespace SharpLiebThirring.MatrixFlow +open Matrix Set ODEProof MeasureTheory +variable {N : ℕ} + +def symCongr (C : Matrix (Fin N) (Fin N) ℝ) : Sym N →L[ℝ] Sym N := + LinearMap.toContinuousLinearMap + { toFun := fun A ↦ ⟨C * A.val * C.transpose, + by + change (C * A.val * C.transpose).IsHermitian + simpa only [conjTranspose_eq_transpose_of_trivial] using isHermitian_mul_mul_conjTranspose C A.prop⟩ + map_add' := by + intro A B; apply Subtype.ext + change C * (A.val + B.val) * C.transpose = C * A.val * C.transpose + C * B.val * C.transpose + rw [mul_add,add_mul] + map_smul' := by + intro r A; apply Subtype.ext + change C * (r • A.val) * C.transpose = r • (C * A.val * C.transpose) + rw [Matrix.mul_smul,Matrix.smul_mul] } +@[simp] lemma symCongr_apply (C : Matrix (Fin N) (Fin N) ℝ) (A : Sym N) : + (symCongr C A).val = C * A.val * C.transpose := rfl + +lemma symCongr_outer (C : Matrix (Fin N) (Fin N) ℝ) (a : Fin N → ℝ) : + symCongr C (symOuter a) = symOuter (C *ᵥ a) := by + apply Subtype.ext + simp only [symCongr_apply,symOuter,mul_vecMulVec,vecMulVec_mul,vecMul_transpose] + +lemma integral_outer_identity {l r : ℝ} (hlr : l ≤ r) + (u : ℝ → Fin N → ℝ) (hu : ContinuousOn u (Icc l r)) + (ho : ∀ i j, (∫ t in l..r, u t i * u t j) = if i=j then 1 else 0) : + (∫ t in l..r, symOuter (u t)) = symDiag (fun _ ↦ 1) := by + have hc : ContinuousOn (fun t ↦ symOuter (u t)) (Icc l r) := continuous_symOuter.comp_continuousOn hu + apply Subtype.ext + ext i j + have hh := (symEntry i j).intervalIntegral_comp_comm (hc.intervalIntegrable_of_Icc (μ := volume) hlr) + change (∫ t in l..r, u t i*u t j) = (∫ t in l..r, symOuter (u t)).val i j at hh + rw [← hh,ho] + exact (diagonal_apply (fun _ : Fin N ↦ (1 : ℝ)) i j).symm + +lemma integral_outer_mulVec {l r : ℝ} (hlr : l ≤ r) + (u : ℝ → Fin N → ℝ) (hu : ContinuousOn u (Icc l r)) + (ho : ∀ i j, (∫ t in l..r, u t i * u t j) = if i=j then 1 else 0) + (C : Matrix (Fin N) (Fin N) ℝ) : + (∫ t in l..r, symOuter (C *ᵥ u t)).val = C * C.transpose := by + have hc : ContinuousOn (fun t ↦ symOuter (u t)) (Icc l r) := continuous_symOuter.comp_continuousOn hu + have hh := (symCongr C).intervalIntegral_comp_comm (hc.intervalIntegrable_of_Icc (μ := volume) hlr) + simp only [symCongr_outer,integral_outer_identity hlr u hu ho] at hh + rw [hh] + simp only [symCongr_apply,symDiag,diagonal_one,mul_one] + +lemma integrate_affine_ode {E : Type u156} [NormedAddCommGroup E] [NormedSpace ℝ E] + [CompleteSpace E] {l r a b : ℝ} (hlr : l ≤ r) (X V W : ℝ → E) + (hV : ContinuousOn V (Icc l r)) (hW : ContinuousOn W (Icc l r)) + (hd : ∀ t ∈ Icc l r, HasDerivWithinAt X (a • V t - b • W t) (Icc l r) t) : + a • (∫ t in l..r, V t) - b • (∫ t in l..r, W t) = X r - X l := by + have hc := (hV.const_smul a).sub (hW.const_smul b) + have hh := intervalIntegral.integral_eq_sub_of_hasDerivAt_of_le hlr + (HasDerivWithinAt.continuousOn hd) + (fun t ht ↦ (hd t (Ioo_subset_Icc_self ht)).hasDerivAt (Icc_mem_nhds ht.1 ht.2)) + (hc.intervalIntegrable_of_Icc (μ := volume) hlr) + have hiV : IntervalIntegrable (fun t ↦ a • V t) volume l r := by + exact (hV.intervalIntegrable_of_Icc (μ := volume) hlr).smul a + have hiW : IntervalIntegrable (fun t ↦ b • W t) volume l r := by + exact (hW.intervalIntegrable_of_Icc (μ := volume) hlr).smul b + rw [intervalIntegral.integral_sub hiV hiW,intervalIntegral.integral_smul, + intervalIntegral.integral_smul] at hh + exact hh + +lemma flow_integral_sub {l r ε θ : ℝ} (hlr : l ≤ r) + (M : Sym N → Sym N) (hM : Continuous M) + (u : ℝ → Fin N → ℝ) (hu : ContinuousOn u (Icc l r)) + (C : Matrix (Fin N) (Fin N) ℝ) (X : ℝ → Sym N) + (hXd : ∀ t ∈ Icc l r, HasDerivWithinAt X (flowRhs ε M u (C,θ) t (X t)) (Icc l r) t) : + (ε⁻¹ * θ) • (∫ t in l..r, M (X t)) - ε⁻¹ • (∫ t in l..r, symOuter (C *ᵥ u t)) = X r - X l := by + apply integrate_affine_ode hlr X (fun t ↦ M (X t)) (fun t ↦ symOuter (C *ᵥ u t)) + (hM.comp_continuousOn (HasDerivWithinAt.continuousOn hXd)) _ hXd + apply continuous_symOuter.comp_continuousOn + exact (show Continuous (fun v : Fin N → ℝ ↦ C *ᵥ v) by fun_prop).comp_continuousOn hu + +lemma flow_integral_identity {l r ε : ℝ} (hlr : l ≤ r) (hε : ε ≠ 0) + (M : Sym N → Sym N) (hM : Continuous M) (k : Fin N → ℝ) + (u : ℝ → Fin N → ℝ) (hu : ContinuousOn u (Icc l r)) + (ho : ∀ i j, (∫ t in l..r, u t i * u t j) = if i=j then 1 else 0) + (C : Matrix (Fin N) (Fin N) ℝ) (θ : ℝ) (X : ℝ → Sym N) + (hXi : X l = symDiag k) + (hXd : ∀ t ∈ Icc l r, HasDerivWithinAt X (flowRhs ε M u (C,θ) t (X t)) (Icc l r) t) : + C * C.transpose = ε • (diagonal k - (X r).val) + θ • (∫ t in l..r, M (X t)).val := by + have hh := flow_integral_sub hlr M hM u hu C X hXd + have he := congrArg (fun Z : Sym N ↦ ε • Z) hh + simp only [smul_sub,smul_smul,mul_inv_cancel₀ hε,one_smul] at he + have hcoef : ε * (ε⁻¹ * θ) = θ := by field_simp + rw [hcoef,hXi] at he + have he' := congrArg (fun Z : Sym N ↦ Z.val) he + change θ • (∫ t in l..r, M (X t)).val - (∫ t in l..r, symOuter (C *ᵥ u t)).val = + ε • (X r).val - ε • diagonal k at he' + rw [integral_outer_mulVec hlr u hu ho C,sub_eq_iff_eq_add] at he' + rw [he',smul_sub] + abel + +end SharpLiebThirring.MatrixFlow +namespace SharpLiebThirring.MatrixFlow +open Matrix Set MeasureTheory +variable {N : ℕ} + +lemma gram_entry_bound (C : Matrix (Fin N) (Fin N) ℝ) {D : ℝ} + (hD : ‖C * C.transpose‖ ≤ D) (i j : Fin N) : |C i j| ≤ max D 0 + 1 := by + have hsq : (C i j)^2 ≤ (C*C.transpose) i i := by + simpa only [mul_apply,transpose_apply,pow_two] using + (Finset.single_le_sum (fun a (_ : a ∈ (Finset.univ : Finset (Fin N))) ↦ mul_self_nonneg (C i a)) + (Finset.mem_univ j)) + have hh := hsq.trans ((le_abs_self _).trans ((matrix_norm_entry _ i i).trans hD)) + have hm := le_max_left D 0 + have hn := le_max_right D 0 + have hs := sq_abs (C i j) + nlinarith [abs_nonneg (C i j)] + +lemma bounded_integral_norm {E : Type u157} [NormedAddCommGroup E] [NormedSpace ℝ E] + {l r B : ℝ} (hlr : l ≤ r) (f : ℝ → E) (hf : ∀ t ∈ Icc l r, ‖f t‖ ≤ B) : + ‖∫ t in l..r, f t‖ ≤ (r-l)*B := by + have hh := intervalIntegral.norm_integral_le_of_norm_le_const + (fun t (ht : t ∈ Set.uIoc l r) ↦ hf t (by + rw [uIoc_of_le hlr] at ht + exact Ioc_subset_Icc_self ht)) + simpa only [abs_of_nonneg (sub_nonneg.mpr hlr),mul_comm] using hh + +lemma matching_gram_norm {l r ε : ℝ} (hlr : l ≤ r) (hε : ε ≠ 0) + (M : Sym N → Sym N) (hM : Continuous M) (B : ℝ≥0) (hB : ∀ A, ‖M A‖ ≤ B) + (k : Fin N → ℝ) (u : ℝ → Fin N → ℝ) (hu : ContinuousOn u (Icc l r)) + (ho : ∀ i j, (∫ t in l..r, u t i * u t j) = if i=j then 1 else 0) + (C : Matrix (Fin N) (Fin N) ℝ) {θ : ℝ} (hθ : θ ∈ Icc (0 : ℝ) 1) (X : ℝ → Sym N) + (hXi : X l = symDiag k) (hXf : X r = -symDiag k) + (hXd : ∀ t ∈ Icc l r, HasDerivWithinAt X (flowRhs ε M u (C,θ) t (X t)) (Icc l r) t) : + ‖C * C.transpose‖ ≤ |ε| *(2*‖k‖) + (r-l)*B := by + rw [flow_integral_identity hlr hε M hM k u hu ho C θ X hXi hXd,hXf] + have hi := bounded_integral_norm hlr (fun t ↦ M (X t)) (fun _ _ ↦ hB _) + have he : (-(symDiag k)).val = -diagonal k := rfl + rw [he,sub_neg_eq_add] + apply (norm_add_le _ _).trans + rw [norm_smul,norm_smul,Real.norm_eq_abs,Real.norm_eq_abs,abs_of_nonneg hθ.1] + apply add_le_add + · have hh := norm_add_le (diagonal k) (diagonal k) + rw [Matrix.l2_opNorm_diagonal] at hh + exact mul_le_mul_of_nonneg_left (hh.trans_eq (by ring)) (abs_nonneg ε) + · exact (mul_le_of_le_one_left (norm_nonneg _) hθ.2).trans hi + +end SharpLiebThirring.MatrixFlow + +end +end +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/MatrixOrder.lean b/lean/OAI/Analysis/LiebThirring/MatrixOrder.lean new file mode 100644 index 0000000000000000000000000000000000000000..bdc2da793323c2706499794f25b974385018cc7c --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/MatrixOrder.lean @@ -0,0 +1,1063 @@ +import OAI.Analysis.LiebThirring.Model + +namespace OAI + +universe u1 u2 u3 u4 u5 + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix +namespace SharpLiebThirring + + +/-! ## The matrix field and action -/ + +/-- The regularized primitive, including beta = 0 without a special convention. -/ +def regularizedPrimitive (σ δ y : ℝ) : ℝ := + ∫ t in 0..y, (max t 0 + δ) ^ (σ - 3 / 2) + +def fieldNormalization (σ : ℝ) : ℝ := + σ / ∫ s : ℝ, (1 + s ^ 2) ^ (σ - 3 / 2) + +def scalarMu (σ δ z : ℝ) : ℝ := + fieldNormalization σ * ∫ s : ℝ, + regularizedPrimitive σ δ (s ^ 2 + z) - regularizedPrimitive σ δ (s ^ 2) + +section FieldDefinitions +variable {N : ℕ} + +def matrixX (k : Fin N → ℝ) (B : Matrix (Fin N) (Fin N) ℝ) (s : ℝ) : + Matrix (Fin N) (Fin N) ℝ := + Matrix.diagonal (fun i ↦ (k i) ^ 2) - (2 * s) • B + (s ^ 2) • 1 + +/-- The symmetric cutoff is part of the definition, not replaced +by a potentially non-absolutely-convergent whole-line Bochner integral. -/ +def truncatedField (σ δ : ℝ) (k : Fin N → ℝ) (B : Matrix (Fin N) (Fin N) ℝ) + (R : ℝ) : Matrix (Fin N) (Fin N) ℝ := + fieldNormalization σ • ∫ s in (-R)..R, + cfc (regularizedPrimitive σ δ) (matrixX k B s) - + regularizedPrimitive σ δ (s ^ 2) • 1 + +/-- The symmetric-cutoff limit, whose convergence and local regularity are proved below. -/ +def matrixField (σ δ : ℝ) (k : Fin N → ℝ) (B : Matrix (Fin N) (Fin N) ℝ) : + Matrix (Fin N) (Fin N) ℝ := + Filter.limUnder Filter.atTop (truncatedField σ δ k B) + +def fieldPrimitive (σ δ : ℝ) (k : Fin N → ℝ) (B : Matrix (Fin N) (Fin N) ℝ) : ℝ := + -(∫ t in (0 : ℝ)..1, Matrix.trace (B * matrixField σ δ k (t • B))) + +/-- The rank-one comparison for the symmetric-cutoff matrix field. -/ +def RankOneClaim : Prop := + ∀ (σ δ : ℝ) (k : Fin N → ℝ) (B : Matrix (Fin N) (Fin N) ℝ) (a : Fin N → ℝ), + 0 < σ → σ < 1 → 0 < δ → (∀ i, 0 < k i) → B.IsHermitian → + matrixField σ δ k B = Matrix.vecMulVec a a → + (∑ i, a i * ((Matrix.diagonal (fun i ↦ (k i) ^ 2) - B ^ 2) *ᵥ a) i) ≥ + (∑ i, (a i) ^ 2) ^ (1 + 1 / σ) +end FieldDefinitions + +/-- The real continuous representative of H¹₀ on a bounded interval. -/ +structure H10 (l r : ℝ) where + val : ℝ → ℝ + grad : ℝ → ℝ + val_memLp : MemLp val 2 (volume.restrict (Set.Ioo l r)) + grad_memLp : MemLp grad 2 (volume.restrict (Set.Ioo l r)) + continuous_val : ContinuousOn val (Set.Icc l r) + left_zero : val l = 0 + right_zero : val r = 0 + weak_derivative : ∀ φ : ℝ → ℝ, ContDiff ℝ (↑(⊤ : ℕ∞) : WithTop ℕ∞) φ → HasCompactSupport φ → + Function.support φ ⊆ Set.Ioo l r → + (∫ x in Set.Ioo l r, val x * deriv φ x) = -(∫ x in Set.Ioo l r, grad x * φ x) + +def LowerTriangular {N : ℕ} (C : Matrix (Fin N) (Fin N) ℝ) : Prop := + ∀ i j, i < j → C i j = 0 + +def finiteIntervalAction {N : ℕ} {l r : ℝ} + (σ : ℝ) (k : Fin N → ℝ) (u : Fin N → H10 l r) + (C : Matrix (Fin N) (Fin N) ℝ) : ℝ := + ∫ x in Set.Ioo l r, + (∑ i, (C *ᵥ (fun j ↦ (u j).grad x)) i ^ 2) + + (∑ i, (k i) ^ 2 * (C *ᵥ (fun j ↦ (u j).val x)) i ^ 2) - + (∑ i, (C *ᵥ (fun j ↦ (u j).val x)) i ^ 2) ^ (1 + 1 / σ) + +/-- The action inequality, with an extended-real supremum so boundedness is not implicit. -/ +def ActionClaim : Prop := + ∀ (N : ℕ) (l r σ : ℝ) (k : Fin N → ℝ) (u : Fin N → H10 l r), + l < r → 0 < σ → σ < 1 → (∀ i, 0 < k i) → + (∀ i j, (∫ x in Set.Ioo l r, (u i).val x * (u j).val x) = + if i = j then 1 else 0) → + (((∑ i, ∫ s in (-(k i))..(k i), ((k i) ^ 2 - s ^ 2) ^ σ) : ℝ) : EReal) ≤ + ⨆ (C : Matrix (Fin N) (Fin N) ℝ) (_ : LowerTriangular C), + (finiteIntervalAction σ k u C : EReal) + + +open Matrix Unitary +namespace MatrixProof +variable {n : Type u1} [Fintype n] [DecidableEq n] + +lemma monotone_sub_mul_nonneg {f : ℝ → ℝ} (hf : Monotone f) (x y : ℝ) : + 0 ≤ (f x - f y) * (x - y) := by + rcases le_total x y with h | h + · exact mul_nonneg_of_nonpos_of_nonpos (sub_nonpos.mpr (hf h)) (sub_nonpos.mpr h) + · exact mul_nonneg (sub_nonneg.mpr (hf h)) (sub_nonneg.mpr h) + +omit [DecidableEq n] in +lemma trace_star_mul_sum (A B : Matrix n n ℂ) : + (trace (star A * B)).re = ∑ i, ∑ j, (star (A i j) * B i j).re := by + simp only [trace, diag, mul_apply, star_eq_conjTranspose, conjTranspose_apply, + Complex.re_sum, Complex.star_def] + exact Finset.sum_comm + +lemma trace_star_mul_change (U V : unitary (Matrix n n ℂ)) (A B : Matrix n n ℂ) : + trace (star (star (U : Matrix n n ℂ) * A * (V : Matrix n n ℂ)) * + (star (U : Matrix n n ℂ) * B * (V : Matrix n n ℂ))) = trace (star A * B) := by + have hu : (U : Matrix n n ℂ) * star (U : Matrix n n ℂ) = 1 := + Unitary.mul_star_self_of_mem U.property + have hv : (V : Matrix n n ℂ) * star (V : Matrix n n ℂ) = 1 := + Unitary.mul_star_self_of_mem V.property + simp only [star_mul, star_star] + calc + _ = trace (star (V : Matrix n n ℂ) * (star A * + ((U : Matrix n n ℂ) * star (U : Matrix n n ℂ))) * B * (V : Matrix n n ℂ)) := by + congr 1 + noncomm_ring + _ = trace (star (V : Matrix n n ℂ) * (star A * B) * (V : Matrix n n ℂ)) := by simp [hu, mul_assoc] + _ = trace ((V : Matrix n n ℂ) * star (V : Matrix n n ℂ) * (star A * B)) := + trace_mul_cycle _ _ _ + _ = trace (star A * B) := by rw [hv, one_mul] + +lemma mixed_diagonal_sub (U V : unitary (Matrix n n ℂ)) (a b : n → ℝ) : + star (U : Matrix n n ℂ) * + (conjStarAlgAut ℂ (Matrix n n ℂ) U (diagonal (fun i ↦ (a i : ℂ))) - + conjStarAlgAut ℂ (Matrix n n ℂ) V (diagonal (fun i ↦ (b i : ℂ)))) * (V : Matrix n n ℂ) = + diagonal (fun i ↦ (a i : ℂ)) * (star (U : Matrix n n ℂ) * (V : Matrix n n ℂ)) - + (star (U : Matrix n n ℂ) * (V : Matrix n n ℂ)) * diagonal (fun i ↦ (b i : ℂ)) := by + simp only [conjStarAlgAut_apply] + calc + _ = (star (U : Matrix n n ℂ) * (U : Matrix n n ℂ)) * diagonal (fun i ↦ (a i : ℂ)) * + (star (U : Matrix n n ℂ) * (V : Matrix n n ℂ)) - + (star (U : Matrix n n ℂ) * (V : Matrix n n ℂ)) * diagonal (fun i ↦ (b i : ℂ)) * + (star (V : Matrix n n ℂ) * (V : Matrix n n ℂ)) := by noncomm_ring + _ = _ := by simp only [Unitary.coe_star_mul_self, one_mul, mul_one] + +lemma mixed_diagonal_sub_apply (U V : unitary (Matrix n n ℂ)) (a b : n → ℝ) + (i j : n) : + (star (U : Matrix n n ℂ) * + (conjStarAlgAut ℂ (Matrix n n ℂ) U (diagonal (fun i ↦ (a i : ℂ))) - + conjStarAlgAut ℂ (Matrix n n ℂ) V (diagonal (fun i ↦ (b i : ℂ)))) * (V : Matrix n n ℂ)) i j = + ((a i - b j : ℝ) : ℂ) * (star (U : Matrix n n ℂ) * (V : Matrix n n ℂ)) i j := by + rw [mixed_diagonal_sub] + simp only [Matrix.sub_apply, diagonal_mul, mul_diagonal, Complex.ofReal_sub] + ring + +lemma trace_functional_monotonicity {A B : Matrix n n ℂ} + (hA : A.IsHermitian) (hB : B.IsHermitian) {f : ℝ → ℝ} (hf : Monotone f) : + 0 ≤ (trace ((hA.cfc f - hB.cfc f) * (A - B))).re := by + let U := hA.eigenvectorUnitary + let V := hB.eigenvectorUnitary + let a := hA.eigenvalues + let b := hB.eigenvalues + have hfab : (hA.cfc f - hB.cfc f).IsHermitian := by + apply IsHermitian.sub + · rw [← hA.cfc_eq] + exact (cfc_predicate f A).isHermitian + · rw [← hB.cfc_eq] + exact (cfc_predicate f B).isHermitian + have ha : A = conjStarAlgAut ℂ (Matrix n n ℂ) U (diagonal (fun i ↦ (a i : ℂ))) := + hA.spectral_theorem + have hb : B = conjStarAlgAut ℂ (Matrix n n ℂ) V (diagonal (fun i ↦ (b i : ℂ))) := + hB.spectral_theorem + have hfm (i j : n) : + (star (U : Matrix n n ℂ) * (hA.cfc f - hB.cfc f) * (V : Matrix n n ℂ)) i j = + ((f (a i) - f (b j) : ℝ) : ℂ) * + (star (U : Matrix n n ℂ) * (V : Matrix n n ℂ)) i j := by + exact mixed_diagonal_sub_apply U V (f ∘ a) (f ∘ b) i j + have hm (i j : n) : + (star (U : Matrix n n ℂ) * (A - B) * (V : Matrix n n ℂ)) i j = + ((a i - b j : ℝ) : ℂ) * (star (U : Matrix n n ℂ) * (V : Matrix n n ℂ)) i j := by + rw [ha, hb] + exact mixed_diagonal_sub_apply U V a b i j + rw [← hfab.star_eq, ← trace_star_mul_change U V, trace_star_mul_sum] + apply Finset.sum_nonneg + intro i _ + apply Finset.sum_nonneg + intro j _ + rw [hfm, hm] + have heq (s t : ℝ) (z : ℂ) : + (star ((s : ℂ) * z) * ((t : ℂ) * z)).re = (s * t) * Complex.normSq z := by + simp [Complex.mul_re, Complex.mul_im, Complex.normSq_apply] + ring + rw [heq] + exact mul_nonneg (monotone_sub_mul_nonneg hf _ _) (Complex.normSq_nonneg _) + + +lemma trace_unitary_conjugate (U : unitary (Matrix n n ℂ)) (A : Matrix n n ℂ) : + trace (conjStarAlgAut ℂ (Matrix n n ℂ) U A) = trace A := by + simp only [conjStarAlgAut_apply] + rw [trace_mul_cycle, Unitary.coe_star_mul_self, one_mul] + +lemma trace_conjugate_pair (U : unitary (Matrix n n ℂ)) (F A : Matrix n n ℂ) : + trace (conjStarAlgAut ℂ (Matrix n n ℂ) U F * A) = + trace (F * conjStarAlgAut ℂ (Matrix n n ℂ) (star U) A) := by + simp only [conjStarAlgAut_apply, Unitary.coe_star, star_star] + calc + _ = trace ((U : Matrix n n ℂ) * (F * (star (U : Matrix n n ℂ) * A))) := by + congr 1 + noncomm_ring + _ = trace ((F * (star (U : Matrix n n ℂ) * A)) * (U : Matrix n n ℂ)) := + trace_mul_comm _ _ + _ = _ := by congr 1; noncomm_ring + +lemma trace_conjugate_difference (U : unitary (Matrix n n ℂ)) (F A : Matrix n n ℂ) : + trace ((conjStarAlgAut ℂ (Matrix n n ℂ) U F - F) * (conjStarAlgAut ℂ (Matrix n n ℂ) U A - A)) = + trace (F * (2 • A - conjStarAlgAut ℂ (Matrix n n ℂ) U A - + conjStarAlgAut ℂ (Matrix n n ℂ) (star U) A)) := by + have h1 : trace (conjStarAlgAut ℂ (Matrix n n ℂ) U F * conjStarAlgAut ℂ (Matrix n n ℂ) U A) = + trace (F * A) := by + rw [← map_mul, trace_unitary_conjugate] + simp only [mul_sub, sub_mul, trace_sub, h1, trace_conjugate_pair, two_smul, + mul_add, trace_add] + ring + +lemma hermitian_unitary_conjugate {A : Matrix n n ℂ} (hA : A.IsHermitian) + (U : unitary (Matrix n n ℂ)) : (conjStarAlgAut ℂ (Matrix n n ℂ) U A).IsHermitian := by + change star (conjStarAlgAut ℂ (Matrix n n ℂ) U A) = conjStarAlgAut ℂ (Matrix n n ℂ) U A + rw [← map_star, hA.star_eq] + +lemma functional_unitary_conjugate {A : Matrix n n ℂ} (hA : A.IsHermitian) + (U : unitary (Matrix n n ℂ)) (f : ℝ → ℝ) : + (hermitian_unitary_conjugate hA U).cfc f = conjStarAlgAut ℂ (Matrix n n ℂ) U (hA.cfc f) := by + rw [← IsHermitian.cfc_eq, ← hA.cfc_eq] + symm + exact StarAlgHomClass.map_cfc (conjStarAlgAut ℂ (Matrix n n ℂ) U) f A + (A.finite_real_spectrum.continuousOn f) (by + change Continuous (fun X : Matrix n n ℂ ↦ conjStarAlgAut ℂ (Matrix n n ℂ) U X) + simp only [conjStarAlgAut_apply] + fun_prop) hA + (hermitian_unitary_conjugate hA U) + +/-- The fixed-unitary trace comparison used before averaging. -/ +lemma trace_unitary_comparison {A : Matrix n n ℂ} (hA : A.IsHermitian) + {f : ℝ → ℝ} (hf : Monotone f) (U : unitary (Matrix n n ℂ)) : + 0 ≤ (trace (hA.cfc f * (2 • A - conjStarAlgAut ℂ (Matrix n n ℂ) U A - + conjStarAlgAut ℂ (Matrix n n ℂ) (star U) A))).re := by + have h := trace_functional_monotonicity (hermitian_unitary_conjugate hA U) hA hf + rw [functional_unitary_conjugate, trace_conjugate_difference] at h + exact h + +/-- Removing any invariant part, such as (s I - B)^2, is an exact identity. -/ +lemma conjugate_difference_sub_invariant (U : unitary (Matrix n n ℂ)) + (D Y : Matrix n n ℂ) (hY : conjStarAlgAut ℂ (Matrix n n ℂ) U Y = Y) : + 2 • (D + Y) - conjStarAlgAut ℂ (Matrix n n ℂ) U (D + Y) - + conjStarAlgAut ℂ (Matrix n n ℂ) (star U) (D + Y) = + 2 • D - conjStarAlgAut ℂ (Matrix n n ℂ) U D - conjStarAlgAut ℂ (Matrix n n ℂ) (star U) D := by + have hYs : conjStarAlgAut ℂ (Matrix n n ℂ) (star U) Y = Y := by + calc + _ = conjStarAlgAut ℂ (Matrix n n ℂ) (star U) (conjStarAlgAut ℂ (Matrix n n ℂ) U Y) := by rw [hY] + _ = Y := by rw [← conjStarAlgAut_mul_apply]; simp + rw [map_add, map_add, hY, hYs] + simp only [two_smul] + abel + +lemma trace_unitary_comparison_sub_invariant {D Y : Matrix n n ℂ} + (hA : (D + Y).IsHermitian) {f : ℝ → ℝ} (hf : Monotone f) + (U : unitary (Matrix n n ℂ)) (hY : conjStarAlgAut ℂ (Matrix n n ℂ) U Y = Y) : + 0 ≤ (trace (hA.cfc f * (2 • D - conjStarAlgAut ℂ (Matrix n n ℂ) U D - + conjStarAlgAut ℂ (Matrix n n ℂ) (star U) D))).re := by + have h := trace_unitary_comparison hA hf U + rwa [conjugate_difference_sub_invariant U D Y hY] at h + + +/-- The squared Hilbert--Schmidt norm, without changing the ambient matrix norm. -/ +def hsSquared (A : Matrix n n ℂ) : ℝ := ∑ i, ∑ j, Complex.normSq (A i j) + +omit [DecidableEq n] in +lemma hsSquared_eq_trace (A : Matrix n n ℂ) : + hsSquared A = (trace (star A * A)).re := by + rw [trace_star_mul_sum] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + rw [Complex.star_def, ← Complex.normSq_eq_conj_mul_self, Complex.ofReal_re] + +lemma hsSquared_change (U V : unitary (Matrix n n ℂ)) (A : Matrix n n ℂ) : + hsSquared (star (U : Matrix n n ℂ) * A * (V : Matrix n n ℂ)) = hsSquared A := by + rw [hsSquared_eq_trace, trace_star_mul_change, hsSquared_eq_trace] + +/-- The finite-dimensional Hilbert--Schmidt calculus estimate, +proved in mixed eigenbases. -/ +lemma hsSquared_cfc_sub {A B : Matrix n n ℂ} + (hA : A.IsHermitian) (hB : B.IsHermitian) (f : ℝ → ℝ) (L : ℝ) (hL : 0 ≤ L) + (hf : ∀ i j, |f (hA.eigenvalues i) - f (hB.eigenvalues j)| ≤ + L * |hA.eigenvalues i - hB.eigenvalues j|) : + hsSquared (hA.cfc f - hB.cfc f) ≤ L ^ 2 * hsSquared (A - B) := by + let U := hA.eigenvectorUnitary + let V := hB.eigenvectorUnitary + let a := hA.eigenvalues + let b := hB.eigenvalues + have ha : A = conjStarAlgAut ℂ (Matrix n n ℂ) U (diagonal (fun i ↦ (a i : ℂ))) := + hA.spectral_theorem + have hb : B = conjStarAlgAut ℂ (Matrix n n ℂ) V (diagonal (fun i ↦ (b i : ℂ))) := + hB.spectral_theorem + have hfm (i j : n) : + (star (U : Matrix n n ℂ) * (hA.cfc f - hB.cfc f) * (V : Matrix n n ℂ)) i j = + ((f (a i) - f (b j) : ℝ) : ℂ) * + (star (U : Matrix n n ℂ) * (V : Matrix n n ℂ)) i j := + mixed_diagonal_sub_apply U V (f ∘ a) (f ∘ b) i j + have hm (i j : n) : + (star (U : Matrix n n ℂ) * (A - B) * (V : Matrix n n ℂ)) i j = + ((a i - b j : ℝ) : ℂ) * (star (U : Matrix n n ℂ) * (V : Matrix n n ℂ)) i j := by + rw [ha, hb] + exact mixed_diagonal_sub_apply U V a b i j + rw [← hsSquared_change U V (hA.cfc f - hB.cfc f), + ← hsSquared_change U V (A - B)] + simp only [hsSquared, Finset.mul_sum] + apply Finset.sum_le_sum + intro i _ + apply Finset.sum_le_sum + intro j _ + rw [hfm, hm, Complex.normSq_mul, Complex.normSq_mul, + Complex.normSq_ofReal, Complex.normSq_ofReal] + have hh := sq_le_sq₀ (abs_nonneg (f (a i) - f (b j))) + (mul_nonneg hL (abs_nonneg (a i - b j))) |>.2 (hf i j) + rw [sq_abs, mul_pow, sq_abs] at hh + nlinarith [mul_le_mul_of_nonneg_right hh + (Complex.normSq_nonneg ((star (U : Matrix n n ℂ) * (V : Matrix n n ℂ)) i j))] + +open MeasureTheory +open scoped Matrix.Norms.L2Operator NNReal + +/-- Real trace pairing as a continuous linear functional. -/ +def tracePairCLM (M : Matrix n n ℂ) : Matrix n n ℂ →L[ℝ] ℝ := + (Complex.reCLM).comp + ((Matrix.traceLinearMap n ℝ ℂ).toContinuousLinearMap.comp + ((LinearMap.mulLeft ℝ M).toContinuousLinearMap)) + +@[simp] lemma tracePairCLM_apply (M Z : Matrix n n ℂ) : + tracePairCLM M Z = (trace (M * Z)).re := rfl + +/-- Trace comparison commutes with limits in matrix norm. -/ +lemma trace_unitary_comparison_limit {ι : Type u2} {l : Filter ι} [l.NeBot] + {F : ι → Matrix n n ℂ} {M D : Matrix n n ℂ} + (hlim : Filter.Tendsto F l (nhds M)) (U : unitary (Matrix n n ℂ)) + (hF : ∀ᶠ i in l, 0 ≤ (trace (F i * (2 • D - conjStarAlgAut ℂ (Matrix n n ℂ) U D - + conjStarAlgAut ℂ (Matrix n n ℂ) (star U) D))).re) : + 0 ≤ (trace (M * (2 • D - conjStarAlgAut ℂ (Matrix n n ℂ) U D - + conjStarAlgAut ℂ (Matrix n n ℂ) (star U) D))).re := by + apply ge_of_tendsto ?_ hF + have hc : Continuous (fun X : Matrix n n ℂ ↦ + (trace (X * (2 • D - conjStarAlgAut ℂ (Matrix n n ℂ) U D - + conjStarAlgAut ℂ (Matrix n n ℂ) (star U) D))).re) := by + unfold trace diag + fun_prop + exact hc.continuousAt.tendsto.comp hlim + +/-- The integration step in `trace-average`, for any symmetric probability +average. The symmetry needed is expressed by equality of the two integrals. -/ +lemma trace_comparison_average {α : Type u3} [MeasurableSpace α] (ν : Measure α) + [IsProbabilityMeasure ν] (U : α → unitary (Matrix n n ℂ)) + (M D : Matrix n n ℂ) + (hU : Integrable (fun t ↦ conjStarAlgAut ℂ (Matrix n n ℂ) (U t) D) ν) + (hUs : Integrable (fun t ↦ conjStarAlgAut ℂ (Matrix n n ℂ) (star (U t)) D) ν) + (hsym : (∫ t, conjStarAlgAut ℂ (Matrix n n ℂ) (star (U t)) D ∂ν) = + ∫ t, conjStarAlgAut ℂ (Matrix n n ℂ) (U t) D ∂ν) + (hpoint : ∀ᵐ t ∂ν, 0 ≤ (trace (M * (2 • D - conjStarAlgAut ℂ (Matrix n n ℂ) (U t) D - + conjStarAlgAut ℂ (Matrix n n ℂ) (star (U t)) D))).re) : + (trace (M * (∫ t, conjStarAlgAut ℂ (Matrix n n ℂ) (U t) D ∂ν))).re ≤ + (trace (M * D)).re := by + have hi : Integrable (fun t ↦ 2 • D - conjStarAlgAut ℂ (Matrix n n ℂ) (U t) D - + conjStarAlgAut ℂ (Matrix n n ℂ) (star (U t)) D) ν := + ((integrable_const (2 • D)).sub hU).sub hUs + have hn := integral_nonneg_of_ae hpoint + change 0 ≤ ∫ t, tracePairCLM M + (2 • D - conjStarAlgAut ℂ (Matrix n n ℂ) (U t) D - conjStarAlgAut ℂ (Matrix n n ℂ) (star (U t)) D) ∂ν at hn + rw [(tracePairCLM M).integral_comp_comm hi, + integral_sub (f := fun t ↦ 2 • D - conjStarAlgAut ℂ (Matrix n n ℂ) (U t) D) + ((integrable_const (2 • D)).sub hU) hUs, + integral_sub (f := fun _ : α ↦ 2 • D) (integrable_const (2 • D)) hU, integral_const, probReal_univ, + one_smul, hsym, map_sub, map_sub, map_nsmul] at hn + norm_num only [tracePairCLM_apply, nsmul_eq_mul, Nat.cast_ofNat] at hn + linarith + + +/-- In a fixed eigenbasis of B, the unitary exp(itB). -/ +def phaseUnitary (z : n → ℝ) (t : ℝ) : unitary (Matrix n n ℂ) := + ⟨diagonal (fun i ↦ Complex.exp ((t * z i : ℝ) * Complex.I)), by + constructor + · simp only [star_eq_conjTranspose, diagonal_conjTranspose, diagonal_mul_diagonal] + rw [← diagonal_one] + congr 1 + funext i + simp only [Pi.star_apply] + rw [Complex.star_def, ← Complex.exp_conj, ← Complex.exp_add] + simp + · simp only [star_eq_conjTranspose, diagonal_conjTranspose, diagonal_mul_diagonal] + rw [← diagonal_one] + congr 1 + funext i + simp only [Pi.star_apply] + rw [Complex.star_def, ← Complex.exp_conj, ← Complex.exp_add] + simp⟩ + +lemma phaseUnitary_conj_apply (z : n → ℝ) (t : ℝ) (D : Matrix n n ℂ) (i j : n) : + conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D i j = + Complex.exp (((z i - z j) * t : ℝ) * Complex.I) * D i j := by + simp only [conjStarAlgAut_apply, phaseUnitary, star_eq_conjTranspose, + diagonal_conjTranspose, diagonal_mul, mul_diagonal] + simp only [Pi.star_apply] + rw [Complex.star_def, ← Complex.exp_conj] + calc _ = (Complex.exp (((t * z i : ℝ) : ℂ) * Complex.I) * + Complex.exp (starRingEnd ℂ (((t * z j : ℝ) : ℂ) * Complex.I))) * D i j := by ring + _ = _ := by + rw [← Complex.exp_add] + congr 2 + simp only [map_mul, Complex.conj_ofReal, Complex.conj_I] + push_cast + ring + +lemma phaseUnitary_star (z : n → ℝ) (t : ℝ) : + star (phaseUnitary z t) = phaseUnitary z (-t) := by + apply Subtype.ext + simp only [Unitary.coe_star, phaseUnitary, star_eq_conjTranspose, diagonal_conjTranspose] + congr 1 + funext i + simp only [Pi.star_apply] + rw [Complex.star_def, ← Complex.exp_conj] + simp + +lemma continuous_phase_conj (z : n → ℝ) (D : Matrix n n ℂ) : + Continuous (fun t : ℝ ↦ conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D) := by + apply continuous_pi + intro i + apply continuous_pi + intro j + simp_rw [phaseUnitary_conj_apply] + fun_prop + +lemma integrable_phase_conj (z : n → ℝ) (D : Matrix n n ℂ) (ν : Measure ℝ) + [IsFiniteMeasure ν] : + Integrable (fun t ↦ conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D) ν := by + apply Integrable.of_bound (continuous_phase_conj z D).aestronglyMeasurable ‖D‖ + filter_upwards [] with t + change ‖(phaseUnitary z t : Matrix n n ℂ) * D * + ((star (phaseUnitary z t) : unitary (Matrix n n ℂ)) : Matrix n n ℂ)‖ ≤ ‖D‖ + rw [CStarRing.norm_mul_coe_unitary, CStarRing.norm_coe_unitary_mul] + +/-- Entry evaluation is a continuous linear functional even for the operator norm. -/ +def entryCLM (i j : n) : Matrix n n ℂ →L[ℝ] ℂ := + ({ toFun := fun D ↦ D i j + map_add' := fun _ _ ↦ rfl + map_smul' := fun _ _ ↦ rfl } : Matrix n n ℂ →ₗ[ℝ] ℂ).toContinuousLinearMap + +omit [DecidableEq n] in +@[simp] lemma entryCLM_apply (i j : n) (D : Matrix n n ℂ) : entryCLM i j D = D i j := rfl + +lemma gaussian_phase_average (z : n → ℝ) (D : Matrix n n ℂ) (v : ℝ≥0) (i j : n) : + (∫ t, conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D ∂ProbabilityTheory.gaussianReal 0 v) i j = + Complex.exp (-((v : ℝ) * (z i - z j) ^ 2 / 2 : ℝ)) * D i j := by + have h := (entryCLM i j).integral_comp_comm + (integrable_phase_conj z D (ProbabilityTheory.gaussianReal 0 v)) + simp only [entryCLM_apply] at h + rw [← h] + simp_rw [phaseUnitary_conj_apply] + rw [integral_mul_const] + simp only [Complex.ofReal_mul] + rw [← charFun_apply_real, ProbabilityTheory.charFun_gaussianReal] + congr 2 + push_cast + ring + +lemma gaussian_phase_star_average (z : n → ℝ) (D : Matrix n n ℂ) (v : ℝ≥0) : + (∫ t, conjStarAlgAut ℂ (Matrix n n ℂ) (star (phaseUnitary z t)) D + ∂ProbabilityTheory.gaussianReal 0 v) = + ∫ t, conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D + ∂ProbabilityTheory.gaussianReal 0 v := by + simp_rw [phaseUnitary_star] + have hm : (ProbabilityTheory.gaussianReal 0 v).map (fun x : ℝ ↦ -x) = + ProbabilityTheory.gaussianReal 0 v := by + simpa using (ProbabilityTheory.gaussianReal_map_neg (μ := 0) (v := v)) + have he := integral_map (μ := ProbabilityTheory.gaussianReal 0 v) + (φ := fun x : ℝ ↦ -x) (by fun_prop) + ((continuous_phase_conj z D).aestronglyMeasurable + (μ := (ProbabilityTheory.gaussianReal 0 v).map (fun x : ℝ ↦ -x))) + rw [hm] at he + exact he.symm + +lemma integrable_gaussian_phase_star (z : n → ℝ) (D : Matrix n n ℂ) (v : ℝ≥0) : + Integrable (fun t ↦ conjStarAlgAut ℂ (Matrix n n ℂ) (star (phaseUnitary z t)) D) + (ProbabilityTheory.gaussianReal 0 v) := by + simp_rw [phaseUnitary_star] + have hm : (ProbabilityTheory.gaussianReal 0 v).map (fun x : ℝ ↦ -x) = + ProbabilityTheory.gaussianReal 0 v := by + simpa using (ProbabilityTheory.gaussianReal_map_neg (μ := 0) (v := v)) + have hi := integrable_phase_conj z D (ProbabilityTheory.gaussianReal 0 v) + rw [← hm] at hi + exact hi.comp_measurable (by fun_prop) + +/-- The Gaussian stage of the even-unitary trace contraction. -/ +lemma gaussian_trace_comparison (z : n → ℝ) (M D : Matrix n n ℂ) (v : ℝ≥0) + (hpoint : ∀ t : ℝ, 0 ≤ (trace (M * (2 • D - + conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D - + conjStarAlgAut ℂ (Matrix n n ℂ) (star (phaseUnitary z t)) D))).re) : + (trace (M * (∫ t, conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D + ∂ProbabilityTheory.gaussianReal 0 v))).re ≤ (trace (M * D)).re := by + exact trace_comparison_average (ProbabilityTheory.gaussianReal 0 v) + (phaseUnitary z) M D (integrable_phase_conj z D _) + (integrable_gaussian_phase_star z D v) (gaussian_phase_star_average z D v) + (Filter.Eventually.of_forall hpoint) + +end MatrixProof + +open MeasureTheory Set Filter +open scoped Topology +namespace ScalarProof + +lemma derivative_continuous (σ : ℝ) {δ : ℝ} (hδ : 0 < δ) : + Continuous (fun t : ℝ ↦ (max t 0 + δ) ^ (σ - 3 / 2)) := by + apply Continuous.rpow_const + · fun_prop + · intro t + left + positivity + +lemma primitive_hasDerivAt (σ : ℝ) {δ : ℝ} (hδ : 0 < δ) (y : ℝ) : + HasDerivAt (regularizedPrimitive σ δ) ((max y 0 + δ) ^ (σ - 3 / 2)) y := by + have hc := derivative_continuous σ hδ + exact intervalIntegral.integral_hasDerivAt_right (hc.intervalIntegrable _ _) + hc.aestronglyMeasurable.stronglyMeasurableAtFilter hc.continuousAt + +lemma primitive_deriv (σ : ℝ) {δ : ℝ} (hδ : 0 < δ) (y : ℝ) : + deriv (regularizedPrimitive σ δ) y = (max y 0 + δ) ^ (σ - 3 / 2) := + (primitive_hasDerivAt σ hδ y).deriv + +lemma primitive_differentiable (σ : ℝ) {δ : ℝ} (hδ : 0 < δ) : + Differentiable ℝ (regularizedPrimitive σ δ) := + fun y ↦ (primitive_hasDerivAt σ hδ y).differentiableAt + +lemma primitive_strictMono (σ : ℝ) {δ : ℝ} (hδ : 0 < δ) : + StrictMono (regularizedPrimitive σ δ) := by + apply strictMono_of_deriv_pos + intro y + rw [primitive_deriv σ hδ] + exact Real.rpow_pos_of_pos (by positivity) _ + +lemma primitive_concave {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) : + ConcaveOn ℝ univ (regularizedPrimitive σ δ) := by + apply Antitone.concaveOn_univ_of_deriv (primitive_differentiable σ hδ) + intro x y hxy + rw [primitive_deriv σ hδ, primitive_deriv σ hδ] + exact Real.rpow_le_rpow_of_nonpos (by positivity) + (add_le_add (max_le_max hxy le_rfl) le_rfl) (by linarith) + +@[simp] lemma primitive_zero (σ δ : ℝ) : regularizedPrimitive σ δ 0 = 0 := by + simp [regularizedPrimitive] + +lemma primitive_nonneg (σ : ℝ) {δ y : ℝ} (hδ : 0 < δ) (hy : 0 ≤ y) : + 0 ≤ regularizedPrimitive σ δ y := by + simpa using (primitive_strictMono σ hδ).monotone hy + +lemma normalization_integrable {σ : ℝ} (hσ : σ < 1) : + Integrable (fun s : ℝ ↦ (1 + s ^ 2) ^ (σ - 3 / 2)) := by + have h : (Module.finrank ℝ ℝ : ℝ) < 3 - 2 * σ := by + norm_num only [Module.finrank_self, Nat.cast_one] + linarith + have he := integrable_rpow_neg_one_add_norm_sq (E := ℝ) (μ := volume) h + convert he using 1 + ext s + congr 1 + · simp + · ring + +lemma normalization_integral_pos {σ : ℝ} (hσ : σ < 1) : + 0 < ∫ s : ℝ, (1 + s ^ 2) ^ (σ - 3 / 2) := by + apply integral_pos_iff_support_of_nonneg + (fun s ↦ Real.rpow_nonneg (by positivity) _) + (normalization_integrable hσ) |>.2 + have hs : Function.support (fun s : ℝ ↦ (1 + s ^ 2) ^ (σ - 3 / 2)) = univ := by + ext s + simp only [Function.mem_support, mem_univ, iff_true] + exact (Real.rpow_pos_of_pos (by positivity) _).ne' + rw [hs] + simp + +lemma normalization_pos {σ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) : + 0 < fieldNormalization σ := + div_pos hσ₀ (normalization_integral_pos hσ₁) + +@[simp] lemma mu_zero (σ δ : ℝ) : scalarMu σ δ 0 = 0 := by + simp [scalarMu] + + +/-- A global comparison with the Japanese-bracket integrable majorant, including +negative shifts. It supplies all scalar dominated-convergence bounds. -/ +lemma shifted_base_lower {δ : ℝ} (hδ : 0 < δ) (z s : ℝ) : + (δ / (δ + |z| + 1)) * (1 + s ^ 2) ≤ max (s ^ 2 + z) 0 + δ := by + have hd : 0 < δ + |z| + 1 := by positivity + rw [div_mul_eq_mul_div, div_le_iff₀ hd] + have hm : 0 ≤ max (s ^ 2 + z) 0 := le_max_right _ _ + have hh : s ^ 2 ≤ max (s ^ 2 + z) 0 + |z| := by + have := le_max_left (s ^ 2 + z) 0 + have := neg_le_abs z + linarith + nlinarith [mul_le_mul_of_nonneg_left hh hδ.le, + mul_nonneg (abs_nonneg z) hm, mul_nonneg (abs_nonneg z) hδ.le] + +lemma shifted_derivative_integrable {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (z : ℝ) : + Integrable (fun s : ℝ ↦ (max (s ^ 2 + z) 0 + δ) ^ (σ - 3 / 2)) := by + have ha : 0 < δ / (δ + |z| + 1) := by positivity + refine ((normalization_integrable hσ).const_mul + ((δ / (δ + |z| + 1)) ^ (σ - 3 / 2))).mono' ?_ ?_ + · exact ((derivative_continuous σ hδ).comp (by fun_prop)).aestronglyMeasurable + · filter_upwards [] with s + rw [Real.norm_eq_abs, abs_of_nonneg (Real.rpow_nonneg (by positivity) _)] + rw [← Real.mul_rpow ha.le (by positivity : 0 ≤ 1 + s ^ 2)] + exact Real.rpow_le_rpow_of_nonpos (by positivity) + (shifted_base_lower hδ z s) (by linarith) + +lemma primitive_difference_bound {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (z s : ℝ) : + ‖regularizedPrimitive σ δ (s ^ 2 + z) - regularizedPrimitive σ δ (s ^ 2)‖ ≤ + (max (s ^ 2 - |z|) 0 + δ) ^ (σ - 3 / 2) * |z| := by + have hd : ∀ y ∈ Ici (s ^ 2 - |z|), + ‖(max y 0 + δ) ^ (σ - 3 / 2)‖ ≤ + (max (s ^ 2 - |z|) 0 + δ) ^ (σ - 3 / 2) := by + intro y hy + rw [Real.norm_eq_abs, abs_of_nonneg (Real.rpow_nonneg (by positivity) _)] + exact Real.rpow_le_rpow_of_nonpos (by positivity) + (add_le_add (max_le_max hy le_rfl) le_rfl) (by linarith) + have hs : s ^ 2 ∈ Ici (s ^ 2 - |z|) := by + simp only [mem_Ici] + have := abs_nonneg z + linarith + have hsz : s ^ 2 + z ∈ Ici (s ^ 2 - |z|) := by + simp only [mem_Ici] + have := neg_le_abs z + linarith + simpa only [add_sub_cancel_left, Real.norm_eq_abs] using + (convex_Ici (s ^ 2 - |z|)).norm_image_sub_le_of_norm_hasDerivWithin_le + (fun y _ ↦ (primitive_hasDerivAt σ hδ y).hasDerivWithinAt) hd hs hsz + +lemma mu_integrand_integrable {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (z : ℝ) : + Integrable (fun s : ℝ ↦ regularizedPrimitive σ δ (s ^ 2 + z) - + regularizedPrimitive σ δ (s ^ 2)) := by + have hi := (shifted_derivative_integrable hσ hδ (-|z|)).mul_const |z| + refine hi.mono' ?_ (Filter.Eventually.of_forall ?_) + · exact (((primitive_differentiable σ hδ).continuous.comp (by fun_prop)).sub + ((primitive_differentiable σ hδ).continuous.comp (by fun_prop))).aestronglyMeasurable + · intro s + simpa only [sub_eq_add_neg] using primitive_difference_bound hσ hδ z s + +lemma mu_hasDerivAt_integral {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (z : ℝ) : + HasDerivAt (scalarMu σ δ) + (fieldNormalization σ * ∫ s : ℝ, (max (s ^ 2 + z) 0 + δ) ^ (σ - 3 / 2)) z := by + have hh := hasDerivAt_integral_of_dominated_loc_of_deriv_le + (μ := volume) (s := Ioi (z - 1)) (x₀ := z) + (F := fun y s : ℝ ↦ regularizedPrimitive σ δ (s ^ 2 + y) - + regularizedPrimitive σ δ (s ^ 2)) + (F' := fun y s : ℝ ↦ (max (s ^ 2 + y) 0 + δ) ^ (σ - 3 / 2)) + (bound := fun s : ℝ ↦ (max (s ^ 2 + (z - 1)) 0 + δ) ^ (σ - 3 / 2)) + (Ioi_mem_nhds (by linarith)) + (Filter.Eventually.of_forall (fun y ↦ (mu_integrand_integrable hσ hδ y).aestronglyMeasurable)) + (mu_integrand_integrable hσ hδ z) + (shifted_derivative_integrable hσ hδ z).aestronglyMeasurable + (Filter.Eventually.of_forall (fun s y hy ↦ ?_)) + (shifted_derivative_integrable hσ hδ (z - 1)) + (Filter.Eventually.of_forall (fun s y _ ↦ ?_)) + · exact hh.2.const_mul (fieldNormalization σ) + · change z - 1 < y at hy + rw [Real.norm_eq_abs, abs_of_nonneg (Real.rpow_nonneg (by positivity) _)] + exact Real.rpow_le_rpow_of_nonpos (by positivity) + (add_le_add (max_le_max (by linarith) le_rfl) le_rfl) (by linarith) + · simpa using ((primitive_hasDerivAt σ hδ (s ^ 2 + y)).comp y + ((hasDerivAt_id y).const_add (s ^ 2))).sub_const (regularizedPrimitive σ δ (s ^ 2)) + +lemma mu_strictMono {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) : + StrictMono (scalarMu σ δ) := by + apply strictMono_of_deriv_pos + intro z + rw [(mu_hasDerivAt_integral hσ₁ hδ z).deriv] + apply mul_pos (normalization_pos hσ₀ hσ₁) + apply (integral_pos_iff_support_of_nonneg + (fun s ↦ Real.rpow_nonneg (by positivity) _) + (shifted_derivative_integrable hσ₁ hδ z)).2 + have hs : Function.support (fun s : ℝ ↦ (max (s ^ 2 + z) 0 + δ) ^ (σ - 3 / 2)) = univ := by + ext s + simp only [Function.mem_support, mem_univ, iff_true] + exact (Real.rpow_pos_of_pos (by positivity) _).ne' + rw [hs] + simp + +/-- The scaling integral used in the evaluation of the scalar field. -/ +lemma quadratic_integral_scale (t : ℝ) {a : ℝ} (ha : 0 < a) : + (∫ s : ℝ, (s ^ 2 + a) ^ t) = + a ^ (t + 1 / 2) * ∫ s : ℝ, (1 + s ^ 2) ^ t := by + have hs : 0 < Real.sqrt a := Real.sqrt_pos.2 ha + have he (s : ℝ) : (s ^ 2 + a) ^ t = + a ^ t * (1 + (s / Real.sqrt a) ^ 2) ^ t := by + rw [← Real.mul_rpow ha.le (by positivity)] + congr 1 + rw [div_pow, Real.sq_sqrt ha.le] + field_simp + ring + simp_rw [he] + rw [integral_const_mul, Measure.integral_comp_div (fun s : ℝ ↦ (1 + s ^ 2) ^ t), + abs_of_pos hs, smul_eq_mul, ← mul_assoc, Real.sqrt_eq_rpow, + ← Real.rpow_add ha] + +lemma mu_hasDerivAt_nonneg {σ δ z : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (hz : 0 ≤ z) : + HasDerivAt (scalarMu σ δ) (σ * (z + δ) ^ (σ - 1)) z := by + have hh := mu_hasDerivAt_integral hσ hδ z + have he (s : ℝ) : (max (s ^ 2 + z) 0 + δ) ^ (σ - 3 / 2) = + (s ^ 2 + (z + δ)) ^ (σ - 3 / 2) := by + rw [max_eq_left (by positivity)] + congr 1 + ring + simp_rw [he] at hh + rw [quadratic_integral_scale _ (by positivity : 0 < z + δ)] at hh + have hp := (normalization_integral_pos hσ).ne' + convert hh using 1 + unfold fieldNormalization + rw [show σ - 3 / 2 + 1 / 2 = σ - 1 by ring] + rw [mul_comm ((z + δ) ^ (σ - 1)), ← mul_assoc, div_mul_cancel₀ _ hp] + +lemma mu_eq_nonneg {σ δ z : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (hz : 0 ≤ z) : + scalarMu σ δ z = (z + δ) ^ σ - δ ^ σ := by + have hd (y : ℝ) (hy : 0 ≤ y) : + HasDerivAt (fun x : ℝ ↦ (x + δ) ^ σ - δ ^ σ) + (σ * (y + δ) ^ (σ - 1)) y := by + convert! (((hasDerivAt_id y).add_const δ).rpow_const (p := σ) + (Or.inl (by positivity : y + δ ≠ 0))).sub_const (δ ^ σ) using 1 + simp + exact eq_of_has_deriv_right_eq + (fun y hy ↦ (mu_hasDerivAt_nonneg hσ hδ hy.1).hasDerivWithinAt) + (fun y hy ↦ (hd y hy.1).hasDerivWithinAt) + (continuous_iff_continuousAt.mpr (fun y ↦ + (mu_hasDerivAt_integral hσ hδ y).continuousAt)).continuousOn + (fun y hy ↦ (hd y hy.1).continuousAt.continuousWithinAt) + (by simp) z ⟨hz, le_rfl⟩ + + +/-- Normalized Gamma mixing density, used only on the positive half-line. -/ +def gammaWeight (σ v : ℝ) : ℝ := + (Real.Gamma (1 - σ))⁻¹ * (v ^ (-σ) * Real.exp (-v)) + +lemma gammaWeight_nonneg {σ v : ℝ} (hσ : σ < 1) (hv : 0 ≤ v) : + 0 ≤ gammaWeight σ v := by + unfold gammaWeight + exact mul_nonneg (inv_nonneg.2 (Real.Gamma_pos_of_pos (by linarith)).le) + (mul_nonneg (Real.rpow_nonneg hv _) (Real.exp_pos _).le) + +lemma gammaWeight_integrable {σ : ℝ} (hσ : σ < 1) : + IntegrableOn (gammaWeight σ) (Ioi 0) := by + have hi := integrableOn_rpow_mul_exp_neg_mul_rpow (s := -σ) (p := 1) (b := 1) + (by linarith) zero_lt_one zero_lt_one + simp only [Real.rpow_one, neg_one_mul] at hi + exact hi.const_mul _ + +lemma gamma_mixture {σ h x : ℝ} (hσ : σ < 1) (hh : 0 ≤ h) : + (∫ v in Ioi (0 : ℝ), gammaWeight σ v * Real.exp (-v * h * x ^ 2)) = + (1 + h * x ^ 2) ^ (σ - 1) := by + have hb : 0 < 1 + h * x ^ 2 := by positivity + have hg : Real.Gamma (1 - σ) ≠ 0 := (Real.Gamma_pos_of_pos (by linarith)).ne' + have he (v : ℝ) : gammaWeight σ v * Real.exp (-v * h * x ^ 2) = + (Real.Gamma (1 - σ))⁻¹ * (v ^ (-σ) * Real.exp (-(1 + h * x ^ 2) * v ^ (1 : ℝ))) := by + unfold gammaWeight + rw [mul_assoc, mul_assoc, ← Real.exp_add, Real.rpow_one] + congr 3 + ring + simp_rw [he] + rw [integral_const_mul, integral_rpow_mul_exp_neg_mul_rpow zero_lt_one (by linarith) hb] + simp only [div_one, mul_one] + rw [show -σ + 1 = 1 - σ by ring, show -(1 - σ) = σ - 1 by ring] + rw [← mul_assoc, mul_comm _ ((1 + h * x ^ 2) ^ (σ - 1)), mul_assoc, + inv_mul_cancel₀ hg, mul_one] + +lemma gammaWeight_integral {σ : ℝ} (hσ : σ < 1) : + (∫ v in Ioi (0 : ℝ), gammaWeight σ v) = 1 := by + simpa using gamma_mixture (h := 0) (x := 0) hσ le_rfl + +/-- Integrability of the scalar kernel used in the matrix resolvent tangent formula. -/ +lemma resolvent_kernel_integrable {β a : ℝ} (hβ₀ : -1 < β) (hβ₁ : β < 1) + (ha : 0 < a) : IntegrableOn (fun v : ℝ ↦ v ^ β / (a + v) ^ 2) (Ioi 0) := by + have hc : ContinuousOn (fun v : ℝ ↦ v ^ β / (a + v) ^ 2) (Ioi 0) := by + apply ContinuousOn.div + · exact continuousOn_id.rpow_const (fun v hv ↦ Or.inl (ne_of_gt hv)) + · fun_prop + · intro v hv + exact pow_ne_zero _ (ne_of_gt (add_pos ha hv) : a + v ≠ 0) + have hn : IntegrableOn (fun v : ℝ ↦ v ^ β / (a + v) ^ 2) (Ioo 0 1) := by + have hi : IntegrableOn (fun v : ℝ ↦ v ^ β * (a ^ 2)⁻¹) (Ioo 0 1) := + ((intervalIntegral.integrableOn_Ioo_rpow_iff zero_lt_one).2 hβ₀).mul_const _ + apply hi.mono' ((hc.mono Ioo_subset_Ioi_self).aestronglyMeasurable measurableSet_Ioo) + filter_upwards [ae_restrict_mem measurableSet_Ioo] with v hv + rw [Real.norm_eq_abs, abs_of_nonneg (div_nonneg (Real.rpow_nonneg hv.1.le _) (sq_nonneg _)), + ← div_eq_mul_inv] + apply div_le_div_of_nonneg_left (Real.rpow_nonneg hv.1.le _) (sq_pos_of_pos ha) + nlinarith [hv.1, hv.2] + have hf : IntegrableOn (fun v : ℝ ↦ v ^ β / (a + v) ^ 2) (Ioi 1) := by + apply (integrableOn_Ioi_rpow_of_lt (show β - 2 < -1 by linarith) zero_lt_one).mono' + ((hc.mono (Ioi_subset_Ioi zero_le_one)).aestronglyMeasurable measurableSet_Ioi) + filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + have hv₀ : 0 < v := lt_trans zero_lt_one hv + rw [Real.norm_eq_abs, abs_of_nonneg (div_nonneg (Real.rpow_nonneg hv₀.le _) (sq_nonneg _)), + Real.rpow_sub hv₀, Real.rpow_two] + apply div_le_div_of_nonneg_left (Real.rpow_nonneg hv₀.le _) (sq_pos_of_pos hv₀) + nlinarith + rw [← Ioc_union_Ioi_eq_Ioi zero_le_one] + exact (hn.congr_set_ae Ioo_ae_eq_Ioc.symm).union hf + +lemma resolvent_kernel_integral_scale (β : ℝ) {a : ℝ} (ha : 0 < a) : + (∫ v in Ioi (0 : ℝ), v ^ β / (a + v) ^ 2) = + a ^ (β - 1) * ∫ v in Ioi (0 : ℝ), v ^ β / (1 + v) ^ 2 := by + have hs := integral_comp_mul_left_Ioi (fun v : ℝ ↦ v ^ β / (a + v) ^ 2) 0 ha + simp only [mul_zero, smul_eq_mul] at hs + have he : (fun v : ℝ ↦ (a * v) ^ β / (a + a * v) ^ 2) =ᵐ[volume.restrict (Ioi 0)] + fun v ↦ (a ^ β / a ^ 2) * (v ^ β / (1 + v) ^ 2) := by + filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + rw [Real.mul_rpow ha.le hv.le, show a + a * v = a * (1 + v) by ring, mul_pow, mul_div_mul_comm] + rw [integral_congr_ae he, integral_const_mul] at hs + have he' : a ^ (β - 1) = a * (a ^ β / a ^ 2) := by + rw [Real.rpow_sub ha, Real.rpow_one] + field_simp + rw [he', mul_assoc, hs, ← mul_assoc, mul_inv_cancel₀ ha.ne', one_mul] + +lemma resolvent_kernel_integral_pos {β a : ℝ} (hβ₀ : -1 < β) (hβ₁ : β < 1) + (ha : 0 < a) : 0 < ∫ v in Ioi (0 : ℝ), v ^ β / (a + v) ^ 2 := by + have hn : 0 ≤ᵐ[volume.restrict (Ioi (0 : ℝ))] (fun v ↦ v ^ β / (a + v) ^ 2) := by + filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + exact div_nonneg (Real.rpow_nonneg hv.le _) (sq_nonneg _) + rw [setIntegral_pos_iff_support_of_nonneg_ae hn + (resolvent_kernel_integrable hβ₀ hβ₁ ha)] + have he : Function.support (fun v : ℝ ↦ v ^ β / (a + v) ^ 2) ∩ Ioi 0 = Ioi 0 := by + apply inter_eq_right.mpr + intro v hv + exact (div_pos (Real.rpow_pos_of_pos hv _) (sq_pos_of_pos (add_pos ha hv))).ne' + rw [he] + simp + +/-- The scalar difference whose positive-matrix functional calculus is integrated. -/ +def resolventDifference (β δ y v : ℝ) : ℝ := + v ^ β * ((δ + v)⁻¹ - (y + δ + v)⁻¹) + +lemma resolvent_difference_eq (β : ℝ) {δ y v : ℝ} + (hδv : δ + v ≠ 0) (hyδv : y + δ + v ≠ 0) : + resolventDifference β δ y v = y * (v ^ β / ((δ + v) * (y + δ + v))) := by + unfold resolventDifference + field_simp + ring + +lemma resolvent_difference_integrable {β δ y : ℝ} (hβ₀ : -1 < β) (hβ₁ : β < 1) + (hδ : 0 < δ) (hy : -δ / 2 < y) : + IntegrableOn (resolventDifference β δ y) (Ioi 0) := by + have hc : ContinuousOn (resolventDifference β δ y) (Ioi 0) := by + unfold resolventDifference + apply ContinuousOn.mul + · exact continuousOn_id.rpow_const (fun _ hv ↦ Or.inl (ne_of_gt hv)) + · apply ContinuousOn.sub + · apply ContinuousOn.inv₀ (by fun_prop) + intro v hv + exact ne_of_gt (add_pos hδ hv) + · apply ContinuousOn.inv₀ (by fun_prop) + intro v hv + have hv' : 0 < v := hv + linarith + apply ((resolvent_kernel_integrable hβ₀ hβ₁ (half_pos hδ)).const_mul |y|).mono' + (hc.aestronglyMeasurable measurableSet_Ioi) + filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + have hv' : 0 < v := hv + have ha : 0 < δ + v := by linarith + have hb : 0 < y + δ + v := by linarith + have hm : 0 < δ / 2 + v := by linarith + rw [resolvent_difference_eq β ha.ne' hb.ne', norm_mul, Real.norm_eq_abs, + Real.norm_eq_abs, abs_of_nonneg (div_nonneg (Real.rpow_nonneg hv'.le _) (mul_pos ha hb).le)] + apply mul_le_mul_of_nonneg_left _ (abs_nonneg y) + apply div_le_div_of_nonneg_left (Real.rpow_nonneg hv'.le _) (sq_pos_of_pos hm) + nlinarith [mul_nonneg (show 0 ≤ δ / 2 by linarith) (show 0 ≤ δ / 2 + v by linarith), + mul_nonneg (show 0 ≤ y + δ / 2 by linarith) (show 0 ≤ δ + v by linarith)] + +lemma resolvent_integral_hasDerivAt {β δ y : ℝ} (hβ₀ : -1 < β) (hβ₁ : β < 1) + (hδ : 0 < δ) (hy : 0 ≤ y) : + HasDerivAt (fun x ↦ ∫ v in Ioi (0 : ℝ), resolventDifference β δ x v) + (∫ v in Ioi (0 : ℝ), v ^ β / (y + δ + v) ^ 2) y := by + have hi x (hx : -δ / 2 < x) := resolvent_difference_integrable hβ₀ hβ₁ hδ hx + have hmeas : ∀ᶠ x in 𝓝 y, AEStronglyMeasurable (resolventDifference β δ x) + (volume.restrict (Ioi 0)) := by + filter_upwards [Ioi_mem_nhds (show -δ / 2 < y by linarith)] with x hx + exact (hi x hx).aestronglyMeasurable + have hdint : IntegrableOn (fun v : ℝ ↦ v ^ β / (y + δ + v) ^ 2) (Ioi 0) := + resolvent_kernel_integrable hβ₀ hβ₁ (by linarith) + apply (hasDerivAt_integral_of_dominated_loc_of_deriv_le + (μ := volume.restrict (Ioi (0 : ℝ))) (s := Ioi (-δ / 2)) + (F' := fun x v : ℝ ↦ v ^ β / (x + δ + v) ^ 2) + (bound := fun v : ℝ ↦ v ^ β / (δ / 2 + v) ^ 2) + (Ioi_mem_nhds (show -δ / 2 < y by linarith)) hmeas + (hi y (by linarith)) hdint.aestronglyMeasurable ?_ + (resolvent_kernel_integrable hβ₀ hβ₁ (half_pos hδ)) ?_).2 + · filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + intro x hx + have hv' : 0 < v := hv + have hx' : -δ / 2 < x := hx + rw [Real.norm_eq_abs, abs_of_nonneg (div_nonneg (Real.rpow_nonneg hv'.le _) (sq_nonneg _))] + apply div_le_div_of_nonneg_left (Real.rpow_nonneg hv'.le _) + (sq_pos_of_pos (by linarith : 0 < δ / 2 + v)) + nlinarith + · filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + intro x hx + have hv' : 0 < v := hv + have hx' : -δ / 2 < x := hx + have he := (((hasDerivAt_id x).add_const δ).add_const v).inv + (by linarith : x + δ + v ≠ 0) + convert! (he.const_sub ((δ + v)⁻¹)).const_mul (v ^ β) using 1 + simp [div_eq_mul_inv] + + +/-- The normalization constant for the resolvent representation. -/ +def resolventNormalization (β : ℝ) : ℝ := + (∫ v in Ioi (0 : ℝ), v ^ β / (1 + v) ^ 2)⁻¹ + +lemma resolvent_normalization_pos {β : ℝ} (hβ₀ : -1 < β) (hβ₁ : β < 1) : + 0 < resolventNormalization β := + inv_pos.2 (resolvent_kernel_integral_pos hβ₀ hβ₁ zero_lt_one) + +/-- Resolvent representation of f, for every nonnegative scalar argument. +The exponent sigma-1/2 may be zero or negative. -/ +lemma primitive_resolvent_representation {σ δ y : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hδ : 0 < δ) (hy : 0 ≤ y) : + regularizedPrimitive σ δ y = resolventNormalization (σ - 1 / 2) * + ∫ v in Ioi (0 : ℝ), resolventDifference (σ - 1 / 2) δ y v := by + have hβ₀ : -1 < σ - 1 / 2 := by linarith + have hβ₁ : σ - 1 / 2 < 1 := by linarith + have hJ := (resolvent_kernel_integral_pos hβ₀ hβ₁ zero_lt_one).ne' + have hd (x : ℝ) (hx : 0 ≤ x) : + HasDerivAt (fun t ↦ resolventNormalization (σ - 1 / 2) * + ∫ v in Ioi (0 : ℝ), resolventDifference (σ - 1 / 2) δ t v) + ((x + δ) ^ (σ - 3 / 2)) x := by + have hh := (resolvent_integral_hasDerivAt hβ₀ hβ₁ hδ hx).const_mul + (resolventNormalization (σ - 1 / 2)) + rw [resolvent_kernel_integral_scale _ (by positivity : 0 < x + δ)] at hh + convert! hh using 1 + unfold resolventNormalization + rw [show σ - 1 / 2 - 1 = σ - 3 / 2 by ring, + mul_comm ((x + δ) ^ (σ - 3 / 2)), ← mul_assoc, inv_mul_cancel₀ hJ, one_mul] + have hf (x : ℝ) (hx : 0 ≤ x) : + HasDerivAt (regularizedPrimitive σ δ) ((x + δ) ^ (σ - 3 / 2)) x := by + simpa only [max_eq_left hx] using primitive_hasDerivAt σ hδ x + exact eq_of_has_deriv_right_eq + (fun x hx ↦ (hf x hx.1).hasDerivWithinAt) + (fun x hx ↦ (hd x hx.1).hasDerivWithinAt) + (primitive_differentiable σ hδ).continuous.continuousOn + (fun x hx ↦ (hd x hx.1).continuousAt.continuousWithinAt) + (by simp [resolventDifference]) y ⟨hy, le_rfl⟩ + +lemma inverse_mu_positive {σ δ m : ℝ} (hσ₀ : 0 < σ) (hδ : 0 < δ) (hm : 0 < m) : + 0 < (m + δ ^ σ) ^ (1 / σ) - δ := by + have hbase : 0 < δ ^ σ := Real.rpow_pos_of_pos hδ _ + have hi : 0 < (1 : ℝ) / σ := one_div_pos.2 hσ₀ + have hc := Real.rpow_lt_rpow hbase.le (show δ ^ σ < m + δ ^ σ by linarith) hi + rw [← Real.rpow_mul hδ.le, mul_one_div_cancel hσ₀.ne', Real.rpow_one] at hc + linarith + +lemma mu_inverse {σ δ m : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) + (hm : 0 < m) : + scalarMu σ δ ((m + δ ^ σ) ^ (1 / σ) - δ) = m := by + rw [mu_eq_nonneg hσ₁ hδ (inverse_mu_positive hσ₀ hδ hm).le, sub_add_cancel, + ← Real.rpow_mul (by positivity : 0 ≤ m + δ ^ σ), + one_div_mul_cancel hσ₀.ne', Real.rpow_one] + ring + +lemma mu_le_rpow {σ δ d : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) + (hd : 0 ≤ d) : scalarMu σ δ d ≤ d ^ σ := by + rw [mu_eq_nonneg hσ₁ hδ hd] + have := Real.rpow_add_le_add_rpow hd hδ.le hσ₀.le hσ₁.le + linarith + +lemma rankone_scalar_power {σ δ m d : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hδ : 0 < δ) (hm : 0 < m) (hd : 0 ≤ d) (he : scalarMu σ δ d = m) : + m ^ (1 + 1 / σ) ≤ d * m := by + have hmd : m ≤ d ^ σ := by rw [← he]; exact mu_le_rpow hσ₀ hσ₁ hδ hd + have hp := Real.rpow_le_rpow hm.le hmd (le_of_lt (one_div_pos.2 hσ₀)) + rw [← Real.rpow_mul hd, mul_one_div_cancel hσ₀.ne', Real.rpow_one] at hp + rw [Real.rpow_add hm, Real.rpow_one, mul_comm d] + exact mul_le_mul_of_nonneg_left hp hm.le + +end ScalarProof + +open scoped MatrixOrder ComplexOrder +namespace MatrixProof +variable {n : Type u4} [Fintype n] [DecidableEq n] + +/-- Exact resolvent remainder. All inverses are the ordinary finite-matrix +inverse; invertibility is provided by the positive-definiteness hypotheses. -/ +lemma resolvent_remainder (A B : Matrix n n ℂ) (hA : IsUnit A) (hB : IsUnit B) : + -A⁻¹ + A⁻¹ * (B - A) * A⁻¹ - (-B⁻¹) = + (A⁻¹ * (B - A)) * B⁻¹ * ((B - A) * A⁻¹) := by + have hAA := Matrix.mul_nonsing_inv A ((Matrix.isUnit_iff_isUnit_det A).mp hA) + have hAA' := Matrix.nonsing_inv_mul A ((Matrix.isUnit_iff_isUnit_det A).mp hA) + have hBB := Matrix.mul_nonsing_inv B ((Matrix.isUnit_iff_isUnit_det B).mp hB) + have hBB' := Matrix.nonsing_inv_mul B ((Matrix.isUnit_iff_isUnit_det B).mp hB) + have hb (C : Matrix n n ℂ) : B⁻¹ * (B * C) = C := by + rw [← mul_assoc, hBB', one_mul] + simp only [mul_sub, sub_mul, hAA, hAA', mul_one, one_mul] + simp only [mul_assoc, hb, hBB, mul_one] + noncomm_ring + +/-- The resolvent tangent inequality before integration. -/ +lemma resolvent_tangent {A B : Matrix n n ℂ} (hA : A.PosDef) (hB : B.PosDef) : + -B⁻¹ ≤ -A⁻¹ + A⁻¹ * (B - A) * A⁻¹ := by + rw [← sub_nonneg, resolvent_remainder A B hA.isUnit hB.isUnit] + have hp := hB.inv.posSemidef.conjTranspose_mul_mul_same ((B - A) * A⁻¹) + have he : (((B - A) * A⁻¹)ᴴ) = A⁻¹ * (B - A) := by + rw [conjTranspose_mul, hA.inv.isHermitian.eq, (hB.isHermitian.sub hA.isHermitian).eq] + rw [he] at hp + exact hp.nonneg + + +end MatrixProof + +/-- The compact penalty lemma. No differentiability or +convergence of the selected paths is required. -/ +lemma compact_penalty {X : Type u5} [TopologicalSpace X] {K : Set X} + (hK : IsCompact K) {f g : X → ℝ} (hf : Continuous f) (hg : Continuous g) + (hg₀ : ∀ x ∈ K, 0 ≤ g x) (hzero : ∀ x ∈ K, g x = 0 → f x ≤ 0) + {η : ℝ} (hη : 0 < η) : + ∃ t₀ : ℝ, 0 < t₀ ∧ ∀ t : ℝ, 0 < t → t ≤ t₀ → + ∀ x ∈ K, f x - g x / t ≤ η := by + let S := K ∩ {x | η ≤ f x} + have hS : IsCompact S := hK.inter_right (isClosed_le continuous_const hf) + by_cases hne : S.Nonempty + · obtain ⟨y, hy, hmin⟩ := hS.exists_isMinOn hne hg.continuousOn + obtain ⟨z, hz, hmax⟩ := hK.exists_isMaxOn ⟨y, hy.1⟩ hf.continuousOn + have hgy : 0 < g y := by + apply lt_of_le_of_ne (hg₀ y hy.1) + intro h + have := hzero y hy.1 h.symm + exact (not_le_of_gt hη) (le_trans hy.2 this) + refine ⟨g y / (max (f z) 0 + 1), div_pos hgy (by positivity), ?_⟩ + intro t ht htt x hx + by_cases hfx : η ≤ f x + · have hxS : x ∈ S := ⟨hx, hfx⟩ + have hxg : g y ≤ g x := hmin hxS + have hxf : f x ≤ f z := hmax hx + have hc : 0 < max (f z) 0 + 1 := by positivity + have htm : t * (max (f z) 0 + 1) ≤ g y := (le_div_iff₀ hc).1 htt + have hgquot : max (f z) 0 + 1 ≤ g x / t := + (le_div_iff₀ ht).2 (by nlinarith) + have := le_max_left (f z) 0 + linarith + · have := div_nonneg (hg₀ x hx) ht.le + linarith + · refine ⟨1, zero_lt_one, ?_⟩ + intro t ht _ x hx + have hfx : f x < η := by + by_contra hn + apply hne + exact ⟨x, hx, le_of_not_gt hn⟩ + have := div_nonneg (hg₀ x hx) ht.le + linarith + + +end SharpLiebThirring + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/MatrixTangent.lean b/lean/OAI/Analysis/LiebThirring/MatrixTangent.lean new file mode 100644 index 0000000000000000000000000000000000000000..9d0ba8a45c5642b7d6eba1be452c4f52ec3746b9 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/MatrixTangent.lean @@ -0,0 +1,326 @@ +import OAI.Analysis.LiebThirring.ResolventCalculus + +namespace OAI + +universe u12 u13 u14 u15 + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +noncomputable section +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder CStarAlgebra + + +namespace SharpLiebThirring.MatrixProof +open ScalarProof MeasureTheory Set Filter Unitary +open scoped Matrix.Norms.L2Operator NNReal Topology +variable {n : Type u12} [Fintype n] [DecidableEq n] + +/-- The Schur action obtained by one Gaussian average. -/ +def gaussianSchur (z : n → ℝ) (v h : ℝ) (D : Matrix n n ℂ) : Matrix n n ℂ := + fun i j ↦ (Real.exp (-v * h * (z i - z j) ^ 2) : ℂ) * D i j + +lemma gaussianSchur_eq_average (z : n → ℝ) (D : Matrix n n ℂ) {v h : ℝ} + (hv : 0 ≤ v) (hh : 0 ≤ h) : + gaussianSchur z v h D = ∫ t, + conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D + ∂ProbabilityTheory.gaussianReal 0 ⟨2 * v * h, by positivity⟩ := by + ext i j + have he := (gaussian_phase_average z D (⟨2 * v * h, by positivity⟩ : ℝ≥0) i j).symm + convert! he using 1 + change (Real.exp (-v * h * (z i - z j) ^ 2) : ℂ) * D i j = + Complex.exp (-((2 * v * h) * (z i - z j) ^ 2 / 2 : ℝ)) * D i j + rw [Complex.ofReal_exp] + congr 2 + push_cast + ring + +lemma gaussianSchur_norm_le (z : n → ℝ) (D : Matrix n n ℂ) {v h : ℝ} + (hv : 0 ≤ v) (hh : 0 ≤ h) : ‖gaussianSchur z v h D‖ ≤ ‖D‖ := by + rw [gaussianSchur_eq_average z D hv hh] + apply (norm_integral_le_integral_norm _).trans + have he (t : ℝ) : + ‖conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D‖ = ‖D‖ := by + change ‖(phaseUnitary z t : Matrix n n ℂ) * D * + ((star (phaseUnitary z t) : unitary (Matrix n n ℂ)) : Matrix n n ℂ)‖ = ‖D‖ + rw [CStarRing.norm_mul_coe_unitary, CStarRing.norm_coe_unitary_mul] + simp_rw [he] + rw [integral_const] + have hp : (ProbabilityTheory.gaussianReal 0 (⟨2 * v * h, by positivity⟩ : ℝ≥0)).real univ = 1 := + @probReal_univ ℝ _ _ (ProbabilityTheory.instIsProbabilityMeasureGaussianReal 0 _) + erw [hp] + simp only [one_smul, le_refl] + +omit [Fintype n] [DecidableEq n] in +lemma continuous_gaussianSchur (z : n → ℝ) (h : ℝ) (D : Matrix n n ℂ) : + Continuous (fun v ↦ gaussianSchur z v h D) := by + apply continuous_pi + intro i + apply continuous_pi + intro j + unfold gaussianSchur + fun_prop + +lemma gamma_integrable_gaussianSchur {σ h : ℝ} (hσ : σ < 1) (hh : 0 ≤ h) + (z : n → ℝ) (D : Matrix n n ℂ) : + IntegrableOn (fun v ↦ gammaWeight σ v • gaussianSchur z v h D) (Ioi 0) := by + apply ((gammaWeight_integrable hσ).norm.mul_const ‖D‖).mono' + · exact (gammaWeight_integrable hσ).aestronglyMeasurable.smul + (continuous_gaussianSchur z h D).aestronglyMeasurable + · filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + rw [norm_smul] + exact mul_le_mul_of_nonneg_left (gaussianSchur_norm_le z D (le_of_lt hv) hh) (norm_nonneg _) + +def powerSchur (σ : ℝ) (z : n → ℝ) (h : ℝ) (D : Matrix n n ℂ) : Matrix n n ℂ := + fun i j ↦ (((1 + h * (z i - z j) ^ 2) ^ (σ - 1) : ℝ) : ℂ) * D i j + +lemma gamma_gaussianSchur_integral {σ h : ℝ} (hσ : σ < 1) (hh : 0 ≤ h) + (z : n → ℝ) (D : Matrix n n ℂ) : + (∫ v in Ioi (0 : ℝ), gammaWeight σ v • gaussianSchur z v h D) = + powerSchur σ z h D := by + ext i j + have he := (entryCLM i j).integral_comp_comm (gamma_integrable_gaussianSchur hσ hh z D) + simp only [entryCLM_apply] at he + rw [← he] + simp only [Matrix.smul_apply, gaussianSchur, powerSchur, Complex.real_smul, + ← mul_assoc, ← Complex.ofReal_mul] + erw [integral_mul_const, integral_ofReal, gamma_mixture hσ hh] + rfl + +lemma powerSchur_trace_comparison {σ h : ℝ} (hσ : σ < 1) (hh : 0 ≤ h) + (z : n → ℝ) (M D : Matrix n n ℂ) + (hpoint : ∀ t : ℝ, 0 ≤ (trace (M * (2 • D - + conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D - + conjStarAlgAut ℂ (Matrix n n ℂ) (star (phaseUnitary z t)) D))).re) : + (trace (M * powerSchur σ z h D)).re ≤ (trace (M * D)).re := by + have hi := gamma_integrable_gaussianSchur hσ hh z D + have hp (v : ℝ) (hv : 0 < v) : + gammaWeight σ v * (trace (M * gaussianSchur z v h D)).re ≤ + gammaWeight σ v * (trace (M * D)).re := by + apply mul_le_mul_of_nonneg_left _ (gammaWeight_nonneg hσ hv.le) + rw [gaussianSchur_eq_average z D hv.le hh] + exact gaussian_trace_comparison z M D _ hpoint + have hle := integral_mono_ae ((tracePairCLM M).integrable_comp hi) + ((gammaWeight_integrable hσ).mul_const ((trace (M * D)).re)) + (by filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + simpa only [map_smul, tracePairCLM_apply, smul_eq_mul] using hp v hv) + rw [(tracePairCLM M).integral_comp_comm hi, gamma_gaussianSchur_integral hσ hh z D, + integral_mul_const, gammaWeight_integral hσ, one_mul] at hle + exact hle + +end SharpLiebThirring.MatrixProof + + +namespace SharpLiebThirring.MatrixProof +open ScalarProof MeasureTheory Set +open scoped Matrix.Norms.L2Operator +variable {n : Type u13} [Fintype n] [DecidableEq n] + +def tangentSchur (σ a : ℝ) (z : n → ℝ) (D : Matrix n n ℂ) : Matrix n n ℂ := + ∫ τ in Icc (0 : ℝ) 1, powerSchur σ z (τ * (1 - τ) / a) D + +omit [Fintype n] [DecidableEq n] in +lemma continuousOn_powerSchur_tau (σ : ℝ) {a : ℝ} (ha : 0 < a) + (z : n → ℝ) (D : Matrix n n ℂ) : + ContinuousOn (fun τ ↦ powerSchur σ z (τ * (1 - τ) / a) D) (Icc (0 : ℝ) 1) := by + apply continuousOn_pi.2 + intro i + apply continuousOn_pi.2 + intro j + apply ContinuousOn.mul _ continuousOn_const + apply Complex.continuous_ofReal.comp_continuousOn + apply ContinuousOn.rpow_const (by fun_prop) + intro τ hτ + left + have hp : 0 ≤ τ * (1 - τ) / a * (z i - z j) ^ 2 := + mul_nonneg (div_nonneg (mul_nonneg hτ.1 (sub_nonneg.2 hτ.2)) ha.le) (sq_nonneg _) + linarith + +lemma integrable_powerSchur_tau (σ : ℝ) {a : ℝ} (ha : 0 < a) + (z : n → ℝ) (D : Matrix n n ℂ) : + IntegrableOn (fun τ ↦ powerSchur σ z (τ * (1 - τ) / a) D) (Icc (0 : ℝ) 1) := + (continuousOn_powerSchur_tau σ ha z D).integrableOn_Icc + +lemma tangentSchur_trace_comparison {σ a : ℝ} (hσ : σ < 1) (ha : 0 < a) + (z : n → ℝ) (M D : Matrix n n ℂ) + (hpoint : ∀ t : ℝ, 0 ≤ (trace (M * (2 • D - + Unitary.conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D - + Unitary.conjStarAlgAut ℂ (Matrix n n ℂ) (star (phaseUnitary z t)) D))).re) : + (trace (M * tangentSchur σ a z D)).re ≤ (trace (M * D)).re := by + have hi := integrable_powerSchur_tau σ ha z D + have hle := integral_mono_ae ((tracePairCLM M).integrable_comp hi) + (integrableOn_const (C := (trace (M * D)).re) (s := Icc (0 : ℝ) 1) (by simp)) (by + filter_upwards [ae_restrict_mem measurableSet_Icc] with τ hτ + exact powerSchur_trace_comparison hσ + (div_nonneg (mul_nonneg hτ.1 (sub_nonneg.2 hτ.2)) ha.le) z M D hpoint) + rw [(tracePairCLM M).integral_comp_comm hi] at hle + simpa [tangentSchur, tracePairCLM_apply] using hle + +lemma tangentSchur_one (σ a : ℝ) (z : n → ℝ) : + tangentSchur σ a z 1 = 1 := by + have he : ∀ τ : ℝ, powerSchur σ z (τ * (1 - τ) / a) (1 : Matrix n n ℂ) = 1 := by + intro τ + ext i j + by_cases hij : i = j + · subst j; simp [powerSchur] + · simp [powerSchur, hij] + simp only [tangentSchur, he] + simp + +lemma tangentSchur_selfAdjoint (σ : ℝ) {a : ℝ} (ha : 0 < a) + (z : n → ℝ) (D M : Matrix n n ℂ) : + trace (M * tangentSchur σ a z D) = trace (tangentSchur σ a z M * D) := by + have he (i j) (A : Matrix n n ℂ) : + tangentSchur σ a z A i j = + (∫ τ in Icc (0 : ℝ) 1, (((1 + τ * (1 - τ) / a * (z i - z j) ^ 2) ^ + (σ - 1) : ℝ) : ℂ)) * A i j := by + have hc := (entryCLM i j).integral_comp_comm (integrable_powerSchur_tau σ ha z A) + simp only [entryCLM_apply] at hc + rw [tangentSchur, ← hc] + simp only [powerSchur] + exact integral_mul_const _ _ + simp only [Matrix.trace] + apply Finset.sum_congr rfl + intro i _ + apply Finset.sum_congr rfl + intro j _ + change M i j * tangentSchur σ a z D j i = tangentSchur σ a z M i j * D j i + rw [he, he, show (z j - z i) ^ 2 = (z i - z j) ^ 2 by ring] + ring + +end SharpLiebThirring.MatrixProof + + +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {n : Type u14} [Fintype n] [DecidableEq n] + +def quadraticTangent (σ δ d : ℝ) (z : n → ℝ) (Z : Matrix n n ℂ) (s : ℝ) : Matrix n n ℂ := + fun i j ↦ (dividedPrimitive σ δ ((s - z i) ^ 2 + d) ((s - z j) ^ 2 + d) : ℂ) * Z i j + +lemma integrable_quadraticTangent {σ δ d : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (hd : 0 ≤ d) (z : n → ℝ) (Z : Matrix n n ℂ) : + Integrable (quadraticTangent σ δ d z Z) := by + let e : (n → n → ℂ) →L[ℝ] Matrix n n ℂ := + ({ toFun := Matrix.of + map_add' := by intros; rfl + map_smul' := by intros; rfl } : (n → n → ℂ) →ₗ[ℝ] Matrix n n ℂ).toContinuousLinearMap + apply e.integrable_comp + apply integrable_pi_iff.2 + intro i + apply integrable_pi_iff.2 + intro j + exact (Complex.ofRealCLM.integrable_comp (integrable_divided_quadratic hσ hδ hd (z i) (z j))).mul_const _ + +lemma tangentSchur_apply (σ : ℝ) {a : ℝ} (ha : 0 < a) (z : n → ℝ) (Z : Matrix n n ℂ) (i j : n) : + tangentSchur σ a z Z i j = + ((∫ τ in Icc (0 : ℝ) 1, (1 + τ * (1 - τ) / a * (z i - z j) ^ 2) ^ + (σ - 1) : ℝ) : ℂ) * Z i j := by + have he := (entryCLM i j).integral_comp_comm (integrable_powerSchur_tau σ ha z Z) + simp only [entryCLM_apply] at he + rw [tangentSchur, ← he] + simp only [powerSchur] + rw [integral_mul_const] + exact congrArg (fun t : ℂ ↦ t * Z i j) (integral_ofReal (f := fun τ : ℝ ↦ + (1 + τ * (1 - τ) / a * (z i - z j) ^ 2) ^ (σ - 1))) + +/-- Exact integrated tangent map in any diagonalizing basis, not only simple spectrum. -/ +lemma integral_quadraticTangent {σ δ d : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (hd : 0 ≤ d) (z : n → ℝ) (Z : Matrix n n ℂ) : + fieldNormalization σ • ∫ s : ℝ, quadraticTangent σ δ d z Z s = + (σ * (d + δ) ^ (σ - 1)) • tangentSchur σ (d + δ) z Z := by + ext i j + have he := (entryCLM i j).integral_comp_comm (integrable_quadraticTangent hσ hδ hd z Z) + simp only [entryCLM_apply] at he + simp only [Matrix.smul_apply] + rw [← he, tangentSchur_apply σ (by linarith) z Z i j] + simp only [quadraticTangent] + rw [integral_mul_const] + erw [integral_ofReal (f := fun s : ℝ ↦ dividedPrimitive σ δ + ((s - z i) ^ 2 + d) ((s - z j) ^ 2 + d))] + simp only [Complex.real_smul, ← mul_assoc] + have h := congrArg (fun t : ℝ ↦ (t : ℂ) * Z i j) + (integral_divided_quadratic hσ hδ hd (z i) (z j)) + push_cast at h + push_cast + convert! h using 1 + + +lemma primitive_diagonal_tangent {σ δ d : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hδ : 0 < δ) (hd : 0 ≤ d) (z : n → ℝ) (s : ℝ) {X : Matrix n n ℂ} + (hX : X.PosSemidef) : + hX.isHermitian.cfc (regularizedPrimitive σ δ) ≤ + cfc (regularizedPrimitive σ δ) (diagonal (fun i ↦ (((s - z i) ^ 2 + d : ℝ) : ℂ))) + + quadraticTangent σ δ d z (X - diagonal (fun i ↦ (((s - z i) ^ 2 + d : ℝ) : ℂ))) s := by + have hY := diagonal_real_posSemidef (fun i ↦ (s - z i) ^ 2 + d) + (fun i ↦ add_nonneg (sq_nonneg _) hd) + have ht := primitive_cfc_tangent hX hY hσ₀ hσ₁ hδ + rw [← hY.isHermitian.cfc_eq, integral_resolventTangent_diagonal hσ₀ hσ₁ hδ _ + (fun i ↦ add_nonneg (sq_nonneg _) hd)] at ht + exact ht + +end SharpLiebThirring.MatrixProof + +namespace SharpLiebThirring.ScalarProof + +lemma primitive_le_tangent {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) (x y : ℝ) : + regularizedPrimitive σ δ y ≤ regularizedPrimitive σ δ x + + (max x 0 + δ) ^ (σ - 3 / 2) * (y - x) := by + have hc := (primitive_concave hσ hδ).neg + have hd := (primitive_hasDerivAt σ hδ x).neg + rcases lt_trichotomy x y with hxy | rfl | hyx + · have hs := hc.le_slope_of_hasDerivAt (mem_univ x) (mem_univ y) hxy hd + rw [slope_def_field] at hs + have := (le_div_iff₀ (sub_pos.2 hxy)).1 hs + dsimp at this + nlinarith + · simp + · have hs := hc.slope_le_of_hasDerivAt (mem_univ y) (mem_univ x) hyx hd + rw [slope_def_field] at hs + have := (div_le_iff₀ (sub_pos.2 hyx)).1 hs + dsimp at this + nlinarith + +end SharpLiebThirring.ScalarProof + +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {n : Type u15} [Fintype n] [DecidableEq n] + +/-- Scalar Jensen inequality for every positive unital real-linear matrix state. +No assertion of operator concavity on the whole line is used. -/ +lemma primitive_state_jensen {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (φ : Matrix n n ℂ →ₗ[ℝ] ℝ) (hφ : ∀ A, A.PosSemidef → 0 ≤ φ A) + (hφ₁ : φ 1 = 1) {A : Matrix n n ℂ} (hA : A.IsHermitian) : + φ (cfc (regularizedPrimitive σ δ) A) ≤ regularizedPrimitive σ δ (φ A) := by + let f := regularizedPrimitive σ δ + let x := φ A + let d := (max x 0 + δ) ^ (σ - 3 / 2) + have ht : cfc f A ≤ cfc (fun y : ℝ ↦ f x + d * (y - x)) A := + cfc_mono (fun y _ ↦ primitive_le_tangent hσ hδ x y) + (primitive_differentiable σ hδ).continuous.continuousOn (by fun_prop) + have he : cfc (fun y : ℝ ↦ f x + d * (y - x)) A = + f x • 1 + d • (A - x • 1) := by + erw [cfc_const_add (f x) (fun y : ℝ ↦ d * (y - x)) A (by fun_prop) hA, + cfc_const_mul d (fun y : ℝ ↦ y - x) A (by fun_prop), + cfc_sub id (fun _ : ℝ ↦ x) A (by fun_prop) (by fun_prop), + cfc_id ℝ A hA, cfc_const x A hA, + Algebra.algebraMap_eq_smul_one, Algebra.algebraMap_eq_smul_one] + rw [he] at ht + have hp := hφ _ (Matrix.nonneg_iff_posSemidef.1 (sub_nonneg.2 ht)) + simp only [map_sub, map_add, map_smul, hφ₁, smul_eq_mul, mul_one] at hp + dsimp [x] at hp + linarith + +end SharpLiebThirring.MatrixProof + +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/Model.lean b/lean/OAI/Analysis/LiebThirring/Model.lean new file mode 100644 index 0000000000000000000000000000000000000000..4d4867d7b07af954e309cec53fe5b46195c79b28 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/Model.lean @@ -0,0 +1,95 @@ +import Mathlib + +namespace OAI + + +/-! +The form domain is H¹(R;C), represented by an L² function together with its L² +weak derivative. Null-set changes do not affect any definition below. +`negativeMoment` is the extended nonnegative sum over negative eigenvalues, +counting multiplicities: equivalently the supremum over all finite orthonormal +families of weak eigenfunctions of the form. This does not assume in advance +finiteness of the moment or a finite number of eigenvalues. +-/ + + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix + +namespace SharpLiebThirring + +structure H1 where + val : ℝ → ℂ + grad : ℝ → ℂ + val_memLp : MemLp val 2 volume + grad_memLp : MemLp grad 2 volume + weak_derivative : ∀ φ : ℝ → ℂ, ContDiff ℝ (↑(⊤ : ℕ∞) : WithTop ℕ∞) φ → HasCompactSupport φ → + (∫ x : ℝ, val x * deriv φ x) = -(∫ x : ℝ, grad x * φ x) + +def l2Pairing (u v : H1) : ℂ := ∫ x : ℝ, star (u.val x) * v.val x + +/-- The polarized form of -d²/dx² - W, on exactly H¹. -/ +def schrodingerForm (W : ℝ → ℝ) (u v : H1) : ℂ := + (∫ x : ℝ, star (u.grad x) * v.grad x) - + ∫ x : ℝ, (W x : ℂ) * star (u.val x) * v.val x + +/-- Weak eigenfunction at the negative energy -k². -/ +def IsNegativeEigenfunction (W : ℝ → ℝ) (k : ℝ) (u : H1) : Prop := + 0 < k ∧ ∀ v : H1, schrodingerForm W v u = -(k ^ 2 : ℝ) * l2Pairing v u + +def IsOrthonormalFamily {N : ℕ} (u : Fin N → H1) : Prop := + ∀ i j, l2Pairing (u i) (u j) = if i = j then 1 else 0 + +/-- An unlimited finite-family-size supremum, in ℝ≥0∞, includes the entire sum. -/ +def negativeMoment (γ : ℝ) (W : ℝ → ℝ) : ℝ≥0∞ := + ⨆ (N : ℕ) (u : Fin N → H1) (k : Fin N → ℝ) + (_ : IsOrthonormalFamily u) (_ : ∀ i, IsNegativeEigenfunction W (k i) (u i)), + ∑ i, (ENNReal.ofReal (k i)) ^ (2 * γ) + +/-- The moment retaining at most one negative eigenvalue. -/ +def oneStateMoment (γ : ℝ) (W : ℝ → ℝ) : ℝ≥0∞ := + ⨆ (u : H1) (k : ℝ) (_ : l2Pairing u u = 1) + (_ : IsNegativeEigenfunction W k u), (ENNReal.ofReal k) ^ (2 * γ) + +def Admissible (γ : ℝ) (W : ℝ → ℝ) : Prop := + (∀ᵐ x : ℝ, 0 ≤ W x) ∧ MemLp W (ENNReal.ofReal (γ + 1 / 2)) volume + +def potentialMass (γ : ℝ) (W : ℝ → ℝ) : ℝ≥0∞ := + ∫⁻ x : ℝ, (ENNReal.ofReal (W x)) ^ (γ + 1 / 2) + +def semiclassicalConstant (γ : ℝ) : ℝ := + Real.Gamma (γ + 1) / (2 * Real.sqrt Real.pi * Real.Gamma (γ + 3 / 2)) + +def sharpConstant (γ : ℝ) : ℝ := + 2 * ((γ - 1 / 2) / (γ + 1 / 2)) ^ (γ - 1 / 2) * semiclassicalConstant γ + +def optimalConstant (γ : ℝ) : ℝ≥0∞ := + ⨆ (W : ℝ → ℝ) (_ : Admissible γ W) (_ : 0 < potentialMass γ W), + negativeMoment γ W / potentialMass γ W + +def oneStateConstant (γ : ℝ) : ℝ≥0∞ := + ⨆ (W : ℝ → ℝ) (_ : Admissible γ W) (_ : 0 < potentialMass γ W), + oneStateMoment γ W / potentialMass γ W + +def equalityPotential (γ : ℝ) (x : ℝ) : ℝ := + let r := (γ - 1 / 2)⁻¹ + (r + 1) * (Real.cosh (r * x))⁻¹ ^ 2 + +/-- The full spectral bound, optimal constants, and attainment at the explicit potential. -/ +def MainClaim : Prop := + ∀ γ : ℝ, 1 / 2 < γ → γ < 3 / 2 → + (∀ W : ℝ → ℝ, Admissible γ W → + negativeMoment γ W ≤ ENNReal.ofReal (sharpConstant γ) * potentialMass γ W) ∧ + optimalConstant γ = ENNReal.ofReal (sharpConstant γ) ∧ + oneStateConstant γ = ENNReal.ofReal (sharpConstant γ) ∧ + Admissible γ (equalityPotential γ) ∧ + 0 < potentialMass γ (equalityPotential γ) ∧ + negativeMoment γ (equalityPotential γ) = + ENNReal.ofReal (sharpConstant γ) * potentialMass γ (equalityPotential γ) + +end SharpLiebThirring +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/MomentBound.lean b/lean/OAI/Analysis/LiebThirring/MomentBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..a1c1947b1c05f84e699b5f2250caf3ab1697c91f --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/MomentBound.lean @@ -0,0 +1,86 @@ +import OAI.Analysis.LiebThirring.ComplexFamilies + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring +open MeasureTheory Set +open SobolevProof SobolevProof.C1L2 SpectralProof ConstantProof + +lemma Admissible.locallyIntegrable {γ : ℝ} {W : ℝ → ℝ} + (hW : Admissible γ W) (hγ : 1/2 < γ) : LocallyIntegrable W volume := by + apply hW.2.locallyIntegrable + rw [← ENNReal.ofReal_one] + exact ENNReal.ofReal_le_ofReal (by linarith) + +lemma Admissible.integrable_rpow {γ : ℝ} {W : ℝ → ℝ} + (hW : Admissible γ W) (hγ : 1/2 < γ) : + Integrable (fun x ↦ W x^(γ+1/2)) := by + have hp : 0 < γ+1/2 := by linarith + have hh := hW.2.integrable_norm_rpow (ENNReal.ofReal_pos.mpr hp).ne' ENNReal.ofReal_ne_top + rw [ENNReal.toReal_ofReal hp.le] at hh + apply hh.congr + filter_upwards [hW.1] with x hx + rw [Real.norm_eq_abs,abs_of_nonneg hx] + +lemma Admissible.mass_eq_ofReal {γ : ℝ} {W : ℝ → ℝ} + (hW : Admissible γ W) (hγ : 1/2 < γ) : + potentialMass γ W = ENNReal.ofReal (∫ x, W x^(γ+1/2)) := by + rw [ofReal_integral_eq_lintegral_ofReal (hW.integrable_rpow hγ)] + · apply lintegral_congr_ae + filter_upwards [hW.1] with x hx + exact ENNReal.ofReal_rpow_of_nonneg hx (by linarith) + · filter_upwards [hW.1] with x hx + exact Real.rpow_nonneg hx _ + +lemma Admissible.mass_ne_top {γ : ℝ} {W : ℝ → ℝ} + (hW : Admissible γ W) (hγ : 1/2 < γ) : potentialMass γ W ≠ ⊤ := by + rw [hW.mass_eq_ofReal hγ] + exact ENNReal.ofReal_ne_top + +lemma sharpConstant_pos {γ : ℝ} (hγ : 1/2 < γ) : 0 < sharpConstant γ := by + have hσ : 0 < γ-1/2 := by linarith + have he := action_constant_eq_sharp hσ + rw [sub_add_cancel] at he + rw [← he] + apply div_pos _ (betaAction_pos hσ) + unfold actionYoungConstant + positivity + +lemma finite_complex_eigenfamily_bound {N : ℕ} {γ : ℝ} + (hγ₀ : 1/2 < γ) (hγ₁ : γ < 3/2) {W : ℝ → ℝ} + (hW : Admissible γ W) (u : Fin N → H1) (k : Fin N → ℝ) + (ho : IsOrthonormalFamily u) (he : ∀ i, IsNegativeEigenfunction W (k i) (u i)) : + (∑ i, k i^(2*γ)) ≤ sharpConstant γ*∫ x, W x^(γ+1/2) := by + have hWl := hW.locallyIntegrable hγ₀ + choose a ha har using (fun i ↦ eigen_C1_representative hWl (he i) Complex.reCLM) + choose b hb hbi using (fun i ↦ eigen_C1_representative hWl (he i) Complex.imCLM) + have hr (i j : Fin N) : inner ℝ (a i) (a j)+inner ℝ (b i) (b j) = if i=j then 1 else 0 := by + have hh := congrArg Complex.re (ho i j) + rw [re_l2Pairing (har i) (hbi i) (har j) (hbi j)] at hh + simpa only [apply_ite,Complex.one_re,Complex.zero_re] using hh + have hi (i j : Fin N) : inner ℝ (a i) (b j)-inner ℝ (b i) (a j) = 0 := by + have hh := congrArg Complex.im (ho i j) + rw [im_l2Pairing (har i) (hbi i) (har j) (hbi j)] at hh + simpa only [apply_ite,Complex.one_im,Complex.zero_im,ite_self] using hh + obtain ⟨J,hJ,v,l,hvo,hve,hl,hs⟩ := realify_finite_family hWl k (fun i ↦ (he i).1) a b ha hb hr hi (2*γ) + let := hJ + exact hs.trans (real_family_bound hγ₀ hγ₁ hWl hW.1 (hW.integrable_rpow hγ₀) v l hvo hve hl) + +/-- The full (unlimited-family-size) negative spectral moment estimate. -/ +lemma negativeMoment_bound {γ : ℝ} (hγ₀ : 1/2 < γ) (hγ₁ : γ < 3/2) + {W : ℝ → ℝ} (hW : Admissible γ W) : + negativeMoment γ W ≤ ENNReal.ofReal (sharpConstant γ)*potentialMass γ W := by + unfold negativeMoment + refine iSup_le (fun N ↦ iSup_le (fun u ↦ iSup_le (fun k ↦ iSup_le (fun ho ↦ iSup_le (fun he ↦ ?_))))) + have hh := ENNReal.ofReal_le_ofReal (finite_complex_eigenfamily_bound hγ₀ hγ₁ hW u k ho he) + rw [ENNReal.ofReal_sum_of_nonneg (fun i _ ↦ Real.rpow_nonneg (he i).1.le _), + ENNReal.ofReal_mul (sharpConstant_pos hγ₀).le,← hW.mass_eq_ofReal hγ₀] at hh + simpa only [ENNReal.ofReal_rpow_of_nonneg (he _).1.le (show 0 ≤ 2*γ by linarith)] using hh + +end SharpLiebThirring + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/Multiplication.lean b/lean/OAI/Analysis/LiebThirring/Multiplication.lean new file mode 100644 index 0000000000000000000000000000000000000000..76800ad737e986d8690619c4da61b24c3f8dacee --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/Multiplication.lean @@ -0,0 +1,130 @@ +import OAI.Analysis.LiebThirring.PotentialSplit + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set Filter +open scoped Topology + +structure PotentialData (W : ℝ → ℝ) where + measurable : AEStronglyMeasurable W volume + nonneg : ∀ᵐ x, 0 ≤ W x + b : ℝ + b_nonneg : 0 ≤ b + V : ℝ → ℝ + V_nonneg : ∀ x, 0 ≤ V x + V_integrable : Integrable V + V_small : (∫ x, V x) ≤ 1/32 + decomp : ∀ x, ‖W x‖ ≤ b+V x + +def potentialData {γ : ℝ} {W : ℝ → ℝ} (hγ : 1/2 < γ) (hW : Admissible γ W) : + PotentialData W := Classical.choice (by + obtain ⟨b,hb,V,hV,hVI,hVs,hD⟩ := potential_decomposition hγ hW (ε := 1/32) (by norm_num) + exact ⟨⟨hW.2.aestronglyMeasurable,hW.1,b,hb,V,hV,hVI,hVs,hD⟩⟩) + +lemma memLp_integral_norm_sq {f : ℝ → ℂ} (hf : MemLp f 2 volume) : + (∫ x, ‖f x‖^2) = ‖hf.toLp f‖^2 := by + rw [L2_norm_sq_eq_integral] + exact integral_congr_ae (hf.coeFn_toLp.symm.mono (fun x hx ↦ by simp only [hx])) + +lemma potential_quadratic_bound {W : ℝ → ℝ} (d : PotentialData W) (u : H1) : + Integrable (fun x ↦ ‖W x‖*‖u.val x‖^2) ∧ + (∫ x, ‖W x‖*‖u.val x‖^2) ≤ + (d.b+1/4)*‖u.val_memLp.toLp u.val‖^2+(1/4)*‖u.grad_memLp.toLp u.grad‖^2 := by + let C := 8*(‖u.val_memLp.toLp u.val‖^2+‖u.grad_memLp.toLp u.grad‖^2) + have hC : 0 ≤ C := by positivity + have hdom : Integrable (fun x ↦ d.b*‖u.val x‖^2+d.V x*C) := + ((u.val_memLp.integrable_norm_pow (by norm_num)).const_mul d.b).add + (d.V_integrable.mul_const C) + have hle : ∀ᵐ x, ‖W x‖*‖u.val x‖^2 ≤ d.b*‖u.val x‖^2+d.V x*C := by + filter_upwards [h1_ae_sq_bound u] with x hx + calc + _ ≤ (d.b+d.V x)*‖u.val x‖^2 := mul_le_mul_of_nonneg_right (d.decomp x) (sq_nonneg _) + _ ≤ _ := by nlinarith [mul_le_mul_of_nonneg_left hx (d.V_nonneg x)] + have hi : Integrable (fun x ↦ ‖W x‖*‖u.val x‖^2) := hdom.mono' + (d.measurable.norm.mul (u.val_memLp.aestronglyMeasurable.norm.pow 2)) + (hle.mono (fun x hx ↦ by simpa only [Real.norm_of_nonneg (mul_nonneg (norm_nonneg _) (sq_nonneg _))] using hx)) + refine ⟨hi,?_⟩ + calc + _ ≤ ∫ x, (d.b*‖u.val x‖^2+d.V x*C) := integral_mono_ae hi hdom hle + _ = d.b*‖u.val_memLp.toLp u.val‖^2+(∫ x, d.V x)*C := by + rw [integral_add ((u.val_memLp.integrable_norm_pow (by norm_num)).const_mul d.b) + (d.V_integrable.mul_const C),integral_const_mul,integral_mul_const,memLp_integral_norm_sq] + _ ≤ d.b*‖u.val_memLp.toLp u.val‖^2+(1/32)*C := + add_le_add le_rfl (mul_le_mul_of_nonneg_right d.V_small hC) + _ = _ := by dsimp [C]; ring + +def weightedVal {W : ℝ → ℝ} (_d : PotentialData W) (u : H1C) (x : ℝ) : ℂ := + (Real.sqrt ‖W x‖ : ℂ)*valL u x + +lemma weightedVal_norm_sq {W : ℝ → ℝ} (d : PotentialData W) (u : H1C) (x : ℝ) : + ‖weightedVal d u x‖^2 = ‖W x‖*‖valL u x‖^2 := by + simp only [weightedVal,norm_mul,Complex.norm_real, + Real.norm_of_nonneg (Real.sqrt_nonneg _),mul_pow,Real.sq_sqrt (norm_nonneg _)] + +lemma weightedVal_memLp {W : ℝ → ℝ} (d : PotentialData W) (u : H1C) : + MemLp (weightedVal d u) 2 volume := by + apply (memLp_two_iff_integrable_sq_norm (by + exact (Complex.continuous_ofReal.comp_aestronglyMeasurable + (Real.continuous_sqrt.comp_aestronglyMeasurable d.measurable.norm)).mul + (Lp.aestronglyMeasurable (valL u)))).mpr + have h := (potential_quadratic_bound d (toH1 u)).1 + change Integrable (fun x ↦ ‖W x‖*‖valL u x‖^2) at h + simpa only [weightedVal_norm_sq] using h + +def weightedLM {W : ℝ → ℝ} (d : PotentialData W) : H1C →ₗ[ℂ] L2C where + toFun u := (weightedVal_memLp d u).toLp (weightedVal d u) + map_add' u v := by + apply Lp.ext + filter_upwards [(weightedVal_memLp d (u+v)).coeFn_toLp, + (weightedVal_memLp d u).coeFn_toLp,(weightedVal_memLp d v).coeFn_toLp, + Lp.coeFn_add ((weightedVal_memLp d u).toLp (weightedVal d u)) + ((weightedVal_memLp d v).toLp (weightedVal d v)), + Lp.coeFn_add (valL u) (valL v)] with x h1 h2 h3 h4 h5 + simp only [Pi.add_apply] at h4 h5 + rw [h1,h4,h2,h3] + simp only [weightedVal,map_add] + rw [h5,mul_add] + map_smul' c u := by + apply Lp.ext + filter_upwards [(weightedVal_memLp d (c • u)).coeFn_toLp, + (weightedVal_memLp d u).coeFn_toLp, + Lp.coeFn_smul c ((weightedVal_memLp d u).toLp (weightedVal d u)), + Lp.coeFn_smul c (valL u)] with x h1 h2 h3 h4 + simp only [Pi.smul_apply] at h3 h4 + simp only [RingHom.id_apply] + rw [h1,h3,h2] + simp only [weightedVal,map_smul] + rw [h4] + simp only [smul_eq_mul] + ring + +lemma weightedLM_norm_sq {W : ℝ → ℝ} (d : PotentialData W) (u : H1C) : + ‖weightedLM d u‖^2 ≤ (d.b+1/4)*‖valL u‖^2+(1/4)*‖gradL u‖^2 := by + change ‖(weightedVal_memLp d u).toLp (weightedVal d u)‖^2 ≤ _ + rw [← memLp_integral_norm_sq] + simp only [weightedVal_norm_sq] + have h := (potential_quadratic_bound d (toH1 u)).2 + simp only [toLp_toH1,grad_toLp_toH1] at h + exact h + +lemma h1_norm_sq (u : H1C) : ‖u‖^2 = ‖valL u‖^2+‖gradL u‖^2 := + WithLp.prod_norm_sq_eq_of_L2 u.1 + +lemma weightedLM_bound {W : ℝ → ℝ} (d : PotentialData W) (u : H1C) : + ‖weightedLM d u‖ ≤ Real.sqrt (d.b+1)*‖u‖ := by + apply (sq_le_sq₀ (norm_nonneg _) (mul_nonneg (Real.sqrt_nonneg _) (norm_nonneg _))).mp + rw [mul_pow,Real.sq_sqrt (by linarith [d.b_nonneg]),h1_norm_sq] + have h := weightedLM_norm_sq d u + nlinarith [mul_nonneg d.b_nonneg (sq_nonneg ‖gradL u‖)] + +def weightedL {W : ℝ → ℝ} (d : PotentialData W) : H1C →L[ℂ] L2C := + (weightedLM d).mkContinuous (Real.sqrt (d.b+1)) (weightedLM_bound d) + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/NegativeResolvent.lean b/lean/OAI/Analysis/LiebThirring/NegativeResolvent.lean new file mode 100644 index 0000000000000000000000000000000000000000..6d8839d923b94bf0633bde01b16ad1fb8057bc27 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/NegativeResolvent.lean @@ -0,0 +1,90 @@ +import OAI.Analysis.LiebThirring.FreeForm + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set +open scoped Topology + +/-- Standard bounded-resolvent condition for a partially defined operator: +`R` is a bounded everywhere-defined inverse of `A-e` on its full domain. +The graph equivalence includes both inverse identities and domain membership. -/ +def HasBoundedResolventAt (A : L2C →ₗ.[ℂ] L2C) (e : ℝ) : Prop := + ∃ R : L2C →L[ℂ] L2C, ∀ f g : L2C, + (∃ hf : f ∈ A.domain, A ⟨f,hf⟩ = (e:ℂ) • f+g) ↔ R g = f + +lemma hasBoundedResolventAt_not_eigenvalue {A : L2C →ₗ.[ℂ] L2C} {e : ℝ} + (h : HasBoundedResolventAt A e) : + ¬ ∃ f : L2C, f ≠ 0 ∧ IsOperatorEigenfunction A e f := by + obtain ⟨R,hR⟩ := h + rintro ⟨f,hf,haf,hv⟩ + have he : R 0 = f := (hR f 0).mp ⟨haf,by simpa only [add_zero] using hv⟩ + exact hf (he.symm.trans (map_zero R)) + +lemma energy_operator_graph {W : ℝ → ℝ} (d : PotentialData W) (a : ℝ) (f g : L2C) : + (∃ hf : f ∈ (operator d).domain, operator d ⟨f,hf⟩ = (-a:ℂ) • f+g) ↔ + ∃ u : H1C, valL u = f ∧ energyFormMap d a u = valL.adjoint g := by + rw [operator_graph] + constructor + · rintro ⟨u,hu,hq⟩ + refine ⟨u,hu,?_⟩ + apply ext_inner_left ℂ + intro v + rw [energyFormMap_inner,hq v,ContinuousLinearMap.adjoint_inner_right,hu, + inner_add_right,inner_smul_right] + ring + · rintro ⟨u,hu,hq⟩ + refine ⟨u,hu,fun v ↦ ?_⟩ + have hh := congrArg (fun t ↦ inner ℂ v t) hq + rw [energyFormMap_inner,ContinuousLinearMap.adjoint_inner_right] at hh + rw [inner_add_right,inner_smul_right,← hu] + linear_combination hh + +lemma energyFormMap_bijective_resolvent {W : ℝ → ℝ} (d : PotentialData W) (a : ℝ) + (h : Function.Bijective (energyFormMap d a)) : HasBoundedResolventAt (operator d) (-a) := by + let E : H1C ≃L[ℂ] H1C := ContinuousLinearEquiv.ofBijective (energyFormMap d a) + (LinearMap.ker_eq_bot.mpr h.1) (LinearMap.range_eq_top.mpr h.2) + let R : L2C →L[ℂ] L2C := valL.comp (E.symm.toContinuousLinearMap.comp valL.adjoint) + refine ⟨R,fun f g ↦ ?_⟩ + rw [Complex.ofReal_neg,energy_operator_graph] + constructor + · rintro ⟨u,hu,hq⟩ + have he : E u = valL.adjoint g := hq + change valL (E.symm (valL.adjoint g)) = f + rw [← he,ContinuousLinearEquiv.symm_apply_apply,hu] + · intro hr + refine ⟨E.symm (valL.adjoint g),hr,?_⟩ + exact E.apply_symm_apply _ + +lemma energyFormMap_alternative {γ : ℝ} {W : ℝ → ℝ} (hγ : 1/2 < γ) + (hW : Admissible γ W) (d : PotentialData W) {a : ℝ} (ha : 0 < a) : + (∃ u : H1C, u ≠ 0 ∧ energyFormMap d a u = 0) ∨ + Function.Bijective (energyFormMap d a) := by + have hC : IsCompactOperator ((weightedL d).adjoint.comp (weightedL d)) := + (weightedL_compact hγ hW d).clm_comp (weightedL d).adjoint + exact compact_perturbation_alternative (freeFormEquiv ha) + ((weightedL d).adjoint.comp (weightedL d)) hC + +/-- Below zero there is no continuous or residual spectrum: each real negative +energy is an actual eigenvalue, or has a bounded inverse on the full L² space. -/ +theorem negative_resolvent_or_eigenvalue {γ : ℝ} {W : ℝ → ℝ} (hγ : 1/2 < γ) + (hW : Admissible γ W) (d : PotentialData W) {e : ℝ} (he : e < 0) : + HasBoundedResolventAt (operator d) e ∨ + ∃ f : L2C, f ≠ 0 ∧ IsOperatorEigenfunction (operator d) e f := by + have ha : 0 < -e := neg_pos.mpr he + rcases energyFormMap_alternative hγ hW d ha with ⟨u,hu,hq⟩ | hb + · right + refine ⟨valL u,fun hz ↦ hu (valL_injective (hz.trans (map_zero valL).symm)),?_⟩ + have hg := (energy_operator_graph d (-e) (valL u) 0).mpr + ⟨u,rfl,by simpa only [map_zero] using hq⟩ + simpa only [IsOperatorEigenfunction,neg_neg,Complex.ofReal_neg,add_zero] using hg + · left + simpa only [neg_neg] using energyFormMap_bijective_resolvent d (-e) hb + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/OneState.lean b/lean/OAI/Analysis/LiebThirring/OneState.lean new file mode 100644 index 0000000000000000000000000000000000000000..1f18b5056edacbbb7b242d7f9c75716da4bc0901 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/OneState.lean @@ -0,0 +1,53 @@ +import OAI.Analysis.LiebThirring.EigenvalueSum + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set +open scoped Topology ENNReal + +/-- Retain the largest weight of a single negative eigenvalue of the actual +operator. The supremum of the empty family is zero. -/ +def oneEigenvalueMoment (γ : ℝ) (A : L2C →ₗ.[ℂ] L2C) : ℝ≥0∞ := + ⨆ (f : L2C) (e : ℝ) (_ : inner ℂ f f = 1) + (_ : e < 0 ∧ IsOperatorEigenfunction A e f), (ENNReal.ofReal |e|)^γ + +lemma oneStateMoment_eq_oneEigenvalueMoment {W : ℝ → ℝ} {A : L2C →ₗ.[ℂ] L2C} + (hA : IsAssociated W A) (γ : ℝ) : oneStateMoment γ W = oneEigenvalueMoment γ A := by + apply le_antisymm + · unfold oneStateMoment + refine iSup_le (fun u ↦ iSup_le (fun k ↦ iSup_le (fun hu ↦ iSup_le (fun hk ↦ ?_)))) + let f := u.val_memLp.toLp u.val + have hf : inner ℂ f f = 1 := by simpa only [f,← l2Pairing_eq_inner] using hu + have he : -(k^2) < 0 ∧ IsOperatorEigenfunction A (-(k^2)) f := by + refine ⟨neg_neg_of_pos (sq_pos_of_pos hk.1),?_⟩ + simpa only [IsOperatorEigenfunction,f,Complex.ofReal_neg] using + ((negativeEigenfunction_iff_operator hA k u).mp hk).2 + have hle : (ENNReal.ofReal |-(k^2)|)^γ ≤ oneEigenvalueMoment γ A := + le_iSup_of_le f (le_iSup_of_le (-(k^2)) (le_iSup_of_le hf (le_iSup_of_le he le_rfl))) + simpa only [energy_weight _ γ hk.1.le] using hle + · unfold oneEigenvalueMoment + refine iSup_le (fun f ↦ iSup_le (fun e ↦ iSup_le (fun hf ↦ iSup_le (fun he ↦ ?_)))) + obtain ⟨u,hu,hq⟩ := (hA f ((e:ℂ) • f)).mp he.2 + let k := Real.sqrt (-e) + have hk : 0 < k := Real.sqrt_pos.mpr (neg_pos.mpr he.1) + have hks : -(k^2) = e := by + rw [show k^2 = -e from Real.sq_sqrt (le_of_lt (neg_pos.mpr he.1)),neg_neg] + have hne : IsNegativeEigenfunction W k u := by + rw [negativeEigenfunction_iff_operator hA] + refine ⟨hk,?_⟩ + have hc : -(↑(k^2):ℂ) = (e:ℂ) := by exact_mod_cast hks + simpa only [IsOperatorEigenfunction,hc,hu] using he.2 + have hon : l2Pairing u u = 1 := by rw [l2Pairing_eq_inner,hu]; exact hf + have hle : (ENNReal.ofReal k)^(2*γ) ≤ oneStateMoment γ W := + le_iSup_of_le u (le_iSup_of_le k (le_iSup_of_le hon (le_iSup_of_le hne le_rfl))) + rw [← hks,energy_weight _ _ hk.le] + exact hle + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/OperatorForm.lean b/lean/OAI/Analysis/LiebThirring/OperatorForm.lean new file mode 100644 index 0000000000000000000000000000000000000000..1d9ff1f2faf532be25a6fd8ec954d80ad6121b55 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/OperatorForm.lean @@ -0,0 +1,78 @@ +import OAI.Analysis.LiebThirring.CoerciveInverse + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set Filter +open scoped Topology + +lemma weightedL_inner {W : ℝ → ℝ} (d : PotentialData W) (u v : H1C) : + inner ℂ (weightedL d u) (weightedL d v) = + ∫ x, (W x : ℂ)*star (valL u x)*valL v x := by + rw [L2.inner_def] + apply integral_congr_ae + filter_upwards [(weightedVal_memLp d u).coeFn_toLp, + (weightedVal_memLp d v).coeFn_toLp,d.nonneg] with x hx hy hw + change inner ℂ ((weightedVal_memLp d u).toLp (weightedVal d u) x) + ((weightedVal_memLp d v).toLp (weightedVal d v) x) = _ + rw [hx,hy,RCLike.inner_apply] + change weightedVal d v x*star (weightedVal d u x) = _ + have hs : (Real.sqrt ‖W x‖ : ℂ)^2 = (W x : ℂ) := by + rw [← Complex.ofReal_pow,Real.sq_sqrt (norm_nonneg _),Real.norm_of_nonneg hw] + simp only [weightedVal,star_mul,Complex.star_def,Complex.conj_ofReal] + calc + _ = (Real.sqrt ‖W x‖ : ℂ)^2*star (valL u x)*valL v x := by simp only [Complex.star_def]; ring + _ = _ := by rw [hs]; rfl + +lemma form_eq_inner {W : ℝ → ℝ} (d : PotentialData W) (u v : H1C) : + schrodingerForm W (toH1 u) (toH1 v) = + inner ℂ (gradL u) (gradL v)-inner ℂ (weightedL d u) (weightedL d v) := by + rw [schrodingerForm,gradPairing_eq_inner,grad_toLp_toH1,grad_toLp_toH1,weightedL_inner] + rfl + +def shiftedFormMap {W : ℝ → ℝ} (d : PotentialData W) : H1C →L[ℂ] H1C := + gradL.adjoint.comp gradL - (weightedL d).adjoint.comp (weightedL d) + + ((d.b+1 : ℝ) : ℂ) • (valL.adjoint.comp valL) + +lemma shiftedFormMap_inner {W : ℝ → ℝ} (d : PotentialData W) (u v : H1C) : + inner ℂ u (shiftedFormMap d v) = + inner ℂ (gradL u) (gradL v)-inner ℂ (weightedL d u) (weightedL d v)+ + (d.b+1 : ℂ)*inner ℂ (valL u) (valL v) := by + change inner ℂ u ((gradL.adjoint (gradL v) - + (weightedL d).adjoint (weightedL d v)) + + ((d.b+1 : ℝ) : ℂ) • (valL.adjoint (valL v))) = _ + rw [inner_add_right,inner_sub_right] + rw [inner_smul_right u (valL.adjoint (valL v)) (((d.b+1 : ℝ) : ℂ))] + rw [ContinuousLinearMap.adjoint_inner_right, + ContinuousLinearMap.adjoint_inner_right,ContinuousLinearMap.adjoint_inner_right] + simp only [Complex.ofReal_add,Complex.ofReal_one] + +lemma shiftedFormMap_coercive {W : ℝ → ℝ} (d : PotentialData W) (u : H1C) : + (3/4)*‖u‖^2 ≤ (inner ℂ u (shiftedFormMap d u)).re := by + rw [shiftedFormMap_inner,Complex.add_re,Complex.sub_re] + have hi (v : L2C) : (inner ℂ v v).re = ‖v‖^2 := (norm_sq_eq_re_inner (𝕜 := ℂ) v).symm + have hm : ((d.b+1 : ℂ)*inner ℂ (valL u) (valL u)).re = (d.b+1)*‖valL u‖^2 := by + rw [Complex.mul_re] + simp only [Complex.add_re,Complex.ofReal_re,Complex.one_re,Complex.add_im, + Complex.ofReal_im,Complex.one_im,zero_add,zero_mul,sub_zero,hi] + rw [hi,hi,hm,h1_norm_sq] + have h := weightedLM_norm_sq d u + change ‖weightedL d u‖^2 ≤ _ at h + linarith + +lemma shiftedFormMap_symmetric {W : ℝ → ℝ} (d : PotentialData W) : + (shiftedFormMap d).IsSymmetric := by + intro u v + change inner ℂ (shiftedFormMap d u) v = inner ℂ u (shiftedFormMap d v) + rw [← inner_conj_symm (𝕜 := ℂ) (shiftedFormMap d u) v, shiftedFormMap_inner, + shiftedFormMap_inner] + simp only [map_add,map_sub,map_mul,inner_conj_symm] + simp + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/OperatorGraph.lean b/lean/OAI/Analysis/LiebThirring/OperatorGraph.lean new file mode 100644 index 0000000000000000000000000000000000000000..9dc84e5d13cbaa2587509ca8e02abe41440a17e1 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/OperatorGraph.lean @@ -0,0 +1,141 @@ +import OAI.Analysis.LiebThirring.Main + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set +open scoped ComplexConjugate Topology + +abbrev L2C := Lp ℂ 2 (volume : Measure ℝ) +abbrev ProductL2 := WithLp 2 (L2C × L2C) +abbrev TestFunction := {φ : ℝ → ℂ // ContDiff ℝ (↑(⊤ : ℕ∞) : WithTop ℕ∞) φ ∧ HasCompactSupport φ} + +def testLp (φ : ℝ → ℂ) (hc : Continuous φ) (hs : HasCompactSupport φ) : L2C := + (hc.memLp_of_hasCompactSupport hs (p := 2)).toLp φ + +lemma inner_star_testLp (φ : ℝ → ℂ) (hc : Continuous φ) (hs : HasCompactSupport φ) + (f : L2C) : inner ℂ (testLp (star φ) hc.star (hs.comp_left (star_zero ℂ))) f = ∫ x, f x*φ x := by + rw [L2.inner_def] + apply integral_congr_ae + filter_upwards [(hc.star.memLp_of_hasCompactSupport (hs.comp_left (star_zero ℂ)) (p := 2)).coeFn_toLp] with x hx + simp only [RCLike.inner_apply] + change f x*star ((testLp (star φ) hc.star (hs.comp_left (star_zero ℂ))) x) = f x*φ x + rw [show (testLp (star φ) hc.star (hs.comp_left (star_zero ℂ))) x = star (φ x) from hx,star_star] + +def constraint (φ : TestFunction) : ProductL2 →L[ℂ] ℂ := + (innerSL ℂ (testLp (star (deriv φ.1)) + (φ.2.1.continuous_deriv (by simp)).star (φ.2.2.deriv.comp_left (star_zero ℂ)))).comp (WithLp.fstL 2 ℂ L2C L2C) + + (innerSL ℂ (testLp (star φ.1) φ.2.1.continuous.star (φ.2.2.comp_left (star_zero ℂ)))).comp (WithLp.sndL 2 ℂ L2C L2C) + +lemma constraint_eq (φ : TestFunction) (u : ProductL2) : constraint φ u = + (∫ x, (WithLp.ofLp u).1 x * deriv φ.1 x) + (∫ x, (WithLp.ofLp u).2 x * φ.1 x) := by + simp only [constraint,add_apply,ContinuousLinearMap.comp_apply, + innerSL_apply_apply,WithLp.fstL_apply,WithLp.sndL_apply] + exact congrArg₂ (· + ·) + (inner_star_testLp (deriv φ.1) (φ.2.1.continuous_deriv (by simp)) φ.2.2.deriv _) + (inner_star_testLp φ.1 φ.2.1.continuous φ.2.2 _) + +def h1Graph : Submodule ℂ ProductL2 := ⨅ φ : TestFunction, (constraint φ).ker + +lemma mem_h1Graph_iff (u : ProductL2) : u ∈ h1Graph ↔ ∀ φ : TestFunction, + (∫ x, (WithLp.ofLp u).1 x * deriv φ.1 x) = -(∫ x, (WithLp.ofLp u).2 x * φ.1 x) := by + simp only [h1Graph,Submodule.mem_iInf,LinearMap.mem_ker,ContinuousLinearMap.coe_coe,constraint_eq, + add_eq_zero_iff_eq_neg] + +lemma h1Graph_closed : IsClosed (h1Graph : Set ProductL2) := by + rw [h1Graph,Submodule.coe_iInf] + exact isClosed_iInter (fun φ ↦ (constraint φ).isClosed_ker) + +abbrev H1C := ↥h1Graph +instance : CompleteSpace H1C := h1Graph_closed.completeSpace_coe + +def valL : H1C →L[ℂ] L2C := (WithLp.fstL 2 ℂ L2C L2C).comp h1Graph.subtypeL +def gradL : H1C →L[ℂ] L2C := (WithLp.sndL 2 ℂ L2C L2C).comp h1Graph.subtypeL + +def toH1 (u : H1C) : H1 where + val := valL u + grad := gradL u + val_memLp := Lp.memLp _ + grad_memLp := Lp.memLp _ + weak_derivative φ hc hs := (mem_h1Graph_iff u.1).mp u.2 ⟨φ,hc,hs⟩ + +def ofH1 (u : H1) : H1C := ⟨WithLp.toLp 2 (u.val_memLp.toLp u.val,u.grad_memLp.toLp u.grad),by + rw [mem_h1Graph_iff] + intro φ + convert u.weak_derivative φ.1 φ.2.1 φ.2.2 using 1 + · exact integral_congr_ae (u.val_memLp.coeFn_toLp.mono (fun x hx ↦ by simp [hx])) + · congr 1 + exact integral_congr_ae (u.grad_memLp.coeFn_toLp.mono (fun x hx ↦ by simp [hx]))⟩ + +@[simp] lemma valL_ofH1 (u : H1) : valL (ofH1 u) = u.val_memLp.toLp u.val := rfl +@[simp] lemma gradL_ofH1 (u : H1) : gradL (ofH1 u) = u.grad_memLp.toLp u.grad := rfl + +lemma valL_injective : Function.Injective valL := by + apply (LinearMap.ker_eq_bot).mp + rw [Submodule.eq_bot_iff] + intro u hu + have hv : valL u = 0 := hu + have hg : (fun x ↦ gradL u x) =ᵐ[volume] (0 : ℝ → ℂ) := by + apply ae_eq_zero_of_integral_contDiff_smul_eq_zero ((Lp.memLp (gradL u)).locallyIntegrable (by norm_num)) + intro φ hc hs + have h := (toH1 u).weak_derivative (fun x ↦ (φ x : ℂ)) + (Complex.ofRealCLM.contDiff.comp hc) (hs.comp_left Complex.ofReal_zero) + have hi : (∫ x, (toH1 u).val x*deriv (fun x ↦ (φ x : ℂ)) x) = 0 := by + apply integral_eq_zero_of_ae + filter_upwards [Lp.coeFn_zero ℂ 2 (volume : Measure ℝ)] with x hx + change valL u x*_ = 0 + rw [hv,hx] + simp + rw [hi,eq_neg_iff_add_eq_zero,zero_add] at h + simpa [toH1,Complex.real_smul,mul_comm] using h + have hgz : gradL u = 0 := Lp.ext (hg.trans (Lp.coeFn_zero ℂ 2 (volume : Measure ℝ)).symm) + apply (Submodule.mem_bot ℂ).mpr + apply Subtype.ext + apply (WithLp.equiv 2 (L2C × L2C)).injective + apply Prod.ext + · exact hv + · exact hgz + + +lemma valL_dense : Dense (Set.range valL) := by + have hd := Lp.dense_hasCompactSupport_contDiff (E := ℝ) (F := ℂ) + (μ := volume) (p := 2) (by norm_num) + apply hd.mono + rintro f ⟨g,hfg,hgc,hgd⟩ + let u : H1 := SobolevProof.smoothH1 g (deriv g) hgd + (fun x ↦ (hgd.differentiable (by simp) x).hasDerivAt) + (hgd.continuous_deriv (by simp)) + (hgd.continuous.memLp_of_hasCompactSupport hgc) + ((hgd.continuous_deriv (by simp)).memLp_of_hasCompactSupport hgc.deriv) + refine ⟨ofH1 u,?_⟩ + apply Lp.ext + exact u.val_memLp.coeFn_toLp.trans hfg.symm + +@[simp] lemma toLp_toH1 (u : H1C) : (toH1 u).val_memLp.toLp (toH1 u).val = valL u := + Lp.toLp_coeFn _ _ +@[simp] lemma grad_toLp_toH1 (u : H1C) : (toH1 u).grad_memLp.toLp (toH1 u).grad = gradL u := + Lp.toLp_coeFn _ _ + +lemma l2Pairing_eq_inner (u v : H1) : + l2Pairing u v = inner ℂ (u.val_memLp.toLp u.val) (v.val_memLp.toLp v.val) := by + rw [l2Pairing,L2.inner_def] + apply integral_congr_ae + filter_upwards [u.val_memLp.coeFn_toLp,v.val_memLp.coeFn_toLp] with x hx hy + rw [hx,hy,RCLike.inner_apply,mul_comm] + rfl + +lemma gradPairing_eq_inner (u v : H1) : + (∫ x, star (u.grad x)*v.grad x) = inner ℂ (u.grad_memLp.toLp u.grad) (v.grad_memLp.toLp v.grad) := by + rw [L2.inner_def] + apply integral_congr_ae + filter_upwards [u.grad_memLp.coeFn_toLp,v.grad_memLp.coeFn_toLp] with x hx hy + rw [hx,hy,RCLike.inner_apply,mul_comm] + rfl + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/PotentialCompactness.lean b/lean/OAI/Analysis/LiebThirring/PotentialCompactness.lean new file mode 100644 index 0000000000000000000000000000000000000000..c63d757ee6e781ffd96ac84815b08e49c15a83a8 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/PotentialCompactness.lean @@ -0,0 +1,134 @@ +import OAI.Analysis.LiebThirring.LocalWeight + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set Filter +open scoped Topology ENNReal + +lemma small_bounded_plus_L1 {γ : ℝ} {W : ℝ → ℝ} (hγ : 1/2 < γ) + (hW : Admissible γ W) {δ : ℝ} (hδ : 0 < δ) : + ∃ V : ℝ → ℝ, (∀ x, 0 ≤ V x) ∧ Integrable V ∧ ∀ x, ‖W x‖ ≤ δ+V x := by + let p := γ+1/2 + let V := fun x ↦ ‖W x‖^p / δ^(p-1) + have hc : 0 < δ^(p-1) := Real.rpow_pos_of_pos hδ _ + have hi : Integrable (fun x ↦ ‖W x‖^p) := by + have hh := hW.2.integrable_norm_rpow + (ENNReal.ofReal_pos.mpr (show 0 < γ+1/2 by linarith)).ne' ENNReal.ofReal_ne_top + simpa only [ENNReal.toReal_ofReal (show 0 ≤ γ+1/2 by linarith)] using hh + refine ⟨V,fun x ↦ div_nonneg (Real.rpow_nonneg (norm_nonneg _) _) hc.le,hi.div_const _,?_⟩ + intro x + by_cases hx : ‖W x‖ ≤ δ + · exact hx.trans (le_add_of_nonneg_right (div_nonneg (Real.rpow_nonneg (norm_nonneg _) _) hc.le)) + · have hxδ : δ ≤ ‖W x‖ := (not_le.mp hx).le + have hm : δ^(p-1) ≤ ‖W x‖^(p-1) := Real.rpow_le_rpow hδ.le hxδ (by dsimp [p]; linarith) + have ht : ‖W x‖*δ^(p-1) ≤ ‖W x‖^p := by + calc + _ ≤ ‖W x‖*‖W x‖^(p-1) := mul_le_mul_of_nonneg_left hm (norm_nonneg _) + _ = ‖W x‖^p := by + conv_lhs => lhs; rw [← Real.rpow_one ‖W x‖] + rw [← Real.rpow_add (lt_of_lt_of_le hδ hxδ)] + congr 1 + ring + have hv : ‖W x‖ ≤ V x := (le_div_iff₀ hc).mpr ht + exact hv.trans (le_add_of_nonneg_left hδ.le) + +lemma integrable_tail_small {V : ℝ → ℝ} (hV : Integrable V) {δ : ℝ} (hδ : 0 < δ) : + ∃ R : ℝ, 0 ≤ R ∧ (∫ x, ((Interval R)ᶜ).indicator V x) ≤ δ := by + let F := fun (n : ℕ) ↦ ((Interval (n:ℝ))ᶜ).indicator V + have hm (n : ℕ) : AEStronglyMeasurable (F n) volume := + hV.aestronglyMeasurable.indicator measurableSet_Icc.compl + have hd (n : ℕ) : ∀ᵐ x, ‖F n x‖ ≤ ‖V x‖ := + Eventually.of_forall fun x ↦ norm_indicator_le_norm_self _ _ + have ht (x : ℝ) : Tendsto (fun n ↦ F n x) atTop (𝓝 0) := by + apply tendsto_const_nhds.congr' + obtain ⟨N,hN⟩ := exists_nat_gt |x| + filter_upwards [eventually_ge_atTop N] with n hn + have hlarge : |x| ≤ (n:ℝ) := hN.le.trans (Nat.cast_le.mpr hn) + have hx : x ∈ Interval (n:ℝ) := ⟨by linarith [(neg_abs_le x)],(le_abs_self x).trans hlarge⟩ + simp only [F,indicator_of_notMem (show x ∉ (Interval (n:ℝ))ᶜ from not_not_intro hx)] + have hlim : Tendsto (fun n ↦ ∫ x, F n x) atTop (𝓝 0) := by + simpa only [integral_zero] using tendsto_integral_of_dominated_convergence + (fun x ↦ ‖V x‖) hm hV.norm hd (Eventually.of_forall ht) + obtain ⟨n,hn⟩ := (hlim.eventually (gt_mem_nhds hδ)).exists + exact ⟨n,Nat.cast_nonneg _,hn.le⟩ + +lemma h1Graph_ae_sq_bound (u : H1C) : ∀ᵐ x, ‖valL u x‖^2 ≤ 8*‖u‖^2 := by + have h := h1_ae_sq_bound (toH1 u) + simp only [toLp_toH1,grad_toLp_toH1,← h1_norm_sq] at h + exact h + +lemma tail_weighted_norm_sq {W : ℝ → ℝ} (d : PotentialData W) {δ : ℝ} + (hδ : 0 ≤ δ) {V : ℝ → ℝ} (hV : Integrable V) (hV₀ : ∀ x, 0 ≤ V x) + (hWV : ∀ x, ‖W x‖ ≤ δ+V x) (R : ℝ) (u : H1C) : + ‖weightedL d u-localWeightedL d R u‖^2 ≤ + (δ+8*(∫ x, ((Interval R)ᶜ).indicator V x))*‖u‖^2 := by + let G := fun x ↦ δ*‖valL u x‖^2 + ((Interval R)ᶜ).indicator V x * (8*‖u‖^2) + have hVG : Integrable (((Interval R)ᶜ).indicator V) := hV.indicator measurableSet_Icc.compl + have hG : Integrable G := + ((Lp.memLp (valL u)).integrable_norm_pow (by norm_num)).const_mul δ |>.add + (hVG.mul_const _) + have hdom : ∀ᵐ x, ‖(weightedL d u-localWeightedL d R u) x‖^2 ≤ G x := by + filter_upwards [Lp.coeFn_sub (weightedL d u) (localWeightedL d R u), + (weightedVal_memLp d u).coeFn_toLp,localWeightedL_ae d R u,h1Graph_ae_sq_bound u] + with x hx hy hz hu + simp only [Pi.sub_apply] at hx + change weightedL d u x = weightedVal d u x at hy + rw [hx,hy,hz] + by_cases hs : x ∈ Interval R + · simp only [localSqrt,indicator_of_mem hs,weightedVal,sub_self,norm_zero, + zero_pow (by decide : 2 ≠ 0),G,indicator_of_notMem (show x ∉ (Interval R)ᶜ from not_not_intro hs), + zero_mul,add_zero] + exact mul_nonneg hδ (sq_nonneg _) + · simp only [localSqrt,indicator_of_notMem hs,zero_mul,sub_zero,weightedVal_norm_sq, + G,indicator_of_mem (show x ∈ (Interval R)ᶜ from hs)] + have hm := mul_le_mul_of_nonneg_right (hWV x) (sq_nonneg ‖valL u x‖) + have hv := mul_le_mul_of_nonneg_left hu (hV₀ x) + nlinarith + rw [L2_norm_sq_eq_integral] + calc + _ ≤ ∫ x, G x := integral_mono_ae + ((Lp.memLp (weightedL d u-localWeightedL d R u)).integrable_norm_pow (by norm_num)) hG hdom + _ = δ*‖valL u‖^2 + (∫ x, ((Interval R)ᶜ).indicator V x)*(8*‖u‖^2) := by + rw [integral_add (((Lp.memLp (valL u)).integrable_norm_pow (by norm_num)).const_mul δ) + (hVG.mul_const _),integral_const_mul,integral_mul_const,← L2_norm_sq_eq_integral] + _ ≤ _ := by + have hn := mul_le_mul_of_nonneg_left + ((sq_le_sq₀ (norm_nonneg _) (norm_nonneg _)).mpr (valL_norm_le u)) hδ + nlinarith + +lemma weightedL_compact {γ : ℝ} {W : ℝ → ℝ} (hγ : 1/2 < γ) + (hW : Admissible γ W) (d : PotentialData W) : IsCompactOperator (weightedL d) := by + change weightedL d ∈ {f : H1C →L[ℂ] L2C | IsCompactOperator f} + have hc : IsClosed {f : H1C →L[ℂ] L2C | IsCompactOperator f} := + isClosed_setOfPred_isCompactOperator + rw [← hc.closure_eq] + apply (Metric.mem_closure_iff (α := H1C →L[ℂ] L2C)).mpr + intro ε hε + let δ := ε^2/36 + have hδ : 0 < δ := div_pos (sq_pos_of_pos hε) (by norm_num) + obtain ⟨V,hV₀,hV,hWV⟩ := small_bounded_plus_L1 hγ hW hδ + obtain ⟨R,hR,hVR⟩ := integrable_tail_small hV hδ + refine ⟨localWeightedL d R,localWeightedL_compact d (hW.locallyIntegrable hγ) hR,?_⟩ + have hb : ‖weightedL d-localWeightedL d R‖ ≤ ε/2 := by + apply ContinuousLinearMap.opNorm_le_bound _ (by positivity) + intro u + apply (sq_le_sq₀ (norm_nonneg _) (mul_nonneg (by positivity) (norm_nonneg _))).mp + have hi := tail_weighted_norm_sq d hδ.le hV hV₀ hWV R u + change ‖weightedL d u-localWeightedL d R u‖^2 ≤ _ + rw [mul_pow] + calc + _ ≤ (δ+8*(∫ x, ((Interval R)ᶜ).indicator V x))*‖u‖^2 := hi + _ ≤ (δ+8*δ)*‖u‖^2 := mul_le_mul_of_nonneg_right + (by linarith [hVR]) (sq_nonneg _) + _ = (ε/2)^2*‖u‖^2 := by dsimp only [δ]; ring + rw [dist_eq_norm (weightedL d) (localWeightedL d R)] + exact hb.trans_lt (by linarith) + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/PotentialSplit.lean b/lean/OAI/Analysis/LiebThirring/PotentialSplit.lean new file mode 100644 index 0000000000000000000000000000000000000000..384f598dfa785d65b96cf2008d5fc1b74a6274c5 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/PotentialSplit.lean @@ -0,0 +1,59 @@ +import OAI.Analysis.LiebThirring.SobolevBound + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set Filter +open scoped Topology ENNReal + +/-- The only potential-approximation fact needed for the associated operator: + an Lᵖ potential, p>1, is bounded plus an arbitrarily small L¹ remainder. -/ +lemma potential_decomposition {γ : ℝ} {W : ℝ → ℝ} (hγ : 1/2 < γ) + (hW : Admissible γ W) {ε : ℝ} (hε : 0 < ε) : + ∃ b : ℝ, 0 ≤ b ∧ ∃ V : ℝ → ℝ, (∀ x, 0 ≤ V x) ∧ Integrable V ∧ + (∫ x, V x) ≤ ε ∧ ∀ x, ‖W x‖ ≤ b+V x := by + let V : ℕ → ℝ → ℝ := fun n x ↦ max (‖W x‖-((n:ℝ)+1)) 0 + have hm (n : ℕ) : AEStronglyMeasurable (V n) volume := + (continuous_id.max continuous_const).comp_aestronglyMeasurable + (hW.2.aestronglyMeasurable.norm.sub aestronglyMeasurable_const) + have hpos (n : ℕ) (x : ℝ) : 0 ≤ V n x := le_max_right _ _ + have hd (n : ℕ) (x : ℝ) : ‖V n x‖ ≤ ‖W x‖^(γ+1/2) := by + rw [Real.norm_of_nonneg (hpos n x)] + change max (‖W x‖-((n:ℝ)+1)) 0 ≤ ‖W x‖^(γ+1/2) + apply max_le + · by_cases hw : 1 ≤ ‖W x‖ + · exact (sub_le_self _ (by positivity)).trans + (Real.self_le_rpow_of_one_le hw (by linarith)) + · have hp : 0 ≤ ‖W x‖^(γ+1/2) := Real.rpow_nonneg (norm_nonneg _) _ + have hn : (0:ℝ) ≤ n := Nat.cast_nonneg _ + linarith [not_le.mp hw] + · exact Real.rpow_nonneg (norm_nonneg _) _ + have hdom : Integrable (fun x ↦ ‖W x‖^(γ+1/2)) := by + have hh := hW.2.integrable_norm_rpow + (ENNReal.ofReal_pos.mpr (show 0 < γ+1/2 by linarith)).ne' ENNReal.ofReal_ne_top + simpa only [ENNReal.toReal_ofReal (show 0 ≤ γ+1/2 by linarith)] using hh + have hV (n : ℕ) : Integrable (V n) := hdom.mono' (hm n) (Eventually.of_forall (hd n)) + have ht (x : ℝ) : Tendsto (fun n ↦ V n x) atTop (𝓝 0) := by + apply tendsto_const_nhds.congr' + obtain ⟨N,hN⟩ := exists_nat_gt ‖W x‖ + filter_upwards [eventually_ge_atTop N] with n hn + change 0 = max (‖W x‖-((n:ℝ)+1)) 0 + have hnn : (N:ℝ) ≤ n := Nat.cast_le.mpr hn + rw [max_eq_right (by linarith)] + have hlim : Tendsto (fun n ↦ ∫ x, V n x) atTop (𝓝 0) := by + simpa only [integral_zero] using tendsto_integral_of_dominated_convergence + (fun x ↦ ‖W x‖^(γ+1/2)) hm hdom (fun n ↦ Eventually.of_forall (hd n)) + (Eventually.of_forall ht) + obtain ⟨n,hn⟩ := (hlim.eventually (gt_mem_nhds hε)).exists + refine ⟨(n:ℝ)+1,by positivity,V n,hpos n,hV n,hn.le,?_⟩ + intro x + change ‖W x‖ ≤ (n:ℝ)+1+max (‖W x‖-((n:ℝ)+1)) 0 + linarith [le_max_left (‖W x‖-((n:ℝ)+1)) 0] + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/QuadraticForms.lean b/lean/OAI/Analysis/LiebThirring/QuadraticForms.lean new file mode 100644 index 0000000000000000000000000000000000000000..38969da91b38c0fb5e534127ad41815b75271176 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/QuadraticForms.lean @@ -0,0 +1,117 @@ +import OAI.Analysis.LiebThirring.Gamma + +namespace OAI + +universe u166 u167 u168 u169 u170 + + +noncomputable section +open Filter Set +open scoped Topology +namespace SharpLiebThirring.SpectralProof + +lemma quadratic_error_bound {ι : Type u166} [Fintype ι] (M : ι → ι → ℝ) {ε : ℝ} + (hε : 0 ≤ ε) (hM : ∀ i j, |M i j| ≤ ε) (c : ι → ℝ) : + (∑ i, ∑ j, c i*c j*M i j) ≤ ε*(Fintype.card ι)*∑ i, c i^2 := by + classical + calc + _ ≤ ∑ i, ∑ j, ε*(|c i| *|c j|) := by + apply Finset.sum_le_sum; intro i _ + apply Finset.sum_le_sum; intro j _ + calc + _ ≤ |c i*c j*M i j| := le_abs_self _ + _ = |c i| *|c j| *|M i j| := by rw [abs_mul,abs_mul] + _ ≤ |c i| *|c j| *ε := mul_le_mul_of_nonneg_left (hM i j) (by positivity) + _ = _ := by ring + _ = ε*(∑ i, |c i|)^2 := by simp_rw [← Finset.mul_sum]; rw [← Finset.sum_mul,pow_two] + _ ≤ ε*((Fintype.card ι)*∑ i, c i^2) := by + apply mul_le_mul_of_nonneg_left _ hε + simpa only [one_mul,one_pow,Finset.sum_const,Finset.card_univ,nsmul_eq_mul,mul_one,sq_abs] using + Finset.sum_mul_sq_le_sq_mul_sq Finset.univ (fun _ : ι ↦ (1 : ℝ)) (fun i ↦ |c i|) + _ = _ := by ring + +/-- A strict negative diagonal is stable under entrywise perturbations. -/ +lemma eventually_negative_quadratic {ι : Type u167} [Fintype ι] [DecidableEq ι] (M : ℕ → ι → ι → ℝ) + (d : ι → ℝ) (hd : ∀ i, d i < 0) + (hM : ∀ i j, Tendsto (fun n ↦ M n i j) atTop (𝓝 (if i=j then d i else 0))) : + ∀ᶠ n in atTop, ∀ c : ι → ℝ, (∑ i, ∑ j, c i*c j*M n i j) ≤ 0 := by + classical + by_cases hi : IsEmpty ι + · simp + let : Nonempty ι := not_isEmpty_iff.mp hi + obtain ⟨a,ha⟩ := Finite.exists_max d + let ε := -d a/((Fintype.card ι : ℝ)+1) + have he : 0 < ε := div_pos (neg_pos.mpr (hd a)) (by positivity) + have hε : ε*(Fintype.card ι : ℝ) ≤ -d a := by + have hh : ε*((Fintype.card ι : ℝ)+1) = -d a := by dsimp [ε]; field_simp + nlinarith + have hev : ∀ᶠ n in atTop, ∀ i j, |M n i j-(if i=j then d i else 0)| ≤ ε := by + apply eventually_all.mpr + intro i + apply eventually_all.mpr + intro j + exact ((tendsto_order.1 (((hM i j).sub_const (if i=j then d i else 0)).abs)).2 ε (by simpa using he)).mono + (fun n hn ↦ le_of_lt (by simpa using hn)) + filter_upwards [hev] with n hn c + have hb := quadratic_error_bound (fun i j ↦ M n i j-(if i=j then d i else 0)) he.le hn c + have hid : (∑ i, ∑ j, c i*c j*(if i=j then d i else 0)) = ∑ i, c i^2*d i := by + apply Finset.sum_congr rfl + intro i _ + simp [mul_ite,pow_two] + have hsplit : (∑ i, ∑ j, c i*c j*M n i j) = + (∑ i, ∑ j, c i*c j*(M n i j-(if i=j then d i else 0))) + ∑ i, c i^2*d i := by + rw [← hid,← Finset.sum_add_distrib] + apply Finset.sum_congr rfl; intro i _ + rw [← Finset.sum_add_distrib] + apply Finset.sum_congr rfl; intro j _; ring + rw [hsplit] + have hd' : (∑ i, c i^2*d i) ≤ d a*∑ i, c i^2 := by + rw [Finset.mul_sum] + apply Finset.sum_le_sum; intro i _ + exact (mul_le_mul_of_nonneg_left (ha i) (sq_nonneg _)).trans_eq (mul_comm _ _) + have hs : 0 ≤ ∑ i, c i^2 := Finset.sum_nonneg (fun _ _ ↦ sq_nonneg _) + nlinarith [mul_le_mul_of_nonneg_right hε hs] + +end SharpLiebThirring.SpectralProof + +end + + +noncomputable section +open Module +namespace SharpLiebThirring.SpectralProof + +variable {E : Type u168} [NormedAddCommGroup E] [InnerProductSpace ℝ E] + +/-- Complex orthonormal vectors give twice as many real orthonormal vectors. -/ +lemma doubled_orthonormal {ι : Type u169} [DecidableEq ι] (a b : ι → E) + (hr : ∀ i j, inner ℝ (a i) (a j)+inner ℝ (b i) (b j) = if i=j then 1 else 0) + (hi : ∀ i j, inner ℝ (a i) (b j)-inner ℝ (b i) (a j) = 0) : + Orthonormal ℝ (fun z : ι × Bool ↦ + WithLp.toLp 2 (if z.2 then (-b z.1,a z.1) else (a z.1,b z.1))) := by + rw [orthonormal_iff_ite] + rintro ⟨i,p⟩ ⟨j,q⟩ + cases p <;> cases q <;> + simp only [Bool.false_eq_true,Bool.true_eq_false,ite_false,ite_true,WithLp.prod_inner_apply, + inner_neg_left,inner_neg_right,neg_neg, + Prod.mk.injEq,and_true,and_false,ite_false] + · exact hr i j + · linarith [hi i j] + · linarith [hi j i,real_inner_comm (a j) (b i),real_inner_comm (b j) (a i)] + · simpa only [add_comm] using hr i j + +lemma complex_family_card_le_real_dimension {ι : Type u170} [Fintype ι] [DecidableEq ι] + [FiniteDimensional ℝ E] (a b : ι → E) + (hr : ∀ i j, inner ℝ (a i) (a j)+inner ℝ (b i) (b j) = if i=j then 1 else 0) + (hi : ∀ i j, inner ℝ (a i) (b j)-inner ℝ (b i) (a j) = 0) : + Fintype.card ι ≤ finrank ℝ E := by + have h := (doubled_orthonormal a b hr hi).linearIndependent.fintype_card_le_finrank + rw [(WithLp.linearEquiv 2 ℝ (E×E)).finrank_eq,finrank_prod] at h + simp only [Fintype.card_prod,Fintype.card_bool] at h + omega + +end SharpLiebThirring.SpectralProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/RankOne.lean b/lean/OAI/Analysis/LiebThirring/RankOne.lean new file mode 100644 index 0000000000000000000000000000000000000000..1f8798320d3fd5f0f0aae13d59641414f2525709 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/RankOne.lean @@ -0,0 +1,626 @@ +import OAI.Analysis.LiebThirring.FieldLimit + +namespace OAI + +universe u19 u20 u21 u22 u23 u24 + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +noncomputable section +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder CStarAlgebra +noncomputable section +open MeasureTheory Set Filter +open scoped Topology + + +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {n : Type u19} [Fintype n] [DecidableEq n] + +lemma hermitianField_state_jensen {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) + (φ : Matrix n n ℂ →L[ℝ] ℝ) (hφ : ∀ A, A.PosSemidef → 0 ≤ φ A) (hφ₁ : φ 1 = 1) + {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) : + φ (hermitianField σ δ C B) ≤ scalarMu σ δ (φ C - (φ B) ^ 2) := by + have hlim := φ.continuous.continuousAt.tendsto.comp (hermitianField_cutoff_limit hσ₁ hδ hC hB) + have hs := primitive_shift_limit hσ₁ hδ (φ C - (φ B) ^ 2) (φ B) + apply le_of_tendsto_of_tendsto hlim hs + filter_upwards [eventually_ge_atTop (0 : ℝ)] with R hR + have hc := continuous_fieldIntegrand hδ σ hC hB + dsimp only [Function.comp_apply] + rw [map_smul, ← φ.intervalIntegral_comp_comm (hc.intervalIntegrable _ _), smul_eq_mul] + apply mul_le_mul_of_nonneg_left _ (normalization_pos hσ₀ hσ₁).le + apply intervalIntegral.integral_mono (by linarith : -R ≤ R) + ((φ.continuous.comp hc).intervalIntegrable _ _) + ((by have hf := (primitive_differentiable σ hδ).continuous; fun_prop : Continuous + (fun s : ℝ ↦ regularizedPrimitive σ δ ((s - φ B) ^ 2 + (φ C - (φ B) ^ 2)) - + regularizedPrimitive σ δ (s ^ 2))).intervalIntegrable _ _) + intro s + have hp := primitive_state_jensen hσ₁ hδ φ.toLinearMap hφ hφ₁ (quadraticMatrix_hermitian hC hB s) + have he : φ (quadraticMatrix C B s) = (s - φ B) ^ 2 + (φ C - (φ B) ^ 2) := by + simp only [quadraticMatrix, map_add, map_sub, map_smul, hφ₁, smul_eq_mul, mul_one] + ring + change φ (cfc (regularizedPrimitive σ δ) (quadraticMatrix C B s)) ≤ + regularizedPrimitive σ δ (φ (quadraticMatrix C B s)) at hp + rw [he] at hp + simpa only [Function.comp_apply, fieldIntegrand, map_sub, map_smul, hφ₁, smul_eq_mul, mul_one] using + sub_le_sub_right hp (regularizedPrimitive σ δ (s ^ 2)) + +/-- A diagonal entry after unitary conjugation is a positive unital state. -/ +def unitaryState (U : unitary (Matrix n n ℂ)) (i : n) : Matrix n n ℂ →L[ℝ] ℝ := + LinearMap.toContinuousLinearMap + { toFun := fun A ↦ (conjStarAlgAut ℂ (Matrix n n ℂ) U A i i).re + map_add' := by intros; simp only [map_add, Matrix.add_apply, Complex.add_re] + map_smul' := by intros; simp } + +@[simp] lemma unitaryState_apply (U : unitary (Matrix n n ℂ)) (i : n) (A : Matrix n n ℂ) : + unitaryState U i A = (conjStarAlgAut ℂ (Matrix n n ℂ) U A i i).re := rfl + +lemma unitaryState_positive (U : unitary (Matrix n n ℂ)) (i : n) + {A : Matrix n n ℂ} (hA : A.PosSemidef) : 0 ≤ unitaryState U i A := by + have hp := hA.mul_mul_conjTranspose_same (U : Matrix n n ℂ) + have hd := hp.diag_nonneg (i := i) + exact (Complex.nonneg_iff.1 hd).1 + +@[simp] lemma unitaryState_one (U : unitary (Matrix n n ℂ)) (i : n) : + unitaryState U i 1 = 1 := by simp + +lemma state_quadratic_nonneg {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) + (φ : Matrix n n ℂ →L[ℝ] ℝ) (hφ : ∀ A, A.PosSemidef → 0 ≤ φ A) (hφ₁ : φ 1 = 1) + {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) + (hM : (hermitianField σ δ C B).PosSemidef) (s : ℝ) : + 0 ≤ φ (quadraticMatrix C B s) := by + have hj := hermitianField_state_jensen hσ₀ hσ₁ hδ φ hφ hφ₁ hC hB + have hn := (hφ _ hM).trans hj + have hz : 0 ≤ φ C - (φ B) ^ 2 := by + apply (mu_strictMono hσ₀ hσ₁ hδ).le_iff_le.1 + simpa only [mu_zero] using hn + simp only [quadraticMatrix, map_add, map_sub, map_smul, hφ₁, smul_eq_mul, mul_one] + nlinarith [sq_nonneg (s - φ B)] + +lemma hermitianField_nonneg_implies_quadratic {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hδ : 0 < δ) {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) + (hM : (hermitianField σ δ C B).PosSemidef) (s : ℝ) : + (quadraticMatrix C B s).PosSemidef := by + let X := quadraticMatrix C B s + have hX : X.IsHermitian := quadraticMatrix_hermitian hC hB s + apply hX.posSemidef_iff_eigenvalues_nonneg.2 + intro i + have hp := state_quadratic_nonneg hσ₀ hσ₁ hδ + (unitaryState (star hX.eigenvectorUnitary) i) + (fun A hA ↦ unitaryState_positive _ _ hA) (unitaryState_one _ _) hC hB hM s + change 0 ≤ unitaryState (star hX.eigenvectorUnitary) i X at hp + rw [unitaryState_apply, hX.conjStarAlgAut_star_eigenvectorUnitary] at hp + simpa using hp + +end SharpLiebThirring.MatrixProof + +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder Topology +variable {n : Type u20} [Fintype n] [DecidableEq n] + +def diagonalFieldIntegrand (σ δ d : ℝ) (z : n → ℝ) (s : ℝ) : Matrix n n ℂ := + diagonal (fun i ↦ ((regularizedPrimitive σ δ ((s - z i) ^ 2 + d) - + regularizedPrimitive σ δ (s ^ 2) : ℝ) : ℂ)) + +omit [Fintype n] in +lemma continuous_diagonalFieldIntegrand {δ : ℝ} (hδ : 0 < δ) (σ d : ℝ) (z : n → ℝ) : + Continuous (diagonalFieldIntegrand σ δ d z) := by + have hf := (primitive_differentiable σ hδ).continuous + unfold diagonalFieldIntegrand + fun_prop + +lemma diagonalField_cutoff_limit {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (d : ℝ) (z : n → ℝ) : + Tendsto (fun R : ℝ ↦ fieldNormalization σ • ∫ s in -R..R, diagonalFieldIntegrand σ δ d z s) + atTop (𝓝 (scalarMu σ δ d • (1 : Matrix n n ℂ))) := by + apply tendsto_pi_nhds.2 + intro i + apply tendsto_pi_nhds.2 + intro j + have he (R : ℝ) := (entryCLM i j).intervalIntegral_comp_comm (μ := volume) + ((continuous_diagonalFieldIntegrand hδ σ d z).intervalIntegrable (-R) R) + simp only [entryCLM_apply] at he + have he' (R : ℝ) : (fieldNormalization σ • ∫ s in -R..R, diagonalFieldIntegrand σ δ d z s) i j = + fieldNormalization σ • ∫ s in -R..R, diagonalFieldIntegrand σ δ d z s i j := by + simp only [Matrix.smul_apply] + rw [← he R] + simp only [he'] + by_cases hij : i = j + · subst j + simp only [diagonalFieldIntegrand, diagonal_apply_eq, Matrix.smul_apply, one_apply_eq] + have hs := Complex.continuous_ofReal.continuousAt.tendsto.comp (primitive_shift_limit hσ hδ d (z i)) + convert! hs using 1 + · funext R + rw [intervalIntegral.integral_ofReal] + simp [Complex.real_smul] + · simp + · simp only [diagonalFieldIntegrand, diagonal_apply_ne _ hij, intervalIntegral.integral_zero, + smul_zero, Matrix.smul_apply, one_apply_ne hij] + exact tendsto_const_nhds + +omit [Fintype n] in +lemma quadraticMatrix_sub_diagonal (C : Matrix n n ℂ) (z : n → ℝ) (s d : ℝ) : + quadraticMatrix C (diagonal (fun i ↦ (z i : ℂ))) s - + diagonal (fun i ↦ (((s - z i) ^ 2 + d : ℝ) : ℂ)) = + C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ)) - d • 1 := by + ext i j + by_cases hij : i = j + · subst j + simp only [quadraticMatrix, Matrix.add_apply, Matrix.sub_apply, Matrix.smul_apply, + diagonal_apply_eq, one_apply_eq, Complex.real_smul] + push_cast + ring + · simp [quadraticMatrix, hij] + +lemma fieldIntegrand_tangent {σ δ d : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hδ : 0 < δ) (hd : 0 ≤ d) (C : Matrix n n ℂ) (z : n → ℝ) (s : ℝ) + (hX : (quadraticMatrix C (diagonal (fun i ↦ (z i : ℂ))) s).PosSemidef) : + fieldIntegrand σ δ C (diagonal (fun i ↦ (z i : ℂ))) s ≤ + diagonalFieldIntegrand σ δ d z s + + quadraticTangent σ δ d z (C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ)) - d • 1) s := by + have ht := primitive_diagonal_tangent hσ₀ hσ₁ hδ hd z s hX + rw [quadraticMatrix_sub_diagonal, ← hX.isHermitian.cfc_eq, + cfc_diagonal_real _ _ (primitive_differentiable σ hδ).continuous] at ht + have hh := sub_le_sub_right ht (regularizedPrimitive σ δ (s ^ 2) • (1 : Matrix n n ℂ)) + convert! hh using 1 + unfold diagonalFieldIntegrand + ext i j + by_cases hij : i = j + · subst j + simp only [Matrix.add_apply, Matrix.sub_apply, Matrix.smul_apply, + diagonal_apply_eq, one_apply_eq, Complex.real_smul] + push_cast + ring + · simp [hij] + +lemma hermitianField_diagonal_tangent {σ δ d : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hδ : 0 < δ) (hd : 0 ≤ d) {C : Matrix n n ℂ} (hC : C.IsHermitian) (z : n → ℝ) + (hX : ∀ s, (quadraticMatrix C (diagonal (fun i ↦ (z i : ℂ))) s).PosSemidef) : + hermitianField σ δ C (diagonal (fun i ↦ (z i : ℂ))) ≤ + scalarMu σ δ d • 1 + (σ * (d + δ) ^ (σ - 1)) • + tangentSchur σ (d + δ) z (C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ)) - d • 1) := by + have hB : (diagonal (fun i ↦ (z i : ℂ))).IsHermitian := + isHermitian_diagonal_iff.2 (fun i ↦ by simp [IsSelfAdjoint]) + let Z := C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ)) - d • 1 + have hiT := integrable_quadraticTangent hσ₁ hδ hd z Z + have hlimT := (intervalIntegral_tendsto_integral hiT tendsto_neg_atTop_atBot tendsto_id).const_smul + (fieldNormalization σ) + rw [integral_quadraticTangent hσ₁ hδ hd] at hlimT + have hlimY := diagonalField_cutoff_limit hσ₁ hδ d z + apply le_of_tendsto_of_tendsto (hermitianField_cutoff_limit hσ₁ hδ hC hB) (hlimY.add hlimT) + filter_upwards [eventually_ge_atTop (0 : ℝ)] with R hR + have hc := continuous_fieldIntegrand hδ σ hC hB + have hy := continuous_diagonalFieldIntegrand hδ σ d z + have hab : -R ≤ R := by linarith + have hi := MeasureTheory.integral_mono (μ := volume.restrict (Ioc (-R) R)) + (hc.intervalIntegrable (-R) R).1 + (((hy.intervalIntegrable (-R) R).add (hiT.intervalIntegrable (a := -R) (b := R))).1) + (fun s ↦ fieldIntegrand_tangent hσ₀ hσ₁ hδ hd C z s (hX s)) + rw [← intervalIntegral.integral_of_le hab, ← intervalIntegral.integral_of_le hab] at hi + rw [intervalIntegral.integral_add (hy.intervalIntegrable _ _) hiT.intervalIntegrable] at hi + simpa only [smul_add, id_eq] using smul_le_smul_of_nonneg_left hi (normalization_pos hσ₀ hσ₁).le + +end SharpLiebThirring.MatrixProof + +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder Topology +variable {n : Type u21} [Fintype n] [DecidableEq n] + +lemma phaseUnitary_conj_diagonal (z x : n → ℝ) (t : ℝ) : + conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) (diagonal (fun i ↦ (x i : ℂ))) = + diagonal (fun i ↦ (x i : ℂ)) := by + ext i j + rw [phaseUnitary_conj_apply] + by_cases hij : i = j + · subst j; simp + · simp [hij] + +lemma trace_conjugate_difference_zero (U : unitary (Matrix n n ℂ)) (D : Matrix n n ℂ) : + trace (2 • D - conjStarAlgAut ℂ (Matrix n n ℂ) U D - + conjStarAlgAut ℂ (Matrix n n ℂ) (star U) D) = 0 := by + rw [trace_sub, trace_sub, trace_smul, trace_unitary_conjugate, trace_unitary_conjugate] + simp only [two_smul] + abel + +lemma fieldIntegrand_trace_phase_nonneg {σ δ : ℝ} (hδ : 0 < δ) + {C : Matrix n n ℂ} (hC : C.IsHermitian) (z : n → ℝ) (s t : ℝ) : + 0 ≤ (trace (fieldIntegrand σ δ C (diagonal (fun i ↦ (z i : ℂ))) s * + (2 • (C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ))) - + conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) (C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ))) - + conjStarAlgAut ℂ (Matrix n n ℂ) (star (phaseUnitary z t)) + (C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ)))))).re := by + let B := diagonal (fun i ↦ (z i : ℂ)) + let D := C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ)) + let Y := diagonal (fun i ↦ (((s - z i) ^ 2 : ℝ) : ℂ)) + let H := 2 • D - conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D - + conjStarAlgAut ℂ (Matrix n n ℂ) (star (phaseUnitary z t)) D + have hB : B.IsHermitian := isHermitian_diagonal_iff.2 (fun i ↦ by simp [IsSelfAdjoint]) + have he : quadraticMatrix C B s = D + Y := by + have hh := quadraticMatrix_sub_diagonal C z s 0 + simp only [add_zero, zero_smul, sub_zero] at hh + exact (sub_eq_iff_eq_add.1 hh) + have hA : (D + Y).IsHermitian := he ▸ quadraticMatrix_hermitian hC hB s + have hp := trace_unitary_comparison_sub_invariant hA (primitive_strictMono σ hδ).monotone + (phaseUnitary z t) (phaseUnitary_conj_diagonal z (fun i ↦ (s - z i) ^ 2) t) + rw [← hA.cfc_eq, ← he] at hp + have hH : trace H = 0 := trace_conjugate_difference_zero _ _ + change 0 ≤ (trace ((cfc (regularizedPrimitive σ δ) (quadraticMatrix C B s) - + regularizedPrimitive σ δ (s ^ 2) • 1) * H)).re + rw [sub_mul, trace_sub, smul_mul_assoc, one_mul, trace_smul, hH, smul_zero, sub_zero] + exact hp + +lemma hermitianField_trace_phase_nonneg {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hδ : 0 < δ) {C : Matrix n n ℂ} (hC : C.IsHermitian) (z : n → ℝ) (t : ℝ) : + 0 ≤ (trace (hermitianField σ δ C (diagonal (fun i ↦ (z i : ℂ))) * + (2 • (C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ))) - + conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) (C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ))) - + conjStarAlgAut ℂ (Matrix n n ℂ) (star (phaseUnitary z t)) + (C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ)))))).re := by + have hB : (diagonal (fun i ↦ (z i : ℂ))).IsHermitian := + isHermitian_diagonal_iff.2 (fun i ↦ by simp [IsSelfAdjoint]) + apply trace_unitary_comparison_limit (hermitianField_cutoff_limit hσ₁ hδ hC hB) (phaseUnitary z t) + filter_upwards [eventually_ge_atTop (0 : ℝ)] with R hR + let D := C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ)) + let H := 2 • D - conjStarAlgAut ℂ (Matrix n n ℂ) (phaseUnitary z t) D - + conjStarAlgAut ℂ (Matrix n n ℂ) (star (phaseUnitary z t)) D + have hc := continuous_fieldIntegrand hδ σ hC hB + have hn : 0 ≤ ∫ s in -R..R, tracePairCLM H (fieldIntegrand σ δ C (diagonal (fun i ↦ (z i : ℂ))) s) := by + apply intervalIntegral.integral_nonneg (by linarith) + intro s hs + rw [tracePairCLM_apply, trace_mul_comm] + exact fieldIntegrand_trace_phase_nonneg hδ hC z s t + rw [(tracePairCLM H).intervalIntegral_comp_comm (hc.intervalIntegrable _ _)] at hn + change 0 ≤ (trace ((fieldNormalization σ • ∫ s in -R..R, + fieldIntegrand σ δ C (diagonal (fun i ↦ (z i : ℂ))) s) * H)).re + rw [smul_mul_assoc, trace_smul, Complex.real_smul, Complex.mul_re] + simp only [Complex.ofReal_re, Complex.ofReal_im, zero_mul, sub_zero] + rw [tracePairCLM_apply, trace_mul_comm] at hn + exact mul_nonneg (normalization_pos hσ₀ hσ₁).le hn + +lemma hermitianField_tangentSchur_contraction {σ δ a : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hδ : 0 < δ) (ha : 0 < a) {C : Matrix n n ℂ} (hC : C.IsHermitian) (z : n → ℝ) : + (trace (hermitianField σ δ C (diagonal (fun i ↦ (z i : ℂ))) * + tangentSchur σ a z (C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ))))).re ≤ + (trace (hermitianField σ δ C (diagonal (fun i ↦ (z i : ℂ))) * + (C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ))))).re := + tangentSchur_trace_comparison hσ₁ ha z _ _ (hermitianField_trace_phase_nonneg hσ₀ hσ₁ hδ hC z) + +end SharpLiebThirring.MatrixProof +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder Topology +variable {n : Type u22} [Fintype n] [DecidableEq n] + +lemma tangentSchur_sub_smul_one (σ : ℝ) {a : ℝ} (ha : 0 < a) + (z : n → ℝ) (D : Matrix n n ℂ) (d : ℝ) : + tangentSchur σ a z (D - d • 1) = tangentSchur σ a z D - d • 1 := by + calc + _ = tangentSchur σ a z D - d • tangentSchur σ a z 1 := by + ext i j + simp only [tangentSchur_apply σ ha, Matrix.sub_apply, Matrix.smul_apply, Complex.real_smul] + ring + _ = _ := by rw [tangentSchur_one] + +def vectorMass (a : n → ℂ) : ℝ := ∑ i, Complex.normSq (a i) + +omit [DecidableEq n] in +lemma vectorMass_nonneg (a : n → ℂ) : 0 ≤ vectorMass a := + Finset.sum_nonneg (fun i _ ↦ Complex.normSq_nonneg (a i)) + +omit [DecidableEq n] in +lemma vectorMass_eq_zero {a : n → ℂ} : vectorMass a = 0 ↔ a = 0 := by + rw [vectorMass, Finset.sum_eq_zero_iff_of_nonneg (fun i _ ↦ Complex.normSq_nonneg (a i))] + simp [funext_iff] + +omit [DecidableEq n] in +lemma dot_star_self_vectorMass (a : n → ℂ) : star a ⬝ᵥ a = (vectorMass a : ℂ) := by + simp only [dotProduct, Pi.star_apply, Complex.star_def, ← Complex.normSq_eq_conj_mul_self, + vectorMass, Complex.ofReal_sum] + +omit [DecidableEq n] in +lemma rankone_trace (a : n → ℂ) : trace (vecMulVec a (star a)) = (vectorMass a : ℂ) := by + rw [trace_vecMulVec, dotProduct_comm, dot_star_self_vectorMass] + +omit [DecidableEq n] in +lemma rankone_square (a : n → ℂ) : + vecMulVec a (star a) * vecMulVec a (star a) = vectorMass a • vecMulVec a (star a) := by + rw [vecMulVec_mul_vecMulVec, dot_star_self_vectorMass, vecMulVec_smul] + ext i j + simp [Complex.real_smul] + +lemma rankone_tracePair_positive (a : n → ℂ) {A : Matrix n n ℂ} (hA : A.PosSemidef) : + 0 ≤ tracePairCLM (vecMulVec a (star a)) A := by + rw [tracePairCLM_apply, trace_mul_comm, mul_vecMulVec, trace_vecMulVec, dotProduct_comm] + exact (Complex.nonneg_iff.1 (hA.dotProduct_mulVec_nonneg a)).1 + +lemma rankone_tracePair_monotone (a : n → ℂ) : Monotone (tracePairCLM (vecMulVec a (star a))) := by + intro A B hAB + have h := rankone_tracePair_positive a (le_iff.1 hAB) + rw [map_sub] at h + linarith + +lemma rankone_tracePair_one (a : n → ℂ) : tracePairCLM (vecMulVec a (star a)) 1 = vectorMass a := by + rw [tracePairCLM_apply, mul_one, rankone_trace, Complex.ofReal_re] + +lemma rankone_tracePair_self (a : n → ℂ) : + tracePairCLM (vecMulVec a (star a)) (vecMulVec a (star a)) = (vectorMass a) ^ 2 := by + rw [tracePairCLM_apply, rankone_square, trace_smul, rankone_trace, Complex.real_smul] + simp [pow_two] + +/-- The rank-one comparison in an arbitrary eigenbasis of B. No positivity of +C - B² is assumed; its needed trace bound is obtained by contraction. -/ +lemma rankone_diagonal_comparison {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) + {C : Matrix n n ℂ} (hC : C.IsHermitian) (z : n → ℝ) (a : n → ℂ) + (hM : hermitianField σ δ C (diagonal (fun i ↦ (z i : ℂ))) = vecMulVec a (star a)) : + (vectorMass a) ^ (1 + 1 / σ) ≤ + (trace (vecMulVec a (star a) * (C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ))))).re := by + by_cases ha : a = 0 + · subst a + have hexp : (1 + 1 / σ : ℝ) ≠ 0 := by positivity + have hz : vecMulVec (0 : n → ℂ) (star (0 : n → ℂ)) = 0 := by + ext i j + simp [vecMulVec] + rw [hz, zero_mul, trace_zero, Complex.zero_re] + simpa only [vectorMass, Pi.zero_apply, Complex.normSq_zero, Finset.sum_const_zero] + using (le_of_eq (Real.zero_rpow hexp)) + have hm : 0 < vectorMass a := lt_of_le_of_ne (vectorMass_nonneg a) + (Ne.symm (mt vectorMass_eq_zero.1 ha)) + let d := (vectorMass a + δ ^ σ) ^ (1 / σ) - δ + have hd : 0 < d := inverse_mu_positive hσ₀ hδ hm + have he : scalarMu σ δ d = vectorMass a := mu_inverse hσ₀ hσ₁ hδ hm + have hB : (diagonal (fun i ↦ (z i : ℂ))).IsHermitian := + isHermitian_diagonal_iff.2 (fun i ↦ by simp [IsSelfAdjoint]) + have hMP : (hermitianField σ δ C (diagonal (fun i ↦ (z i : ℂ)))).PosSemidef := by + rw [hM] + exact posSemidef_vecMulVec_self_star a + have ht := hermitianField_diagonal_tangent hσ₀ hσ₁ hδ hd.le hC z + (hermitianField_nonneg_implies_quadratic hσ₀ hσ₁ hδ hC hB hMP) + rw [hM, he, tangentSchur_sub_smul_one σ (by linarith) z _ d] at ht + have hp := rankone_tracePair_monotone a ht + rw [map_add, map_smul, map_smul, map_sub, map_smul, rankone_tracePair_one, + rankone_tracePair_self] at hp + simp only [smul_eq_mul] at hp + have hc := hermitianField_tangentSchur_contraction hσ₀ hσ₁ hδ (show 0 < d + δ by linarith) hC z + rw [hM] at hc + have hk : 0 < σ * (d + δ) ^ (σ - 1) := mul_pos hσ₀ (Real.rpow_pos_of_pos (by linarith) _) + have hpd : d * vectorMass a ≤ tracePairCLM (vecMulVec a (star a)) + (tangentSchur σ (d + δ) z (C - diagonal (fun i ↦ ((z i ^ 2 : ℝ) : ℂ)))) := by + nlinarith + exact (rankone_scalar_power hσ₀ hσ₁ hδ hm hd.le he).trans (hpd.trans hc) + +end SharpLiebThirring.MatrixProof +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder Topology +variable {n : Type u23} [Fintype n] [DecidableEq n] + +def unitaryConjCLM (U : unitary (Matrix n n ℂ)) : Matrix n n ℂ →L[ℝ] Matrix n n ℂ := + LinearMap.toContinuousLinearMap + { toFun := conjStarAlgAut ℂ (Matrix n n ℂ) U + map_add' := by intros; exact map_add _ _ _ + map_smul' := by intros; simp } + +@[simp] lemma unitaryConjCLM_apply (U : unitary (Matrix n n ℂ)) (A : Matrix n n ℂ) : + unitaryConjCLM U A = conjStarAlgAut ℂ (Matrix n n ℂ) U A := rfl + +lemma quadraticMatrix_conj (U : unitary (Matrix n n ℂ)) (C B : Matrix n n ℂ) (s : ℝ) : + quadraticMatrix (conjStarAlgAut ℂ (Matrix n n ℂ) U C) + (conjStarAlgAut ℂ (Matrix n n ℂ) U B) s = + conjStarAlgAut ℂ (Matrix n n ℂ) U (quadraticMatrix C B s) := by + have hs (r : ℝ) (A : Matrix n n ℂ) : + conjStarAlgAut ℂ (Matrix n n ℂ) U (r • A) = + r • conjStarAlgAut ℂ (Matrix n n ℂ) U A := (unitaryConjCLM U).map_smul r A + simp only [quadraticMatrix, map_add, map_sub, hs, map_one] + +lemma cfc_unitary_conj {A : Matrix n n ℂ} (hA : A.IsHermitian) + (U : unitary (Matrix n n ℂ)) (f : ℝ → ℝ) : + cfc f (conjStarAlgAut ℂ (Matrix n n ℂ) U A) = conjStarAlgAut ℂ (Matrix n n ℂ) U (cfc f A) := by + have h := functional_unitary_conjugate hA U f + rwa [← IsHermitian.cfc_eq, ← hA.cfc_eq] at h + +lemma pairedFieldIntegrand_conj (σ δ : ℝ) {C B : Matrix n n ℂ} + (hC : C.IsHermitian) (hB : B.IsHermitian) (U : unitary (Matrix n n ℂ)) (s : ℝ) : + pairedFieldIntegrand σ δ (conjStarAlgAut ℂ (Matrix n n ℂ) U C) + (conjStarAlgAut ℂ (Matrix n n ℂ) U B) s = + unitaryConjCLM U (pairedFieldIntegrand σ δ C B s) := by + simp only [pairedFieldIntegrand, quadraticMatrix_conj, unitaryConjCLM_apply, + cfc_unitary_conj (quadraticMatrix_hermitian hC hB _), map_sub, map_add, map_smul, map_one] + +lemma hermitianField_conj {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) + (U : unitary (Matrix n n ℂ)) : + hermitianField σ δ (conjStarAlgAut ℂ (Matrix n n ℂ) U C) + (conjStarAlgAut ℂ (Matrix n n ℂ) U B) = + conjStarAlgAut ℂ (Matrix n n ℂ) U (hermitianField σ δ C B) := by + change _ = unitaryConjCLM U (hermitianField σ δ C B) + simp only [hermitianField, pairedFieldIntegrand_conj σ δ hC hB, map_smul] + rw [(unitaryConjCLM U).integral_comp_comm (integrable_pairedFieldIntegrand hσ hδ hC hB)] + +lemma unitary_conj_rankone (U : unitary (Matrix n n ℂ)) (a : n → ℂ) : + conjStarAlgAut ℂ (Matrix n n ℂ) U (vecMulVec a (star a)) = + vecMulVec ((U : Matrix n n ℂ) *ᵥ a) (star ((U : Matrix n n ℂ) *ᵥ a)) := by + rw [conjStarAlgAut_apply, mul_vecMulVec, vecMulVec_mul, star_mulVec] + rfl + +lemma vectorMass_unitary (U : unitary (Matrix n n ℂ)) (a : n → ℂ) : + vectorMass ((U : Matrix n n ℂ) *ᵥ a) = vectorMass a := by + apply Complex.ofReal_injective + rw [← rankone_trace, ← unitary_conj_rankone, trace_unitary_conjugate, rankone_trace] + +/-- The complete complex Hermitian rank-one comparison, before identifying the +real symmetric field with its complexification. -/ +lemma rankone_hermitian_comparison {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) + {C B : Matrix n n ℂ} (hC : C.IsHermitian) (hB : B.IsHermitian) (a : n → ℂ) + (hM : hermitianField σ δ C B = vecMulVec a (star a)) : + (vectorMass a) ^ (1 + 1 / σ) ≤ (trace (vecMulVec a (star a) * (C - B ^ 2))).re := by + let U := star hB.eigenvectorUnitary + let C' := conjStarAlgAut ℂ (Matrix n n ℂ) U C + let a' := (U : Matrix n n ℂ) *ᵥ a + have hb : conjStarAlgAut ℂ (Matrix n n ℂ) U B = + diagonal (fun i ↦ (hB.eigenvalues i : ℂ)) := hB.conjStarAlgAut_star_eigenvectorUnitary + have hm : hermitianField σ δ C' (diagonal (fun i ↦ (hB.eigenvalues i : ℂ))) = + vecMulVec a' (star a') := by + rw [← hb, hermitianField_conj hσ₁ hδ hC hB, hM, unitary_conj_rankone] + have hp := rankone_diagonal_comparison hσ₀ hσ₁ hδ (hermitian_unitary_conjugate hC U) + hB.eigenvalues a' hm + have hsq : conjStarAlgAut ℂ (Matrix n n ℂ) U (B ^ 2) = + diagonal (fun i ↦ ((hB.eigenvalues i ^ 2 : ℝ) : ℂ)) := by + rw [map_pow, hb, pow_two, diagonal_mul_diagonal] + congr 1 + funext i + simp [pow_two] + rw [vectorMass_unitary U a] at hp + have ht : trace (vecMulVec a' (star a') * + (C' - diagonal (fun i ↦ ((hB.eigenvalues i ^ 2 : ℝ) : ℂ)))) = + trace (vecMulVec a (star a) * (C - B ^ 2)) := by + rw [← unitary_conj_rankone U a, ← hsq] + change trace (conjStarAlgAut ℂ (Matrix n n ℂ) U (vecMulVec a (star a)) * + (conjStarAlgAut ℂ (Matrix n n ℂ) U C - conjStarAlgAut ℂ (Matrix n n ℂ) U (B ^ 2))) = _ + rw [← map_sub, ← map_mul, trace_unitary_conjugate] + rwa [ht] at hp + +end SharpLiebThirring.MatrixProof +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder Topology +variable {n : Type u24} [Fintype n] [DecidableEq n] + +def complexify : Matrix n n ℝ →⋆ₐ[ℝ] Matrix n n ℂ := + { (Algebra.ofId ℝ ℂ).mapMatrix with + map_star' := by + intro A + ext i j + simp [Matrix.star_apply] } + +@[simp] lemma complexify_apply (A : Matrix n n ℝ) (i j : n) : complexify A i j = (A i j : ℂ) := rfl + +def complexifyCLM : Matrix n n ℝ →L[ℝ] Matrix n n ℂ := + complexify.toLinearMap.toContinuousLinearMap + +@[simp] lemma complexifyCLM_apply (A : Matrix n n ℝ) : complexifyCLM A = complexify A := rfl + +def realPartCLM : Matrix n n ℂ →L[ℝ] Matrix n n ℝ := + LinearMap.toContinuousLinearMap + { toFun := fun A ↦ A.map Complex.re + map_add' := by intros; ext i j; simp + map_smul' := by intros; ext i j; simp } + +@[simp] lemma realPartCLM_complexify (A : Matrix n n ℝ) : realPartCLM (complexify A) = A := by + ext i j + exact Complex.ofReal_re _ + +lemma complexify_hermitian {A : Matrix n n ℝ} (hA : A.IsHermitian) : (complexify A).IsHermitian := by + change star (complexify A) = complexify A + rw [← map_star, hA.star_eq] + +lemma complexify_cfc {A : Matrix n n ℝ} (hA : A.IsHermitian) (f : ℝ → ℝ) : + complexify (cfc f A) = cfc f (complexify A) := + StarAlgHomClass.map_cfc complexify f A (A.finite_real_spectrum.continuousOn f) + complexifyCLM.continuous hA (complexify_hermitian hA) + +lemma complexify_diagonal (x : n → ℝ) : + complexify (diagonal x) = diagonal (fun i ↦ (x i : ℂ)) := by + ext i j + by_cases hij : i = j <;> simp [hij] + +lemma complexify_vecMulVec (a : n → ℝ) : + complexify (vecMulVec a a) = vecMulVec (fun i ↦ (a i : ℂ)) (star (fun i ↦ (a i : ℂ))) := by + ext i j + simp [vecMulVec] + +omit [DecidableEq n] in +lemma vectorMass_ofReal (a : n → ℝ) : vectorMass (fun i ↦ (a i : ℂ)) = ∑ i, a i ^ 2 := by + simp [vectorMass, Complex.normSq_ofReal, pow_two] + +lemma complexify_trace_real (A : Matrix n n ℝ) : (trace (complexify A)).re = trace A := by + simp only [trace, diag, complexify_apply, Complex.re_sum, Complex.ofReal_re] + +lemma matrixX_hermitian {N : ℕ} (k : Fin N → ℝ) {B : Matrix (Fin N) (Fin N) ℝ} + (hB : B.IsHermitian) (s : ℝ) : (matrixX k B s).IsHermitian := by + exact ((isHermitian_diagonal (fun i ↦ k i ^ 2)).sub (hB.smul (isSelfAdjoint_iff.2 rfl : IsSelfAdjoint (2 * s)))).add + (isHermitian_one.smul (isSelfAdjoint_iff.2 rfl : IsSelfAdjoint (s ^ 2))) + +lemma complexify_matrixX {N : ℕ} (k : Fin N → ℝ) (B : Matrix (Fin N) (Fin N) ℝ) (s : ℝ) : + complexify (matrixX k B s) = quadraticMatrix (complexify (diagonal (fun i ↦ k i ^ 2))) + (complexify B) s := by + simp only [matrixX, quadraticMatrix, map_add, map_sub, map_smul, map_one] + abel + +lemma complexify_truncatedField {N : ℕ} {σ δ : ℝ} (hδ : 0 < δ) (k : Fin N → ℝ) + {B : Matrix (Fin N) (Fin N) ℝ} (hB : B.IsHermitian) (R : ℝ) : + complexify (truncatedField σ δ k B R) = fieldNormalization σ • ∫ s in -R..R, + fieldIntegrand σ δ (complexify (diagonal (fun i ↦ k i ^ 2))) (complexify B) s := by + have hc : Continuous (fun s ↦ cfc (regularizedPrimitive σ δ) (matrixX k B s) - + regularizedPrimitive σ δ (s ^ 2) • (1 : Matrix (Fin N) (Fin N) ℝ)) := by + have hx : Continuous (fun s ↦ cfc (regularizedPrimitive σ δ) (matrixX k B s)) := + Continuous.cfc_of_mem_nhdsSet (s := Set.univ) _ Filter.univ_mem + (by unfold matrixX; fun_prop) (matrixX_hermitian k hB) + (primitive_differentiable σ hδ).continuous.continuousOn + exact hx.sub (((primitive_differentiable σ hδ).continuous.comp (continuous_pow 2)).smul continuous_const) + change complexifyCLM (truncatedField σ δ k B R) = _ + rw [truncatedField, map_smul, ← complexifyCLM.intervalIntegral_comp_comm (hc.intervalIntegrable _ _)] + congr 1 + apply intervalIntegral.integral_congr + intro s hs + simp only [complexifyCLM_apply, map_sub, map_smul, map_one, + complexify_cfc (matrixX_hermitian k hB s), complexify_matrixX, fieldIntegrand] + +lemma complexify_matrixField {N : ℕ} {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (k : Fin N → ℝ) {B : Matrix (Fin N) (Fin N) ℝ} (hB : B.IsHermitian) : + complexify (matrixField σ δ k B) = + hermitianField σ δ (complexify (diagonal (fun i ↦ k i ^ 2))) (complexify B) := by + have hC := complexify_hermitian (isHermitian_diagonal (fun i ↦ k i ^ 2)) + have hl := hermitianField_cutoff_limit hσ hδ hC (complexify_hermitian hB) + have ht : Tendsto (fun R ↦ complexify (truncatedField σ δ k B R)) atTop (𝓝 + (hermitianField σ δ (complexify (diagonal (fun i ↦ k i ^ 2))) (complexify B))) := by + simpa only [complexify_truncatedField hδ k hB] using hl + have hr := realPartCLM.continuous.continuousAt.tendsto.comp ht + change Tendsto (fun R ↦ realPartCLM (complexify (truncatedField σ δ k B R))) atTop + (𝓝 (realPartCLM (hermitianField σ δ + (complexify (diagonal (fun i ↦ k i ^ 2))) (complexify B)))) at hr + simp only [realPartCLM_complexify] at hr + have he : matrixField σ δ k B = realPartCLM + (hermitianField σ δ (complexify (diagonal (fun i ↦ k i ^ 2))) (complexify B)) := hr.limUnder_eq + have hh := complexifyCLM.continuous.continuousAt.tendsto.comp hr + change Tendsto (fun R ↦ complexify (truncatedField σ δ k B R)) atTop + (𝓝 (complexify (realPartCLM (hermitianField σ δ + (complexify (diagonal (fun i ↦ k i ^ 2))) (complexify B))))) at hh + rw [he] + exact tendsto_nhds_unique hh ht + +/-- The rank-one comparison for the real field +with its symmetric-cutoff definition. -/ +theorem source_rankone_comparison {N : ℕ} {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hδ : 0 < δ) (k : Fin N → ℝ) {B : Matrix (Fin N) (Fin N) ℝ} (hB : B.IsHermitian) + (a : Fin N → ℝ) (hM : matrixField σ δ k B = vecMulVec a a) : + (∑ i, a i ^ 2) ^ (1 + 1 / σ) ≤ + ∑ i, a i * ((diagonal (fun i ↦ k i ^ 2) - B ^ 2) *ᵥ a) i := by + have hm : hermitianField σ δ (complexify (diagonal (fun i ↦ k i ^ 2))) (complexify B) = + vecMulVec (fun i ↦ (a i : ℂ)) (star (fun i ↦ (a i : ℂ))) := by + rw [← complexify_matrixField hσ₁ hδ k hB, hM, complexify_vecMulVec] + have hp := rankone_hermitian_comparison hσ₀ hσ₁ hδ + (complexify_hermitian (isHermitian_diagonal (fun i ↦ k i ^ 2))) (complexify_hermitian hB) + (fun i ↦ (a i : ℂ)) hm + rw [vectorMass_ofReal, ← complexify_vecMulVec, ← map_pow, ← map_sub, ← map_mul, + complexify_trace_real, trace_mul_comm, mul_vecMulVec, trace_vecMulVec, dotProduct_comm] at hp + exact hp + +theorem rankOneClaim {N : ℕ} : @RankOneClaim N := by + intro σ δ k B a hσ₀ hσ₁ hδ _ hB hM + exact source_rankone_comparison hσ₀ hσ₁ hδ k hB a hM + +end SharpLiebThirring.MatrixProof + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/Resolvent.lean b/lean/OAI/Analysis/LiebThirring/Resolvent.lean new file mode 100644 index 0000000000000000000000000000000000000000..8fd7648f3e1d6f3a5adb119278e0c2693334474e --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/Resolvent.lean @@ -0,0 +1,72 @@ +import OAI.Analysis.LiebThirring.OperatorForm + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set Filter +open scoped Topology + +lemma shiftedFormMap_bijective {W : ℝ → ℝ} (d : PotentialData W) : + Function.Bijective (shiftedFormMap d) := + coercive_bijective _ (by norm_num : (0:ℝ) < 3/4) (shiftedFormMap_coercive d) + +def formEquiv {W : ℝ → ℝ} (d : PotentialData W) : H1C ≃L[ℂ] H1C := + ContinuousLinearEquiv.ofBijective (shiftedFormMap d) + (LinearMap.ker_eq_bot.mpr (shiftedFormMap_bijective d).1) + (LinearMap.range_eq_top.mpr (shiftedFormMap_bijective d).2) + +def solveL {W : ℝ → ℝ} (d : PotentialData W) : L2C →L[ℂ] H1C := + (formEquiv d).symm.toContinuousLinearMap.comp valL.adjoint + +@[simp] lemma shifted_solve {W : ℝ → ℝ} (d : PotentialData W) (f : L2C) : + shiftedFormMap d (solveL d f) = valL.adjoint f := + (formEquiv d).apply_symm_apply _ + +@[simp] lemma solve_shifted {W : ℝ → ℝ} (d : PotentialData W) (u : H1C) : + (formEquiv d).symm (shiftedFormMap d u) = u := + (formEquiv d).symm_apply_apply u + +def resolvent {W : ℝ → ℝ} (d : PotentialData W) : L2C →L[ℂ] L2C := valL.comp (solveL d) + +lemma val_adjoint_injective : Function.Injective valL.adjoint := by + intro f g h + apply valL_dense.eq_of_inner_left ℂ + rintro z ⟨u,rfl⟩ + rw [← ContinuousLinearMap.adjoint_inner_left,← ContinuousLinearMap.adjoint_inner_left,h] + +lemma resolvent_injective {W : ℝ → ℝ} (d : PotentialData W) : + Function.Injective (resolvent d) := + valL_injective.comp ((formEquiv d).symm.injective.comp val_adjoint_injective) + +lemma resolvent_symmetric {W : ℝ → ℝ} (d : PotentialData W) : + (resolvent d).IsSymmetric := by + intro f g + change inner ℂ (valL (solveL d f)) g = inner ℂ f (valL (solveL d g)) + rw [← ContinuousLinearMap.adjoint_inner_right valL (solveL d f) g, + ← ContinuousLinearMap.adjoint_inner_left valL (solveL d g) f, + ← shifted_solve d f,← shifted_solve d g] + exact ((shiftedFormMap_symmetric d) (solveL d f) (solveL d g)).symm + +lemma resolvent_dense {W : ℝ → ℝ} (d : PotentialData W) : + Dense (Set.range (resolvent d)) := by + have hk : (resolvent d).ker = ⊥ := LinearMap.ker_eq_bot.mpr (resolvent_injective d) + have he := (resolvent d).orthogonal_ker + rw [hk,Submodule.bot_orthogonal_eq_top,(resolvent_symmetric d).clm_adjoint_eq] at he + rw [dense_iff_closure_eq] + exact congrArg (fun S : Submodule ℂ L2C ↦ (S : Set L2C)) he.symm + +lemma solve_form {W : ℝ → ℝ} (d : PotentialData W) (f : L2C) (v : H1C) : + schrodingerForm W (toH1 v) (toH1 (solveL d f))+ + (d.b+1 : ℂ)*inner ℂ (valL v) (resolvent d f) = inner ℂ (valL v) f := by + have h := congrArg (fun u ↦ inner ℂ v u) (shifted_solve d f) + rw [shiftedFormMap_inner,ContinuousLinearMap.adjoint_inner_right] at h + rw [form_eq_inner] + exact h + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/ResolventCalculus.lean b/lean/OAI/Analysis/LiebThirring/ResolventCalculus.lean new file mode 100644 index 0000000000000000000000000000000000000000..faab870eb280d452d2c8de15c565d943f797bcda --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/ResolventCalculus.lean @@ -0,0 +1,574 @@ +import OAI.Analysis.LiebThirring.MatrixOrder + +namespace OAI + +universe u6 u7 u8 u9 u10 u11 + +noncomputable section +open MeasureTheory +open scoped ENNReal Matrix.Norms.L2Operator +open Matrix + + +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +namespace SharpLiebThirring.MatrixProof +variable {n : Type u6} [Fintype n] [DecidableEq n] + +/-- Finite spectral synthesis as a real continuous linear map. -/ +def spectralCLM {A : Matrix n n ℂ} (hA : A.IsHermitian) : + (n → ℝ) →L[ℝ] Matrix n n ℂ := + ({ toFun := fun x ↦ conjStarAlgAut ℂ (Matrix n n ℂ) hA.eigenvectorUnitary + (diagonal (fun i ↦ (x i : ℂ))) + map_add' := by + intro x y + simp only [Pi.add_apply, Complex.ofReal_add, conjStarAlgAut_apply] + rw [show diagonal (fun i ↦ (x i : ℂ) + (y i : ℂ)) = + diagonal (fun i ↦ (x i : ℂ)) + diagonal (fun i ↦ (y i : ℂ)) from + (diagonal_add _ _).symm] + simp only [mul_add, add_mul] + map_smul' := by + intro r x + simp only [RingHom.id_apply, Pi.smul_apply, smul_eq_mul, Complex.ofReal_mul] + rw [show diagonal (fun i ↦ (r : ℂ) * (x i : ℂ)) = + r • diagonal (fun i ↦ (x i : ℂ)) by ext i j; simp [diagonal_apply]] + simp [conjStarAlgAut_apply] } : (n → ℝ) →ₗ[ℝ] Matrix n n ℂ).toContinuousLinearMap + +@[simp] lemma spectralCLM_apply {A : Matrix n n ℂ} (hA : A.IsHermitian) (x : n → ℝ) : + spectralCLM hA x = conjStarAlgAut ℂ (Matrix n n ℂ) hA.eigenvectorUnitary + (diagonal (fun i ↦ (x i : ℂ))) := rfl + +lemma integrable_hermitian_cfc {X : Type u7} [MeasurableSpace X] {μ : Measure X} + {A : Matrix n n ℂ} (hA : A.IsHermitian) (f : X → ℝ → ℝ) + (hf : ∀ i, Integrable (fun x ↦ f x (hA.eigenvalues i)) μ) : + Integrable (fun x ↦ hA.cfc (f x)) μ := + (spectralCLM hA).integrable_comp (integrable_pi_iff.2 hf) + +lemma integral_hermitian_cfc {X : Type u8} [MeasurableSpace X] {μ : Measure X} + {A : Matrix n n ℂ} (hA : A.IsHermitian) (f : X → ℝ → ℝ) + (hf : ∀ i, Integrable (fun x ↦ f x (hA.eigenvalues i)) μ) : + ∫ x, hA.cfc (f x) ∂μ = hA.cfc (fun t ↦ ∫ x, f x t ∂μ) := by + have hi := integrable_pi_iff.2 hf + calc + _ = ∫ x, spectralCLM hA (fun i ↦ f x (hA.eigenvalues i)) ∂μ := rfl + _ = spectralCLM hA (∫ x, fun i ↦ f x (hA.eigenvalues i) ∂μ) := + (spectralCLM hA).integral_comp_comm hi + _ = _ := by + apply congrArg (spectralCLM hA) + ext i + exact ((ContinuousLinearMap.proj i : (n → ℝ) →L[ℝ] ℝ).integral_comp_comm hi).symm + +lemma cfc_shifted_inverse {A : Matrix n n ℂ} (hA : A.PosSemidef) {a : ℝ} (ha : 0 < a) : + hA.isHermitian.cfc (fun y ↦ (y + a)⁻¹) = (A + a • 1)⁻¹ := by + have hn : ∀ x ∈ spectrum ℝ A, x + a ≠ 0 := by + intro x hx + have hx₀ : 0 ≤ x := spectrum_nonneg_of_nonneg hA.nonneg hx + linarith + erw [← hA.isHermitian.cfc_eq, + cfc_inv (fun y : ℝ ↦ y + a) A hn (by fun_prop) hA.isHermitian, + cfc_add A id (fun _ ↦ a) (by fun_prop) (by fun_prop), + cfc_const a A hA.isHermitian, cfc_id ℝ A hA.isHermitian, + Matrix.nonsing_inv_eq_ringInverse, Algebra.algebraMap_eq_smul_one] + +open ScalarProof + +lemma shifted_inverse_norm_le {A : Matrix n n ℂ} (hA : A.PosSemidef) {a : ℝ} (ha : 0 < a) : + ‖(A + a • 1)⁻¹‖ ≤ a⁻¹ := by + rw [← cfc_shifted_inverse hA ha, ← hA.isHermitian.cfc_eq] + apply norm_cfc_le (inv_nonneg.2 ha.le) + intro x hx + have hx₀ : 0 ≤ x := spectrum_nonneg_of_nonneg hA.nonneg hx + rw [Real.norm_eq_abs, abs_of_pos (inv_pos.2 (by linarith : 0 < x + a))] + exact inv_anti₀ ha (by linarith) + +def resolventMatrix (β δ : ℝ) (A : Matrix n n ℂ) (v : ℝ) : Matrix n n ℂ := + v ^ β • ((δ + v)⁻¹ • 1 - (A + (δ + v) • 1)⁻¹) + +lemma cfc_resolventDifference {A : Matrix n n ℂ} (hA : A.PosSemidef) + (β : ℝ) {δ v : ℝ} (hδ : 0 < δ) (hv : 0 ≤ v) : + hA.isHermitian.cfc (fun y ↦ resolventDifference β δ y v) = + resolventMatrix β δ A v := by + have ha : 0 < δ + v := by linarith + have hn : ∀ x ∈ spectrum ℝ A, x + (δ + v) ≠ 0 := by + intro x hx + have hx₀ : 0 ≤ x := spectrum_nonneg_of_nonneg hA.nonneg hx + linarith + have hc : ContinuousOn (fun x : ℝ ↦ (x + (δ + v))⁻¹) (spectrum ℝ A) := + (continuousOn_id.add continuousOn_const).inv₀ hn + unfold resolventDifference resolventMatrix + simp only [add_assoc] + erw [← hA.isHermitian.cfc_eq, + cfc_const_mul (v ^ β) (fun y ↦ (δ + v)⁻¹ - (y + (δ + v))⁻¹) A + (continuousOn_const.sub hc), + cfc_sub (fun _ ↦ (δ + v)⁻¹) (fun y ↦ (y + (δ + v))⁻¹) A + continuousOn_const hc, + cfc_const (δ + v)⁻¹ A hA.isHermitian, + hA.isHermitian.cfc_eq, cfc_shifted_inverse hA ha, + Algebra.algebraMap_eq_smul_one] + +lemma integrable_resolventMatrix {A : Matrix n n ℂ} (hA : A.PosSemidef) + {β δ : ℝ} (hβ₀ : -1 < β) (hβ₁ : β < 1) (hδ : 0 < δ) : + IntegrableOn (resolventMatrix β δ A) (Ioi 0) := by + have hi := integrable_hermitian_cfc hA.isHermitian + (fun v y ↦ resolventDifference β δ y v) (μ := volume.restrict (Ioi (0 : ℝ))) + (fun i ↦ resolvent_difference_integrable hβ₀ hβ₁ hδ (by + have := hA.eigenvalues_nonneg i + linarith)) + apply hi.congr + filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + exact cfc_resolventDifference hA β hδ (le_of_lt hv) + +/-- Matrix-valued resolvent representation, not only a scalar or commuting case. -/ +lemma primitive_cfc_resolvent_representation {A : Matrix n n ℂ} (hA : A.PosSemidef) + {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) : + hA.isHermitian.cfc (regularizedPrimitive σ δ) = + resolventNormalization (σ - 1 / 2) • + ∫ v in Ioi (0 : ℝ), resolventMatrix (σ - 1 / 2) δ A v := by + have hβ₀ : -1 < σ - 1 / 2 := by linarith + have hβ₁ : σ - 1 / 2 < 1 := by linarith + have hi (i : n) : IntegrableOn + (fun v ↦ resolventDifference (σ - 1 / 2) δ (hA.isHermitian.eigenvalues i) v) (Ioi 0) := + resolvent_difference_integrable hβ₀ hβ₁ hδ (by + have := hA.eigenvalues_nonneg i + linarith) + have he : (∫ v in Ioi (0 : ℝ), resolventMatrix (σ - 1 / 2) δ A v) = + hA.isHermitian.cfc (fun y ↦ ∫ v in Ioi (0 : ℝ), resolventDifference (σ - 1 / 2) δ y v) := by + rw [← integral_hermitian_cfc hA.isHermitian + (fun v y ↦ resolventDifference (σ - 1 / 2) δ y v) hi] + apply integral_congr_ae + filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + exact (cfc_resolventDifference hA _ hδ (le_of_lt hv)).symm + rw [he] + change spectralCLM hA.isHermitian (fun i ↦ regularizedPrimitive σ δ (hA.isHermitian.eigenvalues i)) = + _ • spectralCLM hA.isHermitian _ + rw [← map_smul] + apply congrArg (spectralCLM hA.isHermitian) + ext i + exact primitive_resolvent_representation hσ₀ hσ₁ hδ (hA.eigenvalues_nonneg i) + +end SharpLiebThirring.MatrixProof + + +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder Topology +variable {n : Type u9} [Fintype n] [DecidableEq n] + +def resolventTangentKernel (β δ : ℝ) (Y Z : Matrix n n ℂ) (v : ℝ) : Matrix n n ℂ := + v ^ β • ((Y + (δ + v) • 1)⁻¹ * Z * (Y + (δ + v) • 1)⁻¹) + +lemma continuousOn_shifted_inverse {Y : Matrix n n ℂ} (hY : Y.PosSemidef) + {δ : ℝ} (hδ : 0 < δ) : + ContinuousOn (fun v : ℝ ↦ (Y + (δ + v) • 1)⁻¹) (Ioi 0) := by + have hc : ContinuousOn (fun v : ℝ ↦ fun i ↦ (hY.isHermitian.eigenvalues i + (δ + v))⁻¹) + (Ioi 0) := by + apply continuousOn_pi.2 + intro i + apply (continuousOn_const.add (continuousOn_const.add continuousOn_id)).inv₀ + intro v hv + change hY.isHermitian.eigenvalues i + (δ + v) ≠ 0 + have hv' : 0 < v := hv + have := hY.eigenvalues_nonneg i + linarith + apply ((spectralCLM hY.isHermitian).continuous.comp_continuousOn hc).congr + intro v hv + change (Y + (δ + v) • 1)⁻¹ = hY.isHermitian.cfc (fun y ↦ (y + (δ + v))⁻¹) + exact (cfc_shifted_inverse hY (by have hv' : 0 < v := hv; linarith)).symm + +lemma integrable_resolventTangentKernel {Y : Matrix n n ℂ} (hY : Y.PosSemidef) + (Z : Matrix n n ℂ) {β δ : ℝ} (hβ₀ : -1 < β) (hβ₁ : β < 1) (hδ : 0 < δ) : + IntegrableOn (resolventTangentKernel β δ Y Z) (Ioi 0) := by + have hc := continuousOn_shifted_inverse hY hδ + have ht : ContinuousOn (resolventTangentKernel β δ Y Z) (Ioi 0) := + (continuousOn_id.rpow_const (fun _ hv ↦ Or.inl (ne_of_gt hv))).smul + ((hc.mul continuousOn_const).mul hc) + apply ((resolvent_kernel_integrable hβ₀ hβ₁ hδ).const_mul ‖Z‖).mono' + (ht.aestronglyMeasurable measurableSet_Ioi) + filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + have hv' : 0 < v := hv + have hb := shifted_inverse_norm_le hY (show 0 < δ + v by linarith) + have hn : 0 ≤ v ^ β := Real.rpow_nonneg hv'.le _ + unfold resolventTangentKernel + rw [norm_smul, Real.norm_eq_abs, abs_of_nonneg hn] + calc + _ ≤ v ^ β * ((‖(Y + (δ + v) • 1)⁻¹‖ * ‖Z‖) * ‖(Y + (δ + v) • 1)⁻¹‖) := by + gcongr + exact (norm_mul_le _ _).trans (mul_le_mul_of_nonneg_right (norm_mul_le _ _) (norm_nonneg _)) + _ ≤ v ^ β * (((δ + v)⁻¹ * ‖Z‖) * (δ + v)⁻¹) := by gcongr + _ = ‖Z‖ * (v ^ β / (δ + v) ^ 2) := by rw [div_eq_mul_inv, ← inv_pow]; ring + +omit [Fintype n] in +lemma shifted_posDef {Y : Matrix n n ℂ} (hY : Y.PosSemidef) {a : ℝ} (ha : 0 < a) : + (Y + a • 1).PosDef := + PosDef.posSemidef_add hY ((PosDef.one : (1 : Matrix n n ℂ).PosDef).smul ha) + +lemma resolventMatrix_le {X Y : Matrix n n ℂ} (hX : X.PosSemidef) (hY : Y.PosSemidef) + {β δ v : ℝ} (hδ : 0 < δ) (hv : 0 < v) : + resolventMatrix β δ X v ≤ resolventMatrix β δ Y v + resolventTangentKernel β δ Y (X - Y) v := by + have ha : 0 < δ + v := by linarith + have ht := resolvent_tangent (shifted_posDef hY ha) (shifted_posDef hX ha) + have he : (X + (δ + v) • 1) - (Y + (δ + v) • 1) = X - Y := by abel + rw [he] at ht + have hh := add_le_add_left ht ((δ + v)⁻¹ • (1 : Matrix n n ℂ)) + have hsm := smul_le_smul_of_nonneg_left hh (Real.rpow_nonneg hv.le β) + convert! hsm using 1 <;> simp only [resolventMatrix, resolventTangentKernel, sub_eq_add_neg, + smul_add, add_assoc] <;> abel + +/-- Operator tangent inequality for every pair of positive Hermitian matrices, +with a fully convergent resolvent integral. -/ +lemma primitive_cfc_tangent {X Y : Matrix n n ℂ} (hX : X.PosSemidef) (hY : Y.PosSemidef) + {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) (hδ : 0 < δ) : + hX.isHermitian.cfc (regularizedPrimitive σ δ) ≤ + hY.isHermitian.cfc (regularizedPrimitive σ δ) + + resolventNormalization (σ - 1 / 2) • + ∫ v in Ioi (0 : ℝ), resolventTangentKernel (σ - 1 / 2) δ Y (X - Y) v := by + have hβ₀ : -1 < σ - 1 / 2 := by linarith + have hβ₁ : σ - 1 / 2 < 1 := by linarith + have hiX := integrable_resolventMatrix hX hβ₀ hβ₁ hδ + have hiY := integrable_resolventMatrix hY hβ₀ hβ₁ hδ + have hiT := integrable_resolventTangentKernel hY (X - Y) hβ₀ hβ₁ hδ + have hle := integral_mono_ae hiX (hiY.add hiT) (by + filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + exact resolventMatrix_le hX hY hδ hv) + simp only [Pi.add_apply] at hle + rw [integral_add hiY hiT] at hle + rw [primitive_cfc_resolvent_representation hX hσ₀ hσ₁ hδ, + primitive_cfc_resolvent_representation hY hσ₀ hσ₁ hδ, ← smul_add] + exact smul_le_smul_of_nonneg_left hle (resolvent_normalization_pos hβ₀ hβ₁).le + +end SharpLiebThirring.MatrixProof + + +namespace SharpLiebThirring.ScalarProof +open MeasureTheory Set + +def dividedPrimitive (σ δ x y : ℝ) : ℝ := + ∫ τ in Icc (0 : ℝ) 1, (τ * x + (1 - τ) * y + δ) ^ (σ - 3 / 2) + +lemma convex_combo_nonneg {x y τ : ℝ} (hx : 0 ≤ x) (hy : 0 ≤ y) + (hτ : τ ∈ Icc (0 : ℝ) 1) : 0 ≤ τ * x + (1 - τ) * y := + add_nonneg (mul_nonneg hτ.1 hx) (mul_nonneg (sub_nonneg.2 hτ.2) hy) + +lemma continuousOn_divided_integrand (σ : ℝ) {δ x y : ℝ} (hδ : 0 < δ) + (hx : 0 ≤ x) (hy : 0 ≤ y) : + ContinuousOn (fun τ : ℝ ↦ (τ * x + (1 - τ) * y + δ) ^ (σ - 3 / 2)) (Icc 0 1) := by + apply ContinuousOn.rpow_const (by fun_prop) + intro τ hτ + left + exact ne_of_gt (add_pos_of_nonneg_of_pos (convex_combo_nonneg hx hy hτ) hδ) + +lemma dividedPrimitive_self (σ δ x : ℝ) : + dividedPrimitive σ δ x x = (x + δ) ^ (σ - 3 / 2) := by + simp only [dividedPrimitive, show ∀ τ : ℝ, τ * x + (1 - τ) * x = x by intro τ; ring] + simp + +lemma dividedPrimitive_mul_sub (σ : ℝ) {δ x y : ℝ} (hδ : 0 < δ) + (hx : 0 ≤ x) (hy : 0 ≤ y) : + (x - y) * dividedPrimitive σ δ x y = + regularizedPrimitive σ δ x - regularizedPrimitive σ δ y := by + have hd (τ : ℝ) (hτ : τ ∈ uIcc (0 : ℝ) 1) : + HasDerivAt (fun t : ℝ ↦ regularizedPrimitive σ δ (t * x + (1 - t) * y)) + ((x - y) * (τ * x + (1 - τ) * y + δ) ^ (σ - 3 / 2)) τ := by + have hc : HasDerivAt (fun t : ℝ ↦ t * x + (1 - t) * y) (x - y) τ := by + convert! ((hasDerivAt_id τ).mul_const x).add + (((hasDerivAt_const τ (1 : ℝ)).sub (hasDerivAt_id τ)).mul_const y) using 1; ring + have hp := (primitive_hasDerivAt σ hδ (τ * x + (1 - τ) * y)).comp τ hc + rw [max_eq_left (convex_combo_nonneg hx hy (by simpa using hτ))] at hp + convert! hp using 1; ring + have he := intervalIntegral.integral_eq_sub_of_hasDerivAt hd + (((continuousOn_divided_integrand σ hδ hx hy).const_mul (x - y)).intervalIntegrable_of_Icc zero_le_one) + simp only [one_mul, sub_self, zero_mul, add_zero, sub_zero, zero_add] at he + rw [intervalIntegral.integral_const_mul, intervalIntegral.integral_of_le zero_le_one, + ← integral_Icc_eq_integral_Ioc] at he + exact he + +lemma mixed_resolvent_integrable {β δ x y : ℝ} (hβ₀ : -1 < β) (hβ₁ : β < 1) + (hδ : 0 < δ) (hx : 0 ≤ x) (hy : 0 ≤ y) : + IntegrableOn (fun v : ℝ ↦ v ^ β / ((x + δ + v) * (y + δ + v))) (Ioi 0) := by + have hc : ContinuousOn (fun v : ℝ ↦ v ^ β / ((x + δ + v) * (y + δ + v))) (Ioi 0) := by + apply ContinuousOn.div + · exact continuousOn_id.rpow_const (fun _ hv ↦ Or.inl (ne_of_gt hv)) + · fun_prop + · intro v hv + have hv' : 0 < v := hv + exact mul_ne_zero (by linarith) (by linarith) + apply (resolvent_kernel_integrable hβ₀ hβ₁ hδ).mono' + (hc.aestronglyMeasurable measurableSet_Ioi) + filter_upwards [ae_restrict_mem measurableSet_Ioi] with v hv + have hv' : 0 < v := hv + have h1 : 0 < x + δ + v := by linarith + have h2 : 0 < y + δ + v := by linarith + rw [Real.norm_eq_abs, abs_of_nonneg (div_nonneg (Real.rpow_nonneg hv'.le _) (mul_pos h1 h2).le)] + apply div_le_div_of_nonneg_left (Real.rpow_nonneg hv'.le _) (sq_pos_of_pos (add_pos hδ hv')) + nlinarith [mul_nonneg hx hy, mul_nonneg hx (add_pos hδ hv').le, + mul_nonneg hy (add_pos hδ hv').le] + +/-- The divided-difference coefficient, including coincident eigenvalues. -/ +lemma mixed_resolvent_eq_divided {σ δ x y : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hδ : 0 < δ) (hx : 0 ≤ x) (hy : 0 ≤ y) : + resolventNormalization (σ - 1 / 2) * + (∫ v in Ioi (0 : ℝ), v ^ (σ - 1 / 2) / ((x + δ + v) * (y + δ + v))) = + dividedPrimitive σ δ x y := by + have hβ₀ : -1 < σ - 1 / 2 := by linarith + have hβ₁ : σ - 1 / 2 < 1 := by linarith + by_cases hxy : x = y + · subst y + simp only [dividedPrimitive_self, ← pow_two] + rw [resolvent_kernel_integral_scale _ (show 0 < x + δ by linarith)] + unfold resolventNormalization + have hn := (resolvent_kernel_integral_pos hβ₀ hβ₁ zero_lt_one).ne' + rw [mul_left_comm, inv_mul_cancel₀ hn, mul_one] + congr 1 + ring + · apply mul_left_cancel₀ (sub_ne_zero.mpr hxy) + rw [dividedPrimitive_mul_sub _ hδ hx hy, + primitive_resolvent_representation hσ₀ hσ₁ hδ hx, + primitive_resolvent_representation hσ₀ hσ₁ hδ hy, ← mul_sub, + ← integral_sub (resolvent_difference_integrable hβ₀ hβ₁ hδ (by linarith)) + (resolvent_difference_integrable hβ₀ hβ₁ hδ (by linarith))] + rw [mul_left_comm, ← integral_const_mul] + congr 1 + apply setIntegral_congr_fun measurableSet_Ioi + intro v hv + have hv' : 0 < v := hv + unfold resolventDifference + have ha : x + δ + v ≠ 0 := by linarith + have hb : y + δ + v ≠ 0 := by linarith + field_simp + ring + +end SharpLiebThirring.ScalarProof + +noncomputable section +open Matrix Unitary MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder CStarAlgebra +namespace SharpLiebThirring.MatrixProof +variable {n : Type u10} [Fintype n] [DecidableEq n] + +def diagonalStarAlgHom : (n → ℂ) →⋆ₐ[ℝ] Matrix n n ℂ := + { diagonalAlgHom ℝ with + map_star' := by + intro x + ext i j + by_cases hij : i = j + · subst j; simp [star_apply] + · simp [star_apply, hij, Ne.symm hij] } + +lemma cfc_diagonal_real (f : ℝ → ℝ) (x : n → ℝ) (hf : Continuous f) : + cfc f (diagonal (fun i ↦ (x i : ℂ))) = diagonal (fun i ↦ (f (x i) : ℂ)) := by + have : ContinuousFunctionalCalculus ℝ (n → ℂ) IsSelfAdjoint := + (IsSelfAdjoint.instIsometricContinuousFunctionalCalculus (A := n → ℂ)).toContinuousFunctionalCalculus + have hself : IsSelfAdjoint (fun i ↦ (x i : ℂ)) := by ext i; simp + change cfc f (diagonalStarAlgHom (fun i ↦ (x i : ℂ))) = _ + erw [← (diagonalStarAlgHom (n := n)).map_cfc f (fun i ↦ (x i : ℂ)) hf.continuousOn + (by change Continuous (diagonal : (n → ℂ) → Matrix n n ℂ); fun_prop) hself + (isHermitian_diagonal_iff.2 fun i ↦ by simp [IsSelfAdjoint])] + rw [cfc_map_pi (S := ℝ) f _ hf.continuousOn hself (fun i ↦ by simp [IsSelfAdjoint])] + change diagonal (fun i ↦ cfc f (x i : ℂ)) = diagonal (fun i ↦ (f (x i) : ℂ)) + apply congrArg diagonal + funext i + exact cfc_algebraMap (R := ℝ) (A := ℂ) (x i) f + +lemma inverse_diagonal_real (x : n → ℝ) (hx : ∀ i, x i ≠ 0) : + (diagonal (fun i ↦ (x i : ℂ)))⁻¹ = diagonal (fun i ↦ ((x i)⁻¹ : ℂ)) := by + apply Matrix.inv_eq_right_inv + ext i j + simp only [diagonal_mul_diagonal] + by_cases hij : i = j + · subst j; simp [hx] + · simp [hij] + +omit [Fintype n] in +lemma shifted_diagonal_real (x : n → ℝ) (a : ℝ) : + diagonal (fun i ↦ (x i : ℂ)) + a • (1 : Matrix n n ℂ) = + diagonal (fun i ↦ ((x i + a : ℝ) : ℂ)) := by + ext i j + by_cases hij : i = j + · subst j; simp + · simp [hij] + +end SharpLiebThirring.MatrixProof + + +namespace SharpLiebThirring.MatrixProof +open ScalarProof Matrix MeasureTheory Set +open scoped Matrix.Norms.L2Operator MatrixOrder ComplexOrder +variable {n : Type u11} [Fintype n] [DecidableEq n] + +omit [Fintype n] in +lemma diagonal_real_posSemidef (x : n → ℝ) (hx : ∀ i, 0 ≤ x i) : + (diagonal (fun i ↦ (x i : ℂ))).PosSemidef := + posSemidef_diagonal_iff.2 (fun i ↦ by exact_mod_cast hx i) + +lemma resolventTangentKernel_diagonal {δ : ℝ} (hδ : 0 < δ) (β : ℝ) + (x : n → ℝ) (hx : ∀ i, 0 ≤ x i) (Z : Matrix n n ℂ) {v : ℝ} (hv : 0 < v) (i j : n) : + resolventTangentKernel β δ (diagonal (fun i ↦ (x i : ℂ))) Z v i j = + ((v ^ β / ((x i + δ + v) * (x j + δ + v)) : ℝ) : ℂ) * Z i j := by + unfold resolventTangentKernel + rw [shifted_diagonal_real, inverse_diagonal_real _ (fun i ↦ by have := hx i; linarith)] + simp only [Matrix.smul_apply, Complex.real_smul, mul_diagonal, diagonal_mul] + simp only [div_eq_mul_inv, _root_.mul_inv_rev] + push_cast + ring + +lemma integral_resolventTangent_diagonal {σ δ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hδ : 0 < δ) (x : n → ℝ) (hx : ∀ i, 0 ≤ x i) (Z : Matrix n n ℂ) : + resolventNormalization (σ - 1 / 2) • + ∫ v in Ioi (0 : ℝ), resolventTangentKernel (σ - 1 / 2) δ + (diagonal (fun i ↦ (x i : ℂ))) Z v = + fun i j ↦ (dividedPrimitive σ δ (x i) (x j) : ℂ) * Z i j := by + have hi := integrable_resolventTangentKernel (diagonal_real_posSemidef x hx) Z + (show -1 < σ - 1 / 2 by linarith) (show σ - 1 / 2 < 1 by linarith) hδ + ext i j + have he := (entryCLM i j).integral_comp_comm hi + simp only [entryCLM_apply] at he + simp only [Matrix.smul_apply] + rw [← he] + have he' : (∫ v in Ioi (0 : ℝ), resolventTangentKernel (σ - 1 / 2) δ + (diagonal (fun i ↦ (x i : ℂ))) Z v i j) = + (∫ v in Ioi (0 : ℝ), ((v ^ (σ - 1 / 2) / ((x i + δ + v) * + (x j + δ + v)) : ℝ) : ℂ)) * Z i j := by + rw [← integral_mul_const] + apply setIntegral_congr_fun measurableSet_Ioi + intro v hv + exact resolventTangentKernel_diagonal hδ _ x hx Z hv i j + rw [he'] + erw [integral_ofReal] + rw [Complex.real_smul, ← mul_assoc] + change (resolventNormalization (σ - 1 / 2) : ℂ) * + ((∫ v in Ioi (0 : ℝ), v ^ (σ - 1 / 2) / ((x i + δ + v) * (x j + δ + v)) : ℝ) : ℂ) * + Z i j = _ + rw [← Complex.ofReal_mul, mixed_resolvent_eq_divided hσ₀ hσ₁ hδ (hx i) (hx j)] + +end SharpLiebThirring.MatrixProof + + +namespace SharpLiebThirring.ScalarProof +open MeasureTheory Set + +def quadraticDividedIntegrand (σ δ d x y s τ : ℝ) : ℝ := + (max (τ * ((s - x) ^ 2 + d) + (1 - τ) * ((s - y) ^ 2 + d)) 0 + δ) ^ (σ - 3 / 2) + +lemma quadratic_combo (d x y s τ : ℝ) : + τ * ((s - x) ^ 2 + d) + (1 - τ) * ((s - y) ^ 2 + d) = + (s - (τ * x + (1 - τ) * y)) ^ 2 + (d + τ * (1 - τ) * (x - y) ^ 2) := by ring + +lemma quadraticDivided_integrable_left {σ δ : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (d x y τ : ℝ) : Integrable (fun s ↦ quadraticDividedIntegrand σ δ d x y s τ) := by + have hi := shifted_derivative_integrable hσ hδ (d + τ * (1 - τ) * (x - y) ^ 2) + have hp := (measurePreserving_sub_right (volume : Measure ℝ) (τ * x + (1 - τ) * y)).integrable_comp + hi.aestronglyMeasurable |>.2 hi + simpa only [Function.comp_def, quadraticDividedIntegrand, quadratic_combo] using hp + +lemma integral_quadraticDivided_left {σ δ d τ : ℝ} (hδ : 0 < δ) (hd : 0 ≤ d) + (hτ : τ ∈ Icc (0 : ℝ) 1) (x y : ℝ) : + (∫ s : ℝ, quadraticDividedIntegrand σ δ d x y s τ) = + (d + δ + τ * (1 - τ) * (x - y) ^ 2) ^ (σ - 1) * + ∫ s : ℝ, (1 + s ^ 2) ^ (σ - 3 / 2) := by + have hz : 0 ≤ d + τ * (1 - τ) * (x - y) ^ 2 := by + exact add_nonneg hd (mul_nonneg (mul_nonneg hτ.1 (sub_nonneg.2 hτ.2)) (sq_nonneg _)) + have ha : 0 < d + δ + τ * (1 - τ) * (x - y) ^ 2 := by linarith + have he (s : ℝ) : quadraticDividedIntegrand σ δ d x y s τ = + ((s - (τ * x + (1 - τ) * y)) ^ 2 + (d + δ + τ * (1 - τ) * (x - y) ^ 2)) ^ + (σ - 3 / 2) := by + unfold quadraticDividedIntegrand + rw [quadratic_combo, max_eq_left (add_nonneg (sq_nonneg _) hz)] + congr 1 + ring + simp_rw [he] + rw [integral_sub_right_eq_self (fun s : ℝ ↦ (s ^ 2 + (d + δ + τ * (1 - τ) * (x - y) ^ 2)) ^ + (σ - 3 / 2)), quadratic_integral_scale _ ha] + congr 2 + ring + +lemma quadraticDivided_integrable_prod {σ δ d : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (hd : 0 ≤ d) (x y : ℝ) : + Integrable (fun p : ℝ × ℝ ↦ quadraticDividedIntegrand σ δ d x y p.1 p.2) + (volume.prod (volume.restrict (Icc (0 : ℝ) 1))) := by + have hc : Continuous (fun p : ℝ × ℝ ↦ quadraticDividedIntegrand σ δ d x y p.1 p.2) := + (derivative_continuous σ hδ).comp (by fun_prop) + apply (integrable_prod_iff' hc.aestronglyMeasurable).2 + constructor + · exact Filter.Eventually.of_forall (quadraticDivided_integrable_left hσ hδ d x y) + · have hv : ContinuousOn (fun τ : ℝ ↦ + (d + δ + τ * (1 - τ) * (x - y) ^ 2) ^ (σ - 1) * + ∫ s : ℝ, (1 + s ^ 2) ^ (σ - 3 / 2)) (Icc 0 1) := by + apply ContinuousOn.mul _ continuousOn_const + apply ContinuousOn.rpow_const (by fun_prop) + intro τ hτ + left + have hz : 0 ≤ τ * (1 - τ) * (x - y) ^ 2 := + mul_nonneg (mul_nonneg hτ.1 (sub_nonneg.2 hτ.2)) (sq_nonneg _) + linarith + apply hv.integrableOn_Icc.congr + filter_upwards [ae_restrict_mem measurableSet_Icc] with τ hτ + rw [← integral_quadraticDivided_left hδ hd hτ x y] + apply integral_congr_ae + filter_upwards [] with s + rw [Real.norm_eq_abs, abs_of_nonneg (show 0 ≤ quadraticDividedIntegrand σ δ d x y s τ by + unfold quadraticDividedIntegrand; positivity)] + +/-- Absolute convergence of the integrated tangent coefficients. -/ +lemma integrable_divided_quadratic {σ δ d : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (hd : 0 ≤ d) (x y : ℝ) : + Integrable (fun s ↦ dividedPrimitive σ δ ((s - x) ^ 2 + d) ((s - y) ^ 2 + d)) := by + have hi := (quadraticDivided_integrable_prod hσ hδ hd x y).integral_prod_left + apply hi.congr + filter_upwards [] with s + unfold dividedPrimitive + apply setIntegral_congr_fun measurableSet_Icc + intro τ hτ + unfold quadraticDividedIntegrand + rw [max_eq_left (convex_combo_nonneg (add_nonneg (sq_nonneg _) hd) + (add_nonneg (sq_nonneg _) hd) hτ)] + +/-- The integrated tangent kernel. -/ +lemma integral_divided_quadratic {σ δ d : ℝ} (hσ : σ < 1) (hδ : 0 < δ) + (hd : 0 ≤ d) (x y : ℝ) : + fieldNormalization σ * + (∫ s : ℝ, dividedPrimitive σ δ ((s - x) ^ 2 + d) ((s - y) ^ 2 + d)) = + σ * (d + δ) ^ (σ - 1) * + ∫ τ in Icc (0 : ℝ) 1, + (1 + τ * (1 - τ) / (d + δ) * (x - y) ^ 2) ^ (σ - 1) := by + have ha : 0 < d + δ := by linarith + have hn := (normalization_integral_pos hσ).ne' + have he (s : ℝ) : dividedPrimitive σ δ ((s - x) ^ 2 + d) ((s - y) ^ 2 + d) = + ∫ τ in Icc (0 : ℝ) 1, quadraticDividedIntegrand σ δ d x y s τ := by + unfold dividedPrimitive + apply setIntegral_congr_fun measurableSet_Icc + intro τ hτ + unfold quadraticDividedIntegrand + rw [max_eq_left (convex_combo_nonneg (add_nonneg (sq_nonneg _) hd) + (add_nonneg (sq_nonneg _) hd) hτ)] + simp_rw [he] + rw [integral_integral_swap (quadraticDivided_integrable_prod hσ hδ hd x y)] + have he' : (∫ τ in Icc (0 : ℝ) 1, ∫ s : ℝ, quadraticDividedIntegrand σ δ d x y s τ) = + ((d + δ) ^ (σ - 1) * ∫ s : ℝ, (1 + s ^ 2) ^ (σ - 3 / 2)) * + ∫ τ in Icc (0 : ℝ) 1, + (1 + τ * (1 - τ) / (d + δ) * (x - y) ^ 2) ^ (σ - 1) := by + rw [← integral_const_mul] + apply setIntegral_congr_fun measurableSet_Icc + intro τ hτ + dsimp only + rw [integral_quadraticDivided_left (σ := σ) hδ hd hτ x y] + have hp : 0 ≤ 1 + τ * (1 - τ) / (d + δ) * (x - y) ^ 2 := by + have := mul_nonneg (div_nonneg (mul_nonneg hτ.1 (sub_nonneg.2 hτ.2)) ha.le) (sq_nonneg (x - y)) + linarith + rw [show d + δ + τ * (1 - τ) * (x - y) ^ 2 = + (d + δ) * (1 + τ * (1 - τ) / (d + δ) * (x - y) ^ 2) by field_simp, + Real.mul_rpow ha.le hp] + ring + rw [he'] + unfold fieldNormalization + calc + _ = (σ / (∫ s : ℝ, (1 + s ^ 2) ^ (σ - 3 / 2)) * + (∫ s : ℝ, (1 + s ^ 2) ^ (σ - 3 / 2))) * ((d + δ) ^ (σ - 1) * + ∫ τ in Icc (0 : ℝ) 1, (1 + τ * (1 - τ) / (d + δ) * (x - y) ^ 2) ^ (σ - 1)) := by ring + _ = _ := by rw [div_mul_cancel₀ _ hn]; ring + +end SharpLiebThirring.ScalarProof + +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/RowSigns.lean b/lean/OAI/Analysis/LiebThirring/RowSigns.lean new file mode 100644 index 0000000000000000000000000000000000000000..c14c3a55ed21145d8332ee60841e4b4b60518840 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/RowSigns.lean @@ -0,0 +1,532 @@ +import OAI.Analysis.LiebThirring.Continuation + +namespace OAI + +noncomputable section +open Finset +noncomputable section +open Finset +noncomputable section +open Finset + +namespace SharpLiebThirring.ContinuationGap +open Matrix Set + +abbrev LowerSpace (N : ℕ) := + {C : Matrix (Fin N) (Fin N) ℝ // ∀ i j, i < j → C i j = 0} + +def rowSign {N : ℕ} (s : Fin N → ℝ) (C : LowerSpace N) : LowerSpace N := + ⟨fun i j ↦ s i * C.val i j, by + intro i j hij + change s i * C.val i j = 0 + rw [C.prop i j hij, mul_zero]⟩ + +def signConjugate {N : ℕ} (s : Fin N → ℝ) (Z : Matrix (Fin N) (Fin N) ℝ) : + Matrix (Fin N) (Fin N) ℝ := fun i j ↦ s i * Z i j * s j + +def NonzeroRows {N : ℕ} (C : LowerSpace N) : Prop := ∀ i, ∃ j, C.val i j ≠ 0 + +end SharpLiebThirring.ContinuationGap +namespace SharpLiebThirring.PathTopology +open Matrix SharpLiebThirring.CubeFlags SharpLiebThirring.ContinuationGap + +abbrev LowerIndex (N : ℕ) := {a : Fin N × Fin N // a.2 ≤ a.1} +abbrev lowerDim (N : ℕ) := Fintype.card (LowerIndex N) +noncomputable def indexEquiv (N : ℕ) : LowerIndex N ≃ Fin (lowerDim N) := Fintype.equivFin _ + +def diagonalIndex {N : ℕ} (i : Fin N) : Fin (lowerDim N) := indexEquiv N ⟨(i,i),le_refl _⟩ +def rowIndex {N : ℕ} (a : Fin (lowerDim N)) : Fin N := ((indexEquiv N).symm a).val.1 +def colIndex {N : ℕ} (a : Fin (lowerDim N)) : Fin N := ((indexEquiv N).symm a).val.2 + +@[simp] lemma rowIndex_diagonal {N : ℕ} (i : Fin N) : rowIndex (diagonalIndex i) = i := by + simp [rowIndex,diagonalIndex] +@[simp] lemma colIndex_diagonal {N : ℕ} (i : Fin N) : colIndex (diagonalIndex i) = i := by + simp [colIndex,diagonalIndex] +lemma colIndex_le_rowIndex {N : ℕ} (a : Fin (lowerDim N)) : colIndex a ≤ rowIndex a := + ((indexEquiv N).symm a).prop + +/-- Exact linear coordinates on the entire lower-triangular coefficient space; +no nonvanishing or invertibility restriction is imposed. -/ +def lowerOfCoords {N : ℕ} (x : Fin (lowerDim N) → ℝ) : LowerSpace N := + ⟨fun i j ↦ if h : j ≤ i then x (indexEquiv N ⟨(i,j),h⟩) else 0, + by intro i j hij; simp only [not_le.mpr hij,↓reduceDIte]⟩ +def lowerCoords {N : ℕ} (C : LowerSpace N) : Fin (lowerDim N) → ℝ := + fun a ↦ C.val (rowIndex a) (colIndex a) + +@[simp] lemma lowerCoords_lowerOfCoords {N : ℕ} (x : Fin (lowerDim N) → ℝ) : + lowerCoords (lowerOfCoords x) = x := by + funext a + have he : (⟨(rowIndex a,colIndex a),colIndex_le_rowIndex a⟩ : LowerIndex N) = (indexEquiv N).symm a := rfl + simp only [lowerCoords,lowerOfCoords,colIndex_le_rowIndex,↓reduceDIte,he,Equiv.apply_symm_apply] + +@[simp] lemma lowerOfCoords_lowerCoords {N : ℕ} (C : LowerSpace N) : + lowerOfCoords (lowerCoords C) = C := by + apply Subtype.ext + funext i j + dsimp [lowerOfCoords] + split_ifs with h + · simp [lowerCoords,rowIndex,colIndex] + · exact (C.prop i j (lt_of_not_ge h)).symm + +lemma continuous_lowerCoords {N : ℕ} : Continuous (lowerCoords (N := N)) := by + apply continuous_pi + intro a + exact (continuous_apply _).comp ((continuous_apply _).comp continuous_subtype_val) +lemma continuous_lowerOfCoords {N : ℕ} : Continuous (lowerOfCoords (N := N)) := by + apply Continuous.subtype_mk + apply continuous_pi + intro i + apply continuous_pi + intro j + by_cases h : j ≤ i + · simpa only [lowerOfCoords,h,↓reduceDIte] using (continuous_apply (indexEquiv N ⟨(i,j),h⟩)) + · simpa only [lowerOfCoords,h,↓reduceDIte] using (continuous_const : Continuous (fun _ : Fin (lowerDim N) → ℝ ↦ (0 : ℝ))) + +def lowerHomeomorph (N : ℕ) : (Fin (lowerDim N) → ℝ) ≃ₜ LowerSpace N where + toFun := lowerOfCoords + invFun := lowerCoords + left_inv := lowerCoords_lowerOfCoords + right_inv := lowerOfCoords_lowerCoords + continuous_toFun := continuous_lowerOfCoords + continuous_invFun := continuous_lowerCoords + +/-- Coordinate reflections that flip whole rows and fix the homotopy time. -/ +def rowSubgroup (N : ℕ) : Subgroup (Signs (lowerDim N + 1)) where + carrier := {s | s.val (Fin.last (lowerDim N)) = false ∧ + ∀ a : Fin (lowerDim N), s.val a.castSucc = s.val (diagonalIndex (rowIndex a)).castSucc} + one_mem' := ⟨rfl,fun _ ↦ rfl⟩ + mul_mem' hs ht := ⟨by simp only [Signs.mul_val,hs.1,ht.1,Bool.false_xor], + fun a ↦ by simp only [Signs.mul_val,hs.2 a,ht.2 a]⟩ + inv_mem' hs := hs + +def rowBool {N : ℕ} (s : rowSubgroup N) (i : Fin N) : Bool := + s.val.val (diagonalIndex i).castSucc +lemma rowSubgroup_time {N : ℕ} (s : rowSubgroup N) : s.val.val (Fin.last (lowerDim N)) = false := s.prop.1 +lemma rowSubgroup_coord {N : ℕ} (s : rowSubgroup N) (a : Fin (lowerDim N)) : + s.val.val a.castSucc = rowBool s (rowIndex a) := s.prop.2 a + +@[simp] lemma rowBool_one {N : ℕ} (i : Fin N) : rowBool (1 : rowSubgroup N) i = false := rfl +@[simp] lemma rowBool_mul {N : ℕ} (s t : rowSubgroup N) (i : Fin N) : + rowBool (s*t) i = xor (rowBool s i) (rowBool t i) := rfl + +lemma rowBool_injective {N : ℕ} : Function.Injective (rowBool (N := N)) := by + intro s t h + apply Subtype.ext + apply Signs.ext + funext a + refine Fin.lastCases ?_ (fun b ↦ ?_) a + · rw [rowSubgroup_time,rowSubgroup_time] + · rw [rowSubgroup_coord,rowSubgroup_coord,h] + +def rowElement {N : ℕ} (s : Fin N → Bool) : rowSubgroup N := + ⟨⟨Fin.snoc (fun a ↦ s (rowIndex a)) false⟩,by + constructor + · simp only [Fin.snoc_last] + · intro a + simp only [Fin.snoc_castSucc,rowIndex_diagonal]⟩ +@[simp] lemma rowBool_rowElement {N : ℕ} (s : Fin N → Bool) : rowBool (rowElement s) = s := by + funext i + simp only [rowBool,rowElement,Fin.snoc_castSucc,rowIndex_diagonal] + +def signValue (b : Bool) : ℝ := if b then -1 else 1 +@[simp] lemma signValue_false : signValue false = 1 := rfl +@[simp] lemma signValue_true : signValue true = -1 := rfl +lemma signValue_cases (b : Bool) : signValue b = 1 ∨ signValue b = -1 := by cases b <;> simp [signValue] +lemma signValue_xor (b c : Bool) : signValue (xor b c) = signValue b * signValue c := by + cases b <;> cases c <;> norm_num [signValue] +lemma signValue_smul (b : Bool) (x : ℝ) : (if b then -x else x) = signValue b * x := by + cases b <;> simp [signValue] + +def conjugateSigns {N : ℕ} (s : rowSubgroup N) : Signs (lowerDim N) := + ⟨fun a ↦ xor (rowBool s (rowIndex a)) (rowBool s (colIndex a))⟩ + +def conjugateRepresentation (N : ℕ) : rowSubgroup N →* ((Fin (lowerDim N) → ℝ) ≃ₗ[ℝ] (Fin (lowerDim N) → ℝ)) where + toFun s := (conjugateSigns s).linearIsometry.toLinearEquiv + map_one' := by + ext x a + simp only [conjugateSigns,Signs.linearIsometry,rowBool_one,Bool.false_xor,Bool.false_eq_true,↓reduceIte] + rfl + map_mul' s t := by + ext x a + change (if xor (rowBool (s*t) (rowIndex a)) (rowBool (s*t) (colIndex a)) then -x a else x a) = + if xor (rowBool s (rowIndex a)) (rowBool s (colIndex a)) then + -(if xor (rowBool t (rowIndex a)) (rowBool t (colIndex a)) then -x a else x a) else + if xor (rowBool t (rowIndex a)) (rowBool t (colIndex a)) then -x a else x a + simp only [rowBool_mul] + rcases Bool.eq_false_or_eq_true (rowBool s (rowIndex a)) with h₁ | h₁ <;> + rcases Bool.eq_false_or_eq_true (rowBool s (colIndex a)) with h₂ | h₂ <;> + rcases Bool.eq_false_or_eq_true (rowBool t (rowIndex a)) with h₃ | h₃ <;> + rcases Bool.eq_false_or_eq_true (rowBool t (colIndex a)) with h₄ | h₄ <;> simp [h₁,h₂,h₃,h₄] + +lemma conjugateRepresentation_norm {N : ℕ} (s : rowSubgroup N) (x : Fin (lowerDim N) → ℝ) : + ‖conjugateRepresentation N s x‖ = ‖x‖ := (conjugateSigns s).linearIsometry.norm_map x +lemma conjugateRepresentation_apply {N : ℕ} (s : rowSubgroup N) (x : Fin (lowerDim N) → ℝ) + (a : Fin (lowerDim N)) : + conjugateRepresentation N s x a = signValue (rowBool s (rowIndex a)) * x a * signValue (rowBool s (colIndex a)) := by + change (if xor (rowBool s (rowIndex a)) (rowBool s (colIndex a)) then -x a else x a) = _ + rw [signValue_smul,signValue_xor] + ring + +end SharpLiebThirring.PathTopology +namespace SharpLiebThirring.PathTopology +open Matrix SharpLiebThirring.CubeFlags SharpLiebThirring.ContinuationGap + +/-- Lower-coordinate restriction is faithful on symmetric matrices. -/ +def matrixCoords {N : ℕ} (A : Matrix (Fin N) (Fin N) ℝ) : Fin (lowerDim N) → ℝ := + fun a ↦ A (rowIndex a) (colIndex a) +lemma continuous_matrixCoords {N : ℕ} : Continuous (matrixCoords (N := N)) := by + apply continuous_pi + intro a + exact (continuous_apply _).comp (continuous_apply _) +lemma matrixCoords_eq_zero {N : ℕ} {A : Matrix (Fin N) (Fin N) ℝ} + (hA : A.IsHermitian) (h : matrixCoords A = 0) : A = 0 := by + have hl (i j : Fin N) (hji : j ≤ i) : A i j = 0 := by + have he := congrFun h (indexEquiv N ⟨(i,j),hji⟩) + simpa [matrixCoords,rowIndex,colIndex] using he + ext i j + rcases le_total j i with hj | hi + · exact hl i j hj + · have hs : A j i = A i j := by simpa using congrArg (fun B ↦ B i j) hA + exact hs.symm.trans (hl j i hi) + +def diagonalLower {N : ℕ} (c : Fin N → ℝ) : LowerSpace N := + ⟨diagonal c,fun _i _j hij ↦ diagonal_apply_ne c (ne_of_lt hij)⟩ +def diagonalPoint {N : ℕ} (c : Fin N → ℝ) : Fin (lowerDim N) → ℝ := lowerCoords (diagonalLower c) +@[simp] lemma lowerOfCoords_diagonalPoint {N : ℕ} (c : Fin N → ℝ) : + lowerOfCoords (diagonalPoint c) = diagonalLower c := lowerOfCoords_lowerCoords _ + +def lowerEntry {N : ℕ} (i j : Fin N) : (Fin (lowerDim N) → ℝ) →L[ℝ] ℝ := + if h : j ≤ i then ContinuousLinearMap.proj (indexEquiv N ⟨(i,j),h⟩) else 0 +lemma lowerEntry_apply {N : ℕ} (i j : Fin N) (x : Fin (lowerDim N) → ℝ) : + lowerEntry i j x = (lowerOfCoords x).val i j := by + dsimp [lowerEntry,lowerOfCoords] + split_ifs <;> rfl +lemma lowerEntry_diagonal {N : ℕ} (i j : Fin N) (c : Fin N → ℝ) : + lowerEntry i j (diagonalPoint c) = diagonal c i j := by + rw [lowerEntry_apply,lowerOfCoords_diagonalPoint] + rfl + +def initialMap {N : ℕ} (β : ℝ) (k : Fin N → ℝ) (x : Fin (lowerDim N) → ℝ) : Fin (lowerDim N) → ℝ := + matrixCoords (2 • diagonal k - β • ((lowerOfCoords x).val * (lowerOfCoords x).val.transpose)) + +def jacobianWeight {N : ℕ} (β : ℝ) (c : Fin N → ℝ) (a : Fin (lowerDim N)) : ℝ := + -β * (c (colIndex a) + if rowIndex a = colIndex a then c (rowIndex a) else 0) +lemma jacobianWeight_ne_zero {N : ℕ} {β : ℝ} (hβ : β ≠ 0) (c : Fin N → ℝ) + (hc : ∀ i, 0 < c i) (a : Fin (lowerDim N)) : jacobianWeight β c a ≠ 0 := by + unfold jacobianWeight + apply mul_ne_zero (neg_ne_zero.mpr hβ) + apply ne_of_gt + split_ifs + · exact add_pos (hc _) (hc _) + · simpa using hc (colIndex a) + +def initialLinearEquiv {N : ℕ} (β : ℝ) (hβ : β ≠ 0) (c : Fin N → ℝ) (hc : ∀ i, 0 < c i) : + (Fin (lowerDim N) → ℝ) ≃ₗ[ℝ] (Fin (lowerDim N) → ℝ) := + LinearEquiv.piCongrRight (fun a ↦ LinearEquiv.smulOfNeZero ℝ ℝ (jacobianWeight β c a) (jacobianWeight_ne_zero hβ c hc a)) + +lemma initialLinearEquiv_apply {N : ℕ} (β : ℝ) (hβ : β ≠ 0) (c : Fin N → ℝ) (hc : ∀ i, 0 < c i) + (x : Fin (lowerDim N) → ℝ) (a : Fin (lowerDim N)) : + initialLinearEquiv β hβ c hc x a = jacobianWeight β c a * x a := rfl + +lemma initialMap_hasFDerivAt {N : ℕ} (β : ℝ) (hβ : β ≠ 0) (k c : Fin N → ℝ) (hc : ∀ i, 0 < c i) : + HasFDerivAt (initialMap β k) + (initialLinearEquiv β hβ c hc).toContinuousLinearEquiv.toContinuousLinearMap (diagonalPoint c) := by + classical + let p := diagonalPoint c + let D := fun a : Fin (lowerDim N) ↦ -(β • ∑ m : Fin N, + ((lowerEntry (rowIndex a) m p) • lowerEntry (colIndex a) m + + (lowerEntry (colIndex a) m p) • lowerEntry (rowIndex a) m)) + have hd : HasFDerivAt (initialMap β k) (ContinuousLinearMap.pi D) p := by + apply hasFDerivAt_pi.mpr + intro a + have hsum := HasFDerivAt.fun_sum (x := p) (u := Finset.univ) (fun m _ ↦ + (lowerEntry (rowIndex a) m).hasFDerivAt.mul (lowerEntry (colIndex a) m).hasFDerivAt) + convert (hsum.const_mul β).const_sub ((2 • diagonal k) (rowIndex a) (colIndex a)) using 1 + · funext x + simp only [initialMap,matrixCoords,Matrix.sub_apply,Matrix.smul_apply,Matrix.mul_apply, + transpose_apply,smul_eq_mul,Pi.mul_apply,lowerEntry_apply] + have hD : ContinuousLinearMap.pi D = + (initialLinearEquiv β hβ c hc).toContinuousLinearEquiv.toContinuousLinearMap := by + ext x a + simp only [ContinuousLinearMap.pi_apply,ContinuousLinearEquiv.coe_coe] + change D a x = jacobianWeight β c a * x a + dsimp [D,p] + simp only [_root_.neg_apply,_root_.smul_apply,_root_.sum_apply, + _root_.add_apply,smul_eq_mul,lowerEntry_diagonal,Finset.sum_add_distrib] + rw [Finset.sum_eq_single (rowIndex a),Finset.sum_eq_single (colIndex a)] + · simp only [diagonal_apply_eq,lowerEntry_apply] + have ha : (lowerOfCoords x).val (rowIndex a) (colIndex a) = x a := + congrFun (lowerCoords_lowerOfCoords x) a + rw [ha] + by_cases he : rowIndex a = colIndex a + · rw [he] at ha ⊢ + rw [ha] + simp only [jacobianWeight,he,↓reduceIte] + ring + · have hlt : colIndex a < rowIndex a := lt_of_le_of_ne (colIndex_le_rowIndex a) (Ne.symm he) + rw [(lowerOfCoords x).prop _ _ hlt] + simp only [jacobianWeight,he,↓reduceIte] + ring + · intro m _ hm + rw [diagonal_apply_ne _ hm.symm,zero_mul] + · simp only [Finset.mem_univ,not_true_eq_false,false_implies] + · intro m _ hm + rw [diagonal_apply_ne _ hm.symm,zero_mul] + · simp only [Finset.mem_univ,not_true_eq_false,false_implies] + rwa [hD] at hd + +end SharpLiebThirring.PathTopology +namespace SharpLiebThirring.PathTopology +open Matrix SharpLiebThirring.CubeFlags SharpLiebThirring.ContinuationGap + +def spaceTimeHomeomorph (N : ℕ) : (Fin (lowerDim N + 1) → ℝ) ≃ₜ (LowerSpace N × ℝ) where + toFun x := (lowerOfCoords (spatial x),x (Fin.last (lowerDim N))) + invFun z := Fin.snoc (lowerCoords z.1) z.2 + left_inv x := by + simp only [lowerCoords_lowerOfCoords] + exact Fin.snoc_init_self x + right_inv z := by + change (lowerOfCoords (Fin.init (Fin.snoc (α := fun _ : Fin (lowerDim N + 1) ↦ ℝ) (lowerCoords z.1) z.2)), + Fin.snoc (α := fun _ : Fin (lowerDim N + 1) ↦ ℝ) (lowerCoords z.1) z.2 (Fin.last (lowerDim N))) = z + simp only [Fin.init_snoc,Fin.snoc_last,lowerOfCoords_lowerCoords] + continuous_toFun := (continuous_lowerOfCoords.comp spatial.continuous_of_finiteDimensional).prodMk (continuous_apply _) + continuous_invFun := by + apply continuous_pi + intro a + refine Fin.lastCases ?_ (fun b ↦ ?_) a + · simpa only [Fin.snoc_last] using (continuous_snd : Continuous (fun z : LowerSpace N × ℝ ↦ z.2)) + · simpa only [Fin.snoc_castSucc,Function.comp_def] using ((continuous_apply b).comp (continuous_lowerCoords.comp continuous_fst)) + +def clampTime (t : ℝ) : ℝ := max 0 (min t 1) +lemma continuous_clampTime : Continuous clampTime := continuous_const.max (continuous_id.min continuous_const) +lemma clampTime_mem (t : ℝ) : clampTime t ∈ Set.Icc (0 : ℝ) 1 := + ⟨le_max_left _ _,max_le zero_le_one (min_le_right _ _)⟩ +lemma clampTime_eq {t : ℝ} (ht : t ∈ Set.Icc (0 : ℝ) 1) : clampTime t = t := by + rw [clampTime,min_eq_left ht.2,max_eq_right ht.1] +@[simp] lemma clampTime_zero : clampTime 0 = 0 := clampTime_eq ⟨le_refl _,zero_le_one⟩ +@[simp] lemma clampTime_one : clampTime 1 = 1 := clampTime_eq ⟨zero_le_one,le_refl _⟩ + +def homotopyCoords {N : ℕ} (Φ : ℝ → LowerSpace N → Matrix (Fin N) (Fin N) ℝ) + (x : Fin (lowerDim N + 1) → ℝ) : Fin (lowerDim N) → ℝ := + matrixCoords (Φ (clampTime (x (Fin.last (lowerDim N)))) (lowerOfCoords (spatial x))) +lemma continuous_homotopyCoords {N : ℕ} (Φ : ℝ → LowerSpace N → Matrix (Fin N) (Fin N) ℝ) + (hΦ : ContinuousOn (fun z : LowerSpace N × ℝ ↦ Φ z.2 z.1) (Set.univ ×ˢ Set.Icc 0 1)) : + Continuous (homotopyCoords Φ) := by + apply continuous_matrixCoords.comp + exact hΦ.comp_continuous + ((continuous_lowerOfCoords.comp spatial.continuous_of_finiteDimensional).prodMk + (continuous_clampTime.comp (continuous_apply _))) + (fun x ↦ ⟨Set.mem_univ _,clampTime_mem _⟩) + +lemma lowerOfCoords_smul {N : ℕ} (s : rowSubgroup N) (x : Fin (lowerDim N + 1) → ℝ) : + lowerOfCoords (spatial (s • x)) = rowSign (fun i ↦ signValue (rowBool s i)) (lowerOfCoords (spatial x)) := by + apply Subtype.ext + funext i j + by_cases hji : j ≤ i + · change (if h : j ≤ i then spatial (s • x) (indexEquiv N ⟨(i,j),h⟩) else 0) = _ + simp only [hji,↓reduceDIte] + change (s.val • x) (indexEquiv N ⟨(i,j),hji⟩).castSucc = + signValue (rowBool s i) * (if h : j ≤ i then spatial x (indexEquiv N ⟨(i,j),h⟩) else 0) + rw [Signs.smul_real,rowSubgroup_coord] + have hr : rowIndex (indexEquiv N ⟨(i,j),hji⟩) = i := by simp [rowIndex] + rw [hr,signValue_smul] + simp only [hji,↓reduceDIte] + rfl + · change (if h : j ≤ i then spatial (s • x) (indexEquiv N ⟨(i,j),h⟩) else 0) = _ + simp only [hji,↓reduceDIte,rowSign,lowerOfCoords,mul_zero] + +lemma time_smul {N : ℕ} (s : rowSubgroup N) (x : Fin (lowerDim N + 1) → ℝ) : + (s • x) (Fin.last (lowerDim N)) = x (Fin.last (lowerDim N)) := by + change (s.val • x) _ = _ + rw [Signs.smul_real,rowSubgroup_time] + rfl + +lemma homotopyCoords_equivariant {N : ℕ} (Φ : ℝ → LowerSpace N → Matrix (Fin N) (Fin N) ℝ) + (he : ∀ θ ∈ Set.Icc (0 : ℝ) 1, ∀ C, ∀ s : Fin N → ℝ, + (∀ i, s i = 1 ∨ s i = -1) → Φ θ (rowSign s C) = signConjugate s (Φ θ C)) + (s : rowSubgroup N) (x : Fin (lowerDim N + 1) → ℝ) : + homotopyCoords Φ (s • x) = conjugateRepresentation N s (homotopyCoords Φ x) := by + unfold homotopyCoords + rw [time_smul,lowerOfCoords_smul,he _ (clampTime_mem _) _ _ (fun _ ↦ signValue_cases _)] + ext a + rw [conjugateRepresentation_apply] + rfl + +lemma homotopyCoords_eq_zero {N : ℕ} (Φ : ℝ → LowerSpace N → Matrix (Fin N) (Fin N) ℝ) + (hs : ∀ θ ∈ Set.Icc (0 : ℝ) 1, ∀ C, (Φ θ C).IsHermitian) + {x : Fin (lowerDim N + 1) → ℝ} (ht : x (Fin.last (lowerDim N)) ∈ Set.Icc (0 : ℝ) 1) : + homotopyCoords Φ x = 0 ↔ Φ (x (Fin.last (lowerDim N))) (lowerOfCoords (spatial x)) = 0 := by + rw [homotopyCoords,clampTime_eq ht] + constructor + · exact matrixCoords_eq_zero (hs _ ht _) + · intro h + rw [h] + rfl + +lemma compact_homotopyCoords_zeros {N : ℕ} (Φ : ℝ → LowerSpace N → Matrix (Fin N) (Fin N) ℝ) + (hs : ∀ θ ∈ Set.Icc (0 : ℝ) 1, ∀ C, (Φ θ C).IsHermitian) + (hK : IsCompact {z : LowerSpace N × ℝ | z.2 ∈ Set.Icc (0 : ℝ) 1 ∧ Φ z.2 z.1 = 0}) : + IsCompact {x : Fin (lowerDim N + 1) → ℝ | x (Fin.last (lowerDim N)) ∈ Set.Icc (0 : ℝ) 1 ∧ homotopyCoords Φ x = 0} := by + have hh := (spaceTimeHomeomorph N).isCompact_preimage.mpr hK + convert hh using 1 + ext x + change (_ ∧ _) ↔ (_ ∧ _) + constructor + · rintro ⟨ht,hx⟩ + exact ⟨ht,(homotopyCoords_eq_zero Φ hs ht).mp hx⟩ + · rintro ⟨ht,hx⟩ + exact ⟨ht,(homotopyCoords_eq_zero Φ hs ht).mpr hx⟩ + +lemma rowAction_free {N : ℕ} (x : Fin (lowerDim N + 1) → ℝ) + (hx : NonzeroRows (lowerOfCoords (spatial x))) + (s : rowSubgroup N) (he : s • x = x) : s = 1 := by + apply rowBool_injective + funext i + rw [rowBool_one] + obtain ⟨j,hj⟩ := hx i + have heC := congrArg (fun y ↦ (lowerOfCoords (spatial y)).val i j) he + rw [lowerOfCoords_smul] at heC + change signValue (rowBool s i) * (lowerOfCoords (spatial x)).val i j = (lowerOfCoords (spatial x)).val i j at heC + rcases Bool.eq_false_or_eq_true (rowBool s i) with hb | hb + · rw [hb,signValue_true,neg_one_mul] at heC + exact False.elim (hj (by linarith)) + · exact hb + +lemma homotopyCoords_initial {N : ℕ} (ε : ℝ) (k : Fin N → ℝ) + (Φ : ℝ → LowerSpace N → Matrix (Fin N) (Fin N) ℝ) + (h0 : ∀ C, Φ 0 C = 2 • diagonal k - ε⁻¹ • (C.val * C.val.transpose)) + (u : Fin (lowerDim N) → ℝ) : + homotopyCoords Φ (embedSpatial u) = initialMap ε⁻¹ k u := by + unfold homotopyCoords + have ht : embedSpatial u (Fin.last (lowerDim N)) = 0 := by + change Fin.snoc (α := fun _ : Fin (lowerDim N + 1) ↦ ℝ) u 0 (Fin.last (lowerDim N)) = 0 + exact Fin.snoc_last _ _ + rw [ht,clampTime_zero,spatial_embed,h0] + rfl + +end SharpLiebThirring.PathTopology +namespace SharpLiebThirring.PathTopology +open Matrix SharpLiebThirring.CubeFlags SharpLiebThirring.ContinuationGap + +lemma initial_matrix_zero {N : ℕ} {ε : ℝ} (hε : 0 < ε) (k : Fin N → ℝ) (hk : ∀ i, 0 < k i) : + 2 • diagonal k - ε⁻¹ • ((diagonalLower (fun i ↦ Real.sqrt (2*ε*k i))).val * + (diagonalLower (fun i ↦ Real.sqrt (2*ε*k i))).val.transpose) = 0 := by + change 2 • diagonal k - ε⁻¹ • (diagonal (fun i ↦ Real.sqrt (2*ε*k i)) * + (diagonal (fun i ↦ Real.sqrt (2*ε*k i))).transpose) = 0 + rw [diagonal_transpose,diagonal_mul_diagonal] + ext i j + by_cases hij : i = j + · subst j + simp only [Matrix.sub_apply,Matrix.smul_apply,diagonal_apply_eq,smul_eq_mul,Matrix.zero_apply] + rw [← sq,Real.sq_sqrt (le_of_lt (mul_pos (mul_pos (by norm_num) hε) (hk i)))] + field_simp [ne_of_gt hε] + ring + · simp only [Matrix.sub_apply,Matrix.smul_apply,diagonal_apply_ne _ hij,smul_eq_mul,smul_zero,mul_zero,sub_self,Matrix.zero_apply] + +lemma gram_of_initial_zero {N : ℕ} {ε : ℝ} (hε : 0 < ε) (k : Fin N → ℝ) (C : LowerSpace N) + (h : 2 • diagonal k - ε⁻¹ • (C.val * C.val.transpose) = 0) : + C.val * C.val.transpose = diagonal (fun i ↦ 2*ε*k i) := by + have he : ε • (2 • diagonal k) = C.val * C.val.transpose := by + have he := congrArg (fun A : Matrix (Fin N) (Fin N) ℝ ↦ ε • A) (sub_eq_zero.mp h) + simpa only [smul_smul,mul_inv_cancel₀ (ne_of_gt hε),one_smul] using he + rw [← he] + ext i j + by_cases hij : i = j + · subst j + simp only [Matrix.smul_apply,diagonal_apply_eq,smul_eq_mul] + ring + · simp only [Matrix.smul_apply,diagonal_apply_ne _ hij,smul_eq_mul,smul_zero,mul_zero] + +lemma homotopyCoords_initial_orbit {N : ℕ} {ε : ℝ} (hε : 0 < ε) (k : Fin N → ℝ) (hk : ∀ i, 0 < k i) + (Φ : ℝ → LowerSpace N → Matrix (Fin N) (Fin N) ℝ) + (hs : ∀ θ ∈ Set.Icc (0 : ℝ) 1, ∀ C, (Φ θ C).IsHermitian) + (h0 : ∀ C, Φ 0 C = 2 • diagonal k - ε⁻¹ • (C.val * C.val.transpose)) + (x : Fin (lowerDim N + 1) → ℝ) (ht : x (Fin.last (lowerDim N)) = 0) + (hx : homotopyCoords Φ x = 0) : + ∃ s : rowSubgroup N, s • embedSpatial (diagonalPoint (fun i ↦ Real.sqrt (2*ε*k i))) = x := by + classical + let C := lowerOfCoords (spatial x) + have hΦ : Φ 0 C = 0 := by + have hh := (homotopyCoords_eq_zero Φ hs (by rw [ht]; exact ⟨le_refl _,zero_le_one⟩)).mp hx + simpa only [ht] using hh + rw [h0] at hΦ + obtain ⟨s,hsign,hC⟩ := PathProof.lower_gram_initial_orbit hε k hk C.prop (gram_of_initial_zero hε k C hΦ) + let b : Fin N → Bool := fun i ↦ decide (s i = -1) + have hb (i : Fin N) : signValue (b i) = s i := by + rcases hsign i with hi | hi + · norm_num [b,hi,signValue] + · norm_num [b,hi,signValue] + have hrow : rowSign (fun i ↦ signValue (rowBool (rowElement b) i)) + (diagonalLower (fun i ↦ Real.sqrt (2*ε*k i))) = C := by + apply Subtype.ext + change (fun i j ↦ signValue (rowBool (rowElement b) i) * diagonal (fun i ↦ Real.sqrt (2*ε*k i)) i j) = C.val + rw [hC] + ext i j + rw [rowBool_rowElement,hb] + by_cases hij : i = j + · subst j + simp only [diagonal_apply_eq] + · simp only [diagonal_apply_ne _ hij,mul_zero] + refine ⟨rowElement b,?_⟩ + apply (spaceTimeHomeomorph N).injective + apply Prod.ext + · change lowerOfCoords (spatial ((rowElement b) • embedSpatial (diagonalPoint _))) = C + rw [lowerOfCoords_smul,spatial_embed,lowerOfCoords_diagonalPoint,hrow] + · change ((rowElement b) • embedSpatial (diagonalPoint (fun i ↦ Real.sqrt (2*ε*k i)))) (Fin.last (lowerDim N)) = x (Fin.last (lowerDim N)) + rw [time_smul,ht] + change Fin.snoc (α := fun _ : Fin (lowerDim N + 1) ↦ ℝ) _ 0 (Fin.last (lowerDim N)) = 0 + exact Fin.snoc_last _ _ + +end SharpLiebThirring.PathTopology +namespace SharpLiebThirring.PathTopology +open Matrix SharpLiebThirring.CubeFlags SharpLiebThirring.ContinuationGap + +/-- Row-sign continuation. Rank +deficiency is allowed throughout; only zero rows at matching solutions are excluded. -/ +theorem equivariant_continuation (N : ℕ) (ε : ℝ) (k : Fin N → ℝ) + (hε : 0 < ε) (hk : ∀ i, 0 < k i) + (Φ : ℝ → LowerSpace N → Matrix (Fin N) (Fin N) ℝ) + (hΦ : ContinuousOn (fun z : LowerSpace N × ℝ ↦ Φ z.2 z.1) (Set.univ ×ˢ Set.Icc 0 1)) + (hs : ∀ θ ∈ Set.Icc (0 : ℝ) 1, ∀ C, (Φ θ C).IsHermitian) + (he : ∀ θ ∈ Set.Icc (0 : ℝ) 1, ∀ C, ∀ s : Fin N → ℝ, + (∀ i, s i = 1 ∨ s i = -1) → Φ θ (rowSign s C) = signConjugate s (Φ θ C)) + (h0 : ∀ C, Φ 0 C = 2 • diagonal k - ε⁻¹ • (C.val * C.val.transpose)) + (hK : IsCompact {z : LowerSpace N × ℝ | z.2 ∈ Set.Icc (0 : ℝ) 1 ∧ Φ z.2 z.1 = 0}) + (hn : ∀ θ ∈ Set.Icc (0 : ℝ) 1, ∀ C, Φ θ C = 0 → NonzeroRows C) : + ∃ C, Φ 1 C = 0 := by + let c := fun i ↦ Real.sqrt (2*ε*k i) + have hc (i : Fin N) : 0 < c i := Real.sqrt_pos.mpr (mul_pos (mul_pos (by norm_num) hε) (hk i)) + have hβ : ε⁻¹ ≠ 0 := inv_ne_zero (ne_of_gt hε) + let L := initialLinearEquiv ε⁻¹ hβ c hc + let p := diagonalPoint c + let f := homotopyCoords Φ + have hp0 : f (embedSpatial p) = 0 := by + change homotopyCoords Φ (embedSpatial p) = 0 + rw [homotopyCoords_initial ε k Φ h0] + dsimp only [initialMap, p] + rw [lowerOfCoords_diagonalPoint] + rw [initial_matrix_zero hε k hk] + rfl + have hd : HasFDerivAt (fun u ↦ f (embedSpatial u)) L.toContinuousLinearEquiv.toContinuousLinearMap p := by + have hh : (fun u ↦ f (embedSpatial u)) = initialMap ε⁻¹ k := + funext (homotopyCoords_initial ε k Φ h0) + rw [hh] + exact initialMap_hasFDerivAt ε⁻¹ hβ k c hc + obtain ⟨x,ht,hx⟩ := exists_terminal_zero_simple (rowSubgroup N) rowSubgroup_time + (conjugateRepresentation N) L conjugateRepresentation_norm p f + (continuous_homotopyCoords Φ hΦ) (homotopyCoords_equivariant Φ he) hp0 hd + (homotopyCoords_initial_orbit hε k hk Φ hs h0) + (compact_homotopyCoords_zeros Φ hs hK) + (fun x ht hx ↦ rowAction_free x + (hn _ ht _ ((homotopyCoords_eq_zero Φ hs ht).mp hx))) + refine ⟨lowerOfCoords (spatial x),?_⟩ + have hh := (homotopyCoords_eq_zero Φ hs (by rw [ht]; exact ⟨zero_le_one,le_refl _⟩)).mp hx + simpa only [ht] using hh + +end SharpLiebThirring.PathTopology + +end +end +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/SchrodingerOperator.lean b/lean/OAI/Analysis/LiebThirring/SchrodingerOperator.lean new file mode 100644 index 0000000000000000000000000000000000000000..e1d9a6adbad1207830c26e94ea0016f7cb812335 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/SchrodingerOperator.lean @@ -0,0 +1,70 @@ +import OAI.Analysis.LiebThirring.FormCongruence + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set Filter +open scoped Topology + +/-- The self-adjoint realization of `-d²/dx²-W`, obtained by inverting the +coercively shifted H¹ form. The graph identity below characterizes it without +reference to the choice of potential decomposition or shift. -/ +def operator {W : ℝ → ℝ} (d : PotentialData W) : L2C →ₗ.[ℂ] L2C := + inverseShift (resolvent d) (resolvent_injective d) (d.b+1) + +lemma operator_selfAdjoint {W : ℝ → ℝ} (d : PotentialData W) : + IsSelfAdjoint (operator d) := + inverseShift_selfAdjoint _ (resolvent_injective d) (resolvent_symmetric d) + (resolvent_dense d) (d.b+1) + +lemma operator_dense {W : ℝ → ℝ} (d : PotentialData W) : + Dense ((operator d).domain : Set L2C) := resolvent_dense d + +lemma operator_graph {W : ℝ → ℝ} (d : PotentialData W) (f g : L2C) : + (∃ hf : f ∈ (operator d).domain, operator d ⟨f,hf⟩ = g) ↔ + ∃ u : H1C, valL u = f ∧ + ∀ v : H1C, schrodingerForm W (toH1 v) (toH1 u) = inner ℂ (valL v) g := by + constructor + · rintro ⟨hf,hg⟩ + obtain ⟨x,rfl⟩ := hf + have ha := inverseShift_apply (resolvent d) (resolvent_injective d) (d.b+1) x + have he : x-((d.b+1 : ℝ):ℂ) • resolvent d x = g := ha.symm.trans hg + refine ⟨solveL d x,rfl,fun v ↦ ?_⟩ + rw [← he,inner_sub_right,inner_smul_right] + have h := solve_form d x v + simpa only [Complex.ofReal_add,Complex.ofReal_one] using eq_sub_of_add_eq h + · rintro ⟨u,rfl,hq⟩ + let x := g+((d.b+1 : ℝ):ℂ) • valL u + have hb : shiftedFormMap d u = valL.adjoint x := by + apply ext_inner_left ℂ + intro v + rw [shiftedFormMap_inner,← form_eq_inner d v u,hq v, + ContinuousLinearMap.adjoint_inner_right] + dsimp only [x] + rw [inner_add_right,inner_smul_right] + simp only [Complex.ofReal_add,Complex.ofReal_one] + have hs : solveL d x = u := (shiftedFormMap_bijective d).1 + ((shifted_solve d x).trans hb.symm) + have hr : resolvent d x = valL u := congrArg valL hs + refine ⟨⟨x,hr⟩,?_⟩ + have ha := inverseShift_apply (resolvent d) (resolvent_injective d) (d.b+1) x + calc + operator d ⟨valL u,⟨x,hr⟩⟩ = + inverseShift (resolvent d) (resolvent_injective d) (d.b+1) + ⟨resolvent d x,⟨x,rfl⟩⟩ := by + apply congrArg (operator d) + exact Subtype.ext hr.symm + _ = x-((d.b+1 : ℝ):ℂ) • resolvent d x := ha + _ = g := by rw [hr]; dsimp only [x]; abel + +lemma operator_associated {W : ℝ → ℝ} (d : PotentialData W) : + IsAssociated W (operator d) := + (isAssociated_iff_graph W (operator d)).mpr (operator_graph d) + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/SobolevBound.lean b/lean/OAI/Analysis/LiebThirring/SobolevBound.lean new file mode 100644 index 0000000000000000000000000000000000000000..12c645ac01e1cfbda79881e607f29b41fb50244b --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/SobolevBound.lean @@ -0,0 +1,137 @@ +import OAI.Analysis.LiebThirring.OperatorGraph + +namespace OAI + +universe u181 + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set Filter +open scoped Topology + +lemma integral_norm_Icc_le_L2 {E : Type u181} [NormedAddCommGroup E] {f : ℝ → E} + (hf : MemLp f 2 volume) {a b : ℝ} (hab : a ≤ b) (hlen : b-a ≤ 1) : + (∫ x in Icc a b, ‖f x‖) ≤ ‖hf.toLp f‖ := by + let q : Lp ℝ 2 (volume : Measure ℝ) := + indicatorConstLp (s := Icc a b) 2 measurableSet_Icc (measure_Icc_lt_top.ne) (1 : ℝ) + have hq : ‖q‖ ≤ 1 := by + rw [show q = indicatorConstLp (s := Icc a b) 2 measurableSet_Icc (measure_Icc_lt_top.ne) (1 : ℝ) from rfl, + norm_indicatorConstLp (by norm_num) (by norm_num)] + simp only [norm_one,one_mul,ENNReal.toReal_ofNat,Real.volume_real_Icc,max_eq_left (sub_nonneg.mpr hab)] + calc + (b-a)^(1/(2:ℝ)) ≤ 1^(1/(2:ℝ)) := Real.rpow_le_rpow (sub_nonneg.mpr hab) hlen (by norm_num) + _ = 1 := by simp + have hi : inner ℝ (hf.norm.toLp (fun x ↦ ‖f x‖)) q = ∫ x in Icc a b, ‖f x‖ := by + rw [L2.inner_def,← integral_indicator measurableSet_Icc] + apply integral_congr_ae + filter_upwards [hf.norm.coeFn_toLp,indicatorConstLp_coeFn (p := 2) + (s := Icc a b) (hs := measurableSet_Icc) (hμs := measure_Icc_lt_top.ne) (c := (1:ℝ))] with x hx hy + change q x * (hf.norm.toLp (fun x ↦ ‖f x‖)) x = (Icc a b).indicator (fun x ↦ ‖f x‖) x + rw [hx,show q x = (Icc a b).indicator (fun _ ↦ (1:ℝ)) x from hy] + by_cases h : x ∈ Icc a b <;> simp [h] + rw [← hi] + calc + _ ≤ ‖hf.norm.toLp (fun x ↦ ‖f x‖)‖*‖q‖ := real_inner_le_norm _ _ + _ ≤ ‖hf.norm.toLp (fun x ↦ ‖f x‖)‖*1 := mul_le_mul_of_nonneg_left hq (norm_nonneg _) + _ = ‖hf.toLp f‖ := by + simp only [mul_one,Lp.norm_toLp,eLpNorm_norm f hf.aestronglyMeasurable] + +lemma primitive_pointwise_bound {f g : ℝ → ℝ} (hf : MemLp f 2 volume) + (hg : MemLp g 2 volume) (c : ℝ) + (hrep : f =ᵐ[volume] (fun x ↦ c+∫ t in (0:ℝ)..x, g t)) (x : ℝ) : + |c+∫ t in (0:ℝ)..x, g t| ≤ ‖hf.toLp f‖+‖hg.toLp g‖ := by + let F : ℝ → ℝ := fun x ↦ c+∫ t in (0:ℝ)..x, g t + have hgI := SobolevProof.locallyIntegrable_intervalIntegrable (hg.locallyIntegrable (by norm_num)) + have hFc : Continuous F := continuous_const.add (intervalIntegral.continuous_primitive hgI 0) + have hFL : MemLp F 2 volume := hf.ae_eq hrep + have hnorm : ‖hFL.toLp F‖ = ‖hf.toLp f‖ := by + congr 1 + exact (MemLp.toLp_eq_toLp_iff hFL hf).mpr hrep.symm + have hvol : volume (Icc x (x+1)) = 1 := by simp [Real.volume_Icc] + obtain ⟨y,hy,hmean⟩ := exists_le_setAverage (μ := volume) (s := Icc x (x+1)) (by simp [hvol]) + (by simp [hvol]) (hFc.norm.integrableOn_Icc) + have hFy : |F y| ≤ ‖hf.toLp f‖ := by + have hInt := integral_norm_Icc_le_L2 hFL (a := x) (b := x+1) (by linarith) (by linarith) + rw [setAverage_eq,Measure.real,hvol] at hmean + simp only [ENNReal.toReal_one,inv_one,one_smul] at hmean + exact hmean.trans (hnorm ▸ hInt) + have hdiff : F y-F x = ∫ t in x..y, g t := by + dsimp [F] + rw [← intervalIntegral.integral_add_adjacent_intervals (hgI 0 x) (hgI x y)] + ring + have hdif : |F y-F x| ≤ ‖hg.toLp g‖ := by + rw [hdiff] + calc + _ ≤ ∫ t in x..y, ‖g t‖ := intervalIntegral.norm_integral_le_integral_norm hy.1 + _ = ∫ t in Icc x y, ‖g t‖ := by + rw [intervalIntegral.integral_of_le hy.1,integral_Icc_eq_integral_Ioc] + _ ≤ ‖hg.toLp g‖ := integral_norm_Icc_le_L2 hg hy.1 (by linarith [hy.2]) + have hFx : |F x| ≤ |F y|+|F y-F x| := by + calc + _ = |F y + (F x-F y)| := by congr 1; ring + _ ≤ |F y|+|F x-F y| := abs_add_le _ _ + _ = _ := by rw [abs_sub_comm (F x) (F y)] + exact hFx.trans (add_le_add hFy hdif) + + +lemma project_L2_norm_le (L : ℂ →L[ℝ] ℝ) (hL : ∀ z, ‖L z‖ ≤ ‖z‖) + {f : ℝ → ℂ} (hf : MemLp f 2 volume) : + ‖(L.comp_memLp' hf).toLp (fun x ↦ L (f x))‖ ≤ ‖hf.toLp f‖ := by + simp only [Lp.norm_toLp] + exact ENNReal.toReal_mono hf.eLpNorm_ne_top + (eLpNorm_mono_ae (L.comp_memLp' hf).aestronglyMeasurable + (Filter.Eventually.of_forall (fun x ↦ hL (f x)))) + +lemma h1_ae_bound (u : H1) : ∀ᵐ x : ℝ, + ‖u.val x‖ ≤ 2*(‖u.val_memLp.toLp u.val‖+‖u.grad_memLp.toLp u.grad‖) := by + obtain ⟨cr,hr⟩ := SobolevProof.weak_derivative_representation + ((Complex.reCLM.comp_memLp' u.val_memLp).locallyIntegrable (by norm_num)) + ((Complex.reCLM.comp_memLp' u.grad_memLp).locallyIntegrable (by norm_num)) + (SobolevProof.h1_project_weak u Complex.reCLM) + obtain ⟨ci,hi⟩ := SobolevProof.weak_derivative_representation + ((Complex.imCLM.comp_memLp' u.val_memLp).locallyIntegrable (by norm_num)) + ((Complex.imCLM.comp_memLp' u.grad_memLp).locallyIntegrable (by norm_num)) + (SobolevProof.h1_project_weak u Complex.imCLM) + have hrv := project_L2_norm_le Complex.reCLM (fun z ↦ Complex.abs_re_le_norm z) u.val_memLp + have hrg := project_L2_norm_le Complex.reCLM (fun z ↦ Complex.abs_re_le_norm z) u.grad_memLp + have hiv := project_L2_norm_le Complex.imCLM (fun z ↦ Complex.abs_im_le_norm z) u.val_memLp + have hig := project_L2_norm_le Complex.imCLM (fun z ↦ Complex.abs_im_le_norm z) u.grad_memLp + filter_upwards [hr,hi] with x hx hy + have hxr := primitive_pointwise_bound (Complex.reCLM.comp_memLp' u.val_memLp) + (Complex.reCLM.comp_memLp' u.grad_memLp) cr hr x + have hxi := primitive_pointwise_bound (Complex.imCLM.comp_memLp' u.val_memLp) + (Complex.imCLM.comp_memLp' u.grad_memLp) ci hi x + change (u.val x).re = _ at hx + change (u.val x).im = _ at hy + rw [← hx] at hxr + rw [← hy] at hxi + calc + ‖u.val x‖ ≤ |(u.val x).re|+|(u.val x).im| := Complex.norm_le_abs_re_add_abs_im _ + _ ≤ _ := add_le_add hxr hxi + _ ≤ (‖u.val_memLp.toLp u.val‖+‖u.grad_memLp.toLp u.grad‖)+ + (‖u.val_memLp.toLp u.val‖+‖u.grad_memLp.toLp u.grad‖) := + add_le_add (add_le_add hrv hrg) (add_le_add hiv hig) + _ = _ := by ring + +lemma h1_ae_sq_bound (u : H1) : ∀ᵐ x : ℝ, + ‖u.val x‖^2 ≤ 8*(‖u.val_memLp.toLp u.val‖^2+‖u.grad_memLp.toLp u.grad‖^2) := by + filter_upwards [h1_ae_bound u] with x hx + have hpos : 0 ≤ 2*(‖u.val_memLp.toLp u.val‖+‖u.grad_memLp.toLp u.grad‖) := by positivity + have hsq := sq_le_sq₀ (norm_nonneg (u.val x)) hpos |>.mpr hx + nlinarith [sq_nonneg (‖u.val_memLp.toLp u.val‖-‖u.grad_memLp.toLp u.grad‖)] + +lemma L2_norm_sq_eq_integral (f : Lp ℂ 2 (volume : Measure ℝ)) : + ‖f‖^2 = ∫ x, ‖f x‖^2 := by + rw [@norm_sq_eq_re_inner ℂ,L2.inner_def] + change Complex.reCLM (∫ x, inner ℂ (f x) (f x)) = _ + rw [← Complex.reCLM.integral_comp_comm (L2.integrable_inner f f)] + congr 1 + ext x + exact (norm_sq_eq_re_inner (𝕜 := ℂ) (f x)).symm + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/SobolevProjection.lean b/lean/OAI/Analysis/LiebThirring/SobolevProjection.lean new file mode 100644 index 0000000000000000000000000000000000000000..213c1015af429fdecbf68ec484eac85154b5f0aa --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/SobolevProjection.lean @@ -0,0 +1,359 @@ +import OAI.Analysis.LiebThirring.CutoffEnergy + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.SobolevProof +open MeasureTheory Set Filter ContinuousLinearMap +open scoped Topology Convolution ContDiff + +/-- A locally integrable function whose distributional derivative vanishes is constant. +This uses only smooth compact tests, hence applies to the H¹ definition. -/ +lemma ae_const_of_weak_derivative_zero {f : ℝ → ℝ} (hf : LocallyIntegrable f volume) + (hw : ∀ φ : ℝ → ℝ, ContDiff ℝ ∞ φ → HasCompactSupport φ → + (∫ x, f x * deriv φ x) = 0) : ∃ c : ℝ, f =ᵐ[volume] fun _ ↦ c := by + have hc (ρ : ℝ → ℝ) (hρ : ContDiff ℝ ∞ ρ) (hρc : HasCompactSupport ρ) : + ∀ x y : ℝ, (ρ ⋆[lsmul ℝ ℝ, volume] f) x = (ρ ⋆[lsmul ℝ ℝ, volume] f) y := by + have hder (x : ℝ) : HasDerivAt (ρ ⋆[lsmul ℝ ℝ, volume] f) 0 x := by + have hd := hρc.hasDerivAt_convolution_left (lsmul ℝ ℝ) (hρ.of_le (by simp)) hf x + have ht := hw (fun y ↦ ρ (x-y)) (hρ.comp (contDiff_const.sub contDiff_id)) + (hρc.comp_homeomorph (Homeomorph.subLeft x)) + have hdφ (y : ℝ) : deriv (fun y ↦ ρ (x-y)) y = -deriv ρ (x-y) := by + simpa only [Function.comp_def, zero_sub, mul_neg, mul_one] using + ((hρ.differentiable (by simp) (x-y)).hasDerivAt.comp y + ((hasDerivAt_const y x).sub (hasDerivAt_id y))).deriv + simp_rw [hdφ,mul_neg,integral_neg] at ht + have hz : ((deriv ρ ⋆[lsmul ℝ ℝ, volume] f) x) = 0 := by + rw [convolution_eq_swap] + simpa only [lsmul_apply,smul_eq_mul,mul_comm,neg_eq_zero] using ht + rwa [hz] at hd + exact is_const_of_deriv_eq_zero (fun x ↦ (hder x).differentiableAt) + (fun x ↦ (hder x).deriv) + let b : ℕ → ContDiffBump (0 : ℝ) := fun n ↦ + ⟨(n+1 : ℝ)⁻¹,2*(n+1 : ℝ)⁻¹,by positivity,by nlinarith [inv_pos.mpr (show (0 : ℝ) apply image_eq_zero_of_notMem_tsupport <;> + intro h <;> have := hs h <;> simp_all + let F := fun x ↦ ∫ t in (0 : ℝ)..x, g t + have hgi := locallyIntegrable_intervalIntegrable hg (-R) R + have h0 : (0 : ℝ) ∈ uIcc (-R) R := by rw [uIcc_of_le (by linarith)]; constructor <;> linarith + have hF : AbsolutelyContinuousOnInterval F (-R) R := + hgi.absolutelyContinuousOnInterval_intervalIntegral h0 + have hφa : AbsolutelyContinuousOnInterval φ (-R) R := + (hφ.of_le (by simp)).contDiffOn.absolutelyContinuousOnInterval + have hfd : ∀ᵐ x, x ∈ uIcc (-R) R → deriv F x = g x := by + filter_upwards [hgi.ae_hasDerivAt_integral] with x hx hmem + exact (hx hmem 0 h0).deriv + have he := hF.integral_mul_deriv_eq_deriv_mul hφa + rw [hzero.1,hzero.2,mul_zero,mul_zero,sub_self,zero_sub] at he + have hi : (∫ x in (-R)..R, deriv F x * φ x) = ∫ x in (-R)..R, g x * φ x := by + apply intervalIntegral.integral_congr_ae + filter_upwards [hfd] with x hx hmem + rw [hx (uIoc_subset_uIcc hmem)] + rw [hi] at he + have hleft : Function.support (fun x ↦ F x * deriv φ x) ⊆ Ioc (-R) R := by + intro x hx + have hd : x ∈ tsupport (deriv φ) := + subset_tsupport _ (Function.mem_support.mpr (mul_ne_zero_iff.mp hx).2) + exact Ioo_subset_Ioc_self (hs (tsupport_deriv_subset hd)) + have hright : Function.support (fun x ↦ g x * φ x) ⊆ Ioc (-R) R := by + intro x hx + exact Ioo_subset_Ioc_self (hs (subset_tsupport _ (Function.mem_support.mpr (mul_ne_zero_iff.mp hx).2))) + rwa [intervalIntegral.integral_eq_integral_of_support_subset hleft, + intervalIntegral.integral_eq_integral_of_support_subset hright] at he + +/-- The precise one-dimensional Sobolev representative, obtained from the weak derivative +without assuming any pointwise regularity or adding a representative to the domain. -/ +lemma weak_derivative_representation {f g : ℝ → ℝ} + (hf : LocallyIntegrable f volume) (hg : LocallyIntegrable g volume) + (hw : ∀ φ : ℝ → ℝ, ContDiff ℝ ∞ φ → HasCompactSupport φ → + (∫ x, f x * deriv φ x) = -(∫ x, g x * φ x)) : + ∃ c : ℝ, f =ᵐ[volume] fun x ↦ c + ∫ t in (0 : ℝ)..x, g t := by + let F := fun x ↦ ∫ t in (0 : ℝ)..x, g t + have hFc : Continuous F := intervalIntegral.continuous_primitive (locallyIntegrable_intervalIntegrable hg) 0 + obtain ⟨c,hc⟩ := ae_const_of_weak_derivative_zero (hf.sub hFc.locallyIntegrable) (fun φ hφ hφc ↦ by + have hi₁ : Integrable (fun x ↦ f x * deriv φ x) volume := + hf.integrable_smul_right_of_hasCompactSupport (hφ.continuous_deriv (by simp)) hφc.deriv + have hi₂ : Integrable (fun x ↦ F x * deriv φ x) volume := + hFc.locallyIntegrable.integrable_smul_right_of_hasCompactSupport + (hφ.continuous_deriv (by simp)) hφc.deriv + simp only [Pi.sub_apply,sub_mul,integral_sub hi₁ hi₂,hw φ hφ hφc] + change -(∫ x, g x * φ x) - (∫ x, (∫ t in (0 : ℝ)..x, g t) * deriv φ x) = 0 + rw [primitive_weak_derivative hg φ hφ hφc,sub_self]) + refine ⟨c,?_⟩ + filter_upwards [hc] with x hx + exact sub_eq_iff_eq_add.mp hx + +end SharpLiebThirring.SobolevProof +namespace SharpLiebThirring.SobolevProof +open MeasureTheory Set Filter +open scoped Topology ContDiff + +lemma h1_project_weak (u : H1) (L : ℂ →L[ℝ] ℝ) (φ : ℝ → ℝ) + (hφ : ContDiff ℝ ∞ φ) (hφc : HasCompactSupport φ) : + (∫ x, L (u.val x) * deriv φ x) = -(∫ x, L (u.grad x) * φ x) := by + have hp : ContDiff ℝ ∞ (fun x ↦ (φ x : ℂ)) := Complex.ofRealCLM.contDiff.comp hφ + have hpc : HasCompactSupport (fun x ↦ (φ x : ℂ)) := hφc.comp_left Complex.ofReal_zero + have hd (x : ℝ) : deriv (fun x ↦ (φ x : ℂ)) x = ((deriv φ x : ℝ) : ℂ) := + ((hφ.differentiable (by simp) x).hasDerivAt.ofReal_comp).deriv + have hi₁ : Integrable (fun x ↦ u.val x * ((deriv φ x : ℝ) : ℂ)) := + (u.val_memLp.locallyIntegrable (by norm_num)).integrable_smul_right_of_hasCompactSupport + (Complex.continuous_ofReal.comp (hφ.continuous_deriv (by simp))) + (hφc.deriv.comp_left Complex.ofReal_zero) + have hi₂ : Integrable (fun x ↦ u.grad x * (φ x : ℂ)) := + (u.grad_memLp.locallyIntegrable (by norm_num)).integrable_smul_right_of_hasCompactSupport + hp.continuous hpc + have he := congrArg L (u.weak_derivative _ hp hpc) + simp only [hd,map_neg,← L.integral_comp_comm hi₁,← L.integral_comp_comm hi₂] at he + have hm (z : ℂ) (a : ℝ) : L (z*(a : ℂ)) = L z*a := by + rw [mul_comm,← Complex.real_smul,map_smul,smul_eq_mul,mul_comm] + simpa only [hm] using he + +lemma h1_continuous_representative (u : H1) : + ∃ f : ℝ → ℂ, Continuous f ∧ u.val =ᵐ[volume] f := by + have hr := weak_derivative_representation + ((Complex.reCLM.comp_memLp' u.val_memLp).locallyIntegrable (by norm_num)) + ((Complex.reCLM.comp_memLp' u.grad_memLp).locallyIntegrable (by norm_num)) + (h1_project_weak u Complex.reCLM) + have hi := weak_derivative_representation + ((Complex.imCLM.comp_memLp' u.val_memLp).locallyIntegrable (by norm_num)) + ((Complex.imCLM.comp_memLp' u.grad_memLp).locallyIntegrable (by norm_num)) + (h1_project_weak u Complex.imCLM) + obtain ⟨cr,hr⟩ := hr + obtain ⟨ci,hi⟩ := hi + let fr := fun x ↦ cr + ∫ t in (0 : ℝ)..x, (u.grad t).re + let fi := fun x ↦ ci + ∫ t in (0 : ℝ)..x, (u.grad t).im + have hfr : Continuous fr := continuous_const.add (intervalIntegral.continuous_primitive + (locallyIntegrable_intervalIntegrable ((Complex.reCLM.comp_memLp' u.grad_memLp).locallyIntegrable (by norm_num))) 0) + have hfi : Continuous fi := continuous_const.add (intervalIntegral.continuous_primitive + (locallyIntegrable_intervalIntegrable ((Complex.imCLM.comp_memLp' u.grad_memLp).locallyIntegrable (by norm_num))) 0) + refine ⟨fun x ↦ (fr x : ℂ)+(fi x : ℂ)*Complex.I, + (Complex.continuous_ofReal.comp hfr).add ((Complex.continuous_ofReal.comp hfi).mul continuous_const),?_⟩ + filter_upwards [hr,hi] with x hx hy + apply Complex.ext + · simpa [fr,fi] using (show (u.val x).re = fr x from hx) + · simpa [fr,fi] using (show (u.val x).im = fi x from hy) + +/-- Classical representative of a real weak second-order eigenfunction. -/ +structure RealEigenfunction (W : ℝ → ℝ) (k : ℝ) where + val : ℝ → ℝ + grad : ℝ → ℝ + val_memLp : MemLp val 2 volume + grad_memLp : MemLp grad 2 volume + grad_continuous : Continuous grad + hasDerivAt : ∀ x, HasDerivAt val (grad x) x + grad_ac : ∀ a b, AbsolutelyContinuousOnInterval grad a b + grad_deriv : ∀ᵐ x, deriv grad x = (k^2-W x)*val x + +lemma real_eigen_of_weak {W f g : ℝ → ℝ} {k : ℝ} + (hf : MemLp f 2 volume) (hg : MemLp g 2 volume) + (hW : LocallyIntegrable W volume) + (hw : ∀ φ : ℝ → ℝ, ContDiff ℝ ∞ φ → HasCompactSupport φ → + (∫ x, f x*deriv φ x) = -(∫ x, g x*φ x)) + (hwe : ∀ φ : ℝ → ℝ, ContDiff ℝ ∞ φ → HasCompactSupport φ → + (∫ x, g x*deriv φ x) = -(∫ x, (k^2-W x)*f x*φ x)) : + ∃ u : RealEigenfunction W k, f =ᵐ[volume] u.val ∧ g =ᵐ[volume] u.grad := by + obtain ⟨c,hc⟩ := weak_derivative_representation (hf.locallyIntegrable (by norm_num)) + (hg.locallyIntegrable (by norm_num)) hw + let F := fun x ↦ c+∫ t in (0 : ℝ)..x, g t + have hFc : Continuous F := continuous_const.add (intervalIntegral.continuous_primitive + (locallyIntegrable_intervalIntegrable (hg.locallyIntegrable (by norm_num))) 0) + let J := fun x ↦ (k^2-W x)*F x + have hJ : LocallyIntegrable J volume := ((locallyIntegrable_const (c := k^2)).sub hW).mul_continuous hFc + obtain ⟨d,hd⟩ := weak_derivative_representation (hg.locallyIntegrable (by norm_num)) hJ (fun φ hφ hφc ↦ by + rw [hwe φ hφ hφc]; congr 1 + apply integral_congr_ae + filter_upwards [hc] with x hx + rw [hx]) + let G := fun x ↦ d+∫ t in (0 : ℝ)..x, J t + have hGc : Continuous G := continuous_const.add (intervalIntegral.continuous_primitive + (locallyIntegrable_intervalIntegrable hJ) 0) + have hFG (x : ℝ) : F x = c+∫ t in (0 : ℝ)..x, G t := by + change c+(∫ t in (0 : ℝ)..x, g t) = c+∫ t in (0 : ℝ)..x, G t + congr 1 + exact intervalIntegral.integral_congr_ae (hd.mono fun _ hx _ ↦ hx) + have hFd (x : ℝ) : HasDerivAt F (G x) x := by + simp_rw [show F = fun x ↦ c+∫ t in (0 : ℝ)..x, G t from funext hFG] + exact (intervalIntegral.integral_hasDerivAt_right (hGc.intervalIntegrable _ _) (hGc.stronglyMeasurableAtFilter _ _) hGc.continuousAt).const_add c + have hGa (a b : ℝ) : AbsolutelyContinuousOnInterval G a b := by + have hi := locallyIntegrable_intervalIntegrable hJ (min 0 (min a b)) (max 0 (max a b)) + have h0 : (0 : ℝ) ∈ uIcc (min 0 (min a b)) (max 0 (max a b)) := by + rw [uIcc_of_le (by exact (min_le_left _ _).trans (le_max_left _ _))] + exact ⟨min_le_left _ _,le_max_left _ _⟩ + have h := hi.absolutelyContinuousOnInterval_intervalIntegral h0 + exact (((contDiff_const : ContDiff ℝ 1 (fun _ : ℝ ↦ d)).contDiffOn.absolutelyContinuousOnInterval).add h).mono (by + intro x hx + rw [uIcc_of_le (by exact (min_le_left _ _).trans (le_max_left _ _))] + exact ⟨(min_le_right _ _).trans hx.1,hx.2.trans (le_max_right _ _)⟩) + have hGd : ∀ᵐ x, deriv G x = J x := by + have hi : LocallyIntegrable J volume := hJ + have hd' := LocallyIntegrable.ae_hasDerivAt_integral hi + filter_upwards [hd'] with x hx + exact ((hx 0).const_add d).deriv + exact ⟨⟨F,G,hf.ae_eq hc,hg.ae_eq hd,hGc,hFd,hGa,hGd⟩,hc,hd⟩ + +end SharpLiebThirring.SobolevProof +namespace SharpLiebThirring.SobolevProof +open MeasureTheory Set Filter +open scoped Topology ContDiff + +lemma clm_mul_real (L : ℂ →L[ℝ] ℝ) (z : ℂ) (a : ℝ) : L (z*(a : ℂ)) = L z*a := by + rw [mul_comm,← Complex.real_smul,map_smul,smul_eq_mul,mul_comm] + +lemma integrable_h1_test (u : H1) (φ : ℝ → ℝ) (hφ : Continuous φ) + (hφc : HasCompactSupport φ) : Integrable (fun x ↦ u.val x*(φ x : ℂ)) := + (u.val_memLp.locallyIntegrable (by norm_num)).integrable_smul_right_of_hasCompactSupport + (Complex.continuous_ofReal.comp hφ) (hφc.comp_left Complex.ofReal_zero) + +lemma integrable_potential_h1_test (u : H1) {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) + (φ : ℝ → ℝ) (hφ : Continuous φ) (hφc : HasCompactSupport φ) : + Integrable (fun x ↦ (W x : ℂ)*u.val x*(φ x : ℂ)) := by + obtain ⟨F,hF,hFe⟩ := h1_continuous_representative u + have h := hW.integrable_smul_right_of_hasCompactSupport + (hF.mul (Complex.continuous_ofReal.comp hφ)) + ((hφc.comp_left Complex.ofReal_zero).mul_left (f := F)) + apply h.congr + filter_upwards [hFe] with x hx + simp only [Complex.real_smul,hx,mul_assoc,Pi.mul_apply,Function.comp_apply] + +lemma eigen_weak_second {W : ℝ → ℝ} {k : ℝ} {u : H1} + (hW : LocallyIntegrable W volume) (hu : IsNegativeEigenfunction W k u) + (φ : ℝ → ℝ) (hφ : ContDiff ℝ ∞ φ) (hφc : HasCompactSupport φ) : + (∫ x, u.grad x*((deriv φ x : ℝ) : ℂ)) = + -(∫ x, ((k^2-W x : ℝ) : ℂ)*u.val x*(φ x : ℂ)) := by + have hφd : Continuous (deriv φ) := hφ.continuous_deriv (by simp) + let v := smoothH1 (fun x ↦ (φ x : ℂ)) (fun x ↦ ((deriv φ x : ℝ) : ℂ)) + (Complex.ofRealCLM.contDiff.comp hφ) + (fun x ↦ (hφ.differentiable (by simp) x).hasDerivAt.ofReal_comp) + (Complex.continuous_ofReal.comp hφd) + ((hφ.continuous.memLp_of_hasCompactSupport hφc).ofReal) + ((hφd.memLp_of_hasCompactSupport hφc.deriv).ofReal) + have he := hu.2 v + change (∫ x, star (((deriv φ x : ℝ) : ℂ))*u.grad x) - + (∫ x, (W x : ℂ)*star (φ x : ℂ)*u.val x) = + -(k^2 : ℝ)*(∫ x, star (φ x : ℂ)*u.val x) at he + simp only [Complex.star_def,Complex.conj_ofReal] at he + have hi := (integrable_h1_test u φ hφ.continuous hφc).const_mul ((k^2 : ℝ) : ℂ) + have hwi := integrable_potential_h1_test u hW φ hφ.continuous hφc + have hid : Integrable (fun x ↦ ((k^2 : ℝ) : ℂ)*u.val x*(φ x : ℂ)) := by + simpa only [mul_assoc] using hi + simp_rw [Complex.ofReal_sub,sub_mul] + rw [integral_sub hid hwi] + simp_rw [mul_assoc] at he ⊢ + rw [integral_const_mul] + simp_rw [mul_comm (u.grad _),mul_comm (u.val _)] + simpa only [neg_sub,sub_eq_add_neg,neg_mul,neg_add_rev,neg_neg,add_comm] using (sub_eq_iff_eq_add.mp he) + +lemma eigen_project_weak_second {W : ℝ → ℝ} {k : ℝ} {u : H1} + (hW : LocallyIntegrable W volume) (hu : IsNegativeEigenfunction W k u) + (L : ℂ →L[ℝ] ℝ) (φ : ℝ → ℝ) (hφ : ContDiff ℝ ∞ φ) + (hφc : HasCompactSupport φ) : + (∫ x, L (u.grad x)*deriv φ x) = -(∫ x, (k^2-W x)*L (u.val x)*φ x) := by + have hi : Integrable (fun x ↦ u.grad x*((deriv φ x : ℝ) : ℂ)) := + (u.grad_memLp.locallyIntegrable (by norm_num)).integrable_smul_right_of_hasCompactSupport + (Complex.continuous_ofReal.comp (hφ.continuous_deriv (by simp))) + (hφc.deriv.comp_left Complex.ofReal_zero) + have hj := integrable_potential_h1_test u ((locallyIntegrable_const (c := k^2)).sub hW) + φ hφ.continuous hφc + change Integrable (fun x ↦ ((k^2-W x : ℝ) : ℂ)*u.val x*(φ x : ℂ)) at hj + have he := congrArg L (eigen_weak_second hW hu φ hφ hφc) + rw [map_neg,← L.integral_comp_comm hi,← L.integral_comp_comm hj] at he + have hm (z : ℂ) (a : ℝ) : L ((a : ℂ)*z) = a*L z := by + rw [mul_comm,clm_mul_real,mul_comm] + simpa only [clm_mul_real,hm] using he + +lemma eigen_project_representative {W : ℝ → ℝ} {k : ℝ} {u : H1} + (hW : LocallyIntegrable W volume) (hu : IsNegativeEigenfunction W k u) + (L : ℂ →L[ℝ] ℝ) : + ∃ v : RealEigenfunction W k, + (fun x ↦ L (u.val x)) =ᵐ[volume] v.val ∧ + (fun x ↦ L (u.grad x)) =ᵐ[volume] v.grad := + real_eigen_of_weak (L.comp_memLp' u.val_memLp) (L.comp_memLp' u.grad_memLp) hW + (h1_project_weak u L) (eigen_project_weak_second hW hu L) + +end SharpLiebThirring.SobolevProof +namespace SharpLiebThirring.SobolevProof +open MeasureTheory Set + +def RealEigenfunction.toC1L2 {W : ℝ → ℝ} {k : ℝ} (u : RealEigenfunction W k) : C1L2 := + ⟨(u.val,u.grad),u.val_memLp,u.grad_memLp,u.grad_continuous,u.hasDerivAt⟩ + +lemma RealEigenfunction.toC1L2_eigen {W : ℝ → ℝ} {k : ℝ} (u : RealEigenfunction W k) : + u.toC1L2.IsEigen W k := by + intro a b + change u.grad b-u.grad a = ∫ x in a..b, (k^2-W x)*u.val x + rw [← (u.grad_ac a b).integral_deriv_eq_sub] + apply intervalIntegral.integral_congr_ae + filter_upwards [u.grad_deriv] with x hx _ + exact hx + +lemma eigen_C1_representative {W : ℝ → ℝ} {k : ℝ} {u : H1} + (hW : LocallyIntegrable W volume) (hu : IsNegativeEigenfunction W k u) + (L : ℂ →L[ℝ] ℝ) : + ∃ v : C1L2, v.IsEigen W k ∧ (fun x ↦ L (u.val x)) =ᵐ[volume] v.val := by + obtain ⟨v,hv,_⟩ := eigen_project_representative hW hu L + exact ⟨v.toC1L2,v.toC1L2_eigen,hv⟩ + +lemma re_l2Pairing {u v : H1} {ur ui vr vi : C1L2} + (hur : (fun x ↦ (u.val x).re) =ᵐ[volume] ur.val) + (hui : (fun x ↦ (u.val x).im) =ᵐ[volume] ui.val) + (hvr : (fun x ↦ (v.val x).re) =ᵐ[volume] vr.val) + (hvi : (fun x ↦ (v.val x).im) =ᵐ[volume] vi.val) : + (l2Pairing u v).re = inner ℝ ur vr+inner ℝ ui vi := by + have hint : Integrable (fun x ↦ star (u.val x)*v.val x) := + u.val_memLp.star.integrable_mul v.val_memLp + have hreal := Complex.reCLM.integral_comp_comm hint + simp only [Complex.reCLM_apply] at hreal + rw [l2Pairing,← hreal,C1L2.inner_eq_integral,C1L2.inner_eq_integral, + ← integral_add (ur.integrable_val_mul vr) (ui.integrable_val_mul vi)] + apply integral_congr_ae + filter_upwards [hur,hui,hvr,hvi] with x h1 h2 h3 h4 + simp only [Complex.mul_re,Complex.star_def,Complex.conj_re,Complex.conj_im,h1,h2,h3,h4] + ring + +lemma im_l2Pairing {u v : H1} {ur ui vr vi : C1L2} + (hur : (fun x ↦ (u.val x).re) =ᵐ[volume] ur.val) + (hui : (fun x ↦ (u.val x).im) =ᵐ[volume] ui.val) + (hvr : (fun x ↦ (v.val x).re) =ᵐ[volume] vr.val) + (hvi : (fun x ↦ (v.val x).im) =ᵐ[volume] vi.val) : + (l2Pairing u v).im = inner ℝ ur vi-inner ℝ ui vr := by + have hint : Integrable (fun x ↦ star (u.val x)*v.val x) := + u.val_memLp.star.integrable_mul v.val_memLp + have himag := Complex.imCLM.integral_comp_comm hint + simp only [Complex.imCLM_apply] at himag + rw [l2Pairing,← himag,C1L2.inner_eq_integral,C1L2.inner_eq_integral, + ← integral_sub (ur.integrable_val_mul vi) (ui.integrable_val_mul vr)] + apply integral_congr_ae + filter_upwards [hur,hui,hvr,hvi] with x h1 h2 h3 h4 + simp only [Complex.mul_im,Complex.star_def,Complex.conj_re,Complex.conj_im,h1,h2,h3,h4] + ring + +end SharpLiebThirring.SobolevProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/SpectralMain.lean b/lean/OAI/Analysis/LiebThirring/SpectralMain.lean new file mode 100644 index 0000000000000000000000000000000000000000..9bf879e5ef5e6dc9230b589178497a63b94f347f --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/SpectralMain.lean @@ -0,0 +1,110 @@ +import OAI.Analysis.LiebThirring.OneState + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set +open scoped Topology ENNReal + +/-- The unbounded self-adjoint operator associated with exactly the H¹ form. -/ +def schrodingerOperator {γ : ℝ} (hγ : 1/2 < γ) {W : ℝ → ℝ} (hW : Admissible γ W) : + L2C →ₗ.[ℂ] L2C := operator (potentialData hγ hW) + +lemma schrodingerOperator_selfAdjoint {γ : ℝ} (hγ : 1/2 < γ) {W : ℝ → ℝ} + (hW : Admissible γ W) : IsSelfAdjoint (schrodingerOperator hγ hW) := + operator_selfAdjoint (potentialData hγ hW) + +lemma schrodingerOperator_associated {γ : ℝ} (hγ : 1/2 < γ) {W : ℝ → ℝ} + (hW : Admissible γ W) : IsAssociated W (schrodingerOperator hγ hW) := + operator_associated (potentialData hγ hW) + +lemma eigenvalueSum_eq_negativeMoment {γ : ℝ} (hγ₀ : 1/2 < γ) (hγ₁ : γ < 3/2) + {W : ℝ → ℝ} (hW : Admissible γ W) {A : L2C →ₗ.[ℂ] L2C} + (hA : IsSelfAdjoint A) (ha : IsAssociated W A) : + eigenvalueSum γ A hA = negativeMoment γ W := by + have hbound : eigenvalueSum γ A hA ≤ + ENNReal.ofReal (sharpConstant γ)*potentialMass γ W := by + calc + _ ≤ eigenvalueMoment γ A := eigenvalueSum_le_moment γ A hA + _ = negativeMoment γ W := (negativeMoment_eq_eigenvalueMoment ha γ).symm + _ ≤ _ := negativeMoment_bound hγ₀ hγ₁ hW + have hfin : eigenvalueSum γ A hA ≠ ∞ := ne_top_of_le_ne_top + (ENNReal.mul_ne_top ENNReal.ofReal_ne_top (hW.mass_ne_top hγ₀)) hbound + exact (eigenvalueMoment_eq_sum hA hfin).symm.trans + (negativeMoment_eq_eigenvalueMoment ha γ).symm + +/-- The trace: sum of every negative eigenvalue of the form +operator, counted once for each member of a full eigenspace basis. -/ +def spectralMoment {γ : ℝ} (hγ : 1/2 < γ) {W : ℝ → ℝ} (hW : Admissible γ W) : ℝ≥0∞ := + eigenvalueSum γ (schrodingerOperator hγ hW) (schrodingerOperator_selfAdjoint hγ hW) + +lemma spectralMoment_eq {γ : ℝ} (hγ₀ : 1/2 < γ) (hγ₁ : γ < 3/2) + {W : ℝ → ℝ} (hW : Admissible γ W) : spectralMoment hγ₀ hW = negativeMoment γ W := + eigenvalueSum_eq_negativeMoment hγ₀ hγ₁ hW (schrodingerOperator_selfAdjoint hγ₀ hW) + (schrodingerOperator_associated hγ₀ hW) + +def spectralOptimalConstant {γ : ℝ} (hγ : 1/2 < γ) : ℝ≥0∞ := + ⨆ (W : ℝ → ℝ) (hW : Admissible γ W) (_ : 0 < potentialMass γ W), + spectralMoment hγ hW / potentialMass γ W + +def spectralOneStateConstant {γ : ℝ} (hγ : 1/2 < γ) : ℝ≥0∞ := + ⨆ (W : ℝ → ℝ) (hW : Admissible γ W) (_ : 0 < potentialMass γ W), + oneEigenvalueMoment γ (schrodingerOperator hγ hW) / potentialMass γ W + +lemma spectralOptimalConstant_eq {γ : ℝ} (hγ₀ : 1/2 < γ) (hγ₁ : γ < 3/2) : + spectralOptimalConstant hγ₀ = optimalConstant γ := by + unfold spectralOptimalConstant optimalConstant + congr 1 + funext W + congr 1 + funext hW + simp only [spectralMoment_eq hγ₀ hγ₁ hW] + +lemma spectralOneStateConstant_eq {γ : ℝ} (hγ : 1/2 < γ) : + spectralOneStateConstant hγ = oneStateConstant γ := by + unfold spectralOneStateConstant oneStateConstant + congr 1 + funext W + congr 1 + funext hW + simp only [← oneStateMoment_eq_oneEigenvalueMoment (schrodingerOperator_associated hγ hW)] + +/-- The sharp bound for the infinite eigenvalue sum of any self-adjoint +operator associated with the form, together with finite multiplicities. -/ +theorem sharp_bound_for_associated_operator {γ : ℝ} (hγ₀ : 1/2 < γ) (hγ₁ : γ < 3/2) + {W : ℝ → ℝ} (hW : Admissible γ W) {A : L2C →ₗ.[ℂ] L2C} + (hA : IsSelfAdjoint A) (ha : IsAssociated W A) : + eigenvalueSum γ A hA ≤ ENNReal.ofReal (sharpConstant γ)*potentialMass γ W ∧ + ∀ e : NegativeEnergy, FiniteDimensional ℂ (eigenSpace A e.1) := by + have hb : eigenvalueSum γ A hA ≤ ENNReal.ofReal (sharpConstant γ)*potentialMass γ W := by + rw [eigenvalueSum_eq_negativeMoment hγ₀ hγ₁ hW hA ha] + exact negativeMoment_bound hγ₀ hγ₁ hW + exact ⟨hb,fun e ↦ eigenSpace_finiteDimensional hA + (ne_top_of_le_ne_top (ENNReal.mul_ne_top ENNReal.ofReal_ne_top (hW.mass_ne_top hγ₀)) hb) e⟩ + +/-- All main conclusions in the actual-operator formulation. Its operator is +constructed unconditionally; no existence, trace equivalence, spectral estimate, +or finiteness assumption is used as an input. -/ +theorem sharp_lieb_thirring_spectral {γ : ℝ} (hγ₀ : 1/2 < γ) (hγ₁ : γ < 3/2) : + (∀ (W : ℝ → ℝ) (hW : Admissible γ W), + spectralMoment hγ₀ hW ≤ ENNReal.ofReal (sharpConstant γ)*potentialMass γ W) ∧ + spectralOptimalConstant hγ₀ = ENNReal.ofReal (sharpConstant γ) ∧ + spectralOneStateConstant hγ₀ = ENNReal.ofReal (sharpConstant γ) ∧ + ∃ hW : Admissible γ (equalityPotential γ), + 0 < potentialMass γ (equalityPotential γ) ∧ + spectralMoment hγ₀ hW = ENNReal.ofReal (sharpConstant γ)*potentialMass γ (equalityPotential γ) := by + obtain ⟨hb,ho,hs,hW,hp,he⟩ := sharp_lieb_thirring γ hγ₀ hγ₁ + refine ⟨fun W hW ↦ ?_,?_,?_,hW,hp,?_⟩ + · rw [spectralMoment_eq hγ₀ hγ₁ hW] + exact hb W hW + · rw [spectralOptimalConstant_eq hγ₀ hγ₁]; exact ho + · rw [spectralOneStateConstant_eq hγ₀]; exact hs + · rw [spectralMoment_eq hγ₀ hγ₁ hW]; exact he + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/SpectralMoment.lean b/lean/OAI/Analysis/LiebThirring/SpectralMoment.lean new file mode 100644 index 0000000000000000000000000000000000000000..4e68f239f5bf9d2e8673b669d2e837e41509c7f2 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/SpectralMoment.lean @@ -0,0 +1,81 @@ +import OAI.Analysis.LiebThirring.SchrodingerOperator + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set +open scoped Topology ENNReal + +def IsOperatorEigenfunction (A : L2C →ₗ.[ℂ] L2C) (e : ℝ) (f : L2C) : Prop := + ∃ hf : f ∈ A.domain, A ⟨f,hf⟩ = (e:ℂ) • f + +/-- The entire negative eigenvalue moment, with multiplicity, of an actual +partially defined operator. Energies here are the eigenvalues `e`, not scales. -/ +def eigenvalueMoment (γ : ℝ) (A : L2C →ₗ.[ℂ] L2C) : ℝ≥0∞ := + ⨆ (N : ℕ) (f : Fin N → L2C) (e : Fin N → ℝ) + (_ : Orthonormal ℂ f) (_ : ∀ i, e i < 0 ∧ IsOperatorEigenfunction A (e i) (f i)), + ∑ i, (ENNReal.ofReal |e i|)^γ + +lemma energy_weight (k γ : ℝ) (hk : 0 ≤ k) : + (ENNReal.ofReal |-(k^2)|)^γ = (ENNReal.ofReal k)^(2*γ) := by + rw [abs_neg,abs_of_nonneg (sq_nonneg _),ENNReal.ofReal_pow hk] + simpa only [Nat.cast_ofNat] using (ENNReal.rpow_natCast_mul (ENNReal.ofReal k) 2 γ).symm + +lemma negativeMoment_eq_eigenvalueMoment {W : ℝ → ℝ} {A : L2C →ₗ.[ℂ] L2C} + (hA : IsAssociated W A) (γ : ℝ) : negativeMoment γ W = eigenvalueMoment γ A := by + classical + apply le_antisymm + · unfold negativeMoment + refine iSup_le (fun N ↦ iSup_le (fun u ↦ iSup_le (fun k ↦ + iSup_le (fun hu ↦ iSup_le (fun hk ↦ ?_))))) + let f := fun i ↦ (u i).val_memLp.toLp (u i).val + have hf : Orthonormal ℂ f := orthonormal_iff_ite.mpr (fun i j ↦ by + simpa only [f,l2Pairing_eq_inner] using hu i j) + have he : ∀ i, -(k i)^2 < 0 ∧ IsOperatorEigenfunction A (-(k i)^2) (f i) := by + intro i + refine ⟨neg_neg_of_pos (sq_pos_of_pos (hk i).1),?_⟩ + simpa only [IsOperatorEigenfunction,f,Complex.ofReal_neg] using + ((negativeEigenfunction_iff_operator hA (k i) (u i)).mp (hk i)).2 + have hle : (∑ i, (ENNReal.ofReal |-(k i)^2|)^γ) ≤ eigenvalueMoment γ A := + le_iSup_of_le N (le_iSup_of_le f (le_iSup_of_le (fun i ↦ -(k i)^2) + (le_iSup_of_le hf (le_iSup_of_le he le_rfl)))) + simpa only [energy_weight _ γ ((hk _).1.le)] using hle + · unfold eigenvalueMoment + refine iSup_le (fun N ↦ iSup_le (fun f ↦ iSup_le (fun e ↦ + iSup_le (fun hf ↦ iSup_le (fun he ↦ ?_))))) + have hex : ∀ i, ∃ u : H1, u.val_memLp.toLp u.val = f i ∧ + ∀ v : H1, schrodingerForm W v u = inner ℂ (v.val_memLp.toLp v.val) ((e i : ℂ) • f i) := by + intro i + exact (hA _ _).mp (he i).2 + choose u hu hq using hex + let k := fun i ↦ Real.sqrt (-e i) + have hkp : ∀ i, 0 < k i := fun i ↦ Real.sqrt_pos.mpr (neg_pos.mpr (he i).1) + have hks : ∀ i, -(k i)^2 = e i := fun i ↦ by + rw [show (k i)^2 = -e i from Real.sq_sqrt (le_of_lt (neg_pos.mpr (he i).1)),neg_neg] + have hne : ∀ i, IsNegativeEigenfunction W (k i) (u i) := by + intro i + rw [negativeEigenfunction_iff_operator hA] + refine ⟨hkp i,?_⟩ + have hc : -(↑((k i)^2):ℂ) = (e i:ℂ) := by exact_mod_cast hks i + simpa only [IsOperatorEigenfunction,hc,hu i] using (he i).2 + have hon : IsOrthonormalFamily u := by + intro i j + rw [l2Pairing_eq_inner,hu i,hu j] + exact orthonormal_iff_ite.mp hf i j + have hle : (∑ i, (ENNReal.ofReal (k i))^(2*γ)) ≤ negativeMoment γ W := + le_iSup_of_le N (le_iSup_of_le u (le_iSup_of_le k + (le_iSup_of_le hon (le_iSup_of_le hne le_rfl)))) + calc + _ = ∑ i, (ENNReal.ofReal (k i))^(2*γ) := by + apply Finset.sum_congr rfl + intro i _ + rw [← hks i,energy_weight _ _ (hkp i).le] + _ ≤ _ := hle + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/SpectralTrials.lean b/lean/OAI/Analysis/LiebThirring/SpectralTrials.lean new file mode 100644 index 0000000000000000000000000000000000000000..7ff99cea1e239a9a27200a5c81a0a19a1a085657 --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/SpectralTrials.lean @@ -0,0 +1,189 @@ +import OAI.Analysis.LiebThirring.FlagApproximation + +namespace OAI + +universe u179 + + +noncomputable section +namespace SharpLiebThirring.SpectralProof +open Matrix MatrixProof MatrixFlow MeasureTheory Set ContinuationGap ActionProof +open scoped Matrix.Norms.L2Operator +variable {N : ℕ} + +lemma triangular_action_upper {σ l r : ℝ} (hσ : 0 < σ) (hlr : l ≤ r) + (k : Fin N → ℝ) (a v : ℝ → Fin N → ℝ) + (ha : ContinuousOn a (Icc l r)) (hv : ContinuousOn v (Icc l r)) + {W : ℝ → ℝ} (hW : IntervalIntegrable W volume l r) + (hWn : ∀ᵐ x ∂volume, 0 ≤ W x) + (hWp : Integrable (fun x ↦ W x^(1+σ))) + (he : (∫ t in l..r, (∑ i, v t i^2)+(∑ i, k i^2*a t i^2)) ≤ + ∫ t in l..r, W t*(∑ i, a t i^2)) : + (∫ t in l..r, actionDensity σ k (a t) (v t)) ≤ + actionYoungConstant σ * ∫ t, W t^(1+σ) := by + let m := fun t ↦ ∑ i, a t i^2 + have hm : ContinuousOn m (Icc l r) := continuousOn_finsetSum Finset.univ (fun i _ ↦ (continuousOn_pi.mp ha i).pow 2) + have hm0 (t : ℝ) : 0 ≤ m t := Finset.sum_nonneg (fun _ _ ↦ sq_nonneg _) + have hmr : ContinuousOn (fun t ↦ m t^(1+1/σ)) (Icc l r) := + hm.rpow_const (fun _ _ ↦ Or.inr (by positivity)) + have hE : ContinuousOn (fun t ↦ (∑ i, v t i^2)+(∑ i, k i^2*a t i^2)) (Icc l r) := + (continuousOn_finsetSum Finset.univ (fun i _ ↦ (continuousOn_pi.mp hv i).pow 2)).add + (continuousOn_finsetSum Finset.univ (fun i _ ↦ ((continuousOn_pi.mp ha i).pow 2).const_mul _)) + have hEi : IntervalIntegrable (fun t ↦ (∑ i, v t i^2)+(∑ i, k i^2*a t i^2)) volume l r := hE.intervalIntegrable_of_Icc hlr + have hmri : IntervalIntegrable (fun t ↦ m t^(1+1/σ)) volume l r := hmr.intervalIntegrable_of_Icc hlr + have hWmi : IntervalIntegrable (fun t ↦ W t*m t) volume l r := by + rw [intervalIntegrable_iff_integrableOn_Icc_of_le hlr] at hW ⊢ + exact hW.mul_continuousOn hm isCompact_Icc + have hAi : IntervalIntegrable (fun t ↦ actionYoungConstant σ * W t^(1+σ)) volume l r := hWp.intervalIntegrable.const_mul (actionYoungConstant σ) + calc + (∫ t in l..r, actionDensity σ k (a t) (v t)) = + (∫ t in l..r, (∑ i, v t i^2)+(∑ i, k i^2*a t i^2)) - + ∫ t in l..r, m t^(1+1/σ) := intervalIntegral.integral_sub hEi hmri + _ ≤ (∫ t in l..r, W t*m t) - ∫ t in l..r, m t^(1+1/σ) := sub_le_sub_right he _ + _ = ∫ t in l..r, W t*m t-m t^(1+1/σ) := + (intervalIntegral.integral_sub hWmi hmri).symm + _ ≤ ∫ t in l..r, actionYoungConstant σ * W t^(1+σ) := by + apply intervalIntegral.integral_mono_ae_restrict hlr (hWmi.sub hmri) hAi + filter_upwards [ae_restrict_of_ae hWn] with t ht + exact young_action_bound hσ ht (hm0 t) + _ = actionYoungConstant σ * ∫ t in l..r, W t^(1+σ) := intervalIntegral.integral_const_mul _ _ + _ ≤ actionYoungConstant σ * ∫ t, W t^(1+σ) := by + apply mul_le_mul_of_nonneg_left _ (by unfold actionYoungConstant; positivity) + rw [intervalIntegral.integral_of_le hlr] + exact integral_mono_measure Measure.restrict_le_self + (hWn.mono fun x hx ↦ Real.rpow_nonneg hx _) hWp + +lemma finite_spectral_trial {σ l r : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + (hlr : l ≤ r) (k : Fin N → ℝ) (hk : ∀ i, 0 < k i) + (u v : ℝ → Fin N → ℝ) (hu : ContinuousOn u (Icc l r)) (hv : ContinuousOn v (Icc l r)) + (hud : ∀ t ∈ Ioo l r, ∀ i, HasDerivAt (fun t ↦ u t i) (v t i) t) + (hul : u l = 0) (hur : u r = 0) + (ho : ∀ i j, (∫ t in l..r, u t i*u t j) = if i=j then 1 else 0) + {W : ℝ → ℝ} (hW : IntervalIntegrable W volume l r) + (hWn : ∀ᵐ x ∂volume, 0 ≤ W x) (hWp : Integrable (fun x ↦ W x^(1+σ))) + (he : ∀ C : LowerSpace N, + (∫ t in l..r, (∑ i, (C.val *ᵥ v t) i^2)+(∑ i, k i^2*(C.val *ᵥ u t) i^2)) ≤ + ∫ t in l..r, W t*(∑ i, (C.val *ᵥ u t) i^2)) : + (∑ i, ∫ s in -(k i)..k i, (k i^2-s^2)^σ) ≤ + actionYoungConstant σ * ∫ t, W t^(1+σ) := by + apply finite_action_upper_test hσ₀ hσ₁ hlr k hk u v hu hv hud hul hur ho + intro C + exact triangular_action_upper hσ₀ hlr k _ _ + ((show Continuous (fun a : Fin N → ℝ ↦ C.val *ᵥ a) by fun_prop).comp_continuousOn hu) + ((show Continuous (fun a : Fin N → ℝ ↦ C.val *ᵥ a) by fun_prop).comp_continuousOn hv) + hW hWn hWp (he C) + +end SharpLiebThirring.SpectralProof + +end + + +noncomputable section +namespace SharpLiebThirring.SpectralProof +open SobolevProof SobolevProof.C1L2 MeasureTheory Set Filter Matrix MatrixProof ContinuationGap +open scoped Topology Matrix.Norms.L2Operator + +lemma compact_family_radius {ι : Type u179} [Fintype ι] (u : ι → C1L2) + (hu : ∀ i, HasCompactSupport (u i).val) : + ∃ R : ℝ, 0 < R ∧ ∀ i x, R ≤ |x| → (u i).val x = 0 ∧ (u i).grad x = 0 := by + have hc : IsCompact (⋃ i, tsupport (u i).val) := isCompact_iUnion hu + obtain ⟨R,hR,hs⟩ := hc.isBounded.subset_ball_lt 0 0 + refine ⟨R,hR,fun i x hx ↦ ?_⟩ + have hn : x ∉ tsupport (u i).val := by + intro hm + have hxb := hs (mem_iUnion.2 ⟨i,hm⟩) + rw [Metric.mem_ball,dist_zero_right,Real.norm_eq_abs] at hxb + linarith + refine ⟨image_eq_zero_of_notMem_tsupport hn,?_⟩ + rw [← deriv_val] + apply Function.notMem_support.mp + exact fun hd ↦ hn (support_deriv_subset hd) + +lemma integral_eq_interval_of_vanish {R : ℝ} (_hR : 0 ≤ R) {f : ℝ → ℝ} + (hf : ∀ x, R ≤ |x| → f x = 0) : (∫ x, f x) = ∫ x in -R..R, f x := by + symm + apply intervalIntegral.integral_eq_integral_of_support_subset + intro x hx + have hn : |x| < R := lt_of_not_ge (fun h ↦ hx (hf x h)) + exact ⟨by rw [abs_lt] at hn; linarith [hn.1],by rw [abs_lt] at hn; linarith [hn.2]⟩ + +lemma row_mem_prefix {N : ℕ} (q : Fin N → C1L2) (C : LowerSpace N) (i : Fin N) : + (∑ j, C.val i j • q j) ∈ Submodule.span ℝ (q '' Iic i) := by + classical + apply Submodule.sum_mem + intro j _ + by_cases hj : j ≤ i + · exact Submodule.smul_mem _ _ (Submodule.subset_span (mem_image_of_mem q (mem_Iic.mpr hj))) + · rw [C.property i j (lt_of_not_ge hj),zero_smul] + exact Submodule.zero_mem _ + +lemma compact_trial_energy {N : ℕ} {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) + (κ : Fin N → ℝ) (p : Fin N → C1L2) (hp : ∀ i, HasCompactSupport (p i).val) + (he : ∀ i, energy W (p i) (p i)+κ i^2*inner ℝ (p i) (p i) ≤ 0) : + (∫ x, (∑ i, (p i).grad x^2)+(∑ i, κ i^2*(p i).val x^2)) ≤ + ∫ x, W x*(∑ i, (p i).val x^2) := by + have hgi (i : Fin N) : Integrable (fun x ↦ (p i).grad x^2) := by + simpa only [pow_two] using (p i).integrable_grad_mul (p i) + have hvi (i : Fin N) : Integrable (fun x ↦ κ i^2*(p i).val x^2) := by + simpa only [pow_two] using ((p i).integrable_val_mul (p i)).const_mul (κ i*κ i) + have hwi (i : Fin N) : Integrable (fun x ↦ W x*(p i).val x^2) := by + simpa only [pow_two,mul_assoc] using integrable_potential hW (p i) (p i) (hp i) + rw [integral_add (integrable_finsetSum _ (fun i _ ↦ hgi i)) + (integrable_finsetSum _ (fun i _ ↦ hvi i)),integral_finsetSum _ (fun i _ ↦ hgi i), + integral_finsetSum _ (fun i _ ↦ hvi i)] + simp_rw [Finset.mul_sum] + rw [integral_finsetSum _ (fun i _ ↦ hwi i),← Finset.sum_add_distrib] + apply Finset.sum_le_sum + intro i _ + have hh := he i + simp only [energy,inner_eq_integral,mul_assoc,← pow_two] at hh + rw [integral_const_mul] + linarith + +lemma compact_trial_bound {N : ℕ} {σ : ℝ} (hσ₀ : 0 < σ) (hσ₁ : σ < 1) + {W : ℝ → ℝ} (hW : LocallyIntegrable W volume) + (hWn : ∀ᵐ x, 0 ≤ W x) (hWp : Integrable (fun x ↦ W x^(1+σ))) + (κ : Fin N → ℝ) (hκ : ∀ i, 0 < κ i) + (q : Fin N → C1L2) (ho : Orthonormal ℝ q) + (hc : ∀ i, HasCompactSupport (q i).val) + (he : ∀ i (v : C1L2), v ∈ Submodule.span ℝ (q '' Iic i) → + energy W v v+κ i^2*inner ℝ v v ≤ 0) : + (∑ i, ∫ s in -(κ i)..κ i, (κ i^2-s^2)^σ) ≤ + actionYoungConstant σ * ∫ x, W x^(1+σ) := by + classical + obtain ⟨R,hR,hvan⟩ := compact_family_radius q hc + apply finite_spectral_trial hσ₀ hσ₁ (l := -R) (r := R) (by linarith) κ hκ + (fun x i ↦ (q i).val x) (fun x i ↦ (q i).grad x) + ((continuous_pi (fun i ↦ (q i).continuous)).continuousOn) + ((continuous_pi (fun i ↦ (q i).grad_continuous)).continuousOn) + (fun x _ i ↦ (q i).hasDerivAt x) + · ext i; exact (hvan i (-R) (by simp [abs_of_pos hR])).1 + · ext i; exact (hvan i R (by simp [abs_of_pos hR])).1 + · intro i j + rw [← integral_eq_interval_of_vanish hR.le (fun x hx ↦ by rw [(hvan i x hx).1,zero_mul]), + ← inner_eq_integral] + exact orthonormal_iff_ite.mp ho i j + · exact locallyIntegrable_intervalIntegrable hW _ _ + · exact hWn + · exact hWp + · intro C + let p := fun i ↦ ∑ j, C.val i j • q j + have hp (i : Fin N) : HasCompactSupport (p i).val := + compact_sum _ _ (fun j _ ↦ compact_smul _ (hc j)) + have hpv (i : Fin N) (x : ℝ) : (p i).val x = (C.val *ᵥ (fun j ↦ (q j).val x)) i := by + simp only [p,val_sum,val_smul,mulVec,dotProduct] + have hpg (i : Fin N) (x : ℝ) : (p i).grad x = (C.val *ᵥ (fun j ↦ (q j).grad x)) i := by + simp only [p,grad_sum,grad_smul,mulVec,dotProduct] + have he' := compact_trial_energy hW κ p hp (fun i ↦ he i (p i) (row_mem_prefix q C i)) + have hz (i : Fin N) (x : ℝ) (hx : R ≤ |x|) : (p i).val x = 0 ∧ (p i).grad x = 0 := by + constructor <;> simp only [p,val_sum,grad_sum,val_smul,grad_smul] <;> + apply Finset.sum_eq_zero <;> intro j _ <;> simp [(hvan j x hx).1,(hvan j x hx).2] + rw [integral_eq_interval_of_vanish hR.le (fun x hx ↦ by simp [(fun i ↦ (hz i x hx).1),(fun i ↦ (hz i x hx).2)]), + integral_eq_interval_of_vanish hR.le (fun x hx ↦ by simp [(fun i ↦ (hz i x hx).1)])] at he' + simpa only [hpv,hpg] using he' + +end SharpLiebThirring.SpectralProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LiebThirring/WeightedCutoff.lean b/lean/OAI/Analysis/LiebThirring/WeightedCutoff.lean new file mode 100644 index 0000000000000000000000000000000000000000..f4dfd9be5f8039f66ee6dbf34aa84963de33819b --- /dev/null +++ b/lean/OAI/Analysis/LiebThirring/WeightedCutoff.lean @@ -0,0 +1,114 @@ +import OAI.Analysis.LiebThirring.LocalCompactness + +namespace OAI + + +noncomputable section +namespace SharpLiebThirring.OperatorProof +open MeasureTheory Set Filter +open scoped Topology BoundedContinuousFunction + +lemma cutoff_memLp (s : Set ℝ) (hs : MeasurableSet s) (f : L2C) : + MemLp (s.indicator f) 2 volume := (Lp.memLp f).indicator hs + +def cutoffLM (s : Set ℝ) (hs : MeasurableSet s) : L2C →ₗ[ℂ] L2C where + toFun f := (cutoff_memLp s hs f).toLp (s.indicator f) + map_add' f g := by + apply Lp.ext + filter_upwards [(cutoff_memLp s hs (f+g)).coeFn_toLp, + (cutoff_memLp s hs f).coeFn_toLp,(cutoff_memLp s hs g).coeFn_toLp, + Lp.coeFn_add ((cutoff_memLp s hs f).toLp (s.indicator f)) + ((cutoff_memLp s hs g).toLp (s.indicator g)),Lp.coeFn_add f g] with x h1 h2 h3 h4 h5 + simp only [Pi.add_apply] at h4 h5 + rw [h1,h4,h2,h3] + by_cases hx : x ∈ s + · simp only [indicator_of_mem hx] + exact h5 + · simp only [indicator_of_notMem hx,zero_add] + map_smul' c f := by + apply Lp.ext + filter_upwards [(cutoff_memLp s hs (c • f)).coeFn_toLp, + (cutoff_memLp s hs f).coeFn_toLp, + Lp.coeFn_smul c ((cutoff_memLp s hs f).toLp (s.indicator f)), + Lp.coeFn_smul c f] with x h1 h2 h3 h4 + simp only [Pi.smul_apply] at h3 h4 + simp only [RingHom.id_apply] + rw [h1,h3,h2] + by_cases hx : x ∈ s <;> simp [hx,h4] + +lemma cutoffLM_norm (s : Set ℝ) (hs : MeasurableSet s) (f : L2C) : + ‖cutoffLM s hs f‖ ≤ ‖f‖ := by + apply Lp.norm_le_norm_of_ae_le + filter_upwards [(cutoff_memLp s hs f).coeFn_toLp] with x hx + change ‖((cutoff_memLp s hs f).toLp (s.indicator f)) x‖ ≤ _ + rw [hx] + exact norm_indicator_le_norm_self _ _ + +def cutoffL (s : Set ℝ) (hs : MeasurableSet s) : L2C →L[ℂ] L2C := + (cutoffLM s hs).mkContinuous 1 (by simpa only [one_mul] using cutoffLM_norm s hs) + +lemma cutoffL_ae (s : Set ℝ) (hs : MeasurableSet s) (f : L2C) : + cutoffL s hs f =ᵐ[volume] s.indicator f := (cutoff_memLp s hs f).coeFn_toLp + +variable {R : ℝ} (hR : 0 ≤ R) {g : ℝ → ℂ} (hg : MemLp g 2 volume) + +private def extendedBCF (f : Interval R →ᵇ ℂ) (x : ℝ) : ℂ := + f (projIcc (-R) R (by linarith) x) + +private lemma extendedBCF_continuous (f : Interval R →ᵇ ℂ) : Continuous (extendedBCF hR f) := + f.continuous.comp continuous_projIcc + +include hg in +private lemma weightedBCF_memLp (f : Interval R →ᵇ ℂ) : + MemLp (fun x ↦ g x*extendedBCF hR f x) 2 volume := by + apply hg.of_le_mul (c := ‖f‖) (hg.aestronglyMeasurable.mul (extendedBCF_continuous hR f).aestronglyMeasurable) + exact Eventually.of_forall fun x ↦ by + change ‖g x * extendedBCF hR f x‖ ≤ ‖f‖ * ‖g x‖ + rw [norm_mul,mul_comm ‖g x‖] + exact mul_le_mul_of_nonneg_right (f.norm_coe_le_norm _) (norm_nonneg _) + +def weightedBCF (f : Interval R →ᵇ ℂ) : L2C := + (weightedBCF_memLp hR hg f).toLp _ + +lemma weightedBCF_ae (f : Interval R →ᵇ ℂ) : + weightedBCF hR hg f =ᵐ[volume] (fun x ↦ g x*extendedBCF hR f x) := + (weightedBCF_memLp hR hg f).coeFn_toLp + +lemma weightedBCF_lipschitz (f f' : Interval R →ᵇ ℂ) : + dist (weightedBCF hR hg f) (weightedBCF hR hg f') ≤ ‖hg.toLp g‖*dist f f' := by + rw [dist_eq_norm,dist_eq_norm,mul_comm] + apply Lp.norm_le_mul_norm_of_ae_le_mul + filter_upwards [weightedBCF_ae hR hg f,weightedBCF_ae hR hg f', + Lp.coeFn_sub (weightedBCF hR hg f) (weightedBCF hR hg f'),hg.coeFn_toLp] with x h1 h2 h3 h4 + simp only [Pi.sub_apply] at h3 + rw [h3,h1,h2,h4,← mul_sub,norm_mul,mul_comm ‖g x‖] + exact mul_le_mul_of_nonneg_right ((f-f').norm_coe_le_norm _) (norm_nonneg _) + +lemma weightedBCF_continuous : Continuous (weightedBCF hR hg) := + (show LipschitzWith ⟨‖hg.toLp g‖,norm_nonneg _⟩ (weightedBCF hR hg) from + LipschitzWith.of_dist_le_mul (weightedBCF_lipschitz hR hg)).continuous + +lemma weightedBCF_localRep_ae (hsupp : ∀ x ∉ Interval R, g x = 0) (u : H1C) : + weightedBCF hR hg (localRep R u) =ᵐ[volume] (fun x ↦ g x * valL u x) := by + filter_upwards [weightedBCF_ae hR hg (localRep R u), continuousRep_ae u] with x hx hu + rw [hx] + by_cases hs : x ∈ Interval R + · simp only [extendedBCF,projIcc_of_mem _ hs,localRep, + BoundedContinuousFunction.mkOfCompact_apply,ContinuousMap.coe_mk] + rw [hu] + · rw [hsupp x hs,zero_mul,zero_mul] + +lemma localRep_isCompact (R : ℝ) : IsCompactOperator (localRep R) := by + apply (isCompactOperator_iff_exists_mem_nhds_image_subset_compact (localRep R)).mpr + exact ⟨Metric.closedBall 0 1,Metric.closedBall_mem_nhds 0 zero_lt_one, + closure (localRep R '' Metric.closedBall 0 1),localRep_compact R,subset_closure⟩ + +lemma weightedBCF_localRep_isCompact : + IsCompactOperator (fun u : H1C ↦ weightedBCF hR hg (localRep R u)) := + (localRep_isCompact R).continuous_comp (weightedBCF_continuous hR hg) + +end SharpLiebThirring.OperatorProof + +end + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ActualCharacteristic.lean b/lean/OAI/Analysis/LienardCycles/ActualCharacteristic.lean new file mode 100644 index 0000000000000000000000000000000000000000..7c01a0cb5fa67bc88c128b026dcb28e89cf0d8f8 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ActualCharacteristic.lean @@ -0,0 +1,145 @@ +import OAI.Analysis.LienardCycles.PositiveBase + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ActualCharacteristic +open PartialCalculus QuinticFit +noncomputable def b (a : Fin 6 → ℝ) (t s : ℝ) : ℝ := PositiveWidth.baseAtWidth (QuinticProfile.profile a) ((0,t),s) +def Adm (a : Fin 6 → ℝ) (t s : ℝ) : Prop := PositiveWidth.Admissible (QuinticProfile.profile a) ((0,t),s) +noncomputable def point (a : Fin 6 → ℝ) (t s : ℝ) : ℝ × ℝ := (b a t s,s) +noncomputable def m (a : Fin 6 → ℝ) (t s : ℝ) : ℝ := M a (point a t s) +noncomputable def v (a : Fin 6 → ℝ) (t s : ℝ) : ℝ := V a (point a t s) +noncomputable def A (a : Fin 6 → ℝ) (t s : ℝ) : ℝ := m a t s/s +noncomputable def g (a : Fin 6 → ℝ) (t s : ℝ) : ℝ := s^2-(m a t s)^2 +noncomputable def k (a : Fin 6 → ℝ) (t s : ℝ) : ℝ := ScaledProfile.slope a (b a t s) +noncomputable def c (a : Fin 6 → ℝ) (t s : ℝ) : ℝ := ScaledProfile.curvature a (b a t s) +lemma base_spec {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : + 0 QuinticProfile.analytic a h) (base_spec he).1 (base_spec he).2.1 +lemma m_abs_lt {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : |m a t r| QuinticProfile.analytic a h) (QuinticProfile.local_flow a) he).comp r + (contDiffAt_const.prodMk contDiffAt_id) +lemma adm_eventually {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : ∀ᶠ s in 𝓝 r, Adm a t s := + (continuousAt_const.prodMk continuousAt_id).eventually + (PositiveWidth.base_local _ (fun _ h => QuinticProfile.analytic a h) (QuinticProfile.local_flow a) he).2 +lemma point_analytic {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : ContDiffAt ℝ ω (point a t) r := + (base_analytic he).prodMk contDiffAt_id +lemma m_analytic {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : ContDiffAt ℝ ω (m a t) r := + (M_analytic a (base_spec he).1 (radius_pos he)).comp (f:=point a t) r (point_analytic he) +lemma v_analytic {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : ContDiffAt ℝ ω (v a t) r := + (V_analytic a (base_spec he).1 (radius_pos he)).comp (f:=point a t) r (point_analytic he) +lemma A_analytic {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : ContDiffAt ℝ ω (A a t) r := + (m_analytic he).div contDiffAt_id (radius_pos he).ne' +lemma k_analytic {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : ContDiffAt ℝ ω (k a t) r := + (ScaledProfile.slope_analytic a (base_spec he).1).comp r (base_analytic he) +lemma c_analytic {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : ContDiffAt ℝ ω (c a t) r := + (ScaledProfile.curvature_analytic a (base_spec he).1).comp r (base_analytic he) +lemma base_deriv {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : HasDerivAt (b a t) (-g a t r/r) r := by + have hd := PositiveWidth.base_width_deriv _ (fun _ h => QuinticProfile.analytic a h) (QuinticProfile.local_flow a) he + have hm := PositiveWidth.base_midpoint _ (fun _ h => QuinticProfile.analytic a h) (QuinticProfile.local_flow a) he + change m a t r=_ at hm + rw [←hm] at hd + exact hd +lemma along_deriv {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) {f : ℝ × ℝ → ℝ} + (hf : DifferentiableAt ℝ f (point a t r)) : + HasDerivAt (fun s => f (point a t s)) (-g a t r/r*D a f (point a t r)) r := by + have hd := hf.hasFDerivAt.comp_hasDerivAt r ((base_deriv he).prodMk (hasDerivAt_id r)) + rw [fderiv_pair] at hd + convert! hd using 1 + change -g a t r/r*(first f (point a t r)-r/g a t r*second f (point a t r)) = _ + field_simp [(radius_pos he).ne',(g_pos he).ne'] + ring +lemma m_deriv {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : + HasDerivAt (m a t) (-m a t r/r+g a t r/r*k a t r) r := by + have ht := PositiveTransport.transport_midpoint (QuinticProfile.profile a) (fun _ h => QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) (p:=0) (base_spec he).1 (radius_pos he) + have hp : HasDerivAt (fun u => QuinticProfile.profile a (0,u)) (ScaledProfile.slope a (b a t r)) (b a t r) := ScaledProfile.profile_hasDerivAt a (base_spec he).1 + rw [hp.deriv] at ht + change D a (M a) (point a t r)=m a t r/g a t r-k a t r at ht + have hd := along_deriv he ((M_analytic a (base_spec he).1 (radius_pos he)).differentiableAt (by simp)) + rw [ht] at hd + convert! hd using 1 + field_simp [(radius_pos he).ne',(g_pos he).ne'] + ring +lemma v_deriv {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : + HasDerivAt (v a t) (2*m a t r*(1-(v a t r)^2)/g a t r) r := by + have ht := PositiveTransport.transport_v (QuinticProfile.profile a) (fun _ h => QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) (p:=0) (base_spec he).1 (radius_pos he) + change D a (V a) (point a t r)= -2*m a t r*r*(1-(v a t r)^2)/(g a t r)^2 at ht + have hd := along_deriv he ((V_analytic a (base_spec he).1 (radius_pos he)).differentiableAt (by simp)) + rw [ht] at hd + convert! hd using 1 + field_simp [(radius_pos he).ne',(g_pos he).ne'] +lemma A_deriv {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : + HasDerivAt (A a t) (k a t r*(1-(A a t r)^2)-2*A a t r/r) r := by + convert! (m_deriv he).div (hasDerivAt_id r) (radius_pos he).ne' using 1 + dsimp only [A,g,id_eq] + field_simp [(radius_pos he).ne'] + ring +lemma k_deriv {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : + HasDerivAt (k a t) (-g a t r/r*c a t r) r := by + convert! (ScaledProfile.slope_hasDerivAt a (base_spec he).1).comp r (base_deriv he) using 1 + exact mul_comm _ _ +lemma c_deriv {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : + HasDerivAt (c a t) (-g a t r/r*ScaledProfile.third a (b a t r)) r := by + convert! (ScaledProfile.curvature_hasDerivAt a (base_spec he).1).comp r (base_deriv he) using 1 + exact mul_comm _ _ +noncomputable def L (a : Fin 6 → ℝ) (t s : ℝ) : ℝ := angle (v a t s) +noncomputable def rate (a : Fin 6 → ℝ) (t s : ℝ) : ℝ := 2*A a t s/(s*(1-(A a t s)^2)) +lemma L_deriv {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : HasDerivAt (L a t) (rate a t r) r := by + have hd := (angle_deriv (v_abs_lt he)).comp r (v_deriv he) + convert! hd using 1 + dsimp only [rate,A,g] + have hv : 1-(v a t r)^2≠0 := by + have ht := sq_lt_sq₀ (abs_nonneg _) (by norm_num : (0:ℝ)≤1) |>.mpr (v_abs_lt he) + nlinarith [sq_abs (v a t r)] + field_simp [(radius_pos he).ne',hv] +lemma adm_le {a : Fin 6 → ℝ} {t r s : ℝ} (he : Adm a t r) (hs : 0 QuinticProfile.analytic a h) (QuinticProfile.local_flow a) hb.1 hb.2.1 hs + rw [hb.2.2] + exact hsr +lemma base_tendsto {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : + Tendsto (b a t) (𝓝[>] (0:ℝ)) (𝓝 t) := + PositiveWidth.base_tendsto _ (fun _ h => QuinticProfile.analytic a h) (QuinticProfile.local_flow a) (base_spec he).1 (base_spec he).2.1 +lemma small_limits {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : + Tendsto (A a t) (𝓝[>] (0:ℝ)) (𝓝 0) ∧ Tendsto (L a t) (𝓝[>] (0:ℝ)) (𝓝 0) ∧ + Tendsto (k a t) (𝓝[>] (0:ℝ)) (𝓝 (ScaledProfile.slope a t)) ∧ + Tendsto (c a t) (𝓝[>] (0:ℝ)) (𝓝 (ScaledProfile.curvature a t)) := by + have ht : 0angle (V a (b a t s,s))) (𝓝[>] (0:ℝ)) (𝓝 0) + simpa only [angle_zero,Function.comp_def,id_eq] using + (angle_analytic (by norm_num : |(0:ℝ)|<1)).continuousAt.tendsto.comp hl.2 +end QuinticLienard.ActualCharacteristic + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ActualError.lean b/lean/OAI/Analysis/LienardCycles/ActualError.lean new file mode 100644 index 0000000000000000000000000000000000000000..4a1814f232d3c6a66eceec6f59d97f151a5aa892 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ActualError.lean @@ -0,0 +1,117 @@ +import OAI.Analysis.LienardCycles.FixedSlopeLimit + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ActualCharacteristic +open PartialCalculus QuadraticCoordinates +noncomputable def j (a : Fin 6 → ℝ) (t κ s : ℝ) : ℝ := QuadraticFit.slope ((κ,s),m a t s) +noncomputable def err (a : Fin 6 → ℝ) (t κ s : ℝ) : ℝ := k a t s-j a t κ s +noncomputable def coeff (a : Fin 6 → ℝ) (t κ s : ℝ) : ℝ := g a t s/(s*P ((j a t κ s,κ),s)) +noncomputable def label (a : Fin 6 → ℝ) (t κ s : ℝ) : ℝ := QuadraticFit.label ((κ,s),A a t s) +lemma j_analytic {a : Fin 6 → ℝ} {t κ r : ℝ} (he : Adm a t r) : ContDiffAt ℝ ω (j a t κ) r := + (QuadraticFit.slope_analytic (k:=κ) (radius_pos he) (m_abs_lt he)).comp + (f:=fun s=>((κ,s),m a t s)) r ((contDiffAt_const.prodMk contDiffAt_id).prodMk (m_analytic he)) +lemma j_spec {a : Fin 6 → ℝ} {t κ r : ℝ} (he : Adm a t r) : H ((j a t κ r,κ),r)=m a t r := + QuadraticFit.slope_spec (radius_pos he) (m_abs_lt he) +lemma j_deriv {a : Fin 6 → ℝ} {t κ r : ℝ} (he : Adm a t r) : + HasDerivAt (j a t κ) (-κ*g a t r/r+coeff a t κ r*err a t κ r) r := by + have hj := (j_analytic (κ:=κ) he).differentiableAt (by simp) + have hd := (H_analytic (d:=j a t κ r) (k:=κ) (radius_pos he)).differentiableAt (by simp) + |>.hasFDerivAt.comp_hasDerivAt (f:=fun s=>((j a t κ s,κ),s)) r + ((hj.hasDerivAt.prodMk (hasDerivAt_const r κ)).prodMk (hasDerivAt_id r)) + have hev : (fun s=>H ((j a t κ s,κ),s)) =ᶠ[𝓝 r] m a t := by + filter_upwards [adm_eventually he] with s hs + exact j_spec hs + have hq := hd.unique ((m_deriv he).congr_of_eventuallyEq hev) + rw [fderiv_model] at hq + change deriv (j a t κ) r*P ((j a t κ r,κ),r)+0*Q ((j a t κ r,κ),r)+1*Hr ((j a t κ r,κ),r)=_ at hq + have hw := width_identity (d:=j a t κ r) (k:=κ) (radius_pos he) + change κ*P ((j a t κ r,κ),r)+j a t κ r=(r*Hr ((j a t κ r,κ),r)+H ((j a t κ r,κ),r))/(r^2-H ((j a t κ r,κ),r)^2) at hw + rw [j_spec he] at hw + have hP := (QuadraticVariation.P_pos (d:=j a t κ r) (k:=κ) (radius_pos he)).ne' + have heq : deriv (j a t κ) r = -κ*g a t r/r+coeff a t κ r*err a t κ r := by + dsimp only [coeff,err] + change κ*P ((j a t κ r,κ),r)+j a t κ r=(r*Hr ((j a t κ r,κ),r)+m a t r)/g a t r at hw + have hw' := (eq_div_iff (g_pos he).ne').mp hw + have hq' : (deriv (j a t κ) r*P ((j a t κ r,κ),r)+Hr ((j a t κ r,κ),r))*r = -m a t r+g a t r*k a t r := by + calc + _ = (-m a t r/r+g a t r/r*k a t r)*r := by + congr 1 + simpa only [zero_mul,one_mul,add_zero] using hq + _ = _ := by field_simp [(radius_pos he).ne'] + field_simp [(radius_pos he).ne',hP] + nlinarith [hw',hq'] + rw [←heq] + exact hj.hasDerivAt +lemma err_deriv {a : Fin 6 → ℝ} {t κ r : ℝ} (he : Adm a t r) : + HasDerivAt (err a t κ) (-coeff a t κ r*err a t κ r-g a t r/r*(c a t r-κ)) r := by + convert! (k_deriv he).sub (j_deriv (κ:=κ) he) using 1 + ring +lemma coeff_pos {a : Fin 6 → ℝ} {t κ r : ℝ} (he : Adm a t r) : 0((j a t κ s,κ),s)) r := + (((j_analytic he).continuousAt.prodMk continuousAt_const).prodMk continuousAt_id) + have hP : ContinuousAt (fun s=>P ((j a t κ s,κ),s)) r := + (P_analytic (d:=j a t κ r) (k:=κ) (radius_pos he)).continuousAt.comp (f:=fun s=>((j a t κ s,κ),s)) hq + exact ((continuousAt_id.pow 2).sub ((m_analytic he).continuousAt.pow 2)).div + (continuousAt_id.mul hP) (mul_ne_zero (radius_pos he).ne' (QuadraticVariation.P_pos (radius_pos he)).ne') +lemma err_tendsto {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) (κ : ℝ) : + Tendsto (err a t κ) (𝓝[>] (0:ℝ)) (𝓝 0) := by + have hj := QuinticFit.fixed_slope_limit (a:=a) ((base_spec he).1.trans (base_spec he).2.1) κ + (base_tendsto he) (tendsto_id.mono_left inf_le_left) self_mem_nhdsWithin + change Tendsto (fun s=>k a t s-QuadraticFit.slope ((κ,s),QuinticFit.M a (b a t s,s))) (𝓝[>] (0:ℝ)) (𝓝 0) + simpa only [sub_self,id_eq] using (small_limits he).2.2.1.sub hj +lemma label_analytic {a : Fin 6 → ℝ} {t κ r : ℝ} (he : Adm a t r) : ContDiffAt ℝ ω (label a t κ) r := + (QuadraticFit.label_analytic (k:=κ) (radius_pos he) (A_abs_lt he)).comp + (f:=fun s=>((κ,s),A a t s)) r ((contDiffAt_const.prodMk contDiffAt_id).prodMk (A_analytic he)) +lemma label_spec {a : Fin 6 → ℝ} {t κ r : ℝ} (he : Adm a t r) : + ReferenceCharacteristic.A ((label a t κ r,κ),r)=A a t r := + QuadraticFit.label_spec (radius_pos he) (A_abs_lt he) +lemma label_J {a : Fin 6 → ℝ} {t κ r : ℝ} (he : Adm a t r) : + ReferenceCharacteristic.J ((label a t κ r,κ),r)=j a t κ r := by + symm + apply QuadraticFit.slope_eq (radius_pos he) (m_abs_lt he) + have hh := label_spec (κ:=κ) he + change H ((ReferenceCharacteristic.J ((label a t κ r,κ),r),κ),r)/r=m a t r/r at hh + exact (div_left_inj' (radius_pos he).ne').mp hh +lemma label_deriv {a : Fin 6 → ℝ} {t κ r : ℝ} (he : Adm a t r) : + HasDerivAt (label a t κ) (err a t κ r*(1-(A a t r)^2)/ReferenceCharacteristic.Az ((label a t κ r,κ),r)) r := by + have hz := (label_analytic (κ:=κ) he).differentiableAt (by simp) + have hd := (ReferenceCharacteristic.A_analytic (q:=((label a t κ r,κ),r)) (radius_pos he)).differentiableAt (by simp) + |>.hasFDerivAt.comp_hasDerivAt (f:=fun s=>((label a t κ s,κ),s)) r + ((hz.hasDerivAt.prodMk (hasDerivAt_const r κ)).prodMk (hasDerivAt_id r)) + have hev : (fun s=>ReferenceCharacteristic.A ((label a t κ s,κ),s)) =ᶠ[𝓝 r] A a t := by + filter_upwards [adm_eventually he] with s hs + exact label_spec hs + have hq := hd.unique ((A_deriv he).congr_of_eventuallyEq hev) + rw [fderiv_model] at hq + have hs := (ReferenceCharacteristic.A_analytic (q:=((label a t κ r,κ),r)) (radius_pos he)).differentiableAt (by simp) + |>.hasFDerivAt.comp_hasDerivAt r ((hasDerivAt_const r (label a t κ r,κ)).prodMk (hasDerivAt_id r)) + have hs' := hs.unique (ReferenceCharacteristic.A_deriv (radius_pos he)) + change direction ((0,0),1) ReferenceCharacteristic.A ((label a t κ r,κ),r)=_ at hs' + rw [hs',label_spec he,label_J he] at hq + have hn := (ReferenceCharacteristic.Az_pos (z:=label a t κ r) (k:=κ) (radius_pos he)).ne' + have heq : deriv (label a t κ) r=err a t κ r*(1-(A a t r)^2)/ReferenceCharacteristic.Az ((label a t κ r,κ),r) := by + apply (eq_div_iff hn).mpr + dsimp only [ReferenceCharacteristic.Az,err] at hq ⊢ + linarith + rw [←heq] + exact hz.hasDerivAt +end QuinticLienard.ActualCharacteristic + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ActualFitLimits.lean b/lean/OAI/Analysis/LienardCycles/ActualFitLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..1ce299cfdffb54f08aa1644059f43fbd14d66616 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ActualFitLimits.lean @@ -0,0 +1,86 @@ +import OAI.Analysis.LienardCycles.CurvatureTransport + +namespace OAI + +universe uι + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuinticFit +open ScaledProfile SmallWidth QuadraticCoordinates +lemma fit_limits {a : Fin 6 → ℝ} {h₀ : ℝ} (hh₀ : 0 lambda a (h z,r z)) l (𝓝 (slope a h₀)) ∧ + Tendsto (fun z => kappa a (h z,r z)) l (𝓝 (curvature a h₀)) := by + let c := h₀/2 + have hc : 0 (r z)^5) l (𝓝 0) := by simpa using hr.pow 5 + have hn : ∀ᶠ z in l, (r z)^5≠0 := hp.mono (fun _ hz => pow_ne_zero _ hz.ne') + have hqF := fiber_quotient_tendsto (hF.hasStrictFDerivAt (by simp)) (hh.prodMk_nhds hr) he hn + have hqG := fiber_quotient_tendsto (hG.hasStrictFDerivAt (by simp)) (hh.prodMk_nhds hr) he hn + have hlF := (hr.pow 4).mul hqF + have hlG := (hr.pow 2).mul hqG + have hb : ∀ᶠ z in l, c+(r z)^2 h z-c-(r z)^2) l (𝓝 (h₀-c)) := by + simpa using (hh.sub tendsto_const_nhds).sub (hr.pow 2) + filter_upwards [ht.eventually (eventually_gt_nhds (sub_pos.mpr hch))] with z hz + linarith + constructor + · have ht := ((slope_analytic a hh₀).continuousAt.tendsto.comp hh).add hlF + simp only [zero_pow (by norm_num : (4:ℕ)≠0),zero_mul,add_zero] at ht + apply ht.congr' + filter_upwards [hp,hb] with z hz hbz + dsimp + rw [(pulled_actual hc hbz.le hz).1,(pulled_zero hc hbz.le).1] + field_simp + ring + · have ht := ((curvature_analytic a hh₀).continuousAt.tendsto.comp hh).add hlG + simp only [zero_pow (by norm_num : (2:ℕ)≠0),zero_mul,add_zero] at ht + apply ht.congr' + filter_upwards [hp,hb] with z hz hbz + dsimp + rw [(pulled_actual hc hbz.le hz).2,(pulled_zero hc hbz.le).2] + field_simp + ring +lemma normalized_limits {a : Fin 6 → ℝ} {h₀ : ℝ} (hh₀ : 0 M a (h z,r z)/r z) l (𝓝 0) ∧ + Tendsto (fun z => V a (h z,r z)) l (𝓝 0) := by + have hf := fit_limits (a:=a) hh₀ hh hr hp + have hd : Tendsto (fun z => r z*lambda a (h z,r z)) l (𝓝 0) := by simpa using hr.mul hf.1 + have hk : Tendsto (fun z => (r z)^3*kappa a (h z,r z)) l (𝓝 0) := by simpa using (hr.pow 3).mul hf.2 + have ht := (hd.prodMk_nhds hk).prodMk_nhds (tendsto_const_nhds (x:=(1:ℝ))) + have hM := (H_analytic (d:=0) (k:=0) (by norm_num : (0:ℝ)<1)).continuousAt.tendsto.comp ht + have hV := (Hr_analytic (d:=0) (k:=0) (by norm_num : (0:ℝ)<1)).continuousAt.tendsto.comp ht + rw [(zero_data (by norm_num : (0:ℝ)<1)).2] at hM + rw [Hr_zero (by norm_num : (0:ℝ)<1)] at hV + constructor + · apply hM.congr' + filter_upwards [hp,hh.eventually (eventually_gt_nhds hh₀)] with z hz hhz + have he := scaling (lambda a (h z,r z)) (kappa a (h z,r z)) hz + rw [show H ((lambda a (h z,r z),kappa a (h z,r z)),r z)=M a (h z,r z) from (spec a hhz hz).1] at he + exact (eq_div_iff hz.ne').mpr (by simpa only [Function.comp_apply,mul_comm] using he.symm) + · apply hV.congr' + filter_upwards [hp,hh.eventually (eventually_gt_nhds hh₀)] with z hz hhz + have he := Hr_scaling (lambda a (h z,r z)) (kappa a (h z,r z)) hz (by norm_num : (0:ℝ)<1) + simpa only [Function.comp_apply,mul_one,show Hr ((lambda a (h z,r z),kappa a (h z,r z)),r z)=V a (h z,r z) from (spec a hhz hz).2] using he.symm +end QuinticLienard.QuinticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ActualFitTransport.lean b/lean/OAI/Analysis/LienardCycles/ActualFitTransport.lean new file mode 100644 index 0000000000000000000000000000000000000000..f35acb3d15f1fe6bf557ba8468533ecfd241f32b --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ActualFitTransport.lean @@ -0,0 +1,149 @@ +import OAI.Analysis.LienardCycles.ProfileDerivatives + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open scoped Topology +open Set Filter MeasureTheory +open Set Filter Asymptotics +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuinticFit +open ScaledProfile PartialCalculus QuadraticCoordinates +noncomputable def M (a : Fin 6 → ℝ) : ℝ × ℝ → ℝ := PositiveTransport.M (QuinticProfile.profile a) 0 +noncomputable def V (a : Fin 6 → ℝ) : ℝ × ℝ → ℝ := PositiveTransport.v (QuinticProfile.profile a) 0 +lemma M_analytic (a : Fin 6 → ℝ) {h r : ℝ} (hh : 0 QuinticProfile.analytic a h) (QuinticProfile.local_flow a) hh hr +lemma V_analytic (a : Fin 6 → ℝ) {h r : ℝ} (hh : 0 QuinticProfile.analytic a h) (QuinticProfile.local_flow a) hh hr +lemma M_abs_lt (a : Fin 6 → ℝ) {h r : ℝ} (hh : 0 QuinticProfile.analytic a h) (QuinticProfile.local_flow a) hh hr +lemma V_abs_lt (a : Fin 6 → ℝ) {h r : ℝ} (hh : 0 QuinticProfile.analytic a h) (QuinticProfile.local_flow a) hh hr +lemma n_eq_V (a : Fin 6 → ℝ) {h r : ℝ} (hh : 0 QuinticProfile.analytic a h) (QuinticProfile.local_flow a) hh hr).unique + (second_hasDerivAt ((M_analytic a hh hr).differentiableAt (by simp))) +lemma fit_eq (a : Fin 6 → ℝ) {h r : ℝ} (hh : 0 ((L (h,s),K (h,s)),s)) + (((second_hasDerivAt hL).prodMk (second_hasDerivAt hK)).prodMk (hasDerivAt_id r)) + rw [fderiv_model] at hd₁ hd₂ + simp only [zero_mul,add_zero,one_mul] at hd₁ hd₂ + exact ⟨(first_hasDerivAt hX).unique (hd₁.congr_of_eventuallyEq + ((continuousAt_id.prodMk continuousAt_const).eventually he)), + (second_hasDerivAt hX).unique (hd₂.congr_of_eventuallyEq + ((continuousAt_const.prodMk continuousAt_id).eventually he))⟩ +lemma chain_M (a : Fin 6 → ℝ) {h r : ℝ} (hh : 0 QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) (p:=0) hh hr + have htv := PositiveTransport.transport_v (QuinticProfile.profile a) (fun _ h => QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) (p:=0) hh hr + have hder : deriv (fun u => QuinticProfile.profile a (0,u)) h=slope a h := (profile_hasDerivAt a hh).deriv + rw [hder] at ht + change first (M a) (h,r)-α a (h,r)*V a (h,r)=M a (h,r)/(r^2-M a (h,r)^2)-slope a h at ht + change first (V a) (h,r)-α a (h,r)*second (V a) (h,r)= -2*M a (h,r)*r*(1-V a (h,r)^2)/(r^2-M a (h,r)^2)^2 at htv + have hb := transport_H (d:=lambda a (h,r)) (k:=kappa a (h,r)) hr + have hbv := transport_Hr (d:=lambda a (h,r)) (k:=kappa a (h,r)) hr + change kappa a (h,r)*P (fit a (h,r))-alpha (fit a (h,r))*Hr (fit a (h,r)) = _ at hb + change kappa a (h,r)*R (fit a (h,r))-alpha (fit a (h,r))*Hrr (fit a (h,r)) = _ at hbv + have hal : alpha (fit a (h,r))=α a (h,r) := by dsimp only [alpha,gap]; rw [hs.1]; rfl + have hg : gap (fit a (h,r))=r^2-M a (h,r)^2 := by dsimp only [gap]; rw [hs.1]; rfl + change _ = H (fit a (h,r))/gap (fit a (h,r))-lambda a (h,r) at hb + change _ = -2*H (fit a (h,r))*r*(1-Hr (fit a (h,r))^2)/gap (fit a (h,r))^2 at hbv + rw [hal,hg,hs.1,hs.2] at hb + rw [hal,hg,hs.1,hs.2] at hbv + have h₁ : P (fit a (h,r))*(D a (lambda a) (h,r)-kappa a (h,r))+Q (fit a (h,r))*D a (kappa a) (h,r)=lambda a (h,r)-slope a h := by + dsimp only [D] + linear_combination -hm.1 + ht - hb + α a (h,r)*hm.2 + α a (h,r)*hs.2 + have h₂ : R (fit a (h,r))*(D a (lambda a) (h,r)-kappa a (h,r))+S (fit a (h,r))*D a (kappa a) (h,r)=0 := by + dsimp only [D] + linear_combination -hv.1 + htv - hbv + α a (h,r)*hv.2 + have hG : G (fit a (h,r))≠0 := (G_pos hr).ne' + refine ⟨?_,?_,?_⟩ + · linear_combination -hs.2 - hm.2 + · rw [div_mul_eq_mul_div] + apply (eq_div_iff hG).mpr + dsimp only [G] + linear_combination P (fit a (h,r))*h₂-R (fit a (h,r))*h₁ + · rw [div_mul_eq_mul_div] + apply (eq_div_iff hG).mpr + dsimp only [G] + linear_combination S (fit a (h,r))*h₁-Q (fit a (h,r))*h₂ +end QuinticLienard.QuinticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ActualReflection.lean b/lean/OAI/Analysis/LienardCycles/ActualReflection.lean new file mode 100644 index 0000000000000000000000000000000000000000..922a624c9a790f684e233aaf938005a186c7f77f --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ActualReflection.lean @@ -0,0 +1,106 @@ +import OAI.Analysis.LienardCycles.CurvaturePositive + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuinticFit +open ScalarArcs PartialCalculus QuadraticCoordinates +lemma profile_neg (a : Fin 6 → ℝ) (q : ℝ × ℝ) : + QuinticProfile.profile (-a) q = -QuinticProfile.profile a q := by + dsimp [QuinticProfile.profile,ScaledProfile.poly] + ring +lemma M_neg (a : Fin 6 → ℝ) {h r : ℝ} (hh : 0QuinticProfile.analytic a ht) + (QuinticProfile.local_flow a) (p:=0) hh hr + have ha := chosen_arch (positive_arch_exists (PositiveWidth.profile_C1 Φ + (fun _ ht=>QuinticProfile.analytic a ht) 0) hh hs.1) + have hb := ArchSymmetries.IsArch.reflect ha + have hf : (fun x=> -Φ (0,x)) = (fun x=>QuinticProfile.profile (-a) (0,x)) := by + funext x + exact (profile_neg a (0,x)).symm + rw [hf] at hb + have hw : (-lower (fun x=>Φ (0,x)) h t- -upper (fun x=>Φ (0,x)) h t)/2=r := by + have hs2 := hs.2 + change (upper (fun x=>Φ (0,x)) h t-lower (fun x=>Φ (0,x)) h t)/2=r at hs2 + linarith [hs2] + have hm := PositiveWidth.midpoint_of_arch (QuinticProfile.profile (-a)) + (fun _ ht=>QuinticProfile.analytic (-a) ht) (QuinticProfile.local_flow (-a)) hb hh hs.1 hr hw + change M (-a) (h,r)=_ at hm + rw [hm,profile_neg] + dsimp [M,PositiveTransport.M,PositiveWidth.midpointAtWidth,PositiveWidth.midpointFamily,ScalarArcs.midpoint,t,Φ] + ring +lemma V_neg (a : Fin 6 → ℝ) {h r : ℝ} (hh : 0 (c_deriv (adm_le he hs.1 hs.2)).continuousAt.continuousWithinAt) + intro s hs + have he' := adm_le he (interior_subset hs).1 (interior_subset hs).2 + rw [(c_deriv he').deriv] + exact mul_neg_of_neg_of_pos (div_neg_of_neg_of_pos (neg_neg_of_pos (g_pos he')) (radius_pos he')) + (hthird _ (base_spec he').1) +lemma label_strictAnti_of_error {a : Fin 6 → ℝ} {t r κ : ℝ} (he : Adm a t r) + (hthird : ∀ h, 0 (coeff_continuous (adm_le he hs.1 hs.2)).continuousWithinAt) + (fun s hs => coeff_pos (adm_le he hs.1 hs.2)) + (fun s hs => div_pos (g_pos (adm_le he hs.1 hs.2)) hs.1) + (c_strictAnti he hthird) (fun s hs => err_deriv (adm_le he hs.1 hs.2)) + (err_tendsto he κ) herr + apply strictAntiOn_of_deriv_neg (convex_Ioc 0 r) + (fun s hs => (label_deriv (adm_le he hs.1 hs.2)).continuousAt.continuousWithinAt) + intro s hs + rw [interior_Ioc] at hs + have he' := adm_le he hs.1 hs.2.le + rw [(label_deriv (κ:=κ) he').deriv] + have hg : 0<1-(A a t s)^2 := by + have hh := sq_lt_sq₀ (abs_nonneg _) (by norm_num : (0:ℝ)≤1) |>.mpr (A_abs_lt he') + nlinarith [sq_abs (A a t s)] + exact div_neg_of_neg_of_pos (mul_neg_of_neg_of_pos (hn hs.1 hs.2) hg) + (ReferenceCharacteristic.Az_pos (radius_pos he')) +lemma j_eq_lambda {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : + j a t (QuinticFit.kappa a (point a t r)) r=QuinticFit.lambda a (point a t r) := by + apply QuadraticFit.slope_eq (radius_pos he) (m_abs_lt he) + exact (QuinticFit.spec a (base_spec he).1 (radius_pos he)).1 +lemma L_matched {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : + ReferenceCharacteristic.L ((label a t (QuinticFit.kappa a (point a t r)) r, + QuinticFit.kappa a (point a t r)),r)=L a t r := by + dsimp only [ReferenceCharacteristic.L,ReferenceCharacteristic.D,L] + rw [label_J he,j_eq_lambda he] + congr 1 + exact (QuinticFit.spec a (base_spec he).1 (radius_pos he)).2 +lemma rate_gt_reference {a : Fin 6 → ℝ} {t r κ s : ℝ} (he : Adm a t r) + (hthird : ∀ h, 0ReferenceCharacteristic.E ((z,κ),s)) := by + apply strictMono_of_deriv_pos + intro z + rw [(ReferenceCharacteristic.E_z_deriv (z:=z) (k:=κ) hs).deriv] + exact mul_pos (ReferenceCharacteristic.K_pos hs) (ReferenceCharacteristic.Az_pos hs) + have hh := hm hz + change _ < 2*ReferenceCharacteristic.A ((label a t κ s,κ),s)/(s*(1-ReferenceCharacteristic.A ((label a t κ s,κ),s)^2)) at hh + rw [label_spec (adm_le he hs hsr.le)] at hh + exact hh + +theorem fitted_slope_lt {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) + (hthird : ∀ h, 0L a t s-ReferenceCharacteristic.L ((label a t κ r,κ),s)) (radius_pos he) + (by simpa only [sub_self] using ((small_limits he).2.1.sub + (ReferenceCharacteristic.L_tendsto_zero (label a t κ r) κ))) + apply strictMonoOn_of_deriv_pos (convex_Ioc 0 r) + (fun s hs => ((L_deriv (adm_le he hs.1 hs.2)).sub + (ReferenceCharacteristic.L_deriv hs.1)).continuousAt.continuousWithinAt) + intro s hs + rw [interior_Ioc] at hs + rw [((L_deriv (adm_le he hs.1 hs.2.le)).sub + (ReferenceCharacteristic.L_deriv (z:=label a t κ r) (k:=κ) hs.1)).deriv] + exact sub_pos.mpr (rate_gt_reference he hthird herr hs.1 hs.2) + rw [L_matched he,sub_self] at hp + exact (lt_irrefl 0) hp +end QuinticLienard.ActualCharacteristic + +namespace QuinticLienard.QuinticFit + +theorem lambda_lt_slope {a : Fin 6 → ℝ} {h r : ℝ} (hh : 0QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) (p:=0) hh hr + have he : ActualCharacteristic.Adm a t r := ⟨h,hh,ht.1,ht.2⟩ + have hb : ActualCharacteristic.b a t r=h := PositiveWidth.base_eq _ + (fun _ h=>QuinticProfile.analytic a h) (QuinticProfile.local_flow a) hh ht.1 ht.2 + simpa only [ActualCharacteristic.point,ActualCharacteristic.k,hb] using + ActualCharacteristic.fitted_slope_lt he hthird +end QuinticLienard.QuinticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ActualSmallWidth.lean b/lean/OAI/Analysis/LienardCycles/ActualSmallWidth.lean new file mode 100644 index 0000000000000000000000000000000000000000..0527ec0d958bac68cfde7aac52acd59c919d9030 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ActualSmallWidth.lean @@ -0,0 +1,62 @@ +import OAI.Analysis.LienardCycles.ScaledActual + +namespace OAI + +universe uι + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open scoped Topology +open Set Filter MeasureTheory +open Set Filter Asymptotics +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuinticFit +open ScaledProfile SmallWidth PartialCalculus +lemma pulled_fiber {a : Fin 6 → ℝ} {c h : ℝ} (hc : 0 pulledCurvature a c ((h,0),e)) + (fiber (pulledCurvature a c) ((h,0),0)) 0 := + hs.hasFDerivAt.comp_hasDerivAt 0 ((hasDerivAt_const 0 (h,0)).prodMk (hasDerivAt_id 0)) + have hcub := (fit_cubic (a:=a) hc (Real.sqrt (h-c))).2 + have hh' : c+(Real.sqrt (h-c))^2=h := by rw [Real.sq_sqrt (by linarith)]; ring + rw [hh'] at hcub + apply hd.unique + simpa only [pulledCurvature,Function.comp_def,pull,zero_pow (by norm_num : (2:ℕ)≠0),sub_zero] using! hcub +lemma kappa_deriv_correction {a : Fin 6 → ℝ} {c h r : ℝ} + (hc : 0 kappa a (h,s)) r=deriv (fun s => correction (pulledCurvature a c) (h,s)) r := by + have hev : (fun s => kappa a (h,s)) =ᶠ[𝓝 r] + (fun s => curvature a h+correction (pulledCurvature a c) (h,s)) := by + filter_upwards [continuousAt_const.eventually_lt continuousAt_id hr, + (continuousAt_const.add (continuousAt_id.pow 2)).eventually_lt continuousAt_const hh] with s hs hh' + exact kappa_correction hc hh'.le hs + rw [hev.deriv_eq,deriv_const_add] +lemma kappa_deriv_limit {a : Fin 6 → ℝ} {h₀ : ℝ} (hh₀ : 0 deriv (fun s => kappa a (h z,s)) (r z)/r z) l (𝓝 (4*third a h₀/7)) := by + let c := h₀/2 + have hc : 0 hz.ne')) + rw [pulled_fiber hc hch] at hl + have he : 2*(2*third a h₀/7)=4*third a h₀/7 := by ring + rw [he] at hl + apply hl.congr' + have hlim : Tendsto (fun z => h z-c-(r z)^2) l (𝓝 (h₀-c)) := by + simpa using (hh.sub tendsto_const_nhds).sub (hr.pow 2) + filter_upwards [hp,hlim.eventually (eventually_gt_nhds (sub_pos.mpr hch))] with z hz hh' + rw [kappa_deriv_correction hc (by linarith) hz] +end QuinticLienard.QuinticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AlgebraicFlow.lean b/lean/OAI/Analysis/LienardCycles/AlgebraicFlow.lean new file mode 100644 index 0000000000000000000000000000000000000000..73b96a545457f4637b17b34ae8db667c54f2b73f --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AlgebraicFlow.lean @@ -0,0 +1,146 @@ +import OAI.Analysis.LienardCycles.SqrtPaths + +namespace OAI + +universe uE uF uP + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter +open Set Filter Metric +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.SmoothFlow +variable {E : Type uE} [NormedAddCommGroup E] [NormedSpace ℝ E] +noncomputable def pathMap {F : Type uF} [NormedAddCommGroup F] [NormedSpace ℝ F] + (L : E →L[ℝ] F) : Path E →L[ℝ] Path F := + ContinuousLinearMap.compLeftContinuous ℝ UnitInterval L +@[simp] lemma pathMap_apply {F : Type uF} [NormedAddCommGroup F] [NormedSpace ℝ F] + (L : E →L[ℝ] F) (u : Path E) (s : UnitInterval) : pathMap L u s=L (u s) := rfl +@[simp] lemma pathMap_const {F : Type uF} [NormedAddCommGroup F] [NormedSpace ℝ F] + (L : E →L[ℝ] F) (x : E) : pathMap L (constCLM x)=constCLM (L x) := rfl +inductive AlgebraicExpr (E : Type uE) [NormedAddCommGroup E] [NormedSpace ℝ E] where + | const : ℝ → AlgebraicExpr E + | linear : (E →L[ℝ] ℝ) → AlgebraicExpr E + | add : AlgebraicExpr E → AlgebraicExpr E → AlgebraicExpr E + | mul : AlgebraicExpr E → AlgebraicExpr E → AlgebraicExpr E + | inv : AlgebraicExpr E → AlgebraicExpr E + | sqrt : AlgebraicExpr E → AlgebraicExpr E +namespace AlgebraicExpr +noncomputable def eval : AlgebraicExpr E → E → ℝ + | const c, _ => c + | linear L, x => L x + | add p q,x => p.eval x+q.eval x + | mul p q,x => p.eval x*q.eval x + | inv p,x => (p.eval x)⁻¹ + | sqrt p,x => Real.sqrt (p.eval x) +def RegularAt : AlgebraicExpr E → E → Prop + | const _,_ => True + | linear _,_ => True + | add p q,x => p.RegularAt x ∧ q.RegularAt x + | mul p q,x => p.RegularAt x ∧ q.RegularAt x + | inv p,x => p.RegularAt x ∧ p.eval x≠0 + | sqrt p,x => p.RegularAt x ∧ 0 exact contDiffAt_const + | linear L => exact L.contDiff.contDiffAt + | add p q ihp ihq => exact (ihp hp.1).add (ihq hp.2) + | mul p q ihp ihq => exact (ihp hp.1).mul (ihq hp.2) + | inv p ih => exact (ih hp.1).inv hp.2 + | sqrt p ih => exact (ih hp.1).sqrt (ne_of_gt hp.2) +noncomputable def onPaths : AlgebraicExpr E → Path E → Path ℝ + | const c,_ => constCLM c + | linear L,u => pathMap L u + | add p q,u => p.onPaths u+q.onPaths u + | mul p q,u => p.onPaths u*q.onPaths u + | inv p,u => Ring.inverse (p.onPaths u) + | sqrt p,u => sqrtPath (p.onPaths u) +lemma path_properties (p : AlgebraicExpr E) {x : E} (hp : p.RegularAt x) : + p.onPaths (constCLM x)=constCLM (p.eval x) ∧ + ContDiffAt ℝ ω p.onPaths (constCLM x) ∧ + ∀ᶠ u in 𝓝 (constCLM x), ∀ s, p.onPaths u s=p.eval (u s) := by + induction p with + | const c => exact ⟨rfl,contDiffAt_const,Eventually.of_forall (fun _ _ => rfl)⟩ + | linear L => exact ⟨rfl,(pathMap L).contDiff.contDiffAt,Eventually.of_forall (fun _ _ => rfl)⟩ + | add p q ihp ihq => + obtain ⟨hp0,hpd,hpe⟩ := ihp hp.1 + obtain ⟨hq0,hqd,hqe⟩ := ihq hp.2 + refine ⟨?_,hpd.add hqd,?_⟩ + · simp only [onPaths,hp0,hq0]; ext s; rfl + · filter_upwards [hpe,hqe] with u hu hv s + exact congrArg₂ (·+·) (hu s) (hv s) + | mul p q ihp ihq => + obtain ⟨hp0,hpd,hpe⟩ := ihp hp.1 + obtain ⟨hq0,hqd,hqe⟩ := ihq hp.2 + refine ⟨?_,hpd.mul hqd,?_⟩ + · simp only [onPaths,hp0,hq0]; ext s; rfl + · filter_upwards [hpe,hqe] with u hu hv s + exact congrArg₂ (·*·) (hu s) (hv s) + | inv p ih => + obtain ⟨hp0,hpd,hpe⟩ := ih hp.1 + have hunit : IsUnit (p.onPaths (constCLM x)) := by + rw [hp0] + exact (ContinuousMap.isUnit_iff_forall_ne_zero _).mpr (fun _ => hp.2) + have hinv : ContDiffAt ℝ ω Ring.inverse (p.onPaths (constCLM x)) := by + have hh := contDiffAt_ringInverse ℝ (n:=ω) hunit.unit + rw [hunit.unit_spec] at hh + exact hh + refine ⟨?_,hinv.comp _ hpd,?_⟩ + · ext s + rw [onPaths,RationalExpr.inverse_eval _ hunit,hp0] + rfl + · have hu : ∀ᶠ u in 𝓝 (constCLM x), IsUnit (p.onPaths u) := + hpd.continuousAt.eventually (Units.isOpen.mem_nhds hunit) + filter_upwards [hpe,hu] with u he hunit s + rw [onPaths,RationalExpr.inverse_eval _ hunit,he s] + rfl + | sqrt p ih => + obtain ⟨hp0,hpd,hpe⟩ := ih hp.1 + refine ⟨?_,?_,?_⟩ + · simp only [onPaths,hp0,sqrtPath_const,eval] + · apply (show ContDiffAt ℝ ω sqrtPath (p.onPaths (constCLM x)) by rw [hp0]; exact sqrtPath_analytic hp.2).comp _ hpd + · filter_upwards [hpe] with u hu s + exact congrArg Real.sqrt (hu s) +end AlgebraicExpr + +open ArcFamilies +variable {P : Type uP} [NormedAddCommGroup P] [NormedSpace ℝ P] [CompleteSpace P] + +theorem algebraic_profile_flow (e : AlgebraicExpr (P × ℝ)) (x : State P) + (he : e.RegularAt (x.1,x.2.1)) : + ∃ f : State P × ℝ → State P, ContDiffAt ℝ ω f (x,0) ∧ + ∀ᶠ q in 𝓝 (x,(0:ℝ)), f (q.1,0)=q.1 ∧ + HasDerivAt (fun s => f (q.1,s)) (field e.eval (f q)) q.2 := by + let L : State P →L[ℝ] P × ℝ := + (ContinuousLinearMap.fst ℝ P (ℝ×ℝ)).prod + ((ContinuousLinearMap.fst ℝ ℝ ℝ).comp (ContinuousLinearMap.snd ℝ P (ℝ×ℝ))) + let Y : State P →L[ℝ] ℝ := + (ContinuousLinearMap.snd ℝ ℝ ℝ).comp (ContinuousLinearMap.snd ℝ P (ℝ×ℝ)) + let I : ℝ →L[ℝ] State P := + (ContinuousLinearMap.inr ℝ P (ℝ×ℝ)).comp (ContinuousLinearMap.inl ℝ ℝ ℝ) + let W : Path (State P) → Path (State P) := fun u => + constCLM (0,(0,1)) + pathMap I (e.onPaths (pathMap L u)-pathMap Y u) + have hL : L x=(x.1,x.2.1) := rfl + have hep := AlgebraicExpr.path_properties e he + have hed : ContDiffAt ℝ ω e.onPaths (pathMap L (constCLM x)) := by + simpa only [pathMap_const,hL] using hep.2.1 + have hW : ContDiffAt ℝ ω W (constCLM x) := + contDiffAt_const.add ((pathMap I).contDiff.contDiffAt.comp _ + ((hed.comp _ (pathMap L).contDiff.contDiffAt).sub (pathMap Y).contDiff.contDiffAt)) + apply exists_analytic_local_flow_eventually W (field e.eval) x _ hW + have ht : Tendsto (pathMap L) (𝓝 (constCLM x)) (𝓝 (constCLM (x.1,x.2.1))) := by + exact (pathMap L).continuous.continuousAt.tendsto + filter_upwards [ht.eventually hep.2.2] with u hu s + simp only [W,ContinuousMap.add_apply,pathMap_apply,ContinuousMap.sub_apply,hu s,constCLM_apply] + simp [I,L,Y,field] +end QuinticLienard.SmoothFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AlgebraicNotation.lean b/lean/OAI/Analysis/LienardCycles/AlgebraicNotation.lean new file mode 100644 index 0000000000000000000000000000000000000000..3f70c0269c6765a6193c3b57d563daa0db7cb7c0 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AlgebraicNotation.lean @@ -0,0 +1,63 @@ +import OAI.Analysis.LienardCycles.AlgebraicFlow + +namespace OAI + +universe uE + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +namespace QuinticLienard.SmoothFlow.AlgebraicExpr +variable {E : Type uE} [NormedAddCommGroup E] [NormedSpace ℝ E] +instance : Add (AlgebraicExpr E) := ⟨add⟩ +instance : Mul (AlgebraicExpr E) := ⟨mul⟩ +instance : Inv (AlgebraicExpr E) := ⟨inv⟩ +instance : Neg (AlgebraicExpr E) := ⟨fun p => mul (const (-1)) p⟩ +instance : Sub (AlgebraicExpr E) := ⟨fun p q => p + -q⟩ +instance : Div (AlgebraicExpr E) := ⟨fun p q => p*q⁻¹⟩ +instance (n : ℕ) : OfNat (AlgebraicExpr E) n := ⟨const n⟩ +def pow (p : AlgebraicExpr E) : ℕ → AlgebraicExpr E + | 0 => const 1 + | n+1 => pow p n*p +instance : Pow (AlgebraicExpr E) ℕ := ⟨pow⟩ +@[simp] lemma eval_const (c : ℝ) (x : E) : (const c : AlgebraicExpr E).eval x=c := rfl +@[simp] lemma eval_linear (L : E →L[ℝ] ℝ) (x : E) : (linear L).eval x=L x := rfl +@[simp] lemma eval_add (p q : AlgebraicExpr E) (x : E) : (p+q).eval x=p.eval x+q.eval x := rfl +@[simp] lemma eval_mul (p q : AlgebraicExpr E) (x : E) : (p*q).eval x=p.eval x*q.eval x := rfl +@[simp] lemma eval_inv (p : AlgebraicExpr E) (x : E) : p⁻¹.eval x=(p.eval x)⁻¹ := rfl +@[simp] lemma eval_neg (p : AlgebraicExpr E) (x : E) : (-p).eval x= -p.eval x := by change (-1:ℝ)*p.eval x= -p.eval x; ring +@[simp] lemma eval_sub (p q : AlgebraicExpr E) (x : E) : (p-q).eval x=p.eval x-q.eval x := by change (p+ -q).eval x=_; rw [eval_add,eval_neg,sub_eq_add_neg] +@[simp] lemma eval_div (p q : AlgebraicExpr E) (x : E) : (p/q).eval x=p.eval x/q.eval x := by change (p*q⁻¹).eval x=_; rw [eval_mul,eval_inv,div_eq_mul_inv] +@[simp] lemma eval_ofNat (n : ℕ) (x : E) : (OfNat.ofNat n : AlgebraicExpr E).eval x=n := rfl +@[simp] lemma eval_pow (p : AlgebraicExpr E) (n : ℕ) (x : E) : (p^n).eval x=(p.eval x)^n := by + induction n with + | zero => + rw [pow_zero] + change (pow p 0).eval x=1 + rfl + | succ n ih => change (p^n).eval x*p.eval x=_; rw [ih,pow_succ] +@[simp] lemma eval_sqrt (p : AlgebraicExpr E) (x : E) : (sqrt p).eval x=Real.sqrt (p.eval x) := rfl +@[simp] lemma regular_const (c : ℝ) (x : E) : (const c : AlgebraicExpr E).RegularAt x := trivial +@[simp] lemma regular_linear (L : E →L[ℝ] ℝ) (x : E) : (linear L).RegularAt x := trivial +@[simp] lemma regular_add (p q : AlgebraicExpr E) (x : E) : (p+q).RegularAt x ↔ p.RegularAt x ∧ q.RegularAt x := Iff.rfl +@[simp] lemma regular_mul (p q : AlgebraicExpr E) (x : E) : (p*q).RegularAt x ↔ p.RegularAt x ∧ q.RegularAt x := Iff.rfl +@[simp] lemma regular_inv (p : AlgebraicExpr E) (x : E) : p⁻¹.RegularAt x ↔ p.RegularAt x ∧ p.eval x≠0 := Iff.rfl +@[simp] lemma regular_neg (p : AlgebraicExpr E) (x : E) : (-p).RegularAt x ↔ p.RegularAt x := by change (True ∧ p.RegularAt x) ↔ p.RegularAt x; simp +@[simp] lemma regular_sub (p q : AlgebraicExpr E) (x : E) : (p-q).RegularAt x ↔ p.RegularAt x ∧ q.RegularAt x := by change (p+ -q).RegularAt x ↔ _; rw [regular_add,regular_neg] +@[simp] lemma regular_div (p q : AlgebraicExpr E) (x : E) : (p/q).RegularAt x ↔ p.RegularAt x ∧ q.RegularAt x ∧ q.eval x≠0 := Iff.rfl +@[simp] lemma regular_ofNat (n : ℕ) (x : E) : (OfNat.ofNat n : AlgebraicExpr E).RegularAt x := trivial +lemma regular_pow (p : AlgebraicExpr E) (n : ℕ) {x : E} (hp : p.RegularAt x) : (p^n).RegularAt x := by + induction n with + | zero => trivial + | succ n ih => exact ⟨ih,hp⟩ +@[simp] lemma regular_sqrt (p : AlgebraicExpr E) (x : E) : (sqrt p).RegularAt x ↔ p.RegularAt x ∧ 0 2*u n/(s*(1-(u n)^2))))) : + BddAbove (range (fun n => angle (u n))) := by + obtain ⟨B,hB⟩ := hB + let C := s*max B 0+1/(1+u 0)+1 + have hlow : 0 < 1+u 0 := by linarith [(abs_lt.mp (hu 0)).1] + have hC : 1 < C := by + dsimp only [C] + have := mul_nonneg hs.le (le_max_right B 0) + linarith [one_div_pos.mpr hlow] + have ht : 1-1/C ∈ Ioo (-1:ℝ) 1 := by + have h₁ := one_div_pos.mpr (show 0 < C by linarith) + have h₂ := one_div_lt_one_div_of_lt (by norm_num : (0:ℝ)<1) hC + norm_num only [div_one] at h₂ + constructor <;> linarith + refine ⟨angle (1-1/C),?_⟩ + rintro y ⟨n,rfl⟩ + apply angle_strictMono.monotoneOn (abs_lt.mp (hu n)) ht + have hrange := hB (mem_range_self n) + have hi := one_div_le_one_div_of_le hlow (show 1+u 0 ≤ 1+u n by linarith [hm (Nat.zero_le n)]) + have hc : 1/(1-u n) ≤ C := by + rw [rate_inverse_identity hs (hu n)] + have hmul := mul_le_mul_of_nonneg_left (hrange.trans (le_max_left B 0)) hs.le + dsimp only [C] + linarith + have hden : 0 < 1-u n := by linarith [(abs_lt.mp (hu n)).2] + have hc' : 1/C ≤ 1-u n := by + have hprod := (div_le_iff₀ hden).mp hc + apply (div_le_iff₀ (show 0 < C by linarith)).mpr + nlinarith + linarith + +lemma exists_mem_Ioo_of_ae {l u a b : ℝ} {p : ℝ → Prop} + (hab : a < b) (hsub : Ioo a b ⊆ Ioc l u) + (hp : ∀ᵐ s ∂volume.restrict (Ioc l u), p s) : ∃ s ∈ Ioo a b, p s := by + apply Measure.exists_mem_of_measure_ne_zero_of_ae + (show volume (Ioo a b) ≠ 0 by rw [Real.volume_Ioo]; exact ne_of_gt (ENNReal.ofReal_pos.mpr (sub_pos.mpr hab))) + exact hp.filter_mono (ae_mono (Measure.restrict_mono hsub le_rfl)) + +lemma uniform_integral_pos_of_reciprocal {a b B : ℝ} (hab : a < b) {g : ℕ → ℝ → ℝ} + (hg : ∀ n, ContinuousOn (g n) (Icc a b)) + (hp : ∀ n x, x ∈ Icc a b → 0 < g n x) + (hB : ∀ n, (∫ x in a..b, 1/(g n x)) ≤ B) : + ∃ ε > 0, ∀ n, ε ≤ ∫ x in a..b, g n x := by + have hi (n : ℕ) : IntervalIntegrable (fun x => 1/(g n x)) volume a b := + (continuousOn_const.div (hg n) (fun x hx => ne_of_gt (hp n x hx))).intervalIntegrable_of_Icc hab.le + have hB0 : 0 ≤ B := (intervalIntegral.integral_nonneg hab.le + (fun x hx => le_of_lt (one_div_pos.mpr (hp 0 x hx)))).trans (hB 0) + let δ := (b-a)/(B+1) + have hδ : 0 < δ := div_pos (sub_pos.mpr hab) (by linarith) + have hδB : δ*B ≤ b-a := by + have he : δ*(B+1)=b-a := by dsimp only [δ]; field_simp + nlinarith + refine ⟨δ*(b-a),mul_pos hδ (sub_pos.mpr hab),?_⟩ + intro n + have hpoint (x : ℝ) (hx : x ∈ Icc a b) : 2*δ ≤ g n x+δ^2*(1/g n x) := by + apply (mul_le_mul_iff_left₀ (hp n x hx)).mp + have he : (g n x+δ^2*(1/g n x))*g n x=(g n x)^2+δ^2 := by + field_simp [ne_of_gt (hp n x hx)] + rw [he] + nlinarith [sq_nonneg (g n x-δ)] + have hineq := intervalIntegral.integral_mono_on hab.le intervalIntegrable_const + (((hg n).intervalIntegrable_of_Icc hab.le).add ((hi n).const_mul (δ^2))) hpoint + rw [intervalIntegral.integral_const,intervalIntegral.integral_add + ((hg n).intervalIntegrable_of_Icc hab.le) ((hi n).const_mul (δ^2)),intervalIntegral.integral_const_mul] at hineq + simp only [smul_eq_mul] at hineq + have hbound := mul_le_mul_of_nonneg_left (hB n) (sq_nonneg δ) + have hbound' := mul_le_mul_of_nonneg_left hδB hδ.le + nlinarith +end QuinticLienard.RealAnalysis + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ArcEndpoints.lean b/lean/OAI/Analysis/LienardCycles/ArcEndpoints.lean new file mode 100644 index 0000000000000000000000000000000000000000..97e8451ded16ff0bb4dcf44afd892f63feda2537 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ArcEndpoints.lean @@ -0,0 +1,119 @@ +import OAI.Analysis.LienardCycles.ArcFamilies + +namespace OAI + +universe uP + +open Set Filter MeasureTheory +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ArcEndpoints +open PartialCalculus ScalarArcs + +variable {P : Type uP} [NormedAddCommGroup P] [NormedSpace ℝ P] [CompleteSpace P] + +lemma level_hit {w : P × ℝ → ℝ} {p : P} {y h d : ℝ} + (hw : ContDiffAt ℝ ω w (p,y)) (hd : HasDerivAt (fun s => w (p,s)) d y) + (hu : w (p,y) = h) (hne : d ≠ 0) : + ∃ Y : P × ℝ → ℝ, ContDiffAt ℝ ω Y (p,h) ∧ Y (p,h) = y ∧ + ∀ᶠ q in 𝓝 (p,h), w (q.1,Y q) = q.2 := by + let f : (P × ℝ) × ℝ → ℝ := fun q => w (q.1.1,q.2)-q.1.2 + have hf : ContDiffAt ℝ ω f ((p,h),y) := + (hw.comp ((p,h),y) (contDiffAt_fst.fst.prodMk contDiffAt_snd)).sub contDiffAt_fst.snd + obtain ⟨Y,hY,hY0,he,_⟩ := transverse_hit hf (hd.sub_const h) hne + refine ⟨Y,hY,hY0,?_⟩ + filter_upwards [he] with q hq + change w (q.1,Y q)-q.2 = w (p,y)-h at hq + rw [hu,sub_self,sub_eq_zero] at hq + exact hq + +theorem actual_endpoint_families (Φ : P × ℝ → ℝ) + (hΦ : ∀ p, ContDiff ℝ 1 (fun x => Φ (p,x))) + {w : (P × ℝ) × ℝ → ℝ} {p : P} {t h a b A B : ℝ} + (hwc : ∀ q, Continuous (fun y => w (q,y))) + (hpeak : ∀ q, w (q,Φ q) = q.2) + (hw : ∀ y ∈ Icc A B, ContDiffAt ℝ ω w ((p,t),y)) + (he : ∀ y ∈ Icc A B, ∀ᶠ q in 𝓝 ((p,t),y), + HasDerivAt (fun s => w (q.1,s)) (Φ (q.1.1,w q)-q.2) q.2) + (hu : IsArch (fun x => Φ (p,x)) (fun y => w ((p,t),y)) h t a b) + (hA : A < a) (hB : b < B) (hΦp : ContinuousAt Φ (p,t)) : + ∃ l r : (P × ℝ) × ℝ → ℝ, + ContDiffAt ℝ ω l ((p,t),h) ∧ ContDiffAt ℝ ω r ((p,t),h) ∧ + l ((p,t),h) = a ∧ r ((p,t),h) = b ∧ + ∀ᶠ q in 𝓝 ((p,t),h), + IsArch (fun x => Φ (q.1.1,x)) (fun y => w (q.1,y)) + q.2 q.1.2 (l q) (r q) := by + have hab : a < b := hu.lower_lt_peak.trans hu.peak_lt_upper + have haAB : a ∈ Icc A B := ⟨hA.le,(hab.trans hB).le⟩ + have hbAB : b ∈ Icc A B := ⟨(hA.trans hab).le,hB.le⟩ + have had : HasDerivAt (fun y => w ((p,t),y)) (Φ (p,h)-a) a := by + simpa only [hu.lower] using hu.equation a ⟨le_rfl,hab.le⟩ + have hbd : HasDerivAt (fun y => w ((p,t),y)) (Φ (p,h)-b) b := by + simpa only [hu.upper] using hu.equation b ⟨hab.le,le_rfl⟩ + obtain ⟨l,hld,hl0,hle⟩ := level_hit (hw a haAB) had hu.lower (by + have hh := hu.lower_transverse + exact ne_of_gt (sub_pos.mpr hh)) + obtain ⟨r,hrd,hr0,hre⟩ := level_hit (hw b hbAB) hbd hu.upper (by + have hh := hu.upper_transverse + exact ne_of_lt (sub_neg.mpr hh)) + have hode : ∀ᶠ q in 𝓝 (p,t), ∀ y ∈ Icc A B, + HasDerivAt (fun s => w (q,s)) (Φ (q.1,w (q,y))-y) y := + isCompact_Icc.eventually_forall_of_forall_eventually he + have hpcont : ContinuousAt (fun q : (P × ℝ) × ℝ => Φ q.1) ((p,t),h) := + ContinuousAt.comp (f := Prod.fst) (g := Φ) (x := ((p,t),h)) hΦp continuousAt_fst + have hnear : ∀ᶠ q in 𝓝 ((p,t),h), + A < l q ∧ l q < Φ q.1 ∧ Φ q.1 < r q ∧ r q < B := by + have ha' : A < l ((p,t),h) := by simpa only [hl0] using hA + have hl' : l ((p,t),h) < Φ ((p,t),h).1 := by simpa only [hl0] using hu.lower_lt_peak + have hr' : Φ ((p,t),h).1 < r ((p,t),h) := by simpa only [hr0] using hu.peak_lt_upper + have hb' : r ((p,t),h) < B := by simpa only [hr0] using hB + filter_upwards [continuousAt_const.eventually_lt hld.continuousAt ha', + hld.continuousAt.eventually_lt hpcont hl', + hpcont.eventually_lt hrd.continuousAt hr', + hrd.continuousAt.eventually_lt continuousAt_const hb'] with q h₁ h₂ h₃ h₄ + exact ⟨h₁,h₂,h₃,h₄⟩ + refine ⟨l,r,hld,hrd,hl0,hr0,?_⟩ + filter_upwards [hle,hre,hnear,continuousAt_fst.eventually hode] with q hl hr hq ho + apply IsArch.of_solution_and_hits (hΦ q.1.1) (hwc q.1) + (fun y hy => ho y ⟨hq.1.le.trans hy.1,hy.2.trans hq.2.2.2.le⟩) + hq.2.1 hq.2.2.1 (hpeak q.1) hl hr + +noncomputable def lowerFamily (Φ : P × ℝ → ℝ) (q : (P × ℝ) × ℝ) : ℝ := + lower (fun x => Φ (q.1.1,x)) q.2 q.1.2 +noncomputable def upperFamily (Φ : P × ℝ → ℝ) (q : (P × ℝ) × ℝ) : ℝ := + upper (fun x => Φ (q.1.1,x)) q.2 q.1.2 + +omit [CompleteSpace P] in + +theorem canonical_endpoints_contDiffAt (Φ : P × ℝ → ℝ) + (hΦ : ∀ p, ContDiff ℝ 1 (fun x => Φ (p,x))) + {p : P} {t h : ℝ} (hht : h < t) + {l r : (P × ℝ) × ℝ → ℝ} + (hl : ContDiffAt ℝ ω l ((p,t),h)) (hr : ContDiffAt ℝ ω r ((p,t),h)) + (he : ∀ᶠ q in 𝓝 ((p,t),h), + ∃ u, IsArch (fun x => Φ (q.1.1,x)) u q.2 q.1.2 (l q) (r q)) : + ContDiffAt ℝ ω (lowerFamily Φ) ((p,t),h) ∧ + ContDiffAt ℝ ω (upperFamily Φ) ((p,t),h) := by + have ht : ∀ᶠ q : (P × ℝ) × ℝ in 𝓝 ((p,t),h), q.2 < q.1.2 := + continuousAt_snd.eventually_lt continuousAt_fst.snd hht + have heq : ∀ᶠ q in 𝓝 ((p,t),h), lowerFamily Φ q = l q ∧ upperFamily Φ q = r q := by + filter_upwards [he,ht] with q hq hqt + obtain ⟨u,hu⟩ := hq + obtain ⟨ψ,K,B,hs,hK,_,hψ⟩ := entire_profile_extension (hΦ q.1.1) hqt + have hc := chosen_arch (entire_arch_exists (hΦ q.1.1) hqt) + have hh := hc.unique hu hK hψ + exact ⟨hh.1,hh.2.1⟩ + exact ⟨hl.congr_of_eventuallyEq (heq.mono fun _ h => h.1), + hr.congr_of_eventuallyEq (heq.mono fun _ h => h.2)⟩ + +end QuinticLienard.ArcEndpoints + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ArcFamilies.lean b/lean/OAI/Analysis/LienardCycles/ArcFamilies.lean new file mode 100644 index 0000000000000000000000000000000000000000..e0196ec9d78e1df74b29ed6dfe4d5a0ccc1f0a73 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ArcFamilies.lean @@ -0,0 +1,133 @@ +import OAI.Analysis.LienardCycles.ScalarArcs + +namespace OAI + +universe uP + +open Set Filter MeasureTheory +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open scoped Topology ContDiff +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff + +open Set Filter +open scoped Topology ContDiff + +namespace QuinticLienard.ArcFamilies +open PartialCalculus + +variable {P : Type uP} [NormedAddCommGroup P] [NormedSpace ℝ P] + [FiniteDimensional ℝ P] + +abbrev State (P : Type uP) := P × (ℝ × ℝ) + +def field (Φ : P × ℝ → ℝ) (z : State P) : State P := + (0,(Φ (z.1,z.2.1)-z.2.2,1)) + +theorem peak_family (Φ : P × ℝ → ℝ) {U : Set (State P)} + (hU : IsOpen U) (hV : ContDiffOn ℝ 1 (field Φ) U) + (hloc : ∀ x ∈ U, ∃ f : State P × ℝ → State P, + ContDiffAt ℝ ω f (x,0) ∧ ∀ᶠ q in 𝓝 (x,(0:ℝ)), + f (q.1,0) = q.1 ∧ HasDerivAt (fun s => f (q.1,s)) (field Φ (f q)) q.2) + {p : P} {t a b : ℝ} {u : ℝ → ℝ} + (hΦ : ContDiffAt ℝ ω Φ (p,t)) + (ha : a < Φ (p,t)) (hb : Φ (p,t) < b) + (hu : Continuous u) (hpeak : u (Φ (p,t)) = t) + (hueq : ∀ y ∈ Icc a b, HasDerivAt u (Φ (p,u y)-y) y) + (huU : ∀ y ∈ Icc a b, (p,(u y,y)) ∈ U) : + ∃ w : (P × ℝ) × ℝ → ℝ, + (∀ q, Continuous (fun y => w (q,y))) ∧ + (∀ q, w (q,Φ q) = q.2) ∧ + (∀ y ∈ Icc a b, w ((p,t),y) = u y) ∧ + (∀ y ∈ Icc a b, ContDiffAt ℝ ω w ((p,t),y)) ∧ + ∀ y ∈ Ioo a b, ∀ᶠ q in 𝓝 ((p,t),y), + HasDerivAt (fun s => w (q.1,s)) (Φ (q.1.1,w q)-q.2) q.2 := by + let c := Φ (p,t) + let γ : ℝ → State P := fun y => (p,(u y,y)) + have hγ : Continuous γ := continuous_const.prodMk (hu.prodMk continuous_id) + have hγd : ∀ y ∈ Icc a b, HasDerivAt γ (field Φ (γ y)) y := by + intro y hy + exact (hasDerivAt_const y p).prodMk ((hueq y hy).prodMk (hasDerivAt_id y)) + obtain ⟨f,hfc,hzero,hmatch,hd,he⟩ := GlobalODE.analytic_family_along_compact_solution + (field Φ) hU hV hloc ha hb hγ huU hγd + have hinit : γ c = (p,(t,c)) := by simp [γ,c,hpeak] + have hode : ∀ᶠ x in 𝓝 (γ c), ∀ s ∈ Icc (a-c) (b-c), + HasDerivAt (fun z => f (x,z)) (field Φ (f (x,s))) s := by + apply isCompact_Icc.eventually_forall_of_forall_eventually + intro s hs + have hs' : s+c ∈ Icc a b := by constructor <;> linarith [hs.1,hs.2] + have hx := he (s+c) hs' + simpa only [c,add_sub_cancel_right] using hx + have hcoord : ∀ᶠ x in 𝓝 (γ c), ∀ s ∈ Icc (a-c) (b-c), + (f (x,s)).1 = x.1 ∧ (f (x,s)).2.2 = x.2.2+s := by + filter_upwards [hode] with x hx + have h0 : (0:ℝ) ∈ Icc (a-c) (b-c) := by + constructor <;> dsimp [c] <;> linarith + have hpd : ∀ s ∈ Icc (a-c) (b-c), HasDerivAt (fun z => (f (x,z)).1) 0 s := + fun s hs => (hx s hs).fst + have htd : ∀ s ∈ Icc (a-c) (b-c), HasDerivAt (fun z => (f (x,z)).2.2) 1 s := + fun s hs => (hx s hs).snd.snd + have hpconst := eq_of_hasDerivAt_eq_on_Icc + (fun s hs => (hpd s hs).continuousAt.continuousWithinAt) + continuousOn_const hpd (fun s _ => hasDerivAt_const s x.1) h0 + (by simp only [hzero]) + have htconst := eq_of_hasDerivAt_eq_on_Icc + (fun s hs => (htd s hs).continuousAt.continuousWithinAt) + (continuous_const.add continuous_id).continuousOn htd + (fun s _ => (hasDerivAt_id s).const_add x.2.2) h0 + (by simp [hzero]) + exact fun s hs => ⟨hpconst hs,htconst hs⟩ + let init : P × ℝ → State P := fun q => (q.1,(q.2,Φ q)) + let lift : (P × ℝ) × ℝ → State P × ℝ := fun q => (init q.1,q.2-Φ q.1) + let w : (P × ℝ) × ℝ → ℝ := fun q => (f (lift q)).2.1 + have hlift (y : ℝ) : lift ((p,t),y) = (γ c,y-c) := by + simp [lift,init,hinit,c] + have hld (y : ℝ) : ContDiffAt ℝ ω lift ((p,t),y) := by + have hp := hΦ.comp ((p,t),y) contDiffAt_fst + exact (contDiffAt_fst.fst.prodMk (contDiffAt_fst.snd.prodMk hp)).prodMk + (contDiffAt_snd.sub hp) + refine ⟨w,?_,?_,?_,?_,?_⟩ + · intro q + change Continuous (fun y => (f (init q,y-Φ q)).2.1) + exact (hfc.comp (continuous_const.prodMk (continuous_id.sub continuous_const))).snd.fst + · intro q + simp [w,lift,init,hzero] + · intro y hy + change (f (lift ((p,t),y))).2.1 = u y + rw [hlift y,hmatch y hy] + · intro y hy + have hf := hd y hy + rw [←hlift y] at hf + exact (hf.comp ((p,t),y) (hld y)).snd.fst + · intro y hy + have ho : ∀ᶠ q in 𝓝 ((p,t),y), + HasDerivAt (fun s => f ((lift q).1,s)) (field Φ (f (lift q))) (lift q).2 := by + have hc := (hld y).continuousAt.tendsto + rw [hlift y] at hc + exact hc.eventually (he y (Ioo_subset_Icc_self hy)) + have hi : Tendsto (fun q : (P × ℝ) × ℝ => init q.1) + (𝓝 ((p,t),y)) (𝓝 (γ c)) := by + have hc := (hld y).fst.continuousAt.tendsto + simpa only [hlift y] using hc + have ht : ∀ᶠ q in 𝓝 ((p,t),y), (lift q).2 ∈ Icc (a-c) (b-c) := by + have hc := (hld y).snd.continuousAt.tendsto + have hyt : y-c ∈ Ioo (a-c) (b-c) := by constructor <;> linarith [hy.1,hy.2] + rw [hlift y] at hc + exact hc.eventually (mem_of_superset (Ioo_mem_nhds hyt.1 hyt.2) Ioo_subset_Icc_self) + filter_upwards [ho,hi.eventually hcoord,ht] with q hq hqcoord hqt + have hcoords := hqcoord _ hqt + have hdq0 : HasDerivAt (fun s => (f ((lift q).1,s)).2.1) + (Φ ((f (lift q)).1,(f (lift q)).2.1)-(f (lift q)).2.2) (lift q).2 := hq.snd.fst + have hdq := hdq0.scomp q.2 ((hasDerivAt_id q.2).sub_const (Φ q.1)) + have hp : (f (lift q)).1 = q.1.1 := hcoords.1 + have ht : (f (lift q)).2.2 = q.2 := by + calc + (f (lift q)).2.2 = (init q.1).2.2+(lift q).2 := hcoords.2 + _ = q.2 := by simp [lift,init] + simpa only [Function.comp_def,id_eq,smul_eq_mul,one_mul,hp,ht] using hdq + +end QuinticLienard.ArcFamilies + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ArchSymmetries.lean b/lean/OAI/Analysis/LienardCycles/ArchSymmetries.lean new file mode 100644 index 0000000000000000000000000000000000000000..d57acfebddf3031e1aba9241a72a5e74b6582840 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ArchSymmetries.lean @@ -0,0 +1,188 @@ +import OAI.Analysis.LienardCycles.WidthTransport + +namespace OAI + +universe uP + +open Set Filter MeasureTheory +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ArchSymmetries +open ScalarArcs CanonicalVariation ArcEndpoints ArcFamilies WidthCoordinates WidthTransport + +lemma affine_cancel {c : ℝ} (hc : c ≠ 0) (C y : ℝ) : (C+c*y-C)/c = y := by + field_simp + ring + +theorem IsArch.affine {φ ψ u : ℝ → ℝ} {h t a b c H C : ℝ} + (hu : IsArch φ u h t a b) (hc : 0 < c) + (he : ∀ x, ψ (H+c^2*x) = C+c*φ x) : + IsArch ψ (fun y => H+c^2*u ((y-C)/c)) + (H+c^2*h) (H+c^2*t) (C+c*a) (C+c*b) := by + have hc2 : 0 < c^2 := sq_pos_of_pos hc + have hpre {y : ℝ} (hy : y ∈ Icc (C+c*a) (C+c*b)) : + (y-C)/c ∈ Icc a b := by + constructor + · apply (le_div_iff₀ hc).mpr + nlinarith [hy.1] + · apply (div_le_iff₀ hc).mpr + nlinarith [hy.2] + constructor + · exact continuous_const.add (continuous_const.mul + (hu.continuous.comp ((continuous_id.sub continuous_const).div_const c))) + · rw [he] + nlinarith [hu.lower_lt_peak] + · rw [he] + nlinarith [hu.peak_lt_upper] + · rw [he,affine_cancel hc.ne',hu.peak] + · rw [affine_cancel hc.ne',hu.lower] + · rw [affine_cancel hc.ne',hu.upper] + · rw [he] + nlinarith [hu.lower_transverse] + · rw [he] + nlinarith [hu.upper_transverse] + · intro y hy + have hd := (((hu.equation _ (hpre hy)).comp y + (((hasDerivAt_id y).sub_const C).div_const c)).const_mul (c^2)).const_add H + have hd' : HasDerivAt (fun y => H+c^2*u ((y-C)/c)) + (c^2*((φ (u ((y-C)/c))-(y-C)/c)*(1/c))) y := by + simpa using! hd + convert hd' using 1 + rw [he] + field_simp + ring + · intro y hy + have hh := hu.range_mem _ (hpre hy) + constructor <;> nlinarith [hh.1,hh.2] + · intro y₁ hy₁ y₂ hy₂ hyy + rw [he] at hy₁ hy₂ + have hm : (y₁-C)/c < (y₂-C)/c := (div_lt_div_iff_of_pos_right hc).mpr (by linarith) + have hh := hu.inc (show (y₁-C)/c ∈ Icc a (φ t) from + ⟨(le_div_iff₀ hc).mpr (by nlinarith [hy₁.1]), (div_le_iff₀ hc).mpr (by nlinarith [hy₁.2])⟩) + (show (y₂-C)/c ∈ Icc a (φ t) from + ⟨(le_div_iff₀ hc).mpr (by nlinarith [hy₂.1]), (div_le_iff₀ hc).mpr (by nlinarith [hy₂.2])⟩) hm + nlinarith + · intro y₁ hy₁ y₂ hy₂ hyy + rw [he] at hy₁ hy₂ + have hm : (y₁-C)/c < (y₂-C)/c := (div_lt_div_iff_of_pos_right hc).mpr (by linarith) + have hh := hu.dec (show (y₁-C)/c ∈ Icc (φ t) b from + ⟨(le_div_iff₀ hc).mpr (by nlinarith [hy₁.1]), (div_le_iff₀ hc).mpr (by nlinarith [hy₁.2])⟩) + (show (y₂-C)/c ∈ Icc (φ t) b from + ⟨(le_div_iff₀ hc).mpr (by nlinarith [hy₂.1]), (div_le_iff₀ hc).mpr (by nlinarith [hy₂.2])⟩) hm + nlinarith + +theorem IsArch.reflect {φ u : ℝ → ℝ} {h t a b : ℝ} + (hu : IsArch φ u h t a b) : + IsArch (fun x => -φ x) (fun y => u (-y)) h t (-b) (-a) := by + constructor + · exact hu.continuous.comp continuous_neg + · simpa using hu.peak_lt_upper + · simpa using hu.lower_lt_peak + · simpa using hu.peak + · simpa using hu.upper + · simpa using hu.lower + · simpa using hu.upper_transverse + · simpa using hu.lower_transverse + · intro y hy + have hd := (hu.equation (-y) (by constructor <;> linarith [hy.1,hy.2])).comp y (hasDerivAt_neg y) + have hd' : HasDerivAt (fun y => u (-y)) ((φ (u (-y))- -y)*(-1)) y := by + simpa using! hd + convert hd' using 1 + ring + · intro y hy + exact hu.range_mem (-y) (by constructor <;> linarith [hy.1,hy.2]) + · intro y₁ hy₁ y₂ hy₂ hyy + exact hu.dec (show -y₂ ∈ Icc (φ t) b by constructor <;> linarith [hy₂.1,hy₂.2]) + (show -y₁ ∈ Icc (φ t) b by constructor <;> linarith [hy₁.1,hy₁.2]) (by linarith) + · intro y₁ hy₁ y₂ hy₂ hyy + exact hu.inc (show -y₂ ∈ Icc a (φ t) by constructor <;> linarith [hy₂.1,hy₂.2]) + (show -y₁ ∈ Icc a (φ t) by constructor <;> linarith [hy₁.1,hy₁.2]) (by linarith) + +theorem canonical_affine {φ ψ : ℝ → ℝ} {h t c H C : ℝ} + (hφ : ContDiff ℝ 1 φ) (hψ : ContDiff ℝ 1 ψ) (hht : h < t) + (hc : 0 < c) (he : ∀ x, ψ (H+c^2*x) = C+c*φ x) : + lower ψ (H+c^2*h) (H+c^2*t) = C+c*lower φ h t ∧ + upper ψ (H+c^2*h) (H+c^2*t) = C+c*upper φ h t := by + have hu := chosen_arch (entire_arch_exists hφ hht) + exact canonical_of_arch (IsArch.affine hu hc he) hψ (by nlinarith [sq_pos_of_pos hc]) + +theorem canonical_reflect {φ : ℝ → ℝ} {h t : ℝ} + (hφ : ContDiff ℝ 1 φ) (hht : h < t) : + lower (fun x => -φ x) h t = -upper φ h t ∧ + upper (fun x => -φ x) h t = -lower φ h t := + canonical_of_arch (IsArch.reflect (chosen_arch (entire_arch_exists hφ hht))) hφ.neg hht + +variable {P : Type uP} [NormedAddCommGroup P] [NormedSpace ℝ P] + [FiniteDimensional ℝ P] +variable (Φ : P × ℝ → ℝ) (hΦ : ContDiff ℝ ω Φ) + (hloc : ∀ x : State P, ∃ f : State P × ℝ → State P, + ContDiffAt ℝ ω f (x,0) ∧ ∀ᶠ q in 𝓝 (x,(0:ℝ)), + f (q.1,0) = q.1 ∧ HasDerivAt (fun s => f (q.1,s)) (field Φ (f q)) q.2) +include hΦ hloc + +omit hloc [FiniteDimensional ℝ P] in +lemma profile_C1 (p : P) : ContDiff ℝ 1 (fun u => Φ (p,u)) := + (hΦ.comp (contDiff_const.prodMk contDiff_id)).of_le (by simp) + +omit hloc [FiniteDimensional ℝ P] in +theorem width_affine {p q : P} {h t c H C : ℝ} (hht : h < t) (hc : 0 < c) + (he : ∀ x, Φ (q,H+c^2*x) = C+c*Φ (p,x)) : + widthFamily Φ ((q,H+c^2*t),H+c^2*h) = c*widthFamily Φ ((p,t),h) := by + have hh := canonical_affine (profile_C1 Φ hΦ p) (profile_C1 Φ hΦ q) hht hc he + dsimp [widthFamily,width] + rw [hh.1,hh.2] + ring + +omit hloc [FiniteDimensional ℝ P] in +theorem midpoint_affine {p q : P} {h t c H C : ℝ} (hht : h < t) (hc : 0 < c) + (he : ∀ x, Φ (q,H+c^2*x) = C+c*Φ (p,x)) : + midpointFamily Φ ((q,H+c^2*t),H+c^2*h) = c*midpointFamily Φ ((p,t),h) := by + have hh := canonical_affine (profile_C1 Φ hΦ p) (profile_C1 Φ hΦ q) hht hc he + dsimp [midpointFamily,ScalarArcs.midpoint] + rw [hh.1,hh.2,he] + ring + +theorem fixed_width_affine {p q : P} {h r c H C : ℝ} (hr : 0 < r) (hc : 0 < c) + (he : ∀ x, Φ (q,H+c^2*x) = C+c*Φ (p,x)) : + peakAtWidth Φ ((q,H+c^2*h),c*r) = H+c^2*peakAtWidth Φ ((p,h),r) ∧ + midpointAtWidth Φ ((q,H+c^2*h),c*r) = c*midpointAtWidth Φ ((p,h),r) := by + have hs := peak_spec Φ hΦ hloc (p := p) (h := h) hr + have hw := width_affine Φ hΦ hs.1 hc he + rw [hs.2] at hw + have hp := peak_eq Φ hΦ hloc (mul_pos hc hr) + (show H+c^2*h < H+c^2*peakAtWidth Φ ((p,h),r) by nlinarith [sq_pos_of_pos hc]) hw + refine ⟨hp,?_⟩ + dsimp [midpointAtWidth] + rw [hp] + exact midpoint_affine Φ hΦ hs.1 hc he + +theorem fixed_width_reflect {p q : P} {h r : ℝ} (hr : 0 < r) + (he : ∀ x, Φ (q,x) = -Φ (p,x)) : + peakAtWidth Φ ((q,h),r) = peakAtWidth Φ ((p,h),r) ∧ + midpointAtWidth Φ ((q,h),r) = -midpointAtWidth Φ ((p,h),r) := by + have hs := peak_spec Φ hΦ hloc (p := p) (h := h) hr + have hf : (fun x => Φ (q,x)) = (fun x => -Φ (p,x)) := funext he + have hh := canonical_reflect (profile_C1 Φ hΦ p) hs.1 + have hw : widthFamily Φ ((q,peakAtWidth Φ ((p,h),r)),h) = r := by + dsimp [widthFamily,width] at hs ⊢ + rw [hf,hh.1,hh.2] + linarith [hs.2] + have hp := peak_eq Φ hΦ hloc hr hs.1 hw + refine ⟨hp,?_⟩ + dsimp [midpointAtWidth] + rw [hp] + dsimp [midpointFamily,ScalarArcs.midpoint] + rw [hf,hh.1,hh.2,he] + ring + +end QuinticLienard.ArchSymmetries + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ArchVariation.lean b/lean/OAI/Analysis/LienardCycles/ArchVariation.lean new file mode 100644 index 0000000000000000000000000000000000000000..8d5c8738f7c03d608c2e7726b8612a8b37a62041 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ArchVariation.lean @@ -0,0 +1,138 @@ +import OAI.Analysis.LienardCycles.PolynomialModel + +namespace OAI + +open Set Filter MeasureTheory +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ArchVariation +open PartialCalculus + +lemma fixed_profile_variation {w : ℝ × ℝ → ℝ} {φ : ℝ → ℝ} {t y : ℝ} + (hw : ContDiffAt ℝ ω w (t,y)) (hφ : DifferentiableAt ℝ φ (w (t,y))) + (he : ∀ᶠ q in 𝓝 (t,y), HasDerivAt (fun s => w (q.1,s)) (φ (w q)-q.2) q.2) : + HasDerivAt (fun s => first w (t,s)) (deriv φ (w (t,y))*first w (t,y)) y := by + let Φ : ℝ × ℝ → ℝ := fun q => φ q.2 + have hd : DifferentiableAt ℝ Φ (t,w (t,y)) := hφ.comp (t,w (t,y)) differentiableAt_snd + have h₁ : first Φ (t,w (t,y)) = 0 := + (first_hasDerivAt hd).unique (hasDerivAt_const t (φ (w (t,y)))) + have h₂ : second Φ (t,w (t,y)) = deriv φ (w (t,y)) := + (second_hasDerivAt hd).unique hφ.hasDerivAt + simpa only [h₁,h₂,zero_add] using scalar_ode_variation hw hd he + +lemma moving_peak_variation {w : ℝ × ℝ → ℝ} {φ : ℝ → ℝ} {t : ℝ} + (hw : ContDiffAt ℝ ω w (t,φ t)) (hφ : DifferentiableAt ℝ φ t) + (hp : ∀ᶠ s in 𝓝 t, w (s,φ s) = s) + (he : HasDerivAt (fun y => w (t,y)) 0 (φ t)) : first w (t,φ t) = 1 := by + have hs : second w (t,φ t) = 0 := + (second_hasDerivAt (hw.differentiableAt (by simp))).unique he + have hd := (hw.differentiableAt (by simp)).hasFDerivAt.comp_hasDerivAt t + ((hasDerivAt_id t).prodMk hφ.hasDerivAt) + have heq := hd.unique ((hasDerivAt_id t).congr_of_eventuallyEq hp) + simpa only [fderiv_pair,hs,mul_zero,one_mul,add_zero] using heq + +theorem positive_homogeneous {f a : ℝ → ℝ} {l r c : ℝ} + (ha : Continuous a) (hf : ContinuousOn f (Icc l r)) + (hd : ∀ y ∈ Icc l r, HasDerivAt f (a y*f y) y) + (hc : c ∈ Icc l r) (hinit : f c = 1) : + ∀ y ∈ Icc l r, f y = Real.exp (∫ s in c..y, a s) := by + let g : ℝ → ℝ := fun y => Real.exp (-(∫ s in c..y, a s))*f y + have hg (y : ℝ) (hy : y ∈ Icc l r) : HasDerivAt g 0 y := by + have hh := ((ha.integral_hasStrictDerivAt c y).hasDerivAt.neg.exp).mul (hd y hy) + convert hh using 1; (first | rfl | (dsimp; ring)) + have hgc : ContinuousOn g (Icc l r) := + ((continuous_iff_continuousAt.mpr (fun y => + ((ha.integral_hasStrictDerivAt c y).hasDerivAt.neg.exp).continuousAt)).continuousOn).mul hf + have heq := eq_of_hasDerivAt_eq_on_Icc hgc continuousOn_const hg + (fun y _ => hasDerivAt_const y (1:ℝ)) hc (by simp [g,hinit]) + intro y hy + have h := heq hy + change Real.exp (-(∫ s in c..y, a s))*f y=1 at h + have he : Real.exp (∫ s in c..y, a s)*Real.exp (-(∫ s in c..y, a s))=1 := by + rw [←Real.exp_add,add_neg_cancel,Real.exp_zero] + calc + f y = (Real.exp (∫ s in c..y, a s)*Real.exp (-(∫ s in c..y, a s)))*f y := by rw [he,one_mul] + _ = Real.exp (∫ s in c..y, a s) := by rw [mul_assoc,h,mul_one] + +lemma hit_variation {w : ℝ × ℝ → ℝ} {Y h : ℝ → ℝ} {t d : ℝ} + (hw : DifferentiableAt ℝ w (t,Y t)) (hY : DifferentiableAt ℝ Y t) + (hh : HasDerivAt h d t) (he : ∀ᶠ s in 𝓝 t, w (s,Y s) = h s) : + first w (t,Y t) + deriv Y t*second w (t,Y t) = d := by + have hd := hw.hasFDerivAt.comp_hasDerivAt t ((hasDerivAt_id t).prodMk hY.hasDerivAt) + have hq := hd.unique (hh.congr_of_eventuallyEq he) + simpa only [fderiv_pair,one_mul] using hq + +theorem peak_derivative_positive {w : ℝ × ℝ → ℝ} {φ : ℝ → ℝ} + {t a b : ℝ} (hφ : ContDiff ℝ 1 φ) + (hwc : Continuous (fun y => w (t,y))) + (hw : ∀ y ∈ Icc a b, ContDiffAt ℝ ω w (t,y)) + (he : ∀ y ∈ Icc a b, ∀ᶠ q in 𝓝 (t,y), + HasDerivAt (fun s => w (q.1,s)) (φ (w q)-q.2) q.2) + (hp : ∀ᶠ s in 𝓝 t, w (s,φ s) = s) + (hc : φ t ∈ Icc a b) : ∀ y ∈ Icc a b, 0 < first w (t,y) := by + have hφd := hφ.differentiable (by norm_num) + have init : first w (t,φ t) = 1 := by + apply moving_peak_variation (hw _ hc) (hφd t) hp + have hd := (he _ hc).self_of_nhds + simpa only [hp.self_of_nhds,sub_self] using hd + have hcoeff : Continuous (fun y => deriv φ (w (t,y))) := + (hφ.continuous_deriv (by norm_num)).comp hwc + have hfirst : ContinuousOn (fun y => first w (t,y)) (Icc a b) := by + intro y hy + exact (((first_contDiffAt (hw y hy)).continuousAt).comp + (continuousAt_const.prodMk continuousAt_id)).continuousWithinAt + have hd := positive_homogeneous hcoeff hfirst + (fun y hy => fixed_profile_variation (hw y hy) (hφd _) (he y hy)) hc init + intro y hy + rw [hd y hy] + exact Real.exp_pos _ + +theorem endpoint_peak_signs {w : ℝ × ℝ → ℝ} {φ : ℝ → ℝ} + {l r : ℝ → ℝ} {t h : ℝ} + (hl : DifferentiableAt ℝ l t) (hr : DifferentiableAt ℝ r t) + (hwl : DifferentiableAt ℝ w (t,l t)) (hwr : DifferentiableAt ℝ w (t,r t)) + (hel : ∀ᶠ s in 𝓝 t, w (s,l s) = h) (her : ∀ᶠ s in 𝓝 t, w (s,r s) = h) + (hdl : HasDerivAt (fun y => w (t,y)) (φ h-l t) (l t)) + (hdr : HasDerivAt (fun y => w (t,y)) (φ h-r t) (r t)) + (hxl : 0 < first w (t,l t)) (hxr : 0 < first w (t,r t)) + (hlt : l t < φ h) (htr : φ h < r t) : deriv l t < 0 ∧ 0 < deriv r t := by + have hlv := hit_variation hwl hl (hasDerivAt_const t h) hel + have hrv := hit_variation hwr hr (hasDerivAt_const t h) her + rw [(second_hasDerivAt hwl).unique hdl] at hlv + rw [(second_hasDerivAt hwr).unique hdr] at hrv + constructor + · by_contra hn + have hnon := mul_nonneg (le_of_not_gt hn) (sub_nonneg.mpr hlt.le) + linarith + · by_contra hn + have hnon := mul_nonneg_of_nonpos_of_nonpos (le_of_not_gt hn) (sub_nonpos.mpr htr.le) + linarith + +lemma width_midpoint_peak_bounds {l r : ℝ → ℝ} {t : ℝ} + (hl : DifferentiableAt ℝ l t) (hr : DifferentiableAt ℝ r t) + (hlneg : deriv l t < 0) (hrpos : 0 < deriv r t) : + 0 < deriv (fun s => (r s-l s)/2) t ∧ + |deriv (fun s => (r s+l s)/2) t / deriv (fun s => (r s-l s)/2) t| < 1 := by + have hd₁ : HasDerivAt (fun s => (r s-l s)/2) ((deriv r t-deriv l t)/2) t := + (hr.hasDerivAt.sub hl.hasDerivAt).div_const 2 + have hd₂ : HasDerivAt (fun s => (r s+l s)/2) ((deriv r t+deriv l t)/2) t := + (hr.hasDerivAt.add hl.hasDerivAt).div_const 2 + rw [hd₁.deriv,hd₂.deriv] + have hd : 0 < (deriv r t-deriv l t)/2 := by linarith + refine ⟨hd,?_⟩ + rw [abs_lt] + constructor + · rw [lt_div_iff₀ hd]; linarith + · rw [div_lt_iff₀ hd]; linarith + +end QuinticLienard.ArchVariation + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AxisBranches.lean b/lean/OAI/Analysis/LienardCycles/AxisBranches.lean new file mode 100644 index 0000000000000000000000000000000000000000..81c2e522a1ac88336b1e0437a100267c6f56750f --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AxisBranches.lean @@ -0,0 +1,127 @@ +import OAI.Analysis.LienardCycles.BoundaryGerm + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter +open Set Filter Metric +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.AxisFlow +open ScaledProfile ScalarArcs ArcFamilies PartialCalculus +noncomputable def φ (a : Fin 6 → ℝ) (h : ℝ) : ℝ := poly a (root h) +noncomputable def endpoint (a : Fin 6 → ℝ) (upper : Bool) (h t : ℝ) : ℝ := + if upper then ScalarArcs.upper (φ a) h t else lower (φ a) h t +noncomputable def branch (a : Fin 6 → ℝ) (upper : Bool) (q : ℝ×ℝ) : ℝ := endpoint a upper (q.2^2/2) q.1 +noncomputable def axisEndpoint (a : Fin 6 → ℝ) (upper : Bool) (t : ℝ) : ℝ := + if upper then axisUpper (φ a) t else axisLower (φ a) t +lemma φ_continuous (a : Fin 6 → ℝ) : Continuous (φ a) := by + unfold φ poly root + fun_prop +lemma φ_smooth (a : Fin 6 → ℝ) : ContDiffOn ℝ 1 (φ a) (Ioi 0) := by + intro h hh + exact (((QuinticProfile.analytic a (q:=((0:ℝ),h)) hh).comp h + (contDiffAt_const.prodMk contDiffAt_id)).of_le (by simp)).contDiffWithinAt +lemma φ_square (a : Fin 6 → ℝ) {x : ℝ} (hx : 0≤x) : φ a (x^2/2)=poly a x := by + have he : 2*(x^2/2)=x^2 := by ring + simp only [φ,root,he,Real.sqrt_sq hx] +lemma branch_analytic (a : Fin 6 → ℝ) (u : Bool) {t x : ℝ} (hx : 0QuinticProfile.analytic a h) (QuinticProfile.local_flow a) (p:=(0:ℝ)) hh ht + have hc : ContDiffAt ℝ ω (fun q : ℝ×ℝ=>(((0:ℝ),q.1),q.2^2/2)) (t,x) := by fun_prop + cases u + · exact hl.comp (t,x) hc + · exact hr.comp (t,x) hc +lemma branch_equation (a : Fin 6 → ℝ) (u : Bool) {t x : ℝ} (hx : 0(s,branch a u (t,s))) (field a (x,branch a u (t,x))) x ∧ + (x,branch a u (t,x)) ∈ domain a := by + have hh : 0QuinticProfile.analytic a h) (QuinticProfile.local_flow a) (p:=(0:ℝ)) hh ht + have hd : HasDerivAt (fun s : ℝ=>s^2/2) x x := by convert! ((hasDerivAt_id x).pow 2).div_const 2 using 1; simp + have hu := chosen_arch (positive_arch_exists (φ_smooth a) hh ht) + have he : HasDerivAt (fun s=>branch a u (t,s)) (x/(poly a x-branch a u (t,x))) x := by + cases u + · convert! hl.comp x hd using 1 + change x/(poly a x-branch a false (t,x))=1/(φ a (x^2/2)-_) * x + rw [φ_square a hx.le] + change x/(poly a x-branch a false (t,x))=1/(poly a x-branch a false (t,x))*x + ring + · convert! hr.comp x hd using 1 + change x/(poly a x-branch a true (t,x))=1/(φ a (x^2/2)-_) * x + rw [φ_square a hx.le] + change x/(poly a x-branch a true (t,x))=1/(poly a x-branch a true (t,x))*x + ring + refine ⟨(hasDerivAt_id x).prodMk he,?_⟩ + cases u + · exact ne_of_gt (by change 0QuinticProfile.analytic a h) (QuinticProfile.local_flow a) (p:=(0:ℝ)) hh ht + have hd := (first_hasDerivAt ((branch_analytic a u hx ht).differentiableAt (by simp))).deriv + cases u + · change first (branch a false) (t,x)<0 + rw [←hd] + exact hl + · change 0branch a u (t,x)) (𝓝[>] 0) (𝓝 (axisEndpoint a u t)) := by + have hc : Tendsto (fun x : ℝ=>x^2/2) (𝓝[>] (0:ℝ)) (𝓝 (0:ℝ)) := by + have hh := (((continuousAt_id.pow 2).div_const 2 : ContinuousAt (fun x : ℝ=>x^2/2) 0).tendsto).mono_left (show 𝓝[>] (0:ℝ) ≤ 𝓝 (0:ℝ) from inf_le_left) + simpa only [Pi.pow_apply,id_eq,zero_pow (by norm_num : (2:ℕ)≠0),zero_div] using hh + have he : ∀ᶠ x : ℝ in 𝓝[>] (0:ℝ), x^2/2 ∈ Ioi (0:ℝ) := by + filter_upwards [self_mem_nhdsWithin] with x hx + exact div_pos (sq_pos_of_pos (show 0x^2/2) (𝓝[>] (0:ℝ)) (𝓝[>] (0:ℝ)) := + tendsto_nhdsWithin_iff.mpr ⟨hc,he⟩ + cases u + · exact (lower_axis_tendsto (φ_smooth a) (φ_continuous a).continuousOn ht).comp hs + · exact (upper_axis_tendsto (φ_smooth a) (φ_continuous a).continuousOn ht).comp hs + +theorem endpoint_germ (a : Fin 6 → ℝ) (u : Bool) {t : ℝ} (ht : 0.mpr hx.2 + dsimp only [T] at hs + rw [Real.sq_sqrt ht.le] at hs + linarith + have hAU : (0,axisEndpoint a u t) ∈ domain a := sub_ne_zero.mpr htr.symm + obtain ⟨G,hG,h0,he,δ,hδ,k,hk,hD⟩ := boundary_germ (V:=field a) (domain_open a) + (fun z hz=>(field_analytic a hz).of_le (by simp) |>.contDiffWithinAt) + (y:=branch a u) (J:=Ioi (t/2)) (Ioi_mem_nhds (by linarith)) hT + (fun x hx=>branch_analytic a u hx.1 (by linarith [hbound hx])) + (fun p hp x hx=>branch_equation a u hx.1 ((hbound hx).trans hp)) + (branch_tendsto a u ht) (local_flow a hAU) hAU + refine ⟨G,hG,h0,he,?_⟩ + have hs := branch_peak_sign a u hδ.1 (show δ^2/2third_pos_case2 h1 h3 h5 hh) + intro h hh + rw [reflectX_third a hh] + exact neg_neg_of_pos (third_pos_case2 h1 h3 h5 hh) +lemma matching_case3_gap {a : Fin 6 → ℝ} (h1 : a 1<0) (h3 : 0≤a 3) (h5 : 0≤a 5) + {r : ℝ} (hr : r ∈ matchingDomain a (reflectX a)) : axisKappa (reflectX a) rcurvature_lower_case3 h1 h3 h5 hu.1 hu.2) + have hb : axisKappa (reflectX a) r≤8*a 4-δ := axisKappa_upper hr.2 hTb (fun h hu=>by + rw [reflectX_curvature a hu.1] + linarith [curvature_lower_case3 h1 h3 h5 hu.1 hu.2]) + linarith +lemma matching_zeros_case3 {a : Fin 6 → ℝ} (h1 : a 1<0) (h3 : 0≤a 3) (h5 : 0≤a 5) : + {r ∈ matchingDomain a (reflectX a) | matchingDelta a (reflectX a) r=0}.encard≤1 := + matchingDelta_zero_bound (fun _ hr _=>matching_case3_gap h1 h3 h5 hr) +lemma matching_zeros_case4 {a : Fin 6 → ℝ} (h1 : a 1<0) (h3 : a 3<0) (h5 : 0≤a 5) : + {r ∈ matchingDomain a (reflectX a) | matchingDelta a (reflectX a) r=0}.encard≤1 := by + apply matchingDelta_zero_bound_of_lambda + intro r hr + have ha := axisLambda_lt hr.1 (fun _ hh=>intercept_pos_case4 h1 h3 h5 hh) (slope_atBot h1) + have hb := axisLambda_gt (d:=2*a 2) hr.2 (fun h hh=>by + rw [reflectX_intercept a hh] + exact neg_neg_of_pos (intercept_pos_case4 h1 h3 h5 hh)) + (slope_atTop (a:=reflectX a) (by simpa using neg_pos.mpr h1)) + exact ha.trans hb +lemma matching_isolated_case3 {a : Fin 6 → ℝ} (h1 : a 1<0) (h3 : 0≤a 3) (h5 : 0≤a 5) : + {r | IsIsolatedZeroOn (matchingDelta a (reflectX a)) (matchingDomain a (reflectX a)) r}.encard≤2 := by + have hs : {r | IsIsolatedZeroOn (matchingDelta a (reflectX a)) (matchingDomain a (reflectX a)) r} ⊆ + {r ∈ matchingDomain a (reflectX a) | matchingDelta a (reflectX a) r=0} := fun _ hr=>⟨hr.1,hr.2.1⟩ + exact (encard_mono hs).trans ((matching_zeros_case3 h1 h3 h5).trans (by norm_num)) +lemma matching_isolated_case4 {a : Fin 6 → ℝ} (h1 : a 1<0) (h3 : a 3<0) (h5 : 0≤a 5) : + {r | IsIsolatedZeroOn (matchingDelta a (reflectX a)) (matchingDomain a (reflectX a)) r}.encard≤2 := by + have hs : {r | IsIsolatedZeroOn (matchingDelta a (reflectX a)) (matchingDomain a (reflectX a)) r} ⊆ + {r ∈ matchingDomain a (reflectX a) | matchingDelta a (reflectX a) r=0} := fun _ hr=>⟨hr.1,hr.2.1⟩ + exact (encard_mono hs).trans ((matching_zeros_case4 h1 h3 h5).trans (by norm_num)) +end QuinticLienard.AxisFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AxisComparison.lean b/lean/OAI/Analysis/LienardCycles/AxisComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..4601cca79c078d772ce82106774e775024ff0f82 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AxisComparison.lean @@ -0,0 +1,106 @@ +import OAI.Analysis.LienardCycles.CurvatureRange + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.AxisFlow +open ScaledProfile PositiveWidth PartialCalculus +lemma kappa_monotone_height {a : Fin 6 → ℝ} {h : ℝ} (hh : 0QuinticFit.kappa a (h,r)) (Ioi 0) := by + apply monotoneOn_of_deriv_nonneg (convex_Ioi 0) + (fun r hr=>((QuinticFit.kappa_analytic a hh hr).comp r (contDiffAt_const.prodMk contDiffAt_id)).continuousAt.continuousWithinAt) + (fun r hr=>((QuinticFit.kappa_analytic a hh (interior_subset hr)).comp r (contDiffAt_const.prodMk contDiffAt_id)).differentiableAt (by simp) |>.differentiableWithinAt) + intro r hr + have hr' : 0QuinticFit.kappa a (h,s)) r + rw [(second_hasDerivAt ((QuinticFit.kappa_analytic a hh hr').differentiableAt (by simp))).deriv] + exact (QuinticFit.kappa_width_pos hh hr' hp).le +lemma kappa_antitone_height {a : Fin 6 → ℝ} {h : ℝ} (hh : 0QuinticFit.kappa a (h,r)) (Ioi 0) := by + apply antitoneOn_of_deriv_nonpos (convex_Ioi 0) + (fun r hr=>((QuinticFit.kappa_analytic a hh hr).comp r (contDiffAt_const.prodMk contDiffAt_id)).continuousAt.continuousWithinAt) + (fun r hr=>((QuinticFit.kappa_analytic a hh (interior_subset hr)).comp r (contDiffAt_const.prodMk contDiffAt_id)).differentiableAt (by simp) |>.differentiableWithinAt) + intro r hr + have hr' : 0QuinticFit.kappa a (h,s)) r≤0 + rw [(second_hasDerivAt ((QuinticFit.kappa_analytic a hh hr').differentiableAt (by simp))).deriv] + exact (QuinticFit.kappa_width_neg hh hr' hp).le +lemma axisKappa_monotone {a : Fin 6 → ℝ} (hp : ∀ u,0] (0:ℝ)) (h:=id) (r:=fun _ : ℝ=>r) self_mem_nhdsWithin + (tendsto_id.mono_left inf_le_left) tendsto_const_nhds).2.2.2.1 + have hls := (joint_limits a hs (l:=𝓝[>] (0:ℝ)) (h:=id) (r:=fun _ : ℝ=>s) self_mem_nhdsWithin + (tendsto_id.mono_left inf_le_left) tendsto_const_nhds).2.2.2.1 + exact le_of_tendsto_of_tendsto hlr hls ((show ∀ᶠ h : ℝ in 𝓝[>] 0, 0 + kappa_monotone_height hh hp (axisM_abs_lt a hr).1 (axisM_abs_lt a hs).1 hrs) +lemma axisKappa_antitone {a : Fin 6 → ℝ} (hp : ∀ u,0] (0:ℝ)) (h:=id) (r:=fun _ : ℝ=>r) self_mem_nhdsWithin + (tendsto_id.mono_left inf_le_left) tendsto_const_nhds).2.2.2.1 + have hls := (joint_limits a hs (l:=𝓝[>] (0:ℝ)) (h:=id) (r:=fun _ : ℝ=>s) self_mem_nhdsWithin + (tendsto_id.mono_left inf_le_left) tendsto_const_nhds).2.2.2.1 + exact le_of_tendsto_of_tendsto hls hlr ((show ∀ᶠ h : ℝ in 𝓝[>] 0, 0 + kappa_antitone_height hh hp (axisM_abs_lt a hr).1 (axisM_abs_lt a hs).1 hrs) +lemma kappa_range_height {a : Fin 6 → ℝ} {h r T C D : ℝ} (hh : 0QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) (p:=0) hh hr + have he : ActualCharacteristic.Adm a t r := ⟨h,hh,hs.1,hs.2⟩ + have hb : ActualCharacteristic.b a t r=h := base_eq _ + (fun _ h=>QuinticProfile.analytic a h) (QuinticProfile.local_flow a) hh hs.1 hs.2 + have hl := ActualCharacteristic.curvature_lower he (C:=C) (fun u hu=> + (hc u ⟨(show 0 + (hc u ⟨(show 0] (0:ℝ)) (h:=id) (r:=fun _ : ℝ=>r) self_mem_nhdsWithin + (tendsto_id.mono_left inf_le_left) tendsto_const_nhds + apply ge_of_tendsto hl.2.2.2.1 + filter_upwards [self_mem_nhdsWithin,hl.2.2.2.2.eventually (eventually_lt_nhds ht)] with h hh hht + let t := peakAtWidth (QuinticProfile.profile a) ((0,h),r) + have hs := peak_spec (QuinticProfile.profile a) (fun _ h=>QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) (p:=0) hh (axisM_abs_lt a hr).1 + have he : ActualCharacteristic.Adm a t r := ⟨h,hh,hs.1,hs.2⟩ + have hb : ActualCharacteristic.b a t r=h := base_eq _ + (fun _ h=>QuinticProfile.analytic a h) (QuinticProfile.local_flow a) hh hs.1 hs.2 + have hh' : 0hc u ⟨hh'.trans_le hu.1,hu.2.trans_lt hht⟩) +lemma axisKappa_upper {a : Fin 6 → ℝ} {r T C : ℝ} (hr : r ∈ axisWidths a) + (ht : axisPeak a r] (0:ℝ)) (h:=id) (r:=fun _ : ℝ=>r) self_mem_nhdsWithin + (tendsto_id.mono_left inf_le_left) tendsto_const_nhds + apply le_of_tendsto hl.2.2.2.1 + filter_upwards [self_mem_nhdsWithin,hl.2.2.2.2.eventually (eventually_lt_nhds ht)] with h hh hht + let t := peakAtWidth (QuinticProfile.profile a) ((0,h),r) + have hs := peak_spec (QuinticProfile.profile a) (fun _ h=>QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) (p:=0) hh (axisM_abs_lt a hr).1 + have he : ActualCharacteristic.Adm a t r := ⟨h,hh,hs.1,hs.2⟩ + have hb : ActualCharacteristic.b a t r=h := base_eq _ + (fun _ h=>QuinticProfile.analytic a h) (QuinticProfile.local_flow a) hh hs.1 hs.2 + have hh' : 0hc u ⟨hh'.trans_le hu.1,hu.2.trans_lt hht⟩) +end QuinticLienard.AxisFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AxisFit.lean b/lean/OAI/Analysis/LienardCycles/AxisFit.lean new file mode 100644 index 0000000000000000000000000000000000000000..06e7ea3928a41ce6d7254794a00708fc58de7094 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AxisFit.lean @@ -0,0 +1,93 @@ +import OAI.Analysis.LienardCycles.AxisWidthRegularity + +namespace OAI + +universe uι + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.AxisFlow +open ScalarArcs ScaledProfile PartialCalculus PositiveWidth QuadraticCoordinates +noncomputable def axisLambda (a : Fin 6 → ℝ) (r : ℝ) : ℝ := QuadraticFit.fitD ((r,axisM a r),axisV a r) +noncomputable def axisKappa (a : Fin 6 → ℝ) (r : ℝ) : ℝ := QuadraticFit.fitK ((r,axisM a r),axisV a r) +lemma axisLambda_analytic (a : Fin 6 → ℝ) {r : ℝ} (hr : r ∈ axisWidths a) : + ContDiffAt ℝ ω (axisLambda a) r := + (QuadraticFit.fitD_analytic (axisM_abs_lt a hr).1 (axisM_abs_lt a hr).2 (axisV_abs_lt a hr)).comp r + ((contDiffAt_id.prodMk (axisM_analytic a hr)).prodMk (axisV_analytic a hr)) +lemma axisKappa_analytic (a : Fin 6 → ℝ) {r : ℝ} (hr : r ∈ axisWidths a) : + ContDiffAt ℝ ω (axisKappa a) r := + (QuadraticFit.fitK_analytic (axisM_abs_lt a hr).1 (axisM_abs_lt a hr).2 (axisV_abs_lt a hr)).comp r + ((contDiffAt_id.prodMk (axisM_analytic a hr)).prodMk (axisV_analytic a hr)) +lemma axisFit_spec (a : Fin 6 → ℝ) {r : ℝ} (hr : r ∈ axisWidths a) : + H ((axisLambda a r,axisKappa a r),r)=axisM a r ∧ + Hr ((axisLambda a r,axisKappa a r),r)=axisV a r := + QuadraticFit.fit_spec (axisM_abs_lt a hr).1 (axisM_abs_lt a hr).2 (axisV_abs_lt a hr) + +theorem joint_limits (a : Fin 6 → ℝ) {r₀ : ℝ} (hr₀ : r₀ ∈ axisWidths a) + {ι : Type uι} {l : Filter ι} {h r : ι → ℝ} + (hh : ∀ᶠ i in l, 0QuinticFit.M a (h i,r i)) l (𝓝 (axisM a r₀)) ∧ + Tendsto (fun i=>QuinticFit.V a (h i,r i)) l (𝓝 (axisV a r₀)) ∧ + Tendsto (fun i=>QuinticFit.lambda a (h i,r i)) l (𝓝 (axisLambda a r₀)) ∧ + Tendsto (fun i=>QuinticFit.kappa a (h i,r i)) l (𝓝 (axisKappa a r₀)) ∧ + Tendsto (fun i=>peakAtWidth (QuinticProfile.profile a) ((0,h i),r i)) l (𝓝 (axisPeak a r₀)) := by + have ht := axisPeak_spec a hr₀ + obtain ⟨Y,G,hY,hG,hY0,_,hes,hep⟩ := width_germ a ht.1 + rw [ht.2] at hY hG hY0 hes hep + have hG0 : G (0,r₀)=axisM a r₀ := hes.self_of_nhds.2.2 + have hGD0 : second G (0,r₀)=axisV a r₀ := width_germ_axis_derivative a hG (hes.mono fun _ he=>he.2.2) + have heD := width_germ_derivative a (axisM_abs_lt a hr₀).1 hG (hep.mono fun _ he hx=>(he hx).2) + have hx0 : Tendsto (fun i=>root (h i)) l (𝓝 0) := by + have hc : Continuous (fun s : ℝ=>root s) := by unfold root; fun_prop + simpa [root,Function.comp_def] using hc.continuousAt.tendsto.comp hh0 + have hq := hx0.prodMk_nhds hrr + have hx : ∀ᶠ i in l, 0Real.sqrt_pos.mpr (mul_pos (by norm_num) hi) + have hEq : ∀ᶠ i in l, + G (root (h i),r i)=QuinticFit.M a (h i,r i) ∧ + second G (root (h i),r i)=QuinticFit.V a (h i,r i) ∧ + Y (root (h i),r i)=peakAtWidth (QuinticProfile.profile a) ((0,h i),r i) := by + filter_upwards [hq.eventually hep,hq.eventually heD,hh,hx] with i he hd hi hxi + have hs : root (h i)^2/2=h i := by rw [root_sq hi.le]; ring + have hm := (he hxi).2 + have hv := hd hxi + have hy := (he hxi).1 + rw [hs] at hm hv hy + exact ⟨hm,hv,hy⟩ + have hm : Tendsto (fun i=>QuinticFit.M a (h i,r i)) l (𝓝 (axisM a r₀)) := by + have hg := hG.continuousAt.tendsto.comp hq + rw [hG0] at hg + exact hg.congr' (hEq.mono fun _ he=>he.1) + have hv : Tendsto (fun i=>QuinticFit.V a (h i,r i)) l (𝓝 (axisV a r₀)) := by + have hg := (second_contDiffAt hG).continuousAt.tendsto.comp hq + rw [hGD0] at hg + exact hg.congr' (hEq.mono fun _ he=>he.2.1) + have hyp : Tendsto (fun i=>peakAtWidth (QuinticProfile.profile a) ((0,h i),r i)) l (𝓝 (axisPeak a r₀)) := by + have hy := hY.continuousAt.tendsto.comp hq + rw [hY0] at hy + exact hy.congr' (hEq.mono fun _ he=>he.2.2) + have hr : ∀ᶠ i in l, 0QuinticProfile.analytic a h) hh ht +lemma heightWidth_limit (a : Fin 6 → ℝ) {t : ℝ} (ht : 0] 0) (𝓝 (axisWidth a t)) := by + exact ((upper_axis_tendsto (φ_smooth a) (φ_continuous a).continuousOn ht).sub + (lower_axis_tendsto (φ_smooth a) (φ_continuous a).continuousOn ht)).div_const 2 +lemma heightWidth_midpoint (a : Fin 6 → ℝ) {t h : ℝ} (hh : 0QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) (p:=(0:ℝ)) (heightWidth_pos a hh ht) hh ht rfl + exact congrArg (fun t=>midpointFamily (QuinticProfile.profile a) ((0,t),h)) he +lemma heightWidth_deriv (a : Fin 6 → ℝ) {t h : ℝ} (hh : 0QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) (p:=(0:ℝ)) hh ht + change HasDerivAt (heightWidth a t) (-(heightWidth a t h/(heightWidth a t h^2-QuinticFit.M a (h,heightWidth a t h)^2))) h + rw [heightWidth_midpoint a hh ht] + change HasDerivAt (fun s=>widthFamily (QuinticProfile.profile a) ((0,t),s)) + (-(widthFamily (QuinticProfile.profile a) ((0,t),h)/(widthFamily (QuinticProfile.profile a) ((0,t),h)^2-midpointFamily (QuinticProfile.profile a) ((0,t),h)^2))) h + simpa only [neg_div] using hd +lemma along_height_deriv {a : Fin 6 → ℝ} {t h : ℝ} (hh : 0f (u,heightWidth a t u)) (QuinticFit.D a f (h,heightWidth a t h)) h := by + have hd := hf.hasFDerivAt.comp_hasDerivAt h ((hasDerivAt_id h).prodMk (heightWidth_deriv a hh ht)) + simpa only [Function.comp_def,fderiv_pair,one_mul,QuinticFit.D,id_eq,neg_mul,sub_eq_add_neg] using hd +lemma intercept_height_deriv {a : Fin 6 → ℝ} {t h d : ℝ} (hh : 0QuinticFit.intercept a d (u,heightWidth a t u)) + ((S (QuinticFit.fit a (h,heightWidth a t h))+h*R (QuinticFit.fit a (h,heightWidth a t h)))/ + G (QuinticFit.fit a (h,heightWidth a t h))* + (QuinticFit.lambda a (h,heightWidth a t h)-slope a h)) h := by + have hr := heightWidth_pos a hh ht + have hl := along_height_deriv hh ht ((QuinticFit.lambda_analytic a hh hr).differentiableAt (by simp)) + have hk := along_height_deriv hh ht ((QuinticFit.kappa_analytic a hh hr).differentiableAt (by simp)) + have hd := (hl.sub ((hasDerivAt_id h).mul hk)).sub_const d + have hg := QuinticFit.fit_transport a hh hr + have hL : QuinticFit.D a (QuinticFit.lambda a) (h,heightWidth a t h)= + QuinticFit.kappa a (h,heightWidth a t h)+S (QuinticFit.fit a (h,heightWidth a t h))/G (QuinticFit.fit a (h,heightWidth a t h))* + (QuinticFit.lambda a (h,heightWidth a t h)-slope a h) := by linarith only [hg.2.2] + rw [hg.2.1,hL] at hd + convert! hd using 1 + simp only [id_eq] + ring + +lemma axisLambda_lt {a : Fin 6 → ℝ} {r d : ℝ} (hr : r ∈ axisWidths a) + (hp : ∀ u,0] 0) atBot) : axisLambda a r] 0) (𝓝 r) := by + rw [←ht.2] + exact heightWidth_limit a ht.1.1 + have hl := joint_limits a hr (l:=𝓝[>] (0:ℝ)) (h:=id) (r:=heightWidth a t) + self_mem_nhdsWithin (tendsto_id.mono_left inf_le_left) hw + have hI : Tendsto (fun u=>QuinticFit.intercept a d (u,heightWidth a t u)) (𝓝[>] 0) (𝓝 (axisLambda a r-d)) := by + simpa only [QuinticFit.intercept,zero_mul,sub_zero,id_eq] using + (hl.2.2.1.sub ((tendsto_id.mono_left inf_le_left).mul hl.2.2.2.1)).sub_const d + have hev : ∀ᶠ u in 𝓝[>] (0:ℝ), uQuinticFit.intercept a d (u,heightWidth a t u)) (Ioo 0 ε) := by + apply monotoneOn_of_deriv_nonneg (convex_Ioo 0 ε) + (fun u hu=>(intercept_height_deriv hu.1 (hεprop hu).1).continuousAt.continuousWithinAt) + (fun u hu=>(intercept_height_deriv (interior_subset hu).1 (hεprop (interior_subset hu)).1).differentiableAt.differentiableWithinAt) + intro u hu + have hu' := interior_subset hu + rw [(intercept_height_deriv (d:=d) hu'.1 (hεprop hu').1).deriv] + have hru := heightWidth_pos a hu'.1 (hεprop hu').1 + exact (mul_pos (div_pos (add_pos (S_pos hru) (mul_pos hu'.1 (R_pos hru))) (G_pos hru)) + (sub_pos.mpr (hεprop hu').2)).le + have hle : axisLambda a r-d≤QuinticFit.intercept a d (ε/2,heightWidth a t (ε/2)) := by + apply le_of_tendsto hI + filter_upwards [self_mem_nhdsWithin,(eventually_lt_nhds (half_pos hε)).filter_mono inf_le_left] with u hu hue + exact hm ⟨hu,hue.trans (half_lt_self hε)⟩ ⟨half_pos hε,half_lt_self hε⟩ hue.le + have hi := QuinticFit.intercept_negative (half_pos hε) (heightWidth_pos a (half_pos hε) hεt) hp + dsimp only [QuinticFit.intercept] at hle + linarith +end QuinticLienard.AxisFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AxisLimits.lean b/lean/OAI/Analysis/LienardCycles/AxisLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..b128d58238a8f5d7458bcf0b83c32ae98cdc5d2f --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AxisLimits.lean @@ -0,0 +1,148 @@ +import OAI.Analysis.LienardCycles.Intercept + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ScalarArcs +lemma IsArch.endpoint_bounds {φ u : ℝ → ℝ} {h t a b B : ℝ} + (hu : IsArch φ u h t a b) (hh : 0≤h) (ht : hu y+(y-B)^2/2) (φ (u y)-B) y := by + convert! (hu.equation y hy).add ((((hasDerivAt_id y).sub_const B).pow 2).div_const 2) using 1 + simp only [id_eq] + ring + have hdm (y : ℝ) (hy : y ∈ Icc a b) : + HasDerivAt (fun y=>u y+(y+B)^2/2) (φ (u y)+B) y := by + convert! (hu.equation y hy).add ((((hasDerivAt_id y).add_const B).pow 2).div_const 2) using 1 + simp only [id_eq] + ring + have hmp : AntitoneOn (fun y=>u y+(y-B)^2/2) (Icc a b) := by + apply antitoneOn_of_deriv_nonpos (convex_Icc a b) + (fun y hy=>(hdp y hy).continuousAt.continuousWithinAt) + (fun y hy=>(hdp y (interior_subset hy)).differentiableAt.differentiableWithinAt) + intro y hy + rw [(hdp y (interior_subset hy)).deriv] + exact sub_nonpos.mpr (abs_le.mp (hb _ (hu.range_mem y (interior_subset hy)))).2 + have hmm : MonotoneOn (fun y=>u y+(y+B)^2/2) (Icc a b) := by + apply monotoneOn_of_deriv_nonneg (convex_Icc a b) + (fun y hy=>(hdm y hy).continuousAt.continuousWithinAt) + (fun y hy=>(hdm y (interior_subset hy)).differentiableAt.differentiableWithinAt) + intro y hy + rw [(hdm y (interior_subset hy)).deriv] + have hx := (abs_le.mp (hb _ (hu.range_mem y (interior_subset hy)))).1 + linarith + have hl := hmm (show a ∈ Icc a b from ⟨le_rfl,hab.le⟩) + (show φ t ∈ Icc a b from ⟨hu.lower_lt_peak.le,hu.peak_lt_upper.le⟩) hu.lower_lt_peak.le + have hr := hmp (show φ t ∈ Icc a b from ⟨hu.lower_lt_peak.le,hu.peak_lt_upper.le⟩) + (show b ∈ Icc a b from ⟨hab.le,le_rfl⟩) hu.peak_lt_upper.le + dsimp only at hl hr + rw [hu.lower,hu.peak] at hl + rw [hu.upper,hu.peak] at hr + have hsq : (φ t)^2≤B^2 := by nlinarith [mul_nonneg (sub_nonneg.mpr hc.2) (show 0≤φ t+B by linarith [hc.1])] + have hBc : |B*φ t|≤B^2 := by rw [abs_mul,abs_of_nonneg hB,pow_two]; exact mul_le_mul_of_nonneg_left hct hB + have hBc' := abs_le.mp hBc + have htl : 0≤t := hh.trans ht.le + have hBt : 0≤B*t := mul_nonneg hB htl + constructor + · by_contra! hn + have hcomp : (4*(B+t+1)-B)^2<(a+B)^2 := by nlinarith [sq_nonneg (a+B+4*(B+t+1)-B)] + nlinarith [sq_nonneg t,sq_nonneg B] + · by_contra! hn + have hcomp : (4*(B+t+1)-B)^2<(b-B)^2 := by nlinarith [sq_nonneg (b-B-(4*(B+t+1)-B))] + nlinarith [sq_nonneg t,sq_nonneg B] + +lemma lower_strictMono_base {φ : ℝ → ℝ} (hφ : ContDiffOn ℝ 1 φ (Ioi 0)) (t : ℝ) : + StrictMonoOn (fun h=>lower φ h t) (Ioo 0 t) := by + intro h hh k hk hhk + have hu := chosen_arch (positive_arch_exists hφ hh.1 hh.2) + obtain ⟨a,b,ha,_,hab⟩ := hu.subarch_positive hφ hh.1 hhk hk.2 + dsimp only + rw [(canonical_of_positive_arch hab hφ hk.1 hk.2).1] + exact ha +lemma upper_strictAnti_base {φ : ℝ → ℝ} (hφ : ContDiffOn ℝ 1 φ (Ioi 0)) (t : ℝ) : + StrictAntiOn (fun h=>upper φ h t) (Ioo 0 t) := by + intro h hh k hk hhk + have hu := chosen_arch (positive_arch_exists hφ hh.1 hh.2) + obtain ⟨a,b,_,hb,hab⟩ := hu.subarch_positive hφ hh.1 hhk hk.2 + dsimp only + rw [(canonical_of_positive_arch hab hφ hk.1 hk.2).2] + exact hb + +noncomputable def axisLower (φ : ℝ → ℝ) (t : ℝ) : ℝ := sInf ((fun h=>lower φ h t) '' Ioo 0 t) +noncomputable def axisUpper (φ : ℝ → ℝ) (t : ℝ) : ℝ := sSup ((fun h=>upper φ h t) '' Ioo 0 t) +lemma axis_bounded {φ : ℝ → ℝ} (hφ : ContDiffOn ℝ 1 φ (Ioi 0)) + (hc : ContinuousOn φ (Ici 0)) {t : ℝ} (ht : 0lower φ h t) '' Ioo 0 t) ∧ BddAbove ((fun h=>upper φ h t) '' Ioo 0 t) := by + obtain ⟨v,hv,hmax⟩ := isCompact_Icc.exists_isMaxOn (nonempty_Icc.mpr ht.le) + (hc.abs.mono (show Icc 0 t ⊆ Ici 0 from fun _ h=>h.1)) + have hb (h : ℝ) (hh : h ∈ Ioo 0 t) := + (chosen_arch (positive_arch_exists hφ hh.1 hh.2)).endpoint_bounds hh.1.le hh.2 (abs_nonneg (φ v)) + (fun x hx=>hmax ⟨hh.1.le.trans hx.1,hx.2⟩) + exact ⟨⟨-4*(|φ v|+t+1),fun x hx=> by obtain ⟨h,hh,rfl⟩:=hx; exact (hb h hh).1⟩, + ⟨4*(|φ v|+t+1),fun x hx=> by obtain ⟨h,hh,rfl⟩:=hx; exact (hb h hh).2⟩⟩ + +lemma lower_axis_tendsto {φ : ℝ → ℝ} (hφ : ContDiffOn ℝ 1 φ (Ioi 0)) + (hc : ContinuousOn φ (Ici 0)) {t : ℝ} (ht : 0lower φ h t) (𝓝[>] 0) (𝓝 (axisLower φ t)) := by + have hb := (axis_bounded hφ hc ht).1 + have hne : ((fun h=>lower φ h t) '' Ioo 0 t).Nonempty := + (nonempty_Ioo.mpr ht).image _ + apply tendsto_order.2 + constructor + · intro a ha + filter_upwards [self_mem_nhdsWithin,(eventually_lt_nhds ht).filter_mono inf_le_left] with h hh hht + exact ha.trans_le (csInf_le hb (mem_image_of_mem _ ⟨hh,hht⟩)) + · intro b hb' + obtain ⟨x,hx,hxb⟩ := exists_lt_of_csInf_lt hne hb' + obtain ⟨k,hk,rfl⟩ := hx + filter_upwards [self_mem_nhdsWithin,(eventually_lt_nhds hk.1).filter_mono inf_le_left] with h hh hhk + exact ((lower_strictMono_base hφ t) ⟨hh,hhk.trans hk.2⟩ hk hhk).trans hxb +lemma upper_axis_tendsto {φ : ℝ → ℝ} (hφ : ContDiffOn ℝ 1 φ (Ioi 0)) + (hc : ContinuousOn φ (Ici 0)) {t : ℝ} (ht : 0upper φ h t) (𝓝[>] 0) (𝓝 (axisUpper φ t)) := by + have hb := (axis_bounded hφ hc ht).2 + have hne : ((fun h=>upper φ h t) '' Ioo 0 t).Nonempty := + (nonempty_Ioo.mpr ht).image _ + apply tendsto_order.2 + constructor + · intro a ha + obtain ⟨x,hx,hax⟩ := exists_lt_of_lt_csSup hne ha + obtain ⟨k,hk,rfl⟩ := hx + filter_upwards [self_mem_nhdsWithin,(eventually_lt_nhds hk.1).filter_mono inf_le_left] with h hh hhk + exact hax.trans ((upper_strictAnti_base hφ t) ⟨hh,hhk.trans hk.2⟩ hk hhk) + · intro b hb' + filter_upwards [self_mem_nhdsWithin,(eventually_lt_nhds ht).filter_mono inf_le_left] with h hh hht + exact (le_csSup hb (mem_image_of_mem _ ⟨hh,hht⟩)).trans_lt hb' + +lemma axis_signs {φ : ℝ → ℝ} (hφ : ContDiffOn ℝ 1 φ (Ioi 0)) + (hc : ContinuousOn φ (Ici 0)) (h0 : φ 0=0) {t : ℝ} (ht : 0] 0) (𝓝 (0:ℝ)) := by + simpa only [h0] using (hc 0 (show (0:ℝ) ∈ Set.Ici (0:ℝ) by simp)).mono_left (nhdsWithin_mono (0:ℝ) Ioi_subset_Ici_self) + have he : ∀ᶠ h in 𝓝[>] (0:ℝ), lower φ h t≤φ h ∧ φ h≤upper φ h t := by + filter_upwards [self_mem_nhdsWithin,(eventually_lt_nhds ht).filter_mono inf_le_left] with h hh hht + have hu := chosen_arch (positive_arch_exists hφ hh hht) + exact ⟨hu.lower_transverse.le,hu.upper_transverse.le⟩ + exact ⟨le_of_tendsto_of_tendsto (lower_axis_tendsto hφ hc ht) hlim (he.mono fun _ h=>h.1), + le_of_tendsto_of_tendsto hlim (upper_axis_tendsto hφ hc ht) (he.mono fun _ h=>h.2)⟩ +end QuinticLienard.ScalarArcs + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AxisReflection.lean b/lean/OAI/Analysis/LienardCycles/AxisReflection.lean new file mode 100644 index 0000000000000000000000000000000000000000..10c25c8c9979b2b44a38eca887d0d6fa59ec29c1 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AxisReflection.lean @@ -0,0 +1,89 @@ +import OAI.Analysis.LienardCycles.AxisIntercept + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.AxisFlow +open ScaledProfile ScalarArcs +lemma poly_neg (a : Fin 6 → ℝ) (x : ℝ) : poly (-a) x= -poly a x := by + dsimp [poly] + ring +lemma endpoint_neg (a : Fin 6 → ℝ) {h t : ℝ} (hh : 0-φ a x)=φ (-a) := by funext x; exact (poly_neg a _).symm + rw [he] at hb + exact canonical_of_positive_arch hb (φ_smooth (-a)) hh ht +lemma axisEndpoint_neg (a : Fin 6 → ℝ) {t : ℝ} (ht : 0] (0:ℝ), endpoint (-a) false h t= -endpoint a true h t ∧ + endpoint (-a) true h t= -endpoint a false h t := by + filter_upwards [self_mem_nhdsWithin,(eventually_lt_nhds ht).filter_mono inf_le_left] with h hh hht + exact endpoint_neg a hh hht + constructor + · exact tendsto_nhds_unique (lower_axis_tendsto (φ_smooth (-a)) (φ_continuous (-a)).continuousOn ht) + (((upper_axis_tendsto (φ_smooth a) (φ_continuous a).continuousOn ht).neg).congr' (he.mono fun _ h=>h.1.symm)) + · exact tendsto_nhds_unique (upper_axis_tendsto (φ_smooth (-a)) (φ_continuous (-a)).continuousOn ht) + (((lower_axis_tendsto (φ_smooth a) (φ_continuous a).continuousOn ht).neg).congr' (he.mono fun _ h=>h.2.symm)) +lemma transversePeaks_neg (a : Fin 6 → ℝ) : transversePeaks (-a)=transversePeaks a := by + ext t + change (0 intro ht + · rw [(axisEndpoint_neg a ht.1).1,(axisEndpoint_neg a ht.1).2,poly_neg] at ht + exact ⟨ht.1,by linarith [ht.2.2],by linarith [ht.2.1]⟩ + · refine ⟨ht.1,?_,?_⟩ <;> simp only [(axisEndpoint_neg a ht.1).1,(axisEndpoint_neg a ht.1).2,poly_neg] <;> linarith [ht.2.1,ht.2.2] +lemma axisWidth_neg (a : Fin 6 → ℝ) {t : ℝ} (ht : 0] (0:ℝ)) (h:=id) (r:=fun _=>r) + self_mem_nhdsWithin (tendsto_id.mono_left inf_le_left) tendsto_const_nhds + have hb := joint_limits (-a) hr' (l:=𝓝[>] (0:ℝ)) (h:=id) (r:=fun _=>r) + self_mem_nhdsWithin (tendsto_id.mono_left inf_le_left) tendsto_const_nhds + have he : ∀ᶠ h in 𝓝[>] (0:ℝ), QuinticFit.lambda (-a) (h,r)= -QuinticFit.lambda a (h,r) ∧ + QuinticFit.kappa (-a) (h,r)= -QuinticFit.kappa a (h,r) := by + filter_upwards [self_mem_nhdsWithin] with h hh + exact QuinticFit.fit_neg a hh (axisM_abs_lt a hr).1 + constructor + · exact tendsto_nhds_unique hb.2.2.1 (ha.2.2.1.neg.congr' (he.mono fun _ h=>h.1.symm)) + · exact tendsto_nhds_unique hb.2.2.2.1 (ha.2.2.2.1.neg.congr' (he.mono fun _ h=>h.2.symm)) +lemma axisLambda_gt {a : Fin 6 → ℝ} {r d : ℝ} (hr : r ∈ axisWidths a) + (hp : ∀ u,0] 0) atTop) : d] 0) atBot := by + change Tendsto (fun x=>slope (-a) x) _ _ + simpa only [slope_neg,Function.comp_def] using tendsto_neg_atTop_atBot.comp hs + have hl := axisLambda_lt hr' hp' hs' + rw [(axisFit_neg a hr).1] at hl + linarith +end QuinticLienard.AxisFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AxisRegularity.lean b/lean/OAI/Analysis/LienardCycles/AxisRegularity.lean new file mode 100644 index 0000000000000000000000000000000000000000..d953377af138da73c1a2d133b03e9a25944b733d --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AxisRegularity.lean @@ -0,0 +1,138 @@ +import OAI.Analysis.LienardCycles.AxisBranches + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.AxisFlow +open ScalarArcs ScaledProfile PartialCalculus +lemma endpoint_germ_eq {a : Fin 6 → ℝ} {u : Bool} {t : ℝ} {G : ℝ×ℝ → ℝ} + (ht : 0G (s,x)) (𝓝[>] 0) (𝓝 (G (s,0))) := + (hsc.comp (f:=fun x : ℝ=>(s,x)) (continuousAt_const.prodMk continuousAt_id)).tendsto.mono_left inf_le_left + have hEq : (fun x=>G (s,x)) =ᶠ[𝓝[>] 0] (fun x=>branch a u (s,x)) := by + filter_upwards [hse.filter_mono inf_le_left,self_mem_nhdsWithin] with x hx hx0 + exact hx hx0 + exact tendsto_nhds_unique hlim ((branch_tendsto a u hs).congr' hEq.symm) +lemma axisEndpoint_analytic (a : Fin 6 → ℝ) (u : Bool) {t : ℝ} (ht : 0h.symm) +lemma axisEndpoint_sign (a : Fin 6 → ℝ) (u : Bool) {t : ℝ} (ht : 0h.symm)).deriv + rwa [hde] + +lemma endpoint_peak_order (a : Fin 6 → ℝ) {h s t : ℝ} (hh : 0endpoint a u h q) p := by + obtain ⟨hl,hr⟩ := PositiveVariation.endpoints (QuinticProfile.profile a) + (fun _ h=>QuinticProfile.analytic a h) (QuinticProfile.local_flow a) (p:=(0:ℝ)) hh hp + cases u + · exact hl.comp p ((contDiffAt_const.prodMk contDiffAt_id).prodMk contDiffAt_const) + · exact hr.comp p ((contDiffAt_const.prodMk contDiffAt_id).prodMk contDiffAt_const) + have hd (p : ℝ) (hp : hQuinticProfile.analytic a h) (QuinticProfile.local_flow a) (p:=(0:ℝ)) hh hp + have hl : AntitoneOn (endpoint a false h) (Ioi h) := by + apply antitoneOn_of_deriv_nonpos (convex_Ioi h) + (fun p hp=>(ha false p hp).continuousAt.continuousWithinAt) + (fun p hp=>(ha false p (interior_subset hp)).differentiableAt (by simp) |>.differentiableWithinAt) + intro p hp + exact (hd p (interior_subset hp)).1.le + have hr : MonotoneOn (endpoint a true h) (Ioi h) := by + apply monotoneOn_of_deriv_nonneg (convex_Ioi h) + (fun p hp=>(ha true p hp).continuousAt.continuousWithinAt) + (fun p hp=>(ha true p (interior_subset hp)).differentiableAt (by simp) |>.differentiableWithinAt) + intro p hp + exact (hd p (interior_subset hp)).2.le + exact ⟨hl hs (hs.trans_le hst) hst,hr hs (hs.trans_le hst) hst⟩ +lemma axis_peak_order (a : Fin 6 → ℝ) {s t : ℝ} (hs : 0] (0:ℝ), endpoint a false h t≤endpoint a false h s ∧ + endpoint a true h s≤endpoint a true h t := by + filter_upwards [self_mem_nhdsWithin,(eventually_lt_nhds hs).filter_mono inf_le_left] with h hh hs' + exact endpoint_peak_order a hh hs' hst + have hls := lower_axis_tendsto (φ_smooth a) (φ_continuous a).continuousOn hs + have hlt := lower_axis_tendsto (φ_smooth a) (φ_continuous a).continuousOn (hs.trans_le hst) + have hrs := upper_axis_tendsto (φ_smooth a) (φ_continuous a).continuousOn hs + have hrt := upper_axis_tendsto (φ_smooth a) (φ_continuous a).continuousOn (hs.trans_le hst) + exact ⟨le_of_tendsto_of_tendsto hlt hls (hE.mono fun _ h=>h.1), + le_of_tendsto_of_tendsto hrs hrt (hE.mono fun _ h=>h.2)⟩ + +def transversePeaks (a : Fin 6 → ℝ) : Set ℝ := + {t | 0 linarith [ht.2.1,ht.2.2] + · rw [hwd,hcd] + rw [abs_div,abs_of_pos (show 0<(deriv (axisEndpoint a true) t-deriv (axisEndpoint a false) t)/2 by linarith),div_lt_one] + · rw [abs_lt]; constructor <;> linarith + · linarith +lemma axisWidth_strictMono (a : Fin 6 → ℝ) : StrictMonoOn (axisWidth a) (transversePeaks a) := by + apply strictMonoOn_of_deriv_pos (convex_iff_ordConnected.mpr (transversePeaks_ordConnected a)) + (fun t ht=>(axisWidth_analytic a ht).continuousAt.continuousWithinAt) + intro t ht + exact (axisWidth_pos_deriv a (interior_subset ht)).2.1 +end QuinticLienard.AxisFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AxisSecants.lean b/lean/OAI/Analysis/LienardCycles/AxisSecants.lean new file mode 100644 index 0000000000000000000000000000000000000000..31b326848364b5d12193fd3c5248784b975a51a1 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AxisSecants.lean @@ -0,0 +1,122 @@ +import OAI.Analysis.LienardCycles.SecantIntegral + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.AxisFlow +open PartialCalculus QuadraticFit QuadraticCoordinates RealAnalysis +noncomputable def Vm : (ℝ×ℝ)×ℝ → ℝ := direction ((0,0),1) conditionalV +noncomputable def Vk : (ℝ×ℝ)×ℝ → ℝ := direction ((1,0),0) conditionalV +lemma Vm_deriv {k r M : ℝ} (hr : 0conditionalV ((k,r),u)) (Vm ((k,r),M)) M := by + simpa [Vm,direction] using! + ((conditionalV_analytic hr hM).differentiableAt (by simp)).hasFDerivAt.comp_hasDerivAt M + ((hasDerivAt_const M (k,r)).prodMk (hasDerivAt_id M)) +lemma Vk_deriv {k r M : ℝ} (hr : 0conditionalV ((u,r),M)) (Vk ((k,r),M)) k := by + simpa [Vk,direction] using! + ((conditionalV_analytic hr hM).differentiableAt (by simp)).hasFDerivAt.comp_hasDerivAt k + (((hasDerivAt_id k).prodMk (hasDerivAt_const k r)).prodMk (hasDerivAt_const k M)) +lemma Vk_pos {k r M : ℝ} (hr : 0 ((axisKappa a q.1,q.1),axisM b q.1+q.2*(axisM a q.1-axisM b q.1))) (r,s) + exact (((axisKappa_analytic a hr.1).continuousAt.comp (x := (r,s)) continuousAt_fst).prodMk continuousAt_fst).prodMk + (((axisM_analytic b hr.2).continuousAt.comp (x := (r,s)) continuousAt_fst).add + (continuousAt_snd.mul (((axisM_analytic a hr.1).continuousAt.comp (x := (r,s)) continuousAt_fst).sub + ((axisM_analytic b hr.2).continuousAt.comp (x := (r,s)) continuousAt_fst)))) +lemma kSegment_continuousAt {a b : Fin 6 → ℝ} {r s : ℝ} (hr : r ∈ matchingDomain a b) : + ContinuousAt (kSegment a b) (r,s) := by + change ContinuousAt (fun q : ℝ×ℝ => ((axisKappa b q.1+q.2*(axisKappa a q.1-axisKappa b q.1),q.1),axisM b q.1)) (r,s) + exact ((((axisKappa_analytic b hr.2).continuousAt.comp (x := (r,s)) continuousAt_fst).add + (continuousAt_snd.mul (((axisKappa_analytic a hr.1).continuousAt.comp (x := (r,s)) continuousAt_fst).sub + ((axisKappa_analytic b hr.2).continuousAt.comp (x := (r,s)) continuousAt_fst)))).prodMk continuousAt_fst).prodMk + ((axisM_analytic b hr.2).continuousAt.comp (x := (r,s)) continuousAt_fst) +lemma secant_integrands_continuous {a b : Fin 6 → ℝ} {R : Set ℝ} (hR : R ⊆ matchingDomain a b) : + ContinuousOn (fun q=>Vm (mSegment a b q)) (R ×ˢ Icc 0 1) ∧ + ContinuousOn (fun q=>Vk (kSegment a b q)) (R ×ˢ Icc 0 1) := by + constructor + · intro q hq + have hr := hR hq.1 + have hM := abs_segment_lt (axisM_abs_lt a hr.1).2 (axisM_abs_lt b hr.2).2 hq.2 + have hv : ContinuousAt Vm (mSegment a b q) := + (direction_contDiffAt (conditionalV_analytic (axisM_abs_lt a hr.1).1 hM) ((0,0),1)).continuousAt + exact (hv.comp (mSegment_continuousAt hr)).continuousWithinAt + · intro q hq + have hr := hR hq.1 + have hv : ContinuousAt Vk (kSegment a b q) := + (direction_contDiffAt (conditionalV_analytic (axisM_abs_lt b hr.2).1 (axisM_abs_lt b hr.2).2) ((1,0),0)).continuousAt + exact (hv.comp (kSegment_continuousAt hr)).continuousWithinAt +lemma secantA_continuousOn {a b : Fin 6 → ℝ} {l r : ℝ} (hl : l ∈ matchingDomain a b) (hr : r ∈ matchingDomain a b) : + ContinuousOn (secantA a b) (Icc l r) := + continuousOn_segment_integral (secant_integrands_continuous ((matchingDomain_ordConnected a b).out hl hr)).1 +lemma secantB_pos {a b : Fin 6 → ℝ} {r : ℝ} (hr : r ∈ matchingDomain a b) : 0Vk (kSegment a b (r,s))) (Icc 0 1) := + (secant_integrands_continuous (Subset.refl (matchingDomain a b))).2.comp + (continuous_const.prodMk continuous_id).continuousOn (fun s hs=>⟨hr,hs⟩) + exact intervalIntegral.integral_pos (by norm_num) hc + (fun s _=>(Vk_pos (axisM_abs_lt b hr.2).1 (axisM_abs_lt b hr.2).2).le) + ⟨1/2,by norm_num,Vk_pos (axisM_abs_lt b hr.2).1 (axisM_abs_lt b hr.2).2⟩ +lemma secant_identity {a b : Fin 6 → ℝ} {r : ℝ} (hr : r ∈ matchingDomain a b) : + axisV a r-axisV b r=secantA a b r*(axisM a r-axisM b r)+ + secantB a b r*(axisKappa a r-axisKappa b r) := by + have hM (s : ℝ) (hs : s ∈ Icc 0 1) := abs_segment_lt (axisM_abs_lt a hr.1).2 (axisM_abs_lt b hr.2).2 hs + have hdm (s : ℝ) (hs : s ∈ Icc 0 1) : HasDerivAt + (fun u=>conditionalV (mSegment a b (r,u))) + (Vm (mSegment a b (r,s))*(axisM a r-axisM b r)) s := by + simpa [mSegment] using! (Vm_deriv (k := axisKappa a r) (axisM_abs_lt a hr.1).1 (hM s hs)).comp s + ((hasDerivAt_const s (axisM b r)).add ((hasDerivAt_id s).mul_const (axisM a r-axisM b r))) + have hdk (s : ℝ) (_hs : s ∈ Icc 0 1) : HasDerivAt + (fun u=>conditionalV (kSegment a b (r,u))) + (Vk (kSegment a b (r,s))*(axisKappa a r-axisKappa b r)) s := by + simpa [kSegment] using! (Vk_deriv (k := axisKappa b r+s*(axisKappa a r-axisKappa b r)) (axisM_abs_lt b hr.2).1 (axisM_abs_lt b hr.2).2).comp s + ((hasDerivAt_const s (axisKappa b r)).add ((hasDerivAt_id s).mul_const (axisKappa a r-axisKappa b r))) + have hc := secant_integrands_continuous (Subset.refl (matchingDomain a b)) + have hcm := hc.1.comp (continuous_const.prodMk continuous_id).continuousOn (fun s hs=>⟨hr,hs⟩) + have hck := hc.2.comp (continuous_const.prodMk continuous_id).continuousOn (fun s hs=>⟨hr,hs⟩) + have hm := intervalIntegral.integral_eq_sub_of_hasDerivAt + (f:=fun u=>conditionalV (mSegment a b (r,u))) + (fun s hs=>hdm s (by simpa using hs)) ((hcm.mul_const _).intervalIntegrable_of_Icc (by norm_num)) + have hk := intervalIntegral.integral_eq_sub_of_hasDerivAt + (f:=fun u=>conditionalV (kSegment a b (r,u))) + (fun s hs=>hdk s (by simpa using hs)) ((hck.mul_const _).intervalIntegrable_of_Icc (by norm_num)) + rw [intervalIntegral.integral_mul_const] at hm hk + simp only [mSegment,kSegment,zero_mul,add_zero,one_mul,add_sub_cancel] at hm hk + rw [axisV_conditional a hr.1,axisV_conditional b hr.2] + change _=secantA a b r*(axisM a r-axisM b r)+secantB a b r*(axisKappa a r-axisKappa b r) + change secantA a b r*(axisM a r-axisM b r)=_ at hm + change secantB a b r*(axisKappa a r-axisKappa b r)=_ at hk + linarith +end QuinticLienard.AxisFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AxisWidthGerm.lean b/lean/OAI/Analysis/LienardCycles/AxisWidthGerm.lean new file mode 100644 index 0000000000000000000000000000000000000000..1d300d3eceb17028469698ebb27c0cfde12996d5 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AxisWidthGerm.lean @@ -0,0 +1,114 @@ +import OAI.Analysis.LienardCycles.AxisRegularity + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.AxisFlow +open ScalarArcs ScaledProfile PartialCalculus PositiveWidth + +def axisWidths (a : Fin 6 → ℝ) : Set ℝ := axisWidth a '' transversePeaks a +noncomputable def axisPeak (a : Fin 6 → ℝ) (r : ℝ) : ℝ := + Classical.epsilon (fun t=>t ∈ transversePeaks a ∧ axisWidth a t=r) +lemma axisPeak_spec (a : Fin 6 → ℝ) {r : ℝ} (hr : r ∈ axisWidths a) : + axisPeak a r ∈ transversePeaks a ∧ axisWidth a (axisPeak a r)=r := + Classical.epsilon_spec hr +lemma axisPeak_eq (a : Fin 6 → ℝ) {r t : ℝ} (ht : t ∈ transversePeaks a) (he : axisWidth a t=r) : + axisPeak a r=t := by + have hs := axisPeak_spec a (mem_image_of_mem (axisWidth a) ht) + rw [he] at hs + exact (axisWidth_strictMono a).injOn hs.1 ht (hs.2.trans he.symm) +noncomputable def axisM (a : Fin 6 → ℝ) (r : ℝ) : ℝ := axisCenter a (axisPeak a r) +lemma axisM_abs_lt (a : Fin 6 → ℝ) {r : ℝ} (hr : r ∈ axisWidths a) : 0(b (q.2,q.1)-l (q.2,q.1))/2 + have hWa : ContDiffAt ℝ ω W (0,t) := ((hba.sub hla).div_const 2).comp (0,t) + (contDiffAt_snd.prodMk contDiffAt_fst) + have hW0 : W (0,t)=axisWidth a t := by dsimp [W,axisWidth]; rw [hl0,hb0] + have hWslice : (fun s=>W (0,s)) =ᶠ[𝓝 t] axisWidth a := by + filter_upwards [hle0,hbe0] with s hls hbs + simp only [W,axisWidth,hls,hbs] + have hWd : HasDerivAt (fun s=>W (0,s)) (deriv (axisWidth a) t) t := + ((axisWidth_analytic a ht).differentiableAt (by simp)).hasDerivAt.congr_of_eventuallyEq hWslice + obtain ⟨Y,hY,hY0,hYe⟩ := ArcEndpoints.level_hit hWa hWd hW0 (axisWidth_pos_deriv a ht).2.1.ne' + let G : ℝ×ℝ → ℝ := fun q=>(b (Y q,q.1)+l (Y q,q.1))/2-poly a q.1 + have hYa : ContDiffAt ℝ ω (fun q=>(Y q,q.1)) (0,axisWidth a t) := hY.prodMk contDiffAt_fst + have hGa : ContDiffAt ℝ ω G (0,axisWidth a t) := by + have hh : ContDiffAt ℝ ω (fun q=>(b q+l q)/2) (t,0) := (hba.add hla).div_const 2 + have hc : ContDiffAt ℝ ω (fun q : ℝ×ℝ=>poly a q.1) (0,axisWidth a t) := by unfold poly; fun_prop + exact (show ContDiffAt ℝ ω (fun q=>(b (Y q,q.1)+l (Y q,q.1))/2) (0,axisWidth a t) from + (by + have hh' : ContDiffAt ℝ ω (fun q=>(b q+l q)/2) (Y (0,axisWidth a t),0) := by rw [hY0]; exact hh + exact hh'.comp (f:=fun q : ℝ×ℝ=>(Y q,q.1)) (0,axisWidth a t) hYa)).sub hc + have hG0 : G (0,axisWidth a t)=axisCenter a t := by dsimp [G,axisCenter]; rw [hY0,hl0,hb0] + have hYlim : ContinuousAt (fun r=>Y (0,r)) (axisWidth a t) := + hY.continuousAt.comp (f:=fun r : ℝ=>(0,r)) (continuousAt_const.prodMk continuousAt_id) + have hYt : Tendsto (fun r=>Y (0,r)) (𝓝 (axisWidth a t)) (𝓝 t) := by simpa only [hY0] using hYlim.tendsto + have hYtrans : ∀ᶠ r in 𝓝 (axisWidth a t), Y (0,r) ∈ transversePeaks a := + hYlim.eventually ((transversePeaks_open a).mem_nhds (by simpa only [hY0] using ht)) + have hslice : ∀ᶠ r in 𝓝 (axisWidth a t), r ∈ axisWidths a ∧ Y (0,r)=axisPeak a r ∧ G (0,r)=axisM a r := by + have hNb : ∀ᶠ r in 𝓝 (axisWidth a t), b (Y (0,r),0)=axisEndpoint a true (Y (0,r)) := hYt.eventually hbe0 + have hNl : ∀ᶠ r in 𝓝 (axisWidth a t), l (Y (0,r),0)=axisEndpoint a false (Y (0,r)) := hYt.eventually hle0 + filter_upwards [hYtrans,(continuousAt_const.prodMk continuousAt_id).eventually hYe,hNb,hNl] with r htr he hb hl + have hwr : axisWidth a (Y (0,r))=r := by simpa only [W,axisWidth,id_eq,hb,hl] using he + have hpeak := (axisPeak_eq a htr hwr).symm + refine ⟨⟨Y (0,r),htr,hwr⟩,hpeak,?_⟩ + dsimp only [G,axisM,axisCenter] + rw [hb,hl,hpeak] + have hposr : 0QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) hr hh0 hh hwr + refine ⟨hp.symm,?_⟩ + dsimp only [G,QuinticFit.M,PositiveTransport.M,midpointAtWidth,midpointFamily] + rw [hp] + rw [hb hx,hl hx] + change (endpoint a true (q.1^2/2) (Y q)+endpoint a false (q.1^2/2) (Y q))/2-poly a q.1= + ScalarArcs.midpoint (φ a) (q.1^2/2) (Y q) + dsimp only [ScalarArcs.midpoint] + rw [φ_square a hx.le] + rfl + exact ⟨Y,G,hY,hGa,hY0,hG0,hslice,hposEq⟩ +end QuinticLienard.AxisFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AxisWidthRegularity.lean b/lean/OAI/Analysis/LienardCycles/AxisWidthRegularity.lean new file mode 100644 index 0000000000000000000000000000000000000000..c8f4b79f562953988c0fcc103c0db87e0133ff14 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AxisWidthRegularity.lean @@ -0,0 +1,79 @@ +import OAI.Analysis.LienardCycles.AxisWidthGerm + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.AxisFlow +open ScalarArcs ScaledProfile PartialCalculus PositiveWidth +lemma axisWidths_open (a : Fin 6 → ℝ) : IsOpen (axisWidths a) := by + apply isOpen_iff_mem_nhds.mpr + rintro r ⟨t,ht,rfl⟩ + obtain ⟨Y,G,_,_,_,_,he,_⟩ := width_germ a ht + exact he.mono fun _ h=>h.1 +lemma axisWidths_ordConnected (a : Fin 6 → ℝ) : OrdConnected (axisWidths a) := by + have hc : IsPreconnected (transversePeaks a) := (convex_iff_ordConnected.mpr (transversePeaks_ordConnected a)).isPreconnected + exact (hc.image (axisWidth a) (fun t ht=>(axisWidth_analytic a ht).continuousAt.continuousWithinAt)).ordConnected +lemma axisPeak_analytic (a : Fin 6 → ℝ) {r : ℝ} (hr : r ∈ axisWidths a) : ContDiffAt ℝ ω (axisPeak a) r := by + obtain ⟨t,ht,rfl⟩ := hr + obtain ⟨Y,G,hY,_,_,_,he,_⟩ := width_germ a ht + exact (hY.comp _ (contDiffAt_const.prodMk contDiffAt_id)).congr_of_eventuallyEq (he.mono fun _ h=>h.2.1.symm) +lemma axisM_analytic (a : Fin 6 → ℝ) {r : ℝ} (hr : r ∈ axisWidths a) : ContDiffAt ℝ ω (axisM a) r := by + obtain ⟨t,ht,rfl⟩ := hr + obtain ⟨Y,G,_,hG,_,_,he,_⟩ := width_germ a ht + exact (hG.comp _ (contDiffAt_const.prodMk contDiffAt_id)).congr_of_eventuallyEq (he.mono fun _ h=>h.2.2.symm) +noncomputable def axisV (a : Fin 6 → ℝ) (r : ℝ) : ℝ := deriv (axisM a) r +lemma axisV_analytic (a : Fin 6 → ℝ) {r : ℝ} (hr : r ∈ axisWidths a) : ContDiffAt ℝ ω (axisV a) r := + ((axisM_analytic a hr).fderiv_right (m:=ω) (by simp)).clm_apply contDiffAt_const +lemma axisV_ratio (a : Fin 6 → ℝ) {r : ℝ} (hr : r ∈ axisWidths a) : + axisV a r=deriv (axisCenter a) (axisPeak a r)/deriv (axisWidth a) (axisPeak a r) := by + have ht := (axisPeak_spec a hr).1 + have hpd := (axisPeak_analytic a hr).differentiableAt (by simp) + have hd := ((axisWidth_analytic a ht).differentiableAt (by simp)).hasDerivAt.comp r hpd.hasDerivAt + have he : (axisWidth a ∘ axisPeak a) =ᶠ[𝓝 r] (fun s=>s) := by + filter_upwards [(axisWidths_open a).mem_nhds hr] with s hs + exact (axisPeak_spec a hs).2 + have hdp : deriv (axisWidth a) (axisPeak a r)*deriv (axisPeak a) r=1 := + (hd.congr_of_eventuallyEq he.symm).unique (hasDerivAt_id r) + have hc := ((axisCenter_analytic a ht).differentiableAt (by simp)).hasDerivAt.comp r hpd.hasDerivAt + have hdc : axisV a r=deriv (axisCenter a) (axisPeak a r)*deriv (axisPeak a) r := hc.deriv + rw [hdc] + apply (eq_div_iff (axisWidth_pos_deriv a ht).2.1.ne').mpr + calc + _ = deriv (axisCenter a) (axisPeak a r)*(deriv (axisWidth a) (axisPeak a r)*deriv (axisPeak a) r) := by ring + _ = _ := by rw [hdp,mul_one] +lemma axisV_abs_lt (a : Fin 6 → ℝ) {r : ℝ} (hr : r ∈ axisWidths a) : |axisV a r|<1 := by + rw [axisV_ratio a hr] + exact (axisWidth_pos_deriv a (axisPeak_spec a hr).1).2.2.2 + +lemma width_germ_derivative (a : Fin 6 → ℝ) {r : ℝ} {G : ℝ×ℝ → ℝ} + (hr : 0G (q.1,s)) =ᶠ[𝓝 q.2] (fun s=>QuinticFit.M a (q.1^2/2,s)) := by + filter_upwards [(continuousAt_const.prodMk continuousAt_id).eventually hqe] with s hs + exact hs hqx + have hh : 0h.symm)).deriv.symm +end QuinticLienard.AxisFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AxisZeroCount.lean b/lean/OAI/Analysis/LienardCycles/AxisZeroCount.lean new file mode 100644 index 0000000000000000000000000000000000000000..3ee3a68e4d9d7a4e3bf1e9ec6d3ec9b05ac325be --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AxisZeroCount.lean @@ -0,0 +1,37 @@ +import OAI.Analysis.LienardCycles.AxisComparison + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.AxisFlow +open RealAnalysis ScaledProfile +lemma matchingDelta_zero_bound_of_third {a b : Fin 6 → ℝ} + (ha : ∀ u,0axisKappa a r-axisKappa b r) (matchingDomain_ordConnected a b) + (fun _ hl _ hr _=>secantA_continuousOn hl hr) + · intro r hr + change HasDerivAt (matchingDelta a b) (secantA a b r*(axisM a r-axisM b r)+secantB a b r*(axisKappa a r-axisKappa b r)) r + rw [←secant_identity hr] + exact matchingDelta_deriv a b hr + · exact fun _ hr=>secantB_pos hr + · intro r hr s hs hrs + exact sub_le_sub (axisKappa_monotone ha hr.1 hs.1 hrs) + (axisKappa_antitone hb hr.2 hs.2 hrs) +end QuinticLienard.AxisFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/AxisZeros.lean b/lean/OAI/Analysis/LienardCycles/AxisZeros.lean new file mode 100644 index 0000000000000000000000000000000000000000..cbe9ae0cbe376a63a15d9f6bbc9e7aca45ebf312 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/AxisZeros.lean @@ -0,0 +1,71 @@ +import OAI.Analysis.LienardCycles.AxisFit + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.AxisFlow +open PartialCalculus QuadraticCoordinates QuadraticFit RealAnalysis + +def matchingDomain (a b : Fin 6 → ℝ) : Set ℝ := axisWidths a ∩ axisWidths b +noncomputable def matchingDelta (a b : Fin 6 → ℝ) (r : ℝ) : ℝ := axisM a r-axisM b r +lemma matchingDomain_open (a b : Fin 6 → ℝ) : IsOpen (matchingDomain a b) := + (axisWidths_open a).inter (axisWidths_open b) +lemma matchingDomain_ordConnected (a b : Fin 6 → ℝ) : OrdConnected (matchingDomain a b) := + (axisWidths_ordConnected a).inter (axisWidths_ordConnected b) +lemma matchingDelta_deriv (a b : Fin 6 → ℝ) {r : ℝ} (hr : r ∈ matchingDomain a b) : + HasDerivAt (matchingDelta a b) (axisV a r-axisV b r) r := + ((axisM_analytic a hr.1).differentiableAt (by simp)).hasDerivAt.sub + ((axisM_analytic b hr.2).differentiableAt (by simp)).hasDerivAt +lemma axisV_conditional (a : Fin 6 → ℝ) {r : ℝ} (hr : r ∈ axisWidths a) : + axisV a r=conditionalV ((axisKappa a r,r),axisM a r) := by + have hf := axisFit_spec a hr + have hs := slope_eq (axisM_abs_lt a hr).1 (axisM_abs_lt a hr).2 hf.1 + dsimp only [conditionalV] + rw [hs] + exact hf.2.symm +lemma matchingDelta_crossing {a b : Fin 6 → ℝ} {r : ℝ} (hr : r ∈ matchingDomain a b) + (hz : matchingDelta a b r=0) (hk : axisKappa b rmatchingDelta_deriv a b hr) + (fun _ hr hz=>matchingDelta_crossing hr hz (hk _ hr hz)) +lemma H_curvature_strictMono (d : ℝ) {r : ℝ} (hr : 0H ((d,k),r)) := by + apply strictMono_of_deriv_pos + intro k + rw [(Q_hasDerivAt hr).deriv] + exact QuadraticVariation.Q_pos hr +lemma matchingDelta_kappa_of_lambda {a b : Fin 6 → ℝ} {r : ℝ} (hr : r ∈ matchingDomain a b) + (hz : matchingDelta a b r=0) (hl : axisLambda a rmatchingDelta_kappa_of_lambda hr hz (hl r hr)) +end QuinticLienard.AxisFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/BaseLimits.lean b/lean/OAI/Analysis/LienardCycles/BaseLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..15abdb7c288c82bf026670f69cdb4b17b3760243 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/BaseLimits.lean @@ -0,0 +1,106 @@ +import OAI.Analysis.LienardCycles.RadiusLimits + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology +open Set Filter MeasureTheory +open Set Filter +open scoped Topology ContDiff + +namespace QuinticLienard.ReferenceCharacteristic +open ScalarArcs CanonicalVariation PolynomialModel WidthCoordinates + WidthTransport PartialCalculus QuadraticCoordinates ArchSymmetries + +lemma base_bounds {z k r : ℝ} (hr : 0 < r) : -r^2/2 ≤ base ((z,k),r) ∧ base ((z,k),r) < 0 := by + have hs := base_spec profile profile_contDiff model_local_flow (p := (z,k)) (t := 0) hr + have hh := height_bound profile profile_contDiff model_local_flow (p := (z,k)) hs.1 + rw [hs.2] at hh + exact ⟨by dsimp [base]; linarith,hs.1⟩ + +lemma base_tendsto_zero (z k : ℝ) : Tendsto (fun r => base ((z,k),r)) (𝓝[>] (0:ℝ)) (𝓝 0) := by + apply tendsto_of_tendsto_of_tendsto_of_le_of_le' + (g := fun r : ℝ => -r^2/2) (h := fun _ : ℝ => (0:ℝ)) + · simpa using! (((tendsto_id.mono_left inf_le_left).pow 2).neg.div_const (2:ℝ) : + Tendsto (fun r : ℝ => -r^2/2) (𝓝[>] (0:ℝ)) (𝓝 (-0^2/2))) + · exact tendsto_const_nhds + · filter_upwards [self_mem_nhdsWithin] with r hr + exact (base_bounds (z := z) (k := k) hr).1 + · filter_upwards [self_mem_nhdsWithin] with r hr + exact (base_bounds (z := z) (k := k) hr).2.le + +lemma model_tendsto (z k : ℝ) : + Tendsto (fun r => ((J ((z,k),r),k),r)) (𝓝[>] (0:ℝ)) (𝓝 ((z,k),(0:ℝ))) := by + have hj : Tendsto (fun r => J ((z,k),r)) (𝓝[>] (0:ℝ)) (𝓝 z) := by + simpa [J] using (tendsto_const_nhds.add (tendsto_const_nhds.mul (base_tendsto_zero z k))) + exact (hj.prodMk_nhds tendsto_const_nhds).prodMk_nhds (tendsto_id.mono_left inf_le_left) + +lemma U_B_positive_near_zero (z k : ℝ) : + ∀ᶠ r in 𝓝[>] (0:ℝ), 0 < U ((z,k),r) ∧ 0 < B ((z,k),r) := by + filter_upwards [(model_tendsto z k).eventually (R_G_positive_near_zero z k), + self_mem_nhdsWithin] with r hh hr + obtain ⟨hR,hG⟩ := hh hr + constructor + · dsimp only [U] + rw [Dz_formula hr] + exact div_pos (mul_pos hR (Jz_pos hr)) (D_gap_pos hr) + · rw [B_formula hr] + exact div_pos hG (mul_pos (QuadraticVariation.P_pos hr) (D_gap_pos hr)) + +lemma K_pos {q : (ℝ × ℝ) × ℝ} (hr : 0 < q.2) : 0 < K q := by + dsimp [K] + exact div_pos (mul_pos (by norm_num) (by positivity)) + (mul_pos hr (sq_pos_of_pos (A_gap_pos hr))) + +lemma U_pos {z k r : ℝ} (hr : 0 < r) : 0 < U ((z,k),r) := by + have hm : MonotoneOn (fun s => U ((z,k),s)) (Ioi 0) := by + apply monotoneOn_of_deriv_nonneg (convex_Ioi 0) + (fun s hs => (U_deriv hs).continuousAt.continuousWithinAt) + (fun s hs => (U_deriv (interior_subset (s := Ioi 0) hs)).differentiableAt.differentiableWithinAt) + intro s hs + have hs' : 0 < s := interior_subset hs + rw [(U_deriv (z := z) (k := k) hs').deriv] + exact (mul_pos (K_pos hs') (Az_pos hs')).le + have he : ∀ᶠ s in 𝓝[>] (0:ℝ), 0 < s ∧ s < r ∧ 0 < U ((z,k),s) := by + filter_upwards [U_B_positive_near_zero z k,self_mem_nhdsWithin, + (eventually_lt_nhds hr).filter_mono inf_le_left] with s hs hpos hlt + exact ⟨hpos,hlt,hs.1⟩ + obtain ⟨s,hs,hlt,hU⟩ := he.exists + exact hU.trans_le (hm hs hr hlt.le) + +lemma B_pos {z k r : ℝ} (hr : 0 < r) : 0 < B ((z,k),r) := by + have hm : MonotoneOn (fun s => B ((z,k),s)) (Ioi 0) := by + apply monotoneOn_of_deriv_nonneg (convex_Ioi 0) + (fun s hs => (B_deriv hs).continuousAt.continuousWithinAt) + (fun s hs => (B_deriv (interior_subset (s := Ioi 0) hs)).differentiableAt.differentiableWithinAt) + intro s hs + have hs' : 0 < s := interior_subset hs + rw [(B_deriv (z := z) (k := k) hs').deriv] + exact (mul_pos (div_pos (mul_pos (mul_pos (A_gap_pos hs') + (QuadraticVariation.Q_pos hs')) (Jz_pos hs')) + (mul_pos hs' (sq_pos_of_pos (Az_pos hs')))) (U_pos hs')).le + have he : ∀ᶠ s in 𝓝[>] (0:ℝ), 0 < s ∧ s < r ∧ 0 < B ((z,k),s) := by + filter_upwards [U_B_positive_near_zero z k,self_mem_nhdsWithin, + (eventually_lt_nhds hr).filter_mono inf_le_left] with s hs hpos hlt + exact ⟨hpos,hlt,hs.2⟩ + obtain ⟨s,hs,hlt,hB⟩ := he.exists + exact hB.trans_le (hm hs hr hlt.le) + +lemma J_surjective (d k : ℝ) {r : ℝ} (hr : 0 < r) : ∃ z : ℝ, J ((z,k),r)=d := by + let t := peakAtWidth profile (((d,k),0),r) + have hs := peak_spec profile profile_contDiff model_local_flow (p := (d,k)) (h := 0) hr + have he : baseAtWidth profile (((d,k),t),r)=0 := + base_eq profile profile_contDiff model_local_flow hr hs.1 hs.2 + have ht := base_translation d k t hr + refine ⟨d+k*t,?_⟩ + dsimp [J,base] + rw [he] at ht + linear_combination -k*ht + +end QuinticLienard.ReferenceCharacteristic + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/BaseSymmetry.lean b/lean/OAI/Analysis/LienardCycles/BaseSymmetry.lean new file mode 100644 index 0000000000000000000000000000000000000000..6102bb6947481a2ff99873d3a4d2e0faf078e100 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/BaseSymmetry.lean @@ -0,0 +1,39 @@ +import OAI.Analysis.LienardCycles.BaseTransport + +namespace OAI + +universe uP + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology +open Set Filter MeasureTheory +open Set Filter +open scoped Topology ContDiff + +namespace QuinticLienard.ArchSymmetries +open ScalarArcs ArcFamilies CanonicalVariation WidthCoordinates +variable {P : Type uP} [NormedAddCommGroup P] [NormedSpace ℝ P] + [FiniteDimensional ℝ P] +variable (Φ : P × ℝ → ℝ) (hΦ : ContDiff ℝ ω Φ) + (hloc : ∀ x : State P, ∃ f : State P × ℝ → State P, + ContDiffAt ℝ ω f (x,0) ∧ ∀ᶠ q in 𝓝 (x,(0:ℝ)), + f (q.1,0) = q.1 ∧ HasDerivAt (fun s => f (q.1,s)) (field Φ (f q)) q.2) + +include hΦ hloc + +theorem base_affine {p q : P} {t r c H C : ℝ} (hr : 0 < r) (hc : 0 < c) + (he : ∀ x, Φ (q,H+c^2*x) = C+c*Φ (p,x)) : + baseAtWidth Φ ((q,H+c^2*t),c*r) = H+c^2*baseAtWidth Φ ((p,t),r) := by + have hs := base_spec Φ hΦ hloc (p := p) (t := t) hr + have hw := width_affine Φ hΦ hs.1 hc he + rw [hs.2] at hw + exact base_eq Φ hΦ hloc (mul_pos hc hr) + (by nlinarith [sq_pos_of_pos hc]) hw + +end QuinticLienard.ArchSymmetries + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/BaseTransport.lean b/lean/OAI/Analysis/LienardCycles/BaseTransport.lean new file mode 100644 index 0000000000000000000000000000000000000000..f881a2d2645affa7e711176ca5936bc1b16618dd --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/BaseTransport.lean @@ -0,0 +1,57 @@ +import OAI.Analysis.LienardCycles.QuadraticSlices + +namespace OAI + +universe uP + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology +open Set Filter MeasureTheory +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.WidthTransport +open ScalarArcs CanonicalVariation WidthCoordinates PartialCalculus +variable {P : Type uP} [NormedAddCommGroup P] [NormedSpace ℝ P] + [FiniteDimensional ℝ P] +variable (Φ : P × ℝ → ℝ) (hΦ : ContDiff ℝ ω Φ) + (hloc : ∀ x : ArcFamilies.State P, ∃ f : ArcFamilies.State P × ℝ → ArcFamilies.State P, + ContDiffAt ℝ ω f (x,0) ∧ ∀ᶠ q in 𝓝 (x,(0:ℝ)), + f (q.1,0) = q.1 ∧ HasDerivAt (fun s => f (q.1,s)) (ArcFamilies.field Φ (f q)) q.2) +include hΦ hloc + +theorem base_width_deriv {p : P} {t r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => baseAtWidth Φ ((p,t),s)) + (-(r^2-(M Φ p (baseAtWidth Φ ((p,t),r),r))^2)/r) r := by + let h := baseAtWidth Φ ((p,t),r) + have hs := base_spec Φ hΦ hloc (p := p) (t := t) hr + let f : ℝ → ℝ := fun h => widthFamily Φ ((p,t),h) + let g : ℝ → ℝ := fun s => baseAtWidth Φ ((p,t),s) + have hg : DifferentiableAt ℝ g r := + ((base_analytic Φ hΦ hloc hr).comp r + (contDiffAt_const.prodMk contDiffAt_id)).differentiableAt (by simp) + have hf := width_base_deriv Φ hΦ hloc (p := p) hs.1 + have hm := midpoint_reparam Φ hΦ hloc (p := p) hs.1 + rw [hs.2] at hm hf + rw [←hm] at hf + have he : (f ∘ g) =ᶠ[𝓝 r] id := by + filter_upwards [continuousAt_const.eventually_lt continuousAt_id hr] with s hsr + exact (base_spec Φ hΦ hloc hsr).2 + have hc := (hf.comp r hg.hasDerivAt).unique + ((hasDerivAt_id r).congr_of_eventuallyEq he) + have hgap := ne_of_gt (M_gap_pos Φ hΦ hloc (p := p) (h := h) hr) + have hg' : deriv g r = -(r^2-M Φ p (h,r)^2)/r := by + change (-r / (r^2-M Φ p (h,r)^2))*deriv g r = 1 at hc + field_simp [hgap, ne_of_gt hr] at hc ⊢ + nlinarith [hc] + simpa only [hg'] using hg.hasDerivAt + +end QuinticLienard.WidthTransport + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/BoundaryFlow.lean b/lean/OAI/Analysis/LienardCycles/BoundaryFlow.lean new file mode 100644 index 0000000000000000000000000000000000000000..c8c2d05af60c537ad502ec977e01043e04387be7 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/BoundaryFlow.lean @@ -0,0 +1,91 @@ +import OAI.Analysis.LienardCycles.AxisLimits + +namespace OAI + +universe uE + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter Metric +open scoped Topology ContDiff +namespace QuinticLienard.GlobalODE +variable {E : Type uE} [NormedAddCommGroup E] [NormedSpace ℝ E] [FiniteDimensional ℝ E] + +theorem unique_on_open_interval (V : E → E) {U : Set E} (hU : IsOpen U) + (hV : ContDiffOn ℝ 1 V U) {f g : ℝ → E} {a b c : ℝ} + (hc : c ∈ Ioo a b) + (hf : ∀ t ∈ Ioo a b, HasDerivAt f (V (f t)) t ∧ f t ∈ U) + (hg : ∀ t ∈ Ioo a b, HasDerivAt g (V (g t)) t ∧ g t ∈ U) + (he : f c=g c) : EqOn f g (Ioo a b) := by + intro t ht + let A := (a+min t c)/2 + let B := (b+max t c)/2 + have hA : a linarith [lt_min ht.1 hc.1] + have hB : max t c < B ∧ B linarith [max_lt ht.2 hc.2] + have hs : Icc A B ⊆ Ioo a b := fun _ h=>⟨hA.1.trans_le h.1,h.2.trans_lt hB.2⟩ + have hfc : ContinuousOn f (Icc A B) := fun x hx=>(hf x (hs hx)).1.continuousAt.continuousWithinAt + have hgc : ContinuousOn g (Icc A B) := fun x hx=>(hg x (hs hx)).1.continuousAt.continuousWithinAt + obtain ⟨W,K,L,hK,_,hW⟩ := exists_bounded_lipschitz_cutoff_on V + ((isCompact_Icc.image_of_continuousOn hfc).union (isCompact_Icc.image_of_continuousOn hgc)) hU + (by rintro _ (⟨x,hx,rfl⟩|⟨x,hx,rfl⟩); exact (hf x (hs hx)).2; exact (hg x (hs hx)).2) hV + have hct : c ∈ Ioo A B := ⟨hA.2.trans_le (min_le_right _ _),(le_max_right _ _).trans_lt hB.1⟩ + have heq := ODE_solution_unique_of_mem_Icc (v:=fun _=>W) (s:=fun _=>(Set.univ : Set E)) + (fun _ _=>hK.lipschitzOnWith) hct hfc + (fun x hx=>by rw [(hW (f x) (Or.inl (mem_image_of_mem _ (Ioo_subset_Icc_self hx)))).self_of_nhds]; exact (hf x (hs (Ioo_subset_Icc_self hx))).1) + (fun _ _=>mem_univ _) hgc + (fun x hx=>by rw [(hW (g x) (Or.inr (mem_image_of_mem _ (Ioo_subset_Icc_self hx)))).self_of_nhds]; exact (hg x (hs (Ioo_subset_Icc_self hx))).1) + (fun _ _=>mem_univ _) he + exact heq ⟨(hA.2.trans_le (min_le_left _ _)).le,((le_max_left _ _).trans_lt hB.1).le⟩ +end QuinticLienard.GlobalODE +namespace QuinticLienard.AxisFlow +open SmoothFlow SmoothFlow.AlgebraicExpr ScaledProfile +noncomputable def X : AlgebraicExpr (ℝ×ℝ) := linear (ContinuousLinearMap.fst ℝ ℝ ℝ) +noncomputable def Y : AlgebraicExpr (ℝ×ℝ) := linear (ContinuousLinearMap.snd ℝ ℝ ℝ) +noncomputable def polynomial (a : Fin 6 → ℝ) : AlgebraicExpr (ℝ×ℝ) := + const (a 0)+const (a 1)*X+const (a 2)*X^2+const (a 3)*X^3+const (a 4)*X^4+const (a 5)*X^5 +noncomputable def rhs (a : Fin 6 → ℝ) : AlgebraicExpr (ℝ×ℝ) := X*(polynomial a+const (-1)*Y)⁻¹ +noncomputable def field (a : Fin 6 → ℝ) (z : ℝ×ℝ) : ℝ×ℝ := (1,z.1/(poly a z.1-z.2)) +def domain (a : Fin 6 → ℝ) : Set (ℝ×ℝ) := {z | poly a z.1-z.2≠0} +lemma polynomial_eval (a : Fin 6 → ℝ) (z : ℝ×ℝ) : (polynomial a).eval z=poly a z.1 := by + simp [polynomial,poly,X] +lemma polynomial_regular (a : Fin 6 → ℝ) (z : ℝ×ℝ) : (polynomial a).RegularAt z := by + simp [polynomial,X,regular_pow] +lemma rhs_eval (a : Fin 6 → ℝ) (z : ℝ×ℝ) : (rhs a).eval z=z.1/(poly a z.1-z.2) := by + simp [rhs,X,Y,polynomial_eval,div_eq_mul_inv,sub_eq_add_neg] +lemma rhs_regular (a : Fin 6 → ℝ) {z : ℝ×ℝ} (hz : z ∈ domain a) : (rhs a).RegularAt z := by + simp only [rhs,regular_mul,regular_inv,regular_add,regular_const,polynomial_regular,true_and] + simpa [domain,X,Y,polynomial_eval,sub_eq_add_neg] using hz +lemma domain_open (a : Fin 6 → ℝ) : IsOpen (domain a) := by + apply isOpen_ne_fun + · unfold poly + fun_prop + · fun_prop +lemma field_analytic (a : Fin 6 → ℝ) {z : ℝ×ℝ} (hz : z ∈ domain a) : ContDiffAt ℝ ω (field a) z := by + have he := (rhs a).eval_analytic (rhs_regular a hz) + change ContDiffAt ℝ ω (fun q : ℝ×ℝ=>(1,q.1/(poly a q.1-q.2))) z + simpa only [rhs_eval] using (contDiffAt_const.prodMk he : ContDiffAt ℝ ω (fun q=>((1:ℝ),(rhs a).eval q)) z) +lemma local_flow (a : Fin 6 → ℝ) {z : ℝ×ℝ} (hz : z ∈ domain a) : + ∃ f : ((ℝ×ℝ)×ℝ) → ℝ×ℝ, ContDiffAt ℝ ω f (z,0) ∧ + ∀ᶠ q in 𝓝 (z,(0:ℝ)), f (q.1,0)=q.1 ∧ HasDerivAt (fun s=>f (q.1,s)) (field a (f q)) q.2 := by + let I : ℝ →L[ℝ] ℝ×ℝ := ContinuousLinearMap.inr ℝ ℝ ℝ + let W : Path (ℝ×ℝ) → Path (ℝ×ℝ) := fun u=>constCLM (1,0)+pathMap I ((rhs a).onPaths u) + have hp := AlgebraicExpr.path_properties (rhs a) (rhs_regular a hz) + have hW : ContDiffAt ℝ ω W (constCLM z) := contDiffAt_const.add + ((pathMap I).contDiff.contDiffAt.comp _ hp.2.1) + apply exists_analytic_local_flow_eventually W (field a) z _ hW + filter_upwards [hp.2.2] with u hu s + simp only [W,ContinuousMap.add_apply,constCLM_apply,pathMap_apply,hu s,rhs_eval] + simp [I,field] +end QuinticLienard.AxisFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/BoundaryGerm.lean b/lean/OAI/Analysis/LienardCycles/BoundaryGerm.lean new file mode 100644 index 0000000000000000000000000000000000000000..61bd9c15e884205e21bd5c37de61c4eb37af6d2e --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/BoundaryGerm.lean @@ -0,0 +1,129 @@ +import OAI.Analysis.LienardCycles.BoundaryFlow + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter +open Set Filter Metric +open scoped Topology ContDiff + +open Set Filter Metric +open scoped Topology ContDiff +namespace QuinticLienard.AxisFlow +open PartialCalculus + +theorem boundary_germ {V : (ℝ×ℝ) → ℝ×ℝ} {U : Set (ℝ×ℝ)} + (hU : IsOpen U) (hV : ContDiffOn ℝ 1 V U) + {y : ℝ×ℝ → ℝ} {t₀ A T : ℝ} {J : Set ℝ} (hJ : J ∈ 𝓝 t₀) (hT : 0(s,y (t,s))) (V (x,y (t,x))) x ∧ (x,y (t,x)) ∈ U) + (hlim : Tendsto (fun x=>y (t₀,x)) (𝓝[>] 0) (𝓝 A)) + (hf : ∃ f : ((ℝ×ℝ)×ℝ) → ℝ×ℝ, ContDiffAt ℝ ω f ((0,A),0) ∧ + ∀ᶠ q in 𝓝 ((0,A),(0:ℝ)), f (q.1,0)=q.1 ∧ + HasDerivAt (fun s=>f (q.1,s)) (V (f q)) q.2) + (hAU : (0,A) ∈ U) : + ∃ G : ℝ×ℝ → ℝ, ContDiffAt ℝ ω G (t₀,0) ∧ G (t₀,0)=A ∧ + (∀ᶠ q in 𝓝 (t₀,(0:ℝ)), 0(f q).2 + have hFa : ContDiffAt ℝ ω F ((0,A),0) := hfa.snd + have hD : direction e F ((0,A),0)=1 := by + have hpath : HasDerivAt (fun s=>F ((0,s),0)) (direction e F ((0,A),0)) A := by + simpa only [direction,e,Function.comp_def,id_eq] using hFa.differentiableAt (by simp) |>.hasFDerivAt.comp_hasDerivAt A + (((hasDerivAt_const A (0:ℝ)).prodMk (hasDerivAt_id A)).prodMk (hasDerivAt_const A (0:ℝ))) + have heq : (fun s=>F ((0,s),0)) =ᶠ[𝓝 A] (fun s=>s) := by + filter_upwards [((continuousAt_const.prodMk continuousAt_id).prodMk continuousAt_const).eventually hfe] with s hs + exact congrArg Prod.snd hs.1 + exact (hpath.congr_of_eventuallyEq heq.symm).unique (hasDerivAt_id A) + have hpos : ∀ᶠ q in 𝓝 ((0,A),(0:ℝ)), 0(x,y (t₀,x))) (𝓝[>] 0) (𝓝 (0,A)) := + ((continuousAt_id : ContinuousAt (fun x : ℝ=>x) 0).tendsto.mono_left inf_le_left).prodMk_nhds hlim + have hzsmall : ∀ᶠ x in 𝓝[>] (0:ℝ), dist (x,y (t₀,x)) (0,A)<ρ/2 := + hzl (Metric.ball_mem_nhds _ (by linarith)) + have hex : ∀ᶠ x in 𝓝[>] (0:ℝ), 0(δ,y (t,δ))) t₀ := continuousAt_const.prodMk + ((ha δ ⟨hδ,hδT⟩).continuousAt.comp (f:=fun t : ℝ=>(t,δ)) (continuousAt_id.prodMk continuousAt_const)) + + have hzN' : ∀ᶠ t in 𝓝 t₀, dist (δ,y (t,δ)) (0,A)<ρ/2 := + (hzcont.dist continuousAt_const).eventually (eventually_lt_nhds hδz) + let G : ℝ×ℝ → ℝ := fun q=>F ((δ,y (q.1,δ)),q.2-δ) + have hnear (t x : ℝ) (ht : dist (δ,y (t,δ)) (0,A)<ρ/2) (hx : |x|<2*δ) : + ((δ,y (t,δ)),x-δ) ∈ ball ((0,A),0) ρ := by + rw [mem_ball,Prod.dist_eq,max_lt_iff,Real.dist_eq,sub_zero] + constructor + · linarith + · have hb := abs_le.mp (le_of_lt hx) + rw [abs_lt] + constructor <;> linarith + have hzero := hball (hnear t₀ 0 hδz (by simpa only [abs_zero] using mul_pos (by norm_num : (0:ℝ)<2) hδ)) + have hinner : ContDiffAt ℝ ω (fun q : ℝ×ℝ=>((δ,y (q.1,δ)),q.2-δ)) (t₀,0) := + (contDiffAt_const.prodMk ((ha δ ⟨hδ,hδT⟩).comp (t₀,(0:ℝ)) + (contDiffAt_fst.prodMk contDiffAt_const))).prodMk (contDiffAt_snd.sub contDiffAt_const) + have hGF : ContDiffAt ℝ ω F ((δ,y (t₀,δ)),0-δ) := hzero.1.snd + have hGa : ContDiffAt ℝ ω G (t₀,0) := hGF.comp (f:=fun q : ℝ×ℝ=>((δ,y (q.1,δ)),q.2-δ)) (t₀,0) hinner + have hag : ∀ᶠ q in 𝓝 (t₀,(0:ℝ)), 0(s,y (q.1,s)) + let ψ : ℝ → ℝ×ℝ := fun s=>f ((δ,y (q.1,δ)),s-δ) + have hdomain : ∀ s ∈ Ioo 0 (min T (2*δ)), |s|<2*δ := by + intro s hs + simpa only [abs_of_pos hs.1] using hs.2.trans_le (min_le_right _ _) + have hc : δ ∈ Ioo 0 (min T (2*δ)) := ⟨hδ,lt_min hδT (by linarith)⟩ + have heq := GlobalODE.unique_on_open_interval V hU hV hc + (fun s hs=>he q.1 hq.1 s ⟨hs.1,hs.2.trans_le (min_le_left _ _)⟩) + (fun s hs=>by + have hfq := hball (hnear q.1 s hq.2 (hdomain s hs)) + refine ⟨?_,hfq.2.2.2⟩ + have hd : HasDerivAt (fun v=>f ((δ,y (q.1,δ)),v)) (V (f ((δ,y (q.1,δ)),s-δ))) (s-δ) := hfq.2.1.2 + simpa only [one_smul,Function.comp_def,id_eq] using hd.scomp (h:=fun v : ℝ=>v-δ) s ((hasDerivAt_id s).sub_const δ)) + (show γ δ=ψ δ by + dsimp only [γ,ψ] + rw [sub_self] + exact (hball (hnear q.1 δ hq.2 (by rw [abs_of_pos hδ]; linarith))).2.1.1.symm) + have hxx : q.2 ∈ Ioo 0 (min T (2*δ)) := ⟨hx,lt_min + ((lt_of_le_of_lt (le_abs_self _) hqx).trans hδT) (by linarith [le_abs_self q.2])⟩ + exact (congrArg Prod.snd (heq hxx)).symm + have hGlim : Tendsto (fun x=>G (t₀,x)) (𝓝[>] 0) (𝓝 (G (t₀,0))) := + ((hGa.continuousAt.comp (continuousAt_const.prodMk continuousAt_id))).tendsto.mono_left inf_le_left + have heq0 : (fun x=>G (t₀,x)) =ᶠ[𝓝[>] 0] (fun x=>y (t₀,x)) := by + filter_upwards [((continuousAt_const.prodMk continuousAt_id).eventually hag).filter_mono inf_le_left, + self_mem_nhdsWithin] with x hx hx0 + exact hx hx0 + have hzero' := hzero + simp only [zero_sub] at hzero' + refine ⟨G,hGa,tendsto_nhds_unique hGlim (hlim.congr' heq0.symm),hag,δ,⟨hδ,hδT⟩, + direction e F ((δ,y (t₀,δ)),-δ),hzero'.2.2.1,?_⟩ + have hdy := first_hasDerivAt ((ha δ ⟨hδ,hδT⟩).differentiableAt (by simp)) + have hdG := hzero'.1.snd.differentiableAt (by simp) |>.hasFDerivAt.comp_hasDerivAt t₀ + (((hasDerivAt_const t₀ δ).prodMk hdy).prodMk (hasDerivAt_const t₀ (-δ))) + have heqD : ((0,first y (t₀,δ)),0)=first y (t₀,δ) • e := by ext <;> simp [e] + have hdval : first G (t₀,0)=fderiv ℝ F ((δ,y (t₀,δ)),-δ) ((0,first y (t₀,δ)),0) := by + exact (first_hasDerivAt (hGa.differentiableAt (by simp))).unique (by simpa only [G,F,Function.comp_def,zero_sub] using hdG) + rw [hdval,heqD,map_smul] + simp only [smul_eq_mul, direction] + ring +end QuinticLienard.AxisFlow + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CanonicalAnalytic.lean b/lean/OAI/Analysis/LienardCycles/CanonicalAnalytic.lean new file mode 100644 index 0000000000000000000000000000000000000000..d5a91ed8a281de81e4b6ecf7543d6aaa33b8bc48 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CanonicalAnalytic.lean @@ -0,0 +1,64 @@ +import OAI.Analysis.LienardCycles.ArcEndpoints + +namespace OAI + +universe uP + +open Set Filter MeasureTheory +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.CanonicalAnalytic +open ScalarArcs ArcEndpoints ArcFamilies +variable {P : Type uP} [NormedAddCommGroup P] [NormedSpace ℝ P] + [FiniteDimensional ℝ P] + +theorem endpoints (Φ : P × ℝ → ℝ) (hΦ : ContDiff ℝ ω Φ) + (hloc : ∀ x : State P, ∃ f : State P × ℝ → State P, + ContDiffAt ℝ ω f (x,0) ∧ ∀ᶠ q in 𝓝 (x,(0:ℝ)), + f (q.1,0) = q.1 ∧ HasDerivAt (fun s => f (q.1,s)) (field Φ (f q)) q.2) + {p : P} {t h : ℝ} (hht : h < t) : + ContDiffAt ℝ ω (lowerFamily Φ) ((p,t),h) ∧ + ContDiffAt ℝ ω (upperFamily Φ) ((p,t),h) := by + have hφ (p : P) : ContDiff ℝ 1 (fun x => Φ (p,x)) := + (hΦ.comp (contDiff_const.prodMk contDiff_id)).of_le (by simp) + obtain ⟨u,a₀,b₀,hu⟩ := entire_arch_exists (hφ p) (show h-1 < t by linarith) + obtain ⟨a,b,ha,hb,harch⟩ := hu.subarch (hφ p) (show h-1 < h by linarith) hht + have hV : ContDiffOn ℝ 1 (field Φ) univ := by + have hd : ContDiff ℝ ω (field Φ) := + contDiff_const.prodMk (((hΦ.comp (contDiff_fst.prodMk contDiff_snd.fst)).sub + contDiff_snd.snd).prodMk contDiff_const) + exact (hd.of_le (by simp)).contDiffOn + obtain ⟨w,hwc,hwpeak,hwmatch,hwd,hwe⟩ := peak_family Φ isOpen_univ hV + (fun x _ => hloc x) hΦ.contDiffAt hu.lower_lt_peak hu.peak_lt_upper + hu.continuous hu.peak hu.equation (fun _ _ => mem_univ _) + let A := (a₀+a)/2 + let B := (b+b₀)/2 + have hA : a₀ < A ∧ A < a := by dsimp [A]; constructor <;> linarith + have hB : b < B ∧ B < b₀ := by dsimp [B]; constructor <;> linarith + have hsub : Icc A B ⊆ Ioo a₀ b₀ := + fun _ hy => ⟨hA.1.trans_le hy.1,hy.2.trans_lt hB.2⟩ + have hwb : IsArch (fun x => Φ (p,x)) (fun y => w ((p,t),y)) h t a b := by + apply IsArch.of_solution_and_hits (hφ p) (hwc (p,t)) + (fun y hy => (hwe y (hsub ⟨hA.2.le.trans hy.1,hy.2.trans hB.1.le⟩)).self_of_nhds) + harch.lower_lt_peak harch.peak_lt_upper (hwpeak (p,t)) + · rw [hwmatch a ⟨ha.le,(harch.lower_lt_peak.trans hu.peak_lt_upper).le⟩] + exact harch.lower + · rw [hwmatch b ⟨(hu.lower_lt_peak.trans harch.peak_lt_upper).le,hb.le⟩] + exact harch.upper + obtain ⟨l,r,hl,hr,_,_,he⟩ := actual_endpoint_families Φ hφ hwc hwpeak + (fun y hy => hwd y (Ioo_subset_Icc_self (hsub hy))) + (fun y hy => hwe y (hsub hy)) hwb hA.2 hB.1 hΦ.continuous.continuousAt + exact canonical_endpoints_contDiffAt Φ hφ hht hl hr + (he.mono fun q hq => ⟨fun y => w (q.1,y),hq⟩) + +end QuinticLienard.CanonicalAnalytic + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CanonicalVariation.lean b/lean/OAI/Analysis/LienardCycles/CanonicalVariation.lean new file mode 100644 index 0000000000000000000000000000000000000000..e6fbc420e14dd5b392c1bcc91235d866064cb1d8 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CanonicalVariation.lean @@ -0,0 +1,210 @@ +import OAI.Analysis.LienardCycles.ArchVariation + +namespace OAI + +universe uP + +open Set Filter MeasureTheory +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.CanonicalVariation +open ScalarArcs ArcEndpoints ArcFamilies PartialCalculus ArchVariation + +lemma canonical_of_arch {φ u : ℝ → ℝ} {h t a b : ℝ} + (hu : IsArch φ u h t a b) (hφ : ContDiff ℝ 1 φ) (hht : h < t) : + lower φ h t = a ∧ upper φ h t = b := by + obtain ⟨ψ,K,B,_,hK,_,hψ⟩ := entire_profile_extension hφ hht + have hc := chosen_arch (entire_arch_exists hφ hht) + have hh := hc.unique hu hK hψ + exact ⟨hh.1,hh.2.1⟩ + +variable {P : Type uP} [NormedAddCommGroup P] [NormedSpace ℝ P] + [FiniteDimensional ℝ P] + +theorem endpoint_witness (Φ : P × ℝ → ℝ) (hΦ : ContDiff ℝ ω Φ) + (hloc : ∀ x : State P, ∃ f : State P × ℝ → State P, + ContDiffAt ℝ ω f (x,0) ∧ ∀ᶠ q in 𝓝 (x,(0:ℝ)), + f (q.1,0) = q.1 ∧ HasDerivAt (fun s => f (q.1,s)) (field Φ (f q)) q.2) + {p : P} {t h : ℝ} (hht : h < t) : + ∃ w : (P × ℝ) × ℝ → ℝ, + (∀ q, Continuous (fun y => w (q,y))) ∧ + (∀ q, w (q,Φ q) = q.2) ∧ + (∀ y ∈ Icc (lowerFamily Φ ((p,t),h)) (upperFamily Φ ((p,t),h)), + ContDiffAt ℝ ω w ((p,t),y)) ∧ + (∀ y ∈ Icc (lowerFamily Φ ((p,t),h)) (upperFamily Φ ((p,t),h)), + ∀ᶠ q in 𝓝 ((p,t),y), + HasDerivAt (fun s => w (q.1,s)) (Φ (q.1.1,w q)-q.2) q.2) ∧ + ∀ᶠ q in 𝓝 ((p,t),h), + IsArch (fun x => Φ (q.1.1,x)) (fun y => w (q.1,y)) + q.2 q.1.2 (lowerFamily Φ q) (upperFamily Φ q) := by + have hφ (p : P) : ContDiff ℝ 1 (fun x => Φ (p,x)) := + (hΦ.comp (contDiff_const.prodMk contDiff_id)).of_le (by simp) + obtain ⟨u,a₀,b₀,hu⟩ := entire_arch_exists (hφ p) (show h-1 < t by linarith) + obtain ⟨a,b,ha,hb,harch⟩ := hu.subarch (hφ p) (show h-1 < h by linarith) hht + have hV : ContDiffOn ℝ 1 (field Φ) univ := by + have hd : ContDiff ℝ ω (field Φ) := + contDiff_const.prodMk (((hΦ.comp (contDiff_fst.prodMk contDiff_snd.fst)).sub + contDiff_snd.snd).prodMk contDiff_const) + exact (hd.of_le (by simp)).contDiffOn + obtain ⟨w,hwc,hwpeak,hwmatch,hwd,hwe⟩ := peak_family Φ isOpen_univ hV + (fun x _ => hloc x) hΦ.contDiffAt hu.lower_lt_peak hu.peak_lt_upper + hu.continuous hu.peak hu.equation (fun _ _ => mem_univ _) + let A := (a₀+a)/2 + let B := (b+b₀)/2 + have hA : a₀ < A ∧ A < a := by dsimp [A]; constructor <;> linarith + have hB : b < B ∧ B < b₀ := by dsimp [B]; constructor <;> linarith + have hsub : Icc A B ⊆ Ioo a₀ b₀ := + fun _ hy => ⟨hA.1.trans_le hy.1,hy.2.trans_lt hB.2⟩ + have hwb : IsArch (fun x => Φ (p,x)) (fun y => w ((p,t),y)) h t a b := by + apply IsArch.of_solution_and_hits (hφ p) (hwc (p,t)) + (fun y hy => (hwe y (hsub ⟨hA.2.le.trans hy.1,hy.2.trans hB.1.le⟩)).self_of_nhds) + harch.lower_lt_peak harch.peak_lt_upper (hwpeak (p,t)) + · rw [hwmatch a ⟨ha.le,(harch.lower_lt_peak.trans hu.peak_lt_upper).le⟩] + exact harch.lower + · rw [hwmatch b ⟨(hu.lower_lt_peak.trans harch.peak_lt_upper).le,hb.le⟩] + exact harch.upper + obtain ⟨l,r,_,_,_,_,he⟩ := actual_endpoint_families Φ hφ hwc hwpeak + (fun y hy => hwd y (Ioo_subset_Icc_self (hsub hy))) + (fun y hy => hwe y (hsub hy)) hwb hA.2 hB.1 hΦ.continuous.continuousAt + have hlr := canonical_of_arch hwb (hφ p) hht + change lowerFamily Φ ((p,t),h) = a ∧ upperFamily Φ ((p,t),h) = b at hlr + have hinc : Icc (lowerFamily Φ ((p,t),h)) (upperFamily Φ ((p,t),h)) ⊆ + Ioo a₀ b₀ := by + rw [hlr.1,hlr.2] + exact fun _ hy => ⟨ha.trans_le hy.1,hy.2.trans_lt hb⟩ + refine ⟨w,hwc,hwpeak,fun y hy => hwd y (Ioo_subset_Icc_self (hinc hy)), + fun y hy => hwe y (hinc hy),?_⟩ + have ht : ∀ᶠ q : (P × ℝ) × ℝ in 𝓝 ((p,t),h), q.2 < q.1.2 := + continuousAt_snd.eventually_lt continuousAt_fst.snd hht + filter_upwards [he,ht] with q hq hqt + have hcanon := canonical_of_arch hq (hφ q.1.1) hqt + change lowerFamily Φ q = l q ∧ upperFamily Φ q = r q at hcanon + rwa [hcanon.1,hcanon.2] + +theorem peak_signs (Φ : P × ℝ → ℝ) (hΦ : ContDiff ℝ ω Φ) + (hloc : ∀ x : State P, ∃ f : State P × ℝ → State P, + ContDiffAt ℝ ω f (x,0) ∧ ∀ᶠ q in 𝓝 (x,(0:ℝ)), + f (q.1,0) = q.1 ∧ HasDerivAt (fun s => f (q.1,s)) (field Φ (f q)) q.2) + {p : P} {t h : ℝ} (hht : h < t) : + deriv (fun s => lowerFamily Φ ((p,s),h)) t < 0 ∧ + 0 < deriv (fun s => upperFamily Φ ((p,s),h)) t := by + obtain ⟨w,hwc,hpeak,hwd,hwe,harch⟩ := endpoint_witness Φ hΦ hloc hht + have hu := harch.self_of_nhds + have hφ : ContDiff ℝ 1 (fun x => Φ (p,x)) := + (hΦ.comp (contDiff_const.prodMk contDiff_id)).of_le (by simp) + let w₀ : ℝ × ℝ → ℝ := fun q => w ((p,q.1),q.2) + let l : ℝ → ℝ := fun s => lowerFamily Φ ((p,s),h) + let r : ℝ → ℝ := fun s => upperFamily Φ ((p,s),h) + have hw₀ (y : ℝ) (hy : y ∈ Icc (l t) (r t)) : ContDiffAt ℝ ω w₀ (t,y) := + (hwd y hy).comp (t,y) ((contDiffAt_const.prodMk contDiffAt_fst).prodMk contDiffAt_snd) + have he₀ (y : ℝ) (hy : y ∈ Icc (l t) (r t)) : + ∀ᶠ q in 𝓝 (t,y), HasDerivAt (fun s => w₀ (q.1,s)) (Φ (p,w₀ q)-q.2) q.2 := by + have hc : ContinuousAt (fun q : ℝ × ℝ => ((p,q.1),q.2)) (t,y) := + (continuousAt_const.prodMk continuousAt_fst).prodMk continuousAt_snd + exact hc.eventually (hwe y hy) + have hh := peak_derivative_positive hφ (hwc (p,t)) hw₀ he₀ + (Eventually.of_forall (fun s => hpeak (p,s))) + ⟨hu.lower_lt_peak.le,hu.peak_lt_upper.le⟩ + obtain ⟨hl,hr⟩ := CanonicalAnalytic.endpoints Φ hΦ hloc (p := p) hht + have hld : DifferentiableAt ℝ l t := + (hl.comp t ((contDiffAt_const.prodMk contDiffAt_id).prodMk contDiffAt_const)).differentiableAt (by simp) + have hrd : DifferentiableAt ℝ r t := + (hr.comp t ((contDiffAt_const.prodMk contDiffAt_id).prodMk contDiffAt_const)).differentiableAt (by simp) + have hag : ∀ᶠ s in 𝓝 t, + IsArch (fun x => Φ (p,x)) (fun y => w₀ (s,y)) h s (l s) (r s) := + ((continuousAt_const.prodMk continuousAt_id).prodMk continuousAt_const).eventually harch + have hab := hu.lower_lt_peak.le.trans hu.peak_lt_upper.le + have hal : l t ∈ Icc (l t) (r t) := ⟨le_rfl,hab⟩ + have har : r t ∈ Icc (l t) (r t) := ⟨hab,le_rfl⟩ + have hel0 : w ((p,t),l t) = h := hu.lower + have her0 : w ((p,t),r t) = h := hu.upper + apply endpoint_peak_signs (φ := fun s => Φ (p,s)) hld hrd ((hw₀ _ hal).differentiableAt (by simp)) + ((hw₀ _ har).differentiableAt (by simp)) + (hag.mono fun _ hq => hq.lower) (hag.mono fun _ hq => hq.upper) + · simpa only [hel0] using hu.equation _ hal + · simpa only [her0] using hu.equation _ har + · exact hh _ hal + · exact hh _ har + · exact hu.lower_transverse + · exact hu.upper_transverse + +theorem base_derivatives (Φ : P × ℝ → ℝ) (hΦ : ContDiff ℝ ω Φ) + (hloc : ∀ x : State P, ∃ f : State P × ℝ → State P, + ContDiffAt ℝ ω f (x,0) ∧ ∀ᶠ q in 𝓝 (x,(0:ℝ)), + f (q.1,0) = q.1 ∧ HasDerivAt (fun s => f (q.1,s)) (field Φ (f q)) q.2) + {p : P} {t h : ℝ} (hht : h < t) : + HasDerivAt (fun s => lowerFamily Φ ((p,t),s)) + (1/(Φ (p,h)-lowerFamily Φ ((p,t),h))) h ∧ + HasDerivAt (fun s => upperFamily Φ ((p,t),s)) + (1/(Φ (p,h)-upperFamily Φ ((p,t),h))) h := by + obtain ⟨w,_,_,_,_,he⟩ := endpoint_witness Φ hΦ hloc hht + have hu := he.self_of_nhds + obtain ⟨hl,hr⟩ := CanonicalAnalytic.endpoints Φ hΦ hloc (p := p) hht + let l : ℝ → ℝ := fun s => lowerFamily Φ ((p,t),s) + let r : ℝ → ℝ := fun s => upperFamily Φ ((p,t),s) + have hld : DifferentiableAt ℝ l h := + (hl.comp h (contDiffAt_const.prodMk contDiffAt_id)).differentiableAt (by simp) + have hrd : DifferentiableAt ℝ r h := + (hr.comp h (contDiffAt_const.prodMk contDiffAt_id)).differentiableAt (by simp) + have hag : ∀ᶠ s in 𝓝 h, + IsArch (fun x => Φ (p,x)) (fun y => w ((p,t),y)) s t (l s) (r s) := + (continuousAt_const.prodMk continuousAt_id).eventually he + have hab := hu.lower_lt_peak.le.trans hu.peak_lt_upper.le + have hal : l h ∈ Icc (l h) (r h) := ⟨le_rfl,hab⟩ + have har : r h ∈ Icc (l h) (r h) := ⟨hab,le_rfl⟩ + have hel : w ((p,t),l h) = h := hu.lower + have her : w ((p,t),r h) = h := hu.upper + have hdl : HasDerivAt (fun y => w ((p,t),y)) (Φ (p,h)-l h) (l h) := by + simpa only [hel] using hu.equation _ hal + have hdr : HasDerivAt (fun y => w ((p,t),y)) (Φ (p,h)-r h) (r h) := by + simpa only [her] using hu.equation _ har + have hlv := (hdl.comp h hld.hasDerivAt).unique + ((hasDerivAt_id h).congr_of_eventuallyEq (hag.mono fun _ hq => hq.lower)) + have hrv := (hdr.comp h hrd.hasDerivAt).unique + ((hasDerivAt_id h).congr_of_eventuallyEq (hag.mono fun _ hq => hq.upper)) + have hlne : Φ (p,h)-l h ≠ 0 := ne_of_gt (sub_pos.mpr hu.lower_transverse) + have hrne : Φ (p,h)-r h ≠ 0 := ne_of_lt (sub_neg.mpr hu.upper_transverse) + have hleq : deriv l h = 1/(Φ (p,h)-l h) := by + apply (eq_div_iff hlne).mpr + simpa only [mul_comm] using hlv + have hreq : deriv r h = 1/(Φ (p,h)-r h) := by + apply (eq_div_iff hrne).mpr + simpa only [mul_comm] using hrv + exact ⟨by simpa only [hleq] using hld.hasDerivAt, + by simpa only [hreq] using hrd.hasDerivAt⟩ + +theorem peak_width_midpoint_bounds (Φ : P × ℝ → ℝ) (hΦ : ContDiff ℝ ω Φ) + (hloc : ∀ x : State P, ∃ f : State P × ℝ → State P, + ContDiffAt ℝ ω f (x,0) ∧ ∀ᶠ q in 𝓝 (x,(0:ℝ)), + f (q.1,0) = q.1 ∧ HasDerivAt (fun s => f (q.1,s)) (field Φ (f q)) q.2) + {p : P} {t h : ℝ} (hht : h < t) : + 0 < deriv (fun s => width (fun u => Φ (p,u)) h s) t ∧ + |deriv (fun s => midpoint (fun u => Φ (p,u)) h s) t / + deriv (fun s => width (fun u => Φ (p,u)) h s) t| < 1 := by + obtain ⟨hl,hr⟩ := CanonicalAnalytic.endpoints Φ hΦ hloc (p := p) hht + have hld := (hl.comp t + ((contDiffAt_const.prodMk contDiffAt_id).prodMk contDiffAt_const)).differentiableAt + (by simp) + have hrd := (hr.comp t + ((contDiffAt_const.prodMk contDiffAt_id).prodMk contDiffAt_const)).differentiableAt + (by simp) + obtain ⟨hls,hrs⟩ := peak_signs Φ hΦ hloc hht + have hb := width_midpoint_peak_bounds hld hrd hls hrs + have hmid : deriv (fun s => midpoint (fun u => Φ (p,u)) h s) t = + deriv (fun s => (upperFamily Φ ((p,s),h)+lowerFamily Φ ((p,s),h))/2) t := by + exact (((hrd.hasDerivAt.add hld.hasDerivAt).div_const 2).sub_const (Φ (p,h))).deriv.trans + (((hrd.hasDerivAt.add hld.hasDerivAt).div_const 2).deriv.symm) + rw [hmid] + exact hb + +end QuinticLienard.CanonicalVariation + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CaseOne.lean b/lean/OAI/Analysis/LienardCycles/CaseOne.lean new file mode 100644 index 0000000000000000000000000000000000000000..9e33a1e67f33137f209cccc351cd109082d8b7dd --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CaseOne.lean @@ -0,0 +1,102 @@ +import OAI.Analysis.LienardCycles.CycleIsolation + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open Set Filter Metric +open scoped Topology NNReal +open scoped Topology +open scoped Topology ContDiff +open Set Filter +open scoped Topology ContDiff NNReal + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard +open ScaledProfile ScalarArcs AxisFlow RealAnalysis ScalarComparison +lemma linear_pos_open {a E F : ℝ → ℝ} {l r : ℝ} (hlr : la (projIcc l r hlr.le s) + have hc : Continuous ac := (continuousOn_iff_continuous_domRestrict.mp ha).comp continuous_projIcc + let w : ℝ → ℝ := fun s=>Real.exp (∫ u in l..s,ac u) + have hw : Continuous w := continuous_iff_continuousAt.mpr fun s=>((hc.integral_hasStrictDerivAt l s).hasDerivAt.exp).continuousAt + have hwd (s : ℝ) (hs : s ∈ Ioo l r) : HasDerivAt (fun s=>w s*E s) (w s*F s) s := by + have H := ((hc.integral_hasStrictDerivAt l s).hasDerivAt.exp).mul (hd s hs) + have he : ac s=a s := by simp only [ac,projIcc_of_mem hlr.le (Ioo_subset_Icc_self hs)] + rw [he] at H + convert! H using 1 + dsimp only [w] + ring + have hm : StrictMonoOn (fun s=>w s*E s) (Icc l r) := by + apply strictMonoOn_of_deriv_pos (convex_Icc _ _) (hw.continuousOn.mul hE) + intro s hs + have hs' : s ∈ Ioo l r := by simpa using hs + change 0w s*E s) s + rw [(hwd s hs').deriv] + exact mul_pos (Real.exp_pos _) (hF s hs') + have hp := hm ⟨le_rfl,hlr.le⟩ ⟨hlr.le,le_rfl⟩ hlr + have hw0 : w l=1 := by simp [w] + dsimp only at hp + rw [hw0,one_mul] at hp + exact (mul_pos_iff_of_pos_left (Real.exp_pos _)).mp (h0.trans_lt hp) +noncomputable def oddPart (a : Fin 6 → ℝ) (u : ℝ) : ℝ := a 1*root u+a 3*(root u)^3+a 5*(root u)^5 +lemma oddPart_pos {a : Fin 6 → ℝ} (h1 : 0≤a 1) (h3 : 0≤a 3) (h5 : 0≤a 5) + (hne : a 1≠0 ∨ a 3≠0 ∨ a 5≠0) {u : ℝ} (hu : 0by rw [polynomialReflect_eval,hF,reflectX_poly]) hz.reverseX + simp only [QuinticLienard.reverseX,neg_neg,hzT] at hvA hvB hvd + have hpos := linear_pos_open (a:=fun y=>-(2*a 2+4*a 4*(u y+v y))) + (E:=fun y=>u y-v y) (F:=fun y=>oddPart a (u y)+oddPart a (v y)) (hr.y_lt hz) + (by fun_prop) (hu.sub hv).continuousOn + (fun y hy=>by + convert! (hud y hy).2.sub (hvd y hy).2 using 1 + rw [show (φ a (u y)-y)-(φ (reflectX a) (v y)-y)=φ a (u y)-φ (reflectX a) (v y) by ring] + rw [profile_odd_difference a (hud y hy).1.le (hvd y hy).1.le] + ring) + (fun y hy=>add_pos (oddPart_pos h1 h3 h5 hne (hud y hy).1) (oddPart_pos h1 h3 h5 hne (hvd y hy).1)) + (by rw [huA,hvA,sub_self]) + rw [huB,hvB,sub_self] at hpos + exact lt_irrefl _ hpos +end QuinticLienard + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/Characteristic.lean b/lean/OAI/Analysis/LienardCycles/Characteristic.lean new file mode 100644 index 0000000000000000000000000000000000000000..50a3d6dad3d5bc1dec31b986ef6f86dfe640342c --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/Characteristic.lean @@ -0,0 +1,127 @@ +import OAI.Analysis.LienardCycles.BaseSymmetry + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology +open Set Filter MeasureTheory +open Set Filter +open scoped Topology ContDiff + +namespace QuinticLienard.ReferenceCharacteristic +open ScalarArcs CanonicalVariation PolynomialModel WidthCoordinates + WidthTransport PartialCalculus QuadraticCoordinates ArchSymmetries + +noncomputable def base (q : (ℝ × ℝ) × ℝ) : ℝ := + baseAtWidth profile ((q.1,0),q.2) +noncomputable def J (q : (ℝ × ℝ) × ℝ) : ℝ := q.1.1+q.1.2*base q +noncomputable def A (q : (ℝ × ℝ) × ℝ) : ℝ := H ((J q,q.1.2),q.2)/q.2 +noncomputable def D (q : (ℝ × ℝ) × ℝ) : ℝ := Hr ((J q,q.1.2),q.2) +noncomputable def Jz : (ℝ × ℝ) × ℝ → ℝ := direction ((1,0),0) J +noncomputable def Jk : (ℝ × ℝ) × ℝ → ℝ := direction ((0,1),0) J +noncomputable def Az : (ℝ × ℝ) × ℝ → ℝ := direction ((1,0),0) A +noncomputable def Ak : (ℝ × ℝ) × ℝ → ℝ := direction ((0,1),0) A +noncomputable def Dz : (ℝ × ℝ) × ℝ → ℝ := direction ((1,0),0) D +noncomputable def Dk : (ℝ × ℝ) × ℝ → ℝ := direction ((0,1),0) D + +lemma base_analytic {q : (ℝ × ℝ) × ℝ} (hr : 0 < q.2) : ContDiffAt ℝ ω base q := + (WidthCoordinates.base_analytic profile profile_contDiff model_local_flow hr).comp q + ((contDiffAt_fst.prodMk contDiffAt_const).prodMk contDiffAt_snd) +lemma J_analytic {q : (ℝ × ℝ) × ℝ} (hr : 0 < q.2) : ContDiffAt ℝ ω J q := by + unfold J + have hb := base_analytic hr + fun_prop +lemma A_analytic {q : (ℝ × ℝ) × ℝ} (hr : 0 < q.2) : ContDiffAt ℝ ω A q := by + exact ((H_analytic (d := J q) (k := q.1.2) hr).comp q + (((J_analytic hr).prodMk contDiffAt_fst.snd).prodMk contDiffAt_snd)).div + contDiffAt_snd (ne_of_gt hr) +lemma D_analytic {q : (ℝ × ℝ) × ℝ} (hr : 0 < q.2) : ContDiffAt ℝ ω D q := + (Hr_analytic (d := J q) (k := q.1.2) hr).comp q + (((J_analytic hr).prodMk contDiffAt_fst.snd).prodMk contDiffAt_snd) + +lemma Jz_hasDerivAt {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => J ((s,k),r)) (Jz ((z,k),r)) z := + slice_d ((J_analytic hr).differentiableAt (by simp)) +lemma Jk_hasDerivAt {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => J ((z,s),r)) (Jk ((z,k),r)) k := + slice_k ((J_analytic hr).differentiableAt (by simp)) +lemma Az_hasDerivAt {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => A ((s,k),r)) (Az ((z,k),r)) z := + slice_d ((A_analytic hr).differentiableAt (by simp)) +lemma Ak_hasDerivAt {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => A ((z,s),r)) (Ak ((z,k),r)) k := + slice_k ((A_analytic hr).differentiableAt (by simp)) +lemma Dz_hasDerivAt {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => D ((s,k),r)) (Dz ((z,k),r)) z := + slice_d ((D_analytic hr).differentiableAt (by simp)) +lemma Dk_hasDerivAt {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => D ((z,s),r)) (Dk ((z,k),r)) k := + slice_k ((D_analytic hr).differentiableAt (by simp)) + +lemma A_abs_lt {q : (ℝ × ℝ) × ℝ} (hr : 0 < q.2) : |A q| < 1 := by + dsimp [A] + rw [abs_div,abs_of_pos hr,div_lt_one hr] + exact H_abs_lt hr +lemma D_abs_lt {q : (ℝ × ℝ) × ℝ} (hr : 0 < q.2) : |D q| < 1 := Hr_abs_lt hr +lemma A_gap_pos {q : (ℝ × ℝ) × ℝ} (hr : 0 < q.2) : 0 < 1-(A q)^2 := by + have ht := sq_lt_sq₀ (abs_nonneg (A q)) (by norm_num : (0:ℝ) ≤ 1) |>.mpr (A_abs_lt hr) + nlinarith [sq_abs (A q)] +lemma D_gap_pos {q : (ℝ × ℝ) × ℝ} (hr : 0 < q.2) : 0 < 1-(D q)^2 := by + have ht := sq_lt_sq₀ (abs_nonneg (D q)) (by norm_num : (0:ℝ) ≤ 1) |>.mpr (D_abs_lt hr) + nlinarith [sq_abs (D q)] + +lemma base_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => base ((z,k),s)) (-r*(1-(A ((z,k),r))^2)) r := by + have hb := base_width_deriv profile profile_contDiff model_local_flow + (p := (z,k)) (t := 0) hr + rw [translation z k _ hr] at hb + convert! hb using 1 + dsimp only [J,A,base] + field_simp [ne_of_gt hr] + +lemma J_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => J ((z,k),s)) (-k*r*(1-(A ((z,k),r))^2)) r := by + convert! (base_deriv (z := z) (k := k) hr).const_mul k |>.const_add z using 1 + ring + +lemma A_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => A ((z,k),s)) + (J ((z,k),r)*(1-(A ((z,k),r))^2)-2*A ((z,k),r)/r) r := by + have hd := (((H_analytic (d := J ((z,k),r)) (k := k) hr).differentiableAt (by simp)).hasFDerivAt.comp_hasDerivAt (f := fun s => ((J ((z,k),s),k),s)) r + (((J_deriv (z := z) (k := k) hr).prodMk (hasDerivAt_const r k)).prodMk (hasDerivAt_id r))).div + (hasDerivAt_id r) (ne_of_gt hr) + rw [fderiv_model] at hd + have ht := width_identity (d := J ((z,k),r)) (k := k) hr + change k*P ((J ((z,k),r),k),r)+J ((z,k),r)= + (r*Hr ((J ((z,k),r),k),r)+H ((J ((z,k),r),k),r))/(r^2-H ((J ((z,k),r),k),r)^2) at ht + have hg := ne_of_gt (H_gap_pos (d := J ((z,k),r)) (k := k) hr) + convert! hd using 1 + dsimp [A,P,Hr,Q,direction] at ht ⊢ + field_simp [ne_of_gt hr,hg] at ht ⊢ + nlinarith [ht] + +lemma D_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => D ((z,k),s)) + (2*A ((z,k),r)*(1-(D ((z,k),r))^2)/(r*(1-(A ((z,k),r))^2))) r := by + have hd := (Hr_analytic (d := J ((z,k),r)) (k := k) hr).differentiableAt (by simp) + have hc := hd.hasFDerivAt.comp_hasDerivAt (f := fun s => ((J ((z,k),s),k),s)) r + (((J_deriv (z := z) (k := k) hr).prodMk (hasDerivAt_const r k)).prodMk (hasDerivAt_id r)) + rw [fderiv_model] at hc + have hR : direction ((1,0),0) Hr ((J ((z,k),r),k),r)=R ((J ((z,k),r),k),r) := + direction_comm (H_analytic hr) _ _ + rw [hR] at hc + have ht := transport_Hr (d := J ((z,k),r)) (k := k) hr + have hg := ne_of_gt (H_gap_pos (d := J ((z,k),r)) (k := k) hr) + have ha := ne_of_gt (A_gap_pos (q := ((z,k),r)) hr) + convert! hc using 1 + dsimp [A,D,Hrr,alpha,gap] at ht ⊢ + field_simp [ne_of_gt hr,hg] at ht ⊢ + nlinarith [ht] + +end QuinticLienard.ReferenceCharacteristic + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CharacteristicJets.lean b/lean/OAI/Analysis/LienardCycles/CharacteristicJets.lean new file mode 100644 index 0000000000000000000000000000000000000000..9f2c7a804460fc3b31ed1b2ef04e0f9937af40ca --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CharacteristicJets.lean @@ -0,0 +1,147 @@ +import OAI.Analysis.LienardCycles.MixedDerivatives + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology +open Set Filter MeasureTheory +open Set Filter +open scoped Topology ContDiff + +namespace QuinticLienard.ReferenceCharacteristic +open PartialCalculus QuadraticCoordinates + +noncomputable def C (q : (ℝ × ℝ) × ℝ) : ℝ := -2*(J q*A q+1/q.2) +noncomputable def E (q : (ℝ × ℝ) × ℝ) : ℝ := 2*A q/(q.2*(1-(A q)^2)) +noncomputable def K (q : (ℝ × ℝ) × ℝ) : ℝ := 2*(1+(A q)^2)/(q.2*(1-(A q)^2)^2) +noncomputable def U (q : (ℝ × ℝ) × ℝ) : ℝ := Dz q/(1-(D q)^2) +noncomputable def V (q : (ℝ × ℝ) × ℝ) : ℝ := Dk q/(1-(D q)^2) +noncomputable def T (q : (ℝ × ℝ) × ℝ) : ℝ := Ak q/Az q +noncomputable def B (q : (ℝ × ℝ) × ℝ) : ℝ := V q-T q*U q + +lemma Az_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => Az ((z,k),s)) + ((1-(A ((z,k),r))^2)*Jz ((z,k),r)+C ((z,k),r)*Az ((z,k),r)) r := by + apply mixed_z_radius (f := A) + (fr := fun q => J q*(1-(A q)^2)-2*A q/q.2) (fun _ hp => A_analytic hp) hr + (fun a => A_deriv hr) + convert! ((Jz_hasDerivAt (z := z) (k := k) hr).mul + (((Az_hasDerivAt (z := z) (k := k) hr).pow 2).const_sub 1)).sub + (((Az_hasDerivAt (z := z) (k := k) hr).const_mul 2).div_const r) using 1 + dsimp [C] + ring + +lemma Ak_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => Ak ((z,k),s)) + ((1-(A ((z,k),r))^2)*Jk ((z,k),r)+C ((z,k),r)*Ak ((z,k),r)) r := by + apply mixed_k_radius (f := A) + (fr := fun q => J q*(1-(A q)^2)-2*A q/q.2) (fun _ hp => A_analytic hp) hr + (fun a => A_deriv hr) + convert! ((Jk_hasDerivAt (z := z) (k := k) hr).mul + (((Ak_hasDerivAt (z := z) (k := k) hr).pow 2).const_sub 1)).sub + (((Ak_hasDerivAt (z := z) (k := k) hr).const_mul 2).div_const r) using 1 + dsimp [C] + ring + +lemma E_z_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => E ((s,k),r)) (K ((z,k),r)*Az ((z,k),r)) z := by + convert! ((Az_hasDerivAt (z := z) (k := k) hr).const_mul 2).div + ((((Az_hasDerivAt (z := z) (k := k) hr).pow 2).const_sub 1).const_mul r) + (ne_of_gt (mul_pos hr (A_gap_pos (q := ((z,k),r)) hr))) using 1 + dsimp [E,K] + field_simp + ring + +lemma E_k_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => E ((z,s),r)) (K ((z,k),r)*Ak ((z,k),r)) k := by + convert! ((Ak_hasDerivAt (z := z) (k := k) hr).const_mul 2).div + ((((Ak_hasDerivAt (z := z) (k := k) hr).pow 2).const_sub 1).const_mul r) + (ne_of_gt (mul_pos hr (A_gap_pos (q := ((z,k),r)) hr))) using 1 + dsimp [E,K] + field_simp + ring + +lemma D_deriv' {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => D ((z,k),s)) (E ((z,k),r)*(1-(D ((z,k),r))^2)) r := by + convert D_deriv (z := z) (k := k) hr using 1 + dsimp [E] + ring + +lemma Dz_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => Dz ((z,k),s)) + (K ((z,k),r)*Az ((z,k),r)*(1-(D ((z,k),r))^2)- + 2*E ((z,k),r)*D ((z,k),r)*Dz ((z,k),r)) r := by + apply mixed_z_radius (f := D) (fr := fun q => E q*(1-(D q)^2)) + (fun _ hp => D_analytic hp) hr (fun a => D_deriv' hr) + convert! (E_z_deriv (z := z) (k := k) hr).mul + (((Dz_hasDerivAt (z := z) (k := k) hr).pow 2).const_sub 1) using 1 + dsimp only [Pi.pow_apply] + ring + +lemma Dk_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => Dk ((z,k),s)) + (K ((z,k),r)*Ak ((z,k),r)*(1-(D ((z,k),r))^2)- + 2*E ((z,k),r)*D ((z,k),r)*Dk ((z,k),r)) r := by + apply mixed_k_radius (f := D) (fr := fun q => E q*(1-(D q)^2)) + (fun _ hp => D_analytic hp) hr (fun a => D_deriv' hr) + convert! (E_k_deriv (z := z) (k := k) hr).mul + (((Dk_hasDerivAt (z := z) (k := k) hr).pow 2).const_sub 1) using 1 + dsimp only [Pi.pow_apply] + ring + +lemma U_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => U ((z,k),s)) (K ((z,k),r)*Az ((z,k),r)) r := by + convert! (Dz_deriv (z := z) (k := k) hr).div + (((D_deriv' (z := z) (k := k) hr).pow 2).const_sub 1) + (ne_of_gt (D_gap_pos (q := ((z,k),r)) hr)) using 1 + dsimp only [Pi.pow_apply] + field_simp [ne_of_gt (D_gap_pos (q := ((z,k),r)) hr)] + ring + +lemma V_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => V ((z,k),s)) (K ((z,k),r)*Ak ((z,k),r)) r := by + convert! (Dk_deriv (z := z) (k := k) hr).div + (((D_deriv' (z := z) (k := k) hr).pow 2).const_sub 1) + (ne_of_gt (D_gap_pos (q := ((z,k),r)) hr)) using 1 + dsimp only [Pi.pow_apply] + field_simp [ne_of_gt (D_gap_pos (q := ((z,k),r)) hr)] + ring + +lemma T_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => T ((z,k),s)) + (-(1-(A ((z,k),r))^2)*Q ((J ((z,k),r),k),r)*Jz ((z,k),r)/ + (r*(Az ((z,k),r))^2)) r := by + convert! (Ak_deriv (z := z) (k := k) hr).div (Az_deriv (z := z) (k := k) hr) + (ne_of_gt (Az_pos (z := z) (k := k) hr)) using 1 + have h1 := Az_formula (z := z) (k := k) hr + have h2 := Ak_formula (z := z) (k := k) hr + rw [h1,h2] + field_simp + ring + +lemma B_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => B ((z,k),s)) + ((1-(A ((z,k),r))^2)*Q ((J ((z,k),r),k),r)*Jz ((z,k),r)/ + (r*(Az ((z,k),r))^2)*U ((z,k),r)) r := by + convert! (V_deriv (z := z) (k := k) hr).sub + ((T_deriv (z := z) (k := k) hr).mul (U_deriv (z := z) (k := k) hr)) using 1 + dsimp [B,T] + field_simp [ne_of_gt (Az_pos (z := z) (k := k) hr)] + ring + +lemma B_formula {z k r : ℝ} (hr : 0 < r) : + B ((z,k),r) = G ((J ((z,k),r),k),r)/(P ((J ((z,k),r),k),r)*(1-(D ((z,k),r))^2)) := by + dsimp only [B,V,T,U] + rw [Dk_formula hr,Dz_formula hr,Az_formula hr,Ak_formula hr] + dsimp [G] + field_simp [ne_of_gt (QuadraticVariation.P_pos (d := J ((z,k),r)) (k := k) hr), + ne_of_gt (Jz_pos (z := z) (k := k) hr),ne_of_gt hr] + ring + +end QuinticLienard.ReferenceCharacteristic + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CharacteristicLimit.lean b/lean/OAI/Analysis/LienardCycles/CharacteristicLimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..ccc852ac7ac97c111184f7b1bce11900ffbc05f4 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CharacteristicLimit.lean @@ -0,0 +1,26 @@ +import OAI.Analysis.LienardCycles.HeightLimits + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +namespace QuinticLienard.ReferenceCharacteristic +open QuadraticCoordinates +lemma D_tendsto_zero (z k : ℝ) : + Tendsto (fun r => D ((z,k),r)) (𝓝[>] (0:ℝ)) (𝓝 0) := by + have ht := (DN_analytic ((z,k),0)).continuousAt.tendsto.comp (model_tendsto z k) + rw [DN_zero] at ht + apply ht.congr' + filter_upwards [self_mem_nhdsWithin] with r hr + exact (Hr_DN hr).symm +end QuinticLienard.ReferenceCharacteristic + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CharacteristicPositive.lean b/lean/OAI/Analysis/LienardCycles/CharacteristicPositive.lean new file mode 100644 index 0000000000000000000000000000000000000000..25f5a38340f84ee7a7613d14e2bf7c207079fc49 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CharacteristicPositive.lean @@ -0,0 +1,30 @@ +import OAI.Analysis.LienardCycles.Schwarzian + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ReferenceCharacteristic +lemma D_pos_of_A_nonneg {z k r : ℝ} (hk : 0 < k) (hr : 0 < r) + (hA : 0 ≤ A ((z,k),r)) : 0 < D ((z,k),r) := by + apply strictMono_zero_pos hr (D_tendsto_zero z k) + apply strictMonoOn_of_deriv_pos (convex_Ioc 0 r) + (fun s hs => (D_deriv hs.1).continuousAt.continuousWithinAt) + intro s hs + rw [interior_Ioc] at hs + rw [(D_deriv (z := z) (k := k) hs.1).deriv] + exact div_pos (mul_pos (mul_pos (by norm_num) (A_pos_before hk hr hA hs.1 hs.2)) + (D_gap_pos hs.1)) (mul_pos hs.1 (A_gap_pos hs.1)) +end QuinticLienard.ReferenceCharacteristic + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CharacteristicScaling.lean b/lean/OAI/Analysis/LienardCycles/CharacteristicScaling.lean new file mode 100644 index 0000000000000000000000000000000000000000..219b93267be87a1200e5cc83606ee6f6a31b02d1 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CharacteristicScaling.lean @@ -0,0 +1,94 @@ +import OAI.Analysis.LienardCycles.Characteristic + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology +open Set Filter MeasureTheory +open Set Filter +open scoped Topology ContDiff + +namespace QuinticLienard.ReferenceCharacteristic +open ScalarArcs CanonicalVariation PolynomialModel WidthCoordinates + WidthTransport PartialCalculus QuadraticCoordinates ArchSymmetries + +lemma base_translation (z k t : ℝ) {r : ℝ} (hr : 0 < r) : + baseAtWidth profile (((z,k),t),r) = t+baseAtWidth profile (((z+k*t,k),0),r) := by + have hh := base_affine profile profile_contDiff model_local_flow + (p := (z+k*t,k)) (q := (z,k)) (t := 0) (H := t) + (C := z*t+k/2*t^2) hr (show 0 < (1:ℝ) by norm_num) + (by intro x; dsimp [profile]; ring) + simpa using hh + +lemma J_reparam {z k r : ℝ} (hr : 0 < r) (hk : k ≠ 0) : + J ((z,k),r)=k*baseAtWidth profile (((0,k),z/k),r) := by + have hh := base_translation 0 k (z/k) hr + simp only [zero_add,mul_div_cancel₀ _ hk] at hh + rw [hh] + dsimp [J,base] + field_simp + +lemma Jz_pos {z k r : ℝ} (hr : 0 < r) : 0 < Jz ((z,k),r) := by + by_cases hk : k = 0 + · subst k + have he : (fun s => J ((s,0),r))=id := by ext s; simp [J] + have hh := (Jz_hasDerivAt (z := z) (k := 0) hr).unique (he ▸ hasDerivAt_id z) + rw [hh]; norm_num + · have hb : DifferentiableAt ℝ (fun t => baseAtWidth profile (((0,k),t),r)) (z/k) := + ((WidthCoordinates.base_analytic profile profile_contDiff model_local_flow hr).comp (z/k) + ((contDiffAt_const.prodMk contDiffAt_id).prodMk contDiffAt_const)).differentiableAt (by simp) + have hc := (hb.hasDerivAt.comp z ((hasDerivAt_id z).div_const k)).const_mul k + have he : (fun s => J ((s,k),r))=(fun s => k*baseAtWidth profile (((0,k),s/k),r)) := + funext (fun s => J_reparam hr hk) + have hh := (Jz_hasDerivAt (z := z) (k := k) hr).unique (he ▸ hc) + have hp := base_peak_deriv_pos profile profile_contDiff model_local_flow + (p := (0,k)) (t := z/k) hr + rw [hh] + convert hp using 1 + field_simp + +lemma Az_formula {z k r : ℝ} (hr : 0 < r) : + Az ((z,k),r) = P ((J ((z,k),r),k),r)*Jz ((z,k),r)/r := by + have hc := ((P_hasDerivAt (d := J ((z,k),r)) (k := k) hr).comp z + (Jz_hasDerivAt (z := z) (k := k) hr)).div_const r + exact (Az_hasDerivAt hr).unique hc + +lemma Ak_formula {z k r : ℝ} (hr : 0 < r) : + Ak ((z,k),r) = (P ((J ((z,k),r),k),r)*Jk ((z,k),r)+Q ((J ((z,k),r),k),r))/r := by + have hc := ((H_analytic (d := J ((z,k),r)) (k := k) hr).differentiableAt (by simp)).hasFDerivAt.comp_hasDerivAt + (f := fun s => ((J ((z,s),r),s),r)) k + (((Jk_hasDerivAt (z := z) (k := k) hr).prodMk (hasDerivAt_id k)).prodMk (hasDerivAt_const k r)) + have hh := (Ak_hasDerivAt (z := z) (k := k) hr).unique (hc.div_const r) + rw [fderiv_model] at hh + simpa [P,Q,mul_comm] using hh + +lemma Dz_formula {z k r : ℝ} (hr : 0 < r) : + Dz ((z,k),r) = R ((J ((z,k),r),k),r)*Jz ((z,k),r) := by + have hc := (Hr_d_hasDerivAt (d := J ((z,k),r)) (k := k) hr).comp z + (Jz_hasDerivAt (z := z) (k := k) hr) + exact (Dz_hasDerivAt hr).unique hc + +lemma Dk_formula {z k r : ℝ} (hr : 0 < r) : + Dk ((z,k),r) = R ((J ((z,k),r),k),r)*Jk ((z,k),r)+S ((J ((z,k),r),k),r) := by + have hc := ((Hr_analytic (d := J ((z,k),r)) (k := k) hr).differentiableAt (by simp)).hasFDerivAt.comp_hasDerivAt + (f := fun s => ((J ((z,s),r),s),r)) k + (((Jk_hasDerivAt (z := z) (k := k) hr).prodMk (hasDerivAt_id k)).prodMk (hasDerivAt_const k r)) + have hh := (Dk_hasDerivAt (z := z) (k := k) hr).unique hc + rw [fderiv_model] at hh + have hR : direction ((1,0),0) Hr ((J ((z,k),r),k),r)=R ((J ((z,k),r),k),r) := + direction_comm (H_analytic hr) _ _ + have hS : direction ((0,1),0) Hr ((J ((z,k),r),k),r)=S ((J ((z,k),r),k),r) := + direction_comm (H_analytic hr) _ _ + simpa [hR,hS,mul_comm] using hh + +lemma Az_pos {z k r : ℝ} (hr : 0 < r) : 0 < Az ((z,k),r) := by + rw [Az_formula hr] + exact div_pos (mul_pos (QuadraticVariation.P_pos hr) (Jz_pos hr)) hr + +end QuinticLienard.ReferenceCharacteristic + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CharacteristicSigns.lean b/lean/OAI/Analysis/LienardCycles/CharacteristicSigns.lean new file mode 100644 index 0000000000000000000000000000000000000000..511a05594fda7fa05b0f21b1091dbc6390115e40 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CharacteristicSigns.lean @@ -0,0 +1,105 @@ +import OAI.Analysis.LienardCycles.RegionBarrier + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology ContDiff +open Set Filter +open scoped Topology + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ReferenceCharacteristic +open QuadraticCoordinates PartialCalculus + +lemma monotone_zero_nonneg {f : ℝ → ℝ} {r : ℝ} (hr : 0 < r) + (hf : Tendsto f (𝓝[>] (0:ℝ)) (𝓝 0)) + (hm : MonotoneOn f (Ioc 0 r)) : 0 ≤ f r := by + apply le_of_tendsto hf + filter_upwards [self_mem_nhdsWithin,(eventually_lt_nhds hr).filter_mono inf_le_left] with s hs hsr + exact hm ⟨hs,hsr.le⟩ ⟨hr,le_rfl⟩ hsr.le + +lemma strictMono_zero_pos {f : ℝ → ℝ} {r : ℝ} (hr : 0 < r) + (hf : Tendsto f (𝓝[>] (0:ℝ)) (𝓝 0)) + (hm : StrictMonoOn f (Ioc 0 r)) : 0 < f r := by + have hhalf : 0 < r/2 := half_pos hr + have hle : r/2 ≤ r := by linarith + have hn := monotone_zero_nonneg hhalf hf (hm.monotoneOn.mono (Ioc_subset_Ioc_right hle)) + exact hn.trans_lt (hm ⟨hhalf,hle⟩ ⟨hr,le_rfl⟩ (by linarith)) + +lemma J_strictAnti {z k : ℝ} (hk : 0 < k) : + StrictAntiOn (fun r => J ((z,k),r)) (Ioi 0) := by + apply strictAntiOn_of_deriv_neg (convex_Ioi 0) + (fun s hs => (J_deriv hs).continuousAt.continuousWithinAt) + intro s hs + have hs' : 0 < s := interior_subset hs + rw [(J_deriv (z := z) (k := k) hs').deriv] + have h := mul_pos (mul_pos hk hs') (A_gap_pos (q := ((z,k),s)) hs') + linarith + +lemma AH_tendsto (z k : ℝ) : + Tendsto (fun r => r^2*A ((z,k),r)) (𝓝[>] (0:ℝ)) (𝓝 0) := by + have hlow : Tendsto (fun r : ℝ => -r^2) (𝓝[>] (0:ℝ)) (𝓝 0) := by + simpa using! (((tendsto_id.mono_left inf_le_left).pow 2).neg : + Tendsto (fun r : ℝ => -r^2) (𝓝[>] (0:ℝ)) (𝓝 (-0^2))) + have hupp : Tendsto (fun r : ℝ => r^2) (𝓝[>] (0:ℝ)) (𝓝 0) := by + simpa using! ((tendsto_id.mono_left inf_le_left).pow 2 : + Tendsto (fun r : ℝ => r^2) (𝓝[>] (0:ℝ)) (𝓝 (0^2))) + apply tendsto_of_tendsto_of_tendsto_of_le_of_le' hlow hupp + · filter_upwards [self_mem_nhdsWithin] with r hr + have h := (abs_lt.mp (A_abs_lt (q := ((z,k),r)) hr)).1 + nlinarith [mul_nonneg (sq_nonneg r) (show 0 ≤ A ((z,k),r)+1 by linarith)] + · filter_upwards [self_mem_nhdsWithin] with r hr + have h := (abs_lt.mp (A_abs_lt (q := ((z,k),r)) hr)).2 + nlinarith [mul_nonneg (sq_nonneg r) (show 0 ≤ 1-A ((z,k),r) by linarith)] + +lemma AH_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => s^2*A ((z,k),s)) (r^2*J ((z,k),r)*(1-A ((z,k),r)^2)) r := by + have hd := ((hasDerivAt_id r).pow 2).mul (A_deriv (z := z) (k := k) hr) + convert! hd using 1 + dsimp only [Pi.pow_apply,id_eq] + field_simp + ring + +lemma A_pos_before {z k r : ℝ} (hk : 0 < k) (_hr : 0 < r) + (hA : 0 ≤ A ((z,k),r)) {s : ℝ} (hs : 0 < s) (hsr : s < r) : + 0 < A ((z,k),s) := by + have hj := J_strictAnti (z := z) hk + have hpos (t : ℝ) (ht : 0 < t) (hjt : 0 ≤ J ((z,k),t)) : 0 < A ((z,k),t) := by + have hm : StrictMonoOn (fun u => u^2*A ((z,k),u)) (Ioc 0 t) := by + apply strictMonoOn_of_deriv_pos (convex_Ioc 0 t) + (fun u hu => (AH_deriv hu.1).continuousAt.continuousWithinAt) + intro u hu + rw [interior_Ioc] at hu + rw [(AH_deriv (z := z) (k := k) hu.1).deriv] + exact mul_pos (mul_pos (sq_pos_of_pos hu.1) + (hjt.trans_lt (hj hu.1 ht hu.2))) (A_gap_pos hu.1) + have hmul : 0 < t^2*A ((z,k),t) := strictMono_zero_pos (f := fun u => u^2*A ((z,k),u)) (r := t) ht (AH_tendsto z k) hm + exact (mul_pos_iff_of_pos_left (sq_pos_of_pos ht)).mp hmul + by_contra! hnon + have hjs : J ((z,k),s) < 0 := by + by_contra! h + exact (hpos s hs h).not_ge hnon + have hm : StrictAntiOn (fun u => u^2*A ((z,k),u)) (Icc s r) := by + apply strictAntiOn_of_deriv_neg (convex_Icc s r) + (fun u hu => (AH_deriv (hs.trans_le hu.1)).continuousAt.continuousWithinAt) + intro u hu + have hu' := interior_subset (s := Icc s r) hu + have hu0 := hs.trans_le hu'.1 + rw [(AH_deriv (z := z) (k := k) hu0).deriv] + exact mul_neg_of_neg_of_pos + (mul_neg_of_pos_of_neg (sq_pos_of_pos hu0) + ((hj.antitoneOn hs hu0 hu'.1).trans_lt hjs)) (A_gap_pos hu0) + have hh := hm ⟨le_rfl,hsr.le⟩ ⟨hsr.le,le_rfl⟩ hsr + have hleft := mul_nonpos_of_nonneg_of_nonpos (sq_nonneg s) hnon + have hright := mul_nonneg (sq_nonneg r) hA + linarith + +end QuinticLienard.ReferenceCharacteristic + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ClosedCutoff.lean b/lean/OAI/Analysis/LienardCycles/ClosedCutoff.lean new file mode 100644 index 0000000000000000000000000000000000000000..052dcb84867b243bb5a03830bdecb06016d6882c --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ClosedCutoff.lean @@ -0,0 +1,49 @@ +import OAI.Analysis.LienardCycles.PhysicalFlow + +namespace OAI + +universe uE + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open scoped Topology ContDiff +open Set Filter +open scoped Topology ContDiff NNReal + +open Set Filter +open scoped Topology NNReal +namespace QuinticLienard +open GlobalODE +lemma flow_periodic_of_hit {E : Type uE} [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E] + (W : E → E) {K L : ℝ≥0} (hK : LipschitzWith K W) (hL : ∀ x,‖W x‖≤L) + {x : E} {T : ℝ} (he : flow W hK hL x T=x) : Function.Periodic (flow W hK hL x) T := by + intro t + rw [add_comm,flow_add,he] +lemma flow_true_of_closed {F : Polynomial ℝ} (W : Plane → Plane) {K L : ℝ≥0} + (hK : LipschitzWith K W) (hL : ∀ x,‖W x‖≤L) {x : Plane} {T : ℝ} + (hT : 0] (0:ℝ)) (𝓝 0) := by + have hc : Continuous root := Real.continuous_sqrt.comp (continuous_const.mul continuous_id) + have hc0 : Tendsto root (𝓝 (0:ℝ)) (𝓝 0) := by + have H : Tendsto root (𝓝 (0:ℝ)) (𝓝 (root 0)) := hc.continuousAt + simpa [root] using H + exact hc0.mono_left inf_le_left +lemma root_tendsto_zero_pos : Tendsto root (𝓝[>] (0:ℝ)) (𝓝[>] 0) := + tendsto_nhdsWithin_iff.mpr ⟨root_tendsto_zero,(show ∀ᶠ h : ℝ in 𝓝[>] 0, 0root_pos hh⟩ +lemma slope_rest_limit (a : Fin 6 → ℝ) : + Tendsto (fun h=>2*a 2+3*a 3*root h+4*a 4*(root h)^2+5*a 5*(root h)^3) + (𝓝[>] (0:ℝ)) (𝓝 (2*a 2)) := by + simpa using ((tendsto_const_nhds.add (root_tendsto_zero.const_mul (3*a 3))).add + ((root_tendsto_zero.pow 2).const_mul (4*a 4))).add + ((root_tendsto_zero.pow 3).const_mul (5*a 5)) +lemma slope_atBot {a : Fin 6 → ℝ} (h1 : a 1<0) : Tendsto (slope a) (𝓝[>] (0:ℝ)) atBot := by + have hi := tendsto_inv_nhdsGT_zero.comp root_tendsto_zero_pos + have ht := (hi.const_mul_atTop_of_neg h1).atBot_add (slope_rest_limit a) + apply ht.congr' + filter_upwards [self_mem_nhdsWithin] with h hh + rw [slope_formula a hh,div_eq_mul_inv] + simp only [Function.comp_apply] + ring +lemma slope_atTop {a : Fin 6 → ℝ} (h1 : 0] (0:ℝ)) atTop := by + have hi := tendsto_inv_nhdsGT_zero.comp root_tendsto_zero_pos + have ht := (hi.const_mul_atTop h1).atTop_add (slope_rest_limit a) + apply ht.congr' + filter_upwards [self_mem_nhdsWithin] with h hh + rw [slope_formula a hh,div_eq_mul_inv] + simp only [Function.comp_apply] + ring +end QuinticLienard.ScaledProfile + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ConditionalFit.lean b/lean/OAI/Analysis/LienardCycles/ConditionalFit.lean new file mode 100644 index 0000000000000000000000000000000000000000..001f662501bddf992c42b22926537069a6534e05 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ConditionalFit.lean @@ -0,0 +1,173 @@ +import OAI.Analysis.LienardCycles.PositiveTransport + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuadraticFit +open PartialCalculus QuadraticCoordinates ReferenceCharacteristic + +lemma slope_curvature_deriv {k r M : ℝ} (hr : 0 < r) (hM : |M| < r) : + HasDerivAt (fun a => slope ((a,r),M)) + (-Q ((slope ((k,r),M),k),r)/P ((slope ((k,r),M),k),r)) k := by + have hs := ((slope_analytic hr hM).comp (f := fun a : ℝ => ((a,r),M)) k + ((contDiffAt_id.prodMk contDiffAt_const).prodMk contDiffAt_const)).differentiableAt (by simp) + have hprod := (H_analytic (d := slope ((k,r),M)) (k := k) hr).differentiableAt (by simp) + |>.hasFDerivAt.comp_hasDerivAt (f := fun a => ((slope ((a,r),M),a),r)) k + ((hs.hasDerivAt.prodMk (hasDerivAt_id k)).prodMk (hasDerivAt_const k r)) + have he := hprod.unique ((hasDerivAt_const k M).congr_of_eventuallyEq + (Eventually.of_forall (fun a => slope_spec (k := a) hr hM))) + rw [fderiv_model] at he + have hP := ne_of_gt (QuadraticVariation.P_pos (d := slope ((k,r),M)) (k := k) hr) + have hd : deriv (fun a => slope ((a,r),M)) k = -Q ((slope ((k,r),M),k),r)/P ((slope ((k,r),M),k),r) := by + dsimp only [P,Q,Hr] at hP ⊢ + field_simp [hP] + simp only [one_mul,zero_mul,add_zero,Function.comp_def] at he + linarith + rw [←hd] + exact hs.hasDerivAt + +noncomputable def conditionalV (q : (ℝ × ℝ) × ℝ) : ℝ := Hr ((slope q,q.1.1),q.1.2) + +lemma conditionalV_analytic {k r M : ℝ} (hr : 0 < r) (hM : |M| < r) : + ContDiffAt ℝ ω conditionalV ((k,r),M) := + (Hr_analytic (d := slope ((k,r),M)) (k := k) hr).comp + (f := fun q : (ℝ × ℝ) × ℝ => ((slope q,q.1.1),q.1.2)) ((k,r),M) + (((slope_analytic hr hM).prodMk contDiffAt_fst.fst).prodMk contDiffAt_fst.snd) + +lemma conditionalV_deriv {k r M : ℝ} (hr : 0 < r) (hM : |M| < r) : + HasDerivAt (fun a => conditionalV ((a,r),M)) + (G ((slope ((k,r),M),k),r)/P ((slope ((k,r),M),k),r)) k := by + have h := (Hr_analytic (d := slope ((k,r),M)) (k := k) hr).differentiableAt (by simp) + |>.hasFDerivAt.comp_hasDerivAt (f := fun a => ((slope ((a,r),M),a),r)) k + (((slope_curvature_deriv hr hM).prodMk (hasDerivAt_id k)).prodMk (hasDerivAt_const k r)) + rw [fderiv_model] at h + have hR := direction_comm (H_analytic (d := slope ((k,r),M)) (k := k) hr) ((1,0),0) ((0,0),1) + have hS := direction_comm (H_analytic (d := slope ((k,r),M)) (k := k) hr) ((0,1),0) ((0,0),1) + change direction ((1,0),0) Hr _=R _ at hR + change direction ((0,1),0) Hr _=S _ at hS + convert! h using 1 + rw [hR,hS] + dsimp only [G] + field_simp [ne_of_gt (QuadraticVariation.P_pos (d := slope ((k,r),M)) (k := k) hr)] + ring + +lemma conditionalV_strictMono {r M : ℝ} (hr : 0 < r) (hM : |M| < r) : + StrictMono (fun k => conditionalV ((k,r),M)) := by + apply strictMono_of_deriv_pos + intro k + rw [(conditionalV_deriv hr hM).deriv] + exact div_pos (G_pos hr) (QuadraticVariation.P_pos hr) + +lemma reference_midpoint_exists {k r A₀ : ℝ} (hr : 0 < r) (hA : |A₀| < 1) : + ∃ z, A ((z,k),r)=A₀ := by + have hm : |r*A₀| A ((z,k),r)) := by + apply strictMono_of_deriv_pos + intro z + rw [(Az_hasDerivAt hr).deriv] + exact Az_pos hr + +noncomputable def label (q : (ℝ × ℝ) × ℝ) : ℝ := by + classical + exact if h : ∃ z, A ((z,q.1.1),q.1.2)=q.2 then h.choose else 0 + +lemma label_spec {k r A₀ : ℝ} (hr : 0 < r) (hA : |A₀| < 1) : + A ((label ((k,r),A₀),k),r)=A₀ := by + have he := reference_midpoint_exists (k := k) hr hA + simp only [label,dite_eq_left he] + exact he.choose_spec + +lemma label_eq {k r A₀ z : ℝ} (hr : 0 < r) (hA : |A₀| < 1) + (hz : A ((z,k),r)=A₀) : label ((k,r),A₀)=z := + (reference_midpoint_strictMono k hr).injective ((label_spec hr hA).trans hz.symm) + +lemma label_analytic {k r A₀ : ℝ} (hr : 0 < r) (hA : |A₀| < 1) : + ContDiffAt ℝ ω label ((k,r),A₀) := by + let z := label ((k,r),A₀) + let f : (ℝ × ℝ) × ℝ → ℝ := fun q => A ((q.2,q.1.1),q.1.2) + have hf : ContDiffAt ℝ ω f ((k,r),z) := + (A_analytic (q := ((z,k),r)) hr).comp (g := A) + (f := fun q : (ℝ × ℝ) × ℝ => ((q.2,q.1.1),q.1.2)) ((k,r),z) + ((contDiffAt_snd.prodMk contDiffAt_fst.fst).prodMk contDiffAt_fst.snd) + obtain ⟨Y,hY,hY₀,he⟩ := ArcEndpoints.level_hit hf (Az_hasDerivAt hr) + (label_spec hr hA) (ne_of_gt (Az_pos hr)) + apply hY.congr_of_eventuallyEq + have hpos : ∀ᶠ q : (ℝ × ℝ) × ℝ in 𝓝 ((k,r),A₀), 0 < q.1.2 := + continuousAt_const.eventually_lt continuousAt_fst.snd hr + have habs : ∀ᶠ q : (ℝ × ℝ) × ℝ in 𝓝 ((k,r),A₀), |q.2| < 1 := + continuousAt_snd.abs.eventually_lt continuousAt_const hA + filter_upwards [he,hpos,habs] with q hq hqr hqA + exact label_eq hqr hqA hq + +lemma label_curvature_deriv {k r A₀ : ℝ} (hr : 0 < r) (hA : |A₀| < 1) : + HasDerivAt (fun a => label ((a,r),A₀)) (-T ((label ((k,r),A₀),k),r)) k := by + have hs := ((label_analytic hr hA).comp (f := fun a : ℝ => ((a,r),A₀)) k + ((contDiffAt_id.prodMk contDiffAt_const).prodMk contDiffAt_const)).differentiableAt (by simp) + have hprod := (A_analytic (q := ((label ((k,r),A₀),k),r)) hr).differentiableAt (by simp) + |>.hasFDerivAt.comp_hasDerivAt (f := fun a => ((label ((a,r),A₀),a),r)) k + ((hs.hasDerivAt.prodMk (hasDerivAt_id k)).prodMk (hasDerivAt_const k r)) + have he := hprod.unique ((hasDerivAt_const k A₀).congr_of_eventuallyEq + (Eventually.of_forall (fun a => label_spec (k := a) hr hA))) + rw [fderiv_model] at he + have hP := ne_of_gt (Az_pos (z := label ((k,r),A₀)) (k := k) hr) + have hd : deriv (fun a => label ((a,r),A₀)) k = -T ((label ((k,r),A₀),k),r) := by + dsimp only [T,Az,Ak] at hP ⊢ + field_simp [hP] + simp only [one_mul,zero_mul,add_zero,Function.comp_def] at he + linarith + rw [←hd] + exact hs.hasDerivAt + +lemma T_strictAnti (z k : ℝ) : StrictAntiOn (fun s => T ((z,k),s)) (Ioi 0) := by + apply strictAntiOn_of_deriv_neg (convex_Ioi 0) + (fun s hs => (T_deriv hs).continuousAt.continuousWithinAt) + intro s hs + have hs' : 0 < s := interior_subset hs + rw [(T_deriv (z := z) (k := k) hs').deriv] + exact div_neg_of_neg_of_pos + (mul_neg_of_neg_of_pos (mul_neg_of_neg_of_pos (neg_neg_of_pos (A_gap_pos hs')) + (QuadraticVariation.Q_pos hs')) (Jz_pos hs')) + (mul_pos hs' (sq_pos_of_pos (Az_pos hs'))) + +lemma conditionalA_deriv {k r A₀ s : ℝ} (hr : 0 < r) (hA : |A₀| < 1) (hs : 0 < s) : + HasDerivAt (fun a => A ((label ((a,r),A₀),a),s)) + (Az ((label ((k,r),A₀),k),s)*(T ((label ((k,r),A₀),k),s)-T ((label ((k,r),A₀),k),r))) k := by + have h := (A_analytic (q := ((label ((k,r),A₀),k),s)) hs).differentiableAt (by simp) + |>.hasFDerivAt.comp_hasDerivAt (f := fun a => ((label ((a,r),A₀),a),s)) k + (((label_curvature_deriv hr hA).prodMk (hasDerivAt_id k)).prodMk (hasDerivAt_const k s)) + rw [fderiv_model] at h + convert! h using 1 + have h₁ := ne_of_gt (Az_pos (z := label ((k,r),A₀)) (k := k) hs) + have h₂ := ne_of_gt (Az_pos (z := label ((k,r),A₀)) (k := k) hr) + dsimp only [T,Az,Ak] at h₁ h₂ ⊢ + field_simp [h₁,h₂] + ring + +lemma conditionalA_strictMono {r A₀ s : ℝ} (hr : 0 < r) (hA : |A₀| < 1) + (hs : 0 < s) (hsr : s < r) : StrictMono (fun k => A ((label ((k,r),A₀),k),s)) := by + apply strictMono_of_deriv_pos + intro k + rw [(conditionalA_deriv hr hA hs).deriv] + exact mul_pos (Az_pos hs) (sub_pos.mpr (T_strictAnti _ _ hs hr hsr)) +end QuinticLienard.QuadraticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CubicVariation.lean b/lean/OAI/Analysis/LienardCycles/CubicVariation.lean new file mode 100644 index 0000000000000000000000000000000000000000..a337e55162724022d74236c8c8c16fdbc3c6f11e --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CubicVariation.lean @@ -0,0 +1,68 @@ +import OAI.Analysis.LienardCycles.PositiveZero + +namespace OAI + +universe uP + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open scoped Topology +open Set Filter MeasureTheory +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.PositiveZero +open ScalarArcs ArcFamilies PositiveWidth PartialCalculus +variable {P : Type uP} [NormedAddCommGroup P] [NormedSpace ℝ P] [FiniteDimensional ℝ P] +variable (Φ : P × ℝ → ℝ) (hΦ : ∀ q, 0 f (q.1,s)) (field Φ (f q)) q.2) +include hΦ hloc +lemma cubic_direction {γ : ℝ → P} (hγ : ContDiff ℝ ω γ) {h r β : ℝ} + (hbase : ∀ p, Φ (p,h)=0) (hz : ∀ x, Φ (γ 0,x)=0) (hh : 0 Φ (γ q.1,q.2)) (0,x)=β*(x-h)^3/6) : + deriv (fun s => midpointAtWidth Φ ((γ s,h),r)) 0=β*r^6/105 := by + apply zero_direction Φ hΦ hloc hγ hbase hz hh hr + (B:=fun y => β*(r^6*y/48-r^4*y^3/48+r^2*y^5/80-y^7/336)) + · intro y hy + have hy2 : y^2≤r^2 := by nlinarith [mul_nonneg (show 0≤r-y by linarith [hy.2]) (show 0≤r+y by linarith [hy.1])] + rw [hβ _ (by linarith)] + convert ((((((hasDerivAt_id y).const_mul (r^6)).div_const 48).sub + ((((hasDerivAt_id y).pow 3).const_mul (r^4)).div_const 48)).add + ((((hasDerivAt_id y).pow 5).const_mul (r^2)).div_const 80)).sub + (((hasDerivAt_id y).pow 7).div_const 336)).const_mul β using 1 <;> + (first | rfl | (dsimp; ring)) + · ring + +noncomputable def pathMidpoint (γ : ℝ → P) (h : ℝ) (q : ℝ × ℝ) : ℝ := + midpointAtWidth Φ ((γ q.1,h),q.2) +lemma pathMidpoint_analytic {γ : ℝ → P} (hγ : ContDiff ℝ ω γ) {h θ r : ℝ} + (hh : 0 Φ (γ q.1,q.2)) (0,x)=β*(x-h)^3/6) : + first (second (pathMidpoint Φ γ h)) (0,r)=6*β*r^5/105 := by + have ha := pathMidpoint_analytic Φ hΦ hloc (θ:=0) hγ hh hr + rw [mixed_comm ha] + apply (second_hasDerivAt ((first_contDiffAt ha).differentiableAt (by simp))).unique + have hd : HasDerivAt (fun s => β*s^6/105) (6*β*r^5/105) r := by + convert (((hasDerivAt_id r).pow 6).const_mul β).div_const 105 using 1 <;> + (first | rfl | (dsimp; ring)) + apply hd.congr_of_eventuallyEq + filter_upwards [continuousAt_const.eventually_lt continuousAt_id hr] with s hs + have hd := (first_hasDerivAt ((pathMidpoint_analytic Φ hΦ hloc (θ:=0) hγ hh hs).differentiableAt (by simp))).deriv + simp only [id_eq] at hd + rw [←hd] + exact cubic_direction Φ hΦ hloc hγ hbase hz hh hs hβ +end QuinticLienard.PositiveZero + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CurvatureComparison.lean b/lean/OAI/Analysis/LienardCycles/CurvatureComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..c70732baf770d9cfe0709e06b05713b8cadf7cdd --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CurvatureComparison.lean @@ -0,0 +1,118 @@ +import OAI.Analysis.LienardCycles.CurvatureJets + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuadraticCoordinates +open PartialCalculus ModelEndpoint + +lemma transport_W_at_zero {d k r : ℝ} (hr : 0 < r) (hW : W ((d,k),r)=0) : + transport W ((d,k),r) = -G ((d,k),r)*(grr ((d,k),r)-Rr ((d,k),r)/R ((d,k),r)*gr ((d,k),r)) := by + have hR := ne_of_gt (R_pos (d := d) (k := k) hr) + rw [transport_W hr,hW,mul_zero,zero_add] + dsimp only [W] at hW + dsimp only [G] + field_simp + linear_combination gr ((d,k),r)*P ((d,k),r)*hW + +lemma characteristic_deriv {f : (ℝ × ℝ) × ℝ → ℝ} {z k r : ℝ} (hr : 0 < r) + (hf : ContDiffAt ℝ ω f ((ReferenceCharacteristic.J ((z,k),r),k),r)) : + HasDerivAt (fun s => f ((ReferenceCharacteristic.J ((z,k),s),k),s)) + (-transport f ((ReferenceCharacteristic.J ((z,k),r),k),r)/ + alpha ((ReferenceCharacteristic.J ((z,k),r),k),r)) r := by + have hd := (hf.differentiableAt (by simp)).hasFDerivAt.comp_hasDerivAt (f := fun s => ((ReferenceCharacteristic.J ((z,k),s),k),s)) r + (((ReferenceCharacteristic.J_deriv (z := z) (k := k) hr).prodMk (hasDerivAt_const r k)).prodMk (hasDerivAt_id r)) + rw [fderiv_model] at hd + convert! hd using 1 + have hg := ne_of_gt (H_gap_pos (d := ReferenceCharacteristic.J ((z,k),r)) (k := k) hr) + dsimp [transport,alpha,ReferenceCharacteristic.A,gap] + field_simp [ne_of_gt hr,hg] + ring + +lemma W_pos_of_curvature_pos {d k r : ℝ} (hk : 0 < k) (hr : 0 < r) : 0 < W ((d,k),r) := by + obtain ⟨z,hz⟩ := ReferenceCharacteristic.J_surjective d k hr + have he : ∀ᶠ s in 𝓝[>] (0:ℝ), 0 < s ∧ s < r ∧ + 0 < W ((ReferenceCharacteristic.J ((z,k),s),k),s) := by + filter_upwards [self_mem_nhdsWithin,(eventually_lt_nhds hr).filter_mono inf_le_left, + (ReferenceCharacteristic.model_tendsto z k).eventually (W_positive_near_zero z k)] with s hs hsr hW + exact ⟨hs,hsr,hW hs⟩ + obtain ⟨a,ha,har,hWa⟩ := he.exists + have hd (s : ℝ) (hs : s ∈ Icc a r) := + characteristic_deriv (ha.trans_le hs.1) (W_analytic (d := ReferenceCharacteristic.J ((z,k),s)) (k := k) (ha.trans_le hs.1)) + have hpos := RealAnalysis.positive_of_deriv_pos_at_zero har + (fun s hs => (hd s hs).continuousAt.continuousWithinAt) hd hWa.le (by + intro s hs hzero + have hs0 := ha.trans_le hs.1 + rw [transport_W_at_zero hs0 hzero,neg_mul,neg_neg] + exact div_pos (mul_pos (G_pos hs0) (gamma_source_sign hk hs0 hzero)) + (div_pos hs0 (H_gap_pos hs0))) + simpa only [hz] using hpos + +lemma P_reflection (d k : ℝ) {r : ℝ} (hr : 0 < r) : P ((-d,-k),r)=P ((d,k),r) := by + have h1 := (P_hasDerivAt (d := -d) (k := -k) hr).comp d (hasDerivAt_neg d) + have h2 := (P_hasDerivAt (d := d) (k := k) hr).neg + have hh := h1.unique (h2.congr_of_eventuallyEq (Eventually.of_forall (fun s => reflection s k hr))) + linarith +lemma Q_reflection (d k : ℝ) {r : ℝ} (hr : 0 < r) : Q ((-d,-k),r)=Q ((d,k),r) := by + have h1 := (Q_hasDerivAt (d := -d) (k := -k) hr).comp k (hasDerivAt_neg k) + have h2 := (Q_hasDerivAt (d := d) (k := k) hr).neg + have hh := h1.unique (h2.congr_of_eventuallyEq (Eventually.of_forall (fun s => reflection d s hr))) + linarith +lemma R_reflection (d k : ℝ) {r : ℝ} (hr : 0 < r) : R ((-d,-k),r)=R ((d,k),r) := by + exact (R_hasDerivAt hr).unique ((R_hasDerivAt hr).congr_of_eventuallyEq + ((eventually_gt_nhds hr).mono (fun s hs => P_reflection d k hs))) +lemma S_reflection (d k : ℝ) {r : ℝ} (hr : 0 < r) : S ((-d,-k),r)=S ((d,k),r) := by + exact (S_hasDerivAt hr).unique ((S_hasDerivAt hr).congr_of_eventuallyEq + ((eventually_gt_nhds hr).mono (fun s hs => Q_reflection d k hs))) +lemma Rr_reflection (d k : ℝ) {r : ℝ} (hr : 0 < r) : Rr ((-d,-k),r)=Rr ((d,k),r) := by + exact (Rr_hasDerivAt hr).unique ((Rr_hasDerivAt hr).congr_of_eventuallyEq + ((eventually_gt_nhds hr).mono (fun s hs => R_reflection d k hs))) +lemma Sr_reflection (d k : ℝ) {r : ℝ} (hr : 0 < r) : Sr ((-d,-k),r)=Sr ((d,k),r) := by + exact (Sr_hasDerivAt hr).unique ((Sr_hasDerivAt hr).congr_of_eventuallyEq + ((eventually_gt_nhds hr).mono (fun s hs => S_reflection d k hs))) +lemma W_reflection (d k : ℝ) {r : ℝ} (hr : 0 < r) : W ((-d,-k),r)=W ((d,k),r) := by + simp only [W,R_reflection d k hr,S_reflection d k hr,Rr_reflection d k hr,Sr_reflection d k hr] + +lemma W_nonneg {d k r : ℝ} (hr : 0 < r) : 0 ≤ W ((d,k),r) := by + rcases lt_trichotomy k 0 with hk | rfl | hk + · have hh := W_pos_of_curvature_pos (d := -d) (neg_pos.mpr hk) hr + simpa only [W_reflection d k hr] using hh.le + · have ht : Tendsto (fun a : ℝ => W ((d,a),r)) (𝓝[>] (0:ℝ)) (𝓝 (W ((d,0),r))) := + (((W_analytic (d := d) (k := 0) hr).continuousAt).comp (f := fun a : ℝ => ((d,a),r)) + ((continuousAt_const.prodMk continuousAt_id).prodMk continuousAt_const)).tendsto.mono_left inf_le_left + apply ge_of_tendsto ht + filter_upwards [self_mem_nhdsWithin] with a ha + exact (W_pos_of_curvature_pos (d := d) ha hr).le + · exact (W_pos_of_curvature_pos hk hr).le + +lemma G_deriv {d k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => G ((d,k),s)) (P ((d,k),r)*Sr ((d,k),r)-Q ((d,k),r)*Rr ((d,k),r)) r := by + convert! ((R_hasDerivAt hr).mul (Sr_hasDerivAt hr)).sub + ((S_hasDerivAt hr).mul (Rr_hasDerivAt hr)) using 1 + ring + +theorem model_inequality {d k r : ℝ} (hr : 0 < r) : + deriv (fun s => R ((d,k),s)/G ((d,k),s)) r ≤ 0 := by + have hG := G_pos (d := d) (k := k) hr + have hd := ((Rr_hasDerivAt (d := d) (k := k) hr).div (G_deriv hr) (ne_of_gt hG)) + change deriv ((fun s => R ((d,k),s)) / (fun s => G ((d,k),s))) r ≤ 0 + rw [hd.deriv] + have he : Rr ((d,k),r)*G ((d,k),r)-R ((d,k),r)*(P ((d,k),r)*Sr ((d,k),r)-Q ((d,k),r)*Rr ((d,k),r))= + -P ((d,k),r)*W ((d,k),r) := by dsimp [G,W]; ring + rw [he] + exact div_nonpos_of_nonpos_of_nonneg + (mul_nonpos_of_nonpos_of_nonneg (neg_nonpos.mpr (QuadraticVariation.P_pos hr).le) (W_nonneg hr)) (sq_nonneg _) +end QuinticLienard.QuadraticCoordinates + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CurvatureJets.lean b/lean/OAI/Analysis/LienardCycles/CurvatureJets.lean new file mode 100644 index 0000000000000000000000000000000000000000..b6cf9d0551b57c344a13e7fbcaaf1bda3fe3fa78 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CurvatureJets.lean @@ -0,0 +1,160 @@ +import OAI.Analysis.LienardCycles.EndpointSigns + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuadraticCoordinates +open PartialCalculus ModelEndpoint +noncomputable def ar := direction ((0,0),1) alpha +noncomputable def arr := direction ((0,0),1) ar +noncomputable def transport (f : (ℝ × ℝ) × ℝ → ℝ) (q : (ℝ × ℝ) × ℝ) : ℝ := + q.1.2*direction ((1,0),0) f q-alpha q*direction ((0,0),1) f q +lemma alpha_analytic {d k r : ℝ} (hr : 0 < r) : ContDiffAt ℝ ω alpha ((d,k),r) := by + unfold alpha gap + have hH := H_analytic (d := d) (k := k) hr + fun_prop (disch := exact ne_of_gt (H_gap_pos hr)) +lemma ar_analytic {d k r : ℝ} (hr : 0 < r) : ContDiffAt ℝ ω ar ((d,k),r) := + direction_contDiffAt (alpha_analytic hr) _ +lemma ar_deriv {d k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => alpha ((d,k),s)) (ar ((d,k),r)) r := + slice_r ((alpha_analytic hr).differentiableAt (by simp)) +lemma arr_deriv {d k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => ar ((d,k),s)) (arr ((d,k),r)) r := + slice_r ((ar_analytic hr).differentiableAt (by simp)) +lemma Rr_analytic {d k r : ℝ} (hr : 0 < r) : ContDiffAt ℝ ω Rr ((d,k),r) := + direction_contDiffAt (R_analytic hr) _ +lemma Sr_analytic {d k r : ℝ} (hr : 0 < r) : ContDiffAt ℝ ω Sr ((d,k),r) := + direction_contDiffAt (S_analytic hr) _ +lemma W_analytic {d k r : ℝ} (hr : 0 < r) : ContDiffAt ℝ ω W ((d,k),r) := + ((R_analytic hr).mul (Sr_analytic hr)).sub ((S_analytic hr).mul (Rr_analytic hr)) + +lemma transport_P {d k r : ℝ} (hr : 0 < r) : + transport P ((d,k),r)=gamma ((d,k),r)*P ((d,k),r)-1 := by + have hp := slice_d ((P_analytic (d := d) (k := k) hr).differentiableAt (by simp)) + have hH := P_hasDerivAt (d := d) (k := k) hr + have hg := ne_of_gt (H_gap_pos (d := d) (k := k) hr) + have ht := (((Hr_d_hasDerivAt (d := d) (k := k) hr).const_mul r).add hH).div + ((hasDerivAt_const d (r^2)).sub (hH.pow 2)) hg + have he : (fun s => k*P ((s,k),r)+s) =ᶠ[𝓝 d] + (fun s => (r*Hr ((s,k),r)+H ((s,k),r))/(r^2-(H ((s,k),r))^2)) := + Eventually.of_forall (fun s => width_identity (d := s) (k := k) hr) + have hh := ((hp.const_mul k).add (hasDerivAt_id d)).unique (ht.congr_of_eventuallyEq he) + dsimp [transport,alpha,gamma,gap] + change k*direction ((1,0),0) P ((d,k),r)-r/(r^2-H ((d,k),r)^2)*R ((d,k),r)=_ + dsimp at hh + norm_num only [Nat.cast_ofNat, show 2-1=1 from rfl, pow_one] at hh + field_simp [hg] at hh ⊢ + nlinarith only [hh] + +lemma transport_Q {d k r : ℝ} (hr : 0 < r) : + transport Q ((d,k),r)=gamma ((d,k),r)*Q ((d,k),r)-P ((d,k),r) := by + have hp := slice_k ((P_analytic (d := d) (k := k) hr).differentiableAt (by simp)) + have hH := Q_hasDerivAt (d := d) (k := k) hr + have hg := ne_of_gt (H_gap_pos (d := d) (k := k) hr) + have ht := (((Hr_k_hasDerivAt (d := d) (k := k) hr).const_mul r).add hH).div + ((hasDerivAt_const k (r^2)).sub (hH.pow 2)) hg + have he : (fun s => s*P ((d,s),r)+d) =ᶠ[𝓝 k] + (fun s => (r*Hr ((d,s),r)+H ((d,s),r))/(r^2-(H ((d,s),r))^2)) := + Eventually.of_forall (fun s => width_identity (d := d) (k := s) hr) + have hh := (((hasDerivAt_id k).mul hp).add_const d).unique (ht.congr_of_eventuallyEq he) + have hc : direction ((0,1),0) P ((d,k),r)=direction ((1,0),0) Q ((d,k),r) := + direction_comm (H_analytic hr) _ _ + rw [hc] at hh + dsimp [transport,alpha,gamma,gap] + change k*direction ((1,0),0) Q ((d,k),r)-r/(r^2-H ((d,k),r)^2)*S ((d,k),r)=_ + dsimp at hh + norm_num only [Nat.cast_ofNat, show 2-1=1 from rfl, pow_one] at hh + field_simp [hg] at hh ⊢ + nlinarith only [hh] + +lemma transport_deriv {f : (ℝ × ℝ) × ℝ → ℝ} {d k r : ℝ} (hr : 0 < r) + (hf : ContDiffAt ℝ ω f ((d,k),r)) : + HasDerivAt (fun s => transport f ((d,k),s)) + (transport (direction ((0,0),1) f) ((d,k),r)-ar ((d,k),r)*direction ((0,0),1) f ((d,k),r)) r := by + have hfd := direction_contDiffAt hf (((1,0),0) : (ℝ × ℝ) × ℝ) + have hfr := direction_contDiffAt hf (((0,0),1) : (ℝ × ℝ) × ℝ) + have hd := ((slice_r (hfd.differentiableAt (by simp))).const_mul k).sub + ((ar_deriv (d := d) (k := k) hr).mul (slice_r (hfr.differentiableAt (by simp)))) + have hc := direction_comm hf (((0,0),1) : (ℝ × ℝ) × ℝ) (((1,0),0) : (ℝ × ℝ) × ℝ) + convert! hd using 1 + dsimp [transport] + rw [hc] + ring + +lemma transport_R {d k r : ℝ} (hr : 0 < r) : + transport R ((d,k),r)=(gamma ((d,k),r)+ar ((d,k),r))*R ((d,k),r)+gr ((d,k),r)*P ((d,k),r) := by + have hh := (transport_deriv hr (P_analytic (d := d) (k := k) hr)).unique + ((((gr_deriv hr).mul (R_hasDerivAt hr)).sub_const 1).congr_of_eventuallyEq + ((eventually_gt_nhds hr).mono (fun s hs => transport_P (d := d) (k := k) hs))) + change transport R ((d,k),r)-ar ((d,k),r)*R ((d,k),r)=_ at hh + nlinarith only [hh] +lemma transport_S {d k r : ℝ} (hr : 0 < r) : + transport S ((d,k),r)=(gamma ((d,k),r)+ar ((d,k),r))*S ((d,k),r)+gr ((d,k),r)*Q ((d,k),r)-R ((d,k),r) := by + have hh := (transport_deriv hr (Q_analytic (d := d) (k := k) hr)).unique + ((((gr_deriv hr).mul (S_hasDerivAt hr)).sub (R_hasDerivAt hr)).congr_of_eventuallyEq + ((eventually_gt_nhds hr).mono (fun s hs => transport_Q (d := d) (k := k) hs))) + change transport S ((d,k),r)-ar ((d,k),r)*S ((d,k),r)=_ at hh + nlinarith only [hh] +lemma transport_Rr {d k r : ℝ} (hr : 0 < r) : + transport Rr ((d,k),r)=(gamma ((d,k),r)+2*ar ((d,k),r))*Rr ((d,k),r)+ + (2*gr ((d,k),r)+arr ((d,k),r))*R ((d,k),r)+grr ((d,k),r)*P ((d,k),r) := by + have hh := (transport_deriv hr (R_analytic (d := d) (k := k) hr)).unique + (((((gr_deriv hr).add (arr_deriv hr)).mul (Rr_hasDerivAt hr)).add + ((grr_deriv hr).mul (R_hasDerivAt hr))).congr_of_eventuallyEq + ((eventually_gt_nhds hr).mono (fun s hs => transport_R (d := d) (k := k) hs))) + change transport Rr ((d,k),r)-ar ((d,k),r)*Rr ((d,k),r)=_ at hh + dsimp at hh + nlinarith only [hh] +lemma transport_Sr {d k r : ℝ} (hr : 0 < r) : + transport Sr ((d,k),r)=(gamma ((d,k),r)+2*ar ((d,k),r))*Sr ((d,k),r)+ + (2*gr ((d,k),r)+arr ((d,k),r))*S ((d,k),r)+grr ((d,k),r)*Q ((d,k),r)-Rr ((d,k),r) := by + have hh := (transport_deriv hr (S_analytic (d := d) (k := k) hr)).unique + ((((((gr_deriv hr).add (arr_deriv hr)).mul (Sr_hasDerivAt hr)).add + ((grr_deriv hr).mul (S_hasDerivAt hr))).sub (Rr_hasDerivAt hr)).congr_of_eventuallyEq + ((eventually_gt_nhds hr).mono (fun s hs => transport_S (d := d) (k := k) hs))) + change transport Sr ((d,k),r)-ar ((d,k),r)*Sr ((d,k),r)=_ at hh + dsimp at hh + nlinarith only [hh] + +lemma direction_mul_sub {f g h j : (ℝ × ℝ) × ℝ → ℝ} {q : (ℝ × ℝ) × ℝ} + (hf : DifferentiableAt ℝ f q) (hg : DifferentiableAt ℝ g q) + (hh : DifferentiableAt ℝ h q) (hj : DifferentiableAt ℝ j q) (v : (ℝ × ℝ) × ℝ) : + direction v (fun q => f q*g q-h q*j q) q= + direction v f q*g q+f q*direction v g q-direction v h q*j q-h q*direction v j q := by + change (fderiv ℝ (f*g-h*j) q) v=_ + rw [fderiv_sub (hf.mul hg) (hh.mul hj),fderiv_mul hf hg,fderiv_mul hh hj] + dsimp only [direction] + simp only [sub_apply,add_apply,smul_apply,smul_eq_mul] + ring + +lemma transport_W {d k r : ℝ} (hr : 0 < r) : + transport W ((d,k),r)=(2*gamma ((d,k),r)+3*ar ((d,k),r))*W ((d,k),r)+ + gr ((d,k),r)*(P ((d,k),r)*Sr ((d,k),r)-Q ((d,k),r)*Rr ((d,k),r))- + grr ((d,k),r)*G ((d,k),r) := by + have hR := (R_analytic (d := d) (k := k) hr).differentiableAt (by simp) + have hS := (S_analytic (d := d) (k := k) hr).differentiableAt (by simp) + have hRr := (Rr_analytic (d := d) (k := k) hr).differentiableAt (by simp) + have hSr := (Sr_analytic (d := d) (k := k) hr).differentiableAt (by simp) + have he : transport W ((d,k),r)=transport R ((d,k),r)*Sr ((d,k),r)+R ((d,k),r)*transport Sr ((d,k),r)- + transport S ((d,k),r)*Rr ((d,k),r)-S ((d,k),r)*transport Rr ((d,k),r) := by + dsimp only [transport] + rw [show W = (fun q => R q*Sr q-S q*Rr q) from rfl] + rw [direction_mul_sub hR hSr hS hRr,direction_mul_sub hR hSr hS hRr] + ring + rw [he,transport_R hr,transport_S hr,transport_Rr hr,transport_Sr hr] + dsimp [W,G] + ring +end QuinticLienard.QuadraticCoordinates + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CurvaturePositive.lean b/lean/OAI/Analysis/LienardCycles/CurvaturePositive.lean new file mode 100644 index 0000000000000000000000000000000000000000..3dba5599128229783403a9a2992eec7644180c14 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CurvaturePositive.lean @@ -0,0 +1,87 @@ +import OAI.Analysis.LienardCycles.ActualSlopeComparison + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ActualCharacteristic +open PartialCalculus QuadraticCoordinates +noncomputable def w (a : Fin 6 → ℝ) (t s : ℝ) : ℝ := QuinticFit.w a (point a t s) +noncomputable def damp (a : Fin 6 → ℝ) (t s : ℝ) : ℝ := g a t s/s*QuinticFit.T a (point a t s) +noncomputable def feed (a : Fin 6 → ℝ) (t s : ℝ) : ℝ := g a t s/s*Cr (QuinticFit.fit a (point a t s))*(QuinticFit.lambda a (point a t s)-k a t s) +lemma w_analytic {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : ContDiffAt ℝ ω (w a t) r := + (QuinticFit.w_analytic a (base_spec he).1 (radius_pos he)).comp (f:=point a t) r (point_analytic he) +lemma damp_continuous {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : ContinuousAt (damp a t) r := by + have hT : ContinuousAt (fun s=>QuinticFit.T a (point a t s)) r := + (QuinticFit.T_analytic a (base_spec he).1 (radius_pos he)).continuousAt.comp (f:=point a t) (point_analytic he).continuousAt + exact (((continuousAt_id.pow 2).sub ((m_analytic he).continuousAt.pow 2)).div continuousAt_id (radius_pos he).ne').mul hT +lemma w_deriv {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : + HasDerivAt (w a t) (-damp a t r*w a t r+feed a t r) r := by + have hd := along_deriv he ((QuinticFit.w_analytic a (base_spec he).1 (radius_pos he)).differentiableAt (by simp)) + dsimp only [point] at hd + rw [QuinticFit.w_transport a (base_spec he).1 (radius_pos he)] at hd + convert! hd using 1 + dsimp only [damp,w,feed,k,point] + ring +lemma feed_nonneg {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) + (hthird : ∀ h, 0] (0:ℝ), 0] (0:ℝ), 0 (damp_continuous (adm_le he (hs.trans_le hu.1) hu.2)).continuousWithinAt) + (fun u hu => w_deriv (adm_le he (hs.trans_le hu.1) hu.2)) + (fun u hu => feed_nonneg (adm_le he (hs.trans hu.1) hu.2.le) hthird) hws +end QuinticLienard.ActualCharacteristic +namespace QuinticLienard.QuinticFit + +theorem kappa_width_pos {a : Fin 6 → ℝ} {h r : ℝ} (hh : 0QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) (p:=0) hh hr + have he : ActualCharacteristic.Adm a t r := ⟨h,hh,ht.1,ht.2⟩ + have hb : ActualCharacteristic.b a t r=h := PositiveWidth.base_eq _ + (fun _ h=>QuinticProfile.analytic a h) (QuinticProfile.local_flow a) hh ht.1 ht.2 + simpa only [ActualCharacteristic.w,ActualCharacteristic.point,hb] using + ActualCharacteristic.w_pos he hthird +end QuinticLienard.QuinticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CurvatureRange.lean b/lean/OAI/Analysis/LienardCycles/CurvatureRange.lean new file mode 100644 index 0000000000000000000000000000000000000000..496e205745448f545ded6ff900c3bcae65816cc0 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CurvatureRange.lean @@ -0,0 +1,136 @@ +import OAI.Analysis.LienardCycles.AxisSecants + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ActualCharacteristic +open PartialCalculus QuadraticCoordinates +lemma base_strictAnti {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) : StrictAntiOn (b a t) (Ioc 0 r) := by + apply strictAntiOn_of_deriv_neg (convex_Ioc 0 r) + (fun s hs=>(base_deriv (adm_le he hs.1 hs.2)).continuousAt.continuousWithinAt) + intro s hs + have he' := adm_le he (interior_subset hs).1 (interior_subset hs).2 + rw [(base_deriv he').deriv] + exact div_neg_of_neg_of_pos (neg_neg_of_pos (g_pos he')) (radius_pos he') +lemma rate_model_strictMono {κ s : ℝ} (hs : 0ReferenceCharacteristic.E ((z,κ),s)) := by + apply strictMono_of_deriv_pos + intro z + rw [(ReferenceCharacteristic.E_z_deriv (z:=z) (k:=κ) hs).deriv] + exact mul_pos (ReferenceCharacteristic.K_pos hs) (ReferenceCharacteristic.Az_pos hs) +lemma rate_label {a : Fin 6 → ℝ} {t κ s : ℝ} (he : Adm a t s) : + ReferenceCharacteristic.E ((label a t κ s,κ),s)=rate a t s := by + change 2*ReferenceCharacteristic.A ((label a t κ s,κ),s)/(s*(1-ReferenceCharacteristic.A ((label a t κ s,κ),s)^2))=_ + rw [label_spec he] + rfl +lemma label_factor_pos {a : Fin 6 → ℝ} {t κ s : ℝ} (he : Adm a t s) : + 0<(1-(A a t s)^2)/ReferenceCharacteristic.Az ((label a t κ s,κ),s) := by + have hh := (sq_lt_sq₀ (abs_nonneg _) (by norm_num : (0:ℝ)≤1)).mpr (A_abs_lt he) + have hg : 0<1-(A a t s)^2 := by nlinarith [sq_abs (A a t s)] + exact div_pos hg (ReferenceCharacteristic.Az_pos (radius_pos he)) +lemma not_all_error_neg {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) + (hn : ∀ s ∈ Ioo 0 r, err a t (QuinticFit.kappa a (point a t r)) s<0) : False := by + let κ := QuinticFit.kappa a (point a t r) + have hz : StrictAntiOn (label a t κ) (Ioc 0 r) := by + apply strictAntiOn_of_deriv_neg (convex_Ioc 0 r) + (fun s hs=>(label_deriv (κ:=κ) (adm_le he hs.1 hs.2)).continuousAt.continuousWithinAt) + intro s hs + rw [interior_Ioc] at hs + rw [(label_deriv (κ:=κ) (adm_le he hs.1 hs.2.le)).deriv] + rw [mul_div_assoc] + exact mul_neg_of_neg_of_pos (hn s hs) (label_factor_pos (adm_le he hs.1 hs.2.le)) + have hp : 0L a t s-ReferenceCharacteristic.L ((label a t κ r,κ),s)) (radius_pos he) + (by simpa only [sub_self] using ((small_limits he).2.1.sub + (ReferenceCharacteristic.L_tendsto_zero (label a t κ r) κ))) + apply strictMonoOn_of_deriv_pos (convex_Ioc 0 r) + (fun s hs=>((L_deriv (adm_le he hs.1 hs.2)).sub (ReferenceCharacteristic.L_deriv hs.1)).continuousAt.continuousWithinAt) + intro s hs + rw [interior_Ioc] at hs + rw [((L_deriv (adm_le he hs.1 hs.2.le)).sub (ReferenceCharacteristic.L_deriv (z:=label a t κ r) (k:=κ) hs.1)).deriv] + apply sub_pos.mpr + rw [←rate_label (κ:=κ) (adm_le he hs.1 hs.2.le)] + exact rate_model_strictMono hs.1 (hz ⟨hs.1,hs.2.le⟩ ⟨radius_pos he,le_rfl⟩ hs.2) + rw [L_matched he,sub_self] at hp + exact (lt_irrefl 0) hp +lemma not_all_error_pos {a : Fin 6 → ℝ} {t r : ℝ} (he : Adm a t r) + (hn : ∀ s ∈ Ioo 0 r, 0(label_deriv (κ:=κ) (adm_le he hs.1 hs.2)).continuousAt.continuousWithinAt) + intro s hs + rw [interior_Ioc] at hs + rw [(label_deriv (κ:=κ) (adm_le he hs.1 hs.2.le)).deriv] + rw [mul_div_assoc] + exact mul_pos (hn s hs) (label_factor_pos (adm_le he hs.1 hs.2.le)) + have hp : 0ReferenceCharacteristic.L ((label a t κ r,κ),s)-L a t s) (radius_pos he) + (by simpa only [sub_self] using ((ReferenceCharacteristic.L_tendsto_zero (label a t κ r) κ).sub (small_limits he).2.1)) + apply strictMonoOn_of_deriv_pos (convex_Ioc 0 r) + (fun s hs=>((ReferenceCharacteristic.L_deriv (z:=label a t κ r) (k:=κ) hs.1).sub (L_deriv (adm_le he hs.1 hs.2))).continuousAt.continuousWithinAt) + intro s hs + rw [interior_Ioc] at hs + rw [((ReferenceCharacteristic.L_deriv (z:=label a t κ r) (k:=κ) hs.1).sub (L_deriv (adm_le he hs.1 hs.2.le))).deriv] + apply sub_pos.mpr + rw [←rate_label (κ:=κ) (adm_le he hs.1 hs.2.le)] + exact rate_model_strictMono hs.1 (hz ⟨hs.1,hs.2.le⟩ ⟨radius_pos he,le_rfl⟩ hs.2) + rw [L_matched he,sub_self] at hp + exact (lt_irrefl 0) hp + +theorem curvature_lower {a : Fin 6 → ℝ} {t r C : ℝ} (he : Adm a t r) + (hC : ∀ u ∈ Icc (b a t r) t, C≤ScaledProfile.curvature a u) : + C≤QuinticFit.kappa a (point a t r) := by + by_contra! hn + let κ := QuinticFit.kappa a (point a t r) + apply not_all_error_neg he + intro s hs + have he' := adm_le he hs.1 hs.2.le + apply ScalarComparison.linear_negative_from_zero hs.1 + (fun u hu=>(coeff_continuous (κ:=κ) (adm_le he' hu.1 hu.2)).continuousWithinAt) + (fun u hu=>coeff_pos (κ:=κ) (adm_le he' hu.1 hu.2)) + (fun u hu=>err_deriv (κ:=κ) (adm_le he' hu.1 hu.2)) + (fun u hu=>?_) (err_tendsto he κ) + have heu := adm_le he hu.1 (hu.2.le.trans hs.2.le) + have hb : b a t r≤b a t u := (base_strictAnti he).antitoneOn + ⟨hu.1,hu.2.le.trans hs.2.le⟩ ⟨radius_pos he,le_rfl⟩ (hu.2.le.trans hs.2.le) + exact neg_neg_of_pos (mul_pos (div_pos (g_pos heu) (radius_pos heu)) + (sub_pos.mpr (hn.trans_le (hC _ ⟨hb,(base_spec heu).2.1.le⟩)))) + +theorem curvature_upper {a : Fin 6 → ℝ} {t r C : ℝ} (he : Adm a t r) + (hC : ∀ u ∈ Icc (b a t r) t, ScaledProfile.curvature a u≤C) : + QuinticFit.kappa a (point a t r)≤C := by + by_contra! hn + let κ := QuinticFit.kappa a (point a t r) + apply not_all_error_pos he + intro s hs + have he' := adm_le he hs.1 hs.2.le + have hneg : -err a t κ s<0 := by + apply ScalarComparison.linear_negative_from_zero (E:=fun u=> -err a t κ u) + (F:=fun u=>g a t u/u*(c a t u-κ)) hs.1 + (fun u hu=>(coeff_continuous (κ:=κ) (adm_le he' hu.1 hu.2)).continuousWithinAt) + (fun u hu=>coeff_pos (κ:=κ) (adm_le he' hu.1 hu.2)) + (fun u hu=>?_) (fun u hu=>?_) (by simpa using (err_tendsto he κ).neg) + · convert! (err_deriv (κ:=κ) (adm_le he' hu.1 hu.2)).neg using 1 + ring + · have heu := adm_le he hu.1 (hu.2.le.trans hs.2.le) + have hb : b a t r≤b a t u := (base_strictAnti he).antitoneOn + ⟨hu.1,hu.2.le.trans hs.2.le⟩ ⟨radius_pos he,le_rfl⟩ (hu.2.le.trans hs.2.le) + exact mul_neg_of_pos_of_neg (div_pos (g_pos heu) (radius_pos heu)) + (sub_neg.mpr ((hC _ ⟨hb,(base_spec heu).2.1.le⟩).trans_lt hn)) + linarith +end QuinticLienard.ActualCharacteristic + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CurvatureTransport.lean b/lean/OAI/Analysis/LienardCycles/CurvatureTransport.lean new file mode 100644 index 0000000000000000000000000000000000000000..4b702fde49ff02304ee6ac38a9dbc6c8fbe59700 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CurvatureTransport.lean @@ -0,0 +1,99 @@ +import OAI.Analysis.LienardCycles.ProfileComparison + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuadraticCoordinates +open PartialCalculus +noncomputable def C (q : (ℝ × ℝ) × ℝ) : ℝ := R q/G q +noncomputable def Cr : (ℝ × ℝ) × ℝ → ℝ := direction ((0,0),1) C +noncomputable def Cd : (ℝ × ℝ) × ℝ → ℝ := direction ((1,0),0) C +noncomputable def Ck : (ℝ × ℝ) × ℝ → ℝ := direction ((0,1),0) C +lemma G_analytic {d k r : ℝ} (hr : 0P (fit a q)) (h,r) := (P_analytic hr).comp (f:=fit a) (h,r) hf + have hQ : ContDiffAt ℝ ω (fun q=>Q (fit a q)) (h,r) := (Q_analytic hr).comp (f:=fit a) (h,r) hf + have hC : ContDiffAt ℝ ω (fun q=>C (fit a q)) (h,r) := (C_analytic hr).comp (f:=fit a) (h,r) hf + have hd : ContDiffAt ℝ ω (fun q=>Cd (fit a q)) (h,r) := (Cd_analytic hr).comp (f:=fit a) (h,r) hf + have hk : ContDiffAt ℝ ω (fun q=>Ck (fit a q)) (h,r) := (Ck_analytic hr).comp (f:=fit a) (h,r) hf + exact ((second_contDiffAt (α_analytic a hh hr)).add ((hC.mul hQ).div hP (QuadraticVariation.P_pos hr).ne')).sub + ((hk.sub ((hQ.div hP (QuadraticVariation.P_pos hr).ne').mul hd)).mul + ((lambda_analytic a hh hr).sub ((ScaledProfile.slope_analytic a hh).comp (h,r) contDiffAt_fst))) + +theorem w_transport (a : Fin 6 → ℝ) {h r : ℝ} (hh : 0.hasFDerivAt.comp_hasDerivAt (f:=fun s=>fit a (h,s)) r + (((second_hasDerivAt (hL.differentiableAt (by simp))).prodMk + (second_hasDerivAt (hK.differentiableAt (by simp)))).prodMk (hasDerivAt_id r)) + rw [fderiv_model] at hC + have hd := ((second_hasDerivAt ((first_contDiffAt hK).differentiableAt (by simp))).sub + ((second_hasDerivAt (hα.differentiableAt (by simp))).mul + (second_hasDerivAt ((second_contDiffAt hK).differentiableAt (by simp))))) + have hc := hC.neg.mul ((second_hasDerivAt (hL.differentiableAt (by simp))).sub_const (ScaledProfile.slope a h)) + have he : (fun s=>first (kappa a) (h,s)-α a (h,s)*second (kappa a) (h,s)) =ᶠ[𝓝 r] + (fun s=>-C (fit a (h,s))*(lambda a (h,s)-ScaledProfile.slope a h)) := by + filter_upwards [eventually_gt_nhds hr] with s hs + simpa only [D,C,neg_div] using (fit_transport a hh hs).2.1 + have hq := hd.unique (hc.congr_of_eventuallyEq he) + rw [←mixed_comm hK] at hq + have hp := (fit_transport a hh hr).1 + have hPe : P (fit a (h,r))≠0 := (QuadraticVariation.P_pos (d:=lambda a (h,r)) (k:=kappa a (h,r)) hr).ne' + change _ = -(second (lambda a) (h,r)*Cd (fit a (h,r))+second (kappa a) (h,r)*Ck (fit a (h,r))+1*Cr (fit a (h,r)))* + (lambda a (h,r)-ScaledProfile.slope a h)+-C (fit a (h,r))*second (lambda a) (h,r) at hq + have hlam : second (lambda a) (h,r)= -Q (fit a (h,r))/P (fit a (h,r))*w a (h,r) := by + rw [div_mul_eq_mul_div] + apply (eq_div_iff hPe).mpr + dsimp only [w] + nlinarith only [hp] + rw [hlam] at hq + dsimp only [D,T,w] at hq ⊢ + field_simp [hPe] at hq ⊢ + linear_combination hq +end QuinticLienard.QuinticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CycleIsolation.lean b/lean/OAI/Analysis/LienardCycles/CycleIsolation.lean new file mode 100644 index 0000000000000000000000000000000000000000..82ae3bfc55dd602849ec9da87f02ae8afdef8185 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CycleIsolation.lean @@ -0,0 +1,90 @@ +import OAI.Analysis.LienardCycles.OvalMatching + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open Set Filter Metric +open scoped Topology NNReal +open scoped Topology +open scoped Topology ContDiff NNReal +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff NNReal +namespace QuinticLienard +open ScaledProfile ScalarArcs AxisFlow RealAnalysis GlobalODE +lemma IsLimitCycle.matching {F : Polynomial ℝ} {a : Fin 6 → ℝ} + (hF : ∀ x,F.eval x=poly a x) {C : Set Plane} (hC : IsLimitCycle F C) : + ∃ r,IsIsolatedZeroOn (matchingDelta a (reflectX a)) (matchingDomain a (reflectX a)) r ∧ + (0,poly a 0+axisM a r+r) ∈ C := by + obtain ⟨z,S,T,hz,hS,hST,hp,hr,hl,hCz⟩ := hC.1.oval hF + obtain ⟨hr0,hd0,hb0⟩ := hz.oval_matching hF hp hr hl + let r0 := ((z 0).2-(z S).2)/2 + let b : ℝ → ℝ := fun r=>poly a 0+axisM a r+r + change b r0=(z 0).2 at hb0 + obtain ⟨U,hU,hCU,hiso⟩ := hC.2 + have hzU : range z ⊆ U := hCz ▸ hCU + obtain ⟨R,_,_,_,_,_,hne,hnear⟩ := hz.return_neighborhood hF hS hST hp hr hl + have hbc : ContinuousAt b r0 := + (continuousAt_const.add (axisM_analytic a hr0.1).continuousAt).add continuousAt_id + have hbt : Tendsto b (𝓝 r0) (𝓝 (z 0).2) := by simpa only [hb0] using hbc.tendsto + have hne' := hbt.eventually hne + have hnear' := hbt.eventually (hnear U hU hzU) + have isolated : ∀ᶠ r in 𝓝 r0,r ∈ matchingDomain a (reflectX a) → matchingDelta a (reflectX a) r=0 → r=r0 := by + filter_upwards [hne',hnear'] with r hn hu hmem hdelta + obtain ⟨hs,hst,hR,hL,hlo,hhi,hhi',hW⟩ := hn + have hfix := R.fixed_of_matching hF hmem hdelta hs hst hR hL hlo hhi hhi' hW + have hper : Function.Periodic (R.path (b r)) (R.σ (b r)) := flow_periodic_of_hit R.W R.lip R.bound hfix + have hsol : IsSolution F (R.path (b r)) := flow_true_of_closed R.W R.lip R.bound (hs.trans hst) hfix hW + have horbit : IsPeriodicOrbit F (range (R.path (b r))) := + ⟨R.path (b r),R.σ (b r),hsol,hs.trans hst,hper,hR.nonconstant,rfl⟩ + have hin : range (R.path (b r)) ⊆ U := periodic_range_subset hper (hs.trans hst) hu + have he : range (R.path (b r))=C := hiso _ horbit hin + have hstart : ((0,b r):Plane) ∈ range z := by + rw [←hCz,←he] + exact ⟨0,R.path_zero _⟩ + have hpoint := hz.oval_axis_positive hS hST hp hr hl hstart rfl hhi + have hbeq : b r=b r0 := (congrArg Prod.snd hpoint).trans hb0.symm + have hPeq : axisPeak a r=axisPeak a r0 := + (axisUpper_strictMono a).injOn (axisPeak_spec a hmem.1).1 (axisPeak_spec a hr0.1).1 + (by rw [(axisPeak_endpoints hmem.1).2,(axisPeak_endpoints hr0.1).2];exact hbeq) + calc r=axisWidth a (axisPeak a r) := (axisPeak_spec a hmem.1).2.symm + _=axisWidth a (axisPeak a r0) := congrArg (axisWidth a) hPeq + _=r0 := (axisPeak_spec a hr0.1).2 + obtain ⟨ε,hε,hball⟩ := Metric.mem_nhds_iff.mp isolated + refine ⟨r0,⟨hr0,hd0,ε,hε,?_⟩,?_⟩ + · intro r hr hmem hd + apply hball ?_ hmem hd + rw [Metric.mem_ball,Real.dist_eq,abs_lt] + constructor <;> linarith [hr.1,hr.2] + · rw [hCz] + refine ⟨0,Prod.ext hr.left ?_⟩ + exact hb0.symm +lemma limitCycle_encard_le_matching {F : Polynomial ℝ} {a : Fin 6 → ℝ} + (hF : ∀ x,F.eval x=poly a x) : + {C : Set Plane | IsLimitCycle F C}.encard ≤ + {r | IsIsolatedZeroOn (matchingDelta a (reflectX a)) (matchingDomain a (reflectX a)) r}.encard := by + classical + let f : {C : Set Plane // IsLimitCycle F C} → ℝ := fun C=>Classical.choose (C.prop.matching hF) + have hf (C : {C : Set Plane // IsLimitCycle F C}) : + IsIsolatedZeroOn (matchingDelta a (reflectX a)) (matchingDomain a (reflectX a)) (f C) ∧ + (0,poly a 0+axisM a (f C)+f C) ∈ (C : Set Plane) := Classical.choose_spec (C.prop.matching hF) + have hi : Function.Injective f := by + intro C D he + apply Subtype.ext + exact C.prop.1.eq_of_common D.prop.1 (hf C).2 (by rw [he];exact (hf D).2) + have hm : Set.MapsTo f univ {r | IsIsolatedZeroOn (matchingDelta a (reflectX a)) (matchingDomain a (reflectX a)) r} := + fun C _=>(hf C).1 + have H := Set.encard_le_encard_of_injOn hm hi.injOn + rw [Set.encard_univ] at H + exact H +end QuinticLienard + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CycleSection.lean b/lean/OAI/Analysis/LienardCycles/CycleSection.lean new file mode 100644 index 0000000000000000000000000000000000000000..d5f19433469b620aa7933d5e1fc60057312e7943 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CycleSection.lean @@ -0,0 +1,109 @@ +import OAI.Analysis.LienardCycles.UpperAssembly + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open Set Filter Metric +open scoped Topology NNReal +open scoped Topology ContDiff NNReal +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard +open ScaledProfile +lemma solution_unique_Icc (F : Polynomial ℝ) {z w : ℝ → Plane} {T : ℝ} + (hzc : ContinuousOn z (Icc 0 T)) (hwc : ContinuousOn w (Icc 0 T)) + (hz : ∀ t ∈ Icc 0 T,HasDerivAt z (vectorField F (z t)) t) + (hw : ∀ t ∈ Icc 0 T,HasDerivAt w (vectorField F (w t)) t) + (he : z 0=w 0) : EqOn z w (Icc 0 T) := by + obtain ⟨W,K,L,hK,_,hW⟩ := GlobalODE.exists_bounded_lipschitz_cutoff_on (vectorField F) + ((isCompact_Icc.image_of_continuousOn hzc).union (isCompact_Icc.image_of_continuousOn hwc)) isOpen_univ + (subset_univ _) ((vectorField_contDiff F).of_le (by simp)).contDiffOn + apply ODE_solution_unique_of_mem_Icc_right (v:=fun _=>W) (s:=fun _=>(univ : Set Plane)) + (fun _ _=>hK.lipschitzOnWith) hzc _ (fun _ _=>mem_univ _) hwc _ (fun _ _=>mem_univ _) he + · intro t ht + rw [(hW (z t) (Or.inl (mem_image_of_mem _ (Ico_subset_Icc_self ht)))).self_of_nhds] + exact (hz t (Ico_subset_Icc_self ht)).hasDerivWithinAt + · intro t ht + rw [(hW (w t) (Or.inr (mem_image_of_mem _ (Ico_subset_Icc_self ht)))).self_of_nhds] + exact (hw t (Ico_subset_Icc_self ht)).hasDerivWithinAt +lemma IsPeriodicOrbit.positive_axis {F : Polynomial ℝ} {a : Fin 6 → ℝ} + (hF : ∀ x,F.eval x=poly a x) {C : Set Plane} (hC : IsPeriodicOrbit F C) : + ∃ b,F.eval 0.abs) continuous_const)) + refine ⟨hC,U,hU,?_,?_⟩ + · intro p hp + by_cases hx : p.1=0 + · by_cases hy : p.2(hz.shift t) u) (by simpa using h0.trans ht.symm) + have hm : g s (τ s) ∈ range z := ⟨τ s+t,(he ⟨hT.le,le_rfl⟩).symm⟩ + apply hiso + exact (show IsPeriodicOrbit F (range z) from ⟨z,T,hz,hper,hp,hn,rfl⟩).axis_unique hF + hsb ⟨t,ht⟩ hm hx hy +end QuinticLienard + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/CycleTransform.lean b/lean/OAI/Analysis/LienardCycles/CycleTransform.lean new file mode 100644 index 0000000000000000000000000000000000000000..874882956f1ca8f55f6f8a97d772b05ca2b3ac87 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/CycleTransform.lean @@ -0,0 +1,67 @@ +import OAI.Analysis.LienardCycles.CaseOne + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open Set Filter Metric +open scoped Topology NNReal +open scoped Topology +open scoped Topology ContDiff NNReal +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology +namespace QuinticLienard +noncomputable def flipY : Plane ≃ₜ Plane where + toFun p := (p.1,-p.2) + invFun p := (p.1,-p.2) + left_inv p := by simp + right_inv p := by simp + continuous_toFun := continuous_fst.prodMk continuous_snd.neg + continuous_invFun := continuous_fst.prodMk continuous_snd.neg +@[simp] lemma flipY_apply (p : Plane) : flipY p=(p.1,-p.2) := rfl +@[simp] lemma flipY_symm : flipY.symm=flipY := rfl +lemma IsPeriodicOrbit.flipY {F : Polynomial ℝ} {C : Set Plane} (hC : IsPeriodicOrbit F C) : + IsPeriodicOrbit (-F) (QuinticLienard.flipY '' C) := by + obtain ⟨z,T,hz,hT,hp,hn,rfl⟩ := hC + refine ⟨reverseY z,T,hz.reverseY,hT,reverseY_periodic hp,reverseY_nonconstant hn,?_⟩ + ext p + constructor + · rintro ⟨q,⟨t,rfl⟩,rfl⟩ + exact ⟨-t,by simp [reverseY]⟩ + · rintro ⟨t,rfl⟩ + exact ⟨z (-t),mem_range_self _,rfl⟩ +lemma IsLimitCycle.map_homeomorph {F G : Polynomial ℝ} (e : Plane ≃ₜ Plane) + (he : ∀ C,IsPeriodicOrbit F C → IsPeriodicOrbit G (e '' C)) + (he' : ∀ C,IsPeriodicOrbit G C → IsPeriodicOrbit F (e.symm '' C)) + {C : Set Plane} (hC : IsLimitCycle F C) : IsLimitCycle G (e '' C) := by + obtain ⟨U,hU,hCU,hiso⟩ := hC.2 + refine ⟨he C hC.1,e '' U,e.isOpenMap U hU,image_mono hCU,?_⟩ + intro D hD hDU + have hi : e.symm '' D ⊆ U := by + rintro p ⟨q,hq,rfl⟩ + obtain ⟨v,hv,hvq⟩ := hDU hq + simpa only [←hvq,e.symm_apply_apply] using hv + have H := congrArg (fun S=>e '' S) (hiso _ (he' D hD) hi) + simpa only [image_image,Function.comp_def,e.apply_symm_apply,image_id'] using H +lemma IsLimitCycle.flipY {F : Polynomial ℝ} {C : Set Plane} (hC : IsLimitCycle F C) : + IsLimitCycle (-F) (QuinticLienard.flipY '' C) := by + apply hC.map_homeomorph QuinticLienard.flipY (fun _ h=>h.flipY) + intro D hD + simpa only [flipY_symm,neg_neg] using hD.flipY +lemma limitCycle_encard_neg (F : Polynomial ℝ) : + {C : Set Plane | IsLimitCycle F C}.encard={C : Set Plane | IsLimitCycle (-F) C}.encard := by + have h (G : Polynomial ℝ) : {C : Set Plane | IsLimitCycle G C}.encard≤{C : Set Plane | IsLimitCycle (-G) C}.encard := by + apply encard_le_encard_of_injOn (f:=fun C=>flipY '' C) (fun _ h=>h.flipY) + exact (Set.image_injective.mpr flipY.injective).injOn + exact le_antisymm (h F) (by simpa only [neg_neg] using h (-F)) +end QuinticLienard + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/EndpointAlgebra.lean b/lean/OAI/Analysis/LienardCycles/EndpointAlgebra.lean new file mode 100644 index 0000000000000000000000000000000000000000..e9fb4528ef57257352099904268fe96eb819af8e --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/EndpointAlgebra.lean @@ -0,0 +1,66 @@ +import OAI.Analysis.LienardCycles.ModelAlgebra + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +namespace QuinticLienard.EndpointAlgebra +open ModelAlgebra +noncomputable def X (m n l : ℝ) : ℝ := (l/m-1/n)/(1+l) +noncomputable def Z (m n l : ℝ) : ℝ := (l*m-n)/(1+l) +noncomputable def gamma (m n l : ℝ) : ℝ := (l/m^2+1/n^2)/(1+l) +noncomputable def Z1 (m n l w : ℝ) : ℝ := l*w*(m+n)/(1+l)^2 +noncomputable def Z2 (m n l w s : ℝ) : ℝ := + l*(s+3/2*w^2)*(m+n)/(1+l)^2+l*w/(1+l)-2*l^2*w^2*(m+n)/(1+l)^3 +noncomputable def X1 (m n l w : ℝ) : ℝ := l*(1/n^2-1/m^2)/(1+l)+Z1 m n l w/(m*n) +noncomputable def X2 (m n l w s : ℝ) : ℝ := + l*w*(1/n^2-1/m^2)/(1+l)^2+l*(2/m^3-2*l/n^3)/(1+l)+ + Z2 m n l w s/(m*n)-Z1 m n l w*(n+m*l)/(m^2*n^2) +noncomputable def N0 (m n l : ℝ) : ℝ := l/m^2+1/n^2 +noncomputable def N1 (m n l w : ℝ) : ℝ := l*w/m^2-2*l/m^3-2*l/n^3 +noncomputable def N2 (m n l w s : ℝ) : ℝ := + l*(s+3/2*w^2)/m^2-4*l*w/m^3+6*l/m^4-2*l*w/n^3+6*l^2/n^4 +noncomputable def gamma1 (m n l w : ℝ) : ℝ := N1 m n l w/(1+l)-N0 m n l*l*w/(1+l)^2 +noncomputable def gamma2 (m n l w s : ℝ) : ℝ := + N2 m n l w s/(1+l)-2*N1 m n l w*l*w/(1+l)^2- + N0 m n l*l*(s+3/2*w^2)/(1+l)^2+2*N0 m n l*(l*w)^2/(1+l)^3 + +lemma determinant {m n l w s : ℝ} (hm : m ≠ 0) (hn : n ≠ 0) (hl : 1+l ≠ 0) : + X1 m n l w*Z2 m n l w s-Z1 m n l w*X2 m n l w s = + l^2*(m+n)^2/(m^2*n^2*(1+l)^3)*dStar m n l w s := by + dsimp [X1,X2,Z1,Z2,dStar] + field_simp + ring + +lemma gamma_identity {m n l w s : ℝ} (hm : m ≠ 0) (hn : n ≠ 0) + (hl : 1+l ≠ 0) (hmn : m+n ≠ 0) : + (m-n)*(gamma2 m n l w s*X1 m n l w-gamma1 m n l w*X2 m n l w s)- + l*(m+n)^2/((1+l)*m^2*n^2)*(wStar m n l-w)*X1 m n l w = + l^2*(m+n)^2*(m^2+n^2)/((1+l)^3*m^4*n^4)*dStar m n l w s := by + dsimp [gamma2,gamma1,N0,N1,N2,X1,X2,Z1,Z2,wStar,dStar] + field_simp + ring + +lemma gamma_factor {m n l w s : ℝ} (hm : m ≠ 0) (hn : n ≠ 0) + (hl : 1+l ≠ 0) (hmn : m+n ≠ 0) (hneq : m ≠ n) + (hx : X1 m n l w ≠ 0) (hd : dStar m n l w s=0) : + gamma2 m n l w s-X2 m n l w s/X1 m n l w*gamma1 m n l w = + l*(m+n)^2/((1+l)*m^2*n^2)*(wStar m n l-w)/(m-n) := by + have hh := gamma_identity (w := w) (s := s) hm hn hl hmn + rw [hd,mul_zero] at hh + have hdiff : m-n ≠ 0 := sub_ne_zero.mpr hneq + apply (eq_div_iff hdiff).mpr + field_simp [hx] at * + nlinarith only [hh] + +end QuinticLienard.EndpointAlgebra + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/EndpointComparison.lean b/lean/OAI/Analysis/LienardCycles/EndpointComparison.lean new file mode 100644 index 0000000000000000000000000000000000000000..15532dd3de0e3de61783d3c608a14c6ac3315240 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/EndpointComparison.lean @@ -0,0 +1,70 @@ +import OAI.Analysis.LienardCycles.RiccatiComparison + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter +open scoped Topology +open Set Filter MeasureTheory +open scoped Topology ContDiff + +namespace QuinticLienard.ModelEndpoint +open Set Filter +open scoped Topology ContDiff +open PartialCalculus QuadraticCoordinates RiccatiJets + +theorem LowerChart.formulas {d k r : ℝ} (hr : 0 < r) (c : LowerChart d k r) : + schwarzian c.upper (m ((d,k),r)) = + k*(m ((d,k),r)+n ((d,k),r)*(ell ((d,k),r))^2)+ + (d^2/2)*((ell ((d,k),r))^2-1)- + d*(1/m ((d,k),r)+(ell ((d,k),r))^2/n ((d,k),r))+ + (3/2)*((ell ((d,k),r))^2/(n ((d,k),r))^2-1/(m ((d,k),r))^2) ∧ + deriv (deriv c.upper) (m ((d,k),r))/ell ((d,k),r) = + 1/m ((d,k),r)-ell ((d,k),r)/n ((d,k),r)+d*(1+ell ((d,k),r))+ + k*m ((d,k),r)*(∫ y in (-m ((d,k),r))..(n ((d,k),r)), + 1/(Riccati.multiplier (fun s => c.solution (m ((d,k),r),s)) (k/2) d + (-m ((d,k),r)) y)^2) := by + have hn : 0 < c.upper (m ((d,k),r)) := by rw [c.upper_base]; exact n_pos hr + have hl : 0 < deriv c.upper (m ((d,k),r)) := by + rw [c.upper_derivative.deriv]; exact ell_pos hr + have hu : ∀ y ∈ Icc (-m ((d,k),r)) (c.upper (m ((d,k),r))), + ContDiffAt ℝ ω c.solution (m ((d,k),r),y) := by + rw [c.upper_base]; exact c.solution_analytic + have he : ∀ y ∈ Icc (-m ((d,k),r)) (c.upper (m ((d,k),r))), + ∀ᶠ q in 𝓝 (m ((d,k),r),y), HasDerivAt (fun s => c.solution (q.1,s)) + (d*c.solution q+(k/2)*(c.solution q)^2-q.2) q.2 := by + rw [c.upper_base]; exact c.equation + have hh := RiccatiJets.endpoint_formulas (m_pos hr) hn hl + (c.solution_continuous _) hu he c.upper_analytic c.lower_zero c.upper_zero + rw [c.upper_base,c.upper_derivative.deriv] at hh + constructor + · convert hh.1 using 1; ring + · convert hh.2.1 using 1; ring + +theorem LowerChart.variation_bound {d k r ν : ℝ} (hr : 0 < r) + (hk : 0 < k) (hd : d < 0) (hν : 0 ≤ ν) + (hνsq : ν^2=d^2/4-(k/2)*m ((d,k),r)) (c : LowerChart d k r) : + deriv (deriv c.upper) (m ((d,k),r))/ell ((d,k),r) ≤ + 1/m ((d,k),r)-ell ((d,k),r)/n ((d,k),r)+d*ell ((d,k),r)-2*ν := by + have he : ∀ y ∈ Icc (-m ((d,k),r)) (n ((d,k),r)), + HasDerivAt (fun s => c.solution (m ((d,k),r),s)) + (d*c.solution (m ((d,k),r),y)+(k/2)*(c.solution (m ((d,k),r),y))^2-y) y := + fun y hy => (c.equation y hy).self_of_nhds + have hz : c.solution (m ((d,k),r),-m ((d,k),r))=0 := c.lower_zero.self_of_nhds + have hf := (c.formulas hr).2 + have hv := Riccati.endpoint_variation_bound (c.solution_continuous _) + (show 0 < k/2 by linarith) (m_pos hr) (n_pos hr) hd hν hνsq hz he + (show deriv (deriv c.upper) (m ((d,k),r))/ell ((d,k),r) = + 1/m ((d,k),r)-ell ((d,k),r)/n ((d,k),r)+d*(1+ell ((d,k),r))+ + 2*(k/2)*m ((d,k),r)*(∫ y in (-m ((d,k),r))..(n ((d,k),r)), + 1/(Riccati.multiplier (fun s => c.solution (m ((d,k),r),s)) (k/2) d + (-m ((d,k),r)) y)^2) by convert hf using 1; ring) + exact hv + +end QuinticLienard.ModelEndpoint + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/EndpointJets.lean b/lean/OAI/Analysis/LienardCycles/EndpointJets.lean new file mode 100644 index 0000000000000000000000000000000000000000..a0bebc1abeb4e42323ca356a84c4224419350c42 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/EndpointJets.lean @@ -0,0 +1,172 @@ +import OAI.Analysis.LienardCycles.EndpointScaling + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ModelEndpoint +open PartialCalculus QuadraticCoordinates +noncomputable def Xj (q : (ℝ × ℝ) × ℝ) := EndpointAlgebra.X1 (m q) (n q) (ell q) (w q) +noncomputable def Xjj (q : (ℝ × ℝ) × ℝ) := EndpointAlgebra.X2 (m q) (n q) (ell q) (w q) (sch q) +noncomputable def Zj (q : (ℝ × ℝ) × ℝ) := EndpointAlgebra.Z1 (m q) (n q) (ell q) (w q) +noncomputable def Zjj (q : (ℝ × ℝ) × ℝ) := EndpointAlgebra.Z2 (m q) (n q) (ell q) (w q) (sch q) +noncomputable def gj (q : (ℝ × ℝ) × ℝ) := EndpointAlgebra.gamma1 (m q) (n q) (ell q) (w q) +noncomputable def gjj (q : (ℝ × ℝ) × ℝ) := EndpointAlgebra.gamma2 (m q) (n q) (ell q) (w q) (sch q) +noncomputable def gr := direction ((0,0),1) QuadraticCoordinates.gamma +noncomputable def grr := direction ((0,0),1) gr + +lemma endpoint_identities {d k r : ℝ} (hr : 0 < r) : + EndpointAlgebra.X (m ((d,k),r)) (n ((d,k),r)) (ell ((d,k),r))=k*P ((d,k),r)+d ∧ + EndpointAlgebra.Z (m ((d,k),r)) (n ((d,k),r)) (ell ((d,k),r))=d*P ((d,k),r)+3*k*Q ((d,k),r) ∧ + EndpointAlgebra.gamma (m ((d,k),r)) (n ((d,k),r)) (ell ((d,k),r))=QuadraticCoordinates.gamma ((d,k),r) := by + have hm := ne_of_gt (m_pos (d := d) (k := k) hr) + have hn := ne_of_gt (n_pos (d := d) (k := k) hr) + have hv := ne_of_gt (mr_pos (d := d) (k := k) hr) + have hg := ne_of_gt (H_gap_pos (d := d) (k := k) hr) + dsimp only [m,n] at hm hn + constructor + · rw [width_identity hr] + dsimp [EndpointAlgebra.X,m,n,ell,gap] + field_simp + ring + constructor + · rw [← euler_identity hr] + dsimp [EndpointAlgebra.Z,m,n,ell] + field_simp + ring + · dsimp [EndpointAlgebra.gamma,QuadraticCoordinates.gamma,m,n,ell,gap] + field_simp + ring + +lemma m_deriv {d k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => m ((d,k),s)) (1-Hr ((d,k),r)) r := + (hasDerivAt_id r).sub (Hr_hasDerivAt hr) +lemma n_deriv {d k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => n ((d,k),s)) (ell ((d,k),r)*(1-Hr ((d,k),r))) r := by + convert! (hasDerivAt_id r).add (Hr_hasDerivAt (d := d) (k := k) hr) using 1 + dsimp [ell] + field_simp [ne_of_gt (mr_pos (d := d) (k := k) hr)] +lemma ell_deriv_scaled {d k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => ell ((d,k),s)) (ell ((d,k),r)*w ((d,k),r)*(1-Hr ((d,k),r))) r := by + have hm := ne_of_gt (mr_pos (d := d) (k := k) hr) + have hp : 1+Hr ((d,k),r) ≠ 0 := by + have hh := (abs_lt.mp (Hr_abs_lt (d := d) (k := k) hr)).1 + linarith + convert! ell_deriv (d := d) (k := k) hr using 1 + dsimp [ell,w] + field_simp +lemma w_deriv_scaled {d k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => w ((d,k),s)) ((sch ((d,k),r)+(1/2)*(w ((d,k),r))^2)*(1-Hr ((d,k),r))) r := by + simpa only [mul_comm] using w_deriv (d := d) (k := k) hr + +lemma endpoint_first_derivs {d k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => EndpointAlgebra.X (m ((d,k),s)) (n ((d,k),s)) (ell ((d,k),s))) + (Xj ((d,k),r)*(1-Hr ((d,k),r))) r ∧ + HasDerivAt (fun s => EndpointAlgebra.Z (m ((d,k),s)) (n ((d,k),s)) (ell ((d,k),s))) + (Zj ((d,k),r)*(1-Hr ((d,k),r))) r ∧ + HasDerivAt (fun s => EndpointAlgebra.gamma (m ((d,k),s)) (n ((d,k),s)) (ell ((d,k),s))) + (gj ((d,k),r)*(1-Hr ((d,k),r))) r := by + have hm := ne_of_gt (m_pos (d := d) (k := k) hr) + have hn := ne_of_gt (n_pos (d := d) (k := k) hr) + have hl : 1+ell ((d,k),r) ≠ 0 := by have := ell_pos (d := d) (k := k) hr; positivity + exact ⟨EndpointAlgebra.X_reparam (m_deriv hr) (n_deriv hr) (ell_deriv_scaled hr) rfl rfl rfl hm hn hl, + EndpointAlgebra.Z_reparam (m_deriv hr) (n_deriv hr) (ell_deriv_scaled hr) rfl rfl rfl hl, + EndpointAlgebra.gamma_reparam (m_deriv hr) (n_deriv hr) (ell_deriv_scaled hr) rfl rfl rfl hm hn hl⟩ + +lemma endpoint_second_derivs {d k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => Xj ((d,k),s)) (Xjj ((d,k),r)*(1-Hr ((d,k),r))) r ∧ + HasDerivAt (fun s => Zj ((d,k),s)) (Zjj ((d,k),r)*(1-Hr ((d,k),r))) r ∧ + HasDerivAt (fun s => gj ((d,k),s)) (gjj ((d,k),r)*(1-Hr ((d,k),r))) r := by + have hm := ne_of_gt (m_pos (d := d) (k := k) hr) + have hn := ne_of_gt (n_pos (d := d) (k := k) hr) + have hl : 1+ell ((d,k),r) ≠ 0 := by have := ell_pos (d := d) (k := k) hr; positivity + exact ⟨EndpointAlgebra.X1_reparam (m_deriv hr) (n_deriv hr) (ell_deriv_scaled hr) + (w_deriv_scaled hr) rfl rfl rfl rfl hm hn hl, + EndpointAlgebra.Z1_reparam (m_deriv hr) (n_deriv hr) (ell_deriv_scaled hr) + (w_deriv_scaled hr) rfl rfl rfl rfl hl, + EndpointAlgebra.gamma1_reparam (m_deriv hr) (n_deriv hr) (ell_deriv_scaled hr) + (w_deriv_scaled hr) rfl rfl rfl rfl hm hn hl⟩ + +lemma gamma_analytic {d k r : ℝ} (hr : 0 < r) : + ContDiffAt ℝ ω QuadraticCoordinates.gamma ((d,k),r) := by + unfold QuadraticCoordinates.gamma gap + have hH := H_analytic (d := d) (k := k) hr + have hHr := Hr_analytic (d := d) (k := k) hr + fun_prop (disch := exact pow_ne_zero _ (ne_of_gt (H_gap_pos hr))) +lemma gr_analytic {d k r : ℝ} (hr : 0 < r) : ContDiffAt ℝ ω gr ((d,k),r) := + direction_contDiffAt (gamma_analytic hr) _ +lemma gr_deriv {d k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => QuadraticCoordinates.gamma ((d,k),s)) (gr ((d,k),r)) r := + slice_r ((gamma_analytic hr).differentiableAt (by simp)) +lemma grr_deriv {d k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => gr ((d,k),s)) (grr ((d,k),r)) r := + slice_r ((gr_analytic hr).differentiableAt (by simp)) + +lemma first_jets {d k r : ℝ} (hr : 0 < r) : + Xj ((d,k),r)*(1-Hr ((d,k),r))=k*R ((d,k),r) ∧ + Zj ((d,k),r)*(1-Hr ((d,k),r))=d*R ((d,k),r)+3*k*S ((d,k),r) ∧ + gj ((d,k),r)*(1-Hr ((d,k),r))=gr ((d,k),r) := by + have he : ∀ᶠ s in 𝓝 r, 0 < s := eventually_gt_nhds hr + have h1 := (endpoint_first_derivs (d := d) (k := k) hr).1 + have h2 := (endpoint_first_derivs (d := d) (k := k) hr).2.1 + have h3 := (endpoint_first_derivs (d := d) (k := k) hr).2.2 + constructor + · have ht := (((R_hasDerivAt (d := d) (k := k) hr).const_mul k).add_const d).congr_of_eventuallyEq + (he.mono (fun s hs => (endpoint_identities (d := d) (k := k) hs).1)) + exact h1.unique ht + constructor + · have ht := (((R_hasDerivAt (d := d) (k := k) hr).const_mul d).add + ((S_hasDerivAt (d := d) (k := k) hr).const_mul (3*k))).congr_of_eventuallyEq + (he.mono (fun s hs => (endpoint_identities (d := d) (k := k) hs).2.1)) + exact h2.unique ht + · exact h3.unique ((gr_deriv (d := d) (k := k) hr).congr_of_eventuallyEq + (he.mono (fun s hs => (endpoint_identities (d := d) (k := k) hs).2.2))) + +lemma second_jets {d k r : ℝ} (hr : 0 < r) : + Xjj ((d,k),r)*(1-Hr ((d,k),r))^2-Xj ((d,k),r)*Hrr ((d,k),r)=k*Rr ((d,k),r) ∧ + Zjj ((d,k),r)*(1-Hr ((d,k),r))^2-Zj ((d,k),r)*Hrr ((d,k),r)=d*Rr ((d,k),r)+3*k*Sr ((d,k),r) ∧ + gjj ((d,k),r)*(1-Hr ((d,k),r))^2-gj ((d,k),r)*Hrr ((d,k),r)=grr ((d,k),r) := by + have he : ∀ᶠ s in 𝓝 r, 0 < s := eventually_gt_nhds hr + have hm := (Hrr_hasDerivAt (d := d) (k := k) hr).const_sub 1 + have h1 := ((endpoint_second_derivs (d := d) (k := k) hr).1.mul hm).unique + (((Rr_hasDerivAt (d := d) (k := k) hr).const_mul k).congr_of_eventuallyEq + (he.mono (fun s hs => (first_jets (d := d) (k := k) hs).1))) + have h2 := ((endpoint_second_derivs (d := d) (k := k) hr).2.1.mul hm).unique + ((((Rr_hasDerivAt (d := d) (k := k) hr).const_mul d).add + ((Sr_hasDerivAt (d := d) (k := k) hr).const_mul (3*k))).congr_of_eventuallyEq + (he.mono (fun s hs => (first_jets (d := d) (k := k) hs).2.1))) + have h3 := ((endpoint_second_derivs (d := d) (k := k) hr).2.2.mul hm).unique + ((grr_deriv (d := d) (k := k) hr).congr_of_eventuallyEq + (he.mono (fun s hs => (first_jets (d := d) (k := k) hs).2.2))) + constructor + · nlinarith only [h1] + constructor + · nlinarith only [h2] + · nlinarith only [h3] + +lemma Xj_pos {d k r : ℝ} (hk : 0 < k) (hr : 0 < r) : 0 < Xj ((d,k),r) := by + have h := (first_jets (d := d) (k := k) hr).1 + exact pos_of_mul_pos_left (h.symm ▸ mul_pos hk (R_pos hr)) (mr_pos hr).le + +lemma determinant_W {d k r : ℝ} (hr : 0 < r) : + (Xj ((d,k),r)*Zjj ((d,k),r)-Zj ((d,k),r)*Xjj ((d,k),r))*(1-Hr ((d,k),r))^3= + 3*k^2*W ((d,k),r) := by + obtain ⟨hx,hz,_⟩ := first_jets (d := d) (k := k) hr + obtain ⟨hxx,hzz,_⟩ := second_jets (d := d) (k := k) hr + dsimp only [W] + linear_combination (Zjj ((d,k),r)*(1-Hr ((d,k),r))^2-Hrr ((d,k),r)*Zj ((d,k),r))*hx + + (-Xjj ((d,k),r)*(1-Hr ((d,k),r))^2+Hrr ((d,k),r)*Xj ((d,k),r))*hz + + k*R ((d,k),r)*hzz-(d*R ((d,k),r)+3*k*S ((d,k),r))*hxx +end QuinticLienard.ModelEndpoint + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/EndpointScaling.lean b/lean/OAI/Analysis/LienardCycles/EndpointScaling.lean new file mode 100644 index 0000000000000000000000000000000000000000..a60b9302f5d6b43d0e25f52a91cc80eed6c9f865 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/EndpointScaling.lean @@ -0,0 +1,137 @@ +import OAI.Analysis.LienardCycles.RealAnalysis + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology ContDiff +open Set Filter +open scoped Topology + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.EndpointAlgebra + +lemma X_reparam {M N L : ℝ → ℝ} {x m n l w a : ℝ} + (hM : HasDerivAt M a x) (hN : HasDerivAt N (l*a) x) (hL : HasDerivAt L (l*w*a) x) + (hMv : M x=m) (hNv : N x=n) (hLv : L x=l) (hm : m ≠ 0) (hn : n ≠ 0) (hl : 1+l ≠ 0) : + HasDerivAt (fun t => X (M t) (N t) (L t)) (X1 m n l w*a) x := by + have hm' : M x ≠ 0 := by rwa [hMv] + have hn' : N x ≠ 0 := by rwa [hNv] + have hl' : 1+L x ≠ 0 := by rwa [hLv] + have hd := ((hL.div hM hm').sub ((hasDerivAt_const x (1:ℝ)).div hN hn')).div + (hL.const_add 1) hl' + convert! hd using 1 + simp only [Pi.div_apply,Pi.sub_apply,hMv,hNv,hLv] + dsimp [X1,Z1] + field_simp + ring + +lemma Z_reparam {M N L : ℝ → ℝ} {x m n l w a : ℝ} + (hM : HasDerivAt M a x) (hN : HasDerivAt N (l*a) x) (hL : HasDerivAt L (l*w*a) x) + (hMv : M x=m) (hNv : N x=n) (hLv : L x=l) (hl : 1+l ≠ 0) : + HasDerivAt (fun t => Z (M t) (N t) (L t)) (Z1 m n l w*a) x := by + have hl' : 1+L x ≠ 0 := by rwa [hLv] + have hd := ((hL.mul hM).sub hN).div (hL.const_add 1) hl' + convert! hd using 1 + simp only [Pi.sub_apply,Pi.mul_apply,hMv,hNv,hLv] + dsimp [Z1] + field_simp + ring + +lemma N0_reparam {M N L : ℝ → ℝ} {x m n l w a : ℝ} + (hM : HasDerivAt M a x) (hN : HasDerivAt N (l*a) x) (hL : HasDerivAt L (l*w*a) x) + (hMv : M x=m) (hNv : N x=n) (hLv : L x=l) (hm : m ≠ 0) (hn : n ≠ 0) : + HasDerivAt (fun t => N0 (M t) (N t) (L t)) (N1 m n l w*a) x := by + have hm' : M x ≠ 0 := by rwa [hMv] + have hn' : N x ≠ 0 := by rwa [hNv] + have hd := (hL.div (hM.pow 2) (pow_ne_zero _ hm')).add + ((hasDerivAt_const x (1:ℝ)).div (hN.pow 2) (pow_ne_zero _ hn')) + convert! hd using 1 + simp only [Pi.pow_apply,hMv,hNv,hLv] + dsimp [N1] + field_simp + ring + +lemma gamma_reparam {M N L : ℝ → ℝ} {x m n l w a : ℝ} + (hM : HasDerivAt M a x) (hN : HasDerivAt N (l*a) x) (hL : HasDerivAt L (l*w*a) x) + (hMv : M x=m) (hNv : N x=n) (hLv : L x=l) (hm : m ≠ 0) (hn : n ≠ 0) (hl : 1+l ≠ 0) : + HasDerivAt (fun t => gamma (M t) (N t) (L t)) (gamma1 m n l w*a) x := by + have hl' : 1+L x ≠ 0 := by rwa [hLv] + have hd := (N0_reparam hM hN hL hMv hNv hLv hm hn).div (hL.const_add 1) hl' + convert! hd using 1 + simp only [hMv,hNv,hLv] + dsimp [gamma1] + field_simp + +lemma Z1_reparam {M N L W : ℝ → ℝ} {x m n l w s a : ℝ} + (hM : HasDerivAt M a x) (hN : HasDerivAt N (l*a) x) (hL : HasDerivAt L (l*w*a) x) + (hW : HasDerivAt W ((s+(1/2)*w^2)*a) x) + (hMv : M x=m) (hNv : N x=n) (hLv : L x=l) (hWv : W x=w) (hl : 1+l ≠ 0) : + HasDerivAt (fun t => Z1 (M t) (N t) (L t) (W t)) (Z2 m n l w s*a) x := by + have hl' : 1+L x ≠ 0 := by rwa [hLv] + have hd := (((hL.mul hW).mul (hM.add hN)).div + ((hL.const_add 1).pow 2) (pow_ne_zero _ hl')) + convert! hd using 1 + simp only [Pi.add_apply,Pi.mul_apply,Pi.pow_apply,hMv,hNv,hLv,hWv] + dsimp [Z2] + field_simp + ring + +lemma X1_reparam {M N L W : ℝ → ℝ} {x m n l w s a : ℝ} + (hM : HasDerivAt M a x) (hN : HasDerivAt N (l*a) x) (hL : HasDerivAt L (l*w*a) x) + (hW : HasDerivAt W ((s+(1/2)*w^2)*a) x) + (hMv : M x=m) (hNv : N x=n) (hLv : L x=l) (hWv : W x=w) + (hm : m ≠ 0) (hn : n ≠ 0) (hl : 1+l ≠ 0) : + HasDerivAt (fun t => X1 (M t) (N t) (L t) (W t)) (X2 m n l w s*a) x := by + have hm' : M x ≠ 0 := by rwa [hMv] + have hn' : N x ≠ 0 := by rwa [hNv] + have hl' : 1+L x ≠ 0 := by rwa [hLv] + have hB := ((hasDerivAt_const x (1:ℝ)).div (hN.pow 2) (pow_ne_zero _ hn')).sub + ((hasDerivAt_const x (1:ℝ)).div (hM.pow 2) (pow_ne_zero _ hm')) + have hd := ((hL.mul hB).div (hL.const_add 1) hl').add + ((Z1_reparam hM hN hL hW hMv hNv hLv hWv hl).div (hM.mul hN) (mul_ne_zero hm' hn')) + convert! hd using 1 + simp only [Pi.div_apply,Pi.sub_apply,Pi.mul_apply,Pi.pow_apply,hMv,hNv,hLv,hWv] + dsimp [X2] + field_simp + ring + +lemma N1_reparam {M N L W : ℝ → ℝ} {x m n l w s a : ℝ} + (hM : HasDerivAt M a x) (hN : HasDerivAt N (l*a) x) (hL : HasDerivAt L (l*w*a) x) + (hW : HasDerivAt W ((s+(1/2)*w^2)*a) x) + (hMv : M x=m) (hNv : N x=n) (hLv : L x=l) (hWv : W x=w) (hm : m ≠ 0) (hn : n ≠ 0) : + HasDerivAt (fun t => N1 (M t) (N t) (L t) (W t)) (N2 m n l w s*a) x := by + have hm' : M x ≠ 0 := by rwa [hMv] + have hn' : N x ≠ 0 := by rwa [hNv] + have hd := (((hL.mul hW).div (hM.pow 2) (pow_ne_zero _ hm')).sub + ((hL.const_mul 2).div (hM.pow 3) (pow_ne_zero _ hm'))).sub + ((hL.const_mul 2).div (hN.pow 3) (pow_ne_zero _ hn')) + convert! hd using 1 + simp only [Pi.mul_apply,Pi.pow_apply,hMv,hNv,hLv,hWv] + dsimp [N2] + field_simp + ring + +lemma gamma1_reparam {M N L W : ℝ → ℝ} {x m n l w s a : ℝ} + (hM : HasDerivAt M a x) (hN : HasDerivAt N (l*a) x) (hL : HasDerivAt L (l*w*a) x) + (hW : HasDerivAt W ((s+(1/2)*w^2)*a) x) + (hMv : M x=m) (hNv : N x=n) (hLv : L x=l) (hWv : W x=w) + (hm : m ≠ 0) (hn : n ≠ 0) (hl : 1+l ≠ 0) : + HasDerivAt (fun t => gamma1 (M t) (N t) (L t) (W t)) (gamma2 m n l w s*a) x := by + have hl' : 1+L x ≠ 0 := by rwa [hLv] + have hd := ((N1_reparam hM hN hL hW hMv hNv hLv hWv hm hn).div (hL.const_add 1) hl').sub + ((((N0_reparam hM hN hL hMv hNv hLv hm hn).mul hL).mul hW).div + ((hL.const_add 1).pow 2) (pow_ne_zero _ hl')) + convert! hd using 1 + simp only [Pi.mul_apply,Pi.pow_apply,hMv,hNv,hLv,hWv] + dsimp [gamma2] + field_simp + ring +end QuinticLienard.EndpointAlgebra + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/EndpointSigns.lean b/lean/OAI/Analysis/LienardCycles/EndpointSigns.lean new file mode 100644 index 0000000000000000000000000000000000000000..2537eb9196c5114e098494542b19fc40c621cf97 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/EndpointSigns.lean @@ -0,0 +1,112 @@ +import OAI.Analysis.LienardCycles.SchwarzianScaling + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ModelEndpoint +open PartialCalculus QuadraticCoordinates + +lemma sch_eq {d k r : ℝ} : sch ((d,k),r)= + ModelAlgebra.schwarzian (m ((d,k),r)) (n ((d,k),r)) (ell ((d,k),r)) (k/2) d := by + dsimp [sch,ModelAlgebra.schwarzian] + ring + +lemma actual_zero_sign {d k r : ℝ} (hk : 0 < k) (hr : 0 < r) + (hZero : ModelAlgebra.dStar (m ((d,k),r)) (n ((d,k),r)) (ell ((d,k),r)) + (w ((d,k),r)) (sch ((d,k),r))=0) : + m ((d,k),r) ≠ n ((d,k),r) ∧ + 0 < (ModelAlgebra.wStar (m ((d,k),r)) (n ((d,k),r)) (ell ((d,k),r))-w ((d,k),r))/ + (m ((d,k),r)-n ((d,k),r)) := by + have hm := m_pos (d := d) (k := k) hr + have hn := n_pos (d := d) (k := k) hr + have hl := ell_pos (d := d) (k := k) hr + apply ModelAlgebra.zero_sign_unscaled hm hn hl (show 0 < k/2 by linarith) + · intro hmn + have hH : 0 ≤ H ((d,k),r) := by dsimp [m,n] at hmn; linarith + have hHr := Hr_pos_of_H_nonneg hk hr hH + refine ⟨?_,w_pos_of_H_nonneg hk hr hH⟩ + exact (lt_div_iff₀ (mr_pos hr)).mpr (by linarith) + · intro hnm + apply d_neg_of_H_neg hk hr + dsimp [m,n] at hnm + linarith + · intro hnm hl1 + have hH : H ((d,k),r) < 0 := by dsimp [m,n] at hnm; linarith + have hHr : 0 ≤ Hr ((d,k),r) := by + have hh := (le_div_iff₀ (mr_pos (d := d) (k := k) hr)).mp hl1 + linarith + exact w_nonneg_of_H_neg_Hr_nonneg hk hr hH hHr + · change d < EndpointAlgebra.X (m ((d,k),r)) (n ((d,k),r)) (ell ((d,k),r)) + rw [(endpoint_identities hr).1] + have hh := mul_pos hk (QuadraticVariation.P_pos (d := d) (k := k) hr) + linarith + · intro hnm hdisc + have hH : H ((d,k),r) < 0 := by dsimp [m,n] at hnm; linarith + have hd := d_neg_of_H_neg hk hr hH + obtain ⟨c⟩ := lower_chart (d := d) (k := k) hr + have hh := c.variation_bound hr hk hd (Real.sqrt_nonneg (d^2/4-(k/2)*m ((d,k),r))) + (Real.sq_sqrt (show 0 ≤ d^2/4-(k/2)*m ((d,k),r) by linarith)) + rwa [c.log_deriv hr] at hh + · rwa [← sch_eq] + +lemma dStar_zero_of_W_zero {d k r : ℝ} (hr : 0 < r) (hW : W ((d,k),r)=0) : + ModelAlgebra.dStar (m ((d,k),r)) (n ((d,k),r)) (ell ((d,k),r)) + (w ((d,k),r)) (sch ((d,k),r))=0 := by + have hm := m_pos (d := d) (k := k) hr + have hn := n_pos (d := d) (k := k) hr + have hl := ell_pos (d := d) (k := k) hr + have hln : 1+ell ((d,k),r) ≠ 0 := by positivity + have hh := determinant_W (d := d) (k := k) hr + rw [hW,mul_zero] at hh + have hd : Xj ((d,k),r)*Zjj ((d,k),r)-Zj ((d,k),r)*Xjj ((d,k),r)=0 := + (mul_eq_zero.mp hh).resolve_right (pow_ne_zero _ (ne_of_gt (mr_pos hr))) + rw [Xj,Xjj,Zj,Zjj,EndpointAlgebra.determinant (ne_of_gt hm) (ne_of_gt hn) hln] at hd + exact (mul_eq_zero.mp hd).resolve_left (ne_of_gt (by positivity)) + +lemma gamma_zero_sign {d k r : ℝ} (hk : 0 < k) (hr : 0 < r) (hW : W ((d,k),r)=0) : + 0 < gjj ((d,k),r)-Xjj ((d,k),r)/Xj ((d,k),r)*gj ((d,k),r) := by + have hm := m_pos (d := d) (k := k) hr + have hn := n_pos (d := d) (k := k) hr + have hl := ell_pos (d := d) (k := k) hr + have hln : 1+ell ((d,k),r) ≠ 0 := by positivity + have hmn : m ((d,k),r)+n ((d,k),r) ≠ 0 := ne_of_gt (add_pos hm hn) + have hd := dStar_zero_of_W_zero hr hW + obtain ⟨hne,hpos⟩ := actual_zero_sign hk hr hd + have hf := EndpointAlgebra.gamma_factor (ne_of_gt hm) (ne_of_gt hn) hln hmn hne + (ne_of_gt (Xj_pos hk hr)) hd + change 0 < EndpointAlgebra.gamma2 _ _ _ _ _ - EndpointAlgebra.X2 _ _ _ _ _ / + EndpointAlgebra.X1 _ _ _ _ * EndpointAlgebra.gamma1 _ _ _ _ + rw [hf, mul_div_assoc] + exact mul_pos (by positivity) hpos + +lemma gamma_source_sign {d k r : ℝ} (hk : 0 < k) (hr : 0 < r) (hW : W ((d,k),r)=0) : + 0 < grr ((d,k),r)-Rr ((d,k),r)/R ((d,k),r)*gr ((d,k),r) := by + have ha := mr_pos (d := d) (k := k) hr + have hR := R_pos (d := d) (k := k) hr + have hX := Xj_pos (d := d) hk hr + obtain ⟨hx,_,hg⟩ := first_jets (d := d) (k := k) hr + obtain ⟨hxx,_,hgg⟩ := second_jets (d := d) (k := k) hr + have heq : grr ((d,k),r)-Rr ((d,k),r)/R ((d,k),r)*gr ((d,k),r)= + (1-Hr ((d,k),r))^2*(gjj ((d,k),r)-Xjj ((d,k),r)/Xj ((d,k),r)*gj ((d,k),r)) := by + apply (mul_right_inj' (ne_of_gt (mul_pos hR hX))).mp + field_simp + linear_combination -R ((d,k),r)*Xj ((d,k),r)*hgg + + Xj ((d,k),r)*Rr ((d,k),r)*hg + + gj ((d,k),r)*R ((d,k),r)*hxx - + gj ((d,k),r)*Rr ((d,k),r)*hx + rw [heq] + exact mul_pos (sq_pos_of_pos ha) (gamma_zero_sign hk hr hW) +end QuinticLienard.ModelEndpoint + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ExcursionAxis.lean b/lean/OAI/Analysis/LienardCycles/ExcursionAxis.lean new file mode 100644 index 0000000000000000000000000000000000000000..ef45d9794cde380749be497bbf8c0afa4284a595 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ExcursionAxis.lean @@ -0,0 +1,67 @@ +import OAI.Analysis.LienardCycles.OpenArchAxis + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open Set Filter Metric +open scoped Topology NNReal +open scoped Topology ContDiff NNReal +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard +open ScaledProfile ScalarArcs AxisFlow +lemma IsRightExcursion.axis_peak {F : Polynomial ℝ} {a : Fin 6 → ℝ} + (hF : ∀ x,F.eval x=poly a x) {z : ℝ → Plane} {s t : ℝ} + (hz : IsSolution F z) (hn : ∃ s t,z s≠z t) (he : IsRightExcursion z s t) : + ∃ H ∈ transversePeaks a,axisEndpoint a false H=(z t).2 ∧ axisEndpoint a true H=(z s).2 := by + obtain ⟨u,huc,hul,hur,hud,_⟩ := he.graph hF hz + have hu : IsOpenArch (φ a) u (z t).2 (z s).2 := + ⟨he.y_lt hz,huc,hul,hur,fun y hy=>(hud y hy).1,fun y hy=>(hud y hy).2⟩ + obtain ⟨H,hH,hp,hpeak,_⟩ := hu.peak_exists + obtain ⟨hl,hr⟩ := hu.axis_endpoints (φ_smooth a) (φ_continuous a).continuousOn hH hp hpeak + have hs := he.endpoint_signs hz hn + refine ⟨H,⟨hH,?_,?_⟩,hl,hr⟩ + · change axisLower (φ a) H(axisEndpoint_analytic a false ht.1 ht.2.1.ne).continuousAt.continuousWithinAt) + intro t ht + exact axisEndpoint_sign a false (interior_subset ht).1 (interior_subset ht).2.1.ne +lemma axisUpper_strictMono (a : Fin 6 → ℝ) : StrictMonoOn (axisEndpoint a true) (transversePeaks a) := by + apply strictMonoOn_of_deriv_pos (convex_iff_ordConnected.mpr (transversePeaks_ordConnected a)) + (fun t ht=>(axisEndpoint_analytic a true ht.1 ht.2.2.ne').continuousAt.continuousWithinAt) + intro t ht + exact axisEndpoint_sign a true (interior_subset ht).1 (interior_subset ht).2.2.ne' +lemma axis_order {a : Fin 6 → ℝ} {s t : ℝ} (hs : s ∈ transversePeaks a) (ht : t ∈ transversePeaks a) : + (axisEndpoint a true s≤axisEndpoint a true t ↔ axisEndpoint a false t≤axisEndpoint a false s) := by + constructor + · intro h + have hst : s≤t := by + by_contra! hn + exact (not_lt_of_ge h) (axisUpper_strictMono a ht hs hn) + exact (axisLower_strictAnti a).antitoneOn hs ht hst + · intro h + have hst : s≤t := by + by_contra! hn + exact (not_lt_of_ge h) (axisLower_strictAnti a ht hs hn) + exact (axisUpper_strictMono a).monotoneOn hs ht hst +end AxisFlow +end QuinticLienard + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ExcursionGraph.lean b/lean/OAI/Analysis/LienardCycles/ExcursionGraph.lean new file mode 100644 index 0000000000000000000000000000000000000000..cf60362c184b68287ee10c39ce9b09b099c7f25a --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ExcursionGraph.lean @@ -0,0 +1,85 @@ +import OAI.Analysis.LienardCycles.IntervalInverse + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open Set Filter Metric +open scoped Topology ContDiff +open scoped Topology NNReal +open scoped Topology ContDiff NNReal +open Set Filter +open scoped Topology + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard +open RealAnalysis ScaledProfile AxisFlow + +structure IsRightExcursion (z : ℝ → Plane) (s t : ℝ) : Prop where + lt : s(z v).2) (Icc s t) := by + apply strictAntiOn_of_deriv_neg (convex_Icc s t) hz.continuous.snd.continuousOn + intro v hv + have hv' : v ∈ Ioo s t := by simpa using hv + rw [(hz.y_deriv v).deriv] + exact neg_neg_of_pos (he.positive v hv') +lemma IsRightExcursion.y_lt {F : Polynomial ℝ} {z : ℝ → Plane} {s t : ℝ} + (hz : IsSolution F z) (he : IsRightExcursion z s t) : (z t).2<(z s).2 := + he.y_strictAnti hz ⟨le_rfl,he.lt.le⟩ ⟨he.lt.le,le_rfl⟩ he.lt +lemma IsRightExcursion.graph {F : Polynomial ℝ} {a : Fin 6 → ℝ} + (hF : ∀ x,F.eval x=poly a x) {z : ℝ → Plane} {s t : ℝ} + (hz : IsSolution F z) (he : IsRightExcursion z s t) : + ∃ u : ℝ → ℝ, Continuous u ∧ u (z t).2=0 ∧ u (z s).2=0 ∧ + (∀ y ∈ Ioo (z t).2 (z s).2,0(z v).2) (Icc s t) (Icc (z t).2 (z s).2) := by + refine ⟨?_,hanti.injOn,?_⟩ + · intro v hv + exact ⟨hanti.antitoneOn hv ⟨he.lt.le,le_rfl⟩ hv.2, + hanti.antitoneOn ⟨le_rfl,he.lt.le⟩ hv hv.1⟩ + · intro y hy + exact intermediate_value_Icc' he.lt.le hz.continuous.snd.continuousOn hy + obtain ⟨τ,hτc,hτmem,hτr,hτl⟩ := continuous_interval_inverse hylt.le hz.continuous.snd.continuousOn hb + have hτint (y : ℝ) (hy : y ∈ Ioo (z t).2 (z s).2) : τ y ∈ Ioo s t := by + have hm := hτmem y + refine ⟨lt_of_le_of_ne hm.1 ?_,lt_of_le_of_ne hm.2 ?_⟩ + · intro hn + have hh := hτr y (Ioo_subset_Icc_self hy) + rw [←hn] at hh + exact hy.2.ne hh.symm + · intro hn + have hh := hτr y (Ioo_subset_Icc_self hy) + rw [hn] at hh + exact hy.1.ne hh + let u : ℝ → ℝ := fun y=>(z (τ y)).1^2/2 + have hu : ∀ v ∈ Icc s t,u (z v).2=(z v).1^2/2 := fun v hv=>by dsimp [u];rw [hτl v hv] + refine ⟨u,(hz.continuous.fst.comp hτc).pow 2 |>.div_const 2,?_,?_,?_,hu⟩ + · rw [hu t ⟨he.lt.le,le_rfl⟩,he.right];norm_num + · rw [hu s ⟨le_rfl,he.lt.le⟩,he.left];norm_num + · intro y hy + have hx := he.positive (τ y) (hτint y hy) + have hτd : HasDerivAt τ (-(z (τ y)).1)⁻¹ y := + HasDerivAt.of_local_left_inverse hτc.continuousAt (hz.y_deriv (τ y)) (neg_ne_zero.mpr hx.ne') + ((show ∀ᶠ v in 𝓝 y,v ∈ Ioo (z t).2 (z s).2 from Ioo_mem_nhds hy.1 hy.2).mono fun v hv=>hτr v (Ioo_subset_Icc_self hv)) + refine ⟨div_pos (sq_pos_of_pos hx) (by norm_num),?_⟩ + convert! (((hz.x_deriv (τ y)).pow 2).div_const 2).comp y hτd using 1 + symm + change (2*(z (τ y)).1^(2-1)*((z (τ y)).2-F.eval (z (τ y)).1)/2)*(-(z (τ y)).1)⁻¹=φ a ((z (τ y)).1^2/2)-y + rw [AxisFlow.φ_square a hx.le,←hF,hτr y (Ioo_subset_Icc_self hy)] + field_simp [hx.ne'] + ring +end QuinticLienard + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ExcursionSigns.lean b/lean/OAI/Analysis/LienardCycles/ExcursionSigns.lean new file mode 100644 index 0000000000000000000000000000000000000000..e2aae6acaaefdc03f98261f7ed5853783b9a593d --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ExcursionSigns.lean @@ -0,0 +1,73 @@ +import OAI.Analysis.LienardCycles.ExcursionGraph + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open Set Filter Metric +open scoped Topology NNReal +open scoped Topology ContDiff NNReal +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard +lemma HasDerivAt.pos_right_of_pos {f : ℝ → ℝ} {s d : ℝ} + (hd : HasDerivAt f d s) (h0 : f s=0) (hpos : 0] s,0 (not_lt_of_ge (sub_nonneg.mpr hst.le)) h.2) |>.1 +lemma HasDerivAt.nonneg_of_pos_right {f : ℝ → ℝ} {s t d : ℝ} + (hd : HasDerivAt f d s) (h0 : f s=0) (hst : s⟨⟨h.1.1.le,h.1.2⟩,h.2⟩) + have hne : S.Nonempty := ⟨s+T,⟨by constructor <;> linarith,hp s ▸ hs⟩⟩ + obtain ⟨t,ht,hmin⟩ := hS.isCompact.exists_isMinOn hne continuous_id.continuousOn + have hst : s] s,s (f (p z,t z)-f (p z,(0:ℝ)))/t z) l (𝓝 (D (0,1))) := by + have hmap : Tendsto (fun z => ((p z,t z),(p z,(0:ℝ)))) l (𝓝 ((p₀,(0:ℝ)),(p₀,(0:ℝ)))) := + (hp.prodMk_nhds ht).prodMk_nhds (hp.prodMk_nhds tendsto_const_nhds) + have ho := hf.isLittleO.comp_tendsto hmap + have he (z : α) : D ((p z,t z)-(p z,(0:ℝ)))=t z*D (0,1) := by + rw [show (p z,t z)-(p z,(0:ℝ))=t z • (0,1) by ext <;> simp] + simp only [map_smul,smul_eq_mul] + have ho' : (fun z => f (p z,t z)-f (p z,(0:ℝ))-t z*D (0,1)) =o[l] t := by + apply Asymptotics.isLittleO_iff.mpr + intro c hc + filter_upwards [ho.bound hc] with z hz + simp only [Function.comp_apply] at hz + rw [he z] at hz + simpa only [Prod.mk_sub_mk,sub_self,sub_zero, + Prod.norm_def,norm_zero,max_eq_right (norm_nonneg (t z))] using hz + have hh := ho'.tendsto_div_nhds_zero.add_const (D (0,1)) + simp only [zero_add] at hh + apply hh.congr' + filter_upwards [hne] with z hz + field_simp [hz] + ring + +end QuinticLienard.SmallWidth + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/FiniteFlow.lean b/lean/OAI/Analysis/LienardCycles/FiniteFlow.lean new file mode 100644 index 0000000000000000000000000000000000000000..fb5c75accde80750a82eb49dedeb76f77fe893b1 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/FiniteFlow.lean @@ -0,0 +1,84 @@ +import OAI.Analysis.LienardCycles.AxisCases + +namespace OAI + +universe uE + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff NNReal +namespace QuinticLienard.GlobalODE +variable {E : Type uE} [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E] +theorem analytic_cutoff_along_compact_solution [FiniteDimensional ℝ E] + (V : E → E) {U : Set E} (hU : IsOpen U) (hV : ContDiffOn ℝ 1 V U) + (hloc : ∀ x ∈ U, ∃ f : E × ℝ → E, ContDiffAt ℝ ω f (x,0) ∧ + ∀ᶠ p in 𝓝 (x,(0:ℝ)), f (p.1,0) = p.1 ∧ + HasDerivAt (fun t => f (p.1,t)) (V (f p)) p.2) + {γ : ℝ → E} {a b c : ℝ} (ha : a < c) (hb : c < b) + (hγ : Continuous γ) (hγU : ∀ y ∈ Icc a b, γ y ∈ U) + (hγd : ∀ y ∈ Icc a b, HasDerivAt γ (V (γ y)) y) : + ∃ (W : E → E) (K L : ℝ≥0) (hK : LipschitzWith K W) (hL : ∀ x, ‖W x‖ ≤ L), + (∀ y ∈ Icc a b, flow W hK hL (γ c) (y-c) = γ y) ∧ + (∀ y ∈ Icc a b, ContDiffAt ℝ ω (fun p : E × ℝ=>flow W hK hL p.1 p.2) (γ c,y-c)) ∧ + ∀ y ∈ Icc a b, ∀ᶠ p : E × ℝ in 𝓝 (γ c,y-c), + W (flow W hK hL p.1 p.2)=V (flow W hK hL p.1 p.2) := by + obtain ⟨W,K,L,hK,hL,hW⟩ := exists_bounded_lipschitz_cutoff_on V + (isCompact_Icc.image hγ) hU (by rintro _ ⟨y,hy,rfl⟩; exact hγU y hy) hV + let f : E × ℝ → E := fun p => flow W hK hL p.1 p.2 + have hmatch : ∀ y ∈ Icc a b, f (γ c,y-c) = γ y := by + apply ODE_solution_unique_of_mem_Icc + (v := fun _ => W) (s := fun _ => Set.univ) (K := K) + (fun _ _ => hK.lipschitzOnWith) ⟨ha,hb⟩ + ((continuous_flow W hK hL).comp (by fun_prop)).continuousOn + _ (fun _ _ => mem_univ _) hγ.continuousOn _ (fun _ _ => mem_univ _) + (by simp) + · intro y _ + simpa [f,Function.comp_def] using + (flow_deriv W hK hL (γ c) (y-c)).scomp y ((hasDerivAt_id y).sub_const c) + · intro y hy + rw [(hW (γ y) ⟨y,Ioo_subset_Icc_self hy,rfl⟩).self_of_nhds] + exact hγd y (Ioo_subset_Icc_self hy) + have hlocalW (y : ℝ) (hy : y ∈ Icc a b) : + ContDiffAt ℝ ω f (γ y,0) := by + obtain ⟨g,hgd,hge⟩ := hloc (γ y) (hγU y hy) + have hg0 : g (γ y,0) = γ y := hge.self_of_nhds.1 + have heV : ∀ᶠ p in 𝓝 (γ y,(0:ℝ)), W (g p) = V (g p) := by + have ht := hgd.continuousAt.tendsto + rw [hg0] at ht + exact ht.eventually (hW (γ y) ⟨y,hy,rfl⟩) + have heq : g =ᶠ[𝓝 (γ y,(0:ℝ))] f := by + apply local_family_eq W hK hL (γ y) g + filter_upwards [hge,heV] with p hp hp' + exact ⟨hp.1,hp' ▸ hp.2⟩ + exact hgd.congr_of_eventuallyEq heq.symm + have hd : ∀ y ∈ Icc a b, ContDiffAt ℝ ω f (γ c,y-c) := by + have hh := analytic_flow_on_trajectory W hK hL (γ c) + (I := Icc (a-c) (b-c)) isPreconnected_Icc + (show (0:ℝ) ∈ Icc (a-c) (b-c) by constructor <;> linarith) + (fun s hs => by + have hs' : s+c ∈ Icc a b := by constructor <;> linarith [hs.1,hs.2] + have heq : flow W hK hL (γ c) s = γ (s+c) := by + simpa [f] using hmatch (s+c) hs' + rw [heq] + exact hlocalW (s+c) hs') + exact fun y hy => hh (y-c) (by constructor <;> linarith [hy.1,hy.2]) + refine ⟨W,K,L,hK,hL,hmatch,hd,?_⟩ + intro y hy + have hfc : Tendsto f (𝓝 (γ c,y-c)) (𝓝 (γ y)) := by + have hc : ContinuousAt f (γ c,y-c) := (continuous_flow W hK hL).continuousAt + simpa only [hmatch y hy] using hc.tendsto + exact hfc.eventually (hW (γ y) ⟨y,hy,rfl⟩) +end QuinticLienard.GlobalODE + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/FitAngles.lean b/lean/OAI/Analysis/LienardCycles/FitAngles.lean new file mode 100644 index 0000000000000000000000000000000000000000..a78cda044ceabccf4270b9352ff37593a14c1ab5 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/FitAngles.lean @@ -0,0 +1,117 @@ +import OAI.Analysis.LienardCycles.HyperbolicCoordinate + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter MeasureTheory +open scoped Topology ContDiff +namespace QuinticLienard.ReferenceCharacteristic +open QuadraticCoordinates PartialCalculus +noncomputable def θ (q : (ℝ × ℝ) × ℝ) : ℝ := angle (A q) +noncomputable def L (q : (ℝ × ℝ) × ℝ) : ℝ := angle (D q) +lemma E_analytic {q : (ℝ × ℝ) × ℝ} (hr : 0 < q.2) : ContDiffAt ℝ ω E q := by + apply ContDiffAt.div + · exact contDiffAt_const.mul (A_analytic hr) + · exact contDiffAt_snd.mul (contDiffAt_const.sub ((A_analytic hr).pow 2)) + · exact ne_of_gt (mul_pos hr (A_gap_pos hr)) +lemma θ_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => θ ((z,k),s)) (J ((z,k),r)-E ((z,k),r)) r := by + change HasDerivAt (fun s => angle (A ((z,k),s))) _ r + have h := (angle_deriv (A_abs_lt (q := ((z,k),r)) hr)).comp (h := fun s => A ((z,k),s)) r (A_deriv (z := z) (k := k) hr) + convert! h using 1 + dsimp only [E] + field_simp [ne_of_gt (A_gap_pos (q := ((z,k),r)) hr),ne_of_gt hr] +lemma L_deriv {z k r : ℝ} (hr : 0 < r) : + HasDerivAt (fun s => L ((z,k),s)) (E ((z,k),r)) r := by + change HasDerivAt (fun s => angle (D ((z,k),s))) _ r + have h := (angle_deriv (D_abs_lt (q := ((z,k),r)) hr)).comp (h := fun s => D ((z,k),s)) r (D_deriv' (z := z) (k := k) hr) + convert! h using 1 + field_simp [ne_of_gt (D_gap_pos (q := ((z,k),r)) hr)] +lemma L_tendsto_zero (z k : ℝ) : + Tendsto (fun r => L ((z,k),r)) (𝓝[>] (0:ℝ)) (𝓝 0) := by + simpa only [angle_zero,Function.comp_def,L] using ((angle_analytic (by norm_num : |(0:ℝ)|<1)).continuousAt.tendsto.comp (D_tendsto_zero z k)) +lemma E_continuousOn (z k : ℝ) : ContinuousOn (fun s => E ((z,k),s)) (Ioi 0) := + fun x hs => ((E_analytic (q := ((z,k),x)) hs).continuousAt.comp (continuousAt_const.prodMk continuousAt_id)).continuousWithinAt +lemma J_continuousOn (z k : ℝ) : ContinuousOn (fun s => J ((z,k),s)) (Ioi 0) := + fun _ hs => (J_deriv hs).continuousAt.continuousWithinAt +lemma integral_E {z k a b : ℝ} (ha : 0 < a) (hab : a ≤ b) : + (∫ s in a..b, E ((z,k),s))=L ((z,k),b)-L ((z,k),a) := by + apply intervalIntegral.integral_eq_sub_of_hasDerivAt + · intro s hs + rw [uIcc_of_le hab] at hs + exact L_deriv (ha.trans_le hs.1) + · exact ((E_continuousOn z k).mono (fun _ hs => ha.trans_le hs.1)).intervalIntegrable_of_Icc hab +lemma integral_J {z k a b : ℝ} (ha : 0 < a) (hab : a ≤ b) : + (∫ s in a..b, J ((z,k),s)) = θ ((z,k),b)-θ ((z,k),a)+(∫ s in a..b, E ((z,k),s)) := by + have hJ : IntervalIntegrable (fun s => J ((z,k),s)) volume a b := ((J_continuousOn z k).mono (fun _ hs => ha.trans_le hs.1)).intervalIntegrable_of_Icc hab + have hE : IntervalIntegrable (fun s => E ((z,k),s)) volume a b := ((E_continuousOn z k).mono (fun _ hs => ha.trans_le hs.1)).intervalIntegrable_of_Icc hab + have he := intervalIntegral.integral_eq_sub_of_hasDerivAt + (f := fun s => θ ((z,k),s)) (f' := fun s => J ((z,k),s)-E ((z,k),s)) + (a := a) (b := b) (fun s hs => θ_deriv (ha.trans_le ((uIcc_of_le hab) ▸ hs).1)) (hJ.sub hE) + rw [intervalIntegral.integral_sub hJ hE] at he + linarith +end QuinticLienard.ReferenceCharacteristic + +namespace QuinticLienard.QuadraticFit +open QuadraticCoordinates ReferenceCharacteristic +lemma conditionalE_strictMono {r A₀ s : ℝ} (hr : 0 < r) (hA : |A₀| < 1) + (hs : 0 < s) (hsr : s < r) : StrictMono (fun k => E ((label ((k,r),A₀),k),s)) := by + apply strictMono_of_deriv_pos + intro k + let a' := Az ((label ((k,r),A₀),k),s)*(T ((label ((k,r),A₀),k),s)-T ((label ((k,r),A₀),k),r)) + have hd := conditionalA_deriv (k := k) hr hA hs + have he : HasDerivAt (fun k => E ((label ((k,r),A₀),k),s)) + (K ((label ((k,r),A₀),k),s)*a') k := by + convert! (hd.const_mul 2).div (((hd.pow 2).const_sub 1).const_mul s) + (ne_of_gt (mul_pos hs (A_gap_pos (q := ((label ((k,r),A₀),k),s)) hs))) using 1 + dsimp only [E,K,a',Pi.pow_apply] + field_simp [ne_of_gt hs,ne_of_gt (A_gap_pos (q := ((label ((k,r),A₀),k),s)) hs)] + ring + rw [he.deriv] + exact mul_pos (K_pos hs) (mul_pos (Az_pos hs) (sub_pos.mpr (T_strictAnti _ _ hs hr hsr))) + +lemma L_difference_nonneg {r A₀ k₁ k₂ s : ℝ} (hr : 0 < r) (hA : |A₀| < 1) + (hk : k₁ ≤ k₂) (hs : 0 < s) (hsr : s ≤ r) : + 0 ≤ L ((label ((k₂,r),A₀),k₂),s)-L ((label ((k₁,r),A₀),k₁),s) := by + apply monotone_zero_nonneg hs + (by simpa using (L_tendsto_zero (label ((k₂,r),A₀)) k₂).sub (L_tendsto_zero (label ((k₁,r),A₀)) k₁)) + apply monotoneOn_of_deriv_nonneg (convex_Ioc 0 s) + (fun t ht => ((L_deriv ht.1).sub (L_deriv ht.1)).continuousAt.continuousWithinAt) + (fun t ht => ((L_deriv (interior_subset ht).1).sub (L_deriv (interior_subset ht).1)).differentiableAt.differentiableWithinAt) + intro t ht + rw [interior_Ioc] at ht + rw [((L_deriv (z := label ((k₂,r),A₀)) (k := k₂) ht.1).sub (L_deriv ht.1)).deriv] + exact sub_nonneg.mpr ((conditionalE_strictMono hr hA ht.1 (ht.2.trans_le hsr)).monotone hk) + +lemma integral_E_difference_bound {r A₀ k₁ k₂ a b : ℝ} (hr : 0 < r) (hA : |A₀| < 1) + (hk : k₁ ≤ k₂) (ha : 0 < a) (hab : a ≤ b) (hbr : b ≤ r) : + 0 ≤ (∫ s in a..b, E ((label ((k₂,r),A₀),k₂),s)-E ((label ((k₁,r),A₀),k₁),s)) ∧ + (∫ s in a..b, E ((label ((k₂,r),A₀),k₂),s)-E ((label ((k₁,r),A₀),k₁),s)) ≤ + L ((label ((k₂,r),A₀),k₂),r)-L ((label ((k₁,r),A₀),k₁),r) := by + have hE (k : ℝ) : IntervalIntegrable (fun s => E ((label ((k,r),A₀),k),s)) volume a b := ((E_continuousOn (label ((k,r),A₀)) k).mono + (fun t (ht : t ∈ Icc a b) => ha.trans_le ht.1)).intervalIntegrable_of_Icc hab + have hmono : MonotoneOn (fun t => L ((label ((k₂,r),A₀),k₂),t)-L ((label ((k₁,r),A₀),k₁),t)) (Ioc 0 r) := by + apply monotoneOn_of_deriv_nonneg (convex_Ioc 0 r) + (fun t ht => ((L_deriv ht.1).sub (L_deriv ht.1)).continuousAt.continuousWithinAt) + (fun t ht => ((L_deriv (interior_subset ht).1).sub (L_deriv (interior_subset ht).1)).differentiableAt.differentiableWithinAt) + intro t ht + rw [interior_Ioc] at ht + rw [((L_deriv (z := label ((k₂,r),A₀)) (k := k₂) ht.1).sub (L_deriv ht.1)).deriv] + exact sub_nonneg.mpr ((conditionalE_strictMono hr hA ht.1 ht.2).monotone hk) + rw [intervalIntegral.integral_sub (hE k₂) (hE k₁),integral_E ha hab,integral_E ha hab] + have h₁ := hmono ⟨ha,hab.trans hbr⟩ ⟨ha.trans_le hab,hbr⟩ hab + have h₂ := hmono ⟨ha.trans_le hab,hbr⟩ ⟨hr,le_rfl⟩ hbr + have h₃ := L_difference_nonneg hr hA hk ha (hab.trans hbr) + constructor <;> linarith +end QuinticLienard.QuadraticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/FitProperness.lean b/lean/OAI/Analysis/LienardCycles/FitProperness.lean new file mode 100644 index 0000000000000000000000000000000000000000..1459347465d430c95e35f44b1768fc542e1e173a --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/FitProperness.lean @@ -0,0 +1,204 @@ +import OAI.Analysis.LienardCycles.AngleBounds + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open scoped Topology + +open Set Filter MeasureTheory +open scoped Topology ContDiff +namespace QuinticLienard.QuadraticFit +open QuadraticCoordinates ReferenceCharacteristic RealAnalysis + +noncomputable def seqA (r M : ℝ) (n : ℕ) (s : ℝ) : ℝ := A ((label ((((n:ℝ)+1),r),M),(n:ℝ)+1),s) +noncomputable def seqE (r M : ℝ) (n : ℕ) (s : ℝ) : ℝ := E ((label ((((n:ℝ)+1),r),M),(n:ℝ)+1),s) +noncomputable def seqJ (r M : ℝ) (n : ℕ) (s : ℝ) : ℝ := J ((label ((((n:ℝ)+1),r),M),(n:ℝ)+1),s) +noncomputable def seqL (r M : ℝ) (n : ℕ) (s : ℝ) : ℝ := L ((label ((((n:ℝ)+1),r),M),(n:ℝ)+1),s) +noncomputable def seqθ (r M : ℝ) (n : ℕ) (s : ℝ) : ℝ := angle (seqA r M n s) +noncomputable def seqg (r M : ℝ) (n : ℕ) (s : ℝ) : ℝ := s*(1-(seqA r M n s)^2) + +lemma seqA_abs {r M s : ℝ} (n : ℕ) (hs : 0 < s) : |seqA r M n s|<1 := A_abs_lt hs +lemma seqA_mono {r M s : ℝ} (hr : 0 < r) (hM : |M|<1) (hs : 0 < s) (hsr : s < r) : + Monotone (fun n => seqA r M n s) := by + intro n m hnm + exact (conditionalA_strictMono hr hM hs hsr).monotone (by exact_mod_cast Nat.add_le_add_right hnm 1) +lemma seqE_mono {r M s : ℝ} (hr : 0 < r) (hM : |M|<1) (hs : 0 < s) (hsr : s < r) : + Monotone (fun n => seqE r M n s) := by + intro n m hnm + exact (conditionalE_strictMono hr hM hs hsr).monotone (by exact_mod_cast Nat.add_le_add_right hnm 1) +lemma seqθ_lower {r M s : ℝ} (hr : 0 < r) (hM : |M|<1) (hs : 0 < s) (hsr : s < r) (n : ℕ) : + seqθ r M 0 s ≤ seqθ r M n s := + angle_strictMono.monotoneOn (abs_lt.mp (seqA_abs 0 hs)) (abs_lt.mp (seqA_abs n hs)) + (seqA_mono hr hM hs hsr (Nat.zero_le n)) +lemma seqE_continuousOn (r M : ℝ) (n : ℕ) : ContinuousOn (seqE r M n) (Ioi 0) := E_continuousOn _ _ +lemma seqJ_continuousOn (r M : ℝ) (n : ℕ) : ContinuousOn (seqJ r M n) (Ioi 0) := J_continuousOn _ _ +lemma seqA_continuousOn (r M : ℝ) (n : ℕ) : ContinuousOn (seqA r M n) (Ioi 0) := by + intro s hs + exact (A_deriv (z := label ((((n:ℝ)+1),r),M)) (k := (n:ℝ)+1) hs).continuousAt.continuousWithinAt +lemma seqg_continuousOn (r M : ℝ) (n : ℕ) : ContinuousOn (seqg r M n) (Ioi 0) := + continuousOn_id.mul (continuousOn_const.sub ((seqA_continuousOn r M n).pow 2)) +lemma seqg_pos {r M s : ℝ} (n : ℕ) (hs : 0 < s) : 0 < seqg r M n s := + mul_pos hs (A_gap_pos hs) +lemma seqE_integrable {r M a b : ℝ} (n : ℕ) (ha : 0 < a) (hab : a ≤ b) : + IntervalIntegrable (seqE r M n) volume a b := + ((seqE_continuousOn r M n).mono (fun _ hs => ha.trans_le hs.1)).intervalIntegrable_of_Icc hab +lemma seqJ_integrable {r M a b : ℝ} (n : ℕ) (ha : 0 < a) (hab : a ≤ b) : + IntervalIntegrable (seqJ r M n) volume a b := + ((seqJ_continuousOn r M n).mono (fun _ hs => ha.trans_le hs.1)).intervalIntegrable_of_Icc hab +lemma seqE_integral_bounds {r M C a b : ℝ} (hr : 0 < r) (hM : |M|<1) + (hC : ∀ n, seqL r M n r ≤ C) (ha : 0 < a) (hab : a ≤ b) (hbr : b ≤ r) (n : ℕ) : + (∫ s in a..b, seqE r M 0 s) ≤ (∫ s in a..b, seqE r M n s) ∧ + (∫ s in a..b, seqE r M n s) ≤ (∫ s in a..b, seqE r M 0 s)+C-seqL r M 0 r := by + have h := integral_E_difference_bound (k₁ := ((0:ℕ):ℝ)+1) (k₂ := (n:ℝ)+1) hr hM + (by simp only [Nat.cast_zero]; linarith [Nat.cast_nonneg (α := ℝ) n]) ha hab hbr + change 0 ≤ (∫ s in a..b, seqE r M n s-seqE r M 0 s) ∧ + (∫ s in a..b, seqE r M n s-seqE r M 0 s) ≤ seqL r M n r-seqL r M 0 r at h + rw [intervalIntegral.integral_sub (seqE_integrable n ha hab) (seqE_integrable 0 ha hab)] at h + constructor <;> linarith [h.1,h.2,hC n] + +lemma seqθ_ae_bdd {r M C a b : ℝ} (hr : 0 < r) (hM : |M|<1) + (hC : ∀ n, seqL r M n r ≤ C) (ha : 0 < a) (hab : a ≤ b) (hbr : b < r) : + ∀ᵐ s ∂volume.restrict (Ioc a b), BddAbove (range (fun n => seqθ r M n s)) := by + have hmem : ∀ᵐ s ∂volume.restrict (Ioc a b), s ∈ Ioc a b := ae_restrict_mem measurableSet_Ioc + have hbd := ae_bddAbove_of_integral_bounded + (μ := volume.restrict (Ioc a b)) (f := fun n s => seqE r M n s-seqE r M 0 s) + (C := C-seqL r M 0 r) + (fun n => ((seqE_integrable n ha hab).sub (seqE_integrable 0 ha hab)).1) + (hmem.mono (fun s hs n => sub_nonneg.mpr (seqE_mono hr hM (ha.trans hs.1) (hs.2.trans_lt hbr) (Nat.zero_le n)))) + (hmem.mono (fun s hs n m hnm => sub_le_sub_right (seqE_mono hr hM (ha.trans hs.1) (hs.2.trans_lt hbr) hnm) _)) + (by intro n; rw [←intervalIntegral.integral_of_le hab,intervalIntegral.integral_sub + (seqE_integrable n ha hab) (seqE_integrable 0 ha hab)] + have h := (seqE_integral_bounds hr hM hC ha hab hbr.le n).2 + linarith) + filter_upwards [hbd,hmem] with s hs hsm + have hrates : BddAbove (range (fun n => 2*seqA r M n s/(s*(1-(seqA r M n s)^2)))) := by + obtain ⟨B,hB⟩ := hs + refine ⟨B+seqE r M 0 s,?_⟩ + rintro y ⟨n,rfl⟩ + have h := hB (mem_range_self n) + change 2*seqA r M n s/(s*(1-(seqA r M n s)^2))-seqE r M 0 s ≤ B at h + linarith + exact bddAbove_angle_of_rate (ha.trans hsm.1) (fun n => seqA_abs n (ha.trans hsm.1)) + (seqA_mono hr hM (ha.trans hsm.1) (hsm.2.trans_lt hbr)) hrates + +lemma seqg_uniform_integral_pos {r M C a b : ℝ} (hr : 0 < r) (hM : |M|<1) + (hC : ∀ n, seqL r M n r ≤ C) (ha : 0 < a) (hab : a < b) (hbr : b < r) : + ∃ ε > 0, ∀ n, ε ≤ ∫ s in a..b, seqg r M n s := by + let q : ℝ → ℝ := fun s => 1/(s*(1+seqA r M 0 s)) + have hq : ContinuousOn q (Icc a b) := by + apply continuousOn_const.div + (continuousOn_id.mul (continuousOn_const.add ((seqA_continuousOn r M 0).mono (fun _ hs => ha.trans_le hs.1)))) + intro s hs + apply ne_of_gt (mul_pos (ha.trans_le hs.1) _) + change 0 < 1+seqA r M 0 s + linarith [(abs_lt.mp (seqA_abs (r := r) (M := M) 0 (ha.trans_le hs.1))).1] + apply uniform_integral_pos_of_reciprocal hab + (fun n => (seqg_continuousOn r M n).mono (fun _ hs => ha.trans_le hs.1)) + (fun n s hs => seqg_pos n (ha.trans_le hs.1)) + (B := ((∫ s in a..b, seqE r M 0 s)+C-seqL r M 0 r)/2+(∫ s in a..b, q s)) + intro n + have h₁ := seqE_integrable (r := r) (M := M) n ha hab.le + have h₂ : IntervalIntegrable q volume a b := hq.intervalIntegrable_of_Icc hab.le + have hg : IntervalIntegrable (fun s => 1/seqg r M n s) volume a b := + (continuousOn_const.div ((seqg_continuousOn r M n).mono (fun _ hs => ha.trans_le hs.1)) + (fun s hs => ne_of_gt (seqg_pos n (ha.trans_le hs.1)))).intervalIntegrable_of_Icc hab.le + have hpoint (s : ℝ) (hs : s ∈ Icc a b) : 1/seqg r M n s ≤ seqE r M n s/2+q s := by + have hs0 := ha.trans_le hs.1 + have hin : 0 < 1+seqA r M n s := by linarith [(abs_lt.mp (seqA_abs (r := r) (M := M) n hs0)).1] + have hi0 : 0 < 1+seqA r M 0 s := by linarith [(abs_lt.mp (seqA_abs (r := r) (M := M) 0 hs0)).1] + have hgap : 0 < 1-(seqA r M n s)^2 := A_gap_pos hs0 + have hid : 1/seqg r M n s=seqE r M n s/2+1/(s*(1+seqA r M n s)) := by + change 1/(s*(1-(seqA r M n s)^2))= (2*seqA r M n s/(s*(1-(seqA r M n s)^2)))/2+1/(s*(1+seqA r M n s)) + field_simp [ne_of_gt hs0,ne_of_gt hin,ne_of_gt hgap] + ring + rw [hid] + have hinv : 1/(s*(1+seqA r M n s)) ≤ 1/(s*(1+seqA r M 0 s)) := one_div_le_one_div_of_le (mul_pos hs0 hi0) + (mul_le_mul_of_nonneg_left (by linarith [seqA_mono hr hM hs0 (hs.2.trans_lt hbr) (Nat.zero_le n)]) hs0.le) + dsimp only [q] + linarith + have hle := intervalIntegral.integral_mono_on hab.le hg ((h₁.div_const 2).add h₂) hpoint + rw [intervalIntegral.integral_add (h₁.div_const 2) h₂,intervalIntegral.integral_div] at hle + linarith [(seqE_integral_bounds hr hM hC ha hab.le hbr.le n).2] + +lemma seqJ_drop {r M a b : ℝ} (n : ℕ) (ha : 0 < a) (hab : a ≤ b) : + seqJ r M n a-seqJ r M n b=((n:ℝ)+1)*(∫ s in a..b, seqg r M n s) := by + have hg : IntervalIntegrable (seqg r M n) volume a b := + ((seqg_continuousOn r M n).mono (fun _ hs => ha.trans_le hs.1)).intervalIntegrable_of_Icc hab + have hd (s : ℝ) (hs : s ∈ uIcc a b) : HasDerivAt (seqJ r M n) (-((n:ℝ)+1)*seqg r M n s) s := by + have h := J_deriv (z := label ((((n:ℝ)+1),r),M)) (k := (n:ℝ)+1) (ha.trans_le (((uIcc_of_le hab) ▸ hs).1)) + convert! h using 1 + dsimp only [seqg,seqA] + ring + have he := intervalIntegral.integral_eq_sub_of_hasDerivAt hd (hg.const_mul (-((n:ℝ)+1))) + rw [intervalIntegral.integral_const_mul] at he + linarith + +theorem seqL_not_bddAbove {r M : ℝ} (hr : 0 < r) (hM : |M|<1) : + ¬ BddAbove (range (fun n => seqL r M n r)) := by + rintro ⟨C,hC⟩ + have hCn (n : ℕ) : seqL r M n r ≤ C := hC (mem_range_self n) + have hgood := seqθ_ae_bdd hr hM hCn (show 0 linarith [hs.1,hs.2]) hgood + obtain ⟨c,hc,hθc⟩ := exists_mem_Ioo_of_ae (a := 7*r/12) (b := 2*r/3) + (by linarith) (by intro s hs; constructor <;> linarith [hs.1,hs.2]) hgood + obtain ⟨Bθb,hBθb⟩ := hθb + obtain ⟨Bθc,hBθc⟩ := hθc + let a := r/4 + let d := 3*r/4 + have ha : 0 + (J_strictAnti (z := label ((((n:ℝ)+1),r),M)) (by positivity : (0:ℝ)<(n:ℝ)+1)).antitoneOn + (ha.trans_le hs.1) (ha.trans hab) hs.2) + rw [intervalIntegral.integral_const] at hI + simp only [smul_eq_mul] at hI + change (b-a)*seqJ r M n b ≤ (∫ s in a..b, seqJ r M n s) at hI + apply (le_div_iff₀ (sub_pos.mpr hab)).mpr + have hLow := seqθ_lower hr hM ha (hab.trans (hbc.trans (hcd.trans hdr))) n + have hHigh := hBθb (mem_range_self n) + have hEB := (seqE_integral_bounds hr hM hCn ha hab.le (hbc.trans (hcd.trans hdr)).le n).2 + dsimp only [U] + nlinarith + have hlower (n : ℕ) : V/(d-c) ≤ seqJ r M n c := by + have hc0 := ha.trans (hab.trans hbc) + have he : (∫ s in c..d, seqJ r M n s)=seqθ r M n d-seqθ r M n c+(∫ s in c..d, seqE r M n s) := integral_J hc0 hcd.le + have hI := intervalIntegral.integral_mono_on hcd.le (seqJ_integrable n hc0 hcd.le) + intervalIntegrable_const (fun s hs => + (J_strictAnti (z := label ((((n:ℝ)+1),r),M)) (by positivity : (0:ℝ)<(n:ℝ)+1)).antitoneOn + hc0 (hc0.trans_le hs.1) hs.1) + rw [intervalIntegral.integral_const] at hI + simp only [smul_eq_mul] at hI + change (∫ s in c..d, seqJ r M n s) ≤ (d-c)*seqJ r M n c at hI + apply (div_le_iff₀ (sub_pos.mpr hcd)).mpr + have hLow := seqθ_lower hr hM (hc0.trans hcd) hdr n + have hHigh := hBθc (mem_range_self n) + have hEB := (seqE_integral_bounds hr hM hCn hc0 hcd.le hdr.le n).1 + dsimp only [V] + nlinarith + obtain ⟨ε,hε,hbound⟩ := seqg_uniform_integral_pos hr hM hCn (ha.trans hab) hbc (hcd.trans hdr) + obtain ⟨n,hn⟩ := exists_nat_gt ((U/(b-a)-V/(d-c))/ε) + have hmul := mul_le_mul_of_nonneg_left (hbound n) (show (0:ℝ) ≤ (n:ℝ)+1 by positivity) + rw [←seqJ_drop n (ha.trans hab) hbc.le] at hmul + have hn' := (div_lt_iff₀ hε).mp hn + nlinarith [hupper n,hlower n] +end QuinticLienard.QuadraticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/FitSmall.lean b/lean/OAI/Analysis/LienardCycles/FitSmall.lean new file mode 100644 index 0000000000000000000000000000000000000000..1fdafef398f9d09a55eb6d216587308685ef6545 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/FitSmall.lean @@ -0,0 +1,96 @@ +import OAI.Analysis.LienardCycles.CubicVariation + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open scoped Topology +open Set Filter MeasureTheory +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuadraticCoordinates +open PartialCalculus QuadraticVariation +lemma Hr_zero {r : ℝ} (hr : 0 s^2/3) (2*r/3) r := by + convert ((hasDerivAt_id r).pow 2).div_const 3 using 1 <;> (first | rfl | (dsimp; ring)) + apply (R_hasDerivAt hr).unique (hd.congr_of_eventuallyEq ?_) + filter_upwards [continuousAt_const.eventually_lt continuousAt_id hr] with s hs + exact P_zero hs +lemma S_zero {r : ℝ} (hr : 0 s^4/15) (4*r^3/15) r := by + convert ((hasDerivAt_id r).pow 4).div_const 15 using 1 <;> (first | rfl | (dsimp; ring)) + apply (S_hasDerivAt hr).unique (hd.congr_of_eventuallyEq ?_) + filter_upwards [continuousAt_const.eventually_lt continuousAt_id hr] with s hs + exact Q_zero hs +lemma fderiv_Hr {d k r : ℝ} (hr : 0 fitD (((1:ℝ),μ t),ν t)) (3*(4*m-n)/2) θ ∧ + HasDerivAt (fun t => fitK (((1:ℝ),μ t),ν t)) (15*(n-2*m)/2) θ := by + let d : ℝ → ℝ := fun t => fitD (((1:ℝ),μ t),ν t) + let k : ℝ → ℝ := fun t => fitK (((1:ℝ),μ t),ν t) + have hpos : (0:ℝ)<1 := by norm_num + have hz : |(0:ℝ)|<1 := by norm_num + have hd0 : d θ=0 := by simpa only [d,hμ,hν] using (fit_zero hpos).1 + have hk0 : k θ=0 := by simpa only [k,hμ,hν] using (fit_zero hpos).2 + have hfd : DifferentiableAt ℝ d θ := by + have hf : DifferentiableAt ℝ fitD (((1:ℝ),μ θ),ν θ) := by + rw [hμ,hν] + exact (fitD_analytic hpos hz hz).differentiableAt (by simp) + have hg : DifferentiableAt ℝ (fun t => (((1:ℝ),μ t),ν t)) θ := + (((differentiableAt_const (1:ℝ)).prodMk hm.differentiableAt).prodMk hn.differentiableAt) + exact DifferentiableAt.comp (g := fitD) (f := fun t => (((1:ℝ),μ t),ν t)) θ hf hg + have hfk : DifferentiableAt ℝ k θ := by + have hf : DifferentiableAt ℝ fitK (((1:ℝ),μ θ),ν θ) := by + rw [hμ,hν] + exact (fitK_analytic hpos hz hz).differentiableAt (by simp) + have hg : DifferentiableAt ℝ (fun t => (((1:ℝ),μ t),ν t)) θ := + (((differentiableAt_const (1:ℝ)).prodMk hm.differentiableAt).prodMk hn.differentiableAt) + exact DifferentiableAt.comp (g := fitK) (f := fun t => (((1:ℝ),μ t),ν t)) θ hf hg + have he : ∀ᶠ t in 𝓝 θ, H ((d t,k t),1)=μ t ∧ Hr ((d t,k t),1)=ν t := by + have hμb : |μ θ|<1 := by rw [hμ]; exact hz + have hνb : |ν θ|<1 := by rw [hν]; exact hz + filter_upwards [hm.continuousAt.abs.eventually_lt continuousAt_const hμb, + hn.continuousAt.abs.eventually_lt continuousAt_const hνb] with t ht hu + exact fit_spec hpos ht hu + have hh := ((H_analytic (d:=d θ) (k:=k θ) hpos).differentiableAt (by simp)).hasFDerivAt.comp_hasDerivAt θ + ((hfd.hasDerivAt.prodMk hfk.hasDerivAt).prodMk (hasDerivAt_const θ (1:ℝ))) + have hv := ((Hr_analytic (d:=d θ) (k:=k θ) hpos).differentiableAt (by simp)).hasFDerivAt.comp_hasDerivAt θ + ((hfd.hasDerivAt.prodMk hfk.hasDerivAt).prodMk (hasDerivAt_const θ (1:ℝ))) + have heh := hh.unique (hm.congr_of_eventuallyEq (he.mono fun _ h => h.1)) + have hev := hv.unique (hn.congr_of_eventuallyEq (he.mono fun _ h => h.2)) + rw [hd0,hk0,fderiv_model] at heh + change deriv d θ*P ((0,0),1)+deriv k θ*Q ((0,0),1)+0*Hr ((0,0),1)=m at heh + rw [hd0,hk0,fderiv_Hr hpos] at hev + norm_num only [P_zero hpos,Q_zero hpos,R_zero hpos,S_zero hpos,one_pow,mul_one,zero_mul,add_zero] at heh hev + constructor + · have hed : deriv d θ=3*(4*m-n)/2 := by linarith only [heh,hev] + simpa only [hed] using hfd.hasDerivAt + · have hek : deriv k θ=15*(n-2*m)/2 := by linarith only [heh,hev] + simpa only [hek] using hfk.hasDerivAt +end QuinticLienard.QuadraticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/FixedSlopeLimit.lean b/lean/OAI/Analysis/LienardCycles/FixedSlopeLimit.lean new file mode 100644 index 0000000000000000000000000000000000000000..a0ef6fc2f26342c7f1239a5d5545d99c1d7ad5ae --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/FixedSlopeLimit.lean @@ -0,0 +1,70 @@ +import OAI.Analysis.LienardCycles.ActualCharacteristic + +namespace OAI + +universe uι + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuadraticFit +open QuadraticCoordinates +lemma slope_scaled {κ r m : ℝ} (hr : 0 slope ((κ,r z),M a (h z,r z))) l (𝓝 (ScaledProfile.slope a h₀)) := by + have hf := fit_limits (a:=a) hh₀ hh hr hp + have hn := (normalized_limits (a:=a) hh₀ hh hr hp).1 + have hx : Tendsto (fun z => (((r z)^3*κ,(1:ℝ)),M a (h z,r z)/r z)) l (𝓝 (((0:ℝ),(1:ℝ)),0)) := by + have h0 : Tendsto (fun z => (r z)^3*κ) l (𝓝 (0:ℝ)) := by simpa using ((hr.pow 3).mul_const κ) + exact (h0.prodMk_nhds tendsto_const_nhds).prodMk_nhds hn + have hy : Tendsto (fun z => (((r z)^3*kappa a (h z,r z),(1:ℝ)),M a (h z,r z)/r z)) l (𝓝 (((0:ℝ),(1:ℝ)),0)) := by + have h0 : Tendsto (fun z => (r z)^3*kappa a (h z,r z)) l (𝓝 (0:ℝ)) := by simpa using ((hr.pow 3).mul hf.2) + exact (h0.prodMk_nhds tendsto_const_nhds).prodMk_nhds hn + obtain ⟨K,U,hU,hLip⟩ := ((slope_analytic (k:=0) (by norm_num : (0:ℝ)<1) (by norm_num : |(0:ℝ)|<1)).of_le (by simp : (1:WithTop ℕ∞)≤ω)).exists_lipschitzOnWith + have hbound : ∀ᶠ z in l, + |slope ((κ,r z),M a (h z,r z))-lambda a (h z,r z)| ≤ + K*(r z)^2*|κ-kappa a (h z,r z)| := by + filter_upwards [hp,hh.eventually (eventually_gt_nhds hh₀),hx.eventually hU,hy.eventually hU] with z hz hhz hxz hyz + have hl := hLip.dist_le_mul _ hxz _ hyz + have hm := M_abs_lt a hhz hz + have hs : slope ((kappa a (h z,r z),r z),M a (h z,r z))=lambda a (h z,r z) := + slope_eq hz hm (spec a hhz hz).1 + rw [slope_scaled hz hm,slope_scaled hz hm,hs] at hl + simp only [Prod.dist_eq,dist_self,Real.dist_eq] at hl + simp only [max_eq_left (abs_nonneg (r z^3*κ-r z^3*kappa a (h z,r z)))] at hl + rw [←mul_sub,abs_mul,abs_of_pos hz] at hl + have hd : |r z^3*κ-r z^3*kappa a (h z,r z)|=(r z)^3*|κ-kappa a (h z,r z)| := by + rw [←mul_sub,abs_mul,abs_of_pos (pow_pos hz 3)] + rw [hd] at hl + apply (mul_le_mul_iff_right₀ hz).mp + nlinarith [hl] + have hb : Tendsto (fun z => (K:ℝ)*(r z)^2*|κ-kappa a (h z,r z)|) l (𝓝 0) := by + simpa using ((hr.pow 2).const_mul (K:ℝ)).mul ((tendsto_const_nhds.sub hf.2).abs) + have he : Tendsto (fun z => slope ((κ,r z),M a (h z,r z))-lambda a (h z,r z)) l (𝓝 0) := + tendsto_zero_iff_norm_tendsto_zero.mpr (by simpa only [Real.norm_eq_abs] using squeeze_zero' (Eventually.of_forall (fun _ => abs_nonneg _)) hbound hb) + simpa only [sub_add_cancel,zero_add] using he.add hf.1 +end QuinticLienard.QuinticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/FixedWidthFamilies.lean b/lean/OAI/Analysis/LienardCycles/FixedWidthFamilies.lean new file mode 100644 index 0000000000000000000000000000000000000000..dd41843939b46725d6354c73b5d7ae1f4e54e3ec --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/FixedWidthFamilies.lean @@ -0,0 +1,76 @@ +import OAI.Analysis.LienardCycles.QuadraticCoordinates + +namespace OAI + +universe uP + +open Set Filter MeasureTheory +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.FixedWidthFamilies +open ScalarArcs ArcEndpoints ArcFamilies CanonicalVariation WidthCoordinates PartialCalculus ArchVariation + +variable {P : Type uP} [NormedAddCommGroup P] [NormedSpace ℝ P] + [FiniteDimensional ℝ P] +variable (Φ : P × ℝ → ℝ) (hΦ : ContDiff ℝ ω Φ) + (hloc : ∀ x : State P, ∃ f : State P × ℝ → State P, + ContDiffAt ℝ ω f (x,0) ∧ ∀ᶠ q in 𝓝 (x,(0:ℝ)), + f (q.1,0) = q.1 ∧ HasDerivAt (fun s => f (q.1,s)) (field Φ (f q)) q.2) +include hΦ hloc + +lemma endpoint_formulas {p : P} {h r : ℝ} (hr : 0 < r) : + lowerFamily Φ ((p,peakAtWidth Φ ((p,h),r)),h) = + midpointAtWidth Φ ((p,h),r)+Φ (p,h)-r ∧ + upperFamily Φ ((p,peakAtWidth Φ ((p,h),r)),h) = + midpointAtWidth Φ ((p,h),r)+Φ (p,h)+r := by + have hs := (peak_spec Φ hΦ hloc (p := p) (h := h) hr).2 + dsimp [widthFamily,width] at hs + dsimp [lowerFamily,upperFamily,midpointAtWidth,midpointFamily,ScalarArcs.midpoint] + constructor <;> linarith + +theorem witness {γ : ℝ → P} {θ h r : ℝ} (hγ : ContDiffAt ℝ ω γ θ) (hr : 0 < r) : + ∃ u : ℝ × ℝ → ℝ, + (∀ s, Continuous (fun y => u (s,y))) ∧ + (∀ y ∈ Icc (midpointAtWidth Φ ((γ θ,h),r)+Φ (γ θ,h)-r) + (midpointAtWidth Φ ((γ θ,h),r)+Φ (γ θ,h)+r), ContDiffAt ℝ ω u (θ,y)) ∧ + (∀ y ∈ Icc (midpointAtWidth Φ ((γ θ,h),r)+Φ (γ θ,h)-r) + (midpointAtWidth Φ ((γ θ,h),r)+Φ (γ θ,h)+r), + ∀ᶠ q in 𝓝 (θ,y), HasDerivAt (fun s => u (q.1,s)) (Φ (γ q.1,u q)-q.2) q.2) ∧ + ∀ᶠ s in 𝓝 θ, IsArch (fun x => Φ (γ s,x)) (fun y => u (s,y)) h + (peakAtWidth Φ ((γ s,h),r)) + (midpointAtWidth Φ ((γ s,h),r)+Φ (γ s,h)-r) + (midpointAtWidth Φ ((γ s,h),r)+Φ (γ s,h)+r) := by + let T : ℝ → ℝ := fun s => peakAtWidth Φ ((γ s,h),r) + have hmap : ContDiffAt ℝ ω (fun s => ((γ s,h),r)) θ := + (hγ.prodMk contDiffAt_const).prodMk contDiffAt_const + have hT : ContDiffAt ℝ ω T θ := by + have hh := (peak_analytic Φ hΦ hloc (p := γ θ) (h := h) hr).comp θ hmap + exact hh + have hs := peak_spec Φ hΦ hloc (p := γ θ) (h := h) hr + obtain ⟨w,hwc,_,hwd,hwe,hwa⟩ := endpoint_witness Φ hΦ hloc hs.1 + let u : ℝ × ℝ → ℝ := fun q => w ((γ q.1,T q.1),q.2) + have hlift (y : ℝ) : ContDiffAt ℝ ω (fun q : ℝ × ℝ => ((γ q.1,T q.1),q.2)) (θ,y) := + ((hγ.comp (θ,y) contDiffAt_fst).prodMk (hT.comp (θ,y) contDiffAt_fst)).prodMk contDiffAt_snd + have hf := endpoint_formulas Φ hΦ hloc (p := γ θ) (h := h) hr + rw [hf.1,hf.2] at hwd hwe + refine ⟨u,fun s => hwc (γ s,T s),fun y hy => (hwd y hy).comp (θ,y) (hlift y),?_,?_⟩ + · intro y hy + filter_upwards [(hlift y).continuousAt.eventually (hwe y hy)] with q hq + exact hq + · have hc : ContinuousAt (fun s => ((γ s,T s),h)) θ := + (hγ.continuousAt.prodMk hT.continuousAt).prodMk continuousAt_const + filter_upwards [hc.eventually hwa] with s hs + have hh := endpoint_formulas Φ hΦ hloc (p := γ s) (h := h) hr + simpa only [T,hh.1,hh.2] using hs + +end QuinticLienard.FixedWidthFamilies + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/GlobalFit.lean b/lean/OAI/Analysis/LienardCycles/GlobalFit.lean new file mode 100644 index 0000000000000000000000000000000000000000..9fdee21198f351c0ce0897569a59beaaa1809232 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/GlobalFit.lean @@ -0,0 +1,135 @@ +import OAI.Analysis.LienardCycles.FitProperness + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open Set Filter +open scoped Topology ENNReal +open scoped Topology +open Set Filter MeasureTheory +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuadraticFit +open QuadraticCoordinates ReferenceCharacteristic + +lemma label_model_slope {r M k : ℝ} (hr : 0 < r) (hM : |M| reflection d k hs)) + +lemma conditionalV_reflection {r M k : ℝ} (hr : 0 < r) (hM : |M| conditionalV ((k,r),M)) := by + apply continuous_iff_continuousAt.mpr + intro k + exact ((conditionalV_analytic hr hM).comp (f := fun k : ℝ => ((k,r),M)) k + ((contDiffAt_id.prodMk contDiffAt_const).prodMk contDiffAt_const)).continuousAt + obtain ⟨k,_,hk⟩ := intermediate_value_Icc hab.le hc.continuousOn ⟨ha.le,hb.le⟩ + exact ⟨k,hk⟩ + +noncomputable def fitK (q : (ℝ × ℝ) × ℝ) : ℝ := by + classical + exact if h : ∃ k, conditionalV ((k,q.1.1),q.1.2)=q.2 then h.choose else 0 +noncomputable def fitD (q : (ℝ × ℝ) × ℝ) : ℝ := slope ((fitK q,q.1.1),q.1.2) + +lemma fitK_spec {r M v : ℝ} (hr : 0 < r) (hM : |M| conditionalV ((q.2,q.1.1),q.1.2) + have hf : ContDiffAt ℝ ω f ((r,M),k) := + (conditionalV_analytic (k := k) hr hM).comp + (f := fun q : (ℝ × ℝ) × ℝ => ((q.2,q.1.1),q.1.2)) ((r,M),k) + ((contDiffAt_snd.prodMk contDiffAt_fst.fst).prodMk contDiffAt_fst.snd) + obtain ⟨Y,hY,hY₀,he⟩ := ArcEndpoints.level_hit hf (conditionalV_deriv hr hM) + (fitK_spec hr hM hv) (ne_of_gt (div_pos (G_pos hr) (QuadraticVariation.P_pos hr))) + apply hY.congr_of_eventuallyEq + have hp : ∀ᶠ q : (ℝ × ℝ) × ℝ in 𝓝 ((r,M),v), 0 < q.1.1 := + continuousAt_const.eventually_lt continuousAt_fst.fst hr + have hm : ∀ᶠ q : (ℝ × ℝ) × ℝ in 𝓝 ((r,M),v), |q.1.2| ((fitK q,q.1.1),q.1.2)) ((r,M),v) + (((fitK_analytic hr hM hv).prodMk contDiffAt_fst.fst).prodMk contDiffAt_fst.snd) +end QuinticLienard.QuadraticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/GlobalODE.lean b/lean/OAI/Analysis/LienardCycles/GlobalODE.lean new file mode 100644 index 0000000000000000000000000000000000000000..56f474101320889536df45919fd2ae806c243a1e --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/GlobalODE.lean @@ -0,0 +1,321 @@ +import OAI.Analysis.LienardCycles.SmoothFlow + +namespace OAI + +universe uE + +open Set Filter MeasureTheory +open scoped Topology ContDiff + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold + +namespace QuinticLienard.GlobalODE + +variable {E : Type uE} [NormedAddCommGroup E] [NormedSpace ℝ E] [CompleteSpace E] + +theorem bounded_lipschitz_global_solution (V : E → E) {K L : ℝ≥0} + (hK : LipschitzWith K V) (hL : ∀ x, ‖V x‖ ≤ L) (x₀ : E) : + ∃ u : ℝ → E, u 0 = x₀ ∧ ∀ t, HasDerivAt u (V (u t)) t := by + have hex (N : ℕ) : ∃ u : ℝ → E, u 0 = x₀ ∧ + ∀ t, |t| < (N:ℝ)+1 → HasDerivAt u (V (u t)) t := by + let T : ℝ := (N:ℝ)+1 + have hT : 0 < T := by dsimp [T]; positivity + let t₀ : Icc (-T) T := ⟨0, by constructor <;> linarith⟩ + have hpl : IsPicardLindelof (fun _ : ℝ => V) t₀ x₀ (L * (N+1)) 0 L K := by + constructor + · exact fun _ _ => hK.lipschitzOnWith + · exact fun _ _ => continuous_const.continuousOn + · exact fun _ _ x _ => hL x + · simp [t₀, T, mul_add] + obtain ⟨u,hu,hdu⟩ := hpl.exists_eq_forall_mem_Icc_hasDerivWithinAt₀ + refine ⟨u,hu,fun t ht => ?_⟩ + have ht' : t ∈ Ioo (-T) T := abs_lt.mp ht + exact (hdu t (Ioo_subset_Icc_self ht')).hasDerivAt (Icc_mem_nhds ht'.1 ht'.2) + choose u hu hdu using hex + have hmatch (N M : ℕ) {t : ℝ} (htN : |t| < (N:ℝ)+1) (htM : |t| < (M:ℝ)+1) : + u N t = u M t := by + let R : ℝ := min ((N:ℝ)+1) ((M:ℝ)+1) + have hR : 0 < R := lt_min (by positivity) (by positivity) + have hsubN {s : ℝ} (hs : s ∈ Ioo (-R) R) : |s| < (N:ℝ)+1 := + (abs_lt.mpr hs).trans_le (min_le_left _ _) + have hsubM {s : ℝ} (hs : s ∈ Ioo (-R) R) : |s| < (M:ℝ)+1 := + (abs_lt.mpr hs).trans_le (min_le_right _ _) + have he := ODE_solution_unique_of_mem_Ioo + (v := fun _ : ℝ => V) (s := fun _ => (Set.univ : Set E)) + (fun _ _ => hK.lipschitzOnWith) + (show (0:ℝ) ∈ Ioo (-R) R by constructor <;> linarith) + (fun s hs => ⟨hdu N s (hsubN hs), mem_univ _⟩) + (fun s hs => ⟨hdu M s (hsubM hs), mem_univ _⟩) + (by rw [hu N, hu M]) + exact he (abs_lt.mp (lt_min htN htM)) + let U : ℝ → E := fun t => u ⌈|t|⌉₊ t + have hpoint (N : ℕ) {t : ℝ} (ht : |t| < (N:ℝ)+1) : U t = u N t := by + apply hmatch _ N _ ht + exact (Nat.le_ceil _).trans_lt (by linarith) + refine ⟨U,by simp [U,hu],fun t => ?_⟩ + let N := ⌈|t|⌉₊ + have ht : |t| < (N:ℝ)+1 := (Nat.le_ceil _).trans_lt (by linarith) + have hevent : U =ᶠ[𝓝 t] u N := by + filter_upwards [Ioo_mem_nhds (abs_lt.mp ht).1 (abs_lt.mp ht).2] with s hs + exact hpoint N (abs_lt.mpr hs) + rw [hpoint N ht] + exact (hdu N t ht).congr_of_eventuallyEq hevent + +section Flow +variable (V : E → E) {K L : ℝ≥0} (hK : LipschitzWith K V) (hL : ∀ x, ‖V x‖ ≤ L) + +noncomputable def flow (x : E) : ℝ → E := + Classical.choose (bounded_lipschitz_global_solution V hK hL x) + +@[simp] theorem flow_zero (x : E) : flow V hK hL x 0 = x := + (Classical.choose_spec (bounded_lipschitz_global_solution V hK hL x)).1 + + theorem flow_deriv (x : E) (t : ℝ) : + HasDerivAt (flow V hK hL x) (V (flow V hK hL x t)) t := + (Classical.choose_spec (bounded_lipschitz_global_solution V hK hL x)).2 t + + theorem flow_unique {x : E} {u : ℝ → E} (hu : ∀ t, HasDerivAt u (V (u t)) t) + (h0 : u 0 = x) : u = flow V hK hL x := by + apply ODE_solution_unique_univ (v := fun _ : ℝ => V) (s := fun _ => Set.univ) (t₀ := 0) + · exact fun _ => hK.lipschitzOnWith + · exact fun t => ⟨hu t, mem_univ _⟩ + · exact fun t => ⟨flow_deriv V hK hL x t, mem_univ _⟩ + · simpa using h0 + + theorem flow_add (x : E) (s t : ℝ) : + flow V hK hL x (s+t) = flow V hK hL (flow V hK hL x s) t := by + have hu : ∀ t, HasDerivAt (fun t => flow V hK hL x (s+t)) + (V (flow V hK hL x (s+t))) t := by + intro t + simpa [Function.comp_def] using (flow_deriv V hK hL x (s+t)).scomp t ((hasDerivAt_id t).const_add s) + exact congrFun (flow_unique V hK hL hu (by simp)) t + + theorem flow_lipschitz_time (x : E) : LipschitzWith L (flow V hK hL x) := by + apply lipschitzWith_of_nnnorm_deriv_le + · exact fun t => (flow_deriv V hK hL x t).differentiableAt + · intro t + rw [(flow_deriv V hK hL x t).deriv] + exact_mod_cast hL (flow V hK hL x t) + + theorem flow_dist_initial (x y : E) (t : ℝ) : + dist (flow V hK hL x t) (flow V hK hL y t) ≤ dist x y * Real.exp (K * |t|) := by + have hpos {W : E → E} (hW : LipschitzWith K W) {f g : ℝ → E} + (hf : ∀ s, HasDerivAt f (W (f s)) s) (hg : ∀ s, HasDerivAt g (W (g s)) s) + {t : ℝ} (ht : 0 ≤ t) : dist (f t) (g t) ≤ dist (f 0) (g 0) * Real.exp (K*t) := by + simpa using dist_le_of_trajectories_ODE (v := fun _ : ℝ => W) + (fun _ => hW) (fun z _ => (hf z).continuousAt.continuousWithinAt) + (fun z _ => (hf z).hasDerivWithinAt) + (fun z _ => (hg z).continuousAt.continuousWithinAt) + (fun z _ => (hg z).hasDerivWithinAt) (le_refl (dist (f 0) (g 0))) t ⟨ht,le_rfl⟩ + rcases le_total 0 t with ht | ht + · simpa [abs_of_nonneg ht] using hpos hK (flow_deriv V hK hL x) + (flow_deriv V hK hL y) ht + · have hder (a : E) (s : ℝ) : HasDerivAt (fun s => flow V hK hL a (-s)) + (-V (flow V hK hL a (-s))) s := by + simpa [Function.comp_def] using (flow_deriv V hK hL a (-s)).scomp s (hasDerivAt_id s).neg + simpa [abs_of_nonpos ht] using + hpos hK.neg (hder x) (hder y) (neg_nonneg.mpr ht) + + theorem continuous_flow : Continuous (fun p : E × ℝ => flow V hK hL p.1 p.2) := by + rw [continuous_iff_continuousAt] + intro p + apply tendsto_iff_dist_tendsto_zero.mpr + have hbound (q : E × ℝ) : dist (flow V hK hL q.1 q.2) (flow V hK hL p.1 p.2) ≤ + L * dist q.2 p.2 + dist q.1 p.1 * Real.exp (K * |p.2|) := by + calc + _ ≤ dist (flow V hK hL q.1 q.2) (flow V hK hL q.1 p.2) + + dist (flow V hK hL q.1 p.2) (flow V hK hL p.1 p.2) := dist_triangle _ _ _ + _ ≤ _ := add_le_add ((flow_lipschitz_time V hK hL q.1).dist_le_mul _ _) + (flow_dist_initial V hK hL q.1 p.1 p.2) + apply squeeze_zero (fun _ => dist_nonneg) hbound + have hc : Continuous (fun q : E × ℝ => + L * dist q.2 p.2 + dist q.1 p.1 * Real.exp (K * |p.2|)) := by fun_prop + simpa using hc.tendsto p + +theorem local_family_eq (x₀ : E) (f : E × ℝ → E) + (hf : ∀ᶠ p in 𝓝 (x₀,(0:ℝ)), f (p.1,0) = p.1 ∧ + HasDerivAt (fun t => f (p.1,t)) (V (f p)) p.2) : + f =ᶠ[𝓝 (x₀,(0:ℝ))] (fun p => flow V hK hL p.1 p.2) := by + obtain ⟨r,hr,hrf⟩ := Metric.mem_nhds_iff.mp hf + have he (x : E) (hx : dist x x₀ < r) (t : ℝ) (ht : |t| < r) : + f (x,t) = flow V hK hL x t := by + have hdo (s : ℝ) (hs : s ∈ Ioo (-r) r) := hrf + (show (x,s) ∈ ball (x₀,(0:ℝ)) r by + simpa only [mem_ball, Prod.dist_eq, Real.dist_eq, sub_zero, max_lt_iff] + using And.intro hx (abs_lt.mpr hs)) + apply ODE_solution_unique_of_mem_Ioo + (v := fun _ : ℝ => V) (s := fun _ => Set.univ) + (fun _ _ => hK.lipschitzOnWith) + (show (0:ℝ) ∈ Ioo (-r) r by constructor <;> linarith) + (fun s hs => ⟨(hdo s hs).2, mem_univ _⟩) + (fun s _ => ⟨flow_deriv V hK hL x s, mem_univ _⟩) + (by simpa using (hdo 0 (by constructor <;> linarith)).1) + (abs_lt.mp ht) + filter_upwards [Metric.ball_mem_nhds (x₀,(0:ℝ)) hr] with p hp + have hp' : dist p.1 x₀ < r ∧ |p.2| < r := by + simpa only [mem_ball, Prod.dist_eq, Real.dist_eq, sub_zero, max_lt_iff] using hp + exact he p.1 hp'.1 p.2 hp'.2 + +theorem analytic_flow_on_trajectory (x : E) {I : Set ℝ} (hI : IsPreconnected I) + (h0 : 0 ∈ I) + (hloc : ∀ t ∈ I, ContDiffAt ℝ ω (fun p : E × ℝ => flow V hK hL p.1 p.2) + (flow V hK hL x t,0)) : + ∀ t ∈ I, ContDiffAt ℝ ω (fun p : E × ℝ => flow V hK hL p.1 p.2) (x,t) := by + let F : E × ℝ → E := fun p => flow V hK hL p.1 p.2 + let A : Set ℝ := {t | ContDiffAt ℝ ω F (x,t)} + have hA : IsOpen A := by + rw [isOpen_iff_mem_nhds] + intro t ht + change ContDiffAt ℝ ω F (x,t) at ht + have hc : ContinuousAt (fun s : ℝ => (x,s)) t := by fun_prop + exact hc.eventually ((ht : ContDiffAt ℝ ω F (x,t)).eventually (by simp)) + have hA0 : (I ∩ A).Nonempty := by + refine ⟨0,h0,?_⟩ + simpa [A,F] using hloc 0 h0 + apply hI.subset_of_closure_inter_subset hA hA0 + intro t ht + have hc : ContinuousAt (fun s : ℝ => (flow V hK hL x s,t-s)) t := + ((flow_lipschitz_time V hK hL x).continuous.continuousAt).prodMk + (continuousAt_const.sub continuousAt_id) + have he : ∀ᶠ s in 𝓝 t, ContDiffAt ℝ ω F (flow V hK hL x s,t-s) := by + apply hc.eventually + simpa only [sub_self] using (hloc t ht.2).eventually (by simp) + obtain ⟨s,hs,hsA⟩ := mem_closure_iff_nhds.mp ht.1 _ he + change ContDiffAt ℝ ω F (x,s) at hsA + have hslice : ContDiffAt ℝ ω (fun z : E => flow V hK hL z s) x := + (hsA : ContDiffAt ℝ ω F (x,s)).comp x (contDiffAt_id.prodMk contDiffAt_const) + have hpair : ContDiffAt ℝ ω (fun p : E × ℝ => (flow V hK hL p.1 s,p.2-s)) (x,t) := + (hslice.comp (x,t) contDiffAt_fst).prodMk (contDiffAt_snd.sub contDiffAt_const) + change ContDiffAt ℝ ω F (flow V hK hL x s,t-s) at hs + have ht' := hs.comp (x,t) hpair + change ContDiffAt ℝ ω F (x,t) + convert ht' using 1 + ext p + simp only [F, Function.comp_def] + rw [← flow_add V hK hL p.1 s (p.2-s)] + congr 1 + ring +end Flow + +omit [CompleteSpace E] in + +theorem exists_bounded_lipschitz_cutoff [FiniteDimensional ℝ E] (V : E → E) + (hV : ContDiff ℝ 1 V) (r : ℝ) : + ∃ (W : E → E) (K L : ℝ≥0), LipschitzWith K W ∧ (∀ x, ‖W x‖ ≤ L) ∧ + EqOn W V (closedBall 0 r) := by + let b : ContDiffBump (0 : E) := ⟨max r 0 + 1,max r 0 + 2, + by positivity,by linarith⟩ + let W : E → E := fun x => b x • V x + have hs : HasCompactSupport W := b.hasCompactSupport.smul_right + have hd : ContDiff ℝ 1 W := b.contDiff.smul hV + obtain ⟨K,hK⟩ := hd.lipschitzWith_of_hasCompactSupport hs (by norm_num) + obtain ⟨L,hL⟩ := hs.exists_bound_of_continuous hd.continuous + refine ⟨W,K,⟨max L 0,le_max_right _ _⟩,hK,fun x => (hL x).trans (le_max_left _ _),?_⟩ + intro x hx + have hb : b x = 1 := b.one_of_mem_closedBall (closedBall_subset_closedBall + (show r ≤ b.rIn by dsimp [b]; exact (le_max_left _ _).trans (by linarith)) hx) + simp [W,hb] + +omit [CompleteSpace E] in + +theorem exists_bounded_lipschitz_cutoff_on [FiniteDimensional ℝ E] + (V : E → E) {s U : Set E} (hs : IsCompact s) (hU : IsOpen U) + (hsub : s ⊆ U) (hV : ContDiffOn ℝ 1 V U) : + ∃ (W : E → E) (K L : ℝ≥0), LipschitzWith K W ∧ (∀ x, ‖W x‖ ≤ L) ∧ + ∀ x ∈ s, W =ᶠ[𝓝 x] V := by + obtain ⟨f,hf0,hf1,_⟩ := exists_contMDiffMap_zero_one_nhds_of_isClosed + (𝓘(ℝ,E)) (n := 1) hU.isClosed_compl hs.isClosed + (disjoint_compl_left_iff.mpr hsub) + have hfd : ContDiff ℝ 1 (fun x => f x) := contMDiff_iff_contDiff.mp f.contMDiff + obtain ⟨r,hr⟩ := hs.isBounded.subset_closedBall (0:E) + let b : ContDiffBump (0:E) := ⟨max r 0+1,max r 0+2,by positivity,by linarith⟩ + let W : E → E := fun x => b x • (f x • V x) + have hWd : ContDiff ℝ 1 W := by + apply contDiff_iff_contDiffAt.mpr + intro x + by_cases hx : x ∈ U + · exact b.contDiff.contDiffAt.smul (hfd.contDiffAt.smul + (hV.contDiffAt (hU.mem_nhds hx))) + · apply (contDiffAt_const (c := (0:E))).congr_of_eventuallyEq + filter_upwards [hf0.filter_mono (nhds_le_nhdsSet hx)] with y hy + simp [W,hy] + have hWs : HasCompactSupport W := b.hasCompactSupport.smul_right + obtain ⟨K,hK⟩ := hWd.lipschitzWith_of_hasCompactSupport hWs (by norm_num) + obtain ⟨L,hL⟩ := hWs.exists_bound_of_continuous hWd.continuous + refine ⟨W,K,⟨max L 0,le_max_right _ _⟩,hK, + fun x => (hL x).trans (le_max_left _ _),?_⟩ + intro x hx + have hb : (fun y => b y) =ᶠ[𝓝 x] 1 := b.eventuallyEq_one_of_mem_ball (by + have hx' := hr hx + change dist x 0 ≤ r at hx' + change dist x 0 < max r 0+1 + exact hx'.trans_lt ((le_max_left _ _).trans_lt (by linarith))) + filter_upwards [hb,hf1.filter_mono (nhds_le_nhdsSet hx)] with y hy hy' + simp [W,hy,hy'] + +theorem analytic_family_along_compact_solution [FiniteDimensional ℝ E] + (V : E → E) {U : Set E} (hU : IsOpen U) (hV : ContDiffOn ℝ 1 V U) + (hloc : ∀ x ∈ U, ∃ f : E × ℝ → E, ContDiffAt ℝ ω f (x,0) ∧ + ∀ᶠ p in 𝓝 (x,(0:ℝ)), f (p.1,0) = p.1 ∧ + HasDerivAt (fun t => f (p.1,t)) (V (f p)) p.2) + {γ : ℝ → E} {a b c : ℝ} (ha : a < c) (hb : c < b) + (hγ : Continuous γ) (hγU : ∀ y ∈ Icc a b, γ y ∈ U) + (hγd : ∀ y ∈ Icc a b, HasDerivAt γ (V (γ y)) y) : + ∃ f : E × ℝ → E, Continuous f ∧ (∀ x, f (x,0) = x) ∧ + (∀ y ∈ Icc a b, f (γ c,y-c) = γ y) ∧ + (∀ y ∈ Icc a b, ContDiffAt ℝ ω f (γ c,y-c)) ∧ + ∀ y ∈ Icc a b, ∀ᶠ p in 𝓝 (γ c,y-c), + HasDerivAt (fun t => f (p.1,t)) (V (f p)) p.2 := by + obtain ⟨W,K,L,hK,hL,hW⟩ := exists_bounded_lipschitz_cutoff_on V + (isCompact_Icc.image hγ) hU (by rintro _ ⟨y,hy,rfl⟩; exact hγU y hy) hV + let f : E × ℝ → E := fun p => flow W hK hL p.1 p.2 + have hmatch : ∀ y ∈ Icc a b, f (γ c,y-c) = γ y := by + apply ODE_solution_unique_of_mem_Icc + (v := fun _ => W) (s := fun _ => Set.univ) (K := K) + (fun _ _ => hK.lipschitzOnWith) ⟨ha,hb⟩ + ((continuous_flow W hK hL).comp (by fun_prop)).continuousOn + _ (fun _ _ => mem_univ _) hγ.continuousOn _ (fun _ _ => mem_univ _) + (by simp) + · intro y _ + simpa [f,Function.comp_def] using + (flow_deriv W hK hL (γ c) (y-c)).scomp y ((hasDerivAt_id y).sub_const c) + · intro y hy + rw [(hW (γ y) ⟨y,Ioo_subset_Icc_self hy,rfl⟩).self_of_nhds] + exact hγd y (Ioo_subset_Icc_self hy) + have hlocalW (y : ℝ) (hy : y ∈ Icc a b) : + ContDiffAt ℝ ω f (γ y,0) := by + obtain ⟨g,hgd,hge⟩ := hloc (γ y) (hγU y hy) + have hg0 : g (γ y,0) = γ y := hge.self_of_nhds.1 + have heV : ∀ᶠ p in 𝓝 (γ y,(0:ℝ)), W (g p) = V (g p) := by + have ht := hgd.continuousAt.tendsto + rw [hg0] at ht + exact ht.eventually (hW (γ y) ⟨y,hy,rfl⟩) + have heq : g =ᶠ[𝓝 (γ y,(0:ℝ))] f := by + apply local_family_eq W hK hL (γ y) g + filter_upwards [hge,heV] with p hp hp' + exact ⟨hp.1,hp' ▸ hp.2⟩ + exact hgd.congr_of_eventuallyEq heq.symm + have hd : ∀ y ∈ Icc a b, ContDiffAt ℝ ω f (γ c,y-c) := by + have hh := analytic_flow_on_trajectory W hK hL (γ c) + (I := Icc (a-c) (b-c)) isPreconnected_Icc + (show (0:ℝ) ∈ Icc (a-c) (b-c) by constructor <;> linarith) + (fun s hs => by + have hs' : s+c ∈ Icc a b := by constructor <;> linarith [hs.1,hs.2] + have heq : flow W hK hL (γ c) s = γ (s+c) := by + simpa [f] using hmatch (s+c) hs' + rw [heq] + exact hlocalW (s+c) hs') + exact fun y hy => hh (y-c) (by constructor <;> linarith [hy.1,hy.2]) + refine ⟨f,continuous_flow W hK hL,fun x => flow_zero W hK hL x,hmatch,hd,?_⟩ + intro y hy + have hfc : Tendsto f (𝓝 (γ c,y-c)) (𝓝 (γ y)) := by + have hc : ContinuousAt f (γ c,y-c) := (continuous_flow W hK hL).continuousAt + simpa only [hmatch y hy] using hc.tendsto + filter_upwards [hfc.eventually (hW (γ y) ⟨y,hy,rfl⟩)] with p hp + rw [←hp] + exact flow_deriv W hK hL p.1 p.2 + +end QuinticLienard.GlobalODE + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/HeightLimits.lean b/lean/OAI/Analysis/LienardCycles/HeightLimits.lean new file mode 100644 index 0000000000000000000000000000000000000000..c15c9f99c28bd4bb872f747835c9b5ee9755c646 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/HeightLimits.lean @@ -0,0 +1,73 @@ +import OAI.Analysis.LienardCycles.CharacteristicSigns + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuadraticCoordinates +open PartialCalculus +noncomputable def HN (q : (ℝ × ℝ) × ℝ) : ℝ := H ((q.1.1*q.2,q.1.2*q.2^3),1) +noncomputable def DN (q : (ℝ × ℝ) × ℝ) : ℝ := + HN q+q.1.1*q.2*PN q+3*q.1.2*q.2^3*QN q +lemma HN_analytic (q : (ℝ × ℝ) × ℝ) : ContDiffAt ℝ ω HN q := by + apply (H_analytic (by norm_num : (0:ℝ)<1)).comp q + fun_prop +lemma DN_analytic (q : (ℝ × ℝ) × ℝ) : ContDiffAt ℝ ω DN q := by + unfold DN + have h1 := HN_analytic q + have h2 := PN_analytic q + have h3 := QN_analytic q + fun_prop +lemma HN_zero (d k : ℝ) : HN ((d,k),0)=0 := by + simpa [HN] using (zero_data (by norm_num : (0:ℝ)<1)).2 +lemma DN_zero (d k : ℝ) : DN ((d,k),0)=0 := by simp [DN,HN_zero] +lemma Hr_DN {d k r : ℝ} (hr : 0 < r) : Hr ((d,k),r)=DN ((d,k),r) := by + have he := euler_identity (d := d) (k := k) hr + rw [scaling d k hr,P_scaling d k hr,Q_scaling d k hr] at he + dsimp [DN,HN,PN,QN] + apply (mul_left_cancel₀ (ne_of_gt hr)) + nlinarith only [he] +lemma HN_deriv_zero (d k : ℝ) : HasDerivAt (fun r => HN ((d,k),r)) (d/3) 0 := by + have hm : HasDerivAt (fun s : ℝ => ((d*s,k*s^3),(1:ℝ))) ((d,0),0) 0 := by + convert! (((hasDerivAt_id (0:ℝ)).const_mul d).prodMk + (((hasDerivAt_id (0:ℝ)).pow 3).const_mul k)).prodMk (hasDerivAt_const (0:ℝ) (1:ℝ)) using 1 + norm_num [id_eq] + have hH : HasFDerivAt H (fderiv ℝ H ((0,0),1)) ((d*0,k*0^3),1) := by + simpa using ((H_analytic (d := 0) (k := 0) (by norm_num : (0:ℝ)<1)).differentiableAt (by simp)).hasFDerivAt + have hd := hH.comp_hasDerivAt (f := fun s : ℝ => ((d*s,k*s^3),(1:ℝ))) 0 hm + rw [fderiv_model] at hd + change HasDerivAt (fun r => HN ((d,k),r)) + (d*P ((0,0),1)+0*Q ((0,0),1)+0*Hr ((0,0),1)) 0 at hd + simpa [QuadraticVariation.P_zero (by norm_num : (0:ℝ)<1),div_eq_mul_inv] using hd +lemma DN_deriv_zero (d k : ℝ) : HasDerivAt (fun r => DN ((d,k),r)) (2*d/3) 0 := by + have hd := ((HN_deriv_zero d k).add + (((hasDerivAt_id (0:ℝ)).const_mul d).mul (PNr_hasDerivAt d k 0))).add + ((((hasDerivAt_id (0:ℝ)).pow 3).const_mul (3*k)).mul (QNr_hasDerivAt d k 0)) + convert! hd using 1 + dsimp [DN,Pi.pow_apply,id_eq] + norm_num [PN,QuadraticVariation.P_zero (by norm_num : (0:ℝ)<1)] + ring +lemma Hr_negative_near_zero {d k : ℝ} (hd : d < 0) : + ∀ᶠ r in 𝓝[>] (0:ℝ), Hr ((d,k),r) < 0 := by + have ht := (DN_deriv_zero d k).hasDerivWithinAt (s := Ioi 0) + have hlim := (hasDerivWithinAt_iff_tendsto_slope' (show (0:ℝ) ∉ Ioi 0 by simp)).mp ht + have hn : (2:ℝ)*d/3 < 0 := by linarith + filter_upwards [hlim.eventually (eventually_lt_nhds hn),self_mem_nhdsWithin] with r hh hr + rw [Hr_DN hr] + have hh' : DN ((d,k),r)/r < 0 := by + simpa [slope,DN_zero,vsub_eq_sub,div_eq_mul_inv,mul_comm] using hh + have h := (div_lt_iff₀ hr).mp hh' + simpa using h +end QuinticLienard.QuadraticCoordinates + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/HeightSigns.lean b/lean/OAI/Analysis/LienardCycles/HeightSigns.lean new file mode 100644 index 0000000000000000000000000000000000000000..a67d1a5d868b209654c0225110d6558982816631 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/HeightSigns.lean @@ -0,0 +1,116 @@ +import OAI.Analysis.LienardCycles.CharacteristicPositive + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +namespace QuinticLienard.ModelEndpoint +open PartialCalculus QuadraticCoordinates +lemma d_neg_of_H_neg {d k r : ℝ} (hk : 0 < k) (hr : 0 < r) + (hH : H ((d,k),r) < 0) : d < 0 := by + have hmd : StrictMono (fun d => H ((d,k),r)) := by + apply strictMono_of_deriv_pos + intro a; rw [(P_hasDerivAt hr).deriv]; exact QuadraticVariation.P_pos hr + have hmk : StrictMono (fun k => H ((0,k),r)) := by + apply strictMono_of_deriv_pos + intro a; rw [(Q_hasDerivAt hr).deriv]; exact QuadraticVariation.Q_pos hr + have hH0 : 0 < H ((0,k),r) := by + have hh := hmk hk + simpa only [(zero_data hr).2] using hh + by_contra! hd + have hh := hmd.monotone hd + exact hH.not_ge (hH0.le.trans hh) + +lemma Hr_pos_of_H_nonneg {d k r : ℝ} (hk : 0 < k) (hr : 0 < r) + (hH : 0 ≤ H ((d,k),r)) : 0 < Hr ((d,k),r) := by + obtain ⟨z,hz⟩ := ReferenceCharacteristic.J_surjective d k hr + have hA : 0 ≤ ReferenceCharacteristic.A ((z,k),r) := by + dsimp [ReferenceCharacteristic.A] + rw [hz] + exact div_nonneg hH hr.le + simpa only [ReferenceCharacteristic.D,hz] using ReferenceCharacteristic.D_pos_of_A_nonneg hk hr hA + +lemma w_pos_of_H_nonneg {d k r : ℝ} (hk : 0 < k) (hr : 0 < r) + (hH : 0 ≤ H ((d,k),r)) : 0 < w ((d,k),r) := by + have ha : 0 < alpha ((d,k),r) := div_pos hr (H_gap_pos hr) + have ht := transport_Hr (d := d) (k := k) hr + have hgap : 0 < 1-(Hr ((d,k),r))^2 := by + have hh := abs_lt.mp (Hr_abs_lt (d := d) (k := k) hr) + nlinarith [sq_nonneg (Hr ((d,k),r))] + have hnon : -2*H ((d,k),r)*r*(1-(Hr ((d,k),r))^2)/(gap ((d,k),r))^2 ≤ 0 := + div_nonpos_of_nonpos_of_nonneg + (mul_nonpos_of_nonpos_of_nonneg + (mul_nonpos_of_nonpos_of_nonneg (mul_nonpos_of_nonpos_of_nonneg (by norm_num) hH) hr.le) hgap.le) + (sq_nonneg _) + have hpr := mul_pos hk (R_pos (d := d) (k := k) hr) + have hHrr : 0 < Hrr ((d,k),r) := + pos_of_mul_pos_right (by linarith : 0 < alpha ((d,k),r)*Hrr ((d,k),r)) ha.le + have hplus : 0 < 1+Hr ((d,k),r) := by + have hh := (abs_lt.mp (Hr_abs_lt (d := d) (k := k) hr)).1 + linarith + exact div_pos (mul_pos (by norm_num) hHrr) (mul_pos (sq_pos_of_pos (mr_pos hr)) hplus) + +lemma sch_pos_of_H_neg_Hr_nonneg {d k r : ℝ} (hk : 0 < k) (hr : 0 < r) + (hH : H ((d,k),r) < 0) (hHr : 0 ≤ Hr ((d,k),r)) : 0 < sch ((d,k),r) := by + have hd := d_neg_of_H_neg hk hr hH + have hm := m_pos (d := d) (k := k) hr + have hn := n_pos (d := d) (k := k) hr + have hmn : n ((d,k),r) < m ((d,k),r) := by dsimp [m,n]; linarith + have hl : 1 ≤ ell ((d,k),r) := by + apply (le_div_iff₀ (mr_pos hr)).mpr + linarith + have hl2 : 1 ≤ (ell ((d,k),r))^2 := by nlinarith + have hbase : 0 ≤ (ell ((d,k),r))^2/(n ((d,k),r))^2-1/(m ((d,k),r))^2 := by + have hsq : (n ((d,k),r))^2 ≤ (m ((d,k),r))^2 := sq_le_sq₀ hn.le hm.le |>.mpr hmn.le + have hh : (1:ℝ)/(m ((d,k),r))^2 ≤ (ell ((d,k),r))^2/(n ((d,k),r))^2 := by + apply (div_le_div_iff₀ (sq_pos_of_pos hm) (sq_pos_of_pos hn)).mpr + nlinarith [mul_nonneg (sq_nonneg (m ((d,k),r))) (sub_nonneg.mpr hl2)] + linarith + have hkn : 0 < k*(m ((d,k),r)+n ((d,k),r)*(ell ((d,k),r))^2) := by positivity + have hd2 : 0 ≤ d^2/2*((ell ((d,k),r))^2-1) := mul_nonneg (by positivity) (by linarith) + have hdp : 0 ≤ -d*(1/m ((d,k),r)+(ell ((d,k),r))^2/n ((d,k),r)) := mul_nonneg (neg_nonneg.mpr hd.le) (by positivity) + dsimp only [sch,Prod.fst] at * + nlinarith + +lemma w_nonneg_of_H_neg_Hr_nonneg {d k r : ℝ} (hk : 0 < k) (hr : 0 < r) + (hH : H ((d,k),r) < 0) (hHr : 0 ≤ Hr ((d,k),r)) : 0 ≤ w ((d,k),r) := by + have hd := d_neg_of_H_neg hk hr hH + obtain ⟨a,ha0,har,ha⟩ : ∃ a : ℝ, 0 < a ∧ a < r ∧ Hr ((d,k),a) < 0 := by + have he : ∀ᶠ a in 𝓝[>] (0:ℝ), 0 < a ∧ a < r ∧ Hr ((d,k),a) < 0 := by + filter_upwards [self_mem_nhdsWithin,(eventually_lt_nhds hr).filter_mono inf_le_left, + Hr_negative_near_zero (k := k) hd] with a ha0 har ha + exact ⟨ha0,har,ha⟩ + exact he.exists + let C : ℝ → ℝ := fun s => (1-Hr ((d,k),s))^2*(1+Hr ((d,k),s))/2 + have hC (s : ℝ) (hs : 0 < s) : 0 < C s := by + have hm := mr_pos (d := d) (k := k) hs + have hp : 0 < 1+Hr ((d,k),s) := by + have ht := (abs_lt.mp (Hr_abs_lt (d := d) (k := k) hs)).1 + linarith + dsimp [C]; positivity + apply RegionBarrier.no_negative_w har + (fun s hs => Hr_hasDerivAt (ha0.trans_le hs.1)) + (C := C) (w' := fun s => (1-Hr ((d,k),s))*(sch ((d,k),s)+(1/2)*(w ((d,k),s))^2)) + _ (fun s hs => w_deriv (ha0.trans_le hs.1)) (fun s hs => hC s (ha0.trans_le hs.1)) _ ha hH hHr + · intro s hs + convert! Hrr_hasDerivAt (d := d) (k := k) (ha0.trans_le hs.1) using 1 + dsimp [C,w] + have hm := mr_pos (d := d) (k := k) (ha0.trans_le hs.1) + have hp : 0 < 1+Hr ((d,k),s) := by + have ht := (abs_lt.mp (Hr_abs_lt (d := d) (k := k) (ha0.trans_le hs.1))).1 + linarith + field_simp [ne_of_gt hm,ne_of_gt hp] + · intro s hs hHs hHrs + have hsch := sch_pos_of_H_neg_Hr_nonneg hk (ha0.trans_le hs.1) hHs hHrs + exact mul_pos (mr_pos (ha0.trans_le hs.1)) (by nlinarith [sq_nonneg (w ((d,k),s))]) +end QuinticLienard.ModelEndpoint + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/HyperbolicCoordinate.lean b/lean/OAI/Analysis/LienardCycles/HyperbolicCoordinate.lean new file mode 100644 index 0000000000000000000000000000000000000000..d4a45e73a92ecfba5514c3bc7102e5cd61e12c26 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/HyperbolicCoordinate.lean @@ -0,0 +1,52 @@ +import OAI.Analysis.LienardCycles.ConditionalFit + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter Metric +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard +noncomputable def angle (x : ℝ) : ℝ := (Real.log (1+x)-Real.log (1-x))/2 + +lemma angle_analytic {x : ℝ} (hx : |x| < 1) : ContDiffAt ℝ ω angle x := by + have h := abs_lt.mp hx + apply ContDiffAt.div_const + apply ContDiffAt.sub + · exact (contDiffAt_const.add contDiffAt_id).log (by dsimp only [id_eq]; linarith [h.1,h.2]) + · exact (contDiffAt_const.sub contDiffAt_id).log (by dsimp only [id_eq]; linarith [h.1,h.2]) + +lemma angle_deriv {x : ℝ} (hx : |x| < 1) : HasDerivAt angle (1/(1-x^2)) x := by + have h := abs_lt.mp hx + have h₁ : 1+x ≠ 0 := by linarith + have h₂ : 1-x ≠ 0 := by linarith + have h₃ : 1-x^2 ≠ 0 := by nlinarith [mul_pos (show 0 < 1+x by linarith) (show 0 < 1-x by linarith)] + convert! (((hasDerivAt_id x).const_add 1).log h₁).sub + (((hasDerivAt_id x).const_sub 1).log h₂) |>.div_const 2 using 1 + dsimp only [id_eq] + field_simp [h₁,h₂,h₃] + ring + +@[simp] lemma angle_zero : angle 0=0 := by simp [angle] +lemma angle_neg (x : ℝ) : angle (-x) = -angle x := by + simp only [angle,sub_neg_eq_add,←sub_eq_add_neg] + ring + +lemma angle_strictMono : StrictMonoOn angle (Ioo (-1) 1) := by + apply strictMonoOn_of_deriv_pos (convex_Ioo _ _) + (fun x hx => (angle_deriv (abs_lt.mpr hx)).continuousAt.continuousWithinAt) + intro x hx + have hx' := interior_subset (s := Ioo (-1) 1) hx + rw [(angle_deriv (abs_lt.mpr hx')).deriv] + exact div_pos one_pos (by nlinarith [mul_pos (sub_pos.mpr hx'.2) (show 0 < 1+x by linarith [hx'.1])]) +end QuinticLienard + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/Intercept.lean b/lean/OAI/Analysis/LienardCycles/Intercept.lean new file mode 100644 index 0000000000000000000000000000000000000000..a50384212e5d7c92c6adae8eb57c981ac0743190 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/Intercept.lean @@ -0,0 +1,145 @@ +import OAI.Analysis.LienardCycles.ActualReflection + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ScaledProfile +lemma intercept_ratio_strictMono {a : Fin 6 → ℝ} {d : ℝ} + (hp : ∀ u, 0(slope a u-d)/u) (Ioi 0) := by + have hd (u : ℝ) (hu : 0(hd u hu).continuousAt.continuousWithinAt) + intro u hu + have hu' : 0 + (d+h*κ)*(u-h)+κ*(u-h)^2/2 := by + let f : ℝ → ℝ := fun u=>QuinticProfile.profile a (0,u)-(d+h*κ)*(u-h)-κ*(u-h)^2/2 + have hd (u : ℝ) (hu : h≤u) : HasDerivAt f (slope a u-d-κ*u) u := by + convert! ((profile_hasDerivAt a (hh.trans_le hu)).sub + (((hasDerivAt_id u).sub_const h).const_mul (d+h*κ))).sub + ((((hasDerivAt_id u).sub_const h).pow 2).const_mul κ |>.div_const 2) using 1 + simp only [id_eq] + ring + have hm : StrictMonoOn f (Ici h) := by + apply strictMonoOn_of_deriv_pos (convex_Ici h) + (fun u hu=>(hd u hu).continuousAt.continuousWithinAt) + intro u hu + have hhu : hQuinticFit.intercept a d (point a t s)) (-interceptRate a t r) r := by + have hl := along_deriv he ((QuinticFit.lambda_analytic a (base_spec he).1 (radius_pos he)).differentiableAt (by simp)) + have hk := along_deriv he ((QuinticFit.kappa_analytic a (base_spec he).1 (radius_pos he)).differentiableAt (by simp)) + have htr := QuinticFit.fit_transport a (base_spec he).1 (radius_pos he) + have hL : QuinticFit.D a (QuinticFit.lambda a) (point a t r)=QuinticFit.kappa a (point a t r)+ + S (QuinticFit.fit a (point a t r))/G (QuinticFit.fit a (point a t r))*(QuinticFit.lambda a (point a t r)-k a t r) := by + dsimp only [point,k] + linarith only [htr.2.2] + dsimp only [point] at hk + rw [htr.2.1] at hk + rw [hL] at hl + convert! (hl.sub ((base_deriv he).mul hk)).sub_const d using 1 + dsimp only [interceptRate,point,k] + ring +lemma intercept_small {a : Fin 6 → ℝ} {t r d : ℝ} (he : Adm a t r) + (hp : ∀ u, 0] (0:ℝ), QuinticFit.intercept a d (point a t s)<0 := by + have ht : 0] (0:ℝ), 0-QuinticFit.intercept a d (point a t v)) (interceptRate a t u) u := by + convert! (intercept_deriv (adm_le he (hs.trans_le hu.1) hu.2) d).const_mul (-1) using 1 <;> simp + have hit := RealAnalysis.positive_of_deriv_pos_at_zero hsr + (fun u hu=>(hd u hu).continuousAt.continuousWithinAt) hd (neg_pos.mpr hIs).le (fun u hu hz=>?_) + · exact neg_pos.mp hit + · have heu := adm_le he (hs.trans_le hu.1) hu.2 + have hI : QuinticFit.intercept a d (point a t u)=0 := neg_eq_zero.mp hz + have hslope := QuinticFit.intercept_zero_slope_gt (base_spec heu).1 (radius_pos heu) hp hI + dsimp only [interceptRate] + exact mul_pos (mul_pos (div_pos (g_pos heu) (radius_pos heu)) + (div_pos (add_pos (S_pos (radius_pos heu)) (mul_pos (base_spec heu).1 (R_pos (radius_pos heu)))) + (G_pos (radius_pos heu)))) (sub_pos.mpr hslope) +end QuinticLienard.ActualCharacteristic +namespace QuinticLienard.QuinticFit +theorem intercept_negative {a : Fin 6 → ℝ} {h r d : ℝ} (hh : 0QuinticProfile.analytic a h) + (QuinticProfile.local_flow a) (p:=0) hh hr + have he : ActualCharacteristic.Adm a t r := ⟨h,hh,ht.1,ht.2⟩ + have hb : ActualCharacteristic.b a t r=h := PositiveWidth.base_eq _ + (fun _ h=>QuinticProfile.analytic a h) (QuinticProfile.local_flow a) hh ht.1 ht.2 + have hi := ActualCharacteristic.intercept_lt he hp + dsimp only [intercept,ActualCharacteristic.point] at hi + rw [hb] at hi + linarith +end QuinticLienard.QuinticFit + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/IntervalInverse.lean b/lean/OAI/Analysis/LienardCycles/IntervalInverse.lean new file mode 100644 index 0000000000000000000000000000000000000000..c3914ee5eaf7bfd2efbe6e39dc3dc2a58e0d3a28 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/IntervalInverse.lean @@ -0,0 +1,54 @@ +import OAI.Analysis.LienardCycles.SharpPhysical + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open scoped Topology +open Set Filter Metric +open scoped Topology ContDiff +open scoped Topology NNReal +open Set Filter +open scoped Topology ContDiff NNReal + +open Set Filter +open scoped Topology +namespace QuinticLienard.RealAnalysis + +theorem continuous_interval_inverse {f : ℝ → ℝ} {a b c d : ℝ} (hcd : c≤d) + (hc : ContinuousOn f (Icc a b)) (hb : BijOn f (Icc a b) (Icc c d)) : + ∃ g : ℝ → ℝ, Continuous g ∧ (∀ y,g y ∈ Icc a b) ∧ + (∀ y ∈ Icc c d,f (g y)=y) ∧ (∀ t ∈ Icc a b,g (f t)=t) := by + let F : Icc a b → Icc c d := fun t=>⟨f t,hb.mapsTo t.property⟩ + have hF : Function.Bijective F := by + constructor + · intro x y h + exact Subtype.ext (hb.injOn x.property y.property (congrArg Subtype.val h)) + · intro y + obtain ⟨x,hx,he⟩ := hb.surjOn y.property + exact ⟨⟨x,hx⟩,Subtype.ext he⟩ + let e : Icc a b ≃ Icc c d := Equiv.ofBijective F hF + have hec : Continuous e := by + exact (hc.domRestrict).subtype_mk _ + let H : Icc a b ≃ₜ Icc c d := hec.homeoOfEquivCompactToT2 + let clamp : ℝ → Icc c d := fun y=>⟨max c (min d y),le_max_left _ _,max_le hcd (min_le_left _ _)⟩ + have hcl : Continuous clamp := (continuous_const.max (continuous_const.min continuous_id)).subtype_mk _ + have hcl_eq (y : ℝ) (hy : y ∈ Icc c d) : (clamp y : ℝ)=y := by simp [clamp,max_eq_right hy.1,min_eq_right hy.2] + let g : ℝ → ℝ := fun y=>H.symm (clamp y) + refine ⟨g,continuous_subtype_val.comp (H.symm.continuous.comp hcl),fun y=>(H.symm (clamp y)).property,?_,?_⟩ + · intro y hy + have h := congrArg Subtype.val (H.apply_symm_apply (clamp y)) + change f (g y)=(clamp y : ℝ) at h + exact h.trans (hcl_eq y hy) + · intro t ht + have hclt : clamp (f t)=H ⟨t,ht⟩ := Subtype.ext (hcl_eq (f t) (hb.mapsTo ht)) + dsimp [g] + rw [hclt,H.symm_apply_apply] +end QuinticLienard.RealAnalysis + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/LocalExcursion.lean b/lean/OAI/Analysis/LienardCycles/LocalExcursion.lean new file mode 100644 index 0000000000000000000000000000000000000000..e951f08584c6788205628d0e65aef03937f674aa --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/LocalExcursion.lean @@ -0,0 +1,95 @@ +import OAI.Analysis.LienardCycles.ReturnNeighborhood + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open Set Filter Metric +open scoped Topology NNReal +open scoped Topology ContDiff +open scoped Topology +open Set Filter +open scoped Topology ContDiff NNReal + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard +open RealAnalysis ScaledProfile ScalarArcs AxisFlow +lemma IsRightExcursion.graph_on {F : Polynomial ℝ} {a : Fin 6 → ℝ} + (hF : ∀ x,F.eval x=poly a x) {z : ℝ → Plane} {s t : ℝ} + (hc : Continuous z) (hz : ∀ v ∈ Icc s t, HasDerivAt z (vectorField F (z v)) v) (he : IsRightExcursion z s t) : + ∃ u : ℝ → ℝ, Continuous u ∧ u (z t).2=0 ∧ u (z s).2=0 ∧ + (∀ y ∈ Ioo (z t).2 (z s).2,0(z w).1) ((z v).2-F.eval (z v).1) v := by + simpa [vectorField] using! (ContinuousLinearMap.fst ℝ ℝ ℝ).hasFDerivAt.comp_hasDerivAt v (hz v hv) + have hyd (v : ℝ) (hv : v ∈ Icc s t) : HasDerivAt (fun w=>(z w).2) (-(z v).1) v := by + simpa [vectorField] using! (ContinuousLinearMap.snd ℝ ℝ ℝ).hasFDerivAt.comp_hasDerivAt v (hz v hv) + have hanti : StrictAntiOn (fun v=>(z v).2) (Icc s t) := by + apply strictAntiOn_of_deriv_neg (convex_Icc s t) hc.snd.continuousOn + intro v hv + rw [(hyd v (interior_subset hv)).deriv] + exact neg_neg_of_pos (he.positive v (by simpa using hv)) + have hylt := hanti ⟨le_rfl,he.lt.le⟩ ⟨he.lt.le,le_rfl⟩ he.lt + have hb : BijOn (fun v=>(z v).2) (Icc s t) (Icc (z t).2 (z s).2) := by + refine ⟨?_,hanti.injOn,?_⟩ + · intro v hv + exact ⟨hanti.antitoneOn hv ⟨he.lt.le,le_rfl⟩ hv.2, + hanti.antitoneOn ⟨le_rfl,he.lt.le⟩ hv hv.1⟩ + · intro y hy + exact intermediate_value_Icc' he.lt.le hc.snd.continuousOn hy + obtain ⟨τ,hτc,hτmem,hτr,hτl⟩ := continuous_interval_inverse hylt.le hc.snd.continuousOn hb + have hτint (y : ℝ) (hy : y ∈ Ioo (z t).2 (z s).2) : τ y ∈ Ioo s t := by + have hm := hτmem y + refine ⟨lt_of_le_of_ne hm.1 ?_,lt_of_le_of_ne hm.2 ?_⟩ + · intro hn + have hh := hτr y (Ioo_subset_Icc_self hy) + rw [←hn] at hh + exact hy.2.ne hh.symm + · intro hn + have hh := hτr y (Ioo_subset_Icc_self hy) + rw [hn] at hh + exact hy.1.ne hh + let u : ℝ → ℝ := fun y=>(z (τ y)).1^2/2 + have hu : ∀ v ∈ Icc s t,u (z v).2=(z v).1^2/2 := fun v hv=>by dsimp [u];rw [hτl v hv] + refine ⟨u,(hc.fst.comp hτc).pow 2 |>.div_const 2,?_,?_,?_,hu⟩ + · rw [hu t ⟨he.lt.le,le_rfl⟩,he.right];norm_num + · rw [hu s ⟨le_rfl,he.lt.le⟩,he.left];norm_num + · intro y hy + have hx := he.positive (τ y) (hτint y hy) + have hτd : HasDerivAt τ (-(z (τ y)).1)⁻¹ y := + HasDerivAt.of_local_left_inverse hτc.continuousAt (hyd (τ y) (Ioo_subset_Icc_self (hτint y hy))) (neg_ne_zero.mpr hx.ne') + ((show ∀ᶠ v in 𝓝 y,v ∈ Ioo (z t).2 (z s).2 from Ioo_mem_nhds hy.1 hy.2).mono fun v hv=>hτr v (Ioo_subset_Icc_self hv)) + refine ⟨div_pos (sq_pos_of_pos hx) (by norm_num),?_⟩ + convert! (((hxd (τ y) (Ioo_subset_Icc_self (hτint y hy))).pow 2).div_const 2).comp y hτd using 1 + symm + change (2*(z (τ y)).1^(2-1)*((z (τ y)).2-F.eval (z (τ y)).1)/2)*(-(z (τ y)).1)⁻¹=φ a ((z (τ y)).1^2/2)-y + rw [AxisFlow.φ_square a hx.le,←hF,hτr y (Ioo_subset_Icc_self hy)] + field_simp [hx.ne'] + ring +lemma IsRightExcursion.axis_peak_on {F : Polynomial ℝ} {a : Fin 6 → ℝ} + (hF : ∀ x,F.eval x=poly a x) {z : ℝ → Plane} {s t : ℝ} + (hc : Continuous z) (hz : ∀ v ∈ Icc s t, HasDerivAt z (vectorField F (z v)) v) + (hl : (z t).2(hud y hy).1,fun y hy=>(hud y hy).2⟩ + obtain ⟨H,hH,hp,hpeak,_⟩ := hu.peak_exists + obtain ⟨hlo,hro⟩ := hu.axis_endpoints (φ_smooth a) (φ_continuous a).continuousOn hH hp hpeak + refine ⟨H,⟨hH,?_,?_⟩,hlo,hro⟩ + · change axisLower (φ a) H f ((a,k),s)) (fr ((a,k),r)) r) + (hb : HasDerivAt (fun a => fr ((a,k),r)) b z) : + HasDerivAt (fun s => direction ((1,0),0) f ((z,k),s)) b r := by + have he : (fun a => direction ((0,0),1) f ((a,k),r)) = (fun a => fr ((a,k),r)) := by + ext a + exact (slice_r ((hf ((a,k),r) hr).differentiableAt (by simp))).unique (hfr a) + have hcross := (slice_d ((direction_contDiffAt (hf ((z,k),r) hr) ((0,0),1)).differentiableAt + (by simp))).unique (he ▸ hb) + have hh := slice_r ((direction_contDiffAt (hf ((z,k),r) hr) ((1,0),0)).differentiableAt (by simp)) + rw [←direction_comm (hf ((z,k),r) hr) ((1,0),0) ((0,0),1),hcross] at hh + exact hh + +lemma mixed_k_radius {f fr : (ℝ × ℝ) × ℝ → ℝ} {z k r b : ℝ} + (hf : ∀ q, 0 < q.2 → ContDiffAt ℝ ω f q) (hr : 0 < r) + (hfr : ∀ a, HasDerivAt (fun s => f ((z,a),s)) (fr ((z,a),r)) r) + (hb : HasDerivAt (fun a => fr ((z,a),r)) b k) : + HasDerivAt (fun s => direction ((0,1),0) f ((z,k),s)) b r := by + have he : (fun a => direction ((0,0),1) f ((z,a),r)) = (fun a => fr ((z,a),r)) := by + ext a + exact (slice_r ((hf ((z,a),r) hr).differentiableAt (by simp))).unique (hfr a) + have hcross := (slice_k ((direction_contDiffAt (hf ((z,k),r) hr) ((0,0),1)).differentiableAt + (by simp))).unique (he ▸ hb) + have hh := slice_r ((direction_contDiffAt (hf ((z,k),r) hr) ((0,1),0)).differentiableAt (by simp)) + rw [←direction_comm (hf ((z,k),r) hr) ((0,1),0) ((0,0),1),hcross] at hh + exact hh + +end QuinticLienard.QuadraticCoordinates + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/Model.lean b/lean/OAI/Analysis/LienardCycles/Model.lean new file mode 100644 index 0000000000000000000000000000000000000000..f14d759292211c2138b548652bfa4c1dcc46dd2f --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/Model.lean @@ -0,0 +1,27 @@ +import Mathlib + +namespace OAI + +namespace QuinticLienard + +abbrev Plane := ℝ × ℝ + +def vectorField (F : Polynomial ℝ) (z : Plane) : Plane := + (z.2 - F.eval z.1, -z.1) + +def IsSolution (F : Polynomial ℝ) (z : ℝ → Plane) : Prop := + ∀ t : ℝ, HasDerivAt z (vectorField F (z t)) t + +def IsPeriodicOrbit (F : Polynomial ℝ) (C : Set Plane) : Prop := + ∃ (z : ℝ → Plane) (T : ℝ), + IsSolution F z ∧ 0 < T ∧ Function.Periodic z T ∧ + (∃ s t : ℝ, z s ≠ z t) ∧ C = Set.range z + +def IsLimitCycle (F : Polynomial ℝ) (C : Set Plane) : Prop := + IsPeriodicOrbit F C ∧ + ∃ U : Set Plane, IsOpen U ∧ C ⊆ U ∧ + ∀ C' : Set Plane, IsPeriodicOrbit F C' → C' ⊆ U → C' = C + +end QuinticLienard + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ModelAlgebra.lean b/lean/OAI/Analysis/LienardCycles/ModelAlgebra.lean new file mode 100644 index 0000000000000000000000000000000000000000..373f0621b57424955d98ad1b7463b4c82b15d9dd --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ModelAlgebra.lean @@ -0,0 +1,342 @@ +import OAI.Analysis.LienardCycles.HeightSigns + +namespace OAI + +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter MeasureTheory +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +namespace QuinticLienard.ModelAlgebra + +noncomputable def wStar (m n l : ℝ) : ℝ := + 2 * (l * m^4 - 2*l*m^3*n + 2*m*n^3 - n^4) / (m^2*n^2*(m+n)) + +noncomputable def dStar (m n l w S : ℝ) : ℝ := + (m-n)*S + (1-2*n/m+l*(2*m/n-1))*w + (m+n)/2*w^2 + +noncomputable def schwarzian (m n l b d : ℝ) : ℝ := + 2*b*(m+n*l^2) + d^2/2*(l^2-1) - d*(1/m+l^2/n) + + 3/2*(l^2/n^2-1/m^2) + +noncomputable def A (z l : ℝ) : ℝ := 2*l*z^3-3*l*z^2+3*z-2 +noncomputable def T (z l : ℝ) : ℝ := 2*l*z^3-l*z^2-z+2 +noncomputable def J (z l : ℝ) : ℝ := 2*l*z^4-2*l*z^3-l*z^2+z^2+2*z-2 +noncomputable def S₀ (z l : ℝ) : ℝ := 3/2*(l^2-z⁻¹^2) + +lemma A_pos {z l : ℝ} (hz : 1 < z) (hl : 0 < l) (hl1 : l < 1) : 0 < A z l := by + have hz1 : 0 < z - 1 := by linarith + have hA : A z l = (1-l)*(3*(z-1)+1) + + l * (z-1) * (2*(z-1)^2+3*(z-1)+3) := by unfold A; ring + rw [hA] + positivity + +lemma J_pos {z l : ℝ} (hz : 1 < z) (hl : 0 < l) (hl1 : l < 1) : 0 < J z l := by + have hz1 : 0 < z - 1 := by linarith + have hz2 : 0 < z + 1 := by linarith + have hJ : J z l = (1-l)*((z-1)^2+4*(z-1)+1) + + l * (2*(z-1)*(z+1)*((z-1)^2+(z-1)+1)) := by unfold J; ring + rw [hJ] + positivity + +lemma wStar_normalized (z l : ℝ) : + wStar z 1 l = 2*(l*z^3*(z-2)+2*z-1) / (z^2*(z+1)) := by + unfold wStar + congr 1 <;> ring + +lemma wStar_pos {z l : ℝ} (hz : 1 < z) (hl : 0 < l) (hl1 : l < 1) : + 0 < wStar z 1 l := by + have hz0 : 0 < z := by linarith + have hz1 : 0 < z - 1 := by linarith + have hz2 : 0 < z + 1 := by linarith + rw [wStar_normalized] + have heq : l*z^3*(z-2)+2*z-1 = + (1-l)*(2*(z-1)+1)+l*(z-1)^3*(z+1) := by ring + rw [heq] + positivity + +lemma baseline {z l : ℝ} (hz : 0 < z) : + dStar z 1 l (wStar z 1 l) (S₀ z l) = + (z-1)/(2*z^4) * A z l * T z l := by + have hz0 : z ≠ 0 := ne_of_gt hz + have hz1 : z + 1 ≠ 0 := by positivity + unfold dStar S₀ A T + rw [wStar_normalized] + field_simp + ring + +lemma delta_factor {z l : ℝ} (hz : 0 < z) : + 1/z-l-wStar z 1 l = -(z-1)/((z+1)*z^2) * T z l := by + have hz0 : z ≠ 0 := ne_of_gt hz + have hz1 : z + 1 ≠ 0 := by positivity + rw [wStar_normalized] + unfold T + field_simp + ring + +lemma derivative_at_wStar {z l : ℝ} (hz : 0 < z) : + (1-2/z+l*(2*z-1)) + (z+1)*wStar z 1 l = J z l / z^2 := by + have hz0 : z ≠ 0 := ne_of_gt hz + have hz1 : z + 1 ≠ 0 := by positivity + rw [wStar_normalized] + unfold J + field_simp + ring + +lemma dStar_mono_from_wStar {z l w S : ℝ} + (hz : 1 < z) (hl : 0 < l) (hl1 : l < 1) (hw : wStar z 1 l ≤ w) : + dStar z 1 l (wStar z 1 l) S ≤ dStar z 1 l w S := by + have hz0 : 0 < z := by linarith + have hz1 : 0 < z + 1 := by linarith + have hp : 0 < 1-2/z+l*(2*z-1)+(z+1)*wStar z 1 l := by + rw [derivative_at_wStar hz0] + exact div_pos (J_pos hz hl hl1) (sq_pos_of_pos hz0) + have heq : dStar z 1 l w S - dStar z 1 l (wStar z 1 l) S = + (w-wStar z 1 l) * ((1-2/z+l*(2*z-1)+(z+1)*wStar z 1 l) + + (z+1)/2*(w-wStar z 1 l)) := by unfold dStar; ring + have hw0 : 0 ≤ w-wStar z 1 l := sub_nonneg.mpr hw + have : 0 ≤ dStar z 1 l w S - dStar z 1 l (wStar z 1 l) S := by + rw [heq] + positivity + linarith + +lemma schwarzian_improvement (z l b d : ℝ) : + schwarzian z 1 l b d - S₀ z l = + (2*b*z-d^2/2)+l^2*(2*b+d^2/2-d)-d/z := by + unfold schwarzian S₀ + simp only [div_one, one_pow, one_div] + ring + +lemma schwarzian_last (z l b d : ℝ) : + schwarzian z 1 l b d = + (2*b*z-d^2/2)+l^2*(2*b+d^2/2-d+3/2)-d/z-3/(2*z^2) := by + unfold schwarzian + simp only [div_one, one_pow] + ring + +lemma riccati_consequence {z l b d w : ℝ} + (hl : 0 < l) (hd : d < 0) (hw : wStar z 1 l ≤ w) + (hR : w ≤ 1/z-l+d*l-2*Real.sqrt (d^2/4-b*z)) : + 2*Real.sqrt (d^2/4-b*z) < 1/z-l-wStar z 1 l := by + have hdl : d*l < 0 := mul_neg_of_neg_of_pos hd hl + linarith + +lemma last_case_nonneg_T {z l b d w : ℝ} + (hz : 1 < z) (hl : 0 < l) (hl1 : l < 1) (hb : 0 < b) (hd : d < 0) + (hw : wStar z 1 l ≤ w) (hT : 0 ≤ T z l) + (hRic : 4*b*z ≤ d^2 → + w ≤ 1/z-l+d*l-2*Real.sqrt (d^2/4-b*z)) : + 0 < dStar z 1 l w (schwarzian z 1 l b d) := by + have hz0 : 0 < z := by linarith + have hz1 : 0 < z - 1 := by linarith + have hdelta : 1/z-l-wStar z 1 l ≤ 0 := by + rw [delta_factor hz0] + apply mul_nonpos_of_nonpos_of_nonneg + · exact div_nonpos_of_nonpos_of_nonneg (by linarith) (by positivity) + · exact hT + have hd2 : d^2 < 4*b*z := by + by_contra! h + have hstrict := riccati_consequence hl hd hw (hRic h) + have hs := Real.sqrt_nonneg (d^2/4-b*z) + linarith + have hbase : 0 ≤ dStar z 1 l (wStar z 1 l) (S₀ z l) := by + rw [baseline hz0] + exact mul_nonneg (mul_nonneg (by positivity) (A_pos hz hl hl1).le) hT + have hS : 0 < schwarzian z 1 l b d - S₀ z l := by + rw [schwarzian_improvement] + have ht1 : 0 < 2*b*z-d^2/2 := by linarith + have ht2 : 0 ≤ l^2*(2*b+d^2/2-d) := by + apply mul_nonneg (sq_nonneg _) + nlinarith only [sq_nonneg d, hb, hd] + have ht3 : 0 < -(d/z) := by + simpa only [neg_div] using div_pos (neg_pos.mpr hd) hz0 + linarith + have heq : dStar z 1 l (wStar z 1 l) (schwarzian z 1 l b d) = + dStar z 1 l (wStar z 1 l) (S₀ z l) + + (z-1)*(schwarzian z 1 l b d - S₀ z l) := by unfold dStar; ring + have hpos : 0 < dStar z 1 l (wStar z 1 l) (schwarzian z 1 l b d) := by + rw [heq] + exact add_pos_of_nonneg_of_pos hbase (mul_pos hz1 hS) + exact hpos.trans_le (dStar_mono_from_wStar hz hl hl1 hw) + +lemma negative_T_estimates {z l : ℝ} (hz : 1 < z) (hl : 0 < l) + (hT : T z l < 0) : 2 < z ∧ 2+3*l < z := by + have hz0 : 0 < z := by linarith + have hzpow : 0 < z^2 := sq_pos_of_pos hz0 + have ht : 0 < l*z^2*(2*z-1) := mul_pos (mul_pos hl hzpow) (by linarith) + have hTwo : 2 < z := by unfold T at hT; nlinarith only [hT, ht] + have hSquare : 4 < z^2 := by nlinarith only [hTwo] + have hrest : 0 < z^2*(2*z-1)-3 := by + have : 0 < z^2*(2*z-4) := mul_pos hzpow (by linarith) + nlinarith only [this, hSquare] + have hprod : 0 < l * (z^2*(2*z-1)-3) := mul_pos hl hrest + exact ⟨hTwo, by unfold T at hT; nlinarith only [hT, hprod]⟩ + +lemma slope_estimate {z l d : ℝ} (hz : 0 < z) (hl : 0 < l) + (hzl : 2 + 3*l < z) (hX : d < (l/z-1)/(1+l)) : 2 < -d*z := by + have hl1 : 0 < 1+l := by linarith + have h1 : d*(1+l) < l/z-1 := (lt_div_iff₀ hl1).mp hX + have h2 := mul_lt_mul_of_pos_right h1 hz + have heq : (l/z-1)*z = l-z := by field_simp + rw [heq] at h2 + have hh : (2+d*z)*(1+l) < 0 := by nlinarith only [h2, hzl] + have hneg : 2+d*z < 0 := by + by_contra hn + have hnonneg := mul_nonneg (le_of_not_gt hn) hl1.le + linarith only [hnonneg, hh] + linarith + +lemma last_case_neg_T {z l b d w : ℝ} + (hz : 1 < z) (hl : 0 < l) (hl1 : l < 1) (hb : 0 < b) (hd : d < 0) + (hw : wStar z 1 l ≤ w) (hT : T z l < 0) + (hX : d < (l/z-1)/(1+l)) + (hRic : 4*b*z ≤ d^2 → + w ≤ 1/z-l+d*l-2*Real.sqrt (d^2/4-b*z)) : + 0 < dStar z 1 l w (schwarzian z 1 l b d) := by + have hz0 : 0 < z := by linarith + have hzsq : 0 < z^2 := sq_pos_of_pos hz0 + obtain ⟨hz2, hzl⟩ := negative_T_estimates hz hl hT + have hdz : 2 < -d*z := slope_estimate hz0 hl hzl hX + have hddiv : 2/z^2 < -d/z := by + have heq : -d/z = (-d*z)/z^2 := by field_simp + rw [heq] + exact div_lt_div_of_pos_right hdz hzsq + have hfirst : -(1/(2*z^2)) < 2*b*z-d^2/2 := by + by_cases hnonneg : 0 ≤ 2*b*z-d^2/2 + · have : 0 < 1/(2*z^2) := by positivity + linarith + · have hlarge : 4*b*z ≤ d^2 := by linarith + have hrad : 0 ≤ d^2/4-b*z := by linarith + have hroot := Real.sq_sqrt hrad + have hroot0 := Real.sqrt_nonneg (d^2/4-b*z) + have hstrict := riccati_consequence hl hd hw (hRic hlarge) + have hws := wStar_pos hz hl hl1 + have hupper : 2*Real.sqrt (d^2/4-b*z) < 1/z := by linarith + have hrecip : 0 < 1/z := by positivity + have hsquare : 4*(Real.sqrt (d^2/4-b*z))^2 < (1/z)^2 := by + nlinarith only [sq_nonneg (2*Real.sqrt (d^2/4-b*z)-1/z), + mul_pos (by linarith : 0 < 1/z-2*Real.sqrt (d^2/4-b*z)) + (by linarith : 0 < 1/z+2*Real.sqrt (d^2/4-b*z))] + have heq : (1/z)^2 = 1/z^2 := by ring + rw [heq] at hsquare + have heq2 : 1/(2*z^2) = (1/z^2)/2 := by ring + rw [heq2] + nlinarith only [hsquare, hroot] + have hS : 0 < schwarzian z 1 l b d := by + rw [schwarzian_last] + have hterm : 0 ≤ l^2*(2*b+d^2/2-d+3/2) := by + apply mul_nonneg (sq_nonneg _) + nlinarith only [sq_nonneg d, hb, hd] + have heq : 3/(2*z^2) = -(1/(2*z^2))+2/z^2 := by ring + rw [heq] + simp only [neg_div] at hddiv + linarith + have hwpos : 0 < w := (wStar_pos hz hl hl1).trans_le hw + have hcoeff : 0 < 1-2/z+l*(2*z-1) := by + have hdiv : 2/z < 1 := (div_lt_one hz0).mpr hz2 + have : 0 < l*(2*z-1) := mul_pos hl (by linarith) + linarith + unfold dStar + simp only [mul_one, div_one] + have : 0 < z-1 := by linarith + positivity + +lemma last_case {z l b d w : ℝ} + (hz : 1 < z) (hl : 0 < l) (hl1 : l < 1) (hb : 0 < b) (hd : d < 0) + (hw : wStar z 1 l ≤ w) + (hX : d < (l/z-1)/(1+l)) + (hRic : 4*b*z ≤ d^2 → + w ≤ 1/z-l+d*l-2*Real.sqrt (d^2/4-b*z)) : + 0 < dStar z 1 l w (schwarzian z 1 l b d) := by + rcases le_or_gt 0 (T z l) with hT | hT + · exact last_case_nonneg_T hz hl hl1 hb hd hw hT hRic + · exact last_case_neg_T hz hl hl1 hb hd hw hT hX hRic + +lemma wStar_neg {z l : ℝ} (hz : 0 < z) (hz1 : z < 1) (hl : 1 ≤ l) : + wStar z 1 l < 0 := by + rw [wStar_normalized] + have ht : z^3*(z-2) < 0 := mul_neg_of_pos_of_neg (pow_pos hz _) (by linarith) + have hb : l*z^3*(z-2) ≤ z^3*(z-2) := by + nlinarith only [mul_nonpos_of_nonneg_of_nonpos (sub_nonneg.mpr hl) ht.le] + have heq : z^3*(z-2)+2*z-1 = (z-1)^3*(z+1) := by ring + have hbase : z^3*(z-2)+2*z-1 < 0 := by + rw [heq] + exact mul_neg_of_neg_of_pos ((show Odd (3 : ℕ) by decide).pow_neg (by linarith)) (by positivity) + apply div_neg_of_neg_of_pos _ (by positivity) + linarith + +lemma equal_endpoints_pos {l w S : ℝ} (hl : 1 < l) (hw : 0 < w) : + 0 < dStar 1 1 l w S := by + have heq : dStar 1 1 l w S = (l-1)*w+w^2 := by unfold dStar; ring + rw [heq] + exact add_pos_of_pos_of_nonneg (mul_pos (by linarith) hw) (sq_nonneg _) + +lemma schwarzian_pos_of_one_le {z l b d : ℝ} + (hz : 1 < z) (hl : 1 ≤ l) (hb : 0 < b) (hd : d < 0) : + 0 < schwarzian z 1 l b d := by + have hz0 : 0 < z := by linarith + have hl0 : 0 ≤ l := by linarith + have hl2 : 1 ≤ l^2 := by nlinarith + have hz2 : 1 < z^2 := by nlinarith + have hiz : 1/z^2 < 1 := (div_lt_one (sq_pos_of_pos hz0)).mpr hz2 + have hi : 0 < 1/z+l^2 := add_pos_of_pos_of_nonneg (one_div_pos.mpr hz0) (sq_nonneg _) + have h1 : 0 < 2*b*(z+l^2) := mul_pos (by positivity) (by positivity) + have h2 : 0 ≤ d^2/2*(l^2-1) := mul_nonneg (by positivity) (by linarith) + have h3 : 0 < -d*(1/z+l^2) := mul_pos (neg_pos.mpr hd) hi + have h4 : 0 < (3:ℝ)/2*(l^2-1/z^2) := mul_pos (by norm_num) (by linarith) + unfold schwarzian + simp only [one_pow, div_one] + linarith + +lemma second_case {z l b d w : ℝ} + (hz : 1 < z) (hl : 1 ≤ l) (hb : 0 < b) (hd : d < 0) (hw : 0 ≤ w) : + 0 < dStar z 1 l w (schwarzian z 1 l b d) := by + have hz0 : 0 < z := by linarith + have hlow : l*(2*z-1) ≥ 2*z-1 := by + have := mul_nonneg (sub_nonneg.mpr hl) (show 0 ≤ 2*z-1 by linarith) + nlinarith only [this] + have hi : 2/z < 2 := (div_lt_iff₀ hz0).mpr (by linarith) + have hcoeff : 0 < 1-2/z+l*(2*z-1) := by linarith + have hS := schwarzian_pos_of_one_le hz hl hb hd + unfold dStar + simp only [div_one, mul_one] + exact add_pos_of_pos_of_nonneg + (add_pos_of_pos_of_nonneg (mul_pos (by linarith) hS) (mul_nonneg hcoeff.le hw)) + (mul_nonneg (by positivity) (sq_nonneg _)) + +lemma zero_sign {z l b d w : ℝ} + (hz : 0 < z) (hl : 0 < l) (hb : 0 < b) + (hSmall : z ≤ 1 → 1 < l ∧ 0 < w) + (hLarge : 1 < z → d < 0) + (hSlope : 1 < z → 1 ≤ l → 0 ≤ w) + (hX : d < (l/z-1)/(1+l)) + (hRic : 4*b*z ≤ d^2 → w ≤ 1/z-l+d*l-2*Real.sqrt (d^2/4-b*z)) + (hZero : dStar z 1 l w (schwarzian z 1 l b d) = 0) : + z ≠ 1 ∧ 0 < (wStar z 1 l-w)/(z-1) := by + rcases lt_trichotomy z 1 with hlt | rfl | hgt + · obtain ⟨hl1, hw⟩ := hSmall hlt.le + refine ⟨ne_of_lt hlt, div_pos_of_neg_of_neg ?_ (by linarith)⟩ + have hstar := wStar_neg hz hlt hl1.le + linarith + · obtain ⟨hl1, hw⟩ := hSmall le_rfl + have := equal_endpoints_pos (S := schwarzian 1 1 l b d) hl1 hw + simp only [hZero, lt_self_iff_false] at this + · have hd := hLarge hgt + have hl1 : l < 1 := by + by_contra! hl1 + have := second_case hgt hl1 hb hd (hSlope hgt hl1) + linarith + have hw : w < wStar z 1 l := by + by_contra! hw + have := last_case hgt hl hl1 hb hd hw hX hRic + linarith + exact ⟨ne_of_gt hgt, div_pos (sub_pos.mpr hw) (by linarith)⟩ + +end QuinticLienard.ModelAlgebra + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ModelEndpoint.lean b/lean/OAI/Analysis/LienardCycles/ModelEndpoint.lean new file mode 100644 index 0000000000000000000000000000000000000000..5e202d34df5ac5f7ffc612492b2a7f73c7283465 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ModelEndpoint.lean @@ -0,0 +1,185 @@ +import OAI.Analysis.LienardCycles.QuadraticDerivatives + +namespace OAI + +open Set Filter MeasureTheory +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ModelEndpoint +open ScalarArcs ArcEndpoints CanonicalVariation PolynomialModel WidthCoordinates + PartialCalculus QuadraticCoordinates + +noncomputable def m (q : (ℝ × ℝ) × ℝ) : ℝ := q.2-H q +noncomputable def n (q : (ℝ × ℝ) × ℝ) : ℝ := q.2+H q +noncomputable def ell (q : (ℝ × ℝ) × ℝ) : ℝ := (1+Hr q)/(1-Hr q) + +lemma m_pos {d k r : ℝ} (hr : 0 < r) : 0 < m ((d,k),r) := by + have hh := (abs_lt.mp (H_abs_lt (d := d) (k := k) hr)).2 + dsimp [m]; linarith +lemma n_pos {d k r : ℝ} (hr : 0 < r) : 0 < n ((d,k),r) := by + have hh := (abs_lt.mp (H_abs_lt (d := d) (k := k) hr)).1 + dsimp [n]; linarith +lemma mr_pos {d k r : ℝ} (hr : 0 < r) : 0 < 1-Hr ((d,k),r) := by + have hh := (abs_lt.mp (Hr_abs_lt (d := d) (k := k) hr)).2 + linarith +lemma ell_pos {d k r : ℝ} (hr : 0 < r) : 0 < ell ((d,k),r) := by + apply div_pos _ (mr_pos hr) + have hh := (abs_lt.mp (Hr_abs_lt (d := d) (k := k) hr)).1 + linarith + +theorem radius_chart {d k r : ℝ} (hr : 0 < r) : + ∃ ρ : ℝ → ℝ, ContDiffAt ℝ ω ρ (m ((d,k),r)) ∧ + ρ (m ((d,k),r)) = r ∧ + (∀ᶠ s in 𝓝 (m ((d,k),r)), m ((d,k),ρ s)=s) ∧ + HasDerivAt ρ (1/(1-Hr ((d,k),r))) (m ((d,k),r)) := by + let f : ℝ × ℝ → ℝ := fun q => m ((d,k),q.2)-q.1 + have hf : ContDiffAt ℝ ω f (m ((d,k),r),r) := + (contDiffAt_snd.sub ((H_analytic (d := d) (k := k) hr).comp (m ((d,k),r),r) + (contDiffAt_const.prodMk contDiffAt_snd))).sub + contDiffAt_fst + have hd : HasDerivAt (fun s => f (m ((d,k),r),s)) (1-Hr ((d,k),r)) r := + ((hasDerivAt_id r).sub (Hr_hasDerivAt hr)).sub_const _ + obtain ⟨ρ,hρ,hρ0,he,_⟩ := transverse_hit hf hd (ne_of_gt (mr_pos hr)) + have he0 : ∀ᶠ s in 𝓝 (m ((d,k),r)), m ((d,k),ρ s)=s := by + filter_upwards [he] with s hs + dsimp [f] at hs + linarith + have hdρ := (hρ.differentiableAt (by simp)).hasDerivAt + have hmD : HasDerivAt (fun s => m ((d,k),s)) (1-Hr ((d,k),r)) + (ρ (m ((d,k),r))) := by + rw [hρ0] + exact (hasDerivAt_id r).sub (Hr_hasDerivAt hr) + have hcomp := hmD.comp (m ((d,k),r)) hdρ + have hder := hcomp.unique ((hasDerivAt_id _).congr_of_eventuallyEq he0) + have heder : deriv ρ (m ((d,k),r))=1/(1-Hr ((d,k),r)) := by + apply (eq_div_iff (ne_of_gt (mr_pos hr))).mpr + simpa only [mul_comm] using hder + exact ⟨ρ,hρ,hρ0,he0,by simpa only [heder] using hdρ⟩ + +structure LowerChart (d k r : ℝ) where + radius : ℝ → ℝ + upper : ℝ → ℝ + solution : ℝ × ℝ → ℝ + radius_analytic : ContDiffAt ℝ ω radius (m ((d,k),r)) + radius_base : radius (m ((d,k),r)) = r + radius_relation : ∀ᶠ s in 𝓝 (m ((d,k),r)), m ((d,k),radius s)=s + radius_derivative : HasDerivAt radius (1/(1-Hr ((d,k),r))) (m ((d,k),r)) + upper_def : ∀ s, upper s=n ((d,k),radius s) + upper_analytic : ContDiffAt ℝ ω upper (m ((d,k),r)) + upper_base : upper (m ((d,k),r)) = n ((d,k),r) + upper_derivative : HasDerivAt upper (ell ((d,k),r)) (m ((d,k),r)) + solution_continuous : ∀ s, Continuous (fun y => solution (s,y)) + solution_analytic : ∀ y ∈ Icc (-m ((d,k),r)) (n ((d,k),r)), + ContDiffAt ℝ ω solution (m ((d,k),r),y) + equation : ∀ y ∈ Icc (-m ((d,k),r)) (n ((d,k),r)), + ∀ᶠ q in 𝓝 (m ((d,k),r),y), HasDerivAt (fun s => solution (q.1,s)) + (d*solution q+(k/2)*(solution q)^2-q.2) q.2 + lower_zero : ∀ᶠ s in 𝓝 (m ((d,k),r)), solution (s,-s)=0 + upper_zero : ∀ᶠ s in 𝓝 (m ((d,k),r)), solution (s,upper s)=0 + +theorem lower_chart {d k r : ℝ} (hr : 0 < r) : Nonempty (LowerChart d k r) := by + obtain ⟨ρ,hρ,hρ0,hρeq,hρd⟩ := radius_chart (d := d) (k := k) hr + let m₀ := m ((d,k),r) + have hρbase : ρ m₀ = r := hρ0 + let Y : ℝ → ℝ := fun s => n ((d,k),ρ s) + have hY : ContDiffAt ℝ ω Y m₀ := by + have hH0 : ContDiffAt ℝ ω H ((d,k),ρ m₀) := by + rw [hρbase]; exact H_analytic hr + exact hρ.add (ContDiffAt.comp m₀ (g := H) + (f := fun s => ((d,k),ρ s)) hH0 (contDiffAt_const.prodMk hρ)) + have hY0 : Y m₀=n ((d,k),r) := by simp only [Y,m₀,hρ0] + have hYd : HasDerivAt Y (ell ((d,k),r)) m₀ := by + have hnD : HasDerivAt (fun s => n ((d,k),s)) (1+Hr ((d,k),r)) (ρ m₀) := by + rw [hρbase] + exact (hasDerivAt_id r).add (Hr_hasDerivAt hr) + have hd := hnD.comp m₀ hρd + convert! hd using 1 + dsimp [ell] + ring + let T : ℝ → ℝ := fun s => peakAtWidth profile (((d,k),0),ρ s) + have hT : ContDiffAt ℝ ω T m₀ := by + have hT0 : ContDiffAt ℝ ω (peakAtWidth profile) (((d,k),0),ρ m₀) := by + rw [hρbase] + exact peak_analytic profile profile_contDiff model_local_flow hr + exact ContDiffAt.comp m₀ (g := peakAtWidth profile) + (f := fun s => (((d,k),(0:ℝ)),ρ s)) hT0 (contDiffAt_const.prodMk hρ) + have hTs : 0 < T m₀ := by + simpa only [T,m₀,hρ0] using (peak_spec profile profile_contDiff model_local_flow + (p := (d,k)) (h := 0) hr).1 + obtain ⟨w,hwc,_,hwd,hwe,hwa⟩ := endpoint_witness profile profile_contDiff model_local_flow hTs + let u : ℝ × ℝ → ℝ := fun q => w (((d,k),T q.1),q.2) + have hlift (y : ℝ) : ContDiffAt ℝ ω + (fun q : ℝ × ℝ => (((d,k),T q.1),q.2)) (m₀,y) := + (contDiffAt_const.prodMk (hT.comp (m₀,y) contDiffAt_fst)).prodMk contDiffAt_snd + have href := FixedWidthFamilies.endpoint_formulas profile profile_contDiff model_local_flow + (p := (d,k)) (h := 0) hr + have hlower : lowerFamily profile (((d,k),T m₀),0) = -m ((d,k),r) := by + dsimp only [T] + rw [hρbase] + have h0 : profile ((d,k),(0:ℝ)) = 0 := by simp [profile] + rw [href.1,h0,add_zero] + dsimp [m,H]; ring + have hupper : upperFamily profile (((d,k),T m₀),0) = n ((d,k),r) := by + dsimp only [T] + rw [hρbase] + have h0 : profile ((d,k),(0:ℝ)) = 0 := by simp [profile] + rw [href.2,h0,add_zero] + exact add_comm _ _ + rw [hlower,hupper] at hwd hwe + have hua (y : ℝ) (hy : y ∈ Icc (-m ((d,k),r)) (n ((d,k),r))) : + ContDiffAt ℝ ω u (m₀,y) := (hwd y hy).comp (m₀,y) (hlift y) + have hue (y : ℝ) (hy : y ∈ Icc (-m ((d,k),r)) (n ((d,k),r))) : + ∀ᶠ q in 𝓝 (m₀,y), HasDerivAt (fun s => u (q.1,s)) + (d*u q+(k/2)*(u q)^2-q.2) q.2 := by + filter_upwards [(hlift y).continuousAt.eventually (hwe y hy)] with q hq + simpa only [profile] using hq + have harch : ∀ᶠ s in 𝓝 m₀, + IsArch (fun x => profile ((d,k),x)) (fun y => u (s,y)) 0 (T s) (-s) (Y s) := by + have hmap : ContinuousAt (fun s => (((d,k),T s),(0:ℝ))) m₀ := + (continuousAt_const.prodMk hT.continuousAt).prodMk continuousAt_const + have hpos : ∀ᶠ s in 𝓝 m₀, 0 < ρ s := + continuousAt_const.eventually_lt hρ.continuousAt (by simpa only [hρbase] using hr) + filter_upwards [hmap.eventually hwa,hpos,hρeq] with s hs hps heq + have hf := FixedWidthFamilies.endpoint_formulas profile profile_contDiff model_local_flow + (p := (d,k)) (h := 0) hps + have hl : lowerFamily profile (((d,k),T s),0) = -s := by + have h0 : profile ((d,k),(0:ℝ)) = 0 := by simp [profile] + change ρ s-H ((d,k),ρ s)=s at heq + change lowerFamily profile (((d,k),T s),0) = -s + rw [show lowerFamily profile (((d,k),T s),0) = + H ((d,k),ρ s)+profile ((d,k),0)-ρ s from hf.1,h0] + linarith + have hu : upperFamily profile (((d,k),T s),0) = Y s := by + have h0 : profile ((d,k),(0:ℝ)) = 0 := by simp [profile] + change upperFamily profile (((d,k),T s),0) = ρ s+H ((d,k),ρ s) + rw [hf.2,h0,add_zero] + exact add_comm _ _ + simpa only [hl,hu] using hs + exact ⟨{ radius := ρ + upper := Y + solution := u + radius_analytic := hρ + radius_base := hρ0 + radius_relation := hρeq + radius_derivative := hρd + upper_def := fun _ => rfl + upper_analytic := hY + upper_base := hY0 + upper_derivative := hYd + solution_continuous := fun s => hwc ((d,k),T s) + solution_analytic := hua + equation := hue + lower_zero := harch.mono (fun _ hs => hs.lower) + upper_zero := harch.mono (fun _ hs => hs.upper) }⟩ + +end QuinticLienard.ModelEndpoint + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ModelScaling.lean b/lean/OAI/Analysis/LienardCycles/ModelScaling.lean new file mode 100644 index 0000000000000000000000000000000000000000..39144fc4eab22b3b220f7d074671cf0bb4a983fd --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ModelScaling.lean @@ -0,0 +1,56 @@ +import OAI.Analysis.LienardCycles.PositiveScaling + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open scoped Topology +open Set Filter MeasureTheory +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuadraticCoordinates +open PolynomialModel ArchSymmetries WidthCoordinates +lemma scaling_width (d k : ℝ) {r s : ℝ} (hr : 0 H ((d,k),r*t)) =ᶠ[𝓝 s] (fun t => r*H ((r*d,r^3*k),t)) := by + filter_upwards [continuousAt_const.eventually_lt continuousAt_id hs] with t ht + exact scaling_width d k hr ht + have hc := hd.unique (he.congr_of_eventuallyEq hev) + apply mul_right_cancel₀ hr.ne' + calc + _ = r*Hr ((r*d,r^3*k),s) := by simpa only [mul_one] using hc + _ = _ := mul_comm _ _ +end QuinticLienard.QuadraticCoordinates +namespace QuinticLienard.QuadraticFit +open QuadraticCoordinates +lemma fit_scaled {r M v : ℝ} (hr : 0 f n x)) + (hI : ∀ n, (∫ x, f n x ∂μ) ≤ C) : + ∀ᵐ x ∂μ, BddAbove (Set.range (fun n => f n x)) := by + let F : ℕ → α → ℝ≥0∞ := fun n x => ENNReal.ofReal (f n x) + have hFm : ∀ n, AEMeasurable (F n) μ := fun n => (hf n).aemeasurable.ennreal_ofReal + have hFM : ∀ᵐ x ∂μ, Monotone (fun n => F n x) := by + filter_upwards [hm] with x hx n m hnm + exact ENNReal.ofReal_le_ofReal (hx hnm) + have hfin : (∫⁻ x, ⨆ n, F n x ∂μ) < ⊤ := by + rw [lintegral_iSup' hFm hFM] + apply lt_of_le_of_lt (b := ENNReal.ofReal C) _ ENNReal.ofReal_lt_top + apply iSup_le + intro n + rw [←ofReal_integral_eq_lintegral_ofReal (hf n) (hn.mono (fun x hx => hx n))] + exact ENNReal.ofReal_le_ofReal (hI n) + filter_upwards [ae_lt_top' (AEMeasurable.iSup hFm) hfin.ne,hn] with x hx hxn + refine ⟨(⨆ n, F n x).toReal,?_⟩ + rintro y ⟨n,rfl⟩ + have ht := ENNReal.toReal_mono hx.ne (le_iSup (fun n => F n x) n) + simpa only [F,ENNReal.toReal_ofReal (hxn n)] using ht + +lemma integral_pos_of_ae_pos {α : Type uα} [MeasurableSpace α] {μ : Measure α} + (hμ : μ Set.univ ≠ 0) {f : α → ℝ} (hf : Integrable f μ) + (hp : ∀ᵐ x ∂μ, 0 < f x) : 0 < ∫ x, f x ∂μ := by + rw [integral_pos_iff_support_of_nonneg_ae (hp.mono (fun _ h => h.le)) hf] + have he : Function.support f =ᵐ[μ] Set.univ := by + filter_upwards [hp] with x hx + exact propext (iff_true_intro (ne_of_gt hx)) + rw [measure_congr he] + exact pos_iff_ne_zero.mpr hμ +end QuinticLienard.RealAnalysis + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/OpenArch.lean b/lean/OAI/Analysis/LienardCycles/OpenArch.lean new file mode 100644 index 0000000000000000000000000000000000000000..fa9c96971a4159b745f0e518bbb588ec1e1ae3d2 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/OpenArch.lean @@ -0,0 +1,128 @@ +import OAI.Analysis.LienardCycles.PeriodicSymmetry + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open Set Filter Metric +open scoped Topology NNReal +open scoped Topology ContDiff NNReal +open scoped Topology +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.ScalarArcs + +structure IsOpenArch (φ u : ℝ → ℝ) (A B : ℝ) : Prop where + lt : Ahmax hy⟩ +lemma profile_extension_along_compact {φ u : ℝ → ℝ} {S : Set ℝ} + (hφ : ContDiffOn ℝ 1 φ (Ioi 0)) (hu : Continuous u) (hS : IsCompact S) (hn : S.Nonempty) + (hp : ∀ y ∈ S,0he ⟨by have hv : u m ≤ u y := hmin hy; linarith [hp m hm],by have hv : u y ≤ u M := hmax hy; linarith⟩⟩ +lemma IsOpenArch.derivative_signs {φ u : ℝ → ℝ} {A B H : ℝ} + (hu : IsOpenArch φ u A B) (hφ : ContDiffOn ℝ 1 φ (Ioi 0)) + (hp : φ H ∈ Ioo A B) (hpeak : u (φ H)=H) : + (∀ y ∈ Ioo A B,y<φ H → 0<φ (u y)-y) ∧ + (∀ y ∈ Ioo A B,φ Hhu.positive v (hsub hv)) + have heH : ψ H=φ H := by simpa only [hpeak] using he _ hpp + have hd : ∀ v ∈ Icc l r,HasDerivAt u (ψ (u v)-v) v := fun v hv=>by + rw [he v hv]; exact hu.equation v (hsub hv) + have signs := derivative_signs_on_Icc (t := H) hψ hu.continuous hd + (by simpa only [heH] using hpeak) (by simpa only [heH] using hpp) + constructor + · intro h + have hh := signs.1 y hyp (by simpa only [heH] using h) + simpa only [he y hyp] using hh + · intro h + have hh := signs.2 y hyp (by simpa only [heH] using h) + simpa only [he y hyp] using hh + exact ⟨fun y hy=> (hs y hy).1,fun y hy=> (hs y hy).2⟩ +lemma IsOpenArch.monotonicity {φ u : ℝ → ℝ} {A B H : ℝ} + (hu : IsOpenArch φ u A B) (hφ : ContDiffOn ℝ 1 φ (Ioi 0)) + (hp : φ H ∈ Ioo A B) (hpeak : u (φ H)=H) : + StrictMonoOn u (Icc A (φ H)) ∧ StrictAntiOn u (Icc (φ H) B) := by + have hs := hu.derivative_signs hφ hp hpeak + constructor + · apply strictMonoOn_of_deriv_pos (convex_Icc _ _) hu.continuous.continuousOn + intro y hy + have hy' : y ∈ Ioo A (φ H) := by simpa using hy + have hyab : y ∈ Ioo A B := ⟨hy'.1,hy'.2.trans hp.2⟩ + rw [(hu.equation y hyab).deriv] + exact hs.1 y hyab hy'.2 + · apply strictAntiOn_of_deriv_neg (convex_Icc _ _) hu.continuous.continuousOn + intro y hy + have hy' : y ∈ Ioo (φ H) B := by simpa using hy + have hyab : y ∈ Ioo A B := ⟨hp.1.trans hy'.1,hy'.2⟩ + rw [(hu.equation y hyab).deriv] + exact hs.2 y hyab hy'.1 +lemma IsOpenArch.subarch {φ u : ℝ → ℝ} {A B H h : ℝ} + (hu : IsOpenArch φ u A B) (hφ : ContDiffOn ℝ 1 φ (Ioi 0)) + (hp : φ H ∈ Ioo A B) (hpeak : u (φ H)=H) (hh : 0] (0:ℝ), + Ah.1.le) + have hlp : axisLower φ H≤φ H := le_of_tendsto hl (he.mono fun _ h=>h.2.1.le) + have hpr : φ H≤axisUpper φ H := ge_of_tendsto hr (he.mono fun _ h=>h.2.2.1.le) + have hrb : axisUpper φ H≤B := le_of_tendsto hr (he.mono fun _ h=>h.2.2.2.1.le) + have hul : u (axisLower φ H)=0 := tendsto_nhds_unique (hu.continuous.continuousAt.tendsto.comp hl) + ((tendsto_id.mono_left inf_le_left : Tendsto (fun h : ℝ=>h) (𝓝[>] 0) (𝓝 0)).congr' + (he.mono fun _ h=>h.2.2.2.2.1.symm)) + have hur : u (axisUpper φ H)=0 := tendsto_nhds_unique (hu.continuous.continuousAt.tendsto.comp hr) + ((tendsto_id.mono_left inf_le_left : Tendsto (fun h : ℝ=>h) (𝓝[>] 0) (𝓝 0)).congr' + (he.mono fun _ h=>h.2.2.2.2.2.symm)) + constructor + · apply le_antisymm _ hal + by_contra! hn + have hh := hu.positive _ ⟨hn,hlp.trans_lt hp.2⟩ + rw [hul] at hh + exact lt_irrefl _ hh + · apply le_antisymm hrb + by_contra! hn + have hh := hu.positive _ ⟨hp.1.trans_le hpr,hn⟩ + rw [hur] at hh + exact lt_irrefl _ hh +end QuinticLienard.ScalarArcs + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/OriginalProfile.lean b/lean/OAI/Analysis/LienardCycles/OriginalProfile.lean new file mode 100644 index 0000000000000000000000000000000000000000..f35e594fcee8b052ca848aa23a4a5ce524918335 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/OriginalProfile.lean @@ -0,0 +1,45 @@ +import OAI.Analysis.LienardCycles.ScaledCoefficients + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter Metric +open scoped Topology ENNReal +open scoped Topology +open Set Filter MeasureTheory +open Set Filter +open scoped Topology ContDiff + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard.QuinticProfile +open SmoothFlow SmoothFlow.AlgebraicExpr ArcFamilies ScaledProfile +noncomputable def xExpr : AlgebraicExpr (ℝ × ℝ) := sqrt (const 2*linear (ContinuousLinearMap.snd ℝ ℝ ℝ)) +noncomputable def expr (a : Fin 6 → ℝ) : AlgebraicExpr (ℝ × ℝ) := + const (a 0)+const (a 1)*xExpr+const (a 2)*xExpr^2+const (a 3)*xExpr^3+ + const (a 4)*xExpr^4+const (a 5)*xExpr^5 +noncomputable def profile (a : Fin 6 → ℝ) (q : ℝ × ℝ) : ℝ := poly a (root q.2) +lemma representation (a : Fin 6 → ℝ) : (expr a).eval=profile a := by + funext q + simp [expr,xExpr,profile,poly,root] +lemma regular (a : Fin 6 → ℝ) {q : ℝ × ℝ} (hq : 0 f (q.1,s)) (field (profile a) (f q)) q.2 := by + simpa only [representation] using algebraic_profile_flow (expr a) x (regular a hx) +lemma profile_eq (a : Fin 6 → ℝ) (p h : ℝ) : profile a (p,h)=poly a (Real.sqrt (2*h)) := rfl +end QuinticLienard.QuinticProfile + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/OvalMatching.lean b/lean/OAI/Analysis/LienardCycles/OvalMatching.lean new file mode 100644 index 0000000000000000000000000000000000000000..8c82f0e9d770474f94ad7f433f8643fff117580a --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/OvalMatching.lean @@ -0,0 +1,76 @@ +import OAI.Analysis.LienardCycles.ReturnMatching + +namespace OAI + +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open scoped Topology ENNReal +open Set Filter MeasureTheory +open Set Filter Asymptotics +open Set Filter Metric +open scoped Topology NNReal +open scoped Topology +open scoped Topology ContDiff +open Set Filter +open scoped Topology ContDiff NNReal + +open Set Filter +open scoped Topology ContDiff +namespace QuinticLienard +open ScaledProfile ScalarArcs AxisFlow RealAnalysis +lemma IsRightExcursion.nonconstant {z : ℝ → Plane} {s t : ℝ} (hr : IsRightExcursion z s t) : ∃ u v,z u≠z v := by + refine ⟨s,(s+t)/2,?_⟩ + intro he + have hh := hr.positive ((s+t)/2) ⟨by linarith [hr.lt],by linarith [hr.lt]⟩ + rw [←he,hr.left] at hh + exact lt_irrefl _ hh +lemma IsSolution.oval_axis_positive {F : Polynomial ℝ} {z : ℝ → Plane} (hz : IsSolution F z) + {S T : ℝ} (hS : 0by rw [polynomialReflect_eval,hF,reflectX_poly]) hz.reverseX (reverseX_nonconstant hr.nonconstant) + simp only [QuinticLienard.reverseX,neg_neg,hzT] at hKa hKb + dsimp only + have hwH : axisWidth a H=((z 0).2-(z S).2)/2 := by rw [axisWidth,hHa,hHb] + have hwK : axisWidth (reflectX a) K=((z 0).2-(z S).2)/2 := by rw [axisWidth,hKa,hKb] + have hpa := axisPeak_eq a hH hwH + have hpb := axisPeak_eq (reflectX a) hK hwK + have hM : axisM a (((z 0).2-(z S).2)/2)=((z 0).2+(z S).2)/2-poly a 0 := by + rw [axisM,hpa,axisCenter,hHa,hHb] + have hMb : axisM (reflectX a) (((z 0).2-(z S).2)/2)=((z 0).2+(z S).2)/2-poly a 0 := by + rw [axisM,hpb,axisCenter,hKa,hKb,reflectX_poly] + simp + refine ⟨⟨⟨H,hH,hwH⟩,⟨K,hK,hwK⟩⟩,?_,?_⟩ + · rw [matchingDelta,hM,hMb,sub_self] + · rw [hM];ring +end QuinticLienard + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/ParameterVariation.lean b/lean/OAI/Analysis/LienardCycles/ParameterVariation.lean new file mode 100644 index 0000000000000000000000000000000000000000..a2bf1ccd16b5c20630a6b6c83fdd9a367889c47a --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/ParameterVariation.lean @@ -0,0 +1,102 @@ +import OAI.Analysis.LienardCycles.FixedWidthFamilies + +namespace OAI + +open Set Filter MeasureTheory +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold +open Filter Set +open Set Filter Metric MeasureTheory +open scoped Topology NNReal ContDiff +open Set Filter +open scoped Topology ContDiff + +namespace QuinticLienard.ParameterVariation +open ScalarArcs PartialCalculus ArchVariation + +lemma arch_interior_pos {φ u : ℝ → ℝ} {h t a b y : ℝ} + (hu : IsArch φ u h t a b) (hy : y ∈ Ioo a b) : h < u y := by + by_cases hh : y ≤ φ t + · have hi := hu.inc (show a ∈ Icc a (φ t) from ⟨le_rfl,hu.lower_lt_peak.le⟩) + (show y ∈ Icc a (φ t) from ⟨hy.1.le,hh⟩) hy.1 + simpa only [hu.lower] using hi + · have hi := hu.dec (show y ∈ Icc (φ t) b from ⟨(le_of_not_ge hh),hy.2.le⟩) + (show b ∈ Icc (φ t) b from ⟨hu.peak_lt_upper.le,le_rfl⟩) hy.2 + simpa only [hu.upper] using hi + +theorem positive_displacement {z a f : ℝ → ℝ} {l r δ : ℝ} + (ha : Continuous a) (hz : ContinuousOn z (Icc l r)) + (hd : ∀ y ∈ Icc l r, HasDerivAt z (a y*z y+f y) y) + (hf : ∀ y ∈ Ioo l r, 0 < f y) (hl : l < 0) (hr : 0 < r) + (hzl : z l = δ*l) (hzr : z r = δ*r) : 0 < δ := by + let w : ℝ → ℝ := fun y => Real.exp (-(∫ s in l..y, a s)) + let g : ℝ → ℝ := fun y => w y*z y + have hwd (y : ℝ) : HasDerivAt w (-a y*w y) y := by + convert (ha.integral_hasStrictDerivAt l y).hasDerivAt.neg.exp using 1; + (first | rfl | (dsimp [w]; ring)) + have hgc : ContinuousOn g (Icc l r) := + (continuous_iff_continuousAt.mpr (fun y => (hwd y).continuousAt)).continuousOn.mul hz + have hgd (y : ℝ) (hy : y ∈ Icc l r) : HasDerivAt g (w y*f y) y := by + convert (hwd y).mul (hd y hy) using 1; (first | rfl | ring) + have hm : StrictMonoOn g (Icc l r) := by + apply strictMonoOn_of_deriv_pos (convex_Icc _ _) hgc + intro y hy + rw [(hgd y (interior_subset hy)).deriv] + exact mul_pos (Real.exp_pos _) (hf y (by simpa only [interior_Icc] using hy)) + have hh := hm (show l ∈ Icc l r from ⟨le_rfl,(hl.trans hr).le⟩) + (show r ∈ Icc l r from ⟨(hl.trans hr).le,le_rfl⟩) (hl.trans hr) + dsimp [g] at hh + rw [hzl,hzr] at hh + have hwpos : 0 < w r := Real.exp_pos _ + have hwnon : 0 < w l := Real.exp_pos _ + have hden : 0 < w r*r-w l*l := by nlinarith + nlinarith + +theorem midpoint_positive {Φ u : ℝ × ℝ → ℝ} {Y : ℝ → ℝ} {θ r t : ℝ} + (hΦ : ContDiff ℝ ω Φ) (hbase : ∀ s, Φ (s,0) = 0) + (hY : DifferentiableAt ℝ Y θ) (hr : 0 < r) + (ha : IsArch (fun x => Φ (θ,x)) (fun y => u (θ,y)) 0 t (Y θ-r) (Y θ+r)) + (hu : ∀ y ∈ Icc (Y θ-r) (Y θ+r), ContDiffAt ℝ ω u (θ,y)) + (he : ∀ y ∈ Icc (Y θ-r) (Y θ+r), ∀ᶠ q in 𝓝 (θ,y), + HasDerivAt (fun s => u (q.1,s)) (Φ (q.1,u q)-q.2) q.2) + (hl : ∀ᶠ s in 𝓝 θ, u (s,Y s-r) = 0) + (hb : ∀ᶠ s in 𝓝 θ, u (s,Y s+r) = 0) + (hpos : ∀ x, 0 < x → 0 < first Φ (θ,x)) : 0 < deriv Y θ := by + let l := Y θ-r + let b := Y θ+r + have hlb : l < b := by dsimp [l,b]; linarith + have hll : l ∈ Icc l b := ⟨le_rfl,hlb.le⟩ + have hbb : b ∈ Icc l b := ⟨hlb.le,le_rfl⟩ + have ha0 : l < 0 := by simpa only [hbase] using ha.lower_transverse + have hb0 : 0 < b := by simpa only [hbase] using ha.upper_transverse + have hac : Continuous (fun y => second Φ (θ,u (θ,y))) := by + apply continuous_iff_continuousAt.mpr + intro y + exact (second_contDiffAt (hΦ.contDiffAt)).continuousAt.comp + (continuousAt_const.prodMk ha.continuous.continuousAt) + have hzc : ContinuousOn (fun y => first u (θ,y)) (Icc l b) := by + intro y hy + exact ((first_contDiffAt (hu y hy)).continuousAt.comp + (continuousAt_const.prodMk continuousAt_id)).continuousWithinAt + have hzdl : HasDerivAt (fun y => u (θ,y)) (-l) l := by + simpa only [show u (θ,l) = 0 from ha.lower,hbase,zero_sub] using ha.equation l hll + have hzdb : HasDerivAt (fun y => u (θ,y)) (-b) b := by + simpa only [show u (θ,b) = 0 from ha.upper,hbase,zero_sub] using ha.equation b hbb + have hel := hit_variation ((hu l hll).differentiableAt (by simp)) + (hY.sub_const r) (hasDerivAt_const θ (0:ℝ)) hl + have heb := hit_variation ((hu b hbb).differentiableAt (by simp)) + (hY.add_const r) (hasDerivAt_const θ (0:ℝ)) hb + rw [(second_hasDerivAt ((hu l hll).differentiableAt (by simp))).unique hzdl, + (hY.hasDerivAt.sub_const r).deriv] at hel + rw [(second_hasDerivAt ((hu b hbb).differentiableAt (by simp))).unique hzdb, + (hY.hasDerivAt.add_const r).deriv] at heb + apply positive_displacement hac hzc + (fun y hy => ?_) (fun y hy => hpos _ (arch_interior_pos ha hy)) ha0 hb0 + (show first u (θ,l) = deriv Y θ*l by linarith) + (show first u (θ,b) = deriv Y θ*b by linarith) + convert scalar_ode_variation (hu y hy) (hΦ.differentiable (by simp) _) (he y hy) using 1 + ring + +end QuinticLienard.ParameterVariation + +end OAI diff --git a/lean/OAI/Analysis/LienardCycles/PartialCalculus.lean b/lean/OAI/Analysis/LienardCycles/PartialCalculus.lean new file mode 100644 index 0000000000000000000000000000000000000000..f172319b1f40836f7adeb4bc9f29cab95ac70432 --- /dev/null +++ b/lean/OAI/Analysis/LienardCycles/PartialCalculus.lean @@ -0,0 +1,142 @@ +import OAI.Analysis.LienardCycles.GlobalODE + +namespace OAI + +universe uE uF + +open Set Filter MeasureTheory +open scoped Topology ContDiff +open Set Filter Metric +open scoped Topology NNReal ContDiff Manifold + +open Filter Set +open scoped Topology ContDiff + +namespace QuinticLienard.PartialCalculus + +variable {E : Type uE} {F : Type uF} [NormedAddCommGroup E] [NormedSpace ℝ E] + [NormedAddCommGroup F] [NormedSpace ℝ F] + +noncomputable def direction (v : E) (f : E → F) (x : E) : F := fderiv ℝ f x v + +lemma direction_contDiffAt {f : E → F} {x : E} (hf : ContDiffAt ℝ ω f x) (v : E) : + ContDiffAt ℝ ω (direction v f) x := + (hf.fderiv_right (by simp)).clm_apply contDiffAt_const + +lemma direction_hasFDerivAt {f : E → F} {x : E} (hf : ContDiffAt ℝ ω f x) (v : E) : + HasFDerivAt (direction v f) ((fderiv ℝ (fderiv ℝ f) x).flip v) x := by + have hd : HasFDerivAt (fderiv ℝ f) (fderiv ℝ (fderiv ℝ f) x) x := + ((hf.fderiv_right (m := ω) (by simp)).differentiableAt (by simp)).hasFDerivAt + change HasFDerivAt (fun y => fderiv ℝ f y v) _ x + convert hd.clm_apply (hasFDerivAt_const v x) using 1 + ext y + simp + +lemma direction_direction {f : E → F} {x : E} (hf : ContDiffAt ℝ ω f x) (v w : E) : + direction v (direction w f) x = (fderiv ℝ (fderiv ℝ f) x v) w := by + rw [direction,(direction_hasFDerivAt hf w).fderiv] + rfl + +lemma direction_comm {f : E → F} {x : E} (hf : ContDiffAt ℝ ω f x) (v w : E) : + direction v (direction w f) x = direction w (direction v f) x := by + rw [direction_direction hf,direction_direction hf] + exact hf.isSymmSndFDerivAt_of_omega.eq v w + +noncomputable def first (f : ℝ × ℝ → F) : ℝ × ℝ → F := direction (1,0) f +noncomputable def second (f : ℝ × ℝ → F) : ℝ × ℝ → F := direction (0,1) f + +lemma first_contDiffAt {f : ℝ × ℝ → F} {p : ℝ × ℝ} (hf : ContDiffAt ℝ ω f p) : + ContDiffAt ℝ ω (first f) p := direction_contDiffAt hf _ +lemma second_contDiffAt {f : ℝ × ℝ → F} {p : ℝ × ℝ} (hf : ContDiffAt ℝ ω f p) : + ContDiffAt ℝ ω (second f) p := direction_contDiffAt hf _ + +lemma first_hasDerivAt {f : ℝ × ℝ → F} {x y : ℝ} + (hf : DifferentiableAt ℝ f (x,y)) : + HasDerivAt (fun s => f (s,y)) (first f (x,y)) x := by + simpa [first,direction,Function.comp_def] using + hf.hasFDerivAt.comp_hasDerivAt x ((hasDerivAt_id x).prodMk (hasDerivAt_const x y)) + +lemma second_hasDerivAt {f : ℝ × ℝ → F} {x y : ℝ} + (hf : DifferentiableAt ℝ f (x,y)) : + HasDerivAt (fun s => f (x,s)) (second f (x,y)) y := by + simpa [second,direction,Function.comp_def] using + hf.hasFDerivAt.comp_hasDerivAt y ((hasDerivAt_const y x).prodMk (hasDerivAt_id y)) + +lemma mixed_comm {f : ℝ × ℝ → F} {p : ℝ × ℝ} (hf : ContDiffAt ℝ ω f p) : + first (second f) p = second (first f) p := direction_comm hf _ _ + +lemma fderiv_pair (f : ℝ × ℝ → ℝ) (p : ℝ × ℝ) (a b : ℝ) : + fderiv ℝ f p (a,b) = a * first f p + b * second f p := by + have he : (a,b) = a • (1,0) + b • (0,1) := by ext <;> simp + rw [he,map_add,map_smul,map_smul] + rfl + +theorem scalar_ode_variation {u Φ : ℝ × ℝ → ℝ} {θ y : ℝ} + (hu : ContDiffAt ℝ ω u (θ,y)) (hΦ : DifferentiableAt ℝ Φ (θ,u (θ,y))) + (he : ∀ᶠ p in 𝓝 (θ,y), HasDerivAt (fun s => u (p.1,s)) + (Φ (p.1,u p)-p.2) p.2) : + HasDerivAt (fun s => first u (θ,s)) + (first Φ (θ,u (θ,y)) + second Φ (θ,u (θ,y))*first u (θ,y)) y := by + have huN : ∀ᶠ p in 𝓝 (θ,y), ContDiffAt ℝ ω u p := hu.eventually (by simp) + have heq : ∀ᶠ p in 𝓝 (θ,y), second u p = Φ (p.1,u p)-p.2 := by + filter_upwards [he,huN] with p hp hpu + exact (second_hasDerivAt (hpu.differentiableAt (by simp))).unique hp + have hslice : (fun s => second u (s,y)) =ᶠ[𝓝 θ] (fun s => Φ (s,u (s,y))-y) := + (continuousAt_id.prodMk continuousAt_const).eventually heq + have hcomp := hΦ.hasFDerivAt.comp_hasDerivAt θ + ((hasDerivAt_id θ).prodMk (first_hasDerivAt (hu.differentiableAt (by simp)))) + have hcoeff : HasDerivAt (fun s => Φ (s,u (s,y))-y) + (first Φ (θ,u (θ,y))+second Φ (θ,u (θ,y))*first u (θ,y)) θ := by + have hc : HasDerivAt (fun s => Φ (s,u (s,y))-y) + (fderiv ℝ Φ (θ,u (θ,y)) (1,first u (θ,y))) θ := hcomp.sub_const y + convert hc using 1 + rw [fderiv_pair] + ring + have hd1 := first_hasDerivAt ((second_contDiffAt hu).differentiableAt (by simp)) + have hecoeff := hd1.unique (hcoeff.congr_of_eventuallyEq hslice) + have hd2 := second_hasDerivAt ((first_contDiffAt hu).differentiableAt (by simp)) + rw [←mixed_comm hu,hecoeff] at hd2 + exact hd2 + +theorem transverse_hit [CompleteSpace E] {f : E × ℝ → ℝ} {p : E} {y a : ℝ} + (hf : ContDiffAt ℝ ω f (p,y)) (hd : HasDerivAt (fun s => f (p,s)) a y) + (ha : a ≠ 0) : + ∃ Y : E → ℝ, ContDiffAt ℝ ω Y p ∧ Y p = y ∧ + (∀ᶠ q in 𝓝 p, f (q,Y q) = f (p,y)) ∧ + ∀ᶠ q in 𝓝 (p,y), f q = f (p,y) ↔ Y q.1 = q.2 := by + have hpartial : fderiv ℝ f (p,y) ∘L ContinuousLinearMap.inr ℝ E ℝ = + ContinuousLinearMap.toSpanSingleton ℝ a := by + have hc := (hf.differentiableAt (by simp)).hasFDerivAt.comp y + ((hasFDerivAt_const p y).prodMk (hasFDerivAt_id y)) + exact hc.unique hd.hasFDerivAt + have hi : (fderiv ℝ f (p,y) ∘L ContinuousLinearMap.inr ℝ E ℝ).IsInvertible := by + rw [hpartial] + refine ⟨(LinearEquiv.smulOfNeZero ℝ ℝ a ha).toContinuousLinearEquiv, ?_⟩ + apply ContinuousLinearMap.ext + intro z + change a*z=z*a + ring + exact ⟨hf.implicitFunction (by simp) hi, + hf.contDiffAt_implicitFunction (by simp) hi, + hf.implicitFunction_apply_self (by simp) hi, + hf.eventually_apply_implicitFunction (by simp) hi, + hf.eventually_apply_eq_iff_implicitFunction (by simp) hi⟩ + +lemma eq_of_hasDerivAt_eq_on_Icc {f g : ℝ → F} {a b c : ℝ} + (hf : ContinuousOn f (Icc a b)) (hg : ContinuousOn g (Icc a b)) + {d : ℝ → F} + (hdf : ∀ y ∈ Icc a b, HasDerivAt f (d y) y) + (hdg : ∀ y ∈ Icc a b, HasDerivAt g (d y) y) + (hc : c ∈ Icc a b) (he : f c = g c) : EqOn f g (Icc a b) := by + have hconst := constant_of_has_deriv_right_zero (hf.sub hg) + (fun y hy => (by simpa only [sub_self] using + ((hdf y (Ico_subset_Icc_self hy)).sub + (hdg y (Ico_subset_Icc_self hy))).hasDerivWithinAt)) + intro y hy + have hh := (hconst y hy).trans (hconst c hc).symm + change f y-g y=f c-g c at hh + simpa only [he, sub_self, sub_eq_zero] using hh + +end QuinticLienard.PartialCalculus + +end OAI